LMFDB - Embedded newform 405.2.r.a.278.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(8,405)] 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("405.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.23394128186$
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			278.9
Character	$\chi$	$=$	405.278
Dual form			405.2.r.a.287.9

$q$-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} +(1.96939 - 0.347256i) q^{4} +(-0.516124 - 2.17569i) q^{5} +(-0.148030 - 0.211408i) q^{7} +(-0.0158044 - 0.0589827i) q^{8} +(-0.0324025 + 0.0107445i) q^{10} +(-1.49616 - 4.11066i) q^{11} +(2.14258 + 0.187451i) q^{13} +(-0.00301826 + 0.00253263i) q^{14} +(3.75746 - 1.36760i) q^{16} +(-0.456091 + 1.70216i) q^{17} +(-4.91894 - 2.83995i) q^{19} +(-1.77197 - 4.10554i) q^{20} +(-0.0605267 + 0.0282241i) q^{22} +(4.74660 + 3.32360i) q^{23} +(-4.46723 + 2.24585i) q^{25} -0.0328351i q^{26} +(-0.364940 - 0.364940i) q^{28} +(3.59567 + 3.01712i) q^{29} +(-0.912568 - 5.17543i) q^{31} +(-0.0774120 - 0.166010i) q^{32} +(0.0264943 + 0.00467167i) q^{34} +(-0.383557 + 0.431179i) q^{35} +(3.12552 + 0.837479i) q^{37} +(-0.0366467 + 0.0785891i) q^{38} +(-0.120171 + 0.0648277i) q^{40} +(-0.241984 - 0.288386i) q^{41} +(8.25395 + 3.84888i) q^{43} +(-4.37396 - 7.57592i) q^{44} +(0.0442317 - 0.0766116i) q^{46} +(3.28345 - 2.29910i) q^{47} +(2.37136 - 6.51526i) q^{49} +(0.0401003 + 0.0649522i) q^{50} +(4.28465 - 0.374859i) q^{52} +(-8.15900 + 8.15900i) q^{53} +(-8.17131 + 5.37678i) q^{55} +(-0.0101299 + 0.0120724i) q^{56} +(0.0411020 - 0.0586997i) q^{58} +(10.6146 + 3.86341i) q^{59} +(-2.10712 + 11.9501i) q^{61} +(-0.0774969 + 0.0207652i) q^{62} +(6.92336 - 3.99720i) q^{64} +(-0.697999 - 4.75832i) q^{65} +(0.160052 - 1.82940i) q^{67} +(-0.307136 + 3.51058i) q^{68} +(0.00706800 + 0.00525965i) q^{70} +(-4.44360 + 2.56551i) q^{71} +(-13.8702 + 3.71651i) q^{73} +(0.00857816 - 0.0486492i) q^{74} +(-10.6735 - 3.88483i) q^{76} +(-0.647552 + 0.924799i) q^{77} +(-1.98949 + 2.37099i) q^{79} +(-4.91479 - 7.46920i) q^{80} +(-0.00406398 + 0.00406398i) q^{82} +(-4.94812 + 0.432904i) q^{83} +(3.93876 + 0.113789i) q^{85} +(0.0475536 - 0.130653i) q^{86} +(-0.218812 + 0.153214i) q^{88} +(-1.44584 + 2.50426i) q^{89} +(-0.277536 - 0.480707i) q^{91} +(10.5020 + 4.89717i) q^{92} +(-0.0393351 - 0.0468777i) q^{94} +(-3.64006 + 12.1678i) q^{95} +(-1.99162 + 4.27105i) q^{97} +(-0.102243 - 0.0273961i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

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	$0.973940\pi$
$3$		0			0
$3$		0			0
$4$	1.96939	−	0.347256i	0.984693	−	0.173628i
$5$	−0.516124	−	2.17569i	−0.230818	−	0.972997i
$5$	−0.516124	−	2.17569i	−0.230818	−	0.972997i
$6$		0			0
$7$	−0.148030	−	0.211408i	−0.0559499	−	0.0799048i	0.790202	−	0.612846i	$-0.209975\pi$
$7$	−0.148030	−	0.211408i	−0.0559499	−	0.0799048i	−0.846152	+	0.532941i	$0.821087\pi$
$8$	−0.0158044	−	0.0589827i	−0.00558769	−	0.0208535i
$9$		0			0
$10$	−0.0324025	+	0.0107445i	−0.0102466	+	0.00339770i
$11$	−1.49616	−	4.11066i	−0.451108	−	1.23941i	−0.931945	−	0.362600i	$-0.881889\pi$
$11$	−1.49616	−	4.11066i	−0.451108	−	1.23941i	0.480836	−	0.876810i	$-0.340333\pi$
$12$		0			0
$13$	2.14258	+	0.187451i	0.594244	+	0.0519896i	0.380311	−	0.924859i	$-0.375817\pi$
$13$	2.14258	+	0.187451i	0.594244	+	0.0519896i	0.213933	+	0.976848i	$0.431373\pi$
$14$	−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			0
$19$	−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	$0.892539\pi$
$20$	−1.77197	−	4.10554i	−0.396224	−	0.918027i
$21$		0			0
$22$	−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			0
$25$	−4.46723	+	2.24585i	−0.893447	+	0.449170i
$26$		−	0.0328351i		−	0.00643949i
$27$		0			0
$28$	−0.364940	−	0.364940i	−0.0689672	−	0.0689672i
$29$	3.59567	+	3.01712i	0.667699	+	0.560266i	0.912383	−	0.409337i	$-0.134240\pi$
$29$	3.59567	+	3.01712i	0.667699	+	0.560266i	−0.244685	+	0.969603i	$0.578684\pi$
$30$		0			0
$31$	−0.912568	−	5.17543i	−0.163902	−	0.929534i	−0.950189	−	0.311673i	$-0.899111\pi$
$31$	−0.912568	−	5.17543i	−0.163902	−	0.929534i	0.786287	−	0.617861i	$-0.212001\pi$
$32$	−0.0774120	−	0.166010i	−0.0136846	−	0.0293468i
$33$		0			0
$34$	0.0264943	+	0.00467167i	0.00454374	+	0.000801184i
$35$	−0.383557	+	0.431179i	−0.0648329	+	0.0728826i
$36$		0			0
$37$	3.12552	+	0.837479i	0.513832	+	0.137681i	0.506412	−	0.862292i	$-0.330972\pi$
$37$	3.12552	+	0.837479i	0.513832	+	0.137681i	0.00741968	+	0.999972i	$0.497638\pi$
$38$	−0.0366467	+	0.0785891i	−0.00594488	+	0.0127488i
$39$		0			0
$40$	−0.120171	+	0.0648277i	−0.0190007	+	0.0102502i
$41$	−0.241984	−	0.288386i	−0.0377916	−	0.0450383i	0.746818	−	0.665029i	$-0.231581\pi$
$41$	−0.241984	−	0.288386i	−0.0377916	−	0.0450383i	−0.784609	+	0.619991i	$0.787136\pi$
$42$		0			0
$43$	8.25395	+	3.84888i	1.25872	+	0.586948i	0.933461	−	0.358678i	$-0.116772\pi$
$43$	8.25395	+	3.84888i	1.25872	+	0.586948i	0.325254	+	0.945627i	$0.394550\pi$
$44$	−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	$0.211122\pi$
$48$		0			0
$49$	2.37136	−	6.51526i	0.338766	−	0.930751i
$50$	0.0401003	+	0.0649522i	0.00567104	+	0.00918563i
$51$		0			0
$52$	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			0
$55$	−8.17131	+	5.37678i	−1.10182	+	0.725005i
$56$	−0.0101299	+	0.0120724i	−0.00135367	+	0.00161324i
$57$		0			0
$58$	0.0411020	−	0.0586997i	0.00539696	−	0.00770765i
$59$	10.6146	+	3.86341i	1.38191	+	0.502973i	0.922756	−	0.385385i	$-0.125931\pi$
$59$	10.6146	+	3.86341i	1.38191	+	0.502973i	0.459152	+	0.888358i	$0.348153\pi$
$60$		0			0
$61$	−2.10712	+	11.9501i	−0.269790	+	1.53005i	0.485251	+	0.874375i	$0.338728\pi$
$61$	−2.10712	+	11.9501i	−0.269790	+	1.53005i	−0.755040	+	0.655678i	$0.772383\pi$
$62$	−0.0774969	+	0.0207652i	−0.00984212	+	0.00263719i
$63$		0			0
$64$	6.92336	−	3.99720i	0.865420	−	0.499650i
$65$	−0.697999	−	4.75832i	−0.0865761	−	0.590197i
$66$		0			0
$67$	0.160052	−	1.82940i	0.0195534	−	0.223497i	−0.980130	−	0.198354i	$-0.936440\pi$
$67$	0.160052	−	1.82940i	0.0195534	−	0.223497i	0.999684	−	0.0251426i	$-0.00800398\pi$
