LMFDB - Embedded newform 702.2.bb.a.71.7

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			71.7
Character	$\chi$	$=$	702.71
Dual form			702.2.bb.a.89.7

$q$-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 $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

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

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	0.590337	−	0.807157i	$-0.298995\pi$
$5$	3.36565	−	0.901822i	1.50516	−	0.403307i	0.914825	+	0.403850i	$0.132328\pi$
$6$		0			0
$7$	0.0541850	−	0.0145188i	0.0204800	−	0.00548760i	−0.248564	−	0.968615i	$-0.579959\pi$
$7$	0.0541850	−	0.0145188i	0.0204800	−	0.00548760i	0.269045	+	0.963128i	$0.413292\pi$
$8$	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	0.106426	−	0.994321i	$-0.466059\pi$
$11$	3.65076	−	3.65076i	1.10075	−	1.10075i	0.994321	−	0.106426i	$-0.0339406\pi$
$12$		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	0.997980	−	0.0635211i	$-0.0202330\pi$
$17$	1.83057	+	3.17065i	0.443979	+	0.768995i	−0.554001	+	0.832516i	$0.686900\pi$
$18$		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	$0.557694\pi$
$20$	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	−0.992313	−	0.123754i	$-0.960507\pi$
$23$	−2.89347	−	5.01164i	−0.603330	−	1.04500i	0.388982	−	0.921245i	$-0.372827\pi$
$24$		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	$0.103892\pi$
$29$			3.45319i			0.641242i	−0.947208	+	0.320621i	$0.896108\pi$
$30$		0			0
$31$	1.54108	+	5.75138i	0.276786	+	1.03298i	0.954635	+	0.297778i	$0.0962454\pi$
$31$	1.54108	+	5.75138i	0.276786	+	1.03298i	−0.677850	+	0.735201i	$0.737088\pi$
$32$	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	0.396134	−	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
$41$	0.780112	−	2.91142i	0.121833	−	0.454687i	−0.877874	−	0.478892i	$-0.841039\pi$
$41$	0.780112	−	2.91142i	0.121833	−	0.454687i	0.999707	+	0.0242048i	$0.00770537\pi$
$42$		0			0
$43$	−4.70232	−	2.71489i	−0.717097	−	0.414016i	0.0965863	−	0.995325i	$-0.469208\pi$
$43$	−4.70232	−	2.71489i	−0.717097	−	0.414016i	−0.813683	+	0.581309i	$0.802541\pi$
$44$	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	0.593123	−	0.805112i	$-0.297895\pi$
$47$	4.82793	+	1.29364i	0.704226	+	0.188697i	0.111103	+	0.993809i	$0.464561\pi$
$48$		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	$-0.913794\pi$
$53$		−	3.89525i		−	0.535053i	0.963550	−	0.267527i	$-0.0862064\pi$
$54$		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	−0.753969	−	0.656910i	$-0.771863\pi$
$59$	−0.745519	+	0.745519i	−0.0970583	+	0.0970583i	0.656910	+	0.753969i	$0.271863\pi$
$60$		0			0
$61$	1.50195	−	2.60145i	0.192305	−	0.333082i	−0.753709	−	0.657209i	$-0.771737\pi$
$61$	1.50195	−	2.60145i	0.192305	−	0.333082i	0.946014	+	0.324127i	$0.105070\pi$
$62$	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	−0.448784	−	0.893640i	$-0.648143\pi$
$67$	−10.5121	−	2.81672i	−1.28426	−	0.344117i	−0.835478	+	0.549524i	$0.814809\pi$
$68$	−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	−0.154865	−	0.987936i	$-0.549494\pi$
$71$	3.98742	−	14.8813i	0.473220	−	1.76608i	0.628085	−	0.778145i	$-0.283839\pi$
$72$		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	$0.588671\pi$
$74$	−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	0.978652	−	0.205523i	$-0.0658896\pi$
$79$	2.76723	+	4.79298i	0.311338	+	0.539253i	−0.667314	+	0.744776i	$0.732556\pi$
$80$	−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	−0.238184	−	0.971220i	$-0.576552\pi$
$83$	4.13340	−	15.4261i	0.453699	−	1.69323i	0.691883	−	0.722009i	$-0.256781\pi$
$84$		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	0.647955	+	0.761679i	$0.275625\pi$
