LMFDB - Embedded newform 441.2.i.d.68.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(68,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

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

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

chi := DirichletCharacter("441.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.2
Character	$\chi$	$=$	441.68
Dual form			441.2.i.d.227.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70883i q^{2} +(0.572034 + 1.63486i) q^{3} -5.33776 q^{4} +(0.601464 + 1.04177i) q^{5} +(4.42857 - 1.54954i) q^{6} +9.04141i q^{8} +(-2.34556 + 1.87039i) q^{9} +O(q^{10})$	\(q-2.70883i q^{2} +(0.572034 + 1.63486i) q^{3} -5.33776 q^{4} +(0.601464 + 1.04177i) q^{5} +(4.42857 - 1.54954i) q^{6} +9.04141i q^{8} +(-2.34556 + 1.87039i) q^{9} +(2.82197 - 1.62926i) q^{10} +(2.15351 + 1.24333i) q^{11} +(-3.05338 - 8.72650i) q^{12} +(1.63211 + 0.942300i) q^{13} +(-1.35909 + 1.57924i) q^{15} +13.8161 q^{16} +(0.601863 + 1.04246i) q^{17} +(5.06658 + 6.35371i) q^{18} +(6.46933 + 3.73507i) q^{19} +(-3.21047 - 5.56070i) q^{20} +(3.36797 - 5.83350i) q^{22} +(-2.63359 + 1.52050i) q^{23} +(-14.7815 + 5.17199i) q^{24} +(1.77648 - 3.07696i) q^{25} +(2.55253 - 4.42111i) q^{26} +(-4.39957 - 2.76473i) q^{27} +(-0.173847 + 0.100371i) q^{29} +(4.27788 + 3.68154i) q^{30} +3.50314i q^{31} -19.3427i q^{32} +(-0.800795 + 4.23193i) q^{33} +(2.82384 - 1.63034i) q^{34} +(12.5200 - 9.98370i) q^{36} +(-0.865458 + 1.49902i) q^{37} +(10.1177 - 17.5243i) q^{38} +(-0.606909 + 3.20731i) q^{39} +(-9.41904 + 5.43809i) q^{40} +(3.36029 - 5.82020i) q^{41} +(0.00656005 + 0.0113623i) q^{43} +(-11.4949 - 6.63660i) q^{44} +(-3.35928 - 1.31855i) q^{45} +(4.11878 + 7.13394i) q^{46} +1.43481 q^{47} +(7.90329 + 22.5875i) q^{48} +(-8.33495 - 4.81219i) q^{50} +(-1.35999 + 1.58028i) q^{51} +(-8.71182 - 5.02977i) q^{52} +(-8.58085 + 4.95416i) q^{53} +(-7.48919 + 11.9177i) q^{54} +2.99128i q^{55} +(-2.40565 + 12.7130i) q^{57} +(0.271887 + 0.470923i) q^{58} -12.2191 q^{59} +(7.25448 - 8.42958i) q^{60} +11.2457i q^{61} +9.48942 q^{62} -24.7638 q^{64} +2.26704i q^{65} +(11.4636 + 2.16922i) q^{66} -5.15865 q^{67} +(-3.21260 - 5.56438i) q^{68} +(-3.99231 - 3.43578i) q^{69} -12.0452i q^{71} +(-16.9110 - 21.2071i) q^{72} +(7.51020 - 4.33602i) q^{73} +(4.06058 + 2.34438i) q^{74} +(6.04661 + 1.14418i) q^{75} +(-34.5317 - 19.9369i) q^{76} +(8.68805 + 1.64401i) q^{78} +5.49601 q^{79} +(8.30991 + 14.3932i) q^{80} +(2.00326 - 8.77422i) q^{81} +(-15.7659 - 9.10246i) q^{82} +(1.60854 + 2.78607i) q^{83} +(-0.723998 + 1.25400i) q^{85} +(0.0307786 - 0.0177700i) q^{86} +(-0.263539 - 0.226801i) q^{87} +(-11.2415 + 19.4708i) q^{88} +(3.98364 - 6.89986i) q^{89} +(-3.57172 + 9.09972i) q^{90} +(14.0574 - 8.11607i) q^{92} +(-5.72716 + 2.00392i) q^{93} -3.88665i q^{94} +8.98604i q^{95} +(31.6227 - 11.0647i) q^{96} +(2.06260 - 1.19084i) q^{97} +(-7.37671 + 1.11162i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 - 8 * q^9	$ 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	2.70883i		−	1.91543i	−0.287716	−	0.957716i	$-0.592896\pi$
$2$		−	2.70883i		−	1.91543i	0.287716	−	0.957716i	$-0.407104\pi$
$3$	0.572034	+	1.63486i	0.330264	+	0.943889i
$3$	0.572034	+	1.63486i	0.330264	+	0.943889i
$4$	−5.33776			−2.66888
$5$	0.601464	+	1.04177i	0.268983	+	0.465892i	0.968599	−	0.248626i	$-0.0799791\pi$
$5$	0.601464	+	1.04177i	0.268983	+	0.465892i	−0.699616	+	0.714519i	$0.746646\pi$
$6$	4.42857	−	1.54954i	1.80795	−	0.632598i
$7$		0			0
$7$		0			0
$8$			9.04141i			3.19662i
$9$	−2.34556	+	1.87039i	−0.781852	+	0.623464i
$10$	2.82197	−	1.62926i	0.892385	−	0.515219i
$11$	2.15351	+	1.24333i	0.649309	+	0.374879i	0.788191	−	0.615430i	$-0.211018\pi$
$11$	2.15351	+	1.24333i	0.649309	+	0.374879i	−0.138882	+	0.990309i	$0.544351\pi$
$12$	−3.05338	−	8.72650i	−0.881434	−	2.51912i
$13$	1.63211	+	0.942300i	0.452666	+	0.261347i	0.708956	−	0.705253i	$-0.249167\pi$
$13$	1.63211	+	0.942300i	0.452666	+	0.261347i	−0.256289	+	0.966600i	$0.582500\pi$
$14$		0			0
$15$	−1.35909	+	1.57924i	−0.350915	+	0.407757i
$16$	13.8161			3.45403
$17$	0.601863	+	1.04246i	0.145973	+	0.252833i	0.929736	−	0.368228i	$-0.120035\pi$
$17$	0.601863	+	1.04246i	0.145973	+	0.252833i	−0.783762	+	0.621061i	$0.786702\pi$
$18$	5.06658	+	6.35371i	1.19420	+	1.49758i
$19$	6.46933	+	3.73507i	1.48417	+	0.856883i	0.999838	−	0.0180038i	$-0.00573111\pi$
$19$	6.46933	+	3.73507i	1.48417	+	0.856883i	0.484327	+	0.874887i	$0.339064\pi$
$20$	−3.21047	−	5.56070i	−0.717883	−	1.24341i
$21$		0			0
$22$	3.36797	−	5.83350i	0.718054	−	1.24371i
$23$	−2.63359	+	1.52050i	−0.549141	+	0.317047i	−0.748775	−	0.662824i	$-0.769358\pi$
$23$	−2.63359	+	1.52050i	−0.549141	+	0.317047i	0.199634	+	0.979870i	$0.436025\pi$
$24$	−14.7815	+	5.17199i	−3.01725	+	1.05573i
$25$	1.77648	−	3.07696i	0.355296	−	0.615391i
$26$	2.55253	−	4.42111i	0.500592	−	0.867052i
$27$	−4.39957	−	2.76473i	−0.846698	−	0.532073i
$28$		0			0
$29$	−0.173847	+	0.100371i	−0.0322826	+	0.0186384i	−0.516054	−	0.856556i	$-0.672600\pi$
$29$	−0.173847	+	0.100371i	−0.0322826	+	0.0186384i	0.483772	+	0.875194i	$0.339266\pi$
$30$	4.27788	+	3.68154i	0.781031	+	0.672154i
$31$			3.50314i			0.629183i	0.949227	+	0.314592i	$0.101868\pi$
$31$			3.50314i			0.629183i	−0.949227	+	0.314592i	$0.898132\pi$
$32$		−	19.3427i		−	3.41934i
$33$	−0.800795	+	4.23193i	−0.139401	+	0.736684i
$34$	2.82384	−	1.63034i	0.484285	−	0.279602i
$35$		0			0
$36$	12.5200	−	9.98370i	2.08667	−	1.66395i
$37$	−0.865458	+	1.49902i	−0.142280	+	0.246437i	−0.928355	−	0.371695i	$-0.878777\pi$
$37$	−0.865458	+	1.49902i	−0.142280	+	0.246437i	0.786075	+	0.618132i	$0.212110\pi$
$38$	10.1177	−	17.5243i	1.64130	−	2.84282i
$39$	−0.606909	+	3.20731i	−0.0971832	+	0.513580i
$40$	−9.41904	+	5.43809i	−1.48928	+	0.859837i
$41$	3.36029	−	5.82020i	0.524790	−	0.908963i	−0.474793	−	0.880097i	$-0.657477\pi$
$41$	3.36029	−	5.82020i	0.524790	−	0.908963i	0.999583	−	0.0288655i	$-0.00918944\pi$
$42$		0			0
$43$	0.00656005	+	0.0113623i	0.00100040	+	0.00173274i	0.866525	−	0.499133i	$-0.166348\pi$
$43$	0.00656005	+	0.0113623i	0.00100040	+	0.00173274i	−0.865525	+	0.500866i	$0.833015\pi$
$44$	−11.4949	−	6.63660i	−1.73293	−	1.00051i
$45$	−3.35928	−	1.31855i	−0.500772	−	0.196557i
$46$	4.11878	+	7.13394i	0.607281	+	1.05184i
$47$	1.43481			0.209288			0.104644	−	0.994510i	$-0.466630\pi$
$47$	1.43481			0.209288			0.104644	+	0.994510i	$0.466630\pi$
$48$	7.90329	+	22.5875i	1.14074	+	3.26022i
$49$		0			0
$50$	−8.33495	−	4.81219i	−1.17874	−	0.680546i
$51$	−1.35999	+	1.58028i	−0.190437	+	0.221284i
$52$	−8.71182	−	5.02977i	−1.20811	−	0.697504i
$53$	−8.58085	+	4.95416i	−1.17867	+	0.680506i	−0.955707	−	0.294321i	$-0.904906\pi$
$53$	−8.58085	+	4.95416i	−1.17867	+	0.680506i	−0.222964	+	0.974827i	$0.571573\pi$
$54$	−7.48919	+	11.9177i	−1.01915	+	1.62179i
$55$			2.99128i			0.403344i
$56$		0			0
$57$	−2.40565	+	12.7130i	−0.318636	+	1.68388i
$58$	0.271887	+	0.470923i	0.0357005	+	0.0618352i
$59$	−12.2191			−1.59079			−0.795394	−	0.606092i	$-0.792736\pi$
$59$	−12.2191			−1.59079			−0.795394	+	0.606092i	$0.792736\pi$
$60$	7.25448	−	8.42958i	0.936549	−	1.08825i
$61$			11.2457i			1.43986i	0.694047	+	0.719930i	$0.255826\pi$
$61$			11.2457i			1.43986i	−0.694047	+	0.719930i	$0.744174\pi$
$62$	9.48942			1.20516
$63$		0			0
$64$	−24.7638			−3.09548
$65$			2.26704i			0.281192i
$66$	11.4636	+	2.16922i	1.41107	+	0.267012i
$67$	−5.15865			−0.630229			−0.315115	−	0.949054i	$-0.602043\pi$
$67$	−5.15865			−0.630229			−0.315115	+	0.949054i	$0.602043\pi$
$68$	−3.21260	−	5.56438i	−0.389585	−	0.674781i
$69$	−3.99231	−	3.43578i	−0.480618	−	0.413619i
$70$		0			0
$71$		−	12.0452i		−	1.42950i	−0.699379	−	0.714751i	$-0.746540\pi$
$71$		−	12.0452i		−	1.42950i	0.699379	−	0.714751i	$-0.253460\pi$
$72$	−16.9110	−	21.2071i	−1.99298	−	2.49928i
$73$	7.51020	−	4.33602i	0.879003	−	0.507493i	0.00867336	−	0.999962i	$-0.497239\pi$
$73$	7.51020	−	4.33602i	0.879003	−	0.507493i	0.870330	+	0.492470i	$0.163906\pi$
$74$	4.06058	+	2.34438i	0.472033	+	0.272528i
$75$	6.04661	+	1.14418i	0.698202	+	0.132119i
$76$	−34.5317	−	19.9369i	−3.96106	−	2.28692i
$77$		0			0
$78$	8.68805	+	1.64401i	0.983728	+	0.186148i
$79$	5.49601			0.618350			0.309175	−	0.951005i	$-0.399947\pi$
