LMFDB - Embedded newform 950.2.bb.e.857.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			857.7
Character	$\chi$	$=$	950.857
Dual form			950.2.bb.e.143.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573576 + 0.819152i) q^{2} +(-0.0418747 - 0.478630i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(0.368052 - 0.308832i) q^{6} +(0.971585 - 3.62600i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(2.72709 - 0.480860i) q^{9} +O(q^{10})$	\(q+(0.573576 + 0.819152i) q^{2} +(-0.0418747 - 0.478630i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(0.368052 - 0.308832i) q^{6} +(0.971585 - 3.62600i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(2.72709 - 0.480860i) q^{9} +(-2.49403 + 4.31978i) q^{11} +(0.464087 + 0.124352i) q^{12} +(-1.33531 - 0.116824i) q^{13} +(3.52753 - 1.28391i) q^{14} +(-0.766044 - 0.642788i) q^{16} +(3.85053 - 2.69617i) q^{17} +(1.95809 + 1.95809i) q^{18} +(3.89880 - 1.94919i) q^{19} +(-1.77620 - 0.313191i) q^{21} +(-4.96907 + 0.434737i) q^{22} +(2.34802 - 1.09490i) q^{23} +(0.164326 + 0.451483i) q^{24} +(-0.670204 - 1.16083i) q^{26} +(-0.717405 - 2.67739i) q^{27} +(3.07503 + 2.15316i) q^{28} +(-0.303332 - 1.72028i) q^{29} +(1.63635 - 0.944744i) q^{31} +(0.0871557 - 0.996195i) q^{32} +(2.17201 + 1.01283i) q^{33} +(4.41715 + 1.60771i) q^{34} +(-0.480860 + 2.72709i) q^{36} +(5.79340 - 5.79340i) q^{37} +(3.83295 + 2.07570i) q^{38} +0.644009i q^{39} +(6.01261 - 7.16555i) q^{41} +(-0.762233 - 1.63461i) q^{42} +(0.825480 - 1.77025i) q^{43} +(-3.20626 - 3.82107i) q^{44} +(2.24366 + 1.29538i) q^{46} +(-3.92548 + 5.60617i) q^{47} +(-0.275579 + 0.393568i) q^{48} +(-6.14174 - 3.54594i) q^{49} +(-1.45171 - 1.73008i) q^{51} +(0.566481 - 1.21482i) q^{52} +(4.44595 + 9.53438i) q^{53} +(1.78170 - 2.12335i) q^{54} +3.75391i q^{56} +(-1.09620 - 1.78446i) q^{57} +(1.23519 - 1.23519i) q^{58} +(-1.59029 + 9.01900i) q^{59} +(-2.01691 - 0.734095i) q^{61} +(1.71246 + 0.798532i) q^{62} +(0.906001 - 10.3556i) q^{63} +(0.866025 - 0.500000i) q^{64} +(0.416156 + 2.36014i) q^{66} +(-0.207335 - 0.145177i) q^{67} +(1.21661 + 4.54046i) q^{68} +(-0.622375 - 1.07799i) q^{69} +(4.08948 + 11.2357i) q^{71} +(-2.50971 + 1.17030i) q^{72} +(-10.4597 + 0.915101i) q^{73} +(8.06863 + 1.42272i) q^{74} +(0.498175 + 4.33034i) q^{76} +(13.2404 + 13.2404i) q^{77} +(-0.527542 + 0.369389i) q^{78} +(7.35519 + 6.17174i) q^{79} +(6.55504 - 2.38584i) q^{81} +(9.31836 + 0.815251i) q^{82} +(-14.4402 - 3.86923i) q^{83} +(0.901799 - 1.56196i) q^{84} +(1.92358 - 0.339179i) q^{86} +(-0.810675 + 0.217220i) q^{87} +(1.29100 - 4.81809i) q^{88} +(10.2071 - 8.56479i) q^{89} +(-1.72097 + 4.72832i) q^{91} +(0.225799 + 2.58090i) q^{92} +(-0.520704 - 0.743642i) q^{93} -6.84386 q^{94} -0.480458 q^{96} +(-8.07300 - 11.5294i) q^{97} +(-0.618097 - 7.06489i) q^{98} +(-4.72423 + 12.9797i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^7	$ 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) $ 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{18}\right)$

Coefficient data

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

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

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

$2$	0.573576	+	0.819152i	0.405580	+	0.579228i
$2$	0.573576	+	0.819152i	0.405580	+	0.579228i
$3$	−0.0418747	−	0.478630i	−0.0241763	−	0.276337i	−0.998655	−	0.0518551i	$-0.983487\pi$
$3$	−0.0418747	−	0.478630i	−0.0241763	−	0.276337i	0.974478	−	0.224482i	$-0.0720689\pi$
$4$	−0.342020	+	0.939693i	−0.171010	+	0.469846i
$5$		0			0
$5$		0			0
$6$	0.368052	−	0.308832i	0.150257	−	0.126080i
$7$	0.971585	−	3.62600i	0.367224	−	1.37050i	−0.497156	−	0.867661i	$-0.665622\pi$
$7$	0.971585	−	3.62600i	0.367224	−	1.37050i	0.864380	−	0.502839i	$-0.167711\pi$
$8$	−0.965926	+	0.258819i	−0.341506	+	0.0915064i
$9$	2.72709	−	0.480860i	0.909030	−	0.160287i
$10$		0			0
$11$	−2.49403	+	4.31978i	−0.751977	+	1.30246i	0.194886	+	0.980826i	$0.437566\pi$
$11$	−2.49403	+	4.31978i	−0.751977	+	1.30246i	−0.946863	+	0.321637i	$0.895767\pi$
$12$	0.464087	+	0.124352i	0.133970	+	0.0358972i
$13$	−1.33531	−	0.116824i	−0.370347	−	0.0324012i	−0.0995369	−	0.995034i	$-0.531736\pi$
$13$	−1.33531	−	0.116824i	−0.370347	−	0.0324012i	−0.270811	+	0.962633i	$0.587292\pi$
$14$	3.52753	−	1.28391i	0.942771	−	0.343141i
$15$		0			0
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	3.85053	−	2.69617i	0.933891	−	0.653917i	−0.00431668	−	0.999991i	$-0.501374\pi$
$17$	3.85053	−	2.69617i	0.933891	−	0.653917i	0.938207	+	0.346073i	$0.112485\pi$
$18$	1.95809	+	1.95809i	0.461527	+	0.461527i
$19$	3.89880	−	1.94919i	0.894446	−	0.447176i
$19$	3.89880	−	1.94919i	0.894446	−	0.447176i
$20$		0			0
$21$	−1.77620	−	0.313191i	−0.387598	−	0.0683440i
$22$	−4.96907	+	0.434737i	−1.05941	+	0.0926863i
$23$	2.34802	−	1.09490i	0.489597	−	0.228303i	−0.162111	−	0.986772i	$-0.551830\pi$
$23$	2.34802	−	1.09490i	0.489597	−	0.228303i	0.651708	+	0.758470i	$0.274053\pi$
$24$	0.164326	+	0.451483i	0.0335430	+	0.0921585i
$25$		0			0
$26$	−0.670204	−	1.16083i	−0.131438	−	0.227657i
$27$	−0.717405	−	2.67739i	−0.138065	−	0.515264i
$28$	3.07503	+	2.15316i	0.581125	+	0.406908i
$29$	−0.303332	−	1.72028i	−0.0563273	−	0.319448i	0.943605	−	0.331073i	$-0.107411\pi$
$29$	−0.303332	−	1.72028i	−0.0563273	−	0.319448i	−0.999932	+	0.0116251i	$0.996300\pi$
$30$		0			0
$31$	1.63635	−	0.944744i	0.293896	−	0.169681i	−0.345801	−	0.938308i	$-0.612393\pi$
$31$	1.63635	−	0.944744i	0.293896	−	0.169681i	0.639698	+	0.768627i	$0.279060\pi$
$32$	0.0871557	−	0.996195i	0.0154071	−	0.176104i
$33$	2.17201	+	1.01283i	0.378099	+	0.176310i
$34$	4.41715	+	1.60771i	0.757534	+	0.275720i
$35$		0			0
$36$	−0.480860	+	2.72709i	−0.0801433	+	0.454515i
$37$	5.79340	−	5.79340i	0.952429	−	0.952429i	−0.0464896	−	0.998919i	$-0.514803\pi$
$37$	5.79340	−	5.79340i	0.952429	−	0.952429i	0.998919	+	0.0464896i	$0.0148034\pi$
$38$	3.83295	+	2.07570i	0.621786	+	0.336723i
$39$			0.644009i			0.103124i
$40$		0			0
$41$	6.01261	−	7.16555i	0.939012	−	1.11907i	−0.0537001	−	0.998557i	$-0.517101\pi$
$41$	6.01261	−	7.16555i	0.939012	−	1.11907i	0.992712	−	0.120513i	$-0.0384541\pi$
$42$	−0.762233	−	1.63461i	−0.117615	−	0.252227i
$43$	0.825480	−	1.77025i	0.125885	−	0.269960i	−0.833258	−	0.552885i	$-0.813527\pi$
$43$	0.825480	−	1.77025i	0.125885	−	0.269960i	0.959142	+	0.282925i	$0.0913047\pi$
$44$	−3.20626	−	3.82107i	−0.483362	−	0.576048i
$45$		0			0
$46$	2.24366	+	1.29538i	0.330810	+	0.190993i
$47$	−3.92548	+	5.60617i	−0.572590	+	0.817743i	−0.996108	−	0.0881446i	$-0.971906\pi$
$47$	−3.92548	+	5.60617i	−0.572590	+	0.817743i	0.423518	+	0.905888i	$0.360795\pi$
$48$	−0.275579	+	0.393568i	−0.0397764	+	0.0568067i
$49$	−6.14174	−	3.54594i	−0.877392	−	0.506562i
$50$		0			0
$51$	−1.45171	−	1.73008i	−0.203280	−	0.242259i
$52$	0.566481	−	1.21482i	0.0785567	−	0.168465i
$53$	4.44595	+	9.53438i	0.610699	+	1.30965i	0.931927	+	0.362646i	$0.118127\pi$
$53$	4.44595	+	9.53438i	0.610699	+	1.30965i	−0.321228	+	0.947002i	$0.604096\pi$
$54$	1.78170	−	2.12335i	0.242459	−	0.288952i
$55$		0			0
$56$			3.75391i			0.501638i
$57$	−1.09620	−	1.78446i	−0.145196	−	0.236357i
$58$	1.23519	−	1.23519i	0.162188	−	0.162188i
$59$	−1.59029	+	9.01900i	−0.207039	+	1.17417i	0.687161	+	0.726505i	$0.258857\pi$
$59$	−1.59029	+	9.01900i	−0.207039	+	1.17417i	−0.894199	+	0.447669i	$0.852254\pi$
$60$		0			0
$61$	−2.01691	−	0.734095i	−0.258239	−	0.0939912i	0.209657	−	0.977775i	$-0.432765\pi$
$61$	−2.01691	−	0.734095i	−0.258239	−	0.0939912i	−0.467895	+	0.883784i	$0.654988\pi$
$62$	1.71246	+	0.798532i	0.217482	+	0.101414i
$63$	0.906001	−	10.3556i	0.114145	−	1.30469i
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$		0			0
$66$	0.416156	+	2.36014i	0.0512253	+	0.290513i
$67$	−0.207335	−	0.145177i	−0.0253300	−	0.0177363i	0.560843	−	0.827922i	$-0.310477\pi$
$67$	−0.207335	−	0.145177i	−0.0253300	−	0.0177363i	−0.586173	+	0.810186i	$0.699366\pi$
$68$	1.21661	+	4.54046i	0.147536	+	0.550612i
$69$	−0.622375	−	1.07799i	−0.0749252	−	0.129774i
$70$		0			0
$71$	4.08948	+	11.2357i	0.485332	+	1.33344i	0.904865	+	0.425698i	$0.139971\pi$
$71$	4.08948	+	11.2357i	0.485332	+	1.33344i	−0.419534	+	0.907740i	$0.637806\pi$
$72$	−2.50971	+	1.17030i	−0.295772	+	0.137921i
$73$	−10.4597	+	0.915101i	−1.22421	+	0.107104i	−0.680867	−	0.732407i	$-0.738397\pi$
$73$	−10.4597	+	0.915101i	−1.22421	+	0.107104i	−0.543343	+	0.839511i	$0.682841\pi$
