LMFDB - Embedded newform 354.4.c.b.353.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,4,Mod(353,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.353");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	354.c (of order $2$, degree $1$, 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:	$20.8866761420$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.14
Character	$\chi$	$=$	354.353
Dual form			354.4.c.b.353.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +(-1.46648 + 4.98492i) q^{3} +4.00000 q^{4} +18.9931i q^{5} +(-2.93296 + 9.96984i) q^{6} -10.1890 q^{7} +8.00000 q^{8} +(-22.6989 - 14.6206i) q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +(-1.46648 + 4.98492i) q^{3} +4.00000 q^{4} +18.9931i q^{5} +(-2.93296 + 9.96984i) q^{6} -10.1890 q^{7} +8.00000 q^{8} +(-22.6989 - 14.6206i) q^{9} +37.9861i q^{10} +10.1714 q^{11} +(-5.86593 + 19.9397i) q^{12} +82.2827i q^{13} -20.3780 q^{14} +(-94.6789 - 27.8530i) q^{15} +16.0000 q^{16} -92.4725i q^{17} +(-45.3977 - 29.2412i) q^{18} +23.3309 q^{19} +75.9722i q^{20} +(14.9420 - 50.7914i) q^{21} +20.3427 q^{22} -39.6956 q^{23} +(-11.7319 + 39.8794i) q^{24} -235.736 q^{25} +164.565i q^{26} +(106.170 - 91.7112i) q^{27} -40.7560 q^{28} +118.325i q^{29} +(-189.358 - 55.7060i) q^{30} -30.7291i q^{31} +32.0000 q^{32} +(-14.9161 + 50.7034i) q^{33} -184.945i q^{34} -193.520i q^{35} +(-90.7954 - 58.4824i) q^{36} -221.478i q^{37} +46.6619 q^{38} +(-410.173 - 120.666i) q^{39} +151.944i q^{40} -63.0445i q^{41} +(29.8840 - 101.583i) q^{42} -147.338i q^{43} +40.6854 q^{44} +(277.690 - 431.121i) q^{45} -79.3912 q^{46} +37.8072 q^{47} +(-23.4637 + 79.7587i) q^{48} -239.184 q^{49} -471.472 q^{50} +(460.968 + 135.609i) q^{51} +329.131i q^{52} +409.038i q^{53} +(212.340 - 183.422i) q^{54} +193.185i q^{55} -81.5120 q^{56} +(-34.2144 + 116.303i) q^{57} +236.651i q^{58} +(-170.128 - 420.042i) q^{59} +(-378.715 - 111.412i) q^{60} +709.628i q^{61} -61.4582i q^{62} +(231.279 + 148.969i) q^{63} +64.0000 q^{64} -1562.80 q^{65} +(-29.8322 + 101.407i) q^{66} +1044.75i q^{67} -369.890i q^{68} +(58.2129 - 197.880i) q^{69} -387.041i q^{70} +361.984i q^{71} +(-181.591 - 116.965i) q^{72} +327.686i q^{73} -442.955i q^{74} +(345.703 - 1175.13i) q^{75} +93.3238 q^{76} -103.636 q^{77} +(-820.345 - 241.332i) q^{78} -238.712 q^{79} +303.889i q^{80} +(301.476 + 663.742i) q^{81} -126.089i q^{82} +156.436 q^{83} +(59.7680 - 203.165i) q^{84} +1756.34 q^{85} -294.677i q^{86} +(-589.843 - 173.522i) q^{87} +81.3709 q^{88} +1097.96 q^{89} +(555.379 - 862.241i) q^{90} -838.379i q^{91} -158.782 q^{92} +(153.182 + 45.0637i) q^{93} +75.6143 q^{94} +443.126i q^{95} +(-46.9274 + 159.517i) q^{96} -1334.04i q^{97} -478.368 q^{98} +(-230.878 - 148.711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 60 q^{2} + 5 q^{3} + 120 q^{4} + 10 q^{6} + 6 q^{7} + 240 q^{8} + 27 q^{9}+O(q^{10}) $ 30 * q + 60 * q^2 + 5 * q^3 + 120 * q^4 + 10 * q^6 + 6 * q^7 + 240 * q^8 + 27 * q^9	$ 30 q + 60 q^{2} + 5 q^{3} + 120 q^{4} + 10 q^{6} + 6 q^{7} + 240 q^{8} + 27 q^{9} + 60 q^{11} + 20 q^{12} + 12 q^{14} + 20 q^{15} + 480 q^{16} + 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} - 24 q^{23} + 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} + 40 q^{30} + 960 q^{32} - 336 q^{33} + 108 q^{36} + 180 q^{38} - 652 q^{39} + 264 q^{42} + 240 q^{44} - 878 q^{45} - 48 q^{46} - 792 q^{47} + 80 q^{48} + 2016 q^{49} - 2160 q^{50} + 650 q^{51} - 110 q^{54} + 48 q^{56} + 846 q^{57} + 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} + 1416 q^{65} - 672 q^{66} + 590 q^{69} + 216 q^{72} - 952 q^{75} + 360 q^{76} - 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} - 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} + 300 q^{89} - 1756 q^{90} - 96 q^{92} - 1684 q^{93} - 1584 q^{94} + 160 q^{96} + 4032 q^{98} - 730 q^{99}+O(q^{100}) $ 30 * q + 60 * q^2 + 5 * q^3 + 120 * q^4 + 10 * q^6 + 6 * q^7 + 240 * q^8 + 27 * q^9 + 60 * q^11 + 20 * q^12 + 12 * q^14 + 20 * q^15 + 480 * q^16 + 54 * q^18 + 90 * q^19 + 132 * q^21 + 120 * q^22 - 24 * q^23 + 40 * q^24 - 1080 * q^25 - 55 * q^27 + 24 * q^28 + 40 * q^30 + 960 * q^32 - 336 * q^33 + 108 * q^36 + 180 * q^38 - 652 * q^39 + 264 * q^42 + 240 * q^44 - 878 * q^45 - 48 * q^46 - 792 * q^47 + 80 * q^48 + 2016 * q^49 - 2160 * q^50 + 650 * q^51 - 110 * q^54 + 48 * q^56 + 846 * q^57 + 480 * q^59 + 80 * q^60 + 887 * q^63 + 1920 * q^64 + 1416 * q^65 - 672 * q^66 + 590 * q^69 + 216 * q^72 - 952 * q^75 + 360 * q^76 - 864 * q^77 - 1304 * q^78 + 738 * q^79 - 1217 * q^81 - 876 * q^83 + 528 * q^84 + 1176 * q^85 + 534 * q^87 + 480 * q^88 + 300 * q^89 - 1756 * q^90 - 96 * q^92 - 1684 * q^93 - 1584 * q^94 + 160 * q^96 + 4032 * q^98 - 730 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	2.00000			0.707107
$2$	2.00000			0.707107
$3$	−1.46648	+	4.98492i	−0.282225	+	0.959348i
$3$	−1.46648	+	4.98492i	−0.282225	+	0.959348i
$4$	4.00000			0.500000
$5$			18.9931i			1.69879i	0.527757	+	0.849395i	$0.323033\pi$
$5$			18.9931i			1.69879i	−0.527757	+	0.849395i	$0.676967\pi$
$6$	−2.93296	+	9.96984i	−0.199563	+	0.678362i
$7$	−10.1890			−0.550154			−0.275077	−	0.961422i	$-0.588703\pi$
$7$	−10.1890			−0.550154			−0.275077	+	0.961422i	$0.588703\pi$
$8$	8.00000			0.353553
$9$	−22.6989	−	14.6206i	−0.840699	−	0.541503i
$10$			37.9861i			1.20123i
$11$	10.1714			0.278798			0.139399	−	0.990236i	$-0.455483\pi$
$11$	10.1714			0.278798			0.139399	+	0.990236i	$0.455483\pi$
$12$	−5.86593	+	19.9397i	−0.141112	+	0.479674i
$13$			82.2827i			1.75547i	0.479146	+	0.877735i	$0.340946\pi$
$13$			82.2827i			1.75547i	−0.479146	+	0.877735i	$0.659054\pi$
$14$	−20.3780			−0.389018
$15$	−94.6789	−	27.8530i	−1.62973	−	0.479441i
$16$	16.0000			0.250000
$17$		−	92.4725i		−	1.31929i	−0.751579	−	0.659644i	$-0.770707\pi$
$17$		−	92.4725i		−	1.31929i	0.751579	−	0.659644i	$-0.229293\pi$
$18$	−45.3977	−	29.2412i	−0.594464	−	0.382901i
$19$	23.3309			0.281710			0.140855	−	0.990030i	$-0.455015\pi$
$19$	23.3309			0.281710			0.140855	+	0.990030i	$0.455015\pi$
$20$			75.9722i			0.849395i
$21$	14.9420	−	50.7914i	0.155267	−	0.527790i
$22$	20.3427			0.197140
$23$	−39.6956			−0.359874			−0.179937	−	0.983678i	$-0.557589\pi$
$23$	−39.6956			−0.359874			−0.179937	+	0.983678i	$0.557589\pi$
$24$	−11.7319	+	39.8794i	−0.0997815	+	0.339181i
$25$	−235.736			−1.88589
$26$			164.565i			1.24131i
$27$	106.170	−	91.7112i	0.756756	−	0.653697i
$28$	−40.7560			−0.275077
$29$			118.325i			0.757672i	0.925464	+	0.378836i	$0.123675\pi$
$29$			118.325i			0.757672i	−0.925464	+	0.378836i	$0.876325\pi$
$30$	−189.358	−	55.7060i	−1.15239	−	0.339016i
$31$		−	30.7291i		−	0.178036i	−0.996030	−	0.0890179i	$-0.971627\pi$
$31$		−	30.7291i		−	0.178036i	0.996030	−	0.0890179i	$-0.0283728\pi$
$32$	32.0000			0.176777
$33$	−14.9161	+	50.7034i	−0.0786837	+	0.267465i
$34$		−	184.945i		−	0.932877i
$35$		−	193.520i		−	0.934597i
$36$	−90.7954	−	58.4824i	−0.420349	−	0.270752i
$37$		−	221.478i		−	0.984073i	−0.870575	−	0.492036i	$-0.836253\pi$
$37$		−	221.478i		−	0.984073i	0.870575	−	0.492036i	$-0.163747\pi$
$38$	46.6619			0.199199
$39$	−410.173	−	120.666i	−1.68411	−	0.495437i
$40$			151.944i			0.600613i
$41$		−	63.0445i		−	0.240144i	−0.992765	−	0.120072i	$-0.961687\pi$
$41$		−	63.0445i		−	0.240144i	0.992765	−	0.120072i	$-0.0383125\pi$
$42$	29.8840	−	101.583i	0.109790	−	0.373204i
$43$		−	147.338i		−	0.522532i	−0.965267	−	0.261266i	$-0.915860\pi$
$43$		−	147.338i		−	0.522532i	0.965267	−	0.261266i	$-0.0841400\pi$
$44$	40.6854			0.139399
$45$	277.690	−	431.121i	0.919901	−	1.42817i
$46$	−79.3912			−0.254470
$47$	37.8072			0.117335			0.0586675	−	0.998278i	$-0.481315\pi$
$47$	37.8072			0.117335			0.0586675	+	0.998278i	$0.481315\pi$
