LMFDB - Embedded newform 74.6.h.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(3,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("74.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.h (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.8
Character	$\chi$	$=$	74.3
Dual form			74.6.h.a.25.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.57115 + 3.06418i) q^{2} +(20.6376 - 17.3170i) q^{3} +(-2.77837 - 15.7569i) q^{4} +(-28.8625 + 79.2990i) q^{5} +107.762i q^{6} +(-209.650 - 76.3065i) q^{7} +(55.4256 + 32.0000i) q^{8} +(83.8350 - 475.452i) q^{9} +O(q^{10})$	\(q+(-2.57115 + 3.06418i) q^{2} +(20.6376 - 17.3170i) q^{3} +(-2.77837 - 15.7569i) q^{4} +(-28.8625 + 79.2990i) q^{5} +107.762i q^{6} +(-209.650 - 76.3065i) q^{7} +(55.4256 + 32.0000i) q^{8} +(83.8350 - 475.452i) q^{9} +(-168.776 - 292.329i) q^{10} +(-333.667 + 577.929i) q^{11} +(-330.201 - 277.071i) q^{12} +(-578.886 + 102.073i) q^{13} +(772.859 - 446.211i) q^{14} +(777.567 + 2136.35i) q^{15} +(-240.561 + 87.5572i) q^{16} +(1416.90 + 249.838i) q^{17} +(1241.32 + 1479.34i) q^{18} +(-343.842 - 409.775i) q^{19} +(1329.70 + 234.462i) q^{20} +(-5648.07 + 2055.73i) q^{21} +(-912.968 - 2508.36i) q^{22} +(-2243.78 + 1295.45i) q^{23} +(1697.99 - 299.402i) q^{24} +(-3061.40 - 2568.82i) q^{25} +(1175.63 - 2036.25i) q^{26} +(-3229.97 - 5594.47i) q^{27} +(-619.869 + 3515.45i) q^{28} +(-828.415 - 478.286i) q^{29} +(-8545.40 - 3110.27i) q^{30} -2938.08i q^{31} +(350.229 - 962.245i) q^{32} +(3121.90 + 17705.1i) q^{33} +(-4408.62 + 3699.27i) q^{34} +(12102.1 - 14422.7i) q^{35} -7724.58 q^{36} +(-8070.95 - 2050.31i) q^{37} +2139.69 q^{38} +(-10179.2 + 12131.1i) q^{39} +(-4137.29 + 3471.60i) q^{40} +(1616.38 + 9166.95i) q^{41} +(8222.92 - 22592.3i) q^{42} -2964.85i q^{43} +(10033.4 + 3651.87i) q^{44} +(35283.2 + 20370.7i) q^{45} +(1799.62 - 10206.1i) q^{46} +(-2483.17 - 4300.97i) q^{47} +(-3448.37 + 5972.76i) q^{48} +(25255.7 + 21192.0i) q^{49} +(15742.6 - 2775.85i) q^{50} +(33567.9 - 19380.4i) q^{51} +(3216.72 + 8837.86i) q^{52} +(-17855.4 + 6498.85i) q^{53} +(25447.2 + 4487.03i) q^{54} +(-36198.7 - 43140.0i) q^{55} +(-9178.20 - 10938.1i) q^{56} +(-14192.1 - 2502.45i) q^{57} +(3595.53 - 1308.67i) q^{58} +(-5300.03 - 14561.7i) q^{59} +(31501.9 - 18187.6i) q^{60} +(27819.3 - 4905.30i) q^{61} +(9002.79 + 7554.23i) q^{62} +(-53856.1 + 93281.5i) q^{63} +(2048.00 + 3547.24i) q^{64} +(8613.77 - 48851.1i) q^{65} +(-62278.6 - 35956.6i) q^{66} +(35139.3 + 12789.7i) q^{67} -23020.2i q^{68} +(-23872.9 + 65590.3i) q^{69} +(13077.4 + 74165.7i) q^{70} +(-11568.7 + 9707.31i) q^{71} +(19861.1 - 23669.5i) q^{72} -25600.1 q^{73} +(27034.1 - 19459.2i) q^{74} -107664. q^{75} +(-5501.47 + 6556.40i) q^{76} +(114053. - 95702.0i) q^{77} +(-10999.6 - 62381.7i) q^{78} +(34237.8 - 94067.7i) q^{79} -21603.4i q^{80} +(-53296.1 - 19398.2i) q^{81} +(-32245.1 - 18616.7i) q^{82} +(-1222.93 + 6935.60i) q^{83} +(48084.4 + 83284.6i) q^{84} +(-60707.3 + 105148. i) q^{85} +(9084.83 + 7623.08i) q^{86} +(-25378.9 + 4474.99i) q^{87} +(-36987.4 + 21354.7i) q^{88} +(12599.5 + 34616.9i) q^{89} +(-153138. + 55737.6i) q^{90} +(129152. + 22773.1i) q^{91} +(26646.3 + 31755.8i) q^{92} +(-50878.6 - 60634.7i) q^{93} +(19563.5 + 3449.58i) q^{94} +(42418.9 - 15439.2i) q^{95} +(-9435.31 - 25923.3i) q^{96} +(-17014.7 + 9823.46i) q^{97} +(-129872. + 22900.0i) q^{98} +(246804. + 207093. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{3} + 90 q^{5} - 228 q^{7} - 186 q^{9}+O(q^{10}) $ 96 * q + 6 * q^3 + 90 * q^5 - 228 * q^7 - 186 * q^9	\( 96 q + 6 q^{3} + 90 q^{5} - 228 q^{7} - 186 q^{9} + 600 q^{10} - 726 q^{11} - 96 q^{12} - 246 q^{13} + 3960 q^{14} - 3960 q^{15} - 1530 q^{17} + 3222 q^{19} + 1440 q^{20} - 16110 q^{21} + 8232 q^{25} + 13632 q^{26} + 2154 q^{27} - 10464 q^{28} - 18378 q^{29} - 25056 q^{30} + 78198 q^{33} + 37296 q^{34} + 82170 q^{35} - 124416 q^{36} - 5586 q^{37} - 39936 q^{38} + 58686 q^{39} - 16128 q^{40} - 59598 q^{41} - 26304 q^{42} + 480 q^{44} - 74646 q^{45} - 22536 q^{46} - 1266 q^{47} + 193320 q^{49} + 18864 q^{50} + 68352 q^{52} - 57432 q^{53} + 101520 q^{54} + 133830 q^{55} - 228936 q^{57} - 79224 q^{58} - 52800 q^{59} + 68664 q^{61} - 72720 q^{62} - 166254 q^{63} + 196608 q^{64} - 122058 q^{65} + 254946 q^{67} - 218094 q^{69} - 25872 q^{70} + 200052 q^{71} - 32244 q^{73} + 124368 q^{74} - 234036 q^{75} + 51552 q^{76} + 397188 q^{77} - 16584 q^{78} + 267462 q^{79} - 371496 q^{81} + 121440 q^{83} + 84672 q^{84} - 337260 q^{85} + 43920 q^{86} - 667500 q^{87} - 135936 q^{88} + 377850 q^{89} - 576408 q^{90} + 875826 q^{91} + 233376 q^{92} + 365868 q^{93} - 80256 q^{94} + 764592 q^{95} - 823212 q^{97} - 342192 q^{98} - 928650 q^{99}+O(q^{100}) \) 96 * q + 6 * q^3 + 90 * q^5 - 228 * q^7 - 186 * q^9 + 600 * q^10 - 726 * q^11 - 96 * q^12 - 246 * q^13 + 3960 * q^14 - 3960 * q^15 - 1530 * q^17 + 3222 * q^19 + 1440 * q^20 - 16110 * q^21 + 8232 * q^25 + 13632 * q^26 + 2154 * q^27 - 10464 * q^28 - 18378 * q^29 - 25056 * q^30 + 78198 * q^33 + 37296 * q^34 + 82170 * q^35 - 124416 * q^36 - 5586 * q^37 - 39936 * q^38 + 58686 * q^39 - 16128 * q^40 - 59598 * q^41 - 26304 * q^42 + 480 * q^44 - 74646 * q^45 - 22536 * q^46 - 1266 * q^47 + 193320 * q^49 + 18864 * q^50 + 68352 * q^52 - 57432 * q^53 + 101520 * q^54 + 133830 * q^55 - 228936 * q^57 - 79224 * q^58 - 52800 * q^59 + 68664 * q^61 - 72720 * q^62 - 166254 * q^63 + 196608 * q^64 - 122058 * q^65 + 254946 * q^67 - 218094 * q^69 - 25872 * q^70 + 200052 * q^71 - 32244 * q^73 + 124368 * q^74 - 234036 * q^75 + 51552 * q^76 + 397188 * q^77 - 16584 * q^78 + 267462 * q^79 - 371496 * q^81 + 121440 * q^83 + 84672 * q^84 - 337260 * q^85 + 43920 * q^86 - 667500 * q^87 - 135936 * q^88 + 377850 * q^89 - 576408 * q^90 + 875826 * q^91 + 233376 * q^92 + 365868 * q^93 - 80256 * q^94 + 764592 * q^95 - 823212 * q^97 - 342192 * q^98 - 928650 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−2.57115	+	3.06418i	−0.454519	+	0.541675i
$2$	−2.57115	+	3.06418i	−0.454519	+	0.541675i
$3$	20.6376	−	17.3170i	1.32390	−	1.11088i	0.338438	−	0.940989i	$-0.390101\pi$
$3$	20.6376	−	17.3170i	1.32390	−	1.11088i	0.985462	−	0.169895i	$-0.0543430\pi$
$4$	−2.77837	−	15.7569i	−0.0868241	−	0.492404i
$5$	−28.8625	+	79.2990i	−0.516308	+	1.41854i	0.358251	+	0.933625i	$0.383373\pi$
$5$	−28.8625	+	79.2990i	−0.516308	+	1.41854i	−0.874559	+	0.484919i	$0.838849\pi$
$6$			107.762i			1.22204i
$7$	−209.650	−	76.3065i	−1.61715	−	0.588595i	−0.634315	−	0.773075i	$-0.718718\pi$
$7$	−209.650	−	76.3065i	−1.61715	−	0.588595i	−0.982836	+	0.184480i	$0.940940\pi$
$8$	55.4256	+	32.0000i	0.306186	+	0.176777i
$9$	83.8350	−	475.452i	0.345000	−	1.95659i
$10$	−168.776	−	292.329i	−0.533718	−	0.924427i
$11$	−333.667	+	577.929i	−0.831442	+	1.44010i	0.0654524	+	0.997856i	$0.479151\pi$
$11$	−333.667	+	577.929i	−0.831442	+	1.44010i	−0.896895	+	0.442244i	$0.854182\pi$
$12$	−330.201	−	277.071i	−0.661950	−	0.555442i
$13$	−578.886	+	102.073i	−0.950023	+	0.167515i	−0.627125	−	0.778919i	$-0.715768\pi$
$13$	−578.886	+	102.073i	−0.950023	+	0.167515i	−0.322899	+	0.946434i	$0.604657\pi$
$14$	772.859	−	446.211i	1.05385	−	0.608443i
$15$	777.567	+	2136.35i	0.892298	+	2.45157i
$16$	−240.561	+	87.5572i	−0.234923	+	0.0855050i
$17$	1416.90	+	249.838i	1.18910	+	0.209670i	0.732981	−	0.680249i	$-0.238128\pi$
$17$	1416.90	+	249.838i	1.18910	+	0.209670i	0.456118	+	0.889919i	$0.349240\pi$
$18$	1241.32	+	1479.34i	0.903028	+	1.07619i
$19$	−343.842	−	409.775i	−0.218512	−	0.260412i	0.645642	−	0.763641i	$-0.276590\pi$
$19$	−343.842	−	409.775i	−0.218512	−	0.260412i	−0.864154	+	0.503228i	$0.832146\pi$
$20$	1329.70	+	234.462i	0.743324	+	0.131068i
$21$	−5648.07	+	2055.73i	−2.79481	+	1.01723i
$22$	−912.968	−	2508.36i	−0.402160	−	1.10493i
$23$	−2243.78	+	1295.45i	−0.884424	+	0.510622i	−0.872114	−	0.489302i	$-0.837252\pi$
$23$	−2243.78	+	1295.45i	−0.884424	+	0.510622i	−0.0123094	+	0.999924i	$0.503918\pi$
$24$	1697.99	−	299.402i	0.601738	−	0.106103i
$25$	−3061.40	−	2568.82i	−0.979649	−	0.822023i
$26$	1175.63	−	2036.25i	0.341066	−	0.590743i
$27$	−3229.97	−	5594.47i	−0.852686	−	1.47690i
$28$	−619.869	+	3515.45i	−0.149419	+	0.847396i
$29$	−828.415	−	478.286i	−0.182917	−	0.105607i	0.405746	−	0.913986i	$-0.367012\pi$
$29$	−828.415	−	478.286i	−0.182917	−	0.105607i	−0.588662	+	0.808379i	$0.700345\pi$
$30$	−8545.40	−	3110.27i	−1.73352	−	0.630950i
$31$		−	2938.08i		−	0.549109i	−0.961572	−	0.274555i	$-0.911470\pi$
$31$		−	2938.08i		−	0.549109i	0.961572	−	0.274555i	$-0.0885304\pi$
$32$	350.229	−	962.245i	0.0604612	−	0.166116i
$33$	3121.90	+	17705.1i	0.499038	+	2.83018i
$34$	−4408.62	+	3699.27i	−0.654042	+	0.548806i
$35$	12102.1	−	14422.7i	1.66989	−	1.99010i
$36$	−7724.58			−0.993387
$37$	−8070.95	−	2050.31i	−0.969215	−	0.246215i
$37$	−8070.95	−	2050.31i	−0.969215	−	0.246215i
$38$	2139.69			0.240377
$39$	−10179.2	+	12131.1i	−1.07165	+	1.27714i
$40$	−4137.29	+	3471.60i	−0.408852	+	0.343067i
$41$	1616.38	+	9166.95i	0.150170	+	0.851658i	0.963069	+	0.269253i	$0.0867769\pi$
$41$	1616.38	+	9166.95i	0.150170	+	0.851658i	−0.812899	+	0.582405i	$0.802112\pi$
$42$	8222.92	−	22592.3i	0.719288	−	1.97623i
$43$		−	2964.85i		−	0.244530i	−0.992498	−	0.122265i	$-0.960984\pi$
$43$		−	2964.85i		−	0.244530i	0.992498	−	0.122265i	$-0.0390158\pi$
$44$	10033.4	+	3651.87i	0.781300	+	0.284370i
$45$	35283.2	+	20370.7i	2.59738	+	1.49960i
$46$	1799.62	−	10206.1i	0.125396	−	0.711158i
$47$	−2483.17	−	4300.97i	−0.163969	−	0.284003i	0.772320	−	0.635234i	$-0.219096\pi$
$47$	−2483.17	−	4300.97i	−0.163969	−	0.284003i	−0.936289	+	0.351231i	$0.885763\pi$
$48$	−3448.37	+	5972.76i	−0.216029	+	0.374173i
$49$	25255.7	+	21192.0i	1.50269	+	1.26091i
$50$	15742.6	−	2775.85i	0.890539	−	0.157026i
$51$	33567.9	−	19380.4i	1.80717	−	1.04337i
$52$	3216.72	+	8837.86i	0.164970	+	0.453251i
$53$	−17855.4	+	6498.85i	−0.873134	+	0.317795i	−0.739436	−	0.673227i	$-0.764908\pi$
$53$	−17855.4	+	6498.85i	−0.873134	+	0.317795i	−0.133699	+	0.991022i	$0.542685\pi$