$74$	8.06863	+	1.42272i	0.937960	+	0.165388i
$75$		0			0
$76$	0.498175	+	4.33034i	0.0571446	+	0.496724i
$77$	13.2404	+	13.2404i	1.50888	+	1.50888i
$78$	−0.527542	+	0.369389i	−0.0597323	+	0.0418250i
$79$	7.35519	+	6.17174i	0.827523	+	0.694375i	0.954721	−	0.297503i	$-0.0961537\pi$
$79$	7.35519	+	6.17174i	0.827523	+	0.694375i	−0.127197	+	0.991877i	$0.540598\pi$
$80$		0			0
$81$	6.55504	−	2.38584i	0.728338	−	0.265093i
$82$	9.31836	+	0.815251i	1.02904	+	0.0900294i
$83$	−14.4402	−	3.86923i	−1.58501	−	0.424703i	−0.644539	−	0.764571i	$-0.722951\pi$
$83$	−14.4402	−	3.86923i	−1.58501	−	0.424703i	−0.940473	+	0.339868i	$0.889618\pi$
$84$	0.901799	−	1.56196i	0.0983943	−	0.170424i
$85$		0			0
$86$	1.92358	−	0.339179i	0.207425	−	0.0365746i
$87$	−0.810675	+	0.217220i	−0.0869134	+	0.0232884i
$88$	1.29100	−	4.81809i	0.137621	−	0.513610i
$89$	10.2071	−	8.56479i	1.08195	−	0.907866i	0.0858712	−	0.996306i	$-0.472633\pi$
$89$	10.2071	−	8.56479i	1.08195	−	0.907866i	0.996081	+	0.0884402i	$0.0281882\pi$
$90$		0			0
$91$	−1.72097	+	4.72832i	−0.180406	+	0.495663i
$92$	0.225799	+	2.58090i	0.0235412	+	0.269077i
$93$	−0.520704	−	0.743642i	−0.0539945	−	0.0771121i
$94$	−6.84386			−0.705891
$95$		0			0
$96$	−0.480458			−0.0490365
$97$	−8.07300	−	11.5294i	−0.819689	−	1.17064i	−0.982917	−	0.184048i	$-0.941080\pi$
$97$	−8.07300	−	11.5294i	−0.819689	−	1.17064i	0.163229	−	0.986588i	$-0.447809\pi$
$98$	−0.618097	−	7.06489i	−0.0624373	−	0.713661i
$99$	−4.72423	+	12.9797i	−0.474803	+	1.30451i
$100$		0			0
$101$	−8.61490	+	7.22876i	−0.857214	+	0.719288i	−0.961366	−	0.275273i	$-0.911232\pi$
$101$	−8.61490	+	7.22876i	−0.857214	+	0.719288i	0.104152	+	0.994561i	$0.466787\pi$
$102$	0.584531	−	2.18150i	0.0578772	−	0.216001i
$103$	−2.30555	+	0.617770i	−0.227173	+	0.0608707i	−0.370610	−	0.928789i	$-0.620851\pi$
$103$	−2.30555	+	0.617770i	−0.227173	+	0.0608707i	0.143437	+	0.989659i	$0.454185\pi$
$104$	1.32004	−	0.232759i	0.129441	−	0.0228239i
$105$		0			0
$106$	−5.26001	+	9.11061i	−0.510898	+	0.884901i
$107$	−6.81684	−	1.82657i	−0.659009	−	0.176581i	−0.0862101	−	0.996277i	$-0.527476\pi$
$107$	−6.81684	−	1.82657i	−0.659009	−	0.176581i	−0.572799	+	0.819696i	$0.694142\pi$
$108$	2.76129	+	0.241582i	0.265705	+	0.0232462i
$109$	−2.80009	+	1.01915i	−0.268200	+	0.0976167i	−0.472620	−	0.881267i	$-0.656691\pi$
$109$	−2.80009	+	1.01915i	−0.268200	+	0.0976167i	0.204420	+	0.978883i	$0.434469\pi$
$110$		0			0
$111$	−3.01549	−	2.53030i	−0.286218	−	0.240165i
$112$	−3.07503	+	2.15316i	−0.290563	+	0.203454i
$113$	6.03088	+	6.03088i	0.567338	+	0.567338i	0.931382	−	0.364044i	$-0.118604\pi$
$113$	6.03088	+	6.03088i	0.567338	+	0.567338i	−0.364044	+	0.931382i	$0.618604\pi$
$114$	0.832987	−	1.92148i	0.0780164	−	0.179963i
$115$		0			0
$116$	1.72028	+	0.303332i	0.159724	+	0.0281636i
$117$	−3.69768	+	0.323505i	−0.341850	+	0.0299080i
$118$	−8.30009	+	3.87040i	−0.764085	+	0.356299i
$119$	−6.03521	−	16.5816i	−0.553246	−	1.52003i
$120$		0			0
$121$	−6.94033	−	12.0210i	−0.630939	−	1.09282i
$122$	−0.555516	−	2.07321i	−0.0502941	−	0.187700i
$123$	−3.68142	−	2.57776i	−0.331942	−	0.232429i
$124$	0.328106	+	1.86078i	0.0294648	+	0.167103i
$125$		0			0
$126$	9.00250	−	5.19760i	0.802006	−	0.463039i
$127$	−0.663010	+	7.57824i	−0.0588326	+	0.672460i	0.908322	+	0.418271i	$0.137364\pi$
$127$	−0.663010	+	7.57824i	−0.0588326	+	0.672460i	−0.967155	+	0.254188i	$0.918192\pi$
$128$	0.906308	+	0.422618i	0.0801070	+	0.0373545i
$129$	−0.881860	−	0.320971i	−0.0776434	−	0.0282599i
$130$		0			0
$131$	1.78830	−	10.1420i	0.156245	−	0.886107i	−0.801394	−	0.598136i	$-0.795908\pi$
$131$	1.78830	−	10.1420i	0.156245	−	0.886107i	0.957639	−	0.287971i	$-0.0929807\pi$
$132$	−1.69462	+	1.69462i	−0.147497	+	0.147497i
$133$	−3.27977	−	16.0309i	−0.284392	−	1.39005i
$134$		−	0.253109i		−	0.0218653i
$135$		0			0
$136$	−3.02151	+	3.60089i	−0.259092	+	0.308774i
$137$	−5.94775	−	12.7550i	−0.508150	−	1.08973i	−0.978309	−	0.207150i	$-0.933581\pi$
$137$	−5.94775	−	12.7550i	−0.508150	−	1.08973i	0.470159	−	0.882582i	$-0.344197\pi$
$138$	0.526054	−	1.12813i	0.0447807	−	0.0960325i
$139$	−11.9222	−	14.2084i	−1.01123	−	1.20514i	−0.978621	−	0.205670i	$-0.934062\pi$
$139$	−11.9222	−	14.2084i	−1.01123	−	1.20514i	−0.0326101	−	0.999468i	$-0.510382\pi$
$140$		0			0
$141$	2.84765	+	1.64409i	0.239816	+	0.138458i
$142$	−6.85816	+	9.79446i	−0.575524	+	0.821933i
$143$	3.83494	−	5.47687i	0.320694	−	0.457999i
$144$	−2.39816	−	1.38458i	−0.199847	−	0.115382i
$145$		0			0
$146$	−6.74902	−	8.04317i	−0.558553	−	0.665657i
$147$	−1.44001	+	3.08810i	−0.118770	+	0.254703i
$148$	3.46256	+	7.42548i	0.284620	+	0.610370i
$149$	−5.19534	+	6.19156i	−0.425618	+	0.507232i	−0.935653	−	0.352922i	$-0.885188\pi$
$149$	−5.19534	+	6.19156i	−0.425618	+	0.507232i	0.510034	+	0.860154i	$0.329633\pi$
$150$		0			0
$151$			11.3814i			0.926208i	0.886304	+	0.463104i	$0.153264\pi$
$151$			11.3814i			0.926208i	−0.886304	+	0.463104i	$0.846736\pi$
$152$	−3.26146	+	2.89186i	−0.264540	+	0.234561i
$153$	9.20427	−	9.20427i	0.744121	−	0.744121i
$154$	−3.25151	+	18.4402i	−0.262014	+	1.48596i
$155$		0			0
$156$	−0.605171	−	0.220264i	−0.0484524	−	0.0176352i
$157$	2.27098	+	1.05898i	0.181244	+	0.0845154i	0.511122	−	0.859508i	$-0.329230\pi$
$157$	2.27098	+	1.05898i	0.181244	+	0.0845154i	−0.329878	+	0.944023i	$0.607008\pi$
$158$	−0.836827	+	9.56498i	−0.0665744	+	0.760949i
$159$	4.37726	−	2.52721i	0.347140	−	0.200421i
$160$		0			0
$161$	−1.68881	−	9.57773i	−0.133097	−	0.754831i
$162$	5.71418	+	4.00111i	0.448949	+	0.314357i
$163$	3.42920	+	12.7979i	0.268596	+	1.00241i	0.960013	+	0.279956i	$0.0903200\pi$
$163$	3.42920	+	12.7979i	0.268596	+	1.00241i	−0.691417	+	0.722456i	$0.743013\pi$
$164$	4.67698	+	8.10076i	0.365211	+	0.632563i
$165$		0			0
$166$	−5.11305	−	14.0480i	−0.396849	−	1.09033i
$167$	9.96206	−	4.64539i	0.770888	−	0.359471i	0.00295017	−	0.999996i	$-0.499061\pi$
$167$	9.96206	−	4.64539i	0.770888	−	0.359471i	0.767937	+	0.640525i	$0.221283\pi$
$168$	1.79673	−	0.157194i	0.138621	−	0.0121278i
$169$	−11.0331	−	1.94543i	−0.848700	−	0.149649i
$170$		0			0
$171$	9.69509	−	7.19040i	0.741402	−	0.549864i
$172$	1.38116	+	1.38116i	0.105312	+	0.105312i
$173$	−14.4251	+	10.1006i	−1.09672	+	0.767934i	−0.974459	−	0.224563i	$-0.927904\pi$
$173$	−14.4251	+	10.1006i	−1.09672	+	0.767934i	−0.122264	+	0.992498i	$0.539015\pi$
$174$	−0.642920	−	0.539474i	−0.0487396	−	0.0408974i
$175$		0			0
$176$	4.68724	−	1.70601i	0.353314	−	0.128596i
$177$	4.38336	+	0.383494i	0.329473	+	0.0288252i
$178$	12.8704	+	3.44862i	0.964680	+	0.258485i
$179$	−9.94971	+	17.2334i	−0.743676	+	1.28808i	0.207135	+	0.978312i	$0.433586\pi$
$179$	−9.94971	+	17.2334i	−0.743676	+	1.28808i	−0.950811	+	0.309772i	$0.899747\pi$
$180$		0			0
$181$	7.23169	−	1.27514i	0.537527	−	0.0947805i	0.101707	−	0.994814i	$-0.467570\pi$
$181$	7.23169	−	1.27514i	0.537527	−	0.0947805i	0.435820	+	0.900034i	$0.356458\pi$
$182$	−4.86032	+	1.30232i	−0.360271	+	0.0965343i
$183$	−0.266902	+	0.996092i	−0.0197300	+	0.0736333i
$184$	−1.98464	+	1.66531i	−0.146309	+	0.122768i
$185$		0			0
$186$	0.310493	−	0.853071i	0.0227664	−	0.0625502i
$187$	2.04354	+	23.3578i	0.149438	+	1.70809i
$188$	−3.92548	−	5.60617i	−0.286295	−	0.408872i
$189$	−10.4052			−0.756870
$190$		0			0
$191$	2.96590			0.214605			0.107303	−	0.994226i	$-0.465779\pi$
$191$	2.96590			0.214605			0.107303	+	0.994226i	$0.465779\pi$
$192$	−0.275579	−	0.393568i	−0.0198882	−	0.0284033i
$193$	0.855286	+	9.77596i	0.0615648	+	0.703689i	0.962774	+	0.270306i	$0.0871248\pi$
$193$	0.855286	+	9.77596i	0.0615648	+	0.703689i	−0.901210	+	0.433383i	$0.857320\pi$
$194$	4.81388	−	13.2260i	0.345616	−	0.949573i
$195$		0			0
$196$	5.43269	−	4.55857i	0.388049	−	0.325612i
$197$	−2.39954	+	8.95519i	−0.170960	+	0.638031i	0.826245	+	0.563311i	$0.190473\pi$
$197$	−2.39954	+	8.95519i	−0.170960	+	0.638031i	−0.997205	+	0.0747197i	$0.976194\pi$
$198$	−13.3421	+	3.57499i	−0.948179	+	0.254064i
$199$	9.86381	−	1.73926i	0.699227	−	0.123293i	0.187276	−	0.982307i	$-0.440034\pi$
$199$	9.86381	−	1.73926i	0.699227	−	0.123293i	0.511951	+	0.859015i	$0.328923\pi$
$200$		0			0
$201$	−0.0608042	+	0.105316i	−0.00428879	+	0.00742841i
$202$	−10.8628	−	2.91067i	−0.764301	−	0.204794i
$203$	−6.53245	−	0.571515i	−0.458488	−	0.0401125i
$204$	2.12225	−	0.772437i	0.148587	−	0.0540814i
$205$		0			0
$206$	−1.82846	−	1.53426i	−0.127395	−	0.106897i
$207$	5.87678	−	4.11497i	0.408465	−	0.286010i
