LMFDB - Embedded newform 675.2.ba.b.443.9

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			443.9
Character	$\chi$	$=$	675.443
Dual form			675.2.ba.b.32.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.00133058 - 0.0152086i) q^{2} +(1.71244 - 0.259886i) q^{3} +(1.96939 - 0.347256i) q^{4} +(-0.00623106 - 0.0256981i) q^{6} +(0.148030 + 0.211408i) q^{7} +(-0.0158044 - 0.0589827i) q^{8} +(2.86492 - 0.890079i) q^{9} +(1.49616 + 4.11066i) q^{11} +(3.28221 - 1.10647i) q^{12} +(-2.14258 - 0.187451i) q^{13} +(0.00301826 - 0.00253263i) q^{14} +(3.75746 - 1.36760i) q^{16} +(-0.456091 + 1.70216i) q^{17} +(-0.0173489 - 0.0423872i) q^{18} +(-4.91894 - 2.83995i) q^{19} +(0.308434 + 0.323554i) q^{21} +(0.0605267 - 0.0282241i) q^{22} +(4.74660 + 3.32360i) q^{23} +(-0.0423928 - 0.0968971i) q^{24} +0.0328351i q^{26} +(4.67469 - 2.26876i) q^{27} +(0.364940 + 0.364940i) q^{28} +(-3.59567 - 3.01712i) q^{29} +(-0.912568 - 5.17543i) q^{31} +(-0.0774120 - 0.166010i) q^{32} +(3.63039 + 6.65044i) q^{33} +(0.0264943 + 0.00467167i) q^{34} +(5.33305 - 2.74777i) q^{36} +(-3.12552 - 0.837479i) q^{37} +(-0.0366467 + 0.0785891i) q^{38} +(-3.71775 + 0.235826i) q^{39} +(0.241984 + 0.288386i) q^{41} +(0.00451041 - 0.00512138i) q^{42} +(-8.25395 - 3.84888i) q^{43} +(4.37396 + 7.57592i) q^{44} +(0.0442317 - 0.0766116i) q^{46} +(3.28345 - 2.29910i) q^{47} +(6.07901 - 3.31845i) q^{48} +(2.37136 - 6.51526i) q^{49} +(-0.338664 + 3.03338i) q^{51} +(-4.28465 + 0.374859i) q^{52} +(-8.15900 + 8.15900i) q^{53} +(-0.0407248 - 0.0680769i) q^{54} +(0.0101299 - 0.0120724i) q^{56} +(-9.16146 - 3.58489i) q^{57} +(-0.0411020 + 0.0586997i) q^{58} +(-10.6146 - 3.86341i) q^{59} +(-2.10712 + 11.9501i) q^{61} +(-0.0774969 + 0.0207652i) q^{62} +(0.612263 + 0.473909i) q^{63} +(6.92336 - 3.99720i) q^{64} +(0.0963135 - 0.0640622i) q^{66} +(-0.160052 + 1.82940i) q^{67} +(-0.307136 + 3.51058i) q^{68} +(8.99203 + 4.45790i) q^{69} +(4.44360 - 2.56551i) q^{71} +(-0.0977775 - 0.154913i) q^{72} +(13.8702 - 3.71651i) q^{73} +(-0.00857816 + 0.0486492i) q^{74} +(-10.6735 - 3.88483i) q^{76} +(-0.647552 + 0.924799i) q^{77} +(0.00853337 + 0.0562282i) q^{78} +(-1.98949 + 2.37099i) q^{79} +(7.41552 - 5.10001i) q^{81} +(0.00406398 - 0.00406398i) q^{82} +(-4.94812 + 0.432904i) q^{83} +(0.719782 + 0.530096i) q^{84} +(-0.0475536 + 0.130653i) q^{86} +(-6.94148 - 4.23219i) q^{87} +(0.218812 - 0.153214i) q^{88} +(1.44584 - 2.50426i) q^{89} +(-0.277536 - 0.480707i) q^{91} +(10.5020 + 4.89717i) q^{92} +(-2.90774 - 8.62546i) q^{93} +(-0.0393351 - 0.0468777i) q^{94} +(-0.175707 - 0.264165i) q^{96} +(1.99162 - 4.27105i) q^{97} +(-0.102243 - 0.0273961i) 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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.00133058	−	0.0152086i	−0.000940864	−	0.0107541i	0.995710	−	0.0925315i	$-0.0294959\pi$
$2$	−0.00133058	−	0.0152086i	−0.000940864	−	0.0107541i	−0.996651	+	0.0817774i	$0.973940\pi$
$3$	1.71244	−	0.259886i	0.988679	−	0.150045i
$3$	1.71244	−	0.259886i	0.988679	−	0.150045i
$4$	1.96939	−	0.347256i	0.984693	−	0.173628i
$5$		0			0
$5$		0			0
$6$	−0.00623106	−	0.0256981i	−0.00254382	−	0.0104912i
$7$	0.148030	+	0.211408i	0.0559499	+	0.0799048i	0.846152	−	0.532941i	$-0.178913\pi$
$7$	0.148030	+	0.211408i	0.0559499	+	0.0799048i	−0.790202	+	0.612846i	$0.790025\pi$
$8$	−0.0158044	−	0.0589827i	−0.00558769	−	0.0208535i
$9$	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	$0.659667\pi$
$12$	3.28221	−	1.10647i	0.947493	−	0.319411i
$13$	−2.14258	−	0.187451i	−0.594244	−	0.0519896i	−0.213933	−	0.976848i	$-0.568627\pi$
$13$	−2.14258	−	0.187451i	−0.594244	−	0.0519896i	−0.380311	+	0.924859i	$0.624183\pi$
$14$	0.00301826	−	0.00253263i	0.000806665	−	0.000676873i
$15$		0			0
$16$	3.75746	−	1.36760i	0.939364	−	0.341901i
$17$	−0.456091	+	1.70216i	−0.110618	+	0.412833i	−0.998922	−	0.0464236i	$-0.985218\pi$
$17$	−0.456091	+	1.70216i	−0.110618	+	0.412833i	0.888303	+	0.459257i	$0.151884\pi$
$18$	−0.0173489	−	0.0423872i	−0.00408918	−	0.00999075i
$19$	−4.91894	−	2.83995i	−1.12848	−	0.651529i	−0.184929	−	0.982752i	$-0.559206\pi$
$19$	−4.91894	−	2.83995i	−1.12848	−	0.651529i	−0.943553	+	0.331222i	$0.892539\pi$
$20$		0			0
$21$	0.308434	+	0.323554i	0.0673059	+	0.0706052i
$22$	0.0605267	−	0.0282241i	0.0129043	−	0.00601740i
$23$	4.74660	+	3.32360i	0.989734	+	0.693019i	0.951946	−	0.306267i	$-0.0990800\pi$
$23$	4.74660	+	3.32360i	0.989734	+	0.693019i	0.0377879	+	0.999286i	$0.487969\pi$
$24$	−0.0423928	−	0.0968971i	−0.00865340	−	0.0197790i
$25$		0			0
$26$			0.0328351i			0.00643949i
$27$	4.67469	−	2.26876i	0.899644	−	0.436623i
$28$	0.364940	+	0.364940i	0.0689672	+	0.0689672i
$29$	−3.59567	−	3.01712i	−0.667699	−	0.560266i	0.244685	−	0.969603i	$-0.421316\pi$
$29$	−3.59567	−	3.01712i	−0.667699	−	0.560266i	−0.912383	+	0.409337i	$0.865760\pi$
$30$		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	$-0.212001\pi$
$32$	−0.0774120	−	0.166010i	−0.0136846	−	0.0293468i
$33$	3.63039	+	6.65044i	0.631969	+	1.15769i
$34$	0.0264943	+	0.00467167i	0.00454374	+	0.000801184i
$35$		0			0
$36$	5.33305	−	2.74777i	0.888841	−	0.457962i
$37$	−3.12552	−	0.837479i	−0.513832	−	0.137681i	−0.00741968	−	0.999972i	$-0.502362\pi$
$37$	−3.12552	−	0.837479i	−0.513832	−	0.137681i	−0.506412	+	0.862292i	$0.669028\pi$
$38$	−0.0366467	+	0.0785891i	−0.00594488	+	0.0127488i
$39$	−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	$0.768419\pi$
$42$	0.00451041	−	0.00512138i	0.000695972	−	0.000790246i
$43$	−8.25395	−	3.84888i	−1.25872	−	0.586948i	−0.325254	−	0.945627i	$-0.605450\pi$
$43$	−8.25395	−	3.84888i	−1.25872	−	0.586948i	−0.933461	+	0.358678i	$0.883228\pi$
$44$	4.37396	+	7.57592i	0.659400	+	1.14211i
$45$		0			0
$46$	0.0442317	−	0.0766116i	0.00652161	−	0.0112958i
$47$	3.28345	−	2.29910i	0.478941	−	0.335358i	−0.309049	−	0.951046i	$-0.600011\pi$
$47$	3.28345	−	2.29910i	0.478941	−	0.335358i	0.787990	+	0.615688i	$0.211122\pi$
$48$	6.07901	−	3.31845i	0.877429	−	0.478977i
$49$	2.37136	−	6.51526i	0.338766	−	0.930751i
$50$		0			0
$51$	−0.338664	+	3.03338i	−0.0474224	+	0.424757i
$52$	−4.28465	+	0.374859i	−0.594174	+	0.0519835i
$53$	−8.15900	+	8.15900i	−1.12072	+	1.12072i	−0.129092	+	0.991633i	$0.541206\pi$
$53$	−8.15900	+	8.15900i	−1.12072	+	1.12072i	−0.991633	+	0.129092i	$0.958794\pi$
$54$	−0.0407248	−	0.0680769i	−0.00554195	−	0.00926409i
$55$		0			0
$56$	0.0101299	−	0.0120724i	0.00135367	−	0.00161324i
$57$	−9.16146	−	3.58489i	−1.21347	−	0.474830i
$58$	−0.0411020	+	0.0586997i	−0.00539696	+	0.00770765i
$59$	−10.6146	−	3.86341i	−1.38191	−	0.502973i	−0.459152	−	0.888358i	$-0.651847\pi$
$59$	−10.6146	−	3.86341i	−1.38191	−	0.502973i	−0.922756	+	0.385385i	$0.874069\pi$
$60$		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	$0.772383\pi$
$62$	−0.0774969	+	0.0207652i	−0.00984212	+	0.00263719i
$63$	0.612263	+	0.473909i	0.0771379	+	0.0597070i
$64$	6.92336	−	3.99720i	0.865420	−	0.499650i
$65$		0			0
$66$	0.0963135	−	0.0640622i	0.0118554	−	0.00788551i
$67$	−0.160052	+	1.82940i	−0.0195534	+	0.223497i	0.980130	+	0.198354i	$0.0635595\pi$
$67$	−0.160052	+	1.82940i	−0.0195534	+	0.223497i	−0.999684	+	0.0251426i	$0.991996\pi$
$68$	−0.307136	+	3.51058i	−0.0372457	+	0.425721i
$69$	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	$0.234854\pi$
$72$	−0.0977775	−	0.154913i	−0.0115232	−	0.0182567i
$73$	13.8702	−	3.71651i	1.62338	−	0.434984i	0.671390	−	0.741104i	$-0.265697\pi$