$89$	4.41179	+	16.4650i	0.467649	+	1.74529i	−0.180306	+	0.983611i	$0.557709\pi$
$90$		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	0.929072	−	0.369898i	$-0.120607\pi$
$97$	−0.595628	−	2.22292i	−0.0604769	−	0.225703i	−0.989549	+	0.144195i	$0.953941\pi$
$98$	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	0.734090	−	0.679052i	$-0.237609\pi$
$103$	5.20698	+	3.00625i	0.513059	+	0.296215i	−0.221031	+	0.975267i	$0.570942\pi$
$104$	−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	−0.412024	−	0.911173i	$-0.635178\pi$
$107$	−14.5555	−	8.40363i	−1.40714	−	0.812410i	−0.995111	+	0.0987630i	$0.968511\pi$
$108$		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	$0.848277\pi$
$110$	−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	$0.372143\pi$
$113$			19.5681i			1.84082i	−0.390960	+	0.920408i	$0.627857\pi$
$114$		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	0.499890	−	0.866089i	$-0.333374\pi$
$127$	−0.00248320	−	0.00143368i	−0.000220349	−	0.000127218i	−0.500110	+	0.865962i	$0.666707\pi$
$128$	−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	0.893255	−	0.449550i	$-0.148416\pi$
$131$	10.8797	+	6.28138i	0.950562	+	0.548807i	0.0573063	+	0.998357i	$0.481749\pi$
$132$		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	0.927700	+	0.373327i	$0.121783\pi$
$137$	3.63959	+	13.5832i	0.310952	+	1.16049i	−0.616748	+	0.787160i	$0.711550\pi$
$138$		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	0.508014	−	0.861349i	$-0.330380\pi$
$149$	−4.31299	−	4.31299i	−0.353334	−	0.353334i	−0.861349	+	0.508014i	$0.830380\pi$
$150$		0			0
$151$	−2.90331	+	10.8353i	−0.236268	+	0.881766i	0.741305	+	0.671169i	$0.234207\pi$
$151$	−2.90331	+	10.8353i	−0.236268	+	0.881766i	−0.977573	+	0.210597i	$0.932459\pi$
$152$	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	0.479366	+	0.877615i	$0.340867\pi$
$157$	−6.52002	+	11.2930i	−0.520354	+	0.901280i	−0.999720	+	0.0236645i	$0.992467\pi$
$158$	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	−0.999172	−	0.0406802i	$-0.987048\pi$
$163$	−1.44937	+	5.40913i	−0.113524	+	0.423676i	0.885649	+	0.464356i	$0.153714\pi$
$164$	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	−0.104627	−	0.994512i	$-0.533365\pi$
$167$	−8.94898	−	2.39787i	−0.692493	−	0.185553i	−0.587866	+	0.808959i	$0.700032\pi$
$168$		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	−0.615916	−	0.787812i	$-0.711214\pi$
$173$	4.92325	−	8.52731i	0.374307	−	0.648319i	0.990223	+	0.139493i	$0.0445471\pi$
$174$		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	0.420642	+	0.907227i	$0.361805\pi$
$179$	−7.69779	+	13.3330i	−0.575360	+	0.996553i	−0.996002	+	0.0893264i	$0.971529\pi$
$180$		0			0
$181$			17.1903i			1.27774i	0.769314	+	0.638871i	$0.220598\pi$
$181$			17.1903i			1.27774i	−0.769314	+	0.638871i	$0.779402\pi$
$182$	0.128971	+	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	0.743227	−	0.669039i	$-0.233294\pi$
$191$	7.39988	+	4.27232i	0.535436	+	0.309134i	−0.207791	+	0.978173i	$0.566627\pi$
$192$		0			0
$193$	0.157908	−	0.589319i	0.0113664	−	0.0424201i	−0.960010	−	0.279967i	$-0.909677\pi$
$193$	0.157908	−	0.589319i	0.0113664	−	0.0424201i	0.971376	+	0.237547i	$0.0763432\pi$
$194$	−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	−0.816244	−	0.577707i	$-0.803948\pi$
$197$	−17.3239	+	4.64193i	−1.23428	+	0.330724i	−0.418035	+	0.908431i	$0.637281\pi$
$198$		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	$0.0835675\pi$
$200$	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	0.839908	−	0.542728i	$-0.182609\pi$
$211$	−0.727198	−	1.25954i	−0.0500623	−	0.0867105i	−0.889971	+	0.456018i	$0.849275\pi$
