LMFDB - Embedded newform 693.2.by.b.487.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(37,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 10, 6]))

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

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

chi := DirichletCharacter("693.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.by (of order $15$, degree $8$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			487.1
Character	$\chi$	$=$	693.487
Dual form			693.2.by.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.04369 - 0.909911i) q^{2} +(2.01049 + 2.23287i) q^{4} +(-0.0905565 + 0.861587i) q^{5} +(-2.63985 + 0.176636i) q^{7} +(-0.694498 - 2.13745i) q^{8} +O(q^{10})$	\(q+(-2.04369 - 0.909911i) q^{2} +(2.01049 + 2.23287i) q^{4} +(-0.0905565 + 0.861587i) q^{5} +(-2.63985 + 0.176636i) q^{7} +(-0.694498 - 2.13745i) q^{8} +(0.969038 - 1.67842i) q^{10} +(-1.89678 - 2.72071i) q^{11} +(2.73539 - 1.98738i) q^{13} +(5.55577 + 2.04104i) q^{14} +(0.102593 - 0.976110i) q^{16} +(2.00586 - 0.893065i) q^{17} +(-2.40122 + 2.66683i) q^{19} +(-2.10587 + 1.53001i) q^{20} +(1.40083 + 7.28619i) q^{22} +(0.834837 + 1.44598i) q^{23} +(4.15661 + 0.883514i) q^{25} +(-7.39864 + 1.57263i) q^{26} +(-5.70178 - 5.53931i) q^{28} +(-0.473517 + 1.45734i) q^{29} +(0.927888 + 8.82827i) q^{31} +(-3.34529 + 5.79421i) q^{32} -4.91197 q^{34} +(0.0868681 - 2.29046i) q^{35} +(-3.01788 + 0.641471i) q^{37} +(7.33394 - 3.26528i) q^{38} +(1.90449 - 0.404811i) q^{40} +(-0.203209 - 0.625414i) q^{41} -9.76359 q^{43} +(2.26154 - 9.70519i) q^{44} +(-0.390438 - 3.71477i) q^{46} +(-8.82952 + 9.80618i) q^{47} +(6.93760 - 0.932584i) q^{49} +(-7.69091 - 5.58777i) q^{50} +(9.93702 + 2.11218i) q^{52} +(0.686100 + 6.52780i) q^{53} +(2.51589 - 1.38786i) q^{55} +(2.21092 + 5.51986i) q^{56} +(2.29377 - 2.54749i) q^{58} +(9.74869 + 10.8270i) q^{59} +(-0.605886 + 5.76462i) q^{61} +(6.13662 - 18.8866i) q^{62} +(10.5209 - 7.64386i) q^{64} +(1.46459 + 2.53675i) q^{65} +(-2.64188 + 4.57587i) q^{67} +(6.02684 + 2.68332i) q^{68} +(-2.26164 + 4.60195i) q^{70} +(6.33800 + 4.60483i) q^{71} +(-3.95947 - 4.39744i) q^{73} +(6.75131 + 1.43504i) q^{74} -10.7823 q^{76} +(5.48778 + 6.84721i) q^{77} +(10.7382 + 4.78095i) q^{79} +(0.831714 + 0.176786i) q^{80} +(-0.153773 + 1.46306i) q^{82} +(-0.455953 - 0.331269i) q^{83} +(0.587810 + 1.80909i) q^{85} +(19.9538 + 8.88400i) q^{86} +(-4.49805 + 5.94378i) q^{88} +(1.76101 + 3.05016i) q^{89} +(-6.86998 + 5.72955i) q^{91} +(-1.55026 + 4.77120i) q^{92} +(26.9676 - 12.0067i) q^{94} +(-2.08026 - 2.31036i) q^{95} +(11.2566 - 8.17838i) q^{97} +(-15.0269 - 4.40668i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 3 q^{2} - 3 q^{4} - 4 q^{5} - 2 q^{7} + 38 q^{8}+O(q^{10}) $ 40 * q + 3 * q^2 - 3 * q^4 - 4 * q^5 - 2 * q^7 + 38 * q^8	$ 40 q + 3 q^{2} - 3 q^{4} - 4 q^{5} - 2 q^{7} + 38 q^{8} + 14 q^{10} + 9 q^{11} + 6 q^{13} + 3 q^{14} - 5 q^{16} + 7 q^{17} - 4 q^{19} + 30 q^{20} + 44 q^{22} + 14 q^{23} + 21 q^{25} + 16 q^{28} - 17 q^{31} + 30 q^{32} + 48 q^{34} + 14 q^{35} + 24 q^{37} - 12 q^{38} + 10 q^{40} - 60 q^{41} - 72 q^{43} - 18 q^{44} + 8 q^{46} - 13 q^{47} - 10 q^{49} - 6 q^{50} + 2 q^{52} - 33 q^{53} - 6 q^{55} - 24 q^{56} - 17 q^{58} - 21 q^{59} + 52 q^{62} + 94 q^{64} + 40 q^{65} - 38 q^{67} + 23 q^{68} - 3 q^{70} - 20 q^{71} + 11 q^{73} + 41 q^{74} - 96 q^{76} - 36 q^{77} + 21 q^{79} - 12 q^{80} + 6 q^{82} + 46 q^{83} - 78 q^{85} - 7 q^{86} + 32 q^{88} + 10 q^{89} - 14 q^{91} + 110 q^{92} + 37 q^{94} - 7 q^{95} - 54 q^{97} - 116 q^{98}+O(q^{100}) $ 40 * q + 3 * q^2 - 3 * q^4 - 4 * q^5 - 2 * q^7 + 38 * q^8 + 14 * q^10 + 9 * q^11 + 6 * q^13 + 3 * q^14 - 5 * q^16 + 7 * q^17 - 4 * q^19 + 30 * q^20 + 44 * q^22 + 14 * q^23 + 21 * q^25 + 16 * q^28 - 17 * q^31 + 30 * q^32 + 48 * q^34 + 14 * q^35 + 24 * q^37 - 12 * q^38 + 10 * q^40 - 60 * q^41 - 72 * q^43 - 18 * q^44 + 8 * q^46 - 13 * q^47 - 10 * q^49 - 6 * q^50 + 2 * q^52 - 33 * q^53 - 6 * q^55 - 24 * q^56 - 17 * q^58 - 21 * q^59 + 52 * q^62 + 94 * q^64 + 40 * q^65 - 38 * q^67 + 23 * q^68 - 3 * q^70 - 20 * q^71 + 11 * q^73 + 41 * q^74 - 96 * q^76 - 36 * q^77 + 21 * q^79 - 12 * q^80 + 6 * q^82 + 46 * q^83 - 78 * q^85 - 7 * q^86 + 32 * q^88 + 10 * q^89 - 14 * q^91 + 110 * q^92 + 37 * q^94 - 7 * q^95 - 54 * q^97 - 116 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−2.04369	−	0.909911i	−1.44511	−	0.643404i	−0.473673	−	0.880701i	$-0.657072\pi$
$2$	−2.04369	−	0.909911i	−1.44511	−	0.643404i	−0.971437	+	0.237297i	$0.923739\pi$
$3$		0			0
$3$		0			0
$4$	2.01049	+	2.23287i	1.00524	+	1.11643i
$5$	−0.0905565	+	0.861587i	−0.0404981	+	0.385314i	0.955434	+	0.295205i	$0.0953880\pi$
$5$	−0.0905565	+	0.861587i	−0.0404981	+	0.385314i	−0.995932	+	0.0901084i	$0.971279\pi$
$6$		0			0
$7$	−2.63985	+	0.176636i	−0.997769	+	0.0667621i
$7$	−2.63985	+	0.176636i	−0.997769	+	0.0667621i
$8$	−0.694498	−	2.13745i	−0.245542	−	0.755701i
$9$		0			0
$10$	0.969038	−	1.67842i	0.306437	−	0.530764i
$11$	−1.89678	−	2.72071i	−0.571900	−	0.820323i
$11$	−1.89678	−	2.72071i	−0.571900	−	0.820323i
$12$		0			0
$13$	2.73539	−	1.98738i	0.758661	−	0.551200i	−0.139838	−	0.990174i	$-0.544658\pi$
$13$	2.73539	−	1.98738i	0.758661	−	0.551200i	0.898499	+	0.438975i	$0.144658\pi$
$14$	5.55577	+	2.04104i	1.48484	+	0.545490i
$15$		0			0
$16$	0.102593	−	0.976110i	0.0256483	−	0.244028i
$17$	2.00586	−	0.893065i	0.486492	−	0.216600i	−0.148808	−	0.988866i	$-0.547543\pi$
$17$	2.00586	−	0.893065i	0.486492	−	0.216600i	0.635299	+	0.772266i	$0.280877\pi$
$18$		0			0
$19$	−2.40122	+	2.66683i	−0.550878	+	0.611813i	−0.952703	−	0.303904i	$-0.901710\pi$
$19$	−2.40122	+	2.66683i	−0.550878	+	0.611813i	0.401824	+	0.915717i	$0.368376\pi$
$20$	−2.10587	+	1.53001i	−0.470888	+	0.342120i
$21$		0			0
$22$	1.40083	+	7.28619i	0.298658	+	1.55342i
$23$	0.834837	+	1.44598i	0.174076	+	0.301508i	0.939841	−	0.341612i	$-0.110973\pi$
$23$	0.834837	+	1.44598i	0.174076	+	0.301508i	−0.765765	+	0.643120i	$0.777640\pi$
$24$		0			0
$25$	4.15661	+	0.883514i	0.831321	+	0.176703i
$26$	−7.39864	+	1.57263i	−1.45099	+	0.308418i
$27$		0			0
$28$	−5.70178	−	5.53931i	−1.07754	−	1.04683i
$29$	−0.473517	+	1.45734i	−0.0879300	+	0.270621i	−0.985347	−	0.170563i	$-0.945441\pi$
$29$	−0.473517	+	1.45734i	−0.0879300	+	0.270621i	0.897417	+	0.441184i	$0.145441\pi$
$30$		0			0
$31$	0.927888	+	8.82827i	0.166654	+	1.58560i	0.683776	+	0.729692i	$0.260337\pi$
$31$	0.927888	+	8.82827i	0.166654	+	1.58560i	−0.517122	+	0.855912i	$0.672997\pi$
$32$	−3.34529	+	5.79421i	−0.591369	+	1.02428i
$33$		0			0
$34$	−4.91197			−0.842395
$35$	0.0868681	−	2.29046i	0.0146834	−	0.387158i
$36$		0			0
$37$	−3.01788	+	0.641471i	−0.496137	+	0.105457i	−0.449183	−	0.893440i	$-0.648285\pi$
$37$	−3.01788	+	0.641471i	−0.496137	+	0.105457i	−0.0469542	+	0.998897i	$0.514951\pi$
$38$	7.33394	−	3.26528i	1.18972	−	0.529699i
$39$		0			0
$40$	1.90449	−	0.404811i	0.301126	−	0.0640063i
$41$	−0.203209	−	0.625414i	−0.0317360	−	0.0976732i	0.933934	−	0.357446i	$-0.116352\pi$
$41$	−0.203209	−	0.625414i	−0.0317360	−	0.0976732i	−0.965670	+	0.259773i	$0.916352\pi$
$42$		0			0
$43$	−9.76359			−1.48893			−0.744467	−	0.667660i	$-0.767296\pi$
$43$	−9.76359			−1.48893			−0.744467	+	0.667660i	$0.767296\pi$
$44$	2.26154	−	9.70519i	0.340940	−	1.46311i
$45$		0			0
$46$	−0.390438	−	3.71477i	−0.0575669	−	0.547713i
$47$	−8.82952	+	9.80618i	−1.28792	+	1.43038i	−0.442046	+	0.896992i	$0.645747\pi$
$47$	−8.82952	+	9.80618i	−1.28792	+	1.43038i	−0.845872	+	0.533385i	$0.820920\pi$
$48$		0			0
$49$	6.93760	−	0.932584i	0.991086	−	0.133226i
$50$	−7.69091	−	5.58777i	−1.08766	−	0.790231i
$51$		0			0
$52$	9.93702	+	2.11218i	1.37802	+	0.292907i
$53$	0.686100	+	6.52780i	0.0942430	+	0.896663i	0.934856	+	0.355027i	$0.115528\pi$
$53$	0.686100	+	6.52780i	0.0942430	+	0.896663i	−0.840613	+	0.541636i	$0.817805\pi$
$54$		0			0
$55$	2.51589	−	1.38786i	0.339243	−	0.187139i
$56$	2.21092	+	5.51986i	0.295447	+	0.737622i
$57$		0			0
$58$	2.29377	−	2.54749i	0.301187	−	0.334502i
$59$	9.74869	+	10.8270i	1.26917	+	1.40956i	0.870278	+	0.492560i	$0.163939\pi$
$59$	9.74869	+	10.8270i	1.26917	+	1.40956i	0.398893	+	0.916998i	$0.369395\pi$
$60$		0			0
$61$	−0.605886	+	5.76462i	−0.0775758	+	0.738084i	0.884728	+	0.466108i	$0.154344\pi$