$54$	25447.2	+	4487.03i	1.18756	+	0.209399i
$55$	−36198.7	−	43140.0i	−1.61357	−	1.92297i
$56$	−9178.20	−	10938.1i	−0.391099	−	0.466094i
$57$	−14192.1	−	2502.45i	−0.578576	−	0.102019i
$58$	3595.53	−	1308.67i	0.140344	−	0.0510810i
$59$	−5300.03	−	14561.7i	−0.198221	−	0.544606i	0.800264	−	0.599648i	$-0.204693\pi$
$59$	−5300.03	−	14561.7i	−0.198221	−	0.544606i	−0.998484	+	0.0550421i	$0.982471\pi$
$60$	31501.9	−	18187.6i	1.12969	−	0.652226i
$61$	27819.3	−	4905.30i	0.957243	−	0.168788i	0.326861	−	0.945072i	$-0.394009\pi$
$61$	27819.3	−	4905.30i	0.957243	−	0.168788i	0.630383	+	0.776285i	$0.282898\pi$
$62$	9002.79	+	7554.23i	0.297439	+	0.249581i
$63$	−53856.1	+	93281.5i	−1.70956	+	2.96104i
$64$	2048.00	+	3547.24i	0.0625000	+	0.108253i
$65$	8613.77	−	48851.1i	0.252877	−	1.43414i
$66$	−62278.6	−	35956.6i	−1.75986	−	1.01606i
$67$	35139.3	+	12789.7i	0.956326	+	0.348074i	0.772593	−	0.634902i	$-0.218959\pi$
$67$	35139.3	+	12789.7i	0.956326	+	0.348074i	0.183733	+	0.982976i	$0.441182\pi$
$68$		−	23020.2i		−	0.603721i
$69$	−23872.9	+	65590.3i	−0.603647	+	1.65851i
$70$	13077.4	+	74165.7i	0.318990	+	1.80908i
$71$	−11568.7	+	9707.31i	−0.272358	+	0.228535i	−0.768728	−	0.639576i	$-0.779110\pi$
$71$	−11568.7	+	9707.31i	−0.272358	+	0.228535i	0.496371	+	0.868111i	$0.334666\pi$
$72$	19861.1	−	23669.5i	0.451514	−	0.538093i
$73$	−25600.1			−0.562257			−0.281128	−	0.959670i	$-0.590709\pi$
$73$	−25600.1			−0.562257			−0.281128	+	0.959670i	$0.590709\pi$
$74$	27034.1	−	19459.2i	0.573896	−	0.413090i
$75$	−107664.			−2.21013
$76$	−5501.47	+	6556.40i	−0.109256	+	0.130206i
$77$	114053.	−	95702.0i	2.19220	−	1.83948i
$78$	−10999.6	−	62381.7i	−0.204710	−	1.16097i
$79$	34237.8	−	94067.7i	0.617218	−	1.69579i	−0.0964769	−	0.995335i	$-0.530757\pi$
$79$	34237.8	−	94067.7i	0.617218	−	1.69579i	0.713695	−	0.700457i	$-0.247020\pi$
$80$		−	21603.4i		−	0.377396i
$81$	−53296.1	−	19398.2i	−0.902574	−	0.328510i
$82$	−32245.1	−	18616.7i	−0.529577	−	0.305752i
$83$	−1222.93	+	6935.60i	−0.0194853	+	0.110507i	−0.992999	−	0.118121i	$-0.962313\pi$
$83$	−1222.93	+	6935.60i	−0.0194853	+	0.110507i	0.973514	+	0.228628i	$0.0734240\pi$
$84$	48084.4	+	83284.6i	0.743543	+	1.28785i
$85$	−60707.3	+	105148.i	−0.911367	+	1.57853i
$86$	9084.83	+	7623.08i	0.132456	+	0.111144i
$87$	−25378.9	+	4474.99i	−0.359480	+	0.0633861i
$88$	−36987.4	+	21354.7i	−0.509152	+	0.293959i
$89$	12599.5	+	34616.9i	0.168608	+	0.463248i	0.995003	−	0.0998433i	$-0.0318342\pi$
$89$	12599.5	+	34616.9i	0.168608	+	0.463248i	−0.826395	+	0.563091i	$0.809612\pi$
$90$	−153138.	+	55737.6i	−1.99286	+	0.725341i
$91$	129152.	+	22773.1i	1.63493	+	0.288282i
$92$	26646.3	+	31755.8i	0.328222	+	0.391159i
$93$	−50878.6	−	60634.7i	−0.609997	−	0.726966i
$94$	19563.5	+	3449.58i	0.228364	+	0.0402668i
$95$	42418.9	−	15439.2i	0.482226	−	0.175516i
$96$	−9435.31	−	25923.3i	−0.104491	−	0.287086i
$97$	−17014.7	+	9823.46i	−0.183610	+	0.106007i	−0.588988	−	0.808142i	$-0.700473\pi$
$97$	−17014.7	+	9823.46i	−0.183610	+	0.106007i	0.405378	+	0.914149i	$0.367140\pi$
$98$	−129872.	+	22900.0i	−1.36600	+	0.240863i
$99$	246804.	+	207093.i	2.53084	+	2.12363i
$100$	−31971.0	+	55375.4i	−0.319710	+	0.553754i
$101$	−20233.6	−	35045.7i	−0.197365	−	0.341846i	0.750308	−	0.661088i	$-0.229905\pi$
$101$	−20233.6	−	35045.7i	−0.197365	−	0.341846i	−0.947673	+	0.319242i	$0.896572\pi$
$102$	−26923.0	+	152688.i	−0.256226	+	1.45313i
$103$	119562.	+	69029.2i	1.11045	+	0.641121i	0.938947	−	0.344062i	$-0.111803\pi$
$103$	119562.	+	69029.2i	1.11045	+	0.641121i	0.171507	+	0.985183i	$0.445136\pi$
$104$	−35351.4	−	12866.9i	−0.320497	−	0.116651i
$105$		−	507220.i		−	4.48976i
$106$	25995.4	−	71421.8i	0.224715	−	0.617399i
$107$	−14945.6	−	84760.9i	−0.126199	−	0.715708i	−0.980589	−	0.196076i	$-0.937180\pi$
$107$	−14945.6	−	84760.9i	−0.126199	−	0.715708i	0.854390	−	0.519632i	$-0.173931\pi$
$108$	−79177.7	+	66437.9i	−0.653196	+	0.548096i
$109$	−74454.7	+	88731.6i	−0.600241	+	0.715339i	−0.977540	−	0.210752i	$-0.932409\pi$
$109$	−74454.7	+	88731.6i	−0.600241	+	0.715339i	0.377298	+	0.926092i	$0.376853\pi$
$110$	225261.			1.77502
$111$	−202070.	+	97451.0i	−1.55666	+	0.750721i
$112$	57114.9			0.430234
$113$	−122476.	+	145961.i	−0.902305	+	1.07533i	0.0945059	+	0.995524i	$0.469873\pi$
$113$	−122476.	+	145961.i	−0.902305	+	1.07533i	−0.996811	+	0.0798008i	$0.974572\pi$
$114$	44158.1	−	37053.0i	0.318235	−	0.267031i
$115$	−37966.6	−	215319.i	−0.267705	−	1.51823i
$116$	−5234.67	+	14382.1i	−0.0361197	+	0.0992380i
$117$			283789.i			1.91660i
$118$	58246.9	+	21200.1i	0.385095	+	0.140163i
$119$	−277990.	−	160498.i	−1.79954	−	1.03897i
$120$	−25266.0	+	143291.i	−0.160171	+	0.908374i
$121$	−142142.	−	246198.i	−0.882592	−	1.52869i
$122$	−56497.0	+	97855.7i	−0.343658	+	0.595232i
$123$	192102.	+	161193.i	1.14490	+	0.960688i
$124$	−46295.0	+	8163.06i	−0.270384	+	0.0476759i
$125$	63682.2	−	36766.9i	0.364538	−	0.210466i
$126$	−147359.	−	404865.i	−0.826894	−	2.27187i
$127$	−115223.	+	41937.9i	−0.633916	+	0.230726i	−0.638935	−	0.769261i	$-0.720625\pi$
$127$	−115223.	+	41937.9i	−0.633916	+	0.230726i	0.00501905	+	0.999987i	$0.498402\pi$
$128$	−16135.1	−	2845.05i	−0.0870455	−	0.0153485i
$129$	−51342.2	−	61187.3i	−0.271644	−	0.323733i
$130$	127541.	+	151998.i	0.661900	+	0.788822i
$131$	21012.9	+	3705.15i	0.106981	+	0.0188637i	0.226883	−	0.973922i	$-0.427147\pi$
$131$	21012.9	+	3705.15i	0.106981	+	0.0188637i	−0.119901	+	0.992786i	$0.538258\pi$
$132$	270305.	−	98382.9i	1.35027	−	0.491456i
$133$	40818.1	+	112147.i	0.200089	+	0.549741i
$134$	−129538.	+	74788.9i	−0.623212	+	0.359812i
$135$	536861.	−	94663.1i	2.53529	−	0.447040i
$136$	70537.9	+	59188.3i	0.327021	+	0.274403i
$137$	−183324.	+	317527.i	−0.834486	+	1.44537i	0.0599625	+	0.998201i	$0.480902\pi$
$137$	−183324.	+	317527.i	−0.834486	+	1.44537i	−0.894448	+	0.447171i	$0.852431\pi$
$138$	−139599.	−	241793.i	−0.624002	−	1.08080i
$139$	33122.8	−	187849.i	0.145409	−	0.824653i	−0.821630	−	0.570022i	$-0.806935\pi$
$139$	33122.8	−	187849.i	0.145409	−	0.824653i	0.967038	−	0.254631i	$-0.0819541\pi$
$140$	−260881.	−	150620.i	−1.12492	−	0.649474i
$141$	−125726.	−	45760.7i	−0.532572	−	0.193840i
$142$		−	60407.6i		−	0.251403i
$143$	134164.	−	368613.i	0.548652	−	1.50741i
$144$	21461.7	+	121716.i	0.0862500	+	0.489148i
$145$	61837.7	−	51888.0i	0.244249	−	0.204949i
$146$	65821.7	−	78443.3i	0.255557	−	0.304560i
$147$	888198.			3.39013
$148$	−9882.48	+	132870.i	−0.0370862	+	0.498623i
$149$	189920.			0.700817			0.350409	−	0.936597i	$-0.386043\pi$
$149$	189920.			0.700817			0.350409	+	0.936597i	$0.386043\pi$
$150$	276820.	−	329902.i	1.00455	−	1.19717i
$151$	−394813.	+	331287.i	−1.40912	+	1.18239i	−0.452249	+	0.891892i	$0.649378\pi$
$151$	−394813.	+	331287.i	−1.40912	+	1.18239i	−0.956874	+	0.290503i	$0.906177\pi$
$152$	−5944.86	−	33715.0i	−0.0208705	−	0.118362i
$153$	237572.	−	652724.i	0.820478	−	2.25424i
$154$			595544.i			2.02354i
$155$	232987.	+	84800.2i	0.778936	+	0.283509i
$156$	219430.	+	126688.i	0.721913	+	0.416797i
$157$	−89191.0	+	505827.i	−0.288783	+	1.63777i	0.402667	+	0.915347i	$0.368083\pi$
$157$	−89191.0	+	505827.i	−0.288783	+	1.63777i	−0.691450	+	0.722424i	$0.743028\pi$
$158$	200209.	+	346773.i	0.638031	+	1.10510i
$159$	−255952.	+	443323.i	−0.802909	+	1.39068i
$160$	66196.6	+	55545.6i	0.204426	+	0.171534i
$161$	569260.	−	100376.i	1.73080	−	0.305186i
$162$	196472.	−	113433.i	0.588183	−	0.339588i
$163$	46845.2	+	128706.i	0.138101	+	0.379429i	0.989393	−	0.145263i	$-0.0464029\pi$
$163$	46845.2	+	128706.i	0.138101	+	0.379429i	−0.851292	+	0.524692i	$0.824181\pi$
$164$	139952.	−	50938.4i	0.406321	−	0.147889i
$165$	−1.49411e6	−	263451.i	−4.27240	−	0.753339i
$166$	−18107.6	−	21579.8i	−0.0510023	−	0.0607822i
$167$	124910.	+	148861.i	0.346581	+	0.413039i	0.910972	−	0.412469i	$-0.135333\pi$
$167$	124910.	+	148861.i	0.346581	+	0.413039i	−0.564391	+	0.825508i	$0.690889\pi$
$168$	−378831.	−	66798.1i	−1.03555	−	0.182596i
$169$	−24211.7	+	8812.36i	−0.0652093	+	0.0237342i
$170$	−166105.	−	456369.i	−0.440819	−	1.21114i
$171$	−223654.	+	129127.i	−0.584907	+	0.337696i
$172$	−46716.9	+	8237.46i	−0.120407	+	0.0212311i
$173$	−191427.	−	160627.i	−0.486282	−	0.408039i	0.366409	−	0.930454i	$-0.380587\pi$
$173$	−191427.	−	160627.i	−0.486282	−	0.408039i	−0.852692	+	0.522414i	$0.825031\pi$
$174$	51540.9	−	89271.4i	0.129056	−	0.223532i
$175$	445806.	+	772159.i	1.10040	+	1.90595i
$176$	29665.7	−	168242.i	0.0721892	−	0.409405i
$177$	−361545.	−	208738.i	−0.867419	−	0.500804i
$178$	−138468.	−	50398.1i	−0.327566	−	0.119224i
$179$		−	585713.i		−	1.36632i	−0.730269	−	0.683160i	$-0.760605\pi$
$179$		−	585713.i		−	1.36632i	0.730269	−	0.683160i	$-0.239395\pi$
$180$	222951.	−	612552.i	0.512894	−	1.40916i
$181$	−76543.0	−	434097.i	−0.173664	−	0.984896i	−0.939675	−	0.342069i	$-0.888872\pi$
$181$	−76543.0	−	434097.i	−0.173664	−	0.984896i	0.766011	−	0.642827i	$-0.222239\pi$
$182$	−401851.	+	337193.i	−0.899263	+	0.754571i
$183$	489179.	−	582980.i	1.07979	−	1.28684i
$184$	−165817.			−0.361065
$185$	395535.	−	580841.i	0.849681	−	1.24775i
$186$	316612.			0.671035
$187$	−617163.	+	735506.i	−1.29061	+	1.53809i
$188$	−60871.0	+	51076.8i	−0.125607	+	0.105397i
$189$	250270.	+	1.41935e6i	0.509629	+	2.89025i
$190$	−61756.9	+	169676.i	−0.124108	+	0.340985i
$191$			675668.i			1.34014i	0.742298	+	0.670069i	$0.233736\pi$
$191$			675668.i			1.34014i	−0.742298	+	0.670069i	$0.766264\pi$
$192$	103693.	+	37741.2i	0.203000	+	0.0738861i
$193$	327254.	+	188940.i	0.632400	+	0.365116i	0.781681	−	0.623679i	$-0.214363\pi$
$193$	327254.	+	188940.i	0.632400	+	0.365116i	−0.149281	+	0.988795i	$0.547696\pi$
$194$	13646.6	−	77393.7i	0.0260328	−	0.147639i
$195$	−668186.	−	1.15733e6i	−1.25838	−	2.17957i
$196$	263752.	−	456831.i	0.490405	−	0.849407i
$197$	−525992.	−	441360.i	−0.965637	−	0.810265i	0.0162243	−	0.999868i	$-0.494835\pi$
$197$	−525992.	−	441360.i	−0.965637	−	0.810265i	−0.981861	+	0.189603i	$0.939280\pi$
