LMFDB - Embedded newform 756.2.be.d.107.12

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			107.12
Character	$\chi$	$=$	756.107
Dual form			756.2.be.d.431.12

$q$-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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

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

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	0.998657	+	0.0518089i	$0.0164987\pi$
$5$	3.44992	+	1.99182i	1.54285	+	0.890767i	0.544196	+	0.838958i	$0.316835\pi$
$6$		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	$-0.257782\pi$
$11$	−0.936467	−	1.62201i	−0.282356	−	0.489054i	−0.971964	+	0.235128i	$0.924449\pi$
$12$		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	$-0.562100\pi$
$17$	2.30404	−	1.33024i	0.558811	−	0.322630i	0.752668	+	0.658400i	$0.228766\pi$
$18$		0			0
$19$	−0.628053	−	0.362606i	−0.144085	−	0.0831876i	0.426224	−	0.904617i	$-0.359843\pi$
$19$	−0.628053	−	0.362606i	−0.144085	−	0.0831876i	−0.570310	+	0.821430i	$0.693177\pi$
$20$	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	0.361884	+	0.932223i	$0.382134\pi$
$23$	−3.00404	+	5.20316i	−0.626387	+	1.08493i	−0.988271	+	0.152711i	$0.951200\pi$
$24$		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	−0.153741	−	0.988111i	$-0.549132\pi$
$31$	3.48051	−	2.00948i	0.625119	−	0.360912i	0.778859	+	0.627199i	$0.215799\pi$
$32$	−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	−0.217241	−	0.976118i	$-0.569706\pi$
$37$	4.48131	−	7.76185i	0.736722	−	1.27604i	0.953963	−	0.299923i	$-0.0969609\pi$
$38$	−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	$-0.612302\pi$
$43$		−	12.3071i		−	1.87681i	0.345533	−	0.938407i	$-0.387698\pi$
$44$	−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	$-0.929347\pi$
$47$	−2.03670	+	3.52767i	−0.297084	+	0.514564i	0.678384	+	0.734708i	$0.262681\pi$
$48$		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	−0.544841	+	0.838539i	$0.683410\pi$
$53$	−11.2365	+	6.48742i	−1.54346	+	0.891116i	−0.998617	+	0.0525765i	$0.983257\pi$
$54$		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	−0.993652	−	0.112499i	$-0.964114\pi$
$59$	−4.56454	−	7.90602i	−0.594253	−	1.02928i	0.399399	−	0.916777i	$-0.369219\pi$
$60$		0			0
$61$	−5.21274	+	9.02873i	−0.667423	+	1.15601i	0.311199	+	0.950345i	$0.399269\pi$
$61$	−5.21274	+	9.02873i	−0.667423	+	1.15601i	−0.978622	+	0.205666i	$0.934064\pi$
$62$	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	−0.162306	−	0.986740i	$-0.551893\pi$
$67$	5.00193	−	2.88786i	0.611083	−	0.352809i	0.773389	+	0.633932i	$0.218560\pi$
$68$	−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	$-0.620755\pi$
$71$	−6.24090			−0.740658			−0.370329	+	0.928901i	$0.620755\pi$
$72$		0			0
$73$	−7.37051	−	12.7661i	−0.862653	−	1.49416i	−0.869359	−	0.494181i	$-0.835468\pi$
$73$	−7.37051	−	12.7661i	−0.862653	−	1.49416i	0.00670577	−	0.999978i	$-0.497865\pi$
$74$	−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	0.750746	−	0.660591i	$-0.229694\pi$
$79$	4.92434	+	2.84307i	0.554031	+	0.319870i	−0.196715	+	0.980461i	$0.563027\pi$
$80$	−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	$-0.557489\pi$
$83$	−3.27295			−0.359253			−0.179626	+	0.983735i	$0.557489\pi$
$84$		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	$-0.152179\pi$
$89$	8.80546	+	5.08384i	0.933377	+	0.538886i	0.0454992	+	0.998964i	$0.485512\pi$
$90$		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	$-0.833398\pi$
