LMFDB - Embedded newform 819.2.fm.f.748.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			748.1
Character	$\chi$	$=$	819.748
Dual form			819.2.fm.f.496.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.37607 + 0.636667i) q^{2} +(3.50833 - 2.02554i) q^{4} +(-0.498430 + 0.498430i) q^{5} +(-2.12397 - 1.57758i) q^{7} +(-3.56765 + 3.56765i) q^{8} +O(q^{10})$	\(q+(-2.37607 + 0.636667i) q^{2} +(3.50833 - 2.02554i) q^{4} +(-0.498430 + 0.498430i) q^{5} +(-2.12397 - 1.57758i) q^{7} +(-3.56765 + 3.56765i) q^{8} +(0.866973 - 1.50164i) q^{10} +(-0.184478 - 0.688480i) q^{11} +(3.17894 + 1.70127i) q^{13} +(6.05110 + 2.39618i) q^{14} +(2.15452 - 3.73174i) q^{16} +(-2.27300 - 3.93695i) q^{17} +(-3.25000 - 0.870835i) q^{19} +(-0.739070 + 2.75825i) q^{20} +(0.876665 + 1.51843i) q^{22} +(1.67026 + 0.964326i) q^{23} +4.50313i q^{25} +(-8.63655 - 2.01842i) q^{26} +(-10.6470 - 1.23248i) q^{28} +(-0.185925 + 0.322032i) q^{29} +(-3.53994 + 3.53994i) q^{31} +(-0.131724 + 0.491600i) q^{32} +(7.90735 + 7.90735i) q^{34} +(1.84496 - 0.272339i) q^{35} +(-0.545727 - 2.03668i) q^{37} +8.27667 q^{38} -3.55645i q^{40} +(3.11983 + 11.6434i) q^{41} +(6.38504 - 3.68640i) q^{43} +(-2.04175 - 2.04175i) q^{44} +(-4.58262 - 1.22791i) q^{46} +(-3.55898 - 3.55898i) q^{47} +(2.02250 + 6.70145i) q^{49} +(-2.86700 - 10.6998i) q^{50} +(14.5988 - 0.470438i) q^{52} +4.97712 q^{53} +(0.435109 + 0.251210i) q^{55} +(13.2058 - 1.94934i) q^{56} +(0.236745 - 0.883543i) q^{58} +(-1.03416 + 3.85953i) q^{59} +(-10.0720 + 5.81509i) q^{61} +(6.15739 - 10.6649i) q^{62} +7.36614i q^{64} +(-2.43245 + 0.736516i) q^{65} +(-12.5870 + 3.37267i) q^{67} +(-15.9489 - 9.20809i) q^{68} +(-4.21038 + 1.82173i) q^{70} +(-2.10681 + 7.86274i) q^{71} +(-0.608899 - 0.608899i) q^{73} +(2.59337 + 4.49186i) q^{74} +(-13.1660 + 3.52781i) q^{76} +(-0.694305 + 1.75334i) q^{77} +9.81537 q^{79} +(0.786133 + 2.93389i) q^{80} +(-14.8259 - 25.6792i) q^{82} +(-2.25452 + 2.25452i) q^{83} +(3.09523 + 0.829364i) q^{85} +(-12.8243 + 12.8243i) q^{86} +(3.11441 + 1.79810i) q^{88} +(-17.5524 + 4.70315i) q^{89} +(-4.06809 - 8.62848i) q^{91} +7.81311 q^{92} +(10.7223 + 6.19052i) q^{94} +(2.05395 - 1.18585i) q^{95} +(-8.73810 - 2.34137i) q^{97} +(-9.07221 - 14.6355i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$

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 $