$79$	5.49601			0.618350			0.309175	+	0.951005i	$0.399947\pi$
$80$	8.30991	+	14.3932i	0.929076	+	1.60921i
$81$	2.00326	−	8.77422i	0.222584	−	0.974913i
$82$	−15.7659	−	9.10246i	−1.74106	−	1.00520i
$83$	1.60854	+	2.78607i	0.176560	+	0.305811i	0.940700	−	0.339239i	$-0.110170\pi$
$83$	1.60854	+	2.78607i	0.176560	+	0.305811i	−0.764140	+	0.645051i	$0.776836\pi$
$84$		0			0
$85$	−0.723998	+	1.25400i	−0.0785286	+	0.136016i
$86$	0.0307786	−	0.0177700i	0.00331894	−	0.00191619i
$87$	−0.263539	−	0.226801i	−0.0282543	−	0.0243156i
$88$	−11.2415	+	19.4708i	−1.19835	+	2.07559i
$89$	3.98364	−	6.89986i	0.422265	−	0.731384i	−0.573896	−	0.818928i	$-0.694569\pi$
$89$	3.98364	−	6.89986i	0.422265	−	0.731384i	0.996161	+	0.0875442i	$0.0279019\pi$
$90$	−3.57172	+	9.09972i	−0.376492	+	0.959195i
$91$		0			0
$92$	14.0574	−	8.11607i	1.46559	−	0.846159i
$93$	−5.72716	+	2.00392i	−0.593879	+	0.207796i
$94$		−	3.88665i		−	0.400877i
$95$			8.98604i			0.921948i
$96$	31.6227	−	11.0647i	3.22748	−	1.12928i
$97$	2.06260	−	1.19084i	0.209425	−	0.120912i	−0.391619	−	0.920128i	$-0.628085\pi$
$97$	2.06260	−	1.19084i	0.209425	−	0.120912i	0.601044	+	0.799216i	$0.294751\pi$
$98$		0			0
$99$	−7.37671	+	1.11162i	−0.741387	+	0.111722i
$100$	−9.48242	+	16.4240i	−0.948242	+	1.64240i
$101$	−4.73272	+	8.19730i	−0.470923	+	0.815662i	−0.999447	−	0.0332561i	$-0.989412\pi$
$101$	−4.73272	+	8.19730i	−0.470923	+	0.815662i	0.528524	+	0.848918i	$0.322746\pi$
$102$	4.28072	+	3.68398i	0.423855	+	0.364768i
$103$	14.9460	−	8.62908i	1.47267	−	0.850249i	0.473147	−	0.880984i	$-0.343118\pi$
$103$	14.9460	−	8.62908i	1.47267	−	0.850249i	0.999528	+	0.0307347i	$0.00978469\pi$
$104$	−8.51973	+	14.7566i	−0.835428	+	1.44700i
$105$		0			0
$106$	13.4200	+	23.2441i	1.30346	+	2.25766i
$107$	8.55935	+	4.94175i	0.827464	+	0.477737i	0.852984	−	0.521938i	$-0.174791\pi$
$107$	8.55935	+	4.94175i	0.827464	+	0.477737i	−0.0255196	+	0.999674i	$0.508124\pi$
$108$	23.4839	+	14.7575i	2.25973	+	1.42004i
$109$	−5.20678	−	9.01841i	−0.498719	−	0.863807i	0.501280	−	0.865285i	$-0.332863\pi$
$109$	−5.20678	−	9.01841i	−0.498719	−	0.863807i	−0.999999	+	0.00147852i	$0.999529\pi$
$110$	8.10286			0.772578
$111$	−2.94576	−	0.557417i	−0.279599	−	0.0529077i
$112$		0			0
$113$	−9.56137	−	5.52026i	−0.899458	−	0.519303i	−0.0224339	−	0.999748i	$-0.507142\pi$
$113$	−9.56137	−	5.52026i	−0.899458	−	0.519303i	−0.877024	+	0.480446i	$0.840475\pi$
$114$	34.4375	+	6.51650i	3.22536	+	0.610326i
$115$	−3.16802	−	1.82906i	−0.295419	−	0.170560i
$116$	0.927954	−	0.535755i	0.0861584	−	0.0497436i
$117$	−5.59068	+	0.842474i	−0.516859	+	0.0778868i
$118$			33.0994i			3.04705i
$119$		0			0
$120$	−14.2785	−	12.2881i	−1.30345	−	1.12174i
$121$	−2.40825	−	4.17121i	−0.218932	−	0.379201i
$122$	30.4626			2.75795
$123$	11.4374	+	2.16427i	1.03128	+	0.195146i
$124$		−	18.6989i		−	1.67921i
$125$	10.2886			0.920241
$126$		0			0
$127$	13.8634			1.23018			0.615090	−	0.788457i	$-0.289119\pi$
$127$	13.8634			1.23018			0.615090	+	0.788457i	$0.289119\pi$
$128$			28.3956i			2.50984i
$129$	−0.0148233	+	0.0172244i	−0.00130512	+	0.00151653i
$130$	6.14102			0.538603
$131$	−6.17975	−	10.7036i	−0.539927	−	0.935181i	−0.998907	−	0.0467344i	$-0.985119\pi$
$131$	−6.17975	−	10.7036i	−0.539927	−	0.935181i	0.458981	−	0.888446i	$-0.348215\pi$
$132$	4.27445	−	22.5890i	0.372043	−	1.96612i
$133$		0			0
$134$			13.9739i			1.20716i
$135$	0.234021	−	6.24622i	0.0201413	−	0.537589i
$136$	−9.42529	+	5.44169i	−0.808212	+	0.466621i
$137$	−10.0991	−	5.83070i	−0.862822	−	0.498150i	0.00213432	−	0.999998i	$-0.499321\pi$
$137$	−10.0991	−	5.83070i	−0.862822	−	0.498150i	−0.864956	+	0.501847i	$0.832654\pi$
$138$	−9.30693	+	10.8145i	−0.792259	+	0.920591i
$139$	8.73893	+	5.04543i	0.741227	+	0.427947i	0.822515	−	0.568743i	$-0.192570\pi$
$139$	8.73893	+	5.04543i	0.741227	+	0.427947i	−0.0812884	+	0.996691i	$0.525903\pi$
$140$		0			0
$141$	0.820757	+	2.34571i	0.0691202	+	0.197545i
$142$	−32.6284			−2.73811
$143$	2.34318	+	4.05851i	0.195947	+	0.339390i
$144$	−32.4065	+	25.8416i	−2.70054	+	2.15347i
$145$	−0.209126	−	0.120739i	−0.0173670	−	0.0100268i
$146$	−11.7455	−	20.3439i	−0.972067	−	1.68367i
$147$		0			0
$148$	4.61960	−	8.00138i	0.379729	−	0.657710i
$149$	−4.15010	+	2.39606i	−0.339990	+	0.196293i	−0.660267	−	0.751031i	$-0.729557\pi$
$149$	−4.15010	+	2.39606i	−0.339990	+	0.196293i	0.320278	+	0.947324i	$0.396224\pi$
$150$	3.09939	−	16.3792i	0.253064	−	1.33736i
$151$	5.65924	−	9.80209i	0.460542	−	0.797683i	−0.538446	−	0.842660i	$-0.680988\pi$
$151$	5.65924	−	9.80209i	0.460542	−	0.797683i	0.998988	+	0.0449774i	$0.0143216\pi$
$152$	−33.7703	+	58.4918i	−2.73913	+	4.74431i
$153$	−3.36151	−	1.31942i	−0.271762	−	0.106669i
$154$		0			0
$155$	−3.64946	+	2.10702i	−0.293132	+	0.169240i
$156$	3.23953	−	17.1198i	0.259370	−	1.37068i
$157$			14.7316i			1.17571i	0.808966	+	0.587856i	$0.200028\pi$
$157$			14.7316i			1.17571i	−0.808966	+	0.587856i	$0.799972\pi$
$158$		−	14.8878i		−	1.18441i
$159$	−13.0079	−	11.1946i	−1.03159	−	0.887787i
$160$	20.1506	−	11.6339i	1.59304	−	0.919744i
$161$		0			0
$162$	−23.7679	−	5.42648i	−1.86738	−	0.426345i
$163$	9.07900	−	15.7253i	0.711122	−	1.23170i	−0.253314	−	0.967384i	$-0.581521\pi$
$163$	9.07900	−	15.7253i	0.711122	−	1.23170i	0.964436	−	0.264316i	$-0.0851460\pi$
$164$	−17.9364	+	31.0668i	−1.40060	+	2.42591i
$165$	−4.89033	+	1.71111i	−0.380712	+	0.133210i
$166$	7.54700	−	4.35726i	0.585761	−	0.338189i
$167$	0.599436	−	1.03825i	0.0463857	−	0.0803425i	−0.841900	−	0.539633i	$-0.818563\pi$
$167$	0.599436	−	1.03825i	0.0463857	−	0.0803425i	0.888286	+	0.459291i	$0.151896\pi$
$168$		0			0
$169$	−4.72414	−	8.18245i	−0.363395	−	0.629419i
$170$	3.39688	+	1.96119i	0.260529	+	0.150416i
$171$	−22.1602	+	3.33938i	−1.69463	+	0.255369i
$172$	−0.0350159	−	0.0606494i	−0.00266994	−	0.00462447i
$173$	−18.0081			−1.36913			−0.684564	−	0.728953i	$-0.740007\pi$
$173$	−18.0081			−1.36913			−0.684564	+	0.728953i	$0.740007\pi$
$174$	−0.614365	+	0.713882i	−0.0465749	+	0.0541193i
$175$		0			0
$176$	29.7532	+	17.1780i	2.24273	+	1.29484i
$177$	−6.98973	−	19.9765i	−0.525380	−	1.50153i
$178$	−18.6906	−	10.7910i	−1.40092	−	0.808819i
$179$	13.1137	−	7.57118i	0.980162	−	0.565897i	0.0778428	−	0.996966i	$-0.475197\pi$
$179$	13.1137	−	7.57118i	0.980162	−	0.565897i	0.902319	+	0.431069i	$0.141863\pi$
$180$	17.9310	+	7.03808i	1.33650	+	0.524587i
$181$			7.98716i			0.593681i	0.954927	+	0.296840i	$0.0959329\pi$
$181$			7.98716i			0.593681i	−0.954927	+	0.296840i	$0.904067\pi$
$182$		0			0
$183$	−18.3851	+	6.43290i	−1.35907	+	0.475534i
$184$	−13.7475	−	23.8114i	−1.01348	−	1.75540i
$185$	−2.08217			−0.153084
$186$	5.42827	+	15.5139i	0.398020	+	1.13753i
$187$			2.99326i			0.218889i
$188$	−7.65865			−0.558564
$189$		0			0
$190$	24.3416			1.76593
$191$			16.0170i			1.15895i	0.814991	+	0.579473i	$0.196742\pi$
$191$			16.0170i			1.15895i	−0.814991	+	0.579473i	$0.803258\pi$
$192$	−14.1657	−	40.4855i	−1.02232	−	2.92179i
$193$	−13.7094			−0.986821			−0.493410	−	0.869797i	$-0.664250\pi$
$193$	−13.7094			−0.986821			−0.493410	+	0.869797i	$0.664250\pi$
$194$	−3.22579	−	5.58724i	−0.231598	−	0.401140i
$195$	−3.70630	+	1.29682i	−0.265414	+	0.0928674i
$196$		0			0
$197$		−	18.9248i		−	1.34834i	−0.738577	−	0.674170i	$-0.764502\pi$
$197$		−	18.9248i		−	1.34834i	0.738577	−	0.674170i	$-0.235498\pi$
$198$	3.01118	+	19.9822i	0.213995	+	1.42008i
$199$	21.5055	−	12.4162i	1.52449	−	0.880163i	0.524908	−	0.851159i	$-0.324100\pi$
$199$	21.5055	−	12.4162i	1.52449	−	0.880163i	0.999579	−	0.0290036i	$-0.00923344\pi$
$200$	27.8200	+	16.0619i	1.96717	+	1.13575i
$201$	−2.95092	−	8.43368i	−0.208142	−	0.594866i
$202$	22.2051	+	12.8201i	1.56235	+	0.902020i
$203$		0			0
$204$	7.25929	−	8.43517i	0.508252	−	0.590580i
$205$	8.08439			0.564638
$206$	−23.3747	−	40.4862i	−1.62859	−	2.82081i
$207$	3.33329	−	8.49227i	0.231679	−	0.590253i
$208$	22.5495	+	13.0189i	1.56352	+	0.902701i
$209$	9.28786	+	16.0870i	0.642454	+	1.11276i
$210$		0			0
$211$	3.60761	−	6.24857i	0.248358	−	0.430169i	−0.714712	−	0.699419i	$-0.753442\pi$
$211$	3.60761	−	6.24857i	0.248358	−	0.430169i	0.963070	+	0.269250i	$0.0867757\pi$
$212$	45.8025	−	26.4441i	3.14573	−	1.81619i