$101$	−8.70650	+	5.02670i	−0.866330	+	0.500176i	−0.000202762		1.00000i	$0.500065\pi$
$102$		0			0
$103$	8.29973	+	4.79185i	0.817796	+	0.472155i	0.849656	−	0.527337i	$-0.176810\pi$
$103$	8.29973	+	4.79185i	0.817796	+	0.472155i	−0.0318595	+	0.999492i	$0.510143\pi$
$104$	−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	$-0.902021\pi$
$107$	−2.21486	+	3.83624i	−0.214118	+	0.370863i	0.738881	+	0.673836i	$0.235354\pi$
$108$		0			0
$109$	3.40807	+	5.90294i	0.326433	+	0.565399i	0.981801	−	0.189910i	$-0.0608198\pi$
$109$	3.40807	+	5.90294i	0.326433	+	0.565399i	−0.655368	+	0.755310i	$0.727486\pi$
$110$	−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	$0.228281\pi$
$127$			14.8137i			1.31450i	−0.753670	+	0.657252i	$0.771719\pi$
$128$	−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	$-0.867484\pi$
$131$	−1.22561	+	2.12281i	−0.107082	+	0.185471i	0.807505	+	0.589861i	$0.200817\pi$
$132$		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	$-0.658236\pi$
$137$	0.536858	−	0.309955i	0.0458669	−	0.0264812i	0.522758	+	0.852481i	$0.324903\pi$
$138$		0			0
$139$		−	2.00673i		−	0.170209i	−0.996372	−	0.0851044i	$-0.972878\pi$
$139$		−	2.00673i		−	0.170209i	0.996372	−	0.0851044i	$-0.0271224\pi$
$140$	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	$-0.425228\pi$
$149$	−6.01927	−	3.47523i	−0.493118	−	0.284702i	−0.725867	+	0.687835i	$0.758561\pi$
$150$		0			0
$151$	−12.9420	+	7.47207i	−1.05320	+	0.608068i	−0.923545	−	0.383490i	$-0.874722\pi$
$151$	−12.9420	+	7.47207i	−1.05320	+	0.608068i	−0.129660	+	0.991559i	$0.541389\pi$
$152$	−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	−0.988665	−	0.150135i	$-0.952029\pi$
$157$	−7.82313	−	13.5501i	−0.624354	−	1.08141i	0.364312	−	0.931277i	$-0.381304\pi$
$158$	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	0.725271	−	0.688464i	$-0.241715\pi$
$163$	6.27734	+	3.62422i	0.491679	+	0.283871i	−0.233592	+	0.972335i	$0.575048\pi$
$164$	−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	$-0.747183\pi$
$167$	−18.1132			−1.40164			−0.700822	+	0.713337i	$0.747183\pi$
$168$		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	$-0.200041\pi$
$173$	9.26339	+	5.34822i	0.704283	+	0.406618i	−0.104658	+	0.994508i	$0.533375\pi$
$174$		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	0.860364	+	0.509681i	$0.170236\pi$
$179$	11.6609	+	20.1973i	0.871578	+	1.50962i	0.0112146	+	0.999937i	$0.496430\pi$
$180$		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	$-0.942535\pi$
$191$	−4.64881	+	8.05197i	−0.336376	+	0.582620i	0.647372	+	0.762174i	$0.275868\pi$
$192$		0			0
$193$	3.54336	+	6.13728i	0.255056	+	0.441771i	0.964911	−	0.262578i	$-0.0845726\pi$
$193$	3.54336	+	6.13728i	0.255056	+	0.441771i	−0.709854	+	0.704348i	$0.751239\pi$
$194$	−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	0.394201	−	0.919024i	$-0.371021\pi$
$199$	19.5689	−	11.2981i	1.38720	−	0.800900i	0.992999	+	0.118124i	$0.0376880\pi$
$200$	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	$0.0387676\pi$
$211$			3.52953i			0.242983i	−0.992592	+	0.121491i	$0.961232\pi$
$212$	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	$-0.944616\pi$
$223$		−	5.17037i		−	0.346234i	0.984901	−	0.173117i	$-0.0553839\pi$
$224$	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	−0.974521	−	0.224296i	$-0.927992\pi$
$227$	−10.2679	−	17.7846i	−0.681507	−	1.18040i	0.293014	−	0.956108i	$-0.405342\pi$
$228$		0			0
$229$	5.10463	−	8.84148i	0.337323	−	0.584261i	−0.646605	−	0.762825i	$-0.723812\pi$
