LMFDB - Embedded newform 75.6.i.a.4.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,6,Mod(4,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("75.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	75.i (of order $10$, degree $4$, 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:	$12.0287864860$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			4.18
Character	$\chi$	$=$	75.4
Dual form			75.6.i.a.19.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.18267 + 1.68395i) q^{2} +(5.29007 - 7.28115i) q^{3} +(-1.86417 - 1.35440i) q^{4} +(-41.4891 - 37.4654i) q^{5} +(39.6778 - 28.8276i) q^{6} +121.054i q^{7} +(-109.879 - 151.235i) q^{8} +(-25.0304 - 77.0356i) q^{9} +O(q^{10})$	\(q+(5.18267 + 1.68395i) q^{2} +(5.29007 - 7.28115i) q^{3} +(-1.86417 - 1.35440i) q^{4} +(-41.4891 - 37.4654i) q^{5} +(39.6778 - 28.8276i) q^{6} +121.054i q^{7} +(-109.879 - 151.235i) q^{8} +(-25.0304 - 77.0356i) q^{9} +(-151.934 - 264.036i) q^{10} +(212.022 - 652.537i) q^{11} +(-19.7232 + 6.40844i) q^{12} +(-953.707 + 309.878i) q^{13} +(-203.849 + 627.384i) q^{14} +(-492.271 + 103.894i) q^{15} +(-292.007 - 898.705i) q^{16} +(-690.177 - 949.947i) q^{17} -441.400i q^{18} +(464.056 - 337.156i) q^{19} +(26.5997 + 126.035i) q^{20} +(881.414 + 640.385i) q^{21} +(2197.68 - 3024.85i) q^{22} +(1217.89 + 395.718i) q^{23} -1682.43 q^{24} +(317.692 + 3108.81i) q^{25} -5464.57 q^{26} +(-693.320 - 225.273i) q^{27} +(163.955 - 225.665i) q^{28} +(1841.56 + 1337.97i) q^{29} +(-2726.23 - 290.512i) q^{30} +(4922.19 - 3576.18i) q^{31} +832.561i q^{32} +(-3629.61 - 4995.73i) q^{33} +(-1977.29 - 6085.48i) q^{34} +(4535.34 - 5022.43i) q^{35} +(-57.6760 + 177.508i) q^{36} +(627.273 - 203.813i) q^{37} +(2972.80 - 965.922i) q^{38} +(-2788.90 + 8583.36i) q^{39} +(-1107.31 + 10391.3i) q^{40} +(1731.94 + 5330.36i) q^{41} +(3489.70 + 4803.16i) q^{42} -10057.6i q^{43} +(-1279.04 + 929.277i) q^{44} +(-1847.68 + 4133.91i) q^{45} +(5645.57 + 4101.75i) q^{46} +(12527.2 - 17242.2i) q^{47} +(-8088.35 - 2628.06i) q^{48} +2152.90 q^{49} +(-3588.59 + 16646.9i) q^{50} -10567.8 q^{51} +(2197.57 + 714.033i) q^{52} +(-14219.8 + 19571.8i) q^{53} +(-3213.90 - 2335.04i) q^{54} +(-33244.2 + 19129.7i) q^{55} +(18307.6 - 13301.3i) q^{56} -5162.44i q^{57} +(7291.10 + 10035.3i) q^{58} +(2099.29 + 6460.96i) q^{59} +(1058.39 + 473.055i) q^{60} +(1771.48 - 5452.06i) q^{61} +(31532.2 - 10245.4i) q^{62} +(9325.48 - 3030.03i) q^{63} +(-10746.2 + 33073.5i) q^{64} +(51178.1 + 22874.4i) q^{65} +(-10398.5 - 32003.3i) q^{66} +(-8867.14 - 12204.6i) q^{67} +2705.63i q^{68} +(9324.02 - 6774.30i) q^{69} +(31962.7 - 18392.3i) q^{70} +(44614.3 + 32414.2i) q^{71} +(-8900.18 + 12250.0i) q^{72} +(-40715.8 - 13229.4i) q^{73} +3594.16 q^{74} +(24316.3 + 14132.6i) q^{75} -1321.72 q^{76} +(78992.3 + 25666.2i) q^{77} +(-28907.9 + 39788.4i) q^{78} +(-33092.5 - 24043.1i) q^{79} +(-21555.2 + 48226.6i) q^{80} +(-5307.96 + 3856.46i) q^{81} +30542.0i q^{82} +(-65625.0 - 90325.1i) q^{83} +(-775.768 - 2387.57i) q^{84} +(-6955.29 + 65270.2i) q^{85} +(16936.5 - 52125.1i) q^{86} +(19483.9 - 6330.71i) q^{87} +(-121983. + 39634.8i) q^{88} +(42234.0 - 129983. i) q^{89} +(-16537.2 + 18313.3i) q^{90} +(-37512.0 - 115450. i) q^{91} +(-1734.40 - 2387.20i) q^{92} -54757.4i q^{93} +(93959.2 - 68265.3i) q^{94} +(-31884.9 - 3397.71i) q^{95} +(6062.00 + 4404.30i) q^{96} +(-70860.5 + 97531.2i) q^{97} +(11157.8 + 3625.37i) q^{98} -55575.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 352 q^{4} - 120 q^{5} + 72 q^{6} - 1230 q^{8} + 1944 q^{9}+O(q^{10}) $ 96 * q + 352 * q^4 - 120 * q^5 + 72 * q^6 - 1230 * q^8 + 1944 * q^9	\( 96 q + 352 q^{4} - 120 q^{5} + 72 q^{6} - 1230 q^{8} + 1944 q^{9} - 890 q^{10} + 474 q^{11} + 2748 q^{14} - 780 q^{16} + 1910 q^{17} - 5522 q^{19} - 19220 q^{20} + 1764 q^{21} + 6170 q^{22} + 21980 q^{23} + 13824 q^{24} + 11790 q^{25} - 11028 q^{26} - 9120 q^{28} - 24304 q^{29} - 22860 q^{30} + 1566 q^{31} - 3690 q^{33} + 24224 q^{34} + 10250 q^{35} - 28512 q^{36} + 16490 q^{37} + 68730 q^{38} - 12168 q^{39} - 106480 q^{40} + 26126 q^{41} - 43560 q^{42} - 10814 q^{44} + 9720 q^{45} + 22956 q^{46} + 66440 q^{47} - 123480 q^{49} + 329620 q^{50} - 83232 q^{51} + 251240 q^{52} - 91690 q^{53} - 5832 q^{54} - 123470 q^{55} + 116100 q^{56} - 483290 q^{58} - 97428 q^{59} + 119610 q^{60} + 91560 q^{61} - 138410 q^{62} + 47790 q^{63} + 127738 q^{64} - 235130 q^{65} + 118296 q^{66} + 163960 q^{67} - 73332 q^{69} + 209520 q^{70} + 155672 q^{71} - 99630 q^{72} + 18980 q^{73} + 100588 q^{74} - 464032 q^{76} + 119560 q^{77} - 112020 q^{79} - 66300 q^{80} - 157464 q^{81} + 148010 q^{83} - 61128 q^{84} + 346980 q^{85} - 295956 q^{86} - 371160 q^{87} - 189090 q^{88} - 494082 q^{89} - 144180 q^{90} - 79494 q^{91} + 599810 q^{92} + 234622 q^{94} + 605800 q^{95} + 210744 q^{96} + 372140 q^{97} + 891060 q^{98} + 25596 q^{99}+O(q^{100}) \) 96 * q + 352 * q^4 - 120 * q^5 + 72 * q^6 - 1230 * q^8 + 1944 * q^9 - 890 * q^10 + 474 * q^11 + 2748 * q^14 - 780 * q^16 + 1910 * q^17 - 5522 * q^19 - 19220 * q^20 + 1764 * q^21 + 6170 * q^22 + 21980 * q^23 + 13824 * q^24 + 11790 * q^25 - 11028 * q^26 - 9120 * q^28 - 24304 * q^29 - 22860 * q^30 + 1566 * q^31 - 3690 * q^33 + 24224 * q^34 + 10250 * q^35 - 28512 * q^36 + 16490 * q^37 + 68730 * q^38 - 12168 * q^39 - 106480 * q^40 + 26126 * q^41 - 43560 * q^42 - 10814 * q^44 + 9720 * q^45 + 22956 * q^46 + 66440 * q^47 - 123480 * q^49 + 329620 * q^50 - 83232 * q^51 + 251240 * q^52 - 91690 * q^53 - 5832 * q^54 - 123470 * q^55 + 116100 * q^56 - 483290 * q^58 - 97428 * q^59 + 119610 * q^60 + 91560 * q^61 - 138410 * q^62 + 47790 * q^63 + 127738 * q^64 - 235130 * q^65 + 118296 * q^66 + 163960 * q^67 - 73332 * q^69 + 209520 * q^70 + 155672 * q^71 - 99630 * q^72 + 18980 * q^73 + 100588 * q^74 - 464032 * q^76 + 119560 * q^77 - 112020 * q^79 - 66300 * q^80 - 157464 * q^81 + 148010 * q^83 - 61128 * q^84 + 346980 * q^85 - 295956 * q^86 - 371160 * q^87 - 189090 * q^88 - 494082 * q^89 - 144180 * q^90 - 79494 * q^91 + 599810 * q^92 + 234622 * q^94 + 605800 * q^95 + 210744 * q^96 + 372140 * q^97 + 891060 * q^98 + 25596 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	5.18267	+	1.68395i	0.916175	+	0.297683i	0.728897	−	0.684623i	$-0.240033\pi$
$2$	5.18267	+	1.68395i	0.916175	+	0.297683i	0.187278	+	0.982307i	$0.440033\pi$
$3$	5.29007	−	7.28115i	0.339358	−	0.467086i
$3$	5.29007	−	7.28115i	0.339358	−	0.467086i
$4$	−1.86417	−	1.35440i	−0.0582553	−	0.0423249i
$5$	−41.4891	−	37.4654i	−0.742180	−	0.670201i
$5$	−41.4891	−	37.4654i	−0.742180	−	0.670201i
$6$	39.6778	−	28.8276i	0.449955	−	0.326912i
$7$			121.054i			0.933758i	0.884321	+	0.466879i	$0.154622\pi$
$7$			121.054i			0.933758i	−0.884321	+	0.466879i	$0.845378\pi$
$8$	−109.879	−	151.235i	−0.607000	−	0.835464i
$9$	−25.0304	−	77.0356i	−0.103006	−	0.317019i
$10$	−151.934	−	264.036i	−0.480459	−	0.834956i
$11$	212.022	−	652.537i	0.528323	−	1.62601i	−0.229327	−	0.973349i	$-0.573652\pi$
$11$	212.022	−	652.537i	0.528323	−	1.62601i	0.757650	−	0.652661i	$-0.226348\pi$
$12$	−19.7232	+	6.40844i	−0.0395388	+	0.0128469i
$13$	−953.707	+	309.878i	−1.56515	+	0.508549i	−0.958178	−	0.286173i	$-0.907617\pi$
$13$	−953.707	+	309.878i	−1.56515	+	0.508549i	−0.606974	+	0.794722i	$0.707617\pi$
$14$	−203.849	+	627.384i	−0.277964	+	0.855486i
$15$	−492.271	+	103.894i	−0.564906	+	0.119224i
$16$	−292.007	−	898.705i	−0.285163	−	0.877642i
$17$	−690.177	−	949.947i	−0.579213	−	0.797218i	0.414396	−	0.910097i	$-0.363993\pi$
$17$	−690.177	−	949.947i	−0.579213	−	0.797218i	−0.993609	+	0.112879i	$0.963993\pi$
$18$		−	441.400i		−	0.321108i
$19$	464.056	−	337.156i	0.294908	−	0.214263i	−0.430486	−	0.902597i	$-0.641658\pi$
$19$	464.056	−	337.156i	0.294908	−	0.214263i	0.725394	+	0.688334i	$0.241658\pi$
$20$	26.5997	+	126.035i	0.0148697	+	0.0704554i
$21$	881.414	+	640.385i	0.436146	+	0.316878i
$22$	2197.68	−	3024.85i	0.968073	−	1.33244i
$23$	1217.89	+	395.718i	0.480054	+	0.155979i	0.539041	−	0.842280i	$-0.318787\pi$
$23$	1217.89	+	395.718i	0.480054	+	0.155979i	−0.0589867	+	0.998259i	$0.518787\pi$
$24$	−1682.43			−0.596224
$25$	317.692	+	3108.81i	0.101661	+	0.994819i
$26$	−5464.57			−1.58534
$27$	−693.320	−	225.273i	−0.183031	−	0.0594703i
$28$	163.955	−	225.665i	0.0395213	−	0.0543963i
$29$	1841.56	+	1337.97i	0.406621	+	0.295428i	0.772233	−	0.635340i	$-0.219140\pi$
$29$	1841.56	+	1337.97i	0.406621	+	0.295428i	−0.365611	+	0.930768i	$0.619140\pi$
$30$	−2726.23	−	290.512i	−0.553044	−	0.0589333i
$31$	4922.19	−	3576.18i	0.919929	−	0.668367i	−0.0235777	−	0.999722i	$-0.507506\pi$
$31$	4922.19	−	3576.18i	0.919929	−	0.668367i	0.943506	+	0.331355i	$0.107506\pi$
$32$			832.561i			0.143728i
$33$	−3629.61	−	4995.73i	−0.580197	−	0.798572i
$34$	−1977.29	−	6085.48i	−0.293342	−	0.902813i
$35$	4535.34	−	5022.43i	0.625806	−	0.693017i
$36$	−57.6760	+	177.508i	−0.00741718	+	0.0228277i
$37$	627.273	−	203.813i	0.0753273	−	0.0244753i	−0.271111	−	0.962548i	$-0.587391\pi$
$37$	627.273	−	203.813i	0.0753273	−	0.0244753i	0.346438	+	0.938073i	$0.387391\pi$
$38$	2972.80	−	965.922i	0.333970	−	0.108513i
$39$	−2788.90	+	8583.36i	−0.293611	+	0.903641i
$40$	−1107.31	+	10391.3i	−0.109426	+	1.02688i
$41$	1731.94	+	5330.36i	0.160906	+	0.495218i	0.998711	−	0.0507511i	$-0.0161615\pi$
$41$	1731.94	+	5330.36i	0.160906	+	0.495218i	−0.837805	+	0.545969i	$0.816162\pi$
$42$	3489.70	+	4803.16i	0.305256	+	0.420149i
$43$		−	10057.6i		−	0.829512i	−0.909933	−	0.414756i	$-0.863867\pi$
$43$		−	10057.6i		−	0.829512i	0.909933	−	0.414756i	$-0.136133\pi$
$44$	−1279.04	+	929.277i	−0.0995984	+	0.0723625i
$45$	−1847.68	+	4133.91i	−0.136018	+	0.304319i
$46$	5645.57	+	4101.75i	0.393381	+	0.285808i
$47$	12527.2	−	17242.2i	0.827196	−	1.13854i	−0.161242	−	0.986915i	$-0.551550\pi$
$47$	12527.2	−	17242.2i	0.827196	−	1.13854i	0.988438	−	0.151623i	$-0.0484499\pi$
