LMFDB - Embedded newform 675.2.ba.b.32.9

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			32.9
Character	$\chi$	$=$	675.32
Dual form			675.2.ba.b.443.9

$q$-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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.00133058	+	0.0152086i	−0.000940864	+	0.0107541i	−0.996651	−	0.0817774i	$-0.973940\pi$
$2$	−0.00133058	+	0.0152086i	−0.000940864	+	0.0107541i	0.995710	+	0.0925315i	$0.0294959\pi$
$3$	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	−0.790202	−	0.612846i	$-0.790025\pi$
$7$	0.148030	−	0.211408i	0.0559499	−	0.0799048i	0.846152	+	0.532941i	$0.178913\pi$
$8$	−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	−0.480836	−	0.876810i	$-0.659667\pi$
$11$	1.49616	−	4.11066i	0.451108	−	1.23941i	0.931945	−	0.362600i	$-0.118111\pi$
$12$	3.28221	+	1.10647i	0.947493	+	0.319411i
$13$	−2.14258	+	0.187451i	−0.594244	+	0.0519896i	−0.380311	−	0.924859i	$-0.624183\pi$
$13$	−2.14258	+	0.187451i	−0.594244	+	0.0519896i	−0.213933	+	0.976848i	$0.568627\pi$
$14$	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	0.888303	−	0.459257i	$-0.151884\pi$
$17$	−0.456091	−	1.70216i	−0.110618	−	0.412833i	−0.998922	+	0.0464236i	$0.985218\pi$
$18$	−0.0173489	+	0.0423872i	−0.00408918	+	0.00999075i
$19$	−4.91894	+	2.83995i	−1.12848	+	0.651529i	−0.943553	−	0.331222i	$-0.892539\pi$
$19$	−4.91894	+	2.83995i	−1.12848	+	0.651529i	−0.184929	+	0.982752i	$0.559206\pi$
$20$		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	0.0377879	−	0.999286i	$-0.487969\pi$
$23$	4.74660	−	3.32360i	0.989734	−	0.693019i	0.951946	+	0.306267i	$0.0990800\pi$
$24$	−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	−0.912383	−	0.409337i	$-0.865760\pi$
$29$	−3.59567	+	3.01712i	−0.667699	+	0.560266i	0.244685	+	0.969603i	$0.421316\pi$
$30$		0			0
$31$	−0.912568	+	5.17543i	−0.163902	+	0.929534i	0.786287	+	0.617861i	$0.212001\pi$
$31$	−0.912568	+	5.17543i	−0.163902	+	0.929534i	−0.950189	+	0.311673i	$0.899111\pi$
$32$	−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	−0.506412	−	0.862292i	$-0.669028\pi$
$37$	−3.12552	+	0.837479i	−0.513832	+	0.137681i	−0.00741968	+	0.999972i	$0.502362\pi$
$38$	−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	−0.746818	−	0.665029i	$-0.768419\pi$
$41$	0.241984	−	0.288386i	0.0377916	−	0.0450383i	0.784609	+	0.619991i	$0.212864\pi$
$42$	0.00451041	+	0.00512138i	0.000695972	+	0.000790246i
$43$	−8.25395	+	3.84888i	−1.25872	+	0.586948i	−0.933461	−	0.358678i	$-0.883228\pi$
$43$	−8.25395	+	3.84888i	−1.25872	+	0.586948i	−0.325254	+	0.945627i	$0.605450\pi$
$44$	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	0.787990	−	0.615688i	$-0.211122\pi$
$47$	3.28345	+	2.29910i	0.478941	+	0.335358i	−0.309049	+	0.951046i	$0.600011\pi$
$48$	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	−0.991633	−	0.129092i	$-0.958794\pi$
$53$	−8.15900	−	8.15900i	−1.12072	−	1.12072i	−0.129092	−	0.991633i	$-0.541206\pi$
$54$	−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	−0.922756	−	0.385385i	$-0.874069\pi$
$59$	−10.6146	+	3.86341i	−1.38191	+	0.502973i	−0.459152	+	0.888358i	$0.651847\pi$
$60$		0			0
$61$	−2.10712	−	11.9501i	−0.269790	−	1.53005i	−0.755040	−	0.655678i	$-0.772383\pi$
$61$	−2.10712	−	11.9501i	−0.269790	−	1.53005i	0.485251	−	0.874375i	$-0.338728\pi$
$62$	−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	−0.999684	−	0.0251426i	$-0.991996\pi$
$67$	−0.160052	−	1.82940i	−0.0195534	−	0.223497i	0.980130	−	0.198354i	$-0.0635595\pi$
$68$	−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	0.739940	−	0.672673i	$-0.234854\pi$
$71$	4.44360	+	2.56551i	0.527358	+	0.304471i	−0.212582	+	0.977143i	$0.568187\pi$
$72$	−0.0977775	+	0.154913i	−0.0115232	+	0.0182567i
$73$	13.8702	+	3.71651i	1.62338	+	0.434984i	0.951993	−	0.306120i	$-0.0990308\pi$
$73$	13.8702	+	3.71651i	1.62338	+	0.434984i	0.671390	+	0.741104i	$0.265697\pi$
