LMFDB - Embedded newform 756.2.be.d.431.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(107,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("756.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.be (of order $6$, degree $2$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.3
Character	$\chi$	$=$	756.431
Dual form			756.2.be.d.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16654 - 0.799486i) q^{2} +(0.721643 + 1.86527i) q^{4} +(-3.44992 + 1.99182i) q^{5} +(-0.212727 - 2.63719i) q^{7} +(0.649430 - 2.75286i) q^{8} +O(q^{10})$	\(q+(-1.16654 - 0.799486i) q^{2} +(0.721643 + 1.86527i) q^{4} +(-3.44992 + 1.99182i) q^{5} +(-0.212727 - 2.63719i) q^{7} +(0.649430 - 2.75286i) q^{8} +(5.61691 + 0.434631i) q^{10} +(0.936467 - 1.62201i) q^{11} +1.05785 q^{13} +(-1.86024 + 3.24646i) q^{14} +(-2.95846 + 2.69212i) q^{16} +(-2.30404 - 1.33024i) q^{17} +(-0.628053 + 0.362606i) q^{19} +(-6.20489 - 4.99766i) q^{20} +(-2.38920 + 1.14345i) q^{22} +(3.00404 + 5.20316i) q^{23} +(5.43465 - 9.41310i) q^{25} +(-1.23402 - 0.845733i) q^{26} +(4.76555 - 2.29990i) q^{28} +5.09494i q^{29} +(3.48051 + 2.00948i) q^{31} +(5.60348 - 0.775220i) q^{32} +(1.62425 + 3.39382i) q^{34} +(5.98668 + 8.67438i) q^{35} +(4.48131 + 7.76185i) q^{37} +(1.02255 + 0.0791238i) q^{38} +(3.24270 + 10.7907i) q^{40} -6.19225i q^{41} +12.3071i q^{43} +(3.70128 + 0.576252i) q^{44} +(0.655508 - 8.47140i) q^{46} +(2.03670 + 3.52767i) q^{47} +(-6.90949 + 1.12200i) q^{49} +(-13.8654 + 6.63585i) q^{50} +(0.763387 + 1.97317i) q^{52} +(11.2365 + 6.48742i) q^{53} +7.46108i q^{55} +(-7.39795 - 1.12706i) q^{56} +(4.07333 - 5.94346i) q^{58} +(4.56454 - 7.90602i) q^{59} +(-5.21274 - 9.02873i) q^{61} +(-2.45362 - 5.12676i) q^{62} +(-7.15648 - 3.57558i) q^{64} +(-3.64949 + 2.10703i) q^{65} +(5.00193 + 2.88786i) q^{67} +(0.818557 - 5.25761i) q^{68} +(-0.0486684 - 14.9053i) q^{70} +6.24090 q^{71} +(-7.37051 + 12.7661i) q^{73} +(0.977859 - 12.6373i) q^{74} +(-1.12959 - 0.909815i) q^{76} +(-4.47675 - 2.12459i) q^{77} +(4.92434 - 2.84307i) q^{79} +(4.84427 - 15.1803i) q^{80} +(-4.95062 + 7.22352i) q^{82} +3.27295 q^{83} +10.5983 q^{85} +(9.83935 - 14.3567i) q^{86} +(-3.85699 - 3.63135i) q^{88} +(-8.80546 + 5.08384i) q^{89} +(-0.225033 - 2.78973i) q^{91} +(-7.53745 + 9.35818i) q^{92} +(0.444426 - 5.74350i) q^{94} +(1.44449 - 2.50193i) q^{95} -2.03772 q^{97} +(8.95724 + 4.21518i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{4} + 2 q^{7}+O(q^{10}) $ 28 * q - 4 * q^4 + 2 * q^7	$ 28 q - 4 q^{4} + 2 q^{7} + 4 q^{10} + 8 q^{13} + 12 q^{16} - 42 q^{19} + 4 q^{22} + 6 q^{25} + 24 q^{28} + 30 q^{31} + 24 q^{34} + 12 q^{37} + 24 q^{46} - 14 q^{49} - 24 q^{52} - 44 q^{58} + 6 q^{61} + 8 q^{64} + 24 q^{67} - 32 q^{70} - 22 q^{73} + 48 q^{79} + 36 q^{82} - 24 q^{85} - 4 q^{88} + 16 q^{91} + 60 q^{94} - 4 q^{97}+O(q^{100}) $ 28 * q - 4 * q^4 + 2 * q^7 + 4 * q^10 + 8 * q^13 + 12 * q^16 - 42 * q^19 + 4 * q^22 + 6 * q^25 + 24 * q^28 + 30 * q^31 + 24 * q^34 + 12 * q^37 + 24 * q^46 - 14 * q^49 - 24 * q^52 - 44 * q^58 + 6 * q^61 + 8 * q^64 + 24 * q^67 - 32 * q^70 - 22 * q^73 + 48 * q^79 + 36 * q^82 - 24 * q^85 - 4 * q^88 + 16 * q^91 + 60 * q^94 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.16654	−	0.799486i	−0.824870	−	0.565322i
$2$	−1.16654	−	0.799486i	−0.824870	−	0.565322i
$3$		0			0
$3$		0			0
$4$	0.721643	+	1.86527i	0.360822	+	0.932635i
$5$	−3.44992	+	1.99182i	−1.54285	+	0.890767i	−0.544196	+	0.838958i	$0.683165\pi$
$5$	−3.44992	+	1.99182i	−1.54285	+	0.890767i	−0.998657	+	0.0518089i	$0.983501\pi$
$6$		0			0
$7$	−0.212727	−	2.63719i	−0.0804033	−	0.996762i
$7$	−0.212727	−	2.63719i	−0.0804033	−	0.996762i
$8$	0.649430	−	2.75286i	0.229608	−	0.973283i
$9$		0			0
$10$	5.61691	+	0.434631i	1.77622	+	0.137442i
$11$	0.936467	−	1.62201i	0.282356	−	0.489054i	−0.689609	−	0.724182i	$-0.742218\pi$
$11$	0.936467	−	1.62201i	0.282356	−	0.489054i	0.971964	+	0.235128i	$0.0755509\pi$
$12$		0			0
$13$	1.05785			0.293394			0.146697	−	0.989182i	$-0.453136\pi$
$13$	1.05785			0.293394			0.146697	+	0.989182i	$0.453136\pi$
$14$	−1.86024	+	3.24646i	−0.497170	+	0.867653i
$15$		0			0
$16$	−2.95846	+	2.69212i	−0.739616	+	0.673030i
$17$	−2.30404	−	1.33024i	−0.558811	−	0.322630i	0.193857	−	0.981030i	$-0.437900\pi$
$17$	−2.30404	−	1.33024i	−0.558811	−	0.322630i	−0.752668	+	0.658400i	$0.771234\pi$
$18$		0			0
$19$	−0.628053	+	0.362606i	−0.144085	+	0.0831876i	−0.570310	−	0.821430i	$-0.693177\pi$
$19$	−0.628053	+	0.362606i	−0.144085	+	0.0831876i	0.426224	+	0.904617i	$0.359843\pi$
$20$	−6.20489	−	4.99766i	−1.38745	−	1.11751i
$21$		0			0
$22$	−2.38920	+	1.14345i	−0.509380	+	0.243784i
$23$	3.00404	+	5.20316i	0.626387	+	1.08493i	0.988271	+	0.152711i	$0.0488002\pi$
$23$	3.00404	+	5.20316i	0.626387	+	1.08493i	−0.361884	+	0.932223i	$0.617866\pi$
$24$		0			0
$25$	5.43465	−	9.41310i	1.08693	−	1.88262i
$26$	−1.23402	−	0.845733i	−0.242012	−	0.165862i
$27$		0			0
$28$	4.76555	−	2.29990i	0.900604	−	0.434640i
$29$			5.09494i			0.946106i	0.881034	+	0.473053i	$0.156848\pi$
$29$			5.09494i			0.946106i	−0.881034	+	0.473053i	$0.843152\pi$
$30$		0			0
$31$	3.48051	+	2.00948i	0.625119	+	0.360912i	0.778859	−	0.627199i	$-0.215799\pi$
$31$	3.48051	+	2.00948i	0.625119	+	0.360912i	−0.153741	+	0.988111i	$0.549132\pi$
$32$	5.60348	−	0.775220i	0.990565	−	0.137041i
$33$		0			0
$34$	1.62425	+	3.39382i	0.278557	+	0.582036i
$35$	5.98668	+	8.67438i	1.01193	+	1.46624i
$36$		0			0
$37$	4.48131	+	7.76185i	0.736722	+	1.27604i	0.953963	+	0.299923i	$0.0969609\pi$
$37$	4.48131	+	7.76185i	0.736722	+	1.27604i	−0.217241	+	0.976118i	$0.569706\pi$
$38$	1.02255	+	0.0791238i	0.165879	+	0.0128356i
$39$		0			0
$40$	3.24270	+	10.7907i	0.512716	+	1.70616i
$41$		−	6.19225i		−	0.967067i	−0.875326	−	0.483534i	$-0.839353\pi$
$41$		−	6.19225i		−	0.967067i	0.875326	−	0.483534i	$-0.160647\pi$
$42$		0			0
$43$			12.3071i			1.87681i	0.345533	+	0.938407i	$0.387698\pi$
$43$			12.3071i			1.87681i	−0.345533	+	0.938407i	$0.612302\pi$
$44$	3.70128	+	0.576252i	0.557989	+	0.0868733i
$45$		0			0
$46$	0.655508	−	8.47140i	0.0966494	−	1.24904i
$47$	2.03670	+	3.52767i	0.297084	+	0.514564i	0.975467	−	0.220144i	$-0.0706526\pi$
$47$	2.03670	+	3.52767i	0.297084	+	0.514564i	−0.678384	+	0.734708i	$0.737319\pi$
$48$		0			0
$49$	−6.90949	+	1.12200i	−0.987071	+	0.160286i
$50$	−13.8654	+	6.63585i	−1.96086	+	0.938451i
$51$		0			0
$52$	0.763387	+	1.97317i	0.105863	+	0.273629i
$53$	11.2365	+	6.48742i	1.54346	+	0.891116i	0.998617	+	0.0525765i	$0.0167433\pi$
$53$	11.2365	+	6.48742i	1.54346	+	0.891116i	0.544841	+	0.838539i	$0.316590\pi$
$54$		0			0
$55$			7.46108i			1.00605i
$56$	−7.39795	−	1.12706i	−0.988593	−	0.150610i
$57$		0			0
$58$	4.07333	−	5.94346i	0.534855	−	0.780415i
$59$	4.56454	−	7.90602i	0.594253	−	1.02928i	−0.399399	−	0.916777i	$-0.630781\pi$
$59$	4.56454	−	7.90602i	0.594253	−	1.02928i	0.993652	−	0.112499i	$-0.0358856\pi$
$60$		0			0
$61$	−5.21274	−	9.02873i	−0.667423	−	1.15601i	−0.978622	−	0.205666i	$-0.934064\pi$
$61$	−5.21274	−	9.02873i	−0.667423	−	1.15601i	0.311199	−	0.950345i	$-0.399269\pi$
$62$	−2.45362	−	5.12676i	−0.311610	−	0.651099i
$63$		0			0
$64$	−7.15648	−	3.57558i	−0.894560	−	0.446948i
$65$	−3.64949	+	2.10703i	−0.452663	+	0.261345i
$66$		0			0
$67$	5.00193	+	2.88786i	0.611083	+	0.352809i	0.773389	−	0.633932i	$-0.218560\pi$
$67$	5.00193	+	2.88786i	0.611083	+	0.352809i	−0.162306	+	0.986740i	$0.551893\pi$
$68$	0.818557	−	5.25761i	0.0992647	−	0.637579i
$69$		0			0
$70$	−0.0486684	−	14.9053i	−0.00581699	−	1.78152i
