LMFDB - Embedded newform 325.2.m.d.49.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(49,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 16 x^{18} + 172 x^{16} + 1018 x^{14} + 4330 x^{12} + 9943 x^{10} + 16225 x^{8} + 14698 x^{6} + \cdots + 729 $ x^20 + 16x^18 + 172x^16 + 1018x^14 + 4330x^12 + 9943x^10 + 16225x^8 + 14698x^6 + 9523x^4 + 3186*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.10
Root			$-1.31626 + 2.27983i$ of defining polynomial
Character	$\chi$	$=$	325.49
Dual form			325.2.m.d.199.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.31626 + 2.27983i) q^{2} +(2.33745 - 1.34953i) q^{3} +(-2.46508 + 4.26964i) q^{4} +(6.15337 + 3.55265i) q^{6} +(1.37037 - 2.37354i) q^{7} -7.71370 q^{8} +(2.14244 - 3.71081i) q^{9} +(-1.59372 + 0.920132i) q^{11} +13.3067i q^{12} +(0.149035 + 3.60247i) q^{13} +7.21503 q^{14} +(-5.22307 - 9.04662i) q^{16} +(-3.30556 - 1.90847i) q^{17} +11.2800 q^{18} +(-4.91151 - 2.83566i) q^{19} -7.39738i q^{21} +(-4.19549 - 2.42227i) q^{22} +(-0.120718 + 0.0696968i) q^{23} +(-18.0304 + 10.4098i) q^{24} +(-8.01684 + 5.08156i) q^{26} -3.46794i q^{27} +(6.75612 + 11.7019i) q^{28} +(0.583497 + 1.01065i) q^{29} -5.69034i q^{31} +(6.03614 - 10.4549i) q^{32} +(-2.48348 + 4.30152i) q^{33} -10.0481i q^{34} +(10.5626 + 18.2949i) q^{36} +(1.23046 + 2.13121i) q^{37} -14.9299i q^{38} +(5.20999 + 8.21945i) q^{39} +(8.01584 - 4.62795i) q^{41} +(16.8648 - 9.73687i) q^{42} +(1.81644 + 1.04872i) q^{43} -9.07280i q^{44} +(-0.317794 - 0.183478i) q^{46} -3.66621 q^{47} +(-24.4173 - 14.0973i) q^{48} +(-0.255809 - 0.443075i) q^{49} -10.3021 q^{51} +(-15.7486 - 8.24405i) q^{52} +9.97820i q^{53} +(7.90632 - 4.56471i) q^{54} +(-10.5706 + 18.3088i) q^{56} -15.3072 q^{57} +(-1.53607 + 2.66055i) q^{58} +(-2.19087 - 1.26490i) q^{59} +(4.17536 - 7.23193i) q^{61} +(12.9730 - 7.48996i) q^{62} +(-5.87185 - 10.1703i) q^{63} +10.8882 q^{64} -13.0756 q^{66} +(2.99082 + 5.18026i) q^{67} +(16.2969 - 9.40904i) q^{68} +(-0.188115 + 0.325825i) q^{69} +(-7.58786 - 4.38085i) q^{71} +(-16.5261 + 28.6241i) q^{72} +10.7918 q^{73} +(-3.23920 + 5.61046i) q^{74} +(24.2145 - 13.9803i) q^{76} +5.04367i q^{77} +(-11.8813 + 22.6968i) q^{78} +9.64672 q^{79} +(1.74723 + 3.02630i) q^{81} +(21.1018 + 12.1832i) q^{82} -15.6113 q^{83} +(31.5842 + 18.2351i) q^{84} +5.52156i q^{86} +(2.72779 + 1.57489i) q^{87} +(12.2934 - 7.09762i) q^{88} +(-2.91690 + 1.68407i) q^{89} +(8.75486 + 4.58296i) q^{91} -0.687233i q^{92} +(-7.67925 - 13.3009i) q^{93} +(-4.82569 - 8.35833i) q^{94} -32.5837i q^{96} +(-0.156577 + 0.271200i) q^{97} +(0.673423 - 1.16640i) q^{98} +7.88531i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 12 q^{4} + 18 q^{6} + 16 q^{9} - 18 q^{11} + 16 q^{14} - 24 q^{16} - 84 q^{24} - 34 q^{26} - 14 q^{29} - 6 q^{36} - 16 q^{39} + 24 q^{41} + 78 q^{46} + 2 q^{49} + 32 q^{51} + 18 q^{54} - 42 q^{56}+ \cdots - 10 q^{94}+O(q^{100}) $ 20 * q - 12 * q^4 + 18 * q^6 + 16 * q^9 - 18 * q^11 + 16 * q^14 - 24 * q^16 - 84 * q^24 - 34 * q^26 - 14 * q^29 - 6 * q^36 - 16 * q^39 + 24 * q^41 + 78 * q^46 + 2 * q^49 + 32 * q^51 + 18 * q^54 - 42 * q^56 + 96 * q^59 + 26 * q^61 + 68 * q^64 - 84 * q^66 - 40 * q^69 - 54 * q^71 + 52 * q^74 - 24 * q^76 - 8 * q^79 - 34 * q^81 + 180 * q^84 - 48 * q^89 + 26 * q^91 - 10 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.31626	+	2.27983i	0.930736	+	1.61208i	0.782066	+	0.623195i	$0.214166\pi$
$2$	1.31626	+	2.27983i	0.930736	+	1.61208i	0.148670	+	0.988887i	$0.452501\pi$
$3$	2.33745	−	1.34953i	1.34953	−	0.779149i	0.361343	−	0.932433i	$-0.382318\pi$
$3$	2.33745	−	1.34953i	1.34953	−	0.779149i	0.988182	+	0.153284i	$0.0489849\pi$
$4$	−2.46508	+	4.26964i	−1.23254	+	2.13482i
$5$		0			0
$5$		0			0
$6$	6.15337	+	3.55265i	2.51210	+	1.45036i
$7$	1.37037	−	2.37354i	0.517950	−	0.897116i	−0.481833	−	0.876263i	$-0.660029\pi$
$7$	1.37037	−	2.37354i	0.517950	−	0.897116i	0.999783	−	0.0208523i	$-0.00663797\pi$
$8$	−7.71370			−2.72720
$9$	2.14244	−	3.71081i	0.714146	−	1.23694i
$10$		0			0
$11$	−1.59372	+	0.920132i	−0.480523	+	0.277430i	−0.720635	−	0.693315i	$-0.756149\pi$
$11$	−1.59372	+	0.920132i	−0.480523	+	0.277430i	0.240111	+	0.970745i	$0.422816\pi$
$12$			13.3067i			3.84133i
$13$	0.149035	+	3.60247i	0.0413349	+	0.999145i
$13$	0.149035	+	3.60247i	0.0413349	+	0.999145i
$14$	7.21503			1.92830
$15$		0			0
$16$	−5.22307	−	9.04662i	−1.30577	−	2.26166i
$17$	−3.30556	−	1.90847i	−0.801716	−	0.462871i	0.0423549	−	0.999103i	$-0.486514\pi$
$17$	−3.30556	−	1.90847i	−0.801716	−	0.462871i	−0.844071	+	0.536232i	$0.819847\pi$
$18$	11.2800			2.65873
$19$	−4.91151	−	2.83566i	−1.12678	−	0.650545i	−0.183655	−	0.982991i	$-0.558793\pi$
$19$	−4.91151	−	2.83566i	−1.12678	−	0.650545i	−0.943123	+	0.332445i	$0.892126\pi$
$20$		0			0
$21$		−	7.39738i		−	1.61424i
$22$	−4.19549	−	2.42227i	−0.894481	−	0.516429i
$23$	−0.120718	+	0.0696968i	−0.0251715	+	0.0145328i	−0.512533	−	0.858668i	$-0.671293\pi$
$23$	−0.120718	+	0.0696968i	−0.0251715	+	0.0145328i	0.487361	+	0.873200i	$0.337959\pi$
$24$	−18.0304	+	10.4098i	−3.68043	+	2.12490i
$25$		0			0
$26$	−8.01684	+	5.08156i	−1.57223	+	0.996576i
$27$		−	3.46794i		−	0.667406i
$28$	6.75612	+	11.7019i	1.27679	+	2.21146i
$29$	0.583497	+	1.01065i	0.108353	+	0.187672i	0.915103	−	0.403220i	$-0.132109\pi$
$29$	0.583497	+	1.01065i	0.108353	+	0.187672i	−0.806750	+	0.590892i	$0.798776\pi$
$30$		0			0
$31$		−	5.69034i		−	1.02201i	−0.859576	−	0.511007i	$-0.829273\pi$
$31$		−	5.69034i		−	1.02201i	0.859576	−	0.511007i	$-0.170727\pi$
$32$	6.03614	−	10.4549i	1.06705	−	1.84818i
$33$	−2.48348	+	4.30152i	−0.432319	+	0.748799i
$34$		−	10.0481i		−	1.72324i
$35$		0			0
$36$	10.5626	+	18.2949i	1.76043	+	3.04915i
$37$	1.23046	+	2.13121i	0.202286	+	0.350369i	0.949265	−	0.314479i	$-0.101830\pi$
$37$	1.23046	+	2.13121i	0.202286	+	0.350369i	−0.746979	+	0.664848i	$0.768496\pi$
$38$		−	14.9299i		−	2.42194i
$39$	5.20999	+	8.21945i	0.834265	+	1.31617i
$40$		0			0
$41$	8.01584	−	4.62795i	1.25186	−	0.722764i	0.280384	−	0.959888i	$-0.409538\pi$
$41$	8.01584	−	4.62795i	1.25186	−	0.722764i	0.971479	+	0.237124i	$0.0762048\pi$
$42$	16.8648	−	9.73687i	2.60229	−	1.50243i
$43$	1.81644	+	1.04872i	0.277004	+	0.159929i	0.632066	−	0.774914i	$-0.282207\pi$
$43$	1.81644	+	1.04872i	0.277004	+	0.159929i	−0.355062	+	0.934843i	$0.615540\pi$
$44$		−	9.07280i		−	1.36778i
$45$		0			0
$46$	−0.317794	−	0.183478i	−0.0468561	−	0.0270524i
$47$	−3.66621			−0.534772			−0.267386	−	0.963590i	$-0.586160\pi$
$47$	−3.66621			−0.534772			−0.267386	+	0.963590i	$0.586160\pi$
$48$	−24.4173	−	14.0973i	−3.52433	−	2.03477i
$49$	−0.255809	−	0.443075i	−0.0365442	−	0.0632964i
$50$		0			0
$51$	−10.3021			−1.44258
$52$	−15.7486	−	8.24405i	−2.18394	−	1.14324i
$53$			9.97820i			1.37061i	0.728256	+	0.685305i	$0.240331\pi$
$53$			9.97820i			1.37061i	−0.728256	+	0.685305i	$0.759669\pi$
$54$	7.90632	−	4.56471i	1.07591	−	0.621179i
$55$		0			0
$56$	−10.5706	+	18.3088i	−1.41255	+	2.44662i
$57$	−15.3072			−2.02749
$58$	−1.53607	+	2.66055i	−0.201696	+	0.349347i
$59$	−2.19087	−	1.26490i	−0.285227	−	0.164676i	0.350560	−	0.936540i	$-0.385991\pi$
$59$	−2.19087	−	1.26490i	−0.285227	−	0.164676i	−0.635787	+	0.771864i	$0.719324\pi$
$60$		0			0
$61$	4.17536	−	7.23193i	0.534600	−	0.925954i	−0.464583	−	0.885530i	$-0.653796\pi$
$61$	4.17536	−	7.23193i	0.534600	−	0.925954i	0.999183	−	0.0404240i	$-0.0128709\pi$
$62$	12.9730	−	7.48996i	1.64757	−	0.951226i
$63$	−5.87185	−	10.1703i	−0.739784	−	1.28134i
$64$	10.8882			1.36103
$65$		0			0
$66$	−13.0756			−1.60950
$67$	2.99082	+	5.18026i	0.365387	+	0.632869i	0.988838	−	0.148993i	$-0.0476033\pi$
$67$	2.99082	+	5.18026i	0.365387	+	0.632869i	−0.623451	+	0.781862i	$0.714270\pi$
$68$	16.2969	−	9.40904i	1.97629	−	1.14101i
$69$	−0.188115	+	0.325825i	−0.0226464	+	0.0392248i