$48$	−8088.35	−	2628.06i	−0.506707	−	0.164639i
$49$	2152.90			0.128095
$50$	−3588.59	+	16646.9i	−0.203001	+	0.941692i
$51$	−10567.8			−0.568930
$52$	2197.57	+	714.033i	0.112703	+	0.0366193i
$53$	−14219.8	+	19571.8i	−0.695350	+	0.957067i	0.304640	+	0.952468i	$0.401464\pi$
$53$	−14219.8	+	19571.8i	−0.695350	+	0.957067i	−0.999989	+	0.00459899i	$0.998536\pi$
$54$	−3213.90	−	2335.04i	−0.149985	−	0.108971i
$55$	−33244.2	+	19129.7i	−1.48186	+	0.852710i
$56$	18307.6	−	13301.3i	0.780121	−	0.566791i
$57$		−	5162.44i		−	0.210459i
$58$	7291.10	+	10035.3i	0.284592	+	0.391708i
$59$	2099.29	+	6460.96i	0.0785133	+	0.241639i	0.982608	−	0.185694i	$-0.0594532\pi$
$59$	2099.29	+	6460.96i	0.0785133	+	0.241639i	−0.904094	+	0.427333i	$0.859453\pi$
$60$	1058.39	+	473.055i	0.0379549	+	0.0169642i
$61$	1771.48	−	5452.06i	0.0609554	−	0.187601i	−0.915942	−	0.401311i	$-0.868555\pi$
$61$	1771.48	−	5452.06i	0.0609554	−	0.187601i	0.976897	+	0.213710i	$0.0685546\pi$
$62$	31532.2	−	10245.4i	1.04178	−	0.338494i
$63$	9325.48	−	3030.03i	0.296019	−	0.0961824i
$64$	−10746.2	+	33073.5i	−0.327949	+	1.00932i
$65$	51178.1	+	22874.4i	1.50245	+	0.671532i
$66$	−10398.5	−	32003.3i	−0.293840	−	0.904347i
$67$	−8867.14	−	12204.6i	−0.241322	−	0.332151i	0.671127	−	0.741343i	$-0.265811\pi$
$67$	−8867.14	−	12204.6i	−0.241322	−	0.332151i	−0.912448	+	0.409192i	$0.865811\pi$
$68$			2705.63i			0.0709573i
$69$	9324.02	−	6774.30i	0.235766	−	0.171294i
$70$	31962.7	−	18392.3i	0.779647	−	0.448633i
$71$	44614.3	+	32414.2i	1.05033	+	0.763113i	0.972276	−	0.233836i	$-0.0751278\pi$
$71$	44614.3	+	32414.2i	1.05033	+	0.763113i	0.0780587	+	0.996949i	$0.475128\pi$
$72$	−8900.18	+	12250.0i	−0.202333	+	0.278488i
$73$	−40715.8	−	13229.4i	−0.894243	−	0.290557i	−0.174384	−	0.984678i	$-0.555793\pi$
$73$	−40715.8	−	13229.4i	−0.894243	−	0.290557i	−0.719859	+	0.694120i	$0.755793\pi$
$74$	3594.16			0.0762989
$75$	24316.3	+	14132.6i	0.499166	+	0.290115i
$76$	−1321.72			−0.0262486
$77$	78992.3	+	25666.2i	1.51830	+	0.493326i
$78$	−28907.9	+	39788.4i	−0.537998	+	0.740490i
$79$	−33092.5	−	24043.1i	−0.596571	−	0.433434i	0.248089	−	0.968737i	$-0.420197\pi$
$79$	−33092.5	−	24043.1i	−0.596571	−	0.433434i	−0.844660	+	0.535303i	$0.820197\pi$
$80$	−21555.2	+	48226.6i	−0.376554	+	0.842485i
$81$	−5307.96	+	3856.46i	−0.0898908	+	0.0653095i
$82$			30542.0i			0.501606i
$83$	−65625.0	−	90325.1i	−1.04562	−	1.43917i	−0.892544	−	0.450959i	$-0.851082\pi$
$83$	−65625.0	−	90325.1i	−1.04562	−	1.43917i	−0.153077	−	0.988214i	$-0.548918\pi$
$84$	−775.768	−	2387.57i	−0.0119959	−	0.0369197i
$85$	−6955.29	+	65270.2i	−0.104416	+	0.979868i
$86$	16936.5	−	52125.1i	0.246932	−	0.759978i
$87$	19483.9	−	6330.71i	0.275980	−	0.0896714i
$88$	−121983.	+	39634.8i	−1.67917	+	0.545594i
$89$	42234.0	−	129983.i	0.565181	−	1.73945i	−0.102234	−	0.994760i	$-0.532599\pi$
$89$	42234.0	−	129983.i	0.565181	−	1.73945i	0.667415	−	0.744686i	$-0.267401\pi$
$90$	−16537.2	+	18313.3i	−0.215207	+	0.238320i
$91$	−37512.0	−	115450.i	−0.474862	−	1.46147i
$92$	−1734.40	−	2387.20i	−0.0213639	−	0.0294048i
$93$		−	54757.4i		−	0.656502i
$94$	93959.2	−	68265.3i	1.09678	−	0.796857i
$95$	−31884.9	−	3397.71i	−0.362474	−	0.0386258i
$96$	6062.00	+	4404.30i	0.0671333	+	0.0487752i
$97$	−70860.5	+	97531.2i	−0.764672	+	1.05248i	0.232139	+	0.972683i	$0.425428\pi$
$97$	−70860.5	+	97531.2i	−0.764672	+	1.05248i	−0.996811	+	0.0797979i	$0.974572\pi$
$98$	11157.8	+	3625.37i	0.117358	+	0.0381318i
$99$	−55575.6			−0.569896
$100$	3618.33	−	6225.63i	0.0361833	−	0.0622563i
$101$	−38128.9			−0.371921			−0.185960	−	0.982557i	$-0.559540\pi$
$101$	−38128.9			−0.371921			−0.185960	+	0.982557i	$0.559540\pi$
$102$	−54769.4	−	17795.6i	−0.521239	−	0.169361i
$103$	49770.8	−	68503.6i	0.462255	−	0.636239i	−0.512720	−	0.858556i	$-0.671362\pi$
$103$	49770.8	−	68503.6i	0.462255	−	0.636239i	0.974974	+	0.222317i	$0.0713620\pi$
$104$	151657.	+	110185.i	1.37492	+	0.998939i
$105$	−12576.8	−	59591.5i	−0.111326	−	0.527486i
$106$	−106654.	+	77489.0i	−0.921965	+	0.669847i
$107$		−	29163.7i		−	0.246254i	−0.992391	−	0.123127i	$-0.960708\pi$
$107$		−	29163.7i		−	0.246254i	0.992391	−	0.123127i	$-0.0392923\pi$
$108$	987.356	+	1358.98i	0.00814544	+	0.0112112i
$109$	−60605.2	−	186524.i	−0.488589	−	1.50372i	−0.826714	−	0.562622i	$-0.809793\pi$
$109$	−60605.2	−	186524.i	−0.488589	−	1.50372i	0.338125	−	0.941101i	$-0.390207\pi$
$110$	−204507.	+	43161.3i	−1.61149	+	0.340105i
$111$	1834.32	−	5645.46i	0.0141308	−	0.0434902i
$112$	108792.	−	35348.7i	0.819506	−	0.266274i
$113$	−106500.	+	34604.1i	−0.784613	+	0.254936i	−0.673808	−	0.738906i	$-0.735343\pi$
$113$	−106500.	+	34604.1i	−0.784613	+	0.254936i	−0.110804	+	0.993842i	$0.535343\pi$
$114$	8693.30	−	26755.2i	0.0626502	−	0.192817i
$115$	−35703.6	−	62046.8i	−0.251749	−	0.437497i
$116$	−1620.83	−	4988.40i	−0.0111839	−	0.0344204i
$117$	47743.3	+	65713.0i	0.322439	+	0.443799i
$118$			37020.2i			0.244756i
$119$	114995.	−	83548.7i	0.744409	−	0.540845i
$120$	69802.6	+	63032.9i	0.442505	+	0.399590i
$121$	−250558.	−	182041.i	−1.55577	−	1.13033i
$122$	18362.0	−	25273.1i	0.111692	−	0.153730i
$123$	47973.2	+	15587.4i	0.285914	+	0.0928992i
$124$	−14019.4			−0.0818793
$125$	103292.	−	140884.i	0.591278	−	0.806468i
$126$	53433.3			0.299837
$127$	317567.	+	103184.i	1.74714	+	0.567679i	0.995743	−	0.0921756i	$-0.0293821\pi$
$127$	317567.	+	103184.i	1.74714	+	0.567679i	0.751393	+	0.659855i	$0.229382\pi$
$128$	−95728.5	+	131759.i	−0.516436	+	0.710813i
$129$	−73230.8	−	53205.3i	−0.387454	−	0.281501i
$130$	226720.	+	204732.i	1.17661	+	1.06250i
$131$	103330.	−	75073.8i	0.526076	−	0.382217i	−0.292812	−	0.956170i	$-0.594591\pi$
$131$	103330.	−	75073.8i	0.526076	−	0.382217i	0.818888	+	0.573953i	$0.194591\pi$
$132$			14228.8i			0.0710778i
$133$	40814.1	+	56175.9i	0.200070	+	0.275373i
$134$	−25403.6	−	78184.1i	−0.122217	−	0.376146i
$135$	20325.3	+	35321.9i	0.0959847	+	0.166805i
$136$	−67829.6	+	208758.i	−0.314465	+	0.967822i
$137$	−187186.	+	60820.6i	−0.852066	+	0.276853i	−0.702311	−	0.711870i	$-0.747848\pi$
$137$	−187186.	+	60820.6i	−0.852066	+	0.276853i	−0.149755	+	0.988723i	$0.547848\pi$
$138$	59730.9	−	19407.8i	0.266994	−	0.0867516i
$139$	−27052.9	+	83260.1i	−0.118762	+	0.365511i	−0.992713	−	0.120503i	$-0.961549\pi$
$139$	−27052.9	+	83260.1i	−0.118762	+	0.365511i	0.873951	+	0.486013i	$0.161549\pi$
$140$	−15257.0	+	3220.00i	−0.0657884	+	0.0138847i
$141$	−59273.3	−	182425.i	−0.251080	−	0.772744i
$142$	176637.	+	243120.i	0.735125	+	1.01181i
$143$			688030.i			2.81363i
$144$	−61923.2	+	44989.9i	−0.248856	+	0.180804i
$145$	−26277.0	−	124506.i	−0.103790	−	0.491778i
$146$	−188739.	−	137127.i	−0.732789	−	0.532403i
$147$	11389.0	−	15675.6i	0.0434701	−	0.0598315i
$148$	−1445.39	−	469.635i	−0.00542413	−	0.00176241i
$149$	452241.			1.66880			0.834400	−	0.551160i	$-0.185815\pi$
$149$	452241.			1.66880			0.834400	+	0.551160i	$0.185815\pi$
$150$	102225.	+	114192.i	0.370961	+	0.414390i
$151$	298537.			1.06551			0.532753	−	0.846271i	$-0.321158\pi$
$151$	298537.			1.06551			0.532753	+	0.846271i	$0.321158\pi$
$152$	−101980.	−	33135.2i	−0.358018	−	0.116327i
$153$	−55904.3	+	76945.7i	−0.193071	+	0.265739i
$154$	366170.	+	266038.i	1.24418	+	0.903946i
$155$	−338200.	−	36039.2i	−1.13069	−	0.120488i
$156$	16824.3	−	12223.5i	0.0553509	−	0.0402148i
$157$			176303.i			0.570836i	0.958403	+	0.285418i	$0.0921323\pi$
$157$			176303.i			0.570836i	−0.958403	+	0.285418i	$0.907868\pi$
$158$	−131020.	−	180334.i	−0.417538	−	0.574691i
$159$	67282.0	+	207073.i	0.211060	+	0.649576i
$160$	31192.2	−	34542.2i	0.0963266	−	0.106672i
$161$	−47903.3	+	147431.i	−0.145647	+	0.448254i
$162$	−34003.5	+	11048.4i	−0.101797	+	0.0330759i
$163$	422725.	−	137352.i	1.24620	−	0.404916i	0.389645	−	0.920965i	$-0.372598\pi$
$163$	422725.	−	137352.i	1.24620	−	0.404916i	0.856559	+	0.516049i	$0.172598\pi$
$164$	3990.80	−	12282.4i	0.0115864	−	0.0356594i
$165$	−36577.6	+	343253.i	−0.104594	+	0.981532i
$166$	−188010.	−	578635.i	−0.529554	−	1.62980i
$167$	164036.	+	225777.i	0.455144	+	0.626452i	0.973493	−	0.228717i	$-0.0734530\pi$
$167$	164036.	+	225777.i	0.455144	+	0.626452i	−0.518349	+	0.855169i	$0.673453\pi$
$168$		−	203665.i		−	0.556729i
$169$	513150.	−	372825.i	1.38206	−	1.00413i
$170$	−145959.	+	326561.i	−0.387354	+	0.866647i
$171$	−37588.5	−	27309.6i	−0.0983026	−	0.0714210i
$172$	−13622.0	+	18749.0i	−0.0351090	+	0.0483234i
$173$	−582203.	−	189169.i	−1.47897	−	0.480546i	−0.545165	−	0.838329i	$-0.683533\pi$
$173$	−582203.	−	189169.i	−1.47897	−	0.480546i	−0.933805	+	0.357782i	$0.883533\pi$
$174$	111639.			0.279540
$175$	−376334.	+	38457.9i	−0.928921	+	0.0949272i
$176$	−648351.			−1.57771
$177$	58148.7	+	18893.7i	0.139510	+	0.0453297i
$178$	437770.	−	602538.i	1.03561	−	1.42539i
$179$	−276766.	−	201083.i	−0.645626	−	0.469075i	0.216153	−	0.976360i	$-0.430649\pi$
$179$	−276766.	−	201083.i	−0.645626	−	0.469075i	−0.861778	+	0.507285i	$0.830649\pi$
$180$	9043.34	−	5203.81i	0.0208040	−	0.0119713i
$181$	−61864.9	+	44947.5i	−0.140361	+	0.101979i	−0.655750	−	0.754978i	$-0.727648\pi$
$181$	−61864.9	+	44947.5i	−0.140361	+	0.101979i	0.515389	+	0.856956i	$0.327648\pi$
$182$		−	661509.i		−	1.48032i
$183$	−30326.0	−	41740.2i	−0.0669403	−	0.0921355i
$184$	−73974.2	−	227669.i	−0.161078	−	0.495747i
$185$	−33661.0	−	15045.0i	−0.0723098	−	0.0323193i
$186$	92208.9	−	283790.i	0.195430	−	0.601471i
$187$	−766208.	+	248956.i	−1.60230	+	0.520618i
$188$	−46705.5	+	15175.5i	−0.0963770	+	0.0313148i
$189$	27270.3	−	83929.3i	0.0555309	−	0.170907i
$190$	−159528.	−	71301.9i	−0.320591	−	0.143290i
$191$	219720.	+	676229.i	0.435799	+	1.34125i	0.892265	+	0.451511i	$0.149115\pi$
$191$	219720.	+	676229.i	0.435799	+	1.34125i	−0.456466	+	0.889741i	$0.650885\pi$
$192$	183965.	+	253206.i	0.360148	+	0.495702i
$193$			656362.i			1.26838i	0.773176	+	0.634191i	$0.218667\pi$
$193$			656362.i			1.26838i	−0.773176	+	0.634191i	$0.781333\pi$
