LMFDB - Embedded newform 325.2.x.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(7,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 11]))

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

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

chi := DirichletCharacter("325.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.x (of order $12$, degree $4$, 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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.2
Root			$0.274809i$ of defining polynomial
Character	$\chi$	$=$	325.7
Dual form			325.2.x.b.93.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.237991 + 0.137404i) q^{2} +(-0.611610 - 2.28256i) q^{3} +(-0.962240 - 1.66665i) q^{4} +(0.168076 - 0.627267i) q^{6} +(0.193052 + 0.334376i) q^{7} -1.07848i q^{8} +(-2.23793 + 1.29207i) q^{9} +O(q^{10})$	\(q+(0.237991 + 0.137404i) q^{2} +(-0.611610 - 2.28256i) q^{3} +(-0.962240 - 1.66665i) q^{4} +(0.168076 - 0.627267i) q^{6} +(0.193052 + 0.334376i) q^{7} -1.07848i q^{8} +(-2.23793 + 1.29207i) q^{9} +(-1.12873 - 4.21249i) q^{11} +(-3.21571 + 3.21571i) q^{12} +(1.35750 + 3.34024i) q^{13} +0.106105i q^{14} +(-1.77629 + 3.07663i) q^{16} +(-1.90527 - 0.510514i) q^{17} -0.710144 q^{18} +(-4.83947 - 1.29673i) q^{19} +(0.645159 - 0.645159i) q^{21} +(0.310185 - 1.15763i) q^{22} +(-0.322241 + 0.0863441i) q^{23} +(-2.46170 + 0.659609i) q^{24} +(-0.135891 + 0.981474i) q^{26} +(-0.694880 - 0.694880i) q^{27} +(0.371524 - 0.643499i) q^{28} +(7.07031 + 4.08205i) q^{29} +(-2.54187 - 2.54187i) q^{31} +(-2.71347 + 1.56662i) q^{32} +(-8.92491 + 5.15280i) q^{33} +(-0.383290 - 0.383290i) q^{34} +(4.30685 + 2.48656i) q^{36} +(2.41251 - 4.17859i) q^{37} +(-0.973575 - 0.973575i) q^{38} +(6.79403 - 5.14149i) q^{39} +(4.49768 - 1.20515i) q^{41} +(0.242190 - 0.0648946i) q^{42} +(1.76471 - 6.58600i) q^{43} +(-5.93462 + 5.93462i) q^{44} +(-0.0885545 - 0.0237281i) q^{46} +9.83310 q^{47} +(8.10898 + 2.17280i) q^{48} +(3.42546 - 5.93307i) q^{49} +4.66112i q^{51} +(4.26077 - 5.47658i) q^{52} +(7.17155 - 7.17155i) q^{53} +(-0.0698958 - 0.260855i) q^{54} +(0.360618 - 0.208203i) q^{56} +11.8395i q^{57} +(1.12178 + 1.94298i) q^{58} +(-0.628209 + 2.34451i) q^{59} +(-5.32338 - 9.22037i) q^{61} +(-0.255679 - 0.954209i) q^{62} +(-0.864073 - 0.498873i) q^{63} +6.24413 q^{64} -2.83207 q^{66} +(-5.52170 - 3.18796i) q^{67} +(0.982475 + 3.66665i) q^{68} +(0.394171 + 0.682724i) q^{69} +(-1.12684 + 4.20542i) q^{71} +(1.39347 + 2.41357i) q^{72} +6.08593i q^{73} +(1.14831 - 0.662979i) q^{74} +(2.49554 + 9.31346i) q^{76} +(1.19065 - 1.19065i) q^{77} +(2.32338 - 0.290100i) q^{78} -3.34944i q^{79} +(-5.03732 + 8.72489i) q^{81} +(1.23600 + 0.331185i) q^{82} -5.18834 q^{83} +(-1.69605 - 0.454456i) q^{84} +(1.32493 - 1.32493i) q^{86} +(4.99324 - 18.6350i) q^{87} +(-4.54309 + 1.21732i) q^{88} +(4.82829 - 1.29374i) q^{89} +(-0.854827 + 1.09875i) q^{91} +(0.453978 + 0.453978i) q^{92} +(-4.24734 + 7.35661i) q^{93} +(2.34019 + 1.35111i) q^{94} +(5.23549 + 5.23549i) q^{96} +(-12.7722 + 7.37402i) q^{97} +(1.63046 - 0.941346i) q^{98} +(7.96886 + 7.96886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 8 * q^6 + 2 * q^7 + 12 * q^9	$ 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9} - 16 q^{11} + 24 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 4 q^{21} - 16 q^{22} + 10 q^{23} + 32 q^{24} - 24 q^{26} - 4 q^{27} - 18 q^{28} - 48 q^{32} - 18 q^{33} + 2 q^{34} + 36 q^{36} + 4 q^{37} + 8 q^{38} + 4 q^{39} + 10 q^{41} - 40 q^{42} - 10 q^{43} - 36 q^{44} + 4 q^{46} + 40 q^{47} + 56 q^{48} + 18 q^{49} + 30 q^{52} + 10 q^{53} - 48 q^{54} - 16 q^{59} - 16 q^{61} + 44 q^{62} + 36 q^{63} + 20 q^{64} - 32 q^{66} - 18 q^{67} - 22 q^{68} - 16 q^{69} - 16 q^{71} - 4 q^{72} + 18 q^{74} - 64 q^{76} + 28 q^{77} - 68 q^{78} - 14 q^{81} - 56 q^{82} - 48 q^{83} - 40 q^{84} + 60 q^{86} + 34 q^{87} - 82 q^{88} - 6 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 48 q^{94} + 56 q^{96} - 66 q^{97} + 30 q^{98} + 60 q^{99}+O(q^{100}) $ 20 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 8 * q^6 + 2 * q^7 + 12 * q^9 - 16 * q^11 + 24 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 4 * q^21 - 16 * q^22 + 10 * q^23 + 32 * q^24 - 24 * q^26 - 4 * q^27 - 18 * q^28 - 48 * q^32 - 18 * q^33 + 2 * q^34 + 36 * q^36 + 4 * q^37 + 8 * q^38 + 4 * q^39 + 10 * q^41 - 40 * q^42 - 10 * q^43 - 36 * q^44 + 4 * q^46 + 40 * q^47 + 56 * q^48 + 18 * q^49 + 30 * q^52 + 10 * q^53 - 48 * q^54 - 16 * q^59 - 16 * q^61 + 44 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 - 22 * q^68 - 16 * q^69 - 16 * q^71 - 4 * q^72 + 18 * q^74 - 64 * q^76 + 28 * q^77 - 68 * q^78 - 14 * q^81 - 56 * q^82 - 48 * q^83 - 40 * q^84 + 60 * q^86 + 34 * q^87 - 82 * q^88 - 6 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 48 * q^94 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.237991	+	0.137404i	0.168285	+	0.0971595i	0.581777	−	0.813348i	$-0.302358\pi$
$2$	0.237991	+	0.137404i	0.168285	+	0.0971595i	−0.413492	+	0.910508i	$0.635691\pi$
$3$	−0.611610	−	2.28256i	−0.353113	−	1.31784i	−0.882842	−	0.469669i	$-0.844373\pi$
$3$	−0.611610	−	2.28256i	−0.353113	−	1.31784i	0.529729	−	0.848167i	$-0.322293\pi$
$4$	−0.962240	−	1.66665i	−0.481120	−	0.833324i
$5$		0			0
$5$		0			0
$6$	0.168076	−	0.627267i	0.0686166	−	0.256081i
$7$	0.193052	+	0.334376i	0.0729667	+	0.126382i	0.900200	−	0.435476i	$-0.143420\pi$
$7$	0.193052	+	0.334376i	0.0729667	+	0.126382i	−0.827234	+	0.561858i	$0.810087\pi$
$8$		−	1.07848i		−	0.381301i
$9$	−2.23793	+	1.29207i	−0.745977	+	0.430690i
$10$		0			0
$11$	−1.12873	−	4.21249i	−0.340326	−	1.27011i	−0.897979	−	0.440039i	$-0.854965\pi$
$11$	−1.12873	−	4.21249i	−0.340326	−	1.27011i	0.557653	−	0.830074i	$-0.311702\pi$
$12$	−3.21571	+	3.21571i	−0.928295	+	0.928295i
$13$	1.35750	+	3.34024i	0.376502	+	0.926416i
$13$	1.35750	+	3.34024i	0.376502	+	0.926416i
$14$			0.106105i			0.0283576i
$15$		0			0
$16$	−1.77629	+	3.07663i	−0.444073	+	0.769157i
$17$	−1.90527	−	0.510514i	−0.462095	−	0.123818i	0.0202583	−	0.999795i	$-0.493551\pi$
$17$	−1.90527	−	0.510514i	−0.462095	−	0.123818i	−0.482353	+	0.875977i	$0.660218\pi$
$18$	−0.710144			−0.167383
$19$	−4.83947	−	1.29673i	−1.11025	−	0.297491i	−0.343318	−	0.939219i	$-0.611551\pi$
$19$	−4.83947	−	1.29673i	−1.11025	−	0.297491i	−0.766932	+	0.641728i	$0.778218\pi$
$20$		0			0
$21$	0.645159	−	0.645159i	0.140785	−	0.140785i
$22$	0.310185	−	1.15763i	0.0661318	−	0.246807i
$23$	−0.322241	+	0.0863441i	−0.0671918	+	0.0180040i	−0.292258	−	0.956339i	$-0.594407\pi$
$23$	−0.322241	+	0.0863441i	−0.0671918	+	0.0180040i	0.225067	+	0.974343i	$0.427740\pi$
$24$	−2.46170	+	0.659609i	−0.502492	+	0.134642i
$25$		0			0
$26$	−0.135891	+	0.981474i	−0.0266504	+	0.192483i
$27$	−0.694880	−	0.694880i	−0.133730	−	0.133730i
$28$	0.371524	−	0.643499i	0.0702115	−	0.121610i
$29$	7.07031	+	4.08205i	1.31292	+	0.758017i	0.982579	−	0.185843i	$-0.0595016\pi$
$29$	7.07031	+	4.08205i	1.31292	+	0.758017i	0.330345	+	0.943860i	$0.392835\pi$
$30$		0			0
$31$	−2.54187	−	2.54187i	−0.456534	−	0.456534i	0.440982	−	0.897516i	$-0.354630\pi$
$31$	−2.54187	−	2.54187i	−0.456534	−	0.456534i	−0.897516	+	0.440982i	$0.854630\pi$
$32$	−2.71347	+	1.56662i	−0.479678	+	0.276942i
$33$	−8.92491	+	5.15280i	−1.55363	+	0.896987i
$34$	−0.383290	−	0.383290i	−0.0657336	−	0.0657336i
$35$		0			0
$36$	4.30685	+	2.48656i	0.717809	+	0.414427i
$37$	2.41251	−	4.17859i	0.396614	−	0.686956i	−0.596691	−	0.802471i	$-0.703518\pi$
$37$	2.41251	−	4.17859i	0.396614	−	0.686956i	0.993306	+	0.115514i	$0.0368517\pi$
$38$	−0.973575	−	0.973575i	−0.157935	−	0.157935i
$39$	6.79403	−	5.14149i	1.08792	−	0.823297i
$40$		0			0
$41$	4.49768	−	1.20515i	0.702419	−	0.188213i	0.110105	−	0.993920i	$-0.464881\pi$
$41$	4.49768	−	1.20515i	0.702419	−	0.188213i	0.592314	+	0.805707i	$0.298214\pi$
$42$	0.242190	−	0.0648946i	0.0373707	−	0.0100135i
$43$	1.76471	−	6.58600i	0.269116	−	1.00436i	−0.690566	−	0.723269i	$-0.742638\pi$
$43$	1.76471	−	6.58600i	0.269116	−	1.00436i	0.959682	−	0.281087i	$-0.0906948\pi$
$44$	−5.93462	+	5.93462i	−0.894678	+	0.894678i
$45$		0			0
$46$	−0.0885545	−	0.0237281i	−0.0130566	−	0.00349852i
$47$	9.83310			1.43430			0.717152	−	0.696917i	$-0.245445\pi$
$47$	9.83310			1.43430			0.717152	+	0.696917i	$0.245445\pi$
$48$	8.10898	+	2.17280i	1.17043	+	0.313616i
$49$	3.42546	−	5.93307i	0.489352	−	0.847582i
$50$		0			0
$51$			4.66112i			0.652687i
$52$	4.26077	−	5.47658i	0.590862	−	0.759466i
$53$	7.17155	−	7.17155i	0.985088	−	0.985088i	−0.0148021	−	0.999890i	$-0.504712\pi$
$53$	7.17155	−	7.17155i	0.985088	−	0.985088i	0.999890	+	0.0148021i	$0.00471182\pi$
$54$	−0.0698958	−	0.260855i	−0.00951161	−	0.0354978i
$55$		0			0
$56$	0.360618	−	0.208203i	0.0481896	−	0.0278223i
$57$			11.8395i			1.56818i