$208$	0.947811	+	0.947811i	0.0657189	+	0.0657189i
$209$	−1.30362	+	21.7033i	−0.0901732	+	1.50125i
$210$		0			0
$211$	−23.8211	−	4.20030i	−1.63991	−	0.289160i	−0.723776	−	0.690035i	$-0.757595\pi$
$211$	−23.8211	−	4.20030i	−1.63991	−	0.289160i	−0.916133	+	0.400874i	$0.868706\pi$
$212$	−10.4800	+	0.916881i	−0.719769	+	0.0629716i
$213$	5.20651	−	2.42784i	0.356744	−	0.166353i
$214$	−2.41374	−	6.63170i	−0.165000	−	0.453334i
$215$		0			0
$216$	1.38592	+	2.40048i	0.0942999	+	0.163332i
$217$	−1.83580	−	6.85129i	−0.124622	−	0.465096i
$218$	−2.44090	−	1.70914i	−0.165319	−	0.115757i
$219$	0.875989	+	4.96798i	0.0591939	+	0.335705i
$220$		0			0
$221$	−5.45662	+	3.15038i	−0.367052	+	0.211917i
$222$	0.343084	−	3.92146i	0.0230263	−	0.263191i
$223$	−1.50444	−	0.701532i	−0.100745	−	0.0469780i	0.371593	−	0.928396i	$-0.378812\pi$
$223$	−1.50444	−	0.701532i	−0.100745	−	0.0469780i	−0.472337	+	0.881418i	$0.656590\pi$
$224$	−3.52753	−	1.28391i	−0.235693	−	0.0857851i
$225$		0			0
$226$	−1.48104	+	8.39938i	−0.0985171	+	0.558719i
$227$	−11.1061	+	11.1061i	−0.737139	+	0.737139i	−0.972023	−	0.234885i	$-0.924529\pi$
$227$	−11.1061	+	11.1061i	−0.737139	+	0.737139i	0.234885	+	0.972023i	$0.424529\pi$
$228$	2.05177	−	0.419773i	0.135882	−	0.0278001i
$229$		−	3.84236i		−	0.253911i	−0.991908	−	0.126955i	$-0.959480\pi$
$229$		−	3.84236i		−	0.253911i	0.991908	−	0.126955i	$-0.0405205\pi$
$230$		0			0
$231$	5.78280	−	6.89167i	0.380480	−	0.453439i
$232$	0.738237	+	1.58315i	0.0484676	+	0.103939i
$233$	2.99274	−	6.41796i	0.196061	−	0.420454i	−0.783558	−	0.621319i	$-0.786597\pi$
$233$	2.99274	−	6.41796i	0.196061	−	0.420454i	0.979619	+	0.200864i	$0.0643750\pi$
$234$	−2.38590	−	2.84341i	−0.155971	−	0.185879i
$235$		0			0
$236$	−7.93118	−	4.57907i	−0.516276	−	0.298072i
$237$	2.64598	−	3.77885i	0.171875	−	0.245463i
$238$	10.1212	−	14.4546i	0.656059	−	0.936950i
$239$	−7.49094	−	4.32489i	−0.484548	−	0.279754i	0.237762	−	0.971324i	$-0.423586\pi$
$239$	−7.49094	−	4.32489i	−0.484548	−	0.279754i	−0.722310	+	0.691569i	$0.756920\pi$
$240$		0			0
$241$	13.2053	+	15.7374i	0.850625	+	1.01374i	0.999690	+	0.0249084i	$0.00792942\pi$
$241$	13.2053	+	15.7374i	0.850625	+	1.01374i	−0.149064	+	0.988828i	$0.547626\pi$
$242$	5.86622	−	12.5801i	0.377095	−	0.808683i
$243$	−4.93071	−	10.5739i	−0.316305	−	0.678319i
$244$	1.37965	−	1.64420i	0.0883229	−	0.105259i
$245$		0			0
$246$		−	4.49418i		−	0.286539i
$247$	−5.43381	+	2.14730i	−0.345745	+	0.136629i
$248$	−1.33607	+	1.33607i	−0.0848405	+	0.0848405i
$249$	−1.24725	+	7.07351i	−0.0790413	+	0.448265i
$250$		0			0
$251$	−1.95128	−	0.710207i	−0.123163	−	0.0448278i	0.279703	−	0.960087i	$-0.409764\pi$
$251$	−1.95128	−	0.710207i	−0.123163	−	0.0448278i	−0.402867	+	0.915259i	$0.631986\pi$
$252$	9.42124	+	4.39320i	0.593482	+	0.276745i
$253$	−1.12630	+	12.8737i	−0.0708098	+	0.809360i
$254$	−6.58801	+	3.80359i	−0.413369	+	0.238659i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	13.0723	+	9.15332i	0.815427	+	0.570968i	0.905196	−	0.424994i	$-0.139724\pi$
$257$	13.0723	+	9.15332i	0.815427	+	0.570968i	−0.0897689	+	0.995963i	$0.528613\pi$
$258$	−0.242890	−	0.906478i	−0.0151217	−	0.0564349i
$259$	−15.3781	−	26.6357i	−0.955549	−	1.65506i
$260$		0			0
$261$	−1.65443	−	4.54550i	−0.102406	−	0.281359i
$262$	9.33354	−	4.35230i	0.576628	−	0.268886i
$263$	−6.43268	+	0.562787i	−0.396656	+	0.0347029i	−0.283739	−	0.958901i	$-0.591575\pi$
$263$	−6.43268	+	0.562787i	−0.396656	+	0.0347029i	−0.112917	+	0.993604i	$0.536019\pi$
$264$	−2.36014	−	0.416156i	−0.145257	−	0.0256126i
$265$		0			0
$266$	11.2505	−	11.8816i	0.689814	−	0.728505i
$267$	−4.52678	−	4.52678i	−0.277035	−	0.277035i
$268$	0.207335	−	0.145177i	0.0126650	−	0.00886813i
$269$	16.5823	+	13.9142i	1.01104	+	0.848366i	0.988476	−	0.151380i	$-0.0483716\pi$
$269$	16.5823	+	13.9142i	1.01104	+	0.848366i	0.0225671	+	0.999745i	$0.492816\pi$
$270$		0			0
$271$	−24.3332	+	8.85654i	−1.47813	+	0.537997i	−0.950296	−	0.311348i	$-0.899219\pi$
$271$	−24.3332	+	8.85654i	−1.47813	+	0.537997i	−0.527838	+	0.849345i	$0.676997\pi$
$272$	−4.68274	−	0.409687i	−0.283933	−	0.0248409i
$273$	2.33518	+	0.625709i	0.141331	+	0.0378697i
$274$	7.03679	−	12.1881i	0.425108	−	0.736308i
$275$		0			0
$276$	1.22584	−	0.216149i	0.0737869	−	0.0130106i
$277$	8.01321	−	2.14713i	0.481467	−	0.129009i	−0.00991869	−	0.999951i	$-0.503157\pi$
$277$	8.01321	−	2.14713i	0.481467	−	0.129009i	0.491386	+	0.870942i	$0.336491\pi$
$278$	4.80050	−	17.9157i	0.287915	−	1.07451i
$279$	4.00817	−	3.36326i	0.239963	−	0.201353i
$280$		0			0
$281$	8.25824	−	22.6893i	0.492645	−	1.35353i	−0.405605	−	0.914048i	$-0.632939\pi$
$281$	8.25824	−	22.6893i	0.492645	−	1.35353i	0.898251	−	0.439484i	$-0.144839\pi$
$282$	0.286584	+	3.27568i	0.0170659	+	0.195064i
$283$	5.09656	+	7.27864i	0.302959	+	0.432670i	0.941549	−	0.336877i	$-0.109371\pi$
$283$	5.09656	+	7.27864i	0.302959	+	0.432670i	−0.638590	+	0.769547i	$0.720482\pi$
$284$	−11.9568			−0.709507
$285$		0			0
$286$	6.68602			0.395353
$287$	−20.1405	−	28.7637i	−1.18886	−	1.69787i
$288$	−0.241348	−	2.75862i	−0.0142216	−	0.162553i
$289$	1.74291	−	4.78860i	0.102524	−	0.281682i
$290$		0			0
$291$	−5.18027	+	4.34677i	−0.303673	+	0.254812i
$292$	2.71750	−	10.1418i	0.159030	−	0.593507i
$293$	13.2971	−	3.56296i	0.776827	−	0.208150i	0.151441	−	0.988466i	$-0.451608\pi$
$293$	13.2971	−	3.56296i	0.776827	−	0.208150i	0.625385	+	0.780316i	$0.284942\pi$
$294$	−3.35558	+	0.591679i	−0.195701	+	0.0345074i
$295$		0			0
$296$	−4.09655	+	7.09544i	−0.238107	+	0.412414i
$297$	13.3550	+	3.57845i	0.774933	+	0.207643i
$298$	−8.05175	−	0.704437i	−0.466425	−	0.0408069i
$299$	−3.26324	+	1.18772i	−0.188718	+	0.0686878i
$300$		0			0
$301$	−5.61690	−	4.71314i	−0.323753	−	0.271661i
$302$	−9.32312	+	6.52812i	−0.536486	+	0.375651i
$303$	3.82064	+	3.82064i	0.219490	+	0.219490i
$304$	−4.23957	−	1.01293i	−0.243156	−	0.0580956i
$305$		0			0
$306$	12.8190	+	2.26034i	0.732816	+	0.129215i
$307$	−5.34855	+	0.467937i	−0.305258	+	0.0267066i	−0.238756	−	0.971080i	$-0.576739\pi$
$307$	−5.34855	+	0.467937i	−0.305258	+	0.0267066i	−0.0665022	+	0.997786i	$0.521184\pi$
$308$	−16.9704	+	7.91341i	−0.966976	+	0.450908i
$309$	0.392227	+	1.07764i	0.0223130	+	0.0613045i
$310$		0			0
$311$	5.24325	+	9.08157i	0.297317	+	0.514969i	0.975521	−	0.219905i	$-0.0705748\pi$
$311$	5.24325	+	9.08157i	0.297317	+	0.514969i	−0.678204	+	0.734874i	$0.737241\pi$
$312$	−0.166682	−	0.622065i	−0.00943650	−	0.0352175i
$313$	−5.10972	−	3.57786i	−0.288818	−	0.202233i	0.420184	−	0.907439i	$-0.361966\pi$
$313$	−5.10972	−	3.57786i	−0.288818	−	0.202233i	−0.709002	+	0.705206i	$0.750854\pi$
$314$	0.435119	+	2.46768i	0.0245552	+	0.139259i
$315$		0			0
$316$	−8.31516	+	4.80076i	−0.467764	+	0.270064i
$317$	1.13557	−	12.9797i	0.0637802	−	0.729012i	−0.895223	−	0.445618i	$-0.852984\pi$
$317$	1.13557	−	12.9797i	0.0637802	−	0.729012i	0.959004	−	0.283394i	$-0.0914604\pi$
$318$	4.58087	+	2.13609i	0.256882	+	0.119786i
$319$	8.18774	+	2.98010i	0.458426	+	0.166853i
$320$		0			0
$321$	−0.588796	+	3.33923i	−0.0328634	+	0.186378i
$322$	6.87696	−	6.87696i	0.383238	−	0.383238i
$323$	9.75709	−	18.0173i	0.542899	−	1.00251i
$324$			6.97573i			0.387541i
$325$		0			0
$326$	−8.51655	+	10.1496i	−0.471688	+	0.562136i
$327$	0.605047	+	1.29753i	0.0334592	+	0.0717535i
$328$	−3.95315	+	8.47756i	−0.218276	+	0.468095i
$329$	16.5140	+	19.6807i	0.910448	+	1.08503i
$330$		0			0
$331$	−13.6536	−	7.88293i	−0.750471	−	0.433285i	0.0753928	−	0.997154i	$-0.475979\pi$
$331$	−13.6536	−	7.88293i	−0.750471	−	0.433285i	−0.825864	+	0.563869i	$0.809312\pi$
$332$	8.57471	−	12.2460i	0.470598	−	0.672084i
$333$	13.0133	−	18.5849i	0.713125	−	1.01845i
$334$	9.51928	+	5.49596i	0.520872	+	0.300726i
$335$		0			0
$336$	1.15933	+	1.38164i	0.0632466	+	0.0753744i
$337$	−11.8506	+	25.4137i	−0.645544	+	1.38437i	0.262268	+	0.964995i	$0.415530\pi$
$337$	−11.8506	+	25.4137i	−0.645544	+	1.38437i	−0.907812	+	0.419378i	$0.862248\pi$
$338$	−4.73472	−	10.1536i	−0.257535	−	0.552285i
$339$	2.63402	−	3.13910i	0.143060	−	0.170492i
$340$		0			0
$341$			9.42487i			0.510385i
$342$	11.4509	+	3.81751i	0.619194	+	0.206427i
$343$	−0.243870	+	0.243870i	−0.0131678	+	0.0131678i
$344$	−0.339179	+	1.92358i	−0.0182873	+	0.103712i
$345$		0			0
$346$	−16.5478	−	6.02292i	−0.889618	−	0.323794i
$347$	−1.77554	−	0.827948i	−0.0953160	−	0.0444466i	0.374376	−	0.927277i	$-0.377857\pi$
$347$	−1.77554	−	0.827948i	−0.0953160	−	0.0444466i	−0.469692	+	0.882831i	$0.655635\pi$
