LMFDB - Embedded newform 405.2.r.a.197.8

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			197.8
Character	$\chi$	$=$	405.197
Dual form			405.2.r.a.368.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0152086 - 0.00133058i) q^{2} +(-1.96939 + 0.347256i) q^{4} +(1.79388 - 1.33492i) q^{5} +(0.211408 - 0.148030i) q^{7} +(-0.0589827 + 0.0158044i) q^{8} +(0.0255062 - 0.0226891i) q^{10} +(-1.49616 - 4.11066i) q^{11} +(0.187451 - 2.14258i) q^{13} +(0.00301826 - 0.00253263i) q^{14} +(3.75746 - 1.36760i) q^{16} +(-1.70216 - 0.456091i) q^{17} +(4.91894 + 2.83995i) q^{19} +(-3.06928 + 3.25190i) q^{20} +(-0.0282241 - 0.0605267i) q^{22} +(3.32360 - 4.74660i) q^{23} +(1.43600 - 4.78935i) q^{25} -0.0328351i q^{26} +(-0.364940 + 0.364940i) q^{28} +(-3.59567 - 3.01712i) q^{29} +(-0.912568 - 5.17543i) q^{31} +(0.166010 - 0.0774120i) q^{32} +(-0.0264943 - 0.00467167i) q^{34} +(0.181634 - 0.547759i) q^{35} +(-0.837479 + 3.12552i) q^{37} +(0.0785891 + 0.0366467i) q^{38} +(-0.0847103 + 0.107088i) q^{40} +(-0.241984 - 0.288386i) q^{41} +(3.84888 - 8.25395i) q^{43} +(4.37396 + 7.57592i) q^{44} +(0.0442317 - 0.0766116i) q^{46} +(2.29910 + 3.28345i) q^{47} +(-2.37136 + 6.51526i) q^{49} +(0.0154670 - 0.0747502i) q^{50} +(0.374859 + 4.28465i) q^{52} +(8.15900 + 8.15900i) q^{53} +(-8.17131 - 5.37678i) q^{55} +(-0.0101299 + 0.0120724i) q^{56} +(-0.0586997 - 0.0411020i) q^{58} +(-10.6146 - 3.86341i) q^{59} +(-2.10712 + 11.9501i) q^{61} +(-0.0207652 - 0.0774969i) q^{62} +(-6.92336 + 3.99720i) q^{64} +(-2.52389 - 4.09375i) q^{65} +(1.82940 + 0.160052i) q^{67} +(3.51058 + 0.307136i) q^{68} +(0.00203356 - 0.00857235i) q^{70} +(-4.44360 + 2.56551i) q^{71} +(3.71651 + 13.8702i) q^{73} +(-0.00857816 + 0.0486492i) q^{74} +(-10.6735 - 3.88483i) q^{76} +(-0.924799 - 0.647552i) q^{77} +(1.98949 - 2.37099i) q^{79} +(4.91479 - 7.46920i) q^{80} +(-0.00406398 - 0.00406398i) q^{82} +(0.432904 + 4.94812i) q^{83} +(-3.66230 + 1.45406i) q^{85} +(0.0475536 - 0.130653i) q^{86} +(0.153214 + 0.218812i) q^{88} +(1.44584 - 2.50426i) q^{89} +(-0.277536 - 0.480707i) q^{91} +(-4.89717 + 10.5020i) q^{92} +(0.0393351 + 0.0468777i) q^{94} +(12.6151 - 1.47184i) q^{95} +(-4.27105 - 1.99162i) q^{97} +(-0.0273961 + 0.102243i) 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.0152086	−	0.00133058i	0.0107541	−	0.000940864i	−0.0817774	−	0.996651i	$-0.526060\pi$
$2$	0.0152086	−	0.00133058i	0.0107541	−	0.000940864i	0.0925315	+	0.995710i	$0.470504\pi$
$3$		0			0
$3$		0			0
$4$	−1.96939	+	0.347256i	−0.984693	+	0.173628i
$5$	1.79388	−	1.33492i	0.802247	−	0.596992i
$5$	1.79388	−	1.33492i	0.802247	−	0.596992i
$6$		0			0
$7$	0.211408	−	0.148030i	0.0799048	−	0.0559499i	−0.532941	−	0.846152i	$-0.678913\pi$
$7$	0.211408	−	0.148030i	0.0799048	−	0.0559499i	0.612846	+	0.790202i	$0.290025\pi$
$8$	−0.0589827	+	0.0158044i	−0.0208535	+	0.00558769i
$9$		0			0
$10$	0.0255062	−	0.0226891i	0.00806578	−	0.00717494i
$11$	−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
$13$	0.187451	−	2.14258i	0.0519896	−	0.594244i	−0.924859	−	0.380311i	$-0.875817\pi$
$13$	0.187451	−	2.14258i	0.0519896	−	0.594244i	0.976848	−	0.213933i	$-0.0686274\pi$
$14$	0.00301826	−	0.00253263i	0.000806665	−	0.000676873i
$15$		0			0
$16$	3.75746	−	1.36760i	0.939364	−	0.341901i
$17$	−1.70216	−	0.456091i	−0.412833	−	0.110618i	0.0464236	−	0.998922i	$-0.485218\pi$
$17$	−1.70216	−	0.456091i	−0.412833	−	0.110618i	−0.459257	+	0.888303i	$0.651884\pi$
$18$		0			0
$19$	4.91894	+	2.83995i	1.12848	+	0.651529i	0.943553	−	0.331222i	$-0.107461\pi$
$19$	4.91894	+	2.83995i	1.12848	+	0.651529i	0.184929	+	0.982752i	$0.440794\pi$
$20$	−3.06928	+	3.25190i	−0.686312	+	0.727147i
$21$		0			0
$22$	−0.0282241	−	0.0605267i	−0.00601740	−	0.0129043i
$23$	3.32360	−	4.74660i	0.693019	−	0.989734i	−0.306267	−	0.951946i	$-0.599080\pi$
$23$	3.32360	−	4.74660i	0.693019	−	0.989734i	0.999286	−	0.0377879i	$-0.0120311\pi$
$24$		0			0
$25$	1.43600	−	4.78935i	0.287200	−	0.957871i
$26$		−	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	0.244685	−	0.969603i	$-0.421316\pi$
$29$	−3.59567	−	3.01712i	−0.667699	−	0.560266i	−0.912383	+	0.409337i	$0.865760\pi$
$30$		0			0
$31$	−0.912568	−	5.17543i	−0.163902	−	0.929534i	−0.950189	−	0.311673i	$-0.899111\pi$
$31$	−0.912568	−	5.17543i	−0.163902	−	0.929534i	0.786287	−	0.617861i	$-0.212001\pi$
$32$	0.166010	−	0.0774120i	0.0293468	−	0.0136846i
$33$		0			0
$34$	−0.0264943	−	0.00467167i	−0.00454374	−	0.000801184i
$35$	0.181634	−	0.547759i	0.0307017	−	0.0925882i
$36$		0			0
$37$	−0.837479	+	3.12552i	−0.137681	+	0.513832i	0.862292	+	0.506412i	$0.169028\pi$
$37$	−0.837479	+	3.12552i	−0.137681	+	0.513832i	−0.999972	+	0.00741968i	$0.997638\pi$
$38$	0.0785891	+	0.0366467i	0.0127488	+	0.00594488i
$39$		0			0
$40$	−0.0847103	+	0.107088i	−0.0133939	+	0.0169321i
$41$	−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
$43$	3.84888	−	8.25395i	0.586948	−	1.25872i	−0.358678	−	0.933461i	$-0.616772\pi$
$43$	3.84888	−	8.25395i	0.586948	−	1.25872i	0.945627	−	0.325254i	$-0.105450\pi$
$44$	4.37396	+	7.57592i	0.659400	+	1.14211i
$45$		0			0
$46$	0.0442317	−	0.0766116i	0.00652161	−	0.0112958i
$47$	2.29910	+	3.28345i	0.335358	+	0.478941i	0.951046	−	0.309049i	$-0.100011\pi$
$47$	2.29910	+	3.28345i	0.335358	+	0.478941i	−0.615688	+	0.787990i	$0.711122\pi$
$48$		0			0
$49$	−2.37136	+	6.51526i	−0.338766	+	0.930751i
$50$	0.0154670	−	0.0747502i	0.00218736	−	0.0105713i
$51$		0			0
$52$	0.374859	+	4.28465i	0.0519835	+	0.594174i
$53$	8.15900	+	8.15900i	1.12072	+	1.12072i	0.991633	+	0.129092i	$0.0412062\pi$
$53$	8.15900	+	8.15900i	1.12072	+	1.12072i	0.129092	+	0.991633i	$0.458794\pi$
$54$		0			0
$55$	−8.17131	−	5.37678i	−1.10182	−	0.725005i
$56$	−0.0101299	+	0.0120724i	−0.00135367	+	0.00161324i
$57$		0			0
$58$	−0.0586997	−	0.0411020i	−0.00770765	−	0.00539696i
$59$	−10.6146	−	3.86341i	−1.38191	−	0.502973i	−0.459152	−	0.888358i	$-0.651847\pi$
$59$	−10.6146	−	3.86341i	−1.38191	−	0.502973i	−0.922756	+	0.385385i	$0.874069\pi$
$60$		0			0
$61$	−2.10712	+	11.9501i	−0.269790	+	1.53005i	0.485251	+	0.874375i	$0.338728\pi$
$61$	−2.10712	+	11.9501i	−0.269790	+	1.53005i	−0.755040	+	0.655678i	$0.772383\pi$
$62$	−0.0207652	−	0.0774969i	−0.00263719	−	0.00984212i
$63$		0			0
$64$	−6.92336	+	3.99720i	−0.865420	+	0.499650i
$65$	−2.52389	−	4.09375i	−0.313050	−	0.507768i
$66$		0			0
$67$	1.82940	+	0.160052i	0.223497	+	0.0195534i	0.198354	−	0.980130i	$-0.436440\pi$
$67$	1.82940	+	0.160052i	0.223497	+	0.0195534i	0.0251426	+	0.999684i	$0.491996\pi$
$68$	3.51058	+	0.307136i	0.425721	+	0.0372457i
$69$		0			0
$70$	0.00203356	−	0.00857235i	0.000243057	−	0.00102459i
$71$	−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
$73$	3.71651	+	13.8702i	0.434984	+	1.62338i	0.741104	+	0.671390i	$0.234303\pi$
$73$	3.71651	+	13.8702i	0.434984	+	1.62338i	−0.306120	+	0.951993i	$0.599031\pi$
$74$	−0.00857816	+	0.0486492i	−0.000997191	+	0.00565535i
$75$		0			0
$76$	−10.6735	−	3.88483i	−1.22433	−	0.445620i
$77$	−0.924799	−	0.647552i	−0.105391	−	0.0737953i
$78$		0			0
$79$	1.98949	−	2.37099i	0.223835	−	0.266757i	−0.642426	−	0.766348i	$-0.722072\pi$
$79$	1.98949	−	2.37099i	0.223835	−	0.266757i	0.866261	+	0.499591i	$0.166516\pi$
$80$	4.91479	−	7.46920i	0.549490	−	0.835082i