$58$	1.12178	+	1.94298i	0.147297	+	0.255126i
$59$	−0.628209	+	2.34451i	−0.0817858	+	0.305229i	−0.994686	−	0.102954i	$-0.967171\pi$
$59$	−0.628209	+	2.34451i	−0.0817858	+	0.305229i	0.912900	+	0.408183i	$0.133837\pi$
$60$		0			0
$61$	−5.32338	−	9.22037i	−0.681589	−	1.18055i	−0.974496	−	0.224406i	$-0.927956\pi$
$61$	−5.32338	−	9.22037i	−0.681589	−	1.18055i	0.292906	−	0.956141i	$-0.405378\pi$
$62$	−0.255679	−	0.954209i	−0.0324713	−	0.121185i
$63$	−0.864073	−	0.498873i	−0.108863	−	0.0628521i
$64$	6.24413			0.780516
$65$		0			0
$66$	−2.83207			−0.348603
$67$	−5.52170	−	3.18796i	−0.674583	−	0.389471i	0.123228	−	0.992378i	$-0.460675\pi$
$67$	−5.52170	−	3.18796i	−0.674583	−	0.389471i	−0.797811	+	0.602908i	$0.794009\pi$
$68$	0.982475	+	3.66665i	0.119143	+	0.444646i
$69$	0.394171	+	0.682724i	0.0474526	+	0.0821903i
$70$		0			0
$71$	−1.12684	+	4.20542i	−0.133731	+	0.499091i	−1.00000		0.000486883i	$-0.999845\pi$
$71$	−1.12684	+	4.20542i	−0.133731	+	0.499091i	0.866269	+	0.499578i	$0.166512\pi$
$72$	1.39347	+	2.41357i	0.164222	+	0.284442i
$73$			6.08593i			0.712304i	0.934428	+	0.356152i	$0.115912\pi$
$73$			6.08593i			0.712304i	−0.934428	+	0.356152i	$0.884088\pi$
$74$	1.14831	−	0.662979i	0.133489	−	0.0770697i
$75$		0			0
$76$	2.49554	+	9.31346i	0.286258	+	1.06833i
$77$	1.19065	−	1.19065i	0.135687	−	0.135687i
$78$	2.32338	−	0.290100i	0.263071	−	0.0328474i
$79$		−	3.34944i		−	0.376842i	−0.982088	−	0.188421i	$-0.939663\pi$
$79$		−	3.34944i		−	0.376842i	0.982088	−	0.188421i	$-0.0603369\pi$
$80$		0			0
$81$	−5.03732	+	8.72489i	−0.559702	+	0.969433i
$82$	1.23600	+	0.331185i	0.136493	+	0.0365733i
$83$	−5.18834			−0.569494			−0.284747	−	0.958603i	$-0.591910\pi$
$83$	−5.18834			−0.569494			−0.284747	+	0.958603i	$0.591910\pi$
$84$	−1.69605	−	0.454456i	−0.185054	−	0.0495852i
$85$		0			0
$86$	1.32493	−	1.32493i	0.142871	−	0.142871i
$87$	4.99324	−	18.6350i	0.535332	−	1.99788i
$88$	−4.54309	+	1.21732i	−0.484295	+	0.129766i
$89$	4.82829	−	1.29374i	0.511798	−	0.137136i	0.00632782	−	0.999980i	$-0.497986\pi$
$89$	4.82829	−	1.29374i	0.511798	−	0.137136i	0.505470	+	0.862844i	$0.331319\pi$
$90$		0			0
$91$	−0.854827	+	1.09875i	−0.0896102	+	0.115181i
$92$	0.453978	+	0.453978i	0.0473305	+	0.0473305i
$93$	−4.24734	+	7.35661i	−0.440429	+	0.762845i
$94$	2.34019	+	1.35111i	0.241372	+	0.139356i
$95$		0			0
$96$	5.23549	+	5.23549i	0.534345	+	0.534345i
$97$	−12.7722	+	7.37402i	−1.29682	+	0.748718i	−0.979853	−	0.199719i	$-0.935997\pi$
$97$	−12.7722	+	7.37402i	−1.29682	+	0.748718i	−0.316965	+	0.948437i	$0.602664\pi$
$98$	1.63046	−	0.941346i	0.164701	−	0.0950903i
$99$	7.96886	+	7.96886i	0.800900	+	0.800900i
$100$		0			0
$101$	4.57218	+	2.63975i	0.454949	+	0.262665i	0.709918	−	0.704284i	$-0.248732\pi$
$101$	4.57218	+	2.63975i	0.454949	+	0.262665i	−0.254969	+	0.966949i	$0.582065\pi$
$102$	−0.640458	+	1.10930i	−0.0634147	+	0.109838i
$103$	1.21001	+	1.21001i	0.119226	+	0.119226i	0.764203	−	0.644976i	$-0.223133\pi$
$103$	1.21001	+	1.21001i	0.119226	+	0.119226i	−0.644976	+	0.764203i	$0.723133\pi$
$104$	3.60238	−	1.46404i	0.353243	−	0.143560i
$105$		0			0
$106$	2.69217	−	0.721364i	0.261487	−	0.0700651i
$107$	3.91480	−	1.04897i	0.378458	−	0.101408i	−0.0645749	−	0.997913i	$-0.520569\pi$
$107$	3.91480	−	1.04897i	0.378458	−	0.101408i	0.443033	+	0.896505i	$0.353902\pi$
$108$	−0.489479	+	1.82676i	−0.0471002	+	0.175780i
$109$	−5.02898	+	5.02898i	−0.481689	+	0.481689i	−0.905671	−	0.423982i	$-0.860632\pi$
$109$	−5.02898	+	5.02898i	−0.481689	+	0.481689i	0.423982	+	0.905671i	$0.360632\pi$
$110$		0			0
$111$	−11.0134	−	2.95103i	−1.04535	−	0.280099i
$112$	−1.37167			−0.129610
$113$	−3.83891	−	1.02863i	−0.361134	−	0.0967655i	0.0736896	−	0.997281i	$-0.476523\pi$
$113$	−3.83891	−	1.02863i	−0.361134	−	0.0967655i	−0.434824	+	0.900516i	$0.643189\pi$
$114$	−1.62679	+	2.81769i	−0.152363	+	0.263901i
$115$		0			0
$116$		−	15.7116i		−	1.45879i
$117$	−7.35381	−	5.72124i	−0.679860	−	0.528929i
$118$	−0.471653	+	0.471653i	−0.0434192	+	0.0434192i
$119$	−0.197111	−	0.735630i	−0.0180692	−	0.0674351i
$120$		0			0
$121$	−6.94473	+	4.00954i	−0.631339	+	0.364504i
$122$		−	2.92582i		−	0.264892i
$123$	−5.50165	−	9.52914i	−0.496067	−	0.859213i
$124$	−1.79052	+	6.68231i	−0.160793	+	0.600089i
$125$		0			0
$126$	−0.137095	−	0.237455i	−0.0122134	−	0.0211542i
$127$	2.95156	+	11.0154i	0.261908	+	0.977455i	0.964116	+	0.265483i	$0.0855313\pi$
$127$	2.95156	+	11.0154i	0.261908	+	0.977455i	−0.702207	+	0.711972i	$0.747802\pi$
$128$	6.91298	+	3.99121i	0.611027	+	0.352777i
$129$	−16.1123			−1.41860
$130$		0			0
$131$	20.8627			1.82279			0.911393	−	0.411536i	$-0.135008\pi$
$131$	20.8627			1.82279			0.911393	+	0.411536i	$0.135008\pi$
$132$	17.1758	+	9.91645i	1.49496	+	0.863117i
$133$	−0.500673	−	1.86854i	−0.0434138	−	0.162023i
$134$	−0.876078	−	1.51741i	−0.0756816	−	0.131084i
$135$		0			0
$136$	−0.550580	+	2.05479i	−0.0472119	+	0.176197i
$137$	−0.121975	−	0.211266i	−0.0104210	−	0.0180497i	0.860768	−	0.508998i	$-0.169984\pi$
$137$	−0.121975	−	0.211266i	−0.0104210	−	0.0180497i	−0.871189	+	0.490948i	$0.836651\pi$
$138$			0.216643i			0.0184419i
$139$	10.1187	−	5.84202i	0.858255	−	0.495514i	−0.00517263	−	0.999987i	$-0.501647\pi$
$139$	10.1187	−	5.84202i	0.858255	−	0.495514i	0.863428	+	0.504473i	$0.168313\pi$
$140$		0			0
$141$	−6.01402	−	22.4446i	−0.506472	−	1.89018i
$142$	−0.846020	+	0.846020i	−0.0709965	+	0.0709965i
$143$	12.5385	−	9.48868i	1.04852	−	0.793483i
$144$		−	9.18038i		−	0.765032i
$145$		0			0
$146$	−0.836233	+	1.44840i	−0.0692071	+	0.119870i
$147$	−15.6376	−	4.19009i	−1.28977	−	0.345593i
$148$	−9.28566			−0.763277
$149$	−2.44620	−	0.655457i	−0.200400	−	0.0536971i	0.157223	−	0.987563i	$-0.449746\pi$
$149$	−2.44620	−	0.655457i	−0.200400	−	0.0536971i	−0.357623	+	0.933866i	$0.616413\pi$
$150$		0			0
$151$	2.58498	−	2.58498i	0.210362	−	0.210362i	−0.594059	−	0.804421i	$-0.702475\pi$
$151$	2.58498	−	2.58498i	0.210362	−	0.210362i	0.804421	+	0.594059i	$0.202475\pi$
$152$	−1.39850	+	5.21928i	−0.113433	+	0.423339i
$153$	4.92348	−	1.31924i	0.398039	−	0.106654i
$154$	0.446964	−	0.119764i	0.0360174	−	0.00965083i
$155$		0			0
$156$	−15.1066	−	6.37592i	−1.20949	−	0.510482i
$157$	2.21767	+	2.21767i	0.176990	+	0.176990i	0.790042	−	0.613053i	$-0.210059\pi$
$157$	2.21767	+	2.21767i	0.176990	+	0.176990i	−0.613053	+	0.790042i	$0.710059\pi$
$158$	0.460228	−	0.797137i	0.0366137	−	0.0634169i
$159$	−20.7557	−	11.9833i	−1.64603	−	0.950337i
$160$		0			0
$161$	−0.0910805	−	0.0910805i	−0.00717815	−	0.00717815i
$162$	−2.39768	+	1.38430i	−0.188379	+	0.108761i
$163$	12.8283	−	7.40642i	1.00479	−	0.580116i	0.0951279	−	0.995465i	$-0.469674\pi$
$163$	12.8283	−	7.40642i	1.00479	−	0.580116i	0.909662	+	0.415349i	$0.136341\pi$
$164$	−6.33641	−	6.33641i	−0.494790	−	0.494790i
$165$		0			0
$166$	−1.23478	−	0.712900i	−0.0958374	−	0.0553318i
$167$	1.73406	−	3.00348i	0.134186	−	0.232417i	−0.791100	−	0.611686i	$-0.790491\pi$
$167$	1.73406	−	3.00348i	0.134186	−	0.232417i	0.925286	+	0.379270i	$0.123825\pi$
$168$	−0.695792	−	0.695792i	−0.0536815	−	0.0536815i
$169$	−9.31440	+	9.06873i	−0.716492	+	0.697595i
$170$		0			0
$171$	12.5059	−	3.35094i	0.956348	−	0.256253i
$172$	−12.6746	+	3.39616i	−0.966432	+	0.258955i
$173$	1.01194	−	3.77661i	0.0769362	−	0.287130i	−0.916729	−	0.399509i	$-0.869181\pi$
$173$	1.01194	−	3.77661i	0.0769362	−	0.287130i	0.993665	+	0.112379i	$0.0358472\pi$
$174$	3.74888	−	3.74888i	0.284202	−	0.284202i
$175$		0			0
$176$	14.9652	+	4.00992i	1.12805	+	0.302259i
$177$	5.73569			0.431121
$178$	1.32686	+	0.355530i	0.0994521	+	0.0266481i
$179$	−3.24880	+	5.62708i	−0.242827	+	0.420588i	−0.961518	−	0.274741i	$-0.911408\pi$
$179$	−3.24880	+	5.62708i	−0.242827	+	0.420588i	0.718692	+	0.695329i	$0.244741\pi$
$180$		0			0
$181$			11.9845i			0.890802i	0.895331	+	0.445401i	$0.146939\pi$
$181$			11.9845i			0.890802i	−0.895331	+	0.445401i	$0.853061\pi$
$182$	−0.354415	+	0.144037i	−0.0262710	+	0.0106767i
$183$	−17.7902	+	17.7902i	−1.31509	+	1.31509i
$184$	0.0931205	+	0.347530i	0.00686493	+	0.0256203i
$185$		0			0
$186$	−2.02166	+	1.16721i	−0.148235	+	0.0855837i
$187$			8.60214i			0.629051i
$188$	−9.46180	−	16.3883i	−0.690073	−	1.19524i
$189$	0.0982030	−	0.366499i	0.00714322	−	0.0266588i
$190$		0			0
$191$	2.59646	+	4.49719i	0.187873	+	0.325405i	0.944541	−	0.328394i	$-0.106507\pi$
$191$	2.59646	+	4.49719i	0.187873	+	0.325405i	−0.756668	+	0.653799i	$0.773174\pi$
$192$	−3.81897	−	14.2526i	−0.275610	−	1.02859i
$193$	−5.77996	−	3.33706i	−0.416051	−	0.240207i	0.277335	−	0.960773i	$-0.410549\pi$
$193$	−5.77996	−	3.33706i	−0.416051	−	0.240207i	−0.693386	+	0.720566i	$0.743882\pi$
$194$	−4.05289			−0.290980
$195$		0			0
$196$	−13.1845			−0.941748
$197$	16.9716	+	9.79857i	1.20918	+	0.698119i	0.962580	−	0.270999i	$-0.0873540\pi$