$61$	−0.605886	+	5.76462i	−0.0775758	+	0.738084i	−0.962304	+	0.271977i	$0.912323\pi$
$62$	6.13662	−	18.8866i	0.779351	−	2.39860i
$63$		0			0
$64$	10.5209	−	7.64386i	1.31511	−	0.955483i
$65$	1.46459	+	2.53675i	0.181660	+	0.314645i
$66$		0			0
$67$	−2.64188	+	4.57587i	−0.322757	+	0.559032i	−0.981056	−	0.193725i	$-0.937943\pi$
$67$	−2.64188	+	4.57587i	−0.322757	+	0.559032i	0.658299	+	0.752757i	$0.271276\pi$
$68$	6.02684	+	2.68332i	0.730862	+	0.325401i
$69$		0			0
$70$	−2.26164	+	4.60195i	−0.270318	+	0.550038i
$71$	6.33800	+	4.60483i	0.752183	+	0.546493i	0.896503	−	0.443038i	$-0.146099\pi$
$71$	6.33800	+	4.60483i	0.752183	+	0.546493i	−0.144320	+	0.989531i	$0.546099\pi$
$72$		0			0
$73$	−3.95947	−	4.39744i	−0.463421	−	0.514681i	0.465455	−	0.885071i	$-0.345891\pi$
$73$	−3.95947	−	4.39744i	−0.463421	−	0.514681i	−0.928876	+	0.370390i	$0.879224\pi$
$74$	6.75131	+	1.43504i	0.784824	+	0.166820i
$75$		0			0
$76$	−10.7823			−1.23682
$77$	5.48778	+	6.84721i	0.625390	+	0.780312i
$78$		0			0
$79$	10.7382	+	4.78095i	1.20814	+	0.537899i	0.909194	−	0.416372i	$-0.136699\pi$
$79$	10.7382	+	4.78095i	1.20814	+	0.537899i	0.298945	+	0.954270i	$0.403365\pi$
$80$	0.831714	+	0.176786i	0.0929884	+	0.0197653i
$81$		0			0
$82$	−0.153773	+	1.46306i	−0.0169814	+	0.161568i
$83$	−0.455953	−	0.331269i	−0.0500473	−	0.0363615i	0.562480	−	0.826811i	$-0.309847\pi$
$83$	−0.455953	−	0.331269i	−0.0500473	−	0.0363615i	−0.612528	+	0.790449i	$0.709847\pi$
$84$		0			0
$85$	0.587810	+	1.80909i	0.0637569	+	0.196224i
$86$	19.9538	+	8.88400i	2.15167	+	0.957986i
$87$		0			0
$88$	−4.49805	+	5.94378i	−0.479494	+	0.633609i
$89$	1.76101	+	3.05016i	0.186667	+	0.323317i	0.944137	−	0.329553i	$-0.106898\pi$
$89$	1.76101	+	3.05016i	0.186667	+	0.323317i	−0.757470	+	0.652870i	$0.773565\pi$
$90$		0			0
$91$	−6.86998	+	5.72955i	−0.720169	+	0.600620i
$92$	−1.55026	+	4.77120i	−0.161626	+	0.497432i
$93$		0			0
$94$	26.9676	−	12.0067i	2.78149	−	1.23840i
$95$	−2.08026	−	2.31036i	−0.213430	−	0.237038i
$96$		0			0
$97$	11.2566	−	8.17838i	1.14293	−	0.830388i	0.155406	−	0.987851i	$-0.450331\pi$
$97$	11.2566	−	8.17838i	1.14293	−	0.830388i	0.987525	+	0.157462i	$0.0503313\pi$
$98$	−15.0269	−	4.40668i	−1.51795	−	0.445142i
$99$		0			0
$100$	6.38402	+	11.0575i	0.638402	+	1.10575i
$101$	−1.26876	−	12.0714i	−0.126246	−	1.20115i	−0.855829	−	0.517259i	$-0.826953\pi$
$101$	−1.26876	−	12.0714i	−0.126246	−	1.20115i	0.729583	−	0.683892i	$-0.239714\pi$
$102$		0			0
$103$	−2.81798	+	0.598981i	−0.277664	+	0.0590193i	−0.344639	−	0.938735i	$-0.611999\pi$
$103$	−2.81798	+	0.598981i	−0.277664	+	0.0590193i	0.0669748	+	0.997755i	$0.478665\pi$
$104$	−6.14764	−	4.46652i	−0.602825	−	0.437978i
$105$		0			0
$106$	4.53754	−	13.9651i	0.440725	−	1.35641i
$107$	0.624629	−	0.693721i	0.0603852	−	0.0670645i	−0.712195	−	0.701981i	$-0.752299\pi$
$107$	0.624629	−	0.693721i	0.0603852	−	0.0670645i	0.772580	+	0.634917i	$0.218966\pi$
$108$		0			0
$109$	−6.08365	+	10.5372i	−0.582708	+	1.00928i	0.412449	+	0.910981i	$0.364673\pi$
$109$	−6.08365	+	10.5372i	−0.582708	+	1.00928i	−0.995157	+	0.0982988i	$0.968660\pi$
$110$	−6.40454	+	0.547128i	−0.610649	+	0.0521666i
$111$		0			0
$112$	−0.0984147	+	2.59490i	−0.00929932	+	0.245195i
$113$	−3.95376	−	12.1684i	−0.371939	−	1.14471i	−0.945521	−	0.325562i	$-0.894447\pi$
$113$	−3.95376	−	12.1684i	−0.371939	−	1.14471i	0.573582	−	0.819148i	$-0.305553\pi$
$114$		0			0
$115$	−1.32144	+	0.588342i	−0.123225	+	0.0548632i
$116$	−4.20604	+	1.87265i	−0.390521	+	0.173871i
$117$		0			0
$118$	−10.0717	−	30.9975i	−0.927176	−	2.85356i
$119$	−5.13741	+	2.71186i	−0.470946	+	0.248596i
$120$		0			0
$121$	−3.80447	+	10.3211i	−0.345861	+	0.938286i
$122$	6.48354	−	11.2298i	0.586992	−	1.01670i
$123$		0			0
$124$	−17.8469	+	19.8210i	−1.60270	+	1.77997i
$125$	−2.47619	+	7.62093i	−0.221477	+	0.681637i
$126$		0			0
$127$	−1.79504	−	1.30417i	−0.159284	−	0.115727i	0.505288	−	0.862951i	$-0.331386\pi$
$127$	−1.79504	−	1.30417i	−0.159284	−	0.115727i	−0.664572	+	0.747224i	$0.731386\pi$
$128$	−15.3679	+	3.26656i	−1.35835	+	0.288726i
$129$		0			0
$130$	−0.684963	−	6.51699i	−0.0600752	−	0.571578i
$131$	0.633382	+	1.09705i	0.0553388	+	0.0958497i	0.892368	−	0.451309i	$-0.149043\pi$
$131$	0.633382	+	1.09705i	0.0553388	+	0.0958497i	−0.837029	+	0.547159i	$0.815709\pi$
$132$		0			0
$133$	5.86781	−	7.46417i	0.508804	−	0.647225i
$134$	9.56284	−	6.94781i	0.826103	−	0.600199i
$135$		0			0
$136$	−3.30194	−	3.66718i	−0.283139	−	0.314458i
$137$	−5.95895	+	2.65309i	−0.509107	+	0.226669i	−0.645181	−	0.764030i	$-0.723218\pi$
$137$	−5.95895	+	2.65309i	−0.509107	+	0.226669i	0.136074	+	0.990699i	$0.456551\pi$
$138$		0			0
$139$	−4.39304	+	13.5204i	−0.372613	+	1.14678i	0.572463	+	0.819931i	$0.305988\pi$
$139$	−4.39304	+	13.5204i	−0.372613	+	1.14678i	−0.945075	+	0.326853i	$0.894012\pi$
$140$	5.28894	−	4.41096i	0.446997	−	0.372794i
$141$		0			0
$142$	−8.76295	−	15.1779i	−0.735371	−	1.27370i
$143$	−10.5955	−	3.67258i	−0.886040	−	0.307117i
$144$		0			0
$145$	−1.21274	−	0.539948i	−0.100713	−	0.0448402i
$146$	4.09067	+	12.5898i	0.338546	+	1.04194i
$147$		0			0
$148$	−7.49973	−	5.44888i	−0.616474	−	0.447895i
$149$	0.384261	−	3.65599i	0.0314798	−	0.299511i	−0.967442	−	0.253092i	$-0.918552\pi$
$149$	0.384261	−	3.65599i	0.0314798	−	0.299511i	0.998922	−	0.0464188i	$-0.0147809\pi$
$150$		0			0
$151$	8.65413	+	1.83949i	0.704263	+	0.149696i	0.546103	−	0.837718i	$-0.316111\pi$
$151$	8.65413	+	1.83949i	0.704263	+	0.149696i	0.158160	+	0.987414i	$0.449444\pi$
$152$	7.36785	+	3.28038i	0.597611	+	0.266074i
$153$		0			0
$154$	−4.98499	−	18.9870i	−0.401702	−	1.53002i
$155$	−7.69035			−0.617704
$156$		0			0
$157$	−2.25627	−	0.479585i	−0.180070	−	0.0382750i	0.116994	−	0.993133i	$-0.462674\pi$
$157$	−2.25627	−	0.479585i	−0.180070	−	0.0382750i	−0.297064	+	0.954858i	$0.596007\pi$
$158$	−17.5953	−	19.5416i	−1.39981	−	1.55464i
$159$		0			0
$160$	−4.68928	−	3.40696i	−0.370720	−	0.269344i
$161$	−2.45926	−	3.66971i	−0.193816	−	0.289213i
$162$		0			0
$163$	−5.23657	−	2.33147i	−0.410160	−	0.182615i	0.191275	−	0.981536i	$-0.438738\pi$
$163$	−5.23657	−	2.33147i	−0.410160	−	0.182615i	−0.601435	+	0.798921i	$0.705404\pi$
$164$	0.987918	−	1.71112i	0.0771435	−	0.133616i
$165$		0			0
$166$	0.630402	+	1.09189i	0.0489287	+	0.0847470i
$167$	2.60856	−	1.89523i	0.201857	−	0.146657i	−0.482265	−	0.876025i	$-0.660186\pi$
$167$	2.60856	−	1.89523i	0.201857	−	0.146657i	0.684122	+	0.729368i	$0.260186\pi$
$168$		0			0
$169$	−0.484526	+	1.49122i	−0.0372713	+	0.114709i
$170$	0.444810	−	4.23209i	0.0341154	−	0.324586i
$171$		0			0
$172$	−19.6295	−	21.8008i	−1.49674	−	1.66230i
$173$	5.62096	−	6.24271i	0.427354	−	0.474624i	−0.490558	−	0.871408i	$-0.663207\pi$
$173$	5.62096	−	6.24271i	0.427354	−	0.474624i	0.917912	+	0.396784i	$0.129874\pi$
$174$		0			0
$175$	−11.1289	−	1.59814i	−0.841263	−	0.120808i
$176$	−2.85030	+	1.57234i	−0.214850	+	0.118519i
$177$		0			0
$178$	−0.823593	−	7.83597i	−0.0617309	−	0.587331i
$179$	−2.51173	−	0.533884i	−0.187735	−	0.0399044i	0.113084	−	0.993585i	$-0.463927\pi$
$179$	−2.51173	−	0.533884i	−0.187735	−	0.0399044i	−0.300820	+	0.953681i	$0.597260\pi$
$180$		0			0
$181$	−1.43468	−	1.04235i	−0.106639	−	0.0774775i	0.533188	−	0.845997i	$-0.320994\pi$
$181$	−1.43468	−	1.04235i	−0.106639	−	0.0774775i	−0.639827	+	0.768519i	$0.720994\pi$
$182$	19.2535	−	5.45837i	1.42716	−	0.404601i
$183$		0			0
$184$	2.51091	−	2.78865i	0.185107	−	0.205582i
$185$	−0.279394	−	2.65826i	−0.0205415	−	0.195439i
$186$		0			0
$187$	−6.23443	−	3.76340i	−0.455907	−	0.275207i
$188$	−39.6475			−2.89159
$189$		0			0
$190$	2.14919	+	6.61452i	0.155919	+	0.479868i
$191$	−8.09990	+	1.72169i	−0.586088	+	0.124577i	−0.491406	−	0.870931i	$-0.663517\pi$
$191$	−8.09990	+	1.72169i	−0.586088	+	0.124577i	−0.0946822	+	0.995508i	$0.530184\pi$
$192$		0			0
$193$	−17.3810	+	7.73850i	−1.25111	+	0.557029i	−0.921973	−	0.387253i	$-0.873424\pi$
$193$	−17.3810	+	7.73850i	−1.25111	+	0.557029i	−0.329135	+	0.944283i	$0.606757\pi$
$194$	−30.4466	+	6.47162i	−2.18594	+	0.464635i
$195$		0			0
$196$	16.0303	+	13.6158i	1.14502	+	0.972558i
$197$	−15.1831			−1.08175			−0.540877	−	0.841102i	$-0.681907\pi$
$197$	−15.1831			−1.08175			−0.540877	+	0.841102i	$0.681907\pi$
$198$		0			0
$199$	12.3023	−	21.3082i	0.872086	−	1.51050i	0.0122517	−	0.999925i	$-0.496100\pi$
