LMFDB - Embedded newform 400.3.bg.f.33.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(17,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("400.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$, degree $8$, not 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:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			33.4
Character	$\chi$	$=$	400.33
Dual form			400.3.bg.f.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.535050 - 0.0847436i) q^{3} +(2.05203 - 4.55951i) q^{5} +(-4.47022 + 4.47022i) q^{7} +(-8.28041 - 2.69047i) q^{9} +O(q^{10})$	\(q+(-0.535050 - 0.0847436i) q^{3} +(2.05203 - 4.55951i) q^{5} +(-4.47022 + 4.47022i) q^{7} +(-8.28041 - 2.69047i) q^{9} +(1.20728 + 3.71563i) q^{11} +(-8.27903 + 4.21838i) q^{13} +(-1.48433 + 2.26567i) q^{15} +(11.2207 - 1.77718i) q^{17} +(-20.6896 + 28.4767i) q^{19} +(2.77061 - 2.01297i) q^{21} +(-4.19198 + 8.22722i) q^{23} +(-16.5783 - 18.7125i) q^{25} +(8.54651 + 4.35467i) q^{27} +(23.1727 + 31.8945i) q^{29} +(-16.1948 - 11.7662i) q^{31} +(-0.331080 - 2.09036i) q^{33} +(11.2090 + 29.5550i) q^{35} +(-10.4140 - 20.4385i) q^{37} +(4.78718 - 1.55545i) q^{39} +(-16.0730 + 49.4677i) q^{41} +(-17.2999 - 17.2999i) q^{43} +(-29.2589 + 32.2337i) q^{45} +(-2.99450 + 18.9065i) q^{47} +9.03431i q^{49} -6.15422 q^{51} +(-75.9092 - 12.0228i) q^{53} +(19.4189 + 2.11998i) q^{55} +(13.4832 - 13.4832i) q^{57} +(-101.199 - 32.8817i) q^{59} +(10.5593 + 32.4981i) q^{61} +(49.0422 - 24.9883i) q^{63} +(2.24491 + 46.4046i) q^{65} +(-58.9216 + 9.33226i) q^{67} +(2.94012 - 4.04673i) q^{69} +(88.8498 - 64.5532i) q^{71} +(-27.0876 + 53.1624i) q^{73} +(7.28447 + 11.4170i) q^{75} +(-22.0065 - 11.2129i) q^{77} +(14.1699 + 19.5033i) q^{79} +(59.1899 + 43.0040i) q^{81} +(-17.1948 - 108.564i) q^{83} +(14.9221 - 54.8076i) q^{85} +(-9.69572 - 19.0289i) q^{87} +(-3.07504 + 0.999140i) q^{89} +(18.1520 - 55.8661i) q^{91} +(7.66789 + 7.66789i) q^{93} +(87.3844 + 152.769i) q^{95} +(24.7036 - 155.972i) q^{97} -34.0151i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{20}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.535050	−	0.0847436i	−0.178350	−	0.0282479i	0.0666206	−	0.997778i	$-0.478778\pi$
$3$	−0.535050	−	0.0847436i	−0.178350	−	0.0282479i	−0.244971	+	0.969531i	$0.578778\pi$
$4$		0			0
$5$	2.05203	−	4.55951i	0.410406	−	0.911903i
$5$	2.05203	−	4.55951i	0.410406	−	0.911903i
$6$		0			0
$7$	−4.47022	+	4.47022i	−0.638602	+	0.638602i	−0.950211	−	0.311608i	$-0.899132\pi$
$7$	−4.47022	+	4.47022i	−0.638602	+	0.638602i	0.311608	+	0.950211i	$0.399132\pi$
$8$		0			0
$9$	−8.28041	−	2.69047i	−0.920046	−	0.298941i
$10$		0			0
$11$	1.20728	+	3.71563i	0.109753	+	0.337785i	0.990817	−	0.135213i	$-0.0431719\pi$
$11$	1.20728	+	3.71563i	0.109753	+	0.337785i	−0.881064	+	0.472998i	$0.843172\pi$
$12$		0			0
$13$	−8.27903	+	4.21838i	−0.636848	+	0.324491i	−0.742433	−	0.669920i	$-0.766328\pi$
$13$	−8.27903	+	4.21838i	−0.636848	+	0.324491i	0.105585	+	0.994410i	$0.466328\pi$
$14$		0			0
$15$	−1.48433	+	2.26567i	−0.0989553	+	0.151045i
$16$		0			0
$17$	11.2207	−	1.77718i	0.660040	−	0.104540i	0.182576	−	0.983192i	$-0.441556\pi$
$17$	11.2207	−	1.77718i	0.660040	−	0.104540i	0.477463	+	0.878652i	$0.341556\pi$
$18$		0			0
$19$	−20.6896	+	28.4767i	−1.08892	+	1.49878i	−0.239623	+	0.970866i	$0.577024\pi$
$19$	−20.6896	+	28.4767i	−1.08892	+	1.49878i	−0.849301	+	0.527909i	$0.822976\pi$
$20$		0			0
$21$	2.77061	−	2.01297i	0.131934	−	0.0958556i
$22$		0			0
$23$	−4.19198	+	8.22722i	−0.182260	+	0.357705i	−0.964001	−	0.265897i	$-0.914332\pi$
$23$	−4.19198	+	8.22722i	−0.182260	+	0.357705i	0.781741	+	0.623603i	$0.214332\pi$
$24$		0			0
$25$	−16.5783	−	18.7125i	−0.663133	−	0.748501i
$26$		0			0
$27$	8.54651	+	4.35467i	0.316538	+	0.161284i
$28$		0			0
$29$	23.1727	+	31.8945i	0.799060	+	1.09981i	0.992920	+	0.118783i	$0.0378992\pi$
$29$	23.1727	+	31.8945i	0.799060	+	1.09981i	−0.193860	+	0.981029i	$0.562101\pi$
$30$		0			0
$31$	−16.1948	−	11.7662i	−0.522411	−	0.379554i	0.295100	−	0.955466i	$-0.404647\pi$
$31$	−16.1948	−	11.7662i	−0.522411	−	0.379554i	−0.817512	+	0.575912i	$0.804647\pi$
$32$		0			0
$33$	−0.331080	−	2.09036i	−0.0100327	−	0.0633442i
$34$		0			0
$35$	11.2090	+	29.5550i	0.320257	+	0.844430i
$36$		0			0
$37$	−10.4140	−	20.4385i	−0.281458	−	0.552393i	0.706388	−	0.707824i	$-0.250323\pi$
$37$	−10.4140	−	20.4385i	−0.281458	−	0.552393i	−0.987847	+	0.155432i	$0.950323\pi$
$38$		0			0
$39$	4.78718	−	1.55545i	0.122748	−	0.0398833i
$40$		0			0
$41$	−16.0730	+	49.4677i	−0.392026	+	1.20653i	0.539228	+	0.842160i	$0.318716\pi$
$41$	−16.0730	+	49.4677i	−0.392026	+	1.20653i	−0.931254	+	0.364371i	$0.881284\pi$
$42$		0			0
$43$	−17.2999	−	17.2999i	−0.402323	−	0.402323i	0.476728	−	0.879051i	$-0.341823\pi$
$43$	−17.2999	−	17.2999i	−0.402323	−	0.402323i	−0.879051	+	0.476728i	$0.841823\pi$
$44$		0			0
$45$	−29.2589	+	32.2337i	−0.650198	+	0.716305i
$46$		0			0
$47$	−2.99450	+	18.9065i	−0.0637127	+	0.402266i	0.935136	+	0.354290i	$0.115277\pi$
$47$	−2.99450	+	18.9065i	−0.0637127	+	0.402266i	−0.998848	+	0.0479767i	$0.984723\pi$
$48$		0			0
$49$			9.03431i			0.184374i
$50$		0			0
$51$	−6.15422			−0.120671
$52$		0			0
$53$	−75.9092	−	12.0228i	−1.43225	−	0.226846i	−0.608389	−	0.793639i	$-0.708184\pi$
$53$	−75.9092	−	12.0228i	−1.43225	−	0.226846i	−0.823860	+	0.566793i	$0.808184\pi$
$54$		0			0
$55$	19.4189	+	2.11998i	0.353070	+	0.0385450i
$56$		0			0
$57$	13.4832	−	13.4832i	0.236547	−	0.236547i
$58$		0			0
$59$	−101.199	−	32.8817i	−1.71524	−	0.557317i	−0.724051	−	0.689746i	$-0.757722\pi$
$59$	−101.199	−	32.8817i	−1.71524	−	0.557317i	−0.991192	+	0.132430i	$0.957722\pi$
$60$		0			0
$61$	10.5593	+	32.4981i	0.173103	+	0.532755i	0.999542	−	0.0302710i	$-0.00963702\pi$
$61$	10.5593	+	32.4981i	0.173103	+	0.532755i	−0.826439	+	0.563026i	$0.809637\pi$
$62$		0			0
$63$	49.0422	−	24.9883i	0.778448	−	0.396639i
$64$		0			0
$65$	2.24491	+	46.4046i	0.0345371	+	0.713917i
$66$		0			0
$67$	−58.9216	+	9.33226i	−0.879426	+	0.139287i	−0.579790	−	0.814766i	$-0.696865\pi$
$67$	−58.9216	+	9.33226i	−0.879426	+	0.139287i	−0.299636	+	0.954053i	$0.596865\pi$
$68$		0			0
$69$	2.94012	−	4.04673i	0.0426105	−	0.0586483i
$70$		0			0
$71$	88.8498	−	64.5532i	1.25141	−	0.909200i	0.253104	−	0.967439i	$-0.418549\pi$
$71$	88.8498	−	64.5532i	1.25141	−	0.909200i	0.998303	+	0.0582393i	$0.0185487\pi$
$72$		0			0
$73$	−27.0876	+	53.1624i	−0.371063	+	0.728252i	−0.998738	−	0.0502232i	$-0.984007\pi$
$73$	−27.0876	+	53.1624i	−0.371063	+	0.728252i	0.627675	+	0.778476i	$0.284007\pi$
$74$		0			0
$75$	7.28447	+	11.4170i	0.0971262	+	0.152227i
$76$		0			0
$77$	−22.0065	−	11.2129i	−0.285799	−	0.145622i
$78$		0			0
$79$	14.1699	+	19.5033i	0.179366	+	0.246877i	0.889228	−	0.457465i	$-0.151242\pi$