$198$	−1.26914e6	+	223784.i	−2.30063	+	0.405664i
$199$	−164030.	+	94702.9i	−0.293624	+	0.169524i	−0.639575	−	0.768729i	$-0.720890\pi$
$199$	−164030.	+	94702.9i	−0.293624	+	0.169524i	0.345951	+	0.938253i	$0.387556\pi$
$200$	−87477.8	−	240343.i	−0.154640	−	0.424871i
$201$	946667.	−	344559.i	1.65275	−	0.601552i
$202$	159410.	+	28108.3i	0.274876	+	0.0484680i
$203$	137181.	+	163486.i	0.233644	+	0.278446i
$204$	−398640.	−	475080.i	−0.670664	−	0.799266i
$205$	−773583.	−	136404.i	−1.28565	−	0.226694i
$206$	−518930.	+	188875.i	−0.852002	+	0.310103i
$207$	427815.	+	1.17541e6i	0.693953	+	1.90662i
$208$	130320.	−	75240.4i	0.208859	−	0.120585i
$209$	351550.	−	61987.7i	0.556700	−	0.0981612i
$210$	1.55421e6	+	1.30414e6i	2.43199	+	2.04068i
$211$	−337457.	+	584493.i	−0.521810	+	0.903801i	0.477868	+	0.878431i	$0.341410\pi$
$211$	−337457.	+	584493.i	−0.521810	+	0.903801i	−0.999678	+	0.0253695i	$0.991924\pi$
$212$	152011.	+	263291.i	0.232293	+	0.402343i
$213$	−70649.0	+	400670.i	−0.106698	+	0.605115i
$214$	298150.	+	172137.i	0.445041	+	0.256945i
$215$	235110.	+	85573.0i	0.346876	+	0.126253i
$216$		−	413436.i		−	0.602940i
$217$	−224194.	+	615969.i	−0.323203	+	0.887992i
$218$	−80455.3	−	456285.i	−0.114660	−	0.650271i
$219$	−528324.	+	443316.i	−0.744371	+	0.624602i
$220$	−579180.	+	690239.i	−0.806783	+	0.961486i
$221$	−845726.			−1.16479
$222$	220945.	−	869739.i	0.300886	−	1.18442i
$223$	76919.1			0.103579			0.0517895	−	0.998658i	$-0.483508\pi$
$223$	76919.1			0.103579			0.0517895	+	0.998658i	$0.483508\pi$
$224$	−146851.	+	175010.i	−0.195550	+	0.233047i
$225$	−1.47800e6	+	1.24019e6i	−1.94634	+	1.63317i
$226$	−132346.	−	750574.i	−0.172362	−	0.977512i
$227$	207494.	−	570086.i	0.267264	−	0.734303i	−0.731366	−	0.681985i	$-0.761117\pi$
$227$	207494.	−	570086.i	0.267264	−	0.734303i	0.998630	−	0.0523180i	$-0.0166609\pi$
$228$			230577.i			0.293751i
$229$	1.35415e6	+	492872.i	1.70639	+	0.621077i	0.996528	−	0.0832599i	$-0.0265332\pi$
$229$	1.35415e6	+	492872.i	1.70639	+	0.621077i	0.709866	+	0.704337i	$0.248755\pi$
$230$	757394.	+	437282.i	0.944066	+	0.545057i
$231$	696511.	−	3.95011e6i	0.858812	−	4.87057i
$232$	−30610.3	−	53018.6i	−0.0373377	−	0.0646708i
$233$	−587466.	+	1.01752e6i	−0.708913	+	1.22787i	0.256348	+	0.966585i	$0.417481\pi$
$233$	−587466.	+	1.01752e6i	−0.708913	+	1.22787i	−0.965261	+	0.261288i	$0.915853\pi$
$234$	−869581.	−	729665.i	−1.03817	−	0.871132i
$235$	412733.	−	72776.0i	0.487528	−	0.0859644i
$236$	−214723.	+	123970.i	−0.250956	+	0.144890i
$237$	−922381.	−	2.53422e6i	−1.06669	−	2.93072i
$238$	1.20655e6	−	439147.i	1.38071	−	0.502537i
$239$	−418234.	−	73745.9i	−0.473614	−	0.0835109i	−0.0682537	−	0.997668i	$-0.521743\pi$
$239$	−418234.	−	73745.9i	−0.473614	−	0.0835109i	−0.405360	+	0.914157i	$0.632854\pi$
$240$	−374105.	−	445841.i	−0.419243	−	0.499634i
$241$	198000.	+	235967.i	0.219595	+	0.261703i	0.864583	−	0.502489i	$-0.167582\pi$
$241$	198000.	+	235967.i	0.219595	+	0.261703i	−0.644989	+	0.764192i	$0.723138\pi$
$242$	1.11986e6	+	197462.i	1.22921	+	0.216743i
$243$	39278.4	−	14296.2i	0.0426715	−	0.0155312i
$244$	−154585.	−	424719.i	−0.166224	−	0.456696i
$245$	−2.40945e6	+	1.39110e6i	−2.56450	+	1.48061i
$246$	−987846.	+	174184.i	−1.04076	+	0.183514i
$247$	240872.	+	202116.i	0.251214	+	0.210794i
$248$	94018.4	−	162845.i	0.0970697	−	0.168130i
$249$	94865.2	+	164311.i	0.0969636	+	0.167946i
$250$	−51076.1	+	289667.i	−0.0516854	+	0.293122i
$251$	−187319.	−	108149.i	−0.187671	−	0.108352i	0.403221	−	0.915103i	$-0.367891\pi$
$251$	−187319.	−	108149.i	−0.187671	−	0.108352i	−0.590892	+	0.806751i	$0.701224\pi$
$252$	1.61946e6	+	589436.i	1.60646	+	0.584703i
$253$		−	1.72899e6i		−	1.69821i
$254$	167752.	−	460894.i	0.163148	−	0.448246i
$255$	567996.	+	3.22127e6i	0.547009	+	3.10224i
$256$	50203.5	−	42125.7i	0.0478778	−	0.0401742i
$257$	−116650.	+	139018.i	−0.110167	+	0.131292i	−0.818310	−	0.574777i	$-0.805089\pi$
$257$	−116650.	+	139018.i	−0.110167	+	0.131292i	0.708143	+	0.706069i	$0.249533\pi$
$258$	319497.			0.298826
$259$	1.53563e6	+	1.04571e6i	1.42245	+	0.968642i
$260$	−793676.			−0.728131
$261$	−296852.	+	353774.i	−0.269736	+	0.321459i
$262$	−65380.7	+	54860.9i	−0.0588432	+	0.0493753i
$263$	−134355.	−	761964.i	−0.119774	−	0.679274i	−0.984275	−	0.176642i	$-0.943476\pi$
$263$	−134355.	−	761964.i	−0.119774	−	0.679274i	0.864501	−	0.502632i	$-0.167635\pi$
$264$	−393532.	+	1.08122e6i	−0.347512	+	0.954782i
$265$		−	1.60349e6i		−	1.40266i
$266$	−448588.	−	163273.i	−0.388726	−	0.141485i
$267$	859484.	+	496223.i	0.737836	+	0.425990i
$268$	103896.	−	589222.i	0.0883610	−	0.501120i
$269$	997994.	+	1.72858e6i	0.840905	+	1.45649i	0.889130	+	0.457654i	$0.151310\pi$
$269$	997994.	+	1.72858e6i	0.840905	+	1.45649i	−0.0482248	+	0.998837i	$0.515356\pi$
$270$	−1.09029e6	+	1.88843e6i	−0.910188	+	1.57649i
$271$	−1.15333e6	−	967759.i	−0.953960	−	0.800468i	0.0259997	−	0.999662i	$-0.491723\pi$
$271$	−1.15333e6	−	967759.i	−0.953960	−	0.800468i	−0.979960	+	0.199194i	$0.936168\pi$
$272$	−362727.	+	63958.6i	−0.297275	+	0.0524175i
$273$	3.05975e6	−	1.76655e6i	2.48473	−	1.43456i
$274$	−501605.	−	1.37815e6i	−0.403632	−	1.10897i
$275$	2.50609e6	−	912141.i	1.99832	−	0.727328i
$276$	1.09983e6	+	193930.i	0.869066	+	0.153240i
$277$	950435.	+	1.13268e6i	0.744257	+	0.886971i	0.996744	−	0.0806293i	$-0.0256930\pi$
$277$	950435.	+	1.13268e6i	0.744257	+	0.886971i	−0.252487	+	0.967600i	$0.581249\pi$
$278$	490438.	+	584481.i	0.380603	+	0.453585i
$279$	−1.39691e6	−	246313.i	−1.07438	−	0.189443i
$280$	1.13229e6	−	412120.i	0.863103	−	0.314144i
$281$	−252130.	−	692721.i	−0.190484	−	0.523350i	0.807281	−	0.590167i	$-0.200938\pi$
$281$	−252130.	−	692721.i	−0.190484	−	0.523350i	−0.997765	+	0.0668164i	$0.978716\pi$
$282$	463480.	−	267590.i	0.347063	−	0.200377i
$283$	−1.80837e6	+	318864.i	−1.34221	+	0.236668i	−0.798191	−	0.602404i	$-0.794210\pi$
$283$	−1.80837e6	+	318864.i	−1.34221	+	0.236668i	−0.544020	+	0.839072i	$0.683098\pi$
$284$	185100.	+	155317.i	0.136179	+	0.114268i
$285$	608062.	−	1.05319e6i	0.443441	−	0.768062i
$286$	784540.	+	1.35886e6i	0.567153	+	0.982337i
$287$	360623.	−	2.04519e6i	0.258433	−	1.46565i
$288$	−428140.	−	247187.i	−0.304162	−	0.175608i
$289$	610966.	+	222373.i	0.430301	+	0.156617i
$290$			322893.i			0.225457i
$291$	−181030.	+	497376.i	−0.125319	+	0.344312i
$292$	71126.6	+	403379.i	0.0488174	+	0.276857i
$293$	1.37287e6	−	1.15197e6i	0.934242	−	0.783922i	−0.0423319	−	0.999104i	$-0.513479\pi$
$293$	1.37287e6	−	1.15197e6i	0.934242	−	0.783922i	0.976574	+	0.215181i	$0.0690342\pi$
$294$	−2.28369e6	+	2.72160e6i	−1.54088	+	1.83635i
$295$	1.30770e6			0.874891
$296$	−381727.	−	371910.i	−0.253235	−	0.246722i
$297$	4.31094e6			2.83584
$298$	−488313.	+	581948.i	−0.318535	+	0.379615i
$299$	1.16666e6	−	978945.i	0.754687	−	0.633257i
$300$	299131.	+	1.69645e6i	0.191892	+	1.08828i
$301$	−226237.	+	621582.i	−0.143929	+	0.395442i
$302$		−	2.06157e6i		−	1.30071i
$303$	−1.02446e6	−	372872.i	−0.641043	−	0.233321i
$304$	118594.	+	68470.2i	0.0736001	+	0.0424930i
$305$	−413950.	+	2.34763e6i	−0.254799	+	1.44504i
$306$	1.38923e6	+	2.40621e6i	0.848145	+	1.46903i
$307$	116585.	−	201931.i	0.0705986	−	0.122280i	−0.828565	−	0.559893i	$-0.810842\pi$
$307$	116585.	−	201931.i	0.0705986	−	0.122280i	0.899164	+	0.437612i	$0.144176\pi$
$308$	−1.82485e6	−	1.53123e6i	−1.09610	−	0.919738i
$309$	3.66285e6	−	645859.i	2.18234	−	0.384805i
$310$	−858886.	+	495878.i	−0.507611	+	0.293070i
$311$	656607.	+	1.80401e6i	0.384950	+	1.05764i	0.969244	+	0.246101i	$0.0791493\pi$
$311$	656607.	+	1.80401e6i	0.384950	+	1.05764i	−0.584294	+	0.811542i	$0.698628\pi$
$312$	−952383.	+	346639.i	−0.553892	+	0.201600i
$313$	−2.53714e6	−	447366.i	−1.46381	−	0.258108i	−0.615719	−	0.787966i	$-0.711134\pi$
$313$	−2.53714e6	−	447366.i	−1.46381	−	0.258108i	−0.848087	+	0.529858i	$0.822245\pi$
$314$	−1.32062e6	−	1.57386e6i	−0.755882	−	0.900826i
$315$	−5.84271e6	−	6.96307e6i	−3.31771	−	3.95389i
$316$	−1.57734e6	−	278128.i	−0.888604	−	0.156685i
$317$	−1.52066e6	+	553475.i	−0.849931	+	0.309350i	−0.730012	−	0.683434i	$-0.760486\pi$
$317$	−1.52066e6	+	553475.i	−0.849931	+	0.309350i	−0.119919	+	0.992784i	$0.538263\pi$
$318$	−700327.	−	1.92413e6i	−0.388359	−	1.06701i
$319$	552830.	−	319177.i	0.304169	−	0.175612i
$320$	−340403.	+	60022.2i	−0.185831	+	0.0327670i
$321$	−1.77624e6	−	1.49045e6i	−0.962144	−	0.807334i
$322$	−1.15608e6	+	2.00240e6i	−0.621369	+	1.07624i
$323$	−384813.	−	666517.i	−0.205231	−	0.355471i
$324$	−157580.	+	893678.i	−0.0833945	+	0.472954i
$325$	2.03441e6	+	1.17457e6i	1.06839	+	0.616835i
$326$	−514824.	−	187381.i	−0.268297	−	0.0976519i
$327$			3.12053e6i			1.61384i
$328$	−203753.	+	559808.i	−0.104573	+	0.287313i
$329$	192405.	+	1.09118e6i	0.0980001	+	0.555786i
$330$	4.64883e6	−	3.90084e6i	2.34995	−	1.97184i
$331$	861188.	−	1.02632e6i	0.432044	−	0.514890i	−0.505467	−	0.862846i	$-0.668680\pi$
$331$	861188.	−	1.02632e6i	0.432044	−	0.514890i	0.937511	+	0.347956i	$0.113124\pi$
$332$	112682.			0.0561058
$333$	−1.65145e6	+	3.66546e6i	−0.816122	+	1.81141i
$334$	−777299.			−0.381261
$335$	−2.02841e6	+	2.41737e6i	−0.987517	+	1.17688i
$336$	1.17871e6	−	989058.i	0.569587	−	0.477940i
$337$	−163940.	−	929750.i	−0.0786339	−	0.445955i	−0.998550	−	0.0538390i	$-0.982854\pi$
$337$	−163940.	−	929750.i	−0.0786339	−	0.445955i	0.919916	−	0.392116i	$-0.128257\pi$
$338$	35249.4	−	96847.0i	0.0167826	−	0.0461099i
$339$			5.13318e6i			2.42598i
$340$	1.82548e6	+	664419.i	0.856405	+	0.311706i
$341$	1.69800e6	+	980340.i	0.790772	+	0.456553i
$342$	179381.	−	1.01732e6i	0.0829300	−	0.470319i
$343$	−1.80291e6	−	3.12273e6i	−0.827444	−	1.43317i
$344$	94875.3	−	164329.i	0.0432272	−	0.0748717i
$345$	−4.51221e6	−	3.78620e6i	−2.04100	−	1.71260i
$346$	984377.	−	173572.i	0.442050	−	0.0779453i
$347$	847698.	−	489419.i	0.377935	−	0.218201i	−0.298984	−	0.954258i	$-0.596648\pi$
$347$	847698.	−	489419.i	0.377935	−	0.218201i	0.676920	+	0.736057i	$0.263314\pi$
$348$	141024.	+	387461.i	0.0624231	+	0.171506i