$229$	5.10463	−	8.84148i	0.337323	−	0.584261i	0.983928	+	0.178564i	$0.0571451\pi$
$230$	−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	$-0.267586\pi$
$233$	5.42215	+	3.13048i	0.355217	+	0.205085i	−0.311764	+	0.950160i	$0.600920\pi$
$234$		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	$-0.448373\pi$
$239$	4.99283			0.322959			0.161480	+	0.986876i	$0.448373\pi$
$240$		0			0
$241$	3.48576	+	6.03752i	0.224538	+	0.388911i	0.956181	−	0.292777i	$-0.0945795\pi$
$241$	3.48576	+	6.03752i	0.224538	+	0.388911i	−0.731643	+	0.681688i	$0.761246\pi$
$242$	−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	$-0.296128\pi$
$251$	18.9350			1.19516			0.597582	+	0.801808i	$0.296128\pi$
$252$		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	$-0.340933\pi$
$257$	−0.662857	−	0.382701i	−0.0413479	−	0.0238722i	−0.520531	+	0.853842i	$0.674266\pi$
$258$		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	$-0.0218342\pi$
$263$	7.12695	+	12.3442i	0.439466	+	0.761178i	−0.558182	+	0.829719i	$0.688501\pi$
$264$		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	$-0.572796\pi$
$269$	8.25667	−	4.76699i	0.503418	−	0.290649i	0.730124	+	0.683315i	$0.239462\pi$
$270$		0			0
$271$	−2.98753	−	1.72485i	−0.181479	−	0.104777i	0.406508	−	0.913647i	$-0.366746\pi$
$271$	−2.98753	−	1.72485i	−0.181479	−	0.104777i	−0.587988	+	0.808870i	$0.700080\pi$
$272$	−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	0.531841	−	0.846844i	$-0.321501\pi$
$277$	−7.78023	−	13.4757i	−0.467469	−	0.809679i	−0.999309	+	0.0371652i	$0.988167\pi$
$278$	−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	0.652940	−	0.757410i	$-0.273535\pi$
$283$	27.5108	−	15.8834i	1.63535	−	0.944167i	0.982406	−	0.186758i	$-0.0597979\pi$
$284$	−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	$-0.852010\pi$
$307$		−	15.7116i		−	0.896709i	0.893856	−	0.448355i	$-0.147990\pi$
$308$	−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	$-0.0419820\pi$
$311$	6.73255	+	11.6611i	0.381768	+	0.661241i	−0.609547	+	0.792750i	$0.708649\pi$
$312$		0			0
$313$	−6.18899	+	10.7196i	−0.349822	+	0.605910i	−0.986218	−	0.165453i	$-0.947091\pi$
$313$	−6.18899	+	10.7196i	−0.349822	+	0.605910i	0.636395	+	0.771363i	$0.280425\pi$
$314$	−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	$-0.160004\pi$
$317$	15.9748	+	9.22303i	0.897232	+	0.518017i	0.0209310	+	0.999781i	$0.493337\pi$
$318$		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	0.965329	−	0.261037i	$-0.0840646\pi$
$331$	22.2310	+	12.8351i	1.22193	+	0.705480i	0.256599	+	0.966518i	$0.417398\pi$
$332$	−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	$-0.185547\pi$
$347$	−1.10428	−	1.91268i	−0.0592811	−	0.102678i	−0.894143	+	0.447782i	$0.852214\pi$
$348$		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	−0.566922	+	0.823771i	$0.691866\pi$
$353$	−29.3810	+	16.9631i	−1.56379	+	0.902855i	−0.996868	+	0.0790836i	$0.974801\pi$
$354$		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	$-0.774461\pi$
$359$	3.48440	−	6.03516i	0.183900	−	0.318523i	0.943205	+	0.332211i	$0.107795\pi$
$360$		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	−0.542621	−	0.839978i	$-0.682568\pi$
$367$	−1.65689	+	0.956605i	−0.0864889	+	0.0499344i	0.456132	+	0.889912i	$0.349235\pi$
$368$	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	−0.952259	−	0.305291i	$-0.901246\pi$
$373$	−4.08938	+	7.08301i	−0.211740	+	0.366745i	0.740519	+	0.672035i	$0.234580\pi$
