LMFDB - Embedded newform 950.2.l.i.351.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 24 x^{16} - 12 x^{15} + 393 x^{14} - 222 x^{13} + 3518 x^{12} - 2478 x^{11} + 22809 x^{10} + \cdots + 64 $ x^18 + 24x^16 - 12x^15 + 393x^14 - 222x^13 + 3518x^12 - 2478x^11 + 22809x^10 - 12862x^9 + 77397x^8 - 24822x^7 + 178501x^6 - 39408x^5 + 132588x^4 + 45584x^3 + 50640x^2 + 1824x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			351.2
Root			$0.554587 + 0.960572i$ of defining polynomial
Character	$\chi$	$=$	950.351
Dual form			950.2.l.i.701.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(0.849676 - 0.712963i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.849676 + 0.712963i) q^{6} +(2.46456 - 4.26875i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.307311 + 1.74285i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(0.849676 - 0.712963i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.849676 + 0.712963i) q^{6} +(2.46456 - 4.26875i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.307311 + 1.74285i) q^{9} +(-2.20561 - 3.82023i) q^{11} +(-0.554587 + 0.960572i) q^{12} +(-2.02230 - 1.69691i) q^{13} +(4.63187 + 1.68586i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-0.872649 - 4.94904i) q^{17} -1.76973 q^{18} +(-4.21347 + 1.11656i) q^{19} +(-0.949379 - 5.38420i) q^{21} +(3.37919 - 2.83548i) q^{22} +(-0.964570 + 0.351075i) q^{23} +(-1.04228 - 0.379360i) q^{24} +(1.31996 - 2.28624i) q^{26} +(2.64523 + 4.58167i) q^{27} +(-0.855934 + 4.85424i) q^{28} +(0.462691 - 2.62405i) q^{29} +(-1.01615 + 1.76003i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-4.59773 - 1.67344i) q^{33} +(4.72232 - 1.71878i) q^{34} +(-0.307311 - 1.74285i) q^{36} -2.00107 q^{37} +(-1.83126 - 3.95557i) q^{38} -2.92813 q^{39} +(1.65005 - 1.38456i) q^{41} +(5.13754 - 1.86991i) q^{42} +(1.41929 + 0.516578i) q^{43} +(3.37919 + 2.83548i) q^{44} +(-0.513237 - 0.888952i) q^{46} +(-0.310895 + 1.76317i) q^{47} +(0.192606 - 1.09232i) q^{48} +(-8.64815 - 14.9790i) q^{49} +(-4.26995 - 3.58291i) q^{51} +(2.48072 + 0.902907i) q^{52} +(5.28457 - 1.92343i) q^{53} +(-4.05273 + 3.40064i) q^{54} -4.92913 q^{56} +(-2.78402 + 3.95276i) q^{57} +2.66453 q^{58} +(2.44041 + 13.8402i) q^{59} +(13.6360 - 4.96308i) q^{61} +(-1.90974 - 0.695088i) q^{62} +(6.68240 + 5.60720i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.849627 - 4.81847i) q^{66} +(2.36894 - 13.4349i) q^{67} +(2.51269 + 4.35211i) q^{68} +(-0.569269 + 0.986002i) q^{69} +(14.6575 + 5.33488i) q^{71} +(1.66301 - 0.605285i) q^{72} +(9.66157 - 8.10702i) q^{73} +(-0.347483 - 1.97067i) q^{74} +(3.57748 - 2.49031i) q^{76} -21.7435 q^{77} +(-0.508465 - 2.88365i) q^{78} +(-2.17143 + 1.82205i) q^{79} +(0.525132 + 0.191132i) q^{81} +(1.65005 + 1.38456i) q^{82} +(-3.64153 + 6.30732i) q^{83} +(2.73363 + 4.73478i) q^{84} +(-0.262274 + 1.48743i) q^{86} +(-1.47771 - 2.55947i) q^{87} +(-2.20561 + 3.82023i) q^{88} +(7.72995 + 6.48620i) q^{89} +(-12.2278 + 4.45054i) q^{91} +(0.786325 - 0.659805i) q^{92} +(0.391433 + 2.21993i) q^{93} -1.79037 q^{94} +1.10917 q^{96} +(-2.06772 - 11.7266i) q^{97} +(13.2497 - 11.1179i) q^{98} +(7.33589 - 2.67005i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 18 * q - 9 * q^8 - 18 * q^9	$ 18 q - 9 q^{8} - 18 q^{9} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 42 q^{18} + 12 q^{21} + 3 q^{22} - 9 q^{23} - 9 q^{26} + 18 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{31} - 66 q^{33} + 18 q^{34} - 18 q^{36} + 12 q^{37} + 6 q^{38} + 48 q^{39} - 21 q^{41} - 42 q^{42} - 18 q^{43} + 3 q^{44} + 18 q^{46} + 54 q^{47} - 39 q^{49} + 42 q^{51} - 12 q^{52} + 24 q^{53} - 54 q^{54} + 18 q^{57} - 30 q^{59} + 48 q^{61} + 30 q^{62} + 57 q^{63} - 9 q^{64} + 24 q^{66} + 6 q^{67} + 6 q^{68} - 30 q^{69} + 30 q^{71} - 6 q^{73} - 3 q^{74} - 21 q^{76} - 30 q^{77} + 24 q^{78} + 30 q^{79} + 18 q^{81} - 21 q^{82} - 6 q^{83} + 6 q^{84} + 36 q^{86} - 24 q^{87} - 12 q^{88} + 30 q^{89} - 60 q^{91} + 18 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{97} + 18 q^{98} + 171 q^{99}+O(q^{100}) $ 18 * q - 9 * q^8 - 18 * q^9 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 42 * q^18 + 12 * q^21 + 3 * q^22 - 9 * q^23 - 9 * q^26 + 18 * q^27 - 3 * q^28 - 6 * q^29 - 6 * q^31 - 66 * q^33 + 18 * q^34 - 18 * q^36 + 12 * q^37 + 6 * q^38 + 48 * q^39 - 21 * q^41 - 42 * q^42 - 18 * q^43 + 3 * q^44 + 18 * q^46 + 54 * q^47 - 39 * q^49 + 42 * q^51 - 12 * q^52 + 24 * q^53 - 54 * q^54 + 18 * q^57 - 30 * q^59 + 48 * q^61 + 30 * q^62 + 57 * q^63 - 9 * q^64 + 24 * q^66 + 6 * q^67 + 6 * q^68 - 30 * q^69 + 30 * q^71 - 6 * q^73 - 3 * q^74 - 21 * q^76 - 30 * q^77 + 24 * q^78 + 30 * q^79 + 18 * q^81 - 21 * q^82 - 6 * q^83 + 6 * q^84 + 36 * q^86 - 24 * q^87 - 12 * q^88 + 30 * q^89 - 60 * q^91 + 18 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^97 + 18 * q^98 + 171 * 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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	0.849676	−	0.712963i	0.490561	−	0.411629i	−0.363667	−	0.931529i	$-0.618475\pi$
$3$	0.849676	−	0.712963i	0.490561	−	0.411629i	0.854227	+	0.519900i	$0.174031\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	0.849676	+	0.712963i	0.346879	+	0.291066i
$7$	2.46456	−	4.26875i	0.931518	−	1.61344i	0.150789	−	0.988566i	$-0.451819\pi$
$7$	2.46456	−	4.26875i	0.931518	−	1.61344i	0.780729	−	0.624870i	$-0.214848\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−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	$-0.398242\pi$
$12$	−0.554587	+	0.960572i	−0.160095	+	0.277293i
$13$	−2.02230	−	1.69691i	−0.560884	−	0.470638i	0.317722	−	0.948184i	$-0.397082\pi$
$13$	−2.02230	−	1.69691i	−0.560884	−	0.470638i	−0.878607	+	0.477546i	$0.841526\pi$
$14$	4.63187	+	1.68586i	1.23792	+	0.450565i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.872649	−	4.94904i	−0.211649	−	1.20032i	−0.886628	−	0.462483i	$-0.846959\pi$
$17$	−0.872649	−	4.94904i	−0.211649	−	1.20032i	0.674980	−	0.737836i	$-0.264152\pi$
$18$	−1.76973			−0.417131
$19$	−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
$22$	3.37919	−	2.83548i	0.720446	−	0.604526i
$23$	−0.964570	+	0.351075i	−0.201127	+	0.0732041i	−0.440619	−	0.897694i	$-0.645241\pi$
$23$	−0.964570	+	0.351075i	−0.201127	+	0.0732041i	0.239493	+	0.970898i	$0.423019\pi$
$24$	−1.04228	−	0.379360i	−0.212755	−	0.0774364i
$25$		0			0
$26$	1.31996	−	2.28624i	0.258866	−	0.448368i
$27$	2.64523	+	4.58167i	0.509075	+	0.881744i
$28$	−0.855934	+	4.85424i	−0.161756	+	0.917366i
$29$	0.462691	−	2.62405i	0.0859196	−	0.487274i	−0.911235	−	0.411887i	$-0.864870\pi$
$29$	0.462691	−	2.62405i	0.0859196	−	0.487274i	0.997154	−	0.0753868i	$-0.0240192\pi$
$30$		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	$0.225088\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−4.59773	−	1.67344i	−0.800363	−	0.291308i
$34$	4.72232	−	1.71878i	0.809871	−	0.294769i
$35$		0			0
$36$	−0.307311	−	1.74285i	−0.0512185	−	0.290475i
$37$	−2.00107			−0.328975			−0.164487	−	0.986379i	$-0.552597\pi$
$37$	−2.00107			−0.328975			−0.164487	+	0.986379i	$0.552597\pi$
$38$	−1.83126	−	3.95557i	−0.297069	−	0.641678i
$39$	−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	$0.223983\pi$
$42$	5.13754	−	1.86991i	0.792740	−	0.288534i
$43$	1.41929	+	0.516578i	0.216439	+	0.0787775i	0.447964	−	0.894052i	$-0.352149\pi$
$43$	1.41929	+	0.516578i	0.216439	+	0.0787775i	−0.231525	+	0.972829i	$0.574371\pi$
$44$	3.37919	+	2.83548i	0.509432	+	0.427464i
$45$		0			0
$46$	−0.513237	−	0.888952i	−0.0756727	−	0.131069i
$47$	−0.310895	+	1.76317i	−0.0453486	+	0.257185i	−0.999050	−	0.0435690i	$-0.986127\pi$
$47$	−0.310895	+	1.76317i	−0.0453486	+	0.257185i	0.953702	+	0.300754i	$0.0972383\pi$
$48$	0.192606	−	1.09232i	0.0278003	−	0.157663i
$49$	−8.64815	−	14.9790i	−1.23545	−	2.13986i
$50$		0			0
$51$	−4.26995	−	3.58291i	−0.597913	−	0.501708i
$52$	2.48072	+	0.902907i	0.344013	+	0.125211i
$53$	5.28457	−	1.92343i	0.725891	−	0.264203i	0.0474667	−	0.998873i	$-0.484885\pi$
