LMFDB - Embedded newform 675.2.ba.b.632.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			632.8
Character	$\chi$	$=$	675.632
Dual form			675.2.ba.b.518.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0152086 - 0.00133058i) q^{2} +(-0.259886 - 1.71244i) q^{3} +(-1.96939 + 0.347256i) q^{4} +(-0.00623106 - 0.0256981i) q^{6} +(-0.211408 + 0.148030i) q^{7} +(-0.0589827 + 0.0158044i) q^{8} +(-2.86492 + 0.890079i) q^{9} +(1.49616 + 4.11066i) q^{11} +(1.10647 + 3.28221i) q^{12} +(-0.187451 + 2.14258i) q^{13} +(-0.00301826 + 0.00253263i) q^{14} +(3.75746 - 1.36760i) q^{16} +(-1.70216 - 0.456091i) q^{17} +(-0.0423872 + 0.0173489i) q^{18} +(4.91894 + 2.83995i) q^{19} +(0.308434 + 0.323554i) q^{21} +(0.0282241 + 0.0605267i) q^{22} +(3.32360 - 4.74660i) q^{23} +(0.0423928 + 0.0968971i) q^{24} +0.0328351i q^{26} +(2.26876 + 4.67469i) q^{27} +(0.364940 - 0.364940i) q^{28} +(3.59567 + 3.01712i) q^{29} +(-0.912568 - 5.17543i) q^{31} +(0.166010 - 0.0774120i) q^{32} +(6.65044 - 3.63039i) q^{33} +(-0.0264943 - 0.00467167i) q^{34} +(5.33305 - 2.74777i) q^{36} +(0.837479 - 3.12552i) q^{37} +(0.0785891 + 0.0366467i) q^{38} +(3.71775 - 0.235826i) q^{39} +(0.241984 + 0.288386i) q^{41} +(0.00512138 + 0.00451041i) q^{42} +(-3.84888 + 8.25395i) q^{43} +(-4.37396 - 7.57592i) q^{44} +(0.0442317 - 0.0766116i) q^{46} +(2.29910 + 3.28345i) q^{47} +(-3.31845 - 6.07901i) q^{48} +(-2.37136 + 6.51526i) q^{49} +(-0.338664 + 3.03338i) q^{51} +(-0.374859 - 4.28465i) q^{52} +(8.15900 + 8.15900i) q^{53} +(0.0407248 + 0.0680769i) q^{54} +(0.0101299 - 0.0120724i) q^{56} +(3.58489 - 9.16146i) q^{57} +(0.0586997 + 0.0411020i) q^{58} +(10.6146 + 3.86341i) q^{59} +(-2.10712 + 11.9501i) q^{61} +(-0.0207652 - 0.0774969i) q^{62} +(0.473909 - 0.612263i) q^{63} +(-6.92336 + 3.99720i) q^{64} +(0.0963135 - 0.0640622i) q^{66} +(-1.82940 - 0.160052i) q^{67} +(3.51058 + 0.307136i) q^{68} +(-8.99203 - 4.45790i) q^{69} +(4.44360 - 2.56551i) q^{71} +(0.154913 - 0.0977775i) q^{72} +(-3.71651 - 13.8702i) q^{73} +(0.00857816 - 0.0486492i) q^{74} +(-10.6735 - 3.88483i) q^{76} +(-0.924799 - 0.647552i) q^{77} +(0.0562282 - 0.00853337i) q^{78} +(1.98949 - 2.37099i) q^{79} +(7.41552 - 5.10001i) q^{81} +(0.00406398 + 0.00406398i) q^{82} +(0.432904 + 4.94812i) q^{83} +(-0.719782 - 0.530096i) q^{84} +(-0.0475536 + 0.130653i) q^{86} +(4.23219 - 6.94148i) q^{87} +(-0.153214 - 0.218812i) q^{88} +(-1.44584 + 2.50426i) q^{89} +(-0.277536 - 0.480707i) q^{91} +(-4.89717 + 10.5020i) q^{92} +(-8.62546 + 2.90774i) q^{93} +(0.0393351 + 0.0468777i) q^{94} +(-0.175707 - 0.264165i) q^{96} +(4.27105 + 1.99162i) q^{97} +(-0.0273961 + 0.102243i) q^{98} +(-7.94518 - 10.4450i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0152086	−	0.00133058i	0.0107541	−	0.000940864i	−0.0817774	−	0.996651i	$-0.526060\pi$
$2$	0.0152086	−	0.00133058i	0.0107541	−	0.000940864i	0.0925315	+	0.995710i	$0.470504\pi$
$3$	−0.259886	−	1.71244i	−0.150045	−	0.988679i
$3$	−0.259886	−	1.71244i	−0.150045	−	0.988679i
$4$	−1.96939	+	0.347256i	−0.984693	+	0.173628i
$5$		0			0
$5$		0			0
$6$	−0.00623106	−	0.0256981i	−0.00254382	−	0.0104912i
$7$	−0.211408	+	0.148030i	−0.0799048	+	0.0559499i	−0.612846	−	0.790202i	$-0.709975\pi$
$7$	−0.211408	+	0.148030i	−0.0799048	+	0.0559499i	0.532941	+	0.846152i	$0.321087\pi$
$8$	−0.0589827	+	0.0158044i	−0.0208535	+	0.00558769i
$9$	−2.86492	+	0.890079i	−0.954973	+	0.296693i
$10$		0			0
$11$	1.49616	+	4.11066i	0.451108	+	1.23941i	0.931945	+	0.362600i	$0.118111\pi$
$11$	1.49616	+	4.11066i	0.451108	+	1.23941i	−0.480836	+	0.876810i	$0.659667\pi$
$12$	1.10647	+	3.28221i	0.319411	+	0.947493i
$13$	−0.187451	+	2.14258i	−0.0519896	+	0.594244i	0.924859	+	0.380311i	$0.124183\pi$
$13$	−0.187451	+	2.14258i	−0.0519896	+	0.594244i	−0.976848	+	0.213933i	$0.931373\pi$
$14$	−0.00301826	+	0.00253263i	−0.000806665	+	0.000676873i
$15$		0			0
$16$	3.75746	−	1.36760i	0.939364	−	0.341901i
$17$	−1.70216	−	0.456091i	−0.412833	−	0.110618i	0.0464236	−	0.998922i	$-0.485218\pi$
$17$	−1.70216	−	0.456091i	−0.412833	−	0.110618i	−0.459257	+	0.888303i	$0.651884\pi$
$18$	−0.0423872	+	0.0173489i	−0.00999075	+	0.00408918i
$19$	4.91894	+	2.83995i	1.12848	+	0.651529i	0.943553	−	0.331222i	$-0.107461\pi$
$19$	4.91894	+	2.83995i	1.12848	+	0.651529i	0.184929	+	0.982752i	$0.440794\pi$
$20$		0			0
$21$	0.308434	+	0.323554i	0.0673059	+	0.0706052i
$22$	0.0282241	+	0.0605267i	0.00601740	+	0.0129043i
$23$	3.32360	−	4.74660i	0.693019	−	0.989734i	−0.306267	−	0.951946i	$-0.599080\pi$
$23$	3.32360	−	4.74660i	0.693019	−	0.989734i	0.999286	−	0.0377879i	$-0.0120311\pi$
$24$	0.0423928	+	0.0968971i	0.00865340	+	0.0197790i
$25$		0			0
$26$			0.0328351i			0.00643949i
$27$	2.26876	+	4.67469i	0.436623	+	0.899644i
$28$	0.364940	−	0.364940i	0.0689672	−	0.0689672i
$29$	3.59567	+	3.01712i	0.667699	+	0.560266i	0.912383	−	0.409337i	$-0.134240\pi$
$29$	3.59567	+	3.01712i	0.667699	+	0.560266i	−0.244685	+	0.969603i	$0.578684\pi$
$30$		0			0
$31$	−0.912568	−	5.17543i	−0.163902	−	0.929534i	−0.950189	−	0.311673i	$-0.899111\pi$
$31$	−0.912568	−	5.17543i	−0.163902	−	0.929534i	0.786287	−	0.617861i	$-0.212001\pi$
$32$	0.166010	−	0.0774120i	0.0293468	−	0.0136846i
$33$	6.65044	−	3.63039i	1.15769	−	0.631969i
$34$	−0.0264943	−	0.00467167i	−0.00454374	−	0.000801184i
$35$		0			0
$36$	5.33305	−	2.74777i	0.888841	−	0.457962i
$37$	0.837479	−	3.12552i	0.137681	−	0.513832i	−0.862292	−	0.506412i	$-0.830972\pi$
$37$	0.837479	−	3.12552i	0.137681	−	0.513832i	0.999972	−	0.00741968i	$-0.00236178\pi$
$38$	0.0785891	+	0.0366467i	0.0127488	+	0.00594488i
$39$	3.71775	−	0.235826i	0.595317	−	0.0377624i
$40$		0			0
$41$	0.241984	+	0.288386i	0.0377916	+	0.0450383i	0.784609	−	0.619991i	$-0.212864\pi$
$41$	0.241984	+	0.288386i	0.0377916	+	0.0450383i	−0.746818	+	0.665029i	$0.768419\pi$
$42$	0.00512138	+	0.00451041i	0.000790246	+	0.000695972i
$43$	−3.84888	+	8.25395i	−0.586948	+	1.25872i	0.358678	+	0.933461i	$0.383228\pi$
$43$	−3.84888	+	8.25395i	−0.586948	+	1.25872i	−0.945627	+	0.325254i	$0.894550\pi$
$44$	−4.37396	−	7.57592i	−0.659400	−	1.14211i
$45$		0			0
$46$	0.0442317	−	0.0766116i	0.00652161	−	0.0112958i
$47$	2.29910	+	3.28345i	0.335358	+	0.478941i	0.951046	−	0.309049i	$-0.100011\pi$
$47$	2.29910	+	3.28345i	0.335358	+	0.478941i	−0.615688	+	0.787990i	$0.711122\pi$
$48$	−3.31845	−	6.07901i	−0.478977	−	0.877429i
$49$	−2.37136	+	6.51526i	−0.338766	+	0.930751i
$50$		0			0
$51$	−0.338664	+	3.03338i	−0.0474224	+	0.424757i
$52$	−0.374859	−	4.28465i	−0.0519835	−	0.594174i
$53$	8.15900	+	8.15900i	1.12072	+	1.12072i	0.991633	+	0.129092i	$0.0412062\pi$
$53$	8.15900	+	8.15900i	1.12072	+	1.12072i	0.129092	+	0.991633i	$0.458794\pi$
$54$	0.0407248	+	0.0680769i	0.00554195	+	0.00926409i
$55$		0			0
$56$	0.0101299	−	0.0120724i	0.00135367	−	0.00161324i
$57$	3.58489	−	9.16146i	0.474830	−	1.21347i
$58$	0.0586997	+	0.0411020i	0.00770765	+	0.00539696i
$59$	10.6146	+	3.86341i	1.38191	+	0.502973i	0.922756	−	0.385385i	$-0.125931\pi$
$59$	10.6146	+	3.86341i	1.38191	+	0.502973i	0.459152	+	0.888358i	$0.348153\pi$
$60$		0			0
$61$	−2.10712	+	11.9501i	−0.269790	+	1.53005i	0.485251	+	0.874375i	$0.338728\pi$
$61$	−2.10712	+	11.9501i	−0.269790	+	1.53005i	−0.755040	+	0.655678i	$0.772383\pi$
$62$	−0.0207652	−	0.0774969i	−0.00263719	−	0.00984212i
$63$	0.473909	−	0.612263i	0.0597070	−	0.0771379i
$64$	−6.92336	+	3.99720i	−0.865420	+	0.499650i
$65$		0			0
$66$	0.0963135	−	0.0640622i	0.0118554	−	0.00788551i
$67$	−1.82940	−	0.160052i	−0.223497	−	0.0195534i	−0.0251426	−	0.999684i	$-0.508004\pi$
$67$	−1.82940	−	0.160052i	−0.223497	−	0.0195534i	−0.198354	+	0.980130i	$0.563560\pi$
$68$	3.51058	+	0.307136i	0.425721	+	0.0372457i
$69$	−8.99203	−	4.45790i	−1.08251	−	0.536669i
$70$		0			0
$71$	4.44360	−	2.56551i	0.527358	−	0.304471i	−0.212582	−	0.977143i	$-0.568187\pi$
$71$	4.44360	−	2.56551i	0.527358	−	0.304471i	0.739940	+	0.672673i	$0.234854\pi$
$72$	0.154913	−	0.0977775i	0.0182567	−	0.0115232i
$73$	−3.71651	−	13.8702i	−0.434984	−	1.62338i	−0.741104	−	0.671390i	$-0.765697\pi$
$73$	−3.71651	−	13.8702i	−0.434984	−	1.62338i	0.306120	−	0.951993i	$-0.400969\pi$
$74$	0.00857816	−	0.0486492i	0.000997191	−	0.00565535i
$75$		0			0
$76$	−10.6735	−	3.88483i	−1.22433	−	0.445620i
$77$	−0.924799	−	0.647552i	−0.105391	−	0.0737953i
$78$	0.0562282	−	0.00853337i	0.00636659	−	0.000966214i
$79$	1.98949	−	2.37099i	0.223835	−	0.266757i	−0.642426	−	0.766348i	$-0.722072\pi$
$79$	1.98949	−	2.37099i	0.223835	−	0.266757i	0.866261	+	0.499591i	$0.166516\pi$
$80$		0			0
$81$	7.41552	−	5.10001i	0.823946	−	0.566668i