$70$		0			0
$71$	−7.58786	−	4.38085i	−0.900513	−	0.519912i	−0.0231467	−	0.999732i	$-0.507368\pi$
$71$	−7.58786	−	4.38085i	−0.900513	−	0.519912i	−0.877367	+	0.479820i	$0.840702\pi$
$72$	−16.5261	+	28.6241i	−1.94762	+	3.37338i
$73$	10.7918			1.26309			0.631544	−	0.775340i	$-0.282422\pi$
$73$	10.7918			1.26309			0.631544	+	0.775340i	$0.282422\pi$
$74$	−3.23920	+	5.61046i	−0.376549	+	0.652202i
$75$		0			0
$76$	24.2145	−	13.9803i	2.77760	−	1.60365i
$77$			5.04367i			0.574780i
$78$	−11.8813	+	22.6968i	−1.34529	+	2.56991i
$79$	9.64672			1.08534			0.542670	−	0.839946i	$-0.317413\pi$
$79$	9.64672			1.08534			0.542670	+	0.839946i	$0.317413\pi$
$80$		0			0
$81$	1.74723	+	3.02630i	0.194137	+	0.336255i
$82$	21.1018	+	12.1832i	2.33031	+	1.34540i
$83$	−15.6113			−1.71356			−0.856779	−	0.515684i	$-0.827538\pi$
$83$	−15.6113			−1.71356			−0.856779	+	0.515684i	$0.827538\pi$
$84$	31.5842	+	18.2351i	3.44611	+	1.98961i
$85$		0			0
$86$			5.52156i			0.595405i
$87$	2.72779	+	1.57489i	0.292450	+	0.168846i
$88$	12.2934	−	7.09762i	1.31049	−	0.756609i
$89$	−2.91690	+	1.68407i	−0.309190	+	0.178511i	−0.646564	−	0.762860i	$-0.723795\pi$
$89$	−2.91690	+	1.68407i	−0.309190	+	0.178511i	0.337374	+	0.941371i	$0.390461\pi$
$90$		0			0
$91$	8.75486	+	4.58296i	0.917758	+	0.480425i
$92$		−	0.687233i		−	0.0716490i
$93$	−7.67925	−	13.3009i	−0.796302	−	1.37923i
$94$	−4.82569	−	8.35833i	−0.497731	−	0.862096i
$95$		0			0
$96$		−	32.5837i		−	3.32556i
$97$	−0.156577	+	0.271200i	−0.0158980	+	0.0275362i	−0.873865	−	0.486169i	$-0.838394\pi$
$97$	−0.156577	+	0.271200i	−0.0158980	+	0.0275362i	0.857967	+	0.513705i	$0.171727\pi$
$98$	0.673423	−	1.16640i	0.0680260	−	0.117824i
$99$			7.88531i			0.792503i
$100$		0			0
$101$	7.91794	+	13.7143i	0.787864	+	1.36462i	0.927273	+	0.374386i	$0.122146\pi$
$101$	7.91794	+	13.7143i	0.787864	+	1.36462i	−0.139409	+	0.990235i	$0.544520\pi$
$102$	−13.5602	−	23.4870i	−1.34266	−	2.32556i
$103$		−	7.37659i		−	0.726837i	−0.931626	−	0.363418i	$-0.881610\pi$
$103$		−	7.37659i		−	0.726837i	0.931626	−	0.363418i	$-0.118390\pi$
$104$	−1.14961	−	27.7884i	−0.112729	−	2.72487i
$105$		0			0
$106$	−22.7486	+	13.1339i	−2.20954	+	1.27568i
$107$	−8.34292	+	4.81679i	−0.806540	+	0.465656i	−0.845753	−	0.533575i	$-0.820848\pi$
$107$	−8.34292	+	4.81679i	−0.806540	+	0.465656i	0.0392127	+	0.999231i	$0.487515\pi$
$108$	14.8069	+	8.54876i	1.42479	+	0.822604i
$109$		−	8.73514i		−	0.836674i	−0.908292	−	0.418337i	$-0.862613\pi$
$109$		−	8.73514i		−	0.836674i	0.908292	−	0.418337i	$-0.137387\pi$
$110$		0			0
$111$	5.75225	+	3.32106i	0.545979	+	0.315221i
$112$	−28.6301			−2.70529
$113$	15.8213	+	9.13443i	1.48834	+	0.859295i	0.999911	−	0.0133068i	$-0.00423583\pi$
$113$	15.8213	+	9.13443i	1.48834	+	0.859295i	0.488432	+	0.872602i	$0.337569\pi$
$114$	−20.1482	−	34.8978i	−1.88706	−	3.26848i
$115$		0			0
$116$	−5.75347			−0.534196
$117$	13.6874	+	7.16503i	1.26540	+	0.662407i
$118$		−	6.65974i		−	0.613079i
$119$	−9.05966	+	5.23060i	−0.830497	+	0.479488i
$120$		0			0
$121$	−3.80671	+	6.59342i	−0.346065	+	0.599402i
$122$	21.9834			1.99028
$123$	12.4911	−	21.6352i	1.12628	−	1.95078i
$124$	24.2957	+	14.0271i	2.18182	+	1.25967i
$125$		0			0
$126$	15.4578	−	26.7736i	1.37709	−	2.38518i
$127$	9.64353	−	5.56769i	0.855725	−	0.494053i	−0.00685350	−	0.999977i	$-0.502182\pi$
$127$	9.64353	−	5.56769i	0.855725	−	0.494053i	0.862578	+	0.505924i	$0.168848\pi$
$128$	2.25944	+	3.91346i	0.199708	+	0.345904i
$129$	5.66111			0.498433
$130$		0			0
$131$	4.16563			0.363953			0.181976	−	0.983303i	$-0.441751\pi$
$131$	4.16563			0.363953			0.181976	+	0.983303i	$0.441751\pi$
$132$	−12.2440	−	21.2072i	−1.06570	−	1.84585i
$133$	−13.4611	+	7.77179i	−1.16723	+	0.673900i
$134$	−7.87340	+	13.6371i	−0.680158	+	1.17807i
$135$		0			0
$136$	25.4981	+	14.7213i	2.18644	+	1.26234i
$137$	−0.200396	+	0.347097i	−0.0171210	+	0.0296545i	−0.874459	−	0.485099i	$-0.838783\pi$
$137$	−0.200396	+	0.347097i	−0.0171210	+	0.0296545i	0.857338	+	0.514754i	$0.172117\pi$
$138$	−0.990434			−0.0843114
$139$	−5.57346	+	9.65351i	−0.472735	+	0.818800i	−0.999513	−	0.0312024i	$-0.990066\pi$
$139$	−5.57346	+	9.65351i	−0.472735	+	0.818800i	0.526779	+	0.850003i	$0.323400\pi$
$140$		0			0
$141$	−8.56957	+	4.94764i	−0.721688	+	0.416667i
$142$		−	23.0654i		−	1.93560i
$143$	−3.55227	−	5.60418i	−0.297056	−	0.468645i
$144$	−44.7604			−3.73003
$145$		0			0
$146$	14.2048	+	24.6035i	1.17560	+	2.03620i
$147$	−1.19588	−	0.690442i	−0.0986346	−	0.0569467i
$148$	−12.1327			−0.997300
$149$	−15.4824	−	8.93879i	−1.26837	−	0.732294i	−0.293691	−	0.955900i	$-0.594884\pi$
$149$	−15.4824	−	8.93879i	−1.26837	−	0.732294i	−0.974680	+	0.223606i	$0.928217\pi$
$150$		0			0
$151$		−	6.29273i		−	0.512095i	−0.966664	−	0.256048i	$-0.917580\pi$
$151$		−	6.29273i		−	0.512095i	0.966664	−	0.256048i	$-0.0824204\pi$
$152$	37.8859	+	21.8734i	3.07295	+	1.77417i
$153$	−14.1639	+	8.17754i	−1.14508	+	0.661115i
$154$	−11.4987	+	6.63879i	−0.926593	+	0.534969i
$155$		0			0
$156$	−47.9372	+	1.98317i	−3.83804	+	0.158781i
$157$		−	16.1516i		−	1.28904i	−0.764589	−	0.644518i	$-0.777058\pi$
$157$		−	16.1516i		−	1.28904i	0.764589	−	0.644518i	$-0.222942\pi$
$158$	12.6976	+	21.9929i	1.01017	+	1.74966i
$159$	13.4658	+	23.3235i	1.06791	+	1.84967i
$160$		0			0
$161$			0.382041i			0.0301090i
$162$	−4.59963	+	7.96679i	−0.361381	+	0.625930i
$163$	−11.9167	+	20.6404i	−0.933390	+	1.61668i	−0.155910	+	0.987771i	$0.549831\pi$
$163$	−11.9167	+	20.6404i	−0.933390	+	1.61668i	−0.777480	+	0.628908i	$0.783502\pi$
$164$			45.6330i			3.56334i
$165$		0			0
$166$	−20.5485	−	35.5910i	−1.59487	−	2.76240i
$167$	0.558448	+	0.967261i	0.0432140	+	0.0748489i	0.886823	−	0.462108i	$-0.152907\pi$
$167$	0.558448	+	0.967261i	0.0432140	+	0.0748489i	−0.843609	+	0.536957i	$0.819574\pi$
$168$			57.0611i			4.40236i
$169$	−12.9556	+	1.07379i	−0.996583	+	0.0825992i
$170$		0			0
$171$	−21.0452	+	12.1505i	−1.60937	+	0.929169i
$172$	−8.95533	+	5.17036i	−0.682838	+	0.394236i
$173$	1.86266	+	1.07541i	0.141615	+	0.0817616i	0.569134	−	0.822245i	$-0.307279\pi$
$173$	1.86266	+	1.07541i	0.141615	+	0.0817616i	−0.427518	+	0.904007i	$0.640612\pi$
$174$			8.29185i			0.628604i
$175$		0			0
$176$	16.6482	+	9.61183i	1.25490	+	0.724519i
$177$	−6.82805			−0.513228
$178$	−7.67878	−	4.43335i	−0.575549	−	0.332293i
$179$	1.08264	+	1.87518i	0.0809199	+	0.140157i	0.903645	−	0.428282i	$-0.140881\pi$
$179$	1.08264	+	1.87518i	0.0809199	+	0.140157i	−0.822725	+	0.568439i	$0.807548\pi$
$180$		0			0
$181$	−19.8242			−1.47352			−0.736759	−	0.676155i	$-0.763645\pi$
$181$	−19.8242			−1.47352			−0.736759	+	0.676155i	$0.763645\pi$
$182$	1.07529	+	25.9919i	0.0797061	+	1.92665i
$183$		−	22.5390i		−	1.66613i
$184$	0.931186	−	0.537620i	0.0686479	−	0.0396339i
$185$		0			0
$186$	20.2158	−	35.0148i	1.48229	−	2.56741i
$187$	7.02416			0.513658
$188$	9.03750	−	15.6534i	0.659127	−	1.14164i
$189$	−8.23132	−	4.75235i	−0.598740	−	0.345683i
$190$		0			0
$191$	1.38158	−	2.39297i	0.0999677	−	0.173149i	−0.811703	−	0.584070i	$-0.801459\pi$
$191$	1.38158	−	2.39297i	0.0999677	−	0.173149i	0.911671	+	0.410921i	$0.134793\pi$
$192$	25.4506	−	14.6939i	1.83674	−	1.06044i
$193$	−0.611391	−	1.05896i	−0.0440089	−	0.0762257i	0.843182	−	0.537628i	$-0.180680\pi$
$193$	−0.611391	−	1.05896i	−0.0440089	−	0.0762257i	−0.887191	+	0.461403i	$0.847346\pi$
$194$	−0.824386			−0.0591875
$195$		0			0
$196$	2.52236			0.180169
$197$	8.42195	+	14.5872i	0.600039	+	1.03930i	0.992815	+	0.119663i	$0.0381815\pi$
$197$	8.42195	+	14.5872i	0.600039	+	1.03930i	−0.392776	+	0.919634i	$0.628485\pi$
$198$	−17.9771	+	10.3791i	−1.27758	+	0.737611i
$199$	11.5992	−	20.0904i	0.822245	−	1.42417i	−0.0817623	−	0.996652i	$-0.526055\pi$
$199$	11.5992	−	20.0904i	0.822245	−	1.42417i	0.904007	−	0.427518i	$-0.140612\pi$