$348$	0.0731474	−	0.836078i	0.00392111	−	0.0448185i
$349$	15.6149	−	9.01529i	0.835848	−	0.482577i	−0.0200025	−	0.999800i	$-0.506367\pi$
$349$	15.6149	−	9.01529i	0.835848	−	0.482577i	0.855851	+	0.517223i	$0.173034\pi$
$350$		0			0
$351$	0.645171	+	3.65895i	0.0344367	+	0.195300i
$352$	4.08597	+	2.86103i	0.217783	+	0.152493i
$353$	−1.67238	−	6.24143i	−0.0890121	−	0.332198i	0.907032	−	0.421063i	$-0.138343\pi$
$353$	−1.67238	−	6.24143i	−0.0890121	−	0.332198i	−0.996044	+	0.0888650i	$0.971676\pi$
$354$	2.20005	+	3.81060i	0.116931	+	0.202531i
$355$		0			0
$356$	4.55723	+	12.5209i	0.241533	+	0.663606i
$357$	−7.68372	+	3.58298i	−0.406665	+	0.189631i
$358$	−19.8237	+	1.73435i	−1.04771	+	0.0916632i
$359$	−19.3534	−	3.41253i	−1.02143	−	0.180106i	−0.362244	−	0.932083i	$-0.617989\pi$
$359$	−19.3534	−	3.41253i	−1.02143	−	0.180106i	−0.659190	+	0.751977i	$0.729101\pi$
$360$		0			0
$361$	11.4013	−	15.1990i	0.600068	−	0.799949i
$362$	5.19246	+	5.19246i	0.272910	+	0.272910i
$363$	−5.46298	+	3.82522i	−0.286732	+	0.200772i
$364$	−3.85456	−	3.23436i	−0.202034	−	0.169527i
$365$		0			0
$366$	−0.969040	+	0.352702i	−0.0506525	+	0.0184360i
$367$	−14.0514	−	1.22934i	−0.733479	−	0.0641711i	−0.285704	−	0.958318i	$-0.592228\pi$
$367$	−14.0514	−	1.22934i	−0.733479	−	0.0641711i	−0.447774	+	0.894147i	$0.647783\pi$
$368$	−2.50248	−	0.670538i	−0.130451	−	0.0349542i
$369$	12.9513	−	22.4323i	0.674218	−	1.16778i
$370$		0			0
$371$	38.8913	−	6.85759i	2.01914	−	0.356028i
$372$	0.876887	−	0.234961i	0.0454644	−	0.0121822i
$373$	−9.39261	+	35.0537i	−0.486331	+	1.81501i	0.0876618	+	0.996150i	$0.472061\pi$
$373$	−9.39261	+	35.0537i	−0.486331	+	1.81501i	−0.573993	+	0.818861i	$0.694606\pi$
$374$	−17.9614	+	15.0714i	−0.928763	+	0.779325i
$375$		0			0
$376$	2.34074	−	6.43113i	0.120714	−	0.331660i
$377$	0.204071	+	2.33254i	0.0105102	+	0.120132i
$378$	−5.96820	−	8.52348i	−0.306971	−	0.438400i
$379$	8.38366			0.430640			0.215320	−	0.976544i	$-0.430921\pi$
$379$	8.38366			0.430640			0.215320	+	0.976544i	$0.430921\pi$
$380$		0			0
$381$	3.65493			0.187248
$382$	1.70117	+	2.42952i	0.0870395	+	0.124305i
$383$	1.39172	+	15.9074i	0.0711136	+	0.812832i	0.945079	+	0.326843i	$0.105985\pi$
$383$	1.39172	+	15.9074i	0.0711136	+	0.812832i	−0.873965	+	0.485989i	$0.838460\pi$
$384$	0.164326	−	0.451483i	0.00838574	−	0.0230396i
$385$		0			0
$386$	−7.51743	+	6.30787i	−0.382627	+	0.321062i
$387$	1.39992	−	5.22457i	0.0711618	−	0.265580i
$388$	13.5953	−	3.64284i	0.690194	−	0.184937i
$389$	27.1705	−	4.79090i	1.37760	−	0.242908i	0.564693	−	0.825301i	$-0.308994\pi$
$389$	27.1705	−	4.79090i	1.37760	−	0.242908i	0.812908	+	0.582392i	$0.197883\pi$
$390$		0			0
$391$	6.08910	−	10.5466i	0.307939	−	0.533366i
$392$	6.85022	+	1.83551i	0.345989	+	0.0927074i
$393$	−4.92913	−	0.431243i	−0.248642	−	0.0217533i
$394$	−8.71198	+	3.17090i	−0.438903	+	0.159748i
$395$		0			0
$396$	−10.5812	−	8.87864i	−0.531723	−	0.446169i
$397$	11.1433	−	7.80262i	0.559266	−	0.391602i	−0.259489	−	0.965746i	$-0.583554\pi$
$397$	11.1433	−	7.80262i	0.559266	−	0.391602i	0.818754	+	0.574144i	$0.194665\pi$
$398$	7.08236	+	7.08236i	0.355007	+	0.355007i
$399$	−7.53551	+	2.24108i	−0.377247	+	0.112194i
$400$		0			0
$401$	23.9183	+	4.21744i	1.19442	+	0.210609i	0.735286	−	0.677757i	$-0.237048\pi$
$401$	23.9183	+	4.21744i	1.19442	+	0.210609i	0.459136	+	0.888366i	$0.348159\pi$
$402$	−0.121146	+	0.0105989i	−0.00604219	+	0.000528623i
$403$	−2.29539	+	1.07036i	−0.114342	+	0.0533184i
$404$	−3.84634	−	10.5677i	−0.191363	−	0.525764i
$405$		0			0
$406$	−3.27870	−	5.67888i	−0.162719	−	0.281838i
$407$	10.5773	+	39.4751i	0.524298	+	1.95671i
$408$	1.85002	+	1.29540i	0.0915895	+	0.0641317i
$409$	−1.91034	−	10.8341i	−0.0944600	−	0.535709i	−0.994911	−	0.100753i	$-0.967875\pi$
$409$	−1.91034	−	10.8341i	−0.0944600	−	0.535709i	0.900451	−	0.434956i	$-0.143236\pi$
$410$		0			0
$411$	−5.85585	+	3.38088i	−0.288848	+	0.166766i
$412$	0.208030	−	2.37780i	0.0102489	−	0.117146i
$413$	31.1578	+	14.5291i	1.53318	+	0.714932i
$414$	6.74157	+	2.45373i	0.331330	+	0.120594i
$415$		0			0
$416$	−0.232759	+	1.32004i	−0.0114120	+	0.0647205i
$417$	−6.30131	+	6.30131i	−0.308576	+	0.308576i
$418$	−18.5260	+	11.3806i	−0.906138	+	0.556645i
$419$			20.2401i			0.988793i	0.869237	+	0.494396i	$0.164611\pi$
$419$			20.2401i			0.988793i	−0.869237	+	0.494396i	$0.835389\pi$
$420$		0			0
$421$	−18.3645	+	21.8860i	−0.895032	+	1.06666i	0.102378	+	0.994746i	$0.467355\pi$
$421$	−18.3645	+	21.8860i	−0.895032	+	1.06666i	−0.997411	+	0.0719127i	$0.977090\pi$
$422$	−10.2225	−	21.9223i	−0.497624	−	1.06716i
$423$	−8.00936	+	17.1761i	−0.389428	+	0.835132i
$424$	−6.76214	−	8.05881i	−0.328399	−	0.391370i
$425$		0			0
$426$	4.97510	+	2.87238i	0.241044	+	0.139167i
$427$	−4.62143	+	6.60008i	−0.223647	+	0.319400i
$428$	4.04791	−	5.78101i	0.195663	−	0.279436i
$429$	−2.78198	−	1.60618i	−0.134315	−	0.0775469i
$430$		0			0
$431$	−11.0078	−	13.1186i	−0.530229	−	0.631903i	0.432738	−	0.901520i	$-0.357547\pi$
$431$	−11.0078	−	13.1186i	−0.530229	−	0.631903i	−0.962968	+	0.269617i	$0.913103\pi$
$432$	−1.17143	+	2.51214i	−0.0563604	+	0.120865i
$433$	1.73279	+	3.71598i	0.0832725	+	0.178578i	0.943535	−	0.331273i	$-0.107478\pi$
$433$	1.73279	+	3.71598i	0.0832725	+	0.178578i	−0.860262	+	0.509851i	$0.829700\pi$
$434$	4.55928	−	5.43354i	0.218852	−	0.260818i
$435$		0			0
$436$		−	2.97979i		−	0.142706i
$437$	7.02030	−	8.84556i	0.335827	−	0.423140i
$438$	−3.56708	+	3.56708i	−0.170442	+	0.170442i
$439$	3.06889	−	17.4045i	0.146470	−	0.830673i	−0.819705	−	0.572786i	$-0.805863\pi$
$439$	3.06889	−	17.4045i	0.146470	−	0.830673i	0.966175	−	0.257887i	$-0.0830262\pi$
$440$		0			0
$441$	−18.4542	−	6.71677i	−0.878771	−	0.319846i
$442$	−5.71043	−	2.66282i	−0.271617	−	0.126657i
$443$	0.839479	−	9.59529i	0.0398849	−	0.455886i	−0.949823	−	0.312787i	$-0.898738\pi$
$443$	0.839479	−	9.59529i	0.0398849	−	0.455886i	0.989708	−	0.143100i	$-0.0457069\pi$
$444$	3.40906	−	1.96822i	0.161787	−	0.0934076i
$445$		0			0
$446$	−0.288250	−	1.63475i	−0.0136490	−	0.0774075i
$447$	3.18102	+	2.22737i	0.150457	+	0.105351i
$448$	−0.971585	−	3.62600i	−0.0459031	−	0.171313i
$449$	10.4806	+	18.1529i	0.494610	+	0.856689i	0.999981	−	0.00621314i	$-0.00197772\pi$
$449$	10.4806	+	18.1529i	0.494610	+	0.856689i	−0.505371	+	0.862902i	$0.668644\pi$
$450$		0			0
$451$	15.9580	+	43.8442i	0.751432	+	2.06454i
$452$	−7.72986	+	3.60449i	−0.363582	+	0.169541i
$453$	5.44749	−	0.476594i	0.255945	−	0.0223923i
$454$	−15.4678	−	2.72739i	−0.725940	−	0.128003i
$455$		0			0
$456$	1.52070	+	1.43994i	0.0712134	+	0.0674312i
$457$	−23.9786	−	23.9786i	−1.12167	−	1.12167i	−0.991491	−	0.130179i	$-0.958445\pi$
$457$	−23.9786	−	23.9786i	−1.12167	−	1.12167i	−0.130179	−	0.991491i	$-0.541555\pi$
$458$	3.14748	−	2.20389i	0.147072	−	0.102981i
$459$	−9.98109	−	8.37513i	−0.465877	−	0.390917i
$460$		0			0
$461$	10.5002	−	3.82175i	0.489042	−	0.177997i	−0.0857169	−	0.996320i	$-0.527318\pi$
$461$	10.5002	−	3.82175i	0.489042	−	0.177997i	0.574759	+	0.818323i	$0.305096\pi$
$462$	8.96220	+	0.784091i	0.416959	+	0.0364792i
$463$	27.8891	+	7.47287i	1.29612	+	0.347294i	0.839981	−	0.542616i	$-0.182566\pi$
$463$	27.8891	+	7.47287i	1.29612	+	0.347294i	0.456137	+	0.889910i	$0.349233\pi$
$464$	−0.873409	+	1.51279i	−0.0405470	+	0.0702294i
$465$		0			0
$466$	6.97385	−	1.22968i	0.323057	−	0.0569637i
$467$	−14.8914	+	3.99015i	−0.689094	+	0.184642i	−0.586341	−	0.810065i	$-0.699432\pi$
$467$	−14.8914	+	3.99015i	−0.689094	+	0.184642i	−0.102753	+	0.994707i	$0.532765\pi$
$468$	0.960685	−	3.58533i	0.0444077	−	0.165732i
$469$	−0.727857	+	0.610745i	−0.0336093	+	0.0282016i
$470$		0			0
$471$	0.411760	−	1.13130i	0.0189729	−	0.0521277i
$472$	−0.798184	−	9.12329i	−0.0367394	−	0.419933i
$473$	5.58831	+	7.98093i	0.256951	+	0.366964i
$474$	4.61312			0.211888
$475$		0			0
$476$	17.6458			0.808792
$477$	16.7092	+	23.8632i	0.765063	+	1.09262i
$478$	−0.753879	−	8.61687i	−0.0344816	−	0.394127i
$479$	3.53261	−	9.70577i	0.161409	−	0.443468i	−0.832453	−	0.554096i	$-0.813064\pi$
$479$	3.53261	−	9.70577i	0.161409	−	0.443468i	0.993862	+	0.110628i	$0.0352863\pi$
$480$		0			0
$481$	−8.41278	+	7.05916i	−0.383590	+	0.321870i
$482$	−5.31711	+	19.8437i	−0.242188	+	0.903857i
$483$	−4.51347	+	1.20938i	−0.205370	+	0.0550287i
$484$	13.6698	−	2.41035i	0.621354	−	0.109561i
$485$		0			0
$486$	5.83353	−	10.1040i	0.264614	−	0.458325i