$48$	−23.4637	+	79.7587i	−0.0705562	+	0.239837i
$49$	−239.184			−0.697330
$50$	−471.472			−1.33353
$51$	460.968	+	135.609i	1.26566	+	0.372335i
$52$			329.131i			0.877735i
$53$			409.038i			1.06011i	0.847964	+	0.530054i	$0.177828\pi$
$53$			409.038i			1.06011i	−0.847964	+	0.530054i	$0.822172\pi$
$54$	212.340	−	183.422i	0.535108	−	0.462234i
$55$			193.185i			0.473620i
$56$	−81.5120			−0.194509
$57$	−34.2144	+	116.303i	−0.0795054	+	0.270258i
$58$			236.651i			0.535755i
$59$	−170.128	−	420.042i	−0.375403	−	0.926862i
$59$	−170.128	−	420.042i	−0.375403	−	0.926862i
$60$	−378.715	−	111.412i	−0.814866	−	0.239720i
$61$			709.628i			1.48949i	0.667352	+	0.744743i	$0.267428\pi$
$61$			709.628i			1.48949i	−0.667352	+	0.744743i	$0.732572\pi$
$62$		−	61.4582i		−	0.125890i
$63$	231.279	+	148.969i	0.462514	+	0.297911i
$64$	64.0000			0.125000
$65$	−1562.80			−2.98218
$66$	−29.8322	+	101.407i	−0.0556378	+	0.189126i
$67$			1044.75i			1.90502i	0.304513	+	0.952508i	$0.401506\pi$
$67$			1044.75i			1.90502i	−0.304513	+	0.952508i	$0.598494\pi$
$68$		−	369.890i		−	0.659644i
$69$	58.2129	−	197.880i	0.101565	−	0.345245i
$70$		−	387.041i		−	0.660860i
$71$			361.984i			0.605064i	0.953139	+	0.302532i	$0.0978319\pi$
$71$			361.984i			0.605064i	−0.953139	+	0.302532i	$0.902168\pi$
$72$	−181.591	−	116.965i	−0.297232	−	0.191450i
$73$			327.686i			0.525380i	0.964880	+	0.262690i	$0.0846097\pi$
$73$			327.686i			0.525380i	−0.964880	+	0.262690i	$0.915390\pi$
$74$		−	442.955i		−	0.695844i
$75$	345.703	−	1175.13i	0.532244	−	1.80922i
$76$	93.3238			0.140855
$77$	−103.636			−0.153382
$78$	−820.345	−	241.332i	−1.19084	−	0.350327i
$79$	−238.712			−0.339964			−0.169982	−	0.985447i	$-0.554371\pi$
$79$	−238.712			−0.339964			−0.169982	+	0.985447i	$0.554371\pi$
$80$			303.889i			0.424698i
$81$	301.476	+	663.742i	0.413548	+	0.910482i
$82$		−	126.089i		−	0.169807i
$83$	156.436			0.206880			0.103440	−	0.994636i	$-0.467015\pi$
$83$	156.436			0.206880			0.103440	+	0.994636i	$0.467015\pi$
$84$	59.7680	−	203.165i	0.0776336	−	0.263895i
$85$	1756.34			2.24119
$86$		−	294.677i		−	0.369486i
$87$	−589.843	−	173.522i	−0.726871	−	0.213834i
$88$	81.3709			0.0985701
$89$	1097.96			1.30768			0.653838	−	0.756634i	$-0.273158\pi$
$89$	1097.96			1.30768			0.653838	+	0.756634i	$0.273158\pi$
$90$	555.379	−	862.241i	0.650468	−	1.00987i
$91$		−	838.379i		−	0.965780i
$92$	−158.782			−0.179937
$93$	153.182	+	45.0637i	0.170798	+	0.0502461i
$94$	75.6143			0.0829683
$95$			443.126i			0.478566i
$96$	−46.9274	+	159.517i	−0.0498907	+	0.169590i
$97$		−	1334.04i		−	1.39640i	−0.715902	−	0.698201i	$-0.753984\pi$
$97$		−	1334.04i		−	1.39640i	0.715902	−	0.698201i	$-0.246016\pi$
$98$	−478.368			−0.493087
$99$	−230.878	−	148.711i	−0.234385	−	0.150970i
$100$	−942.945			−0.942945
$101$	−807.886			−0.795917			−0.397958	−	0.917403i	$-0.630281\pi$
$101$	−807.886			−0.795917			−0.397958	+	0.917403i	$0.630281\pi$
$102$	921.936	+	271.219i	0.894954	+	0.263281i
$103$			1915.68i			1.83260i	0.400492	+	0.916300i	$0.368839\pi$
$103$			1915.68i			1.83260i	−0.400492	+	0.916300i	$0.631161\pi$
$104$			658.262i			0.620653i
$105$	964.683	+	283.794i	0.896604	+	0.263766i
$106$			818.076i			0.749609i
$107$		−	1003.68i		−	0.906815i	−0.891303	−	0.453407i	$-0.850208\pi$
$107$		−	1003.68i		−	0.906815i	0.891303	−	0.453407i	$-0.149792\pi$
$108$	424.680	−	366.845i	0.378378	−	0.326849i
$109$			1972.94i			1.73370i	0.498567	+	0.866851i	$0.333860\pi$
$109$			1972.94i			1.73370i	−0.498567	+	0.866851i	$0.666140\pi$
$110$			386.370i			0.334900i
$111$	1104.05	+	324.793i	0.944069	+	0.277730i
$112$	−163.024			−0.137539
$113$	−524.671			−0.436787			−0.218393	−	0.975861i	$-0.570082\pi$
$113$	−524.671			−0.436787			−0.218393	+	0.975861i	$0.570082\pi$
$114$	−68.4288	+	232.606i	−0.0562188	+	0.191101i
$115$		−	753.941i		−	0.611351i
$116$			473.302i			0.378836i
$117$	1203.02	−	1867.72i	0.950593	−	1.47582i
$118$	−340.256	−	840.084i	−0.265450	−	0.655390i
$119$			942.203i			0.725812i
$120$	−757.431	−	222.824i	−0.576197	−	0.169508i
$121$	−1227.54			−0.922272
$122$			1419.26i			1.05322i
$123$	314.272	+	92.4537i	0.230382	+	0.0677745i
$124$		−	122.916i		−	0.0890179i
$125$		−	2103.22i		−	1.50494i
$126$	462.558	+	297.939i	0.327047	+	0.210655i
$127$	1399.78			0.978037			0.489018	−	0.872273i	$-0.337355\pi$
$127$	1399.78			0.978037			0.489018	+	0.872273i	$0.337355\pi$
$128$	128.000			0.0883883
$129$	734.470	+	216.069i	0.501291	+	0.147472i
$130$	−3125.60			−2.10872
$131$	2065.19			1.37738			0.688689	−	0.725057i	$-0.258187\pi$
$131$	2065.19			1.37738			0.688689	+	0.725057i	$0.258187\pi$
$132$	−59.6645	+	202.814i	−0.0393419	+	0.133732i
$133$	−237.719			−0.154984
$134$			2089.49i			1.34705i
$135$	1741.88	+	2016.49i	1.11049	+	1.28557i
$136$		−	739.780i		−	0.466438i
$137$		−	438.983i		−	0.273758i	−0.990588	−	0.136879i	$-0.956293\pi$
$137$		−	438.983i		−	0.273758i	0.990588	−	0.136879i	$-0.0437071\pi$
$138$	116.426	−	395.759i	0.0718176	−	0.244125i
$139$	2717.07			1.65798			0.828989	−	0.559266i	$-0.188917\pi$
$139$	2717.07			1.65798			0.828989	+	0.559266i	$0.188917\pi$
$140$		−	774.081i		−	0.467299i
$141$	−55.4435	+	188.466i	−0.0331148	+	0.112565i
$142$			723.967i			0.427845i
$143$			836.927i			0.489422i
$144$	−363.182	−	233.929i	−0.210175	−	0.135376i
$145$	−2247.36			−1.28713
$146$			655.372i			0.371500i
$147$	350.759	−	1192.31i	0.196804	−	0.668982i
$148$		−	885.910i		−	0.492036i
$149$	2675.78			1.47120			0.735600	−	0.677417i	$-0.236901\pi$
$149$	2675.78			1.47120			0.735600	+	0.677417i	$0.236901\pi$
$150$	691.406	−	2350.25i	0.376354	−	1.27932i
$151$			2596.05i			1.39910i	0.714585	+	0.699548i	$0.246615\pi$
$151$			2596.05i			1.39910i	−0.714585	+	0.699548i	$0.753385\pi$
$152$	186.648			0.0995995
$153$	−1352.00	+	2099.02i	−0.714399	+	1.10912i
$154$	−207.272			−0.108458
$155$	583.639			0.302445
$156$	−1640.69	−	482.664i	−0.842054	−	0.247719i
$157$		−	1973.10i		−	1.00300i	−0.865158	−	0.501499i	$-0.832782\pi$
$157$		−	1973.10i		−	1.00300i	0.865158	−	0.501499i	$-0.167218\pi$
$158$	−477.423			−0.240391
$159$	−2039.02	−	599.847i	−1.01701	−	0.299189i
$160$			607.778i			0.300307i
$161$	404.459			0.197986
$162$	602.953	+	1327.48i	0.292423	+	0.643808i
$163$	1338.42			0.643150			0.321575	−	0.946884i	$-0.395788\pi$
$163$	1338.42			0.643150			0.321575	+	0.946884i	$0.395788\pi$
$164$		−	252.178i		−	0.120072i
$165$	−963.013	−	283.303i	−0.454366	−	0.133667i
$166$	312.872			0.146286
$167$			916.784i			0.424808i	0.977182	+	0.212404i	$0.0681292\pi$
$167$			916.784i			0.424808i	−0.977182	+	0.212404i	$0.931871\pi$
$168$	119.536	−	406.331i	0.0548952	−	0.186602i
$169$	−4573.44			−2.08168
$170$	3512.67			1.58476
$171$	−529.586	−	341.112i	−0.236833	−	0.152547i
$172$		−	589.354i		−	0.261266i
$173$	−1781.69			−0.783004			−0.391502	−	0.920177i	$-0.628044\pi$
$173$	−1781.69			−0.783004			−0.391502	+	0.920177i	$0.628044\pi$
$174$	−1179.69	−	347.044i	−0.513975	−	0.151203i
$175$	2401.92			1.03753
$176$	162.742			0.0696996
$177$	2343.37	−	232.090i	0.995131	−	0.0985591i
$178$	2195.91			0.924667
$179$	870.852			0.363634			0.181817	−	0.983332i	$-0.441802\pi$
$179$	870.852			0.363634			0.181817	+	0.983332i	$0.441802\pi$
$180$	1110.76	−	1724.48i	0.459950	−	0.714085i
$181$	−3247.54			−1.33364			−0.666818	−	0.745221i	$-0.732344\pi$
$181$	−3247.54			−1.33364			−0.666818	+	0.745221i	$0.732344\pi$
$182$		−	1676.76i		−	0.682910i
$183$	−3537.44	−	1040.66i	−1.42894	−	0.420369i
$184$	−317.565			−0.127235
$185$	4206.54			1.67173
$186$	306.364	+	90.1273i	0.120773	+	0.0355293i
$187$		−	940.572i		−	0.367815i
$188$	151.229			0.0586675
$189$	−1081.77	+	934.445i	−0.416333	+	0.359634i
$190$			886.252i			0.338397i
