LMFDB - Embedded newform 950.2.u.g.549.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			549.2
Character	$\chi$	$=$	950.549
Dual form			950.2.u.g.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(-0.712963 + 0.849676i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.849676 - 0.712963i) q^{6} +(4.26875 - 2.46456i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.307311 + 1.74285i) q^{9} +O(q^{10})$	\(q+(-0.984808 - 0.173648i) q^{2} +(-0.712963 + 0.849676i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.849676 - 0.712963i) q^{6} +(4.26875 - 2.46456i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.307311 + 1.74285i) q^{9} +(-2.20561 + 3.82023i) q^{11} +(-0.960572 + 0.554587i) q^{12} +(-1.69691 - 2.02230i) q^{13} +(-4.63187 + 1.68586i) q^{14} +(0.766044 + 0.642788i) q^{16} +(4.94904 + 0.872649i) q^{17} -1.76973i q^{18} +(4.21347 + 1.11656i) q^{19} +(-0.949379 + 5.38420i) q^{21} +(2.83548 - 3.37919i) q^{22} +(0.351075 - 0.964570i) q^{23} +(1.04228 - 0.379360i) q^{24} +(1.31996 + 2.28624i) q^{26} +(-4.58167 - 2.64523i) q^{27} +(4.85424 - 0.855934i) q^{28} +(-0.462691 - 2.62405i) q^{29} +(-1.01615 - 1.76003i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-1.67344 - 4.59773i) q^{33} +(-4.72232 - 1.71878i) q^{34} +(-0.307311 + 1.74285i) q^{36} +2.00107i q^{37} +(-3.95557 - 1.83126i) q^{38} +2.92813 q^{39} +(1.65005 + 1.38456i) q^{41} +(1.86991 - 5.13754i) q^{42} +(0.516578 + 1.41929i) q^{43} +(-3.37919 + 2.83548i) q^{44} +(-0.513237 + 0.888952i) q^{46} +(-1.76317 + 0.310895i) q^{47} +(-1.09232 + 0.192606i) q^{48} +(8.64815 - 14.9790i) q^{49} +(-4.26995 + 3.58291i) q^{51} +(-0.902907 - 2.48072i) q^{52} +(-1.92343 + 5.28457i) q^{53} +(4.05273 + 3.40064i) q^{54} -4.92913 q^{56} +(-3.95276 + 2.78402i) q^{57} +2.66453i q^{58} +(-2.44041 + 13.8402i) q^{59} +(13.6360 + 4.96308i) q^{61} +(0.695088 + 1.90974i) q^{62} +(5.60720 + 6.68240i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.849627 + 4.81847i) q^{66} +(13.4349 - 2.36894i) q^{67} +(4.35211 + 2.51269i) q^{68} +(0.569269 + 0.986002i) q^{69} +(14.6575 - 5.33488i) q^{71} +(0.605285 - 1.66301i) q^{72} +(-8.10702 + 9.66157i) q^{73} +(0.347483 - 1.97067i) q^{74} +(3.57748 + 2.49031i) q^{76} +21.7435i q^{77} +(-2.88365 - 0.508465i) q^{78} +(2.17143 + 1.82205i) q^{79} +(0.525132 - 0.191132i) q^{81} +(-1.38456 - 1.65005i) q^{82} +(6.30732 - 3.64153i) q^{83} +(-2.73363 + 4.73478i) q^{84} +(-0.262274 - 1.48743i) q^{86} +(2.55947 + 1.47771i) q^{87} +(3.82023 - 2.20561i) q^{88} +(-7.72995 + 6.48620i) q^{89} +(-12.2278 - 4.45054i) q^{91} +(0.659805 - 0.786325i) q^{92} +(2.21993 + 0.391433i) q^{93} +1.79037 q^{94} +1.10917 q^{96} +(11.7266 + 2.06772i) q^{97} +(-11.1179 + 13.2497i) q^{98} +(-7.33589 - 2.67005i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 36 q^{9}+O(q^{10}) $ 36 * q + 36 * q^9	$ 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) $ 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$3$	−0.712963	+	0.849676i	−0.411629	+	0.490561i	−0.931529	−	0.363667i	$-0.881525\pi$
$3$	−0.712963	+	0.849676i	−0.411629	+	0.490561i	0.519900	+	0.854227i	$0.325969\pi$
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	0.849676	−	0.712963i	0.346879	−	0.291066i
$7$	4.26875	−	2.46456i	1.61344	−	0.931518i	0.624870	−	0.780729i	$-0.285152\pi$
$7$	4.26875	−	2.46456i	1.61344	−	0.931518i	0.988566	−	0.150789i	$-0.0481814\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	0.307311	+	1.74285i	0.102437	+	0.580950i
$10$		0			0
$11$	−2.20561	+	3.82023i	−0.665016	+	1.15184i	0.314264	+	0.949336i	$0.398242\pi$
$11$	−2.20561	+	3.82023i	−0.665016	+	1.15184i	−0.979281	+	0.202507i	$0.935091\pi$
$12$	−0.960572	+	0.554587i	−0.277293	+	0.160095i
$13$	−1.69691	−	2.02230i	−0.470638	−	0.560884i	0.477546	−	0.878607i	$-0.341526\pi$
$13$	−1.69691	−	2.02230i	−0.470638	−	0.560884i	−0.948184	+	0.317722i	$0.897082\pi$
$14$	−4.63187	+	1.68586i	−1.23792	+	0.450565i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	4.94904	+	0.872649i	1.20032	+	0.211649i	0.737836	−	0.674980i	$-0.235848\pi$
$17$	4.94904	+	0.872649i	1.20032	+	0.211649i	0.462483	+	0.886628i	$0.346959\pi$
$18$		−	1.76973i		−	0.417131i
$19$	4.21347	+	1.11656i	0.966635	+	0.256156i
$19$	4.21347	+	1.11656i	0.966635	+	0.256156i
$20$		0			0
$21$	−0.949379	+	5.38420i	−0.207172	+	1.17493i
$22$	2.83548	−	3.37919i	0.604526	−	0.720446i
$23$	0.351075	−	0.964570i	0.0732041	−	0.201127i	−0.897694	−	0.440619i	$-0.854759\pi$
$23$	0.351075	−	0.964570i	0.0732041	−	0.201127i	0.970898	+	0.239493i	$0.0769811\pi$
$24$	1.04228	−	0.379360i	0.212755	−	0.0774364i
$25$		0			0
$26$	1.31996	+	2.28624i	0.258866	+	0.448368i
$27$	−4.58167	−	2.64523i	−0.881744	−	0.509075i
$28$	4.85424	−	0.855934i	0.917366	−	0.161756i
$29$	−0.462691	−	2.62405i	−0.0859196	−	0.487274i	−0.997154	−	0.0753868i	$-0.975981\pi$
$29$	−0.462691	−	2.62405i	−0.0859196	−	0.487274i	0.911235	−	0.411887i	$-0.135130\pi$
$30$		0			0
$31$	−1.01615	−	1.76003i	−0.182506	−	0.316110i	0.760227	−	0.649657i	$-0.225088\pi$
$31$	−1.01615	−	1.76003i	−0.182506	−	0.316110i	−0.942733	+	0.333547i	$0.891754\pi$
$32$	−0.642788	−	0.766044i	−0.113630	−	0.135419i
$33$	−1.67344	−	4.59773i	−0.291308	−	0.800363i
$34$	−4.72232	−	1.71878i	−0.809871	−	0.294769i
$35$		0			0
$36$	−0.307311	+	1.74285i	−0.0512185	+	0.290475i
$37$			2.00107i			0.328975i	0.986379	+	0.164487i	$0.0525970\pi$
$37$			2.00107i			0.328975i	−0.986379	+	0.164487i	$0.947403\pi$
$38$	−3.95557	−	1.83126i	−0.641678	−	0.297069i
$39$	2.92813			0.468876
$40$		0			0
$41$	1.65005	+	1.38456i	0.257695	+	0.216232i	0.762477	−	0.647015i	$-0.223983\pi$
$41$	1.65005	+	1.38456i	0.257695	+	0.216232i	−0.504782	+	0.863247i	$0.668427\pi$
$42$	1.86991	−	5.13754i	0.288534	−	0.792740i
$43$	0.516578	+	1.41929i	0.0787775	+	0.216439i	0.972829	−	0.231525i	$-0.0743714\pi$
$43$	0.516578	+	1.41929i	0.0787775	+	0.216439i	−0.894052	+	0.447964i	$0.852149\pi$
$44$	−3.37919	+	2.83548i	−0.509432	+	0.427464i
$45$		0			0
$46$	−0.513237	+	0.888952i	−0.0756727	+	0.131069i
$47$	−1.76317	+	0.310895i	−0.257185	+	0.0453486i	−0.300754	−	0.953702i	$-0.597238\pi$
$47$	−1.76317	+	0.310895i	−0.257185	+	0.0453486i	0.0435690	+	0.999050i	$0.486127\pi$
$48$	−1.09232	+	0.192606i	−0.157663	+	0.0278003i
$49$	8.64815	−	14.9790i	1.23545	−	2.13986i
$50$		0			0
$51$	−4.26995	+	3.58291i	−0.597913	+	0.501708i
$52$	−0.902907	−	2.48072i	−0.125211	−	0.344013i
$53$	−1.92343	+	5.28457i	−0.264203	+	0.725891i	0.734670	+	0.678425i	$0.237337\pi$
$53$	−1.92343	+	5.28457i	−0.264203	+	0.725891i	−0.998873	+	0.0474667i	$0.984885\pi$
$54$	4.05273	+	3.40064i	0.551507	+	0.462769i
$55$		0			0
$56$	−4.92913			−0.658683
$57$	−3.95276	+	2.78402i	−0.523555	+	0.368752i
$58$			2.66453i			0.349870i
$59$	−2.44041	+	13.8402i	−0.317714	+	1.80184i	0.238869	+	0.971052i	$0.423223\pi$
$59$	−2.44041	+	13.8402i	−0.317714	+	1.80184i	−0.556583	+	0.830792i	$0.687888\pi$
$60$		0			0
$61$	13.6360	+	4.96308i	1.74590	+	0.635457i	0.999547	−	0.0300876i	$-0.00957861\pi$
$61$	13.6360	+	4.96308i	1.74590	+	0.635457i	0.746358	+	0.665545i	$0.231801\pi$
$62$	0.695088	+	1.90974i	0.0882763	+	0.242537i
$63$	5.60720	+	6.68240i	0.706441	+	0.841903i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	0.849627	+	4.81847i	0.104582	+	0.593113i
$67$	13.4349	−	2.36894i	1.64134	−	0.289412i	0.724679	−	0.689086i	$-0.241988\pi$
$67$	13.4349	−	2.36894i	1.64134	−	0.289412i	0.916657	+	0.399674i	$0.130877\pi$
$68$	4.35211	+	2.51269i	0.527771	+	0.304709i
$69$	0.569269	+	0.986002i	0.0685319	+	0.118701i
$70$		0			0
$71$	14.6575	−	5.33488i	1.73952	−	0.633134i	0.740287	−	0.672291i	$-0.234690\pi$
$71$	14.6575	−	5.33488i	1.73952	−	0.633134i	0.999233	+	0.0391574i	$0.0124674\pi$
$72$	0.605285	−	1.66301i	0.0713335	−	0.195987i
$73$	−8.10702	+	9.66157i	−0.948855	+	1.13080i	0.0424348	+	0.999099i	$0.486489\pi$
$73$	−8.10702	+	9.66157i	−0.948855	+	1.13080i	−0.991289	+	0.131702i	$0.957956\pi$
$74$	0.347483	−	1.97067i	0.0403941	−	0.229086i
$75$		0			0
$76$	3.57748	+	2.49031i	0.410365	+	0.285658i
$77$			21.7435i			2.47790i
$78$	−2.88365	−	0.508465i	−0.326509	−	0.0575723i
$79$	2.17143	+	1.82205i	0.244305	+	0.204996i	0.756716	−	0.653744i	$-0.226803\pi$
$79$	2.17143	+	1.82205i	0.244305	+	0.204996i	−0.512410	+	0.858741i	$0.671247\pi$
