LMFDB - Embedded newform 950.2.u.g.199.2

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			199.2
Character	$\chi$	$=$	950.199
Dual form			950.2.u.g.549.2

$q$-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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$

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	0.519900	−	0.854227i	$-0.325969\pi$
$3$	−0.712963	−	0.849676i	−0.411629	−	0.490561i	−0.931529	+	0.363667i	$0.881525\pi$
$4$	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	0.988566	+	0.150789i	$0.0481814\pi$
$7$	4.26875	+	2.46456i	1.61344	+	0.931518i	0.624870	+	0.780729i	$0.285152\pi$
$8$	−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	−0.979281	−	0.202507i	$-0.935091\pi$
$11$	−2.20561	−	3.82023i	−0.665016	−	1.15184i	0.314264	−	0.949336i	$-0.398242\pi$
$12$	−0.960572	−	0.554587i	−0.277293	−	0.160095i
$13$	−1.69691	+	2.02230i	−0.470638	+	0.560884i	−0.948184	−	0.317722i	$-0.897082\pi$
$13$	−1.69691	+	2.02230i	−0.470638	+	0.560884i	0.477546	+	0.878607i	$0.341526\pi$
$14$	−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	0.462483	−	0.886628i	$-0.346959\pi$
$17$	4.94904	−	0.872649i	1.20032	−	0.211649i	0.737836	+	0.674980i	$0.235848\pi$
$18$			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	0.970898	−	0.239493i	$-0.0769811\pi$
$23$	0.351075	+	0.964570i	0.0732041	+	0.201127i	−0.897694	+	0.440619i	$0.854759\pi$
$24$	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	0.911235	+	0.411887i	$0.135130\pi$
$29$	−0.462691	+	2.62405i	−0.0859196	+	0.487274i	−0.997154	+	0.0753868i	$0.975981\pi$
$30$		0			0
$31$	−1.01615	+	1.76003i	−0.182506	+	0.316110i	−0.942733	−	0.333547i	$-0.891754\pi$
$31$	−1.01615	+	1.76003i	−0.182506	+	0.316110i	0.760227	+	0.649657i	$0.225088\pi$
$32$	−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	$-0.947403\pi$
$37$		−	2.00107i		−	0.328975i	0.986379	−	0.164487i	$-0.0525970\pi$
$38$	−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	−0.504782	−	0.863247i	$-0.668427\pi$
$41$	1.65005	−	1.38456i	0.257695	−	0.216232i	0.762477	+	0.647015i	$0.223983\pi$
$42$	1.86991	+	5.13754i	0.288534	+	0.792740i
$43$	0.516578	−	1.41929i	0.0787775	−	0.216439i	−0.894052	−	0.447964i	$-0.852149\pi$
$43$	0.516578	−	1.41929i	0.0787775	−	0.216439i	0.972829	+	0.231525i	$0.0743714\pi$
$44$	−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	0.0435690	−	0.999050i	$-0.486127\pi$
$47$	−1.76317	−	0.310895i	−0.257185	−	0.0453486i	−0.300754	+	0.953702i	$0.597238\pi$
$48$	−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	−0.998873	−	0.0474667i	$-0.984885\pi$
$53$	−1.92343	−	5.28457i	−0.264203	−	0.725891i	0.734670	−	0.678425i	$-0.237337\pi$
$54$	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	−0.556583	−	0.830792i	$-0.687888\pi$
$59$	−2.44041	−	13.8402i	−0.317714	−	1.80184i	0.238869	−	0.971052i	$-0.423223\pi$
$60$		0			0
$61$	13.6360	−	4.96308i	1.74590	−	0.635457i	0.746358	−	0.665545i	$-0.231801\pi$
$61$	13.6360	−	4.96308i	1.74590	−	0.635457i	0.999547	+	0.0300876i	$0.00957861\pi$
$62$	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	0.916657	−	0.399674i	$-0.130877\pi$
$67$	13.4349	+	2.36894i	1.64134	+	0.289412i	0.724679	+	0.689086i	$0.241988\pi$
$68$	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	0.999233	−	0.0391574i	$-0.0124674\pi$
$71$	14.6575	+	5.33488i	1.73952	+	0.633134i	0.740287	+	0.672291i	$0.234690\pi$
$72$	0.605285	+	1.66301i	0.0713335	+	0.195987i
$73$	−8.10702	−	9.66157i	−0.948855	−	1.13080i	−0.991289	−	0.131702i	$-0.957956\pi$
$73$	−8.10702	−	9.66157i	−0.948855	−	1.13080i	0.0424348	−	0.999099i	$-0.486489\pi$
$74$	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	−0.512410	−	0.858741i	$-0.671247\pi$
$79$	2.17143	−	1.82205i	0.244305	−	0.204996i	0.756716	+	0.653744i	$0.226803\pi$