$212$	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	−0.800496	−	0.599339i	$-0.795430\pi$
$223$	−3.00391	+	3.00391i	−0.201157	+	0.201157i	0.599339	+	0.800496i	$0.295430\pi$
$224$	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	−0.912364	−	0.409380i	$-0.865745\pi$
$227$	−22.5667	+	6.04673i	−1.49780	+	0.401335i	−0.585440	+	0.810716i	$0.699078\pi$
$228$		0			0
$229$	5.96935	−	1.59948i	0.394466	−	0.105697i	−0.0561332	−	0.998423i	$-0.517877\pi$
$229$	5.96935	−	1.59948i	0.394466	−	0.105697i	0.450599	+	0.892727i	$0.351210\pi$
$230$			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	−0.657246	−	0.753676i	$-0.728279\pi$
$239$	−13.1345	+	3.51937i	−0.849599	+	0.227649i	−0.192353	+	0.981326i	$0.561612\pi$
$240$		0			0
$241$	−6.88614	+	1.84513i	−0.443575	+	0.118856i	−0.473692	−	0.880691i	$-0.657079\pi$
$241$	−6.88614	+	1.84513i	−0.443575	+	0.118856i	0.0301165	+	0.999546i	$0.490412\pi$
$242$	−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	0.775873	−	0.630889i	$-0.217310\pi$
$251$	−2.50999	−	4.34744i	−0.158429	−	0.274408i	−0.934302	+	0.356481i	$0.883976\pi$
$252$		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	0.778625	−	0.627489i	$-0.215917\pi$
$257$	−2.47055	−	4.27912i	−0.154109	−	0.266924i	−0.932734	+	0.360565i	$0.882584\pi$
$258$		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	$0.130269\pi$
$263$			12.9065i			0.795849i	−0.917418	+	0.397925i	$0.869731\pi$
$264$		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	0.378558	−	0.925577i	$-0.376420\pi$
$269$	22.4600	−	12.9673i	1.36941	−	0.790630i	0.990853	+	0.134948i	$0.0430866\pi$
$270$		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
$275$	9.54212	−	35.6117i	0.575412	−	2.14747i
$276$		0			0
$277$	−14.7653	−	8.52472i	−0.887158	−	0.512201i	−0.0141462	−	0.999900i	$-0.504503\pi$
$277$	−14.7653	−	8.52472i	−0.887158	−	0.512201i	−0.873012	+	0.487699i	$0.837836\pi$
$278$	−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	0.371843	−	0.928296i	$-0.378726\pi$
$281$	3.85082	+	1.03182i	0.229721	+	0.0615535i	−0.142122	+	0.989849i	$0.545393\pi$
$282$		0			0
$283$	−15.7258	+	9.07928i	−0.934801	+	0.539707i	−0.888327	−	0.459212i	$-0.848132\pi$
$283$	−15.7258	+	9.07928i	−0.934801	+	0.539707i	−0.0464740	+	0.998920i	$0.514798\pi$
$284$	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	−0.989497	−	0.144557i	$-0.953824\pi$
$293$	−14.4630	+	14.4630i	−0.844940	+	0.844940i	0.144557	+	0.989497i	$0.453824\pi$
$294$		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	0.488822	−	0.872384i	$-0.337427\pi$
$307$	−6.72055	−	6.72055i	−0.383562	−	0.383562i	−0.872384	+	0.488822i	$0.837427\pi$
$308$	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	−0.810145	−	0.586230i	$-0.800612\pi$
$311$	1.80968	−	3.13446i	0.102618	−	0.177739i	0.912762	+	0.408491i	$0.133945\pi$
$312$		0			0
$313$	−9.03947	−	15.6568i	−0.510941	−	0.884975i	−0.999920	−	0.0126797i	$-0.995964\pi$
$313$	−9.03947	−	15.6568i	−0.510941	−	0.884975i	0.488979	−	0.872296i	$-0.337370\pi$
$314$	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	−0.843830	−	0.536610i	$-0.819705\pi$
$317$	2.76420	−	10.3161i	0.155253	−	0.579412i	0.999084	−	0.0428025i	$-0.0136286\pi$
$318$		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	0.938215	−	0.346054i	$-0.112479\pi$
$331$	−0.861097	−	3.21366i	−0.0473301	−	0.176639i	−0.985545	+	0.169416i	$0.945812\pi$
$332$	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	0.566672	−	0.823943i	$-0.308231\pi$
$337$	2.50494	+	1.44623i	0.136453	+	0.0787811i	−0.430220	+	0.902724i	$0.641564\pi$
$338$	−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	$-0.839561\pi$
