LMFDB - Embedded newform 585.2.j.g.406.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(406,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("585.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.j (of order $3$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.591408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4x^{4} + x^{3} + 10x^{2} - 3x + 1 $ x^6 - x^5 + 4x^4 + x^3 + 10x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.3
Root			$0.155554 - 0.269427i$ of defining polynomial
Character	$\chi$	$=$	585.406
Dual form			585.2.j.g.451.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.10716 + 1.91766i) q^{2} +(-1.45161 + 2.51426i) q^{4} +1.00000 q^{5} +(1.91827 - 3.32254i) q^{7} -2.00000 q^{8} +(1.10716 + 1.91766i) q^{10} +(2.90321 + 5.02851i) q^{11} +(0.533338 - 3.56589i) q^{13} +8.49532 q^{14} +(0.688892 + 1.19320i) q^{16} +(-1.79605 + 3.11085i) q^{17} +(-1.07382 + 1.85991i) q^{19} +(-1.45161 + 2.51426i) q^{20} +(-6.42864 + 11.1347i) q^{22} +(-3.11753 - 5.39972i) q^{23} +1.00000 q^{25} +(7.42864 - 2.92525i) q^{26} +(5.56914 + 9.64603i) q^{28} +(1.03334 + 1.78979i) q^{29} -5.28100 q^{31} +(-3.52543 + 6.10622i) q^{32} -7.95407 q^{34} +(1.91827 - 3.32254i) q^{35} +(2.37778 + 4.11844i) q^{37} -4.75557 q^{38} -2.00000 q^{40} +(-5.55877 - 9.62806i) q^{41} +(4.74766 - 8.22318i) q^{43} -16.8573 q^{44} +(6.90321 - 11.9567i) q^{46} -2.21432 q^{47} +(-3.85950 - 6.68485i) q^{49} +(1.10716 + 1.91766i) q^{50} +(8.19135 + 6.51721i) q^{52} +0.815792 q^{53} +(2.90321 + 5.02851i) q^{55} +(-3.83654 + 6.64507i) q^{56} +(-2.28814 + 3.96318i) q^{58} +(-4.98741 + 8.63844i) q^{59} +(-2.64050 + 4.57348i) q^{61} +(-5.84691 - 10.1271i) q^{62} -12.8573 q^{64} +(0.533338 - 3.56589i) q^{65} +(1.77777 + 3.07919i) q^{67} +(-5.21432 - 9.03147i) q^{68} +8.49532 q^{70} +(2.86987 - 4.97077i) q^{71} -2.78568 q^{73} +(-5.26517 + 9.11955i) q^{74} +(-3.11753 - 5.39972i) q^{76} +22.2766 q^{77} +12.3319 q^{79} +(0.688892 + 1.19320i) q^{80} +(12.3089 - 21.3196i) q^{82} -0.622216 q^{83} +(-1.79605 + 3.11085i) q^{85} +21.0257 q^{86} +(-5.80642 - 10.0570i) q^{88} +(-8.08419 - 14.0022i) q^{89} +(-10.8247 - 8.61236i) q^{91} +18.1017 q^{92} +(-2.45161 - 4.24631i) q^{94} +(-1.07382 + 1.85991i) q^{95} +(-2.12544 + 3.68137i) q^{97} +(8.54617 - 14.8024i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} + 6 q^{5} + 5 q^{7} - 12 q^{8} + 4 q^{11} + 3 q^{13} + 24 q^{14} + 4 q^{16} - 4 q^{17} - 2 q^{20} - 12 q^{22} + 8 q^{23} + 6 q^{25} + 18 q^{26} + 6 q^{29} - 18 q^{31} - 8 q^{32} - 8 q^{34}+ \cdots - 2 q^{98}+O(q^{100}) $ 6 * q - 2 * q^4 + 6 * q^5 + 5 * q^7 - 12 * q^8 + 4 * q^11 + 3 * q^13 + 24 * q^14 + 4 * q^16 - 4 * q^17 - 2 * q^20 - 12 * q^22 + 8 * q^23 + 6 * q^25 + 18 * q^26 + 6 * q^29 - 18 * q^31 - 8 * q^32 - 8 * q^34 + 5 * q^35 + 14 * q^37 - 28 * q^38 - 12 * q^40 - 20 * q^41 + 15 * q^43 - 48 * q^44 + 28 * q^46 - 30 * q^49 + 16 * q^52 + 32 * q^53 + 4 * q^55 - 10 * q^56 + 6 * q^58 + 10 * q^59 - 9 * q^61 - 2 * q^62 - 24 * q^64 + 3 * q^65 + 11 * q^67 - 18 * q^68 + 24 * q^70 + 4 * q^71 - 30 * q^73 + 8 * q^74 + 8 * q^76 + 34 * q^79 + 4 * q^80 + 14 * q^82 - 4 * q^83 - 4 * q^85 + 20 * q^86 - 8 * q^88 - 22 * q^89 - 31 * q^91 + 56 * q^92 - 8 * q^94 + q^97 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.10716	+	1.91766i	0.782880	+	1.35599i	0.930257	+	0.366908i	$0.119584\pi$
$2$	1.10716	+	1.91766i	0.782880	+	1.35599i	−0.147377	+	0.989080i	$0.547083\pi$
$3$		0			0
$3$		0			0
$4$	−1.45161	+	2.51426i	−0.725803	+	1.25713i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	1.91827	−	3.32254i	0.725037	−	1.25580i	−0.233922	−	0.972255i	$-0.575156\pi$
$7$	1.91827	−	3.32254i	0.725037	−	1.25580i	0.958959	−	0.283546i	$-0.0915107\pi$
$8$	−2.00000			−0.707107
$9$		0			0
$10$	1.10716	+	1.91766i	0.350115	+	0.606416i
$11$	2.90321	+	5.02851i	0.875351	+	1.51615i	0.856388	+	0.516333i	$0.172703\pi$
$11$	2.90321	+	5.02851i	0.875351	+	1.51615i	0.0189633	+	0.999820i	$0.493963\pi$
$12$		0			0
$13$	0.533338	−	3.56589i	0.147921	−	0.988999i
$13$	0.533338	−	3.56589i	0.147921	−	0.988999i
$14$	8.49532			2.27047
$15$		0			0
$16$	0.688892	+	1.19320i	0.172223	+	0.298299i
$17$	−1.79605	+	3.11085i	−0.435607	+	0.754493i	−0.997345	−	0.0728222i	$-0.976799\pi$
$17$	−1.79605	+	3.11085i	−0.435607	+	0.754493i	0.561738	+	0.827315i	$0.310133\pi$
$18$		0			0
$19$	−1.07382	+	1.85991i	−0.246352	+	0.426693i	−0.962511	−	0.271244i	$-0.912565\pi$
$19$	−1.07382	+	1.85991i	−0.246352	+	0.426693i	0.716159	+	0.697937i	$0.245898\pi$
$20$	−1.45161	+	2.51426i	−0.324589	+	0.562205i
$21$		0			0
$22$	−6.42864	+	11.1347i	−1.37059	+	2.37393i
$23$	−3.11753	−	5.39972i	−0.650050	−	1.12592i	−0.983110	−	0.183014i	$-0.941414\pi$
$23$	−3.11753	−	5.39972i	−0.650050	−	1.12592i	0.333060	−	0.942906i	$-0.391919\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	7.42864	−	2.92525i	1.45688	−	0.573688i
$27$		0			0
$28$	5.56914	+	9.64603i	1.05247	+	1.82293i
$29$	1.03334	+	1.78979i	0.191886	+	0.332356i	0.945875	−	0.324530i	$-0.105206\pi$
$29$	1.03334	+	1.78979i	0.191886	+	0.332356i	−0.753989	+	0.656887i	$0.771873\pi$
$30$		0			0
$31$	−5.28100			−0.948495			−0.474247	−	0.880392i	$-0.657280\pi$
$31$	−5.28100			−0.948495			−0.474247	+	0.880392i	$0.657280\pi$
$32$	−3.52543	+	6.10622i	−0.623213	+	1.07944i
$33$		0			0
$34$	−7.95407			−1.36411
$35$	1.91827	−	3.32254i	0.324246	−	0.561611i
$36$		0			0
$37$	2.37778	+	4.11844i	0.390905	+	0.677068i	0.992569	−	0.121681i	$-0.0388286\pi$
$37$	2.37778	+	4.11844i	0.390905	+	0.677068i	−0.601664	+	0.798749i	$0.705495\pi$
$38$	−4.75557			−0.771455
$39$		0			0
$40$	−2.00000			−0.316228
$41$	−5.55877	−	9.62806i	−0.868133	−	1.50365i	−0.863902	−	0.503660i	$-0.831986\pi$
$41$	−5.55877	−	9.62806i	−0.868133	−	1.50365i	−0.00423144	−	0.999991i	$-0.501347\pi$
$42$		0			0
$43$	4.74766	−	8.22318i	0.724011	−	1.25402i	−0.235369	−	0.971906i	$-0.575630\pi$
$43$	4.74766	−	8.22318i	0.724011	−	1.25402i	0.959380	−	0.282118i	$-0.0910369\pi$
$44$	−16.8573			−2.54133
$45$		0			0
$46$	6.90321	−	11.9567i	1.01782	−	1.76292i
$47$	−2.21432			−0.322992			−0.161496	−	0.986873i	$-0.551632\pi$
$47$	−2.21432			−0.322992			−0.161496	+	0.986873i	$0.551632\pi$
$48$		0			0
$49$	−3.85950	−	6.68485i	−0.551357	−	0.954979i
$50$	1.10716	+	1.91766i	0.156576	+	0.271198i
$51$		0			0
$52$	8.19135	+	6.51721i	1.13594	+	0.903775i
$53$	0.815792			0.112058			0.0560288	−	0.998429i	$-0.482156\pi$
$53$	0.815792			0.112058			0.0560288	+	0.998429i	$0.482156\pi$
$54$		0			0
$55$	2.90321	+	5.02851i	0.391469	+	0.678044i
$56$	−3.83654	+	6.64507i	−0.512679	+	0.887985i
$57$		0			0
$58$	−2.28814	+	3.96318i	−0.300448	+	0.520391i
$59$	−4.98741	+	8.63844i	−0.649305	+	1.12463i	0.333984	+	0.942579i	$0.391607\pi$
$59$	−4.98741	+	8.63844i	−0.649305	+	1.12463i	−0.983289	+	0.182050i	$0.941727\pi$
$60$		0			0
$61$	−2.64050	+	4.57348i	−0.338081	+	0.585574i	−0.984072	−	0.177772i	$-0.943111\pi$
$61$	−2.64050	+	4.57348i	−0.338081	+	0.585574i	0.645991	+	0.763345i	$0.276445\pi$
$62$	−5.84691	−	10.1271i	−0.742558	−	1.28615i
$63$		0			0
$64$	−12.8573			−1.60716
$65$	0.533338	−	3.56589i	0.0661525	−	0.442294i
$66$		0			0
$67$	1.77777	+	3.07919i	0.217189	+	0.376183i	0.953948	−	0.299973i	$-0.0969778\pi$