$68$	−0.307136	+	3.51058i	−0.0372457	+	0.425721i
$69$		0			0
$70$	0.00706800	+	0.00525965i	0.000844787	+	0.000628649i
$71$	−4.44360	+	2.56551i	−0.527358	+	0.304471i	−0.739940	−	0.672673i	$-0.765146\pi$
$71$	−4.44360	+	2.56551i	−0.527358	+	0.304471i	0.212582	+	0.977143i	$0.431813\pi$
$72$		0			0
$73$	−13.8702	+	3.71651i	−1.62338	+	0.434984i	−0.951993	−	0.306120i	$-0.900969\pi$
$73$	−13.8702	+	3.71651i	−1.62338	+	0.434984i	−0.671390	+	0.741104i	$0.734303\pi$
$74$	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			0
$79$	−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	$0.277928\pi$
$80$	−4.91479	−	7.46920i	−0.549490	−	0.835082i
$81$		0			0
$82$	−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			0
$85$	3.93876	+	0.113789i	0.427218	+	0.0123422i
$86$	0.0475536	−	0.130653i	0.00512784	−	0.0140886i
$87$		0			0
$88$	−0.218812	+	0.153214i	−0.0233254	+	0.0163326i
$89$	−1.44584	+	2.50426i	−0.153259	+	0.265452i	−0.932424	−	0.361367i	$-0.882310\pi$
$89$	−1.44584	+	2.50426i	−0.153259	+	0.265452i	0.779165	+	0.626819i	$0.215643\pi$
$90$		0			0
$91$	−0.277536	−	0.480707i	−0.0290937	−	0.0503917i
$92$	10.5020	+	4.89717i	1.09491	+	0.510565i
$93$		0			0
$94$	−0.0393351	−	0.0468777i	−0.00405710	−	0.00483507i
$95$	−3.64006	+	12.1678i	−0.373463	+	1.24839i
$96$		0			0
$97$	−1.99162	+	4.27105i	−0.202219	+	0.433659i	−0.981097	−	0.193516i	$-0.938011\pi$
$97$	−1.99162	+	4.27105i	−0.202219	+	0.433659i	0.778879	+	0.627175i	$0.215789\pi$
$98$	−0.102243	−	0.0273961i	−0.0103282	−	0.00276742i
$99$		0			0
$100$	−8.01782	+	5.97421i	−0.801782	+	0.597421i
$101$	−2.84523	−	0.501690i	−0.283110	−	0.0499200i	0.0302897	−	0.999541i	$-0.490357\pi$
$101$	−2.84523	−	0.501690i	−0.283110	−	0.0499200i	−0.313400	+	0.949621i	$0.601468\pi$
$102$		0			0
$103$	4.26799	+	9.15274i	0.420538	+	0.901846i	0.996438	+	0.0843263i	$0.0268738\pi$
$103$	4.26799	+	9.15274i	0.420538	+	0.901846i	−0.575900	+	0.817520i	$0.695348\pi$
$104$	−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	$0.491198\pi$
$108$		0			0
$109$			12.0030i			1.14968i	0.818265	+	0.574841i	$0.194936\pi$
$109$			12.0030i			1.14968i	−0.818265	+	0.574841i	$0.805064\pi$
$110$	0.0926461	+	0.117120i	0.00883346	+	0.0111670i
$111$		0			0
$112$	−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			0
$115$	4.78129	−	12.0425i	0.445858	−	1.12297i
$116$	8.12897	+	4.69326i	0.754756	+	0.435759i
$117$		0			0
$118$	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			0
$124$	−3.59440	−	9.87552i	−0.322786	−	0.886848i
$125$	7.19191	+	8.56017i	0.643264	+	0.765645i
$126$		0			0
$127$	−5.03035	−	18.7735i	−0.446371	−	1.66588i	−0.712290	−	0.701885i	$-0.752342\pi$
$127$	−5.03035	−	18.7735i	−0.446371	−	1.66588i	0.265918	−	0.963996i	$-0.414325\pi$
$128$	−0.280131	−	0.400068i	−0.0247603	−	0.0353614i
$129$		0			0
$130$	−0.0714389	+	0.0169470i	−0.00626560	+	0.00148635i
$131$	4.49710	−	0.792959i	0.392913	−	0.0692812i	0.0262986	−	0.999654i	$-0.491628\pi$
$131$	4.49710	−	0.792959i	0.392913	−	0.0692812i	0.366614	+	0.930373i	$0.380517\pi$
$132$		0			0
$133$	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			0
$139$	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	$0.331929\pi$
$140$	−0.605642	+	0.982350i	−0.0511861	+	0.0830238i
$141$		0			0
$142$	0.0449306	+	0.0641675i	0.00377049	+	0.00538482i
$143$	−2.43508	−	9.08786i	−0.203632	−	0.759965i
$144$		0			0
$145$	4.70851	−	9.38026i	0.391020	−	0.778988i
$146$	0.0749784	+	0.206002i	0.00620526	+	0.0170488i
$147$		0			0
$148$	6.44617	+	0.563966i	0.529872	+	0.0463578i
$149$	14.7726	−	12.3956i	1.21021	−	1.01549i	0.210937	−	0.977500i	$-0.432349\pi$
$149$	14.7726	−	12.3956i	1.21021	−	1.01549i	0.999278	−	0.0379911i	$-0.0120959\pi$
$150$		0			0
$151$	−14.1147	+	5.13734i	−1.14864	+	0.418070i	−0.845026	−	0.534725i	$-0.820415\pi$
$151$	−14.1147	+	5.13734i	−1.14864	+	0.418070i	−0.303613	+	0.952795i	$0.598193\pi$
$152$	−0.0897672	+	0.335016i	−0.00728108	+	0.0271734i
$153$		0			0
$154$	0.0149266	+	0.00861785i	0.00120282	+	0.000694446i
$155$	−10.7891	+	4.65662i	−0.866603	+	0.374029i
$156$		0			0
$157$	2.11753	−	0.987420i	0.168997	−	0.0788047i	−0.336279	−	0.941762i	$-0.609168\pi$
$157$	2.11753	−	0.987420i	0.168997	−	0.0788047i	0.505276	+	0.862958i	$0.331391\pi$
$158$	0.0387066	+	0.0271027i	0.00307933	+	0.00215617i
$159$		0			0
$160$	−0.321233	+	0.254106i	−0.0253957	+	0.0200889i
$161$		−	1.49546i		−	0.117859i
$162$		0			0
$163$	10.7302	+	10.7302i	0.840451	+	0.840451i	0.988917	−	0.148467i	$-0.0474338\pi$
$163$	10.7302	+	10.7302i	0.840451	+	0.840451i	−0.148467	+	0.988917i	$0.547434\pi$
$164$	−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			0
$169$	−8.24701	−	1.45417i	−0.634385	−	0.111859i
$170$	−0.00351027	−	0.0600545i	−0.000269225	−	0.00460597i
$171$		0			0
$172$	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			0
$175$	1.13607	+	0.611958i	0.0858791	+	0.0462597i
$176$	−11.2435	−	13.3995i	−0.847510	−	1.01002i
$177$		0			0
$178$	0.0400103	+	0.0186571i	0.00299890	+	0.00139841i
$179$	−4.77974	−	8.27875i	−0.357254	−	0.618783i	0.630247	−	0.776395i	$-0.282954\pi$
$179$	−4.77974	−	8.27875i	−0.357254	−	0.618783i	−0.987501	+	0.157612i	$0.949620\pi$
$180$		0			0
$181$	6.93879	−	12.0183i	0.515756	−	0.893315i	−0.484077	−	0.875026i	$-0.660844\pi$
$181$	6.93879	−	12.0183i	0.515756	−	0.893315i	0.999833	−	0.0182899i	$-0.00582219\pi$
$182$	−0.00694161	+	0.00486056i	−0.000514546	+	0.000360289i
$183$		0			0
$184$	0.121018	−	0.332494i	0.00892157	−	0.0245118i
$185$	0.208941	−	7.23239i	0.0153616	−	0.531736i
$186$		0			0
$187$	7.67937	−	0.671857i	0.561571	−	0.0491311i
$188$	5.66801	−	5.66801i	0.413382	−	0.413382i
$189$		0			0
$190$	0.189900	+	0.0391701i	0.0137768	+	0.00284170i
$191$	7.63489	−	9.09890i	0.552441	−	0.658374i	−0.415488	−	0.909599i	$-0.636389\pi$
$191$	7.63489	−	9.09890i	0.552441	−	0.658374i	0.967929	+	0.251225i	$0.0808335\pi$
$192$		0			0
$193$	−6.94425	+	9.91741i	−0.499858	+	0.713871i	−0.987226	−	0.159325i	$-0.949068\pi$
$193$	−6.94425	+	9.91741i	−0.499858	+	0.713871i	0.487368	+	0.873197i	$0.337957\pi$