$374$	−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	$0.145428\pi$
$379$			17.1764i			0.882295i	−0.897435	+	0.441147i	$0.854572\pi$
$380$	−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	−0.406133	−	0.913814i	$-0.633123\pi$
$383$	11.5136	−	19.9422i	0.588320	−	1.01900i	0.994453	−	0.105186i	$-0.0335437\pi$
$384$		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	$-0.826448\pi$
$389$	−16.4368	+	9.48980i	−0.833380	+	0.481152i	0.0216286	+	0.999766i	$0.493115\pi$
$390$		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	−0.0166054	−	0.999862i	$-0.505286\pi$
$397$	17.0876	−	29.5966i	0.857603	−	1.48541i	0.874209	−	0.485550i	$-0.161381\pi$
$398$	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	$-0.439955\pi$
$401$	−11.4019	−	6.58287i	−0.569382	−	0.328733i	−0.756902	+	0.653528i	$0.773288\pi$
$402$		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	0.971774	+	0.235912i	$0.0758076\pi$
$409$	13.9583	+	24.1765i	0.690193	+	1.19545i	−0.281582	+	0.959537i	$0.590859\pi$
$410$	−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	$-0.211192\pi$
$419$	32.2539			1.57571			0.787854	+	0.615863i	$0.211192\pi$
$420$		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	−0.996457	−	0.0841006i	$-0.973198\pi$
$431$	−11.8556	−	20.5344i	−0.571062	−	0.989108i	0.425395	−	0.905008i	$-0.360135\pi$
$432$		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	0.467953	−	0.883753i	$-0.344992\pi$
$439$	−1.32885	−	0.767212i	−0.0634225	−	0.0366170i	−0.531376	+	0.847136i	$0.678325\pi$
$440$	−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	−0.273141	−	0.961974i	$-0.588063\pi$
$443$	14.6601	−	25.3921i	0.696523	−	1.20641i	0.969664	−	0.244440i	$-0.0786041\pi$
$444$		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	−0.915259	−	0.402866i	$-0.868014\pi$
$457$	−2.32454	+	4.02622i	−0.108737	+	0.188339i	0.806522	+	0.591205i	$0.201347\pi$
$458$	−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	$0.143311\pi$
$463$			18.7274i			0.870335i	−0.900349	+	0.435168i	$0.856689\pi$
$464$	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	$-0.974726\pi$
$467$	−9.28665	+	16.0849i	−0.429735	+	0.744323i	0.567115	+	0.823639i	$0.308060\pi$
$468$		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	$-0.0895835\pi$
$479$	5.24836	+	9.09043i	0.239804	+	0.415352i	−0.720854	+	0.693087i	$0.756250\pi$
$480$		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	−0.926185	−	0.377070i	$-0.876932\pi$
$487$	−23.4523	+	13.5402i	−1.06273	+	0.613565i	−0.136540	+	0.990635i	$0.543598\pi$
$488$	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	$-0.560644\pi$
$491$	−8.39226			−0.378737			−0.189369	+	0.981906i	$0.560644\pi$
$492$		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	0.804489	−	0.593967i	$-0.202439\pi$
$499$	15.4658	+	8.92917i	0.692343	+	0.399724i	−0.112146	+	0.993692i	$0.535772\pi$
$500$	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	$-0.611171\pi$
$503$	−15.3493			−0.684392			−0.342196	+	0.939629i	$0.611171\pi$
$504$		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	$-0.109240\pi$
$509$	25.2937	+	14.6033i	1.12112	+	0.647281i	0.179436	+	0.983770i	$0.442573\pi$
$510$		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	$-0.560069\pi$
$521$	12.9936	−	7.50183i	0.569258	−	0.328661i	0.756853	+	0.653585i	$0.226736\pi$
$522$		0			0
$523$	10.6638	+	6.15676i	0.466296	+	0.269216i	0.714688	−	0.699443i	$-0.246569\pi$
$523$	10.6638	+	6.15676i	0.466296	+	0.269216i	−0.248392	+	0.968660i	$0.579902\pi$