$80$		0			0
$81$	0.525132	−	0.191132i	0.0583480	−	0.0212369i
$82$	−1.38456	−	1.65005i	−0.152899	−	0.182218i
$83$	6.30732	−	3.64153i	0.692318	−	0.399710i	−0.112162	−	0.993690i	$-0.535778\pi$
$83$	6.30732	−	3.64153i	0.692318	−	0.399710i	0.804480	+	0.593980i	$0.202444\pi$
$84$	−2.73363	+	4.73478i	−0.298263	+	0.516607i
$85$		0			0
$86$	−0.262274	−	1.48743i	−0.0282817	−	0.160394i
$87$	2.55947	+	1.47771i	0.274404	+	0.158428i
$88$	3.82023	−	2.20561i	0.407238	−	0.235119i
$89$	−7.72995	+	6.48620i	−0.819373	+	0.687536i	−0.952825	−	0.303520i	$-0.901838\pi$
$89$	−7.72995	+	6.48620i	−0.819373	+	0.687536i	0.133452	+	0.991055i	$0.457394\pi$
$90$		0			0
$91$	−12.2278	−	4.45054i	−1.28182	−	0.466544i
$92$	0.659805	−	0.786325i	0.0687894	−	0.0819800i
$93$	2.21993	+	0.391433i	0.230196	+	0.0405897i
$94$	1.79037			0.184663
$95$		0			0
$96$	1.10917			0.113205
$97$	11.7266	+	2.06772i	1.19066	+	0.209945i	0.733656	−	0.679521i	$-0.237812\pi$
$97$	11.7266	+	2.06772i	1.19066	+	0.209945i	0.457002	+	0.889466i	$0.348923\pi$
$98$	−11.1179	+	13.2497i	−1.12307	+	1.33843i
$99$	−7.33589	−	2.67005i	−0.737285	−	0.268350i
$100$		0			0
$101$	−1.10632	+	0.928316i	−0.110083	+	0.0923709i	−0.696168	−	0.717879i	$-0.745113\pi$
$101$	−1.10632	+	0.928316i	−0.110083	+	0.0923709i	0.586085	+	0.810250i	$0.300669\pi$
$102$	4.82725	−	2.78701i	0.477969	−	0.275955i
$103$	−3.86364	−	2.23068i	−0.380696	−	0.219795i	0.297425	−	0.954745i	$-0.403872\pi$
$103$	−3.86364	−	2.23068i	−0.380696	−	0.219795i	−0.678121	+	0.734950i	$0.737206\pi$
$104$	0.458418	+	2.59982i	0.0449515	+	0.254933i
$105$		0			0
$106$	2.81186	−	4.87029i	0.273112	−	0.473044i
$107$	−6.80951	+	3.93147i	−0.658300	+	0.380070i	−0.791629	−	0.611002i	$-0.790767\pi$
$107$	−6.80951	+	3.93147i	−0.658300	+	0.380070i	0.133329	+	0.991072i	$0.457433\pi$
$108$	−3.40064	−	4.05273i	−0.327227	−	0.389974i
$109$	−2.37019	+	0.862678i	−0.227023	+	0.0826296i	−0.453027	−	0.891497i	$-0.649656\pi$
$109$	−2.37019	+	0.862678i	−0.227023	+	0.0826296i	0.226004	+	0.974126i	$0.427434\pi$
$110$		0			0
$111$	−1.70027	−	1.42669i	−0.161382	−	0.135416i
$112$	4.85424	+	0.855934i	0.458683	+	0.0808782i
$113$		−	2.59814i		−	0.244413i	−0.992505	−	0.122206i	$-0.961003\pi$
$113$		−	2.59814i		−	0.244413i	0.992505	−	0.122206i	$-0.0389970\pi$
$114$	4.37615	−	2.05533i	0.409864	−	0.192499i
$115$		0			0
$116$	0.462691	−	2.62405i	0.0429598	−	0.243637i
$117$	3.00308	−	3.57893i	0.277635	−	0.330872i
$118$	4.80666	−	13.2062i	0.442489	−	1.21573i
$119$	23.2769	−	8.47211i	2.13379	−	0.776637i
$120$		0			0
$121$	−4.22943	−	7.32559i	−0.384494	−	0.665963i
$122$	−12.5670	−	7.25554i	−1.13776	−	0.656886i
$123$	−2.35285	+	0.414871i	−0.212150	+	0.0374077i
$124$	−0.352906	−	2.00143i	−0.0316919	−	0.179733i
$125$		0			0
$126$	−4.36163	−	7.55456i	−0.388564	−	0.673013i
$127$	−13.3209	−	15.8752i	−1.18204	−	1.40869i	−0.892213	−	0.451614i	$-0.850848\pi$
$127$	−13.3209	−	15.8752i	−1.18204	−	1.40869i	−0.289822	−	0.957080i	$-0.593596\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$	−1.57424	−	0.572975i	−0.138604	−	0.0504476i
$130$		0			0
$131$	−0.301638	+	1.71068i	−0.0263543	+	0.149462i	−0.995145	−	0.0984163i	$-0.968622\pi$
$131$	−0.301638	+	1.71068i	−0.0263543	+	0.149462i	0.968791	+	0.247879i	$0.0797334\pi$
$132$		−	4.89281i		−	0.425864i
$133$	20.7381	−	5.61805i	1.79822	−	0.487147i
$134$	−13.6422			−1.17850
$135$		0			0
$136$	−3.84967	−	3.23026i	−0.330107	−	0.276992i
$137$	0.854249	−	2.34703i	0.0729834	−	0.200520i	−0.897837	−	0.440328i	$-0.854862\pi$
$137$	0.854249	−	2.34703i	0.0729834	−	0.200520i	0.970820	+	0.239808i	$0.0770844\pi$
$138$	−0.389403	−	1.06988i	−0.0331482	−	0.0910738i
$139$	−9.06390	+	7.60552i	−0.768790	+	0.645092i	−0.940399	−	0.340074i	$-0.889548\pi$
$139$	−9.06390	+	7.60552i	−0.768790	+	0.645092i	0.171609	+	0.985165i	$0.445104\pi$
$140$		0			0
$141$	0.992916	−	1.71978i	0.0836186	−	0.144832i
$142$	−15.3612	+	2.70859i	−1.28908	+	0.227300i
$143$	11.4684	−	2.02218i	0.959032	−	0.169103i
$144$	−0.884867	+	1.53264i	−0.0737390	+	0.127720i
$145$		0			0
$146$	9.66157	−	8.10702i	0.799597	−	0.670942i
$147$	6.56152	+	18.0276i	0.541185	+	1.48689i
$148$	−0.684408	+	1.88040i	−0.0562580	+	0.154568i
$149$	15.4299	+	12.9472i	1.26406	+	1.06068i	0.995237	+	0.0974880i	$0.0310808\pi$
$149$	15.4299	+	12.9472i	1.26406	+	1.06068i	0.268828	+	0.963188i	$0.413364\pi$
$150$		0			0
$151$	−7.67871			−0.624885			−0.312442	−	0.949937i	$-0.601147\pi$
$151$	−7.67871			−0.624885			−0.312442	+	0.949937i	$0.601147\pi$
$152$	−3.09069	−	3.07370i	−0.250688	−	0.249310i
$153$			8.89360i			0.719005i
$154$	3.77571	−	21.4131i	0.304256	−	1.72552i
$155$		0			0
$156$	2.75154	+	1.00148i	0.220300	+	0.0801825i
$157$	1.98396	+	5.45088i	0.158337	+	0.435027i	0.993340	−	0.115218i	$-0.0367565\pi$
$157$	1.98396	+	5.45088i	0.158337	+	0.435027i	−0.835003	+	0.550245i	$0.814534\pi$
$158$	−1.82205	−	2.17143i	−0.144954	−	0.172750i
$159$	−3.11884	−	5.40199i	−0.247340	−	0.428406i
$160$		0			0
$161$	−0.878594	−	4.98275i	−0.0692429	−	0.392696i
$162$	−0.550344	+	0.0970404i	−0.0432391	+	0.00762422i
$163$	−9.28767	−	5.36224i	−0.727466	−	0.420003i	0.0900283	−	0.995939i	$-0.471304\pi$
$163$	−9.28767	−	5.36224i	−0.727466	−	0.420003i	−0.817495	+	0.575936i	$0.804638\pi$
$164$	1.07700	+	1.86541i	0.0840992	+	0.145664i
$165$		0			0
$166$	−6.84384	+	2.49095i	−0.531185	+	0.193335i
$167$	3.38367	−	9.29655i	0.261836	−	0.719389i	−0.737208	−	0.675666i	$-0.763856\pi$
$167$	3.38367	−	9.29655i	0.261836	−	0.719389i	0.999044	−	0.0437226i	$-0.0139218\pi$
$168$	3.51429	−	4.18816i	0.271133	−	0.323124i
$169$	1.04724	−	5.93919i	0.0805569	−	0.456861i
$170$		0			0
$171$	−0.651146	+	7.68657i	−0.0497944	+	0.587806i
$172$			1.51037i			0.115165i
$173$	15.4634	+	2.72662i	1.17566	+	0.207301i	0.727151	−	0.686477i	$-0.240844\pi$
$173$	15.4634	+	2.72662i	1.17566	+	0.207301i	0.448510	+	0.893778i	$0.351955\pi$
$174$	−2.26399	−	1.89971i	−0.171633	−	0.144017i
$175$		0			0
$176$	−4.14519	+	1.50873i	−0.312456	+	0.113725i
$177$	−10.0198	−	11.9411i	−0.753134	−	0.897550i
$178$	8.73883	−	5.04537i	0.655003	−	0.378166i
$179$	5.05642	−	8.75798i	0.377935	−	0.654602i	−0.612827	−	0.790217i	$-0.709968\pi$
$179$	5.05642	−	8.75798i	0.377935	−	0.654602i	0.990762	+	0.135615i	$0.0433010\pi$
$180$		0			0
$181$	0.465151	+	2.63800i	0.0345744	+	0.196081i	0.997203	−	0.0747449i	$-0.0238142\pi$
$181$	0.465151	+	2.63800i	0.0345744	+	0.196081i	−0.962628	+	0.270826i	$0.912703\pi$
$182$	11.2692	+	6.50626i	0.835326	+	0.482276i
$183$	−13.9389	+	8.04765i	−1.03040	+	0.594899i
$184$	−0.786325	+	0.659805i	−0.0579686	+	0.0486414i
$185$		0			0
$186$	−2.11823	−	0.770973i	−0.155316	−	0.0565305i
$187$	−14.2494	+	16.9817i	−1.04202	+	1.24183i
$188$	−1.76317	−	0.310895i	−0.128592	−	0.0226743i
$189$	−26.0774			−1.89685
$190$		0			0
$191$	3.75100			0.271413			0.135706	−	0.990749i	$-0.456670\pi$
$191$	3.75100			0.271413			0.135706	+	0.990749i	$0.456670\pi$
$192$	−1.09232	−	0.192606i	−0.0788316	−	0.0139001i
$193$	−9.27700	+	11.0559i	−0.667773	+	0.795821i	−0.988479	−	0.151358i	$-0.951635\pi$
$193$	−9.27700	+	11.0559i	−0.667773	+	0.795821i	0.320706	+	0.947179i	$0.396080\pi$
$194$	−11.1894	−	4.07261i	−0.803353	−	0.292397i
$195$		0			0
$196$	13.2497	−	11.1179i	0.946410	−	0.794132i
$197$	−17.1473	+	9.89999i	−1.22169	+	0.705345i	−0.965279	−	0.261222i	$-0.915875\pi$
$197$	−17.1473	+	9.89999i	−1.22169	+	0.705345i	−0.256415	+	0.966567i	$0.582541\pi$
$198$	6.76079	+	3.90335i	0.480469	+	0.277399i
$199$	−3.46951	−	19.6766i	−0.245947	−	1.39484i	−0.818282	−	0.574817i	$-0.805073\pi$
$199$	−3.46951	−	19.6766i	−0.245947	−	1.39484i	0.572335	−	0.820020i	$-0.306038\pi$
$200$		0			0
$201$	−7.56577	+	13.1043i	−0.533648	+	0.924305i
$202$	1.25072	−	0.722101i	0.0880001	−	0.0508069i
$203$	−8.44226	−	10.0611i	−0.592530	−	0.706150i
$204$	−5.23787	+	1.90643i	−0.366724	+	0.133477i
$205$		0			0
$206$	3.41759	+	2.86770i	0.238115	+	0.199802i
$207$	1.78899	+	0.315447i	0.124343	+	0.0219251i
$208$		−	2.63992i		−	0.183046i
$209$	−13.5588	+	13.6337i	−0.937880	+	0.943064i
$210$		0			0
$211$	2.37072	−	13.4450i	0.163207	−	0.925594i	−0.787687	−	0.616076i	$-0.788721\pi$
$211$	2.37072	−	13.4450i	0.163207	−	0.925594i	0.950894	−	0.309518i	$-0.100168\pi$