$79$	14.1699	+	19.5033i	0.179366	+	0.246877i	−0.709861	+	0.704341i	$0.751242\pi$
$80$		0			0
$81$	59.1899	+	43.0040i	0.730739	+	0.530913i
$82$		0			0
$83$	−17.1948	−	108.564i	−0.207167	−	1.30800i	−0.843728	−	0.536772i	$-0.819644\pi$
$83$	−17.1948	−	108.564i	−0.207167	−	1.30800i	0.636561	−	0.771226i	$-0.280356\pi$
$84$		0			0
$85$	14.9221	−	54.8076i	0.175554	−	0.644796i
$86$		0			0
$87$	−9.69572	−	19.0289i	−0.111445	−	0.218723i
$88$		0			0
$89$	−3.07504	+	0.999140i	−0.0345510	+	0.0112263i	−0.326241	−	0.945286i	$-0.605782\pi$
$89$	−3.07504	+	0.999140i	−0.0345510	+	0.0112263i	0.291691	+	0.956513i	$0.405782\pi$
$90$		0			0
$91$	18.1520	−	55.8661i	0.199473	−	0.613913i
$92$		0			0
$93$	7.66789	+	7.66789i	0.0824505	+	0.0824505i
$94$		0			0
$95$	87.3844	+	152.769i	0.919836	+	1.60810i
$96$		0			0
$97$	24.7036	−	155.972i	0.254676	−	1.60796i	−0.446371	−	0.894848i	$-0.647284\pi$
$97$	24.7036	−	155.972i	0.254676	−	1.60796i	0.701047	−	0.713115i	$-0.252716\pi$
$98$		0			0
$99$		−	34.0151i		−	0.343587i
$100$		0			0
$101$	114.519			1.13385			0.566926	−	0.823769i	$-0.308132\pi$
$101$	114.519			1.13385			0.566926	+	0.823769i	$0.308132\pi$
$102$		0			0
$103$	108.622	+	17.2040i	1.05458	+	0.167030i	0.659568	−	0.751645i	$-0.270739\pi$
$103$	108.622	+	17.2040i	1.05458	+	0.167030i	0.395015	+	0.918674i	$0.370739\pi$
$104$		0			0
$105$	−3.49277	−	16.7633i	−0.0332645	−	0.159651i
$106$		0			0
$107$	26.5080	−	26.5080i	0.247738	−	0.247738i	−0.572304	−	0.820042i	$-0.693950\pi$
$107$	26.5080	−	26.5080i	0.247738	−	0.247738i	0.820042	+	0.572304i	$0.193950\pi$
$108$		0			0
$109$	54.8106	+	17.8091i	0.502850	+	0.163386i	0.549448	−	0.835528i	$-0.314838\pi$
$109$	54.8106	+	17.8091i	0.502850	+	0.163386i	−0.0465982	+	0.998914i	$0.514838\pi$
$110$		0			0
$111$	3.83995	+	11.8182i	0.0345942	+	0.106470i
$112$		0			0
$113$	−44.0704	+	22.4550i	−0.390003	+	0.198717i	−0.637986	−	0.770048i	$-0.720232\pi$
$113$	−44.0704	+	22.4550i	−0.390003	+	0.198717i	0.247983	+	0.968764i	$0.420232\pi$
$114$		0			0
$115$	28.9101	+	35.9959i	0.251392	+	0.313008i
$116$		0			0
$117$	79.9032	−	12.6554i	0.682933	−	0.108166i
$118$		0			0
$119$	−42.2145	+	58.1032i	−0.354743	+	0.488262i
$120$		0			0
$121$	85.5427	−	62.1504i	0.706964	−	0.513640i
$122$		0			0
$123$	12.7920	−	25.1056i	0.104000	−	0.204111i
$124$		0			0
$125$	−119.339	+	37.1904i	−0.954715	+	0.297523i
$126$		0			0
$127$	−44.6680	−	22.7595i	−0.351717	−	0.179209i	0.269202	−	0.963084i	$-0.413240\pi$
$127$	−44.6680	−	22.7595i	−0.351717	−	0.179209i	−0.620918	+	0.783875i	$0.713240\pi$
$128$		0			0
$129$	7.79024	+	10.7223i	0.0603895	+	0.0831190i
$130$		0			0
$131$	−15.2962	−	11.1134i	−0.116765	−	0.0848348i	0.527870	−	0.849325i	$-0.322991\pi$
$131$	−15.2962	−	11.1134i	−0.116765	−	0.0848348i	−0.644635	+	0.764490i	$0.722991\pi$
$132$		0			0
$133$	−34.8104	−	219.784i	−0.261732	−	1.65251i
$134$		0			0
$135$	37.3929	−	30.0320i	0.276984	−	0.222460i
$136$		0			0
$137$	−73.0810	−	143.430i	−0.533438	−	1.04693i	−0.987744	−	0.156085i	$-0.950113\pi$
$137$	−73.0810	−	143.430i	−0.533438	−	1.04693i	0.454306	−	0.890846i	$-0.349887\pi$
$138$		0			0
$139$	−210.438	+	68.3754i	−1.51394	+	0.491909i	−0.944048	−	0.329809i	$-0.893016\pi$
$139$	−210.438	+	68.3754i	−1.51394	+	0.491909i	−0.569894	+	0.821719i	$0.693016\pi$
$140$		0			0
$141$	3.20441	−	9.86217i	0.0227263	−	0.0699445i
$142$		0			0
$143$	−25.6691	−	25.6691i	−0.179504	−	0.179504i
$144$		0			0
$145$	192.975	−	40.2078i	1.33086	−	0.277295i
$146$		0			0
$147$	0.765600	−	4.83381i	0.00520816	−	0.0328831i
$148$		0			0
$149$			32.1217i			0.215582i	0.994174	+	0.107791i	$0.0343777\pi$
$149$			32.1217i			0.215582i	−0.994174	+	0.107791i	$0.965622\pi$
$150$		0			0
$151$	6.98536			0.0462607			0.0231303	−	0.999732i	$-0.492637\pi$
$151$	6.98536			0.0462607			0.0231303	+	0.999732i	$0.492637\pi$
$152$		0			0
$153$	−97.6932	−	15.4731i	−0.638518	−	0.101131i
$154$		0			0
$155$	−86.8802	+	49.6956i	−0.560517	+	0.320617i
$156$		0			0
$157$	182.197	−	182.197i	1.16049	−	1.16049i	0.176120	−	0.984369i	$-0.443645\pi$
$157$	182.197	−	182.197i	1.16049	−	1.16049i	0.984369	−	0.176120i	$-0.0563546\pi$
$158$		0			0
$159$	39.5964	+	12.8656i	0.249034	+	0.0809160i
$160$		0			0
$161$	−18.0384	−	55.5165i	−0.112040	−	0.344823i
$162$		0			0
$163$	−201.043	+	102.437i	−1.23340	+	0.628446i	−0.944373	−	0.328876i	$-0.893330\pi$
$163$	−201.043	+	102.437i	−1.23340	+	0.628446i	−0.289022	+	0.957322i	$0.593330\pi$
$164$		0			0
$165$	−10.2104	−	2.77992i	−0.0618812	−	0.0168480i
$166$		0			0
$167$	265.889	−	42.1126i	1.59215	−	0.252171i	0.703477	−	0.710718i	$-0.251630\pi$
$167$	265.889	−	42.1126i	1.59215	−	0.252171i	0.888670	+	0.458546i	$0.151630\pi$
$168$		0			0
$169$	−48.5881	+	66.8757i	−0.287503	+	0.395714i
$170$		0			0
$171$	247.934	−	180.134i	1.44990	−	1.05342i
$172$		0			0
$173$	−45.2751	+	88.8573i	−0.261706	+	0.513626i	−0.984047	−	0.177911i	$-0.943066\pi$
$173$	−45.2751	+	88.8573i	−0.261706	+	0.513626i	0.722341	+	0.691537i	$0.243066\pi$
$174$		0			0
$175$	157.758	+	9.54035i	0.901473	+	0.0545163i
$176$		0			0
$177$	51.3602	+	26.1693i	0.290171	+	0.147849i
$178$		0			0
$179$	−47.7452	−	65.7156i	−0.266733	−	0.367126i	0.654551	−	0.756018i	$-0.272858\pi$
$179$	−47.7452	−	65.7156i	−0.266733	−	0.367126i	−0.921283	+	0.388892i	$0.872858\pi$
$180$		0			0
$181$	84.0670	+	61.0782i	0.464458	+	0.337449i	0.795278	−	0.606245i	$-0.207325\pi$
$181$	84.0670	+	61.0782i	0.464458	+	0.337449i	−0.330819	+	0.943694i	$0.607325\pi$
$182$		0			0
$183$	−2.89573	−	18.2829i	−0.0158237	−	0.0999067i
$184$		0			0
$185$	−114.560	+	5.54204i	−0.619241	+	0.0299570i
$186$		0			0
$187$	20.1499	+	39.5463i	0.107753	+	0.211478i
$188$		0			0
$189$	−57.6711	+	18.7385i	−0.305138	+	0.0991453i
$190$		0			0
$191$	8.81351	−	27.1252i	0.0461440	−	0.142017i	−0.925330	−	0.379163i	$-0.876212\pi$
$191$	8.81351	−	27.1252i	0.0461440	−	0.142017i	0.971474	+	0.237146i	$0.0762120\pi$
$192$		0			0
$193$	11.4314	+	11.4314i	0.0592299	+	0.0592299i	0.736101	−	0.676871i	$-0.236665\pi$
$193$	11.4314	+	11.4314i	0.0592299	+	0.0592299i	−0.676871	+	0.736101i	$0.736665\pi$
$194$		0			0
$195$	2.73135	−	25.0190i	0.0140069	−	0.128303i
$196$		0			0
$197$	−32.8279	+	207.267i	−0.166639	+	1.05212i	0.752617	+	0.658459i	$0.228791\pi$
$197$	−32.8279	+	207.267i	−0.166639	+	1.05212i	−0.919256	+	0.393660i	$0.871209\pi$
$198$		0			0
$199$			164.539i			0.826829i	0.910543	+	0.413414i	$0.135664\pi$
$199$			164.539i			0.826829i	−0.910543	+	0.413414i	$0.864336\pi$
$200$		0			0
$201$	32.3168			0.160780
$202$		0			0
$203$	−246.163	−	38.9883i	−1.21262	−	0.192061i
$204$		0			0
$205$	192.566	+	174.795i	0.939349	+	0.852657i
$206$		0			0
$207$	56.8464	−	56.8464i	0.274620	−	0.274620i
$208$		0			0
