LMFDB - Embedded newform 702.2.bb.a.89.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(71,702)]

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([10, 5]))

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

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

chi := DirichletCharacter("702.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (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			89.7
Character	$\chi$	$=$	702.89
Dual form			702.2.bb.a.71.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(3.36565 + 0.901822i) q^{5} +(0.0541850 + 0.0145188i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(3.36565 + 0.901822i) q^{5} +(0.0541850 + 0.0145188i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.01756 + 1.74219i) q^{10} +(3.65076 + 3.65076i) q^{11} +(-3.37979 + 1.25580i) q^{13} +(-0.0485810 + 0.0280482i) q^{14} -1.00000 q^{16} +(1.83057 - 3.17065i) q^{17} +(0.677531 - 0.181544i) q^{19} +(0.901822 - 3.36565i) q^{20} -5.16296 q^{22} +(-2.89347 + 5.01164i) q^{23} +(6.18416 + 3.57043i) q^{25} +(1.50189 - 3.27785i) q^{26} +(0.0145188 - 0.0541850i) q^{28} -3.45319i q^{29} +(1.54108 - 5.75138i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.947575 + 3.53640i) q^{34} +(0.169274 + 0.0977305i) q^{35} +(7.28892 + 1.95306i) q^{37} +(-0.350716 + 0.607458i) q^{38} +(1.74219 + 3.01756i) q^{40} +(0.780112 + 2.91142i) q^{41} +(-4.70232 + 2.71489i) q^{43} +(3.65076 - 3.65076i) q^{44} +(-1.49777 - 5.58976i) q^{46} +(4.82793 - 1.29364i) q^{47} +(-6.05945 - 3.49843i) q^{49} +(-6.89754 + 1.84819i) q^{50} +(1.25580 + 3.37979i) q^{52} +3.89525i q^{53} +(8.99483 + 15.5795i) q^{55} +(0.0280482 + 0.0485810i) q^{56} +(2.44178 + 2.44178i) q^{58} +(-0.745519 - 0.745519i) q^{59} +(1.50195 + 2.60145i) q^{61} +(2.97713 + 5.15654i) q^{62} +1.00000i q^{64} +(-12.5077 + 1.17860i) q^{65} +(-10.5121 + 2.81672i) q^{67} +(-3.17065 - 1.83057i) q^{68} +(-0.188801 + 0.0505890i) q^{70} +(3.98742 + 14.8813i) q^{71} +(5.86521 - 5.86521i) q^{73} +(-6.53507 + 3.77302i) q^{74} +(-0.181544 - 0.677531i) q^{76} +(0.144812 + 0.250821i) q^{77} +(2.76723 - 4.79298i) q^{79} +(-3.36565 - 0.901822i) q^{80} +(-2.61030 - 1.50706i) q^{82} +(4.13340 + 15.4261i) q^{83} +(9.02042 - 9.02042i) q^{85} +(1.40533 - 5.24476i) q^{86} +5.16296i q^{88} +(4.41179 - 16.4650i) q^{89} +(-0.201367 + 0.0189747i) q^{91} +(5.01164 + 2.89347i) q^{92} +(-2.49912 + 4.32861i) q^{94} +2.44405 q^{95} +(-0.595628 + 2.22292i) q^{97} +(6.75844 - 1.81092i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73} - 48 q^{74} + 4 q^{76} + 24 q^{77} - 24 q^{79} + 60 q^{83} - 48 q^{86} + 4 q^{91} + 24 q^{92} + 20 q^{97} + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	3.36565	+	0.901822i	1.50516	+	0.403307i	0.914825	−	0.403850i	$-0.132328\pi$
$5$	3.36565	+	0.901822i	1.50516	+	0.403307i	0.590337	+	0.807157i	$0.298995\pi$
$6$		0			0
$7$	0.0541850	+	0.0145188i	0.0204800	+	0.00548760i	0.269045	−	0.963128i	$-0.413292\pi$
$7$	0.0541850	+	0.0145188i	0.0204800	+	0.00548760i	−0.248564	+	0.968615i	$0.579959\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−3.01756	+	1.74219i	−0.954235	+	0.550928i
$11$	3.65076	+	3.65076i	1.10075	+	1.10075i	0.994321	+	0.106426i	$0.0339406\pi$
$11$	3.65076	+	3.65076i	1.10075	+	1.10075i	0.106426	+	0.994321i	$0.466059\pi$
$12$		0			0
$13$	−3.37979	+	1.25580i	−0.937385	+	0.348295i
$13$	−3.37979	+	1.25580i	−0.937385	+	0.348295i
$14$	−0.0485810	+	0.0280482i	−0.0129838	+	0.00749621i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.83057	−	3.17065i	0.443979	−	0.768995i	−0.554001	−	0.832516i	$-0.686900\pi$
$17$	1.83057	−	3.17065i	0.443979	−	0.768995i	0.997980	+	0.0635211i	$0.0202330\pi$
$18$		0			0
$19$	0.677531	−	0.181544i	0.155436	−	0.0416491i	−0.180262	−	0.983619i	$-0.557694\pi$
$19$	0.677531	−	0.181544i	0.155436	−	0.0416491i	0.335698	+	0.941970i	$0.391028\pi$
$20$	0.901822	−	3.36565i	0.201654	−	0.752581i
$21$		0			0
$22$	−5.16296			−1.10075
$23$	−2.89347	+	5.01164i	−0.603330	+	1.04500i	0.388982	+	0.921245i	$0.372827\pi$
$23$	−2.89347	+	5.01164i	−0.603330	+	1.04500i	−0.992313	+	0.123754i	$0.960507\pi$
$24$		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
$29$		−	3.45319i		−	0.641242i	−0.947208	−	0.320621i	$-0.896108\pi$
$29$		−	3.45319i		−	0.641242i	0.947208	−	0.320621i	$-0.103892\pi$
$30$		0			0
$31$	1.54108	−	5.75138i	0.276786	−	1.03298i	−0.677850	−	0.735201i	$-0.737088\pi$
$31$	1.54108	−	5.75138i	0.276786	−	1.03298i	0.954635	−	0.297778i	$-0.0962454\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	0.947575	+	3.53640i	0.162508	+	0.606487i
$35$	0.169274	+	0.0977305i	0.0286126	+	0.0165195i
$36$		0			0
$37$	7.28892	+	1.95306i	1.19829	+	0.321081i	0.802158	−	0.597112i	$-0.203685\pi$
$37$	7.28892	+	1.95306i	1.19829	+	0.321081i	0.396134	+	0.918193i	$0.370352\pi$
$38$	−0.350716	+	0.607458i	−0.0568937	+	0.0985427i
$39$		0			0
$40$	1.74219	+	3.01756i	0.275464	+	0.477117i
$41$	0.780112	+	2.91142i	0.121833	+	0.454687i	0.999707	−	0.0242048i	$-0.00770537\pi$
$41$	0.780112	+	2.91142i	0.121833	+	0.454687i	−0.877874	+	0.478892i	$0.841039\pi$
$42$		0			0
$43$	−4.70232	+	2.71489i	−0.717097	+	0.414016i	−0.813683	−	0.581309i	$-0.802541\pi$
$43$	−4.70232	+	2.71489i	−0.717097	+	0.414016i	0.0965863	+	0.995325i	$0.469208\pi$
$44$	3.65076	−	3.65076i	0.550373	−	0.550373i
$45$		0			0
$46$	−1.49777	−	5.58976i	−0.220834	−	0.824165i
$47$	4.82793	−	1.29364i	0.704226	−	0.188697i	0.111103	−	0.993809i	$-0.464561\pi$
$47$	4.82793	−	1.29364i	0.704226	−	0.188697i	0.593123	+	0.805112i	$0.297895\pi$
$48$		0			0
$49$	−6.05945	−	3.49843i	−0.865636	−	0.499775i
$50$	−6.89754	+	1.84819i	−0.975459	+	0.261373i
$51$		0			0
$52$	1.25580	+	3.37979i	0.174148	+	0.468692i
$53$			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
$56$	0.0280482	+	0.0485810i	0.00374810	+	0.00649190i
$57$		0			0
$58$	2.44178	+	2.44178i	0.320621	+	0.320621i
$59$	−0.745519	−	0.745519i	−0.0970583	−	0.0970583i	0.656910	−	0.753969i	$-0.271863\pi$
$59$	−0.745519	−	0.745519i	−0.0970583	−	0.0970583i	−0.753969	+	0.656910i	$0.771863\pi$
$60$		0			0
$61$	1.50195	+	2.60145i	0.192305	+	0.333082i	0.946014	−	0.324127i	$-0.105070\pi$
$61$	1.50195	+	2.60145i	0.192305	+	0.333082i	−0.753709	+	0.657209i	$0.771737\pi$
$62$	2.97713	+	5.15654i	0.378096	+	0.654882i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−12.5077	+	1.17860i	−1.55139	+	0.146187i
$66$		0			0
$67$	−10.5121	+	2.81672i	−1.28426	+	0.344117i	−0.835478	−	0.549524i	$-0.814809\pi$
$67$	−10.5121	+	2.81672i	−1.28426	+	0.344117i	−0.448784	+	0.893640i	$0.648143\pi$
$68$	−3.17065	−	1.83057i	−0.384497	−	0.221990i
$69$		0			0
$70$	−0.188801	+	0.0505890i	−0.0225660	+	0.00604655i
$71$	3.98742	+	14.8813i	0.473220	+	1.76608i	0.628085	+	0.778145i	$0.283839\pi$
$71$	3.98742	+	14.8813i	0.473220	+	1.76608i	−0.154865	+	0.987936i	$0.549494\pi$
$72$		0			0