$82$	0.00406398	+	0.00406398i	0.000448791	+	0.000448791i
$83$	0.432904	+	4.94812i	0.0475174	+	0.543127i	0.982225	+	0.187708i	$0.0601060\pi$
$83$	0.432904	+	4.94812i	0.0475174	+	0.543127i	−0.934707	+	0.355418i	$0.884338\pi$
$84$	−0.719782	−	0.530096i	−0.0785347	−	0.0578383i
$85$		0			0
$86$	−0.0475536	+	0.130653i	−0.00512784	+	0.0140886i
$87$	4.23219	−	6.94148i	0.453738	−	0.744205i
$88$	−0.153214	−	0.218812i	−0.0163326	−	0.0233254i
$89$	−1.44584	+	2.50426i	−0.153259	+	0.265452i	−0.932424	−	0.361367i	$-0.882310\pi$
$89$	−1.44584	+	2.50426i	−0.153259	+	0.265452i	0.779165	+	0.626819i	$0.215643\pi$
$90$		0			0
$91$	−0.277536	−	0.480707i	−0.0290937	−	0.0503917i
$92$	−4.89717	+	10.5020i	−0.510565	+	1.09491i
$93$	−8.62546	+	2.90774i	−0.894418	+	0.301519i
$94$	0.0393351	+	0.0468777i	0.00405710	+	0.00483507i
$95$		0			0
$96$	−0.175707	−	0.264165i	−0.0179331	−	0.0269612i
$97$	4.27105	+	1.99162i	0.433659	+	0.202219i	0.627175	−	0.778879i	$-0.284211\pi$
$97$	4.27105	+	1.99162i	0.433659	+	0.202219i	−0.193516	+	0.981097i	$0.561989\pi$
$98$	−0.0273961	+	0.102243i	−0.00276742	+	0.0103282i
$99$	−7.94518	−	10.4450i	−0.798521	−	1.04976i
$100$		0			0
$101$	2.84523	+	0.501690i	0.283110	+	0.0499200i	0.313400	−	0.949621i	$-0.398532\pi$
$101$	2.84523	+	0.501690i	0.283110	+	0.0499200i	−0.0302897	+	0.999541i	$0.509643\pi$
$102$	−0.00111446	+	0.0465841i	−0.000110348	+	0.00461251i
$103$	−9.15274	+	4.26799i	−0.901846	+	0.420538i	−0.817520	−	0.575900i	$-0.804652\pi$
$103$	−9.15274	+	4.26799i	−0.901846	+	0.420538i	−0.0843263	+	0.996438i	$0.526874\pi$
$104$	−0.0228057	−	0.129337i	−0.00223628	−	0.0126826i
$105$		0			0
$106$	0.134943	+	0.113231i	0.0131069	+	0.0109980i
$107$	−10.6261	+	10.6261i	−1.02727	+	1.02727i	−0.0276498	+	0.999618i	$0.508802\pi$
$107$	−10.6261	+	10.6261i	−1.02727	+	1.02727i	−0.999618	+	0.0276498i	$0.991198\pi$
$108$	−6.09138	−	8.41843i	−0.586143	−	0.810064i
$109$		−	12.0030i		−	1.14968i	−0.818265	−	0.574841i	$-0.805064\pi$
$109$		−	12.0030i		−	1.14968i	0.818265	−	0.574841i	$-0.194936\pi$
$110$		0			0
$111$	−5.56991	−	0.621858i	−0.528673	−	0.0590241i
$112$	−0.591912	+	0.845337i	−0.0559304	+	0.0798769i
$113$	3.92562	+	8.41851i	0.369291	+	0.791947i	0.999875	+	0.0158260i	$0.00503778\pi$
$113$	3.92562	+	8.41851i	0.369291	+	0.791947i	−0.630584	+	0.776121i	$0.717184\pi$
$114$	0.0423312	−	0.144103i	0.00396468	−	0.0134965i
$115$		0			0
$116$	−8.12897	−	4.69326i	−0.754756	−	0.435759i
$117$	−1.37003	−	6.30515i	−0.126659	−	0.582912i
$118$	0.166575	+	0.0446336i	0.0153344	+	0.00410885i
$119$	0.427365	−	0.155548i	0.0391765	−	0.0142591i
$120$		0			0
$121$	−6.23254	+	5.22972i	−0.566595	+	0.475429i
$122$	−0.0161459	+	0.184548i	−0.00146178	+	0.0167082i
$123$	0.430956	−	0.489332i	0.0388580	−	0.0441216i
$124$	3.59440	+	9.87552i	0.322786	+	0.886848i
$125$		0			0
$126$	0.00639285	−	0.00994226i	0.000569520	−	0.000885727i
$127$	−18.7735	+	5.03035i	−1.66588	+	0.446371i	−0.963996	−	0.265918i	$-0.914325\pi$
$127$	−18.7735	+	5.03035i	−1.66588	+	0.446371i	−0.701885	+	0.712290i	$0.747658\pi$
$128$	−0.400068	+	0.280131i	−0.0353614	+	0.0247603i
$129$	15.1347	+	4.44590i	1.33253	+	0.391440i
$130$		0			0
$131$	−4.49710	+	0.792959i	−0.392913	+	0.0692812i	−0.366614	−	0.930373i	$-0.619483\pi$
$131$	−4.49710	+	0.792959i	−0.392913	+	0.0692812i	−0.0262986	+	0.999654i	$0.508372\pi$
$132$	−11.8366	+	9.45903i	−1.03024	+	0.823303i
$133$	−1.46030	+	0.127760i	−0.126624	+	0.0110782i
$134$	−0.0280356			−0.00242191
$135$		0			0
$136$	0.107606			0.00922713
$137$	6.96948	−	0.609750i	0.595443	−	0.0520945i	0.214549	−	0.976713i	$-0.431172\pi$
$137$	6.96948	−	0.609750i	0.595443	−	0.0520945i	0.380894	+	0.924619i	$0.375616\pi$
$138$	−0.142688	−	0.0558340i	−0.0121464	−	0.00475291i
$139$	−8.03836	+	1.41738i	−0.681805	+	0.120221i	−0.503815	−	0.863812i	$-0.668071\pi$
$139$	−8.03836	+	1.41738i	−0.681805	+	0.120221i	−0.177990	+	0.984032i	$0.556959\pi$
$140$		0			0
$141$	5.02522	−	4.79040i	0.423200	−	0.403424i
$142$	0.0641675	−	0.0449306i	0.00538482	−	0.00377049i
$143$	−9.08786	+	2.43508i	−0.759965	+	0.203632i
$144$	−9.54753	+	7.26250i	−0.795628	+	0.605209i
$145$		0			0
$146$	−0.0749784	−	0.206002i	−0.00620526	−	0.0170488i
$147$	11.7733	+	2.36759i	0.971045	+	0.195276i
$148$	−0.563966	+	6.44617i	−0.0463578	+	0.529872i
$149$	14.7726	−	12.3956i	1.21021	−	1.01549i	0.210937	−	0.977500i	$-0.432349\pi$
$149$	14.7726	−	12.3956i	1.21021	−	1.01549i	0.999278	−	0.0379911i	$-0.0120959\pi$
$150$		0			0
$151$	−14.1147	+	5.13734i	−1.14864	+	0.418070i	−0.845026	−	0.534725i	$-0.820415\pi$
$151$	−14.1147	+	5.13734i	−1.14864	+	0.418070i	−0.303613	+	0.952795i	$0.598193\pi$
$152$	−0.335016	−	0.0897672i	−0.0271734	−	0.00728108i
$153$	5.28249	−	0.208389i	0.427064	−	0.0168473i
$154$	−0.0149266	−	0.00861785i	−0.00120282	−	0.000694446i
$155$		0			0
$156$	−7.23980	+	1.75544i	−0.579648	+	0.140548i
$157$	−0.987420	−	2.11753i	−0.0788047	−	0.168997i	0.862958	−	0.505276i	$-0.168609\pi$
$157$	−0.987420	−	2.11753i	−0.0788047	−	0.168997i	−0.941762	+	0.336279i	$0.890832\pi$
$158$	0.0271027	−	0.0387066i	0.00215617	−	0.00307933i
$159$	11.8514	−	16.0922i	0.939878	−	1.27620i
$160$		0			0
$161$			1.49546i			0.117859i
$162$	0.105994	−	0.0874311i	0.00832767	−	0.00686924i
$163$	−10.7302	+	10.7302i	−0.840451	+	0.840451i	−0.988917	−	0.148467i	$-0.952566\pi$
$163$	−10.7302	+	10.7302i	−0.840451	+	0.840451i	0.148467	+	0.988917i	$0.452566\pi$
$164$	−0.576705	−	0.483913i	−0.0450331	−	0.0377872i
$165$		0			0
$166$	0.0131678	+	0.0746781i	0.00102202	+	0.00579615i
$167$	17.5852	−	8.20013i	1.36079	−	0.634545i	0.401208	−	0.915987i	$-0.368590\pi$
$167$	17.5852	−	8.20013i	1.36079	−	0.634545i	0.959578	+	0.281442i	$0.0908126\pi$
$168$	−0.0233058	−	0.0142095i	−0.00179808	−	0.00109628i
$169$	8.24701	+	1.45417i	0.634385	+	0.111859i
$170$		0			0
$171$	−16.6201	−	3.75798i	−1.27097	−	0.287380i
$172$	4.71370	−	17.5918i	0.359416	−	1.34136i
$173$	5.26921	+	2.45707i	0.400610	+	0.186808i	0.612472	−	0.790492i	$-0.290175\pi$
$173$	5.26921	+	2.45707i	0.400610	+	0.186808i	−0.211862	+	0.977300i	$0.567953\pi$
$174$	0.0551296	−	0.111202i	0.00417936	−	0.00843018i
$175$		0			0
$176$	11.2435	+	13.3995i	0.847510	+	1.01002i
$177$	3.85728	−	19.1810i	0.289931	−	1.44173i
$178$	−0.0186571	+	0.0400103i	−0.00139841	+	0.00299890i
$179$	−4.77974	−	8.27875i	−0.357254	−	0.618783i	0.630247	−	0.776395i	$-0.282954\pi$
$179$	−4.77974	−	8.27875i	−0.357254	−	0.618783i	−0.987501	+	0.157612i	$0.949620\pi$
$180$		0			0
$181$	6.93879	−	12.0183i	0.515756	−	0.893315i	−0.484077	−	0.875026i	$-0.660844\pi$
$181$	6.93879	−	12.0183i	0.515756	−	0.893315i	0.999833	−	0.0182899i	$-0.00582219\pi$
$182$	−0.00486056	−	0.00694161i	−0.000360289	−	0.000514546i
$183$	21.0115	+	0.502668i	1.55321	+	0.0371583i
$184$	−0.121018	+	0.332494i	−0.00892157	+	0.0245118i
$185$		0			0
$186$	−0.127312	+	0.0556997i	−0.00933500	+	0.00408410i
$187$	−0.671857	−	7.67937i	−0.0491311	−	0.561571i
$188$	−5.66801	−	5.66801i	−0.413382	−	0.413382i
$189$	−1.17163	−	0.652424i	−0.0852234	−	0.0474569i
$190$		0			0
$191$	−7.63489	+	9.09890i	−0.552441	+	0.658374i	−0.967929	−	0.251225i	$-0.919167\pi$
$191$	−7.63489	+	9.09890i	−0.552441	+	0.658374i	0.415488	+	0.909599i	$0.363611\pi$
$192$	8.64426	+	10.8170i	0.623846	+	0.780652i
$193$	−9.91741	−	6.94425i	−0.713871	−	0.499858i	0.159325	−	0.987226i	$-0.449068\pi$
$193$	−9.91741	−	6.94425i	−0.713871	−	0.499858i	−0.873197	+	0.487368i	$0.837957\pi$
$194$	0.0676068	+	0.0246069i	0.00485389	+	0.00176667i
$195$		0			0
$196$	2.40766	−	13.6545i	0.171976	−	0.975323i
$197$	−1.53862	−	5.74222i	−0.109622	−	0.409116i	0.889206	−	0.457507i	$-0.151257\pi$
$197$	−1.53862	−	5.74222i	−0.109622	−	0.409116i	−0.998828	+	0.0483907i	$0.984591\pi$
$198$	−0.134733	−	0.148283i	−0.00957508	−	0.0105380i
$199$	−4.84519	+	2.79737i	−0.343466	+	0.198300i	−0.661804	−	0.749677i	$-0.730209\pi$
$199$	−4.84519	+	2.79737i	−0.343466	+	0.198300i	0.318337	+	0.947977i	$0.396876\pi$
$200$		0			0
$201$	0.201356	+	3.17433i	0.0142025	+	0.223900i
$202$	0.0439395	+	0.00384421i	0.00309157	+	0.000270478i
$203$	−1.20678	−	0.105579i	−0.0846992	−	0.00741022i
$204$	−0.386398	−	6.09149i	−0.0270533	−	0.426490i
$205$		0			0
$206$	−0.133522	+	0.0770888i	−0.00930290	+	0.00537103i
$207$	−5.29700	+	16.5569i	−0.368167	+	1.15078i
$208$	2.22585	+	8.30699i	0.154335	+	0.575986i
$209$	−4.31456	+	24.4691i	−0.298444	+	1.69256i
$210$		0			0
$211$	5.33826	+	1.94297i	0.367501	+	0.133759i	0.519168	−	0.854672i	$-0.326242\pi$
$211$	5.33826	+	1.94297i	0.367501	+	0.133759i	−0.151667	+	0.988432i	$0.548464\pi$
$212$	−18.9015	−	13.2350i	−1.29816	−	0.908980i