$209$	−130.787	−	42.4953i	−0.625776	−	0.203327i
$210$		0			0
$211$	99.8963	+	307.449i	0.473442	+	1.45710i	0.848047	+	0.529920i	$0.177778\pi$
$211$	99.8963	+	307.449i	0.473442	+	1.45710i	−0.374605	+	0.927184i	$0.622222\pi$
$212$		0			0
$213$	−53.0096	+	27.0097i	−0.248871	+	0.126806i
$214$		0			0
$215$	−114.379	+	43.3791i	−0.531995	+	0.201763i
$216$		0			0
$217$	124.991	−	19.7967i	0.575997	−	0.0912290i
$218$		0			0
$219$	18.9984	−	26.1491i	0.0867507	−	0.119402i
$220$		0			0
$221$	−85.3995	+	62.0463i	−0.386423	+	0.280753i
$222$		0			0
$223$	160.585	−	315.167i	0.720114	−	1.41330i	−0.182655	−	0.983177i	$-0.558469\pi$
$223$	160.585	−	315.167i	0.720114	−	1.41330i	0.902769	−	0.430126i	$-0.141531\pi$
$224$		0			0
$225$	86.9299	+	199.551i	0.386355	+	0.886893i
$226$		0			0
$227$	−195.419	−	99.5712i	−0.860879	−	0.438640i	−0.0329393	−	0.999457i	$-0.510487\pi$
$227$	−195.419	−	99.5712i	−0.860879	−	0.438640i	−0.827939	+	0.560818i	$0.810487\pi$
$228$		0			0
$229$	−50.5254	−	69.5422i	−0.220635	−	0.303678i	0.684323	−	0.729179i	$-0.260098\pi$
$229$	−50.5254	−	69.5422i	−0.220635	−	0.303678i	−0.904958	+	0.425501i	$0.860098\pi$
$230$		0			0
$231$	10.8244	+	7.86436i	0.0468587	+	0.0340448i
$232$		0			0
$233$	−28.3610	−	179.064i	−0.121721	−	0.768515i	−0.970736	−	0.240147i	$-0.922804\pi$
$233$	−28.3610	−	179.064i	−0.121721	−	0.768515i	0.849016	−	0.528368i	$-0.177196\pi$
$234$		0			0
$235$	80.0597	+	52.4502i	0.340680	+	0.223193i
$236$		0			0
$237$	−5.92885	−	11.6360i	−0.0250163	−	0.0490972i
$238$		0			0
$239$	25.4329	−	8.26364i	0.106414	−	0.0345759i	−0.255326	−	0.966855i	$-0.582183\pi$
$239$	25.4329	−	8.26364i	0.106414	−	0.0345759i	0.361740	+	0.932279i	$0.382183\pi$
$240$		0			0
$241$	−44.3238	+	136.415i	−0.183916	+	0.566036i	−0.999928	−	0.0119991i	$-0.996180\pi$
$241$	−44.3238	+	136.415i	−0.183916	+	0.566036i	0.816012	+	0.578035i	$0.196180\pi$
$242$		0			0
$243$	−89.0682	−	89.0682i	−0.366536	−	0.366536i
$244$		0			0
$245$	41.1921	+	18.5387i	0.168131	+	0.0756682i
$246$		0			0
$247$	51.1639	−	323.036i	0.207141	−	1.30784i
$248$		0			0
$249$			59.5442i			0.239133i
$250$		0			0
$251$	−299.489			−1.19318			−0.596591	−	0.802546i	$-0.703478\pi$
$251$	−299.489			−1.19318			−0.596591	+	0.802546i	$0.703478\pi$
$252$		0			0
$253$	−35.6302	−	5.64328i	−0.140831	−	0.0223054i
$254$		0			0
$255$	−12.6287	+	28.0603i	−0.0495242	+	0.110040i
$256$		0			0
$257$	−255.355	+	255.355i	−0.993599	+	0.993599i	−0.999980	−	0.00638078i	$-0.997969\pi$
$257$	−255.355	+	255.355i	−0.993599	+	0.993599i	0.00638078	+	0.999980i	$0.497969\pi$
$258$		0			0
$259$	137.917	+	44.8121i	0.532499	+	0.173020i
$260$		0			0
$261$	−106.069	−	326.445i	−0.406393	−	1.25075i
$262$		0			0
$263$	−235.389	+	119.937i	−0.895017	+	0.456034i	−0.840084	−	0.542456i	$-0.817494\pi$
$263$	−235.389	+	119.937i	−0.895017	+	0.456034i	−0.0549329	+	0.998490i	$0.517494\pi$
$264$		0			0
$265$	−210.586	+	321.438i	−0.794666	+	1.21297i
$266$		0			0
$267$	1.72997	−	0.274000i	0.00647928	−	0.00102622i
$268$		0			0
$269$	−291.307	+	400.950i	−1.08293	+	1.49052i	−0.226666	+	0.973972i	$0.572783\pi$
$269$	−291.307	+	400.950i	−1.08293	+	1.49052i	−0.856259	+	0.516547i	$0.827217\pi$
$270$		0			0
$271$	−15.9470	+	11.5862i	−0.0588450	+	0.0427534i	−0.616819	−	0.787105i	$-0.711579\pi$
$271$	−15.9470	+	11.5862i	−0.0588450	+	0.0427534i	0.557974	+	0.829858i	$0.311579\pi$
$272$		0			0
$273$	−14.4465	+	28.3529i	−0.0529177	+	0.103857i
$274$		0			0
$275$	49.5142	−	84.1903i	0.180052	−	0.306147i
$276$		0			0
$277$	−358.051	−	182.436i	−1.29260	−	0.658615i	−0.333790	−	0.942647i	$-0.608328\pi$
$277$	−358.051	−	182.436i	−1.29260	−	0.658615i	−0.958815	+	0.284033i	$0.908328\pi$
$278$		0			0
$279$	102.443	+	141.000i	0.367178	+	0.505377i
$280$		0			0
$281$	124.614	+	90.5371i	0.443465	+	0.322196i	0.787010	−	0.616940i	$-0.211628\pi$
$281$	124.614	+	90.5371i	0.443465	+	0.322196i	−0.343545	+	0.939136i	$0.611628\pi$
$282$		0			0
$283$	47.7692	+	301.603i	0.168796	+	1.06574i	0.916011	+	0.401153i	$0.131390\pi$
$283$	47.7692	+	301.603i	0.168796	+	1.06574i	−0.747215	+	0.664582i	$0.768610\pi$
$284$		0			0
$285$	−33.8088	−	89.1446i	−0.118627	−	0.312788i
$286$		0			0
$287$	−149.282	−	292.982i	−0.520145	−	1.02084i
$288$		0			0
$289$	−152.110	+	49.4236i	−0.526333	+	0.171016i
$290$		0			0
$291$	−26.4353	+	81.3596i	−0.0908430	+	0.279586i
$292$		0			0
$293$	−21.3000	−	21.3000i	−0.0726964	−	0.0726964i	0.669824	−	0.742520i	$-0.266370\pi$
$293$	−21.3000	−	21.3000i	−0.0726964	−	0.0726964i	−0.742520	+	0.669824i	$0.766370\pi$
$294$		0			0
$295$	−357.589	+	393.946i	−1.21217	+	1.33541i
$296$		0			0
$297$	−5.86229	+	37.0130i	−0.0197383	+	0.124623i
$298$		0			0
$299$		−	85.7968i		−	0.286946i
$300$		0			0
$301$	154.668			0.513848
$302$		0			0
$303$	−61.2734	−	9.70476i	−0.202223	−	0.0320289i
$304$		0			0
$305$	169.843	+	18.5420i	0.556863	+	0.0607933i
$306$		0			0
$307$	167.701	−	167.701i	0.546256	−	0.546256i	−0.379100	−	0.925356i	$-0.623766\pi$
$307$	167.701	−	167.701i	0.546256	−	0.546256i	0.925356	+	0.379100i	$0.123766\pi$
$308$		0			0
$309$	−56.6603	−	18.4101i	−0.183367	−	0.0595795i
$310$		0			0
$311$	106.128	+	326.629i	0.341249	+	1.05025i	0.963562	+	0.267487i	$0.0861931\pi$
$311$	106.128	+	326.629i	0.341249	+	1.05025i	−0.622313	+	0.782768i	$0.713807\pi$
$312$		0			0
$313$	520.031	−	264.969i	1.66144	−	0.846546i	0.666564	−	0.745448i	$-0.267764\pi$
$313$	520.031	−	264.969i	1.66144	−	0.846546i	0.994876	−	0.101098i	$-0.0322357\pi$
$314$		0			0
$315$	−13.2981	−	274.885i	−0.0422162	−	0.872652i
$316$		0			0
$317$	116.010	−	18.3742i	0.365963	−	0.0579628i	0.0292550	−	0.999572i	$-0.490687\pi$
$317$	116.010	−	18.3742i	0.365963	−	0.0579628i	0.336708	+	0.941609i	$0.390687\pi$
$318$		0			0
$319$	−90.5324	+	124.607i	−0.283801	+	0.390618i
$320$		0			0
$321$	−16.4295	+	11.9367i	−0.0511821	+	0.0371860i
$322$		0			0
$323$	−181.542	+	356.297i	−0.562051	+	1.10309i
$324$		0			0
$325$	216.189	+	84.9880i	0.665197	+	0.261502i
$326$		0			0
$327$	−27.8172	−	14.1736i	−0.0850680	−	0.0433443i
$328$		0			0
$329$	−71.1302	−	97.9023i	−0.216201	−	0.297575i
$330$		0			0
$331$	377.587	+	274.333i	1.14075	+	0.828800i	0.987223	−	0.159345i	$-0.0509383\pi$
$331$	377.587	+	274.333i	1.14075	+	0.828800i	0.153522	+	0.988145i	$0.450938\pi$
$332$		0			0
$333$	31.2426	+	197.258i	0.0938216	+	0.592366i
$334$		0			0
$335$	−78.3584	+	287.804i	−0.233906	+	0.859116i
$336$		0			0
$337$	162.607	+	319.134i	0.482513	+	0.946984i	0.996040	+	0.0889108i	$0.0283386\pi$
$337$	162.607	+	319.134i	0.482513	+	0.946984i	−0.513527	+	0.858073i	$0.671661\pi$
$338$		0			0
$339$	25.4828	−	8.27985i	0.0751704	−	0.0244243i
$340$		0			0
$341$	24.1672	−	74.3789i	0.0708714	−	0.218120i
$342$		0			0
$343$	−259.426	−	259.426i	−0.756344	−	0.756344i
$344$		0			0