$194$	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			0
$199$	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	$0.269791\pi$
$200$	0.203068	+	0.227995i	0.0143591	+	0.0161217i
$201$		0			0
$202$	−0.00384421	+	0.0439395i	−0.000270478	+	0.00309157i
$203$	0.105579	−	1.20678i	0.00741022	−	0.0846992i
$204$		0			0
$205$	−0.502544	+	0.675325i	−0.0350992	+	0.0471668i
$206$	0.133522	−	0.0770888i	0.00930290	−	0.00537103i
$207$		0			0
$208$	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
$213$		0			0
$214$	0.147470	−	0.175748i	0.0100808	−	0.0120139i
$215$	4.11390	−	19.9445i	0.280566	−	1.36020i
$216$		0			0
$217$	−0.959041	+	0.959041i	−0.0651039	+	0.0651039i
$218$	0.182550	−	0.0159710i	0.0123638	−	0.00108169i
$219$		0			0
$220$	−14.2253	+	13.4265i	−0.959072	+	0.905214i
$221$	−1.29628	+	3.56150i	−0.0871973	+	0.239573i
$222$		0			0
$223$	10.8010	−	7.56295i	0.723289	−	0.506452i	−0.153007	−	0.988225i	$-0.548896\pi$
$223$	10.8010	−	7.56295i	0.723289	−	0.506452i	0.876296	+	0.481773i	$0.160007\pi$
$224$	−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	$0.799573\pi$
$228$		0			0
$229$	−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	$0.866508\pi$
$230$	−0.189512	−	0.0566933i	−0.0124960	−	0.00373825i
$231$		0			0
$232$	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			0
$235$	−6.69679	−	5.95715i	−0.436850	−	0.388602i
$236$	22.2459	+	3.92255i	1.44808	+	0.255336i
$237$		0			0
$238$	−0.00293432	−	0.00629266i	−0.000190204	−	0.000407893i
$239$	−3.76477	−	21.3510i	−0.243522	−	1.38108i	−0.823899	−	0.566736i	$-0.808206\pi$
$239$	−3.76477	−	21.3510i	−0.243522	−	1.38108i	0.580377	−	0.814348i	$-0.302905\pi$
$240$		0			0
$241$	3.99926	+	3.35578i	0.257615	+	0.216165i	0.762443	−	0.647055i	$-0.224000\pi$
$241$	3.99926	+	3.35578i	0.257615	+	0.216165i	−0.504828	+	0.863220i	$0.668444\pi$
$242$	0.0878299	+	0.0878299i	0.00564592	+	0.00564592i
$243$		0			0
$244$			24.2661i			1.55348i
$245$	−15.3991	−	1.79666i	−0.983811	−	0.114784i
$246$		0			0
$247$	−10.0068	−	7.00687i	−0.636721	−	0.445837i
$248$	−0.290838	+	0.135620i	−0.0184682	+	0.00861188i
$249$		0			0
$250$	0.120619	−	0.120769i	0.00762862	−	0.00763811i
$251$	−12.0778	−	6.97313i	−0.762345	−	0.440140i	0.0677923	−	0.997699i	$-0.478404\pi$
$251$	−12.0778	−	6.97313i	−0.762345	−	0.440140i	−0.830137	+	0.557560i	$0.811738\pi$
$252$		0			0
$253$	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			0
$259$	−0.285619	−	0.784731i	−0.0177475	−	0.0487608i
$260$	−3.02699	−	9.12859i	−0.187726	−	0.566131i
$261$		0			0
$262$	−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			0
$265$	21.9625	+	13.5404i	1.34914	+	0.831779i
$266$	0.0220392	−	0.00388610i	0.00135131	−	0.000238272i
$267$		0			0
$268$	−0.320066	−	3.65837i	−0.0195511	−	0.223470i
$269$	−1.84882			−0.112724			−0.0563622	−	0.998410i	$-0.517950\pi$
$269$	−1.84882			−0.112724			−0.0563622	+	0.998410i	$0.517950\pi$
$270$		0			0
$271$	14.0068			0.850851			0.425426	−	0.904993i	$-0.360124\pi$
$271$	14.0068			0.850851			0.425426	+	0.904993i	$0.360124\pi$
$272$	0.614129	+	7.01953i	0.0372370	+	0.425621i
$273$		0			0
$274$	−0.105185	+	0.0185469i	−0.00635445	+	0.00112046i
$275$	15.9156	+	15.0031i	0.959747	+	0.904723i
$276$		0			0
$277$	10.4313	+	14.8975i	0.626758	+	0.895103i	0.999460	−	0.0328481i	$-0.0104577\pi$
$277$	10.4313	+	14.8975i	0.626758	+	0.895103i	−0.372703	+	0.927951i	$0.621569\pi$
$278$	−0.0322521	−	0.120367i	−0.00193435	−	0.00721911i
$279$		0			0
$280$	0.0314940	+	0.0158087i	0.00188212	+	0.000944750i
$281$	8.98091	+	24.6748i	0.535756	+	1.47198i	0.852124	+	0.523341i	$0.175314\pi$
$281$	8.98091	+	24.6748i	0.535756	+	1.47198i	−0.316368	+	0.948637i	$0.602463\pi$
$282$		0			0
$283$	−18.2738	−	1.59875i	−1.08627	−	0.0950360i	−0.470071	−	0.882629i	$-0.655772\pi$
$283$	−18.2738	−	1.59875i	−1.08627	−	0.0950360i	−0.616196	+	0.787593i	$0.711327\pi$
$284$	−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			0
$289$	12.0331	+	6.94732i	0.707830	+	0.408666i
$290$	−0.148926	−	0.0591288i	−0.00874523	−	0.00347216i
$291$		0			0
$292$	−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			0
$295$	2.92711	−	25.0881i	0.170423	−	1.46069i
$296$		−	0.197587i		−	0.0114845i
$297$		0			0
$298$	−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
$303$		0			0
$304$	−22.3666	−	3.94384i	−1.28281	−	0.226195i
$305$	27.0872	−	1.58328i	1.55101	−	0.0906586i
$306$		0			0
$307$	−12.3714	−	3.31491i	−0.706074	−	0.189192i	−0.112124	−	0.993694i	$-0.535765\pi$
$307$	−12.3714	−	3.31491i	−0.706074	−	0.189192i	−0.593949	+	0.804502i	$0.702432\pi$
$308$	−0.954137	+	2.04615i	−0.0543670	+	0.116590i
$309$		0			0
$310$	0.0851767	+	0.157892i	0.00483771	+	0.00896765i
$311$	−13.5014	−	16.0903i	−0.765592	−	0.912397i	0.232596	−	0.972573i	$-0.425278\pi$
$311$	−13.5014	−	16.0903i	−0.765592	−	0.912397i	−0.998188	+	0.0601768i	$0.980834\pi$
$312$		0			0
$313$	−26.7887	−	12.4918i	−1.51419	−	0.706078i	−0.524781	−	0.851237i	$-0.675853\pi$
$313$	−26.7887	−	12.4918i	−1.51419	−	0.706078i	−0.989408	+	0.145159i	$0.953631\pi$
$314$	−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			0
$319$	7.02268	−	19.2947i	0.393195	−	1.08029i
$320$	−12.2700	−	13.0000i	−0.685912	−	0.726723i
$321$		0			0
$322$	−0.0227439	+	0.00198984i	−0.00126747	+	0.000110889i
$323$	7.07752	−	7.07752i	0.393804	−	0.393804i
$324$		0			0
$325$	−9.99237	+	3.97451i	−0.554277	+	0.220466i
$326$	0.148914	−	0.177468i	0.00824756	−	0.00982906i
$327$		0			0
$328$	−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
$333$		0			0
$334$	−0.256536	+	0.148111i	−0.0140371	+	0.00810430i
$335$	−4.06280	+	0.595973i	−0.221975	+	0.0325615i
$336$		0			0
$337$	−1.22264	+	13.9748i	−0.0666015	+	0.761258i	0.887311	+	0.461172i	$0.152571\pi$
$337$	−1.22264	+	13.9748i	−0.0666015	+	0.761258i	−0.953912	+	0.300086i	$0.902985\pi$
$338$	−0.0111426	+	0.127361i	−0.000606078	+	0.00692750i
$339$		0			0
$340$	7.79645	−	1.14366i	0.422822	−	0.0620238i
$341$	−19.9091	+	11.4945i	−1.07814	+	0.622463i
$342$		0			0
$343$	−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	$0.246847\pi$