$2$	−2.37607	+	0.636667i	−1.68014	+	0.450192i	−0.967816	−	0.251661i	$-0.919023\pi$
$2$	−2.37607	+	0.636667i	−1.68014	+	0.450192i	−0.712322	+	0.701852i	$0.752357\pi$
$3$		0			0
$3$		0			0
$4$	3.50833	−	2.02554i	1.75417	−	1.01277i
$5$	−0.498430	+	0.498430i	−0.222905	+	0.222905i	−0.809721	−	0.586816i	$-0.800381\pi$
$5$	−0.498430	+	0.498430i	−0.222905	+	0.222905i	0.586816	+	0.809721i	$0.300381\pi$
$6$		0			0
$7$	−2.12397	−	1.57758i	−0.802785	−	0.596268i
$7$	−2.12397	−	1.57758i	−0.802785	−	0.596268i
$8$	−3.56765	+	3.56765i	−1.26135	+	1.26135i
$9$		0			0
$10$	0.866973	−	1.50164i	0.274161	−	0.474861i
$11$	−0.184478	−	0.688480i	−0.0556221	−	0.207585i	0.932522	−	0.361113i	$-0.117603\pi$
$11$	−0.184478	−	0.688480i	−0.0556221	−	0.207585i	−0.988144	+	0.153528i	$0.950936\pi$
$12$		0			0
$13$	3.17894	+	1.70127i	0.881680	+	0.471848i
$13$	3.17894	+	1.70127i	0.881680	+	0.471848i
$14$	6.05110	+	2.39618i	1.61723	+	0.640405i
$15$		0			0
$16$	2.15452	−	3.73174i	0.538630	−	0.932934i
$17$	−2.27300	−	3.93695i	−0.551284	−	0.954852i	−0.998182	−	0.0602669i	$-0.980805\pi$
$17$	−2.27300	−	3.93695i	−0.551284	−	0.954852i	0.446898	−	0.894585i	$-0.352529\pi$
$18$		0			0
$19$	−3.25000	−	0.870835i	−0.745601	−	0.199783i	−0.134035	−	0.990977i	$-0.542793\pi$
$19$	−3.25000	−	0.870835i	−0.745601	−	0.199783i	−0.611566	+	0.791193i	$0.709460\pi$
$20$	−0.739070	+	2.75825i	−0.165261	+	0.616763i
$21$		0			0
$22$	0.876665	+	1.51843i	0.186906	+	0.323730i
$23$	1.67026	+	0.964326i	0.348274	+	0.201076i	0.663925	−	0.747799i	$-0.268890\pi$
$23$	1.67026	+	0.964326i	0.348274	+	0.201076i	−0.315651	+	0.948875i	$0.602223\pi$
$24$		0			0
$25$			4.50313i			0.900627i
$26$	−8.63655	−	2.01842i	−1.69377	−	0.395845i
$27$		0			0
$28$	−10.6470	−	1.23248i	−2.01210	−	0.232917i
$29$	−0.185925	+	0.322032i	−0.0345254	+	0.0597998i	−0.882772	−	0.469802i	$-0.844325\pi$
$29$	−0.185925	+	0.322032i	−0.0345254	+	0.0597998i	0.848246	+	0.529602i	$0.177659\pi$
$30$		0			0
$31$	−3.53994	+	3.53994i	−0.635792	+	0.635792i	−0.949515	−	0.313723i	$-0.898424\pi$
$31$	−3.53994	+	3.53994i	−0.635792	+	0.635792i	0.313723	+	0.949515i	$0.398424\pi$
$32$	−0.131724	+	0.491600i	−0.0232857	+	0.0869034i
$33$		0			0
$34$	7.90735	+	7.90735i	1.35610	+	1.35610i
$35$	1.84496	−	0.272339i	0.311856	−	0.0460337i
$36$		0			0
$37$	−0.545727	−	2.03668i	−0.0897169	−	0.334828i	0.906449	−	0.422316i	$-0.138783\pi$
$37$	−0.545727	−	2.03668i	−0.0897169	−	0.334828i	−0.996166	+	0.0874879i	$0.972116\pi$