$487$	−19.9832	−	5.35450i	−0.905527	−	0.242635i	−0.224139	−	0.974557i	$-0.571957\pi$
$487$	−19.9832	−	5.35450i	−0.905527	−	0.242635i	−0.681389	+	0.731922i	$0.738624\pi$
$488$	2.13818	+	0.187067i	0.0967910	+	0.00846811i
$489$	5.98188	−	2.17723i	0.270510	−	0.0984575i
$490$		0			0
$491$	27.5015	+	23.0765i	1.24112	+	1.04143i	0.997435	+	0.0715726i	$0.0228018\pi$
$491$	27.5015	+	23.0765i	1.24112	+	1.04143i	0.243688	+	0.969854i	$0.421643\pi$
$492$	3.68142	−	2.57776i	0.165971	−	0.116214i
$493$	−5.80615	−	5.80615i	−0.261496	−	0.261496i
$494$	−4.87567	−	3.21947i	−0.219367	−	0.144851i
$495$		0			0
$496$	−1.86078	−	0.328106i	−0.0835516	−	0.0147324i
$497$	44.7141	−	3.91198i	2.00570	−	0.175476i
$498$	−6.50967	+	3.03551i	−0.291705	+	0.136024i
$499$	3.78694	+	10.4045i	0.169527	+	0.465771i	0.995141	−	0.0984645i	$-0.0313931\pi$
$499$	3.78694	+	10.4045i	0.169527	+	0.465771i	−0.825614	+	0.564236i	$0.809171\pi$
$500$		0			0
$501$	−2.64058	−	4.57361i	−0.117972	−	0.204334i
$502$	−0.537439	−	2.00575i	−0.0239871	−	0.0895210i
$503$	25.1961	+	17.6425i	1.12344	+	0.786640i	0.979199	−	0.202902i	$-0.0650374\pi$
$503$	25.1961	+	17.6425i	1.12344	+	0.786640i	0.144240	+	0.989543i	$0.453926\pi$
$504$	1.80511	+	10.2373i	0.0804058	+	0.456004i
$505$		0			0
$506$	−11.1915	+	6.46142i	−0.497523	+	0.287245i
$507$	−0.469135	+	5.36223i	−0.0208350	+	0.238145i
$508$	−6.89445	−	3.21493i	−0.305892	−	0.142640i
$509$	36.5051	+	13.2868i	1.61806	+	0.588925i	0.983011	−	0.183548i	$-0.0587581\pi$
$509$	36.5051	+	13.2868i	1.61806	+	0.588925i	0.635048	+	0.772473i	$0.280980\pi$
$510$		0			0
$511$	−6.84428	+	38.8158i	−0.302773	+	1.71711i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−8.01577	−	9.04025i	−0.353905	−	0.399137i
$514$			15.9583i			0.703891i
$515$		0			0
$516$	0.603227	−	0.718898i	0.0265556	−	0.0316477i
$517$	−14.4272	−	30.9391i	−0.634505	−	1.36070i
$518$	12.9981	−	27.8746i	0.571105	−	1.22474i
$519$	5.43849	+	6.48134i	0.238723	+	0.284499i
$520$		0			0
$521$	−14.3093	−	8.26150i	−0.626904	−	0.361943i	0.152648	−	0.988281i	$-0.451220\pi$
$521$	−14.3093	−	8.26150i	−0.626904	−	0.361943i	−0.779552	+	0.626338i	$0.784553\pi$
$522$	2.77451	−	3.96242i	0.121437	−	0.173430i
$523$	4.58197	−	6.54373i	0.200356	−	0.286137i	−0.706384	−	0.707829i	$-0.749675\pi$
$523$	4.58197	−	6.54373i	0.200356	−	0.286137i	0.906739	+	0.421692i	$0.138564\pi$
$524$	8.91869	+	5.14921i	0.389615	+	0.224944i
$525$		0			0
$526$	−4.15064	−	4.94655i	−0.180977	−	0.215680i
$527$	3.75361	−	8.04963i	0.163510	−	0.350648i
$528$	−1.01283	−	2.17201i	−0.0440776	−	0.0945246i
$529$	−10.4697	+	12.4773i	−0.455205	+	0.542492i
$530$		0			0
$531$			25.3603i			1.10055i
$532$	16.1858	+	2.40090i	0.701745	+	0.104092i
$533$	−8.86579	+	8.86579i	−0.384020	+	0.384020i
$534$	1.11167	−	6.30458i	0.0481065	−	0.272826i
$535$		0			0
$536$	0.237845	+	0.0865685i	0.0102733	+	0.00373919i
$537$	8.66506	+	4.04058i	0.373925	+	0.174364i
$538$	−1.88663	+	21.5643i	−0.0813386	+	0.929704i
$539$	30.6353	−	17.6873i	1.31956	−	0.761847i
$540$		0			0
$541$	1.47824	+	8.38349i	0.0635543	+	0.360434i	0.999955	+	0.00950131i	$0.00302441\pi$
$541$	1.47824	+	8.38349i	0.0635543	+	0.360434i	−0.936401	+	0.350933i	$0.885864\pi$
$542$	−21.2118	−	14.8526i	−0.911124	−	0.637976i
$543$	−0.913145	−	3.40790i	−0.0391868	−	0.146247i
$544$	−2.35031	−	4.07086i	−0.100769	−	0.174537i
$545$		0			0
$546$	0.826853	+	2.27176i	0.0353860	+	0.0972223i
$547$	32.4549	−	15.1340i	1.38767	−	0.647082i	0.421940	−	0.906624i	$-0.361349\pi$
$547$	32.4549	−	15.1340i	1.38767	−	0.647082i	0.965732	+	0.259542i	$0.0835716\pi$
$548$	14.0200	−	1.22659i	0.598905	−	0.0523974i
$549$	−5.85329	−	1.03209i	−0.249812	−	0.0440487i
$550$		0			0
$551$	−4.53579	−	6.11577i	−0.193231	−	0.260541i
$552$	0.880171	+	0.880171i	0.0374626	+	0.0374626i
$553$	29.5249	−	20.6736i	1.25553	−	0.879130i
$554$	6.35501	+	5.33249i	0.269999	+	0.226556i
$555$		0			0
$556$	17.4292	−	6.34369i	0.739161	−	0.269032i
$557$	−9.40447	−	0.822784i	−0.398480	−	0.0348625i	−0.113845	−	0.993498i	$-0.536317\pi$
$557$	−9.40447	−	0.822784i	−0.398480	−	0.0348625i	−0.284635	+	0.958636i	$0.591872\pi$
$558$	5.05401	+	1.35422i	0.213953	+	0.0573286i
$559$	−1.30908	+	2.26739i	−0.0553680	+	0.0959003i
$560$		0			0
$561$	11.0941	−	1.95620i	0.468395	−	0.0825907i
$562$	23.3227	−	6.24931i	0.983811	−	0.263611i
$563$	0.717612	−	2.67816i	0.0302437	−	0.112871i	−0.949154	−	0.314813i	$-0.898058\pi$
$563$	0.717612	−	2.67816i	0.0302437	−	0.112871i	0.979398	+	0.201941i	$0.0647250\pi$
$564$	−2.51890	+	2.11361i	−0.106065	+	0.0889989i
$565$		0			0
$566$	−3.03904	+	8.34971i	−0.127741	+	0.350964i
$567$	−2.28229	−	26.0866i	−0.0958470	−	1.09554i
$568$	−6.85816	−	9.79446i	−0.287762	−	0.410966i
$569$	−5.49736			−0.230461			−0.115231	−	0.993339i	$-0.536761\pi$
$569$	−5.49736			−0.230461			−0.115231	+	0.993339i	$0.536761\pi$
$570$		0			0
$571$	−4.01384			−0.167974			−0.0839871	−	0.996467i	$-0.526765\pi$
$571$	−4.01384			−0.167974			−0.0839871	+	0.996467i	$0.526765\pi$
$572$	3.83494	+	5.47687i	0.160347	+	0.228999i
$573$	−0.124196	−	1.41957i	−0.00518837	−	0.0593033i
$574$	12.0097	−	32.9963i	0.501274	−	1.37724i
$575$		0			0
$576$	2.12130	−	1.77998i	0.0883875	−	0.0741659i
$577$	−3.50041	+	13.0637i	−0.145724	+	0.543849i	0.853998	+	0.520276i	$0.174171\pi$
$577$	−3.50041	+	13.0637i	−0.145724	+	0.543849i	−0.999722	+	0.0235733i	$0.992496\pi$
$578$	4.92228	−	1.31892i	0.204740	−	0.0548599i
$579$	4.64325	−	0.818730i	0.192967	−	0.0340253i
$580$		0			0
$581$	−28.0597	+	48.6008i	−1.16411	+	2.01630i
$582$	−6.53195	−	1.75023i	−0.270758	−	0.0725494i
$583$	−52.2747	−	4.57345i	−2.16500	−	0.189413i
$584$	9.86641	−	3.59108i	0.408275	−	0.148600i
$585$		0			0
$586$	10.5455	+	8.84875i	0.435632	+	0.365538i
$587$	1.69635	−	1.18780i	0.0700160	−	0.0490257i	−0.538044	−	0.842916i	$-0.680837\pi$
$587$	1.69635	−	1.18780i	0.0700160	−	0.0490257i	0.608060	+	0.793891i	$0.291948\pi$
$588$	−2.40936	−	2.40936i	−0.0993602	−	0.0993602i
$589$	4.53829	−	6.87292i	0.186997	−	0.283194i
$590$		0			0
$591$	4.38670	+	0.773494i	0.180445	+	0.0318173i
$592$	−8.16193	+	0.714076i	−0.335453	+	0.0293483i
$593$	−29.7681	+	13.8811i	−1.22243	+	0.570028i	−0.923261	−	0.384173i	$-0.874487\pi$
$593$	−29.7681	+	13.8811i	−1.22243	+	0.570028i	−0.299167	+	0.954201i	$0.596709\pi$
$594$	4.72880	+	12.9923i	0.194025	+	0.533079i
$595$		0			0
$596$	−4.04125	−	6.99966i	−0.165536	−	0.286717i
$597$	−1.24550	−	4.64828i	−0.0509750	−	0.190241i
$598$	−2.84465	−	1.99184i	−0.116326	−	0.0814525i
$599$	0.983279	+	5.57645i	0.0401757	+	0.227848i	0.998284	−	0.0585585i	$-0.0186504\pi$
$599$	0.983279	+	5.57645i	0.0401757	+	0.227848i	−0.958108	+	0.286406i	$0.907539\pi$
$600$		0			0
$601$	−0.0640903	+	0.0370026i	−0.00261430	+	0.00150937i	−0.501307	−	0.865270i	$-0.667147\pi$
$601$	−0.0640903	+	0.0370026i	−0.00261430	+	0.00150937i	0.498692	+	0.866779i	$0.333814\pi$
$602$	0.639056	−	7.30444i	0.0260460	−	0.297707i
$603$	−0.635231	−	0.296213i	−0.0258686	−	0.0120627i
$604$	−10.6950	−	3.89268i	−0.435175	−	0.158391i
$605$		0			0
$606$	−0.938257	+	5.32112i	−0.0381141	+	0.216156i
$607$	−27.7146	+	27.7146i	−1.12490	+	1.12490i	−0.133908	+	0.990994i	$0.542753\pi$
$607$	−27.7146	+	27.7146i	−1.12490	+	1.12490i	−0.990994	+	0.133908i	$0.957247\pi$
$608$	−1.60197	−	4.05385i	−0.0649686	−	0.164405i
$609$			3.15056i			0.127667i
$610$		0			0
$611$	5.89665	−	7.02736i	0.238553	−	0.284297i
$612$	5.50114	+	11.7972i	0.222370	+	0.476875i
$613$	−1.11748	+	2.39644i	−0.0451345	+	0.0967913i	−0.927582	−	0.373620i	$-0.878117\pi$
$613$	−1.11748	+	2.39644i	−0.0451345	+	0.0967913i	0.882447	+	0.470411i	$0.155894\pi$
$614$	−3.45111	−	4.11288i	−0.139276	−	0.165982i
$615$		0			0
$616$	−16.2161	−	9.36236i	−0.653365	−	0.377220i
$617$	21.9732	−	31.3810i	0.884608	−	1.26335i	−0.0792280	−	0.996857i	$-0.525246\pi$
$617$	21.9732	−	31.3810i	0.884608	−	1.26335i	0.963836	−	0.266495i	$-0.0858656\pi$
$618$	−0.657775	+	0.939400i	−0.0264596	+	0.0377882i
$619$	−6.00501	−	3.46700i	−0.241362	−	0.139350i	0.374441	−	0.927251i	$-0.377835\pi$
$619$	−6.00501	−	3.46700i	−0.241362	−	0.139350i	−0.615802	+	0.787901i	$0.711168\pi$
$620$		0			0
$621$	−4.61596	−	5.50109i	−0.185232	−	0.220751i
$622$	−4.43178	+	9.50399i	−0.177698	+	0.381075i
$623$	−21.1389	−	45.3325i	−0.846911	−	1.81621i
$624$	0.413961	−	0.493340i	0.0165717	−	0.0197494i
$625$		0			0
$626$		−	6.23781i		−	0.249313i
$627$	10.4424	−	0.284867i	0.417030	−	0.0113765i
$628$	−1.77183	+	1.77183i	−0.0707038	+	0.0707038i