$73$	13.8702	−	3.71651i	1.62338	−	0.434984i	0.951993	+	0.306120i	$0.0990308\pi$
$74$	−0.00857816	+	0.0486492i	−0.000997191	+	0.00565535i
$75$		0			0
$76$	−10.6735	−	3.88483i	−1.22433	−	0.445620i
$77$	−0.647552	+	0.924799i	−0.0737953	+	0.105391i
$78$	0.00853337	+	0.0562282i	0.000966214	+	0.00636659i
$79$	−1.98949	+	2.37099i	−0.223835	+	0.266757i	−0.866261	−	0.499591i	$-0.833484\pi$
$79$	−1.98949	+	2.37099i	−0.223835	+	0.266757i	0.642426	+	0.766348i	$0.277928\pi$
$80$		0			0
$81$	7.41552	−	5.10001i	0.823946	−	0.566668i
$82$	0.00406398	−	0.00406398i	0.000448791	−	0.000448791i
$83$	−4.94812	+	0.432904i	−0.543127	+	0.0475174i	−0.355418	−	0.934707i	$-0.615662\pi$
$83$	−4.94812	+	0.432904i	−0.543127	+	0.0475174i	−0.187708	+	0.982225i	$0.560106\pi$
$84$	0.719782	+	0.530096i	0.0785347	+	0.0578383i
$85$		0			0
$86$	−0.0475536	+	0.130653i	−0.00512784	+	0.0140886i
$87$	−6.94148	−	4.23219i	−0.744205	−	0.453738i
$88$	0.218812	−	0.153214i	0.0233254	−	0.0163326i
$89$	1.44584	−	2.50426i	0.153259	−	0.265452i	−0.779165	−	0.626819i	$-0.784357\pi$
$89$	1.44584	−	2.50426i	0.153259	−	0.265452i	0.932424	+	0.361367i	$0.117690\pi$
$90$		0			0
$91$	−0.277536	−	0.480707i	−0.0290937	−	0.0503917i
$92$	10.5020	+	4.89717i	1.09491	+	0.510565i
$93$	−2.90774	−	8.62546i	−0.301519	−	0.894418i
$94$	−0.0393351	−	0.0468777i	−0.00405710	−	0.00483507i
$95$		0			0
$96$	−0.175707	−	0.264165i	−0.0179331	−	0.0269612i
$97$	1.99162	−	4.27105i	0.202219	−	0.433659i	−0.778879	−	0.627175i	$-0.784211\pi$
$97$	1.99162	−	4.27105i	0.202219	−	0.433659i	0.981097	+	0.193516i	$0.0619890\pi$
$98$	−0.102243	−	0.0273961i	−0.0103282	−	0.00276742i
$99$	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	$0.509643\pi$
$102$	0.0465841	+	0.00111446i	0.00461251	+	0.000110348i
$103$	−4.26799	−	9.15274i	−0.420538	−	0.901846i	−0.996438	−	0.0843263i	$-0.973126\pi$
$103$	−4.26799	−	9.15274i	−0.420538	−	0.901846i	0.575900	−	0.817520i	$-0.304652\pi$
$104$	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	0.999618	+	0.0276498i	$0.00880233\pi$
$107$	10.6261	+	10.6261i	1.02727	+	1.02727i	0.0276498	+	0.999618i	$0.491198\pi$
$108$	8.41843	−	6.09138i	0.810064	−	0.586143i
$109$			12.0030i			1.14968i	0.818265	+	0.574841i	$0.194936\pi$
$109$			12.0030i			1.14968i	−0.818265	+	0.574841i	$0.805064\pi$
$110$		0			0
$111$	−5.56991	−	0.621858i	−0.528673	−	0.0590241i
$112$	0.845337	+	0.591912i	0.0798769	+	0.0559304i
$113$	−8.41851	+	3.92562i	−0.791947	+	0.369291i	−0.776121	−	0.630584i	$-0.782816\pi$
$113$	−8.41851	+	3.92562i	−0.791947	+	0.369291i	−0.0158260	+	0.999875i	$0.505038\pi$
$114$	−0.0423312	+	0.144103i	−0.00396468	+	0.0134965i
$115$		0			0
$116$	−8.12897	−	4.69326i	−0.754756	−	0.435759i
$117$	−6.30515	+	1.37003i	−0.582912	+	0.126659i
$118$	−0.0446336	+	0.166575i	−0.00410885	+	0.0153344i
$119$	−0.427365	+	0.155548i	−0.0391765	+	0.0142591i
$120$		0			0
$121$	−6.23254	+	5.22972i	−0.566595	+	0.475429i
$122$	0.184548	+	0.0161459i	0.0167082	+	0.00146178i
$123$	0.489332	+	0.430956i	0.0441216	+	0.0388580i
$124$	−3.59440	−	9.87552i	−0.322786	−	0.886848i
$125$		0			0
$126$	0.00639285	−	0.00994226i	0.000569520	−	0.000885727i
$127$	5.03035	+	18.7735i	0.446371	+	1.66588i	0.712290	+	0.701885i	$0.247658\pi$
$127$	5.03035	+	18.7735i	0.446371	+	1.66588i	−0.265918	+	0.963996i	$0.585675\pi$
$128$	−0.280131	−	0.400068i	−0.0247603	−	0.0353614i
$129$	−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	$0.508372\pi$
$132$	9.45903	+	11.8366i	0.823303	+	1.03024i
$133$	−0.127760	−	1.46030i	−0.0110782	−	0.126624i
$134$	0.0280356			0.00242191
$135$		0			0
$136$	0.107606			0.00922713
$137$	−0.609750	−	6.96948i	−0.0520945	−	0.595443i	−0.976713	−	0.214549i	$-0.931172\pi$
$137$	−0.609750	−	6.96948i	−0.0520945	−	0.595443i	0.924619	−	0.380894i	$-0.124384\pi$
$138$	0.0558340	−	0.142688i	0.00475291	−	0.0121464i
$139$	8.03836	−	1.41738i	0.681805	−	0.120221i	0.177990	−	0.984032i	$-0.443041\pi$
$139$	8.03836	−	1.41738i	0.681805	−	0.120221i	0.503815	+	0.863812i	$0.331929\pi$
$140$		0			0
$141$	5.02522	−	4.79040i	0.423200	−	0.403424i
$142$	−0.0449306	−	0.0641675i	−0.00377049	−	0.00538482i
$143$	−2.43508	−	9.08786i	−0.203632	−	0.759965i
$144$	9.54753	−	7.26250i	0.795628	−	0.605209i
$145$		0			0
$146$	−0.0749784	−	0.206002i	−0.00620526	−	0.0170488i
$147$	2.36759	−	11.7733i	0.195276	−	0.971045i
$148$	−6.44617	−	0.563966i	−0.529872	−	0.0463578i
$149$	−14.7726	+	12.3956i	−1.21021	+	1.01549i	−0.210937	+	0.977500i	$0.567651\pi$
$149$	−14.7726	+	12.3956i	−1.21021	+	1.01549i	−0.999278	+	0.0379911i	$0.987904\pi$
$150$		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	$0.598193\pi$
$152$	−0.0897672	+	0.335016i	−0.00728108	+	0.0271734i
$153$	0.208389	+	5.28249i	0.0168473	+	0.427064i
$154$	0.0149266	+	0.00861785i	0.00120282	+	0.000694446i
$155$		0			0
$156$	−7.23980	+	1.75544i	−0.579648	+	0.140548i
$157$	−2.11753	+	0.987420i	−0.168997	+	0.0788047i	−0.505276	−	0.862958i	$-0.668609\pi$
$157$	−2.11753	+	0.987420i	−0.168997	+	0.0788047i	0.336279	+	0.941762i	$0.390832\pi$
$158$	0.0387066	+	0.0271027i	0.00307933	+	0.00215617i
$159$	−11.8514	+	16.0922i	−0.939878	+	1.27620i
$160$		0			0
$161$			1.49546i			0.117859i
$162$	−0.0874311	−	0.105994i	−0.00686924	−	0.00832767i
$163$	−10.7302	−	10.7302i	−0.840451	−	0.840451i	0.148467	−	0.988917i	$-0.452566\pi$
$163$	−10.7302	−	10.7302i	−0.840451	−	0.840451i	−0.988917	+	0.148467i	$0.952566\pi$
$164$	0.576705	+	0.483913i	0.0450331	+	0.0377872i
$165$		0			0
$166$	0.0131678	+	0.0746781i	0.00102202	+	0.00579615i
$167$	−8.20013	−	17.5852i	−0.634545	−	1.36079i	−0.915987	−	0.401208i	$-0.868590\pi$
$167$	−8.20013	−	17.5852i	−0.634545	−	1.36079i	0.281442	−	0.959578i	$-0.409187\pi$
$168$	0.0142095	−	0.0233058i	0.00109628	−	0.00179808i
$169$	−8.24701	−	1.45417i	−0.634385	−	0.111859i
$170$		0			0
$171$	−16.6201	−	3.75798i	−1.27097	−	0.287380i
$172$	−17.5918	−	4.71370i	−1.34136	−	0.359416i
$173$	−2.45707	+	5.26921i	−0.186808	+	0.400610i	−0.977300	−	0.211862i	$-0.932047\pi$
$173$	−2.45707	+	5.26921i	−0.186808	+	0.400610i	0.790492	+	0.612472i	$0.209825\pi$
$174$	−0.0551296	+	0.111202i	−0.00417936	+	0.00843018i
$175$		0			0
$176$	11.2435	+	13.3995i	0.847510	+	1.01002i
$177$	−19.1810	−	3.85728i	−1.44173	−	0.289931i
$178$	−0.0400103	−	0.0186571i	−0.00299890	−	0.00139841i
$179$	4.77974	+	8.27875i	0.357254	+	0.618783i	0.987501	−	0.157612i	$-0.0503796\pi$
$179$	4.77974	+	8.27875i	0.357254	+	0.618783i	−0.630247	+	0.776395i	$0.717046\pi$
$180$		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	$-0.00582219\pi$
$182$	−0.00694161	+	0.00486056i	−0.000514546	+	0.000360289i
$183$	−0.502668	+	21.0115i	−0.0371583	+	1.55321i
$184$	0.121018	−	0.332494i	0.00892157	−	0.0245118i
$185$		0			0
$186$	−0.127312	+	0.0556997i	−0.00933500	+	0.00408410i
$187$	−7.67937	+	0.671857i	−0.561571	+	0.0491311i
$188$	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	$0.363611\pi$
$192$	10.8170	−	8.64426i	0.780652	−	0.623846i
$193$	6.94425	−	9.91741i	0.499858	−	0.713871i	−0.487368	−	0.873197i	$-0.662043\pi$
$193$	6.94425	−	9.91741i	0.499858	−	0.713871i	0.987226	+	0.159325i	$0.0509319\pi$
$194$	−0.0676068	−	0.0246069i	−0.00485389	−	0.00176667i
$195$		0			0
$196$	2.40766	−	13.6545i	0.171976	−	0.975323i
$197$	−5.74222	+	1.53862i	−0.409116	+	0.109622i	−0.457507	−	0.889206i	$-0.651257\pi$
$197$	−5.74222	+	1.53862i	−0.409116	+	0.109622i	0.0483907	+	0.998828i	$0.484591\pi$