$38$	8.27667			1.34265
$39$		0			0
$40$		−	3.55645i		−	0.562324i
$41$	3.11983	+	11.6434i	0.487236	+	1.81839i	0.569776	+	0.821800i	$0.307030\pi$
$41$	3.11983	+	11.6434i	0.487236	+	1.81839i	−0.0825406	+	0.996588i	$0.526303\pi$
$42$		0			0
$43$	6.38504	−	3.68640i	0.973709	−	0.562171i	0.0733440	−	0.997307i	$-0.476633\pi$
$43$	6.38504	−	3.68640i	0.973709	−	0.562171i	0.900365	+	0.435136i	$0.143300\pi$
$44$	−2.04175	−	2.04175i	−0.307805	−	0.307805i
$45$		0			0
$46$	−4.58262	−	1.22791i	−0.675671	−	0.181045i
$47$	−3.55898	−	3.55898i	−0.519131	−	0.519131i	0.398177	−	0.917308i	$-0.369643\pi$
$47$	−3.55898	−	3.55898i	−0.519131	−	0.519131i	−0.917308	+	0.398177i	$0.869643\pi$
$48$		0			0
$49$	2.02250	+	6.70145i	0.288929	+	0.957351i
$50$	−2.86700	−	10.6998i	−0.405455	−	1.51318i
$51$		0			0
$52$	14.5988	−	0.470438i	2.02449	−	0.0652380i
$53$	4.97712			0.683660			0.341830	−	0.939762i	$-0.388953\pi$
$53$	4.97712			0.683660			0.341830	+	0.939762i	$0.388953\pi$
$54$		0			0
$55$	0.435109	+	0.251210i	0.0586700	+	0.0338732i
$56$	13.2058	−	1.94934i	1.76470	−	0.260492i
$57$		0			0
$58$	0.236745	−	0.883543i	0.0310861	−	0.116015i
$59$	−1.03416	+	3.85953i	−0.134636	+	0.502467i	0.865363	+	0.501145i	$0.167088\pi$
$59$	−1.03416	+	3.85953i	−0.134636	+	0.502467i	−0.999999	+	0.00132252i	$0.999579\pi$
$60$		0			0
$61$	−10.0720	+	5.81509i	−1.28959	+	0.744546i	−0.978581	−	0.205860i	$-0.934001\pi$
$61$	−10.0720	+	5.81509i	−1.28959	+	0.744546i	−0.311011	+	0.950406i	$0.600667\pi$
$62$	6.15739	−	10.6649i	0.781990	−	1.35445i
$63$		0			0
$64$			7.36614i			0.920767i
$65$	−2.43245	+	0.736516i	−0.301708	+	0.0913536i
$66$		0			0
$67$	−12.5870	+	3.37267i	−1.53774	+	0.412037i	−0.925536	−	0.378660i	$-0.876385\pi$
$67$	−12.5870	+	3.37267i	−1.53774	+	0.412037i	−0.612207	+	0.790697i	$0.709718\pi$
$68$	−15.9489	−	9.20809i	−1.93409	−	1.11665i
$69$		0			0
$70$	−4.21038	+	1.82173i	−0.503237	+	0.217738i
$71$	−2.10681	+	7.86274i	−0.250033	+	0.933135i	0.720754	+	0.693191i	$0.243796\pi$
$71$	−2.10681	+	7.86274i	−0.250033	+	0.933135i	−0.970787	+	0.239944i	$0.922871\pi$
$72$		0			0
$73$	−0.608899	−	0.608899i	−0.0712663	−	0.0712663i	0.670575	−	0.741842i	$-0.266047\pi$
$73$	−0.608899	−	0.608899i	−0.0712663	−	0.0712663i	−0.741842	+	0.670575i	$0.766047\pi$
$74$	2.59337	+	4.49186i	0.301474	+	0.522168i
$75$		0			0
$76$	−13.1660	+	3.52781i	−1.51024	+	0.404668i