$348$		0			0
$349$	−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	$0.254845\pi$
$350$	0.00779540	−	0.0180924i	0.000416682	−	0.000967079i
$351$		0			0
$352$	−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			0
$355$	7.87521	+	8.34377i	0.417973	+	0.442841i
$356$	−1.97779	+	5.43394i	−0.104823	+	0.287998i
$357$		0			0
$358$	−0.119549	+	0.0837088i	−0.00631834	+	0.00442415i
$359$	−5.90045	+	10.2199i	−0.311414	+	0.539385i	−0.978669	−	0.205445i	$-0.934136\pi$
$359$	−5.90045	+	10.2199i	−0.311414	+	0.539385i	0.667255	+	0.744829i	$0.267469\pi$
$360$		0			0
$361$	6.63064	+	11.4846i	0.348981	+	0.604453i
$362$	−0.192015	−	0.0895381i	−0.0100921	−	0.00470602i
$363$		0			0
$364$	−0.713504	−	0.850321i	−0.0373978	−	0.0445689i
$365$	15.2447	+	28.2590i	0.797944	+	1.47915i
$366$		0			0
$367$	−0.896047	+	1.92158i	−0.0467733	+	0.100306i	−0.928306	−	0.371818i	$-0.878735\pi$
$367$	−0.896047	+	1.92158i	−0.0467733	+	0.100306i	0.881532	+	0.472123i	$0.156512\pi$
$368$	22.3805	+	5.99683i	1.16666	+	0.312607i
$369$		0			0
$370$	−0.110273	+	0.00644559i	−0.00573281	+	0.000335090i
$371$	2.93265	+	0.517106i	0.152256	+	0.0268468i
$372$		0			0
$373$	1.40277	+	3.00825i	0.0726328	+	0.155762i	0.939272	−	0.343174i	$-0.111502\pi$
$373$	1.40277	+	3.00825i	0.0726328	+	0.155762i	−0.866639	+	0.498936i	$0.833724\pi$
$374$	−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			0
$379$			15.7634i			0.809713i	0.914380	+	0.404856i	$0.132678\pi$
$379$			15.7634i			0.809713i	−0.914380	+	0.404856i	$0.867322\pi$
$380$	−2.94334	+	25.2272i	−0.150990	+	1.29413i
$381$		0			0
$382$	−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			0
$385$	2.34629	+	0.931559i	0.119578	+	0.0474766i
$386$	0.160070	+	0.0924166i	0.00814736	+	0.00470388i
$387$		0			0
$388$	−2.43913	+	9.10294i	−0.123828	+	0.462132i
$389$	−28.2091	+	10.2673i	−1.43026	+	0.520571i	−0.937005	−	0.349315i	$-0.886414\pi$
$389$	−28.2091	+	10.2673i	−1.43026	+	0.520571i	−0.493252	+	0.869886i	$0.664192\pi$
$390$		0			0
$391$	−7.82217	+	6.56358i	−0.395584	+	0.331934i
$392$	−0.421765	−	0.0368997i	−0.0213024	−	0.00186372i
$393$		0			0
$394$	0.0310408	+	0.0852840i	0.00156382	+	0.00429655i
$395$	6.18535	+	3.10479i	0.311219	+	0.156219i
$396$		0			0
$397$	−1.23812	−	4.62074i	−0.0621397	−	0.231908i	0.927871	−	0.372902i	$-0.121637\pi$
$397$	−1.23812	−	4.62074i	−0.0621397	−	0.231908i	−0.990011	+	0.140993i	$0.954970\pi$
$398$	−0.0489911	−	0.0699666i	−0.00245570	−	0.00350711i
$399$		0			0
$400$	−13.7140	+	14.5481i	−0.685700	+	0.727404i
$401$	8.47214	−	1.49387i	0.423078	−	0.0746001i	0.0419444	−	0.999120i	$-0.486645\pi$
$401$	8.47214	−	1.49387i	0.423078	−	0.0746001i	0.381134	+	0.924520i	$0.375534\pi$
$402$		0			0
$403$	−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			0
$409$	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	$0.377377\pi$
$410$	0.0109395	+	0.00674443i	0.000540261	+	0.000333083i
$411$		0			0
$412$	11.5837	+	16.5432i	0.570686	+	0.815024i
$413$	−0.754524	−	2.81592i	−0.0371277	−	0.138562i
$414$		0			0
$415$	3.49571	+	10.5421i	0.171597	+	0.517493i
$416$	−0.134742	−	0.370201i	−0.00660628	−	0.0181506i
$417$		0			0
$418$	0.377882	+	0.0330604i	0.0184828	+	0.00161704i
$419$	−6.72816	+	5.64560i	−0.328692	+	0.275806i	−0.792167	−	0.610305i	$-0.791047\pi$
$419$	−6.72816	+	5.64560i	−0.328692	+	0.275806i	0.463475	+	0.886110i	$0.346603\pi$
$420$		0			0
$421$	0.538899	−	0.196143i	0.0262643	−	0.00955944i	−0.328855	−	0.944381i	$-0.606663\pi$
$421$	0.538899	−	0.196143i	0.0262643	−	0.00955944i	0.355119	+	0.934821i	$0.384440\pi$
$422$	0.0224469	−	0.0837730i	0.00109270	−	0.00407800i
$423$		0			0
$424$	0.610187	+	0.352292i	0.0296333	+	0.0171088i
$425$	−1.78532	−	8.62824i	−0.0866006	−	0.418531i
$426$		0			0
$427$	2.83827	−	1.32351i	0.137353	−	0.0640489i
$428$	24.6170	+	17.2370i	1.18991	+	0.833181i
$429$		0			0
$430$	−0.308803	−	0.0360290i	−0.0148918	−	0.00173747i
$431$			25.0117i			1.20477i	0.798205	+	0.602386i	$0.205783\pi$
$431$			25.0117i			1.20477i	−0.798205	+	0.602386i	$0.794217\pi$
$432$		0			0
$433$	−24.9892	−	24.9892i	−1.20090	−	1.20090i	−0.973892	−	0.227011i	$-0.927105\pi$
$433$	−24.9892	−	24.9892i	−1.20090	−	1.20090i	−0.227011	−	0.973892i	$-0.572895\pi$
$434$	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			0
$439$	−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	$0.591492\pi$
$440$	0.446279	+	0.396989i	0.0212755	+	0.0189257i
$441$		0			0
$442$	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	$-0.109002\pi$
$444$		0			0
$445$	6.19473	+	1.85318i	0.293658	+	0.0878492i
$446$	−0.129394	−	0.154205i	−0.00612697	−	0.00730184i
$447$		0			0
$448$	−1.86990	−	0.871951i	−0.0883447	−	0.0411958i
$449$	−3.36725	−	5.83225i	−0.158910	−	0.275241i	0.775566	−	0.631267i	$-0.217465\pi$
$449$	−3.36725	−	5.83225i	−0.158910	−	0.275241i	−0.934476	+	0.356026i	$0.884131\pi$
$450$		0			0
$451$	−0.823409	+	1.42619i	−0.0387728	+	0.0671565i
$452$	−15.2161	+	10.6544i	−0.715706	+	0.501142i
$453$		0			0
$454$	−0.0760955	+	0.209071i	−0.00357134	+	0.00981217i
$455$	−0.902624	+	0.851936i	−0.0423157	+	0.0399394i
$456$		0			0
$457$	−36.1208	+	3.16016i	−1.68966	+	0.147826i	−0.891015	−	0.453974i	$-0.850006\pi$
$457$	−36.1208	+	3.16016i	−1.68966	+	0.147826i	−0.798647	+	0.601800i	$0.794450\pi$
$458$	−0.0899006	+	0.0899006i	−0.00420078	+	0.00420078i
$459$		0			0
$460$	5.23438	−	25.3767i	0.244054	−	1.18319i
$461$	−16.9825	+	20.2390i	−0.790956	+	0.942625i	−0.999373	−	0.0354156i	$-0.988725\pi$
$461$	−16.9825	+	20.2390i	−0.790956	+	0.942625i	0.208417	+	0.978040i	$0.433169\pi$
$462$		0			0
$463$	6.89825	−	9.85172i	0.320589	−	0.457848i	−0.626219	−	0.779647i	$-0.715399\pi$
$463$	6.89825	−	9.85172i	0.320589	−	0.457848i	0.946808	+	0.321799i	$0.104287\pi$
$464$	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	$0.334340\pi$
$468$		0			0
$469$	−0.410442	+	0.236969i	−0.0189525	+	0.0109422i
$470$	−0.0816895	+	0.109775i	−0.00376805	+	0.00506357i
$471$		0			0
$472$	0.0601168	−	0.687138i	0.00276710	−	0.0316281i
$473$	3.47222	−	39.6877i	0.159653	−	1.82484i