$213$	−5.54813	−	6.94267i	−0.380151	−	0.475704i
$214$	−0.147470	+	0.175748i	−0.0100808	+	0.0120139i
$215$		0			0
$216$	−0.207698	−	0.239869i	−0.0141321	−	0.0163210i
$217$	0.959041	+	0.959041i	0.0651039	+	0.0651039i
$218$	−0.0159710	−	0.182550i	−0.00108169	−	0.0123638i
$219$	−22.7860	+	9.96897i	−1.53974	+	0.673641i
$220$		0			0
$221$	1.29628	−	3.56150i	0.0871973	−	0.239573i
$222$	−0.0855382	−	0.00204637i	−0.00574095	−	0.000137344i
$223$	7.56295	+	10.8010i	0.506452	+	0.723289i	0.988225	−	0.153007i	$-0.0488958\pi$
$223$	7.56295	+	10.8010i	0.506452	+	0.723289i	−0.481773	+	0.876296i	$0.660007\pi$
$224$	−0.0236367	+	0.0409400i	−0.00157929	+	0.00273542i
$225$		0			0
$226$	0.0709048	+	0.122811i	0.00471652	+	0.00816925i
$227$	6.15899	−	13.2080i	0.408787	−	0.876646i	−0.588870	−	0.808228i	$-0.700427\pi$
$227$	6.15899	−	13.2080i	0.408787	−	0.876646i	0.997657	−	0.0684181i	$-0.0217952\pi$
$228$	−3.87866	+	19.2873i	−0.256870	+	1.27733i
$229$	5.35302	+	6.37948i	0.353738	+	0.421568i	0.913343	−	0.407191i	$-0.133492\pi$
$229$	5.35302	+	6.37948i	0.353738	+	0.421568i	−0.559605	+	0.828759i	$0.689047\pi$
$230$		0			0
$231$	−0.868552	+	1.75196i	−0.0571466	+	0.115270i
$232$	−0.259766	−	0.121131i	−0.0170545	−	0.00795262i
$233$	7.15675	−	26.7094i	0.468854	−	1.74979i	−0.174930	−	0.984581i	$-0.555970\pi$
$233$	7.15675	−	26.7094i	0.468854	−	1.74979i	0.643784	−	0.765207i	$-0.277363\pi$
$234$	−0.0292258	−	0.0940698i	−0.00191055	−	0.00614954i
$235$		0			0
$236$	−22.2459	−	3.92255i	−1.44808	−	0.255336i
$237$	−4.57722	−	2.79071i	−0.297322	−	0.181276i
$238$	0.00629266	−	0.00293432i	0.000407893	−	0.000190204i
$239$	−3.76477	−	21.3510i	−0.243522	−	1.38108i	−0.823899	−	0.566736i	$-0.808206\pi$
$239$	−3.76477	−	21.3510i	−0.243522	−	1.38108i	0.580377	−	0.814348i	$-0.302905\pi$
$240$		0			0
$241$	3.99926	+	3.35578i	0.257615	+	0.216165i	0.762443	−	0.647055i	$-0.224000\pi$
$241$	3.99926	+	3.35578i	0.257615	+	0.216165i	−0.504828	+	0.863220i	$0.668444\pi$
$242$	−0.0878299	+	0.0878299i	−0.00564592	+	0.00564592i
$243$	−10.6607	−	11.3732i	−0.683882	−	0.729593i
$244$		−	24.2661i		−	1.55348i
$245$		0			0
$246$	0.00590315	−	0.00801549i	0.000376371	−	0.000511049i
$247$	−7.00687	+	10.0068i	−0.445837	+	0.636721i
$248$	0.135620	+	0.290838i	0.00861188	+	0.0184682i
$249$	8.36086	−	2.02727i	0.529848	−	0.128473i
$250$		0			0
$251$	12.0778	+	6.97313i	0.762345	+	0.440140i	0.830137	−	0.557560i	$-0.188262\pi$
$251$	12.0778	+	6.97313i	0.762345	+	0.440140i	−0.0677923	+	0.997699i	$0.521596\pi$
$252$	−0.720698	+	1.37035i	−0.0453997	+	0.0863239i
$253$	24.4843	+	6.56054i	1.53931	+	0.412458i
$254$	−0.278826	+	0.101484i	−0.0174951	+	0.00636770i
$255$		0			0
$256$	12.2424	−	10.2726i	0.765152	−	0.642039i
$257$	−0.816897	+	9.33717i	−0.0509566	+	0.582437i	0.927200	+	0.374567i	$0.122209\pi$
$257$	−0.816897	+	9.33717i	−0.0509566	+	0.582437i	−0.978156	+	0.207870i	$0.933347\pi$
$258$	0.236093	+	0.0474781i	0.0146985	+	0.00295586i
$259$	0.285619	+	0.784731i	0.0177475	+	0.0487608i
$260$		0			0
$261$	−12.9868	−	5.44338i	−0.803861	−	0.336937i
$262$	−0.0673396	+	0.0180436i	−0.00416025	+	0.00111474i
$263$	−8.22122	+	5.75656i	−0.506942	+	0.354965i	−0.798897	−	0.601467i	$-0.794583\pi$
$263$	−8.22122	+	5.75656i	−0.506942	+	0.354965i	0.291955	+	0.956432i	$0.405694\pi$
$264$	−0.334885	+	0.319236i	−0.0206107	+	0.0196476i
$265$		0			0
$266$	−0.0220392	+	0.00388610i	−0.00135131	+	0.000238272i
$267$	4.66416	+	1.82509i	0.285442	+	0.111694i
$268$	3.65837	−	0.320066i	0.223470	−	0.0195511i
$269$	−1.84882			−0.112724			−0.0563622	−	0.998410i	$-0.517950\pi$
$269$	−1.84882			−0.112724			−0.0563622	+	0.998410i	$0.517950\pi$
$270$		0			0
$271$	14.0068			0.850851			0.425426	−	0.904993i	$-0.360124\pi$
$271$	14.0068			0.850851			0.425426	+	0.904993i	$0.360124\pi$
$272$	−7.01953	+	0.614129i	−0.425621	+	0.0372370i
$273$	−0.751055	+	0.600193i	−0.0454559	+	0.0363254i
$274$	0.105185	−	0.0185469i	0.00635445	−	0.00112046i
$275$		0			0
$276$	19.2568	+	5.65680i	1.15912	+	0.340499i
$277$	14.8975	−	10.4313i	0.895103	−	0.626758i	−0.0328481	−	0.999460i	$-0.510458\pi$
$277$	14.8975	−	10.4313i	0.895103	−	0.626758i	0.927951	+	0.372703i	$0.121569\pi$
$278$	−0.120367	+	0.0322521i	−0.00721911	+	0.00193435i
$279$	7.22097	+	14.0149i	0.432308	+	0.839051i
$280$		0			0
$281$	−8.98091	−	24.6748i	−0.535756	−	1.47198i	−0.852124	−	0.523341i	$-0.824686\pi$
$281$	−8.98091	−	24.6748i	−0.535756	−	1.47198i	0.316368	−	0.948637i	$-0.397537\pi$
$282$	0.0700527	−	0.0795419i	0.00417158	−	0.00473665i
$283$	1.59875	−	18.2738i	0.0950360	−	1.08627i	−0.787593	−	0.616196i	$-0.788673\pi$
$283$	1.59875	−	18.2738i	0.0950360	−	1.08627i	0.882629	−	0.470071i	$-0.155772\pi$
$284$	−7.86028	+	6.59556i	−0.466422	+	0.391374i
$285$		0			0
$286$	−0.134974	+	0.0491264i	−0.00798117	+	0.00290491i
$287$	−0.0938472	−	0.0251463i	−0.00553962	−	0.00148434i
$288$	−0.406704	+	0.369541i	−0.0239652	+	0.0217754i
$289$	−12.0331	−	6.94732i	−0.707830	−	0.408666i
$290$		0			0
$291$	2.30055	−	7.83152i	0.134861	−	0.459092i
$292$	12.1357	+	26.0252i	0.710191	+	1.52301i
$293$	−6.02781	+	8.60861i	−0.352149	+	0.502920i	−0.955675	−	0.294422i	$-0.904873\pi$
$293$	−6.02781	+	8.60861i	−0.352149	+	0.502920i	0.603527	+	0.797343i	$0.293762\pi$
$294$	0.182206	+	0.0203425i	0.0106265	+	0.00118640i
$295$		0			0
$296$			0.197587i			0.0114845i
$297$	−15.8216	+	16.3202i	−0.918064	+	0.946993i
$298$	0.208177	−	0.208177i	0.0120594	−	0.0120594i
$299$	9.54693	+	8.01082i	0.552113	+	0.463278i
$300$		0			0
$301$	−0.408144	−	2.31470i	−0.0235250	−	0.133417i
$302$	−0.207830	+	0.0969127i	−0.0119593	+	0.00557670i
$303$	0.119681	−	5.00267i	0.00687551	−	0.287396i
$304$	22.3666	+	3.94384i	1.28281	+	0.226195i
$305$		0			0
$306$	0.0800623	−	0.0101981i	0.00457685	−	0.000582987i
$307$	−3.31491	+	12.3714i	−0.189192	+	0.706074i	0.804502	+	0.593949i	$0.202432\pi$
$307$	−3.31491	+	12.3714i	−0.189192	+	0.706074i	−0.993694	+	0.112124i	$0.964235\pi$
$308$	2.04615	+	0.954137i	0.116590	+	0.0543670i
$309$	9.68736	+	14.5643i	0.551095	+	0.828537i
$310$		0			0
$311$	13.5014	+	16.0903i	0.765592	+	0.912397i	0.998188	−	0.0601768i	$-0.0191664\pi$
$311$	13.5014	+	16.0903i	0.765592	+	0.912397i	−0.232596	+	0.972573i	$0.574722\pi$
$312$	−0.215556	+	0.0726664i	−0.0122035	+	0.00411392i
$313$	12.4918	−	26.7887i	0.706078	−	1.51419i	−0.145159	−	0.989408i	$-0.546369\pi$
$313$	12.4918	−	26.7887i	0.706078	−	1.51419i	0.851237	−	0.524781i	$-0.175853\pi$
$314$	−0.0178349	−	0.0308909i	−0.00100648	−	0.00174327i
$315$		0			0
$316$	−3.09474	+	5.36025i	−0.174093	+	0.301538i
$317$	15.2311	+	21.7523i	0.855465	+	1.22173i	0.973492	+	0.228720i	$0.0734540\pi$
$317$	15.2311	+	21.7523i	0.855465	+	1.22173i	−0.118027	+	0.993010i	$0.537657\pi$
$318$	0.158832	−	0.260510i	0.00890684	−	0.0146087i
$319$	−7.02268	+	19.2947i	−0.393195	+	1.08029i
$320$		0			0
$321$	20.9582	+	15.4351i	1.16977	+	0.861501i
$322$	0.00198984	+	0.0227439i	0.000110889	+	0.00126747i
$323$	−7.07752	−	7.07752i	−0.393804	−	0.393804i
$324$	−12.8330	+	12.6190i	−0.712945	+	0.701054i
$325$		0			0
$326$	−0.148914	+	0.177468i	−0.00824756	+	0.00982906i
$327$	−20.5545	+	3.11942i	−1.13667	+	0.172504i
$328$	−0.0188306	−	0.0131854i	−0.00103975	−	0.000728040i
$329$	−0.972097	−	0.353814i	−0.0535934	−	0.0195064i
$330$		0			0
$331$	−1.72647	+	9.79132i	−0.0948956	+	0.538179i	0.899884	+	0.436130i	$0.143651\pi$
$331$	−1.72647	+	9.79132i	−0.0948956	+	0.538179i	−0.994779	+	0.102050i	$0.967460\pi$
$332$	−2.57082	−	9.59443i	−0.141092	−	0.526563i
$333$	0.382646	+	9.69977i	0.0209689	+	0.531544i
$334$	0.256536	−	0.148111i	0.0140371	−	0.00810430i
$335$		0			0
$336$	1.60142	+	0.793923i	0.0873647	+	0.0433121i
$337$	13.9748	+	1.22264i	0.761258	+	0.0666015i	0.461172	−	0.887311i	$-0.347429\pi$
$337$	13.9748	+	1.22264i	0.761258	+	0.0666015i	0.300086	+	0.953912i	$0.402985\pi$
$338$	0.127361	+	0.0111426i	0.00692750	+	0.000606078i
$339$	13.3960	−	8.91025i	0.727571	−	0.483938i
$340$		0			0
$341$	19.9091	−	11.4945i	1.07814	−	0.622463i
$342$	−0.257770	−	0.0350393i	−0.0139386	−	0.00189471i
$343$	−0.930702	−	3.47343i	−0.0502532	−	0.187547i
$344$	0.0965688	−	0.547669i	0.00520664	−	0.0295283i
$345$		0			0
$346$	0.0834068	+	0.0303576i	0.00448397	+	0.00163203i
$347$	−5.00149	−	3.50208i	−0.268494	−	0.188001i	0.431574	−	0.902077i	$-0.357958\pi$
$347$	−5.00149	−	3.50208i	−0.268494	−	0.188001i	−0.700068	+	0.714076i	$0.746847\pi$
$348$	−5.92434	+	15.1401i	−0.317578	+	0.811595i
$349$	2.45708	−	2.92823i	0.131524	−	0.156745i	−0.696263	−	0.717787i	$-0.745155\pi$
$349$	2.45708	−	2.92823i	0.131524	−	0.156745i	0.827787	+	0.561042i	$0.189600\pi$