$80$		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	0.804480	−	0.593980i	$-0.202444\pi$
$83$	6.30732	+	3.64153i	0.692318	+	0.399710i	−0.112162	+	0.993690i	$0.535778\pi$
$84$	−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	0.133452	−	0.991055i	$-0.457394\pi$
$89$	−7.72995	−	6.48620i	−0.819373	−	0.687536i	−0.952825	+	0.303520i	$0.901838\pi$
$90$		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	0.457002	−	0.889466i	$-0.348923\pi$
$97$	11.7266	−	2.06772i	1.19066	−	0.209945i	0.733656	+	0.679521i	$0.237812\pi$
$98$	−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	0.586085	−	0.810250i	$-0.300669\pi$
$101$	−1.10632	−	0.928316i	−0.110083	−	0.0923709i	−0.696168	+	0.717879i	$0.745113\pi$
$102$	4.82725	+	2.78701i	0.477969	+	0.275955i
$103$	−3.86364	+	2.23068i	−0.380696	+	0.219795i	−0.678121	−	0.734950i	$-0.737206\pi$
$103$	−3.86364	+	2.23068i	−0.380696	+	0.219795i	0.297425	+	0.954745i	$0.403872\pi$
$104$	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	0.133329	−	0.991072i	$-0.457433\pi$
$107$	−6.80951	−	3.93147i	−0.658300	−	0.380070i	−0.791629	+	0.611002i	$0.790767\pi$
$108$	−3.40064	+	4.05273i	−0.327227	+	0.389974i
$109$	−2.37019	−	0.862678i	−0.227023	−	0.0826296i	0.226004	−	0.974126i	$-0.427434\pi$
$109$	−2.37019	−	0.862678i	−0.227023	−	0.0826296i	−0.453027	+	0.891497i	$0.649656\pi$
$110$		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	$0.0389970\pi$
$113$			2.59814i			0.244413i	−0.992505	+	0.122206i	$0.961003\pi$
$114$	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	−0.289822	+	0.957080i	$0.593596\pi$
$127$	−13.3209	+	15.8752i	−1.18204	+	1.40869i	−0.892213	+	0.451614i	$0.850848\pi$
$128$	−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	0.968791	−	0.247879i	$-0.0797334\pi$
$131$	−0.301638	−	1.71068i	−0.0263543	−	0.149462i	−0.995145	+	0.0984163i	$0.968622\pi$
$132$			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	0.970820	−	0.239808i	$-0.0770844\pi$
$137$	0.854249	+	2.34703i	0.0729834	+	0.200520i	−0.897837	+	0.440328i	$0.854862\pi$
$138$	−0.389403	+	1.06988i	−0.0331482	+	0.0910738i
$139$	−9.06390	−	7.60552i	−0.768790	−	0.645092i	0.171609	−	0.985165i	$-0.445104\pi$
$139$	−9.06390	−	7.60552i	−0.768790	−	0.645092i	−0.940399	+	0.340074i	$0.889548\pi$
$140$		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	0.268828	−	0.963188i	$-0.413364\pi$
$149$	15.4299	−	12.9472i	1.26406	−	1.06068i	0.995237	−	0.0974880i	$-0.0310808\pi$
$150$		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	−0.835003	−	0.550245i	$-0.814534\pi$
$157$	1.98396	−	5.45088i	0.158337	−	0.435027i	0.993340	+	0.115218i	$0.0367565\pi$
$158$	−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	−0.817495	−	0.575936i	$-0.804638\pi$
$163$	−9.28767	+	5.36224i	−0.727466	+	0.420003i	0.0900283	+	0.995939i	$0.471304\pi$
$164$	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	0.999044	+	0.0437226i	$0.0139218\pi$
$167$	3.38367	+	9.29655i	0.261836	+	0.719389i	−0.737208	+	0.675666i	$0.763856\pi$
$168$	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	0.448510	−	0.893778i	$-0.351955\pi$
$173$	15.4634	−	2.72662i	1.17566	−	0.207301i	0.727151	+	0.686477i	$0.240844\pi$
$174$	−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	0.990762	−	0.135615i	$-0.0433010\pi$
$179$	5.05642	+	8.75798i	0.377935	+	0.654602i	−0.612827	+	0.790217i	$0.709968\pi$
$180$		0			0
$181$	0.465151	−	2.63800i	0.0345744	−	0.196081i	−0.962628	−	0.270826i	$-0.912703\pi$
$181$	0.465151	−	2.63800i	0.0345744	−	0.196081i	0.997203	+	0.0747449i	$0.0238142\pi$
$182$	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	0.320706	−	0.947179i	$-0.396080\pi$
$193$	−9.27700	−	11.0559i	−0.667773	−	0.795821i	−0.988479	+	0.151358i	$0.951635\pi$