$194$	−531485.	+	386146.i	−1.01388	+	0.736627i
$195$	437288.	−	251629.i	0.823533	−	0.473886i
$196$	−4013.36	−	2915.88i	−0.00746222	−	0.00542162i
$197$	615766.	−	847529.i	1.13045	−	1.55593i	0.343228	−	0.939252i	$-0.388480\pi$
$197$	615766.	−	847529.i	1.13045	−	1.55593i	0.787219	−	0.616674i	$-0.211520\pi$
$198$	−288030.	−	93586.6i	−0.522125	−	0.169649i
$199$	−625733.			−1.12010			−0.560050	−	0.828459i	$-0.689218\pi$
$199$	−625733.			−1.12010			−0.560050	+	0.828459i	$0.689218\pi$
$200$	435254.	−	389638.i	0.769427	−	0.688790i
$201$	−135771.			−0.237038
$202$	−197609.	−	64207.2i	−0.340745	−	0.110715i
$203$	−161967.	+	222928.i	−0.275858	+	0.379686i
$204$	19700.1	+	14313.0i	0.0331432	+	0.0240799i
$205$	127847.	−	286039.i	0.212474	−	0.475380i
$206$	373302.	−	271220.i	0.612904	−	0.445301i
$207$		−	103726.i		−	0.168253i
$208$	556978.	+	766615.i	0.892648	+	1.22862i
$209$	−121617.	−	374298.i	−0.192587	−	0.592723i
$210$	35167.6	−	330022.i	0.0550294	−	0.516410i
$211$	−61781.8	+	190145.i	−0.0955332	+	0.294021i	−0.987392	−	0.158292i	$-0.949401\pi$
$211$	−61781.8	+	190145.i	−0.0955332	+	0.294021i	0.891859	+	0.452313i	$0.149401\pi$
$212$	53016.1	−	17226.0i	0.0810156	−	0.0263235i
$213$	472025.	−	153370.i	0.712879	−	0.231628i
$214$	49110.3	−	151146.i	0.0733057	−	0.225612i
$215$	−376811.	+	417280.i	−0.555940	+	0.615647i
$216$	42111.9	+	129607.i	0.0614144	+	0.189014i
$217$	432911.	+	595851.i	0.624094	+	0.858991i
$218$		−	1.06875e6i		−	1.52312i
$219$	−311714.	+	226474.i	−0.439184	+	0.319086i
$220$	87881.9	+	9364.84i	0.122417	+	0.0130450i
$221$	952594.	+	692100.i	1.31198	+	0.953209i
$222$	19013.4	−	26169.6i	0.0258926	−	0.0356382i
$223$	−1.11524e6	−	362362.i	−1.50177	−	0.487956i	−0.561239	−	0.827654i	$-0.689675\pi$
$223$	−1.11524e6	−	362362.i	−1.50177	−	0.487956i	−0.940535	+	0.339698i	$0.889675\pi$
$224$	−100785.			−0.134207
$225$	231537.	−	102288.i	0.304905	−	0.134701i
$226$	−610229.			−0.794733
$227$	−171630.	−	55765.9i	−0.221069	−	0.0718297i	0.196388	−	0.980526i	$-0.437079\pi$
$227$	−171630.	−	55765.9i	−0.221069	−	0.0718297i	−0.417457	+	0.908696i	$0.637079\pi$
$228$	−6992.00	+	9623.66i	−0.00890767	+	0.0122604i
$229$	−650573.	−	472669.i	−0.819799	−	0.595619i	0.0968556	−	0.995298i	$-0.469121\pi$
$229$	−650573.	−	472669.i	−0.819799	−	0.595619i	−0.916655	+	0.399679i	$0.869121\pi$
$230$	−80556.2	−	381691.i	−0.100411	−	0.475765i
$231$	604754.	−	439379.i	0.745673	−	0.541763i
$232$		−	425522.i		−	0.519042i
$233$	457536.	+	629744.i	0.552122	+	0.759931i	0.990298	−	0.138958i	$-0.0443753\pi$
$233$	457536.	+	629744.i	0.552122	+	0.759931i	−0.438176	+	0.898889i	$0.644375\pi$
$234$	136780.	+	420966.i	0.163299	+	0.502583i
$235$	−1.16573e6	+	246027.i	−1.37698	+	0.290612i
$236$	4837.28	−	14887.6i	0.00565355	−	0.0173998i
$237$	−350124.	+	113762.i	−0.404902	+	0.131561i
$238$	736673.	−	239360.i	0.843009	−	0.273910i
$239$	−387865.	+	1.19373e6i	−0.439224	+	1.35179i	0.449471	+	0.893295i	$0.351612\pi$
$239$	−387865.	+	1.19373e6i	−0.439224	+	1.35179i	−0.888695	+	0.458498i	$0.848388\pi$
$240$	237117.	+	412069.i	0.265726	+	0.461787i
$241$	289848.	+	892059.i	0.321460	+	0.989352i	0.973013	+	0.230749i	$0.0741177\pi$
$241$	289848.	+	892059.i	0.321460	+	0.989352i	−0.651553	+	0.758603i	$0.725882\pi$
$242$	−992012.	−	1.36539e6i	−1.08888	−	1.49871i
$243$			59049.0i			0.0641500i
$244$	−10686.6	+	7764.27i	−0.0114912	+	0.00834884i
$245$	−89321.7	−	80659.1i	−0.0950697	−	0.0858495i
$246$	222381.	+	161569.i	0.234293	+	0.170224i
$247$	−338096.	+	465349.i	−0.352612	+	0.485329i
$248$	−1.08169e6	−	351462.i	−1.11679	−	0.362868i
$249$	−1.00483e6			−1.02706
$250$	772570.	−	556218.i	0.781786	−	0.562853i
$251$	1.70388e6			1.70708			0.853540	−	0.521028i	$-0.174451\pi$
$251$	1.70388e6			1.70708			0.853540	+	0.521028i	$0.174451\pi$
$252$	−21488.1	−	6981.91i	−0.0213156	−	0.00692585i
$253$	516441.	−	710820.i	0.507247	−	0.698165i
$254$	1.47209e6	+	1.06954e6i	1.43169	+	1.04019i
$255$	438448.	+	395926.i	0.422248	+	0.381297i
$256$	182282.	−	132436.i	0.173838	−	0.126301i
$257$		−	13617.2i		−	0.0128604i	−0.999979	−	0.00643019i	$-0.997953\pi$
$257$		−	13617.2i		−	0.0128604i	0.999979	−	0.00643019i	$-0.00204681\pi$
$258$	−289936.	−	399063.i	−0.271177	−	0.373243i
$259$	24672.5	+	75934.0i	0.0228540	+	0.0703375i
$260$	−64423.6	−	111957.i	−0.0591033	−	0.102712i
$261$	56976.4	−	175355.i	0.0517718	−	0.159337i
$262$	661947.	−	215080.i	0.595758	−	0.193573i
$263$	1.03158e6	−	335182.i	0.919634	−	0.298807i	0.189317	−	0.981916i	$-0.439372\pi$
$263$	1.03158e6	−	335182.i	0.919634	−	0.298807i	0.730317	+	0.683109i	$0.239372\pi$
$264$	−356713.	+	1.09785e6i	−0.314999	+	0.969467i
$265$	1.32323e6	−	279269.i	1.15750	−	0.244291i
$266$	116929.	+	359870.i	0.101325	+	0.311847i
$267$	−723005.	−	995130.i	−0.620673	−	0.854283i
$268$			34761.0i			0.0295635i
$269$	194487.	−	141303.i	0.163874	−	0.119062i	−0.502826	−	0.864388i	$-0.667706\pi$
$269$	194487.	−	141303.i	0.163874	−	0.119062i	0.666700	+	0.745326i	$0.267706\pi$
$270$	45858.9	+	217288.i	0.0382837	+	0.181396i
$271$	−457120.	−	332117.i	−0.378100	−	0.274706i	0.382462	−	0.923971i	$-0.375076\pi$
$271$	−457120.	−	332117.i	−0.378100	−	0.274706i	−0.760562	+	0.649265i	$0.775076\pi$
$272$	−652186.	+	897657.i	−0.534502	+	0.735678i
$273$	−1.03905e6	−	337608.i	−0.843782	−	0.274162i
$274$	−1.07254e6			−0.863056
$275$	2.09597e6	+	451831.i	1.67130	+	0.360283i
$276$	−26556.6			−0.0209846
$277$	−460867.	−	149745.i	−0.360891	−	0.117261i	0.122959	−	0.992412i	$-0.460762\pi$
$277$	−460867.	−	149745.i	−0.360891	−	0.117261i	−0.483849	+	0.875151i	$0.660762\pi$
$278$	−280412.	+	385954.i	−0.217613	+	0.299519i
$279$	−398697.	−	289671.i	−0.306643	−	0.222789i
$280$	−1.25790e6	−	134044.i	−0.958854	−	0.102177i
$281$	666102.	−	483952.i	0.503240	−	0.365625i	−0.307013	−	0.951705i	$-0.599330\pi$
$281$	666102.	−	483952.i	0.503240	−	0.365625i	0.810253	+	0.586080i	$0.199330\pi$
$282$		−	1.04526e6i		−	0.782711i
$283$	−154838.	−	213117.i	−0.114924	−	0.158180i	0.747680	−	0.664060i	$-0.231168\pi$
$283$	−154838.	−	213117.i	−0.114924	−	0.158180i	−0.862604	+	0.505880i	$0.831168\pi$
$284$	−39266.8	−	120851.i	−0.0288888	−	0.0889107i
$285$	−193413.	+	214185.i	−0.141050	+	0.156198i
$286$	−1.15861e6	+	3.56583e6i	−0.837572	+	2.57778i
$287$	−645262.	+	209658.i	−0.462414	+	0.150247i
$288$	64136.8	−	20839.3i	0.0455645	−	0.0148048i
$289$	12705.1	−	39102.1i	0.00894812	−	0.0275395i
$290$	73476.5	−	689521.i	0.0513043	−	0.481452i
$291$	335282.	+	1.03189e6i	0.232102	+	0.714335i
$292$	57983.3	+	79807.1i	0.0397966	+	0.0547753i
$293$			1.10577e6i			0.752478i	0.926523	+	0.376239i	$0.122783\pi$
$293$			1.10577e6i			0.752478i	−0.926523	+	0.376239i	$0.877217\pi$
$294$	85422.2	−	62062.8i	0.0576371	−	0.0418758i
$295$	154965.	−	346711.i	0.103676	−	0.231959i
$296$	−99747.8	−	72471.0i	−0.0661719	−	0.0480767i
$297$	−293998.	+	404654.i	−0.193399	+	0.266191i
$298$	2.34382e6	+	761552.i	1.52891	+	0.496774i
$299$	−1.28414e6			−0.830680
$300$	−26188.5	−	59279.6i	−0.0167999	−	0.0380279i
$301$	1.21751e6			0.774564
$302$	1.54722e6	+	502722.i	0.976190	+	0.317183i
$303$	−201704.	+	277622.i	−0.126214	+	0.173719i
$304$	−438512.	−	318597.i	−0.272143	−	0.197723i
$305$	−277761.	+	159832.i	−0.170970	+	0.0983816i
$306$	−419306.	+	304644.i	−0.255993	+	0.185990i
$307$			1.25478e6i			0.759840i	0.925019	+	0.379920i	$0.124048\pi$
$307$			1.25478e6i			0.759840i	−0.925019	+	0.379920i	$0.875952\pi$
$308$	−112493.	−	154833.i	−0.0675691	−	0.0930008i
$309$	−235494.	−	724777.i	−0.140309	−	0.431826i
$310$	−1.69209e6	−	756292.i	−1.00005	−	0.446977i
$311$	−413243.	+	1.27183e6i	−0.242272	+	0.745638i	0.753801	+	0.657103i	$0.228218\pi$
$311$	−413243.	+	1.27183e6i	−0.242272	+	0.745638i	−0.996073	+	0.0885348i	$0.971782\pi$
$312$	1.60455e6	−	521349.i	0.933181	−	0.303209i
$313$	2.71498e6	−	882152.i	1.56641	−	0.508959i	0.607902	−	0.794012i	$-0.292011\pi$
$313$	2.71498e6	−	882152.i	1.56641	−	0.508959i	0.958512	+	0.285054i	$0.0920115\pi$
$314$	−296886.	+	913721.i	−0.169928	+	0.522985i
$315$	−500427.	−	223669.i	−0.284161	−	0.127008i
$316$	29126.1	+	89640.9i	0.0164083	+	0.0504997i
$317$	−708997.	−	975850.i	−0.396274	−	0.545425i	0.563530	−	0.826096i	$-0.309443\pi$
$317$	−708997.	−	975850.i	−0.396274	−	0.545425i	−0.959804	+	0.280671i	$0.909443\pi$
$318$			1.18649e6i			0.657955i
$319$	1.26353e6	−	918005.i	0.695196	−	0.505089i
$320$	1.68496e6	−	969577.i	0.919845	−	0.529307i
$321$	−212345.	−	154278.i	−0.115022	−	0.0835683i
$322$	−496534.	+	683420.i	−0.266876	+	0.367323i
$323$	−640561.	−	208131.i	−0.341628	−	0.111002i
$324$	15118.1			0.00800083
$325$	−1.26634e6	−	2.86645e6i	−0.665030	−	1.50534i
$326$	2.42214e6			1.26228
$327$	−1.67871e6	−	545447.i	−0.868175	−	0.282087i
$328$	615834.	−	847623.i	0.316067	−	0.435029i
$329$	2.08724e6	+	1.51647e6i	1.06312	+	0.772401i
$330$	−767591.	+	1.71737e6i	−0.388012	+	0.868120i
$331$	−435134.	+	316144.i	−0.218300	+	0.158604i	−0.691561	−	0.722318i	$-0.743077\pi$
$331$	−435134.	+	316144.i	−0.218300	+	0.158604i	0.473261	+	0.880922i	$0.343077\pi$
$332$			257264.i			0.128095i
$333$	−31401.8	−	43220.8i	−0.0155183	−	0.0213591i
$334$	469950.	+	1.44636e6i	0.230507	+	0.709429i
$335$	−89359.1	+	838568.i	−0.0435038	+	0.408250i
$336$	318138.	−	979128.i	0.153733	−	0.473142i
$337$	−1.14550e6	+	372197.i	−0.549442	+	0.178524i	−0.570565	−	0.821252i	$-0.693276\pi$
$337$	−1.14550e6	+	372197.i	−0.549442	+	0.178524i	0.0211233	+	0.999777i	$0.493276\pi$
$338$	3.28731e6	−	1.06811e6i	1.56512	−	0.508539i
$339$	−311437.	+	958504.i	−0.147187	+	0.452997i
$340$	101368.	−	112254.i	0.0475556	−	0.0526630i
$341$	−1.28998e6	−	3.97014e6i	−0.600753	−	1.84893i
$342$	−148821.	−	204834.i	−0.0688015	−	0.0946972i
$343$			2.29517e6i			1.05337i
$344$	−1.52106e6	+	1.10511e6i	−0.693027	+	0.503514i
$345$	−640647.	−	68268.4i	−0.289782	−	0.0308796i
$346$	−2.69882e6	−	1.96080e6i	−1.21194	−	0.880530i
