LMFDB - Embedded newform 702.2.bc.a.305.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(305,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("702.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bc (of order $12$, degree $4$, 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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.14
Character	$\chi$	$=$	702.305
Dual form			702.2.bc.a.557.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.901822 - 3.36565i) q^{5} +(-0.0396662 - 0.0396662i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.901822 - 3.36565i) q^{5} +(-0.0396662 - 0.0396662i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-3.01756 - 1.74219i) q^{10} +(4.98703 + 1.33627i) q^{11} +(2.77745 - 2.29909i) q^{13} +(-0.0485810 + 0.0280482i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.83057 - 3.17065i) q^{17} +(0.677531 + 0.181544i) q^{19} +(-2.46382 + 2.46382i) q^{20} +(2.58148 - 4.47125i) q^{22} -5.78694 q^{23} +(-6.18416 - 3.57043i) q^{25} +(-1.50189 - 3.27785i) q^{26} +(0.0145188 + 0.0541850i) q^{28} +(-2.99055 + 1.72660i) q^{29} +(-5.75138 - 1.54108i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-3.53640 + 0.947575i) q^{34} +(-0.169274 + 0.0977305i) q^{35} +(7.28892 - 1.95306i) q^{37} +(0.350716 - 0.607458i) q^{38} +(1.74219 + 3.01756i) q^{40} +(-2.13130 - 2.13130i) q^{41} +5.42977i q^{43} +(-3.65076 - 3.65076i) q^{44} +(-1.49777 + 5.58976i) q^{46} +(1.29364 + 4.82793i) q^{47} -6.99685i q^{49} +(-5.04935 + 5.04935i) q^{50} +(-3.55488 + 0.602344i) q^{52} +3.89525i q^{53} +(8.99483 - 15.5795i) q^{55} +0.0560965 q^{56} +(0.893752 + 3.33553i) q^{58} +(0.272879 + 1.01840i) q^{59} -3.00390 q^{61} +(-2.97713 + 5.15654i) q^{62} -1.00000i q^{64} +(-5.23315 - 11.4213i) q^{65} +(7.69542 - 7.69542i) q^{67} +3.66115i q^{68} +(0.0505890 + 0.188801i) q^{70} +(-3.98742 + 14.8813i) q^{71} +(5.86521 + 5.86521i) q^{73} -7.54605i q^{74} +(-0.495987 - 0.495987i) q^{76} +(-0.144812 - 0.250821i) q^{77} +(2.76723 - 4.79298i) q^{79} +(3.36565 - 0.901822i) q^{80} +(-2.61030 + 1.50706i) q^{82} +(15.4261 - 4.13340i) q^{83} +(-12.3221 + 3.30170i) q^{85} +(5.24476 + 1.40533i) q^{86} +(-4.47125 + 2.58148i) q^{88} +(-4.41179 - 16.4650i) q^{89} +(-0.201367 - 0.0189747i) q^{91} +(5.01164 + 2.89347i) q^{92} +4.99824 q^{94} +(1.22203 - 2.11661i) q^{95} +(-1.62729 + 1.62729i) q^{97} +(-6.75844 - 1.81092i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7}+O(q^{10}) $ 56 * q - 8 * q^7	$ 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73} + 4 q^{76} - 24 q^{77} - 24 q^{79} + 96 q^{83} - 72 q^{85} + 4 q^{91} + 24 q^{92} - 52 q^{97} - 48 q^{98}+O(q^{100}) $ 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.901822	−	3.36565i	0.403307	−	1.50516i	−0.403850	−	0.914825i	$-0.632328\pi$
$5$	0.901822	−	3.36565i	0.403307	−	1.50516i	0.807157	−	0.590337i	$-0.201005\pi$
$6$		0			0
$7$	−0.0396662	−	0.0396662i	−0.0149924	−	0.0149924i	0.699571	−	0.714563i	$-0.253375\pi$
$7$	−0.0396662	−	0.0396662i	−0.0149924	−	0.0149924i	−0.714563	+	0.699571i	$0.753375\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−3.01756	−	1.74219i	−0.954235	−	0.550928i
$11$	4.98703	+	1.33627i	1.50365	+	0.402901i	0.914320	−	0.404993i	$-0.132726\pi$
$11$	4.98703	+	1.33627i	1.50365	+	0.402901i	0.589328	+	0.807894i	$0.299393\pi$
$12$		0			0
$13$	2.77745	−	2.29909i	0.770325	−	0.637652i
$13$	2.77745	−	2.29909i	0.770325	−	0.637652i
$14$	−0.0485810	+	0.0280482i	−0.0129838	+	0.00749621i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.83057	−	3.17065i	−0.443979	−	0.768995i	0.554001	−	0.832516i	$-0.313100\pi$
$17$	−1.83057	−	3.17065i	−0.443979	−	0.768995i	−0.997980	+	0.0635211i	$0.979767\pi$
$18$		0			0
$19$	0.677531	+	0.181544i	0.155436	+	0.0416491i	0.335698	−	0.941970i	$-0.391028\pi$
$19$	0.677531	+	0.181544i	0.155436	+	0.0416491i	−0.180262	+	0.983619i	$0.557694\pi$
$20$	−2.46382	+	2.46382i	−0.550928	+	0.550928i
$21$		0			0
$22$	2.58148	−	4.47125i	0.550373	−	0.953274i
$23$	−5.78694			−1.20666			−0.603330	−	0.797491i	$-0.706160\pi$
$23$	−5.78694			−1.20666			−0.603330	+	0.797491i	$0.706160\pi$
$24$		0			0
$25$	−6.18416	−	3.57043i	−1.23683	−	0.714085i
$26$	−1.50189	−	3.27785i	−0.294545	−	0.642840i
$27$		0			0
$28$	0.0145188	+	0.0541850i	0.00274380	+	0.0102400i
$29$	−2.99055	+	1.72660i	−0.555332	+	0.320621i	−0.751270	−	0.659995i	$-0.770558\pi$
$29$	−2.99055	+	1.72660i	−0.555332	+	0.320621i	0.195938	+	0.980616i	$0.437225\pi$
$30$		0			0
$31$	−5.75138	−	1.54108i	−1.03298	−	0.276786i	−0.297778	−	0.954635i	$-0.596245\pi$
$31$	−5.75138	−	1.54108i	−1.03298	−	0.276786i	−0.735201	+	0.677850i	$0.762912\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$		0			0
$34$	−3.53640	+	0.947575i	−0.606487	+	0.162508i
$35$	−0.169274	+	0.0977305i	−0.0286126	+	0.0165195i
$36$		0			0
$37$	7.28892	−	1.95306i	1.19829	−	0.321081i	0.396134	−	0.918193i	$-0.370352\pi$
$37$	7.28892	−	1.95306i	1.19829	−	0.321081i	0.802158	+	0.597112i	$0.203685\pi$
$38$	0.350716	−	0.607458i	0.0568937	−	0.0985427i
$39$		0			0
$40$	1.74219	+	3.01756i	0.275464	+	0.477117i
$41$	−2.13130	−	2.13130i	−0.332854	−	0.332854i	0.520815	−	0.853669i	$-0.325628\pi$
$41$	−2.13130	−	2.13130i	−0.332854	−	0.332854i	−0.853669	+	0.520815i	$0.825628\pi$
$42$		0			0
$43$			5.42977i			0.828032i	0.910270	+	0.414016i	$0.135874\pi$
$43$			5.42977i			0.828032i	−0.910270	+	0.414016i	$0.864126\pi$
$44$	−3.65076	−	3.65076i	−0.550373	−	0.550373i
$45$		0			0
$46$	−1.49777	+	5.58976i	−0.220834	+	0.824165i
$47$	1.29364	+	4.82793i	0.188697	+	0.704226i	0.993809	+	0.111103i	$0.0354385\pi$
$47$	1.29364	+	4.82793i	0.188697	+	0.704226i	−0.805112	+	0.593123i	$0.797895\pi$
$48$		0			0
$49$		−	6.99685i		−	0.999550i
$50$	−5.04935	+	5.04935i	−0.714085	+	0.714085i
$51$		0			0
$52$	−3.55488	+	0.602344i	−0.492973	+	0.0835300i
$53$			3.89525i			0.535053i	0.963550	+	0.267527i	$0.0862064\pi$
$53$			3.89525i			0.535053i	−0.963550	+	0.267527i	$0.913794\pi$
$54$		0			0
$55$	8.99483	−	15.5795i	1.21286	−	2.10074i
$56$	0.0560965			0.00749621
$57$		0			0
$58$	0.893752	+	3.33553i	0.117355	+	0.437976i
$59$	0.272879	+	1.01840i	0.0355258	+	0.132584i	0.981411	−	0.191917i	$-0.0614703\pi$
$59$	0.272879	+	1.01840i	0.0355258	+	0.132584i	−0.945885	+	0.324501i	$0.894804\pi$
$60$		0			0
$61$	−3.00390			−0.384610			−0.192305	−	0.981335i	$-0.561596\pi$
$61$	−3.00390			−0.384610			−0.192305	+	0.981335i	$0.561596\pi$
$62$	−2.97713	+	5.15654i	−0.378096	+	0.654882i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−5.23315	−	11.4213i	−0.649092	−	1.41663i
$66$		0			0
$67$	7.69542	−	7.69542i	0.940145	−	0.940145i	−0.0581622	−	0.998307i	$-0.518524\pi$
$67$	7.69542	−	7.69542i	0.940145	−	0.940145i	0.998307	+	0.0581622i	$0.0185241\pi$
$68$			3.66115i			0.443979i
$69$		0			0
$70$	0.0505890	+	0.188801i	0.00604655	+	0.0225660i
$71$	−3.98742	+	14.8813i	−0.473220	+	1.76608i	0.154865	+	0.987936i	$0.450506\pi$
$71$	−3.98742	+	14.8813i	−0.473220	+	1.76608i	−0.628085	+	0.778145i	$0.716161\pi$
$72$		0			0
$73$	5.86521	+	5.86521i	0.686471	+	0.686471i	0.961450	−	0.274979i	$-0.0886710\pi$
$73$	5.86521	+	5.86521i	0.686471	+	0.686471i	−0.274979	+	0.961450i	$0.588671\pi$
$74$		−	7.54605i		−	0.877210i
$75$		0			0
$76$	−0.495987	−	0.495987i	−0.0568937	−	0.0568937i
$77$	−0.144812	−	0.250821i	−0.0165028	−	0.0285838i
$78$		0			0
$79$	2.76723	−	4.79298i	0.311338	−	0.539253i	−0.667314	−	0.744776i	$-0.732556\pi$
$79$	2.76723	−	4.79298i	0.311338	−	0.539253i	0.978652	+	0.205523i	$0.0658896\pi$