$194$	−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	−0.256415	−	0.966567i	$-0.582541\pi$
$197$	−17.1473	−	9.89999i	−1.22169	−	0.705345i	−0.965279	+	0.261222i	$0.915875\pi$
$198$	6.76079	−	3.90335i	0.480469	−	0.277399i
$199$	−3.46951	+	19.6766i	−0.245947	+	1.39484i	0.572335	+	0.820020i	$0.306038\pi$
$199$	−3.46951	+	19.6766i	−0.245947	+	1.39484i	−0.818282	+	0.574817i	$0.805073\pi$
$200$		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	0.950894	+	0.309518i	$0.100168\pi$
$211$	2.37072	+	13.4450i	0.163207	+	0.925594i	−0.787687	+	0.616076i	$0.788721\pi$
$212$	−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	0.327054	+	0.945006i	$0.393944\pi$
$223$	−7.92835	+	21.7830i	−0.530922	+	1.45870i	−0.857976	+	0.513690i	$0.828278\pi$
$224$	−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	$0.0787479\pi$
$227$			7.37892i			0.489756i	−0.969554	+	0.244878i	$0.921252\pi$
$228$	−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	−0.646375	−	0.763020i	$-0.723716\pi$
$233$	5.17822	−	14.2271i	0.339237	−	0.932045i	0.985612	−	0.169025i	$-0.0540620\pi$
$234$	−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	0.990766	−	0.135583i	$-0.0432909\pi$
$239$	5.84319	+	10.1207i	0.377964	+	0.654653i	−0.612802	+	0.790237i	$0.709958\pi$
$240$		0			0
$241$	9.77297	+	8.20049i	0.629532	+	0.528240i	0.900784	−	0.434268i	$-0.142993\pi$
$241$	9.77297	+	8.20049i	0.629532	+	0.528240i	−0.271251	+	0.962509i	$0.587437\pi$
$242$	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	−0.977963	−	0.208778i	$-0.933051\pi$
$251$	−25.2367	+	9.18541i	−1.59293	+	0.579778i	−0.614964	+	0.788556i	$0.710829\pi$
$252$	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	0.178551	−	0.983931i	$-0.442859\pi$
$257$	0.157270	+	0.0277309i	0.00981023	+	0.00172981i	−0.168741	+	0.985660i	$0.553970\pi$
$258$	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	0.917663	−	0.397360i	$-0.130073\pi$
$263$	5.95157	+	7.09280i	0.366990	+	0.437361i	−0.550673	+	0.834721i	$0.685629\pi$
$264$	−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	−0.885872	−	0.463930i	$-0.846439\pi$
$269$	−9.55896	+	8.02092i	−0.582820	+	0.489044i	0.303052	+	0.952974i	$0.401995\pi$
$270$		0			0
$271$	26.5079	+	9.64808i	1.61024	+	0.586079i	0.981487	−	0.191526i	$-0.0613437\pi$
$271$	26.5079	+	9.64808i	1.61024	+	0.586079i	0.628752	+	0.777606i	$0.283566\pi$
$272$	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	−0.702624	−	0.711562i	$-0.747988\pi$
$277$	−7.28486	+	4.20592i	−0.437705	+	0.252709i	0.264919	+	0.964271i	$0.414655\pi$
$278$	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	−0.881266	−	0.472621i	$-0.843308\pi$
$281$	−20.9967	+	7.64218i	−1.25256	+	0.455894i	−0.371294	+	0.928515i	$0.621086\pi$
$282$	−1.27647	−	1.52123i	−0.0760125	−	0.0905882i
$283$	−12.5725	+	2.21687i	−0.747357	+	0.131779i	−0.534340	−	0.845269i	$-0.679440\pi$
$283$	−12.5725	+	2.21687i	−0.747357	+	0.131779i	−0.213016	+	0.977049i	$0.568329\pi$
$284$	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	−0.999136	−	0.0415616i	$-0.986767\pi$
$293$	−25.0376	+	14.4554i	−1.46271	+	0.844496i	−0.463575	+	0.886058i	$0.653433\pi$
$294$	−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	−0.999367	−	0.0355713i	$-0.988675\pi$
$307$	−15.0835	−	17.9758i	−0.860860	−	1.02593i	0.138507	−	0.990361i	$-0.455770\pi$
$308$	−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	−0.919910	−	0.392130i	$-0.871738\pi$
$311$	−2.12258	+	3.67642i	−0.120360	+	0.208470i	0.799549	+	0.600600i	$0.205072\pi$
$312$	−2.53584	+	1.46407i	−0.143563	+	0.0828864i
$313$	−11.4384	−	2.01689i	−0.646534	−	0.114001i	−0.159241	−	0.987240i	$-0.550905\pi$
$313$	−11.4384	−	2.01689i	−0.646534	−	0.114001i	−0.487293	+	0.873238i	$0.662016\pi$
$314$	−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	−0.804899	−	0.593411i	$-0.797781\pi$