$200$		0			0
$201$	13.9818	+	8.07238i	0.986199	+	0.569382i
$202$	−20.8441	+	36.1031i	−1.46659	+	2.54020i
$203$	3.19842			0.224485
$204$	25.3955	−	43.9862i	1.77804	−	3.07965i
$205$		0			0
$206$	16.8174	−	9.70951i	1.17172	−	0.676493i
$207$			0.597285i			0.0415141i
$208$	31.8118	−	20.1642i	2.20575	−	1.39814i
$209$	10.4367			0.721924
$210$		0			0
$211$	−13.4892	−	23.3639i	−0.928632	−	1.60844i	−0.785614	−	0.618717i	$-0.787653\pi$
$211$	−13.4892	−	23.3639i	−0.928632	−	1.60844i	−0.143017	−	0.989720i	$-0.545680\pi$
$212$	−42.6033	−	24.5970i	−2.92601	−	1.68933i
$213$	−23.6483			−1.62035
$214$	−21.9629	−	12.6803i	−1.50135	−	0.866806i
$215$		0			0
$216$			26.7507i			1.82015i
$217$	−13.5063	−	7.79785i	−0.916865	−	0.529352i
$218$	19.9146	−	11.4977i	1.34879	−	0.778723i
$219$	25.2253	−	14.5638i	1.70457	−	0.984134i
$220$		0			0
$221$	6.38255	−	12.1926i	0.429336	−	0.820164i
$222$			17.4855i			1.17355i
$223$	0.440345	+	0.762699i	0.0294877	+	0.0510741i	0.880393	−	0.474246i	$-0.157279\pi$
$223$	0.440345	+	0.762699i	0.0294877	+	0.0510741i	−0.850905	+	0.525320i	$0.823946\pi$
$224$	−16.5434	−	28.6541i	−1.10535	−	1.91453i
$225$		0			0
$226$			48.0931i			3.19911i
$227$	1.73934	−	3.01263i	0.115444	−	0.199955i	−0.802513	−	0.596635i	$-0.796504\pi$
$227$	1.73934	−	3.01263i	0.115444	−	0.199955i	0.917957	+	0.396679i	$0.129838\pi$
$228$	37.7334	−	65.3562i	2.49896	−	4.32832i
$229$		−	7.25190i		−	0.479219i	−0.970869	−	0.239610i	$-0.922981\pi$
$229$		−	7.25190i		−	0.479219i	0.970869	−	0.239610i	$-0.0770194\pi$
$230$		0			0
$231$	6.80657	+	11.7893i	0.447839	+	0.775680i
$232$	−4.50092	−	7.79583i	−0.295500	−	0.511821i
$233$			14.3236i			0.938371i	0.883100	+	0.469185i	$0.155452\pi$
$233$			14.3236i			0.938371i	−0.883100	+	0.469185i	$0.844548\pi$
$234$	1.68112	+	40.6359i	0.109898	+	2.65645i
$235$		0			0
$236$	10.8013	−	6.23615i	0.703107	−	0.405939i
$237$	22.5487	−	13.0185i	1.46469	−	0.845642i
$238$	−23.8497	−	13.7696i	−1.54595	−	0.892553i
$239$			3.62106i			0.234227i	0.993119	+	0.117114i	$0.0373642\pi$
$239$			3.62106i			0.234227i	−0.993119	+	0.117114i	$0.962636\pi$
$240$		0			0
$241$	2.36360	+	1.36462i	0.152253	+	0.0879031i	0.574191	−	0.818721i	$-0.305317\pi$
$241$	2.36360	+	1.36462i	0.152253	+	0.0879031i	−0.421938	+	0.906625i	$0.638650\pi$
$242$	−20.0425			−1.28838
$243$	17.1781	+	9.91779i	1.10198	+	0.636227i
$244$	20.5852	+	35.6545i	1.31783	+	2.28255i
$245$		0			0
$246$	65.7659			4.19308
$247$	9.48340	−	18.1162i	0.603414	−	1.15270i
$248$			43.8935i			2.78724i
$249$	−36.4905	+	21.0678i	−2.31249	+	1.33512i
$250$		0			0
$251$	−5.54338	+	9.60142i	−0.349895	+	0.606036i	−0.986231	−	0.165376i	$-0.947116\pi$
$251$	−5.54338	+	9.60142i	−0.349895	+	0.606036i	0.636335	+	0.771413i	$0.280450\pi$
$252$	57.8983			3.64725
$253$	0.128261	−	0.222154i	0.00806368	−	0.0139667i
$254$	25.3868	+	14.6571i	1.59291	+	0.919666i
$255$		0			0
$256$	4.94020	−	8.55667i	0.308762	−	0.534792i
$257$	−25.3401	+	14.6301i	−1.58067	+	0.912601i	−0.585910	+	0.810376i	$0.699263\pi$
$257$	−25.3401	+	14.6301i	−1.58067	+	0.912601i	−0.994761	+	0.102224i	$0.967404\pi$
$258$	7.45149	+	12.9064i	0.463909	+	0.803514i
$259$	6.74470			0.419095
$260$		0			0
$261$	5.00043			0.309519
$262$	5.48305	+	9.49692i	0.338744	+	0.586722i
$263$	12.4749	−	7.20239i	0.769235	−	0.444118i	−0.0633665	−	0.997990i	$-0.520184\pi$
$263$	12.4749	−	7.20239i	0.769235	−	0.444118i	0.832602	+	0.553872i	$0.186850\pi$
$264$	19.1568	−	33.1806i	1.17902	−	2.04213i
$265$		0			0
$266$	−35.4367	−	20.4594i	−2.17276	−	1.25445i
$267$	−4.54539	+	7.87285i	−0.278173	+	0.481810i
$268$	−29.4905			−1.80142
$269$	6.56252	−	11.3666i	0.400124	−	0.693035i	−0.593616	−	0.804748i	$-0.702300\pi$
$269$	6.56252	−	11.3666i	0.400124	−	0.693035i	0.993741	+	0.111713i	$0.0356337\pi$
$270$		0			0
$271$	−1.64683	+	0.950797i	−0.100038	+	0.0577568i	−0.549184	−	0.835701i	$-0.685061\pi$
$271$	−1.64683	+	0.950797i	−0.100038	+	0.0577568i	0.449147	+	0.893458i	$0.351728\pi$
$272$			39.8722i			2.41761i
$273$	26.6488	−	1.10247i	1.61286	−	0.0667245i
$274$	−1.05509			−0.0637406
$275$		0			0
$276$	−0.927438	−	1.60637i	−0.0558252	−	0.0966921i
$277$	24.7847	+	14.3095i	1.48917	+	0.859772i	0.999923	−	0.0123732i	$-0.00393863\pi$
$277$	24.7847	+	14.3095i	1.48917	+	0.859772i	0.489246	+	0.872146i	$0.337272\pi$
$278$	−29.3445			−1.75996
$279$	−21.1158	−	12.1912i	−1.26417	−	0.729868i
$280$		0			0
$281$			0.841175i			0.0501803i	0.999685	+	0.0250901i	$0.00798728\pi$
$281$			0.841175i			0.0501803i	−0.999685	+	0.0250901i	$0.992013\pi$
$282$	−22.5596	−	13.0248i	−1.34340	−	0.775614i
$283$	2.83957	−	1.63943i	0.168795	−	0.0974538i	−0.413223	−	0.910630i	$-0.635597\pi$
$283$	2.83957	−	1.63943i	0.168795	−	0.0974538i	0.582018	+	0.813176i	$0.302264\pi$
$284$	37.4094	−	21.5983i	2.21984	−	1.28162i
$285$		0			0
$286$	8.10087	−	15.4751i	0.479014	−	0.915063i
$287$		−	25.3679i		−	1.49742i
$288$	−25.8641	−	44.7979i	−1.52406	−	2.63974i
$289$	−1.21552	−	2.10534i	−0.0715010	−	0.123843i
$290$		0			0
$291$			0.845221i			0.0495477i
$292$	−26.6027	+	46.0772i	−1.55681	+	2.69647i
$293$	4.20020	−	7.27496i	0.245378	−	0.425008i	−0.716860	−	0.697217i	$-0.754421\pi$
$293$	4.20020	−	7.27496i	0.245378	−	0.425008i	0.962238	+	0.272210i	$0.0877545\pi$
$294$		−	3.63521i		−	0.212010i
$295$		0			0
$296$	−9.49136	−	16.4395i	−0.551674	−	0.955528i
$297$	3.19097	+	5.52692i	0.185159	+	0.320704i
$298$		−	47.0631i		−	2.72629i
$299$	−0.269072	−	0.424497i	−0.0155608	−	0.0245493i
$300$		0			0
$301$	4.97838	−	2.87427i	0.286949	−	0.165670i
$302$	14.3464	−	8.28287i	0.825540	−	0.476626i
$303$	37.0155	+	21.3709i	2.12649	+	1.22773i
$304$			59.2434i			3.39784i
$305$		0			0
$306$	−37.2868	−	21.5275i	−2.13154	−	1.23065i
$307$	32.8251			1.87343			0.936714	−	0.350095i	$-0.113851\pi$
$307$	32.8251			1.87343			0.936714	+	0.350095i	$0.113851\pi$
$308$	−21.5347	−	12.4331i	−1.22705	−	0.708439i
$309$	−9.95489	−	17.2424i	−0.566314	−	0.980885i
$310$		0			0
$311$	18.5990			1.05465			0.527327	−	0.849662i	$-0.323194\pi$
$311$	18.5990			1.05465			0.527327	+	0.849662i	$0.323194\pi$
$312$	−40.1883	−	63.4024i	−2.27521	−	3.58945i
$313$		−	6.55565i		−	0.370547i	−0.982687	−	0.185274i	$-0.940683\pi$
$313$		−	6.55565i		−	0.370547i	0.982687	−	0.185274i	$-0.0593172\pi$
$314$	36.8228	−	21.2597i	2.07803	−	1.19975i
$315$		0			0
$316$	−23.7799	+	41.1880i	−1.33772	+	2.31701i
$317$	−28.3918			−1.59464			−0.797321	−	0.603555i	$-0.793750\pi$
$317$	−28.3918			−1.59464			−0.797321	+	0.603555i	$0.793750\pi$
$318$	−35.4491	+	61.3996i	−1.98788	+	3.44312i
$319$	−1.85986	−	1.07379i	−0.104132	−	0.0601207i
$320$		0			0
$321$	−13.0008	+	22.5180i	−0.725631	+	1.25683i
$322$	−0.870988	+	0.502865i	−0.0485382	+	0.0280236i
$323$	10.8235	+	18.7469i	0.602237	+	1.04311i
$324$	−17.2283			−0.957127
$325$		0			0
$326$	−62.7420			−3.47496
$327$	−11.7883	−	20.4179i	−0.651894	−	1.12911i
$328$	−61.8317	+	35.6986i	−3.41409	+	1.97112i
$329$	−5.02405	+	8.70191i	−0.276985	+	0.479752i
$330$		0			0
$331$	−2.08424	−	1.20334i	−0.114560	−	0.0661413i	0.441625	−	0.897200i	$-0.354402\pi$
$331$	−2.08424	−	1.20334i	−0.114560	−	0.0661413i	−0.556185	+	0.831058i	$0.687735\pi$
$332$	38.4830	−	66.6545i	2.11203	−	3.65814i
$333$	10.5447			0.577846
$334$	−1.47013	+	2.54633i	−0.0804417	+	0.139329i
$335$		0			0
$336$	−66.9213	+	38.6370i	−3.65086	+	2.10782i
$337$			3.33555i			0.181699i	0.995865	+	0.0908496i	$0.0289582\pi$
$337$			3.33555i			0.181699i	−0.995865	+	0.0908496i	$0.971042\pi$
$338$	−19.5010	−	28.1231i	−1.06071	−	1.52970i
$339$	49.3086			2.67808
$340$		0			0
$341$	5.23586	+	9.06878i	0.283538	+	0.491102i
$342$	−55.4019	−	31.9863i	−2.99579	−	1.72962i
$343$	17.7829			0.960188
$344$	−14.0115	−	8.08952i	−0.755447	−	0.436158i
$345$		0			0
$346$			5.66206i			0.304394i