$474$		0			0
$475$	28.3521	+	1.63953i	1.30089	+	0.0752269i
$476$	0.787631	−	0.454739i	0.0361010	−	0.0208429i
$477$		0			0
$478$	−0.319711	+	0.0856663i	−0.0146232	+	0.00391828i
$479$	0.735877	−	4.17337i	0.0336231	−	0.190686i	−0.963370	−	0.268175i	$-0.913579\pi$
$479$	0.735877	−	4.17337i	0.0336231	−	0.190686i	0.996993	+	0.0774895i	$0.0246904\pi$
$480$		0			0
$481$	6.53967	+	2.38024i	0.298183	+	0.108530i
$482$	0.0457155	−	0.0652884i	0.00208228	−	0.00297381i
$483$		0			0
$484$	−10.4582	+	12.4636i	−0.475374	+	0.566529i
$485$	10.3204	+	2.12876i	0.468625	+	0.0966619i
$486$		0			0
$487$	16.7646	−	16.7646i	0.759676	−	0.759676i	−0.216587	−	0.976263i	$-0.569493\pi$
$487$	16.7646	−	16.7646i	0.759676	−	0.759676i	0.976263	+	0.216587i	$0.0694925\pi$
$488$	0.738151	−	0.0645798i	0.0334145	−	0.00292339i
$489$		0			0
$490$	−0.00683498	+	0.236590i	−0.000308773	+	0.0106880i
$491$	−0.697417	+	1.91614i	−0.0314740	+	0.0864740i	−0.954434	−	0.298421i	$-0.903540\pi$
$491$	−0.697417	+	1.91614i	−0.0314740	+	0.0864740i	0.922960	+	0.384895i	$0.125762\pi$
$492$		0			0
$493$	−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			0
$499$	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	$0.678922\pi$
$500$	17.1362	+	14.3608i	0.766355	+	0.642236i
$501$		0			0
$502$	−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			0
$505$	0.376968	+	6.44926i	0.0167748	+	0.286988i
$506$	−0.381102	−	0.0671985i	−0.0169420	−	0.00298734i
$507$		0			0
$508$	−16.4259	−	35.2255i	−0.728782	−	1.56288i
$509$	−0.883595	−	5.01112i	−0.0391647	−	0.222114i	0.958943	−	0.283597i	$-0.0915279\pi$
$509$	−0.883595	−	5.01112i	−0.0391647	−	0.222114i	−0.998108	+	0.0614836i	$0.980417\pi$
$510$		0			0
$511$	2.83890	+	2.38212i	0.125586	+	0.105379i
$512$	−0.863214	−	0.863214i	−0.0381490	−	0.0381490i
$513$		0			0
$514$		−	0.143093i		−	0.00631155i
$515$	17.7107	−	14.0098i	0.780426	−	0.617344i
$516$		0			0
$517$	−14.3634	−	10.0573i	−0.631700	−	0.442321i
$518$	−0.0115547	+	0.00538802i	−0.000507682	+	0.000236736i
$519$		0			0
$520$	−0.269627	+	0.116372i	−0.0118239	+	0.00510326i
$521$	14.9219	+	8.61518i	0.653742	+	0.377438i	0.789888	−	0.613251i	$-0.210138\pi$
$521$	14.9219	+	8.61518i	0.653742	+	0.377438i	−0.136146	+	0.990689i	$0.543472\pi$
$522$		0			0
$523$	−3.45799	+	12.9054i	−0.151207	+	0.564314i	0.848193	+	0.529688i	$0.177691\pi$
$523$	−3.45799	+	12.9054i	−0.151207	+	0.564314i	−0.999400	+	0.0346265i	$0.988976\pi$
$524$	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
$528$		0			0
$529$	3.61738	+	9.93866i	0.157277	+	0.432116i
$530$	0.176708	−	0.352036i	0.00767569	−	0.0152915i
$531$		0			0
$532$	0.758707	+	2.83153i	0.0328941	+	0.122762i
$533$	−0.464412	−	0.663249i	−0.0201159	−	0.0287285i
$534$		0			0
$535$	17.6348	−	28.6036i	0.762417	−	1.23664i
$536$	−0.110432	+	0.0194722i	−0.00476995	+	0.000841071i
$537$		0			0
$538$	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
$543$		0			0
$544$	0.317883	−	0.0560513i	0.0136291	−	0.00240318i
$545$	26.1148	−	6.19505i	1.11864	−	0.265367i
$546$		0			0
$547$	−5.89172	−	8.41425i	−0.251912	−	0.359767i	0.673201	−	0.739459i	$-0.264919\pi$
$547$	−5.89172	−	8.41425i	−0.251912	−	0.359767i	−0.925113	+	0.379692i	$0.876030\pi$
$548$	−3.62103	−	13.5139i	−0.154683	−	0.577283i
$549$		0			0
$550$	0.207000	−	0.262017i	0.00882651	−	0.0111725i
$551$	−9.11839	−	25.0526i	−0.388456	−	1.06728i
$552$		0			0
$553$	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			0
$559$	16.9632	+	9.79373i	0.717468	+	0.414230i
$560$	−0.851516	+	2.14469i	−0.0359831	+	0.0906297i
$561$		0			0
$562$	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	$0.520365\pi$
$564$		0			0
$565$	12.8859	+	16.2900i	0.542114	+	0.685323i
$566$			0.280047i			0.0117713i
$567$		0			0
$568$	0.221549	+	0.221549i	0.00929600	+	0.00929600i
$569$	1.46173	+	1.22654i	0.0612790	+	0.0514192i	0.672913	−	0.739722i	$-0.265043\pi$
$569$	1.46173	+	1.22654i	0.0612790	+	0.0514192i	−0.611634	+	0.791141i	$0.709487\pi$
$570$		0			0
$571$	−7.82276	−	44.3651i	−0.327372	−	1.85662i	−0.492452	−	0.870340i	$-0.663899\pi$
$571$	−7.82276	−	44.3651i	−0.327372	−	1.85662i	0.165080	−	0.986280i	$-0.447212\pi$
$572$	−7.95143	−	17.0519i	−0.332466	−	0.712976i
$573$		0			0
$574$	0.00146075		0.000257569i	6.09704e−5		1.07507e-5i
$575$	−28.6685	−	4.18717i	−1.19556	−	0.174617i
$576$		0			0
$577$	−21.9121	−	5.87132i	−0.912211	−	0.244426i	−0.227958	−	0.973671i	$-0.573205\pi$
$577$	−21.9121	−	5.87132i	−0.912211	−	0.244426i	−0.684253	+	0.729245i	$0.739872\pi$
$578$	0.0896482	−	0.192251i	0.00372888	−	0.00799660i
$579$		0			0
$580$	6.01552	−	20.1084i	0.249781	−	0.834956i
$581$	0.823988	+	0.981990i	0.0341848	+	0.0407398i
$582$		0			0
$583$	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			0
$589$	−10.2091	+	28.0493i	−0.420659	+	1.15575i
$590$	−0.385451	−	0.0111355i	−0.0158688	−	0.000458442i
$591$		0			0
$592$	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			0
$595$	−0.558997	−	0.849530i	−0.0229166	−	0.0348273i
$596$	24.7884	−	29.5417i	1.01537	−	1.21007i
$597$		0			0
$598$	0.109131	−	0.155855i	0.00446269	−	0.00637338i
$599$	13.5981	+	4.94929i	0.555602	+	0.202223i	0.604534	−	0.796580i	$-0.293359\pi$
$599$	13.5981	+	4.94929i	0.555602	+	0.202223i	−0.0489318	+	0.998802i	$0.515582\pi$
$600$		0			0
$601$	−2.11215	+	11.9786i	−0.0861565	+	0.488618i	0.910944	+	0.412529i	$0.135354\pi$
$601$	−2.11215	+	11.9786i	−0.0861565	+	0.488618i	−0.997101	+	0.0760891i	$0.975757\pi$
$602$	−0.0346604	+	0.00928722i	−0.00141265	+	0.000378519i
$603$		0			0
$604$	−26.0133	+	15.0188i	−1.05847	+	0.611107i
$605$	14.5950	+	10.8609i	0.593371	+	0.441557i
$606$		0			0
$607$	1.69592	−	19.3845i	0.0688354	−	0.786792i	−0.880811	−	0.473468i	$-0.843002\pi$
$607$	1.69592	−	19.3845i	0.0688354	−	0.786792i	0.949646	−	0.313324i	$-0.101443\pi$
$608$	−0.0906769	+	1.03644i	−0.00367743	+	0.0420333i
$609$		0			0
$610$	−0.0601214	−	0.409853i	−0.00243424	−	0.0165945i
$611$	7.46602	−	4.31051i	0.302043	−	0.174384i
$612$		0			0
$613$	−13.0162	+	3.48768i	−0.525720	+	0.140866i	−0.511911	−	0.859038i	$-0.671062\pi$
