LMFDB - Embedded newform 325.2.m.d.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(49,325)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			49.1
Root			$1.31626 - 2.27983i$ of defining polynomial
Character	$\chi$	$=$	325.49
Dual form			325.2.m.d.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31626 - 2.27983i) q^{2} +(-2.33745 + 1.34953i) q^{3} +(-2.46508 + 4.26964i) q^{4} +(6.15337 + 3.55265i) q^{6} +(-1.37037 + 2.37354i) q^{7} +7.71370 q^{8} +(2.14244 - 3.71081i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 20 * q - 12 * q^4 + 18 * q^6 + 16 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.785834\pi$
$2$	−1.31626	−	2.27983i	−0.930736	−	1.61208i	−0.148670	−	0.988887i	$-0.547499\pi$
$3$	−2.33745	+	1.34953i	−1.34953	+	0.779149i	−0.988182	−	0.153284i	$-0.951015\pi$
$3$	−2.33745	+	1.34953i	−1.34953	+	0.779149i	−0.361343	+	0.932433i	$0.617682\pi$
$4$	−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	$0.339971\pi$
$7$	−1.37037	+	2.37354i	−0.517950	+	0.897116i	−0.999783	+	0.0208523i	$0.993362\pi$
$8$	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	0.844071	−	0.536232i	$-0.180153\pi$
$17$	3.30556	+	1.90847i	0.801716	+	0.462871i	−0.0423549	+	0.999103i	$0.513486\pi$
$18$	−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	−0.487361	−	0.873200i	$-0.662041\pi$
$23$	0.120718	−	0.0696968i	0.0251715	−	0.0145328i	0.512533	+	0.858668i	$0.328707\pi$
$24$	−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	0.746979	−	0.664848i	$-0.231504\pi$
$37$	−1.23046	−	2.13121i	−0.202286	−	0.350369i	−0.949265	+	0.314479i	$0.898170\pi$
$38$			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	0.355062	−	0.934843i	$-0.384460\pi$
$43$	−1.81644	−	1.04872i	−0.277004	−	0.159929i	−0.632066	+	0.774914i	$0.717793\pi$
$44$		−	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	$-0.413840\pi$
$47$	3.66621			0.534772			0.267386	+	0.963590i	$0.413840\pi$
$48$	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	$-0.759669\pi$
$53$		−	9.97820i		−	1.37061i	0.728256	−	0.685305i	$-0.240331\pi$
$54$	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	0.623451	−	0.781862i	$-0.285730\pi$
$67$	−2.99082	−	5.18026i	−0.365387	−	0.632869i	−0.988838	+	0.148993i	$0.952397\pi$
$68$	−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	$-0.717578\pi$
$73$	−10.7918			−1.26309			−0.631544	+	0.775340i	$0.717578\pi$
$74$	−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	$-0.172462\pi$
$83$	15.6113			1.71356			0.856779	+	0.515684i	$0.172462\pi$
$84$	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	−0.857967	−	0.513705i	$-0.828273\pi$
$97$	0.156577	−	0.271200i	0.0158980	−	0.0275362i	0.873865	+	0.486169i	$0.161606\pi$
$98$	−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	$0.118390\pi$
$103$			7.37659i			0.726837i	−0.931626	+	0.363418i	$0.881610\pi$
$104$	−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	−0.0392127	−	0.999231i	$-0.512485\pi$
$107$	8.34292	−	4.81679i	0.806540	−	0.465656i	0.845753	+	0.533575i	$0.179152\pi$
$108$	−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	−0.488432	−	0.872602i	$-0.662431\pi$
$113$	−15.8213	−	9.13443i	−1.48834	−	0.859295i	−0.999911	+	0.0133068i	$0.995764\pi$
$114$	−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	−0.862578	−	0.505924i	$-0.831152\pi$
