LMFDB - Embedded newform 138.4.e.d.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,4,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	138.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:	$8.14226358079$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	138.25
Dual form			138.4.e.d.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68251 - 1.08128i) q^{2} +(0.426945 + 2.96946i) q^{3} +(1.66166 + 3.63853i) q^{4} +(15.3096 + 4.49530i) q^{5} +(2.49249 - 5.45779i) q^{6} +(7.46958 - 8.62035i) q^{7} +(1.13852 - 7.91857i) q^{8} +(-8.63544 + 2.53559i) q^{9} +O(q^{10})$	\(q+(-1.68251 - 1.08128i) q^{2} +(0.426945 + 2.96946i) q^{3} +(1.66166 + 3.63853i) q^{4} +(15.3096 + 4.49530i) q^{5} +(2.49249 - 5.45779i) q^{6} +(7.46958 - 8.62035i) q^{7} +(1.13852 - 7.91857i) q^{8} +(-8.63544 + 2.53559i) q^{9} +(-20.8978 - 24.1174i) q^{10} +(-17.4771 + 11.2319i) q^{11} +(-10.0950 + 6.48769i) q^{12} +(21.0583 + 24.3026i) q^{13} +(-21.8886 + 6.42709i) q^{14} +(-6.81229 + 47.3805i) q^{15} +(-10.4778 + 12.0920i) q^{16} +(17.6463 - 38.6401i) q^{17} +(17.2709 + 5.07119i) q^{18} +(45.8759 + 100.454i) q^{19} +(9.08306 + 63.1741i) q^{20} +(28.7869 + 18.5002i) q^{21} +41.5502 q^{22} +(106.701 - 27.9606i) q^{23} +24.0000 q^{24} +(109.019 + 70.0624i) q^{25} +(-9.15283 - 63.6593i) q^{26} +(-11.2162 - 24.5601i) q^{27} +(43.7773 + 12.8542i) q^{28} +(42.1837 - 92.3694i) q^{29} +(62.6934 - 72.3521i) q^{30} +(-36.7561 + 255.644i) q^{31} +(30.7038 - 9.01544i) q^{32} +(-40.8144 - 47.1023i) q^{33} +(-71.4710 + 45.9316i) q^{34} +(153.107 - 98.3961i) q^{35} +(-23.5750 - 27.2070i) q^{36} +(-92.4320 + 27.1405i) q^{37} +(31.4328 - 218.620i) q^{38} +(-63.1750 + 72.9079i) q^{39} +(53.0266 - 116.112i) q^{40} +(307.995 + 90.4356i) q^{41} +(-28.4302 - 62.2535i) q^{42} +(19.9357 + 138.656i) q^{43} +(-69.9085 - 44.9275i) q^{44} -143.603 q^{45} +(-209.759 - 68.3305i) q^{46} -438.764 q^{47} +(-40.3802 - 25.9508i) q^{48} +(30.2981 + 210.728i) q^{49} +(-107.668 - 235.761i) q^{50} +(122.274 + 35.9030i) q^{51} +(-53.4340 + 117.004i) q^{52} +(181.385 - 209.329i) q^{53} +(-7.68500 + 53.4504i) q^{54} +(-318.058 + 93.3903i) q^{55} +(-59.7566 - 68.9628i) q^{56} +(-278.709 + 179.115i) q^{57} +(-170.852 + 109.800i) q^{58} +(-254.757 - 294.006i) q^{59} +(-183.715 + 53.9436i) q^{60} +(96.4226 - 670.634i) q^{61} +(338.266 - 390.380i) q^{62} +(-42.6454 + 93.3803i) q^{63} +(-61.4076 - 18.0309i) q^{64} +(213.147 + 466.727i) q^{65} +(17.7396 + 123.382i) q^{66} +(86.8368 + 55.8066i) q^{67} +169.915 q^{68} +(128.584 + 304.909i) q^{69} -363.998 q^{70} +(-985.791 - 633.530i) q^{71} +(10.2467 + 71.2671i) q^{72} +(-178.144 - 390.081i) q^{73} +(184.864 + 54.2810i) q^{74} +(-161.503 + 353.642i) q^{75} +(-289.276 + 333.842i) q^{76} +(-33.7241 + 234.556i) q^{77} +(185.126 - 54.3580i) q^{78} +(-418.542 - 483.023i) q^{79} +(-214.768 + 138.023i) q^{80} +(68.1415 - 43.7919i) q^{81} +(-420.418 - 485.188i) q^{82} +(28.2736 - 8.30187i) q^{83} +(-19.4795 + 135.483i) q^{84} +(443.857 - 512.239i) q^{85} +(116.384 - 254.845i) q^{86} +(292.298 + 85.8263i) q^{87} +(69.0423 + 151.182i) q^{88} +(-142.970 - 994.378i) q^{89} +(241.614 + 155.276i) q^{90} +366.794 q^{91} +(279.037 + 341.775i) q^{92} -774.820 q^{93} +(738.223 + 474.427i) q^{94} +(250.770 + 1744.14i) q^{95} +(39.8798 + 87.3247i) q^{96} +(627.003 + 184.105i) q^{97} +(176.880 - 387.312i) q^{98} +(122.443 - 141.307i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} + 24 q^{8} - 27 q^{9}+O(q^{10}) $ 30 * q + 6 * q^2 + 9 * q^3 - 12 * q^4 - 2 * q^5 - 18 * q^6 + 24 * q^8 - 27 * q^9	\( 30 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} + 24 q^{8} - 27 q^{9} + 48 q^{10} + 51 q^{11} + 36 q^{12} - 61 q^{13} + 44 q^{14} - 126 q^{15} - 48 q^{16} + 45 q^{17} + 54 q^{18} + 305 q^{19} + 168 q^{20} - 33 q^{21} + 8 q^{22} + 282 q^{23} + 720 q^{24} + 709 q^{25} + 210 q^{26} + 81 q^{27} - 88 q^{28} - 471 q^{29} - 144 q^{30} - 463 q^{31} + 96 q^{32} + 771 q^{33} + 724 q^{34} - 1424 q^{35} - 108 q^{36} - 483 q^{37} + 270 q^{38} + 183 q^{39} + 104 q^{40} + 886 q^{41} - 974 q^{43} + 204 q^{44} - 18 q^{45} + 382 q^{46} - 122 q^{47} + 144 q^{48} + 791 q^{49} - 450 q^{50} - 729 q^{51} - 200 q^{52} - 1117 q^{53} - 162 q^{54} - 2104 q^{55} - 354 q^{57} + 788 q^{58} - 4103 q^{59} + 24 q^{60} - 870 q^{61} - 592 q^{62} - 192 q^{64} - 2058 q^{65} - 24 q^{66} + 1365 q^{67} - 304 q^{68} + 2091 q^{69} - 584 q^{70} - 119 q^{71} + 216 q^{72} - 3314 q^{73} + 966 q^{74} - 675 q^{75} + 208 q^{76} + 606 q^{77} + 1218 q^{78} + 4040 q^{79} - 32 q^{80} - 243 q^{81} - 2300 q^{82} - 2365 q^{83} - 132 q^{84} + 4242 q^{85} - 1946 q^{86} - 402 q^{87} - 1992 q^{88} - 4963 q^{89} + 36 q^{90} + 8054 q^{91} + 3768 q^{92} - 2406 q^{93} - 1450 q^{94} + 1623 q^{95} - 288 q^{96} + 2287 q^{97} - 2748 q^{98} - 2313 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 9 * q^3 - 12 * q^4 - 2 * q^5 - 18 * q^6 + 24 * q^8 - 27 * q^9 + 48 * q^10 + 51 * q^11 + 36 * q^12 - 61 * q^13 + 44 * q^14 - 126 * q^15 - 48 * q^16 + 45 * q^17 + 54 * q^18 + 305 * q^19 + 168 * q^20 - 33 * q^21 + 8 * q^22 + 282 * q^23 + 720 * q^24 + 709 * q^25 + 210 * q^26 + 81 * q^27 - 88 * q^28 - 471 * q^29 - 144 * q^30 - 463 * q^31 + 96 * q^32 + 771 * q^33 + 724 * q^34 - 1424 * q^35 - 108 * q^36 - 483 * q^37 + 270 * q^38 + 183 * q^39 + 104 * q^40 + 886 * q^41 - 974 * q^43 + 204 * q^44 - 18 * q^45 + 382 * q^46 - 122 * q^47 + 144 * q^48 + 791 * q^49 - 450 * q^50 - 729 * q^51 - 200 * q^52 - 1117 * q^53 - 162 * q^54 - 2104 * q^55 - 354 * q^57 + 788 * q^58 - 4103 * q^59 + 24 * q^60 - 870 * q^61 - 592 * q^62 - 192 * q^64 - 2058 * q^65 - 24 * q^66 + 1365 * q^67 - 304 * q^68 + 2091 * q^69 - 584 * q^70 - 119 * q^71 + 216 * q^72 - 3314 * q^73 + 966 * q^74 - 675 * q^75 + 208 * q^76 + 606 * q^77 + 1218 * q^78 + 4040 * q^79 - 32 * q^80 - 243 * q^81 - 2300 * q^82 - 2365 * q^83 - 132 * q^84 + 4242 * q^85 - 1946 * q^86 - 402 * q^87 - 1992 * q^88 - 4963 * q^89 + 36 * q^90 + 8054 * q^91 + 3768 * q^92 - 2406 * q^93 - 1450 * q^94 + 1623 * q^95 - 288 * q^96 + 2287 * q^97 - 2748 * q^98 - 2313 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−1.68251	−	1.08128i	−0.594856	−	0.382291i
$2$	−1.68251	−	1.08128i	−0.594856	−	0.382291i
$3$	0.426945	+	2.96946i	0.0821655	+	0.571474i
$3$	0.426945	+	2.96946i	0.0821655	+	0.571474i
$4$	1.66166	+	3.63853i	0.207708	+	0.454816i
$5$	15.3096	+	4.49530i	1.36933	+	0.402072i	0.882043	−	0.471169i	$-0.156168\pi$
$5$	15.3096	+	4.49530i	1.36933	+	0.402072i	0.487289	+	0.873241i	$0.337986\pi$
$6$	2.49249	−	5.45779i	0.169592	−	0.371356i
$7$	7.46958	−	8.62035i	0.403319	−	0.465455i	−0.517364	−	0.855765i	$-0.673087\pi$
$7$	7.46958	−	8.62035i	0.403319	−	0.465455i	0.920683	+	0.390310i	$0.127632\pi$
$8$	1.13852	−	7.91857i	0.0503159	−	0.349955i
$9$	−8.63544	+	2.53559i	−0.319831	+	0.0939109i
$10$	−20.8978	−	24.1174i	−0.660847	−	0.762658i
$11$	−17.4771	+	11.2319i	−0.479050	+	0.307867i	−0.757788	−	0.652500i	$-0.773720\pi$
$11$	−17.4771	+	11.2319i	−0.479050	+	0.307867i	0.278738	+	0.960367i	$0.410084\pi$
$12$	−10.0950	+	6.48769i	−0.242849	+	0.156070i
$13$	21.0583	+	24.3026i	0.449272	+	0.518487i	0.934530	−	0.355883i	$-0.115820\pi$
$13$	21.0583	+	24.3026i	0.449272	+	0.518487i	−0.485259	+	0.874371i	$0.661275\pi$
$14$	−21.8886	+	6.42709i	−0.417856	+	0.122694i
$15$	−6.81229	+	47.3805i	−0.117262	+	0.815574i
$16$	−10.4778	+	12.0920i	−0.163715	+	0.188937i
$17$	17.6463	−	38.6401i	0.251757	−	0.551271i	−0.740987	−	0.671520i	$-0.765642\pi$
$17$	17.6463	−	38.6401i	0.251757	−	0.551271i	0.992744	+	0.120249i	$0.0383692\pi$
$18$	17.2709	+	5.07119i	0.226155	+	0.0664050i
$19$	45.8759	+	100.454i	0.553930	+	1.21294i	0.954922	+	0.296856i	$0.0959380\pi$
$19$	45.8759	+	100.454i	0.553930	+	1.21294i	−0.400993	+	0.916081i	$0.631335\pi$
$20$	9.08306	+	63.1741i	0.101552	+	0.706307i
$21$	28.7869	+	18.5002i	0.299134	+	0.192242i
$22$	41.5502			0.402660
$23$	106.701	−	27.9606i	0.967339	−	0.253486i
$23$	106.701	−	27.9606i	0.967339	−	0.253486i
$24$	24.0000			0.204124
$25$	109.019	+	70.0624i	0.872154	+	0.560499i
$26$	−9.15283	−	63.6593i	−0.0690391	−	0.480178i
$27$	−11.2162	−	24.5601i	−0.0799467	−	0.175059i
$28$	43.7773	+	12.8542i	0.295469	+	0.0867575i
$29$	42.1837	−	92.3694i	0.270114	−	0.591468i	−0.725159	−	0.688581i	$-0.758234\pi$
$29$	42.1837	−	92.3694i	0.270114	−	0.591468i	0.995273	+	0.0971137i	$0.0309611\pi$
$30$	62.6934	−	72.3521i	0.381540	−	0.440321i
$31$	−36.7561	+	255.644i	−0.212955	+	1.48113i	0.550263	+	0.834991i	$0.314527\pi$
$31$	−36.7561	+	255.644i	−0.212955	+	1.48113i	−0.763218	+	0.646141i	$0.776382\pi$
$32$	30.7038	−	9.01544i	0.169616	−	0.0498038i
$33$	−40.8144	−	47.1023i	−0.215299	−	0.248468i
$34$	−71.4710	+	45.9316i	−0.360505	+	0.231682i
$35$	153.107	−	98.3961i	0.739425	−	0.475199i
$36$	−23.5750	−	27.2070i	−0.109143	−	0.125958i
$37$	−92.4320	+	27.1405i	−0.410695	+	0.120591i	−0.480552	−	0.876966i	$-0.659564\pi$
$37$	−92.4320	+	27.1405i	−0.410695	+	0.120591i	0.0698571	+	0.997557i	$0.477746\pi$
$38$	31.4328	−	218.620i	0.134186	−	0.933285i
$39$	−63.1750	+	72.9079i	−0.259387	+	0.299349i
$40$	53.0266	−	116.112i	0.209606	−	0.458974i
$41$	307.995	+	90.4356i	1.17319	+	0.344480i	0.809545	−	0.587058i	$-0.199714\pi$
$41$	307.995	+	90.4356i	1.17319	+	0.344480i	0.363645	+	0.931538i	$0.381532\pi$
$42$	−28.4302	−	62.2535i	−0.104450	−	0.228713i
$43$	19.9357	+	138.656i	0.0707015	+	0.491740i	0.994149	+	0.108015i	$0.0344496\pi$
$43$	19.9357	+	138.656i	0.0707015	+	0.491740i	−0.923448	+	0.383724i	$0.874641\pi$
$44$	−69.9085	−	44.9275i	−0.239525	−	0.153933i
$45$	−143.603			−0.475714
$46$	−209.759	−	68.3305i	−0.672333	−	0.219017i
$47$	−438.764			−1.36171			−0.680854	−	0.732420i	$-0.738391\pi$
$47$	−438.764			−1.36171			−0.680854	+	0.732420i	$0.738391\pi$
$48$	−40.3802	−	25.9508i	−0.121424	−	0.0780348i