$350$		0			0
$351$	−10.4412	+	3.98472i	−0.557308	+	0.212689i
$352$	0.566592	+	0.566592i	0.0301995	+	0.0301995i
$353$	−0.194119	−	2.21879i	−0.0103319	−	0.118094i	0.989277	−	0.146050i	$-0.0466559\pi$
$353$	−0.194119	−	2.21879i	−0.0103319	−	0.118094i	−0.999609	+	0.0279554i	$0.991100\pi$
$354$	0.0331420	−	0.296849i	0.00176148	−	0.0157774i
$355$		0			0
$356$	1.97779	−	5.43394i	0.104823	−	0.287998i
$357$	−0.377433	−	0.691413i	−0.0199759	−	0.0365934i
$358$	−0.0837088	−	0.119549i	−0.00442415	−	0.00631834i
$359$	−5.90045	+	10.2199i	−0.311414	+	0.539385i	−0.978669	−	0.205445i	$-0.934136\pi$
$359$	−5.90045	+	10.2199i	−0.311414	+	0.539385i	0.667255	+	0.744829i	$0.267469\pi$
$360$		0			0
$361$	6.63064	+	11.4846i	0.348981	+	0.604453i
$362$	0.0895381	−	0.192015i	0.00470602	−	0.0100921i
$363$	10.5753	+	9.31374i	0.555062	+	0.488844i
$364$	0.713504	+	0.850321i	0.0373978	+	0.0445689i
$365$		0			0
$366$	0.320225	−	0.0203126i	0.0167384	−	0.00106176i
$367$	1.92158	+	0.896047i	0.100306	+	0.0467733i	0.472123	−	0.881532i	$-0.343488\pi$
$367$	1.92158	+	0.896047i	0.100306	+	0.0467733i	−0.371818	+	0.928306i	$0.621265\pi$
$368$	5.99683	−	22.3805i	0.312607	−	1.16666i
$369$	−0.949952	−	0.610817i	−0.0494525	−	0.0317978i
$370$		0			0
$371$	−2.93265	−	0.517106i	−0.152256	−	0.0268468i
$372$	15.9771	−	8.72170i	0.828376	−	0.452199i
$373$	−3.00825	+	1.40277i	−0.155762	+	0.0726328i	−0.498936	−	0.866639i	$-0.666276\pi$
$373$	−3.00825	+	1.40277i	−0.155762	+	0.0726328i	0.343174	+	0.939272i	$0.388498\pi$
$374$	−0.0204361	−	0.115899i	−0.00105672	−	0.00599298i
$375$		0			0
$376$	−0.187500	−	0.157331i	−0.00966957	−	0.00811373i
$377$	−7.13843	+	7.13843i	−0.367648	+	0.367648i
$378$	−0.0186870	−	0.00836353i	−0.000961153	−	0.000430173i
$379$		−	15.7634i		−	0.809713i	−0.914380	−	0.404856i	$-0.867322\pi$
$379$		−	15.7634i		−	0.809713i	0.914380	−	0.404856i	$-0.132678\pi$
$380$		0			0
$381$	13.4932	+	30.8413i	0.691276	+	1.58005i
$382$	−0.104009	+	0.148541i	−0.00532158	+	0.00760001i
$383$	11.6401	+	24.9622i	0.594781	+	1.27551i	0.941333	+	0.337480i	$0.109575\pi$
$383$	11.6401	+	24.9622i	0.594781	+	1.27551i	−0.346552	+	0.938031i	$0.612648\pi$
$384$	0.583680	+	0.612292i	0.0297858	+	0.0312459i
$385$		0			0
$386$	−0.160070	−	0.0924166i	−0.00814736	−	0.00470388i
$387$	3.68006	−	27.0727i	0.187068	−	1.37618i
$388$	−9.10294	−	2.43913i	−0.462132	−	0.123828i
$389$	−28.2091	+	10.2673i	−1.43026	+	0.520571i	−0.937005	−	0.349315i	$-0.886414\pi$
$389$	−28.2091	+	10.2673i	−1.43026	+	0.520571i	−0.493252	+	0.869886i	$0.664192\pi$
$390$		0			0
$391$	−7.82217	+	6.56358i	−0.395584	+	0.331934i
$392$	0.0368997	−	0.421765i	0.00186372	−	0.0213024i
$393$	2.52663	+	7.49494i	0.127452	+	0.378070i
$394$	−0.0310408	−	0.0852840i	−0.00156382	−	0.00429655i
$395$		0			0
$396$	19.2742	+	17.8112i	0.968566	+	0.895048i
$397$	−4.62074	+	1.23812i	−0.231908	+	0.0621397i	−0.372902	−	0.927871i	$-0.621637\pi$
$397$	−4.62074	+	1.23812i	−0.231908	+	0.0621397i	0.140993	+	0.990011i	$0.454970\pi$
$398$	−0.0699666	+	0.0489911i	−0.00350711	+	0.00245570i
$399$	0.598293	+	2.46748i	0.0299521	+	0.123528i
$400$		0			0
$401$	−8.47214	+	1.49387i	−0.423078	+	0.0746001i	−0.381134	−	0.924520i	$-0.624466\pi$
$401$	−8.47214	+	1.49387i	−0.423078	+	0.0746001i	−0.0419444	+	0.999120i	$0.513355\pi$
$402$	0.00728606	+	0.0480094i	0.000363396	+	0.00239449i
$403$	11.2598	−	0.985106i	0.560891	−	0.0490716i
$404$	−5.77756			−0.287444
$405$		0			0
$406$	−0.0184939			−0.000917838
$407$	14.1009	−	1.23367i	0.698957	−	0.0611508i
$408$	−0.0279653	−	0.184269i	−0.00138449	−	0.00912267i
$409$	−8.33076	+	1.46894i	−0.411930	+	0.0726343i	−0.375773	−	0.926712i	$-0.622623\pi$
$409$	−8.33076	+	1.46894i	−0.411930	+	0.0726343i	−0.0361568	+	0.999346i	$0.511512\pi$
$410$		0			0
$411$	−2.85543	−	11.7764i	−0.140848	−	0.580885i
$412$	16.5432	−	11.5837i	0.815024	−	0.570686i
$413$	−2.81592	+	0.754524i	−0.138562	+	0.0371277i
$414$	−0.0585299	+	0.258856i	−0.00287659	+	0.0127221i
$415$		0			0
$416$	0.134742	+	0.370201i	0.00660628	+	0.0181506i
$417$	4.51624	+	13.3969i	0.221161	+	0.656048i
$418$	−0.0330604	+	0.377882i	−0.00161704	+	0.0184828i
$419$	−6.72816	+	5.64560i	−0.328692	+	0.275806i	−0.792167	−	0.610305i	$-0.791047\pi$
$419$	−6.72816	+	5.64560i	−0.328692	+	0.275806i	0.463475	+	0.886110i	$0.346603\pi$
$420$		0			0
$421$	0.538899	−	0.196143i	0.0262643	−	0.00955944i	−0.328855	−	0.944381i	$-0.606663\pi$
$421$	0.538899	−	0.196143i	0.0262643	−	0.00955944i	0.355119	+	0.934821i	$0.384440\pi$
$422$	0.0837730	+	0.0224469i	0.00407800	+	0.00109270i
$423$	−9.50926	−	7.36045i	−0.462356	−	0.357877i
$424$	−0.610187	−	0.352292i	−0.0296333	−	0.0171088i
$425$		0			0
$426$	−0.0936172	−	0.0982063i	−0.00453577	−	0.00475811i
$427$	−1.32351	−	2.83827i	−0.0640489	−	0.137353i
$428$	17.2370	−	24.6170i	0.833181	−	1.18991i
$429$	6.53175	+	14.9296i	0.315356	+	0.720807i
$430$		0			0
$431$		−	25.0117i		−	1.20477i	−0.798205	−	0.602386i	$-0.794217\pi$
$431$		−	25.0117i		−	1.20477i	0.798205	−	0.602386i	$-0.205783\pi$
$432$	14.9179	+	14.4622i	0.717737	+	0.695812i
$433$	24.9892	−	24.9892i	1.20090	−	1.20090i	0.227011	−	0.973892i	$-0.427105\pi$
$433$	24.9892	−	24.9892i	1.20090	−	1.20090i	0.973892	−	0.227011i	$-0.0728954\pi$
$434$	0.0158618	+	0.0133096i	0.000761390	+	0.000638882i
$435$		0			0
$436$	4.16812	+	23.6386i	0.199617	+	1.13208i
$437$	29.8287	−	13.9093i	1.42690	−	0.665374i
$438$	−0.333280	+	0.181933i	−0.0159247	+	0.00869310i
$439$	4.64923	+	0.819785i	0.221896	+	0.0391262i	0.283491	−	0.958975i	$-0.408508\pi$
$439$	4.64923	+	0.819785i	0.221896	+	0.0391262i	−0.0615948	+	0.998101i	$0.519619\pi$
$440$		0			0
$441$	0.994657	−	20.7764i	0.0473646	−	0.989352i
$442$	0.0149758	−	0.0558904i	0.000712326	−	0.00265844i
$443$	−26.7976	−	12.4959i	−1.27319	−	0.593700i	−0.335787	−	0.941938i	$-0.609002\pi$
$443$	−26.7976	−	12.4959i	−1.27319	−	0.593700i	−0.937406	+	0.348238i	$0.886780\pi$
$444$	11.1853	−	0.709507i	0.530829	−	0.0336717i
$445$		0			0
$446$	0.129394	+	0.154205i	0.00612697	+	0.00730184i
$447$	−25.0660	−	22.0757i	−1.18558	−	1.04414i
$448$	0.871951	−	1.86990i	0.0411958	−	0.0883447i
$449$	−3.36725	−	5.83225i	−0.158910	−	0.275241i	0.775566	−	0.631267i	$-0.217465\pi$
$449$	−3.36725	−	5.83225i	−0.158910	−	0.275241i	−0.934476	+	0.356026i	$0.884131\pi$
$450$		0			0
$451$	−0.823409	+	1.42619i	−0.0387728	+	0.0671565i
$452$	−10.6544	−	15.2161i	−0.501142	−	0.715706i
$453$	12.4656	+	22.8355i	0.585685	+	1.07291i
$454$	0.0760955	−	0.209071i	0.00357134	−	0.00981217i
$455$		0			0
$456$	−0.0666553	+	0.597025i	−0.00312142	+	0.0279582i
$457$	3.16016	+	36.1208i	0.147826	+	1.68966i	0.601800	+	0.798647i	$0.294450\pi$
$457$	3.16016	+	36.1208i	0.147826	+	1.68966i	−0.453974	+	0.891015i	$0.649994\pi$
$458$	0.0899006	+	0.0899006i	0.00420078	+	0.00420078i
$459$	−1.72970	−	8.99181i	−0.0807355	−	0.419702i
$460$		0			0
$461$	16.9825	−	20.2390i	0.790956	−	0.942625i	−0.208417	−	0.978040i	$-0.566831\pi$
$461$	16.9825	−	20.2390i	0.790956	−	0.942625i	0.999373	+	0.0354156i	$0.0112755\pi$
$462$	−0.0108784	+	0.0278005i	−0.000506108	+	0.00129340i
$463$	9.85172	+	6.89825i	0.457848	+	0.320589i	0.779647	−	0.626219i	$-0.215399\pi$
$463$	9.85172	+	6.89825i	0.457848	+	0.320589i	−0.321799	+	0.946808i	$0.604287\pi$
$464$	17.6368	+	6.41927i	0.818767	+	0.298007i
$465$		0			0
$466$	0.0733054	−	0.415735i	0.00339581	−	0.0192586i
$467$	2.86104	+	10.6775i	0.132393	+	0.494098i	0.999995	−	0.00316149i	$-0.00100633\pi$
$467$	2.86104	+	10.6775i	0.132393	+	0.494098i	−0.867602	+	0.497260i	$0.834340\pi$
$468$	4.88762	+	11.9415i	0.225930	+	0.551997i
$469$	0.410442	−	0.236969i	0.0189525	−	0.0109422i
$470$		0			0
$471$	−3.36953	+	2.24122i	−0.155260	+	0.103270i
$472$	−0.687138	−	0.0601168i	−0.0316281	−	0.00276710i
$473$	−39.6877	−	3.47222i	−1.82484	−	0.159653i
$474$	−0.0733265	−	0.0363525i	−0.00336800	−	0.00166972i
$475$		0			0
$476$	−0.787631	+	0.454739i	−0.0361010	+	0.0208429i
$477$	−30.6370	−	16.1127i	−1.40277	−	0.737750i
$478$	−0.0856663	−	0.319711i	−0.00391828	−	0.0146232i
$479$	0.735877	−	4.17337i	0.0336231	−	0.190686i	−0.963370	−	0.268175i	$-0.913579\pi$
$479$	0.735877	−	4.17337i	0.0336231	−	0.190686i	0.996993	+	0.0774895i	$0.0246904\pi$
$480$		0			0
$481$	6.53967	+	2.38024i	0.298183	+	0.108530i
$482$	0.0652884	+	0.0457155i	0.00297381	+	0.00208228i
$483$	2.56089	−	0.388649i	0.116525	−	0.0176842i
$484$	10.4582	−	12.4636i	0.475374	−	0.566529i
$485$		0			0
$486$	−0.177267	−	0.158786i	−0.00804100	−	0.00720270i
$487$	−16.7646	−	16.7646i	−0.759676	−	0.759676i	0.216587	−	0.976263i	$-0.430507\pi$