$613$	−13.0162	+	3.48768i	−0.525720	+	0.140866i	−0.0138088	+	0.999905i	$0.504396\pi$
$614$	−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			0
$619$	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	$0.214605\pi$
$620$	−19.6309	+	12.9173i	−0.788396	+	0.518770i
$621$		0			0
$622$	−0.226747	+	0.226747i	−0.00909171	+	0.00909171i
$623$	0.743449	−	0.0650434i	0.0297857	−	0.00260591i
$624$		0			0
$625$	14.9123	−	20.0654i	0.596493	−	0.802618i
$626$	−0.154339	+	0.424042i	−0.00616861	+	0.0169481i
$627$		0			0
$628$	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
$633$		0			0
$634$	−0.260588	−	0.310556i	−0.0103493	−	0.0123338i
$635$	−38.2490	+	20.6339i	−1.51787	+	0.818833i
$636$		0			0
$637$	6.30211	−	13.5149i	0.249699	−	0.535481i
$638$	−0.302790	−	0.0811322i	−0.0119876	−	0.00321206i
$639$		0			0
$640$	−0.725841	+	0.815962i	−0.0286914	+	0.0322537i
$641$	−11.0540	−	1.94912i	−0.436606	−	0.0769855i	−0.0489751	−	0.998800i	$-0.515595\pi$
$641$	−11.0540	−	1.94912i	−0.436606	−	0.0769855i	−0.387631	+	0.921815i	$0.626707\pi$
$642$		0			0
$643$	10.0815	+	21.6198i	0.397575	+	0.852602i	0.998576	+	0.0533535i	$0.0169910\pi$
$643$	10.0815	+	21.6198i	0.397575	+	0.852602i	−0.601001	+	0.799248i	$0.705231\pi$
$644$	−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			0
$649$		−	49.4134i		−	1.93965i
$650$	0.0737426	+	0.146682i	0.00289242	+	0.00575334i
$651$		0			0
$652$	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			0
$655$	−4.04629	−	9.37501i	−0.158102	−	0.366312i
$656$	−1.30364	−	0.752659i	−0.0508987	−	0.0293864i
$657$		0			0
$658$	−0.00408758	+	0.0152550i	−0.000159350	+	0.000594704i
$659$	32.1808	−	11.7129i	1.25359	−	0.456269i	0.371975	−	0.928243i	$-0.378681\pi$
$659$	32.1808	−	11.7129i	1.25359	−	0.456269i	0.881612	+	0.471974i	$0.156458\pi$
$660$		0			0
$661$	3.43935	−	2.88596i	0.133775	−	0.112251i	−0.573445	−	0.819244i	$-0.694393\pi$
$661$	3.43935	−	2.88596i	0.133775	−	0.112251i	0.707220	+	0.706993i	$0.249949\pi$
$662$	0.151210	+	0.0132291i	0.00587693	+	0.000514165i
$663$		0			0
$664$	0.103736	+	0.285012i	0.00402573	+	0.0110606i
$665$	3.11122	−	1.03166i	0.120648	−	0.0400061i
$666$		0			0
$667$	7.03946	+	26.2716i	0.272569	+	1.01724i
$668$	−22.2558	−	31.7846i	−0.861103	−	1.22978i
$669$		0			0
$670$	0.0144698	+	0.0609967i	0.000559019	+	0.00235651i
$671$	52.2754	−	9.21756i	2.01807	−	0.355840i
$672$		0			0
$673$	1.31952	+	15.0821i	0.0508636	+	0.581374i	0.978272	+	0.207324i	$0.0664755\pi$
$673$	1.31952	+	15.0821i	0.0508636	+	0.581374i	−0.927409	+	0.374050i	$0.877969\pi$
$674$	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			0
$679$	1.19775	−	0.211196i	0.0459656	−	0.00810497i
$680$	−0.0555380	−	0.234117i	−0.00212978	−	0.00897797i
$681$		0			0
$682$	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	$0.769714\pi$
$684$		0			0
$685$	−14.8487	+	4.92374i	−0.567340	+	0.188126i
$686$	0.0187764	+	0.0515877i	0.000716886	+	0.00196963i
$687$		0			0
$688$	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
$693$		0			0
$694$	0.0807256	+	0.0466069i	0.00306430	+	0.00176918i
$695$	−7.23256	−	16.7574i	−0.274347	−	0.635645i
$696$		0			0
$697$	0.601245	−	0.280365i	0.0227738	−	0.0106196i
$698$	0.0478038	+	0.0334725i	0.00180940	+	0.00126695i
$699$		0			0
$700$	2.44987	+	0.810673i	0.0925965	+	0.0306405i
$701$		−	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			0
$703$	−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
$708$		0			0
$709$	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	$0.376300\pi$
$710$	0.116419	−	0.130873i	0.00436911	−	0.00491158i
$711$		0			0
$712$	0.170559	+	0.0457011i	0.00639196	+	0.00171272i
$713$	12.8695	−	27.5987i	0.481966	−	1.03358i
$714$		0			0
$715$	−18.5155	+	9.98844i	−0.692442	+	0.373546i
$716$	−12.2880	−	14.6443i	−0.459224	−	0.547282i
$717$		0			0
$718$	0.163281	+	0.0761394i	0.00609361	+	0.00284150i
$719$	−8.97949	−	15.5529i	−0.334878	−	0.580026i	0.648583	−	0.761144i	$-0.275362\pi$
$719$	−8.97949	−	15.5529i	−0.334878	−	0.580026i	−0.983461	+	0.181118i	$0.942029\pi$
$720$		0			0
$721$	1.30318	−	2.25717i	0.0485328	−	0.0840612i
$722$	0.165843	−	0.116124i	0.00617202	−	0.00432170i
$723$		0			0
$724$	9.49171	−	26.0783i	0.352757	−	0.969191i
$725$	−22.8387	−	5.40287i	−0.848207	−	0.200658i
$726$		0			0
$727$	28.2887	−	2.47494i	1.04917	−	0.0917905i	0.450492	−	0.892780i	$-0.351249\pi$
$727$	28.2887	−	2.47494i	1.04917	−	0.0917905i	0.598678	+	0.800990i	$0.295693\pi$
$728$	−0.0239671	+	0.0239671i	−0.000888279	+	0.000888279i
$729$		0			0
$730$	0.409497	−	0.269452i	0.0151562	−	0.00997286i
$731$	−10.3159	+	12.2941i	−0.381549	+	0.454712i
$732$		0			0
$733$	5.80448	−	8.28966i	0.214393	−	0.306185i	−0.697522	−	0.716563i	$-0.745714\pi$
$733$	5.80448	−	8.28966i	0.214393	−	0.306185i	0.911916	+	0.410378i	$0.134603\pi$
$734$	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			0
$739$	−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	$0.608601\pi$
$740$	−2.10000	−	14.3159i	−0.0771977	−	0.526264i
$741$		0			0
$742$	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			0
$745$	−34.5935	−	25.7428i	−1.26741	−	0.943142i
$746$	0.0438849	−	0.0253370i	0.00160674	−	0.000927653i
$747$		0			0
$748$	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
$753$		0			0
$754$	0.0990675	−	0.118064i	0.00360782	−	0.00429964i
$755$	18.4622	+	28.0577i	0.671907	+	1.02112i
$756$		0			0
$757$	−10.7021	+	10.7021i	−0.388975	+	0.388975i	−0.874322	−	0.485347i	$-0.838693\pi$
$757$	−10.7021	+	10.7021i	−0.388975	+	0.388975i	0.485347	+	0.874322i	$0.338693\pi$
$758$	0.239740	−	0.0209745i	0.00870775	−	0.000761830i
$759$		0			0
$760$	0.775221	+	0.0223958i	0.0281202	+	0.000812382i
$761$	−16.8761	+	46.3666i	−0.611756	+	1.68079i	0.114551	+	0.993417i	$0.463457\pi$
$761$	−16.8761	+	46.3666i	−0.611756	+	1.68079i	−0.726308	+	0.687370i	$0.758765\pi$
$762$		0			0
$763$	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
$768$		0			0
$769$	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	$0.736969\pi$
$770$	0.0110458	−	0.0369234i	0.000398063	−	0.00133063i
