LMFDB - Embedded newform 69.6.e.b.58.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,6,Mod(4,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0664835671$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			58.9
Character	$\chi$	$=$	69.58
Dual form			69.6.e.b.25.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.30485 - 4.05188i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(10.0401 - 21.9848i) q^{4} +(-78.9416 + 23.1793i) q^{5} +(28.0203 + 61.3559i) q^{6} +(-51.3024 - 59.2061i) q^{7} +(8.35258 + 58.0934i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})$	\(q+(6.30485 - 4.05188i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(10.0401 - 21.9848i) q^{4} +(-78.9416 + 23.1793i) q^{5} +(28.0203 + 61.3559i) q^{6} +(-51.3024 - 59.2061i) q^{7} +(8.35258 + 58.0934i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(-403.795 + 466.004i) q^{10} +(-206.531 - 132.729i) q^{11} +(182.990 + 117.600i) q^{12} +(-697.303 + 804.731i) q^{13} +(-563.350 - 165.415i) q^{14} +(-105.380 - 732.931i) q^{15} +(794.522 + 916.927i) q^{16} +(97.3598 + 213.188i) q^{17} +(-582.472 + 171.029i) q^{18} +(373.064 - 816.897i) q^{19} +(-282.990 + 1968.24i) q^{20} +(593.141 - 381.189i) q^{21} -1839.95 q^{22} +(-1090.25 - 2290.78i) q^{23} -528.218 q^{24} +(3065.57 - 1970.12i) q^{25} +(-1135.72 + 7899.10i) q^{26} +(302.838 - 663.122i) q^{27} +(-1816.72 + 533.437i) q^{28} +(2229.47 + 4881.86i) q^{29} +(-3634.15 - 4194.04i) q^{30} +(-207.222 - 1441.26i) q^{31} +(6922.60 + 2032.66i) q^{32} +(1446.94 - 1669.85i) q^{33} +(1477.65 + 949.630i) q^{34} +(5422.25 + 3484.67i) q^{35} +(-1282.01 + 1479.52i) q^{36} +(10129.1 + 2974.17i) q^{37} +(-957.854 - 6662.02i) q^{38} +(-6275.73 - 7242.58i) q^{39} +(-2005.93 - 4392.38i) q^{40} +(-13778.0 + 4045.59i) q^{41} +(2195.14 - 4806.68i) q^{42} +(-349.293 + 2429.38i) q^{43} +(-4991.62 + 3207.92i) q^{44} +6664.21 q^{45} +(-16155.9 - 10025.5i) q^{46} -14668.4 q^{47} +(-9186.00 + 5903.48i) q^{48} +(1518.46 - 10561.1i) q^{49} +(11345.3 - 24842.7i) q^{50} +(-2023.87 + 594.261i) q^{51} +(10690.8 + 23409.7i) q^{52} +(-10453.7 - 12064.2i) q^{53} +(-777.545 - 5407.95i) q^{54} +(19380.4 + 5690.61i) q^{55} +(3010.98 - 3474.86i) q^{56} +(6799.40 + 4369.71i) q^{57} +(33837.2 + 21745.9i) q^{58} +(-2980.70 + 3439.91i) q^{59} +(-17171.4 - 5041.97i) q^{60} +(3426.95 + 23835.0i) q^{61} +(-7146.31 - 8247.28i) q^{62} +(2636.06 + 5772.17i) q^{63} +(14630.1 - 4295.79i) q^{64} +(36393.1 - 79689.8i) q^{65} +(2356.67 - 16391.0i) q^{66} +(48121.3 - 30925.7i) q^{67} +5664.41 q^{68} +(21803.6 - 6778.28i) q^{69} +48305.9 q^{70} +(-18560.9 + 11928.4i) q^{71} +(676.559 - 4705.57i) q^{72} +(-34608.6 + 75782.2i) q^{73} +(75913.3 - 22290.2i) q^{74} +(13624.1 + 29832.7i) q^{75} +(-14213.7 - 16403.5i) q^{76} +(2737.14 + 19037.2i) q^{77} +(-68913.6 - 20234.9i) q^{78} +(-64841.5 + 74831.1i) q^{79} +(-83974.6 - 53967.2i) q^{80} +(5519.46 + 3547.14i) q^{81} +(-70476.1 + 81333.7i) q^{82} +(-71187.8 - 20902.6i) q^{83} +(-2425.15 - 16867.3i) q^{84} +(-12627.3 - 14572.7i) q^{85} +(7641.34 + 16732.2i) q^{86} +(-46345.2 + 13608.2i) q^{87} +(5985.64 - 13106.7i) q^{88} +(-16861.4 + 117273. i) q^{89} +(42016.9 - 27002.6i) q^{90} +83418.4 q^{91} +(-61308.7 + 969.207i) q^{92} +13104.7 q^{93} +(-92482.2 + 59434.7i) q^{94} +(-10515.1 + 73134.5i) q^{95} +(-26974.4 + 59065.7i) q^{96} +(138195. - 40577.7i) q^{97} +(-33218.7 - 72738.8i) q^{98} +(13022.4 + 15028.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9}+O(q^{10}) $ 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9	\( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9} - 38 q^{10} + 404 q^{11} - 1332 q^{12} - 2850 q^{13} - 724 q^{14} + 639 q^{15} - 5556 q^{16} - 2519 q^{17} + 972 q^{18} + 1117 q^{19} - 22411 q^{20} - 702 q^{21} + 32798 q^{22} + 12040 q^{23} - 756 q^{24} - 5928 q^{25} - 788 q^{26} - 7290 q^{27} - 54024 q^{28} + 13774 q^{29} - 342 q^{30} + 12501 q^{31} + 37412 q^{32} - 4185 q^{33} + 9441 q^{34} + 28894 q^{35} - 21789 q^{36} - 38902 q^{37} - 15042 q^{38} - 25650 q^{39} - 133835 q^{40} - 19456 q^{41} + 85950 q^{42} - 8126 q^{43} + 120643 q^{44} + 40500 q^{45} + 90500 q^{46} + 60846 q^{47} + 62955 q^{48} - 25762 q^{49} - 110197 q^{50} - 51084 q^{51} + 91725 q^{52} - 83896 q^{53} - 31347 q^{54} + 190331 q^{55} - 358140 q^{56} - 40437 q^{57} + 150977 q^{58} + 248368 q^{59} + 122625 q^{60} - 81516 q^{61} + 82657 q^{62} - 6318 q^{63} - 298028 q^{64} - 25475 q^{65} - 6669 q^{66} + 51337 q^{67} + 491228 q^{68} + 17082 q^{69} + 395832 q^{70} - 206653 q^{71} - 149364 q^{72} - 121007 q^{73} + 716844 q^{74} - 59490 q^{75} + 171145 q^{76} + 71982 q^{77} + 11916 q^{78} - 661118 q^{79} - 1386592 q^{80} - 65610 q^{81} - 136394 q^{82} - 368400 q^{83} + 165204 q^{84} + 45505 q^{85} - 99668 q^{86} + 50112 q^{87} - 474416 q^{88} + 328408 q^{89} - 3078 q^{90} + 1042320 q^{91} + 1554071 q^{92} + 160722 q^{93} - 299081 q^{94} - 434011 q^{95} + 412740 q^{96} - 88136 q^{97} + 515807 q^{98} - 37665 q^{99}+O(q^{100}) \) 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9 - 38 * q^10 + 404 * q^11 - 1332 * q^12 - 2850 * q^13 - 724 * q^14 + 639 * q^15 - 5556 * q^16 - 2519 * q^17 + 972 * q^18 + 1117 * q^19 - 22411 * q^20 - 702 * q^21 + 32798 * q^22 + 12040 * q^23 - 756 * q^24 - 5928 * q^25 - 788 * q^26 - 7290 * q^27 - 54024 * q^28 + 13774 * q^29 - 342 * q^30 + 12501 * q^31 + 37412 * q^32 - 4185 * q^33 + 9441 * q^34 + 28894 * q^35 - 21789 * q^36 - 38902 * q^37 - 15042 * q^38 - 25650 * q^39 - 133835 * q^40 - 19456 * q^41 + 85950 * q^42 - 8126 * q^43 + 120643 * q^44 + 40500 * q^45 + 90500 * q^46 + 60846 * q^47 + 62955 * q^48 - 25762 * q^49 - 110197 * q^50 - 51084 * q^51 + 91725 * q^52 - 83896 * q^53 - 31347 * q^54 + 190331 * q^55 - 358140 * q^56 - 40437 * q^57 + 150977 * q^58 + 248368 * q^59 + 122625 * q^60 - 81516 * q^61 + 82657 * q^62 - 6318 * q^63 - 298028 * q^64 - 25475 * q^65 - 6669 * q^66 + 51337 * q^67 + 491228 * q^68 + 17082 * q^69 + 395832 * q^70 - 206653 * q^71 - 149364 * q^72 - 121007 * q^73 + 716844 * q^74 - 59490 * q^75 + 171145 * q^76 + 71982 * q^77 + 11916 * q^78 - 661118 * q^79 - 1386592 * q^80 - 65610 * q^81 - 136394 * q^82 - 368400 * q^83 + 165204 * q^84 + 45505 * q^85 - 99668 * q^86 + 50112 * q^87 - 474416 * q^88 + 328408 * q^89 - 3078 * q^90 + 1042320 * q^91 + 1554071 * q^92 + 160722 * q^93 - 299081 * q^94 - 434011 * q^95 + 412740 * q^96 - 88136 * q^97 + 515807 * q^98 - 37665 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	6.30485	−	4.05188i	1.11455	−	0.716278i	0.152271	−	0.988339i	$-0.451341\pi$
$2$	6.30485	−	4.05188i	1.11455	−	0.716278i	0.962280	+	0.272060i	$0.0877051\pi$
$3$	−1.28083	+	8.90839i	−0.0821655	+	0.571474i
$3$	−1.28083	+	8.90839i	−0.0821655	+	0.571474i
$4$	10.0401	−	21.9848i	0.313754	−	0.687025i
$5$	−78.9416	+	23.1793i	−1.41215	+	0.414645i	−0.896838	−	0.442359i	$-0.854142\pi$
$5$	−78.9416	+	23.1793i	−1.41215	+	0.414645i	−0.515311	+	0.857003i	$0.672324\pi$
$6$	28.0203	+	61.3559i	0.317757	+	0.695790i
$7$	−51.3024	−	59.2061i	−0.395724	−	0.456690i	0.522566	−	0.852599i	$-0.324975\pi$
$7$	−51.3024	−	59.2061i	−0.395724	−	0.456690i	−0.918290	+	0.395909i	$0.870430\pi$
$8$	8.35258	+	58.0934i	0.0461419	+	0.320924i
$9$	−77.7189	−	22.8203i	−0.319831	−	0.0939109i
$10$	−403.795	+	466.004i	−1.27691	+	1.47363i
$11$	−206.531	−	132.729i	−0.514639	−	0.330739i	0.257409	−	0.966303i	$-0.417131\pi$
$11$	−206.531	−	132.729i	−0.514639	−	0.330739i	−0.772048	+	0.635564i	$0.780768\pi$
$12$	182.990	+	117.600i	0.366837	+	0.235752i
$13$	−697.303	+	804.731i	−1.14436	+	1.32066i	−0.204596	+	0.978847i	$0.565588\pi$
$13$	−697.303	+	804.731i	−1.14436	+	1.32066i	−0.939766	+	0.341818i	$0.888957\pi$
$14$	−563.350	−	165.415i	−0.768172	−	0.225556i
$15$	−105.380	−	732.931i	−0.120928	−	0.841076i
$16$	794.522	+	916.927i	0.775901	+	0.895437i
$17$	97.3598	+	213.188i	0.0817066	+	0.178913i	0.946076	−	0.323945i	$-0.105009\pi$
$17$	97.3598	+	213.188i	0.0817066	+	0.178913i	−0.864369	+	0.502858i	$0.832282\pi$
$18$	−582.472	+	171.029i	−0.423734	+	0.124420i
$19$	373.064	−	816.897i	0.237083	−	0.519138i	−0.753270	−	0.657712i	$-0.771524\pi$
$19$	373.064	−	816.897i	0.237083	−	0.519138i	0.990352	+	0.138574i	$0.0442517\pi$
$20$	−282.990	+	1968.24i	−0.158196	+	1.10028i
$21$	593.141	−	381.189i	0.293501	−	0.188622i
$22$	−1839.95			−0.810493
$23$	−1090.25	−	2290.78i	−0.429741	−	0.902952i
$23$	−1090.25	−	2290.78i	−0.429741	−	0.902952i
$24$	−528.218			−0.187191
$25$	3065.57	−	1970.12i	0.980983	−	0.630439i
$26$	−1135.72	+	7899.10i	−0.329487	+	2.29163i
$27$	302.838	−	663.122i	0.0799467	−	0.175059i
$28$	−1816.72	+	533.437i	−0.437918	+	0.128584i
$29$	2229.47	+	4881.86i	0.492274	+	1.07793i	0.978904	+	0.204322i	$0.0654989\pi$
$29$	2229.47	+	4881.86i	0.492274	+	1.07793i	−0.486629	+	0.873608i	$0.661774\pi$
$30$	−3634.15	−	4194.04i	−0.737225	−	0.850803i
$31$	−207.222	−	1441.26i	−0.0387285	−	0.269363i	0.961252	−	0.275673i	$-0.0889006\pi$
$31$	−207.222	−	1441.26i	−0.0387285	−	0.269363i	−0.999980	+	0.00630992i	$0.997991\pi$
$32$	6922.60	+	2032.66i	1.19507	+	0.350905i
$33$	1446.94	−	1669.85i	0.231294	−	0.266928i
$34$	1477.65	+	949.630i	0.219217	+	0.140882i
$35$	5422.25	+	3484.67i	0.748186	+	0.480830i
$36$	−1282.01	+	1479.52i	−0.164867	+	0.190267i
$37$	10129.1	+	2974.17i	1.21637	+	0.357158i	0.826090	−	0.563538i	$-0.190560\pi$
$37$	10129.1	+	2974.17i	1.21637	+	0.357158i	0.390280	+	0.920696i	$0.372378\pi$
$38$	−957.854	−	6662.02i	−0.107607	−	0.748423i
$39$	−6275.73	−	7242.58i	−0.660698	−	0.762486i
$40$	−2005.93	−	4392.38i	−0.198229	−	0.434060i
$41$	−13778.0	+	4045.59i	−1.28005	+	0.375857i	−0.849921	−	0.526911i	$-0.823350\pi$
$41$	−13778.0	+	4045.59i	−1.28005	+	0.375857i	−0.430129	+	0.902767i	$0.641532\pi$
$42$	2195.14	−	4806.68i	0.192016	−	0.420457i
$43$	−349.293	+	2429.38i	−0.0288083	+	0.200366i	−0.999143	−	0.0414008i	$-0.986818\pi$
$43$	−349.293	+	2429.38i	−0.0288083	+	0.200366i	0.970334	+	0.241767i	$0.0777270\pi$
$44$	−4991.62	+	3207.92i	−0.388696	+	0.249800i
$45$	6664.21			0.490589
$46$	−16155.9	−	10025.5i	−1.12573	−	0.698572i
$47$	−14668.4			−0.968587			−0.484294	−	0.874906i	$-0.660923\pi$