$73$	5.86521	−	5.86521i	0.686471	−	0.686471i	−0.274979	−	0.961450i	$-0.588671\pi$
$73$	5.86521	−	5.86521i	0.686471	−	0.686471i	0.961450	+	0.274979i	$0.0886710\pi$
$74$	−6.53507	+	3.77302i	−0.759687	+	0.438605i
$75$		0			0
$76$	−0.181544	−	0.677531i	−0.0208245	−	0.0777182i
$77$	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
$83$	4.13340	+	15.4261i	0.453699	+	1.69323i	0.691883	+	0.722009i	$0.256781\pi$
$83$	4.13340	+	15.4261i	0.453699	+	1.69323i	−0.238184	+	0.971220i	$0.576552\pi$
$84$		0			0
$85$	9.02042	−	9.02042i	0.978402	−	0.978402i
$86$	1.40533	−	5.24476i	0.151540	−	0.565556i
$87$		0			0
$88$			5.16296i			0.550373i
$89$	4.41179	−	16.4650i	0.467649	−	1.74529i	−0.180306	−	0.983611i	$-0.557709\pi$
$89$	4.41179	−	16.4650i	0.467649	−	1.74529i	0.647955	−	0.761679i	$-0.275625\pi$
$90$		0			0
$91$	−0.201367	+	0.0189747i	−0.0211090	+	0.00198909i
$92$	5.01164	+	2.89347i	0.522500	+	0.301665i
$93$		0			0
$94$	−2.49912	+	4.32861i	−0.257765	+	0.446462i
$95$	2.44405			0.250754
$96$		0			0
$97$	−0.595628	+	2.22292i	−0.0604769	+	0.225703i	−0.989549	−	0.144195i	$-0.953941\pi$
$97$	−0.595628	+	2.22292i	−0.0604769	+	0.225703i	0.929072	+	0.369898i	$0.120607\pi$
$98$	6.75844	−	1.81092i	0.682706	−	0.182930i
$99$		0			0
$100$	3.57043	−	6.18416i	0.357043	−	0.618416i
$101$	3.52328			0.350580			0.175290	−	0.984517i	$-0.443914\pi$
$101$	3.52328			0.350580			0.175290	+	0.984517i	$0.443914\pi$
$102$		0			0
$103$	5.20698	−	3.00625i	0.513059	−	0.296215i	−0.221031	−	0.975267i	$-0.570942\pi$
$103$	5.20698	−	3.00625i	0.513059	−	0.296215i	0.734090	+	0.679052i	$0.237609\pi$
$104$	−3.27785	−	1.50189i	−0.321420	−	0.147272i
$105$		0			0
$106$	−2.75436	−	2.75436i	−0.267527	−	0.267527i
$107$	−14.5555	+	8.40363i	−1.40714	+	0.812410i	−0.995111	−	0.0987630i	$-0.968511\pi$
$107$	−14.5555	+	8.40363i	−1.40714	+	0.812410i	−0.412024	+	0.911173i	$0.635178\pi$
$108$		0			0
$109$	−14.0667	−	14.0667i	−1.34734	−	1.34734i	−0.888537	−	0.458806i	$-0.848277\pi$
$109$	−14.0667	−	14.0667i	−1.34734	−	1.34734i	−0.458806	−	0.888537i	$-0.651723\pi$
$110$	−17.3767	−	4.65607i	−1.65680	−	0.443939i
$111$		0			0
$112$	−0.0541850	−	0.0145188i	−0.00512000	−	0.00137190i
$113$		−	19.5681i		−	1.84082i	−0.390960	−	0.920408i	$-0.627857\pi$
$113$		−	19.5681i		−	1.84082i	0.390960	−	0.920408i	$-0.372143\pi$
$114$		0			0
$115$	−14.2580	+	14.2580i	−1.32957	+	1.32957i
$116$	−3.45319			−0.320621
$117$		0			0
$118$	1.05432			0.0970583
$119$	0.145224	−	0.145224i	0.0133126	−	0.0133126i
$120$		0			0
$121$			15.6561i			1.42328i
$122$	−2.90154	−	0.777466i	−0.262693	−	0.0703885i
$123$		0			0
$124$	−5.75138	−	1.54108i	−0.516489	−	0.138393i
$125$	5.27469	+	5.27469i	0.471782	+	0.471782i
$126$		0			0
$127$	−0.00248320	+	0.00143368i	−0.000220349	+	0.000127218i	−0.500110	−	0.865962i	$-0.666707\pi$
$127$	−0.00248320	+	0.00143368i	−0.000220349	+	0.000127218i	0.499890	+	0.866089i	$0.333374\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	8.01087	−	9.67766i	0.702600	−	0.848787i
$131$	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
$133$	0.0393479			0.00341189
$134$	5.44148	−	9.42492i	0.470072	−	0.814189i
$135$		0			0
$136$	3.53640	−	0.947575i	0.303244	−	0.0812539i
$137$	3.63959	−	13.5832i	0.310952	−	1.16049i	−0.616748	−	0.787160i	$-0.711550\pi$
$137$	3.63959	−	13.5832i	0.310952	−	1.16049i	0.927700	−	0.373327i	$-0.121783\pi$
$138$		0			0
$139$	0.313887			0.0266236			0.0133118	−	0.999911i	$-0.495763\pi$
$139$	0.313887			0.0266236			0.0133118	+	0.999911i	$0.495763\pi$
$140$	0.0977305	−	0.169274i	0.00825973	−	0.0143063i
$141$		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
$146$			8.29466i			0.686471i
$147$		0			0
$148$	1.95306	−	7.28892i	0.160541	−	0.599146i
$149$	−4.31299	+	4.31299i	−0.353334	+	0.353334i	−0.861349	−	0.508014i	$-0.830380\pi$
$149$	−4.31299	+	4.31299i	−0.353334	+	0.353334i	0.508014	+	0.861349i	$0.330380\pi$
$150$		0			0
$151$	−2.90331	−	10.8353i	−0.236268	−	0.881766i	−0.977573	−	0.210597i	$-0.932459\pi$
$151$	−2.90331	−	10.8353i	−0.236268	−	0.881766i	0.741305	−	0.671169i	$-0.234207\pi$
$152$	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	$-0.340867\pi$
$158$	1.43242	+	5.34588i	0.113958	+	0.425295i
$159$		0			0
$160$	3.01756	−	1.74219i	0.238559	−	0.137732i
$161$	−0.229546	+	0.229546i	−0.0180908	+	0.0180908i
$162$		0			0
$163$	−1.44937	−	5.40913i	−0.113524	−	0.423676i	0.885649	−	0.464356i	$-0.153714\pi$
$163$	−1.44937	−	5.40913i	−0.113524	−	0.423676i	−0.999172	+	0.0406802i	$0.987048\pi$
$164$	2.91142	−	0.780112i	0.227343	−	0.0609165i
$165$		0			0
$166$	−13.8306	−	7.98511i	−1.07346	−	0.619765i
$167$	−8.94898	+	2.39787i	−0.692493	+	0.185553i	−0.587866	−	0.808959i	$-0.700032\pi$
$167$	−8.94898	+	2.39787i	−0.692493	+	0.185553i	−0.104627	+	0.994512i	$0.533365\pi$
$168$		0			0
$169$	9.84595	−	8.48865i	0.757381	−	0.652973i
$170$			12.7568i			0.978402i
$171$		0			0
$172$	2.71489	+	4.70232i	0.207008	+	0.358548i
$173$	4.92325	+	8.52731i	0.374307	+	0.648319i	0.990223	−	0.139493i	$-0.0445471\pi$
$173$	4.92325	+	8.52731i	0.374307	+	0.648319i	−0.615916	+	0.787812i	$0.711214\pi$
$174$		0			0
$175$	0.283250	+	0.283250i	0.0214117	+	0.0214117i
$176$	−3.65076	−	3.65076i	−0.275187	−	0.275187i
$177$		0			0
$178$	8.52292	+	14.7621i	0.638820	+	1.10647i
$179$	−7.69779	−	13.3330i	−0.575360	−	0.996553i	−0.996002	−	0.0893264i	$-0.971529\pi$
$179$	−7.69779	−	13.3330i	−0.575360	−	0.996553i	0.420642	−	0.907227i	$-0.361805\pi$
$180$		0			0
$181$		−	17.1903i		−	1.27774i	−0.769314	−	0.638871i	$-0.779402\pi$
$181$		−	17.1903i		−	1.27774i	0.769314	−	0.638871i	$-0.220598\pi$
$182$	0.128971	−	0.155805i	0.00955993	−	0.0115490i
$183$		0			0
$184$	−5.58976	+	1.49777i	−0.412082	+	0.110417i
$185$	22.7706	+	13.1466i	1.67413	+	0.966559i
$186$		0			0
$187$	18.2583	−	4.89229i	1.33518	−	0.357760i
$188$	−1.29364	−	4.82793i	−0.0943484	−	0.352113i
$189$		0			0
$190$	−1.72821	+	1.72821i	−0.125377	+	0.125377i
$191$	7.39988	−	4.27232i	0.535436	−	0.309134i	−0.207791	−	0.978173i	$-0.566627\pi$
$191$	7.39988	−	4.27232i	0.535436	−	0.309134i	0.743227	+	0.669039i	$0.233294\pi$
$192$		0			0
$193$	0.157908	+	0.589319i	0.0113664	+	0.0424201i	0.971376	−	0.237547i	$-0.0763432\pi$
$193$	0.157908	+	0.589319i	0.0113664	+	0.0424201i	−0.960010	+	0.279967i	$0.909677\pi$
$194$	−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	$-0.637281\pi$
$197$	−17.3239	−	4.64193i	−1.23428	−	0.330724i	−0.816244	+	0.577707i	$0.803948\pi$
$198$		0			0
$199$	17.2644	+	9.96763i	1.22384	+	0.706586i	0.965735	−	0.259530i	$-0.0835675\pi$
$199$	17.2644	+	9.96763i	1.22384	+	0.706586i	0.258108	+	0.966116i	$0.416901\pi$
$200$	1.84819	+	6.89754i	0.130687	+	0.487729i
$201$		0			0
$202$	−2.49134	+	2.49134i	−0.175290	+	0.175290i
$203$	0.0501363	−	0.187111i	0.00351888	−	0.0131326i
$204$		0			0
$205$			10.5023i			0.733514i
$206$	−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