$67$	1.77777	+	3.07919i	0.217189	+	0.376183i	−0.736758	+	0.676156i	$0.763645\pi$
$68$	−5.21432	−	9.03147i	−0.632329	−	1.09523i
$69$		0			0
$70$	8.49532			1.01538
$71$	2.86987	−	4.97077i	0.340591	−	0.589922i	−0.643951	−	0.765066i	$-0.722706\pi$
$71$	2.86987	−	4.97077i	0.340591	−	0.589922i	0.984543	+	0.175145i	$0.0560394\pi$
$72$		0			0
$73$	−2.78568			−0.326039			−0.163020	−	0.986623i	$-0.552123\pi$
$73$	−2.78568			−0.326039			−0.163020	+	0.986623i	$0.552123\pi$
$74$	−5.26517	+	9.11955i	−0.612064	+	1.06013i
$75$		0			0
$76$	−3.11753	−	5.39972i	−0.357605	−	0.619391i
$77$	22.2766			2.53865
$78$		0			0
$79$	12.3319			1.38744			0.693721	−	0.720244i	$-0.255970\pi$
$79$	12.3319			1.38744			0.693721	+	0.720244i	$0.255970\pi$
$80$	0.688892	+	1.19320i	0.0770205	+	0.133403i
$81$		0			0
$82$	12.3089	−	21.3196i	1.35929	−	2.35436i
$83$	−0.622216			−0.0682970			−0.0341485	−	0.999417i	$-0.510872\pi$
$83$	−0.622216			−0.0682970			−0.0341485	+	0.999417i	$0.510872\pi$
$84$		0			0
$85$	−1.79605	+	3.11085i	−0.194809	+	0.337419i
$86$	21.0257			2.26726
$87$		0			0
$88$	−5.80642	−	10.0570i	−0.618967	−	1.07208i
$89$	−8.08419	−	14.0022i	−0.856923	−	1.48423i	−0.874850	−	0.484395i	$-0.839040\pi$
$89$	−8.08419	−	14.0022i	−0.856923	−	1.48423i	0.0179269	−	0.999839i	$-0.494293\pi$
$90$		0			0
$91$	−10.8247	−	8.61236i	−1.13474	−	0.902821i
$92$	18.1017			1.88723
$93$		0			0
$94$	−2.45161	−	4.24631i	−0.252864	−	0.437973i
$95$	−1.07382	+	1.85991i	−0.110172	+	0.190823i
$96$		0			0
$97$	−2.12544	+	3.68137i	−0.215806	+	0.373787i	−0.953522	−	0.301325i	$-0.902571\pi$
$97$	−2.12544	+	3.68137i	−0.215806	+	0.373787i	0.737716	+	0.675112i	$0.235905\pi$
$98$	8.54617	−	14.8024i	0.863294	−	1.49527i
$99$		0			0
$100$	−1.45161	+	2.51426i	−0.145161	+	0.251426i
$101$	−1.11753	−	1.93562i	−0.111199	−	0.192602i	0.805055	−	0.593200i	$-0.202136\pi$
$101$	−1.11753	−	1.93562i	−0.111199	−	0.192602i	−0.916254	+	0.400598i	$0.868802\pi$
$102$		0			0
$103$	−2.44446			−0.240860			−0.120430	−	0.992722i	$-0.538427\pi$
$103$	−2.44446			−0.240860			−0.120430	+	0.992722i	$0.538427\pi$
$104$	−1.06668	+	7.13177i	−0.104596	+	0.699328i
$105$		0			0
$106$	0.903212	+	1.56441i	0.0877277	+	0.151949i
$107$	0.826164	+	1.43096i	0.0798682	+	0.138336i	0.903193	−	0.429235i	$-0.141217\pi$
$107$	0.826164	+	1.43096i	0.0798682	+	0.138336i	−0.823325	+	0.567571i	$0.807883\pi$
$108$		0			0
$109$	−2.61285			−0.250265			−0.125133	−	0.992140i	$-0.539936\pi$
$109$	−2.61285			−0.250265			−0.125133	+	0.992140i	$0.539936\pi$
$110$	−6.42864	+	11.1347i	−0.612947	+	1.06165i
$111$		0			0
$112$	5.28592			0.499472
$113$	1.21432	−	2.10326i	0.114234	−	0.197858i	−0.803240	−	0.595656i	$-0.796892\pi$
$113$	1.21432	−	2.10326i	0.114234	−	0.197858i	0.917473	+	0.397798i	$0.130225\pi$
$114$		0			0
$115$	−3.11753	−	5.39972i	−0.290711	−	0.503527i
$116$	−6.00000			−0.557086
$117$		0			0
$118$	−22.0874			−2.03331
$119$	6.89062	+	11.9349i	0.631662	+	1.09407i
$120$		0			0
$121$	−11.3573	+	19.6714i	−1.03248	+	1.78831i
$122$	−11.6938			−1.05871
$123$		0			0
$124$	7.66593	−	13.2778i	0.688420	−	1.19238i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−9.62790	−	16.6760i	−0.854338	−	1.47976i	−0.877258	−	0.480020i	$-0.840629\pi$
$127$	−9.62790	−	16.6760i	−0.854338	−	1.47976i	0.0229193	−	0.999737i	$-0.492704\pi$
$128$	−7.18421	−	12.4434i	−0.635000	−	1.09985i
$129$		0			0
$130$	7.42864	−	2.92525i	0.651535	−	0.256561i
$131$	−13.4128			−1.17188			−0.585942	−	0.810353i	$-0.699275\pi$
$131$	−13.4128			−1.17188			−0.585942	+	0.810353i	$0.699275\pi$
$132$		0			0
$133$	4.11975	+	7.13562i	0.357228	+	0.618737i
$134$	−3.93655	+	6.81830i	−0.340066	+	0.589012i
$135$		0			0
$136$	3.59210	−	6.22171i	0.308020	−	0.533507i
$137$	−2.36741	+	4.10048i	−0.202262	+	0.350328i	−0.949257	−	0.314502i	$-0.898162\pi$
$137$	−2.36741	+	4.10048i	−0.202262	+	0.350328i	0.746995	+	0.664830i	$0.231496\pi$
$138$		0			0
$139$	5.52074	−	9.56221i	0.468263	−	0.811056i	−0.531079	−	0.847322i	$-0.678213\pi$
$139$	5.52074	−	9.56221i	0.468263	−	0.811056i	0.999342	+	0.0362665i	$0.0115465\pi$
$140$	5.56914	+	9.64603i	0.470678	+	0.815238i
$141$		0			0
$142$	12.7096			1.06657
$143$	19.4795	−	7.67063i	1.62896	−	0.641450i
$144$		0			0
$145$	1.03334	+	1.78979i	0.0858141	+	0.148634i
$146$	−3.08419	−	5.34198i	−0.255250	−	0.442105i
$147$		0			0
$148$	−13.8064			−1.13488
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	−0.904076	−	0.427372i	$-0.859440\pi$
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	0.822153	+	0.569267i	$0.192773\pi$
$150$		0			0
$151$	8.81135			0.717057			0.358529	−	0.933519i	$-0.383279\pi$
$151$	8.81135			0.717057			0.358529	+	0.933519i	$0.383279\pi$
$152$	2.14764	−	3.71983i	0.174197	−	0.301718i
$153$		0			0
$154$	24.6637	+	42.7188i	1.98746	+	3.44238i
$155$	−5.28100			−0.424180
$156$		0			0
$157$	−2.73975			−0.218656			−0.109328	−	0.994006i	$-0.534870\pi$
$157$	−2.73975			−0.218656			−0.109328	+	0.994006i	$0.534870\pi$
$158$	13.6533	+	23.6483i	1.08620	+	1.88135i
$159$		0			0
$160$	−3.52543	+	6.10622i	−0.278710	+	0.482739i
$161$	−23.9210			−1.88524
$162$		0			0
$163$	12.3469	−	21.3855i	0.967084	−	1.67504i	0.263177	−	0.964748i	$-0.415230\pi$
$163$	12.3469	−	21.3855i	0.967084	−	1.67504i	0.703907	−	0.710292i	$-0.251437\pi$
$164$	32.2766			2.52038
$165$		0			0
$166$	−0.688892	−	1.19320i	−0.0534684	−	0.0926100i
$167$	3.95407	+	6.84865i	0.305975	+	0.529964i	0.977478	−	0.211038i	$-0.0676843\pi$
$167$	3.95407	+	6.84865i	0.305975	+	0.529964i	−0.671503	+	0.741002i	$0.734351\pi$
$168$		0			0
$169$	−12.4311	−	3.80365i	−0.956239	−	0.292588i
$170$	−7.95407			−0.610049
$171$		0			0
$172$	13.7835	+	23.8736i	1.05098	+	1.82035i
$173$	−1.82616	+	3.16301i	−0.138841	+	0.240479i	−0.927058	−	0.374918i	$-0.877671\pi$
$173$	−1.82616	+	3.16301i	−0.138841	+	0.240479i	0.788217	+	0.615397i	$0.211004\pi$
$174$		0			0
$175$	1.91827	−	3.32254i	0.145007	−	0.251160i
$176$	−4.00000	+	6.92820i	−0.301511	+	0.522233i
$177$		0			0
$178$	17.9010	−	31.0054i	1.34174	−	2.32395i
$179$	−2.92073	−	5.05885i	−0.218306	−	0.378116i	0.735985	−	0.676998i	$-0.236720\pi$
$179$	−2.92073	−	5.05885i	−0.218306	−	0.378116i	−0.954290	+	0.298882i	$0.903386\pi$
$180$		0			0
$181$	10.0874			0.749792			0.374896	−	0.927067i	$-0.377678\pi$
$181$	10.0874			0.749792			0.374896	+	0.927067i	$0.377678\pi$
$182$	4.53088	−	30.2933i	0.335851	−	2.24549i
$183$		0			0
$184$	6.23506	+	10.7994i	0.459655	+	0.796146i
$185$	2.37778	+	4.11844i	0.174818	+	0.302794i
$186$		0			0
$187$	−20.8573			−1.52524
$188$	3.21432	−	5.56737i	0.234428	−	0.406042i
$189$		0			0
$190$	−4.75557			−0.345005
$191$	7.98741	−	13.8346i	0.577948	−	1.00104i	−0.417766	−	0.908555i	$-0.637187\pi$
$191$	7.98741	−	13.8346i	0.577948	−	1.00104i	0.995714	−	0.0924813i	$-0.0294798\pi$
$192$		0			0
$193$	1.85159	+	3.20705i	0.133280	+	0.230849i	0.924939	−	0.380115i	$-0.124116\pi$
$193$	1.85159	+	3.20705i	0.133280	+	0.230849i	−0.791659	+	0.610963i	$0.790782\pi$
$194$	−9.41282			−0.675801
$195$		0			0
$196$	22.4099			1.60071
$197$	8.19850	+	14.2002i	0.584119	+	1.01172i	0.994985	+	0.100028i	$0.0318931\pi$
$197$	8.19850	+	14.2002i	0.584119	+	1.01172i	−0.410866	+	0.911696i	$0.634774\pi$
$198$		0			0
$199$	−2.64764	+	4.58585i	−0.187686	+	0.325082i	−0.944478	−	0.328573i	$-0.893432\pi$