$47$	−14668.4			−0.968587			−0.484294	+	0.874906i	$0.660923\pi$
$48$	−9186.00	+	5903.48i	−0.575471	+	0.369833i
$49$	1518.46	−	10561.1i	0.0903467	−	0.628375i
$50$	11345.3	−	24842.7i	0.641785	−	1.40531i
$51$	−2023.87	+	594.261i	−0.108957	+	0.0319928i
$52$	10690.8	+	23409.7i	0.548282	+	1.20057i
$53$	−10453.7	−	12064.2i	−0.511185	−	0.589939i	0.440217	−	0.897892i	$-0.354902\pi$
$53$	−10453.7	−	12064.2i	−0.511185	−	0.589939i	−0.951402	+	0.307952i	$0.900356\pi$
$54$	−777.545	−	5407.95i	−0.0362862	−	0.252376i
$55$	19380.4	+	5690.61i	0.863887	+	0.253660i
$56$	3010.98	−	3474.86i	0.128303	−	0.148070i
$57$	6799.40	+	4369.71i	0.277194	+	0.178142i
$58$	33837.2	+	21745.9i	1.32076	+	0.848803i
$59$	−2980.70	+	3439.91i	−0.111478	+	0.128652i	−0.808746	−	0.588158i	$-0.799853\pi$
$59$	−2980.70	+	3439.91i	−0.111478	+	0.128652i	0.697268	+	0.716810i	$0.254399\pi$
$60$	−17171.4	−	5041.97i	−0.615782	−	0.180810i
$61$	3426.95	+	23835.0i	0.117919	+	0.820143i	0.959841	+	0.280544i	$0.0905150\pi$
$61$	3426.95	+	23835.0i	0.117919	+	0.820143i	−0.841922	+	0.539599i	$0.818576\pi$
$62$	−7146.31	−	8247.28i	−0.236104	−	0.272478i
$63$	2636.06	+	5772.17i	0.0836767	+	0.183226i
$64$	14630.1	−	4295.79i	0.446475	−	0.131097i
$65$	36393.1	−	79689.8i	1.06840	−	2.33948i
$66$	2356.67	−	16391.0i	0.0665946	−	0.463175i
$67$	48121.3	−	30925.7i	1.30964	−	0.841652i	0.315410	−	0.948956i	$-0.397858\pi$
$67$	48121.3	−	30925.7i	1.30964	−	0.841652i	0.994226	+	0.107304i	$0.0342217\pi$
$68$	5664.41			0.148553
$69$	21803.6	−	6778.28i	0.551323	−	0.171394i
$70$	48305.9			1.17830
$71$	−18560.9	+	11928.4i	−0.436972	+	0.280825i	−0.740575	−	0.671974i	$-0.765447\pi$
$71$	−18560.9	+	11928.4i	−0.436972	+	0.280825i	0.303603	+	0.952799i	$0.401810\pi$
$72$	676.559	−	4705.57i	0.0153806	−	0.106975i
$73$	−34608.6	+	75782.2i	−0.760110	+	1.66441i	−0.0128138	+	0.999918i	$0.504079\pi$
$73$	−34608.6	+	75782.2i	−0.760110	+	1.66441i	−0.747296	+	0.664491i	$0.768648\pi$
$74$	75913.3	−	22290.2i	1.61153	−	0.473188i
$75$	13624.1	+	29832.7i	0.279677	+	0.612406i
$76$	−14213.7	−	16403.5i	−0.282276	−	0.325763i
$77$	2737.14	+	19037.2i	0.0526102	+	0.365912i
$78$	−68913.6	−	20234.9i	−1.28253	−	0.376586i
$79$	−64841.5	+	74831.1i	−1.16892	+	1.34901i	−0.243576	+	0.969882i	$0.578320\pi$
$79$	−64841.5	+	74831.1i	−1.16892	+	1.34901i	−0.925346	+	0.379125i	$0.876225\pi$
$80$	−83974.6	−	53967.2i	−1.46698	−	0.942768i
$81$	5519.46	+	3547.14i	0.0934726	+	0.0600712i
$82$	−70476.1	+	81333.7i	−1.15746	+	1.33578i
$83$	−71187.8	−	20902.6i	−1.13425	−	0.333047i	−0.339875	−	0.940471i	$-0.610385\pi$
$83$	−71187.8	−	20902.6i	−1.13425	−	0.333047i	−0.794378	+	0.607424i	$0.792203\pi$
$84$	−2425.15	−	16867.3i	−0.0375008	−	0.260824i
$85$	−12627.3	−	14572.7i	−0.189567	−	0.218772i
$86$	7641.34	+	16732.2i	0.111410	+	0.243953i
$87$	−46345.2	+	13608.2i	−0.656457	+	0.192753i
$88$	5985.64	−	13106.7i	0.0823955	−	0.180421i
$89$	−16861.4	+	117273.i	−0.225641	+	1.56937i	0.490520	+	0.871430i	$0.336807\pi$
$89$	−16861.4	+	117273.i	−0.225641	+	1.56937i	−0.716160	+	0.697936i	$0.754102\pi$
$90$	42016.9	−	27002.6i	0.546786	−	0.351398i
$91$	83418.4			1.05599
$92$	−61308.7	+	969.207i	−0.755184	+	0.0119384i
$93$	13104.7			0.157116
$94$	−92482.2	+	59434.7i	−1.07954	+	0.693778i
$95$	−10515.1	+	73134.5i	−0.119538	+	0.831406i
$96$	−26974.4	+	59065.7i	−0.298727	+	0.654120i
$97$	138195.	−	40577.7i	1.49129	−	0.437883i	0.568339	−	0.822794i	$-0.307586\pi$
$97$	138195.	−	40577.7i	1.49129	−	0.437883i	0.922954	+	0.384911i	$0.125768\pi$
$98$	−33218.7	−	72738.8i	−0.349395	−	0.765069i
$99$	13022.4	+	15028.7i	0.133538	+	0.154111i
$100$	−12534.1	−	87176.3i	−0.125341	−	0.871763i
$101$	10603.2	+	3113.38i	0.103427	+	0.0303688i	0.333036	−	0.942914i	$-0.391927\pi$
$101$	10603.2	+	3113.38i	0.103427	+	0.0303688i	−0.229610	+	0.973283i	$0.573745\pi$
$102$	−10352.3	+	11947.2i	−0.0985228	+	0.113701i
$103$	−24893.8	−	15998.3i	−0.231206	−	0.148587i	0.419909	−	0.907566i	$-0.362062\pi$
$103$	−24893.8	−	15998.3i	−0.231206	−	0.148587i	−0.651115	+	0.758979i	$0.725698\pi$
$104$	−52573.9	−	33787.2i	−0.476636	−	0.306315i
$105$	−37987.8	+	43840.3i	−0.336257	+	0.388061i
$106$	−114791.	−	33705.8i	−0.992303	−	0.291366i
$107$	−3463.16	−	24086.8i	−0.0292424	−	0.203386i	0.969962	−	0.243255i	$-0.0782151\pi$
$107$	−3463.16	−	24086.8i	−0.0292424	−	0.203386i	−0.999205	+	0.0398689i	$0.987306\pi$
$108$	−11538.1	−	13315.7i	−0.0951862	−	0.109851i
$109$	41635.9	+	91170.0i	0.335662	+	0.734997i	0.999922	−	0.0125046i	$-0.00398044\pi$
$109$	41635.9	+	91170.0i	0.335662	+	0.734997i	−0.664260	+	0.747502i	$0.731253\pi$
$110$	145248.	−	42648.8i	1.14454	−	0.336066i
$111$	−39468.7	+	86424.4i	−0.304050	+	0.665777i
$112$	13526.8	−	94081.2i	0.101895	−	0.708692i
$113$	−139802.	+	89845.5i	−1.02996	+	0.661912i	−0.942483	−	0.334255i	$-0.891515\pi$
$113$	−139802.	+	89845.5i	−1.02996	+	0.661912i	−0.0874725	+	0.996167i	$0.527879\pi$
$114$	60574.8			0.436546
$115$	139165.	+	155567.i	0.981263	+	1.09691i
$116$	129711.			0.895019
$117$	72557.9	−	46630.1i	0.490027	−	0.314921i
$118$	−4854.76	+	33765.6i	−0.0320968	+	0.223238i
$119$	7627.26	−	16701.4i	0.0493743	−	0.108115i
$120$	41698.3	−	12243.7i	0.264342	−	0.0776177i
$121$	−41865.1	−	91671.8i	−0.259949	−	0.569210i
$122$	118183.	+	136390.i	0.718878	+	0.829629i
$123$	−18392.4	−	127922.i	−0.109616	−	0.762397i
$124$	−33766.3	−	9914.68i	−0.197210	−	0.0579062i
$125$	−27965.5	+	32273.9i	−0.160084	+	0.184747i
$126$	40008.2	+	25711.7i	0.224503	+	0.144279i
$127$	136466.	+	87701.4i	0.750785	+	0.482500i	0.859222	−	0.511603i	$-0.170948\pi$
$127$	136466.	+	87701.4i	0.750785	+	0.482500i	−0.108437	+	0.994103i	$0.534585\pi$
$128$	−76356.5	+	88120.1i	−0.411928	+	0.475390i
$129$	−21194.5	−	6223.27i	−0.112137	−	0.0329264i
$130$	−93440.5	−	649893.i	−0.484927	−	3.37274i
$131$	−13139.0	−	15163.2i	−0.0668937	−	0.0771994i	0.721316	−	0.692606i	$-0.243537\pi$
$131$	−13139.0	−	15163.2i	−0.0668937	−	0.0771994i	−0.788210	+	0.615406i	$0.788992\pi$
$132$	−22184.0	−	48576.2i	−0.110817	−	0.242654i
$133$	−67504.4	+	19821.1i	−0.330905	+	0.0971623i
$134$	178091.	−	389964.i	0.856799	−	1.87613i
$135$	−8535.75	+	59367.4i	−0.0403095	+	0.280359i
$136$	−11571.6	+	7436.64i	−0.0536472	+	0.0344770i
$137$	167155.			0.760883			0.380442	−	0.924805i	$-0.375772\pi$
$137$	167155.			0.760883			0.380442	+	0.924805i	$0.375772\pi$
$138$	110004.	−	131082.i	0.491712	−	0.585929i
$139$	63123.2			0.277110			0.138555	−	0.990355i	$-0.455754\pi$
$139$	63123.2			0.277110			0.138555	+	0.990355i	$0.455754\pi$
$140$	131050.	−	84220.6i	0.565089	−	0.363160i
$141$	18787.8	−	130672.i	0.0795845	−	0.553522i
$142$	−68691.4	+	150413.i	−0.285878	+	0.625986i
$143$	250826.	−	73649.2i	1.02573	−	0.301181i
$144$	−40824.8	−	89393.9i	−0.164066	−	0.359254i
$145$	−289156.	−	333704.i	−1.14212	−	1.31808i
$146$	88858.6	+	618025.i	0.344999	+	2.39952i
$147$	92137.5	+	27054.0i	0.351676	+	0.103261i
$148$	167084.	−	192825.i	0.627018	−	0.723617i
$149$	−115727.	−	74373.0i	−0.427039	−	0.274441i	0.309417	−	0.950926i	$-0.399866\pi$
$149$	−115727.	−	74373.0i	−0.427039	−	0.274441i	−0.736456	+	0.676485i	$0.763502\pi$
$150$	206777.	+	132887.i	0.750367	+	0.482232i
$151$	25289.6	−	29185.8i	0.0902609	−	0.104167i	−0.708822	−	0.705387i	$-0.750773\pi$
$151$	25289.6	−	29185.8i	0.0902609	−	0.104167i	0.799083	+	0.601220i	$0.205319\pi$
$152$	50572.4	+	14849.4i	0.177543	+	0.0521314i
$153$	−2701.67	−	18790.5i	−0.00933048	−	0.0648949i
$154$	94393.8	+	108936.i	0.320732	+	0.370144i
$155$	49765.8	+	108972.i	0.166380	+	0.364322i
$156$	−222236.	+	65254.4i	−0.731144	+	0.214683i
$157$	144763.	−	316987.i	0.468715	−	1.02634i	−0.516699	−	0.856167i	$-0.672839\pi$
$157$	144763.	−	316987.i	0.468715	−	1.02634i	0.985414	−	0.170175i	$-0.0544334\pi$
$158$	−105609.	+	734529.i	−0.336558	+	2.34081i
$159$	120862.	−	77673.1i	0.379137	−	0.243656i
$160$	−593596.			−1.83312
$161$	−79696.0	+	182072.i	−0.242310	+	0.553579i
$162$	49172.0			0.147208
$163$	−54175.5	+	34816.5i	−0.159711	+	0.102640i	−0.618055	−	0.786135i	$-0.712079\pi$
$163$	−54175.5	+	34816.5i	−0.159711	+	0.102640i	0.458344	+	0.888775i	$0.348443\pi$
$164$	−49391.5	+	343525.i	−0.143398	+	0.997353i
$165$	−75517.3	+	165360.i	−0.215942	+	0.472846i
$166$	−533523.	+	156657.i	−1.50274	+	0.441243i
$167$	−2018.37	−	4419.62i	−0.00560028	−	0.0122629i	0.906811	−	0.421537i	$-0.138509\pi$
$167$	−2018.37	−	4419.62i	−0.00560028	−	0.0122629i	−0.912411	+	0.409274i	$0.865782\pi$
$168$	27098.8	+	31273.7i	0.0740760	+	0.0854882i
$169$	−108520.	−	754770.i	−0.292275	−	2.03281i
$170$	−138660.	−	40714.2i	−0.367984	−	0.108050i
$171$	−47636.0	+	54974.9i	−0.124579	+	0.143772i
$172$	49902.6	+	32070.4i	0.128618	+	0.0826578i
$173$	−574896.	−	369463.i	−1.46041	−	0.938548i	−0.998671	−	0.0515306i	$-0.983590\pi$
$173$	−574896.	−	369463.i	−1.46041	−	0.938548i	−0.461737	−	0.887017i	$-0.652774\pi$
$174$	−237061.	+	273583.i	−0.593590	+	0.685039i
$175$	−273914.	−	80428.6i	−0.676114	−	0.198525i
$176$	−42390.2	−	294830.i	−0.103153	−	0.717448i
$177$	−26826.3	−	30959.2i	−0.0643617	−	0.0742774i
$178$	368869.	+	807711.i	0.872615	+	1.91076i
$179$	688784.	−	202245.i	1.60676	−	0.471787i	0.649341	−	0.760497i	$-0.275045\pi$
$179$	688784.	−	202245.i	1.60676	−	0.471787i	0.957416	+	0.288711i	$0.0932265\pi$
$180$	66909.6	−	146511.i	0.153924	−	0.337047i
$181$	−79226.6	+	551033.i	−0.179752	+	1.25020i	0.677583	+	0.735446i	$0.263027\pi$
$181$	−79226.6	+	551033.i	−0.179752	+	1.25020i	−0.857335	+	0.514758i	$0.827882\pi$
$182$	525940.	−	338001.i	1.17695	−	0.756380i
$183$	−216721.			−0.478379
$184$	123973.	−	82470.4i	0.269950	−	0.179578i
$185$	−868544.			−1.86579
$186$	82623.2	−	53098.7i	0.175114	−	0.112539i
$187$	8188.52	−	56952.4i	0.0171239	−	0.119099i
$188$	−147273.	+	322482.i	−0.303898	+	0.665444i
$189$	−54797.2	+	16089.9i	−0.111584	+	0.0327641i
$190$	230036.	+	503708.i	0.462287	+	1.01227i
$191$	−392976.	−	453519.i	−0.779440	−	0.899522i	0.217629	−	0.976032i	$-0.430168\pi$
$191$	−392976.	−	453519.i	−0.779440	−	0.899522i	−0.997069	+	0.0765097i	$0.975622\pi$
$192$	19529.8	+	135833.i	0.0382336	+	0.265921i
$193$	141990.	+	41692.0i	0.274388	+	0.0805675i	0.416031	−	0.909350i	$-0.363421\pi$
$193$	141990.	+	41692.0i	0.274388	+	0.0805675i	−0.141644	+	0.989918i	$0.545239\pi$