$211$	−0.727198	+	1.25954i	−0.0500623	+	0.0867105i	−0.889971	−	0.456018i	$-0.849275\pi$
$211$	−0.727198	+	1.25954i	−0.0500623	+	0.0867105i	0.839908	+	0.542728i	$0.182609\pi$
$212$	3.89525			0.267527
$213$		0			0
$214$	4.35004	−	16.2346i	0.297363	−	1.10977i
$215$	−18.2747	+	4.89669i	−1.24632	+	0.333951i
$216$		0			0
$217$	0.167007	−	0.289264i	0.0113371	−	0.0196365i
$218$	19.8933			1.34734
$219$		0			0
$220$	15.5795	−	8.99483i	1.05037	−	0.606432i
$221$	−2.20527	+	13.0149i	−0.148342	+	0.875480i
$222$		0			0
$223$	−3.00391	−	3.00391i	−0.201157	−	0.201157i	0.599339	−	0.800496i	$-0.295430\pi$
$223$	−3.00391	−	3.00391i	−0.201157	−	0.201157i	−0.800496	+	0.599339i	$0.795430\pi$
$224$	0.0485810	−	0.0280482i	0.00324595	−	0.00187405i
$225$		0			0
$226$	13.8368	+	13.8368i	0.920408	+	0.920408i
$227$	−22.5667	−	6.04673i	−1.49780	−	0.401335i	−0.585440	−	0.810716i	$-0.699078\pi$
$227$	−22.5667	−	6.04673i	−1.49780	−	0.401335i	−0.912364	+	0.409380i	$0.865745\pi$
$228$		0			0
$229$	5.96935	+	1.59948i	0.394466	+	0.105697i	0.450599	−	0.892727i	$-0.351210\pi$
$229$	5.96935	+	1.59948i	0.394466	+	0.105697i	−0.0561332	+	0.998423i	$0.517877\pi$
$230$		−	20.1639i		−	1.32957i
$231$		0			0
$232$	2.44178	−	2.44178i	0.160310	−	0.160310i
$233$	−1.20969			−0.0792497			−0.0396249	−	0.999215i	$-0.512616\pi$
$233$	−1.20969			−0.0792497			−0.0396249	+	0.999215i	$0.512616\pi$
$234$		0			0
$235$	17.4157			1.13608
$236$	−0.745519	+	0.745519i	−0.0485292	+	0.0485292i
$237$		0			0
$238$			0.205377i			0.0133126i
$239$	−13.1345	−	3.51937i	−0.849599	−	0.227649i	−0.192353	−	0.981326i	$-0.561612\pi$
$239$	−13.1345	−	3.51937i	−0.849599	−	0.227649i	−0.657246	+	0.753676i	$0.728279\pi$
$240$		0			0
$241$	−6.88614	−	1.84513i	−0.443575	−	0.118856i	0.0301165	−	0.999546i	$-0.490412\pi$
$241$	−6.88614	−	1.84513i	−0.443575	−	0.118856i	−0.473692	+	0.880691i	$0.657079\pi$
$242$	−11.0706	−	11.0706i	−0.711642	−	0.711642i
$243$		0			0
$244$	2.60145	−	1.50195i	0.166541	−	0.0961524i
$245$	−17.2390	−	17.2390i	−1.10136	−	1.10136i
$246$		0			0
$247$	−2.06193	+	1.46442i	−0.131198	+	0.0931789i
$248$	5.15654	−	2.97713i	0.327441	−	0.189048i
$249$		0			0
$250$	−7.45953			−0.471782
$251$	−2.50999	+	4.34744i	−0.158429	+	0.274408i	−0.934302	−	0.356481i	$-0.883976\pi$
$251$	−2.50999	+	4.34744i	−0.158429	+	0.274408i	0.775873	+	0.630889i	$0.217310\pi$
$252$		0			0
$253$	−28.8597	+	7.73293i	−1.81439	+	0.486165i
$254$	0.000742127	−	0.00276966i	4.65652e−5	−	0.000173784i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−2.47055	+	4.27912i	−0.154109	+	0.266924i	−0.932734	−	0.360565i	$-0.882584\pi$
$257$	−2.47055	+	4.27912i	−0.154109	+	0.266924i	0.778625	+	0.627489i	$0.215917\pi$
$258$		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
$263$		−	12.9065i		−	0.795849i	−0.917418	−	0.397925i	$-0.869731\pi$
$263$		−	12.9065i		−	0.795849i	0.917418	−	0.397925i	$-0.130269\pi$
$264$		0			0
$265$	−3.51282	+	13.1100i	−0.215791	+	0.805342i
$266$	−0.0278231	+	0.0278231i	−0.00170595	+	0.00170595i
$267$		0			0
$268$	2.81672	+	10.5121i	0.172058	+	0.642131i
$269$	22.4600	+	12.9673i	1.36941	+	0.790630i	0.990853	−	0.134948i	$-0.0430866\pi$
$269$	22.4600	+	12.9673i	1.36941	+	0.790630i	0.378558	+	0.925577i	$0.376420\pi$
$270$		0			0
$271$	−15.7870	−	4.23012i	−0.958992	−	0.256961i	−0.254819	−	0.966989i	$-0.582016\pi$
$271$	−15.7870	−	4.23012i	−0.958992	−	0.256961i	−0.704174	+	0.710028i	$0.748682\pi$
$272$	−1.83057	+	3.17065i	−0.110995	+	0.192249i
$273$		0			0
$274$	7.03116	+	12.1783i	0.424768	+	0.735719i
$275$	9.54212	+	35.6117i	0.575412	+	2.14747i
$276$		0			0
$277$	−14.7653	+	8.52472i	−0.887158	+	0.512201i	−0.873012	−	0.487699i	$-0.837836\pi$
$277$	−14.7653	+	8.52472i	−0.887158	+	0.512201i	−0.0141462	+	0.999900i	$0.504503\pi$
$278$	−0.221952	+	0.221952i	−0.0133118	+	0.0133118i
$279$		0			0
$280$	0.0505890	+	0.188801i	0.00302327	+	0.0112830i
$281$	3.85082	−	1.03182i	0.229721	−	0.0615535i	−0.142122	−	0.989849i	$-0.545393\pi$
$281$	3.85082	−	1.03182i	0.229721	−	0.0615535i	0.371843	+	0.928296i	$0.378726\pi$
$282$		0			0
$283$	−15.7258	−	9.07928i	−0.934801	−	0.539707i	−0.0464740	−	0.998920i	$-0.514798\pi$
$283$	−15.7258	−	9.07928i	−0.934801	−	0.539707i	−0.888327	+	0.459212i	$0.848132\pi$
$284$	14.8813	−	3.98742i	0.883040	−	0.236610i
$285$		0			0
$286$	17.4497	−	6.48362i	1.03182	−	0.383385i
$287$			0.169081i			0.00998056i
$288$		0			0
$289$	1.79800	+	3.11423i	0.105765	+	0.183190i
$290$	6.01611	+	10.4202i	0.353278	+	0.611895i
$291$		0			0
$292$	−5.86521	−	5.86521i	−0.343235	−	0.343235i
$293$	−14.4630	−	14.4630i	−0.844940	−	0.844940i	0.144557	−	0.989497i	$-0.453824\pi$
$293$	−14.4630	−	14.4630i	−0.844940	−	0.844940i	−0.989497	+	0.144557i	$0.953824\pi$
$294$		0			0
$295$	−1.83683	−	3.18148i	−0.106944	−	0.185233i
$296$	3.77302	+	6.53507i	0.219303	+	0.379843i
$297$		0			0
$298$		−	6.09950i		−	0.353334i
$299$	3.48573	−	20.5719i	0.201585	−	1.18970i
$300$		0			0
$301$	−0.294212	+	0.0788339i	−0.0169581	+	0.00454391i
$302$	9.71468	+	5.60877i	0.559017	+	0.322749i
$303$		0			0
$304$	−0.677531	+	0.181544i	−0.0388591	+	0.0104123i
$305$	2.70898	+	10.1101i	0.155116	+	0.578900i
$306$		0			0
$307$	−6.72055	+	6.72055i	−0.383562	+	0.383562i	−0.872384	−	0.488822i	$-0.837427\pi$
$307$	−6.72055	+	6.72055i	−0.383562	+	0.383562i	0.488822	+	0.872384i	$0.337427\pi$
$308$	0.250821	−	0.144812i	0.0142919	−	0.00825142i
$309$		0			0
$310$	5.36969	+	20.0399i	0.304978	+	1.13819i
$311$	1.80968	+	3.13446i	0.102618	+	0.177739i	0.912762	−	0.408491i	$-0.133945\pi$
$311$	1.80968	+	3.13446i	0.102618	+	0.177739i	−0.810145	+	0.586230i	$0.800612\pi$
$312$		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
$317$	2.76420	+	10.3161i	0.155253	+	0.579412i	0.999084	+	0.0428025i	$0.0136286\pi$
$317$	2.76420	+	10.3161i	0.155253	+	0.579412i	−0.843830	+	0.536610i	$0.819705\pi$
$318$		0			0
$319$	12.6068	−	12.6068i	0.705845	−	0.705845i
$320$	−0.901822	+	3.36565i	−0.0504134	+	0.188145i
$321$		0			0
$322$		−	0.324627i		−	0.0180908i
$323$	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
$328$	−1.50706	+	2.61030i	−0.0832135	+	0.144130i
$329$	0.280384			0.0154581
$330$		0			0
$331$	−0.861097	+	3.21366i	−0.0473301	+	0.176639i	−0.985545	−	0.169416i	$-0.945812\pi$
$331$	−0.861097	+	3.21366i	−0.0473301	+	0.176639i	0.938215	+	0.346054i	$0.112479\pi$
$332$	15.4261	−	4.13340i	0.846615	−	0.226850i
$333$		0			0
$334$	4.63233	−	8.02344i	0.253470	−	0.439023i
$335$	−37.9203			−2.07181
$336$		0			0
$337$	2.50494	−	1.44623i	0.136453	−	0.0787811i	−0.430220	−	0.902724i	$-0.641564\pi$
$337$	2.50494	−	1.44623i	0.136453	−	0.0787811i	0.566672	+	0.823943i	$0.308231\pi$
$338$	−0.959757	+	12.9645i	−0.0522039	+	0.705177i
$339$		0			0
$340$	−9.02042	−	9.02042i	−0.489201	−	0.489201i
$341$	26.6230	−	15.3708i	1.44172	−	0.832376i
$342$		0			0
$343$	−0.555202	−	0.555202i	−0.0299781	−	0.0299781i