$213$	19.6923	−	6.89026i	1.34929	−	0.472113i
$214$	13.3863	−	23.1858i	0.915072	−	1.58495i
$215$	−0.00789127	+	0.0136681i	−0.000538180	+	0.000932155i
$216$	24.9971	−	39.7784i	1.70084	−	2.70657i
$217$		0			0
$218$	−24.4293	+	14.1043i	−1.65456	+	0.955262i
$219$	11.3849	+	9.79781i	0.769319	+	0.662074i
$220$		−	15.9667i		−	1.07648i
$221$			2.26854i			0.152599i
$222$	−1.50995	+	7.97956i	−0.101341	+	0.535553i
$223$	−21.0706	+	12.1651i	−1.41099	+	0.814635i	−0.995482	−	0.0949545i	$-0.969729\pi$
$223$	−21.0706	+	12.1651i	−1.41099	+	0.814635i	−0.415508	+	0.909590i	$0.636396\pi$
$224$		0			0
$225$	1.58828	+	10.5399i	0.105886	+	0.702659i
$226$	−14.9534	+	25.9001i	−0.994688	+	1.72285i
$227$	−0.240288	+	0.416192i	−0.0159485	+	0.0276236i	−0.873890	−	0.486125i	$-0.838410\pi$
$227$	−0.240288	+	0.416192i	−0.0159485	+	0.0276236i	0.857941	+	0.513748i	$0.171743\pi$
$228$	12.8408	−	67.8591i	0.850401	−	4.49408i
$229$	−7.80442	+	4.50588i	−0.515730	+	0.297757i	−0.735186	−	0.677865i	$-0.762905\pi$
$229$	−7.80442	+	4.50588i	−0.515730	+	0.297757i	0.219456	+	0.975622i	$0.429572\pi$
$230$	−4.95460	+	8.58162i	−0.326697	+	0.565855i
$231$		0			0
$232$	−0.907493	−	1.57182i	−0.0595799	−	0.103195i
$233$	−9.62742	−	5.55840i	−0.630713	−	0.364143i	0.150315	−	0.988638i	$-0.451971\pi$
$233$	−9.62742	−	5.55840i	−0.630713	−	0.364143i	−0.781028	+	0.624496i	$0.785305\pi$
$234$	2.28212	+	15.1442i	0.149187	+	0.990007i
$235$	0.862985	+	1.49473i	0.0562949	+	0.0975057i
$236$	65.2225			4.24562
$237$	3.14390	+	8.98523i	0.204219	+	0.583653i
$238$		0			0
$239$	12.0446	+	6.95395i	0.779100	+	0.449813i	0.836111	−	0.548560i	$-0.184824\pi$
$239$	12.0446	+	6.95395i	0.779100	+	0.449813i	−0.0570114	+	0.998374i	$0.518157\pi$
$240$	−18.7773	+	21.8189i	−1.21207	+	1.40841i
$241$	−10.7181	−	6.18807i	−0.690411	−	0.398609i	0.113355	−	0.993555i	$-0.463840\pi$
$241$	−10.7181	−	6.18807i	−0.690411	−	0.398609i	−0.803766	+	0.594946i	$0.797173\pi$
$242$	−11.2991	+	6.52354i	−0.726334	+	0.419349i
$243$	15.4906	−	1.74410i	0.993721	−	0.111884i
$244$		−	60.0266i		−	3.84281i
$245$		0			0
$246$	5.86264	−	30.9821i	0.373788	−	1.97534i
$247$	7.03911	+	12.1921i	0.447888	+	0.775764i
$248$	−31.6734			−2.01126
$249$	−3.63471	+	4.22347i	−0.230340	+	0.267652i
$250$		−	27.8701i		−	1.76266i
$251$	−19.7147			−1.24438			−0.622191	−	0.782866i	$-0.713757\pi$
$251$	−19.7147			−1.24438			−0.622191	+	0.782866i	$0.713757\pi$
$252$		0			0
$253$	−7.56196			−0.475416
$254$		−	37.5537i		−	2.35633i
$255$	−2.46427	−	0.466307i	−0.154319	−	0.0292013i
$256$	27.3911			1.71195
$257$	−5.62025	−	9.73456i	−0.350581	−	0.607225i	0.635770	−	0.771879i	$-0.280683\pi$
$257$	−5.62025	−	9.73456i	−0.350581	−	0.607225i	−0.986351	+	0.164654i	$0.947349\pi$
$258$	0.0466580	+	0.0401538i	0.00290480	+	0.00249987i
$259$		0			0
$260$		−	12.1009i		−	0.750466i
$261$	0.220036	−	0.560588i	0.0136199	−	0.0346995i
$262$	−28.9943	+	16.7399i	−1.79127	+	1.03419i
$263$	2.82146	+	1.62897i	0.173979	+	0.100447i	0.584461	−	0.811422i	$-0.301306\pi$
$263$	2.82146	+	1.62897i	0.173979	+	0.100447i	−0.410482	+	0.911869i	$0.634640\pi$
$264$	−38.2626	−	7.24032i	−2.35490	−	0.445611i
$265$	−10.3221	−	5.95949i	−0.634084	−	0.366089i
$266$		0			0
$267$	13.5591	+	2.56575i	0.829804	+	0.157021i
$268$	27.5356			1.68200
$269$	−0.121147	−	0.209832i	−0.00738644	−	0.0127937i	0.862309	−	0.506383i	$-0.169018\pi$
$269$	−0.121147	−	0.209832i	−0.00738644	−	0.0127937i	−0.869695	+	0.493590i	$0.835685\pi$
$270$	−16.9199	−	0.633923i	−1.02971	−	0.0385793i
$271$	0.929287	+	0.536524i	0.0564502	+	0.0325915i	0.527959	−	0.849270i	$-0.322957\pi$
$271$	0.929287	+	0.536524i	0.0564502	+	0.0325915i	−0.471509	+	0.881861i	$0.656291\pi$
$272$	8.31542	+	14.4027i	0.504196	+	0.873294i
$273$		0			0
$274$	−15.7944	+	27.3567i	−0.954173	+	1.65268i
$275$	7.65136	−	4.41751i	0.461394	−	0.266386i
$276$	21.3100	+	18.3393i	1.28271	+	1.10390i
$277$	2.45076	−	4.24485i	0.147252	−	0.255048i	−0.782959	−	0.622074i	$-0.786290\pi$
$277$	2.45076	−	4.24485i	0.147252	−	0.255048i	0.930211	+	0.367025i	$0.119624\pi$
$278$	13.6672	−	23.6723i	0.819704	−	1.41977i
$279$	−6.55226	−	8.21682i	−0.392273	−	0.491928i
$280$		0			0
$281$	11.5613	−	6.67494i	0.689691	−	0.398194i	−0.113805	−	0.993503i	$-0.536304\pi$
$281$	11.5613	−	6.67494i	0.689691	−	0.398194i	0.803496	+	0.595310i	$0.202971\pi$
$282$	6.35413	−	2.22329i	0.378383	−	0.132395i
$283$			3.75657i			0.223305i	0.993747	+	0.111653i	$0.0356144\pi$
$283$			3.75657i			0.223305i	−0.993747	+	0.111653i	$0.964386\pi$
$284$			64.2943i			3.81517i
$285$	−14.6909	+	5.14032i	−0.870216	+	0.304486i
$286$	10.9938	−	6.34729i	0.650078	−	0.375323i
$287$		0			0
$288$	36.1785	+	45.3694i	2.13184	+	2.67342i
$289$	7.77552	−	13.4676i	0.457384	−	0.792212i
$290$	−0.327061	+	0.566486i	−0.0192057	+	0.0332652i
$291$	3.12674	+	2.69087i	0.183293	+	0.157742i
$292$	−40.0876	+	23.1446i	−2.34595	+	1.35444i
$293$	6.38430	−	11.0579i	0.372975	−	0.646011i	−0.617047	−	0.786926i	$-0.711671\pi$
$293$	6.38430	−	11.0579i	0.372975	−	0.646011i	0.990022	+	0.140915i	$0.0450045\pi$
$294$		0			0
$295$	−7.34934	−	12.7294i	−0.427895	−	0.741136i
$296$	−13.5532	−	7.82496i	−0.787765	−	0.454816i
$297$	−6.03706	−	11.4240i	−0.350306	−	0.662889i
$298$	6.49052	+	11.2419i	0.375986	+	0.651227i
$299$	−5.73108			−0.331437
$300$	−32.2753	−	6.10736i	−1.86342	−	0.352609i
$301$		0			0
$302$	−26.5522	−	15.3299i	−1.52791	−	0.882137i
$303$	−16.1087	−	3.04821i	−0.925423	−	0.175115i
$304$	89.3810	+	51.6042i	5.12635	+	2.95970i
$305$	−11.7154	+	6.76387i	−0.670819	+	0.387298i
$306$	−3.57409	+	9.10575i	−0.204317	+	0.520541i
$307$		−	10.7257i		−	0.612148i	−0.952008	−	0.306074i	$-0.900984\pi$
$307$		−	10.7257i		−	0.612148i	0.952008	−	0.306074i	$-0.0990155\pi$
$308$		0			0
$309$	22.6570	+	19.4986i	1.28891	+	1.10923i
$310$	5.70755	+	9.88576i	0.324167	+	0.561473i
$311$	18.8349			1.06803			0.534013	−	0.845476i	$-0.320683\pi$
$311$	18.8349			1.06803			0.534013	+	0.845476i	$0.320683\pi$
$312$	−28.9986	−	5.48731i	−1.64172	−	0.310658i
$313$			26.0702i			1.47357i	0.676125	+	0.736787i	$0.263658\pi$
$313$			26.0702i			1.47357i	−0.676125	+	0.736787i	$0.736342\pi$
$314$	39.9054			2.25199
$315$		0			0
$316$	−29.3364			−1.65030
$317$			13.8899i			0.780134i	0.920786	+	0.390067i	$0.127548\pi$
$317$			13.8899i			0.780134i	−0.920786	+	0.390067i	$0.872452\pi$
$318$	−30.3242	+	35.2362i	−1.70050	+	1.97595i
$319$	−0.499177			−0.0279485
$320$	−14.8946	−	25.7981i	−0.832631	−	1.44216i
$321$	−3.18284	+	16.8202i	−0.177649	+	0.938813i
$322$		0			0
$323$			8.99200i			0.500328i
$324$	−10.6929	+	46.8347i	−0.594050	+	2.60193i
$325$	5.79883	−	3.34796i	0.321661	−	0.185711i
$326$	−42.5971	−	24.5935i	−2.35924	−	1.36211i
$327$	11.7654	−	13.6712i	0.650629	−	0.756019i
$328$	52.6228	+	30.3818i	2.90561	+	1.67755i
$329$		0			0
$330$	4.63511	+	13.2471i	0.255154	+	0.729227i
$331$	4.48460			0.246496			0.123248	−	0.992376i	$-0.460669\pi$
$331$	4.48460			0.246496			0.123248	+	0.992376i	$0.460669\pi$
$332$	−8.58600	−	14.8714i	−0.471218	−	0.816173i
$333$	−0.773772	−	5.13477i	−0.0424025	−	0.281384i
$334$	−2.81245	−	1.62377i	−0.153891	−	0.0888487i
$335$	−3.10274	−	5.37411i	−0.169521	−	0.293619i
$336$		0			0
$337$	−16.4010	+	28.4074i	−0.893420	+	1.54745i	−0.0576723	+	0.998336i	$0.518368\pi$
$337$	−16.4010	+	28.4074i	−0.893420	+	1.54745i	−0.835748	+	0.549113i	$0.814965\pi$
$338$	−22.1649	+	12.7969i	−1.20561	+	0.696059i
$339$	3.55544	−	18.7893i	0.193105	−	1.02050i
$340$	3.86453	−	6.69356i	0.209583	−	0.363009i
$341$	−4.35557	+	7.54407i	−0.235867	+	0.408534i
$342$	9.04581	+	60.0282i	0.489141	+	3.24595i
$343$		0			0
$344$	−0.102732	+	0.0593121i	−0.00553891	+	0.00319789i
$345$	1.17804	−	6.22556i	0.0634237	−	0.335173i
$346$			48.7807i			2.62247i
$347$		−	13.4075i		−	0.719751i	−0.933000	−	0.359876i	$-0.882819\pi$
$347$		−	13.4075i		−	0.719751i	0.933000	−	0.359876i	$-0.117181\pi$
$348$	1.40671	+	1.21061i	0.0754074	+	0.0648954i
$349$	19.3276	−	11.1588i	1.03458	−	0.597316i	0.116288	−	0.993215i	$-0.462900\pi$
$349$	19.3276	−	11.1588i	1.03458	−	0.597316i	0.918294	+	0.395899i	$0.129567\pi$
$350$		0			0
$351$	−4.57539	−	8.65807i	−0.244216	−	0.462134i
$352$	24.0494	−	41.6548i	1.28184	−	2.22021i
$353$	8.60842	−	14.9102i	0.458180	−	0.793591i	−0.540685	−	0.841225i	$-0.681835\pi$