$347$		−	17.9932i		−	0.965923i	0.875642	−	0.482962i	$-0.160439\pi$
$348$		0			0
$349$	18.3144	+	18.3144i	0.980348	+	0.980348i	0.999811	−	0.0194630i	$-0.00619566\pi$
$349$	18.3144	+	18.3144i	0.980348	+	0.980348i	−0.0194630	+	0.999811i	$0.506196\pi$
$350$	−0.400577			−0.0214117
$351$		0			0
$352$	5.16296			0.275187
$353$	2.10008	+	2.10008i	0.111776	+	0.111776i	0.760783	−	0.649007i	$-0.224815\pi$
$353$	2.10008	+	2.10008i	0.111776	+	0.111776i	−0.649007	+	0.760783i	$0.724815\pi$
$354$		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	−0.707988	−	0.706225i	$-0.750397\pi$
$359$	−0.0334095	+	0.0334095i	−0.00176329	+	0.00176329i	0.706225	+	0.707988i	$0.250397\pi$
$360$		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	0.969036	+	0.246921i	$0.0794189\pi$
$379$	4.93097	+	18.4026i	0.253287	+	0.945279i	−0.715749	+	0.698358i	$0.753914\pi$
$380$			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	0.858570	−	0.512697i	$-0.171354\pi$
$383$	6.76886	+	6.76886i	0.345873	+	0.345873i	−0.512697	+	0.858570i	$0.671354\pi$
$384$		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	0.725308	−	0.688425i	$-0.241698\pi$
$389$	−4.60612	−	7.97804i	−0.233540	−	0.404502i	−0.958847	+	0.283922i	$0.908364\pi$
$390$		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	−0.506859	−	0.862029i	$-0.669194\pi$
$397$	7.23488	−	27.0009i	0.363108	−	1.35514i	0.869967	−	0.493110i	$-0.164140\pi$
$398$	−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	0.466849	−	0.884337i	$-0.345389\pi$
$401$	8.59039	+	2.30179i	0.428984	+	0.114946i	−0.0378654	+	0.999283i	$0.512056\pi$
$402$		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	−0.250692	+	0.968067i	$0.580658\pi$
$409$	−24.6479	+	24.6479i	−1.21876	+	1.21876i	−0.968067	+	0.250692i	$0.919342\pi$
$410$	−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	−0.817757	−	0.575564i	$-0.804783\pi$
$419$	−14.9055	+	8.60570i	−0.728182	+	0.420416i	0.0895746	+	0.995980i	$0.471449\pi$
$420$		0			0
$421$	3.68017	+	0.986098i	0.179360	+	0.0480595i	0.347381	−	0.937724i	$-0.387071\pi$
$421$	3.68017	+	0.986098i	0.179360	+	0.0480595i	−0.168021	+	0.985783i	$0.553738\pi$
$422$	−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	0.282687	−	0.959212i	$-0.408774\pi$
$431$	20.9081	−	5.60231i	1.00711	−	0.269854i	0.724420	+	0.689358i	$0.242107\pi$
$432$		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	$0.195319\pi$
$434$	0.0864490	−	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	$0.0480372\pi$
$439$			6.29999i			0.300682i	−0.988634	+	0.150341i	$0.951963\pi$
$440$	−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	−0.130414	−	0.991460i	$-0.541631\pi$
$443$	13.9547	−	8.05675i	0.663007	−	0.382788i	0.793422	+	0.608672i	$0.208297\pi$
$444$		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	0.663685	−	0.748012i	$-0.268991\pi$
$449$	18.3173	+	4.90811i	0.864447	+	0.231628i	0.200762	+	0.979640i	$0.435658\pi$
$450$		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	−0.929316	−	0.369285i	$-0.879603\pi$
$457$	−11.9721	+	11.9721i	−0.560032	+	0.560032i	0.369285	+	0.929316i	$0.379603\pi$
$458$	−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	−0.538120	−	0.842868i	$-0.680865\pi$
$461$	−12.5113	+	3.35240i	−0.582711	+	0.156137i	−0.0445913	+	0.999005i	$0.514199\pi$
$462$		0			0
$463$	17.0527	−	4.56925i	0.792505	−	0.212351i	0.160214	−	0.987082i	$-0.448782\pi$
$463$	17.0527	−	4.56925i	0.792505	−	0.212351i	0.632291	+	0.774731i	$0.282115\pi$
$464$		−	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	−0.413583	−	0.910466i	$-0.635723\pi$
$479$	10.8748	−	10.8748i	0.496883	−	0.496883i	0.910466	+	0.413583i	$0.135723\pi$
