LMFDB - Embedded newform 819.2.et.b.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.1
Character	$\chi$	$=$	819.271
Dual form			819.2.et.b.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.74384 - 1.74384i) q^{2} +4.08193i q^{4} +(0.638637 + 2.38343i) q^{5} +(-2.04541 - 1.67818i) q^{7} +(3.63054 - 3.63054i) q^{8} +O(q^{10})$	\(q+(-1.74384 - 1.74384i) q^{2} +4.08193i q^{4} +(0.638637 + 2.38343i) q^{5} +(-2.04541 - 1.67818i) q^{7} +(3.63054 - 3.63054i) q^{8} +(3.04263 - 5.26998i) q^{10} +(-1.17950 - 4.40195i) q^{11} +(1.54835 + 3.25617i) q^{13} +(0.640394 + 6.49333i) q^{14} -4.49827 q^{16} -0.112710 q^{17} +(-3.32660 - 0.891360i) q^{19} +(-9.72897 + 2.60687i) q^{20} +(-5.61943 + 9.73314i) q^{22} -0.652493i q^{23} +(-0.942740 + 0.544291i) q^{25} +(2.97816 - 8.37828i) q^{26} +(6.85021 - 8.34922i) q^{28} +(2.82213 + 4.88807i) q^{29} +(5.34937 + 1.43336i) q^{31} +(0.583169 + 0.583169i) q^{32} +(0.196548 + 0.196548i) q^{34} +(2.69354 - 5.94684i) q^{35} +(1.09952 - 1.09952i) q^{37} +(4.24666 + 7.35543i) q^{38} +(10.9717 + 6.33453i) q^{40} +(10.6793 + 2.86152i) q^{41} +(6.08601 + 3.51376i) q^{43} +(17.9684 - 4.81463i) q^{44} +(-1.13784 + 1.13784i) q^{46} +(5.72325 - 1.53354i) q^{47} +(1.36743 + 6.86514i) q^{49} +(2.59314 + 0.694830i) q^{50} +(-13.2914 + 6.32024i) q^{52} +(2.41079 + 4.17561i) q^{53} +(9.73846 - 5.62250i) q^{55} +(-13.5186 + 1.33325i) q^{56} +(3.60266 - 13.4453i) q^{58} +(-2.79191 - 2.79191i) q^{59} +(13.2845 - 7.66982i) q^{61} +(-6.82887 - 11.8280i) q^{62} +6.96264i q^{64} +(-6.77201 + 5.76988i) q^{65} +(-6.07826 + 1.62866i) q^{67} -0.460075i q^{68} +(-15.0674 + 5.67322i) q^{70} +(-3.56578 + 0.955449i) q^{71} +(-0.651157 + 2.43015i) q^{73} -3.83477 q^{74} +(3.63847 - 13.5789i) q^{76} +(-4.97470 + 10.9832i) q^{77} +(6.11315 - 10.5883i) q^{79} +(-2.87276 - 10.7213i) q^{80} +(-13.6330 - 23.6130i) q^{82} +(3.34105 - 3.34105i) q^{83} +(-0.0719809 - 0.268637i) q^{85} +(-4.48558 - 16.7404i) q^{86} +(-20.2637 - 11.6992i) q^{88} +(6.14338 + 6.14338i) q^{89} +(2.29743 - 9.25861i) q^{91} +2.66343 q^{92} +(-12.6547 - 7.30617i) q^{94} -8.49797i q^{95} +(1.04426 + 3.89722i) q^{97} +(9.58711 - 14.3562i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.74384	−	1.74384i	−1.23308	−	1.23308i	−0.962775	−	0.270303i	$-0.912876\pi$
$2$	−1.74384	−	1.74384i	−1.23308	−	1.23308i	−0.270303	−	0.962775i	$-0.587124\pi$
$3$		0			0
$3$		0			0
$4$			4.08193i			2.04096i
$5$	0.638637	+	2.38343i	0.285607	+	1.06590i	0.948394	+	0.317093i	$0.102707\pi$
$5$	0.638637	+	2.38343i	0.285607	+	1.06590i	−0.662787	+	0.748808i	$0.730627\pi$
$6$		0			0
$7$	−2.04541	−	1.67818i	−0.773093	−	0.634292i
$7$	−2.04541	−	1.67818i	−0.773093	−	0.634292i
$8$	3.63054	−	3.63054i	1.28359	−	1.28359i
$9$		0			0
$10$	3.04263	−	5.26998i	0.962163	−	1.66652i
$11$	−1.17950	−	4.40195i	−0.355633	−	1.32724i	−0.879687	−	0.475554i	$-0.842248\pi$
$11$	−1.17950	−	4.40195i	−0.355633	−	1.32724i	0.524054	−	0.851685i	$-0.324419\pi$
$12$		0			0
$13$	1.54835	+	3.25617i	0.429434	+	0.903098i
$13$	1.54835	+	3.25617i	0.429434	+	0.903098i
$14$	0.640394	+	6.49333i	0.171152	+	1.73542i
$15$		0			0
$16$	−4.49827			−1.12457
$17$	−0.112710			−0.0273362			−0.0136681	−	0.999907i	$-0.504351\pi$
$17$	−0.112710			−0.0273362			−0.0136681	+	0.999907i	$0.504351\pi$
$18$		0			0
$19$	−3.32660	−	0.891360i	−0.763175	−	0.204492i	−0.143820	−	0.989604i	$-0.545939\pi$
$19$	−3.32660	−	0.891360i	−0.763175	−	0.204492i	−0.619354	+	0.785112i	$0.712605\pi$
$20$	−9.72897	+	2.60687i	−2.17546	+	0.582914i
$21$		0			0
$22$	−5.61943	+	9.73314i	−1.19807	+	2.07511i
$23$		−	0.652493i		−	0.136054i	−0.997683	−	0.0680271i	$-0.978330\pi$
$23$		−	0.652493i		−	0.136054i	0.997683	−	0.0680271i	$-0.0216704\pi$
$24$		0			0
$25$	−0.942740	+	0.544291i	−0.188548	+	0.108858i
$26$	2.97816	−	8.37828i	0.584065	−	1.64312i
$27$		0			0
$28$	6.85021	−	8.34922i	1.29457	−	1.57785i
$29$	2.82213	+	4.88807i	0.524056	+	0.907691i	0.999608	+	0.0280035i	$0.00891495\pi$
$29$	2.82213	+	4.88807i	0.524056	+	0.907691i	−0.475552	+	0.879688i	$0.657752\pi$
$30$		0			0
$31$	5.34937	+	1.43336i	0.960774	+	0.257439i	0.704928	−	0.709279i	$-0.250979\pi$
$31$	5.34937	+	1.43336i	0.960774	+	0.257439i	0.255846	+	0.966717i	$0.417646\pi$
$32$	0.583169	+	0.583169i	0.103091	+	0.103091i
$33$		0			0
$34$	0.196548	+	0.196548i	0.0337077	+	0.0337077i
$35$	2.69354	−	5.94684i	0.455292	−	1.00520i
$36$		0			0
$37$	1.09952	−	1.09952i	0.180760	−	0.180760i	−0.610927	−	0.791687i	$-0.709203\pi$
$37$	1.09952	−	1.09952i	0.180760	−	0.180760i	0.791687	+	0.610927i	$0.209203\pi$
$38$	4.24666	+	7.35543i	0.688899	+	1.19321i
$39$		0			0
$40$	10.9717	+	6.33453i	1.73478	+	1.00158i
$41$	10.6793	+	2.86152i	1.66783	+	0.446894i	0.964525	−	0.263993i	$-0.0850396\pi$
$41$	10.6793	+	2.86152i	1.66783	+	0.446894i	0.703306	+	0.710887i	$0.251706\pi$
$42$		0			0
$43$	6.08601	+	3.51376i	0.928108	+	0.535843i	0.886213	−	0.463279i	$-0.153327\pi$
$43$	6.08601	+	3.51376i	0.928108	+	0.535843i	0.0418951	+	0.999122i	$0.486660\pi$
$44$	17.9684	−	4.81463i	2.70885	−	0.725833i
$45$		0			0
$46$	−1.13784	+	1.13784i	−0.167766	+	0.167766i
$47$	5.72325	−	1.53354i	0.834822	−	0.223690i	0.184006	−	0.982925i	$-0.441093\pi$
$47$	5.72325	−	1.53354i	0.834822	−	0.223690i	0.650816	+	0.759235i	$0.274427\pi$
$48$		0			0
$49$	1.36743	+	6.86514i	0.195347	+	0.980734i
$50$	2.59314	+	0.694830i	0.366725	+	0.0982637i
$51$		0			0
$52$	−13.2914	+	6.32024i	−1.84319	+	0.876459i
$53$	2.41079	+	4.17561i	0.331147	+	0.573564i	0.982737	−	0.185008i	$-0.0592310\pi$
$53$	2.41079	+	4.17561i	0.331147	+	0.573564i	−0.651590	+	0.758571i	$0.725898\pi$
$54$		0			0
$55$	9.73846	−	5.62250i	1.31313	−	0.758138i
$56$	−13.5186	+	1.33325i	−1.80650	+	0.178163i
$57$		0			0
$58$	3.60266	−	13.4453i	0.473052	−	1.76546i
$59$	−2.79191	−	2.79191i	−0.363476	−	0.363476i	0.501615	−	0.865091i	$-0.332739\pi$
$59$	−2.79191	−	2.79191i	−0.363476	−	0.363476i	−0.865091	+	0.501615i	$0.832739\pi$
$60$		0			0
$61$	13.2845	−	7.66982i	1.70091	−	0.982020i	0.756067	−	0.654495i	$-0.227119\pi$
$61$	13.2845	−	7.66982i	1.70091	−	0.982020i	0.944842	−	0.327526i	$-0.106215\pi$
$62$	−6.82887	−	11.8280i	−0.867268	−	1.50215i
$63$		0			0
$64$			6.96264i			0.870330i
$65$	−6.77201	+	5.76988i	−0.839964	+	0.715666i
$66$		0			0
$67$	−6.07826	+	1.62866i	−0.742577	+	0.198973i	−0.610223	−	0.792230i	$-0.708920\pi$
$67$	−6.07826	+	1.62866i	−0.742577	+	0.198973i	−0.132354	+	0.991203i	$0.542254\pi$
$68$		−	0.460075i		−	0.0557923i
$69$		0			0
$70$	−15.0674	+	5.67322i	−1.80090	+	0.678079i
$71$	−3.56578	+	0.955449i	−0.423181	+	0.113391i	−0.464123	−	0.885771i	$-0.653631\pi$
$71$	−3.56578	+	0.955449i	−0.423181	+	0.113391i	0.0409427	+	0.999161i	$0.486964\pi$
$72$		0			0
$73$	−0.651157	+	2.43015i	−0.0762122	+	0.284428i	−0.993505	−	0.113785i	$-0.963703\pi$
$73$	−0.651157	+	2.43015i	−0.0762122	+	0.284428i	0.917293	+	0.398212i	$0.130369\pi$
$74$	−3.83477			−0.445783
$75$		0			0
$76$	3.63847	−	13.5789i	0.417361	−	1.55761i
$77$	−4.97470	+	10.9832i	−0.566920	+	1.25165i
$78$		0			0
$79$	6.11315	−	10.5883i	0.687783	−	1.19128i	−0.284770	−	0.958596i	$-0.591917\pi$
$79$	6.11315	−	10.5883i	0.687783	−	1.19128i	0.972553	−	0.232680i	$-0.0747493\pi$
$80$	−2.87276	−	10.7213i	−0.321185	−	1.19868i
$81$		0			0
$82$	−13.6330	−	23.6130i	−1.50551	−	2.60762i
$83$	3.34105	−	3.34105i	0.366728	−	0.366728i	−0.499554	−	0.866283i	$-0.666503\pi$
$83$	3.34105	−	3.34105i	0.366728	−	0.366728i	0.866283	+	0.499554i	$0.166503\pi$
$84$		0			0