$344$	−5.24476	−	1.40533i	−0.282778	−	0.0757702i
$345$		0			0
$346$	−9.51098	−	2.54846i	−0.511313	−	0.137006i
$347$			17.9932i			0.965923i	0.875642	+	0.482962i	$0.160439\pi$
$347$			17.9932i			0.965923i	−0.875642	+	0.482962i	$0.839561\pi$
$348$		0			0
$349$	18.3144	−	18.3144i	0.980348	−	0.980348i	−0.0194630	−	0.999811i	$-0.506196\pi$
$349$	18.3144	−	18.3144i	0.980348	−	0.980348i	0.999811	+	0.0194630i	$0.00619566\pi$
$350$	−0.400577			−0.0214117
$351$		0			0
$352$	5.16296			0.275187
$353$	2.10008	−	2.10008i	0.111776	−	0.111776i	−0.649007	−	0.760783i	$-0.724815\pi$
$353$	2.10008	−	2.10008i	0.111776	−	0.111776i	0.760783	+	0.649007i	$0.224815\pi$
$354$		0			0
$355$			53.6810i			2.84909i
$356$	−16.4650	−	4.41179i	−0.872645	−	0.233824i
$357$		0			0
$358$	14.8710	+	3.98467i	0.785957	+	0.210596i
$359$	−0.0334095	−	0.0334095i	−0.00176329	−	0.00176329i	0.706225	−	0.707988i	$-0.250397\pi$
$359$	−0.0334095	−	0.0334095i	−0.00176329	−	0.00176329i	−0.707988	+	0.706225i	$0.750397\pi$
$360$		0			0
$361$	−16.0284	+	9.25400i	−0.843600	+	0.487052i
$362$	12.1554	+	12.1554i	0.638871	+	0.638871i
$363$		0			0
$364$	0.0189747	+	0.201367i	0.000994546	+	0.0105545i
$365$	25.0296	−	14.4508i	1.31011	−	0.756392i
$366$		0			0
$367$	−9.50010			−0.495901			−0.247951	−	0.968773i	$-0.579757\pi$
$367$	−9.50010			−0.495901			−0.247951	+	0.968773i	$0.579757\pi$
$368$	2.89347	−	5.01164i	0.150833	−	0.261250i
$369$		0			0
$370$	−25.3973	+	6.80519i	−1.32034	+	0.353785i
$371$	−0.0565545	+	0.211064i	−0.00293616	+	0.0109579i
$372$		0			0
$373$	26.8580			1.39066			0.695328	−	0.718693i	$-0.255259\pi$
$373$	26.8580			1.39066			0.695328	+	0.718693i	$0.255259\pi$
$374$	−9.45117	+	16.3699i	−0.488709	+	0.846468i
$375$		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	−0.715749	−	0.698358i	$-0.753914\pi$
$379$	4.93097	−	18.4026i	0.253287	−	0.945279i	0.969036	−	0.246921i	$-0.0794189\pi$
$380$		−	2.44405i		−	0.125377i
$381$		0			0
$382$	−2.21152	+	8.25349i	−0.113151	+	0.422285i
$383$	6.76886	−	6.76886i	0.345873	−	0.345873i	−0.512697	−	0.858570i	$-0.671354\pi$
$383$	6.76886	−	6.76886i	0.345873	−	0.345873i	0.858570	+	0.512697i	$0.171354\pi$
$384$		0			0
$385$	0.261189	+	0.974771i	0.0133114	+	0.0496789i
$386$	−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	−0.958847	−	0.283922i	$-0.908364\pi$
$389$	−4.60612	+	7.97804i	−0.233540	+	0.404502i	0.725308	+	0.688425i	$0.241698\pi$
$390$		0			0
$391$	10.5934	+	18.3484i	0.535733	+	0.927916i
$392$	−1.81092	−	6.75844i	−0.0914652	−	0.341353i
$393$		0			0
$394$	15.5322	−	8.96753i	0.782502	−	0.451777i
$395$	13.6359	−	13.6359i	0.686098	−	0.686098i
$396$		0			0
$397$	7.23488	+	27.0009i	0.363108	+	1.35514i	0.869967	+	0.493110i	$0.164140\pi$
$397$	7.23488	+	27.0009i	0.363108	+	1.35514i	−0.506859	+	0.862029i	$0.669194\pi$
$398$	−19.2560	+	5.15962i	−0.965215	+	0.258629i
$399$		0			0
$400$	−6.18416	−	3.57043i	−0.309208	−	0.178521i
$401$	8.59039	−	2.30179i	0.428984	−	0.114946i	−0.0378654	−	0.999283i	$-0.512056\pi$
$401$	8.59039	−	2.30179i	0.428984	−	0.114946i	0.466849	+	0.884337i	$0.345389\pi$
$402$		0			0
$403$	2.01404	+	21.3737i	0.100327	+	1.06470i
$404$		−	3.52328i		−	0.175290i
$405$		0			0
$406$	0.0968559	+	0.167759i	0.00480688	+	0.00832576i
$407$	19.4800	+	33.7403i	0.965586	+	1.67244i
$408$		0			0
$409$	−24.6479	−	24.6479i	−1.21876	−	1.21876i	−0.968067	−	0.250692i	$-0.919342\pi$
$409$	−24.6479	−	24.6479i	−1.21876	−	1.21876i	−0.250692	−	0.968067i	$-0.580658\pi$
$410$	−7.42626	−	7.42626i	−0.366757	−	0.366757i
$411$		0			0
$412$	−3.00625	−	5.20698i	−0.148107	−	0.256529i
$413$	−0.0295719	−	0.0512200i	−0.00145514	−	0.00252037i
$414$		0			0
$415$			55.6462i			2.73157i
$416$	−1.50189	+	3.27785i	−0.0736362	+	0.160710i
$417$		0			0
$418$	−3.49807	+	0.937304i	−0.171096	+	0.0458450i
$419$	−14.9055	−	8.60570i	−0.728182	−	0.420416i	0.0895746	−	0.995980i	$-0.471449\pi$
$419$	−14.9055	−	8.60570i	−0.728182	−	0.420416i	−0.817757	+	0.575564i	$0.804783\pi$
$420$		0			0
$421$	3.68017	−	0.986098i	0.179360	−	0.0480595i	−0.168021	−	0.985783i	$-0.553738\pi$
$421$	3.68017	−	0.986098i	0.179360	−	0.0480595i	0.347381	+	0.937724i	$0.387071\pi$
$422$	−0.376425	−	1.40484i	−0.0183241	−	0.0683864i
$423$		0			0
$424$	−2.75436	+	2.75436i	−0.133763	+	0.133763i
$425$	22.6411	−	13.0719i	1.09826	−	0.634078i
$426$		0			0
$427$	0.0436131	+	0.162766i	0.00211059	+	0.00787681i
$428$	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	$-0.242107\pi$
$431$	20.9081	+	5.60231i	1.00711	+	0.269854i	0.282687	+	0.959212i	$0.408774\pi$
$432$		0			0
$433$	15.1421	+	8.74227i	0.727681	+	0.420127i	0.817573	−	0.575825i	$-0.195319\pi$
$433$	15.1421	+	8.74227i	0.727681	+	0.420127i	−0.0898923	+	0.995951i	$0.528652\pi$
$434$	0.0864490	+	0.322632i	0.00414968	+	0.0154868i
$435$		0			0
$436$	−14.0667	+	14.0667i	−0.673671	+	0.673671i
$437$	−1.05058	+	3.92084i	−0.0502563	+	0.187559i
$438$		0			0
$439$		−	6.29999i		−	0.300682i	−0.988634	−	0.150341i	$-0.951963\pi$
$439$		−	6.29999i		−	0.300682i	0.988634	−	0.150341i	$-0.0480372\pi$
$440$	−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
$445$	29.6970	−	51.4368i	1.40778	−	2.43834i
$446$	4.24818			0.201157
$447$		0			0
$448$	−0.0145188	+	0.0541850i	−0.000685950	+	0.00256000i
$449$	18.3173	−	4.90811i	0.864447	−	0.231628i	0.200762	−	0.979640i	$-0.435658\pi$
$449$	18.3173	−	4.90811i	0.864447	−	0.231628i	0.663685	+	0.748012i	$0.268991\pi$
$450$		0			0
$451$	−7.78089	+	13.4769i	−0.366388	+	0.634602i
$452$	−19.5681			−0.920408
$453$		0			0
$454$	20.2327	−	11.6814i	0.949570	−	0.548234i
$455$	−0.694841	−	0.117735i	−0.0325746	−	0.00551949i
$456$		0			0
$457$	−11.9721	−	11.9721i	−0.560032	−	0.560032i	0.369285	−	0.929316i	$-0.379603\pi$
$457$	−11.9721	−	11.9721i	−0.560032	−	0.560032i	−0.929316	+	0.369285i	$0.879603\pi$
$458$	−5.35197	+	3.08996i	−0.250081	+	0.144384i
$459$		0			0
$460$	14.2580	+	14.2580i	0.664783	+	0.664783i
$461$	−12.5113	−	3.35240i	−0.582711	−	0.156137i	−0.0445913	−	0.999005i	$-0.514199\pi$
$461$	−12.5113	−	3.35240i	−0.582711	−	0.156137i	−0.538120	+	0.842868i	$0.680865\pi$
$462$		0			0
$463$	17.0527	+	4.56925i	0.792505	+	0.212351i	0.632291	−	0.774731i	$-0.282115\pi$
$463$	17.0527	+	4.56925i	0.792505	+	0.212351i	0.160214	+	0.987082i	$0.448782\pi$
$464$			3.45319i			0.160310i
$465$		0			0
$466$	0.855383	−	0.855383i	0.0396249	−	0.0396249i
$467$	−21.1177			−0.977210			−0.488605	−	0.872505i	$-0.662494\pi$
$467$	−21.1177			−0.977210			−0.488605	+	0.872505i	$0.662494\pi$
$468$		0			0
$469$	−0.610496			−0.0281901
$470$	−12.3148	+	12.3148i	−0.568039	+	0.568039i
$471$		0			0
$472$		−	1.05432i		−	0.0485292i
$473$	−27.0784	−	7.25565i	−1.24507	−	0.333615i
$474$		0			0
$475$	4.83815	+	1.29638i	0.221990	+	0.0594820i
$476$	−0.145224	−	0.145224i	−0.00665632	−	0.00665632i
$477$		0			0
$478$	11.7761	−	6.79891i	0.538624	−	0.310975i
