LMFDB - Embedded newform 775.2.bl.b.76.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(51,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("775.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.bl (of order $15$, degree $8$, 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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			76.4
Character	$\chi$	$=$	775.76
Dual form			775.2.bl.b.51.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.437416 - 1.34623i) q^{2} +(-2.08671 + 2.31753i) q^{3} +(-0.00296283 - 0.00215262i) q^{4} +(2.20716 + 3.82291i) q^{6} +(0.0992859 - 0.944642i) q^{7} +(2.28615 - 1.66098i) q^{8} +(-0.702986 - 6.68846i) q^{9} +O(q^{10})$	\(q+(0.437416 - 1.34623i) q^{2} +(-2.08671 + 2.31753i) q^{3} +(-0.00296283 - 0.00215262i) q^{4} +(2.20716 + 3.82291i) q^{6} +(0.0992859 - 0.944642i) q^{7} +(2.28615 - 1.66098i) q^{8} +(-0.702986 - 6.68846i) q^{9} +(2.64680 - 1.17843i) q^{11} +(0.0111713 - 0.00237454i) q^{12} +(-3.97302 - 0.844492i) q^{13} +(-1.22827 - 0.546863i) q^{14} +(-1.23833 - 3.81118i) q^{16} +(5.39849 + 2.40356i) q^{17} +(-9.31169 - 1.97926i) q^{18} +(-3.85426 + 0.819249i) q^{19} +(1.98205 + 2.20129i) q^{21} +(-0.428684 - 4.07866i) q^{22} +(5.74196 - 4.17178i) q^{23} +(-0.921154 + 8.76420i) q^{24} +(-2.87474 + 4.97920i) q^{26} +(9.39877 + 6.82861i) q^{27} +(-0.00232762 + 0.00258509i) q^{28} +(-0.690565 + 2.12534i) q^{29} +(4.68304 - 3.01150i) q^{31} -0.0207168 q^{32} +(-2.79206 + 8.59307i) q^{33} +(5.59713 - 6.21624i) q^{34} +(-0.0123149 + 0.0213300i) q^{36} +(-0.728076 - 1.26106i) q^{37} +(-0.583021 + 5.54707i) q^{38} +(10.2477 - 7.44538i) q^{39} +(0.928592 + 1.03131i) q^{41} +(3.83043 - 1.70542i) q^{42} +(12.5437 - 2.66625i) q^{43} +(-0.0103787 - 0.00220606i) q^{44} +(-3.10454 - 9.55479i) q^{46} +(0.462894 + 1.42464i) q^{47} +(11.4165 + 5.08297i) q^{48} +(5.96454 + 1.26780i) q^{49} +(-16.8354 + 7.49561i) q^{51} +(0.00995351 + 0.0110545i) q^{52} +(0.282850 + 2.69114i) q^{53} +(13.3040 - 9.66595i) q^{54} +(-1.34205 - 2.32450i) q^{56} +(6.14411 - 10.6419i) q^{57} +(2.55913 + 1.85931i) q^{58} +(-2.76666 + 3.07268i) q^{59} +5.75919 q^{61} +(-2.00573 - 7.62172i) q^{62} -6.38800 q^{63} +(2.46759 - 7.59447i) q^{64} +(10.3469 + 7.51749i) q^{66} +(-4.59142 + 7.95257i) q^{67} +(-0.0108208 - 0.0187422i) q^{68} +(-2.31360 + 22.0125i) q^{69} +(-1.16123 - 11.0483i) q^{71} +(-12.7165 - 14.1232i) q^{72} +(-4.92960 + 2.19480i) q^{73} +(-2.01615 + 0.428546i) q^{74} +(0.0131831 + 0.00586947i) q^{76} +(-0.850405 - 2.61728i) q^{77} +(-5.54068 - 17.0525i) q^{78} +(3.76376 + 1.67573i) q^{79} +(-15.7030 + 3.33777i) q^{81} +(1.79455 - 0.798986i) q^{82} +(-11.3186 - 12.5706i) q^{83} +(-0.00113393 - 0.0107887i) q^{84} +(1.89744 - 18.0529i) q^{86} +(-3.48452 - 6.03537i) q^{87} +(4.09361 - 7.09035i) q^{88} +(6.19419 + 4.50034i) q^{89} +(-1.19221 + 3.66924i) q^{91} -0.0259927 q^{92} +(-2.79291 + 17.1372i) q^{93} +2.12037 q^{94} +(0.0432300 - 0.0480118i) q^{96} +(-0.00275399 - 0.00200089i) q^{97} +(4.31574 - 7.47508i) q^{98} +(-9.74255 - 16.8746i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 12 q^{6} + 2 q^{7} + 31 q^{8} + 6 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 12 * q^6 + 2 * q^7 + 31 * q^8 + 6 * q^9	$ 40 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 12 q^{6} + 2 q^{7} + 31 q^{8} + 6 q^{9} + 16 q^{11} + q^{12} - 2 q^{13} - 10 q^{14} - 16 q^{16} - 4 q^{17} - 37 q^{18} - 9 q^{19} - 24 q^{21} + 2 q^{22} + 4 q^{23} + 110 q^{24} - 4 q^{26} + 9 q^{27} - 38 q^{28} - 22 q^{29} - 6 q^{31} + 60 q^{32} - 9 q^{33} - 16 q^{34} - q^{36} + 38 q^{37} + 32 q^{38} - 55 q^{39} - 24 q^{41} + 68 q^{42} - 26 q^{43} - 52 q^{44} - 50 q^{46} - 4 q^{47} - 105 q^{48} + 93 q^{49} - 42 q^{51} - 15 q^{52} - 13 q^{53} + 102 q^{54} + 5 q^{56} + 36 q^{57} + 37 q^{58} + 31 q^{59} + 68 q^{61} - 47 q^{62} + 10 q^{63} - 23 q^{64} + 2 q^{67} + 28 q^{68} - 48 q^{69} - 30 q^{71} - 39 q^{72} - 25 q^{73} + 50 q^{74} + 14 q^{76} + 64 q^{77} + 22 q^{78} + 49 q^{79} + 25 q^{81} + 66 q^{82} + 18 q^{83} - 18 q^{84} + 163 q^{86} + 36 q^{87} + 124 q^{88} + 4 q^{89} - 37 q^{91} - 110 q^{92} - 7 q^{93} - 94 q^{94} + 22 q^{96} - 46 q^{97} + 13 q^{98} + 17 q^{99}+O(q^{100}) $ 40 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 12 * q^6 + 2 * q^7 + 31 * q^8 + 6 * q^9 + 16 * q^11 + q^12 - 2 * q^13 - 10 * q^14 - 16 * q^16 - 4 * q^17 - 37 * q^18 - 9 * q^19 - 24 * q^21 + 2 * q^22 + 4 * q^23 + 110 * q^24 - 4 * q^26 + 9 * q^27 - 38 * q^28 - 22 * q^29 - 6 * q^31 + 60 * q^32 - 9 * q^33 - 16 * q^34 - q^36 + 38 * q^37 + 32 * q^38 - 55 * q^39 - 24 * q^41 + 68 * q^42 - 26 * q^43 - 52 * q^44 - 50 * q^46 - 4 * q^47 - 105 * q^48 + 93 * q^49 - 42 * q^51 - 15 * q^52 - 13 * q^53 + 102 * q^54 + 5 * q^56 + 36 * q^57 + 37 * q^58 + 31 * q^59 + 68 * q^61 - 47 * q^62 + 10 * q^63 - 23 * q^64 + 2 * q^67 + 28 * q^68 - 48 * q^69 - 30 * q^71 - 39 * q^72 - 25 * q^73 + 50 * q^74 + 14 * q^76 + 64 * q^77 + 22 * q^78 + 49 * q^79 + 25 * q^81 + 66 * q^82 + 18 * q^83 - 18 * q^84 + 163 * q^86 + 36 * q^87 + 124 * q^88 + 4 * q^89 - 37 * q^91 - 110 * q^92 - 7 * q^93 - 94 * q^94 + 22 * q^96 - 46 * q^97 + 13 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{11}{15}\right)$	$1$

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 $

$2$	0.437416	−	1.34623i	0.309300	−	0.951927i	−0.668738	−	0.743498i	$-0.733165\pi$
$2$	0.437416	−	1.34623i	0.309300	−	0.951927i	0.978038	−	0.208429i	$-0.0668349\pi$
$3$	−2.08671	+	2.31753i	−1.20476	+	1.33803i	−0.278830	+	0.960341i	$0.589946\pi$
$3$	−2.08671	+	2.31753i	−1.20476	+	1.33803i	−0.925934	+	0.377685i	$0.876720\pi$
$4$	−0.00296283	−	0.00215262i	−0.00148141	−	0.00107631i
$5$		0			0
$5$		0			0
$6$	2.20716	+	3.82291i	0.901069	+	1.56070i
$7$	0.0992859	−	0.944642i	0.0375265	−	0.357041i	−0.959605	−	0.281351i	$-0.909217\pi$
$7$	0.0992859	−	0.944642i	0.0375265	−	0.357041i	0.997131	−	0.0756900i	$-0.0241159\pi$
$8$	2.28615	−	1.66098i	0.808275	−	0.587246i
$9$	−0.702986	−	6.68846i	−0.234329	−	2.22949i
$10$		0			0
$11$	2.64680	−	1.17843i	0.798039	−	0.355310i	0.0331325	−	0.999451i	$-0.489452\pi$
$11$	2.64680	−	1.17843i	0.798039	−	0.355310i	0.764907	+	0.644141i	$0.222785\pi$
$12$	0.0111713	−	0.00237454i	0.00322488	−	0.000685470i
$13$	−3.97302	−	0.844492i	−1.10192	−	0.234220i	−0.379167	−	0.925328i	$-0.623789\pi$
$13$	−3.97302	−	0.844492i	−1.10192	−	0.234220i	−0.722751	+	0.691108i	$0.757123\pi$
$14$	−1.22827	−	0.546863i	−0.328270	−	0.146155i
$15$		0			0
$16$	−1.23833	−	3.81118i	−0.309582	−	0.952795i
$17$	5.39849	+	2.40356i	1.30933	+	0.582949i	0.938348	−	0.345692i	$-0.112356\pi$
$17$	5.39849	+	2.40356i	1.30933	+	0.582949i	0.370978	+	0.928642i	$0.379023\pi$
$18$	−9.31169	−	1.97926i	−2.19479	−	0.466516i
$19$	−3.85426	+	0.819249i	−0.884229	+	0.187949i	−0.627576	−	0.778555i	$-0.715953\pi$
$19$	−3.85426	+	0.819249i	−0.884229	+	0.187949i	−0.256653	+	0.966504i	$0.582620\pi$
$20$		0			0
$21$	1.98205	+	2.20129i	0.432520	+	0.480362i
$22$	−0.428684	−	4.07866i	−0.0913957	−	0.869572i
$23$	5.74196	−	4.17178i	1.19728	−	0.869876i	0.203267	−	0.979123i	$-0.434844\pi$
$23$	5.74196	−	4.17178i	1.19728	−	0.869876i	0.994015	+	0.109247i	$0.0348441\pi$
$24$	−0.921154	+	8.76420i	−0.188030	+	1.78898i
$25$		0			0
$26$	−2.87474	+	4.97920i	−0.563783	+	0.976501i
$27$	9.39877	+	6.82861i	1.80879	+	1.31417i
$28$	−0.00232762	+	0.00258509i	−0.000439879	+	0.000488536i
$29$	−0.690565	+	2.12534i	−0.128235	+	0.394666i	−0.994477	−	0.104959i	$-0.966529\pi$
$29$	−0.690565	+	2.12534i	−0.128235	+	0.394666i	0.866242	+	0.499625i	$0.166529\pi$
$30$		0			0
$31$	4.68304	−	3.01150i	0.841099	−	0.540882i
$31$	4.68304	−	3.01150i	0.841099	−	0.540882i
$32$	−0.0207168			−0.00366225
$33$	−2.79206	+	8.59307i	−0.486035	+	1.49586i
$34$	5.59713	−	6.21624i	0.959899	−	1.06608i
$35$		0			0
$36$	−0.0123149	+	0.0213300i	−0.00205248	+	0.00355500i
$37$	−0.728076	−	1.26106i	−0.119695	−	0.207318i	0.799952	−	0.600064i	$-0.204858\pi$
$37$	−0.728076	−	1.26106i	−0.119695	−	0.207318i	−0.919647	+	0.392746i	$0.871525\pi$
$38$	−0.583021	+	5.54707i	−0.0945784	+	0.899854i
$39$	10.2477	−	7.44538i	1.64094	−	1.19222i
$40$		0			0
$41$	0.928592	+	1.03131i	0.145022	+	0.161063i	0.811279	−	0.584659i	$-0.198772\pi$
$41$	0.928592	+	1.03131i	0.145022	+	0.161063i	−0.666258	+	0.745722i	$0.732105\pi$
$42$	3.83043	−	1.70542i	0.591048	−	0.263151i
$43$	12.5437	−	2.66625i	1.91290	−	0.406599i	0.912899	−	0.408186i	$-0.133838\pi$
$43$	12.5437	−	2.66625i	1.91290	−	0.406599i	0.999999	+	0.00158676i	$0.000505081\pi$
$44$	−0.0103787	−	0.00220606i	−0.00156465	−	0.000332577i
$45$		0			0
$46$	−3.10454	−	9.55479i	−0.457739	−	1.40878i
$47$	0.462894	+	1.42464i	0.0675201	+	0.207805i	0.979124	−	0.203265i	$-0.0651552\pi$
$47$	0.462894	+	1.42464i	0.0675201	+	0.207805i	−0.911604	+	0.411070i	$0.865155\pi$
$48$	11.4165	+	5.08297i	1.64784	+	0.733664i
$49$	5.96454	+	1.26780i	0.852077	+	0.181115i
$50$		0			0
$51$	−16.8354	+	7.49561i	−2.35743	+	1.04960i
$52$	0.00995351	+	0.0110545i	0.00138030	+	0.00153298i