$80$	3.36565	−	0.901822i	0.376291	−	0.100827i
$81$		0			0
$82$	−2.61030	+	1.50706i	−0.288260	+	0.166427i
$83$	15.4261	−	4.13340i	1.69323	−	0.453699i	0.722009	−	0.691883i	$-0.243219\pi$
$83$	15.4261	−	4.13340i	1.69323	−	0.453699i	0.971220	+	0.238184i	$0.0765521\pi$
$84$		0			0
$85$	−12.3221	+	3.30170i	−1.33652	+	0.358120i
$86$	5.24476	+	1.40533i	0.565556	+	0.151540i
$87$		0			0
$88$	−4.47125	+	2.58148i	−0.476637	+	0.275187i
$89$	−4.41179	−	16.4650i	−0.467649	−	1.74529i	−0.647955	−	0.761679i	$-0.724375\pi$
$89$	−4.41179	−	16.4650i	−0.467649	−	1.74529i	0.180306	−	0.983611i	$-0.442291\pi$
$90$		0			0
$91$	−0.201367	−	0.0189747i	−0.0211090	−	0.00198909i
$92$	5.01164	+	2.89347i	0.522500	+	0.301665i
$93$		0			0
$94$	4.99824			0.515529
$95$	1.22203	−	2.11661i	0.125377	−	0.217160i
$96$		0			0
$97$	−1.62729	+	1.62729i	−0.165226	+	0.165226i	−0.784877	−	0.619651i	$-0.787274\pi$
$97$	−1.62729	+	1.62729i	−0.165226	+	0.165226i	0.619651	+	0.784877i	$0.287274\pi$
$98$	−6.75844	−	1.81092i	−0.682706	−	0.182930i
$99$		0			0
$100$	3.57043	+	6.18416i	0.357043	+	0.618416i
$101$	1.76164	+	3.05125i	0.175290	+	0.303611i	0.940262	−	0.340453i	$-0.110580\pi$
$101$	1.76164	+	3.05125i	0.175290	+	0.303611i	−0.764972	+	0.644064i	$0.777247\pi$
$102$		0			0
$103$	−5.20698	+	3.00625i	−0.513059	+	0.296215i	−0.734090	−	0.679052i	$-0.762391\pi$
$103$	−5.20698	+	3.00625i	−0.513059	+	0.296215i	0.221031	+	0.975267i	$0.429058\pi$
$104$	−0.338252	+	3.58965i	−0.0331683	+	0.351994i
$105$		0			0
$106$	3.76252	+	1.00816i	0.365448	+	0.0979216i
$107$	14.5555	+	8.40363i	1.40714	+	0.812410i	0.995111	−	0.0987630i	$-0.0314886\pi$
$107$	14.5555	+	8.40363i	1.40714	+	0.812410i	0.412024	+	0.911173i	$0.364822\pi$
$108$		0			0
$109$	−14.0667	+	14.0667i	−1.34734	+	1.34734i	−0.458806	+	0.888537i	$0.651723\pi$
$109$	−14.0667	+	14.0667i	−1.34734	+	1.34734i	−0.888537	+	0.458806i	$0.848277\pi$
$110$	−12.7206	−	12.7206i	−1.21286	−	1.21286i
$111$		0			0
$112$	0.0145188	−	0.0541850i	0.00137190	−	0.00512000i
$113$	16.9465	+	9.78407i	1.59419	+	0.920408i	0.992576	+	0.121623i	$0.0388099\pi$
$113$	16.9465	+	9.78407i	1.59419	+	0.920408i	0.601617	+	0.798785i	$0.294523\pi$
$114$		0			0
$115$	−5.21879	+	19.4768i	−0.486655	+	1.81622i
$116$	3.45319			0.320621
$117$		0			0
$118$	1.05432			0.0970583
$119$	−0.0531556	+	0.198379i	−0.00487276	+	0.0181854i
$120$		0			0
$121$	13.5586	+	7.82807i	1.23260	+	0.711642i
$122$	−0.777466	+	2.90154i	−0.0703885	+	0.262693i
$123$		0			0
$124$	4.21030	+	4.21030i	0.378096	+	0.378096i
$125$	−5.27469	+	5.27469i	−0.471782	+	0.471782i
$126$		0			0
$127$	−0.00248320	−	0.00143368i	−0.000220349	−	0.000127218i	0.499890	−	0.866089i	$-0.333374\pi$
$127$	−0.00248320	−	0.00143368i	−0.000220349	−	0.000127218i	−0.500110	+	0.865962i	$0.666707\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$		0			0
$130$	−12.3865	+	2.09879i	−1.08637	+	0.184076i
$131$	10.8797	−	6.28138i	0.950562	−	0.548807i	0.0573063	−	0.998357i	$-0.481749\pi$
$131$	10.8797	−	6.28138i	0.950562	−	0.548807i	0.893255	+	0.449550i	$0.148416\pi$
$132$		0			0
$133$	−0.0196739	−	0.0340762i	−0.00170595	−	0.00295479i
$134$	−5.44148	−	9.42492i	−0.470072	−	0.814189i
$135$		0			0
$136$	3.53640	+	0.947575i	0.303244	+	0.0812539i
$137$	−9.94356	+	9.94356i	−0.849535	+	0.849535i	−0.990075	−	0.140540i	$-0.955116\pi$
$137$	−9.94356	+	9.94356i	−0.849535	+	0.849535i	0.140540	+	0.990075i	$0.455116\pi$
$138$		0			0
$139$	−0.156944	+	0.271834i	−0.0133118	+	0.0230567i	−0.872605	−	0.488427i	$-0.837571\pi$
$139$	−0.156944	+	0.271834i	−0.0133118	+	0.0230567i	0.859293	+	0.511484i	$0.170904\pi$
$140$	0.195461			0.0165195
$141$		0			0
$142$	13.3422	+	7.70311i	1.11965	+	0.646430i
$143$	16.9234	−	7.75420i	1.41521	−	0.648438i
$144$		0			0
$145$	3.11417	+	11.6222i	0.258617	+	0.965173i
$146$	7.18339	−	4.14733i	0.594501	−	0.343235i
$147$		0			0
$148$	−7.28892	−	1.95306i	−0.599146	−	0.160541i
$149$	−5.89166	+	1.57867i	−0.482664	+	0.129329i	−0.491943	−	0.870628i	$-0.663713\pi$
$149$	−5.89166	+	1.57867i	−0.482664	+	0.129329i	0.00927899	+	0.999957i	$0.497046\pi$
$150$		0			0
$151$	10.8353	−	2.90331i	0.881766	−	0.236268i	0.210597	−	0.977573i	$-0.432459\pi$
$151$	10.8353	−	2.90331i	0.881766	−	0.236268i	0.671169	+	0.741305i	$0.265793\pi$
$152$	−0.607458	+	0.350716i	−0.0492714	+	0.0284468i
$153$		0			0
$154$	−0.279755	+	0.0749601i	−0.0225433	+	0.00604046i
$155$	−10.3734	+	17.9673i	−0.833215	+	1.44317i
$156$		0			0
$157$	−6.52002	−	11.2930i	−0.520354	−	0.901280i	−0.999720	−	0.0236645i	$-0.992467\pi$
$157$	−6.52002	−	11.2930i	−0.520354	−	0.901280i	0.479366	−	0.877615i	$-0.340867\pi$
$158$	−3.91346	−	3.91346i	−0.311338	−	0.311338i
$159$		0			0
$160$		−	3.48437i		−	0.275464i
$161$	0.229546	+	0.229546i	0.0180908	+	0.0180908i
$162$		0			0
$163$	−1.44937	+	5.40913i	−0.113524	+	0.423676i	−0.999172	−	0.0406802i	$-0.987048\pi$
$163$	−1.44937	+	5.40913i	−0.113524	+	0.423676i	0.885649	+	0.464356i	$0.153714\pi$
$164$	0.780112	+	2.91142i	0.0609165	+	0.227343i
$165$		0			0
$166$		−	15.9702i		−	1.23953i
$167$	−6.55111	+	6.55111i	−0.506940	+	0.506940i	−0.913586	−	0.406646i	$-0.866698\pi$
$167$	−6.55111	+	6.55111i	−0.506940	+	0.506940i	0.406646	+	0.913586i	$0.366698\pi$
$168$		0			0
$169$	2.42841	−	12.7712i	0.186801	−	0.982398i
$170$			12.7568i			0.978402i
$171$		0			0
$172$	2.71489	−	4.70232i	0.207008	−	0.358548i
$173$	9.84649			0.748615			0.374307	−	0.927305i	$-0.377880\pi$
$173$	9.84649			0.748615			0.374307	+	0.927305i	$0.377880\pi$
$174$		0			0
$175$	0.103677	+	0.386927i	0.00783723	+	0.0292490i
$176$	1.33627	+	4.98703i	0.100725	+	0.375912i
$177$		0			0
$178$	−17.0458			−1.27764
$179$	7.69779	−	13.3330i	0.575360	−	0.996553i	−0.420642	−	0.907227i	$-0.638195\pi$
$179$	7.69779	−	13.3330i	0.575360	−	0.996553i	0.996002	−	0.0893264i	$-0.0284714\pi$
$180$		0			0
$181$			17.1903i			1.27774i	0.769314	+	0.638871i	$0.220598\pi$
$181$			17.1903i			1.27774i	−0.769314	+	0.638871i	$0.779402\pi$
$182$	−0.0704457	+	0.189594i	−0.00522178	+	0.0140537i
$183$		0			0
$184$	4.09199	−	4.09199i	0.301665	−	0.301665i
$185$		−	26.2933i		−	1.93312i
$186$		0			0
$187$	−4.89229	−	18.2583i	−0.357760	−	1.33518i
$188$	1.29364	−	4.82793i	0.0943484	−	0.352113i
$189$		0			0
$190$	−1.72821	−	1.72821i	−0.125377	−	0.125377i
$191$			8.54464i			0.618269i	0.951018	+	0.309134i	$0.100039\pi$
$191$			8.54464i			0.618269i	−0.951018	+	0.309134i	$0.899961\pi$
$192$		0			0
$193$	0.431411	+	0.431411i	0.0310537	+	0.0310537i	0.722463	−	0.691409i	$-0.243010\pi$
$193$	0.431411	+	0.431411i	0.0310537	+	0.0310537i	−0.691409	+	0.722463i	$0.743010\pi$
$194$	1.15067	+	1.99301i	0.0826130	+	0.143090i
$195$		0			0
$196$	−3.49843	+	6.05945i	−0.249888	+	0.432818i
$197$	17.3239	−	4.64193i	1.23428	−	0.330724i	0.418035	−	0.908431i	$-0.362719\pi$
$197$	17.3239	−	4.64193i	1.23428	−	0.330724i	0.816244	+	0.577707i	$0.196052\pi$
$198$		0			0
$199$	17.2644	−	9.96763i	1.22384	−	0.706586i	0.258108	−	0.966116i	$-0.416901\pi$
$199$	17.2644	−	9.96763i	1.22384	−	0.706586i	0.965735	+	0.259530i	$0.0835675\pi$
$200$	6.89754	−	1.84819i	0.487729	−	0.130687i
$201$		0			0
$202$	3.40323	−	0.911892i	0.239450	−	0.0641605i
$203$	0.187111	+	0.0501363i	0.0131326	+	0.00351888i
$204$		0			0
$205$	−9.09527	+	5.25116i	−0.635241	+	0.366757i
$206$	1.55615	+	5.80763i	0.108422	+	0.404637i
$207$		0			0
$208$	3.37979	+	1.25580i	0.234346	+	0.0870738i
$209$	3.13628	+	1.81073i	0.216941	+	0.125251i
$210$		0			0
$211$	1.45440			0.100125			0.0500623	−	0.998746i	$-0.484058\pi$