$212$	−3.61486	+	4.30802i	−0.248269	+	0.295876i
$213$	−5.91730	+	16.2577i	−0.405447	+	1.11396i
$214$	7.38875	−	2.68928i	0.505084	−	0.183836i
$215$		0			0
$216$	2.64523	+	4.58167i	0.179985	+	0.311743i
$217$	−8.67539	−	5.00874i	−0.588924	−	0.340015i
$218$	2.48398	−	0.437993i	0.168237	−	0.0296646i
$219$	−2.42920	−	13.7767i	−0.164150	−	0.930941i
$220$		0			0
$221$	−6.63332	−	11.4892i	−0.446205	−	0.772850i
$222$	1.42669	+	1.70027i	0.0957533	+	0.114114i
$223$	−7.92835	−	21.7830i	−0.530922	−	1.45870i	−0.857976	−	0.513690i	$-0.828278\pi$
$223$	−7.92835	−	21.7830i	−0.530922	−	1.45870i	0.327054	−	0.945006i	$-0.393944\pi$
$224$	−4.63187	−	1.68586i	−0.309480	−	0.112641i
$225$		0			0
$226$	−0.451163	+	2.55867i	−0.0300109	+	0.170200i
$227$		−	7.37892i		−	0.489756i	−0.969554	−	0.244878i	$-0.921252\pi$
$227$		−	7.37892i		−	0.489756i	0.969554	−	0.244878i	$-0.0787479\pi$
$228$	−4.66657	+	1.26420i	−0.309051	+	0.0837235i
$229$	13.2440			0.875188			0.437594	−	0.899173i	$-0.355831\pi$
$229$	13.2440			0.875188			0.437594	+	0.899173i	$0.355831\pi$
$230$		0			0
$231$	−18.4749	−	15.5023i	−1.21556	−	1.01998i
$232$	−0.911323	+	2.50384i	−0.0598313	+	0.164385i
$233$	5.17822	+	14.2271i	0.339237	+	0.932045i	0.985612	+	0.169025i	$0.0540620\pi$
$233$	5.17822	+	14.2271i	0.339237	+	0.932045i	−0.646375	+	0.763020i	$0.723716\pi$
$234$	−3.57893	+	3.00308i	−0.233962	+	0.196317i
$235$		0			0
$236$	−7.02687	+	12.1709i	−0.457410	+	0.792258i
$237$	−3.09630	+	0.545962i	−0.201126	+	0.0354640i
$238$	−24.3945	+	4.30140i	−1.58126	+	0.278818i
$239$	5.84319	−	10.1207i	0.377964	−	0.654653i	−0.612802	−	0.790237i	$-0.709958\pi$
$239$	5.84319	−	10.1207i	0.377964	−	0.654653i	0.990766	+	0.135583i	$0.0432909\pi$
$240$		0			0
$241$	9.77297	−	8.20049i	0.629532	−	0.528240i	−0.271251	−	0.962509i	$-0.587437\pi$
$241$	9.77297	−	8.20049i	0.629532	−	0.528240i	0.900784	+	0.434268i	$0.142993\pi$
$242$	2.89310	+	7.94873i	0.185976	+	0.510964i
$243$	5.21633	−	14.3318i	0.334628	−	0.919383i
$244$	11.1161	+	9.32754i	0.711637	+	0.597135i
$245$		0			0
$246$	2.38915			0.152327
$247$	−4.89186	−	10.4156i	−0.311261	−	0.662727i
$248$			2.03230i			0.129051i
$249$	−1.40276	+	7.95545i	−0.0888963	+	0.504156i
$250$		0			0
$251$	−25.2367	−	9.18541i	−1.59293	−	0.579778i	−0.614964	−	0.788556i	$-0.710829\pi$
$251$	−25.2367	−	9.18541i	−1.59293	−	0.579778i	−0.977963	+	0.208778i	$0.933051\pi$
$252$	2.98353	+	8.19717i	0.187945	+	0.516373i
$253$	2.91054	+	3.46865i	0.182984	+	0.218072i
$254$	10.3618	+	17.9471i	0.650157	+	1.12610i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	0.157270	−	0.0277309i	0.00981023	−	0.00172981i	−0.168741	−	0.985660i	$-0.553970\pi$
$257$	0.157270	−	0.0277309i	0.00981023	−	0.00172981i	0.178551	+	0.983931i	$0.442859\pi$
$258$	1.45082	+	0.837633i	0.0903243	+	0.0521488i
$259$	4.93178	+	8.54209i	0.306446	+	0.530780i
$260$		0			0
$261$	4.43113	−	1.61280i	0.274280	−	0.0998299i
$262$	0.594111	−	1.63231i	0.0367043	−	0.100844i
$263$	5.95157	−	7.09280i	0.366990	−	0.437361i	−0.550673	−	0.834721i	$-0.685629\pi$
$263$	5.95157	−	7.09280i	0.366990	−	0.437361i	0.917663	+	0.397360i	$0.130073\pi$
$264$	−0.849627	+	4.81847i	−0.0522909	+	0.296557i
$265$		0			0
$266$	−21.3986	+	1.93157i	−1.31203	+	0.118432i
$267$		−	11.1924i		−	0.684962i
$268$	13.4349	+	2.36894i	0.820668	+	0.144706i
$269$	−9.55896	−	8.02092i	−0.582820	−	0.489044i	0.303052	−	0.952974i	$-0.401995\pi$
$269$	−9.55896	−	8.02092i	−0.582820	−	0.489044i	−0.885872	+	0.463930i	$0.846439\pi$
$270$		0			0
$271$	26.5079	−	9.64808i	1.61024	−	0.586079i	0.628752	−	0.777606i	$-0.283566\pi$
$271$	26.5079	−	9.64808i	1.61024	−	0.586079i	0.981487	+	0.191526i	$0.0613437\pi$
$272$	3.23026	+	3.84967i	0.195863	+	0.233421i
$273$	12.4995	−	7.21657i	0.756502	−	0.436766i
$274$	−1.24883	+	2.16303i	−0.0754445	+	0.130674i
$275$		0			0
$276$	0.197705	+	1.12124i	0.0119004	+	0.0674907i
$277$	−7.28486	−	4.20592i	−0.437705	−	0.252709i	0.264919	−	0.964271i	$-0.414655\pi$
$277$	−7.28486	−	4.20592i	−0.437705	−	0.252709i	−0.702624	+	0.711562i	$0.747988\pi$
$278$	10.2469	−	5.91604i	0.614567	−	0.354821i
$279$	2.75518	−	2.31187i	0.164948	−	0.138408i
$280$		0			0
$281$	−20.9967	−	7.64218i	−1.25256	−	0.455894i	−0.371294	−	0.928515i	$-0.621086\pi$
$281$	−20.9967	−	7.64218i	−1.25256	−	0.455894i	−0.881266	+	0.472621i	$0.843308\pi$
$282$	−1.27647	+	1.52123i	−0.0760125	+	0.0905882i
$283$	−12.5725	−	2.21687i	−0.747357	−	0.131779i	−0.213016	−	0.977049i	$-0.568329\pi$
$283$	−12.5725	−	2.21687i	−0.747357	−	0.131779i	−0.534340	+	0.845269i	$0.679440\pi$
$284$	15.5981			0.925579
$285$		0			0
$286$	−11.6453			−0.688600
$287$	10.4560	+	1.84368i	0.617198	+	0.108829i
$288$	1.13756	−	1.35570i	0.0670316	−	0.0798851i
$289$	7.75671	+	2.82321i	0.456277	+	0.166071i
$290$		0			0
$291$	−10.1175	+	8.48962i	−0.593100	+	0.497670i
$292$	−10.9226	+	6.30614i	−0.639194	+	0.369039i
$293$	−25.0376	−	14.4554i	−1.46271	−	0.844496i	−0.463575	−	0.886058i	$-0.653433\pi$
$293$	−25.0376	−	14.4554i	−1.46271	−	0.844496i	−0.999136	+	0.0415616i	$0.986767\pi$
$294$	−3.33137	−	18.8931i	−0.194289	−	1.10187i
$295$		0			0
$296$	1.00054	−	1.73298i	0.0581551	−	0.100728i
$297$	20.2108	−	11.6687i	1.17275	−	0.677086i
$298$	−12.9472	−	15.4299i	−0.750011	−	0.893829i
$299$	−2.54639	+	0.926810i	−0.147261	+	0.0535988i
$300$		0			0
$301$	5.70307	+	4.78544i	0.328719	+	0.275828i
$302$	7.56206	+	1.33339i	0.435147	+	0.0767282i
$303$		−	1.60187i		−	0.0920251i
$304$	2.50999	+	3.56370i	0.143958	+	0.204392i
$305$		0			0
$306$	1.54436	−	8.75849i	0.0882851	−	0.500690i
$307$	−15.0835	+	17.9758i	−0.860860	+	1.02593i	0.138507	+	0.990361i	$0.455770\pi$
$307$	−15.0835	+	17.9758i	−0.860860	+	1.02593i	−0.999367	+	0.0355713i	$0.988675\pi$
$308$	−7.43671	+	20.4322i	−0.423746	+	1.16423i
$309$	4.64999	−	1.69246i	0.264528	−	0.0962805i
$310$		0			0
$311$	−2.12258	−	3.67642i	−0.120360	−	0.208470i	0.799549	−	0.600600i	$-0.205072\pi$
$311$	−2.12258	−	3.67642i	−0.120360	−	0.208470i	−0.919910	+	0.392130i	$0.871738\pi$
$312$	−2.53584	−	1.46407i	−0.143563	−	0.0828864i
$313$	−11.4384	+	2.01689i	−0.646534	+	0.114001i	−0.487293	−	0.873238i	$-0.662016\pi$
$313$	−11.4384	+	2.01689i	−0.646534	+	0.114001i	−0.159241	+	0.987240i	$0.550905\pi$
$314$	−1.00728	−	5.71258i	−0.0568442	−	0.322379i
$315$		0			0
$316$	1.41730	+	2.45484i	0.0797295	+	0.138096i
$317$	−1.43742	−	1.71306i	−0.0807338	−	0.0962148i	0.724165	−	0.689626i	$-0.242225\pi$
$317$	−1.43742	−	1.71306i	−0.0807338	−	0.0962148i	−0.804899	+	0.593411i	$0.797781\pi$
$318$	2.13341	+	5.86150i	0.119636	+	0.328697i
$319$	11.0450	+	4.02005i	0.618401	+	0.225080i
$320$		0			0
$321$	1.51445	−	8.58887i	0.0845283	−	0.479384i
$322$			5.05962i			0.281962i
$323$	19.8783	+	9.20277i	1.10606	+	0.512056i
$324$	0.558833			0.0310463
$325$		0			0
$326$	8.21542	+	6.89356i	0.455010	+	0.381799i
$327$	0.956860	−	2.62895i	0.0529145	−	0.145381i
$328$	−0.736709	−	2.02409i	−0.0406779	−	0.111762i
$329$	−6.76032	+	5.67258i	−0.372708	+	0.312739i
$330$		0			0
$331$	0.254634	−	0.441039i	0.0139959	−	0.0242417i	−0.858943	−	0.512072i	$-0.828878\pi$
$331$	0.254634	−	0.441039i	0.0139959	−	0.0242417i	0.872939	+	0.487830i	$0.162211\pi$
$332$	7.17241	−	1.26469i	0.393637	−	0.0694089i
$333$	−3.48757	+	0.614953i	−0.191118	+	0.0336992i
$334$	−4.94659	+	8.56775i	−0.270666	+	0.468806i
$335$		0			0
$336$	−4.18816	+	3.51429i	−0.228483	+	0.191720i
$337$	5.15806	+	14.1717i	0.280977	+	0.771979i	0.997247	+	0.0741552i	$0.0236260\pi$
$337$	5.15806	+	14.1717i	0.280977	+	0.771979i	−0.716269	+	0.697824i	$0.754152\pi$
$338$	−2.06266	+	5.66711i	−0.112194	+	0.308250i
$339$	2.20758	+	1.85238i	0.119899	+	0.100607i
$340$		0			0
$341$	8.96493			0.485478
$342$	1.97601	−	7.45672i	0.106850	−	0.403213i
$343$		−	50.7518i		−	2.74034i
$344$	0.262274	−	1.48743i	0.0141409	−	0.0801968i
$345$		0			0
$346$	−14.7550	−	5.37038i	−0.793234	−	0.288714i
$347$	−11.5530	−	31.7415i	−0.620196	−	1.70398i	−0.706506	−	0.707707i	$-0.749730\pi$
$347$	−11.5530	−	31.7415i	−0.620196	−	1.70398i	0.0863093	−	0.996268i	$-0.472493\pi$
$348$	1.89971	+	2.26399i	0.101835	+	0.121363i
$349$	−0.0164139	−	0.0284297i	−0.000878615	−	0.00152181i	0.865586	−	0.500761i	$-0.166946\pi$
$349$	−0.0164139	−	0.0284297i	−0.000878615	−	0.00152181i	−0.866464	+	0.499239i	$0.833613\pi$