$53$	0.282850	+	2.69114i	0.0388525	+	0.369657i	0.996622	+	0.0821209i	$0.0261693\pi$
$53$	0.282850	+	2.69114i	0.0388525	+	0.369657i	−0.957770	+	0.287536i	$0.907164\pi$
$54$	13.3040	−	9.66595i	1.81045	−	1.31537i
$55$		0			0
$56$	−1.34205	−	2.32450i	−0.179339	−	0.310625i
$57$	6.14411	−	10.6419i	0.813807	−	1.40955i
$58$	2.55913	+	1.85931i	0.336030	+	0.244140i
$59$	−2.76666	+	3.07268i	−0.360188	+	0.400029i	−0.895816	−	0.444425i	$-0.853408\pi$
$59$	−2.76666	+	3.07268i	−0.360188	+	0.400029i	0.535628	+	0.844454i	$0.320075\pi$
$60$		0			0
$61$	5.75919			0.737389			0.368695	−	0.929551i	$-0.379805\pi$
$61$	5.75919			0.737389			0.368695	+	0.929551i	$0.379805\pi$
$62$	−2.00573	−	7.62172i	−0.254728	−	0.967959i
$63$	−6.38800			−0.804813
$64$	2.46759	−	7.59447i	0.308449	−	0.949309i
$65$		0			0
$66$	10.3469	+	7.51749i	1.27362	+	0.925339i
$67$	−4.59142	+	7.95257i	−0.560931	+	0.971561i	0.436484	+	0.899712i	$0.356223\pi$
$67$	−4.59142	+	7.95257i	−0.560931	+	0.971561i	−0.997415	+	0.0718494i	$0.977110\pi$
$68$	−0.0108208	−	0.0187422i	−0.00131222	−	0.00227283i
$69$	−2.31360	+	22.0125i	−0.278525	+	2.64999i
$70$		0			0
$71$	−1.16123	−	11.0483i	−0.137812	−	1.31119i	−0.816747	−	0.576996i	$-0.804225\pi$
$71$	−1.16123	−	11.0483i	−0.137812	−	1.31119i	0.678935	−	0.734198i	$-0.262442\pi$
$72$	−12.7165	−	14.1232i	−1.49866	−	1.66443i
$73$	−4.92960	+	2.19480i	−0.576966	+	0.256882i	−0.674407	−	0.738359i	$-0.735601\pi$
$73$	−4.92960	+	2.19480i	−0.576966	+	0.256882i	0.0974413	+	0.995241i	$0.468934\pi$
$74$	−2.01615	+	0.428546i	−0.234373	+	0.0498175i
$75$		0			0
$76$	0.0131831	+	0.00586947i	0.00151220	+	0.000673275i
$77$	−0.850405	−	2.61728i	−0.0969127	−	0.298267i
$78$	−5.54068	−	17.0525i	−0.627358	−	1.93081i
$79$	3.76376	+	1.67573i	0.423456	+	0.188535i	0.607390	−	0.794404i	$-0.292217\pi$
$79$	3.76376	+	1.67573i	0.423456	+	0.188535i	−0.183934	+	0.982939i	$0.558883\pi$
$80$		0			0
$81$	−15.7030	+	3.33777i	−1.74478	+	0.370864i
$82$	1.79455	−	0.798986i	0.198175	−	0.0882333i
$83$	−11.3186	−	12.5706i	−1.24238	−	1.37981i	−0.897413	−	0.441192i	$-0.854556\pi$
$83$	−11.3186	−	12.5706i	−1.24238	−	1.37981i	−0.344970	−	0.938614i	$-0.612111\pi$
$84$	−0.00113393	−	0.0107887i	−0.000123722	−	0.00117714i
$85$		0			0
$86$	1.89744	−	18.0529i	0.204606	−	1.94670i
$87$	−3.48452	−	6.03537i	−0.373580	−	0.647060i
$88$	4.09361	−	7.09035i	0.436381	−	0.755833i
$89$	6.19419	+	4.50034i	0.656583	+	0.477036i	0.865507	−	0.500896i	$-0.166996\pi$
$89$	6.19419	+	4.50034i	0.656583	+	0.477036i	−0.208924	+	0.977932i	$0.566996\pi$
$90$		0			0
$91$	−1.19221	+	3.66924i	−0.124977	+	0.384641i
$92$	−0.0259927			−0.00270992
$93$	−2.79291	+	17.1372i	−0.289611	+	1.77705i
$94$	2.12037			0.218700
$95$		0			0
$96$	0.0432300	−	0.0480118i	0.00441215	−	0.00490019i
$97$	−0.00275399	−	0.00200089i	−0.000279625	−	0.000203160i	0.587645	−	0.809119i	$-0.300055\pi$
$97$	−0.00275399	−	0.00200089i	−0.000279625	−	0.000203160i	−0.587925	+	0.808915i	$0.700055\pi$
$98$	4.31574	−	7.47508i	0.435955	−	0.755097i
$99$	−9.74255	−	16.8746i	−0.979163	−	1.69596i
$100$		0			0
$101$	−3.87721	+	2.81696i	−0.385797	+	0.280298i	−0.763731	−	0.645535i	$-0.776635\pi$
$101$	−3.87721	+	2.81696i	−0.385797	+	0.280298i	0.377934	+	0.925833i	$0.376635\pi$
$102$	2.72672	+	25.9430i	0.269985	+	2.56874i
$103$	5.53023	+	6.14194i	0.544909	+	0.605183i	0.951205	−	0.308558i	$-0.0998465\pi$
$103$	5.53023	+	6.14194i	0.544909	+	0.605183i	−0.406296	+	0.913741i	$0.633180\pi$
$104$	−10.4856	+	4.66849i	−1.02820	+	0.457783i
$105$		0			0
$106$	3.74661	+	0.796367i	0.363903	+	0.0773500i
$107$	−14.6727	−	6.53269i	−1.41846	−	0.631539i	−0.452862	−	0.891580i	$-0.649597\pi$
$107$	−14.6727	−	6.53269i	−1.41846	−	0.631539i	−0.965597	+	0.260042i	$0.916264\pi$
$108$	−0.0131475	−	0.0404640i	−0.00126512	−	0.00389365i
$109$	2.11356	+	6.50487i	0.202442	+	0.623054i	0.999809	+	0.0195581i	$0.00622595\pi$
$109$	2.11356	+	6.50487i	0.202442	+	0.623054i	−0.797366	+	0.603496i	$0.793774\pi$
$110$		0			0
$111$	4.44184	+	0.944142i	0.421601	+	0.0896140i
$112$	−3.72315	+	0.791380i	−0.351805	+	0.0747784i
$113$	−13.0068	+	5.79099i	−1.22357	+	0.544770i	−0.913848	−	0.406056i	$-0.866904\pi$
$113$	−13.0068	+	5.79099i	−1.22357	+	0.544770i	−0.309725	+	0.950826i	$0.600237\pi$
$114$	−11.6389	−	12.9263i	−1.09008	−	1.21066i
$115$		0			0
$116$	0.00662107	−	0.00481049i	0.000614751	−	0.000446643i
$117$	−2.85538	+	27.1671i	−0.263980	+	2.51160i
$118$	2.92635	+	5.06859i	0.269393	+	0.466602i
$119$	2.80650	−	4.86100i	0.257271	−	0.445607i
$120$		0			0
$121$	−1.74360	+	1.93646i	−0.158509	+	0.176042i
$122$	2.51916	−	7.75319i	0.228074	−	0.701941i
$123$	−4.32778			−0.390223
$124$	−0.0203577	−	0.00115824i	−0.00182817	−	0.000104013i
$125$		0			0
$126$	−2.79421	+	8.59971i	−0.248928	+	0.766123i
$127$	4.39184	−	4.87763i	0.389713	−	0.432820i	−0.516080	−	0.856540i	$-0.672609\pi$
$127$	4.39184	−	4.87763i	0.389713	−	0.432820i	0.905793	+	0.423720i	$0.139276\pi$
$128$	−9.17804	−	6.66824i	−0.811232	−	0.589395i
$129$	−19.9960	+	34.6341i	−1.76055	+	3.04936i
$130$		0			0
$131$	0.929302	−	8.84171i	0.0811935	−	0.772504i	−0.875855	−	0.482575i	$-0.839702\pi$
$131$	0.929302	−	8.84171i	0.0811935	−	0.772504i	0.957048	−	0.289929i	$-0.0936318\pi$
$132$	0.0267700	−	0.0194495i	0.00233003	−	0.00169287i
$133$	0.391223	+	3.72224i	0.0339234	+	0.322759i
$134$	8.69761	+	9.65968i	0.751359	+	0.834469i
$135$		0			0
$136$	16.3340	−	3.47190i	1.40063	−	0.297713i
$137$	17.2383	+	3.66411i	1.47277	+	0.313046i	0.873233	−	0.487304i	$-0.162020\pi$
$137$	17.2383	+	3.66411i	1.47277	+	0.313046i	0.599533	+	0.800350i	$0.295353\pi$
$138$	28.6218	+	12.7432i	2.43645	+	1.08478i
$139$	−5.13638	−	15.8081i	−0.435662	−	1.34083i	−0.892407	−	0.451232i	$-0.850985\pi$
$139$	−5.13638	−	15.8081i	−0.435662	−	1.34083i	0.456745	−	0.889598i	$-0.349015\pi$
$140$		0			0
$141$	−4.26758	−	1.90005i	−0.359395	−	0.160013i
$142$	−15.3815	−	3.26944i	−1.29079	−	0.274365i
$143$	−11.5110	+	2.44673i	−0.962595	+	0.204606i
$144$	−24.6204	+	10.9617i	−2.05170	+	0.913476i
$145$		0			0
$146$	0.798415	+	7.59641i	0.0660773	+	0.628683i
$147$	−15.3844	+	11.1775i	−1.26889	+	0.921901i
$148$	−0.000557429		0.00530359i	−4.58204e−5		0.000435952i
$149$	−2.06741	−	3.58085i	−0.169369	−	0.293355i	0.768829	−	0.639454i	$-0.220839\pi$
$149$	−2.06741	−	3.58085i	−0.169369	−	0.293355i	−0.938198	+	0.346099i	$0.887506\pi$
$150$		0			0
$151$	8.12460	+	5.90287i	0.661171	+	0.480369i	0.867058	−	0.498207i	$-0.166008\pi$
$151$	8.12460	+	5.90287i	0.661171	+	0.480369i	−0.205887	+	0.978576i	$0.566008\pi$
$152$	−7.45065	+	8.27479i	−0.604328	+	0.671174i
$153$	12.2811	−	37.7973i	0.992866	−	3.05573i
$154$	−3.89543			−0.313903
$155$		0			0
$156$	−0.0463892			−0.00371411
$157$	7.22255	−	22.2287i	0.576422	−	1.77404i	−0.0548631	−	0.998494i	$-0.517472\pi$
$157$	7.22255	−	22.2287i	0.576422	−	1.77404i	0.631285	−	0.775551i	$-0.282528\pi$
$158$	3.90224	−	4.33388i	0.310446	−	0.344785i
$159$	−6.82702	−	4.96012i	−0.541418	−	0.393363i
$160$		0			0
$161$	−3.37074	−	5.83830i	−0.265652	−	0.460122i
$162$	−2.37533	+	22.5998i	−0.186624	+	1.77561i
$163$	−0.200354	+	0.145566i	−0.0156929	+	0.0114016i	−0.595604	−	0.803278i	$-0.703087\pi$
$163$	−0.200354	+	0.145566i	−0.0156929	+	0.0114016i	0.579911	+	0.814680i	$0.303087\pi$
$164$	−0.000531248	−	0.00505448i	−4.14835e−5	−	0.000394689i
$165$		0			0
$166$	−21.8739	+	9.73888i	−1.69774	+	0.755884i
$167$	−0.0560777	+	0.0119197i	−0.00433943	+	0.000922373i	−0.210081	−	0.977684i	$-0.567373\pi$
$167$	−0.0560777	+	0.0119197i	−0.00433943	+	0.000922373i	0.205741	+	0.978606i	$0.434039\pi$
$168$	8.18758	+	1.74032i	0.631685	+	0.134269i
$169$	3.19565	+	1.42280i	0.245819	+	0.109446i
$170$		0			0
$171$	8.18901	+	25.2032i	0.626229	+	1.92734i
$172$	−0.0429043	−	0.0191022i	−0.00327142	−	0.00145653i
$173$	−13.1701	−	2.79938i	−1.00130	−	0.212833i	−0.322037	−	0.946727i	$-0.604368\pi$
$173$	−13.1701	−	2.79938i	−1.00130	−	0.212833i	−0.679264	+	0.733894i	$0.737701\pi$
$174$	−9.64918	+	2.05100i	−0.731502	+	0.155486i
$175$		0			0
$176$	−7.76881	−	8.62814i	−0.585596	−	0.650370i
$177$	−1.34782	−	12.8236i	−0.101308	−	0.963881i
$178$	8.76793	−	6.37027i	0.657184	−	0.477472i
$179$	0.316693	−	3.01313i	0.0236707	−	0.225212i	−0.976291	−	0.216462i	$-0.930548\pi$
$179$	0.316693	−	3.01313i	0.0236707	−	0.225212i	0.999962	−	0.00874979i	$-0.00278518\pi$
$180$		0			0
$181$	−3.39081	+	5.87305i	−0.252037	+	0.436540i	−0.964086	−	0.265589i	$-0.914434\pi$
$181$	−3.39081	+	5.87305i	−0.252037	+	0.436540i	0.712050	+	0.702129i	$0.247767\pi$
$182$	4.41814	+	3.20997i	0.327494	+	0.237939i
$183$	−12.0178	+	13.3471i	−0.888380	+	0.986646i
$184$	6.19771	−	19.0746i	0.456901	−	1.40620i
$185$		0			0
$186$	21.8489	+	11.2560i	1.60204	+	0.825329i
$187$	17.1211			1.25202
$188$	0.00169524	−	0.00521741i	0.000123638	−	0.000380518i
$189$	7.38376	−	8.20049i	0.537089	−	0.596498i
$190$		0			0
$191$	5.60468	−	9.70760i	0.405541	−	0.702417i	−0.588843	−	0.808247i	$-0.700417\pi$
$191$	5.60468	−	9.70760i	0.405541	−	0.702417i	0.994384	+	0.105830i	$0.0337499\pi$