$345$	−12.4179	−	21.7096i	−0.0359939	−	0.0629262i
$346$		0			0
$347$	−86.5803	+	546.646i	−0.249511	+	1.57535i	0.471144	+	0.882056i	$0.343841\pi$
$347$	−86.5803	+	546.646i	−0.249511	+	1.57535i	−0.720655	+	0.693294i	$0.756159\pi$
$348$		0			0
$349$		−	373.660i		−	1.07066i	−0.844643	−	0.535330i	$-0.820187\pi$
$349$		−	373.660i		−	1.07066i	0.844643	−	0.535330i	$-0.179813\pi$
$350$		0			0
$351$	−89.1265			−0.253922
$352$		0			0
$353$	−253.460	−	40.1442i	−0.718018	−	0.113723i	−0.213275	−	0.976992i	$-0.568413\pi$
$353$	−253.460	−	40.1442i	−0.718018	−	0.113723i	−0.504743	+	0.863269i	$0.668413\pi$
$354$		0			0
$355$	−112.008	−	537.577i	−0.315517	−	1.51430i
$356$		0			0
$357$	27.5107	−	27.5107i	0.0770608	−	0.0770608i
$358$		0			0
$359$	106.124	+	34.4817i	0.295610	+	0.0960494i	0.453067	−	0.891476i	$-0.350330\pi$
$359$	106.124	+	34.4817i	0.295610	+	0.0960494i	−0.157458	+	0.987526i	$0.550330\pi$
$360$		0			0
$361$	−271.311	−	835.010i	−0.751555	−	2.31305i
$362$		0			0
$363$	−51.0364	+	26.0044i	−0.140596	+	0.0716374i
$364$		0			0
$365$	186.810	+	232.597i	0.511809	+	0.637253i
$366$		0			0
$367$	122.755	−	19.4425i	0.334482	−	0.0529768i	0.0130656	−	0.999915i	$-0.495841\pi$
$367$	122.755	−	19.4425i	0.334482	−	0.0529768i	0.321417	+	0.946938i	$0.395841\pi$
$368$		0			0
$369$	266.183	−	366.369i	0.721363	−	0.992871i
$370$		0			0
$371$	393.075	−	285.586i	1.05950	−	0.769773i
$372$		0			0
$373$	−14.9317	+	29.3052i	−0.0400315	+	0.0785661i	−0.910156	−	0.414266i	$-0.864038\pi$
$373$	−14.9317	+	29.3052i	−0.0400315	+	0.0785661i	0.870124	+	0.492832i	$0.164038\pi$
$374$		0			0
$375$	67.0041	−	9.78549i	0.178678	−	0.0260946i
$376$		0			0
$377$	−326.391	−	166.305i	−0.865759	−	0.441126i
$378$		0			0
$379$	−110.421	−	151.982i	−0.291349	−	0.401008i	0.638103	−	0.769951i	$-0.279720\pi$
$379$	−110.421	−	151.982i	−0.291349	−	0.401008i	−0.929452	+	0.368944i	$0.879720\pi$
$380$		0			0
$381$	21.9709	+	15.9628i	0.0576664	+	0.0418971i
$382$		0			0
$383$	98.4544	+	621.616i	0.257061	+	1.62302i	0.691541	+	0.722338i	$0.256932\pi$
$383$	98.4544	+	621.616i	0.257061	+	1.62302i	−0.434480	+	0.900682i	$0.643068\pi$
$384$		0			0
$385$	−96.2833	+	77.3298i	−0.250086	+	0.200857i
$386$		0			0
$387$	96.7053	+	189.795i	0.249884	+	0.490426i
$388$		0			0
$389$	−362.815	+	117.886i	−0.932686	+	0.303048i	−0.735660	−	0.677351i	$-0.763128\pi$
$389$	−362.815	+	117.886i	−0.932686	+	0.303048i	−0.197025	+	0.980398i	$0.563128\pi$
$390$		0			0
$391$	−32.4156	+	99.7649i	−0.0829043	+	0.255153i
$392$		0			0
$393$	7.24246	+	7.24246i	0.0184286	+	0.0184286i
$394$		0			0
$395$	118.003	−	24.5868i	0.298741	−	0.0622449i
$396$		0			0
$397$	−50.3324	+	317.786i	−0.126782	+	0.800469i	0.839571	+	0.543250i	$0.182806\pi$
$397$	−50.3324	+	317.786i	−0.126782	+	0.800469i	−0.966353	+	0.257219i	$0.917194\pi$
$398$		0			0
$399$			120.545i			0.302119i
$400$		0			0
$401$	531.357			1.32508			0.662539	−	0.749027i	$-0.269479\pi$
$401$	531.357			1.32508			0.662539	+	0.749027i	$0.269479\pi$
$402$		0			0
$403$	183.711	+	29.0970i	0.455859	+	0.0722009i
$404$		0			0
$405$	317.537	−	181.632i	0.784041	−	0.448473i
$406$		0			0
$407$	63.3695	−	63.3695i	0.155699	−	0.155699i
$408$		0			0
$409$	−85.0625	−	27.6385i	−0.207977	−	0.0675757i	0.203176	−	0.979142i	$-0.434874\pi$
$409$	−85.0625	−	27.6385i	−0.207977	−	0.0675757i	−0.411153	+	0.911567i	$0.634874\pi$
$410$		0			0
$411$	26.9472	+	82.9351i	0.0655651	+	0.201789i
$412$		0			0
$413$	599.371	−	305.395i	1.45126	−	0.739455i
$414$		0			0
$415$	−530.283	−	144.376i	−1.27779	−	0.347895i
$416$		0			0
$417$	118.389	−	18.7510i	0.283907	−	0.0449664i
$418$		0			0
$419$	120.959	−	166.486i	0.288685	−	0.397341i	−0.639901	−	0.768457i	$-0.721025\pi$
$419$	120.959	−	166.486i	0.288685	−	0.397341i	0.928587	+	0.371116i	$0.121025\pi$
$420$		0			0
$421$	−383.527	+	278.649i	−0.910991	+	0.661873i	−0.941265	−	0.337668i	$-0.890362\pi$
$421$	−383.527	+	278.649i	−0.910991	+	0.661873i	0.0302746	+	0.999542i	$0.490362\pi$
$422$		0			0
$423$	75.6631	−	148.497i	0.178873	−	0.351057i
$424$		0			0
$425$	−219.276	−	180.505i	−0.515942	−	0.424717i
$426$		0			0
$427$	−192.476	−	98.0712i	−0.450763	−	0.229675i
$428$		0			0
$429$	11.5589	+	15.9095i	0.0269439	+	0.0370851i
$430$		0			0
$431$	−506.113	−	367.713i	−1.17428	−	0.853162i	−0.182762	−	0.983157i	$-0.558504\pi$
$431$	−506.113	−	367.713i	−1.17428	−	0.853162i	−0.991515	+	0.129995i	$0.958504\pi$
$432$		0			0
$433$	25.5566	+	161.358i	0.0590222	+	0.372651i	0.999465	+	0.0327001i	$0.0104106\pi$
$433$	25.5566	+	161.358i	0.0590222	+	0.372651i	−0.940443	+	0.339951i	$0.889589\pi$
$434$		0			0
$435$	−106.659	+	5.15981i	−0.245192	+	0.0118616i
$436$		0			0
$437$	−147.554	−	289.591i	−0.337653	−	0.662681i
$438$		0			0
$439$	508.414	−	165.194i	1.15812	−	0.376295i	0.333923	−	0.942600i	$-0.391628\pi$
$439$	508.414	−	165.194i	1.15812	−	0.376295i	0.824196	+	0.566305i	$0.191628\pi$
$440$		0			0
$441$	24.3065	−	74.8078i	0.0551169	−	0.169632i
$442$		0			0
$443$	−301.059	−	301.059i	−0.679592	−	0.679592i	0.280316	−	0.959908i	$-0.409561\pi$
$443$	−301.059	−	301.059i	−0.679592	−	0.679592i	−0.959908	+	0.280316i	$0.909561\pi$
$444$		0			0
$445$	−1.75448	+	16.0709i	−0.00394265	+	0.0361145i
$446$		0			0
$447$	2.72211	−	17.1867i	0.00608973	−	0.0384490i
$448$		0			0
$449$			574.659i			1.27986i	0.768431	+	0.639932i	$0.221038\pi$
$449$			574.659i			1.27986i	−0.768431	+	0.639932i	$0.778962\pi$
$450$		0			0
$451$	−203.209			−0.450574
$452$		0			0
$453$	−3.73752	−	0.591965i	−0.00825059	−	0.00130677i
$454$		0			0
$455$	−217.474	−	197.403i	−0.477965	−	0.433854i
$456$		0			0
$457$	192.683	−	192.683i	0.421626	−	0.421626i	−0.464138	−	0.885763i	$-0.653636\pi$
$457$	192.683	−	192.683i	0.421626	−	0.421626i	0.885763	+	0.464138i	$0.153636\pi$
$458$		0			0
$459$	103.637	+	33.6736i	0.225788	+	0.0733629i
$460$		0			0
$461$	−109.731	−	337.718i	−0.238029	−	0.732578i	−0.996705	−	0.0811100i	$-0.974153\pi$
$461$	−109.731	−	337.718i	−0.238029	−	0.732578i	0.758676	−	0.651468i	$-0.225847\pi$
$462$		0			0
$463$	541.260	−	275.786i	1.16903	−	0.595649i	0.241866	−	0.970310i	$-0.422241\pi$
$463$	541.260	−	275.786i	1.16903	−	0.595649i	0.927162	+	0.374660i	$0.122241\pi$
$464$		0			0
$465$	50.6966	−	19.2271i	0.109025	−	0.0413486i
$466$		0			0
$467$	827.775	−	131.107i	1.77254	−	0.280742i	0.817220	−	0.576326i	$-0.195514\pi$
$467$	827.775	−	131.107i	1.77254	−	0.280742i	0.955317	+	0.295583i	$0.0955140\pi$
$468$		0			0
$469$	221.675	−	305.109i	0.472655	−	0.650553i
$470$		0			0
$471$	−112.924	+	82.0443i	−0.239754	+	0.174192i
$472$		0			0
$473$	43.3941	−	85.1658i	0.0917424	−	0.180055i
$474$		0			0
$475$	875.870	−	84.9426i	1.84394	−	0.178827i
$476$		0			0
$477$	596.212	+	303.785i	1.24992	+	0.636867i
$478$		0			0