$191$	−1580.55			−0.598766			−0.299383	−	0.954133i	$-0.596781\pi$
$191$	−1580.55			−0.598766			−0.299383	+	0.954133i	$0.596781\pi$
$192$	−93.8549	+	319.035i	−0.0352781	+	0.119919i
$193$	1657.33			0.618120			0.309060	−	0.951043i	$-0.399986\pi$
$193$	1657.33			0.618120			0.309060	+	0.951043i	$0.399986\pi$
$194$		−	2668.08i		−	0.987405i
$195$	2291.82	−	7790.43i	0.841644	−	2.86095i
$196$	−956.737			−0.348665
$197$		−	1740.87i		−	0.629602i	−0.949158	−	0.314801i	$-0.898062\pi$
$197$		−	1740.87i		−	0.629602i	0.949158	−	0.314801i	$-0.101938\pi$
$198$	−461.757	−	297.423i	−0.165735	−	0.106752i
$199$	614.923			0.219049			0.109524	−	0.993984i	$-0.465067\pi$
$199$	614.923			0.219049			0.109524	+	0.993984i	$0.465067\pi$
$200$	−1885.89			−0.666763
$201$	−5207.98	−	1532.10i	−1.82757	−	0.537643i
$202$	−1615.77			−0.562798
$203$		−	1205.62i		−	0.416836i
$204$	1843.87	+	542.437i	0.632828	+	0.186168i
$205$	1197.41			0.407954
$206$			3831.37i			1.29584i
$207$	901.045	+	580.374i	0.302546	+	0.194873i
$208$			1316.52i			0.438868i
$209$	237.308			0.0785402
$210$	1929.37	+	567.588i	0.633995	+	0.186511i
$211$			3523.30i			1.14954i	0.818313	+	0.574772i	$0.194909\pi$
$211$			3523.30i			1.14954i	−0.818313	+	0.574772i	$0.805091\pi$
$212$			1636.15i			0.530054i
$213$	−1804.46	−	530.842i	−0.580467	−	0.170764i
$214$		−	2007.36i		−	0.641215i
$215$	2798.41			0.887673
$216$	849.360	−	733.689i	0.267554	−	0.231117i
$217$			313.099i			0.0979471i
$218$			3945.88i			1.22591i
$219$	−1633.49	−	480.546i	−0.504022	−	0.148275i
$220$			772.741i			0.236810i
$221$	7608.89			2.31597
$222$	2208.10	+	649.586i	0.667557	+	0.196384i
$223$	4805.24			1.44297			0.721485	−	0.692430i	$-0.243460\pi$
$223$	4805.24			1.44297			0.721485	+	0.692430i	$0.243460\pi$
$224$	−326.048			−0.0972545
$225$	5350.94	+	3446.60i	1.58546	+	1.02122i
$226$	−1049.34			−0.308855
$227$	−4618.27			−1.35033			−0.675166	−	0.737665i	$-0.735928\pi$
$227$	−4618.27			−1.35033			−0.675166	+	0.737665i	$0.735928\pi$
$228$	−136.858	+	465.212i	−0.0397527	+	0.135129i
$229$			3653.07i			1.05415i	0.849817	+	0.527077i	$0.176712\pi$
$229$			3653.07i			1.05415i	−0.849817	+	0.527077i	$0.823288\pi$
$230$		−	1507.88i		−	0.432291i
$231$	151.980	−	516.617i	0.0432882	−	0.147147i
$232$			946.603i			0.267877i
$233$	−1303.90			−0.366615			−0.183307	−	0.983056i	$-0.558680\pi$
$233$	−1303.90			−0.366615			−0.183307	+	0.983056i	$0.558680\pi$
$234$	2406.04	−	3735.45i	0.672171	−	1.04356i
$235$			718.074i			0.199327i
$236$	−680.512	−	1680.17i	−0.187702	−	0.463431i
$237$	350.066	−	1189.96i	0.0959462	−	0.326144i
$238$			1884.41i			0.513226i
$239$			6935.79i			1.87715i	0.345073	+	0.938576i	$0.387854\pi$
$239$			6935.79i			1.87715i	−0.345073	+	0.938576i	$0.612146\pi$
$240$	−1514.86	−	445.648i	−0.407433	−	0.119860i
$241$	974.319			0.260421			0.130210	−	0.991486i	$-0.458435\pi$
$241$	974.319			0.260421			0.130210	+	0.991486i	$0.458435\pi$
$242$	−2455.09			−0.652144
$243$	−3750.81	+	529.471i	−0.990183	+	0.139776i
$244$			2838.51i			0.744743i
$245$		−	4542.84i		−	1.18462i
$246$	628.544	+	184.907i	0.162904	+	0.0479238i
$247$			1919.73i			0.494533i
$248$		−	245.833i		−	0.0629451i
$249$	−229.410	+	779.820i	−0.0583867	+	0.198470i
$250$		−	4206.44i		−	1.06415i
$251$		−	2287.55i		−	0.575254i	−0.957742	−	0.287627i	$-0.907134\pi$
$251$		−	2287.55i		−	0.575254i	0.957742	−	0.287627i	$-0.0928664\pi$
$252$	925.115	+	595.877i	0.231257	+	0.148955i
$253$	−403.759			−0.100332
$254$	2799.57			0.691577
$255$	−2575.64	+	8755.19i	−0.632520	+	2.15008i
$256$	256.000			0.0625000
$257$		−	6990.89i		−	1.69681i	−0.529349	−	0.848404i	$-0.677564\pi$
$257$		−	6990.89i		−	1.69681i	0.529349	−	0.848404i	$-0.322436\pi$
$258$	1468.94	+	432.138i	0.354466	+	0.104278i
$259$			2256.64i			0.541392i
$260$	−6251.20			−1.49109
$261$	1729.99	−	2685.85i	0.410282	−	0.636973i
$262$	4130.38			0.973953
$263$		−	2946.13i		−	0.690747i	−0.938465	−	0.345373i	$-0.887752\pi$
$263$		−	2946.13i		−	0.690747i	0.938465	−	0.345373i	$-0.112248\pi$
$264$	−119.329	+	405.627i	−0.0278189	+	0.0945630i
$265$	−7768.89			−1.80090
$266$	−475.438			−0.109590
$267$	−1610.13	+	5473.23i	−0.369059	+	1.25452i
$268$			4178.99i			0.952508i
$269$	1274.53			0.288882			0.144441	−	0.989513i	$-0.453862\pi$
$269$	1274.53			0.288882			0.144441	+	0.989513i	$0.453862\pi$
$270$	3483.75	+	4032.98i	0.785238	+	0.909036i
$271$	−4929.25			−1.10491			−0.552455	−	0.833543i	$-0.686309\pi$
$271$	−4929.25			−1.10491			−0.552455	+	0.833543i	$0.686309\pi$
$272$		−	1479.56i		−	0.329822i
$273$	4179.25	+	1229.47i	0.926519	+	0.272567i
$274$		−	877.966i		−	0.193576i
$275$	−2397.76			−0.525783
$276$	232.852	−	791.518i	0.0507827	−	0.172622i
$277$	−6811.99			−1.47759			−0.738796	−	0.673929i	$-0.764605\pi$
$277$	−6811.99			−1.47759			−0.738796	+	0.673929i	$0.764605\pi$
$278$	5434.14			1.17237
$279$	−449.278	+	697.515i	−0.0964070	+	0.149674i
$280$		−	1548.16i		−	0.330430i
$281$		−	4763.12i		−	1.01119i	−0.862771	−	0.505594i	$-0.831273\pi$
$281$		−	4763.12i		−	1.01119i	0.862771	−	0.505594i	$-0.168727\pi$
$282$	−110.887	+	376.931i	−0.0234157	+	0.0795955i
$283$			6042.10i			1.26914i	0.772867	+	0.634568i	$0.218822\pi$
$283$			6042.10i			1.26914i	−0.772867	+	0.634568i	$0.781178\pi$
$284$			1447.93i			0.302532i
$285$	−2208.95	−	649.836i	−0.459111	−	0.135063i
$286$			1673.85i			0.346074i
$287$			642.361i			0.132116i
$288$	−726.364	−	467.859i	−0.148616	−	0.0957252i
$289$	−3638.17			−0.740519
$290$	−4494.72			−0.910135
$291$	6650.07	+	1956.34i	1.33964	+	0.394099i
$292$			1310.74i			0.262690i
$293$			1472.96i			0.293691i	0.989159	+	0.146845i	$0.0469120\pi$
$293$			1472.96i			0.293691i	−0.989159	+	0.146845i	$0.953088\pi$
$294$	701.519	−	2384.63i	0.139161	−	0.473042i
$295$	7977.89	−	3231.25i	1.57454	−	0.637731i
$296$		−	1771.82i		−	0.347922i
$297$	1079.89	−	932.827i	0.210982	−	0.182250i
$298$	5351.57			1.04029
$299$		−	3266.26i		−	0.631749i
$300$	1382.81	−	4700.50i	0.266122	−	0.904612i
$301$			1501.23i			0.287474i
$302$			5192.10i			0.989311i
$303$	1184.75	−	4027.24i	0.224627	−	0.763562i
$304$	373.295			0.0704275
$305$	−13478.0			−2.53032
$306$	−2704.01	+	4198.04i	−0.505156	+	0.784268i
$307$	2075.53			0.385852			0.192926	−	0.981213i	$-0.438202\pi$
$307$	2075.53			0.385852			0.192926	+	0.981213i	$0.438202\pi$
$308$	−414.544			−0.0766911
$309$	−9549.53	−	2809.31i	−1.75810	−	0.517205i
$310$	1167.28			0.213861
$311$		−	5120.23i		−	0.933575i	−0.884370	−	0.466787i	$-0.845411\pi$
$311$		−	5120.23i		−	0.933575i	0.884370	−	0.466787i	$-0.154589\pi$
$312$	−3281.38	−	965.329i	−0.595422	−	0.175163i
$313$			4181.55i			0.755128i	0.925984	+	0.377564i	$0.123238\pi$
$313$			4181.55i			0.755128i	−0.925984	+	0.377564i	$0.876762\pi$
$314$		−	3946.21i		−	0.709227i
$315$	−2829.38	+	4392.69i	−0.506088	+	0.785714i
$316$	−954.846			−0.169982
$317$			5414.77i			0.959380i	0.877438	+	0.479690i	$0.159251\pi$
$317$			5414.77i			0.959380i	−0.877438	+	0.479690i	$0.840749\pi$
$318$	−4078.05	−	1199.69i	−0.719137	−	0.211558i
$319$			1203.53i			0.211238i
$320$			1215.56i			0.212349i
$321$	5003.25	+	1471.88i	0.869951	+	0.255925i
$322$	808.918			0.139998
$323$		−	2157.47i		−	0.371656i
$324$	1205.91	+	2654.97i	0.206774	+	0.455241i
$325$		−	19397.0i		−	3.31062i
$326$	2676.85			0.454776
$327$	−9834.96	−	2893.28i	−1.66322	−	0.489293i
$328$		−	504.356i		−	0.0849037i
$329$	−385.217			−0.0645523
$330$	−1926.03	−	566.605i	−0.321286	−	0.0945170i
$331$	1106.67			0.183770			0.0918852	−	0.995770i	$-0.470711\pi$
$331$	1106.67			0.183770			0.0918852	+	0.995770i	$0.470711\pi$
$332$	625.743			0.103440
$333$	−3238.13	+	5027.29i	−0.532879	+	0.827308i
$334$			1833.57i			0.300384i
$335$	−19842.9			−3.23622