$199$	12.3023	−	21.3082i	0.872086	−	1.51050i	0.859835	−	0.510573i	$-0.170567\pi$
$200$	−0.998292	−	9.49812i	−0.0705899	−	0.671618i
$201$		0			0
$202$	−8.39097	+	25.8247i	−0.590386	+	1.81702i
$203$	0.992596	−	3.93079i	0.0696666	−	0.275887i
$204$		0			0
$205$	0.557250	−	0.118447i	0.0389201	−	0.00827271i
$206$	6.30411	+	1.33998i	0.439228	+	0.0933609i
$207$		0			0
$208$	−1.65927	−	2.87394i	−0.115049	−	0.199272i
$209$	11.8102	+	1.47464i	0.816931	+	0.102003i
$210$		0			0
$211$	14.0745	−	10.2257i	0.968930	−	0.703969i	0.0137227	−	0.999906i	$-0.495632\pi$
$211$	14.0745	−	10.2257i	0.968930	−	0.703969i	0.955208	+	0.295937i	$0.0956318\pi$
$212$	−13.1963	+	14.6560i	−0.906328	+	1.00658i
$213$		0			0
$214$	−1.90777	+	0.849396i	−0.130413	+	0.0580635i
$215$	0.884156	−	8.41218i	0.0602989	−	0.573706i
$216$		0			0
$217$	−4.00887	−	23.1414i	−0.272140	−	1.57094i
$218$	22.0210	−	15.9992i	1.49145	−	1.08360i
$219$		0			0
$220$	8.15708	+	2.82738i	0.549950	+	0.190622i
$221$	3.71194	−	6.42928i	0.249692	−	0.432480i
$222$		0			0
$223$	0.832077	+	2.56087i	0.0557200	+	0.171488i	0.975043	−	0.222014i	$-0.0712632\pi$
$223$	0.832077	+	2.56087i	0.0557200	+	0.171488i	−0.919323	+	0.393503i	$0.871263\pi$
$224$	7.80758	−	15.8867i	0.521666	−	1.06148i
$225$		0			0
$226$	−2.99191	+	28.4661i	−0.199019	+	1.89354i
$227$	15.3932	+	17.0959i	1.02168	+	1.13469i	0.990822	+	0.135170i	$0.0431582\pi$
$227$	15.3932	+	17.0959i	1.02168	+	1.13469i	0.0308607	+	0.999524i	$0.490175\pi$
$228$		0			0
$229$	16.3594	+	7.28370i	1.08106	+	0.481320i	0.868430	−	0.495812i	$-0.165130\pi$
$229$	16.3594	+	7.28370i	1.08106	+	0.481320i	0.212633	+	0.977132i	$0.431796\pi$
$230$	3.23595			0.213372
$231$		0			0
$232$	3.44384			0.226099
$233$	18.6946	+	8.32336i	1.22472	+	0.545281i	0.914192	−	0.405282i	$-0.132827\pi$
$233$	18.6946	+	8.32336i	1.22472	+	0.545281i	0.310530	+	0.950563i	$0.399493\pi$
$234$		0			0
$235$	−7.64931	−	8.49542i	−0.498986	−	0.554180i
$236$	−4.57572	+	43.5351i	−0.297854	+	2.83389i
$237$		0			0
$238$	12.9668	−	0.867629i	0.840516	−	0.0562401i
$239$	−2.16824	−	6.67315i	−0.140252	−	0.431650i	0.856118	−	0.516780i	$-0.172870\pi$
$239$	−2.16824	−	6.67315i	−0.140252	−	0.431650i	−0.996370	+	0.0851298i	$0.972870\pi$
$240$		0			0
$241$	−5.56584	+	9.64031i	−0.358527	+	0.620987i	−0.987715	−	0.156266i	$-0.950054\pi$
$241$	−5.56584	+	9.64031i	−0.358527	+	0.620987i	0.629188	+	0.777253i	$0.283388\pi$
$242$	17.1665	−	17.6315i	1.10350	−	1.13340i
$243$		0			0
$244$	−14.0898	+	10.2368i	−0.902006	+	0.655346i
$245$	0.175258	+	6.06180i	0.0111968	+	0.387274i
$246$		0			0
$247$	−1.26829	+	12.0670i	−0.0806993	+	0.767802i
$248$	18.2255	−	8.11453i	1.15732	−	0.515273i
$249$		0			0
$250$	11.9949	−	13.3217i	0.758627	−	0.842540i
$251$	8.56766	−	6.22477i	0.540786	−	0.392904i	−0.283591	−	0.958945i	$-0.591526\pi$
$251$	8.56766	−	6.22477i	0.540786	−	0.392904i	0.824377	+	0.566041i	$0.191526\pi$
$252$		0			0
$253$	2.35059	−	5.01405i	0.147780	−	0.315230i
$254$	2.48183	+	4.29866i	0.155724	+	0.269722i
$255$		0			0
$256$	8.93898	+	1.90004i	0.558687	+	0.118752i
$257$	0.588165	−	0.125018i	0.0366887	−	0.00779843i	−0.189531	−	0.981875i	$-0.560697\pi$
$257$	0.588165	−	0.125018i	0.0366887	−	0.00779843i	0.226219	+	0.974076i	$0.427363\pi$
$258$		0			0
$259$	7.85345	−	2.22645i	0.487990	−	0.138345i
$260$	−2.71969	+	8.37034i	−0.168668	+	0.519106i
$261$		0			0
$262$	−0.296221	−	2.81835i	−0.0183006	−	0.174119i
$263$	−8.60688	+	14.9076i	−0.530723	+	0.919240i	0.468634	+	0.883392i	$0.344746\pi$
$263$	−8.60688	+	14.9076i	−0.530723	+	0.919240i	−0.999357	+	0.0358472i	$0.988587\pi$
$264$		0			0
$265$	−5.68640			−0.349313
$266$	−18.7837	+	9.91529i	−1.15170	+	0.607945i
$267$		0			0
$268$	−15.5288	+	3.30075i	−0.948572	+	0.201625i
$269$	−19.0273	+	8.47152i	−1.16012	+	0.516517i	−0.894283	−	0.447501i	$-0.852314\pi$
$269$	−19.0273	+	8.47152i	−1.16012	+	0.516517i	−0.265834	+	0.964019i	$0.585647\pi$
$270$		0			0
$271$	22.7170	−	4.82865i	1.37996	−	0.293320i	0.542610	−	0.839985i	$-0.317436\pi$
$271$	22.7170	−	4.82865i	1.37996	−	0.293320i	0.837351	+	0.546665i	$0.184103\pi$
$272$	−0.665942	−	2.04956i	−0.0403787	−	0.124273i
$273$		0			0
$274$	14.5923			0.881556
$275$	−5.48037	−	12.9847i	−0.330479	−	0.783009i
$276$		0			0
$277$	−0.828505	−	7.88270i	−0.0497800	−	0.473625i	−0.990806	−	0.135291i	$-0.956803\pi$
$277$	−0.828505	−	7.88270i	−0.0497800	−	0.473625i	0.941026	−	0.338335i	$-0.109864\pi$
$278$	21.2804	−	23.6342i	1.27631	−	1.41749i
$279$		0			0
$280$	−4.95605	+	1.40504i	−0.296181	+	0.0839673i
$281$	7.85059	+	5.70379i	0.468327	+	0.340260i	0.796789	−	0.604258i	$-0.206530\pi$
$281$	7.85059	+	5.70379i	0.468327	+	0.340260i	−0.328462	+	0.944517i	$0.606530\pi$
$282$		0			0
$283$	−12.2682	−	2.60768i	−0.729266	−	0.155010i	−0.171708	−	0.985148i	$-0.554928\pi$
$283$	−12.2682	−	2.60768i	−0.729266	−	0.155010i	−0.557558	+	0.830138i	$0.688262\pi$
$284$	2.46048	+	23.4099i	0.146002	+	1.38912i
$285$		0			0
$286$	18.3122	+	17.1466i	1.08283	+	1.01390i
$287$	0.646912	+	1.61510i	0.0381860	+	0.0953365i
$288$		0			0
$289$	−8.14933	+	9.05074i	−0.479372	+	0.532397i
$290$	1.98717	+	2.20698i	0.116691	+	0.129598i
$291$		0			0
$292$	1.85845	−	17.6820i	0.108758	−	1.03476i
$293$	2.05861	−	6.33575i	0.120265	−	0.370138i	−0.872744	−	0.488179i	$-0.837661\pi$
$293$	2.05861	−	6.33575i	0.120265	−	0.370138i	0.993009	+	0.118041i	$0.0376613\pi$
$294$		0			0
$295$	−10.2112	+	7.41889i	−0.594521	+	0.431945i
$296$	3.46702	+	6.00506i	0.201517	+	0.349037i
$297$		0			0
$298$	−4.11194	+	7.12209i	−0.238198	+	0.412572i
$299$	5.15732	+	2.29619i	0.298255	+	0.132792i
$300$		0			0
$301$	25.7744	−	1.72460i	1.48561	−	0.0994043i
$302$	−16.0126	−	11.6338i	−0.921422	−	0.669453i
$303$		0			0
$304$	2.35677	+	2.61746i	0.135170	+	0.150121i
$305$	−4.91186	−	1.04405i	−0.281252	−	0.0597820i
$306$		0			0
$307$	−2.06252			−0.117714			−0.0588572	−	0.998266i	$-0.518746\pi$
$307$	−2.06252			−0.117714			−0.0588572	+	0.998266i	$0.518746\pi$
$308$	−4.25583	+	26.0197i	−0.242499	+	1.48261i
$309$		0			0
$310$	15.7167	+	6.99753i	0.892650	+	0.397433i
$311$	3.46666	+	0.736862i	0.196576	+	0.0417836i	0.305148	−	0.952305i	$-0.401294\pi$
$311$	3.46666	+	0.736862i	0.196576	+	0.0417836i	−0.108571	+	0.994089i	$0.534628\pi$
$312$		0			0
$313$	1.62599	−	15.4702i	0.0919063	−	0.874430i	−0.847309	−	0.531101i	$-0.821779\pi$
$313$	1.62599	−	15.4702i	0.0919063	−	0.874430i	0.939215	−	0.343329i	$-0.111555\pi$
$314$	4.17474	+	3.03313i	0.235594	+	0.171169i
$315$		0			0
$316$	10.9137	+	33.5890i	0.613945	+	1.88953i
$317$	15.1841	+	6.76041i	0.852826	+	0.379702i	0.786123	−	0.618071i	$-0.212085\pi$
$317$	15.1841	+	6.76041i	0.852826	+	0.379702i	0.0667028	+	0.997773i	$0.478752\pi$
$318$		0			0
$319$	4.86314	−	1.47594i	0.272284	−	0.0826369i
$320$	5.63312	+	9.75685i	0.314901	+	0.545425i
$321$		0			0
$322$	1.68686	+	9.73746i	0.0940049	+	0.542647i
$323$	−2.43486	+	7.49372i	−0.135479	+	0.416962i
$324$		0			0
$325$	13.1258	−	5.84399i	0.728090	−	0.324166i
$326$	8.58052	+	9.52963i	0.475231	+	0.527797i
$327$		0			0
$328$	−1.19566	+	0.868697i	−0.0660192	+	0.0479658i
$329$	21.5765	−	27.4464i	1.18955	−	1.51317i
$330$		0			0
$331$	−10.5203	−	18.2217i	−0.578249	−	1.00156i	−0.995680	−	0.0928482i	$-0.970403\pi$
$331$	−10.5203	−	18.2217i	−0.578249	−	1.00156i	0.417431	−	0.908709i	$-0.362930\pi$
$332$	−0.177005	−	1.68409i	−0.00971444	−	0.0924267i
$333$		0			0
$334$	−7.05559	+	1.49971i	−0.386065	+	0.0820606i
$335$	−3.70328	−	2.69059i	−0.202332	−	0.147002i
$336$		0			0
$337$	−9.35330	+	28.7865i	−0.509507	+	1.56810i	0.283553	+	0.958957i	$0.408487\pi$
$337$	−9.35330	+	28.7865i	−0.509507	+	1.56810i	−0.793060	+	0.609144i	$0.791513\pi$
$338$	2.34710	−	2.60672i	0.127665	−	0.141787i
$339$		0			0
$340$	−2.85769	+	4.94966i	−0.154980	+	0.268433i
$341$	22.2591	−	19.2698i	1.20540	−	1.04352i
$342$		0			0
$343$	−18.1495	+	3.68731i	−0.979980	+	0.199096i
$344$	6.78079	+	20.8691i	0.365596	+	1.12519i
$345$		0			0
$346$	−17.1678	+	7.64361i	−0.922949	+	0.410923i
$347$	−23.9532	+	10.6647i	−1.28588	+	0.572509i	−0.931890	−	0.362741i	$-0.881841\pi$
$347$	−23.9532	+	10.6647i	−1.28588	+	0.572509i	−0.353987	+	0.935251i	$0.615174\pi$
$348$		0			0
$349$	−3.29993	−	10.1562i	−0.176641	−	0.543646i	0.823063	−	0.567950i	$-0.192263\pi$
$349$	−3.29993	−	10.1562i	−0.176641	−	0.543646i	−0.999705	+	0.0243034i	$0.992263\pi$