$487$	−16.7646	−	16.7646i	−0.759676	−	0.759676i	−0.976263	+	0.216587i	$0.930507\pi$
$488$	−0.0645798	−	0.738151i	−0.00292339	−	0.0334145i
$489$	21.1634	+	15.5862i	0.957041	+	0.704830i
$490$		0			0
$491$	0.697417	−	1.91614i	0.0314740	−	0.0864740i	−0.922960	−	0.384895i	$-0.874238\pi$
$491$	0.697417	−	1.91614i	0.0314740	−	0.0864740i	0.954434	+	0.298421i	$0.0964599\pi$
$492$	−0.678795	+	1.11334i	−0.0306024	+	0.0501930i
$493$	−4.74430	−	6.77556i	−0.213673	−	0.305156i
$494$	−0.0932500	+	0.161514i	−0.00419552	+	0.00726685i
$495$		0			0
$496$	−10.5069	−	18.1984i	−0.471772	−	0.817133i
$497$	−0.559642	+	1.20016i	−0.0251034	+	0.0538343i
$498$	0.124460	−	0.0419568i	0.00557718	−	0.00188013i
$499$	−8.77600	−	10.4588i	−0.392868	−	0.468202i	0.532964	−	0.846138i	$-0.321078\pi$
$499$	−8.77600	−	10.4588i	−0.392868	−	0.468202i	−0.925832	+	0.377937i	$0.876634\pi$
$500$		0			0
$501$	−18.6124	−	27.9826i	−0.831541	−	1.25017i
$502$	0.192965	+	0.0899812i	0.00861246	+	0.00401606i
$503$	−11.4964	+	42.9050i	−0.512597	+	1.91304i	−0.121825	+	0.992552i	$0.538875\pi$
$503$	−11.4964	+	42.9050i	−0.512597	+	1.91304i	−0.390772	+	0.920487i	$0.627792\pi$
$504$	−0.0182760	+	0.0436027i	−0.000814078	+	0.00194222i
$505$		0			0
$506$	0.381102	+	0.0671985i	0.0169420	+	0.00298734i
$507$	0.346901	−	14.5004i	0.0154064	−	0.643987i
$508$	35.2255	−	16.4259i	1.56288	−	0.728782i
$509$	−0.883595	−	5.01112i	−0.0391647	−	0.222114i	0.958943	−	0.283597i	$-0.0915279\pi$
$509$	−0.883595	−	5.01112i	−0.0391647	−	0.222114i	−0.998108	+	0.0614836i	$0.980417\pi$
$510$		0			0
$511$	2.83890	+	2.38212i	0.125586	+	0.105379i
$512$	0.863214	−	0.863214i	0.0381490	−	0.0381490i
$513$	−2.11599	+	29.4377i	−0.0934231	+	1.29971i
$514$			0.143093i			0.00631155i
$515$		0			0
$516$	−31.3499	−	3.50008i	−1.38010	−	0.154083i
$517$	−10.0573	+	14.3634i	−0.442321	+	0.631700i
$518$	0.00538802	+	0.0115547i	0.000236736	+	0.000507682i
$519$	2.83820	−	9.66177i	0.124583	−	0.424105i
$520$		0			0
$521$	−14.9219	−	8.61518i	−0.653742	−	0.377438i	0.136146	−	0.990689i	$-0.456528\pi$
$521$	−14.9219	−	8.61518i	−0.653742	−	0.377438i	−0.789888	+	0.613251i	$0.789862\pi$
$522$	−0.204754	−	0.0655064i	−0.00896184	−	0.00286714i
$523$	−12.9054	−	3.45799i	−0.564314	−	0.151207i	−0.0346265	−	0.999400i	$-0.511024\pi$
$523$	−12.9054	−	3.45799i	−0.564314	−	0.151207i	−0.529688	+	0.848193i	$0.677691\pi$
$524$	8.58116	−	3.12329i	0.374870	−	0.136441i
$525$		0			0
$526$	−0.117374	+	0.0984884i	−0.00511775	+	0.00429430i
$527$	−0.807135	+	9.22560i	−0.0351594	+	0.401873i
$528$	20.0238	−	22.7362i	0.871424	−	0.989465i
$529$	−3.61738	−	9.93866i	−0.157277	−	0.432116i
$530$		0			0
$531$	−33.8488	−	1.62049i	−1.46891	−	0.0703233i
$532$	2.83153	−	0.758707i	0.122762	−	0.0328941i
$533$	−0.663249	+	0.464412i	−0.0287285	+	0.0201159i
$534$	0.0733640	+	0.0215511i	0.00317477	+	0.000932607i
$535$		0			0
$536$	0.110432	−	0.0194722i	0.00476995	−	0.000841071i
$537$	−12.9347	+	10.3366i	−0.558173	+	0.446055i
$538$	−0.0281180	+	0.00246001i	−0.00121225	+	0.000106058i
$539$	−30.3299			−1.30640
$540$		0			0
$541$	7.10549			0.305489			0.152745	−	0.988266i	$-0.451189\pi$
$541$	7.10549			0.305489			0.152745	+	0.988266i	$0.451189\pi$
$542$	0.213024	−	0.0186372i	0.00915016	−	0.000800535i
$543$	−22.3840	−	8.75888i	−0.960589	−	0.375879i
$544$	−0.317883	+	0.0560513i	−0.0136291	+	0.00240318i
$545$		0			0
$546$	−0.0106239	+	0.0101275i	−0.000454661	+	0.000433415i
$547$	−8.41425	+	5.89172i	−0.359767	+	0.251912i	−0.739459	−	0.673201i	$-0.764919\pi$
$547$	−8.41425	+	5.89172i	−0.359767	+	0.251912i	0.379692	+	0.925113i	$0.376030\pi$
$548$	−13.5139	+	3.62103i	−0.577283	+	0.154683i
$549$	−4.59979	−	36.1116i	−0.196314	−	1.54120i
$550$		0			0
$551$	9.11839	+	25.0526i	0.388456	+	1.06728i
$552$	0.600828	+	0.120826i	0.0255730	+	0.00514269i
$553$	−0.0696191	+	0.795750i	−0.00296050	+	0.0338387i
$554$	0.212691	−	0.178469i	0.00903636	−	0.00758240i
$555$		0			0
$556$	15.3384	−	5.58274i	0.650495	−	0.236761i
$557$	5.55174	+	1.48759i	0.235235	+	0.0630310i	0.374511	−	0.927223i	$-0.377811\pi$
$557$	5.55174	+	1.48759i	0.235235	+	0.0630310i	−0.139276	+	0.990254i	$0.544477\pi$
$558$	0.128469	+	0.203540i	0.00543853	+	0.00861652i
$559$	−16.9632	−	9.79373i	−0.717468	−	0.414230i
$560$		0			0
$561$	−12.9759	+	3.14628i	−0.547841	+	0.132836i
$562$	−0.169419	−	0.363321i	−0.00714652	−	0.0153258i
$563$	14.1548	−	20.2152i	0.596555	−	0.851969i	−0.401399	−	0.915903i	$-0.631476\pi$
$563$	14.1548	−	20.2152i	0.596555	−	0.851969i	0.997954	+	0.0639343i	$0.0203648\pi$
$564$	−8.23311	+	11.1792i	−0.346676	+	0.470728i
$565$		0			0
$566$		−	0.280047i		−	0.0117713i
$567$	−0.812749	+	2.17590i	−0.0341322	+	0.0913792i
$568$	−0.221549	+	0.221549i	−0.00929600	+	0.00929600i
$569$	1.46173	+	1.22654i	0.0612790	+	0.0514192i	0.672913	−	0.739722i	$-0.265043\pi$
$569$	1.46173	+	1.22654i	0.0612790	+	0.0514192i	−0.611634	+	0.791141i	$0.709487\pi$
$570$		0			0
$571$	−7.82276	−	44.3651i	−0.327372	−	1.85662i	−0.492452	−	0.870340i	$-0.663899\pi$
$571$	−7.82276	−	44.3651i	−0.327372	−	1.85662i	0.165080	−	0.986280i	$-0.447212\pi$
$572$	17.0519	−	7.95143i	0.712976	−	0.332466i
$573$	17.5655	+	10.7096i	0.733811	+	0.447401i
$574$	−0.00146075		0.000257569i	−6.09704e−5		1.07507e-5i
$575$		0			0
$576$	16.2770	−	17.6140i	0.678210	−	0.733917i
$577$	−5.87132	+	21.9121i	−0.244426	+	0.912211i	0.729245	+	0.684253i	$0.239872\pi$
$577$	−5.87132	+	21.9121i	−0.244426	+	0.912211i	−0.973671	+	0.227958i	$0.926795\pi$
$578$	−0.192251	−	0.0896482i	−0.00799660	−	0.00372888i
$579$	−9.31423	+	18.7877i	−0.387086	+	0.780791i
$580$		0			0
$581$	−0.823988	−	0.981990i	−0.0341848	−	0.0407398i
$582$	0.0245678	−	0.122168i	0.00101837	−	0.00506402i
$583$	−21.3317	+	45.7460i	−0.883469	+	1.89461i
$584$	0.438419	+	0.759364i	0.0181419	+	0.0314227i
$585$		0			0
$586$	−0.0802204	+	0.138946i	−0.00331387	+	0.00573980i
$587$	−4.91190	−	7.01492i	−0.202736	−	0.289537i	0.704890	−	0.709316i	$-0.250996\pi$
$587$	−4.91190	−	7.01492i	−0.202736	−	0.289537i	−0.907626	+	0.419780i	$0.862107\pi$
$588$	−24.0083	−	0.574363i	−0.990086	−	0.0236863i
$589$	10.2091	−	28.0493i	0.420659	−	1.15575i
$590$		0			0
$591$	−9.43335	+	4.12712i	−0.388036	+	0.169767i
$592$	−1.12767	−	12.8893i	−0.0463469	−	0.529748i
$593$	−4.26261	−	4.26261i	−0.175044	−	0.175044i	0.614147	−	0.789192i	$-0.289500\pi$
$593$	−4.26261	−	4.26261i	−0.175044	−	0.175044i	−0.789192	+	0.614147i	$0.789500\pi$
$594$	−0.218910	+	0.269260i	−0.00898199	+	0.0110479i
$595$		0			0
$596$	−24.7884	+	29.5417i	−1.01537	+	1.21007i
$597$	6.04953	+	7.57011i	0.247591	+	0.309824i
$598$	0.155855	+	0.109131i	0.00637338	+	0.00446269i
$599$	13.5981	+	4.94929i	0.555602	+	0.202223i	0.604534	−	0.796580i	$-0.293359\pi$
$599$	13.5981	+	4.94929i	0.555602	+	0.202223i	−0.0489318	+	0.998802i	$0.515582\pi$
$600$		0			0
$601$	−2.11215	+	11.9786i	−0.0861565	+	0.488618i	0.910944	+	0.412529i	$0.135354\pi$
$601$	−2.11215	+	11.9786i	−0.0861565	+	0.488618i	−0.997101	+	0.0760891i	$0.975757\pi$
$602$	−0.00928722	−	0.0346604i	−0.000378519	−	0.00141265i
$603$	5.38353	−	1.16977i	0.219234	−	0.0476369i
$604$	26.0133	−	15.0188i	1.05847	−	0.611107i
$605$		0			0
$606$	−0.00483627	−	0.0762430i	−0.000196460	−	0.00309716i
$607$	−19.3845	−	1.69592i	−0.786792	−	0.0688354i	−0.313324	−	0.949646i	$-0.601443\pi$
$607$	−19.3845	−	1.69592i	−0.786792	−	0.0688354i	−0.473468	+	0.880811i	$0.656998\pi$
$608$	1.03644	+	0.0906769i	0.0420333	+	0.00367743i
$609$	0.132826	+	2.09398i	0.00538238	+	0.0848522i
$610$		0			0
$611$	−7.46602	+	4.31051i	−0.302043	+	0.174384i
$612$	−10.3309	+	2.24478i	−0.417602	+	0.0907397i
$613$	−3.48768	−	13.0162i	−0.140866	−	0.525720i	−0.999905	−	0.0138088i	$-0.995604\pi$
$613$	−3.48768	−	13.0162i	−0.140866	−	0.525720i	0.859038	−	0.511911i	$-0.171062\pi$
$614$	−0.0339541	+	0.192563i	−0.00137027	+	0.00777121i
$615$		0			0
$616$	0.0647813	+	0.0235785i	0.00261011	+	0.000950003i
$617$	−37.1967	−	26.0454i	−1.49748	−	1.04855i	−0.981392	−	0.192014i	$-0.938498\pi$
$617$	−37.1967	−	26.0454i	−1.49748	−	1.04855i	−0.516090	−	0.856535i	$-0.672613\pi$
$618$	0.166711	+	0.208614i	0.00670608	+	0.00839169i
$619$	−0.765342	+	0.912099i	−0.0307617	+	0.0366604i	−0.781206	−	0.624273i	$-0.785395\pi$
$619$	−0.765342	+	0.912099i	−0.0307617	+	0.0366604i	0.750444	+	0.660934i	$0.229840\pi$
$620$		0			0
$621$	29.7293	+	4.76791i	1.19300	+	0.191330i
$622$	0.226747	+	0.226747i	0.00909171	+	0.00909171i
$623$	−0.0650434	−	0.743449i	−0.00260591	−	0.0297857i
$624$	13.6468	−	5.97052i	0.546309	−	0.239012i
$625$		0			0
$626$	0.154339	−	0.424042i	0.00616861	−	0.0169481i
$627$	43.0232	+	1.02927i	1.71818	+	0.0411049i