$336$	239.072	−	812.662i	0.0388168	−	0.131947i
$337$		−	8283.09i		−	1.33890i	−0.742858	−	0.669449i	$-0.766530\pi$
$337$		−	8283.09i		−	1.33890i	0.742858	−	0.669449i	$-0.233470\pi$
$338$	−9146.89			−1.47197
$339$	769.421	−	2615.44i	0.123272	−	0.419031i
$340$	7025.34			1.12060
$341$		−	312.557i		−	0.0496360i
$342$	−1059.17	−	682.225i	−0.167466	−	0.107867i
$343$	5931.88			0.933794
$344$		−	1178.71i		−	0.184743i
$345$	3758.34	+	1105.64i	0.586499	+	0.172538i
$346$	−3563.39			−0.553668
$347$	3871.50			0.598943			0.299471	−	0.954105i	$-0.403190\pi$
$347$	3871.50			0.598943			0.299471	+	0.954105i	$0.403190\pi$
$348$	−2359.37	−	694.088i	−0.363435	−	0.106917i
$349$		−	10305.7i		−	1.58067i	−0.612678	−	0.790333i	$-0.709908\pi$
$349$		−	10305.7i		−	1.58067i	0.612678	−	0.790333i	$-0.290092\pi$
$350$	4803.83			0.733645
$351$	7546.24	+	8735.95i	1.14755	+	1.32846i
$352$	325.484			0.0492850
$353$	5062.97			0.763385			0.381692	−	0.924289i	$-0.375341\pi$
$353$	5062.97			0.763385			0.381692	+	0.924289i	$0.375341\pi$
$354$	4686.73	−	464.180i	0.703664	−	0.0696918i
$355$	−6875.17			−1.02788
$356$	4391.83			0.653838
$357$	−4696.81	−	1381.72i	−0.696306	−	0.204842i
$358$	1741.70			0.257128
$359$			7093.69i			1.04287i	0.853291	+	0.521435i	$0.174603\pi$
$359$			7093.69i			1.04287i	−0.853291	+	0.521435i	$0.825397\pi$
$360$	2221.52	−	3448.97i	0.325234	−	0.504935i
$361$	−6314.67			−0.920640
$362$	−6495.09			−0.943022
$363$	1800.17	−	6119.21i	0.260288	−	0.884780i
$364$		−	3353.52i		−	0.482890i
$365$	−6223.76			−0.892511
$366$	−7074.88	−	2081.31i	−1.01041	−	0.297246i
$367$		−	7928.64i		−	1.12772i	−0.825872	−	0.563858i	$-0.809317\pi$
$367$		−	7928.64i		−	1.12772i	0.825872	−	0.563858i	$-0.190683\pi$
$368$	−635.130			−0.0899686
$369$	−921.749	+	1431.04i	−0.130039	+	0.201889i
$370$	8413.07			1.18209
$371$		−	4167.69i		−	0.583223i
$372$	612.728	+	180.255i	0.0853991	+	0.0251230i
$373$	−8719.31			−1.21037			−0.605186	−	0.796084i	$-0.706901\pi$
$373$	−8719.31			−1.21037			−0.605186	+	0.796084i	$0.706901\pi$
$374$		−	1881.14i		−	0.260084i
$375$	10484.4	+	3084.33i	1.44376	+	0.424731i
$376$	302.457			0.0414842
$377$	−9736.13			−1.33007
$378$	−2163.53	+	1868.89i	−0.294392	+	0.254300i
$379$	−789.446			−0.106995			−0.0534975	−	0.998568i	$-0.517037\pi$
$379$	−789.446			−0.106995			−0.0534975	+	0.998568i	$0.517037\pi$
$380$			1772.50i			0.239283i
$381$	−2052.76	+	6977.81i	−0.276026	+	0.938278i
$382$	−3161.09			−0.423392
$383$		−	4907.40i		−	0.654717i	−0.944900	−	0.327359i	$-0.893842\pi$
$383$		−	4907.40i		−	0.654717i	0.944900	−	0.327359i	$-0.106158\pi$
$384$	−187.710	+	638.070i	−0.0249454	+	0.0847952i
$385$		−	1968.37i		−	0.260564i
$386$	3314.66			0.437077
$387$	−2154.17	+	3344.41i	−0.282953	+	0.439292i
$388$		−	5336.15i		−	0.698201i
$389$			2497.38i			0.325507i	0.986667	+	0.162754i	$0.0520376\pi$
$389$			2497.38i			0.325507i	−0.986667	+	0.162754i	$0.947962\pi$
$390$	4583.64	−	15580.9i	0.595132	−	2.02299i
$391$			3670.75i			0.474778i
$392$	−1913.47			−0.246543
$393$	−3028.56	+	10294.8i	−0.388730	+	1.32139i
$394$		−	3481.73i		−	0.445196i
$395$		−	4533.86i		−	0.577527i
$396$	−923.513	−	594.845i	−0.117193	−	0.0754851i
$397$			6068.25i			0.767145i	0.923511	+	0.383573i	$0.125306\pi$
$397$			6068.25i			0.767145i	−0.923511	+	0.383573i	$0.874694\pi$
$398$	1229.85			0.154891
$399$	348.611	−	1185.01i	0.0437403	−	0.148684i
$400$	−3771.78			−0.471472
$401$	9709.46			1.20915			0.604573	−	0.796550i	$-0.293344\pi$
$401$	9709.46			1.20915			0.604573	+	0.796550i	$0.293344\pi$
$402$	−10416.0	−	3064.20i	−1.29229	−	0.380171i
$403$	2528.47			0.312536
$404$	−3231.54			−0.397958
$405$	−12606.5	+	5725.96i	−1.54672	+	0.702531i
$406$		−	2411.24i		−	0.294748i
$407$		−	2252.73i		−	0.274358i
$408$	3687.75	+	1084.87i	0.447477	+	0.131640i
$409$		−	5832.59i		−	0.705142i	−0.935785	−	0.352571i	$-0.885307\pi$
$409$		−	5832.59i		−	0.705142i	0.935785	−	0.352571i	$-0.114693\pi$
$410$	2394.82			0.288467
$411$	2188.29	+	643.761i	0.262629	+	0.0772612i
$412$			7662.73i			0.916300i
$413$	1733.43	+	4279.81i	0.206530	+	0.509917i
$414$	1802.09	+	1160.75i	0.213932	+	0.137796i
$415$			2971.19i			0.351446i
$416$			2633.05i			0.310326i
$417$	−3984.53	+	13544.4i	−0.467922	+	1.59058i
$418$	474.615			0.0555363
$419$	6572.59			0.766330			0.383165	−	0.923680i	$-0.374834\pi$
$419$	6572.59			0.766330			0.383165	+	0.923680i	$0.374834\pi$
$420$	3858.73	+	1135.18i	0.448302	+	0.131883i
$421$			8822.88i			1.02138i	0.859765	+	0.510690i	$0.170610\pi$
$421$			8822.88i			1.02138i	−0.859765	+	0.510690i	$0.829390\pi$
$422$			7046.60i			0.812851i
$423$	−858.179	−	552.763i	−0.0986433	−	0.0635373i
$424$			3272.31i			0.374805i
$425$			21799.1i			2.48803i
$426$	−3608.92	−	1061.68i	−0.410452	−	0.120748i
$427$		−	7230.40i		−	0.819447i
$428$		−	4014.71i		−	0.453407i
$429$	−4172.02	−	1227.34i	−0.469526	−	0.138127i
$430$	5596.81			0.627680
$431$	9519.82			1.06393			0.531965	−	0.846767i	$-0.321454\pi$
$431$	9519.82			1.06393			0.531965	+	0.846767i	$0.321454\pi$
$432$	1698.72	−	1467.38i	0.189189	−	0.163424i
$433$	−4618.05			−0.512539			−0.256269	−	0.966605i	$-0.582493\pi$
$433$	−4618.05			−0.512539			−0.256269	+	0.966605i	$0.582493\pi$
$434$			626.198i			0.0692591i
$435$	3295.71	−	11202.9i	0.363258	−	1.23480i
$436$			7891.77i			0.866851i
$437$	−926.136			−0.101380
$438$	−3266.98	−	961.091i	−0.356398	−	0.104846i
$439$	−6509.93			−0.707749			−0.353875	−	0.935293i	$-0.615136\pi$
$439$	−6509.93			−0.707749			−0.353875	+	0.935293i	$0.615136\pi$
$440$			1545.48i			0.167450i
$441$	5429.21	+	3497.02i	0.586244	+	0.377607i
$442$	15217.8			1.63764
$443$	13277.5			1.42401			0.712003	−	0.702176i	$-0.247788\pi$
$443$	13277.5			1.42401			0.712003	+	0.702176i	$0.247788\pi$
$444$	4416.19	+	1299.17i	0.472034	+	0.138865i
$445$			20853.6i			2.22147i
$446$	9610.47			1.02033
$447$	−3923.99	+	13338.6i	−0.415209	+	1.41139i
$448$	−652.096			−0.0687693
$449$			12397.8i			1.30310i	0.758607	+	0.651548i	$0.225880\pi$
$449$			12397.8i			1.30310i	−0.758607	+	0.651548i	$0.774120\pi$
$450$	10701.9	+	6893.21i	1.12109	+	0.722108i
$451$		−	641.249i		−	0.0669517i
$452$	−2098.69			−0.218393
$453$	−12941.1	−	3807.06i	−1.34222	−	0.394860i
$454$	−9236.55			−0.954829
$455$	15923.4			1.64066
$456$	−273.715	+	930.423i	−0.0281094	+	0.0955506i
$457$		−	2877.48i		−	0.294536i	−0.989097	−	0.147268i	$-0.952952\pi$
$457$		−	2877.48i		−	0.294536i	0.989097	−	0.147268i	$-0.0470479\pi$
$458$			7306.13i			0.745400i
$459$	−8480.76	−	9817.81i	−0.862414	−	0.998379i
$460$		−	3015.76i		−	0.305676i
$461$		−	5221.95i		−	0.527571i	−0.964581	−	0.263786i	$-0.915029\pi$
$461$		−	5221.95i		−	0.527571i	0.964581	−	0.263786i	$-0.0849712\pi$
$462$	303.961	−	1033.23i	0.0306094	−	0.104049i
$463$		−	16063.6i		−	1.61240i	−0.591645	−	0.806198i	$-0.701521\pi$
$463$		−	16063.6i		−	1.61240i	0.591645	−	0.806198i	$-0.298479\pi$
$464$			1893.21i			0.189418i
$465$	−855.897	+	2909.40i	−0.0853575	+	0.290150i
$466$	−2607.80			−0.259236
$467$	19210.6			1.90356			0.951778	−	0.306787i	$-0.0992538\pi$
$467$	19210.6			1.90356			0.951778	+	0.306787i	$0.0992538\pi$
$468$	4812.09	−	7470.89i	0.475297	−	0.737911i
$469$		−	10644.9i		−	1.04805i
$470$			1436.15i			0.140946i
$471$	9835.76	+	2893.52i	0.962225	+	0.283071i
$472$	−1361.02	−	3360.34i	−0.132725	−	0.327695i
$473$		−	1498.63i		−	0.145681i
$474$	700.132	−	2379.92i	0.0678442	−	0.230618i
$475$	−5499.95			−0.531273
$476$			3768.81i			0.362906i
$477$	5980.38	−	9284.70i	0.574052	−	0.891231i
$478$			13871.6i			1.32735i
$479$		−	11153.0i		−	1.06387i	−0.846786	−	0.531934i	$-0.821466\pi$
$479$		−	11153.0i		−	1.06387i	0.846786	−	0.531934i	$-0.178534\pi$
$480$	−3029.72	−	891.295i	−0.288099	−	0.0847539i