$85$	−0.0719809	−	0.268637i	−0.00780743	−	0.0291377i
$86$	−4.48558	−	16.7404i	−0.483693	−	1.80517i
$87$		0			0
$88$	−20.2637	−	11.6992i	−2.16011	−	1.24714i
$89$	6.14338	+	6.14338i	0.651197	+	0.651197i	0.953281	−	0.302084i	$-0.0976824\pi$
$89$	6.14338	+	6.14338i	0.651197	+	0.651197i	−0.302084	+	0.953281i	$0.597682\pi$
$90$		0			0
$91$	2.29743	−	9.25861i	0.240836	−	0.970566i
$92$	2.66343			0.277682
$93$		0			0
$94$	−12.6547	−	7.30617i	−1.30523	−	0.753574i
$95$		−	8.49797i		−	0.871873i
$96$		0			0
$97$	1.04426	+	3.89722i	0.106028	+	0.395703i	0.998460	−	0.0554799i	$-0.0176689\pi$
$97$	1.04426	+	3.89722i	0.106028	+	0.395703i	−0.892431	+	0.451183i	$0.851002\pi$
$98$	9.58711	−	14.3562i	0.968444	−	1.45020i
$99$		0			0
$100$	−2.22176	−	3.84820i	−0.222176	−	0.384820i
$101$	−2.26018	+	3.91475i	−0.224897	+	0.389532i	−0.956288	−	0.292425i	$-0.905538\pi$
$101$	−2.26018	+	3.91475i	−0.224897	+	0.389532i	0.731392	+	0.681957i	$0.238871\pi$
$102$		0			0
$103$	−6.72989	+	11.6565i	−0.663115	+	1.14855i	0.316677	+	0.948533i	$0.397433\pi$
$103$	−6.72989	+	11.6565i	−0.663115	+	1.14855i	−0.979793	+	0.200016i	$0.935901\pi$
$104$	17.4430	+	6.20031i	1.71042	+	0.607990i
$105$		0			0
$106$	3.07755	−	11.4856i	0.298919	−	1.11558i
$107$	−8.25997			−0.798521			−0.399261	−	0.916837i	$-0.630733\pi$
$107$	−8.25997			−0.798521			−0.399261	+	0.916837i	$0.630733\pi$
$108$		0			0
$109$	3.48535	−	13.0075i	0.333836	−	1.24589i	−0.571289	−	0.820749i	$-0.693557\pi$
$109$	3.48535	−	13.0075i	0.333836	−	1.24589i	0.905125	−	0.425145i	$-0.139777\pi$
$110$	−26.7870	−	7.17755i	−2.55404	−	0.684353i
$111$		0			0
$112$	9.20082	+	7.54891i	0.869396	+	0.713305i
$113$	−1.14314	+	1.97997i	−0.107537	+	0.186260i	−0.914772	−	0.403970i	$-0.867630\pi$
$113$	−1.14314	+	1.97997i	−0.107537	+	0.186260i	0.807235	+	0.590231i	$0.200963\pi$
$114$		0			0
$115$	1.55517	−	0.416707i	0.145020	−	0.0388581i
$116$	−19.9527	+	11.5197i	−1.85256	+	1.06958i
$117$		0			0
$118$			9.73726i			0.896388i
$119$	0.230539	+	0.189148i	0.0211335	+	0.0173392i
$120$		0			0
$121$	−8.45969	+	4.88420i	−0.769063	+	0.444018i
$122$	−36.5409	−	9.79112i	−3.30826	−	0.886446i
$123$		0			0
$124$	−5.85086	+	21.8357i	−0.525423	+	1.96091i
$125$	6.82460	+	6.82460i	0.610411	+	0.610411i
$126$		0			0
$127$	−4.38857	+	2.53374i	−0.389422	+	0.224833i	−0.681910	−	0.731436i	$-0.738850\pi$
$127$	−4.38857	+	2.53374i	−0.389422	+	0.224833i	0.292488	+	0.956269i	$0.405517\pi$
$128$	13.3080	−	13.3080i	1.17628	−	1.17628i
$129$		0			0
$130$	21.8710	+	1.74754i	1.91821	+	0.153269i
$131$	4.92213	+	2.84179i	0.430048	+	0.248288i	0.699367	−	0.714763i	$-0.253465\pi$
$131$	4.92213	+	2.84179i	0.430048	+	0.248288i	−0.269319	+	0.963051i	$0.586799\pi$
$132$		0			0
$133$	5.30841	+	7.40583i	0.460297	+	0.642167i
$134$	13.4396	+	7.75936i	1.16100	+	0.670306i
$135$		0			0
$136$	−0.409199	+	0.409199i	−0.0350885	+	0.0350885i
$137$	6.04202	−	6.04202i	0.516205	−	0.516205i	−0.400216	−	0.916421i	$-0.631065\pi$
$137$	6.04202	−	6.04202i	0.516205	−	0.516205i	0.916421	+	0.400216i	$0.131065\pi$
$138$		0			0
$139$	9.91348	+	5.72355i	0.840850	+	0.485465i	0.857553	−	0.514395i	$-0.171984\pi$
$139$	9.91348	+	5.72355i	0.840850	+	0.485465i	−0.0167030	+	0.999860i	$0.505317\pi$
$140$	24.2746	+	10.9948i	2.05158	+	0.929234i
$141$		0			0
$142$	7.88429	+	4.55200i	0.661635	+	0.381995i
$143$	12.5072	−	10.6564i	1.04591	−	0.891133i
$144$		0			0
$145$	−9.84803	+	9.84803i	−0.817835	+	0.817835i
$146$	5.37330	−	3.10227i	0.444697	−	0.256746i
$147$		0			0
$148$	4.48817	+	4.48817i	0.368925	+	0.368925i
$149$	1.97417	−	7.36771i	0.161730	−	0.603586i	−0.836704	−	0.547655i	$-0.815521\pi$
$149$	1.97417	−	7.36771i	0.161730	−	0.603586i	0.998435	−	0.0559311i	$-0.0178127\pi$
$150$		0			0
$151$	6.37363	+	1.70781i	0.518679	+	0.138980i	0.508656	−	0.860970i	$-0.330143\pi$
$151$	6.37363	+	1.70781i	0.518679	+	0.138980i	0.0100235	+	0.999950i	$0.496809\pi$
$152$	−15.3135	+	8.84123i	−1.24209	+	0.717119i
$153$		0			0
$154$	27.8280	−	10.4779i	2.24244	−	0.844331i
$155$			13.6652i			1.09762i
$156$		0			0
$157$	8.20626	−	4.73788i	0.654931	−	0.378124i	−0.135412	−	0.990789i	$-0.543236\pi$
$157$	8.20626	−	4.73788i	0.654931	−	0.378124i	0.790343	+	0.612665i	$0.209903\pi$
$158$	−29.1246	+	7.80390i	−2.31703	+	0.620845i
$159$		0			0
$160$	−1.01751	+	1.76238i	−0.0804411	+	0.139328i
$161$	−1.09500	+	1.33462i	−0.0862982	+	0.105183i
$162$		0			0
$163$	−17.8485	−	4.78249i	−1.39800	−	0.374594i	−0.520376	−	0.853937i	$-0.674208\pi$
$163$	−17.8485	−	4.78249i	−1.39800	−	0.374594i	−0.877627	+	0.479344i	$0.840875\pi$
$164$	−11.6805	+	43.5922i	−0.912094	+	3.40398i
$165$		0			0
$166$	−11.6525			−0.904409
$167$	4.24807	−	15.8540i	0.328725	−	1.22682i	−0.581788	−	0.813341i	$-0.697647\pi$
$167$	4.24807	−	15.8540i	0.328725	−	1.22682i	0.910513	−	0.413480i	$-0.135687\pi$
$168$		0			0
$169$	−8.20525	+	10.0833i	−0.631173	+	0.775642i
$170$	−0.342935	+	0.593981i	−0.0263019	+	0.0455563i
$171$		0			0
$172$	−14.3429	+	24.8426i	−1.09364	+	1.89423i
$173$	−9.11872	−	15.7941i	−0.693283	−	1.20080i	−0.970756	−	0.240068i	$-0.922830\pi$
$173$	−9.11872	−	15.7941i	−0.693283	−	1.20080i	0.277473	−	0.960733i	$-0.410503\pi$
$174$		0			0
$175$	2.84171	+	0.468787i	0.214813	+	0.0354370i
$176$	5.30571	+	19.8012i	0.399933	+	1.49257i
$177$		0			0
$178$		−	21.4261i		−	1.60595i
$179$	20.4226	+	11.7910i	1.52645	+	0.881299i	0.999507	+	0.0314008i	$0.00999682\pi$
$179$	20.4226	+	11.7910i	1.52645	+	0.881299i	0.526947	+	0.849898i	$0.323337\pi$
$180$		0			0
$181$	4.65138			0.345735			0.172867	−	0.984945i	$-0.444697\pi$
$181$	4.65138			0.345735			0.172867	+	0.984945i	$0.444697\pi$
$182$	−20.1518	+	12.1392i	−1.49375	+	0.899814i
$183$		0			0
$184$	−2.36890	−	2.36890i	−0.174638	−	0.174638i
$185$	3.32282	+	1.91843i	0.244299	+	0.141046i
$186$		0			0
$187$	0.132942	+	0.496145i	0.00972165	+	0.0362817i
$188$	6.25980	+	23.3619i	0.456543	+	1.70384i
$189$		0			0
$190$	−14.8191	+	14.8191i	−1.07509	+	1.07509i
$191$	3.84978	+	6.66801i	0.278560	+	0.482480i	0.971027	−	0.238969i	$-0.0768095\pi$
$191$	3.84978	+	6.66801i	0.278560	+	0.482480i	−0.692467	+	0.721450i	$0.743476\pi$
$192$		0			0
$193$	0.0645055	+	0.240738i	0.00464321	+	0.0173287i	0.968209	−	0.250144i	$-0.0804781\pi$
$193$	0.0645055	+	0.240738i	0.00464321	+	0.0173287i	−0.963565	+	0.267473i	$0.913811\pi$
$194$	4.97510	−	8.61713i	0.357192	−	0.618674i
$195$		0			0
$196$	−28.0230	+	5.58173i	−2.00164	+	0.398695i
$197$	1.72653	−	6.44350i	0.123010	−	0.459081i	−0.876751	−	0.480945i	$-0.840294\pi$
$197$	1.72653	−	6.44350i	0.123010	−	0.459081i	0.999761	+	0.0218645i	$0.00696025\pi$
$198$		0			0
$199$	−5.38835			−0.381970			−0.190985	−	0.981593i	$-0.561168\pi$
$199$	−5.38835			−0.381970			−0.190985	+	0.981593i	$0.561168\pi$
$200$	−1.44658	+	5.39873i	−0.102289	+	0.381748i
$201$		0			0
$202$	10.7681	−	2.88530i	0.757639	−	0.203009i
$203$	2.43064	−	14.7341i	0.170598	−	1.03413i
$204$		0			0
$205$			27.2809i			1.90538i
$206$	32.0628	−	8.59121i	2.23392	−	0.598578i
$207$		0			0
$208$	−6.96488	−	14.6471i	−0.482928	−	1.01560i
$209$			15.6949i			1.08564i
$210$		0			0
$211$	−1.44964	−	2.51085i	−0.0997974	−	0.172854i	0.811803	−	0.583931i	$-0.198486\pi$
$211$	−1.44964	−	2.51085i	−0.0997974	−	0.172854i	−0.911601	+	0.411077i	$0.865153\pi$
$212$	−17.0445	+	9.84066i	−1.17062	+	0.675859i
$213$		0			0
$214$	14.4040	+	14.4040i	0.984639	+	0.984639i
$215$	−4.48804	+	16.7496i	−0.306081	+	1.14231i
$216$		0			0
$217$	−8.53623	−	11.9090i	−0.579477	−	0.808436i