$71$	6.24090			0.740658			0.370329	−	0.928901i	$-0.379245\pi$
$71$	6.24090			0.740658			0.370329	+	0.928901i	$0.379245\pi$
$72$		0			0
$73$	−7.37051	+	12.7661i	−0.862653	+	1.49416i	0.00670577	+	0.999978i	$0.497865\pi$
$73$	−7.37051	+	12.7661i	−0.862653	+	1.49416i	−0.869359	+	0.494181i	$0.835468\pi$
$74$	0.977859	−	12.6373i	0.113674	−	1.46905i
$75$		0			0
$76$	−1.12959	−	0.909815i	−0.129573	−	0.104363i
$77$	−4.47675	−	2.12459i	−0.510173	−	0.242120i
$78$		0			0
$79$	4.92434	−	2.84307i	0.554031	−	0.319870i	−0.196715	−	0.980461i	$-0.563027\pi$
$79$	4.92434	−	2.84307i	0.554031	−	0.319870i	0.750746	+	0.660591i	$0.229694\pi$
$80$	4.84427	−	15.1803i	0.541606	−	1.69721i
$81$		0			0
$82$	−4.95062	+	7.22352i	−0.546705	+	0.797705i
$83$	3.27295			0.359253			0.179626	−	0.983735i	$-0.442511\pi$
$83$	3.27295			0.359253			0.179626	+	0.983735i	$0.442511\pi$
$84$		0			0
$85$	10.5983			1.14955
$86$	9.83935	−	14.3567i	1.06100	−	1.54813i
$87$		0			0
$88$	−3.85699	−	3.63135i	−0.411157	−	0.387103i
$89$	−8.80546	+	5.08384i	−0.933377	+	0.538886i	−0.887878	−	0.460079i	$-0.847821\pi$
$89$	−8.80546	+	5.08384i	−0.933377	+	0.538886i	−0.0454992	+	0.998964i	$0.514488\pi$
$90$		0			0
$91$	−0.225033	−	2.78973i	−0.0235898	−	0.292444i
$92$	−7.53745	+	9.35818i	−0.785833	+	0.975657i
$93$		0			0
$94$	0.444426	−	5.74350i	0.0458390	−	0.592397i
$95$	1.44449	−	2.50193i	0.148202	−	0.256693i
$96$		0			0
$97$	−2.03772			−0.206900			−0.103450	−	0.994635i	$-0.532988\pi$
$97$	−2.03772			−0.206900			−0.103450	+	0.994635i	$0.532988\pi$
$98$	8.95724	+	4.21518i	0.904818	+	0.425798i
$99$		0			0
$100$	21.4798	+	3.34420i	2.14798	+	0.334420i
$101$	8.70650	+	5.02670i	0.866330	+	0.500176i	0.866127	−	0.499824i	$-0.166602\pi$
$101$	8.70650	+	5.02670i	0.866330	+	0.500176i	0.000202762		1.00000i	$0.499935\pi$
$102$		0			0
$103$	8.29973	−	4.79185i	0.817796	−	0.472155i	−0.0318595	−	0.999492i	$-0.510143\pi$
$103$	8.29973	−	4.79185i	0.817796	−	0.472155i	0.849656	+	0.527337i	$0.176810\pi$
$104$	0.686997	−	2.91210i	0.0673656	−	0.285555i
$105$		0			0
$106$	−7.92130	−	16.5513i	−0.769385	−	1.60761i
$107$	2.21486	+	3.83624i	0.214118	+	0.370863i	0.952999	−	0.302972i	$-0.0979789\pi$
$107$	2.21486	+	3.83624i	0.214118	+	0.370863i	−0.738881	+	0.673836i	$0.764646\pi$
$108$		0			0
$109$	3.40807	−	5.90294i	0.326433	−	0.565399i	−0.655368	−	0.755310i	$-0.727486\pi$
$109$	3.40807	−	5.90294i	0.326433	−	0.565399i	0.981801	+	0.189910i	$0.0608198\pi$
$110$	5.96503	−	8.70367i	0.568743	−	0.829862i
$111$		0			0
$112$	7.72896	+	7.22933i	0.730318	+	0.683107i
$113$		−	11.0586i		−	1.04030i	−0.854074	−	0.520151i	$-0.825875\pi$
$113$		−	11.0586i		−	1.04030i	0.854074	−	0.520151i	$-0.174125\pi$
$114$		0			0
$115$	−20.7275	−	11.9670i	−1.93285	−	1.11593i
$116$	−9.50344	+	3.67673i	−0.882372	+	0.341376i
$117$		0			0
$118$	−11.6455	+	5.57342i	−1.07205	+	0.513075i
$119$	−3.01795	+	6.35915i	−0.276655	+	0.582943i
$120$		0			0
$121$	3.74606	+	6.48836i	0.340551	+	0.589851i
$122$	−1.13746	+	14.6999i	−0.102981	+	1.33087i
$123$		0			0
$124$	−1.23652	+	7.94222i	−0.111043	+	0.713232i
$125$			23.3812i			2.09127i
$126$		0			0
$127$		−	14.8137i		−	1.31450i	−0.753670	−	0.657252i	$-0.771719\pi$
$127$		−	14.8137i		−	1.31450i	0.753670	−	0.657252i	$-0.228281\pi$
$128$	5.48971	+	9.89258i	0.485226	+	0.874389i
$129$		0			0
$130$	5.94183	+	0.459772i	0.521133	+	0.0403247i
$131$	1.22561	+	2.12281i	0.107082	+	0.185471i	0.914587	−	0.404390i	$-0.132516\pi$
$131$	1.22561	+	2.12281i	0.107082	+	0.185471i	−0.807505	+	0.589861i	$0.799183\pi$
$132$		0			0
$133$	1.08986	+	1.57916i	0.0945032	+	0.136930i
$134$	−3.52615	−	7.36779i	−0.304613	−	0.636480i
$135$		0			0
$136$	−5.15827	+	5.47880i	−0.442318	+	0.469803i
$137$	−0.536858	−	0.309955i	−0.0458669	−	0.0264812i	0.476891	−	0.878962i	$-0.341764\pi$
$137$	−0.536858	−	0.309955i	−0.0458669	−	0.0264812i	−0.522758	+	0.852481i	$0.675097\pi$
$138$		0			0
$139$			2.00673i			0.170209i	0.996372	+	0.0851044i	$0.0271224\pi$
$139$			2.00673i			0.170209i	−0.996372	+	0.0851044i	$0.972878\pi$
$140$	−11.8598	+	17.4266i	−1.00234	+	1.47281i
$141$		0			0
$142$	−7.28027	−	4.98951i	−0.610947	−	0.418710i
$143$	0.990638	−	1.71583i	0.0828413	−	0.143485i
$144$		0			0
$145$	−10.1482	−	17.5772i	−0.842760	−	1.45970i
$146$	18.8043	−	8.99958i	1.55626	−	0.744810i
$147$		0			0
$148$	−11.2440	+	13.9601i	−0.924255	+	1.14752i
$149$	6.01927	−	3.47523i	0.493118	−	0.284702i	−0.232749	−	0.972537i	$-0.574772\pi$
$149$	6.01927	−	3.47523i	0.493118	−	0.284702i	0.725867	+	0.687835i	$0.241439\pi$
$150$		0			0
$151$	−12.9420	−	7.47207i	−1.05320	−	0.608068i	−0.129660	−	0.991559i	$-0.541389\pi$
$151$	−12.9420	−	7.47207i	−1.05320	−	0.608068i	−0.923545	+	0.383490i	$0.874722\pi$
$152$	0.590328	+	1.96443i	0.0478820	+	0.159336i
$153$		0			0
$154$	3.52374	+	6.05753i	0.283951	+	0.488130i
$155$	−16.0100			−1.28596
$156$		0			0
$157$	−7.82313	+	13.5501i	−0.624354	+	1.08141i	0.364312	+	0.931277i	$0.381304\pi$
$157$	−7.82313	+	13.5501i	−0.624354	+	1.08141i	−0.988665	+	0.150135i	$0.952029\pi$
$158$	−8.01744	−	0.620381i	−0.637833	−	0.0493549i
$159$		0			0
$160$	−17.7875	+	13.8356i	−1.40623	+	1.09380i
$161$	13.0827	−	9.02908i	1.03106	−	0.711591i
$162$		0			0
$163$	6.27734	−	3.62422i	0.491679	−	0.283871i	−0.233592	−	0.972335i	$-0.575048\pi$
$163$	6.27734	−	3.62422i	0.491679	−	0.283871i	0.725271	+	0.688464i	$0.241715\pi$
$164$	11.5502	−	4.46860i	0.901921	−	0.348939i
$165$		0			0
$166$	−3.81803	−	2.61668i	−0.296337	−	0.203094i
$167$	18.1132			1.40164			0.700822	−	0.713337i	$-0.252817\pi$
$167$	18.1132			1.40164			0.700822	+	0.713337i	$0.252817\pi$
$168$		0			0
$169$	−11.8810			−0.913920
$170$	−12.3634	−	8.47323i	−0.948231	−	0.649867i
$171$		0			0
$172$	−22.9560	+	8.88133i	−1.75038	+	0.677195i
$173$	−9.26339	+	5.34822i	−0.704283	+	0.406618i	−0.808941	−	0.587890i	$-0.799959\pi$
$173$	−9.26339	+	5.34822i	−0.704283	+	0.406618i	0.104658	+	0.994508i	$0.466625\pi$
$174$		0			0
$175$	−25.9802	−	12.3298i	−1.96392	−	0.932043i
$176$	1.59614	+	7.31973i	0.120313	+	0.551746i
$177$		0			0
$178$	14.3364	+	1.10934i	1.07456	+	0.0831482i
$179$	−11.6609	+	20.1973i	−0.871578	+	1.50962i	−0.0112146	+	0.999937i	$0.503570\pi$
$179$	−11.6609	+	20.1973i	−0.871578	+	1.50962i	−0.860364	+	0.509681i	$0.829764\pi$
$180$		0			0
$181$	−2.90143			−0.215662			−0.107831	−	0.994169i	$-0.534391\pi$
$181$	−2.90143			−0.215662			−0.107831	+	0.994169i	$0.534391\pi$
$182$	−1.96784	+	3.43425i	−0.145866	+	0.254564i
$183$		0			0
$184$	16.2745	−	4.89063i	1.19977	−	0.360542i
$185$	−30.9204	−	17.8519i	−2.27331	−	1.31250i
$186$		0			0
$187$	−4.31531	+	2.49145i	−0.315567	+	0.182193i
$188$	−5.11029	+	6.34472i	−0.372706	+	0.462736i
$189$		0			0
$190$	−3.68532	+	1.76376i	−0.267361	+	0.127956i
$191$	4.64881	+	8.05197i	0.336376	+	0.582620i	0.983748	−	0.179554i	$-0.0574654\pi$
$191$	4.64881	+	8.05197i	0.336376	+	0.582620i	−0.647372	+	0.762174i	$0.724132\pi$
$192$		0			0
$193$	3.54336	−	6.13728i	0.255056	−	0.441771i	−0.709854	−	0.704348i	$-0.751239\pi$
$193$	3.54336	−	6.13728i	0.255056	−	0.441771i	0.964911	+	0.262578i	$0.0845726\pi$
$194$	2.37709	+	1.62913i	0.170665	+	0.116965i
$195$		0			0
$196$	−7.07903	−	12.0784i	−0.505645	−	0.862742i
$197$		−	4.03120i		−	0.287211i	−0.989635	−	0.143606i	$-0.954130\pi$
$197$		−	4.03120i		−	0.287211i	0.989635	−	0.143606i	$-0.0458697\pi$
$198$		0			0
$199$	19.5689	+	11.2981i	1.38720	+	0.800900i	0.992999	−	0.118124i	$-0.0376880\pi$
$199$	19.5689	+	11.2981i	1.38720	+	0.800900i	0.394201	+	0.919024i	$0.371021\pi$
$200$	−22.3835	−	21.0740i	−1.58275	−	1.49016i
$201$		0			0