$479$	10.8748	+	10.8748i	0.496883	+	0.496883i	0.910466	−	0.413583i	$-0.135723\pi$
$479$	10.8748	+	10.8748i	0.496883	+	0.496883i	−0.413583	+	0.910466i	$0.635723\pi$
$480$		0			0
$481$	−27.0877	+	2.55246i	−1.23509	+	0.116382i
$482$	6.17394	−	3.56453i	0.281215	−	0.162360i
$483$		0			0
$484$	15.6561			0.711642
$485$	−4.00935	+	6.94439i	−0.182055	+	0.315329i
$486$		0			0
$487$	−15.1707	+	4.06498i	−0.687450	+	0.184202i	−0.585603	−	0.810598i	$-0.699142\pi$
$487$	−15.1707	+	4.06498i	−0.687450	+	0.184202i	−0.101848	+	0.994800i	$0.532475\pi$
$488$	−0.777466	+	2.90154i	−0.0351942	+	0.131347i
$489$		0			0
$490$	24.3796			1.10136
$491$	3.19734	−	5.53796i	0.144294	−	0.249925i	−0.784815	−	0.619730i	$-0.787242\pi$
$491$	3.19734	−	5.53796i	0.144294	−	0.249925i	0.929109	+	0.369805i	$0.120576\pi$
$492$		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
$497$			0.864234i			0.0387662i
$498$		0			0
$499$	−1.98095	+	7.39299i	−0.0886794	+	0.330956i	−0.995985	−	0.0895148i	$-0.971468\pi$
$499$	−1.98095	+	7.39299i	−0.0886794	+	0.330956i	0.907306	+	0.420471i	$0.138135\pi$
$500$	5.27469	−	5.27469i	0.235891	−	0.235891i
$501$		0			0
$502$	−1.29927	−	4.84894i	−0.0579892	−	0.216419i
$503$	−6.97222	−	4.02541i	−0.310876	−	0.179484i	0.336442	−	0.941704i	$-0.390776\pi$
$503$	−6.97222	−	4.02541i	−0.310876	−	0.179484i	−0.647318	+	0.762220i	$0.724110\pi$
$504$		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
$509$	8.37966	+	31.2733i	0.371422	+	1.38617i	0.858503	+	0.512809i	$0.171395\pi$
$509$	8.37966	+	31.2733i	0.371422	+	1.38617i	−0.487081	+	0.873357i	$0.661938\pi$
$510$		0			0
$511$	0.402962	−	0.232651i	0.0178260	−	0.0102919i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−1.27885	−	4.77274i	−0.0564077	−	0.210517i
$515$	20.2359	−	5.42221i	0.891702	−	0.238931i
$516$		0			0
$517$	22.3484	+	12.9029i	0.982882	+	0.567467i
$518$	−0.408883	+	0.109560i	−0.0179653	+	0.00481378i
$519$		0			0
$520$	−9.67766	−	8.01087i	−0.424393	−	0.351300i
$521$		−	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	−0.868868	−	0.495044i	$-0.835152\pi$
$523$	−19.7397	−	34.1901i	−0.863155	−	1.49503i	0.00571276	−	0.999984i	$-0.498182\pi$
$524$	−6.28138	−	10.8797i	−0.274403	−	0.475281i
$525$		0			0
$526$	9.12628	+	9.12628i	0.397925	+	0.397925i
$527$	−15.4145	−	15.4145i	−0.671468	−	0.671468i
$528$		0			0
$529$	−5.24435	−	9.08349i	−0.228015	−	0.394934i
$530$	−6.78625	−	11.7541i	−0.294776	−	0.510567i
$531$		0			0
$532$		−	0.0393479i		−	0.00170595i
$533$	−6.29276	−	8.86031i	−0.272570	−	0.383783i
$534$		0			0
$535$	−56.5673	+	15.1572i	−2.44562	+	0.655301i
$536$	−9.42492	−	5.44148i	−0.407095	−	0.235036i
$537$		0			0
$538$	−25.0509	+	6.71236i	−1.08002	+	0.289391i
$539$	−9.34970	−	34.8935i	−0.402720	−	1.50297i
$540$		0			0
$541$	8.65093	−	8.65093i	0.371933	−	0.371933i	−0.496248	−	0.868181i	$-0.665289\pi$
$541$	8.65093	−	8.65093i	0.371933	−	0.371933i	0.868181	+	0.496248i	$0.165289\pi$
$542$	14.1542	−	8.17196i	0.607977	−	0.351016i
$543$		0			0
$544$	−0.947575	−	3.53640i	−0.0406269	−	0.151622i
$545$	−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
$551$	−0.626906	−	2.33965i	−0.0267071	−	0.0996723i
$552$		0			0
$553$	0.219531	−	0.219531i	0.00933541	−	0.00933541i
$554$	4.41272	−	16.4685i	0.187479	−	0.699680i
$555$		0			0
$556$		−	0.313887i		−	0.0133118i
$557$	2.76078	−	10.3034i	0.116978	−	0.436567i	−0.882449	−	0.470407i	$-0.844107\pi$
$557$	2.76078	−	10.3034i	0.116978	−	0.436567i	0.999427	+	0.0338399i	$0.0107736\pi$
$558$		0			0
$559$	12.4835	−	15.0809i	0.527996	−	0.637854i
$560$	−0.169274	−	0.0977305i	−0.00715314	−	0.00412987i
$561$		0			0
$562$	−1.99333	+	3.45255i	−0.0840836	+	0.145637i
$563$	29.8646			1.25864			0.629322	−	0.777144i	$-0.283333\pi$
$563$	29.8646			1.25864			0.629322	+	0.777144i	$0.283333\pi$
$564$		0			0
$565$	17.6470	−	65.8594i	0.742414	−	2.77073i
$566$	17.5398	−	4.69978i	0.737254	−	0.197547i
$567$		0			0
$568$	−7.70311	+	13.3422i	−0.323215	+	0.559825i
$569$	−45.0588			−1.88896			−0.944482	−	0.328563i	$-0.893436\pi$
$569$	−45.0588			−1.88896			−0.944482	+	0.328563i	$0.893436\pi$
$570$		0			0
$571$	23.2043	−	13.3970i	0.971071	−	0.560648i	0.0715081	−	0.997440i	$-0.477219\pi$
$571$	23.2043	−	13.3970i	0.971071	−	0.560648i	0.899562	+	0.436792i	$0.143885\pi$
$572$	−7.75420	+	16.9234i	−0.324219	+	0.707604i
$573$		0			0
$574$	−0.119559	−	0.119559i	−0.00499028	−	0.00499028i
$575$	−35.7874	+	20.6619i	−1.49244	+	0.861659i
$576$		0			0
$577$	−20.9051	−	20.9051i	−0.870292	−	0.870292i	0.122212	−	0.992504i	$-0.461001\pi$
$577$	−20.9051	−	20.9051i	−0.870292	−	0.870292i	−0.992504	+	0.122212i	$0.961001\pi$
$578$	−3.47347	−	0.930713i	−0.144477	−	0.0387126i
$579$		0			0
$580$	−11.6222	−	3.11417i	−0.482587	−	0.129309i
$581$			0.895873i			0.0371671i
$582$		0			0
$583$	−14.2206	+	14.2206i	−0.588958	+	0.588958i
$584$	8.29466			0.343235
$585$		0			0
$586$	20.4538			0.844940
$587$	17.7153	−	17.7153i	0.731190	−	0.731190i	−0.239665	−	0.970856i	$-0.577038\pi$
$587$	17.7153	−	17.7153i	0.731190	−	0.731190i	0.970856	+	0.239665i	$0.0770378\pi$
$588$		0			0
$589$		−	4.17651i		−	0.172090i
$590$	3.54848	+	0.950812i	0.146089	+	0.0391443i
$591$		0			0
$592$	−7.28892	−	1.95306i	−0.299573	−	0.0802703i
$593$	13.5809	+	13.5809i	0.557700	+	0.557700i	0.928652	−	0.370952i	$-0.120969\pi$
$593$	13.5809	+	13.5809i	0.557700	+	0.557700i	−0.370952	+	0.928652i	$0.620969\pi$
$594$		0			0
$595$	0.619738	−	0.357806i	0.0254068	−	0.0146686i
$596$	4.31299	+	4.31299i	0.176667	+	0.176667i
$597$		0			0
$598$	12.0817	+	17.0113i	0.494059	+	0.695644i
$599$	−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
$601$	−23.1090			−0.942636			−0.471318	−	0.881963i	$-0.656222\pi$
$601$	−23.1090			−0.942636			−0.471318	+	0.881963i	$0.656222\pi$
$602$	0.152295	−	0.263783i	0.00620710	−	0.0107510i
$603$		0			0
$604$	−10.8353	+	2.90331i	−0.440883	+	0.118134i
$605$	−14.1190	+	52.6930i	−0.574021	+	2.14228i
$606$		0			0
$607$	29.8697			1.21238			0.606188	−	0.795322i	$-0.292698\pi$
$607$	29.8697			1.21238			0.606188	+	0.795322i	$0.292698\pi$
$608$	0.350716	−	0.607458i	0.0142234	−	0.0246357i
$609$		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	0.516832	+	0.856087i	$0.327111\pi$
$613$	−8.88349	+	33.1536i	−0.358801	+	1.33906i	−0.875633	+	0.482977i	$0.839556\pi$
$614$		−	9.50429i		−	0.383562i
$615$		0			0
$616$	−0.0749601	+	0.279755i	−0.00302023	+	0.0112716i
$617$	−1.94352	+	1.94352i	−0.0782432	+	0.0782432i	−0.745145	−	0.666902i	$-0.767620\pi$
$617$	−1.94352	+	1.94352i	−0.0782432	+	0.0782432i	0.666902	+	0.745145i	$0.267620\pi$
$618$		0			0
$619$	4.73494	+	17.6710i	0.190313	+	0.710259i	0.993430	+	0.114438i	$0.0365066\pi$
$619$	4.73494	+	17.6710i	0.190313	+	0.710259i	−0.803117	+	0.595821i	$0.796827\pi$
$620$	−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
$626$	−4.67917	−	17.4629i	−0.187017	−	0.697958i
$627$		0			0