$218$	−28.7608	+	16.6051i	−1.94793	+	1.12464i
$219$		0			0
$220$	22.9506	+	39.7517i	1.54733	+	2.68006i
$221$	−0.174514	−	0.367003i	−0.0117391	−	0.0246873i
$222$		0			0
$223$	−18.1024	−	4.85053i	−1.21223	−	0.324816i	−0.404593	−	0.914497i	$-0.632587\pi$
$223$	−18.1024	−	4.85053i	−1.21223	−	0.324816i	−0.807636	+	0.589681i	$0.799253\pi$
$224$	−0.214159	−	2.17148i	−0.0143091	−	0.145088i
$225$		0			0
$226$	5.44619	−	1.45930i	0.362275	−	0.0970714i
$227$	−4.51374	+	4.51374i	−0.299587	+	0.299587i	−0.840852	−	0.541265i	$-0.817946\pi$
$227$	−4.51374	+	4.51374i	−0.299587	+	0.299587i	0.541265	+	0.840852i	$0.317946\pi$
$228$		0			0
$229$	16.7169	−	4.47928i	1.10468	−	0.295999i	0.340014	−	0.940420i	$-0.389568\pi$
$229$	16.7169	−	4.47928i	1.10468	−	0.295999i	0.764671	+	0.644421i	$0.222902\pi$
$230$	−3.43863	−	1.98529i	−0.226737	−	0.130906i
$231$		0			0
$232$	27.9921	+	7.50047i	1.83777	+	0.492430i
$233$	−1.08707	−	0.627620i	−0.0712163	−	0.0411167i	0.463969	−	0.885851i	$-0.346425\pi$
$233$	−1.08707	−	0.627620i	−0.0712163	−	0.0411167i	−0.535185	+	0.844735i	$0.679758\pi$
$234$		0			0
$235$	7.31017	+	12.6616i	0.476863	+	0.825950i
$236$	11.3964	−	11.3964i	0.741840	−	0.741840i
$237$		0			0
$238$	−0.0721789	−	0.731865i	−0.00467866	−	0.0474398i
$239$	8.59429	+	8.59429i	0.555918	+	0.555918i	0.928143	−	0.372225i	$-0.121405\pi$
$239$	8.59429	+	8.59429i	0.555918	+	0.555918i	−0.372225	+	0.928143i	$0.621405\pi$
$240$		0			0
$241$	−1.71820	−	1.71820i	−0.110679	−	0.110679i	0.649599	−	0.760277i	$-0.274937\pi$
$241$	−1.71820	−	1.71820i	−0.110679	−	0.110679i	−0.760277	+	0.649599i	$0.774937\pi$
$242$	23.2696	+	6.23506i	1.49582	+	0.400805i
$243$		0			0
$244$	31.3077	+	54.2264i	2.00427	+	3.47149i
$245$	−15.4893	+	7.64349i	−0.989573	+	0.488325i
$246$		0			0
$247$	−2.24831	−	12.2121i	−0.143057	−	0.777037i
$248$	24.6249	−	14.2172i	1.56368	−	0.902794i
$249$		0			0
$250$		−	23.8020i		−	1.50537i
$251$	−7.94802	+	13.7664i	−0.501675	+	0.868926i	0.498323	+	0.866991i	$0.333949\pi$
$251$	−7.94802	+	13.7664i	−0.501675	+	0.868926i	−0.999998	+	0.00193499i	$0.999384\pi$
$252$		0			0
$253$	−2.87225	+	0.769616i	−0.180577	+	0.0483853i
$254$	12.0714	+	3.23451i	0.757425	+	0.202951i
$255$		0			0
$256$	−32.4888			−2.03055
$257$	−14.1941			−0.885401			−0.442701	−	0.896670i	$-0.645980\pi$
$257$	−14.1941			−0.885401			−0.442701	+	0.896670i	$0.645980\pi$
$258$		0			0
$259$	−4.09417	+	0.403780i	−0.254399	+	0.0250897i
$260$	−23.5522	−	27.6428i	−1.46065	−	1.71434i
$261$		0			0
$262$	−3.62776	−	13.5390i	−0.224124	−	0.836442i
$263$	−9.46835	+	16.3997i	−0.583843	+	1.01125i	0.411175	+	0.911556i	$0.365118\pi$
$263$	−9.46835	+	16.3997i	−0.583843	+	1.01125i	−0.995019	+	0.0996901i	$0.968215\pi$
$264$		0			0
$265$	−8.41264	+	8.41264i	−0.516784	+	0.516784i
$266$	3.65756	−	22.1716i	0.224260	−	1.35942i
$267$		0			0
$268$	−6.64809	−	24.8110i	−0.406096	−	1.51557i
$269$		−	24.2202i		−	1.47673i	−0.674400	−	0.738366i	$-0.735598\pi$
$269$		−	24.2202i		−	1.47673i	0.674400	−	0.738366i	$-0.264402\pi$
$270$		0			0
$271$	11.1386	+	11.1386i	0.676624	+	0.676624i	0.959235	−	0.282610i	$-0.0912004\pi$
$271$	11.1386	+	11.1386i	0.676624	+	0.676624i	−0.282610	+	0.959235i	$0.591200\pi$
$272$	0.507001			0.0307414
$273$		0			0
$274$	−21.0726			−1.27304
$275$	3.50791	+	3.50791i	0.211535	+	0.211535i
$276$		0			0
$277$			0.746768i			0.0448689i	0.999748	+	0.0224345i	$0.00714171\pi$
$277$			0.746768i			0.0448689i	−0.999748	+	0.0224345i	$0.992858\pi$
$278$	−7.30655	−	27.2684i	−0.438218	−	1.63545i
$279$		0			0
$280$	−11.8112	−	31.3692i	−0.705856	−	1.87467i
$281$	0.536856	−	0.536856i	0.0320261	−	0.0320261i	−0.690912	−	0.722939i	$-0.742791\pi$
$281$	0.536856	−	0.536856i	0.0320261	−	0.0320261i	0.722939	+	0.690912i	$0.242791\pi$
$282$		0			0
$283$	9.63432	−	16.6871i	0.572701	−	0.991947i	−0.423587	−	0.905856i	$-0.639229\pi$
$283$	9.63432	−	16.6871i	0.572701	−	0.991947i	0.996287	−	0.0860911i	$-0.0274376\pi$
$284$	−3.90007	−	14.5553i	−0.231427	−	0.863696i
$285$		0			0
$286$	−40.3935	−	3.22753i	−2.38852	−	0.190848i
$287$	−17.0415	−	23.7748i	−1.00593	−	1.40338i
$288$		0			0
$289$	−16.9873			−0.999253
$290$	34.3467			2.01691
$291$		0			0
$292$	−9.91970	−	2.65798i	−0.580507	−	0.155546i
$293$	−14.0543	+	3.76584i	−0.821062	+	0.220003i	−0.644811	−	0.764342i	$-0.723064\pi$
$293$	−14.0543	+	3.76584i	−0.821062	+	0.220003i	−0.176251	+	0.984345i	$0.556397\pi$
$294$		0			0
$295$	4.87129	−	8.43733i	0.283618	−	0.491240i
$296$		−	7.98371i		−	0.464044i
$297$		0			0
$298$	−16.2907	+	9.40544i	−0.943695	+	0.544843i
$299$	2.12463	−	1.01029i	0.122870	−	0.0584263i
$300$		0			0
$301$	−6.55168	−	17.4005i	−0.377633	−	1.00295i
$302$	−8.13643	−	14.0927i	−0.468199	−	0.810944i
$303$		0			0
$304$	14.9639	+	4.00958i	0.858241	+	0.229965i
$305$	26.7645	+	26.7645i	1.53253	+	1.53253i
$306$		0			0
$307$	9.47209	+	9.47209i	0.540601	+	0.540601i	0.923705	−	0.383104i	$-0.125145\pi$
$307$	9.47209	+	9.47209i	0.540601	+	0.540601i	−0.383104	+	0.923705i	$0.625145\pi$
$308$	−44.8327	−	20.3064i	−2.55458	−	1.15706i
$309$		0			0
$310$	23.8299	−	23.8299i	1.35345	−	1.35345i
$311$	4.14087	+	7.17220i	0.234807	+	0.406698i	0.959217	−	0.282672i	$-0.0912207\pi$
$311$	4.14087	+	7.17220i	0.234807	+	0.406698i	−0.724409	+	0.689370i	$0.757887\pi$
$312$		0			0
$313$	−4.98156	−	2.87611i	−0.281574	−	0.162567i	0.352562	−	0.935789i	$-0.385311\pi$
$313$	−4.98156	−	2.87611i	−0.281574	−	0.162567i	−0.634136	+	0.773222i	$0.718644\pi$
$314$	−22.5725	−	6.04827i	−1.27384	−	0.341324i
$315$		0			0
$316$	43.2206	+	24.9534i	2.43135	+	1.40374i
$317$	−9.94515	+	2.66479i	−0.558575	+	0.149670i	−0.527052	−	0.849833i	$-0.676703\pi$
$317$	−9.94515	+	2.66479i	−0.558575	+	0.149670i	−0.0315235	+	0.999503i	$0.510036\pi$
$318$		0			0
$319$	18.1883	−	18.1883i	1.01835	−	1.01835i
$320$	−16.5949	+	4.44660i	−0.927685	+	0.248573i
$321$		0			0
$322$	4.23686	−	0.417853i	0.236111	−	0.0232860i
$323$	0.374942	+	0.100465i	0.0208623	+	0.00559004i
$324$		0			0
$325$	−3.23199	−	2.22697i	−0.179279	−	0.123530i
$326$	22.7850	+	39.4647i	1.26194	+	2.18575i
$327$		0			0
$328$	49.1605	−	28.3829i	2.71444	−	1.56718i
$329$	−14.2800	−	6.46792i	−0.787280	−	0.356588i
$330$		0			0
$331$	−4.48552	+	16.7402i	−0.246547	+	0.920125i	0.726053	+	0.687639i	$0.241353\pi$
$331$	−4.48552	+	16.7402i	−0.246547	+	0.920125i	−0.972600	+	0.232486i	$0.925314\pi$
$332$	13.6379	+	13.6379i	0.748479	+	0.748479i
$333$		0			0
$334$	−35.0547	+	20.2389i	−1.91811	+	1.10742i
$335$	−7.76360	−	13.4470i	−0.424171	−	0.734686i
$336$		0			0
$337$			12.1069i			0.659506i	0.944067	+	0.329753i	$0.106965\pi$
$337$			12.1069i			0.659506i	−0.944067	+	0.329753i	$0.893035\pi$
$338$	31.8923	−	3.27510i	1.73471	−	0.178142i
$339$		0			0
$340$	1.09655	−	0.293821i	0.0594690	−	0.0159347i
$341$		−	25.2383i		−	1.36673i
$342$		0			0
$343$	8.72399	−	16.3368i	0.471051	−	0.882106i
$344$	34.8523	−	9.33865i	1.87911	−	0.503506i
$345$		0			0
$346$	−11.6407	+	43.4438i	−0.625810	+	2.33555i
$347$	2.86789			0.153957			0.0769783	−	0.997033i	$-0.475473\pi$
$347$	2.86789			0.153957			0.0769783	+	0.997033i	$0.475473\pi$
$348$		0			0
$349$	3.12009	−	11.6443i	0.167014	−	0.623306i	−0.830760	−	0.556630i	$-0.812094\pi$
$349$	3.12009	−	11.6443i	0.167014	−	0.623306i	0.997775	−	0.0666760i	$-0.0212394\pi$
$350$	−4.13799	−	5.77297i	−0.221185	−	0.308578i
$351$		0			0
$352$	1.87924	−	3.25493i	0.100164	−	0.173488i
$353$	−7.89564	−	29.4669i	−0.420242	−	1.56837i	−0.774098	−	0.633066i	$-0.781796\pi$