$127$	−9.64353	+	5.56769i	−0.855725	+	0.494053i	0.00685350	+	0.999977i	$0.497818\pi$
$128$	−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	−0.857338	−	0.514754i	$-0.827883\pi$
$137$	0.200396	−	0.347097i	0.0171210	−	0.0296545i	0.874459	+	0.485099i	$0.161217\pi$
$138$	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	$0.222942\pi$
$157$			16.1516i			1.28904i	−0.764589	+	0.644518i	$0.777058\pi$
$158$	−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	$-0.450169\pi$
$163$	11.9167	−	20.6404i	0.933390	−	1.61668i	0.777480	−	0.628908i	$-0.216498\pi$
$164$			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	0.843609	−	0.536957i	$-0.180426\pi$
$167$	−0.558448	−	0.967261i	−0.0432140	−	0.0748489i	−0.886823	+	0.462108i	$0.847093\pi$
$168$		−	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	0.427518	−	0.904007i	$-0.359388\pi$
$173$	−1.86266	−	1.07541i	−0.141615	−	0.0817616i	−0.569134	+	0.822245i	$0.692721\pi$
$174$			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	0.887191	−	0.461403i	$-0.152654\pi$
$193$	0.611391	+	1.05896i	0.0440089	+	0.0762257i	−0.843182	+	0.537628i	$0.819320\pi$
$194$	−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	$-0.961818\pi$
$197$	−8.42195	−	14.5872i	−0.600039	−	1.03930i	0.392776	−	0.919634i	$-0.371515\pi$
$198$	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	0.850905	−	0.525320i	$-0.176054\pi$
$223$	−0.440345	−	0.762699i	−0.0294877	−	0.0510741i	−0.880393	+	0.474246i	$0.842721\pi$
$224$	−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	−0.917957	−	0.396679i	$-0.870162\pi$
$227$	−1.73934	+	3.01263i	−0.115444	+	0.199955i	0.802513	+	0.596635i	$0.203496\pi$
$228$	−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	$-0.844548\pi$
$233$		−	14.3236i		−	0.938371i	0.883100	−	0.469185i	$-0.155452\pi$
$234$	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	$-0.300737\pi$
$257$	25.3401	−	14.6301i	1.58067	−	0.912601i	0.994761	−	0.102224i	$-0.0325960\pi$
$258$	−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	−0.832602	−	0.553872i	$-0.813150\pi$
$263$	−12.4749	+	7.20239i	−0.769235	+	0.444118i	0.0633665	+	0.997990i	$0.479816\pi$
$264$	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	−0.489246	−	0.872146i	$-0.662728\pi$
$277$	−24.7847	−	14.3095i	−1.48917	−	0.859772i	−0.999923	+	0.0123732i	$0.996061\pi$
$278$	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	−0.582018	−	0.813176i	$-0.697736\pi$
$283$	−2.83957	+	1.63943i	−0.168795	+	0.0974538i	0.413223	+	0.910630i	$0.364403\pi$
$284$	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	−0.962238	−	0.272210i	$-0.912245\pi$
$293$	−4.20020	+	7.27496i	−0.245378	+	0.425008i	0.716860	+	0.697217i	$0.245579\pi$
$294$		−	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	$-0.886149\pi$
$307$	−32.8251			−1.87343			−0.936714	+	0.350095i	$0.886149\pi$
$308$	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	$0.0593172\pi$
$313$			6.55565i			0.370547i	−0.982687	+	0.185274i	$0.940683\pi$
$314$	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	$-0.206250\pi$
$317$	28.3918			1.59464			0.797321	+	0.603555i	$0.206250\pi$
$318$	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	$-0.971042\pi$
$337$		−	3.33555i		−	0.181699i	0.995865	−	0.0908496i	$-0.0289582\pi$
$338$	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	−0.0444861	−	0.999010i	$-0.514165\pi$