$349$	−109288.	+	39777.7i	−0.0480298	+	0.0174814i	−0.365923	−	0.930645i	$-0.619247\pi$
$349$	−109288.	+	39777.7i	−0.0480298	+	0.0174814i	0.317894	+	0.948126i	$0.397025\pi$
$350$	−3.51227e6	−	619308.i	−1.53256	−	0.270232i
$351$	2.44083e6	+	2.90887e6i	1.05747	+	1.26025i
$352$	439249.	+	523477.i	0.188953	+	0.225186i
$353$	−3.67511e6	−	648021.i	−1.56976	−	0.276791i	−0.679998	−	0.733214i	$-0.738019\pi$
$353$	−3.67511e6	−	648021.i	−1.56976	−	0.276791i	−0.889763	+	0.456423i	$0.849131\pi$
$354$	1.56920e6	−	571141.i	0.665532	−	0.242234i
$355$	−435878.	−	1.19757e6i	−0.183567	−	0.504346i
$356$	510450.	−	294709.i	0.213466	−	0.123245i
$357$	−8.51637e6	+	1.50167e6i	−3.53658	+	0.623595i
$358$	1.79473e6	+	1.50596e6i	0.740101	+	0.621019i
$359$	−42230.8	+	73146.0i	−0.0172939	+	0.0299540i	−0.874543	−	0.484948i	$-0.838838\pi$
$359$	−42230.8	+	73146.0i	−0.0172939	+	0.0299540i	0.857249	+	0.514902i	$0.172172\pi$
$360$	1.30373e6	+	2.25812e6i	0.530189	+	0.918314i
$361$	380282.	−	2.15669e6i	0.153581	−	0.871001i
$362$	1.52695e6	+	881587.i	0.612427	+	0.353585i
$363$	−7.19687e6	−	2.61945e6i	−2.86667	−	1.04338i
$364$		−	2.09832e6i		−	0.830075i
$365$	738882.	−	2.03006e6i	0.290297	−	0.797586i
$366$	528604.	+	2.99786e6i	0.206266	+	1.16979i
$367$	−1.77103e6	+	1.48607e6i	−0.686373	+	0.575935i	−0.917861	−	0.396902i	$-0.870085\pi$
$367$	−1.77103e6	+	1.48607e6i	−0.686373	+	0.575935i	0.231488	+	0.972838i	$0.425641\pi$
$368$	426341.	−	508093.i	0.164111	−	0.195580i
$369$	4.49395e6			1.71816
$370$	762820.	+	2.70542e6i	0.289680	+	1.02738i
$371$	4.23931e6			1.59904
$372$	−814057.	+	970155.i	−0.304998	+	0.363483i
$373$	1.49787e6	−	1.25687e6i	0.557446	−	0.467753i	−0.320007	−	0.947415i	$-0.603685\pi$
$373$	1.49787e6	−	1.25687e6i	0.557446	−	0.467753i	0.877453	+	0.479662i	$0.159241\pi$
$374$	−666903.	−	3.78219e6i	−0.246538	−	1.39819i
$375$	677554.	−	1.86156e6i	0.248809	−	0.683596i
$376$		−	317846.i		−	0.115944i
$377$	528378.	+	192314.i	0.191466	+	0.0696878i
$378$	−4.99263e6	−	2.88249e6i	−1.79721	−	1.03762i
$379$	49371.6	−	280000.i	0.0176555	−	0.100129i	−0.974707	−	0.223488i	$-0.928256\pi$
$379$	49371.6	−	280000.i	0.0176555	−	0.100129i	0.992362	+	0.123359i	$0.0393667\pi$
$380$	−361130.	−	625495.i	−0.128293	−	0.222211i
$381$	−1.65169e6	+	2.86082e6i	−0.582931	+	1.00967i
$382$	−2.07037e6	−	1.73724e6i	−0.725920	−	0.609119i
$383$	2.59842e6	−	458171.i	0.905132	−	0.159599i	0.298340	−	0.954460i	$-0.403567\pi$
$383$	2.59842e6	−	458171.i	0.905132	−	0.159599i	0.606792	+	0.794860i	$0.292456\pi$
$384$	−382257.	+	220696.i	−0.132290	+	0.0763776i
$385$	4.29722e6	+	1.18065e7i	1.47753	+	4.05947i
$386$	−1.42037e6	+	516971.i	−0.485212	+	0.176603i
$387$	−1.40964e6	−	248558.i	−0.478445	−	0.0843628i
$388$	202061.	+	240807.i	0.0681400	+	0.0812061i
$389$	1.95679e6	+	2.33202e6i	0.655649	+	0.781372i	0.986754	−	0.162222i	$-0.0518661\pi$
$389$	1.95679e6	+	2.33202e6i	0.655649	+	0.781372i	−0.331106	+	0.943594i	$0.607422\pi$
$390$	5.26428e6	+	928235.i	1.75258	+	0.309027i
$391$	−3.50287e6	+	1.27494e6i	−1.15873	+	0.421743i
$392$	721667.	+	1.98276e6i	0.237204	+	0.651712i
$393$	497818.	−	287415.i	0.162588	−	0.0938703i
$394$	2.70481e6	−	476931.i	0.877801	−	0.154780i
$395$	6.47128e6	+	5.43005e6i	2.08688	+	1.75110i
$396$	2.57744e6	−	4.46426e6i	0.825944	−	1.43058i
$397$	−2.80166e6	−	4.85262e6i	−0.892153	−	1.54525i	−0.837289	−	0.546761i	$-0.815861\pi$
$397$	−2.80166e6	−	4.85262e6i	−0.892153	−	1.54525i	−0.0548646	−	0.998494i	$-0.517473\pi$
$398$	131560.	−	746113.i	0.0416309	−	0.236101i
$399$	2.78443e6	+	1.60759e6i	0.875597	+	0.505526i
$400$	961373.	+	349911.i	0.300429	+	0.109347i
$401$			835833.i			0.259573i	0.991542	+	0.129786i	$0.0414291\pi$
$401$			835833.i			0.259573i	−0.991542	+	0.129786i	$0.958571\pi$
$402$	−1.37824e6	+	3.78667e6i	−0.425362	+	1.16867i
$403$	299899.	+	1.70081e6i	0.0919839	+	0.521667i
$404$	−495995.	+	416190.i	−0.151190	+	0.126864i
$405$	3.07652e6	−	3.66645e6i	0.932012	−	1.11073i
$406$	−853664.			−0.257023
$407$	3.87794e6	−	3.98031e6i	1.16042	−	1.19105i
$408$	2.48069e6			0.737773
$409$	2.44006e6	−	2.90795e6i	0.721260	−	0.859564i	−0.273493	−	0.961874i	$-0.588179\pi$
$409$	2.44006e6	−	2.90795e6i	0.721260	−	0.859564i	0.994753	+	0.102310i	$0.0326234\pi$
$410$	2.40696e6	−	2.01968e6i	0.707147	−	0.593367i
$411$	1.71524e6	+	9.72761e6i	0.500865	+	2.84055i
$412$	755500.	−	2.07572e6i	0.219276	−	0.602456i
$413$			3.45730e6i			0.997382i
$414$	−4.70165e6	−	1.71126e6i	−1.34818	−	0.490699i
$415$	−514689.	−	297156.i	−0.146698	−	0.0846963i
$416$	−104523.	+	592779.i	−0.0296127	+	0.167942i
$417$	−2.56940e6	−	4.45033e6i	−0.723587	−	1.25329i
$418$	−713946.	+	1.23659e6i	−0.199859	+	0.346167i
$419$	2.42148e6	+	2.03186e6i	0.673823	+	0.565404i	0.914194	−	0.405277i	$-0.132825\pi$
$419$	2.42148e6	+	2.03186e6i	0.673823	+	0.565404i	−0.240372	+	0.970681i	$0.577269\pi$
$420$	−7.99222e6	+	1.40924e6i	−2.21077	+	0.389819i
$421$	2.08592e6	−	1.20431e6i	0.573579	−	0.331156i	−0.184999	−	0.982739i	$-0.559228\pi$
$421$	2.08592e6	−	1.20431e6i	0.573579	−	0.331156i	0.758577	+	0.651583i	$0.225895\pi$
$422$	−923336.	−	2.53685e6i	−0.252394	−	0.693447i
$423$	−2.25308e6	+	820055.i	−0.612246	+	0.222839i
$424$	−1.19761e6	−	211171.i	−0.323520	−	0.0570454i
$425$	−3.69592e6	−	4.40463e6i	−0.992545	−	1.18287i
$426$	−1.04608e6	−	1.24666e6i	−0.279280	−	0.332832i
$427$	−6.20664e6	−	1.09440e6i	−1.64735	−	0.290473i
$428$	−1.29405e6	+	470994.i	−0.341461	+	0.124281i
$429$	−3.61444e6	−	9.93059e6i	−0.948195	−	2.60515i
$430$	−866714.	+	500397.i	−0.226050	+	0.130510i
$431$	1.17176e6	−	206613.i	0.303841	−	0.0535754i	−0.0196491	−	0.999807i	$-0.506255\pi$
$431$	1.17176e6	−	206613.i	0.303841	−	0.0535754i	0.323490	+	0.946232i	$0.395144\pi$
$432$	1.26684e6	+	1.06301e6i	0.326598	+	0.274048i
$433$	−797930.	+	1.38205e6i	−0.204524	+	0.354246i	−0.949981	−	0.312308i	$-0.898898\pi$
$433$	−797930.	+	1.38205e6i	−0.204524	+	0.354246i	0.745457	+	0.666554i	$0.232231\pi$
$434$	−1.31100e6	−	2.27072e6i	−0.334102	−	0.578681i
$435$	377636.	−	2.14168e6i	0.0956865	−	0.542665i
$436$	1.60500e6	+	926647.i	0.404351	+	0.233452i
$437$	1.30235e6	+	474016.i	0.326230	+	0.118738i
$438$		−	2.75871e6i		−	0.687101i
$439$	406532.	−	1.11694e6i	0.100678	−	0.276610i	−0.879120	−	0.476600i	$-0.841869\pi$
$439$	406532.	−	1.11694e6i	0.100678	−	0.276610i	0.979798	+	0.199990i	$0.0640911\pi$
$440$	−625858.	−	3.54942e6i	−0.154115	−	0.874028i
$441$	1.21931e7	−	1.02312e7i	2.98550	−	2.50514i
$442$	2.17449e6	−	2.59146e6i	0.529422	−	0.630940i
$443$	−5.50854e6			−1.33361			−0.666803	−	0.745234i	$-0.732338\pi$
$443$	−5.50854e6			−1.33361			−0.666803	+	0.745234i	$0.732338\pi$
$444$	2.09695e6	+	2.91324e6i	0.504814	+	0.701325i
$445$	−3.10874e6			−0.744191
$446$	−197771.	+	235694.i	−0.0470787	+	0.0561062i
$447$	3.91948e6	−	3.28884e6i	0.927812	−	0.778527i
$448$	−158687.	−	899956.i	−0.0373547	−	0.211849i
$449$	−1.74161e6	+	4.78503e6i	−0.407694	+	1.12013i	0.550705	+	0.834700i	$0.314359\pi$
$449$	−1.74161e6	+	4.78503e6i	−0.407694	+	1.12013i	−0.958399	+	0.285431i	$0.907863\pi$
$450$		−	7.71758e6i		−	1.79659i
$451$	−5.83718e6	−	2.12456e6i	−1.35133	−	0.491844i
$452$	2.64017e6	+	1.52431e6i	0.607836	+	0.350934i
$453$	−2.41108e6	+	1.36739e7i	−0.552035	+	3.13075i
$454$	1.21334e6	+	2.10157e6i	0.276277	+	0.478526i
$455$	−5.53354e6	+	9.58437e6i	−1.25307	+	2.17038i
$456$	−706529.	−	592848.i	−0.159117	−	0.133515i
$457$	−5.34347e6	+	942198.i	−1.19683	+	0.211034i	−0.736328	−	0.676625i	$-0.763442\pi$
$457$	−5.34347e6	+	942198.i	−1.19683	+	0.211034i	−0.460503	+	0.887658i	$0.652331\pi$
$458$	−4.99198e6	+	2.88212e6i	−1.11201	+	0.642020i
$459$	−3.17884e6	−	8.73380e6i	−0.704267	−	1.93496i
$460$	−3.28728e6	+	1.19647e6i	−0.724340	+	0.263638i
$461$	5.97790e6	+	1.05407e6i	1.31008	+	0.231002i	0.784704	−	0.619871i	$-0.212815\pi$
$461$	5.97790e6	+	1.05407e6i	1.31008	+	0.231002i	0.525372	+	0.850872i	$0.323926\pi$
$462$	1.03130e7	+	1.22906e7i	2.24792	+	2.67896i
$463$	−729486.	−	869368.i	−0.158148	−	0.188474i	0.681152	−	0.732142i	$-0.261479\pi$
$463$	−729486.	−	869368.i	−0.158148	−	0.188474i	−0.839300	+	0.543668i	$0.817035\pi$
$464$	241162.	+	42523.4i	0.0520013	+	0.00916922i
$465$	6.27675e6	−	2.28455e6i	1.34618	−	0.489969i
$466$	−1.60740e6	−	4.41630e6i	−0.342894	−	0.942093i
$467$	3.65505e6	−	2.11024e6i	0.775534	−	0.447755i	−0.0593110	−	0.998240i	$-0.518890\pi$
$467$	3.65505e6	−	2.11024e6i	0.775534	−	0.447755i	0.834845	+	0.550485i	$0.185557\pi$
$468$	4.47165e6	−	788472.i	0.943741	−	0.166407i
$469$	−6.39103e6	−	5.36271e6i	−1.34165	−	1.12578i
$470$	−838201.	+	1.45181e6i	−0.175026	+	0.303155i
$471$	6.91871e6	+	1.19836e7i	1.43705	+	2.48905i
$472$	172217.	−	976694.i	0.0355813	−	0.201792i
$473$	1.71347e6	+	989274.i	0.352147	+	0.203312i
$474$	1.01369e7	+	3.68953e6i	2.07233	+	0.754266i
$475$			2.13776e6i			0.434734i
$476$	−1.75659e6	+	4.82619e6i	−0.355347	+	0.976308i
$477$	1.59298e6	+	9.03423e6i	0.320564	+	1.81801i
$478$	1.30131e6	−	1.09193e6i	0.260502	−	0.218588i
$479$	4.90578e6	−	5.84648e6i	0.976943	−	1.16428i	−0.00946353	−	0.999955i	$-0.503012\pi$
$479$	4.90578e6	−	5.84648e6i	0.976943	−	1.16428i	0.986407	−	0.164321i	$-0.0525432\pi$
$480$	2.32802e6			0.461194
$481$	4.88144e6	+	363067.i	0.962022	+	0.0715525i
$482$	−1.23213e6			−0.241568
$483$	1.00099e7	−	1.19294e7i	1.95238	−	2.32675i
$484$	−3.48440e6	+	2.92376e6i	−0.676105	+	0.567319i
$485$	−287903.	−	1.63278e6i	−0.0555766	−	0.315191i
$486$	−57184.7	+	157114.i	−0.0109822	+	0.0301733i
$487$		−	1.96632e6i		−	0.375693i	−0.982198	−	0.187846i	$-0.939849\pi$
$487$		−	1.96632e6i		−	0.375693i	0.982198	−	0.187846i	$-0.0601507\pi$
$488$	1.69887e6	+	618340.i	0.322932	+	0.117538i
$489$	3.19557e6	+	1.84496e6i	0.604333	+	0.348912i
$490$	1.93249e6	−	1.09597e7i	0.363603	−	2.06209i
$491$	−1.51422e6	−	2.62270e6i	−0.283456	−	0.490959i	0.688778	−	0.724972i	$-0.258147\pi$
$491$	−1.51422e6	−	2.62270e6i	−0.283456	−	0.490959i	−0.972233	+	0.234013i	$0.924814\pi$
$492$	2.00617e6	−	3.47479e6i	0.373641	−	0.647166i