$197$	16.9716	+	9.79857i	1.20918	+	0.698119i	0.246598	+	0.969118i	$0.420687\pi$
$198$	0.801563	+	2.99147i	0.0569646	+	0.212595i
$199$	−7.35302	−	12.7358i	−0.521242	−	0.902817i	−0.999695	−	0.0247042i	$-0.992136\pi$
$199$	−7.35302	−	12.7358i	−0.521242	−	0.902817i	0.478453	−	0.878113i	$-0.341198\pi$
$200$		0			0
$201$	−3.89957	+	14.5534i	−0.275054	+	1.02652i
$202$	0.725425	+	1.25647i	0.0510408	+	0.0884052i
$203$			3.15219i			0.221240i
$204$	7.76844	−	4.48511i	0.543900	−	0.314021i
$205$		0			0
$206$	0.121712	+	0.454234i	0.00848005	+	0.0316480i
$207$	0.609590	−	0.609590i	0.0423694	−	0.0423694i
$208$	−12.6880	−	1.75673i	−0.879754	−	0.121807i
$209$			21.8499i			1.51139i
$210$		0			0
$211$	10.7072	−	18.5453i	0.737111	−	1.27671i	−0.216679	−	0.976243i	$-0.569523\pi$
$211$	10.7072	−	18.5453i	0.737111	−	1.27671i	0.953791	−	0.300471i	$-0.0971440\pi$
$212$	−18.8532	−	5.05170i	−1.29484	−	0.346952i
$213$	10.2883			0.704943
$214$	1.07582	+	0.288265i	0.0735416	+	0.0197054i
$215$		0			0
$216$	−0.749414	+	0.749414i	−0.0509912	+	0.0509912i
$217$	0.359227	−	1.34065i	0.0243859	−	0.0910095i
$218$	−1.88786	+	0.505850i	−0.127862	+	0.0342605i
$219$	13.8915	−	3.72221i	0.938700	−	0.251524i
$220$		0			0
$221$	−0.881153	−	7.05707i	−0.0592728	−	0.474710i
$222$	−2.21561	−	2.21561i	−0.148702	−	0.148702i
$223$	−13.6678	+	23.6733i	−0.915264	+	1.58528i	−0.108749	+	0.994069i	$0.534685\pi$
$223$	−13.6678	+	23.6733i	−0.915264	+	1.58528i	−0.806515	+	0.591214i	$0.798649\pi$
$224$	−1.04768	−	0.604878i	−0.0700010	−	0.0404151i
$225$		0			0
$226$	−0.772287	−	0.772287i	−0.0513718	−	0.0513718i
$227$	−5.99928	+	3.46369i	−0.398186	+	0.229893i	−0.685701	−	0.727883i	$-0.740504\pi$
$227$	−5.99928	+	3.46369i	−0.398186	+	0.229893i	0.287515	+	0.957776i	$0.407171\pi$
$228$	19.7322	−	11.3924i	1.30680	−	0.754481i
$229$	4.56825	+	4.56825i	0.301879	+	0.301879i	0.841749	−	0.539870i	$-0.181527\pi$
$229$	4.56825	+	4.56825i	0.301879	+	0.301879i	−0.539870	+	0.841749i	$0.681527\pi$
$230$		0			0
$231$	−3.44594	−	1.98951i	−0.226726	−	0.130900i
$232$	4.40241	−	7.62520i	0.289032	−	0.500619i
$233$	−5.49074	−	5.49074i	−0.359711	−	0.359711i	0.503996	−	0.863706i	$-0.331863\pi$
$233$	−5.49074	−	5.49074i	−0.359711	−	0.359711i	−0.863706	+	0.503996i	$0.831863\pi$
$234$	−0.964019	−	2.37205i	−0.0630199	−	0.155066i
$235$		0			0
$236$	4.51196	−	1.20898i	0.293703	−	0.0786976i
$237$	−7.64529	+	2.04855i	−0.496615	+	0.133068i
$238$	0.0541679	−	0.202157i	0.00351119	−	0.0131039i
$239$	8.33949	−	8.33949i	0.539437	−	0.539437i	−0.383927	−	0.923363i	$-0.625429\pi$
$239$	8.33949	−	8.33949i	0.539437	−	0.539437i	0.923363	+	0.383927i	$0.125429\pi$
$240$		0			0
$241$	−1.40952	−	0.377680i	−0.0907952	−	0.0243285i	0.213135	−	0.977023i	$-0.431632\pi$
$241$	−1.40952	−	0.377680i	−0.0907952	−	0.0243285i	−0.303931	+	0.952694i	$0.598299\pi$
$242$	−2.20371			−0.141660
$243$	20.1483	+	5.39872i	1.29251	+	0.346328i
$244$	−10.2447	+	17.7444i	−0.655853	+	1.13597i
$245$		0			0
$246$		−	3.02380i		−	0.192791i
$247$	−2.23817	−	17.9253i	−0.142412	−	1.14056i
$248$	−2.74136	+	2.74136i	−0.174077	+	0.174077i
$249$	3.17324	+	11.8427i	0.201096	+	0.750500i
$250$		0			0
$251$	−11.2668	+	6.50488i	−0.711153	+	0.410585i	−0.811488	−	0.584369i	$-0.801342\pi$
$251$	−11.2668	+	6.50488i	−0.711153	+	0.410585i	0.100335	+	0.994954i	$0.468009\pi$
$252$			1.92014i			0.120958i
$253$	0.727447	+	1.25997i	0.0457342	+	0.0792139i
$254$	−0.811113	+	3.02712i	−0.0508938	+	0.189938i
$255$		0			0
$256$	−5.14731	−	8.91540i	−0.321707	−	0.557212i
$257$	7.62518	+	28.4576i	0.475646	+	1.77513i	0.618922	+	0.785452i	$0.287570\pi$
$257$	7.62518	+	28.4576i	0.475646	+	1.77513i	−0.143276	+	0.989683i	$0.545764\pi$
$258$	−3.83458	−	2.21389i	−0.238730	−	0.137831i
$259$	1.86296			0.115759
$260$		0			0
$261$	−21.0972			−1.30588
$262$	4.96515	+	2.86663i	0.306748	+	0.177101i
$263$	1.30768	+	4.88034i	0.0806351	+	0.300934i	0.994452	−	0.105192i	$-0.0335458\pi$
$263$	1.30768	+	4.88034i	0.0806351	+	0.300934i	−0.913817	+	0.406127i	$0.866879\pi$
$264$	5.55719	+	9.62534i	0.342022	+	0.592399i
$265$		0			0
$266$	0.137589	−	0.513490i	0.00843614	−	0.0314841i
$267$	−5.90606	−	10.2296i	−0.361445	−	0.626041i
$268$			12.2703i			0.749529i
$269$	7.49111	−	4.32499i	0.456741	−	0.263699i	−0.253932	−	0.967222i	$-0.581724\pi$
$269$	7.49111	−	4.32499i	0.456741	−	0.263699i	0.710673	+	0.703523i	$0.248391\pi$
$270$		0			0
$271$	5.96047	+	22.2448i	0.362073	+	1.35127i	0.871346	+	0.490669i	$0.163248\pi$
$271$	5.96047	+	22.2448i	0.362073	+	1.35127i	−0.509273	+	0.860605i	$0.670086\pi$
$272$	4.95497	−	4.95497i	0.300439	−	0.300439i
$273$	3.03079	+	1.27918i	0.183432	+	0.0774198i
$274$		−	0.0670394i		−	0.00405000i
$275$		0			0
$276$	0.758574	−	1.31389i	0.0456608	−	0.0790868i
$277$	20.9037	+	5.60114i	1.25598	+	0.336540i	0.824645	−	0.565650i	$-0.191375\pi$
$277$	20.9037	+	5.60114i	1.25598	+	0.336540i	0.431338	+	0.902190i	$0.358042\pi$
$278$	3.21087			0.192575
$279$	8.97282	+	2.40426i	0.537189	+	0.143939i
$280$		0			0
$281$	8.17717	−	8.17717i	0.487809	−	0.487809i	−0.419805	−	0.907614i	$-0.637902\pi$
$281$	8.17717	−	8.17717i	0.487809	−	0.487809i	0.907614	+	0.419805i	$0.137902\pi$
$282$	1.65270	−	6.16797i	0.0984171	−	0.367298i
$283$	4.34603	−	1.16452i	0.258345	−	0.0692233i	−0.127322	−	0.991861i	$-0.540638\pi$
$283$	4.34603	−	1.16452i	0.258345	−	0.0692233i	0.385667	+	0.922638i	$0.373971\pi$
$284$	8.09325	−	2.16858i	0.480246	−	0.128681i
$285$		0			0
$286$	4.28783	−	0.535383i	0.253545	−	0.0316579i
$287$	1.27126	+	1.27126i	0.0750400	+	0.0750400i
$288$	4.04837	−	7.01198i	0.238552	−	0.413185i
$289$	−11.3530	−	6.55467i	−0.667825	−	0.385569i
$290$		0			0
$291$	24.6432	+	24.6432i	1.44461	+	1.44461i
$292$	10.1431	−	5.85613i	0.593580	−	0.342704i
$293$	−11.3497	+	6.55274i	−0.663056	+	0.382815i	−0.793440	−	0.608648i	$-0.791712\pi$
$293$	−11.3497	+	6.55274i	−0.663056	+	0.382815i	0.130385	+	0.991463i	$0.458379\pi$
$294$	−3.14588	−	3.14588i	−0.183472	−	0.183472i
$295$		0			0
$296$	−4.50653	−	2.60185i	−0.261937	−	0.151229i
$297$	−2.14284	+	3.71150i	−0.124340	+	0.215363i
$298$	−0.492111	−	0.492111i	−0.0285072	−	0.0285072i
$299$	−0.725851	−	0.959149i	−0.0419770	−	0.0554690i
$300$		0			0
$301$	2.54288	−	0.681363i	0.146569	−	0.0392731i
$302$	0.970388	−	0.260015i	0.0558396	−	0.0149622i
$303$	3.22899	−	12.0508i	0.185501	−	0.692298i
$304$	12.5859	−	12.5859i	0.721849	−	0.721849i
$305$		0			0
$306$	1.35301	+	0.362539i	0.0773466	+	0.0207250i
$307$	−7.75447			−0.442571			−0.221285	−	0.975209i	$-0.571025\pi$
$307$	−7.75447			−0.442571			−0.221285	+	0.975209i	$0.571025\pi$
$308$	−3.13008	−	0.838703i	−0.178353	−	0.0477896i
$309$	2.02187	−	3.50198i	0.115020	−	0.199221i
$310$		0			0
$311$			11.6030i			0.657947i	0.944339	+	0.328974i	$0.106703\pi$
$311$			11.6030i			0.657947i	−0.944339	+	0.328974i	$0.893297\pi$
$312$	−5.54500	−	7.32724i	−0.313924	−	0.414823i
$313$	10.1565	−	10.1565i	0.574078	−	0.574078i	−0.359188	−	0.933265i	$-0.616946\pi$
$313$	10.1565	−	10.1565i	0.574078	−	0.574078i	0.933265	+	0.359188i	$0.116946\pi$
$314$	0.223069	+	0.832505i	0.0125885	+	0.0469810i
$315$		0			0
$316$	−5.58234	+	3.22297i	−0.314031	+	0.181306i
$317$		−	21.7686i		−	1.22265i	−0.791381	−	0.611323i	$-0.790638\pi$
$317$		−	21.7686i		−	1.22265i	0.791381	−	0.611323i	$-0.209362\pi$
$318$	−3.29311	−	5.70384i	−0.184669	−	0.319855i
$319$	9.21508	−	34.3911i	0.515945	−	1.92553i
$320$		0			0
$321$	−4.78866	−	8.29420i	−0.267277	−	0.462937i
$322$	−0.00916151	−	0.0341912i	−0.000510551	−	0.00190540i
$323$	8.55848	+	4.94124i	0.476206	+	0.274938i
$324$	19.3884			1.07714
$325$		0			0
$326$	4.07070			0.225455
$327$	14.5547	+	8.40318i	0.804878	+	0.464697i
$328$	−1.29973	−	4.85066i	−0.0717656	−	0.267833i
$329$	1.89830	+	3.28795i	0.104657	+	0.181270i
$330$		0			0
$331$	−5.07792	+	18.9511i	−0.279108	+	1.04164i	0.673931	+	0.738795i	$0.264605\pi$
$331$	−5.07792	+	18.9511i	−0.279108	+	1.04164i	−0.953038	+	0.302850i	$0.902062\pi$
$332$	4.99243	+	8.64714i	0.273995	+	0.474573i
$333$			12.4685i			0.683272i
$334$	0.825383	−	0.476535i	0.0451630	−	0.0260748i
$335$		0			0
$336$	0.838924	+	3.13091i	0.0457671	+	0.170805i
$337$	9.35946	−	9.35946i	0.509842	−	0.509842i	−0.404636	−	0.914478i	$-0.632602\pi$
$337$	9.35946	−	9.35946i	0.509842	−	0.509842i	0.914478	+	0.404636i	$0.132602\pi$
$338$	−3.46283	+	0.878441i	−0.188353	+	0.0477809i
$339$			9.39165i			0.510084i
$340$		0			0
$341$	−7.83852	+	13.5767i	−0.424480	+	0.735220i
$342$	3.43672	+	0.920867i	0.185837	+	0.0497948i
$343$	5.34789			0.288759
$344$	−7.10288	−	1.90321i	−0.382962	−	0.102614i
$345$		0			0
$346$	0.759754	−	0.759754i	0.0408446	−	0.0408446i
$347$	7.15698	−	26.7102i	0.384207	−	1.43388i	−0.455207	−	0.890386i	$-0.650435\pi$
$347$	7.15698	−	26.7102i	0.384207	−	1.43388i	0.839414	−	0.543493i	$-0.182899\pi$