$74$	−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	0.642426	−	0.766348i	$-0.277928\pi$
$79$	−1.98949	−	2.37099i	−0.223835	−	0.266757i	−0.866261	+	0.499591i	$0.833484\pi$
$80$		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	−0.187708	−	0.982225i	$-0.560106\pi$
$83$	−4.94812	−	0.432904i	−0.543127	−	0.0475174i	−0.355418	+	0.934707i	$0.615662\pi$
$84$	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	0.932424	−	0.361367i	$-0.117690\pi$
$89$	1.44584	+	2.50426i	0.153259	+	0.265452i	−0.779165	+	0.626819i	$0.784357\pi$
$90$		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	0.981097	−	0.193516i	$-0.0619890\pi$
$97$	1.99162	+	4.27105i	0.202219	+	0.433659i	−0.778879	+	0.627175i	$0.784211\pi$
$98$	−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	−0.0302897	−	0.999541i	$-0.509643\pi$
$101$	2.84523	−	0.501690i	0.283110	−	0.0499200i	0.313400	+	0.949621i	$0.398532\pi$
$102$	0.0465841	−	0.00111446i	0.00461251	−	0.000110348i
$103$	−4.26799	+	9.15274i	−0.420538	+	0.901846i	0.575900	+	0.817520i	$0.304652\pi$
$103$	−4.26799	+	9.15274i	−0.420538	+	0.901846i	−0.996438	+	0.0843263i	$0.973126\pi$
$104$	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	$-0.491198\pi$
$107$	10.6261	−	10.6261i	1.02727	−	1.02727i	0.999618	−	0.0276498i	$-0.00880233\pi$
$108$	8.41843	+	6.09138i	0.810064	+	0.586143i
$109$		−	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
$112$	0.845337	−	0.591912i	0.0798769	−	0.0559304i
$113$	−8.41851	−	3.92562i	−0.791947	−	0.369291i	−0.0158260	−	0.999875i	$-0.505038\pi$
$113$	−8.41851	−	3.92562i	−0.791947	−	0.369291i	−0.776121	+	0.630584i	$0.782816\pi$
$114$	−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	−0.265918	−	0.963996i	$-0.585675\pi$
$127$	5.03035	−	18.7735i	0.446371	−	1.66588i	0.712290	−	0.701885i	$-0.247658\pi$
$128$	−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	−0.0262986	−	0.999654i	$-0.508372\pi$
$131$	−4.49710	−	0.792959i	−0.392913	−	0.0692812i	−0.366614	+	0.930373i	$0.619483\pi$
$132$	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	0.924619	+	0.380894i	$0.124384\pi$
$137$	−0.609750	+	6.96948i	−0.0520945	+	0.595443i	−0.976713	+	0.214549i	$0.931172\pi$
$138$	0.0558340	+	0.142688i	0.00475291	+	0.0121464i
$139$	8.03836	+	1.41738i	0.681805	+	0.120221i	0.503815	−	0.863812i	$-0.331929\pi$
$139$	8.03836	+	1.41738i	0.681805	+	0.120221i	0.177990	+	0.984032i	$0.443041\pi$
$140$		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	−0.999278	−	0.0379911i	$-0.987904\pi$
$149$	−14.7726	−	12.3956i	−1.21021	−	1.01549i	−0.210937	−	0.977500i	$-0.567651\pi$
$150$		0			0
$151$	−14.1147	−	5.13734i	−1.14864	−	0.418070i	−0.303613	−	0.952795i	$-0.598193\pi$
$151$	−14.1147	−	5.13734i	−1.14864	−	0.418070i	−0.845026	+	0.534725i	$0.820415\pi$
$152$	−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	0.336279	−	0.941762i	$-0.390832\pi$
$157$	−2.11753	−	0.987420i	−0.168997	−	0.0788047i	−0.505276	+	0.862958i	$0.668609\pi$
$158$	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	−0.988917	−	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
$167$	−8.20013	+	17.5852i	−0.634545	+	1.36079i	0.281442	+	0.959578i	$0.409187\pi$
$167$	−8.20013	+	17.5852i	−0.634545	+	1.36079i	−0.915987	+	0.401208i	$0.868590\pi$
$168$	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	0.790492	−	0.612472i	$-0.209825\pi$
$173$	−2.45707	−	5.26921i	−0.186808	−	0.400610i	−0.977300	+	0.211862i	$0.932047\pi$
$174$	−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	−0.630247	−	0.776395i	$-0.717046\pi$
$179$	4.77974	−	8.27875i	0.357254	−	0.618783i	0.987501	+	0.157612i	$0.0503796\pi$
$180$		0			0
$181$	6.93879	+	12.0183i	0.515756	+	0.893315i	0.999833	+	0.0182899i	$0.00582219\pi$
$181$	6.93879	+	12.0183i	0.515756	+	0.893315i	−0.484077	+	0.875026i	$0.660844\pi$
$182$	−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	0.415488	−	0.909599i	$-0.363611\pi$
$191$	−7.63489	−	9.09890i	−0.552441	−	0.658374i	−0.967929	+	0.251225i	$0.919167\pi$