$350$	21.2898	+	13.3924i	1.13799	+	0.715853i
$351$		0			0
$352$	22.1096	−	1.88878i	1.17845	−	0.100672i
$353$	1.94930	−	3.37628i	0.103751	−	0.179701i	−0.809476	−	0.587152i	$-0.800249\pi$
$353$	1.94930	−	3.37628i	0.103751	−	0.179701i	0.913227	+	0.407451i	$0.133582\pi$
$354$		0			0
$355$	−4.54141	+	5.04375i	−0.241033	+	0.267694i
$356$	−3.27013	+	10.0644i	−0.173317	+	0.533413i
$357$		0			0
$358$	4.64742	+	3.37655i	0.245624	+	0.178456i
$359$	−20.8679	+	4.43560i	−1.10136	+	0.234102i	−0.722514	−	0.691356i	$-0.757014\pi$
$359$	−20.8679	+	4.43560i	−1.10136	+	0.234102i	−0.378850	+	0.925458i	$0.623680\pi$
$360$		0			0
$361$	0.639939	+	6.08861i	0.0336810	+	0.320453i
$362$	1.98359	+	3.43568i	0.104255	+	0.180575i
$363$		0			0
$364$	−26.6053	−	3.82060i	−1.39450	−	0.200254i
$365$	4.14733	−	3.01321i	0.217081	−	0.157719i
$366$		0			0
$367$	0.393460	+	0.436981i	0.0205384	+	0.0228102i	0.753327	−	0.657647i	$-0.228448\pi$
$367$	0.393460	+	0.436981i	0.0205384	+	0.0228102i	−0.732788	+	0.680457i	$0.761781\pi$
$368$	1.49708	−	0.666545i	0.0780409	−	0.0347461i
$369$		0			0
$370$	−1.84778	+	5.68689i	−0.0960617	+	0.295648i
$371$	−2.96424	−	17.1112i	−0.153896	−	0.888370i
$372$		0			0
$373$	6.65785	+	11.5317i	0.344730	+	0.597090i	0.985305	−	0.170806i	$-0.0546371\pi$
$373$	6.65785	+	11.5317i	0.344730	+	0.597090i	−0.640575	+	0.767896i	$0.721304\pi$
$374$	9.31690	+	13.3640i	0.481766	+	0.691036i
$375$		0			0
$376$	27.0923	+	12.0623i	1.39718	+	0.622063i
$377$	1.60102	+	4.92744i	0.0824569	+	0.253776i
$378$		0			0
$379$	−7.03443	−	5.11081i	−0.361334	−	0.262525i	0.392274	−	0.919848i	$-0.371689\pi$
$379$	−7.03443	−	5.11081i	−0.361334	−	0.262525i	−0.753608	+	0.657324i	$0.771689\pi$
$380$	0.976408	−	9.28990i	0.0500887	−	0.476562i
$381$		0			0
$382$	18.1203	+	3.85159i	0.927115	+	0.197064i
$383$	−28.1944	−	12.5529i	−1.44067	−	0.641426i	−0.470177	−	0.882572i	$-0.655810\pi$
$383$	−28.1944	−	12.5529i	−1.44067	−	0.641426i	−0.970489	+	0.241147i	$0.922477\pi$
$384$		0			0
$385$	−6.39642	+	4.10814i	−0.325992	+	0.209370i
$386$	42.5627			2.16638
$387$		0			0
$388$	40.8924	+	8.69195i	2.07600	+	0.441267i
$389$	−3.43117	−	3.81070i	−0.173967	−	0.193210i	0.649856	−	0.760058i	$-0.274829\pi$
$389$	−3.43117	−	3.81070i	−0.173967	−	0.193210i	−0.823822	+	0.566848i	$0.808163\pi$
$390$		0			0
$391$	2.96592	+	2.15486i	0.149993	+	0.108976i
$392$	−6.81150	−	14.1811i	−0.344033	−	0.716252i
$393$		0			0
$394$	31.0297	+	13.8153i	1.56325	+	0.696005i
$395$	−5.09161	+	8.81894i	−0.256187	+	0.443729i
$396$		0			0
$397$	14.6266	+	25.3340i	0.734088	+	1.27148i	0.955122	+	0.296212i	$0.0957234\pi$
$397$	14.6266	+	25.3340i	0.734088	+	1.27148i	−0.221034	+	0.975266i	$0.570943\pi$
$398$	−44.5307	+	32.3534i	−2.23212	+	1.62173i
$399$		0			0
$400$	1.28885	−	3.96666i	0.0644423	−	0.198333i
$401$	1.51804	−	14.4432i	0.0758075	−	0.721260i	−0.888929	−	0.458044i	$-0.848550\pi$
$401$	1.51804	−	14.4432i	0.0758075	−	0.721260i	0.964737	−	0.263216i	$-0.0847832\pi$
$402$		0			0
$403$	20.0832	+	22.3047i	1.00042	+	1.11108i
$404$	24.4031	−	27.1024i	1.21410	−	1.34839i
$405$		0			0
$406$	−5.60523	+	7.13015i	−0.278183	+	0.353864i
$407$	7.46951	+	6.99405i	0.370250	+	0.346682i
$408$		0			0
$409$	−1.24752	−	11.8694i	−0.0616860	−	0.586903i	−0.981085	−	0.193577i	$-0.937991\pi$
$409$	−1.24752	−	11.8694i	−0.0616860	−	0.586903i	0.919399	−	0.393326i	$-0.128676\pi$
$410$	−1.24663	−	0.264978i	−0.0615665	−	0.0130864i
$411$		0			0
$412$	−7.00296	−	5.08795i	−0.345011	−	0.250665i
$413$	−27.6475	−	26.8597i	−1.36044	−	1.32168i
$414$		0			0
$415$	0.326707	−	0.362844i	0.0160374	−	0.0178113i
$416$	2.36461	+	22.4978i	0.115935	+	1.10304i
$417$		0			0
$418$	−22.7947	−	13.7600i	−1.11493	−	0.673023i
$419$	15.3521			0.749999			0.374999	−	0.927025i	$-0.377643\pi$
$419$	15.3521			0.749999			0.374999	+	0.927025i	$0.377643\pi$
$420$		0			0
$421$	−2.34650	−	7.22177i	−0.114361	−	0.351968i	0.877452	−	0.479664i	$-0.159242\pi$
$421$	−2.34650	−	7.22177i	−0.114361	−	0.351968i	−0.991813	+	0.127697i	$0.959242\pi$
$422$	−38.0685	+	8.09172i	−1.85315	+	0.393899i
$423$		0			0
$424$	13.4763	−	6.00005i	0.654468	−	0.291388i
$425$	9.12659	−	1.93992i	0.442705	−	0.0940998i
$426$		0			0
$427$	0.581209	−	15.3248i	0.0281267	−	0.741617i
$428$	2.80480			0.135575
$429$		0			0
$430$	−9.46128	+	16.3874i	−0.456264	+	0.790272i
$431$	2.75406	+	26.2031i	0.132658	+	1.26216i	0.834972	+	0.550292i	$0.185484\pi$
$431$	2.75406	+	26.2031i	0.132658	+	1.26216i	−0.702314	+	0.711867i	$0.747850\pi$
$432$		0			0
$433$	2.29633	−	7.06737i	0.110354	−	0.339636i	−0.880595	−	0.473869i	$-0.842857\pi$
$433$	2.29633	−	7.06737i	0.110354	−	0.339636i	0.990950	+	0.134233i	$0.0428571\pi$
$434$	−12.8637	+	50.9416i	−0.617477	+	2.44528i
$435$		0			0
$436$	−35.7593	+	7.60086i	−1.71256	+	0.364015i
$437$	−5.86081	−	1.24575i	−0.280361	−	0.0595925i
$438$		0			0
$439$	−9.49372	−	16.4436i	−0.453111	−	0.784811i	0.545467	−	0.838133i	$-0.316352\pi$
$439$	−9.49372	−	16.4436i	−0.453111	−	0.784811i	−0.998577	+	0.0533218i	$0.983019\pi$
$440$	−4.71376	−	4.41371i	−0.224720	−	0.210415i
$441$		0			0
$442$	−13.4361	+	9.76193i	−0.639092	+	0.464328i
$443$	3.49964	−	3.88675i	0.166273	−	0.184665i	−0.654250	−	0.756278i	$-0.727016\pi$
$443$	3.49964	−	3.88675i	0.166273	−	0.184665i	0.820523	+	0.571613i	$0.193682\pi$
$444$		0			0
$445$	−2.78745	+	1.24105i	−0.132138	+	0.0588316i
$446$	0.629653	−	5.99075i	0.0298149	−	0.283670i
$447$		0			0
$448$	−26.4233	+	22.0370i	−1.24839	+	1.04115i
$449$	−11.4942	+	8.35101i	−0.542444	+	0.394109i	−0.824992	−	0.565145i	$-0.808820\pi$
$449$	−11.4942	+	8.35101i	−0.542444	+	0.394109i	0.282548	+	0.959253i	$0.408820\pi$
$450$		0			0
$451$	−1.31612	+	1.73914i	−0.0619738	+	0.0818930i
$452$	19.2215	−	33.2927i	0.904106	−	1.56596i
$453$		0			0
$454$	−15.9033	−	48.9452i	−0.746377	−	2.29711i
$455$	−4.31438	−	6.43793i	−0.202261	−	0.301815i
$456$		0			0
$457$	3.26591	−	31.0730i	0.152773	−	1.45353i	−0.602497	−	0.798121i	$-0.705828\pi$
$457$	3.26591	−	31.0730i	0.152773	−	1.45353i	0.755270	−	0.655414i	$-0.227506\pi$
$458$	−26.8062	−	29.7713i	−1.25257	−	1.39112i
$459$		0			0
$460$	−3.97042	−	1.76775i	−0.185122	−	0.0824216i
$461$	24.4883			1.14053			0.570266	−	0.821460i	$-0.306840\pi$
$461$	24.4883			1.14053			0.570266	+	0.821460i	$0.306840\pi$
$462$		0			0
$463$	−4.68038			−0.217516			−0.108758	−	0.994068i	$-0.534687\pi$
$463$	−4.68038			−0.217516			−0.108758	+	0.994068i	$0.534687\pi$
$464$	1.37394	+	0.611718i	0.0637836	+	0.0283983i
$465$		0			0
$466$	−30.6325	−	34.0208i	−1.41902	−	1.57598i
$467$	3.65829	−	34.8063i	0.169286	−	1.61065i	−0.498906	−	0.866656i	$-0.666265\pi$
$467$	3.65829	−	34.8063i	0.169286	−	1.61065i	0.668192	−	0.743989i	$-0.267069\pi$
$468$		0			0
$469$	6.16590	−	12.5463i	0.284715	−	0.579333i
$470$	7.90277	+	24.3222i	0.364528	+	1.12190i
$471$		0			0
$472$	16.3717	−	28.3566i	0.753569	−	1.30522i
$473$	18.5193	+	26.5638i	0.851521	+	1.22141i
$474$		0			0
$475$	−12.3371	+	8.96344i	−0.566066	+	0.411271i
$476$	−16.3839	−	6.01901i	−0.750956	−	0.275881i
$477$		0			0
$478$	−1.64076	+	15.6108i	−0.0750466	+	0.714021i
$479$	38.8676	−	17.3050i	1.77591	−	0.790684i	0.792354	−	0.610062i	$-0.208855\pi$
$479$	38.8676	−	17.3050i	1.77591	−	0.790684i	0.983552	−	0.180623i	$-0.0578113\pi$
$480$		0			0
$481$	−6.98025	+	7.75235i	−0.318272	+	0.353477i
$482$	20.1467	−	14.6374i	0.917657	−	0.666717i
$483$		0			0
$484$	−30.6946	+	12.2556i	−1.39521	+	0.557073i
$485$	6.02703	+	10.4391i	0.273673	+	0.474016i
$486$		0			0
$487$	20.4533	+	4.34749i	0.926828	+	0.197003i	0.646512	−	0.762904i	$-0.276227\pi$
$487$	20.4533	+	4.34749i	0.926828	+	0.197003i	0.280317	+	0.959908i	$0.409561\pi$
$488$	12.7424	−	2.70847i	0.576819	−	0.122607i
$489$		0			0
$490$	5.15753	−	12.5479i	0.232993	−	0.566858i
$491$	−3.71603	+	11.4368i	−0.167702	+	0.516134i	−0.999225	−	0.0393561i	$-0.987469\pi$
$491$	−3.71603	+	11.4368i	−0.167702	+	0.516134i	0.831523	+	0.555490i	$0.187469\pi$
$492$		0			0
$493$	0.351688	+	3.34609i	0.0158392	+	0.150700i
$494$	13.5719	−	23.5071i	0.610627	−	1.05764i
$495$		0			0
$496$	8.71256			0.391205
$497$	−17.5447	−	11.0365i	−0.786989	−	0.495056i
$498$		0			0
$499$	−19.7300	+	4.19373i	−0.883234	+	0.187737i	−0.627132	−	0.778913i	$-0.715772\pi$
$499$	−19.7300	+	4.19373i	−0.883234	+	0.187737i	−0.256102	+	0.966650i	$0.582438\pi$