$199$	−2.64764	+	4.58585i	−0.187686	+	0.325082i	0.756792	+	0.653656i	$0.226766\pi$
$200$	−2.00000			−0.141421
$201$		0			0
$202$	2.47457	−	4.28609i	0.174110	−	0.301568i
$203$	7.92888			0.556498
$204$		0			0
$205$	−5.55877	−	9.62806i	−0.388241	−	0.672453i
$206$	−2.70641	−	4.68764i	−0.188564	−	0.326603i
$207$		0			0
$208$	4.62222	−	1.82013i	0.320493	−	0.126204i
$209$	−12.4701			−0.862577
$210$		0			0
$211$	−3.99532	−	6.92009i	−0.275049	−	0.476399i	0.695099	−	0.718914i	$-0.255361\pi$
$211$	−3.99532	−	6.92009i	−0.275049	−	0.476399i	−0.970147	+	0.242516i	$0.922027\pi$
$212$	−1.18421	+	2.05111i	−0.0813318	+	0.140871i
$213$		0			0
$214$	−1.82939	+	3.16860i	−0.125055	+	0.216601i
$215$	4.74766	−	8.22318i	0.323788	−	0.560817i
$216$		0			0
$217$	−10.1304	+	17.5463i	−0.687694	+	1.19112i
$218$	−2.89284	−	5.01055i	−0.195928	−	0.339357i
$219$		0			0
$220$	−16.8573			−1.13652
$221$	10.1350	+	8.06366i	0.681757	+	0.542420i
$222$		0			0
$223$	4.68889	+	8.12140i	0.313991	+	0.543849i	0.979223	−	0.202788i	$-0.0650003\pi$
$223$	4.68889	+	8.12140i	0.313991	+	0.543849i	−0.665231	+	0.746637i	$0.731667\pi$
$224$	13.5254	+	23.4267i	0.903706	+	1.56526i
$225$		0			0
$226$	5.37778			0.357725
$227$	7.20395	−	12.4776i	0.478143	−	0.828168i	−0.521543	−	0.853225i	$-0.674643\pi$
$227$	7.20395	−	12.4776i	0.478143	−	0.828168i	0.999686	+	0.0250572i	$0.00797680\pi$
$228$		0			0
$229$	−17.9541			−1.18644			−0.593219	−	0.805041i	$-0.702143\pi$
$229$	−17.9541			−1.18644			−0.593219	+	0.805041i	$0.702143\pi$
$230$	6.90321	−	11.9567i	0.455184	−	0.788402i
$231$		0			0
$232$	−2.06668	−	3.57959i	−0.135684	−	0.235012i
$233$	−27.5210			−1.80296			−0.901480	−	0.432821i	$-0.857518\pi$
$233$	−27.5210			−1.80296			−0.901480	+	0.432821i	$0.857518\pi$
$234$		0			0
$235$	−2.21432			−0.144446
$236$	−14.4795	−	25.0792i	−0.942535	−	1.63252i
$237$		0			0
$238$	−15.2580	+	26.4277i	−0.989031	+	1.71305i
$239$	19.0321			1.23109			0.615543	−	0.788104i	$-0.288937\pi$
$239$	19.0321			1.23109			0.615543	+	0.788104i	$0.288937\pi$
$240$		0			0
$241$	−11.6407	+	20.1623i	−0.749846	+	1.29877i	0.198051	+	0.980192i	$0.436539\pi$
$241$	−11.6407	+	20.1623i	−0.749846	+	1.29877i	−0.947896	+	0.318579i	$0.896794\pi$
$242$	−50.2973			−3.23323
$243$		0			0
$244$	−7.66593	−	13.2778i	−0.490761	−	0.850022i
$245$	−3.85950	−	6.68485i	−0.246575	−	0.427080i
$246$		0			0
$247$	6.05953	+	4.82109i	0.385559	+	0.306759i
$248$	10.5620			0.670687
$249$		0			0
$250$	1.10716	+	1.91766i	0.0700229	+	0.121283i
$251$	−13.3620	+	23.1436i	−0.843400	+	1.46081i	0.0436042	+	0.999049i	$0.486116\pi$
$251$	−13.3620	+	23.1436i	−0.843400	+	1.46081i	−0.887004	+	0.461762i	$0.847217\pi$
$252$		0			0
$253$	18.1017	−	31.3531i	1.13804	−	1.97115i
$254$	21.3193	−	36.9260i	1.33769	−	2.31695i
$255$		0			0
$256$	3.05086	−	5.28424i	0.190678	−	0.330265i
$257$	−5.95952	−	10.3222i	−0.371744	−	0.643880i	0.618090	−	0.786108i	$-0.287907\pi$
$257$	−5.95952	−	10.3222i	−0.371744	−	0.643880i	−0.989834	+	0.142227i	$0.954574\pi$
$258$		0			0
$259$	18.2449			1.13368
$260$	8.19135	+	6.51721i	0.508006	+	0.404180i
$261$		0			0
$262$	−14.8501	−	25.7212i	−0.917444	−	1.58906i
$263$	7.96444	+	13.7948i	0.491108	+	0.850625i	0.999948	−	0.0102370i	$-0.00325858\pi$
$263$	7.96444	+	13.7948i	0.491108	+	0.850625i	−0.508839	+	0.860862i	$0.669925\pi$
$264$		0			0
$265$	0.815792			0.0501137
$266$	−9.12245	+	15.8006i	−0.559334	+	0.968794i
$267$		0			0
$268$	−10.3225			−0.630546
$269$	−4.79383	+	8.30316i	−0.292285	+	0.506252i	−0.974350	−	0.225039i	$-0.927749\pi$
$269$	−4.79383	+	8.30316i	−0.292285	+	0.506252i	0.682065	+	0.731292i	$0.261082\pi$
$270$		0			0
$271$	−6.86196	−	11.8853i	−0.416835	−	0.721979i	0.578785	−	0.815481i	$-0.303527\pi$
$271$	−6.86196	−	11.8853i	−0.416835	−	0.721979i	−0.995619	+	0.0935019i	$0.970194\pi$
$272$	−4.94914			−0.300086
$273$		0			0
$274$	−10.4844			−0.633387
$275$	2.90321	+	5.02851i	0.175070	+	0.303231i
$276$		0			0
$277$	−5.90321	+	10.2247i	−0.354690	+	0.614340i	−0.987065	−	0.160322i	$-0.948747\pi$
$277$	−5.90321	+	10.2247i	−0.354690	+	0.614340i	0.632375	+	0.774662i	$0.282080\pi$
$278$	24.4494			1.46638
$279$		0			0
$280$	−3.83654	+	6.64507i	−0.229277	+	0.397119i
$281$	10.7906			0.643713			0.321857	−	0.946788i	$-0.395693\pi$
$281$	10.7906			0.643713			0.321857	+	0.946788i	$0.395693\pi$
$282$		0			0
$283$	15.5978	+	27.0162i	0.927192	+	1.60594i	0.787997	+	0.615680i	$0.211118\pi$
$283$	15.5978	+	27.0162i	0.927192	+	1.60594i	0.139196	+	0.990265i	$0.455548\pi$
$284$	8.33185	+	14.4312i	0.494404	+	0.856334i
$285$		0			0
$286$	36.2766	+	28.8624i	2.14508	+	1.70667i
$287$	−42.6528			−2.51772
$288$		0			0
$289$	2.04839	+	3.54792i	0.120494	+	0.208701i
$290$	−2.28814	+	3.96318i	−0.134364	+	0.232726i
$291$		0			0
$292$	4.04371	−	7.00391i	0.236640	−	0.409873i
$293$	2.95952	−	5.12603i	0.172897	−	0.299466i	−0.766535	−	0.642203i	$-0.778021\pi$
$293$	2.95952	−	5.12603i	0.172897	−	0.299466i	0.939431	+	0.342737i	$0.111354\pi$
$294$		0			0
$295$	−4.98741	+	8.63844i	−0.290378	+	0.502949i
$296$	−4.75557	−	8.23689i	−0.276412	−	0.478759i
$297$		0			0
$298$	−4.42864			−0.256544
$299$	−20.9175	+	8.23689i	−1.20969	+	0.476351i
$300$		0			0
$301$	−18.2146	−	31.5485i	−1.04987	−	1.81843i
$302$	9.75557	+	16.8971i	0.561370	+	0.972321i
$303$		0			0
$304$	−2.95899			−0.169710
$305$	−2.64050	+	4.57348i	−0.151194	+	0.261877i
$306$		0			0
$307$	14.5877			0.832562			0.416281	−	0.909236i	$-0.363333\pi$
$307$	14.5877			0.832562			0.416281	+	0.909236i	$0.363333\pi$
$308$	−32.3368	+	56.0089i	−1.84256	+	3.19141i
$309$		0			0
$310$	−5.84691	−	10.1271i	−0.332082	−	0.575183i
$311$	−17.9748			−1.01926			−0.509629	−	0.860394i	$-0.670217\pi$
$311$	−17.9748			−1.01926			−0.509629	+	0.860394i	$0.670217\pi$
$312$		0			0
$313$	−5.79060			−0.327304			−0.163652	−	0.986518i	$-0.552327\pi$
$313$	−5.79060			−0.327304			−0.163652	+	0.986518i	$0.552327\pi$
$314$	−3.03334	−	5.25390i	−0.171181	−	0.296495i
$315$		0			0
$316$	−17.9010	+	31.0054i	−1.00701	+	1.74419i
$317$	−4.78415			−0.268705			−0.134352	−	0.990934i	$-0.542895\pi$
$317$	−4.78415			−0.268705			−0.134352	+	0.990934i	$0.542895\pi$
$318$		0			0
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$	−12.8573			−0.718744
$321$		0			0
$322$	−26.4844	−	45.8724i	−1.47592	−	2.55637i
$323$	−3.85728	−	6.68100i	−0.214625	−	0.371741i
$324$		0			0
$325$	0.533338	−	3.56589i	0.0295843	−	0.197800i
$326$	54.6800			3.02845
$327$		0			0
$328$	11.1175	+	19.2561i	0.613863	+	1.06324i
$329$	−4.24766	+	7.35716i	−0.234181	+	0.405613i
$330$		0			0
$331$	−1.33654	+	2.31495i	−0.0734626	+	0.127241i	−0.900417	−	0.435028i	$-0.856738\pi$
$331$	−1.33654	+	2.31495i	−0.0734626	+	0.127241i	0.826954	+	0.562269i	$0.190072\pi$
$332$	0.903212	−	1.56441i	0.0495702	−	0.0858581i
$333$		0			0
$334$	−8.75557	+	15.1651i	−0.479083	+	0.829797i
$335$	1.77777	+	3.07919i	0.0971299	+	0.168234i
$336$		0			0
$337$	−29.0350			−1.58164			−0.790820	−	0.612049i	$-0.790345\pi$
$337$	−29.0350			−1.58164			−0.790820	+	0.612049i	$0.790345\pi$
$338$	−6.46912	−	28.0498i	−0.351874	−	1.52571i
$339$		0			0
$340$	−5.21432	−	9.03147i	−0.282786	−	0.489800i
$341$	−15.3319	−	26.5555i	−0.830266	−	1.43806i
$342$		0			0
$343$	−2.75848			−0.148944
$344$	−9.49532	+	16.4464i	−0.511953	+	0.886729i