$350$		0			0
$351$	2.42524	+	13.7542i	0.129450	+	0.734146i
$352$	4.34420	−	0.766000i	0.231547	−	0.0408280i
$353$	−0.243332	−	0.140488i	−0.0129512	−	0.00747740i	0.493510	−	0.869740i	$-0.335713\pi$
$353$	−0.243332	−	0.140488i	−0.0129512	−	0.00747740i	−0.506462	+	0.862262i	$0.669047\pi$
$354$	7.79401	+	13.4996i	0.414247	+	0.717497i
$355$		0			0
$356$	−9.48219	+	3.45123i	−0.502555	+	0.182915i
$357$	−9.39703	+	25.8181i	−0.497344	+	1.36644i
$358$	−6.50041	+	7.74689i	−0.343557	+	0.409436i
$359$	−2.29364	+	13.0079i	−0.121054	+	0.686530i	0.862520	+	0.506023i	$0.168885\pi$
$359$	−2.29364	+	13.0079i	−0.121054	+	0.686530i	−0.983574	+	0.180507i	$0.942226\pi$
$360$		0			0
$361$	16.5066	+	9.40916i	0.868768	+	0.495219i
$362$		−	2.67870i		−	0.140789i
$363$	9.23981	+	1.62923i	0.484964	+	0.0855122i
$364$	−9.96816	−	8.36428i	−0.522474	−	0.438408i
$365$		0			0
$366$	15.1246	−	5.50492i	0.790577	−	0.287747i
$367$	6.62354	+	7.89363i	0.345746	+	0.412044i	0.910693	−	0.413083i	$-0.135548\pi$
$367$	6.62354	+	7.89363i	0.345746	+	0.412044i	−0.564948	+	0.825127i	$0.691104\pi$
$368$	0.888952	−	0.513237i	0.0463398	−	0.0267543i
$369$	−1.90600	+	3.30128i	−0.0992222	+	0.171858i
$370$		0			0
$371$	4.81354	+	27.2989i	0.249906	+	1.41729i
$372$	1.95217	+	1.12709i	0.101215	+	0.0584368i
$373$	−24.5861	+	14.1948i	−1.27302	+	0.734977i	−0.975555	−	0.219756i	$-0.929474\pi$
$373$	−24.5861	+	14.1948i	−1.27302	+	0.734977i	−0.297463	+	0.954733i	$0.596141\pi$
$374$	16.9817	−	14.2494i	0.878105	−	0.736818i
$375$		0			0
$376$	1.68240	+	0.612343i	0.0867631	+	0.0315792i
$377$	−4.52147	+	5.38848i	−0.232867	+	0.277521i
$378$	25.6812	+	4.52829i	1.32090	+	0.232910i
$379$	−19.1984			−0.986157			−0.493079	−	0.869985i	$-0.664129\pi$
$379$	−19.1984			−0.986157			−0.493079	+	0.869985i	$0.664129\pi$
$380$		0			0
$381$	22.9860			1.17761
$382$	−3.69402	−	0.651355i	−0.189002	−	0.0333262i
$383$	13.4201	−	15.9934i	0.685734	−	0.817226i	−0.305099	−	0.952321i	$-0.598689\pi$
$383$	13.4201	−	15.9934i	0.685734	−	0.817226i	0.990833	+	0.135095i	$0.0431339\pi$
$384$	1.04228	+	0.379360i	0.0531887	+	0.0193591i
$385$		0			0
$386$	11.0559	−	9.27700i	0.562731	−	0.472187i
$387$	−2.31485	+	1.33648i	−0.117671	+	0.0679371i
$388$	10.3122	+	5.95376i	0.523523	+	0.302256i
$389$	−2.69629	−	15.2914i	−0.136707	−	0.775304i	−0.973656	−	0.228023i	$-0.926774\pi$
$389$	−2.69629	−	15.2914i	−0.136707	−	0.775304i	0.836949	−	0.547281i	$-0.184337\pi$
$390$		0			0
$391$	2.57921	−	4.46733i	0.130436	−	0.225923i
$392$	−14.9790	+	8.64815i	−0.756556	+	0.436798i
$393$	−1.23846	−	1.47594i	−0.0624722	−	0.0744515i
$394$	18.6059	−	6.77199i	0.937351	−	0.341168i
$395$		0			0
$396$	−5.98027	−	5.01804i	−0.300520	−	0.252166i
$397$	4.74331	+	0.836373i	0.238060	+	0.0419764i	0.291405	−	0.956600i	$-0.405877\pi$
$397$	4.74331	+	0.836373i	0.238060	+	0.0419764i	−0.0533453	+	0.998576i	$0.516988\pi$
$398$			19.9801i			1.00151i
$399$	−10.0119	+	21.6261i	−0.501224	+	1.08266i
$400$		0			0
$401$	−2.15856	+	12.2418i	−0.107793	+	0.611326i	0.882275	+	0.470735i	$0.156011\pi$
$401$	−2.15856	+	12.2418i	−0.107793	+	0.611326i	−0.990068	+	0.140591i	$0.955100\pi$
$402$	9.72636	−	11.5914i	0.485107	−	0.578128i
$403$	−1.83498	+	5.04156i	−0.0914068	+	0.251138i
$404$	−1.35711	+	0.493947i	−0.0675186	+	0.0245748i
$405$		0			0
$406$	6.56691	+	11.3742i	0.325910	+	0.564493i
$407$	−7.64456	−	4.41359i	−0.378927	−	0.218774i
$408$	5.48934	−	0.967919i	0.271763	−	0.0479191i
$409$	2.99828	+	17.0041i	0.148255	+	0.840797i	0.964696	+	0.263367i	$0.0848332\pi$
$409$	2.99828	+	17.0041i	0.148255	+	0.840797i	−0.816440	+	0.577430i	$0.804056\pi$
$410$		0			0
$411$	1.38517	+	2.39918i	0.0683253	+	0.118343i
$412$	−2.86770	−	3.41759i	−0.141282	−	0.168373i
$413$	23.6926	+	65.0950i	1.16584	+	3.20312i
$414$	−1.70703	−	0.621309i	−0.0838961	−	0.0305357i
$415$		0			0
$416$	−0.458418	+	2.59982i	−0.0224758	+	0.127466i
$417$		−	13.1238i		−	0.642677i
$418$	15.7203	−	11.0721i	0.768903	−	0.541556i
$419$	−18.2962			−0.893827			−0.446914	−	0.894577i	$-0.647477\pi$
$419$	−18.2962			−0.893827			−0.446914	+	0.894577i	$0.647477\pi$
$420$		0			0
$421$	21.4711	+	18.0164i	1.04644	+	0.878067i	0.992715	−	0.120489i	$-0.0384462\pi$
$421$	21.4711	+	18.0164i	1.04644	+	0.878067i	0.0537246	+	0.998556i	$0.482891\pi$
$422$	−4.66941	+	12.8291i	−0.227303	+	0.624510i
$423$	−1.08368	−	2.97740i	−0.0526905	−	0.144766i
$424$	4.30802	−	3.61486i	0.209216	−	0.175553i
$425$		0			0
$426$	8.65052	−	14.9831i	0.419119	−	0.725935i
$427$	70.4403	−	12.4205i	3.40885	−	0.601072i
$428$	−7.74349	+	1.36539i	−0.374296	+	0.0659984i
$429$	−6.45831	+	11.1861i	−0.311810	+	0.540071i
$430$		0			0
$431$	11.8489	−	9.94239i	0.570740	−	0.478908i	−0.311151	−	0.950360i	$-0.600715\pi$
$431$	11.8489	−	9.94239i	0.570740	−	0.478908i	0.881892	+	0.471452i	$0.156270\pi$
$432$	−1.80944	−	4.97141i	−0.0870569	−	0.239187i
$433$	−4.81630	+	13.2327i	−0.231457	+	0.635922i	−0.999992	−	0.00388467i	$-0.998763\pi$
$433$	−4.81630	+	13.2327i	−0.231457	+	0.635922i	0.768536	+	0.639807i	$0.220986\pi$
$434$	7.67383	+	6.43911i	0.368356	+	0.309087i
$435$		0			0
$436$	−2.52230			−0.120796
$437$	2.55624	−	3.67219i	0.122282	−	0.175665i
$438$			13.9892i			0.668430i
$439$	−1.61433	+	9.15534i	−0.0770479	+	0.436961i	0.921743	+	0.387801i	$0.126765\pi$
$439$	−1.61433	+	9.15534i	−0.0770479	+	0.436961i	−0.998791	+	0.0491593i	$0.984346\pi$
$440$		0			0
$441$	28.7639	+	10.4692i	1.36971	+	0.498533i
$442$	4.53746	+	12.4666i	0.215825	+	0.592974i
$443$	7.64795	+	9.11448i	0.363365	+	0.433042i	0.916491	−	0.400056i	$-0.131009\pi$
$443$	7.64795	+	9.11448i	0.363365	+	0.433042i	−0.553125	+	0.833098i	$0.686565\pi$
$444$	−1.10977	−	1.92218i	−0.0526673	−	0.0912225i
$445$		0			0
$446$	4.02533	+	22.8288i	0.190605	+	1.08097i
$447$	−22.0019	+	3.87952i	−1.04065	+	0.183495i
$448$	4.26875	+	2.46456i	0.201680	+	0.116440i
$449$	−9.95157	−	17.2366i	−0.469644	−	0.813446i	0.529754	−	0.848151i	$-0.322284\pi$
$449$	−9.95157	−	17.2366i	−0.469644	−	0.813446i	−0.999398	+	0.0347048i	$0.988951\pi$
$450$		0			0
$451$	−8.92871	+	3.24978i	−0.420436	+	0.153026i
$452$	0.888617	−	2.44146i	0.0417970	−	0.114836i
$453$	5.47464	−	6.52442i	0.257221	−	0.306544i
$454$	−1.28134	+	7.26682i	−0.0601361	+	0.341049i
$455$		0			0
$456$	4.81520	−	0.434651i	0.225492	−	0.0203544i
$457$		−	36.8095i		−	1.72188i	−0.508708	−	0.860939i	$-0.669877\pi$
$457$		−	36.8095i		−	1.72188i	0.508708	−	0.860939i	$-0.330123\pi$
$458$	−13.0428	−	2.29980i	−0.609449	−	0.107462i
$459$	−20.3665	−	17.0896i	−0.950628	−	0.797672i
$460$		0			0
$461$	−28.6287	+	10.4200i	−1.33337	+	0.485308i	−0.907719	−	0.419578i	$-0.862178\pi$
$461$	−28.6287	+	10.4200i	−1.33337	+	0.485308i	−0.425653	+	0.904886i	$0.639956\pi$
$462$	15.5023	+	18.4749i	0.721232	+	0.859530i
$463$	19.3969	−	11.1988i	0.901452	−	0.520454i	0.0237813	−	0.999717i	$-0.492429\pi$
$463$	19.3969	−	11.1988i	0.901452	−	0.520454i	0.877671	+	0.479263i	$0.159096\pi$
$464$	1.33227	−	2.30755i	0.0618489	−	0.107125i
$465$		0			0
$466$	−2.62905	−	14.9101i	−0.121789	−	0.690697i
$467$	12.8027	+	7.39165i	0.592439	+	0.342045i	0.766061	−	0.642768i	$-0.222214\pi$
$467$	12.8027	+	7.39165i	0.592439	+	0.342045i	−0.173623	+	0.984812i	$0.555547\pi$
$468$	4.04604	−	2.33598i	0.187028	−	0.107981i
$469$	51.5119	−	43.2236i	2.37860	−	1.99588i
$470$		0			0
$471$	−6.04597	−	2.20055i	−0.278583	−	0.101396i
$472$	9.03357	−	10.7658i	0.415804	−	0.495535i
$473$	−6.56137	−	1.15695i	−0.301692	−	0.0531965i
$474$	3.14407			0.144412
$475$		0			0
$476$	24.7708			1.13537
$477$	−9.80130	−	1.72823i	−0.448770	−	0.0791303i
$478$	−7.51186	+	8.95228i	−0.343584	+	0.409468i
$479$	−25.2882	−	9.20416i	−1.15545	−	0.420549i	−0.307979	−	0.951393i	$-0.599653\pi$
$479$	−25.2882	−	9.20416i	−1.15545	−	0.420549i	−0.847469	+	0.530844i	$0.821875\pi$
$480$		0			0
$481$	4.04677	−	3.39564i	0.184517	−	0.154828i
$482$	−11.0485	+	6.37885i	−0.503245	+	0.290549i
$483$	4.86013	+	2.80600i	0.221144	+	0.127677i
$484$	−1.46887	−	8.33035i	−0.0667667	−	0.378652i
$485$		0			0
$486$	−7.62577	+	13.2082i	−0.345912	+	0.599137i
$487$	−12.2827	+	7.09140i	−0.556581	+	0.321342i	−0.751772	−	0.659423i	$-0.770801\pi$
$487$	−12.2827	+	7.09140i	−0.556581	+	0.321342i	0.195191	+	0.980765i	$0.437467\pi$
$488$	−9.32754	−	11.1161i	−0.422238	−	0.503204i