$481$	18223.8			1.72751
$482$	1948.64			0.184145
$483$	−593.132	+	2016.20i	−0.0558767	+	0.189938i
$484$	−4910.17			−0.461136
$485$	25337.4			2.37219
$486$	−7501.62	+	1058.94i	−0.700165	+	0.0988366i
$487$	7355.98			0.684459			0.342229	−	0.939616i	$-0.388818\pi$
$487$	7355.98			0.684459			0.342229	+	0.939616i	$0.388818\pi$
$488$			5677.03i			0.526612i
$489$	−1962.77	+	6671.94i	−0.181513	+	0.617005i
$490$		−	9085.68i		−	0.837651i
$491$		−	2400.04i		−	0.220596i	−0.993899	−	0.110298i	$-0.964820\pi$
$491$		−	2400.04i		−	0.220596i	0.993899	−	0.110298i	$-0.0351805\pi$
$492$	1257.09	+	369.815i	0.115191	+	0.0338873i
$493$	10941.8			0.999586
$494$			3839.47i			0.349688i
$495$	2824.48	−	4385.08i	0.256467	−	0.398172i
$496$		−	491.665i		−	0.0445089i
$497$		−	3688.25i		−	0.332879i
$498$	−458.821	+	1559.64i	−0.0412856	+	0.140340i
$499$	18219.5			1.63450			0.817252	−	0.576280i	$-0.195496\pi$
$499$	18219.5			1.63450			0.817252	+	0.576280i	$0.195496\pi$
$500$		−	8412.87i		−	0.752470i
$501$	−4570.09	−	1344.45i	−0.407538	−	0.119891i
$502$		−	4575.10i		−	0.406766i
$503$	812.931			0.0720612			0.0360306	−	0.999351i	$-0.488529\pi$
$503$	812.931			0.0720612			0.0360306	+	0.999351i	$0.488529\pi$
$504$	1850.23	+	1191.75i	0.163523	+	0.105327i
$505$		−	15344.2i		−	1.35210i
$506$	−807.517			−0.0709457
$507$	6706.87	−	22798.3i	0.587500	−	1.99705i
$508$	5599.13			0.489018
$509$	7475.46			0.650971			0.325485	−	0.945547i	$-0.394472\pi$
$509$	7475.46			0.650971			0.325485	+	0.945547i	$0.394472\pi$
$510$	−5151.27	+	17510.4i	−0.447259	+	1.52034i
$511$		−	3338.79i		−	0.289040i
$512$	512.000			0.0441942
$513$	2477.05	−	2139.71i	0.213186	−	0.184153i
$514$		−	13981.8i		−	1.19983i
$515$	−36384.7			−3.11320
$516$	2937.88	+	864.277i	0.250645	+	0.0737358i
$517$	384.550			0.0327128
$518$			4513.27i			0.382822i
$519$	2612.82	−	8881.61i	0.220983	−	0.751174i
$520$	−12502.4			−1.05436
$521$			13918.5i			1.17041i	0.810886	+	0.585204i	$0.198986\pi$
$521$			13918.5i			1.17041i	−0.810886	+	0.585204i	$0.801014\pi$
$522$	3459.98	−	5371.70i	0.290113	−	0.450408i
$523$	10698.0			0.894438			0.447219	−	0.894425i	$-0.352415\pi$
$523$	10698.0			0.894438			0.447219	+	0.894425i	$0.352415\pi$
$524$	8260.76			0.688689
$525$	−3522.37	+	11973.4i	−0.292817	+	0.995353i
$526$		−	5892.27i		−	0.488432i
$527$	−2841.60			−0.234880
$528$	−238.658	+	811.255i	−0.0196709	+	0.0668662i
$529$	−10591.3			−0.870490
$530$	−15537.8			−1.27343
$531$	−2279.55	+	12021.9i	−0.186298	+	0.982493i
$532$	−950.876			−0.0774920
$533$	5187.48			0.421566
$534$	−3220.27	+	10946.5i	−0.260964	+	0.887078i
$535$	19062.9			1.54049
$536$			8357.97i			0.673525i
$537$	−1277.09	+	4341.13i	−0.102627	+	0.348852i
$538$	2549.06			0.204271
$539$	−2432.83			−0.194414
$540$	6967.50	+	8065.97i	0.555247	+	0.642785i
$541$			11634.8i			0.924616i	0.886720	+	0.462308i	$0.152978\pi$
$541$			11634.8i			0.924616i	−0.886720	+	0.462308i	$0.847022\pi$
$542$	−9858.49			−0.781289
$543$	4762.46	−	16188.7i	0.376385	−	1.27942i
$544$		−	2959.12i		−	0.233219i
$545$	−37472.2			−2.94520
$546$	8358.50	+	2458.94i	0.655148	+	0.192734i
$547$	−19199.4			−1.50074			−0.750371	−	0.661016i	$-0.770125\pi$
$547$	−19199.4			−1.50074			−0.750371	+	0.661016i	$0.770125\pi$
$548$		−	1755.93i		−	0.136879i
$549$	10375.2	−	16107.8i	0.806561	−	1.25221i
$550$	−4795.52			−0.371784
$551$			2760.64i			0.213444i
$552$	465.703	−	1583.04i	0.0359088	−	0.122062i
$553$	2432.23			0.187033
$554$	−13624.0			−1.04482
$555$	−6168.81	+	20969.2i	−0.471804	+	1.60377i
$556$	10868.3			0.828989
$557$		−	12237.1i		−	0.930883i	−0.885079	−	0.465442i	$-0.845896\pi$
$557$		−	12237.1i		−	0.930883i	0.885079	−	0.465442i	$-0.154104\pi$
$558$	−898.555	+	1395.03i	−0.0681700	+	0.105836i
$559$	12123.4			0.917290
$560$		−	3096.32i		−	0.233649i
$561$	4688.67	+	1379.33i	0.352863	+	0.103806i
$562$		−	9526.24i		−	0.715018i
$563$	1826.20			0.136705			0.0683527	−	0.997661i	$-0.478226\pi$
$563$	1826.20			0.136705			0.0683527	+	0.997661i	$0.478226\pi$
$564$	−221.774	+	753.863i	−0.0165574	+	0.0562825i
$565$		−	9965.11i		−	0.742010i
$566$			12084.2i			0.897415i
$567$	−3071.74	−	6762.87i	−0.227515	−	0.500906i
$568$			2895.87i			0.213922i
$569$	4352.74			0.320696			0.160348	−	0.987061i	$-0.448738\pi$
$569$	4352.74			0.320696			0.160348	+	0.987061i	$0.448738\pi$
$570$	−4417.90	−	1299.67i	−0.324641	−	0.0955040i
$571$		−	5189.16i		−	0.380315i	−0.981754	−	0.190157i	$-0.939100\pi$
$571$		−	5189.16i		−	0.380315i	0.981754	−	0.190157i	$-0.0608998\pi$
$572$			3347.71i			0.244711i
$573$	2317.84	−	7878.90i	0.168987	−	0.574426i
$574$			1284.72i			0.0934203i
$575$	9357.69			0.678683
$576$	−1452.73	−	935.718i	−0.105087	−	0.0676879i
$577$	9056.33			0.653414			0.326707	−	0.945126i	$-0.394061\pi$
$577$	9056.33			0.653414			0.326707	+	0.945126i	$0.394061\pi$
$578$	−7276.34			−0.523626
$579$	−2430.44	+	8261.66i	−0.174449	+	0.592993i
$580$	−8989.44			−0.643563
$581$	−1593.93			−0.113816
$582$	13300.1	+	3912.68i	0.947266	+	0.278670i
$583$			4160.48i			0.295556i
$584$			2621.49i			0.185750i
$585$	35473.8	+	22849.1i	2.50711	+	1.61486i
$586$			2945.93i			0.207671i
$587$	25369.7			1.78385			0.891925	−	0.452183i	$-0.149355\pi$
$587$	25369.7			1.78385			0.891925	+	0.452183i	$0.149355\pi$
$588$	1403.04	−	4769.26i	0.0984019	−	0.334491i
$589$		−	716.939i		−	0.0501544i
$590$	15955.8	−	6462.50i	1.11337	−	0.450944i
$591$	8678.08	+	2552.95i	0.604008	+	0.177689i
$592$		−	3543.64i		−	0.246018i
$593$			556.620i			0.0385457i	0.999814	+	0.0192729i	$0.00613512\pi$
$593$			556.620i			0.0385457i	−0.999814	+	0.0192729i	$0.993865\pi$
$594$	2159.79	−	1865.65i	0.149187	−	0.128870i
$595$	−17895.3			−1.23300
$596$	10703.1			0.735600
$597$	−901.773	+	3065.34i	−0.0618210	+	0.210144i
$598$		−	6532.53i		−	0.446714i
$599$		−	15541.0i		−	1.06008i	−0.847973	−	0.530039i	$-0.822177\pi$
$599$		−	15541.0i		−	1.06008i	0.847973	−	0.530039i	$-0.177823\pi$
$600$	2765.62	−	9401.01i	0.188177	−	0.639658i
$601$			3882.45i			0.263508i	0.991282	+	0.131754i	$0.0420609\pi$
$601$			3882.45i			0.263508i	−0.991282	+	0.131754i	$0.957939\pi$
$602$			3002.46i			0.203275i
$603$	15274.8	−	23714.6i	1.03157	−	1.60154i
$604$			10384.2i			0.699548i
$605$		−	23314.8i		−	1.56675i
$606$	2369.50	−	8054.49i	0.158836	−	0.539920i
$607$	−2132.51			−0.142596			−0.0712982	−	0.997455i	$-0.522714\pi$
$607$	−2132.51			−0.142596			−0.0712982	+	0.997455i	$0.522714\pi$
$608$	746.590			0.0497997
$609$	6009.91	+	1768.02i	0.399891	+	0.117642i
$610$	−26956.0			−1.78921
$611$			3110.88i			0.205978i
$612$	−5408.01	+	8396.08i	−0.357199	+	0.554561i
$613$			842.437i			0.0555069i	0.999615	+	0.0277534i	$0.00883533\pi$
$613$			842.437i			0.0555069i	−0.999615	+	0.0277534i	$0.991165\pi$
$614$	4151.05			0.272838
$615$	−1755.98	+	5968.99i	−0.115135	+	0.391370i
$616$	−829.088			−0.0542288
$617$		−	22352.9i		−	1.45850i	−0.684250	−	0.729248i	$-0.739870\pi$
$617$		−	22352.9i		−	1.45850i	0.684250	−	0.729248i	$-0.260130\pi$
$618$	−19099.1	−	5618.63i	−1.24317	−	0.365719i
$619$	−12127.3			−0.787458			−0.393729	−	0.919227i	$-0.628815\pi$
$619$	−12127.3			−0.787458			−0.393729	+	0.919227i	$0.628815\pi$
$620$	2334.56			0.151223
$621$	−4214.48	+	3640.53i	−0.272337	+	0.235249i
$622$		−	10240.5i		−	0.660137i
$623$	−11187.1			−0.719424
$624$	−6562.76	−	1930.66i	−0.421027	−	0.123859i
$625$	10479.5			0.670689
$626$			8363.09i			0.533956i
$627$	−348.007	+	1182.96i	−0.0221660	+	0.0753474i
$628$		−	7892.41i		−	0.501499i
$629$	−20480.6			−1.29827
$630$	−5658.76	+	8785.38i	−0.357858	+	0.555584i
$631$	18241.3			1.15083			0.575414	−	0.817862i	$-0.304841\pi$
$631$	18241.3			1.15083			0.575414	+	0.817862i	$0.304841\pi$
$632$	−1909.69			−0.120195