$345$		0			0
$346$	−8.08742			−0.434782
$347$	14.1541	−	24.5156i	0.759832	−	1.31607i	−0.183104	−	0.983093i	$-0.558615\pi$
$347$	14.1541	−	24.5156i	0.759832	−	1.31607i	0.942936	−	0.332974i	$-0.108052\pi$
$348$		0			0
$349$	16.0232	+	27.7530i	0.857702	+	1.48558i	0.874115	+	0.485719i	$0.161442\pi$
$349$	16.0232	+	27.7530i	0.857702	+	1.48558i	−0.0164125	+	0.999865i	$0.505225\pi$
$350$	8.49532			0.454094
$351$		0			0
$352$	−40.9403			−2.18212
$353$	−7.24443	−	12.5477i	−0.385582	−	0.667848i	0.606268	−	0.795261i	$-0.292666\pi$
$353$	−7.24443	−	12.5477i	−0.385582	−	0.667848i	−0.991850	+	0.127413i	$0.959333\pi$
$354$		0			0
$355$	2.86987	−	4.97077i	0.152317	−	0.263821i
$356$	46.9403			2.48783
$357$		0			0
$358$	6.46743	−	11.2019i	0.341814	−	0.592039i
$359$	24.2701			1.28093			0.640463	−	0.767989i	$-0.278742\pi$
$359$	24.2701			1.28093			0.640463	+	0.767989i	$0.278742\pi$
$360$		0			0
$361$	7.19381	+	12.4601i	0.378622	+	0.655792i
$362$	11.1684	+	19.3442i	0.586997	+	1.01671i
$363$		0			0
$364$	37.3669	−	14.7143i	1.95856	−	0.771240i
$365$	−2.78568			−0.145809
$366$		0			0
$367$	1.11899	+	1.93815i	0.0584107	+	0.101170i	0.893752	−	0.448561i	$-0.148063\pi$
$367$	1.11899	+	1.93815i	0.0584107	+	0.101170i	−0.835341	+	0.549732i	$0.814730\pi$
$368$	4.29529	−	7.43965i	0.223907	−	0.387819i
$369$		0			0
$370$	−5.26517	+	9.11955i	−0.273723	+	0.474103i
$371$	1.56491	−	2.71050i	0.0812459	−	0.140722i
$372$		0			0
$373$	−14.0565	+	24.3466i	−0.727820	+	1.26062i	0.229982	+	0.973195i	$0.426133\pi$
$373$	−14.0565	+	24.3466i	−0.727820	+	1.26062i	−0.957803	+	0.287427i	$0.907200\pi$
$374$	−23.0923	−	39.9971i	−1.19408	−	2.06820i
$375$		0			0
$376$	4.42864			0.228390
$377$	6.93332	−	2.73020i	0.357084	−	0.140613i
$378$		0			0
$379$	9.80888	+	16.9895i	0.503849	+	0.872691i	0.999990	+	0.00444967i	$0.00141638\pi$
$379$	9.80888	+	16.9895i	0.503849	+	0.872691i	−0.496142	+	0.868242i	$0.665250\pi$
$380$	−3.11753	−	5.39972i	−0.159926	−	0.277000i
$381$		0			0
$382$	35.3733			1.80986
$383$	−9.72001	+	16.8355i	−0.496669	+	0.860256i	−0.999993	−	0.00384183i	$-0.998777\pi$
$383$	−9.72001	+	16.8355i	−0.496669	+	0.860256i	0.503323	+	0.864098i	$0.332110\pi$
$384$		0			0
$385$	22.2766			1.13532
$386$	−4.10001	+	7.10143i	−0.208685	+	0.361453i
$387$		0			0
$388$	−6.17061	−	10.6878i	−0.313265	−	0.542591i
$389$	2.81579			0.142766			0.0713832	−	0.997449i	$-0.477259\pi$
$389$	2.81579			0.142766			0.0713832	+	0.997449i	$0.477259\pi$
$390$		0			0
$391$	22.3970			1.13266
$392$	7.71900	+	13.3697i	0.389869	+	0.675272i
$393$		0			0
$394$	−18.1541	+	31.4438i	−0.914590	+	1.58412i
$395$	12.3319			0.620483
$396$		0			0
$397$	6.33976	−	10.9808i	0.318184	−	0.551110i	−0.661926	−	0.749570i	$-0.730261\pi$
$397$	6.33976	−	10.9808i	0.318184	−	0.551110i	0.980109	+	0.198460i	$0.0635938\pi$
$398$	−11.7255			−0.587744
$399$		0			0
$400$	0.688892	+	1.19320i	0.0344446	+	0.0596598i
$401$	0.453829	+	0.786055i	0.0226631	+	0.0392537i	0.877135	−	0.480245i	$-0.159452\pi$
$401$	0.453829	+	0.786055i	0.0226631	+	0.0392537i	−0.854471	+	0.519498i	$0.826119\pi$
$402$		0			0
$403$	−2.81656	+	18.8314i	−0.140303	+	0.938061i
$404$	6.48886			0.322833
$405$		0			0
$406$	8.77854	+	15.2049i	0.435671	+	0.754605i
$407$	−13.8064	+	23.9134i	−0.684359	+	1.18534i
$408$		0			0
$409$	16.7881	−	29.0779i	0.830120	−	1.43781i	−0.0678223	−	0.997697i	$-0.521605\pi$
$409$	16.7881	−	29.0779i	0.830120	−	1.43781i	0.897942	−	0.440113i	$-0.145062\pi$
$410$	12.3089	−	21.3196i	0.607892	−	1.05290i
$411$		0			0
$412$	3.54839	−	6.14600i	0.174817	−	0.302792i
$413$	19.1344	+	33.1417i	0.941540	+	1.63080i
$414$		0			0
$415$	−0.622216			−0.0305434
$416$	19.8938	+	15.8280i	0.975376	+	0.776029i
$417$		0			0
$418$	−13.8064	−	23.9134i	−0.675294	−	1.16964i
$419$	11.4763	+	19.8775i	0.560652	+	0.971078i	0.997440	+	0.0715136i	$0.0227829\pi$
$419$	11.4763	+	19.8775i	0.560652	+	0.971078i	−0.436787	+	0.899565i	$0.643884\pi$
$420$		0			0
$421$	−31.0874			−1.51511			−0.757554	−	0.652772i	$-0.773606\pi$
$421$	−31.0874			−1.51511			−0.757554	+	0.652772i	$0.773606\pi$
$422$	8.84691	−	15.3233i	0.430661	−	0.745926i
$423$		0			0
$424$	−1.63158			−0.0792367
$425$	−1.79605	+	3.11085i	−0.0871213	+	0.150899i
$426$		0			0
$427$	10.1304	+	17.5463i	0.490243	+	0.849125i
$428$	−4.79706			−0.231874
$429$		0			0
$430$	21.0257			1.01395
$431$	8.52543	+	14.7665i	0.410655	+	0.711276i	0.994962	−	0.100257i	$-0.0319666\pi$
$431$	8.52543	+	14.7665i	0.410655	+	0.711276i	−0.584306	+	0.811533i	$0.698633\pi$
$432$		0			0
$433$	1.29605	−	2.24483i	0.0622843	−	0.107880i	−0.833202	−	0.552969i	$-0.813495\pi$
$433$	1.29605	−	2.24483i	0.0622843	−	0.107880i	0.895486	+	0.445089i	$0.146828\pi$
$434$	−44.8637			−2.15353
$435$		0			0
$436$	3.79283	−	6.56937i	0.181643	−	0.314616i
$437$	13.3907			0.640564
$438$		0			0
$439$	6.88493	+	11.9250i	0.328600	+	0.569151i	0.982234	−	0.187659i	$-0.0600900\pi$
$439$	6.88493	+	11.9250i	0.328600	+	0.569151i	−0.653635	+	0.756810i	$0.726757\pi$
$440$	−5.80642	−	10.0570i	−0.276810	−	0.479450i
$441$		0			0
$442$	−4.24221	+	28.3633i	−0.201781	+	1.34910i
$443$	−4.71609			−0.224068			−0.112034	−	0.993704i	$-0.535737\pi$
$443$	−4.71609			−0.224068			−0.112034	+	0.993704i	$0.535737\pi$
$444$		0			0
$445$	−8.08419	−	14.0022i	−0.383228	−	0.663770i
$446$	−10.3827	+	17.9834i	−0.491635	+	0.851537i
$447$		0			0
$448$	−24.6637	+	42.7188i	−1.16525	+	2.01827i
$449$	−5.16839	+	8.95191i	−0.243911	+	0.422467i	−0.961825	−	0.273665i	$-0.911764\pi$
$449$	−5.16839	+	8.95191i	−0.243911	+	0.422467i	0.717914	+	0.696132i	$0.245097\pi$
$450$		0			0
$451$	32.2766	−	55.9046i	1.51984	−	2.63245i
$452$	3.52543	+	6.10622i	0.165822	+	0.287212i
$453$		0			0
$454$	31.9037			1.49731
$455$	−10.8247	−	8.61236i	−0.507470	−	0.403754i
$456$		0			0
$457$	9.81433	+	16.9989i	0.459095	+	0.795176i	0.998913	−	0.0466054i	$-0.0148403\pi$
$457$	9.81433	+	16.9989i	0.459095	+	0.795176i	−0.539818	+	0.841782i	$0.681507\pi$
$458$	−19.8780	−	34.4297i	−0.928839	−	1.60880i
$459$		0			0
$460$	18.1017			0.843997
$461$	12.6003	−	21.8243i	0.586852	−	1.01646i	−0.407789	−	0.913076i	$-0.633700\pi$
$461$	12.6003	−	21.8243i	0.586852	−	1.01646i	0.994642	−	0.103382i	$-0.0329664\pi$
$462$		0			0
$463$	28.8129			1.33905			0.669524	−	0.742790i	$-0.266498\pi$
$463$	28.8129			1.33905			0.669524	+	0.742790i	$0.266498\pi$
$464$	−1.42372	+	2.46595i	−0.0660944	+	0.114479i
$465$		0			0
$466$	−30.4701	−	52.7758i	−1.41150	−	2.44479i
$467$	32.3575			1.49733			0.748664	−	0.662950i	$-0.230696\pi$
$467$	32.3575			1.49733			0.748664	+	0.662950i	$0.230696\pi$
$468$		0			0
$469$	13.6410			0.629881
$470$	−2.45161	−	4.24631i	−0.113084	−	0.195867i
$471$		0			0
$472$	9.97481	−	17.2769i	0.459128	−	0.795233i
$473$	55.1338			2.53506
$474$		0			0
$475$	−1.07382	+	1.85991i	−0.0492703	+	0.0853387i
$476$	−40.0098			−1.83385
$477$		0			0
$478$	21.0716	+	36.4971i	0.963792	+	1.66934i
$479$	2.96666	+	5.13841i	0.135550	+	0.234780i	0.925808	−	0.377995i	$-0.123386\pi$
$479$	2.96666	+	5.13841i	0.135550	+	0.234780i	−0.790257	+	0.612775i	$0.790053\pi$
$480$		0			0
$481$	15.9541	−	6.28239i	0.727443	−	0.286452i
$482$	−51.5526			−2.34816
$483$		0			0
$484$	−32.9726	−	57.1102i	−1.49875	−	2.59592i
$485$	−2.12544	+	3.68137i	−0.0965114	+	0.167163i
$486$		0			0