$192$	10.8170	+	8.64426i	0.780652	+	0.623846i
$193$	6.94425	+	9.91741i	0.499858	+	0.713871i	0.987226	−	0.159325i	$-0.0509319\pi$
$193$	6.94425	+	9.91741i	0.499858	+	0.713871i	−0.487368	+	0.873197i	$0.662043\pi$
$194$	−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	0.0483907	−	0.998828i	$-0.484591\pi$
$197$	−5.74222	−	1.53862i	−0.409116	−	0.109622i	−0.457507	+	0.889206i	$0.651257\pi$
$198$	0.148283	+	0.134733i	0.0105380	+	0.00957508i
$199$	4.84519	+	2.79737i	0.343466	+	0.198300i	0.661804	−	0.749677i	$-0.269791\pi$
$199$	4.84519	+	2.79737i	0.343466	+	0.198300i	−0.318337	+	0.947977i	$0.603124\pi$
$200$		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	−0.151667	−	0.988432i	$-0.548464\pi$
$211$	5.33826	−	1.94297i	0.367501	−	0.133759i	0.519168	+	0.854672i	$0.326242\pi$
$212$	−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	0.153007	−	0.988225i	$-0.451104\pi$
$223$	−10.8010	−	7.56295i	−0.723289	−	0.506452i	−0.876296	+	0.481773i	$0.839993\pi$
$224$	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	−0.808228	−	0.588870i	$-0.799573\pi$
$227$	−13.2080	+	6.15899i	−0.876646	+	0.408787i	−0.0684181	+	0.997657i	$0.521795\pi$
$228$	−19.2873	+	3.87866i	−1.27733	+	0.256870i
$229$	−5.35302	+	6.37948i	−0.353738	+	0.421568i	−0.913343	−	0.407191i	$-0.866508\pi$
$229$	−5.35302	+	6.37948i	−0.353738	+	0.421568i	0.559605	+	0.828759i	$0.310953\pi$
$230$		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	0.765207	−	0.643784i	$-0.222637\pi$
$233$	26.7094	−	7.15675i	1.74979	−	0.468854i	0.984581	+	0.174930i	$0.0559699\pi$
$234$	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	−0.580377	−	0.814348i	$-0.697095\pi$
$239$	3.76477	−	21.3510i	0.243522	−	1.38108i	0.823899	−	0.566736i	$-0.191794\pi$
$240$		0			0
$241$	3.99926	−	3.35578i	0.257615	−	0.216165i	−0.504828	−	0.863220i	$-0.668444\pi$
$241$	3.99926	−	3.35578i	0.257615	−	0.216165i	0.762443	+	0.647055i	$0.224000\pi$
$242$	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	−0.0677923	−	0.997699i	$-0.521596\pi$
$251$	12.0778	−	6.97313i	0.762345	−	0.440140i	0.830137	+	0.557560i	$0.188262\pi$
$252$	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	0.207870	−	0.978156i	$-0.433347\pi$
$257$	9.33717	−	0.816897i	0.582437	−	0.0509566i	0.374567	+	0.927200i	$0.377791\pi$
$258$	−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	−0.956432	−	0.291955i	$-0.905694\pi$
$263$	−5.75656	+	8.22122i	−0.354965	+	0.506942i	0.601467	+	0.798897i	$0.294583\pi$
$264$	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	−0.999460	−	0.0328481i	$-0.989542\pi$
$277$	−10.4313	+	14.8975i	−0.626758	+	0.895103i	0.372703	+	0.927951i	$0.378431\pi$
$278$	−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	0.316368	+	0.948637i	$0.397537\pi$
$281$	−8.98091	+	24.6748i	−0.535756	+	1.47198i	−0.852124	+	0.523341i	$0.824686\pi$
$282$	−0.0795419	+	0.0700527i	−0.00473665	+	0.00417158i
$283$	18.2738	−	1.59875i	1.08627	−	0.0950360i	0.470071	−	0.882629i	$-0.344228\pi$
$283$	18.2738	−	1.59875i	1.08627	−	0.0950360i	0.616196	+	0.787593i	$0.288673\pi$
$284$	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	−0.797343	−	0.603527i	$-0.793762\pi$
$293$	−8.60861	+	6.02781i	−0.502920	+	0.352149i	0.294422	+	0.955675i	$0.404873\pi$
$294$	−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	0.112124	−	0.993694i	$-0.464235\pi$
$307$	12.3714	−	3.31491i	0.706074	−	0.189192i	0.593949	+	0.804502i	$0.297568\pi$
$308$	−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	−0.232596	−	0.972573i	$-0.574722\pi$
$311$	13.5014	−	16.0903i	0.765592	−	0.912397i	0.998188	+	0.0601768i	$0.0191664\pi$
$312$	0.0726664	−	0.215556i	0.00411392	−	0.0122035i
$313$	26.7887	−	12.4918i	1.51419	−	0.706078i	0.524781	−	0.851237i	$-0.324147\pi$
$313$	26.7887	−	12.4918i	1.51419	−	0.706078i	0.989408	+	0.145159i	$0.0463694\pi$
$314$	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	0.993010	−	0.118027i	$-0.0376571\pi$