$317$	−1.43742	+	1.71306i	−0.0807338	+	0.0962148i	0.724165	+	0.689626i	$0.242225\pi$
$318$	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	0.872939	−	0.487830i	$-0.162211\pi$
$331$	0.254634	+	0.441039i	0.0139959	+	0.0242417i	−0.858943	+	0.512072i	$0.828878\pi$
$332$	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	−0.716269	−	0.697824i	$-0.754152\pi$
$337$	5.15806	−	14.1717i	0.280977	−	0.771979i	0.997247	−	0.0741552i	$-0.0236260\pi$
$338$	−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	0.0863093	+	0.996268i	$0.472493\pi$
$347$	−11.5530	+	31.7415i	−0.620196	+	1.70398i	−0.706506	+	0.707707i	$0.749730\pi$
$348$	1.89971	−	2.26399i	0.101835	−	0.121363i
$349$	−0.0164139	+	0.0284297i	−0.000878615	+	0.00152181i	−0.866464	−	0.499239i	$-0.833613\pi$
$349$	−0.0164139	+	0.0284297i	−0.000878615	+	0.00152181i	0.865586	+	0.500761i	$0.166946\pi$
$350$		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	−0.506462	−	0.862262i	$-0.669047\pi$
$353$	−0.243332	+	0.140488i	−0.0129512	+	0.00747740i	0.493510	+	0.869740i	$0.335713\pi$
$354$	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	−0.983574	−	0.180507i	$-0.942226\pi$
$359$	−2.29364	−	13.0079i	−0.121054	−	0.686530i	0.862520	−	0.506023i	$-0.168885\pi$
$360$		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	−0.564948	−	0.825127i	$-0.691104\pi$
$367$	6.62354	−	7.89363i	0.345746	−	0.412044i	0.910693	+	0.413083i	$0.135548\pi$
$368$	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	−0.297463	−	0.954733i	$-0.596141\pi$
$373$	−24.5861	−	14.1948i	−1.27302	−	0.734977i	−0.975555	+	0.219756i	$0.929474\pi$
$374$	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	0.990833	−	0.135095i	$-0.0431339\pi$
$383$	13.4201	+	15.9934i	0.685734	+	0.817226i	−0.305099	+	0.952321i	$0.598689\pi$
$384$	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	0.836949	+	0.547281i	$0.184337\pi$
$389$	−2.69629	+	15.2914i	−0.136707	+	0.775304i	−0.973656	+	0.228023i	$0.926774\pi$
$390$		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	−0.0533453	−	0.998576i	$-0.516988\pi$
$397$	4.74331	−	0.836373i	0.238060	−	0.0419764i	0.291405	+	0.956600i	$0.405877\pi$
$398$		−	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	−0.990068	−	0.140591i	$-0.955100\pi$
$401$	−2.15856	−	12.2418i	−0.107793	−	0.611326i	0.882275	−	0.470735i	$-0.156011\pi$
$402$	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	−0.816440	−	0.577430i	$-0.804056\pi$
$409$	2.99828	−	17.0041i	0.148255	−	0.840797i	0.964696	−	0.263367i	$-0.0848332\pi$
$410$		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	0.0537246	−	0.998556i	$-0.482891\pi$
$421$	21.4711	−	18.0164i	1.04644	−	0.878067i	0.992715	+	0.120489i	$0.0384462\pi$
$422$	−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	0.881892	−	0.471452i	$-0.156270\pi$
$431$	11.8489	+	9.94239i	0.570740	+	0.478908i	−0.311151	+	0.950360i	$0.600715\pi$
$432$	−1.80944	+	4.97141i	−0.0870569	+	0.239187i
$433$	−4.81630	−	13.2327i	−0.231457	−	0.635922i	0.768536	−	0.639807i	$-0.220986\pi$
$433$	−4.81630	−	13.2327i	−0.231457	−	0.635922i	−0.999992	+	0.00388467i	$0.998763\pi$
$434$	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	−0.998791	−	0.0491593i	$-0.984346\pi$
$439$	−1.61433	−	9.15534i	−0.0770479	−	0.436961i	0.921743	−	0.387801i	$-0.126765\pi$
$440$		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	−0.553125	−	0.833098i	$-0.686565\pi$
$443$	7.64795	−	9.11448i	0.363365	−	0.433042i	0.916491	+	0.400056i	$0.131009\pi$
$444$	−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	−0.999398	−	0.0347048i	$-0.988951\pi$
$449$	−9.95157	+	17.2366i	−0.469644	+	0.813446i	0.529754	+	0.848151i	$0.322284\pi$
$450$		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	$0.330123\pi$