$487$	2.42149	−	4.19415i	0.109728	−	0.190055i	−0.805932	−	0.592008i	$-0.798335\pi$
$487$	2.42149	−	4.19415i	0.109728	−	0.190055i	0.915660	+	0.401953i	$0.131669\pi$
$488$	5.28100	−	9.14695i	0.239059	−	0.414063i
$489$		0			0
$490$	8.54617	−	14.8024i	0.386077	−	0.668704i
$491$	0.0382604	+	0.0662690i	0.00172667	+	0.00299068i	0.866887	−	0.498504i	$-0.166117\pi$
$491$	0.0382604	+	0.0662690i	0.00172667	+	0.00299068i	−0.865161	+	0.501495i	$0.832784\pi$
$492$		0			0
$493$	−7.42372			−0.334347
$494$	−2.53633	+	16.9578i	−0.114115	+	0.762968i
$495$		0			0
$496$	−3.63804	−	6.30127i	−0.163353	−	0.282935i
$497$	−11.0104	−	19.0705i	−0.493883	−	0.855430i
$498$		0			0
$499$	38.0687			1.70419			0.852094	−	0.523388i	$-0.175332\pi$
$499$	38.0687			1.70419			0.852094	+	0.523388i	$0.175332\pi$
$500$	−1.45161	+	2.51426i	−0.0649178	+	0.112441i
$501$		0			0
$502$	−59.1753			−2.64112
$503$	6.62714	−	11.4785i	0.295489	−	0.511803i	−0.679609	−	0.733574i	$-0.737851\pi$
$503$	6.62714	−	11.4785i	0.295489	−	0.511803i	0.975099	+	0.221772i	$0.0711839\pi$
$504$		0			0
$505$	−1.11753	−	1.93562i	−0.0497295	−	0.0861340i
$506$	80.1659			3.56381
$507$		0			0
$508$	55.9037			2.48033
$509$	−14.2351	−	24.6559i	−0.630958	−	1.09285i	−0.987356	−	0.158517i	$-0.949329\pi$
$509$	−14.2351	−	24.6559i	−0.630958	−	1.09285i	0.356398	−	0.934334i	$-0.384005\pi$
$510$		0			0
$511$	−5.34368	+	9.25553i	−0.236391	+	0.409440i
$512$	−15.2257			−0.672887
$513$		0			0
$514$	13.1963	−	22.8566i	0.582063	−	1.00816i
$515$	−2.44446			−0.107716
$516$		0			0
$517$	−6.42864	−	11.1347i	−0.282731	−	0.489705i
$518$	20.2000	+	34.9875i	0.887538	+	1.53726i
$519$		0			0
$520$	−1.06668	+	7.13177i	−0.0467769	+	0.312749i
$521$	−17.1175			−0.749933			−0.374966	−	0.927038i	$-0.622346\pi$
$521$	−17.1175			−0.749933			−0.374966	+	0.927038i	$0.622346\pi$
$522$		0			0
$523$	−0.0666765	−	0.115487i	−0.00291556	−	0.00504990i	0.864564	−	0.502523i	$-0.167595\pi$
$523$	−0.0666765	−	0.115487i	−0.00291556	−	0.00504990i	−0.867480	+	0.497473i	$0.834261\pi$
$524$	19.4701	−	33.7232i	0.850556	−	1.47321i
$525$		0			0
$526$	−17.6358	+	30.5461i	−0.768958	+	1.33187i
$527$	9.48494	−	16.4284i	0.413171	−	0.715633i
$528$		0			0
$529$	−7.93801	+	13.7490i	−0.345131	+	0.597784i
$530$	0.903212	+	1.56441i	0.0392330	+	0.0679536i
$531$		0			0
$532$	−23.9210			−1.03711
$533$	−37.2973	+	14.6869i	−1.61553	+	0.636161i
$534$		0			0
$535$	0.826164	+	1.43096i	0.0357182	+	0.0618657i
$536$	−3.55554	−	6.15837i	−0.153576	−	0.266001i
$537$		0			0
$538$	−21.2301			−0.915296
$539$	22.4099	−	38.8151i	0.965263	−	1.67188i
$540$		0			0
$541$	−26.3876			−1.13449			−0.567246	−	0.823548i	$-0.691991\pi$
$541$	−26.3876			−1.13449			−0.567246	+	0.823548i	$0.691991\pi$
$542$	15.1946	−	26.3178i	0.652663	−	1.13045i
$543$		0			0
$544$	−12.6637	−	21.9342i	−0.542952	−	0.940420i
$545$	−2.61285			−0.111922
$546$		0			0
$547$	−0.0573086			−0.00245034			−0.00122517	−	0.999999i	$-0.500390\pi$
$547$	−0.0573086			−0.00245034			−0.00122517	+	0.999999i	$0.500390\pi$
$548$	−6.87310	−	11.9046i	−0.293604	−	0.508538i
$549$		0			0
$550$	−6.42864	+	11.1347i	−0.274118	+	0.474786i
$551$	−4.43848			−0.189086
$552$		0			0
$553$	23.6558	−	40.9730i	1.00595	−	1.74235i
$554$	−26.1432			−1.11072
$555$		0			0
$556$	16.0279	+	27.7611i	0.679734	+	1.17733i
$557$	20.5210	+	35.5434i	0.869502	+	1.50602i	0.862507	+	0.506046i	$0.168893\pi$
$557$	20.5210	+	35.5434i	0.869502	+	1.50602i	0.00699538	+	0.999976i	$0.497773\pi$
$558$		0			0
$559$	−26.7908	−	21.3154i	−1.13313	−	0.901543i
$560$	5.28592			0.223371
$561$		0			0
$562$	11.9469	+	20.6927i	0.503950	+	0.872868i
$563$	10.6128	−	18.3820i	0.447278	−	0.774709i	−0.550930	−	0.834552i	$-0.685727\pi$
$563$	10.6128	−	18.3820i	0.447278	−	0.774709i	0.998208	+	0.0598432i	$0.0190601\pi$
$564$		0			0
$565$	1.21432	−	2.10326i	0.0510868	−	0.0884850i
$566$	−34.5385	+	59.8224i	−1.45176	+	2.51452i
$567$		0			0
$568$	−5.73975	+	9.94153i	−0.240834	+	0.417137i
$569$	8.18098	+	14.1699i	0.342965	+	0.594032i	0.984982	−	0.172658i	$-0.0552356\pi$
$569$	8.18098	+	14.1699i	0.342965	+	0.594032i	−0.642017	+	0.766690i	$0.721902\pi$
$570$		0			0
$571$	−37.7101			−1.57812			−0.789060	−	0.614317i	$-0.789432\pi$
$571$	−37.7101			−1.57812			−0.789060	+	0.614317i	$0.789432\pi$
$572$	−8.99063	+	60.1112i	−0.375917	+	2.51337i
$573$		0			0
$574$	−47.2235	−	81.7935i	−1.97107	−	3.41399i
$575$	−3.11753	−	5.39972i	−0.130010	−	0.225184i
$576$		0			0
$577$	42.7150			1.77825			0.889125	−	0.457664i	$-0.151314\pi$
$577$	42.7150			1.77825			0.889125	+	0.457664i	$0.151314\pi$
$578$	−4.53580	+	7.85623i	−0.188664	+	0.326776i
$579$		0			0
$580$	−6.00000			−0.249136
$581$	−1.19358	+	2.06733i	−0.0495179	+	0.0857675i
$582$		0			0
$583$	2.36842	+	4.10222i	0.0980898	+	0.169896i
$584$	5.57136			0.230545
$585$		0			0
$586$	13.1066			0.541430
$587$	4.81187	+	8.33441i	0.198607	+	0.343998i	0.948077	−	0.318041i	$-0.103025\pi$
$587$	4.81187	+	8.33441i	0.198607	+	0.343998i	−0.749470	+	0.662039i	$0.769692\pi$
$588$		0			0
$589$	5.67085	−	9.82220i	0.233663	−	0.404717i
$590$	−22.0874			−0.909325
$591$		0			0
$592$	−3.27607	+	5.67433i	−0.134646	+	0.233213i
$593$	24.5018			1.00617			0.503084	−	0.864238i	$-0.332199\pi$
$593$	24.5018			1.00617			0.503084	+	0.864238i	$0.332199\pi$
$594$		0			0
$595$	6.89062	+	11.9349i	0.282488	+	0.489283i
$596$	−2.90321	−	5.02851i	−0.118920	−	0.205976i
$597$		0			0
$598$	−38.9545	−	30.9930i	−1.59297	−	1.26740i
$599$	16.9654			0.693189			0.346595	−	0.938015i	$-0.387338\pi$
$599$	16.9654			0.693189			0.346595	+	0.938015i	$0.387338\pi$
$600$		0			0
$601$	10.7835	+	18.6775i	0.439866	+	0.761871i	0.997679	−	0.0680961i	$-0.0216925\pi$
$601$	10.7835	+	18.6775i	0.439866	+	0.761871i	−0.557812	+	0.829967i	$0.688359\pi$
$602$	40.3329	−	69.8586i	1.64384	−	2.84722i
$603$		0			0
$604$	−12.7906	+	22.1540i	−0.520442	+	0.901432i
$605$	−11.3573	+	19.6714i	−0.461739	+	0.799755i
$606$		0			0
$607$	9.99285	−	17.3081i	0.405597	−	0.702515i	−0.588793	−	0.808284i	$-0.700397\pi$
$607$	9.99285	−	17.3081i	0.405597	−	0.702515i	0.994391	+	0.105768i	$0.0337301\pi$
$608$	−7.57136	−	13.1140i	−0.307059	−	0.531842i
$609$		0			0
$610$	−11.6938			−0.473469
$611$	−1.18098	+	7.89601i	−0.0477774	+	0.319439i
$612$		0			0
$613$	−5.60001	−	9.69951i	−0.226182	−	0.391760i	0.730491	−	0.682922i	$-0.239291\pi$
$613$	−5.60001	−	9.69951i	−0.226182	−	0.391760i	−0.956674	+	0.291163i	$0.905958\pi$
$614$	16.1509	+	27.9741i	0.651796	+	1.12894i
$615$		0			0
$616$	−44.5531			−1.79510
$617$	0.295286	−	0.511451i	0.0118878	−	0.0205902i	−0.860020	−	0.510260i	$-0.829549\pi$
$617$	0.295286	−	0.511451i	0.0118878	−	0.0205902i	0.871908	+	0.489670i	$0.162883\pi$
$618$		0			0
$619$	−12.2573			−0.492664			−0.246332	−	0.969186i	$-0.579225\pi$
$619$	−12.2573			−0.492664			−0.246332	+	0.969186i	$0.579225\pi$
$620$	7.66593	−	13.2778i	0.307871	−	0.533248i
$621$		0			0
$622$	−19.9010	−	34.4695i	−0.797957	−	1.38210i
$623$	−62.0306			−2.48520
$624$		0			0
$625$	1.00000			0.0400000
$626$	−6.41112	−	11.1044i	−0.256240	−	0.443821i
$627$		0			0
$628$	3.97703	−	6.88842i	0.158701	−	0.274878i
$629$	−17.0825			−0.681124
$630$		0			0
$631$	−18.3200	+	31.7312i	−0.729309	+	1.26320i	0.227867	+	0.973692i	$0.426825\pi$