$628$	2.67993	+	3.82734i	0.106941	+	0.152728i
$629$	−2.85104	+	4.93815i	−0.113678	+	0.196897i
$630$		0			0
$631$	10.8669	+	18.8220i	0.432605	+	0.749293i	0.997097	−	0.0761454i	$-0.0242613\pi$
$631$	10.8669	+	18.8220i	0.432605	+	0.749293i	−0.564492	+	0.825438i	$0.690928\pi$
$632$	−0.0798737	+	0.171290i	−0.00317721	+	0.00681354i
$633$	1.93988	−	9.64642i	0.0771034	−	0.383411i
$634$	0.260588	+	0.310556i	0.0103493	+	0.0123338i
$635$		0			0
$636$	−17.7519	+	35.8073i	−0.703908	+	1.41985i
$637$	−13.5149	−	6.30211i	−0.535481	−	0.249699i
$638$	−0.0811322	+	0.302790i	−0.00321206	+	0.0119876i
$639$	−10.4470	+	11.3051i	−0.413279	+	0.447225i
$640$		0			0
$641$	11.0540	+	1.94912i	0.436606	+	0.0769855i	0.387631	−	0.921815i	$-0.373293\pi$
$641$	11.0540	+	1.94912i	0.436606	+	0.0769855i	0.0489751	+	0.998800i	$0.484405\pi$
$642$	0.339284	+	0.206860i	0.0133905	+	0.00816410i
$643$	−21.6198	+	10.0815i	−0.852602	+	0.397575i	−0.799248	−	0.601001i	$-0.794769\pi$
$643$	−21.6198	+	10.0815i	−0.852602	+	0.397575i	−0.0533535	+	0.998576i	$0.516991\pi$
$644$	−0.519308	−	2.94514i	−0.0204636	−	0.116055i
$645$		0			0
$646$	−0.117057	−	0.0982222i	−0.00460553	−	0.00386450i
$647$	17.7336	−	17.7336i	0.697179	−	0.697179i	−0.266622	−	0.963801i	$-0.585908\pi$
$647$	17.7336	−	17.7336i	0.697179	−	0.697179i	0.963801	+	0.266622i	$0.0859076\pi$
$648$	−0.356785	+	0.418010i	−0.0140158	+	0.0164210i
$649$			49.4134i			1.93965i
$650$		0			0
$651$	1.39306	−	1.89154i	0.0545984	−	0.0741355i
$652$	17.4057	−	24.8579i	0.681660	−	0.973511i
$653$	−7.70684	−	16.5274i	−0.301592	−	0.646766i	0.695855	−	0.718183i	$-0.255026\pi$
$653$	−7.70684	−	16.5274i	−0.301592	−	0.646766i	−0.997447	+	0.0714165i	$0.977248\pi$
$654$	−0.308455	+	0.0747915i	−0.0120616	+	0.00292458i
$655$		0			0
$656$	1.30364	+	0.752659i	0.0508987	+	0.0293864i
$657$	22.9931	+	36.4290i	0.897045	+	1.42123i
$658$	−0.0152550	−	0.00408758i	−0.000594704	−	0.000159350i
$659$	32.1808	−	11.7129i	1.25359	−	0.456269i	0.371975	−	0.928243i	$-0.378681\pi$
$659$	32.1808	−	11.7129i	1.25359	−	0.456269i	0.881612	+	0.471974i	$0.156458\pi$
$660$		0			0
$661$	3.43935	−	2.88596i	0.133775	−	0.112251i	−0.573445	−	0.819244i	$-0.694393\pi$
$661$	3.43935	−	2.88596i	0.133775	−	0.112251i	0.707220	+	0.706993i	$0.249949\pi$
$662$	−0.0132291	+	0.151210i	−0.000514165	+	0.00587693i
$663$	−6.43575	−	1.29422i	−0.249944	−	0.0502634i
$664$	−0.103736	−	0.285012i	−0.00402573	−	0.0110606i
$665$		0			0
$666$	0.0187259	+	0.147011i	0.000725613	+	0.00569656i
$667$	26.2716	−	7.03946i	1.01724	−	0.272569i
$668$	−31.7846	+	22.2558i	−1.22978	+	0.861103i
$669$	16.5306	−	15.7581i	0.639110	−	0.609245i
$670$		0			0
$671$	−52.2754	+	9.21756i	−2.01807	+	0.355840i
$672$	0.0762502	+	0.0298368i	0.00294142	+	0.00115098i
$673$	−15.0821	+	1.31952i	−0.581374	+	0.0508636i	−0.374050	−	0.927409i	$-0.622031\pi$
$673$	−15.0821	+	1.31952i	−0.581374	+	0.0508636i	−0.207324	+	0.978272i	$0.566475\pi$
$674$	0.214165			0.00824933
$675$		0			0
$676$	−16.7465			−0.644096
$677$	9.69800	−	0.848465i	0.372724	−	0.0326092i	0.100745	−	0.994912i	$-0.467877\pi$
$677$	9.69800	−	0.848465i	0.372724	−	0.0326092i	0.271979	+	0.962303i	$0.412322\pi$
$678$	0.191879	−	0.153337i	0.00736908	−	0.00588888i
$679$	−1.19775	+	0.211196i	−0.0459656	+	0.00810497i
$680$		0			0
$681$	−24.2186	−	7.11435i	−0.928058	−	0.272622i
$682$	0.287495	−	0.201306i	0.0110088	−	0.00770842i
$683$	22.4891	−	6.02595i	0.860523	−	0.230577i	0.198538	−	0.980093i	$-0.436381\pi$
$683$	22.4891	−	6.02595i	0.860523	−	0.230577i	0.661985	+	0.749517i	$0.269714\pi$
$684$	34.0365	+	1.62948i	1.30142	+	0.0623045i
$685$		0			0
$686$	−0.0187764	−	0.0515877i	−0.000716886	−	0.00196963i
$687$	9.53332	−	10.8247i	0.363719	−	0.412987i
$688$	−3.17388	+	36.2776i	−0.121003	+	1.38307i
$689$	−19.0107	+	15.9519i	−0.724249	+	0.607717i
$690$		0			0
$691$	−4.24724	+	1.54587i	−0.161573	+	0.0588077i	−0.421540	−	0.906810i	$-0.638510\pi$
$691$	−4.24724	+	1.54587i	−0.161573	+	0.0588077i	0.259968	+	0.965617i	$0.416288\pi$
$692$	−11.2303	−	3.00916i	−0.426913	−	0.114391i
$693$	3.22585	+	1.03204i	0.122540	+	0.0392039i
$694$	−0.0807256	−	0.0466069i	−0.00306430	−	0.00176918i
$695$		0			0
$696$	−0.139920	+	0.476314i	−0.00530365	+	0.0180546i
$697$	−0.280365	−	0.601245i	−0.0106196	−	0.0227738i
$698$	0.0334725	−	0.0478038i	0.00126695	−	0.00180940i
$699$	−47.5982	−	5.31414i	−1.80033	−	0.200999i
$700$		0			0
$701$			28.3612i			1.07119i	0.844476	+	0.535593i	$0.179912\pi$
$701$			28.3612i			1.07119i	−0.844476	+	0.535593i	$0.820088\pi$
$702$	−0.153494	+	0.0744950i	−0.00579325	+	0.00281163i
$703$	12.9958	−	12.9958i	0.490147	−	0.490147i
$704$	−26.7896	−	22.4791i	−1.00967	−	0.847214i
$705$		0			0
$706$	−0.00590457	−	0.0334865i	−0.000222221	−	0.00126028i
$707$	−0.675769	+	0.315116i	−0.0254149	+	0.0118512i
$708$	−0.935750	+	39.1142i	−0.0351676	+	1.47000i
$709$	−27.9978	−	4.93677i	−1.05148	−	0.185404i	−0.378907	−	0.925435i	$-0.623700\pi$
$709$	−27.9978	−	4.93677i	−1.05148	−	0.185404i	−0.672574	+	0.740030i	$0.734811\pi$
$710$		0			0
$711$	−3.58937	+	8.56349i	−0.134612	+	0.321156i
$712$	0.0457011	−	0.170559i	0.00171272	−	0.00639196i
$713$	−27.5987	−	12.8695i	−1.03358	−	0.481966i
$714$	−0.00666022	−	0.0100132i	−0.000249253	−	0.000374736i
$715$		0			0
$716$	12.2880	+	14.6443i	0.459224	+	0.547282i
$717$	−35.5840	+	11.9958i	−1.32891	+	0.447991i
$718$	−0.0761394	+	0.163281i	−0.00284150	+	0.00609361i
$719$	−8.97949	−	15.5529i	−0.334878	−	0.580026i	0.648583	−	0.761144i	$-0.275362\pi$
$719$	−8.97949	−	15.5529i	−0.334878	−	0.580026i	−0.983461	+	0.181118i	$0.942029\pi$
$720$		0			0
$721$	1.30318	−	2.25717i	0.0485328	−	0.0840612i
$722$	0.116124	+	0.165843i	0.00432170	+	0.00617202i
$723$	4.70723	−	7.72062i	0.175064	−	0.287133i
$724$	−9.49171	+	26.0783i	−0.352757	+	0.969191i
$725$		0			0
$726$	0.173229	+	0.127578i	0.00642914	+	0.00473486i
$727$	−2.47494	−	28.2887i	−0.0917905	−	1.04917i	−0.892780	−	0.450492i	$-0.851249\pi$
$727$	−2.47494	−	28.2887i	−0.0917905	−	1.04917i	0.800990	−	0.598678i	$-0.204307\pi$
$728$	0.0239671	+	0.0239671i	0.000888279	+	0.000888279i
$729$	−16.7054	+	21.2115i	−0.618720	+	0.785612i
$730$		0			0
$731$	10.3159	−	12.2941i	0.381549	−	0.454712i
$732$	−41.5542	+	6.30641i	−1.53589	+	0.233092i
$733$	8.28966	+	5.80448i	0.306185	+	0.214393i	0.716563	−	0.697522i	$-0.245714\pi$
$733$	8.28966	+	5.80448i	0.306185	+	0.214393i	−0.410378	+	0.911916i	$0.634603\pi$
$734$	0.0304169	+	0.0110708i	0.00112271	+	0.000408632i
$735$		0			0
$736$	0.184310	−	1.04527i	0.00679374	−	0.0385292i
$737$	−2.07915	−	7.75949i	−0.0765865	−	0.285825i
$738$	−0.0152602	−	0.00802570i	−0.000561736	−	0.000295430i
$739$	35.8294	−	20.6861i	1.31801	−	0.760951i	0.334598	−	0.942361i	$-0.391399\pi$
$739$	35.8294	−	20.6861i	1.31801	−	0.760951i	0.983408	+	0.181410i	$0.0580660\pi$
$740$		0			0
$741$	18.9571	+	9.39823i	0.696408	+	0.345252i
$742$	−0.0452897	−	0.00396233i	−0.00166264	−	0.000145462i
$743$	7.70953	+	0.674496i	0.282835	+	0.0247449i	0.227691	−	0.973734i	$-0.426882\pi$
$743$	7.70953	+	0.674496i	0.282835	+	0.0247449i	0.0551445	+	0.998478i	$0.482438\pi$
$744$	0.462798	−	0.307826i	0.0169670	−	0.0112855i
$745$		0			0
$746$	−0.0438849	+	0.0253370i	−0.00160674	+	0.000927653i
$747$	−5.64445	−	13.7906i	−0.206520	−	0.504573i
$748$	3.98985	+	14.8903i	0.145883	+	0.544444i
$749$	0.673470	−	3.81944i	0.0246080	−	0.139559i
$750$		0			0
$751$	−38.8916	−	14.1554i	−1.41918	−	0.516537i	−0.485367	−	0.874311i	$-0.661314\pi$
$751$	−38.8916	−	14.1554i	−1.41918	−	0.516537i	−0.933808	+	0.357773i	$0.883536\pi$
$752$	13.1292	+	9.19318i	0.478773	+	0.335241i
$753$	8.80223	−	22.4948i	0.320771	−	0.819755i
$754$	−0.0990675	+	0.118064i	−0.00360782	+	0.00429964i
$755$		0			0
$756$	2.53394	+	0.878020i	0.0921587	+	0.0319333i
$757$	10.7021	+	10.7021i	0.388975	+	0.388975i	0.874322	−	0.485347i	$-0.161307\pi$
$757$	10.7021	+	10.7021i	0.388975	+	0.388975i	−0.485347	+	0.874322i	$0.661307\pi$
$758$	−0.0209745	−	0.239740i	−0.000761830	−	0.00870775i
$759$	4.87143	−	43.6329i	0.176822	−	1.58377i
$760$		0			0
$761$	16.8761	−	46.3666i	0.611756	−	1.68079i	−0.114551	−	0.993417i	$-0.536543\pi$
$761$	16.8761	−	46.3666i	0.611756	−	1.68079i	0.726308	−	0.687370i	$-0.241235\pi$
$762$	0.246249	+	0.451100i	0.00892067	+	0.0163416i
$763$	1.77680	+	2.53754i	0.0643246	+	0.0918651i
$764$	11.8764	−	20.5705i	0.429673	−	0.744215i
$765$		0			0
$766$	0.210244	+	0.364154i	0.00759643	+	0.0131574i
$767$	−10.2674	+	22.0185i	−0.370733	+	0.795040i
$768$	−20.7729	−	18.2947i	−0.749578	−	0.660155i
$769$	−4.55804	−	5.43206i	−0.164367	−	0.195885i	0.677574	−	0.735455i	$-0.263031\pi$