$348$	−35.8627	+	9.60939i	−1.92244	+	0.515118i
$349$	−28.5113	+	7.63958i	−1.52618	+	0.408938i	−0.921769	−	0.387739i	$-0.873256\pi$
$349$	−28.5113	+	7.63958i	−1.52618	+	0.408938i	−0.604406	+	0.796676i	$0.706590\pi$
$350$		0			0
$351$	1.37777	−	3.26436i	0.0735398	−	0.174239i
$352$	9.66215	+	9.66215i	0.514994	+	0.514994i
$353$	7.81777	−	13.5408i	0.416098	−	0.720702i	−0.579445	−	0.815011i	$-0.696731\pi$
$353$	7.81777	−	13.5408i	0.416098	−	0.720702i	0.995543	+	0.0943088i	$0.0300641\pi$
$354$	1.36504	+	0.788109i	0.0725513	+	0.0418875i
$355$		0			0
$356$	−6.80218	−	6.80218i	−0.360515	−	0.360515i
$357$	−1.55856	+	0.899837i	−0.0824879	+	0.0476244i
$358$	−1.54637	+	0.892798i	−0.0817282	+	0.0471858i
$359$	14.0592	+	14.0592i	0.742017	+	0.742017i	0.972966	−	0.230949i	$-0.0741830\pi$
$359$	14.0592	+	14.0592i	0.742017	+	0.742017i	−0.230949	+	0.972966i	$0.574183\pi$
$360$		0			0
$361$	5.28447	+	3.05099i	0.278130	+	0.160578i
$362$	−1.64672	+	2.85221i	−0.0865499	+	0.149909i
$363$	13.3995	+	13.3995i	0.703290	+	0.703290i
$364$	2.65378	+	0.367432i	0.139096	+	0.0192587i
$365$		0			0
$366$	−6.67836	+	1.78946i	−0.349084	+	0.0935367i
$367$	−21.2746	+	5.70052i	−1.11053	+	0.297565i	−0.767045	−	0.641594i	$-0.778273\pi$
$367$	−21.2746	+	5.70052i	−1.11053	+	0.297565i	−0.343483	+	0.939159i	$0.611607\pi$
$368$	0.306745	−	1.14479i	0.0159902	−	0.0596761i
$369$	−8.50836	+	8.50836i	−0.442928	+	0.442928i
$370$		0			0
$371$	3.78247	+	1.01351i	0.196376	+	0.0526188i
$372$	16.3479			0.847597
$373$	−1.12584	−	0.301668i	−0.0582937	−	0.0156198i	0.229554	−	0.973296i	$-0.426273\pi$
$373$	−1.12584	−	0.301668i	−0.0582937	−	0.0156198i	−0.287848	+	0.957676i	$0.592940\pi$
$374$	−1.18197	+	2.04723i	−0.0611183	+	0.105860i
$375$		0			0
$376$		−	10.6048i		−	0.546901i
$377$	−4.03708	+	29.1579i	−0.207920	+	1.50171i
$378$	0.0737299	−	0.0737299i	0.00379226	−	0.00379226i
$379$	6.82640	+	25.4765i	0.350649	+	1.30864i	0.885873	+	0.463928i	$0.153560\pi$
$379$	6.82640	+	25.4765i	0.350649	+	1.30864i	−0.535224	+	0.844710i	$0.679773\pi$
$380$		0			0
$381$	23.3380	−	13.4742i	1.19564	−	0.690304i
$382$			1.42706i			0.0730146i
$383$	16.4001	+	28.4058i	0.838004	+	1.45147i	0.891561	+	0.452901i	$0.149611\pi$
$383$	16.4001	+	28.4058i	0.838004	+	1.45147i	−0.0535563	+	0.998565i	$0.517056\pi$
$384$	4.88213	−	18.2204i	0.249140	−	0.929804i
$385$		0			0
$386$	−0.917054	−	1.58838i	−0.0466768	−	0.0808466i
$387$	4.56027	+	17.0192i	0.231812	+	0.865132i
$388$	24.5798	+	14.1912i	1.24785	+	0.720447i
$389$	9.36826			0.474989			0.237495	−	0.971389i	$-0.423674\pi$
$389$	9.36826			0.474989			0.237495	+	0.971389i	$0.423674\pi$
$390$		0			0
$391$	0.658034			0.0332782
$392$	−6.39871	−	3.69430i	−0.323184	−	0.186590i
$393$	−12.7599	−	47.6205i	−0.643650	−	2.40213i
$394$	2.69273	+	4.66395i	0.135658	+	0.234966i
$395$		0			0
$396$	5.61333	−	20.9492i	0.282080	−	1.05274i
$397$	−5.82600	−	10.0909i	−0.292399	−	0.506449i	0.681978	−	0.731373i	$-0.261120\pi$
$397$	−5.82600	−	10.0909i	−0.292399	−	0.506449i	−0.974376	+	0.224924i	$0.927787\pi$
$398$		−	4.04135i		−	0.202574i
$399$	−3.95883	+	2.28563i	−0.198189	+	0.114425i
$400$		0			0
$401$	−5.33600	−	19.9142i	−0.266467	−	0.994469i	−0.961346	−	0.275342i	$-0.911209\pi$
$401$	−5.33600	−	19.9142i	−0.266467	−	0.994469i	0.694879	−	0.719126i	$-0.255458\pi$
$402$	−2.92776	+	2.92776i	−0.146024	+	0.146024i
$403$	5.03988	−	11.9411i	0.251054	−	0.594827i
$404$		−	10.1603i		−	0.505493i
$405$		0			0
$406$	−0.433124	+	0.750193i	−0.0214956	+	0.0372314i
$407$	−20.3253	−	5.44616i	−1.00749	−	0.269956i
$408$	5.02693			0.248870
$409$	4.40250	+	1.17965i	0.217689	+	0.0583297i	0.366015	−	0.930609i	$-0.380722\pi$
$409$	4.40250	+	1.17965i	0.217689	+	0.0583297i	−0.148326	+	0.988939i	$0.547388\pi$
$410$		0			0
$411$	−0.407627	+	0.407627i	−0.0201067	+	0.0201067i
$412$	0.852344	−	3.18099i	0.0419920	−	0.156716i
$413$	−0.905223	+	0.242554i	−0.0445431	+	0.0119353i
$414$	0.228837	−	0.0613168i	0.0112467	−	0.00301355i
$415$		0			0
$416$	−8.91642	−	6.93695i	−0.437163	−	0.340112i
$417$	−19.5234	−	19.5234i	−0.956067	−	0.956067i
$418$	−3.00227	+	5.20008i	−0.146846	+	0.254344i
$419$	0.564687	+	0.326022i	0.0275868	+	0.0159272i	0.513730	−	0.857952i	$-0.328263\pi$
$419$	0.564687	+	0.326022i	0.0275868	+	0.0159272i	−0.486143	+	0.873879i	$0.661597\pi$
$420$		0			0
$421$	−5.58095	−	5.58095i	−0.271999	−	0.271999i	0.557906	−	0.829904i	$-0.311605\pi$
$421$	−5.58095	−	5.58095i	−0.271999	−	0.271999i	−0.829904	+	0.557906i	$0.811605\pi$
$422$	5.09642	−	2.94242i	0.248090	−	0.143235i
$423$	−22.0058	+	12.7051i	−1.06996	+	0.617741i
$424$	−7.73438	−	7.73438i	−0.375615	−	0.375615i
$425$		0			0
$426$	2.44853	+	1.41366i	0.118631	+	0.0684919i
$427$	2.05538	−	3.56002i	0.0994667	−	0.172281i
$428$	−5.51524	−	5.51524i	−0.266589	−	0.266589i
$429$	−29.3271	−	22.8164i	−1.41593	−	1.10159i
$430$		0			0
$431$	−34.5325	+	9.25295i	−1.66337	+	0.445699i	−0.963312	−	0.268385i	$-0.913510\pi$
$431$	−34.5325	+	9.25295i	−1.66337	+	0.445699i	−0.700060	+	0.714084i	$0.746843\pi$
$432$	3.37220	−	0.903577i	0.162245	−	0.0434734i
$433$	−6.82761	+	25.4810i	−0.328114	+	1.22454i	0.583031	+	0.812450i	$0.301867\pi$
$433$	−6.82761	+	25.4810i	−0.328114	+	1.22454i	−0.911144	+	0.412087i	$0.864800\pi$
$434$	0.269705	−	0.269705i	0.0129462	−	0.0129462i
$435$		0			0
$436$	13.2206	+	3.54246i	0.633154	+	0.169653i
$437$	1.67144			0.0799558
$438$	3.81750	+	1.02290i	0.182407	+	0.0488759i
$439$	−0.864675	+	1.49766i	−0.0412687	+	0.0714794i	−0.885922	−	0.463834i	$-0.846473\pi$
$439$	−0.864675	+	1.49766i	−0.0412687	+	0.0714794i	0.844653	+	0.535314i	$0.179807\pi$
$440$		0			0
$441$			17.7038i			0.843036i
$442$	0.759965	−	1.80059i	0.0361478	−	0.0856455i
$443$	−2.86737	+	2.86737i	−0.136233	+	0.136233i	−0.771935	−	0.635702i	$-0.780711\pi$
$443$	−2.86737	+	2.86737i	−0.136233	+	0.136233i	0.635702	+	0.771935i	$0.280711\pi$
$444$	5.67920	+	21.1951i	0.269523	+	1.00587i
$445$		0			0
$446$	−6.50564	+	3.75603i	−0.308051	+	0.177853i
$447$			5.98448i			0.283056i
$448$	1.20544	+	2.08788i	0.0569517	+	0.0986432i
$449$	−5.22508	+	19.5003i	−0.246587	+	0.920274i	0.725993	+	0.687702i	$0.241381\pi$
$449$	−5.22508	+	19.5003i	−0.246587	+	0.920274i	−0.972579	+	0.232571i	$0.925286\pi$
$450$		0			0
$451$	−10.1534	−	17.5861i	−0.478103	−	0.828098i
$452$	1.97958	+	7.38790i	0.0931117	+	0.347497i
$453$	−7.48135	−	4.31936i	−0.351505	−	0.202941i
$454$	−1.90370			−0.0893452
$455$		0			0
$456$	12.7686			0.597946
$457$	−12.8012	−	7.39079i	−0.598816	−	0.345727i	0.169759	−	0.985486i	$-0.445701\pi$
$457$	−12.8012	−	7.39079i	−0.598816	−	0.345727i	−0.768576	+	0.639759i	$0.779034\pi$
$458$	0.459507	+	1.71490i	0.0214713	+	0.0801321i
$459$	0.969184	+	1.67868i	0.0452377	+	0.0783539i
$460$		0			0
$461$	−1.57205	+	5.86696i	−0.0732175	+	0.273252i	−0.992823	−	0.119591i	$-0.961842\pi$
$461$	−1.57205	+	5.86696i	−0.0732175	+	0.273252i	0.919606	+	0.392843i	$0.128508\pi$
$462$	−0.546735	−	0.946973i	−0.0254364	−	0.0440572i
$463$		−	36.0148i		−	1.67375i	−0.547396	−	0.836874i	$-0.684381\pi$
$463$		−	36.0148i		−	1.67375i	0.547396	−	0.836874i	$-0.315619\pi$
$464$	−25.1179	+	14.5018i	−1.16607	+	0.673230i
$465$		0			0
$466$	−0.552297	−	2.06120i	−0.0255847	−	0.0954833i
$467$	−7.68952	+	7.68952i	−0.355829	+	0.355829i	−0.862273	−	0.506444i	$-0.830960\pi$
$467$	−7.68952	+	7.68952i	−0.355829	+	0.355829i	0.506444	+	0.862273i	$0.330960\pi$
$468$	−2.45917	+	17.7614i	−0.113675	+	0.821022i
$469$		−	2.46176i		−	0.113674i
$470$		0			0
$471$	3.70562	−	6.41832i	0.170746	−	0.295741i
$472$	2.52851	+	0.677511i	0.116384	+	0.0311850i
$473$	−29.7353			−1.36723
$474$	−2.10099	−	0.562959i	−0.0965018	−	0.0258576i
$475$		0			0
$476$	−1.03637	+	1.03637i	−0.0475019	+	0.0475019i
$477$	−6.78329	+	25.3156i	−0.310586	+	1.15912i
$478$	3.13061	−	0.838843i	0.143191	−	0.0383678i
$479$	−8.87096	+	2.37697i	−0.405324	+	0.108606i	−0.455720	−	0.890123i	$-0.650618\pi$
$479$	−8.87096	+	2.37697i	−0.405324	+	0.108606i	0.0503960	+	0.998729i	$0.483952\pi$
$480$		0			0
$481$	17.2325	+	2.38594i	0.785733	+	0.108789i
$482$	−0.283559	−	0.283559i	−0.0129157	−	0.0129157i
$483$	−0.152191	+	0.263602i	−0.00692492	+	0.0119943i
$484$	13.3650	+	7.71629i	0.607500	+	0.350740i
$485$		0			0
$486$	4.05331	+	4.05331i	0.183862	+	0.183862i
$487$	−22.2840	+	12.8657i	−1.00978	+	0.582998i	−0.911128	−	0.412123i	$-0.864787\pi$
$487$	−22.2840	+	12.8657i	−1.00978	+	0.582998i	−0.0986549	+	0.995122i	$0.531454\pi$
$488$	−9.94399	+	5.74117i	−0.450143	+	0.259890i
$489$	−24.7515	−	24.7515i	−1.11930	−	1.11930i
$490$		0			0
$491$	11.4291	+	6.59859i	0.515788	+	0.297790i	0.735210	−	0.677840i	$-0.237084\pi$
$491$	11.4291	+	6.59859i	0.515788	+	0.297790i	−0.219422	+	0.975630i	$0.570417\pi$
$492$	−10.5878	+	18.3386i	−0.477336	+	0.826769i
$493$	−11.3869	−	11.3869i	−0.512839	−	0.512839i