$631$	−18.3200	+	31.7312i	−0.729309	+	1.26320i	−0.957176	+	0.289507i	$0.906509\pi$
$632$	−24.6637			−0.981069
$633$		0			0
$634$	−5.29682	−	9.17436i	−0.210364	−	0.364360i
$635$	−9.62790	−	16.6760i	−0.382072	−	0.661768i
$636$		0			0
$637$	−25.8959	+	10.1973i	−1.02603	+	0.404030i
$638$	−26.5718			−1.05199
$639$		0			0
$640$	−7.18421	−	12.4434i	−0.283981	−	0.491869i
$641$	−10.5827	+	18.3298i	−0.417993	+	0.723985i	−0.995737	−	0.0922326i	$-0.970600\pi$
$641$	−10.5827	+	18.3298i	−0.417993	+	0.723985i	0.577745	+	0.816218i	$0.303933\pi$
$642$		0			0
$643$	−6.09602	+	10.5586i	−0.240404	+	0.416391i	−0.960829	−	0.277141i	$-0.910613\pi$
$643$	−6.09602	+	10.5586i	−0.240404	+	0.416391i	0.720426	+	0.693532i	$0.243946\pi$
$644$	34.7239	−	60.1436i	1.36831	−	2.36999i
$645$		0			0
$646$	8.54125	−	14.7939i	0.336051	−	0.582057i
$647$	4.73038	+	8.19326i	0.185970	+	0.322110i	0.943903	−	0.330223i	$-0.107124\pi$
$647$	4.73038	+	8.19326i	0.185970	+	0.322110i	−0.757933	+	0.652333i	$0.773790\pi$
$648$		0			0
$649$	−57.9180			−2.27348
$650$	7.42864	−	2.92525i	0.291375	−	0.114738i
$651$		0			0
$652$	35.8457	+	62.0866i	1.40383	+	2.43150i
$653$	10.1995	+	17.6661i	0.399137	+	0.691326i	0.993620	−	0.112782i	$-0.0359763\pi$
$653$	10.1995	+	17.6661i	0.399137	+	0.691326i	−0.594482	+	0.804109i	$0.702643\pi$
$654$		0			0
$655$	−13.4128			−0.524082
$656$	7.65878	−	13.2654i	0.299025	−	0.517927i
$657$		0			0
$658$	−18.8113			−0.733343
$659$	17.4859	−	30.2866i	0.681156	−	1.17980i	−0.293473	−	0.955967i	$-0.594811\pi$
$659$	17.4859	−	30.2866i	0.681156	−	1.17980i	0.974628	−	0.223829i	$-0.0718557\pi$
$660$		0			0
$661$	9.73014	+	16.8531i	0.378459	+	0.655510i	0.990838	−	0.135054i	$-0.0431209\pi$
$661$	9.73014	+	16.8531i	0.378459	+	0.655510i	−0.612380	+	0.790564i	$0.709788\pi$
$662$	−5.91903			−0.230050
$663$		0			0
$664$	1.24443			0.0482933
$665$	4.11975	+	7.13562i	0.159757	+	0.276708i
$666$		0			0
$667$	6.44293	−	11.1595i	0.249471	−	0.432097i
$668$	−22.9590			−0.888310
$669$		0			0
$670$	−3.93655	+	6.81830i	−0.152082	+	0.263414i
$671$	−30.6637			−1.18376
$672$		0			0
$673$	−7.13259	−	12.3540i	−0.274941	−	0.476212i	0.695179	−	0.718836i	$-0.255325\pi$
$673$	−7.13259	−	12.3540i	−0.274941	−	0.476212i	−0.970120	+	0.242625i	$0.921992\pi$
$674$	−32.1464	−	55.6792i	−1.23823	−	2.14468i
$675$		0			0
$676$	27.6084	−	25.7336i	1.06186	−	0.989752i
$677$	34.0415			1.30832			0.654160	−	0.756356i	$-0.273022\pi$
$677$	34.0415			1.30832			0.654160	+	0.756356i	$0.273022\pi$
$678$		0			0
$679$	8.15433	+	14.1237i	0.312935	+	0.542019i
$680$	3.59210	−	6.22171i	0.137751	−	0.238592i
$681$		0			0
$682$	33.9496	−	58.8025i	1.30000	−	2.25166i
$683$	14.6692	−	25.4077i	0.561300	−	0.972199i	−0.436084	−	0.899906i	$-0.643635\pi$
$683$	14.6692	−	25.4077i	0.561300	−	0.972199i	0.997383	−	0.0722933i	$-0.0230318\pi$
$684$		0			0
$685$	−2.36741	+	4.10048i	−0.0904542	+	0.156671i
$686$	−3.05408	−	5.28982i	−0.116605	−	0.201966i
$687$		0			0
$688$	13.0825			0.498766
$689$	0.435093	−	2.90902i	0.0165757	−	0.110825i
$690$		0			0
$691$	−1.59457	−	2.76187i	−0.0606601	−	0.105066i	0.834101	−	0.551612i	$-0.185987\pi$
$691$	−1.59457	−	2.76187i	−0.0606601	−	0.105066i	−0.894761	+	0.446546i	$0.852654\pi$
$692$	−5.30174	−	9.18288i	−0.201542	−	0.349081i
$693$		0			0
$694$	62.6834			2.37943
$695$	5.52074	−	9.56221i	0.209414	−	0.362715i
$696$		0			0
$697$	39.9353			1.51266
$698$	−35.4805	+	61.4540i	−1.34296	+	2.32607i
$699$		0			0
$700$	5.56914	+	9.64603i	0.210494	+	0.364586i
$701$	−2.44738			−0.0924361			−0.0462180	−	0.998931i	$-0.514717\pi$
$701$	−2.44738			−0.0924361			−0.0462180	+	0.998931i	$0.514717\pi$
$702$		0			0
$703$	−10.2133			−0.385201
$704$	−37.3274	−	64.6530i	−1.40683	−	2.43670i
$705$		0			0
$706$	16.0415	−	27.7847i	0.603729	−	1.04569i
$707$	−8.57490			−0.322492
$708$		0			0
$709$	0.301502	−	0.522216i	0.0113231	−	0.0196122i	−0.860308	−	0.509774i	$-0.829729\pi$
$709$	0.301502	−	0.522216i	0.0113231	−	0.0196122i	0.871631	+	0.490162i	$0.163062\pi$
$710$	12.7096			0.476984
$711$		0			0
$712$	16.1684	+	28.0045i	0.605936	+	1.04951i
$713$	16.4637	+	28.5159i	0.616569	+	1.06793i
$714$		0			0
$715$	19.4795	−	7.67063i	0.728492	−	0.286865i
$716$	16.9590			0.633787
$717$		0			0
$718$	26.8709	+	46.5417i	1.00281	+	1.73692i
$719$	21.7988	−	37.7565i	0.812956	−	1.40808i	−0.0978299	−	0.995203i	$-0.531190\pi$
$719$	21.7988	−	37.7565i	0.812956	−	1.40808i	0.910786	−	0.412878i	$-0.135477\pi$
$720$		0			0
$721$	−4.68913	+	8.12181i	−0.174632	+	0.302472i
$722$	−15.9294	+	27.5905i	−0.592831	+	1.02681i
$723$		0			0
$724$	−14.6430	+	25.3623i	−0.544201	+	0.942584i
$725$	1.03334	+	1.78979i	0.0383772	+	0.0664713i
$726$		0			0
$727$	32.8642			1.21887			0.609433	−	0.792838i	$-0.291397\pi$
$727$	32.8642			1.21887			0.609433	+	0.792838i	$0.291397\pi$
$728$	21.6494	+	17.2247i	0.802381	+	0.638391i
$729$		0			0
$730$	−3.08419	−	5.34198i	−0.114151	−	0.197716i
$731$	17.0541	+	29.5385i	0.630768	+	1.09252i
$732$		0			0
$733$	17.4035			0.642811			0.321406	−	0.946942i	$-0.395845\pi$
$733$	17.4035			0.642811			0.321406	+	0.946942i	$0.395845\pi$
$734$	−2.47780	+	4.29167i	−0.0914572	+	0.158409i
$735$		0			0
$736$	43.9625			1.62048
$737$	−10.3225	+	17.8791i	−0.380234	+	0.658584i
$738$		0			0
$739$	−21.2924	−	36.8795i	−0.783253	−	1.35663i	−0.930037	−	0.367465i	$-0.880226\pi$
$739$	−21.2924	−	36.8795i	−0.783253	−	1.35663i	0.146785	−	0.989168i	$-0.453107\pi$
$740$	−13.8064			−0.507534
$741$		0			0
$742$	6.93041			0.254423
$743$	−16.4232	−	28.4458i	−0.602508	−	1.04358i	−0.992440	−	0.122731i	$-0.960835\pi$
$743$	−16.4232	−	28.4458i	−0.602508	−	1.04358i	0.389932	−	0.920844i	$-0.372499\pi$
$744$		0			0
$745$	−1.00000	+	1.73205i	−0.0366372	+	0.0634574i
$746$	−62.2514			−2.27918
$747$		0			0
$748$	30.2766	−	52.4405i	1.10702	−	1.91742i
$749$	6.33921			0.231630
$750$		0			0
$751$	−6.23729	−	10.8033i	−0.227602	−	0.394218i	0.729495	−	0.683986i	$-0.239755\pi$
$751$	−6.23729	−	10.8033i	−0.227602	−	0.394218i	−0.957097	+	0.289768i	$0.906422\pi$
$752$	−1.52543	−	2.64212i	−0.0556266	−	0.0963481i
$753$		0			0
$754$	12.9119	+	10.2730i	0.470223	+	0.374119i
$755$	8.81135			0.320678
$756$		0			0
$757$	2.43732	+	4.22155i	0.0885858	+	0.153435i	0.906914	−	0.421317i	$-0.138432\pi$
$757$	2.43732	+	4.22155i	0.0885858	+	0.153435i	−0.818328	+	0.574752i	$0.805099\pi$
$758$	−21.7200	+	37.6202i	−0.788906	+	1.36643i
$759$		0			0
$760$	2.14764	−	3.71983i	0.0779032	−	0.134932i
$761$	−2.05086	+	3.55219i	−0.0743434	+	0.128767i	−0.900801	−	0.434233i	$-0.857019\pi$
$761$	−2.05086	+	3.55219i	−0.0743434	+	0.128767i	0.826457	+	0.563000i	$0.190353\pi$
$762$		0			0
$763$	−5.01214	+	8.68128i	−0.181452	+	0.314284i
$764$	23.1891	+	40.1648i	0.838953	+	1.45311i
$765$		0			0
$766$	−43.0464			−1.55533
$767$	28.1437	+	22.3917i	1.01621	+	0.808519i
$768$		0			0
$769$	24.0486	+	41.6535i	0.867216	+	1.50206i	0.864830	+	0.502065i	$0.167426\pi$
$769$	24.0486	+	41.6535i	0.867216	+	1.50206i	0.00238584	+	0.999997i	$0.499241\pi$
$770$	24.6637	+	42.7188i	0.888818	+	1.53948i
$771$		0			0
$772$	−10.7511			−0.386941
$773$	9.09679	−	15.7561i	0.327189	−	0.566707i	−0.654764	−	0.755833i	$-0.727232\pi$
$773$	9.09679	−	15.7561i	0.327189	−	0.566707i	0.981953	+	0.189126i	$0.0605654\pi$
$774$		0			0
$775$	−5.28100			−0.189699