$771$		0			0
$772$	−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			0
$775$	15.6999	+	21.0704i	0.563956	+	0.756869i
$776$	0.283394	+	0.0499700i	0.0101733	+	0.00179382i
$777$		0			0
$778$	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
$783$		0			0
$784$		−	27.7239i		−	0.990139i
$785$	−3.24122	−	4.09745i	−0.115684	−	0.146244i
$786$		0			0
$787$	−0.568328	−	0.397947i	−0.0202587	−	0.0141853i	0.563403	−	0.826182i	$-0.309492\pi$
$787$	−0.568328	−	0.397947i	−0.0202587	−	0.0141853i	−0.583662	+	0.811997i	$0.698381\pi$
$788$	−10.7743	+	5.02416i	−0.383820	+	0.178978i
$789$		0			0
$790$	0.0389895	−	0.0982019i	0.00138719	−	0.00349387i
$791$	2.07610	+	1.19864i	0.0738175	+	0.0426186i
$792$		0			0
$793$	−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			0
$799$	2.41587	+	6.63755i	0.0854673	+	0.234820i
$800$	0.718651	+	0.567752i	0.0254082	+	0.0200731i
$801$		0			0
$802$	−0.0339926	−	0.126862i	−0.00120032	−	0.00447965i
$803$	36.0293	+	51.4551i	1.27145	+	1.81581i
$804$		0			0
$805$	−3.25366	+	0.771843i	−0.114676	+	0.0272039i
$806$	−0.169936	+	0.0299642i	−0.00598573	+	0.00105544i
$807$		0			0
$808$	0.0153759	+	0.175748i	0.000540924	+	0.00618279i
$809$	9.19706			0.323351			0.161676	−	0.986844i	$-0.448310\pi$
$809$	9.19706			0.323351			0.161676	+	0.986844i	$0.448310\pi$
$810$		0			0
$811$	−3.49413			−0.122695			−0.0613477	−	0.998116i	$-0.519540\pi$
$811$	−3.49413			−0.122695			−0.0613477	+	0.998116i	$0.519540\pi$
$812$	−0.211134	−	2.41327i	−0.00740935	−	0.0846893i
$813$		0			0
$814$	−0.212814	+	0.0375249i	−0.00745914	+	0.00131525i
$815$	17.8074	−	28.8835i	0.623765	−	1.01175i
$816$		0			0
$817$	−29.6700	−	42.3732i	−1.03802	−	1.48245i
$818$	−0.0334253	−	0.124745i	−0.00116869	−	0.00436160i
$819$		0			0
$820$	−0.755192	+	1.50449i	−0.0263724	+	0.0525390i
$821$	5.34053	+	14.6730i	0.186386	+	0.512091i	0.997329	−	0.0730336i	$-0.0232680\pi$
$821$	5.34053	+	14.6730i	0.186386	+	0.512091i	−0.810944	+	0.585124i	$0.801046\pi$
$822$		0			0
$823$	−29.7914	−	2.60641i	−1.03846	−	0.0908536i	−0.444850	−	0.895605i	$-0.646743\pi$
$823$	−29.7914	−	2.60641i	−1.03846	−	0.0908536i	−0.593612	+	0.804752i	$0.702298\pi$
$824$	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	$0.858968\pi$
$828$		0			0
$829$	−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	$0.710367\pi$
$830$	0.155680	−	0.0671921i	0.00540373	−	0.00233227i
$831$		0			0
$832$	15.5831	−	7.26652i	0.540247	−	0.251921i
$833$	10.0084	+	7.00798i	0.346771	+	0.242812i
$834$		0			0
$835$	−34.0277	+	26.9171i	−1.17758	+	0.931504i
$836$			49.6874i			1.71847i
$837$		0			0
$838$	0.0948142	+	0.0948142i	0.00327530	+	0.00327530i
$839$	26.9906	+	22.6478i	0.931819	+	0.781889i	0.976143	−	0.217128i	$-0.0696689\pi$
$839$	26.9906	+	22.6478i	0.931819	+	0.781889i	−0.0443239	+	0.999017i	$0.514113\pi$
$840$		0			0
$841$	−1.21001	−	6.86229i	−0.0417244	−	0.236631i
$842$	−0.00370012	−	0.00793494i	−0.000127515	−	0.000273456i
$843$		0			0
$844$	11.1878	+	1.97271i	0.385100	+	0.0679035i
$845$	1.09266	+	18.6934i	0.0375885	+	0.643074i
$846$		0			0
$847$	2.02821	+	0.543456i	0.0696900	+	0.0186734i
$848$	−19.4988	+	41.8153i	−0.669592	+	1.43594i
$849$		0			0
$850$	−0.128848	+	0.0386328i	−0.00441946	+	0.00132509i
$851$	12.0521	+	14.3631i	0.413141	+	0.492362i
$852$		0			0
$853$	−22.1725	−	10.3392i	−0.759171	−	0.354007i	0.00417979	−	0.999991i	$-0.498670\pi$
$853$	−22.1725	−	10.3392i	−0.759171	−	0.354007i	−0.763351	+	0.645984i	$0.776447\pi$
$854$	−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			0
$859$	−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	$0.160627\pi$
$860$	1.17601	−	40.7070i	0.0401016	−	1.38810i
$861$		0			0
$862$	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			0
$865$	12.7323	+	2.62626i	0.432911	+	0.0892954i
$866$	−0.346801	+	0.413302i	−0.0117848	+	0.0140446i
$867$		0			0
$868$	−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
$873$		0			0
$874$	−0.435146	+	0.251232i	−0.0147190	+	0.00849804i
$875$	0.745074	−	2.78759i	0.0251881	−	0.0942376i
$876$		0			0
$877$	−3.98890	+	45.5933i	−0.134696	+	1.53958i	0.564973	+	0.825110i	$0.308887\pi$
$877$	−3.98890	+	45.5933i	−0.134696	+	1.53958i	−0.699668	+	0.714468i	$0.746669\pi$
$878$	−0.00628162	+	0.0717992i	−0.000211994	+	0.00242311i
$879$		0			0
$880$	−23.3500	+	31.3781i	−0.787129	+	1.05776i
$881$	33.3855	−	19.2752i	1.12479	−	0.649396i	0.182169	−	0.983267i	$-0.441688\pi$
$881$	33.3855	−	19.2752i	1.12479	−	0.649396i	0.942619	+	0.333871i	$0.108355\pi$
$882$		0			0
$883$	18.1259	−	4.85682i	0.609986	−	0.163445i	0.0594144	−	0.998233i	$-0.481077\pi$
$883$	18.1259	−	4.85682i	0.609986	−	0.163445i	0.550571	+	0.834788i	$0.314410\pi$
$884$	−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			0
$889$	−3.22424	+	3.84250i	−0.108137	+	0.128873i
$890$	0.0199418	−	0.0966792i	0.000668449	−	0.00324069i
$891$		0			0
$892$	18.6451	−	18.6451i	0.624283	−	0.624283i
$893$	−22.6804	+	1.98428i	−0.758972	+	0.0664014i
$894$		0			0
$895$	−15.5450	+	14.6721i	−0.519613	+	0.490433i
$896$	−0.0431100	+	0.118444i	−0.00144021	+	0.00395693i
$897$		0			0
$898$	−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
$903$		0			0
$904$	0.364593	+	0.434505i	0.0121262	+	0.0144514i
$905$	−29.7294	−	8.89369i	−0.988239	−	0.295636i
$906$		0			0
$907$	−8.15736	+	17.4935i	−0.270861	+	0.580863i	−0.993943	−	0.109900i	$-0.964947\pi$
$907$	−8.15736	+	17.4935i	−0.270861	+	0.580863i	0.723082	+	0.690762i	$0.242725\pi$
$908$	−28.1504	−	7.54288i	−0.934204	−	0.250319i
$909$		0			0
$910$	0.0141578	+	0.0125941i	0.000469326	+	0.000417491i
$911$	−39.2363	−	6.91842i	−1.29996	−	0.229217i	−0.519523	−	0.854456i	$-0.673890\pi$
$911$	−39.2363	−	6.91842i	−1.29996	−	0.229217i	−0.780433	+	0.625239i	$0.785001\pi$
$912$		0			0
$913$	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			0
$919$		−	43.5953i		−	1.43808i	−0.694971	−	0.719038i	$-0.744583\pi$
$919$		−	43.5953i		−	1.43808i	0.694971	−	0.719038i	$-0.255417\pi$
$920$	−0.785864	−	0.0916892i	−0.0259092	−	0.00302290i
$921$		0			0
$922$	0.330404	+	0.231352i	0.0108813	+	0.00761916i