$317$	21.7523	+	15.2311i	1.22173	+	0.855465i	0.228720	+	0.973492i	$0.426546\pi$
$318$	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	−0.994779	−	0.102050i	$-0.967460\pi$
$331$	−1.72647	−	9.79132i	−0.0948956	−	0.538179i	0.899884	−	0.436130i	$-0.143651\pi$
$332$	−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	0.953912	+	0.300086i	$0.0970154\pi$
$337$	1.22264	+	13.9748i	0.0666015	+	0.761258i	−0.887311	+	0.461172i	$0.847429\pi$
$338$	−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	0.714076	−	0.700068i	$-0.246847\pi$
$347$	−3.50208	−	5.00149i	−0.188001	−	0.268494i	−0.902077	+	0.431574i	$0.857958\pi$
$348$	−15.1401	+	5.92434i	−0.811595	+	0.317578i
$349$	−2.45708	−	2.92823i	−0.131524	−	0.156745i	0.696263	−	0.717787i	$-0.254845\pi$
$349$	−2.45708	−	2.92823i	−0.131524	−	0.156745i	−0.827787	+	0.561042i	$0.810400\pi$
$350$		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	0.146050	−	0.989277i	$-0.453344\pi$
$353$	2.21879	+	0.194119i	0.118094	+	0.0103319i	−0.0279554	+	0.999609i	$0.508900\pi$
$354$	−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	0.978669	−	0.205445i	$-0.0658641\pi$
$359$	5.90045	+	10.2199i	0.311414	+	0.539385i	−0.667255	+	0.744829i	$0.732531\pi$
$360$		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	0.928306	−	0.371818i	$-0.121265\pi$
$367$	0.896047	+	1.92158i	0.0467733	+	0.100306i	−0.881532	+	0.472123i	$0.843488\pi$
$368$	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	−0.939272	−	0.343174i	$-0.888498\pi$
$373$	−1.40277	+	3.00825i	−0.0726328	+	0.155762i	0.866639	+	0.498936i	$0.166276\pi$
$374$	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	$-0.867322\pi$
$379$		−	15.7634i		−	0.809713i	0.914380	−	0.404856i	$-0.132678\pi$
$380$		0			0
$381$	13.4932	−	30.8413i	0.691276	−	1.58005i
$382$	0.148541	−	0.104009i	0.00760001	−	0.00532158i
$383$	−24.9622	−	11.6401i	−1.27551	−	0.594781i	−0.337480	−	0.941333i	$-0.609575\pi$
$383$	−24.9622	−	11.6401i	−1.27551	−	0.594781i	−0.938031	+	0.346552i	$0.887352\pi$
$384$	−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	0.937005	−	0.349315i	$-0.113586\pi$
$389$	28.2091	+	10.2673i	1.43026	+	0.520571i	0.493252	+	0.869886i	$0.335808\pi$
$390$		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	−0.927871	−	0.372902i	$-0.878363\pi$
$397$	1.23812	−	4.62074i	0.0621397	−	0.231908i	0.990011	+	0.140993i	$0.0450296\pi$
$398$	−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	−0.0419444	−	0.999120i	$-0.513355\pi$
$401$	−8.47214	−	1.49387i	−0.423078	−	0.0746001i	−0.381134	+	0.924520i	$0.624466\pi$
$402$	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	0.375773	−	0.926712i	$-0.377377\pi$
$409$	8.33076	+	1.46894i	0.411930	+	0.0726343i	0.0361568	+	0.999346i	$0.488488\pi$
$410$		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	0.792167	−	0.610305i	$-0.208953\pi$
$419$	6.72816	+	5.64560i	0.328692	+	0.275806i	−0.463475	+	0.886110i	$0.653397\pi$
$420$		0			0
$421$	0.538899	+	0.196143i	0.0262643	+	0.00955944i	0.355119	−	0.934821i	$-0.384440\pi$
$421$	0.538899	+	0.196143i	0.0262643	+	0.00955944i	−0.328855	+	0.944381i	$0.606663\pi$
$422$	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	$0.205783\pi$
$431$			25.0117i			1.20477i	−0.798205	+	0.602386i	$0.794217\pi$
$432$	14.4622	+	14.9179i	0.695812	+	0.717737i
$433$	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
$437$	−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	−0.283491	−	0.958975i	$-0.591492\pi$
$439$	−4.64923	+	0.819785i	−0.221896	+	0.0391262i	0.0615948	+	0.998101i	$0.480381\pi$
$440$		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	0.941938	+	0.335787i	$0.109002\pi$
$443$	12.4959	+	26.7976i	0.593700	+	1.27319i	−0.348238	+	0.937406i	$0.613220\pi$
$444$	−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	−0.775566	−	0.631267i	$-0.782535\pi$
$449$	3.36725	−	5.83225i	0.158910	−	0.275241i	0.934476	+	0.356026i	$0.115869\pi$