$776$	4.25088	−	7.36275i	0.152598	−	0.264307i
$777$		0			0
$778$	3.11753	+	5.39972i	0.111769	+	0.193589i
$779$	23.8765			0.855464
$780$		0			0
$781$	33.3274			1.19255
$782$	24.7971	+	42.9498i	0.886741	+	1.53588i
$783$		0			0
$784$	5.31756	−	9.21029i	0.189913	−	0.328939i
$785$	−2.73975			−0.0977858
$786$		0			0
$787$	14.6486	−	25.3722i	0.522168	−	0.904421i	−0.477500	−	0.878632i	$-0.658457\pi$
$787$	14.6486	−	25.3722i	0.522168	−	0.904421i	0.999667	−	0.0257893i	$-0.00820989\pi$
$788$	−47.6040			−1.69582
$789$		0			0
$790$	13.6533	+	23.6483i	0.485764	+	0.841367i
$791$	−4.65878	−	8.06924i	−0.165647	−	0.286909i
$792$		0			0
$793$	14.9002	+	11.8549i	0.529122	+	0.420981i
$794$	28.0765			0.996398
$795$		0			0
$796$	−7.68667	−	13.3137i	−0.272447	−	0.471892i
$797$	13.4390	−	23.2771i	0.476034	−	0.824515i	−0.523589	−	0.851971i	$-0.675407\pi$
$797$	13.4390	−	23.2771i	0.476034	−	0.824515i	0.999623	+	0.0274557i	$0.00874051\pi$
$798$		0			0
$799$	3.97703	−	6.88842i	0.140697	−	0.243695i
$800$	−3.52543	+	6.10622i	−0.124643	+	0.215887i
$801$		0			0
$802$	−1.00492	+	1.74058i	−0.0354850	+	0.0614619i
$803$	−8.08742	−	14.0078i	−0.285399	−	0.494325i
$804$		0			0
$805$	−23.9210			−0.843106
$806$	−39.2306	+	15.4482i	−1.38184	+	0.544140i
$807$		0			0
$808$	2.23506	+	3.87124i	0.0786293	+	0.136190i
$809$	−14.2286	−	24.6447i	−0.500251	−	0.866461i	−1.00000		0.000290180i	$-0.999908\pi$
$809$	−14.2286	−	24.6447i	−0.500251	−	0.866461i	0.499749	−	0.866170i	$-0.333426\pi$
$810$		0			0
$811$	−16.6316			−0.584014			−0.292007	−	0.956416i	$-0.594323\pi$
$811$	−16.6316			−0.584014			−0.292007	+	0.956416i	$0.594323\pi$
$812$	−11.5096	+	19.9352i	−0.403908	+	0.699589i
$813$		0			0
$814$	−61.1437			−2.14308
$815$	12.3469	−	21.3855i	0.432493	−	0.749100i
$816$		0			0
$817$	10.1963	+	17.6605i	0.356723	+	0.617862i
$818$	74.3486			2.59954
$819$		0			0
$820$	32.2766			1.12715
$821$	−17.4844	−	30.2839i	−0.610210	−	1.05692i	−0.991205	−	0.132338i	$-0.957752\pi$
$821$	−17.4844	−	30.2839i	−0.610210	−	1.05692i	0.380994	−	0.924577i	$-0.375582\pi$
$822$		0			0
$823$	−9.33185	+	16.1632i	−0.325288	+	0.563415i	−0.981571	−	0.191100i	$-0.938795\pi$
$823$	−9.33185	+	16.1632i	−0.325288	+	0.563415i	0.656283	+	0.754515i	$0.272128\pi$
$824$	4.88892			0.170314
$825$		0			0
$826$	−42.3696	+	73.3863i	−1.47423	+	2.55344i
$827$	−21.2968			−0.740563			−0.370281	−	0.928920i	$-0.620739\pi$
$827$	−21.2968			−0.740563			−0.370281	+	0.928920i	$0.620739\pi$
$828$		0			0
$829$	3.59610	+	6.22862i	0.124898	+	0.216329i	0.921693	−	0.387920i	$-0.126806\pi$
$829$	3.59610	+	6.22862i	0.124898	+	0.216329i	−0.796795	+	0.604249i	$0.793473\pi$
$830$	−0.688892	−	1.19320i	−0.0239118	−	0.0414164i
$831$		0			0
$832$	−6.85728	+	45.8476i	−0.237733	+	1.58948i
$833$	27.7275			0.960700
$834$		0			0
$835$	3.95407	+	6.84865i	0.136836	+	0.237007i
$836$	18.1017	−	31.3531i	0.626061	−	1.08437i
$837$		0			0
$838$	−25.4121	+	44.0151i	−0.877847	+	1.52048i
$839$	−0.790602	+	1.36936i	−0.0272946	+	0.0472757i	−0.879350	−	0.476176i	$-0.842023\pi$
$839$	−0.790602	+	1.36936i	−0.0272946	+	0.0472757i	0.852055	+	0.523452i	$0.175356\pi$
$840$		0			0
$841$	12.3644	−	21.4158i	0.426359	−	0.738476i
$842$	−34.4187	−	59.6150i	−1.18615	−	2.05447i
$843$		0			0
$844$	23.1985			0.798525
$845$	−12.4311	−	3.80365i	−0.427643	−	0.130849i
$846$		0			0
$847$	43.5726	+	75.4700i	1.49717	+	2.59318i
$848$	0.561993	+	0.973400i	0.0192989	+	0.0334267i
$849$		0			0
$850$	−7.95407			−0.272822
$851$	14.8256	−	25.6788i	0.508216	−	0.880256i
$852$		0			0
$853$	−23.0207			−0.788215			−0.394108	−	0.919064i	$-0.628946\pi$
$853$	−23.0207			−0.788215			−0.394108	+	0.919064i	$0.628946\pi$
$854$	−22.4319	+	38.8531i	−0.767603	+	1.32953i
$855$		0			0
$856$	−1.65233	−	2.86191i	−0.0564754	−	0.0978182i
$857$	−47.4499			−1.62086			−0.810428	−	0.585838i	$-0.800765\pi$
$857$	−47.4499			−1.62086			−0.810428	+	0.585838i	$0.800765\pi$
$858$		0			0
$859$	−49.0241			−1.67268			−0.836341	−	0.548210i	$-0.815310\pi$
$859$	−49.0241			−1.67268			−0.836341	+	0.548210i	$0.815310\pi$
$860$	13.7835	+	23.8736i	0.470012	+	0.814085i
$861$		0			0
$862$	−18.8780	+	32.6977i	−0.642988	+	1.11369i
$863$	37.3590			1.27172			0.635858	−	0.771806i	$-0.280646\pi$
$863$	37.3590			1.27172			0.635858	+	0.771806i	$0.280646\pi$
$864$		0			0
$865$	−1.82616	+	3.16301i	−0.0620914	+	0.107546i
$866$	5.73975			0.195045
$867$		0			0
$868$	−29.4106	−	50.9406i	−0.998261	−	1.72904i
$869$	35.8020	+	62.0108i	1.21450	+	2.10357i
$870$		0			0
$871$	11.9282	−	4.69708i	0.404171	−	0.159154i
$872$	5.22570			0.176964
$873$		0			0
$874$	14.8256	+	25.6788i	0.501485	+	0.868597i
$875$	1.91827	−	3.32254i	0.0648493	−	0.112322i
$876$		0			0
$877$	−10.3985	+	18.0108i	−0.351133	+	0.608181i	−0.986448	−	0.164072i	$-0.947537\pi$
$877$	−10.3985	+	18.0108i	−0.351133	+	0.608181i	0.635315	+	0.772253i	$0.280870\pi$
$878$	−15.2454	+	26.4059i	−0.514509	+	0.891155i
$879$		0			0
$880$	−4.00000	+	6.92820i	−0.134840	+	0.233550i
$881$	14.8780	+	25.7695i	0.501253	+	0.868196i	0.999999	+	0.00144781i	$0.000460852\pi$
$881$	14.8780	+	25.7695i	0.501253	+	0.868196i	−0.498746	+	0.866748i	$0.666206\pi$
$882$		0			0
$883$	−40.5975			−1.36621			−0.683107	−	0.730318i	$-0.739372\pi$
$883$	−40.5975			−1.36621			−0.683107	+	0.730318i	$0.739372\pi$
$884$	−34.9862	+	13.7768i	−1.17671	+	0.463366i
$885$		0			0
$886$	−5.22146	−	9.04384i	−0.175419	−	0.303834i
$887$	24.2153	+	41.9422i	0.813071	+	1.40828i	0.910705	+	0.413058i	$0.135539\pi$
$887$	24.2153	+	41.9422i	0.813071	+	1.40828i	−0.0976338	+	0.995222i	$0.531127\pi$
$888$		0			0
$889$	−73.8756			−2.47771
$890$	17.9010	−	31.0054i	0.600043	−	1.03930i
$891$		0			0
$892$	−27.2257			−0.911584
$893$	2.37778	−	4.11844i	0.0795695	−	0.137818i
$894$		0			0
$895$	−2.92073	−	5.05885i	−0.0976292	−	0.169099i
$896$	−55.1249			−1.84159
$897$		0			0
$898$	−22.8889			−0.763813
$899$	−5.45706	−	9.45190i	−0.182003	−	0.315238i
$900$		0			0
$901$	−1.46520	+	2.53781i	−0.0488130	+	0.0845467i
$902$	142.941			4.75942
$903$		0			0
$904$	−2.42864	+	4.20653i	−0.0807753	+	0.139907i
$905$	10.0874			0.335317
$906$		0			0
$907$	5.14987	+	8.91983i	0.170998	+	0.296178i	0.938769	−	0.344547i	$-0.111967\pi$
$907$	5.14987	+	8.91983i	0.170998	+	0.296178i	−0.767771	+	0.640725i	$0.778634\pi$
$908$	20.9146	+	36.2251i	0.694075	+	1.20217i
$909$		0			0
$910$	4.53088	−	30.2933i	0.150197	−	1.00421i
$911$	−7.35905			−0.243816			−0.121908	−	0.992541i	$-0.538901\pi$
$911$	−7.35905			−0.243816			−0.121908	+	0.992541i	$0.538901\pi$
$912$		0			0
$913$	−1.80642	−	3.12882i	−0.0597839	−	0.103549i
$914$	−21.7321	+	37.6411i	−0.718833	+	1.24506i
$915$		0			0
$916$	26.0622	−	45.1411i	0.861120	−	1.49150i
$917$	−25.7294	+	44.5646i	−0.849659	+	1.47165i
$918$		0			0
$919$	−0.391383	+	0.677895i	−0.0129105	+	0.0223617i	−0.872408	−	0.488777i	$-0.837443\pi$
$919$	−0.391383	+	0.677895i	−0.0129105	+	0.0223617i	0.859498	+	0.511139i	$0.170776\pi$
$920$	6.23506	+	10.7994i	0.205564	+	0.356047i
$921$		0			0
$922$	55.8020			1.83774
$923$	−16.1946	−	12.8847i	−0.533051	−	0.424107i
$924$		0			0
$925$	2.37778	+	4.11844i	0.0781811	+	0.135414i
$926$	31.9005	+	55.2532i	1.04831	+	1.81573i
$927$		0			0
$928$	−14.5718			−0.478344
$929$	−14.2208	+	24.6311i	−0.466568	+	0.808120i	−0.999271	−	0.0381824i	$-0.987843\pi$