$77$	−0.694305	+	1.75334i	−0.0791234	+	0.199812i
$78$		0			0
$79$	9.81537			1.10432			0.552158	−	0.833740i	$-0.313805\pi$
$79$	9.81537			1.10432			0.552158	+	0.833740i	$0.313805\pi$
$80$	0.786133	+	2.93389i	0.0878924	+	0.328019i
$81$		0			0
$82$	−14.8259	−	25.6792i	−1.63725	−	2.83579i
$83$	−2.25452	+	2.25452i	−0.247465	+	0.247465i	−0.819930	−	0.572464i	$-0.805988\pi$
$83$	−2.25452	+	2.25452i	−0.247465	+	0.247465i	0.572464	+	0.819930i	$0.305988\pi$
$84$		0			0
$85$	3.09523	+	0.829364i	0.335725	+	0.0899572i
$86$	−12.8243	+	12.8243i	−1.38288	+	1.38288i
$87$		0			0
$88$	3.11441	+	1.79810i	0.331997	+	0.191678i
$89$	−17.5524	+	4.70315i	−1.86055	+	0.498533i	−0.999942	−	0.0107329i	$-0.996584\pi$
$89$	−17.5524	+	4.70315i	−1.86055	+	0.498533i	−0.860609	+	0.509266i	$0.829917\pi$
$90$		0			0
$91$	−4.06809	−	8.62848i	−0.426452	−	0.904510i
$92$	7.81311			0.814573
$93$		0			0
$94$	10.7223	+	6.19052i	1.10592	+	0.638503i
$95$	2.05395	−	1.18585i	0.210731	−	0.121665i
$96$		0			0
$97$	−8.73810	−	2.34137i	−0.887220	−	0.237730i	−0.213700	−	0.976899i	$-0.568552\pi$
$97$	−8.73810	−	2.34137i	−0.887220	−	0.237730i	−0.673520	+	0.739169i	$0.735218\pi$
$98$	−9.07221	−	14.6355i	−0.916432	−	1.47841i
$99$		0			0
$100$	9.12126	+	15.7985i	0.912126	+	1.57985i
$101$	−6.77353	+	11.7321i	−0.673991	+	1.16739i	0.302772	+	0.953063i	$0.402088\pi$
$101$	−6.77353	+	11.7321i	−0.673991	+	1.16739i	−0.976763	+	0.214324i	$0.931245\pi$
$102$		0			0
$103$	−16.4565			−1.62151			−0.810756	−	0.585385i	$-0.800944\pi$
$103$	−16.4565			−1.62151			−0.810756	+	0.585385i	$0.800944\pi$
$104$	−17.4109	+	5.27181i	−1.70728	+	0.516943i
$105$		0			0
$106$	−11.8260	+	3.16877i	−1.14864	+	0.307778i
$107$	−8.35835	+	14.4771i	−0.808033	+	1.39955i	0.106192	+	0.994346i	$0.466134\pi$
$107$	−8.35835	+	14.4771i	−0.808033	+	1.39955i	−0.914225	+	0.405208i	$0.867199\pi$
$108$		0			0
$109$	1.77768	+	1.77768i	0.170271	+	0.170271i	0.787099	−	0.616827i	$-0.211582\pi$
$109$	1.77768	+	1.77768i	0.170271	+	0.170271i	−0.616827	+	0.787099i	$0.711582\pi$
$110$	−1.19379	−	0.319874i	−0.113823	−	0.0304988i
$111$		0			0
$112$	−10.4632	+	4.52718i	−0.988683	+	0.427778i
$113$	2.96252	+	5.13124i	0.278691	+	0.482706i	0.971060	−	0.238837i	$-0.0767662\pi$
$113$	2.96252	+	5.13124i	0.278691	+	0.482706i	−0.692369	+	0.721544i	$0.743433\pi$
$114$		0			0
$115$	−1.31316	+	0.351860i	−0.122453	+	0.0328111i
$116$			1.50639i			0.139865i