$480$		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	−0.101848	−	0.994800i	$-0.532475\pi$
$487$	−15.1707	−	4.06498i	−0.687450	−	0.184202i	−0.585603	+	0.810598i	$0.699142\pi$
$488$	−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	0.929109	−	0.369805i	$-0.120576\pi$
$491$	3.19734	+	5.53796i	0.144294	+	0.249925i	−0.784815	+	0.619730i	$0.787242\pi$
$492$		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	0.907306	−	0.420471i	$-0.138135\pi$
$499$	−1.98095	−	7.39299i	−0.0886794	−	0.330956i	−0.995985	+	0.0895148i	$0.971468\pi$
$500$	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	−0.647318	−	0.762220i	$-0.724110\pi$
$503$	−6.97222	+	4.02541i	−0.310876	+	0.179484i	0.336442	+	0.941704i	$0.390776\pi$
$504$		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	−0.487081	−	0.873357i	$-0.661938\pi$
$509$	8.37966	−	31.2733i	0.371422	−	1.38617i	0.858503	−	0.512809i	$-0.171395\pi$
$510$		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	$0.0275999\pi$
$521$			3.95332i			0.173198i	−0.996243	+	0.0865990i	$0.972400\pi$
$522$		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	$0.835152\pi$
$524$	−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	0.868181	−	0.496248i	$-0.165289\pi$
$541$	8.65093	+	8.65093i	0.371933	+	0.371933i	−0.496248	+	0.868181i	$0.665289\pi$
$542$	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	0.999080	+	0.0428870i	$0.0136556\pi$
$547$	12.5519	+	21.7406i	0.536681	+	0.929559i	−0.462399	+	0.886672i	$0.653011\pi$
$548$	−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	0.999427	−	0.0338399i	$-0.0107736\pi$
$557$	2.76078	+	10.3034i	0.116978	+	0.436567i	−0.882449	+	0.470407i	$0.844107\pi$
$558$		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	0.899562	−	0.436792i	$-0.143885\pi$
$571$	23.2043	+	13.3970i	0.971071	+	0.560648i	0.0715081	+	0.997440i	$0.477219\pi$
$572$	−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	−0.992504	−	0.122212i	$-0.961001\pi$
$577$	−20.9051	+	20.9051i	−0.870292	+	0.870292i	0.122212	+	0.992504i	$0.461001\pi$
$578$	−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	0.970856	−	0.239665i	$-0.0770378\pi$
$587$	17.7153	+	17.7153i	0.731190	+	0.731190i	−0.239665	+	0.970856i	$0.577038\pi$
$588$		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	−0.370952	−	0.928652i	$-0.620969\pi$
$593$	13.5809	−	13.5809i	0.557700	−	0.557700i	0.928652	+	0.370952i	$0.120969\pi$
$594$		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	0.213282	−	0.976991i	$-0.431585\pi$
$599$	−12.8779	−	7.43506i	−0.526176	−	0.303788i	−0.739458	+	0.673203i	$0.764918\pi$
$600$		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	−0.875633	−	0.482977i	$-0.839556\pi$
$613$	−8.88349	−	33.1536i	−0.358801	−	1.33906i	0.516832	−	0.856087i	$-0.327111\pi$
$614$			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	0.666902	−	0.745145i	$-0.267620\pi$
$617$	−1.94352	−	1.94352i	−0.0782432	−	0.0782432i	−0.745145	+	0.666902i	$0.767620\pi$
$618$		0			0
$619$	4.73494	−	17.6710i	0.190313	−	0.710259i	−0.803117	−	0.595821i	$-0.796827\pi$
$619$	4.73494	−	17.6710i	0.190313	−	0.710259i	0.993430	−	0.114438i	$-0.0365066\pi$
$620$	−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	0.526902	+	0.849926i	$0.323353\pi$
$631$	−8.90171	+	33.2216i	−0.354371	+	1.32253i	−0.881274	+	0.472606i	$0.843313\pi$
$632$	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	−0.700562	−	0.713592i	$-0.747067\pi$
$641$	6.77781	−	11.7395i	0.267707	−	0.463683i	0.968269	+	0.249909i	$0.0804006\pi$
$642$		0			0
$643$	28.1744	−	28.1744i	1.11109	−	1.11109i	0.118088	−	0.993003i	$-0.462324\pi$