$198$	0.148283	−	0.134733i	0.0105380	−	0.00957508i
$199$	4.84519	−	2.79737i	0.343466	−	0.198300i	−0.318337	−	0.947977i	$-0.603124\pi$
$199$	4.84519	−	2.79737i	0.343466	−	0.198300i	0.661804	+	0.749677i	$0.269791\pi$
$200$		0			0
$201$	0.201356	+	3.17433i	0.0142025	+	0.223900i
$202$	0.00384421	−	0.0439395i	0.000270478	−	0.00309157i
$203$	0.105579	−	1.20678i	0.00741022	−	0.0846992i
$204$	0.386398	+	6.09149i	0.0270533	+	0.426490i
$205$		0			0
$206$	−0.133522	+	0.0770888i	−0.00930290	+	0.00537103i
$207$	16.5569	+	5.29700i	1.15078	+	0.368167i
$208$	−8.30699	+	2.22585i	−0.575986	+	0.154335i
$209$	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	$0.548464\pi$
$212$	−13.2350	+	18.9015i	−0.908980	+	1.29816i
$213$	6.94267	−	5.54813i	0.475704	−	0.380151i
$214$	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
$218$	0.182550	−	0.0159710i	0.0123638	−	0.00108169i
$219$	22.7860	−	9.96897i	1.53974	−	0.673641i
$220$		0			0
$221$	1.29628	−	3.56150i	0.0871973	−	0.239573i
$222$	−0.00204637	+	0.0855382i	−0.000137344	+	0.00574095i
$223$	−10.8010	+	7.56295i	−0.723289	+	0.506452i	−0.876296	−	0.481773i	$-0.839993\pi$
$223$	−10.8010	+	7.56295i	−0.723289	+	0.506452i	0.153007	+	0.988225i	$0.451104\pi$
$224$	0.0236367	−	0.0409400i	0.00157929	−	0.00273542i
$225$		0			0
$226$	0.0709048	+	0.122811i	0.00471652	+	0.00816925i
$227$	−13.2080	−	6.15899i	−0.876646	−	0.408787i	−0.0684181	−	0.997657i	$-0.521795\pi$
$227$	−13.2080	−	6.15899i	−0.876646	−	0.408787i	−0.808228	+	0.588870i	$0.799573\pi$
$228$	−19.2873	−	3.87866i	−1.27733	−	0.256870i
$229$	−5.35302	−	6.37948i	−0.353738	−	0.421568i	0.559605	−	0.828759i	$-0.310953\pi$
$229$	−5.35302	−	6.37948i	−0.353738	−	0.421568i	−0.913343	+	0.407191i	$0.866508\pi$
$230$		0			0
$231$	−0.868552	+	1.75196i	−0.0571466	+	0.115270i
$232$	−0.121131	+	0.259766i	−0.00795262	+	0.0170545i
$233$	26.7094	+	7.15675i	1.74979	+	0.468854i	0.984581	−	0.174930i	$-0.0559699\pi$
$233$	26.7094	+	7.15675i	1.74979	+	0.468854i	0.765207	+	0.643784i	$0.222637\pi$
$234$	0.0292258	+	0.0940698i	0.00191055	+	0.00614954i
$235$		0			0
$236$	−22.2459	−	3.92255i	−1.44808	−	0.255336i
$237$	−2.79071	+	4.57722i	−0.181276	+	0.297322i
$238$	0.00293432	+	0.00629266i	0.000190204	+	0.000407893i
$239$	3.76477	+	21.3510i	0.243522	+	1.38108i	0.823899	+	0.566736i	$0.191794\pi$
$239$	3.76477	+	21.3510i	0.243522	+	1.38108i	−0.580377	+	0.814348i	$0.697095\pi$
$240$		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
$243$	11.3732	−	10.6607i	0.729593	−	0.683882i
$244$			24.2661i			1.55348i
$245$		0			0
$246$	0.00590315	−	0.00801549i	0.000376371	−	0.000511049i
$247$	10.0068	+	7.00687i	0.636721	+	0.445837i
$248$	−0.290838	+	0.135620i	−0.0184682	+	0.00861188i
$249$	−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	$0.521596\pi$
$252$	1.37035	+	0.720698i	0.0863239	+	0.0453997i
$253$	−6.56054	+	24.4843i	−0.412458	+	1.53931i
$254$	0.278826	−	0.101484i	0.0174951	−	0.00636770i
$255$		0			0
$256$	12.2424	−	10.2726i	0.765152	−	0.642039i
$257$	9.33717	+	0.816897i	0.582437	+	0.0509566i	0.374567	−	0.927200i	$-0.377791\pi$
$257$	9.33717	+	0.816897i	0.582437	+	0.0509566i	0.207870	+	0.978156i	$0.433347\pi$
$258$	−0.0474781	+	0.236093i	−0.00295586	+	0.0146985i
$259$	−0.285619	−	0.784731i	−0.0177475	−	0.0487608i
$260$		0			0
$261$	−12.9868	−	5.44338i	−0.803861	−	0.336937i
$262$	0.0180436	+	0.0673396i	0.00111474	+	0.00416025i
$263$	−5.75656	−	8.22122i	−0.354965	−	0.506942i	0.601467	−	0.798897i	$-0.294583\pi$
$263$	−5.75656	−	8.22122i	−0.354965	−	0.506942i	−0.956432	+	0.291955i	$0.905694\pi$
$264$	0.334885	−	0.319236i	0.0206107	−	0.0196476i
$265$		0			0
$266$	−0.0220392	+	0.00388610i	−0.00135131	+	0.000238272i
$267$	1.82509	−	4.66416i	0.111694	−	0.285442i
$268$	0.320066	+	3.65837i	0.0195511	+	0.223470i
$269$	1.84882			0.112724			0.0563622	−	0.998410i	$-0.482050\pi$
$269$	1.84882			0.112724			0.0563622	+	0.998410i	$0.482050\pi$
$270$		0			0
$271$	14.0068			0.850851			0.425426	−	0.904993i	$-0.360124\pi$
$271$	14.0068			0.850851			0.425426	+	0.904993i	$0.360124\pi$
$272$	0.614129	+	7.01953i	0.0372370	+	0.425621i
$273$	−0.600193	−	0.751055i	−0.0363254	−	0.0454559i
$274$	−0.105185	+	0.0185469i	−0.00635445	+	0.00112046i
$275$		0			0
$276$	19.2568	+	5.65680i	1.15912	+	0.340499i
$277$	−10.4313	−	14.8975i	−0.626758	−	0.895103i	0.372703	−	0.927951i	$-0.378431\pi$
$277$	−10.4313	−	14.8975i	−0.626758	−	0.895103i	−0.999460	+	0.0328481i	$0.989542\pi$
$278$	−0.0322521	−	0.120367i	−0.00193435	−	0.00721911i
$279$	−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	$-0.397537\pi$
$282$	−0.0795419	−	0.0700527i	−0.00473665	−	0.00417158i
$283$	18.2738	+	1.59875i	1.08627	+	0.0950360i	0.616196	−	0.787593i	$-0.288673\pi$
$283$	18.2738	+	1.59875i	1.08627	+	0.0950360i	0.470071	+	0.882629i	$0.344228\pi$
$284$	7.86028	−	6.59556i	0.466422	−	0.391374i
$285$		0			0
$286$	−0.134974	+	0.0491264i	−0.00798117	+	0.00290491i
$287$	−0.0251463	+	0.0938472i	−0.00148434	+	0.00553962i
$288$	−0.369541	−	0.406704i	−0.0217754	−	0.0239652i
$289$	12.0331	+	6.94732i	0.707830	+	0.408666i
$290$		0			0
$291$	2.30055	−	7.83152i	0.134861	−	0.459092i
$292$	26.0252	−	12.1357i	1.52301	−	0.710191i
$293$	−8.60861	−	6.02781i	−0.502920	−	0.352149i	0.294422	−	0.955675i	$-0.404873\pi$
$293$	−8.60861	−	6.02781i	−0.502920	−	0.352149i	−0.797343	+	0.603527i	$0.793762\pi$
$294$	−0.182206	−	0.0203425i	−0.0106265	−	0.00118640i
$295$		0			0
$296$			0.197587i			0.0114845i
$297$	16.3202	+	15.8216i	0.946993	+	0.918064i
$298$	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
$302$	0.0969127	+	0.207830i	0.00557670	+	0.0119593i
$303$	5.00267	+	0.119681i	0.287396	+	0.00687551i
$304$	−22.3666	−	3.94384i	−1.28281	−	0.226195i
$305$		0			0
$306$	0.0800623	−	0.0101981i	0.00457685	−	0.000582987i
$307$	12.3714	+	3.31491i	0.706074	+	0.189192i	0.593949	−	0.804502i	$-0.297568\pi$
$307$	12.3714	+	3.31491i	0.706074	+	0.189192i	0.112124	+	0.993694i	$0.464235\pi$
$308$	−0.954137	+	2.04615i	−0.0543670	+	0.116590i
$309$	−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	$0.574722\pi$
$312$	0.0726664	+	0.215556i	0.00411392	+	0.0122035i
$313$	26.7887	+	12.4918i	1.51419	+	0.706078i	0.989408	−	0.145159i	$-0.0463694\pi$
$313$	26.7887	+	12.4918i	1.51419	+	0.706078i	0.524781	+	0.851237i	$0.324147\pi$
$314$	0.0178349	+	0.0308909i	0.00100648	+	0.00174327i
$315$		0			0
$316$	−3.09474	+	5.36025i	−0.174093	+	0.301538i
$317$	21.7523	−	15.2311i	1.22173	−	0.855465i	0.228720	−	0.973492i	$-0.426546\pi$
$317$	21.7523	−	15.2311i	1.22173	−	0.855465i	0.993010	+	0.118027i	$0.0376571\pi$
$318$	0.260510	+	0.158832i	0.0146087	+	0.00890684i
$319$	7.02268	−	19.2947i	0.393195	−	1.08029i
$320$		0			0
$321$	20.9582	+	15.4351i	1.16977	+	0.861501i
$322$	0.0227439	−	0.00198984i	0.00126747	−	0.000110889i
$323$	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
$327$	3.11942	+	20.5545i	0.172504	+	1.13667i
$328$	0.0131854	−	0.0188306i	0.000728040	−	0.00103975i
$329$	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	$0.967460\pi$
$332$	−9.59443	+	2.57082i	−0.526563	+	0.141092i
$333$	−9.69977	+	0.382646i	−0.531544	+	0.0209689i
$334$	−0.256536	+	0.148111i	−0.0140371	+	0.00810430i
$335$		0			0
$336$	1.60142	+	0.793923i	0.0873647	+	0.0433121i
$337$	1.22264	−	13.9748i	0.0666015	−	0.761258i	−0.887311	−	0.461172i	$-0.847429\pi$
$337$	1.22264	−	13.9748i	0.0666015	−	0.761258i	0.953912	−	0.300086i	$-0.0970154\pi$