$923$	−10.0017	+	4.66385i	−0.329209	+	0.153513i
$924$		0			0
$925$	−15.8433	+	3.27822i	−0.520923	+	0.107787i
$926$	−0.159010	−	0.0918044i	−0.00522539	−	0.00301688i
$927$		0			0
$928$	0.222526	−	0.830480i	0.00730479	−	0.0272618i
$929$	−32.4046	+	11.7943i	−1.06316	+	0.386959i	−0.813615	−	0.581404i	$-0.802504\pi$
$929$	−32.4046	+	11.7943i	−1.06316	+	0.386959i	−0.249546	+	0.968363i	$0.580281\pi$
$930$		0			0
$931$	−30.1676	+	25.3136i	−0.988703	+	0.829620i
$932$	55.0863	+	4.81942i	1.80441	+	0.157865i
$933$		0			0
$934$	−0.0577199	−	0.158584i	−0.00188865	−	0.00518903i
$935$	−5.42525	−	16.3611i	−0.177425	−	0.535066i
$936$		0			0
$937$	11.9945	+	44.7642i	0.391845	+	1.46238i	0.827089	+	0.562072i	$0.189995\pi$
$937$	11.9945	+	44.7642i	0.391845	+	1.46238i	−0.435244	+	0.900313i	$0.643338\pi$
$938$	0.00415010	+	0.00592696i	0.000135506	+	0.000193522i
$939$		0			0
$940$	−15.2572	−	9.40643i	−0.497635	−	0.306804i
$941$	−8.77614	+	1.54747i	−0.286094	+	0.0504461i	−0.314854	−	0.949140i	$-0.601955\pi$
$941$	−8.77614	+	1.54747i	−0.286094	+	0.0504461i	0.0287596	+	0.999586i	$0.490844\pi$
$942$		0			0
$943$	−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	$0.767959\pi$
$948$		0			0
$949$	−30.4146	+	5.36292i	−0.987300	+	0.174088i
$950$	−0.0127898	−	0.433379i	−0.000414957	−	0.0140607i
$951$		0			0
$952$	−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			0
$955$	−23.7369	−	11.9150i	−0.768109	−	0.385559i
$956$	−14.8286	−	40.7411i	−0.479590	−	1.31766i
$957$		0			0
$958$	−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
$963$		0			0
$964$	9.04140	+	5.22006i	0.291204	+	0.168127i
$965$	25.1613	+	9.98990i	0.809970	+	0.321586i
$966$		0			0
$967$	19.0304	−	8.87400i	0.611975	−	0.285369i	−0.0918158	−	0.995776i	$-0.529267\pi$
$967$	19.0304	−	8.87400i	0.611975	−	0.285369i	0.703791	+	0.710407i	$0.251489\pi$
$968$	0.406964	+	0.284960i	0.0130803	+	0.00915895i
$969$		0			0
$970$	0.0186434	−	0.159791i	0.000598603	−	0.00513059i
$971$		−	58.1766i		−	1.86697i	−0.358610	−	0.933487i	$-0.616749\pi$
$971$		−	58.1766i		−	1.86697i	0.358610	−	0.933487i	$-0.383251\pi$
$972$		0			0
$973$	−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			0
$979$	12.4574	+	2.19657i	0.398140	+	0.0702028i
$980$	−30.9506	+	1.80911i	−0.988682	+	0.0577898i
$981$		0			0
$982$	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			0
$985$	6.31126	+	11.6992i	0.201093	+	0.372766i
$986$	0.0811698	+	0.0967344i	0.00258497	+	0.00308065i
$987$		0			0
$988$	−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			0
$994$	0.00691448	−	0.0189974i	0.000219314	−	0.000602560i
$995$	−8.58692	−	9.09783i	−0.272224	−	0.288421i
$996$		0			0
$997$	23.3597	−	2.04371i	0.739808	−	0.0647248i	0.288979	−	0.957335i	$-0.406684\pi$
$997$	23.3597	−	2.04371i	0.739808	−	0.0647248i	0.450829	+	0.892610i	$0.351129\pi$
$998$	0.147387	−	0.147387i	0.00466546	−	0.00466546i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.278.9		192
3.2	odd	2		135.2.q.a.38.8	yes	192
5.2	odd	4	inner	405.2.r.a.197.8		192
15.2	even	4		135.2.q.a.92.9	yes	192
15.8	even	4		675.2.ba.b.632.8		192
15.14	odd	2		675.2.ba.b.443.9		192
27.5	odd	18	inner	405.2.r.a.368.8		192
27.22	even	9		135.2.q.a.113.9	yes	192
135.22	odd	36		135.2.q.a.32.8	✓	192
135.32	even	36	inner	405.2.r.a.287.9		192
135.49	even	18		675.2.ba.b.518.8		192
135.103	odd	36		675.2.ba.b.32.9		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.8	✓	192	135.22	odd	36
135.2.q.a.38.8	yes	192	3.2	odd	2
135.2.q.a.92.9	yes	192	15.2	even	4
135.2.q.a.113.9	yes	192	27.22	even	9
405.2.r.a.197.8		192	5.2	odd	4	inner
405.2.r.a.278.9		192	1.1	even	1	trivial
405.2.r.a.287.9		192	135.32	even	36	inner
405.2.r.a.368.8		192	27.5	odd	18	inner
675.2.ba.b.32.9		192	135.103	odd	36
675.2.ba.b.443.9		192	15.14	odd	2
675.2.ba.b.518.8		192	135.49	even	18
675.2.ba.b.632.8		192	15.8	even	4

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.00133058 - 0.0152086i) q^{2} +(1.96939 - 0.347256i) q^{4} +(-0.516124 - 2.17569i) q^{5} +(-0.148030 - 0.211408i) q^{7} +(-0.0158044 - 0.0589827i) q^{8} +(-0.0324025 + 0.0107445i) q^{10} +(-1.49616 - 4.11066i) q^{11} +(2.14258 + 0.187451i) q^{13} +(-0.00301826 + 0.00253263i) q^{14} +(3.75746 - 1.36760i) q^{16} +(-0.456091 + 1.70216i) q^{17} +(-4.91894 - 2.83995i) q^{19} +(-1.77197 - 4.10554i) q^{20} +(-0.0605267 + 0.0282241i) q^{22} +(4.74660 + 3.32360i) q^{23} +(-4.46723 + 2.24585i) q^{25} -0.0328351i q^{26} +(-0.364940 - 0.364940i) q^{28} +(3.59567 + 3.01712i) q^{29} +(-0.912568 - 5.17543i) q^{31} +(-0.0774120 - 0.166010i) q^{32} +(0.0264943 + 0.00467167i) q^{34} +(-0.383557 + 0.431179i) q^{35} +(3.12552 + 0.837479i) q^{37} +(-0.0366467 + 0.0785891i) q^{38} +(-0.120171 + 0.0648277i) q^{40} +(-0.241984 - 0.288386i) q^{41} +(8.25395 + 3.84888i) q^{43} +(-4.37396 - 7.57592i) q^{44} +(0.0442317 - 0.0766116i) q^{46} +(3.28345 - 2.29910i) q^{47} +(2.37136 - 6.51526i) q^{49} +(0.0401003 + 0.0649522i) q^{50} +(4.28465 - 0.374859i) q^{52} +(-8.15900 + 8.15900i) q^{53} +(-8.17131 + 5.37678i) q^{55} +(-0.0101299 + 0.0120724i) q^{56} +(0.0411020 - 0.0586997i) q^{58} +(10.6146 + 3.86341i) q^{59} +(-2.10712 + 11.9501i) q^{61} +(-0.0774969 + 0.0207652i) q^{62} +(6.92336 - 3.99720i) q^{64} +(-0.697999 - 4.75832i) q^{65} +(0.160052 - 1.82940i) q^{67} +(-0.307136 + 3.51058i) q^{68} +(0.00706800 + 0.00525965i) q^{70} +(-4.44360 + 2.56551i) q^{71} +(-13.8702 + 3.71651i) q^{73} +(0.00857816 - 0.0486492i) q^{74} +(-10.6735 - 3.88483i) q^{76} +(-0.647552 + 0.924799i) q^{77} +(-1.98949 + 2.37099i) q^{79} +(-4.91479 - 7.46920i) q^{80} +(-0.00406398 + 0.00406398i) q^{82} +(-4.94812 + 0.432904i) q^{83} +(3.93876 + 0.113789i) q^{85} +(0.0475536 - 0.130653i) q^{86} +(-0.218812 + 0.153214i) q^{88} +(-1.44584 + 2.50426i) q^{89} +(-0.277536 - 0.480707i) q^{91} +(10.5020 + 4.89717i) q^{92} +(-0.0393351 - 0.0468777i) q^{94} +(-3.64006 + 12.1678i) q^{95} +(-1.99162 + 4.27105i) q^{97} +(-0.102243 - 0.0273961i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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