$494$	1.93035	−	4.57360i	0.0868504	−	0.205776i
$495$		0			0
$496$	12.3355	−	3.30529i	0.553881	−	0.148412i
$497$	−1.62373	+	0.435076i	−0.0728341	+	0.0195158i
$498$	−0.872033	+	3.25447i	−0.0390767	+	0.145836i
$499$	16.7683	−	16.7683i	0.750650	−	0.750650i	−0.223950	−	0.974601i	$-0.571895\pi$
$499$	16.7683	−	16.7683i	0.750650	−	0.750650i	0.974601	+	0.223950i	$0.0718954\pi$
$500$		0			0
$501$	−7.91620	−	2.12114i	−0.353670	−	0.0947655i
$502$	−3.57520			−0.159569
$503$	7.28214	+	1.95124i	0.324695	+	0.0870017i	0.417485	−	0.908684i	$-0.362912\pi$
$503$	7.28214	+	1.95124i	0.324695	+	0.0870017i	−0.0927898	+	0.995686i	$0.529578\pi$
$504$	−0.538025	+	0.931887i	−0.0239655	+	0.0415095i
$505$		0			0
$506$			0.399817i			0.0177740i
$507$	26.3967	+	15.7141i	1.17232	+	0.697889i
$508$	15.5186	−	15.5186i	0.688528	−	0.688528i
$509$	−7.93327	−	29.6074i	−0.351636	−	1.31232i	−0.884666	−	0.466226i	$-0.845613\pi$
$509$	−7.93327	−	29.6074i	−0.351636	−	1.31232i	0.533030	−	0.846097i	$-0.321053\pi$
$510$		0			0
$511$	−2.03499	+	1.17490i	−0.0900225	+	0.0519745i
$512$		−	18.7939i		−	0.830581i
$513$	2.46178	+	4.26392i	0.108690	+	0.188257i
$514$	−2.09547	+	7.82039i	−0.0924271	+	0.344942i
$515$		0			0
$516$	15.5039	+	26.8535i	0.682519	+	1.18216i
$517$	−11.0989	−	41.4218i	−0.488131	−	1.82173i
$518$	0.443368	+	0.255979i	0.0194805	+	0.0112471i
$519$	−9.23923			−0.405557
$520$		0			0
$521$	−7.16076			−0.313719			−0.156859	−	0.987621i	$-0.550137\pi$
$521$	−7.16076			−0.313719			−0.156859	+	0.987621i	$0.550137\pi$
$522$	−5.02094	−	2.89884i	−0.219761	−	0.126879i
$523$	−2.78390	−	10.3897i	−0.121731	−	0.454308i	0.877971	−	0.478714i	$-0.158897\pi$
$523$	−2.78390	−	10.3897i	−0.121731	−	0.454308i	−0.999702	+	0.0244065i	$0.992230\pi$
$524$	−20.0750	−	34.7709i	−0.876979	−	1.51897i
$525$		0			0
$526$	−0.359362	+	1.34116i	−0.0156689	+	0.0584773i
$527$	3.54528	+	6.14061i	0.154435	+	0.267489i
$528$		−	36.6115i		−	1.59331i
$529$	−19.8222	+	11.4444i	−0.861835	+	0.497581i
$530$		0			0
$531$	−1.62338	−	6.05854i	−0.0704487	−	0.262918i
$532$	−2.63243	+	2.63243i	−0.114130	+	0.114130i
$533$	10.1311	+	13.3873i	0.438826	+	0.579870i
$534$		−	3.24607i		−	0.140471i
$535$		0			0
$536$	−3.43815	+	5.95505i	−0.148505	+	0.257219i
$537$	14.8311	+	3.97399i	0.640011	+	0.171490i
$538$	2.37709			0.102484
$539$	−28.8594	−	7.73286i	−1.24306	−	0.333078i
$540$		0			0
$541$	11.1986	−	11.1986i	0.481464	−	0.481464i	−0.424135	−	0.905599i	$-0.639422\pi$
$541$	11.1986	−	11.1986i	0.481464	−	0.481464i	0.905599	+	0.424135i	$0.139422\pi$
$542$	−1.63799	+	6.11306i	−0.0703576	+	0.262578i
$543$	27.3554	−	7.32985i	1.17393	−	0.314554i
$544$	5.96966	−	1.59957i	0.255947	−	0.0685808i
$545$		0			0
$546$	0.545536	+	0.720878i	0.0233468	+	0.0308507i
$547$	23.6205	+	23.6205i	1.00994	+	1.00994i	0.999950	+	0.00999077i	$0.00318021\pi$
$547$	23.6205	+	23.6205i	1.00994	+	1.00994i	0.00999077	+	0.999950i	$0.496820\pi$
$548$	−0.234738	+	0.406578i	−0.0100275	+	0.0173681i
$549$	23.8267	+	13.7564i	1.01690	+	0.587108i
$550$		0			0
$551$	−28.9232	−	28.9232i	−1.23217	−	1.23217i
$552$	0.736305	−	0.425106i	0.0313392	−	0.0180937i
$553$	1.11997	−	0.646616i	0.0476260	−	0.0274969i
$554$	4.20528	+	4.20528i	0.178665	+	0.178665i
$555$		0			0
$556$	−19.4732	−	11.2429i	−0.825847	−	0.476803i
$557$	15.5732	−	26.9736i	0.659859	−	1.14291i	−0.320793	−	0.947149i	$-0.603950\pi$
$557$	15.5732	−	26.9736i	0.659859	−	1.14291i	0.980652	−	0.195759i	$-0.0627172\pi$
$558$	1.80510	+	1.80510i	0.0764159	+	0.0764159i
$559$	24.3944	−	3.04592i	1.03177	−	0.128829i
$560$		0			0
$561$	19.6349	−	5.26115i	0.828986	−	0.222126i
$562$	3.06967	−	0.822517i	0.129486	−	0.0346958i
$563$	5.39509	−	20.1348i	0.227376	−	0.848579i	−0.754063	−	0.656802i	$-0.771909\pi$
$563$	5.39509	−	20.1348i	0.227376	−	0.848579i	0.981439	−	0.191776i	$-0.0614248\pi$
$564$	−31.6204	+	31.6204i	−1.33146	+	1.33146i
$565$		0			0
$566$	1.19433	+	0.320019i	0.0502013	+	0.0134514i
$567$	−3.88985			−0.163359
$568$	4.53546	+	1.21527i	0.190304	+	0.0509918i
$569$	20.8728	−	36.1527i	0.875031	−	1.51560i	0.0183019	−	0.999833i	$-0.494174\pi$
$569$	20.8728	−	36.1527i	0.875031	−	1.51560i	0.856729	−	0.515766i	$-0.172493\pi$
$570$		0			0
$571$		−	19.2151i		−	0.804127i	−0.915612	−	0.402064i	$-0.868293\pi$
$571$		−	19.2151i		−	0.804127i	0.915612	−	0.402064i	$-0.131707\pi$
$572$	−27.8793	−	11.7668i	−1.16569	−	0.491996i
$573$	8.67709	−	8.67709i	0.362491	−	0.362491i
$574$	0.127872	+	0.477224i	0.00533727	+	0.0199190i
$575$		0			0
$576$	−13.9739	+	8.06785i	−0.582247	+	0.336160i
$577$			21.8168i			0.908243i	0.890940	+	0.454122i	$0.150047\pi$
$577$			21.8168i			0.908243i	−0.890940	+	0.454122i	$0.849953\pi$
$578$	−1.80128	−	3.11991i	−0.0749233	−	0.129771i
$579$	−4.08196	+	15.2341i	−0.169640	+	0.633107i
$580$		0			0
$581$	−1.00162	−	1.73485i	−0.0415541	−	0.0719738i
$582$	2.47879	+	9.25095i	0.102749	+	0.383464i
$583$	−38.3048	−	22.1153i	−1.58642	−	0.915922i
$584$	6.56356			0.271602
$585$		0			0
$586$	−3.60150			−0.148777
$587$	−5.07084	−	2.92765i	−0.209296	−	0.120837i	0.391688	−	0.920098i	$-0.371891\pi$
$587$	−5.07084	−	2.92765i	−0.209296	−	0.120837i	−0.600984	+	0.799261i	$0.705225\pi$
$588$	8.06375	+	30.0943i	0.332543	+	1.24107i
$589$	9.00520	+	15.5975i	0.371053	+	0.642682i
$590$		0			0
$591$	11.9858	−	44.7316i	0.493030	−	1.84001i
$592$	8.57065	+	14.8448i	0.352252	+	0.610118i
$593$			45.6277i			1.87370i	0.349727	+	0.936852i	$0.386274\pi$
$593$			45.6277i			1.87370i	−0.349727	+	0.936852i	$0.613726\pi$
$594$	−1.01995	+	0.588870i	−0.0418492	+	0.0241616i
$595$		0			0
$596$	1.26141	+	4.70766i	0.0516695	+	0.192833i
$597$	−24.5730	+	24.5730i	−1.00571	+	1.00571i
$598$	−0.0409550	−	0.328004i	−0.00167477	−	0.0134131i
$599$		−	12.7240i		−	0.519888i	−0.965624	−	0.259944i	$-0.916296\pi$
$599$		−	12.7240i		−	0.519888i	0.965624	−	0.259944i	$-0.0837041\pi$
$600$		0			0
$601$	12.3636	−	21.4144i	0.504321	−	0.873510i	−0.495666	−	0.868513i	$-0.665076\pi$
$601$	12.3636	−	21.4144i	0.504321	−	0.873510i	0.999988	−	0.00499702i	$-0.00159061\pi$
$602$	0.698805	+	0.187244i	0.0284812	+	0.00763151i
$603$	16.4763			0.670965
$604$	−6.79561	−	1.82088i	−0.276510	−	0.0740905i
$605$		0			0
$606$	2.42430	−	2.42430i	0.0984804	−	0.0984804i
$607$	−1.13924	+	4.25169i	−0.0462402	+	0.172571i	−0.985184	−	0.171499i	$-0.945139\pi$
$607$	−1.13924	+	4.25169i	−0.0462402	+	0.172571i	0.938944	+	0.344070i	$0.111806\pi$
$608$	15.1632	−	4.06298i	0.614950	−	0.164775i
$609$	7.19505	−	1.92791i	0.291558	−	0.0781228i
$610$		0			0
$611$	13.3484	+	32.8449i	0.540019	+	1.32876i
$612$	−6.93628	−	6.93628i	−0.280382	−	0.280382i
$613$	0.580288	−	1.00509i	0.0234376	−	0.0405951i	−0.854069	−	0.520160i	$-0.825872\pi$
$613$	0.580288	−	1.00509i	0.0234376	−	0.0405951i	0.877506	+	0.479565i	$0.159206\pi$
$614$	−1.84550	−	1.06550i	−0.0744781	−	0.0430000i
$615$		0			0
$616$	−1.28409	−	1.28409i	−0.0517375	−	0.0517375i
$617$	33.3212	−	19.2380i	1.34146	−	0.774493i	0.354439	−	0.935079i	$-0.384672\pi$
$617$	33.3212	−	19.2380i	1.34146	−	0.774493i	0.987022	+	0.160587i	$0.0513386\pi$
$618$	0.962375	−	0.555628i	0.0387124	−	0.0223506i
$619$	24.7229	+	24.7229i	0.993698	+	0.993698i	0.999980	−	0.00628240i	$-0.00199976\pi$
$619$	24.7229	+	24.7229i	0.993698	+	0.993698i	−0.00628240	+	0.999980i	$0.502000\pi$
$620$		0			0
$621$	0.283917	+	0.163920i	0.0113932	+	0.00657787i
$622$	−1.59431	+	2.76142i	−0.0639258	+	0.110723i
$623$	1.36470	+	1.36470i	0.0546757	+	0.0546757i
$624$	3.75027	+	30.0355i	0.150131	+	1.20238i
$625$		0			0
$626$	3.81269	−	1.02161i	0.152386	−	0.0408317i
$627$	49.8736	−	13.3636i	1.99176	−	0.533690i
$628$	1.56215	−	5.83002i	0.0623365	−	0.232643i
$629$	−6.72971	+	6.72971i	−0.268331	+	0.268331i
$630$		0			0
$631$	−7.05694	−	1.89090i	−0.280933	−	0.0752756i	0.115601	−	0.993296i	$-0.463120\pi$
$631$	−7.05694	−	1.89090i	−0.280933	−	0.0752756i	−0.396534	+	0.918020i	$0.629787\pi$
$632$	−3.61231			−0.143690
$633$	−48.8794	−	13.0972i	−1.94278	−	0.520567i
$634$	2.99110	−	5.18074i	0.118792	−	0.205753i
$635$		0			0
$636$			46.1232i			1.82891i
$637$	24.4679	+	3.38773i	0.969455	+	0.134227i
$638$	6.91860	−	6.91860i	0.273910	−	0.273910i
$639$	−2.91191	−	10.8674i	−0.115193	−	0.429907i
$640$		0			0
$641$	−7.19858	+	4.15610i	−0.284327	+	0.164156i	−0.635381	−	0.772199i	$-0.719157\pi$
$641$	−7.19858	+	4.15610i	−0.284327	+	0.164156i	0.351054	+	0.936355i	$0.385823\pi$
$642$		−	2.63193i		−	0.103874i
$643$	5.57779	+	9.66101i	0.219967	+	0.380993i	0.954797	−	0.297257i	$-0.0960719\pi$
$643$	5.57779	+	9.66101i	0.219967	+	0.380993i	−0.734831	+	0.678250i	$0.762739\pi$
$644$	−0.0641579	+	0.239440i	−0.00252817	+	0.00943528i
$645$		0			0
$646$	1.35789	+	2.35194i	0.0534257	+	0.0925360i
$647$	−10.8961	−	40.6647i	−0.428369	−	1.59870i	−0.756454	−	0.654047i	$-0.773070\pi$