$489$	11.1779	−	4.06843i	0.505483	−	0.183981i
$490$		0			0
$491$	7.44701	+	6.24878i	0.336079	+	0.282004i	0.795171	−	0.606385i	$-0.207381\pi$
$491$	7.44701	+	6.24878i	0.336079	+	0.282004i	−0.459092	+	0.888389i	$0.651825\pi$
$492$	−2.35285	−	0.414871i	−0.106075	−	0.0187039i
$493$		−	13.3903i		−	0.603069i
$494$	3.00889	+	11.1068i	0.135376	+	0.499719i
$495$		0			0
$496$	0.352906	−	2.00143i	0.0158459	−	0.0898667i
$497$	49.4209	−	58.8975i	2.21683	−	2.64191i
$498$	2.76290	−	7.59100i	0.123808	−	0.340161i
$499$	−11.5577	+	4.20666i	−0.517394	+	0.188316i	−0.587501	−	0.809223i	$-0.699888\pi$
$499$	−11.5577	+	4.20666i	−0.517394	+	0.188316i	0.0701069	+	0.997539i	$0.477666\pi$
$500$		0			0
$501$	5.48663	+	9.50312i	0.245124	+	0.424568i
$502$	23.2583	+	13.4282i	1.03807	+	0.599329i
$503$	−24.5454	+	4.32801i	−1.09442	+	0.192976i	−0.691586	−	0.722295i	$-0.743087\pi$
$503$	−24.5454	+	4.32801i	−1.09442	+	0.192976i	−0.402839	+	0.915271i	$0.631976\pi$
$504$	−1.51478	−	8.59073i	−0.0674735	−	0.382661i
$505$		0			0
$506$	−2.26400	−	3.92136i	−0.100647	−	0.174326i
$507$	4.29974	+	5.12424i	0.190958	+	0.227575i
$508$	−7.08788	−	19.4738i	−0.314474	−	0.864010i
$509$	−12.5923	−	4.58321i	−0.558142	−	0.203147i	0.0475184	−	0.998870i	$-0.484869\pi$
$509$	−12.5923	−	4.58321i	−0.558142	−	0.203147i	−0.605660	+	0.795723i	$0.707091\pi$
$510$		0			0
$511$	−10.7953	+	61.2231i	−0.477555	+	2.70835i
$512$		−	1.00000i		−	0.0441942i
$513$	−16.3512	−	16.2613i	−0.721922	−	0.717954i
$514$	−0.159696			−0.00704389
$515$		0			0
$516$	−1.28333	−	1.07684i	−0.0564954	−	0.0474053i
$517$	2.70118	−	7.42143i	0.118798	−	0.326394i
$518$	−3.37353	−	9.26871i	−0.148225	−	0.407244i
$519$	−13.3416	+	11.1949i	−0.585630	+	0.491402i
$520$		0			0
$521$	−0.583692	+	1.01098i	−0.0255720	+	0.0442920i	−0.878528	−	0.477690i	$-0.841474\pi$
$521$	−0.583692	+	1.01098i	−0.0255720	+	0.0442920i	0.852956	+	0.521983i	$0.174807\pi$
$522$	−4.64388	+	0.818841i	−0.203257	+	0.0358397i
$523$	−9.28028	+	1.63636i	−0.405798	+	0.0715532i	−0.372822	−	0.927903i	$-0.621610\pi$
$523$	−9.28028	+	1.63636i	−0.405798	+	0.0715532i	−0.0329765	+	0.999456i	$0.510499\pi$
$524$	−0.868533	+	1.50434i	−0.0379420	+	0.0657175i
$525$		0			0
$526$	−7.09280	+	5.95157i	−0.309261	+	0.259501i
$527$	−3.49309	−	9.59718i	−0.152161	−	0.418060i
$528$	1.67344	−	4.59773i	0.0728271	−	0.200091i
$529$	16.8119	+	14.1068i	0.730951	+	0.613341i
$530$		0			0
$531$	−24.8714			−1.07933
$532$	21.4089	+	1.81359i	0.928193	+	0.0786293i
$533$		−	5.68637i		−	0.246304i
$534$	−1.94353	+	11.0223i	−0.0841050	+	0.476983i
$535$		0			0
$536$	−12.8194	−	4.66590i	−0.553716	−	0.201536i
$537$	3.83640	+	10.5404i	0.165553	+	0.454853i
$538$	8.02092	+	9.55896i	0.345807	+	0.412116i
$539$	38.1489	+	66.0759i	1.64319	+	2.84609i
$540$		0			0
$541$	−7.26524	−	41.2032i	−0.312357	−	1.77147i	−0.586671	−	0.809825i	$-0.699562\pi$
$541$	−7.26524	−	41.2032i	−0.312357	−	1.77147i	0.274314	−	0.961640i	$-0.411549\pi$
$542$	−27.7806	+	4.89846i	−1.19328	+	0.210407i
$543$	−2.57308	−	1.48557i	−0.110422	−	0.0637520i
$544$	−2.51269	−	4.35211i	−0.107731	−	0.186595i
$545$		0			0
$546$	−13.5627	+	4.93642i	−0.580430	+	0.211259i
$547$	9.61418	−	26.4147i	0.411073	−	1.12941i	−0.545549	−	0.838079i	$-0.683679\pi$
$547$	9.61418	−	26.4147i	0.411073	−	1.12941i	0.956622	−	0.291334i	$-0.0940990\pi$
$548$	1.60546	−	1.91332i	0.0685820	−	0.0817328i
$549$	−4.45942	+	25.2906i	−0.190323	+	1.07938i
$550$		0			0
$551$	0.980372	−	11.5730i	0.0417653	−	0.493025i
$552$		−	1.13854i		−	0.0484594i
$553$	13.7599	+	2.42623i	0.585129	+	0.103174i
$554$	6.44384	+	5.40702i	0.273772	+	0.229722i
$555$		0			0
$556$	−11.1185	+	4.04681i	−0.471530	+	0.171623i
$557$	7.93117	+	9.45200i	0.336055	+	0.400494i	0.907436	−	0.420190i	$-0.138037\pi$
$557$	7.93117	+	9.45200i	0.336055	+	0.400494i	−0.571381	+	0.820685i	$0.693592\pi$
$558$	−3.11478	+	1.79832i	−0.131859	+	0.0761289i
$559$	1.99364	−	3.45308i	0.0843218	−	0.146050i
$560$		0			0
$561$	−4.26971	−	24.2147i	−0.180267	−	1.02235i
$562$	19.3507	+	11.1721i	0.816259	+	0.471268i
$563$	12.5114	−	7.22347i	0.527293	−	0.304433i	−0.212620	−	0.977135i	$-0.568200\pi$
$563$	12.5114	−	7.22347i	0.527293	−	0.304433i	0.739914	+	0.672702i	$0.234866\pi$
$564$	1.52123	−	1.27647i	0.0640555	−	0.0537490i
$565$		0			0
$566$	11.9965	+	4.36638i	0.504252	+	0.183533i
$567$	1.77060	−	2.11012i	0.0743581	−	0.0886166i
$568$	−15.3612	−	2.70859i	−0.644540	−	0.113650i
$569$	−31.8303			−1.33439			−0.667197	−	0.744881i	$-0.732506\pi$
$569$	−31.8303			−1.33439			−0.667197	+	0.744881i	$0.732506\pi$
$570$		0			0
$571$	−9.10909			−0.381204			−0.190602	−	0.981667i	$-0.561044\pi$
$571$	−9.10909			−0.381204			−0.190602	+	0.981667i	$0.561044\pi$
$572$	11.4684	+	2.02218i	0.479516	+	0.0845516i
$573$	−2.67432	+	3.18714i	−0.111722	+	0.133145i
$574$	−9.97700	−	3.63133i	−0.416432	−	0.151569i
$575$		0			0
$576$	−1.35570	+	1.13756i	−0.0564873	+	0.0473985i
$577$	10.1300	−	5.84857i	0.421718	−	0.243479i	−0.274094	−	0.961703i	$-0.588378\pi$
$577$	10.1300	−	5.84857i	0.421718	−	0.243479i	0.695812	+	0.718224i	$0.255045\pi$
$578$	−7.14863	−	4.12726i	−0.297344	−	0.171671i
$579$	−2.77978	−	15.7649i	−0.115524	−	0.655167i
$580$		0			0
$581$	17.9496	−	31.0896i	0.744674	−	1.28981i
$582$	11.4380	−	6.60375i	0.474122	−	0.273734i
$583$	−15.9459	−	19.0036i	−0.660413	−	0.787050i
$584$	11.8517	−	4.31365i	0.490425	−	0.178500i
$585$		0			0
$586$	22.1470	+	18.5836i	0.914885	+	0.767680i
$587$	−30.2839	−	5.33986i	−1.24995	−	0.220400i	−0.490774	−	0.871287i	$-0.663286\pi$
$587$	−30.2839	−	5.33986i	−1.24995	−	0.220400i	−0.759175	+	0.650887i	$0.774397\pi$
$588$			19.1846i			0.791160i
$589$	−2.31635	−	8.55040i	−0.0954435	−	0.352313i
$590$		0			0
$591$	3.81359	−	21.6280i	0.156870	−	0.889655i
$592$	−1.28627	+	1.53291i	−0.0528652	+	0.0630023i
$593$	−2.12039	+	5.82573i	−0.0870741	+	0.239234i	−0.975585	−	0.219621i	$-0.929518\pi$
$593$	−2.12039	+	5.82573i	−0.0870741	+	0.239234i	0.888511	+	0.458855i	$0.151740\pi$
$594$	−21.9300	+	7.98186i	−0.899798	+	0.327500i
$595$		0			0
$596$	10.0711	+	17.4437i	0.412530	+	0.714523i
$597$	19.1924	+	11.0807i	0.785491	+	0.453503i
$598$	2.66864	−	0.470554i	0.109129	−	0.0192424i
$599$	5.09116	+	28.8734i	0.208019	+	1.17973i	0.892618	+	0.450815i	$0.148866\pi$
$599$	5.09116	+	28.8734i	0.208019	+	1.17973i	−0.684599	+	0.728920i	$0.740022\pi$
$600$		0			0
$601$	23.1718	+	40.1348i	0.945199	+	1.63713i	0.755353	+	0.655318i	$0.227466\pi$
$601$	23.1718	+	40.1348i	0.945199	+	1.63713i	0.189846	+	0.981814i	$0.439201\pi$
$602$	−4.78544	−	5.70307i	−0.195040	−	0.232440i
$603$	8.25740	+	22.6870i	0.336267	+	0.923887i
$604$	−7.21563	−	2.62627i	−0.293600	−	0.106862i
$605$		0			0
$606$	−0.278162	+	1.57754i	−0.0112996	+	0.0640830i
$607$			25.4409i			1.03262i	0.856403	+	0.516308i	$0.172694\pi$
$607$			25.4409i			1.03262i	−0.856403	+	0.516308i	$0.827306\pi$
$608$	−1.85303	−	3.94541i	−0.0751503	−	0.160008i
$609$	14.5677			0.590312
$610$		0			0
$611$	3.62066	+	3.03810i	0.146476	+	0.122908i
$612$	−3.04179	+	8.35725i	−0.122957	+	0.337822i
$613$	−10.4412	−	28.6870i	−0.421717	−	1.15866i	−0.950723	−	0.310041i	$-0.899657\pi$
$613$	−10.4412	−	28.6870i	−0.421717	−	1.15866i	0.529006	−	0.848618i	$-0.322565\pi$
$614$	17.9758	−	15.0835i	0.725444	−	0.608720i
$615$		0			0
$616$	10.8717	−	18.8304i	0.438035	−	0.758698i
$617$	−6.00494	+	1.05883i	−0.241750	+	0.0426270i	−0.293210	−	0.956048i	$-0.594724\pi$
$617$	−6.00494	+	1.05883i	−0.241750	+	0.0426270i	0.0514603	+	0.998675i	$0.483612\pi$
$618$	−4.87323	+	0.859283i	−0.196030	+	0.0345654i
$619$	9.07568	−	15.7195i	0.364782	−	0.631821i	−0.623959	−	0.781457i	$-0.714477\pi$
$619$	9.07568	−	15.7195i	0.364782	−	0.631821i	0.988741	+	0.149636i	$0.0478101\pi$
$620$		0			0
$621$	−4.16002	+	3.49067i	−0.166936	+	0.140076i
$622$	1.45193	+	3.98914i	0.0582171	+	0.159950i
$623$	−17.0116	+	46.7389i	−0.681554	+	1.87255i
$624$	2.24308	+	1.88217i	0.0897950	+	0.0753469i
$625$		0			0
$626$	11.6148			0.464221
$627$	−1.91734	−	21.2409i	−0.0765712	−	0.848279i
$628$			5.80070i			0.231473i
$629$	−1.74624	+	9.90340i	−0.0696270	+	0.394874i
$630$		0			0
$631$	−14.9306	−	5.43428i	−0.594376	−	0.216335i	0.0272768	−	0.999628i	$-0.491316\pi$
$631$	−14.9306	−	5.43428i	−0.594376	−	0.216335i	−0.621653	+	0.783293i	$0.713539\pi$