$353$	8.60842	−	14.9102i	0.458180	−	0.793591i	0.998865	+	0.0476341i	$0.0151682\pi$
$354$	−54.1130	+	18.9340i	−2.87607	+	1.00633i
$355$	12.5483	−	7.24476i	0.665994	−	0.384512i
$356$	−21.2637	+	36.8298i	−1.12697	+	1.95198i
$357$		0			0
$358$	−20.5090	−	35.5227i	−1.08394	−	1.87743i
$359$	−5.62867	−	3.24971i	−0.297070	−	0.171513i	0.344056	−	0.938949i	$-0.388199\pi$
$359$	−5.62867	−	3.24971i	−0.297070	−	0.171513i	−0.641126	+	0.767436i	$0.721532\pi$
$360$	11.9215	−	30.3726i	0.628319	−	1.60078i
$361$	18.4015	+	31.8722i	0.968497	+	1.67749i
$362$	21.6358			1.13715
$363$	5.44176	−	6.32324i	0.285619	−	0.331884i
$364$		0			0
$365$	9.03424	+	5.21592i	0.472874	+	0.273014i
$366$	17.4256	+	49.8022i	0.910852	+	2.60320i
$367$	7.79734	+	4.50180i	0.407018	+	0.234992i	0.689508	−	0.724278i	$-0.257827\pi$
$367$	7.79734	+	4.50180i	0.407018	+	0.234992i	−0.282490	+	0.959270i	$0.591160\pi$
$368$	−36.3860	+	21.0075i	−1.89675	+	1.09509i
$369$	3.00431	+	19.9367i	0.156398	+	1.03786i
$370$			5.64024i			0.293222i
$371$		0			0
$372$	30.5702	−	10.6964i	1.58499	−	0.554583i
$373$	−5.75312	−	9.96470i	−0.297885	−	0.515953i	0.677767	−	0.735277i	$-0.262948\pi$
$373$	−5.75312	−	9.96470i	−0.297885	−	0.515953i	−0.975652	+	0.219324i	$0.929615\pi$
$374$	8.10824			0.419267
$375$	5.88543	+	16.8205i	0.303922	+	0.868605i
$376$			12.9727i			0.669015i
$377$	−0.378318			−0.0194844
$378$		0			0
$379$	17.0982			0.878275			0.439138	−	0.898420i	$-0.355284\pi$
$379$	17.0982			0.878275			0.439138	+	0.898420i	$0.355284\pi$
$380$		−	47.9653i		−	2.46057i
$381$	7.93035	+	22.6648i	0.406284	+	1.16115i
$382$	43.3872			2.21988
$383$	8.10778	+	14.0431i	0.414288	+	0.717569i	0.995353	−	0.0962885i	$-0.0306971\pi$
$383$	8.10778	+	14.0431i	0.414288	+	0.717569i	−0.581065	+	0.813857i	$0.697364\pi$
$384$	−46.4229	+	16.2432i	−2.36901	+	0.828909i
$385$		0			0
$386$			37.1363i			1.89019i
$387$	−0.0366390	−	0.0143811i	−0.00186246	−	0.000731033i
$388$	−11.0097	+	6.35643i	−0.558931	+	0.322699i
$389$	16.2358	+	9.37376i	0.823189	+	0.475269i	0.851515	−	0.524330i	$-0.175684\pi$
$389$	16.2358	+	9.37376i	0.823189	+	0.475269i	−0.0283257	+	0.999599i	$0.509018\pi$
$390$	3.51287	+	10.0397i	0.177881	+	0.508382i
$391$	−3.17012	−	1.83027i	−0.160320	−	0.0925607i
$392$		0			0
$393$	13.9640	−	16.2259i	0.704388	−	0.818487i
$394$	−51.2642			−2.58265
$395$	3.30565	+	5.72556i	0.166326	+	0.288084i
$396$	39.3751	−	5.93353i	1.97867	−	0.298171i
$397$	−26.8216	−	15.4854i	−1.34614	−	0.777192i	−0.358436	−	0.933554i	$-0.616690\pi$
$397$	−26.8216	−	15.4854i	−1.34614	−	0.777192i	−0.987700	+	0.156362i	$0.950023\pi$
$398$	−33.6334	−	58.2548i	−1.68589	−	2.92005i
$399$		0			0
$400$	24.5441	−	42.5116i	1.22720	−	2.12558i
$401$	0.801065	−	0.462495i	0.0400033	−	0.0230959i	−0.479865	−	0.877342i	$-0.659314\pi$
$401$	0.801065	−	0.462495i	0.0400033	−	0.0230959i	0.519868	+	0.854246i	$0.325981\pi$
$402$	−22.8454	+	7.99354i	−1.13943	+	0.398681i
$403$	−3.30101	+	5.71752i	−0.164435	+	0.284810i
$404$	25.2621	−	43.7552i	1.25684	−	2.17690i
$405$	10.3456	−	3.19045i	0.514076	−	0.158535i
$406$		0			0
$407$	−3.72755	+	2.15210i	−0.184768	+	0.106676i
$408$	−14.2880	−	12.2962i	−0.707362	−	0.608754i
$409$		−	7.58159i		−	0.374885i	−0.982276	−	0.187443i	$-0.939980\pi$
$409$		−	7.58159i		−	0.374885i	0.982276	−	0.187443i	$-0.0600199\pi$
$410$		−	21.8992i		−	1.08153i
$411$	3.75539	−	19.8460i	0.185240	−	0.978929i
$412$	−79.7782	+	46.0599i	−3.93039	+	2.26921i
$413$		0			0
$414$	−23.0041	−	9.02931i	−1.13059	−	0.443766i
$415$	−1.93496	+	3.35145i	−0.0949834	+	0.164516i
$416$	18.2266	−	31.5695i	0.893635	−	1.54782i
$417$	−3.24962	+	17.1731i	−0.159134	+	0.840971i
$418$	43.5770	−	25.1592i	2.13142	−	1.23058i
$419$	2.85061	−	4.93740i	0.139262	−	0.241208i	−0.787956	−	0.615732i	$-0.788860\pi$
$419$	2.85061	−	4.93740i	0.139262	−	0.241208i	0.927217	+	0.374524i	$0.122194\pi$
$420$		0			0
$421$	−5.86189	−	10.1531i	−0.285691	−	0.494832i	0.687085	−	0.726577i	$-0.258890\pi$
$421$	−5.86189	−	10.1531i	−0.285691	−	0.494832i	−0.972777	+	0.231745i	$0.925557\pi$
$422$	−16.9263	−	9.77240i	−0.823959	−	0.475713i
$423$	−3.36542	+	2.68365i	−0.163632	+	0.130484i
$424$	−44.7926	−	77.5830i	−2.17532	−	3.76776i
$425$	4.27680			0.207455
$426$	−18.6645	−	53.3430i	−0.904300	−	2.58447i
$427$		0			0
$428$	−45.6877	−	26.3778i	−2.20840	−	1.27502i
$429$	−5.29473	+	6.15239i	−0.255632	+	0.297040i
$430$	0.0370245	+	0.0213761i	0.00178548	+	0.00103085i
$431$	23.2973	−	13.4507i	1.12219	−	0.647897i	0.180231	−	0.983624i	$-0.442315\pi$
$431$	23.2973	−	13.4507i	1.12219	−	0.647897i	0.941959	+	0.335728i	$0.108982\pi$
$432$	−60.7851	−	38.1979i	−2.92452	−	1.83780i
$433$		−	28.1028i		−	1.35053i	−0.737574	−	0.675266i	$-0.764029\pi$
$433$		−	28.1028i		−	1.35053i	0.737574	−	0.675266i	$-0.235971\pi$
$434$		0			0
$435$	0.0777645	−	0.410959i	0.00372852	−	0.0197040i
$436$	27.7925	+	48.1381i	1.33102	+	2.30539i
$437$	−22.7167			−1.08669
$438$	26.5406	−	30.8397i	1.26816	−	1.47358i
$439$			9.32629i			0.445120i	0.974919	+	0.222560i	$0.0714412\pi$
$439$			9.32629i			0.445120i	−0.974919	+	0.222560i	$0.928559\pi$
$440$	−27.0454			−1.28934
$441$		0			0
$442$	6.14510			0.292292
$443$			11.3407i			0.538812i	0.963027	+	0.269406i	$0.0868273\pi$
$443$			11.3407i			0.538812i	−0.963027	+	0.269406i	$0.913173\pi$
$444$	15.7237	+	2.97536i	0.746216	+	0.141204i
$445$	9.58406			0.454328
$446$	32.9532	+	57.0766i	1.56038	+	2.70265i
$447$	−6.29123	−	5.41422i	−0.297565	−	0.256084i
$448$		0			0
$449$			15.3295i			0.723444i	0.932286	+	0.361722i	$0.117811\pi$
$449$			15.3295i			0.723444i	−0.932286	+	0.361722i	$0.882189\pi$
$450$	28.5508	−	4.30239i	1.34590	−	0.202817i
$451$	14.4729	−	8.35592i	0.681501	−	0.393465i
$452$	51.0363	+	29.4658i	2.40054	+	1.38596i
$453$	19.2624	+	3.64496i	0.905024	+	0.171255i
$454$	1.12739	+	0.650900i	0.0529111	+	0.0305483i
$455$		0			0
$456$	−114.944	−	21.7505i	−5.38274	−	1.01856i
$457$	−9.17299			−0.429094			−0.214547	−	0.976714i	$-0.568828\pi$
$457$	−9.17299			−0.429094			−0.214547	+	0.976714i	$0.568828\pi$
$458$	12.2057	+	21.1408i	0.570333	+	0.987846i
$459$	0.234176	−	6.25036i	0.0109304	−	0.291742i
$460$	16.9101	+	9.76305i	0.788438	+	0.455205i
$461$	16.5365	+	28.6420i	0.770181	+	1.33399i	0.937464	+	0.348083i	$0.113167\pi$
$461$	16.5365	+	28.6420i	0.770181	+	1.33399i	−0.167283	+	0.985909i	$0.553499\pi$
$462$		0			0
$463$	3.91594	−	6.78260i	0.181989	−	0.315214i	−0.760569	−	0.649257i	$-0.775080\pi$
$463$	3.91594	−	6.78260i	0.181989	−	0.315214i	0.942558	+	0.334043i	$0.108413\pi$
$464$	−2.40190	+	1.38674i	−0.111505	+	0.0643776i
$465$	−5.53229	−	4.76108i	−0.256554	−	0.220790i
$466$	−15.0567	+	26.0790i	−0.697490	+	1.20809i
$467$	−10.3385	+	17.9068i	−0.478408	+	0.828627i	−0.999694	−	0.0247555i	$-0.992119\pi$
$467$	−10.3385	+	17.9068i	−0.478408	+	0.828627i	0.521286	+	0.853382i	$0.325453\pi$
$468$	29.8417	−	4.49692i	1.37943	−	0.207870i
$469$		0			0
$470$	4.04898	−	2.33768i	0.186765	−	0.107829i
$471$	−24.0842	+	8.42698i	−1.10974	+	0.388295i
$472$		−	110.478i		−	5.08515i
$473$			0.0326253i			0.00150011i
$474$	24.3394	−	8.51630i	1.11795	−	0.391167i
$475$	22.9853	−	13.2706i	1.05464	−	0.608895i
$476$		0			0
$477$	10.8606	−	27.6698i	0.497274	−	1.26691i
$478$	18.8371	−	32.6267i	0.861587	−	1.49231i
$479$	−1.32999	+	2.30361i	−0.0607688	+	0.105255i	−0.894809	−	0.446449i	$-0.852689\pi$
$479$	−1.32999	+	2.30361i	−0.0607688	+	0.105255i	0.834040	+	0.551703i	$0.186022\pi$
$480$	30.5467	+	26.2884i	1.39426	+	1.19990i
$481$	−2.82505	+	1.63104i	−0.128811	+	0.0743691i
$482$	−16.7624	+	29.0334i	−0.763508	+	1.32243i
$483$		0			0
$484$	12.8547	+	22.2649i	0.584303	+	1.01204i
$485$	2.48116	+	1.43250i	0.112664	+	0.0650465i
$486$	−4.72447	−	41.9613i	−0.214306	−	1.90341i
$487$	0.521900	+	0.903957i	0.0236495	+	0.0409622i	0.877608	−	0.479379i	$-0.159138\pi$
$487$	0.521900	+	0.903957i	0.0236495	+	0.0409622i	−0.853958	+	0.520341i	$0.825805\pi$
$488$	−101.677			−4.60269
$489$	30.9022	+	5.84753i	1.39745	+	0.264434i
$490$		0			0
$491$	36.0415	+	20.8085i	1.62653	+	0.939076i	0.985118	+	0.171878i	$0.0549835\pi$
$491$	36.0415	+	20.8085i	1.62653	+	0.939076i	0.641410	+	0.767198i	$0.278350\pi$
$492$	−61.0502	−	11.5524i	−2.75236	−	0.520820i
$493$	−0.209265	−	0.120819i	−0.00942480	−	0.00544141i