$53$	5.28457	−	1.92343i	0.725891	−	0.264203i	0.678425	+	0.734670i	$0.262663\pi$
$54$	−4.05273	+	3.40064i	−0.551507	+	0.462769i
$55$		0			0
$56$	−4.92913			−0.658683
$57$	−2.78402	+	3.95276i	−0.368752	+	0.523555i
$58$	2.66453			0.349870
$59$	2.44041	+	13.8402i	0.317714	+	1.80184i	0.556583	+	0.830792i	$0.312112\pi$
$59$	2.44041	+	13.8402i	0.317714	+	1.80184i	−0.238869	+	0.971052i	$0.576777\pi$
$60$		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	$0.00957861\pi$
$62$	−1.90974	−	0.695088i	−0.242537	−	0.0882763i
$63$	6.68240	+	5.60720i	0.841903	+	0.706441i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	0.849627	−	4.81847i	0.104582	−	0.593113i
$67$	2.36894	−	13.4349i	0.289412	−	1.64134i	−0.399674	−	0.916657i	$-0.630877\pi$
$67$	2.36894	−	13.4349i	0.289412	−	1.64134i	0.689086	−	0.724679i	$-0.258012\pi$
$68$	2.51269	+	4.35211i	0.304709	+	0.527771i
$69$	−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	$0.234690\pi$
$72$	1.66301	−	0.605285i	0.195987	−	0.0713335i
$73$	9.66157	−	8.10702i	1.13080	−	0.948855i	0.131702	−	0.991289i	$-0.457956\pi$
$73$	9.66157	−	8.10702i	1.13080	−	0.948855i	0.999099	+	0.0424348i	$0.0135115\pi$
$74$	−0.347483	−	1.97067i	−0.0403941	−	0.229086i
$75$		0			0
$76$	3.57748	−	2.49031i	0.410365	−	0.285658i
$77$	−21.7435			−2.47790
$78$	−0.508465	−	2.88365i	−0.0575723	−	0.326509i
$79$	−2.17143	+	1.82205i	−0.244305	+	0.204996i	−0.756716	−	0.653744i	$-0.773197\pi$
$79$	−2.17143	+	1.82205i	−0.244305	+	0.204996i	0.512410	+	0.858741i	$0.328753\pi$
$80$		0			0
$81$	0.525132	+	0.191132i	0.0583480	+	0.0212369i
$82$	1.65005	+	1.38456i	0.182218	+	0.152899i
$83$	−3.64153	+	6.30732i	−0.399710	+	0.692318i	−0.993690	−	0.112162i	$-0.964222\pi$
$83$	−3.64153	+	6.30732i	−0.399710	+	0.692318i	0.593980	+	0.804480i	$0.297556\pi$
$84$	2.73363	+	4.73478i	0.298263	+	0.516607i
$85$		0			0
$86$	−0.262274	+	1.48743i	−0.0282817	+	0.160394i
$87$	−1.47771	−	2.55947i	−0.158428	−	0.274404i
$88$	−2.20561	+	3.82023i	−0.235119	+	0.407238i
$89$	7.72995	+	6.48620i	0.819373	+	0.687536i	0.952825	−	0.303520i	$-0.0981618\pi$
$89$	7.72995	+	6.48620i	0.819373	+	0.687536i	−0.133452	+	0.991055i	$0.542606\pi$
$90$		0			0
$91$	−12.2278	+	4.45054i	−1.28182	+	0.466544i
$92$	0.786325	−	0.659805i	0.0819800	−	0.0687894i
$93$	0.391433	+	2.21993i	0.0405897	+	0.230196i
$94$	−1.79037			−0.184663
$95$		0			0
$96$	1.10917			0.113205
$97$	−2.06772	−	11.7266i	−0.209945	−	1.19066i	−0.889466	−	0.457002i	$-0.848923\pi$
$97$	−2.06772	−	11.7266i	−0.209945	−	1.19066i	0.679521	−	0.733656i	$-0.262188\pi$
$98$	13.2497	−	11.1179i	1.33843	−	1.12307i
$99$	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	$0.745113\pi$
$102$	2.78701	−	4.82725i	0.275955	−	0.477969i
$103$	−2.23068	−	3.86364i	−0.219795	−	0.380696i	0.734950	−	0.678121i	$-0.237206\pi$
$103$	−2.23068	−	3.86364i	−0.219795	−	0.380696i	−0.954745	+	0.297425i	$0.903872\pi$
$104$	−0.458418	+	2.59982i	−0.0449515	+	0.254933i
$105$		0			0
$106$	2.81186	+	4.87029i	0.273112	+	0.473044i
$107$	−3.93147	+	6.80951i	−0.380070	+	0.658300i	−0.991072	−	0.133329i	$-0.957433\pi$
$107$	−3.93147	+	6.80951i	−0.380070	+	0.658300i	0.611002	+	0.791629i	$0.290767\pi$
$108$	−4.05273	−	3.40064i	−0.389974	−	0.327227i
$109$	2.37019	+	0.862678i	0.227023	+	0.0826296i	0.453027	−	0.891497i	$-0.350344\pi$
$109$	2.37019	+	0.862678i	0.227023	+	0.0826296i	−0.226004	+	0.974126i	$0.572566\pi$
$110$		0			0
$111$	−1.70027	+	1.42669i	−0.161382	+	0.135416i
$112$	−0.855934	−	4.85424i	−0.0808782	−	0.458683i
$113$	−2.59814			−0.244413			−0.122206	−	0.992505i	$-0.538997\pi$
$113$	−2.59814			−0.244413			−0.122206	+	0.992505i	$0.538997\pi$
$114$	−4.37615	−	2.05533i	−0.409864	−	0.192499i
$115$		0			0
$116$	0.462691	+	2.62405i	0.0429598	+	0.243637i
$117$	3.57893	−	3.00308i	0.330872	−	0.277635i
$118$	−13.2062	+	4.80666i	−1.21573	+	0.442489i
$119$	−23.2769	−	8.47211i	−2.13379	−	0.776637i
$120$		0			0
$121$	−4.22943	+	7.32559i	−0.384494	+	0.665963i
$122$	7.25554	+	12.5670i	0.656886	+	1.13776i
$123$	0.414871	−	2.35285i	0.0374077	−	0.212150i
$124$	0.352906	−	2.00143i	0.0316919	−	0.179733i
$125$		0			0
$126$	−4.36163	+	7.55456i	−0.388564	+	0.673013i
$127$	15.8752	+	13.3209i	1.40869	+	1.18204i	0.957080	+	0.289822i	$0.0935962\pi$
$127$	15.8752	+	13.3209i	1.40869	+	1.18204i	0.451614	+	0.892213i	$0.350848\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	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	$0.968622\pi$
$132$	4.89281			0.425864
$133$	−5.61805	+	20.7381i	−0.487147	+	1.79822i
$134$	13.6422			1.17850
$135$		0			0
$136$	−3.84967	+	3.23026i	−0.330107	+	0.276992i
$137$	2.34703	−	0.854249i	0.200520	−	0.0729834i	−0.239808	−	0.970820i	$-0.577084\pi$
$137$	2.34703	−	0.854249i	0.200520	−	0.0729834i	0.440328	+	0.897837i	$0.354862\pi$
$138$	−1.06988	−	0.389403i	−0.0910738	−	0.0331482i
$139$	9.06390	+	7.60552i	0.768790	+	0.645092i	0.940399	−	0.340074i	$-0.110452\pi$
$139$	9.06390	+	7.60552i	0.768790	+	0.645092i	−0.171609	+	0.985165i	$0.554896\pi$
$140$		0			0
$141$	0.992916	+	1.71978i	0.0836186	+	0.144832i
$142$	−2.70859	+	15.3612i	−0.227300	+	1.28908i
$143$	−2.02218	+	11.4684i	−0.169103	+	0.959032i
$144$	0.884867	+	1.53264i	0.0737390	+	0.127720i
$145$		0			0
$146$	9.66157	+	8.10702i	0.799597	+	0.670942i
$147$	−18.0276	−	6.56152i	−1.48689	−	0.541185i
$148$	1.88040	−	0.684408i	0.154568	−	0.0562580i
$149$	−15.4299	+	12.9472i	−1.26406	+	1.06068i	−0.268828	+	0.963188i	$0.586636\pi$
$149$	−15.4299	+	12.9472i	−1.26406	+	1.06068i	−0.995237	+	0.0974880i	$0.968919\pi$
$150$		0			0
$151$	−7.67871			−0.624885			−0.312442	−	0.949937i	$-0.601147\pi$
$151$	−7.67871			−0.624885			−0.312442	+	0.949937i	$0.601147\pi$
$152$	3.07370	+	3.09069i	0.249310	+	0.250688i
$153$	8.89360			0.719005
$154$	−3.77571	−	21.4131i	−0.304256	−	1.72552i
$155$		0			0
$156$	2.75154	−	1.00148i	0.220300	−	0.0801825i
$157$	−5.45088	−	1.98396i	−0.435027	−	0.158337i	0.115218	−	0.993340i	$-0.463243\pi$
$157$	−5.45088	−	1.98396i	−0.435027	−	0.158337i	−0.550245	+	0.835003i	$0.685466\pi$
$158$	−2.17143	−	1.82205i	−0.172750	−	0.144954i
$159$	3.11884	−	5.40199i	0.247340	−	0.428406i
$160$		0			0
$161$	−0.878594	+	4.98275i	−0.0692429	+	0.392696i
$162$	−0.0970404	+	0.550344i	−0.00762422	+	0.0432391i
$163$	−5.36224	−	9.28767i	−0.420003	−	0.727466i	0.575936	−	0.817495i	$-0.304638\pi$
$163$	−5.36224	−	9.28767i	−0.420003	−	0.727466i	−0.995939	+	0.0900283i	$0.971304\pi$
$164$	−1.07700	+	1.86541i	−0.0840992	+	0.145664i
$165$		0			0
$166$	−6.84384	−	2.49095i	−0.531185	−	0.193335i
$167$	9.29655	−	3.38367i	0.719389	−	0.261836i	0.0437226	−	0.999044i	$-0.486078\pi$
$167$	9.29655	−	3.38367i	0.719389	−	0.261836i	0.675666	+	0.737208i	$0.263856\pi$
$168$	−4.18816	+	3.51429i	−0.323124	+	0.271133i
$169$	−1.04724	−	5.93919i	−0.0805569	−	0.456861i
$170$		0			0
$171$	−0.651146	−	7.68657i	−0.0497944	−	0.587806i
$172$	−1.51037			−0.115165
$173$	2.72662	+	15.4634i	0.207301	+	1.17566i	0.893778	+	0.448510i	$0.148045\pi$
$173$	2.72662	+	15.4634i	0.207301	+	1.17566i	−0.686477	+	0.727151i	$0.740844\pi$
$174$	2.26399	−	1.89971i	0.171633	−	0.144017i
$175$		0			0
$176$	−4.14519	−	1.50873i	−0.312456	−	0.113725i
$177$	11.9411	+	10.0198i	0.897550	+	0.753134i
$178$	−5.04537	+	8.73883i	−0.378166	+	0.655003i
$179$	−5.05642	−	8.75798i	−0.377935	−	0.654602i	0.612827	−	0.790217i	$-0.290032\pi$
$179$	−5.05642	−	8.75798i	−0.377935	−	0.654602i	−0.990762	+	0.135615i	$0.956699\pi$
$180$		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	$0.0238142\pi$
$182$	−6.50626	−	11.2692i	−0.482276	−	0.835326i
$183$	8.04765	−	13.9389i	0.594899	−	1.03040i
$184$	0.786325	+	0.659805i	0.0579686	+	0.0486414i
$185$		0			0
$186$	−2.11823	+	0.770973i	−0.155316	+	0.0565305i
$187$	−16.9817	+	14.2494i	−1.24183	+	1.04202i
$188$	−0.310895	−	1.76317i	−0.0226743	−	0.128592i
$189$	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	$0.456670\pi$
$192$	0.192606	+	1.09232i	0.0139001	+	0.0788316i
$193$	11.0559	−	9.27700i	0.795821	−	0.667773i	−0.151358	−	0.988479i	$-0.548365\pi$