$211$	1.45440			0.100125			0.0500623	+	0.998746i	$0.484058\pi$
$212$	1.94762	−	3.37338i	0.133763	−	0.231685i
$213$		0			0
$214$	11.8845	−	11.8845i	0.812410	−	0.812410i
$215$	18.2747	+	4.89669i	1.24632	+	0.333951i
$216$		0			0
$217$	0.167007	+	0.289264i	0.0113371	+	0.0196365i
$218$	9.94664	+	17.2281i	0.673671	+	1.16683i
$219$		0			0
$220$	−15.5795	+	8.99483i	−1.05037	+	0.606432i
$221$	−12.3739	−	4.59765i	−0.832359	−	0.309272i
$222$		0			0
$223$	4.10342	+	1.09951i	0.274786	+	0.0736286i	0.393580	−	0.919290i	$-0.371236\pi$
$223$	4.10342	+	1.09951i	0.274786	+	0.0736286i	−0.118795	+	0.992919i	$0.537903\pi$
$224$	−0.0485810	−	0.0280482i	−0.00324595	−	0.00187405i
$225$		0			0
$226$	13.8368	−	13.8368i	0.920408	−	0.920408i
$227$	−16.5200	−	16.5200i	−1.09647	−	1.09647i	−0.994820	−	0.101648i	$-0.967588\pi$
$227$	−16.5200	−	16.5200i	−1.09647	−	1.09647i	−0.101648	−	0.994820i	$-0.532412\pi$
$228$		0			0
$229$	−1.59948	+	5.96935i	−0.105697	+	0.394466i	−0.998423	−	0.0561332i	$-0.982123\pi$
$229$	−1.59948	+	5.96935i	−0.105697	+	0.394466i	0.892727	+	0.450599i	$0.148790\pi$
$230$	17.4624	+	10.0819i	1.15144	+	0.664783i
$231$		0			0
$232$	0.893752	−	3.33553i	0.0586777	−	0.218988i
$233$	1.20969			0.0792497			0.0396249	−	0.999215i	$-0.487384\pi$
$233$	1.20969			0.0792497			0.0396249	+	0.999215i	$0.487384\pi$
$234$		0			0
$235$	17.4157			1.13608
$236$	0.272879	−	1.01840i	0.0177629	−	0.0662921i
$237$		0			0
$238$	0.177862	+	0.102689i	0.0115291	+	0.00665632i
$239$	−3.51937	+	13.1345i	−0.227649	+	0.849599i	0.753676	+	0.657246i	$0.228279\pi$
$239$	−3.51937	+	13.1345i	−0.227649	+	0.849599i	−0.981326	+	0.192353i	$0.938388\pi$
$240$		0			0
$241$	5.04100	+	5.04100i	0.324719	+	0.324719i	0.850574	−	0.525855i	$-0.176255\pi$
$241$	5.04100	+	5.04100i	0.324719	+	0.324719i	−0.525855	+	0.850574i	$0.676255\pi$
$242$	11.0706	−	11.0706i	0.711642	−	0.711642i
$243$		0			0
$244$	2.60145	+	1.50195i	0.166541	+	0.0961524i
$245$	−23.5489	−	6.30992i	−1.50449	−	0.403126i
$246$		0			0
$247$	2.29919	−	1.05347i	0.146294	−	0.0670310i
$248$	5.15654	−	2.97713i	0.327441	−	0.189048i
$249$		0			0
$250$	3.72977	+	6.46015i	0.235891	+	0.408575i
$251$	2.50999	+	4.34744i	0.158429	+	0.274408i	0.934302	−	0.356481i	$-0.116024\pi$
$251$	2.50999	+	4.34744i	0.158429	+	0.274408i	−0.775873	+	0.630889i	$0.782690\pi$
$252$		0			0
$253$	−28.8597	−	7.73293i	−1.81439	−	0.486165i
$254$	−0.00202753	+	0.00202753i	−0.000127218	+	0.000127218i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.94110			−0.308218			−0.154109	−	0.988054i	$-0.549251\pi$
$257$	−4.94110			−0.308218			−0.154109	+	0.988054i	$0.549251\pi$
$258$		0			0
$259$	−0.366594	−	0.211653i	−0.0227791	−	0.0131515i
$260$	−1.17860	+	12.5077i	−0.0730934	+	0.775693i
$261$		0			0
$262$	−3.25148	−	12.1347i	−0.200877	−	0.749684i
$263$	−11.1774	+	6.45325i	−0.689226	+	0.397925i	−0.803322	−	0.595545i	$-0.796936\pi$
$263$	−11.1774	+	6.45325i	−0.689226	+	0.397925i	0.114096	+	0.993470i	$0.463603\pi$
$264$		0			0
$265$	13.1100	+	3.51282i	0.805342	+	0.215791i
$266$	−0.0380071	+	0.0101840i	−0.00233037	+	0.000624420i
$267$		0			0
$268$	−10.5121	+	2.81672i	−0.642131	+	0.172058i
$269$	−22.4600	+	12.9673i	−1.36941	+	0.790630i	−0.990853	−	0.134948i	$-0.956913\pi$
$269$	−22.4600	+	12.9673i	−1.36941	+	0.790630i	−0.378558	+	0.925577i	$0.623580\pi$
$270$		0			0
$271$	−15.7870	+	4.23012i	−0.958992	+	0.256961i	−0.704174	−	0.710028i	$-0.748682\pi$
$271$	−15.7870	+	4.23012i	−0.958992	+	0.256961i	−0.254819	+	0.966989i	$0.582016\pi$
$272$	1.83057	−	3.17065i	0.110995	−	0.192249i
$273$		0			0
$274$	7.03116	+	12.1783i	0.424768	+	0.735719i
$275$	−26.0696	−	26.0696i	−1.57205	−	1.57205i
$276$		0			0
$277$			17.0494i			1.02440i	0.858866	+	0.512201i	$0.171170\pi$
$277$			17.0494i			1.02440i	−0.858866	+	0.512201i	$0.828830\pi$
$278$	0.221952	+	0.221952i	0.0133118	+	0.0133118i
$279$		0			0
$280$	0.0505890	−	0.188801i	0.00302327	−	0.0112830i
$281$	1.03182	+	3.85082i	0.0615535	+	0.229721i	0.989849	−	0.142122i	$-0.0453926\pi$
$281$	1.03182	+	3.85082i	0.0615535	+	0.229721i	−0.928296	+	0.371843i	$0.878726\pi$
$282$		0			0
$283$		−	18.1586i		−	1.07941i	−0.841853	−	0.539707i	$-0.818535\pi$
$283$		−	18.1586i		−	1.07941i	0.841853	−	0.539707i	$-0.181465\pi$
$284$	10.8938	−	10.8938i	0.646430	−	0.646430i
$285$		0			0
$286$	−3.10987	−	18.3537i	−0.183891	−	1.08528i
$287$			0.169081i			0.00998056i
$288$		0			0
$289$	1.79800	−	3.11423i	0.105765	−	0.183190i
$290$	12.0322			0.706556
$291$		0			0
$292$	−2.14682	−	8.01203i	−0.125633	−	0.468868i
$293$	5.29384	+	19.7569i	0.309269	+	1.15421i	0.929208	+	0.369558i	$0.120491\pi$
$293$	5.29384	+	19.7569i	0.309269	+	1.15421i	−0.619938	+	0.784651i	$0.712842\pi$
$294$		0			0
$295$	3.67366			0.213888
$296$	−3.77302	+	6.53507i	−0.219303	+	0.379843i
$297$		0			0
$298$			6.09950i			0.353334i
$299$	−16.0729	+	13.3047i	−0.929521	+	0.769429i
$300$		0			0
$301$	0.215378	−	0.215378i	0.0124142	−	0.0124142i
$302$		−	11.2175i		−	0.645497i
$303$		0			0
$304$	0.181544	+	0.677531i	0.0104123	+	0.0388591i
$305$	−2.70898	+	10.1101i	−0.155116	+	0.578900i
$306$		0			0
$307$	−6.72055	−	6.72055i	−0.383562	−	0.383562i	0.488822	−	0.872384i	$-0.337427\pi$
$307$	−6.72055	−	6.72055i	−0.383562	−	0.383562i	−0.872384	+	0.488822i	$0.837427\pi$
$308$			0.289624i			0.0165028i
$309$		0			0
$310$	14.6703	+	14.6703i	0.833215	+	0.833215i
$311$	−1.80968	−	3.13446i	−0.102618	−	0.177739i	0.810145	−	0.586230i	$-0.199388\pi$
$311$	−1.80968	−	3.13446i	−0.102618	−	0.177739i	−0.912762	+	0.408491i	$0.866055\pi$
$312$		0			0
$313$	−9.03947	+	15.6568i	−0.510941	+	0.884975i	0.488979	+	0.872296i	$0.337370\pi$
$313$	−9.03947	+	15.6568i	−0.510941	+	0.884975i	−0.999920	+	0.0126797i	$0.995964\pi$
$314$	−12.5957	+	3.37501i	−0.710817	+	0.190463i
$315$		0			0
$316$	−4.79298	+	2.76723i	−0.269626	+	0.155669i
$317$	10.3161	−	2.76420i	0.579412	−	0.155253i	0.0428025	−	0.999084i	$-0.486371\pi$
$317$	10.3161	−	2.76420i	0.579412	−	0.155253i	0.536610	+	0.843830i	$0.319705\pi$
$318$		0			0
$319$	−17.2212	+	4.61440i	−0.964202	+	0.258357i
$320$	−3.36565	−	0.901822i	−0.188145	−	0.0504134i
$321$		0			0
$322$	0.281135	−	0.162314i	0.0156671	−	0.00904538i
$323$	−0.664659	−	2.48054i	−0.0369826	−	0.138021i
$324$		0			0
$325$	−25.3849	+	4.30125i	−1.40810	+	0.238590i
$326$	4.84969	+	2.79997i	0.268600	+	0.155076i
$327$		0			0
$328$	3.01412			0.166427
$329$	0.140192	−	0.242819i	0.00772903	−	0.0133871i
$330$		0			0
$331$	−2.35256	+	2.35256i	−0.129308	+	0.129308i	−0.768799	−	0.639491i	$-0.779145\pi$
$331$	−2.35256	+	2.35256i	−0.129308	+	0.129308i	0.639491	+	0.768799i	$0.279145\pi$
$332$	−15.4261	−	4.13340i	−0.846615	−	0.226850i
$333$		0			0
$334$	4.63233	+	8.02344i	0.253470	+	0.439023i
$335$	−18.9602	−	32.8399i	−1.03590	−	1.79424i
$336$		0			0
$337$	−2.50494	+	1.44623i	−0.136453	+	0.0787811i	−0.566672	−	0.823943i	$-0.691769\pi$
$337$	−2.50494	+	1.44623i	−0.136453	+	0.0787811i	0.430220	+	0.902724i	$0.358436\pi$
$338$	−11.7075	−	5.65109i	−0.636803	−	0.307379i
$339$		0			0
$340$	12.3221	+	3.30170i	0.668261	+	0.179060i
$341$	−26.6230	−	15.3708i	−1.44172	−	0.832376i
$342$		0			0
$343$	−0.555202	+	0.555202i	−0.0299781	+	0.0299781i
$344$	−3.83943	−	3.83943i	−0.207008	−	0.207008i
$345$		0			0
$346$	2.54846	−	9.51098i	0.137006	−	0.511313i
$347$	−15.5825	−	8.99658i	−0.836514	−	0.482962i	0.0195637	−	0.999809i	$-0.493772\pi$
$347$	−15.5825	−	8.99658i	−0.836514	−	0.482962i	−0.856078	+	0.516847i	$0.827106\pi$
$348$		0			0