$493$	−1.05429e6	−	884654.i	−0.195363	−	0.163929i
$494$	−1.23864e6	+	218405.i	−0.228364	+	0.0402667i
$495$	−2.35457e7	+	1.35941e7i	−4.31915	+	2.49366i
$496$	257250.	+	706787.i	0.0469516	+	0.128998i
$497$	3.16612e6	−	1.15237e6i	0.574958	−	0.209268i
$498$	−747392.	−	131785.i	−0.135044	−	0.0238119i
$499$	−1.48848e6	−	1.77390e6i	−0.267604	−	0.318917i	0.615463	−	0.788166i	$-0.288969\pi$
$499$	−1.48848e6	−	1.77390e6i	−0.267604	−	0.318917i	−0.883066	+	0.469249i	$0.844525\pi$
$500$	−756267.	−	901284.i	−0.135285	−	0.161227i
$501$	5.15566e6	+	909082.i	0.917677	+	0.161811i
$502$	813013.	−	295913.i	0.143992	−	0.0524088i
$503$	−1.70541e6	−	4.68558e6i	−0.300545	−	0.825741i	−0.994405	−	0.105631i	$-0.966314\pi$
$503$	−1.70541e6	−	4.68558e6i	−0.300545	−	0.825741i	0.693860	−	0.720110i	$-0.255909\pi$
$504$	−5.97001e6	+	3.44679e6i	−1.04689	+	0.604419i
$505$	3.36308e6	−	593002.i	0.586825	−	0.103473i
$506$	5.29794e6	+	4.44550e6i	0.919879	+	0.771870i
$507$	−347068.	+	601140.i	−0.0599646	+	0.103862i
$508$	980946.	+	1.69905e6i	0.168650	+	0.292110i
$509$	−1.17588e6	+	6.66877e6i	−0.201173	+	1.14091i	0.702176	+	0.712004i	$0.252212\pi$
$509$	−1.17588e6	+	6.66877e6i	−0.201173	+	1.14091i	−0.903349	+	0.428906i	$0.858899\pi$
$510$	−1.13309e7	−	6.54192e6i	−1.92904	−	1.11373i
$511$	5.36707e6	+	1.95345e6i	0.909254	+	0.330941i
$512$			262144.i			0.0441942i
$513$	−1.18188e6	+	3.24718e6i	−0.198280	+	0.544769i
$514$	−126051.	−	714870.i	−0.0210445	−	0.119349i
$515$	−8.92481e6	+	7.48880e6i	−1.48279	+	1.24421i
$516$	−821476.	+	978997.i	−0.135822	+	0.161867i
$517$	3.31421e6			0.545323
$518$	−7.15258e6	+	2.01674e6i	−1.17122	+	0.330237i
$519$	−6.73216e6			−1.09707
$520$	2.04066e6	−	2.43196e6i	0.330950	−	0.394411i
$521$	−5.47420e6	+	4.59340e6i	−0.883540	+	0.741378i	−0.966904	−	0.255141i	$-0.917878\pi$
$521$	−5.47420e6	+	4.59340e6i	−0.883540	+	0.741378i	0.0833642	+	0.996519i	$0.473434\pi$
$522$	−320776.	−	1.81921e6i	−0.0515260	−	0.292218i
$523$	2.74513e6	−	7.54219e6i	0.438843	−	1.20571i	−0.501403	−	0.865214i	$-0.667182\pi$
$523$	2.74513e6	−	7.54219e6i	0.438843	−	1.20571i	0.940246	−	0.340497i	$-0.110595\pi$
$524$		−	341394.i		−	0.0543159i
$525$	2.25718e7	+	8.21547e6i	3.57411	+	1.30087i
$526$	2.68024e6	+	1.54744e6i	0.422386	+	0.243864i
$527$	734044.	−	4.16297e6i	0.115132	−	0.652945i
$528$	−2.30122e6	−	3.98583e6i	−0.359231	−	0.622206i
$529$	138191.	−	239354.i	0.0214704	−	0.0371878i
$530$	4.91339e6	+	4.12282e6i	0.759786	+	0.637536i
$531$	−7.36772e6	+	1.29913e6i	−1.13396	+	0.199947i
$532$	1.65368e6	−	954754.i	0.253322	−	0.146256i
$533$	−1.87140e6	−	5.14163e6i	−0.285331	−	0.783939i
$534$	−3.73038e6	+	1.35775e6i	−0.566109	+	0.206047i
$535$	7.15282e6	+	1.26124e6i	1.08042	+	0.190507i
$536$	1.53835e6	+	1.83333e6i	0.231282	+	0.275632i
$537$	−1.01428e7	−	1.20877e7i	−1.51782	−	1.80887i
$538$	−7.86266e6	−	1.38640e6i	−1.17115	−	0.206506i
$539$	−2.06745e7	+	7.52490e6i	−3.06523	+	1.11565i
$540$	−2.98320e6	−	8.19627e6i	−0.440249	−	1.20957i
$541$	9.18314e6	−	5.30189e6i	1.34896	−	0.778820i	0.360855	−	0.932622i	$-0.382485\pi$
$541$	9.18314e6	−	5.30189e6i	1.34896	−	0.778820i	0.988102	+	0.153802i	$0.0491517\pi$
$542$	5.93077e6	−	1.04575e6i	0.867187	−	0.152908i
$543$	−9.09690e6	−	7.63321e6i	−1.32402	−	1.11098i
$544$	736646.	−	1.27591e6i	0.106724	−	0.184851i
$545$	−4.88738e6	−	8.46520e6i	−0.704831	−	1.22080i
$546$	−2.45406e6	+	1.39177e7i	−0.352293	+	1.99795i
$547$	−1.07837e7	−	6.22599e6i	−1.54099	−	0.889692i	−0.998776	−	0.0494531i	$-0.984252\pi$
$547$	−1.07837e7	−	6.22599e6i	−1.54099	−	0.889692i	−0.542216	−	0.840239i	$-0.682414\pi$
$548$	5.51260e6	+	2.00642e6i	0.784160	+	0.285411i
$549$		−	1.36380e7i		−	1.93117i
$550$	−3.64856e6	+	1.00243e7i	−0.514298	+	1.41302i
$551$	88854.4	+	503919.i	0.0124681	+	0.0707101i
$552$	−3.42206e6	+	2.87145e6i	−0.478013	+	0.401101i
$553$	−1.43559e7	+	1.71088e7i	−1.99627	+	2.37906i
$554$	−5.91446e6			−0.818729
$555$	−1.89553e6	−	1.88366e7i	−0.261215	−	2.59579i
$556$	−3.05195e6			−0.418687
$557$	6.38394e6	−	7.60808e6i	0.871867	−	1.03905i	−0.127020	−	0.991900i	$-0.540541\pi$
$557$	6.38394e6	−	7.60808e6i	0.871867	−	1.03905i	0.998888	−	0.0471511i	$-0.0150142\pi$
$558$	4.34642e6	−	3.64708e6i	0.590944	−	0.495861i
$559$	302632.	+	1.71631e6i	0.0409624	+	0.232309i
$560$	−1.64848e6	+	4.52916e6i	−0.222133	+	0.610306i
$561$			2.58665e7i			3.47000i
$562$	2.77088e6	+	1.00852e6i	0.370065	+	0.134693i
$563$	8.35104e6	+	4.82148e6i	1.11037	+	0.641075i	0.938926	−	0.344118i	$-0.111822\pi$
$563$	8.35104e6	+	4.82148e6i	1.11037	+	0.641075i	0.171448	+	0.985193i	$0.445155\pi$
$564$	−371733.	+	2.10820e6i	−0.0492077	+	0.279071i
$565$	−8.03959e6	−	1.39250e7i	−1.05953	−	1.83516i
$566$	3.67253e6	−	6.36101e6i	0.481864	−	0.834613i
$567$	9.69334e6	+	8.13368e6i	1.26624	+	1.06250i
$568$	−951837.	+	167835.i	−0.123792	+	0.0218278i
$569$	−7.84262e6	+	4.52794e6i	−1.01550	+	0.586300i	−0.912798	−	0.408412i	$-0.866083\pi$
$569$	−7.84262e6	+	4.52794e6i	−1.01550	+	0.586300i	−0.102704	+	0.994712i	$0.532749\pi$
$570$	1.66376e6	+	4.57113e6i	0.214488	+	0.589300i
$571$	8.11248e6	−	2.95270e6i	1.04127	−	0.378991i	0.235908	−	0.971775i	$-0.424194\pi$
$571$	8.11248e6	−	2.95270e6i	1.04127	−	0.378991i	0.805361	+	0.592784i	$0.201971\pi$
$572$	−6.18097e6	−	1.08987e6i	−0.789890	−	0.139279i
$573$	1.17005e7	+	1.39441e7i	1.48874	+	1.77421i
$574$	5.33962e6	+	6.36352e6i	0.676443	+	0.806153i
$575$	1.01969e7	+	1.79798e6i	1.28617	+	0.226786i
$576$	1.85824e6	−	676342.i	0.233370	−	0.0849396i
$577$	3.96923e6	+	1.09054e7i	0.496325	+	1.36364i	0.894801	+	0.446464i	$0.147317\pi$
$577$	3.96923e6	+	1.09054e7i	0.496325	+	1.36364i	−0.398476	+	0.917179i	$0.630461\pi$
$578$	−2.25228e6	+	1.30035e6i	−0.280416	+	0.161898i
$579$	1.00256e7	−	1.76778e6i	1.24284	−	0.219146i
$580$	−989403.	−	830208.i	−0.122125	−	0.102475i
$581$	785620.	−	1.36073e6i	0.0965544	−	0.167237i
$582$	−1.05859e6	−	1.83354e6i	−0.129545	−	0.224379i
$583$	2.20191e6	−	1.24876e7i	0.268304	−	1.52163i
$584$	−1.41890e6	−	819203.i	−0.172155	−	0.0993939i
$585$	−2.25042e7	−	8.19087e6i	−2.71878	−	0.989555i
$586$			7.16860e6i			0.862364i
$587$	2.90748e6	−	7.98823e6i	0.348274	−	0.956876i	−0.634639	−	0.772808i	$-0.718851\pi$
$587$	2.90748e6	−	7.98823e6i	0.348274	−	0.956876i	0.982914	−	0.184067i	$-0.0589264\pi$
$588$	−2.46774e6	−	1.39953e7i	−0.294345	−	1.66931i
$589$	−1.20395e6	+	1.01023e6i	−0.142995	+	0.119987i
$590$	−3.36230e6	+	4.00703e6i	−0.397655	+	0.473907i
$591$	−1.84982e7			−2.17852
$592$	2.12108e6	−	213444.i	0.248744	−	0.0250311i
$593$	490456.			0.0572748			0.0286374	−	0.999590i	$-0.490883\pi$
$593$	490456.			0.0572748			0.0286374	+	0.999590i	$0.490883\pi$
$594$	−1.10841e7	+	1.32095e7i	−1.28894	+	1.53610i
$595$	2.07508e7	−	1.74120e7i	2.40293	−	2.01630i
$596$	−527668.	−	2.99255e6i	−0.0608478	−	0.345085i
$597$	−1.74522e6	+	4.79494e6i	−0.200407	+	0.550615i
$598$			6.09187e6i			0.696623i
$599$	3.86044e6	+	1.40509e6i	0.439612	+	0.160006i	0.552338	−	0.833620i	$-0.313736\pi$
$599$	3.86044e6	+	1.40509e6i	0.439612	+	0.160006i	−0.112726	+	0.993626i	$0.535958\pi$
$600$	−5.96735e6	−	3.44525e6i	−0.676711	−	0.390699i
$601$	−1.06334e6	+	6.03048e6i	−0.120084	+	0.681029i	0.864023	+	0.503452i	$0.167937\pi$
$601$	−1.06334e6	+	6.03048e6i	−0.120084	+	0.681029i	−0.984107	+	0.177577i	$0.943174\pi$
$602$	−1.32295e6	−	2.29141e6i	−0.148782	−	0.257699i
$603$	9.02677e6	−	1.56348e7i	1.01097	−	1.75105i
$604$	6.31701e6	+	5.30060e6i	0.704562	+	0.591197i
$605$	2.36258e7	−	4.16587e6i	2.62421	−	0.462719i
$606$	3.77658e6	−	2.18041e6i	0.417751	−	0.241188i
$607$	750744.	+	2.06265e6i	0.0827028	+	0.227224i	0.974151	−	0.225899i	$-0.0725320\pi$
$607$	750744.	+	2.06265e6i	0.0827028	+	0.227224i	−0.891448	+	0.453123i	$0.850310\pi$
$608$	−514728.	+	187345.i	−0.0564701	+	0.0205534i
$609$	5.66217e6	+	998393.i	0.618642	+	0.109083i
$610$	−6.12922e6	−	7.30452e6i	−0.666930	−	0.794816i
$611$	1.87648e6	+	2.23631e6i	0.203349	+	0.242342i
$612$	−1.09450e7	−	1.92990e6i	−1.18124	−	0.208284i
$613$	−1.32579e6	+	482547.i	−0.142502	+	0.0518667i	−0.412287	−	0.911054i	$-0.635270\pi$
$613$	−1.32579e6	+	482547.i	−0.142502	+	0.0518667i	0.269784	+	0.962921i	$0.413048\pi$
$614$	318995.	+	876431.i	0.0341478	+	0.0938203i
$615$	−1.83270e7	+	1.05811e7i	−1.95390	+	1.12809i
$616$	9.38394e6	−	1.65464e6i	0.996399	−	0.175692i
$617$	1.48184e6	+	1.24341e6i	0.156707	+	0.131493i	0.717770	−	0.696280i	$-0.245163\pi$
$617$	1.48184e6	+	1.24341e6i	0.156707	+	0.131493i	−0.561063	+	0.827773i	$0.689607\pi$
$618$	−7.43870e6	+	1.28842e7i	−0.783477	+	1.35702i
$619$	−1.30418e6	−	2.25890e6i	−0.136807	−	0.236957i	0.789479	−	0.613778i	$-0.210351\pi$
$619$	−1.30418e6	−	2.25890e6i	−0.136807	−	0.236957i	−0.926286	+	0.376820i	$0.877017\pi$
$620$	688867.	−	3.90676e6i	0.0719707	−	0.408166i
$621$	1.44947e7	+	8.36851e6i	1.50827	+	0.870801i
$622$	−7.21606e6	−	2.62643e6i	−0.747866	−	0.272201i
$623$		−	8.21888e6i		−	0.848384i
$624$	1.38656e6	−	3.80953e6i	0.142553	−	0.391661i
$625$	−1.09108e6	−	6.18782e6i	−0.111727	−	0.633633i
$626$	7.89417e6	−	6.62400e6i	0.805139	−	0.675592i
$627$	6.18169e6	−	7.36705e6i	0.627969	−	0.748385i
$628$	8.21809e6			0.831518
$629$	−1.09235e7	−	4.92152e6i	−1.10087	−	0.495990i
$630$	3.63586e7			3.64968
$631$	−2.05894e6	+	2.45374e6i	−0.205859	+	0.245333i	−0.859089	−	0.511827i	$-0.828969\pi$
$631$	−2.05894e6	+	2.45374e6i	−0.205859	+	0.245333i	0.653230	+	0.757160i	$0.273413\pi$
$632$	4.90782e6	−	4.11815e6i	0.488760	−	0.410118i
$633$	3.15735e6	+	1.79062e7i	0.313194	+	1.77621i
$634$	2.21390e6	−	6.08264e6i	0.218743	−	0.600992i
$635$		−	1.03475e7i		−	1.01836i
$636$	7.69653e6	+	2.80131e6i	0.754488	+	0.274611i
$637$	−1.67833e7	−	9.68984e6i	−1.63881	−	0.946167i
$638$	−443396.	+	2.51462e6i	−0.0431260	+	0.244580i
$639$	3.64549e6	+	6.31418e6i	0.353187	+	0.611737i
$640$	691309.	−	1.19738e6i	0.0667148	−	0.115553i
$641$	−1.96694e6	−	1.65046e6i	−0.189081	−	0.158657i	0.543333	−	0.839517i	$-0.317162\pi$
$641$	−1.96694e6	−	1.65046e6i	−0.189081	−	0.158657i	−0.732414	+	0.680860i	$0.761606\pi$