$202$	−6.13773	−	12.8246i	−0.431849	−	0.902335i
$203$	13.4363	−	1.08383i	0.943043	−	0.0760701i
$204$		0			0
$205$	12.3338	+	21.3628i	0.861431	+	1.49204i
$206$	−13.5130	−	1.04562i	−0.941496	−	0.0728519i
$207$		0			0
$208$	−3.12960	+	2.84785i	−0.216998	+	0.197463i
$209$			1.35828i			0.0939539i
$210$		0			0
$211$		−	3.52953i		−	0.242983i	−0.992592	−	0.121491i	$-0.961232\pi$
$211$		−	3.52953i		−	0.242983i	0.992592	−	0.121491i	$-0.0387676\pi$
$212$	−3.99202	+	25.6408i	−0.274173	+	1.76102i
$213$		0			0
$214$	0.483300	−	6.24589i	0.0330377	−	0.426960i
$215$	−24.5134	−	42.4585i	−1.67180	−	2.89565i
$216$		0			0
$217$	4.55896	−	9.60623i	0.309482	−	0.652113i
$218$	−8.69497	+	4.16133i	−0.588898	+	0.281841i
$219$		0			0
$220$	−13.9169	+	5.38424i	−0.938279	+	0.363005i
$221$	−2.43732	−	1.40719i	−0.163952	−	0.0946575i
$222$		0			0
$223$			5.17037i			0.346234i	0.984901	+	0.173117i	$0.0553839\pi$
$223$			5.17037i			0.346234i	−0.984901	+	0.173117i	$0.944616\pi$
$224$	−3.23641	−	14.6125i	−0.216242	−	0.976340i
$225$		0			0
$226$	−8.84118	+	12.9003i	−0.588106	+	0.858115i
$227$	10.2679	−	17.7846i	0.681507	−	1.18040i	−0.293014	−	0.956108i	$-0.594658\pi$
$227$	10.2679	−	17.7846i	0.681507	−	1.18040i	0.974521	−	0.224296i	$-0.0720084\pi$
$228$		0			0
$229$	5.10463	+	8.84148i	0.337323	+	0.584261i	0.983928	−	0.178564i	$-0.0571451\pi$
$229$	5.10463	+	8.84148i	0.337323	+	0.584261i	−0.646605	+	0.762825i	$0.723812\pi$
$230$	14.6120	+	30.5313i	0.963487	+	2.01318i
$231$		0			0
$232$	14.0257	+	3.30881i	0.920829	+	0.217234i
$233$	−5.42215	+	3.13048i	−0.355217	+	0.205085i	−0.666981	−	0.745075i	$-0.732414\pi$
$233$	−5.42215	+	3.13048i	−0.355217	+	0.205085i	0.311764	+	0.950160i	$0.399080\pi$
$234$		0			0
$235$	−14.0529	−	8.11347i	−0.916713	−	0.529265i
$236$	18.0408	+	2.80878i	1.17436	+	0.182836i
$237$		0			0
$238$	8.60462	−	5.00541i	0.557755	−	0.324453i
$239$	−4.99283			−0.322959			−0.161480	−	0.986876i	$-0.551627\pi$
$239$	−4.99283			−0.322959			−0.161480	+	0.986876i	$0.551627\pi$
$240$		0			0
$241$	3.48576	−	6.03752i	0.224538	−	0.388911i	−0.731643	−	0.681688i	$-0.761246\pi$
$241$	3.48576	−	6.03752i	0.224538	−	0.388911i	0.956181	+	0.292777i	$0.0945795\pi$
$242$	0.817421	−	10.5639i	0.0525458	−	0.679072i
$243$		0			0
$244$	13.0793	−	16.2387i	0.837315	−	1.03958i
$245$	21.6024	−	17.6333i	1.38013	−	1.12655i
$246$		0			0
$247$	−0.664383	+	0.383582i	−0.0422737	+	0.0244067i
$248$	7.79215	−	8.27635i	0.494802	−	0.525549i
$249$		0			0
$250$	18.6929	−	27.2751i	1.18224	−	1.72503i
$251$	−18.9350			−1.19516			−0.597582	−	0.801808i	$-0.703872\pi$
$251$	−18.9350			−1.19516			−0.597582	+	0.801808i	$0.703872\pi$
$252$		0			0
$253$	11.2528			0.707455
$254$	−11.8434	+	17.2808i	−0.743119	+	1.08430i
$255$		0			0
$256$	1.50500	−	15.9291i	0.0940624	−	0.995566i
$257$	0.662857	−	0.382701i	0.0413479	−	0.0238722i	−0.479184	−	0.877715i	$-0.659067\pi$
$257$	0.662857	−	0.382701i	0.0413479	−	0.0238722i	0.520531	+	0.853842i	$0.325734\pi$
$258$		0			0
$259$	19.5161	−	13.4692i	1.21267	−	0.836935i
$260$	−6.56381	−	5.28675i	−0.407070	−	0.327871i
$261$		0			0
$262$	0.267438	−	3.45621i	0.0165224	−	0.213525i
$263$	−7.12695	+	12.3442i	−0.439466	+	0.761178i	−0.997648	−	0.0685403i	$-0.978166\pi$
$263$	−7.12695	+	12.3442i	−0.439466	+	0.761178i	0.558182	+	0.829719i	$0.311499\pi$
$264$		0			0
$265$	−51.6870			−3.17511
$266$	−0.00886000	−	2.71348i	−0.000543241	−	0.166374i
$267$		0			0
$268$	−1.77704	+	11.4139i	−0.108550	+	0.697218i
$269$	−8.25667	−	4.76699i	−0.503418	−	0.290649i	0.226706	−	0.973963i	$-0.427204\pi$
$269$	−8.25667	−	4.76699i	−0.503418	−	0.290649i	−0.730124	+	0.683315i	$0.760538\pi$
$270$		0			0
$271$	−2.98753	+	1.72485i	−0.181479	+	0.104777i	−0.587988	−	0.808870i	$-0.700080\pi$
$271$	−2.98753	+	1.72485i	−0.181479	+	0.104777i	0.406508	+	0.913647i	$0.366746\pi$
$272$	10.3976	−	2.26729i	0.630445	−	0.137474i
$273$		0			0
$274$	0.378463	+	0.790786i	0.0228638	+	0.0477731i
$275$	−10.1788	−	17.6301i	−0.613802	−	1.06314i
$276$		0			0
$277$	−7.78023	+	13.4757i	−0.467469	+	0.809679i	−0.999309	−	0.0371652i	$-0.988167\pi$
$277$	−7.78023	+	13.4757i	−0.467469	+	0.809679i	0.531841	+	0.846844i	$0.321501\pi$
$278$	1.60435	−	2.34094i	0.0962228	−	0.140400i
$279$		0			0
$280$	27.7673	−	10.8471i	1.65941	−	0.648237i
$281$		−	7.65968i		−	0.456938i	−0.973551	−	0.228469i	$-0.926628\pi$
$281$		−	7.65968i		−	0.456938i	0.973551	−	0.228469i	$-0.0733720\pi$
$282$		0			0
$283$	27.5108	+	15.8834i	1.63535	+	0.944167i	0.982406	+	0.186758i	$0.0597979\pi$
$283$	27.5108	+	15.8834i	1.63535	+	0.944167i	0.652940	+	0.757410i	$0.273535\pi$
$284$	4.50370	+	11.6410i	0.267245	+	0.690764i
$285$		0			0
$286$	−2.52741	+	1.20959i	−0.149449	+	0.0715247i
$287$	−16.3301	+	1.31726i	−0.963936	+	0.0777554i
$288$		0			0
$289$	−4.96094	−	8.59260i	−0.291820	−	0.505447i
$290$	−2.21442	+	28.6178i	−0.130035	+	1.68050i
$291$		0			0
$292$	−29.1311	−	4.53542i	−1.70477	−	0.265416i
$293$			8.77681i			0.512747i	0.966578	+	0.256373i	$0.0825277\pi$
$293$			8.77681i			0.512747i	−0.966578	+	0.256373i	$0.917472\pi$
$294$		0			0
$295$			36.3669i			2.11736i
$296$	24.2776	−	7.29563i	1.41111	−	0.424050i
$297$		0			0
$298$	−9.80013	−	0.758323i	−0.567706	−	0.0439285i
$299$	3.17782	+	5.50414i	0.183778	+	0.318313i
$300$		0			0
$301$	32.4561	−	2.61805i	1.87074	−	0.150902i
$302$	9.12358	+	19.0634i	0.525003	+	1.09698i
$303$		0			0
$304$	0.881891	−	2.76355i	0.0505799	−	0.158500i
$305$	35.9671	+	20.7656i	2.05947	+	1.18904i
$306$		0			0
$307$			15.7116i			0.896709i	0.893856	+	0.448355i	$0.147990\pi$
$307$			15.7116i			0.896709i	−0.893856	+	0.448355i	$0.852010\pi$
$308$	0.732322	−	9.88354i	0.0417279	−	0.563167i
$309$		0			0
$310$	18.6764	+	12.7998i	1.06075	+	0.726979i
$311$	−6.73255	+	11.6611i	−0.381768	+	0.661241i	−0.991315	−	0.131508i	$-0.958018\pi$
$311$	−6.73255	+	11.6611i	−0.381768	+	0.661241i	0.609547	+	0.792750i	$0.291351\pi$
$312$		0			0
$313$	−6.18899	−	10.7196i	−0.349822	−	0.605910i	0.636395	−	0.771363i	$-0.280425\pi$
$313$	−6.18899	−	10.7196i	−0.349822	−	0.605910i	−0.986218	+	0.165453i	$0.947091\pi$
$314$	19.9591	−	9.55224i	1.12636	−	0.539064i
$315$		0			0
$316$	8.85670	+	7.13354i	0.498228	+	0.401293i
$317$	−15.9748	+	9.22303i	−0.897232	+	0.518017i	−0.876301	−	0.481764i	$-0.839996\pi$
$317$	−15.9748	+	9.22303i	−0.897232	+	0.518017i	−0.0209310	+	0.999781i	$0.506663\pi$
$318$		0			0
$319$	8.26404	+	4.77124i	0.462697	+	0.267138i
$320$	31.8112	−	1.91890i	1.77830	−	0.107270i
$321$		0			0
$322$	−22.4801	+	0.0734014i	−1.25277	+	0.00409050i
$323$	1.92941			0.107355
$324$		0			0
$325$	5.74903	−	9.95760i	0.318899	−	0.552348i
$326$	−10.2203	−	0.790836i	−0.566050	−	0.0438003i
$327$		0			0
$328$	−17.0464	−	4.02144i	−0.941230	−	0.222047i
$329$	8.86987	−	6.12160i	0.489012	−	0.337495i
$330$		0			0
$331$	22.2310	−	12.8351i	1.22193	−	0.705480i	0.256599	−	0.966518i	$-0.417398\pi$
$331$	22.2310	−	12.8351i	1.22193	−	0.705480i	0.965329	+	0.261037i	$0.0840646\pi$
$332$	2.36190	+	6.10493i	0.129626	+	0.335052i
$333$		0			0
$334$	−21.1298	−	14.4813i	−1.15617	−	0.792380i
$335$	−23.0084			−1.25708
$336$		0			0
$337$	1.12521			0.0612942			0.0306471	−	0.999530i	$-0.490243\pi$
$337$	1.12521			0.0612942			0.0306471	+	0.999530i	$0.490243\pi$
$338$	13.8596	+	9.49867i	0.753866	+	0.516659i
$339$		0			0
$340$	7.64822	+	19.7688i	0.414783	+	1.07211i
$341$	6.51877	−	3.76362i	0.353011	−	0.203811i
$342$		0			0
$343$	4.42877	+	17.9829i	0.239131	+	0.970987i
$344$	33.8797	+	7.99259i	1.82667	+	0.430932i
$345$		0			0
$346$	15.0820	+	1.16703i	0.810812	+	0.0627398i