$347$	17.3593	+	10.0224i	0.931897	+	0.538031i	0.887411	−	0.460979i	$-0.152502\pi$
$347$	17.3593	+	10.0224i	0.931897	+	0.538031i	0.0444861	+	0.999010i	$0.485835\pi$
$348$	−13.4484	+	7.76445i	−0.720911	+	0.416218i
$349$	−12.8911	+	7.44270i	−0.690047	+	0.398399i	−0.803630	−	0.595130i	$-0.797101\pi$
$349$	−12.8911	+	7.44270i	−0.690047	+	0.398399i	0.113583	+	0.993529i	$0.463767\pi$
$350$		0			0
$351$	12.4932	−	0.516846i	0.666836	−	0.0275872i
$352$			22.2162i			1.18413i
$353$	−9.58417	−	16.6003i	−0.510114	−	0.883543i	−0.999931	−	0.0117179i	$-0.996270\pi$
$353$	−9.58417	−	16.6003i	−0.510114	−	0.883543i	0.489818	−	0.871825i	$-0.337063\pi$
$354$	−8.98749	−	15.5668i	−0.477680	−	0.827365i
$355$		0			0
$356$		−	16.6055i		−	0.880088i
$357$	−14.1176	+	24.4525i	−0.747185	+	1.29416i
$358$	−2.85006	+	4.93645i	−0.150630	+	0.260899i
$359$		−	15.1897i		−	0.801683i	−0.916147	−	0.400842i	$-0.868718\pi$
$359$		−	15.1897i		−	0.801683i	0.916147	−	0.400842i	$-0.131282\pi$
$360$		0			0
$361$	6.58195	+	11.4003i	0.346419	+	0.600014i
$362$	−26.0937	−	45.1957i	−1.37146	−	2.37543i
$363$			20.5490i			1.07854i
$364$	−41.1490	+	26.0827i	−2.15679	+	1.36711i
$365$		0			0
$366$	51.3850	−	29.6672i	2.68594	−	1.55073i
$367$	−3.69540	+	2.13354i	−0.192898	+	0.111370i	−0.593339	−	0.804953i	$-0.702190\pi$
$367$	−3.69540	+	2.13354i	−0.192898	+	0.111370i	0.400440	+	0.916323i	$0.368857\pi$
$368$	1.26104	+	0.728063i	0.0657364	+	0.0379529i
$369$		−	39.6603i		−	2.06463i
$370$		0			0
$371$	23.6837	+	13.6738i	1.22960	+	0.709908i
$372$	75.7199			3.92589
$373$	−11.8675	−	6.85171i	−0.614476	−	0.354768i	0.160239	−	0.987078i	$-0.448773\pi$
$373$	−11.8675	−	6.85171i	−0.614476	−	0.354768i	−0.774715	+	0.632310i	$0.782107\pi$
$374$	9.24562	+	16.0139i	0.478080	+	0.828059i
$375$		0			0
$376$	28.2800			1.45843
$377$	−3.55386	+	2.25265i	−0.183033	+	0.116018i
$378$		−	25.0213i		−	1.28696i
$379$	16.5632	−	9.56275i	0.850792	−	0.491205i	−0.0101257	−	0.999949i	$-0.503223\pi$
$379$	16.5632	−	9.56275i	0.850792	−	0.491205i	0.860918	+	0.508744i	$0.169890\pi$
$380$		0			0
$381$	15.0275	−	26.0284i	0.769882	−	1.33347i
$382$	7.27408			0.372174
$383$	−4.95147	+	8.57619i	−0.253008	+	0.438223i	−0.964353	−	0.264621i	$-0.914753\pi$
$383$	−4.95147	+	8.57619i	−0.253008	+	0.438223i	0.711344	+	0.702844i	$0.248087\pi$
$384$	10.5626	+	6.09833i	0.539022	+	0.311204i
$385$		0			0
$386$	1.60950	−	2.78773i	0.0819213	−	0.141892i
$387$	7.78322	−	4.49364i	0.395643	−	0.228425i
$388$	−0.771951	−	1.33706i	−0.0391899	−	0.0678789i
$389$	19.3750			0.982350			0.491175	−	0.871061i	$-0.336568\pi$
$389$	19.3750			0.982350			0.491175	+	0.871061i	$0.336568\pi$
$390$		0			0
$391$	0.532056			0.0269072
$392$	1.97324	+	3.41774i	0.0996635	+	0.172622i
$393$	9.73693	−	5.62162i	0.491163	−	0.283573i
$394$	−22.1709	+	38.4012i	−1.11696	+	1.93462i
$395$		0			0
$396$	−33.6674	−	19.4379i	−1.69185	−	0.976791i
$397$	9.78940	−	16.9557i	0.491316	−	0.850984i	−0.508634	−	0.860983i	$-0.669849\pi$
$397$	9.78940	−	16.9557i	0.491316	−	0.850984i	0.999950	+	0.00999849i	$0.00318267\pi$
$398$	61.0702			3.06117
$399$	−20.9765	+	36.3323i	−1.05014	+	1.81889i
$400$		0			0
$401$	−27.1719	+	15.6877i	−1.35690	+	0.783406i	−0.989205	−	0.146541i	$-0.953186\pi$
$401$	−27.1719	+	15.6877i	−1.35690	+	0.783406i	−0.367694	+	0.929947i	$0.619852\pi$
$402$			42.5014i			2.11978i
$403$	20.4993	−	0.848060i	1.02114	−	0.0422449i
$404$	−78.0734			−3.88429
$405$		0			0
$406$	4.20995	+	7.29185i	0.208936	+	0.361889i
$407$	−3.92199	−	2.26436i	−0.194406	−	0.112240i
$408$	79.4672			3.93421
$409$	16.8069	+	9.70347i	0.831048	+	0.479806i	0.854211	−	0.519926i	$-0.174041\pi$
$409$	16.8069	+	9.70347i	0.831048	+	0.479806i	−0.0231636	+	0.999732i	$0.507374\pi$
$410$		0			0
$411$			1.08176i			0.0533593i
$412$	31.4954	+	18.1839i	1.55167	+	0.895855i
$413$	−6.00459	+	3.46675i	−0.295466	+	0.170588i
$414$	−1.36171	+	0.786182i	−0.0669242	+	0.0386387i
$415$		0			0
$416$	38.5630	+	20.1868i	1.89071	+	0.989742i
$417$			30.0861i			1.47332i
$418$	13.7375	+	23.7940i	0.671921	+	1.16380i
$419$	4.07630	+	7.06036i	0.199140	+	0.344921i	0.948250	−	0.317525i	$-0.102852\pi$
$419$	4.07630	+	7.06036i	0.199140	+	0.344921i	−0.749110	+	0.662446i	$0.769518\pi$
$420$		0			0
$421$		−	15.3225i		−	0.746771i	−0.927676	−	0.373385i	$-0.878197\pi$
$421$		−	15.3225i		−	0.746771i	0.927676	−	0.373385i	$-0.121803\pi$
$422$	35.5105	−	61.5059i	1.72862	−	2.99406i
$423$	−7.85463	+	13.6046i	−0.381905	+	0.661479i
$424$		−	76.9688i		−	3.73793i
$425$		0			0
$426$	−31.1273	−	53.9141i	−1.50812	−	2.61214i
$427$	−11.4435	−	19.8208i	−0.553792	−	0.959195i
$428$		−	47.4950i		−	2.29576i
$429$	−15.8662	−	8.30560i	−0.766029	−	0.400998i
$430$		0			0
$431$	12.4274	−	7.17495i	0.598606	−	0.345605i	−0.169887	−	0.985464i	$-0.554340\pi$
$431$	12.4274	−	7.17495i	0.598606	−	0.345605i	0.768493	+	0.639858i	$0.221007\pi$
$432$	−31.3732	+	18.1133i	−1.50944	+	0.871477i
$433$	−13.2409	−	7.64462i	−0.636316	−	0.367377i	0.146878	−	0.989155i	$-0.453077\pi$
$433$	−13.2409	−	7.64462i	−0.636316	−	0.367377i	−0.783194	+	0.621778i	$0.786411\pi$
$434$		−	41.0560i		−	1.97075i
$435$		0			0
$436$	37.2959	+	21.5328i	1.78615	+	1.03123i
$437$	0.790547			0.0378170
$438$	66.4061	+	38.3396i	3.17301	+	1.83194i
$439$	−0.394002	−	0.682432i	−0.0188047	−	0.0325707i	0.856470	−	0.516197i	$-0.172653\pi$
$439$	−0.394002	−	0.682432i	−0.0188047	−	0.0325707i	−0.875275	+	0.483626i	$0.839319\pi$
$440$		0			0
$441$	−2.19222			−0.104392
$442$	36.1981	−	1.49753i	1.72177	−	0.0712301i
$443$		−	16.1718i		−	0.768343i	−0.923262	−	0.384172i	$-0.874487\pi$
$443$		−	16.1718i		−	0.768343i	0.923262	−	0.384172i	$-0.125513\pi$
$444$	−28.3595	+	16.3734i	−1.34588	+	0.777045i
$445$		0			0
$446$	−1.15922	+	2.00782i	−0.0548905	+	0.0950731i
$447$	−48.2525			−2.28227
$448$	14.9208	−	25.8436i	0.704943	−	1.22100i
$449$	5.14701	+	2.97163i	0.242903	+	0.140240i	0.616510	−	0.787347i	$-0.288546\pi$
$449$	5.14701	+	2.97163i	0.242903	+	0.140240i	−0.373607	+	0.927587i	$0.621879\pi$
$450$		0			0
$451$	−8.51665	+	14.7513i	−0.401033	+	0.694610i
$452$	−78.0015	+	45.0342i	−3.66888	+	2.11823i
$453$	−8.49221	−	14.7089i	−0.398999	−	0.691086i
$454$	9.15770			0.429792
$455$		0			0
$456$	118.075			5.52937
$457$	−4.32602	−	7.49289i	−0.202363	−	0.350503i	0.746926	−	0.664907i	$-0.231529\pi$
$457$	−4.32602	−	7.49289i	−0.202363	−	0.350503i	−0.949289	+	0.314404i	$0.898195\pi$
$458$	16.5331	−	9.54539i	0.772541	−	0.446027i
$459$	−6.61845	+	11.4635i	−0.308923	+	0.535070i
$460$		0			0
$461$	−0.600268	−	0.346565i	−0.0279573	−	0.0161411i	0.485956	−	0.873983i	$-0.338471\pi$
$461$	−0.600268	−	0.346565i	−0.0279573	−	0.0161411i	−0.513913	+	0.857842i	$0.671805\pi$
$462$	−17.9184	+	31.0356i	−0.833640	+	1.44391i
$463$	−33.6025			−1.56164			−0.780821	−	0.624754i	$-0.785199\pi$
$463$	−33.6025			−1.56164			−0.780821	+	0.624754i	$0.785199\pi$
$464$	6.09530	−	10.5574i	0.282967	−	0.490113i
$465$		0			0
$466$	−32.6554	+	18.8536i	−1.51273	+	0.873375i
$467$			2.48505i			0.114995i	0.998346	+	0.0574973i	$0.0183120\pi$
$467$			2.48505i			0.114995i	−0.998346	+	0.0574973i	$0.981688\pi$
$468$	−64.3326	+	40.7779i	−2.97377	+	1.88496i
$469$	16.3941			0.757009
$470$		0			0
$471$	−21.7970	−	37.7534i	−1.00435	−	1.73959i
$472$	16.8997	+	9.75704i	0.777872	+	0.449104i
$473$	−3.85985			−0.177476
$474$	59.3598	+	34.2714i	2.72649	+	1.57414i
$475$		0			0
$476$		−	51.5753i		−	2.36395i
$477$	37.0272	+	21.3777i	1.69536	+	0.978816i
$478$	−8.25541	+	4.76626i	−0.377593	+	0.218004i
$479$	29.0171	−	16.7530i	1.32583	−	0.765465i	0.341174	−	0.940000i	$-0.389175\pi$
$479$	29.0171	−	16.7530i	1.32583	−	0.765465i	0.984651	+	0.174535i	$0.0558421\pi$
$480$		0			0
$481$	−7.49424	+	4.75030i	−0.341708	+	0.216595i
$482$			7.18479i			0.327258i
$483$	0.515574	+	0.893000i	0.0234594	+	0.0406329i
$484$	−18.7677	−	32.5066i	−0.853077	−	1.47757i