$769$	−4.55804	−	5.43206i	−0.164367	−	0.195885i	−0.841941	+	0.539570i	$0.818587\pi$
$770$		0			0
$771$	16.2017	−	1.02771i	0.583489	−	0.0370121i
$772$	21.9426	+	10.2320i	0.789733	+	0.368259i
$773$	−2.31145	+	8.62644i	−0.0831370	+	0.310272i	−0.994955	−	0.100323i	$-0.968012\pi$
$773$	−2.31145	+	8.62644i	−0.0831370	+	0.310272i	0.911818	+	0.410595i	$0.134679\pi$
$774$	0.0199462	−	0.416635i	0.000716950	−	0.0149756i
$775$		0			0
$776$	−0.283394	−	0.0499700i	−0.0101733	−	0.00179382i
$777$	1.26958	−	0.693047i	0.0455459	−	0.0248629i
$778$	−0.415360	+	0.193686i	−0.0148914	+	0.00694397i
$779$	0.371305	+	2.10578i	0.0133034	+	0.0754473i
$780$		0			0
$781$	17.1943	+	14.4277i	0.615260	+	0.516264i
$782$	−0.110231	+	0.110231i	−0.00394186	+	0.00394186i
$783$	−5.94640	+	23.6538i	−0.212507	+	0.845316i
$784$			27.7239i			0.990139i
$785$		0			0
$786$	0.0483992	+	0.110626i	0.00172634	+	0.00394589i
$787$	−0.397947	+	0.568328i	−0.0141853	+	0.0202587i	−0.826182	−	0.563403i	$-0.809492\pi$
$787$	−0.397947	+	0.568328i	−0.0141853	+	0.0202587i	0.811997	+	0.583662i	$0.198381\pi$
$788$	5.02416	+	10.7743i	0.178978	+	0.383820i
$789$	11.9944	+	12.5823i	0.427010	+	0.447942i
$790$		0			0
$791$	−2.07610	−	1.19864i	−0.0738175	−	0.0426186i
$792$	0.633705	+	0.490506i	0.0225177	+	0.0174294i
$793$	−25.2090	−	6.75473i	−0.895198	−	0.239868i
$794$	−0.0686278	+	0.0249785i	−0.00243551	+	0.000886453i
$795$		0			0
$796$	8.57065	−	7.19163i	0.303778	−	0.254900i
$797$	−3.24018	+	37.0354i	−0.114773	+	1.31186i	0.692385	+	0.721528i	$0.256560\pi$
$797$	−3.24018	+	37.0354i	−0.114773	+	1.31186i	−0.807158	+	0.590335i	$0.798996\pi$
$798$	0.0123824	+	0.0367309i	0.000438332	+	0.00130026i
$799$	−2.41587	−	6.63755i	−0.0854673	−	0.234820i
$800$		0			0
$801$	1.91321	−	8.46143i	0.0676001	−	0.298970i
$802$	−0.126862	+	0.0339926i	−0.00447965	+	0.00120032i
$803$	51.4551	−	36.0293i	1.81581	−	1.27145i
$804$	−1.49885	−	6.18157i	−0.0528605	−	0.218007i
$805$		0			0
$806$	0.169936	−	0.0299642i	0.00598573	−	0.00105544i
$807$	0.480482	+	3.16599i	0.0169138	+	0.111448i
$808$	−0.175748	+	0.0153759i	−0.00618279	+	0.000540924i
$809$	9.19706			0.323351			0.161676	−	0.986844i	$-0.448310\pi$
$809$	9.19706			0.323351			0.161676	+	0.986844i	$0.448310\pi$
$810$		0			0
$811$	−3.49413			−0.122695			−0.0613477	−	0.998116i	$-0.519540\pi$
$811$	−3.49413			−0.122695			−0.0613477	+	0.998116i	$0.519540\pi$
$812$	2.41327	−	0.211134i	0.0846893	−	0.00740935i
$813$	−3.64016	−	23.9858i	−0.127666	−	0.841219i
$814$	0.212814	−	0.0375249i	0.00745914	−	0.00131525i
$815$		0			0
$816$	2.87594	+	11.8609i	0.100678	+	0.415216i
$817$	−42.3732	+	29.6700i	−1.48245	+	1.03802i
$818$	−0.124745	+	0.0334253i	−0.00436160	+	0.00116869i
$819$	1.22299	+	1.13016i	0.0427346	+	0.0394908i
$820$		0			0
$821$	−5.34053	−	14.6730i	−0.186386	−	0.512091i	0.810944	−	0.585124i	$-0.198954\pi$
$821$	−5.34053	−	14.6730i	−0.186386	−	0.512091i	−0.997329	+	0.0730336i	$0.976732\pi$
$822$	−0.0590967	−	0.175303i	−0.00206123	−	0.00611440i
$823$	2.60641	−	29.7914i	0.0908536	−	1.03846i	−0.804752	−	0.593612i	$-0.797702\pi$
$823$	2.60641	−	29.7914i	0.0908536	−	1.03846i	0.895605	−	0.444850i	$-0.146743\pi$
$824$	0.472400	−	0.396391i	0.0164568	−	0.0138089i
$825$		0			0
$826$	−0.0418223	+	0.0152221i	−0.00145519	+	0.000529644i
$827$	−35.9960	−	9.64511i	−1.25171	−	0.335393i	−0.428710	−	0.903442i	$-0.641032\pi$
$827$	−35.9960	−	9.64511i	−1.25171	−	0.335393i	−0.822995	+	0.568049i	$0.807699\pi$
$828$	4.68237	−	34.4463i	0.162724	−	1.19709i
$829$	6.82502	+	3.94043i	0.237043	+	0.136857i	0.613817	−	0.789448i	$-0.289633\pi$
$829$	6.82502	+	3.94043i	0.237043	+	0.136857i	−0.376774	+	0.926305i	$0.622967\pi$
$830$		0			0
$831$	−21.7347	−	22.8001i	−0.753968	−	0.790927i
$832$	−7.26652	−	15.5831i	−0.251921	−	0.540247i
$833$	7.00798	−	10.0084i	0.242812	−	0.346771i
$834$	0.0865115	+	0.197739i	0.00299565	+	0.00684714i
$835$		0			0
$836$		−	49.6874i		−	1.71847i
$837$	22.1231	−	16.0078i	0.764687	−	0.553310i
$838$	−0.0948142	+	0.0948142i	−0.00327530	+	0.00327530i
$839$	26.9906	+	22.6478i	0.931819	+	0.781889i	0.976143	−	0.217128i	$-0.0696689\pi$
$839$	26.9906	+	22.6478i	0.931819	+	0.781889i	−0.0443239	+	0.999017i	$0.514113\pi$
$840$		0			0
$841$	−1.21001	−	6.86229i	−0.0417244	−	0.236631i
$842$	0.00793494	−	0.00370012i	0.000273456	−	0.000127515i
$843$	−39.9202	+	21.7919i	−1.37493	+	0.750554i
$844$	−11.1878	−	1.97271i	−0.385100	−	0.0679035i
$845$		0			0
$846$	−0.154417	−	0.0992895i	−0.00530895	−	0.00341364i
$847$	0.543456	−	2.02821i	0.0186734	−	0.0696900i
$848$	41.8153	+	19.4988i	1.43594	+	0.669592i
$849$	−31.7084	+	2.01134i	−1.08823	+	0.0690290i
$850$		0			0
$851$	−12.0521	−	14.3631i	−0.413141	−	0.492362i
$852$	13.3373	+	11.7462i	0.456928	+	0.402417i
$853$	10.3392	−	22.1725i	0.354007	−	0.759171i	−0.645984	−	0.763351i	$-0.723553\pi$
$853$	10.3392	−	22.1725i	0.354007	−	0.759171i	0.999991	+	0.00417979i	$0.00133047\pi$
$854$	−0.0239053	−	0.0414051i	−0.000818021	−	0.00141685i
$855$		0			0
$856$	0.458819	−	0.794697i	0.0156821	−	0.0271622i
$857$	−2.59518	−	3.70630i	−0.0886496	−	0.126605i	0.772378	−	0.635164i	$-0.219067\pi$
$857$	−2.59518	−	3.70630i	−0.0886496	−	0.126605i	−0.861027	+	0.508559i	$0.830178\pi$
$858$	0.119204	+	0.218368i	0.00406956	+	0.00745495i
$859$	3.10612	−	8.53399i	0.105979	−	0.291176i	−0.875356	−	0.483478i	$-0.839373\pi$
$859$	3.10612	−	8.53399i	0.105979	−	0.291176i	0.981336	+	0.192302i	$0.0615954\pi$
$860$		0			0
$861$	−0.0186720	+	0.167243i	−0.000636340	+	0.00569963i
$862$	−0.0332801	−	0.380394i	−0.00113353	−	0.0129563i
$863$	21.0851	+	21.0851i	0.717746	+	0.717746i	0.968143	−	0.250398i	$-0.0805613\pi$
$863$	21.0851	+	21.0851i	0.717746	+	0.717746i	−0.250398	+	0.968143i	$0.580561\pi$
$864$	0.738515	+	0.600418i	0.0251248	+	0.0204266i
$865$		0			0
$866$	0.346801	−	0.413302i	0.0117848	−	0.0140446i
$867$	−8.76965	+	22.4115i	−0.297833	+	0.761136i
$868$	−2.22175	−	1.55569i	−0.0754113	−	0.0528035i
$869$	12.7229	+	4.63076i	0.431595	+	0.157088i
$870$		0			0
$871$	0.685845	−	3.88962i	0.0232390	−	0.131795i
$872$	0.189700	+	0.707971i	0.00642406	+	0.0239749i
$873$	−14.0089	−	1.90426i	−0.474130	−	0.0644496i
$874$	0.435146	−	0.251232i	0.0147190	−	0.00849804i
$875$		0			0
$876$	41.4127	−	27.5453i	1.39921	−	0.930671i
$877$	45.5933	+	3.98890i	1.53958	+	0.134696i	0.825110	−	0.564973i	$-0.191113\pi$
$877$	45.5933	+	3.98890i	1.53958	+	0.134696i	0.714468	+	0.699668i	$0.246669\pi$
$878$	0.0717992	+	0.00628162i	0.00242311	+	0.000211994i
$879$	16.3083	+	8.08503i	0.550065	+	0.272701i
$880$		0			0
$881$	−33.3855	+	19.2752i	−1.12479	+	0.649396i	−0.942619	−	0.333871i	$-0.891645\pi$
$881$	−33.3855	+	19.2752i	−1.12479	+	0.649396i	−0.182169	+	0.983267i	$0.558312\pi$
$882$	−0.0125173	−	0.317304i	−0.000421480	−	0.0106842i
$883$	4.85682	+	18.1259i	0.163445	+	0.609986i	0.998233	+	0.0594144i	$0.0189233\pi$
$883$	4.85682	+	18.1259i	0.163445	+	0.609986i	−0.834788	+	0.550571i	$0.814410\pi$
$884$	−1.31612	+	7.46412i	−0.0442661	+	0.251045i
$885$		0			0
$886$	−0.424182	−	0.154390i	−0.0142507	−	0.00518682i
$887$	−30.0349	−	21.0306i	−1.00847	−	0.706140i	−0.0522057	−	0.998636i	$-0.516625\pi$
$887$	−30.0349	−	21.0306i	−1.00847	−	0.706140i	−0.956267	+	0.292496i	$0.905514\pi$
$888$	0.338357	−	0.0513501i	0.0113545	−	0.00172320i
$889$	3.22424	−	3.84250i	0.108137	−	0.128873i
$890$		0			0
$891$	32.0592	+	22.8522i	1.07402	+	0.765579i
$892$	−18.6451	−	18.6451i	−0.624283	−	0.624283i
$893$	1.98428	+	22.6804i	0.0664014	+	0.758972i
$894$	−0.410593	−	0.302389i	−0.0137323	−	0.0101134i
$895$		0			0
$896$	0.0431100	−	0.118444i	0.00144021	−	0.00395693i
$897$	11.2370	−	18.4305i	0.375191	−	0.615375i
$898$	−0.0589716	−	0.0842201i	−0.00196791	−	0.00281046i
$899$	12.3336	−	21.3624i	0.411349	−	0.712477i
$900$		0			0
$901$	−10.1666	−	17.6091i	−0.338700	−	0.586645i
$902$	−0.0106253	+	0.0227860i	−0.000353783	+	0.000758690i
$903$	−3.85772	+	1.30048i	−0.128377	+	0.0432773i
$904$	−0.364593	−	0.434505i	−0.0121262	−	0.0144514i
$905$		0			0
$906$	0.219969	+	0.330710i	0.00730799	+	0.0109871i
$907$	17.4935	+	8.15736i	0.580863	+	0.270861i	0.690762	−	0.723082i	$-0.257275\pi$
$907$	17.4935	+	8.15736i	0.580863	+	0.270861i	−0.109900	+	0.993943i	$0.535053\pi$
$908$	−7.54288	+	28.1504i	−0.250319	+	0.934204i
$909$	−8.59788	+	1.09518i	−0.285174	+	0.0363247i
$910$		0			0
$911$	39.2363	+	6.91842i	1.29996	+	0.229217i	0.780433	−	0.625239i	$-0.214999\pi$
$911$	39.2363	+	6.91842i	1.29996	+	0.229217i	0.519523	+	0.854456i	$0.326110\pi$
$912$	0.940828	−	39.3265i	0.0311539	−	1.30223i