$479$	61.1061	+	84.1053i	0.127570	+	0.175585i	0.868024	−	0.496521i	$-0.165390\pi$
$479$	61.1061	+	84.1053i	0.127570	+	0.175585i	−0.740454	+	0.672107i	$0.765390\pi$
$480$		0			0
$481$	172.435	+	125.281i	0.358492	+	0.260460i
$482$		0			0
$483$	4.94678	+	31.2328i	0.0102418	+	0.0646641i
$484$		0			0
$485$	−660.466	−	432.697i	−1.36178	−	0.892158i
$486$		0			0
$487$	−356.543	−	699.756i	−0.732122	−	1.43687i	−0.893075	−	0.449908i	$-0.851457\pi$
$487$	−356.543	−	699.756i	−0.732122	−	1.43687i	0.160953	−	0.986962i	$-0.448543\pi$
$488$		0			0
$489$	116.249	−	37.7716i	0.237728	−	0.0772426i
$490$		0			0
$491$	−59.2346	+	182.305i	−0.120641	+	0.371294i	−0.993082	−	0.117426i	$-0.962536\pi$
$491$	−59.2346	+	182.305i	−0.120641	+	0.371294i	0.872441	+	0.488720i	$0.162536\pi$
$492$		0			0
$493$	316.696	+	316.696i	0.642385	+	0.642385i
$494$		0			0
$495$	−155.092	−	69.8001i	−0.313318	−	0.141010i
$496$		0			0
$497$	−108.611	+	685.745i	−0.218534	+	1.37977i
$498$		0			0
$499$		−	327.619i		−	0.656550i	−0.944582	−	0.328275i	$-0.893533\pi$
$499$		−	327.619i		−	0.656550i	0.944582	−	0.328275i	$-0.106467\pi$
$500$		0			0
$501$	−145.832			−0.291083
$502$		0			0
$503$	789.677	+	125.072i	1.56993	+	0.248653i	0.879912	−	0.475136i	$-0.157601\pi$
$503$	789.677	+	125.072i	1.56993	+	0.248653i	0.690021	+	0.723789i	$0.257601\pi$
$504$		0			0
$505$	234.997	−	522.151i	0.465340	−	1.03396i
$506$		0			0
$507$	31.6643	−	31.6643i	0.0624543	−	0.0624543i
$508$		0			0
$509$	343.256	+	111.531i	0.674373	+	0.219117i	0.626130	−	0.779719i	$-0.284638\pi$
$509$	343.256	+	111.531i	0.674373	+	0.219117i	0.0482429	+	0.998836i	$0.484638\pi$
$510$		0			0
$511$	−116.560	−	358.735i	−0.228102	−	0.702026i
$512$		0			0
$513$	−300.830	+	153.281i	−0.586414	+	0.298793i
$514$		0			0
$515$	301.338	−	459.961i	0.585122	−	0.893128i
$516$		0			0
$517$	−73.8649	+	11.6990i	−0.142872	+	0.0226287i
$518$		0			0
$519$	31.7545	−	43.7063i	0.0611840	−	0.0842126i
$520$		0			0
$521$	−362.148	+	263.116i	−0.695103	+	0.505022i	−0.878334	−	0.478048i	$-0.841344\pi$
$521$	−362.148	+	263.116i	−0.695103	+	0.505022i	0.183231	+	0.983070i	$0.441344\pi$
$522$		0			0
$523$	342.507	−	672.208i	0.654889	−	1.28529i	−0.289725	−	0.957110i	$-0.593564\pi$
$523$	342.507	−	672.208i	0.654889	−	1.28529i	0.944614	−	0.328182i	$-0.106436\pi$
$524$		0			0
$525$	−83.5998	−	18.4735i	−0.159238	−	0.0351877i
$526$		0			0
$527$	−202.627	−	103.243i	−0.384491	−	0.195908i
$528$		0			0
$529$	260.824	+	358.993i	0.493051	+	0.678626i
$530$		0			0
$531$	749.505	+	544.548i	1.41150	+	1.02551i
$532$		0			0
$533$	−75.6044	−	477.347i	−0.141847	−	0.895586i
$534$		0			0
$535$	−66.4682	−	175.259i	−0.124240	−	0.327586i
$536$		0			0
$537$	19.9771	+	39.2072i	0.0372012	+	0.0730116i
$538$		0			0
$539$	−33.5682	+	10.9070i	−0.0622786	+	0.0202356i
$540$		0			0
$541$	−299.830	+	922.782i	−0.554215	+	1.70570i	0.143793	+	0.989608i	$0.454070\pi$
$541$	−299.830	+	922.782i	−0.554215	+	1.70570i	−0.698008	+	0.716090i	$0.745930\pi$
$542$		0			0
$543$	−39.8040	−	39.8040i	−0.0733040	−	0.0733040i
$544$		0			0
$545$	193.674	−	213.365i	0.355365	−	0.391496i
$546$		0			0
$547$	−160.828	+	1015.43i	−0.294019	+	1.85636i	0.190640	+	0.981660i	$0.438944\pi$
$547$	−160.828	+	1015.43i	−0.294019	+	1.85636i	−0.484659	+	0.874703i	$0.661056\pi$
$548$		0			0
$549$		−	297.507i		−	0.541907i
$550$		0			0
$551$	−1387.69			−2.51849
$552$		0			0
$553$	−150.527	−	23.8411i	−0.272200	−	0.0431122i
$554$		0			0
$555$	61.7647	+	6.74292i	0.111288	+	0.0121494i
$556$		0			0
$557$	−188.199	+	188.199i	−0.337879	+	0.337879i	−0.855569	−	0.517689i	$-0.826792\pi$
$557$	−188.199	+	188.199i	−0.337879	+	0.337879i	0.517689	+	0.855569i	$0.326792\pi$
$558$		0			0
$559$	216.203	+	70.2488i	0.386768	+	0.125669i
$560$		0			0
$561$	−7.42989	−	22.8668i	−0.0132440	−	0.0407609i
$562$		0			0
$563$	−930.107	+	473.913i	−1.65206	+	0.841764i	−0.655835	+	0.754904i	$0.727683\pi$
$563$	−930.107	+	473.913i	−1.65206	+	0.841764i	−0.996221	+	0.0868603i	$0.972317\pi$
$564$		0			0
$565$	11.9500	+	247.018i	0.0211504	+	0.437200i
$566$		0			0
$567$	−456.829	+	72.3545i	−0.805694	+	0.127609i
$568$		0			0
$569$	236.953	−	326.137i	0.416437	−	0.573176i	−0.548337	−	0.836258i	$-0.684739\pi$
$569$	236.953	−	326.137i	0.416437	−	0.573176i	0.964774	+	0.263081i	$0.0847387\pi$
$570$		0			0
$571$	671.899	−	488.163i	1.17671	−	0.854926i	0.184909	−	0.982756i	$-0.440801\pi$
$571$	671.899	−	488.163i	1.17671	−	0.854926i	0.991796	+	0.127829i	$0.0408010\pi$
$572$		0			0
$573$	−7.01435	+	13.7664i	−0.0122414	+	0.0240252i
$574$		0			0
$575$	223.448	−	57.9511i	0.388606	−	0.100784i
$576$		0			0
$577$	−728.209	−	371.041i	−1.26206	−	0.643052i	−0.310517	−	0.950568i	$-0.600502\pi$
$577$	−728.209	−	371.041i	−1.26206	−	0.643052i	−0.951543	+	0.307516i	$0.900502\pi$
$578$		0			0
$579$	−5.14762	−	7.08509i	−0.00889053	−	0.0122368i
$580$		0			0
$581$	562.169	+	408.439i	0.967588	+	0.702994i
$582$		0			0
$583$	−46.9714	−	296.566i	−0.0805684	−	0.508689i
$584$		0			0
$585$	106.261	−	390.289i	0.181643	−	0.667161i
$586$		0			0
$587$	421.251	+	826.752i	0.717634	+	1.40844i	0.904683	+	0.426085i	$0.140107\pi$
$587$	421.251	+	826.752i	0.717634	+	1.40844i	−0.187050	+	0.982350i	$0.559893\pi$
$588$		0			0
$589$	670.124	−	217.737i	1.13773	−	0.369672i
$590$		0			0
$591$	35.1292	−	108.116i	0.0594402	−	0.182938i
$592$		0			0
$593$	645.208	+	645.208i	1.08804	+	1.08804i	0.995730	+	0.0923095i	$0.0294249\pi$
$593$	645.208	+	645.208i	1.08804	+	1.08804i	0.0923095	+	0.995730i	$0.470575\pi$
$594$		0			0
$595$	178.297	+	311.707i	0.299659	+	0.523877i
$596$		0			0
$597$	13.9436	−	88.0365i	0.0233561	−	0.147465i
$598$		0			0
$599$		−	248.911i		−	0.415545i	−0.978177	−	0.207772i	$-0.933379\pi$
$599$		−	248.911i		−	0.415545i	0.978177	−	0.207772i	$-0.0666213\pi$
$600$		0			0
$601$	−749.209			−1.24660			−0.623302	−	0.781981i	$-0.714209\pi$
$601$	−749.209			−1.24660			−0.623302	+	0.781981i	$0.714209\pi$
$602$		0			0
$603$	513.003	+	81.2517i	0.850751	+	0.134746i
$604$		0			0
$605$	−107.839	−	517.567i	−0.178247	−	0.855483i
$606$		0			0
$607$	−515.561	+	515.561i	−0.849358	+	0.849358i	−0.990053	−	0.140695i	$-0.955066\pi$
$607$	−515.561	+	515.561i	−0.849358	+	0.849358i	0.140695	+	0.990053i	$0.455066\pi$
$608$		0			0
$609$	128.405	+	41.7214i	0.210846	+	0.0685081i
$610$		0			0
$611$	−54.9633	−	169.160i	−0.0899563	−	0.276857i
$612$		0			0
$613$	−773.223	+	393.977i	−1.26138	+	0.642703i	−0.951375	−	0.308034i	$-0.900329\pi$
$613$	−773.223	+	393.977i	−1.26138	+	0.642703i	−0.310000	+	0.950737i	$0.600329\pi$
$614$		0			0
$615$	−88.2200	−	109.843i	−0.143447	−	0.178606i
$616$		0			0
$617$	576.870	−	91.3672i	0.934959	−	0.148083i	0.329677	−	0.944094i	$-0.393060\pi$
$617$	576.870	−	91.3672i	0.934959	−	0.148083i	0.605282	+	0.796011i	$0.293060\pi$