$500$	−21.9949	+	9.79276i	−0.983641	+	0.437945i
$501$		0			0
$502$	−23.1737	+	4.92571i	−1.03429	+	0.219845i
$503$	−1.03536	−	3.18651i	−0.0461644	−	0.142079i	0.925317	−	0.379193i	$-0.123798\pi$
$503$	−1.03536	−	3.18651i	−0.0461644	−	0.142079i	−0.971482	+	0.237114i	$0.923798\pi$
$504$		0			0
$505$	10.5155			0.467932
$506$	−9.36622	+	8.10835i	−0.416379	+	0.360460i
$507$		0			0
$508$	−0.696853	−	6.63012i	−0.0309179	−	0.294164i
$509$	−19.5478	+	21.7100i	−0.866440	+	0.962279i	−0.999585	−	0.0288172i	$-0.990826\pi$
$509$	−19.5478	+	21.7100i	−0.866440	+	0.962279i	0.133144	+	0.991097i	$0.457493\pi$
$510$		0			0
$511$	11.2291	+	10.9092i	0.496748	+	0.482594i
$512$	8.88170	+	6.45293i	0.392519	+	0.285182i
$513$		0			0
$514$	−1.31578	−	0.279679i	−0.0580368	−	0.0123361i
$515$	−0.260888	−	2.48218i	−0.0114961	−	0.109378i
$516$		0			0
$517$	43.4274	+	5.42239i	1.90993	+	0.238476i
$518$	−18.0759	−	2.59575i	−0.794210	−	0.114051i
$519$		0			0
$520$	4.40501	−	4.89225i	0.193172	−	0.214540i
$521$	−25.4302	−	28.2431i	−1.11412	−	1.23735i	−0.968767	−	0.247973i	$-0.920235\pi$
$521$	−25.4302	−	28.2431i	−1.11412	−	1.23735i	−0.145351	−	0.989380i	$-0.546431\pi$
$522$		0			0
$523$	−0.0630228	+	0.599622i	−0.00275579	+	0.0262196i	−0.995813	−	0.0914096i	$-0.970863\pi$
$523$	−0.0630228	+	0.599622i	−0.00275579	+	0.0262196i	0.993058	+	0.117629i	$0.0375294\pi$
$524$	−1.17616	+	3.61986i	−0.0513810	+	0.158134i
$525$		0			0
$526$	31.1544	−	22.6350i	1.35840	−	0.986932i
$527$	9.74542	+	16.8796i	0.424517	+	0.735286i
$528$		0			0
$529$	10.1061	−	17.5043i	0.439395	−	0.761055i
$530$	11.6213	+	5.17412i	0.504795	+	0.224749i
$531$		0			0
$532$	28.4637	−	1.90454i	1.23406	−	0.0825724i
$533$	−1.79879	−	1.30690i	−0.0779143	−	0.0566080i
$534$		0			0
$535$	0.541137	+	0.600993i	0.0233954	+	0.0259832i
$536$	11.6155	+	2.46894i	0.501712	+	0.106642i
$537$		0			0
$538$	46.5944			2.00883
$539$	−15.6964	−	17.1063i	−0.676090	−	0.736819i
$540$		0			0
$541$	−5.74408	−	2.55743i	−0.246957	−	0.109952i	0.279526	−	0.960138i	$-0.409823\pi$
$541$	−5.74408	−	2.55743i	−0.246957	−	0.109952i	−0.526483	+	0.850186i	$0.676489\pi$
$542$	−50.8203	−	10.8022i	−2.18292	−	0.463994i
$543$		0			0
$544$	−1.53556	+	14.6099i	−0.0658367	+	0.626394i
$545$	−8.52779	−	6.19580i	−0.365291	−	0.265399i
$546$		0			0
$547$	0.941825	+	2.89864i	0.0402695	+	0.123937i	0.969170	−	0.246392i	$-0.0792450\pi$
$547$	0.941825	+	2.89864i	0.0402695	+	0.123937i	−0.928901	+	0.370329i	$0.879245\pi$
$548$	−17.9044	−	7.97155i	−0.764838	−	0.340528i
$549$		0			0
$550$	−0.614740	+	31.5235i	−0.0262126	+	1.34416i
$551$	−2.74945	−	4.76218i	−0.117130	−	0.202876i
$552$		0			0
$553$	−29.1917	−	10.7242i	−1.24136	−	0.456040i
$554$	−5.47934	+	16.8637i	−0.232795	+	0.716469i
$555$		0			0
$556$	−39.0214	+	17.3734i	−1.65488	+	0.736798i
$557$	22.7399	+	25.2552i	0.963521	+	1.07010i	0.997499	+	0.0706761i	$0.0225157\pi$
$557$	22.7399	+	25.2552i	0.963521	+	1.07010i	−0.0339782	+	0.999423i	$0.510818\pi$
$558$		0			0
$559$	−26.7072	+	19.4039i	−1.12960	+	0.820699i
$560$	−2.22682	−	0.319778i	−0.0941005	−	0.0135131i
$561$		0			0
$562$	−10.8543	−	18.8001i	−0.457860	−	0.793036i
$563$	−4.40357	−	41.8972i	−0.185588	−	1.76575i	−0.550617	−	0.834758i	$-0.685607\pi$
$563$	−4.40357	−	41.8972i	−0.185588	−	1.76575i	0.365029	−	0.930996i	$-0.381059\pi$
$564$		0			0
$565$	10.8422	−	2.30458i	0.456135	−	0.0969545i
$566$	22.6996	+	16.4922i	0.954135	+	0.693220i
$567$		0			0
$568$	5.44084	−	16.7452i	0.228293	−	0.702612i
$569$	−14.9611	+	16.6160i	−0.627201	+	0.696578i	−0.970075	−	0.242804i	$-0.921933\pi$
$569$	−14.9611	+	16.6160i	−0.627201	+	0.696578i	0.342874	+	0.939381i	$0.388600\pi$
$570$		0			0
$571$	−9.49191	+	16.4405i	−0.397224	+	0.688012i	−0.993382	−	0.114855i	$-0.963360\pi$
$571$	−9.49191	+	16.4405i	−0.397224	+	0.688012i	0.596158	+	0.802867i	$0.296693\pi$
$572$	−13.1017	−	31.0420i	−0.547810	−	1.29793i
$573$		0			0
$574$	0.147510	−	3.88941i	0.00615696	−	0.162341i
$575$	2.19255	+	6.74796i	0.0914355	+	0.281409i
$576$		0			0
$577$	25.2676	−	11.2499i	1.05190	−	0.468338i	0.193387	−	0.981122i	$-0.438053\pi$
$577$	25.2676	−	11.2499i	1.05190	−	0.468338i	0.858518	+	0.512784i	$0.171386\pi$
$578$	24.8901	−	11.0818i	1.03529	−	0.460942i
$579$		0			0
$580$	−1.23257	−	3.79345i	−0.0511796	−	0.157515i
$581$	1.26216	+	0.793962i	0.0523632	+	0.0329391i
$582$		0			0
$583$	16.4588	−	14.2485i	0.681656	−	0.590111i
$584$	−6.64944	+	11.5172i	−0.275156	+	0.476584i
$585$		0			0
$586$	−9.97213	+	11.0752i	−0.411945	+	0.457511i
$587$	6.84645	−	21.0712i	0.282583	−	0.869701i	−0.704530	−	0.709675i	$-0.748842\pi$
$587$	6.84645	−	21.0712i	0.282583	−	0.869701i	0.987113	−	0.160027i	$-0.0511581\pi$
$588$		0			0
$589$	−25.7715	−	18.7241i	−1.06190	−	0.771514i
$590$	27.6192	−	5.87063i	1.13706	−	0.241690i
$591$		0			0
$592$	0.316532	+	3.01160i	0.0130094	+	0.123776i
$593$	−6.11706	−	10.5951i	−0.251198	−	0.435087i	0.712658	−	0.701511i	$-0.247491\pi$
$593$	−6.11706	−	10.5951i	−0.251198	−	0.435087i	−0.963856	+	0.266424i	$0.914158\pi$
$594$		0			0
$595$	−1.87128	−	4.67190i	−0.0767150	−	0.191529i
$596$	8.93591	−	6.49232i	0.366029	−	0.265936i
$597$		0			0
$598$	−8.45065	−	9.38540i	−0.345573	−	0.383798i
$599$	6.98887	−	3.11165i	0.285558	−	0.127138i	−0.258959	−	0.965888i	$-0.583380\pi$
$599$	6.98887	−	3.11165i	0.285558	−	0.127138i	0.544517	+	0.838750i	$0.316713\pi$
$600$		0			0
$601$	−0.852504	+	2.62374i	−0.0347744	+	0.107025i	−0.966937	−	0.255015i	$-0.917920\pi$
$601$	−0.852504	+	2.62374i	−0.0347744	+	0.107025i	0.932163	+	0.362040i	$0.117920\pi$
$602$	−54.2442	−	19.9279i	−2.21083	−	0.812199i
$603$		0			0
$604$	13.2917	+	23.0218i	0.540830	+	0.936744i
$605$	−8.54805	−	4.21253i	−0.347527	−	0.171264i
$606$		0			0
$607$	2.71592	+	1.20921i	0.110236	+	0.0490802i	0.461114	−	0.887341i	$-0.347450\pi$
$607$	2.71592	+	1.20921i	0.110236	+	0.0490802i	−0.350878	+	0.936421i	$0.614117\pi$
$608$	−7.41938	−	22.8345i	−0.300895	−	0.926061i
$609$		0			0
$610$	9.08835	+	6.60307i	0.367976	+	0.267351i
$611$	−4.66362	+	44.3713i	−0.188670	+	1.79507i
$612$		0			0
$613$	14.2952	+	3.03853i	0.577376	+	0.122725i	0.487338	−	0.873213i	$-0.337968\pi$
$613$	14.2952	+	3.03853i	0.577376	+	0.122725i	0.0900377	+	0.995938i	$0.471301\pi$
$614$	4.21517	+	1.87671i	0.170110	+	0.0757380i
$615$		0			0
$616$	10.8243	−	16.4852i	0.436123	−	0.664208i
$617$	8.43040			0.339395			0.169697	−	0.985496i	$-0.445721\pi$
$617$	8.43040			0.339395			0.169697	+	0.985496i	$0.445721\pi$
$618$		0			0
$619$	−43.4276	−	9.23083i	−1.74550	−	0.371018i	−0.778871	−	0.627184i	$-0.784207\pi$
$619$	−43.4276	−	9.23083i	−1.74550	−	0.371018i	−0.966633	+	0.256166i	$0.917541\pi$
$620$	−15.4613	−	17.1715i	−0.620942	−	0.689626i
$621$		0			0
$622$	−6.41432	−	4.66028i	−0.257191	−	0.186860i
$623$	−5.18758	−	7.74091i	−0.207836	−	0.310133i
$624$		0			0
$625$	13.0685	+	5.81849i	0.522742	+	0.232740i
$626$	−17.3996	+	30.1369i	−0.695427	+	1.20451i
$627$		0			0
$628$	−3.46534	−	6.00215i	−0.138282	−	0.239512i
$629$	−5.48057	+	3.98186i	−0.218524	+	0.158767i
$630$		0			0
$631$	−12.0351	+	37.0403i	−0.479110	+	1.47455i	0.361223	+	0.932479i	$0.382359\pi$
$631$	−12.0351	+	37.0403i	−0.479110	+	1.47455i	−0.840333	+	0.542070i	$0.817641\pi$
$632$	2.76137	−	26.2726i	0.109841	−	1.04507i
$633$		0			0
$634$	−24.8803	−	27.6324i	−0.988124	−	1.09742i
$635$	1.28621	−	1.42848i	0.0510418	−	0.0566876i
$636$		0			0
$637$	17.1237	−	16.3386i	0.678464	−	0.647360i
$638$	−11.2817	−	1.40865i	−0.446649	−	0.0557691i
$639$		0			0
$640$	−1.42276	−	13.5366i	−0.0562394	−	0.535083i
$641$	−11.1353	−	2.36687i	−0.439816	−	0.0934859i	−0.0173191	−	0.999850i	$-0.505513\pi$
$641$	−11.1353	−	2.36687i	−0.439816	−	0.0934859i	−0.422497	+	0.906364i	$0.638846\pi$
$642$		0			0
$643$	−15.4231	−	11.2055i	−0.608227	−	0.441903i	0.240563	−	0.970634i	$-0.422668\pi$
$643$	−15.4231	−	11.2055i	−0.608227	−	0.441903i	−0.848789	+	0.528731i	$0.822668\pi$
$644$	3.24968	−	12.8691i	0.128055	−	0.507113i
$645$		0			0
$646$	11.7947	−	13.0994i	0.464057	−	0.515388i
$647$	2.88324	+	27.4322i	0.113352	+	1.07847i	0.892319	+	0.451405i	$0.149077\pi$
$647$	2.88324	+	27.4322i	0.113352	+	1.07847i	−0.778967	+	0.627064i	$0.784256\pi$
$648$		0			0
$649$	10.9660	−	47.0597i	0.430454	−	1.84726i
$650$	−32.1427			−1.26074
$651$		0			0
$652$	−5.32218	−	16.3800i	−0.208432	−	0.641489i