$457$			36.8095i			1.72188i	−0.508708	+	0.860939i	$0.669877\pi$
$458$	−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	−0.425653	−	0.904886i	$-0.639956\pi$
$461$	−28.6287	−	10.4200i	−1.33337	−	0.485308i	−0.907719	+	0.419578i	$0.862178\pi$
$462$	15.5023	−	18.4749i	0.721232	−	0.859530i
$463$	19.3969	+	11.1988i	0.901452	+	0.520454i	0.877671	−	0.479263i	$-0.159096\pi$
$463$	19.3969	+	11.1988i	0.901452	+	0.520454i	0.0237813	+	0.999717i	$0.492429\pi$
$464$	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	−0.173623	−	0.984812i	$-0.555547\pi$
$467$	12.8027	−	7.39165i	0.592439	−	0.342045i	0.766061	+	0.642768i	$0.222214\pi$
$468$	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	−0.847469	−	0.530844i	$-0.821875\pi$
$479$	−25.2882	+	9.20416i	−1.15545	+	0.420549i	−0.307979	+	0.951393i	$0.599653\pi$
$480$		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	0.195191	−	0.980765i	$-0.437467\pi$
$487$	−12.2827	−	7.09140i	−0.556581	−	0.321342i	−0.751772	+	0.659423i	$0.770801\pi$
$488$	−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	−0.459092	−	0.888389i	$-0.651825\pi$
$491$	7.44701	−	6.24878i	0.336079	−	0.282004i	0.795171	+	0.606385i	$0.207381\pi$
$492$	−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	0.0701069	−	0.997539i	$-0.477666\pi$
$499$	−11.5577	−	4.20666i	−0.517394	−	0.188316i	−0.587501	+	0.809223i	$0.699888\pi$
$500$		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	−0.402839	−	0.915271i	$-0.631976\pi$
$503$	−24.5454	−	4.32801i	−1.09442	−	0.192976i	−0.691586	+	0.722295i	$0.743087\pi$
$504$	−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	−0.605660	−	0.795723i	$-0.707091\pi$
$509$	−12.5923	+	4.58321i	−0.558142	+	0.203147i	0.0475184	+	0.998870i	$0.484869\pi$
$510$		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	0.852956	−	0.521983i	$-0.174807\pi$
$521$	−0.583692	−	1.01098i	−0.0255720	−	0.0442920i	−0.878528	+	0.477690i	$0.841474\pi$
$522$	−4.64388	−	0.818841i	−0.203257	−	0.0358397i
$523$	−9.28028	−	1.63636i	−0.405798	−	0.0715532i	−0.0329765	−	0.999456i	$-0.510499\pi$
$523$	−9.28028	−	1.63636i	−0.405798	−	0.0715532i	−0.372822	+	0.927903i	$0.621610\pi$
$524$	−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	0.274314	+	0.961640i	$0.411549\pi$
$541$	−7.26524	+	41.2032i	−0.312357	+	1.77147i	−0.586671	+	0.809825i	$0.699562\pi$
$542$	−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	0.956622	+	0.291334i	$0.0940990\pi$
$547$	9.61418	+	26.4147i	0.411073	+	1.12941i	−0.545549	+	0.838079i	$0.683679\pi$
$548$	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	−0.571381	−	0.820685i	$-0.693592\pi$
$557$	7.93117	−	9.45200i	0.336055	−	0.400494i	0.907436	+	0.420190i	$0.138037\pi$
$558$	−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	0.739914	−	0.672702i	$-0.234866\pi$
$563$	12.5114	+	7.22347i	0.527293	+	0.304433i	−0.212620	+	0.977135i	$0.568200\pi$
$564$	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	0.695812	−	0.718224i	$-0.255045\pi$
$577$	10.1300	+	5.84857i	0.421718	+	0.243479i	−0.274094	+	0.961703i	$0.588378\pi$
$578$	−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	−0.759175	−	0.650887i	$-0.774397\pi$
$587$	−30.2839	+	5.33986i	−1.24995	+	0.220400i	−0.490774	+	0.871287i	$0.663286\pi$
$588$		−	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	0.888511	−	0.458855i	$-0.151740\pi$
$593$	−2.12039	−	5.82573i	−0.0870741	−	0.239234i	−0.975585	+	0.219621i	$0.929518\pi$
$594$	−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	−0.684599	−	0.728920i	$-0.740022\pi$
$599$	5.09116	−	28.8734i	0.208019	−	1.17973i	0.892618	−	0.450815i	$-0.148866\pi$
$600$		0			0
$601$	23.1718	−	40.1348i	0.945199	−	1.63713i	0.189846	−	0.981814i	$-0.439201\pi$