$81$		0			0
$82$	−0.00406398	−	0.00406398i	−0.000448791	−	0.000448791i
$83$	0.432904	+	4.94812i	0.0475174	+	0.543127i	0.982225	+	0.187708i	$0.0601060\pi$
$83$	0.432904	+	4.94812i	0.0475174	+	0.543127i	−0.934707	+	0.355418i	$0.884338\pi$
$84$		0			0
$85$	−3.66230	+	1.45406i	−0.397233	+	0.157715i
$86$	0.0475536	−	0.130653i	0.00512784	−	0.0140886i
$87$		0			0
$88$	0.153214	+	0.218812i	0.0163326	+	0.0233254i
$89$	1.44584	−	2.50426i	0.153259	−	0.265452i	−0.779165	−	0.626819i	$-0.784357\pi$
$89$	1.44584	−	2.50426i	0.153259	−	0.265452i	0.932424	+	0.361367i	$0.117690\pi$
$90$		0			0
$91$	−0.277536	−	0.480707i	−0.0290937	−	0.0503917i
$92$	−4.89717	+	10.5020i	−0.510565	+	1.09491i
$93$		0			0
$94$	0.0393351	+	0.0468777i	0.00405710	+	0.00483507i
$95$	12.6151	−	1.47184i	1.29428	−	0.151008i
$96$		0			0
$97$	−4.27105	−	1.99162i	−0.433659	−	0.202219i	0.193516	−	0.981097i	$-0.438011\pi$
$97$	−4.27105	−	1.99162i	−0.433659	−	0.202219i	−0.627175	+	0.778879i	$0.715789\pi$
$98$	−0.0273961	+	0.102243i	−0.00276742	+	0.0103282i
$99$		0			0
$100$	−1.16491	+	9.93074i	−0.116491	+	0.993074i
$101$	−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
$103$	9.15274	−	4.26799i	0.901846	−	0.420538i	0.0843263	−	0.996438i	$-0.473126\pi$
$103$	9.15274	−	4.26799i	0.901846	−	0.420538i	0.817520	+	0.575900i	$0.195348\pi$
$104$	0.0228057	+	0.129337i	0.00223628	+	0.0126826i
$105$		0			0
$106$	0.134943	+	0.113231i	0.0131069	+	0.0109980i
$107$	−10.6261	+	10.6261i	−1.02727	+	1.02727i	−0.0276498	+	0.999618i	$0.508802\pi$
$107$	−10.6261	+	10.6261i	−1.02727	+	1.02727i	−0.999618	+	0.0276498i	$0.991198\pi$
$108$		0			0
$109$		−	12.0030i		−	1.14968i	−0.818265	−	0.574841i	$-0.805064\pi$
$109$		−	12.0030i		−	1.14968i	0.818265	−	0.574841i	$-0.194936\pi$
$110$	−0.131429	−	0.0709009i	−0.0125312	−	0.00676013i
$111$		0			0
$112$	0.591912	−	0.845337i	0.0559304	−	0.0798769i
$113$	3.92562	+	8.41851i	0.369291	+	0.791947i	0.999875	+	0.0158260i	$0.00503778\pi$
$113$	3.92562	+	8.41851i	0.369291	+	0.791947i	−0.630584	+	0.776121i	$0.717184\pi$
$114$		0			0
$115$	−0.374165	−	12.9515i	−0.0348911	−	1.20774i
$116$	8.12897	+	4.69326i	0.754756	+	0.435759i
$117$		0			0
$118$	−0.166575	−	0.0446336i	−0.0153344	−	0.00410885i
$119$	−0.427365	+	0.155548i	−0.0391765	+	0.0142591i
$120$		0			0
$121$	−6.23254	+	5.22972i	−0.566595	+	0.475429i
$122$	−0.0161459	+	0.184548i	−0.00146178	+	0.0167082i
$123$		0			0
$124$	3.59440	+	9.87552i	0.322786	+	0.886848i
$125$	−3.81737	−	10.5085i	−0.341436	−	0.939905i
$126$		0			0
$127$	18.7735	−	5.03035i	1.66588	−	0.446371i	0.701885	−	0.712290i	$-0.252342\pi$
$127$	18.7735	−	5.03035i	1.66588	−	0.446371i	0.963996	+	0.265918i	$0.0856752\pi$
$128$	−0.400068	+	0.280131i	−0.0353614	+	0.0247603i
$129$		0			0
$130$	−0.0438320	−	0.0589021i	−0.00384433	−	0.00516606i
$131$	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
$133$	1.46030	−	0.127760i	0.126624	−	0.0110782i
$134$	0.0280356			0.00242191
$135$		0			0
$136$	0.107606			0.00922713
$137$	6.96948	−	0.609750i	0.595443	−	0.0520945i	0.214549	−	0.976713i	$-0.431172\pi$
$137$	6.96948	−	0.609750i	0.595443	−	0.0520945i	0.380894	+	0.924619i	$0.375616\pi$
$138$		0			0
$139$	−8.03836	+	1.41738i	−0.681805	+	0.120221i	−0.503815	−	0.863812i	$-0.668071\pi$
$139$	−8.03836	+	1.41738i	−0.681805	+	0.120221i	−0.177990	+	0.984032i	$0.556959\pi$
$140$	−0.167494	+	1.14182i	−0.0141558	+	0.0965017i
$141$		0			0
$142$	−0.0641675	+	0.0449306i	−0.00538482	+	0.00377049i
$143$	−9.08786	+	2.43508i	−0.759965	+	0.203632i
$144$		0			0
$145$	−10.4778	−	0.612441i	−0.870133	−	0.0508605i
$146$	0.0749784	+	0.206002i	0.00620526	+	0.0170488i
$147$		0			0
$148$	0.563966	−	6.44617i	0.0463578	−	0.529872i
$149$	−14.7726	+	12.3956i	−1.21021	+	1.01549i	−0.210937	+	0.977500i	$0.567651\pi$
$149$	−14.7726	+	12.3956i	−1.21021	+	1.01549i	−0.999278	+	0.0379911i	$0.987904\pi$
$150$		0			0
$151$	−14.1147	+	5.13734i	−1.14864	+	0.418070i	−0.845026	−	0.534725i	$-0.820415\pi$
$151$	−14.1147	+	5.13734i	−1.14864	+	0.418070i	−0.303613	+	0.952795i	$0.598193\pi$
$152$	−0.335016	−	0.0897672i	−0.0271734	−	0.00728108i
$153$		0			0
$154$	−0.0149266	−	0.00861785i	−0.00120282	−	0.000694446i
$155$	−8.54579	−	8.06589i	−0.686415	−	0.647868i
$156$		0			0
$157$	0.987420	+	2.11753i	0.0788047	+	0.168997i	0.941762	−	0.336279i	$-0.109168\pi$
$157$	0.987420	+	2.11753i	0.0788047	+	0.168997i	−0.862958	+	0.505276i	$0.831391\pi$
$158$	0.0271027	−	0.0387066i	0.00215617	−	0.00307933i
$159$		0			0
$160$	0.194464	−	0.360478i	0.0153737	−	0.0284983i
$161$		−	1.49546i		−	0.117859i
$162$		0			0
$163$	10.7302	−	10.7302i	0.840451	−	0.840451i	−0.148467	−	0.988917i	$-0.547434\pi$
$163$	10.7302	−	10.7302i	0.840451	−	0.840451i	0.988917	+	0.148467i	$0.0474338\pi$
$164$	0.576705	+	0.483913i	0.0450331	+	0.0377872i
$165$		0			0
$166$	0.0131678	+	0.0746781i	0.00102202	+	0.00579615i
$167$	17.5852	−	8.20013i	1.36079	−	0.634545i	0.401208	−	0.915987i	$-0.368590\pi$
$167$	17.5852	−	8.20013i	1.36079	−	0.634545i	0.959578	+	0.281442i	$0.0908126\pi$
$168$		0			0
$169$	8.24701	+	1.45417i	0.634385	+	0.111859i
$170$	−0.0537639	+	0.0269873i	−0.00412350	+	0.00206983i
$171$		0			0
$172$	−4.71370	+	17.5918i	−0.359416	+	1.34136i
$173$	5.26921	+	2.45707i	0.400610	+	0.186808i	0.612472	−	0.790492i	$-0.290175\pi$
$173$	5.26921	+	2.45707i	0.400610	+	0.186808i	−0.211862	+	0.977300i	$0.567953\pi$
$174$		0			0
$175$	−0.405384	−	1.22508i	−0.0306441	−	0.0926073i
$176$	−11.2435	−	13.3995i	−0.847510	−	1.01002i
$177$		0			0
$178$	0.0186571	−	0.0400103i	0.00139841	−	0.00299890i
$179$	4.77974	+	8.27875i	0.357254	+	0.618783i	0.987501	−	0.157612i	$-0.0503796\pi$
$179$	4.77974	+	8.27875i	0.357254	+	0.618783i	−0.630247	+	0.776395i	$0.717046\pi$
$180$		0			0
$181$	6.93879	−	12.0183i	0.515756	−	0.893315i	−0.484077	−	0.875026i	$-0.660844\pi$
$181$	6.93879	−	12.0183i	0.515756	−	0.893315i	0.999833	−	0.0182899i	$-0.00582219\pi$
$182$	−0.00486056	−	0.00694161i	−0.000360289	−	0.000514546i
$183$		0			0
$184$	−0.121018	+	0.332494i	−0.00892157	+	0.0245118i
$185$	2.66996	+	6.72476i	0.196300	+	0.494414i
$186$		0			0
$187$	0.671857	+	7.67937i	0.0491311	+	0.561571i
$188$	−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
$193$	9.91741	+	6.94425i	0.713871	+	0.499858i	0.873197	−	0.487368i	$-0.162043\pi$
$193$	9.91741	+	6.94425i	0.713871	+	0.499858i	−0.159325	+	0.987226i	$0.550932\pi$
$194$	−0.0676068	−	0.0246069i	−0.00485389	−	0.00176667i
$195$		0			0
$196$	2.40766	−	13.6545i	0.171976	−	0.975323i
$197$	−1.53862	−	5.74222i	−0.109622	−	0.409116i	0.889206	−	0.457507i	$-0.151257\pi$
$197$	−1.53862	−	5.74222i	−0.109622	−	0.409116i	−0.998828	+	0.0483907i	$0.984591\pi$
$198$		0			0
$199$	−4.84519	+	2.79737i	−0.343466	+	0.198300i	−0.661804	−	0.749677i	$-0.730209\pi$
$199$	−4.84519	+	2.79737i	−0.343466	+	0.198300i	0.318337	+	0.947977i	$0.396876\pi$
$200$	−0.00900656	+	0.305184i	−0.000636860	+	0.0215798i
$201$		0			0
$202$	−0.0439395	−	0.00384421i	−0.00309157	−	0.000270478i
$203$	−1.20678	−	0.105579i	−0.0846992	−	0.00741022i
$204$		0			0
$205$	−0.819062	−	0.194300i	−0.0572057	−	0.0135705i
$206$	0.133522	−	0.0770888i	0.00930290	−	0.00537103i
$207$		0			0
$208$	−2.22585	−	8.30699i	−0.154335	−	0.575986i
$209$	4.31456	−	24.4691i	0.298444	−	1.69256i