$192$	12.4512	+	21.5662i	0.898591	+	1.55641i
$193$	0.488048	−	4.64346i	0.0351304	−	0.334244i	−0.962814	−	0.270164i	$-0.912922\pi$
$193$	0.488048	−	4.64346i	0.0351304	−	0.334244i	0.997945	−	0.0640799i	$-0.0204113\pi$
$194$	−0.00389829	+	0.00283228i	−0.000279881	+	0.000203346i
$195$		0			0
$196$	−0.0149428	−	0.0165957i	−0.00106734	−	0.00118541i
$197$	−12.4099	+	5.52524i	−0.884168	+	0.393657i	−0.798024	−	0.602626i	$-0.794121\pi$
$197$	−12.4099	+	5.52524i	−0.884168	+	0.393657i	−0.0861438	+	0.996283i	$0.527454\pi$
$198$	−26.9786	+	5.73447i	−1.91728	+	0.407531i
$199$	−7.46756	−	1.58728i	−0.529361	−	0.112519i	−0.0645254	−	0.997916i	$-0.520553\pi$
$199$	−7.46756	−	1.58728i	−0.529361	−	0.112519i	−0.464836	+	0.885397i	$0.653887\pi$
$200$		0			0
$201$	−8.84934	−	27.2355i	−0.624184	−	1.92104i
$202$	2.09632	+	6.45180i	0.147496	+	0.453947i
$203$	1.93912	+	0.863353i	0.136100	+	0.0605955i
$204$	0.0660156	+	0.0140321i	0.00462202	+	0.000982440i
$205$		0			0
$206$	10.6875	−	4.75836i	0.744630	−	0.331531i
$207$	−31.9393	−	35.4722i	−2.21993	−	2.46549i
$208$	1.70139	+	16.1877i	0.117970	+	1.12241i
$209$	−9.23603	+	6.71037i	−0.638869	+	0.464166i
$210$		0			0
$211$	−9.30466	−	16.1161i	−0.640559	−	1.10948i	−0.985308	−	0.170786i	$-0.945369\pi$
$211$	−9.30466	−	16.1161i	−0.640559	−	1.10948i	0.344749	−	0.938695i	$-0.387964\pi$
$212$	0.00495497	−	0.00858225i	0.000340308	−	0.000589432i
$213$	28.0279	+	20.3635i	1.92044	+	1.39528i
$214$	−15.2125	+	16.8952i	−1.03991	+	1.15494i
$215$		0			0
$216$	32.8292			2.23374
$217$	−2.37983	−	4.72280i	−0.161554	−	0.320604i
$218$	9.68155			0.655717
$219$	5.20015	−	16.0044i	0.351393	−	1.08148i
$220$		0			0
$221$	−19.4185	−	14.1084i	−1.30623	−	0.949033i
$222$	3.21396	−	5.56674i	0.215707	−	0.373615i
$223$	−9.85023	−	17.0611i	−0.659620	−	1.14250i	−0.980714	−	0.195448i	$-0.937384\pi$
$223$	−9.85023	−	17.0611i	−0.659620	−	1.14250i	0.321094	−	0.947047i	$-0.395949\pi$
$224$	−0.00205689	+	0.0195700i	−0.000137432	+	0.00130757i
$225$		0			0
$226$	2.10662	+	20.0431i	0.140130	+	1.33325i
$227$	17.2574	+	19.1662i	1.14541	+	1.27211i	0.957022	+	0.290014i	$0.0936600\pi$
$227$	17.2574	+	19.1662i	1.14541	+	1.27211i	0.188389	+	0.982094i	$0.439673\pi$
$228$	−0.0411119	+	0.0183042i	−0.00272270	+	0.00121222i
$229$	−0.296092	+	0.0629363i	−0.0195663	+	0.00415895i	−0.217684	−	0.976019i	$-0.569850\pi$
$229$	−0.296092	+	0.0629363i	−0.0195663	+	0.00415895i	0.198118	+	0.980178i	$0.436517\pi$
$230$		0			0
$231$	7.84017	+	3.49067i	0.515845	+	0.229669i
$232$	1.95142	+	6.00585i	0.128117	+	0.394303i
$233$	−0.136360	−	0.419673i	−0.00893324	−	0.0274937i	0.946491	−	0.322732i	$-0.104601\pi$
$233$	−0.136360	−	0.419673i	−0.00893324	−	0.0274937i	−0.955424	+	0.295238i	$0.904601\pi$
$234$	35.3241	+	15.7273i	2.30921	+	1.02813i
$235$		0			0
$236$	0.0148114	−	0.00314827i	0.000964143	−	0.000204935i
$237$	−11.7374	+	5.22584i	−0.762428	+	0.339455i
$238$	−5.31641	−	5.90447i	−0.344612	−	0.382730i
$239$	1.37323	+	13.0654i	0.0888270	+	0.845133i	0.944698	+	0.327943i	$0.106355\pi$
$239$	1.37323	+	13.0654i	0.0888270	+	0.845133i	−0.855871	+	0.517190i	$0.826978\pi$
$240$		0			0
$241$	−2.71749	+	25.8552i	−0.175049	+	1.66548i	0.456185	+	0.889885i	$0.349216\pi$
$241$	−2.71749	+	25.8552i	−0.175049	+	1.66548i	−0.631234	+	0.775593i	$0.717451\pi$
$242$	1.84424	+	3.19432i	0.118552	+	0.205339i
$243$	7.60596	−	13.1739i	0.487922	−	0.845106i
$244$	−0.0170635	−	0.0123974i	−0.00109238	−	0.000793659i
$245$		0			0
$246$	−1.89304	+	5.82618i	−0.120696	+	0.371464i
$247$	16.0049			1.01837
$248$	5.70406	−	14.6632i	0.362208	−	0.931113i
$249$	52.7515			3.34299
$250$		0			0
$251$	−11.3115	+	12.5627i	−0.713976	+	0.792951i	−0.985535	−	0.169471i	$-0.945794\pi$
$251$	−11.3115	+	12.5627i	−0.713976	+	0.792951i	0.271559	+	0.962422i	$0.412461\pi$
$252$	0.0189265	+	0.0137509i	0.00119226	+	0.000866228i
$253$	10.2817	−	17.8083i	0.646402	−	1.11960i
$254$	−4.64534	−	8.04597i	−0.291475	−	0.504849i
$255$		0			0
$256$	−0.0711076	+	0.0516627i	−0.00444423	+	0.00322892i
$257$	0.436951	+	4.15731i	0.0272562	+	0.259326i	0.999661	+	0.0260267i	$0.00828548\pi$
$257$	0.436951	+	4.15731i	0.0272562	+	0.259326i	−0.972405	+	0.233299i	$0.925048\pi$
$258$	37.8788	+	42.0687i	2.35823	+	2.61908i
$259$	−1.26354	+	0.562566i	−0.0785127	+	0.0349561i
$260$		0			0
$261$	14.7007	+	3.12473i	0.909951	+	0.193416i
$262$	−11.4965	−	5.11856i	−0.710254	−	0.316226i
$263$	5.68182	+	17.4868i	0.350356	+	1.07828i	0.958654	+	0.284575i	$0.0918526\pi$
$263$	5.68182	+	17.4868i	0.350356	+	1.07828i	−0.608298	+	0.793709i	$0.708147\pi$
$264$	7.88989	+	24.2826i	0.485589	+	1.49449i
$265$		0			0
$266$	5.18211	+	1.10149i	0.317736	+	0.0675368i
$267$	−23.3552	+	4.96429i	−1.42931	+	0.303810i
$268$	0.0307224	−	0.0136785i	0.00187667	−	0.000835548i
$269$	15.0877	+	16.7566i	0.919911	+	1.02167i	0.999691	+	0.0248525i	$0.00791161\pi$
$269$	15.0877	+	16.7566i	0.919911	+	1.02167i	−0.0797798	+	0.996813i	$0.525422\pi$
$270$		0			0
$271$	−7.89808	+	5.73829i	−0.479774	+	0.348576i	−0.801238	−	0.598345i	$-0.795825\pi$
$271$	−7.89808	+	5.73829i	−0.479774	+	0.348576i	0.321464	+	0.946922i	$0.395825\pi$
$272$	2.47531	−	23.5510i	0.150088	−	1.42799i
$273$	−6.01577	−	10.4196i	−0.364091	−	0.630624i
$274$	12.4730	−	21.6039i	0.753523	−	1.30514i
$275$		0			0
$276$	0.0542392	−	0.0602388i	0.00326482	−	0.00362595i
$277$	−7.94542	+	24.4535i	−0.477394	+	1.46927i	0.365308	+	0.930887i	$0.380964\pi$
$277$	−7.94542	+	24.4535i	−0.477394	+	1.46927i	−0.842702	+	0.538381i	$0.819036\pi$
$278$	−23.5281			−1.41112
$279$	−23.4344	−	29.2053i	−1.40298	−	1.74847i
$280$		0			0
$281$	0.0465029	−	0.143121i	0.00277413	−	0.00853790i	−0.949660	−	0.313283i	$-0.898571\pi$
$281$	0.0465029	−	0.143121i	0.00277413	−	0.00853790i	0.952434	+	0.304745i	$0.0985712\pi$
$282$	−4.42460	+	4.91402i	−0.263481	+	0.292626i
$283$	12.2037	+	8.86651i	0.725435	+	0.527059i	0.888116	−	0.459620i	$-0.152014\pi$
$283$	12.2037	+	8.86651i	0.725435	+	0.527059i	−0.162681	+	0.986679i	$0.552014\pi$
$284$	−0.0203423	+	0.0352339i	−0.00120709	+	0.00209075i
$285$		0			0
$286$	−1.74122	+	16.5666i	−0.102961	+	0.979604i
$287$	1.06641	−	0.774793i	0.0629482	−	0.0457346i
$288$	0.0145636	+	0.138564i	0.000858170	+	0.00816494i
$289$	11.9914	+	13.3177i	0.705374	+	0.783397i
$290$		0			0
$291$	0.0103839	−	0.00220717i	0.000608715	−	0.000129386i
$292$	0.0193301	+	0.00410875i	0.00113121	+	0.000240446i
$293$	3.77774	+	1.68196i	0.220698	+	0.0982610i	0.514107	−	0.857726i	$-0.328123\pi$
$293$	3.77774	+	1.68196i	0.220698	+	0.0982610i	−0.293410	+	0.955987i	$0.594790\pi$
$294$	8.31800	+	25.6002i	0.485116	+	1.49303i
$295$		0			0
$296$	−3.75909	−	1.67366i	−0.218493	−	0.0972793i
$297$	32.9237	+	6.99814i	1.91043	+	0.406073i
$298$	−5.72496	+	1.21688i	−0.331638	+	0.0704919i
$299$	−26.3360	+	11.7255i	−1.52305	+	0.678105i
$300$		0			0
$301$	−1.27324	−	12.1140i	−0.0733882	−	0.698242i
$302$	11.5004	−	8.35556i	0.661776	−	0.480808i
$303$	1.56224	−	14.8637i	0.0897484	−	0.853899i
$304$	7.89515	+	13.6748i	0.452818	+	0.784303i
$305$		0			0
$306$	−45.5118	−	33.0662i	−2.60174	−	1.89027i
$307$	6.95706	−	7.72660i	0.397060	−	0.440980i	−0.511152	−	0.859491i	$-0.670781\pi$
$307$	6.95706	−	7.72660i	0.397060	−	0.440980i	0.908212	+	0.418510i	$0.137448\pi$
$308$	−0.00311440	+	0.00958514i	−0.000177459	+	0.000546164i
$309$	−25.7741			−1.46624
$310$		0			0
$311$	−21.5627			−1.22271			−0.611353	−	0.791358i	$-0.709375\pi$
$311$	−21.5627			−1.22271			−0.611353	+	0.791358i	$0.709375\pi$
$312$	11.0611	−	34.0425i	0.626209	−	1.92727i
$313$	1.38020	−	1.53286i	0.0780134	−	0.0866426i	−0.702874	−	0.711314i	$-0.748100\pi$
$313$	1.38020	−	1.53286i	0.0780134	−	0.0866426i	0.780888	+	0.624671i	$0.214767\pi$
$314$	−26.7657	−	19.4464i	−1.51047	−	1.09742i
$315$		0			0
$316$	−0.00754414	−	0.0130668i	−0.000424391	−	0.000735067i
$317$	−2.27052	+	21.6026i	−0.127525	+	1.21332i	0.724295	+	0.689490i	$0.242165\pi$
$317$	−2.27052	+	21.6026i	−0.127525	+	1.21332i	−0.851821	+	0.523833i	$0.824501\pi$
$318$	−9.66370	+	7.02109i	−0.541914	+	0.393723i
$319$	0.676779	+	6.43912i	0.0378924	+	0.360522i
$320$		0			0
$321$	45.7573	−	20.3725i	2.55392	−	1.13708i
$322$	−9.33410	+	1.98402i	−0.520169	+	0.110565i
$323$	−22.7763	−	4.84126i	−1.26731	−	0.269375i
$324$	0.0537102	+	0.0239133i	0.00298390	+	0.00132852i
$325$		0			0
$326$	0.108327	+	0.333395i	0.00599966	+	0.0184650i
$327$	−19.4856	−	8.67556i	−1.07756	−	0.479759i
$328$	3.83588	+	0.815340i	0.211801	+	0.0450196i
$329$	1.39174	−	0.295823i	0.0767289	−	0.0163092i
$330$		0			0
$331$	−11.3089	−	12.5598i	−0.621594	−	0.690350i	0.347320	−	0.937747i	$-0.387092\pi$
$331$	−11.3089	−	12.5598i	−0.621594	−	0.690350i	−0.968914	+	0.247396i	$0.920425\pi$
$332$	0.00647540	+	0.0616093i	0.000355384	+	0.00338125i
$333$	−7.92276	+	5.75622i	−0.434164	+	0.315439i
$334$	−0.00848268	+	0.0807073i	−0.000464151	+	0.00441611i
$335$		0			0
$336$	5.93510	−	10.2799i	0.323786	−	0.560814i