$347$	−17.3593	−	10.0224i	−0.931897	−	0.538031i	−0.887411	+	0.460979i	$0.847498\pi$
$348$	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	$0.00373000\pi$
$353$	9.58417	+	16.6003i	0.510114	+	0.883543i	−0.489818	+	0.871825i	$0.662937\pi$
$354$	−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	−0.400440	−	0.916323i	$-0.631143\pi$
$367$	3.69540	−	2.13354i	0.192898	−	0.111370i	0.593339	+	0.804953i	$0.297810\pi$
$368$	−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	0.774715	−	0.632310i	$-0.217893\pi$
$373$	11.8675	+	6.85171i	0.614476	+	0.354768i	−0.160239	+	0.987078i	$0.551227\pi$
$374$	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	−0.711344	−	0.702844i	$-0.751913\pi$
$383$	4.95147	−	8.57619i	0.253008	−	0.438223i	0.964353	+	0.264621i	$0.0852467\pi$
$384$	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	−0.999950	−	0.00999849i	$-0.996817\pi$
$397$	−9.78940	+	16.9557i	−0.491316	+	0.850984i	0.508634	+	0.860983i	$0.330151\pi$
$398$	−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	0.783194	−	0.621778i	$-0.213589\pi$
$433$	13.2409	+	7.64462i	0.636316	+	0.367377i	−0.146878	+	0.989155i	$0.546923\pi$
$434$		−	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	$0.125513\pi$
$443$			16.1718i			0.768343i	−0.923262	+	0.384172i	$0.874487\pi$
$444$	−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	0.949289	−	0.314404i	$-0.101805\pi$
$457$	4.32602	+	7.49289i	0.202363	+	0.350503i	−0.746926	+	0.664907i	$0.768471\pi$
$458$	−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	$-0.214801\pi$
$463$	33.6025			1.56164			0.780821	+	0.624754i	$0.214801\pi$
$464$	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	$-0.981688\pi$
$467$		−	2.48505i		−	0.114995i	0.998346	−	0.0574973i	$-0.0183120\pi$
$468$	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	−0.866255	−	0.499601i	$-0.833480\pi$
$487$	−0.0101571	+	0.0175926i	−0.000460263	+	0.000797199i	0.865795	+	0.500399i	$0.166813\pi$
$488$	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	0.836108	−	0.548566i	$-0.184826\pi$
$503$	17.4732	+	10.0881i	0.779090	+	0.449808i	−0.0570180	+	0.998373i	$0.518159\pi$
$504$	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	$0.676078\pi$
$523$	−34.8743	+	20.1347i	−1.52495	+	0.880428i	−0.999563	+	0.0295625i	$0.990589\pi$
$524$	−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	$0.239379\pi$
$547$			31.9538i			1.36625i	−0.730303	+	0.683123i	$0.760621\pi$
$548$	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	0.559515	−	0.828820i	$-0.310988\pi$
$557$	−10.3377	−	17.9054i	−0.438022	−	0.758677i	−0.997537	+	0.0701438i	$0.977654\pi$
$558$			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	0.968435	−	0.249266i	$-0.0801895\pi$
$563$	29.3459	+	16.9429i	1.23678	+	0.714056i	0.268346	+	0.963322i	$0.413523\pi$
$564$		−	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	$-0.455545\pi$
$577$	6.68771			0.278413			0.139206	+	0.990263i	$0.455545\pi$
$578$	−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	0.516568	−	0.856246i	$-0.327209\pi$
$587$	−11.7081	−	20.2791i	−0.483247	−	0.837008i	−0.999815	+	0.0192383i	$0.993876\pi$
$588$	−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	$-0.547335\pi$
$593$	−7.21585			−0.296319			−0.148160	+	0.988963i	$0.547335\pi$
$594$	−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	−0.0478390	−	0.998855i	$-0.515233\pi$