$347$	1.10428	−	1.91268i	0.0592811	−	0.102678i	−0.834862	−	0.550460i	$-0.814453\pi$
$347$	1.10428	−	1.91268i	0.0592811	−	0.102678i	0.894143	+	0.447782i	$0.147786\pi$
$348$		0			0
$349$	15.3373			0.820986			0.410493	−	0.911864i	$-0.365357\pi$
$349$	15.3373			0.820986			0.410493	+	0.911864i	$0.365357\pi$
$350$	20.4495	+	35.1540i	1.09307	+	1.87906i
$351$		0			0
$352$	3.99007	−	9.81487i	0.212671	−	0.523134i
$353$	29.3810	+	16.9631i	1.56379	+	0.902855i	0.996868	+	0.0790836i	$0.0251994\pi$
$353$	29.3810	+	16.9631i	1.56379	+	0.902855i	0.566922	+	0.823771i	$0.308134\pi$
$354$		0			0
$355$	−21.5306	+	12.4307i	−1.14273	+	0.659754i
$356$	−15.8371	−	12.7558i	−0.839366	−	0.676059i
$357$		0			0
$358$	29.7504	−	14.2383i	1.57236	−	0.752516i
$359$	−3.48440	−	6.03516i	−0.183900	−	0.318523i	0.759306	−	0.650734i	$-0.225539\pi$
$359$	−3.48440	−	6.03516i	−0.183900	−	0.318523i	−0.943205	+	0.332211i	$0.892205\pi$
$360$		0			0
$361$	−9.23703	+	15.9990i	−0.486160	+	0.842053i
$362$	3.38465	+	2.31966i	0.177893	+	0.121918i
$363$		0			0
$364$	5.04121	−	2.43294i	0.264231	−	0.127521i
$365$		−	58.7228i		−	3.07369i
$366$		0			0
$367$	−1.65689	−	0.956605i	−0.0864889	−	0.0499344i	0.456132	−	0.889912i	$-0.349235\pi$
$367$	−1.65689	−	0.956605i	−0.0864889	−	0.0499344i	−0.542621	+	0.839978i	$0.682568\pi$
$368$	−22.8949	−	7.30610i	−1.19348	−	0.380857i
$369$		0			0
$370$	21.7976	+	45.5454i	1.13320	+	2.36779i
$371$	14.7182	−	31.0129i	0.764132	−	1.61011i
$372$		0			0
$373$	−4.08938	−	7.08301i	−0.211740	−	0.366745i	0.740519	−	0.672035i	$-0.234580\pi$
$373$	−4.08938	−	7.08301i	−0.211740	−	0.366745i	−0.952259	+	0.305291i	$0.901246\pi$
$374$	7.02587	+	0.543655i	0.363299	+	0.0281117i
$375$		0			0
$376$	11.0339	−	3.31578i	0.569029	−	0.170998i
$377$			5.38966i			0.277582i
$378$		0			0
$379$		−	17.1764i		−	0.882295i	−0.897435	−	0.441147i	$-0.854572\pi$
$379$		−	17.1764i		−	0.882295i	0.897435	−	0.441147i	$-0.145428\pi$
$380$	5.70918	+	0.888863i	0.292875	+	0.0455977i
$381$		0			0
$382$	1.01441	−	13.1096i	0.0519017	−	0.670747i
$383$	−11.5136	−	19.9422i	−0.588320	−	1.01900i	−0.994453	−	0.105186i	$-0.966456\pi$
$383$	−11.5136	−	19.9422i	−0.588320	−	1.01900i	0.406133	−	0.913814i	$-0.366877\pi$
$384$		0			0
$385$	19.6762	−	1.58717i	1.00279	−	0.0808899i
$386$	−9.04015	+	4.32653i	−0.460131	+	0.220214i
$387$		0			0
$388$	−1.47051	−	3.80091i	−0.0746538	−	0.192962i
$389$	16.4368	+	9.48980i	0.833380	+	0.481152i	0.855009	−	0.518614i	$-0.173552\pi$
$389$	16.4368	+	9.48980i	0.833380	+	0.481152i	−0.0216286	+	0.999766i	$0.506885\pi$
$390$		0			0
$391$		−	15.9844i		−	0.808364i
$392$	−1.39852	+	19.7495i	−0.0706359	+	0.997502i
$393$		0			0
$394$	−3.22289	+	4.70257i	−0.162367	+	0.236912i
$395$	−11.3257	+	19.6167i	−0.569859	+	0.987025i
$396$		0			0
$397$	17.0876	+	29.5966i	0.857603	+	1.48541i	0.874209	+	0.485550i	$0.161381\pi$
$397$	17.0876	+	29.5966i	0.857603	+	1.48541i	−0.0166054	+	0.999862i	$0.505286\pi$
$398$	−13.7952	−	28.8247i	−0.691493	−	1.44485i
$399$		0			0
$400$	9.26295	+	42.4790i	0.463148	+	2.12395i
$401$	11.4019	−	6.58287i	0.569382	−	0.328733i	−0.187521	−	0.982261i	$-0.560045\pi$
$401$	11.4019	−	6.58287i	0.569382	−	0.328733i	0.756902	+	0.653528i	$0.226712\pi$
$402$		0			0
$403$	3.68184	+	2.12571i	0.183406	+	0.105889i
$404$	−3.09317	+	19.8675i	−0.153891	+	0.988443i
$405$		0			0
$406$	−16.5405	−	9.47780i	−0.820892	−	0.470375i
$407$	16.7864			0.832071
$408$		0			0
$409$	13.9583	−	24.1765i	0.690193	−	1.19545i	−0.281582	−	0.959537i	$-0.590859\pi$
$409$	13.9583	−	24.1765i	0.690193	−	1.19545i	0.971774	−	0.235912i	$-0.0758076\pi$
$410$	2.69134	−	34.7813i	0.132916	−	1.71773i
$411$		0			0
$412$	14.9275	+	12.0232i	0.735427	+	0.592342i
$413$	−21.8206	−	10.3557i	−1.07372	−	0.509572i
$414$		0			0
$415$	−11.2914	+	6.51911i	−0.554274	+	0.320010i
$416$	5.92762	−	0.820063i	0.290626	−	0.0402069i
$417$		0			0
$418$	1.08592	−	1.58449i	0.0531142	−	0.0774998i
$419$	−32.2539			−1.57571			−0.787854	−	0.615863i	$-0.788808\pi$
$419$	−32.2539			−1.57571			−0.787854	+	0.615863i	$0.788808\pi$
$420$		0			0
$421$	−20.3473			−0.991667			−0.495833	−	0.868418i	$-0.665137\pi$
$421$	−20.3473			−0.991667			−0.495833	+	0.868418i	$0.665137\pi$
$422$	−2.82181	+	4.11734i	−0.137363	+	0.200429i
$423$		0			0
$424$	25.1563	−	26.7195i	1.22170	−	1.29761i
$425$	−25.0433	+	14.4588i	−1.21478	+	0.701353i
$426$		0			0
$427$	−22.7015	+	15.6676i	−1.09860	+	0.758209i
$428$	−5.55729	+	6.89970i	−0.268622	+	0.333510i
$429$		0			0
$430$	−5.34904	+	69.1278i	−0.257954	+	3.33364i
$431$	11.8556	−	20.5344i	0.571062	−	0.989108i	−0.425395	−	0.905008i	$-0.639865\pi$
$431$	11.8556	−	20.5344i	0.571062	−	0.989108i	0.996457	−	0.0841006i	$-0.0268017\pi$
$432$		0			0
$433$	12.4523			0.598417			0.299209	−	0.954188i	$-0.403277\pi$
$433$	12.4523			0.598417			0.299209	+	0.954188i	$0.403277\pi$
$434$	−12.9983	+	7.56125i	−0.623937	+	0.362952i
$435$		0			0
$436$	13.4700	+	2.09714i	0.645095	+	0.100435i
$437$	−3.77340	−	2.17857i	−0.180506	−	0.104215i
$438$		0			0
$439$	−1.32885	+	0.767212i	−0.0634225	+	0.0366170i	−0.531376	−	0.847136i	$-0.678325\pi$
$439$	−1.32885	+	0.767212i	−0.0634225	+	0.0366170i	0.467953	+	0.883753i	$0.344992\pi$
$440$	20.5393	+	4.84545i	0.979173	+	0.230998i
$441$		0			0
$442$	1.71821	+	3.59014i	0.0817268	+	0.170766i
$443$	−14.6601	−	25.3921i	−0.696523	−	1.20641i	−0.969664	−	0.244440i	$-0.921396\pi$
$443$	−14.6601	−	25.3921i	−0.696523	−	1.20641i	0.273141	−	0.961974i	$-0.411937\pi$
$444$		0			0
$445$	20.2521	−	35.0777i	0.960043	−	1.66284i
$446$	4.13364	−	6.03146i	0.195734	−	0.285598i
$447$		0			0
$448$	−7.90709	+	19.6336i	−0.373575	+	0.927600i
$449$			4.29939i			0.202901i	0.994841	+	0.101450i	$0.0323483\pi$
$449$			4.29939i			0.202901i	−0.994841	+	0.101450i	$0.967652\pi$
$450$		0			0
$451$	−10.0439	−	5.79884i	−0.472948	−	0.273057i
$452$	20.6272	−	7.98034i	0.970223	−	0.375364i
$453$		0			0
$454$	−26.1965	+	12.5374i	−1.22946	+	0.588409i
$455$	6.33298	+	9.17615i	0.296895	+	0.430185i
$456$		0			0
$457$	−2.32454	−	4.02622i	−0.108737	−	0.188339i	0.806522	−	0.591205i	$-0.201347\pi$
$457$	−2.32454	−	4.02622i	−0.108737	−	0.188339i	−0.915259	+	0.402866i	$0.868014\pi$
$458$	1.11387	−	14.3950i	0.0520479	−	0.672636i
$459$		0			0
$460$	7.36386	−	47.2982i	0.343342	−	2.20529i
$461$		−	24.2351i		−	1.12874i	−0.825521	−	0.564371i	$-0.809119\pi$
$461$		−	24.2351i		−	1.12874i	0.825521	−	0.564371i	$-0.190881\pi$
$462$		0			0
$463$		−	18.7274i		−	0.870335i	−0.900349	−	0.435168i	$-0.856689\pi$
$463$		−	18.7274i		−	0.870335i	0.900349	−	0.435168i	$-0.143311\pi$
$464$	−13.7162	−	15.0732i	−0.636758	−	0.699755i
$465$		0			0
$466$	8.82795	+	0.683097i	0.408947	+	0.0316439i
$467$	9.28665	+	16.0849i	0.429735	+	0.744323i	0.996850	−	0.0793162i	$-0.0252737\pi$
$467$	9.28665	+	16.0849i	0.429735	+	0.744323i	−0.567115	+	0.823639i	$0.691940\pi$
$468$		0			0
$469$	6.55179	−	13.8053i	0.302533	−	0.637471i
$470$	9.90675	+	20.6999i	0.456964	+	0.954813i
$471$		0			0
$472$	−18.7998	−	17.7000i	−0.865332	−	0.814707i
$473$	19.9622	+	11.5252i	0.917863	+	0.529929i
$474$		0			0
$475$			7.88256i			0.361677i
$476$	−14.0394	−	1.04025i	−0.643496	−	0.0476798i
$477$		0			0
$478$	5.82435	+	3.99170i	0.266400	+	0.182576i
$479$	−5.24836	+	9.09043i	−0.239804	+	0.415352i	−0.960658	−	0.277734i	$-0.910416\pi$
$479$	−5.24836	+	9.09043i	−0.239804	+	0.415352i	0.720854	+	0.693087i	$0.243750\pi$
$480$		0			0
$481$	4.74053	+	8.21084i	0.216150	+	0.374382i
$482$	−8.89321	+	4.25620i	−0.405074	+	0.193865i
$483$		0			0
$484$	−9.39923	+	11.6697i	−0.427238	+	0.530441i