$450$		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	0.891015	−	0.453974i	$-0.149994\pi$
$457$	36.1208	+	3.16016i	1.68966	+	0.147826i	0.798647	+	0.601800i	$0.205550\pi$
$458$	−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	0.999373	−	0.0354156i	$-0.0112755\pi$
$461$	16.9825	+	20.2390i	0.790956	+	0.942625i	−0.208417	+	0.978040i	$0.566831\pi$
$462$	0.0278005	−	0.0108784i	0.00129340	−	0.000506108i
$463$	−6.89825	−	9.85172i	−0.320589	−	0.457848i	0.626219	−	0.779647i	$-0.284601\pi$
$463$	−6.89825	−	9.85172i	−0.320589	−	0.457848i	−0.946808	+	0.321799i	$0.895713\pi$
$464$	−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	0.497260	−	0.867602i	$-0.334340\pi$
$467$	10.6775	+	2.86104i	0.494098	+	0.132393i	−0.00316149	+	0.999995i	$0.501006\pi$
$468$	−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	0.963370	−	0.268175i	$-0.0864207\pi$
$479$	−0.735877	−	4.17337i	−0.0336231	−	0.190686i	−0.996993	+	0.0774895i	$0.975310\pi$
$480$		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	0.216587	−	0.976263i	$-0.430507\pi$
$487$	−16.7646	−	16.7646i	−0.759676	−	0.759676i	−0.976263	+	0.216587i	$0.930507\pi$
$488$	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	0.954434	−	0.298421i	$-0.0964599\pi$
$491$	0.697417	+	1.91614i	0.0314740	+	0.0864740i	−0.922960	+	0.384895i	$0.874238\pi$
$492$	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	−0.532964	−	0.846138i	$-0.678922\pi$
$499$	8.77600	−	10.4588i	0.392868	−	0.468202i	0.925832	+	0.377937i	$0.123366\pi$
$500$		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	−0.920487	+	0.390772i	$0.872208\pi$
$503$	−42.9050	+	11.4964i	−1.91304	+	0.512597i	−0.992552	+	0.121825i	$0.961125\pi$
$504$	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	−0.958943	−	0.283597i	$-0.908472\pi$
$509$	0.883595	−	5.01112i	0.0391647	−	0.222114i	0.998108	+	0.0614836i	$0.0195832\pi$
$510$		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	−0.789888	−	0.613251i	$-0.789862\pi$
$521$	−14.9219	+	8.61518i	−0.653742	+	0.377438i	0.136146	+	0.990689i	$0.456528\pi$
$522$	−0.0655064	−	0.204754i	−0.00286714	−	0.00896184i
$523$	3.45799	+	12.9054i	0.151207	+	0.564314i	0.999400	+	0.0346265i	$0.0110241\pi$
$523$	3.45799	+	12.9054i	0.151207	+	0.564314i	−0.848193	+	0.529688i	$0.822309\pi$
$524$	−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	−0.673201	−	0.739459i	$-0.735081\pi$
$547$	5.89172	−	8.41425i	0.251912	−	0.359767i	0.925113	+	0.379692i	$0.123970\pi$
$548$	−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	0.990254	−	0.139276i	$-0.0444774\pi$
$557$	1.48759	+	5.55174i	0.0630310	+	0.235235i	−0.927223	+	0.374511i	$0.877811\pi$
$558$	−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	−0.0639343	−	0.997954i	$-0.520365\pi$
$563$	20.2152	−	14.1548i	0.851969	−	0.596555i	0.915903	+	0.401399i	$0.131476\pi$
$564$	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	−0.672913	−	0.739722i	$-0.734957\pi$
$569$	−1.46173	+	1.22654i	−0.0612790	+	0.0514192i	0.611634	+	0.791141i	$0.290513\pi$
$570$		0			0
$571$	−7.82276	+	44.3651i	−0.327372	+	1.85662i	0.165080	+	0.986280i	$0.447212\pi$
$571$	−7.82276	+	44.3651i	−0.327372	+	1.85662i	−0.492452	+	0.870340i	$0.663899\pi$
$572$	−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	0.227958	−	0.973671i	$-0.426795\pi$
$577$	21.9121	−	5.87132i	0.912211	−	0.244426i	0.684253	+	0.729245i	$0.260128\pi$
$578$	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	0.419780	−	0.907626i	$-0.362107\pi$
$587$	−7.01492	−	4.91190i	−0.289537	−	0.202736i	−0.709316	+	0.704890i	$0.750996\pi$
$588$	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	0.789192	−	0.614147i	$-0.210500\pi$
$593$	4.26261	+	4.26261i	0.175044	+	0.175044i	−0.614147	+	0.789192i	$0.710500\pi$
$594$	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	−0.604534	−	0.796580i	$-0.706641\pi$
$599$	−13.5981	+	4.94929i	−0.555602	+	0.202223i	0.0489318	+	0.998802i	$0.484418\pi$