$194$	706883.	−	815786.i	1.34848	−	1.55622i
$195$	663294.	+	426273.i	1.24916	+	0.802789i
$196$	−216938.	−	139418.i	−0.403363	−	0.259226i
$197$	−441017.	+	508960.i	−0.809635	+	0.934369i	−0.998868	−	0.0475635i	$-0.984854\pi$
$197$	−441017.	+	508960.i	−0.809635	+	0.934369i	0.189233	+	0.981932i	$0.439400\pi$
$198$	142999.	+	41988.3i	0.259221	+	0.0761141i
$199$	63624.5	+	442518.i	0.113892	+	0.792133i	0.964072	+	0.265642i	$0.0855838\pi$
$199$	63624.5	+	442518.i	0.113892	+	0.792133i	−0.850180	+	0.526492i	$0.823507\pi$
$200$	140057.	+	161634.i	0.247588	+	0.285731i
$201$	213863.	+	468294.i	0.373375	+	0.817577i
$202$	79466.5	−	23333.5i	0.137027	−	0.0402347i
$203$	174659.	−	382450.i	0.297475	−	0.651380i
$204$	−7255.16	+	50460.8i	−0.0122060	+	0.0848943i
$205$	993884.	−	638730.i	1.65178	−	1.06153i
$206$	−221775.			−0.364120
$207$	32456.7	+	202917.i	0.0526476	+	0.329149i
$208$	−1.29190e6			−2.07048
$209$	−185475.	+	119198.i	−0.293711	+	0.188757i
$210$	−61871.9	+	430328.i	−0.0968155	+	0.673367i
$211$	283933.	−	621726.i	0.439045	−	0.961375i	−0.552727	−	0.833362i	$-0.686413\pi$
$211$	283933.	−	621726.i	0.439045	−	0.961375i	0.991773	−	0.128013i	$-0.0408598\pi$
$212$	−370184.	+	108696.i	−0.565690	+	0.166101i
$213$	−82489.1	−	180626.i	−0.124580	−	0.272792i
$214$	−119432.	−	137832.i	−0.178273	−	0.205738i
$215$	−28737.8	−	199876.i	−0.0423991	−	0.294893i
$216$	41052.5	+	12054.1i	0.0598694	+	0.0175793i
$217$	−74700.3	+	86208.8i	−0.107689	+	0.124280i
$218$	631918.	+	406109.i	0.900575	+	0.578764i
$219$	−630770.	−	405371.i	−0.888711	−	0.571140i
$220$	319689.	−	368941.i	0.445319	−	0.513925i
$221$	−239449.	−	70308.4i	−0.329785	−	0.0968338i
$222$	101337.	+	704815.i	0.138002	+	0.959827i
$223$	726487.	+	838411.i	0.978286	+	1.12900i	0.991633	+	0.129091i	$0.0412059\pi$
$223$	726487.	+	838411.i	0.978286	+	1.12900i	−0.0133471	+	0.999911i	$0.504249\pi$
$224$	−234800.	−	514140.i	−0.312664	−	0.684639i
$225$	−283212.	+	83158.5i	−0.372954	+	0.109509i
$226$	−517390.	+	1.13293e6i	−0.673824	+	1.47547i
$227$	164720.	−	1.14565e6i	0.212169	−	1.47567i	−0.553725	−	0.832700i	$-0.686794\pi$
$227$	164720.	−	1.14565e6i	0.212169	−	1.47567i	0.765894	−	0.642967i	$-0.222297\pi$
$228$	164334.	−	105611.i	0.209359	−	0.134547i
$229$	−203271.			−0.256146			−0.128073	−	0.991765i	$-0.540879\pi$
$229$	−203271.			−0.256146			−0.128073	+	0.991765i	$0.540879\pi$
$230$	1.50775e6	+	416945.i	1.87936	+	0.519708i
$231$	−173097.			−0.213432
$232$	−264982.	+	170294.i	−0.323219	+	0.207720i
$233$	−34755.8	+	241732.i	−0.0419409	+	0.291706i	0.958046	+	0.286614i	$0.0925298\pi$
$233$	−34755.8	+	241732.i	−0.0419409	+	0.291706i	−0.999987	+	0.00509146i	$0.998379\pi$
$234$	268527.	−	587992.i	0.320589	−	0.701992i
$235$	1.15795e6	−	340004.i	1.36779	−	0.401619i
$236$	45699.2	+	100067.i	0.0534107	+	0.116953i
$237$	−583573.	−	673480.i	−0.674877	−	0.778849i
$238$	−19583.2	−	136204.i	−0.0224100	−	0.155865i
$239$	−1.25049e6	−	367177.i	−1.41607	−	0.415797i	−0.517902	−	0.855440i	$-0.673287\pi$
$239$	−1.25049e6	−	367177.i	−1.41607	−	0.415797i	−0.898172	+	0.439643i	$0.855105\pi$
$240$	588318.	−	678956.i	0.659302	−	0.760875i
$241$	−861971.	−	553955.i	−0.955983	−	0.614373i	−0.0330996	−	0.999452i	$-0.510538\pi$
$241$	−861971.	−	553955.i	−0.955983	−	0.614373i	−0.922884	+	0.385079i	$0.874174\pi$
$242$	−635397.	−	408345.i	−0.697439	−	0.448217i
$243$	−38668.9	+	44626.3i	−0.0420093	+	0.0484814i
$244$	558414.	+	163965.i	0.600457	+	0.176310i
$245$	124930.	+	868906.i	0.132969	+	0.924821i
$246$	−634285.	−	732003.i	−0.668261	−	0.771215i
$247$	397243.	+	869841.i	0.414299	+	0.907189i
$248$	81996.8	−	24076.4i	0.0846579	−	0.0248578i
$249$	277388.	−	607396.i	0.283524	−	0.620831i
$250$	−45548.3	+	316796.i	−0.0460917	+	0.320575i
$251$	−272664.	+	175231.i	−0.273177	+	0.175560i	−0.670055	−	0.742311i	$-0.733730\pi$
$251$	−272664.	+	175231.i	−0.273177	+	0.175560i	0.396879	+	0.917871i	$0.370093\pi$
$252$	153367.			0.152135
$253$	−78883.7	+	617826.i	−0.0774793	+	0.606827i
$254$	1.21575e6			1.18239
$255$	145993.	−	93823.7i	0.140598	−	0.0903571i
$256$	−193803.	+	1.34793e6i	−0.184825	+	1.28549i
$257$	−6322.39	+	13844.1i	−0.00597102	+	0.0130747i	−0.912594	−	0.408867i	$-0.865924\pi$
$257$	−6322.39	+	13844.1i	−0.00597102	+	0.0130747i	0.906623	+	0.421942i	$0.138651\pi$
$258$	−158844.	+	46640.9i	−0.148567	+	0.0436232i
$259$	−343557.	−	752285.i	−0.318236	−	0.696840i
$260$	−1.38657e6	−	1.60019e6i	−1.27207	−	1.46804i
$261$	−61866.4	−	430291.i	−0.0562152	−	0.390985i
$262$	−144279.	−	42364.2i	−0.129853	−	0.0381282i
$263$	774738.	−	894095.i	0.690662	−	0.797066i	−0.296798	−	0.954940i	$-0.595919\pi$
$263$	774738.	−	894095.i	0.690662	−	0.797066i	0.987459	+	0.157874i	$0.0504641\pi$
$264$	109093.	+	70109.9i	0.0963358	+	0.0619113i
$265$	1.10487e6	+	710055.i	0.966485	+	0.621122i
$266$	−345292.	+	398489.i	−0.299215	+	0.345312i
$267$	−1.02312e6	−	300415.i	−0.878311	−	0.257895i
$268$	−196751.	−	1.36844e6i	−0.167333	−	1.16382i
$269$	1.41077e6	+	1.62812e6i	1.18871	+	1.37185i	0.911636	+	0.410999i	$0.134820\pi$
$269$	1.41077e6	+	1.62812e6i	1.18871	+	1.37185i	0.277076	+	0.960848i	$0.410635\pi$
$270$	186733.	+	408889.i	0.155888	+	0.341347i
$271$	661565.	−	194253.i	0.547204	−	0.160674i	0.00356650	−	0.999994i	$-0.498865\pi$
$271$	661565.	−	194253.i	0.547204	−	0.160674i	0.543638	+	0.839320i	$0.317047\pi$
$272$	−118124.	+	258655.i	−0.0968087	+	0.211982i
$273$	−106845.	+	743123.i	−0.0867656	+	0.603468i
$274$	1.05389e6	−	677293.i	0.848043	−	0.545004i
$275$	−894628.			−0.713363
$276$	69892.2	−	547404.i	0.0552276	−	0.432549i
$277$	−229067.			−0.179376			−0.0896878	−	0.995970i	$-0.528587\pi$
$277$	−229067.			−0.179376			−0.0896878	+	0.995970i	$0.528587\pi$
$278$	397983.	−	255768.i	0.308853	−	0.198488i
$279$	−16784.9	+	116742.i	−0.0129095	+	0.0897876i
$280$	−157147.	+	344103.i	−0.119787	+	0.262297i
$281$	−624578.	+	183393.i	−0.471869	+	0.138553i	−0.509017	−	0.860757i	$-0.669991\pi$
$281$	−624578.	+	183393.i	−0.471869	+	0.138553i	0.0371481	+	0.999310i	$0.488173\pi$
$282$	−411013.	−	899994.i	−0.307775	−	0.673933i
$283$	−1.15203e6	−	1.32951e6i	−0.855060	−	0.986792i	0.144937	−	0.989441i	$-0.453702\pi$
$283$	−1.15203e6	−	1.32951e6i	−0.855060	−	0.986792i	−0.999996	+	0.00264925i	$0.999157\pi$
$284$	75889.1	+	527820.i	0.0558320	+	0.388320i
$285$	−638042.	−	187346.i	−0.465305	−	0.136626i
$286$	1.28300e6	−	1.48066e6i	0.927497	−	1.07039i
$287$	946369.	+	608194.i	0.678197	+	0.435851i
$288$	−491631.	−	315952.i	−0.349267	−	0.224460i
$289$	893838.	−	1.03154e6i	0.629527	−	0.726513i
$290$	−3.17522e6	−	932328.i	−2.21707	−	0.650989i
$291$	184477.	+	1.28307e6i	0.127706	+	0.888214i
$292$	1.31858e6	+	1.52173e6i	0.905004	+	1.04443i
$293$	519525.	+	1.13760e6i	0.353539	+	0.774142i	0.999938	+	0.0111428i	$0.00354692\pi$
$293$	519525.	+	1.13760e6i	0.353539	+	0.774142i	−0.646399	+	0.763000i	$0.723726\pi$
$294$	690533.	−	202759.i	0.465925	−	0.136808i
$295$	155566.	−	340643.i	0.104078	−	0.227900i
$296$	−88175.6	+	613275.i	−0.0584951	+	0.406842i
$297$	−150561.	+	96759.6i	−0.0990424	+	0.0636507i
$298$	−1.03099e6			−0.672533
$299$	2.60370e6	+	720013.i	1.68428	+	0.465760i
$300$	792655.			0.508488
$301$	161754.	−	103953.i	0.102905	−	0.0661333i
$302$	41190.0	−	286482.i	0.0259881	−	0.180751i
$303$	−41316.1	+	90469.6i	−0.0258531	+	0.0566104i
$304$	1.04544e6	−	306970.i	0.648808	−	0.190507i
$305$	−823007.	−	1.80213e6i	−0.506587	−	1.10927i
$306$	−93170.7	−	107525.i	−0.0568821	−	0.0656455i
$307$	312948.	+	2.17660e6i	0.189507	+	1.31805i	0.833287	+	0.552840i	$0.186456\pi$
$307$	312948.	+	2.17660e6i	0.189507	+	1.31805i	−0.643780	+	0.765211i	$0.722635\pi$
$308$	446011.	+	130961.i	0.267897	+	0.0786618i
$309$	174404.	−	201273.i	0.103911	−	0.119919i
$310$	755307.	+	485406.i	0.446395	+	0.286881i
$311$	2.11365e6	+	1.35836e6i	1.23917	+	0.796367i	0.985294	−	0.170870i	$-0.0546578\pi$
$311$	2.11365e6	+	1.35836e6i	1.23917	+	0.796367i	0.253877	+	0.967237i	$0.418294\pi$
$312$	368328.	−	425073.i	0.214214	−	0.247216i
$313$	−2.86574e6	−	841457.i	−1.65339	−	0.485480i	−0.683691	−	0.729772i	$-0.739626\pi$
$313$	−2.86574e6	−	841457.i	−1.65339	−	0.485480i	−0.969702	+	0.244292i	$0.921445\pi$
$314$	−371684.	−	2.58512e6i	−0.212740	−	1.47964i
$315$	−341890.	−	394562.i	−0.194138	−	0.224047i
$316$	994130.	+	2.17684e6i	0.560048	+	1.22633i
$317$	−135902.	+	39904.3i	−0.0759585	+	0.0223034i	−0.319491	−	0.947589i	$-0.603512\pi$
$317$	−135902.	+	39904.3i	−0.0759585	+	0.0223034i	0.243533	+	0.969893i	$0.421694\pi$
$318$	447293.	−	979434.i	0.248041	−	0.543135i
$319$	187512.	−	1.30417e6i	0.103169	−	0.717560i
$320$	−1.05535e6	+	678232.i	−0.576131	+	0.370257i
$321$	219011.			0.118632
$322$	235264.	+	1.47086e6i	0.126449	+	0.790553i
$323$	210474.			0.112252
$324$	133399.	−	85730.6i	0.0705978	−	0.0453705i
$325$	−552214.	+	3.84073e6i	−0.290001	+	2.01700i
$326$	−200496.	+	439025.i	−0.104487	+	0.228794i
$327$	−865507.	+	254136.i	−0.447611	+	0.131431i
$328$	−350104.	−	766621.i	−0.179685	−	0.393456i
$329$	752525.	+	868460.i	0.383293	+	0.442344i
$330$	193893.	+	1.34856e6i	0.0980116	+	0.681686i
$331$	1.12796e6	+	331198.i	0.565877	+	0.166156i	0.552143	−	0.833749i	$-0.313810\pi$
$331$	1.12796e6	+	331198.i	0.565877	+	0.166156i	0.0137336	+	0.999906i	$0.495628\pi$
$332$	−1.17427e6	+	1.35518e6i	−0.584688	+	0.674766i
$333$	−719350.	−	462298.i	−0.355492	−	0.228461i
$334$	−30633.3	−	19686.8i	−0.0150255	−	0.00965627i
$335$	−3.08194e6	+	3.55674e6i	−1.50042	+	1.73157i
$336$	820786.	+	241005.i	0.396627	+	0.116460i
$337$	−273759.	−	1.90404e6i	−0.131309	−	0.913273i	−0.943851	−	0.330371i	$-0.892826\pi$
$337$	−273759.	−	1.90404e6i	−0.131309	−	0.913273i	0.812542	−	0.582902i	$-0.198083\pi$
$338$	−3.74244e6	−	4.31900e6i	−1.78182	−	2.05633i
$339$	−621316.	−	1.36049e6i	−0.293638	−	0.642979i
$340$	−447157.	+	131297.i	−0.209779	+	0.0615968i
$341$	−148499.	+	325168.i	−0.0691574	+	0.151434i
$342$	−77586.2	+	539624.i	−0.0358690	+	0.249474i
$343$	−1.81084e6	+	1.16376e6i	−0.831084	+	0.534105i
$344$	−144049.			−0.0656317
$345$	−1.56410e6	+	1.04048e6i	−0.707483	+	0.470638i
$346$	−5.12166e6			−2.29996
$347$	1.25446e6	−	806194.i	0.559286	−	0.359431i	−0.230254	−	0.973131i	$-0.573956\pi$