$601$	23.1718	−	40.1348i	0.945199	−	1.63713i	0.755353	−	0.655318i	$-0.227466\pi$
$602$	−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	$-0.827306\pi$
$607$		−	25.4409i		−	1.03262i	0.856403	−	0.516308i	$-0.172694\pi$
$608$	−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	0.529006	+	0.848618i	$0.322565\pi$
$613$	−10.4412	+	28.6870i	−0.421717	+	1.15866i	−0.950723	+	0.310041i	$0.899657\pi$
$614$	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	0.0514603	−	0.998675i	$-0.483612\pi$
$617$	−6.00494	−	1.05883i	−0.241750	−	0.0426270i	−0.293210	+	0.956048i	$0.594724\pi$
$618$	−4.87323	−	0.859283i	−0.196030	−	0.0345654i
$619$	9.07568	+	15.7195i	0.364782	+	0.631821i	0.988741	−	0.149636i	$-0.0478101\pi$
$619$	9.07568	+	15.7195i	0.364782	+	0.631821i	−0.623959	+	0.781457i	$0.714477\pi$
$620$		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	−0.621653	−	0.783293i	$-0.713539\pi$
$631$	−14.9306	+	5.43428i	−0.594376	+	0.216335i	0.0272768	+	0.999628i	$0.491316\pi$
$632$	−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	0.899976	−	0.435940i	$-0.143584\pi$
$641$	33.1458	+	12.0641i	1.30918	+	0.476503i	0.409205	+	0.912443i	$0.365806\pi$
$642$	−2.98288	−	8.19540i	−0.117725	−	0.323447i
$643$	−5.36891	−	6.39841i	−0.211729	−	0.252329i	0.649719	−	0.760174i	$-0.274887\pi$
$643$	−5.36891	−	6.39841i	−0.211729	−	0.252329i	−0.861448	+	0.507846i	$0.830442\pi$
$644$	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	$0.0758350\pi$
$647$			12.0057i			0.471991i	−0.971754	+	0.235995i	$0.924165\pi$
$648$	−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	0.984196	−	0.177081i	$-0.0566655\pi$
$653$	33.8062	+	19.5180i	1.32294	+	0.763798i	0.338741	+	0.940880i	$0.389999\pi$
$654$	−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	0.706354	−	0.707859i	$-0.250339\pi$
$659$	3.38617	+	2.84133i	0.131906	+	0.110683i	−0.574448	+	0.818541i	$0.694783\pi$
$660$		0			0
$661$	5.32012	−	1.93636i	0.206929	−	0.0753159i	−0.236476	−	0.971637i	$-0.575993\pi$
$661$	5.32012	−	1.93636i	0.206929	−	0.0753159i	0.443405	+	0.896321i	$0.353770\pi$
$662$	−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	−0.201240	−	0.979542i	$-0.564497\pi$
$673$	14.1761	−	8.18457i	0.546448	−	0.315492i	0.747688	+	0.664050i	$0.231164\pi$
$674$	−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	0.154556	−	0.987984i	$-0.450605\pi$
$677$	−16.2304	−	9.37064i	−0.623786	−	0.360143i	−0.778341	+	0.627841i	$0.783939\pi$
$678$	−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	$0.0682422\pi$
$683$			11.1202i			0.425501i	−0.977107	+	0.212751i	$0.931758\pi$
$684$	−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	−0.957040	−	0.289956i	$-0.906359\pi$
$691$	−5.97792	+	10.3541i	−0.227411	+	0.393887i	0.729629	+	0.683843i	$0.239693\pi$
$692$	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	0.977821	+	0.209443i	$0.0671650\pi$
$701$	3.45791	+	19.6108i	0.130603	+	0.740689i	−0.847217	+	0.531246i	$0.821724\pi$
$702$			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	0.800062	−	0.599917i	$-0.204800\pi$
$709$	9.27123	+	7.77949i	0.348188	+	0.292165i	−0.451874	+	0.892082i	$0.649244\pi$
$710$		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	−0.961404	−	0.275141i	$-0.911275\pi$
$719$	−22.9902	+	19.2911i	−0.857389	+	0.719435i	0.104015	+	0.994576i	$0.466831\pi$
$720$		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	−0.319175	−	0.947696i	$-0.603406\pi$
$727$	14.4115	−	39.5954i	0.534494	−	1.46851i	0.853669	−	0.520815i	$-0.174372\pi$
$728$	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	−0.627732	−	0.778429i	$-0.716017\pi$
$733$	−7.24116	+	4.18069i	−0.267458	+	0.154417i	0.360274	+	0.932847i	$0.382683\pi$
$734$	−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	0.988414	+	0.151784i	$0.0485019\pi$