$642$	9.13398e6	−	1.61057e6i	0.874626	−	0.154220i
$643$	−2.78021e6	+	1.60515e6i	−0.265185	+	0.153105i	−0.626698	−	0.779263i	$-0.715594\pi$
$643$	−2.78021e6	+	1.60515e6i	−0.265185	+	0.153105i	0.361512	+	0.932367i	$0.382261\pi$
$644$	−3.16323e6	−	8.69091e6i	−0.300550	−	0.825753i
$645$	6.33396e6	−	2.30537e6i	0.599482	−	0.218193i
$646$	3.03174e6	+	534577.i	0.285832	+	0.0503998i
$647$	8.73974e6	+	1.04156e7i	0.820801	+	0.978192i	0.999984	−	0.00562328i	$-0.00178995\pi$
$647$	8.73974e6	+	1.04156e7i	0.820801	+	0.978192i	−0.179183	+	0.983816i	$0.557346\pi$
$648$	−2.33323e6	−	2.78063e6i	−0.218283	−	0.260139i
$649$	1.01841e7	+	1.79573e6i	0.949097	+	0.167351i
$650$	−8.82985e6	+	3.21380e6i	−0.819728	+	0.298357i
$651$	6.03989e6	+	1.65945e7i	0.558568	+	1.53465i
$652$	1.89786e6	−	1.09573e6i	0.174842	−	0.100945i
$653$	1.11407e7	−	1.96440e6i	1.02242	−	0.180280i	0.362790	−	0.931871i	$-0.381824\pi$
$653$	1.11407e7	−	1.96440e6i	1.02242	−	0.180280i	0.659629	+	0.751591i	$0.270713\pi$
$654$	−9.56187e6	−	8.02336e6i	−0.874175	−	0.733520i
$655$	−900300.	+	1.55937e6i	−0.0819944	+	0.142018i
$656$	−1.19147e6	−	2.06369e6i	−0.108100	−	0.187234i
$657$	−2.14618e6	+	1.21716e7i	−0.193978	+	1.10011i
$658$	−3.83828e6	−	2.21603e6i	−0.345599	−	0.199531i
$659$	1.51619e7	+	5.51849e6i	1.36001	+	0.495002i	0.916056	−	0.401049i	$-0.131354\pi$
$659$	1.51619e7	+	5.51849e6i	1.36001	+	0.495002i	0.443950	+	0.896051i	$0.353577\pi$
$660$			2.42745e7i			2.16915i
$661$	−1.81019e6	+	4.97346e6i	−0.161146	+	0.442746i	−0.993818	−	0.111021i	$-0.964588\pi$
$661$	−1.81019e6	+	4.97346e6i	−0.161146	+	0.442746i	0.832672	+	0.553767i	$0.186810\pi$
$662$	930595.	+	5.27767e6i	0.0825308	+	0.468055i
$663$	−1.74537e7	+	1.46454e7i	−1.54207	+	1.29395i
$664$	−289721.	+	345276.i	−0.0255012	+	0.0303911i
$665$	−1.00712e7			−0.883139
$666$	−6.98549e6	−	1.44848e7i	−0.610255	−	1.26540i
$667$	2.47837e6			0.215701
$668$	1.99855e6	−	2.38178e6i	0.173290	−	0.206520i
$669$	1.58742e6	−	1.33201e6i	0.137128	−	0.115064i
$670$	−2.19189e6	−	1.24308e7i	−0.188639	−	1.06983i
$671$	−6.44749e6	+	1.77143e7i	−0.552821	+	1.51886i
$672$			6.15480e6i			0.525764i
$673$	2.84730e6	+	1.03633e6i	0.242324	+	0.0881987i	0.460327	−	0.887749i	$-0.347732\pi$
$673$	2.84730e6	+	1.03633e6i	0.242324	+	0.0881987i	−0.218003	+	0.975948i	$0.569954\pi$
$674$	3.27043e6	+	1.88819e6i	0.277304	+	0.160101i
$675$	−4.48296e6	+	2.54242e7i	−0.378709	+	2.14777i
$676$	206125.	+	357019.i	0.0173486	+	0.0300486i
$677$	2.09872e6	−	3.63508e6i	0.175988	−	0.304819i	−0.764515	−	0.644606i	$-0.777021\pi$
$677$	2.09872e6	−	3.63508e6i	0.175988	−	0.304819i	0.940503	+	0.339786i	$0.110355\pi$
$678$	−1.57290e7	−	1.31982e7i	−1.31409	−	1.10265i
$679$	4.31674e6	−	761157.i	0.359320	−	0.0633578i
$680$	−6.72948e6	+	3.88526e6i	−0.558096	+	0.322217i
$681$	−5.58998e6	−	1.53583e7i	−0.461894	−	1.26904i
$682$	−7.36975e6	+	2.68237e6i	−0.606725	+	0.220830i
$683$	−2.05708e7	−	3.62718e6i	−1.68732	−	0.297521i	−0.754085	−	0.656777i	$-0.771919\pi$
$683$	−2.05708e7	−	3.62718e6i	−1.68732	−	0.297521i	−0.933239	+	0.359256i	$0.883031\pi$
$684$	2.65604e6	+	3.16534e6i	0.217067	+	0.258690i
$685$	−1.98884e7	−	2.37021e7i	−1.61947	−	1.93001i
$686$	1.42041e7	+	2.50457e6i	1.15240	+	0.203200i
$687$	3.64815e7	−	1.32782e7i	2.94904	−	1.07336i
$688$	259594.	+	713229.i	0.0209085	+	0.0574457i
$689$	9.67290e6	−	5.58465e6i	0.776263	−	0.448176i
$690$	2.32032e7	−	4.09134e6i	1.85534	−	0.327147i
$691$	−8.47410e6	−	7.11061e6i	−0.675147	−	0.566516i	0.239437	−	0.970912i	$-0.423037\pi$
$691$	−8.47410e6	−	7.11061e6i	−0.675147	−	0.566516i	−0.914584	+	0.404396i	$0.867482\pi$
$692$	−1.99912e6	+	3.46258e6i	−0.158699	+	0.274875i
$693$	−3.59400e7	−	6.22500e7i	−2.84279	−	4.92386i
$694$	−679893.	+	3.85587e6i	−0.0535849	+	0.303895i
$695$	1.39402e7	+	8.04839e6i	1.09473	+	0.632043i
$696$	−1.54984e6	−	564096.i	−0.121273	−	0.0441398i
$697$			1.33925e7i			1.04419i
$698$	159111.	−	437154.i	0.0123612	−	0.0339622i
$699$	5.49651e6	+	3.11723e7i	0.425495	+	2.41310i
$700$	1.09282e7	−	9.16988e6i	0.842956	−	0.707324i
$701$	−1.09394e7	+	1.30370e7i	−0.840808	+	1.00204i	0.159083	+	0.987265i	$0.449146\pi$
$701$	−1.09394e7	+	1.30370e7i	−0.840808	+	1.00204i	−0.999891	+	0.0147704i	$0.995298\pi$
$702$	−1.51890e7			−1.16329
$703$	1.93497e6	+	4.01226e6i	0.147668	+	0.306197i
$704$	−2.73340e6			−0.207861
$705$	7.25755e6	−	8.64921e6i	0.549942	−	0.655396i
$706$	1.14349e7	−	9.59503e6i	0.863418	−	0.724494i
$707$	1.56778e6	+	8.89129e6i	0.117960	+	0.668985i
$708$	−2.28456e6	+	6.27678e6i	−0.171285	+	0.470602i
$709$		−	1.44631e7i		−	1.08056i	−0.841487	−	0.540278i	$-0.818319\pi$
$709$		−	1.44631e7i		−	1.08056i	0.841487	−	0.540278i	$-0.181681\pi$
$710$	4.79026e6	+	1.74351e6i	0.356626	+	0.129801i
$711$	−4.18543e7	−	2.41646e7i	−3.10503	−	1.79269i
$712$	−409405.	+	2.32185e6i	−0.0302659	+	0.171646i
$713$	3.80612e6	+	6.59239e6i	0.280387	+	0.485645i
$714$	1.72955e7	−	2.99567e7i	1.26966	−	2.19912i
$715$	2.53583e7	+	2.12782e7i	1.85505	+	1.55657i
$716$	−9.22904e6	+	1.62733e6i	−0.672781	+	0.118629i
$717$	−9.90838e6	+	5.72061e6i	−0.719788	+	0.415570i
$718$	−115550.	−	317472.i	−0.00836489	−	0.0229823i
$719$	9.54854e6	−	3.47538e6i	0.688834	−	0.250715i	0.0261981	−	0.999657i	$-0.491660\pi$
$719$	9.54854e6	−	3.47538e6i	0.688834	−	0.250715i	0.662636	+	0.748942i	$0.269438\pi$
$720$	−1.02714e7	−	1.81112e6i	−0.738409	−	0.130201i
$721$	−1.97989e7	−	2.35954e7i	−1.41841	−	1.69040i
$722$	5.63071e6	+	6.71041e6i	0.401994	+	0.479078i
$723$	8.17246e6	+	1.44102e6i	0.581443	+	0.102524i
$724$	−6.62737e6	+	2.41216e6i	−0.469888	+	0.171025i
$725$	1.30748e6	+	3.59227e6i	0.0923826	+	0.253819i
$726$	2.65307e7	−	1.53175e7i	1.86813	−	1.07857i
$727$	1.85045e7	−	3.26284e6i	1.29850	−	0.228960i	0.518681	−	0.854968i	$-0.326423\pi$
$727$	1.85045e7	−	3.26284e6i	1.29850	−	0.228960i	0.779817	+	0.626007i	$0.215312\pi$
$728$	6.42962e6	+	5.39509e6i	0.449631	+	0.377285i
$729$	7.45410e6	−	1.29109e7i	0.519489	−	0.899782i
$730$	4.32070e6	+	7.48366e6i	0.300087	+	0.519765i
$731$	740733.	−	4.20091e6i	0.0512706	−	0.290770i
$732$	−1.05451e7	−	6.08821e6i	−0.727399	−	0.419964i
$733$	−1.11286e7	−	4.05048e6i	−0.765035	−	0.278450i	−0.0701166	−	0.997539i	$-0.522337\pi$
$733$	−1.11286e7	−	4.05048e6i	−0.765035	−	0.278450i	−0.694918	+	0.719089i	$0.744559\pi$
$734$		−	9.24765e6i		−	0.633565i
$735$	−2.56356e7	+	7.04332e7i	−1.75035	+	4.80905i
$736$	460701.	+	2.61277e6i	0.0313491	+	0.177790i
$737$	−1.91164e7	+	1.60405e7i	−1.29639	+	1.08780i
$738$	−1.15546e7	+	1.37703e7i	−0.780935	+	0.930682i
$739$	1.07538e7			0.724355			0.362177	−	0.932109i	$-0.382033\pi$
$739$	1.07538e7			0.724355			0.362177	+	0.932109i	$0.382033\pi$
$740$	−1.02512e7	−	4.61862e6i	−0.688170	−	0.310051i
$741$	8.47105e6			0.566750
$742$	−1.08999e7	+	1.29900e7i	−0.726796	+	0.866162i
$743$	−1.13008e7	+	9.48253e6i	−0.750998	+	0.630162i	−0.935767	−	0.352620i	$-0.885291\pi$
$743$	−1.13008e7	+	9.48253e6i	−0.750998	+	0.630162i	0.184769	+	0.982782i	$0.440846\pi$
$744$	−879666.	−	4.98883e6i	−0.0582620	−	0.330420i
$745$	−5.48156e6	+	1.50605e7i	−0.361837	+	0.994140i
$746$			7.82134e6i			0.514558i
$747$	3.19502e6	+	1.16289e6i	0.209494	+	0.0762496i
$748$	1.33040e7	+	7.68108e6i	0.869419	+	0.501959i
$749$	−3.33445e6	+	1.89106e7i	−0.217180	+	1.23169i
$750$	3.96207e6	+	6.86250e6i	0.257199	+	0.445481i
$751$	−1.28258e7	+	2.22149e7i	−0.829821	+	1.43729i	0.0683571	+	0.997661i	$0.478224\pi$
$751$	−1.28258e7	+	2.22149e7i	−0.829821	+	1.43729i	−0.898178	+	0.439631i	$0.855109\pi$
$752$	973935.	+	817229.i	0.0628037	+	0.0526986i
$753$	−5.73862e6	+	1.01187e6i	−0.368825	+	0.0650338i
$754$	−1.94782e6	+	1.12458e6i	−0.124773	+	0.0720378i
$755$	−1.48755e7	−	4.08701e7i	−0.949738	−	2.60938i
$756$	2.16693e7	−	7.88697e6i	1.37892	−	0.501887i
$757$	5.38727e6	+	949922.i	0.341688	+	0.0602487i	0.341859	−	0.939751i	$-0.388943\pi$
$757$	5.38727e6	+	949922.i	0.341688	+	0.0602487i	−0.000171420		1.00000i	$0.500055\pi$
$758$	731029.	+	871206.i	0.0462127	+	0.0550742i
$759$	−2.99409e7	−	3.56822e7i	−1.88652	−	2.24826i
$760$	2.84515e6	+	501677.i	0.178678	+	0.0315057i
$761$	−1.75886e7	+	6.40171e6i	−1.10095	+	0.400714i	−0.827667	−	0.561219i	$-0.810332\pi$
$761$	−1.75886e7	+	6.40171e6i	−1.10095	+	0.400714i	−0.273285	+	0.961933i	$0.588110\pi$
$762$	−4.51930e6	−	1.24167e7i	−0.281957	−	0.774672i
$763$	2.23802e7	−	1.29212e7i	1.39173	−	0.803513i
$764$	1.06464e7	−	1.87726e6i	0.659890	−	0.116356i
$765$	4.49034e7	+	3.76785e7i	2.77412	+	2.32777i
$766$	−5.27701e6	+	9.14004e6i	−0.324949	+	0.562829i
$767$	4.55447e6	+	7.88858e6i	0.279544	+	0.484184i
$768$	306588.	−	1.73874e6i	0.0187565	−	0.106373i
$769$	5.34753e6	+	3.08740e6i	0.326090	+	0.188268i	0.654104	−	0.756405i	$-0.273046\pi$
$769$	5.34753e6	+	3.08740e6i	0.326090	+	0.188268i	−0.328014	+	0.944673i	$0.606379\pi$
$770$	−4.72260e7	−	1.71889e7i	−2.87048	−	1.04477i
$771$			4.88900e6i			0.296199i
$772$	2.06788e6	−	5.68146e6i	0.124877	−	0.343097i
$773$	−3.89512e6	−	2.20903e7i	−0.234462	−	1.32970i	−0.843744	−	0.536745i	$-0.819654\pi$
$773$	−3.89512e6	−	2.20903e7i	−0.234462	−	1.32970i	0.609283	−	0.792953i	$-0.291457\pi$
$774$	4.38603e6	−	3.68032e6i	0.263160	−	0.220817i
$775$	−7.54739e6	+	8.99463e6i	−0.451380	+	0.537934i
$776$	−1.25740e6			−0.0749583
$777$	4.98001e7	−	5.01139e6i	2.95923	−	0.297787i
$778$	−1.21769e7			−0.721255
$779$	3.20061e6	−	3.81434e6i	0.188968	−	0.225204i
$780$	−1.63795e7	+	1.37441e7i	−0.963973	+	0.808870i
$781$	−1.75003e6	−	9.92491e6i	−0.102664	−	0.582236i
$782$	5.09976e6	−	1.40115e7i	0.298217	−	0.819345i
$783$			6.17940e6i			0.360198i
$784$	−7.93106e6	−	2.88667e6i	−0.460830	−	0.167728i
$785$	−3.75373e7	−	2.16722e7i	−2.17415	−	1.25525i
$786$	−399273.	+	2.26439e6i	−0.0230523	+	0.130736i
$787$	1.56470e7	+	2.71013e7i	0.900520	+	1.55975i	0.826821	+	0.562466i	$0.190147\pi$
$787$	1.56470e7	+	2.71013e7i	0.900520	+	1.55975i	0.0736991	+	0.997281i	$0.476520\pi$
$788$	−5.49307e6	+	9.51428e6i	−0.315137	+	0.545834i
$789$	−1.59677e7	−	1.33985e7i	−0.913164	−	0.766235i