$347$	774665.	−	1.06623e6i	0.345374	−	0.475367i	−0.600627	−	0.799529i	$-0.705082\pi$
$347$	774665.	−	1.06623e6i	0.345374	−	0.475367i	0.946001	+	0.324162i	$0.105082\pi$
$348$	−44895.6	−	14587.5i	−0.0198726	−	0.00645701i
$349$	2.39129e6			1.05092			0.525459	−	0.850819i	$-0.323894\pi$
$349$	2.39129e6			1.05092			0.525459	+	0.850819i	$0.323894\pi$
$350$	−2.01518e6	−	434414.i	−0.879312	−	0.189554i
$351$	731032.			0.316715
$352$	543277.	+	176521.i	0.233703	+	0.0759348i
$353$	746374.	−	1.02730e6i	0.318801	−	0.438792i	−0.619300	−	0.785155i	$-0.712583\pi$
$353$	746374.	−	1.02730e6i	0.318801	−	0.438792i	0.938101	+	0.346363i	$0.112583\pi$
$354$	269549.	+	195839.i	0.114322	+	0.0830599i
$355$	−636597.	−	3.01632e6i	−0.268098	−	1.27030i
$356$	−254780.	+	185108.i	−0.106547	+	0.0774107i
$357$		−	1.27927e6i		−	0.531243i
$358$	−1.09578e6	−	1.50821e6i	−0.451871	−	0.621947i
$359$	−1.19661e6	−	3.68279e6i	−0.490023	−	1.50814i	−0.824572	−	0.565757i	$-0.808584\pi$
$359$	−1.19661e6	−	3.68279e6i	−0.490023	−	1.50814i	0.334549	−	0.942378i	$-0.391416\pi$
$360$	828213.	−	174795.i	0.336811	−	0.0710841i
$361$	−663483.	+	2.04199e6i	−0.267955	+	0.824681i
$362$	−396315.	+	128770.i	−0.158953	+	0.0516470i
$363$	−2.65094e6	+	861342.i	−1.05593	+	0.343091i
$364$	−86436.7	+	266025.i	−0.0341936	+	0.105237i
$365$	1.19362e6	+	2.07431e6i	0.468957	+	0.814968i
$366$	−86881.3	−	267393.i	−0.0339019	−	0.104339i
$367$	−241753.	−	332744.i	−0.0936929	−	0.128957i	0.759597	−	0.650394i	$-0.225396\pi$
$367$	−241753.	−	332744.i	−0.0936929	−	0.128957i	−0.853290	+	0.521437i	$0.825396\pi$
$368$		−	1.21008e6i		−	0.465795i
$369$	367276.	−	266842.i	0.140419	−	0.102021i
$370$	−149119.	−	134657.i	−0.0566275	−	0.0511356i
$371$	−2.36925e6	−	1.72136e6i	−0.893669	−	0.649289i
$372$	−74163.4	+	102077.i	−0.0277864	+	0.0382447i
$373$	2.76454e6	+	898253.i	1.02885	+	0.334292i	0.774334	−	0.632777i	$-0.218085\pi$
$373$	2.76454e6	+	898253.i	1.02885	+	0.334292i	0.254512	+	0.967070i	$0.418085\pi$
$374$	−4.39023e6			−1.62296
$375$	−479378.	−	1.49737e6i	−0.176035	−	0.549859i
$376$	−3.98409e6			−1.45332
$377$	−2.17091e6	−	705372.i	−0.786663	−	0.255602i
$378$	282666.	−	389056.i	0.101752	−	0.140050i
$379$	−696510.	−	506044.i	−0.249075	−	0.180963i	0.456242	−	0.889856i	$-0.349195\pi$
$379$	−696510.	−	506044.i	−0.249075	−	0.180963i	−0.705317	+	0.708892i	$0.749195\pi$
$380$	54837.0	+	49518.8i	0.0194812	+	0.0175918i
$381$	2.43125e6	−	1.76641e6i	0.858060	−	0.623417i
$382$			3.87467e6i			1.35855i
$383$	1.94292e6	+	2.67420e6i	0.676795	+	0.931529i	0.999890	−	0.0148380i	$-0.00472326\pi$
$383$	1.94292e6	+	2.67420e6i	0.676795	+	0.931529i	−0.323095	+	0.946367i	$0.604723\pi$
$384$	452947.	+	1.39403e6i	0.156754	+	0.482440i
$385$	−2.31573e6	−	4.02434e6i	−0.796225	−	1.38370i
$386$	−1.10528e6	+	3.40171e6i	−0.377577	+	1.16206i
$387$	−774792.	+	251745.i	−0.262971	+	0.0854444i
$388$	264192.	−	85841.2i	0.0890923	−	0.0289479i
$389$	−467654.	+	1.43929e6i	−0.156693	+	0.482253i	−0.998329	−	0.0577939i	$-0.981593\pi$
$389$	−467654.	+	1.43929e6i	−0.156693	+	0.482253i	0.841635	+	0.540047i	$0.181593\pi$
$390$	2.69005e6	−	567737.i	0.895568	−	0.189010i
$391$	−464651.	−	1.43005e6i	−0.153704	−	0.473052i
$392$	−236558.	−	325594.i	−0.0777538	−	0.107019i
$393$		−	1.14951e6i		−	0.375431i
$394$	4.61851e6	−	3.35554e6i	1.49886	−	1.08899i
$395$	472195.	+	2.23735e6i	0.152275	+	0.721509i
$396$	103602.	+	75271.4i	0.0331995	+	0.0241208i
$397$	597867.	−	822893.i	0.190383	−	0.262040i	−0.703146	−	0.711046i	$-0.748222\pi$
$397$	597867.	−	822893.i	0.190383	−	0.262040i	0.893529	+	0.449006i	$0.148222\pi$
$398$	−3.24297e6	−	1.05370e6i	−1.02621	−	0.333435i
$399$	624935.			0.196518
$400$	2.70114e6	−	1.19331e6i	0.844105	−	0.372908i
$401$	1.79183e6			0.556464			0.278232	−	0.960514i	$-0.410252\pi$
$401$	1.79183e6			0.556464			0.278232	+	0.960514i	$0.410252\pi$
$402$	−703657.	−	228632.i	−0.217168	−	0.0705622i
$403$	−3.58615e6	+	4.93591e6i	−1.09993	+	1.51392i
$404$	71078.7	+	51641.7i	0.0216664	+	0.0157415i
$405$	364706.	+	38863.7i	0.110486	+	0.0117735i
$406$	−1.21482e6	+	882618.i	−0.365761	+	0.265741i
$407$		−	452532.i		−	0.135414i
$408$	1.16118e6	+	1.59822e6i	0.345340	+	0.475320i
$409$	−1.79493e6	−	5.52422e6i	−0.530565	−	1.63291i	−0.753041	−	0.657973i	$-0.771414\pi$
$409$	−1.79493e6	−	5.52422e6i	−0.530565	−	1.63291i	0.222476	−	0.974938i	$-0.428586\pi$
$410$	1.14427e6	−	1.26716e6i	0.336177	−	0.372282i
$411$	−547385.	+	1.68468e6i	−0.159841	+	0.491940i
$412$	−185562.	+	60292.8i	−0.0538575	+	0.0174994i
$413$	−782127.	+	254128.i	−0.225633	+	0.0733125i
$414$	174670.	−	537578.i	0.0500861	−	0.154149i
$415$	−661340.	+	6.20617e6i	−0.188497	+	1.76890i
$416$	−257992.	−	794019.i	−0.0730926	−	0.224956i
$417$	463118.	+	637428.i	0.130422	+	0.179511i
$418$		−	2.14466e6i		−	0.600368i
$419$	−90782.4	+	65957.3i	−0.0252619	+	0.0183539i	−0.600345	−	0.799741i	$-0.704970\pi$
$419$	−90782.4	+	65957.3i	−0.0252619	+	0.0183539i	0.575083	+	0.818095i	$0.304970\pi$
$420$	−57265.2	+	128123.i	−0.0158405	+	0.0354407i
$421$	1.36869e6	+	994411.i	0.376357	+	0.273439i	0.759842	−	0.650108i	$-0.225276\pi$
$421$	1.36869e6	+	994411.i	0.376357	+	0.273439i	−0.383485	+	0.923547i	$0.625276\pi$
$422$	−640389.	+	881420.i	−0.175050	+	0.240936i
$423$	−1.64182e6	−	533460.i	−0.446144	−	0.144961i
$424$	4.52240e6			1.22167
$425$	2.73394e6	−	2.44742e6i	0.734204	−	0.657258i
$426$	2.70462e6			0.722074
$427$	659994.	+	214445.i	0.175174	+	0.0569176i
$428$	−39499.3	+	54366.1i	−0.0104227	+	0.0143456i
$429$	5.00965e6	+	3.63973e6i	1.31421	+	0.954829i
$430$	−2.65557e6	+	1.52809e6i	−0.692606	+	0.398546i
$431$	−468246.	+	340201.i	−0.121417	+	0.0882149i	−0.646837	−	0.762629i	$-0.723908\pi$
$431$	−468246.	+	340201.i	−0.121417	+	0.0882149i	0.525419	+	0.850843i	$0.323908\pi$
$432$			688872.i			0.177594i
$433$	3.49469e6	+	4.81002e6i	0.895753	+	1.23290i	0.971803	+	0.235795i	$0.0757692\pi$
$433$	3.49469e6	+	4.81002e6i	0.895753	+	1.23290i	−0.0760497	+	0.997104i	$0.524231\pi$
$434$	1.24025e6	+	3.81710e6i	0.316072	+	0.972769i
$435$	−1.04555e6	−	467317.i	−0.264925	−	0.118410i
$436$	−139649.	+	429795.i	−0.0351821	+	0.108279i
$437$	698589.	−	226985.i	0.174992	−	0.0568584i
$438$	−1.99688e6	+	648826.i	−0.497356	+	0.161601i
$439$	1.10823e6	−	3.41079e6i	0.274454	−	0.844684i	−0.714909	−	0.699218i	$-0.753532\pi$
$439$	1.10823e6	−	3.41079e6i	0.274454	−	0.844684i	0.989363	−	0.145466i	$-0.0464681\pi$
$440$	6.54591e6	+	2.92574e6i	1.61190	+	0.720450i
$441$	−53887.8	−	165850.i	−0.0131945	−	0.0406086i
$442$	3.77152e6	+	5.19105e6i	0.918249	+	1.26386i
$443$		−	460184.i		−	0.111409i	−0.998447	−	0.0557047i	$-0.982259\pi$
$443$		−	460184.i		−	0.111409i	0.998447	−	0.0557047i	$-0.0177405\pi$
$444$	−11065.7	+	8039.69i	−0.00266392	+	0.00193545i
$445$	−6.62211e6	+	3.81056e6i	−1.58524	+	0.912198i
$446$	−5.16970e6	−	3.75601e6i	−1.23063	−	0.894106i
$447$	2.39238e6	−	3.29283e6i	0.566320	−	0.779473i
$448$	−4.00368e6	−	1.30087e6i	−0.942463	−	0.306225i
$449$	513162.			0.120126			0.0600632	−	0.998195i	$-0.480870\pi$
$449$	513162.			0.120126			0.0600632	+	0.998195i	$0.480870\pi$
$450$	1.37223e6	−	140229.i	0.319444	−	0.0326443i
$451$	3.84546e6			0.890241
$452$	245403.	+	79736.1i	0.0564980	+	0.0183573i
$453$	1.57928e6	−	2.17369e6i	0.361588	−	0.497683i
$454$	−795594.	−	578033.i	−0.181156	−	0.131617i
$455$	−2.76904e6	+	6.19533e6i	−0.627049	+	1.40293i
$456$	−780742.	+	567242.i	−0.175831	+	0.127749i
$457$			1.67468e6i			0.375094i	0.982256	+	0.187547i	$0.0600537\pi$
$457$			1.67468e6i			0.375094i	−0.982256	+	0.187547i	$0.939946\pi$
$458$	−2.57576e6	−	3.54522e6i	−0.573774	−	0.789732i
$459$	264516.	+	814096.i	0.0586030	+	0.180361i
$460$	−17478.5	+	164023.i	−0.00385132	+	0.0361418i
$461$	2.19323e6	−	6.75007e6i	0.480654	−	1.47930i	−0.357525	−	0.933904i	$-0.616379\pi$
$461$	2.19323e6	−	6.75007e6i	0.480654	−	1.47930i	0.838179	−	0.545396i	$-0.183621\pi$
$462$	3.87413e6	−	1.25878e6i	0.844442	−	0.274376i
$463$	6.93427e6	−	2.25308e6i	1.50331	−	0.488455i	0.562328	−	0.826914i	$-0.309906\pi$
$463$	6.93427e6	−	2.25308e6i	1.50331	−	0.488455i	0.940981	+	0.338459i	$0.109906\pi$
$464$	664693.	−	2.04571e6i	0.143326	−	0.441113i
$465$	−2.05151e6	+	2.27184e6i	−0.439988	+	0.487242i
$466$	1.31080e6	+	4.03422e6i	0.279622	+	0.860588i
$467$	5.43734e6	+	7.48386e6i	1.15370	+	1.58794i	0.732164	+	0.681128i	$0.238510\pi$
$467$	5.43734e6	+	7.48386e6i	1.15370	+	1.58794i	0.421540	+	0.906810i	$0.361490\pi$
$468$		−	187164.i		−	0.0395009i
$469$	1.47741e6	−	1.07340e6i	0.310149	−	0.225336i
$470$	−6.45587e6	−	687948.i	−1.34806	−	0.143652i
$471$	1.28369e6	+	932656.i	0.266629	+	0.193718i
$472$	746457.	−	1.02741e6i	0.154223	−	0.212270i
$473$	−6.56295e6	−	2.13243e6i	−1.34880	−	0.438250i
$474$	−2.00614e6			−0.410125
$475$	1.19558e6	+	1.33555e6i	0.243134	+	0.271598i
$476$	−327528.			−0.0662569
$477$	1.86366e6	+	605538.i	0.375033	+	0.121856i
$478$	−4.02036e6	+	5.53354e6i	−0.804813	+	1.10773i
$479$	−3.35825e6	−	2.43991e6i	−0.668765	−	0.485887i	0.200846	−	0.979623i	$-0.435631\pi$
$479$	−3.35825e6	−	2.43991e6i	−0.668765	−	0.485887i	−0.869612	+	0.493736i	$0.835631\pi$
$480$	−86498.2	−	409846.i	−0.0171358	−	0.0811928i
$481$	−535078.	+	388757.i	−0.105452	+	0.0766152i
$482$			5.11134e6i			1.00211i
$483$	820057.	+	1.12871e6i	0.159947	+	0.220148i
$484$	220527.	+	678711.i	0.0427905	+	0.131696i
$485$	6.59398e6	−	1.39166e6i	1.27290	−	0.268646i
$486$	−99435.7	+	306031.i	−0.0190964	+	0.0587727i
$487$	52657.5	−	17109.5i	0.0100609	−	0.00326899i	−0.303982	−	0.952678i	$-0.598316\pi$
$487$	52657.5	−	17109.5i	0.0100609	−	0.00326899i	0.314043	+	0.949409i	$0.398316\pi$
$488$	−1.01919e6	+	331155.i	−0.193734	+	0.0629480i
$489$	1.23617e6	−	3.80453e6i	0.233779	−	0.719496i
$490$	−327099.	−	568443.i	−0.0615445	−	0.106954i
$491$	−14929.7	−	45949.0i	−0.00279479	−	0.00860147i	0.949649	−	0.313315i	$-0.101439\pi$
$491$	−14929.7	−	45949.0i	−0.00279479	−	0.00860147i	−0.952444	+	0.304713i	$0.901439\pi$