$338$	−0.0111426	+	0.127361i	−0.000606078	+	0.00692750i
$339$	−13.3960	+	8.91025i	−0.727571	+	0.483938i
$340$		0			0
$341$	19.9091	−	11.4945i	1.07814	−	0.622463i
$342$	−0.0350393	+	0.257770i	−0.00189471	+	0.0139386i
$343$	3.47343	−	0.930702i	0.187547	−	0.0502532i
$344$	−0.0965688	+	0.547669i	−0.00520664	+	0.0295283i
$345$		0			0
$346$	0.0834068	+	0.0303576i	0.00448397	+	0.00163203i
$347$	−3.50208	+	5.00149i	−0.188001	+	0.268494i	−0.902077	−	0.431574i	$-0.857958\pi$
$347$	−3.50208	+	5.00149i	−0.188001	+	0.268494i	0.714076	+	0.700068i	$0.246847\pi$
$348$	−15.1401	−	5.92434i	−0.811595	−	0.317578i
$349$	−2.45708	+	2.92823i	−0.131524	+	0.156745i	−0.827787	−	0.561042i	$-0.810400\pi$
$349$	−2.45708	+	2.92823i	−0.131524	+	0.156745i	0.696263	+	0.717787i	$0.254845\pi$
$350$		0			0
$351$	−10.4412	+	3.98472i	−0.557308	+	0.212689i
$352$	0.566592	−	0.566592i	0.0301995	−	0.0301995i
$353$	2.21879	−	0.194119i	0.118094	−	0.0103319i	−0.0279554	−	0.999609i	$-0.508900\pi$
$353$	2.21879	−	0.194119i	0.118094	−	0.0103319i	0.146050	+	0.989277i	$0.453344\pi$
$354$	−0.0331420	+	0.296849i	−0.00176148	+	0.0157774i
$355$		0			0
$356$	1.97779	−	5.43394i	0.104823	−	0.287998i
$357$	−0.691413	+	0.377433i	−0.0365934	+	0.0199759i
$358$	0.119549	−	0.0837088i	0.00631834	−	0.00442415i
$359$	5.90045	−	10.2199i	0.311414	−	0.539385i	−0.667255	−	0.744829i	$-0.732531\pi$
$359$	5.90045	−	10.2199i	0.311414	−	0.539385i	0.978669	+	0.205445i	$0.0658641\pi$
$360$		0			0
$361$	6.63064	+	11.4846i	0.348981	+	0.604453i
$362$	−0.192015	−	0.0895381i	−0.0100921	−	0.00470602i
$363$	−9.31374	+	10.5753i	−0.488844	+	0.555062i
$364$	−0.713504	−	0.850321i	−0.0373978	−	0.0445689i
$365$		0			0
$366$	0.320225	−	0.0203126i	0.0167384	−	0.00106176i
$367$	0.896047	−	1.92158i	0.0467733	−	0.100306i	−0.881532	−	0.472123i	$-0.843488\pi$
$367$	0.896047	−	1.92158i	0.0467733	−	0.100306i	0.928306	+	0.371818i	$0.121265\pi$
$368$	22.3805	+	5.99683i	1.16666	+	0.312607i
$369$	0.949952	+	0.610817i	0.0494525	+	0.0317978i
$370$		0			0
$371$	−2.93265	−	0.517106i	−0.152256	−	0.0268468i
$372$	−8.72170	−	15.9771i	−0.452199	−	0.828376i
$373$	−1.40277	−	3.00825i	−0.0726328	−	0.155762i	0.866639	−	0.498936i	$-0.166276\pi$
$373$	−1.40277	−	3.00825i	−0.0726328	−	0.155762i	−0.939272	+	0.343174i	$0.888498\pi$
$374$	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
$378$	0.00836353	−	0.0186870i	0.000430173	−	0.000961153i
$379$			15.7634i			0.809713i	0.914380	+	0.404856i	$0.132678\pi$
$379$			15.7634i			0.809713i	−0.914380	+	0.404856i	$0.867322\pi$
$380$		0			0
$381$	13.4932	+	30.8413i	0.691276	+	1.58005i
$382$	0.148541	+	0.104009i	0.00760001	+	0.00532158i
$383$	−24.9622	+	11.6401i	−1.27551	+	0.594781i	−0.938031	−	0.346552i	$-0.887352\pi$
$383$	−24.9622	+	11.6401i	−1.27551	+	0.594781i	−0.337480	+	0.941333i	$0.609575\pi$
$384$	−0.583680	−	0.612292i	−0.0297858	−	0.0312459i
$385$		0			0
$386$	−0.160070	−	0.0924166i	−0.00814736	−	0.00470388i
$387$	−27.0727	−	3.68006i	−1.37618	−	0.187068i
$388$	2.43913	−	9.10294i	0.123828	−	0.462132i
$389$	28.2091	−	10.2673i	1.43026	−	0.520571i	0.493252	−	0.869886i	$-0.335808\pi$
$389$	28.2091	−	10.2673i	1.43026	−	0.520571i	0.937005	+	0.349315i	$0.113586\pi$
$390$		0			0
$391$	−7.82217	+	6.56358i	−0.395584	+	0.331934i
$392$	−0.421765	−	0.0368997i	−0.0213024	−	0.00186372i
$393$	−7.49494	+	2.52663i	−0.378070	+	0.127452i
$394$	0.0310408	+	0.0852840i	0.00156382	+	0.00429655i
$395$		0			0
$396$	19.2742	+	17.8112i	0.968566	+	0.895048i
$397$	1.23812	+	4.62074i	0.0621397	+	0.231908i	0.990011	−	0.140993i	$-0.0450296\pi$
$397$	1.23812	+	4.62074i	0.0621397	+	0.231908i	−0.927871	+	0.372902i	$0.878363\pi$
$398$	−0.0489911	−	0.0699666i	−0.00245570	−	0.00350711i
$399$	−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	$0.513355\pi$
$402$	0.0480094	−	0.00728606i	0.00239449	−	0.000363396i
$403$	0.985106	+	11.2598i	0.0490716	+	0.560891i
$404$	5.77756			0.287444
$405$		0			0
$406$	−0.0184939			−0.000917838
$407$	−1.23367	−	14.1009i	−0.0611508	−	0.698957i
$408$	0.184269	−	0.0279653i	0.00912267	−	0.00138449i
$409$	8.33076	−	1.46894i	0.411930	−	0.0726343i	0.0361568	−	0.999346i	$-0.488488\pi$
$409$	8.33076	−	1.46894i	0.411930	−	0.0726343i	0.375773	+	0.926712i	$0.377377\pi$
$410$		0			0
$411$	−2.85543	−	11.7764i	−0.140848	−	0.580885i
$412$	−11.5837	−	16.5432i	−0.570686	−	0.815024i
$413$	−0.754524	−	2.81592i	−0.0371277	−	0.138562i
$414$	0.0585299	−	0.258856i	0.00287659	−	0.0127221i
$415$		0			0
$416$	0.134742	+	0.370201i	0.00660628	+	0.0181506i
$417$	13.3969	−	4.51624i	0.656048	−	0.221161i
$418$	−0.377882	−	0.0330604i	−0.0184828	−	0.00161704i
$419$	6.72816	−	5.64560i	0.328692	−	0.275806i	−0.463475	−	0.886110i	$-0.653397\pi$
$419$	6.72816	−	5.64560i	0.328692	−	0.275806i	0.792167	+	0.610305i	$0.208953\pi$
$420$		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	$0.384440\pi$
$422$	0.0224469	−	0.0837730i	0.00109270	−	0.00407800i
$423$	7.36045	−	9.50926i	0.357877	−	0.462356i
$424$	0.610187	+	0.352292i	0.0296333	+	0.0171088i
$425$		0			0
$426$	−0.0936172	−	0.0982063i	−0.00453577	−	0.00475811i
$427$	−2.83827	+	1.32351i	−0.137353	+	0.0640489i
$428$	24.6170	+	17.2370i	1.18991	+	0.833181i
$429$	−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	$-0.205783\pi$
$432$	14.4622	−	14.9179i	0.695812	−	0.717737i
$433$	24.9892	+	24.9892i	1.20090	+	1.20090i	0.973892	+	0.227011i	$0.0728954\pi$
$433$	24.9892	+	24.9892i	1.20090	+	1.20090i	0.227011	+	0.973892i	$0.427105\pi$
$434$	−0.0158618	−	0.0133096i	−0.000761390	−	0.000638882i
$435$		0			0
$436$	4.16812	+	23.6386i	0.199617	+	1.13208i
$437$	−13.9093	−	29.8287i	−0.665374	−	1.42690i
$438$	−0.181933	−	0.333280i	−0.00869310	−	0.0159247i
$439$	−4.64923	−	0.819785i	−0.221896	−	0.0391262i	0.0615948	−	0.998101i	$-0.480381\pi$
$439$	−4.64923	−	0.819785i	−0.221896	−	0.0391262i	−0.283491	+	0.958975i	$0.591492\pi$
$440$		0			0
$441$	0.994657	−	20.7764i	0.0473646	−	0.989352i
$442$	−0.0558904	−	0.0149758i	−0.00265844	−	0.000712326i
$443$	12.4959	−	26.7976i	0.593700	−	1.27319i	−0.348238	−	0.937406i	$-0.613220\pi$
$443$	12.4959	−	26.7976i	0.593700	−	1.27319i	0.941938	−	0.335787i	$-0.109002\pi$
$444$	−11.1853	+	0.709507i	−0.530829	+	0.0336717i
$445$		0			0
$446$	0.129394	+	0.154205i	0.00612697	+	0.00730184i
$447$	−22.0757	+	25.0660i	−1.04414	+	1.18558i
$448$	1.86990	+	0.871951i	0.0883447	+	0.0411958i
$449$	3.36725	+	5.83225i	0.158910	+	0.275241i	0.934476	−	0.356026i	$-0.115869\pi$
$449$	3.36725	+	5.83225i	0.158910	+	0.275241i	−0.775566	+	0.631267i	$0.782535\pi$
$450$		0			0
$451$	−0.823409	+	1.42619i	−0.0387728	+	0.0671565i
$452$	−15.2161	+	10.6544i	−0.715706	+	0.501142i
$453$	−22.8355	+	12.4656i	−1.07291	+	0.585685i
$454$	−0.0760955	+	0.209071i	−0.00357134	+	0.00981217i
$455$		0			0
$456$	−0.0666553	+	0.597025i	−0.00312142	+	0.0279582i
$457$	36.1208	−	3.16016i	1.68966	−	0.147826i	0.798647	−	0.601800i	$-0.205550\pi$
$457$	36.1208	−	3.16016i	1.68966	−	0.147826i	0.891015	+	0.453974i	$0.149994\pi$
$458$	−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	$0.0112755\pi$
$462$	0.0278005	+	0.0108784i	0.00129340	+	0.000506108i
$463$	−6.89825	+	9.85172i	−0.320589	+	0.457848i	−0.946808	−	0.321799i	$-0.895713\pi$
$463$	−6.89825	+	9.85172i	−0.320589	+	0.457848i	0.626219	+	0.779647i	$0.284601\pi$
$464$	−17.6368	−	6.41927i	−0.818767	−	0.298007i
$465$		0			0