$647$	−10.8961	−	40.6647i	−0.428369	−	1.59870i	0.328085	−	0.944648i	$-0.393597\pi$
$648$	9.40963	+	5.43265i	0.369645	+	0.213415i
$649$	10.5853			0.415509
$650$		0			0
$651$	−3.27983			−0.128547
$652$	−24.6878	−	14.2535i	−0.966849	−	0.558211i
$653$	11.0577	+	41.2678i	0.432721	+	1.61494i	0.746463	+	0.665427i	$0.231750\pi$
$653$	11.0577	+	41.2678i	0.432721	+	1.61494i	−0.313742	+	0.949508i	$0.601583\pi$
$654$	2.30926	+	3.99976i	0.0902994	+	0.156403i
$655$		0			0
$656$	−4.28140	+	15.9784i	−0.167160	+	0.623851i
$657$	−7.86345	−	13.6199i	−0.306782	−	0.531363i
$658$			1.04334i			0.0406735i
$659$	15.2491	−	8.80408i	0.594021	−	0.342958i	−0.172665	−	0.984981i	$-0.555238\pi$
$659$	15.2491	−	8.80408i	0.594021	−	0.342958i	0.766686	+	0.642023i	$0.221904\pi$
$660$		0			0
$661$	7.21232	+	26.9167i	0.280527	+	1.04694i	0.952047	+	0.305953i	$0.0989751\pi$
$661$	7.21232	+	26.9167i	0.280527	+	1.04694i	−0.671520	+	0.740987i	$0.734358\pi$
$662$	−3.81246	+	3.81246i	−0.148175	+	0.148175i
$663$	−15.5692	+	6.32746i	−0.604659	+	0.245738i
$664$			5.59552i			0.217148i
$665$		0			0
$666$	−1.71323	+	2.96740i	−0.0663863	+	0.114985i
$667$	−2.63080	−	0.704922i	−0.101865	−	0.0272947i
$668$	−6.67434			−0.258238
$669$	62.3951	+	16.7187i	2.41234	+	0.646383i
$670$		0			0
$671$	−32.8320	+	32.8320i	−1.26747	+	1.26747i
$672$	−0.739899	+	2.76134i	−0.0285422	+	0.106521i
$673$	−7.05459	+	1.89027i	−0.271934	+	0.0728646i	−0.392209	−	0.919876i	$-0.628289\pi$
$673$	−7.05459	+	1.89027i	−0.271934	+	0.0728646i	0.120275	+	0.992741i	$0.461622\pi$
$674$	3.51350	−	0.941440i	0.135335	−	0.0362629i
$675$		0			0
$676$	24.0771	+	6.79753i	0.926042	+	0.261444i
$677$	−3.26988	−	3.26988i	−0.125672	−	0.125672i	0.641473	−	0.767145i	$-0.278323\pi$
$677$	−3.26988	−	3.26988i	−0.125672	−	0.125672i	−0.767145	+	0.641473i	$0.778323\pi$
$678$	−1.29045	+	2.23513i	−0.0495595	+	0.0858397i
$679$	−4.93138	−	2.84713i	−0.189249	−	0.109263i
$680$		0			0
$681$	11.5753	+	11.5753i	0.443566	+	0.443566i
$682$	−3.73100	+	2.15409i	−0.142867	+	0.0824845i
$683$	−23.4651	+	13.5476i	−0.897868	+	0.518384i	−0.876508	−	0.481388i	$-0.840133\pi$
$683$	−23.4651	+	13.5476i	−0.897868	+	0.518384i	−0.0213600	+	0.999772i	$0.506800\pi$
$684$	−17.6185	−	17.6185i	−0.673660	−	0.673660i
$685$		0			0
$686$	1.27275	+	0.734823i	0.0485939	+	0.0280557i
$687$	7.63332	−	13.2213i	0.291229	−	0.504424i
$688$	17.1280	+	17.1280i	0.653000	+	0.653000i
$689$	33.6901	+	14.2193i	1.28349	+	0.541714i
$690$		0			0
$691$	−12.1374	+	3.25221i	−0.461729	+	0.123720i	−0.482182	−	0.876071i	$-0.660156\pi$
$691$	−12.1374	+	3.25221i	−0.461729	+	0.123720i	0.0204532	+	0.999791i	$0.493489\pi$
$692$	−7.26800	+	1.94746i	−0.276288	+	0.0740311i
$693$	−1.12619	+	4.20299i	−0.0427804	+	0.159658i
$694$	5.37339	−	5.37339i	0.203971	−	0.203971i
$695$		0			0
$696$	−20.0975	−	5.38511i	−0.761795	−	0.204122i
$697$	−9.18452			−0.347889
$698$	−7.83515	−	2.09942i	−0.296565	−	0.0794643i
$699$	−9.17475	+	15.8911i	−0.347021	+	0.601058i
$700$		0			0
$701$		−	39.3955i		−	1.48795i	−0.668208	−	0.743974i	$-0.732938\pi$
$701$		−	39.3955i		−	1.48795i	0.668208	−	0.743974i	$-0.267062\pi$
$702$	0.776434	−	0.587578i	0.0293046	−	0.0221767i
$703$	−17.0938	+	17.0938i	−0.644705	+	0.644705i
$704$	−7.04795	−	26.3033i	−0.265630	−	0.991343i
$705$		0			0
$706$	3.72112	−	2.14839i	0.140046	−	0.0808557i
$707$			2.03843i			0.0766631i
$708$	−5.51911	−	9.55939i	−0.207421	−	0.359264i
$709$	−6.62303	+	24.7175i	−0.248733	+	0.928285i	0.722737	+	0.691123i	$0.242884\pi$
$709$	−6.62303	+	24.7175i	−0.248733	+	0.928285i	−0.971470	+	0.237162i	$0.923783\pi$
$710$		0			0
$711$	4.32771	+	7.49582i	0.162302	+	0.281115i
$712$	−1.39527	−	5.20722i	−0.0522900	−	0.195149i
$713$	1.03857	+	0.599619i	0.0388948	+	0.0224559i
$714$	−0.494566			−0.0185087
$715$		0			0
$716$	12.5045			0.467315
$717$	−24.1359	−	13.9349i	−0.901371	−	0.520407i
$718$	1.41417	+	5.27777i	0.0527765	+	0.196965i
$719$	4.34268	+	7.52174i	0.161955	+	0.280514i	0.935570	−	0.353142i	$-0.114887\pi$
$719$	4.34268	+	7.52174i	0.161955	+	0.280514i	−0.773615	+	0.633656i	$0.781554\pi$
$720$		0			0
$721$	−0.171004	+	0.638194i	−0.00636851	+	0.0237676i
$722$	0.838438	+	1.45222i	0.0312034	+	0.0540460i
$723$			3.44830i			0.128244i
$724$	19.9740	−	11.5320i	0.742327	−	0.428583i
$725$		0			0
$726$	1.34781	+	5.03011i	0.0500220	+	0.186685i
$727$	17.4677	−	17.4677i	0.647841	−	0.647841i	−0.304630	−	0.952471i	$-0.598533\pi$
$727$	17.4677	−	17.4677i	0.647841	−	0.647841i	0.952471	+	0.304630i	$0.0985327\pi$
$728$	1.18498	+	0.921915i	0.0439184	+	0.0341684i
$729$		−	19.0676i		−	0.706209i
$730$		0			0
$731$	−6.72450	+	11.6472i	−0.248715	+	0.430786i
$732$	46.7685	+	12.5316i	1.72861	+	0.463180i
$733$	34.2413			1.26473			0.632365	−	0.774670i	$-0.282084\pi$
$733$	34.2413			1.26473			0.632365	+	0.774670i	$0.282084\pi$
$734$	−5.84646	−	1.56655i	−0.215797	−	0.0578225i
$735$		0			0
$736$	0.739121	−	0.739121i	0.0272444	−	0.0272444i
$737$	−7.19670	+	26.8584i	−0.265094	+	0.989344i
$738$	−3.19400	+	0.855830i	−0.117573	+	0.0315035i
$739$	−27.2869	+	7.31150i	−1.00376	+	0.268958i	−0.723022	−	0.690825i	$-0.757247\pi$
$739$	−27.2869	+	7.31150i	−1.00376	+	0.268958i	−0.280743	+	0.959783i	$0.590581\pi$
$740$		0			0
$741$	−39.5467	+	16.0720i	−1.45278	+	0.590421i
$742$	0.760935	+	0.760935i	0.0279348	+	0.0279348i
$743$	15.8384	−	27.4329i	0.581055	−	1.00642i	−0.414299	−	0.910141i	$-0.635973\pi$
$743$	15.8384	−	27.4329i	0.581055	−	1.00642i	0.995355	−	0.0962765i	$-0.0306933\pi$
$744$	7.93397	+	4.58068i	0.290873	+	0.167936i
$745$		0			0
$746$	−0.226489	−	0.226489i	−0.00829237	−	0.00829237i
$747$	11.6111	−	6.70370i	0.424830	−	0.245275i
$748$	14.3367	−	8.27733i	0.524203	−	0.302649i
$749$	1.10651	+	1.10651i	0.0404309	+	0.0404309i
$750$		0			0
$751$	2.11351	+	1.22024i	0.0771231	+	0.0445271i	0.538066	−	0.842903i	$-0.319155\pi$
$751$	2.11351	+	1.22024i	0.0771231	+	0.0445271i	−0.460943	+	0.887430i	$0.652489\pi$
$752$	−17.4665	+	30.2528i	−0.636936	+	1.10321i
$753$	21.7387	+	21.7387i	0.792201	+	0.792201i
$754$	−4.96721	+	6.38462i	−0.180895	+	0.232514i
$755$		0			0
$756$	−0.705319	+	0.188990i	−0.0256522	+	0.00687349i
$757$	41.2367	−	11.0493i	1.49877	−	0.401595i	0.586084	−	0.810250i	$-0.300669\pi$
$757$	41.2367	−	11.0493i	1.49877	−	0.401595i	0.912689	+	0.408655i	$0.134002\pi$
$758$	−1.87595	+	7.00115i	−0.0681377	+	0.254293i
$759$	2.43105	−	2.43105i	0.0882416	−	0.0882416i
$760$		0			0
$761$	−38.5996	−	10.3427i	−1.39923	−	0.374923i	−0.521164	−	0.853457i	$-0.674502\pi$
$761$	−38.5996	−	10.3427i	−1.39923	−	0.374923i	−0.878069	+	0.478533i	$0.841169\pi$
$762$	7.40565			0.268279
$763$	−2.65242	−	0.710715i	−0.0960242	−	0.0257296i
$764$	4.99683	−	8.65476i	0.180779	−	0.313118i
$765$		0			0
$766$			9.01376i			0.325680i
$767$	−8.68401	+	1.08429i	−0.313561	+	0.0391516i
$768$	−17.2018	+	17.2018i	−0.620716	+	0.620716i
$769$	−9.91969	−	37.0208i	−0.357713	−	1.33500i	−0.877035	−	0.480426i	$-0.840482\pi$
$769$	−9.91969	−	37.0208i	−0.357713	−	1.33500i	0.519322	−	0.854579i	$-0.326184\pi$
$770$		0			0
$771$	60.2925	−	34.8099i	2.17138	−	1.25365i
$772$			12.8442i			0.462274i
$773$	−7.28940	−	12.6256i	−0.262181	−	0.454111i	0.704640	−	0.709565i	$-0.251109\pi$
$773$	−7.28940	−	12.6256i	−0.262181	−	0.454111i	−0.966821	+	0.255454i	$0.917775\pi$
$774$	−1.25320	+	4.67701i	−0.0450454	+	0.168112i
$775$		0			0
$776$	7.95274	+	13.7745i	0.285487	+	0.494477i
$777$	−1.13940	−	4.25231i	−0.0408759	−	0.152551i
$778$	2.22956	+	1.28724i	0.0799337	+	0.0461497i
$779$	−23.3291			−0.835853
$780$		0			0
$781$	18.9872			0.679414
$782$	0.156606	+	0.0904167i	0.00560023	+	0.00323329i
$783$	−2.07649	−	7.74955i	−0.0742075	−	0.276946i
$784$	12.1692	+	21.0777i	0.434616	+	0.752777i
$785$		0			0
$786$	3.50652	−	13.0865i	0.125073	−	0.466780i
$787$	0.473902	+	0.820823i	0.0168928	+	0.0292592i	0.874348	−	0.485299i	$-0.161289\pi$
$787$	0.473902	+	0.820823i	0.0168928	+	0.0292592i	−0.857455	+	0.514558i	$0.827956\pi$
$788$		−	37.7143i		−	1.34352i
$789$	10.3399	−	5.96972i	0.368109	−	0.212528i
$790$		0			0
$791$	−0.397158	−	1.48222i	−0.0141213	−	0.0527015i
$792$	8.59426	−	8.59426i	0.305384	−	0.305384i
$793$	23.5718	−	30.2980i	0.837058	−	1.07591i
$794$		−	3.20207i		−	0.113637i
$795$		0			0
$796$	−14.1507	+	24.5098i	−0.501560	+	0.868727i
$797$	4.51774	+	1.21053i	0.160027	+	0.0428790i	0.337943	−	0.941167i	$-0.390269\pi$
$797$	4.51774	+	1.21053i	0.160027	+	0.0428790i	−0.177916	+	0.984046i	$0.556936\pi$
$798$	−1.25622			−0.0444698
$799$	−18.7347	−	5.01994i	−0.662785	−	0.177593i
$800$		0			0
$801$	−9.13379	+	9.13379i	−0.322726	+	0.322726i
$802$	1.46638	−	5.47260i	0.0517796	−	0.193244i
$803$	25.6369	−	6.86939i	0.904707	−	0.242415i
$804$	28.0077	−	7.50465i	0.987756	−	0.264668i
$805$		0			0
$806$	2.84020	−	2.14937i	0.100042	−	0.0757082i
$807$	−14.4537	−	14.4537i	−0.508794	−	0.508794i