$485$		0			0
$486$			52.2176i			2.36864i
$487$	0.0101571	−	0.0175926i	0.000460263	−	0.000797199i	−0.865795	−	0.500399i	$-0.833187\pi$
$487$	0.0101571	−	0.0175926i	0.000460263	−	0.000797199i	0.866255	+	0.499601i	$0.166520\pi$
$488$	−32.2074	+	55.7849i	−1.45796	+	2.52526i
$489$			64.3277i			2.90900i
$490$		0			0
$491$	−5.50075	−	9.52758i	−0.248245	−	0.429974i	0.714794	−	0.699335i	$-0.246521\pi$
$491$	−5.50075	−	9.52758i	−0.248245	−	0.429974i	−0.963039	+	0.269362i	$0.913187\pi$
$492$	61.5829	+	106.665i	2.77637	+	4.80882i
$493$		−	4.45434i		−	0.200613i
$494$	53.7844	−	2.22508i	2.41987	−	0.100111i
$495$		0			0
$496$	−51.4783	+	29.7210i	−2.31145	+	1.33451i
$497$	−20.7963	+	12.0068i	−0.932842	+	0.538576i
$498$	−96.0619	−	55.4613i	−4.30464	−	2.48528i
$499$		−	8.95832i		−	0.401030i	−0.979691	−	0.200515i	$-0.935739\pi$
$499$		−	8.95832i		−	0.401030i	0.979691	−	0.200515i	$-0.0642615\pi$
$500$		0			0
$501$	2.61069	+	1.50728i	0.116637	+	0.0673403i
$502$	−29.1861			−1.30264
$503$	−17.4732	−	10.0881i	−0.779090	−	0.449808i	0.0570180	−	0.998373i	$-0.481841\pi$
$503$	−17.4732	−	10.0881i	−0.779090	−	0.449808i	−0.836108	+	0.548566i	$0.815174\pi$
$504$	45.2937	+	78.4509i	2.01754	+	3.49448i
$505$		0			0
$506$	0.675297			0.0300206
$507$	−28.8339	+	19.9938i	−1.28056	+	0.887956i
$508$			54.8992i			2.43576i
$509$	−1.99934	+	1.15432i	−0.0886193	+	0.0511644i	−0.543655	−	0.839309i	$-0.682960\pi$
$509$	−1.99934	+	1.15432i	−0.0886193	+	0.0511644i	0.455035	+	0.890473i	$0.349627\pi$
$510$		0			0
$511$	14.7888	−	25.6149i	0.654216	−	1.13314i
$512$	35.0481			1.54892
$513$	−9.83391	+	17.0328i	−0.434178	+	0.752018i
$514$	−66.7083	−	38.5140i	−2.94238	−	1.69878i
$515$		0			0
$516$	−13.9551	+	24.1709i	−0.614338	+	1.06406i
$517$	5.84290	−	3.37340i	0.256970	−	0.148362i
$518$	8.87778	+	15.3768i	0.390067	+	0.675616i
$519$	5.80515			0.254818
$520$		0			0
$521$	−9.00049			−0.394319			−0.197159	−	0.980371i	$-0.563172\pi$
$521$	−9.00049			−0.394319			−0.197159	+	0.980371i	$0.563172\pi$
$522$	6.58186	+	11.4001i	0.288080	+	0.498970i
$523$	34.8743	−	20.1347i	1.52495	−	0.880428i	0.525383	−	0.850866i	$-0.323922\pi$
$523$	34.8743	−	20.1347i	1.52495	−	0.880428i	0.999563	−	0.0295625i	$-0.00941141\pi$
$524$	−10.2686	+	17.7857i	−0.448586	+	0.776974i
$525$		0			0
$526$	32.8404	+	18.9604i	1.43191	+	0.826714i
$527$	−10.8598	+	18.8097i	−0.473061	+	0.819365i
$528$	51.8856			2.25803
$529$	−11.4903	+	19.9018i	−0.499578	+	0.865294i
$530$		0			0
$531$	−9.38760	+	5.41993i	−0.407387	+	0.235205i
$532$		−	76.6323i		−	3.32243i
$533$	17.8667	+	28.1871i	0.773892	+	1.22092i
$534$	−23.9317			−1.03562
$535$		0			0
$536$	−23.0703	−	39.9589i	−0.996485	−	1.72596i
$537$	5.06120	+	2.92209i	0.218407	+	0.126097i
$538$	34.5519			1.48964
$539$	0.815375	+	0.470757i	0.0351207	+	0.0202769i
$540$		0			0
$541$		−	18.4257i		−	0.792185i	−0.918211	−	0.396092i	$-0.870366\pi$
$541$		−	18.4257i		−	0.792185i	0.918211	−	0.396092i	$-0.129634\pi$
$542$	−4.33531	−	2.50299i	−0.186217	−	0.107513i
$543$	−46.3379	+	26.7532i	−1.98855	+	1.14809i
$544$	−39.9056	+	23.0395i	−1.71094	+	0.987811i
$545$		0			0
$546$	37.5902	+	59.3036i	1.60871	+	2.53796i
$547$		−	31.9538i		−	1.36625i	−0.730303	−	0.683123i	$-0.760621\pi$
$547$		−	31.9538i		−	1.36625i	0.730303	−	0.683123i	$-0.239379\pi$
$548$	−0.987985	−	1.71124i	−0.0422046	−	0.0731006i
$549$	−17.8909	−	30.9879i	−0.763564	−	1.32253i
$550$		0			0
$551$		−	6.61840i		−	0.281953i
$552$	1.45106	−	2.51332i	0.0617614	−	0.106974i
$553$	13.2195	−	22.8969i	0.562152	−	0.973676i
$554$			75.3399i			3.20089i
$555$		0			0
$556$	−27.4780	−	47.5933i	−1.16533	−	2.01841i
$557$	10.3377	+	17.9054i	0.438022	+	0.758677i	0.997537	−	0.0701438i	$-0.0223458\pi$
$557$	10.3377	+	17.9054i	0.438022	+	0.758677i	−0.559515	+	0.828820i	$0.689012\pi$
$558$		−	64.1871i		−	2.71726i
$559$	−3.50727	+	6.69996i	−0.148342	+	0.283378i
$560$		0			0
$561$	16.4186	−	9.47929i	0.693194	−	0.400216i
$562$	−1.91773	+	1.10720i	−0.0808948	+	0.0467046i
$563$	−29.3459	−	16.9429i	−1.23678	−	0.714056i	−0.268346	−	0.963322i	$-0.586477\pi$
$563$	−29.3459	−	16.9429i	−1.23678	−	0.714056i	−0.968435	+	0.249266i	$0.919811\pi$
$564$		−	48.7853i		−	2.05423i
$565$		0			0
$566$	7.47523	+	4.31582i	0.314207	+	0.181408i
$567$	9.57741			0.402213
$568$	58.5305	+	33.7926i	2.45588	+	1.41790i
$569$	−16.4578	−	28.5058i	−0.689949	−	1.19503i	−0.971854	−	0.235584i	$-0.924300\pi$
$569$	−16.4578	−	28.5058i	−0.689949	−	1.19503i	0.281905	−	0.959442i	$-0.409034\pi$
$570$		0			0
$571$	−33.3623			−1.39617			−0.698085	−	0.716015i	$-0.745964\pi$
$571$	−33.3623			−1.39617			−0.698085	+	0.716015i	$0.745964\pi$
$572$	32.6845	−	1.35217i	1.36661	−	0.0565369i
$573$		−	7.45792i		−	0.311559i
$574$	57.8345	−	33.3908i	2.41397	−	1.39370i
$575$		0			0
$576$	23.3273	−	40.4041i	0.971971	−	1.68350i
$577$	−6.68771			−0.278413			−0.139206	−	0.990263i	$-0.544455\pi$
$577$	−6.68771			−0.278413			−0.139206	+	0.990263i	$0.544455\pi$
$578$	3.19987	−	5.54234i	0.133097	−	0.230531i
$579$	−2.85819	−	1.65018i	−0.118782	−	0.0685790i
$580$		0			0
$581$	−21.3931	+	37.0540i	−0.887537	+	1.53726i
$582$	−1.92696	+	1.11253i	−0.0798750	+	0.0461158i
$583$	−9.18126	−	15.9024i	−0.380249	−	0.658611i
$584$	−83.2449			−3.44470
$585$		0			0
$586$	22.1142			0.913530
$587$	11.7081	+	20.2791i	0.483247	+	0.837008i	0.999815	−	0.0192383i	$-0.00612413\pi$
$587$	11.7081	+	20.2791i	0.483247	+	0.837008i	−0.516568	+	0.856246i	$0.672791\pi$
$588$	5.89588	−	3.40399i	0.243142	−	0.140378i
$589$	−16.1359	+	27.9481i	−0.664867	+	1.15158i
$590$		0			0
$591$	39.3717	+	22.7313i	1.61954	+	0.935039i
$592$	12.8535	−	22.2629i	0.528276	−	0.915001i
$593$	7.21585			0.296319			0.148160	−	0.988963i	$-0.452665\pi$
$593$	7.21585			0.296319			0.148160	+	0.988963i	$0.452665\pi$
$594$	−8.40028	+	14.5497i	−0.344668	+	0.596982i
$595$		0			0
$596$	76.3309	−	44.0697i	3.12663	−	1.80516i
$597$		−	62.6136i		−	2.56260i
$598$	0.613612	−	1.17219i	0.0250925	−	0.0479343i
$599$	−37.7682			−1.54317			−0.771584	−	0.636127i	$-0.780535\pi$
$599$	−37.7682			−1.54317			−0.771584	+	0.636127i	$0.780535\pi$
$600$		0			0
$601$	14.1912	+	24.5800i	0.578873	+	1.00264i	0.995609	+	0.0936099i	$0.0298406\pi$
$601$	14.1912	+	24.5800i	0.578873	+	1.00264i	−0.416736	+	0.909028i	$0.636826\pi$
$602$	13.1057	+	7.56656i	0.534147	+	0.308390i
$603$	25.6306			1.04376
$604$	26.8677	+	15.5121i	1.09323	+	0.631178i
$605$		0			0
$606$			112.519i			4.57076i
$607$	23.0801	+	13.3253i	0.936792	+	0.540857i	0.888953	−	0.457998i	$-0.151433\pi$
$607$	23.0801	+	13.3253i	0.936792	+	0.540857i	0.0478390	+	0.998855i	$0.484767\pi$
$608$	−59.2931	+	34.2329i	−2.40465	+	1.38833i
$609$	7.47614	−	4.31635i	0.302948	−	0.174907i
$610$		0			0
$611$	−0.546394	−	13.2074i	−0.0221048	−	0.534315i
$612$		−	80.6331i		−	3.25940i
$613$	2.30095	+	3.98537i	0.0929346	+	0.160967i	0.908745	−	0.417352i	$-0.137042\pi$
$613$	2.30095	+	3.98537i	0.0929346	+	0.160967i	−0.815810	+	0.578320i	$0.803709\pi$
$614$	43.2064	+	74.8356i	1.74367	+	3.02012i
$615$		0			0
$616$		−	38.9054i		−	1.56754i
$617$	13.9270	−	24.1223i	0.560680	−	0.971126i	−0.436757	−	0.899579i	$-0.643873\pi$
$617$	13.9270	−	24.1223i	0.560680	−	0.971126i	0.997437	−	0.0715470i	$-0.0227936\pi$
$618$	26.2064	−	45.3909i	1.05418	−	1.82589i
$619$		−	30.3338i		−	1.21922i	−0.792703	−	0.609608i	$-0.791327\pi$
$619$		−	30.3338i		−	1.21922i	0.792703	−	0.609608i	$-0.208673\pi$
$620$		0			0
$621$	0.241705	+	0.418645i	0.00969928	+	0.0167996i
$622$	24.4812	+	42.4026i	0.981605	+	1.70019i
$623$			9.23117i			0.369839i
$624$	47.1462	−	90.0636i	1.88736	−	3.60543i
$625$		0			0
$626$	14.9458	−	8.62894i	0.597353	−	0.344882i
$627$	24.3953	−	14.0846i	0.974255	−	0.562486i
$628$	68.9614	+	39.8149i	2.75186	+	1.58879i
$629$		−	9.39313i		−	0.374529i
$630$		0			0