$607$	−23.0801	−	13.3253i	−0.936792	−	0.540857i	−0.888953	+	0.457998i	$0.848567\pi$
$608$	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	0.815810	−	0.578320i	$-0.196291\pi$
$613$	−2.30095	−	3.98537i	−0.0929346	−	0.160967i	−0.908745	+	0.417352i	$0.862958\pi$
$614$	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	$0.356127\pi$
$617$	−13.9270	+	24.1223i	−0.560680	+	0.971126i	−0.997437	+	0.0715470i	$0.977206\pi$
$618$	−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	$-0.655391\pi$
$643$	13.4485	−	23.2936i	0.530359	−	0.918608i	0.999373	−	0.0354176i	$-0.0112761\pi$
$644$	−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	−0.469921	−	0.882709i	$-0.655717\pi$
$647$	1.51516	−	0.874779i	0.0595672	−	0.0343911i	0.529488	+	0.848318i	$0.322384\pi$
$648$	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	−0.513658	−	0.857995i	$-0.671710\pi$
$653$	−0.701221	+	0.404850i	−0.0274409	+	0.0158430i	0.486217	+	0.873838i	$0.338377\pi$
$654$	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	0.166300	−	0.986075i	$-0.446818\pi$
$673$	28.6251	−	16.5267i	1.10342	−	0.637057i	0.937116	+	0.349018i	$0.113485\pi$
$674$	−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	$0.0573634\pi$
$677$			9.32729i			0.358477i	−0.983806	+	0.179238i	$0.942637\pi$
$678$	−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	−0.601031	−	0.799226i	$-0.705243\pi$
$683$	10.2351	−	17.7277i	0.391634	−	0.678331i	0.992665	+	0.120895i	$0.0385765\pi$
$684$		−	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	$-0.872100\pi$
$727$		−	21.0896i		−	0.782168i	0.920355	−	0.391084i	$-0.127900\pi$
$728$	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	$-0.556191\pi$
$733$	−9.50914			−0.351228			−0.175614	+	0.984459i	$0.556191\pi$
$734$	−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	$0.0296197\pi$
$743$	15.7635	+	27.3032i	0.578307	+	1.00166i	−0.417367	+	0.908738i	$0.637047\pi$
$744$	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	0.131521	−	0.991313i	$-0.458014\pi$
$757$	29.0485	−	16.7711i	1.05578	−	0.609558i	0.924263	+	0.381756i	$0.124680\pi$
$758$	−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	−0.675722	−	0.737156i	$-0.736168\pi$
$773$	8.35573	−	14.4726i	0.300535	−	0.520542i	0.976257	+	0.216615i	$0.0695015\pi$
$774$	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	$-0.490487\pi$
$787$	24.7034	−	42.7875i	0.880580	−	1.52521i	0.850697	−	0.525656i	$-0.176180\pi$
$788$	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	0.767271	−	0.641323i	$-0.221614\pi$
$797$	16.8118	+	9.70631i	0.595505	+	0.343815i	−0.171766	+	0.985138i	$0.554947\pi$
$798$	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	0.719750	−	0.694233i	$-0.244256\pi$
$823$	13.7244	+	7.92379i	0.478402	+	0.276206i	−0.241348	+	0.970439i	$0.577590\pi$
$824$			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	$-0.526894\pi$
$827$	−4.85361			−0.168777			−0.0843883	+	0.996433i	$0.526894\pi$
$828$	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	$-0.471703\pi$
$853$	5.18588			0.177561			0.0887806	+	0.996051i	$0.471703\pi$
$854$	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	$-0.929461\pi$
$857$		−	12.8688i		−	0.439589i	0.975546	−	0.219795i	$-0.0705387\pi$
$858$	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	$-0.588054\pi$