$629$	6.68767	−	37.9277i	0.266655	−	1.51227i
$630$		0			0
$631$	−38.0296	−	13.8416i	−1.51393	−	0.551026i	−0.554308	−	0.832311i	$-0.687017\pi$
$631$	−38.0296	−	13.8416i	−1.51393	−	0.551026i	−0.959624	+	0.281285i	$0.909239\pi$
$632$	−8.70193	−	4.05778i	−0.346144	−	0.161410i
$633$	−1.01289	+	11.5773i	−0.0402586	+	0.460158i
$634$	11.2837	−	6.51463i	0.448132	−	0.258729i
$635$		0			0
$636$	0.877692	+	4.97764i	0.0348028	+	0.197376i
$637$	7.78686	+	5.45242i	0.308527	+	0.216033i
$638$	2.25515	+	8.41632i	0.0892821	+	0.333205i
$639$	16.5552	+	28.6744i	0.654913	+	1.13434i
$640$		0			0
$641$	−1.32749	−	3.64724i	−0.0524325	−	0.144057i	0.910712	−	0.413043i	$-0.135534\pi$
$641$	−1.32749	−	3.64724i	−0.0524325	−	0.144057i	−0.963144	+	0.268985i	$0.913312\pi$
$642$	−3.07306	+	1.43299i	−0.121284	+	0.0565556i
$643$	41.0713	−	3.59328i	1.61970	−	0.141705i	0.759093	−	0.650982i	$-0.225643\pi$
$643$	41.0713	−	3.59328i	1.61970	−	0.141705i	0.860602	+	0.509278i	$0.170087\pi$
$644$	9.57773	+	1.68881i	0.377416	+	0.0665486i
$645$		0			0
$646$	20.3553	−	2.34174i	0.800869	−	0.0921344i
$647$	4.81659	+	4.81659i	0.189360	+	0.189360i	0.795419	−	0.606060i	$-0.207251\pi$
$647$	4.81659	+	4.81659i	0.189360	+	0.189360i	−0.606060	+	0.795419i	$0.707251\pi$
$648$	−5.71418	+	4.00111i	−0.224474	+	0.157179i
$649$	−34.9939	−	29.3633i	−1.37363	−	1.15261i
$650$		0			0
$651$	−3.20236	+	1.16556i	−0.125510	+	0.0456820i
$652$	−13.1990	−	1.15476i	−0.516912	−	0.0452240i
$653$	−21.3360	−	5.71697i	−0.834944	−	0.223722i	−0.184074	−	0.982912i	$-0.558929\pi$
$653$	−21.3360	−	5.71697i	−0.834944	−	0.223722i	−0.650869	+	0.759190i	$0.725595\pi$
$654$	−0.715832	+	1.23986i	−0.0279913	+	0.0484823i
$655$		0			0
$656$	−9.21185	+	1.62430i	−0.359662	+	0.0634182i
$657$	−28.0844	+	7.52519i	−1.09568	+	0.293586i
$658$	−6.64939	+	24.8159i	−0.259220	+	0.967423i
$659$	−10.2912	+	8.63535i	−0.400889	+	0.336385i	−0.820837	−	0.571163i	$-0.806493\pi$
$659$	−10.2912	+	8.63535i	−0.400889	+	0.336385i	0.419948	+	0.907548i	$0.362048\pi$
$660$		0			0
$661$	16.8993	−	46.4304i	0.657305	−	1.80593i	0.0685088	−	0.997651i	$-0.478176\pi$
$661$	16.8993	−	46.4304i	0.657305	−	1.80593i	0.588797	−	0.808281i	$-0.299602\pi$
$662$	−1.37408	−	15.7059i	−0.0534053	−	0.610426i
$663$	1.73636	+	2.47978i	0.0674346	+	0.0963066i
$664$	14.9495			0.580155
$665$		0			0
$666$	22.6880			0.879143
$667$	−2.59577	−	3.70714i	−0.100509	−	0.143541i
$668$	0.958009	+	10.9501i	0.0370665	+	0.423672i
$669$	−0.272776	+	0.749446i	−0.0105461	+	0.0289752i
$670$		0			0
$671$	8.20135	−	6.88175i	0.316610	−	0.265667i
$672$	−0.466805	+	1.74214i	−0.0180074	+	0.0672046i
$673$	−7.21919	+	1.93437i	−0.278279	+	0.0745647i	−0.395259	−	0.918570i	$-0.629345\pi$
$673$	−7.21919	+	1.93437i	−0.278279	+	0.0745647i	0.116980	+	0.993134i	$0.462679\pi$
$674$	−27.6149	+	4.86926i	−1.06369	+	0.187557i
$675$		0			0
$676$	5.60165	−	9.70235i	0.215448	−	0.373167i
$677$	26.7103	+	7.15701i	1.02656	+	0.275066i	0.732534	−	0.680731i	$-0.238338\pi$
$677$	26.7103	+	7.15701i	1.02656	+	0.275066i	0.294027	+	0.955797i	$0.405004\pi$
$678$	4.08221	+	0.357147i	0.156776	+	0.0137162i
$679$	−49.6494	+	18.0709i	−1.90537	+	0.693497i
$680$		0			0
$681$	5.78078	+	4.85065i	0.221520	+	0.185877i
$682$	−7.72040	+	5.40588i	−0.295629	+	0.207002i
$683$	25.9136	+	25.9136i	0.991557	+	0.991557i	0.999965	−	0.00840797i	$-0.00267637\pi$
$683$	25.9136	+	25.9136i	0.991557	+	0.991557i	−0.00840797	+	0.999965i	$0.502676\pi$
$684$	3.44085	+	11.5697i	0.131564	+	0.442377i
$685$		0			0
$686$	−0.339645	−	0.0598886i	−0.0129677	−	0.00228656i
$687$	−1.83907	+	0.160898i	−0.0701649	+	0.00613863i
$688$	−1.77025	+	0.825480i	−0.0674901	+	0.0314711i
$689$	−4.82287	−	13.2507i	−0.183737	−	0.504812i
$690$		0			0
$691$	−7.30289	−	12.6490i	−0.277815	−	0.481190i	0.693026	−	0.720912i	$-0.256277\pi$
$691$	−7.30289	−	12.6490i	−0.277815	−	0.481190i	−0.970842	+	0.239722i	$0.922944\pi$
$692$	−4.55777	−	17.0098i	−0.173260	−	0.646616i
$693$	42.4745	+	29.7409i	1.61347	+	1.12976i
$694$	−0.340193	−	1.92933i	−0.0129135	−	0.0732363i
$695$		0			0
$696$	0.726831	−	0.419636i	0.0275505	−	0.0159063i
$697$	3.83219	−	43.8022i	0.145155	−	1.65913i
$698$	16.3413	+	7.62005i	0.618526	+	0.288423i
$699$	−3.19714	−	1.16367i	−0.120927	−	0.0440139i
$700$		0			0
$701$	8.46076	−	47.9834i	0.319559	−	1.81231i	−0.225879	−	0.974155i	$-0.572526\pi$
$701$	8.46076	−	47.9834i	0.319559	−	1.81231i	0.545438	−	0.838151i	$-0.316363\pi$
$702$	−2.62718	+	2.62718i	−0.0991565	+	0.0991565i
$703$	11.2948	−	33.8798i	0.425993	−	1.27780i
$704$			4.98805i			0.187994i
$705$		0			0
$706$	4.15344	−	4.94987i	0.156317	−	0.186291i
$707$	17.8414	+	38.2610i	0.670995	+	1.43895i
$708$	−1.85956	+	3.98784i	−0.0698866	+	0.149872i
$709$	11.3359	+	13.5096i	0.425729	+	0.507364i	0.935685	−	0.352836i	$-0.114783\pi$
$709$	11.3359	+	13.5096i	0.425729	+	0.507364i	−0.509956	+	0.860200i	$0.670338\pi$
$710$		0			0
$711$	23.0260	+	13.2941i	0.863543	+	0.498567i
$712$	−7.64259	+	10.9148i	−0.286418	+	0.409048i
$713$	2.80778	−	4.00992i	0.105152	−	0.150173i
$714$	−7.34220	−	4.23902i	−0.274775	−	0.158641i
$715$		0			0
$716$	−12.7911	−	15.2438i	−0.478026	−	0.569689i
$717$	−1.75634	+	3.76649i	−0.0655918	+	0.140662i
$718$	−8.30528	−	17.8107i	−0.309950	−	0.664691i
$719$	9.85702	−	11.7471i	0.367605	−	0.438094i	−0.550256	−	0.834996i	$-0.685470\pi$
$719$	9.85702	−	11.7471i	0.367605	−	0.438094i	0.917861	+	0.396901i	$0.129914\pi$
$720$		0			0
$721$			8.96015i			0.333693i
$722$	18.9898	+	0.621576i	0.706728	+	0.0231327i
$723$	6.97943	−	6.97943i	0.259568	−	0.259568i
$724$	−1.27514	+	7.23169i	−0.0473903	+	0.268764i
$725$		0			0
$726$	−6.26688	−	2.28096i	−0.232586	−	0.0846542i
$727$	31.4152	+	14.6492i	1.16513	+	0.543307i	0.906308	−	0.422619i	$-0.138889\pi$
$727$	31.4152	+	14.6492i	1.16513	+	0.543307i	0.258819	+	0.965926i	$0.416667\pi$
$728$	0.438548	−	5.01263i	0.0162537	−	0.185780i
$729$	13.2689	−	7.66083i	0.491442	−	0.283734i
$730$		0			0
$731$	−1.59435	−	9.04203i	−0.0589693	−	0.334431i
$732$	−0.844735	−	0.591490i	−0.0312223	−	0.0218621i
$733$	1.93064	+	7.20524i	0.0713098	+	0.266132i	0.992371	−	0.123286i	$-0.0393431\pi$
$733$	1.93064	+	7.20524i	0.0713098	+	0.266132i	−0.921061	+	0.389417i	$0.872676\pi$
$734$	−7.05255	−	12.2154i	−0.260314	−	0.450878i
$735$		0			0
$736$	−0.886092	−	2.43452i	−0.0326618	−	0.0897375i
$737$	1.14423	−	0.533565i	0.0421484	−	0.0196541i
$738$	25.8040	−	2.25756i	0.949860	−	0.0831020i
$739$	18.9290	+	3.33770i	0.696315	+	0.122779i	0.510592	−	0.859823i	$-0.329426\pi$
$739$	18.9290	+	3.33770i	0.696315	+	0.122779i	0.185723	+	0.982602i	$0.440537\pi$
$740$		0			0
$741$	1.25530	+	2.51086i	0.0461146	+	0.0922389i
$742$	27.9245	+	27.9245i	1.02514	+	1.02514i
$743$	−29.1705	+	20.4254i	−1.07016	+	0.749334i	−0.969378	−	0.245574i	$-0.921023\pi$
$743$	−29.1705	+	20.4254i	−1.07016	+	0.749334i	−0.100782	+	0.994908i	$0.532135\pi$
$744$	0.695430	+	0.583535i	0.0254957	+	0.0213934i
$745$		0			0
$746$	−34.1017	+	12.4120i	−1.24855	+	0.454435i
$747$	−41.2402	−	3.60805i	−1.50890	−	0.132012i
$748$	−22.6480	−	6.06853i	−0.828095	−	0.221887i
$749$	−13.2463	+	22.9432i	−0.484008	+	0.838327i
$750$		0			0
$751$	1.29307	−	0.228003i	0.0471847	−	0.00831994i	−0.150006	−	0.988685i	$-0.547929\pi$
$751$	1.29307	−	0.228003i	0.0471847	−	0.00831994i	0.197191	+	0.980365i	$0.436818\pi$
$752$	6.61066	−	1.77132i	0.241066	−	0.0645935i
$753$	−0.258217	+	0.963678i	−0.00940994	+	0.0351184i
$754$	−1.79365	+	1.50505i	−0.0653210	+	0.0548108i
$755$		0			0
$756$	3.55880	−	9.77773i	0.129432	−	0.355613i
$757$	−1.68000	−	19.2025i	−0.0610608	−	0.697928i	−0.963605	−	0.267331i	$-0.913858\pi$
$757$	−1.68000	−	19.2025i	−0.0610608	−	0.697928i	0.902544	−	0.430598i	$-0.141697\pi$
$758$	4.80867	+	6.86749i	0.174659	+	0.249439i
$759$	6.20888			0.225368
$760$		0			0
$761$	16.5439			0.599715			0.299857	−	0.953984i	$-0.403061\pi$
$761$	16.5439			0.599715			0.299857	+	0.953984i	$0.403061\pi$
$762$	2.09638	+	2.99394i	0.0759439	+	0.108459i
$763$	0.974914	+	11.1433i	0.0352943	+	0.403415i
$764$	−1.01440	+	2.78704i	−0.0366996	+	0.100831i
$765$		0			0
$766$	−12.2323	+	10.2642i	−0.441973	+	0.370859i
$767$	3.17717	−	11.8574i	0.114721	−	0.428144i
$768$	0.464087	−	0.124352i	0.0167463	−	0.00448715i
$769$	−33.8306	+	5.96525i	−1.21996	+	0.215112i	−0.746310	−	0.665599i	$-0.768176\pi$
$769$	−33.8306	+	5.96525i	−1.21996	+	0.215112i	−0.473653	+	0.880711i	$0.657065\pi$
$770$		0			0
$771$	3.83365	−	6.64008i	0.138066	−	0.239137i