$347$	1.25446e6	−	806194.i	0.559286	−	0.359431i	0.789540	+	0.613699i	$0.210319\pi$
$348$	−166138.	+	1.15552e6i	−0.0735397	+	0.511480i
$349$	−628067.	+	1.37528e6i	−0.276021	+	0.604402i	−0.995976	−	0.0896187i	$-0.971435\pi$
$349$	−628067.	+	1.37528e6i	−0.276021	+	0.604402i	0.719955	+	0.694021i	$0.244162\pi$
$350$	−2.05288e6	+	602779.i	−0.895763	+	0.263020i
$351$	322465.	+	706100.i	0.139706	+	0.305913i
$352$	−1.15994e6	−	1.33864e6i	−0.498973	−	0.575846i
$353$	592773.	+	4.12283e6i	0.253193	+	1.76100i	0.578779	+	0.815485i	$0.303529\pi$
$353$	592773.	+	4.12283e6i	0.253193	+	1.76100i	−0.325586	+	0.945513i	$0.605561\pi$
$354$	−294579.	−	86496.1i	−0.124938	−	0.0366850i
$355$	1.18873e6	−	1.37187e6i	0.500627	−	0.577754i
$356$	2.40894e6	+	1.54813e6i	1.00740	+	0.647416i
$357$	139013.	+	89338.3i	0.0577278	+	0.0370994i
$358$	3.52321e6	−	4.06600e6i	1.45288	−	1.67672i
$359$	1.12066e6	+	329056.i	0.458921	+	0.134751i	0.503018	−	0.864276i	$-0.332223\pi$
$359$	1.12066e6	+	329056.i	0.458921	+	0.134751i	−0.0440970	+	0.999027i	$0.514041\pi$
$360$	55663.4	+	387147.i	0.0226367	+	0.157442i
$361$	1.09336e6	+	1.26180e6i	0.441564	+	0.509592i
$362$	1.73321e6	+	3.79520e6i	0.695152	+	1.52217i
$363$	870271.	−	255534.i	0.346647	−	0.101785i
$364$	837531.	−	1.83394e6i	0.331320	−	0.725489i
$365$	975474.	−	6.78457e6i	0.383251	−	2.66557i
$366$	−1.36639e6	+	878126.i	−0.533178	+	0.342653i
$367$	1.19181e6			0.461893			0.230947	−	0.972966i	$-0.425818\pi$
$367$	1.19181e6			0.461893			0.230947	+	0.972966i	$0.425818\pi$
$368$	1.23425e6	−	2.81976e6i	0.475100	−	1.08541i
$369$	1.16313e6			0.444697
$370$	−5.47604e6	+	3.51924e6i	−2.07952	+	1.33642i
$371$	−177975.	+	1.23784e6i	−0.0671310	+	0.466906i
$372$	131573.	−	288105.i	0.0492957	−	0.107943i
$373$	740809.	−	217521.i	0.275698	−	0.0809523i	−0.140961	−	0.990015i	$-0.545019\pi$
$373$	740809.	−	217521.i	0.275698	−	0.0809523i	0.416659	+	0.909063i	$0.363201\pi$
$374$	−179137.	−	392256.i	−0.0662226	−	0.145007i
$375$	−251690.	−	290466.i	−0.0924246	−	0.106664i
$376$	−122519.	−	852139.i	−0.0446925	−	0.310843i
$377$	−5.48321e6	−	1.61001e6i	−1.98692	−	0.583414i
$378$	−280294.	+	323476.i	−0.100898	+	0.116443i
$379$	−1.05517e6	−	678116.i	−0.377333	−	0.242497i	0.338203	−	0.941073i	$-0.390181\pi$
$379$	−1.05517e6	−	678116.i	−0.377333	−	0.242497i	−0.715536	+	0.698576i	$0.753817\pi$
$380$	1.50227e6	+	965453.i	0.533691	+	0.342983i
$381$	−956069.	+	1.10336e6i	−0.337425	+	0.389409i
$382$	−4.31526e6	−	1.26707e6i	−1.51303	−	0.444267i
$383$	2369.03	+	16476.9i	0.000825226	+	0.00573957i	0.990230	−	0.139444i	$-0.0445317\pi$
$383$	2369.03	+	16476.9i	0.000825226	+	0.00573957i	−0.989405	+	0.145184i	$0.953623\pi$
$384$	−687208.	−	793081.i	−0.237827	−	0.274466i
$385$	−657344.	−	1.43938e6i	−0.226017	−	0.494908i
$386$	1.06416e6	−	312465.i	0.363528	−	0.106741i
$387$	82586.0	−	180838.i	0.0280304	−	0.0613780i
$388$	495402.	−	3.44560e6i	0.167062	−	1.16194i
$389$	1.95187e6	−	1.25439e6i	0.653999	−	0.420300i	−0.171126	−	0.985249i	$-0.554741\pi$
$389$	1.95187e6	−	1.25439e6i	0.653999	−	0.420300i	0.825126	+	0.564949i	$0.191104\pi$
$390$	5.90918e6			1.96728
$391$	382222.	−	455459.i	0.126437	−	0.150663i
$392$	626214.			0.205829
$393$	151909.	−	97626.0i	0.0496138	−	0.0318848i
$394$	−718297.	+	4.99587e6i	−0.233111	+	1.62133i
$395$	3.38415e6	−	7.41026e6i	1.09133	−	2.38969i
$396$	461149.	−	135406.i	0.147776	−	0.0433909i
$397$	1.67945e6	+	3.67748e6i	0.534798	+	1.17105i	0.963527	+	0.267612i	$0.0862344\pi$
$397$	1.67945e6	+	3.67748e6i	0.534798	+	1.17105i	−0.428728	+	0.903433i	$0.641038\pi$
$398$	2.19417e6	+	2.53221e6i	0.694326	+	0.801295i
$399$	−90112.0	−	626743.i	−0.0283368	−	0.197087i
$400$	4.24212e6	+	1.24560e6i	1.32566	+	0.389250i
$401$	−957624.	+	1.10516e6i	−0.297395	+	0.343212i	−0.884706	−	0.466149i	$-0.845641\pi$
$401$	−957624.	+	1.10516e6i	−0.297395	+	0.343212i	0.587311	+	0.809361i	$0.300187\pi$
$402$	3.24585e6	+	2.08598e6i	1.00176	+	0.643791i
$403$	1.30432e6	+	838236.i	0.400057	+	0.257101i
$404$	174904.	−	201850.i	0.0533147	−	0.0615285i
$405$	−517936.	−	152080.i	−0.156906	−	0.0460716i
$406$	−448443.	−	3.11899e6i	−0.135018	−	0.939071i
$407$	−1.69721e6	−	1.95868e6i	−0.507866	−	0.586108i
$408$	−51427.2	−	112610.i	−0.0152947	−	0.0334908i
$409$	−441196.	+	129547.i	−0.130414	+	0.0382929i	−0.346288	−	0.938128i	$-0.612558\pi$
$409$	−441196.	+	129547.i	−0.130414	+	0.0382929i	0.215874	+	0.976421i	$0.430740\pi$
$410$	3.67823e6	−	8.05420e6i	1.08064	−	2.36626i
$411$	−214098.	+	1.48908e6i	−0.0625184	+	0.434825i
$412$	−601657.	+	386661.i	−0.174625	+	0.112224i
$413$	356581.			0.102869
$414$	1.02683e6	+	1.14785e6i	0.294441	+	0.329143i
$415$	6.10418e6			1.73983
$416$	−6.46289e6	+	4.15345e6i	−1.83102	+	1.17673i
$417$	−80850.3	+	562326.i	−0.0227689	+	0.158361i
$418$	−686419.	+	1.50305e6i	−0.192154	+	0.420758i
$419$	5.71376e6	−	1.67771e6i	1.58996	−	0.466855i	0.637232	−	0.770672i	$-0.280079\pi$
$419$	5.71376e6	−	1.67771e6i	1.58996	−	0.466855i	0.952730	+	0.303817i	$0.0982611\pi$
$420$	582417.	+	1.27532e6i	0.161106	+	0.352772i
$421$	−2.51162e6	−	2.89856e6i	−0.690634	−	0.797034i	0.296821	−	0.954933i	$-0.404074\pi$
$421$	−2.51162e6	−	2.89856e6i	−0.690634	−	0.797034i	−0.987455	+	0.157899i	$0.949528\pi$
$422$	−729006.	−	5.07035e6i	−0.199274	−	1.38598i
$423$	1.14001e6	+	334738.i	0.309784	+	0.0909609i
$424$	613534.	−	708055.i	0.165739	−	0.191273i
$425$	718470.	+	461733.i	0.192946	+	0.123999i
$426$	−1.25196e6	−	804584.i	−0.334245	−	0.214807i
$427$	1.23536e6	−	1.42569e6i	0.327888	−	0.378403i
$428$	−564315.	−	165698.i	−0.148906	−	0.0437228i
$429$	334829.	+	2.32879e6i	0.0878376	+	0.610924i
$430$	−991060.	−	1.14374e6i	−0.258481	−	0.298303i
$431$	1.65894e6	+	3.63256e6i	0.430166	+	0.941933i	0.993300	+	0.115567i	$0.0368684\pi$
$431$	1.65894e6	+	3.63256e6i	0.430166	+	0.941933i	−0.563134	+	0.826366i	$0.690404\pi$
$432$	848646.	−	249185.i	0.218785	−	0.0642410i
$433$	2.25438e6	−	4.93639e6i	0.577839	−	1.26529i	−0.364679	−	0.931133i	$-0.618821\pi$
$433$	2.25438e6	−	4.93639e6i	0.577839	−	1.26529i	0.942518	−	0.334157i	$-0.108451\pi$
$434$	−121667.	+	846211.i	−0.0310061	+	0.215652i
$435$	3.34313e6	−	2.14850e6i	0.847091	−	0.544392i
$436$	2.42239e6			0.610277
$437$	−2.27807e6	+	36013.1i	−0.570641	+	0.00902105i
$438$	−5.61943e6			−1.39961
$439$	−4.80343e6	+	3.08698e6i	−1.18957	+	0.764491i	−0.977122	−	0.212681i	$-0.931780\pi$
$439$	−4.80343e6	+	3.08698e6i	−1.18957	+	0.764491i	−0.212449	+	0.977172i	$0.568144\pi$
$440$	−168711.	+	1.17341e6i	−0.0415442	+	0.288946i
$441$	−359021.	+	786145.i	−0.0879069	+	0.192489i
$442$	−1.79457e6	+	526933.i	−0.436923	+	0.128292i
$443$	2.25538e6	+	4.93859e6i	0.546021	+	1.19562i	0.958615	+	0.284705i	$0.0918957\pi$
$443$	2.25538e6	+	4.93859e6i	0.546021	+	1.19562i	−0.412594	+	0.910915i	$0.635377\pi$
$444$	1.50375e6	+	1.73542e6i	0.362009	+	0.417780i
$445$	−1.38726e6	−	9.64857e6i	−0.332090	−	2.30974i
$446$	7.97753e6	+	2.34242e6i	1.89903	+	0.557605i
$447$	810771.	−	935679.i	0.191924	−	0.221492i
$448$	−1.00490e6	−	645808.i	−0.236552	−	0.152023i
$449$	−5.75511e6	−	3.69859e6i	−1.34722	−	0.865805i	−0.349745	−	0.936845i	$-0.613732\pi$
$449$	−5.75511e6	−	3.69859e6i	−1.34722	−	0.865805i	−0.997473	+	0.0710403i	$0.977368\pi$
$450$	−1.44866e6	+	1.67184e6i	−0.337237	+	0.389192i
$451$	3.38255e6	+	993207.i	0.783074	+	0.229931i
$452$	571603.	+	3.97559e6i	0.131598	+	0.915283i
$453$	227606.	+	262672.i	0.0521122	+	0.0601406i
$454$	−3.60351e6	−	7.89059e6i	−0.820515	−	1.79668i
$455$	−6.58518e6	+	1.93358e6i	−1.49121	+	0.437859i
$456$	−197059.	+	431499.i	−0.0443797	+	0.0971780i
$457$	−593515.	+	4.12799e6i	−0.132936	+	0.924588i	0.808764	+	0.588133i	$0.200137\pi$
$457$	−593515.	+	4.12799e6i	−0.132936	+	0.924588i	−0.941700	+	0.336455i	$0.890772\pi$
$458$	−1.28160e6	+	823632.i	−0.285488	+	0.183472i
$459$	170854.			0.0378524
$460$	4.81734e6	−	1.49761e6i	1.06148	−	0.329992i
$461$	3.83997e6			0.841542			0.420771	−	0.907167i	$-0.361760\pi$
$461$	3.83997e6			0.841542			0.420771	+	0.907167i	$0.361760\pi$
$462$	−1.09135e6	+	701368.i	−0.237881	+	0.152877i
$463$	195550.	−	1.36008e6i	0.0423941	−	0.294858i	−0.957583	−	0.288156i	$-0.906958\pi$
$463$	195550.	−	1.36008e6i	0.0423941	−	0.294858i	0.999978	−	0.00670147i	$-0.00213316\pi$
$464$	−2.70495e6	+	5.92301e6i	−0.583263	+	1.27717i
$465$	−1.03451e6	+	303758.i	−0.221871	+	0.0651472i
$466$	760340.	+	1.66491e6i	0.162197	+	0.355162i
$467$	−471573.	−	544224.i	−0.100059	−	0.115474i	0.703511	−	0.710684i	$-0.251614\pi$
$467$	−471573.	−	544224.i	−0.100059	−	0.115474i	−0.803570	+	0.595210i	$0.797069\pi$
$468$	−296664.	−	2.06334e6i	−0.0626110	−	0.435469i
$469$	−4.29973e6	−	1.26251e6i	−0.902629	−	0.265036i
$470$	5.92303e6	−	6.83555e6i	1.23680	−	1.42734i
$471$	2.63843e6	+	1.69561e6i	0.548015	+	0.352188i
$472$	−224733.	−	144427.i	−0.0464314	−	0.0298396i
$473$	394590.	−	455381.i	0.0810948	−	0.0935884i
$474$	−6.40820e6	−	1.88162e6i	−1.31006	−	0.384668i
$475$	−465732.	−	3.23924e6i	−0.0947113	−	0.658732i
$476$	−290598.	−	335368.i	−0.0587861	−	0.0678428i
$477$	537138.	+	1.17617e6i	0.108091	+	0.236687i
$478$	−9.37192e6	+	2.75184e6i	−1.87611	+	0.550876i
$479$	−2.81212e6	+	6.15768e6i	−0.560009	+	1.22625i	0.391940	+	0.919991i	$0.371804\pi$
$479$	−2.81212e6	+	6.15768e6i	−0.560009	+	1.22625i	−0.951949	+	0.306258i	$0.900923\pi$
$480$	760298.	−	5.28799e6i	0.150619	−	1.04758i
$481$	−9.45644e6	+	6.07729e6i	−1.86365	+	1.19770i
$482$	−7.67916e6			−1.50555
$483$	−1.51989e6	−	943167.i	−0.296446	−	0.183959i
$484$	−2.43572e6			−0.472622
$485$	−9.96877e6	+	6.40654e6i	−1.92436	+	1.23671i
$486$	−62981.2	+	438044.i	−0.0120954	+	0.0841253i
$487$	−1.30103e6	+	2.84886e6i	−0.248580	+	0.544314i	−0.992254	−	0.124229i	$-0.960354\pi$
$487$	−1.30103e6	+	2.84886e6i	−0.248580	+	0.544314i	0.743674	+	0.668543i	$0.233082\pi$
$488$	−1.35603e6	+	398167.i	−0.257763	+	0.0756860i
$489$	−240769.	−	527210.i	−0.0455332	−	0.0997038i
$490$	4.30837e6	+	4.97212e6i	0.810630	+	0.935517i
$491$	1.02789e6	+	7.14915e6i	0.192417	+	1.33829i	0.825586	+	0.564277i	$0.190845\pi$
$491$	1.02789e6	+	7.14915e6i	0.192417	+	1.33829i	−0.633168	+	0.774014i	$0.718246\pi$
$492$	−2.99700e6	−	879997.i	−0.558179	−	0.163896i