$492$	−68318.6	−	94032.4i	−0.0127241	−	0.0175132i
$493$		−	2.67282e6i		−	0.495281i
$494$	−2.53586e6	+	1.84241e6i	−0.467529	+	0.339680i
$495$	2.30578e6	+	2.08216e6i	0.422965	+	0.381945i
$496$	−4.65125e6	−	3.37933e6i	−0.848917	−	0.616774i
$497$	−3.92387e6	+	5.40074e6i	−0.712563	+	0.980759i
$498$	−5.20771e6	−	1.69209e6i	−0.940965	−	0.305738i
$499$	1.89880e6			0.341372			0.170686	−	0.985325i	$-0.445402\pi$
$499$	1.89880e6			0.341372			0.170686	+	0.985325i	$0.445402\pi$
$500$	−383367.	+	122733.i	−0.0685787	+	0.0219552i
$501$	2.51168e6			0.447064
$502$	8.83063e6	+	2.86925e6i	1.56398	+	0.508169i
$503$	−2.67384e6	+	3.68023e6i	−0.471211	+	0.648567i	−0.976786	−	0.214216i	$-0.931280\pi$
$503$	−2.67384e6	+	3.68023e6i	−0.471211	+	0.648567i	0.505575	+	0.862783i	$0.331280\pi$
$504$	−1.48292e6	−	1.07740e6i	−0.260040	−	0.188930i
$505$	1.58193e6	+	1.42851e6i	0.276032	+	0.249262i
$506$	3.87353e6	−	2.81428e6i	0.672559	−	0.488643i
$507$		−	5.70860e6i		−	0.986301i
$508$	−452247.	−	622465.i	−0.0777529	−	0.107018i
$509$	−456190.	−	1.40401e6i	−0.0780461	−	0.240201i	0.904420	−	0.426644i	$-0.140304\pi$
$509$	−456190.	−	1.40401e6i	−0.0780461	−	0.240201i	−0.982466	+	0.186443i	$0.940304\pi$
$510$	1.60561e6	+	2.79028e6i	0.273347	+	0.475031i
$511$	1.60147e6	−	4.92881e6i	0.271310	−	0.835007i
$512$	6.12427e6	−	1.98989e6i	1.03247	−	0.335471i
$513$	−397691.	+	129218.i	−0.0667195	+	0.0216785i
$514$	22930.6	−	70573.2i	0.00382832	−	0.0117824i
$515$	−4.63146e6	+	977472.i	−0.769484	+	0.162400i
$516$	64453.4	+	198367.i	0.0106567	+	0.0327979i
$517$	−8.59512e6	−	1.18302e7i	−1.41425	−	1.94655i
$518$			435088.i			0.0712448i
$519$	−4.45726e6	+	3.23839e6i	−0.726357	+	0.527729i
$520$	−2.16398e6	−	1.02533e7i	−0.350949	−	1.66287i
$521$	−6.07192e6	−	4.41151e6i	−0.980013	−	0.712021i	−0.0223016	−	0.999751i	$-0.507099\pi$
$521$	−6.07192e6	−	4.41151e6i	−0.980013	−	0.712021i	−0.957712	+	0.287730i	$0.907099\pi$
$522$	590579.	−	812863.i	0.0948641	−	0.130569i
$523$	−9.03823e6	−	2.93670e6i	−1.44487	−	0.469467i	−0.521459	−	0.853276i	$-0.674612\pi$
$523$	−9.03823e6	−	2.93670e6i	−1.44487	−	0.469467i	−0.923413	+	0.383809i	$0.874612\pi$
$524$	−294305.			−0.0468240
$525$	−1.71082e6	+	2.94359e6i	−0.270897	+	0.466100i
$526$	5.91079e6			0.931496
$527$	−6.79436e6	−	2.20762e6i	−1.06567	−	0.346257i
$528$	−3.42982e6	+	4.72074e6i	−0.535410	+	0.736928i
$529$	−3.88044e6	−	2.81930e6i	−0.602895	−	0.438029i
$530$	7.32815e6	+	780900.i	1.13320	+	0.120755i
$531$	445178.	−	323441.i	0.0685169	−	0.0497804i
$532$		−	160000.i		−	0.0245098i
$533$	−3.30352e6	−	4.54691e6i	−0.503685	−	0.693263i
$534$	−2.07134e6	−	6.37494e6i	−0.314339	−	0.967437i
$535$	−1.09263e6	+	1.20998e6i	−0.165040	+	0.182765i
$536$	−871450.	+	2.68205e6i	−0.131018	+	0.403231i
$537$	−2.92823e6	+	951438.i	−0.438197	+	0.142379i
$538$	1.24591e6	−	404821.i	0.185580	−	0.0602987i
$539$	456462.	−	1.40484e6i	0.0676756	−	0.208284i
$540$	9950.13	−	93374.5i	0.00146840	−	0.0137798i
$541$	2.08563e6	+	6.41890e6i	0.306368	+	0.942903i	0.979163	+	0.203075i	$0.0650934\pi$
$541$	2.08563e6	+	6.41890e6i	0.306368	+	0.942903i	−0.672795	+	0.739829i	$0.734907\pi$
$542$	−1.80983e6	−	2.49102e6i	−0.264631	−	0.364233i
$543$			688223.i			0.100168i
$544$	790889.	−	574614.i	0.114582	−	0.0832490i
$545$	−4.47372e6	+	1.00093e7i	−0.645176	+	1.44349i
$546$	−4.81654e6	−	3.49942e6i	−0.691439	−	0.502360i
$547$	3.42107e6	−	4.70870e6i	0.488870	−	0.672872i	−0.491309	−	0.870985i	$-0.663481\pi$
$547$	3.42107e6	−	4.70870e6i	0.488870	−	0.672872i	0.980179	+	0.198113i	$0.0634814\pi$
$548$	431322.	+	140145.i	0.0613551	+	0.0199355i
$549$	−464343.			−0.0657519
$550$	1.01019e7	+	5.87120e6i	1.42395	+	0.827600i
$551$	1.30569e6			0.183215
$552$	−2.04902e6	−	665768.i	−0.286220	−	0.0929984i
$553$	2.91052e6	−	4.00599e6i	0.404723	−	0.557053i
$554$	−2.13636e6	−	1.55215e6i	−0.295733	−	0.214862i
$555$	−287614.	+	165502.i	−0.0396348	+	0.0228071i
$556$	163198.	−	118571.i	0.0223887	−	0.0162663i
$557$		−	1.38876e7i		−	1.89666i	−0.317291	−	0.948328i	$-0.602773\pi$
$557$		−	1.38876e7i		−	1.89666i	0.317291	−	0.948328i	$-0.397227\pi$
$558$	−1.57853e6	−	2.17265e6i	−0.214618	−	0.295396i
$559$	3.11663e6	+	9.59199e6i	0.421847	+	1.29831i
$560$	−5.83803e6	−	2.60935e6i	−0.786677	−	0.351611i
$561$	−2.24060e6	+	6.89587e6i	−0.300579	+	0.925086i
$562$	4.26714e6	−	1.38648e6i	0.569897	−	0.185171i
$563$	−127004.	+	41266.0i	−0.0168867	+	0.00548683i	−0.317448	−	0.948276i	$-0.602826\pi$
$563$	−127004.	+	41266.0i	−0.0168867	+	0.00548683i	0.300561	+	0.953762i	$0.402826\pi$
$564$	−136580.	+	420350.i	−0.0180796	+	0.0556433i
$565$	5.71507e6	+	2.55439e6i	0.753182	+	0.336640i
$566$	−443597.	−	1.36525e6i	−0.0582033	−	0.179131i
$567$	−466840.	−	642551.i	−0.0609833	−	0.0839363i
$568$		−	1.03089e7i		−	1.34073i
$569$	5.93872e6	−	4.31473e6i	0.768974	−	0.558693i	−0.132675	−	0.991160i	$-0.542357\pi$
$569$	5.93872e6	−	4.31473e6i	0.768974	−	0.558693i	0.901650	+	0.432467i	$0.142357\pi$
$570$	−1.36307e6	+	784352.i	−0.175724	+	0.101117i
$571$	−1.02696e7	−	7.46128e6i	−1.31814	−	0.957686i	−0.999953	−	0.00965878i	$-0.996925\pi$
$571$	−1.02696e7	−	7.46128e6i	−1.31814	−	0.957686i	−0.318189	−	0.948027i	$-0.603075\pi$
$572$	931866.	−	1.28260e6i	0.119087	−	0.163909i
$573$	6.08606e6	+	1.97748e6i	0.774372	+	0.251609i
$574$	−3.69723e6			−0.468379
$575$	−843296.	+	3.91192e6i	−0.106368	+	0.493424i
$576$	2.81682e6			0.353755
$577$	3.07756e6	+	999961.i	0.384829	+	0.125038i	0.495041	−	0.868870i	$-0.335153\pi$
$577$	3.07756e6	+	999961.i	0.384829	+	0.125038i	−0.110212	+	0.993908i	$0.535153\pi$
$578$	131692.	−	181259.i	0.0163961	−	0.0225673i
$579$	4.77907e6	+	3.47220e6i	0.592444	+	0.430436i
$580$	−119645.	+	267689.i	−0.0147682	+	0.0330416i
$581$	1.09342e7	−	7.94418e6i	1.34384	−	0.976357i
$582$			5.91256e6i			0.723549i
$583$	9.75645e6	+	1.34286e7i	1.18883	+	1.63629i
$584$	2.47306e6	+	7.61128e6i	0.300056	+	0.923476i
$585$	481136.	−	4.51509e6i	0.0581270	−	0.545478i
$586$	−1.86206e6	+	5.73082e6i	−0.224000	+	0.689402i
$587$	7.45903e6	−	2.42359e6i	0.893485	−	0.290311i	0.173940	−	0.984756i	$-0.444350\pi$
$587$	7.45903e6	−	2.42359e6i	0.893485	−	0.290311i	0.719545	+	0.694445i	$0.244350\pi$
$588$	−42461.9	+	13796.7i	−0.00506473	+	0.00164563i
$589$	1.07844e6	−	3.31909e6i	0.128088	−	0.394213i
$590$	1.38697e6	−	1.53593e6i	0.164036	−	0.181653i
$591$	−2.91355e6	−	8.96697e6i	−0.343126	−	1.05603i
$592$	−366337.	−	504219.i	−0.0429612	−	0.0591310i
$593$		−	5.12127e6i		−	0.598054i	−0.954245	−	0.299027i	$-0.903338\pi$
$593$		−	5.12127e6i		−	0.598054i	0.954245	−	0.299027i	$-0.0966621\pi$
$594$	−2.20511e6	+	1.60211e6i	−0.256428	+	0.186306i
$595$	−7.90122e6	−	841967.i	−0.914960	−	0.0974996i
$596$	−843053.	−	612514.i	−0.0972163	−	0.0706318i
$597$	−3.31017e6	+	4.55606e6i	−0.380115	+	0.523183i
$598$	−6.65526e6	−	2.16243e6i	−0.761049	−	0.247280i
$599$	9.22719e6			1.05076			0.525379	−	0.850868i	$-0.323924\pi$
$599$	9.22719e6			1.05076			0.525379	+	0.850868i	$0.323924\pi$
$600$	−534495.	−	5.23036e6i	−0.0606129	−	0.593135i
$601$	−1.20617e6			−0.136214			−0.0681071	−	0.997678i	$-0.521696\pi$
$601$	−1.20617e6			−0.136214			−0.0681071	+	0.997678i	$0.521696\pi$
$602$	6.30996e6	+	2.05023e6i	0.709636	+	0.230575i
$603$	−718238.	+	988570.i	−0.0804406	+	0.110717i
$604$	−556523.	−	404338.i	−0.0620713	−	0.0450974i
$605$	3.57519e6	+	1.69400e7i	0.397110	+	1.88159i
$606$	−1.51287e6	+	1.09916e6i	−0.167348	+	0.121585i
$607$			1.73603e7i			1.91243i	0.292661	+	0.956216i	$0.405459\pi$
$607$			1.73603e7i			1.91243i	−0.292661	+	0.956216i	$0.594541\pi$
$608$	280703.	+	386355.i	0.0307956	+	0.0423865i
$609$	766358.	+	2.35861e6i	0.0837315	+	0.257699i
$610$	−1.70869e6	+	360620.i	−0.185925	+	0.0392397i
$611$	−6.60428e6	+	2.03259e7i	−0.715686	+	2.20265i
$612$	208430.	−	67723.0i	0.0224948	−	0.00730900i
$613$	−1.27753e7	+	4.15093e6i	−1.37315	+	0.446164i	−0.900412	−	0.435039i	$-0.856735\pi$
$613$	−1.27753e7	+	4.15093e6i	−1.37315	+	0.446164i	−0.472739	+	0.881202i	$0.656735\pi$
$614$	−2.11299e6	+	6.50312e6i	−0.226192	+	0.696146i
$615$	−1.40638e6	−	2.44404e6i	−0.149939	−	0.260568i
$616$	−4.79795e6	−	1.47666e7i	−0.509453	−	1.56793i
$617$	424802.	+	584689.i	0.0449235	+	0.0618319i	0.830888	−	0.556440i	$-0.187833\pi$
$617$	424802.	+	584689.i	0.0449235	+	0.0618319i	−0.785964	+	0.618272i	$0.787833\pi$
$618$		−	4.15284e6i		−	0.437396i
$619$	−5.45908e6	+	3.96625e6i	−0.572654	+	0.416058i	−0.836068	−	0.548625i	$-0.815151\pi$
$619$	−5.45908e6	+	3.96625e6i	−0.572654	+	0.416058i	0.263414	+	0.964683i	$0.415151\pi$
$620$	581651.	+	525241.i	0.0607691	+	0.0548756i
$621$	−755246.	−	548718.i	−0.0785886	−	0.0570979i
$622$	−4.28340e6	+	5.89559e6i	−0.443928	+	0.611015i
$623$	1.57350e7	+	5.11260e6i	1.62422	+	0.527742i
$624$	8.52829e6			0.876800
$625$	−9.56377e6	+	1.97529e6i	−0.979330	+	0.202269i
$626$	1.55564e7			1.58662
$627$	−3.36868e6	−	1.09455e6i	−0.342209	−	0.111190i
$628$	238785.	−	328659.i	0.0241606	−	0.0332542i
$629$	−626541.	−	455209.i	−0.0631427	−	0.0458759i
$630$	−2.21690e6	−	2.00190e6i	−0.222533	−	0.200951i
$631$	4.95066e6	−	3.59687e6i	0.494982	−	0.359626i	−0.312115	−	0.950044i	$-0.601037\pi$
$631$	4.95066e6	−	3.59687e6i	0.494982	−	0.359626i	0.807097	+	0.590419i	$0.201037\pi$
$632$			7.64658e6i			0.761509i
$633$	1.05764e6	+	1.45572e6i	0.104913	+	0.144401i
$634$	−2.03121e6	−	6.25142e6i	−0.200693	−	0.617669i
$635$	−9.30977e6	−	1.61788e7i	−0.916230	−	1.59225i
$636$	155034.	−	477145.i	0.0151979	−	0.0467744i
$637$	−2.05323e6	+	667136.i	−0.200489	+	0.0651427i
$638$	8.09431e6	−	2.63000e6i	0.787278	−	0.255802i
$639$	1.38033e6	−	4.24822e6i	0.133731	−	0.411581i
$640$	8.90809e6	−	1.88006e6i	0.859675	−	0.181435i
$641$	3.60150e6	+	1.10843e7i	0.346209	+	1.06552i	0.960934	+	0.276779i	$0.0892671\pi$
$641$	3.60150e6	+	1.10843e7i	0.346209	+	1.06552i	−0.614725	+	0.788742i	$0.710733\pi$
$642$	−840720.	−	1.15715e6i	−0.0805033	−	0.110803i