$49$	30.2981	+	210.728i	0.0883327	+	0.614367i
$50$	−107.668	−	235.761i	−0.304532	−	0.666833i
$51$	122.274	+	35.9030i	0.335723	+	0.0985770i
$52$	−53.4340	+	117.004i	−0.142499	+	0.312030i
$53$	181.385	−	209.329i	0.470097	−	0.542521i	−0.470342	−	0.882484i	$-0.655869\pi$
$53$	181.385	−	209.329i	0.470097	−	0.542521i	0.940439	+	0.339963i	$0.110415\pi$
$54$	−7.68500	+	53.4504i	−0.0193666	+	0.134698i
$55$	−318.058	+	93.3903i	−0.779763	+	0.228959i
$56$	−59.7566	−	68.9628i	−0.142595	−	0.164563i
$57$	−278.709	+	179.115i	−0.647648	+	0.416218i
$58$	−170.852	+	109.800i	−0.386792	+	0.248576i
$59$	−254.757	−	294.006i	−0.562145	−	0.648750i	0.401524	−	0.915848i	$-0.368481\pi$
$59$	−254.757	−	294.006i	−0.562145	−	0.648750i	−0.963669	+	0.267098i	$0.913935\pi$
$60$	−183.715	+	53.9436i	−0.395292	+	0.116068i
$61$	96.4226	−	670.634i	0.202388	−	1.40764i	−0.594784	−	0.803885i	$-0.702763\pi$
$61$	96.4226	−	670.634i	0.202388	−	1.40764i	0.797172	−	0.603752i	$-0.206328\pi$
$62$	338.266	−	390.380i	0.692901	−	0.799650i
$63$	−42.6454	+	93.3803i	−0.0852827	+	0.186743i
$64$	−61.4076	−	18.0309i	−0.119937	−	0.0352166i
$65$	213.147	+	466.727i	0.406733	+	0.890621i
$66$	17.7396	+	123.382i	0.0330848	+	0.230110i
$67$	86.8368	+	55.8066i	0.158340	+	0.101759i	0.617412	−	0.786640i	$-0.288181\pi$
$67$	86.8368	+	55.8066i	0.158340	+	0.101759i	−0.459071	+	0.888399i	$0.651818\pi$
$68$	169.915			0.303019
$69$	128.584	+	304.909i	0.224343	+	0.531981i
$70$	−363.998			−0.621515
$71$	−985.791	−	633.530i	−1.64777	−	1.05896i	−0.933174	−	0.359426i	$-0.882973\pi$
$71$	−985.791	−	633.530i	−1.64777	−	1.05896i	−0.714600	−	0.699534i	$-0.753391\pi$
$72$	10.2467	+	71.2671i	0.0167720	+	0.116652i
$73$	−178.144	−	390.081i	−0.285619	−	0.625419i	0.711382	−	0.702806i	$-0.248070\pi$
$73$	−178.144	−	390.081i	−0.285619	−	0.625419i	−0.997001	+	0.0773869i	$0.975342\pi$
$74$	184.864	+	54.2810i	0.290405	+	0.0852707i
$75$	−161.503	+	353.642i	−0.248650	+	0.544467i
$76$	−289.276	+	333.842i	−0.436608	+	0.503872i
$77$	−33.7241	+	234.556i	−0.0499119	+	0.347145i
$78$	185.126	−	54.3580i	0.268736	−	0.0789081i
$79$	−418.542	−	483.023i	−0.596071	−	0.687903i	0.374909	−	0.927062i	$-0.377674\pi$
$79$	−418.542	−	483.023i	−0.596071	−	0.687903i	−0.970981	+	0.239158i	$0.923128\pi$
$80$	−214.768	+	138.023i	−0.300147	+	0.192893i
$81$	68.1415	−	43.7919i	0.0934726	−	0.0600712i
$82$	−420.418	−	485.188i	−0.566188	−	0.653416i
$83$	28.2736	−	8.30187i	0.0373907	−	0.0109789i	−0.262984	−	0.964800i	$-0.584707\pi$
$83$	28.2736	−	8.30187i	0.0373907	−	0.0109789i	0.300374	+	0.953821i	$0.402888\pi$
$84$	−19.4795	+	135.483i	−0.0253023	+	0.175981i
$85$	443.857	−	512.239i	0.566389	−	0.653648i
$86$	116.384	−	254.845i	0.145930	−	0.319543i
$87$	292.298	+	85.8263i	0.360202	+	0.105765i
$88$	69.0423	+	151.182i	0.0836356	+	0.183136i
$89$	−142.970	−	994.378i	−0.170279	−	1.18431i	−0.878296	−	0.478118i	$-0.841319\pi$
$89$	−142.970	−	994.378i	−0.170279	−	1.18431i	0.708017	−	0.706195i	$-0.249590\pi$
$90$	241.614	+	155.276i	0.282981	+	0.181861i
$91$	366.794			0.422533
$92$	279.037	+	341.775i	0.316213	+	0.387310i
$93$	−774.820			−0.863926
$94$	738.223	+	474.427i	0.810020	+	0.520568i
$95$	250.770	+	1744.14i	0.270825	+	1.88363i
$96$	39.8798	+	87.3247i	0.0423981	+	0.0928389i
$97$	627.003	+	184.105i	0.656314	+	0.192711i	0.592900	−	0.805276i	$-0.297983\pi$
$97$	627.003	+	184.105i	0.656314	+	0.192711i	0.0634143	+	0.997987i	$0.479801\pi$
$98$	176.880	−	387.312i	0.182322	−	0.399229i
$99$	122.443	−	141.307i	0.124303	−	0.143453i
$100$	−73.7711	+	513.090i	−0.0737711	+	0.513090i
$101$	844.860	−	248.073i	0.832344	−	0.244398i	0.162321	−	0.986738i	$-0.448102\pi$
$101$	844.860	−	248.073i	0.832344	−	0.244398i	0.670024	+	0.742340i	$0.266284\pi$
$102$	−166.906	−	192.620i	−0.162021	−	0.186983i
$103$	1131.41	−	727.116i	1.08235	−	0.695581i	0.127247	−	0.991871i	$-0.459386\pi$
$103$	1131.41	−	727.116i	1.08235	−	0.695581i	0.955098	+	0.296290i	$0.0957494\pi$
$104$	216.417	−	139.083i	0.204053	−	0.131137i
$105$	357.552	+	412.637i	0.332319	+	0.383517i
$106$	−531.526	+	156.070i	−0.487041	+	0.143008i
$107$	104.617	−	727.628i	0.0945208	−	0.657406i	−0.886389	−	0.462942i	$-0.846794\pi$
$107$	104.617	−	727.628i	0.0945208	−	0.657406i	0.980910	−	0.194465i	$-0.0622970\pi$
$108$	70.7250	−	81.6210i	0.0630140	−	0.0727220i
$109$	−163.172	+	357.296i	−0.143385	+	0.313970i	−0.967676	−	0.252197i	$-0.918847\pi$
$109$	−163.172	+	357.296i	−0.143385	+	0.313970i	0.824291	+	0.566167i	$0.191574\pi$
$110$	636.117	+	186.781i	0.551376	+	0.161899i
$111$	−120.056	−	262.886i	−0.102660	−	0.224793i
$112$	25.9727	+	180.644i	0.0219124	+	0.152404i
$113$	375.187	+	241.118i	0.312342	+	0.200730i	0.687414	−	0.726266i	$-0.258746\pi$
$113$	375.187	+	241.118i	0.312342	+	0.200730i	−0.375072	+	0.926996i	$0.622382\pi$
$114$	662.604			0.544373
$115$	1759.25	+	51.5901i	1.42653	+	0.0418330i
$116$	406.184			0.325114
$117$	−243.470	−	156.468i	−0.192383	−	0.123637i
$118$	110.728	+	770.131i	0.0863843	+	0.600816i
$119$	−201.281	−	440.743i	−0.155053	−	0.339520i
$120$	367.430	+	107.887i	0.279514	+	0.0820726i
$121$	−373.622	+	818.119i	−0.280708	+	0.614665i
$122$	−887.376	+	1024.09i	−0.658518	+	0.759971i
$123$	−137.048	+	953.192i	−0.100465	+	0.698752i
$124$	−991.246	+	291.056i	−0.717875	+	0.210787i
$125$	47.9756	+	55.3668i	0.0343285	+	0.0396172i
$126$	172.722	−	111.001i	0.122121	−	0.0784825i
$127$	−1645.21	+	1057.31i	−1.14952	+	0.738750i	−0.969543	−	0.244921i	$-0.921238\pi$
$127$	−1645.21	+	1057.31i	−1.14952	+	0.738750i	−0.179975	+	0.983671i	$0.557602\pi$
$128$	83.8222	+	96.7359i	0.0578821	+	0.0667995i
$129$	−403.222	+	118.397i	−0.275207	+	0.0808081i
$130$	146.042	−	1015.74i	0.0985286	−	0.685281i
$131$	462.414	−	533.654i	0.308407	−	0.355921i	−0.580295	−	0.814407i	$-0.697063\pi$
$131$	462.414	−	533.654i	0.308407	−	0.355921i	0.888702	+	0.458486i	$0.151608\pi$
$132$	103.563	−	226.772i	0.0682882	−	0.149530i
$133$	1208.63	+	354.884i	0.787978	+	0.231371i
$134$	−85.7608	−	187.790i	−0.0552881	−	0.121064i
$135$	−61.3106	−	426.425i	−0.0390873	−	0.271858i
$136$	−285.884	−	183.726i	−0.180252	−	0.115841i
$137$	−536.108			−0.334327			−0.167164	−	0.985929i	$-0.553461\pi$
$137$	−536.108			−0.334327			−0.167164	+	0.985929i	$0.553461\pi$
$138$	113.349	−	652.046i	0.0699198	−	0.402216i
$139$	−1439.43			−0.878352			−0.439176	−	0.898401i	$-0.644730\pi$
$139$	−1439.43			−0.878352			−0.439176	+	0.898401i	$0.644730\pi$
$140$	612.429	+	393.584i	0.369712	+	0.237600i
$141$	−187.328	−	1302.89i	−0.111885	−	0.778180i
$142$	973.577	+	2131.84i	0.575357	+	1.25986i
$143$	−641.003	−	188.215i	−0.374849	−	0.110065i
$144$	59.8198	−	130.987i	0.0346179	−	0.0758027i
$145$	1061.04	−	1224.51i	0.607689	−	0.701310i
$146$	−122.059	+	848.939i	−0.0691895	+	0.481224i
$147$	−612.814	+	179.938i	−0.343837	+	0.100960i
$148$	−252.342	−	291.218i	−0.140151	−	0.161743i
$149$	−925.649	+	594.879i	−0.508940	+	0.327076i	−0.769784	−	0.638305i	$-0.779636\pi$
$149$	−925.649	+	594.879i	−0.508940	+	0.327076i	0.260843	+	0.965381i	$0.415999\pi$
$150$	654.116	−	420.375i	0.356055	−	0.228823i
$151$	−1649.66	−	1903.81i	−0.889055	−	1.02602i	−0.999483	−	0.0321401i	$-0.989768\pi$
$151$	−1649.66	−	1903.81i	−0.889055	−	1.02602i	0.110428	−	0.993884i	$-0.464778\pi$
$152$	847.685	−	248.903i	0.452344	−	0.132820i
$153$	−54.4083	+	378.418i	−0.0287494	+	0.199956i
$154$	310.362	−	358.177i	0.162401	−	0.187420i
$155$	−1711.92	+	3748.58i	−0.887128	+	1.94254i
$156$	−370.253	−	108.716i	−0.190025	−	0.0557965i
$157$	−1255.11	−	2748.30i	−0.638016	−	1.39706i	−0.901662	−	0.432441i	$-0.857652\pi$
$157$	−1255.11	−	2748.30i	−0.638016	−	1.39706i	0.263646	−	0.964620i	$-0.415075\pi$
$158$	181.916	+	1265.25i	0.0915977	+	0.637076i
$159$	699.038	+	449.244i	0.348662	+	0.224072i
$160$	510.590			0.252285
$161$	555.985	−	1128.66i	0.272160	−	0.552489i
$162$	−162.000			−0.0785674
$163$	2278.75	+	1464.46i	1.09500	+	0.703714i	0.957975	−	0.286853i	$-0.0926092\pi$
$163$	2278.75	+	1464.46i	1.09500	+	0.703714i	0.137026	+	0.990567i	$0.456246\pi$
$164$	182.731	+	1270.92i	0.0870055	+	0.605137i
$165$	−413.112	−	904.590i	−0.194914	−	0.426802i
$166$	−56.5472	−	16.6037i	−0.0264392	−	0.00776326i
$167$	−1121.20	+	2455.08i	−0.519525	+	1.13760i	0.450093	+	0.892981i	$0.351391\pi$
$167$	−1121.20	+	2455.08i	−0.519525	+	1.13760i	−0.969619	+	0.244621i	$0.921337\pi$
$168$	179.270	−	206.888i	0.0823272	−	0.0950107i
$169$	165.502	−	1151.09i	0.0753309	−	0.523938i
$170$	−1300.67	+	381.911i	−0.586804	+	0.172301i
$171$	−650.870	−	751.144i	−0.291072	−	0.335915i
$172$	−471.376	+	302.935i	−0.208966	+	0.134294i
$173$	2728.26	−	1753.35i	1.19899	−	0.770546i	0.220211	−	0.975452i	$-0.429325\pi$
$173$	2728.26	−	1753.35i	1.19899	−	0.770546i	0.978782	+	0.204907i	$0.0656891\pi$
$174$	−398.990	−	460.460i	−0.173836	−	0.200617i
$175$	1418.29	−	416.448i	0.612644	−	0.179889i
$176$	47.3057	−	329.018i	0.0202602	−	0.140913i
$177$	764.272	−	882.017i	0.324555	−	0.374556i
$178$	−834.655	+	1827.64i	−0.351461	+	0.769592i
$179$	−233.154	−	68.4602i	−0.0973562	−	0.0285864i	0.232692	−	0.972551i	$-0.425247\pi$
$179$	−233.154	−	68.4602i	−0.0973562	−	0.0285864i	−0.330048	+	0.943964i	$0.607065\pi$
$180$	−238.620	−	522.505i	−0.0988093	−	0.216362i
$181$	−440.998	−	3067.21i	−0.181100	−	1.25958i	−0.854168	−	0.519998i	$-0.825933\pi$
$181$	−440.998	−	3067.21i	−0.181100	−	1.25958i	0.673068	−	0.739581i	$-0.264976\pi$
$182$	−617.134	−	396.608i	−0.251346	−	0.161530i
$183$	2032.59			0.821057
$184$	−99.9263	−	876.757i	−0.0400362	−	0.351279i
$185$	−1537.10			−0.610865
$186$	1303.64	+	837.799i	0.513911	+	0.330271i
$187$	125.593	+	873.519i	0.0491138	+	0.341594i
$188$	−729.076	−	1596.45i	−0.282837	−	0.619326i
$189$	−295.497	−	86.7657i	−0.113726	−	0.0333930i
$190$	1463.99	−	3205.68i	0.558993	−	1.22402i