$493$	−823695.	+	950595.i	−0.152633	+	0.176148i
$494$	6.02905e6	+	3.87464e6i	1.11156	+	0.714354i
$495$	−1.37637e6	−	884536.i	−0.252476	−	0.162257i
$496$	1.15689e6	−	1.33512e6i	0.211148	−	0.243678i
$497$	1.65845e6	+	486965.i	0.301170	+	0.0884315i
$498$	−712204.	−	4.95349e6i	−0.128686	−	0.895030i
$499$	1.76522e6	+	2.03718e6i	0.317357	+	0.366250i	0.891906	−	0.452220i	$-0.149368\pi$
$499$	1.76522e6	+	2.03718e6i	0.317357	+	0.366250i	−0.574549	+	0.818470i	$0.694822\pi$
$500$	428759.	+	938852.i	0.0766988	+	0.167947i
$501$	41956.9	−	12319.7i	0.00746808	−	0.00219283i
$502$	−1.00909e6	+	2.20960e6i	−0.178719	+	0.391341i
$503$	513129.	−	3.56889e6i	0.0904288	−	0.628946i	−0.893323	−	0.449414i	$-0.851633\pi$
$503$	513129.	−	3.56889e6i	0.0904288	−	0.628946i	0.983752	−	0.179532i	$-0.0574582\pi$
$504$	−313308.	+	201351.i	−0.0549408	+	0.0353083i
$505$	−909198.			−0.158646
$506$	2.00601e6	+	4.21493e6i	0.348302	+	0.731836i
$507$	6.86278e6			1.18572
$508$	3.29824e6	−	2.11965e6i	0.567051	−	0.364422i
$509$	−1.36953e6	+	9.52529e6i	−0.234302	+	1.62961i	0.444845	+	0.895608i	$0.353259\pi$
$509$	−1.36953e6	+	9.52529e6i	−0.234302	+	1.62961i	−0.679147	+	0.734002i	$0.737650\pi$
$510$	540299.	−	1.18309e6i	0.0919832	−	0.201415i
$511$	6.26227e6	−	1.83877e6i	1.06091	−	0.311512i
$512$	2.68977e6	+	5.88978e6i	0.453462	+	0.992943i
$513$	−428724.	−	494774.i	−0.0719257	−	0.0830067i
$514$	16233.0	+	112903.i	0.00271013	+	0.0188493i
$515$	2.33599e6	+	685908.i	0.388108	+	0.113959i
$516$	−349613.	+	403475.i	−0.0578047	+	0.0667102i
$517$	3.02948e6	+	1.94693e6i	0.498473	+	0.320349i
$518$	−5.21425e6	−	3.35099e6i	−0.853822	−	0.548718i
$519$	4.02767e6	−	4.64818e6i	0.656350	−	0.757469i
$520$	4.93343e6	+	1.44859e6i	0.800093	+	0.234929i
$521$	−910848.	−	6.33509e6i	−0.147012	−	1.02249i	−0.921076	−	0.389382i	$-0.872689\pi$
$521$	−910848.	−	6.33509e6i	−0.147012	−	1.02249i	0.774065	−	0.633106i	$-0.218220\pi$
$522$	−2.13355e6	−	2.46224e6i	−0.342709	−	0.395507i
$523$	472683.	+	1.03503e6i	0.0755641	+	0.165462i	0.943644	−	0.330962i	$-0.107373\pi$
$523$	472683.	+	1.03503e6i	0.0755641	+	0.165462i	−0.868080	+	0.496424i	$0.834646\pi$
$524$	−465279.	+	136618.i	−0.0740261	+	0.0217360i
$525$	1.06733e6	−	2.33712e6i	0.169005	−	0.370069i
$526$	1.26184e6	−	8.77628e6i	0.198856	−	1.38308i
$527$	287084.	−	184498.i	0.0450280	−	0.0289377i
$528$	2.68076e6			0.418478
$529$	−4.05905e6	+	4.99506e6i	−0.630645	+	0.776072i
$530$	9.84308e6			1.52209
$531$	310157.	−	199326.i	0.0477359	−	0.0306780i
$532$	−241990.	+	1.68308e6i	−0.0370696	+	0.257825i
$533$	6.35184e6	−	1.39086e7i	0.968460	−	2.12063i
$534$	−7.66787e6	+	2.25149e6i	−1.16365	+	0.341678i
$535$	831705.	+	1.82118e6i	0.125627	+	0.275086i
$536$	2.19852e6	+	2.53722e6i	0.330535	+	0.381458i
$537$	919462.	+	6.39500e6i	0.137594	+	0.956984i
$538$	1.54917e7	+	4.54876e6i	2.30750	+	0.677544i
$539$	−1.71537e6	+	1.97965e6i	−0.254324	+	0.293505i
$540$	1.21948e6	+	783713.i	0.179966	+	0.115657i
$541$	−4.37011e6	−	2.80850e6i	−0.641947	−	0.412554i	0.178769	−	0.983891i	$-0.442789\pi$
$541$	−4.37011e6	−	2.80850e6i	−0.641947	−	0.412554i	−0.820716	+	0.571337i	$0.806425\pi$
$542$	3.38398e6	−	3.90532e6i	0.494800	−	0.571029i
$543$	−4.80734e6	−	1.41156e6i	−0.699690	−	0.205447i
$544$	240644.	+	1.67372e6i	0.0348640	+	0.242485i
$545$	−5.40007e6	−	6.23201e6i	−0.778767	−	0.898745i
$546$	2.33741e6	+	5.11821e6i	0.335546	+	0.734744i
$547$	−1.17321e7	+	3.44485e6i	−1.67651	+	0.492269i	−0.975338	−	0.220718i	$-0.929160\pi$
$547$	−1.17321e7	+	3.44485e6i	−1.67651	+	0.492269i	−0.701177	+	0.712987i	$0.747342\pi$
$548$	1.67826e6	−	3.67487e6i	0.238730	−	0.522746i
$549$	277583.	−	1.93063e6i	0.0393063	−	0.273381i
$550$	−5.64050e6	+	3.62493e6i	−0.795079	+	0.510967i
$551$	4.81971e6			0.676305
$552$	575890.	+	1.21003e6i	0.0804437	+	0.169024i
$553$	7.75698e6			1.07865
$554$	−1.44423e6	+	928153.i	−0.199923	+	0.128483i
$555$	1.11246e6	−	7.73733e6i	0.153304	−	1.06625i
$556$	633765.	−	1.38775e6i	0.0869444	−	0.190382i
$557$	1.37972e6	−	405121.i	0.188431	−	0.0553283i	−0.186156	−	0.982520i	$-0.559603\pi$
$557$	1.37972e6	−	405121.i	0.188431	−	0.0553283i	0.374586	+	0.927192i	$0.377785\pi$
$558$	367198.	+	804051.i	0.0499246	+	0.109320i
$559$	−1.71144e6	−	1.97510e6i	−0.231650	−	0.267338i
$560$	1.11291e6	+	7.74046e6i	0.149965	+	1.04303i
$561$	496866.	+	145893.i	0.0666550	+	0.0195717i
$562$	−3.19479e6	+	3.68698e6i	−0.426679	+	0.492414i
$563$	−8.97462e6	−	5.76764e6i	−1.19329	−	0.766879i	−0.215505	−	0.976503i	$-0.569140\pi$
$563$	−8.97462e6	−	5.76764e6i	−1.19329	−	0.766879i	−0.977782	+	0.209623i	$0.932776\pi$
$564$	−2.68417e6	−	1.72501e6i	−0.355314	−	0.228346i
$565$	8.95366e6	−	1.03331e7i	1.17999	−	1.36178i
$566$	−1.26504e7	−	3.71449e6i	−1.65983	−	0.487369i
$567$	−73149.1	−	508763.i	−0.00955545	−	0.0664596i
$568$	−847991.	−	978634.i	−0.110286	−	0.127277i
$569$	−1.83116e6	−	4.00967e6i	−0.237107	−	0.519192i	0.753249	−	0.657735i	$-0.228485\pi$
$569$	−1.83116e6	−	4.00967e6i	−0.237107	−	0.519192i	−0.990356	+	0.138543i	$0.955758\pi$
$570$	−4.78187e6	+	1.40408e6i	−0.616468	+	0.181011i
$571$	−5.18488e6	+	1.13533e7i	−0.665500	+	1.45724i	0.211806	+	0.977312i	$0.432066\pi$
$571$	−5.18488e6	+	1.13533e7i	−0.665500	+	1.45724i	−0.877306	+	0.479931i	$0.840662\pi$
$572$	899162.	−	6.25381e6i	0.114907	−	0.799198i
$573$	4.54346e6	−	2.91990e6i	0.578096	−	0.371520i
$574$	8.43105e6			1.06807
$575$	−7.85537e6	−	4.87463e6i	−0.990825	−	0.614854i
$576$	−1.23507e6			−0.155108
$577$	1.32121e7	−	8.49088e6i	1.65208	−	1.06173i	0.723688	−	0.690127i	$-0.242445\pi$
$577$	1.32121e7	−	8.49088e6i	1.65208	−	1.06173i	0.928393	−	0.371601i	$-0.121191\pi$
$578$	1.45582e6	−	1.01255e7i	0.181254	−	1.26065i
$579$	−553275.	+	1.21150e6i	−0.0685874	+	0.150185i
$580$	−1.02396e7	+	3.00662e6i	−1.26390	+	0.371115i
$581$	2.41454e6	+	5.28711e6i	0.296752	+	0.649797i
$582$	6.36195e6	+	7.34208e6i	0.778543	+	0.898486i
$583$	557734.	+	3.87912e6i	0.0679604	+	0.472675i
$584$	−4.69152e6	−	1.37755e6i	−0.569222	−	0.167139i
$585$	−4.64698e6	+	5.36290e6i	−0.561411	+	0.647903i
$586$	7.88495e6	+	5.06735e6i	0.948539	+	0.609589i
$587$	−1.29021e7	−	8.29165e6i	−1.54548	−	0.993220i	−0.986448	−	0.164075i	$-0.947536\pi$
$587$	−1.29021e7	−	8.29165e6i	−1.54548	−	0.993220i	−0.559033	−	0.829145i	$-0.688828\pi$
$588$	1.51985e6	−	1.75400e6i	0.181283	−	0.209212i
$589$	−1.25467e6	−	368403.i	−0.149018	−	0.0437557i
$590$	−399421.	−	2.77804e6i	−0.0472391	−	0.328555i
$591$	−3.96915e6	−	4.58064e6i	−0.467443	−	0.539458i
$592$	5.32068e6	+	1.16507e7i	0.623969	+	1.36630i
$593$	5.43404e6	−	1.59558e6i	0.634580	−	0.186329i	0.0514071	−	0.998678i	$-0.483629\pi$
$593$	5.43404e6	−	1.59558e6i	0.634580	−	0.186329i	0.583172	+	0.812348i	$0.301811\pi$
$594$	−557206.	+	1.22011e6i	−0.0647962	+	0.141884i
$595$	−214981.	+	1.49523e6i	−0.0248948	+	0.173147i
$596$	−2.79699e6	+	1.79751e6i	−0.322534	+	0.207280i
$597$	−4.02362e6			−0.462041
$598$	1.93334e7	−	6.01032e6i	2.21083	−	0.687297i
$599$	−2.61791e6			−0.298117			−0.149059	−	0.988828i	$-0.547624\pi$
$599$	−2.61791e6			−0.298117			−0.149059	+	0.988828i	$0.547624\pi$
$600$	−1.61929e6	+	1.04065e6i	−0.183631	+	0.118012i
$601$	−876582.	+	6.09676e6i	−0.0989934	+	0.688514i	0.878530	+	0.477687i	$0.158525\pi$
$601$	−876582.	+	6.09676e6i	−0.0989934	+	0.688514i	−0.977523	+	0.210827i	$0.932384\pi$
$602$	598629.	−	1.31082e6i	0.0673235	−	0.147418i
$603$	−4.44567e6	+	1.30537e6i	−0.497902	+	0.146197i
$604$	−387733.	−	849016.i	−0.0432454	−	0.0946943i
$605$	5.42979e6	+	6.26631e6i	0.603107	+	0.696023i
$606$	106080.	+	737806.i	0.0117342	+	0.0816132i
$607$	3.70721e6	+	1.08854e6i	0.408391	+	0.119914i	0.479474	−	0.877556i	$-0.340827\pi$
$607$	3.70721e6	+	1.08854e6i	0.408391	+	0.119914i	−0.0710834	+	0.997470i	$0.522646\pi$
$608$	4.24304e6	−	4.89673e6i	0.465499	−	0.537214i
$609$	3.18330e6	+	2.04579e6i	0.347804	+	0.223520i
$610$	−1.24910e7	−	8.02746e6i	−1.35916	−	0.873481i
$611$	1.02283e7	−	1.18041e7i	1.10841	−	1.27918i
$612$	−440232.	−	129264.i	−0.0475119	−	0.0139508i
$613$	−1.19533e6	−	8.31369e6i	−0.128480	−	0.893599i	−0.947482	−	0.319809i	$-0.896381\pi$
$613$	−1.19533e6	−	8.31369e6i	−0.128480	−	0.893599i	0.819002	−	0.573791i	$-0.194528\pi$
$614$	1.07924e7	+	1.24551e7i	1.15531	+	1.33330i
$615$	4.41706e6	+	9.67201e6i	0.470918	+	1.03117i
$616$	−1.08308e6	+	318020.i	−0.115002	+	0.0337678i
$617$	3.24243e6	−	7.09994e6i	0.342893	−	0.750830i	−0.657103	−	0.753801i	$-0.728218\pi$
$617$	3.24243e6	−	7.09994e6i	0.342893	−	0.750830i	0.999996	+	0.00297074i	$0.000945618\pi$
$618$	284057.	−	1.97566e6i	0.0299181	−	0.208085i
$619$	−1.31767e7	+	8.46818e6i	−1.38223	+	0.888308i	−0.999370	−	0.0354968i	$-0.988699\pi$
$619$	−1.31767e7	+	8.46818e6i	−1.38223	+	0.888308i	−0.382864	+	0.923805i	$0.625062\pi$
$620$	2.89538e6			0.302501
$621$	−1.84924e6	+	29233.9i	−0.192426	+	0.00304199i
$622$	1.88301e7			1.95154
$623$	7.80833e6	−	5.01811e6i	0.806005	−	0.517988i
$624$	1.65471e6	−	1.15088e7i	0.170122	−	1.18323i
$625$	−3.27105e6	+	7.16260e6i	−0.334956	+	0.733450i
$626$	−2.14776e7	+	6.30638e6i	−2.19053	+	0.643197i
$627$	−824297.	−	1.80496e6i	−0.0837365	−	0.183357i
$628$	−5.51546e6	−	6.36518e6i	−0.558062	−	0.644038i
$629$	352108.	+	2.44896e6i	0.0354854	+	0.246806i
$630$	−3.75429e6	−	1.10236e6i	−0.376857	−	0.110655i
$631$	503981.	−	581625.i	0.0503896	−	0.0581527i	−0.729995	−	0.683452i	$-0.760478\pi$
$631$	503981.	−	581625.i	0.0503896	−	0.0581527i	0.780385	+	0.625300i	$0.215023\pi$
$632$	−4.88879e6	−	3.14183e6i	−0.486865	−	0.312889i
$633$	5.17491e6	+	3.32571e6i	0.513326	+	0.329895i
$634$	−695152.	+	802248.i	−0.0686841	+	0.0792657i
$635$	−1.28057e7	−	3.76009e6i	−1.26029	−	0.370053i
$636$	−494161.	−	3.43697e6i	−0.0484424	−	0.336925i
$637$	7.44002e6	+	8.58624e6i	0.726483	+	0.838406i
$638$	−4.10212e6	−	8.98238e6i	−0.398985	−	0.873655i
$639$	1.71474e6	−	503494.i	0.166130	−	0.0487800i
$640$	3.98513e6	−	8.72623e6i	0.384586	−	0.842125i
$641$	−635787.	+	4.42200e6i	−0.0611176	+	0.425083i	0.936174	+	0.351537i	$0.114341\pi$
$641$	−635787.	+	4.42200e6i	−0.0611176	+	0.425083i	−0.997292	+	0.0735461i	$0.976568\pi$
$642$	1.38083e6	−	887406.i	0.132222	−	0.0849737i
$643$	−1.36692e7			−1.30381			−0.651906	−	0.758300i	$-0.726030\pi$