$929$	−14.2208	+	24.6311i	−0.466568	+	0.808120i	0.532702	+	0.846303i	$0.321177\pi$
$930$		0			0
$931$	16.5777			0.543311
$932$	39.9496	−	69.1948i	1.30859	−	2.26655i
$933$		0			0
$934$	35.8249	+	62.0506i	1.17223	+	2.03036i
$935$	−20.8573			−0.682106
$936$		0			0
$937$	−21.3747			−0.698282			−0.349141	−	0.937070i	$-0.613527\pi$
$937$	−21.3747			−0.698282			−0.349141	+	0.937070i	$0.613527\pi$
$938$	15.1027	+	26.1587i	0.493121	+	0.854111i
$939$		0			0
$940$	3.21432	−	5.56737i	0.104840	−	0.181587i
$941$	38.2830			1.24799			0.623995	−	0.781428i	$-0.285508\pi$
$941$	38.2830			1.24799			0.623995	+	0.781428i	$0.285508\pi$
$942$		0			0
$943$	−34.6593	+	60.0316i	−1.12866	+	1.95490i
$944$	−13.7431			−0.447301
$945$		0			0
$946$	61.0420	+	105.728i	1.98465	+	3.43751i
$947$	3.80251	+	6.58613i	0.123565	+	0.214021i	0.921171	−	0.389158i	$-0.127234\pi$
$947$	3.80251	+	6.58613i	0.123565	+	0.214021i	−0.797606	+	0.603179i	$0.793901\pi$
$948$		0			0
$949$	−1.48571	+	9.93342i	−0.0482282	+	0.322452i
$950$	−4.75557			−0.154291
$951$		0			0
$952$	−13.7812	−	23.8698i	−0.446652	−	0.773625i
$953$	−16.6780	+	28.8871i	−0.540253	+	0.935746i	0.458636	+	0.888624i	$0.348338\pi$
$953$	−16.6780	+	28.8871i	−0.540253	+	0.935746i	−0.998889	+	0.0471217i	$0.984995\pi$
$954$		0			0
$955$	7.98741	−	13.8346i	0.258466	−	0.447677i
$956$	−27.6271	+	47.8516i	−0.893525	+	1.54763i
$957$		0			0
$958$	−6.56914	+	11.3781i	−0.212239	+	0.367609i
$959$	9.08266	+	15.7316i	0.293294	+	0.508001i
$960$		0			0
$961$	−3.11108			−0.100357
$962$	29.7112	+	23.6388i	0.957926	+	0.762146i
$963$		0			0
$964$	−33.7955	−	58.5356i	−1.08848	−	1.88530i
$965$	1.85159	+	3.20705i	0.0596048	+	0.103239i
$966$		0			0
$967$	−40.8988			−1.31522			−0.657608	−	0.753360i	$-0.728432\pi$
$967$	−40.8988			−1.31522			−0.657608	+	0.753360i	$0.728432\pi$
$968$	22.7146	−	39.3428i	0.730074	−	1.26452i
$969$		0			0
$970$	−9.41282			−0.302227
$971$	−2.11753	+	3.66767i	−0.0679548	+	0.117701i	−0.898001	−	0.439994i	$-0.854981\pi$
$971$	−2.11753	+	3.66767i	−0.0679548	+	0.117701i	0.830046	+	0.557695i	$0.188314\pi$
$972$		0			0
$973$	−21.1805	−	36.6858i	−0.679017	−	1.17609i
$974$	10.7239			0.343617
$975$		0			0
$976$	−7.27607			−0.232901
$977$	−19.3941	−	33.5915i	−0.620472	−	1.07469i	−0.989398	−	0.145230i	$-0.953608\pi$
$977$	−19.3941	−	33.5915i	−0.620472	−	1.07469i	0.368926	−	0.929459i	$-0.379725\pi$
$978$		0			0
$979$	46.9403	−	81.3029i	1.50022	−	2.59845i
$980$	22.4099			0.715858
$981$		0			0
$982$	−0.0847209	+	0.146741i	−0.00270355	+	0.00468269i
$983$	−21.4479			−0.684080			−0.342040	−	0.939685i	$-0.611118\pi$
$983$	−21.4479			−0.684080			−0.342040	+	0.939685i	$0.611118\pi$
$984$		0			0
$985$	8.19850	+	14.2002i	0.261226	+	0.452456i
$986$	−8.21924	−	14.2361i	−0.261754	−	0.453371i
$987$		0			0
$988$	−20.9175	+	8.23689i	−0.665474	+	0.262050i
$989$	−59.2039			−1.88257
$990$		0			0
$991$	5.65010	+	9.78627i	0.179481	+	0.310871i	0.941703	−	0.336445i	$-0.109225\pi$
$991$	5.65010	+	9.78627i	0.179481	+	0.310871i	−0.762222	+	0.647316i	$0.775891\pi$
$992$	18.6178	−	32.2469i	0.591115	−	1.02384i
$993$		0			0
$994$	24.3805	−	42.2282i	0.773302	−	1.33940i
$995$	−2.64764	+	4.58585i	−0.0839359	+	0.145381i
$996$		0			0
$997$	27.1123	−	46.9599i	0.858656	−	1.48724i	−0.0145557	−	0.999894i	$-0.504633\pi$
$997$	27.1123	−	46.9599i	0.858656	−	1.48724i	0.873212	−	0.487341i	$-0.162033\pi$
$998$	42.1481	+	73.0027i	1.33418	+	2.31086i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.g.406.3		6
3.2	odd	2		195.2.i.e.16.1	✓	6
13.3	even	3		7605.2.a.bu.1.1		3
13.9	even	3	inner	585.2.j.g.451.3		6
13.10	even	6		7605.2.a.bt.1.3		3
15.2	even	4		975.2.bb.j.874.6		12
15.8	even	4		975.2.bb.j.874.1		12
15.14	odd	2		975.2.i.m.601.3		6
39.23	odd	6		2535.2.a.z.1.1		3
39.29	odd	6		2535.2.a.y.1.3		3
39.35	odd	6		195.2.i.e.61.1	yes	6
195.74	odd	6		975.2.i.m.451.3		6
195.113	even	12		975.2.bb.j.724.6		12
195.152	even	12		975.2.bb.j.724.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.e.16.1	✓	6	3.2	odd	2
195.2.i.e.61.1	yes	6	39.35	odd	6
585.2.j.g.406.3		6	1.1	even	1	trivial
585.2.j.g.451.3		6	13.9	even	3	inner
975.2.i.m.451.3		6	195.74	odd	6
975.2.i.m.601.3		6	15.14	odd	2
975.2.bb.j.724.1		12	195.152	even	12
975.2.bb.j.724.6		12	195.113	even	12
975.2.bb.j.874.1		12	15.8	even	4
975.2.bb.j.874.6		12	15.2	even	4
2535.2.a.y.1.3		3	39.29	odd	6
2535.2.a.z.1.1		3	39.23	odd	6
7605.2.a.bt.1.3		3	13.10	even	6
7605.2.a.bu.1.1		3	13.3	even	3

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10716 + 1.91766i) q^{2} +(-1.45161 + 2.51426i) q^{4} +1.00000 q^{5} +(1.91827 - 3.32254i) q^{7} -2.00000 q^{8} +(1.10716 + 1.91766i) q^{10} +(2.90321 + 5.02851i) q^{11} +(0.533338 - 3.56589i) q^{13} +8.49532 q^{14} +(0.688892 + 1.19320i) q^{16} +(-1.79605 + 3.11085i) q^{17} +(-1.07382 + 1.85991i) q^{19} +(-1.45161 + 2.51426i) q^{20} +(-6.42864 + 11.1347i) q^{22} +(-3.11753 - 5.39972i) q^{23} +1.00000 q^{25} +(7.42864 - 2.92525i) q^{26} +(5.56914 + 9.64603i) q^{28} +(1.03334 + 1.78979i) q^{29} -5.28100 q^{31} +(-3.52543 + 6.10622i) q^{32} -7.95407 q^{34} +(1.91827 - 3.32254i) q^{35} +(2.37778 + 4.11844i) q^{37} -4.75557 q^{38} -2.00000 q^{40} +(-5.55877 - 9.62806i) q^{41} +(4.74766 - 8.22318i) q^{43} -16.8573 q^{44} +(6.90321 - 11.9567i) q^{46} -2.21432 q^{47} +(-3.85950 - 6.68485i) q^{49} +(1.10716 + 1.91766i) q^{50} +(8.19135 + 6.51721i) q^{52} +0.815792 q^{53} +(2.90321 + 5.02851i) q^{55} +(-3.83654 + 6.64507i) q^{56} +(-2.28814 + 3.96318i) q^{58} +(-4.98741 + 8.63844i) q^{59} +(-2.64050 + 4.57348i) q^{61} +(-5.84691 - 10.1271i) q^{62} -12.8573 q^{64} +(0.533338 - 3.56589i) q^{65} +(1.77777 + 3.07919i) q^{67} +(-5.21432 - 9.03147i) q^{68} +8.49532 q^{70} +(2.86987 - 4.97077i) q^{71} -2.78568 q^{73} +(-5.26517 + 9.11955i) q^{74} +(-3.11753 - 5.39972i) q^{76} +22.2766 q^{77} +12.3319 q^{79} +(0.688892 + 1.19320i) q^{80} +(12.3089 - 21.3196i) q^{82} -0.622216 q^{83} +(-1.79605 + 3.11085i) q^{85} +21.0257 q^{86} +(-5.80642 - 10.0570i) q^{88} +(-8.08419 - 14.0022i) q^{89} +(-10.8247 - 8.61236i) q^{91} +18.1017 q^{92} +(-2.45161 - 4.24631i) q^{94} +(-1.07382 + 1.85991i) q^{95} +(-2.12544 + 3.68137i) q^{97} +(8.54617 - 14.8024i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} + 6 q^{5} + 5 q^{7} - 12 q^{8} + 4 q^{11} + 3 q^{13} + 24 q^{14} + 4 q^{16} - 4 q^{17} - 2 q^{20} - 12 q^{22} + 8 q^{23} + 6 q^{25} + 18 q^{26} + 6 q^{29} - 18 q^{31} - 8 q^{32} - 8 q^{34}+ \cdots - 2 q^{98}+O(q^{100}) \) 6 * q - 2 * q^4 + 6 * q^5 + 5 * q^7 - 12 * q^8 + 4 * q^11 + 3 * q^13 + 24 * q^14 + 4 * q^16 - 4 * q^17 - 2 * q^20 - 12 * q^22 + 8 * q^23 + 6 * q^25 + 18 * q^26 + 6 * q^29 - 18 * q^31 - 8 * q^32 - 8 * q^34 + 5 * q^35 + 14 * q^37 - 28 * q^38 - 12 * q^40 - 20 * q^41 + 15 * q^43 - 48 * q^44 + 28 * q^46 - 30 * q^49 + 16 * q^52 + 32 * q^53 + 4 * q^55 - 10 * q^56 + 6 * q^58 + 10 * q^59 - 9 * q^61 - 2 * q^62 - 24 * q^64 + 3 * q^65 + 11 * q^67 - 18 * q^68 + 24 * q^70 + 4 * q^71 - 30 * q^73 + 8 * q^74 + 8 * q^76 + 34 * q^79 + 4 * q^80 + 14 * q^82 - 4 * q^83 - 4 * q^85 + 20 * q^86 - 8 * q^88 - 22 * q^89 - 31 * q^91 + 56 * q^92 - 8 * q^94 + q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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