$191$	−1593.51	+	1839.01i	−0.603676	+	0.696680i	−0.972522	−	0.232811i	$-0.925208\pi$
$191$	−1593.51	+	1839.01i	−0.603676	+	0.696680i	0.368846	+	0.929491i	$0.379753\pi$
$192$	27.3244	−	190.046i	0.0102707	−	0.0714342i
$193$	−169.966	+	49.9065i	−0.0633908	+	0.0186132i	−0.313274	−	0.949663i	$-0.601426\pi$
$193$	−169.966	+	49.9065i	−0.0633908	+	0.0186132i	0.249883	+	0.968276i	$0.419608\pi$
$194$	−855.868	−	987.724i	−0.316741	−	0.365538i
$195$	−1294.93	+	832.199i	−0.475547	+	0.305615i
$196$	−716.394	+	460.399i	−0.261077	+	0.167784i
$197$	−1757.81	−	2028.62i	−0.635731	−	0.733673i	0.342883	−	0.939378i	$-0.388597\pi$
$197$	−1757.81	−	2028.62i	−0.635731	−	0.733673i	−0.978614	+	0.205706i	$0.934051\pi$
$198$	−358.804	+	105.354i	−0.128783	+	0.0378142i
$199$	−224.597	+	1562.11i	−0.0800065	+	0.556457i	0.909910	+	0.414805i	$0.136150\pi$
$199$	−224.597	+	1562.11i	−0.0800065	+	0.556457i	−0.989917	+	0.141652i	$0.954759\pi$
$200$	678.915	−	783.509i	0.240033	−	0.277012i
$201$	−128.641	+	281.685i	−0.0451426	+	0.0988484i
$202$	−1689.72	−	496.147i	−0.588556	−	0.172816i
$203$	−481.162	−	1053.60i	−0.166359	−	0.364276i
$204$	72.5444	+	504.558i	0.0248977	+	0.173167i
$205$	4308.75	+	2769.07i	1.46798	+	0.943414i
$206$	−2689.83			−0.909754
$207$	−850.517	+	512.003i	−0.285580	+	0.171916i
$208$	−514.512			−0.171514
$209$	−1930.07	−	1240.38i	−0.638783	−	0.410521i
$210$	−155.407	−	1080.88i	−0.0510671	−	0.355180i
$211$	−1506.03	−	3297.75i	−0.491372	−	1.07595i	−0.979178	−	0.203003i	$-0.934930\pi$
$211$	−1506.03	−	3297.75i	−0.491372	−	1.07595i	0.487806	−	0.872952i	$-0.337797\pi$
$212$	1063.05	+	312.140i	0.344390	+	0.101122i
$213$	1460.37	−	3197.75i	0.469777	−	1.02867i
$214$	−962.790	+	1111.12i	−0.307547	+	0.354928i
$215$	−318.092	+	2212.38i	−0.100901	+	0.701782i
$216$	−207.250	+	60.8542i	−0.0652852	+	0.0191695i
$217$	1929.19	+	2226.41i	0.603512	+	0.696490i
$218$	660.875	−	424.719i	0.205322	−	0.131952i
$219$	1082.27	−	695.536i	0.333942	−	0.214612i
$220$	−868.308	−	1002.08i	−0.266097	−	0.307092i
$221$	1310.66	−	384.844i	0.398934	−	0.117138i
$222$	−82.2587	+	572.122i	−0.0248687	+	0.172965i
$223$	−2314.53	+	2671.11i	−0.695033	+	0.802111i	−0.988073	−	0.153989i	$-0.950788\pi$
$223$	−2314.53	+	2671.11i	−0.695033	+	0.802111i	0.293039	+	0.956100i	$0.405333\pi$
$224$	151.628	−	332.019i	0.0452280	−	0.0990355i
$225$	−1119.08	−	328.591i	−0.331579	−	0.0973603i
$226$	−370.538	−	811.366i	−0.109061	−	0.238811i
$227$	524.816	+	3650.17i	0.153450	+	1.06727i	0.910380	+	0.413774i	$0.135790\pi$
$227$	524.816	+	3650.17i	0.153450	+	1.06727i	−0.756929	+	0.653497i	$0.773301\pi$
$228$	−1114.84	−	716.462i	−0.323824	−	0.208109i
$229$	6816.96			1.96715			0.983576	−	0.180496i	$-0.0577704\pi$
$229$	6816.96			1.96715			0.983576	+	0.180496i	$0.0577704\pi$
$230$	−2904.16	−	1989.04i	−0.832586	−	0.570233i
$231$	−710.905			−0.202485
$232$	−683.407	−	439.199i	−0.193396	−	0.124288i
$233$	797.908	+	5549.57i	0.224346	+	1.56036i	0.721323	+	0.692599i	$0.243534\pi$
$233$	797.908	+	5549.57i	0.224346	+	1.56036i	−0.496977	+	0.867764i	$0.665557\pi$
$234$	240.453	+	526.518i	0.0671748	+	0.147092i
$235$	−6717.29	−	1972.37i	−1.86463	−	0.547504i
$236$	646.427	−	1415.48i	0.178300	−	0.390423i
$237$	1255.63	−	1449.07i	0.344142	−	0.397161i
$238$	−137.911	+	959.194i	−0.0375608	+	0.261241i
$239$	4073.27	−	1196.02i	1.10242	−	0.323699i	0.320606	−	0.947213i	$-0.396113\pi$
$239$	4073.27	−	1196.02i	1.10242	−	0.323699i	0.781813	+	0.623513i	$0.214295\pi$
$240$	−501.548	−	578.817i	−0.134895	−	0.155677i
$241$	−1536.62	+	987.523i	−0.410714	+	0.263950i	−0.729642	−	0.683829i	$-0.760314\pi$
$241$	−1536.62	+	987.523i	−0.410714	+	0.263950i	0.318928	+	0.947779i	$0.396677\pi$
$242$	1513.24	−	972.500i	0.401962	−	0.258325i
$243$	159.131	+	183.647i	0.0420093	+	0.0484814i
$244$	2600.34	−	763.529i	0.682253	−	0.200328i
$245$	−483.434	+	3362.36i	−0.126063	+	0.876789i
$246$	1261.25	−	1455.57i	0.326889	−	0.377250i
$247$	−1475.23	+	3230.31i	−0.380027	+	0.832144i
$248$	1982.49	+	582.112i	0.507614	+	0.149049i
$249$	36.7234	+	80.4130i	0.00934638	+	0.0204657i
$250$	−20.8522	−	145.030i	−0.00527523	−	0.0366900i
$251$	−1731.01	−	1112.45i	−0.435301	−	0.279751i	0.304583	−	0.952486i	$-0.401483\pi$
$251$	−1731.01	−	1112.45i	−0.435301	−	0.279751i	−0.739884	+	0.672735i	$0.765119\pi$
$252$	−410.629			−0.102648
$253$	−1550.79	+	1687.13i	−0.385364	+	0.419244i
$254$	3911.33			0.966215
$255$	1710.58	+	1099.32i	0.420080	+	0.269969i
$256$	−36.4326	−	253.394i	−0.00889468	−	0.0618638i
$257$	−2888.26	−	6324.40i	−0.701029	−	1.53504i	−0.838719	−	0.544565i	$-0.816695\pi$
$257$	−2888.26	−	6324.40i	−0.701029	−	1.53504i	0.137689	−	0.990475i	$-0.456032\pi$
$258$	806.444	+	236.793i	0.194601	+	0.0571399i
$259$	−456.468	+	999.524i	−0.109512	+	0.239797i
$260$	−1344.02	+	1551.08i	−0.320587	+	0.369977i
$261$	−130.063	+	904.611i	−0.0308457	+	0.214536i
$262$	−1355.05	+	397.877i	−0.319523	+	0.0938204i
$263$	2630.44	+	3035.70i	0.616731	+	0.711745i	0.975083	−	0.221841i	$-0.0712067\pi$
$263$	2630.44	+	3035.70i	0.616731	+	0.711745i	−0.358352	+	0.933587i	$0.616661\pi$
$264$	−419.451	+	269.565i	−0.0977857	+	0.0628430i
$265$	3717.93	−	2389.37i	0.861852	−	0.553878i
$266$	−1649.79	−	1903.96i	−0.380283	−	0.438870i
$267$	2891.73	−	849.089i	0.662813	−	0.194619i
$268$	−58.7607	+	408.690i	−0.0133932	+	0.0931518i
$269$	−3018.77	+	3483.85i	−0.684230	+	0.789644i	−0.986532	−	0.163569i	$-0.947699\pi$
$269$	−3018.77	+	3483.85i	−0.684230	+	0.789644i	0.302302	+	0.953212i	$0.402245\pi$
$270$	−357.930	+	783.757i	−0.0806775	+	0.176659i
$271$	−558.852	−	164.094i	−0.125269	−	0.0367822i	0.218497	−	0.975838i	$-0.429885\pi$
$271$	−558.852	−	164.094i	−0.125269	−	0.0367822i	−0.343766	+	0.939055i	$0.611703\pi$
$272$	282.342	+	618.242i	0.0629392	+	0.137818i
$273$	156.601	+	1089.18i	0.0347176	+	0.241466i
$274$	902.006	+	579.684i	0.198877	+	0.127810i
$275$	−2692.27			−0.590365
$276$	−895.756	+	974.509i	−0.195356	+	0.212531i
$277$	−671.682			−0.145695			−0.0728474	−	0.997343i	$-0.523209\pi$
$277$	−671.682			−0.145695			−0.0728474	+	0.997343i	$0.523209\pi$
$278$	2421.85	+	1556.43i	0.522493	+	0.335786i
$279$	−330.805	−	2300.80i	−0.0709849	−	0.493711i
$280$	−604.841	−	1324.42i	−0.129093	−	0.282675i
$281$	−1051.74	−	308.820i	−0.223280	−	0.0655610i	0.168179	−	0.985756i	$-0.446211\pi$
$281$	−1051.74	−	308.820i	−0.223280	−	0.0655610i	−0.391459	+	0.920196i	$0.628030\pi$
$282$	−1093.61	+	2394.68i	−0.230935	+	0.505678i
$283$	3297.95	−	3806.04i	0.692731	−	0.799454i	−0.295020	−	0.955491i	$-0.595326\pi$
$283$	3297.95	−	3806.04i	0.692731	−	0.799454i	0.987751	+	0.156037i	$0.0498718\pi$
$284$	667.065	−	4639.54i	0.139377	−	0.969387i
$285$	−5072.10	+	1489.30i	−1.05419	+	0.309539i
$286$	874.978	+	1009.78i	0.180904	+	0.208774i
$287$	3080.18	−	1979.51i	0.633510	−	0.407132i
$288$	−242.281	+	155.705i	−0.0495713	+	0.0318576i
$289$	2035.67	+	2349.28i	0.414343	+	0.478177i
$290$	−3109.25	+	912.959i	−0.629592	+	0.184865i
$291$	−278.997	+	1940.47i	−0.0562030	+	0.390901i
$292$	1123.31	−	1296.37i	0.225125	−	0.259808i
$293$	−3176.57	+	6955.71i	−0.633369	+	1.38688i	0.272017	+	0.962293i	$0.412309\pi$
$293$	−3176.57	+	6955.71i	−0.633369	+	1.38688i	−0.905385	+	0.424591i	$0.860418\pi$
$294$	1225.63	+	359.877i	0.243129	+	0.0713892i
$295$	−2578.59	−	5646.32i	−0.508919	−	1.11438i
$296$	109.678	+	762.829i	0.0215369	+	0.149792i
$297$	471.882	+	303.260i	0.0921932	+	0.0592490i
$298$	2200.64			0.427785
$299$	2926.47	+	2004.32i	0.566028	+	0.387669i
$300$	−1555.10			−0.299279
$301$	1344.17	+	863.847i	0.257398	+	0.165420i
$302$	717.010	+	4986.91i	0.136620	+	0.950214i
$303$	1097.35	+	2402.87i	0.208057	+	0.455582i
$304$	−1695.37	−	497.806i	−0.319856	−	0.0939181i
$305$	4490.89	−	9833.68i	0.843108	−	1.84615i
$306$	500.719	−	577.861i	0.0935431	−	0.107955i
$307$	262.999	−	1829.20i	0.0488929	−	0.340058i	−0.950662	−	0.310228i	$-0.899595\pi$
$307$	262.999	−	1829.20i	0.0488929	−	0.340058i	0.999555	−	0.0298294i	$-0.00949640\pi$
$308$	−909.477	+	267.047i	−0.168254	+	0.0494039i
$309$	2642.20	+	3049.26i	0.486438	+	0.561379i
$310$	6933.59	−	4455.95i	1.27033	−	0.816390i
$311$	8869.62	−	5700.16i	1.61720	−	1.03931i	0.659438	−	0.751759i	$-0.270794\pi$
$311$	8869.62	−	5700.16i	1.61720	−	1.03931i	0.957765	−	0.287553i	$-0.0928419\pi$
$312$	505.400	+	583.263i	0.0917072	+	0.105836i
$313$	−1326.23	+	389.416i	−0.239498	+	0.0703230i	−0.399279	−	0.916830i	$-0.630739\pi$
$313$	−1326.23	+	389.416i	−0.239498	+	0.0703230i	0.159781	+	0.987153i	$0.448921\pi$
$314$	−859.962	+	5981.17i	−0.154556	+	1.07496i
$315$	−1072.66	+	1237.91i	−0.191865	+	0.221423i
$316$	1062.02	−	2325.50i	0.189061	−	0.413985i
$317$	8005.77	+	2350.71i	1.41845	+	0.416495i	0.898978	−	0.437993i	$-0.144311\pi$
$317$	8005.77	+	2350.71i	1.41845	+	0.416495i	0.519472	+	0.854488i	$0.326129\pi$
$318$	−690.376	−	1511.71i	−0.121743	−	0.266581i
$319$	300.231	+	2088.15i	0.0526950	+	0.366502i
$320$	−859.070	−	552.091i	−0.150073	−	0.0964463i
$321$	2205.33			0.383457
$322$	−2155.85	+	1297.80i	−0.373107	+	0.224607i
$323$	4691.11			0.808112
$324$	272.566	+	175.168i	0.0467363	+	0.0300356i
$325$	593.064	+	4124.85i	0.101222	+	0.704017i
$326$	−2250.51	−	4927.93i	−0.382344	−	0.837217i
$327$	−1130.64	−	331.987i	−0.191207	−	0.0561435i
$328$	1066.78	−	2335.92i	0.179582	−	0.393231i
$329$	−3277.38	+	3782.30i	−0.549203	+	0.633814i
$330$	−283.052	+	1968.67i	−0.0472167	+	0.328399i
$331$	−5156.42	+	1514.06i	−0.856261	+	0.251421i	−0.680262	−	0.732969i	$-0.738134\pi$
$331$	−5156.42	+	1514.06i	−0.856261	+	0.251421i	−0.176000	+	0.984390i	$0.556316\pi$
$332$	77.1877	+	89.0793i	0.0127597	+	0.0147255i
$333$	729.374	−	468.740i	0.120028	−	0.0771375i
$334$	4541.05	−	2918.36i	0.743938	−	0.478100i
$335$	1078.57	+	1244.73i	0.175906	+	0.203006i
$336$	−525.328	+	154.250i	−0.0852945	+	0.0250447i