$349$	6.70354	−	25.0179i	0.358832	−	1.33918i	−0.516761	−	0.856130i	$-0.672862\pi$
$349$	6.70354	−	25.0179i	0.358832	−	1.33918i	0.875593	−	0.483050i	$-0.160471\pi$
$350$	0.400577			0.0214117
$351$		0			0
$352$	5.16296			0.275187
$353$	−0.768681	+	2.86876i	−0.0409128	+	0.152688i	−0.983360	−	0.181665i	$-0.941851\pi$
$353$	−0.768681	+	2.86876i	−0.0409128	+	0.152688i	0.942448	+	0.334354i	$0.108518\pi$
$354$		0			0
$355$	46.4891	+	26.8405i	2.46739	+	1.42455i
$356$	−4.41179	+	16.4650i	−0.233824	+	0.872645i
$357$		0			0
$358$	−10.8863	−	10.8863i	−0.575360	−	0.575360i
$359$	0.0334095	−	0.0334095i	0.00176329	−	0.00176329i	−0.706225	−	0.707988i	$-0.749603\pi$
$359$	0.0334095	−	0.0334095i	0.00176329	−	0.00176329i	0.707988	+	0.706225i	$0.249603\pi$
$360$		0			0
$361$	−16.0284	−	9.25400i	−0.843600	−	0.487052i
$362$	16.6045	+	4.44917i	0.872714	+	0.233843i
$363$		0			0
$364$	0.164901	+	0.117116i	0.00864318	+	0.00613854i
$365$	25.0296	−	14.4508i	1.31011	−	0.756392i
$366$		0			0
$367$	4.75005	+	8.22733i	0.247951	+	0.429463i	0.962957	−	0.269655i	$-0.0869096\pi$
$367$	4.75005	+	8.22733i	0.247951	+	0.429463i	−0.715006	+	0.699118i	$0.753576\pi$
$368$	−2.89347	−	5.01164i	−0.150833	−	0.261250i
$369$		0			0
$370$	−25.3973	−	6.80519i	−1.32034	−	0.353785i
$371$	0.154510	−	0.154510i	0.00802174	−	0.00802174i
$372$		0			0
$373$	−13.4290	+	23.2597i	−0.695328	+	1.20434i	0.274743	+	0.961518i	$0.411407\pi$
$373$	−13.4290	+	23.2597i	−0.695328	+	1.20434i	−0.970070	+	0.242825i	$0.921926\pi$
$374$	−18.9023			−0.977417
$375$		0			0
$376$	−4.32861	−	2.49912i	−0.223231	−	0.128882i
$377$	−4.33651	+	11.6711i	−0.223341	+	0.601090i
$378$		0			0
$379$	4.93097	+	18.4026i	0.253287	+	0.945279i	0.969036	+	0.246921i	$0.0794189\pi$
$379$	4.93097	+	18.4026i	0.253287	+	0.945279i	−0.715749	+	0.698358i	$0.753914\pi$
$380$	−2.11661	+	1.22203i	−0.108580	+	0.0626886i
$381$		0			0
$382$	8.25349	+	2.21152i	0.422285	+	0.113151i
$383$	9.24644	−	2.47758i	0.472471	−	0.126598i	−0.0147237	−	0.999892i	$-0.504687\pi$
$383$	9.24644	−	2.47758i	0.472471	−	0.126598i	0.487195	+	0.873293i	$0.338020\pi$
$384$		0			0
$385$	−0.974771	+	0.261189i	−0.0496789	+	0.0133114i
$386$	0.528369	−	0.305054i	0.0268933	−	0.0155268i
$387$		0			0
$388$	2.22292	−	0.595628i	0.112851	−	0.0302384i
$389$	4.60612	−	7.97804i	0.233540	−	0.404502i	−0.725308	−	0.688425i	$-0.758302\pi$
$389$	4.60612	−	7.97804i	0.233540	−	0.404502i	0.958847	+	0.283922i	$0.0916358\pi$
$390$		0			0
$391$	10.5934	+	18.3484i	0.535733	+	0.927916i
$392$	4.94752	+	4.94752i	0.249888	+	0.249888i
$393$		0			0
$394$		−	17.9351i		−	0.903555i
$395$	−13.6359	−	13.6359i	−0.686098	−	0.686098i
$396$		0			0
$397$	7.23488	−	27.0009i	0.363108	−	1.35514i	−0.506859	−	0.862029i	$-0.669194\pi$
$397$	7.23488	−	27.0009i	0.363108	−	1.35514i	0.869967	−	0.493110i	$-0.164140\pi$
$398$	−5.15962	−	19.2560i	−0.258629	−	0.965215i
$399$		0			0
$400$		−	7.14085i		−	0.357043i
$401$	6.28860	−	6.28860i	0.314038	−	0.314038i	−0.532434	−	0.846472i	$-0.678722\pi$
$401$	6.28860	−	6.28860i	0.314038	−	0.314038i	0.846472	+	0.532434i	$0.178722\pi$
$402$		0			0
$403$	−19.5172	+	8.94265i	−0.972222	+	0.445465i
$404$		−	3.52328i		−	0.175290i
$405$		0			0
$406$	0.0968559	−	0.167759i	0.00480688	−	0.00832576i
$407$	38.9599			1.93117
$408$		0			0
$409$	−9.02175	−	33.6696i	−0.446097	−	1.66486i	−0.713025	−	0.701139i	$-0.752675\pi$
$409$	−9.02175	−	33.6696i	−0.446097	−	1.66486i	0.266928	−	0.963716i	$-0.413991\pi$
$410$	2.71820	+	10.1445i	0.134242	+	0.500999i
$411$		0			0
$412$	6.01250			0.296215
$413$	0.0295719	−	0.0512200i	0.00145514	−	0.00252037i
$414$		0			0
$415$		−	55.6462i		−	2.73157i
$416$	2.08776	−	2.93960i	0.102361	−	0.144126i
$417$		0			0
$418$	2.56076	−	2.56076i	0.125251	−	0.125251i
$419$			17.2114i			0.840832i	0.907331	+	0.420416i	$0.138116\pi$
$419$			17.2114i			0.840832i	−0.907331	+	0.420416i	$0.861884\pi$
$420$		0			0
$421$	−0.986098	−	3.68017i	−0.0480595	−	0.179360i	0.937724	−	0.347381i	$-0.112929\pi$
$421$	−0.986098	−	3.68017i	−0.0480595	−	0.179360i	−0.985783	+	0.168021i	$0.946262\pi$
$422$	0.376425	−	1.40484i	0.0183241	−	0.0683864i
$423$		0			0
$424$	−2.75436	−	2.75436i	−0.133763	−	0.133763i
$425$			26.1437i			1.26816i
$426$		0			0
$427$	0.119153	+	0.119153i	0.00576623	+	0.00576623i
$428$	−8.40363	−	14.5555i	−0.406205	−	0.703568i
$429$		0			0
$430$	9.45967	−	16.3846i	0.456186	−	0.790137i
$431$	−20.9081	+	5.60231i	−1.00711	+	0.269854i	−0.724420	−	0.689358i	$-0.757893\pi$
$431$	−20.9081	+	5.60231i	−1.00711	+	0.269854i	−0.282687	+	0.959212i	$0.591226\pi$
$432$		0			0
$433$	15.1421	−	8.74227i	0.727681	−	0.420127i	−0.0898923	−	0.995951i	$-0.528652\pi$
$433$	15.1421	−	8.74227i	0.727681	−	0.420127i	0.817573	+	0.575825i	$0.195319\pi$
$434$	0.322632	−	0.0864490i	0.0154868	−	0.00414968i
$435$		0			0
$436$	19.2154	−	5.14876i	0.920252	−	0.246581i
$437$	−3.92084	−	1.05058i	−0.187559	−	0.0502563i
$438$		0			0
$439$	5.45595	−	3.15000i	0.260398	−	0.150341i	−0.364118	−	0.931353i	$-0.618629\pi$
$439$	5.45595	−	3.15000i	0.260398	−	0.150341i	0.624516	+	0.781012i	$0.285296\pi$
$440$	4.65607	+	17.3767i	0.221969	+	0.828401i
$441$		0			0
$442$	−7.64360	+	10.7623i	−0.363569	+	0.511911i
$443$	13.9547	+	8.05675i	0.663007	+	0.382788i	0.793422	−	0.608672i	$-0.208297\pi$
$443$	13.9547	+	8.05675i	0.663007	+	0.382788i	−0.130414	+	0.991460i	$0.541631\pi$
$444$		0			0
$445$	−59.3941			−2.81555
$446$	2.12409	−	3.67903i	0.100579	−	0.174207i
$447$		0			0
$448$	−0.0396662	+	0.0396662i	−0.00187405	+	0.00187405i
$449$	−18.3173	−	4.90811i	−0.864447	−	0.231628i	−0.200762	−	0.979640i	$-0.564342\pi$
$449$	−18.3173	−	4.90811i	−0.864447	−	0.231628i	−0.663685	+	0.748012i	$0.731009\pi$
$450$		0			0
$451$	−7.78089	−	13.4769i	−0.366388	−	0.634602i
$452$	−9.78407	−	16.9465i	−0.460204	−	0.797097i
$453$		0			0
$454$	−20.2327	+	11.6814i	−0.949570	+	0.548234i
$455$	−0.245459	+	0.660617i	−0.0115073	+	0.0309702i
$456$		0			0
$457$	16.3542	+	4.38210i	0.765017	+	0.204986i	0.620169	−	0.784468i	$-0.287064\pi$
$457$	16.3542	+	4.38210i	0.765017	+	0.204986i	0.144848	+	0.989454i	$0.453731\pi$
$458$	5.35197	+	3.08996i	0.250081	+	0.144384i
$459$		0			0
$460$	14.2580	−	14.2580i	0.664783	−	0.664783i
$461$	−9.15894	−	9.15894i	−0.426574	−	0.426574i	0.460885	−	0.887460i	$-0.347532\pi$
$461$	−9.15894	−	9.15894i	−0.426574	−	0.426574i	−0.887460	+	0.460885i	$0.847532\pi$
$462$		0			0
$463$	−4.56925	+	17.0527i	−0.212351	+	0.792505i	0.774731	+	0.632291i	$0.217885\pi$
$463$	−4.56925	+	17.0527i	−0.212351	+	0.792505i	−0.987082	+	0.160214i	$0.948782\pi$
$464$	−2.99055	−	1.72660i	−0.138833	−	0.0801552i
$465$		0			0
$466$	0.313092	−	1.16848i	0.0145037	−	0.0541286i
$467$	21.1177			0.977210			0.488605	−	0.872505i	$-0.337506\pi$
$467$	21.1177			0.977210			0.488605	+	0.872505i	$0.337506\pi$
$468$		0			0
$469$	−0.610496			−0.0281901
$470$	4.50753	−	16.8223i	0.207917	−	0.775956i
$471$		0			0
$472$	−0.913071	−	0.527162i	−0.0420275	−	0.0242646i
$473$	−7.25565	+	27.0784i	−0.333615	+	1.24507i
$474$		0			0
$475$	−3.54177	−	3.54177i	−0.162508	−	0.162508i
$476$	0.145224	−	0.145224i	0.00665632	−	0.00665632i
$477$		0			0
$478$	11.7761	+	6.79891i	0.538624	+	0.310975i
$479$	14.8553	+	3.98046i	0.678755	+	0.181872i	0.581695	−	0.813407i	$-0.302390\pi$
$479$	14.8553	+	3.98046i	0.678755	+	0.181872i	0.0970596	+	0.995279i	$0.469056\pi$
$480$		0			0
$481$	15.7543	−	22.1824i	0.718336	−	1.01143i
$482$	6.17394	−	3.56453i	0.281215	−	0.162360i
$483$		0			0
$484$	−7.82807	−	13.5586i	−0.355821	−	0.616300i