$631$	−2.94868	−	1.70242i	−0.117385	−	0.0677723i	0.440158	−	0.897920i	$-0.354922\pi$
$631$	−2.94868	−	1.70242i	−0.117385	−	0.0677723i	−0.557543	+	0.830148i	$0.688256\pi$
$632$	−74.4118			−2.95994
$633$	−63.0603	−	36.4079i	−2.50642	−	1.44708i
$634$	−37.3710	−	64.7285i	−1.48419	−	2.57070i
$635$		0			0
$636$	−132.777			−5.26496
$637$	1.55804	−	0.987579i	0.0617318	−	0.0391293i
$638$		−	5.65354i		−	0.223826i
$639$	−32.5130	+	18.7714i	−1.28620	+	0.742586i
$640$		0			0
$641$	−3.54843	+	6.14606i	−0.140155	+	0.242755i	−0.927555	−	0.373687i	$-0.878093\pi$
$641$	−3.54843	+	6.14606i	−0.140155	+	0.242755i	0.787400	+	0.616442i	$0.211427\pi$
$642$	−68.4495			−2.70148
$643$	−13.4485	+	23.2936i	−0.530359	+	0.918608i	0.469014	+	0.883191i	$0.344609\pi$
$643$	−13.4485	+	23.2936i	−0.530359	+	0.918608i	−0.999373	+	0.0354176i	$0.988724\pi$
$644$	−1.63118	−	0.941761i	−0.0642774	−	0.0371106i
$645$		0			0
$646$	−28.4931	+	49.3516i	−1.12105	+	1.94171i
$647$	−1.51516	+	0.874779i	−0.0595672	+	0.0343911i	−0.529488	−	0.848318i	$-0.677616\pi$
$647$	−1.51516	+	0.874779i	−0.0595672	+	0.0343911i	0.469921	+	0.882709i	$0.344283\pi$
$648$	−13.4776	−	23.3440i	−0.529452	−	0.917037i
$649$	4.65550			0.182744
$650$		0			0
$651$	−42.0936			−1.64978
$652$	−58.7513	−	101.760i	−2.30088	−	3.98524i
$653$	0.701221	−	0.404850i	0.0274409	−	0.0158430i	−0.486217	−	0.873838i	$-0.661623\pi$
$653$	0.701221	−	0.404850i	0.0274409	−	0.0158430i	0.513658	+	0.857995i	$0.328290\pi$
$654$	31.0329	−	53.7505i	1.21348	−	2.10181i
$655$		0			0
$656$	−83.7346	−	48.3442i	−3.26929	−	1.88752i
$657$	23.1208	−	40.0464i	0.902029	−	1.56236i
$658$	−26.4518			−1.03120
$659$	−19.4927	+	33.7623i	−0.759327	+	1.31519i	0.183867	+	0.982951i	$0.441138\pi$
$659$	−19.4927	+	33.7623i	−0.759327	+	1.31519i	−0.943194	+	0.332242i	$0.892195\pi$
$660$		0			0
$661$	−13.5955	+	7.84937i	−0.528804	+	0.305305i	−0.740529	−	0.672024i	$-0.765425\pi$
$661$	−13.5955	+	7.84937i	−0.528804	+	0.305305i	0.211725	+	0.977329i	$0.432092\pi$
$662$		−	6.33561i		−	0.246240i
$663$	−1.53537	−	37.1130i	−0.0596290	−	1.44135i
$664$	120.420			4.67322
$665$		0			0
$666$	13.8796	+	24.0401i	0.537822	+	0.931535i
$667$	−0.140878	−	0.0813358i	−0.00545481	−	0.00314934i
$668$	−5.50648			−0.213052
$669$	2.05856	+	1.18851i	0.0795887	+	0.0459506i
$670$		0			0
$671$			15.3675i			0.593257i
$672$	−77.3388	−	44.6516i	−2.98341	−	1.72247i
$673$	−28.6251	+	16.5267i	−1.10342	+	0.637057i	−0.937116	−	0.349018i	$-0.886515\pi$
$673$	−28.6251	+	16.5267i	−1.10342	+	0.637057i	−0.166300	+	0.986075i	$0.553182\pi$
$674$	−7.60449	+	4.39045i	−0.292914	+	0.169114i
$675$		0			0
$676$	27.3518	−	57.9627i	1.05199	−	2.22933i
$677$		−	9.32729i		−	0.358477i	−0.983806	−	0.179238i	$-0.942637\pi$
$677$		−	9.32729i		−	0.358477i	0.983806	−	0.179238i	$-0.0573634\pi$
$678$	64.9029	+	112.415i	2.49258	+	4.31728i
$679$	0.429137	+	0.743287i	0.0164688	+	0.0285247i
$680$		0			0
$681$		−	9.38914i		−	0.359793i
$682$	−13.7835	+	23.8737i	−0.527798	+	0.914173i
$683$	−10.2351	+	17.7277i	−0.391634	+	0.678331i	−0.992665	−	0.120895i	$-0.961424\pi$
$683$	−10.2351	+	17.7277i	−0.391634	+	0.678331i	0.601031	+	0.799226i	$0.294757\pi$
$684$		−	119.807i		−	4.58095i
$685$		0			0
$686$	23.4069	+	40.5420i	0.893681	+	1.54790i
$687$	−9.78663	−	16.9509i	−0.373383	−	0.646719i
$688$		−	21.9102i		−	0.835318i
$689$	−35.9462	+	1.48710i	−1.36944	+	0.0566541i
$690$		0			0
$691$	−3.86449	+	2.23116i	−0.147012	+	0.0848774i	−0.571702	−	0.820462i	$-0.693717\pi$
$691$	−3.86449	+	2.23116i	−0.147012	+	0.0848774i	0.424690	+	0.905339i	$0.360383\pi$
$692$	−9.18320	+	5.30192i	−0.349093	+	0.201549i
$693$	18.7161	+	10.8058i	0.710967	+	0.410477i
$694$			52.7684i			2.00306i
$695$		0			0
$696$	−21.0413	−	12.1482i	−0.797569	−	0.460477i
$697$	−35.3291			−1.33819
$698$	−33.9362	−	19.5931i	−1.28450	−	0.741608i
$699$	19.3301	+	33.4807i	0.731130	+	1.26635i
$700$		0			0
$701$	41.2801			1.55913			0.779564	−	0.626323i	$-0.215441\pi$
$701$	41.2801			1.55913			0.779564	+	0.626323i	$0.215441\pi$
$702$	17.6226	+	27.8020i	0.665121	+	1.04932i
$703$		−	13.9566i		−	0.526384i
$704$	−17.3527	+	10.0186i	−0.654005	+	0.377590i
$705$		0			0
$706$	25.2305	−	43.7005i	0.949562	−	1.64469i
$707$	43.4019			1.63230
$708$	16.8317	−	29.1533i	0.632573	−	1.09565i
$709$	24.3714	+	14.0708i	0.915287	+	0.528441i	0.882128	−	0.471009i	$-0.156110\pi$
$709$	24.3714	+	14.0708i	0.915287	+	0.528441i	0.0331583	+	0.999450i	$0.489443\pi$
$710$		0			0
$711$	20.6675	−	35.7971i	0.775091	−	1.34250i
$712$	22.5000	−	12.9904i	0.843225	−	0.486836i
$713$	0.396598	+	0.686929i	0.0148527	+	0.0257257i
$714$	−74.3299			−2.78173
$715$		0			0
$716$	−10.6751			−0.398948
$717$	4.88672	+	8.46404i	0.182498	+	0.316096i
$718$	34.6300	−	19.9936i	1.29238	−	0.746156i
$719$	5.50910	−	9.54204i	0.205455	−	0.355858i	−0.744823	−	0.667262i	$-0.767466\pi$
$719$	5.50910	−	9.54204i	0.205455	−	0.355858i	0.950278	+	0.311404i	$0.100799\pi$
$720$		0			0
$721$	−17.5087	−	10.1086i	−0.652057	−	0.376465i
$722$	−17.3271	+	30.0114i	−0.644848	+	1.11691i
$723$	7.36637			0.273958
$724$	48.8681	−	84.6421i	1.81617	−	3.14570i
$725$		0			0
$726$	−46.8482	+	27.0478i	−1.73870	+	1.00384i
$727$			21.0896i			0.782168i	0.920355	+	0.391084i	$0.127900\pi$
$727$			21.0896i			0.782168i	−0.920355	+	0.391084i	$0.872100\pi$
$728$	−67.5323	−	35.3516i	−2.50291	−	1.31022i
$729$	43.0538			1.59459
$730$		0			0
$731$	−4.00290	−	6.93322i	−0.148053	−	0.256435i
$732$	96.2334	+	55.5604i	3.55689	+	2.05357i
$733$	9.50914			0.351228			0.175614	−	0.984459i	$-0.443809\pi$
$733$	9.50914			0.351228			0.175614	+	0.984459i	$0.443809\pi$
$734$	−9.72820	−	5.61658i	−0.359075	−	0.207312i
$735$		0			0
$736$			1.68280i			0.0620288i
$737$	−9.53305	−	5.50391i	−0.351154	−	0.202739i
$738$	90.4188	−	52.2033i	3.32836	−	1.92163i
$739$	2.97018	−	1.71484i	0.109260	−	0.0630813i	−0.444374	−	0.895841i	$-0.646574\pi$
$739$	2.97018	−	1.71484i	0.109260	−	0.0630813i	0.553634	+	0.832760i	$0.313241\pi$
$740$		0			0
$741$	−2.28131	−	55.1437i	−0.0838060	−	2.02575i
$742$			71.9930i			2.64295i
$743$	−15.7635	−	27.3032i	−0.578307	−	1.00166i	−0.995674	−	0.0929188i	$-0.970380\pi$
$743$	−15.7635	−	27.3032i	−0.578307	−	1.00166i	0.417367	−	0.908738i	$-0.362953\pi$
$744$	59.2354	+	102.599i	2.17168	+	3.76145i
$745$		0			0
$746$		−	36.0745i		−	1.32078i
$747$	−33.4461	+	57.9304i	−1.22373	+	2.11956i
$748$	−17.3151	+	29.9907i	−0.633103	+	1.09657i
$749$			26.4031i			0.964747i
$750$		0			0
$751$	4.49261	+	7.78143i	0.163938	+	0.283948i	0.936278	−	0.351261i	$-0.114247\pi$
$751$	4.49261	+	7.78143i	0.163938	+	0.283948i	−0.772340	+	0.635210i	$0.780914\pi$
$752$	19.1489	+	33.1668i	0.698288	+	1.20947i
$753$			29.9238i			1.09048i
$754$	−9.81347	−	5.13712i	−0.357386	−	0.187083i
$755$		0			0
$756$	40.5817	−	23.4299i	1.47594	−	0.852136i
$757$	−29.0485	+	16.7711i	−1.05578	+	0.609558i	−0.924263	−	0.381756i	$-0.875320\pi$
$757$	−29.0485	+	16.7711i	−1.05578	+	0.609558i	−0.131521	+	0.991313i	$0.541986\pi$
$758$	43.6028	+	25.1741i	1.58373	+	0.914365i
$759$		−	0.692364i		−	0.0251312i
$760$		0			0
$761$	−39.0273	−	22.5324i	−1.41474	−	0.816800i	−0.418909	−	0.908028i	$-0.637587\pi$
$761$	−39.0273	−	22.5324i	−1.41474	−	0.816800i	−0.995830	+	0.0912283i	$0.970921\pi$
$762$	79.1203			2.86623
$763$	−20.7332	−	11.9703i	−0.750593	−	0.433355i
$764$	6.81141	+	11.7977i	0.246428	+	0.426826i
$765$		0			0
$766$	−26.0697			−0.941935
$767$	4.23024	−	8.08105i	0.152745	−	0.291790i
$768$		−	26.6677i		−	0.962287i
$769$	13.7521	−	7.93979i	0.495914	−	0.286316i	−0.231110	−	0.972928i	$-0.574236\pi$
$769$	13.7521	−	7.93979i	0.495914	−	0.286316i	0.727025	+	0.686611i	$0.240903\pi$
$770$		0			0
$771$	−39.4874	+	68.3942i	−1.42210	+	2.46316i
$772$	6.02851			0.216971
$773$	−8.35573	+	14.4726i	−0.300535	+	0.520542i	−0.976257	−	0.216615i	$-0.930498\pi$