$739$	3.03167	+	17.1935i	0.111522	+	0.632472i	−0.876892	+	0.480688i	$0.840387\pi$
$740$		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	0.116899	−	0.993144i	$-0.462705\pi$
$743$	15.4396	−	2.72242i	0.566424	−	0.0998758i	0.449524	+	0.893268i	$0.351593\pi$
$744$	−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	−0.991583	−	0.129476i	$-0.958670\pi$
$751$	−0.425213	+	2.41150i	−0.0155162	+	0.0879970i	0.976066	+	0.217473i	$0.0697815\pi$
$752$	−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	0.338743	−	0.940879i	$-0.389998\pi$
$757$	−17.7921	−	21.2038i	−0.646664	−	0.770664i	−0.985407	+	0.170215i	$0.945554\pi$
$758$	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	−0.956322	−	0.292314i	$-0.905575\pi$
$769$	1.17313	−	6.65313i	0.0423040	−	0.239918i	0.998626	+	0.0523962i	$0.0166859\pi$
$770$		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	−0.887580	−	0.460654i	$-0.847615\pi$
$773$	−7.77917	+	9.27086i	−0.279797	+	0.333450i	0.607782	+	0.794104i	$0.292059\pi$
$774$	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	−0.840085	−	0.542454i	$-0.817495\pi$
$787$	−22.1721	+	12.8010i	−0.790349	+	0.456308i	0.0497367	+	0.998762i	$0.484162\pi$
$788$	−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	$0.170874\pi$
$797$			28.8750i			1.02281i	−0.859341	+	0.511403i	$0.829126\pi$
$798$	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	0.985117	+	0.171888i	$0.0549866\pi$
$809$	18.2438	+	31.5992i	0.641417	+	1.11097i	−0.343699	+	0.939080i	$0.611680\pi$
$810$		0			0
$811$	3.21407	+	2.69693i	0.112861	+	0.0947020i	0.697472	−	0.716612i	$-0.254308\pi$
$811$	3.21407	+	2.69693i	0.112861	+	0.0947020i	−0.584610	+	0.811314i	$0.698753\pi$
$812$	−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	−0.271206	−	0.962521i	$-0.587422\pi$
$821$	4.00386	−	1.45729i	0.139736	−	0.0508597i	0.410941	+	0.911662i	$0.365200\pi$
$822$	−0.947510	+	2.60326i	−0.0330482	+	0.0907992i
$823$	−1.04295	+	1.24294i	−0.0363551	+	0.0433263i	−0.783916	−	0.620867i	$-0.786781\pi$
$823$	−1.04295	+	1.24294i	−0.0363551	+	0.0433263i	0.747561	+	0.664194i	$0.231225\pi$
$824$	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	0.582676	−	0.812704i	$-0.302006\pi$
$827$	24.5087	+	4.32155i	0.852252	+	0.150275i	0.269575	+	0.962979i	$0.413117\pi$
$828$	1.57321	−	0.908293i	0.0546728	−	0.0315654i
$829$	6.75957	−	11.7079i	0.234770	−	0.406633i	−0.724436	−	0.689342i	$-0.757900\pi$
$829$	6.75957	−	11.7079i	0.234770	−	0.406633i	0.959206	+	0.282709i	$0.0912331\pi$
$830$		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	−0.827349	−	0.561689i	$-0.810152\pi$
$839$	−12.1036	+	10.1561i	−0.417861	+	0.350627i	0.409488	+	0.912316i	$0.365707\pi$
$840$		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	−0.344187	−	0.938901i	$-0.611845\pi$
$853$	−10.1197	+	1.78438i	−0.346494	+	0.0610962i	−0.00230672	+	0.999997i	$0.500734\pi$
$854$	−71.5270			−2.44760
$855$		0			0
$856$	7.86294			0.268750
$857$	27.0617	−	4.77171i	0.924410	−	0.162998i	0.308870	−	0.951104i	$-0.400049\pi$
$857$	27.0617	−	4.77171i	0.924410	−	0.162998i	0.615540	+	0.788106i	$0.288938\pi$
$858$	8.30265	+	9.89471i	0.283448	+	0.337800i
$859$	−0.328073	+	0.119409i	−0.0111937	+	0.00407418i	−0.347611	−	0.937639i	$-0.613007\pi$
$859$	−0.328073	+	0.119409i	−0.0111937	+	0.00407418i	0.336417	+	0.941713i	$0.390785\pi$
$860$		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	−0.847679	−	0.530509i	$-0.822001\pi$
$863$	−23.8565	+	13.7736i	−0.812084	+	0.468857i	0.0355949	+	0.999366i	$0.488667\pi$
$864$	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	0.373705	−	0.927548i	$-0.378087\pi$
$877$	−17.9061	−	21.3396i	−0.604645	−	0.720587i	−0.978349	+	0.206960i	$0.933643\pi$
$878$	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	0.426795	+	0.904348i	$0.359642\pi$