$618$		0			0
$619$	325.910	−	448.577i	0.526511	−	0.724681i	−0.460082	−	0.887876i	$-0.652180\pi$
$619$	325.910	−	448.577i	0.526511	−	0.724681i	0.986594	+	0.163196i	$0.0521802\pi$
$620$		0			0
$621$	−71.6536	+	52.0594i	−0.115384	+	0.0838316i
$622$		0			0
$623$	9.27971	−	18.2125i	0.0148952	−	0.0292335i
$624$		0			0
$625$	−75.3179	+	620.445i	−0.120509	+	0.992712i
$626$		0			0
$627$	66.3765	+	33.8205i	0.105864	+	0.0539402i
$628$		0			0
$629$	−153.175	−	210.827i	−0.243521	−	0.335177i
$630$		0			0
$631$	−655.610	−	476.329i	−1.03900	−	0.754879i	−0.0689113	−	0.997623i	$-0.521953\pi$
$631$	−655.610	−	476.329i	−1.03900	−	0.754879i	−0.970090	+	0.242744i	$0.921953\pi$
$632$		0			0
$633$	−27.3952	−	172.966i	−0.0432783	−	0.273248i
$634$		0			0
$635$	−195.432	+	156.961i	−0.307768	+	0.247183i
$636$		0			0
$637$	−38.1101	−	74.7953i	−0.0598275	−	0.117418i
$638$		0			0
$639$	−909.392	+	295.479i	−1.42315	+	0.462409i
$640$		0			0
$641$	−102.361	+	315.034i	−0.159689	+	0.491472i	−0.998606	−	0.0527877i	$-0.983189\pi$
$641$	−102.361	+	315.034i	−0.159689	+	0.491472i	0.838917	+	0.544260i	$0.183189\pi$
$642$		0			0
$643$	664.492	+	664.492i	1.03342	+	1.03342i	0.999422	+	0.0340024i	$0.0108254\pi$
$643$	664.492	+	664.492i	1.03342	+	1.03342i	0.0340024	+	0.999422i	$0.489175\pi$
$644$		0			0
$645$	64.8745	−	13.5171i	0.100581	−	0.0209568i
$646$		0			0
$647$	−78.9653	+	498.567i	−0.122048	+	0.770583i	0.848415	+	0.529332i	$0.177558\pi$
$647$	−78.9653	+	498.567i	−0.122048	+	0.770583i	−0.970463	+	0.241250i	$0.922442\pi$
$648$		0			0
$649$		−	415.717i		−	0.640550i
$650$		0			0
$651$	−68.5543			−0.105306
$652$		0			0
$653$	217.408	+	34.4341i	0.332937	+	0.0527321i	0.320665	−	0.947193i	$-0.396094\pi$
$653$	217.408	+	34.4341i	0.332937	+	0.0527321i	0.0122721	+	0.999925i	$0.496094\pi$
$654$		0			0
$655$	−82.0598	+	46.9384i	−0.125282	+	0.0716616i
$656$		0			0
$657$	367.328	−	367.328i	0.559100	−	0.559100i
$658$		0			0
$659$	−1119.68	−	363.805i	−1.69906	−	0.552057i	−0.710604	−	0.703592i	$-0.751578\pi$
$659$	−1119.68	−	363.805i	−1.69906	−	0.552057i	−0.988452	+	0.151535i	$0.951578\pi$
$660$		0			0
$661$	−383.061	−	1178.94i	−0.579518	−	1.78357i	−0.620253	−	0.784402i	$-0.712970\pi$
$661$	−383.061	−	1178.94i	−0.579518	−	1.78357i	0.0407350	−	0.999170i	$-0.487030\pi$
$662$		0			0
$663$	50.9510	−	25.9608i	0.0768492	−	0.0391566i
$664$		0			0
$665$	−1073.54	−	292.285i	−1.61435	−	0.439527i
$666$		0			0
$667$	−359.543	+	56.9460i	−0.539045	+	0.0853764i
$668$		0			0
$669$	−112.630	+	155.021i	−0.168355	+	0.231721i
$670$		0			0
$671$	−108.003	+	78.4687i	−0.160958	+	0.116943i
$672$		0			0
$673$	−167.300	+	328.345i	−0.248589	+	0.487883i	−0.981257	−	0.192703i	$-0.938275\pi$
$673$	−167.300	+	328.345i	−0.248589	+	0.487883i	0.732669	+	0.680586i	$0.238275\pi$
$674$		0			0
$675$	−60.2001	−	232.120i	−0.0891853	−	0.343882i
$676$		0			0
$677$	−302.604	−	154.184i	−0.446977	−	0.227746i	0.215989	−	0.976396i	$-0.430703\pi$
$677$	−302.604	−	154.184i	−0.446977	−	0.227746i	−0.662966	+	0.748650i	$0.730703\pi$
$678$		0			0
$679$	586.800	+	807.661i	0.864212	+	1.18949i
$680$		0			0
$681$	96.1211	+	69.8361i	0.141147	+	0.102549i
$682$		0			0
$683$	62.2622	+	393.108i	0.0911600	+	0.575561i	0.990414	+	0.138134i	$0.0441104\pi$
$683$	62.2622	+	393.108i	0.0911600	+	0.575561i	−0.899254	+	0.437428i	$0.855890\pi$
$684$		0			0
$685$	−803.933	+	38.8918i	−1.17363	+	0.0567764i
$686$		0			0
$687$	21.1403	+	41.4903i	0.0307720	+	0.0603934i
$688$		0			0
$689$	679.171	−	220.676i	0.985735	−	0.320285i
$690$		0			0
$691$	−26.2446	+	80.7726i	−0.0379806	+	0.116892i	−0.968249	−	0.249987i	$-0.919574\pi$
$691$	−26.2446	+	80.7726i	−0.0379806	+	0.116892i	0.930269	+	0.366879i	$0.119574\pi$
$692$		0			0
$693$	152.055	+	152.055i	0.219416	+	0.219416i
$694$		0			0
$695$	−120.067	+	1099.80i	−0.172758	+	1.58245i
$696$		0			0
$697$	−92.4373	+	583.626i	−0.132622	+	0.837340i
$698$		0			0
$699$			98.2116i			0.140503i
$700$		0			0
$701$	−13.9555			−0.0199080			−0.00995402	−	0.999950i	$-0.503169\pi$
$701$	−13.9555			−0.0199080			−0.00995402	+	0.999950i	$0.503169\pi$
$702$		0			0
$703$	797.483	+	126.309i	1.13440	+	0.179671i
$704$		0			0
$705$	−38.3911	−	34.8480i	−0.0544555	−	0.0494299i
$706$		0			0
$707$	−511.925	+	511.925i	−0.724081	+	0.724081i
$708$		0			0
$709$	1107.30	+	359.783i	1.56177	+	0.507451i	0.957281	−	0.289159i	$-0.0933756\pi$
$709$	1107.30	+	359.783i	1.56177	+	0.507451i	0.604493	+	0.796610i	$0.293376\pi$
$710$		0			0
$711$	−64.8601	−	199.619i	−0.0912237	−	0.280758i
$712$		0			0
$713$	164.691	−	83.9143i	0.230983	−	0.117692i
$714$		0			0
$715$	−169.712	+	64.3647i	−0.237360	+	0.0900206i
$716$		0			0
$717$	−14.3081	+	2.26619i	−0.0199556	+	0.00316065i
$718$		0			0
$719$	138.168	−	190.172i	0.192167	−	0.264495i	−0.702051	−	0.712126i	$-0.747732\pi$
$719$	138.168	−	190.172i	0.192167	−	0.264495i	0.894218	+	0.447631i	$0.147732\pi$
$720$		0			0
$721$	−562.470	+	408.659i	−0.780125	+	0.566794i
$722$		0			0
$723$	35.2757	−	69.2325i	0.0487908	−	0.0957573i
$724$		0			0
$725$	212.662	−	962.379i	0.293327	−	1.32742i
$726$		0			0
$727$	−430.297	−	219.247i	−0.591881	−	0.301578i	0.132277	−	0.991213i	$-0.457771\pi$
$727$	−430.297	−	219.247i	−0.591881	−	0.301578i	−0.724158	+	0.689635i	$0.757771\pi$
$728$		0			0
$729$	−346.928	−	477.505i	−0.475895	−	0.655014i
$730$		0			0
$731$	−224.861	−	163.371i	−0.307608	−	0.223490i
$732$		0			0
$733$	72.9256	+	460.434i	0.0994893	+	0.628150i	0.986166	+	0.165761i	$0.0530079\pi$
$733$	72.9256	+	460.434i	0.0994893	+	0.628150i	−0.886677	+	0.462390i	$0.846992\pi$
$734$		0			0
$735$	−20.4688	−	13.4099i	−0.0278487	−	0.0182448i
$736$		0			0
$737$	−105.810	−	207.664i	−0.143569	−	0.281770i
$738$		0			0
$739$	294.119	−	95.5652i	0.397997	−	0.129317i	−0.103178	−	0.994663i	$-0.532901\pi$
$739$	294.119	−	95.5652i	0.397997	−	0.129317i	0.501175	+	0.865346i	$0.332901\pi$
$740$		0			0
$741$	−54.7505	+	168.505i	−0.0738873	+	0.227402i
$742$		0			0
$743$	355.190	+	355.190i	0.478049	+	0.478049i	0.904507	−	0.426458i	$-0.140239\pi$
$743$	355.190	+	355.190i	0.478049	+	0.478049i	−0.426458	+	0.904507i	$0.640239\pi$
$744$		0			0
$745$	146.459	+	65.9147i	0.196590	+	0.0884761i
$746$		0			0
$747$	−149.707	+	945.215i	−0.200412	+	1.26535i
$748$		0			0
$749$			236.993i			0.316412i
$750$		0			0
$751$	−1365.36			−1.81806			−0.909030	−	0.416731i	$-0.863176\pi$
$751$	−1365.36			−1.81806			−0.909030	+	0.416731i	$0.863176\pi$
$752$		0			0
$753$	160.241	+	25.3797i	0.212804	+	0.0337048i
$754$		0			0
$755$	14.3342	−	31.8498i	0.0189857	−	0.0421852i
$756$		0			0
$757$	48.3671	−	48.3671i	0.0638931	−	0.0638931i	−0.674438	−	0.738331i	$-0.735614\pi$
$757$	48.3671	−	48.3671i	0.0638931	−	0.0638931i	0.738331	+	0.674438i	$0.235614\pi$