$466$	0.0733054	−	0.415735i	0.00339581	−	0.0192586i
$467$	10.6775	−	2.86104i	0.494098	−	0.132393i	−0.00316149	−	0.999995i	$-0.501006\pi$
$467$	10.6775	−	2.86104i	0.494098	−	0.132393i	0.497260	+	0.867602i	$0.334340\pi$
$468$	−11.9415	+	4.88762i	−0.551997	+	0.225930i
$469$	−0.410442	+	0.236969i	−0.0189525	+	0.0109422i
$470$		0			0
$471$	−3.36953	+	2.24122i	−0.155260	+	0.103270i
$472$	−0.0601168	+	0.687138i	−0.00276710	+	0.0316281i
$473$	3.47222	−	39.6877i	0.159653	−	1.82484i
$474$	0.0733265	+	0.0363525i	0.00336800	+	0.00166972i
$475$		0			0
$476$	−0.787631	+	0.454739i	−0.0361010	+	0.0208429i
$477$	−16.1127	+	30.6370i	−0.737750	+	1.40277i
$478$	0.319711	−	0.0856663i	0.0146232	−	0.00391828i
$479$	−0.735877	+	4.17337i	−0.0336231	+	0.190686i	−0.996993	−	0.0774895i	$-0.975310\pi$
$479$	−0.735877	+	4.17337i	−0.0336231	+	0.190686i	0.963370	+	0.268175i	$0.0864207\pi$
$480$		0			0
$481$	6.53967	+	2.38024i	0.298183	+	0.108530i
$482$	0.0457155	−	0.0652884i	0.00208228	−	0.00297381i
$483$	0.388649	+	2.56089i	0.0176842	+	0.116525i
$484$	−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	−0.976263	−	0.216587i	$-0.930507\pi$
$487$	−16.7646	+	16.7646i	−0.759676	+	0.759676i	0.216587	+	0.976263i	$0.430507\pi$
$488$	0.738151	−	0.0645798i	0.0334145	−	0.00292339i
$489$	−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	$0.0964599\pi$
$492$	1.11334	+	0.678795i	0.0501930	+	0.0306024i
$493$	6.77556	−	4.74430i	0.305156	−	0.213673i
$494$	0.0932500	−	0.161514i	0.00419552	−	0.00726685i
$495$		0			0
$496$	−10.5069	−	18.1984i	−0.471772	−	0.817133i
$497$	1.20016	+	0.559642i	0.0538343	+	0.0251034i
$498$	0.0419568	+	0.124460i	0.00188013	+	0.00557718i
$499$	8.77600	+	10.4588i	0.392868	+	0.468202i	0.925832	−	0.377937i	$-0.123366\pi$
$499$	8.77600	+	10.4588i	0.392868	+	0.468202i	−0.532964	+	0.846138i	$0.678922\pi$
$500$		0			0
$501$	−18.6124	−	27.9826i	−0.831541	−	1.25017i
$502$	0.0899812	−	0.192965i	0.00401606	−	0.00861246i
$503$	−42.9050	−	11.4964i	−1.91304	−	0.512597i	−0.992552	−	0.121825i	$-0.961125\pi$
$503$	−42.9050	−	11.4964i	−1.91304	−	0.512597i	−0.920487	−	0.390772i	$-0.872208\pi$
$504$	0.0182760	−	0.0436027i	0.000814078	−	0.00194222i
$505$		0			0
$506$	0.381102	+	0.0671985i	0.0169420	+	0.00298734i
$507$	−14.5004	−	0.346901i	−0.643987	−	0.0154064i
$508$	16.4259	+	35.2255i	0.728782	+	1.56288i
$509$	0.883595	+	5.01112i	0.0391647	+	0.222114i	0.998108	−	0.0614836i	$-0.0195832\pi$
$509$	0.883595	+	5.01112i	0.0391647	+	0.222114i	−0.958943	+	0.283597i	$0.908472\pi$
$510$		0			0
$511$	2.83890	+	2.38212i	0.125586	+	0.105379i
$512$	−0.863214	−	0.863214i	−0.0381490	−	0.0381490i
$513$	−29.4377	−	2.11599i	−1.29971	−	0.0934231i
$514$		−	0.143093i		−	0.00631155i
$515$		0			0
$516$	−31.3499	−	3.50008i	−1.38010	−	0.154083i
$517$	14.3634	+	10.0573i	0.631700	+	0.442321i
$518$	−0.0115547	+	0.00538802i	−0.000507682	+	0.000236736i
$519$	−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	$0.789862\pi$
$522$	−0.0655064	+	0.204754i	−0.00286714	+	0.00896184i
$523$	3.45799	−	12.9054i	0.151207	−	0.564314i	−0.848193	−	0.529688i	$-0.822309\pi$
$523$	3.45799	−	12.9054i	0.151207	−	0.564314i	0.999400	−	0.0346265i	$-0.0110241\pi$
$524$	−8.58116	+	3.12329i	−0.374870	+	0.136441i
$525$		0			0
$526$	−0.117374	+	0.0984884i	−0.00511775	+	0.00429430i
$527$	9.22560	+	0.807135i	0.401873	+	0.0351594i
$528$	22.7362	+	20.0238i	0.989465	+	0.871424i
$529$	3.61738	+	9.93866i	0.157277	+	0.432116i
$530$		0			0
$531$	−33.8488	−	1.62049i	−1.46891	−	0.0703233i
$532$	−0.758707	−	2.83153i	−0.0328941	−	0.122762i
$533$	−0.464412	−	0.663249i	−0.0201159	−	0.0287285i
$534$	−0.0733640	−	0.0215511i	−0.00317477	−	0.000932607i
$535$		0			0
$536$	0.110432	−	0.0194722i	0.00476995	−	0.000841071i
$537$	10.3366	+	12.9347i	0.446055	+	0.558173i
$538$	−0.00246001	−	0.0281180i	−0.000106058	−	0.00121225i
$539$	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	$0.451189\pi$
$542$	−0.0186372	−	0.213024i	−0.000800535	−	0.00915016i
$543$	8.75888	−	22.3840i	0.375879	−	0.960589i
$544$	0.317883	−	0.0560513i	0.0136291	−	0.00240318i
$545$		0			0
$546$	−0.0106239	+	0.0101275i	−0.000454661	+	0.000433415i
$547$	5.89172	+	8.41425i	0.251912	+	0.359767i	0.925113	−	0.379692i	$-0.123970\pi$
$547$	5.89172	+	8.41425i	0.251912	+	0.359767i	−0.673201	+	0.739459i	$0.735081\pi$
$548$	−3.62103	−	13.5139i	−0.154683	−	0.577283i
$549$	4.59979	+	36.1116i	0.196314	+	1.54120i
$550$		0			0
$551$	9.11839	+	25.0526i	0.388456	+	1.06728i
$552$	0.120826	−	0.600828i	0.00514269	−	0.0255730i
$553$	−0.795750	−	0.0696191i	−0.0338387	−	0.00296050i
$554$	−0.212691	+	0.178469i	−0.00903636	+	0.00758240i
$555$		0			0
$556$	15.3384	−	5.58274i	0.650495	−	0.236761i
$557$	1.48759	−	5.55174i	0.0630310	−	0.235235i	−0.927223	−	0.374511i	$-0.877811\pi$
$557$	1.48759	−	5.55174i	0.0630310	−	0.235235i	0.990254	+	0.139276i	$0.0444774\pi$
$558$	−0.203540	+	0.128469i	−0.00861652	+	0.00543853i
$559$	16.9632	+	9.79373i	0.717468	+	0.414230i
$560$		0			0
$561$	−12.9759	+	3.14628i	−0.547841	+	0.132836i
$562$	−0.363321	+	0.169419i	−0.0153258	+	0.00714652i
$563$	20.2152	+	14.1548i	0.851969	+	0.596555i	0.915903	−	0.401399i	$-0.131476\pi$
$563$	20.2152	+	14.1548i	0.851969	+	0.596555i	−0.0639343	+	0.997954i	$0.520365\pi$
$564$	8.23311	−	11.1792i	0.346676	−	0.470728i
$565$		0			0
$566$		−	0.280047i		−	0.0117713i
$567$	2.17590	+	0.812749i	0.0913792	+	0.0341322i
$568$	−0.221549	−	0.221549i	−0.00929600	−	0.00929600i
$569$	−1.46173	−	1.22654i	−0.0612790	−	0.0514192i	0.611634	−	0.791141i	$-0.290513\pi$
$569$	−1.46173	−	1.22654i	−0.0612790	−	0.0514192i	−0.672913	+	0.739722i	$0.734957\pi$
$570$		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	$-0.447212\pi$
$572$	−7.95143	−	17.0519i	−0.332466	−	0.712976i
$573$	−10.7096	+	17.5655i	−0.447401	+	0.733811i
$574$	0.00146075		0.000257569i	6.09704e−5		1.07507e-5i
$575$		0			0
$576$	16.2770	−	17.6140i	0.678210	−	0.733917i
$577$	21.9121	+	5.87132i	0.912211	+	0.244426i	0.684253	−	0.729245i	$-0.260128\pi$
$577$	21.9121	+	5.87132i	0.912211	+	0.244426i	0.227958	+	0.973671i	$0.426795\pi$
$578$	0.0896482	−	0.192251i	0.00372888	−	0.00799660i
$579$	9.31423	−	18.7877i	0.387086	−	0.780791i
$580$		0			0
$581$	−0.823988	−	0.981990i	−0.0341848	−	0.0407398i
$582$	−0.122168	−	0.0245678i	−0.00506402	−	0.00101837i
$583$	−45.7460	−	21.3317i	−1.89461	−	0.883469i
$584$	−0.438419	−	0.759364i	−0.0181419	−	0.0314227i
$585$		0			0
$586$	−0.0802204	+	0.138946i	−0.00331387	+	0.00573980i
$587$	−7.01492	+	4.91190i	−0.289537	+	0.202736i	−0.709316	−	0.704890i	$-0.750996\pi$
$587$	−7.01492	+	4.91190i	−0.289537	+	0.202736i	0.419780	+	0.907626i	$0.362107\pi$
$588$	0.574363	−	24.0083i	0.0236863	−	0.990086i
$589$	−10.2091	+	28.0493i	−0.420659	+	1.15575i
$590$		0			0
$591$	−9.43335	+	4.12712i	−0.388036	+	0.169767i
$592$	−12.8893	+	1.12767i	−0.529748	+	0.0463469i
$593$	4.26261	−	4.26261i	0.175044	−	0.175044i	−0.614147	−	0.789192i	$-0.710500\pi$
$593$	4.26261	−	4.26261i	0.175044	−	0.175044i	0.789192	+	0.614147i	$0.210500\pi$
$594$	0.218910	−	0.269260i	0.00898199	−	0.0110479i
$595$		0			0
$596$	−24.7884	+	29.5417i	−1.01537	+	1.21007i
$597$	7.57011	−	6.04953i	0.309824	−	0.247591i
$598$	−0.109131	+	0.155855i	−0.00446269	+	0.00637338i
$599$	−13.5981	−	4.94929i	−0.555602	−	0.202223i	0.0489318	−	0.998802i	$-0.484418\pi$
$599$	−13.5981	−	4.94929i	−0.555602	−	0.202223i	−0.604534	+	0.796580i	$0.706641\pi$