$643$	−1.36692e7			−1.30381			−0.651906	+	0.758300i	$0.726030\pi$
$644$	3.20267e6	+	3.58013e6i	0.304297	+	0.340161i
$645$	1.81738e6			0.172007
$646$	1.32701e6	−	852817.i	0.125110	−	0.0804034i
$647$	2.28785e6	−	1.59124e7i	0.214866	−	1.49443i	−0.541736	−	0.840549i	$-0.682233\pi$
$647$	2.28785e6	−	1.59124e7i	0.214866	−	1.49443i	0.756602	−	0.653876i	$-0.226858\pi$
$648$	−159964.	+	350273.i	−0.0149653	+	0.0327694i
$649$	1.07218e6	−	314821.i	0.0999211	−	0.0293395i
$650$	1.20806e7	+	2.64528e7i	1.12151	+	2.45577i
$651$	−672303.	−	775879.i	−0.0621745	−	0.0717532i
$652$	221505.	+	1.54060e6i	0.0204063	+	0.141929i
$653$	1.00589e7	+	2.95357e6i	0.923144	+	0.271060i	0.708564	−	0.705647i	$-0.249343\pi$
$653$	1.00589e7	+	2.95357e6i	0.923144	+	0.271060i	0.214580	+	0.976706i	$0.431162\pi$
$654$	−4.42716e6	+	5.10922e6i	−0.404745	+	0.467100i
$655$	1.38869e6	+	892456.i	0.126474	+	0.0812800i
$656$	−1.46564e7	−	9.41913e6i	−1.32975	−	0.854577i
$657$	4.41912e6	−	5.09993e6i	0.399413	−	0.460947i
$658$	8.26346e6	+	2.42637e6i	0.744042	+	0.218470i
$659$	3.02514e6	+	2.10403e7i	0.271351	+	1.88729i	0.434475	+	0.900684i	$0.356934\pi$
$659$	3.02514e6	+	2.10403e7i	0.271351	+	1.88729i	−0.163124	+	0.986606i	$0.552157\pi$
$660$	2.87720e6	+	3.32047e6i	0.257105	+	0.296715i
$661$	−2.68353e6	−	5.87611e6i	−0.238893	−	0.523102i	0.751772	−	0.659423i	$-0.229199\pi$
$661$	−2.68353e6	−	5.87611e6i	−0.238893	−	0.523102i	−0.990665	+	0.136321i	$0.956472\pi$
$662$	8.45357e6	−	2.48219e6i	0.749713	−	0.220136i
$663$	933029.	−	2.04305e6i	0.0824349	−	0.180507i
$664$	619704.	−	4.31013e6i	0.0545461	−	0.379377i
$665$	4.86946e6	−	3.12941e6i	0.426999	−	0.274416i
$666$	−6.40857e6			−0.559855
$667$	8.75261e6	−	1.04297e7i	0.761769	−	0.907731i
$668$	−117429.			−0.0101820
$669$	−8.39940e6	+	5.39797e6i	−0.725576	+	0.466299i
$670$	−5.01964e6	+	3.49124e7i	−0.432002	+	3.00464i
$671$	2.45583e6	−	5.37751e6i	0.210567	−	0.461078i
$672$	4.88090e6	−	1.43316e6i	0.416943	−	0.122426i
$673$	−7.37835e6	−	1.61563e7i	−0.627945	−	1.37501i	−0.909597	−	0.415491i	$-0.863610\pi$
$673$	−7.37835e6	−	1.61563e7i	−0.627945	−	1.37501i	0.281652	−	0.959517i	$-0.409118\pi$
$674$	−9.44095e6	−	1.08954e7i	−0.800508	−	0.923836i
$675$	−378061.	−	2.62947e6i	−0.0319376	−	0.222131i
$676$	−1.76830e7	−	5.19220e6i	−1.48830	−	0.437004i
$677$	−3.91607e6	+	4.51938e6i	−0.328381	+	0.378972i	−0.895800	−	0.444457i	$-0.853397\pi$
$677$	−3.91607e6	+	4.51938e6i	−0.328381	+	0.378972i	0.567419	+	0.823429i	$0.307942\pi$
$678$	−9.42985e6	−	6.06020e6i	−0.787827	−	0.506305i
$679$	−9.49219e6	−	6.10026e6i	−0.790118	−	0.507778i
$680$	741107.	−	855283.i	0.0614622	−	0.0709312i
$681$	9.99494e6	+	2.93478e6i	0.825872	+	0.242498i
$682$	381277.	+	2.65184e6i	0.0313892	+	0.218317i
$683$	−3.03251e6	−	3.49970e6i	−0.248742	−	0.287064i	0.617623	−	0.786474i	$-0.288096\pi$
$683$	−3.03251e6	−	3.49970e6i	−0.248742	−	0.287064i	−0.866366	+	0.499410i	$0.833550\pi$
$684$	730341.	+	1.59922e6i	0.0596878	+	0.130698i
$685$	−1.31955e7	+	3.87454e6i	−1.07448	+	0.315496i
$686$	−6.70168e6	+	1.46746e7i	−0.543717	+	1.19057i
$687$	260357.	−	1.81082e6i	0.0210464	−	0.146381i
$688$	−2.50509e6	+	1.60992e6i	−0.201768	+	0.129668i
$689$	1.69978e7			1.36409
$690$	−5.64549e6	+	1.28976e7i	−0.451418	+	1.03130i
$691$	1.54835e7			1.23360			0.616799	−	0.787121i	$-0.288429\pi$
$691$	1.54835e7			1.23360			0.616799	+	0.787121i	$0.288429\pi$
$692$	−1.38946e7	+	8.92953e6i	−1.10301	+	0.708865i
$693$	221708.	−	1.54201e6i	0.0175367	−	0.121971i
$694$	4.64260e6	−	1.01659e7i	0.365900	−	0.801209i
$695$	−4.98305e6	+	1.46315e6i	−0.391321	+	0.114902i
$696$	−1.17765e6	−	2.57869e6i	−0.0921493	−	0.201779i
$697$	−2.20390e6	−	2.54343e6i	−0.171834	−	0.198307i
$698$	1.61258e6	+	1.12158e7i	0.125280	+	0.871345i
$699$	−2.10893e6	−	619237.i	−0.163256	−	0.0479363i
$700$	−4.51834e6	+	5.21445e6i	−0.348525	+	0.402219i
$701$	1.00924e7	+	6.48600e6i	0.775711	+	0.498519i	0.867608	−	0.497249i	$-0.165657\pi$
$701$	1.00924e7	+	6.48600e6i	0.775711	+	0.498519i	−0.0918968	+	0.995769i	$0.529293\pi$
$702$	4.89413e6	+	3.14527e6i	0.374828	+	0.240888i
$703$	6.20838e6	−	7.16485e6i	0.473795	−	0.546788i
$704$	−3.59174e6	−	1.05463e6i	−0.273133	−	0.0801990i
$705$	1.54575e6	+	1.07509e7i	0.117130	+	0.814655i
$706$	2.04426e7	+	2.35920e7i	1.54356	+	1.78136i
$707$	−359638.	−	787497.i	−0.0270593	−	0.0592517i
$708$	−949972.	+	278937.i	−0.0712242	+	0.0209133i
$709$	2.57267e6	−	5.63336e6i	0.192207	−	0.420874i	−0.788852	−	0.614583i	$-0.789324\pi$
$709$	2.57267e6	−	5.63336e6i	0.192207	−	0.420874i	0.981059	+	0.193709i	$0.0620517\pi$
$710$	1.93613e6	−	1.34661e7i	0.144141	−	1.00252i
$711$	6.74708e6	−	4.33609e6i	0.500544	−	0.321680i
$712$	−6.95365e6			−0.514059
$713$	−3.07569e6	+	2.04603e6i	−0.226578	+	0.150726i
$714$	1.23845e6			0.0909141
$715$	−1.80935e7	+	1.16280e7i	−1.32360	+	0.850625i
$716$	2.46916e6	−	1.71734e7i	0.179997	−	1.25191i
$717$	4.87263e6	−	1.06696e7i	0.353969	−	0.775085i
$718$	8.39890e6	−	2.46614e6i	0.608011	−	0.178528i
$719$	3.69991e6	+	8.10168e6i	0.266913	+	0.584457i	0.994870	−	0.101166i	$-0.0322572\pi$
$719$	3.69991e6	+	8.10168e6i	0.266913	+	0.584457i	−0.727957	+	0.685623i	$0.759530\pi$
$720$	5.29487e6	+	6.11060e6i	0.380648	+	0.439291i
$721$	329916.	+	2.29462e6i	0.0236355	+	0.164389i
$722$	1.20061e7	+	3.52532e6i	0.857156	+	0.251684i
$723$	6.03889e6	−	6.96926e6i	0.429647	−	0.495839i
$724$	1.13189e7	+	7.27422e6i	0.802524	+	0.515751i
$725$	1.64525e7	+	1.05734e7i	1.16248	+	0.747082i
$726$	4.45153e6	−	5.13734e6i	0.313450	−	0.361740i
$727$	−6.59613e6	−	1.93680e6i	−0.462864	−	0.135909i	0.0419826	−	0.999118i	$-0.486633\pi$
$727$	−6.59613e6	−	1.93680e6i	−0.462864	−	0.135909i	−0.504846	+	0.863209i	$0.668451\pi$
$728$	696758.	+	4.84606e6i	0.0487252	+	0.338891i
$729$	−348020.	−	401636.i	−0.0242541	−	0.0279907i
$730$	−2.13401e7	−	4.67282e7i	−1.48214	−	3.24543i
$731$	−551923.	+	162059.i	−0.0382019	+	0.0112171i
$732$	−2.17590e6	+	4.76456e6i	−0.150093	+	0.328659i
$733$	784203.	−	5.45425e6i	0.0539099	−	0.374952i	−0.944950	−	0.327215i	$-0.893890\pi$
$733$	784203.	−	5.45425e6i	0.0539099	−	0.374952i	0.998860	−	0.0477370i	$-0.0152009\pi$
$734$	7.51418e6	−	4.82907e6i	0.514803	−	0.330844i
$735$	−7.90057e6			−0.539436
$736$	−2.89099e6	−	1.80743e7i	−0.196722	−	1.22989i
$737$	−1.40433e7			−0.952357
$738$	7.33339e6	−	4.71288e6i	0.495637	−	0.318527i
$739$	−2.46602e6	+	1.71515e7i	−0.166106	+	1.15529i	0.720733	+	0.693213i	$0.243805\pi$
$739$	−2.46602e6	+	1.71515e7i	−0.166106	+	1.15529i	−0.886839	+	0.462079i	$0.847104\pi$
$740$	−8.72030e6	+	1.90948e7i	−0.585399	+	1.28184i
$741$	−8.25769e6	+	2.42468e6i	−0.552475	+	0.162221i
$742$	3.89348e6	+	8.52553e6i	0.259614	+	0.568475i
$743$	7.74906e6	+	8.94289e6i	0.514964	+	0.594300i	0.952363	−	0.304968i	$-0.0986456\pi$
$743$	7.74906e6	+	8.94289e6i	0.514964	+	0.594300i	−0.437399	+	0.899268i	$0.644100\pi$
$744$	109458.	+	761298.i	0.00724962	+	0.0504222i
$745$	1.08596e7	+	3.18865e6i	0.716839	+	0.210483i
$746$	3.78932e6	−	4.37311e6i	0.249295	−	0.287702i
$747$	5.05563e6	+	3.24906e6i	0.331493	+	0.213037i
$748$	−1.16987e6	−	751833.i	−0.0764514	−	0.0491323i
$749$	−1.24842e6	+	1.44075e6i	−0.0813123	+	0.0938394i
$750$	−2.76380e6	−	811525.i	−0.179413	−	0.0526803i
$751$	3.31823e6	+	2.30788e7i	0.214687	+	1.49318i	0.757226	+	0.653153i	$0.226554\pi$
$751$	3.31823e6	+	2.30788e7i	0.214687	+	1.49318i	−0.542539	+	0.840031i	$0.682537\pi$
$752$	−1.16544e7	−	1.34499e7i	−0.751527	−	0.867309i
$753$	−1.21178e6	−	2.65344e6i	−0.0778822	−	0.170538i
$754$	−4.10944e7	+	1.20664e7i	−2.63241	+	0.772947i
$755$	−1.31989e6	+	2.89017e6i	−0.0842698	+	0.184525i
$756$	−196437.	+	1.36625e6i	−0.0125003	+	0.0869412i
$757$	−1.36645e7	+	8.78166e6i	−0.866672	+	0.556977i	−0.896733	−	0.442572i	$-0.854066\pi$
$757$	−1.36645e7	+	8.78166e6i	−0.866672	+	0.556977i	0.0300608	+	0.999548i	$0.490430\pi$
$758$	−9.40034e6			−0.594252
$759$	−5.40280e6	−	1.49406e6i	−0.340419	−	0.0941376i
$760$	−4.33646e6			−0.272334
$761$	−1.78412e7	+	1.14659e7i	−1.11677	+	0.717704i	−0.962758	−	0.270365i	$-0.912856\pi$
$761$	−1.78412e7	+	1.14659e7i	−1.11677	+	0.717704i	−0.154012	+	0.988069i	$0.549219\pi$
$762$	−1.55718e6	+	1.08304e7i	−0.0971518	+	0.675706i
$763$	3.26180e6	−	7.14234e6i	0.202836	−	0.444150i
$764$	−1.39161e7	+	4.08612e6i	−0.862547	+	0.253267i
$765$	648827.	+	1.42073e6i	0.0400844	+	0.0877725i
$766$	81699.0	+	94285.7i	0.00503089	+	0.00580596i
$767$	−689751.	−	4.79732e6i	−0.0423354	−	0.294449i
$768$	−1.17597e7	−	3.45295e6i	−0.719437	−	0.211246i
$769$	−6.80910e6	+	7.85812e6i	−0.415216	+	0.479185i	−0.924374	−	0.381489i	$-0.875412\pi$
$769$	−6.80910e6	+	7.85812e6i	−0.415216	+	0.479185i	0.509158	+	0.860673i	$0.329957\pi$
$770$	−9.97666e6	−	6.41161e6i	−0.606399	−	0.389709i
$771$	−115231.	−	74054.4i	−0.00698124	−	0.00448657i
$772$	2.34219e6	−	2.70303e6i	0.141442	−	0.163233i
$773$	−9.84577e6	−	2.89098e6i	−0.592653	−	0.174019i	−0.0283667	−	0.999598i	$-0.509031\pi$
$773$	−9.84577e6	−	2.89098e6i	−0.592653	−	0.174019i	−0.564287	+	0.825579i	$0.690849\pi$
$774$	−212042.	−	1.47479e6i	−0.0127224	−	0.0884864i
$775$	−3.47471e6	−	4.01003e6i	−0.207809	−	0.239824i
$776$	3.51158e6	+	7.68930e6i	0.209338	+	0.458387i
$777$	7.14169e6	−	2.09699e6i	0.424374	−	0.124607i
$778$	7.22362e6	−	1.58175e7i	0.427864	−	0.936891i
$779$	−1.83525e6	+	1.27645e7i	−0.108356	+	0.753632i
$780$	1.60311e7	−	1.03026e7i	0.943467	−	0.606329i
$781$	5.41664e6			0.317762
$782$	564384.	−	4.42032e6i	0.0330033	−	0.258486i
$783$	3.91244e6			0.228057
$784$	1.08902e7	−	6.99871e6i	0.632770	−	0.406657i
$785$	−4.08028e6	+	2.83790e7i	−0.236328	+	1.64370i
$786$	562195.	−	1.23104e6i	0.0324587	−	0.0710745i
$787$	9.34857e6	−	2.74499e6i	0.538032	−	0.157981i	−0.00141635	−	0.999999i	$-0.500451\pi$
$787$	9.34857e6	−	2.74499e6i	0.538032	−	0.157981i	0.539449	+	0.842018i	$0.318633\pi$
$788$	6.76153e6	+	1.48057e7i	0.387909	+	0.849402i
$789$	6.97264e6	+	8.04686e6i	0.398754	+	0.460186i
$790$	−8.68892e6	−	6.04328e7i	−0.495334	−	3.44512i
$791$	1.24916e7	+	3.66786e6i	0.709867	+	0.208436i
$792$	−764297.	+	882046.i	−0.0432961	+	0.0499664i
$793$	−2.15704e7	−	1.38624e7i	−1.21808	−	0.782810i
$794$	2.54894e7	+	1.63810e7i	1.43485	+	0.922125i