$210$		0			0
$211$	5.33826	+	1.94297i	0.367501	+	0.133759i	0.519168	−	0.854672i	$-0.326242\pi$
$211$	5.33826	+	1.94297i	0.367501	+	0.133759i	−0.151667	+	0.988432i	$0.548464\pi$
$212$	−18.9015	−	13.2350i	−1.29816	−	0.908980i
$213$		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
$218$	−0.0159710	−	0.182550i	−0.00108169	−	0.0123638i
$219$		0			0
$220$	17.9596	+	7.75142i	1.21083	+	0.522601i
$221$	−1.29628	+	3.56150i	−0.0871973	+	0.239573i
$222$		0			0
$223$	−7.56295	−	10.8010i	−0.506452	−	0.723289i	0.481773	−	0.876296i	$-0.339993\pi$
$223$	−7.56295	−	10.8010i	−0.506452	−	0.723289i	−0.988225	+	0.153007i	$0.951104\pi$
$224$	0.0236367	−	0.0409400i	0.00157929	−	0.00273542i
$225$		0			0
$226$	0.0709048	+	0.122811i	0.00471652	+	0.00816925i
$227$	6.15899	−	13.2080i	0.408787	−	0.876646i	−0.588870	−	0.808228i	$-0.700427\pi$
$227$	6.15899	−	13.2080i	0.408787	−	0.876646i	0.997657	−	0.0684181i	$-0.0217952\pi$
$228$		0			0
$229$	5.35302	+	6.37948i	0.353738	+	0.421568i	0.913343	−	0.407191i	$-0.133492\pi$
$229$	5.35302	+	6.37948i	0.353738	+	0.421568i	−0.559605	+	0.828759i	$0.689047\pi$
$230$	−0.0229236	−	0.196477i	−0.00151154	−	0.0129553i
$231$		0			0
$232$	0.259766	+	0.121131i	0.0170545	+	0.00795262i
$233$	7.15675	−	26.7094i	0.468854	−	1.74979i	−0.174930	−	0.984581i	$-0.555970\pi$
$233$	7.15675	−	26.7094i	0.468854	−	1.74979i	0.643784	−	0.765207i	$-0.277363\pi$
$234$		0			0
$235$	8.50744	+	2.82101i	0.554964	+	0.184023i
$236$	22.2459	+	3.92255i	1.44808	+	0.255336i
$237$		0			0
$238$	−0.00629266	+	0.00293432i	−0.000407893	+	0.000190204i
$239$	3.76477	+	21.3510i	0.243522	+	1.38108i	0.823899	+	0.566736i	$0.191794\pi$
$239$	3.76477	+	21.3510i	0.243522	+	1.38108i	−0.580377	+	0.814348i	$0.697095\pi$
$240$		0			0
$241$	3.99926	+	3.35578i	0.257615	+	0.216165i	0.762443	−	0.647055i	$-0.224000\pi$
$241$	3.99926	+	3.35578i	0.257615	+	0.216165i	−0.504828	+	0.863220i	$0.668444\pi$
$242$	−0.0878299	+	0.0878299i	−0.00564592	+	0.00564592i
$243$		0			0
$244$		−	24.2661i		−	1.55348i
$245$	4.44339	+	14.8531i	0.283878	+	0.948933i
$246$		0			0
$247$	7.00687	−	10.0068i	0.445837	−	0.636721i
$248$	0.135620	+	0.290838i	0.00861188	+	0.0184682i
$249$		0			0
$250$	−0.0720393	−	0.154740i	−0.00455617	−	0.00978662i
$251$	−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
$253$	−24.4843	−	6.56054i	−1.53931	−	0.412458i
$254$	0.278826	−	0.101484i	0.0174951	−	0.00636770i
$255$		0			0
$256$	12.2424	−	10.2726i	0.765152	−	0.642039i
$257$	−0.816897	+	9.33717i	−0.0509566	+	0.582437i	0.927200	+	0.374567i	$0.122209\pi$
$257$	−0.816897	+	9.33717i	−0.0509566	+	0.582437i	−0.978156	+	0.207870i	$0.933347\pi$
$258$		0			0
$259$	0.285619	+	0.784731i	0.0177475	+	0.0487608i
$260$	6.39210	+	7.18574i	0.396421	+	0.445641i
$261$		0			0
$262$	0.0673396	−	0.0180436i	0.00416025	−	0.00111474i
$263$	−8.22122	+	5.75656i	−0.506942	+	0.354965i	−0.798897	−	0.601467i	$-0.794583\pi$
$263$	−8.22122	+	5.75656i	−0.506942	+	0.354965i	0.291955	+	0.956432i	$0.405694\pi$
$264$		0			0
$265$	25.5278	+	3.74468i	1.56816	+	0.230034i
$266$	0.0220392	−	0.00388610i	0.00135131	−	0.000238272i
$267$		0			0
$268$	−3.65837	+	0.320066i	−0.223470	+	0.0195511i
$269$	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	$0.360124\pi$
$272$	−7.01953	+	0.614129i	−0.425621	+	0.0372370i
$273$		0			0
$274$	0.105185	−	0.0185469i	0.00635445	−	0.00112046i
$275$	−21.8359	+	1.26271i	−1.31675	+	0.0761445i
$276$		0			0
$277$	−14.8975	+	10.4313i	−0.895103	+	0.626758i	−0.927951	−	0.372703i	$-0.878431\pi$
$277$	−14.8975	+	10.4313i	−0.895103	+	0.626758i	0.0328481	+	0.999460i	$0.489542\pi$
$278$	−0.120367	+	0.0322521i	−0.00721911	+	0.00193435i
$279$		0			0
$280$	−0.00205625	+	0.0351789i	−0.000122885	+	0.00210234i
$281$	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
$283$	−1.59875	+	18.2738i	−0.0950360	+	1.08627i	0.787593	+	0.616196i	$0.211327\pi$
$283$	−1.59875	+	18.2738i	−0.0950360	+	1.08627i	−0.882629	+	0.470071i	$0.844228\pi$
$284$	7.86028	−	6.59556i	0.466422	−	0.391374i
$285$		0			0
$286$	−0.134974	+	0.0491264i	−0.00798117	+	0.00290491i
$287$	−0.0938472	−	0.0251463i	−0.00553962	−	0.00148434i
$288$		0			0
$289$	−12.0331	−	6.94732i	−0.707830	−	0.408666i
$290$	−0.160168	+	0.00462718i	−0.00940538	+	0.000271718i
$291$		0			0
$292$	−12.1357	−	26.0252i	−0.710191	−	1.52301i
$293$	−6.02781	+	8.60861i	−0.352149	+	0.502920i	−0.955675	−	0.294422i	$-0.904873\pi$
$293$	−6.02781	+	8.60861i	−0.352149	+	0.502920i	0.603527	+	0.797343i	$0.293762\pi$
$294$		0			0
$295$	−24.1987	+	7.23915i	−1.40890	+	0.421480i
$296$		−	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
$302$	−0.207830	+	0.0969127i	−0.0119593	+	0.00557670i
$303$		0			0
$304$	22.3666	+	3.94384i	1.28281	+	0.226195i
$305$	12.1724	+	24.2499i	0.696992	+	1.38854i
$306$		0			0
$307$	3.31491	−	12.3714i	0.189192	−	0.706074i	−0.804502	−	0.593949i	$-0.797568\pi$
$307$	3.31491	−	12.3714i	0.189192	−	0.706074i	0.993694	−	0.112124i	$-0.0357654\pi$
$308$	2.04615	+	0.954137i	0.116590	+	0.0543670i
$309$		0			0
$310$	−0.140702	−	0.111300i	−0.00799135	−	0.00632143i
$311$	−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
$313$	−12.4918	+	26.7887i	−0.706078	+	1.51419i	0.145159	+	0.989408i	$0.453631\pi$
$313$	−12.4918	+	26.7887i	−0.706078	+	1.51419i	−0.851237	+	0.524781i	$0.824147\pi$
$314$	0.0178349	+	0.0308909i	0.00100648	+	0.00174327i
$315$		0			0
$316$	−3.09474	+	5.36025i	−0.174093	+	0.301538i
$317$	15.2311	+	21.7523i	0.855465	+	1.22173i	0.973492	+	0.228720i	$0.0734540\pi$
$317$	15.2311	+	21.7523i	0.855465	+	1.22173i	−0.118027	+	0.993010i	$0.537657\pi$
$318$		0			0
$319$	−7.02268	+	19.2947i	−0.393195	+	1.08029i
$320$	−7.08374	+	16.4126i	−0.395993	+	0.917492i
$321$		0			0
$322$	−0.00198984	−	0.0227439i	−0.000110889	−	0.00126747i
$323$	−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
$328$	0.0188306	+	0.0131854i	0.00103975	+	0.000728040i
$329$	0.972097	+	0.353814i	0.0535934	+	0.0195064i
$330$		0			0
$331$	−1.72647	+	9.79132i	−0.0948956	+	0.538179i	0.899884	+	0.436130i	$0.143651\pi$
$331$	−1.72647	+	9.79132i	−0.0948956	+	0.538179i	−0.994779	+	0.102050i	$0.967460\pi$
$332$	−2.57082	−	9.59443i	−0.141092	−	0.526563i
$333$		0			0
$334$	0.256536	−	0.148111i	0.0140371	−	0.00810430i
$335$	3.49537	−	2.15498i	0.190973	−	0.117739i
$336$		0			0
$337$	−13.9748	−	1.22264i	−0.761258	−	0.0666015i	−0.300086	−	0.953912i	$-0.597015\pi$
$337$	−13.9748	−	1.22264i	−0.761258	−	0.0666015i	−0.461172	+	0.887311i	$0.652571\pi$
$338$	0.127361	+	0.0111426i	0.00692750	+	0.000606078i
$339$		0			0
$340$	6.70756	−	4.13536i	0.363768	−	0.224272i
$341$	−19.9091	+	11.4945i	−1.07814	+	0.622463i
$342$		0			0
$343$	0.930702	+	3.47343i	0.0502532	+	0.187547i
$344$	−0.0965688	+	0.547669i	−0.00520664	+	0.0295283i
$345$		0			0
$346$	0.0834068	+	0.0303576i	0.00448397	+	0.00163203i
$347$	−5.00149	−	3.50208i	−0.268494	−	0.188001i	0.431574	−	0.902077i	$-0.357958\pi$
$347$	−5.00149	−	3.50208i	−0.268494	−	0.188001i	−0.700068	+	0.714076i	$0.746847\pi$
$348$		0			0
$349$	2.45708	−	2.92823i	0.131524	−	0.156745i	−0.696263	−	0.717787i	$-0.745155\pi$
$349$	2.45708	−	2.92823i	0.131524	−	0.156745i	0.827787	+	0.561042i	$0.189600\pi$
$350$	−0.00779540	−	0.0180924i	−0.000416682	−	0.000967079i