$193$	11.0559	−	9.27700i	0.795821	−	0.667773i	0.947179	+	0.320706i	$0.103920\pi$
$194$	11.1894	−	4.07261i	0.803353	−	0.292397i
$195$		0			0
$196$	13.2497	+	11.1179i	0.946410	+	0.794132i
$197$	−9.89999	+	17.1473i	−0.705345	+	1.22169i	0.261222	+	0.965279i	$0.415875\pi$
$197$	−9.89999	+	17.1473i	−0.705345	+	1.22169i	−0.966567	+	0.256415i	$0.917459\pi$
$198$	3.90335	+	6.76079i	0.277399	+	0.480469i
$199$	3.46951	−	19.6766i	0.245947	−	1.39484i	−0.572335	−	0.820020i	$-0.693962\pi$
$199$	3.46951	−	19.6766i	0.245947	−	1.39484i	0.818282	−	0.574817i	$-0.194927\pi$
$200$		0			0
$201$	−7.56577	−	13.1043i	−0.533648	−	0.924305i
$202$	0.722101	−	1.25072i	0.0508069	−	0.0880001i
$203$	−10.0611	−	8.44226i	−0.706150	−	0.592530i
$204$	5.23787	+	1.90643i	0.366724	+	0.133477i
$205$		0			0
$206$	3.41759	−	2.86770i	0.238115	−	0.199802i
$207$	−0.315447	−	1.78899i	−0.0219251	−	0.124343i
$208$	−2.63992			−0.183046
$209$	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	$0.788721\pi$
$212$	−4.30802	+	3.61486i	−0.295876	+	0.248269i
$213$	16.2577	−	5.91730i	1.11396	−	0.405447i
$214$	−7.38875	−	2.68928i	−0.505084	−	0.183836i
$215$		0			0
$216$	2.64523	−	4.58167i	0.179985	−	0.311743i
$217$	5.00874	+	8.67539i	0.340015	+	0.588924i
$218$	−0.437993	+	2.48398i	−0.0296646	+	0.168237i
$219$	2.42920	−	13.7767i	0.164150	−	0.930941i
$220$		0			0
$221$	−6.63332	+	11.4892i	−0.446205	+	0.772850i
$222$	−1.70027	−	1.42669i	−0.114114	−	0.0957533i
$223$	−21.7830	−	7.92835i	−1.45870	−	0.530922i	−0.513690	−	0.857976i	$-0.671722\pi$
$223$	−21.7830	−	7.92835i	−1.45870	−	0.530922i	−0.945006	+	0.327054i	$0.893944\pi$
$224$	4.63187	−	1.68586i	0.309480	−	0.112641i
$225$		0			0
$226$	−0.451163	−	2.55867i	−0.0300109	−	0.170200i
$227$	7.37892			0.489756			0.244878	−	0.969554i	$-0.421252\pi$
$227$	7.37892			0.489756			0.244878	+	0.969554i	$0.421252\pi$
$228$	1.26420	−	4.66657i	0.0837235	−	0.309051i
$229$	−13.2440			−0.875188			−0.437594	−	0.899173i	$-0.644169\pi$
$229$	−13.2440			−0.875188			−0.437594	+	0.899173i	$0.644169\pi$
$230$		0			0
$231$	−18.4749	+	15.5023i	−1.21556	+	1.01998i
$232$	−2.50384	+	0.911323i	−0.164385	+	0.0598313i
$233$	14.2271	+	5.17822i	0.932045	+	0.339237i	0.763020	−	0.646375i	$-0.223716\pi$
$233$	14.2271	+	5.17822i	0.932045	+	0.339237i	0.169025	+	0.985612i	$0.445938\pi$
$234$	3.57893	+	3.00308i	0.233962	+	0.196317i
$235$		0			0
$236$	−7.02687	−	12.1709i	−0.457410	−	0.792258i
$237$	−0.545962	+	3.09630i	−0.0354640	+	0.201126i
$238$	4.30140	−	24.3945i	0.278818	−	1.58126i
$239$	−5.84319	−	10.1207i	−0.377964	−	0.654653i	0.612802	−	0.790237i	$-0.290042\pi$
$239$	−5.84319	−	10.1207i	−0.377964	−	0.654653i	−0.990766	+	0.135583i	$0.956709\pi$
$240$		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	$0.587437\pi$
$242$	−7.94873	−	2.89310i	−0.510964	−	0.185976i
$243$	−14.3318	+	5.21633i	−0.919383	+	0.334628i
$244$	−11.1161	+	9.32754i	−0.711637	+	0.597135i
$245$		0			0
$246$	2.38915			0.152327
$247$	10.4156	+	4.89186i	0.662727	+	0.311261i
$248$	2.03230			0.129051
$249$	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	$0.710829\pi$
$252$	−8.19717	−	2.98353i	−0.516373	−	0.187945i
$253$	3.46865	+	2.91054i	0.218072	+	0.182984i
$254$	−10.3618	+	17.9471i	−0.650157	+	1.12610i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	0.0277309	−	0.157270i	0.00172981	−	0.00981023i	−0.983931	−	0.178551i	$-0.942859\pi$
$257$	0.0277309	−	0.157270i	0.00172981	−	0.00981023i	0.985660	+	0.168741i	$0.0539701\pi$
$258$	0.837633	+	1.45082i	0.0521488	+	0.0903243i
$259$	−4.93178	+	8.54209i	−0.306446	+	0.530780i
$260$		0			0
$261$	4.43113	+	1.61280i	0.274280	+	0.0998299i
$262$	1.63231	−	0.594111i	0.100844	−	0.0367043i
$263$	−7.09280	+	5.95157i	−0.437361	+	0.366990i	−0.834721	−	0.550673i	$-0.814371\pi$
$263$	−7.09280	+	5.95157i	−0.437361	+	0.366990i	0.397360	+	0.917663i	$0.369927\pi$
$264$	0.849627	+	4.81847i	0.0522909	+	0.296557i
$265$		0			0
$266$	−21.3986	−	1.93157i	−1.31203	−	0.118432i
$267$	11.1924			0.684962
$268$	2.36894	+	13.4349i	0.144706	+	0.820668i
$269$	9.55896	−	8.02092i	0.582820	−	0.489044i	−0.303052	−	0.952974i	$-0.598005\pi$
$269$	9.55896	−	8.02092i	0.582820	−	0.489044i	0.885872	+	0.463930i	$0.153561\pi$
$270$		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	$0.283566\pi$
$272$	−3.84967	−	3.23026i	−0.233421	−	0.195863i
$273$	−7.21657	+	12.4995i	−0.436766	+	0.756502i
$274$	1.24883	+	2.16303i	0.0754445	+	0.130674i
$275$		0			0
$276$	0.197705	−	1.12124i	0.0119004	−	0.0674907i
$277$	4.20592	+	7.28486i	0.252709	+	0.437705i	0.964271	−	0.264919i	$-0.0853451\pi$
$277$	4.20592	+	7.28486i	0.252709	+	0.437705i	−0.711562	+	0.702624i	$0.752012\pi$
$278$	−5.91604	+	10.2469i	−0.354821	+	0.614567i
$279$	−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	$0.621086\pi$
$282$	−1.52123	+	1.27647i	−0.0905882	+	0.0760125i
$283$	−2.21687	−	12.5725i	−0.131779	−	0.747357i	−0.977049	−	0.213016i	$-0.931671\pi$
$283$	−2.21687	−	12.5725i	−0.131779	−	0.747357i	0.845269	−	0.534340i	$-0.179440\pi$
$284$	−15.5981			−0.925579
$285$		0			0
$286$	−11.6453			−0.688600
$287$	−1.84368	−	10.4560i	−0.108829	−	0.617198i
$288$	−1.35570	+	1.13756i	−0.0798851	+	0.0670316i
$289$	−7.75671	+	2.82321i	−0.456277	+	0.166071i
$290$		0			0
$291$	−10.1175	−	8.48962i	−0.593100	−	0.497670i
$292$	−6.30614	+	10.9226i	−0.369039	+	0.639194i
$293$	−14.4554	−	25.0376i	−0.844496	−	1.46271i	−0.886058	−	0.463575i	$-0.846567\pi$
$293$	−14.4554	−	25.0376i	−0.844496	−	1.46271i	0.0415616	−	0.999136i	$-0.486767\pi$
$294$	3.33137	−	18.8931i	0.194289	−	1.10187i
$295$		0			0
$296$	1.00054	+	1.73298i	0.0581551	+	0.100728i
$297$	11.6687	−	20.2108i	0.677086	−	1.17275i
$298$	−15.4299	−	12.9472i	−0.893829	−	0.750011i
$299$	2.54639	+	0.926810i	0.147261	+	0.0535988i
$300$		0			0
$301$	5.70307	−	4.78544i	0.328719	−	0.275828i
$302$	−1.33339	−	7.56206i	−0.0767282	−	0.435147i
$303$	−1.60187			−0.0920251
$304$	−2.50999	+	3.56370i	−0.143958	+	0.204392i
$305$		0			0
$306$	1.54436	+	8.75849i	0.0882851	+	0.500690i
$307$	−17.9758	+	15.0835i	−1.02593	+	0.860860i	−0.990361	−	0.138507i	$-0.955770\pi$
$307$	−17.9758	+	15.0835i	−1.02593	+	0.860860i	−0.0355713	+	0.999367i	$0.511325\pi$
$308$	20.4322	−	7.43671i	1.16423	−	0.423746i
$309$	−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	$0.205072\pi$
$312$	1.46407	+	2.53584i	0.0828864	+	0.143563i
$313$	2.01689	−	11.4384i	0.114001	−	0.646534i	−0.873238	−	0.487293i	$-0.837984\pi$
$313$	2.01689	−	11.4384i	0.114001	−	0.646534i	0.987240	−	0.159241i	$-0.0509046\pi$
$314$	1.00728	−	5.71258i	0.0568442	−	0.322379i
$315$		0			0
$316$	1.41730	−	2.45484i	0.0797295	−	0.138096i
$317$	1.71306	+	1.43742i	0.0962148	+	0.0807338i	0.689626	−	0.724165i	$-0.257775\pi$
$317$	1.71306	+	1.43742i	0.0962148	+	0.0807338i	−0.593411	+	0.804899i	$0.702219\pi$
$318$	5.86150	+	2.13341i	0.328697	+	0.119636i
$319$	−11.0450	+	4.02005i	−0.618401	+	0.225080i
$320$		0			0
$321$	1.51445	+	8.58887i	0.0845283	+	0.479384i
$322$	−5.05962			−0.281962
$323$	9.20277	+	19.8783i	0.512056	+	1.10606i
$324$	−0.558833			−0.0310463
$325$		0			0
$326$	8.21542	−	6.89356i	0.455010	−	0.381799i
$327$	2.62895	−	0.956860i	0.145381	−	0.0529145i
$328$	−2.02409	−	0.736709i	−0.111762	−	0.0406779i
$329$	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	$0.828878\pi$
$332$	1.26469	−	7.17241i	0.0694089	−	0.393637i
$333$	0.614953	−	3.48757i	0.0336992	−	0.191118i
$334$	4.94659	+	8.56775i	0.270666	+	0.468806i
$335$		0			0
$336$	−4.18816	−	3.51429i	−0.228483	−	0.191720i
$337$	−14.1717	−	5.15806i	−0.771979	−	0.280977i	−0.0741552	−	0.997247i	$-0.523626\pi$
$337$	−14.1717	−	5.15806i	−0.771979	−	0.280977i	−0.697824	+	0.716269i	$0.745848\pi$
$338$	5.66711	−	2.06266i	0.308250	−	0.112194i
$339$	−2.20758	+	1.85238i	−0.119899	+	0.100607i
$340$		0			0
$341$	8.96493			0.485478
$342$	7.45672	−	1.97601i	0.403213	−	0.106850i
$343$	−50.7518			−2.74034
$344$	−0.262274	−	1.48743i	−0.0141409	−	0.0801968i
$345$		0			0