$653$	−3.35565	+	0.713266i	−0.131317	+	0.0279123i	−0.273101	−	0.961985i	$-0.588049\pi$
$653$	−3.35565	+	0.713266i	−0.131317	+	0.0279123i	0.141784	+	0.989898i	$0.454716\pi$
$654$		0			0
$655$	−1.00256	+	0.446369i	−0.0391733	+	0.0174411i
$656$	−0.631321	+	0.134191i	−0.0246489	+	0.00523929i
$657$		0			0
$658$	−69.0695	+	36.4594i	−2.69261	+	1.42134i
$659$	−12.7090			−0.495073			−0.247536	−	0.968879i	$-0.579621\pi$
$659$	−12.7090			−0.495073			−0.247536	+	0.968879i	$0.579621\pi$
$660$		0			0
$661$	1.25158	−	2.16780i	0.0486808	−	0.0843177i	−0.840658	−	0.541566i	$-0.817832\pi$
$661$	1.25158	−	2.16780i	0.0486808	−	0.0843177i	0.889339	+	0.457248i	$0.151165\pi$
$662$	4.92016	+	46.8122i	0.191227	+	1.81941i
$663$		0			0
$664$	−0.391411	+	1.20464i	−0.0151897	+	0.0467491i
$665$	5.89966	+	5.73156i	0.228779	+	0.222260i
$666$		0			0
$667$	−2.50259	+	0.531942i	−0.0969007	+	0.0205969i
$668$	9.47628	+	2.01425i	0.366648	+	0.0779335i
$669$		0			0
$670$	5.12017	+	8.86839i	0.197809	+	0.342616i
$671$	16.8331	−	9.28577i	0.649834	−	0.358473i
$672$		0			0
$673$	22.9659	−	16.6857i	0.885269	−	0.643185i	−0.0493715	−	0.998780i	$-0.515722\pi$
$673$	22.9659	−	16.6857i	0.885269	−	0.643185i	0.934640	+	0.355595i	$0.115722\pi$
$674$	45.3084	−	50.3201i	1.74522	−	1.93826i
$675$		0			0
$676$	−4.30383	+	1.91619i	−0.165532	+	0.0736996i
$677$	2.78843	−	26.5302i	0.107168	−	1.01964i	−0.800324	−	0.599568i	$-0.795339\pi$
$677$	2.78843	−	26.5302i	0.107168	−	1.01964i	0.907492	−	0.420069i	$-0.137994\pi$
$678$		0			0
$679$	−28.2710	+	23.5780i	−1.08494	+	0.904840i
$680$	3.45861	−	2.51282i	0.132631	−	0.0963624i
$681$		0			0
$682$	−63.0246	+	19.1277i	−2.41334	+	0.732437i
$683$	2.30840	−	3.99827i	0.0883286	−	0.152990i	−0.818476	−	0.574541i	$-0.805181\pi$
$683$	2.30840	−	3.99827i	0.0883286	−	0.152990i	0.906805	+	0.421551i	$0.138514\pi$
$684$		0			0
$685$	−1.74625	−	5.37441i	−0.0667208	−	0.205346i
$686$	40.4471	+	8.97869i	1.54428	+	0.342808i
$687$		0			0
$688$	−1.00168	+	9.53034i	−0.0381886	+	0.363341i
$689$	14.8500	+	16.4926i	0.565739	+	0.628316i
$690$		0			0
$691$	−18.6121	−	8.28665i	−0.708039	−	0.315239i	0.0209349	−	0.999781i	$-0.493336\pi$
$691$	−18.6121	−	8.28665i	−0.708039	−	0.315239i	−0.728974	+	0.684542i	$0.760002\pi$
$692$	25.2400			0.959482
$693$		0			0
$694$	58.6570			2.22659
$695$	−11.2512	−	5.00934i	−0.426781	−	0.190015i
$696$		0			0
$697$	−0.966143	−	1.07301i	−0.0365953	−	0.0406432i
$698$	−2.49714	+	23.7587i	−0.0945182	+	0.899281i
$699$		0			0
$700$	−18.8060	−	28.0623i	−0.710800	−	1.06066i
$701$	13.3158	+	40.9820i	0.502932	+	1.54787i	0.804219	+	0.594333i	$0.202584\pi$
$701$	13.3158	+	40.9820i	0.502932	+	1.54787i	−0.301286	+	0.953534i	$0.597416\pi$
$702$		0			0
$703$	5.53592	−	9.58850i	0.208791	−	0.361637i
$704$	−40.7525	−	14.1255i	−1.53592	−	0.532375i
$705$		0			0
$706$	−7.05588	+	5.12640i	−0.265552	+	0.192935i
$707$	5.48157	+	31.6426i	0.206156	+	1.19004i
$708$		0			0
$709$	2.05380	−	19.5406i	0.0771320	−	0.733862i	−0.885791	−	0.464085i	$-0.846383\pi$
$709$	2.05380	−	19.5406i	0.0771320	−	0.733862i	0.962923	−	0.269777i	$-0.0869501\pi$
$710$	13.8706	−	6.17559i	0.520555	−	0.231766i
$711$		0			0
$712$	5.29654	−	5.88240i	0.198496	−	0.220452i
$713$	−11.9909	+	8.71187i	−0.449061	+	0.326262i
$714$		0			0
$715$	4.12374	−	8.79637i	0.154219	−	0.328966i
$716$	−3.85770	−	6.68173i	−0.144169	−	0.249708i
$717$		0			0
$718$	46.6835	+	9.92289i	1.74221	+	0.370319i
$719$	16.5812	−	3.52443i	0.618373	−	0.131439i	0.111935	−	0.993716i	$-0.464295\pi$
$719$	16.5812	−	3.52443i	0.618373	−	0.131439i	0.506438	+	0.862276i	$0.330962\pi$
$720$		0			0
$721$	7.33325	−	2.07898i	0.273104	−	0.0774251i
$722$	4.23226	−	13.0255i	0.157508	−	0.484761i
$723$		0			0
$724$	−0.556956	−	5.29908i	−0.0206991	−	0.196939i
$725$	−3.25580	+	5.63921i	−0.120917	+	0.209435i
$726$		0			0
$727$	−4.90596			−0.181952			−0.0909760	−	0.995853i	$-0.528999\pi$
$727$	−4.90596			−0.181952			−0.0909760	+	0.995853i	$0.528999\pi$
$728$	17.0178	+	10.7050i	0.630721	+	0.396755i
$729$		0			0
$730$	−11.2176	+	2.38438i	−0.415183	+	0.0882499i
$731$	−19.5844	+	8.71951i	−0.724353	+	0.322503i
$732$		0			0
$733$	−15.1811	+	3.22684i	−0.560726	+	0.119186i	−0.479551	−	0.877514i	$-0.659201\pi$
$733$	−15.1811	+	3.22684i	−0.560726	+	0.119186i	−0.0811750	+	0.996700i	$0.525867\pi$
$734$	−0.406497	−	1.25107i	−0.0150041	−	0.0461778i
$735$		0			0
$736$	−11.1711			−0.411771
$737$	17.4607	−	1.49163i	0.643172	−	0.0549449i
$738$		0			0
$739$	1.54631	+	14.7122i	0.0568820	+	0.541196i	0.985442	+	0.170013i	$0.0543810\pi$
$739$	1.54631	+	14.7122i	0.0568820	+	0.541196i	−0.928560	+	0.371183i	$0.878952\pi$
$740$	5.37383	−	5.96824i	0.197546	−	0.219397i
$741$		0			0
$742$	−9.51168	+	37.6673i	−0.349185	+	1.38281i
$743$	−1.22647	−	0.891080i	−0.0449947	−	0.0326906i	0.565061	−	0.825049i	$-0.308853\pi$
$743$	−1.22647	−	0.891080i	−0.0449947	−	0.0326906i	−0.610055	+	0.792359i	$0.708853\pi$
$744$		0			0
$745$	3.11516	+	0.662148i	0.114131	+	0.0242592i
$746$	−3.11375	−	29.6254i	−0.114003	−	1.08466i
$747$		0			0
$748$	−4.13105	−	21.4869i	−0.151046	−	0.785640i
$749$	−1.52639	+	1.94165i	−0.0557731	+	0.0709463i
$750$		0			0
$751$	28.1583	−	31.2729i	1.02751	−	1.14117i	0.0376258	−	0.999292i	$-0.488021\pi$
$751$	28.1583	−	31.2729i	1.02751	−	1.14117i	0.989885	−	0.141874i	$-0.0453128\pi$
$752$	8.66606	+	9.62463i	0.316019	+	0.350974i
$753$		0			0
$754$	1.21153	−	11.5270i	0.0441215	−	0.419788i
$755$	−2.36857	+	7.28971i	−0.0862011	+	0.265300i
$756$		0			0
$757$	−34.7238	+	25.2283i	−1.26206	+	0.916940i	−0.998857	−	0.0478008i	$-0.984779\pi$
$757$	−34.7238	+	25.2283i	−1.26206	+	0.916940i	−0.263202	+	0.964741i	$0.584779\pi$
$758$	9.72584	+	16.8456i	0.353258	+	0.611861i
$759$		0			0
$760$	−3.49354	+	6.05098i	−0.126724	+	0.219492i
$761$	37.9083	+	16.8779i	1.37418	+	0.611823i	0.955142	−	0.296148i	$-0.0957021\pi$
$761$	37.9083	+	16.8779i	1.37418	+	0.611823i	0.419034	+	0.907970i	$0.362369\pi$
$762$		0			0
$763$	14.1987	−	28.8912i	0.514026	−	1.04593i
$764$	−20.1290	−	14.6246i	−0.728243	−	0.529099i
$765$		0			0
$766$	46.1986	+	51.3088i	1.66922	+	1.85386i
$767$	48.1839	+	10.2418i	1.73982	+	0.369810i
$768$		0			0
$769$	36.1695			1.30430			0.652152	−	0.758088i	$-0.273866\pi$
$769$	36.1695			1.30430			0.652152	+	0.758088i	$0.273866\pi$
$770$	16.8104	−	2.57561i	0.605804	−	0.0928184i
$771$		0			0
$772$	−52.2232	−	23.2513i	−1.87955	−	0.836832i
$773$	1.31846	+	0.280248i	0.0474218	+	0.0100798i	0.231562	−	0.972820i	$-0.425617\pi$
$773$	1.31846	+	0.280248i	0.0474218	+	0.0100798i	−0.184140	+	0.982900i	$0.558950\pi$
$774$		0			0
$775$	−3.94303	+	37.5154i	−0.141638	+	1.34759i
$776$	−25.2985	−	18.3804i	−0.908163	−	0.659819i
$777$		0			0
$778$	3.54486	+	10.9100i	0.127089	+	0.391141i
$779$	2.15582	+	0.959834i	0.0772403	+	0.0343896i
$780$		0			0
$781$	0.506601	−	25.9782i	0.0181276	−	0.929572i
$782$	−4.10069	−	7.10260i	−0.146640	−	0.253989i
$783$		0			0
$784$	−0.198553	−	6.86754i	−0.00709119	−	0.245269i
$785$	0.617524	−	1.90054i	0.0220404	−	0.0678333i
$786$		0			0
$787$	−18.6386	+	8.29845i	−0.664395	+	0.295808i	−0.711090	−	0.703101i	$-0.751798\pi$
$787$	−18.6386	+	8.29845i	−0.664395	+	0.295808i	0.0466945	+	0.998909i	$0.485131\pi$
$788$	−30.5255	−	33.9020i	−1.08742	−	1.20771i
$789$		0			0
$790$	18.4301	−	13.3903i	0.655715	−	0.476405i
$791$	12.5867	+	31.4244i	0.447532	+	1.11732i
$792$		0			0
$793$	9.79915	+	16.9726i	0.347978	+	0.602716i
$794$	−6.84059	−	65.0839i	−0.242764	−	2.30974i
$795$		0			0
$796$	72.3120	−	15.3704i	2.56303	−	0.544789i
$797$	44.3283	+	32.2064i	1.57019	+	1.14081i	0.926977	+	0.375118i	$0.122398\pi$
$797$	44.3283	+	32.2064i	1.57019	+	1.14081i	0.643210	+	0.765690i	$0.277602\pi$
$798$		0			0
$799$	−8.95320	+	27.5551i	−0.316741	+	0.974830i
$800$	−19.0243	+	21.1286i	−0.672610	+	0.747010i
$801$		0			0
$802$	−16.2445	+	28.1363i	−0.573612	+	0.993526i
$803$	−4.45390	+	19.1135i	−0.157175	+	0.674501i
$804$		0			0
$805$	3.38447	−	1.78655i	0.119287	−	0.0629675i
$806$	−20.7487	−	63.8580i	−0.730842	−	2.24930i
$807$		0			0
$808$	−24.9208	+	11.0955i	−0.876712	+	0.390338i
$809$	−21.7007	+	9.66179i	−0.762958	+	0.339691i	−0.751056	−	0.660239i	$-0.770455\pi$
$809$	−21.7007	+	9.66179i	−0.762958	+	0.339691i	−0.0119016	+	0.999929i	$0.503788\pi$
$810$		0			0
$811$	−9.02569	−	27.7782i	−0.316935	−	0.975426i	−0.974951	−	0.222421i	$-0.928604\pi$