$351$		0			0
$352$	−0.566592	−	0.566592i	−0.0301995	−	0.0301995i
$353$	−0.194119	−	2.21879i	−0.0103319	−	0.118094i	0.989277	−	0.146050i	$-0.0466559\pi$
$353$	−0.194119	−	2.21879i	−0.0103319	−	0.118094i	−0.999609	+	0.0279554i	$0.991100\pi$
$354$		0			0
$355$	−4.54654	+	10.5341i	−0.241305	+	0.559090i
$356$	−1.97779	+	5.43394i	−0.104823	+	0.287998i
$357$		0			0
$358$	0.0837088	+	0.119549i	0.00442415	+	0.00631834i
$359$	5.90045	−	10.2199i	0.311414	−	0.539385i	−0.667255	−	0.744829i	$-0.732531\pi$
$359$	5.90045	−	10.2199i	0.311414	−	0.539385i	0.978669	+	0.205445i	$0.0658641\pi$
$360$		0			0
$361$	6.63064	+	11.4846i	0.348981	+	0.604453i
$362$	0.0895381	−	0.192015i	0.00470602	−	0.0100921i
$363$		0			0
$364$	0.713504	+	0.850321i	0.0373978	+	0.0445689i
$365$	25.1825	+	19.9202i	1.31811	+	1.04267i
$366$		0			0
$367$	−1.92158	−	0.896047i	−0.100306	−	0.0467733i	0.371818	−	0.928306i	$-0.378735\pi$
$367$	−1.92158	−	0.896047i	−0.100306	−	0.0467733i	−0.472123	+	0.881532i	$0.656512\pi$
$368$	5.99683	−	22.3805i	0.312607	−	1.16666i
$369$		0			0
$370$	0.0495543	+	0.0987218i	0.00257621	+	0.00513230i
$371$	2.93265	+	0.517106i	0.152256	+	0.0268468i
$372$		0			0
$373$	3.00825	−	1.40277i	0.155762	−	0.0726328i	−0.343174	−	0.939272i	$-0.611502\pi$
$373$	3.00825	−	1.40277i	0.155762	−	0.0726328i	0.498936	+	0.866639i	$0.333724\pi$
$374$	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	$-0.867322\pi$
$379$		−	15.7634i		−	0.809713i	0.914380	−	0.404856i	$-0.132678\pi$
$380$	−24.3328	+	7.27928i	−1.24825	+	0.373419i
$381$		0			0
$382$	0.104009	−	0.148541i	0.00532158	−	0.00760001i
$383$	11.6401	+	24.9622i	0.594781	+	1.27551i	0.941333	+	0.337480i	$0.109575\pi$
$383$	11.6401	+	24.9622i	0.594781	+	1.27551i	−0.346552	+	0.938031i	$0.612648\pi$
$384$		0			0
$385$	−2.52340	+	0.0729001i	−0.128605	+	0.00371533i
$386$	0.160070	+	0.0924166i	0.00814736	+	0.00470388i
$387$		0			0
$388$	9.10294	+	2.43913i	0.462132	+	0.123828i
$389$	28.2091	−	10.2673i	1.43026	−	0.520571i	0.493252	−	0.869886i	$-0.335808\pi$
$389$	28.2091	−	10.2673i	1.43026	−	0.520571i	0.937005	+	0.349315i	$0.113586\pi$
$390$		0			0
$391$	−7.82217	+	6.56358i	−0.395584	+	0.331934i
$392$	0.0368997	−	0.421765i	0.00186372	−	0.0213024i
$393$		0			0
$394$	−0.0310408	−	0.0852840i	−0.00156382	−	0.00429655i
$395$	0.403844	−	6.90906i	0.0203196	−	0.347633i
$396$		0			0
$397$	4.62074	−	1.23812i	0.231908	−	0.0621397i	−0.140993	−	0.990011i	$-0.545030\pi$
$397$	4.62074	−	1.23812i	0.231908	−	0.0621397i	0.372902	+	0.927871i	$0.378363\pi$
$398$	−0.0699666	+	0.0489911i	−0.00350711	+	0.00245570i
$399$		0			0
$400$	−1.15422	−	19.9597i	−0.0577108	−	0.997983i
$401$	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
$403$	−11.2598	+	0.985106i	−0.560891	+	0.0490716i
$404$	5.77756			0.287444
$405$		0			0
$406$	−0.0184939			−0.000917838
$407$	14.1009	−	1.23367i	0.698957	−	0.0611508i
$408$		0			0
$409$	−8.33076	+	1.46894i	−0.411930	+	0.0726343i	−0.375773	−	0.926712i	$-0.622623\pi$
$409$	−8.33076	+	1.46894i	−0.411930	+	0.0726343i	−0.0361568	+	0.999346i	$0.511512\pi$
$410$	−0.0127153	−	0.00186522i	−0.000627966	−	9.21164e-5i
$411$		0			0
$412$	−16.5432	+	11.5837i	−0.815024	+	0.570686i
$413$	−2.81592	+	0.754524i	−0.138562	+	0.0371277i
$414$		0			0
$415$	7.38190	+	8.29843i	0.362363	+	0.407354i
$416$	−0.134742	−	0.370201i	−0.00660628	−	0.0181506i
$417$		0			0
$418$	0.0330604	−	0.377882i	0.00161704	−	0.0184828i
$419$	6.72816	−	5.64560i	0.328692	−	0.275806i	−0.463475	−	0.886110i	$-0.653397\pi$
$419$	6.72816	−	5.64560i	0.328692	−	0.275806i	0.792167	+	0.610305i	$0.208953\pi$
$420$		0			0
$421$	0.538899	−	0.196143i	0.0262643	−	0.00955944i	−0.328855	−	0.944381i	$-0.606663\pi$
$421$	0.538899	−	0.196143i	0.0262643	−	0.00955944i	0.355119	+	0.934821i	$0.384440\pi$
$422$	0.0837730	+	0.0224469i	0.00407800	+	0.00109270i
$423$		0			0
$424$	−0.610187	−	0.352292i	−0.0296333	−	0.0171088i
$425$	−4.62868	+	7.49728i	−0.224524	+	0.363671i
$426$		0			0
$427$	1.32351	+	2.83827i	0.0640489	+	0.137353i
$428$	17.2370	−	24.6170i	0.833181	−	1.18991i
$429$		0			0
$430$	−0.0891046	−	0.297855i	−0.00429701	−	0.0143638i
$431$			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	−0.227011	+	0.973892i	$0.572895\pi$
$433$	−24.9892	+	24.9892i	−1.20090	+	1.20090i	−0.973892	+	0.227011i	$0.927105\pi$
$434$	−0.0158618	−	0.0133096i	−0.000761390	−	0.000638882i
$435$		0			0
$436$	4.16812	+	23.6386i	0.199617	+	1.13208i
$437$	29.8287	−	13.9093i	1.42690	−	0.665374i
$438$		0			0
$439$	4.64923	+	0.819785i	0.221896	+	0.0391262i	0.283491	−	0.958975i	$-0.408508\pi$
$439$	4.64923	+	0.819785i	0.221896	+	0.0391262i	−0.0615948	+	0.998101i	$0.519619\pi$
$440$	0.566942	+	0.187995i	0.0270279	+	0.00896229i
$441$		0			0
$442$	−0.0149758	+	0.0558904i	−0.000712326	+	0.00265844i
$443$	−26.7976	−	12.4959i	−1.27319	−	0.593700i	−0.335787	−	0.941938i	$-0.609002\pi$
$443$	−26.7976	−	12.4959i	−1.27319	−	0.593700i	−0.937406	+	0.348238i	$0.886780\pi$
$444$		0			0
$445$	−0.749324	−	6.42242i	−0.0355214	−	0.304452i
$446$	−0.129394	−	0.154205i	−0.00612697	−	0.00730184i
$447$		0			0
$448$	−0.871951	+	1.86990i	−0.0411958	+	0.0883447i
$449$	3.36725	+	5.83225i	0.158910	+	0.275241i	0.934476	−	0.356026i	$-0.115869\pi$
$449$	3.36725	+	5.83225i	0.158910	+	0.275241i	−0.775566	+	0.631267i	$0.782535\pi$
$450$		0			0
$451$	−0.823409	+	1.42619i	−0.0387728	+	0.0671565i
$452$	−10.6544	−	15.2161i	−0.501142	−	0.715706i
$453$		0			0
$454$	0.0760955	−	0.209071i	0.00357134	−	0.00981217i
$455$	−1.13957	−	0.491842i	−0.0534238	−	0.0230579i
$456$		0			0
$457$	−3.16016	−	36.1208i	−0.147826	−	1.68966i	−0.601800	−	0.798647i	$-0.705550\pi$
$457$	−3.16016	−	36.1208i	−0.147826	−	1.68966i	0.453974	−	0.891015i	$-0.350006\pi$
$458$	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
$463$	−9.85172	−	6.89825i	−0.457848	−	0.320589i	0.321799	−	0.946808i	$-0.395713\pi$
$463$	−9.85172	−	6.89825i	−0.457848	−	0.320589i	−0.779647	+	0.626219i	$0.784601\pi$
$464$	−17.6368	−	6.41927i	−0.818767	−	0.298007i
$465$		0			0
$466$	0.0733054	−	0.415735i	0.00339581	−	0.0192586i
$467$	2.86104	+	10.6775i	0.132393	+	0.494098i	0.999995	−	0.00316149i	$-0.00100633\pi$
$467$	2.86104	+	10.6775i	0.132393	+	0.494098i	−0.867602	+	0.497260i	$0.834340\pi$
$468$		0			0
$469$	0.410442	−	0.236969i	0.0189525	−	0.0109422i
$470$	0.133140	+	0.0315839i	0.00614129	+	0.00145686i
$471$		0			0
$472$	0.687138	+	0.0601168i	0.0316281	+	0.00276710i
$473$	−39.6877	−	3.47222i	−1.82484	−	0.159653i
$474$		0			0
$475$	20.6651	−	19.4804i	0.948181	−	0.893820i
$476$	0.787631	−	0.454739i	0.0361010	−	0.0208429i
$477$		0			0
$478$	0.0856663	+	0.319711i	0.00391828	+	0.0146232i
$479$	−0.735877	+	4.17337i	−0.0336231	+	0.190686i	−0.996993	−	0.0774895i	$-0.975310\pi$
$479$	−0.735877	+	4.17337i	−0.0336231	+	0.190686i	0.963370	+	0.268175i	$0.0864207\pi$
$480$		0			0
$481$	6.53967	+	2.38024i	0.298183	+	0.108530i
$482$	0.0652884	+	0.0457155i	0.00297381	+	0.00208228i
$483$		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	0.976263	−	0.216587i	$-0.0694925\pi$
$487$	16.7646	+	16.7646i	0.759676	+	0.759676i	−0.216587	+	0.976263i	$0.569493\pi$
$488$	−0.0645798	−	0.738151i	−0.00292339	−	0.0334145i
$489$		0			0
$490$	0.0873412	+	0.219984i	0.00394567	+	0.00993786i