$600$		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	$0.975757\pi$
$602$	−0.0346604	+	0.00928722i	−0.00141265	+	0.000378519i
$603$	1.16977	+	5.38353i	0.0476369	+	0.219234i
$604$	−26.0133	+	15.0188i	−1.05847	+	0.611107i
$605$		0			0
$606$	−0.00483627	−	0.0762430i	−0.000196460	−	0.00309716i
$607$	−1.69592	+	19.3845i	−0.0688354	+	0.786792i	0.880811	+	0.473468i	$0.156998\pi$
$607$	−1.69592	+	19.3845i	−0.0688354	+	0.786792i	−0.949646	+	0.313324i	$0.898557\pi$
$608$	−0.0906769	+	1.03644i	−0.00367743	+	0.0420333i
$609$	−0.132826	−	2.09398i	−0.00538238	−	0.0848522i
$610$		0			0
$611$	−7.46602	+	4.31051i	−0.302043	+	0.174384i
$612$	2.24478	+	10.3309i	0.0907397	+	0.417602i
$613$	13.0162	−	3.48768i	0.525720	−	0.140866i	0.0138088	−	0.999905i	$-0.495604\pi$
$613$	13.0162	−	3.48768i	0.525720	−	0.140866i	0.511911	+	0.859038i	$0.328938\pi$
$614$	0.0339541	−	0.192563i	0.00137027	−	0.00777121i
$615$		0			0
$616$	0.0647813	+	0.0235785i	0.00261011	+	0.000950003i
$617$	−26.0454	+	37.1967i	−1.04855	+	1.49748i	−0.192014	+	0.981392i	$0.561502\pi$
$617$	−26.0454	+	37.1967i	−1.04855	+	1.49748i	−0.856535	+	0.516090i	$0.827387\pi$
$618$	−0.208614	+	0.166711i	−0.00839169	+	0.00670608i
$619$	0.765342	−	0.912099i	0.0307617	−	0.0366604i	−0.750444	−	0.660934i	$-0.770160\pi$
$619$	0.765342	−	0.912099i	0.0307617	−	0.0366604i	0.781206	+	0.624273i	$0.214605\pi$
$620$		0			0
$621$	29.7293	+	4.76791i	1.19300	+	0.191330i
$622$	0.226747	−	0.226747i	0.00909171	−	0.00909171i
$623$	0.743449	−	0.0650434i	0.0297857	−	0.00260591i
$624$	−13.6468	+	5.97052i	−0.546309	+	0.239012i
$625$		0			0
$626$	0.154339	−	0.424042i	0.00616861	−	0.0169481i
$627$	1.02927	−	43.0232i	0.0411049	−	1.71818i
$628$	−3.82734	+	2.67993i	−0.152728	+	0.106941i
$629$	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	$0.690928\pi$
$632$	0.171290	+	0.0798737i	0.00681354	+	0.00317721i
$633$	9.64642	+	1.93988i	0.383411	+	0.0771034i
$634$	−0.260588	−	0.310556i	−0.0103493	−	0.0123338i
$635$		0			0
$636$	−17.7519	+	35.8073i	−0.703908	+	1.41985i
$637$	−6.30211	+	13.5149i	−0.249699	+	0.535481i
$638$	−0.302790	−	0.0811322i	−0.0119876	−	0.00321206i
$639$	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	$0.484405\pi$
$642$	0.206860	−	0.339284i	0.00816410	−	0.0133905i
$643$	−10.0815	−	21.6198i	−0.397575	−	0.852602i	−0.998576	−	0.0533535i	$-0.983009\pi$
$643$	−10.0815	−	21.6198i	−0.397575	−	0.852602i	0.601001	−	0.799248i	$-0.294769\pi$
$644$	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	$-0.414092\pi$
$647$	−17.7336	−	17.7336i	−0.697179	−	0.697179i	−0.963801	+	0.266622i	$0.914092\pi$
$648$	−0.418010	−	0.356785i	−0.0164210	−	0.0140158i
$649$		−	49.4134i		−	1.93965i
$650$		0			0
$651$	1.39306	−	1.89154i	0.0545984	−	0.0741355i
$652$	−24.8579	−	17.4057i	−0.973511	−	0.681660i
$653$	16.5274	−	7.70684i	0.646766	−	0.301592i	−0.0714165	−	0.997447i	$-0.522752\pi$
$653$	16.5274	−	7.70684i	0.646766	−	0.301592i	0.718183	+	0.695855i	$0.244974\pi$
$654$	0.308455	−	0.0747915i	0.0120616	−	0.00292458i
$655$		0			0
$656$	1.30364	+	0.752659i	0.0508987	+	0.0293864i
$657$	36.4290	−	22.9931i	1.42123	−	0.897045i
$658$	0.00408758	−	0.0152550i	0.000159350	−	0.000594704i
$659$	−32.1808	+	11.7129i	−1.25359	+	0.456269i	−0.881612	−	0.471974i	$-0.843542\pi$
$659$	−32.1808	+	11.7129i	−1.25359	+	0.456269i	−0.371975	+	0.928243i	$0.621319\pi$
$660$		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	$0.249949\pi$
$662$	0.151210	+	0.0132291i	0.00587693	+	0.000514165i
$663$	1.29422	−	6.43575i	0.0502634	−	0.249944i
$664$	0.103736	+	0.285012i	0.00402573	+	0.0110606i
$665$		0			0
$666$	0.0187259	+	0.147011i	0.000725613	+	0.00569656i
$667$	−7.03946	−	26.2716i	−0.272569	−	1.01724i
$668$	−22.2558	−	31.7846i	−0.861103	−	1.22978i
$669$	−16.5306	+	15.7581i	−0.639110	+	0.609245i
$670$		0			0
$671$	−52.2754	+	9.21756i	−2.01807	+	0.355840i
$672$	0.0298368	−	0.0762502i	0.00115098	−	0.00294142i
$673$	−1.31952	−	15.0821i	−0.0508636	−	0.581374i	−0.978272	−	0.207324i	$-0.933525\pi$
$673$	−1.31952	−	15.0821i	−0.0508636	−	0.581374i	0.927409	−	0.374050i	$-0.122031\pi$
$674$	−0.214165			−0.00824933
$675$		0			0
$676$	−16.7465			−0.644096
$677$	−0.848465	−	9.69800i	−0.0326092	−	0.372724i	−0.994912	−	0.100745i	$-0.967877\pi$
$677$	−0.848465	−	9.69800i	−0.0326092	−	0.372724i	0.962303	−	0.271979i	$-0.0876782\pi$
$678$	0.153337	+	0.191879i	0.00588888	+	0.00736908i
$679$	1.19775	−	0.211196i	0.0459656	−	0.00810497i
$680$		0			0
$681$	−24.2186	−	7.11435i	−0.928058	−	0.272622i
$682$	−0.201306	−	0.287495i	−0.00770842	−	0.0110088i
$683$	6.02595	+	22.4891i	0.230577	+	0.860523i	0.980093	+	0.198538i	$0.0636193\pi$
$683$	6.02595	+	22.4891i	0.230577	+	0.860523i	−0.749517	+	0.661985i	$0.769714\pi$
$684$	−34.0365	−	1.62948i	−1.30142	−	0.0623045i
$685$		0			0
$686$	−0.0187764	−	0.0515877i	−0.000716886	−	0.00196963i
$687$	−10.8247	−	9.53332i	−0.412987	−	0.363719i
$688$	−36.2776	−	3.17388i	−1.38307	−	0.121003i
$689$	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	$0.416288\pi$
$692$	−3.00916	+	11.2303i	−0.114391	+	0.426913i
$693$	−1.03204	+	3.22585i	−0.0392039	+	0.122540i
$694$	0.0807256	+	0.0466069i	0.00306430	+	0.00176918i
$695$		0			0
$696$	−0.139920	+	0.476314i	−0.00530365	+	0.0180546i
$697$	−0.601245	+	0.280365i	−0.0227738	+	0.0106196i
$698$	0.0478038	+	0.0334725i	0.00180940	+	0.00126695i
$699$	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	$0.820088\pi$
$702$	0.0744950	+	0.153494i	0.00281163	+	0.00579325i
$703$	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
$707$	0.315116	+	0.675769i	0.0118512	+	0.0254149i
$708$	−39.1142	−	0.935750i	−1.47000	−	0.0351676i
$709$	27.9978	+	4.93677i	1.05148	+	0.185404i	0.672574	−	0.740030i	$-0.265189\pi$
$709$	27.9978	+	4.93677i	1.05148	+	0.185404i	0.378907	+	0.925435i	$0.376300\pi$
$710$		0			0
$711$	−3.58937	+	8.56349i	−0.134612	+	0.321156i
$712$	−0.170559	−	0.0457011i	−0.00639196	−	0.00171272i
$713$	12.8695	−	27.5987i	0.481966	−	1.03358i
$714$	0.00666022	+	0.0100132i	0.000249253	+	0.000374736i
$715$		0			0
$716$	12.2880	+	14.6443i	0.459224	+	0.547282i
$717$	11.9958	+	35.5840i	0.447991	+	1.32891i
$718$	−0.163281	−	0.0761394i	−0.00609361	−	0.00284150i
$719$	8.97949	+	15.5529i	0.334878	+	0.580026i	0.983461	−	0.181118i	$-0.0579714\pi$
$719$	8.97949	+	15.5529i	0.334878	+	0.580026i	−0.648583	+	0.761144i	$0.724638\pi$
$720$		0			0
$721$	1.30318	−	2.25717i	0.0485328	−	0.0840612i
$722$	0.165843	−	0.116124i	0.00617202	−	0.00432170i
$723$	7.72062	+	4.70723i	0.287133	+	0.175064i
$724$	9.49171	−	26.0783i	0.352757	−	0.969191i
$725$		0			0
$726$	0.173229	+	0.127578i	0.00642914	+	0.00473486i
$727$	−28.2887	+	2.47494i	−1.04917	+	0.0917905i	−0.598678	−	0.800990i	$-0.704307\pi$
$727$	−28.2887	+	2.47494i	−1.04917	+	0.0917905i	−0.450492	+	0.892780i	$0.648751\pi$
$728$	−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
$732$	6.30641	+	41.5542i	0.233092	+	1.53589i
$733$	−5.80448	+	8.28966i	−0.214393	+	0.306185i	−0.911916	−	0.410378i	$-0.865397\pi$
$733$	−5.80448	+	8.28966i	−0.214393	+	0.306185i	0.697522	+	0.716563i	$0.254286\pi$
$734$	−0.0304169	−	0.0110708i	−0.00112271	−	0.000408632i
$735$		0			0
$736$	0.184310	−	1.04527i	0.00679374	−	0.0385292i
$737$	−7.75949	+	2.07915i	−0.285825	+	0.0765865i
$738$	0.00802570	−	0.0152602i	0.000295430	−	0.000561736i
$739$	−35.8294	+	20.6861i	−1.31801	+	0.760951i	−0.983408	−	0.181410i	$-0.941934\pi$