$811$	−9.02569	−	27.7782i	−0.316935	−	0.975426i	0.658016	−	0.753004i	$-0.271396\pi$
$812$	10.7725	−	5.68645i	0.378042	−	0.199555i
$813$		0			0
$814$	−8.90143	−	21.0903i	−0.311995	−	0.739214i
$815$	2.48297	−	4.30063i	0.0869747	−	0.150645i
$816$		0			0
$817$	23.4446	−	26.0378i	0.820221	−	0.910948i
$818$	−8.25053	+	25.3925i	−0.288473	+	0.887829i
$819$		0			0
$820$	1.38482	+	1.00613i	0.0483600	+	0.0351356i
$821$	−11.1890	+	2.37829i	−0.390498	+	0.0830029i	−0.398977	−	0.916961i	$-0.630635\pi$
$821$	−11.1890	+	2.37829i	−0.390498	+	0.0830029i	0.00847849	+	0.999964i	$0.497301\pi$
$822$		0			0
$823$	1.21088	+	11.5208i	0.0422087	+	0.401589i	0.995145	+	0.0984187i	$0.0313784\pi$
$823$	1.21088	+	11.5208i	0.0422087	+	0.401589i	−0.952936	+	0.303170i	$0.901955\pi$
$824$	3.23737	+	5.60730i	0.112779	+	0.195339i
$825$		0			0
$826$	32.0631	+	80.0498i	1.11562	+	2.78529i
$827$	−22.5394	+	16.3758i	−0.783770	+	0.569442i	−0.906108	−	0.423046i	$-0.860961\pi$
$827$	−22.5394	+	16.3758i	−0.783770	+	0.569442i	0.122338	+	0.992489i	$0.460961\pi$
$828$		0			0
$829$	8.52154	+	9.46413i	0.295965	+	0.328703i	0.872726	−	0.488210i	$-0.162350\pi$
$829$	8.52154	+	9.46413i	0.295965	+	0.328703i	−0.576761	+	0.816913i	$0.695683\pi$
$830$	−0.997845	+	0.444269i	−0.0346357	+	0.0154208i
$831$		0			0
$832$	13.5875	−	41.8179i	0.471061	−	1.44978i
$833$	13.0830	−	8.06635i	0.453298	−	0.279483i
$834$		0			0
$835$	1.39668	+	2.41913i	0.0483343	+	0.0837174i
$836$	20.4516	+	29.3355i	0.707335	+	1.01459i
$837$		0			0
$838$	−31.3750	−	13.9690i	−1.08383	−	0.482552i
$839$	−1.11854	−	3.44252i	−0.0386164	−	0.118849i	0.929890	−	0.367838i	$-0.119902\pi$
$839$	−1.11854	−	3.44252i	−0.0386164	−	0.118849i	−0.968506	+	0.248989i	$0.919902\pi$
$840$		0			0
$841$	21.5619	+	15.6656i	0.743513	+	0.540194i
$842$	−1.77565	+	16.8942i	−0.0611930	+	0.582212i
$843$		0			0
$844$	51.1294	+	10.8679i	1.75995	+	0.374088i
$845$	−1.24094	−	0.552501i	−0.0426896	−	0.0190066i
$846$		0			0
$847$	8.22015	−	27.9183i	0.282448	−	0.959283i
$848$	6.44224			0.221228
$849$		0			0
$850$	−20.4171	−	4.33979i	−0.700301	−	0.148854i
$851$	−3.44700	−	3.82828i	−0.118162	−	0.131232i
$852$		0			0
$853$	39.8352	+	28.9420i	1.36393	+	0.990955i	0.998184	+	0.0602414i	$0.0191870\pi$
$853$	39.8352	+	28.9420i	1.36393	+	0.990955i	0.365749	+	0.930714i	$0.380813\pi$
$854$	−15.1320	+	30.7903i	−0.517806	+	1.05362i
$855$		0			0
$856$	−1.91659	−	0.853323i	−0.0655078	−	0.0291660i
$857$	−12.0693	+	20.9046i	−0.412278	+	0.714087i	−0.995138	−	0.0984857i	$-0.968600\pi$
$857$	−12.0693	+	20.9046i	−0.412278	+	0.714087i	0.582860	+	0.812572i	$0.301933\pi$
$858$		0			0
$859$	0.0926485	+	0.160472i	0.00316113	+	0.00547523i	0.867602	−	0.497260i	$-0.165660\pi$
$859$	0.0926485	+	0.160472i	0.00316113	+	0.00547523i	−0.864441	+	0.502735i	$0.832327\pi$
$860$	20.5609	−	14.9384i	0.701121	−	0.509394i
$861$		0			0
$862$	18.2141	−	56.0571i	0.620373	−	1.90931i
$863$	4.00638	−	38.1182i	0.136379	−	1.29756i	−0.685574	−	0.728003i	$-0.740449\pi$
$863$	4.00638	−	38.1182i	0.136379	−	1.29756i	0.821953	−	0.569555i	$-0.192885\pi$
$864$		0			0
$865$	4.86963	+	5.40827i	0.165572	+	0.183887i
$866$	−11.1237	+	12.3541i	−0.377997	+	0.419809i
$867$		0			0
$868$	43.6119	−	55.4767i	1.48029	−	1.88300i
$869$	−7.36039	−	38.2838i	−0.249684	−	1.29869i
$870$		0			0
$871$	1.86741	+	17.7672i	0.0632748	+	0.602019i
$872$	26.7477	+	5.68541i	0.905793	+	0.192532i
$873$		0			0
$874$	10.8442	+	7.87876i	0.366810	+	0.266503i
$875$	5.19064	−	20.5555i	0.175476	−	0.694902i
$876$		0			0
$877$	−17.7953	+	19.7637i	−0.600906	+	0.667373i	−0.964469	−	0.264196i	$-0.914893\pi$
$877$	−17.7953	+	19.7637i	−0.600906	+	0.667373i	0.363563	+	0.931569i	$0.381560\pi$
$878$	4.44004	+	42.2442i	0.149844	+	1.42567i
$879$		0			0
$880$	−1.09659	−	2.59817i	−0.0369661	−	0.0875844i
$881$	−1.78266			−0.0600595			−0.0300297	−	0.999549i	$-0.509560\pi$
$881$	−1.78266			−0.0600595			−0.0300297	+	0.999549i	$0.509560\pi$
$882$		0			0
$883$	13.9329	+	42.8811i	0.468880	+	1.44306i	0.854037	+	0.520213i	$0.174147\pi$
$883$	13.9329	+	42.8811i	0.468880	+	1.44306i	−0.385157	+	0.922851i	$0.625853\pi$
$884$	21.8185	−	4.63768i	0.733837	−	0.155982i
$885$		0			0
$886$	−10.6888	+	4.75896i	−0.359097	+	0.159880i
$887$	−18.1028	+	3.84787i	−0.607832	+	0.129199i	−0.501537	−	0.865136i	$-0.667232\pi$
$887$	−18.1028	+	3.84787i	−0.607832	+	0.129199i	−0.106295	+	0.994335i	$0.533899\pi$
$888$		0			0
$889$	4.96900	+	3.12575i	0.166655	+	0.104834i
$890$	6.82595			0.228806
$891$		0			0
$892$	−4.04521	+	7.00651i	−0.135444	+	0.234595i
$893$	−4.94974	−	47.0936i	−0.165637	−	1.57593i
$894$		0			0
$895$	0.687441	−	2.11573i	0.0229786	−	0.0707210i
$896$	39.9921	−	11.3377i	1.33604	−	0.378768i
$897$		0			0
$898$	31.0893	−	6.60823i	1.03746	−	0.220519i
$899$	−13.3051	−	2.82809i	−0.443751	−	0.0943222i
$900$		0			0
$901$	7.20597	+	12.4811i	0.240066	+	0.415806i
$902$	4.27222	−	2.35672i	0.142249	−	0.0784702i
$903$		0			0
$904$	−23.2635	+	16.9019i	−0.773732	+	0.562149i
$905$	1.02800	−	1.14171i	0.0341718	−	0.0379516i
$906$		0			0
$907$	13.8652	−	6.17318i	0.460386	−	0.204977i	−0.163419	−	0.986557i	$-0.552252\pi$
$907$	13.8652	−	6.17318i	0.460386	−	0.204977i	0.623806	+	0.781580i	$0.285586\pi$
$908$	−7.22508	+	68.7421i	−0.239773	+	2.28129i
$909$		0			0
$910$	2.95933	+	17.0829i	0.0981009	+	0.566292i
$911$	−25.7264	+	18.6913i	−0.852353	+	0.619271i	−0.925794	−	0.378029i	$-0.876602\pi$
$911$	−25.7264	+	18.6913i	−0.852353	+	0.619271i	0.0734407	+	0.997300i	$0.476602\pi$
$912$		0			0
$913$	−0.0364446	+	1.86886i	−0.00120614	+	0.0618501i
$914$	−34.9482	+	60.5321i	−1.15598	+	2.00222i
$915$		0			0
$916$	16.6269	+	51.1723i	0.549368	+	1.69078i
$917$	−1.86581	−	2.78417i	−0.0616145	−	0.0919413i
$918$		0			0
$919$	−2.28580	+	21.7480i	−0.0754017	+	0.717399i	0.889881	+	0.456192i	$0.150787\pi$
$919$	−2.28580	+	21.7480i	−0.0754017	+	0.717399i	−0.965283	+	0.261207i	$0.915880\pi$
$920$	2.17529	+	2.41590i	0.0717171	+	0.0796499i
$921$		0			0
$922$	−50.0465	−	22.2821i	−1.64819	−	0.733823i
$923$	26.4885			0.871878
$924$		0			0
$925$	−13.1109			−0.431084
$926$	9.56527	+	4.25873i	0.314334	+	0.139951i
$927$		0			0
$928$	−6.86006	−	7.61887i	−0.225192	−	0.250102i
$929$	−3.21144	+	30.5548i	−0.105364	+	1.00247i	0.806293	+	0.591517i	$0.201471\pi$
$929$	−3.21144	+	30.5548i	−0.105364	+	1.00247i	−0.911657	+	0.410953i	$0.865196\pi$
$930$		0			0
$931$	−14.1717	+	20.7407i	−0.464458	+	0.679750i
$932$	19.0002	+	58.4765i	0.622372	+	1.91546i
$933$		0			0
$934$	−39.1471	+	67.8048i	−1.28093	+	2.21864i
$935$	3.80706	−	5.03070i	0.124504	−	0.164522i
$936$		0			0
$937$	−35.8545	+	26.0498i	−1.17132	+	0.851010i	−0.991166	−	0.132629i	$-0.957658\pi$
$937$	−35.8545	+	26.0498i	−1.17132	+	0.851010i	−0.180149	+	0.983639i	$0.557658\pi$
$938$	−24.0172	+	20.0303i	−0.784190	+	0.654012i
$939$		0			0
$940$	3.59034	−	34.1598i	0.117104	−	1.11417i
$941$	−22.3006	+	9.92889i	−0.726980	+	0.323673i	−0.736644	−	0.676281i	$-0.763591\pi$
$941$	−22.3006	+	9.92889i	−0.726980	+	0.323673i	0.00966354	+	0.999953i	$0.496924\pi$
$942$		0			0
$943$	0.734689	−	0.815955i	0.0239248	−	0.0265712i
$944$	11.5685	−	8.40502i	0.376523	−	0.273560i
$945$		0			0
$946$	−13.6771	−	71.1393i	−0.444682	−	2.31294i
$947$	−26.4671	−	45.8424i	−0.860066	−	1.48968i	−0.871865	−	0.489747i	$-0.837089\pi$
$947$	−26.4671	−	45.8424i	−0.860066	−	1.48968i	0.0117992	−	0.999930i	$-0.496244\pi$
$948$		0			0
$949$	−19.5701	−	4.15975i	−0.635272	−	0.135031i
$950$	33.3692	−	7.09285i	1.08264	−	0.230122i
$951$		0			0
$952$	9.36438	+	9.09755i	0.303501	+	0.294853i
$953$	1.48389	−	4.56695i	0.0480680	−	0.147938i	−0.924142	−	0.382050i	$-0.875218\pi$
$953$	1.48389	−	4.56695i	0.0480680	−	0.147938i	0.972210	+	0.234112i	$0.0752182\pi$
$954$		0			0
$955$	−0.749885	−	7.13468i	−0.0242657	−	0.230873i
$956$	10.5411	−	18.2577i	0.340922	−	0.590495i
$957$		0			0
$958$	−95.1795			−3.07511
$959$	15.2621	−	8.05633i	0.492839	−	0.260153i
$960$		0			0
$961$	−46.7547	+	9.93803i	−1.50822	+	0.320582i
$962$	21.3194	−	9.49203i	0.687366	−	0.306035i
$963$		0			0
$964$	−32.7156	+	6.95391i	−1.05370	+	0.223970i
$965$	−5.09344	−	15.6760i	−0.163963	−	0.504628i
$966$		0			0
$967$	10.0231			0.322320			0.161160	−	0.986928i	$-0.448477\pi$
$967$	10.0231			0.322320			0.161160	+	0.986928i	$0.448477\pi$