$600$		0			0
$601$	−2.11215	−	11.9786i	−0.0861565	−	0.488618i	−0.997101	−	0.0760891i	$-0.975757\pi$
$601$	−2.11215	−	11.9786i	−0.0861565	−	0.488618i	0.910944	−	0.412529i	$-0.135354\pi$
$602$	−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	−0.949646	−	0.313324i	$-0.898557\pi$
$607$	−1.69592	−	19.3845i	−0.0688354	−	0.786792i	0.880811	−	0.473468i	$-0.156998\pi$
$608$	−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	0.511911	−	0.859038i	$-0.328938\pi$
$613$	13.0162	+	3.48768i	0.525720	+	0.140866i	0.0138088	+	0.999905i	$0.495604\pi$
$614$	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	−0.856535	−	0.516090i	$-0.827387\pi$
$617$	−26.0454	−	37.1967i	−1.04855	−	1.49748i	−0.192014	−	0.981392i	$-0.561502\pi$
$618$	−0.208614	−	0.166711i	−0.00839169	−	0.00670608i
$619$	0.765342	+	0.912099i	0.0307617	+	0.0366604i	0.781206	−	0.624273i	$-0.214605\pi$
$619$	0.765342	+	0.912099i	0.0307617	+	0.0366604i	−0.750444	+	0.660934i	$0.770160\pi$
$620$		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	−0.564492	−	0.825438i	$-0.690928\pi$
$631$	10.8669	−	18.8220i	0.432605	−	0.749293i	0.997097	+	0.0761454i	$0.0242613\pi$
$632$	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	0.0489751	−	0.998800i	$-0.484405\pi$
$641$	11.0540	−	1.94912i	0.436606	−	0.0769855i	0.387631	+	0.921815i	$0.373293\pi$
$642$	0.206860	+	0.339284i	0.00816410	+	0.0133905i
$643$	−10.0815	+	21.6198i	−0.397575	+	0.852602i	0.601001	+	0.799248i	$0.294769\pi$
$643$	−10.0815	+	21.6198i	−0.397575	+	0.852602i	−0.998576	+	0.0533535i	$0.983009\pi$
$644$	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	−0.963801	−	0.266622i	$-0.914092\pi$
$647$	−17.7336	+	17.7336i	−0.697179	+	0.697179i	0.266622	+	0.963801i	$0.414092\pi$
$648$	−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	0.718183	−	0.695855i	$-0.244974\pi$
$653$	16.5274	+	7.70684i	0.646766	+	0.301592i	−0.0714165	+	0.997447i	$0.522752\pi$
$654$	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	−0.371975	−	0.928243i	$-0.621319\pi$
$659$	−32.1808	−	11.7129i	−1.25359	−	0.456269i	−0.881612	+	0.471974i	$0.843542\pi$
$660$		0			0
$661$	3.43935	+	2.88596i	0.133775	+	0.112251i	0.707220	−	0.706993i	$-0.249949\pi$
$661$	3.43935	+	2.88596i	0.133775	+	0.112251i	−0.573445	+	0.819244i	$0.694393\pi$
$662$	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	0.927409	+	0.374050i	$0.122031\pi$
$673$	−1.31952	+	15.0821i	−0.0508636	+	0.581374i	−0.978272	+	0.207324i	$0.933525\pi$
$674$	−0.214165			−0.00824933
$675$		0			0
$676$	−16.7465			−0.644096
$677$	−0.848465	+	9.69800i	−0.0326092	+	0.372724i	0.962303	+	0.271979i	$0.0876782\pi$
$677$	−0.848465	+	9.69800i	−0.0326092	+	0.372724i	−0.994912	+	0.100745i	$0.967877\pi$
$678$	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	−0.749517	−	0.661985i	$-0.769714\pi$
$683$	6.02595	−	22.4891i	0.230577	−	0.860523i	0.980093	−	0.198538i	$-0.0636193\pi$
$684$	−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	0.259968	−	0.965617i	$-0.416288\pi$
$691$	−4.24724	−	1.54587i	−0.161573	−	0.0588077i	−0.421540	+	0.906810i	$0.638510\pi$
$692$	−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	$-0.820088\pi$
$701$		−	28.3612i		−	1.07119i	0.844476	−	0.535593i	$-0.179912\pi$
$702$	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	0.378907	−	0.925435i	$-0.376300\pi$
$709$	27.9978	−	4.93677i	1.05148	−	0.185404i	0.672574	+	0.740030i	$0.265189\pi$
$710$		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	−0.648583	−	0.761144i	$-0.724638\pi$
$719$	8.97949	−	15.5529i	0.334878	−	0.580026i	0.983461	+	0.181118i	$0.0579714\pi$
$720$		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	−0.450492	−	0.892780i	$-0.648751\pi$
$727$	−28.2887	−	2.47494i	−1.04917	−	0.0917905i	−0.598678	+	0.800990i	$0.704307\pi$
$728$	−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	0.697522	−	0.716563i	$-0.254286\pi$
$733$	−5.80448	−	8.28966i	−0.214393	−	0.306185i	−0.911916	+	0.410378i	$0.865397\pi$