$739$	−35.8294	+	20.6861i	−1.31801	+	0.760951i	−0.334598	+	0.942361i	$0.608601\pi$
$740$		0			0
$741$	18.9571	+	9.39823i	0.696408	+	0.345252i
$742$	−0.00396233	+	0.0452897i	−0.000145462	+	0.00166264i
$743$	−0.674496	+	7.70953i	−0.0247449	+	0.282835i	0.973734	+	0.227691i	$0.0731175\pi$
$743$	−0.674496	+	7.70953i	−0.0247449	+	0.282835i	−0.998478	+	0.0551445i	$0.982438\pi$
$744$	−0.462798	+	0.307826i	−0.0169670	+	0.0112855i
$745$		0			0
$746$	−0.0438849	+	0.0253370i	−0.00160674	+	0.000927653i
$747$	−13.7906	+	5.64445i	−0.504573	+	0.206520i
$748$	−14.8903	+	3.98985i	−0.544444	+	0.145883i
$749$	−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	$0.883536\pi$
$752$	9.19318	−	13.1292i	0.335241	−	0.478773i
$753$	22.4948	+	8.80223i	0.819755	+	0.320771i
$754$	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	−0.485347	−	0.874322i	$-0.661307\pi$
$757$	10.7021	−	10.7021i	0.388975	−	0.388975i	0.874322	+	0.485347i	$0.161307\pi$
$758$	0.239740	−	0.0209745i	0.00870775	−	0.000761830i
$759$	−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	$-0.241235\pi$
$762$	0.451100	−	0.246249i	0.0163416	−	0.00892067i
$763$	−2.53754	+	1.77680i	−0.0918651	+	0.0643246i
$764$	−11.8764	+	20.5705i	−0.429673	+	0.744215i
$765$		0			0
$766$	0.210244	+	0.364154i	0.00759643	+	0.0131574i
$767$	22.0185	+	10.2674i	0.795040	+	0.370733i
$768$	18.2947	−	20.7729i	0.660155	−	0.749578i
$769$	4.55804	+	5.43206i	0.164367	+	0.195885i	0.841941	−	0.539570i	$-0.181413\pi$
$769$	4.55804	+	5.43206i	0.164367	+	0.195885i	−0.677574	+	0.735455i	$0.736969\pi$
$770$		0			0
$771$	16.2017	−	1.02771i	0.583489	−	0.0370121i
$772$	10.2320	−	21.9426i	0.368259	−	0.789733i
$773$	−8.62644	−	2.31145i	−0.310272	−	0.0831370i	0.100323	−	0.994955i	$-0.468012\pi$
$773$	−8.62644	−	2.31145i	−0.310272	−	0.0831370i	−0.410595	+	0.911818i	$0.634679\pi$
$774$	−0.0199462	+	0.416635i	−0.000716950	+	0.0149756i
$775$		0			0
$776$	−0.283394	−	0.0499700i	−0.0101733	−	0.00179382i
$777$	−0.693047	−	1.26958i	−0.0248629	−	0.0455459i
$778$	−0.193686	−	0.415360i	−0.00694397	−	0.0148914i
$779$	−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
$783$	−23.6538	−	5.94640i	−0.845316	−	0.212507i
$784$		−	27.7239i		−	0.990139i
$785$		0			0
$786$	0.0483992	+	0.110626i	0.00172634	+	0.00394589i
$787$	0.568328	+	0.397947i	0.0202587	+	0.0141853i	0.583662	−	0.811997i	$-0.301619\pi$
$787$	0.568328	+	0.397947i	0.0202587	+	0.0141853i	−0.563403	+	0.826182i	$0.690508\pi$
$788$	−10.7743	+	5.02416i	−0.383820	+	0.178978i
$789$	−11.9944	−	12.5823i	−0.427010	−	0.447942i
$790$		0			0
$791$	−2.07610	−	1.19864i	−0.0738175	−	0.0426186i
$792$	0.490506	−	0.633705i	0.0174294	−	0.0225177i
$793$	6.75473	−	25.2090i	0.239868	−	0.895198i
$794$	0.0686278	−	0.0249785i	0.00243551	−	0.000886453i
$795$		0			0
$796$	8.57065	−	7.19163i	0.303778	−	0.254900i
$797$	37.0354	+	3.24018i	1.31186	+	0.114773i	0.721528	−	0.692385i	$-0.243440\pi$
$797$	37.0354	+	3.24018i	1.31186	+	0.114773i	0.590335	+	0.807158i	$0.298996\pi$
$798$	−0.0367309	+	0.0123824i	−0.00130026	+	0.000438332i
$799$	2.41587	+	6.63755i	0.0854673	+	0.234820i
$800$		0			0
$801$	1.91321	−	8.46143i	0.0676001	−	0.298970i
$802$	0.0339926	+	0.126862i	0.00120032	+	0.00447965i
$803$	36.0293	+	51.4551i	1.27145	+	1.81581i
$804$	1.49885	+	6.18157i	0.0528605	+	0.218007i
$805$		0			0
$806$	0.169936	−	0.0299642i	0.00598573	−	0.00105544i
$807$	3.16599	−	0.480482i	0.111448	−	0.0169138i
$808$	−0.0153759	−	0.175748i	−0.000540924	−	0.00618279i
$809$	−9.19706			−0.323351			−0.161676	−	0.986844i	$-0.551690\pi$
$809$	−9.19706			−0.323351			−0.161676	+	0.986844i	$0.551690\pi$
$810$		0			0
$811$	−3.49413			−0.122695			−0.0613477	−	0.998116i	$-0.519540\pi$
$811$	−3.49413			−0.122695			−0.0613477	+	0.998116i	$0.519540\pi$
$812$	−0.211134	−	2.41327i	−0.00740935	−	0.0846893i
$813$	23.9858	−	3.64016i	0.841219	−	0.127666i
$814$	−0.212814	+	0.0375249i	−0.00745914	+	0.00131525i
$815$		0			0
$816$	2.87594	+	11.8609i	0.100678	+	0.415216i
$817$	29.6700	+	42.3732i	1.03802	+	1.48245i
$818$	−0.0334253	−	0.124745i	−0.00116869	−	0.00436160i
$819$	−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	$0.976732\pi$
$822$	−0.175303	+	0.0590967i	−0.00611440	+	0.00206123i
$823$	29.7914	+	2.60641i	1.03846	+	0.0908536i	0.593612	−	0.804752i	$-0.297702\pi$
$823$	29.7914	+	2.60641i	1.03846	+	0.0908536i	0.444850	+	0.895605i	$0.353257\pi$
$824$	−0.472400	+	0.396391i	−0.0164568	+	0.0138089i
$825$		0			0
$826$	−0.0418223	+	0.0152221i	−0.00145519	+	0.000529644i
$827$	−9.64511	+	35.9960i	−0.335393	+	1.25171i	0.568049	+	0.822995i	$0.307699\pi$
$827$	−9.64511	+	35.9960i	−0.335393	+	1.25171i	−0.903442	+	0.428710i	$0.858968\pi$
$828$	34.4463	+	4.68237i	1.19709	+	0.162724i
$829$	−6.82502	−	3.94043i	−0.237043	−	0.136857i	0.376774	−	0.926305i	$-0.377033\pi$
$829$	−6.82502	−	3.94043i	−0.237043	−	0.136857i	−0.613817	+	0.789448i	$0.710367\pi$
$830$		0			0
$831$	−21.7347	−	22.8001i	−0.753968	−	0.790927i
$832$	−15.5831	+	7.26652i	−0.540247	+	0.251921i
$833$	10.0084	+	7.00798i	0.346771	+	0.242812i
$834$	−0.0865115	−	0.197739i	−0.00299565	−	0.00684714i
$835$		0			0
$836$		−	49.6874i		−	1.71847i
$837$	−16.0078	−	22.1231i	−0.553310	−	0.764687i
$838$	−0.0948142	−	0.0948142i	−0.00327530	−	0.00327530i
$839$	−26.9906	−	22.6478i	−0.931819	−	0.781889i	0.0443239	−	0.999017i	$-0.485887\pi$
$839$	−26.9906	−	22.6478i	−0.931819	−	0.781889i	−0.976143	+	0.217128i	$0.930331\pi$
$840$		0			0
$841$	−1.21001	−	6.86229i	−0.0417244	−	0.236631i
$842$	−0.00370012	−	0.00793494i	−0.000127515	−	0.000273456i
$843$	−21.7919	−	39.9202i	−0.750554	−	1.37493i
$844$	11.1878	+	1.97271i	0.385100	+	0.0679035i
$845$		0			0
$846$	−0.154417	−	0.0992895i	−0.00530895	−	0.00341364i
$847$	−2.02821	−	0.543456i	−0.0696900	−	0.0186734i
$848$	−19.4988	+	41.8153i	−0.669592	+	1.43594i
$849$	31.7084	−	2.01134i	1.08823	−	0.0690290i
$850$		0			0
$851$	−12.0521	−	14.3631i	−0.413141	−	0.492362i
$852$	11.7462	−	13.3373i	0.402417	−	0.456928i
$853$	22.1725	+	10.3392i	0.759171	+	0.354007i	0.763351	−	0.645984i	$-0.223553\pi$
$853$	22.1725	+	10.3392i	0.759171	+	0.354007i	−0.00417979	+	0.999991i	$0.501330\pi$
$854$	0.0239053	+	0.0414051i	0.000818021	+	0.00141685i
$855$		0			0
$856$	0.458819	−	0.794697i	0.0156821	−	0.0271622i
$857$	−3.70630	+	2.59518i	−0.126605	+	0.0886496i	−0.635164	−	0.772378i	$-0.719067\pi$
$857$	−3.70630	+	2.59518i	−0.126605	+	0.0886496i	0.508559	+	0.861027i	$0.330178\pi$
$858$	−0.218368	+	0.119204i	−0.00745495	+	0.00406956i
$859$	−3.10612	+	8.53399i	−0.105979	+	0.291176i	−0.981336	−	0.192302i	$-0.938405\pi$
$859$	−3.10612	+	8.53399i	−0.105979	+	0.291176i	0.875356	+	0.483478i	$0.160627\pi$
$860$		0			0
$861$	−0.0186720	+	0.167243i	−0.000636340	+	0.00569963i
$862$	−0.380394	+	0.0332801i	−0.0129563	+	0.00113353i
$863$	−21.0851	+	21.0851i	−0.717746	+	0.717746i	−0.968143	−	0.250398i	$-0.919439\pi$
$863$	−21.0851	+	21.0851i	−0.717746	+	0.717746i	0.250398	+	0.968143i	$0.419439\pi$
$864$	−0.738515	−	0.600418i	−0.0251248	−	0.0204266i
$865$		0			0
$866$	0.346801	−	0.413302i	0.0117848	−	0.0140446i
$867$	22.4115	+	8.76965i	0.761136	+	0.297833i
$868$	1.55569	−	2.22175i	0.0528035	−	0.0754113i
$869$	−12.7229	−	4.63076i	−0.431595	−	0.157088i
$870$		0			0
$871$	0.685845	−	3.88962i	0.0232390	−	0.131795i
$872$	0.707971	−	0.189700i	0.0239749	−	0.00642406i
$873$	1.90426	−	14.0089i	0.0644496	−	0.474130i