$968$	24.7031	+	0.963838i	0.793987	+	0.0309789i
$969$		0			0
$970$	−2.81873	−	26.8184i	−0.0905040	−	0.861088i
$971$	−1.01235	+	1.12433i	−0.0324879	+	0.0360814i	−0.759170	−	0.650893i	$-0.774395\pi$
$971$	−1.01235	+	1.12433i	−0.0324879	+	0.0360814i	0.726682	+	0.686974i	$0.241061\pi$
$972$		0			0
$973$	9.20877	−	36.4677i	0.295220	−	1.16910i
$974$	−37.8445	−	27.4956i	−1.21262	−	0.881017i
$975$		0			0
$976$	5.56475	+	1.18282i	0.178123	+	0.0378613i
$977$	−1.91632	−	18.2326i	−0.0613085	−	0.583312i	−0.981449	−	0.191723i	$-0.938592\pi$
$977$	−1.91632	−	18.2326i	−0.0613085	−	0.583312i	0.920140	−	0.391588i	$-0.128074\pi$
$978$		0			0
$979$	4.95835	−	10.5767i	0.158469	−	0.338032i
$980$	−13.1829	+	12.5785i	−0.421111	+	0.401805i
$981$		0			0
$982$	18.0009	−	19.9920i	0.574431	−	0.637970i
$983$	19.5483	+	21.7106i	0.623494	+	0.692460i	0.969310	−	0.245843i	$-0.0790646\pi$
$983$	19.5483	+	21.7106i	0.623494	+	0.692460i	−0.345816	+	0.938302i	$0.612398\pi$
$984$		0			0
$985$	1.37493	−	13.0816i	0.0438090	−	0.416814i
$986$	2.32590	−	7.15839i	0.0740718	−	0.227969i
$987$		0			0
$988$	−29.4938	+	21.4285i	−0.938324	+	0.681732i
$989$	−8.15100	−	14.1180i	−0.259187	−	0.448925i
$990$		0			0
$991$	22.6187	−	39.1768i	0.718508	−	1.24449i	−0.243083	−	0.970005i	$-0.578159\pi$
$991$	22.6187	−	39.1768i	0.718508	−	1.24449i	0.961591	−	0.274487i	$-0.0885079\pi$
$992$	−54.2568	−	24.1567i	−1.72266	−	0.766976i
$993$		0			0
$994$	25.8138	+	38.5195i	0.818765	+	1.22176i
$995$	17.2448	+	12.5291i	0.546697	+	0.397199i
$996$		0			0
$997$	−9.42214	−	10.4643i	−0.298402	−	0.331409i	0.575234	−	0.817989i	$-0.304911\pi$
$997$	−9.42214	−	10.4643i	−0.298402	−	0.331409i	−0.873636	+	0.486580i	$0.838244\pi$
$998$	44.1379	+	9.38180i	1.39716	+	0.296976i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.by.b.487.1		40
3.2	odd	2		77.2.m.b.25.5	yes	40
7.2	even	3	inner	693.2.by.b.289.5		40
11.4	even	5	inner	693.2.by.b.235.5		40
21.2	odd	6		77.2.m.b.58.1	yes	40
21.5	even	6		539.2.q.h.520.1		40
21.11	odd	6		539.2.f.h.344.1		20
21.17	even	6		539.2.f.g.344.1		20
21.20	even	2		539.2.q.h.410.5		40
33.2	even	10		847.2.e.h.606.9		20
33.5	odd	10		847.2.n.i.130.1		40
33.8	even	10		847.2.n.h.753.1		40
33.14	odd	10		847.2.n.i.753.5		40
33.17	even	10		847.2.n.h.130.5		40
33.20	odd	10		847.2.e.i.606.2		20
33.26	odd	10		77.2.m.b.4.1	✓	40
33.29	even	10		847.2.n.j.81.5		40
33.32	even	2		847.2.n.j.487.1		40
77.37	even	15	inner	693.2.by.b.37.1		40
231.2	even	30		847.2.e.h.485.9		20
231.26	even	30		539.2.q.h.422.5		40
231.53	odd	30		5929.2.a.bw.1.9		10
231.59	even	30		539.2.f.g.246.1		20
231.65	even	6		847.2.n.j.366.5		40
231.86	odd	30		847.2.e.i.485.2		20
231.101	odd	30		5929.2.a.bz.1.2		10
231.107	even	30		847.2.n.h.632.5		40
231.125	even	10		539.2.q.h.312.1		40
231.128	even	30		847.2.n.j.807.1		40
231.149	even	30		847.2.n.h.9.1		40
231.158	odd	30		539.2.f.h.246.1		20
231.170	odd	30		847.2.n.i.9.5		40
231.185	even	30		5929.2.a.bx.1.9		10
231.191	odd	30		77.2.m.b.37.5	yes	40
231.200	even	30		5929.2.a.by.1.2		10
231.212	odd	30		847.2.n.i.632.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.4.1	✓	40	33.26	odd	10
77.2.m.b.25.5	yes	40	3.2	odd	2
77.2.m.b.37.5	yes	40	231.191	odd	30
77.2.m.b.58.1	yes	40	21.2	odd	6
539.2.f.g.246.1		20	231.59	even	30
539.2.f.g.344.1		20	21.17	even	6
539.2.f.h.246.1		20	231.158	odd	30
539.2.f.h.344.1		20	21.11	odd	6
539.2.q.h.312.1		40	231.125	even	10
539.2.q.h.410.5		40	21.20	even	2
539.2.q.h.422.5		40	231.26	even	30
539.2.q.h.520.1		40	21.5	even	6
693.2.by.b.37.1		40	77.37	even	15	inner
693.2.by.b.235.5		40	11.4	even	5	inner
693.2.by.b.289.5		40	7.2	even	3	inner
693.2.by.b.487.1		40	1.1	even	1	trivial
847.2.e.h.485.9		20	231.2	even	30
847.2.e.h.606.9		20	33.2	even	10
847.2.e.i.485.2		20	231.86	odd	30
847.2.e.i.606.2		20	33.20	odd	10
847.2.n.h.9.1		40	231.149	even	30
847.2.n.h.130.5		40	33.17	even	10
847.2.n.h.632.5		40	231.107	even	30
847.2.n.h.753.1		40	33.8	even	10
847.2.n.i.9.5		40	231.170	odd	30
847.2.n.i.130.1		40	33.5	odd	10
847.2.n.i.632.1		40	231.212	odd	30
847.2.n.i.753.5		40	33.14	odd	10
847.2.n.j.81.5		40	33.29	even	10
847.2.n.j.366.5		40	231.65	even	6
847.2.n.j.487.1		40	33.32	even	2
847.2.n.j.807.1		40	231.128	even	30
5929.2.a.bw.1.9		10	231.53	odd	30
5929.2.a.bx.1.9		10	231.185	even	30
5929.2.a.by.1.2		10	231.200	even	30
5929.2.a.bz.1.2		10	231.101	odd	30

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.by (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.04369 - 0.909911i) q^{2} +(2.01049 + 2.23287i) q^{4} +(-0.0905565 + 0.861587i) q^{5} +(-2.63985 + 0.176636i) q^{7} +(-0.694498 - 2.13745i) q^{8} +O(q^{10})\)	\(q+(-2.04369 - 0.909911i) q^{2} +(2.01049 + 2.23287i) q^{4} +(-0.0905565 + 0.861587i) q^{5} +(-2.63985 + 0.176636i) q^{7} +(-0.694498 - 2.13745i) q^{8} +(0.969038 - 1.67842i) q^{10} +(-1.89678 - 2.72071i) q^{11} +(2.73539 - 1.98738i) q^{13} +(5.55577 + 2.04104i) q^{14} +(0.102593 - 0.976110i) q^{16} +(2.00586 - 0.893065i) q^{17} +(-2.40122 + 2.66683i) q^{19} +(-2.10587 + 1.53001i) q^{20} +(1.40083 + 7.28619i) q^{22} +(0.834837 + 1.44598i) q^{23} +(4.15661 + 0.883514i) q^{25} +(-7.39864 + 1.57263i) q^{26} +(-5.70178 - 5.53931i) q^{28} +(-0.473517 + 1.45734i) q^{29} +(0.927888 + 8.82827i) q^{31} +(-3.34529 + 5.79421i) q^{32} -4.91197 q^{34} +(0.0868681 - 2.29046i) q^{35} +(-3.01788 + 0.641471i) q^{37} +(7.33394 - 3.26528i) q^{38} +(1.90449 - 0.404811i) q^{40} +(-0.203209 - 0.625414i) q^{41} -9.76359 q^{43} +(2.26154 - 9.70519i) q^{44} +(-0.390438 - 3.71477i) q^{46} +(-8.82952 + 9.80618i) q^{47} +(6.93760 - 0.932584i) q^{49} +(-7.69091 - 5.58777i) q^{50} +(9.93702 + 2.11218i) q^{52} +(0.686100 + 6.52780i) q^{53} +(2.51589 - 1.38786i) q^{55} +(2.21092 + 5.51986i) q^{56} +(2.29377 - 2.54749i) q^{58} +(9.74869 + 10.8270i) q^{59} +(-0.605886 + 5.76462i) q^{61} +(6.13662 - 18.8866i) q^{62} +(10.5209 - 7.64386i) q^{64} +(1.46459 + 2.53675i) q^{65} +(-2.64188 + 4.57587i) q^{67} +(6.02684 + 2.68332i) q^{68} +(-2.26164 + 4.60195i) q^{70} +(6.33800 + 4.60483i) q^{71} +(-3.95947 - 4.39744i) q^{73} +(6.75131 + 1.43504i) q^{74} -10.7823 q^{76} +(5.48778 + 6.84721i) q^{77} +(10.7382 + 4.78095i) q^{79} +(0.831714 + 0.176786i) q^{80} +(-0.153773 + 1.46306i) q^{82} +(-0.455953 - 0.331269i) q^{83} +(0.587810 + 1.80909i) q^{85} +(19.9538 + 8.88400i) q^{86} +(-4.49805 + 5.94378i) q^{88} +(1.76101 + 3.05016i) q^{89} +(-6.86998 + 5.72955i) q^{91} +(-1.55026 + 4.77120i) q^{92} +(26.9676 - 12.0067i) q^{94} +(-2.08026 - 2.31036i) q^{95} +(11.2566 - 8.17838i) q^{97} +(-15.0269 - 4.40668i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 3 q^{2} - 3 q^{4} - 4 q^{5} - 2 q^{7} + 38 q^{8}+O(q^{10}) \) 40 * q + 3 * q^2 - 3 * q^4 - 4 * q^5 - 2 * q^7 + 38 * q^8	\( 40 q + 3 q^{2} - 3 q^{4} - 4 q^{5} - 2 q^{7} + 38 q^{8} + 14 q^{10} + 9 q^{11} + 6 q^{13} + 3 q^{14} - 5 q^{16} + 7 q^{17} - 4 q^{19} + 30 q^{20} + 44 q^{22} + 14 q^{23} + 21 q^{25} + 16 q^{28} - 17 q^{31} + 30 q^{32} + 48 q^{34} + 14 q^{35} + 24 q^{37} - 12 q^{38} + 10 q^{40} - 60 q^{41} - 72 q^{43} - 18 q^{44} + 8 q^{46} - 13 q^{47} - 10 q^{49} - 6 q^{50} + 2 q^{52} - 33 q^{53} - 6 q^{55} - 24 q^{56} - 17 q^{58} - 21 q^{59} + 52 q^{62} + 94 q^{64} + 40 q^{65} - 38 q^{67} + 23 q^{68} - 3 q^{70} - 20 q^{71} + 11 q^{73} + 41 q^{74} - 96 q^{76} - 36 q^{77} + 21 q^{79} - 12 q^{80} + 6 q^{82} + 46 q^{83} - 78 q^{85} - 7 q^{86} + 32 q^{88} + 10 q^{89} - 14 q^{91} + 110 q^{92} + 37 q^{94} - 7 q^{95} - 54 q^{97} - 116 q^{98}+O(q^{100}) \) 40 * q + 3 * q^2 - 3 * q^4 - 4 * q^5 - 2 * q^7 + 38 * q^8 + 14 * q^10 + 9 * q^11 + 6 * q^13 + 3 * q^14 - 5 * q^16 + 7 * q^17 - 4 * q^19 + 30 * q^20 + 44 * q^22 + 14 * q^23 + 21 * q^25 + 16 * q^28 - 17 * q^31 + 30 * q^32 + 48 * q^34 + 14 * q^35 + 24 * q^37 - 12 * q^38 + 10 * q^40 - 60 * q^41 - 72 * q^43 - 18 * q^44 + 8 * q^46 - 13 * q^47 - 10 * q^49 - 6 * q^50 + 2 * q^52 - 33 * q^53 - 6 * q^55 - 24 * q^56 - 17 * q^58 - 21 * q^59 + 52 * q^62 + 94 * q^64 + 40 * q^65 - 38 * q^67 + 23 * q^68 - 3 * q^70 - 20 * q^71 + 11 * q^73 + 41 * q^74 - 96 * q^76 - 36 * q^77 + 21 * q^79 - 12 * q^80 + 6 * q^82 + 46 * q^83 - 78 * q^85 - 7 * q^86 + 32 * q^88 + 10 * q^89 - 14 * q^91 + 110 * q^92 + 37 * q^94 - 7 * q^95 - 54 * q^97 - 116 * q^98

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