$628$	−11.2930	+	6.52002i	−0.450640	+	0.260177i
$629$	19.5354	−	19.5354i	0.778927	−	0.778927i
$630$		0			0
$631$	−8.90171	−	33.2216i	−0.354371	−	1.32253i	−0.881274	−	0.472606i	$-0.843313\pi$
$631$	−8.90171	−	33.2216i	−0.354371	−	1.32253i	0.526902	−	0.849926i	$-0.323353\pi$
$632$	5.34588	−	1.43242i	0.212648	−	0.0569788i
$633$		0			0
$634$	−9.24920	−	5.34003i	−0.367333	−	0.212080i
$635$	−0.00965051	+	0.00258585i	−0.000382969	+	0.000102616i
$636$		0			0
$637$	24.8730	+	4.21451i	0.985503	+	0.166985i
$638$			17.8287i			0.705845i
$639$		0			0
$640$	−1.74219	−	3.01756i	−0.0688660	−	0.119279i
$641$	6.77781	+	11.7395i	0.267707	+	0.463683i	0.968269	−	0.249909i	$-0.0804006\pi$
$641$	6.77781	+	11.7395i	0.267707	+	0.463683i	−0.700562	+	0.713592i	$0.747067\pi$
$642$		0			0
$643$	28.1744	+	28.1744i	1.11109	+	1.11109i	0.993003	+	0.118088i	$0.0376765\pi$
$643$	28.1744	+	28.1744i	1.11109	+	1.11109i	0.118088	+	0.993003i	$0.462324\pi$
$644$	0.229546	+	0.229546i	0.00904538	+	0.00904538i
$645$		0			0
$646$	1.28402	+	2.22399i	0.0505192	+	0.0875019i
$647$	11.0797	+	19.1906i	0.435588	+	0.754460i	0.997343	−	0.0728432i	$-0.0232073\pi$
$647$	11.0797	+	19.1906i	0.435588	+	0.754460i	−0.561756	+	0.827303i	$0.689874\pi$
$648$		0			0
$649$		−	5.44343i		−	0.213673i
$650$	20.9913	−	14.9084i	0.823345	−	0.584755i
$651$		0			0
$652$	−5.40913	+	1.44937i	−0.211838	+	0.0567618i
$653$	29.5307	+	17.0495i	1.15562	+	0.667200i	0.950251	−	0.311484i	$-0.100826\pi$
$653$	29.5307	+	17.0495i	1.15562	+	0.667200i	0.205372	+	0.978684i	$0.434159\pi$
$654$		0			0
$655$	42.2818	−	11.3294i	1.65209	−	0.442675i
$656$	−0.780112	−	2.91142i	−0.0304582	−	0.113672i
$657$		0			0
$658$	−0.198261	+	0.198261i	−0.00772903	+	0.00772903i
$659$	−4.93704	+	2.85040i	−0.192320	+	0.111036i	−0.593068	−	0.805152i	$-0.702084\pi$
$659$	−4.93704	+	2.85040i	−0.192320	+	0.111036i	0.400748	+	0.916188i	$0.368750\pi$
$660$		0			0
$661$	2.37504	+	8.86377i	0.0923783	+	0.344761i	0.996609	−	0.0822839i	$-0.0262214\pi$
$661$	2.37504	+	8.86377i	0.0923783	+	0.344761i	−0.904231	+	0.427044i	$0.859555\pi$
$662$	−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
$668$	2.39787	+	8.94898i	0.0927765	+	0.346246i
$669$		0			0
$670$	26.8137	−	26.8137i	1.03590	−	1.03590i
$671$	−4.01402	+	14.9805i	−0.154960	+	0.578318i
$672$		0			0
$673$		−	30.8722i		−	1.19004i	−0.803713	−	0.595018i	$-0.797145\pi$
$673$		−	30.8722i		−	1.19004i	0.803713	−	0.595018i	$-0.202855\pi$
$674$	−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
$679$	−0.0645483	+	0.111801i	−0.00247714	+	0.00429052i
$680$	12.7568			0.489201
$681$		0			0
$682$	−7.95652	+	29.6941i	−0.304671	+	1.13705i
$683$	−11.2191	+	3.00615i	−0.429287	+	0.115027i	−0.466991	−	0.884262i	$-0.654662\pi$
$683$	−11.2191	+	3.00615i	−0.429287	+	0.115027i	0.0377045	+	0.999289i	$0.487995\pi$
$684$		0			0
$685$	24.4992	−	42.4338i	0.936065	−	1.62131i
$686$	0.785174			0.0299781
$687$		0			0
$688$	4.70232	−	2.71489i	0.179274	−	0.103504i
$689$	−4.89164	−	13.1651i	−0.186356	−	0.501551i
$690$		0			0
$691$	7.51539	+	7.51539i	0.285899	+	0.285899i	0.835456	−	0.549557i	$-0.185204\pi$
$691$	7.51539	+	7.51539i	0.285899	+	0.285899i	−0.549557	+	0.835456i	$0.685204\pi$
$692$	8.52731	−	4.92325i	0.324160	−	0.187154i
$693$		0			0
$694$	−12.7231	−	12.7231i	−0.482962	−	0.482962i
$695$	1.05643	+	0.283070i	0.0400728	+	0.0107375i
$696$		0			0
$697$	10.6591	+	2.85610i	0.403743	+	0.108183i
$698$			25.9005i			0.980348i
$699$		0			0
$700$	0.283250	−	0.283250i	0.0107059	−	0.0107059i
$701$	−10.2778			−0.388185			−0.194093	−	0.980983i	$-0.562176\pi$
$701$	−10.2778			−0.388185			−0.194093	+	0.980983i	$0.562176\pi$
$702$		0			0
$703$	5.29304			0.199631
$704$	−3.65076	+	3.65076i	−0.137593	+	0.137593i
$705$		0			0
$706$			2.96995i			0.111776i
$707$	0.190909	+	0.0511539i	0.00717988	+	0.00192384i
$708$		0			0
$709$	35.0211	+	9.38387i	1.31524	+	0.352419i	0.847194	−	0.531283i	$-0.178290\pi$
$709$	35.0211	+	9.38387i	1.31524	+	0.352419i	0.468050	+	0.883702i	$0.344957\pi$
$710$	−37.9582	−	37.9582i	−1.42455	−	1.42455i
$711$		0			0
$712$	14.7621	−	8.52292i	0.553235	−	0.319410i
$713$	24.3648	+	24.3648i	0.912468	+	0.912468i
$714$		0			0
$715$	−49.9653	−	41.3598i	−1.86860	−	1.54677i
$716$	−13.3330	+	7.69779i	−0.498276	+	0.287680i
$717$		0			0
$718$	0.0472482			0.00176329
$719$	−0.703567	+	1.21861i	−0.0262386	+	0.0454466i	−0.878847	−	0.477105i	$-0.841686\pi$
$719$	−0.703567	+	1.21861i	−0.0262386	+	0.0454466i	0.852608	+	0.522551i	$0.175020\pi$
$720$		0			0
$721$	0.325787	−	0.0872945i	0.0121330	−	0.00325102i
$722$	4.79022	−	17.8773i	0.178274	−	0.665326i
$723$		0			0
$724$	−17.1903			−0.638871
$725$	12.3294	−	21.3551i	0.457901	−	0.793108i
$726$		0			0
$727$	−32.7077	−	18.8838i	−1.21306	−	0.700361i	−0.249636	−	0.968340i	$-0.580311\pi$
$727$	−32.7077	−	18.8838i	−1.21306	−	0.700361i	−0.963425	+	0.267978i	$0.913644\pi$
$728$	−0.155805	−	0.128971i	−0.00577451	−	0.00477997i
$729$		0			0
$730$	−7.48031	+	27.9169i	−0.276859	+	1.03325i
$731$			19.8792i			0.735258i
$732$		0			0
$733$	−8.62288	+	32.1810i	−0.318493	+	1.18863i	0.602199	+	0.798346i	$0.294291\pi$
$733$	−8.62288	+	32.1810i	−0.318493	+	1.18863i	−0.920693	+	0.390288i	$0.872375\pi$
$734$	6.71759	−	6.71759i	0.247951	−	0.247951i
$735$		0			0
$736$	1.49777	+	5.58976i	0.0552086	+	0.206041i
$737$	−48.6605	−	28.0941i	−1.79243	−	1.03486i
$738$		0			0
$739$	−23.0630	−	6.17972i	−0.848388	−	0.227325i	−0.191668	−	0.981460i	$-0.561390\pi$
$739$	−23.0630	−	6.17972i	−0.848388	−	0.227325i	−0.656719	+	0.754135i	$0.728056\pi$
$740$	13.1466	−	22.7706i	0.483280	−	0.837065i
$741$		0			0
$742$	−0.109255	−	0.189235i	−0.00401087	−	0.00694703i
$743$	3.12072	+	11.6467i	0.114488	+	0.427275i	0.999248	−	0.0387716i	$-0.0123445\pi$
$743$	3.12072	+	11.6467i	0.114488	+	0.427275i	−0.884760	+	0.466047i	$0.845678\pi$
$744$		0			0
$745$	−18.4056	+	10.6265i	−0.674328	+	0.389323i
$746$	−18.9915	+	18.9915i	−0.695328	+	0.695328i
$747$		0			0
$748$	−4.89229	−	18.2583i	−0.178880	−	0.667588i
$749$	−0.910702	+	0.244022i	−0.0332763	+	0.00891637i
$750$		0			0
$751$	26.0668	+	15.0497i	0.951192	+	0.549171i	0.893451	−	0.449161i	$-0.148277\pi$
$751$	26.0668	+	15.0497i	0.951192	+	0.549171i	0.0577408	+	0.998332i	$0.481610\pi$
$752$	−4.82793	+	1.29364i	−0.176057	+	0.0471742i
$753$		0			0
$754$	−11.3191	−	5.18632i	−0.412216	−	0.188875i
$755$		−	39.0861i		−	1.42249i
$756$		0			0
$757$	25.3503	+	43.9080i	0.921371	+	1.59586i	0.797296	+	0.603589i	$0.206263\pi$
$757$	25.3503	+	43.9080i	0.921371	+	1.59586i	0.124076	+	0.992273i	$0.460403\pi$
$758$	9.52590	+	16.4993i	0.345996	+	0.599283i
$759$		0			0
$760$	1.72821	+	1.72821i	0.0626886	+	0.0626886i
$761$	−10.5364	−	10.5364i	−0.381943	−	0.381943i	0.489859	−	0.871802i	$-0.337048\pi$
$761$	−10.5364	−	10.5364i	−0.381943	−	0.381943i	−0.871802	+	0.489859i	$0.837048\pi$
$762$		0			0
$763$	−0.557971	−	0.966434i	−0.0201999	−	0.0349873i