$524$	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	−0.475542	−	0.879693i	$-0.657748\pi$
$541$	12.1895	−	21.1128i	0.524066	−	0.907708i	0.999608	−	0.0280151i	$-0.00891864\pi$
$542$	−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	$0.195266\pi$
$547$			26.9284i			1.15138i	−0.817669	+	0.575688i	$0.804734\pi$
$548$	−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	$-0.692850\pi$
$557$	−3.35873	+	1.93917i	−0.142314	+	0.0821651i	0.427152	+	0.904180i	$0.359517\pi$
$558$		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	−0.861755	−	0.507325i	$-0.830634\pi$
$563$	−20.6486	−	35.7644i	−0.870234	−	1.50729i	−0.00847940	−	0.999964i	$-0.502699\pi$
$564$		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	$-0.269346\pi$
$569$	8.24961	+	4.76292i	0.345842	+	0.199672i	−0.317011	+	0.948422i	$0.602679\pi$
$570$		0			0
$571$	22.0822	−	12.7492i	0.924111	−	0.533536i	0.0391670	−	0.999233i	$-0.487530\pi$
$571$	22.0822	−	12.7492i	0.924111	−	0.533536i	0.884944	+	0.465697i	$0.154196\pi$
$572$	−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	0.798254	−	0.602320i	$-0.205757\pi$
$577$	−2.94249	−	5.09654i	−0.122498	−	0.212172i	−0.920752	+	0.390148i	$0.872424\pi$
$578$	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	$-0.391960\pi$
$587$	16.1329			0.665878			0.332939	+	0.942948i	$0.391960\pi$
$588$		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	$-0.275927\pi$
$593$	7.56550	+	4.36794i	0.310678	+	0.179370i	−0.336552	+	0.941665i	$0.609261\pi$
$594$		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	0.969281	+	0.245955i	$0.0791015\pi$
$599$	17.0745	+	29.5738i	0.697644	+	1.20835i	−0.271638	+	0.962400i	$0.587565\pi$
$600$		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	−0.0948125	−	0.995495i	$-0.530225\pi$
$607$	−24.7444	−	14.2862i	−1.00434	−	0.579858i	−0.909530	+	0.415638i	$0.863558\pi$
$608$	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	0.569895	−	0.821717i	$-0.306984\pi$
$613$	−10.5641	−	18.2976i	−0.426680	−	0.739032i	−0.996576	+	0.0826853i	$0.973650\pi$
$614$	−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	−0.242328	−	0.970194i	$-0.577911\pi$
$619$	11.8607	−	6.84777i	0.476721	−	0.275235i	0.719049	+	0.694959i	$0.244578\pi$
$620$	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	$-0.807860\pi$
$631$		−	28.5175i		−	1.13526i	0.823283	−	0.567631i	$-0.192140\pi$
$632$	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	$-0.816622\pi$
$641$	−19.9029	+	11.4909i	−0.786116	+	0.453864i	0.0524773	+	0.998622i	$0.483288\pi$
$642$		0			0
$643$			2.79085i			0.110060i	0.998485	+	0.0550302i	$0.0175255\pi$
$643$			2.79085i			0.110060i	−0.998485	+	0.0550302i	$0.982474\pi$
$644$	−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	0.914000	+	0.405715i	$0.132977\pi$
$647$	20.5616	+	35.6137i	0.808359	+	1.40012i	−0.105640	+	0.994404i	$0.533689\pi$
$648$		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	$-0.177456\pi$
$653$	20.8186	+	12.0196i	0.814694	+	0.470364i	−0.0338892	+	0.999426i	$0.510789\pi$
$654$		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	$-0.405347\pi$
$659$	15.0431			0.585995			0.292997	+	0.956113i	$0.405347\pi$
$660$		0			0
$661$	−10.7083	−	18.5474i	−0.416506	−	0.721409i	0.579079	−	0.815271i	$-0.303412\pi$
$661$	−10.7083	−	18.5474i	−0.416506	−	0.721409i	−0.995585	+	0.0938618i	$0.970079\pi$
$662$	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	0.998802	+	0.0489293i	$0.0155809\pi$
$677$	40.0846	+	23.1429i	1.54058	+	0.889453i	0.541775	+	0.840523i	$0.317752\pi$