$485$	4.00935	+	6.94439i	0.182055	+	0.315329i
$486$		0			0
$487$	−15.1707	−	4.06498i	−0.687450	−	0.184202i	−0.101848	−	0.994800i	$-0.532475\pi$
$487$	−15.1707	−	4.06498i	−0.687450	−	0.184202i	−0.585603	+	0.810598i	$0.699142\pi$
$488$	2.12408	−	2.12408i	0.0961524	−	0.0961524i
$489$		0			0
$490$	−12.1898	+	21.1134i	−0.550680	+	0.953806i
$491$	6.39468			0.288588			0.144294	−	0.989535i	$-0.453909\pi$
$491$	6.39468			0.288588			0.144294	+	0.989535i	$0.453909\pi$
$492$		0			0
$493$	10.9489	+	6.32132i	0.493112	+	0.284698i
$494$	−0.422503	−	2.49351i	−0.0190093	−	0.112188i
$495$		0			0
$496$	−1.54108	−	5.75138i	−0.0691964	−	0.258245i
$497$	0.748449	−	0.432117i	0.0335725	−	0.0193831i
$498$		0			0
$499$	7.39299	+	1.98095i	0.330956	+	0.0886794i	0.420471	−	0.907306i	$-0.361865\pi$
$499$	7.39299	+	1.98095i	0.330956	+	0.0886794i	−0.0895148	+	0.995985i	$0.528532\pi$
$500$	7.20536	−	1.93067i	0.322233	−	0.0863422i
$501$		0			0
$502$	4.84894	−	1.29927i	0.216419	−	0.0579892i
$503$	6.97222	−	4.02541i	0.310876	−	0.179484i	−0.336442	−	0.941704i	$-0.609224\pi$
$503$	6.97222	−	4.02541i	0.310876	−	0.179484i	0.647318	+	0.762220i	$0.275890\pi$
$504$		0			0
$505$	11.8581	−	3.17737i	0.527679	−	0.141391i
$506$	−14.9389	+	25.8749i	−0.664114	+	1.15028i
$507$		0			0
$508$	0.00143368	+	0.00248320i	6.36092e−5	+	0.000110174i
$509$	−22.8937	−	22.8937i	−1.01474	−	1.01474i	−0.999890	−	0.0148538i	$-0.995272\pi$
$509$	−22.8937	−	22.8937i	−1.01474	−	1.01474i	−0.0148538	−	0.999890i	$-0.504728\pi$
$510$		0			0
$511$		−	0.465301i		−	0.0205837i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−1.27885	+	4.77274i	−0.0564077	+	0.210517i
$515$	5.42221	+	20.2359i	0.238931	+	0.891702i
$516$		0			0
$517$			25.8057i			1.13493i
$518$	−0.299323	+	0.299323i	−0.0131515	+	0.0131515i
$519$		0			0
$520$	11.7764	+	4.37566i	0.516431	+	0.191885i
$521$		−	3.95332i		−	0.173198i	−0.996243	−	0.0865990i	$-0.972400\pi$
$521$		−	3.95332i		−	0.173198i	0.996243	−	0.0865990i	$-0.0275999\pi$
$522$		0			0
$523$	−19.7397	+	34.1901i	−0.863155	+	1.49503i	0.00571276	+	0.999984i	$0.498182\pi$
$523$	−19.7397	+	34.1901i	−0.863155	+	1.49503i	−0.868868	+	0.495044i	$0.835152\pi$
$524$	−12.5628			−0.548807
$525$		0			0
$526$	3.34045	+	12.4667i	0.145650	+	0.543575i
$527$	5.64211	+	21.0566i	0.245774	+	0.917242i
$528$		0			0
$529$	10.4887			0.456031
$530$	6.78625	−	11.7541i	0.294776	−	0.510567i
$531$		0			0
$532$			0.0393479i			0.00170595i
$533$	−10.8196	−	1.01953i	−0.468650	−	0.0441608i
$534$		0			0
$535$	41.4101	−	41.4101i	1.79032	−	1.79032i
$536$			10.8830i			0.470072i
$537$		0			0
$538$	6.71236	+	25.0509i	0.289391	+	1.08002i
$539$	9.34970	−	34.8935i	0.402720	−	1.50297i
$540$		0			0
$541$	8.65093	+	8.65093i	0.371933	+	0.371933i	0.868181	−	0.496248i	$-0.165289\pi$
$541$	8.65093	+	8.65093i	0.371933	+	0.371933i	−0.496248	+	0.868181i	$0.665289\pi$
$542$			16.3439i			0.702031i
$543$		0			0
$544$	−2.58882	−	2.58882i	−0.110995	−	0.110995i
$545$	34.6578	+	60.0291i	1.48458	+	2.57136i
$546$		0			0
$547$	12.5519	−	21.7406i	0.536681	−	0.929559i	−0.462399	−	0.886672i	$-0.653011\pi$
$547$	12.5519	−	21.7406i	0.536681	−	0.929559i	0.999080	−	0.0428870i	$-0.0136556\pi$
$548$	13.5832	−	3.63959i	0.580243	−	0.155476i
$549$		0			0
$550$	−31.9286	+	18.4340i	−1.36144	+	0.786027i
$551$	−2.33965	+	0.626906i	−0.0996723	+	0.0267071i
$552$		0			0
$553$	−0.299885	+	0.0803539i	−0.0127524	+	0.00341700i
$554$	16.4685	+	4.41272i	0.699680	+	0.187479i
$555$		0			0
$556$	0.271834	−	0.156944i	0.0115283	−	0.00665589i
$557$	−2.76078	−	10.3034i	−0.116978	−	0.436567i	0.882449	−	0.470407i	$-0.155893\pi$
$557$	−2.76078	−	10.3034i	−0.116978	−	0.436567i	−0.999427	+	0.0338399i	$0.989226\pi$
$558$		0			0
$559$	12.4835	+	15.0809i	0.527996	+	0.637854i
$560$	−0.169274	−	0.0977305i	−0.00715314	−	0.00412987i
$561$		0			0
$562$	3.98666			0.168167
$563$	14.9323	−	25.8635i	0.629322	−	1.09002i	−0.358366	−	0.933581i	$-0.616666\pi$
$563$	14.9323	−	25.8635i	0.629322	−	1.09002i	0.987688	−	0.156437i	$-0.0500008\pi$
$564$		0			0
$565$	48.2124	−	48.2124i	2.02831	−	2.02831i
$566$	−17.5398	−	4.69978i	−0.737254	−	0.197547i
$567$		0			0
$568$	−7.70311	−	13.3422i	−0.323215	−	0.559825i
$569$	−22.5294	−	39.0221i	−0.944482	−	1.63589i	−0.756785	−	0.653664i	$-0.773231\pi$
$569$	−22.5294	−	39.0221i	−0.944482	−	1.63589i	−0.187697	−	0.982227i	$-0.560102\pi$
$570$		0			0
$571$	−23.2043	+	13.3970i	−0.971071	+	0.560648i	−0.899562	−	0.436792i	$-0.856115\pi$
$571$	−23.2043	+	13.3970i	−0.971071	+	0.560648i	−0.0715081	+	0.997440i	$0.522781\pi$
$572$	−18.5332	−	1.74638i	−0.774912	−	0.0730198i
$573$		0			0
$574$	0.163320	+	0.0437615i	0.00681685	+	0.00182657i
$575$	35.7874	+	20.6619i	1.49244	+	0.861659i
$576$		0			0
$577$	−20.9051	+	20.9051i	−0.870292	+	0.870292i	−0.992504	−	0.122212i	$-0.961001\pi$
$577$	−20.9051	+	20.9051i	−0.870292	+	0.870292i	0.122212	+	0.992504i	$0.461001\pi$
$578$	−2.54276	−	2.54276i	−0.105765	−	0.105765i
$579$		0			0
$580$	3.11417	−	11.6222i	0.129309	−	0.482587i
$581$	−0.775849	−	0.447937i	−0.0321876	−	0.0185835i
$582$		0			0
$583$	−5.20511	+	19.4257i	−0.215574	+	0.804532i
$584$	−8.29466			−0.343235
$585$		0			0
$586$	20.4538			0.844940
$587$	−6.48426	+	24.1996i	−0.267634	+	0.998824i	0.692984	+	0.720953i	$0.256296\pi$
$587$	−6.48426	+	24.1996i	−0.267634	+	0.998824i	−0.960618	+	0.277871i	$0.910371\pi$
$588$		0			0
$589$	−3.61697	−	2.08826i	−0.149035	−	0.0860451i
$590$	0.950812	−	3.54848i	0.0391443	−	0.146089i
$591$		0			0
$592$	5.33586	+	5.33586i	0.219303	+	0.219303i
$593$	−13.5809	+	13.5809i	−0.557700	+	0.557700i	−0.928652	−	0.370952i	$-0.879031\pi$
$593$	−13.5809	+	13.5809i	−0.557700	+	0.557700i	0.370952	+	0.928652i	$0.379031\pi$
$594$		0			0
$595$	0.619738	+	0.357806i	0.0254068	+	0.0146686i
$596$	5.89166	+	1.57867i	0.241332	+	0.0646647i
$597$		0			0
$598$	8.69135	+	18.9688i	0.355416	+	0.775690i
$599$	−12.8779	+	7.43506i	−0.526176	+	0.303788i	−0.739458	−	0.673203i	$-0.764918\pi$
$599$	−12.8779	+	7.43506i	−0.526176	+	0.303788i	0.213282	+	0.976991i	$0.431585\pi$
$600$		0			0
$601$	11.5545	+	20.0130i	0.471318	+	0.816346i	0.999462	−	0.0328085i	$-0.0104452\pi$
$601$	11.5545	+	20.0130i	0.471318	+	0.816346i	−0.528144	+	0.849155i	$0.677112\pi$
$602$	−0.152295	−	0.263783i	−0.00620710	−	0.0107510i
$603$		0			0
$604$	−10.8353	−	2.90331i	−0.440883	−	0.118134i
$605$	38.5740	−	38.5740i	1.56825	−	1.56825i
$606$		0			0
$607$	−14.9349	+	25.8680i	−0.606188	+	1.04995i	0.385675	+	0.922635i	$0.373969\pi$
$607$	−14.9349	+	25.8680i	−0.606188	+	1.04995i	−0.991863	+	0.127313i	$0.959365\pi$
$608$	0.701432			0.0284468
$609$		0			0
$610$	9.06443	+	5.23335i	0.367008	+	0.211892i
$611$	14.6928	+	10.4351i	0.594409	+	0.422160i
$612$		0			0
$613$	−8.88349	−	33.1536i	−0.358801	−	1.33906i	−0.875633	−	0.482977i	$-0.839556\pi$
$613$	−8.88349	−	33.1536i	−0.358801	−	1.33906i	0.516832	−	0.856087i	$-0.327111\pi$
$614$	−8.23095	+	4.75214i	−0.332174	+	0.191781i
$615$		0			0
$616$	0.279755	+	0.0749601i	0.0112716	+	0.00302023i
$617$	−2.65490	+	0.711378i	−0.106882	+	0.0286390i	−0.311864	−	0.950127i	$-0.600953\pi$
$617$	−2.65490	+	0.711378i	−0.106882	+	0.0286390i	0.204982	+	0.978766i	$0.434287\pi$
$618$		0			0
$619$	−17.6710	+	4.73494i	−0.710259	+	0.190313i	−0.595821	−	0.803117i	$-0.703173\pi$
$619$	−17.6710	+	4.73494i	−0.710259	+	0.190313i	−0.114438	+	0.993430i	$0.536507\pi$
$620$	17.9673	−	10.3734i	0.721585	−	0.416607i
$621$		0			0
$622$	−3.49603	+	0.936759i	−0.140178	+	0.0375606i