$633$	−17563.4	−	5166.86i	−1.10281	−	0.324430i
$634$			10829.5i			0.678384i
$635$			26586.2i			1.66148i
$636$	−8156.09	−	2399.39i	−0.508506	−	0.149594i
$637$		−	19680.7i		−	1.22414i
$638$			2407.06i			0.149367i
$639$	5292.41	−	8216.61i	0.327644	−	0.508676i
$640$			2431.11i			0.150153i
$641$			27962.8i			1.72303i	0.507728	+	0.861517i	$0.330485\pi$
$641$			27962.8i			1.72303i	−0.507728	+	0.861517i	$0.669515\pi$
$642$	10006.5	+	2943.75i	0.615148	+	0.180967i
$643$	2162.12			0.132606			0.0663031	−	0.997800i	$-0.478880\pi$
$643$	2162.12			0.132606			0.0663031	+	0.997800i	$0.478880\pi$
$644$	1617.84			0.0989932
$645$	−4103.81	+	13949.8i	−0.250523	+	0.851588i
$646$		−	4314.94i		−	0.262801i
$647$		−	1584.19i		−	0.0962614i	−0.998841	−	0.0481307i	$-0.984674\pi$
$647$		−	1584.19i		−	0.0962614i	0.998841	−	0.0481307i	$-0.0153264\pi$
$648$	2411.81	+	5309.93i	0.146211	+	0.321904i
$649$	−1730.43	−	4272.40i	−0.104662	−	0.258407i
$650$		−	38794.0i		−	2.34096i
$651$	−1560.77	−	459.154i	−0.0939654	−	0.0276431i
$652$	5353.69			0.321575
$653$		−	31720.4i		−	1.90094i	−0.310814	−	0.950471i	$-0.600602\pi$
$653$		−	31720.4i		−	1.90094i	0.310814	−	0.950471i	$-0.399398\pi$
$654$	−19669.9	−	5786.57i	−1.17608	−	0.345983i
$655$			39224.3i			2.33988i
$656$		−	1008.71i		−	0.0600360i
$657$	4790.96	−	7438.10i	0.284495	−	0.441686i
$658$	−770.435			−0.0456454
$659$	1761.47			0.104123			0.0520615	−	0.998644i	$-0.483421\pi$
$659$	1761.47			0.104123			0.0520615	+	0.998644i	$0.483421\pi$
$660$	−3852.05	−	1133.21i	−0.227183	−	0.0668336i
$661$	22221.3			1.30758			0.653788	−	0.756677i	$-0.273179\pi$
$661$	22221.3			1.30758			0.653788	+	0.756677i	$0.273179\pi$
$662$	2213.34			0.129945
$663$	−11158.3	+	37929.7i	−0.653624	+	2.22182i
$664$	1251.49			0.0731432
$665$		−	4515.01i		−	0.263285i
$666$	−6476.27	+	10054.6i	−0.376802	+	0.584995i
$667$		−	4697.00i		−	0.272667i
$668$			3667.13i			0.212404i
$669$	−7046.79	+	23953.7i	−0.407242	+	1.38431i
$670$	−39685.9			−2.28836
$671$			7217.89i			0.415266i
$672$	478.144	−	1625.32i	0.0274476	−	0.0933009i
$673$			18991.3i			1.08776i	0.839163	+	0.543880i	$0.183045\pi$
$673$			18991.3i			1.08776i	−0.839163	+	0.543880i	$0.816955\pi$
$674$		−	16566.2i		−	0.946744i
$675$	−25028.1	+	21619.6i	−1.42716	+	1.23280i
$676$	−18293.8			−1.04084
$677$			26193.0i			1.48697i	0.668754	+	0.743484i	$0.266828\pi$
$677$			26193.0i			1.48697i	−0.668754	+	0.743484i	$0.733172\pi$
$678$	1538.84	−	5230.89i	0.0871665	−	0.296300i
$679$			13592.5i			0.768237i
$680$	14050.7			0.792381
$681$	6772.61	−	23021.7i	0.381097	−	1.29544i
$682$		−	625.113i		−	0.0350980i
$683$	−29944.8			−1.67761			−0.838803	−	0.544435i	$-0.816744\pi$
$683$	−29944.8			−1.67761			−0.838803	+	0.544435i	$0.816744\pi$
$684$	−2118.34	−	1364.45i	−0.118417	−	0.0762734i
$685$	8337.63			0.465057
$686$	11863.8			0.660292
$687$	−18210.2	−	5357.16i	−1.01130	−	0.297508i
$688$		−	2357.41i		−	0.130633i
$689$	−33656.8			−1.86099
$690$	7516.67	+	2211.28i	0.414717	+	0.122003i
$691$		−	4559.60i		−	0.251021i	−0.992092	−	0.125510i	$-0.959943\pi$
$691$		−	4559.60i		−	0.251021i	0.992092	−	0.125510i	$-0.0400568\pi$
$692$	−7126.78			−0.391502
$693$	2352.42	+	1515.22i	0.128948	+	0.0830569i
$694$	7743.00			0.423516
$695$			51605.5i			2.81656i
$696$	−4718.74	−	1388.18i	−0.256988	−	0.0756016i
$697$	−5829.89			−0.316819
$698$		−	20611.4i		−	1.11770i
$699$	1912.14	−	6499.83i	0.103468	−	0.351711i
$700$	9607.67			0.518765
$701$	23909.3			1.28822			0.644109	−	0.764934i	$-0.277228\pi$
$701$	23909.3			1.28822			0.644109	+	0.764934i	$0.277228\pi$
$702$	15092.5	+	17471.9i	0.811438	+	0.939365i
$703$		−	5167.28i		−	0.277223i
$704$	650.967			0.0348498
$705$	−3579.54	−	1053.04i	−0.191224	−	0.0562551i
$706$	10125.9			0.539794
$707$	8231.55			0.437877
$708$	9373.47	−	928.361i	0.497566	−	0.0492796i
$709$	7047.67			0.373316			0.186658	−	0.982425i	$-0.440234\pi$
$709$	7047.67			0.373316			0.186658	+	0.982425i	$0.440234\pi$
$710$	−13750.3			−0.726819
$711$	5418.48	+	3490.10i	0.285807	+	0.184092i
$712$	8783.66			0.462334
$713$			1219.81i			0.0640705i
$714$	−9393.61	−	2763.45i	−0.492363	−	0.144845i
$715$	−15895.8			−0.831426
$716$	3483.41			0.181817
$717$	−34574.4	−	10171.2i	−1.80084	−	0.529778i
$718$			14187.4i			0.737421i
$719$	−11771.4			−0.610567			−0.305283	−	0.952262i	$-0.598751\pi$
$719$	−11771.4			−0.610567			−0.305283	+	0.952262i	$0.598751\pi$
$720$	4443.04	−	6897.93i	0.229975	−	0.357043i
$721$		−	19518.9i		−	1.00821i
$722$	−12629.3			−0.650990
$723$	−1428.82	+	4856.90i	−0.0734972	+	0.249834i
$724$	−12990.2			−0.666818
$725$		−	27893.6i		−	1.42888i
$726$	3600.34	−	12238.4i	0.184051	−	0.625634i
$727$	29044.3			1.48170			0.740848	−	0.671673i	$-0.234424\pi$
$727$	29044.3			1.48170			0.740848	+	0.671673i	$0.234424\pi$
$728$		−	6707.03i		−	0.341455i
$729$	2861.12	−	19473.9i	0.145360	−	0.989379i
$730$	−12447.5			−0.631100
$731$	−13624.8			−0.689370
$732$	−14149.8	−	4162.63i	−0.714468	−	0.210185i
$733$	−2188.98			−0.110303			−0.0551514	−	0.998478i	$-0.517564\pi$
$733$	−2188.98			−0.110303			−0.0551514	+	0.998478i	$0.517564\pi$
$734$		−	15857.3i		−	0.797416i
$735$	22645.7	+	6661.99i	1.13646	+	0.334328i
$736$	−1270.26			−0.0636174
$737$			10626.5i			0.531115i
$738$	−1843.50	+	2862.08i	−0.0919513	+	0.142757i
$739$		−	21285.6i		−	1.05955i	−0.848140	−	0.529773i	$-0.822277\pi$
$739$		−	21285.6i		−	1.05955i	0.848140	−	0.529773i	$-0.177723\pi$
$740$	16826.1			0.835867
$741$	−9569.72	−	2815.25i	−0.474430	−	0.139569i
$742$		−	8335.38i		−	0.412401i
$743$		−	28955.4i		−	1.42971i	−0.699275	−	0.714853i	$-0.746494\pi$
$743$		−	28955.4i		−	1.42971i	0.699275	−	0.714853i	$-0.253506\pi$
$744$	1225.46	+	360.509i	0.0603863	+	0.0177647i
$745$			50821.3i			2.49926i
$746$	−17438.6			−0.855862
$747$	−3550.92	−	2287.19i	−0.173924	−	0.112026i
$748$		−	3762.29i		−	0.183907i
$749$			10226.5i			0.498888i
$750$	20968.7	+	6168.66i	1.02089	+	0.300330i
$751$			31748.3i			1.54263i	0.636456	+	0.771313i	$0.280400\pi$
$751$			31748.3i			1.54263i	−0.636456	+	0.771313i	$0.719600\pi$
$752$	604.915			0.0293337
$753$	11403.3	+	3354.65i	0.551869	+	0.162351i
$754$	−19472.3			−0.940502
$755$	−49306.9			−2.37677
$756$	−4327.06	+	3737.78i	−0.208166	+	0.179817i
$757$	−16734.2			−0.803453			−0.401727	−	0.915760i	$-0.631590\pi$
$757$	−16734.2			−0.803453			−0.401727	+	0.915760i	$0.631590\pi$
$758$	−1578.89			−0.0756569
$759$	592.105	−	2012.70i	0.0283163	−	0.0962537i
$760$			3545.01i			0.169199i
$761$		−	25291.3i		−	1.20474i	−0.798216	−	0.602371i	$-0.794223\pi$
$761$		−	25291.3i		−	1.20474i	0.798216	−	0.602371i	$-0.205777\pi$
$762$	−4105.51	+	13955.6i	−0.195180	+	0.663463i
$763$		−	20102.3i		−	0.953804i
$764$	−6322.19			−0.299383
$765$	−39866.8	−	25678.7i	−1.88417	−	1.21361i
$766$		−	9814.81i		−	0.462955i
$767$	34562.2	−	13998.6i	1.62708	−	0.659009i
$768$	−375.419	+	1276.14i	−0.0176390	+	0.0599593i
$769$			18921.8i			0.887307i	0.896198	+	0.443653i	$0.146318\pi$
$769$			18921.8i			0.887307i	−0.896198	+	0.443653i	$0.853682\pi$
$770$		−	3936.73i		−	0.184247i
$771$	34849.0	+	10252.0i	1.62783	+	0.478881i
$772$	6629.32			0.309060
$773$	−29323.8			−1.36443			−0.682215	−	0.731152i	$-0.738983\pi$
$773$	−29323.8			−1.36443			−0.682215	+	0.731152i	$0.738983\pi$
$774$	−4308.35	+	6688.83i	−0.200078	+	0.310627i
$775$			7243.96i			0.335756i
$776$		−	10672.3i		−	0.493703i
$777$	−11249.1	−	3309.32i	−0.519384	−	0.152794i
$778$			4994.77i			0.230169i
$779$		−	1470.89i		−	0.0676509i
$780$	9167.27	−	31161.7i	0.420822	−	1.43047i
$781$			3681.87i			0.168691i
$782$			7341.51i			0.335718i
$783$	10851.8	+	12562.6i	0.495288	+	0.573373i
$784$	−3826.95			−0.174333
$785$	37475.3			1.70388
$786$	−6057.13	+	20589.6i	−0.274874	+	0.934360i