$337$	−1456.67	+	10131.4i	−0.235460	+	1.63766i	0.438385	+	0.898787i	$0.355551\pi$
$337$	−1456.67	+	10131.4i	−0.235460	+	1.63766i	−0.673845	+	0.738873i	$0.735358\pi$
$338$	−1523.11	+	1757.77i	−0.245108	+	0.282869i
$339$	−555.808	+	1217.05i	−0.0890481	+	0.194988i
$340$	2601.34	+	763.821i	0.414933	+	0.121835i
$341$	−2228.97	−	4880.77i	−0.353975	−	0.775098i
$342$	282.895	+	1967.58i	0.0447287	+	0.311095i
$343$	5334.17	+	3428.06i	0.839703	+	0.539644i
$344$	1120.65			0.175644
$345$	597.906	+	5246.05i	0.0933049	+	0.818660i
$346$	−6486.18			−1.00780
$347$	3136.48	+	2015.69i	0.485230	+	0.311839i	0.760285	−	0.649590i	$-0.225059\pi$
$347$	3136.48	+	2015.69i	0.485230	+	0.311839i	−0.275054	+	0.961429i	$0.588696\pi$
$348$	173.418	+	1206.15i	0.0267131	+	0.185794i
$349$	−376.204	−	823.771i	−0.0577012	−	0.126348i	0.878585	−	0.477586i	$-0.158488\pi$
$349$	−376.204	−	823.771i	−0.0577012	−	0.126348i	−0.936286	+	0.351238i	$0.885761\pi$
$350$	−2836.58	−	832.895i	−0.433205	−	0.127200i
$351$	360.679	−	789.777i	0.0548480	−	0.120100i
$352$	−435.353	+	502.425i	−0.0659216	+	0.0760776i
$353$	752.813	−	5235.93i	0.113508	−	0.789463i	−0.850954	−	0.525240i	$-0.823976\pi$
$353$	752.813	−	5235.93i	0.113508	−	0.789463i	0.964462	−	0.264223i	$-0.0851154\pi$
$354$	−2239.60	+	657.606i	−0.336253	+	0.0987327i
$355$	−12244.2	−	14130.5i	−1.83057	−	2.11259i
$356$	3380.51	−	2172.52i	0.503276	−	0.323436i
$357$	1222.84	−	785.868i	0.181287	−	0.116506i
$358$	318.259	+	367.290i	0.0469846	+	0.0542231i
$359$	3968.76	−	1165.33i	0.583463	−	0.171320i	0.0233368	−	0.999728i	$-0.492571\pi$
$359$	3968.76	−	1165.33i	0.583463	−	0.171320i	0.560126	+	0.828408i	$0.310753\pi$
$360$	−163.495	+	1137.13i	−0.0239360	+	0.166478i
$361$	−3494.78	+	4033.19i	−0.509517	+	0.588014i
$362$	−2574.53	+	5637.44i	−0.373797	+	0.818501i
$363$	−2588.89	−	760.167i	−0.374329	−	0.109913i
$364$	609.487	+	1334.59i	0.0877632	+	0.192175i
$365$	−973.781	−	6772.80i	−0.139644	−	0.971245i
$366$	−3419.85	−	2197.80i	−0.488411	−	0.313883i
$367$	6328.79			0.900163			0.450082	−	0.892987i	$-0.351395\pi$
$367$	6328.79			0.900163			0.450082	+	0.892987i	$0.351395\pi$
$368$	−779.894	+	1583.20i	−0.110475	+	0.224266i
$369$	−2888.98			−0.407573
$370$	2586.18	+	1662.04i	0.363376	+	0.233528i
$371$	−449.624	−	3127.21i	−0.0629200	−	0.437618i
$372$	−1287.49	−	2819.20i	−0.179444	−	0.392927i
$373$	−7730.77	−	2269.96i	−1.07315	−	0.315105i	−0.303014	−	0.952986i	$-0.597993\pi$
$373$	−7730.77	−	2269.96i	−1.07315	−	0.315105i	−0.770135	+	0.637881i	$0.779811\pi$
$374$	733.209	−	1605.50i	0.101373	−	0.221975i
$375$	−143.927	+	166.100i	−0.0198196	+	0.0228730i
$376$	−499.541	+	3474.38i	−0.0685155	+	0.476536i
$377$	3133.14	−	919.972i	0.428023	−	0.125679i
$378$	403.357	+	465.499i	0.0548848	+	0.0633404i
$379$	−9175.90	+	5897.00i	−1.24363	+	0.799230i	−0.985956	−	0.167002i	$-0.946591\pi$
$379$	−9175.90	+	5897.00i	−1.24363	+	0.799230i	−0.257670	+	0.966233i	$0.582955\pi$
$380$	−5929.41	+	3810.60i	−0.800454	+	0.514420i
$381$	−3842.06	−	4433.98i	−0.516627	−	0.596219i
$382$	4669.57	−	1371.11i	0.625435	−	0.183644i
$383$	1806.15	−	12562.1i	0.240966	−	1.67596i	−0.406337	−	0.913723i	$-0.633194\pi$
$383$	1806.15	−	12562.1i	0.240966	−	1.67596i	0.647303	−	0.762233i	$-0.275897\pi$
$384$	−251.467	+	290.208i	−0.0334182	+	0.0385667i
$385$	−1570.70	+	3439.36i	−0.207923	+	0.455288i
$386$	339.932	+	99.8131i	0.0448241	+	0.0131615i
$387$	−523.728	−	1146.80i	−0.0687922	−	0.150634i
$388$	371.996	+	2587.29i	0.0486732	+	0.338530i
$389$	−6873.22	−	4417.15i	−0.895852	−	0.575729i	0.00970555	−	0.999953i	$-0.496911\pi$
$389$	−6873.22	−	4417.15i	−0.895852	−	0.575729i	−0.905557	+	0.424224i	$0.860547\pi$
$390$	3078.57			0.399716
$391$	802.491	−	4616.36i	0.103795	−	0.597083i
$392$	1703.16			0.219445
$393$	1782.09	+	1145.28i	0.228740	+	0.147002i
$394$	764.018	+	5313.87i	0.0976921	+	0.679464i
$395$	−4236.37	−	9276.36i	−0.539633	−	1.18163i
$396$	717.608	+	210.709i	0.0910635	+	0.0267387i
$397$	1835.83	−	4019.92i	0.232085	−	0.508196i	−0.757379	−	0.652976i	$-0.773520\pi$
$397$	1835.83	−	4019.92i	0.232085	−	0.508196i	0.989464	+	0.144780i	$0.0462475\pi$
$398$	2066.97	−	2385.41i	0.260321	−	0.300426i
$399$	−537.801	+	3740.49i	−0.0674780	+	0.469320i
$400$	−1989.47	+	584.162i	−0.248684	+	0.0730203i
$401$	−6435.84	−	7427.35i	−0.801472	−	0.924948i	0.196989	−	0.980406i	$-0.436884\pi$
$401$	−6435.84	−	7427.35i	−0.801472	−	0.924948i	−0.998461	+	0.0554573i	$0.982338\pi$
$402$	521.021	−	334.840i	0.0646422	−	0.0415430i
$403$	−6986.85	+	4490.18i	−0.863623	+	0.555017i
$404$	2306.49	+	2661.83i	0.284040	+	0.327800i
$405$	1240.08	−	364.120i	0.152148	−	0.0446747i
$406$	−329.678	+	2292.96i	−0.0402996	+	0.280290i
$407$	1310.61	−	1512.52i	0.159618	−	0.184209i
$408$	423.512	−	927.363i	0.0513897	−	0.112528i
$409$	−3080.60	−	904.544i	−0.372434	−	0.109357i	0.0901585	−	0.995927i	$-0.471263\pi$
$409$	−3080.60	−	904.544i	−0.372434	−	0.109357i	−0.462593	+	0.886571i	$0.653081\pi$
$410$	−4255.36	−	9317.94i	−0.512579	−	1.12239i
$411$	−228.889	−	1591.95i	−0.0274702	−	0.191059i
$412$	4525.66	+	2908.46i	0.541173	+	0.347791i
$413$	−4437.36			−0.528688
$414$	1984.62	+	58.1992i	0.235601	+	0.00690902i
$415$	470.177			0.0556146
$416$	865.670	+	556.332i	0.102026	+	0.0655683i
$417$	−614.557	−	4274.34i	−0.0721703	−	0.501955i
$418$	1906.15	+	4173.90i	0.223046	+	0.488402i
$419$	−14653.2	−	4302.57i	−1.70849	−	0.501657i	−0.725955	−	0.687743i	$-0.758602\pi$
$419$	−14653.2	−	4302.57i	−1.70849	−	0.501657i	−0.982534	+	0.186085i	$0.940420\pi$
$420$	−907.261	+	1986.63i	−0.105404	+	0.230803i
$421$	−5486.39	+	6331.64i	−0.635132	+	0.732981i	−0.978506	−	0.206217i	$-0.933885\pi$
$421$	−5486.39	+	6331.64i	−0.635132	+	0.732981i	0.343374	+	0.939199i	$0.388430\pi$
$422$	−1031.89	+	7176.93i	−0.119032	+	0.827885i
$423$	3788.91	−	1112.53i	0.435516	−	0.127879i
$424$	−1451.08	−	1674.64i	−0.166204	−	0.191810i
$425$	4631.01	−	2976.17i	0.528558	−	0.339683i
$426$	−5914.75	+	3801.18i	−0.672701	+	0.432318i
$427$	−5060.86	−	5840.55i	−0.573565	−	0.661930i
$428$	2821.33	−	828.418i	0.318632	−	0.0935587i
$429$	285.226	−	1983.79i	0.0320999	−	0.223260i
$430$	2927.40	−	3378.40i	0.328306	−	0.378886i
$431$	1118.23	−	2448.58i	0.124973	−	0.273652i	−0.836796	−	0.547515i	$-0.815574\pi$
$431$	1118.23	−	2448.58i	0.124973	−	0.273652i	0.961769	+	0.273862i	$0.0883013\pi$
$432$	414.501	+	121.708i	0.0461636	+	0.0135549i
$433$	5042.94	+	11042.5i	0.559696	+	1.22556i	0.952105	+	0.305772i	$0.0989145\pi$
$433$	5042.94	+	11042.5i	0.559696	+	1.22556i	−0.392409	+	0.919791i	$0.628358\pi$
$434$	−838.507	−	5831.95i	−0.0927411	−	0.645029i
$435$	4089.14	+	2627.93i	0.450711	+	0.289655i
$436$	−1571.17			−0.172581
$437$	7703.79	+	9435.90i	0.843301	+	1.03291i
$438$	−2573.01			−0.280692
$439$	7903.86	+	5079.50i	0.859296	+	0.552236i	0.894461	−	0.447146i	$-0.147559\pi$
$439$	7903.86	+	5079.50i	0.859296	+	0.552236i	−0.0351655	+	0.999382i	$0.511196\pi$
$440$	377.403	+	2624.89i	0.0408908	+	0.284402i
$441$	−795.958	−	1742.90i	−0.0859473	−	0.188198i
$442$	−2621.32	−	769.688i	−0.282089	−	0.0828288i
$443$	3493.82	−	7650.40i	0.374710	−	0.820500i	−0.624510	−	0.781016i	$-0.714701\pi$
$443$	3493.82	−	7650.40i	0.374710	−	0.820500i	0.999220	−	0.0394835i	$-0.0125713\pi$
$444$	757.026	−	873.655i	0.0809164	−	0.0933825i
$445$	2281.22	−	15866.2i	0.243011	−	1.69018i
$446$	6782.44	−	1991.50i	0.720084	−	0.211436i
$447$	−2161.67	−	2494.70i	−0.228733	−	0.263972i
$448$	−614.121	+	394.672i	−0.0647645	+	0.0416216i
$449$	3165.57	−	2034.39i	0.332722	−	0.213828i	−0.363603	−	0.931554i	$-0.618454\pi$
$449$	3165.57	−	2034.39i	0.332722	−	0.213828i	0.696325	+	0.717726i	$0.254817\pi$
$450$	1527.56	+	1762.90i	0.160022	+	0.184675i
$451$	−6398.63	+	1878.81i	−0.668071	+	0.196163i
$452$	−253.882	+	1765.79i	−0.0264194	+	0.183751i
$453$	4948.98	−	5711.42i	0.513296	−	0.592375i
$454$	3063.86	−	6708.91i	0.316727	−	0.693535i
$455$	5615.47	+	1648.85i	0.578587	+	0.169889i
$456$	1101.02	+	2410.90i	0.113070	+	0.247590i
$457$	2613.43	+	18176.8i	0.267508	+	1.86056i	0.471878	+	0.881664i	$0.343576\pi$
$457$	2613.43	+	18176.8i	0.267508	+	1.86056i	−0.204370	+	0.978894i	$0.565515\pi$
$458$	−11469.6	−	7371.06i	−1.17017	−	0.752024i
$459$	−1146.93			−0.116632
$460$	2735.56	+	6486.80i	0.277274	+	0.657497i
$461$	−18099.2			−1.82855			−0.914277	−	0.405090i	$-0.867240\pi$
$461$	−18099.2			−1.82855			−0.914277	+	0.405090i	$0.867240\pi$
$462$	1196.10	+	768.688i	0.120450	+	0.0774082i
$463$	521.885	+	3629.79i	0.0523846	+	0.364343i	0.999105	+	0.0422876i	$0.0134646\pi$
$463$	521.885	+	3629.79i	0.0523846	+	0.364343i	−0.946721	+	0.322055i	$0.895626\pi$
$464$	674.939	+	1477.91i	0.0675286	+	0.147867i
$465$	−11862.2	−	3483.05i	−1.18300	−	0.347360i
$466$	4658.16	−	10200.0i	0.463059	−	1.01396i
$467$	−9994.76	+	11534.6i	−0.990369	+	1.14295i	−0.000638659		1.00000i	$0.500203\pi$
$467$	−9994.76	+	11534.6i	−0.990369	+	1.14295i	−0.989730	+	0.142947i	$0.954342\pi$
$468$	164.751	−	1145.87i	0.0162727	−	0.113179i
$469$	1129.71	−	331.712i	0.111226	−	0.0326589i
$470$	9169.20	+	10581.8i	0.899880	+	1.03852i
$471$	7625.13	−	4900.37i	0.745961	−	0.479400i
$472$	−2618.15	+	1682.58i	−0.255318	+	0.164083i
$473$	−1905.78	−	2199.39i	−0.185260	−	0.213801i
$474$	−3679.45	+	1080.38i	−0.356546	+	0.104691i
$475$	−2036.71	+	14165.6i	−0.196738	+	1.36835i
$476$	1269.20	−	1464.73i	0.122213	−	0.141042i
$477$	−1035.56	+	2267.57i	−0.0994030	+	0.217662i
$478$	−8146.54	−	2392.04i	−0.779528	−	0.228890i
$479$	4391.58	+	9616.23i	0.418907	+	0.917279i	0.994998	+	0.0998934i	$0.0318502\pi$
$479$	4391.58	+	9616.23i	0.418907	+	0.917279i	−0.576091	+	0.817386i	$0.695423\pi$
$480$	217.993	+	1516.18i	0.0207291	+	0.144174i
$481$	−2606.05	−	1674.81i	−0.247039	−	0.158762i
$482$	3653.16			0.345222
$483$	3588.88	+	1169.10i	0.338095	+	0.110137i