$881$	−16.9123	+	29.2930i	−0.569791	+	0.986907i	−0.996586	+	0.0825583i	$0.973691\pi$
$882$	−26.5089	+	15.3049i	−0.892602	+	0.515344i
$883$	27.6813	+	4.88096i	0.931549	+	0.164257i	0.618773	−	0.785570i	$-0.287630\pi$
$883$	27.6813	+	4.88096i	0.931549	+	0.164257i	0.312776	+	0.949827i	$0.398741\pi$
$884$	−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	0.0471192	−	0.998889i	$-0.484996\pi$
$887$	30.4571	−	36.2974i	1.02265	−	1.21875i	0.975532	−	0.219859i	$-0.0705596\pi$
$888$	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	−0.901769	−	0.432219i	$-0.857731\pi$
$907$	2.01331	−	5.53153i	0.0668510	−	0.183672i	0.968620	+	0.248547i	$0.0799531\pi$
$908$	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	−0.00509211	−	0.999987i	$-0.501621\pi$
$919$	26.1760	−	45.3382i	0.863468	−	1.49557i	0.868560	−	0.495584i	$-0.165046\pi$
$920$		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	0.891005	+	0.453993i	$0.150001\pi$
$929$	6.37049	+	36.1288i	0.209009	+	1.18535i	−0.681997	+	0.731355i	$0.738888\pi$
$930$		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	−0.993215	−	0.116292i	$-0.962899\pi$
$937$	−21.6177	+	25.7630i	−0.706219	+	0.841639i	0.286996	+	0.957932i	$0.407343\pi$
$938$	−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	0.544695	+	0.838634i	$0.316645\pi$
$941$	−7.79104	+	44.1852i	−0.253981	+	1.44040i	−0.798676	+	0.601762i	$0.794466\pi$
$942$	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	0.601684	−	0.798734i	$-0.294497\pi$
$947$	−8.90570	−	10.6134i	−0.289396	−	0.344889i	−0.891081	+	0.453845i	$0.850052\pi$
$948$	−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	0.180092	−	0.983650i	$-0.442360\pi$
$953$	−25.3105	−	30.1638i	−0.819886	−	0.977102i	−0.999979	+	0.00654740i	$0.997916\pi$
$954$	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	−0.120178	−	0.992752i	$-0.538346\pi$
$967$	3.30972	−	0.583592i	0.106433	−	0.0187671i	0.226611	+	0.973985i	$0.427235\pi$
$968$		−	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	0.376557	+	0.926393i	$0.377108\pi$
$971$	10.5808	+	60.0068i	0.339554	+	1.92571i	−0.0370028	+	0.999315i	$0.511781\pi$
$972$	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	−0.00172111	−	0.999999i	$-0.500548\pi$
$977$	26.9886	−	15.5819i	0.863442	−	0.498509i	0.865164	+	0.501490i	$0.167215\pi$
$978$	−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	−0.474147	−	0.880446i	$-0.657244\pi$
$983$	14.2659	−	39.1951i	0.455010	−	1.25013i	0.929157	−	0.369685i	$-0.120534\pi$
$984$	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	−0.873774	−	0.486332i	$-0.838334\pi$
$991$	−17.2058	+	14.4374i	−0.546559	+	0.458618i	0.327215	+	0.944950i	$0.393890\pi$
$992$	−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	−0.317377	−	0.948300i	$-0.602802\pi$
$997$	−29.6792	−	5.23325i	−0.939950	−	0.165739i	−0.622574	+	0.782561i	$0.713913\pi$
$998$	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.199.2		36
5.2	odd	4		190.2.k.d.161.2	yes	18
5.3	odd	4		950.2.l.i.351.2		18
5.4	even	2	inner	950.2.u.g.199.5		36
19.17	even	9	inner	950.2.u.g.549.5		36
95.17	odd	36		190.2.k.d.131.2	✓	18
95.32	even	36		3610.2.a.bj.1.6		9
95.74	even	18	inner	950.2.u.g.549.2		36
95.82	odd	36		3610.2.a.bi.1.4		9
95.93	odd	36		950.2.l.i.701.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.131.2	✓	18	95.17	odd	36
190.2.k.d.161.2	yes	18	5.2	odd	4
950.2.l.i.351.2		18	5.3	odd	4
950.2.l.i.701.2		18	95.93	odd	36
950.2.u.g.199.2		36	1.1	even	1	trivial
950.2.u.g.199.5		36	5.4	even	2	inner
950.2.u.g.549.2		36	95.74	even	18	inner
950.2.u.g.549.5		36	19.17	even	9	inner
3610.2.a.bi.1.4		9	95.82	odd	36
3610.2.a.bj.1.6		9	95.32	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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