$491$	−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
$493$	4.74430	+	6.77556i	0.213673	+	0.305156i
$494$	0.0932500	−	0.161514i	0.00419552	−	0.00726685i
$495$		0			0
$496$	−10.5069	−	18.1984i	−0.471772	−	0.817133i
$497$	−0.559642	+	1.20016i	−0.0251034	+	0.0538343i
$498$		0			0
$499$	−8.77600	−	10.4588i	−0.392868	−	0.468202i	0.532964	−	0.846138i	$-0.321078\pi$
$499$	−8.77600	−	10.4588i	−0.392868	−	0.468202i	−0.925832	+	0.377937i	$0.876634\pi$
$500$	11.1670	+	19.3696i	0.499403	+	0.866235i
$501$		0			0
$502$	−0.192965	−	0.0899812i	−0.00861246	−	0.00401606i
$503$	−11.4964	+	42.9050i	−0.512597	+	1.91304i	−0.121825	+	0.992552i	$0.538875\pi$
$503$	−11.4964	+	42.9050i	−0.512597	+	1.91304i	−0.390772	+	0.920487i	$0.627792\pi$
$504$		0			0
$505$	−5.77370	+	2.89816i	−0.256926	+	0.128967i
$506$	−0.381102	−	0.0671985i	−0.0169420	−	0.00298734i
$507$		0			0
$508$	−35.2255	+	16.4259i	−1.56288	+	0.728782i
$509$	0.883595	+	5.01112i	0.0391647	+	0.222114i	0.998108	−	0.0614836i	$-0.0195832\pi$
$509$	0.883595	+	5.01112i	0.0391647	+	0.222114i	−0.958943	+	0.283597i	$0.908472\pi$
$510$		0			0
$511$	2.83890	+	2.38212i	0.125586	+	0.105379i
$512$	0.863214	−	0.863214i	0.0381490	−	0.0381490i
$513$		0			0
$514$			0.143093i			0.00631155i
$515$	10.7215	−	19.8744i	0.472445	−	0.875770i
$516$		0			0
$517$	10.0573	−	14.3634i	0.442321	−	0.631700i
$518$	0.00538802	+	0.0115547i	0.000236736	+	0.000507682i
$519$		0			0
$520$	0.213565	+	0.201572i	0.00936545	+	0.00883952i
$521$	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
$523$	12.9054	+	3.45799i	0.564314	+	0.151207i	0.529688	−	0.848193i	$-0.322309\pi$
$523$	12.9054	+	3.45799i	0.564314	+	0.151207i	0.0346265	+	0.999400i	$0.488976\pi$
$524$	−8.58116	+	3.12329i	−0.374870	+	0.136441i
$525$		0			0
$526$	−0.117374	+	0.0984884i	−0.00511775	+	0.00429430i
$527$	−0.807135	+	9.22560i	−0.0351594	+	0.401873i
$528$		0			0
$529$	−3.61738	−	9.93866i	−0.157277	−	0.432116i
$530$	0.393226	+	0.0229846i	0.0170806	+	0.000998386i
$531$		0			0
$532$	−2.83153	+	0.758707i	−0.122762	+	0.0328941i
$533$	−0.663249	+	0.464412i	−0.0287285	+	0.0201159i
$534$		0			0
$535$	−4.87701	+	33.2470i	−0.210851	+	1.43739i
$536$	−0.110432	+	0.0194722i	−0.00476995	+	0.000841071i
$537$		0			0
$538$	0.0281180	−	0.00246001i	0.00121225	−	0.000106058i
$539$	30.3299			1.30640
$540$		0			0
$541$	7.10549			0.305489			0.152745	−	0.988266i	$-0.451189\pi$
$541$	7.10549			0.305489			0.152745	+	0.988266i	$0.451189\pi$
$542$	0.213024	−	0.0186372i	0.00915016	−	0.000800535i
$543$		0			0
$544$	−0.317883	+	0.0560513i	−0.0136291	+	0.00240318i
$545$	−16.0230	−	21.5320i	−0.686351	−	0.922328i
$546$		0			0
$547$	8.41425	−	5.89172i	0.359767	−	0.251912i	−0.379692	−	0.925113i	$-0.623970\pi$
$547$	8.41425	−	5.89172i	0.359767	−	0.251912i	0.739459	+	0.673201i	$0.235081\pi$
$548$	−13.5139	+	3.62103i	−0.577283	+	0.154683i
$549$		0			0
$550$	−0.330414	+	0.0482586i	−0.0140889	+	0.00205775i
$551$	−9.11839	−	25.0526i	−0.388456	−	1.06728i
$552$		0			0
$553$	0.0696191	−	0.795750i	0.00296050	−	0.0338387i
$554$	−0.212691	+	0.178469i	−0.00903636	+	0.00758240i
$555$		0			0
$556$	15.3384	−	5.58274i	0.650495	−	0.236761i
$557$	5.55174	+	1.48759i	0.235235	+	0.0630310i	0.374511	−	0.927223i	$-0.377811\pi$
$557$	5.55174	+	1.48759i	0.235235	+	0.0630310i	−0.139276	+	0.990254i	$0.544477\pi$
$558$		0			0
$559$	−16.9632	−	9.79373i	−0.717468	−	0.414230i
$560$	−0.0666363	−	2.30658i	−0.00281590	−	0.0974710i
$561$		0			0
$562$	0.169419	+	0.363321i	0.00714652	+	0.0153258i
$563$	14.1548	−	20.2152i	0.596555	−	0.851969i	−0.401399	−	0.915903i	$-0.631476\pi$
$563$	14.1548	−	20.2152i	0.596555	−	0.851969i	0.997954	+	0.0639343i	$0.0203648\pi$
$564$		0			0
$565$	18.2801	+	9.86143i	0.769049	+	0.414873i
$566$			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	0.611634	−	0.791141i	$-0.290513\pi$
$569$	−1.46173	−	1.22654i	−0.0612790	−	0.0514192i	−0.672913	+	0.739722i	$0.734957\pi$
$570$		0			0
$571$	−7.82276	−	44.3651i	−0.327372	−	1.85662i	−0.492452	−	0.870340i	$-0.663899\pi$
$571$	−7.82276	−	44.3651i	−0.327372	−	1.85662i	0.165080	−	0.986280i	$-0.447212\pi$
$572$	17.0519	−	7.95143i	0.712976	−	0.332466i
$573$		0			0
$574$	−0.00146075		0.000257569i	−6.09704e−5		1.07507e-5i
$575$	−17.9604	−	22.7340i	−0.749001	−	0.948074i
$576$		0			0
$577$	5.87132	−	21.9121i	0.244426	−	0.912211i	−0.729245	−	0.684253i	$-0.760128\pi$
$577$	5.87132	−	21.9121i	0.244426	−	0.912211i	0.973671	−	0.227958i	$-0.0732049\pi$
$578$	−0.192251	−	0.0896482i	−0.00799660	−	0.00372888i
$579$		0			0
$580$	20.8475	−	2.43234i	0.865645	−	0.100998i
$581$	0.823988	+	0.981990i	0.0341848	+	0.0407398i
$582$		0			0
$583$	21.3317	−	45.7460i	0.883469	−	1.89461i
$584$	−0.438419	−	0.759364i	−0.0181419	−	0.0314227i
$585$		0			0
$586$	−0.0802204	+	0.138946i	−0.00331387	+	0.00573980i
$587$	−4.91190	−	7.01492i	−0.202736	−	0.289537i	0.704890	−	0.709316i	$-0.250996\pi$
$587$	−4.91190	−	7.01492i	−0.202736	−	0.289537i	−0.907626	+	0.419780i	$0.862107\pi$
$588$		0			0
$589$	10.2091	−	28.0493i	0.420659	−	1.15575i
$590$	−0.358397	+	0.142296i	−0.0147550	+	0.00585823i
$591$		0			0
$592$	1.12767	+	12.8893i	0.0463469	+	0.529748i
$593$	−4.26261	−	4.26261i	−0.175044	−	0.175044i	0.614147	−	0.789192i	$-0.289500\pi$
$593$	−4.26261	−	4.26261i	−0.175044	−	0.175044i	−0.789192	+	0.614147i	$0.789500\pi$
$594$		0			0
$595$	−0.558997	+	0.849530i	−0.0229166	+	0.0348273i
$596$	24.7884	−	29.5417i	1.01537	−	1.21007i
$597$		0			0
$598$	−0.155855	−	0.109131i	−0.00637338	−	0.00446269i
$599$	−13.5981	−	4.94929i	−0.555602	−	0.202223i	0.0489318	−	0.998802i	$-0.484418\pi$
$599$	−13.5981	−	4.94929i	−0.555602	−	0.202223i	−0.604534	+	0.796580i	$0.706641\pi$
$600$		0			0
$601$	−2.11215	+	11.9786i	−0.0861565	+	0.488618i	0.910944	+	0.412529i	$0.135354\pi$
$601$	−2.11215	+	11.9786i	−0.0861565	+	0.488618i	−0.997101	+	0.0760891i	$0.975757\pi$
$602$	−0.00928722	−	0.0346604i	−0.000378519	−	0.00141265i
$603$		0			0
$604$	26.0133	−	15.0188i	1.05847	−	0.611107i
$605$	−4.19918	+	17.7014i	−0.170721	+	0.719664i
$606$		0			0
$607$	19.3845	+	1.69592i	0.786792	+	0.0688354i	0.473468	−	0.880811i	$-0.343002\pi$
$607$	19.3845	+	1.69592i	0.786792	+	0.0688354i	0.313324	+	0.949646i	$0.398557\pi$
$608$	1.03644	+	0.0906769i	0.0420333	+	0.00367743i
$609$		0			0
$610$	0.217393	+	0.352611i	0.00880197	+	0.0142768i
$611$	7.46602	−	4.31051i	0.302043	−	0.174384i
$612$		0			0
$613$	3.48768	+	13.0162i	0.140866	+	0.525720i	0.999905	+	0.0138088i	$0.00439561\pi$
$613$	3.48768	+	13.0162i	0.140866	+	0.525720i	−0.859038	+	0.511911i	$0.828938\pi$
$614$	0.0339541	−	0.192563i	0.00137027	−	0.00777121i
$615$		0			0
$616$	0.0647813	+	0.0235785i	0.00261011	+	0.000950003i
$617$	−37.1967	−	26.0454i	−1.49748	−	1.04855i	−0.981392	−	0.192014i	$-0.938498\pi$
$617$	−37.1967	−	26.0454i	−1.49748	−	1.04855i	−0.516090	−	0.856535i	$-0.672613\pi$
$618$		0			0
$619$	−0.765342	+	0.912099i	−0.0307617	+	0.0366604i	−0.781206	−	0.624273i	$-0.785395\pi$
$619$	−0.765342	+	0.912099i	−0.0307617	+	0.0366604i	0.750444	+	0.660934i	$0.229840\pi$
$620$	19.6309	+	12.9173i	0.788396	+	0.518770i
$621$		0			0
$622$	−0.226747	−	0.226747i	−0.00909171	−	0.00909171i
$623$	−0.0650434	−	0.743449i	−0.00260591	−	0.0297857i
$624$		0			0
$625$	−20.8758	−	13.7550i	−0.835032	−	0.550201i