$734$	−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	−0.334598	−	0.942361i	$-0.608601\pi$
$739$	−35.8294	−	20.6861i	−1.31801	−	0.760951i	−0.983408	+	0.181410i	$0.941934\pi$
$740$		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	−0.998478	−	0.0551445i	$-0.982438\pi$
$743$	−0.674496	−	7.70953i	−0.0247449	−	0.282835i	0.973734	−	0.227691i	$-0.0731175\pi$
$744$	−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	−0.933808	−	0.357773i	$-0.883536\pi$
$751$	−38.8916	+	14.1554i	−1.41918	+	0.516537i	−0.485367	+	0.874311i	$0.661314\pi$
$752$	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	0.874322	−	0.485347i	$-0.161307\pi$
$757$	10.7021	+	10.7021i	0.388975	+	0.388975i	−0.485347	+	0.874322i	$0.661307\pi$
$758$	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	0.726308	+	0.687370i	$0.241235\pi$
$761$	16.8761	+	46.3666i	0.611756	+	1.68079i	−0.114551	+	0.993417i	$0.536543\pi$
$762$	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	−0.677574	−	0.735455i	$-0.736969\pi$
$769$	4.55804	−	5.43206i	0.164367	−	0.195885i	0.841941	+	0.539570i	$0.181413\pi$
$770$		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	−0.410595	−	0.911818i	$-0.634679\pi$
$773$	−8.62644	+	2.31145i	−0.310272	+	0.0831370i	0.100323	+	0.994955i	$0.468012\pi$
$774$	−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	−0.563403	−	0.826182i	$-0.690508\pi$
$787$	0.568328	−	0.397947i	0.0202587	−	0.0141853i	0.583662	+	0.811997i	$0.301619\pi$
$788$	−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	0.590335	−	0.807158i	$-0.298996\pi$
$797$	37.0354	−	3.24018i	1.31186	−	0.114773i	0.721528	+	0.692385i	$0.243440\pi$
$798$	−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	−0.997329	−	0.0730336i	$-0.976732\pi$
$821$	−5.34053	+	14.6730i	−0.186386	+	0.512091i	0.810944	+	0.585124i	$0.198954\pi$
$822$	−0.175303	−	0.0590967i	−0.00611440	−	0.00206123i
$823$	29.7914	−	2.60641i	1.03846	−	0.0908536i	0.444850	−	0.895605i	$-0.353257\pi$
$823$	29.7914	−	2.60641i	1.03846	−	0.0908536i	0.593612	+	0.804752i	$0.297702\pi$
$824$	−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	−0.903442	−	0.428710i	$-0.858968\pi$
$827$	−9.64511	−	35.9960i	−0.335393	−	1.25171i	0.568049	−	0.822995i	$-0.307699\pi$
$828$	34.4463	−	4.68237i	1.19709	−	0.162724i
$829$	−6.82502	+	3.94043i	−0.237043	+	0.136857i	−0.613817	−	0.789448i	$-0.710367\pi$
$829$	−6.82502	+	3.94043i	−0.237043	+	0.136857i	0.376774	+	0.926305i	$0.377033\pi$
$830$		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	−0.976143	−	0.217128i	$-0.930331\pi$
$839$	−26.9906	+	22.6478i	−0.931819	+	0.781889i	0.0443239	+	0.999017i	$0.485887\pi$
$840$		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	−0.00417979	−	0.999991i	$-0.501330\pi$
$853$	22.1725	−	10.3392i	0.759171	−	0.354007i	0.763351	+	0.645984i	$0.223553\pi$
$854$	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	0.508559	−	0.861027i	$-0.330178\pi$
$857$	−3.70630	−	2.59518i	−0.126605	−	0.0886496i	−0.635164	+	0.772378i	$0.719067\pi$
$858$	−0.218368	−	0.119204i	−0.00745495	−	0.00406956i
$859$	−3.10612	−	8.53399i	−0.105979	−	0.291176i	0.875356	−	0.483478i	$-0.160627\pi$
$859$	−3.10612	−	8.53399i	−0.105979	−	0.291176i	−0.981336	+	0.192302i	$0.938405\pi$
$860$		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	0.250398	−	0.968143i	$-0.419439\pi$
$863$	−21.0851	−	21.0851i	−0.717746	−	0.717746i	−0.968143	+	0.250398i	$0.919439\pi$
$864$	−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	0.699668	+	0.714468i	$0.253331\pi$
$877$	3.98890	+	45.5933i	0.134696	+	1.53958i	−0.564973	+	0.825110i	$0.691113\pi$
$878$	−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	−0.182169	−	0.983267i	$-0.558312\pi$
$881$	−33.3855	−	19.2752i	−1.12479	−	0.649396i	−0.942619	+	0.333871i	$0.891645\pi$
$882$	−0.317304	−	0.0125173i	−0.0106842	−	0.000421480i
$883$	−18.1259	−	4.85682i	−0.609986	−	0.163445i	−0.0594144	−	0.998233i	$-0.518923\pi$