$346$	−14.7550	+	5.37038i	−0.793234	+	0.288714i
$347$	31.7415	+	11.5530i	1.70398	+	0.620196i	0.996268	−	0.0863093i	$-0.0275073\pi$
$347$	31.7415	+	11.5530i	1.70398	+	0.620196i	0.707707	+	0.706506i	$0.249730\pi$
$348$	2.26399	+	1.89971i	0.121363	+	0.101835i
$349$	0.0164139	−	0.0284297i	0.000878615	−	0.00152181i	−0.865586	−	0.500761i	$-0.833054\pi$
$349$	0.0164139	−	0.0284297i	0.000878615	−	0.00152181i	0.866464	+	0.499239i	$0.166387\pi$
$350$		0			0
$351$	2.42524	−	13.7542i	0.129450	−	0.734146i
$352$	0.766000	−	4.34420i	0.0408280	−	0.231547i
$353$	−0.140488	−	0.243332i	−0.00747740	−	0.0129512i	0.862262	−	0.506462i	$-0.169047\pi$
$353$	−0.140488	−	0.243332i	−0.00747740	−	0.0129512i	−0.869740	+	0.493510i	$0.835713\pi$
$354$	−7.79401	+	13.4996i	−0.414247	+	0.717497i
$355$		0			0
$356$	−9.48219	−	3.45123i	−0.502555	−	0.182915i
$357$	−25.8181	+	9.39703i	−1.36644	+	0.497344i
$358$	7.74689	−	6.50041i	0.409436	−	0.343557i
$359$	2.29364	+	13.0079i	0.121054	+	0.686530i	0.983574	+	0.180507i	$0.0577738\pi$
$359$	2.29364	+	13.0079i	0.121054	+	0.686530i	−0.862520	+	0.506023i	$0.831115\pi$
$360$		0			0
$361$	16.5066	−	9.40916i	0.868768	−	0.495219i
$362$	2.67870			0.140789
$363$	1.62923	+	9.23981i	0.0855122	+	0.484964i
$364$	9.96816	−	8.36428i	0.522474	−	0.438408i
$365$		0			0
$366$	15.1246	+	5.50492i	0.790577	+	0.287747i
$367$	−7.89363	−	6.62354i	−0.412044	−	0.345746i	0.413083	−	0.910693i	$-0.364452\pi$
$367$	−7.89363	−	6.62354i	−0.412044	−	0.345746i	−0.825127	+	0.564948i	$0.808896\pi$
$368$	−0.513237	+	0.888952i	−0.0267543	+	0.0463398i
$369$	1.90600	+	3.30128i	0.0992222	+	0.171858i
$370$		0			0
$371$	4.81354	−	27.2989i	0.249906	−	1.41729i
$372$	−1.12709	−	1.95217i	−0.0584368	−	0.101215i
$373$	14.1948	−	24.5861i	0.734977	−	1.27302i	−0.219756	−	0.975555i	$-0.570526\pi$
$373$	14.1948	−	24.5861i	0.734977	−	1.27302i	0.954733	−	0.297463i	$-0.0961406\pi$
$374$	−16.9817	−	14.2494i	−0.878105	−	0.736818i
$375$		0			0
$376$	1.68240	−	0.612343i	0.0867631	−	0.0315792i
$377$	−5.38848	+	4.52147i	−0.277521	+	0.232867i
$378$	4.52829	+	25.6812i	0.232910	+	1.32090i
$379$	19.1984			0.986157			0.493079	−	0.869985i	$-0.335871\pi$
$379$	19.1984			0.986157			0.493079	+	0.869985i	$0.335871\pi$
$380$		0			0
$381$	22.9860			1.17761
$382$	0.651355	+	3.69402i	0.0333262	+	0.189002i
$383$	−15.9934	+	13.4201i	−0.817226	+	0.685734i	−0.952321	−	0.305099i	$-0.901311\pi$
$383$	−15.9934	+	13.4201i	−0.817226	+	0.685734i	0.135095	+	0.990833i	$0.456866\pi$
$384$	−1.04228	+	0.379360i	−0.0531887	+	0.0193591i
$385$		0			0
$386$	11.0559	+	9.27700i	0.562731	+	0.472187i
$387$	−1.33648	+	2.31485i	−0.0679371	+	0.117671i
$388$	5.95376	+	10.3122i	0.302256	+	0.523523i
$389$	2.69629	−	15.2914i	0.136707	−	0.775304i	−0.836949	−	0.547281i	$-0.815663\pi$
$389$	2.69629	−	15.2914i	0.136707	−	0.775304i	0.973656	−	0.228023i	$-0.0732261\pi$
$390$		0			0
$391$	2.57921	+	4.46733i	0.130436	+	0.225923i
$392$	−8.64815	+	14.9790i	−0.436798	+	0.756556i
$393$	−1.47594	−	1.23846i	−0.0744515	−	0.0624722i
$394$	−18.6059	−	6.77199i	−0.937351	−	0.341168i
$395$		0			0
$396$	−5.98027	+	5.01804i	−0.300520	+	0.252166i
$397$	−0.836373	−	4.74331i	−0.0419764	−	0.238060i	0.956600	−	0.291405i	$-0.0941227\pi$
$397$	−0.836373	−	4.74331i	−0.0419764	−	0.238060i	−0.998576	+	0.0533453i	$0.983012\pi$
$398$	19.9801			1.00151
$399$	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	$-0.156011\pi$
$402$	11.5914	−	9.72636i	0.578128	−	0.485107i
$403$	5.04156	−	1.83498i	0.251138	−	0.0914068i
$404$	1.35711	+	0.493947i	0.0675186	+	0.0245748i
$405$		0			0
$406$	6.56691	−	11.3742i	0.325910	−	0.564493i
$407$	4.41359	+	7.64456i	0.218774	+	0.378927i
$408$	−0.967919	+	5.48934i	−0.0479191	+	0.271763i
$409$	−2.99828	+	17.0041i	−0.148255	+	0.840797i	0.816440	+	0.577430i	$0.195944\pi$
$409$	−2.99828	+	17.0041i	−0.148255	+	0.840797i	−0.964696	+	0.263367i	$0.915167\pi$
$410$		0			0
$411$	1.38517	−	2.39918i	0.0683253	−	0.118343i
$412$	3.41759	+	2.86770i	0.168373	+	0.141282i
$413$	65.0950	+	23.6926i	3.20312	+	1.16584i
$414$	1.70703	−	0.621309i	0.0838961	−	0.0305357i
$415$		0			0
$416$	−0.458418	−	2.59982i	−0.0224758	−	0.127466i
$417$	13.1238			0.642677
$418$	−11.0721	+	15.7203i	−0.541556	+	0.768903i
$419$	18.2962			0.893827			0.446914	−	0.894577i	$-0.352523\pi$
$419$	18.2962			0.893827			0.446914	+	0.894577i	$0.352523\pi$
$420$		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	$0.0384462\pi$
$422$	−12.8291	+	4.66941i	−0.624510	+	0.227303i
$423$	−2.97740	−	1.08368i	−0.144766	−	0.0526905i
$424$	−4.30802	−	3.61486i	−0.209216	−	0.175553i
$425$		0			0
$426$	8.65052	+	14.9831i	0.419119	+	0.725935i
$427$	12.4205	−	70.4403i	0.601072	−	3.40885i
$428$	1.36539	−	7.74349i	0.0659984	−	0.374296i
$429$	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	$0.600715\pi$
$432$	4.97141	+	1.80944i	0.239187	+	0.0870569i
$433$	13.2327	−	4.81630i	0.635922	−	0.231457i	−0.00388467	−	0.999992i	$-0.501237\pi$
$433$	13.2327	−	4.81630i	0.635922	−	0.231457i	0.639807	+	0.768536i	$0.279014\pi$
$434$	−7.67383	+	6.43911i	−0.368356	+	0.309087i
$435$		0			0
$436$	−2.52230			−0.120796
$437$	3.67219	−	2.55624i	0.175665	−	0.122282i
$438$	13.9892			0.668430
$439$	1.61433	+	9.15534i	0.0770479	+	0.436961i	0.998791	+	0.0491593i	$0.0156542\pi$
$439$	1.61433	+	9.15534i	0.0770479	+	0.436961i	−0.921743	+	0.387801i	$0.873235\pi$
$440$		0			0
$441$	28.7639	−	10.4692i	1.36971	−	0.498533i
$442$	−12.4666	−	4.53746i	−0.592974	−	0.215825i
$443$	9.11448	+	7.64795i	0.433042	+	0.363365i	0.833098	−	0.553125i	$-0.186565\pi$
$443$	9.11448	+	7.64795i	0.433042	+	0.363365i	−0.400056	+	0.916491i	$0.631009\pi$
$444$	1.10977	−	1.92218i	0.0526673	−	0.0912225i
$445$		0			0
$446$	4.02533	−	22.8288i	0.190605	−	1.08097i
$447$	−3.87952	+	22.0019i	−0.183495	+	1.04065i
$448$	2.46456	+	4.26875i	0.116440	+	0.201680i
$449$	9.95157	−	17.2366i	0.469644	−	0.813446i	−0.529754	−	0.848151i	$-0.677716\pi$
$449$	9.95157	−	17.2366i	0.469644	−	0.813446i	0.999398	+	0.0347048i	$0.0110491\pi$
$450$		0			0
$451$	−8.92871	−	3.24978i	−0.420436	−	0.153026i
$452$	2.44146	−	0.888617i	0.114836	−	0.0417970i
$453$	−6.52442	+	5.47464i	−0.306544	+	0.257221i
$454$	1.28134	+	7.26682i	0.0601361	+	0.341049i
$455$		0			0
$456$	4.81520	+	0.434651i	0.225492	+	0.0203544i
$457$	36.8095			1.72188			0.860939	−	0.508708i	$-0.169877\pi$
$457$	36.8095			1.72188			0.860939	+	0.508708i	$0.169877\pi$
$458$	−2.29980	−	13.0428i	−0.107462	−	0.609449i
$459$	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	$0.862178\pi$
$462$	−18.4749	−	15.5023i	−0.859530	−	0.721232i
$463$	−11.1988	+	19.3969i	−0.520454	+	0.901452i	0.479263	+	0.877671i	$0.340904\pi$
$463$	−11.1988	+	19.3969i	−0.520454	+	0.901452i	−0.999717	+	0.0237813i	$0.992429\pi$
$464$	−1.33227	−	2.30755i	−0.0618489	−	0.107125i
$465$		0			0
$466$	−2.62905	+	14.9101i	−0.121789	+	0.690697i
$467$	−7.39165	−	12.8027i	−0.342045	−	0.592439i	0.642768	−	0.766061i	$-0.277786\pi$
$467$	−7.39165	−	12.8027i	−0.342045	−	0.592439i	−0.984812	+	0.173623i	$0.944453\pi$
$468$	−2.33598	+	4.04604i	−0.107981	+	0.187028i
$469$	−51.5119	−	43.2236i	−2.37860	−	1.99588i
$470$		0			0
$471$	−6.04597	+	2.20055i	−0.278583	+	0.101396i
$472$	10.7658	−	9.03357i	0.495535	−	0.415804i
$473$	−1.15695	−	6.56137i	−0.0531965	−	0.301692i
$474$	−3.14407			−0.144412
$475$		0			0
$476$	24.7708			1.13537
$477$	1.72823	+	9.80130i	0.0791303	+	0.448770i
$478$	8.95228	−	7.51186i	0.409468	−	0.343584i
$479$	25.2882	−	9.20416i	1.15545	−	0.420549i	0.307979	−	0.951393i	$-0.400347\pi$
$479$	25.2882	−	9.20416i	1.15545	−	0.420549i	0.847469	+	0.530844i	$0.178125\pi$
$480$		0			0
$481$	4.04677	+	3.39564i	0.184517	+	0.154828i
$482$	−6.37885	+	11.0485i	−0.290549	+	0.503245i
$483$	2.80600	+	4.86013i	0.127677	+	0.221144i
$484$	1.46887	−	8.33035i	0.0667667	−	0.378652i
$485$		0			0
$486$	−7.62577	−	13.2082i	−0.345912	−	0.599137i
$487$	−7.09140	+	12.2827i	−0.321342	+	0.556581i	−0.980765	−	0.195191i	$-0.937467\pi$