$643$		−	6.71359e6i		−	0.640365i	−0.947356	−	0.320182i	$-0.896256\pi$
$643$		−	6.71359e6i		−	0.640365i	0.947356	−	0.320182i	$-0.103744\pi$
$644$	288980.	−	209956.i	0.0274570	−	0.0199487i
$645$	1.04492e6	+	4.95106e6i	0.0988976	+	0.468596i
$646$	−2.96933e6	−	2.15735e6i	−0.279948	−	0.203394i
$647$	4.10498e6	−	5.65002e6i	0.385523	−	0.530627i	−0.571514	−	0.820592i	$-0.693644\pi$
$647$	4.10498e6	−	5.65002e6i	0.385523	−	0.530627i	0.957037	+	0.289965i	$0.0936438\pi$
$648$	1.16646e6	+	379007.i	0.109127	+	0.0354576i
$649$	4.66112e6			0.434388
$650$	−1.73605e6	−	1.69883e7i	−0.161168	−	1.57713i
$651$	6.62862e6			0.613014
$652$	−974060.	−	316491.i	−0.0897360	−	0.0291570i
$653$	−5.89875e6	+	8.11893e6i	−0.541348	+	0.745102i	−0.988807	−	0.149203i	$-0.952329\pi$
$653$	−5.89875e6	+	8.11893e6i	−0.541348	+	0.745102i	0.447458	+	0.894305i	$0.352329\pi$
$654$	−7.78171e6	−	5.65374e6i	−0.711428	−	0.516882i
$655$	−7.09974e6	−	756560.i	−0.646605	−	0.0689033i
$656$	4.28468e6	−	3.11300e6i	0.388740	−	0.282436i
$657$			3.46770e6i			0.313421i
$658$	8.26380e6	+	1.13741e7i	0.744072	+	1.02413i
$659$	−1.96426e6	−	6.04538e6i	−0.176192	−	0.542263i	0.823494	−	0.567325i	$-0.192022\pi$
$659$	−1.96426e6	−	6.04538e6i	−0.176192	−	0.542263i	−0.999686	+	0.0250618i	$0.992022\pi$
$660$	533088.	−	590341.i	0.0476364	−	0.0527525i
$661$	−5.94008e6	+	1.82817e7i	−0.528797	+	1.62747i	0.227886	+	0.973688i	$0.426819\pi$
$661$	−5.94008e6	+	1.82817e7i	−0.528797	+	1.62747i	−0.756683	+	0.653782i	$0.773181\pi$
$662$	−2.78753e6	+	905723.i	−0.247215	+	0.0803249i
$663$	1.00786e7	−	3.27473e6i	0.890462	−	0.289329i
$664$	−6.44953e6	+	1.98496e7i	−0.567686	+	1.74716i
$665$	411307.	−	3.85980e6i	0.0360671	−	0.338463i
$666$	−89963.2	−	276878.i	−0.00785922	−	0.0241882i
$667$	1.71336e6	+	2.35824e6i	0.149120	+	0.205245i
$668$		−	643057.i		−	0.0557581i
$669$	−8.53808e6	+	6.20328e6i	−0.737556	+	0.535866i
$670$	−1.87523e6	+	4.19554e6i	−0.161386	+	0.361078i
$671$	−3.18208e6	−	2.31191e6i	−0.272838	−	0.198228i
$672$	−533159.	+	733831.i	−0.0455443	+	0.0626863i
$673$	6.55011e6	+	2.12826e6i	0.557457	+	0.181129i	0.574177	−	0.818732i	$-0.305322\pi$
$673$	6.55011e6	+	2.12826e6i	0.557457	+	0.181129i	−0.0167198	+	0.999860i	$0.505322\pi$
$674$	−6.56353e6			−0.556529
$675$	480070.	−	2.22697e6i	0.0405551	−	0.188128i
$676$	−1.46155e6			−0.123012
$677$	−1.06524e6	−	346119.i	−0.0893259	−	0.0290237i	0.264013	−	0.964519i	$-0.414954\pi$
$677$	−1.06524e6	−	346119.i	−0.0893259	−	0.0290237i	−0.353339	+	0.935495i	$0.614954\pi$
$678$	−3.22815e6	+	4.44317e6i	−0.269699	+	0.371209i
$679$	−1.18066e7	−	8.57796e6i	−0.982763	−	0.714019i
$680$	1.06354e7	−	6.11992e6i	0.882025	−	0.507544i
$681$	−1.31397e6	+	954658.i	−0.108572	+	0.0788823i
$682$		−	2.27482e7i		−	1.87278i
$683$	9.80334e6	+	1.34931e7i	0.804123	+	1.10678i	0.992204	+	0.124627i	$0.0397733\pi$
$683$	9.80334e6	+	1.34931e7i	0.804123	+	1.10678i	−0.188081	+	0.982154i	$0.560227\pi$
$684$	33083.2	+	101820.i	0.00270375	+	0.00832130i
$685$	1.00449e7	+	4.48962e6i	0.817933	+	0.365581i
$686$	−3.86496e6	+	1.18951e7i	−0.313570	+	0.965070i
$687$	−6.88315e6	+	2.23647e6i	−0.556411	+	0.180789i
$688$	−9.03881e6	+	2.93689e6i	−0.728014	+	0.236546i
$689$	7.49661e6	−	2.30722e7i	0.601613	−	1.85157i
$690$	−3.20530e6	−	1.43263e6i	−0.256299	−	0.114554i
$691$	−1.59208e6	−	4.89991e6i	−0.126844	−	0.390385i	0.867389	−	0.497631i	$-0.165797\pi$
$691$	−1.59208e6	−	4.89991e6i	−0.126844	−	0.390385i	−0.994233	+	0.107246i	$0.965797\pi$
$692$	829114.	+	1.14118e6i	0.0658187	+	0.0905917i
$693$		−	6.72765e6i		−	0.532145i
$694$	5.81032e6	−	4.22144e6i	0.457932	−	0.332707i
$695$	4.24177e6	−	2.44084e6i	0.333108	−	0.191681i
$696$	−3.09829e6	−	2.25104e6i	−0.242437	−	0.176141i
$697$	3.86821e6	−	5.32414e6i	0.301598	−	0.415114i
$698$	1.23933e7	+	4.02682e6i	0.962826	+	0.312841i
$699$	7.00566e6			0.542320
$700$	753638.	+	438014.i	0.0581323	+	0.0337865i
$701$	−2.12211e7			−1.63107			−0.815534	−	0.578709i	$-0.803557\pi$
$701$	−2.12211e7			−1.63107			−0.815534	+	0.578709i	$0.803557\pi$
$702$	3.78870e6	+	1.23102e6i	0.290166	+	0.0942807i
$703$	222373.	−	306070.i	0.0169704	−	0.0233578i
$704$	1.93032e7	+	1.40246e7i	1.46791	+	1.06650i
$705$	−4.37541e6	+	9.78933e6i	−0.331547	+	0.741788i
$706$	5.59813e6	−	4.06728e6i	0.422699	−	0.307109i
$707$		−	4.61566e6i		−	0.347284i
$708$	−82809.4	−	113977.i	−0.00620864	−	0.00854546i
$709$	7.57471e6	+	2.33126e7i	0.565914	+	1.74170i	0.665221	+	0.746647i	$0.268337\pi$
$709$	7.57471e6	+	2.33126e7i	0.565914	+	1.74170i	−0.0993071	+	0.995057i	$0.531663\pi$
$710$	1.78007e6	−	1.67046e7i	0.132523	−	1.24363i
$711$	−1.02386e6	+	3.15111e6i	−0.0759567	+	0.233771i
$712$	−2.42986e7	+	7.89509e6i	−1.79631	+	0.583656i
$713$	7.40986e6	−	2.40761e6i	0.545866	−	0.177363i
$714$	2.15424e6	−	6.63006e6i	0.158142	−	0.486712i
$715$	2.57773e7	−	2.85458e7i	1.88570	−	2.08822i
$716$	243593.	+	749704.i	0.0177576	+	0.0546521i
$717$	6.63987e6	+	9.13900e6i	0.482350	+	0.663897i
$718$		−	2.11017e7i		−	1.52759i
$719$	−2.14645e6	+	1.55949e6i	−0.154845	+	0.112502i	−0.662510	−	0.749053i	$-0.730509\pi$
$719$	−2.14645e6	+	1.55949e6i	−0.154845	+	0.112502i	0.507665	+	0.861555i	$0.330509\pi$
$720$	4.25470e6	+	453388.i	0.305871	+	0.0325941i
$721$	8.29264e6	+	6.02496e6i	0.594094	+	0.431634i
$722$	−6.87723e6	+	9.46570e6i	−0.490988	+	0.675787i
$723$	8.02853e6	+	2.60863e6i	0.571203	+	0.185595i
$724$	176203.			0.0124930
$725$	−3.57444e6	+	6.15011e6i	−0.252559	+	0.434548i
$726$	−1.51894e7			−1.06955
$727$	−2.14918e7	−	6.98310e6i	−1.50812	−	0.490018i	−0.565746	−	0.824579i	$-0.691412\pi$
$727$	−2.14918e7	−	6.98310e6i	−1.50812	−	0.490018i	−0.942374	+	0.334561i	$0.891412\pi$
$728$	−1.33383e7	+	1.83587e7i	−0.932768	+	1.28384i
$729$	429945.	+	312373.i	0.0299636	+	0.0217698i
$730$	2.69310e6	+	1.27604e7i	0.187045	+	0.886255i
$731$	−9.55417e6	+	6.94151e6i	−0.661302	+	0.480464i
$732$			118884.i			0.00820062i
$733$	−6.60962e6	−	9.09737e6i	−0.454377	−	0.625397i	0.518953	−	0.854802i	$-0.326322\pi$
$733$	−6.60962e6	−	9.09737e6i	−0.454377	−	0.625397i	−0.973331	+	0.229406i	$0.926322\pi$
$734$	−692600.	−	2.13160e6i	−0.0474507	−	0.146038i
$735$	−1.05981e6	+	223673.i	−0.0723618	+	0.0152720i
$736$	−329459.	+	1.01397e6i	−0.0224185	+	0.0689971i
$737$	−9.84397e6	+	3.19850e6i	−0.667577	+	0.216909i
$738$	2.35282e6	−	764477.i	0.159018	−	0.0516682i
$739$	−4.27203e6	+	1.31480e7i	−0.287755	+	0.885620i	0.697804	+	0.716289i	$0.254161\pi$
$739$	−4.27203e6	+	1.31480e7i	−0.287755	+	0.885620i	−0.985559	+	0.169331i	$0.945839\pi$
$740$	42372.8	+	73636.7i	0.00284451	+	0.00494328i
$741$	1.59973e6	+	4.92345e6i	0.107029	+	0.329401i
$742$	−9.38037e6	−	1.29110e7i	−0.625475	−	0.860893i
$743$		−	5.06950e6i		−	0.336894i	−0.985711	−	0.168447i	$-0.946125\pi$
$743$		−	5.06950e6i		−	0.336894i	0.985711	−	0.168447i	$-0.0538752\pi$
$744$	−8.28125e6	+	6.01668e6i	−0.548483	+	0.398497i
$745$	−1.87631e7	−	1.69434e7i	−1.23855	−	1.11843i
$746$	1.28151e7	+	9.31070e6i	0.843090	+	0.612541i
$747$	−5.31563e6	+	7.31633e6i	−0.348540	+	0.479725i
$748$	1.76553e6	+	573654.i	0.115377	+	0.0374883i
$749$	3.53039e6			0.229942
$750$	37043.9	−	8.56763e6i	0.00240471	−	0.556170i
$751$	2.41835e7			1.56465			0.782327	−	0.622868i	$-0.214032\pi$
$751$	2.41835e7			1.56465			0.782327	+	0.622868i	$0.214032\pi$
$752$	−1.91537e7	−	6.22340e6i	−1.23511	−	0.401313i
$753$	9.01362e6	−	1.24062e7i	0.579311	−	0.797353i
$754$	−1.00633e7	−	7.31142e6i	−0.644633	−	0.468353i
$755$	−1.23860e7	−	1.11848e7i	−0.790796	−	0.714103i
$756$	−164510.	+	119524.i	−0.0104686	+	0.00760587i
$757$			1.69503e7i			1.07507i	0.843241	+	0.537536i	$0.180645\pi$
$757$			1.69503e7i			1.07507i	−0.843241	+	0.537536i	$0.819355\pi$
$758$	−2.75763e6	−	3.79555e6i	−0.174326	−	0.239939i
$759$	−2.44358e6	−	7.52057e6i	−0.153965	−	0.473856i
$760$	2.98962e6	+	5.19546e6i	0.187751	+	0.326280i
$761$	−2.11236e6	+	6.50118e6i	−0.132223	+	0.406940i	−0.995148	−	0.0983921i	$-0.968630\pi$
$761$	−2.11236e6	+	6.50118e6i	−0.132223	+	0.406940i	0.862925	+	0.505332i	$0.168630\pi$
$762$	1.55749e7	−	5.06060e6i	0.971714	−	0.315729i
$763$	2.25795e7	−	7.33651e6i	1.40411	−	0.456224i
$764$	506288.	−	1.55819e6i	0.0313808	−	0.0965802i
$765$	5.20222e6	−	1.09793e6i	0.321392	−	0.0678300i
$766$	5.56628e6	+	1.71312e7i	0.342762	+	1.05491i
$767$	−4.00422e6	−	5.51134e6i	−0.245771	−	0.338274i
$768$		−	2.02782e6i		−	0.124058i
$769$	−6.40860e6	+	4.65612e6i	−0.390794	+	0.283928i	−0.765781	−	0.643102i	$-0.777647\pi$
$769$	−6.40860e6	+	4.65612e6i	−0.390794	+	0.283928i	0.374987	+	0.927030i	$0.377647\pi$
$770$	−5.22486e6	−	2.47564e7i	−0.317576	−	1.50474i
$771$	−99148.6	−	72035.7i	−0.00600690	−	0.00436427i
$772$	888976.	−	1.22357e6i	0.0536842	−	0.0738900i
$773$	−9.62615e6	−	3.12773e6i	−0.579434	−	0.188269i	0.00461308	−	0.999989i	$-0.498532\pi$
$773$	−9.62615e6	−	3.12773e6i	−0.579434	−	0.188269i	−0.584047	+	0.811720i	$0.698532\pi$
$774$	−4.43942e6			−0.266363
$775$	1.26814e7	+	1.41660e7i	0.758426	+	0.847215i
$776$	2.25362e7			1.34347
$777$	683406.	+	222052.i	0.0406094	+	0.0131948i
$778$	−4.84739e6	+	6.67186e6i	−0.287117	+	0.395183i
$779$	2.60088e6	+	1.88965e6i	0.153559	+	0.111567i
$780$	−1.15598e6	−	123183.i	−0.0680323	−	0.00724963i
$781$	3.06106e7	−	2.22399e7i	1.79575	−	1.30469i
$782$		−	8.19393e6i		−	0.479154i
$783$	−975379.	−	1.34249e6i	−0.0568551	−	0.0782543i
$784$	−628661.	−	1.93482e6i	−0.0365280	−	0.112422i
$785$	6.60526e6	−	7.31466e6i	0.382575	−	0.423663i
$786$	1.93572e6	−	5.95752e6i	0.111760	−	0.343961i
$787$	−5.54776e6	+	1.80258e6i	−0.319287	+	0.103743i	−0.464276	−	0.885691i	$-0.653685\pi$
$787$	−5.54776e6	+	1.80258e6i	−0.319287	+	0.103743i	0.144989	+	0.989433i	$0.453685\pi$
$788$	−2.29578e6	+	745945.i	−0.131709	+	0.0427948i
$789$	3.01664e6	−	9.28425e6i	0.172516	−	0.530951i
$790$	−1.32036e6	+	1.23906e7i	−0.0752707	+	0.706358i
$791$	−4.18897e6	−	1.28923e7i	−0.238049	−	0.732639i
$792$	6.10657e6	+	8.40498e6i	0.345927	+	0.476128i