$494$	33.0263	−	19.0677i	1.48592	−	0.857898i
$495$	−5.59487	−	7.01621i	−0.251471	−	0.315355i
$496$			48.3999i			2.17322i
$497$		0			0
$498$	11.4407	+	9.84581i	0.512668	+	0.441201i
$499$	16.1447	+	27.9635i	0.722738	+	1.25182i	0.959898	+	0.280348i	$0.0904499\pi$
$499$	16.1447	+	27.9635i	0.722738	+	1.25182i	−0.237161	+	0.971470i	$0.576217\pi$
$500$	−54.9181			−2.45601
$501$	2.04030	+	0.386080i	0.0911539	+	0.0172488i
$502$			53.4038i			2.38353i
$503$	−39.9702			−1.78218			−0.891091	−	0.453825i	$-0.850059\pi$
$503$	−39.9702			−1.78218			−0.891091	+	0.453825i	$0.850059\pi$
$504$		0			0
$505$	−11.3862			−0.506681
$506$			20.4841i			0.910627i
$507$	10.6748	−	12.4040i	0.474085	−	0.550879i
$508$	−73.9996			−3.28320
$509$	11.3631	+	19.6815i	0.503661	+	0.872367i	0.999991	+	0.00423260i	$0.00134728\pi$
$509$	11.3631	+	19.6815i	0.503661	+	0.872367i	−0.496330	+	0.868134i	$0.665319\pi$
$510$	−1.26315	+	6.67529i	−0.0559330	+	0.295587i
$511$		0			0
$512$		−	17.4067i		−	0.769277i
$513$	−18.1358	−	34.3187i	−0.800716	−	1.51521i
$514$	−26.3692	+	15.2243i	−1.16310	+	0.671515i
$515$	17.9790	+	10.3802i	0.792249	+	0.457405i
$516$	0.0791231	−	0.0919397i	0.00348320	−	0.00404742i
$517$	3.08988	+	1.78394i	0.135893	+	0.0784576i
$518$		0			0
$519$	−10.3012	−	29.4407i	−0.452173	−	1.29230i
$520$	−20.4972			−0.898863
$521$	15.0179	+	26.0118i	0.657948	+	1.13960i	0.981146	+	0.193268i	$0.0619087\pi$
$521$	15.0179	+	26.0118i	0.657948	+	1.13960i	−0.323198	+	0.946331i	$0.604758\pi$
$522$	−1.51854	−	0.596039i	−0.0664646	−	0.0260879i
$523$	0.675300	+	0.389885i	0.0295288	+	0.0170485i	0.514692	−	0.857375i	$-0.327906\pi$
$523$	0.675300	+	0.389885i	0.0295288	+	0.0170485i	−0.485163	+	0.874424i	$0.661240\pi$
$524$	32.9860	+	57.1334i	1.44100	+	2.49588i
$525$		0			0
$526$	4.41260	−	7.64285i	0.192399	−	0.333244i
$527$	−3.65188	+	2.10841i	−0.159078	+	0.0918439i
$528$	−11.0639	+	58.4689i	−0.481494	+	2.54453i
$529$	−6.87614	+	11.9098i	−0.298963	+	0.517819i
$530$	−16.1433	+	27.9609i	−0.701218	+	1.21455i
$531$	28.6605	−	22.8545i	1.24376	−	0.991800i
$532$		0			0
$533$	10.9688	−	6.33281i	0.475110	−	0.274305i
$534$	6.95018	−	36.7293i	0.300764	−	1.58943i
$535$			11.8891i			0.514012i
$536$		−	46.6415i		−	2.01460i
$537$	19.8793	+	17.1081i	0.857855	+	0.738268i
$538$	−0.568399	+	0.328165i	−0.0245054	+	0.0141482i
$539$		0			0
$540$	−1.24915	+	33.3408i	−0.0537547	+	1.43476i
$541$	−1.02015	+	1.76696i	−0.0438598	+	0.0759674i	−0.887122	−	0.461535i	$-0.847299\pi$
$541$	−1.02015	+	1.76696i	−0.0438598	+	0.0759674i	0.843262	+	0.537503i	$0.180632\pi$
$542$	1.45335	−	2.51728i	0.0624268	−	0.108126i
$543$	−13.0579	+	4.56892i	−0.560368	+	0.196071i
$544$	20.1640	−	11.6417i	0.864522	−	0.499132i
$545$	6.26338	−	10.8485i	0.268294	−	0.464699i
$546$		0			0
$547$	−8.93590	−	15.4774i	−0.382071	−	0.661767i	0.609287	−	0.792950i	$-0.291456\pi$
$547$	−8.93590	−	15.4774i	−0.382071	−	0.661767i	−0.991358	+	0.131183i	$0.958123\pi$
$548$	53.9064	+	31.1229i	2.30277	+	1.32950i
$549$	−21.0338	−	26.3773i	−0.897701	−	1.12576i
$550$	−11.9663	−	20.7262i	−0.510244	−	0.883769i
$551$	−1.49957			−0.0638837
$552$	31.0643	−	36.0962i	1.32218	−	1.53635i
$553$		0			0
$554$	−11.4986	−	6.63870i	−0.488527	−	0.282051i
$555$	−1.19107	−	3.40406i	−0.0505581	−	0.144494i
$556$	−46.6463	−	26.9313i	−1.97824	−	1.14214i
$557$	−37.2049	+	21.4802i	−1.57642	+	0.910147i	−0.581068	+	0.813855i	$0.697365\pi$
$557$	−37.2049	+	21.4802i	−1.57642	+	0.910147i	−0.995353	+	0.0962924i	$0.969302\pi$
$558$	−22.2580	+	17.7489i	−0.942254	+	0.751373i
$559$			0.0247261i			0.00104580i
$560$		0			0
$561$	−4.89357	+	1.71225i	−0.206607	+	0.0722911i
$562$	−18.0813	−	31.3177i	−0.762713	−	1.32106i
$563$	1.54748			0.0652184			0.0326092	−	0.999468i	$-0.489618\pi$
$563$	1.54748			0.0652184			0.0326092	+	0.999468i	$0.489618\pi$
$564$	−4.38100	−	12.5208i	−0.184474	−	0.527222i
$565$		−	13.2810i		−	0.558734i
$566$	10.1759			0.427726
$567$		0			0
$568$	108.906			4.56958
$569$		−	9.99861i		−	0.419164i	−0.977791	−	0.209582i	$-0.932790\pi$
$569$		−	9.99861i		−	0.419164i	0.977791	−	0.209582i	$-0.0672103\pi$
$570$	13.9242	+	39.7952i	0.583222	+	1.66684i
$571$	−2.79430			−0.116938			−0.0584689	−	0.998289i	$-0.518622\pi$
$571$	−2.79430			−0.116938			−0.0584689	+	0.998289i	$0.518622\pi$
$572$	−12.5073	−	21.6634i	−0.522958	−	0.905790i
$573$	−26.1855	+	9.16224i	−1.09392	+	0.382758i
$574$		0			0
$575$			10.8046i			0.450582i
$576$	58.0849	−	46.3181i	2.42021	−	1.92992i
$577$	3.23689	−	1.86882i	0.134754	−	0.0778000i	−0.431108	−	0.902300i	$-0.641877\pi$
$577$	3.23689	−	1.86882i	0.134754	−	0.0778000i	0.565861	+	0.824500i	$0.308544\pi$
$578$	−36.4814	−	21.0626i	−1.51743	−	0.876087i
$579$	−7.84221	−	22.4129i	−0.325911	−	0.931449i
$580$	1.11626	+	0.644475i	0.0463503	+	0.0267604i
$581$		0			0
$582$	7.28910	−	8.46981i	0.302143	−	0.351085i
$583$	−24.6386			−1.02043
$584$	39.2037	+	67.9028i	1.62226	+	2.80984i
$585$	−4.24026	−	5.31747i	−0.175313	−	0.219850i
$586$	−29.9540	−	17.2940i	−1.23739	−	0.714407i
$587$	−13.1249	−	22.7331i	−0.541725	−	0.938295i	−0.998805	−	0.0488692i	$-0.984438\pi$
$587$	−13.1249	−	22.7331i	−0.541725	−	0.938295i	0.457081	−	0.889425i	$-0.348895\pi$
$588$		0			0
$589$	−13.0845	+	22.6630i	−0.539136	+	0.933812i
$590$	−34.4819	+	19.9081i	−1.41960	+	0.819604i
$591$	30.9395	−	10.8256i	1.27268	−	0.445308i
$592$	−11.9573	+	20.7106i	−0.491441	+	0.851201i
$593$	1.79833	−	3.11481i	0.0738488	−	0.127910i	−0.826736	−	0.562590i	$-0.809805\pi$
$593$	1.79833	−	3.11481i	0.0738488	−	0.127910i	0.900585	+	0.434680i	$0.143138\pi$
$594$	−30.9457	+	16.3534i	−1.26972	+	0.670987i
$595$		0			0
$596$	22.1522	−	12.7896i	0.907391	−	0.523882i
$597$	32.6007	+	28.0561i	1.33426	+	1.14826i
$598$			15.5245i			0.634845i
$599$		−	23.8330i		−	0.973789i	−0.873461	−	0.486895i	$-0.838130\pi$
$599$		−	23.8330i		−	0.973789i	0.873461	−	0.486895i	$-0.161870\pi$
$600$	−10.3450	+	54.6699i	−0.422334	+	2.23189i
$601$	−14.6034	+	8.43126i	−0.595684	+	0.343918i	−0.767342	−	0.641238i	$-0.778421\pi$
$601$	−14.6034	+	8.43126i	−0.595684	+	0.343918i	0.171658	+	0.985157i	$0.445088\pi$
$602$		0			0
$603$	12.0999	−	9.64870i	0.492746	−	0.392925i
$604$	−30.2076	+	52.3212i	−1.22913	+	2.12892i
$605$	2.89695	−	5.01767i	0.117778	−	0.203997i
$606$	−8.25708	+	43.6358i	−0.335421	+	1.77258i
$607$	9.07737	−	5.24082i	0.368439	−	0.212718i	−0.304337	−	0.952564i	$-0.598435\pi$
$607$	9.07737	−	5.24082i	0.368439	−	0.212718i	0.672776	+	0.739846i	$0.265102\pi$
$608$	72.2463	−	125.134i	2.92997	−	5.07487i
$609$		0			0
$610$	18.3222	+	31.7349i	0.741842	+	1.28491i
$611$	2.34176	+	1.35202i	0.0947377	+	0.0546968i
$612$	17.9429	+	7.04275i	0.725299	+	0.284686i
$613$	23.9500	+	41.4827i	0.967333	+	1.67547i	0.703213	+	0.710979i	$0.251748\pi$
$613$	23.9500	+	41.4827i	0.967333	+	1.67547i	0.264120	+	0.964490i	$0.414919\pi$
$614$	−29.0541			−1.17253
$615$	4.62454	+	13.2169i	0.186480	+	0.532956i
$616$		0			0
$617$	4.69477	+	2.71053i	0.189004	+	0.109122i	0.591516	−	0.806293i	$-0.298530\pi$
$617$	4.69477	+	2.71053i	0.189004	+	0.109122i	−0.402512	+	0.915415i	$0.631863\pi$
$618$	52.8183	−	61.3739i	2.12466	−	2.46882i
$619$	−27.9729	−	16.1501i	−1.12432	−	0.649129i	−0.181823	−	0.983331i	$-0.558200\pi$
$619$	−27.9729	−	16.1501i	−1.12432	−	0.649129i	−0.942501	+	0.334202i	$0.891533\pi$
$620$	19.4799	−	11.2467i	0.782332	−	0.451680i
$621$	15.7904	+	0.591605i	0.633649	+	0.0237403i
$622$		−	51.0204i		−	2.04573i
$623$		0			0
$624$	−8.38513	+	44.3126i	−0.335674	+	1.77392i
$625$	−2.69418	−	4.66646i	−0.107767	−	0.186658i
$626$	70.6196			2.82253
$627$	−20.9871	+	24.3867i	−0.838146	+	0.973911i
$628$		−	78.6338i		−	3.13783i
$629$	−2.08355			−0.0830765
$630$		0			0
$631$	−18.3539			−0.730656			−0.365328	−	0.930879i	$-0.619043\pi$
$631$	−18.3539			−0.730656			−0.365328	+	0.930879i	$0.619043\pi$
$632$			49.6917i			1.97663i
$633$	12.2792	+	2.32356i	0.488055	+	0.0923532i
$634$	37.6253			1.49429
$635$	8.33836	+	14.4425i	0.330898	+	0.573132i
$636$	69.4330	+	59.7539i	2.75320	+	2.36940i
$637$		0			0
$638$			1.35218i			0.0535335i
$639$	22.5293	+	28.2527i	0.891244	+	1.11766i
$640$	−29.5816	+	17.0789i	−1.16931	+	0.675104i
$641$	−9.07003	−	5.23658i	−0.358245	−	0.206833i	0.310066	−	0.950715i	$-0.399649\pi$