$808$	2.84692	−	4.93101i	0.100154	−	0.173472i
$809$	21.1627	+	12.2183i	0.744040	+	0.429572i	0.823536	−	0.567263i	$-0.191998\pi$
$809$	21.1627	+	12.2183i	0.744040	+	0.429572i	−0.0794964	+	0.996835i	$0.525331\pi$
$810$		0			0
$811$	−9.34795	−	9.34795i	−0.328251	−	0.328251i	0.523670	−	0.851921i	$-0.324562\pi$
$811$	−9.34795	−	9.34795i	−0.328251	−	0.328251i	−0.851921	+	0.523670i	$0.824562\pi$
$812$	5.25359	−	3.03316i	0.184365	−	0.106443i
$813$	47.1295	−	27.2103i	1.65291	−	0.954305i
$814$	−4.08893	−	4.08893i	−0.143317	−	0.143317i
$815$		0			0
$816$	−14.3405	−	8.27951i	−0.502019	−	0.289841i
$817$	−17.0806	+	29.5844i	−0.597573	+	1.03503i
$818$	0.885667	+	0.885667i	0.0309666	+	0.0309666i
$819$	0.493378	−	3.56343i	0.0172400	−	0.124516i
$820$		0			0
$821$	−1.89876	+	0.508771i	−0.0662672	+	0.0177562i	−0.291800	−	0.956479i	$-0.594254\pi$
$821$	−1.89876	+	0.508771i	−0.0662672	+	0.0177562i	0.225533	+	0.974236i	$0.427588\pi$
$822$	−0.153021	+	0.0410019i	−0.00533723	+	0.00143011i
$823$	−4.25627	+	15.8846i	−0.148364	+	0.553703i	0.851218	+	0.524812i	$0.175864\pi$
$823$	−4.25627	+	15.8846i	−0.148364	+	0.553703i	−0.999583	+	0.0288913i	$0.990802\pi$
$824$	1.30498	−	1.30498i	0.0454610	−	0.0454610i
$825$		0			0
$826$	−0.248763	−	0.0666558i	−0.00865557	−	0.00231925i
$827$	−27.3262			−0.950225			−0.475113	−	0.879925i	$-0.657593\pi$
$827$	−27.3262			−0.950225			−0.475113	+	0.879925i	$0.657593\pi$
$828$	−1.60254	−	0.429400i	−0.0556922	−	0.0149227i
$829$	7.27764	−	12.6052i	0.252763	−	0.437798i	−0.711523	−	0.702663i	$-0.751994\pi$
$829$	7.27764	−	12.6052i	0.252763	−	0.437798i	0.964286	+	0.264865i	$0.0853274\pi$
$830$		0			0
$831$		−	51.1397i		−	1.77402i
$832$	8.47639	+	20.8569i	0.293866	+	0.723082i
$833$	−9.55534	+	9.55534i	−0.331073	+	0.331073i
$834$	−1.96380	−	7.32901i	−0.0680009	−	0.253783i
$835$		0			0
$836$	36.4161	−	21.0248i	1.25948	−	0.727159i
$837$			3.53259i			0.122104i
$838$	0.0895937	+	0.155181i	0.00309496	+	0.00536063i
$839$	−6.33030	+	23.6250i	−0.218546	+	0.815625i	0.766342	+	0.642433i	$0.222075\pi$
$839$	−6.33030	+	23.6250i	−0.218546	+	0.815625i	−0.984888	+	0.173192i	$0.944592\pi$
$840$		0			0
$841$	18.8262	+	32.6080i	0.649180	+	1.12441i
$842$	−0.561370	−	2.09506i	−0.0193461	−	0.0722006i
$843$	−23.6661	−	13.6636i	−0.815104	−	0.470601i
$844$	−41.2114			−1.41856
$845$		0			0
$846$	−6.98292			−0.240078
$847$	−2.68139	−	1.54810i	−0.0921335	−	0.0531933i
$848$	9.32543	+	34.8030i	0.320237	+	1.19514i
$849$	−5.31615	−	9.20784i	−0.182450	−	0.316012i
$850$		0			0
$851$	−0.416612	+	1.55482i	−0.0142813	+	0.0532985i
$852$	−9.89982	−	17.1470i	−0.339162	−	0.587446i
$853$			2.94669i			0.100893i	0.998727	+	0.0504464i	$0.0160644\pi$
$853$			2.94669i			0.100893i	−0.998727	+	0.0504464i	$0.983936\pi$
$854$	0.978324	−	0.564835i	0.0334775	−	0.0193283i
$855$		0			0
$856$	−1.13129	−	4.22204i	−0.0386667	−	0.144306i
$857$	13.0632	−	13.0632i	0.446229	−	0.446229i	−0.447870	−	0.894099i	$-0.647817\pi$
$857$	13.0632	−	13.0632i	0.446229	−	0.446229i	0.894099	+	0.447870i	$0.147817\pi$
$858$	−3.84452	−	9.45978i	−0.131250	−	0.322951i
$859$		−	3.08382i		−	0.105219i	−0.998615	−	0.0526093i	$-0.983246\pi$
$859$		−	3.08382i		−	0.105219i	0.998615	−	0.0526093i	$-0.0167538\pi$
$860$		0			0
$861$	2.12421	−	3.67923i	0.0723928	−	0.125388i
$862$	−9.48982	−	2.54279i	−0.323225	−	0.0866078i
$863$	−50.9818			−1.73544			−0.867720	−	0.497053i	$-0.834415\pi$
$863$	−50.9818			−1.73544			−0.867720	+	0.497053i	$0.834415\pi$
$864$	2.97415	+	0.796920i	0.101183	+	0.0271118i
$865$		0			0
$866$	−5.12611	+	5.12611i	−0.174192	+	0.174192i
$867$	−8.01780	+	29.9228i	−0.272299	+	1.01623i
$868$	−2.58006	+	0.691326i	−0.0875730	+	0.0234651i
$869$	−14.1095	+	3.78062i	−0.478631	+	0.128249i
$870$		0			0
$871$	3.15284	−	22.7715i	0.106830	−	0.771581i
$872$	5.42366	+	5.42366i	0.183668	+	0.183668i
$873$	19.0555	−	33.0051i	0.644931	−	1.11705i
$874$	0.397788	+	0.229663i	0.0134554	+	0.00776846i
$875$		0			0
$876$	−19.5706	−	19.5706i	−0.661228	−	0.661228i
$877$	23.1824	−	13.3844i	0.782814	−	0.451958i	−0.0546128	−	0.998508i	$-0.517392\pi$
$877$	23.1824	−	13.3844i	0.782814	−	0.451958i	0.837427	+	0.546550i	$0.184059\pi$
$878$	−0.411570	+	0.237620i	−0.0138898	+	0.00801929i
$879$	21.8986	+	21.8986i	0.738621	+	0.738621i
$880$		0			0
$881$	27.2630	+	15.7403i	0.918512	+	0.530303i	0.883160	−	0.469072i	$-0.155411\pi$
$881$	27.2630	+	15.7403i	0.918512	+	0.530303i	0.0353521	+	0.999375i	$0.488745\pi$
$882$	−2.43257	+	4.21334i	−0.0819089	+	0.141870i
$883$	−27.3576	−	27.3576i	−0.920657	−	0.920657i	0.0764191	−	0.997076i	$-0.475651\pi$
$883$	−27.3576	−	27.3576i	−0.920657	−	0.920657i	−0.997076	+	0.0764191i	$0.975651\pi$
$884$	−10.9138	+	8.25917i	−0.367070	+	0.277786i
$885$		0			0
$886$	−1.07640	+	0.288420i	−0.0361623	+	0.00968965i
$887$	−1.32670	+	0.355489i	−0.0445463	+	0.0119362i	−0.281023	−	0.959701i	$-0.590674\pi$
$887$	−1.32670	+	0.355489i	−0.0445463	+	0.0119362i	0.236477	+	0.971637i	$0.424007\pi$
$888$	−3.18263	+	11.8777i	−0.106802	+	0.398591i
$889$	−3.11346	+	3.11346i	−0.104422	+	0.104422i
$890$		0			0
$891$	42.4393	+	11.3716i	1.42177	+	0.380962i
$892$	52.6068			1.76141
$893$	−47.5870	−	12.7509i	−1.59244	−	0.426692i
$894$	−0.822293	+	1.42425i	−0.0275016	+	0.0476341i
$895$		0			0
$896$			3.08204i			0.102964i
$897$	−1.74538	+	2.24342i	−0.0582764	+	0.0749057i
$898$	−3.92294	+	3.92294i	−0.130910	+	0.130910i
$899$	−7.59580	−	28.3479i	−0.253334	−	0.945456i
$900$		0			0
$901$	−17.3249	+	10.0025i	−0.577176	+	0.333233i
$902$		−	5.58046i		−	0.185809i
$903$	−3.11050	−	5.38754i	−0.103511	−	0.179286i
$904$	−1.10936	+	4.14019i	−0.0368968	+	0.137701i
$905$		0			0
$906$	−1.18700	−	2.05594i	−0.0394354	−	0.0683040i
$907$	6.02625	+	22.4903i	0.200098	+	0.746777i	0.990888	+	0.134689i	$0.0430036\pi$
$907$	6.02625	+	22.4903i	0.200098	+	0.746777i	−0.790790	+	0.612088i	$0.790330\pi$
$908$	11.5455	+	6.66580i	0.383151	+	0.221212i
$909$	−13.6430			−0.452508
$910$		0			0
$911$	2.89704			0.0959832			0.0479916	−	0.998848i	$-0.484718\pi$
$911$	2.89704			0.0959832			0.0479916	+	0.998848i	$0.484718\pi$
$912$	−36.4256	−	21.0304i	−1.20617	−	0.696385i
$913$	5.85624	+	21.8558i	0.193813	+	0.723322i
$914$	−2.03105	−	3.51789i	−0.0671813	−	0.116361i
$915$		0			0
$916$	3.21792	−	12.0094i	0.106323	−	0.396803i
$917$	4.02759	+	6.97599i	0.133003	+	0.230368i
$918$			0.532680i			0.0175811i
$919$	−14.3846	+	8.30494i	−0.474503	+	0.273955i	−0.718123	−	0.695916i	$-0.754998\pi$
$919$	−14.3846	+	8.30494i	−0.474503	+	0.273955i	0.243620	+	0.969871i	$0.421665\pi$
$920$		0			0
$921$	4.74271	+	17.7000i	0.156278	+	0.583236i
$922$	−1.18028	+	1.18028i	−0.0388704	+	0.0388704i
$923$	−15.5768	+	1.94494i	−0.512716	+	0.0640183i
$924$			7.65756i			0.251915i
$925$		0			0
$926$	4.94858	−	8.57120i	0.162621	−	0.281667i
$927$	−4.27135	−	1.14451i	−0.140290	−	0.0375905i
$928$	−25.5801			−0.839708
$929$	41.3672	+	11.0843i	1.35721	+	0.363664i	0.862792	−	0.505559i	$-0.168714\pi$
$929$	41.3672	+	11.0843i	1.35721	+	0.363664i	0.494420	+	0.869223i	$0.335380\pi$
$930$		0			0
$931$	−24.2710	+	24.2710i	−0.795451	+	0.795451i
$932$	−3.86773	+	14.4346i	−0.126692	+	0.472820i
$933$	26.4846	−	7.09653i	0.867067	−	0.232330i
$934$	−2.88661	+	0.773465i	−0.0944528	+	0.0253086i
$935$		0			0
$936$	−6.17025	+	7.93095i	−0.201681	+	0.259231i
$937$	−27.9881	−	27.9881i	−0.914331	−	0.914331i	0.0822783	−	0.996609i	$-0.473780\pi$
$937$	−27.9881	−	27.9881i	−0.914331	−	0.914331i	−0.996609	+	0.0822783i	$0.973780\pi$
$938$	0.338257	−	0.585878i	0.0110445	−	0.0191296i
$939$	−29.3945	−	16.9709i	−0.959254	−	0.553826i
$940$		0			0
$941$	−4.15042	−	4.15042i	−0.135300	−	0.135300i	0.636213	−	0.771513i	$-0.280500\pi$
$941$	−4.15042	−	4.15042i	−0.135300	−	0.135300i	−0.771513	+	0.636213i	$0.780500\pi$
$942$	1.76381	−	1.01834i	0.0574680	−	0.0331792i
$943$	−1.34528	+	0.776696i	−0.0438083	+	0.0252927i
$944$	−6.09729	−	6.09729i	−0.198450	−	0.198450i
$945$		0			0
$946$	−7.07675	−	4.08576i	−0.230085	−	0.132840i
$947$	−12.4299	+	21.5292i	−0.403918	+	0.699606i	−0.994195	−	0.107595i	$-0.965685\pi$
$947$	−12.4299	+	21.5292i	−0.403918	+	0.699606i	0.590277	+	0.807201i	$0.299018\pi$
$948$	10.7708	+	10.7708i	0.349820	+	0.349820i
$949$	−20.3285	+	8.26164i	−0.659890	+	0.268184i
$950$		0			0
$951$	−49.6881	+	13.3139i	−1.61125	+	0.431732i
$952$	−0.793363	+	0.212581i	−0.0257130	+	0.00688979i
$953$	−8.46463	+	31.5904i	−0.274196	+	1.02331i	0.682182	+	0.731182i	$0.261031\pi$
$953$	−8.46463	+	31.5904i	−0.274196	+	1.02331i	−0.956378	+	0.292131i	$0.905636\pi$
$954$	−5.09284	+	5.09284i	−0.164887	+	0.164887i
$955$		0			0
$956$	−21.9236	−	5.87441i	−0.709059	−	0.189992i
$957$	−84.1358			−2.71973
$958$	−2.43782	−	0.653211i	−0.0787622	−	0.0211043i
$959$	0.0470949	−	0.0815707i	0.00152077	−	0.00263405i
$960$		0			0