$626$	−0.154339	+	0.424042i	−0.00616861	+	0.0169481i
$627$		0			0
$628$	−2.67993	−	3.82734i	−0.106941	−	0.152728i
$629$	2.85104	−	4.93815i	0.113678	−	0.196897i
$630$		0			0
$631$	10.8669	+	18.8220i	0.432605	+	0.749293i	0.997097	−	0.0761454i	$-0.0242613\pi$
$631$	10.8669	+	18.8220i	0.432605	+	0.749293i	−0.564492	+	0.825438i	$0.690928\pi$
$632$	−0.0798737	+	0.171290i	−0.00317721	+	0.00681354i
$633$		0			0
$634$	0.260588	+	0.310556i	0.0103493	+	0.0123338i
$635$	26.9623	−	34.0849i	1.06997	−	1.35262i
$636$		0			0
$637$	13.5149	+	6.30211i	0.535481	+	0.249699i
$638$	−0.0811322	+	0.302790i	−0.00321206	+	0.0119876i
$639$		0			0
$640$	−0.343723	+	1.03658i	−0.0135868	+	0.0409743i
$641$	−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
$643$	21.6198	−	10.0815i	0.852602	−	0.397575i	0.0533535	−	0.998576i	$-0.483009\pi$
$643$	21.6198	−	10.0815i	0.852602	−	0.397575i	0.799248	+	0.601001i	$0.205231\pi$
$644$	0.519308	+	2.94514i	0.0204636	+	0.116055i
$645$		0			0
$646$	−0.117057	−	0.0982222i	−0.00460553	−	0.00386450i
$647$	17.7336	−	17.7336i	0.697179	−	0.697179i	−0.266622	−	0.963801i	$-0.585908\pi$
$647$	17.7336	−	17.7336i	0.697179	−	0.697179i	0.963801	+	0.266622i	$0.0859076\pi$
$648$		0			0
$649$			49.4134i			1.93965i
$650$	−0.157259	−	0.0471512i	−0.00616820	−	0.00184942i
$651$		0			0
$652$	−17.4057	+	24.8579i	−0.681660	+	0.973511i
$653$	−7.70684	−	16.5274i	−0.301592	−	0.646766i	0.695855	−	0.718183i	$-0.255026\pi$
$653$	−7.70684	−	16.5274i	−0.301592	−	0.646766i	−0.997447	+	0.0714165i	$0.977248\pi$
$654$		0			0
$655$	7.00871	−	7.42571i	0.273853	−	0.290147i
$656$	−1.30364	−	0.752659i	−0.0508987	−	0.0293864i
$657$		0			0
$658$	0.0152550	+	0.00408758i	0.000594704	+	0.000159350i
$659$	−32.1808	+	11.7129i	−1.25359	+	0.456269i	−0.881612	−	0.471974i	$-0.843542\pi$
$659$	−32.1808	+	11.7129i	−1.25359	+	0.456269i	−0.371975	+	0.928243i	$0.621319\pi$
$660$		0			0
$661$	3.43935	−	2.88596i	0.133775	−	0.112251i	−0.573445	−	0.819244i	$-0.694393\pi$
$661$	3.43935	−	2.88596i	0.133775	−	0.112251i	0.707220	+	0.706993i	$0.249949\pi$
$662$	−0.0132291	+	0.151210i	−0.000514165	+	0.00587693i
$663$		0			0
$664$	−0.103736	−	0.285012i	−0.00402573	−	0.0110606i
$665$	2.44905	−	2.17856i	0.0949703	−	0.0844811i
$666$		0			0
$667$	−26.2716	+	7.03946i	−1.01724	+	0.272569i
$668$	−31.7846	+	22.2558i	−1.22978	+	0.861103i
$669$		0			0
$670$	0.0502925	−	0.0374252i	0.00194297	−	0.00144586i
$671$	52.2754	−	9.21756i	2.01807	−	0.355840i
$672$		0			0
$673$	15.0821	−	1.31952i	0.581374	−	0.0508636i	0.207324	−	0.978272i	$-0.433525\pi$
$673$	15.0821	−	1.31952i	0.581374	−	0.0508636i	0.374050	+	0.927409i	$0.377969\pi$
$674$	−0.214165			−0.00824933
$675$		0			0
$676$	−16.7465			−0.644096
$677$	9.69800	−	0.848465i	0.372724	−	0.0326092i	0.100745	−	0.994912i	$-0.467877\pi$
$677$	9.69800	−	0.848465i	0.372724	−	0.0326092i	0.271979	+	0.962303i	$0.412322\pi$
$678$		0			0
$679$	−1.19775	+	0.211196i	−0.0459656	+	0.00810497i
$680$	0.193032	−	0.143645i	0.00740244	−	0.00550853i
$681$		0			0
$682$	−0.287495	+	0.201306i	−0.0110088	+	0.00770842i
$683$	22.4891	−	6.02595i	0.860523	−	0.230577i	0.198538	−	0.980093i	$-0.436381\pi$
$683$	22.4891	−	6.02595i	0.860523	−	0.230577i	0.661985	+	0.749517i	$0.269714\pi$
$684$		0			0
$685$	11.6884	−	10.3975i	0.446592	−	0.397267i
$686$	0.0187764	+	0.0515877i	0.000716886	+	0.00196963i
$687$		0			0
$688$	3.17388	−	36.2776i	0.121003	−	1.38307i
$689$	19.0107	−	15.9519i	0.724249	−	0.607717i
$690$		0			0
$691$	−4.24724	+	1.54587i	−0.161573	+	0.0588077i	−0.421540	−	0.906810i	$-0.638510\pi$
$691$	−4.24724	+	1.54587i	−0.161573	+	0.0588077i	0.259968	+	0.965617i	$0.416288\pi$
$692$	−11.2303	−	3.00916i	−0.426913	−	0.114391i
$693$		0			0
$694$	−0.0807256	−	0.0466069i	−0.00306430	−	0.00176918i
$695$	−12.5278	+	13.2731i	−0.475205	+	0.503479i
$696$		0			0
$697$	0.280365	+	0.601245i	0.0106196	+	0.0227738i
$698$	0.0334725	−	0.0478038i	0.00126695	−	0.00180940i
$699$		0			0
$700$	1.22377	+	2.27188i	0.0462543	+	0.0858691i
$701$		−	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
$707$	−0.675769	+	0.315116i	−0.0254149	+	0.0118512i
$708$		0			0
$709$	−27.9978	−	4.93677i	−1.05148	−	0.185404i	−0.378907	−	0.925435i	$-0.623700\pi$
$709$	−27.9978	−	4.93677i	−1.05148	−	0.185404i	−0.672574	+	0.740030i	$0.734811\pi$
$710$	−0.0551302	+	0.166258i	−0.00206900	+	0.00623956i
$711$		0			0
$712$	−0.0457011	+	0.170559i	−0.00171272	+	0.00639196i
$713$	−27.5987	−	12.8695i	−1.03358	−	0.481966i
$714$		0			0
$715$	−13.0519	+	16.4998i	−0.488113	+	0.617056i
$716$	−12.2880	−	14.6443i	−0.459224	−	0.547282i
$717$		0			0
$718$	0.0761394	−	0.163281i	0.00284150	−	0.00609361i
$719$	8.97949	+	15.5529i	0.334878	+	0.580026i	0.983461	−	0.181118i	$-0.0579714\pi$
$719$	8.97949	+	15.5529i	0.334878	+	0.580026i	−0.648583	+	0.761144i	$0.724638\pi$
$720$		0			0
$721$	1.30318	−	2.25717i	0.0485328	−	0.0840612i
$722$	0.116124	+	0.165843i	0.00432170	+	0.00617202i
$723$		0			0
$724$	−9.49171	+	26.0783i	−0.352757	+	0.969191i
$725$	−19.6134	+	12.8883i	−0.728425	+	0.478660i
$726$		0			0
$727$	2.47494	+	28.2887i	0.0917905	+	1.04917i	0.892780	+	0.450492i	$0.148751\pi$
$727$	2.47494	+	28.2887i	0.0917905	+	1.04917i	−0.800990	+	0.598678i	$0.795693\pi$
$728$	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
$733$	−8.28966	−	5.80448i	−0.306185	−	0.214393i	0.410378	−	0.911916i	$-0.365397\pi$
$733$	−8.28966	−	5.80448i	−0.306185	−	0.214393i	−0.716563	+	0.697522i	$0.754286\pi$
$734$	−0.0304169	−	0.0110708i	−0.00112271	−	0.000408632i
$735$		0			0
$736$	0.184310	−	1.04527i	0.00679374	−	0.0385292i
$737$	−2.07915	−	7.75949i	−0.0765865	−	0.285825i
$738$		0			0
$739$	35.8294	−	20.6861i	1.31801	−	0.760951i	0.334598	−	0.942361i	$-0.391399\pi$
$739$	35.8294	−	20.6861i	1.31801	−	0.760951i	0.983408	+	0.181410i	$0.0580660\pi$
$740$	−7.59340	−	12.3165i	−0.279139	−	0.452763i
$741$		0			0
$742$	0.0452897	+	0.00396233i	0.00166264	+	0.000145462i
$743$	7.70953	+	0.674496i	0.282835	+	0.0247449i	0.227691	−	0.973734i	$-0.426882\pi$
$743$	7.70953	+	0.674496i	0.282835	+	0.0247449i	0.0551445	+	0.998478i	$0.482438\pi$
$744$		0			0
$745$	−9.95303	+	41.9564i	−0.364651	+	1.53716i
$746$	0.0438849	−	0.0253370i	0.00160674	−	0.000927653i
$747$		0			0
$748$	−3.98985	−	14.8903i	−0.145883	−	0.544444i
$749$	−0.673470	+	3.81944i	−0.0246080	+	0.139559i
$750$		0			0
$751$	−38.8916	−	14.1554i	−1.41918	−	0.516537i	−0.485367	−	0.874311i	$-0.661314\pi$
$751$	−38.8916	−	14.1554i	−1.41918	−	0.516537i	−0.933808	+	0.357773i	$0.883536\pi$
$752$	13.1292	+	9.19318i	0.478773	+	0.335241i
$753$		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	0.485347	−	0.874322i	$-0.338693\pi$
$757$	−10.7021	−	10.7021i	−0.388975	−	0.388975i	−0.874322	+	0.485347i	$0.838693\pi$
$758$	−0.0209745	−	0.239740i	−0.000761830	−	0.00870775i
$759$		0			0
$760$	−0.720809	+	0.286186i	−0.0261465	+	0.0103811i
$761$	−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
$763$	−1.77680	−	2.53754i	−0.0643246	−	0.0918651i
$764$	−11.8764	+	20.5705i	−0.429673	+	0.744215i
$765$		0			0
$766$	0.210244	+	0.364154i	0.00759643	+	0.0131574i
$767$	−10.2674	+	22.0185i	−0.370733	+	0.795040i
$768$		0			0
$769$	−4.55804	−	5.43206i	−0.164367	−	0.195885i	0.677574	−	0.735455i	$-0.263031\pi$