$764$	−4.27232	−	7.39988i	−0.154567	−	0.267718i
$765$		0			0
$766$			9.57262i			0.345873i
$767$	3.45592	+	1.58348i	0.124786	+	0.0571761i
$768$		0			0
$769$	25.6571	−	6.87479i	0.925218	−	0.247911i	0.235404	−	0.971898i	$-0.424359\pi$
$769$	25.6571	−	6.87479i	0.925218	−	0.247911i	0.689814	+	0.723986i	$0.257692\pi$
$770$	−0.873955	−	0.504578i	−0.0314952	−	0.0181837i
$771$		0			0
$772$	0.589319	−	0.157908i	0.0212101	−	0.00568322i
$773$	11.3267	+	42.2718i	0.407393	+	1.52041i	0.799599	+	0.600534i	$0.205045\pi$
$773$	11.3267	+	42.2718i	0.407393	+	1.52041i	−0.392206	+	0.919877i	$0.628288\pi$
$774$		0			0
$775$	30.0651	−	30.0651i	1.07997	−	1.07997i
$776$	−1.99301	+	1.15067i	−0.0715449	+	0.0413065i
$777$		0			0
$778$	−2.38430	−	8.89834i	−0.0854814	−	0.319021i
$779$	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
$785$	−11.7598	−	43.8881i	−0.419725	−	1.56643i
$786$		0			0
$787$	−10.8347	+	10.8347i	−0.386217	+	0.386217i	−0.873336	−	0.487119i	$-0.838048\pi$
$787$	−10.8347	+	10.8347i	−0.386217	+	0.386217i	0.487119	+	0.873336i	$0.338048\pi$
$788$	−4.64193	+	17.3239i	−0.165362	+	0.617139i
$789$		0			0
$790$			19.2841i			0.686098i
$791$	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
$796$	9.96763	−	17.2644i	0.353293	−	0.611922i
$797$	−29.7359			−1.05330			−0.526650	−	0.850083i	$-0.676552\pi$
$797$	−29.7359			−1.05330			−0.526650	+	0.850083i	$0.676552\pi$
$798$		0			0
$799$	4.73621	−	17.6758i	0.167555	−	0.625324i
$800$	6.89754	−	1.84819i	0.243865	−	0.0653433i
$801$		0			0
$802$	−4.44671	+	7.70193i	−0.157019	+	0.271965i
$803$	42.8250			1.51126
$804$		0			0
$805$	−0.979580	+	0.565561i	−0.0345257	+	0.0199334i
$806$	−16.5376	−	13.6894i	−0.582514	−	0.482187i
$807$		0			0
$808$	2.49134	+	2.49134i	0.0876449	+	0.0876449i
$809$	−25.6350	+	14.8004i	−0.901280	+	0.520354i	−0.877615	−	0.479366i	$-0.840867\pi$
$809$	−25.6350	+	14.8004i	−0.901280	+	0.520354i	−0.0236649	+	0.999720i	$0.507533\pi$
$810$		0			0
$811$	−24.2773	−	24.2773i	−0.852492	−	0.852492i	0.137948	−	0.990440i	$-0.455949\pi$
$811$	−24.2773	−	24.2773i	−0.852492	−	0.852492i	−0.990440	+	0.137948i	$0.955949\pi$
$812$	−0.187111	−	0.0501363i	−0.00656632	−	0.00175944i
$813$		0			0
$814$	−37.6324	−	10.0836i	−1.31902	−	0.353429i
$815$		−	19.5123i		−	0.683486i
$816$		0			0
$817$	−2.69310	+	2.69310i	−0.0942196	+	0.0942196i
$818$	34.8574			1.21876
$819$		0			0
$820$	10.5023			0.366757
$821$	−29.2070	+	29.2070i	−1.01933	+	1.01933i	−0.0195210	+	0.999809i	$0.506214\pi$
$821$	−29.2070	+	29.2070i	−1.01933	+	1.01933i	−0.999809	+	0.0195210i	$0.993786\pi$
$822$		0			0
$823$		−	12.6873i		−	0.442251i	−0.975245	−	0.221126i	$-0.929027\pi$
$823$		−	12.6873i		−	0.442251i	0.975245	−	0.221126i	$-0.0709730\pi$
$824$	5.80763	+	1.55615i	0.202318	+	0.0542110i
$825$		0			0
$826$	0.0571285	+	0.0153075i	0.00198776	+	0.000532618i
$827$	36.0824	+	36.0824i	1.25471	+	1.25471i	0.953585	+	0.301123i	$0.0973614\pi$
$827$	36.0824	+	36.0824i	1.25471	+	1.25471i	0.301123	+	0.953585i	$0.402639\pi$
$828$		0			0
$829$	46.6421	−	26.9288i	1.61995	−	0.935276i	0.633014	−	0.774140i	$-0.281817\pi$
$829$	46.6421	−	26.9288i	1.61995	−	0.935276i	0.986932	−	0.161136i	$-0.0515159\pi$
$830$	−39.3478	−	39.3478i	−1.36578	−	1.36578i
$831$		0			0
$832$	−1.25580	−	3.37979i	−0.0435369	−	0.117173i
$833$	−22.1845	+	12.8083i	−0.768649	+	0.443780i
$834$		0			0
$835$	−32.2816			−1.11715
$836$	1.81073	−	3.13628i	0.0626255	−	0.108471i
$837$		0			0
$838$	16.6249	−	4.45464i	0.574299	−	0.153883i
$839$	2.07783	−	7.75457i	0.0717347	−	0.267717i	−0.920738	−	0.390180i	$-0.872413\pi$
$839$	2.07783	−	7.75457i	0.0717347	−	0.267717i	0.992473	+	0.122463i	$0.0390793\pi$
$840$		0			0
$841$	17.0755			0.588809
$842$	−1.90499	+	3.29955i	−0.0656505	+	0.113710i
$843$		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
$848$		−	3.89525i		−	0.133763i
$849$		0			0
$850$	−6.76649	+	25.2529i	−0.232089	+	0.866167i
$851$	−30.8783	+	30.8783i	−1.05850	+	1.05850i
$852$		0			0
$853$	1.59683	+	5.95946i	0.0546745	+	0.204048i	0.987860	−	0.155347i	$-0.0496497\pi$
$853$	1.59683	+	5.95946i	0.0546745	+	0.204048i	−0.933185	+	0.359395i	$0.882983\pi$
$854$	−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	$0.401137\pi$
$857$	−19.6661	+	34.0626i	−0.671780	+	1.16356i	−0.977399	+	0.211404i	$0.932197\pi$
$858$		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	$0.910545\pi$
$860$	4.89669	+	18.2747i	0.166976	+	0.623161i
$861$		0			0
$862$	−18.7457	+	10.8228i	−0.638481	+	0.368627i
$863$	20.5132	−	20.5132i	0.698277	−	0.698277i	−0.265762	−	0.964039i	$-0.585623\pi$
$863$	20.5132	−	20.5132i	0.698277	−	0.698277i	0.964039	+	0.265762i	$0.0856234\pi$
$864$		0			0
$865$	8.87978	+	33.1398i	0.301922	+	1.12679i
$866$	−16.8888	+	4.52533i	−0.573904	+	0.153777i
$867$		0			0
$868$	−0.289264	−	0.167007i	−0.00981826	−	0.00566857i
$869$	27.6006	−	7.39555i	0.936285	−	0.250877i
$870$		0			0
$871$	31.9916	−	22.7210i	1.08399	−	0.769872i
$872$		−	19.8933i		−	0.673671i
$873$		0			0
$874$	−2.02957	−	3.51533i	−0.0686514	−	0.118908i
$875$	0.209227	+	0.362391i	0.00707315	+	0.0122511i
$876$		0			0
$877$	5.47000	+	5.47000i	0.184709	+	0.184709i	0.793404	−	0.608695i	$-0.208307\pi$
$877$	5.47000	+	5.47000i	0.184709	+	0.184709i	−0.608695	+	0.793404i	$0.708307\pi$
$878$	4.45477	+	4.45477i	0.150341	+	0.150341i
$879$		0			0
$880$	−8.99483	−	15.5795i	−0.303216	−	0.525185i
$881$	20.3481	+	35.2439i	0.685544	+	1.18740i	0.973266	+	0.229682i	$0.0737688\pi$
$881$	20.3481	+	35.2439i	0.685544	+	1.18740i	−0.287722	+	0.957714i	$0.592898\pi$
$882$		0			0
$883$			18.4296i			0.620206i	0.950703	+	0.310103i	$0.100364\pi$
$883$			18.4296i			0.620206i	−0.950703	+	0.310103i	$0.899636\pi$
$884$	13.0149	+	2.20527i	0.437740	+	0.0741712i
$885$		0			0
$886$	−15.5644	+	4.17048i	−0.522898	+	0.140110i
$887$	15.2414	+	8.79965i	0.511758	+	0.295463i	0.733556	−	0.679629i	$-0.237859\pi$
$887$	15.2414	+	8.79965i	0.511758	+	0.295463i	−0.221798	+	0.975093i	$0.571193\pi$
$888$		0			0
$889$	−0.000155368	0	4.16307e-5i	−5.21087e−6	0	1.39625e-6i
$890$	15.3723	+	57.3703i	0.515281	+	1.92306i
$891$		0			0
$892$	−3.00391	+	3.00391i	−0.100579	+	0.100579i
$893$	3.03622	−	1.75296i	0.101603	−	0.0586607i
$894$		0			0
$895$	−13.8841	−	51.8161i	−0.464094	−	1.73202i
$896$	−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
$902$	−4.02768	−	15.0315i	−0.134107	−	0.500495i
$903$		0			0
$904$	13.8368	−	13.8368i	0.460204	−	0.460204i
$905$	15.5026	−	57.8564i	0.515323	−	1.92321i
$906$		0			0
$907$			36.3935i			1.20843i	0.796823	+	0.604213i	$0.206512\pi$
$907$			36.3935i			1.20843i	−0.796823	+	0.604213i	$0.793488\pi$
$908$	−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
$913$	−41.2268	+	71.4069i	−1.36441	+	2.36322i
$914$	16.9311			0.560032
$915$		0			0
$916$	1.59948	−	5.96935i	0.0528484	−	0.197233i
$917$	0.680714	−	0.182397i	0.0224791	−	0.00602327i