$790$	−3.32773e7	+	5.86768e6i	−1.89706	+	0.334502i
$791$	3.68148e7	−	2.12550e7i	2.09209	−	1.20787i
$792$	7.05229e6	+	1.93760e7i	0.399501	+	1.09762i
$793$	−1.56035e7	+	5.67922e6i	−0.881129	+	0.320705i
$794$	2.20728e7	+	3.89203e6i	1.24253	+	0.219091i
$795$	−2.77676e7	−	3.30922e7i	−1.55819	−	1.85698i
$796$	1.94796e6	+	2.32149e6i	0.108968	+	0.129863i
$797$	−1.88643e7	−	3.32629e6i	−1.05195	−	0.185487i	−0.379169	−	0.925328i	$-0.623790\pi$
$797$	−1.88643e7	−	3.32629e6i	−1.05195	−	0.185487i	−0.672783	+	0.739840i	$0.734901\pi$
$798$	−1.20851e7	+	4.39863e6i	−0.671807	+	0.244518i
$799$	−2.44386e6	−	6.71445e6i	−0.135428	−	0.372086i
$800$	−3.54403e6	+	2.04614e6i	−0.195782	+	0.113035i
$801$	1.75150e7	−	3.08836e6i	0.964557	−	0.170077i
$802$	−2.56114e6	−	2.14905e6i	−0.140604	−	0.117981i
$803$	8.54192e6	−	1.47950e7i	0.467484	−	0.809706i
$804$	−8.05938e6	−	1.39593e7i	−0.439705	−	0.761592i
$805$	−8.47055e6	+	4.80389e7i	−0.460704	+	2.61278i
$806$	−5.98267e6	−	3.45409e6i	−0.324382	−	0.187282i
$807$	5.05299e7	+	1.83914e7i	2.73127	+	0.994100i
$808$		−	2.58990e6i		−	0.139558i
$809$	−4.92734e6	+	1.35377e7i	−0.264692	+	0.727236i	0.734144	+	0.678994i	$0.237584\pi$
$809$	−4.92734e6	+	1.35377e7i	−0.264692	+	0.727236i	−0.998836	+	0.0482413i	$0.984638\pi$
$810$	3.32447e6	+	1.88540e7i	0.178037	+	1.00970i
$811$	2.46837e7	−	2.07121e7i	1.31783	−	1.10579i	0.331068	−	0.943607i	$-0.392591\pi$
$811$	2.46837e7	−	2.07121e7i	1.31783	−	1.10579i	0.986761	−	0.162182i	$-0.0518533\pi$
$812$	2.19490e6	−	2.61578e6i	0.116822	−	0.139223i
$813$	−4.05606e7			−2.15217
$814$	2.22560e6	+	2.21167e7i	0.117730	+	1.16993i
$815$	−1.15583e7			−0.609538
$816$	−6.37824e6	+	7.60128e6i	−0.335332	+	0.399633i
$817$	−1.21492e6	+	1.01944e6i	−0.0636786	+	0.0534327i
$818$	2.63671e6	+	1.49535e7i	0.137778	+	0.781377i
$819$	2.16550e7	−	5.94966e7i	1.12810	−	3.09943i
$820$			1.25683e7i			0.652741i
$821$	−1.58309e7	−	5.76197e6i	−0.819685	−	0.298341i	−0.102067	−	0.994778i	$-0.532546\pi$
$821$	−1.58309e7	−	5.76197e6i	−0.819685	−	0.298341i	−0.717618	+	0.696437i	$0.754768\pi$
$822$	−3.42173e7	−	1.97554e7i	−1.76631	−	1.01978i
$823$	−2.62881e6	+	1.49087e7i	−0.135288	+	0.767258i	0.839370	+	0.543560i	$0.182924\pi$
$823$	−2.62881e6	+	1.49087e7i	−0.135288	+	0.767258i	−0.974659	+	0.223698i	$0.928187\pi$
$824$	4.41787e6	+	7.65197e6i	0.226670	+	0.392605i
$825$	3.59240e7	−	6.22222e7i	1.83759	−	3.18281i
$826$	−1.05938e7	−	8.88923e6i	−0.540257	−	0.453330i
$827$	−1.41389e7	+	2.49308e6i	−0.718875	+	0.126757i	−0.521106	−	0.853492i	$-0.674480\pi$
$827$	−1.41389e7	+	2.49308e6i	−0.718875	+	0.126757i	−0.197768	+	0.980249i	$0.563369\pi$
$828$	1.73323e7	−	1.00068e7i	0.878576	−	0.507246i
$829$	1.00653e7	+	2.76543e7i	0.508677	+	1.39758i	0.882602	+	0.470120i	$0.155789\pi$
$829$	1.00653e7	+	2.76543e7i	0.508677	+	1.39758i	−0.373925	+	0.927459i	$0.621988\pi$
$830$	2.23388e6	−	813067.i	0.112555	−	0.0409667i
$831$	3.92293e7	+	6.91719e6i	1.97064	+	0.347478i
$832$	−1.54764e6	−	1.84440e6i	−0.0775105	−	0.0923734i
$833$	3.04903e7	+	3.63369e7i	1.52247	+	1.81441i
$834$	2.02429e7	+	3.56937e6i	1.00776	+	0.177695i
$835$	−1.54098e7	+	5.60870e6i	−0.764857	+	0.278385i
$836$	−1.95347e6	−	5.36712e6i	−0.0966699	−	0.265598i
$837$	−1.64370e7	+	9.48990e6i	−0.810977	+	0.468218i
$838$	−1.24520e7	+	2.19562e6i	−0.612531	+	0.108006i
$839$	−2.72588e7	−	2.28728e7i	−1.33691	−	1.12180i	−0.982409	−	0.186743i	$-0.940207\pi$
$839$	−2.72588e7	−	2.28728e7i	−1.33691	−	1.12180i	−0.354500	−	0.935056i	$-0.615349\pi$
$840$	1.62310e7	−	2.81130e7i	0.793685	−	1.37470i
$841$	−9.79806e6	−	1.69707e7i	−0.477694	−	0.827391i
$842$	−1.67301e6	+	9.48810e6i	−0.0813238	+	0.461210i
$843$	−1.71992e7	−	9.92995e6i	−0.833563	−	0.481258i
$844$	1.01474e7	+	3.69335e6i	0.490341	+	0.178469i
$845$		−	2.17431e6i		−	0.104756i
$846$	3.28022e6	−	9.01233e6i	0.157571	−	0.432923i
$847$	1.10137e7	+	6.24618e7i	0.527503	+	2.99162i
$848$	3.72631e6	−	3.12674e6i	0.177946	−	0.149315i
$849$	−3.17986e7	+	3.78960e7i	−1.51404	+	1.80437i
$850$	2.29993e7			1.09186
$851$	2.07655e7	−	5.85504e6i	0.982920	−	0.277144i
$852$	6.50962e6			0.307225
$853$	2.11034e6	−	2.51501e6i	0.0993072	−	0.118350i	−0.714102	−	0.700042i	$-0.753165\pi$
$853$	2.11034e6	−	2.51501e6i	0.0993072	−	0.118350i	0.813409	+	0.581692i	$0.197609\pi$
$854$	1.93116e7	−	1.62044e7i	0.906097	−	0.760305i
$855$	−3.78441e6	−	2.14625e7i	−0.177045	−	1.00407i
$856$	1.88398e6	−	5.17619e6i	0.0878803	−	0.241449i
$857$		−	4.91235e6i		−	0.228474i	−0.993454	−	0.114237i	$-0.963558\pi$
$857$		−	4.91235e6i		−	0.228474i	0.993454	−	0.114237i	$-0.0364423\pi$
$858$	3.97224e7	+	1.44578e7i	1.84212	+	0.670475i
$859$	−1.99735e7	−	1.15317e7i	−0.923572	−	0.533225i	−0.0387993	−	0.999247i	$-0.512353\pi$
$859$	−1.99735e7	−	1.15317e7i	−0.923572	−	0.533225i	−0.884773	+	0.466022i	$0.845687\pi$
$860$	695145.	−	3.94236e6i	0.0320501	−	0.181765i
$861$	−2.79742e7	−	4.84527e7i	−1.28603	−	2.22746i
$862$	−2.37968e6	+	4.12172e6i	−0.109081	+	0.188934i
$863$	2.74308e7	+	2.30172e7i	1.25375	+	1.05202i	0.996319	+	0.0857255i	$0.0273208\pi$
$863$	2.74308e7	+	2.30172e7i	1.25375	+	1.05202i	0.257432	+	0.966296i	$0.417124\pi$
$864$	−6.51449e6	+	1.14868e6i	−0.296890	+	0.0523497i
$865$	1.82626e7	−	1.05439e7i	0.829893	−	0.479139i
$866$	−2.18326e6	−	5.99847e6i	−0.0989262	−	0.271798i
$867$	1.64597e7	−	5.99083e6i	0.743659	−	0.270670i
$868$	1.03287e7	+	1.82122e6i	0.465313	+	0.0820472i
$869$	4.29404e7	+	5.11743e7i	1.92893	+	2.29881i
$870$	5.59154e6	+	6.66373e6i	0.250457	+	0.298483i
$871$	−2.16471e7	−	3.81697e6i	−0.966840	−	0.170480i
$872$	−6.96611e6	+	2.53546e6i	−0.310241	+	0.112918i
$873$	3.24415e6	+	8.91323e6i	0.144067	+	0.395822i
$874$	−4.80100e6	+	2.77186e6i	−0.212595	+	0.122742i
$875$	−1.61566e7	+	2.84884e6i	−0.713393	+	0.125790i
$876$	8.45318e6	+	7.09306e6i	0.372186	+	0.312301i
$877$	−1.86441e6	+	3.22925e6i	−0.0818545	+	0.141776i	−0.904047	−	0.427434i	$-0.859418\pi$
$877$	−1.86441e6	+	3.22925e6i	−0.0818545	+	0.141776i	0.822192	+	0.569210i	$0.192751\pi$
$878$	2.37724e6	+	4.11750e6i	0.104073	+	0.180259i
$879$	8.38396e6	−	4.75478e7i	0.365997	−	2.07567i
$880$	1.24852e7	+	7.20835e6i	0.543488	+	0.313783i
$881$	−1.79604e7	−	6.53705e6i	−0.779607	−	0.283754i	−0.0785985	−	0.996906i	$-0.525044\pi$
$881$	−1.79604e7	−	6.53705e6i	−0.779607	−	0.283754i	−0.701009	+	0.713152i	$0.747267\pi$
$882$			6.36678e7i			2.75581i
$883$	−9.34538e6	+	2.56762e7i	−0.403362	+	1.10823i	0.557252	+	0.830343i	$0.311856\pi$
$883$	−9.34538e6	+	2.56762e7i	−0.403362	+	1.10823i	−0.960614	+	0.277885i	$0.910367\pi$
$884$	2.34974e6	+	1.33260e7i	0.101132	+	0.573549i
$885$	2.69878e7	−	2.26454e7i	1.15827	−	0.971902i
$886$	1.41633e7	−	1.68791e7i	0.606150	−	0.722381i
$887$	−3.77175e7			−1.60966			−0.804829	−	0.593507i	$-0.797743\pi$
$887$	−3.77175e7			−1.60966			−0.804829	+	0.593507i	$0.797743\pi$
$888$	−1.43183e7	−	1.06495e6i	−0.609338	−	0.0453209i
$889$	2.73568e7			1.16094
$890$	7.99304e6	−	9.52574e6i	0.338249	−	0.403110i
$891$	2.89939e7	−	2.43288e7i	1.22353	−	1.02666i
$892$	−213710.	−	1.21201e6i	−0.00899316	−	0.0510027i
$893$	−908614.	+	2.49640e6i	−0.0381286	+	0.104757i
$894$			2.04661e7i			0.856428i
$895$	4.64465e7	+	1.69051e7i	1.93818	+	0.705441i
$896$	3.16563e6	+	1.82768e6i	0.131732	+	0.0760553i
$897$	7.12468e6	−	4.04061e7i	0.295654	−	1.67674i
$898$	−1.01842e7	−	1.76396e7i	−0.421442	−	0.729959i
$899$	−1.40524e6	+	2.43395e6i	−0.0579897	+	0.100441i
$900$	2.36480e7	+	1.98431e7i	0.973171	+	0.816587i
$901$	−2.69231e7	+	4.74727e6i	−1.10487	+	0.194819i
$902$	2.15183e7	−	1.24236e7i	0.880626	−	0.508430i
$903$	6.09493e6	+	1.67457e7i	0.248742	+	0.683414i
$904$	−1.14590e7	+	4.17074e6i	−0.466366	+	0.169743i
$905$	3.66327e7	+	6.45933e6i	1.48678	+	0.262160i
$906$	−3.57001e7	−	4.25457e7i	−1.44494	−	1.72201i
$907$	−1.17062e7	−	1.39509e7i	−0.472496	−	0.563099i	0.476180	−	0.879348i	$-0.342021\pi$
$907$	−1.17062e7	−	1.39509e7i	−0.472496	−	0.563099i	−0.948676	+	0.316249i	$0.897576\pi$
$908$	−9.55929e6	−	1.68556e6i	−0.384779	−	0.0678469i
$909$	−1.83588e7	+	6.68206e6i	−0.736944	+	0.268226i
$910$	−1.51407e7	−	4.15986e7i	−0.606096	−	1.66523i
$911$	−1.73146e7	+	9.99659e6i	−0.691221	+	0.399076i	−0.804069	−	0.594536i	$-0.797336\pi$
$911$	−1.73146e7	+	9.99659e6i	−0.691221	+	0.399076i	0.112849	+	0.993612i	$0.464002\pi$
$912$	3.63318e6	−	640628.i	0.144644	−	0.0255046i
$913$	−3.60023e6	−	3.02095e6i	−0.142940	−	0.119941i
$914$	1.08518e7	−	1.87959e7i	0.429671	−	0.744213i
$915$	3.21109e7	+	5.56176e7i	1.26794	+	2.19614i
$916$	4.00380e6	−	2.27067e7i	0.157664	−	0.894159i
$917$	−4.12264e6	−	2.38021e6i	−0.161902	−	0.0934742i
$918$	3.49352e7	+	1.27154e7i	1.36822	+	0.497992i
$919$			3.41728e7i			1.33473i	0.744732	+	0.667363i	$0.232577\pi$
$919$			3.41728e7i			1.33473i	−0.744732	+	0.667363i	$0.767423\pi$
$920$	4.78589e6	−	1.31491e7i	0.186420	−	0.512186i
$921$	−1.09080e6	−	6.18625e6i	−0.0423738	−	0.240314i
$922$	−1.85999e7	+	1.56072e7i	−0.720583	+	0.604641i
$923$	5.70611e6	−	6.80028e6i	0.220463	−	0.262738i
$924$	−6.41768e7			−2.47285
$925$	1.94415e7	+	2.70096e7i	0.747096	+	1.03792i
$926$	4.53952e6			0.173973
$927$	4.28435e7	−	5.10589e7i	1.63752	−	1.95152i
$928$	−750363.	+	629629.i	−0.0286023	+	0.0240002i
$929$	271764.	+	1.54125e6i	0.0103313	+	0.0585915i	0.989538	−	0.144276i	$-0.0460852\pi$
$929$	271764.	+	1.54125e6i	0.0103313	+	0.0585915i	−0.979206	+	0.202867i	$0.934974\pi$
$930$	−9.13821e6	+	2.51070e7i	−0.346460	+	0.951892i
$931$		−	1.76359e7i		−	0.666841i
$932$	1.76652e7	+	6.42960e6i	0.666160	+	0.242462i
$933$	4.47908e7	+	2.58600e7i	1.68455	+	0.972578i
$934$	−2.93152e6	+	1.66255e7i	−0.109958	+	0.623601i
$935$	−4.05121e7	−	7.01690e7i	−1.51550	−	2.62492i
$936$	−9.08126e6	+	1.57292e7i	−0.338810	+	0.586837i
$937$	1.83536e6	+	1.54005e6i	0.0682925	+	0.0573042i	0.676295	−	0.736631i	$-0.263584\pi$
$937$	1.83536e6	+	1.54005e6i	0.0682925	+	0.0573042i	−0.608002	+	0.793935i	$0.708029\pi$
$938$	3.28646e7	−	5.79492e6i	1.21961	−	0.215050i
$939$	−6.01074e7	+	3.47030e7i	−2.22466	+	1.28441i