$641$	−9.07003	−	5.23658i	−0.358245	−	0.206833i	−0.668310	+	0.743882i	$0.732982\pi$
$642$	45.5631	+	8.62177i	1.79823	+	0.340274i
$643$	3.37572	+	1.94897i	0.133125	+	0.0768600i	0.565084	−	0.825034i	$-0.308844\pi$
$643$	3.37572	+	1.94897i	0.133125	+	0.0768600i	−0.431958	+	0.901894i	$0.642177\pi$
$644$		0			0
$645$	−0.0268595	−	0.00508254i	−0.00105759	−	0.000200125i
$646$	24.3578			0.958344
$647$	−6.20269	−	10.7434i	−0.243853	−	0.422366i	0.717955	−	0.696089i	$-0.245078\pi$
$647$	−6.20269	−	10.7434i	−0.243853	−	0.422366i	−0.961809	+	0.273723i	$0.911745\pi$
$648$	79.3313	+	18.1123i	3.11643	+	0.711517i
$649$	−26.3140	−	15.1924i	−1.03291	−	0.596353i
$650$	−9.06905	−	15.7081i	−0.355717	−	0.616120i
$651$		0			0
$652$	−48.4615	+	83.9377i	−1.89790	+	3.28726i
$653$	12.2749	−	7.08690i	0.480353	−	0.277332i	−0.240211	−	0.970721i	$-0.577216\pi$
$653$	12.2749	−	7.08690i	0.480353	−	0.277332i	0.720564	+	0.693389i	$0.243883\pi$
$654$	−37.0330	−	31.8705i	−1.44810	−	1.24623i
$655$	7.43379	−	12.8757i	0.290462	−	0.503095i
$656$	46.4263	−	80.4126i	1.81264	−	3.13959i
$657$	−9.50554	+	24.2174i	−0.370846	+	0.944811i
$658$		0			0
$659$	−17.2962	+	9.98594i	−0.673763	+	0.388997i	−0.797501	−	0.603318i	$-0.793845\pi$
$659$	−17.2962	+	9.98594i	−0.673763	+	0.388997i	0.123738	+	0.992315i	$0.460512\pi$
$660$	26.1034	−	9.13350i	1.01607	−	0.355521i
$661$			24.3056i			0.945378i	0.881229	+	0.472689i	$0.156717\pi$
$661$			24.3056i			0.945378i	−0.881229	+	0.472689i	$0.843283\pi$
$662$		−	12.1480i		−	0.472146i
$663$	−3.70876	+	1.29768i	−0.144036	+	0.0503978i
$664$	−25.1900	+	14.5435i	−0.977563	+	0.564396i
$665$		0			0
$666$	−13.9092	+	2.09602i	−0.538971	+	0.0812190i
$667$	0.305228	−	0.528670i	0.0118185	−	0.0204702i
$668$	−3.19964	+	5.54194i	−0.123798	+	0.214424i
$669$	−31.9413	−	27.4886i	−1.23492	−	1.06277i
$670$	−14.5575	+	8.40480i	−0.562407	+	0.324706i
$671$	−13.9821	+	24.2177i	−0.539773	+	0.934914i
$672$		0			0
$673$	−1.82521	−	3.16135i	−0.0703566	−	0.121861i	0.828701	−	0.559692i	$-0.189080\pi$
$673$	−1.82521	−	3.16135i	−0.0703566	−	0.121861i	−0.899058	+	0.437830i	$0.855747\pi$
$674$	76.9508	+	44.4275i	2.96403	+	1.71129i
$675$	−16.3227	+	8.62580i	−0.628262	+	0.332007i
$676$	25.2163	+	43.6759i	0.969858	+	1.67984i
$677$	1.93735			0.0744585			0.0372292	−	0.999307i	$-0.488147\pi$
$677$	1.93735			0.0744585			0.0372292	+	0.999307i	$0.488147\pi$
$678$	−50.8970	−	9.63109i	−1.95469	−	0.369880i
$679$		0			0
$680$	−11.3379	−	6.54597i	−0.434790	−	0.251026i
$681$	−0.817869	−	0.154763i	−0.0313408	−	0.00593053i
$682$	20.4356	+	11.7985i	0.782519	+	0.451788i
$683$	16.8815	−	9.74656i	0.645954	−	0.372942i	−0.140950	−	0.990017i	$-0.545016\pi$
$683$	16.8815	−	9.74656i	0.645954	−	0.372942i	0.786905	+	0.617075i	$0.211682\pi$
$684$	118.286	−	17.8248i	4.52277	−	0.681548i
$685$		−	14.0278i		−	0.535976i
$686$		0			0
$687$	−11.8309	−	10.1816i	−0.451377	−	0.388454i
$688$	0.0906345	+	0.156983i	0.00345541	+	0.00598494i
$689$	−18.6732			−0.711393
$690$	−16.8640	−	3.19112i	−0.642000	−	0.121484i
$691$		−	41.3215i		−	1.57194i	−0.618261	−	0.785972i	$-0.712163\pi$
$691$		−	41.3215i		−	1.57194i	0.618261	−	0.785972i	$-0.287837\pi$
$692$	96.1226			3.65403
$693$		0			0
$694$	−36.3186			−1.37863
$695$			12.1386i			0.460442i
$696$	2.05060	−	2.38276i	0.0777279	−	0.0903184i
$697$	8.08975			0.306421
$698$	−30.2273	−	52.3552i	−1.14412	−	1.98167i
$699$	3.58001	−	18.9191i	0.135408	−	0.715586i
$700$		0			0
$701$		−	27.3333i		−	1.03236i	−0.856479	−	0.516182i	$-0.827353\pi$
$701$		−	27.3333i		−	1.03236i	0.856479	−	0.516182i	$-0.172647\pi$
$702$	−23.4532	+	12.3939i	−0.885186	+	0.467779i
$703$	−11.1979	+	6.46508i	−0.422335	+	0.243835i
$704$	−53.3293	−	30.7897i	−2.00992	−	1.16043i
$705$	−1.95003	+	2.26590i	−0.0734423	+	0.0853387i
$706$	−40.3893	−	23.3187i	−1.52007	−	0.877613i
$707$		0			0
$708$	37.3094	+	106.630i	1.40217	+	4.00739i
$709$	2.71269			0.101877			0.0509387	−	0.998702i	$-0.483779\pi$
$709$	2.71269			0.101877			0.0509387	+	0.998702i	$0.483779\pi$
$710$	−19.6248	−	33.9912i	−0.736506	−	1.27567i
$711$	−12.8912	+	10.2797i	−0.483458	+	0.385519i
$712$	62.3845	+	36.0177i	2.33796	+	1.34982i
$713$	−5.32654	−	9.22584i	−0.199480	−	0.345510i
$714$		0			0
$715$	−2.81868	+	4.88210i	−0.105413	+	0.182580i
$716$	−69.9976	+	40.4131i	−2.61593	+	1.51031i
$717$	−4.47884	+	23.6691i	−0.167265	+	0.883941i
$718$	−8.80292	+	15.2471i	−0.328522	+	0.569017i
$719$	−8.13931	+	14.0977i	−0.303545	+	0.525756i	−0.976936	−	0.213531i	$-0.931504\pi$
$719$	−8.13931	+	14.0977i	−0.303545	+	0.525756i	0.673391	+	0.739286i	$0.264837\pi$
$720$	−46.4123	−	18.2172i	−1.72968	−	0.678915i
$721$		0			0
$722$	86.3365	−	49.8464i	3.21311	−	1.85509i
$723$	3.98556	−	21.0623i	0.148225	−	0.783317i
$724$		−	42.6335i		−	1.58446i
$725$			0.713227i			0.0264886i
$726$	−17.1286	−	14.7408i	−0.635701	−	0.547083i
$727$	−0.980123	+	0.565874i	−0.0363508	+	0.0209871i	−0.518065	−	0.855341i	$-0.673348\pi$
$727$	−0.980123	+	0.565874i	−0.0363508	+	0.0209871i	0.481714	+	0.876328i	$0.340014\pi$
$728$		0			0
$729$	11.7125	+	24.3273i	0.433796	+	0.901011i
$730$	14.1290	−	24.4722i	0.522939	−	0.905757i
$731$	−0.00789650	+	0.0136771i	−0.000292063	+	0.000505867i
$732$	98.1353	−	34.3372i	3.62719	−	1.26914i
$733$	−33.2085	+	19.1729i	−1.22658	+	0.708169i	−0.966314	−	0.257367i	$-0.917145\pi$
$733$	−33.2085	+	19.1729i	−1.22658	+	0.708169i	−0.260270	+	0.965536i	$0.583812\pi$
$734$	12.1946	−	21.1217i	0.450111	−	0.779615i
$735$		0			0
$736$	29.4106	+	50.9407i	1.08409	+	1.87770i
$737$	−11.1092	−	6.41391i	−0.409213	−	0.236259i
$738$	54.0051	−	8.13816i	1.98795	−	0.299570i
$739$	−5.36489	−	9.29226i	−0.197351	−	0.341821i	0.750318	−	0.661077i	$-0.229900\pi$
$739$	−5.36489	−	9.29226i	−0.197351	−	0.341821i	−0.947669	+	0.319256i	$0.896567\pi$
$740$	11.1141			0.408562
$741$	−15.9058	+	18.4823i	−0.584314	+	0.678963i
$742$		0			0
$743$	−11.3308	−	6.54185i	−0.415687	−	0.239997i	0.277543	−	0.960713i	$-0.410480\pi$
$743$	−11.3308	−	6.54185i	−0.415687	−	0.239997i	−0.693230	+	0.720716i	$0.743813\pi$
$744$	−18.1182	−	51.7816i	−0.664246	−	1.89841i
$745$	−4.99228	−	2.88229i	−0.182903	−	0.105599i
$746$	−26.9927	+	15.5842i	−0.988272	+	0.570579i
$747$	−8.98397	−	3.52629i	−0.328706	−	0.129020i
$748$		−	15.9773i		−	0.584188i
$749$		0			0
$750$	45.5637	−	15.9426i	1.66375	−	0.582142i
$751$	−13.1677	−	22.8071i	−0.480495	−	0.832242i	0.519254	−	0.854620i	$-0.326210\pi$
$751$	−13.1677	−	22.8071i	−0.480495	−	0.832242i	−0.999750	+	0.0223774i	$0.992876\pi$
$752$	19.8235			0.722887
$753$	−11.2775	−	32.2308i	−0.410974	−	1.17456i
$754$			1.02480i			0.0373209i
$755$	13.6153			0.495512
$756$		0			0
$757$	−32.6280			−1.18588			−0.592942	−	0.805245i	$-0.702034\pi$
$757$	−32.6280			−1.18588			−0.592942	+	0.805245i	$0.702034\pi$
$758$		−	46.3161i		−	1.68228i
$759$	−4.32569	−	12.3628i	−0.157013	−	0.448740i
$760$	−81.2465			−2.94712
$761$	−12.6727	−	21.9498i	−0.459385	−	0.795679i	0.539543	−	0.841958i	$-0.318597\pi$
$761$	−12.6727	−	21.9498i	−0.459385	−	0.795679i	−0.998929	+	0.0462793i	$0.985264\pi$
$762$	61.3951	−	21.4820i	2.22411	−	0.778210i
$763$		0			0
$764$		−	85.4946i		−	3.09309i
$765$	−0.647299	−	4.29549i	−0.0234031	−	0.155304i
$766$	38.0403	−	21.9626i	1.37445	−	0.793541i
$767$	−19.9429	−	11.5140i	−0.720097	−	0.415748i
$768$	15.6687	+	44.7808i	0.565394	+	1.61589i
$769$	−11.4964	−	6.63744i	−0.414570	−	0.239352i	0.278181	−	0.960529i	$-0.410268\pi$
$769$	−11.4964	−	6.63744i	−0.414570	−	0.239352i	−0.692752	+	0.721176i	$0.743602\pi$
$770$		0			0
$771$	12.6997	−	14.7568i	0.457368	−	0.531454i
$772$	73.1772			2.63370
$773$	8.00680	+	13.8682i	0.287985	+	0.498804i	0.973329	−	0.229416i	$-0.0736815\pi$
$773$	8.00680	+	13.8682i	0.287985	+	0.498804i	−0.685344	+	0.728219i	$0.740348\pi$
$774$	−0.0389560	+	0.0992488i	−0.00140024	+	0.00356742i
$775$	10.7790	+	6.22327i	0.387194	+	0.223546i
$776$	10.7669	+	18.6488i	0.386509	+	0.669454i
$777$		0			0
$778$	25.3919	−	43.9801i	0.910344	−	1.57676i
$779$	43.4777	−	25.1019i	1.55775	−	0.899367i
$780$	19.7833	−	6.92213i	0.708357	−	0.247852i
$781$	14.9762	−	25.9395i	0.535890	−	0.928189i
$782$	−4.95789	+	8.58731i	−0.177294	+	0.307082i
$783$	1.04235	+	0.0390528i	0.0372506	+	0.00139563i
$784$		0			0