$918$		0			0
$919$	−9.39060	+	16.2650i	−0.309767	+	0.536533i	−0.978311	−	0.207140i	$-0.933584\pi$
$919$	−9.39060	+	16.2650i	−0.309767	+	0.536533i	0.668544	+	0.743673i	$0.266918\pi$
$920$	−20.1639			−0.664783
$921$		0			0
$922$	11.2174	−	6.47635i	0.369424	−	0.213287i
$923$	−32.1645	−	45.2881i	−1.05871	−	1.49068i
$924$		0			0
$925$	38.1026	+	38.1026i	1.25281	+	1.25281i
$926$	−15.2890	+	8.82711i	−0.502428	+	0.290077i
$927$		0			0
$928$	−2.44178	−	2.44178i	−0.0801552	−	0.0801552i
$929$	5.87987	+	1.57551i	0.192912	+	0.0516907i	0.353982	−	0.935252i	$-0.384828\pi$
$929$	5.87987	+	1.57551i	0.192912	+	0.0516907i	−0.161069	+	0.986943i	$0.551494\pi$
$930$		0			0
$931$	−4.74059	−	1.27024i	−0.155366	−	0.0416303i
$932$			1.20969i			0.0396249i
$933$		0			0
$934$	14.9325	−	14.9325i	0.488605	−	0.488605i
$935$	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	$0.553457\pi$
$938$	0.431686	−	0.431686i	0.0140950	−	0.0140950i
$939$		0			0
$940$		−	17.4157i		−	0.568039i
$941$	36.0693	+	9.66473i	1.17582	+	0.315061i	0.793269	−	0.608871i	$-0.208377\pi$
$941$	36.0693	+	9.66473i	1.17582	+	0.315061i	0.382556	+	0.923932i	$0.375044\pi$
$942$		0			0
$943$	−16.8482	−	4.51446i	−0.548653	−	0.147011i
$944$	0.745519	+	0.745519i	0.0242646	+	0.0242646i
$945$		0			0
$946$	24.2779	−	14.0168i	0.789342	−	0.455727i
$947$	16.6437	+	16.6437i	0.540849	+	0.540849i	0.923778	−	0.382929i	$-0.125085\pi$
$947$	16.6437	+	16.6437i	0.540849	+	0.540849i	−0.382929	+	0.923778i	$0.625085\pi$
$948$		0			0
$949$	−12.4577	+	27.1887i	−0.404393	+	0.882582i
$950$	−4.33777	+	2.50441i	−0.140736	+	0.0812539i
$951$		0			0
$952$	0.205377			0.00665632
$953$	−23.3774	+	40.4908i	−0.757267	+	1.31163i	0.186972	+	0.982365i	$0.440133\pi$
$953$	−23.3774	+	40.4908i	−0.757267	+	1.31163i	−0.944239	+	0.329260i	$0.893201\pi$
$954$		0			0
$955$	28.7582	−	7.70575i	0.930595	−	0.249352i
$956$	−3.51937	+	13.1345i	−0.113825	+	0.424799i
$957$		0			0
$958$	−15.3793			−0.496883
$959$	0.394423	−	0.683161i	0.0127366	−	0.0220604i
$960$		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
$965$			2.12584i			0.0684333i
$966$		0			0
$967$	11.9939	−	44.7620i	0.385699	−	1.43945i	−0.451363	−	0.892340i	$-0.649062\pi$
$967$	11.9939	−	44.7620i	0.385699	−	1.43945i	0.837062	−	0.547108i	$-0.184271\pi$
$968$	−11.0706	+	11.0706i	−0.355821	+	0.355821i
$969$		0			0
$970$	−2.07539	−	7.74546i	−0.0666368	−	0.248692i
$971$	10.9829	+	6.34097i	0.352458	+	0.203491i	0.665767	−	0.746160i	$-0.268104\pi$
$971$	10.9829	+	6.34097i	0.352458	+	0.203491i	−0.313310	+	0.949651i	$0.601438\pi$
$972$		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
$977$	−15.6198	−	58.2939i	−0.499722	−	1.86499i	−0.501791	−	0.864989i	$-0.667325\pi$
$977$	−15.6198	−	58.2939i	−0.499722	−	1.86499i	0.00206974	−	0.999998i	$-0.499341\pi$
$978$		0			0
$979$	76.2163	−	44.0035i	2.43588	−	1.40636i
$980$	−17.2390	+	17.2390i	−0.550680	+	0.550680i
$981$		0			0
$982$	1.65507	+	6.17679i	0.0528153	+	0.197109i
$983$	−21.9948	+	5.89349i	−0.701525	+	0.187973i	−0.591914	−	0.806001i	$-0.701627\pi$
$983$	−21.9948	+	5.89349i	−0.701525	+	0.187973i	−0.109611	+	0.993975i	$0.534961\pi$
$984$		0			0
$985$	−54.1200	−	31.2462i	−1.72441	−	0.995587i
$986$	12.2119	−	3.27216i	0.388905	−	0.104207i
$987$		0			0
$988$	1.46442	+	2.06193i	0.0465895	+	0.0655988i
$989$		−	31.4218i		−	0.999154i
$990$		0			0
$991$	14.2272	+	24.6423i	0.451942	+	0.782787i	0.998507	−	0.0546299i	$-0.0173979\pi$
$991$	14.2272	+	24.6423i	0.451942	+	0.782787i	−0.546564	+	0.837417i	$0.684065\pi$
$992$	−2.97713	−	5.15654i	−0.0945241	−	0.163720i
$993$		0			0
$994$	−0.611106	−	0.611106i	−0.0193831	−	0.0193831i
$995$	49.1170	+	49.1170i	1.55711	+	1.55711i
$996$		0			0
$997$	8.36581	+	14.4900i	0.264948	+	0.458903i	0.967550	−	0.252680i	$-0.0813119\pi$
$997$	8.36581	+	14.4900i	0.264948	+	0.458903i	−0.702602	+	0.711583i	$0.747979\pi$
$998$	−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.bb.a.89.7		56
3.2	odd	2		234.2.y.a.11.8	✓	56
9.4	even	3		234.2.z.a.167.6	yes	56
9.5	odd	6		702.2.bc.a.557.14		56
13.6	odd	12		702.2.bc.a.305.14		56
39.32	even	12		234.2.z.a.227.6	yes	56
117.32	even	12	inner	702.2.bb.a.71.7		56
117.58	odd	12		234.2.y.a.149.8	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.8	✓	56	3.2	odd	2
234.2.y.a.149.8	yes	56	117.58	odd	12
234.2.z.a.167.6	yes	56	9.4	even	3
234.2.z.a.227.6	yes	56	39.32	even	12
702.2.bb.a.71.7		56	117.32	even	12	inner
702.2.bb.a.89.7		56	1.1	even	1	trivial
702.2.bc.a.305.14		56	13.6	odd	12
702.2.bc.a.557.14		56	9.5	odd	6

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.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(3.36565 + 0.901822i) q^{5} +(0.0541850 + 0.0145188i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(3.36565 + 0.901822i) q^{5} +(0.0541850 + 0.0145188i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.01756 + 1.74219i) q^{10} +(3.65076 + 3.65076i) q^{11} +(-3.37979 + 1.25580i) q^{13} +(-0.0485810 + 0.0280482i) q^{14} -1.00000 q^{16} +(1.83057 - 3.17065i) q^{17} +(0.677531 - 0.181544i) q^{19} +(0.901822 - 3.36565i) q^{20} -5.16296 q^{22} +(-2.89347 + 5.01164i) q^{23} +(6.18416 + 3.57043i) q^{25} +(1.50189 - 3.27785i) q^{26} +(0.0145188 - 0.0541850i) q^{28} -3.45319i q^{29} +(1.54108 - 5.75138i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.947575 + 3.53640i) q^{34} +(0.169274 + 0.0977305i) q^{35} +(7.28892 + 1.95306i) q^{37} +(-0.350716 + 0.607458i) q^{38} +(1.74219 + 3.01756i) q^{40} +(0.780112 + 2.91142i) q^{41} +(-4.70232 + 2.71489i) q^{43} +(3.65076 - 3.65076i) q^{44} +(-1.49777 - 5.58976i) q^{46} +(4.82793 - 1.29364i) q^{47} +(-6.05945 - 3.49843i) q^{49} +(-6.89754 + 1.84819i) q^{50} +(1.25580 + 3.37979i) q^{52} +3.89525i q^{53} +(8.99483 + 15.5795i) q^{55} +(0.0280482 + 0.0485810i) q^{56} +(2.44178 + 2.44178i) q^{58} +(-0.745519 - 0.745519i) q^{59} +(1.50195 + 2.60145i) q^{61} +(2.97713 + 5.15654i) q^{62} +1.00000i q^{64} +(-12.5077 + 1.17860i) q^{65} +(-10.5121 + 2.81672i) q^{67} +(-3.17065 - 1.83057i) q^{68} +(-0.188801 + 0.0505890i) q^{70} +(3.98742 + 14.8813i) q^{71} +(5.86521 - 5.86521i) q^{73} +(-6.53507 + 3.77302i) q^{74} +(-0.181544 - 0.677531i) q^{76} +(0.144812 + 0.250821i) q^{77} +(2.76723 - 4.79298i) q^{79} +(-3.36565 - 0.901822i) q^{80} +(-2.61030 - 1.50706i) q^{82} +(4.13340 + 15.4261i) q^{83} +(9.02042 - 9.02042i) q^{85} +(1.40533 - 5.24476i) q^{86} +5.16296i q^{88} +(4.41179 - 16.4650i) q^{89} +(-0.201367 + 0.0189747i) q^{91} +(5.01164 + 2.89347i) q^{92} +(-2.49912 + 4.32861i) q^{94} +2.44405 q^{95} +(-0.595628 + 2.22292i) q^{97} +(6.75844 - 1.81092i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73} - 48 q^{74} + 4 q^{76} + 24 q^{77} - 24 q^{79} + 60 q^{83} - 48 q^{86} + 4 q^{91} + 24 q^{92} + 20 q^{97} + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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