$632$	−0.969492	−	2.66366i	−0.0385643	−	0.105955i
$633$	9.73368	+	11.6001i	0.386879	+	0.461064i
$634$	1.11812	+	1.93664i	0.0444061	+	0.0769137i
$635$		0			0
$636$	−1.08316	−	6.14292i	−0.0429502	−	0.243582i
$637$	−44.9672	+	7.92893i	−1.78167	+	0.314156i
$638$	−10.1791	−	5.87692i	−0.402995	−	0.232669i
$639$	13.8023	+	23.9063i	0.546010	+	0.945717i
$640$		0			0
$641$	33.1458	−	12.0641i	1.30918	−	0.476503i	0.409205	−	0.912443i	$-0.365806\pi$
$641$	33.1458	−	12.0641i	1.30918	−	0.476503i	0.899976	+	0.435940i	$0.143584\pi$
$642$	−2.98288	+	8.19540i	−0.117725	+	0.323447i
$643$	−5.36891	+	6.39841i	−0.211729	+	0.252329i	−0.861448	−	0.507846i	$-0.830442\pi$
$643$	−5.36891	+	6.39841i	−0.211729	+	0.252329i	0.649719	+	0.760174i	$0.274887\pi$
$644$	0.878594	−	4.98275i	0.0346215	−	0.196348i
$645$		0			0
$646$	−17.9782	−	12.5148i	−0.707343	−	0.492387i
$647$		−	12.0057i		−	0.471991i	−0.971754	−	0.235995i	$-0.924165\pi$
$647$		−	12.0057i		−	0.471991i	0.971754	−	0.235995i	$-0.0758350\pi$
$648$	−0.550344	−	0.0970404i	−0.0216195	−	0.00381211i
$649$	−47.4903	−	39.8491i	−1.86416	−	1.56421i
$650$		0			0
$651$	10.4410	−	3.80023i	0.409216	−	0.148943i
$652$	−6.89356	−	8.21542i	−0.269973	−	0.321741i
$653$	33.8062	−	19.5180i	1.32294	−	0.763798i	0.338741	−	0.940880i	$-0.389999\pi$
$653$	33.8062	−	19.5180i	1.32294	−	0.763798i	0.984196	+	0.177081i	$0.0566655\pi$
$654$	−1.39884	+	2.42285i	−0.0546988	+	0.0947411i
$655$		0			0
$656$	0.374037	+	2.12127i	0.0146037	+	0.0828216i
$657$	−19.3300	−	11.1602i	−0.754136	−	0.435401i
$658$	7.64265	−	4.41248i	0.297941	−	0.172017i
$659$	3.38617	−	2.84133i	0.131906	−	0.110683i	−0.574448	−	0.818541i	$-0.694783\pi$
$659$	3.38617	−	2.84133i	0.131906	−	0.110683i	0.706354	+	0.707859i	$0.250339\pi$
$660$		0			0
$661$	5.32012	+	1.93636i	0.206929	+	0.0753159i	0.443405	−	0.896321i	$-0.353770\pi$
$661$	5.32012	+	1.93636i	0.206929	+	0.0753159i	−0.236476	+	0.971637i	$0.575993\pi$
$662$	−0.327351	+	0.390122i	−0.0127229	+	0.0151625i
$663$	14.4914	+	2.55523i	0.562801	+	0.0992370i
$664$	−7.28306			−0.282638
$665$		0			0
$666$	3.54137			0.137225
$667$	−2.69352	−	0.474940i	−0.104294	−	0.0183898i
$668$	6.35922	−	7.57862i	0.246046	−	0.293226i
$669$	24.1611	+	8.79392i	0.934122	+	0.339992i
$670$		0			0
$671$	−49.0357	+	41.1458i	−1.89300	+	1.58842i
$672$	4.73478	−	2.73363i	0.182648	−	0.105452i
$673$	14.1761	+	8.18457i	0.546448	+	0.315492i	0.747688	−	0.664050i	$-0.231164\pi$
$673$	14.1761	+	8.18457i	0.546448	+	0.315492i	−0.201240	+	0.979542i	$0.564497\pi$
$674$	−2.61882	−	14.8520i	−0.100873	−	0.572079i
$675$		0			0
$676$	3.01541	−	5.22284i	0.115977	−	0.200878i
$677$	−16.2304	+	9.37064i	−0.623786	+	0.360143i	−0.778341	−	0.627841i	$-0.783939\pi$
$677$	−16.2304	+	9.37064i	−0.623786	+	0.360143i	0.154556	+	0.987984i	$0.450605\pi$
$678$	−1.85238	−	2.20758i	−0.0711402	−	0.0847816i
$679$	55.1540	−	20.0744i	2.11662	−	0.770386i
$680$		0			0
$681$	6.26969	+	5.26089i	0.240255	+	0.201598i
$682$	−8.82873	−	1.55674i	−0.338070	−	0.0596108i
$683$		−	11.1202i		−	0.425501i	−0.977107	−	0.212751i	$-0.931758\pi$
$683$		−	11.1202i		−	0.425501i	0.977107	−	0.212751i	$-0.0682422\pi$
$684$	−3.24084	+	7.00030i	−0.123917	+	0.267663i
$685$		0			0
$686$	−8.81296	+	49.9808i	−0.336480	+	1.90828i
$687$	−9.44247	+	11.2531i	−0.360253	+	0.429333i
$688$	−0.516578	+	1.41929i	−0.0196944	+	0.0541098i
$689$	13.9509	−	5.07769i	0.531485	−	0.193445i
$690$		0			0
$691$	−5.97792	−	10.3541i	−0.227411	−	0.393887i	0.729629	−	0.683843i	$-0.239693\pi$
$691$	−5.97792	−	10.3541i	−0.227411	−	0.393887i	−0.957040	+	0.289956i	$0.906359\pi$
$692$	13.5983	+	7.85098i	0.516929	+	0.298449i
$693$	−37.8956	+	6.68201i	−1.43953	+	0.253829i
$694$	5.86560	+	33.2655i	0.222655	+	1.26274i
$695$		0			0
$696$	−1.47771	−	2.55947i	−0.0560126	−	0.0970166i
$697$	6.95795	+	8.29216i	0.263551	+	0.314088i
$698$	0.0112278	+	0.0308480i	0.000424977	+	0.00116761i
$699$	−15.7803	−	5.74355i	−0.596865	−	0.217241i
$700$		0			0
$701$	3.45791	−	19.6108i	0.130603	−	0.740689i	−0.847217	−	0.531246i	$-0.821724\pi$
$701$	3.45791	−	19.6108i	0.130603	−	0.740689i	0.977821	−	0.209443i	$-0.0671650\pi$
$702$		−	13.9664i		−	0.527128i
$703$	−2.23432	+	8.43146i	−0.0842688	+	0.317999i
$704$	−4.41122			−0.166254
$705$		0			0
$706$	0.215239	+	0.180607i	0.00810064	+	0.00679725i
$707$	−2.43473	+	6.68935i	−0.0915673	+	0.251579i
$708$	−5.33142	−	14.6480i	−0.200367	−	0.550504i
$709$	9.27123	−	7.77949i	0.348188	−	0.292165i	−0.451874	−	0.892082i	$-0.649244\pi$
$709$	9.27123	−	7.77949i	0.348188	−	0.292165i	0.800062	+	0.599917i	$0.204800\pi$
$710$		0			0
$711$	−2.50825	+	4.34442i	−0.0940667	+	0.162928i
$712$	9.93743	−	1.75224i	0.372421	−	0.0656679i
$713$	−2.05441	+	0.362248i	−0.0769383	+	0.0135663i
$714$	13.7375	−	23.7941i	0.514115	−	0.890473i
$715$		0			0
$716$	7.74689	−	6.50041i	0.289515	−	0.242932i
$717$	4.43334	+	12.1805i	0.165566	+	0.454889i
$718$	4.51759	−	12.4120i	0.168595	−	0.463211i
$719$	−22.9902	−	19.2911i	−0.857389	−	0.719435i	0.104015	−	0.994576i	$-0.466831\pi$
$719$	−22.9902	−	19.2911i	−0.857389	−	0.719435i	−0.961404	+	0.275141i	$0.911275\pi$
$720$		0			0
$721$	−21.9906			−0.818972
$722$	−14.6219	−	12.1326i	−0.544172	−	0.451527i
$723$			14.1505i			0.526263i
$724$	−0.465151	+	2.63800i	−0.0172872	+	0.0980407i
$725$		0			0
$726$	−8.81652	−	3.20895i	−0.327212	−	0.119095i
$727$	14.4115	+	39.5954i	0.534494	+	1.46851i	0.853669	+	0.520815i	$0.174372\pi$
$727$	14.4115	+	39.5954i	0.534494	+	1.46851i	−0.319175	+	0.947696i	$0.603406\pi$
$728$	8.36428	+	9.96816i	0.310001	+	0.369445i
$729$	9.29655	+	16.1021i	0.344317	+	0.596374i
$730$		0			0
$731$	1.31803	+	7.47490i	0.0487490	+	0.276469i
$732$	−15.8508	+	2.79492i	−0.585862	+	0.103303i
$733$	−7.24116	−	4.18069i	−0.267458	−	0.154417i	0.360274	−	0.932847i	$-0.382683\pi$
$733$	−7.24116	−	4.18069i	−0.267458	−	0.154417i	−0.627732	+	0.778429i	$0.716017\pi$
$734$	−5.15220	−	8.92387i	−0.190171	−	0.329386i
$735$		0			0
$736$	−0.964570	+	0.351075i	−0.0355545	+	0.0129408i
$737$	−20.5823	+	56.5494i	−0.758159	+	2.08302i
$738$	2.45030	−	2.92016i	0.0901969	−	0.107492i
$739$	3.03167	−	17.1935i	0.111522	−	0.632472i	−0.876892	−	0.480688i	$-0.840387\pi$
$739$	3.03167	−	17.1935i	0.111522	−	0.632472i	0.988414	−	0.151784i	$-0.0485019\pi$
$740$		0			0
$741$	12.3376	+	3.26943i	0.453232	+	0.120105i
$742$		−	27.7200i		−	1.01763i
$743$	15.4396	+	2.72242i	0.566424	+	0.0998758i	0.449524	−	0.893268i	$-0.351593\pi$
$743$	15.4396	+	2.72242i	0.566424	+	0.0998758i	0.116899	+	0.993144i	$0.462705\pi$
$744$	−1.72680	−	1.44896i	−0.0633075	−	0.0531213i
$745$		0			0
$746$	26.6774	−	9.70980i	0.976731	−	0.355501i
$747$	8.28494	+	9.87361i	0.303130	+	0.361257i
$748$	−19.1981	+	11.0840i	−0.701953	+	0.405273i
$749$	−19.3787	+	33.5649i	−0.708083	+	1.22644i
$750$		0			0
$751$	−0.425213	−	2.41150i	−0.0155162	−	0.0879970i	0.976066	−	0.217473i	$-0.0697815\pi$
$751$	−0.425213	−	2.41150i	−0.0155162	−	0.0879970i	−0.991583	+	0.129476i	$0.958670\pi$
$752$	−1.55051	−	0.895185i	−0.0565412	−	0.0326441i
$753$	25.7975	−	14.8942i	0.940111	−	0.542774i
$754$	5.38848	−	4.52147i	0.196237	−	0.164662i
$755$		0			0
$756$	−24.5047	−	8.91898i	−0.891228	−	0.324380i
$757$	−17.7921	+	21.2038i	−0.646664	+	0.770664i	−0.985407	−	0.170215i	$-0.945554\pi$
$757$	−17.7921	+	21.2038i	−0.646664	+	0.770664i	0.338743	+	0.940879i	$0.389998\pi$
$758$	18.9068	+	3.33377i	0.686725	+	0.121088i
$759$	−5.02234			−0.182299
$760$		0			0
$761$	−34.7738			−1.26055			−0.630275	−	0.776372i	$-0.717058\pi$
$761$	−34.7738			−1.26055			−0.630275	+	0.776372i	$0.717058\pi$
$762$	−22.6368	−	3.99148i	−0.820046	−	0.144596i
$763$	−7.99162	+	9.52404i	−0.289316	+	0.344793i
$764$	3.52479	+	1.28292i	0.127522	+	0.0464143i
$765$		0			0
$766$	−15.9934	+	13.4201i	−0.577866	+	0.484887i
$767$	32.1302	−	18.5504i	1.16015	−	0.669815i
$768$	−0.960572	−	0.554587i	−0.0346617	−	0.0200119i
$769$	1.17313	+	6.65313i	0.0423040	+	0.239918i	0.998626	−	0.0523962i	$-0.0166859\pi$
$769$	1.17313	+	6.65313i	0.0423040	+	0.239918i	−0.956322	+	0.292314i	$0.905575\pi$
$770$		0			0
$771$	−0.0885653	+	0.153400i	−0.00318960	+	0.00552455i
$772$	−12.4989	+	7.21623i	−0.449844	+	0.259718i
$773$	−7.77917	−	9.27086i	−0.279797	−	0.333450i	0.607782	−	0.794104i	$-0.292059\pi$