$623$	−0.478106	+	0.828104i	−0.0191549	+	0.0331773i
$624$		0			0
$625$	−4.85624	−	8.41125i	−0.194250	−	0.336450i
$626$	12.7837	+	12.7837i	0.510941	+	0.510941i
$627$		0			0
$628$			13.0400i			0.520354i
$629$	−19.5354	−	19.5354i	−0.778927	−	0.778927i
$630$		0			0
$631$	−8.90171	+	33.2216i	−0.354371	+	1.32253i	0.526902	+	0.849926i	$0.323353\pi$
$631$	−8.90171	+	33.2216i	−0.354371	+	1.32253i	−0.881274	+	0.472606i	$0.843313\pi$
$632$	1.43242	+	5.34588i	0.0569788	+	0.212648i
$633$		0			0
$634$		−	10.6801i		−	0.424159i
$635$	−0.00706466	+	0.00706466i	−0.000280353	+	0.000280353i
$636$		0			0
$637$	−16.0864	−	19.4334i	−0.637365	−	0.769979i
$638$			17.8287i			0.705845i
$639$		0			0
$640$	−1.74219	+	3.01756i	−0.0688660	+	0.119279i
$641$	13.5556			0.535415			0.267707	−	0.963500i	$-0.413734\pi$
$641$	13.5556			0.535415			0.267707	+	0.963500i	$0.413734\pi$
$642$		0			0
$643$	10.3126	+	38.4870i	0.406688	+	1.51778i	0.800922	+	0.598769i	$0.204343\pi$
$643$	10.3126	+	38.4870i	0.406688	+	1.51778i	−0.394234	+	0.919010i	$0.628990\pi$
$644$	−0.0840197	−	0.313566i	−0.00331084	−	0.0123562i
$645$		0			0
$646$	−2.56805			−0.101038
$647$	−11.0797	+	19.1906i	−0.435588	+	0.754460i	−0.997343	−	0.0728432i	$-0.976793\pi$
$647$	−11.0797	+	19.1906i	−0.435588	+	0.754460i	0.561756	+	0.827303i	$0.310126\pi$
$648$		0			0
$649$			5.44343i			0.213673i
$650$	−2.41541	+	25.6332i	−0.0947400	+	1.00542i
$651$		0			0
$652$	3.95976	−	3.95976i	0.155076	−	0.155076i
$653$		−	34.0991i		−	1.33440i	−0.744879	−	0.667200i	$-0.767493\pi$
$653$		−	34.0991i		−	1.33440i	0.744879	−	0.667200i	$-0.232507\pi$
$654$		0			0
$655$	−11.3294	−	42.2818i	−0.442675	−	1.65209i
$656$	0.780112	−	2.91142i	0.0304582	−	0.113672i
$657$		0			0
$658$	−0.198261	−	0.198261i	−0.00772903	−	0.00772903i
$659$		−	5.70080i		−	0.222072i	−0.993816	−	0.111036i	$-0.964583\pi$
$659$		−	5.70080i		−	0.222072i	0.993816	−	0.111036i	$-0.0354168\pi$
$660$		0			0
$661$	6.48873	+	6.48873i	0.252382	+	0.252382i	0.821947	−	0.569564i	$-0.192888\pi$
$661$	6.48873	+	6.48873i	0.252382	+	0.252382i	−0.569564	+	0.821947i	$0.692888\pi$
$662$	1.66351	+	2.88129i	0.0646542	+	0.111984i
$663$		0			0
$664$	−7.98511	+	13.8306i	−0.309882	+	0.536732i
$665$	−0.132431	+	0.0354848i	−0.00513545	+	0.00137604i
$666$		0			0
$667$	17.3062	−	9.99171i	0.670097	−	0.386881i
$668$	8.94898	−	2.39787i	0.346246	−	0.0927765i
$669$		0			0
$670$	−36.6282	+	9.81450i	−1.41507	+	0.379167i
$671$	−14.9805	−	4.01402i	−0.578318	−	0.154960i
$672$		0			0
$673$	26.7361	−	15.4361i	1.03060	−	0.595018i	0.113444	−	0.993544i	$-0.463812\pi$
$673$	26.7361	−	15.4361i	1.03060	−	0.595018i	0.917157	+	0.398527i	$0.130478\pi$
$674$	0.748623	+	2.79390i	0.0288359	+	0.107617i
$675$		0			0
$676$	−8.48865	+	9.84595i	−0.326487	+	0.378691i
$677$	3.80387	+	2.19617i	0.146195	+	0.0844055i	0.571313	−	0.820732i	$-0.306434\pi$
$677$	3.80387	+	2.19617i	0.146195	+	0.0844055i	−0.425118	+	0.905138i	$0.639768\pi$
$678$		0			0
$679$	0.129097			0.00495427
$680$	6.37840	−	11.0477i	0.244601	−	0.423661i
$681$		0			0
$682$	−21.7376	+	21.7376i	−0.832376	+	0.832376i
$683$	11.2191	+	3.00615i	0.429287	+	0.115027i	0.466991	−	0.884262i	$-0.345338\pi$
$683$	11.2191	+	3.00615i	0.429287	+	0.115027i	−0.0377045	+	0.999289i	$0.512005\pi$
$684$		0			0
$685$	24.4992	+	42.4338i	0.936065	+	1.62131i
$686$	0.392587	+	0.679981i	0.0149890	+	0.0259618i
$687$		0			0
$688$	−4.70232	+	2.71489i	−0.179274	+	0.103504i
$689$	8.95551	+	10.8188i	0.341178	+	0.412165i
$690$		0			0
$691$	−10.2662	−	2.75083i	−0.390545	−	0.104646i	0.0582023	−	0.998305i	$-0.481463\pi$
$691$	−10.2662	−	2.75083i	−0.390545	−	0.104646i	−0.448748	+	0.893658i	$0.648130\pi$
$692$	−8.52731	−	4.92325i	−0.324160	−	0.187154i
$693$		0			0
$694$	−12.7231	+	12.7231i	−0.482962	+	0.482962i
$695$	0.773362	+	0.773362i	0.0293353	+	0.0293353i
$696$		0			0
$697$	−2.85610	+	10.6591i	−0.108183	+	0.403743i
$698$	−22.4305	−	12.9502i	−0.849006	−	0.490174i
$699$		0			0
$700$	0.103677	−	0.386927i	0.00391862	−	0.0146245i
$701$	10.2778			0.388185			0.194093	−	0.980983i	$-0.437824\pi$
$701$	10.2778			0.388185			0.194093	+	0.980983i	$0.437824\pi$
$702$		0			0
$703$	5.29304			0.199631
$704$	1.33627	−	4.98703i	0.0503626	−	0.187956i
$705$		0			0
$706$	2.57206	+	1.48498i	0.0968006	+	0.0558879i
$707$	0.0511539	−	0.190909i	0.00192384	−	0.00717988i
$708$		0			0
$709$	−25.6372	−	25.6372i	−0.962826	−	0.962826i	0.0365077	−	0.999333i	$-0.488377\pi$
$709$	−25.6372	−	25.6372i	−0.962826	−	0.962826i	−0.999333	+	0.0365077i	$0.988377\pi$
$710$	37.9582	−	37.9582i	1.42455	−	1.42455i
$711$		0			0
$712$	14.7621	+	8.52292i	0.553235	+	0.319410i
$713$	33.2829	+	8.91813i	1.24645	+	0.333986i
$714$		0			0
$715$	−10.8360	−	63.9511i	−0.405242	−	2.39164i
$716$	−13.3330	+	7.69779i	−0.498276	+	0.287680i
$717$		0			0
$718$	−0.0236241	−	0.0409182i	−0.000881644	−	0.00152705i
$719$	0.703567	+	1.21861i	0.0262386	+	0.0454466i	0.878847	−	0.477105i	$-0.158314\pi$
$719$	0.703567	+	1.21861i	0.0262386	+	0.0454466i	−0.852608	+	0.522551i	$0.824980\pi$
$720$		0			0
$721$	0.325787	+	0.0872945i	0.0121330	+	0.00325102i
$722$	−13.0871	+	13.0871i	−0.487052	+	0.487052i
$723$		0			0
$724$	8.59513	−	14.8872i	0.319436	−	0.553279i
$725$	24.6587			0.915803
$726$		0			0
$727$	32.7077	+	18.8838i	1.21306	+	0.700361i	0.963425	−	0.267978i	$-0.0863555\pi$
$727$	32.7077	+	18.8838i	1.21306	+	0.700361i	0.249636	+	0.968340i	$0.419689\pi$
$728$	0.155805	−	0.128971i	0.00577451	−	0.00477997i
$729$		0			0
$730$	−7.48031	−	27.9169i	−0.276859	−	1.03325i
$731$	17.2159	−	9.93959i	0.636752	−	0.367629i
$732$		0			0
$733$	32.1810	+	8.62288i	1.18863	+	0.318493i	0.798346	−	0.602199i	$-0.205709\pi$
$733$	32.1810	+	8.62288i	1.18863	+	0.318493i	0.390288	+	0.920693i	$0.372375\pi$
$734$	9.17639	−	2.45881i	0.338707	−	0.0907562i
$735$		0			0
$736$	−5.58976	+	1.49777i	−0.206041	+	0.0552086i
$737$	48.6605	−	28.0941i	1.79243	−	1.03486i
$738$		0			0
$739$	−23.0630	+	6.17972i	−0.848388	+	0.227325i	−0.656719	−	0.754135i	$-0.728056\pi$
$739$	−23.0630	+	6.17972i	−0.848388	+	0.227325i	−0.191668	+	0.981460i	$0.561390\pi$
$740$	−13.1466	+	22.7706i	−0.483280	+	0.837065i
$741$		0			0
$742$	−0.109255	−	0.189235i	−0.00401087	−	0.00694703i
$743$	−8.52596	−	8.52596i	−0.312787	−	0.312787i	0.533201	−	0.845988i	$-0.320989\pi$
$743$	−8.52596	−	8.52596i	−0.312787	−	0.312787i	−0.845988	+	0.533201i	$0.820989\pi$
$744$		0			0
$745$			21.2529i			0.778647i
$746$	18.9915	+	18.9915i	0.695328	+	0.695328i
$747$		0			0
$748$	−4.89229	+	18.2583i	−0.178880	+	0.667588i
$749$	−0.244022	−	0.910702i	−0.00891637	−	0.0332763i
$750$		0			0
$751$			30.0994i			1.09834i	0.835710	+	0.549171i	$0.185056\pi$
$751$			30.0994i			1.09834i	−0.835710	+	0.549171i	$0.814944\pi$
$752$	−3.53429	+	3.53429i	−0.128882	+	0.128882i
$753$		0			0
$754$	10.1510	+	7.20944i	0.369678	+	0.262552i
$755$		−	39.0861i		−	1.42249i
$756$		0			0
$757$	25.3503	−	43.9080i	0.921371	−	1.59586i	0.124076	−	0.992273i	$-0.460403\pi$
$757$	25.3503	−	43.9080i	0.921371	−	1.59586i	0.797296	−	0.603589i	$-0.206263\pi$
$758$	19.0518			0.691992
$759$		0			0
$760$	0.632567	+	2.36077i	0.0229456	+	0.0856342i
$761$	3.85658	+	14.3930i	0.139801	+	0.521744i	0.999932	+	0.0116709i	$0.00371505\pi$
$761$	3.85658	+	14.3930i	0.139801	+	0.521744i	−0.860131	+	0.510073i	$0.829618\pi$
$762$		0			0
$763$	1.11594			0.0403998
$764$	4.27232	−	7.39988i	0.154567	−	0.267718i
$765$		0			0
$766$		−	9.57262i		−	0.345873i
$767$	3.09929	+	2.20117i	0.111909	+	0.0794798i
$768$		0			0