$772$	−9.47893	−	2.53987i	−0.341154	−	0.0914119i
$773$	−11.3638	−	0.994208i	−0.408729	−	0.0357592i	−0.119063	−	0.992887i	$-0.537989\pi$
$773$	−11.3638	−	0.994208i	−0.408729	−	0.0357592i	−0.289667	+	0.957128i	$0.593544\pi$
$774$	5.08267	−	1.84994i	0.182693	−	0.0664948i
$775$		0			0
$776$	10.7820	+	9.04713i	0.387050	+	0.324773i
$777$	−12.1047	+	8.47578i	−0.434252	+	0.304067i
$778$	19.5089	+	19.5089i	0.699426	+	0.699426i
$779$	9.47491	−	39.6568i	0.339474	−	1.42085i
$780$		0			0
$781$	−58.7352	−	10.3566i	−2.10171	−	0.370588i
$782$	12.1319	−	1.06140i	0.433834	−	0.0379556i
$783$	−4.38825	+	2.04627i	−0.156823	+	0.0731278i
$784$	2.42556	+	6.66418i	0.0866273	+	0.238006i
$785$		0			0
$786$	−2.47398	−	4.28506i	−0.0882439	−	0.152843i
$787$	−6.46227	−	24.1175i	−0.230355	−	0.859697i	−0.980188	−	0.198070i	$-0.936533\pi$
$787$	−6.46227	−	24.1175i	−0.230355	−	0.859697i	0.749833	−	0.661627i	$-0.230134\pi$
$788$	−7.59444	−	5.31768i	−0.270541	−	0.189435i
$789$	0.538733	+	3.05531i	0.0191794	+	0.108772i
$790$		0			0
$791$	27.7275	−	16.0085i	0.985877	−	0.569196i
$792$	1.20386	−	13.7602i	0.0427772	−	0.488946i
$793$	2.60743	+	1.21587i	0.0925926	+	0.0431767i
$794$	12.7831	+	4.65265i	0.453654	+	0.165116i
$795$		0			0
$796$	−1.73926	+	9.86381i	−0.0616463	+	0.349613i
$797$	−20.9403	+	20.9403i	−0.741744	+	0.741744i	−0.972913	−	0.231170i	$-0.925745\pi$
$797$	−20.9403	+	20.9403i	−0.741744	+	0.741744i	0.231170	+	0.972913i	$0.425745\pi$
$798$	−6.15798	−	4.88729i	−0.217990	−	0.173008i
$799$			32.1705i			1.13811i
$800$		0			0
$801$	23.7173	−	28.2652i	0.838009	−	0.998700i
$802$	10.2642	+	22.0117i	0.362443	+	0.777262i
$803$	22.1336	−	47.4657i	0.781078	−	1.67503i
$804$	−0.0781683	−	0.0931574i	−0.00275678	−	0.00328541i
$805$		0			0
$806$	−2.19337	−	1.26634i	−0.0772581	−	0.0446050i
$807$	5.96538	−	8.51945i	0.209991	−	0.299899i
$808$	6.45041	−	9.21214i	0.226925	−	0.324082i
$809$	−30.2313	−	17.4540i	−1.06288	−	0.613652i	−0.136649	−	0.990619i	$-0.543633\pi$
$809$	−30.2313	−	17.4540i	−1.06288	−	0.613652i	−0.926226	+	0.376968i	$0.876967\pi$
$810$		0			0
$811$	−27.0249	−	32.2070i	−0.948972	−	1.13094i	−0.991272	−	0.131835i	$-0.957913\pi$
$811$	−27.0249	−	32.2070i	−0.948972	−	1.13094i	0.0423000	−	0.999105i	$-0.486531\pi$
$812$	2.77128	−	5.94303i	0.0972528	−	0.208559i
$813$	5.25795	+	11.2757i	0.184404	+	0.395456i
$814$	−26.2692	+	31.3064i	−0.920735	+	1.09729i
$815$		0			0
$816$			2.25845i			0.0790617i
$817$	−0.232175	−	8.51086i	−0.00812276	−	0.297757i
$818$	7.77901	−	7.77901i	0.271987	−	0.271987i
$819$	−2.41958	+	13.7221i	−0.0845469	+	0.479489i
$820$		0			0
$821$	−34.0120	−	12.3793i	−1.18703	−	0.432042i	−0.328348	−	0.944557i	$-0.606492\pi$
$821$	−34.0120	−	12.3793i	−1.18703	−	0.432042i	−0.858678	+	0.512515i	$0.828714\pi$
$822$	−6.12823	−	2.85764i	−0.213747	−	0.0996717i
$823$	−0.636069	+	7.27030i	−0.0221720	+	0.253427i	0.977017	+	0.213161i	$0.0683760\pi$
$823$	−0.636069	+	7.27030i	−0.0221720	+	0.253427i	−0.999189	+	0.0402656i	$0.987180\pi$
$824$	2.06710	−	1.19344i	0.0720108	−	0.0415755i
$825$		0			0
$826$	5.96983	+	33.8566i	0.207717	+	1.17802i
$827$	3.26292	+	2.28472i	0.113463	+	0.0794475i	0.628931	−	0.777461i	$-0.283493\pi$
$827$	3.26292	+	2.28472i	0.113463	+	0.0794475i	−0.515468	+	0.856909i	$0.672382\pi$
$828$	1.85683	+	6.92977i	0.0645292	+	0.240826i
$829$	5.48124	+	9.49379i	0.190371	+	0.329733i	0.945373	−	0.325990i	$-0.105697\pi$
$829$	5.48124	+	9.49379i	0.190371	+	0.329733i	−0.755002	+	0.655722i	$0.772364\pi$
$830$		0			0
$831$	−1.36323	−	3.74545i	−0.0472900	−	0.129928i
$832$	−1.21482	+	0.566481i	−0.0421164	+	0.0196392i
$833$	−33.2094	+	2.90545i	−1.15064	+	0.100668i
$834$	−8.77601	−	1.54745i	−0.303888	−	0.0535837i
$835$		0			0
$836$	−19.9486	−	8.64797i	−0.689935	−	0.299096i
$837$	−3.70337	−	3.70337i	−0.128007	−	0.128007i
$838$	−16.5797	+	11.6092i	−0.572736	+	0.401034i
$839$	6.03150	+	5.06103i	0.208230	+	0.174726i	0.740938	−	0.671573i	$-0.234381\pi$
$839$	6.03150	+	5.06103i	0.208230	+	0.174726i	−0.532708	+	0.846299i	$0.678826\pi$
$840$		0			0
$841$	24.3837	−	8.87495i	0.840818	−	0.306033i
$842$	−28.4614	−	2.49005i	−0.980845	−	0.0858128i
$843$	−11.2056	−	3.00253i	−0.385941	−	0.103413i
$844$	12.0943	−	20.9479i	0.416302	−	0.721056i
$845$		0			0
$846$	−18.6638	+	3.29094i	−0.641676	+	0.113145i
$847$	−50.3313	+	13.4862i	−1.72940	+	0.463392i
$848$	2.72278	−	10.1616i	0.0935007	−	0.348950i
$849$	3.27035	−	2.74415i	0.112238	−	0.0941791i
$850$		0			0
$851$	7.25984	−	19.9463i	0.248864	−	0.683749i
$852$	0.500688	+	5.72289i	0.0171533	+	0.196063i
$853$	13.9668	+	19.9467i	0.478214	+	0.682961i	0.983688	−	0.179881i	$-0.0575713\pi$
$853$	13.9668	+	19.9467i	0.478214	+	0.682961i	−0.505474	+	0.862842i	$0.668682\pi$
$854$	−8.05721			−0.275712
$855$		0			0
$856$	7.05731			0.241214
$857$	28.6102	+	40.8596i	0.977307	+	1.39574i	0.917592	+	0.397523i	$0.130130\pi$
$857$	28.6102	+	40.8596i	0.977307	+	1.39574i	0.0597146	+	0.998215i	$0.480981\pi$
$858$	−0.279975	−	3.20013i	−0.00955818	−	0.109251i
$859$	16.1613	−	44.4029i	0.551418	−	1.51501i	−0.280357	−	0.959896i	$-0.590453\pi$
$859$	16.1613	−	44.4029i	0.551418	−	1.51501i	0.831775	−	0.555113i	$-0.187325\pi$
$860$		0			0
$861$	−12.9238	+	10.8443i	−0.440441	+	0.369574i
$862$	4.43232	−	16.5416i	0.150965	−	0.563410i
$863$	−24.3265	+	6.51826i	−0.828083	+	0.221884i	−0.647877	−	0.761745i	$-0.724343\pi$
$863$	−24.3265	+	6.51826i	−0.828083	+	0.221884i	−0.180206	+	0.983629i	$0.557676\pi$
$864$	−2.72973	+	0.481325i	−0.0928672	+	0.0163750i
$865$		0			0
$866$	−2.05006	+	3.55081i	−0.0696640	+	0.120662i
$867$	−2.36495	−	0.633686i	−0.0803178	−	0.0215211i
$868$	7.06599	+	0.618194i	0.239835	+	0.0209829i
$869$	−45.0046	+	16.3803i	−1.52668	+	0.555664i
$870$		0			0
$871$	0.259895	+	0.218078i	0.00880622	+	0.00738930i
$872$	2.44090	−	1.70914i	0.0826594	−	0.0578787i
$873$	−27.5598	−	27.5598i	−0.932759	−	0.932759i
$874$	11.2725	+	0.677091i	0.381299	+	0.0229029i
$875$		0			0
$876$	−4.96798	−	0.875989i	−0.167853	−	0.0295969i
$877$	−35.9584	+	3.14595i	−1.21423	+	0.106231i	−0.676214	−	0.736705i	$-0.736381\pi$
$877$	−35.9584	+	3.14595i	−1.21423	+	0.106231i	−0.538014	+	0.842936i	$0.680825\pi$
$878$	16.0172	−	7.46894i	0.540554	−	0.252065i
$879$	−2.26215	−	6.21520i	−0.0763004	−	0.209634i
$880$		0			0
$881$	1.46927	+	2.54486i	0.0495011	+	0.0857384i	0.889714	−	0.456518i	$-0.150904\pi$
$881$	1.46927	+	2.54486i	0.0495011	+	0.0857384i	−0.840213	+	0.542256i	$0.817570\pi$
$882$	−5.08283	−	18.9694i	−0.171148	−	0.638732i
$883$	−37.6354	−	26.3526i	−1.26653	−	0.886836i	−0.269439	−	0.963017i	$-0.586838\pi$
$883$	−37.6354	−	26.3526i	−1.26653	−	0.886836i	−0.997094	+	0.0761812i	$0.975727\pi$
$884$	−1.09412	−	6.20504i	−0.0367991	−	0.208698i
$885$		0			0
$886$	8.34151	−	4.81597i	0.280239	−	0.161796i
$887$	−0.402514	+	4.60075i	−0.0135151	+	0.154478i	−0.999953	−	0.00965430i	$-0.996927\pi$
$887$	−0.402514	+	4.60075i	−0.0135151	+	0.154478i	0.986438	+	0.164132i	$0.0524824\pi$
$888$	3.56763	+	1.66361i	0.119722	+	0.0558272i
$889$	26.8345	+	9.76697i	0.900002	+	0.327574i
$890$		0			0
$891$	−6.04214	+	34.2667i	−0.202419	+	1.14798i
$892$	1.17377	−	1.17377i	0.0393008	−	0.0393008i
$893$	−4.37715	+	29.5088i	−0.146476	+	0.987476i
$894$			3.88330i			0.129877i
$895$		0			0
$896$	2.41297	−	2.87567i	0.0806117	−	0.0960692i
$897$	0.705127	+	1.51215i	0.0235435	+	0.0504892i
$898$	−8.85858	+	18.9973i	−0.295615	+	0.633947i
$899$	−2.12158	−	2.52840i	−0.0707586	−	0.0843269i
$900$		0			0
$901$	42.8256	+	24.7254i	1.42673	+	0.823721i
$902$	−26.7619	+	38.2200i	−0.891075	+	1.27259i
$903$	−2.02064	+	2.88578i	−0.0672427	+	0.0960326i
$904$	−7.38629	−	4.26448i	−0.245664	−	0.141834i
$905$		0			0
$906$	3.51496	+	4.18896i	0.116777	+	0.139169i
$907$	3.91880	−	8.40389i	0.130122	−	0.279047i	−0.830443	−	0.557104i	$-0.811913\pi$
$907$	3.91880	−	8.40389i	0.130122	−	0.279047i	0.960565	+	0.278057i	$0.0896904\pi$
$908$	−6.63782	−	14.2348i	−0.220284	−	0.472400i
$909$	−20.0176	+	23.8560i	−0.663941	+	0.791255i
$910$		0			0
$911$		−	1.34196i		−	0.0444610i	−0.999753	−	0.0222305i	$-0.992923\pi$
$911$		−	1.34196i		−	0.0444610i	0.999753	−	0.0222305i	$-0.00707677\pi$
$912$	−0.307288	+	2.07160i	−0.0101753	+	0.0685976i
$913$	52.7283	−	52.7283i	1.74505	−	1.74505i
$914$	5.88855	−	33.3956i	0.194776	−	1.10463i
$915$		0			0
$916$	3.61064	+	1.31417i	0.119299	+	0.0434213i
$917$	−35.0373	−	16.3382i	−1.15703	−	0.539534i
$918$	1.13559	−	12.9798i	0.0374799	−	0.428397i