$117$		0			0
$118$		−	9.82893i		−	0.904826i
$119$	−1.38306	+	11.9478i	−0.126785	+	1.09525i
$120$		0			0
$121$	9.08631	−	5.24598i	0.826028	−	0.476907i
$122$	20.2296	−	20.2296i	1.83150	−	1.83150i
$123$		0			0
$124$	−5.24901	+	19.5896i	−0.471375	+	1.75919i
$125$	−4.73665	−	4.73665i	−0.423659	−	0.423659i
$126$		0			0
$127$	−17.4169	−	10.0556i	−1.54550	−	0.892293i	−0.998477	−	0.0551724i	$-0.982429\pi$
$127$	−17.4169	−	10.0556i	−1.54550	−	0.892293i	−0.547019	−	0.837120i	$-0.684238\pi$
$128$	−4.95322	−	18.4857i	−0.437807	−	1.63392i
$129$		0			0
$130$	5.31076	−	3.29868i	0.465784	−	0.289313i
$131$		−	12.0796i		−	1.05540i	−0.849430	−	0.527702i	$-0.823054\pi$
$131$		−	12.0796i		−	1.05540i	0.849430	−	0.527702i	$-0.176946\pi$
$132$		0			0
$133$	5.52909	+	6.97675i	0.479433	+	0.604961i
$134$	27.7603	−	16.0274i	2.39813	−	1.38456i
$135$		0			0
$136$	22.1549	+	5.93640i	1.89977	+	0.509042i
$137$	13.9883	+	3.74816i	1.19510	+	0.320227i	0.800901	−	0.598797i	$-0.204354\pi$
$137$	13.9883	+	3.74816i	1.19510	+	0.320227i	0.394202	+	0.919024i	$0.371021\pi$
$138$		0			0
$139$	6.95647	−	4.01632i	0.590040	−	0.340660i	−0.175073	−	0.984555i	$-0.556016\pi$
$139$	6.95647	−	4.01632i	0.590040	−	0.340660i	0.765113	+	0.643896i	$0.222683\pi$
$140$	5.92111	−	4.69250i	0.500425	−	0.396588i
$141$		0			0
$142$		−	20.0238i		−	1.68036i
$143$	0.584848	−	2.50248i	0.0489074	−	0.209268i
$144$		0			0
$145$	−0.0678396	−	0.253181i	−0.00563378	−	0.0210255i
$146$	1.83446	+	1.05912i	0.151821	+	0.0876537i
$147$		0			0
$148$	−6.03996	−	6.03996i	−0.496481	−	0.496481i
$149$	2.13325	−	7.96140i	0.174763	−	0.652223i	−0.821829	−	0.569734i	$-0.807046\pi$
$149$	2.13325	−	7.96140i	0.174763	−	0.652223i	0.996592	−	0.0824894i	$-0.0262870\pi$
$150$		0			0
$151$	−4.15300	+	4.15300i	−0.337966	+	0.337966i	−0.855601	−	0.517635i	$-0.826812\pi$
$151$	−4.15300	+	4.15300i	−0.337966	+	0.337966i	0.517635	+	0.855601i	$0.326812\pi$
$152$	14.7017	−	8.48802i	1.19246	−	0.688469i
$153$		0			0
$154$	0.533427	−	4.60810i	0.0429848	−	0.371332i
$155$		−	3.52883i		−	0.283442i
$156$		0			0
$157$			14.6163i			1.16651i	0.812291	+	0.583253i	$0.198220\pi$
$157$			14.6163i			1.16651i	−0.812291	+	0.583253i	$0.801780\pi$
$158$	−23.3220	+	6.24912i	−1.85540	+	0.497154i
$159$		0			0
$160$	−0.179373	−	0.310684i	−0.0141807	−	0.0245617i
$161$	−2.02629	−	4.68317i	−0.159694	−	0.369085i
$162$		0			0