$769$	−18.7823	+	18.7823i	−0.677307	+	0.677307i	−0.959390	−	0.282083i	$-0.908975\pi$
$769$	−18.7823	+	18.7823i	−0.677307	+	0.677307i	0.282083	+	0.959390i	$0.408975\pi$
$770$			1.00916i			0.0363675i
$771$		0			0
$772$	−0.157908	−	0.589319i	−0.00568322	−	0.0212101i
$773$	−11.3267	+	42.2718i	−0.407393	+	1.52041i	0.392206	+	0.919877i	$0.371712\pi$
$773$	−11.3267	+	42.2718i	−0.407393	+	1.52041i	−0.799599	+	0.600534i	$0.794955\pi$
$774$		0			0
$775$	30.0651	+	30.0651i	1.07997	+	1.07997i
$776$		−	2.30133i		−	0.0826130i
$777$		0			0
$778$	−6.51404	−	6.51404i	−0.233540	−	0.233540i
$779$	−1.05710	−	1.83095i	−0.0378745	−	0.0656006i
$780$		0			0
$781$	−39.7708	+	68.8851i	−1.42311	+	2.46490i
$782$	20.4649	−	5.48356i	0.731824	−	0.196092i
$783$		0			0
$784$	6.05945	−	3.49843i	0.216409	−	0.124944i
$785$	−43.8881	+	11.7598i	−1.56643	+	0.419725i
$786$		0			0
$787$	14.8005	−	3.96579i	0.527582	−	0.141365i	0.0148105	−	0.999890i	$-0.495285\pi$
$787$	14.8005	−	3.96579i	0.527582	−	0.141365i	0.512771	+	0.858525i	$0.328619\pi$
$788$	−17.3239	−	4.64193i	−0.617139	−	0.165362i
$789$		0			0
$790$	−16.7005	+	9.64206i	−0.594179	+	0.343049i
$791$	−0.284107	−	1.06030i	−0.0101017	−	0.0376999i
$792$		0			0
$793$	−8.34317	+	6.90622i	−0.296274	+	0.245247i
$794$	−24.2084	−	13.9767i	−0.859123	−	0.496015i
$795$		0			0
$796$	−19.9353			−0.706586
$797$	−14.8679	+	25.7520i	−0.526650	+	0.912184i	0.472868	+	0.881133i	$0.343219\pi$
$797$	−14.8679	+	25.7520i	−0.526650	+	0.912184i	−0.999518	+	0.0310506i	$0.990115\pi$
$798$		0			0
$799$	12.9396	−	12.9396i	0.457769	−	0.457769i
$800$	−6.89754	−	1.84819i	−0.243865	−	0.0653433i
$801$		0			0
$802$	−4.44671	−	7.70193i	−0.157019	−	0.271965i
$803$	21.4125	+	37.0875i	0.755630	+	1.30879i
$804$		0			0
$805$	0.979580	−	0.565561i	0.0345257	−	0.0199334i
$806$	3.58651	+	21.1667i	0.126330	+	0.745565i
$807$		0			0
$808$	−3.40323	−	0.911892i	−0.119725	−	0.0320803i
$809$	25.6350	+	14.8004i	0.901280	+	0.520354i	0.877615	−	0.479366i	$-0.159133\pi$
$809$	25.6350	+	14.8004i	0.901280	+	0.520354i	0.0236649	+	0.999720i	$0.492467\pi$
$810$		0			0
$811$	−24.2773	+	24.2773i	−0.852492	+	0.852492i	−0.990440	−	0.137948i	$-0.955949\pi$
$811$	−24.2773	+	24.2773i	−0.852492	+	0.852492i	0.137948	+	0.990440i	$0.455949\pi$
$812$	−0.136975	−	0.136975i	−0.00480688	−	0.00480688i
$813$		0			0
$814$	10.0836	−	37.6324i	0.353429	−	1.31902i
$815$	16.8981	+	9.75615i	0.591916	+	0.341743i
$816$		0			0
$817$	−0.985742	+	3.67884i	−0.0344868	+	0.128706i
$818$	−34.8574			−1.21876
$819$		0			0
$820$	10.5023			0.366757
$821$	10.6905	−	39.8975i	0.373101	−	1.39243i	−0.482999	−	0.875621i	$-0.660453\pi$
$821$	10.6905	−	39.8975i	0.373101	−	1.39243i	0.856100	−	0.516810i	$-0.172881\pi$
$822$		0			0
$823$	−10.9875	−	6.34364i	−0.383001	−	0.221126i	0.296122	−	0.955150i	$-0.404306\pi$
$823$	−10.9875	−	6.34364i	−0.383001	−	0.221126i	−0.679123	+	0.734025i	$0.737640\pi$
$824$	1.55615	−	5.80763i	0.0542110	−	0.202318i
$825$		0			0
$826$	−0.0418210	−	0.0418210i	−0.00145514	−	0.00145514i
$827$	−36.0824	+	36.0824i	−1.25471	+	1.25471i	−0.301123	+	0.953585i	$0.597361\pi$
$827$	−36.0824	+	36.0824i	−1.25471	+	1.25471i	−0.953585	+	0.301123i	$0.902639\pi$
$828$		0			0
$829$	46.6421	+	26.9288i	1.61995	+	0.935276i	0.986932	+	0.161136i	$0.0515159\pi$
$829$	46.6421	+	26.9288i	1.61995	+	0.935276i	0.633014	+	0.774140i	$0.281817\pi$
$830$	−53.7501	−	14.4023i	−1.86569	−	0.499911i
$831$		0			0
$832$	−2.29909	−	2.77745i	−0.0797065	−	0.0962906i
$833$	−22.1845	+	12.8083i	−0.768649	+	0.443780i
$834$		0			0
$835$	16.1408	+	27.9566i	0.558575	+	0.967480i
$836$	−1.81073	−	3.13628i	−0.0626255	−	0.108471i
$837$		0			0
$838$	16.6249	+	4.45464i	0.574299	+	0.153883i
$839$	−5.67674	+	5.67674i	−0.195983	+	0.195983i	−0.798275	−	0.602293i	$-0.794254\pi$
$839$	−5.67674	+	5.67674i	−0.195983	+	0.195983i	0.602293	+	0.798275i	$0.294254\pi$
$840$		0			0
$841$	−8.53773	+	14.7878i	−0.294404	+	0.509924i
$842$	−3.80999			−0.131301
$843$		0			0
$844$	−1.25954	−	0.727198i	−0.0433553	−	0.0250312i
$845$	−40.7932	−	19.6905i	−1.40333	−	0.677374i
$846$		0			0
$847$	−0.227309	−	0.848328i	−0.00781042	−	0.0291489i
$848$	−3.37338	+	1.94762i	−0.115842	+	0.0668817i
$849$		0			0
$850$	25.2529	+	6.76649i	0.866167	+	0.232089i
$851$	−42.1806	+	11.3023i	−1.44593	+	0.387436i
$852$		0			0
$853$	−5.95946	+	1.59683i	−0.204048	+	0.0546745i	−0.359395	−	0.933185i	$-0.617017\pi$
$853$	−5.95946	+	1.59683i	−0.204048	+	0.0546745i	0.155347	+	0.987860i	$0.450350\pi$
$854$	0.145932	−	0.0842540i	0.00499370	−	0.00288311i
$855$		0			0
$856$	−16.2346	+	4.35004i	−0.554886	+	0.148681i
$857$	19.6661	−	34.0626i	0.671780	−	1.16356i	−0.305619	−	0.952154i	$-0.598863\pi$
$857$	19.6661	−	34.0626i	0.671780	−	1.16356i	0.977399	−	0.211404i	$-0.0678034\pi$
$858$		0			0
$859$	−7.03986	−	12.1934i	−0.240197	−	0.416033i	0.720573	−	0.693379i	$-0.243879\pi$
$859$	−7.03986	−	12.1934i	−0.240197	−	0.416033i	−0.960770	+	0.277345i	$0.910545\pi$
$860$	−13.3780	−	13.3780i	−0.456186	−	0.456186i
$861$		0			0
$862$			21.6457i			0.737254i
$863$	−20.5132	−	20.5132i	−0.698277	−	0.698277i	0.265762	−	0.964039i	$-0.414377\pi$
$863$	−20.5132	−	20.5132i	−0.698277	−	0.698277i	−0.964039	+	0.265762i	$0.914377\pi$
$864$		0			0
$865$	8.87978	−	33.1398i	0.301922	−	1.12679i
$866$	−4.52533	−	16.8888i	−0.153777	−	0.573904i
$867$		0			0
$868$		−	0.334013i		−	0.0113371i
$869$	20.2050	−	20.2050i	0.685408	−	0.685408i
$870$		0			0
$871$	3.68118	−	39.0660i	0.124732	−	1.32370i
$872$		−	19.8933i		−	0.673671i
$873$		0			0
$874$	−2.02957	+	3.51533i	−0.0686514	+	0.118908i
$875$	0.418453			0.0141463
$876$		0			0
$877$	2.00216	+	7.47216i	0.0676081	+	0.252317i	0.991456	−	0.130444i	$-0.0416401\pi$
$877$	2.00216	+	7.47216i	0.0676081	+	0.252317i	−0.923848	+	0.382760i	$0.874973\pi$
$878$	−1.63056	−	6.08532i	−0.0550287	−	0.205370i
$879$		0			0
$880$	17.9897			0.606432
$881$	−20.3481	+	35.2439i	−0.685544	+	1.18740i	0.287722	+	0.957714i	$0.407102\pi$
$881$	−20.3481	+	35.2439i	−0.685544	+	1.18740i	−0.973266	+	0.229682i	$0.926231\pi$
$882$		0			0
$883$		−	18.4296i		−	0.620206i	−0.950703	−	0.310103i	$-0.899636\pi$
$883$		−	18.4296i		−	0.620206i	0.950703	−	0.310103i	$-0.100364\pi$
$884$	8.41729	+	10.1686i	0.283104	+	0.342008i
$885$		0			0
$886$	11.3940	−	11.3940i	0.382788	−	0.382788i
$887$		−	17.5993i		−	0.590927i	−0.955354	−	0.295463i	$-0.904526\pi$
$887$		−	17.5993i		−	0.590927i	0.955354	−	0.295463i	$-0.0954740\pi$
$888$		0			0
$889$	4.16307e−5	0	0.000155368i	1.39625e−6	0	5.21087e-6i
$890$	−15.3723	+	57.3703i	−0.515281	+	1.92306i
$891$		0			0
$892$	−3.00391	−	3.00391i	−0.100579	−	0.100579i
$893$			3.50593i			0.117321i
$894$		0			0
$895$	−37.9320	−	37.9320i	−1.26793	−	1.26793i
$896$	0.0280482	+	0.0485810i	0.000937026	+	0.00162298i
$897$		0			0
$898$	−9.48174	+	16.4229i	−0.316410	+	0.548038i
$899$	19.8606	−	5.32164i	0.662389	−	0.177487i
$900$		0			0
$901$	12.3505	−	7.13054i	0.411453	−	0.237553i
$902$	−15.0315	+	4.02768i	−0.500495	+	0.134107i
$903$		0			0
$904$	−18.9014	+	5.06461i	−0.628650	+	0.168446i
$905$	57.8564	+	15.5026i	1.92321	+	0.515323i
$906$		0			0
$907$	−31.5177	+	18.1967i	−1.04653	+	0.604213i	−0.921675	−	0.387963i	$-0.873179\pi$
$907$	−31.5177	+	18.1967i	−1.04653	+	0.604213i	−0.124852	+	0.992175i	$0.539846\pi$
$908$	6.04673	+	22.5667i	0.200668	+	0.748902i
$909$		0			0
$910$	0.574578	+	0.408076i	0.0190471	+	0.0135276i
$911$	−30.6958	−	17.7222i	−1.01700	−	0.587164i	−0.103765	−	0.994602i	$-0.533089\pi$
$911$	−30.6958	−	17.7222i	−1.01700	−	0.587164i	−0.913233	+	0.407438i	$0.866422\pi$