$785$	−15.3469	+	8.86054i	−0.547755	+	0.316246i
$786$	−43.9531	−	37.8260i	−1.56776	−	1.34921i
$787$		−	4.90354i		−	0.174792i	−0.996174	−	0.0873961i	$-0.972145\pi$
$787$		−	4.90354i		−	0.174792i	0.996174	−	0.0873961i	$-0.0278546\pi$
$788$			101.016i			3.59855i
$789$	−1.04917	+	5.54453i	−0.0373516	+	0.197390i
$790$	15.5096	−	8.95445i	0.551806	−	0.318585i
$791$		0			0
$792$	−10.0506	−	66.6958i	−0.357131	−	2.36993i
$793$	−10.5968	+	18.3542i	−0.376303	+	0.651776i
$794$	−41.9474	+	72.6551i	−1.48866	+	2.57843i
$795$	3.83834	−	20.2843i	0.136132	−	0.719411i
$796$	−114.791	+	66.2748i	−4.06867	+	2.34905i
$797$	−21.3994	+	37.0649i	−0.758006	+	1.31290i	0.185860	+	0.982576i	$0.440493\pi$
$797$	−21.3994	+	37.0649i	−0.758006	+	1.31290i	−0.943866	+	0.330328i	$0.892841\pi$
$798$		0			0
$799$	0.863557	+	1.49572i	0.0305505	+	0.0529149i
$800$	−59.5167	−	34.3620i	−2.10423	−	1.21488i
$801$	3.56162	+	23.6350i	0.125844	+	0.835101i
$802$	−1.25282	−	2.16995i	−0.0442386	−	0.0766235i
$803$	21.5644			0.760993
$804$	15.7513	+	45.0169i	0.555505	+	1.58763i
$805$		0			0
$806$	15.4878	+	8.94188i	0.545534	+	0.314964i
$807$	0.273747	−	0.318089i	0.00963634	−	0.0111973i
$808$	−74.1152	−	42.7904i	−2.60736	−	1.50536i
$809$	30.5649	−	17.6467i	1.07461	−	0.620424i	0.145169	−	0.989407i	$-0.453627\pi$
$809$	30.5649	−	17.6467i	1.07461	−	0.620424i	0.929436	+	0.368983i	$0.120294\pi$
$810$	−8.64240	−	28.0244i	−0.303663	−	0.984677i
$811$			21.0223i			0.738193i	0.929391	+	0.369096i	$0.120333\pi$
$811$			21.0223i			0.738193i	−0.929391	+	0.369096i	$0.879667\pi$
$812$		0			0
$813$	−0.345560	+	1.82617i	−0.0121193	+	0.0640465i
$814$	5.82968	+	10.0973i	0.204330	+	0.353910i
$815$	21.8428			0.765119
$816$	−18.7898	+	21.8334i	−0.657774	+	0.764322i
$817$			0.0980089i			0.00342890i
$818$	−20.5372			−0.718067
$819$		0			0
$820$	−43.1525			−1.50695
$821$		−	34.4820i		−	1.20343i	−0.798710	−	0.601716i	$-0.794484\pi$
$821$		−	34.4820i		−	1.20343i	0.798710	−	0.601716i	$-0.205516\pi$
$822$	−53.7593	−	10.1727i	−1.87507	−	0.354814i
$823$	−38.9899			−1.35910			−0.679552	−	0.733628i	$-0.737826\pi$
$823$	−38.9899			−1.35910			−0.679552	+	0.733628i	$0.737826\pi$
$824$	78.0191	+	135.133i	2.71792	+	4.70758i
$825$	11.5989	+	9.98195i	0.403820	+	0.347527i
$826$		0			0
$827$			47.2537i			1.64317i	0.570086	+	0.821585i	$0.306910\pi$
$827$			47.2537i			1.64317i	−0.570086	+	0.821585i	$0.693090\pi$
$828$	−17.7923	+	45.3297i	−0.618324	+	1.57531i
$829$	−42.5588	+	24.5713i	−1.47813	+	0.853397i	−0.999694	−	0.0247275i	$-0.992128\pi$
$829$	−42.5588	+	24.5713i	−1.47813	+	0.853397i	−0.478432	+	0.878124i	$0.658795\pi$
$830$	9.07850	+	5.24147i	0.315119	+	0.181934i
$831$	8.34166	+	1.57847i	0.289369	+	0.0547564i
$832$	−40.4174	−	23.3350i	−1.40122	−	0.808995i
$833$		0			0
$834$	46.5190	+	8.80266i	1.61082	+	0.304811i
$835$	1.44216			0.0499079
$836$	−49.5763	−	85.8687i	−1.71463	−	2.96983i
$837$	9.68526	−	15.4123i	0.334771	−	0.532728i
$838$	−13.3746	−	7.72182i	−0.462017	−	0.266746i
$839$	26.0780	+	45.1684i	0.900312	+	1.55939i	0.827090	+	0.562070i	$0.189995\pi$
$839$	26.0780	+	45.1684i	0.900312	+	1.55939i	0.0732219	+	0.997316i	$0.476672\pi$
$840$		0			0
$841$	−14.4799	+	25.0798i	−0.499305	+	0.864822i
$842$	−27.5030	+	15.8789i	−0.947816	+	0.547222i
$843$	17.5261	+	15.0829i	0.603631	+	0.519483i
$844$	−19.2565	+	33.3533i	−0.662838	+	1.14807i
$845$	5.68280	−	9.84290i	0.195494	−	0.338606i
$846$	7.26956	+	9.11634i	0.249932	+	0.313426i
$847$		0			0
$848$	−118.554	+	68.4472i	−4.07116	+	2.35049i
$849$	−6.14148	+	2.14889i	−0.210775	+	0.0737496i
$850$		−	11.5851i		−	0.397366i
$851$		−	5.26372i		−	0.180438i
$852$	−105.112	+	36.7785i	−3.60109	+	1.26001i
$853$	−13.4028	+	7.73808i	−0.458902	+	0.264947i	−0.711582	−	0.702603i	$-0.752021\pi$
$853$	−13.4028	+	7.73808i	−0.458902	+	0.264947i	0.252681	+	0.967550i	$0.418688\pi$
$854$		0			0
$855$	−16.8074	−	21.0772i	−0.574802	−	0.720827i
$856$	−44.6804	+	77.3886i	−1.52714	+	2.64509i
$857$	24.4356	−	42.3238i	0.834706	−	1.44575i	−0.0595642	−	0.998224i	$-0.518971\pi$
$857$	24.4356	−	42.3238i	0.834706	−	1.44575i	0.894270	−	0.447528i	$-0.147696\pi$
$858$	16.6658	+	14.3425i	0.568960	+	0.489646i
$859$	8.45000	−	4.87861i	0.288310	−	0.166456i	−0.348869	−	0.937171i	$-0.613434\pi$
$859$	8.45000	−	4.87861i	0.288310	−	0.166456i	0.637180	+	0.770715i	$0.280101\pi$
$860$	0.0421217	−	0.0729569i	0.00143634	−	0.00248781i
$861$		0			0
$862$	−36.4356	−	63.1083i	−1.24100	−	2.14948i
$863$	−23.9462	−	13.8253i	−0.815138	−	0.470620i	0.0335987	−	0.999435i	$-0.489303\pi$
$863$	−23.9462	−	13.8253i	−0.815138	−	0.470620i	−0.848737	+	0.528815i	$0.822637\pi$
$864$	−53.4774	+	85.0997i	−1.81934	+	2.89515i
$865$	−10.8312	−	18.7602i	−0.368272	−	0.637866i
$866$	−76.1256			−2.58685
$867$	26.4655	+	5.00799i	0.898817	+	0.170080i
$868$		0			0
$869$	11.8357	+	6.83337i	0.401500	+	0.231806i
$870$	−1.11322	−	0.210651i	−0.0377416	−	0.00714173i
$871$	−8.41949	−	4.86100i	−0.285284	−	0.164709i
$872$	81.5391	−	47.0766i	2.76126	−	1.59422i
$873$	−2.61060	+	6.65107i	−0.0883554	+	0.225104i
$874$			61.5357i			2.08148i
$875$		0			0
$876$	−60.7697	−	52.2983i	−2.05322	−	1.76700i
$877$	0.932622	+	1.61535i	0.0314924	+	0.0545465i	0.881342	−	0.472479i	$-0.156641\pi$
$877$	0.932622	+	1.61535i	0.0314924	+	0.0545465i	−0.849850	+	0.527025i	$0.823307\pi$
$878$	25.2633			0.852596
$879$	21.7302	+	4.11195i	0.732942	+	0.138692i
$880$			41.3279i			1.39316i
$881$	0.0273875			0.000922707			0.000461353	−	1.00000i	$-0.499853\pi$
$881$	0.0273875			0.000922707			0.000461353		1.00000i	$0.499853\pi$
$882$		0			0
$883$	36.2074			1.21848			0.609239	−	0.792987i	$-0.291475\pi$
$883$	36.2074			1.21848			0.609239	+	0.792987i	$0.291475\pi$
$884$		−	12.1089i		−	0.407267i
$885$	16.6068	−	19.2968i	0.558232	−	0.648656i
$886$	30.7199			1.03206
$887$	−12.6626	−	21.9323i	−0.425170	−	0.736415i	0.571267	−	0.820765i	$-0.306452\pi$
$887$	−12.6626	−	21.9323i	−0.425170	−	0.736415i	−0.996436	+	0.0843491i	$0.973119\pi$
$888$	5.03984	−	26.6338i	0.169126	−	0.893772i
$889$		0			0
$890$		−	25.9616i		−	0.870235i
$891$	15.2233	−	16.4047i	0.510000	−	0.549578i
$892$	112.470	−	64.9343i	3.76576	−	2.17416i
$893$	9.28223	+	5.35910i	0.310618	+	0.179335i
$894$	−14.6662	+	17.0419i	−0.490511	+	0.569966i
$895$	15.7748	+	9.10759i	0.527294	+	0.304433i
$896$		0			0
$897$	−3.27837	−	9.36953i	−0.109462	−	0.312840i
$898$	41.5250			1.38571
$899$	−0.351613	−	0.609012i	−0.0117270	−	0.0203117i
$900$	−8.47787	−	56.2594i	−0.282596	−	1.87531i
$901$	−10.3290	−	5.96345i	−0.344109	−	0.198671i
$902$	−22.6348	−	39.2046i	−0.753655	−	1.30537i
$903$		0			0
$904$	49.9110	−	86.4483i	1.66001	−	2.87523i
$905$	−8.32075	+	4.80399i	−0.276591	+	0.159690i
$906$	9.87357	−	52.1784i	0.328027	−	1.73351i
$907$	19.4060	−	33.6122i	0.644366	−	1.11608i	−0.340081	−	0.940396i	$-0.610455\pi$
$907$	19.4060	−	33.6122i	0.644366	−	1.11608i	0.984447	−	0.175679i	$-0.0562121\pi$
$908$	1.28260	−	2.22153i	0.0425646	−	0.0737240i
$909$	−4.23134	−	28.0793i	−0.140345	−	0.931331i
$910$		0			0
$911$	−43.6110	+	25.1788i	−1.44490	+	0.834211i	−0.998171	−	0.0604602i	$-0.980743\pi$
$911$	−43.6110	+	25.1788i	−1.44490	+	0.834211i	−0.446725	+	0.894671i	$0.647410\pi$
$912$	−33.2368	+	175.645i	−1.10058	+	5.81619i
$913$			7.99980i			0.264755i
$914$			24.8481i			0.821901i
$915$	−17.7596	−	15.2838i	−0.587113	−	0.505268i
$916$	41.6581	−	24.0513i	1.37642	−	0.794677i
$917$		0			0
$918$	−16.9312	−	0.634343i	−0.558812	−	0.0209364i
$919$	1.49845	−	2.59539i	0.0494293	−	0.0856140i	−0.840252	−	0.542196i	$-0.817593\pi$
$919$	1.49845	−	2.59539i	0.0494293	−	0.0856140i	0.889681	+	0.456582i	$0.150926\pi$
$920$	16.5372	−	28.6434i	0.545217	−	0.944343i
$921$	17.5351	−	6.13546i	0.577800	−	0.202170i
$922$	77.5863	−	44.7945i	2.55517	−	1.47523i
$923$	11.3502	−	19.6591i	0.373596	−	0.647088i
$924$		0			0
$925$	3.07494	+	5.32595i	0.101103	+	0.175116i
$926$	−18.3729	−	10.6076i	−0.603771	−	0.348588i
$927$	−18.9169	+	48.1949i	−0.621313	+	1.58293i
$928$	1.94144	+	3.36268i	0.0637310	+	0.110385i
$929$	32.2215			1.05715			0.528577	−	0.848885i	$-0.322726\pi$
$929$	32.2215			1.05715			0.528577	+	0.848885i	$0.322726\pi$
$930$	−12.8970	+	14.9860i	−0.422908	+	0.491412i
$931$		0			0
$932$	51.3888	+	29.6694i	1.68330	+	0.971852i