$874$	−0.435146	+	0.251232i	−0.0147190	+	0.00849804i
$875$		0			0
$876$	41.4127	−	27.5453i	1.39921	−	0.930671i
$877$	3.98890	−	45.5933i	0.134696	−	1.53958i	−0.564973	−	0.825110i	$-0.691113\pi$
$877$	3.98890	−	45.5933i	0.134696	−	1.53958i	0.699668	−	0.714468i	$-0.253331\pi$
$878$	−0.00628162	+	0.0717992i	−0.000211994	+	0.00242311i
$879$	−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	$0.558312\pi$
$882$	−0.317304	+	0.0125173i	−0.0106842	+	0.000421480i
$883$	−18.1259	+	4.85682i	−0.609986	+	0.163445i	−0.550571	−	0.834788i	$-0.685590\pi$
$883$	−18.1259	+	4.85682i	−0.609986	+	0.163445i	−0.0594144	+	0.998233i	$0.518923\pi$
$884$	1.31612	−	7.46412i	0.0442661	−	0.251045i
$885$		0			0
$886$	−0.424182	−	0.154390i	−0.0142507	−	0.00518682i
$887$	−21.0306	+	30.0349i	−0.706140	+	1.00847i	0.292496	+	0.956267i	$0.405514\pi$
$887$	−21.0306	+	30.0349i	−0.706140	+	1.00847i	−0.998636	+	0.0522057i	$0.983375\pi$
$888$	0.0513501	+	0.338357i	0.00172320	+	0.0113545i
$889$	−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
$893$	−22.6804	+	1.98428i	−0.758972	+	0.0664014i
$894$	0.410593	+	0.302389i	0.0137323	+	0.0101134i
$895$		0			0
$896$	0.0431100	−	0.118444i	0.00144021	−	0.00395693i
$897$	−18.4305	−	11.2370i	−0.615375	−	0.375191i
$898$	0.0842201	−	0.0589716i	0.00281046	−	0.00196791i
$899$	−12.3336	+	21.3624i	−0.411349	+	0.712477i
$900$		0			0
$901$	−10.1666	−	17.6091i	−0.338700	−	0.586645i
$902$	0.0227860	+	0.0106253i	0.000758690	+	0.000353783i
$903$	−1.30048	−	3.85772i	−0.0432773	−	0.128377i
$904$	0.364593	+	0.434505i	0.0121262	+	0.0144514i
$905$		0			0
$906$	0.219969	+	0.330710i	0.00730799	+	0.0109871i
$907$	8.15736	−	17.4935i	0.270861	−	0.580863i	−0.723082	−	0.690762i	$-0.757275\pi$
$907$	8.15736	−	17.4935i	0.270861	−	0.580863i	0.993943	+	0.109900i	$0.0350529\pi$
$908$	−28.1504	−	7.54288i	−0.934204	−	0.250319i
$909$	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	$0.326110\pi$
$912$	−39.3265	−	0.940828i	−1.30223	−	0.0311539i
$913$	−9.18269	−	19.6923i	−0.303903	−	0.651721i
$914$	−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
$918$	0.134452	−	0.0382707i	0.00443757	−	0.00126312i
$919$		−	43.5953i		−	1.43808i	−0.694971	−	0.719038i	$-0.744583\pi$
$919$		−	43.5953i		−	1.43808i	0.694971	−	0.719038i	$-0.255417\pi$
$920$		0			0
$921$	22.0468	+	2.46144i	0.726468	+	0.0811071i
$922$	−0.330404	−	0.231352i	−0.0108813	−	0.00761916i
$923$	−10.0017	+	4.66385i	−0.329209	+	0.153513i
$924$	−1.10214	+	3.75189i	−0.0362577	+	0.123428i
$925$		0			0
$926$	0.159010	+	0.0918044i	0.00522539	+	0.00301688i
$927$	−20.3741	−	22.4230i	−0.669174	−	0.736468i
$928$	−0.222526	+	0.830480i	−0.00730479	+	0.0272618i
$929$	32.4046	−	11.7943i	1.06316	−	0.386959i	0.249546	−	0.968363i	$-0.419719\pi$
$929$	32.4046	−	11.7943i	1.06316	−	0.386959i	0.813615	+	0.581404i	$0.197496\pi$
$930$		0			0
$931$	−30.1676	+	25.3136i	−0.988703	+	0.829620i
$932$	55.0863	+	4.81942i	1.80441	+	0.157865i
$933$	27.3019	+	24.0449i	0.893825	+	0.787194i
$934$	−0.0577199	−	0.158584i	−0.00188865	−	0.00518903i
$935$		0			0
$936$	0.180457	+	0.350242i	0.00589842	+	0.0114480i
$937$	−11.9945	−	44.7642i	−0.391845	−	1.46238i	−0.827089	−	0.562072i	$-0.810005\pi$
$937$	−11.9945	−	44.7642i	−0.391845	−	1.46238i	0.435244	−	0.900313i	$-0.356662\pi$
$938$	0.00415010	+	0.00592696i	0.000135506	+	0.000193522i
$939$	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	$0.398045\pi$
$942$	0.0385693	+	0.0482638i	0.00125665	+	0.00157252i
$943$	0.190123	+	2.17311i	0.00619124	+	0.0707662i
$944$	−45.1676			−1.47008
$945$		0			0
$946$	−0.608216			−0.0197748
$947$	3.21081	+	36.6998i	0.104337	+	1.19258i	0.850192	+	0.526473i	$0.176486\pi$
$947$	3.21081	+	36.6998i	0.104337	+	1.19258i	−0.745854	+	0.666109i	$0.767959\pi$
$948$	−3.90651	+	9.98340i	−0.126878	+	0.324246i
$949$	−30.4146	+	5.36292i	−0.987300	+	0.174088i
$950$		0			0
$951$	33.2912	−	31.7355i	1.07954	−	1.02910i
$952$	0.0159289	+	0.0227488i	0.000516257	+	0.000737292i
$953$	7.47785	+	27.9077i	0.242231	+	0.904020i	0.974755	+	0.223278i	$0.0716758\pi$
$953$	7.47785	+	27.9077i	0.242231	+	0.904020i	−0.732523	+	0.680742i	$0.761658\pi$
$954$	0.487387	+	0.204287i	0.0157797	+	0.00661404i
$955$		0			0
$956$	14.8286	+	40.7411i	0.479590	+	1.31766i
$957$	7.01153	−	34.8661i	0.226650	−	1.12706i
$958$	0.0644504	+	0.00563868i	0.00208230	+	0.000182177i
$959$	1.38314	−	1.16060i	0.0446641	−	0.0374776i
$960$		0			0
$961$	3.17820	−	1.15677i	0.102522	−	0.0373151i
$962$	0.0274987	−	0.102627i	0.000886594	−	0.00330881i
$963$	39.9011	+	20.9849i	1.28580	+	0.676229i
$964$	9.04140	+	5.22006i	0.291204	+	0.168127i
$965$		0			0
$966$	0.0384305	−	0.00931830i	0.00123648	−	0.000299811i
$967$	−19.0304	+	8.87400i	−0.611975	+	0.285369i	−0.703791	−	0.710407i	$-0.748511\pi$
$967$	−19.0304	+	8.87400i	−0.611975	+	0.285369i	0.0918158	+	0.995776i	$0.470733\pi$
$968$	0.406964	+	0.284960i	0.0130803	+	0.00915895i
$969$	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	$0.616749\pi$
$972$	18.6963	−	24.9444i	0.599684	−	0.800091i
$973$	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
$977$	−18.3257	−	39.2996i	−0.586291	−	1.25731i	−0.945977	−	0.324232i	$-0.894894\pi$
$977$	−18.3257	−	39.2996i	−0.586291	−	1.25731i	0.359686	−	0.933073i	$-0.382884\pi$
$978$	−0.208885	+	0.342605i	−0.00667939	+	0.0109553i
$979$	12.4574	+	2.19657i	0.398140	+	0.0702028i
$980$		0			0
$981$	10.6836	+	34.3877i	0.341103	+	1.09791i
$982$	−0.0300698	−	0.00805718i	−0.000959566	−	0.000257115i
$983$	−21.9924	+	47.1628i	−0.701447	+	1.50426i	0.154940	+	0.987924i	$0.450482\pi$
$983$	−21.9924	+	47.1628i	−0.701447	+	1.50426i	−0.856387	+	0.516335i	$0.827296\pi$
$984$	0.0176854	−	0.0356731i	0.000563788	−	0.00113722i
$985$		0			0
$986$	−0.0811698	−	0.0967344i	−0.00258497	−	0.00308065i
$987$	1.75661	+	0.353252i	0.0559135	+	0.0112441i
$988$	22.1405	+	10.3243i	0.704384	+	0.328460i
$989$	−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	$0.183343\pi$
$992$	−0.788532	+	0.552136i	−0.0250359	+	0.0175303i
$993$	−0.411861	+	17.2158i	−0.0130700	+	0.546325i
$994$	0.00691448	−	0.0189974i	0.000219314	−	0.000602560i
$995$		0			0
$996$	−15.7618	+	6.89584i	−0.499431	+	0.218503i
$997$	−23.3597	+	2.04371i	−0.739808	+	0.0647248i	−0.450829	−	0.892610i	$-0.648871\pi$
$997$	−23.3597	+	2.04371i	−0.739808	+	0.0647248i	−0.288979	+	0.957335i	$0.593316\pi$
$998$	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.443.9		192
5.2	odd	4	inner	675.2.ba.b.632.8		192
5.3	odd	4		135.2.q.a.92.9	yes	192
5.4	even	2		135.2.q.a.38.8	yes	192
15.8	even	4		405.2.r.a.197.8		192
15.14	odd	2		405.2.r.a.278.9		192
27.5	odd	18	inner	675.2.ba.b.518.8		192
135.32	even	36	inner	675.2.ba.b.32.9		192
135.49	even	18		405.2.r.a.368.8		192
135.59	odd	18		135.2.q.a.113.9	yes	192
135.103	odd	36		405.2.r.a.287.9		192
135.113	even	36		135.2.q.a.32.8	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.8	✓	192	135.113	even	36
135.2.q.a.38.8	yes	192	5.4	even	2
135.2.q.a.92.9	yes	192	5.3	odd	4
135.2.q.a.113.9	yes	192	135.59	odd	18
405.2.r.a.197.8		192	15.8	even	4
405.2.r.a.278.9		192	15.14	odd	2
405.2.r.a.287.9		192	135.103	odd	36
405.2.r.a.368.8		192	135.49	even	18
675.2.ba.b.32.9		192	135.32	even	36	inner
675.2.ba.b.443.9		192	1.1	even	1	trivial
675.2.ba.b.518.8		192	27.5	odd	18	inner
675.2.ba.b.632.8		192	5.2	odd	4	inner

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

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