$769$	−4.55804	−	5.43206i	−0.164367	−	0.195885i	−0.841941	+	0.539570i	$0.818587\pi$
$770$	−0.0382805	+	0.00446631i	−0.00137953	+	0.000160955i
$771$		0			0
$772$	−21.9426	−	10.2320i	−0.789733	−	0.368259i
$773$	−2.31145	+	8.62644i	−0.0831370	+	0.310272i	−0.994955	−	0.100323i	$-0.968012\pi$
$773$	−2.31145	+	8.62644i	−0.0831370	+	0.310272i	0.911818	+	0.410595i	$0.134679\pi$
$774$		0			0
$775$	−26.0974	−	3.06131i	−0.937446	−	0.109966i
$776$	0.283394	+	0.0499700i	0.0101733	+	0.00179382i
$777$		0			0
$778$	0.415360	−	0.193686i	0.0148914	−	0.00694397i
$779$	−0.371305	−	2.10578i	−0.0133034	−	0.0754473i
$780$		0			0
$781$	17.1943	+	14.4277i	0.615260	+	0.516264i
$782$	−0.110231	+	0.110231i	−0.00394186	+	0.00394186i
$783$		0			0
$784$			27.7239i			0.990139i
$785$	4.59803	+	2.48047i	0.164111	+	0.0885317i
$786$		0			0
$787$	0.397947	−	0.568328i	0.0141853	−	0.0202587i	−0.811997	−	0.583662i	$-0.801619\pi$
$787$	0.397947	−	0.568328i	0.0141853	−	0.0202587i	0.826182	+	0.563403i	$0.190508\pi$
$788$	5.02416	+	10.7743i	0.178978	+	0.383820i
$789$		0			0
$790$	−0.00305117	−	0.105615i	−0.000108556	−	0.00375761i
$791$	2.07610	+	1.19864i	0.0738175	+	0.0426186i
$792$		0			0
$793$	25.2090	+	6.75473i	0.895198	+	0.239868i
$794$	0.0686278	−	0.0249785i	0.00243551	−	0.000886453i
$795$		0			0
$796$	8.57065	−	7.19163i	0.303778	−	0.254900i
$797$	−3.24018	+	37.0354i	−0.114773	+	1.31186i	0.692385	+	0.721528i	$0.256560\pi$
$797$	−3.24018	+	37.0354i	−0.114773	+	1.31186i	−0.807158	+	0.590335i	$0.798996\pi$
$798$		0			0
$799$	−2.41587	−	6.63755i	−0.0854673	−	0.234820i
$800$	−0.132362	−	0.906246i	−0.00467970	−	0.0320406i
$801$		0			0
$802$	0.126862	−	0.0339926i	0.00447965	−	0.00120032i
$803$	51.4551	−	36.0293i	1.81581	−	1.27145i
$804$		0			0
$805$	−1.99631	−	2.68268i	−0.0703608	−	0.0945519i
$806$	−0.169936	+	0.0299642i	−0.00598573	+	0.00105544i
$807$		0			0
$808$	0.175748	−	0.0153759i	0.00618279	−	0.000540924i
$809$	−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	$0.519540\pi$
$812$	2.41327	−	0.211134i	0.0846893	−	0.00740935i
$813$		0			0
$814$	0.212814	−	0.0375249i	0.00745914	−	0.00131525i
$815$	4.92475	−	33.5724i	0.172506	−	1.17599i
$816$		0			0
$817$	42.3732	−	29.6700i	1.48245	−	1.03802i
$818$	−0.124745	+	0.0334253i	−0.00436160	+	0.00116869i
$819$		0			0
$820$	1.68052	+	0.0982287i	0.0586863	+	0.00343029i
$821$	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
$823$	−2.60641	+	29.7914i	−0.0908536	+	1.03846i	0.804752	+	0.593612i	$0.202298\pi$
$823$	−2.60641	+	29.7914i	−0.0908536	+	1.03846i	−0.895605	+	0.444850i	$0.853257\pi$
$824$	−0.472400	+	0.396391i	−0.0164568	+	0.0138089i
$825$		0			0
$826$	−0.0418223	+	0.0152221i	−0.00145519	+	0.000529644i
$827$	−35.9960	−	9.64511i	−1.25171	−	0.335393i	−0.428710	−	0.903442i	$-0.641032\pi$
$827$	−35.9960	−	9.64511i	−1.25171	−	0.335393i	−0.822995	+	0.568049i	$0.807699\pi$
$828$		0			0
$829$	6.82502	+	3.94043i	0.237043	+	0.136857i	0.613817	−	0.789448i	$-0.289633\pi$
$829$	6.82502	+	3.94043i	0.237043	+	0.136857i	−0.376774	+	0.926305i	$0.622967\pi$
$830$	0.123310	+	0.116386i	0.00428016	+	0.00403980i
$831$		0			0
$832$	7.26652	+	15.5831i	0.251921	+	0.540247i
$833$	7.00798	−	10.0084i	0.242812	−	0.346771i
$834$		0			0
$835$	20.5993	−	38.1848i	0.712868	−	1.32144i
$836$			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	0.0443239	−	0.999017i	$-0.485887\pi$
$839$	−26.9906	−	22.6478i	−0.931819	−	0.781889i	−0.976143	+	0.217128i	$0.930331\pi$
$840$		0			0
$841$	−1.21001	−	6.86229i	−0.0417244	−	0.236631i
$842$	0.00793494	−	0.00370012i	0.000273456	−	0.000127515i
$843$		0			0
$844$	−11.1878	−	1.97271i	−0.385100	−	0.0679035i
$845$	16.7353	−	8.40045i	0.575713	−	0.288984i
$846$		0			0
$847$	−0.543456	+	2.02821i	−0.0186734	+	0.0696900i
$848$	41.8153	+	19.4988i	1.43594	+	0.669592i
$849$		0			0
$850$	−0.0604201	+	0.120182i	−0.00207239	+	0.00412221i
$851$	12.0521	+	14.3631i	0.413141	+	0.492362i
$852$		0			0
$853$	−10.3392	+	22.1725i	−0.354007	+	0.759171i	−0.999991	−	0.00417979i	$-0.998670\pi$
$853$	−10.3392	+	22.1725i	−0.354007	+	0.759171i	0.645984	+	0.763351i	$0.276447\pi$
$854$	0.0239053	+	0.0414051i	0.000818021	+	0.00141685i
$855$		0			0
$856$	0.458819	−	0.794697i	0.0156821	−	0.0271622i
$857$	−2.59518	−	3.70630i	−0.0886496	−	0.126605i	0.772378	−	0.635164i	$-0.219067\pi$
$857$	−2.59518	−	3.70630i	−0.0886496	−	0.126605i	−0.861027	+	0.508559i	$0.830178\pi$
$858$		0			0
$859$	3.10612	−	8.53399i	0.105979	−	0.291176i	−0.875356	−	0.483478i	$-0.839373\pi$
$859$	3.10612	−	8.53399i	0.105979	−	0.291176i	0.981336	+	0.192302i	$0.0615954\pi$
$860$	15.0277	+	37.8499i	0.512440	+	1.29067i
$861$		0			0
$862$	0.0332801	+	0.380394i	0.00113353	+	0.0129563i
$863$	21.0851	+	21.0851i	0.717746	+	0.717746i	0.968143	−	0.250398i	$-0.0805613\pi$
$863$	21.0851	+	21.0851i	0.717746	+	0.717746i	−0.250398	+	0.968143i	$0.580561\pi$
$864$		0			0
$865$	12.7323	−	2.62626i	0.432911	−	0.0892954i
$866$	−0.346801	+	0.413302i	−0.0117848	+	0.0140446i
$867$		0			0
$868$	2.22175	+	1.55569i	0.0754113	+	0.0528035i
$869$	−12.7229	−	4.63076i	−0.431595	−	0.157088i
$870$		0			0
$871$	0.685845	−	3.88962i	0.0232390	−	0.131795i
$872$	0.189700	+	0.707971i	0.00642406	+	0.0239749i
$873$		0			0
$874$	0.435146	−	0.251232i	0.0147190	−	0.00849804i
$875$	−2.36259	−	1.65649i	−0.0798700	−	0.0559996i
$876$		0			0
$877$	−45.5933	−	3.98890i	−1.53958	−	0.134696i	−0.714468	−	0.699668i	$-0.753331\pi$
$877$	−45.5933	−	3.98890i	−1.53958	−	0.134696i	−0.825110	+	0.564973i	$0.808887\pi$
$878$	0.0717992	+	0.00628162i	0.00242311	+	0.000211994i
$879$		0			0
$880$	−38.0566	−	9.02792i	−1.28289	−	0.304331i
$881$	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
$883$	−4.85682	−	18.1259i	−0.163445	−	0.609986i	−0.998233	−	0.0594144i	$-0.981077\pi$
$883$	−4.85682	−	18.1259i	−0.163445	−	0.609986i	0.834788	−	0.550571i	$-0.185590\pi$
$884$	1.31612	−	7.46412i	0.0442661	−	0.251045i
$885$		0			0
$886$	−0.424182	−	0.154390i	−0.0142507	−	0.00518682i
$887$	−30.0349	−	21.0306i	−1.00847	−	0.706140i	−0.0522057	−	0.998636i	$-0.516625\pi$
$887$	−30.0349	−	21.0306i	−1.00847	−	0.706140i	−0.956267	+	0.292496i	$0.905514\pi$
$888$		0			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
$893$	1.98428	+	22.6804i	0.0664014	+	0.758972i
$894$		0			0
$895$	19.6257	+	8.47052i	0.656015	+	0.283138i
$896$	−0.0431100	+	0.118444i	−0.00144021	+	0.00395693i
$897$		0			0
$898$	0.0589716	+	0.0842201i	0.00196791	+	0.00281046i
$899$	−12.3336	+	21.3624i	−0.411349	+	0.712477i
$900$		0			0
$901$	−10.1666	−	17.6091i	−0.338700	−	0.586645i
$902$	−0.0106253	+	0.0227860i	−0.000353783	+	0.000758690i
$903$		0			0
$904$	−0.364593	−	0.434505i	−0.0121262	−	0.0144514i
$905$	−3.59611	−	30.8221i	−0.119539	−	1.02456i
$906$		0			0
$907$	−17.4935	−	8.15736i	−0.580863	−	0.270861i	0.109900	−	0.993943i	$-0.464947\pi$
$907$	−17.4935	−	8.15736i	−0.580863	−	0.270861i	−0.690762	+	0.723082i	$0.742725\pi$
$908$	−7.54288	+	28.1504i	−0.250319	+	0.934204i
$909$		0			0
$910$	−0.0179857	−	0.00596396i	−0.000596221	−	0.000197703i
$911$	−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
$913$	19.6923	−	9.18269i	0.651721	−	0.303903i
$914$	−0.0961236	−	0.545144i	−0.00317949	−	0.0180318i
$915$		0			0
$916$	−12.7575	−	10.7048i	−0.421519	−	0.353696i