$484$	−3597.58			−0.337865
$485$	8771.55	+	5637.14i	0.821228	+	0.527771i
$486$	−69.1650	−	481.053i	−0.00645553	−	0.0448992i
$487$	−2779.12	−	6085.41i	−0.258591	−	0.566235i	0.735155	−	0.677899i	$-0.237109\pi$
$487$	−2779.12	−	6085.41i	−0.258591	−	0.566235i	−0.993746	+	0.111664i	$0.964382\pi$
$488$	−5200.68	−	1527.06i	−0.482426	−	0.141653i
$489$	−3375.77	+	7391.90i	−0.312183	+	0.683585i
$490$	4449.04	−	5134.46i	0.410178	−	0.473370i
$491$	−337.267	+	2345.75i	−0.0309993	+	0.215605i	−0.999433	−	0.0336658i	$-0.989282\pi$
$491$	−337.267	+	2345.75i	−0.0309993	+	0.215605i	0.968434	+	0.249271i	$0.0801909\pi$
$492$	−3695.94	+	1085.23i	−0.338671	+	0.0994427i
$493$	−2824.78	−	3259.96i	−0.258056	−	0.297812i
$494$	5974.96	−	3839.87i	0.544182	−	0.349725i
$495$	2509.77	−	1612.93i	0.227891	−	0.146456i
$496$	−2706.13	−	3123.04i	−0.244977	−	0.282719i
$497$	−12824.7	+	3765.67i	−1.15748	+	0.339866i
$498$	25.1617	−	175.004i	0.00226410	−	0.0157472i
$499$	13361.3	−	15419.7i	1.19866	−	1.38333i	0.294773	−	0.955567i	$-0.404756\pi$
$499$	13361.3	−	15419.7i	1.19866	−	1.38333i	0.903890	−	0.427764i	$-0.140699\pi$
$500$	−121.734	+	266.561i	−0.0108883	+	0.0238420i
$501$	−7768.95	−	2281.17i	−0.692797	−	0.203423i
$502$	1709.56	+	3743.42i	0.151995	+	0.332823i
$503$	2920.54	+	20312.8i	0.258887	+	1.80060i	0.540789	+	0.841158i	$0.318126\pi$
$503$	2920.54	+	20312.8i	0.258887	+	1.80060i	−0.281902	+	0.959443i	$0.590965\pi$
$504$	690.886	+	444.006i	0.0610605	+	0.0392412i
$505$	14049.6			1.23802
$506$	4433.47	−	1161.77i	0.389509	−	0.102069i
$507$	3488.79			0.305606
$508$	−6580.84	−	4229.25i	−0.574759	−	0.369375i
$509$	3108.88	+	21622.8i	0.270725	+	1.88293i	0.440959	+	0.897527i	$0.354638\pi$
$509$	3108.88	+	21622.8i	0.270725	+	1.88293i	−0.170235	+	0.985404i	$0.554453\pi$
$510$	−1689.38	−	3699.23i	−0.146681	−	0.321186i
$511$	−4693.30	−	1378.08i	−0.406300	−	0.119300i
$512$	−212.692	+	465.732i	−0.0183589	+	0.0402004i
$513$	1952.61	−	2253.43i	0.168050	−	0.193940i
$514$	−1978.95	+	13763.9i	−0.169820	+	1.18113i
$515$	20590.1	−	6045.80i	1.76176	−	0.517301i
$516$	−1100.81	−	1270.40i	−0.0939154	−	0.108384i
$517$	7668.32	−	4928.13i	0.652326	−	0.419224i
$518$	1848.78	−	1188.14i	0.156816	−	0.100779i
$519$	6371.31	+	7352.89i	0.538862	+	0.621880i
$520$	3938.48	−	1156.44i	0.332142	−	0.0975257i
$521$	1735.93	−	12073.7i	0.145974	−	1.01527i	−0.776749	−	0.629810i	$-0.783133\pi$
$521$	1735.93	−	12073.7i	0.145974	−	1.01527i	0.922723	−	0.385463i	$-0.125958\pi$
$522$	1196.97	−	1381.38i	0.100364	−	0.115826i
$523$	592.515	−	1297.43i	0.0495389	−	0.108475i	−0.883244	−	0.468913i	$-0.844646\pi$
$523$	592.515	−	1297.43i	0.0495389	−	0.108475i	0.932783	+	0.360438i	$0.117373\pi$
$524$	2710.09	+	795.755i	0.225937	+	0.0663410i
$525$	1842.16	+	4033.76i	0.153140	+	0.335329i
$526$	−1143.30	−	7951.83i	−0.0947724	−	0.659156i
$527$	9229.52	+	5931.45i	0.762892	+	0.490281i
$528$	997.204			0.0821927
$529$	10603.4	−	5966.87i	0.871489	−	0.490414i
$530$	−8839.02			−0.724420
$531$	2945.42	+	1892.91i	0.240716	+	0.154699i
$532$	717.068	+	4987.32i	0.0584376	+	0.406443i
$533$	4288.05	+	9389.52i	0.348473	+	0.763049i
$534$	−5783.46	−	1698.18i	−0.468679	−	0.137617i
$535$	4872.56	−	10669.4i	0.393755	−	0.862203i
$536$	540.774	−	624.086i	0.0435781	−	0.0502918i
$537$	103.746	−	721.572i	0.00833703	−	0.0579853i
$538$	8846.13	−	2597.46i	0.708892	−	0.208149i
$539$	−2896.39	−	3342.61i	−0.231459	−	0.267118i
$540$	1449.68	−	931.654i	0.115527	−	0.0742444i
$541$	15802.8	−	10155.8i	1.25585	−	0.807085i	0.268139	−	0.963380i	$-0.413591\pi$
$541$	15802.8	−	10155.8i	1.25585	−	0.807085i	0.987710	+	0.156295i	$0.0499551\pi$
$542$	762.840	+	880.365i	0.0604553	+	0.0697692i
$543$	8919.68	−	2619.05i	0.704936	−	0.206988i
$544$	193.452	−	1345.49i	0.0152467	−	0.106043i
$545$	−4104.25	+	4736.55i	−0.322581	+	0.372278i
$546$	914.231	−	2001.89i	0.0716584	−	0.156910i
$547$	−134.272	−	39.4257i	−0.0104955	−	0.00308176i	0.276481	−	0.961020i	$-0.410832\pi$
$547$	−134.272	−	39.4257i	−0.0104955	−	0.00308176i	−0.286976	+	0.957938i	$0.592650\pi$
$548$	−890.830	−	1950.65i	−0.0694423	−	0.152057i
$549$	867.803	+	6035.71i	0.0674626	+	0.469212i
$550$	4529.77	+	2911.11i	0.351182	+	0.225691i
$551$	11214.1			0.867037
$552$	2560.84	−	671.054i	0.197457	−	0.0517427i
$553$	−7290.16			−0.560595
$554$	1130.11	+	726.278i	0.0866675	+	0.0556978i
$555$	−656.257	−	4564.37i	−0.0501920	−	0.349093i
$556$	−2391.85	−	5237.41i	−0.182440	−	0.399489i
$557$	11381.8	+	3342.01i	0.865824	+	0.254229i	0.684338	−	0.729165i	$-0.260091\pi$
$557$	11381.8	+	3342.01i	0.865824	+	0.254229i	0.181486	+	0.983394i	$0.441909\pi$
$558$	−1931.23	+	4228.81i	−0.146515	+	0.320824i
$559$	−2949.89	+	3404.35i	−0.223197	+	0.257583i
$560$	−414.419	+	2882.34i	−0.0312721	+	0.217502i
$561$	−2540.26	+	745.889i	−0.191176	+	0.0561345i
$562$	1435.64	+	1656.82i	0.107756	+	0.124357i
$563$	−14588.5	+	9375.44i	−1.09206	+	0.701825i	−0.957313	−	0.289055i	$-0.906659\pi$
$563$	−14588.5	+	9375.44i	−1.09206	+	0.701825i	−0.134749	+	0.990880i	$0.543023\pi$
$564$	4429.34	−	2846.56i	0.330689	−	0.212521i
$565$	4660.06	+	5378.00i	0.346992	+	0.400450i
$566$	−9664.23	+	2837.67i	−0.717699	+	0.210736i
$567$	131.487	−	914.511i	0.00973885	−	0.0677352i
$568$	−6138.99	+	7084.77i	−0.453497	+	0.523364i
$569$	−691.283	+	1513.70i	−0.0509316	+	0.111525i	−0.933387	−	0.358871i	$-0.883162\pi$
$569$	−691.283	+	1513.70i	−0.0509316	+	0.111525i	0.882455	+	0.470396i	$0.155889\pi$
$570$	10144.2	+	2978.61i	0.745428	+	0.218877i
$571$	1380.10	+	3022.00i	0.101148	+	0.221483i	0.953440	−	0.301584i	$-0.0975152\pi$
$571$	1380.10	+	3022.00i	0.101148	+	0.221483i	−0.852292	+	0.523066i	$0.824788\pi$
$572$	−380.302	−	2645.06i	−0.0277993	−	0.193349i
$573$	−6141.20	−	3946.71i	−0.447736	−	0.287742i
$574$	−7322.84			−0.532490
$575$	13591.5	+	4427.52i	0.985748	+	0.321114i
$576$	576.000			0.0416667
$577$	−1389.67	−	893.085i	−0.100265	−	0.0644361i	0.489548	−	0.871977i	$-0.337162\pi$
$577$	−1389.67	−	893.085i	−0.100265	−	0.0644361i	−0.589812	+	0.807540i	$0.700798\pi$
$578$	−884.785	−	6153.81i	−0.0636716	−	0.442846i
$579$	−220.762	−	483.401i	−0.0158455	−	0.0346968i
$580$	6218.51	+	1825.92i	0.445189	+	0.130719i
$581$	139.627	−	305.740i	0.00997021	−	0.0218317i
$582$	2567.60	−	2963.17i	0.182870	−	0.211044i
$583$	−818.928	+	5695.77i	−0.0581759	+	0.404622i
$584$	−3291.71	+	966.532i	−0.233239	+	0.0684853i
$585$	−3024.05	−	3489.94i	−0.213725	−	0.246652i
$586$	12865.7	−	8268.27i	0.906956	−	0.582865i
$587$	−518.327	+	333.109i	−0.0364457	+	0.0234222i	−0.558737	−	0.829345i	$-0.688714\pi$
$587$	−518.327	+	333.109i	−0.0364457	+	0.0234222i	0.522291	+	0.852767i	$0.325077\pi$
$588$	−1673.00	−	1930.74i	−0.117336	−	0.135412i
$589$	−27366.8	+	8035.62i	−1.91448	+	0.562143i
$590$	−1766.77	+	12288.1i	−0.123283	+	0.857449i
$591$	5273.44	−	6085.87i	0.367039	−	0.423586i
$592$	640.299	−	1402.06i	0.0444529	−	0.0973383i
$593$	−17311.7	−	5083.18i	−1.19883	−	0.352009i	−0.379426	−	0.925222i	$-0.623879\pi$
$593$	−17311.7	−	5083.18i	−1.19883	−	0.352009i	−0.819407	+	0.573213i	$0.805697\pi$
$594$	−466.035	−	1020.48i	−0.0321914	−	0.0704892i
$595$	−1100.25	−	7652.42i	−0.0758082	−	0.527258i
$596$	−3702.60	−	2379.51i	−0.254470	−	0.163538i
$597$	−4734.52			−0.324574
$598$	−2756.57	−	6536.63i	−0.188503	−	0.446994i
$599$	−1509.91			−0.102994			−0.0514968	−	0.998673i	$-0.516399\pi$
$599$	−1509.91			−0.102994			−0.0514968	+	0.998673i	$0.516399\pi$
$600$	2616.46	+	1681.50i	0.178028	+	0.114411i
$601$	3295.97	+	22924.0i	0.223703	+	1.55589i	0.723855	+	0.689952i	$0.242368\pi$
$601$	3295.97	+	22924.0i	0.223703	+	1.55589i	−0.500152	+	0.865938i	$0.666723\pi$
$602$	−1327.52	−	2906.86i	−0.0898764	−	0.196802i
$603$	−891.376	−	261.732i	−0.0601984	−	0.0176759i
$604$	4185.88	−	9165.81i	0.281989	−	0.617469i
$605$	−9397.70	+	10845.5i	−0.631522	+	0.728815i
$606$	751.873	−	5229.39i	0.0504006	−	0.350544i
$607$	21349.1	−	6268.67i	1.42757	−	0.419172i	0.525510	−	0.850787i	$-0.323874\pi$
$607$	21349.1	−	6268.67i	1.42757	−	0.419172i	0.902058	+	0.431615i	$0.142056\pi$
$608$	2314.20	+	2670.73i	0.154364	+	0.178146i
$609$	2923.19	−	1878.62i	0.194505	−	0.125001i
$610$	−18188.9	+	11689.3i	−1.20729	+	0.775880i
$611$	−9239.63	−	10663.1i	−0.611777	−	0.706028i
$612$	−1467.29	+	430.836i	−0.0969147	+	0.0284567i
$613$	−2902.70	+	20188.7i	−0.191254	+	1.33020i	0.637440	+	0.770500i	$0.279993\pi$
$613$	−2902.70	+	20188.7i	−0.191254	+	1.33020i	−0.828694	+	0.559702i	$0.810916\pi$
$614$	−2420.37	+	2793.26i	−0.159085	+	0.183594i
$615$	−6383.04	+	13976.9i	−0.418519	+	0.916429i
$616$	1818.95	+	534.093i	0.118974	+	0.0349338i
$617$	2312.61	+	5063.92i	0.150895	+	0.330414i	0.969951	−	0.243299i	$-0.0782296\pi$
$617$	2312.61	+	5063.92i	0.150895	+	0.330414i	−0.819056	+	0.573713i	$0.805502\pi$
$618$	−1148.41	−	7987.35i	−0.0747504	−	0.519901i
$619$	−18197.4	−	11694.8i	−1.18161	−	0.759373i	−0.205926	−	0.978568i	$-0.566021\pi$
$619$	−18197.4	−	11694.8i	−1.18161	−	0.759373i	−0.975681	+	0.219195i	$0.929657\pi$
$620$	−16484.0			−1.06776
$621$	−1883.50	−	2306.98i	−0.121711	−	0.149076i
$622$	−21086.7			−1.35932
$623$	−9639.82	−	6195.13i	−0.619921	−	0.398399i
$624$	−219.668	−	1527.82i	−0.0140926	−	0.0980159i
$625$	−6243.68	−	13671.8i	−0.399596	−	0.874993i
$626$	2652.46	+	778.832i	0.169351	+	0.0497259i
$627$	2859.23	−	6260.84i	0.182116	−	0.398778i
$628$	7914.22	−	9133.49i	0.502885	−	0.580360i
$629$	−582.376	+	4050.51i	−0.0369171	+	0.256764i
$630$	3143.28	−	922.951i	0.198780	−	0.0583670i
$631$	−15110.3	−	17438.2i	−0.953298	−	1.10016i	−0.994883	−	0.101030i	$-0.967786\pi$
$631$	−15110.3	−	17438.2i	−0.953298	−	1.10016i	0.0415852	−	0.999135i	$-0.486759\pi$
$632$	−4301.37	+	2764.32i	−0.270727	+	0.173986i
$633$	9149.56	−	5880.06i	0.574506	−	0.369213i
$634$	−10928.0	−	12611.6i	−0.684552	−	0.790015i