$773$	−7.77917	−	9.27086i	−0.279797	−	0.333450i	−0.887580	+	0.460654i	$0.847615\pi$
$774$	2.51176	−	0.914207i	0.0902834	−	0.0328605i
$775$		0			0
$776$	−9.12169	−	7.65401i	−0.327450	−	0.274763i
$777$	−10.7742	−	1.89978i	−0.386522	−	0.0681542i
$778$			15.5273i			0.556680i
$779$	5.40650	+	7.67617i	0.193708	+	0.275027i
$780$		0			0
$781$	−11.9482	+	67.7615i	−0.427540	+	2.42470i
$782$	−3.31577	+	3.95159i	−0.118572	+	0.141308i
$783$	−4.82132	+	13.2465i	−0.172300	+	0.473390i
$784$	16.2532	−	5.91569i	0.580472	−	0.211274i
$785$		0			0
$786$	0.963353	+	1.66858i	0.0343617	+	0.0595162i
$787$	−22.1721	−	12.8010i	−0.790349	−	0.456308i	0.0497367	−	0.998762i	$-0.484162\pi$
$787$	−22.1721	−	12.8010i	−0.790349	−	0.456308i	−0.840085	+	0.542454i	$0.817495\pi$
$788$	−19.4992	+	3.43823i	−0.694629	+	0.122482i
$789$	1.78334	+	10.1138i	0.0634885	+	0.360061i
$790$		0			0
$791$	−6.40329	−	11.0908i	−0.227675	−	0.394344i
$792$	5.01804	+	5.98027i	0.178308	+	0.212500i
$793$	−13.1021	−	35.9979i	−0.465271	−	1.27832i
$794$	−4.52601	−	1.64733i	−0.160622	−	0.0584617i
$795$		0			0
$796$	3.46951	−	19.6766i	0.122974	−	0.697418i
$797$		−	28.8750i		−	1.02281i	−0.859341	−	0.511403i	$-0.829126\pi$
$797$		−	28.8750i		−	1.02281i	0.859341	−	0.511403i	$-0.170874\pi$
$798$	13.6152	−	19.5590i	0.481972	−	0.692381i
$799$	−8.99731			−0.318302
$800$		0			0
$801$	−13.6800	−	11.4788i	−0.483358	−	0.405585i
$802$	4.25153	−	11.6810i	0.150127	−	0.412470i
$803$	−19.0285	−	52.2803i	−0.671500	−	1.84493i
$804$	−11.5914	+	9.72636i	−0.408798	+	0.343022i
$805$		0			0
$806$	2.68256	−	4.64633i	0.0944891	−	0.163660i
$807$	13.6304	−	2.40340i	0.479812	−	0.0846038i
$808$	1.42226	−	0.250783i	0.0500350	−	0.00882252i
$809$	18.2438	−	31.5992i	0.641417	−	1.11097i	−0.343699	−	0.939080i	$-0.611680\pi$
$809$	18.2438	−	31.5992i	0.641417	−	1.11097i	0.985117	−	0.171888i	$-0.0549866\pi$
$810$		0			0
$811$	3.21407	−	2.69693i	0.112861	−	0.0947020i	−0.584610	−	0.811314i	$-0.698753\pi$
$811$	3.21407	−	2.69693i	0.112861	−	0.0947020i	0.697472	+	0.716612i	$0.254308\pi$
$812$	−4.49203	−	12.3418i	−0.157639	−	0.433111i
$813$	−10.7014	+	29.4018i	−0.375314	+	1.03117i
$814$	6.76201	+	5.67400i	0.237008	+	0.198874i
$815$		0			0
$816$	−5.57403			−0.195130
$817$	0.591869	+	6.55691i	0.0207069	+	0.229397i
$818$		−	17.2664i		−	0.603705i
$819$	3.99889	−	22.6788i	0.139733	−	0.792463i
$820$		0			0
$821$	4.00386	+	1.45729i	0.139736	+	0.0508597i	0.410941	−	0.911662i	$-0.365200\pi$
$821$	4.00386	+	1.45729i	0.139736	+	0.0508597i	−0.271206	+	0.962521i	$0.587422\pi$
$822$	−0.947510	−	2.60326i	−0.0330482	−	0.0907992i
$823$	−1.04295	−	1.24294i	−0.0363551	−	0.0433263i	0.747561	−	0.664194i	$-0.231225\pi$
$823$	−1.04295	−	1.24294i	−0.0363551	−	0.0433263i	−0.783916	+	0.620867i	$0.786781\pi$
$824$	2.23068	+	3.86364i	0.0777093	+	0.134596i
$825$		0			0
$826$	−12.0291	−	68.2203i	−0.418545	−	2.37369i
$827$	24.5087	−	4.32155i	0.852252	−	0.150275i	0.269575	−	0.962979i	$-0.413117\pi$
$827$	24.5087	−	4.32155i	0.852252	−	0.150275i	0.582676	+	0.812704i	$0.302006\pi$
$828$	1.57321	+	0.908293i	0.0546728	+	0.0315654i
$829$	6.75957	+	11.7079i	0.234770	+	0.406633i	0.959206	−	0.282709i	$-0.0912331\pi$
$829$	6.75957	+	11.7079i	0.234770	+	0.406633i	−0.724436	+	0.689342i	$0.757900\pi$
$830$		0			0
$831$	8.76750	−	3.19111i	0.304141	−	0.110698i
$832$	0.902907	−	2.48072i	0.0313027	−	0.0860033i
$833$	55.8715	−	66.5851i	1.93583	−	2.30704i
$834$	−2.27893	+	12.9245i	−0.0789129	+	0.447537i
$835$		0			0
$836$	−17.4041	+	8.17413i	−0.601933	+	0.282708i
$837$			10.7518i			0.371637i
$838$	18.0182	+	3.17710i	0.622429	+	0.109751i
$839$	−12.1036	−	10.1561i	−0.417861	−	0.350627i	0.409488	−	0.912316i	$-0.365707\pi$
$839$	−12.1036	−	10.1561i	−0.417861	−	0.350627i	−0.827349	+	0.561689i	$0.810152\pi$
$840$		0			0
$841$	20.5795	−	7.49033i	0.709639	−	0.258287i
$842$	−18.0164	−	21.4711i	−0.620887	−	0.739944i
$843$	21.4633	−	12.3918i	0.739234	−	0.426797i
$844$	6.82622	−	11.8234i	0.234968	−	0.406977i
$845$		0			0
$846$	0.550201	+	3.12035i	0.0189163	+	0.107280i
$847$	−36.1088	−	20.8474i	−1.24071	−	0.716326i
$848$	−4.87029	+	2.81186i	−0.167246	+	0.0965597i
$849$	10.8473	−	9.10199i	0.372280	−	0.312380i
$850$		0			0
$851$	1.93018	+	0.702527i	0.0661656	+	0.0240823i
$852$	−11.1209	+	13.2534i	−0.380996	+	0.454053i
$853$	−10.1197	−	1.78438i	−0.346494	−	0.0610962i	−0.00230672	−	0.999997i	$-0.500734\pi$
$853$	−10.1197	−	1.78438i	−0.346494	−	0.0610962i	−0.344187	+	0.938901i	$0.611845\pi$
$854$	−71.5270			−2.44760
$855$		0			0
$856$	7.86294			0.268750
$857$	27.0617	+	4.77171i	0.924410	+	0.162998i	0.615540	−	0.788106i	$-0.288938\pi$
$857$	27.0617	+	4.77171i	0.924410	+	0.162998i	0.308870	+	0.951104i	$0.400049\pi$
$858$	8.30265	−	9.89471i	0.283448	−	0.337800i
$859$	−0.328073	−	0.119409i	−0.0111937	−	0.00407418i	0.336417	−	0.941713i	$-0.390785\pi$
$859$	−0.328073	−	0.119409i	−0.0111937	−	0.00407418i	−0.347611	+	0.937639i	$0.613007\pi$
$860$		0			0
$861$	−9.02127	+	7.56974i	−0.307444	+	0.257976i
$862$	−13.3953	+	7.73381i	−0.456247	+	0.263415i
$863$	−23.8565	−	13.7736i	−0.812084	−	0.468857i	0.0355949	−	0.999366i	$-0.488667\pi$
$863$	−23.8565	−	13.7736i	−0.812084	−	0.468857i	−0.847679	+	0.530509i	$0.822001\pi$
$864$	0.918679	+	5.21009i	0.0312541	+	0.177251i
$865$		0			0
$866$	7.04096	−	12.1953i	0.239262	−	0.414413i
$867$	−7.92906	+	4.57785i	−0.269285	+	0.155472i
$868$	−6.43911	−	7.67383i	−0.218558	−	0.260467i
$869$	−11.7500	+	4.27664i	−0.398591	+	0.145075i
$870$		0			0
$871$	−27.5885	−	23.1495i	−0.934802	−	0.784392i
$872$	2.48398	+	0.437993i	0.0841183	+	0.0148323i
$873$			21.0732i			0.713218i
$874$	−3.15507	+	3.17251i	−0.106722	+	0.107312i
$875$		0			0
$876$	2.42920	−	13.7767i	0.0820750	−	0.465471i
$877$	−17.9061	+	21.3396i	−0.604645	+	0.720587i	−0.978349	−	0.206960i	$-0.933643\pi$
$877$	−17.9061	+	21.3396i	−0.604645	+	0.720587i	0.373705	+	0.927548i	$0.378087\pi$
$878$	3.17962	−	8.73592i	0.107307	−	0.294823i
$879$	30.1333	−	10.9676i	1.01637	−	0.369929i
$880$		0			0
$881$	−16.9123	−	29.2930i	−0.569791	−	0.986907i	−0.996586	−	0.0825583i	$-0.973691\pi$
$881$	−16.9123	−	29.2930i	−0.569791	−	0.986907i	0.426795	−	0.904348i	$-0.359642\pi$
$882$	−26.5089	−	15.3049i	−0.892602	−	0.515344i
$883$	27.6813	−	4.88096i	0.931549	−	0.164257i	0.312776	−	0.949827i	$-0.398741\pi$
$883$	27.6813	−	4.88096i	0.931549	−	0.164257i	0.618773	+	0.785570i	$0.287630\pi$
$884$	−2.30373	−	13.0651i	−0.0774827	−	0.439426i
$885$		0			0
$886$	−5.94905	−	10.3041i	−0.199862	−	0.346172i
$887$	30.4571	+	36.2974i	1.02265	+	1.21875i	0.975532	+	0.219859i	$0.0705596\pi$
$887$	30.4571	+	36.2974i	1.02265	+	1.21875i	0.0471192	+	0.998889i	$0.484996\pi$
$888$	0.759127	+	2.08568i	0.0254746	+	0.0699910i
$889$	−95.9889	−	34.9371i	−3.21936	−	1.17175i
$890$		0			0
$891$	−0.428067	+	2.42769i	−0.0143408	+	0.0813306i
$892$		−	23.1810i		−	0.776156i
$893$	−7.77619	−	0.658739i	−0.260220	−	0.0220438i
$894$	22.3413			0.747204
$895$		0			0
$896$	−3.77593	−	3.16838i	−0.126145	−	0.105848i
$897$	1.02799	−	2.82439i	0.0343237	−	0.0943035i
$898$	6.80727	+	18.7028i	0.227162	+	0.624122i
$899$	−4.14823	+	3.48078i	−0.138351	+	0.116091i
$900$		0			0
$901$	−14.1307	+	24.4751i	−0.470762	+	0.815383i
$902$	9.35738	−	1.64996i	0.311567	−	0.0549376i
$903$	−8.13215	+	1.43392i	−0.270621	+	0.0477178i
$904$	−1.29907	+	2.25006i	−0.0432065	+	0.0748358i
$905$		0			0
$906$	−6.52442	+	5.47464i	−0.216759	+	0.181883i
$907$	2.01331	+	5.53153i	0.0668510	+	0.183672i	0.968620	−	0.248547i	$-0.0799531\pi$
$907$	2.01331	+	5.53153i	0.0668510	+	0.183672i	−0.901769	+	0.432219i	$0.857731\pi$
$908$	2.52374	−	6.93391i	0.0837532	−	0.230110i
$909$	−1.95790	−	1.64287i	−0.0649394	−	0.0544907i
$910$		0			0
$911$	2.77245			0.0918555			0.0459277	−	0.998945i	$-0.485376\pi$
$911$	2.77245			0.0918555			0.0459277	+	0.998945i	$0.485376\pi$
$912$	−4.81752	−	0.408103i	−0.159524	−	0.0135136i
$913$			32.1272i			1.06325i
$914$	−6.39191	+	36.2503i	−0.211426	+	1.19905i
$915$		0			0
$916$	12.4453	+	4.52971i	0.411204	+	0.149666i
$917$	2.92845	+	8.04585i	0.0967060	+	0.265698i
$918$	17.0896	+	20.3665i	0.564039	+	0.672196i
$919$	26.1760	+	45.3382i	0.863468	+	1.49557i	0.868560	+	0.495584i	$0.165046\pi$