$337$	3.50967	+	2.54993i	0.191184	+	0.138903i	0.679260	−	0.733898i	$-0.262301\pi$
$337$	3.50967	+	2.54993i	0.191184	+	0.138903i	−0.488076	+	0.872801i	$0.662301\pi$
$338$	3.31324	−	3.67972i	0.180216	−	0.200150i
$339$	13.7206	−	42.2277i	0.745201	−	2.29349i
$340$		0			0
$341$	8.84621	−	13.4895i	0.479049	−	0.730496i
$342$	37.5112			2.02837
$343$	3.84444	−	11.8320i	0.207580	−	0.638867i
$344$	24.2482	−	26.9303i	1.30737	−	1.45198i
$345$		0			0
$346$	−9.52940	+	16.5054i	−0.512304	+	0.887336i
$347$	5.24543	+	9.08535i	0.281589	+	0.487727i	0.971776	−	0.235904i	$-0.0758050\pi$
$347$	5.24543	+	9.08535i	0.281589	+	0.487727i	−0.690187	+	0.723631i	$0.742472\pi$
$348$	−0.00266782	+	0.0253826i	−0.000143010	+	0.00136065i
$349$	−4.52158	+	3.28512i	−0.242035	+	0.175849i	−0.702189	−	0.711990i	$-0.747794\pi$
$349$	−4.52158	+	3.28512i	−0.242035	+	0.175849i	0.460155	+	0.887839i	$0.347794\pi$
$350$		0			0
$351$	−31.5748	−	35.0674i	−1.68534	−	1.87176i
$352$	−0.0548332	+	0.0244133i	−0.00292262	+	0.00130123i
$353$	−29.2440	+	6.21600i	−1.55650	+	0.330844i	−0.904197	−	0.427115i	$-0.859530\pi$
$353$	−29.2440	+	6.21600i	−1.55650	+	0.330844i	−0.652302	+	0.757959i	$0.726197\pi$
$354$	−17.8531	−	3.79478i	−0.948879	−	0.201691i
$355$		0			0
$356$	−0.00866479	−	0.0266675i	−0.000459233	−	0.00141337i
$357$	5.40915	+	16.6477i	0.286283	+	0.881087i
$358$	−3.91784	−	1.74433i	−0.207064	−	0.0921909i
$359$	−4.53424	−	0.963782i	−0.239308	−	0.0508665i	0.0866962	−	0.996235i	$-0.472369\pi$
$359$	−4.53424	−	0.963782i	−0.239308	−	0.0508665i	−0.326004	+	0.945368i	$0.605702\pi$
$360$		0			0
$361$	−3.17318	+	1.41279i	−0.167009	+	0.0743574i
$362$	6.42327	+	7.13377i	0.337600	+	0.374942i
$363$	−0.849419	−	8.08168i	−0.0445829	−	0.424178i
$364$	0.0114308	−	0.00830495i	0.000599136	−	0.000435298i
$365$		0			0
$366$	12.7115	+	22.0169i	0.664439	+	1.15084i
$367$	13.2555	−	22.9593i	0.691934	−	1.19846i	−0.279270	−	0.960213i	$-0.590092\pi$
$367$	13.2555	−	22.9593i	0.691934	−	1.19846i	0.971203	−	0.238252i	$-0.0765743\pi$
$368$	−23.0098	−	16.7176i	−1.19947	−	0.871466i
$369$	6.24506	−	6.93584i	0.325105	−	0.361066i
$370$		0			0
$371$	2.57025			0.133441
$372$	0.0451648	−	0.0447625i	0.00234169	−	0.00232083i
$373$	1.86550			0.0965919			0.0482959	−	0.998833i	$-0.484621\pi$
$373$	1.86550			0.0965919			0.0482959	+	0.998833i	$0.484621\pi$
$374$	7.48906	−	23.0489i	0.387250	−	1.19183i
$375$		0			0
$376$	3.42455	+	2.48808i	0.176608	+	0.128313i
$377$	4.53846	−	7.86085i	0.233743	−	0.404854i
$378$	−7.80996	−	13.5272i	−0.401701	−	0.695766i
$379$	−0.152228	+	1.44835i	−0.00781942	+	0.0743968i	−0.997736	−	0.0672569i	$-0.978575\pi$
$379$	−0.152228	+	1.44835i	−0.00781942	+	0.0743968i	0.989916	+	0.141654i	$0.0452419\pi$
$380$		0			0
$381$	2.13955	+	20.3564i	0.109612	+	1.04289i
$382$	−10.6171	−	11.7914i	−0.543216	−	0.603303i
$383$	12.5951	−	5.60769i	0.643578	−	0.286539i	−0.0588794	−	0.998265i	$-0.518753\pi$
$383$	12.5951	−	5.60769i	0.643578	−	0.286539i	0.702458	+	0.711726i	$0.252086\pi$
$384$	34.6058	−	7.35568i	1.76597	−	0.375368i
$385$		0			0
$386$	−6.03768	−	2.68815i	−0.307310	−	0.136823i
$387$	−26.6511	−	82.0238i	−1.35475	−	4.16950i
$388$	3.85244e−6	0	1.18566e-5i	1.95578e−7	0	6.01927e-7i
$389$	−14.7869	−	6.58357i	−0.749727	−	0.333800i	−0.00394702	−	0.999992i	$-0.501256\pi$
$389$	−14.7869	−	6.58357i	−0.749727	−	0.333800i	−0.745780	+	0.666192i	$0.767923\pi$
$390$		0			0
$391$	41.0250	−	8.72014i	2.07473	−	0.440996i
$392$	15.7416	−	7.00862i	0.795071	−	0.353989i
$393$	18.5517	+	20.6038i	0.935812	+	1.03932i
$394$	2.00995	+	19.1234i	0.101260	+	0.963421i
$395$		0			0
$396$	−0.00745909	+	0.0709685i	−0.000374833	+	0.00356630i
$397$	−12.2144	−	21.1560i	−0.613023	−	1.06179i	−0.990728	−	0.135861i	$-0.956620\pi$
$397$	−12.2144	−	21.1560i	−0.613023	−	1.06179i	0.377705	−	0.925926i	$-0.376713\pi$
$398$	−5.40327	+	9.35874i	−0.270841	+	0.469111i
$399$	−9.44277	−	6.86057i	−0.472730	−	0.343458i
$400$		0			0
$401$	−2.02856	+	6.24326i	−0.101301	+	0.311774i	−0.988845	−	0.148951i	$-0.952410\pi$
$401$	−2.02856	+	6.24326i	−0.101301	+	0.311774i	0.887543	+	0.460725i	$0.152410\pi$
$402$	−40.5360			−2.02175
$403$	−21.1490	+	8.00998i	−1.05351	+	0.399006i
$404$	0.0175514			0.000873213
$405$		0			0
$406$	2.01047	−	2.23286i	0.0997781	−	0.110815i
$407$	−3.41315	−	2.47980i	−0.169183	−	0.122919i
$408$	−26.0381	+	45.0994i	−1.28908	+	2.23275i
$409$	−13.9181	−	24.1069i	−0.688208	−	1.19201i	−0.972417	−	0.233248i	$-0.925065\pi$
$409$	−13.9181	−	24.1069i	−0.688208	−	1.19201i	0.284210	−	0.958762i	$-0.408269\pi$
$410$		0			0
$411$	−44.4630	+	32.3043i	−2.19320	+	1.59345i
$412$	−0.00316384	−	0.0301020i	−0.000155871	−	0.00148302i
$413$	2.62790	+	2.91857i	0.129310	+	0.143614i
$414$	−61.7244	+	27.4815i	−3.03359	+	1.35064i
$415$		0			0
$416$	0.0823084	+	0.0174952i	0.00403550	+	0.000857772i
$417$	47.3540	+	21.0833i	2.31893	+	1.03246i
$418$	4.99370	+	15.3690i	0.244250	+	0.751723i
$419$	−6.28700	−	19.3494i	−0.307140	−	0.945279i	−0.978870	−	0.204483i	$-0.934449\pi$
$419$	−6.28700	−	19.3494i	−0.307140	−	0.945279i	0.671730	−	0.740796i	$-0.265551\pi$
$420$		0			0
$421$	13.0345	+	2.77056i	0.635262	+	0.135029i	0.514275	−	0.857625i	$-0.328061\pi$
$421$	13.0345	+	2.77056i	0.635262	+	0.135029i	0.120986	+	0.992654i	$0.461394\pi$
$422$	−25.7660	+	5.47673i	−1.25427	+	0.266603i
$423$	9.20326	−	4.09756i	0.447478	−	0.199230i
$424$	5.11657	+	5.68253i	0.248483	+	0.275968i
$425$		0			0
$426$	39.6738	−	28.8247i	1.92220	−	1.39656i
$427$	0.571807	−	5.44038i	0.0276717	−	0.263278i
$428$	0.0294102	+	0.0509399i	0.00142159	+	0.00246227i
$429$	18.3497	−	31.7826i	0.885931	−	1.53448i
$430$		0			0
$431$	−15.3433	+	17.0405i	−0.739062	+	0.820812i	−0.989072	−	0.147431i	$-0.952899\pi$
$431$	−15.3433	+	17.0405i	−0.739062	+	0.820812i	0.250010	+	0.968243i	$0.419566\pi$
$432$	14.3863	−	44.2764i	0.692161	−	2.13025i
$433$	−6.35044			−0.305183			−0.152591	−	0.988289i	$-0.548762\pi$
$433$	−6.35044			−0.305183			−0.152591	+	0.988289i	$0.548762\pi$
$434$	−7.39894	+	1.13797i	−0.355160	+	0.0546244i
$435$		0			0
$436$	0.00774040	−	0.0238225i	0.000370698	−	0.00114089i
$437$	−18.7133	+	20.7832i	−0.895179	+	0.994197i
$438$	−19.2710	−	14.0012i	−0.920802	−	0.669002i
$439$	−5.60915	+	9.71534i	−0.267710	+	0.463688i	−0.968270	−	0.249906i	$-0.919600\pi$
$439$	−5.60915	+	9.71534i	−0.267710	+	0.463688i	0.700560	+	0.713594i	$0.252934\pi$
$440$		0			0
$441$	4.28666	−	40.7849i	0.204127	−	1.94214i
$442$	−27.4871	+	19.9705i	−1.30743	+	0.949901i
$443$	0.202669	+	1.92826i	0.00962908	+	0.0916146i	0.998281	−	0.0586102i	$-0.0186669\pi$
$443$	0.202669	+	1.92826i	0.00962908	+	0.0916146i	−0.988652	+	0.150225i	$0.952000\pi$
$444$	−0.0111280	−	0.0123589i	−0.000528112	−	0.000586528i
$445$		0			0
$446$	−27.2768	+	5.79786i	−1.29159	+	0.274536i
$447$	12.6128	+	2.68094i	0.596566	+	0.126804i
$448$	−6.92906	−	3.08502i	−0.327367	−	0.145753i
$449$	3.70576	+	11.4052i	0.174886	+	0.538243i	0.999628	−	0.0272656i	$-0.00867999\pi$
$449$	3.70576	+	11.4052i	0.174886	+	0.538243i	−0.824743	+	0.565508i	$0.808680\pi$
$450$		0			0
$451$	3.67311	+	1.63538i	0.172960	+	0.0770068i
$452$	0.0510026	+	0.0108409i	0.00239896	+	0.000509915i
$453$	−30.6338	+	6.51141i	−1.43930	+	0.305933i
$454$	33.3508	−	14.8487i	1.56523	−	0.696885i
$455$		0			0
$456$	−3.62969	−	34.5342i	−0.169976	−	1.61721i
$457$	18.8873	−	13.7224i	0.883510	−	0.641908i	−0.0506677	−	0.998716i	$-0.516135\pi$
$457$	18.8873	−	13.7224i	0.883510	−	0.641908i	0.934178	+	0.356808i	$0.116135\pi$
$458$	−0.0447888	+	0.426137i	−0.00209284	+	0.0199121i
$459$	34.3262	+	59.4547i	1.60221	+	2.77511i
$460$		0			0
$461$	27.2238	+	19.7792i	1.26794	+	0.921210i	0.999118	−	0.0419810i	$-0.0133669\pi$
$461$	27.2238	+	19.7792i	1.26794	+	0.921210i	0.268818	+	0.963191i	$0.413367\pi$
$462$	8.12865	−	9.02778i	0.378179	−	0.420010i
$463$	−8.53149	+	26.2572i	−0.396492	+	1.22028i	0.531301	+	0.847183i	$0.321703\pi$
$463$	−8.53149	+	26.2572i	−0.396492	+	1.22028i	−0.927793	+	0.373094i	$0.878297\pi$
$464$	8.95519			0.415734
$465$		0			0
$466$	−0.624622			−0.0289350
$467$	−10.6023	+	32.6305i	−0.490615	+	1.50996i	0.333065	+	0.942904i	$0.391917\pi$
$467$	−10.6023	+	32.6305i	−0.490615	+	1.50996i	−0.823680	+	0.567055i	$0.808083\pi$
$468$	0.0669404	−	0.0743448i	0.00309432	−	0.00343659i
$469$	7.05647	+	5.12683i	0.325838	+	0.236735i
$470$		0			0
$471$	36.4443	+	63.1234i	1.67926	+	2.90857i
$472$	−1.22131	+	11.6200i	−0.0562153	+	0.534852i
$473$	30.0587	−	21.8389i	1.38210	−	1.00415i
$474$	1.90103	+	18.0871i	0.0873173	+	0.830769i
$475$		0			0
$476$	−0.0187791	+	0.00836098i	−0.000860737	+	0.000383225i
$477$	17.8008	−	3.78367i	0.815041	−	0.173242i
$478$	18.1897	+	3.86635i	0.831979	+	0.176843i
$479$	22.0079	+	9.79853i	1.00556	+	0.447706i	0.842377	−	0.538889i	$-0.181156\pi$
$479$	22.0079	+	9.79853i	1.00556	+	0.447706i	0.163188	+	0.986595i	$0.447822\pi$
$480$		0			0
$481$	1.82770	+	5.62509i	0.0833361	+	0.256482i
$482$	33.6183	+	14.9678i	1.53127	+	0.681766i
$483$	20.5642	+	4.37105i	0.935703	+	0.198890i
$484$	0.00933445	−	0.00198410i	0.000424293	−	9.01863e-5i