$793$			5.74861e6i			0.324624i
$794$	4.48426e6	−	3.25800e6i	0.252429	−	0.183400i
$795$	4.96659e6	−	1.11120e7i	0.278702	−	0.623555i
$796$	1.16647e6	+	847492.i	0.0652517	+	0.0474081i
$797$	2.73112e6	−	3.75906e6i	0.152298	−	0.209620i	−0.726050	−	0.687642i	$-0.758646\pi$
$797$	2.73112e6	−	3.75906e6i	0.152298	−	0.209620i	0.878348	+	0.478021i	$0.158646\pi$
$798$	3.23883e6	+	1.05236e6i	0.180045	+	0.0585001i
$799$	−2.50251e7			−1.38678
$800$	−2.58827e6	+	264498.i	−0.142983	+	0.0146116i
$801$	−1.10704e7			−0.609654
$802$	9.28648e6	+	3.01736e6i	0.509818	+	0.165650i
$803$	−1.72653e7	+	2.37636e7i	−0.944898	+	1.30054i
$804$	253100.	+	183888.i	0.0138087	+	0.0100326i
$805$	7.51103e6	−	4.32207e6i	0.408516	−	0.235073i
$806$	−2.68976e7	+	1.95423e7i	−1.45840	+	1.05959i
$807$		−	2.16360e6i		−	0.116948i
$808$	4.18955e6	+	5.76643e6i	0.225756	+	0.310727i
$809$	244740.	+	753232.i	0.0131472	+	0.0404629i	0.957415	−	0.288716i	$-0.0932282\pi$
$809$	244740.	+	753232.i	0.0131472	+	0.0404629i	−0.944268	+	0.329179i	$0.893228\pi$
$810$	1.82471e6	+	815565.i	0.0977194	+	0.0436763i
$811$	1.17291e6	−	3.60985e6i	0.0626199	−	0.192724i	−0.914852	−	0.403789i	$-0.867693\pi$
$811$	1.17291e6	−	3.60985e6i	0.0626199	−	0.192724i	0.977472	+	0.211065i	$0.0676930\pi$
$812$	603866.	−	196208.i	0.0321404	−	0.0104430i
$813$	−4.83639e6	+	1.57144e6i	−0.256623	+	0.0833818i
$814$	762042.	−	2.34532e6i	0.0403105	−	0.124063i
$815$	−2.26844e7	−	1.01390e7i	−1.19628	−	0.534687i
$816$	3.08587e6	+	9.49733e6i	0.162238	+	0.499317i
$817$	−3.39098e6	−	4.66728e6i	−0.177734	−	0.244629i
$818$		−	3.16528e7i		−	1.65397i
$819$	−7.95483e6	+	5.77952e6i	−0.414401	+	0.301080i
$820$	−625740.	+	360070.i	−0.0324982	+	0.0187004i
$821$	−1.09146e7	−	7.92990e6i	−0.565130	−	0.410591i	0.268203	−	0.963362i	$-0.413570\pi$
$821$	−1.09146e7	−	7.92990e6i	−0.565130	−	0.410591i	−0.833333	+	0.552771i	$0.813570\pi$
$822$	−5.67383e6	+	7.80936e6i	−0.292885	+	0.403121i
$823$	1.47266e6	+	478498.i	0.0757887	+	0.0246252i	0.346666	−	0.937989i	$-0.387314\pi$
$823$	1.47266e6	+	478498.i	0.0757887	+	0.0246252i	−0.270877	+	0.962614i	$0.587314\pi$
$824$	−1.58289e7			−0.812143
$825$	1.43777e7	−	1.28709e7i	0.735451	−	0.658375i
$826$	−4.48144e6			−0.228543
$827$	3.93979e6	+	1.28011e6i	0.200313	+	0.0650856i	0.407455	−	0.913225i	$-0.366416\pi$
$827$	3.93979e6	+	1.28011e6i	0.200313	+	0.0650856i	−0.207142	+	0.978311i	$0.566416\pi$
$828$	−140486.	+	193363.i	−0.00712129	+	0.00980161i
$829$	−9.96688e6	−	7.24136e6i	−0.503701	−	0.365960i	0.306728	−	0.951797i	$-0.400766\pi$
$829$	−9.96688e6	−	7.24136e6i	−0.503701	−	0.365960i	−0.810429	+	0.585837i	$0.800766\pi$
$830$	−1.38784e7	+	3.10509e7i	−0.699269	+	1.56451i
$831$	−3.52833e6	+	2.56348e6i	−0.177242	+	0.128774i
$832$		−	3.48724e7i		−	1.74652i
$833$	−1.48588e6	−	2.04514e6i	−0.0741944	−	0.102120i
$834$	1.32679e6	+	4.08345e6i	0.0660523	+	0.203288i
$835$	1.65309e6	−	1.55130e7i	0.0820501	−	0.769978i
$836$	−280234.	+	862472.i	−0.0138677	+	0.0426805i
$837$	−4.21827e6	+	1.37060e6i	−0.208123	+	0.0676234i
$838$	−581564.	+	188962.i	−0.0286080	+	0.00929531i
$839$	−275220.	+	847041.i	−0.0134982	+	0.0415432i	−0.957579	−	0.288172i	$-0.906953\pi$
$839$	−275220.	+	847041.i	−0.0134982	+	0.0415432i	0.944081	+	0.329715i	$0.106953\pi$
$840$	−7.63040e6	+	8.44989e6i	−0.373120	+	0.413193i
$841$	−4.73712e6	−	1.45794e7i	−0.230954	−	0.710802i
$842$	5.41893e6	+	7.45851e6i	0.263411	+	0.362553i
$843$		−	7.41013e6i		−	0.359134i
$844$	372703.	−	270785.i	0.0180097	−	0.0130848i
$845$	−3.52582e7	−	3.75717e6i	−1.69871	−	0.181017i
$846$	−7.61069e6	−	5.52949e6i	−0.365593	−	0.265619i
$847$	2.20368e7	−	3.03311e7i	1.05546	−	1.45271i
$848$	2.17416e7	+	7.06428e6i	1.03825	+	0.337348i
$849$	−2.37084e6			−0.112884
$850$	1.82904e7	−	8.08034e6i	0.868314	−	0.383603i
$851$	844605.			0.0399788
$852$	−1.08766e6	−	353402.i	−0.0513326	−	0.0166790i
$853$	2.74620e6	−	3.77982e6i	0.129229	−	0.177868i	−0.739499	−	0.673157i	$-0.764938\pi$
$853$	2.74620e6	−	3.77982e6i	0.129229	−	0.177868i	0.868728	+	0.495289i	$0.164938\pi$
$854$	3.05942e6	+	2.22280e6i	0.143547	+	0.104293i
$855$	536347.	+	2.54132e6i	0.0250917	+	0.118890i
$856$	−4.41058e6	+	3.20447e6i	−0.205736	+	0.149476i
$857$		−	2.08225e7i		−	0.968459i	−0.874941	−	0.484229i	$-0.839100\pi$
$857$		−	2.08225e7i		−	0.968459i	0.874941	−	0.484229i	$-0.160900\pi$
$858$	1.98343e7	+	2.72995e7i	0.919809	+	1.26601i
$859$	1.66077e6	+	5.11134e6i	0.0767941	+	0.236348i	0.982083	−	0.188448i	$-0.0603458\pi$
$859$	1.66077e6	+	5.11134e6i	0.0767941	+	0.236348i	−0.905289	+	0.424796i	$0.860346\pi$
$860$	1.26760e6	−	267528.i	0.0584436	−	0.0123346i
$861$	−1.88692e6	+	5.80736e6i	−0.0867454	+	0.266975i
$862$	−2.99964e6	+	974644.i	−0.137500	+	0.0446764i
$863$	1.58281e7	−	5.14285e6i	0.723438	−	0.235059i	0.0759248	−	0.997114i	$-0.475809\pi$
$863$	1.58281e7	−	5.14285e6i	0.723438	−	0.235059i	0.647513	+	0.762054i	$0.275809\pi$
$864$	187554.	−	577231.i	0.00854755	−	0.0263067i
$865$	1.70678e7	+	2.96609e7i	0.775599	+	1.34786i
$866$	1.00120e7	+	3.08136e7i	0.453654	+	1.39620i
$867$	−217498.	−	299360.i	−0.00982670	−	0.0135253i
$868$		−	1.69710e6i		−	0.0764555i
$869$	−2.27054e7	+	1.64964e7i	−1.01995	+	0.741038i
$870$	−4.63182e6	−	4.18261e6i	−0.207469	−	0.187348i
$871$	1.22386e7	+	8.89185e6i	0.546620	+	0.397143i
$872$	−2.15497e7	+	2.96606e7i	−0.959733	+	1.32096i
$873$	9.28704e6	+	3.01754e6i	0.412422	+	0.134004i
$874$	4.00279e6			0.177249
$875$	1.70546e7	+	1.25039e7i	0.753046	+	0.552111i
$876$	887823.			0.0390900
$877$	3.40846e7	+	1.10748e7i	1.49644	+	0.486222i	0.938977	−	0.343980i	$-0.111775\pi$
$877$	3.40846e7	+	1.10748e7i	1.49644	+	0.486222i	0.557462	+	0.830203i	$0.311775\pi$
$878$	1.14872e7	−	1.58108e7i	0.502897	−	0.692178i
$879$	8.05125e6	+	5.84957e6i	0.351472	+	0.255359i
$880$	2.68995e7	+	2.42907e7i	1.17095	+	1.05739i
$881$	1.43712e7	−	1.04413e7i	0.623810	−	0.453225i	−0.230440	−	0.973087i	$-0.574017\pi$
$881$	1.43712e7	−	1.04413e7i	0.623810	−	0.453225i	0.854250	+	0.519862i	$0.174017\pi$
$882$		−	950288.i		−	0.0411324i
$883$	−1.50889e7	−	2.07681e7i	−0.651262	−	0.896385i	0.347891	−	0.937535i	$-0.386898\pi$
$883$	−1.50889e7	−	2.07681e7i	−0.651262	−	0.896385i	−0.999153	+	0.0411496i	$0.986898\pi$
$884$	−838417.	−	2.58038e6i	−0.0360852	−	0.111059i
$885$	−1.70468e6	−	2.96244e6i	−0.0731618	−	0.127143i
$886$	774927.	−	2.38498e6i	0.0331647	−	0.102071i
$887$	7.13888e6	−	2.31956e6i	0.304664	−	0.0989913i	−0.152695	−	0.988273i	$-0.548795\pi$
$887$	7.13888e6	−	2.31956e6i	0.304664	−	0.0989913i	0.457359	+	0.889282i	$0.348795\pi$
$888$	−1.05534e6	+	342902.i	−0.0449120	+	0.0145928i
$889$	−1.24908e7	+	3.84429e7i	−0.530075	+	1.63140i
$890$	−4.07370e7	+	8.59757e6i	−1.72391	+	0.363832i
$891$	1.39108e6	+	4.28130e6i	0.0587026	+	0.180668i
$892$	1.58820e6	+	2.18598e6i	0.0668335	+	0.0919885i
$893$		−	1.22249e7i		−	0.513001i
$894$	1.79439e7	−	1.30370e7i	0.750885	−	0.545550i
$895$	3.94916e6	+	1.87119e7i	0.164796	+	0.780837i
$896$	−1.59500e7	−	1.15883e7i	−0.663727	−	0.482226i
$897$	−6.79318e6	+	9.35001e6i	−0.281898	+	0.387999i
$898$	2.65955e6	+	864140.i	0.110057	+	0.0357596i
$899$	1.38493e7			0.571517
$900$	−570163.	−	122911.i	−0.0234635	−	0.00505805i
$901$	2.84064e7			1.16575
$902$	1.99298e7	+	6.47558e6i	0.815616	+	0.265010i
$903$	6.44072e6	−	8.86489e6i	0.262854	−	0.361788i
$904$	1.69355e7	+	1.23044e7i	0.689250	+	0.500770i
$905$	4.25069e6	+	452961.i	0.172520	+	0.0183840i
$906$	1.18453e7	−	8.60610e6i	0.479430	−	0.348326i
$907$			1.52536e7i			0.615680i	0.951438	+	0.307840i	$0.0996061\pi$
$907$			1.52536e7i			0.615680i	−0.951438	+	0.307840i	$0.900394\pi$
$908$	244418.	+	336412.i	0.00983825	+	0.0135412i
$909$	954380.	+	2.93728e6i	0.0383100	+	0.117906i
$910$	−2.47837e7	+	2.74454e7i	−0.992115	+	1.09867i
$911$	−2.58809e6	+	7.96531e6i	−0.103320	+	0.317985i	−0.989332	−	0.145676i	$-0.953464\pi$
$911$	−2.58809e6	+	7.96531e6i	−0.103320	+	0.317985i	0.886013	+	0.463661i	$0.153464\pi$
$912$	−4.63951e6	+	1.50747e6i	−0.184708	+	0.0600152i
$913$	−7.28544e7	+	2.36718e7i	−2.89254	+	0.939843i
$914$	−2.82007e6	+	8.67930e6i	−0.111659	+	0.343652i
$915$	−305612.	+	2.86794e6i	−0.0120675	+	0.113245i
$916$	572596.	+	1.76227e6i	0.0225481	+	0.0693959i
$917$	9.08799e6	+	1.25085e7i	0.356898	+	0.491228i
$918$			4.66462e6i			0.182688i
$919$	8.66372e6	−	6.29456e6i	0.338389	−	0.245854i	−0.405593	−	0.914054i	$-0.632935\pi$
$919$	8.66372e6	−	6.29456e6i	0.338389	−	0.245854i	0.743982	+	0.668200i	$0.232935\pi$
$920$	−5.46059e6	+	1.22173e7i	−0.212701	+	0.475888i
$921$	9.13625e6	+	6.63788e6i	0.354911	+	0.257858i
$922$	2.27336e7	−	3.12901e7i	0.880726	−	1.21221i
$923$	−5.25934e7	−	1.70886e7i	−2.03201	−	0.660241i
$924$	−1.72246e6			−0.0663695
$925$	832897.	+	1.88532e6i	0.0320064	+	0.0724489i
$926$	3.97321e7			1.52270
$927$	−6.52300e6	−	2.11945e6i	−0.249315	−	0.0810072i
$928$	−1.11394e6	+	1.53321e6i	−0.0424612	+	0.0584428i
$929$	−7.25378e6	−	5.27018e6i	−0.275756	−	0.200349i	0.441308	−	0.897356i	$-0.354515\pi$
$929$	−7.25378e6	−	5.27018e6i	−0.275756	−	0.200349i	−0.717064	+	0.697007i	$0.754515\pi$
$930$	−1.44580e7	+	8.31954e6i	−0.548150	+	0.315422i
$931$	999064.	−	725862.i	0.0377763	−	0.0274461i
$932$		−	1.79363e6i		−	0.0676385i
$933$	7.07431e6	+	9.73695e6i	0.266060	+	0.366200i
$934$	1.55775e7	+	4.79426e7i	0.584293	+	1.79827i
$935$	4.11165e7	+	1.83773e7i	1.53811	+	0.687469i
$936$	4.69214e6	−	1.44409e7i	0.175058	−	0.538772i
$937$	−1.18692e7	+	3.85652e6i	−0.441643	+	0.143498i	−0.521393	−	0.853316i	$-0.674588\pi$
$937$	−1.18692e7	+	3.85652e6i	−0.441643	+	0.143498i	0.0797508	+	0.996815i	$0.474588\pi$
$938$	9.46451e6	−	3.07521e6i	0.351230	−	0.114121i
$939$	7.93936e6	−	2.44349e7i	0.293847	−	0.904369i
$940$	2.50633e6	+	1.12022e6i	0.0925163	+	0.0413508i
$941$	−6.05784e6	−	1.86441e7i	−0.223020	−	0.686384i	−0.998487	−	0.0549960i	$-0.982485\pi$
$941$	−6.05784e6	−	1.86441e7i	−0.223020	−	0.686384i	0.775467	−	0.631388i	$-0.217515\pi$