$961$		−	18.0777i		−	0.583153i
$962$	3.77334	+	2.93565i	0.121657	+	0.0946491i
$963$	−7.40571	+	7.40571i	−0.238646	+	0.238646i
$964$	0.726837	+	2.71259i	0.0234098	+	0.0873667i
$965$		0			0
$966$	−0.0724402	+	0.0418234i	−0.00233072	+	0.00134564i
$967$		−	30.0090i		−	0.965023i	−0.875890	−	0.482512i	$-0.839725\pi$
$967$		−	30.0090i		−	0.965023i	0.875890	−	0.482512i	$-0.160275\pi$
$968$	4.32422	+	7.48976i	0.138986	+	0.240730i
$969$	6.04422	−	22.5573i	0.194168	−	0.724646i
$970$		0			0
$971$	3.13659	+	5.43273i	0.100658	+	0.174345i	0.911956	−	0.410288i	$-0.134572\pi$
$971$	3.13659	+	5.43273i	0.100658	+	0.174345i	−0.811298	+	0.584633i	$0.801239\pi$
$972$	−10.3897	−	38.7750i	−0.333251	−	1.24371i
$973$	3.90686	+	2.25563i	0.125248	+	0.0723120i
$974$	−7.07119			−0.226575
$975$		0			0
$976$	37.8235			1.21070
$977$	−13.4772	−	7.78106i	−0.431174	−	0.248938i	0.268673	−	0.963231i	$-0.413415\pi$
$977$	−13.4772	−	7.78106i	−0.431174	−	0.248938i	−0.699847	+	0.714293i	$0.746748\pi$
$978$	−2.48968	−	9.29160i	−0.0796111	−	0.297113i
$979$	−10.8997	−	18.8788i	−0.348356	−	0.603370i
$980$		0			0
$981$	4.75672	−	17.7523i	0.151870	−	0.566788i
$982$	1.81335	+	3.14082i	0.0578663	+	0.100227i
$983$			53.4558i			1.70498i	0.522746	+	0.852488i	$0.324907\pi$
$983$			53.4558i			1.70498i	−0.522746	+	0.852488i	$0.675093\pi$
$984$	−10.2770	+	5.93342i	−0.327619	+	0.189151i
$985$		0			0
$986$	−1.14537	−	4.27459i	−0.0364761	−	0.136131i
$987$	6.34391	−	6.34391i	0.201929	−	0.201929i
$988$	−27.7215	+	20.9787i	−0.881939	+	0.667421i
$989$			2.27465i			0.0723297i
$990$		0			0
$991$	11.8198	−	20.4726i	0.375470	−	0.650333i	−0.614927	−	0.788584i	$-0.710815\pi$
$991$	11.8198	−	20.4726i	0.375470	−	0.650333i	0.990397	+	0.138251i	$0.0441480\pi$
$992$	10.8795	+	2.91514i	0.345423	+	0.0925558i
$993$	46.3626			1.47127
$994$	−0.446214	−	0.119563i	−0.0141531	−	0.00379230i
$995$		0			0
$996$	16.6842	−	16.6842i	0.528658	−	0.528658i
$997$	−13.3882	+	49.9653i	−0.424007	+	1.58242i	0.342075	+	0.939673i	$0.388870\pi$
$997$	−13.3882	+	49.9653i	−0.424007	+	1.58242i	−0.766082	+	0.642743i	$0.777796\pi$
$998$	6.29473	−	1.68667i	0.199256	−	0.0533905i
$999$	−4.58002	+	1.22721i	−0.144906	+	0.0388273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.x.b.7.2		20
5.2	odd	4		65.2.o.a.33.4	yes	20
5.3	odd	4		325.2.s.b.293.2		20
5.4	even	2		65.2.t.a.7.4	yes	20
13.2	odd	12		325.2.s.b.132.2		20
15.2	even	4		585.2.cf.a.163.2		20
15.14	odd	2		585.2.dp.a.397.2		20
65.2	even	12		65.2.t.a.28.4	yes	20
65.4	even	6		845.2.f.d.437.6		20
65.7	even	12		845.2.f.d.408.5		20
65.9	even	6		845.2.f.e.437.5		20
65.12	odd	4		845.2.o.g.488.2		20
65.17	odd	12		845.2.k.d.268.6		20
65.19	odd	12		845.2.k.e.577.5		20
65.22	odd	12		845.2.k.e.268.5		20
65.24	odd	12		845.2.o.g.587.2		20
65.28	even	12	inner	325.2.x.b.93.2		20
65.29	even	6		845.2.t.f.427.2		20
65.32	even	12		845.2.f.e.408.6		20
65.34	odd	4		845.2.o.f.357.2		20
65.37	even	12		845.2.t.g.418.2		20
65.42	odd	12		845.2.o.e.258.4		20
65.44	odd	4		845.2.o.e.357.4		20
65.47	even	4		845.2.t.e.188.4		20
65.49	even	6		845.2.t.e.427.4		20
65.54	odd	12		65.2.o.a.2.4	✓	20
65.57	even	4		845.2.t.f.188.2		20
65.59	odd	12		845.2.k.d.577.6		20
65.62	odd	12		845.2.o.f.258.2		20
65.64	even	2		845.2.t.g.657.2		20
195.2	odd	12		585.2.dp.a.28.2		20
195.119	even	12		585.2.cf.a.262.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.4	✓	20	65.54	odd	12
65.2.o.a.33.4	yes	20	5.2	odd	4
65.2.t.a.7.4	yes	20	5.4	even	2
65.2.t.a.28.4	yes	20	65.2	even	12
325.2.s.b.132.2		20	13.2	odd	12
325.2.s.b.293.2		20	5.3	odd	4
325.2.x.b.7.2		20	1.1	even	1	trivial
325.2.x.b.93.2		20	65.28	even	12	inner
585.2.cf.a.163.2		20	15.2	even	4
585.2.cf.a.262.2		20	195.119	even	12
585.2.dp.a.28.2		20	195.2	odd	12
585.2.dp.a.397.2		20	15.14	odd	2
845.2.f.d.408.5		20	65.7	even	12
845.2.f.d.437.6		20	65.4	even	6
845.2.f.e.408.6		20	65.32	even	12
845.2.f.e.437.5		20	65.9	even	6
845.2.k.d.268.6		20	65.17	odd	12
845.2.k.d.577.6		20	65.59	odd	12
845.2.k.e.268.5		20	65.22	odd	12
845.2.k.e.577.5		20	65.19	odd	12
845.2.o.e.258.4		20	65.42	odd	12
845.2.o.e.357.4		20	65.44	odd	4
845.2.o.f.258.2		20	65.62	odd	12
845.2.o.f.357.2		20	65.34	odd	4
845.2.o.g.488.2		20	65.12	odd	4
845.2.o.g.587.2		20	65.24	odd	12
845.2.t.e.188.4		20	65.47	even	4
845.2.t.e.427.4		20	65.49	even	6
845.2.t.f.188.2		20	65.57	even	4
845.2.t.f.427.2		20	65.29	even	6
845.2.t.g.418.2		20	65.37	even	12
845.2.t.g.657.2		20	65.64	even	2

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.237991 + 0.137404i) q^{2} +(-0.611610 - 2.28256i) q^{3} +(-0.962240 - 1.66665i) q^{4} +(0.168076 - 0.627267i) q^{6} +(0.193052 + 0.334376i) q^{7} -1.07848i q^{8} +(-2.23793 + 1.29207i) q^{9} +O(q^{10})\)	\(q+(0.237991 + 0.137404i) q^{2} +(-0.611610 - 2.28256i) q^{3} +(-0.962240 - 1.66665i) q^{4} +(0.168076 - 0.627267i) q^{6} +(0.193052 + 0.334376i) q^{7} -1.07848i q^{8} +(-2.23793 + 1.29207i) q^{9} +(-1.12873 - 4.21249i) q^{11} +(-3.21571 + 3.21571i) q^{12} +(1.35750 + 3.34024i) q^{13} +0.106105i q^{14} +(-1.77629 + 3.07663i) q^{16} +(-1.90527 - 0.510514i) q^{17} -0.710144 q^{18} +(-4.83947 - 1.29673i) q^{19} +(0.645159 - 0.645159i) q^{21} +(0.310185 - 1.15763i) q^{22} +(-0.322241 + 0.0863441i) q^{23} +(-2.46170 + 0.659609i) q^{24} +(-0.135891 + 0.981474i) q^{26} +(-0.694880 - 0.694880i) q^{27} +(0.371524 - 0.643499i) q^{28} +(7.07031 + 4.08205i) q^{29} +(-2.54187 - 2.54187i) q^{31} +(-2.71347 + 1.56662i) q^{32} +(-8.92491 + 5.15280i) q^{33} +(-0.383290 - 0.383290i) q^{34} +(4.30685 + 2.48656i) q^{36} +(2.41251 - 4.17859i) q^{37} +(-0.973575 - 0.973575i) q^{38} +(6.79403 - 5.14149i) q^{39} +(4.49768 - 1.20515i) q^{41} +(0.242190 - 0.0648946i) q^{42} +(1.76471 - 6.58600i) q^{43} +(-5.93462 + 5.93462i) q^{44} +(-0.0885545 - 0.0237281i) q^{46} +9.83310 q^{47} +(8.10898 + 2.17280i) q^{48} +(3.42546 - 5.93307i) q^{49} +4.66112i q^{51} +(4.26077 - 5.47658i) q^{52} +(7.17155 - 7.17155i) q^{53} +(-0.0698958 - 0.260855i) q^{54} +(0.360618 - 0.208203i) q^{56} +11.8395i q^{57} +(1.12178 + 1.94298i) q^{58} +(-0.628209 + 2.34451i) q^{59} +(-5.32338 - 9.22037i) q^{61} +(-0.255679 - 0.954209i) q^{62} +(-0.864073 - 0.498873i) q^{63} +6.24413 q^{64} -2.83207 q^{66} +(-5.52170 - 3.18796i) q^{67} +(0.982475 + 3.66665i) q^{68} +(0.394171 + 0.682724i) q^{69} +(-1.12684 + 4.20542i) q^{71} +(1.39347 + 2.41357i) q^{72} +6.08593i q^{73} +(1.14831 - 0.662979i) q^{74} +(2.49554 + 9.31346i) q^{76} +(1.19065 - 1.19065i) q^{77} +(2.32338 - 0.290100i) q^{78} -3.34944i q^{79} +(-5.03732 + 8.72489i) q^{81} +(1.23600 + 0.331185i) q^{82} -5.18834 q^{83} +(-1.69605 - 0.454456i) q^{84} +(1.32493 - 1.32493i) q^{86} +(4.99324 - 18.6350i) q^{87} +(-4.54309 + 1.21732i) q^{88} +(4.82829 - 1.29374i) q^{89} +(-0.854827 + 1.09875i) q^{91} +(0.453978 + 0.453978i) q^{92} +(-4.24734 + 7.35661i) q^{93} +(2.34019 + 1.35111i) q^{94} +(5.23549 + 5.23549i) q^{96} +(-12.7722 + 7.37402i) q^{97} +(1.63046 - 0.941346i) q^{98} +(7.96886 + 7.96886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 8 * q^6 + 2 * q^7 + 12 * q^9	\( 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9} - 16 q^{11} + 24 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 4 q^{21} - 16 q^{22} + 10 q^{23} + 32 q^{24} - 24 q^{26} - 4 q^{27} - 18 q^{28} - 48 q^{32} - 18 q^{33} + 2 q^{34} + 36 q^{36} + 4 q^{37} + 8 q^{38} + 4 q^{39} + 10 q^{41} - 40 q^{42} - 10 q^{43} - 36 q^{44} + 4 q^{46} + 40 q^{47} + 56 q^{48} + 18 q^{49} + 30 q^{52} + 10 q^{53} - 48 q^{54} - 16 q^{59} - 16 q^{61} + 44 q^{62} + 36 q^{63} + 20 q^{64} - 32 q^{66} - 18 q^{67} - 22 q^{68} - 16 q^{69} - 16 q^{71} - 4 q^{72} + 18 q^{74} - 64 q^{76} + 28 q^{77} - 68 q^{78} - 14 q^{81} - 56 q^{82} - 48 q^{83} - 40 q^{84} + 60 q^{86} + 34 q^{87} - 82 q^{88} - 6 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 48 q^{94} + 56 q^{96} - 66 q^{97} + 30 q^{98} + 60 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 8 * q^6 + 2 * q^7 + 12 * q^9 - 16 * q^11 + 24 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 4 * q^21 - 16 * q^22 + 10 * q^23 + 32 * q^24 - 24 * q^26 - 4 * q^27 - 18 * q^28 - 48 * q^32 - 18 * q^33 + 2 * q^34 + 36 * q^36 + 4 * q^37 + 8 * q^38 + 4 * q^39 + 10 * q^41 - 40 * q^42 - 10 * q^43 - 36 * q^44 + 4 * q^46 + 40 * q^47 + 56 * q^48 + 18 * q^49 + 30 * q^52 + 10 * q^53 - 48 * q^54 - 16 * q^59 - 16 * q^61 + 44 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 - 22 * q^68 - 16 * q^69 - 16 * q^71 - 4 * q^72 + 18 * q^74 - 64 * q^76 + 28 * q^77 - 68 * q^78 - 14 * q^81 - 56 * q^82 - 48 * q^83 - 40 * q^84 + 60 * q^86 + 34 * q^87 - 82 * q^88 - 6 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 48 * q^94 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

Introduction

L-functions

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