$795$	−7.74060e6	+	8.93312e6i	−0.434367	+	0.501286i
$796$	1.03675e7	+	3.04417e6i	0.579950	+	0.170289i
$797$	1.14940e6	+	7.99423e6i	0.0640950	+	0.445791i	0.996446	+	0.0842358i	$0.0268449\pi$
$797$	1.14940e6	+	7.99423e6i	0.0640950	+	0.445791i	−0.932351	+	0.361555i	$0.882246\pi$
$798$	−3.10763e6	−	3.58640e6i	−0.172752	−	0.199366i
$799$	−1.42811e6	−	3.12713e6i	−0.0791400	−	0.173292i
$800$	2.52263e7	−	7.40711e6i	1.39357	−	0.409189i
$801$	3.98666e6	−	8.72957e6i	0.219547	−	0.480742i
$802$	−1.55971e6	+	1.08480e7i	−0.0856265	+	0.595545i
$803$	1.72062e7	−	1.10578e7i	0.941667	−	0.605173i
$804$	1.24426e7			0.678844
$805$	2.07101e6	−	1.62204e7i	0.112640	−	0.882208i
$806$	1.16200e7			0.630040
$807$	−1.63109e7	+	1.04824e7i	−0.881646	+	0.566599i
$808$	−92302.8	+	641980.i	−0.00497378	+	0.0345934i
$809$	4.60045e6	−	1.00736e7i	0.247132	−	0.541143i	−0.744893	−	0.667184i	$-0.767500\pi$
$809$	4.60045e6	−	1.00736e7i	0.247132	−	0.541143i	0.992025	+	0.126040i	$0.0402269\pi$
$810$	−3.88172e6	+	1.13977e6i	−0.207879	+	0.0610389i
$811$	−1.21054e7	−	2.65072e7i	−0.646291	−	1.41518i	−0.894763	−	0.446542i	$-0.852655\pi$
$811$	−1.21054e7	−	2.65072e7i	−0.646291	−	1.41518i	0.248471	−	0.968639i	$-0.420072\pi$
$812$	−6.65449e6	−	7.67969e6i	−0.354180	−	0.408746i
$813$	883128.	+	6.14229e6i	0.0468595	+	0.325915i
$814$	−1.86370e7	−	5.47231e6i	−0.985859	−	0.289474i
$815$	3.46967e6	−	4.00422e6i	0.182976	−	0.211166i
$816$	−2.15290e6	−	1.38359e6i	−0.113188	−	0.0727412i
$817$	1.85425e6	+	1.19165e6i	0.0971879	+	0.0624589i
$818$	−2.25677e6	+	2.60445e6i	−0.117924	+	0.136092i
$819$	−6.48319e6	−	1.90364e6i	−0.337737	−	0.0991685i
$820$	−4.06365e6	−	2.82633e7i	−0.211048	−	1.46787i
$821$	4.89085e6	+	5.64435e6i	0.253237	+	0.292251i	0.868107	−	0.496378i	$-0.165337\pi$
$821$	4.89085e6	+	5.64435e6i	0.253237	+	0.292251i	−0.614870	+	0.788629i	$0.710791\pi$
$822$	4.68373e6	+	1.02559e7i	0.241776	+	0.529415i
$823$	1.38620e7	−	4.07025e6i	0.713390	−	0.209470i	0.0951535	−	0.995463i	$-0.469666\pi$
$823$	1.38620e7	−	4.07025e6i	0.713390	−	0.209470i	0.618236	+	0.785993i	$0.287848\pi$
$824$	721468.	−	1.57980e6i	0.0370168	−	0.0810556i
$825$	1.14587e6	−	7.96970e6i	0.0586138	−	0.407668i
$826$	2.24819e6	−	1.44482e6i	0.114652	−	0.0736826i
$827$	−1.30625e7			−0.664142			−0.332071	−	0.943254i	$-0.607747\pi$
$827$	−1.30625e7			−0.664142			−0.332071	+	0.943254i	$0.607747\pi$
$828$	4.78697e6	+	1.32376e6i	0.242652	+	0.0671017i
$829$	2.23284e7			1.12842			0.564209	−	0.825632i	$-0.309181\pi$
$829$	2.23284e7			1.12842			0.564209	+	0.825632i	$0.309181\pi$
$830$	3.84860e7	−	2.47334e7i	1.93913	−	1.24620i
$831$	293397.	−	2.04062e6i	0.0147385	−	0.102508i
$832$	−6.74467e6	+	1.47688e7i	−0.337794	+	0.739666i
$833$	2.39934e6	−	704509.i	0.119806	−	0.0351782i
$834$	1.76873e6	+	3.87298e6i	0.0880535	+	0.192810i
$835$	261777.	+	302107.i	0.0129932	+	0.0149949i
$836$	758344.	+	5.27440e6i	0.0375276	+	0.261010i
$837$	−1.01848e6	−	299054.i	−0.0502505	−	0.0147549i
$838$	2.92265e7	−	3.37292e7i	1.43770	−	1.65919i
$839$	5.91744e6	+	3.80291e6i	0.290221	+	0.186514i	0.677648	−	0.735387i	$-0.262999\pi$
$839$	5.91744e6	+	3.80291e6i	0.290221	+	0.186514i	−0.387426	+	0.921901i	$0.626636\pi$
$840$	−2.86413e6	−	1.84066e6i	−0.140054	−	0.0900070i
$841$	−5.43011e6	+	6.26668e6i	−0.264739	+	0.305525i
$842$	−2.75800e7	−	8.09822e6i	−1.34065	−	0.393649i
$843$	−833754.	−	5.79888e6i	−0.0404081	−	0.281045i
$844$	−1.08178e7	−	1.24844e7i	−0.522737	−	0.603270i
$845$	2.60618e7	+	5.70673e7i	1.25563	+	2.74945i
$846$	8.54394e6	−	2.50873e6i	0.410424	−	0.120511i
$847$	−3.27975e6	+	7.18165e6i	−0.157084	+	0.343966i
$848$	2.75630e6	−	1.91705e7i	0.131624	−	0.915468i
$849$	1.33194e7	−	8.55983e6i	0.634182	−	0.407564i
$850$	6.40074e6			0.303866
$851$	−4.23007e6	−	2.64461e7i	−0.200227	−	1.25181i
$852$	−4.79923e6			−0.226502
$853$	337949.	−	217187.i	0.0159030	−	0.0102202i	−0.532665	−	0.846326i	$-0.678809\pi$
$853$	337949.	−	217187.i	0.0159030	−	0.0102202i	0.548568	+	0.836106i	$0.315173\pi$
$854$	2.01208e6	−	1.39943e7i	0.0944060	−	0.656608i
$855$	2.48618e6	−	5.44397e6i	0.116310	−	0.254683i
$856$	1.37036e6	−	402374.i	0.0639220	−	0.0187692i
$857$	−1.41569e7	−	3.09993e7i	−0.658441	−	1.44178i	−0.883968	−	0.467547i	$-0.845138\pi$
$857$	−1.41569e7	−	3.09993e7i	−0.658441	−	1.44178i	0.225527	−	0.974237i	$-0.427589\pi$
$858$	1.15470e7	+	1.33260e7i	0.535491	+	0.617989i
$859$	2.51711e6	+	1.75069e7i	0.116391	+	0.809517i	0.961477	+	0.274886i	$0.0886402\pi$
$859$	2.51711e6	+	1.75069e7i	0.116391	+	0.809517i	−0.845086	+	0.534631i	$0.820451\pi$
$860$	−4.68276e6	−	1.37498e6i	−0.215902	−	0.0633944i
$861$	−6.63017e6	+	7.65163e6i	−0.304801	+	0.351760i
$862$	2.51781e7	+	1.61810e7i	1.15413	+	0.741713i
$863$	729033.	+	468521.i	0.0333212	+	0.0214142i	0.557195	−	0.830381i	$-0.311877\pi$
$863$	729033.	+	468521.i	0.0333212	+	0.0214142i	−0.523874	+	0.851796i	$0.675514\pi$
$864$	3.44432e6	−	3.97496e6i	0.156971	−	0.181154i
$865$	5.39471e7	+	1.58403e7i	2.45148	+	0.719819i
$866$	−5.78818e6	−	4.02577e7i	−0.262269	−	1.82412i
$867$	8.04454e6	+	9.28390e6i	0.363458	+	0.419452i
$868$	1.14528e6	+	2.50782e6i	0.0515957	+	0.112979i
$869$	2.33240e7	−	6.84855e6i	1.04774	−	0.307645i
$870$	1.23725e7	−	2.70919e7i	0.554190	−	1.21351i
$871$	−8.66830e6	+	6.02893e7i	−0.387158	+	2.69274i
$872$	−4.94861e6	+	3.18028e6i	−0.220390	+	0.141636i
$873$	−1.16664e7			−0.518084
$874$	−1.42170e7	+	9.45752e6i	−0.629547	+	0.418792i
$875$	3.34551e6			0.147721
$876$	−1.52450e7	+	9.79738e6i	−0.671224	+	0.431370i
$877$	1.20633e6	−	8.39022e6i	0.0529624	−	0.368362i	−0.946054	−	0.324010i	$-0.894969\pi$
$877$	1.20633e6	−	8.39022e6i	0.0529624	−	0.368362i	0.999016	−	0.0443515i	$-0.0141222\pi$
$878$	−1.77769e7	+	3.89259e7i	−0.778249	+	1.70413i
$879$	−1.07996e7	+	3.17105e6i	−0.471451	+	0.138430i
$880$	1.01803e7	+	2.22918e7i	0.443154	+	0.970371i
$881$	6.68616e6	+	7.71624e6i	0.290226	+	0.334939i	0.882074	−	0.471111i	$-0.156147\pi$
$881$	6.68616e6	+	7.71624e6i	0.290226	+	0.334939i	−0.591848	+	0.806050i	$0.701601\pi$
$882$	921797.	+	6.41124e6i	0.0398992	+	0.277505i
$883$	−1.46683e7	−	4.30701e6i	−0.633110	−	0.185898i	−0.0505968	−	0.998719i	$-0.516112\pi$
$883$	−1.46683e7	−	4.30701e6i	−0.633110	−	0.185898i	−0.582513	+	0.812821i	$0.697931\pi$
$884$	−3.94981e6	+	4.55833e6i	−0.169999	+	0.196189i
$885$	2.83532e6	+	1.82215e6i	0.121687	+	0.0782035i
$886$	3.42304e7	+	2.19985e7i	1.46497	+	0.941476i
$887$	−3.67356e6	+	4.23951e6i	−0.156775	+	0.180928i	−0.828703	−	0.559688i	$-0.810921\pi$
$887$	−3.67356e6	+	4.23951e6i	−0.156775	+	0.180928i	0.671928	+	0.740616i	$0.265466\pi$
$888$	−5.35036e6	−	1.57101e6i	−0.227693	−	0.0668568i
$889$	−1.80858e6	−	1.25789e7i	−0.0767507	−	0.533813i
$890$	−4.78413e7	−	5.52118e7i	−2.02455	−	2.33645i
$891$	−669129.	−	1.46519e6i	−0.0282368	−	0.0618300i
$892$	2.57263e7	−	7.55393e6i	1.08259	−	0.317878i
$893$	−5.47226e6	+	1.19826e7i	−0.229635	+	0.502831i
$894$	1.32053e6	−	9.18447e6i	0.0552591	−	0.384335i
$895$	−4.96858e7	+	3.19311e7i	−2.07336	+	1.33247i
$896$	9.13452e6			0.380116
$897$	−9.74907e6	+	2.22726e7i	−0.404559	+	0.924250i
$898$	−5.12714e7			−2.12170
$899$	6.57403e6	−	4.22487e6i	0.271289	−	0.174347i
$900$	−1.01526e6	+	7.06128e6i	−0.0417802	+	0.290588i
$901$	1.55417e6	−	3.40316e6i	0.0637803	−	0.139659i
$902$	2.53508e7	−	7.44368e6i	1.03747	−	0.304629i
$903$	718874.	+	1.57411e6i	0.0293382	+	0.0642417i
$904$	−6.38715e6	−	7.37116e6i	−0.259948	−	0.299995i
$905$	−6.51831e6	−	4.53358e7i	−0.264553	−	1.84001i
$906$	2.49934e6	+	733873.i	0.101159	+	0.0297030i
$907$	−9.64032e6	+	1.11255e7i	−0.389111	+	0.449058i	−0.916181	−	0.400764i	$-0.868745\pi$
$907$	−9.64032e6	+	1.11255e7i	−0.389111	+	0.449058i	0.527071	+	0.849821i	$0.323290\pi$
$908$	−2.35331e7	−	1.51238e7i	−0.947252	−	0.608762i
$909$	−753020.	−	483937.i	−0.0302271	−	0.0194258i
$910$	−3.36839e7	+	3.88733e7i	−1.34840	+	1.55614i
$911$	−4.04093e7	−	1.18652e7i	−1.61319	−	0.473675i	−0.654012	−	0.756484i	$-0.726915\pi$
$911$	−4.04093e7	−	1.18652e7i	−1.61319	−	0.473675i	−0.959176	+	0.282809i	$0.908734\pi$
$912$	1.39557e6	+	9.70639e6i	0.0555602	+	0.386430i
$913$	1.19281e7	+	1.37657e7i	0.473580	+	0.546540i
$914$	1.29841e7	+	2.84312e7i	0.514099	+	1.12572i
$915$	1.71083e7	−	5.02344e6i	0.675543	−	0.198357i
$916$	−2.04087e6	+	4.46888e6i	−0.0803668	+	0.175979i
$917$	−223693.	+	1.55582e6i	−0.00878476	+	0.0610993i
$918$	1.07721e6	−	692280.i	0.0421884	−	0.0271128i
$919$	−1.89912e7			−0.741761			−0.370881	−	0.928681i	$-0.620944\pi$
$919$	−1.89912e7			−0.741761			−0.370881	+	0.928681i	$0.620944\pi$
$920$	−7.87503e6	+	9.38396e6i	−0.306748	+	0.365525i
$921$	−1.97908e7			−0.768802
$922$	2.42105e7	−	1.55591e7i	0.937941	−	0.602778i
$923$	3.34345e6	−	2.32542e7i	0.129179	−	0.898458i
$924$	−1.73791e6	+	3.80550e6i	−0.0669651	+	0.146633i
$925$	3.69109e7	−	1.08380e7i	1.41840	−	0.416481i
$926$	−4.27798e6	−	9.36746e6i	−0.163950	−	0.359000i
$927$	1.56964e6	+	1.81146e6i	0.0599928	+	0.0692354i
$928$	5.51058e6	+	3.83269e7i	0.210052	+	1.46095i
$929$	1.24468e7	+	3.65472e6i	0.473172	+	0.138936i	0.509620	−	0.860400i	$-0.329786\pi$
$929$	1.24468e7	+	3.65472e6i	0.473172	+	0.138936i	−0.0364478	+	0.999336i	$0.511604\pi$
$930$	−5.29161e6	+	6.10685e6i	−0.200623	+	0.231531i
$931$	−8.06084e6	−	5.18039e6i	−0.304794	−	0.195879i
$932$	4.96548e6	+	3.19112e6i	0.187250	+	0.120338i
$933$	−1.48080e7	+	1.70894e7i	−0.556920	+	0.642720i
$934$	−5.17833e6	−	1.52049e6i	−0.194233	−	0.0570319i
$935$	673705.	+	4.68572e6i	0.0252023	+	0.175286i
$936$	3.31495e6	+	3.82566e6i	0.123677	+	0.142730i
$937$	−7.01651e6	−	1.53640e7i	−0.261079	−	0.571684i	0.733014	−	0.680214i	$-0.238113\pi$
$937$	−7.01651e6	−	1.53640e7i	−0.261079	−	0.571684i	−0.994093	+	0.108530i	$0.965386\pi$
$938$	−3.22247e7	+	9.46203e6i	−1.19587	+	0.351138i
$939$	1.11666e7	−	2.44514e7i	0.413291	−	0.904981i
$940$	4.15102e6	−	2.88710e7i	0.153227	−	1.06572i
$941$	−2.07684e7	+	1.33471e7i	−0.764592	+	0.491373i	−0.863888	−	0.503685i	$-0.831977\pi$
$941$	−2.07684e7	+	1.33471e7i	−0.764592	+	0.491373i	0.0992957	+	0.995058i	$0.468341\pi$
$942$	2.35053e7			0.863056
$943$	2.42891e7	+	2.71517e7i	0.889471	+	0.994303i
$944$	−5.52238e6			−0.201696
$945$	3.95282e6	−	2.54032e6i	0.143988	−	0.0925357i