$487$	−7.09140	+	12.2827i	−0.321342	+	0.556581i	0.659423	+	0.751772i	$0.270801\pi$
$488$	−11.1161	−	9.32754i	−0.503204	−	0.422238i
$489$	−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	$0.207381\pi$
$492$	0.414871	+	2.35285i	0.0187039	+	0.106075i
$493$	−13.3903			−0.603069
$494$	−3.00889	+	11.1068i	−0.135376	+	0.499719i
$495$		0			0
$496$	0.352906	+	2.00143i	0.0158459	+	0.0898667i
$497$	58.8975	−	49.4209i	2.64191	−	2.21683i
$498$	−7.59100	+	2.76290i	−0.340161	+	0.123808i
$499$	11.5577	+	4.20666i	0.517394	+	0.188316i	0.587501	−	0.809223i	$-0.300112\pi$
$499$	11.5577	+	4.20666i	0.517394	+	0.188316i	−0.0701069	+	0.997539i	$0.522334\pi$
$500$		0			0
$501$	5.48663	−	9.50312i	0.245124	−	0.424568i
$502$	−13.4282	−	23.2583i	−0.599329	−	1.03807i
$503$	4.32801	−	24.5454i	0.192976	−	1.09442i	−0.722295	−	0.691586i	$-0.756913\pi$
$503$	4.32801	−	24.5454i	0.192976	−	1.09442i	0.915271	−	0.402839i	$-0.131976\pi$
$504$	1.51478	−	8.59073i	0.0674735	−	0.382661i
$505$		0			0
$506$	−2.26400	+	3.92136i	−0.100647	+	0.174326i
$507$	−5.12424	−	4.29974i	−0.227575	−	0.190958i
$508$	−19.4738	−	7.08788i	−0.864010	−	0.314474i
$509$	12.5923	−	4.58321i	0.558142	−	0.203147i	−0.0475184	−	0.998870i	$-0.515131\pi$
$509$	12.5923	−	4.58321i	0.558142	−	0.203147i	0.605660	+	0.795723i	$0.292909\pi$
$510$		0			0
$511$	−10.7953	−	61.2231i	−0.477555	−	2.70835i
$512$	1.00000			0.0441942
$513$	−16.2613	−	16.3512i	−0.717954	−	0.721922i
$514$	0.159696			0.00704389
$515$		0			0
$516$	−1.28333	+	1.07684i	−0.0564954	+	0.0474053i
$517$	7.42143	−	2.70118i	0.326394	−	0.118798i
$518$	−9.26871	−	3.37353i	−0.407244	−	0.148225i
$519$	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	$0.841474\pi$
$522$	−0.818841	+	4.64388i	−0.0358397	+	0.203257i
$523$	1.63636	−	9.28028i	0.0715532	−	0.405798i	−0.927903	−	0.372822i	$-0.878390\pi$
$523$	1.63636	−	9.28028i	0.0715532	−	0.405798i	0.999456	−	0.0329765i	$-0.0104986\pi$
$524$	0.868533	+	1.50434i	0.0379420	+	0.0657175i
$525$		0			0
$526$	−7.09280	−	5.95157i	−0.309261	−	0.259501i
$527$	9.59718	+	3.49309i	0.418060	+	0.152161i
$528$	−4.59773	+	1.67344i	−0.200091	+	0.0728271i
$529$	−16.8119	+	14.1068i	−0.730951	+	0.613341i
$530$		0			0
$531$	−24.8714			−1.07933
$532$	−1.81359	−	21.4089i	−0.0786293	−	0.928193i
$533$	−5.68637			−0.246304
$534$	1.94353	+	11.0223i	0.0841050	+	0.476983i
$535$		0			0
$536$	−12.8194	+	4.66590i	−0.553716	+	0.201536i
$537$	−10.5404	−	3.83640i	−0.454853	−	0.165553i
$538$	9.55896	+	8.02092i	0.412116	+	0.345807i
$539$	−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	$0.699562\pi$
$542$	−4.89846	+	27.7806i	−0.210407	+	1.19328i
$543$	−1.48557	−	2.57308i	−0.0637520	−	0.110422i
$544$	2.51269	−	4.35211i	0.107731	−	0.186595i
$545$		0			0
$546$	−13.5627	−	4.93642i	−0.580430	−	0.211259i
$547$	26.4147	−	9.61418i	1.12941	−	0.411073i	0.291334	−	0.956622i	$-0.405901\pi$
$547$	26.4147	−	9.61418i	1.12941	−	0.411073i	0.838079	+	0.545549i	$0.183679\pi$
$548$	−1.91332	+	1.60546i	−0.0817328	+	0.0685820i
$549$	4.45942	+	25.2906i	0.190323	+	1.07938i
$550$		0			0
$551$	0.980372	+	11.5730i	0.0417653	+	0.493025i
$552$	1.13854			0.0484594
$553$	2.42623	+	13.7599i	0.103174	+	0.585129i
$554$	−6.44384	+	5.40702i	−0.273772	+	0.229722i
$555$		0			0
$556$	−11.1185	−	4.04681i	−0.471530	−	0.171623i
$557$	−9.45200	−	7.93117i	−0.400494	−	0.336055i	0.420190	−	0.907436i	$-0.361963\pi$
$557$	−9.45200	−	7.93117i	−0.400494	−	0.336055i	−0.820685	+	0.571381i	$0.806408\pi$
$558$	1.79832	−	3.11478i	0.0761289	−	0.131859i
$559$	−1.99364	−	3.45308i	−0.0843218	−	0.146050i
$560$		0			0
$561$	−4.26971	+	24.2147i	−0.180267	+	1.02235i
$562$	−11.1721	−	19.3507i	−0.471268	−	0.816259i
$563$	−7.22347	+	12.5114i	−0.304433	+	0.527293i	−0.977135	−	0.212620i	$-0.931800\pi$
$563$	−7.22347	+	12.5114i	−0.304433	+	0.527293i	0.672702	+	0.739914i	$0.265134\pi$
$564$	−1.52123	−	1.27647i	−0.0640555	−	0.0537490i
$565$		0			0
$566$	11.9965	−	4.36638i	0.504252	−	0.183533i
$567$	2.11012	−	1.77060i	0.0886166	−	0.0743581i
$568$	−2.70859	−	15.3612i	−0.113650	−	0.644540i
$569$	31.8303			1.33439			0.667197	−	0.744881i	$-0.267494\pi$
$569$	31.8303			1.33439			0.667197	+	0.744881i	$0.267494\pi$
$570$		0			0
$571$	−9.10909			−0.381204			−0.190602	−	0.981667i	$-0.561044\pi$
$571$	−9.10909			−0.381204			−0.190602	+	0.981667i	$0.561044\pi$
$572$	−2.02218	−	11.4684i	−0.0845516	−	0.479516i
$573$	3.18714	−	2.67432i	0.133145	−	0.111722i
$574$	9.97700	−	3.63133i	0.416432	−	0.151569i
$575$		0			0
$576$	−1.35570	−	1.13756i	−0.0564873	−	0.0473985i
$577$	5.84857	−	10.1300i	0.243479	−	0.421718i	−0.718224	−	0.695812i	$-0.755045\pi$
$577$	5.84857	−	10.1300i	0.243479	−	0.421718i	0.961703	+	0.274094i	$0.0883779\pi$
$578$	−4.12726	−	7.14863i	−0.171671	−	0.297344i
$579$	2.77978	−	15.7649i	0.115524	−	0.655167i
$580$		0			0
$581$	17.9496	+	31.0896i	0.744674	+	1.28981i
$582$	6.60375	−	11.4380i	0.273734	−	0.474122i
$583$	−19.0036	−	15.9459i	−0.787050	−	0.660413i
$584$	−11.8517	−	4.31365i	−0.490425	−	0.178500i
$585$		0			0
$586$	22.1470	−	18.5836i	0.914885	−	0.767680i
$587$	5.33986	+	30.2839i	0.220400	+	1.24995i	0.871287	+	0.490774i	$0.163286\pi$
$587$	5.33986	+	30.2839i	0.220400	+	1.24995i	−0.650887	+	0.759175i	$0.725603\pi$
$588$	19.1846			0.791160
$589$	2.31635	−	8.55040i	0.0954435	−	0.352313i
$590$		0			0
$591$	3.81359	+	21.6280i	0.156870	+	0.889655i
$592$	−1.53291	+	1.28627i	−0.0630023	+	0.0528652i
$593$	5.82573	−	2.12039i	0.239234	−	0.0870741i	−0.219621	−	0.975585i	$-0.570482\pi$
$593$	5.82573	−	2.12039i	0.239234	−	0.0870741i	0.458855	+	0.888511i	$0.348260\pi$
$594$	21.9300	+	7.98186i	0.899798	+	0.327500i
$595$		0			0
$596$	10.0711	−	17.4437i	0.412530	−	0.714523i
$597$	−11.0807	−	19.1924i	−0.453503	−	0.785491i
$598$	−0.470554	+	2.66864i	−0.0192424	+	0.109129i
$599$	−5.09116	+	28.8734i	−0.208019	+	1.17973i	0.684599	+	0.728920i	$0.259978\pi$
$599$	−5.09116	+	28.8734i	−0.208019	+	1.17973i	−0.892618	+	0.450815i	$0.851134\pi$
$600$		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	$-0.227466\pi$
$602$	5.70307	+	4.78544i	0.232440	+	0.195040i
$603$	22.6870	+	8.25740i	0.923887	+	0.336267i
$604$	7.21563	−	2.62627i	0.293600	−	0.106862i
$605$		0			0
$606$	−0.278162	−	1.57754i	−0.0112996	−	0.0640830i
$607$	−25.4409			−1.03262			−0.516308	−	0.856403i	$-0.672694\pi$
$607$	−25.4409			−1.03262			−0.516308	+	0.856403i	$0.672694\pi$
$608$	−3.94541	−	1.85303i	−0.160008	−	0.0751503i
$609$	−14.5677			−0.590312
$610$		0			0
$611$	3.62066	−	3.03810i	0.146476	−	0.122908i
$612$	−8.35725	+	3.04179i	−0.337822	+	0.122957i
$613$	−28.6870	−	10.4412i	−1.15866	−	0.421717i	−0.310041	−	0.950723i	$-0.600343\pi$
$613$	−28.6870	−	10.4412i	−1.15866	−	0.421717i	−0.848618	+	0.529006i	$0.822565\pi$
$614$	−17.9758	−	15.0835i	−0.725444	−	0.608720i
$615$		0			0
$616$	10.8717	+	18.8304i	0.438035	+	0.758698i
$617$	−1.05883	+	6.00494i	−0.0426270	+	0.241750i	−0.998675	−	0.0514603i	$-0.983612\pi$
$617$	−1.05883	+	6.00494i	−0.0426270	+	0.241750i	0.956048	+	0.293210i	$0.0947235\pi$
$618$	0.859283	−	4.87323i	0.0345654	−	0.196030i
$619$	−9.07568	−	15.7195i	−0.364782	−	0.631821i	0.623959	−	0.781457i	$-0.285523\pi$
$619$	−9.07568	−	15.7195i	−0.364782	−	0.631821i	−0.988741	+	0.149636i	$0.952190\pi$
$620$		0			0
$621$	−4.16002	−	3.49067i	−0.166936	−	0.140076i
$622$	−3.98914	−	1.45193i	−0.159950	−	0.0582171i
$623$	46.7389	−	17.0116i	1.87255	−	0.681554i
$624$	−2.24308	+	1.88217i	−0.0897950	+	0.0753469i
$625$		0			0
$626$	11.6148			0.464221
$627$	21.2409	+	1.91734i	0.848279	+	0.0765712i
$628$	5.80070			0.231473
$629$	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	$0.491316\pi$
$632$	2.66366	+	0.969492i	0.105955	+	0.0385643i
$633$	11.6001	+	9.73368i	0.461064	+	0.386879i
$634$	−1.11812	+	1.93664i	−0.0444061	+	0.0769137i
$635$		0			0
$636$	−1.08316	+	6.14292i	−0.0429502	+	0.243582i
$637$	−7.92893	+	44.9672i	−0.314156	+	1.78167i
$638$	−5.87692	−	10.1791i	−0.232669	−	0.402995i
$639$	−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	$0.365806\pi$