$485$		0			0
$486$	−14.4081	−	16.0018i	−0.653565	−	0.725858i
$487$	0.398851	+	3.79482i	0.0180737	+	0.171960i	0.999835	−	0.0181573i	$-0.00577997\pi$
$487$	0.398851	+	3.79482i	0.0180737	+	0.171960i	−0.981761	+	0.190117i	$0.939113\pi$
$488$	13.1664	−	9.56592i	0.596013	−	0.433029i
$489$	0.0807285	−	0.768080i	0.00365067	−	0.0347338i
$490$		0			0
$491$	−1.42799	+	2.47336i	−0.0644445	+	0.111621i	−0.896447	−	0.443150i	$-0.853861\pi$
$491$	−1.42799	+	2.47336i	−0.0644445	+	0.111621i	0.832003	+	0.554771i	$0.187194\pi$
$492$	0.0128225	+	0.00931607i	0.000578082	+	0.000420001i
$493$	−8.83639	+	9.81381i	−0.397971	+	0.441992i
$494$	7.00081	−	21.5463i	0.314981	−	0.969413i
$495$		0			0
$496$	−17.2765	−	14.1187i	−0.775738	−	0.633947i
$497$	−10.5520			−0.473322
$498$	23.0744	−	71.0156i	1.03399	−	3.18229i
$499$	−11.4047	+	12.6662i	−0.510545	+	0.567018i	−0.942213	−	0.335015i	$-0.891259\pi$
$499$	−11.4047	+	12.6662i	−0.510545	+	0.567018i	0.431667	+	0.902033i	$0.357925\pi$
$500$		0			0
$501$	0.0893939	−	0.154835i	0.00399382	−	0.00691750i
$502$	11.9644	+	20.7230i	0.533998	+	0.924912i
$503$	2.08330	−	19.8213i	0.0928897	−	0.883786i	−0.844512	−	0.535536i	$-0.820109\pi$
$503$	2.08330	−	19.8213i	0.0928897	−	0.883786i	0.937402	−	0.348250i	$-0.113224\pi$
$504$	−14.6039	+	10.6104i	−0.650510	+	0.472623i
$505$		0			0
$506$	−19.4767	−	21.6311i	−0.865846	−	0.961620i
$507$	−9.96577	+	4.43705i	−0.442596	+	0.197056i
$508$	−0.0235120	+	0.00499762i	−0.00104317	+	0.000221734i
$509$	22.1274	+	4.70332i	0.980780	+	0.208471i	0.670285	−	0.742104i	$-0.266172\pi$
$509$	22.1274	+	4.70332i	0.980780	+	0.208471i	0.310495	+	0.950575i	$0.399505\pi$
$510$		0			0
$511$	1.58386	+	4.87462i	0.0700659	+	0.215641i
$512$	−6.97295	−	21.4605i	−0.308164	−	0.948431i
$513$	−41.8197	−	18.6193i	−1.84638	−	0.822063i
$514$	5.78782	+	1.23024i	0.255290	+	0.0542635i
$515$		0			0
$516$	0.133799	−	0.0595710i	0.00589016	−	0.00262247i
$517$	2.90403	+	3.22525i	0.127719	+	0.141846i
$518$	0.204648	+	1.94709i	0.00899170	+	0.0855503i
$519$	33.9698	−	24.6805i	1.49111	−	1.08335i
$520$		0			0
$521$	−1.76098	−	3.05010i	−0.0771499	−	0.133628i	0.824869	−	0.565324i	$-0.191249\pi$
$521$	−1.76098	−	3.05010i	−0.0771499	−	0.133628i	−0.902019	+	0.431696i	$0.857915\pi$
$522$	10.6369	−	18.4237i	0.465566	−	0.806383i
$523$	31.8259	+	23.1228i	1.39165	+	1.01109i	0.995682	+	0.0928261i	$0.0295901\pi$
$523$	31.8259	+	23.1228i	1.39165	+	1.01109i	0.395966	+	0.918265i	$0.370410\pi$
$524$	−0.0217862	+	0.0241960i	−0.000951735	+	0.00105701i
$525$		0			0
$526$	26.0266			1.13481
$527$	32.5197	−	5.00159i	1.41658	−	0.217873i
$528$	36.2072			1.57572
$529$	8.45898	−	26.0341i	0.367782	−	1.13192i
$530$		0			0
$531$	22.4964	+	16.3446i	0.976263	+	0.709296i
$532$	0.00685344	−	0.0118705i	0.000297134	−	0.000514652i
$533$	−2.81839	−	4.88159i	−0.122078	−	0.211445i
$534$	−3.53285	+	33.6128i	−0.152881	+	1.45457i
$535$		0			0
$536$	2.71243	+	25.8070i	0.117159	+	1.11469i
$537$	6.32217	+	7.02148i	0.272822	+	0.302999i
$538$	29.1577	−	12.9819i	1.25708	−	0.559688i
$539$	17.2809	−	3.67318i	0.744343	−	0.158215i
$540$		0			0
$541$	1.04711	+	0.466202i	0.0450186	+	0.0200436i	0.429122	−	0.903246i	$-0.358823\pi$
$541$	1.04711	+	0.466202i	0.0450186	+	0.0200436i	−0.384104	+	0.923290i	$0.625490\pi$
$542$	4.27030	+	13.1426i	0.183425	+	0.564525i
$543$	−6.53532	−	20.1137i	−0.280458	−	0.863160i
$544$	−0.111840	−	0.0497942i	−0.00479508	−	0.00213491i
$545$		0			0
$546$	−16.6586	+	3.54089i	−0.712921	+	0.151536i
$547$	−24.5971	+	10.9514i	−1.05170	+	0.468246i	−0.858446	−	0.512903i	$-0.828570\pi$
$547$	−24.5971	+	10.9514i	−1.05170	+	0.468246i	−0.193251	+	0.981149i	$0.561903\pi$
$548$	−0.0431866	−	0.0479636i	−0.00184484	−	0.00204890i
$549$	−4.04863	−	38.5202i	−0.172791	−	1.64400i
$550$		0			0
$551$	0.920436	−	8.75736i	0.0392119	−	0.373076i
$552$	31.2731	+	54.1665i	1.33107	+	2.30548i
$553$	1.95666	−	3.38903i	0.0832054	−	0.144116i
$554$	29.4445	+	21.3927i	1.25098	+	0.908888i
$555$		0			0
$556$	−0.0188107	+	0.0578935i	−0.000797753	+	0.00245523i
$557$	−5.09359			−0.215822			−0.107911	−	0.994161i	$-0.534416\pi$
$557$	−5.09359			−0.215822			−0.107911	+	0.994161i	$0.534416\pi$
$558$	−49.5676	+	18.7732i	−2.09836	+	0.794734i
$559$	−52.0881			−2.20309
$560$		0			0
$561$	−35.7269	+	39.6787i	−1.50839	+	1.67524i
$562$	−0.172333	−	0.125207i	−0.00726942	−	0.00528154i
$563$	−14.9324	+	25.8636i	−0.629325	+	1.09002i	0.358363	+	0.933582i	$0.383335\pi$
$563$	−14.9324	+	25.8636i	−0.629325	+	1.09002i	−0.987688	+	0.156440i	$0.949998\pi$
$564$	0.00855401	+	0.0148160i	0.000360189	+	0.000623866i
$565$		0			0
$566$	17.2744	−	12.5506i	0.726098	−	0.527541i
$567$	1.59392	+	15.1651i	0.0669382	+	0.636875i
$568$	−21.0058	−	23.3293i	−0.881384	−	0.978876i
$569$	−12.6321	+	5.62416i	−0.529564	+	0.235777i	−0.654059	−	0.756443i	$-0.726935\pi$
$569$	−12.6321	+	5.62416i	−0.529564	+	0.235777i	0.124496	+	0.992220i	$0.460269\pi$
$570$		0			0
$571$	10.9925	+	2.33652i	0.460020	+	0.0977803i	0.432092	−	0.901830i	$-0.357776\pi$
$571$	10.9925	+	2.33652i	0.460020	+	0.0977803i	0.0279284	+	0.999610i	$0.491109\pi$
$572$	0.0393719	+	0.0175295i	0.00164622	+	0.000732944i
$573$	10.8023	+	33.2460i	0.451271	+	1.38887i
$574$	−0.576583	−	1.77454i	−0.0240661	−	0.0740678i
$575$		0			0
$576$	−52.5300	−	11.1656i	−2.18875	−	0.465233i
$577$	−22.8300	+	4.85267i	−0.950427	+	0.202020i	−0.656939	−	0.753943i	$-0.728149\pi$
$577$	−22.8300	+	4.85267i	−0.950427	+	0.202020i	−0.293488	+	0.955963i	$0.594816\pi$
$578$	23.1739	−	10.3177i	0.963908	−	0.429160i
$579$	9.74295	+	10.8206i	0.404903	+	0.449690i
$580$		0			0
$581$	−12.9985	+	9.44399i	−0.539270	+	0.391803i
$582$	0.00157074	−	0.0149446i	6.51091e−5	−	0.000619472i
$583$	3.91997	+	6.78958i	0.162348	+	0.281196i
$584$	−7.62426	+	13.2056i	−0.315494	+	0.546452i
$585$		0			0
$586$	3.91674	−	4.34998i	0.161799	−	0.179696i
$587$	−0.00933469	+	0.0287292i	−0.000385284	+	0.00118578i	−0.951249	−	0.308424i	$-0.900198\pi$
$587$	−0.00933469	+	0.0287292i	−0.000385284	+	0.00118578i	0.950864	+	0.309610i	$0.100198\pi$
$588$	0.0696423			0.00287200
$589$	−15.5825	+	15.4437i	−0.642066	+	0.636347i
$590$		0			0
$591$	13.0910	−	40.2898i	0.538490	−	1.65730i
$592$	−3.90455	+	4.33644i	−0.160476	+	0.178227i
$593$	−6.17320	−	4.48509i	−0.253503	−	0.184181i	0.453775	−	0.891116i	$-0.350077\pi$
$593$	−6.17320	−	4.48509i	−0.253503	−	0.184181i	−0.707278	+	0.706936i	$0.750077\pi$
$594$	23.8224	−	41.2617i	0.977446	−	1.69299i
$595$		0			0
$596$	−0.00158285	+	0.0150598i	−6.48360e−5	+	0.000616873i
$597$	19.2612	−	13.9941i	0.788309	−	0.572740i
$598$	4.26546	+	40.5832i	0.174428	+	1.65957i
$599$	−5.47027	−	6.07535i	−0.223509	−	0.248232i	0.620952	−	0.783848i	$-0.286746\pi$
$599$	−5.47027	−	6.07535i	−0.223509	−	0.248232i	−0.844462	+	0.535616i	$0.820079\pi$
$600$		0			0
$601$	−0.823421	+	0.175024i	−0.0335880	+	0.00713936i	−0.224675	−	0.974434i	$-0.572132\pi$
$601$	−0.823421	+	0.175024i	−0.0335880	+	0.00713936i	0.191087	+	0.981573i	$0.438799\pi$
$602$	−16.8652	−	3.58481i	−0.687374	−	0.146106i
$603$	56.4182	+	25.1190i	2.29753	+	1.02292i
$604$	−0.0113652	−	0.0349784i	−0.000462442	−	0.00142325i
$605$		0			0
$606$	−19.3266	−	8.60477i	−0.785091	−	0.349545i
$607$	44.0600	+	9.36525i	1.78834	+	0.380124i	0.978455	−	0.206462i	$-0.0661950\pi$
$607$	44.0600	+	9.36525i	1.78834	+	0.380124i	0.809887	+	0.586586i	$0.199528\pi$
$608$	0.0798481	−	0.0169722i	0.00323827	−	0.000688315i
$609$	−6.04723	+	2.69240i	−0.245046	+	0.109102i
$610$		0			0
$611$	−0.635991	−	6.05105i	−0.0257294	−	0.244799i
$612$	−0.117750	+	0.0855503i	−0.00475975	+	0.00345816i
$613$	−4.13767	+	39.3673i	−0.167119	+	1.59003i	0.513956	+	0.857816i	$0.328179\pi$
$613$	−4.13767	+	39.3673i	−0.167119	+	1.59003i	−0.681075	+	0.732213i	$0.738487\pi$
$614$	−7.35863	−	12.7455i	−0.296970	−	0.514368i
$615$		0			0
$616$	−6.29140	−	4.57097i	−0.253488	−	0.184170i
$617$	−19.8433	+	22.0382i	−0.798862	+	0.887226i	−0.995645	−	0.0932207i	$-0.970284\pi$
$617$	−19.8433	+	22.0382i	−0.798862	+	0.887226i	0.196783	+	0.980447i	$0.436950\pi$
$618$	−11.2740	+	34.6978i	−0.453507	+	1.39575i
$619$	−19.6256			−0.788820			−0.394410	−	0.918934i	$-0.629051\pi$
$619$	−19.6256			−0.788820			−0.394410	+	0.918934i	$0.629051\pi$
$620$		0			0
$621$	82.4548			3.30880
$622$	−9.43185	+	29.0283i	−0.378183	+	1.16393i
$623$	4.86621	−	5.40448i	0.194961	−	0.216526i
$624$	−41.0657	−	29.8360i	−1.64394	−	1.19439i
$625$		0			0
$626$	−1.45986	−	2.52856i	−0.0583479	−	0.101062i
$627$	3.72146	−	35.4074i	0.148621	−	1.41403i
$628$	−0.0692491	+	0.0503124i	−0.00276334	+	0.00200769i
$629$	−0.899463	−	8.55782i	−0.0358639	−	0.341223i
$630$		0			0
$631$	18.0599	−	8.04080i	0.718955	−	0.320099i	−0.0144462	−	0.999896i	$-0.504599\pi$
$631$	18.0599	−	8.04080i	0.718955	−	0.320099i	0.733401	+	0.679796i	$0.237932\pi$
$632$	11.3879	−	2.42056i	0.452985	−	0.0962848i
$633$	56.7658	+	12.0659i	2.25624	+	0.479578i
$634$	28.0889	+	12.5060i	1.11555	+	0.496675i
$635$		0			0