$946$	642681.	−	4.46994e6i	0.0233490	−	0.162396i
$947$	1.17503e7	−	2.57296e7i	0.425770	−	0.932306i	−0.568224	−	0.822874i	$-0.692369\pi$
$947$	1.17503e7	−	2.57296e7i	0.425770	−	0.932306i	0.993994	−	0.109433i	$-0.0349034\pi$
$948$	−2.06655e7	+	6.06793e6i	−0.746835	+	0.219290i
$949$	−3.68516e7	−	8.06938e7i	−1.32828	−	2.90854i
$950$	−1.60614e7	−	1.85358e7i	−0.577396	−	0.666350i
$951$	−181416.	−	1.26178e6i	−0.00650465	−	0.0452408i
$952$	1.03395e6	+	303594.i	0.0369748	+	0.0108568i
$953$	7.62418e6	−	8.79878e6i	0.271932	−	0.313827i	−0.603314	−	0.797504i	$-0.706154\pi$
$953$	7.62418e6	−	8.79878e6i	0.271932	−	0.313827i	0.875247	+	0.483677i	$0.160699\pi$
$954$	8.15228e6	+	5.23915e6i	0.290007	+	0.186376i
$955$	4.15344e7	+	2.66925e7i	1.47367	+	0.947069i
$956$	−2.06274e7	+	2.38053e7i	−0.729962	+	0.842421i
$957$	1.13779e7	+	3.34085e6i	0.401589	+	0.117917i
$958$	7.22021e6	+	5.02177e7i	0.254177	+	1.76784i
$959$	−8.57546e6	−	9.89660e6i	−0.301100	−	0.347488i
$960$	−4.69023e6	−	1.02702e7i	−0.164254	−	0.359666i
$961$	2.54352e7	−	7.46844e6i	0.888437	−	0.260869i
$962$	−3.49970e7	+	7.66328e7i	−1.21925	+	2.66979i
$963$	−280516.	+	1.95103e6i	−0.00974748	+	0.0677952i
$964$	−2.08329e7	+	1.33885e7i	−0.722033	+	0.464023i
$965$	−1.21753e7			−0.420883
$966$	−1.34043e7	+	211904.i	−0.462170	+	0.00730627i
$967$	−5.44081e7			−1.87110			−0.935552	−	0.353190i	$-0.885097\pi$
$967$	−5.44081e7			−1.87110			−0.935552	+	0.353190i	$0.885097\pi$
$968$	4.97585e6	−	3.19778e6i	0.170678	−	0.109688i
$969$	−269582.	+	1.87499e6i	−0.00922321	+	0.0641488i
$970$	−3.68931e7	+	8.07845e7i	−1.25897	+	2.75676i
$971$	3.85846e7	−	1.13295e7i	1.31331	−	0.385622i	0.451234	−	0.892406i	$-0.350984\pi$
$971$	3.85846e7	−	1.13295e7i	1.31331	−	0.385622i	0.862073	+	0.506784i	$0.169166\pi$
$972$	592859.	+	1.29818e6i	0.0201273	+	0.0440727i
$973$	−3.23837e6	−	3.73728e6i	−0.109659	−	0.126553i
$974$	3.34044e6	+	2.32333e7i	0.112825	+	0.784718i
$975$	−3.35075e7	−	9.83868e6i	−1.12883	−	0.331456i
$976$	−1.91321e7	+	2.20797e7i	−0.642893	+	0.741939i
$977$	−9.54772e6	−	6.13594e6i	−0.320010	−	0.205658i	0.370767	−	0.928726i	$-0.379095\pi$
$977$	−9.54772e6	−	6.13594e6i	−0.320010	−	0.205658i	−0.690777	+	0.723068i	$0.742731\pi$
$978$	−3.65421e6	−	2.34842e6i	−0.122165	−	0.0785105i
$979$	1.90480e7	−	2.19826e7i	0.635174	−	0.733029i
$980$	2.03571e7	+	5.97737e6i	0.677095	+	0.198813i
$981$	−1.15537e6	−	8.03578e6i	−0.0383309	−	0.266597i
$982$	3.54482e7	+	4.09094e7i	1.17305	+	1.35377i
$983$	3.34064e6	+	7.31499e6i	0.110267	+	0.241452i	0.956719	−	0.291014i	$-0.0939927\pi$
$983$	3.34064e6	+	7.31499e6i	0.110267	+	0.241452i	−0.846451	+	0.532466i	$0.821265\pi$
$984$	7.27779e6	−	2.13695e6i	0.239614	−	0.0703569i
$985$	2.30172e7	−	5.04006e7i	0.755895	−	1.65518i
$986$	−1.34158e6	+	9.33087e6i	−0.0439464	+	0.305654i
$987$	−8.70045e6	+	5.59144e6i	−0.284282	+	0.182697i
$988$	2.31117e7			0.753250
$989$	5.94601e6	−	1.84848e6i	0.193301	−	0.0600932i
$990$	−1.22618e7			−0.397619
$991$	−2.54505e7	+	1.63561e7i	−0.823214	+	0.529048i	−0.883115	−	0.469157i	$-0.844558\pi$
$991$	−2.54505e7	+	1.63561e7i	−0.823214	+	0.529048i	0.0599008	+	0.998204i	$0.480922\pi$
$992$	1.49507e6	−	1.03985e7i	0.0482373	−	0.335498i
$993$	−4.39516e6	+	9.62406e6i	−0.141450	+	0.309731i
$994$	1.24294e7	−	3.64961e6i	0.399011	−	0.117160i
$995$	−1.52799e7	−	3.34583e7i	−0.489286	−	1.07139i
$996$	−1.05685e7	−	1.21967e7i	−0.337570	−	0.389576i
$997$	−447493.	−	3.11238e6i	−0.0142577	−	0.0991641i	0.981450	−	0.191718i	$-0.0614060\pi$
$997$	−447493.	−	3.11238e6i	−0.0142577	−	0.0991641i	−0.995708	+	0.0925541i	$0.970497\pi$
$998$	1.93839e7	+	5.69162e6i	0.616048	+	0.180888i
$999$	5.03970e6	−	5.81612e6i	0.159768	−	0.184383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.6.e.b.58.9	yes	100
23.2	even	11	inner	69.6.e.b.25.9	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.6.e.b.25.9	✓	100	23.2	even	11	inner
69.6.e.b.58.9	yes	100	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(6.30485 - 4.05188i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(10.0401 - 21.9848i) q^{4} +(-78.9416 + 23.1793i) q^{5} +(28.0203 + 61.3559i) q^{6} +(-51.3024 - 59.2061i) q^{7} +(8.35258 + 58.0934i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})\)	\(q+(6.30485 - 4.05188i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(10.0401 - 21.9848i) q^{4} +(-78.9416 + 23.1793i) q^{5} +(28.0203 + 61.3559i) q^{6} +(-51.3024 - 59.2061i) q^{7} +(8.35258 + 58.0934i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(-403.795 + 466.004i) q^{10} +(-206.531 - 132.729i) q^{11} +(182.990 + 117.600i) q^{12} +(-697.303 + 804.731i) q^{13} +(-563.350 - 165.415i) q^{14} +(-105.380 - 732.931i) q^{15} +(794.522 + 916.927i) q^{16} +(97.3598 + 213.188i) q^{17} +(-582.472 + 171.029i) q^{18} +(373.064 - 816.897i) q^{19} +(-282.990 + 1968.24i) q^{20} +(593.141 - 381.189i) q^{21} -1839.95 q^{22} +(-1090.25 - 2290.78i) q^{23} -528.218 q^{24} +(3065.57 - 1970.12i) q^{25} +(-1135.72 + 7899.10i) q^{26} +(302.838 - 663.122i) q^{27} +(-1816.72 + 533.437i) q^{28} +(2229.47 + 4881.86i) q^{29} +(-3634.15 - 4194.04i) q^{30} +(-207.222 - 1441.26i) q^{31} +(6922.60 + 2032.66i) q^{32} +(1446.94 - 1669.85i) q^{33} +(1477.65 + 949.630i) q^{34} +(5422.25 + 3484.67i) q^{35} +(-1282.01 + 1479.52i) q^{36} +(10129.1 + 2974.17i) q^{37} +(-957.854 - 6662.02i) q^{38} +(-6275.73 - 7242.58i) q^{39} +(-2005.93 - 4392.38i) q^{40} +(-13778.0 + 4045.59i) q^{41} +(2195.14 - 4806.68i) q^{42} +(-349.293 + 2429.38i) q^{43} +(-4991.62 + 3207.92i) q^{44} +6664.21 q^{45} +(-16155.9 - 10025.5i) q^{46} -14668.4 q^{47} +(-9186.00 + 5903.48i) q^{48} +(1518.46 - 10561.1i) q^{49} +(11345.3 - 24842.7i) q^{50} +(-2023.87 + 594.261i) q^{51} +(10690.8 + 23409.7i) q^{52} +(-10453.7 - 12064.2i) q^{53} +(-777.545 - 5407.95i) q^{54} +(19380.4 + 5690.61i) q^{55} +(3010.98 - 3474.86i) q^{56} +(6799.40 + 4369.71i) q^{57} +(33837.2 + 21745.9i) q^{58} +(-2980.70 + 3439.91i) q^{59} +(-17171.4 - 5041.97i) q^{60} +(3426.95 + 23835.0i) q^{61} +(-7146.31 - 8247.28i) q^{62} +(2636.06 + 5772.17i) q^{63} +(14630.1 - 4295.79i) q^{64} +(36393.1 - 79689.8i) q^{65} +(2356.67 - 16391.0i) q^{66} +(48121.3 - 30925.7i) q^{67} +5664.41 q^{68} +(21803.6 - 6778.28i) q^{69} +48305.9 q^{70} +(-18560.9 + 11928.4i) q^{71} +(676.559 - 4705.57i) q^{72} +(-34608.6 + 75782.2i) q^{73} +(75913.3 - 22290.2i) q^{74} +(13624.1 + 29832.7i) q^{75} +(-14213.7 - 16403.5i) q^{76} +(2737.14 + 19037.2i) q^{77} +(-68913.6 - 20234.9i) q^{78} +(-64841.5 + 74831.1i) q^{79} +(-83974.6 - 53967.2i) q^{80} +(5519.46 + 3547.14i) q^{81} +(-70476.1 + 81333.7i) q^{82} +(-71187.8 - 20902.6i) q^{83} +(-2425.15 - 16867.3i) q^{84} +(-12627.3 - 14572.7i) q^{85} +(7641.34 + 16732.2i) q^{86} +(-46345.2 + 13608.2i) q^{87} +(5985.64 - 13106.7i) q^{88} +(-16861.4 + 117273. i) q^{89} +(42016.9 - 27002.6i) q^{90} +83418.4 q^{91} +(-61308.7 + 969.207i) q^{92} +13104.7 q^{93} +(-92482.2 + 59434.7i) q^{94} +(-10515.1 + 73134.5i) q^{95} +(-26974.4 + 59065.7i) q^{96} +(138195. - 40577.7i) q^{97} +(-33218.7 - 72738.8i) q^{98} +(13022.4 + 15028.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9}+O(q^{10}) \) 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9	\( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9} - 38 q^{10} + 404 q^{11} - 1332 q^{12} - 2850 q^{13} - 724 q^{14} + 639 q^{15} - 5556 q^{16} - 2519 q^{17} + 972 q^{18} + 1117 q^{19} - 22411 q^{20} - 702 q^{21} + 32798 q^{22} + 12040 q^{23} - 756 q^{24} - 5928 q^{25} - 788 q^{26} - 7290 q^{27} - 54024 q^{28} + 13774 q^{29} - 342 q^{30} + 12501 q^{31} + 37412 q^{32} - 4185 q^{33} + 9441 q^{34} + 28894 q^{35} - 21789 q^{36} - 38902 q^{37} - 15042 q^{38} - 25650 q^{39} - 133835 q^{40} - 19456 q^{41} + 85950 q^{42} - 8126 q^{43} + 120643 q^{44} + 40500 q^{45} + 90500 q^{46} + 60846 q^{47} + 62955 q^{48} - 25762 q^{49} - 110197 q^{50} - 51084 q^{51} + 91725 q^{52} - 83896 q^{53} - 31347 q^{54} + 190331 q^{55} - 358140 q^{56} - 40437 q^{57} + 150977 q^{58} + 248368 q^{59} + 122625 q^{60} - 81516 q^{61} + 82657 q^{62} - 6318 q^{63} - 298028 q^{64} - 25475 q^{65} - 6669 q^{66} + 51337 q^{67} + 491228 q^{68} + 17082 q^{69} + 395832 q^{70} - 206653 q^{71} - 149364 q^{72} - 121007 q^{73} + 716844 q^{74} - 59490 q^{75} + 171145 q^{76} + 71982 q^{77} + 11916 q^{78} - 661118 q^{79} - 1386592 q^{80} - 65610 q^{81} - 136394 q^{82} - 368400 q^{83} + 165204 q^{84} + 45505 q^{85} - 99668 q^{86} + 50112 q^{87} - 474416 q^{88} + 328408 q^{89} - 3078 q^{90} + 1042320 q^{91} + 1554071 q^{92} + 160722 q^{93} - 299081 q^{94} - 434011 q^{95} + 412740 q^{96} - 88136 q^{97} + 515807 q^{98} - 37665 q^{99}+O(q^{100}) \) 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9 - 38 * q^10 + 404 * q^11 - 1332 * q^12 - 2850 * q^13 - 724 * q^14 + 639 * q^15 - 5556 * q^16 - 2519 * q^17 + 972 * q^18 + 1117 * q^19 - 22411 * q^20 - 702 * q^21 + 32798 * q^22 + 12040 * q^23 - 756 * q^24 - 5928 * q^25 - 788 * q^26 - 7290 * q^27 - 54024 * q^28 + 13774 * q^29 - 342 * q^30 + 12501 * q^31 + 37412 * q^32 - 4185 * q^33 + 9441 * q^34 + 28894 * q^35 - 21789 * q^36 - 38902 * q^37 - 15042 * q^38 - 25650 * q^39 - 133835 * q^40 - 19456 * q^41 + 85950 * q^42 - 8126 * q^43 + 120643 * q^44 + 40500 * q^45 + 90500 * q^46 + 60846 * q^47 + 62955 * q^48 - 25762 * q^49 - 110197 * q^50 - 51084 * q^51 + 91725 * q^52 - 83896 * q^53 - 31347 * q^54 + 190331 * q^55 - 358140 * q^56 - 40437 * q^57 + 150977 * q^58 + 248368 * q^59 + 122625 * q^60 - 81516 * q^61 + 82657 * q^62 - 6318 * q^63 - 298028 * q^64 - 25475 * q^65 - 6669 * q^66 + 51337 * q^67 + 491228 * q^68 + 17082 * q^69 + 395832 * q^70 - 206653 * q^71 - 149364 * q^72 - 121007 * q^73 + 716844 * q^74 - 59490 * q^75 + 171145 * q^76 + 71982 * q^77 + 11916 * q^78 - 661118 * q^79 - 1386592 * q^80 - 65610 * q^81 - 136394 * q^82 - 368400 * q^83 + 165204 * q^84 + 45505 * q^85 - 99668 * q^86 + 50112 * q^87 - 474416 * q^88 + 328408 * q^89 - 3078 * q^90 + 1042320 * q^91 + 1554071 * q^92 + 160722 * q^93 - 299081 * q^94 - 434011 * q^95 + 412740 * q^96 - 88136 * q^97 + 515807 * q^98 - 37665 * q^99

Introduction

L-functions

Modular forms

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