$678$		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	−0.979837	−	0.199799i	$-0.935971\pi$
$683$	−17.3257	−	30.0090i	−0.662949	−	1.14826i	0.316888	−	0.948463i	$-0.397362\pi$
$684$		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	0.173941	−	0.984756i	$-0.444350\pi$
$691$	−15.5595	−	8.98330i	−0.591913	−	0.341741i	−0.765853	+	0.643015i	$0.777683\pi$
$692$	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	−0.674771	−	0.738027i	$-0.735757\pi$
$709$	8.03512	−	13.9172i	0.301765	−	0.522673i	0.976536	+	0.215355i	$0.0690908\pi$
$710$	−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	$-0.672744\pi$
$719$	12.9613	−	22.4496i	0.483374	−	0.837229i	0.999818	+	0.0190926i	$0.00607772\pi$
$720$		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	$0.145147\pi$
$727$			23.7464i			0.880706i	−0.897825	+	0.440353i	$0.854853\pi$
$728$	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	−0.644235	−	0.764828i	$-0.722824\pi$
$733$	9.21172	−	15.9552i	0.340243	−	0.589318i	0.984478	+	0.175510i	$0.0561574\pi$
$734$	−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	−0.259725	−	0.965683i	$-0.583632\pi$
$739$	12.1438	−	7.01125i	0.446718	−	0.257913i	0.706443	+	0.707770i	$0.250299\pi$
$740$	−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	$-0.866717\pi$
$743$	−49.8064			−1.82722			−0.913610	+	0.406592i	$0.866717\pi$
$744$		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	0.530433	−	0.847727i	$-0.322029\pi$
$751$	1.68526	+	0.972983i	0.0614959	+	0.0355047i	−0.468937	+	0.883232i	$0.655363\pi$
$752$	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	$-0.125109\pi$
$761$	29.0741	+	16.7859i	1.05393	+	0.608489i	0.130186	+	0.991490i	$0.458443\pi$
$762$		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	$-0.606268\pi$
$773$	9.08272	−	5.24391i	0.326683	−	0.188610i	0.654367	+	0.756177i	$0.272935\pi$
$774$		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	−0.367819	−	0.929898i	$-0.619895\pi$
$787$	7.11401	−	4.10728i	0.253587	−	0.146409i	0.621406	+	0.783489i	$0.286562\pi$
$788$	−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	$-0.453519\pi$
$809$	30.5781	−	17.6543i	1.07507	−	0.620691i	0.929562	+	0.368666i	$0.120185\pi$
$810$		0			0
$811$		−	3.31379i		−	0.116363i	−0.998306	−	0.0581815i	$-0.981470\pi$
$811$		−	3.31379i		−	0.116363i	0.998306	−	0.0581815i	$-0.0185302\pi$
$812$	−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	$-0.396810\pi$
$821$	−9.83140	−	5.67616i	−0.343118	−	0.198099i	−0.661650	+	0.749813i	$0.730144\pi$
$822$		0			0
$823$	−33.0277	+	19.0685i	−1.15127	+	0.664687i	−0.949197	−	0.314682i	$-0.898102\pi$
$823$	−33.0277	+	19.0685i	−1.15127	+	0.664687i	−0.202075	+	0.979370i	$0.564769\pi$
$824$	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	$-0.552905\pi$
$827$	−9.51543			−0.330884			−0.165442	+	0.986220i	$0.552905\pi$
$828$		0			0
$829$	14.5375	+	25.1798i	0.504910	+	0.874529i	0.999984	+	0.00567849i	$0.00180753\pi$
$829$	14.5375	+	25.1798i	0.504910	+	0.874529i	−0.495074	+	0.868851i	$0.664859\pi$
$830$	−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	$-0.505593\pi$
$839$	−1.01793			−0.0351429			−0.0175715	+	0.999846i	$0.505593\pi$
$840$		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	$-0.798486\pi$
$857$	−20.4031	+	11.7797i	−0.696956	+	0.402388i	0.109257	+	0.994014i	$0.465153\pi$
$858$		0			0
$859$	−0.285175	−	0.164646i	−0.00973004	−	0.00561764i	0.495127	−	0.868821i	$-0.335121\pi$