$485$	7.03000	−	4.05877i	0.319216	−	0.184299i
$486$		0			0
$487$	−23.4523	−	13.5402i	−1.06273	−	0.613565i	−0.136540	−	0.990635i	$-0.543598\pi$
$487$	−23.4523	−	13.5402i	−1.06273	−	0.613565i	−0.926185	+	0.377070i	$0.876932\pi$
$488$	−28.2401	+	8.48642i	−1.27837	+	0.384162i
$489$		0			0
$490$	−39.2977	+	3.29911i	−1.77529	+	0.149039i
$491$	8.39226			0.378737			0.189369	−	0.981906i	$-0.439356\pi$
$491$	8.39226			0.378737			0.189369	+	0.981906i	$0.439356\pi$
$492$		0			0
$493$	6.77748	−	11.7389i	0.305242	−	0.528695i
$494$	1.08170	+	0.0837007i	0.0486679	+	0.00376587i
$495$		0			0
$496$	−15.7067	+	3.42500i	−0.705252	+	0.153787i
$497$	−1.32761	−	16.4584i	−0.0595514	−	0.738260i
$498$		0			0
$499$	15.4658	−	8.92917i	0.692343	−	0.399724i	−0.112146	−	0.993692i	$-0.535772\pi$
$499$	15.4658	−	8.92917i	0.692343	−	0.399724i	0.804489	+	0.593967i	$0.202439\pi$
$500$	−43.6122	+	16.8729i	−1.95040	+	0.754577i
$501$		0			0
$502$	22.0884	+	15.1382i	0.985855	+	0.675653i
$503$	15.3493			0.684392			0.342196	−	0.939629i	$-0.388829\pi$
$503$	15.3493			0.684392			0.342196	+	0.939629i	$0.388829\pi$
$504$		0			0
$505$	−40.0490			−1.78216
$506$	−13.1268	−	8.99643i	−0.583558	−	0.399940i
$507$		0			0
$508$	27.6316	−	10.6902i	1.22595	−	0.474302i
$509$	−25.2937	+	14.6033i	−1.12112	+	0.647281i	−0.941687	−	0.336489i	$-0.890760\pi$
$509$	−25.2937	+	14.6033i	−1.12112	+	0.647281i	−0.179436	+	0.983770i	$0.557427\pi$
$510$		0			0
$511$	35.2345	+	16.7217i	1.55868	+	0.739725i
$512$	−14.4907	+	17.3787i	−0.640405	+	0.768037i
$513$		0			0
$514$	−1.07921	−	0.0835085i	−0.0476021	−	0.00368340i
$515$	−19.0890	+	33.0630i	−0.841160	+	1.45693i
$516$		0			0
$517$	7.62922			0.335533
$518$	−33.5349	+	0.109497i	−1.47344	+	0.00481103i
$519$		0			0
$520$	3.43028	+	11.4149i	0.150428	+	0.500577i
$521$	−12.9936	−	7.50183i	−0.569258	−	0.328661i	0.187595	−	0.982246i	$-0.439931\pi$
$521$	−12.9936	−	7.50183i	−0.569258	−	0.328661i	−0.756853	+	0.653585i	$0.773264\pi$
$522$		0			0
$523$	10.6638	−	6.15676i	0.466296	−	0.269216i	−0.248392	−	0.968660i	$-0.579902\pi$
$523$	10.6638	−	6.15676i	0.466296	−	0.269216i	0.714688	+	0.699443i	$0.246569\pi$
$524$	−3.07517	+	3.81800i	−0.134339	+	0.166790i
$525$		0			0
$526$	18.1829	−	8.70218i	0.792814	−	0.379433i
$527$	−5.34616	−	9.25981i	−0.232882	−	0.403364i
$528$		0			0
$529$	−6.54857	+	11.3425i	−0.284720	+	0.493150i
$530$	60.2951	+	41.3230i	2.61905	+	1.79496i
$531$		0			0
$532$	−2.15906	+	3.17248i	−0.0936070	+	0.137544i
$533$		−	6.55045i		−	0.283731i
$534$		0			0
$535$	−15.2822	−	8.82316i	−0.660706	−	0.381459i
$536$	11.1983	−	11.8941i	0.483692	−	0.513749i
$537$		0			0
$538$	5.82061	+	12.1620i	0.250944	+	0.524341i
$539$	−4.65062	+	12.2580i	−0.200316	+	0.527989i
$540$		0			0
$541$	12.1895	+	21.1128i	0.524066	+	0.907708i	0.999608	+	0.0280151i	$0.00891864\pi$
$541$	12.1895	+	21.1128i	0.524066	+	0.907708i	−0.475542	+	0.879693i	$0.657748\pi$
$542$	4.86408	+	0.376377i	0.208930	+	0.0161668i
$543$		0			0
$544$	−13.9419	−	5.66782i	−0.597753	−	0.243006i
$545$			27.1529i			1.16310i
$546$		0			0
$547$		−	26.9284i		−	1.15138i	−0.817669	−	0.575688i	$-0.804734\pi$
$547$		−	26.9284i		−	1.15138i	0.817669	−	0.575688i	$-0.195266\pi$
$548$	0.190730	−	1.22506i	0.00814758	−	0.0523320i
$549$		0			0
$550$	−2.22109	+	28.7041i	−0.0947076	+	1.22395i
$551$	−1.84746	−	3.19989i	−0.0787043	−	0.136320i
$552$		0			0
$553$	−8.54523	−	12.3816i	−0.363380	−	0.526519i
$554$	19.8496	−	9.49985i	0.843331	−	0.403610i
$555$		0			0
$556$	−3.74309	+	1.44814i	−0.158743	+	0.0614150i
$557$	3.35873	+	1.93917i	0.142314	+	0.0821651i	0.569466	−	0.822015i	$-0.307150\pi$
$557$	3.35873	+	1.93917i	0.142314	+	0.0821651i	−0.427152	+	0.904180i	$0.640483\pi$
$558$		0			0
$559$			13.0190i			0.550645i
$560$	−41.0638	−	9.54597i	−1.73526	−	0.403391i
$561$		0			0
$562$	−6.12381	+	8.93535i	−0.258317	+	0.376915i
$563$	20.6486	−	35.7644i	0.870234	−	1.50729i	0.00847940	−	0.999964i	$-0.497301\pi$
$563$	20.6486	−	35.7644i	0.870234	−	1.50729i	0.861755	−	0.507325i	$-0.169366\pi$
$564$		0			0
$565$	22.0266	+	38.1512i	0.926667	+	1.60503i
$566$	−19.3940	−	40.5231i	−0.815189	−	1.70331i
$567$		0			0
$568$	4.05303	−	17.1803i	0.170061	−	0.720870i
$569$	−8.24961	+	4.76292i	−0.345842	+	0.199672i	−0.662852	−	0.748750i	$-0.730654\pi$
$569$	−8.24961	+	4.76292i	−0.345842	+	0.199672i	0.317011	+	0.948422i	$0.397321\pi$
$570$		0			0
$571$	22.0822	+	12.7492i	0.924111	+	0.533536i	0.884944	−	0.465697i	$-0.154196\pi$
$571$	22.0822	+	12.7492i	0.924111	+	0.533536i	0.0391670	+	0.999233i	$0.487530\pi$
$572$	3.91538	+	0.609586i	0.163710	+	0.0254881i
$573$		0			0
$574$	20.1029	+	11.5191i	0.839079	+	0.480796i
$575$	65.3038			2.72336
$576$		0			0
$577$	−2.94249	+	5.09654i	−0.122498	+	0.212172i	−0.920752	−	0.390148i	$-0.872424\pi$
$577$	−2.94249	+	5.09654i	−0.122498	+	0.212172i	0.798254	+	0.602320i	$0.205757\pi$
$578$	−1.08252	+	13.9898i	−0.0450268	+	0.581900i
$579$		0			0
$580$	25.4628	−	31.6135i	1.05728	−	1.31268i
$581$	−0.696245	−	8.63137i	−0.0288851	−	0.358090i
$582$		0			0
$583$	21.0453	−	12.1505i	0.871608	−	0.503223i
$584$	30.3567	+	28.5807i	1.25617	+	1.18268i
$585$		0			0
$586$	7.01694	−	10.2385i	0.289867	−	0.422950i
$587$	−16.1329			−0.665878			−0.332939	−	0.942948i	$-0.608040\pi$
$587$	−16.1329			−0.665878			−0.332939	+	0.942948i	$0.608040\pi$
$588$		0			0
$589$	−2.91459			−0.120094
$590$	29.0748	−	42.4235i	1.19699	−	1.74655i
$591$		0			0
$592$	−34.1536	−	10.8989i	−1.40370	−	0.447944i
$593$	−7.56550	+	4.36794i	−0.310678	+	0.179370i	−0.647230	−	0.762295i	$-0.724073\pi$
$593$	−7.56550	+	4.36794i	−0.310678	+	0.179370i	0.336552	+	0.941665i	$0.390739\pi$
$594$		0			0
$595$	−2.25456	−	27.9498i	−0.0924278	−	1.14583i
$596$	10.8260	+	8.71968i	0.443450	+	0.357172i
$597$		0			0
$598$	0.693426	−	8.96143i	0.0283563	−	0.366460i
$599$	−17.0745	+	29.5738i	−0.697644	+	1.20835i	0.271638	+	0.962400i	$0.412435\pi$
$599$	−17.0745	+	29.5738i	−0.697644	+	1.20835i	−0.969281	+	0.245955i	$0.920899\pi$
$600$		0			0
$601$	−13.8371			−0.564426			−0.282213	−	0.959352i	$-0.591068\pi$
$601$	−13.8371			−0.564426			−0.282213	+	0.959352i	$0.591068\pi$
$602$	−39.9545	−	22.8941i	−1.62842	−	0.933095i
$603$		0			0
$604$	4.59791	−	29.5325i	0.187086	−	1.20166i
$605$	−25.8472	−	14.9229i	−1.05084	−	0.606703i
$606$		0			0
$607$	−24.7444	+	14.2862i	−1.00434	+	0.579858i	−0.909530	−	0.415638i	$-0.863558\pi$
$607$	−24.7444	+	14.2862i	−1.00434	+	0.579858i	−0.0948125	+	0.995495i	$0.530225\pi$
$608$	−3.23818	+	2.51874i	−0.131326	+	0.102148i
$609$		0			0
$610$	−25.3553	−	52.9792i	−1.02661	−	2.14507i
$611$	2.15452	+	3.73173i	0.0871624	+	0.150970i
$612$		0			0
$613$	−10.5641	+	18.2976i	−0.426680	+	0.739032i	−0.996576	−	0.0826853i	$-0.973650\pi$
$613$	−10.5641	+	18.2976i	−0.426680	+	0.739032i	0.569895	+	0.821717i	$0.306984\pi$
$614$	12.5612	−	18.3283i	0.506930	−	0.739669i
$615$		0			0
$616$	−8.75604	+	10.9441i	−0.352791	+	0.440950i
$617$			43.3809i			1.74645i	0.487319	+	0.873224i	$0.337975\pi$
$617$			43.3809i			1.74645i	−0.487319	+	0.873224i	$0.662025\pi$
$618$		0			0
$619$	11.8607	+	6.84777i	0.476721	+	0.275235i	0.719049	−	0.694959i	$-0.244578\pi$
$619$	11.8607	+	6.84777i	0.476721	+	0.275235i	−0.242328	+	0.970194i	$0.577911\pi$
$620$	−11.5535	−	29.8630i	−0.464000	−	1.19933i
$621$		0			0
$622$	17.1767	−	8.22061i	0.688723	−	0.329616i
$623$	15.2802	+	22.1402i	0.612188	+	0.887027i
$624$		0			0
$625$	−19.3977	−	33.5978i	−0.775907	−	1.34391i
$626$	−1.35049	+	17.4529i	−0.0539764	+	0.697559i
$627$		0			0
$628$	−30.9200	−	4.81394i	−1.23384	−	0.192097i
$629$		−	23.8448i		−	0.950755i