$643$	28.1744	−	28.1744i	1.11109	−	1.11109i	0.993003	−	0.118088i	$-0.0376765\pi$
$644$	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	−0.561756	−	0.827303i	$-0.689874\pi$
$647$	11.0797	−	19.1906i	0.435588	−	0.754460i	0.997343	+	0.0728432i	$0.0232073\pi$
$648$		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	0.205372	−	0.978684i	$-0.434159\pi$
$653$	29.5307	−	17.0495i	1.15562	−	0.667200i	0.950251	+	0.311484i	$0.100826\pi$
$654$		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	0.400748	−	0.916188i	$-0.368750\pi$
$659$	−4.93704	−	2.85040i	−0.192320	−	0.111036i	−0.593068	+	0.805152i	$0.702084\pi$
$660$		0			0
$661$	2.37504	−	8.86377i	0.0923783	−	0.344761i	−0.904231	−	0.427044i	$-0.859555\pi$
$661$	2.37504	−	8.86377i	0.0923783	−	0.344761i	0.996609	+	0.0822839i	$0.0262214\pi$
$662$	−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	$0.202855\pi$
$673$			30.8722i			1.19004i	−0.803713	+	0.595018i	$0.797145\pi$
$674$	−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	−0.425118	−	0.905138i	$-0.639768\pi$
$677$	3.80387	−	2.19617i	0.146195	−	0.0844055i	0.571313	+	0.820732i	$0.306434\pi$
$678$		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	0.0377045	−	0.999289i	$-0.487995\pi$
$683$	−11.2191	−	3.00615i	−0.429287	−	0.115027i	−0.466991	+	0.884262i	$0.654662\pi$
$684$		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	−0.549557	−	0.835456i	$-0.685204\pi$
$691$	7.51539	−	7.51539i	0.285899	−	0.285899i	0.835456	+	0.549557i	$0.185204\pi$
$692$	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	0.468050	−	0.883702i	$-0.344957\pi$
$709$	35.0211	−	9.38387i	1.31524	−	0.352419i	0.847194	+	0.531283i	$0.178290\pi$
$710$	−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	0.852608	−	0.522551i	$-0.175020\pi$
$719$	−0.703567	−	1.21861i	−0.0262386	−	0.0454466i	−0.878847	+	0.477105i	$0.841686\pi$
$720$		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	−0.963425	−	0.267978i	$-0.913644\pi$
$727$	−32.7077	+	18.8838i	−1.21306	+	0.700361i	−0.249636	+	0.968340i	$0.580311\pi$
$728$	−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	−0.920693	−	0.390288i	$-0.872375\pi$
$733$	−8.62288	−	32.1810i	−0.318493	−	1.18863i	0.602199	−	0.798346i	$-0.294291\pi$
$734$	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	−0.656719	−	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
$743$	3.12072	−	11.6467i	0.114488	−	0.427275i	−0.884760	−	0.466047i	$-0.845678\pi$
$743$	3.12072	−	11.6467i	0.114488	−	0.427275i	0.999248	+	0.0387716i	$0.0123445\pi$
$744$		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	0.0577408	−	0.998332i	$-0.481610\pi$
$751$	26.0668	−	15.0497i	0.951192	−	0.549171i	0.893451	+	0.449161i	$0.148277\pi$
$752$	−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	0.124076	−	0.992273i	$-0.460403\pi$
$757$	25.3503	−	43.9080i	0.921371	−	1.59586i	0.797296	−	0.603589i	$-0.206263\pi$
$758$	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	−0.871802	−	0.489859i	$-0.837048\pi$
$761$	−10.5364	+	10.5364i	−0.381943	+	0.381943i	0.489859	+	0.871802i	$0.337048\pi$
$762$		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	0.689814	−	0.723986i	$-0.257692\pi$
$769$	25.6571	+	6.87479i	0.925218	+	0.247911i	0.235404	+	0.971898i	$0.424359\pi$
$770$	−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	−0.392206	−	0.919877i	$-0.628288\pi$
$773$	11.3267	−	42.2718i	0.407393	−	1.52041i	0.799599	−	0.600534i	$-0.205045\pi$
$774$		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 <

Overview	Random
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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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