$636$	0.00955003	+	0.0293920i	0.000378683	+	0.00116547i
$637$	−22.6266	−	10.0740i	−0.896499	−	0.399147i
$638$	8.96456	+	1.90548i	0.354910	+	0.0754385i
$639$	−73.0800	+	15.5336i	−2.89100	+	0.614501i
$640$		0			0
$641$	27.0021	+	29.9889i	1.06652	+	1.18449i	0.982158	+	0.188056i	$0.0602187\pi$
$641$	27.0021	+	29.9889i	1.06652	+	1.18449i	0.0843623	+	0.996435i	$0.473115\pi$
$642$	−7.41101	−	70.5110i	−0.292489	−	2.78285i
$643$	23.2581	−	16.8980i	0.917208	−	0.666391i	−0.0256194	−	0.999672i	$-0.508156\pi$
$643$	23.2581	−	16.8980i	0.917208	−	0.666391i	0.942828	+	0.333281i	$0.108156\pi$
$644$	−0.00258071	+	0.0245538i	−0.000101694	+	0.000967555i
$645$		0			0
$646$	−16.4802	+	28.5445i	−0.648403	+	1.12307i
$647$	−31.4131	−	22.8229i	−1.23498	−	0.897262i	−0.237723	−	0.971333i	$-0.576401\pi$
$647$	−31.4131	−	22.8229i	−1.23498	−	0.897262i	−0.997253	+	0.0740708i	$0.976401\pi$
$648$	−30.3553	+	33.7130i	−1.19247	+	1.32437i
$649$	−3.70184	+	11.3931i	−0.145310	+	0.447217i
$650$		0			0
$651$	15.9112	+	4.33978i	0.623611	+	0.170090i
$652$	0.000906962	0		3.55194e−5	0
$653$	13.4677	−	41.4492i	0.527030	−	1.62203i	−0.233235	−	0.972420i	$-0.574931\pi$
$653$	13.4677	−	41.4492i	0.527030	−	1.62203i	0.760266	−	0.649612i	$-0.225069\pi$
$654$	−20.2026	+	22.4373i	−0.789984	+	0.877366i
$655$		0			0
$656$	2.78059	−	4.81612i	0.108564	−	0.188038i
$657$	18.1453	+	31.4285i	0.707915	+	1.22614i
$658$	0.210523	−	2.00299i	0.00820704	−	0.0780848i
$659$	1.37480	−	0.998853i	0.0535548	−	0.0389098i	−0.560686	−	0.828029i	$-0.689462\pi$
$659$	1.37480	−	0.998853i	0.0535548	−	0.0389098i	0.614241	+	0.789119i	$0.289462\pi$
$660$		0			0
$661$	2.18741	+	2.42937i	0.0850804	+	0.0944914i	0.784182	−	0.620531i	$-0.213083\pi$
$661$	2.18741	+	2.42937i	0.0850804	+	0.0944914i	−0.699101	+	0.715023i	$0.746416\pi$
$662$	−21.8551	+	9.73051i	−0.849422	+	0.378187i
$663$	73.2175	−	15.5629i	2.84353	−	0.604411i
$664$	−46.7557	−	9.93822i	−1.81447	−	0.385678i
$665$		0			0
$666$	4.28364	+	13.1837i	0.165988	+	0.510858i
$667$	4.90125	+	15.0845i	0.189777	+	0.584074i
$668$	0.000191807	0	8.53981e-5i	7.42124e−6	0	3.30415e-6i
$669$	60.0942	+	12.7734i	2.32337	+	0.493849i
$670$		0			0
$671$	15.2434	−	6.78681i	0.588466	−	0.262002i
$672$	−0.0410619	−	0.0456038i	−0.00158400	−	0.00175921i
$673$	1.94049	+	18.4625i	0.0748004	+	0.711678i	0.966083	+	0.258231i	$0.0831395\pi$
$673$	1.94049	+	18.4625i	0.0748004	+	0.711678i	−0.891283	+	0.453448i	$0.850194\pi$
$674$	4.96797	−	3.60944i	0.191359	−	0.139031i
$675$		0			0
$676$	−0.00640542	−	0.0110945i	−0.000246362	−	0.000426712i
$677$	12.6762	−	21.9558i	0.487186	−	0.843831i	−0.512705	−	0.858565i	$-0.671357\pi$
$677$	12.6762	−	21.9558i	0.487186	−	0.843831i	0.999891	+	0.0147335i	$0.00468999\pi$
$678$	−50.8465	−	36.9421i	−1.95275	−	1.41875i
$679$	−0.00216356	+	0.00240288i	−8.30298e−5	+	9.22139e-5i
$680$		0			0
$681$	−80.4295			−3.08206
$682$	−14.2904	−	17.8095i	−0.547209	−	0.681962i
$683$	−19.8387			−0.759106			−0.379553	−	0.925170i	$-0.623922\pi$
$683$	−19.8387			−0.759106			−0.379553	+	0.925170i	$0.623922\pi$
$684$	0.0299902	−	0.0923005i	0.00114671	−	0.00352920i
$685$		0			0
$686$	−14.2469	−	10.3510i	−0.543950	−	0.395203i
$687$	0.472002	−	0.817532i	0.0180080	−	0.0311908i
$688$	−25.6948	−	44.5046i	−0.979604	−	1.69672i
$689$	1.14888	−	10.9308i	0.0437687	−	0.416431i
$690$		0			0
$691$	2.77024	+	26.3571i	0.105385	+	1.00267i	0.911608	+	0.411060i	$0.134841\pi$
$691$	2.77024	+	26.3571i	0.105385	+	1.00267i	−0.806223	+	0.591612i	$0.798492\pi$
$692$	0.0329946	+	0.0366442i	0.00125427	+	0.00139300i
$693$	−16.9077	+	7.52781i	−0.642272	+	0.285958i
$694$	14.5254	−	3.08747i	0.551376	−	0.117199i
$695$		0			0
$696$	−17.9908	−	8.01001i	−0.681939	−	0.303619i
$697$	2.53418	+	7.79942i	0.0959891	+	0.295424i
$698$	2.44471	+	7.52404i	0.0925336	+	0.284789i
$699$	1.25715	+	0.559718i	0.0475497	+	0.0211705i
$700$		0			0
$701$	−10.2362	+	2.17576i	−0.386615	+	0.0821775i	−0.397119	−	0.917767i	$-0.629990\pi$
$701$	−10.2362	+	2.17576i	−0.386615	+	0.0821775i	0.0105038	+	0.999945i	$0.496656\pi$
$702$	−61.0200	+	27.1679i	−2.30305	+	1.02539i
$703$	3.83932	+	4.26400i	0.144803	+	0.160820i
$704$	−2.41833	−	23.0089i	−0.0911444	−	0.867181i
$705$		0			0
$706$	−4.42363	+	42.0880i	−0.166486	+	1.58400i
$707$	2.27607	+	3.94226i	0.0856003	+	0.148264i
$708$	−0.0236110	+	0.0408955i	−0.000887356	+	0.00153695i
$709$	0.951875	+	0.691578i	0.0357484	+	0.0259728i	0.605516	−	0.795833i	$-0.292967\pi$
$709$	0.951875	+	0.691578i	0.0357484	+	0.0259728i	−0.569768	+	0.821806i	$0.692967\pi$
$710$		0			0
$711$	8.56220	−	26.3518i	0.321108	−	0.988268i
$712$	21.6358			0.810837
$713$	14.3265	−	36.8285i	0.536532	−	1.37924i
$714$	24.7776			0.927278
$715$		0			0
$716$	−0.00742444	+	0.00824567i	−0.000277464	+	0.000308155i
$717$	−33.1451	−	24.0813i	−1.23783	−	0.899333i
$718$	−3.28082	+	5.68255i	−0.122439	+	0.212071i
$719$	19.4477	+	33.6843i	0.725276	+	1.25621i	0.958860	+	0.283878i	$0.0916210\pi$
$719$	19.4477	+	33.6843i	0.725276	+	1.25621i	−0.233585	+	0.972336i	$0.575046\pi$
$720$		0			0
$721$	6.35101	−	4.61428i	0.236524	−	0.171845i
$722$	0.513939	+	4.88980i	0.0191268	+	0.181980i
$723$	−54.2495	−	60.2501i	−2.01756	−	2.24073i
$724$	0.0226888	−	0.0101017i	0.000843223	−	0.000375427i
$725$		0			0
$726$	−11.2513	−	2.39155i	−0.417576	−	0.0887586i
$727$	7.67746	+	3.41823i	0.284741	+	0.126775i	0.544138	−	0.838996i	$-0.316857\pi$
$727$	7.67746	+	3.41823i	0.284741	+	0.126775i	−0.259396	+	0.965771i	$0.583524\pi$
$728$	3.36898	+	10.3687i	0.124863	+	0.384288i
$729$	−0.223240	−	0.687063i	−0.00826816	−	0.0254468i
$730$		0			0
$731$	74.1256	+	15.7559i	2.74163	+	0.582752i
$732$	0.0643378	−	0.0136754i	0.00237799	−	0.000505458i
$733$	−36.7154	+	16.3468i	−1.35611	+	0.603781i	−0.950632	−	0.310321i	$-0.899563\pi$
$733$	−36.7154	+	16.3468i	−1.35611	+	0.603781i	−0.405483	+	0.914102i	$0.632897\pi$
$734$	−25.1102	−	27.8877i	−0.926835	−	1.02935i
$735$		0			0
$736$	−0.118955	+	0.0864260i	−0.00438475	+	0.00318570i
$737$	−2.78101	+	26.4595i	−0.102440	+	0.974649i
$738$	−6.60554	−	11.4411i	−0.243153	−	0.421154i
$739$	−4.55735	+	7.89357i	−0.167645	+	0.290370i	−0.937591	−	0.347739i	$-0.886950\pi$
$739$	−4.55735	+	7.89357i	−0.167645	+	0.290370i	0.769946	+	0.638109i	$0.220283\pi$
$740$		0			0
$741$	−33.3977	+	37.0919i	−1.22689	+	1.36260i
$742$	1.12427	−	3.46014i	0.0412732	−	0.127026i
$743$	6.65317			0.244081			0.122041	−	0.992525i	$-0.461056\pi$
$743$	6.65317			0.244081			0.122041	+	0.992525i	$0.461056\pi$
$744$	22.0796	+	43.8171i	0.809478	+	1.60641i
$745$		0			0
$746$	0.815999	−	2.51139i	0.0298759	−	0.0919484i
$747$	−76.1213	+	84.5413i	−2.78513	+	3.09321i
$748$	−0.0507270	−	0.0368553i	−0.00185476	−	0.00134756i
$749$	−7.62784	+	13.2118i	−0.278715	+	0.482749i
$750$		0			0
$751$	4.14886	−	39.4738i	0.151394	−	1.44042i	−0.610139	−	0.792294i	$-0.708887\pi$
$751$	4.14886	−	39.4738i	0.151394	−	1.44042i	0.761534	−	0.648125i	$-0.224447\pi$
$752$	4.85635	−	3.52835i	0.177093	−	0.128666i
$753$	−5.51056	−	52.4295i	−0.200816	−	1.91064i
$754$	−8.59729	−	9.54826i	−0.313095	−	0.347727i
$755$		0			0
$756$	−0.0395293	+	0.00840222i	−0.00143767	+	0.000305586i
$757$	13.7095	+	2.91405i	0.498281	+	0.105913i	0.450195	−	0.892930i	$-0.351354\pi$
$757$	13.7095	+	2.91405i	0.498281	+	0.105913i	0.0480862	+	0.998843i	$0.484688\pi$
$758$	1.88322	+	0.838465i	0.0684017	+	0.0304544i
$759$	19.8165	+	60.9889i	0.719293	+	2.21376i
$760$		0			0
$761$	−31.5132	−	14.0306i	−1.14235	−	0.508609i	−0.253743	−	0.967272i	$-0.581662\pi$
$761$	−31.5132	−	14.0306i	−1.14235	−	0.508609i	−0.888610	+	0.458663i	$0.848328\pi$
$762$	28.3403	+	6.02391i	1.02666	+	0.218223i
$763$	6.35463	−	1.35072i	0.230053	−	0.0488993i
$764$	−0.0375025	+	0.0166972i	−0.00135679	+	0.000604083i
$765$		0			0
$766$	−2.03994	−	19.4087i	−0.0737060	−	0.701266i
$767$	13.5868	−	9.87142i	0.490593	−	0.356436i
$768$	0.0286513	−	0.272599i	0.00103387	−	0.00983657i
$769$	13.5658	+	23.4966i	0.489195	+	0.847310i	0.999923	−	0.0124321i	$-0.00395735\pi$
$769$	13.5658	+	23.4966i	0.489195	+	0.847310i	−0.510728	+	0.859742i	$0.670624\pi$
$770$		0			0
$771$	−10.5465	−	7.66246i	−0.379822	−	0.275957i
$772$	−0.0114416	+	0.0127072i	−0.000411793	+	0.000457342i
$773$	8.71995	−	26.8373i	0.313635	−	0.965269i	−0.662678	−	0.748905i	$-0.730580\pi$
$773$	8.71995	−	26.8373i	0.313635	−	0.965269i	0.976313	−	0.216364i	$-0.0694199\pi$
$774$	−122.080			−4.38809
$775$		0			0
$776$	−0.00961947			−0.000345319
$777$	1.33289	−	4.10221i	0.0478171	−	0.147166i
$778$	−15.3310	+	17.0268i	−0.549644	+	0.610441i
$779$	−4.42393	−	3.21418i	−0.158504	−	0.115160i
$780$		0			0
$781$	−16.0932	−	27.8742i	−0.575860	−	0.997419i
$782$	6.20571	−	59.0434i	0.221916	−	2.11139i
$783$	−21.0036	+	15.2600i	−0.750606	+	0.545347i
$784$	−2.55423	−	24.3019i	−0.0912226	−	0.867925i
$785$		0			0
$786$	35.8522	−	15.9624i	1.27881	−	0.569361i
$787$	0.775181	−	0.164770i	0.0276322	−	0.00587341i	−0.194075	−	0.980987i	$-0.562170\pi$
$787$	0.775181	−	0.164770i	0.0276322	−	0.00587341i	0.221707	+	0.975113i	$0.428837\pi$