$919$	1.81672	−	1.04888i	0.0599279	−	0.0345994i	−0.469737	−	0.882807i	$-0.655651\pi$
$919$	1.81672	−	1.04888i	0.0599279	−	0.0345994i	0.529665	+	0.848207i	$0.322318\pi$
$920$		0			0
$921$	0.447937	+	2.54038i	0.0147600	+	0.0837083i
$922$	9.15325	+	6.40918i	0.301446	+	0.211075i
$923$	−4.14810	−	15.4809i	−0.136536	−	0.509561i
$924$	4.49822	+	7.79114i	0.147981	+	0.256310i
$925$		0			0
$926$	9.87513	+	27.1317i	0.324517	+	0.891603i
$927$	−5.99038	+	2.79336i	−0.196750	+	0.0917460i
$928$	−1.74017	+	0.152245i	−0.0571239	+	0.00499769i
$929$	−52.4609	−	9.25027i	−1.72119	−	0.303492i	−0.776172	−	0.630521i	$-0.782841\pi$
$929$	−52.4609	−	9.25027i	−1.72119	−	0.303492i	−0.945014	+	0.327029i	$0.893952\pi$
$930$		0			0
$931$	−30.8571	−	1.85345i	−1.01130	−	0.0607444i
$932$	5.00733	+	5.00733i	0.164020	+	0.164020i
$933$	4.12715	−	2.88986i	0.135117	−	0.0946098i
$934$	−11.8099	−	9.90970i	−0.386432	−	0.324255i
$935$		0			0
$936$	3.48795	−	1.26951i	0.114007	−	0.0414953i
$937$	48.6745	+	4.25846i	1.59013	+	0.139118i	0.847576	−	0.530673i	$-0.178061\pi$
$937$	48.6745	+	4.25846i	1.59013	+	0.139118i	0.742549	+	0.669791i	$0.233617\pi$
$938$	−0.917775	−	0.245917i	−0.0299664	−	0.00802947i
$939$	−1.49850	+	2.59548i	−0.0489018	+	0.0847004i
$940$		0			0
$941$	42.9034	−	7.56502i	1.39861	−	0.246613i	0.577038	−	0.816717i	$-0.304209\pi$
$941$	42.9034	−	7.56502i	1.39861	−	0.246613i	0.821572	+	0.570105i	$0.193097\pi$
$942$	1.16288	−	0.311594i	0.0378888	−	0.0101523i
$943$	6.27218	−	23.4081i	0.204250	−	0.762273i
$944$	7.01554	−	5.88674i	0.228336	−	0.191597i
$945$		0			0
$946$	−3.33228	+	9.15535i	−0.108342	+	0.297666i
$947$	0.241094	+	2.75571i	0.00783449	+	0.0895486i	0.999105	−	0.0422934i	$-0.0134664\pi$
$947$	0.241094	+	2.75571i	0.00783449	+	0.0895486i	−0.991271	+	0.131842i	$0.957911\pi$
$948$	2.64598	+	3.77885i	0.0859374	+	0.122731i
$949$	14.0738			0.456853
$950$		0			0
$951$	−6.26001			−0.202995
$952$	10.1212	+	14.4546i	0.328030	+	0.468475i
$953$	−3.24039	−	37.0378i	−0.104966	−	1.19977i	−0.847808	−	0.530304i	$-0.822078\pi$
$953$	−3.24039	−	37.0378i	−0.104966	−	1.19977i	0.742841	−	0.669468i	$-0.233478\pi$
$954$	−9.96361	+	27.3748i	−0.322584	+	0.886291i
$955$		0			0
$956$	6.62612	−	5.55998i	0.214304	−	0.179823i
$957$	1.08350	−	4.04369i	0.0350247	−	0.130714i
$958$	9.97672	−	2.67325i	0.322333	−	0.0863689i
$959$	−52.0284	+	9.17400i	−1.68008	+	0.296244i
$960$		0			0
$961$	−13.7149	+	23.7549i	−0.442417	+	0.766288i
$962$	−10.6079	−	2.84238i	−0.342012	−	0.0916419i
$963$	−19.4685	−	1.70327i	−0.627362	−	0.0548871i
$964$	−19.3048	+	7.02637i	−0.621766	+	0.226304i
$965$		0			0
$966$	−3.57949	−	3.00354i	−0.115168	−	0.0966375i
$967$	−3.62688	+	2.53957i	−0.116632	+	0.0816669i	−0.630437	−	0.776240i	$-0.717124\pi$
$967$	−3.62688	+	2.53957i	−0.116632	+	0.0816669i	0.513805	+	0.857907i	$0.328236\pi$
$968$	9.81511	+	9.81511i	0.315469	+	0.315469i
$969$	−9.03217	−	3.91556i	−0.290155	−	0.125786i
$970$		0			0
$971$	9.49031	+	1.67340i	0.304558	+	0.0537019i	0.323839	−	0.946112i	$-0.395026\pi$
$971$	9.49031	+	1.67340i	0.304558	+	0.0537019i	−0.0192805	+	0.999814i	$0.506138\pi$
$972$	11.6227	−	1.01685i	0.372797	−	0.0326155i
$973$	−63.1031	+	29.4254i	−2.02299	+	0.943337i
$974$	−7.07577	−	19.4405i	−0.226722	−	0.622915i
$975$		0			0
$976$	1.07317	+	1.85879i	0.0343515	+	0.0594985i
$977$	7.84751	+	29.2873i	0.251064	+	0.936984i	0.970238	+	0.242154i	$0.0778539\pi$
$977$	7.84751	+	29.2873i	0.251064	+	0.936984i	−0.719174	+	0.694830i	$0.755479\pi$
$978$	5.21454	+	3.65126i	0.166743	+	0.116754i
$979$	11.5412	+	65.4533i	0.368858	+	2.09190i
$980$		0			0
$981$	−7.14603	+	4.12576i	−0.228155	+	0.131725i
$982$	−3.12894	+	35.7640i	−0.0998486	+	1.14127i
$983$	−32.3850	−	15.1014i	−1.03292	−	0.481659i	−0.169175	−	0.985586i	$-0.554110\pi$
$983$	−32.3850	−	15.1014i	−1.03292	−	0.481659i	−0.863746	+	0.503927i	$0.831888\pi$
$984$	4.22315	+	1.53710i	0.134629	+	0.0490010i
$985$		0			0
$986$	1.42585	−	8.08640i	0.0454083	−	0.257523i
$987$	8.72823	−	8.72823i	0.277823	−	0.277823i
$988$	−0.159328	−	5.84053i	−0.00506891	−	0.185812i
$989$		−	5.06040i		−	0.160912i
$990$		0			0
$991$	−20.1912	+	24.0629i	−0.641394	+	0.764383i	−0.984590	−	0.174880i	$-0.944046\pi$
$991$	−20.1912	+	24.0629i	−0.641394	+	0.764383i	0.343196	+	0.939264i	$0.388491\pi$
$992$	−0.798532	−	1.71246i	−0.0253534	−	0.0543706i
$993$	−3.20126	+	6.86513i	−0.101589	+	0.217858i
$994$	28.8515	+	34.3838i	0.915113	+	1.09059i
$995$		0			0
$996$	−6.22034	−	3.59131i	−0.197099	−	0.113795i
$997$	−18.5401	+	26.4780i	−0.587170	+	0.838566i	−0.997298	−	0.0734621i	$-0.976595\pi$
$997$	−18.5401	+	26.4780i	−0.587170	+	0.838566i	0.410128	+	0.912028i	$0.365484\pi$
$998$	−6.35080	+	9.06988i	−0.201031	+	0.287102i
$999$	−19.6674	−	11.3550i	−0.622249	−	0.359256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.e.857.7		120
5.2	odd	4		190.2.r.a.173.2	yes	120
5.3	odd	4	inner	950.2.bb.e.743.9		120
5.4	even	2		190.2.r.a.97.4	yes	120
19.10	odd	18	inner	950.2.bb.e.257.9		120
95.29	odd	18		190.2.r.a.67.2	✓	120
95.48	even	36	inner	950.2.bb.e.143.7		120
95.67	even	36		190.2.r.a.143.4	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.r.a.67.2	✓	120	95.29	odd	18
190.2.r.a.97.4	yes	120	5.4	even	2
190.2.r.a.143.4	yes	120	95.67	even	36
190.2.r.a.173.2	yes	120	5.2	odd	4
950.2.bb.e.143.7		120	95.48	even	36	inner
950.2.bb.e.257.9		120	19.10	odd	18	inner
950.2.bb.e.743.9		120	5.3	odd	4	inner
950.2.bb.e.857.7		120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.573576 + 0.819152i) q^{2} +(-0.0418747 - 0.478630i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(0.368052 - 0.308832i) q^{6} +(0.971585 - 3.62600i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(2.72709 - 0.480860i) q^{9} +O(q^{10})\)	\(q+(0.573576 + 0.819152i) q^{2} +(-0.0418747 - 0.478630i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(0.368052 - 0.308832i) q^{6} +(0.971585 - 3.62600i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(2.72709 - 0.480860i) q^{9} +(-2.49403 + 4.31978i) q^{11} +(0.464087 + 0.124352i) q^{12} +(-1.33531 - 0.116824i) q^{13} +(3.52753 - 1.28391i) q^{14} +(-0.766044 - 0.642788i) q^{16} +(3.85053 - 2.69617i) q^{17} +(1.95809 + 1.95809i) q^{18} +(3.89880 - 1.94919i) q^{19} +(-1.77620 - 0.313191i) q^{21} +(-4.96907 + 0.434737i) q^{22} +(2.34802 - 1.09490i) q^{23} +(0.164326 + 0.451483i) q^{24} +(-0.670204 - 1.16083i) q^{26} +(-0.717405 - 2.67739i) q^{27} +(3.07503 + 2.15316i) q^{28} +(-0.303332 - 1.72028i) q^{29} +(1.63635 - 0.944744i) q^{31} +(0.0871557 - 0.996195i) q^{32} +(2.17201 + 1.01283i) q^{33} +(4.41715 + 1.60771i) q^{34} +(-0.480860 + 2.72709i) q^{36} +(5.79340 - 5.79340i) q^{37} +(3.83295 + 2.07570i) q^{38} +0.644009i q^{39} +(6.01261 - 7.16555i) q^{41} +(-0.762233 - 1.63461i) q^{42} +(0.825480 - 1.77025i) q^{43} +(-3.20626 - 3.82107i) q^{44} +(2.24366 + 1.29538i) q^{46} +(-3.92548 + 5.60617i) q^{47} +(-0.275579 + 0.393568i) q^{48} +(-6.14174 - 3.54594i) q^{49} +(-1.45171 - 1.73008i) q^{51} +(0.566481 - 1.21482i) q^{52} +(4.44595 + 9.53438i) q^{53} +(1.78170 - 2.12335i) q^{54} +3.75391i q^{56} +(-1.09620 - 1.78446i) q^{57} +(1.23519 - 1.23519i) q^{58} +(-1.59029 + 9.01900i) q^{59} +(-2.01691 - 0.734095i) q^{61} +(1.71246 + 0.798532i) q^{62} +(0.906001 - 10.3556i) q^{63} +(0.866025 - 0.500000i) q^{64} +(0.416156 + 2.36014i) q^{66} +(-0.207335 - 0.145177i) q^{67} +(1.21661 + 4.54046i) q^{68} +(-0.622375 - 1.07799i) q^{69} +(4.08948 + 11.2357i) q^{71} +(-2.50971 + 1.17030i) q^{72} +(-10.4597 + 0.915101i) q^{73} +(8.06863 + 1.42272i) q^{74} +(0.498175 + 4.33034i) q^{76} +(13.2404 + 13.2404i) q^{77} +(-0.527542 + 0.369389i) q^{78} +(7.35519 + 6.17174i) q^{79} +(6.55504 - 2.38584i) q^{81} +(9.31836 + 0.815251i) q^{82} +(-14.4402 - 3.86923i) q^{83} +(0.901799 - 1.56196i) q^{84} +(1.92358 - 0.339179i) q^{86} +(-0.810675 + 0.217220i) q^{87} +(1.29100 - 4.81809i) q^{88} +(10.2071 - 8.56479i) q^{89} +(-1.72097 + 4.72832i) q^{91} +(0.225799 + 2.58090i) q^{92} +(-0.520704 - 0.743642i) q^{93} -6.84386 q^{94} -0.480458 q^{96} +(-8.07300 - 11.5294i) q^{97} +(-0.618097 - 7.06489i) q^{98} +(-4.72423 + 12.9797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^7	\( 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) \) 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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Database

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