$859$	−0.285175	−	0.164646i	−0.00973004	−	0.00561764i	−0.504857	+	0.863203i	$0.668455\pi$
$860$	−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	0.0258325	+	0.999666i	$0.491776\pi$
$863$	−25.0532	+	43.3934i	−0.852820	+	1.47713i	−0.878653	+	0.477462i	$0.841557\pi$
$864$		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	−0.962836	−	0.270086i	$-0.912948\pi$
$877$	−7.33001	+	12.6959i	−0.247517	+	0.428712i	0.715319	+	0.698798i	$0.246281\pi$
$878$	−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	$0.188458\pi$
$883$			33.1664i			1.11614i	−0.829794	+	0.558070i	$0.811542\pi$
$884$	−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	$-0.716058\pi$
$887$	10.7263	−	18.5785i	0.360154	−	0.623804i	0.987986	+	0.154544i	$0.0493909\pi$
$888$		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	−0.573362	−	0.819302i	$-0.694361\pi$
$907$	−4.53272	+	2.61697i	−0.150507	+	0.0868951i	0.422855	+	0.906197i	$0.361028\pi$
$908$	−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	$-0.755529\pi$
$911$	−43.4199			−1.43857			−0.719283	+	0.694717i	$0.755529\pi$
$912$		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	0.718021	−	0.696022i	$-0.245048\pi$
$919$	14.3771	+	8.30065i	0.474258	+	0.273813i	−0.243762	+	0.969835i	$0.578382\pi$
$920$	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	$-0.451604\pi$
$929$	−19.1671	−	11.0661i	−0.628851	−	0.363067i	−0.780307	+	0.625397i	$0.784937\pi$
$930$		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	$-0.918438\pi$
$941$	−37.7784	+	21.8114i	−1.23154	+	0.711030i	−0.264190	+	0.964471i	$0.585104\pi$
$942$		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	$-0.968724\pi$
$947$	−12.6981	+	21.9938i	−0.412634	+	0.714702i	0.582543	+	0.812800i	$0.302058\pi$
$948$		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	$-0.852086\pi$
$967$		−	27.8714i		−	0.896282i	0.893963	−	0.448141i	$-0.147914\pi$
$968$	−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	$-0.673519\pi$
$971$	14.9960	−	25.9738i	0.481243	−	0.833538i	0.999768	+	0.0215245i	$0.00685200\pi$
$972$		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	$-0.649581\pi$
$977$	2.90454	−	1.67694i	0.0929246	−	0.0536500i	0.545742	+	0.837953i	$0.316248\pi$
$978$		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	$-0.307841\pi$
$983$	−13.4540	−	23.3029i	−0.429115	−	0.743249i	−0.996795	+	0.0800007i	$0.974508\pi$
$984$		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	0.192071	−	0.981381i	$-0.438480\pi$
$991$	35.8246	−	20.6834i	1.13801	−	0.657029i	0.945936	+	0.324352i	$0.105146\pi$
$992$	−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	0.717038	−	0.697034i	$-0.245497\pi$
$997$	−7.74005	−	13.4062i	−0.245130	−	0.424577i	−0.962168	+	0.272457i	$0.912164\pi$
$998$	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.107.12	yes	28
3.2	odd	2	inner	756.2.be.d.107.3	yes	28
4.3	odd	2		756.2.be.c.107.7	✓	28
7.4	even	3		756.2.be.c.431.8	yes	28
12.11	even	2		756.2.be.c.107.8	yes	28
21.11	odd	6		756.2.be.c.431.7	yes	28
28.11	odd	6	inner	756.2.be.d.431.3	yes	28
84.11	even	6	inner	756.2.be.d.431.12	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.7	✓	28	4.3	odd	2
756.2.be.c.107.8	yes	28	12.11	even	2
756.2.be.c.431.7	yes	28	21.11	odd	6
756.2.be.c.431.8	yes	28	7.4	even	3
756.2.be.d.107.3	yes	28	3.2	odd	2	inner
756.2.be.d.107.12	yes	28	1.1	even	1	trivial
756.2.be.d.431.3	yes	28	28.11	odd	6	inner
756.2.be.d.431.12	yes	28	84.11	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more