$940$	−2.29345e6	−	6.30121e6i	−0.0846584	−	0.232597i
$941$	3.40554e7	−	1.23951e7i	1.25375	−	0.456328i	0.372084	−	0.928199i	$-0.378643\pi$
$941$	3.40554e7	−	1.23951e7i	1.25375	−	0.456328i	0.881668	+	0.471871i	$0.156421\pi$
$942$	−5.45088e7	−	9.61137e6i	−2.00143	−	0.352905i
$943$	−1.55021e7	−	1.84747e7i	−0.567690	−	0.676546i
$944$	2.54997e6	+	3.03893e6i	0.0931332	+	0.110992i
$945$	−1.19777e8	−	2.11198e7i	−4.36307	−	0.769327i
$946$	−7.43691e6	+	2.70681e6i	−0.270187	+	0.0983401i
$947$	−1.29824e7	−	3.56689e7i	−0.470415	−	1.29245i	−0.917419	−	0.397922i	$-0.869731\pi$
$947$	−1.29824e7	−	3.56689e7i	−0.470415	−	1.29245i	0.447005	−	0.894532i	$-0.352491\pi$
$948$	−3.73688e7	+	2.15749e7i	−1.35048	+	0.779701i
$949$	1.48195e7	−	2.61308e6i	0.534157	−	0.0941863i
$950$	−6.55046e6	−	5.49649e6i	−0.235485	−	0.197595i
$951$	−2.17982e7	+	3.77556e7i	−0.781572	+	1.35372i
$952$	−1.02718e7	−	1.77914e7i	−0.367330	−	0.636234i
$953$	8.52429e6	−	4.83437e7i	0.304037	−	1.72428i	−0.323967	−	0.946068i	$-0.605017\pi$
$953$	8.52429e6	−	4.83437e7i	0.304037	−	1.72428i	0.628004	−	0.778210i	$-0.283872\pi$
$954$	−3.17783e7	−	1.83472e7i	−1.13047	−	0.652678i
$955$	−5.35798e7	−	1.95014e7i	−1.90105	−	0.691924i
$956$			6.79497e6i			0.240460i
$957$	5.88189e6	−	1.61604e7i	0.207605	−	0.570389i
$958$	5.30116e6	+	3.00644e7i	0.186620	+	1.05837i
$959$	6.26634e7	−	5.25809e7i	2.20023	−	1.84621i
$960$	−5.98568e6	+	7.13346e6i	−0.209621	+	0.249817i
$961$	1.99969e7			0.698479
$962$	−1.36634e7	+	1.40241e7i	−0.476016	+	0.488581i
$963$	−4.15527e7			−1.44389
$964$	3.16799e6	−	3.77547e6i	0.109797	−	0.130851i
$965$	−2.44281e7	+	2.04976e7i	−0.844446	+	0.708575i
$966$	1.08167e7	+	6.13444e7i	0.372950	+	2.11511i
$967$	3.01898e6	−	8.29458e6i	0.103823	−	0.285252i	−0.876894	−	0.480683i	$-0.840389\pi$
$967$	3.01898e6	−	8.29458e6i	0.103823	−	0.285252i	0.980717	+	0.195432i	$0.0626108\pi$
$968$		−	1.81942e7i		−	0.624087i
$969$	−1.94837e7	−	7.09147e6i	−0.666593	−	0.242620i
$970$	5.74337e6	+	3.31594e6i	0.195992	+	0.113156i
$971$	−6.61021e6	+	3.74883e7i	−0.224992	+	1.27599i	0.637709	+	0.770278i	$0.279882\pi$
$971$	−6.61021e6	+	3.74883e7i	−0.224992	+	1.27599i	−0.862701	+	0.505715i	$0.831229\pi$
$972$	−334394.	−	579187.i	−0.0113525	−	0.0196631i
$973$	−2.12783e7	+	3.68551e7i	−0.720534	+	1.24800i
$974$	6.02517e6	+	5.05572e6i	0.203503	+	0.170760i
$975$	6.23252e7	−	1.09896e7i	2.09967	−	0.370229i
$976$	−6.26276e6	+	3.61581e6i	−0.210446	+	0.121501i
$977$	−1.64191e7	−	4.51111e7i	−0.550317	−	1.51198i	−0.833280	−	0.552852i	$-0.813540\pi$
$977$	−1.64191e7	−	4.51111e7i	−0.550317	−	1.51198i	0.282963	−	0.959131i	$-0.408683\pi$
$978$	−1.38696e7	+	5.04812e6i	−0.463678	+	0.168765i
$979$	−2.42102e7	−	4.26891e6i	−0.807312	−	0.142351i
$980$	2.86137e7	+	3.41005e7i	0.951721	+	1.13422i
$981$	3.59457e7	+	4.28384e7i	1.19254	+	1.42122i
$982$	1.19297e7	+	2.10353e6i	0.394777	+	0.0696098i
$983$	−1.18423e7	+	4.31025e6i	−0.390889	+	0.142272i	−0.529985	−	0.848007i	$-0.677802\pi$
$983$	−1.18423e7	+	4.31025e6i	−0.390889	+	0.142272i	0.139096	+	0.990279i	$0.455580\pi$
$984$	5.48921e6	+	1.50815e7i	0.180726	+	0.496542i
$985$	5.01808e7	−	2.89719e7i	1.64796	−	0.951452i
$986$	5.42147e6	−	955952.i	0.177593	−	0.0313144i
$987$	2.28667e7	+	1.91875e7i	0.747156	+	0.626939i
$988$	2.51549e6	−	4.35696e6i	0.0819843	−	0.142001i
$989$	3.84081e6	+	6.65247e6i	0.124862	+	0.216268i
$990$	1.88847e7	−	1.07101e8i	0.612383	−	3.47299i
$991$	3.16266e7	+	1.82596e7i	1.02298	+	0.590619i	0.914966	−	0.403531i	$-0.132217\pi$
$991$	3.16266e7	+	1.82596e7i	1.02298	+	0.590619i	0.108015	+	0.994149i	$0.465550\pi$
$992$	−2.82715e6	−	1.02900e6i	−0.0912157	−	0.0331998i
$993$		−	3.60940e7i		−	1.16161i
$994$	−4.60949e6	+	1.26645e7i	−0.147974	+	0.406557i
$995$	−2.77553e6	−	1.57408e7i	−0.0888767	−	0.504045i
$996$	2.32547e6	−	1.95130e6i	0.0742784	−	0.0623270i
$997$	1.24025e7	−	1.47807e7i	0.395158	−	0.470931i	−0.531379	−	0.847134i	$-0.678326\pi$
$997$	1.24025e7	−	1.47807e7i	0.395158	−	0.470931i	0.926537	+	0.376203i	$0.122771\pi$
$998$	9.26266e6			0.294381
$999$	1.45985e7	+	5.17752e7i	0.462802	+	1.64137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.h.a.3.8	✓	96
37.25	even	18	inner	74.6.h.a.25.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.h.a.3.8	✓	96	1.1	even	1	trivial
74.6.h.a.25.8	yes	96	37.25	even	18	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.57115 + 3.06418i) q^{2} +(20.6376 - 17.3170i) q^{3} +(-2.77837 - 15.7569i) q^{4} +(-28.8625 + 79.2990i) q^{5} +107.762i q^{6} +(-209.650 - 76.3065i) q^{7} +(55.4256 + 32.0000i) q^{8} +(83.8350 - 475.452i) q^{9} +O(q^{10})\)	\(q+(-2.57115 + 3.06418i) q^{2} +(20.6376 - 17.3170i) q^{3} +(-2.77837 - 15.7569i) q^{4} +(-28.8625 + 79.2990i) q^{5} +107.762i q^{6} +(-209.650 - 76.3065i) q^{7} +(55.4256 + 32.0000i) q^{8} +(83.8350 - 475.452i) q^{9} +(-168.776 - 292.329i) q^{10} +(-333.667 + 577.929i) q^{11} +(-330.201 - 277.071i) q^{12} +(-578.886 + 102.073i) q^{13} +(772.859 - 446.211i) q^{14} +(777.567 + 2136.35i) q^{15} +(-240.561 + 87.5572i) q^{16} +(1416.90 + 249.838i) q^{17} +(1241.32 + 1479.34i) q^{18} +(-343.842 - 409.775i) q^{19} +(1329.70 + 234.462i) q^{20} +(-5648.07 + 2055.73i) q^{21} +(-912.968 - 2508.36i) q^{22} +(-2243.78 + 1295.45i) q^{23} +(1697.99 - 299.402i) q^{24} +(-3061.40 - 2568.82i) q^{25} +(1175.63 - 2036.25i) q^{26} +(-3229.97 - 5594.47i) q^{27} +(-619.869 + 3515.45i) q^{28} +(-828.415 - 478.286i) q^{29} +(-8545.40 - 3110.27i) q^{30} -2938.08i q^{31} +(350.229 - 962.245i) q^{32} +(3121.90 + 17705.1i) q^{33} +(-4408.62 + 3699.27i) q^{34} +(12102.1 - 14422.7i) q^{35} -7724.58 q^{36} +(-8070.95 - 2050.31i) q^{37} +2139.69 q^{38} +(-10179.2 + 12131.1i) q^{39} +(-4137.29 + 3471.60i) q^{40} +(1616.38 + 9166.95i) q^{41} +(8222.92 - 22592.3i) q^{42} -2964.85i q^{43} +(10033.4 + 3651.87i) q^{44} +(35283.2 + 20370.7i) q^{45} +(1799.62 - 10206.1i) q^{46} +(-2483.17 - 4300.97i) q^{47} +(-3448.37 + 5972.76i) q^{48} +(25255.7 + 21192.0i) q^{49} +(15742.6 - 2775.85i) q^{50} +(33567.9 - 19380.4i) q^{51} +(3216.72 + 8837.86i) q^{52} +(-17855.4 + 6498.85i) q^{53} +(25447.2 + 4487.03i) q^{54} +(-36198.7 - 43140.0i) q^{55} +(-9178.20 - 10938.1i) q^{56} +(-14192.1 - 2502.45i) q^{57} +(3595.53 - 1308.67i) q^{58} +(-5300.03 - 14561.7i) q^{59} +(31501.9 - 18187.6i) q^{60} +(27819.3 - 4905.30i) q^{61} +(9002.79 + 7554.23i) q^{62} +(-53856.1 + 93281.5i) q^{63} +(2048.00 + 3547.24i) q^{64} +(8613.77 - 48851.1i) q^{65} +(-62278.6 - 35956.6i) q^{66} +(35139.3 + 12789.7i) q^{67} -23020.2i q^{68} +(-23872.9 + 65590.3i) q^{69} +(13077.4 + 74165.7i) q^{70} +(-11568.7 + 9707.31i) q^{71} +(19861.1 - 23669.5i) q^{72} -25600.1 q^{73} +(27034.1 - 19459.2i) q^{74} -107664. q^{75} +(-5501.47 + 6556.40i) q^{76} +(114053. - 95702.0i) q^{77} +(-10999.6 - 62381.7i) q^{78} +(34237.8 - 94067.7i) q^{79} -21603.4i q^{80} +(-53296.1 - 19398.2i) q^{81} +(-32245.1 - 18616.7i) q^{82} +(-1222.93 + 6935.60i) q^{83} +(48084.4 + 83284.6i) q^{84} +(-60707.3 + 105148. i) q^{85} +(9084.83 + 7623.08i) q^{86} +(-25378.9 + 4474.99i) q^{87} +(-36987.4 + 21354.7i) q^{88} +(12599.5 + 34616.9i) q^{89} +(-153138. + 55737.6i) q^{90} +(129152. + 22773.1i) q^{91} +(26646.3 + 31755.8i) q^{92} +(-50878.6 - 60634.7i) q^{93} +(19563.5 + 3449.58i) q^{94} +(42418.9 - 15439.2i) q^{95} +(-9435.31 - 25923.3i) q^{96} +(-17014.7 + 9823.46i) q^{97} +(-129872. + 22900.0i) q^{98} +(246804. + 207093. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{3} + 90 q^{5} - 228 q^{7} - 186 q^{9}+O(q^{10}) \) 96 * q + 6 * q^3 + 90 * q^5 - 228 * q^7 - 186 * q^9	\( 96 q + 6 q^{3} + 90 q^{5} - 228 q^{7} - 186 q^{9} + 600 q^{10} - 726 q^{11} - 96 q^{12} - 246 q^{13} + 3960 q^{14} - 3960 q^{15} - 1530 q^{17} + 3222 q^{19} + 1440 q^{20} - 16110 q^{21} + 8232 q^{25} + 13632 q^{26} + 2154 q^{27} - 10464 q^{28} - 18378 q^{29} - 25056 q^{30} + 78198 q^{33} + 37296 q^{34} + 82170 q^{35} - 124416 q^{36} - 5586 q^{37} - 39936 q^{38} + 58686 q^{39} - 16128 q^{40} - 59598 q^{41} - 26304 q^{42} + 480 q^{44} - 74646 q^{45} - 22536 q^{46} - 1266 q^{47} + 193320 q^{49} + 18864 q^{50} + 68352 q^{52} - 57432 q^{53} + 101520 q^{54} + 133830 q^{55} - 228936 q^{57} - 79224 q^{58} - 52800 q^{59} + 68664 q^{61} - 72720 q^{62} - 166254 q^{63} + 196608 q^{64} - 122058 q^{65} + 254946 q^{67} - 218094 q^{69} - 25872 q^{70} + 200052 q^{71} - 32244 q^{73} + 124368 q^{74} - 234036 q^{75} + 51552 q^{76} + 397188 q^{77} - 16584 q^{78} + 267462 q^{79} - 371496 q^{81} + 121440 q^{83} + 84672 q^{84} - 337260 q^{85} + 43920 q^{86} - 667500 q^{87} - 135936 q^{88} + 377850 q^{89} - 576408 q^{90} + 875826 q^{91} + 233376 q^{92} + 365868 q^{93} - 80256 q^{94} + 764592 q^{95} - 823212 q^{97} - 342192 q^{98} - 928650 q^{99}+O(q^{100}) \) 96 * q + 6 * q^3 + 90 * q^5 - 228 * q^7 - 186 * q^9 + 600 * q^10 - 726 * q^11 - 96 * q^12 - 246 * q^13 + 3960 * q^14 - 3960 * q^15 - 1530 * q^17 + 3222 * q^19 + 1440 * q^20 - 16110 * q^21 + 8232 * q^25 + 13632 * q^26 + 2154 * q^27 - 10464 * q^28 - 18378 * q^29 - 25056 * q^30 + 78198 * q^33 + 37296 * q^34 + 82170 * q^35 - 124416 * q^36 - 5586 * q^37 - 39936 * q^38 + 58686 * q^39 - 16128 * q^40 - 59598 * q^41 - 26304 * q^42 + 480 * q^44 - 74646 * q^45 - 22536 * q^46 - 1266 * q^47 + 193320 * q^49 + 18864 * q^50 + 68352 * q^52 - 57432 * q^53 + 101520 * q^54 + 133830 * q^55 - 228936 * q^57 - 79224 * q^58 - 52800 * q^59 + 68664 * q^61 - 72720 * q^62 - 166254 * q^63 + 196608 * q^64 - 122058 * q^65 + 254946 * q^67 - 218094 * q^69 - 25872 * q^70 + 200052 * q^71 - 32244 * q^73 + 124368 * q^74 - 234036 * q^75 + 51552 * q^76 + 397188 * q^77 - 16584 * q^78 + 267462 * q^79 - 371496 * q^81 + 121440 * q^83 + 84672 * q^84 - 337260 * q^85 + 43920 * q^86 - 667500 * q^87 - 135936 * q^88 + 377850 * q^89 - 576408 * q^90 + 875826 * q^91 + 233376 * q^92 + 365868 * q^93 - 80256 * q^94 + 764592 * q^95 - 823212 * q^97 - 342192 * q^98 - 928650 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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