$642$	−8.19540	+	2.98288i	−0.323447	+	0.117725i
$643$	6.39841	−	5.36891i	0.252329	−	0.211729i	−0.507846	−	0.861448i	$-0.669558\pi$
$643$	6.39841	−	5.36891i	0.252329	−	0.211729i	0.760174	+	0.649719i	$0.225113\pi$
$644$	−0.878594	−	4.98275i	−0.0346215	−	0.196348i
$645$		0			0
$646$	−17.9782	+	12.5148i	−0.707343	+	0.492387i
$647$	12.0057			0.471991			0.235995	−	0.971754i	$-0.424165\pi$
$647$	12.0057			0.471991			0.235995	+	0.971754i	$0.424165\pi$
$648$	−0.0970404	−	0.550344i	−0.00381211	−	0.0216195i
$649$	47.4903	−	39.8491i	1.86416	−	1.56421i
$650$		0			0
$651$	10.4410	+	3.80023i	0.409216	+	0.148943i
$652$	8.21542	+	6.89356i	0.321741	+	0.269973i
$653$	−19.5180	+	33.8062i	−0.763798	+	1.32294i	0.177081	+	0.984196i	$0.443334\pi$
$653$	−19.5180	+	33.8062i	−0.763798	+	1.32294i	−0.940880	+	0.338741i	$0.889999\pi$
$654$	1.39884	+	2.42285i	0.0546988	+	0.0947411i
$655$		0			0
$656$	0.374037	−	2.12127i	0.0146037	−	0.0828216i
$657$	11.1602	+	19.3300i	0.435401	+	0.754136i
$658$	−4.41248	+	7.64265i	−0.172017	+	0.297941i
$659$	−3.38617	−	2.84133i	−0.131906	−	0.110683i	0.574448	−	0.818541i	$-0.305217\pi$
$659$	−3.38617	−	2.84133i	−0.131906	−	0.110683i	−0.706354	+	0.707859i	$0.749661\pi$
$660$		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	$0.353770\pi$
$662$	−0.390122	+	0.327351i	−0.0151625	+	0.0127229i
$663$	2.55523	+	14.4914i	0.0992370	+	0.562801i
$664$	7.28306			0.282638
$665$		0			0
$666$	3.54137			0.137225
$667$	0.474940	+	2.69352i	0.0183898	+	0.104294i
$668$	−7.57862	+	6.35922i	−0.293226	+	0.246046i
$669$	−24.1611	+	8.79392i	−0.934122	+	0.339992i
$670$		0			0
$671$	−49.0357	−	41.1458i	−1.89300	−	1.58842i
$672$	2.73363	−	4.73478i	0.105452	−	0.182648i
$673$	8.18457	+	14.1761i	0.315492	+	0.546448i	0.979542	−	0.201240i	$-0.0644971\pi$
$673$	8.18457	+	14.1761i	0.315492	+	0.546448i	−0.664050	+	0.747688i	$0.731164\pi$
$674$	2.61882	−	14.8520i	0.100873	−	0.572079i
$675$		0			0
$676$	3.01541	+	5.22284i	0.115977	+	0.200878i
$677$	−9.37064	+	16.2304i	−0.360143	+	0.623786i	−0.987984	−	0.154556i	$-0.950605\pi$
$677$	−9.37064	+	16.2304i	−0.360143	+	0.623786i	0.627841	+	0.778341i	$0.283939\pi$
$678$	−2.20758	−	1.85238i	−0.0847816	−	0.0711402i
$679$	−55.1540	−	20.0744i	−2.11662	−	0.770386i
$680$		0			0
$681$	6.26969	−	5.26089i	0.240255	−	0.201598i
$682$	1.55674	+	8.82873i	0.0596108	+	0.338070i
$683$	−11.1202			−0.425501			−0.212751	−	0.977107i	$-0.568242\pi$
$683$	−11.1202			−0.425501			−0.212751	+	0.977107i	$0.568242\pi$
$684$	3.24084	+	7.00030i	0.123917	+	0.267663i
$685$		0			0
$686$	−8.81296	−	49.9808i	−0.336480	−	1.90828i
$687$	−11.2531	+	9.44247i	−0.429333	+	0.360253i
$688$	1.41929	−	0.516578i	0.0541098	−	0.0196944i
$689$	−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	$0.239693\pi$
$692$	−7.85098	−	13.5983i	−0.298449	−	0.516929i
$693$	6.68201	−	37.8956i	0.253829	−	1.43953i
$694$	−5.86560	+	33.2655i	−0.222655	+	1.26274i
$695$		0			0
$696$	−1.47771	+	2.55947i	−0.0560126	+	0.0970166i
$697$	−8.29216	−	6.95795i	−0.314088	−	0.263551i
$698$	0.0308480	+	0.0112278i	0.00116761	+	0.000424977i
$699$	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	$0.821724\pi$
$702$	13.9664			0.527128
$703$	8.43146	−	2.23432i	0.317999	−	0.0842688i
$704$	4.41122			0.166254
$705$		0			0
$706$	0.215239	−	0.180607i	0.00810064	−	0.00679725i
$707$	−6.68935	+	2.43473i	−0.251579	+	0.0915673i
$708$	−14.6480	−	5.33142i	−0.550504	−	0.200367i
$709$	−9.27123	−	7.77949i	−0.348188	−	0.292165i	0.451874	−	0.892082i	$-0.350756\pi$
$709$	−9.27123	−	7.77949i	−0.348188	−	0.292165i	−0.800062	+	0.599917i	$0.795200\pi$
$710$		0			0
$711$	−2.50825	−	4.34442i	−0.0940667	−	0.162928i
$712$	1.75224	−	9.93743i	0.0656679	−	0.372421i
$713$	0.362248	−	2.05441i	0.0135663	−	0.0769383i
$714$	−13.7375	−	23.7941i	−0.514115	−	0.890473i
$715$		0			0
$716$	7.74689	+	6.50041i	0.289515	+	0.242932i
$717$	−12.1805	−	4.43334i	−0.454889	−	0.165566i
$718$	−12.4120	+	4.51759i	−0.463211	+	0.168595i
$719$	22.9902	−	19.2911i	0.857389	−	0.719435i	−0.104015	−	0.994576i	$-0.533169\pi$
$719$	22.9902	−	19.2911i	0.857389	−	0.719435i	0.961404	+	0.275141i	$0.0887245\pi$
$720$		0			0
$721$	−21.9906			−0.818972
$722$	12.1326	+	14.6219i	0.451527	+	0.544172i
$723$	14.1505			0.526263
$724$	0.465151	+	2.63800i	0.0172872	+	0.0980407i
$725$		0			0
$726$	−8.81652	+	3.20895i	−0.327212	+	0.119095i
$727$	−39.5954	−	14.4115i	−1.46851	−	0.534494i	−0.520815	−	0.853669i	$-0.674372\pi$
$727$	−39.5954	−	14.4115i	−1.46851	−	0.534494i	−0.947696	+	0.319175i	$0.896594\pi$
$728$	9.96816	+	8.36428i	0.369445	+	0.310001i
$729$	−9.29655	+	16.1021i	−0.344317	+	0.596374i
$730$		0			0
$731$	1.31803	−	7.47490i	0.0487490	−	0.276469i
$732$	−2.79492	+	15.8508i	−0.103303	+	0.585862i
$733$	−4.18069	−	7.24116i	−0.154417	−	0.267458i	0.778429	−	0.627732i	$-0.216017\pi$
$733$	−4.18069	−	7.24116i	−0.154417	−	0.267458i	−0.932847	+	0.360274i	$0.882683\pi$
$734$	5.15220	−	8.92387i	0.190171	−	0.329386i
$735$		0			0
$736$	−0.964570	−	0.351075i	−0.0355545	−	0.0129408i
$737$	−56.5494	+	20.5823i	−2.08302	+	0.758159i
$738$	−2.92016	+	2.45030i	−0.107492	+	0.0901969i
$739$	−3.03167	−	17.1935i	−0.111522	−	0.632472i	−0.988414	−	0.151784i	$-0.951498\pi$
$739$	−3.03167	−	17.1935i	−0.111522	−	0.632472i	0.876892	−	0.480688i	$-0.159613\pi$
$740$		0			0
$741$	12.3376	−	3.26943i	0.453232	−	0.120105i
$742$	27.7200			1.01763
$743$	2.72242	+	15.4396i	0.0998758	+	0.566424i	0.993144	+	0.116899i	$0.0372954\pi$
$743$	2.72242	+	15.4396i	0.0998758	+	0.566424i	−0.893268	+	0.449524i	$0.851593\pi$
$744$	1.72680	−	1.44896i	0.0633075	−	0.0531213i
$745$		0			0
$746$	26.6774	+	9.70980i	0.976731	+	0.355501i
$747$	−9.87361	−	8.28494i	−0.361257	−	0.303130i
$748$	11.0840	−	19.1981i	0.405273	−	0.701953i
$749$	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	$0.0697815\pi$
$752$	0.895185	+	1.55051i	0.0326441	+	0.0565412i
$753$	−14.8942	+	25.7975i	−0.542774	+	0.940111i
$754$	−5.38848	−	4.52147i	−0.196237	−	0.164662i
$755$		0			0
$756$	−24.5047	+	8.91898i	−0.891228	+	0.324380i
$757$	−21.2038	+	17.7921i	−0.770664	+	0.646664i	−0.940879	−	0.338743i	$-0.889998\pi$
$757$	−21.2038	+	17.7921i	−0.770664	+	0.646664i	0.170215	+	0.985407i	$0.445554\pi$
$758$	3.33377	+	18.9068i	0.121088	+	0.686725i
$759$	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	$0.717058\pi$
$762$	3.99148	+	22.6368i	0.144596	+	0.820046i
$763$	9.52404	−	7.99162i	0.344793	−	0.289316i
$764$	−3.52479	+	1.28292i	−0.127522	+	0.0464143i
$765$		0			0
$766$	−15.9934	−	13.4201i	−0.577866	−	0.484887i
$767$	18.5504	−	32.1302i	0.669815	−	1.16015i
$768$	−0.554587	−	0.960572i	−0.0200119	−	0.0346617i
$769$	−1.17313	+	6.65313i	−0.0423040	+	0.239918i	−0.998626	−	0.0523962i	$-0.983314\pi$
$769$	−1.17313	+	6.65313i	−0.0423040	+	0.239918i	0.956322	+	0.292314i	$0.0944252\pi$
$770$		0			0
$771$	−0.0885653	−	0.153400i	−0.00318960	−	0.00552455i
$772$	−7.21623	+	12.4989i	−0.259718	+	0.449844i
$773$	−9.27086	−	7.77917i	−0.333450	−	0.279797i	0.460654	−	0.887580i	$-0.347615\pi$
$773$	−9.27086	−	7.77917i	−0.333450	−	0.279797i	−0.794104	+	0.607782i	$0.792059\pi$
$774$	−2.51176	−	0.914207i	−0.0902834	−	0.0328605i
$775$		0			0
$776$	−9.12169	+	7.65401i	−0.327450	+	0.274763i
$777$	1.89978	+	10.7742i	0.0681542	+	0.386522i
$778$	15.5273			0.556680
$779$	−5.40650	+	7.67617i	−0.193708	+	0.275027i
$780$		0			0
$781$	−11.9482	−	67.7615i	−0.427540	−	2.42470i
$782$	−3.95159	+	3.31577i	−0.141308	+	0.118572i
$783$	13.2465	−	4.82132i	0.473390	−	0.172300i
$784$	−16.2532	−	5.91569i	−0.580472	−	0.211274i
$785$		0			0
$786$	0.963353	−	1.66858i	0.0343617	−	0.0595162i
$787$	12.8010	+	22.1721i	0.456308	+	0.790349i	0.998762	−	0.0497367i	$-0.0158382\pi$
$787$	12.8010	+	22.1721i	0.456308	+	0.790349i	−0.542454	+	0.840085i	$0.682505\pi$
$788$	3.43823	−	19.4992i	0.122482	−	0.694629i
$789$	−1.78334	+	10.1138i	−0.0634885	+	0.360061i
$790$		0			0
$791$	−6.40329	+	11.0908i	−0.227675	+	0.394344i
$792$	−5.98027	−	5.01804i	−0.212500	−	0.178308i