$353$	−7.89564	−	29.4669i	−0.420242	−	1.56837i	0.353856	−	0.935300i	$-0.384870\pi$
$354$		0			0
$355$	−4.55449	−	7.88860i	−0.241727	−	0.418683i
$356$	−25.0768	+	25.0768i	−1.32907	+	1.32907i
$357$		0			0
$358$	−15.0521	−	56.1751i	−0.795527	−	2.96895i
$359$	4.63302	+	17.2907i	0.244521	+	0.912566i	0.973623	+	0.228161i	$0.0732713\pi$
$359$	4.63302	+	17.2907i	0.244521	+	0.912566i	−0.729102	+	0.684405i	$0.760062\pi$
$360$		0			0
$361$	−6.18273	−	3.56960i	−0.325407	−	0.187874i
$362$	−8.11125	−	8.11125i	−0.426318	−	0.426318i
$363$		0			0
$364$	37.7930	+	9.37793i	1.98089	+	0.491537i
$365$	−6.20794			−0.324939
$366$		0			0
$367$	−6.26259	−	3.61571i	−0.326905	−	0.188738i	0.327561	−	0.944830i	$-0.393773\pi$
$367$	−6.26259	−	3.61571i	−0.326905	−	0.188738i	−0.654466	+	0.756091i	$0.727107\pi$
$368$			2.93509i			0.153002i
$369$		0			0
$370$	−2.44903	−	9.13989i	−0.127319	−	0.475160i
$371$	2.07636	−	12.5866i	0.107799	−	0.653462i
$372$		0			0
$373$	12.2087	+	21.1462i	0.632145	+	1.09491i	0.987112	+	0.160029i	$0.0511586\pi$
$373$	12.2087	+	21.1462i	0.632145	+	1.09491i	−0.354967	+	0.934879i	$0.615508\pi$
$374$	0.633367	−	1.09702i	0.0327506	−	0.0567257i
$375$		0			0
$376$	15.2109	−	26.3461i	0.784443	−	1.35869i
$377$	−11.5467	+	16.7577i	−0.594687	+	0.863067i
$378$		0			0
$379$	−2.27080	+	8.47475i	−0.116643	+	0.435319i	−0.999405	−	0.0345031i	$-0.989015\pi$
$379$	−2.27080	+	8.47475i	−0.116643	+	0.435319i	0.882761	+	0.469822i	$0.155682\pi$
$380$	34.6881			1.77946
$381$		0			0
$382$	4.91454	−	18.3413i	0.251449	−	0.938422i
$383$	16.9913	+	4.55280i	0.868213	+	0.232637i	0.665315	−	0.746563i	$-0.268297\pi$
$383$	16.9913	+	4.55280i	0.868213	+	0.232637i	0.202898	+	0.979200i	$0.434964\pi$
$384$		0			0
$385$	−29.3547	−	4.84255i	−1.49606	−	0.246799i
$386$	0.307320	−	0.532294i	0.0156422	−	0.0270931i
$387$		0			0
$388$	−15.9082	+	4.26258i	−0.807615	+	0.216400i
$389$	−8.77740	+	5.06764i	−0.445032	+	0.256939i	−0.705730	−	0.708481i	$-0.749381\pi$
$389$	−8.77740	+	5.06764i	−0.445032	+	0.256939i	0.260698	+	0.965420i	$0.416047\pi$
$390$		0			0
$391$			0.0735427i			0.00371921i
$392$	29.8886	+	19.9597i	1.50960	+	1.00812i
$393$		0			0
$394$	−14.2472	+	8.22563i	−0.717764	+	0.414401i
$395$	29.1405	+	7.80817i	1.46622	+	0.392872i
$396$		0			0
$397$	2.18723	−	8.16286i	0.109774	−	0.409682i	−0.889069	−	0.457773i	$-0.848647\pi$
$397$	2.18723	−	8.16286i	0.109774	−	0.409682i	0.998843	+	0.0480910i	$0.0153138\pi$
$398$	9.39641	+	9.39641i	0.470999	+	0.470999i
$399$		0			0
$400$	4.24070	−	2.44837i	0.212035	−	0.122419i
$401$	−6.65097	+	6.65097i	−0.332134	+	0.332134i	−0.853396	−	0.521263i	$-0.825461\pi$
$401$	−6.65097	+	6.65097i	−0.332134	+	0.332134i	0.521263	+	0.853396i	$0.325461\pi$
$402$		0			0
$403$	3.61542	+	19.6378i	0.180097	+	0.978227i
$404$	−15.9797	−	9.22590i	−0.795021	−	0.459006i
$405$		0			0
$406$	−29.9326	+	21.4553i	−1.48553	+	1.06481i
$407$	−6.13693	−	3.54316i	−0.304196	−	0.175628i
$408$		0			0
$409$	17.9666	−	17.9666i	0.888390	−	0.888390i	−0.105979	−	0.994368i	$-0.533797\pi$
$409$	17.9666	−	17.9666i	0.888390	−	0.888390i	0.994368	+	0.105979i	$0.0337975\pi$
$410$	47.5734	−	47.5734i	2.34948	−	2.34948i
$411$		0			0
$412$	−47.5810	−	27.4709i	−2.34415	−	1.35339i
$413$	1.02528	+	10.3959i	0.0504508	+	0.511550i
$414$		0			0
$415$	10.0969	+	5.82944i	0.495636	+	0.286156i
$416$	−0.995948	+	2.80184i	−0.0488304	+	0.137372i
$417$		0			0
$418$	27.3693	−	27.3693i	1.33868	−	1.33868i
$419$	17.4075	−	10.0503i	0.850414	−	0.490987i	−0.0103762	−	0.999946i	$-0.503303\pi$
$419$	17.4075	−	10.0503i	0.850414	−	0.490987i	0.860791	+	0.508959i	$0.169970\pi$
$420$		0			0
$421$	−2.51951	−	2.51951i	−0.122793	−	0.122793i	0.643040	−	0.765833i	$-0.277673\pi$
$421$	−2.51951	−	2.51951i	−0.122793	−	0.122793i	−0.765833	+	0.643040i	$0.777673\pi$
$422$	−1.85058	+	6.90645i	−0.0900847	+	0.336201i
$423$		0			0
$424$	23.9122	+	6.40724i	1.16128	+	0.311163i
$425$	0.106256	−	0.0613472i	0.00515419	−	0.00297578i
$426$		0			0
$427$	−40.0437	−	6.60587i	−1.93785	−	0.319680i
$428$		−	33.7166i		−	1.62975i
$429$		0			0
$430$	37.0349	−	21.3821i	1.78598	−	1.03114i
$431$	−23.1558	+	6.20458i	−1.11538	+	0.298864i	−0.769011	−	0.639236i	$-0.779251\pi$
$431$	−23.1558	+	6.20458i	−1.11538	+	0.298864i	−0.346365	+	0.938100i	$0.612584\pi$
$432$		0			0
$433$	−11.7141	+	20.2893i	−0.562941	+	0.975043i	0.434296	+	0.900770i	$0.356997\pi$
$433$	−11.7141	+	20.2893i	−0.562941	+	0.975043i	−0.997238	+	0.0742732i	$0.976336\pi$
$434$	−5.88157	+	35.6531i	−0.282325	+	1.71141i
$435$		0			0
$436$	53.0957	+	14.2269i	2.54282	+	0.681347i
$437$	−0.581607	+	2.17059i	−0.0278220	+	0.103833i
$438$		0			0
$439$	−33.7642			−1.61148			−0.805738	−	0.592272i	$-0.798231\pi$
$439$	−33.7642			−1.61148			−0.805738	+	0.592272i	$0.798231\pi$
$440$	14.9431	−	55.7686i	0.712386	−	2.65866i
$441$		0			0
$442$	−0.335669	+	0.944318i	−0.0159661	+	0.0449166i
$443$	15.5134	−	26.8699i	0.737062	−	1.27663i	−0.216750	−	0.976227i	$-0.569546\pi$
$443$	15.5134	−	26.8699i	0.737062	−	1.27663i	0.953813	−	0.300402i	$-0.0971210\pi$
$444$		0			0
$445$	−10.7189	+	18.5657i	−0.508125	+	0.880098i
$446$	23.1091	+	40.0262i	1.09425	+	1.89530i
$447$		0			0
$448$	11.6846	−	14.2415i	0.552043	−	0.672846i
$449$	0.388197	+	1.44877i	0.0183202	+	0.0683718i	0.974481	−	0.224471i	$-0.0720654\pi$
$449$	0.388197	+	1.44877i	0.0183202	+	0.0683718i	−0.956161	+	0.292843i	$0.905399\pi$
$450$		0			0
$451$		−	50.3851i		−	2.37254i
$452$	−8.08210	−	4.66620i	−0.380150	−	0.219480i
$453$		0			0
$454$	15.7424			0.738829
$455$	23.5344	−	0.437145i	1.10331	−	0.0204937i
$456$		0			0
$457$	21.6961	+	21.6961i	1.01490	+	1.01490i	0.999887	+	0.0150158i	$0.00477986\pi$
$457$	21.6961	+	21.6961i	1.01490	+	1.01490i	0.0150158	+	0.999887i	$0.495220\pi$
$458$	−36.9627	−	21.3404i	−1.72715	−	0.997172i
$459$		0			0
$460$	1.70097	+	6.34809i	0.0793080	+	0.295981i
$461$	−6.69670	−	24.9924i	−0.311896	−	1.16401i	−0.926845	−	0.375445i	$-0.877490\pi$
$461$	−6.69670	−	24.9924i	−0.311896	−	1.16401i	0.614948	−	0.788568i	$-0.289177\pi$
$462$		0			0
$463$	−26.5381	+	26.5381i	−1.23333	+	1.23333i	−0.270652	+	0.962677i	$0.587239\pi$
$463$	−26.5381	+	26.5381i	−1.23333	+	1.23333i	−0.962677	+	0.270652i	$0.912761\pi$
$464$	−12.6947	−	21.9878i	−0.589336	−	1.02076i
$465$		0			0
$466$	0.801205	+	2.99014i	0.0371151	+	0.138515i
$467$	−4.11119	+	7.12080i	−0.190243	+	0.329511i	−0.945331	−	0.326113i	$-0.894261\pi$
$467$	−4.11119	+	7.12080i	−0.190243	+	0.329511i	0.755087	+	0.655624i	$0.227594\pi$
$468$		0			0
$469$	15.1657	+	6.86912i	0.700288	+	0.317186i
$470$	9.33199	−	34.8274i	0.430452	−	1.60647i
$471$		0			0
$472$	−20.2723			−0.933106
$473$	8.28895	−	30.9348i	0.381127	−	1.42238i
$474$		0			0
$475$	3.62128	−	0.970319i	0.166156	−	0.0445213i
$476$	−0.772088	+	0.941043i	−0.0353886	+	0.0431326i
$477$		0			0
$478$		−	29.9740i		−	1.37098i
$479$	−20.9972	+	5.62619i	−0.959388	+	0.257067i	−0.704342	−	0.709861i	$-0.748758\pi$
$479$	−20.9972	+	5.62619i	−0.959388	+	0.257067i	−0.255047	+	0.966929i	$0.582091\pi$
$480$		0			0
$481$	5.28267	+	1.87779i	0.240869	+	0.0856196i
$482$			5.99250i			0.272951i
$483$		0			0
$484$	−19.9370	−	34.5318i	−0.906225	−	1.56963i
$485$	−8.62185	+	4.97782i	−0.391498	+	0.226031i
$486$		0			0
$487$	12.7599	+	12.7599i	0.578206	+	0.578206i	0.934409	−	0.356202i	$-0.115929\pi$
$487$	12.7599	+	12.7599i	0.578206	+	0.578206i	−0.356202	+	0.934409i	$0.615929\pi$
$488$	20.3844	−	76.0755i	0.922758	−	3.44378i
$489$		0			0
$490$	40.3397	+	13.6817i	1.82236	+	0.618078i