$883$	−18.1259	−	4.85682i	−0.609986	−	0.163445i	−0.550571	+	0.834788i	$0.685590\pi$
$884$	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	−0.998636	−	0.0522057i	$-0.983375\pi$
$887$	−21.0306	−	30.0349i	−0.706140	−	1.00847i	0.292496	−	0.956267i	$-0.405514\pi$
$888$	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	0.993943	−	0.109900i	$-0.0350529\pi$
$907$	8.15736	+	17.4935i	0.270861	+	0.580863i	−0.723082	+	0.690762i	$0.757275\pi$
$908$	−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	0.519523	−	0.854456i	$-0.326110\pi$
$911$	39.2363	−	6.91842i	1.29996	−	0.229217i	0.780433	+	0.625239i	$0.214999\pi$
$912$	−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	$0.255417\pi$
$919$			43.5953i			1.43808i	−0.694971	+	0.719038i	$0.744583\pi$
$920$		0			0
$921$	22.0468	−	2.46144i	0.726468	−	0.0811071i
$922$	−0.330404	+	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	0.813615	−	0.581404i	$-0.197496\pi$
$929$	32.4046	+	11.7943i	1.06316	+	0.386959i	0.249546	+	0.968363i	$0.419719\pi$
$930$		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	0.435244	+	0.900313i	$0.356662\pi$
$937$	−11.9945	+	44.7642i	−0.391845	+	1.46238i	−0.827089	+	0.562072i	$0.810005\pi$
$938$	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	0.314854	−	0.949140i	$-0.398045\pi$
$941$	8.77614	+	1.54747i	0.286094	+	0.0504461i	−0.0287596	+	0.999586i	$0.509156\pi$
$942$	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	−0.745854	−	0.666109i	$-0.767959\pi$
$947$	3.21081	−	36.6998i	0.104337	−	1.19258i	0.850192	−	0.526473i	$-0.176486\pi$
$948$	−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	−0.732523	−	0.680742i	$-0.761658\pi$
$953$	7.47785	−	27.9077i	0.242231	−	0.904020i	0.974755	−	0.223278i	$-0.0716758\pi$
$954$	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	0.0918158	−	0.995776i	$-0.470733\pi$
$967$	−19.0304	−	8.87400i	−0.611975	−	0.285369i	−0.703791	+	0.710407i	$0.748511\pi$
$968$	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	$-0.616749\pi$
$971$		−	58.1766i		−	1.86697i	0.358610	−	0.933487i	$-0.383251\pi$
$972$	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	0.359686	+	0.933073i	$0.382884\pi$
$977$	−18.3257	+	39.2996i	−0.586291	+	1.25731i	−0.945977	+	0.324232i	$0.894894\pi$
$978$	−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	−0.856387	−	0.516335i	$-0.827296\pi$
$983$	−21.9924	−	47.1628i	−0.701447	−	1.50426i	0.154940	−	0.987924i	$-0.450482\pi$
$984$	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	0.838654	−	0.544665i	$-0.183343\pi$
$991$	−1.64852	−	2.85532i	−0.0523670	−	0.0907023i	−0.891021	+	0.453963i	$0.850010\pi$
$992$	−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	−0.288979	−	0.957335i	$-0.593316\pi$
$997$	−23.3597	−	2.04371i	−0.739808	−	0.0647248i	−0.450829	+	0.892610i	$0.648871\pi$
$998$	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.32.9		192
5.2	odd	4		135.2.q.a.113.9	yes	192
5.3	odd	4	inner	675.2.ba.b.518.8		192
5.4	even	2		135.2.q.a.32.8	✓	192
15.2	even	4		405.2.r.a.368.8		192
15.14	odd	2		405.2.r.a.287.9		192
27.11	odd	18	inner	675.2.ba.b.632.8		192
135.38	even	36	inner	675.2.ba.b.443.9		192
135.92	even	36		135.2.q.a.38.8	yes	192
135.97	odd	36		405.2.r.a.278.9		192
135.119	odd	18		135.2.q.a.92.9	yes	192
135.124	even	18		405.2.r.a.197.8		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.8	✓	192	5.4	even	2
135.2.q.a.38.8	yes	192	135.92	even	36
135.2.q.a.92.9	yes	192	135.119	odd	18
135.2.q.a.113.9	yes	192	5.2	odd	4
405.2.r.a.197.8		192	135.124	even	18
405.2.r.a.278.9		192	135.97	odd	36
405.2.r.a.287.9		192	15.14	odd	2
405.2.r.a.368.8		192	15.2	even	4
675.2.ba.b.32.9		192	1.1	even	1	trivial
675.2.ba.b.443.9		192	135.38	even	36	inner
675.2.ba.b.518.8		192	5.3	odd	4	inner
675.2.ba.b.632.8		192	27.11	odd	18	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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