$788$	0.0486621	+	0.0103434i	0.00173351	+	0.000368470i
$789$	−52.3825	−	23.3222i	−1.86487	−	0.830293i
$790$		0			0
$791$	4.17902	+	12.8617i	0.148589	+	0.457310i
$792$	−50.3013	−	22.3956i	−1.78738	−	0.795792i
$793$	−22.8814	−	4.86359i	−0.812543	−	0.172711i
$794$	−33.8235	+	7.18941i	−1.20035	+	0.255143i
$795$		0			0
$796$	0.0187083	+	0.0207777i	0.000663097	+	0.000736444i
$797$	2.79155	+	26.5598i	0.0988817	+	0.940796i	0.925682	+	0.378301i	$0.123492\pi$
$797$	2.79155	+	26.5598i	0.0988817	+	0.940796i	−0.826801	+	0.562495i	$0.809842\pi$
$798$	−13.3663	+	9.71120i	−0.473162	+	0.343773i
$799$	−0.925287	+	8.80351i	−0.0327343	+	0.311446i
$800$		0			0
$801$	25.7460	−	44.5933i	0.909689	−	1.57563i
$802$	7.51753	+	5.46181i	0.265453	+	0.192863i
$803$	−10.4612	+	11.6184i	−0.369169	+	0.410004i
$804$	−0.0324086	+	0.0997433i	−0.00114296	+	0.00351767i
$805$		0			0
$806$	1.53235	+	31.9751i	0.0539746	+	1.12627i
$807$	−70.3174			−2.47529
$808$	−4.18495	+	12.8800i	−0.147226	+	0.453116i
$809$	−22.5806	+	25.0783i	−0.793890	+	0.881705i	−0.995204	−	0.0978222i	$-0.968812\pi$
$809$	−22.5806	+	25.0783i	−0.793890	+	0.881705i	0.201313	+	0.979527i	$0.435479\pi$
$810$		0			0
$811$	4.46711	−	7.73726i	0.156861	−	0.271692i	−0.776874	−	0.629656i	$-0.783196\pi$
$811$	4.46711	−	7.73726i	0.156861	−	0.271692i	0.933735	+	0.357964i	$0.116529\pi$
$812$	−0.00388681	−	0.00673216i	−0.000136400	−	0.000236252i
$813$	3.18237	−	30.2782i	0.111610	−	1.06190i
$814$	−4.83133	+	3.51017i	−0.169338	+	0.123031i
$815$		0			0
$816$	49.4149	+	54.8808i	1.72987	+	1.92121i
$817$	−46.1624	+	20.5528i	−1.61502	+	0.719053i
$818$	−38.5414	+	8.19223i	−1.34757	+	0.286435i
$819$	25.3797	+	5.39462i	0.886838	+	0.188503i
$820$		0			0
$821$	−5.15729	−	15.8725i	−0.179991	−	0.553955i	0.819835	−	0.572599i	$-0.194065\pi$
$821$	−5.15729	−	15.8725i	−0.179991	−	0.553955i	−0.999826	+	0.0186447i	$0.994065\pi$
$822$	24.0401	+	73.9878i	0.838494	+	2.58062i
$823$	42.7184	+	19.0195i	1.48907	+	0.662977i	0.980226	−	0.197881i	$-0.0634059\pi$
$823$	42.7184	+	19.0195i	1.48907	+	0.662977i	0.508845	+	0.860858i	$0.330073\pi$
$824$	22.8446	+	4.85576i	0.795828	+	0.169158i
$825$		0			0
$826$	5.07855	−	2.26112i	0.176705	−	0.0786743i
$827$	−15.3547	−	17.0531i	−0.533935	−	0.592994i	0.414468	−	0.910064i	$-0.363968\pi$
$827$	−15.3547	−	17.0531i	−0.533935	−	0.592994i	−0.948402	+	0.317070i	$0.897301\pi$
$828$	0.0182725	+	0.173851i	0.000635013	+	0.00604174i
$829$	10.9766	−	7.97494i	0.381232	−	0.276981i	−0.380621	−	0.924731i	$-0.624290\pi$
$829$	10.9766	−	7.97494i	0.381232	−	0.276981i	0.761853	+	0.647750i	$0.224290\pi$
$830$		0			0
$831$	−40.0918	−	69.4411i	−1.39077	−	2.40889i
$832$	−16.2173	+	28.0891i	−0.562233	+	0.973816i
$833$	29.1523	+	21.1804i	1.01007	+	0.733856i
$834$	49.0964	−	54.5270i	1.70007	−	1.88812i
$835$		0			0
$836$	0.0418096			0.00144602
$837$	64.5792	+	3.67420i	2.23218	+	0.126999i
$838$	−28.7987			−0.994835
$839$	−5.03944	+	15.5098i	−0.173981	+	0.535458i	−0.999585	−	0.0287910i	$-0.990834\pi$
$839$	−5.03944	+	15.5098i	−0.173981	+	0.535458i	0.825605	+	0.564249i	$0.190834\pi$
$840$		0			0
$841$	19.4213	+	14.1104i	0.669700	+	0.486566i
$842$	9.43130	−	16.3355i	0.325024	−	0.562958i
$843$	0.234649	+	0.406425i	0.00808176	+	0.0139980i
$844$	−0.00712383	+	0.0677787i	−0.000245212	+	0.00233304i
$845$		0			0
$846$	−1.49059	−	14.1820i	−0.0512476	−	0.487588i
$847$	1.65615	+	1.83934i	0.0569060	+	0.0632005i
$848$	9.90616	−	4.41051i	0.340179	−	0.151457i
$849$	−46.0140	+	9.78057i	−1.57920	+	0.335668i
$850$		0			0
$851$	−9.44147	−	4.20361i	−0.323649	−	0.144098i
$852$	−0.0392071	−	0.120667i	−0.00134321	−	0.00413398i
$853$	13.4414	+	41.3684i	0.460225	+	1.41643i	0.864890	+	0.501961i	$0.167388\pi$
$853$	13.4414	+	41.3684i	0.460225	+	1.41643i	−0.404665	+	0.914465i	$0.632612\pi$
$854$	−7.07387	−	3.14949i	−0.242063	−	0.107773i
$855$		0			0
$856$	−44.3945	+	9.43635i	−1.51737	+	0.322528i
$857$	−2.73749	+	1.21881i	−0.0935110	+	0.0416338i	−0.452959	−	0.891531i	$-0.649632\pi$
$857$	−2.73749	+	1.21881i	−0.0935110	+	0.0416338i	0.359448	+	0.933165i	$0.382965\pi$
$858$	−34.7602	−	38.6051i	−1.18669	−	1.31796i
$859$	−3.97319	−	37.8023i	−0.135563	−	1.28980i	−0.824867	−	0.565327i	$-0.808750\pi$
$859$	−3.97319	−	37.8023i	−0.135563	−	1.28980i	0.689304	−	0.724472i	$-0.257917\pi$
$860$		0			0
$861$	−0.429688	+	4.08821i	−0.0146437	+	0.139326i
$862$	16.2290	+	28.1094i	0.552761	+	0.957410i
$863$	2.14795	−	3.72036i	0.0731170	−	0.126642i	−0.827149	−	0.561983i	$-0.810039\pi$
$863$	2.14795	−	3.72036i	0.0731170	−	0.126642i	0.900266	+	0.435340i	$0.143372\pi$
$864$	−0.194713	−	0.141467i	−0.00662426	−	0.00481281i
$865$		0			0
$866$	−2.77778	+	8.54914i	−0.0943929	+	0.290512i
$867$	−55.8867			−1.89801
$868$	−0.00311535	+	0.0191157i	−0.000105742	+	0.000648829i
$869$	11.9366			0.404922
$870$		0			0
$871$	24.9577	−	27.7183i	0.845659	−	0.939200i
$872$	15.6364	+	11.3605i	0.529515	+	0.384715i
$873$	−0.0114469	+	0.0198266i	−0.000387418	+	0.000671027i
$874$	19.7935	+	34.2833i	0.669524	+	1.15965i
$875$		0			0
$876$	−0.0498585	+	0.0362243i	−0.00168456	+	0.00122391i
$877$	−0.871320	−	8.29006i	−0.0294224	−	0.279935i	−0.999334	−	0.0364796i	$-0.988386\pi$
$877$	−0.871320	−	8.29006i	−0.0294224	−	0.279935i	0.969912	−	0.243456i	$-0.0782811\pi$
$878$	10.6255	+	11.8008i	0.358594	+	0.398259i
$879$	−11.7810	+	5.24525i	−0.397364	+	0.176918i
$880$		0			0
$881$	−13.6695	−	2.90554i	−0.460537	−	0.0978903i	−0.0282003	−	0.999602i	$-0.508978\pi$
$881$	−13.6695	−	2.90554i	−0.460537	−	0.0978903i	−0.432337	+	0.901712i	$0.642311\pi$
$882$	−53.0307	−	23.6108i	−1.78564	−	0.795016i
$883$	−1.64981	−	5.07760i	−0.0555206	−	0.170875i	0.919451	−	0.393205i	$-0.128634\pi$
$883$	−1.64981	−	5.07760i	−0.0555206	−	0.170875i	−0.974971	+	0.222330i	$0.928634\pi$
$884$	0.0271637	+	0.0836014i	0.000913616	+	0.00281182i
$885$		0			0
$886$	2.68453	+	0.570615i	0.0901887	+	0.0191702i
$887$	−6.86974	+	1.46021i	−0.230663	+	0.0490290i	−0.321793	−	0.946810i	$-0.604286\pi$
$887$	−6.86974	+	1.46021i	−0.230663	+	0.0490290i	0.0911297	+	0.995839i	$0.470952\pi$
$888$	11.7229	−	5.21937i	0.393395	−	0.175151i
$889$	−4.17157	−	4.63300i	−0.139910	−	0.155386i
$890$		0			0
$891$	−37.6293	+	27.3393i	−1.26063	+	0.915901i
$892$	−0.00754153	+	0.0717529i	−0.000252509	+	0.00240246i
$893$	−2.95125	−	5.11172i	−0.0987600	−	0.171057i
$894$	9.12620	−	15.8070i	0.305226	−	0.528666i
$895$		0			0
$896$	−7.21035	+	8.00791i	−0.240881	+	0.267525i
$897$	27.7813	−	85.5022i	0.927592	−	2.85483i
$898$	16.9749			0.566460
$899$	3.16653	+	12.0327i	0.105610	+	0.401312i
$900$		0			0
$901$	−4.94136	+	15.2079i	−0.164621	+	0.506650i
$902$	3.80827	−	4.22951i	0.126801	−	0.140827i
$903$	30.7315	+	22.3277i	1.02268	+	0.743021i
$904$	−20.1166	+	34.8430i	−0.669069	+	1.15886i
$905$		0			0
$906$	−4.63386	+	44.0882i	−0.153950	+	1.46473i
$907$	−22.5261	+	16.3662i	−0.747966	+	0.543429i	−0.895196	−	0.445673i	$-0.852964\pi$
$907$	−22.5261	+	16.3662i	−0.747966	+	0.543429i	0.147230	+	0.989102i	$0.452964\pi$
$908$	−0.00987295	−	0.0939348i	−0.000327645	−	0.00311734i
$909$	21.5668	+	23.9523i	0.715324	+	0.794448i
$910$		0			0
$911$	−20.1754	+	4.28841i	−0.668440	+	0.142081i	−0.529618	−	0.848236i	$-0.677665\pi$
$911$	−20.1754	+	4.28841i	−0.668440	+	0.142081i	−0.138822	+	0.990317i	$0.544331\pi$
$912$	−48.1666	−	10.2381i	−1.59496	−	0.339018i
$913$	−44.7718	−	19.9337i	−1.48173	−	0.659708i
$914$	−10.2119	−	31.4290i	−0.337780	−	1.03958i
$915$		0			0
$916$	0.00101275		0.000450904i	3.34621e−5		1.48983e-5i
$917$	−8.25999	−	1.75572i	−0.272769	−	0.0579788i
$918$	95.0544	−	20.2044i	3.13726	−	0.666846i
$919$	3.16738	−	1.41021i	0.104482	−	0.0465185i	−0.353830	−	0.935310i	$-0.615121\pi$
$919$	3.16738	−	1.41021i	0.104482	−	0.0465185i	0.458312	+	0.888791i	$0.348454\pi$
$920$		0			0
$921$	3.38923	+	32.2464i	0.111679	+	1.06255i
$922$	38.5354	−	27.9976i	1.26910	−	0.922053i
$923$	−4.71664	+	44.8759i	−0.155250	+	1.47711i
$924$	−0.0157150	−	0.0272191i	−0.000516985	−	0.000895444i
$925$		0			0
$926$	31.6164	+	22.9707i	1.03898	+	0.754863i
$927$	37.1925	−	41.3064i	1.22156	−	1.35668i
$928$	0.0143063	−	0.0440303i	0.000469627	−	0.00144536i
$929$	−16.0952			−0.528066			−0.264033	−	0.964514i	$-0.585053\pi$
$929$	−16.0952			−0.528066			−0.264033	+	0.964514i	$0.585053\pi$
$930$		0			0
$931$	−24.0276			−0.787472
$932$	−0.000499385		0.00153695i	−1.63579e−5		5.03445e-5i
$933$	44.9951	−	49.9721i	1.47307	−	1.63601i
$934$	39.2905	+	28.5462i	1.28562	+	0.934060i
$935$		0			0
$936$	38.5962	+	66.8506i	1.26156	+	2.18508i
$937$	−0.305096	+	2.90279i	−0.00996704	+	0.0948300i	−0.998374	−	0.0569946i	$-0.981848\pi$
$937$	−0.305096	+	2.90279i	−0.00996704	+	0.0948300i	0.988407	+	0.151825i	$0.0485149\pi$
$938$	9.98849	−	7.25707i	0.326136	−	0.236952i
$939$	0.672383	+	6.39729i	0.0219424	+	0.208768i
$940$		0			0
$941$	−43.6925	+	19.4531i	−1.42433	+	0.634154i	−0.966915	−	0.255097i	$-0.917892\pi$
$941$	−43.6925	+	19.4531i	−1.42433	+	0.634154i	−0.457418	+	0.889252i	$0.651226\pi$