$942$	5.08240e6	+	6.99532e6i	0.186613	+	0.256850i
$943$			7.17717e6i			0.262829i
$944$	5.19350e6	−	3.77330e6i	0.189684	−	0.137813i
$945$	−4.27586e6	+	2.46046e6i	−0.155756	+	0.0896266i
$946$	−3.04227e7	−	2.21034e7i	−1.10527	−	0.803028i
$947$	1.54221e7	−	2.12267e7i	0.558816	−	0.769144i	−0.432360	−	0.901701i	$-0.642319\pi$
$947$	1.54221e7	−	2.12267e7i	0.558816	−	0.769144i	0.991175	+	0.132557i	$0.0423189\pi$
$948$	806768.	+	262135.i	0.0291560	+	0.00947336i
$949$	4.29304e7			1.54739
$950$	3.94730e6	+	8.93501e6i	0.141903	+	0.321208i
$951$	−1.08560e7			−0.389239
$952$	−2.52710e7	−	8.21105e6i	−0.903712	−	0.293634i
$953$	−2.06041e6	+	2.83591e6i	−0.0734887	+	0.101149i	−0.844179	−	0.536061i	$-0.819912\pi$
$953$	−2.06041e6	+	2.83591e6i	−0.0734887	+	0.101149i	0.770690	+	0.637210i	$0.219912\pi$
$954$	8.63901e6	+	6.27661e6i	0.307322	+	0.223282i
$955$	1.62192e7	−	3.62880e7i	0.575467	−	1.28752i
$956$	2.33983e6	−	1.69998e6i	0.0828016	−	0.0601589i
$957$		−	1.40562e7i		−	0.496122i
$958$	−1.32960e7	−	1.83004e7i	−0.468066	−	0.644238i
$959$	−7.36258e6	−	2.26597e7i	−0.258514	−	0.795623i
$960$	1.85391e6	−	1.73976e7i	0.0649250	−	0.609272i
$961$	2.59199e6	−	7.97733e6i	0.0905368	−	0.278644i
$962$	−3.42778e6	+	1.11375e6i	−0.119419	+	0.0388017i
$963$	−2.24664e6	+	729979.i	−0.0780672	+	0.0253656i
$964$	667878.	−	2.05552e6i	0.0231475	−	0.0712408i
$965$	2.45909e7	−	2.72319e7i	0.850071	−	0.941368i
$966$	2.34939e6	+	7.23068e6i	0.0810050	+	0.249308i
$967$	−1.48384e7	−	2.04233e7i	−0.510293	−	0.702358i	0.473676	−	0.880699i	$-0.342927\pi$
$967$	−1.48384e7	−	2.04233e7i	−0.510293	−	0.702358i	−0.983969	+	0.178341i	$0.942927\pi$
$968$			5.78957e7i			1.98590i
$969$	−4.90404e6	+	3.56299e6i	−0.167782	+	0.121901i
$970$	3.65179e7	+	3.89141e6i	1.24617	+	0.132794i
$971$	3.96708e7	+	2.88226e7i	1.35028	+	0.981035i	0.998998	+	0.0447645i	$0.0142537\pi$
$971$	3.96708e7	+	2.88226e7i	1.35028	+	0.981035i	0.351281	+	0.936270i	$0.385746\pi$
$972$	79975.8	−	110077.i	0.00271515	−	0.00373708i
$973$	−1.00790e7	−	3.27486e6i	−0.341299	−	0.110895i
$974$	301718.			0.0101907
$975$	−2.75701e7	−	5.94331e6i	−0.928808	−	0.200224i
$976$	−5.41708e6			−0.182029
$977$	−876663.	−	284845.i	−0.0293830	−	0.00954711i	0.294289	−	0.955717i	$-0.404917\pi$
$977$	−876663.	−	284845.i	−0.0293830	−	0.00954711i	−0.323672	+	0.946169i	$0.604917\pi$
$978$	1.28133e7	−	1.76360e7i	0.428364	−	0.589593i
$979$	−7.58641e7	−	5.51185e7i	−2.52976	−	1.83798i
$980$	57266.3	+	271339.i	0.00190473	+	0.00902500i
$981$	−1.28520e7	+	9.33752e6i	−0.426381	+	0.309784i
$982$		−	263280.i		−	0.00871242i
$983$	−3.47717e6	−	4.78591e6i	−0.114774	−	0.157972i	0.747765	−	0.663963i	$-0.231127\pi$
$983$	−3.47717e6	−	4.78591e6i	−0.114774	−	0.157972i	−0.862539	+	0.505991i	$0.831127\pi$
$984$	−2.91387e6	−	8.96796e6i	−0.0959361	−	0.295261i
$985$	−5.73006e7	+	1.20933e7i	−1.88178	+	0.397150i
$986$	4.50089e6	−	1.38523e7i	0.147437	−	0.453764i
$987$	2.20832e7	−	7.17528e6i	0.721556	−	0.234448i
$988$	1.26053e6	−	409573.i	0.0410830	−	0.0133487i
$989$	3.97996e6	−	1.22491e7i	0.129386	−	0.398210i
$990$	8.44384e6	+	1.46740e7i	0.273812	+	0.475838i
$991$	−1.02945e7	−	3.16834e7i	−0.332984	−	1.02482i	−0.967707	−	0.252079i	$-0.918886\pi$
$991$	−1.02945e7	−	3.16834e7i	−0.332984	−	1.02482i	0.634723	−	0.772740i	$-0.281114\pi$
$992$	2.97739e6	+	4.09802e6i	0.0960630	+	0.132219i
$993$			4.84070e6i			0.155788i
$994$	−2.94307e7	+	2.13827e7i	−0.944788	+	0.686429i
$995$	2.59611e7	+	2.34433e7i	0.831315	+	0.750692i
$996$	1.87318e6	+	1.36094e6i	0.0598315	+	0.0434702i
$997$	−6.94312e6	+	9.55639e6i	−0.221216	+	0.304478i	−0.905172	−	0.425045i	$-0.860258\pi$
$997$	−6.94312e6	+	9.55639e6i	−0.221216	+	0.304478i	0.683956	+	0.729523i	$0.260258\pi$
$998$	9.84085e6	+	3.19749e6i	0.312757	+	0.101621i
$999$	−480815.			−0.0152428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.6.i.a.4.18	✓	96
25.19	even	10	inner	75.6.i.a.19.18	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.6.i.a.4.18	✓	96	1.1	even	1	trivial
75.6.i.a.19.18	yes	96	25.19	even	10	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	75.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(5.18267 + 1.68395i) q^{2} +(5.29007 - 7.28115i) q^{3} +(-1.86417 - 1.35440i) q^{4} +(-41.4891 - 37.4654i) q^{5} +(39.6778 - 28.8276i) q^{6} +121.054i q^{7} +(-109.879 - 151.235i) q^{8} +(-25.0304 - 77.0356i) q^{9} +O(q^{10})\)	\(q+(5.18267 + 1.68395i) q^{2} +(5.29007 - 7.28115i) q^{3} +(-1.86417 - 1.35440i) q^{4} +(-41.4891 - 37.4654i) q^{5} +(39.6778 - 28.8276i) q^{6} +121.054i q^{7} +(-109.879 - 151.235i) q^{8} +(-25.0304 - 77.0356i) q^{9} +(-151.934 - 264.036i) q^{10} +(212.022 - 652.537i) q^{11} +(-19.7232 + 6.40844i) q^{12} +(-953.707 + 309.878i) q^{13} +(-203.849 + 627.384i) q^{14} +(-492.271 + 103.894i) q^{15} +(-292.007 - 898.705i) q^{16} +(-690.177 - 949.947i) q^{17} -441.400i q^{18} +(464.056 - 337.156i) q^{19} +(26.5997 + 126.035i) q^{20} +(881.414 + 640.385i) q^{21} +(2197.68 - 3024.85i) q^{22} +(1217.89 + 395.718i) q^{23} -1682.43 q^{24} +(317.692 + 3108.81i) q^{25} -5464.57 q^{26} +(-693.320 - 225.273i) q^{27} +(163.955 - 225.665i) q^{28} +(1841.56 + 1337.97i) q^{29} +(-2726.23 - 290.512i) q^{30} +(4922.19 - 3576.18i) q^{31} +832.561i q^{32} +(-3629.61 - 4995.73i) q^{33} +(-1977.29 - 6085.48i) q^{34} +(4535.34 - 5022.43i) q^{35} +(-57.6760 + 177.508i) q^{36} +(627.273 - 203.813i) q^{37} +(2972.80 - 965.922i) q^{38} +(-2788.90 + 8583.36i) q^{39} +(-1107.31 + 10391.3i) q^{40} +(1731.94 + 5330.36i) q^{41} +(3489.70 + 4803.16i) q^{42} -10057.6i q^{43} +(-1279.04 + 929.277i) q^{44} +(-1847.68 + 4133.91i) q^{45} +(5645.57 + 4101.75i) q^{46} +(12527.2 - 17242.2i) q^{47} +(-8088.35 - 2628.06i) q^{48} +2152.90 q^{49} +(-3588.59 + 16646.9i) q^{50} -10567.8 q^{51} +(2197.57 + 714.033i) q^{52} +(-14219.8 + 19571.8i) q^{53} +(-3213.90 - 2335.04i) q^{54} +(-33244.2 + 19129.7i) q^{55} +(18307.6 - 13301.3i) q^{56} -5162.44i q^{57} +(7291.10 + 10035.3i) q^{58} +(2099.29 + 6460.96i) q^{59} +(1058.39 + 473.055i) q^{60} +(1771.48 - 5452.06i) q^{61} +(31532.2 - 10245.4i) q^{62} +(9325.48 - 3030.03i) q^{63} +(-10746.2 + 33073.5i) q^{64} +(51178.1 + 22874.4i) q^{65} +(-10398.5 - 32003.3i) q^{66} +(-8867.14 - 12204.6i) q^{67} +2705.63i q^{68} +(9324.02 - 6774.30i) q^{69} +(31962.7 - 18392.3i) q^{70} +(44614.3 + 32414.2i) q^{71} +(-8900.18 + 12250.0i) q^{72} +(-40715.8 - 13229.4i) q^{73} +3594.16 q^{74} +(24316.3 + 14132.6i) q^{75} -1321.72 q^{76} +(78992.3 + 25666.2i) q^{77} +(-28907.9 + 39788.4i) q^{78} +(-33092.5 - 24043.1i) q^{79} +(-21555.2 + 48226.6i) q^{80} +(-5307.96 + 3856.46i) q^{81} +30542.0i q^{82} +(-65625.0 - 90325.1i) q^{83} +(-775.768 - 2387.57i) q^{84} +(-6955.29 + 65270.2i) q^{85} +(16936.5 - 52125.1i) q^{86} +(19483.9 - 6330.71i) q^{87} +(-121983. + 39634.8i) q^{88} +(42234.0 - 129983. i) q^{89} +(-16537.2 + 18313.3i) q^{90} +(-37512.0 - 115450. i) q^{91} +(-1734.40 - 2387.20i) q^{92} -54757.4i q^{93} +(93959.2 - 68265.3i) q^{94} +(-31884.9 - 3397.71i) q^{95} +(6062.00 + 4404.30i) q^{96} +(-70860.5 + 97531.2i) q^{97} +(11157.8 + 3625.37i) q^{98} -55575.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 352 q^{4} - 120 q^{5} + 72 q^{6} - 1230 q^{8} + 1944 q^{9}+O(q^{10}) \) 96 * q + 352 * q^4 - 120 * q^5 + 72 * q^6 - 1230 * q^8 + 1944 * q^9	\( 96 q + 352 q^{4} - 120 q^{5} + 72 q^{6} - 1230 q^{8} + 1944 q^{9} - 890 q^{10} + 474 q^{11} + 2748 q^{14} - 780 q^{16} + 1910 q^{17} - 5522 q^{19} - 19220 q^{20} + 1764 q^{21} + 6170 q^{22} + 21980 q^{23} + 13824 q^{24} + 11790 q^{25} - 11028 q^{26} - 9120 q^{28} - 24304 q^{29} - 22860 q^{30} + 1566 q^{31} - 3690 q^{33} + 24224 q^{34} + 10250 q^{35} - 28512 q^{36} + 16490 q^{37} + 68730 q^{38} - 12168 q^{39} - 106480 q^{40} + 26126 q^{41} - 43560 q^{42} - 10814 q^{44} + 9720 q^{45} + 22956 q^{46} + 66440 q^{47} - 123480 q^{49} + 329620 q^{50} - 83232 q^{51} + 251240 q^{52} - 91690 q^{53} - 5832 q^{54} - 123470 q^{55} + 116100 q^{56} - 483290 q^{58} - 97428 q^{59} + 119610 q^{60} + 91560 q^{61} - 138410 q^{62} + 47790 q^{63} + 127738 q^{64} - 235130 q^{65} + 118296 q^{66} + 163960 q^{67} - 73332 q^{69} + 209520 q^{70} + 155672 q^{71} - 99630 q^{72} + 18980 q^{73} + 100588 q^{74} - 464032 q^{76} + 119560 q^{77} - 112020 q^{79} - 66300 q^{80} - 157464 q^{81} + 148010 q^{83} - 61128 q^{84} + 346980 q^{85} - 295956 q^{86} - 371160 q^{87} - 189090 q^{88} - 494082 q^{89} - 144180 q^{90} - 79494 q^{91} + 599810 q^{92} + 234622 q^{94} + 605800 q^{95} + 210744 q^{96} + 372140 q^{97} + 891060 q^{98} + 25596 q^{99}+O(q^{100}) \) 96 * q + 352 * q^4 - 120 * q^5 + 72 * q^6 - 1230 * q^8 + 1944 * q^9 - 890 * q^10 + 474 * q^11 + 2748 * q^14 - 780 * q^16 + 1910 * q^17 - 5522 * q^19 - 19220 * q^20 + 1764 * q^21 + 6170 * q^22 + 21980 * q^23 + 13824 * q^24 + 11790 * q^25 - 11028 * q^26 - 9120 * q^28 - 24304 * q^29 - 22860 * q^30 + 1566 * q^31 - 3690 * q^33 + 24224 * q^34 + 10250 * q^35 - 28512 * q^36 + 16490 * q^37 + 68730 * q^38 - 12168 * q^39 - 106480 * q^40 + 26126 * q^41 - 43560 * q^42 - 10814 * q^44 + 9720 * q^45 + 22956 * q^46 + 66440 * q^47 - 123480 * q^49 + 329620 * q^50 - 83232 * q^51 + 251240 * q^52 - 91690 * q^53 - 5832 * q^54 - 123470 * q^55 + 116100 * q^56 - 483290 * q^58 - 97428 * q^59 + 119610 * q^60 + 91560 * q^61 - 138410 * q^62 + 47790 * q^63 + 127738 * q^64 - 235130 * q^65 + 118296 * q^66 + 163960 * q^67 - 73332 * q^69 + 209520 * q^70 + 155672 * q^71 - 99630 * q^72 + 18980 * q^73 + 100588 * q^74 - 464032 * q^76 + 119560 * q^77 - 112020 * q^79 - 66300 * q^80 - 157464 * q^81 + 148010 * q^83 - 61128 * q^84 + 346980 * q^85 - 295956 * q^86 - 371160 * q^87 - 189090 * q^88 - 494082 * q^89 - 144180 * q^90 - 79494 * q^91 + 599810 * q^92 + 234622 * q^94 + 605800 * q^95 + 210744 * q^96 + 372140 * q^97 + 891060 * q^98 + 25596 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more