$635$	−29940.4	+	8791.30i	−1.87110	+	0.549405i
$636$	−473.025	+	3289.96i	−0.0294916	+	0.205119i
$637$	−4483.21	+	5173.91i	−0.278856	+	0.321817i
$638$	1752.74	−	3837.96i	0.108764	−	0.238161i
$639$	10119.1	+	2971.24i	0.626457	+	0.183944i
$640$	848.426	+	1857.79i	0.0524015	+	0.114743i
$641$	−1350.34	−	9391.85i	−0.0832065	−	0.578714i	−0.988186	−	0.153259i	$-0.951023\pi$
$641$	−1350.34	−	9391.85i	−0.0832065	−	0.578714i	0.904980	−	0.425455i	$-0.139886\pi$
$642$	−3710.49	−	2384.58i	−0.228102	−	0.146592i
$643$	28561.0			1.75169			0.875844	−	0.482594i	$-0.160305\pi$
$643$	28561.0			1.75169			0.875844	+	0.482594i	$0.160305\pi$
$644$	5030.51	+	147.520i	0.307810	+	0.00902657i
$645$	−6705.39			−0.409340
$646$	−7892.82	−	5072.41i	−0.480711	−	0.308934i
$647$	−1853.17	−	12889.1i	−0.112605	−	0.783185i	−0.965369	−	0.260889i	$-0.915984\pi$
$647$	−1853.17	−	12889.1i	−0.112605	−	0.783185i	0.852764	−	0.522297i	$-0.174925\pi$
$648$	−269.189	−	589.442i	−0.0163190	−	0.0357337i
$649$	7754.65	+	2276.97i	0.469024	+	0.137718i
$650$	3462.29	−	7581.36i	0.208927	−	0.457485i
$651$	−5787.58	+	6679.22i	−0.348438	+	0.402119i
$652$	−1541.98	+	10724.7i	−0.0926206	+	0.644191i
$653$	−22062.6	+	6478.17i	−1.32217	+	0.388224i	−0.865276	−	0.501296i	$-0.832857\pi$
$653$	−22062.6	+	6478.17i	−1.32217	+	0.388224i	−0.456895	+	0.889521i	$0.651038\pi$
$654$	1543.34	+	1781.11i	0.0922776	+	0.106494i
$655$	9478.31	−	6091.34i	0.565417	−	0.363372i
$656$	−4320.65	+	2776.71i	−0.257154	+	0.165263i
$657$	2527.44	+	2916.82i	0.150083	+	0.173206i
$658$	9603.94	−	2819.97i	0.568998	−	0.167073i
$659$	−2917.04	+	20288.4i	−0.172430	+	1.19928i	0.701299	+	0.712868i	$0.252604\pi$
$659$	−2917.04	+	20288.4i	−0.172430	+	1.19928i	−0.873729	+	0.486413i	$0.838305\pi$
$660$	2604.92	−	3006.24i	0.153631	−	0.177300i
$661$	1663.41	−	3642.35i	0.0978806	−	0.214329i	−0.854357	−	0.519686i	$-0.826049\pi$
$661$	1663.41	−	3642.35i	0.0978806	−	0.214329i	0.952238	+	0.305358i	$0.0987761\pi$
$662$	10312.8	+	3028.12i	0.605468	+	0.177782i
$663$	1702.36	+	3727.65i	0.0997197	+	0.218356i
$664$	−33.5490	−	233.338i	−0.00196077	−	0.0136375i
$665$	16908.3	+	10866.3i	0.985976	+	0.633648i
$666$	−1734.02			−0.100889
$667$	1918.36	−	11035.4i	0.111363	−	0.640620i
$668$	−10795.9			−0.625309
$669$	−8919.94	−	5732.50i	−0.515493	−	0.331287i
$670$	−468.791	−	3260.51i	−0.0270313	−	0.188007i
$671$	5847.28	+	12803.8i	0.336411	+	0.736637i
$672$	1050.66	+	308.500i	0.0603123	+	0.0177093i
$673$	−2967.78	+	6498.54i	−0.169985	+	0.372214i	−0.975382	−	0.220520i	$-0.929224\pi$
$673$	−2967.78	+	6498.54i	−0.169985	+	0.372214i	0.805398	+	0.592735i	$0.201952\pi$
$674$	13405.7	−	15471.0i	0.766127	−	0.884158i
$675$	497.955	−	3463.35i	0.0283945	−	0.197488i
$676$	4463.29	−	1310.54i	0.253942	−	0.0745642i
$677$	1091.84	+	1260.05i	0.0619835	+	0.0715328i	0.785895	−	0.618361i	$-0.212203\pi$
$677$	1091.84	+	1260.05i	0.0619835	+	0.0715328i	−0.723911	+	0.689893i	$0.757657\pi$
$678$	2251.12	−	1446.71i	0.127513	−	0.0819477i
$679$	6270.49	−	4029.80i	0.354403	−	0.227761i
$680$	−3550.86	−	4097.91i	−0.200249	−	0.231100i
$681$	−10615.0	+	3116.84i	−0.597309	+	0.175386i
$682$	−1527.22	+	10622.1i	−0.0857484	+	0.596393i
$683$	12688.2	−	14642.9i	0.710834	−	0.820346i	−0.279339	−	0.960193i	$-0.590115\pi$
$683$	12688.2	−	14642.9i	0.710834	−	0.820346i	0.990173	+	0.139846i	$0.0446608\pi$
$684$	1651.53	−	3616.36i	0.0923216	−	0.202156i
$685$	−8207.60	−	2409.97i	−0.457805	−	0.134424i
$686$	−5268.08	−	11535.5i	−0.293201	−	0.642021i
$687$	2910.47	+	20242.7i	0.161632	+	1.12418i
$688$	−1885.51	−	1211.74i	−0.104483	−	0.0671471i
$689$	8906.92			0.492492
$690$	4666.48	−	9473.02i	0.257463	−	0.522655i
$691$	3116.18			0.171556			0.0857779	−	0.996314i	$-0.472662\pi$
$691$	3116.18			0.171556			0.0857779	+	0.996314i	$0.472662\pi$
$692$	10913.0	+	7013.38i	0.599496	+	0.385273i
$693$	−303.517	−	2111.01i	−0.0166373	−	0.115715i
$694$	−3097.61	−	6782.83i	−0.169429	−	0.370998i
$695$	−22037.1	−	6470.68i	−1.20276	−	0.353161i
$696$	1012.41	−	2216.87i	0.0551368	−	0.120733i
$697$	8929.44	−	10305.1i	0.485260	−	0.560020i
$698$	−257.763	+	1792.78i	−0.0139778	+	0.0972175i
$699$	−16138.6	+	4738.72i	−0.873273	+	0.256416i
$700$	3871.97	+	4468.50i	0.209067	+	0.241276i
$701$	15374.5	−	9880.62i	0.828371	−	0.532362i	−0.0563887	−	0.998409i	$-0.517959\pi$
$701$	15374.5	−	9880.62i	0.828371	−	0.532362i	0.884760	+	0.466047i	$0.154322\pi$
$702$	−1460.82	+	938.810i	−0.0785399	+	0.0504745i
$703$	−6966.79	−	8040.10i	−0.373766	−	0.431349i
$704$	1275.75	−	374.593i	0.0682977	−	0.0200540i
$705$	2988.99	−	20788.9i	0.159676	−	1.11057i
$706$	−6928.13	+	7995.48i	−0.369325	+	0.426224i
$707$	4172.27	−	9136.00i	0.221944	−	0.485989i
$708$	4479.20	+	1315.21i	0.237767	+	0.0698146i
$709$	11122.0	+	24353.8i	0.589133	+	1.29002i	0.935965	+	0.352094i	$0.114530\pi$
$709$	11122.0	+	24353.8i	0.589133	+	1.29002i	−0.346832	+	0.937927i	$0.612743\pi$
$710$	5321.82	+	37014.1i	0.281302	+	1.95650i
$711$	4839.04	+	3109.86i	0.255244	+	0.164035i
$712$	−8036.83			−0.423024
$713$	3226.04	+	28305.4i	0.169448	+	1.48674i
$714$	−2907.17			−0.152379
$715$	−8967.41	−	5763.00i	−0.469038	−	0.301432i
$716$	−138.328	−	962.096i	−0.00722008	−	0.0502168i
$717$	5290.60	+	11584.8i	0.275566	+	0.603406i
$718$	−7937.52	−	2330.67i	−0.412570	−	0.121142i
$719$	9570.59	−	20956.7i	0.496415	−	1.08700i	−0.481202	−	0.876609i	$-0.659800\pi$
$719$	9570.59	−	20956.7i	0.496415	−	1.08700i	0.977618	−	0.210389i	$-0.0674729\pi$
$720$	1504.64	−	1736.45i	0.0778816	−	0.0898801i
$721$	2183.19	−	15184.4i	0.112769	−	0.784325i
$722$	10241.0	−	3007.03i	0.527881	−	0.155000i
$723$	−3588.47	−	4141.31i	−0.184587	−	0.213025i
$724$	10427.3	−	6701.24i	0.535261	−	0.343991i
$725$	11070.5	−	7114.55i	0.567099	−	0.364452i
$726$	3533.87	+	4078.31i	0.180653	+	0.208485i
$727$	10856.4	−	3187.73i	0.553840	−	0.162622i	0.00717603	−	0.999974i	$-0.497716\pi$
$727$	10856.4	−	3187.73i	0.553840	−	0.162622i	0.546664	+	0.837352i	$0.315898\pi$
$728$	417.602	−	2904.49i	0.0212601	−	0.147867i
$729$	−477.393	+	550.941i	−0.0242541	+	0.0279907i
$730$	−5684.91	+	12448.2i	−0.288230	+	0.631136i
$731$	5709.47	+	1676.45i	0.288881	+	0.0848232i
$732$	3377.47	+	7395.64i	0.170540	+	0.373430i
$733$	−4880.71	−	33946.1i	−0.245939	−	1.71054i	−0.621224	−	0.783633i	$-0.713364\pi$
$733$	−4880.71	−	33946.1i	−0.245939	−	1.71054i	0.375285	−	0.926909i	$-0.377545\pi$
$734$	−10648.2	−	6843.20i	−0.535468	−	0.344124i
$735$	−10190.8			−0.511420
$736$	3024.06	−	1820.46i	0.151452	−	0.0911725i
$737$	−2144.47			−0.107181
$738$	4860.73	+	3123.80i	0.242447	+	0.155811i
$739$	−3911.62	−	27205.9i	−0.194711	−	1.35424i	−0.819334	−	0.573317i	$-0.805656\pi$
$739$	−3911.62	−	27205.9i	−0.194711	−	1.35424i	0.624623	−	0.780927i	$-0.285253\pi$
$740$	−2554.14	−	5592.79i	−0.126881	−	0.277831i
$741$	−10222.1	−	3001.49i	−0.506773	−	0.148802i
$742$	−2624.89	+	5747.72i	−0.129869	+	0.284374i
$743$	−14521.8	+	16759.0i	−0.717029	+	0.827496i	−0.990946	−	0.134257i	$-0.957135\pi$
$743$	−14521.8	+	16759.0i	−0.717029	+	0.827496i	0.273917	+	0.961753i	$0.411681\pi$
$744$	−882.147	+	6135.47i	−0.0434692	+	0.302335i
$745$	−16845.5	+	4946.28i	−0.828417	+	0.243245i
$746$	10552.6	+	12178.4i	0.517907	+	0.597697i
$747$	−223.105	+	143.381i	−0.0109277	+	0.00702279i
$748$	−2969.63	+	1908.47i	−0.145161	+	0.0932894i
$749$	−5490.97	−	6336.91i	−0.267871	−	0.309140i
$750$	421.759	−	123.840i	0.0205340	−	0.00602931i
$751$	−678.871	+	4721.65i	−0.0329858	+	0.229421i	−0.999645	−	0.0266452i	$-0.991518\pi$
$751$	−678.871	+	4721.65i	−0.0329858	+	0.229421i	0.966659	+	0.256067i	$0.0824267\pi$
$752$	4597.26	−	5305.53i	0.222932	−	0.257277i
$753$	2564.35	−	5615.14i	0.124104	−	0.271749i
$754$	−6266.27	−	1839.94i	−0.302658	−	0.0888684i
$755$	−16697.4	−	36562.2i	−0.804876	−	1.76243i
$756$	−175.316	−	1219.35i	−0.00843409	−	0.0586604i
$757$	11421.1	+	7339.87i	0.548356	+	0.352407i	0.785299	−	0.619117i	$-0.212509\pi$
$757$	11421.1	+	7339.87i	0.548356	+	0.352407i	−0.236943	+	0.971523i	$0.576146\pi$
$758$	21814.8			1.04532
$759$	−5671.96	−	3884.69i	−0.271251	−	0.185778i
$760$	14096.6			0.672813
$761$	−11392.4	−	7321.44i	−0.542672	−	0.348754i	0.240411	−	0.970671i	$-0.422718\pi$
$761$	−11392.4	−	7321.44i	−0.542672	−	0.348754i	−0.783083	+	0.621917i	$0.786354\pi$
$762$	1669.92	+	11614.6i	0.0793895	+	0.552166i
$763$	1861.20	+	4075.45i	0.0883090	+	0.193370i
$764$	−9339.14	−	2742.22i	−0.442249	−	0.129856i
$765$	−2534.07	+	5548.85i	−0.119764	+	0.262247i
$766$	−16622.0	+	19182.8i	−0.784043	+	0.904834i
$767$	1780.34	−	12382.5i	0.0838127	−	0.582930i
$768$	736.891	−	216.371i	0.0346227	−	0.0101661i
$769$	3664.24	+	4228.75i	0.171828	+	0.198300i	0.835131	−	0.550051i	$-0.185392\pi$
$769$	3664.24	+	4228.75i	0.171828	+	0.198300i	−0.663303	+	0.748351i	$0.730846\pi$
$770$	6361.64	−	4088.38i	0.297737	−	0.191344i
$771$	17547.0	−	11276.7i	0.819635	−	0.526747i
$772$	−464.012	−	535.499i	−0.0216323	−	0.0249651i
$773$	−33562.6	+	9854.88i	−1.56166	+	0.458545i	−0.944560	−	0.328338i	$-0.893511\pi$
$773$	−33562.6	+	9854.88i	−1.56166	+	0.458545i	−0.617101	+	0.786884i	$0.711693\pi$
$774$	−358.842	+	2495.80i	−0.0166645	+	0.115904i
$775$	−21918.2	+	25294.9i	−1.01590	+	1.17241i
$776$	2171.70	−	4755.36i	0.100463	−	0.219984i
$777$	−3162.94	−	928.723i	−0.146036	−	0.0428800i
$778$	6788.06	+	14863.8i	0.312807	+	0.684952i
$779$	5044.93	+	35088.3i	0.232033	+	1.61382i
$780$	−5179.71	−	3328.80i	−0.237773	−	0.152808i
$781$	24344.5			1.11538
$782$	−6341.78	+	6899.34i	−0.290002	+	0.315499i
$783$	−2741.74			−0.125136
$784$	−2865.58	−	1841.60i	−0.130538	−	0.0838919i
$785$	−6860.74	−	47717.5i	−0.311937	−	2.16957i
$786$	−1760.01	−	3853.89i	−0.0798696	−	0.174890i
$787$	6741.11	+	1979.37i	0.305330	+	0.0896529i	0.430808	−	0.902443i	$-0.358228\pi$
$787$	6741.11	+	1979.37i	0.305330	+	0.0896529i	−0.125479	+	0.992096i	$0.540047\pi$