$933$	10.7742	+	30.7924i	0.352730	+	1.00810i
$934$	48.5064	+	28.0052i	1.58718	+	0.916358i
$935$	−3.11828	+	1.80034i	−0.101979	+	0.0588774i
$936$	−7.61716	−	50.5476i	−0.248975	−	1.65220i
$937$			3.07038i			0.100305i	0.998742	+	0.0501525i	$0.0159708\pi$
$937$			3.07038i			0.100305i	−0.998742	+	0.0501525i	$0.984029\pi$
$938$		0			0
$939$	−42.6212	+	14.9130i	−1.39089	+	0.486668i
$940$	−4.60640	−	7.97852i	−0.150244	−	0.260231i
$941$	−38.8272			−1.26573			−0.632865	−	0.774263i	$-0.718121\pi$
$941$	−38.8272			−1.26573			−0.632865	+	0.774263i	$0.718121\pi$
$942$	22.8273	+	65.2399i	0.743752	+	2.12563i
$943$			20.4373i			0.665532i
$944$	−168.820			−5.49464
$945$		0			0
$946$	0.0883763			0.00287336
$947$			18.7513i			0.609337i	0.952459	+	0.304668i	$0.0985456\pi$
$947$			18.7513i			0.609337i	−0.952459	+	0.304668i	$0.901454\pi$
$948$	−16.7814	−	47.9610i	−0.545034	−	1.55770i
$949$	16.3433			0.530527
$950$	−35.9477	−	62.2632i	−1.16630	−	2.02008i
$951$	−22.7081	+	7.94549i	−0.736360	+	0.257650i
$952$		0			0
$953$		−	47.6453i		−	1.54338i	−0.635997	−	0.771692i	$-0.719411\pi$
$953$		−	47.6453i		−	1.54338i	0.635997	−	0.771692i	$-0.280589\pi$
$954$	−74.9528	−	29.4196i	−2.42669	−	0.952495i
$955$	−16.6859	+	9.63362i	−0.539944	+	0.311737i
$956$	−64.2911	−	37.1185i	−2.07932	−	1.20050i
$957$	−0.285546	−	0.816086i	−0.00923039	−	0.0263803i
$958$	6.24009	+	3.60272i	0.201608	+	0.116398i
$959$		0			0
$960$	33.6562	−	39.1080i	1.08625	−	1.26220i
$961$	18.7280			0.604129
$962$	4.41821	+	7.65257i	0.142449	+	0.246729i
$963$	−29.3194	+	4.41822i	−0.944806	+	0.142375i
$964$	57.2104	+	33.0304i	1.84262	+	1.06384i
$965$	−8.24569	−	14.2819i	−0.265438	−	0.459752i
$966$		0			0
$967$	25.8005	−	44.6878i	0.829689	−	1.43706i	−0.0685936	−	0.997645i	$-0.521851\pi$
$967$	25.8005	−	44.6878i	0.829689	−	1.43706i	0.898282	−	0.439419i	$-0.144815\pi$
$968$	37.7137	−	21.7740i	1.21216	−	0.699843i
$969$	−14.7007	+	5.14372i	−0.472254	+	0.165240i
$970$	3.88040	−	6.72104i	0.124592	−	0.215800i
$971$	−14.1933	+	24.5836i	−0.455485	+	0.788924i	−0.998716	−	0.0506597i	$-0.983868\pi$
$971$	−14.1933	+	24.5836i	−0.455485	+	0.788924i	0.543231	+	0.839584i	$0.317201\pi$
$972$	−82.6849	+	9.30958i	−2.65212	+	0.298605i
$973$		0			0
$974$	2.44867	−	1.41374i	0.0784603	−	0.0452991i
$975$	8.79058	+	7.56516i	0.281524	+	0.242279i
$976$			155.372i			4.97332i
$977$		−	41.1908i		−	1.31781i	−0.752227	−	0.658904i	$-0.771020\pi$
$977$		−	41.1908i		−	1.31781i	0.752227	−	0.658904i	$-0.228980\pi$
$978$	15.8400	−	83.7087i	0.506506	−	2.67671i
$979$	17.1576	−	9.90597i	0.548361	−	0.316596i
$980$		0			0
$981$	29.0808	+	11.4144i	0.928477	+	0.364435i
$982$	56.3668	−	97.6302i	1.79874	−	3.11550i
$983$	−26.4017	+	45.7291i	−0.842085	+	1.45853i	0.0460447	+	0.998939i	$0.485338\pi$
$983$	−26.4017	+	45.7291i	−0.842085	+	1.45853i	−0.888129	+	0.459594i	$0.847995\pi$
$984$	−19.5681	+	103.411i	−0.623807	+	3.29661i
$985$	19.7153	−	11.3826i	0.628181	−	0.362680i
$986$	−0.327278	+	0.566862i	−0.0104227	+	0.0180526i
$987$		0			0
$988$	−37.5731	−	65.0784i	−1.19536	−	2.07042i
$989$	−0.0345529	−	0.0199491i	−0.00109872	−	0.000634346i
$990$	−19.0057	+	15.1555i	−0.604041	+	0.481675i
$991$	−8.24486	−	14.2805i	−0.261907	−	0.453636i	0.704842	−	0.709364i	$-0.251018\pi$
$991$	−8.24486	−	14.2805i	−0.261907	−	0.453636i	−0.966749	+	0.255729i	$0.917685\pi$
$992$	67.7603			2.15139
$993$	2.56534	+	7.33171i	0.0814087	+	0.232665i
$994$		0			0
$995$	25.8696	+	14.9358i	0.820122	+	0.473498i
$996$	19.4012	−	22.5439i	0.614750	−	0.714329i
$997$	42.4857	+	24.5291i	1.34553	+	0.776845i	0.987613	−	0.156907i	$-0.0501523\pi$
$997$	42.4857	+	24.5291i	1.34553	+	0.776845i	0.357921	+	0.933752i	$0.383486\pi$
$998$	75.7484	−	43.7333i	2.39777	−	1.38435i
$999$	7.95203	−	4.20227i	0.251591	−	0.132954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.d.68.2		48
3.2	odd	2		1323.2.i.d.1097.6		48
7.2	even	3		441.2.o.e.293.1	yes	48
7.3	odd	6		441.2.s.d.374.23		48
7.4	even	3		441.2.s.d.374.24		48
7.5	odd	6		441.2.o.e.293.2	yes	48
7.6	odd	2	inner	441.2.i.d.68.1		48
9.2	odd	6		441.2.s.d.362.23		48
9.7	even	3		1323.2.s.d.656.2		48
21.2	odd	6		1323.2.o.e.881.23		48
21.5	even	6		1323.2.o.e.881.24		48
21.11	odd	6		1323.2.s.d.962.1		48
21.17	even	6		1323.2.s.d.962.2		48
21.20	even	2		1323.2.i.d.1097.21		48
63.2	odd	6		441.2.o.e.146.2	yes	48
63.11	odd	6	inner	441.2.i.d.227.23		48
63.16	even	3		1323.2.o.e.440.24		48
63.20	even	6		441.2.s.d.362.24		48
63.25	even	3		1323.2.i.d.521.21		48
63.34	odd	6		1323.2.s.d.656.1		48
63.38	even	6	inner	441.2.i.d.227.24		48
63.47	even	6		441.2.o.e.146.1	✓	48
63.52	odd	6		1323.2.i.d.521.6		48
63.61	odd	6		1323.2.o.e.440.23		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.1		48	7.6	odd	2	inner
441.2.i.d.68.2		48	1.1	even	1	trivial
441.2.i.d.227.23		48	63.11	odd	6	inner
441.2.i.d.227.24		48	63.38	even	6	inner
441.2.o.e.146.1	✓	48	63.47	even	6
441.2.o.e.146.2	yes	48	63.2	odd	6
441.2.o.e.293.1	yes	48	7.2	even	3
441.2.o.e.293.2	yes	48	7.5	odd	6
441.2.s.d.362.23		48	9.2	odd	6
441.2.s.d.362.24		48	63.20	even	6
441.2.s.d.374.23		48	7.3	odd	6
441.2.s.d.374.24		48	7.4	even	3
1323.2.i.d.521.6		48	63.52	odd	6
1323.2.i.d.521.21		48	63.25	even	3
1323.2.i.d.1097.6		48	3.2	odd	2
1323.2.i.d.1097.21		48	21.20	even	2
1323.2.o.e.440.23		48	63.61	odd	6
1323.2.o.e.440.24		48	63.16	even	3
1323.2.o.e.881.23		48	21.2	odd	6
1323.2.o.e.881.24		48	21.5	even	6
1323.2.s.d.656.1		48	63.34	odd	6
1323.2.s.d.656.2		48	9.7	even	3
1323.2.s.d.962.1		48	21.11	odd	6
1323.2.s.d.962.2		48	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.70883i q^{2} +(0.572034 + 1.63486i) q^{3} -5.33776 q^{4} +(0.601464 + 1.04177i) q^{5} +(4.42857 - 1.54954i) q^{6} +9.04141i q^{8} +(-2.34556 + 1.87039i) q^{9} +O(q^{10})\)	\(q-2.70883i q^{2} +(0.572034 + 1.63486i) q^{3} -5.33776 q^{4} +(0.601464 + 1.04177i) q^{5} +(4.42857 - 1.54954i) q^{6} +9.04141i q^{8} +(-2.34556 + 1.87039i) q^{9} +(2.82197 - 1.62926i) q^{10} +(2.15351 + 1.24333i) q^{11} +(-3.05338 - 8.72650i) q^{12} +(1.63211 + 0.942300i) q^{13} +(-1.35909 + 1.57924i) q^{15} +13.8161 q^{16} +(0.601863 + 1.04246i) q^{17} +(5.06658 + 6.35371i) q^{18} +(6.46933 + 3.73507i) q^{19} +(-3.21047 - 5.56070i) q^{20} +(3.36797 - 5.83350i) q^{22} +(-2.63359 + 1.52050i) q^{23} +(-14.7815 + 5.17199i) q^{24} +(1.77648 - 3.07696i) q^{25} +(2.55253 - 4.42111i) q^{26} +(-4.39957 - 2.76473i) q^{27} +(-0.173847 + 0.100371i) q^{29} +(4.27788 + 3.68154i) q^{30} +3.50314i q^{31} -19.3427i q^{32} +(-0.800795 + 4.23193i) q^{33} +(2.82384 - 1.63034i) q^{34} +(12.5200 - 9.98370i) q^{36} +(-0.865458 + 1.49902i) q^{37} +(10.1177 - 17.5243i) q^{38} +(-0.606909 + 3.20731i) q^{39} +(-9.41904 + 5.43809i) q^{40} +(3.36029 - 5.82020i) q^{41} +(0.00656005 + 0.0113623i) q^{43} +(-11.4949 - 6.63660i) q^{44} +(-3.35928 - 1.31855i) q^{45} +(4.11878 + 7.13394i) q^{46} +1.43481 q^{47} +(7.90329 + 22.5875i) q^{48} +(-8.33495 - 4.81219i) q^{50} +(-1.35999 + 1.58028i) q^{51} +(-8.71182 - 5.02977i) q^{52} +(-8.58085 + 4.95416i) q^{53} +(-7.48919 + 11.9177i) q^{54} +2.99128i q^{55} +(-2.40565 + 12.7130i) q^{57} +(0.271887 + 0.470923i) q^{58} -12.2191 q^{59} +(7.25448 - 8.42958i) q^{60} +11.2457i q^{61} +9.48942 q^{62} -24.7638 q^{64} +2.26704i q^{65} +(11.4636 + 2.16922i) q^{66} -5.15865 q^{67} +(-3.21260 - 5.56438i) q^{68} +(-3.99231 - 3.43578i) q^{69} -12.0452i q^{71} +(-16.9110 - 21.2071i) q^{72} +(7.51020 - 4.33602i) q^{73} +(4.06058 + 2.34438i) q^{74} +(6.04661 + 1.14418i) q^{75} +(-34.5317 - 19.9369i) q^{76} +(8.68805 + 1.64401i) q^{78} +5.49601 q^{79} +(8.30991 + 14.3932i) q^{80} +(2.00326 - 8.77422i) q^{81} +(-15.7659 - 9.10246i) q^{82} +(1.60854 + 2.78607i) q^{83} +(-0.723998 + 1.25400i) q^{85} +(0.0307786 - 0.0177700i) q^{86} +(-0.263539 - 0.226801i) q^{87} +(-11.2415 + 19.4708i) q^{88} +(3.98364 - 6.89986i) q^{89} +(-3.57172 + 9.09972i) q^{90} +(14.0574 - 8.11607i) q^{92} +(-5.72716 + 2.00392i) q^{93} -3.88665i q^{94} +8.98604i q^{95} +(31.6227 - 11.0647i) q^{96} +(2.06260 - 1.19084i) q^{97} +(-7.37671 + 1.11162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 - 8 * q^9	\( 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Introduction

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