$773$	−8.35573	+	14.4726i	−0.300535	+	0.520542i	0.675722	+	0.737156i	$0.263832\pi$
$774$	20.4895	+	11.8296i	0.736479	+	0.425206i
$775$		0			0
$776$	1.20779	−	2.09195i	0.0433571	−	0.0750968i
$777$	15.7654	−	9.10214i	0.565580	−	0.326538i
$778$	25.5025	+	44.1716i	0.914309	+	1.58363i
$779$	−52.4931			−1.88076
$780$		0			0
$781$	16.1239			0.576957
$782$	0.700324	+	1.21300i	0.0250435	+	0.0433767i
$783$	3.50487	−	2.02354i	0.125254	−	0.0723153i
$784$	−2.67222	+	4.62842i	−0.0954364	+	0.165301i
$785$		0			0
$786$	25.6327	+	14.7990i	0.914287	+	0.527864i
$787$	−24.7034	+	42.7875i	−0.880580	+	1.52521i	−0.0298831	+	0.999553i	$0.509513\pi$
$787$	−24.7034	+	42.7875i	−0.880580	+	1.52521i	−0.850697	+	0.525656i	$0.823820\pi$
$788$	−83.0430			−2.95829
$789$	19.4396	−	33.6704i	0.692068	−	1.19870i
$790$		0			0
$791$	43.3620	−	25.0350i	1.54177	−	0.890144i
$792$		−	60.8249i		−	2.16132i
$793$	26.6751	+	13.9638i	0.947260	+	0.495868i
$794$	51.5416			1.82914
$795$		0			0
$796$	57.1858	+	99.0488i	2.02690	+	3.51069i
$797$	−16.8118	−	9.70631i	−0.595505	−	0.343815i	0.171766	−	0.985138i	$-0.445053\pi$
$797$	−16.8118	−	9.70631i	−0.595505	−	0.343815i	−0.767271	+	0.641323i	$0.778386\pi$
$798$	−110.442			−3.90960
$799$	12.1189	+	6.99684i	0.428735	+	0.247530i
$800$		0			0
$801$			14.4321i			0.509932i
$802$	−71.5305	−	41.2981i	−2.52583	−	1.45829i
$803$	−17.1991	+	9.92991i	−0.606943	+	0.350419i
$804$	−68.9324	+	39.7981i	−2.43106	+	1.40357i
$805$		0			0
$806$	28.9158	+	45.6185i	1.01852	+	1.60684i
$807$		−	35.4252i		−	1.24702i
$808$	−61.0766	−	105.788i	−2.14867	−	3.72160i
$809$	11.0486	+	19.1368i	0.388450	+	0.672814i	0.992241	−	0.124328i	$-0.0396774\pi$
$809$	11.0486	+	19.1368i	0.388450	+	0.672814i	−0.603792	+	0.797142i	$0.706344\pi$
$810$		0			0
$811$		−	13.7950i		−	0.484407i	−0.970225	−	0.242203i	$-0.922130\pi$
$811$		−	13.7950i		−	0.484407i	0.970225	−	0.242203i	$-0.0778702\pi$
$812$	−7.88436	+	13.6561i	−0.276687	+	0.479236i
$813$	−2.56625	+	4.44487i	−0.0900022	+	0.155888i
$814$		−	11.9220i		−	0.417865i
$815$		0			0
$816$	53.8085	+	93.1991i	1.88368	+	3.26262i
$817$	−5.94764	−	10.3016i	−0.208082	−	0.360408i
$818$			51.0891i			1.78629i
$819$	35.7632	−	22.6689i	1.24967	−	0.792116i
$820$		0			0
$821$	−20.2706	+	11.7032i	−0.707450	+	0.408446i	−0.810116	−	0.586270i	$-0.800596\pi$
$821$	−20.2706	+	11.7032i	−0.707450	+	0.408446i	0.102666	+	0.994716i	$0.467263\pi$
$822$	−2.46623	+	1.42388i	−0.0860195	+	0.0496634i
$823$	−13.7244	−	7.92379i	−0.478402	−	0.276206i	0.241348	−	0.970439i	$-0.422410\pi$
$823$	−13.7244	−	7.92379i	−0.478402	−	0.276206i	−0.719750	+	0.694233i	$0.755744\pi$
$824$			56.9008i			1.98223i
$825$		0			0
$826$	−15.8072	−	9.12628i	−0.550002	−	0.317544i
$827$	4.85361			0.168777			0.0843883	−	0.996433i	$-0.473106\pi$
$827$	4.85361			0.168777			0.0843883	+	0.996433i	$0.473106\pi$
$828$	−2.55019	−	1.47235i	−0.0886253	−	0.0511678i
$829$	7.58395	+	13.1358i	0.263401	+	0.456225i	0.967144	−	0.254231i	$-0.0818223\pi$
$829$	7.58395	+	13.1358i	0.263401	+	0.456225i	−0.703742	+	0.710455i	$0.748489\pi$
$830$		0			0
$831$	77.2440			2.67956
$832$	1.62273	+	39.2244i	0.0562579	+	1.35986i
$833$			1.95281i			0.0676610i
$834$	−68.5911	+	39.6011i	−2.37512	+	1.37127i
$835$		0			0
$836$	−25.7274	+	44.5611i	−0.889800	+	1.54118i
$837$	−19.7338			−0.682099
$838$	−10.7309	+	18.5865i	−0.370694	+	0.642061i
$839$	−37.8349	−	21.8440i	−1.30620	−	0.754138i	−0.324744	−	0.945802i	$-0.605278\pi$
$839$	−37.8349	−	21.8440i	−1.30620	−	0.754138i	−0.981461	+	0.191664i	$0.938612\pi$
$840$		0			0
$841$	13.8191	−	23.9353i	0.476519	−	0.825356i
$842$	34.9326	−	20.1683i	1.20386	−	0.695046i
$843$	1.13519	+	1.96620i	0.0390979	+	0.0677196i
$844$	133.007			4.57830
$845$		0			0
$846$	−41.3549			−1.42181
$847$	10.4332	+	18.0708i	0.358488	+	0.620920i
$848$	90.2690	−	52.1168i	3.09985	−	1.78970i
$849$	4.42490	−	7.66415i	0.151862	−	0.263033i
$850$		0			0
$851$	−0.297077	−	0.171518i	−0.0101837	−	0.00587955i
$852$	58.2949	−	100.970i	1.99715	−	3.45917i
$853$	−5.18588			−0.177561			−0.0887806	−	0.996051i	$-0.528297\pi$
$853$	−5.18588			−0.177561			−0.0887806	+	0.996051i	$0.528297\pi$
$854$	30.1253	−	52.1786i	1.03087	−	1.78552i
$855$		0			0
$856$	64.3547	−	37.1552i	2.19960	−	1.26994i
$857$			12.8688i			0.439589i	0.975546	+	0.219795i	$0.0705387\pi$
$857$			12.8688i			0.439589i	−0.975546	+	0.219795i	$0.929461\pi$
$858$	−1.94873	−	47.1046i	−0.0665286	−	1.60812i
$859$	−15.7252			−0.536538			−0.268269	−	0.963344i	$-0.586452\pi$
$859$	−15.7252			−0.536538			−0.268269	+	0.963344i	$0.586452\pi$
$860$		0			0
$861$	−34.2347	−	59.2962i	−1.16671	−	2.02081i
$862$	32.7153	+	18.8882i	1.11429	+	0.643335i
$863$	16.0465			0.546230			0.273115	−	0.961981i	$-0.411946\pi$
$863$	16.0465			0.546230			0.273115	+	0.961981i	$0.411946\pi$
$864$	−36.2570	−	20.9330i	−1.23349	−	0.712154i
$865$		0			0
$866$		−	40.2492i		−	1.36772i
$867$	−5.68241	−	3.28074i	−0.192985	−	0.111420i
$868$	66.5880	−	38.4446i	2.26015	−	1.30490i
$869$	−15.3741	+	8.87626i	−0.521532	+	0.301106i
$870$		0			0
$871$	−18.2160	+	11.5464i	−0.617225	+	0.391235i
$872$			67.3802i			2.28178i
$873$	0.670915	+	1.16206i	0.0227070	+	0.0393297i
$874$	1.04056	+	1.80231i	0.0351976	+	0.0609641i
$875$		0			0
$876$			143.604i			4.85193i
$877$	2.74017	−	4.74612i	0.0925290	−	0.160265i	−0.816046	−	0.577987i	$-0.803838\pi$
$877$	2.74017	−	4.74612i	0.0925290	−	0.160265i	0.908575	+	0.417723i	$0.137172\pi$
$878$	1.03722	−	1.79652i	0.0350044	−	0.0606295i
$879$		−	22.6731i		−	0.764745i
$880$		0			0
$881$	−4.78231	−	8.28321i	−0.161120	−	0.279068i	0.774151	−	0.633002i	$-0.218177\pi$
$881$	−4.78231	−	8.28321i	−0.161120	−	0.279068i	−0.935271	+	0.353933i	$0.884844\pi$
$882$	−2.88553	−	4.99789i	−0.0971610	−	0.168288i
$883$			32.6927i			1.10020i	0.835100	+	0.550098i	$0.185410\pi$
$883$			32.6927i			1.10020i	−0.835100	+	0.550098i	$0.814590\pi$
$884$	36.3246	+	57.3069i	1.22173	+	1.92744i
$885$		0			0
$886$	36.8688	−	21.2862i	1.23863	−	0.715125i
$887$	−39.6612	+	22.8984i	−1.33169	+	0.768854i	−0.985559	−	0.169331i	$-0.945839\pi$
$887$	−39.6612	+	22.8984i	−1.33169	+	0.768854i	−0.346135	+	0.938185i	$0.612506\pi$
$888$	−44.3711	−	25.6177i	−1.48900	−	0.859673i
$889$		−	30.5191i		−	1.02358i
$890$		0			0
$891$	−5.56919	−	3.21537i	−0.186575	−	0.107719i
$892$	−4.34194			−0.145379
$893$	18.0066	+	10.3961i	0.602569	+	0.347893i
$894$	−63.5128	−	110.007i	−2.12419	−	3.67920i
$895$		0			0
$896$	12.3850			0.413755
$897$	−1.20181	−	0.629120i	−0.0401273	−	0.0210057i
$898$			15.6457i			0.522105i
$899$	5.75092	−	3.32030i	0.191804	−	0.110738i
$900$		0			0
$901$	19.0430	−	32.9835i	0.634416	−	1.09884i
$902$	−44.8405			−1.49302
$903$	7.75779	−	13.4369i	0.258163	−	0.447152i
$904$	−122.041	−	70.4603i	−4.05901	−	2.34347i
$905$		0			0
$906$	22.3559	−	38.7215i	0.742725	−	1.28644i
$907$	−10.7434	+	6.20272i	−0.356729	+	0.205958i	−0.667645	−	0.744480i	$-0.732698\pi$
$907$	−10.7434	+	6.20272i	−0.356729	+	0.205958i	0.310916	+	0.950437i	$0.399364\pi$
$908$	8.57523	+	14.8527i	0.284579	+	0.492905i
$909$	67.8547			2.25060
$910$		0			0
$911$	−13.8486			−0.458826			−0.229413	−	0.973329i	$-0.573681\pi$
$911$	−13.8486			−0.458826			−0.229413	+	0.973329i	$0.573681\pi$
$912$	79.9505	+	138.478i	2.64743	+	4.58548i
$913$	24.8799	−	14.3644i	0.823405	−	0.475393i
$914$	11.3883	−	19.7252i	0.376693	−	0.652451i
$915$		0			0
$916$	30.9630	+	17.8765i	1.02305	+	0.590657i
$917$	5.70844	−	9.88730i	0.188509	−	0.326508i
$918$	−34.8464			−1.15010
$919$	−24.2075	+	41.9287i	−0.798533	+	1.38310i	0.122038	+	0.992525i	$0.461057\pi$
$919$	−24.2075	+	41.9287i	−0.798533	+	1.38310i	−0.920571	+	0.390575i	$0.872276\pi$
$920$		0			0
$921$	76.7269	−	44.2983i	2.52824	−	1.45968i
$922$		−	1.82468i		−	0.0600925i
$923$	14.6510	−	27.9879i	0.482245	−	0.921234i