$913$	−19.6923	+	9.18269i	−0.651721	+	0.303903i
$914$	0.0961236	+	0.545144i	0.00317949	+	0.0180318i
$915$		0			0
$916$	−12.7575	−	10.7048i	−0.421519	−	0.353696i
$917$	0.833342	−	0.833342i	0.0275194	−	0.0275194i
$918$	−0.0382707	−	0.134452i	−0.00126312	−	0.00443757i
$919$			43.5953i			1.43808i	0.694971	+	0.719038i	$0.255417\pi$
$919$			43.5953i			1.43808i	−0.694971	+	0.719038i	$0.744583\pi$
$920$		0			0
$921$	22.0468	+	2.46144i	0.726468	+	0.0811071i
$922$	0.231352	−	0.330404i	0.00761916	−	0.0108813i
$923$	4.66385	+	10.0017i	0.153513	+	0.329209i
$924$	1.10214	−	3.75189i	0.0362577	−	0.123428i
$925$		0			0
$926$	0.159010	+	0.0918044i	0.00522539	+	0.00301688i
$927$	22.4230	−	20.3741i	0.736468	−	0.669174i
$928$	0.830480	+	0.222526i	0.0272618	+	0.00730479i
$929$	−32.4046	+	11.7943i	−1.06316	+	0.386959i	−0.813615	−	0.581404i	$-0.802504\pi$
$929$	−32.4046	+	11.7943i	−1.06316	+	0.386959i	−0.249546	+	0.968363i	$0.580281\pi$
$930$		0			0
$931$	−30.1676	+	25.3136i	−0.988703	+	0.829620i
$932$	−4.81942	+	55.0863i	−0.157865	+	1.80441i
$933$	24.0449	−	27.3019i	0.787194	−	0.893825i
$934$	0.0577199	+	0.158584i	0.00188865	+	0.00518903i
$935$		0			0
$936$	0.180457	+	0.350242i	0.00589842	+	0.0114480i
$937$	44.7642	−	11.9945i	1.46238	−	0.391845i	0.562072	−	0.827089i	$-0.310005\pi$
$937$	44.7642	−	11.9945i	1.46238	−	0.391845i	0.900313	+	0.435244i	$0.143338\pi$
$938$	0.00592696	−	0.00415010i	0.000193522	−	0.000135506i
$939$	−49.1206	−	14.4295i	−1.60299	−	0.470888i
$940$		0			0
$941$	8.77614	−	1.54747i	0.286094	−	0.0504461i	−0.0287596	−	0.999586i	$-0.509156\pi$
$941$	8.77614	−	1.54747i	0.286094	−	0.0504461i	0.314854	+	0.949140i	$0.398045\pi$
$942$	−0.0482638	+	0.0385693i	−0.00157252	+	0.00125665i
$943$	2.17311	−	0.190123i	0.0707662	−	0.00619124i
$944$	45.1676			1.47008
$945$		0			0
$946$	−0.608216			−0.0197748
$947$	−36.6998	+	3.21081i	−1.19258	+	0.104337i	−0.666109	−	0.745854i	$-0.732041\pi$
$947$	−36.6998	+	3.21081i	−1.19258	+	0.104337i	−0.526473	+	0.850192i	$0.676486\pi$
$948$	9.98340	+	3.90651i	0.324246	+	0.126878i
$949$	30.4146	−	5.36292i	0.987300	−	0.174088i
$950$		0			0
$951$	33.2912	−	31.7355i	1.07954	−	1.02910i
$952$	−0.0227488	+	0.0159289i	−0.000737292	+	0.000516257i
$953$	27.9077	−	7.47785i	0.904020	−	0.242231i	0.223278	−	0.974755i	$-0.428324\pi$
$953$	27.9077	−	7.47785i	0.904020	−	0.242231i	0.680742	+	0.732523i	$0.261658\pi$
$954$	−0.487387	−	0.204287i	−0.0157797	−	0.00661404i
$955$		0			0
$956$	14.8286	+	40.7411i	0.479590	+	1.31766i
$957$	34.8661	+	7.01153i	1.12706	+	0.226650i
$958$	0.00563868	−	0.0644504i	0.000182177	−	0.00208230i
$959$	−1.38314	+	1.16060i	−0.0446641	+	0.0374776i
$960$		0			0
$961$	3.17820	−	1.15677i	0.102522	−	0.0373151i
$962$	0.102627	+	0.0274987i	0.00330881	+	0.000886594i
$963$	20.9849	−	39.9011i	0.676229	−	1.28580i
$964$	−9.04140	−	5.22006i	−0.291204	−	0.168127i
$965$		0			0
$966$	0.0384305	−	0.00931830i	0.00123648	−	0.000299811i
$967$	−8.87400	−	19.0304i	−0.285369	−	0.611975i	0.710407	−	0.703791i	$-0.248511\pi$
$967$	−8.87400	−	19.0304i	−0.285369	−	0.611975i	−0.995776	+	0.0918158i	$0.970733\pi$
$968$	0.284960	−	0.406964i	0.00915895	−	0.0130803i
$969$	−10.2805	+	13.9592i	−0.330257	+	0.448434i
$970$		0			0
$971$			58.1766i			1.86697i	0.358610	+	0.933487i	$0.383251\pi$
$971$			58.1766i			1.86697i	−0.358610	+	0.933487i	$0.616749\pi$
$972$	24.9444	+	18.6963i	0.800091	+	0.599684i
$973$	1.48956	−	1.48956i	0.0477531	−	0.0477531i
$974$	−0.277273	−	0.232660i	−0.00888441	−	0.00745490i
$975$		0			0
$976$	8.42555	+	47.7837i	0.269695	+	1.52952i
$977$	39.2996	−	18.3257i	1.25731	−	0.586291i	0.324232	−	0.945977i	$-0.394894\pi$
$977$	39.2996	−	18.3257i	1.25731	−	0.586291i	0.933073	+	0.359686i	$0.117116\pi$
$978$	0.342605	+	0.208885i	0.0109553	+	0.00667939i
$979$	−12.4574	−	2.19657i	−0.398140	−	0.0702028i
$980$		0			0
$981$	10.6836	+	34.3877i	0.341103	+	1.09791i
$982$	0.00805718	−	0.0300698i	0.000257115	−	0.000959566i
$983$	47.1628	+	21.9924i	1.50426	+	0.701447i	0.987924	−	0.154940i	$-0.0495183\pi$
$983$	47.1628	+	21.9924i	1.50426	+	0.701447i	0.516335	+	0.856387i	$0.327296\pi$
$984$	−0.0176854	+	0.0356731i	−0.000563788	+	0.00113722i
$985$		0			0
$986$	−0.0811698	−	0.0967344i	−0.00258497	−	0.00308065i
$987$	−0.353252	+	1.75661i	−0.0112441	+	0.0559135i
$988$	10.3243	−	22.1405i	0.328460	−	0.704384i
$989$	26.3860	+	45.7019i	0.839026	+	1.45324i
$990$		0			0
$991$	−1.64852	+	2.85532i	−0.0523670	+	0.0907023i	−0.891021	−	0.453963i	$-0.850010\pi$
$991$	−1.64852	+	2.85532i	−0.0523670	+	0.0907023i	0.838654	+	0.544665i	$0.183343\pi$
$992$	−0.552136	−	0.788532i	−0.0175303	−	0.0250359i
$993$	17.2158	+	0.411861i	0.546325	+	0.0130700i
$994$	−0.00691448	+	0.0189974i	−0.000219314	+	0.000602560i
$995$		0			0
$996$	−15.7618	+	6.89584i	−0.499431	+	0.218503i
$997$	−2.04371	−	23.3597i	−0.0647248	−	0.739808i	−0.957335	−	0.288979i	$-0.906684\pi$
$997$	−2.04371	−	23.3597i	−0.0647248	−	0.739808i	0.892610	−	0.450829i	$-0.148871\pi$
$998$	−0.147387	−	0.147387i	−0.00466546	−	0.00466546i
$999$	16.5109	−	3.17609i	0.522380	−	0.100487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.632.8		192
5.2	odd	4		135.2.q.a.38.8	yes	192
5.3	odd	4	inner	675.2.ba.b.443.9		192
5.4	even	2		135.2.q.a.92.9	yes	192
15.2	even	4		405.2.r.a.278.9		192
15.14	odd	2		405.2.r.a.197.8		192
27.5	odd	18	inner	675.2.ba.b.32.9		192
135.22	odd	36		405.2.r.a.368.8		192
135.32	even	36		135.2.q.a.113.9	yes	192
135.49	even	18		405.2.r.a.287.9		192
135.59	odd	18		135.2.q.a.32.8	✓	192
135.113	even	36	inner	675.2.ba.b.518.8		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.8	✓	192	135.59	odd	18
135.2.q.a.38.8	yes	192	5.2	odd	4
135.2.q.a.92.9	yes	192	5.4	even	2
135.2.q.a.113.9	yes	192	135.32	even	36
405.2.r.a.197.8		192	15.14	odd	2
405.2.r.a.278.9		192	15.2	even	4
405.2.r.a.287.9		192	135.49	even	18
405.2.r.a.368.8		192	135.22	odd	36
675.2.ba.b.32.9		192	27.5	odd	18	inner
675.2.ba.b.443.9		192	5.3	odd	4	inner
675.2.ba.b.518.8		192	135.113	even	36	inner
675.2.ba.b.632.8		192	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0152086 - 0.00133058i) q^{2} +(-0.259886 - 1.71244i) q^{3} +(-1.96939 + 0.347256i) q^{4} +(-0.00623106 - 0.0256981i) q^{6} +(-0.211408 + 0.148030i) q^{7} +(-0.0589827 + 0.0158044i) q^{8} +(-2.86492 + 0.890079i) q^{9} +(1.49616 + 4.11066i) q^{11} +(1.10647 + 3.28221i) q^{12} +(-0.187451 + 2.14258i) q^{13} +(-0.00301826 + 0.00253263i) q^{14} +(3.75746 - 1.36760i) q^{16} +(-1.70216 - 0.456091i) q^{17} +(-0.0423872 + 0.0173489i) q^{18} +(4.91894 + 2.83995i) q^{19} +(0.308434 + 0.323554i) q^{21} +(0.0282241 + 0.0605267i) q^{22} +(3.32360 - 4.74660i) q^{23} +(0.0423928 + 0.0968971i) q^{24} +0.0328351i q^{26} +(2.26876 + 4.67469i) q^{27} +(0.364940 - 0.364940i) q^{28} +(3.59567 + 3.01712i) q^{29} +(-0.912568 - 5.17543i) q^{31} +(0.166010 - 0.0774120i) q^{32} +(6.65044 - 3.63039i) q^{33} +(-0.0264943 - 0.00467167i) q^{34} +(5.33305 - 2.74777i) q^{36} +(0.837479 - 3.12552i) q^{37} +(0.0785891 + 0.0366467i) q^{38} +(3.71775 - 0.235826i) q^{39} +(0.241984 + 0.288386i) q^{41} +(0.00512138 + 0.00451041i) q^{42} +(-3.84888 + 8.25395i) q^{43} +(-4.37396 - 7.57592i) q^{44} +(0.0442317 - 0.0766116i) q^{46} +(2.29910 + 3.28345i) q^{47} +(-3.31845 - 6.07901i) q^{48} +(-2.37136 + 6.51526i) q^{49} +(-0.338664 + 3.03338i) q^{51} +(-0.374859 - 4.28465i) q^{52} +(8.15900 + 8.15900i) q^{53} +(0.0407248 + 0.0680769i) q^{54} +(0.0101299 - 0.0120724i) q^{56} +(3.58489 - 9.16146i) q^{57} +(0.0586997 + 0.0411020i) q^{58} +(10.6146 + 3.86341i) q^{59} +(-2.10712 + 11.9501i) q^{61} +(-0.0207652 - 0.0774969i) q^{62} +(0.473909 - 0.612263i) q^{63} +(-6.92336 + 3.99720i) q^{64} +(0.0963135 - 0.0640622i) q^{66} +(-1.82940 - 0.160052i) q^{67} +(3.51058 + 0.307136i) q^{68} +(-8.99203 - 4.45790i) q^{69} +(4.44360 - 2.56551i) q^{71} +(0.154913 - 0.0977775i) q^{72} +(-3.71651 - 13.8702i) q^{73} +(0.00857816 - 0.0486492i) q^{74} +(-10.6735 - 3.88483i) q^{76} +(-0.924799 - 0.647552i) q^{77} +(0.0562282 - 0.00853337i) q^{78} +(1.98949 - 2.37099i) q^{79} +(7.41552 - 5.10001i) q^{81} +(0.00406398 + 0.00406398i) q^{82} +(0.432904 + 4.94812i) q^{83} +(-0.719782 - 0.530096i) q^{84} +(-0.0475536 + 0.130653i) q^{86} +(4.23219 - 6.94148i) q^{87} +(-0.153214 - 0.218812i) q^{88} +(-1.44584 + 2.50426i) q^{89} +(-0.277536 - 0.480707i) q^{91} +(-4.89717 + 10.5020i) q^{92} +(-8.62546 + 2.90774i) q^{93} +(0.0393351 + 0.0468777i) q^{94} +(-0.175707 - 0.264165i) q^{96} +(4.27105 + 1.99162i) q^{97} +(-0.0273961 + 0.102243i) q^{98} +(-7.94518 - 10.4450i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more