$787$	29548.3			1.33835			0.669177	−	0.743103i	$-0.266647\pi$
$787$	29548.3			1.33835			0.669177	+	0.743103i	$0.266647\pi$
$788$		−	6963.47i		−	0.314801i
$789$	14686.2	+	4320.45i	0.662667	+	0.194946i
$790$		−	9067.72i		−	0.408374i
$791$	5345.88			0.240300
$792$	−1847.03	−	1189.69i	−0.0828677	−	0.0533760i
$793$	−58390.1			−2.61475
$794$			12136.5i			0.542454i
$795$	11392.9	−	38727.3i	0.508259	−	1.72769i
$796$	2459.69			0.109524
$797$	22579.7			1.00353			0.501765	−	0.865004i	$-0.332684\pi$
$797$	22579.7			1.00353			0.501765	+	0.865004i	$0.332684\pi$
$798$	697.222	−	2370.02i	0.0309290	−	0.105135i
$799$		−	3496.12i		−	0.154798i
$800$	−7543.56			−0.333381
$801$	−24922.4	−	16052.8i	−1.09936	−	0.708111i
$802$	19418.9			0.854995
$803$			3333.01i			0.146475i
$804$	−20831.9	−	6128.41i	−0.913787	−	0.268821i
$805$			7681.91i			0.336338i
$806$	5056.95			0.220997
$807$	−1869.07	+	6353.42i	−0.0815297	+	0.277139i
$808$	−6463.08			−0.281399
$809$	11940.1			0.518902			0.259451	−	0.965756i	$-0.416458\pi$
$809$	11940.1			0.518902			0.259451	+	0.965756i	$0.416458\pi$
$810$	−25213.0	+	11451.9i	−1.09370	+	0.496765i
$811$			3871.63i			0.167634i	0.996481	+	0.0838171i	$0.0267111\pi$
$811$			3871.63i			0.167634i	−0.996481	+	0.0838171i	$0.973289\pi$
$812$		−	4822.47i		−	0.208418i
$813$	7228.65	−	24571.9i	0.311833	−	1.05999i
$814$		−	4505.46i		−	0.194000i
$815$			25420.8i			1.09258i
$816$	7375.49	+	2169.75i	0.316414	+	0.0930838i
$817$		−	3437.54i		−	0.147203i
$818$		−	11665.2i		−	0.498611i
$819$	−12257.6	+	19030.2i	−0.522973	+	0.811930i
$820$	4789.63			0.203977
$821$	1641.98			0.0697996			0.0348998	−	0.999391i	$-0.488889\pi$
$821$	1641.98			0.0697996			0.0348998	+	0.999391i	$0.488889\pi$
$822$	4376.59	+	1287.52i	0.185707	+	0.0546319i
$823$		−	34300.1i		−	1.45277i	−0.687289	−	0.726384i	$-0.741199\pi$
$823$		−	34300.1i		−	1.45277i	0.687289	−	0.726384i	$-0.258801\pi$
$824$			15325.5i			0.647922i
$825$	3516.27	−	11952.6i	0.148389	−	0.504409i
$826$	3466.87	+	8559.62i	0.146039	+	0.360566i
$827$			33600.0i			1.41280i	0.707812	+	0.706401i	$0.249682\pi$
$827$			33600.0i			1.41280i	−0.707812	+	0.706401i	$0.750318\pi$
$828$	3604.18	+	2321.49i	0.151273	+	0.0974366i
$829$	−27672.8			−1.15937			−0.579684	−	0.814841i	$-0.696824\pi$
$829$	−27672.8			−1.15937			−0.579684	+	0.814841i	$0.696824\pi$
$830$			5942.39i			0.248510i
$831$	9989.67	−	33957.2i	0.417013	−	1.41753i
$832$			5266.09i			0.219434i
$833$			22118.0i			0.919979i
$834$	−7969.07	+	27088.7i	−0.330871	+	1.12471i
$835$	−17412.5			−0.721659
$836$	949.230			0.0392701
$837$	−2818.20	−	3262.51i	−0.116381	−	0.134730i
$838$	13145.2			0.541877
$839$	22478.3			0.924956			0.462478	−	0.886631i	$-0.346960\pi$
$839$	22478.3			0.924956			0.462478	+	0.886631i	$0.346960\pi$
$840$	7717.47	+	2270.35i	0.316997	+	0.0932555i
$841$	10388.1			0.425934
$842$			17645.8i			0.722224i
$843$	23743.8	+	6985.03i	0.970082	+	0.285382i
$844$			14093.2i			0.574772i
$845$		−	86863.7i		−	3.53633i
$846$	−1716.36	−	1105.53i	−0.0697513	−	0.0449276i
$847$	12507.4			0.507392
$848$			6544.61i			0.265027i
$849$	−30119.4	−	8860.63i	−1.21754	−	0.358181i
$850$			43598.2i			1.75930i
$851$			8791.69i			0.354143i
$852$	−7217.84	−	2123.37i	−0.290234	−	0.0853820i
$853$	35718.4			1.43373			0.716866	−	0.697211i	$-0.245576\pi$
$853$	35718.4			1.43373			0.716866	+	0.697211i	$0.245576\pi$
$854$		−	14460.8i		−	0.579436i
$855$	6478.76	−	10058.5i	0.259145	−	0.402330i
$856$		−	8029.42i		−	0.320607i
$857$	27395.6			1.09197			0.545984	−	0.837796i	$-0.316156\pi$
$857$	27395.6			1.09197			0.545984	+	0.837796i	$0.316156\pi$
$858$	−8344.03	−	2454.68i	−0.332005	−	0.0976705i
$859$			32403.6i			1.28707i	0.765415	+	0.643536i	$0.222534\pi$
$859$			32403.6i			1.28707i	−0.765415	+	0.643536i	$0.777466\pi$
$860$	11193.6			0.443837
$861$	−3202.12	−	942.011i	−0.126746	−	0.0372865i
$862$	19039.6			0.752312
$863$	−21545.2			−0.849835			−0.424917	−	0.905232i	$-0.639697\pi$
$863$	−21545.2			−0.849835			−0.424917	+	0.905232i	$0.639697\pi$
$864$	3397.44	−	2934.76i	0.133777	−	0.115558i
$865$		−	33839.8i		−	1.33016i
$866$	−9236.10			−0.362420
$867$	5335.31	−	18136.0i	0.208993	−	0.710415i
$868$			1252.40i			0.0489736i
$869$	−2428.02			−0.0947813
$870$	6591.43	−	22405.8i	0.256863	−	0.873137i
$871$	−85964.6			−3.34420
$872$			15783.5i			0.612956i
$873$	−19504.4	+	30281.1i	−0.756156	+	1.17395i
$874$	−1852.27			−0.0716866
$875$			21429.7i			0.827950i
$876$	−6533.95	−	1922.18i	−0.252011	−	0.0741376i
$877$	−21365.2			−0.822635			−0.411318	−	0.911492i	$-0.634931\pi$
$877$	−21365.2			−0.822635			−0.411318	+	0.911492i	$0.634931\pi$
$878$	−13019.9			−0.500454
$879$	−7342.60	−	2160.07i	−0.281752	−	0.0828868i
$880$			3090.96i			0.118405i
$881$	39856.6			1.52418			0.762091	−	0.647470i	$-0.224173\pi$
$881$	39856.6			1.52418			0.762091	+	0.647470i	$0.224173\pi$
$882$	10858.4	+	6994.03i	0.414537	+	0.267008i
$883$	3668.31			0.139806			0.0699028	−	0.997554i	$-0.477731\pi$
$883$	3668.31			0.139806			0.0699028	+	0.997554i	$0.477731\pi$
$884$	30435.6			1.15798
$885$	4408.10	+	44507.7i	0.167431	+	1.69052i
$886$	26555.1			1.00692
$887$	−33102.6			−1.25308			−0.626538	−	0.779391i	$-0.715529\pi$
$887$	−33102.6			−1.25308			−0.626538	+	0.779391i	$0.715529\pi$
$888$	8832.38	+	2598.34i	0.333779	+	0.0981922i
$889$	−14262.4			−0.538071
$890$			41707.1i			1.57082i
$891$	3066.43	+	6751.16i	0.115296	+	0.253841i
$892$	19220.9			0.721485
$893$	882.077			0.0330544
$894$	−7847.98	+	26677.1i	−0.293597	+	0.998005i
$895$			16540.1i			0.617738i
$896$	−1304.19			−0.0486272
$897$	16282.1	+	4789.92i	0.606067	+	0.178295i
$898$			24795.7i			0.921429i
$899$	3636.03			0.134893
$900$	21403.8	+	13786.4i	0.792732	+	0.510608i
$901$	37824.8			1.39859
$902$		−	1282.50i		−	0.0473420i
$903$	−7483.52	−	2201.53i	−0.275787	−	0.0811321i
$904$	−4197.37			−0.154428
$905$		−	61680.8i		−	2.26557i
$906$	−25882.2	−	7614.12i	−0.949094	−	0.279208i
$907$	−17757.5			−0.650084			−0.325042	−	0.945700i	$-0.605378\pi$
$907$	−17757.5			−0.650084			−0.325042	+	0.945700i	$0.605378\pi$
$908$	−18473.1			−0.675166
$909$	18338.1	+	11811.8i	0.669126	+	0.430992i
$910$	31846.7			1.16012
$911$		−	32005.8i		−	1.16400i	−0.813190	−	0.581998i	$-0.802271\pi$
$911$		−	32005.8i		−	1.16400i	0.813190	−	0.581998i	$-0.197729\pi$
$912$	−547.431	+	1860.85i	−0.0198764	+	0.0675645i
$913$	1591.17			0.0576779
$914$		−	5754.96i		−	0.208268i
$915$	19765.3	−	67186.8i	0.714120	−	2.42746i
$916$			14612.3i			0.527077i
$917$	−21042.2			−0.757771
$918$	−16961.5	−	19635.6i	−0.609819	−	0.705960i
$919$		−	33130.1i		−	1.18919i	−0.804027	−	0.594593i	$-0.797313\pi$
$919$		−	33130.1i		−	1.18919i	0.804027	−	0.594593i	$-0.202687\pi$
$920$		−	6031.53i		−	0.216145i
$921$	−3043.72	+	10346.3i	−0.108897	+	0.370166i
$922$		−	10443.9i		−	0.373049i
$923$	−29785.0			−1.06217
$924$	607.922	−	2066.47i	0.0216441	−	0.0735734i
$925$			52210.3i			1.85585i
$926$		−	32127.2i		−	1.14014i
$927$	28008.4	−	43483.8i	0.992359	−	1.54066i
$928$			3786.41i			0.133939i
$929$	6394.41			0.225827			0.112914	−	0.993605i	$-0.463982\pi$
$929$	6394.41			0.225827			0.112914	+	0.993605i	$0.463982\pi$
$930$	−1711.79	+	5818.79i	−0.0603569	+	0.205167i
$931$	−5580.39			−0.196445
$932$	−5215.59			−0.183307
$933$	25524.0	+	7508.73i	0.895623	+	0.263478i
$934$	38421.2			1.34602
$935$	17864.3			0.624841
$936$	9624.18	−	14941.8i	0.336086	−	0.521782i
$937$		−	30950.9i		−	1.07910i	−0.841952	−	0.539552i	$-0.818594\pi$
$937$		−	30950.9i		−	1.07910i	0.841952	−	0.539552i	$-0.181406\pi$
$938$		−	21289.9i		−	0.741086i
$939$	−20844.7	−	6132.16i	−0.724431	−	0.213116i
$940$			2872.29i			0.0996637i
$941$	6243.39			0.216290			0.108145	−	0.994135i	$-0.465509\pi$