$924$	−67.1149			−2.20792
$925$		0			0
$926$	−44.2297	−	76.6080i	−1.45348	−	2.51750i
$927$	−27.3731	−	15.8039i	−0.899051	−	0.519068i
$928$	14.0883			0.462470
$929$	−16.1983	−	9.35210i	−0.531450	−	0.306833i	0.210157	−	0.977668i	$-0.432603\pi$
$929$	−16.1983	−	9.35210i	−0.531450	−	0.306833i	−0.741607	+	0.670835i	$0.765936\pi$
$930$		0			0
$931$			2.90156i			0.0950946i
$932$	−61.1567	−	35.3088i	−2.00325	−	1.15658i
$933$	43.4743	−	25.0999i	1.42328	−	0.821733i
$934$	−5.66549	+	3.27097i	−0.185381	+	0.107030i
$935$		0			0
$936$	−105.580	−	55.2688i	−3.45100	−	1.80652i
$937$			32.9941i			1.07787i	0.842347	+	0.538935i	$0.181173\pi$
$937$			32.9941i			1.07787i	−0.842347	+	0.538935i	$0.818827\pi$
$938$	21.5789	+	37.3757i	0.704576	+	1.22036i
$939$	−8.84702	−	15.3235i	−0.288712	−	0.500063i
$940$		0			0
$941$			30.1625i			0.983270i	0.870801	+	0.491635i	$0.163601\pi$
$941$			30.1625i			0.983270i	−0.870801	+	0.491635i	$0.836399\pi$
$942$	57.3809	−	99.3866i	1.86957	−	3.23819i
$943$	−0.645106	+	1.11736i	−0.0210076	+	0.0363861i
$944$			26.4266i			0.860113i
$945$		0			0
$946$	−5.08057	−	8.79980i	−0.165183	−	0.286106i
$947$	−5.22013	−	9.04154i	−0.169632	−	0.293810i	0.768659	−	0.639659i	$-0.220924\pi$
$947$	−5.22013	−	9.04154i	−0.169632	−	0.293810i	−0.938290	+	0.345849i	$0.887591\pi$
$948$			128.366i			4.16915i
$949$	1.60836	+	38.8772i	0.0522097	+	1.26201i
$950$		0			0
$951$	−66.3643	+	38.3155i	−2.15201	+	1.24246i
$952$	69.8834	−	40.3472i	2.26494	−	1.30766i
$953$	30.5345	+	17.6291i	0.989108	+	0.571062i	0.905008	−	0.425396i	$-0.139865\pi$
$953$	30.5345	+	17.6291i	0.989108	+	0.571062i	0.0841005	+	0.996457i	$0.473198\pi$
$954$			112.554i			3.64408i
$955$		0			0
$956$	−15.4606	−	8.92621i	−0.500033	−	0.288694i
$957$	−5.79643			−0.187372
$958$	76.3881	+	44.1027i	2.46799	+	1.42489i
$959$	0.549233	+	0.951299i	0.0177357	+	0.0307191i
$960$		0			0
$961$	−1.37993			−0.0445139
$962$	−20.6942	−	10.8330i	−0.667209	−	0.349269i
$963$			41.2787i			1.33019i
$964$	−11.6529	+	6.72781i	−0.375315	+	0.216688i
$965$		0			0
$966$	−1.35726	+	2.35084i	−0.0436691	+	0.0756370i
$967$	36.8535			1.18513			0.592564	−	0.805523i	$-0.298116\pi$
$967$	36.8535			1.18513			0.592564	+	0.805523i	$0.298116\pi$
$968$	29.3638	−	50.8596i	0.943789	−	1.63469i
$969$	50.5988	+	29.2132i	1.62547	+	0.938465i
$970$		0			0
$971$	−3.00764	+	5.20939i	−0.0965199	+	0.167177i	−0.910242	−	0.414077i	$-0.864104\pi$
$971$	−3.00764	+	5.20939i	−0.0965199	+	0.167177i	0.813722	+	0.581254i	$0.197438\pi$
$972$	−84.6908	+	48.8963i	−2.71646	+	1.56835i
$973$	15.2754	+	26.4577i	0.489706	+	0.848195i
$974$	0.0534776			0.00171353
$975$		0			0
$976$	−87.2327			−2.79225
$977$	17.8807	+	30.9702i	0.572054	+	0.990826i	0.996355	+	0.0853050i	$0.0271865\pi$
$977$	17.8807	+	30.9702i	0.572054	+	0.990826i	−0.424301	+	0.905521i	$0.639480\pi$
$978$	−146.656	+	84.6720i	−4.68955	+	2.70751i
$979$	3.09913	−	5.36786i	0.0990488	−	0.171558i
$980$		0			0
$981$	−32.4144	−	18.7145i	−1.03491	−	0.597507i
$982$	14.4808	−	25.0815i	0.462102	−	0.800384i
$983$	3.54764			0.113152			0.0565760	−	0.998398i	$-0.481982\pi$
$983$	3.54764			0.113152			0.0565760	+	0.998398i	$0.481982\pi$
$984$	−96.3523	+	166.887i	−3.07160	+	5.32016i
$985$		0			0
$986$	10.1551	−	5.86307i	0.323405	−	0.186718i
$987$			27.1203i			0.863250i
$988$	53.9723	+	85.1485i	1.71709	+	2.70894i
$989$	−0.292370			−0.00929684
$990$		0			0
$991$	24.3549	+	42.1839i	0.773658	+	1.34002i	0.935545	+	0.353206i	$0.114909\pi$
$991$	24.3549	+	42.1839i	0.773658	+	1.34002i	−0.161887	+	0.986809i	$0.551758\pi$
$992$	−59.4919	−	34.3476i	−1.88887	−	1.09054i
$993$	−6.49573			−0.206136
$994$	−54.7467	−	31.6080i	−1.73646	−	1.00254i
$995$		0			0
$996$		−	207.735i		−	6.58234i
$997$	−29.5962	−	17.0874i	−0.937320	−	0.541162i	−0.0482007	−	0.998838i	$-0.515349\pi$
$997$	−29.5962	−	17.0874i	−0.937320	−	0.541162i	−0.889119	+	0.457676i	$0.848682\pi$
$998$	20.4234	−	11.7915i	0.646493	−	0.373253i
$999$	7.39092	−	4.26715i	0.233838	−	0.135007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.m.d.49.10		20
5.2	odd	4		325.2.n.e.101.1	✓	10
5.3	odd	4		325.2.n.f.101.5	yes	10
5.4	even	2	inner	325.2.m.d.49.1		20
13.4	even	6	inner	325.2.m.d.199.1		20
65.2	even	12		4225.2.a.bv.1.1		10
65.4	even	6	inner	325.2.m.d.199.10		20
65.17	odd	12		325.2.n.e.251.1	yes	10
65.28	even	12		4225.2.a.bu.1.10		10
65.37	even	12		4225.2.a.bv.1.10		10
65.43	odd	12		325.2.n.f.251.5	yes	10
65.63	even	12		4225.2.a.bu.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.m.d.49.1		20	5.4	even	2	inner
325.2.m.d.49.10		20	1.1	even	1	trivial
325.2.m.d.199.1		20	13.4	even	6	inner
325.2.m.d.199.10		20	65.4	even	6	inner
325.2.n.e.101.1	✓	10	5.2	odd	4
325.2.n.e.251.1	yes	10	65.17	odd	12
325.2.n.f.101.5	yes	10	5.3	odd	4
325.2.n.f.251.5	yes	10	65.43	odd	12
4225.2.a.bu.1.1		10	65.63	even	12
4225.2.a.bu.1.10		10	65.28	even	12
4225.2.a.bv.1.1		10	65.2	even	12
4225.2.a.bv.1.10		10	65.37	even	12

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.31626 + 2.27983i) q^{2} +(2.33745 - 1.34953i) q^{3} +(-2.46508 + 4.26964i) q^{4} +(6.15337 + 3.55265i) q^{6} +(1.37037 - 2.37354i) q^{7} -7.71370 q^{8} +(2.14244 - 3.71081i) q^{9} +(-1.59372 + 0.920132i) q^{11} +13.3067i q^{12} +(0.149035 + 3.60247i) q^{13} +7.21503 q^{14} +(-5.22307 - 9.04662i) q^{16} +(-3.30556 - 1.90847i) q^{17} +11.2800 q^{18} +(-4.91151 - 2.83566i) q^{19} -7.39738i q^{21} +(-4.19549 - 2.42227i) q^{22} +(-0.120718 + 0.0696968i) q^{23} +(-18.0304 + 10.4098i) q^{24} +(-8.01684 + 5.08156i) q^{26} -3.46794i q^{27} +(6.75612 + 11.7019i) q^{28} +(0.583497 + 1.01065i) q^{29} -5.69034i q^{31} +(6.03614 - 10.4549i) q^{32} +(-2.48348 + 4.30152i) q^{33} -10.0481i q^{34} +(10.5626 + 18.2949i) q^{36} +(1.23046 + 2.13121i) q^{37} -14.9299i q^{38} +(5.20999 + 8.21945i) q^{39} +(8.01584 - 4.62795i) q^{41} +(16.8648 - 9.73687i) q^{42} +(1.81644 + 1.04872i) q^{43} -9.07280i q^{44} +(-0.317794 - 0.183478i) q^{46} -3.66621 q^{47} +(-24.4173 - 14.0973i) q^{48} +(-0.255809 - 0.443075i) q^{49} -10.3021 q^{51} +(-15.7486 - 8.24405i) q^{52} +9.97820i q^{53} +(7.90632 - 4.56471i) q^{54} +(-10.5706 + 18.3088i) q^{56} -15.3072 q^{57} +(-1.53607 + 2.66055i) q^{58} +(-2.19087 - 1.26490i) q^{59} +(4.17536 - 7.23193i) q^{61} +(12.9730 - 7.48996i) q^{62} +(-5.87185 - 10.1703i) q^{63} +10.8882 q^{64} -13.0756 q^{66} +(2.99082 + 5.18026i) q^{67} +(16.2969 - 9.40904i) q^{68} +(-0.188115 + 0.325825i) q^{69} +(-7.58786 - 4.38085i) q^{71} +(-16.5261 + 28.6241i) q^{72} +10.7918 q^{73} +(-3.23920 + 5.61046i) q^{74} +(24.2145 - 13.9803i) q^{76} +5.04367i q^{77} +(-11.8813 + 22.6968i) q^{78} +9.64672 q^{79} +(1.74723 + 3.02630i) q^{81} +(21.1018 + 12.1832i) q^{82} -15.6113 q^{83} +(31.5842 + 18.2351i) q^{84} +5.52156i q^{86} +(2.72779 + 1.57489i) q^{87} +(12.2934 - 7.09762i) q^{88} +(-2.91690 + 1.68407i) q^{89} +(8.75486 + 4.58296i) q^{91} -0.687233i q^{92} +(-7.67925 - 13.3009i) q^{93} +(-4.82569 - 8.35833i) q^{94} -32.5837i q^{96} +(-0.156577 + 0.271200i) q^{97} +(0.673423 - 1.16640i) q^{98} +7.88531i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 12 q^{4} + 18 q^{6} + 16 q^{9} - 18 q^{11} + 16 q^{14} - 24 q^{16} - 84 q^{24} - 34 q^{26} - 14 q^{29} - 6 q^{36} - 16 q^{39} + 24 q^{41} + 78 q^{46} + 2 q^{49} + 32 q^{51} + 18 q^{54} - 42 q^{56}+ \cdots - 10 q^{94}+O(q^{100}) \) 20 * q - 12 * q^4 + 18 * q^6 + 16 * q^9 - 18 * q^11 + 16 * q^14 - 24 * q^16 - 84 * q^24 - 34 * q^26 - 14 * q^29 - 6 * q^36 - 16 * q^39 + 24 * q^41 + 78 * q^46 + 2 * q^49 + 32 * q^51 + 18 * q^54 - 42 * q^56 + 96 * q^59 + 26 * q^61 + 68 * q^64 - 84 * q^66 - 40 * q^69 - 54 * q^71 + 52 * q^74 - 24 * q^76 - 8 * q^79 - 34 * q^81 + 180 * q^84 - 48 * q^89 + 26 * q^91 - 10 * q^94

Introduction

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