$919$	26.1760	+	45.3382i	0.863468	+	1.49557i	−0.00509211	+	0.999987i	$0.501621\pi$
$920$		0			0
$921$	−4.51964	−	25.6321i	−0.148927	−	0.844608i
$922$	30.0032	−	5.29037i	0.988103	−	0.174229i
$923$	−35.6611	−	20.5889i	−1.17380	−	0.677693i
$924$	−12.0586	−	20.8862i	−0.396700	−	0.687105i
$925$		0			0
$926$	−21.0469	+	7.66045i	−0.691645	+	0.251738i
$927$	2.70039	−	7.41926i	0.0886924	−	0.243680i
$928$	−1.71273	+	2.04115i	−0.0562230	+	0.0670040i
$929$	6.37049	−	36.1288i	0.209009	−	1.18535i	−0.681997	−	0.731355i	$-0.738888\pi$
$929$	6.37049	−	36.1288i	0.209009	−	1.18535i	0.891005	−	0.453993i	$-0.150001\pi$
$930$		0			0
$931$	53.1637	−	53.4575i	1.74237	−	1.75200i
$932$			15.1401i			0.495931i
$933$	4.63708	+	0.817643i	0.151811	+	0.0267684i
$934$	−11.3247	−	9.50252i	−0.370554	−	0.310932i
$935$		0			0
$936$	−4.39021	+	1.59791i	−0.143498	+	0.0522292i
$937$	−21.6177	−	25.7630i	−0.706219	−	0.841639i	0.286996	−	0.957932i	$-0.407343\pi$
$937$	−21.6177	−	25.7630i	−0.706219	−	0.841639i	−0.993215	+	0.116292i	$0.962899\pi$
$938$	−58.2350	+	33.6220i	−1.90144	+	1.09780i
$939$	6.44142	−	11.1569i	0.210208	−	0.364090i
$940$		0			0
$941$	−7.79104	−	44.1852i	−0.253981	−	1.44040i	−0.798676	−	0.601762i	$-0.794466\pi$
$941$	−7.79104	−	44.1852i	−0.253981	−	1.44040i	0.544695	−	0.838634i	$-0.316645\pi$
$942$	5.57199	+	3.21699i	0.181545	+	0.104815i
$943$	1.91480	−	1.10551i	0.0623543	−	0.0360003i
$944$	−10.7658	+	9.03357i	−0.350396	+	0.294018i
$945$		0			0
$946$	6.26079	+	2.27874i	0.203556	+	0.0740883i
$947$	−8.90570	+	10.6134i	−0.289396	+	0.344889i	−0.891081	−	0.453845i	$-0.850052\pi$
$947$	−8.90570	+	10.6134i	−0.289396	+	0.344889i	0.601684	+	0.798734i	$0.294497\pi$
$948$	−3.09630	−	0.545962i	−0.100563	−	0.0177320i
$949$	33.2954			1.08082
$950$		0			0
$951$	2.48037			0.0804316
$952$	−24.3945	−	4.30140i	−0.790629	−	0.139409i
$953$	−25.3105	+	30.1638i	−0.819886	+	0.977102i	−0.999979	−	0.00654740i	$-0.997916\pi$
$953$	−25.3105	+	30.1638i	−0.819886	+	0.977102i	0.180092	+	0.983650i	$0.442360\pi$
$954$	9.35229	+	3.40395i	0.302791	+	0.110207i
$955$		0			0
$956$	8.95228	−	7.51186i	0.289537	−	0.242951i
$957$	−11.2904	+	6.51852i	−0.364967	+	0.210714i
$958$	23.3058	+	13.4556i	0.752975	+	0.434730i
$959$	−2.13783	−	12.1242i	−0.0690341	−	0.391512i
$960$		0			0
$961$	13.4349	−	23.2699i	0.433383	−	0.750641i
$962$	−4.57494	+	2.64134i	−0.147502	+	0.0851602i
$963$	−8.94460	−	10.6598i	−0.288236	−	0.343506i
$964$	11.9883	−	4.36339i	0.386118	−	0.140535i
$965$		0			0
$966$	−4.29904	−	3.60732i	−0.138319	−	0.116064i
$967$	3.30972	+	0.583592i	0.106433	+	0.0187671i	0.226611	−	0.973985i	$-0.427235\pi$
$967$	3.30972	+	0.583592i	0.106433	+	0.0187671i	−0.120178	+	0.992752i	$0.538346\pi$
$968$			8.45886i			0.271878i
$969$	−21.9918	+	10.3288i	−0.706479	+	0.331810i
$970$		0			0
$971$	10.5808	−	60.0068i	0.339554	−	1.92571i	−0.0370028	−	0.999315i	$-0.511781\pi$
$971$	10.5808	−	60.0068i	0.339554	−	1.92571i	0.376557	−	0.926393i	$-0.377108\pi$
$972$	9.80350	−	11.6834i	0.314447	−	0.374744i
$973$	−19.9473	+	54.8046i	−0.639480	+	1.75696i
$974$	13.3275	−	4.85081i	0.427040	−	0.155430i
$975$		0			0
$976$	7.25554	+	12.5670i	0.232244	+	0.402259i
$977$	26.9886	+	15.5819i	0.863442	+	0.498509i	0.865164	−	0.501490i	$-0.167215\pi$
$977$	26.9886	+	15.5819i	0.863442	+	0.498509i	−0.00172111	+	0.999999i	$0.500548\pi$
$978$	−11.7146	+	2.06560i	−0.374591	+	0.0660505i
$979$	−7.72950	−	43.8362i	−0.247036	−	1.40101i
$980$		0			0
$981$	−2.23190	−	3.86577i	−0.0712592	−	0.123425i
$982$	−6.24878	−	7.44701i	−0.199407	−	0.237644i
$983$	14.2659	+	39.1951i	0.455010	+	1.25013i	0.929157	+	0.369685i	$0.120534\pi$
$983$	14.2659	+	39.1951i	0.455010	+	1.25013i	−0.474147	+	0.880446i	$0.657244\pi$
$984$	2.24507	+	0.817137i	0.0715701	+	0.0260494i
$985$		0			0
$986$	−2.32520	+	13.1869i	−0.0740495	+	0.419956i
$987$		−	9.78842i		−	0.311569i
$988$	−1.03450	−	11.4606i	−0.0329120	−	0.364609i
$989$	1.55036			0.0492986
$990$		0			0
$991$	−17.2058	−	14.4374i	−0.546559	−	0.458618i	0.327215	−	0.944950i	$-0.393890\pi$
$991$	−17.2058	−	14.4374i	−0.546559	−	0.458618i	−0.873774	+	0.486332i	$0.838334\pi$
$992$	−0.695088	+	1.90974i	−0.0220691	+	0.0606343i
$993$	0.193196	+	0.530800i	0.00613088	+	0.0168444i
$994$	−58.8975	+	49.4209i	−1.86812	+	1.56754i
$995$		0			0
$996$	−4.03909	+	6.99590i	−0.127983	+	0.221674i
$997$	−29.6792	+	5.23325i	−0.939950	+	0.165739i	−0.622574	−	0.782561i	$-0.713913\pi$
$997$	−29.6792	+	5.23325i	−0.939950	+	0.165739i	−0.317377	+	0.948300i	$0.602802\pi$
$998$	12.1126	−	2.13578i	0.383418	−	0.0676069i
$999$	5.29331	−	9.16827i	0.167473	−	0.290071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.g.549.2		36
5.2	odd	4		950.2.l.i.701.2		18
5.3	odd	4		190.2.k.d.131.2	✓	18
5.4	even	2	inner	950.2.u.g.549.5		36
19.9	even	9	inner	950.2.u.g.199.5		36
95.3	even	36		3610.2.a.bj.1.6		9
95.9	even	18	inner	950.2.u.g.199.2		36
95.28	odd	36		190.2.k.d.161.2	yes	18
95.47	odd	36		950.2.l.i.351.2		18
95.73	odd	36		3610.2.a.bi.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.131.2	✓	18	5.3	odd	4
190.2.k.d.161.2	yes	18	95.28	odd	36
950.2.l.i.351.2		18	95.47	odd	36
950.2.l.i.701.2		18	5.2	odd	4
950.2.u.g.199.2		36	95.9	even	18	inner
950.2.u.g.199.5		36	19.9	even	9	inner
950.2.u.g.549.2		36	1.1	even	1	trivial
950.2.u.g.549.5		36	5.4	even	2	inner
3610.2.a.bi.1.4		9	95.73	odd	36
3610.2.a.bj.1.6		9	95.3	even	36

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(-0.712963 + 0.849676i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.849676 - 0.712963i) q^{6} +(4.26875 - 2.46456i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.307311 + 1.74285i) q^{9} +O(q^{10})\)	\(q+(-0.984808 - 0.173648i) q^{2} +(-0.712963 + 0.849676i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.849676 - 0.712963i) q^{6} +(4.26875 - 2.46456i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.307311 + 1.74285i) q^{9} +(-2.20561 + 3.82023i) q^{11} +(-0.960572 + 0.554587i) q^{12} +(-1.69691 - 2.02230i) q^{13} +(-4.63187 + 1.68586i) q^{14} +(0.766044 + 0.642788i) q^{16} +(4.94904 + 0.872649i) q^{17} -1.76973i q^{18} +(4.21347 + 1.11656i) q^{19} +(-0.949379 + 5.38420i) q^{21} +(2.83548 - 3.37919i) q^{22} +(0.351075 - 0.964570i) q^{23} +(1.04228 - 0.379360i) q^{24} +(1.31996 + 2.28624i) q^{26} +(-4.58167 - 2.64523i) q^{27} +(4.85424 - 0.855934i) q^{28} +(-0.462691 - 2.62405i) q^{29} +(-1.01615 - 1.76003i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-1.67344 - 4.59773i) q^{33} +(-4.72232 - 1.71878i) q^{34} +(-0.307311 + 1.74285i) q^{36} +2.00107i q^{37} +(-3.95557 - 1.83126i) q^{38} +2.92813 q^{39} +(1.65005 + 1.38456i) q^{41} +(1.86991 - 5.13754i) q^{42} +(0.516578 + 1.41929i) q^{43} +(-3.37919 + 2.83548i) q^{44} +(-0.513237 + 0.888952i) q^{46} +(-1.76317 + 0.310895i) q^{47} +(-1.09232 + 0.192606i) q^{48} +(8.64815 - 14.9790i) q^{49} +(-4.26995 + 3.58291i) q^{51} +(-0.902907 - 2.48072i) q^{52} +(-1.92343 + 5.28457i) q^{53} +(4.05273 + 3.40064i) q^{54} -4.92913 q^{56} +(-3.95276 + 2.78402i) q^{57} +2.66453i q^{58} +(-2.44041 + 13.8402i) q^{59} +(13.6360 + 4.96308i) q^{61} +(0.695088 + 1.90974i) q^{62} +(5.60720 + 6.68240i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.849627 + 4.81847i) q^{66} +(13.4349 - 2.36894i) q^{67} +(4.35211 + 2.51269i) q^{68} +(0.569269 + 0.986002i) q^{69} +(14.6575 - 5.33488i) q^{71} +(0.605285 - 1.66301i) q^{72} +(-8.10702 + 9.66157i) q^{73} +(0.347483 - 1.97067i) q^{74} +(3.57748 + 2.49031i) q^{76} +21.7435i q^{77} +(-2.88365 - 0.508465i) q^{78} +(2.17143 + 1.82205i) q^{79} +(0.525132 - 0.191132i) q^{81} +(-1.38456 - 1.65005i) q^{82} +(6.30732 - 3.64153i) q^{83} +(-2.73363 + 4.73478i) q^{84} +(-0.262274 - 1.48743i) q^{86} +(2.55947 + 1.47771i) q^{87} +(3.82023 - 2.20561i) q^{88} +(-7.72995 + 6.48620i) q^{89} +(-12.2278 - 4.45054i) q^{91} +(0.659805 - 0.786325i) q^{92} +(2.21993 + 0.391433i) q^{93} +1.79037 q^{94} +1.10917 q^{96} +(11.7266 + 2.06772i) q^{97} +(-11.1179 + 13.2497i) q^{98} +(-7.33589 - 2.67005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 36 q^{9}+O(q^{10}) \) 36 * q + 36 * q^9	\( 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) \) 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Introduction

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