$491$	−5.63350	+	3.25250i	−0.254236	+	0.146783i	−0.621703	−	0.783253i	$-0.713559\pi$
$491$	−5.63350	+	3.25250i	−0.254236	+	0.146783i	0.367466	+	0.930037i	$0.380225\pi$
$492$		0			0
$493$	−0.318082	−	0.550935i	−0.0143257	−	0.0248129i
$494$	−17.3752	+	25.2166i	−0.781748	+	1.13455i
$495$		0			0
$496$	−24.0629	−	6.44763i	−1.08046	−	0.289507i
$497$	8.89691	+	4.02974i	0.399081	+	0.180758i
$498$		0			0
$499$	19.4522	−	5.21221i	0.870802	−	0.233331i	0.204367	−	0.978894i	$-0.434486\pi$
$499$	19.4522	−	5.21221i	0.870802	−	0.233331i	0.666434	+	0.745564i	$0.267820\pi$
$500$	−27.8575	+	27.8575i	−1.24583	+	1.24583i
$501$		0			0
$502$	37.8664	−	10.1463i	1.69006	−	0.452850i
$503$	17.1138	+	9.88067i	0.763068	+	0.440557i	0.830396	−	0.557173i	$-0.188114\pi$
$503$	17.1138	+	9.88067i	0.763068	+	0.440557i	−0.0673282	+	0.997731i	$0.521447\pi$
$504$		0			0
$505$	−10.7740	−	2.88687i	−0.479435	−	0.128464i
$506$	6.35081	+	3.66664i	0.282328	+	0.163002i
$507$		0			0
$508$	−10.3425	−	17.9138i	−0.458876	−	0.794796i
$509$	−21.0947	+	21.0947i	−0.935004	+	0.935004i	−0.998013	−	0.0630085i	$-0.979930\pi$
$509$	−21.0947	+	21.0947i	−0.935004	+	0.935004i	0.0630085	+	0.998013i	$0.479930\pi$
$510$		0			0
$511$	5.41012	−	3.87791i	0.239330	−	0.171548i
$512$	30.0390	+	30.0390i	1.32755	+	1.32755i
$513$		0			0
$514$	24.7521	+	24.7521i	1.09177	+	1.09177i
$515$	−32.0804	−	8.59591i	−1.41363	−	0.378781i
$516$		0			0
$517$	−13.5012	−	23.3847i	−0.593780	−	1.02846i
$518$	7.84369	+	6.43543i	0.344632	+	0.282757i
$519$		0			0
$520$	−3.63825	+	45.5338i	−0.159548	+	1.99679i
$521$	−6.67564	+	3.85418i	−0.292465	+	0.168855i	−0.639053	−	0.769163i	$-0.720674\pi$
$521$	−6.67564	+	3.85418i	−0.292465	+	0.168855i	0.346588	+	0.938018i	$0.387340\pi$
$522$		0			0
$523$			0.0152739i			0.000667882i	1.00000		0.000333941i	$0.000106297\pi$
$523$			0.0152739i			0.000667882i	−1.00000		0.000333941i	$0.999894\pi$
$524$	−11.6000	+	20.0918i	−0.506748	+	0.877713i
$525$		0			0
$526$	45.1096	−	12.0871i	1.96687	−	0.527021i
$527$	−0.602928	−	0.161554i	−0.0262640	−	0.00703741i
$528$		0			0
$529$	22.5743			0.981489
$530$	29.3405			1.27447
$531$		0			0
$532$	−30.2301	+	21.6685i	−1.31064	+	0.939450i
$533$	7.21772	+	39.2043i	0.312634	+	1.69813i
$534$		0			0
$535$	−5.27513	−	19.6870i	−0.228064	−	0.851145i
$536$	−16.1544	+	27.9803i	−0.697764	+	1.20856i
$537$		0			0
$538$	−42.2361	+	42.2361i	−1.82093	+	1.82093i
$539$	28.6071	−	14.1168i	1.23220	−	0.608052i
$540$		0			0
$541$	−12.0108	−	44.8251i	−0.516386	−	1.92718i	−0.325325	−	0.945602i	$-0.605474\pi$
$541$	−12.0108	−	44.8251i	−0.516386	−	1.92718i	−0.191061	−	0.981578i	$-0.561193\pi$
$542$		−	38.8479i		−	1.66866i
$543$		0			0
$544$	−0.0657291	−	0.0657291i	−0.00281811	−	0.00281811i
$545$	33.2283			1.42334
$546$		0			0
$547$	22.9225			0.980097			0.490049	−	0.871695i	$-0.336979\pi$
$547$	22.9225			0.980097			0.490049	+	0.871695i	$0.336979\pi$
$548$	24.6631	+	24.6631i	1.05355	+	1.05355i
$549$		0			0
$550$		−	12.2344i		−	0.521678i
$551$	−5.03106	−	18.7762i	−0.214330	−	0.799892i
$552$		0			0
$553$	−30.2730	+	11.3985i	−1.28734	+	0.484711i
$554$	1.30224	−	1.30224i	0.0553269	−	0.0553269i
$555$		0			0
$556$	−23.3631	+	40.4661i	−0.990816	+	1.71614i
$557$	4.20224	+	15.6830i	0.178055	+	0.664509i	0.996011	+	0.0892288i	$0.0284402\pi$
$557$	4.20224	+	15.6830i	0.178055	+	0.664509i	−0.817957	+	0.575280i	$0.804893\pi$
$558$		0			0
$559$	−2.01814	+	25.2576i	−0.0853581	+	1.06828i
$560$	−12.1163	+	26.7505i	−0.512006	+	1.13041i
$561$		0			0
$562$	−1.87238			−0.0789814
$563$	−10.5234			−0.443507			−0.221753	−	0.975103i	$-0.571178\pi$
$563$	−10.5234			−0.443507			−0.221753	+	0.975103i	$0.571178\pi$
$564$		0			0
$565$	−5.44917	−	1.46010i	−0.229248	−	0.0614269i
$566$	−45.9003	+	12.2989i	−1.92933	+	0.516963i
$567$		0			0
$568$	−9.47692	+	16.4145i	−0.397643	+	0.688737i
$569$		−	35.6613i		−	1.49500i	−0.664262	−	0.747500i	$-0.731254\pi$
$569$		−	35.6613i		−	1.49500i	0.664262	−	0.747500i	$-0.268746\pi$
$570$		0			0
$571$	9.54352	−	5.50995i	0.399384	−	0.230584i	−0.286834	−	0.957980i	$-0.592603\pi$
$571$	9.54352	−	5.50995i	0.399384	−	0.230584i	0.686218	+	0.727396i	$0.259270\pi$
$572$	43.4986	+	51.0535i	1.81877	+	2.13466i
$573$		0			0
$574$	−11.7418	+	71.1769i	−0.490094	+	2.97087i
$575$	0.355147	+	0.615132i	0.0148106	+	0.0256528i
$576$		0			0
$577$	−26.6870	−	7.15076i	−1.11099	−	0.297690i	−0.343760	−	0.939057i	$-0.611701\pi$
$577$	−26.6870	−	7.15076i	−1.11099	−	0.297690i	−0.767234	+	0.641367i	$0.778367\pi$
$578$	29.6231	+	29.6231i	1.23216	+	1.23216i
$579$		0			0
$580$	−40.1989	−	40.1989i	−1.66917	−	1.66917i
$581$	−12.4407	+	1.22695i	−0.516128	+	0.0509023i
$582$		0			0
$583$	15.5373	−	15.5373i	0.643489	−	0.643489i
$584$	6.45871	+	11.1868i	0.267263	+	0.462914i
$585$		0			0
$586$	31.0754	+	17.9414i	1.28371	+	0.741153i
$587$	7.45089	+	1.99646i	0.307531	+	0.0824027i	0.409284	−	0.912407i	$-0.365778\pi$
$587$	7.45089	+	1.99646i	0.307531	+	0.0824027i	−0.101753	+	0.994810i	$0.532445\pi$
$588$		0			0
$589$	−16.5176	−	9.53642i	−0.680594	−	0.392941i
$590$	−23.2081	+	6.21858i	−0.955460	+	0.256015i
$591$		0			0
$592$	−4.94594	+	4.94594i	−0.203277	+	0.203277i
$593$	−9.89297	+	2.65081i	−0.406256	+	0.108856i	−0.456159	−	0.889898i	$-0.650775\pi$
$593$	−9.89297	+	2.65081i	−0.406256	+	0.108856i	0.0499035	+	0.998754i	$0.484109\pi$
$594$		0			0
$595$	−0.303590	+	0.670269i	−0.0124460	+	0.0274784i
$596$	30.0744	+	8.05842i	1.23190	+	0.330086i
$597$		0			0
$598$	−5.46677	−	1.94323i	−0.223553	−	0.0794646i
$599$	−19.8784	−	34.4305i	−0.812211	−	1.40679i	−0.911313	−	0.411714i	$-0.864930\pi$
$599$	−19.8784	−	34.4305i	−0.812211	−	1.40679i	0.0991022	−	0.995077i	$-0.468403\pi$
$600$		0			0
$601$	5.65826	−	3.26680i	0.230805	−	0.133255i	−0.380138	−	0.924930i	$-0.624124\pi$
$601$	5.65826	−	3.26680i	0.230805	−	0.133255i	0.610943	+	0.791674i	$0.290790\pi$
$602$	−18.9186	+	41.7687i	−0.771063	+	1.70236i
$603$		0			0
$604$	−6.97116	+	26.0167i	−0.283652	+	1.05860i
$605$	−17.0438	−	17.0438i	−0.692930	−	0.692930i
$606$		0			0
$607$	5.87637	−	3.39272i	0.238514	−	0.137706i	−0.375979	−	0.926628i	$-0.622694\pi$
$607$	5.87637	−	3.39272i	0.238514	−	0.137706i	0.614494	+	0.788922i	$0.289360\pi$
$608$	−1.42016	−	2.45979i	−0.0575950	−	0.0997575i
$609$		0			0
$610$		−	93.3456i		−	3.77945i
$611$	13.8550	+	16.2614i	0.560515	+	0.657866i
$612$		0			0
$613$	19.0899	−	5.11512i	0.771034	−	0.206598i	0.148206	−	0.988957i	$-0.452650\pi$
$613$	19.0899	−	5.11512i	0.771034	−	0.206598i	0.622828	+	0.782359i	$0.285984\pi$
$614$		−	33.0355i		−	1.33321i
$615$		0			0
$616$	21.8142	+	57.9359i	0.878917	+	2.33430i
$617$	2.05438	−	0.550470i	0.0827063	−	0.0221611i	−0.217229	−	0.976121i	$-0.569702\pi$
$617$	2.05438	−	0.550470i	0.0827063	−	0.0221611i	0.299935	+	0.953960i	$0.403035\pi$
$618$		0			0
$619$	−7.70516	+	28.7560i	−0.309696	+	1.15580i	0.619130	+	0.785288i	$0.287485\pi$
$619$	−7.70516	+	28.7560i	−0.309696	+	1.15580i	−0.928827	+	0.370514i	$0.879181\pi$
$620$	−55.7804			−2.24020
$621$		0			0
$622$	5.28614	−	19.7281i	0.211955	−	0.791027i
$623$	−2.25605	−	22.8754i	−0.0903868	−	0.916485i
$624$		0			0
$625$	−14.6290	+	25.3381i	−0.585158	+	1.01352i
$626$	3.67157	+	13.7025i	0.146745	+	0.547661i
$627$		0			0
$628$	19.3397	+	33.4973i	0.771738	+	1.33669i
$629$	−0.123927	+	0.123927i	−0.00494130	+	0.00494130i
$630$		0			0
$631$	6.04595	+	22.5638i	0.240686	+	0.898251i	0.975503	+	0.219986i	$0.0706011\pi$
$631$	6.04595	+	22.5638i	0.240686	+	0.898251i	−0.734817	+	0.678265i	$0.762732\pi$