$630$		0			0
$631$			28.5175i			1.13526i	0.823283	+	0.567631i	$0.192140\pi$
$631$			28.5175i			1.13526i	−0.823283	+	0.567631i	$0.807860\pi$
$632$	−4.62855	−	15.4024i	−0.184114	−	0.612674i
$633$		0			0
$634$	26.0089	+	2.01254i	1.03295	+	0.0799283i
$635$	29.5062	+	51.1062i	1.17092	+	2.02809i
$636$		0			0
$637$	−7.30918	+	1.18691i	−0.289600	+	0.0470269i
$638$	−5.82581	−	12.1728i	−0.230646	−	0.481928i
$639$		0			0
$640$	−38.6433	−	23.1942i	−1.52751	−	0.916830i
$641$	19.9029	+	11.4909i	0.786116	+	0.453864i	0.838593	−	0.544758i	$-0.183378\pi$
$641$	19.9029	+	11.4909i	0.786116	+	0.453864i	−0.0524773	+	0.998622i	$0.516712\pi$
$642$		0			0
$643$		−	2.79085i		−	0.110060i	−0.998485	−	0.0550302i	$-0.982474\pi$
$643$		−	2.79085i		−	0.110060i	0.998485	−	0.0550302i	$-0.0175255\pi$
$644$	26.2827	+	17.8869i	1.03568	+	0.704843i
$645$		0			0
$646$	−2.25074	−	1.54254i	−0.0885541	−	0.0606903i
$647$	−20.5616	+	35.6137i	−0.808359	+	1.40012i	0.105640	+	0.994404i	$0.466311\pi$
$647$	−20.5616	+	35.6137i	−0.808359	+	1.40012i	−0.914000	+	0.405715i	$0.867023\pi$
$648$		0			0
$649$	−8.54909	−	14.8075i	−0.335581	−	0.581244i
$650$	−14.6675	+	7.01970i	−0.575305	+	0.275335i
$651$		0			0
$652$	11.2902	+	9.09353i	0.442156	+	0.356130i
$653$	−20.8186	+	12.0196i	−0.814694	+	0.470364i	−0.848583	−	0.529062i	$-0.822544\pi$
$653$	−20.8186	+	12.0196i	−0.814694	+	0.470364i	0.0338892	+	0.999426i	$0.489211\pi$
$654$		0			0
$655$	−8.45650	−	4.88236i	−0.330423	−	0.190770i
$656$	16.6703	+	18.3195i	0.650865	+	0.715258i
$657$		0			0
$658$	−15.2412	+	0.0497652i	−0.594164	+	0.00194005i
$659$	−15.0431			−0.585995			−0.292997	−	0.956113i	$-0.594653\pi$
$659$	−15.0431			−0.585995			−0.292997	+	0.956113i	$0.594653\pi$
$660$		0			0
$661$	−10.7083	+	18.5474i	−0.416506	+	0.721409i	−0.995585	−	0.0938618i	$-0.970079\pi$
$661$	−10.7083	+	18.5474i	−0.416506	+	0.721409i	0.579079	+	0.815271i	$0.303412\pi$
$662$	−36.1949	−	2.80072i	−1.40676	−	0.108853i
$663$		0			0
$664$	2.12555	−	9.00997i	0.0824874	−	0.349655i
$665$	−6.90533	−	3.27716i	−0.267777	−	0.127083i
$666$		0			0
$667$	−26.5098	+	15.3054i	−1.02646	+	0.592628i
$668$	13.0713	+	33.7860i	0.505743	+	1.30722i
$669$		0			0
$670$	26.8402	+	18.3949i	1.03693	+	0.710656i
$671$	−19.5262			−0.753802
$672$		0			0
$673$	−27.0940			−1.04440			−0.522198	−	0.852824i	$-0.674888\pi$
$673$	−27.0940			−1.04440			−0.522198	+	0.852824i	$0.674888\pi$
$674$	−1.31261	−	0.899591i	−0.0505598	−	0.0346510i
$675$		0			0
$676$	−8.57382	−	22.1612i	−0.329762	−	0.852354i
$677$	−40.0846	+	23.1429i	−1.54058	+	0.889453i	−0.541775	+	0.840523i	$0.682248\pi$
$677$	−40.0846	+	23.1429i	−1.54058	+	0.889453i	−0.998802	+	0.0489293i	$0.984419\pi$
$678$		0			0
$679$	0.433479	+	5.37386i	0.0166354	+	0.206230i
$680$	6.88288	−	29.1758i	0.263947	−	1.11884i
$681$		0			0
$682$	−10.6134	−	0.821252i	−0.406408	−	0.0314474i
$683$	17.3257	−	30.0090i	0.662949	−	1.14826i	−0.316888	−	0.948463i	$-0.602638\pi$
$683$	17.3257	−	30.0090i	0.662949	−	1.14826i	0.979837	−	0.199799i	$-0.0640288\pi$
$684$		0			0
$685$	2.46949			0.0943544
$686$	9.21077	−	24.5186i	0.351669	−	0.936124i
$687$		0			0
$688$	−33.1321	−	36.4101i	−1.26315	−	1.38812i
$689$	11.8865	+	6.86269i	0.452841	+	0.261448i
$690$		0			0
$691$	−15.5595	+	8.98330i	−0.591913	+	0.341741i	−0.765853	−	0.643015i	$-0.777683\pi$
$691$	−15.5595	+	8.98330i	−0.591913	+	0.341741i	0.173941	+	0.984756i	$0.444350\pi$
$692$	−16.6607	−	13.4192i	−0.633346	−	0.510122i
$693$		0			0
$694$	−2.81735	+	1.34836i	−0.106945	+	0.0511830i
$695$	−3.99704	−	6.92307i	−0.151616	−	0.262607i
$696$		0			0
$697$	−8.23716	+	14.2672i	−0.312005	+	0.540408i
$698$	−17.8916	−	12.2619i	−0.677206	−	0.464121i
$699$		0			0
$700$	4.24992	−	57.3577i	0.160632	−	2.16792i
$701$		−	2.58336i		−	0.0975721i	−0.998809	−	0.0487861i	$-0.984465\pi$
$701$		−	2.58336i		−	0.0975721i	0.998809	−	0.0487861i	$-0.0155353\pi$
$702$		0			0
$703$	−5.62899	−	3.24990i	−0.212302	−	0.122572i
$704$	−12.5014	+	8.25946i	−0.471166	+	0.311290i
$705$		0			0
$706$	−20.7124	−	43.2779i	−0.779520	−	1.62878i
$707$	11.4042	−	24.0300i	0.428900	−	0.903740i
$708$		0			0
$709$	8.03512	+	13.9172i	0.301765	+	0.522673i	0.976536	−	0.215355i	$-0.0690908\pi$
$709$	8.03512	+	13.9172i	0.301765	+	0.522673i	−0.674771	+	0.738027i	$0.735757\pi$
$710$	35.0546	+	2.71249i	1.31557	+	0.101798i
$711$		0			0
$712$	8.27656	+	27.5418i	0.310177	+	1.03217i
$713$			24.1462i			0.904283i
$714$		0			0
$715$			7.89267i			0.295169i
$716$	−46.0885	−	7.17551i	−1.72241	−	0.268162i
$717$		0			0
$718$	−0.760325	+	9.82600i	−0.0283751	+	0.366703i
$719$	−12.9613	−	22.4496i	−0.483374	−	0.837229i	0.516444	−	0.856321i	$-0.327256\pi$
$719$	−12.9613	−	22.4496i	−0.483374	−	0.837229i	−0.999818	+	0.0190926i	$0.993922\pi$
$720$		0			0
$721$	−14.4026	−	20.8686i	−0.536380	−	0.777186i
$722$	23.5664	−	11.2786i	0.877050	−	0.419748i
$723$		0			0
$724$	−2.09380	−	5.41196i	−0.0778154	−	0.201134i
$725$	47.9592	+	27.6892i	1.78116	+	1.02835i
$726$		0			0
$727$		−	23.7464i		−	0.880706i	−0.897825	−	0.440353i	$-0.854853\pi$
$727$		−	23.7464i		−	0.880706i	0.897825	−	0.440353i	$-0.145147\pi$
$728$	−7.82589	−	1.19225i	−0.290047	−	0.0441879i
$729$		0			0
$730$	−46.9481	+	68.5026i	−1.73763	+	2.53540i
$731$	16.3713	−	28.3560i	0.605516	−	1.04878i
$732$		0			0
$733$	9.21172	+	15.9552i	0.340243	+	0.589318i	0.984478	−	0.175510i	$-0.0561574\pi$
$733$	9.21172	+	15.9552i	0.340243	+	0.589318i	−0.644235	+	0.764828i	$0.722824\pi$
$734$	1.16804	+	2.44058i	0.0431131	+	0.0900835i
$735$		0			0
$736$	20.8667	+	26.8270i	0.769157	+	0.988857i
$737$	9.36828	−	5.40878i	0.345085	−	0.199235i
$738$		0			0
$739$	12.1438	+	7.01125i	0.446718	+	0.257913i	0.706443	−	0.707770i	$-0.250299\pi$
$739$	12.1438	+	7.01125i	0.446718	+	0.257913i	−0.259725	+	0.965683i	$0.583632\pi$
$740$	10.9851	−	70.5575i	0.403820	−	2.59374i
$741$		0			0
$742$	−41.9638	+	24.4109i	−1.54054	+	0.896151i
$743$	49.8064			1.82722			0.913610	−	0.406592i	$-0.133283\pi$
$743$	49.8064			1.82722			0.913610	+	0.406592i	$0.133283\pi$
$744$		0			0
$745$	−13.8440	+	23.9785i	−0.507205	+	0.878506i
$746$	−0.892337	+	11.5320i	−0.0326708	+	0.422218i
$747$		0			0
$748$	−7.76134	−	6.25129i	−0.283783	−	0.228570i
$749$	9.64572	−	6.65706i	0.352447	−	0.243244i
$750$		0			0
$751$	1.68526	−	0.972983i	0.0614959	−	0.0355047i	−0.468937	−	0.883232i	$-0.655363\pi$
$751$	1.68526	−	0.972983i	0.0614959	−	0.0355047i	0.530433	+	0.847727i	$0.322029\pi$
$752$	−15.5224	−	4.95344i	−0.566045	−	0.180633i
$753$		0			0
$754$	4.30896	−	6.28727i	0.156923	−	0.228969i
$755$	59.5319			2.16659
$756$		0			0
$757$	6.74999			0.245333			0.122666	−	0.992448i	$-0.460855\pi$
$757$	6.74999			0.245333			0.122666	+	0.992448i	$0.460855\pi$
$758$	−13.7323	+	20.0371i	−0.498781	+	0.727779i
$759$		0			0
$760$	−5.94937	−	5.60131i	−0.215806	−	0.203181i
$761$	−29.0741	+	16.7859i	−1.05393	+	0.608489i	−0.923748	−	0.383000i	$-0.874891\pi$
$761$	−29.0741	+	16.7859i	−1.05393	+	0.608489i	−0.130186	+	0.991490i	$0.541557\pi$
$762$		0			0
$763$	−16.2921	−	7.73198i	−0.589815	−	0.279917i
$764$	−11.6643	+	14.4819i	−0.422000	+	0.523938i
$765$		0			0
$766$	−2.51237	+	32.4684i	−0.0907758	+	1.17313i
$767$	4.82858	−	8.36335i	0.174350	−	0.301983i
$768$		0			0
$769$	9.09355			0.327922			0.163961	−	0.986467i	$-0.447573\pi$
$769$	9.09355			0.327922			0.163961	+	0.986467i	$0.447573\pi$
$770$	−24.2221	−	13.8794i	−0.872904	−	0.500178i
$771$		0			0
$772$	14.0047	+	2.18040i	0.504041	+	0.0784741i
$773$	−9.08272	−	5.24391i	−0.326683	−	0.188610i	0.327685	−	0.944787i	$-0.393732\pi$