$758$		0			0
$759$	18.5857	+	6.03887i	0.0244871	+	0.00795635i
$760$		0			0
$761$	229.999	+	707.865i	0.302233	+	0.930177i	0.980695	+	0.195542i	$0.0626465\pi$
$761$	229.999	+	707.865i	0.302233	+	0.930177i	−0.678463	+	0.734635i	$0.737353\pi$
$762$		0			0
$763$	−324.626	+	165.405i	−0.425460	+	0.216783i
$764$		0			0
$765$	−271.019	+	413.682i	−0.354274	+	0.540761i
$766$		0			0
$767$	976.540	−	154.669i	1.27319	−	0.201654i
$768$		0			0
$769$	−111.256	+	153.130i	−0.144676	+	0.199129i	−0.875205	−	0.483752i	$-0.839274\pi$
$769$	−111.256	+	153.130i	−0.144676	+	0.199129i	0.730529	+	0.682882i	$0.239274\pi$
$770$		0			0
$771$	158.267	−	114.988i	0.205275	−	0.149141i
$772$		0			0
$773$	−423.160	+	830.499i	−0.547426	+	1.07438i	0.437144	+	0.899392i	$0.355990\pi$
$773$	−423.160	+	830.499i	−0.547426	+	1.07438i	−0.984570	+	0.174992i	$0.944010\pi$
$774$		0			0
$775$	48.3070	+	498.108i	0.0623316	+	0.642721i
$776$		0			0
$777$	−69.9951	−	35.6643i	−0.0900838	−	0.0459000i
$778$		0			0
$779$	−1076.14	−	1481.17i	−1.38143	−	1.90138i
$780$		0			0
$781$	347.123	+	252.199i	0.444459	+	0.322919i
$782$		0			0
$783$	59.1561	+	373.497i	0.0755505	+	0.477007i
$784$		0			0
$785$	−456.855	−	1204.60i	−0.581981	−	1.53452i
$786$		0			0
$787$	−56.8876	−	111.648i	−0.0722841	−	0.141865i	0.852037	−	0.523482i	$-0.175367\pi$
$787$	−56.8876	−	111.648i	−0.0722841	−	0.141865i	−0.924321	+	0.381617i	$0.875367\pi$
$788$		0			0
$789$	136.109	−	44.2245i	0.172508	−	0.0560513i
$790$		0			0
$791$	96.6255	−	297.383i	0.122156	−	0.375958i
$792$		0			0
$793$	−224.510	−	224.510i	−0.283114	−	0.283114i
$794$		0			0
$795$	139.914	−	154.139i	0.175992	−	0.193886i
$796$		0			0
$797$	−179.352	+	1132.38i	−0.225034	+	1.42081i	0.573671	+	0.819086i	$0.305519\pi$
$797$	−179.352	+	1132.38i	−0.225034	+	1.42081i	−0.798705	+	0.601723i	$0.794481\pi$
$798$		0			0
$799$			217.466i			0.272172i
$800$		0			0
$801$	28.1507			0.0351445
$802$		0			0
$803$	−230.234	−	36.4656i	−0.286718	−	0.0454116i
$804$		0			0
$805$	−290.144	−	31.6753i	−0.360427	−	0.0393482i
$806$		0			0
$807$	189.842	−	189.842i	0.235244	−	0.235244i
$808$		0			0
$809$	−850.288	−	276.275i	−1.05104	−	0.341502i	−0.267961	−	0.963430i	$-0.586350\pi$
$809$	−850.288	−	276.275i	−1.05104	−	0.341502i	−0.783075	+	0.621928i	$0.786350\pi$
$810$		0			0
$811$	132.778	+	408.649i	0.163721	+	0.503883i	0.998940	−	0.0460357i	$-0.0146588\pi$
$811$	132.778	+	408.649i	0.163721	+	0.503883i	−0.835218	+	0.549918i	$0.814659\pi$
$812$		0			0
$813$	9.51429	−	4.84777i	0.0117027	−	0.00596282i
$814$		0			0
$815$	54.5142	+	1126.86i	0.0668886	+	1.38266i
$816$		0			0
$817$	850.570	−	134.717i	1.04109	−	0.164892i
$818$		0			0
$819$	−300.612	+	413.757i	−0.367048	+	0.505198i
$820$		0			0
$821$	885.226	−	643.155i	1.07823	−	0.783380i	0.100856	−	0.994901i	$-0.467842\pi$
$821$	885.226	−	643.155i	1.07823	−	0.783380i	0.977373	+	0.211521i	$0.0678418\pi$
$822$		0			0
$823$	247.845	−	486.422i	0.301148	−	0.591036i	−0.689998	−	0.723811i	$-0.742389\pi$
$823$	247.845	−	486.422i	0.301148	−	0.591036i	0.991146	+	0.132775i	$0.0423888\pi$
$824$		0			0
$825$	−33.6271	+	40.8500i	−0.0407602	+	0.0495152i
$826$		0			0
$827$	−164.809	−	83.9743i	−0.199285	−	0.101541i	0.351500	−	0.936188i	$-0.385672\pi$
$827$	−164.809	−	83.9743i	−0.199285	−	0.101541i	−0.550785	+	0.834647i	$0.685672\pi$
$828$		0			0
$829$	296.115	+	407.567i	0.357195	+	0.491637i	0.949365	−	0.314177i	$-0.101728\pi$
$829$	296.115	+	407.567i	0.357195	+	0.491637i	−0.592170	+	0.805813i	$0.701728\pi$
$830$		0			0
$831$	176.115	+	127.955i	0.211932	+	0.153977i
$832$		0			0
$833$	16.0556	+	101.371i	0.0192744	+	0.121694i
$834$		0			0
$835$	353.599	−	1298.74i	0.423472	−	1.55538i
$836$		0			0
$837$	−87.1709	−	171.083i	−0.104147	−	0.204400i
$838$		0			0
$839$	981.936	−	319.050i	1.17036	−	0.380275i	0.341586	−	0.939851i	$-0.389036\pi$
$839$	981.936	−	319.050i	1.17036	−	0.380275i	0.828779	+	0.559576i	$0.189036\pi$
$840$		0			0
$841$	−220.403	+	678.329i	−0.262072	+	0.806575i
$842$		0			0
$843$	−59.0021	−	59.0021i	−0.0699906	−	0.0699906i
$844$		0			0
$845$	205.217	+	358.769i	0.242860	+	0.424579i
$846$		0			0
$847$	−104.569	+	660.220i	−0.123458	+	0.779481i
$848$		0			0
$849$		−	165.421i		−	0.194842i
$850$		0			0
$851$	211.807			0.248892
$852$		0			0
$853$	−38.3447	−	6.07321i	−0.0449528	−	0.00711982i	0.133918	−	0.990992i	$-0.457244\pi$
$853$	−38.3447	−	6.07321i	−0.0449528	−	0.00711982i	−0.178870	+	0.983873i	$0.557244\pi$
$854$		0			0
$855$	−312.557	−	1500.10i	−0.365564	−	1.75450i
$856$		0			0
$857$	−105.473	+	105.473i	−0.123073	+	0.123073i	−0.765960	−	0.642888i	$-0.777736\pi$
$857$	−105.473	+	105.473i	−0.123073	+	0.123073i	0.642888	+	0.765960i	$0.277736\pi$
$858$		0			0
$859$	454.724	+	147.749i	0.529364	+	0.172001i	0.561491	−	0.827483i	$-0.310228\pi$
$859$	454.724	+	147.749i	0.529364	+	0.172001i	−0.0321268	+	0.999484i	$0.510228\pi$
$860$		0			0
$861$	55.0448	+	169.410i	0.0639312	+	0.196760i
$862$		0			0
$863$	1355.19	−	690.502i	1.57032	−	0.800118i	0.570543	−	0.821268i	$-0.306733\pi$
$863$	1355.19	−	690.502i	1.57032	−	0.800118i	0.999776	+	0.0211502i	$0.00673281\pi$
$864$		0			0
$865$	312.240	+	388.770i	0.360972	+	0.449446i
$866$		0			0
$867$	85.5749	−	13.5537i	0.0987023	−	0.0156329i
$868$		0			0
$869$	−55.3598	+	76.1962i	−0.0637052	+	0.0876827i
$870$		0			0
$871$	448.446	−	325.815i	0.514864	−	0.374070i
$872$		0			0
$873$	−624.195	+	1225.05i	−0.715000	+	1.40327i
$874$		0			0
$875$	367.223	−	699.722i	0.419684	−	0.799682i
$876$		0			0
$877$	−85.8295	−	43.7323i	−0.0978672	−	0.0498658i	0.404372	−	0.914595i	$-0.367490\pi$
$877$	−85.8295	−	43.7323i	−0.0978672	−	0.0498658i	−0.502239	+	0.864729i	$0.667490\pi$
$878$		0			0
$879$	9.59154	+	13.2016i	0.0109119	+	0.0150189i
$880$		0			0
$881$	−457.119	−	332.116i	−0.518864	−	0.376977i	0.297312	−	0.954780i	$-0.403910\pi$
$881$	−457.119	−	332.116i	−0.518864	−	0.376977i	−0.816176	+	0.577804i	$0.803910\pi$
$882$		0			0
$883$	−156.450	−	987.786i	−0.177180	−	1.11867i	−0.902637	−	0.430403i	$-0.858372\pi$
$883$	−156.450	−	987.786i	−0.177180	−	1.11867i	0.725457	−	0.688267i	$-0.241628\pi$
$884$		0			0
$885$	224.712	−	180.477i	0.253912	−	0.203929i
$886$		0			0
$887$	9.75707	+	19.1493i	0.0110001	+	0.0215889i	0.896441	−	0.443163i	$-0.146144\pi$
$887$	9.75707	+	19.1493i	0.0110001	+	0.0215889i	−0.885441	+	0.464752i	$0.846144\pi$
$888$		0			0
$889$	301.416	−	97.9359i	0.339050	−	0.110164i
$890$		0			0
$891$	−88.3280	+	271.846i	−0.0991336	+	0.305102i
$892$		0			0
$893$	−476.441	−	476.441i	−0.533528	−	0.533528i
$894$		0			0
$895$	−397.606	+	82.8443i	−0.444252	+	0.0925634i
$896$		0			0
$897$	−7.27073	+	45.9056i	−0.00810560	+	0.0511768i
$898$		0			0
$899$		−	789.179i		−	0.877841i
$900$		0			0
$901$	−873.119			−0.969055
$902$		0			0