$788$	4460.32	−	9766.73i	0.201640	−	0.441530i
$789$	−7891.33	+	9107.09i	−0.356070	+	0.410926i
$790$	−2902.63	+	20188.3i	−0.130723	+	0.909197i
$791$	4881.01	−	1433.19i	0.219404	−	0.0644229i
$792$	−979.545	−	1130.46i	−0.0439478	−	0.0507184i
$793$	18328.7	−	11779.1i	0.820769	−	0.527476i
$794$	−7435.46	+	4778.48i	−0.332336	+	0.213579i
$795$	8682.50	+	10020.1i	0.387341	+	0.447016i
$796$	−6056.98	+	1778.49i	−0.269704	+	0.0791921i
$797$	1542.60	−	10729.0i	0.0685592	−	0.476839i	−0.926399	−	0.376544i	$-0.877112\pi$
$797$	1542.60	−	10729.0i	0.0685592	−	0.476839i	0.994958	−	0.100295i	$-0.0319787\pi$
$798$	4949.37	−	5711.88i	0.219556	−	0.253381i
$799$	−7742.57	+	16953.9i	−0.342819	+	0.750669i
$800$	3978.95	+	1168.32i	0.175846	+	0.0516331i
$801$	3755.95	+	8224.38i	0.165680	+	0.362789i
$802$	2797.28	+	19455.5i	0.123161	+	0.856607i
$803$	7494.79	+	4816.61i	0.329371	+	0.211674i
$804$	−1238.68			−0.0543343
$805$	13585.6	−	14780.0i	0.594818	−	0.647113i
$806$	16610.6			0.725909
$807$	−11634.0	−	7476.73i	−0.507481	−	0.326138i
$808$	−1002.50	−	6972.52i	−0.0436482	−	0.303580i
$809$	6939.41	+	15195.2i	0.301578	+	0.660364i	0.998380	−	0.0568998i	$-0.0181216\pi$
$809$	6939.41	+	15195.2i	0.301578	+	0.660364i	−0.696802	+	0.717264i	$0.745394\pi$
$810$	−2480.15	−	728.239i	−0.107585	−	0.0315898i
$811$	−6685.08	+	14638.3i	−0.289451	+	0.633810i	−0.997370	−	0.0724846i	$-0.976907\pi$
$811$	−6685.08	+	14638.3i	−0.289451	+	0.633810i	0.707918	+	0.706294i	$0.249634\pi$
$812$	3034.02	−	3501.44i	0.131125	−	0.151326i
$813$	248.672	−	1729.55i	0.0107273	−	0.0746100i
$814$	−3840.57	+	1127.69i	−0.165371	+	0.0485572i
$815$	28303.5	+	32664.0i	1.21648	+	1.40389i
$816$	−1715.30	+	1102.36i	−0.0735878	+	0.0472920i
$817$	−13014.0	+	8363.59i	−0.557285	+	0.358146i
$818$	4205.06	+	4852.89i	0.179739	+	0.207430i
$819$	−3167.43	+	930.041i	−0.135139	+	0.0396804i
$820$	−2915.64	+	20278.8i	−0.124169	+	0.863615i
$821$	8574.65	−	9895.68i	0.364504	−	0.420659i	−0.543640	−	0.839319i	$-0.682954\pi$
$821$	8574.65	−	9895.68i	0.364504	−	0.420659i	0.908144	+	0.418659i	$0.137500\pi$
$822$	−1336.24	+	2925.97i	−0.0566994	+	0.124154i
$823$	−8029.92	−	2357.80i	−0.340104	−	0.0998634i	0.107221	−	0.994235i	$-0.465805\pi$
$823$	−8029.92	−	2357.80i	−0.340104	−	0.0998634i	−0.447324	+	0.894372i	$0.647623\pi$
$824$	−4469.58	−	9787.02i	−0.188963	−	0.413771i
$825$	−1149.45	−	7994.61i	−0.0485076	−	0.337378i
$826$	7465.89	+	4798.04i	0.314493	+	0.202113i
$827$	10185.3			0.428268			0.214134	−	0.976804i	$-0.431307\pi$
$827$	10185.3			0.428268			0.214134	+	0.976804i	$0.431307\pi$
$828$	−3276.21	−	2243.85i	−0.137507	−	0.0941780i
$829$	42788.0			1.79263			0.896313	−	0.443421i	$-0.146235\pi$
$829$	42788.0			1.79263			0.896313	+	0.443421i	$0.146235\pi$
$830$	−791.075	−	508.393i	−0.0330827	−	0.0212609i
$831$	−286.771	−	1994.54i	−0.0119711	−	0.0832608i
$832$	−854.943	−	1872.07i	−0.0356248	−	0.0780074i
$833$	8677.20	+	2547.86i	0.360921	+	0.105976i
$834$	−3587.77	+	7856.12i	−0.148962	+	0.326181i
$835$	−28201.4	+	32546.1i	−1.16880	+	1.34887i
$836$	1306.04	−	9083.70i	0.0540314	−	0.375797i
$837$	6690.91	−	1964.63i	0.276310	−	0.0811320i
$838$	20001.8	+	23083.4i	0.824526	+	0.951553i
$839$	−24460.2	+	15719.6i	−1.00651	+	0.646844i	−0.936487	−	0.350701i	$-0.885943\pi$
$839$	−24460.2	+	15719.6i	−1.00651	+	0.646844i	−0.0700218	+	0.997545i	$0.522307\pi$
$840$	3674.58	−	2361.51i	0.150934	−	0.0969996i
$841$	9218.76	+	10639.0i	0.377988	+	0.436222i
$842$	16077.2	−	4720.69i	0.658024	−	0.193213i
$843$	467.993	−	3254.96i	0.0191204	−	0.132986i
$844$	9496.44	−	10959.5i	0.387300	−	0.446968i
$845$	7708.27	−	16878.8i	0.313814	−	0.687157i
$846$	−7577.83	−	2225.05i	−0.307956	−	0.0904242i
$847$	4261.67	+	9331.76i	0.172884	+	0.378563i
$848$	630.700	+	4386.61i	0.0255405	+	0.177638i
$849$	12709.9	+	8168.18i	0.513786	+	0.330190i
$850$	−11009.8			−0.444274
$851$	−9103.77	+	5480.38i	−0.366713	+	0.220758i
$852$	14061.7			0.565431
$853$	−13431.9	−	8632.16i	−0.539156	−	0.346494i	0.242553	−	0.970138i	$-0.422015\pi$
$853$	−13431.9	−	8632.16i	−0.539156	−	0.346494i	−0.781709	+	0.623644i	$0.785652\pi$
$854$	2199.66	+	15299.0i	0.0881392	+	0.613022i
$855$	−6587.94	−	14425.6i	−0.263512	−	0.577011i
$856$	−5642.67	−	1656.84i	−0.225307	−	0.0661560i
$857$	4128.35	−	9039.83i	0.164553	−	0.360320i	−0.809336	−	0.587346i	$-0.800173\pi$
$857$	4128.35	−	9039.83i	0.164553	−	0.360320i	0.973889	+	0.227026i	$0.0729001\pi$
$858$	−2624.93	+	3029.34i	−0.104445	+	0.120536i
$859$	−52.3810	+	364.318i	−0.00208058	+	0.0144708i	−0.990835	−	0.135076i	$-0.956872\pi$
$859$	−52.3810	+	364.318i	−0.00208058	+	0.0144708i	0.988755	+	0.149546i	$0.0477813\pi$
$860$	−8578.37	+	2518.84i	−0.340139	+	0.0998740i
$861$	7193.16	+	8301.35i	0.284718	+	0.328582i
$862$	−4529.04	+	2910.64i	−0.178956	+	0.115008i
$863$	11183.0	−	7186.90i	0.441106	−	0.283482i	−0.301177	−	0.953568i	$-0.597379\pi$
$863$	11183.0	−	7186.90i	0.441106	−	0.283482i	0.742283	+	0.670087i	$0.233743\pi$
$864$	−565.800	−	652.968i	−0.0222788	−	0.0257111i
$865$	49650.4	−	14578.7i	1.95163	−	0.573051i
$866$	3455.27	−	24031.9i	0.135583	−	0.943000i
$867$	−6107.00	+	7047.85i	−0.239221	+	0.276076i
$868$	−4895.18	+	10719.0i	−0.191421	+	0.419153i
$869$	12740.2	+	3740.85i	0.497331	+	0.146029i
$870$	−4038.48	−	8843.03i	−0.157376	−	0.344606i
$871$	472.392	+	3285.56i	0.0183770	+	0.127815i
$872$	2643.50	+	1698.88i	0.102661	+	0.0659761i
$873$	−5881.26			−0.228007
$874$	−2758.82	−	24205.9i	−0.106772	−	0.936817i
$875$	835.639			0.0322854
$876$	4329.10	+	2782.14i	0.166971	+	0.107306i
$877$	4479.92	+	31158.5i	0.172493	+	1.19971i	0.873595	+	0.486653i	$0.161783\pi$
$877$	4479.92	+	31158.5i	0.172493	+	1.19971i	−0.701102	+	0.713061i	$0.747308\pi$
$878$	−7805.93	−	17092.6i	−0.300043	−	0.657002i
$879$	−22010.9	−	6463.00i	−0.844609	−	0.247999i
$880$	2203.27	−	4824.48i	0.0844001	−	0.184810i
$881$	4424.84	−	5106.53i	0.169213	−	0.195282i	−0.664809	−	0.747013i	$-0.731487\pi$
$881$	4424.84	−	5106.53i	0.169213	−	0.195282i	0.834022	+	0.551731i	$0.186033\pi$
$882$	−545.366	+	3793.10i	−0.0208202	+	0.144808i
$883$	−18065.9	+	5304.63i	−0.688524	+	0.202169i	−0.607236	−	0.794522i	$-0.707722\pi$
$883$	−18065.9	+	5304.63i	−0.688524	+	0.202169i	−0.0812882	+	0.996691i	$0.525903\pi$
$884$	3578.14	+	4129.39i	0.136138	+	0.157111i
$885$	15665.6	−	10067.7i	0.595022	−	0.382397i
$886$	−14150.6	+	9094.05i	−0.536568	+	0.344831i
$887$	−15923.6	−	18376.8i	−0.602775	−	0.695640i	0.369566	−	0.929204i	$-0.379506\pi$
$887$	−15923.6	−	18376.8i	−0.602775	−	0.695640i	−0.972341	+	0.233565i	$0.924961\pi$
$888$	−2218.37	+	651.372i	−0.0838328	+	0.0246155i
$889$	−3174.62	+	22080.0i	−0.119767	+	0.833001i
$890$	−20994.0	+	24228.4i	−0.790698	+	0.912514i
$891$	−699.053	+	1530.71i	−0.0262841	+	0.0575542i
$892$	−13564.9	−	3983.01i	−0.509177	−	0.149508i
$893$	−20128.7	−	44075.7i	−0.754290	−	1.65166i
$894$	939.552	+	6534.73i	0.0351491	+	0.244468i
$895$	−3261.75	−	2096.20i	−0.121819	−	0.0782884i
$896$	1460.01			0.0544371
$897$	−4702.32	+	9545.79i	−0.175035	+	0.355323i
$898$	−7525.83			−0.279666
$899$	22063.2	+	14179.2i	0.818520	+	0.526031i
$900$	−663.940	−	4617.81i	−0.0245904	−	0.171030i
$901$	−4887.73	−	10702.6i	−0.180726	−	0.395734i
$902$	12797.3	+	3757.62i	0.472397	+	0.138708i
$903$	−1991.28	+	4360.29i	−0.0733838	+	0.160688i
$904$	2336.47	−	2696.43i	0.0859622	−	0.0992056i
$905$	7036.53	−	48940.1i	0.258455	−	1.79760i
$906$	−14502.3	+	4258.27i	−0.531797	+	0.156150i
$907$	−27009.5	−	31170.6i	−0.988794	−	1.14113i	−0.989991	−	0.141130i	$-0.954926\pi$
$907$	−27009.5	−	31170.6i	−0.988794	−	1.14113i	0.00119693	−	0.999999i	$-0.499619\pi$
$908$	−12409.2	+	7974.90i	−0.453539	+	0.291472i
$909$	−6666.73	+	4284.44i	−0.243258	+	0.156332i
$910$	−7665.19	−	8846.11i	−0.279229	−	0.322248i
$911$	22227.3	−	6526.52i	0.808368	−	0.237358i	0.148668	−	0.988887i	$-0.452502\pi$
$911$	22227.3	−	6526.52i	0.808368	−	0.237358i	0.659700	+	0.751529i	$0.270683\pi$
$912$	754.387	−	5246.88i	0.0273906	−	0.190506i
$913$	−400.895	+	462.658i	−0.0145320	+	0.0167708i
$914$	15257.1	−	33408.4i	0.552145	−	1.20903i
$915$	31118.1	+	9137.11i	1.12430	+	0.330124i
$916$	11327.5	+	24803.7i	0.408592	+	0.894692i
$917$	−1146.25	−	7972.35i	−0.0412786	−	0.287099i
$918$	1929.72	+	1240.15i	0.0693792	+	0.0445873i
$919$	9030.33			0.324138			0.162069	−	0.986779i	$-0.448183\pi$
$919$	9030.33			0.324138			0.162069	+	0.986779i	$0.448183\pi$
$920$	2411.46	−	13872.0i	0.0864167	−	0.497115i
$921$	5544.02			0.198351
$922$	30452.0	+	19570.3i	1.08773	+	0.699039i
$923$	−5362.70	−	37298.4i	−0.191241	−	1.33011i
$924$	−1181.28	−	2586.65i	−0.0420577	−	0.0920935i
$925$	−11978.4	−	3517.18i	−0.425781	−	0.125021i
$926$	3046.75	−	6671.45i	0.108124	−	0.236758i
$927$	−7926.59	+	9147.77i	−0.280845	+	0.324112i
$928$	462.448	−	3216.39i	0.0163584	−	0.113775i
$929$	−11530.9	+	3385.77i	−0.407229	+	0.119573i	−0.478930	−	0.877853i	$-0.658975\pi$
$929$	−11530.9	+	3385.77i	−0.407229	+	0.119573i	0.0717011	+	0.997426i	$0.477157\pi$
$930$	16192.0	+	18686.6i	0.570923	+	0.658880i
$931$	−19778.6	+	12710.9i	−0.696259	+	0.447458i
$932$	−18866.4	+	12124.7i	−0.663080	+	0.426135i
$933$	20713.2	+	23904.4i	0.726818	+	0.838793i
$934$	29288.4	−	8599.84i	1.02607	−	0.301280i
$935$	−2003.95	+	13937.8i	−0.0700923	+	0.487503i
$936$	−1516.20	+	1749.79i	−0.0529472	+	0.0611043i
$937$	−12528.6	+	27433.7i	−0.436809	+	0.956479i	0.555364	+	0.831608i	$0.312579\pi$
$937$	−12528.6	+	27433.7i	−0.436809	+	0.956479i	−0.992173	+	0.124871i	$0.960148\pi$
$938$	−2259.41	−	663.424i	−0.0786487	−	0.0230933i
$939$	−1722.58	−	3771.93i	−0.0598662	−	0.131089i
$940$	−3985.31	−	27718.5i	−0.138284	−	0.961784i
$941$	23511.4	+	15109.9i	0.814507	+	0.523452i	0.880320	−	0.474380i	$-0.157328\pi$
$941$	23511.4	+	15109.9i	0.814507	+	0.523452i	−0.0658133	+	0.997832i	$0.520964\pi$