$632$	−16.2472	−	60.6352i	−0.646277	−	2.41194i
$633$		0			0
$634$	21.9897	+	12.6957i	0.873321	+	0.504212i
$635$	−8.84168	−	8.84168i	−0.350872	−	0.350872i
$636$		0			0
$637$	−20.2368	+	15.0822i	−0.801811	+	0.597578i
$638$	−63.4349			−2.51141
$639$		0			0
$640$	40.2177	+	23.2197i	1.58975	+	0.917840i
$641$			25.5854i			1.01056i	0.862955	+	0.505280i	$0.168611\pi$
$641$			25.5854i			1.01056i	−0.862955	+	0.505280i	$0.831389\pi$
$642$		0			0
$643$	−7.72960	−	28.8473i	−0.304826	−	1.13763i	−0.933095	−	0.359630i	$-0.882903\pi$
$643$	−7.72960	−	28.8473i	−0.304826	−	1.13763i	0.628269	−	0.777996i	$-0.283764\pi$
$644$	−5.44781	−	4.46971i	−0.214674	−	0.176131i
$645$		0			0
$646$	−0.478642	−	0.829032i	−0.0188319	−	0.0326178i
$647$	−1.41318	+	2.44770i	−0.0555577	+	0.0962288i	−0.892467	−	0.451113i	$-0.851027\pi$
$647$	−1.41318	+	2.44770i	−0.0555577	+	0.0962288i	0.836909	+	0.547342i	$0.184360\pi$
$648$		0			0
$649$	−8.99679	+	15.5829i	−0.353155	+	0.611683i
$650$	1.75260	+	9.51953i	0.0687425	+	0.373387i
$651$		0			0
$652$	19.5218	−	72.8563i	0.764532	−	2.85327i
$653$	−26.1013			−1.02142			−0.510711	−	0.859753i	$-0.670618\pi$
$653$	−26.1013			−1.02142			−0.510711	+	0.859753i	$0.670618\pi$
$654$		0			0
$655$	−3.62975	+	13.5464i	−0.141826	+	0.529302i
$656$	−48.0385	−	12.8719i	−1.87559	−	0.502562i
$657$		0			0
$658$	13.6229	+	36.1809i	0.531077	+	1.41048i
$659$	9.04837	−	15.6722i	0.352475	−	0.610504i	−0.634208	−	0.773163i	$-0.718674\pi$
$659$	9.04837	−	15.6722i	0.352475	−	0.610504i	0.986682	+	0.162659i	$0.0520070\pi$
$660$		0			0
$661$	−1.36965	+	0.366997i	−0.0532733	+	0.0142745i	−0.285357	−	0.958421i	$-0.592112\pi$
$661$	−1.36965	+	0.366997i	−0.0532733	+	0.0142745i	0.232084	+	0.972696i	$0.425446\pi$
$662$	37.0142	−	21.3702i	1.43860	−	0.830574i
$663$		0			0
$664$		−	24.2596i		−	0.941457i
$665$	−14.2611	+	17.3818i	−0.553022	+	0.674039i
$666$		0			0
$667$	3.18943	−	1.84142i	0.123495	−	0.0713000i
$668$	64.7149	+	17.3403i	2.50389	+	0.670917i
$669$		0			0
$670$	−9.91083	+	36.9877i	−0.382889	+	1.42896i
$671$	−49.4313	−	49.4313i	−1.90827	−	1.90827i
$672$		0			0
$673$	−3.78674	+	2.18627i	−0.145968	+	0.0842747i	−0.571205	−	0.820807i	$-0.693524\pi$
$673$	−3.78674	+	2.18627i	−0.145968	+	0.0842747i	0.425237	+	0.905082i	$0.360191\pi$
$674$	21.1125	−	21.1125i	0.813222	−	0.813222i
$675$		0			0
$676$	−41.1595	−	33.4932i	−1.58306	−	1.28820i
$677$	40.1930	+	23.2054i	1.54474	+	0.891857i	0.998530	+	0.0542097i	$0.0172639\pi$
$677$	40.1930	+	23.2054i	1.54474	+	0.891857i	0.546212	+	0.837647i	$0.316069\pi$
$678$		0			0
$679$	4.40430	−	9.72388i	0.169022	−	0.373168i
$680$	−1.23662	−	0.713966i	−0.0474224	−	0.0273793i
$681$		0			0
$682$	−44.0115	+	44.0115i	−1.68529	+	1.68529i
$683$	−2.74654	+	2.74654i	−0.105094	+	0.105094i	−0.757698	−	0.652605i	$-0.773676\pi$
$683$	−2.74654	+	2.74654i	−0.105094	+	0.105094i	0.652605	+	0.757698i	$0.273676\pi$
$684$		0			0
$685$	18.2594	+	10.5421i	0.697655	+	0.402791i
$686$	−43.7020	+	13.2755i	−1.66855	+	0.506863i
$687$		0			0
$688$	−27.3765	−	15.8058i	−1.04372	−	0.602592i
$689$	−9.86374	+	14.3152i	−0.375779	+	0.545366i
$690$		0			0
$691$	−30.7245	+	30.7245i	−1.16882	+	1.16882i	−0.186329	+	0.982487i	$0.559659\pi$
$691$	−30.7245	+	30.7245i	−1.16882	+	1.16882i	−0.982487	+	0.186329i	$0.940341\pi$
$692$	64.4703	−	37.2219i	2.45079	−	1.41497i
$693$		0			0
$694$	−5.00114	−	5.00114i	−0.189841	−	0.189841i
$695$	−7.31054	+	27.2833i	−0.277305	+	1.03492i
$696$		0			0
$697$	−1.20367	−	0.322522i	−0.0455922	−	0.0122164i
$698$	−25.7467	+	14.8649i	−0.974527	+	0.562644i
$699$		0			0
$700$	−1.91356	+	11.5997i	−0.0723256	+	0.438426i
$701$		−	33.2095i		−	1.25430i	−0.778897	−	0.627152i	$-0.784220\pi$
$701$		−	33.2095i		−	1.25430i	0.778897	−	0.627152i	$-0.215780\pi$
$702$		0			0
$703$	−4.63774	+	2.67760i	−0.174916	+	0.100988i
$704$	30.6492	−	8.21243i	1.15514	−	0.309518i
$705$		0			0
$706$	−37.6168	+	65.1542i	−1.41573	+	2.45211i
$707$	11.1927	−	4.21429i	0.420943	−	0.158495i
$708$		0			0
$709$	−21.4384	−	5.74441i	−0.805138	−	0.215736i	−0.167299	−	0.985906i	$-0.553505\pi$
$709$	−21.4384	−	5.74441i	−0.805138	−	0.215736i	−0.637838	+	0.770170i	$0.720171\pi$
$710$	−5.81415	+	21.6987i	−0.218201	+	0.814338i
$711$		0			0
$712$	44.6075			1.67174
$713$	0.935257	−	3.49043i	0.0350256	−	0.130717i
$714$		0			0
$715$	33.3863	+	23.0045i	1.24858	+	0.860319i
$716$	−48.1299	+	83.3634i	−1.79870	+	3.11544i
$717$		0			0
$718$	22.0728	−	38.2313i	0.823751	−	1.42678i
$719$	14.2145	+	24.6202i	0.530111	+	0.918180i	0.999383	+	0.0351257i	$0.0111832\pi$
$719$	14.2145	+	24.6202i	0.530111	+	0.918180i	−0.469272	+	0.883054i	$0.655484\pi$
$720$		0			0
$721$	33.3271	−	12.5484i	1.24117	−	0.467327i
$722$	4.55687	+	17.0065i	0.169589	+	0.632915i
$723$		0			0
$724$			18.9866i			0.705632i
$725$	−5.32106	−	3.07212i	−0.197619	−	0.114096i
$726$		0			0
$727$	−0.462661			−0.0171591			−0.00857957	−	0.999963i	$-0.502731\pi$
$727$	−0.462661			−0.0171591			−0.00857957	+	0.999963i	$0.502731\pi$
$728$	−25.2728	−	41.9546i	−0.936674	−	1.55494i
$729$		0			0
$730$	10.8256	+	10.8256i	0.400675	+	0.400675i
$731$	−0.685955	−	0.396036i	−0.0253710	−	0.0146479i
$732$		0			0
$733$	−9.38272	−	35.0168i	−0.346559	−	1.29337i	−0.890781	−	0.454433i	$-0.849842\pi$
$733$	−9.38272	−	35.0168i	−0.346559	−	1.29337i	0.544222	−	0.838941i	$-0.316825\pi$
$734$	4.61573	+	17.2261i	0.170370	+	0.635828i
$735$		0			0
$736$	0.380514	−	0.380514i	0.0140259	−	0.0140259i
$737$	14.3386	+	24.8352i	0.528169	+	0.914816i
$738$		0			0
$739$	−0.379862	−	1.41767i	−0.0139735	−	0.0521497i	0.958587	−	0.284800i	$-0.0919270\pi$
$739$	−0.379862	−	1.41767i	−0.0139735	−	0.0521497i	−0.972561	+	0.232650i	$0.925260\pi$
$740$	−7.83091	+	13.5635i	−0.287870	+	0.498605i
$741$		0			0
$742$	−25.5698	+	18.3281i	−0.938695	+	0.672845i
$743$	−0.513502	+	1.91642i	−0.0188386	+	0.0703065i	−0.974705	−	0.223494i	$-0.928254\pi$
$743$	−0.513502	+	1.91642i	−0.0188386	+	0.0703065i	0.955867	+	0.293801i	$0.0949202\pi$
$744$		0			0
$745$	18.8212			0.689555
$746$	15.5854	−	58.1655i	0.570622	−	2.12959i
$747$		0			0
$748$	−2.02523	+	0.542658i	−0.0740496	+	0.0198415i
$749$	16.8950	+	13.8617i	0.617332	+	0.506496i
$750$		0			0
$751$		−	18.1843i		−	0.663555i	−0.943358	−	0.331778i	$-0.892352\pi$
$751$		−	18.1843i		−	0.663555i	0.943358	−	0.331778i	$-0.107648\pi$
$752$	−25.7447	+	6.89828i	−0.938814	+	0.251554i
$753$		0			0
$754$	49.3583	−	9.08713i	1.79752	−	0.330934i
$755$			16.2818i			0.592554i
$756$		0			0
$757$	2.77153	+	4.80044i	0.100733	+	0.174475i	0.911987	−	0.410219i	$-0.134548\pi$
$757$	2.77153	+	4.80044i	0.100733	+	0.174475i	−0.811254	+	0.584694i	$0.801215\pi$
$758$	18.7385	−	10.8187i	0.680612	−	0.392952i
$759$		0			0
$760$	−30.8522	−	30.8522i	−1.11913	−	1.11913i
$761$	−11.4195	+	42.6182i	−0.413957	+	1.54491i	0.372960	+	0.927848i	$0.378343\pi$
$761$	−11.4195	+	42.6182i	−0.413957	+	1.54491i	−0.786916	+	0.617060i	$0.788324\pi$
$762$		0			0
$763$	−28.9579	+	20.7567i	−1.04835	+	0.751442i
$764$	−27.2183	+	15.7145i	−0.984725	+	0.568531i
$765$		0			0
$766$	−21.6907	−	37.5693i	−0.783715	−	1.35743i
$767$	4.76808	−	13.4138i	0.172165	−	0.484343i
$768$		0			0
$769$	27.2136	+	7.29187i	0.981348	+	0.262951i	0.713612	−	0.700541i	$-0.247058\pi$
$769$	27.2136	+	7.29187i	0.981348	+	0.262951i	0.267736	+	0.963492i	$0.413725\pi$
$770$	42.7452	+	59.6345i	1.54043	+	2.14908i
$771$		0			0
$772$	−0.982674	+	0.263307i	−0.0353672	+	0.00947661i
$773$	−14.6663	+	14.6663i	−0.527511	+	0.527511i	−0.919829	−	0.392319i	$-0.871673\pi$