$773$	−9.08272	−	5.24391i	−0.326683	−	0.188610i	−0.654367	+	0.756177i	$0.727065\pi$
$774$		0			0
$775$	37.8308	−	21.8416i	1.35892	−	0.784574i
$776$	−1.32336	+	5.60957i	−0.0475058	+	0.201372i
$777$		0			0
$778$	−11.5873	−	24.2113i	−0.415424	−	0.868016i
$779$	2.24535	+	3.88906i	0.0804480	+	0.139340i
$780$		0			0
$781$	5.84440	−	10.1228i	0.209129	−	0.362222i
$782$	−12.7793	+	18.6464i	−0.456986	+	0.666795i
$783$		0			0
$784$	17.4209	−	21.9206i	0.622176	−	0.782878i
$785$		−	62.3289i		−	2.22461i
$786$		0			0
$787$	7.11401	+	4.10728i	0.253587	+	0.146409i	0.621406	−	0.783489i	$-0.286562\pi$
$787$	7.11401	+	4.10728i	0.253587	+	0.146409i	−0.367819	+	0.929898i	$0.619895\pi$
$788$	7.51928	−	2.90909i	0.267863	−	0.103632i
$789$		0			0
$790$	28.8953	−	13.8290i	1.02805	−	0.492013i
$791$	−29.1635	+	2.35246i	−1.03693	+	0.0836438i
$792$		0			0
$793$	−5.51427	−	9.55100i	−0.195818	−	0.339166i
$794$	3.72866	−	48.1871i	0.132325	−	1.71009i
$795$		0			0
$796$	−6.95225	+	44.6544i	−0.246416	+	1.58273i
$797$			27.6583i			0.979709i	0.871804	+	0.489854i	$0.162950\pi$
$797$			27.6583i			0.979709i	−0.871804	+	0.489854i	$0.837050\pi$
$798$		0			0
$799$		−	10.8372i		−	0.383392i
$800$	23.1558	−	56.9592i	0.818680	−	2.01381i
$801$		0			0
$802$	−18.5637	−	1.43644i	−0.655506	−	0.0507223i
$803$	13.8045	+	23.9101i	0.487150	+	0.843768i
$804$		0			0
$805$	−27.1499	+	57.2079i	−0.956909	+	2.01631i
$806$	−2.59555	−	5.42332i	−0.0914243	−	0.191028i
$807$		0			0
$808$	19.4921	−	20.7033i	0.685729	−	0.728339i
$809$	−30.5781	−	17.6543i	−1.07507	−	0.620691i	−0.145507	−	0.989357i	$-0.546481\pi$
$809$	−30.5781	−	17.6543i	−1.07507	−	0.620691i	−0.929562	+	0.368666i	$0.879815\pi$
$810$		0			0
$811$			3.31379i			0.116363i	0.998306	+	0.0581815i	$0.0185302\pi$
$811$			3.31379i			0.116363i	−0.998306	+	0.0581815i	$0.981470\pi$
$812$	11.7179	+	24.2802i	0.411216	+	0.852067i
$813$		0			0
$814$	−19.5820	−	13.4205i	−0.686350	−	0.470388i
$815$	−14.4376	+	25.0066i	−0.505726	+	0.875943i
$816$		0			0
$817$	−4.46263	−	7.72950i	−0.156128	−	0.270421i
$818$	−35.6117	+	17.0434i	−1.24513	+	0.595909i
$819$		0			0
$820$	−30.9468	+	38.4222i	−1.08071	+	1.34176i
$821$	9.83140	−	5.67616i	0.343118	−	0.198099i	−0.318532	−	0.947912i	$-0.603190\pi$
$821$	9.83140	−	5.67616i	0.343118	−	0.198099i	0.661650	+	0.749813i	$0.269856\pi$
$822$		0			0
$823$	−33.0277	−	19.0685i	−1.15127	−	0.664687i	−0.202075	−	0.979370i	$-0.564769\pi$
$823$	−33.0277	−	19.0685i	−1.15127	−	0.664687i	−0.949197	+	0.314682i	$0.898102\pi$
$824$	−7.80120	−	25.9600i	−0.271768	−	0.904358i
$825$		0			0
$826$	17.1755	+	29.5257i	0.597611	+	1.02733i
$827$	9.51543			0.330884			0.165442	−	0.986220i	$-0.447095\pi$
$827$	9.51543			0.330884			0.165442	+	0.986220i	$0.447095\pi$
$828$		0			0
$829$	14.5375	−	25.1798i	0.504910	−	0.874529i	−0.495074	−	0.868851i	$-0.664859\pi$
$829$	14.5375	−	25.1798i	0.504910	−	0.874529i	0.999984	−	0.00567849i	$-0.00180753\pi$
$830$	18.3839	+	1.42252i	0.638113	+	0.0493765i
$831$		0			0
$832$	−7.57045	−	3.78241i	−0.262458	−	0.131132i
$833$	17.4123	+	6.60613i	0.603299	+	0.228889i
$834$		0			0
$835$	−62.4893	+	36.0782i	−2.16253	+	1.24854i
$836$	−2.53355	+	0.980191i	−0.0876247	+	0.0339006i
$837$		0			0
$838$	37.6256	+	25.7866i	1.29975	+	0.890782i
$839$	1.01793			0.0351429			0.0175715	−	0.999846i	$-0.494407\pi$
$839$	1.01793			0.0351429			0.0175715	+	0.999846i	$0.494407\pi$
$840$		0			0
$841$	3.04159			0.104883
$842$	23.7360	+	16.2674i	0.817996	+	0.560611i
$843$		0			0
$844$	6.58352	−	2.54706i	0.226614	−	0.0876733i
$845$	40.9884	−	23.6647i	1.41004	−	0.814090i
$846$		0			0
$847$	16.3141	−	11.2593i	0.560560	−	0.386874i
$848$	−50.7078	+	11.0573i	−1.74131	+	0.379710i
$849$		0			0
$850$	40.7737	+	3.15502i	1.39852	+	0.108216i
$851$	−26.9241	+	46.6339i	−0.922946	+	1.59859i
$852$		0			0
$853$	13.2563			0.453887			0.226944	−	0.973908i	$-0.427127\pi$
$853$	13.2563			0.453887			0.226944	+	0.973908i	$0.427127\pi$
$854$	39.0084	−	0.127369i	1.33484	−	0.00435848i
$855$		0			0
$856$	11.9990	−	3.60582i	0.410118	−	0.123244i
$857$	20.4031	+	11.7797i	0.696956	+	0.402388i	0.806213	−	0.591626i	$-0.201514\pi$
$857$	20.4031	+	11.7797i	0.696956	+	0.402388i	−0.109257	+	0.994014i	$0.534847\pi$
$858$		0			0
$859$	−0.285175	+	0.164646i	−0.00973004	+	0.00561764i	−0.504857	−	0.863203i	$-0.668455\pi$
$859$	−0.285175	+	0.164646i	−0.00973004	+	0.00561764i	0.495127	+	0.868821i	$0.335121\pi$
$860$	61.5067	−	76.3641i	2.09736	−	2.60399i
$861$		0			0
$862$	−30.2470	+	14.4759i	−1.03022	+	0.493052i
$863$	25.0532	+	43.3934i	0.852820	+	1.47713i	0.878653	+	0.477462i	$0.158443\pi$
$863$	25.0532	+	43.3934i	0.852820	+	1.47713i	−0.0258325	+	0.999666i	$0.508224\pi$
$864$		0			0
$865$	21.3053	−	36.9019i	0.724403	−	1.25470i
$866$	−14.5261	−	9.95541i	−0.493617	−	0.338299i
$867$		0			0
$868$	21.2081	+	1.57142i	0.719851	+	0.0533374i
$869$		−	10.6498i		−	0.361268i
$870$		0			0
$871$	5.29127	+	3.05491i	0.179288	+	0.103512i
$872$	−14.0367	−	13.2155i	−0.475342	−	0.447532i
$873$		0			0
$874$	2.66009	+	5.55818i	0.0899789	+	0.188008i
$875$	61.6605	−	4.97381i	2.08450	−	0.168145i
$876$		0			0
$877$	−7.33001	−	12.6959i	−0.247517	−	0.428712i	0.715319	−	0.698798i	$-0.246281\pi$
$877$	−7.33001	−	12.6959i	−0.247517	−	0.428712i	−0.962836	+	0.270086i	$0.912948\pi$
$878$	2.16354	+	0.167412i	0.0730158	+	0.00564988i
$879$		0			0
$880$	−20.0861	−	22.0733i	−0.677103	−	0.744091i
$881$			37.4296i			1.26104i	0.776174	+	0.630518i	$0.217158\pi$
$881$			37.4296i			1.26104i	−0.776174	+	0.630518i	$0.782842\pi$
$882$		0			0
$883$		−	33.1664i		−	1.11614i	−0.829794	−	0.558070i	$-0.811542\pi$
$883$		−	33.1664i		−	1.11614i	0.829794	−	0.558070i	$-0.188458\pi$
$884$	0.865907	−	5.56174i	0.0291236	−	0.187061i
$885$		0			0
$886$	−3.19896	+	41.3415i	−0.107471	+	1.38889i
$887$	−10.7263	−	18.5785i	−0.360154	−	0.623804i	0.627832	−	0.778349i	$-0.283942\pi$
$887$	−10.7263	−	18.5785i	−0.360154	−	0.623804i	−0.987986	+	0.154544i	$0.950609\pi$
$888$		0			0
$889$	−39.0665	+	3.15128i	−1.31025	+	0.105691i
$890$	−51.6691	+	24.7283i	−1.73195	+	0.828896i
$891$		0			0
$892$	−9.64414	+	3.73117i	−0.322910	+	0.124929i
$893$	−2.55831	−	1.47704i	−0.0856107	−	0.0494274i
$894$		0			0
$895$		−	92.9056i		−	3.10549i
$896$	24.9207	−	16.5818i	0.832544	−	0.553959i
$897$		0			0
$898$	3.43730	−	5.01542i	0.114704	−	0.167367i
$899$	−10.2382	+	17.7330i	−0.341462	+	0.591429i
$900$		0			0
$901$	−17.2596	−	29.8945i	−0.575001	−	0.995931i
$902$	7.08053	+	14.7945i	0.235756	+	0.492604i
$903$		0			0
$904$	−30.4427	−	7.18177i	−1.01251	−	0.238862i
$905$	10.0097	−	5.77912i	0.332735	−	0.192104i
$906$		0			0
$907$	−4.53272	−	2.61697i	−0.150507	−	0.0868951i	0.422855	−	0.906197i	$-0.361028\pi$
$907$	−4.53272	−	2.61697i	−0.150507	−	0.0868951i	−0.573362	+	0.819302i	$0.694361\pi$
$908$	40.5828	+	6.31834i	1.34679	+	0.209682i
$909$		0			0
$910$	−0.0514837	−	15.7675i	−0.00170667	−	0.522688i
$911$	43.4199			1.43857			0.719283	−	0.694717i	$-0.244471\pi$
$911$	43.4199			1.43857			0.719283	+	0.694717i	$0.244471\pi$
$912$		0			0
$913$	3.06501	−	5.30875i	0.101437	−	0.175694i
$914$	−0.507234	+	6.55519i	−0.0167778	+	0.216826i
$915$		0			0
$916$	−12.8080	+	15.9019i	−0.423189	+	0.525414i
$917$	5.33753	−	3.68373i	0.176261	−	0.121648i
$918$		0			0
$919$	14.3771	−	8.30065i	0.474258	−	0.273813i	−0.243762	−	0.969835i	$-0.578382\pi$
$919$	14.3771	−	8.30065i	0.474258	−	0.273813i	0.718021	+	0.696022i	$0.245048\pi$
$920$	−46.4045	+	49.2881i	−1.52991	+	1.62498i
$921$		0			0
$922$	−19.3756	+	28.2713i	−0.638103	+	0.931066i
$923$	6.60190			0.217304
$924$		0			0
$925$	97.4174			3.20307