$942$	100.920	−	21.4512i	3.28814	−	0.698917i
$943$	9.63431	+	2.04784i	0.313736	+	0.0666867i
$944$	15.1366	+	6.73924i	0.492653	+	0.219343i
$945$		0			0
$946$	−16.2520	−	50.0185i	−0.528398	−	1.62624i
$947$	32.3961	+	14.4237i	1.05273	+	0.468706i	0.858801	−	0.512309i	$-0.171210\pi$
$947$	32.3961	+	14.4237i	1.05273	+	0.468706i	0.193931	+	0.981015i	$0.437876\pi$
$948$	0.0460252	+	0.00978296i	0.00149483	+	0.000317736i
$949$	21.4389	−	4.55698i	0.695936	−	0.147926i
$950$		0			0
$951$	−45.3267	−	50.3404i	−1.46982	−	1.63240i
$952$	−1.65797	−	15.7745i	−0.0537350	−	0.511255i
$953$	−22.7601	+	16.5362i	−0.737273	+	0.535660i	−0.891856	−	0.452319i	$-0.850597\pi$
$953$	−22.7601	+	16.5362i	−0.737273	+	0.535660i	0.154583	+	0.987980i	$0.450597\pi$
$954$	2.69266	−	25.6189i	0.0871780	−	0.829443i
$955$		0			0
$956$	0.0240563	−	0.0416667i	0.000778035	−	0.00134760i
$957$	−16.3351	−	11.8681i	−0.528039	−	0.383643i
$958$	22.8176	−	25.3416i	0.737204	−	0.818749i
$959$	5.17279	−	15.9202i	0.167038	−	0.514091i
$960$		0			0
$961$	12.8617	−	28.2060i	0.414894	−	0.909870i
$962$	8.37212			0.269928
$963$	−33.3790	+	102.730i	−1.07562	+	3.31043i
$964$	0.0637078	−	0.0707547i	0.00205189	−	0.00227885i
$965$		0			0
$966$	14.8795	−	25.7721i	0.478741	−	0.829204i
$967$	−26.1365	−	45.2698i	−0.840494	−	1.45578i	−0.889478	−	0.456978i	$-0.848932\pi$
$967$	−26.1365	−	45.2698i	−0.840494	−	1.45578i	0.0489843	−	0.998800i	$-0.484402\pi$
$968$	−0.769691	+	7.32313i	−0.0247388	+	0.235374i
$969$	58.7474	−	42.6825i	1.88724	−	1.37116i
$970$		0			0
$971$	−21.2859	−	23.6404i	−0.683097	−	0.758656i	0.297493	−	0.954724i	$-0.403849\pi$
$971$	−21.2859	−	23.6404i	−0.683097	−	0.758656i	−0.980590	+	0.196068i	$0.937183\pi$
$972$	−0.0508935	+	0.0226593i	−0.00163241	+	0.000726796i
$973$	−15.4430	+	3.28251i	−0.495080	+	0.105233i
$974$	5.28315	+	1.12297i	0.169283	+	0.0359822i
$975$		0			0
$976$	−7.13177	−	21.9493i	−0.228282	−	0.702581i
$977$	−12.2419	−	37.6768i	−0.391654	−	1.20539i	−0.931537	−	0.363648i	$-0.881531\pi$
$977$	−12.2419	−	37.6768i	−0.391654	−	1.20539i	0.539882	−	0.841741i	$-0.318469\pi$
$978$	−0.998699	−	0.444649i	−0.0319349	−	0.0142183i
$979$	21.6981	+	4.61208i	0.693475	+	0.147403i
$980$		0			0
$981$	42.0218	−	18.7093i	1.34165	−	0.597342i
$982$	2.70508	+	3.00429i	0.0863225	+	0.0958708i
$983$	1.43588	+	13.6615i	0.0457975	+	0.435734i	0.993264	+	0.115878i	$0.0369680\pi$
$983$	1.43588	+	13.6615i	0.0457975	+	0.435734i	−0.947466	+	0.319856i	$0.896365\pi$
$984$	−9.89394	+	7.18837i	−0.315407	+	0.229157i
$985$		0			0
$986$	9.34644	+	16.1885i	0.297651	+	0.515547i
$987$	−2.21858	+	3.84269i	−0.0706181	+	0.122314i
$988$	−0.0474198	−	0.0344525i	−0.00150863	−	0.00109608i
$989$	60.9025	−	67.6391i	1.93659	−	2.15080i
$990$		0			0
$991$	2.43802			0.0774461			0.0387231	−	0.999250i	$-0.487671\pi$
$991$	2.43802			0.0774461			0.0387231	+	0.999250i	$0.487671\pi$
$992$	−0.0970177	+	0.0623888i	−0.00308031	+	0.00198085i
$993$	52.7062			1.67258
$994$	−4.61562	+	14.2054i	−0.146398	+	0.450568i
$995$		0			0
$996$	−0.156294	−	0.113554i	−0.00495236	−	0.00359810i
$997$	14.5377	−	25.1800i	0.460413	−	0.797458i	−0.538569	−	0.842582i	$-0.681035\pi$
$997$	14.5377	−	25.1800i	0.460413	−	0.797458i	0.998981	+	0.0451235i	$0.0143681\pi$
$998$	12.0630	+	20.8938i	0.381848	+	0.661381i
$999$	1.76829	−	16.8242i	0.0559464	−	0.532294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.bl.b.76.4		40
5.2	odd	4		775.2.ck.b.324.8		80
5.3	odd	4		775.2.ck.b.324.3		80
5.4	even	2		155.2.q.b.76.2	yes	40
31.20	even	15	inner	775.2.bl.b.51.4		40
155.19	even	30		4805.2.a.ba.1.6		20
155.74	odd	30		4805.2.a.z.1.6		20
155.82	odd	60		775.2.ck.b.299.3		80
155.113	odd	60		775.2.ck.b.299.8		80
155.144	even	30		155.2.q.b.51.2	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.b.51.2	✓	40	155.144	even	30
155.2.q.b.76.2	yes	40	5.4	even	2
775.2.bl.b.51.4		40	31.20	even	15	inner
775.2.bl.b.76.4		40	1.1	even	1	trivial
775.2.ck.b.299.3		80	155.82	odd	60
775.2.ck.b.299.8		80	155.113	odd	60
775.2.ck.b.324.3		80	5.3	odd	4
775.2.ck.b.324.8		80	5.2	odd	4
4805.2.a.z.1.6		20	155.74	odd	30
4805.2.a.ba.1.6		20	155.19	even	30

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.bl (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.437416 - 1.34623i) q^{2} +(-2.08671 + 2.31753i) q^{3} +(-0.00296283 - 0.00215262i) q^{4} +(2.20716 + 3.82291i) q^{6} +(0.0992859 - 0.944642i) q^{7} +(2.28615 - 1.66098i) q^{8} +(-0.702986 - 6.68846i) q^{9} +O(q^{10})\)	\(q+(0.437416 - 1.34623i) q^{2} +(-2.08671 + 2.31753i) q^{3} +(-0.00296283 - 0.00215262i) q^{4} +(2.20716 + 3.82291i) q^{6} +(0.0992859 - 0.944642i) q^{7} +(2.28615 - 1.66098i) q^{8} +(-0.702986 - 6.68846i) q^{9} +(2.64680 - 1.17843i) q^{11} +(0.0111713 - 0.00237454i) q^{12} +(-3.97302 - 0.844492i) q^{13} +(-1.22827 - 0.546863i) q^{14} +(-1.23833 - 3.81118i) q^{16} +(5.39849 + 2.40356i) q^{17} +(-9.31169 - 1.97926i) q^{18} +(-3.85426 + 0.819249i) q^{19} +(1.98205 + 2.20129i) q^{21} +(-0.428684 - 4.07866i) q^{22} +(5.74196 - 4.17178i) q^{23} +(-0.921154 + 8.76420i) q^{24} +(-2.87474 + 4.97920i) q^{26} +(9.39877 + 6.82861i) q^{27} +(-0.00232762 + 0.00258509i) q^{28} +(-0.690565 + 2.12534i) q^{29} +(4.68304 - 3.01150i) q^{31} -0.0207168 q^{32} +(-2.79206 + 8.59307i) q^{33} +(5.59713 - 6.21624i) q^{34} +(-0.0123149 + 0.0213300i) q^{36} +(-0.728076 - 1.26106i) q^{37} +(-0.583021 + 5.54707i) q^{38} +(10.2477 - 7.44538i) q^{39} +(0.928592 + 1.03131i) q^{41} +(3.83043 - 1.70542i) q^{42} +(12.5437 - 2.66625i) q^{43} +(-0.0103787 - 0.00220606i) q^{44} +(-3.10454 - 9.55479i) q^{46} +(0.462894 + 1.42464i) q^{47} +(11.4165 + 5.08297i) q^{48} +(5.96454 + 1.26780i) q^{49} +(-16.8354 + 7.49561i) q^{51} +(0.00995351 + 0.0110545i) q^{52} +(0.282850 + 2.69114i) q^{53} +(13.3040 - 9.66595i) q^{54} +(-1.34205 - 2.32450i) q^{56} +(6.14411 - 10.6419i) q^{57} +(2.55913 + 1.85931i) q^{58} +(-2.76666 + 3.07268i) q^{59} +5.75919 q^{61} +(-2.00573 - 7.62172i) q^{62} -6.38800 q^{63} +(2.46759 - 7.59447i) q^{64} +(10.3469 + 7.51749i) q^{66} +(-4.59142 + 7.95257i) q^{67} +(-0.0108208 - 0.0187422i) q^{68} +(-2.31360 + 22.0125i) q^{69} +(-1.16123 - 11.0483i) q^{71} +(-12.7165 - 14.1232i) q^{72} +(-4.92960 + 2.19480i) q^{73} +(-2.01615 + 0.428546i) q^{74} +(0.0131831 + 0.00586947i) q^{76} +(-0.850405 - 2.61728i) q^{77} +(-5.54068 - 17.0525i) q^{78} +(3.76376 + 1.67573i) q^{79} +(-15.7030 + 3.33777i) q^{81} +(1.79455 - 0.798986i) q^{82} +(-11.3186 - 12.5706i) q^{83} +(-0.00113393 - 0.0107887i) q^{84} +(1.89744 - 18.0529i) q^{86} +(-3.48452 - 6.03537i) q^{87} +(4.09361 - 7.09035i) q^{88} +(6.19419 + 4.50034i) q^{89} +(-1.19221 + 3.66924i) q^{91} -0.0259927 q^{92} +(-2.79291 + 17.1372i) q^{93} +2.12037 q^{94} +(0.0432300 - 0.0480118i) q^{96} +(-0.00275399 - 0.00200089i) q^{97} +(4.31574 - 7.47508i) q^{98} +(-9.74255 - 16.8746i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 12 q^{6} + 2 q^{7} + 31 q^{8} + 6 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 12 * q^6 + 2 * q^7 + 31 * q^8 + 6 * q^9	\( 40 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 12 q^{6} + 2 q^{7} + 31 q^{8} + 6 q^{9} + 16 q^{11} + q^{12} - 2 q^{13} - 10 q^{14} - 16 q^{16} - 4 q^{17} - 37 q^{18} - 9 q^{19} - 24 q^{21} + 2 q^{22} + 4 q^{23} + 110 q^{24} - 4 q^{26} + 9 q^{27} - 38 q^{28} - 22 q^{29} - 6 q^{31} + 60 q^{32} - 9 q^{33} - 16 q^{34} - q^{36} + 38 q^{37} + 32 q^{38} - 55 q^{39} - 24 q^{41} + 68 q^{42} - 26 q^{43} - 52 q^{44} - 50 q^{46} - 4 q^{47} - 105 q^{48} + 93 q^{49} - 42 q^{51} - 15 q^{52} - 13 q^{53} + 102 q^{54} + 5 q^{56} + 36 q^{57} + 37 q^{58} + 31 q^{59} + 68 q^{61} - 47 q^{62} + 10 q^{63} - 23 q^{64} + 2 q^{67} + 28 q^{68} - 48 q^{69} - 30 q^{71} - 39 q^{72} - 25 q^{73} + 50 q^{74} + 14 q^{76} + 64 q^{77} + 22 q^{78} + 49 q^{79} + 25 q^{81} + 66 q^{82} + 18 q^{83} - 18 q^{84} + 163 q^{86} + 36 q^{87} + 124 q^{88} + 4 q^{89} - 37 q^{91} - 110 q^{92} - 7 q^{93} - 94 q^{94} + 22 q^{96} - 46 q^{97} + 13 q^{98} + 17 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 12 * q^6 + 2 * q^7 + 31 * q^8 + 6 * q^9 + 16 * q^11 + q^12 - 2 * q^13 - 10 * q^14 - 16 * q^16 - 4 * q^17 - 37 * q^18 - 9 * q^19 - 24 * q^21 + 2 * q^22 + 4 * q^23 + 110 * q^24 - 4 * q^26 + 9 * q^27 - 38 * q^28 - 22 * q^29 - 6 * q^31 + 60 * q^32 - 9 * q^33 - 16 * q^34 - q^36 + 38 * q^37 + 32 * q^38 - 55 * q^39 - 24 * q^41 + 68 * q^42 - 26 * q^43 - 52 * q^44 - 50 * q^46 - 4 * q^47 - 105 * q^48 + 93 * q^49 - 42 * q^51 - 15 * q^52 - 13 * q^53 + 102 * q^54 + 5 * q^56 + 36 * q^57 + 37 * q^58 + 31 * q^59 + 68 * q^61 - 47 * q^62 + 10 * q^63 - 23 * q^64 + 2 * q^67 + 28 * q^68 - 48 * q^69 - 30 * q^71 - 39 * q^72 - 25 * q^73 + 50 * q^74 + 14 * q^76 + 64 * q^77 + 22 * q^78 + 49 * q^79 + 25 * q^81 + 66 * q^82 + 18 * q^83 - 18 * q^84 + 163 * q^86 + 36 * q^87 + 124 * q^88 + 4 * q^89 - 37 * q^91 - 110 * q^92 - 7 * q^93 - 94 * q^94 + 22 * q^96 - 46 * q^97 + 13 * q^98 + 17 * q^99

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