$793$	−35.9979	−	13.1021i	−1.27832	−	0.465271i
$794$	4.52601	−	1.64733i	0.160622	−	0.0584617i
$795$		0			0
$796$	3.46951	+	19.6766i	0.122974	+	0.697418i
$797$	28.8750			1.02281			0.511403	−	0.859341i	$-0.329126\pi$
$797$	28.8750			1.02281			0.511403	+	0.859341i	$0.329126\pi$
$798$	−19.5590	+	13.6152i	−0.692381	+	0.481972i
$799$	8.99731			0.318302
$800$		0			0
$801$	−13.6800	+	11.4788i	−0.483358	+	0.405585i
$802$	11.6810	−	4.25153i	0.412470	−	0.150127i
$803$	−52.2803	−	19.0285i	−1.84493	−	0.671500i
$804$	11.5914	+	9.72636i	0.408798	+	0.343022i
$805$		0			0
$806$	2.68256	+	4.64633i	0.0944891	+	0.163660i
$807$	2.40340	−	13.6304i	0.0846038	−	0.479812i
$808$	−0.250783	+	1.42226i	−0.00882252	+	0.0500350i
$809$	−18.2438	−	31.5992i	−0.641417	−	1.11097i	−0.985117	−	0.171888i	$-0.945013\pi$
$809$	−18.2438	−	31.5992i	−0.641417	−	1.11097i	0.343699	−	0.939080i	$-0.388320\pi$
$810$		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	$0.698753\pi$
$812$	12.3418	+	4.49203i	0.433111	+	0.157639i
$813$	29.4018	−	10.7014i	1.03117	−	0.375314i
$814$	−6.76201	+	5.67400i	−0.237008	+	0.198874i
$815$		0			0
$816$	−5.57403			−0.195130
$817$	−6.55691	−	0.591869i	−0.229397	−	0.0207069i
$818$	−17.2664			−0.603705
$819$	−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	$0.365200\pi$
$822$	2.60326	+	0.947510i	0.0907992	+	0.0330482i
$823$	−1.24294	−	1.04295i	−0.0433263	−	0.0363551i	0.620867	−	0.783916i	$-0.286781\pi$
$823$	−1.24294	−	1.04295i	−0.0433263	−	0.0363551i	−0.664194	+	0.747561i	$0.731225\pi$
$824$	−2.23068	+	3.86364i	−0.0777093	+	0.134596i
$825$		0			0
$826$	−12.0291	+	68.2203i	−0.418545	+	2.37369i
$827$	4.32155	−	24.5087i	0.150275	−	0.852252i	−0.812704	−	0.582676i	$-0.802006\pi$
$827$	4.32155	−	24.5087i	0.150275	−	0.852252i	0.962979	−	0.269575i	$-0.0868834\pi$
$828$	0.908293	+	1.57321i	0.0315654	+	0.0546728i
$829$	−6.75957	+	11.7079i	−0.234770	+	0.406633i	−0.959206	−	0.282709i	$-0.908767\pi$
$829$	−6.75957	+	11.7079i	−0.234770	+	0.406633i	0.724436	+	0.689342i	$0.242100\pi$
$830$		0			0
$831$	8.76750	+	3.19111i	0.304141	+	0.110698i
$832$	2.48072	−	0.902907i	0.0860033	−	0.0313027i
$833$	−66.5851	+	55.8715i	−2.30704	+	1.93583i
$834$	2.27893	+	12.9245i	0.0789129	+	0.447537i
$835$		0			0
$836$	−17.4041	−	8.17413i	−0.601933	−	0.282708i
$837$	−10.7518			−0.371637
$838$	3.17710	+	18.0182i	0.109751	+	0.622429i
$839$	12.1036	−	10.1561i	0.417861	−	0.350627i	−0.409488	−	0.912316i	$-0.634293\pi$
$839$	12.1036	−	10.1561i	0.417861	−	0.350627i	0.827349	+	0.561689i	$0.189848\pi$
$840$		0			0
$841$	20.5795	+	7.49033i	0.709639	+	0.258287i
$842$	21.4711	+	18.0164i	0.739944	+	0.620887i
$843$	−12.3918	+	21.4633i	−0.426797	+	0.739234i
$844$	−6.82622	−	11.8234i	−0.234968	−	0.406977i
$845$		0			0
$846$	0.550201	−	3.12035i	0.0189163	−	0.107280i
$847$	20.8474	+	36.1088i	0.716326	+	1.24071i
$848$	2.81186	−	4.87029i	0.0965597	−	0.167246i
$849$	−10.8473	−	9.10199i	−0.372280	−	0.312380i
$850$		0			0
$851$	1.93018	−	0.702527i	0.0661656	−	0.0240823i
$852$	−13.2534	+	11.1209i	−0.454053	+	0.380996i
$853$	−1.78438	−	10.1197i	−0.0610962	−	0.346494i	−0.999997	−	0.00230672i	$-0.999266\pi$
$853$	−1.78438	−	10.1197i	−0.0610962	−	0.346494i	0.938901	−	0.344187i	$-0.111845\pi$
$854$	71.5270			2.44760
$855$		0			0
$856$	7.86294			0.268750
$857$	−4.77171	−	27.0617i	−0.162998	−	0.924410i	−0.951104	−	0.308870i	$-0.900049\pi$
$857$	−4.77171	−	27.0617i	−0.162998	−	0.924410i	0.788106	−	0.615540i	$-0.211062\pi$
$858$	−9.89471	+	8.30265i	−0.337800	+	0.283448i
$859$	0.328073	−	0.119409i	0.0111937	−	0.00407418i	−0.336417	−	0.941713i	$-0.609215\pi$
$859$	0.328073	−	0.119409i	0.0111937	−	0.00407418i	0.347611	+	0.937639i	$0.386993\pi$
$860$		0			0
$861$	−9.02127	−	7.56974i	−0.307444	−	0.257976i
$862$	−7.73381	+	13.3953i	−0.263415	+	0.456247i
$863$	−13.7736	−	23.8565i	−0.468857	−	0.812084i	0.530509	−	0.847679i	$-0.322001\pi$
$863$	−13.7736	−	23.8565i	−0.468857	−	0.812084i	−0.999366	+	0.0355949i	$0.988667\pi$
$864$	−0.918679	+	5.21009i	−0.0312541	+	0.177251i
$865$		0			0
$866$	7.04096	+	12.1953i	0.239262	+	0.414413i
$867$	−4.57785	+	7.92906i	−0.155472	+	0.269285i
$868$	−7.67383	−	6.43911i	−0.260467	−	0.218558i
$869$	11.7500	+	4.27664i	0.398591	+	0.145075i
$870$		0			0
$871$	−27.5885	+	23.1495i	−0.934802	+	0.784392i
$872$	−0.437993	−	2.48398i	−0.0148323	−	0.0841183i
$873$	21.0732			0.713218
$874$	3.15507	+	3.17251i	0.106722	+	0.107312i
$875$		0			0
$876$	2.42920	+	13.7767i	0.0820750	+	0.465471i
$877$	−21.3396	+	17.9061i	−0.720587	+	0.604645i	−0.927548	−	0.373705i	$-0.878087\pi$
$877$	−21.3396	+	17.9061i	−0.720587	+	0.604645i	0.206960	+	0.978349i	$0.433643\pi$
$878$	−8.73592	+	3.17962i	−0.294823	+	0.107307i
$879$	−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	$0.973691\pi$
$882$	15.3049	+	26.5089i	0.515344	+	0.892602i
$883$	−4.88096	+	27.6813i	−0.164257	+	0.931549i	0.785570	+	0.618773i	$0.212370\pi$
$883$	−4.88096	+	27.6813i	−0.164257	+	0.931549i	−0.949827	+	0.312776i	$0.898741\pi$
$884$	2.30373	−	13.0651i	0.0774827	−	0.439426i
$885$		0			0
$886$	−5.94905	+	10.3041i	−0.199862	+	0.346172i
$887$	−36.2974	−	30.4571i	−1.21875	−	1.02265i	−0.998889	−	0.0471192i	$-0.984996\pi$
$887$	−36.2974	−	30.4571i	−1.21875	−	1.02265i	−0.219859	−	0.975532i	$-0.570560\pi$
$888$	2.08568	+	0.759127i	0.0699910	+	0.0254746i
$889$	95.9889	−	34.9371i	3.21936	−	1.17175i
$890$		0			0
$891$	−0.428067	−	2.42769i	−0.0143408	−	0.0813306i
$892$	23.1810			0.776156
$893$	−0.658739	−	7.77619i	−0.0220438	−	0.260220i
$894$	−22.3413			−0.747204
$895$		0			0
$896$	−3.77593	+	3.16838i	−0.126145	+	0.105848i
$897$	2.82439	−	1.02799i	0.0943035	−	0.0343237i
$898$	18.7028	+	6.80727i	0.624122	+	0.227162i
$899$	4.14823	+	3.48078i	0.138351	+	0.116091i
$900$		0			0
$901$	−14.1307	−	24.4751i	−0.470762	−	0.815383i
$902$	1.64996	−	9.35738i	0.0549376	−	0.311567i
$903$	1.43392	−	8.13215i	0.0477178	−	0.270621i
$904$	1.29907	+	2.25006i	0.0432065	+	0.0748358i
$905$		0			0
$906$	−6.52442	−	5.47464i	−0.216759	−	0.181883i
$907$	−5.53153	−	2.01331i	−0.183672	−	0.0668510i	0.248547	−	0.968620i	$-0.420047\pi$
$907$	−5.53153	−	2.01331i	−0.183672	−	0.0668510i	−0.432219	+	0.901769i	$0.642269\pi$
$908$	−6.93391	+	2.52374i	−0.230110	+	0.0837532i
$909$	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	$0.485376\pi$
$912$	0.408103	+	4.81752i	0.0135136	+	0.159524i
$913$	32.1272			1.06325
$914$	6.39191	+	36.2503i	0.211426	+	1.19905i
$915$		0			0
$916$	12.4453	−	4.52971i	0.411204	−	0.149666i
$917$	−8.04585	−	2.92845i	−0.265698	−	0.0967060i
$918$	20.3665	+	17.0896i	0.672196	+	0.564039i
$919$	−26.1760	+	45.3382i	−0.863468	+	1.49557i	0.00509211	+	0.999987i	$0.498379\pi$
$919$	−26.1760	+	45.3382i	−0.863468	+	1.49557i	−0.868560	+	0.495584i	$0.834954\pi$
$920$		0			0
$921$	−4.51964	+	25.6321i	−0.148927	+	0.844608i
$922$	5.29037	−	30.0032i	0.174229	−	0.988103i
$923$	−20.5889	−	35.6611i	−0.677693	−	1.17380i
$924$	12.0586	−	20.8862i	0.396700	−	0.687105i
$925$		0			0
$926$	−21.0469	−	7.66045i	−0.691645	−	0.251738i
$927$	7.41926	−	2.70039i	0.243680	−	0.0886924i
$928$	2.04115	−	1.71273i	0.0670040	−	0.0562230i
$929$	−6.37049	−	36.1288i	−0.209009	−	1.18535i	−0.891005	−	0.453993i	$-0.849999\pi$
$929$	−6.37049	−	36.1288i	−0.209009	−	1.18535i	0.681997	−	0.731355i	$-0.261112\pi$
$930$		0			0
$931$	53.1637	+	53.4575i	1.74237	+	1.75200i
$932$	−15.1401			−0.495931
$933$	0.817643	+	4.63708i	0.0267684	+	0.151811i
$934$	11.3247	−	9.50252i	0.370554	−	0.310932i
$935$		0			0
$936$	−4.39021	−	1.59791i	−0.143498	−	0.0522292i
$937$	25.7630	+	21.6177i	0.841639	+	0.706219i	0.957932	−	0.286996i	$-0.0926566\pi$
$937$	25.7630	+	21.6177i	0.841639	+	0.706219i	−0.116292	+	0.993215i	$0.537101\pi$
$938$	33.6220	−	58.2350i	1.09780	−	1.90144i
$939$	−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	$0.794466\pi$
$942$	−3.21699	−	5.57199i	−0.104815	−	0.181545i
$943$	−1.10551	+	1.91480i	−0.0360003	+	0.0623543i
$944$	10.7658	+	9.03357i	0.350396	+	0.294018i
$945$		0			0