$863$	−16.0465			−0.546230			−0.273115	+	0.961981i	$0.588054\pi$
$864$	−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	−0.908575	−	0.417723i	$-0.862828\pi$
$877$	−2.74017	+	4.74612i	−0.0925290	+	0.160265i	0.816046	+	0.577987i	$0.196162\pi$
$878$	−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	$-0.814590\pi$
$883$		−	32.6927i		−	1.10020i	0.835100	−	0.550098i	$-0.185410\pi$
$884$	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	0.346135	−	0.938185i	$-0.387494\pi$
$887$	39.6612	−	22.8984i	1.33169	−	0.768854i	0.985559	+	0.169331i	$0.0541607\pi$
$888$	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	−0.310916	−	0.950437i	$-0.600636\pi$
$907$	10.7434	−	6.20272i	0.356729	−	0.205958i	0.667645	+	0.744480i	$0.267302\pi$
$908$	−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	$-0.818827\pi$
$937$		−	32.9941i		−	1.07787i	0.842347	−	0.538935i	$-0.181173\pi$
$938$	−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	0.938290	−	0.345849i	$-0.112409\pi$
$947$	5.22013	+	9.04154i	0.169632	+	0.293810i	−0.768659	+	0.639659i	$0.779076\pi$
$948$		−	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	−0.0841005	−	0.996457i	$-0.526802\pi$
$953$	−30.5345	−	17.6291i	−0.989108	−	0.571062i	−0.905008	+	0.425396i	$0.860135\pi$
$954$			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	$-0.701884\pi$
$967$	−36.8535			−1.18513			−0.592564	+	0.805523i	$0.701884\pi$
$968$	−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	$-0.972814\pi$
$977$	−17.8807	−	30.9702i	−0.572054	−	0.990826i	0.424301	−	0.905521i	$-0.360520\pi$
$978$	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	$-0.518018\pi$
$983$	−3.54764			−0.113152			−0.0565760	+	0.998398i	$0.518018\pi$
$984$	−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	0.889119	−	0.457676i	$-0.151318\pi$
$997$	29.5962	+	17.0874i	0.937320	+	0.541162i	0.0482007	+	0.998838i	$0.484651\pi$
$998$	−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.49.1		20
5.2	odd	4		325.2.n.f.101.5	yes	10
5.3	odd	4		325.2.n.e.101.1	✓	10
5.4	even	2	inner	325.2.m.d.49.10		20
13.4	even	6	inner	325.2.m.d.199.10		20
65.2	even	12		4225.2.a.bu.1.10		10
65.4	even	6	inner	325.2.m.d.199.1		20
65.17	odd	12		325.2.n.f.251.5	yes	10
65.28	even	12		4225.2.a.bv.1.1		10
65.37	even	12		4225.2.a.bu.1.1		10
65.43	odd	12		325.2.n.e.251.1	yes	10
65.63	even	12		4225.2.a.bv.1.10		10

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

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

\(f(q)\)	\(=\)	\(q+(-1.31626 - 2.27983i) q^{2} +(-2.33745 + 1.34953i) q^{3} +(-2.46508 + 4.26964i) q^{4} +(6.15337 + 3.55265i) q^{6} +(-1.37037 + 2.37354i) q^{7} +7.71370 q^{8} +(2.14244 - 3.71081i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 12 q^{4} + 18 q^{6} + 16 q^{9}+O(q^{10}) \) 20 * q - 12 * q^4 + 18 * q^6 + 16 * q^9	\( 20 q - 12 q^{4} + 18 q^{6} + 16 q^{9} - 18 q^{11} + 16 q^{14} - 24 q^{16} - 84 q^{24} - 34 q^{26} - 14 q^{29} - 6 q^{36} - 16 q^{39} + 24 q^{41} + 78 q^{46} + 2 q^{49} + 32 q^{51} + 18 q^{54} - 42 q^{56} + 96 q^{59} + 26 q^{61} + 68 q^{64} - 84 q^{66} - 40 q^{69} - 54 q^{71} + 52 q^{74} - 24 q^{76} - 8 q^{79} - 34 q^{81} + 180 q^{84} - 48 q^{89} + 26 q^{91} - 10 q^{94}+O(q^{100}) \) 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

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