$917$	0.833342	−	0.833342i	0.0275194	−	0.0275194i
$918$		0			0
$919$			43.5953i			1.43808i	0.694971	+	0.719038i	$0.255417\pi$
$919$			43.5953i			1.43808i	−0.694971	+	0.719038i	$0.744583\pi$
$920$	0.226760	+	0.758003i	0.00747606	+	0.0249906i
$921$		0			0
$922$	−0.231352	+	0.330404i	−0.00761916	+	0.0108813i
$923$	4.66385	+	10.0017i	0.153513	+	0.329209i
$924$		0			0
$925$	13.7666	+	8.49923i	0.452642	+	0.279453i
$926$	−0.159010	−	0.0918044i	−0.00522539	−	0.00301688i
$927$		0			0
$928$	−0.830480	−	0.222526i	−0.0272618	−	0.00730479i
$929$	32.4046	−	11.7943i	1.06316	−	0.386959i	0.249546	−	0.968363i	$-0.419719\pi$
$929$	32.4046	−	11.7943i	1.06316	−	0.386959i	0.813615	+	0.581404i	$0.197496\pi$
$930$		0			0
$931$	−30.1676	+	25.3136i	−0.988703	+	0.829620i
$932$	−4.81942	+	55.0863i	−0.157865	+	1.80441i
$933$		0			0
$934$	0.0577199	+	0.158584i	0.00188865	+	0.00518903i
$935$	11.4565	+	12.8790i	0.374669	+	0.421188i
$936$		0			0
$937$	−44.7642	+	11.9945i	−1.46238	+	0.391845i	−0.900313	−	0.435244i	$-0.856662\pi$
$937$	−44.7642	+	11.9945i	−1.46238	+	0.391845i	−0.562072	+	0.827089i	$0.689995\pi$
$938$	0.00592696	−	0.00415010i	0.000193522	−	0.000135506i
$939$		0			0
$940$	−17.7340	−	2.60141i	−0.578421	−	0.0848486i
$941$	−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
$943$	−2.17311	+	0.190123i	−0.0707662	+	0.00619124i
$944$	−45.1676			−1.47008
$945$		0			0
$946$	−0.608216			−0.0197748
$947$	−36.6998	+	3.21081i	−1.19258	+	0.104337i	−0.666109	−	0.745854i	$-0.732041\pi$
$947$	−36.6998	+	3.21081i	−1.19258	+	0.104337i	−0.526473	+	0.850192i	$0.676486\pi$
$948$		0			0
$949$	30.4146	−	5.36292i	0.987300	−	0.174088i
$950$	0.288368	−	0.323766i	0.00935590	−	0.0105044i
$951$		0			0
$952$	0.0227488	−	0.0159289i	0.000737292	−	0.000516257i
$953$	27.9077	−	7.47785i	0.904020	−	0.242231i	0.223278	−	0.974755i	$-0.428324\pi$
$953$	27.9077	−	7.47785i	0.904020	−	0.242231i	0.680742	+	0.732523i	$0.261658\pi$
$954$		0			0
$955$	1.54979	−	26.5143i	0.0501501	−	0.857981i
$956$	−14.8286	−	40.7411i	−0.479590	−	1.31766i
$957$		0			0
$958$	−0.00563868	+	0.0644504i	−0.000182177	+	0.00208230i
$959$	1.38314	−	1.16060i	0.0446641	−	0.0374776i
$960$		0			0
$961$	3.17820	−	1.15677i	0.102522	−	0.0373151i
$962$	0.102627	+	0.0274987i	0.00330881	+	0.000886594i
$963$		0			0
$964$	−9.04140	−	5.22006i	−0.291204	−	0.168127i
$965$	27.0606	−	0.781770i	0.871112	−	0.0251661i
$966$		0			0
$967$	8.87400	+	19.0304i	0.285369	+	0.611975i	0.995776	−	0.0918158i	$-0.0292671\pi$
$967$	8.87400	+	19.0304i	0.285369	+	0.611975i	−0.710407	+	0.703791i	$0.751489\pi$
$968$	0.284960	−	0.406964i	0.00915895	−	0.0130803i
$969$		0			0
$970$	−0.154126	+	0.0461076i	−0.00494870	+	0.00148043i
$971$		−	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
$977$	39.2996	−	18.3257i	1.25731	−	0.586291i	0.324232	−	0.945977i	$-0.394894\pi$
$977$	39.2996	−	18.3257i	1.25731	−	0.586291i	0.933073	+	0.359686i	$0.117116\pi$
$978$		0			0
$979$	−12.4574	−	2.19657i	−0.398140	−	0.0702028i
$980$	−13.9086	−	27.7086i	−0.444294	−	0.885119i
$981$		0			0
$982$	−0.00805718	+	0.0300698i	−0.000257115	+	0.000959566i
$983$	47.1628	+	21.9924i	1.50426	+	0.701447i	0.987924	−	0.154940i	$-0.0495183\pi$
$983$	47.1628	+	21.9924i	1.50426	+	0.701447i	0.516335	+	0.856387i	$0.327296\pi$
$984$		0			0
$985$	−10.4255	−	8.24691i	−0.332183	−	0.262768i
$986$	0.0811698	+	0.0967344i	0.00258497	+	0.00308065i
$987$		0			0
$988$	−10.3243	+	22.1405i	−0.328460	+	0.704384i
$989$	−26.3860	−	45.7019i	−0.839026	−	1.45324i
$990$		0			0
$991$	−1.64852	+	2.85532i	−0.0523670	+	0.0907023i	−0.891021	−	0.453963i	$-0.850010\pi$
$991$	−1.64852	+	2.85532i	−0.0523670	+	0.0907023i	0.838654	+	0.544665i	$0.183343\pi$
$992$	−0.552136	−	0.788532i	−0.0175303	−	0.0250359i
$993$		0			0
$994$	−0.00691448	+	0.0189974i	−0.000219314	+	0.000602560i
$995$	−4.95743	+	11.4861i	−0.157161	+	0.364133i
$996$		0			0
$997$	2.04371	+	23.3597i	0.0647248	+	0.739808i	0.957335	+	0.288979i	$0.0933159\pi$
$997$	2.04371	+	23.3597i	0.0647248	+	0.739808i	−0.892610	+	0.450829i	$0.851129\pi$
$998$	−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.197.8		192
3.2	odd	2		135.2.q.a.92.9	yes	192
5.3	odd	4	inner	405.2.r.a.278.9		192
15.2	even	4		675.2.ba.b.443.9		192
15.8	even	4		135.2.q.a.38.8	yes	192
15.14	odd	2		675.2.ba.b.632.8		192
27.5	odd	18	inner	405.2.r.a.287.9		192
27.22	even	9		135.2.q.a.32.8	✓	192
135.22	odd	36		675.2.ba.b.518.8		192
135.49	even	18		675.2.ba.b.32.9		192
135.103	odd	36		135.2.q.a.113.9	yes	192
135.113	even	36	inner	405.2.r.a.368.8		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.8	✓	192	27.22	even	9
135.2.q.a.38.8	yes	192	15.8	even	4
135.2.q.a.92.9	yes	192	3.2	odd	2
135.2.q.a.113.9	yes	192	135.103	odd	36
405.2.r.a.197.8		192	1.1	even	1	trivial
405.2.r.a.278.9		192	5.3	odd	4	inner
405.2.r.a.287.9		192	27.5	odd	18	inner
405.2.r.a.368.8		192	135.113	even	36	inner
675.2.ba.b.32.9		192	135.49	even	18
675.2.ba.b.443.9		192	15.2	even	4
675.2.ba.b.518.8		192	135.22	odd	36
675.2.ba.b.632.8		192	15.14	odd	2

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+(0.0152086 - 0.00133058i) q^{2} +(-1.96939 + 0.347256i) q^{4} +(1.79388 - 1.33492i) q^{5} +(0.211408 - 0.148030i) q^{7} +(-0.0589827 + 0.0158044i) q^{8} +(0.0255062 - 0.0226891i) q^{10} +(-1.49616 - 4.11066i) q^{11} +(0.187451 - 2.14258i) q^{13} +(0.00301826 - 0.00253263i) q^{14} +(3.75746 - 1.36760i) q^{16} +(-1.70216 - 0.456091i) q^{17} +(4.91894 + 2.83995i) q^{19} +(-3.06928 + 3.25190i) q^{20} +(-0.0282241 - 0.0605267i) q^{22} +(3.32360 - 4.74660i) q^{23} +(1.43600 - 4.78935i) q^{25} -0.0328351i q^{26} +(-0.364940 + 0.364940i) q^{28} +(-3.59567 - 3.01712i) q^{29} +(-0.912568 - 5.17543i) q^{31} +(0.166010 - 0.0774120i) q^{32} +(-0.0264943 - 0.00467167i) q^{34} +(0.181634 - 0.547759i) q^{35} +(-0.837479 + 3.12552i) q^{37} +(0.0785891 + 0.0366467i) q^{38} +(-0.0847103 + 0.107088i) q^{40} +(-0.241984 - 0.288386i) q^{41} +(3.84888 - 8.25395i) q^{43} +(4.37396 + 7.57592i) q^{44} +(0.0442317 - 0.0766116i) q^{46} +(2.29910 + 3.28345i) q^{47} +(-2.37136 + 6.51526i) q^{49} +(0.0154670 - 0.0747502i) q^{50} +(0.374859 + 4.28465i) q^{52} +(8.15900 + 8.15900i) q^{53} +(-8.17131 - 5.37678i) q^{55} +(-0.0101299 + 0.0120724i) q^{56} +(-0.0586997 - 0.0411020i) q^{58} +(-10.6146 - 3.86341i) q^{59} +(-2.10712 + 11.9501i) q^{61} +(-0.0207652 - 0.0774969i) q^{62} +(-6.92336 + 3.99720i) q^{64} +(-2.52389 - 4.09375i) q^{65} +(1.82940 + 0.160052i) q^{67} +(3.51058 + 0.307136i) q^{68} +(0.00203356 - 0.00857235i) q^{70} +(-4.44360 + 2.56551i) q^{71} +(3.71651 + 13.8702i) q^{73} +(-0.00857816 + 0.0486492i) q^{74} +(-10.6735 - 3.88483i) q^{76} +(-0.924799 - 0.647552i) q^{77} +(1.98949 - 2.37099i) q^{79} +(4.91479 - 7.46920i) q^{80} +(-0.00406398 - 0.00406398i) q^{82} +(0.432904 + 4.94812i) q^{83} +(-3.66230 + 1.45406i) q^{85} +(0.0475536 - 0.130653i) q^{86} +(0.153214 + 0.218812i) q^{88} +(1.44584 - 2.50426i) q^{89} +(-0.277536 - 0.480707i) q^{91} +(-4.89717 + 10.5020i) q^{92} +(0.0393351 + 0.0468777i) q^{94} +(12.6151 - 1.47184i) q^{95} +(-4.27105 - 1.99162i) q^{97} +(-0.0273961 + 0.102243i) 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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