$773$	−14.6663	+	14.6663i	−0.527511	+	0.527511i	0.392319	+	0.919829i	$0.371673\pi$
$774$		0			0
$775$	−5.82323	+	1.56033i	−0.209177	+	0.0560487i
$776$	17.9402	+	10.3578i	0.644017	+	0.371823i
$777$		0			0
$778$	24.1435	+	6.46922i	0.865585	+	0.231933i
$779$	−32.9752	−	19.0383i	−1.18146	−	0.682116i
$780$		0			0
$781$	8.41168	+	14.5695i	0.300994	+	0.521336i
$782$	0.128246	−	0.128246i	0.00458608	−	0.00458608i
$783$		0			0
$784$	−6.15105	−	30.8813i	−0.219680	−	1.10290i
$785$	16.5332	+	16.5332i	0.590096	+	0.590096i
$786$		0			0
$787$	32.1068	+	32.1068i	1.14448	+	1.14448i	0.987620	+	0.156863i	$0.0501381\pi$
$787$	32.1068	+	32.1068i	1.14448	+	1.14448i	0.156863	+	0.987620i	$0.449862\pi$
$788$	26.3019	+	7.04758i	0.936967	+	0.251060i
$789$		0			0
$790$	−37.2001	−	64.4324i	−1.32352	−	2.29240i
$791$	5.66094	−	2.13147i	0.201280	−	0.0757864i
$792$		0			0
$793$	45.5433	+	31.3811i	1.61729	+	1.11438i
$794$	−18.0489	+	10.4205i	−0.640530	+	0.369810i
$795$		0			0
$796$		−	21.9949i		−	0.779587i
$797$	15.9452	−	27.6179i	0.564809	−	0.978277i	−0.432259	−	0.901750i	$-0.642283\pi$
$797$	15.9452	−	27.6179i	0.564809	−	0.978277i	0.997067	−	0.0765277i	$-0.0243834\pi$
$798$		0			0
$799$	−0.645069	+	0.172846i	−0.0228209	+	0.00611484i
$800$	−0.867191	−	0.232363i	−0.0306598	−	0.00821528i
$801$		0			0
$802$	23.1964			0.819094
$803$	11.4655			0.404607
$804$		0			0
$805$	−3.88027	−	1.75752i	−0.136762	−	0.0619444i
$806$	27.9403	−	40.5497i	0.984157	−	1.42830i
$807$		0			0
$808$	6.00697	+	22.4183i	0.211325	+	0.788674i
$809$	14.6403	−	25.3577i	0.514726	−	0.891531i	−0.485128	−	0.874443i	$-0.661227\pi$
$809$	14.6403	−	25.3577i	0.514726	−	0.891531i	0.999854	−	0.0170879i	$-0.00543952\pi$
$810$		0			0
$811$	35.8857	−	35.8857i	1.26012	−	1.26012i	0.309082	−	0.951035i	$-0.399978\pi$
$811$	35.8857	−	35.8857i	1.26012	−	1.26012i	0.951035	−	0.309082i	$-0.100022\pi$
$812$	60.1437	+	9.92170i	2.11063	+	0.348183i
$813$		0			0
$814$	4.52311	+	16.8805i	0.158535	+	0.591660i
$815$		−	45.5949i		−	1.59712i
$816$		0			0
$817$	−17.1137	−	17.1137i	−0.598732	−	0.598732i
$818$	−62.6615			−2.19091
$819$		0			0
$820$	−111.359			−3.88881
$821$	6.93408	+	6.93408i	0.242001	+	0.242001i	0.817678	−	0.575677i	$-0.195261\pi$
$821$	6.93408	+	6.93408i	0.242001	+	0.242001i	−0.575677	+	0.817678i	$0.695261\pi$
$822$		0			0
$823$		−	27.5693i		−	0.961006i	−0.876993	−	0.480503i	$-0.840454\pi$
$823$		−	27.5693i		−	0.961006i	0.876993	−	0.480503i	$-0.159546\pi$
$824$	17.8863	+	66.7525i	0.623098	+	2.32543i
$825$		0			0
$826$	16.3409	−	19.9167i	0.568572	−	0.692991i
$827$	−18.9789	+	18.9789i	−0.659961	+	0.659961i	−0.955371	−	0.295410i	$-0.904544\pi$
$827$	−18.9789	+	18.9789i	−0.659961	+	0.659961i	0.295410	+	0.955371i	$0.404544\pi$
$828$		0			0
$829$	14.8153	−	25.6608i	0.514556	−	0.891238i	−0.485301	−	0.874347i	$-0.661290\pi$
$829$	14.8153	−	25.6608i	0.514556	−	0.891238i	0.999857	−	0.0168908i	$-0.00537675\pi$
$830$	−7.44172	−	27.7729i	−0.258306	−	0.964011i
$831$		0			0
$832$	−22.6715	+	10.7806i	−0.785993	+	0.373749i
$833$	−0.154123	−	0.773771i	−0.00534004	−	0.0268096i
$834$		0			0
$835$	40.4999			1.40156
$836$	−64.0654			−2.21575
$837$		0			0
$838$	−47.8819	−	12.8299i	−1.65405	−	0.443202i
$839$	51.8608	−	13.8961i	1.79043	−	0.479745i	0.798014	−	0.602638i	$-0.205884\pi$
$839$	51.8608	−	13.8961i	1.79043	−	0.479745i	0.992420	+	0.122893i	$0.0392172\pi$
$840$		0			0
$841$	−1.42879	+	2.47474i	−0.0492686	+	0.0853357i
$842$			8.78721i			0.302827i
$843$		0			0
$844$	10.2491	−	5.91733i	0.352789	−	0.203683i
$845$	−29.2731	−	13.1170i	−1.00703	−	0.451239i
$846$		0			0
$847$	25.5001	+	4.20667i	0.876195	+	0.144543i
$848$	−10.8444	−	18.7830i	−0.372397	−	0.645011i
$849$		0			0
$850$	−0.292273	−	0.0783144i	−0.0100249	−	0.00268616i
$851$	−0.717431	−	0.717431i	−0.0245932	−	0.0245932i
$852$		0			0
$853$	−36.2761	−	36.2761i	−1.24207	−	1.24207i	−0.959140	−	0.282930i	$-0.908693\pi$
$853$	−36.2761	−	36.2761i	−1.24207	−	1.24207i	−0.282930	−	0.959140i	$-0.591307\pi$
$854$	58.3100	+	81.3491i	1.99533	+	2.78371i
$855$		0			0
$856$	−29.9881	+	29.9881i	−1.02497	+	1.02497i
$857$	23.1941	+	40.1733i	0.792295	+	1.37230i	0.924543	+	0.381079i	$0.124447\pi$
$857$	23.1941	+	40.1733i	0.792295	+	1.37230i	−0.132247	+	0.991217i	$0.542219\pi$
$858$		0			0
$859$	−6.53039	−	3.77032i	−0.222814	−	0.128642i	0.384439	−	0.923151i	$-0.374395\pi$
$859$	−6.53039	−	3.77032i	−0.222814	−	0.128642i	−0.607253	+	0.794509i	$0.707728\pi$
$860$	−68.3705	−	18.3198i	−2.33142	−	0.624701i
$861$		0			0
$862$	51.1997	+	29.5601i	1.74387	+	1.00682i
$863$	−18.4118	+	4.93343i	−0.626745	+	0.167936i	−0.558192	−	0.829712i	$-0.688505\pi$
$863$	−18.4118	+	4.93343i	−0.626745	+	0.167936i	−0.0685528	+	0.997647i	$0.521838\pi$
$864$		0			0
$865$	31.8205	−	31.8205i	1.08193	−	1.08193i
$866$	55.8087	−	14.9539i	1.89646	−	0.508154i
$867$		0			0
$868$	48.6117	−	34.8443i	1.64999	−	1.18269i
$869$	−53.8196	−	14.4209i	−1.82570	−	0.489196i
$870$		0			0
$871$	−14.7144	−	17.2701i	−0.498580	−	0.585174i
$872$	−34.5705	−	59.8779i	−1.17071	−	2.02772i
$873$		0			0
$874$	4.79937	−	2.77092i	0.162341	−	0.0937277i
$875$	−2.50622	−	25.4120i	−0.0847256	−	0.859083i
$876$		0			0
$877$	−4.25400	+	15.8761i	−0.143647	+	0.536099i	0.856165	+	0.516703i	$0.172841\pi$
$877$	−4.25400	+	15.8761i	−0.143647	+	0.536099i	−0.999812	+	0.0193959i	$0.993826\pi$
$878$	58.8792	+	58.8792i	1.98708	+	1.98708i
$879$		0			0
$880$	−43.8062	+	25.2915i	−1.47671	+	0.852578i
$881$	−6.33542	−	10.9733i	−0.213446	−	0.369699i	0.739345	−	0.673327i	$-0.235135\pi$
$881$	−6.33542	−	10.9733i	−0.213446	−	0.369699i	−0.952791	+	0.303628i	$0.901802\pi$
$882$		0			0
$883$		−	48.6526i		−	1.63729i	−0.574300	−	0.818645i	$-0.694726\pi$
$883$		−	48.6526i		−	1.63729i	0.574300	−	0.818645i	$-0.305274\pi$
$884$	1.49808	−	0.712355i	0.0503859	−	0.0239591i
$885$		0			0
$886$	−73.9095	+	19.8040i	−2.48304	+	0.665328i
$887$		−	11.4213i		−	0.383489i	−0.981445	−	0.191744i	$-0.938586\pi$
$887$		−	11.4213i		−	0.383489i	0.981445	−	0.191744i	$-0.0614144\pi$
$888$		0			0
$889$	13.2285	+	2.18226i	0.443670	+	0.0731906i
$890$	51.0675	−	13.6835i	1.71179	−	0.458672i
$891$		0			0
$892$	19.7995	−	73.8928i	0.662937	−	2.47411i
$893$	−20.4059			−0.682858
$894$		0			0
$895$	−15.0603	+	56.2059i	−0.503411	+	1.87875i
$896$	−49.5537	+	4.88715i	−1.65547	+	0.163268i
$897$		0			0
$898$	1.84947	−	3.20337i	0.0617176	−	0.106898i
$899$	8.09024	+	30.1932i	0.269824	+	1.00700i
$900$		0			0
$901$	−0.271720	−	0.470633i	−0.00905232	−	0.0156791i
$902$	−87.8633	+	87.8633i	−2.92553	+	2.92553i
$903$		0			0
$904$	3.03816	+	11.3386i	0.101048	+	0.377115i
$905$	2.97055	+	11.0862i	0.0987443	+	0.368519i
$906$		0			0
$907$	23.0490	+	13.3073i	0.765328	+	0.441862i	0.831205	−	0.555965i	$-0.187651\pi$
$907$	23.0490	+	13.3073i	0.765328	+	0.441862i	−0.0658773	+	0.997828i	$0.520985\pi$
$908$	−18.4247	−	18.4247i	−0.611447	−	0.611447i
$909$		0			0
$910$	−41.8025	−	40.2779i	−1.38574	−	1.33520i
$911$	57.5752			1.90755			0.953775	−	0.300520i	$-0.0971603\pi$
$911$	57.5752			1.90755			0.953775	+	0.300520i	$0.0971603\pi$
$912$		0			0
$913$	−18.6479	−	10.7664i	−0.617157	−	0.356316i
$914$		−	75.6690i		−	2.50291i
$915$		0			0
$916$	18.2841	+	68.2372i	0.604124	+	2.25462i
$917$	−5.29874	−	14.0728i	−0.174980	−	0.464726i
$918$		0			0
$919$	−18.1716	−	31.4741i	−0.599424	−	1.03823i	−0.992906	−	0.118901i	$-0.962063\pi$
$919$	−18.1716	−	31.4741i	−0.599424	−	1.03823i	0.393482	−	0.919332i	$-0.371270\pi$