$903$	−82.7553	−	13.1072i	−0.0916448	−	0.0145151i
$904$		0			0
$905$	450.995	−	257.970i	0.498337	−	0.285050i
$906$		0			0
$907$	−159.176	+	159.176i	−0.175497	+	0.175497i	−0.789390	−	0.613892i	$-0.789603\pi$
$907$	−159.176	+	159.176i	−0.175497	+	0.175497i	0.613892	+	0.789390i	$0.289603\pi$
$908$		0			0
$909$	−948.265	−	308.110i	−1.04320	−	0.338955i
$910$		0			0
$911$	−217.608	−	669.727i	−0.238867	−	0.735156i	−0.996585	−	0.0825742i	$-0.973686\pi$
$911$	−217.608	−	669.727i	−0.238867	−	0.735156i	0.757718	−	0.652582i	$-0.226314\pi$
$912$		0			0
$913$	382.624	−	194.957i	0.419085	−	0.213534i
$914$		0			0
$915$	−89.3034	−	24.3140i	−0.0975993	−	0.0265727i
$916$		0			0
$917$	118.057	−	18.6983i	0.128742	−	0.0203908i
$918$		0			0
$919$	−538.706	+	741.466i	−0.586188	+	0.806818i	−0.994357	−	0.106088i	$-0.966167\pi$
$919$	−538.706	+	741.466i	−0.586188	+	0.806818i	0.408169	+	0.912906i	$0.366167\pi$
$920$		0			0
$921$	−103.940	+	75.5167i	−0.112855	+	0.0819942i
$922$		0			0
$923$	−463.281	+	909.240i	−0.501929	+	0.985092i
$924$		0			0
$925$	−209.811	+	533.708i	−0.226823	+	0.576982i
$926$		0			0
$927$	−853.149	−	434.701i	−0.920333	−	0.468933i
$928$		0			0
$929$	822.223	+	1131.69i	0.885063	+	1.21818i	0.974993	+	0.222236i	$0.0713357\pi$
$929$	822.223	+	1131.69i	0.885063	+	1.21818i	−0.0899299	+	0.995948i	$0.528664\pi$
$930$		0			0
$931$	−257.268	−	186.916i	−0.276335	−	0.200769i
$932$		0			0
$933$	−29.1042	−	183.757i	−0.0311942	−	0.196953i
$934$		0			0
$935$	221.660	−	10.7232i	0.237070	−	0.0114687i
$936$		0			0
$937$	−38.4557	−	75.4735i	−0.0410413	−	0.0805480i	0.869575	−	0.493801i	$-0.164393\pi$
$937$	−38.4557	−	75.4735i	−0.0410413	−	0.0805480i	−0.910616	+	0.413252i	$0.864393\pi$
$938$		0			0
$939$	−300.697	+	97.7024i	−0.320231	+	0.104049i
$940$		0			0
$941$	−143.101	+	440.420i	−0.152073	+	0.468034i	−0.997853	−	0.0654994i	$-0.979136\pi$
$941$	−143.101	+	440.420i	−0.152073	+	0.468034i	0.845779	+	0.533533i	$0.179136\pi$
$942$		0			0
$943$	−339.604	−	339.604i	−0.360132	−	0.360132i
$944$		0			0
$945$	−32.9046	+	301.404i	−0.0348197	+	0.318946i
$946$		0			0
$947$	13.3850	−	84.5096i	0.0141341	−	0.0892393i	−0.979613	−	0.200894i	$-0.935615\pi$
$947$	13.3850	−	84.5096i	0.0141341	−	0.0892393i	0.993747	+	0.111655i	$0.0356152\pi$
$948$		0			0
$949$		−	554.399i		−	0.584193i
$950$		0			0
$951$	−63.6284			−0.0669068
$952$		0			0
$953$	841.092	+	133.216i	0.882572	+	0.139786i	0.581239	−	0.813733i	$-0.302568\pi$
$953$	841.092	+	133.216i	0.882572	+	0.139786i	0.301334	+	0.953519i	$0.402568\pi$
$954$		0			0
$955$	−105.592	−	95.8470i	−0.110568	−	0.100363i
$956$		0			0
$957$	58.9990	−	58.9990i	0.0616499	−	0.0616499i
$958$		0			0
$959$	967.849	+	314.473i	1.00923	+	0.327918i
$960$		0			0
$961$	−173.138	−	532.865i	−0.180165	−	0.554490i
$962$		0			0
$963$	−290.816	+	148.178i	−0.301989	+	0.153871i
$964$		0			0
$965$	75.5790	−	28.6639i	0.0783202	−	0.0297036i
$966$		0			0
$967$	932.351	−	147.670i	0.964169	−	0.152709i	0.345550	−	0.938400i	$-0.387692\pi$
$967$	932.351	−	147.670i	0.964169	−	0.152709i	0.618619	+	0.785691i	$0.287692\pi$
$968$		0			0
$969$	127.328	−	175.252i	0.131402	−	0.180859i
$970$		0			0
$971$	431.922	−	313.810i	0.444822	−	0.323182i	−0.342726	−	0.939435i	$-0.611350\pi$
$971$	431.922	−	313.810i	0.444822	−	0.323182i	0.787548	+	0.616253i	$0.211350\pi$
$972$		0			0
$973$	635.050	−	1246.36i	0.652672	−	1.28094i
$974$		0			0
$975$	−108.470	−	63.7935i	−0.111251	−	0.0654292i
$976$		0			0
$977$	−1043.49	−	531.684i	−1.06805	−	0.544200i	−0.170614	−	0.985338i	$-0.554575\pi$
$977$	−1043.49	−	531.684i	−1.06805	−	0.544200i	−0.897439	+	0.441138i	$0.854575\pi$
$978$		0			0
$979$	−7.42487	−	10.2195i	−0.00758414	−	0.0104387i
$980$		0			0
$981$	−405.940	−	294.933i	−0.413802	−	0.300645i
$982$		0			0
$983$	33.1748	+	209.458i	0.0337486	+	0.213080i	0.998800	−	0.0489817i	$-0.0155976\pi$
$983$	33.1748	+	209.458i	0.0337486	+	0.213080i	−0.965051	+	0.262062i	$0.915598\pi$
$984$		0			0
$985$	877.675	+	574.999i	0.891040	+	0.583755i
$986$		0			0
$987$	29.7616	+	58.4105i	0.0301536	+	0.0591798i
$988$		0			0
$989$	214.851	−	69.8092i	0.217240	−	0.0705856i
$990$		0			0
$991$	−484.152	+	1490.07i	−0.488549	+	1.50360i	0.338225	+	0.941065i	$0.390173\pi$
$991$	−484.152	+	1490.07i	−0.488549	+	1.50360i	−0.826774	+	0.562534i	$0.809827\pi$
$992$		0			0
$993$	−178.780	−	178.780i	−0.180040	−	0.180040i
$994$		0			0
$995$	750.217	+	337.639i	0.753987	+	0.339336i
$996$		0			0
$997$	49.9297	−	315.244i	0.0500799	−	0.316192i	−0.949913	−	0.312514i	$-0.898829\pi$
$997$	49.9297	−	315.244i	0.0500799	−	0.316192i	0.999993	−	0.00367869i	$-0.00117097\pi$
$998$		0			0
$999$		−	220.028i		−	0.220248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.f.33.4		64
4.3	odd	2		200.3.u.b.33.5	✓	64
25.22	odd	20	inner	400.3.bg.f.97.4		64
100.47	even	20		200.3.u.b.97.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.b.33.5	✓	64	4.3	odd	2
200.3.u.b.97.5	yes	64	100.47	even	20
400.3.bg.f.33.4		64	1.1	even	1	trivial
400.3.bg.f.97.4		64	25.22	odd	20	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.535050 - 0.0847436i) q^{3} +(2.05203 - 4.55951i) q^{5} +(-4.47022 + 4.47022i) q^{7} +(-8.28041 - 2.69047i) q^{9} +O(q^{10})\)	\(q+(-0.535050 - 0.0847436i) q^{3} +(2.05203 - 4.55951i) q^{5} +(-4.47022 + 4.47022i) q^{7} +(-8.28041 - 2.69047i) q^{9} +(1.20728 + 3.71563i) q^{11} +(-8.27903 + 4.21838i) q^{13} +(-1.48433 + 2.26567i) q^{15} +(11.2207 - 1.77718i) q^{17} +(-20.6896 + 28.4767i) q^{19} +(2.77061 - 2.01297i) q^{21} +(-4.19198 + 8.22722i) q^{23} +(-16.5783 - 18.7125i) q^{25} +(8.54651 + 4.35467i) q^{27} +(23.1727 + 31.8945i) q^{29} +(-16.1948 - 11.7662i) q^{31} +(-0.331080 - 2.09036i) q^{33} +(11.2090 + 29.5550i) q^{35} +(-10.4140 - 20.4385i) q^{37} +(4.78718 - 1.55545i) q^{39} +(-16.0730 + 49.4677i) q^{41} +(-17.2999 - 17.2999i) q^{43} +(-29.2589 + 32.2337i) q^{45} +(-2.99450 + 18.9065i) q^{47} +9.03431i q^{49} -6.15422 q^{51} +(-75.9092 - 12.0228i) q^{53} +(19.4189 + 2.11998i) q^{55} +(13.4832 - 13.4832i) q^{57} +(-101.199 - 32.8817i) q^{59} +(10.5593 + 32.4981i) q^{61} +(49.0422 - 24.9883i) q^{63} +(2.24491 + 46.4046i) q^{65} +(-58.9216 + 9.33226i) q^{67} +(2.94012 - 4.04673i) q^{69} +(88.8498 - 64.5532i) q^{71} +(-27.0876 + 53.1624i) q^{73} +(7.28447 + 11.4170i) q^{75} +(-22.0065 - 11.2129i) q^{77} +(14.1699 + 19.5033i) q^{79} +(59.1899 + 43.0040i) q^{81} +(-17.1948 - 108.564i) q^{83} +(14.9221 - 54.8076i) q^{85} +(-9.69572 - 19.0289i) q^{87} +(-3.07504 + 0.999140i) q^{89} +(18.1520 - 55.8661i) q^{91} +(7.66789 + 7.66789i) q^{93} +(87.3844 + 152.769i) q^{95} +(24.7036 - 155.972i) q^{97} -34.0151i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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