$926$	−14.9723	+	21.8463i	−0.492020	+	0.717914i
$927$		0			0
$928$	3.94970	+	28.5494i	0.129655	+	0.937180i
$929$	19.1671	−	11.0661i	0.628851	−	0.363067i	−0.151456	−	0.988464i	$-0.548396\pi$
$929$	19.1671	−	11.0661i	0.628851	−	0.363067i	0.780307	+	0.625397i	$0.215063\pi$
$930$		0			0
$931$	3.93268	−	3.21010i	0.128888	−	0.105207i
$932$	−9.75205	−	7.85469i	−0.319439	−	0.257289i
$933$		0			0
$934$	2.02642	−	26.1883i	0.0663066	−	0.856908i
$935$	9.92500	−	17.1906i	0.324582	−	0.562193i
$936$		0			0
$937$	23.3303			0.762167			0.381083	−	0.924541i	$-0.375551\pi$
$937$	23.3303			0.762167			0.381083	+	0.924541i	$0.375551\pi$
$938$	−18.6801	+	10.8664i	−0.609927	+	0.354802i
$939$		0			0
$940$	4.99260	−	32.0676i	0.162841	−	1.04593i
$941$	37.7784	+	21.8114i	1.23154	+	0.711030i	0.967351	−	0.253441i	$-0.0815622\pi$
$941$	37.7784	+	21.8114i	1.23154	+	0.711030i	0.264190	+	0.964471i	$0.414896\pi$
$942$		0			0
$943$	32.2193	−	18.6018i	1.04920	−	0.605758i
$944$	7.77992	+	35.6780i	0.253215	+	1.16122i
$945$		0			0
$946$	−14.0725	−	29.4041i	−0.457538	−	0.956011i
$947$	12.6981	+	21.9938i	0.412634	+	0.714702i	0.995177	−	0.0980973i	$-0.0312756\pi$
$947$	12.6981	+	21.9938i	0.412634	+	0.714702i	−0.582543	+	0.812800i	$0.697942\pi$
$948$		0			0
$949$	−7.79686	+	13.5046i	−0.253097	+	0.438377i
$950$	6.30200	−	9.19534i	0.204464	−	0.298336i
$951$		0			0
$952$	15.5459	+	12.4378i	0.503846	+	0.403112i
$953$		−	1.61704i		−	0.0523809i	−0.999657	−	0.0261905i	$-0.991662\pi$
$953$		−	1.61704i		−	0.0523809i	0.999657	−	0.0261905i	$-0.00833763\pi$
$954$		0			0
$955$	−32.0761	−	18.5191i	−1.03796	−	0.599265i
$956$	−3.60304	−	9.31298i	−0.116531	−	0.301203i
$957$		0			0
$958$	13.3901	−	6.40838i	0.432615	−	0.207045i
$959$	−0.703204	+	1.48173i	−0.0227077	+	0.0478475i
$960$		0			0
$961$	−7.42402	−	12.8588i	−0.239485	−	0.414799i
$962$	1.03442	−	13.3683i	0.0333512	−	0.431011i
$963$		0			0
$964$	13.7771	+	2.14495i	0.443730	+	0.0690843i
$965$			28.2309i			0.908783i
$966$		0			0
$967$			27.8714i			0.896282i	0.893963	+	0.448141i	$0.147914\pi$
$967$			27.8714i			0.896282i	−0.893963	+	0.448141i	$0.852086\pi$
$968$	20.2944	−	6.09864i	0.652285	−	0.196018i
$969$		0			0
$970$	−11.4457	−	0.885658i	−0.367500	−	0.0284368i
$971$	−14.9960	−	25.9738i	−0.481243	−	0.833538i	0.518525	−	0.855062i	$-0.326481\pi$
$971$	−14.9960	−	25.9738i	−0.481243	−	0.833538i	−0.999768	+	0.0215245i	$0.993148\pi$
$972$		0			0
$973$	5.29212	−	0.426886i	0.169658	−	0.0136853i
$974$	16.5329	+	34.5450i	0.529748	+	1.10689i
$975$		0			0
$976$	39.7281	+	12.6778i	1.27167	+	0.405808i
$977$	−2.90454	−	1.67694i	−0.0929246	−	0.0536500i	0.452818	−	0.891603i	$-0.350419\pi$
$977$	−2.90454	−	1.67694i	−0.0929246	−	0.0536500i	−0.545742	+	0.837953i	$0.683752\pi$
$978$		0			0
$979$			19.0434i			0.608629i
$980$	48.4800	+	27.5694i	1.54864	+	0.880673i
$981$		0			0
$982$	−9.78993	−	6.70950i	−0.312409	−	0.214109i
$983$	13.4540	−	23.3029i	0.429115	−	0.743249i	−0.567680	−	0.823249i	$-0.692159\pi$
$983$	13.4540	−	23.3029i	0.429115	−	0.743249i	0.996795	+	0.0800007i	$0.0254923\pi$
$984$		0			0
$985$	8.02941	+	13.9073i	0.255838	+	0.443125i
$986$	−17.2913	+	8.27547i	−0.550668	+	0.263545i
$987$		0			0
$988$	−1.19493	−	0.962444i	−0.0380158	−	0.0306194i
$989$	−64.0357	+	36.9710i	−2.03622	+	1.17561i
$990$		0			0
$991$	35.8246	+	20.6834i	1.13801	+	0.657029i	0.945936	−	0.324352i	$-0.105146\pi$
$991$	35.8246	+	20.6834i	1.13801	+	0.657029i	0.192071	+	0.981381i	$0.438480\pi$
$992$	21.0608	+	8.56190i	0.668681	+	0.271840i
$993$		0			0
$994$	−11.6096	+	20.2608i	−0.368233	+	0.642634i
$995$	−90.0148			−2.85366
$996$		0			0
$997$	−7.74005	+	13.4062i	−0.245130	+	0.424577i	−0.962168	−	0.272457i	$-0.912164\pi$
$997$	−7.74005	+	13.4062i	−0.245130	+	0.424577i	0.717038	+	0.697034i	$0.245497\pi$
$998$	−25.1802	−	1.94842i	−0.797066	−	0.0616761i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.d.431.3	yes	28
3.2	odd	2	inner	756.2.be.d.431.12	yes	28
4.3	odd	2		756.2.be.c.431.8	yes	28
7.2	even	3		756.2.be.c.107.7	✓	28
12.11	even	2		756.2.be.c.431.7	yes	28
21.2	odd	6		756.2.be.c.107.8	yes	28
28.23	odd	6	inner	756.2.be.d.107.12	yes	28
84.23	even	6	inner	756.2.be.d.107.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.7	✓	28	7.2	even	3
756.2.be.c.107.8	yes	28	21.2	odd	6
756.2.be.c.431.7	yes	28	12.11	even	2
756.2.be.c.431.8	yes	28	4.3	odd	2
756.2.be.d.107.3	yes	28	84.23	even	6	inner
756.2.be.d.107.12	yes	28	28.23	odd	6	inner
756.2.be.d.431.3	yes	28	1.1	even	1	trivial
756.2.be.d.431.12	yes	28	3.2	odd	2	inner

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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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16654 - 0.799486i) q^{2} +(0.721643 + 1.86527i) q^{4} +(-3.44992 + 1.99182i) q^{5} +(-0.212727 - 2.63719i) q^{7} +(0.649430 - 2.75286i) q^{8} +O(q^{10})\)	\(q+(-1.16654 - 0.799486i) q^{2} +(0.721643 + 1.86527i) q^{4} +(-3.44992 + 1.99182i) q^{5} +(-0.212727 - 2.63719i) q^{7} +(0.649430 - 2.75286i) q^{8} +(5.61691 + 0.434631i) q^{10} +(0.936467 - 1.62201i) q^{11} +1.05785 q^{13} +(-1.86024 + 3.24646i) q^{14} +(-2.95846 + 2.69212i) q^{16} +(-2.30404 - 1.33024i) q^{17} +(-0.628053 + 0.362606i) q^{19} +(-6.20489 - 4.99766i) q^{20} +(-2.38920 + 1.14345i) q^{22} +(3.00404 + 5.20316i) q^{23} +(5.43465 - 9.41310i) q^{25} +(-1.23402 - 0.845733i) q^{26} +(4.76555 - 2.29990i) q^{28} +5.09494i q^{29} +(3.48051 + 2.00948i) q^{31} +(5.60348 - 0.775220i) q^{32} +(1.62425 + 3.39382i) q^{34} +(5.98668 + 8.67438i) q^{35} +(4.48131 + 7.76185i) q^{37} +(1.02255 + 0.0791238i) q^{38} +(3.24270 + 10.7907i) q^{40} -6.19225i q^{41} +12.3071i q^{43} +(3.70128 + 0.576252i) q^{44} +(0.655508 - 8.47140i) q^{46} +(2.03670 + 3.52767i) q^{47} +(-6.90949 + 1.12200i) q^{49} +(-13.8654 + 6.63585i) q^{50} +(0.763387 + 1.97317i) q^{52} +(11.2365 + 6.48742i) q^{53} +7.46108i q^{55} +(-7.39795 - 1.12706i) q^{56} +(4.07333 - 5.94346i) q^{58} +(4.56454 - 7.90602i) q^{59} +(-5.21274 - 9.02873i) q^{61} +(-2.45362 - 5.12676i) q^{62} +(-7.15648 - 3.57558i) q^{64} +(-3.64949 + 2.10703i) q^{65} +(5.00193 + 2.88786i) q^{67} +(0.818557 - 5.25761i) q^{68} +(-0.0486684 - 14.9053i) q^{70} +6.24090 q^{71} +(-7.37051 + 12.7661i) q^{73} +(0.977859 - 12.6373i) q^{74} +(-1.12959 - 0.909815i) q^{76} +(-4.47675 - 2.12459i) q^{77} +(4.92434 - 2.84307i) q^{79} +(4.84427 - 15.1803i) q^{80} +(-4.95062 + 7.22352i) q^{82} +3.27295 q^{83} +10.5983 q^{85} +(9.83935 - 14.3567i) q^{86} +(-3.85699 - 3.63135i) q^{88} +(-8.80546 + 5.08384i) q^{89} +(-0.225033 - 2.78973i) q^{91} +(-7.53745 + 9.35818i) q^{92} +(0.444426 - 5.74350i) q^{94} +(1.44449 - 2.50193i) q^{95} -2.03772 q^{97} +(8.95724 + 4.21518i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{4} + 2 q^{7}+O(q^{10}) \) 28 * q - 4 * q^4 + 2 * q^7	\( 28 q - 4 q^{4} + 2 q^{7} + 4 q^{10} + 8 q^{13} + 12 q^{16} - 42 q^{19} + 4 q^{22} + 6 q^{25} + 24 q^{28} + 30 q^{31} + 24 q^{34} + 12 q^{37} + 24 q^{46} - 14 q^{49} - 24 q^{52} - 44 q^{58} + 6 q^{61} + 8 q^{64} + 24 q^{67} - 32 q^{70} - 22 q^{73} + 48 q^{79} + 36 q^{82} - 24 q^{85} - 4 q^{88} + 16 q^{91} + 60 q^{94} - 4 q^{97}+O(q^{100}) \) 28 * q - 4 * q^4 + 2 * q^7 + 4 * q^10 + 8 * q^13 + 12 * q^16 - 42 * q^19 + 4 * q^22 + 6 * q^25 + 24 * q^28 + 30 * q^31 + 24 * q^34 + 12 * q^37 + 24 * q^46 - 14 * q^49 - 24 * q^52 - 44 * q^58 + 6 * q^61 + 8 * q^64 + 24 * q^67 - 32 * q^70 - 22 * q^73 + 48 * q^79 + 36 * q^82 - 24 * q^85 - 4 * q^88 + 16 * q^91 + 60 * q^94 - 4 * q^97

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