$941$	6243.39			0.216290			0.108145	+	0.994135i	$0.465509\pi$
$942$	19671.5	+	5787.04i	0.680396	+	0.200161i
$943$			2502.59i			0.0864216i
$944$	−2722.05	−	6720.68i	−0.0938508	−	0.231715i
$945$	−17748.0	−	20546.0i	−0.610944	−	0.707262i
$946$		−	2997.26i		−	0.103012i
$947$			43732.9i			1.50067i	0.661061	+	0.750333i	$0.270107\pi$
$947$			43732.9i			1.50067i	−0.661061	+	0.750333i	$0.729893\pi$
$948$	1400.26	−	4759.83i	0.0479731	−	0.163072i
$949$	−26962.9			−0.922289
$950$	−10999.9			−0.375667
$951$	−26992.2	−	7940.66i	−0.920380	−	0.270761i
$952$			7537.62i			0.256613i
$953$			8829.30i			0.300114i	0.988677	+	0.150057i	$0.0479458\pi$
$953$			8829.30i			0.300114i	−0.988677	+	0.150057i	$0.952054\pi$
$954$	11960.8	−	18569.4i	0.405916	−	0.630196i
$955$		−	30019.4i		−	1.01718i
$956$			27743.2i			0.938576i
$957$	−5999.50	−	1764.96i	−0.202650	−	0.0596164i
$958$		−	22306.0i		−	0.752268i
$959$			4472.80i			0.150609i
$960$	−6059.45	−	1782.59i	−0.203716	−	0.0599301i
$961$	28846.7			0.968303
$962$	36447.5			1.22153
$963$	−14674.4	+	22782.3i	−0.491043	+	0.762358i
$964$	3897.28			0.130210
$965$			31477.8i			1.05006i
$966$	−1186.26	+	4032.39i	−0.0395108	+	0.134306i
$967$			28794.6i			0.957572i	0.877932	+	0.478786i	$0.158923\pi$
$967$			28794.6i			0.957572i	−0.877932	+	0.478786i	$0.841077\pi$
$968$	−9820.35			−0.326072
$969$	10754.8	+	3163.89i	0.356548	+	0.104891i
$970$	50674.9			1.67739
$971$			55951.4i			1.84919i	0.380947	+	0.924597i	$0.375598\pi$
$971$			55951.4i			1.84919i	−0.380947	+	0.924597i	$0.624402\pi$
$972$	−15003.2	+	2117.88i	−0.495092	+	0.0698880i
$973$	−27684.2			−0.912144
$974$	14712.0			0.483986
$975$	96692.5	+	28445.4i	3.17604	+	0.934339i
$976$			11354.1i			0.372371i
$977$	5523.97			0.180888			0.0904440	−	0.995902i	$-0.471171\pi$
$977$	5523.97			0.180888			0.0904440	+	0.995902i	$0.471171\pi$
$978$	−3925.55	+	13343.9i	−0.128349	+	0.436288i
$979$	11167.7			0.364578
$980$		−	18171.4i		−	0.592309i
$981$	28845.6	−	44783.5i	0.938806	−	1.45752i
$982$		−	4800.09i		−	0.155985i
$983$	−22325.7			−0.724394			−0.362197	−	0.932101i	$-0.617973\pi$
$983$	−22325.7			−0.724394			−0.362197	+	0.932101i	$0.617973\pi$
$984$	2514.18	+	739.630i	0.0814522	+	0.0239619i
$985$	33064.4			1.06956
$986$	21883.7			0.706814
$987$	564.914	−	1920.28i	0.0182183	−	0.0619282i
$988$			7678.93i			0.247267i
$989$			5848.69i			0.188046i
$990$	5648.97	−	8770.17i	0.181349	−	0.281550i
$991$			16996.5i			0.544816i	0.962182	+	0.272408i	$0.0878201\pi$
$991$			16996.5i			0.544816i	−0.962182	+	0.272408i	$0.912180\pi$
$992$		−	983.331i		−	0.0314726i
$993$	−1622.91	+	5516.66i	−0.0518645	+	0.176300i
$994$		−	7376.50i		−	0.235381i
$995$			11679.3i			0.372118i
$996$	−917.642	+	3119.28i	−0.0291934	+	0.0992351i
$997$	−19053.3			−0.605241			−0.302621	−	0.953111i	$-0.597861\pi$
$997$	−19053.3			−0.605241			−0.302621	+	0.953111i	$0.597861\pi$
$998$	36439.0			1.15577
$999$	−20312.0	−	23514.3i	−0.643285	−	0.744703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.4.c.b.353.14	yes	30
3.2	odd	2		354.4.c.a.353.13	✓	30
59.58	odd	2		354.4.c.a.353.14	yes	30
177.176	even	2	inner	354.4.c.b.353.13	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.4.c.a.353.13	✓	30	3.2	odd	2
354.4.c.a.353.14	yes	30	59.58	odd	2
354.4.c.b.353.13	yes	30	177.176	even	2	inner
354.4.c.b.353.14	yes	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +(-1.46648 + 4.98492i) q^{3} +4.00000 q^{4} +18.9931i q^{5} +(-2.93296 + 9.96984i) q^{6} -10.1890 q^{7} +8.00000 q^{8} +(-22.6989 - 14.6206i) q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +(-1.46648 + 4.98492i) q^{3} +4.00000 q^{4} +18.9931i q^{5} +(-2.93296 + 9.96984i) q^{6} -10.1890 q^{7} +8.00000 q^{8} +(-22.6989 - 14.6206i) q^{9} +37.9861i q^{10} +10.1714 q^{11} +(-5.86593 + 19.9397i) q^{12} +82.2827i q^{13} -20.3780 q^{14} +(-94.6789 - 27.8530i) q^{15} +16.0000 q^{16} -92.4725i q^{17} +(-45.3977 - 29.2412i) q^{18} +23.3309 q^{19} +75.9722i q^{20} +(14.9420 - 50.7914i) q^{21} +20.3427 q^{22} -39.6956 q^{23} +(-11.7319 + 39.8794i) q^{24} -235.736 q^{25} +164.565i q^{26} +(106.170 - 91.7112i) q^{27} -40.7560 q^{28} +118.325i q^{29} +(-189.358 - 55.7060i) q^{30} -30.7291i q^{31} +32.0000 q^{32} +(-14.9161 + 50.7034i) q^{33} -184.945i q^{34} -193.520i q^{35} +(-90.7954 - 58.4824i) q^{36} -221.478i q^{37} +46.6619 q^{38} +(-410.173 - 120.666i) q^{39} +151.944i q^{40} -63.0445i q^{41} +(29.8840 - 101.583i) q^{42} -147.338i q^{43} +40.6854 q^{44} +(277.690 - 431.121i) q^{45} -79.3912 q^{46} +37.8072 q^{47} +(-23.4637 + 79.7587i) q^{48} -239.184 q^{49} -471.472 q^{50} +(460.968 + 135.609i) q^{51} +329.131i q^{52} +409.038i q^{53} +(212.340 - 183.422i) q^{54} +193.185i q^{55} -81.5120 q^{56} +(-34.2144 + 116.303i) q^{57} +236.651i q^{58} +(-170.128 - 420.042i) q^{59} +(-378.715 - 111.412i) q^{60} +709.628i q^{61} -61.4582i q^{62} +(231.279 + 148.969i) q^{63} +64.0000 q^{64} -1562.80 q^{65} +(-29.8322 + 101.407i) q^{66} +1044.75i q^{67} -369.890i q^{68} +(58.2129 - 197.880i) q^{69} -387.041i q^{70} +361.984i q^{71} +(-181.591 - 116.965i) q^{72} +327.686i q^{73} -442.955i q^{74} +(345.703 - 1175.13i) q^{75} +93.3238 q^{76} -103.636 q^{77} +(-820.345 - 241.332i) q^{78} -238.712 q^{79} +303.889i q^{80} +(301.476 + 663.742i) q^{81} -126.089i q^{82} +156.436 q^{83} +(59.7680 - 203.165i) q^{84} +1756.34 q^{85} -294.677i q^{86} +(-589.843 - 173.522i) q^{87} +81.3709 q^{88} +1097.96 q^{89} +(555.379 - 862.241i) q^{90} -838.379i q^{91} -158.782 q^{92} +(153.182 + 45.0637i) q^{93} +75.6143 q^{94} +443.126i q^{95} +(-46.9274 + 159.517i) q^{96} -1334.04i q^{97} -478.368 q^{98} +(-230.878 - 148.711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 60 q^{2} + 5 q^{3} + 120 q^{4} + 10 q^{6} + 6 q^{7} + 240 q^{8} + 27 q^{9}+O(q^{10}) \) 30 * q + 60 * q^2 + 5 * q^3 + 120 * q^4 + 10 * q^6 + 6 * q^7 + 240 * q^8 + 27 * q^9	\( 30 q + 60 q^{2} + 5 q^{3} + 120 q^{4} + 10 q^{6} + 6 q^{7} + 240 q^{8} + 27 q^{9} + 60 q^{11} + 20 q^{12} + 12 q^{14} + 20 q^{15} + 480 q^{16} + 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} - 24 q^{23} + 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} + 40 q^{30} + 960 q^{32} - 336 q^{33} + 108 q^{36} + 180 q^{38} - 652 q^{39} + 264 q^{42} + 240 q^{44} - 878 q^{45} - 48 q^{46} - 792 q^{47} + 80 q^{48} + 2016 q^{49} - 2160 q^{50} + 650 q^{51} - 110 q^{54} + 48 q^{56} + 846 q^{57} + 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} + 1416 q^{65} - 672 q^{66} + 590 q^{69} + 216 q^{72} - 952 q^{75} + 360 q^{76} - 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} - 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} + 300 q^{89} - 1756 q^{90} - 96 q^{92} - 1684 q^{93} - 1584 q^{94} + 160 q^{96} + 4032 q^{98} - 730 q^{99}+O(q^{100}) \) 30 * q + 60 * q^2 + 5 * q^3 + 120 * q^4 + 10 * q^6 + 6 * q^7 + 240 * q^8 + 27 * q^9 + 60 * q^11 + 20 * q^12 + 12 * q^14 + 20 * q^15 + 480 * q^16 + 54 * q^18 + 90 * q^19 + 132 * q^21 + 120 * q^22 - 24 * q^23 + 40 * q^24 - 1080 * q^25 - 55 * q^27 + 24 * q^28 + 40 * q^30 + 960 * q^32 - 336 * q^33 + 108 * q^36 + 180 * q^38 - 652 * q^39 + 264 * q^42 + 240 * q^44 - 878 * q^45 - 48 * q^46 - 792 * q^47 + 80 * q^48 + 2016 * q^49 - 2160 * q^50 + 650 * q^51 - 110 * q^54 + 48 * q^56 + 846 * q^57 + 480 * q^59 + 80 * q^60 + 887 * q^63 + 1920 * q^64 + 1416 * q^65 - 672 * q^66 + 590 * q^69 + 216 * q^72 - 952 * q^75 + 360 * q^76 - 864 * q^77 - 1304 * q^78 + 738 * q^79 - 1217 * q^81 - 876 * q^83 + 528 * q^84 + 1176 * q^85 + 534 * q^87 + 480 * q^88 + 300 * q^89 - 1756 * q^90 - 96 * q^92 - 1684 * q^93 - 1584 * q^94 + 160 * q^96 + 4032 * q^98 - 730 * q^99

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