$942$	−18128.0			−0.627009
$943$	35392.2	+	1037.88i	1.22219	+	0.0358409i
$944$	6224.40			0.214605
$945$	−4133.90	−	2656.69i	−0.142302	−	0.0914521i
$946$	828.331	+	5761.17i	0.0284687	+	0.198004i
$947$	−7040.59	−	15416.7i	−0.241593	−	0.529014i	0.749529	−	0.661971i	$-0.230280\pi$
$947$	−7040.59	−	15416.7i	−0.241593	−	0.529014i	−0.991122	+	0.132957i	$0.957553\pi$
$948$	7358.90	+	2160.77i	0.252116	+	0.0740280i
$949$	5728.58	−	12543.8i	0.195951	−	0.429073i
$950$	18743.8	−	21631.5i	0.640137	−	0.738757i
$951$	−3562.32	+	24776.5i	−0.121468	+	0.844829i
$952$	−3719.22	+	1092.06i	−0.126618	+	0.0371785i
$953$	−5924.18	−	6836.86i	−0.201367	−	0.232390i	0.646080	−	0.763270i	$-0.276407\pi$
$953$	−5924.18	−	6836.86i	−0.201367	−	0.232390i	−0.847447	+	0.530879i	$0.821862\pi$
$954$	4194.23	−	2695.47i	0.142341	−	0.0914769i
$955$	−32662.9	+	20991.1i	−1.10675	+	0.711264i
$956$	11120.1	+	12833.3i	0.376204	+	0.434163i
$957$	−6072.51	+	1783.05i	−0.205116	+	0.0602276i
$958$	3008.98	−	20927.9i	0.101478	−	0.705793i
$959$	−4004.50	+	4621.44i	−0.134841	+	0.155614i
$960$	1272.64	−	2786.69i	0.0427857	−	0.0936876i
$961$	−35418.8	−	10399.9i	−1.18891	−	0.349096i
$962$	2573.76	+	5635.75i	0.0862592	+	0.188881i
$963$	941.554	+	6548.65i	0.0315069	+	0.219135i
$964$	−6146.47	−	3950.09i	−0.205357	−	0.131975i
$965$	−2826.46			−0.0942869
$966$	−4774.19	−	5847.62i	−0.159014	−	0.194766i
$967$	50371.4			1.67511			0.837557	−	0.546350i	$-0.183983\pi$
$967$	50371.4			1.67511			0.837557	+	0.546350i	$0.183983\pi$
$968$	6052.96	+	3890.00i	0.200981	+	0.129163i
$969$	2002.84	+	13930.1i	0.0663990	+	0.461815i
$970$	−8662.87	−	18969.0i	−0.286751	−	0.627896i
$971$	24355.0	+	7151.27i	0.804932	+	0.236349i	0.658216	−	0.752829i	$-0.271311\pi$
$971$	24355.0	+	7151.27i	0.804932	+	0.236349i	0.146716	+	0.989179i	$0.453130\pi$
$972$	−403.783	+	884.162i	−0.0133244	+	0.0291765i
$973$	−10751.9	+	12408.4i	−0.354256	+	0.408834i
$974$	−1904.16	+	13243.8i	−0.0626421	+	0.435685i
$975$	−11995.4	+	3522.17i	−0.394010	+	0.115692i
$976$	7099.01	+	8192.69i	0.232821	+	0.268690i
$977$	−2454.31	+	1577.29i	−0.0803689	+	0.0516500i	−0.580208	−	0.814468i	$-0.697029\pi$
$977$	−2454.31	+	1577.29i	−0.0803689	+	0.0516500i	0.499839	+	0.866118i	$0.333392\pi$
$978$	13672.5	−	8786.76i	0.447032	−	0.287290i
$979$	13667.4	+	15773.0i	0.446183	+	0.514922i
$980$	−13037.3	+	3828.11i	−0.424962	+	0.124780i
$981$	503.101	−	3499.15i	0.0163739	−	0.113883i
$982$	3103.87	−	3582.05i	0.100864	−	0.116403i
$983$	−21891.4	+	47935.5i	−0.710303	+	1.55535i	0.116711	+	0.993166i	$0.462765\pi$
$983$	−21891.4	+	47935.5i	−0.710303	+	1.55535i	−0.827014	+	0.562181i	$0.809962\pi$
$984$	7391.89	+	2170.45i	0.239476	+	0.0703166i
$985$	−17792.1	−	38959.3i	−0.575537	−	1.26025i
$986$	1227.76	+	8539.29i	0.0396552	+	0.275808i
$987$	−12630.7	−	8117.23i	−0.407333	−	0.261777i
$988$	−14204.9			−0.457407
$989$	6004.06	+	14237.4i	0.193042	+	0.457757i
$990$	−5966.74			−0.191551
$991$	−33741.2	−	21684.1i	−1.08156	−	0.695075i	−0.126641	−	0.991949i	$-0.540420\pi$
$991$	−33741.2	−	21684.1i	−1.08156	−	0.695075i	−0.954917	+	0.296873i	$0.904056\pi$
$992$	1176.20	+	8180.62i	0.0376454	+	0.261830i
$993$	−6697.46	−	14665.4i	−0.214036	−	0.468673i
$994$	25649.4	+	7531.34i	0.818460	+	0.240322i
$995$	−10460.6	+	22905.6i	−0.333291	+	0.729806i
$996$	−231.563	+	267.238i	−0.00736682	+	0.00850177i
$997$	8180.31	−	56895.3i	0.259852	−	1.80731i	−0.273993	−	0.961732i	$-0.588345\pi$
$997$	8180.31	−	56895.3i	0.259852	−	1.80731i	0.533846	−	0.845582i	$-0.320746\pi$
$998$	−39153.5	+	11496.5i	−1.24187	+	0.364645i
$999$	1703.31	+	1965.72i	0.0539442	+	0.0622550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.4.e.d.25.3	✓	30
23.12	even	11	inner	138.4.e.d.127.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.4.e.d.25.3	✓	30	1.1	even	1	trivial
138.4.e.d.127.3	yes	30	23.12	even	11	inner

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68251 - 1.08128i) q^{2} +(0.426945 + 2.96946i) q^{3} +(1.66166 + 3.63853i) q^{4} +(15.3096 + 4.49530i) q^{5} +(2.49249 - 5.45779i) q^{6} +(7.46958 - 8.62035i) q^{7} +(1.13852 - 7.91857i) q^{8} +(-8.63544 + 2.53559i) q^{9} +O(q^{10})\)	\(q+(-1.68251 - 1.08128i) q^{2} +(0.426945 + 2.96946i) q^{3} +(1.66166 + 3.63853i) q^{4} +(15.3096 + 4.49530i) q^{5} +(2.49249 - 5.45779i) q^{6} +(7.46958 - 8.62035i) q^{7} +(1.13852 - 7.91857i) q^{8} +(-8.63544 + 2.53559i) q^{9} +(-20.8978 - 24.1174i) q^{10} +(-17.4771 + 11.2319i) q^{11} +(-10.0950 + 6.48769i) q^{12} +(21.0583 + 24.3026i) q^{13} +(-21.8886 + 6.42709i) q^{14} +(-6.81229 + 47.3805i) q^{15} +(-10.4778 + 12.0920i) q^{16} +(17.6463 - 38.6401i) q^{17} +(17.2709 + 5.07119i) q^{18} +(45.8759 + 100.454i) q^{19} +(9.08306 + 63.1741i) q^{20} +(28.7869 + 18.5002i) q^{21} +41.5502 q^{22} +(106.701 - 27.9606i) q^{23} +24.0000 q^{24} +(109.019 + 70.0624i) q^{25} +(-9.15283 - 63.6593i) q^{26} +(-11.2162 - 24.5601i) q^{27} +(43.7773 + 12.8542i) q^{28} +(42.1837 - 92.3694i) q^{29} +(62.6934 - 72.3521i) q^{30} +(-36.7561 + 255.644i) q^{31} +(30.7038 - 9.01544i) q^{32} +(-40.8144 - 47.1023i) q^{33} +(-71.4710 + 45.9316i) q^{34} +(153.107 - 98.3961i) q^{35} +(-23.5750 - 27.2070i) q^{36} +(-92.4320 + 27.1405i) q^{37} +(31.4328 - 218.620i) q^{38} +(-63.1750 + 72.9079i) q^{39} +(53.0266 - 116.112i) q^{40} +(307.995 + 90.4356i) q^{41} +(-28.4302 - 62.2535i) q^{42} +(19.9357 + 138.656i) q^{43} +(-69.9085 - 44.9275i) q^{44} -143.603 q^{45} +(-209.759 - 68.3305i) q^{46} -438.764 q^{47} +(-40.3802 - 25.9508i) q^{48} +(30.2981 + 210.728i) q^{49} +(-107.668 - 235.761i) q^{50} +(122.274 + 35.9030i) q^{51} +(-53.4340 + 117.004i) q^{52} +(181.385 - 209.329i) q^{53} +(-7.68500 + 53.4504i) q^{54} +(-318.058 + 93.3903i) q^{55} +(-59.7566 - 68.9628i) q^{56} +(-278.709 + 179.115i) q^{57} +(-170.852 + 109.800i) q^{58} +(-254.757 - 294.006i) q^{59} +(-183.715 + 53.9436i) q^{60} +(96.4226 - 670.634i) q^{61} +(338.266 - 390.380i) q^{62} +(-42.6454 + 93.3803i) q^{63} +(-61.4076 - 18.0309i) q^{64} +(213.147 + 466.727i) q^{65} +(17.7396 + 123.382i) q^{66} +(86.8368 + 55.8066i) q^{67} +169.915 q^{68} +(128.584 + 304.909i) q^{69} -363.998 q^{70} +(-985.791 - 633.530i) q^{71} +(10.2467 + 71.2671i) q^{72} +(-178.144 - 390.081i) q^{73} +(184.864 + 54.2810i) q^{74} +(-161.503 + 353.642i) q^{75} +(-289.276 + 333.842i) q^{76} +(-33.7241 + 234.556i) q^{77} +(185.126 - 54.3580i) q^{78} +(-418.542 - 483.023i) q^{79} +(-214.768 + 138.023i) q^{80} +(68.1415 - 43.7919i) q^{81} +(-420.418 - 485.188i) q^{82} +(28.2736 - 8.30187i) q^{83} +(-19.4795 + 135.483i) q^{84} +(443.857 - 512.239i) q^{85} +(116.384 - 254.845i) q^{86} +(292.298 + 85.8263i) q^{87} +(69.0423 + 151.182i) q^{88} +(-142.970 - 994.378i) q^{89} +(241.614 + 155.276i) q^{90} +366.794 q^{91} +(279.037 + 341.775i) q^{92} -774.820 q^{93} +(738.223 + 474.427i) q^{94} +(250.770 + 1744.14i) q^{95} +(39.8798 + 87.3247i) q^{96} +(627.003 + 184.105i) q^{97} +(176.880 - 387.312i) q^{98} +(122.443 - 141.307i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} + 24 q^{8} - 27 q^{9}+O(q^{10}) \) 30 * q + 6 * q^2 + 9 * q^3 - 12 * q^4 - 2 * q^5 - 18 * q^6 + 24 * q^8 - 27 * q^9	\( 30 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} + 24 q^{8} - 27 q^{9} + 48 q^{10} + 51 q^{11} + 36 q^{12} - 61 q^{13} + 44 q^{14} - 126 q^{15} - 48 q^{16} + 45 q^{17} + 54 q^{18} + 305 q^{19} + 168 q^{20} - 33 q^{21} + 8 q^{22} + 282 q^{23} + 720 q^{24} + 709 q^{25} + 210 q^{26} + 81 q^{27} - 88 q^{28} - 471 q^{29} - 144 q^{30} - 463 q^{31} + 96 q^{32} + 771 q^{33} + 724 q^{34} - 1424 q^{35} - 108 q^{36} - 483 q^{37} + 270 q^{38} + 183 q^{39} + 104 q^{40} + 886 q^{41} - 974 q^{43} + 204 q^{44} - 18 q^{45} + 382 q^{46} - 122 q^{47} + 144 q^{48} + 791 q^{49} - 450 q^{50} - 729 q^{51} - 200 q^{52} - 1117 q^{53} - 162 q^{54} - 2104 q^{55} - 354 q^{57} + 788 q^{58} - 4103 q^{59} + 24 q^{60} - 870 q^{61} - 592 q^{62} - 192 q^{64} - 2058 q^{65} - 24 q^{66} + 1365 q^{67} - 304 q^{68} + 2091 q^{69} - 584 q^{70} - 119 q^{71} + 216 q^{72} - 3314 q^{73} + 966 q^{74} - 675 q^{75} + 208 q^{76} + 606 q^{77} + 1218 q^{78} + 4040 q^{79} - 32 q^{80} - 243 q^{81} - 2300 q^{82} - 2365 q^{83} - 132 q^{84} + 4242 q^{85} - 1946 q^{86} - 402 q^{87} - 1992 q^{88} - 4963 q^{89} + 36 q^{90} + 8054 q^{91} + 3768 q^{92} - 2406 q^{93} - 1450 q^{94} + 1623 q^{95} - 288 q^{96} + 2287 q^{97} - 2748 q^{98} - 2313 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 9 * q^3 - 12 * q^4 - 2 * q^5 - 18 * q^6 + 24 * q^8 - 27 * q^9 + 48 * q^10 + 51 * q^11 + 36 * q^12 - 61 * q^13 + 44 * q^14 - 126 * q^15 - 48 * q^16 + 45 * q^17 + 54 * q^18 + 305 * q^19 + 168 * q^20 - 33 * q^21 + 8 * q^22 + 282 * q^23 + 720 * q^24 + 709 * q^25 + 210 * q^26 + 81 * q^27 - 88 * q^28 - 471 * q^29 - 144 * q^30 - 463 * q^31 + 96 * q^32 + 771 * q^33 + 724 * q^34 - 1424 * q^35 - 108 * q^36 - 483 * q^37 + 270 * q^38 + 183 * q^39 + 104 * q^40 + 886 * q^41 - 974 * q^43 + 204 * q^44 - 18 * q^45 + 382 * q^46 - 122 * q^47 + 144 * q^48 + 791 * q^49 - 450 * q^50 - 729 * q^51 - 200 * q^52 - 1117 * q^53 - 162 * q^54 - 2104 * q^55 - 354 * q^57 + 788 * q^58 - 4103 * q^59 + 24 * q^60 - 870 * q^61 - 592 * q^62 - 192 * q^64 - 2058 * q^65 - 24 * q^66 + 1365 * q^67 - 304 * q^68 + 2091 * q^69 - 584 * q^70 - 119 * q^71 + 216 * q^72 - 3314 * q^73 + 966 * q^74 - 675 * q^75 + 208 * q^76 + 606 * q^77 + 1218 * q^78 + 4040 * q^79 - 32 * q^80 - 243 * q^81 - 2300 * q^82 - 2365 * q^83 - 132 * q^84 + 4242 * q^85 - 1946 * q^86 - 402 * q^87 - 1992 * q^88 - 4963 * q^89 + 36 * q^90 + 8054 * q^91 + 3768 * q^92 - 2406 * q^93 - 1450 * q^94 + 1623 * q^95 - 288 * q^96 + 2287 * q^97 - 2748 * q^98 - 2313 * q^99

Introduction

L-functions

Modular forms

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