$912$		0			0
$913$	82.4536			2.72882
$914$	8.46556	−	14.6628i	0.280016	−	0.485002i
$915$		0			0
$916$	4.36987	−	4.36987i	0.144384	−	0.144384i
$917$	−0.680714	−	0.182397i	−0.0224791	−	0.00602327i
$918$		0			0
$919$	−9.39060	−	16.2650i	−0.309767	−	0.536533i	0.668544	−	0.743673i	$-0.266918\pi$
$919$	−9.39060	−	16.2650i	−0.309767	−	0.536533i	−0.978311	+	0.207140i	$0.933584\pi$
$920$	−10.0819	−	17.4624i	−0.332391	−	0.575719i
$921$		0			0
$922$	−11.2174	+	6.47635i	−0.369424	+	0.213287i
$923$	23.1384	+	50.4993i	0.761611	+	1.66221i
$924$		0			0
$925$	−52.0491	−	13.9465i	−1.71137	−	0.458559i
$926$	15.2890	+	8.82711i	0.502428	+	0.290077i
$927$		0			0
$928$	−2.44178	+	2.44178i	−0.0801552	+	0.0801552i
$929$	4.30437	+	4.30437i	0.141222	+	0.141222i	0.774183	−	0.632962i	$-0.218161\pi$
$929$	4.30437	+	4.30437i	0.141222	+	0.141222i	−0.632962	+	0.774183i	$0.718161\pi$
$930$		0			0
$931$	1.27024	−	4.74059i	0.0416303	−	0.155366i
$932$	−1.04763	−	0.604847i	−0.0343161	−	0.0198124i
$933$		0			0
$934$	5.46566	−	20.3981i	0.178842	−	0.667447i
$935$	−65.8628			−2.15394
$936$		0			0
$937$	−10.2331			−0.334301			−0.167150	−	0.985931i	$-0.553457\pi$
$937$	−10.2331			−0.334301			−0.167150	+	0.985931i	$0.553457\pi$
$938$	−0.158008	+	0.589694i	−0.00515914	+	0.0192542i
$939$		0			0
$940$	−15.0825	−	8.70787i	−0.491936	−	0.284019i
$941$	9.66473	−	36.0693i	0.315061	−	1.17582i	−0.608871	−	0.793269i	$-0.708377\pi$
$941$	9.66473	−	36.0693i	0.315061	−	1.17582i	0.923932	−	0.382556i	$-0.124956\pi$
$942$		0			0
$943$	12.3337	+	12.3337i	0.401642	+	0.401642i
$944$	−0.745519	+	0.745519i	−0.0242646	+	0.0242646i
$945$		0			0
$946$	24.2779	+	14.0168i	0.789342	+	0.455727i
$947$	22.7358	+	6.09203i	0.738813	+	0.197964i	0.608550	−	0.793515i	$-0.291751\pi$
$947$	22.7358	+	6.09203i	0.738813	+	0.197964i	0.130262	+	0.991480i	$0.458418\pi$
$948$		0			0
$949$	29.7749	+	2.80568i	0.966535	+	0.0910763i
$950$	−4.33777	+	2.50441i	−0.140736	+	0.0812539i
$951$		0			0
$952$	−0.102689	−	0.177862i	−0.00332816	−	0.00576454i
$953$	23.3774	+	40.4908i	0.757267	+	1.31163i	0.944239	+	0.329260i	$0.106799\pi$
$953$	23.3774	+	40.4908i	0.757267	+	1.31163i	−0.186972	+	0.982365i	$0.559867\pi$
$954$		0			0
$955$	28.7582	+	7.70575i	0.930595	+	0.249352i
$956$	9.61511	−	9.61511i	0.310975	−	0.310975i
$957$		0			0
$958$	7.68966	−	13.3189i	0.248442	−	0.430313i
$959$	0.788846			0.0254732
$960$		0			0
$961$	3.85665	+	2.22664i	0.124408	+	0.0718270i
$962$	−17.3490	−	20.9587i	−0.559355	−	0.675737i
$963$		0			0
$964$	−1.84513	−	6.88614i	−0.0594278	−	0.221788i
$965$	1.84103	−	1.06292i	0.0592650	−	0.0342167i
$966$		0			0
$967$	−44.7620	−	11.9939i	−1.43945	−	0.385699i	−0.547108	−	0.837062i	$-0.684271\pi$
$967$	−44.7620	−	11.9939i	−1.43945	−	0.385699i	−0.892340	+	0.451363i	$0.850938\pi$
$968$	−15.1227	+	4.05211i	−0.486061	+	0.130240i
$969$		0			0
$970$	7.74546	−	2.07539i	0.248692	−	0.0666368i
$971$	−10.9829	+	6.34097i	−0.352458	+	0.203491i	−0.665767	−	0.746160i	$-0.731896\pi$
$971$	−10.9829	+	6.34097i	−0.352458	+	0.203491i	0.313310	+	0.949651i	$0.398562\pi$
$972$		0			0
$973$	0.0170080	−	0.00455727i	0.000545251	−	0.000146099i
$974$	−7.85293	+	13.6017i	−0.251624	+	0.435826i
$975$		0			0
$976$	−1.50195	−	2.60145i	−0.0480762	−	0.0832705i
$977$	42.6741	+	42.6741i	1.36526	+	1.36526i	0.867058	+	0.498206i	$0.166008\pi$
$977$	42.6741	+	42.6741i	1.36526	+	1.36526i	0.498206	+	0.867058i	$0.333992\pi$
$978$		0			0
$979$		−	88.0070i		−	2.81272i
$980$	17.2390	+	17.2390i	0.550680	+	0.550680i
$981$		0			0
$982$	1.65507	−	6.17679i	0.0528153	−	0.197109i
$983$	−5.89349	−	21.9948i	−0.187973	−	0.701525i	−0.993975	−	0.109611i	$-0.965039\pi$
$983$	−5.89349	−	21.9948i	−0.187973	−	0.701525i	0.806001	−	0.591914i	$-0.201627\pi$
$984$		0			0
$985$		−	62.4924i		−	1.99117i
$986$	8.93970	−	8.93970i	0.284698	−	0.284698i
$987$		0			0
$988$	−2.51790	−	0.237261i	−0.0801049	−	0.00754827i
$989$		−	31.4218i		−	0.999154i
$990$		0			0
$991$	14.2272	−	24.6423i	0.451942	−	0.782787i	−0.546564	−	0.837417i	$-0.684065\pi$
$991$	14.2272	−	24.6423i	0.451942	−	0.782787i	0.998507	+	0.0546299i	$0.0173979\pi$
$992$	−5.95427			−0.189048
$993$		0			0
$994$	−0.223680	−	0.834786i	−0.00709471	−	0.0264778i
$995$	−17.9781	−	67.0950i	−0.569943	−	2.12705i
$996$		0			0
$997$	−16.7316			−0.529896			−0.264948	−	0.964263i	$-0.585355\pi$
$997$	−16.7316			−0.529896			−0.264948	+	0.964263i	$0.585355\pi$
$998$	3.82690	−	6.62838i	0.121138	−	0.209818i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bc.a.305.14		56
3.2	odd	2		234.2.z.a.227.6	yes	56
9.4	even	3		234.2.y.a.149.8	yes	56
9.5	odd	6		702.2.bb.a.71.7		56
13.11	odd	12		702.2.bb.a.89.7		56
39.11	even	12		234.2.y.a.11.8	✓	56
117.50	even	12	inner	702.2.bc.a.557.14		56
117.76	odd	12		234.2.z.a.167.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.8	✓	56	39.11	even	12
234.2.y.a.149.8	yes	56	9.4	even	3
234.2.z.a.167.6	yes	56	117.76	odd	12
234.2.z.a.227.6	yes	56	3.2	odd	2
702.2.bb.a.71.7		56	9.5	odd	6
702.2.bb.a.89.7		56	13.11	odd	12
702.2.bc.a.305.14		56	1.1	even	1	trivial
702.2.bc.a.557.14		56	117.50	even	12	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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.901822 - 3.36565i) q^{5} +(-0.0396662 - 0.0396662i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.901822 - 3.36565i) q^{5} +(-0.0396662 - 0.0396662i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-3.01756 - 1.74219i) q^{10} +(4.98703 + 1.33627i) q^{11} +(2.77745 - 2.29909i) q^{13} +(-0.0485810 + 0.0280482i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.83057 - 3.17065i) q^{17} +(0.677531 + 0.181544i) q^{19} +(-2.46382 + 2.46382i) q^{20} +(2.58148 - 4.47125i) q^{22} -5.78694 q^{23} +(-6.18416 - 3.57043i) q^{25} +(-1.50189 - 3.27785i) q^{26} +(0.0145188 + 0.0541850i) q^{28} +(-2.99055 + 1.72660i) q^{29} +(-5.75138 - 1.54108i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-3.53640 + 0.947575i) q^{34} +(-0.169274 + 0.0977305i) q^{35} +(7.28892 - 1.95306i) q^{37} +(0.350716 - 0.607458i) q^{38} +(1.74219 + 3.01756i) q^{40} +(-2.13130 - 2.13130i) q^{41} +5.42977i q^{43} +(-3.65076 - 3.65076i) q^{44} +(-1.49777 + 5.58976i) q^{46} +(1.29364 + 4.82793i) q^{47} -6.99685i q^{49} +(-5.04935 + 5.04935i) q^{50} +(-3.55488 + 0.602344i) q^{52} +3.89525i q^{53} +(8.99483 - 15.5795i) q^{55} +0.0560965 q^{56} +(0.893752 + 3.33553i) q^{58} +(0.272879 + 1.01840i) q^{59} -3.00390 q^{61} +(-2.97713 + 5.15654i) q^{62} -1.00000i q^{64} +(-5.23315 - 11.4213i) q^{65} +(7.69542 - 7.69542i) q^{67} +3.66115i q^{68} +(0.0505890 + 0.188801i) q^{70} +(-3.98742 + 14.8813i) q^{71} +(5.86521 + 5.86521i) q^{73} -7.54605i q^{74} +(-0.495987 - 0.495987i) q^{76} +(-0.144812 - 0.250821i) q^{77} +(2.76723 - 4.79298i) q^{79} +(3.36565 - 0.901822i) q^{80} +(-2.61030 + 1.50706i) q^{82} +(15.4261 - 4.13340i) q^{83} +(-12.3221 + 3.30170i) q^{85} +(5.24476 + 1.40533i) q^{86} +(-4.47125 + 2.58148i) q^{88} +(-4.41179 - 16.4650i) q^{89} +(-0.201367 - 0.0189747i) q^{91} +(5.01164 + 2.89347i) q^{92} +4.99824 q^{94} +(1.22203 - 2.11661i) q^{95} +(-1.62729 + 1.62729i) q^{97} +(-6.75844 - 1.81092i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7}+O(q^{10}) \) 56 * q - 8 * q^7	\( 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73} + 4 q^{76} - 24 q^{77} - 24 q^{79} + 96 q^{83} - 72 q^{85} + 4 q^{91} + 24 q^{92} - 52 q^{97} - 48 q^{98}+O(q^{100}) \) 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more