$920$	4.13324	−	7.15898i	0.136269	−	0.236024i
$921$		0			0
$922$	−31.9047	+	55.2606i	−1.05073	+	1.81991i
$923$	−8.63217	−	10.1314i	−0.284131	−	0.333480i
$924$		0			0
$925$	−0.438103	+	1.63502i	−0.0144047	+	0.0537592i
$926$	92.5561			3.04158
$927$		0			0
$928$	−1.20479	+	4.49635i	−0.0395492	+	0.147600i
$929$	−49.1711	−	13.1754i	−1.61325	−	0.432269i	−0.664242	−	0.747518i	$-0.731246\pi$
$929$	−49.1711	−	13.1754i	−1.61325	−	0.432269i	−0.949009	+	0.315248i	$0.897912\pi$
$930$		0			0
$931$	1.57043	−	24.0564i	0.0514688	−	0.788418i
$932$	2.56190	−	4.43734i	0.0839177	−	0.145350i
$933$		0			0
$934$	19.5867	−	5.24825i	0.640898	−	0.171728i
$935$	−1.09762	+	0.633713i	−0.0358961	+	0.0207246i
$936$		0			0
$937$		−	55.7488i		−	1.82123i	−0.413251	−	0.910617i	$-0.635607\pi$
$937$		−	55.7488i		−	1.82123i	0.413251	−	0.910617i	$-0.364393\pi$
$938$	−14.4679	−	38.4252i	−0.472395	−	1.25463i
$939$		0			0
$940$	−51.6836	+	29.8396i	−1.68573	+	0.973259i
$941$	−7.44082	−	1.99376i	−0.242564	−	0.0649948i	0.135489	−	0.990779i	$-0.456740\pi$
$941$	−7.44082	−	1.99376i	−0.242564	−	0.0649948i	−0.378053	+	0.925784i	$0.623406\pi$
$942$		0			0
$943$	1.86712	−	6.96819i	0.0608018	−	0.226916i
$944$	12.5588	+	12.5588i	0.408753	+	0.408753i
$945$		0			0
$946$	−68.3998	+	39.4906i	−2.22387	+	1.28395i
$947$	27.7853	−	27.7853i	0.902900	−	0.902900i	−0.0927863	−	0.995686i	$-0.529577\pi$
$947$	27.7853	−	27.7853i	0.902900	−	0.902900i	0.995686	+	0.0927863i	$0.0295773\pi$
$948$		0			0
$949$	−8.92120	+	1.64244i	−0.289594	+	0.0533159i
$950$	−8.00700	−	4.62284i	−0.259781	−	0.149985i
$951$		0			0
$952$	1.52369	−	0.150271i	0.0493830	−	0.00487032i
$953$	34.9303	+	20.1670i	1.13150	+	0.653275i	0.944313	−	0.329049i	$-0.106728\pi$
$953$	34.9303	+	20.1670i	1.13150	+	0.653275i	0.187192	+	0.982323i	$0.440061\pi$
$954$		0			0
$955$	−13.4341	+	13.4341i	−0.434717	+	0.434717i
$956$	−35.0812	+	35.0812i	−1.13461	+	1.13461i
$957$		0			0
$958$	46.4269	+	26.8046i	1.49999	+	0.866017i
$959$	−22.4980	+	2.21883i	−0.726499	+	0.0716497i
$960$		0			0
$961$	−0.285588	−	0.164884i	−0.00921252	−	0.00531885i
$962$	−5.93755	−	12.4867i	−0.191434	−	0.402586i
$963$		0			0
$964$	7.01355	−	7.01355i	0.225891	−	0.225891i
$965$	−0.532585	+	0.307488i	−0.0171445	+	0.00989840i
$966$		0			0
$967$	−1.13971	−	1.13971i	−0.0366507	−	0.0366507i	0.688544	−	0.725195i	$-0.258250\pi$
$967$	−1.13971	−	1.13971i	−0.0366507	−	0.0366507i	−0.725195	+	0.688544i	$0.758250\pi$
$968$	−12.9809	+	48.4455i	−0.417223	+	1.55710i
$969$		0			0
$970$	23.7156	+	6.35457i	0.761462	+	0.204033i
$971$	22.6332	−	13.0673i	0.726333	−	0.419348i	−0.0907462	−	0.995874i	$-0.528925\pi$
$971$	22.6332	−	13.0673i	0.726333	−	0.419348i	0.817079	+	0.576526i	$0.195592\pi$
$972$		0			0
$973$	−10.6720	−	28.3436i	−0.342129	−	0.908654i
$974$		−	44.5023i		−	1.42595i
$975$		0			0
$976$	−59.7574	+	34.5009i	−1.91279	+	1.10435i
$977$	−15.3729	+	4.11917i	−0.491824	+	0.131784i	−0.496203	−	0.868207i	$-0.665273\pi$
$977$	−15.3729	+	4.11917i	−0.491824	+	0.131784i	0.00437887	+	0.999990i	$0.498606\pi$
$978$		0			0
$979$	19.7967	−	34.2890i	0.632707	−	1.09588i
$980$	−31.2002	−	63.2261i	−0.996653	−	2.01968i
$981$		0			0
$982$	15.4957	+	4.15207i	0.494489	+	0.132498i
$983$	−2.03290	+	7.58689i	−0.0648395	+	0.241984i	−0.990738	−	0.135788i	$-0.956643\pi$
$983$	−2.03290	+	7.58689i	−0.0648395	+	0.241984i	0.925898	+	0.377773i	$0.123310\pi$
$984$		0			0
$985$	16.4603			0.524467
$986$	−0.406056	+	1.51542i	−0.0129315	+	0.0482609i
$987$		0			0
$988$	49.8489	−	9.17745i	1.58590	−	0.291974i
$989$	2.29270	−	3.97108i	0.0729038	−	0.126273i
$990$		0			0
$991$	−2.27497	+	3.94037i	−0.0722669	+	0.125170i	−0.899894	−	0.436108i	$-0.856357\pi$
$991$	−2.27497	+	3.94037i	−0.0722669	+	0.125170i	0.827628	+	0.561278i	$0.189690\pi$
$992$	2.28370	+	3.95548i	0.0725074	+	0.125586i
$993$		0			0
$994$	−8.48755	−	22.5420i	−0.269209	−	0.714988i
$995$	−3.44120	−	12.8428i	−0.109094	−	0.407143i
$996$		0			0
$997$			20.0987i			0.636534i	0.948001	+	0.318267i	$0.103101\pi$
$997$			20.0987i			0.636534i	−0.948001	+	0.318267i	$0.896899\pi$
$998$	−43.0108	−	24.8323i	−1.36148	−	0.786052i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.b.271.1		28
3.2	odd	2		91.2.ba.a.89.7	yes	28
7.3	odd	6		819.2.gh.b.388.7		28
13.6	odd	12		819.2.gh.b.19.7		28
21.2	odd	6		637.2.bd.b.440.7		28
21.5	even	6		637.2.bd.a.440.7		28
21.11	odd	6		637.2.x.a.570.1		28
21.17	even	6		91.2.w.a.24.1	yes	28
21.20	even	2		637.2.bb.a.362.7		28
39.32	even	12		91.2.w.a.19.1	✓	28
91.45	even	12	inner	819.2.et.b.136.1		28
273.32	even	12		637.2.bb.a.227.7		28
273.110	odd	12		637.2.bd.b.97.7		28
273.149	even	12		637.2.bd.a.97.7		28
273.188	odd	12		637.2.x.a.19.1		28
273.227	odd	12		91.2.ba.a.45.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.1	✓	28	39.32	even	12
91.2.w.a.24.1	yes	28	21.17	even	6
91.2.ba.a.45.7	yes	28	273.227	odd	12
91.2.ba.a.89.7	yes	28	3.2	odd	2
637.2.x.a.19.1		28	273.188	odd	12
637.2.x.a.570.1		28	21.11	odd	6
637.2.bb.a.227.7		28	273.32	even	12
637.2.bb.a.362.7		28	21.20	even	2
637.2.bd.a.97.7		28	273.149	even	12
637.2.bd.a.440.7		28	21.5	even	6
637.2.bd.b.97.7		28	273.110	odd	12
637.2.bd.b.440.7		28	21.2	odd	6
819.2.et.b.136.1		28	91.45	even	12	inner
819.2.et.b.271.1		28	1.1	even	1	trivial
819.2.gh.b.19.7		28	13.6	odd	12
819.2.gh.b.388.7		28	7.3	odd	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.74384 - 1.74384i) q^{2} +4.08193i q^{4} +(0.638637 + 2.38343i) q^{5} +(-2.04541 - 1.67818i) q^{7} +(3.63054 - 3.63054i) q^{8} +O(q^{10})\)	\(q+(-1.74384 - 1.74384i) q^{2} +4.08193i q^{4} +(0.638637 + 2.38343i) q^{5} +(-2.04541 - 1.67818i) q^{7} +(3.63054 - 3.63054i) q^{8} +(3.04263 - 5.26998i) q^{10} +(-1.17950 - 4.40195i) q^{11} +(1.54835 + 3.25617i) q^{13} +(0.640394 + 6.49333i) q^{14} -4.49827 q^{16} -0.112710 q^{17} +(-3.32660 - 0.891360i) q^{19} +(-9.72897 + 2.60687i) q^{20} +(-5.61943 + 9.73314i) q^{22} -0.652493i q^{23} +(-0.942740 + 0.544291i) q^{25} +(2.97816 - 8.37828i) q^{26} +(6.85021 - 8.34922i) q^{28} +(2.82213 + 4.88807i) q^{29} +(5.34937 + 1.43336i) q^{31} +(0.583169 + 0.583169i) q^{32} +(0.196548 + 0.196548i) q^{34} +(2.69354 - 5.94684i) q^{35} +(1.09952 - 1.09952i) q^{37} +(4.24666 + 7.35543i) q^{38} +(10.9717 + 6.33453i) q^{40} +(10.6793 + 2.86152i) q^{41} +(6.08601 + 3.51376i) q^{43} +(17.9684 - 4.81463i) q^{44} +(-1.13784 + 1.13784i) q^{46} +(5.72325 - 1.53354i) q^{47} +(1.36743 + 6.86514i) q^{49} +(2.59314 + 0.694830i) q^{50} +(-13.2914 + 6.32024i) q^{52} +(2.41079 + 4.17561i) q^{53} +(9.73846 - 5.62250i) q^{55} +(-13.5186 + 1.33325i) q^{56} +(3.60266 - 13.4453i) q^{58} +(-2.79191 - 2.79191i) q^{59} +(13.2845 - 7.66982i) q^{61} +(-6.82887 - 11.8280i) q^{62} +6.96264i q^{64} +(-6.77201 + 5.76988i) q^{65} +(-6.07826 + 1.62866i) q^{67} -0.460075i q^{68} +(-15.0674 + 5.67322i) q^{70} +(-3.56578 + 0.955449i) q^{71} +(-0.651157 + 2.43015i) q^{73} -3.83477 q^{74} +(3.63847 - 13.5789i) q^{76} +(-4.97470 + 10.9832i) q^{77} +(6.11315 - 10.5883i) q^{79} +(-2.87276 - 10.7213i) q^{80} +(-13.6330 - 23.6130i) q^{82} +(3.34105 - 3.34105i) q^{83} +(-0.0719809 - 0.268637i) q^{85} +(-4.48558 - 16.7404i) q^{86} +(-20.2637 - 11.6992i) q^{88} +(6.14338 + 6.14338i) q^{89} +(2.29743 - 9.25861i) q^{91} +2.66343 q^{92} +(-12.6547 - 7.30617i) q^{94} -8.49797i q^{95} +(1.04426 + 3.89722i) q^{97} +(9.58711 - 14.3562i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

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