$946$	6.26079	−	2.27874i	0.203556	−	0.0740883i
$947$	−10.6134	+	8.90570i	−0.344889	+	0.289396i	−0.798734	−	0.601684i	$-0.794497\pi$
$947$	−10.6134	+	8.90570i	−0.344889	+	0.289396i	0.453845	+	0.891081i	$0.350052\pi$
$948$	−0.545962	−	3.09630i	−0.0177320	−	0.100563i
$949$	−33.2954			−1.08082
$950$		0			0
$951$	2.48037			0.0804316
$952$	4.30140	+	24.3945i	0.139409	+	0.790629i
$953$	30.1638	−	25.3105i	0.977102	−	0.819886i	−0.00654740	−	0.999979i	$-0.502084\pi$
$953$	30.1638	−	25.3105i	0.977102	−	0.819886i	0.983650	+	0.180092i	$0.0576397\pi$
$954$	−9.35229	+	3.40395i	−0.302791	+	0.110207i
$955$		0			0
$956$	8.95228	+	7.51186i	0.289537	+	0.242951i
$957$	−6.51852	+	11.2904i	−0.210714	+	0.364967i
$958$	13.4556	+	23.3058i	0.434730	+	0.752975i
$959$	2.13783	−	12.1242i	0.0690341	−	0.391512i
$960$		0			0
$961$	13.4349	+	23.2699i	0.433383	+	0.750641i
$962$	−2.64134	+	4.57494i	−0.0851602	+	0.147502i
$963$	−10.6598	−	8.94460i	−0.343506	−	0.288236i
$964$	−11.9883	−	4.36339i	−0.386118	−	0.140535i
$965$		0			0
$966$	−4.29904	+	3.60732i	−0.138319	+	0.116064i
$967$	−0.583592	−	3.30972i	−0.0187671	−	0.106433i	0.973985	−	0.226611i	$-0.0727646\pi$
$967$	−0.583592	−	3.30972i	−0.0187671	−	0.106433i	−0.992752	+	0.120178i	$0.961654\pi$
$968$	8.45886			0.271878
$969$	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	$0.511781\pi$
$972$	11.6834	−	9.80350i	0.374744	−	0.314447i
$973$	54.8046	−	19.9473i	1.75696	−	0.639480i
$974$	−13.3275	−	4.85081i	−0.427040	−	0.155430i
$975$		0			0
$976$	7.25554	−	12.5670i	0.232244	−	0.402259i
$977$	−15.5819	−	26.9886i	−0.498509	−	0.863442i	0.501490	−	0.865164i	$-0.332785\pi$
$977$	−15.5819	−	26.9886i	−0.498509	−	0.863442i	−0.999999	+	0.00172111i	$0.999452\pi$
$978$	2.06560	−	11.7146i	0.0660505	−	0.374591i
$979$	7.72950	−	43.8362i	0.247036	−	1.40101i
$980$		0			0
$981$	−2.23190	+	3.86577i	−0.0712592	+	0.123425i
$982$	7.44701	+	6.24878i	0.237644	+	0.199407i
$983$	39.1951	+	14.2659i	1.25013	+	0.455010i	0.880446	−	0.474147i	$-0.157244\pi$
$983$	39.1951	+	14.2659i	1.25013	+	0.455010i	0.369685	+	0.929157i	$0.379466\pi$
$984$	−2.24507	+	0.817137i	−0.0715701	+	0.0260494i
$985$		0			0
$986$	−2.32520	−	13.1869i	−0.0740495	−	0.419956i
$987$	9.78842			0.311569
$988$	−11.4606	−	1.03450i	−0.364609	−	0.0329120i
$989$	−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	$0.393890\pi$
$992$	−1.90974	+	0.695088i	−0.0606343	+	0.0220691i
$993$	0.530800	+	0.193196i	0.0168444	+	0.00613088i
$994$	58.8975	+	49.4209i	1.86812	+	1.56754i
$995$		0			0
$996$	−4.03909	−	6.99590i	−0.127983	−	0.221674i
$997$	−5.23325	+	29.6792i	−0.165739	+	0.939950i	0.782561	+	0.622574i	$0.213913\pi$
$997$	−5.23325	+	29.6792i	−0.165739	+	0.939950i	−0.948300	+	0.317377i	$0.897198\pi$
$998$	−2.13578	+	12.1126i	−0.0676069	+	0.383418i
$999$	−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.l.i.351.2		18
5.2	odd	4		950.2.u.g.199.2		36
5.3	odd	4		950.2.u.g.199.5		36
5.4	even	2		190.2.k.d.161.2	yes	18
19.17	even	9	inner	950.2.l.i.701.2		18
95.17	odd	36		950.2.u.g.549.5		36
95.44	even	18		3610.2.a.bi.1.4		9
95.74	even	18		190.2.k.d.131.2	✓	18
95.89	odd	18		3610.2.a.bj.1.6		9
95.93	odd	36		950.2.u.g.549.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.131.2	✓	18	95.74	even	18
190.2.k.d.161.2	yes	18	5.4	even	2
950.2.l.i.351.2		18	1.1	even	1	trivial
950.2.l.i.701.2		18	19.17	even	9	inner
950.2.u.g.199.2		36	5.2	odd	4
950.2.u.g.199.5		36	5.3	odd	4
950.2.u.g.549.2		36	95.93	odd	36
950.2.u.g.549.5		36	95.17	odd	36
3610.2.a.bi.1.4		9	95.44	even	18
3610.2.a.bj.1.6		9	95.89	odd	18

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.849676 - 0.712963i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.849676 + 0.712963i) q^{6} +(2.46456 - 4.26875i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.307311 + 1.74285i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.849676 - 0.712963i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.849676 + 0.712963i) q^{6} +(2.46456 - 4.26875i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.307311 + 1.74285i) q^{9} +(-2.20561 - 3.82023i) q^{11} +(-0.554587 + 0.960572i) q^{12} +(-2.02230 - 1.69691i) q^{13} +(4.63187 + 1.68586i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-0.872649 - 4.94904i) q^{17} -1.76973 q^{18} +(-4.21347 + 1.11656i) q^{19} +(-0.949379 - 5.38420i) q^{21} +(3.37919 - 2.83548i) q^{22} +(-0.964570 + 0.351075i) q^{23} +(-1.04228 - 0.379360i) q^{24} +(1.31996 - 2.28624i) q^{26} +(2.64523 + 4.58167i) q^{27} +(-0.855934 + 4.85424i) q^{28} +(0.462691 - 2.62405i) q^{29} +(-1.01615 + 1.76003i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-4.59773 - 1.67344i) q^{33} +(4.72232 - 1.71878i) q^{34} +(-0.307311 - 1.74285i) q^{36} -2.00107 q^{37} +(-1.83126 - 3.95557i) q^{38} -2.92813 q^{39} +(1.65005 - 1.38456i) q^{41} +(5.13754 - 1.86991i) q^{42} +(1.41929 + 0.516578i) q^{43} +(3.37919 + 2.83548i) q^{44} +(-0.513237 - 0.888952i) q^{46} +(-0.310895 + 1.76317i) q^{47} +(0.192606 - 1.09232i) q^{48} +(-8.64815 - 14.9790i) q^{49} +(-4.26995 - 3.58291i) q^{51} +(2.48072 + 0.902907i) q^{52} +(5.28457 - 1.92343i) q^{53} +(-4.05273 + 3.40064i) q^{54} -4.92913 q^{56} +(-2.78402 + 3.95276i) q^{57} +2.66453 q^{58} +(2.44041 + 13.8402i) q^{59} +(13.6360 - 4.96308i) q^{61} +(-1.90974 - 0.695088i) q^{62} +(6.68240 + 5.60720i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.849627 - 4.81847i) q^{66} +(2.36894 - 13.4349i) q^{67} +(2.51269 + 4.35211i) q^{68} +(-0.569269 + 0.986002i) q^{69} +(14.6575 + 5.33488i) q^{71} +(1.66301 - 0.605285i) q^{72} +(9.66157 - 8.10702i) q^{73} +(-0.347483 - 1.97067i) q^{74} +(3.57748 - 2.49031i) q^{76} -21.7435 q^{77} +(-0.508465 - 2.88365i) q^{78} +(-2.17143 + 1.82205i) q^{79} +(0.525132 + 0.191132i) q^{81} +(1.65005 + 1.38456i) q^{82} +(-3.64153 + 6.30732i) q^{83} +(2.73363 + 4.73478i) q^{84} +(-0.262274 + 1.48743i) q^{86} +(-1.47771 - 2.55947i) q^{87} +(-2.20561 + 3.82023i) q^{88} +(7.72995 + 6.48620i) q^{89} +(-12.2278 + 4.45054i) q^{91} +(0.786325 - 0.659805i) q^{92} +(0.391433 + 2.21993i) q^{93} -1.79037 q^{94} +1.10917 q^{96} +(-2.06772 - 11.7266i) q^{97} +(13.2497 - 11.1179i) q^{98} +(7.33589 - 2.67005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 18 * q - 9 * q^8 - 18 * q^9	\( 18 q - 9 q^{8} - 18 q^{9} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 42 q^{18} + 12 q^{21} + 3 q^{22} - 9 q^{23} - 9 q^{26} + 18 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{31} - 66 q^{33} + 18 q^{34} - 18 q^{36} + 12 q^{37} + 6 q^{38} + 48 q^{39} - 21 q^{41} - 42 q^{42} - 18 q^{43} + 3 q^{44} + 18 q^{46} + 54 q^{47} - 39 q^{49} + 42 q^{51} - 12 q^{52} + 24 q^{53} - 54 q^{54} + 18 q^{57} - 30 q^{59} + 48 q^{61} + 30 q^{62} + 57 q^{63} - 9 q^{64} + 24 q^{66} + 6 q^{67} + 6 q^{68} - 30 q^{69} + 30 q^{71} - 6 q^{73} - 3 q^{74} - 21 q^{76} - 30 q^{77} + 24 q^{78} + 30 q^{79} + 18 q^{81} - 21 q^{82} - 6 q^{83} + 6 q^{84} + 36 q^{86} - 24 q^{87} - 12 q^{88} + 30 q^{89} - 60 q^{91} + 18 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{97} + 18 q^{98} + 171 q^{99}+O(q^{100}) \) 18 * q - 9 * q^8 - 18 * q^9 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 42 * q^18 + 12 * q^21 + 3 * q^22 - 9 * q^23 - 9 * q^26 + 18 * q^27 - 3 * q^28 - 6 * q^29 - 6 * q^31 - 66 * q^33 + 18 * q^34 - 18 * q^36 + 12 * q^37 + 6 * q^38 + 48 * q^39 - 21 * q^41 - 42 * q^42 - 18 * q^43 + 3 * q^44 + 18 * q^46 + 54 * q^47 - 39 * q^49 + 42 * q^51 - 12 * q^52 + 24 * q^53 - 54 * q^54 + 18 * q^57 - 30 * q^59 + 48 * q^61 + 30 * q^62 + 57 * q^63 - 9 * q^64 + 24 * q^66 + 6 * q^67 + 6 * q^68 - 30 * q^69 + 30 * q^71 - 6 * q^73 - 3 * q^74 - 21 * q^76 - 30 * q^77 + 24 * q^78 + 30 * q^79 + 18 * q^81 - 21 * q^82 - 6 * q^83 + 6 * q^84 + 36 * q^86 - 24 * q^87 - 12 * q^88 + 30 * q^89 - 60 * q^91 + 18 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^97 + 18 * q^98 + 171 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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