$163$	7.35195	+	1.96995i	0.575849	+	0.154298i	0.534978	−	0.844866i	$-0.320320\pi$
$163$	7.35195	+	1.96995i	0.575849	+	0.154298i	0.0408715	+	0.999164i	$0.486987\pi$
$164$	34.5294	+	34.5294i	2.69630	+	2.69630i
$165$		0			0
$166$	3.92152	−	6.79228i	0.304369	−	0.527183i
$167$	7.60079	−	2.03663i	0.588167	−	0.157599i	0.0475517	−	0.998869i	$-0.484858\pi$
$167$	7.60079	−	2.03663i	0.588167	−	0.157599i	0.540615	+	0.841270i	$0.318191\pi$
$168$		0			0
$169$	7.21135	+	10.8165i	0.554719	+	0.832038i
$170$	−7.88252			−0.604562
$171$		0			0
$172$	14.9339	−	25.8662i	1.13870	−	1.97228i
$173$	5.36019	+	9.28412i	0.407528	+	0.705859i	0.994612	−	0.103667i	$-0.0330577\pi$
$173$	5.36019	+	9.28412i	0.407528	+	0.705859i	−0.587084	+	0.809526i	$0.699724\pi$
$174$		0			0
$175$	7.10404	−	9.56453i	0.537015	−	0.723010i
$176$	−2.96669	−	0.794922i	−0.223623	−	0.0599195i
$177$		0			0
$178$	38.7115	−	22.3501i	2.90155	−	1.67521i
$179$	−8.63169	−	4.98351i	−0.645163	−	0.372485i	0.141438	−	0.989947i	$-0.454828\pi$
$179$	−8.63169	−	4.98351i	−0.645163	−	0.372485i	−0.786601	+	0.617462i	$0.788161\pi$
$180$		0			0
$181$	3.96508			0.294722			0.147361	−	0.989083i	$-0.452922\pi$
$181$	3.96508			0.294722			0.147361	+	0.989083i	$0.452922\pi$
$182$	15.1596	+	17.9119i	1.12370	+	1.32772i
$183$		0			0
$184$	−9.39929	+	2.51853i	−0.692925	+	0.185669i
$185$	1.28715	+	0.743136i	0.0946331	+	0.0546365i
$186$		0			0
$187$	−2.29120	+	2.29120i	−0.167549	+	0.167549i
$188$	−19.6949	−	5.27724i	−1.43640	−	0.384882i
$189$		0			0
$190$	−4.12534	+	4.12534i	−0.299284	+	0.299284i
$191$	9.17881	+	15.8982i	0.664155	+	1.15035i	0.979514	+	0.201378i	$0.0645420\pi$
$191$	9.17881	+	15.8982i	0.664155	+	1.15035i	−0.315358	+	0.948973i	$0.602125\pi$
$192$		0			0
$193$	4.24786	+	15.8532i	0.305767	+	1.14114i	0.932283	+	0.361731i	$0.117814\pi$
$193$	4.24786	+	15.8532i	0.305767	+	1.14114i	−0.626515	+	0.779409i	$0.715519\pi$
$194$	22.2531			1.59768
$195$		0			0
$196$	20.6696	+	19.4143i	1.47640	+	1.38673i
$197$	−5.69553	+	1.52611i	−0.405790	+	0.108731i	−0.455940	−	0.890011i	$-0.650697\pi$
$197$	−5.69553	+	1.52611i	−0.405790	+	0.108731i	0.0501498	+	0.998742i	$0.484030\pi$
$198$		0			0
$199$	9.61483	+	16.6534i	0.681578	+	1.18053i	0.974499	+	0.224391i	$0.0720391\pi$
$199$	9.61483	+	16.6534i	0.681578	+	1.18053i	−0.292922	+	0.956136i	$0.594628\pi$
$200$	−16.0656	−	16.0656i	−1.13601	−	1.13601i
$201$		0			0
$202$	8.62496	−	32.1888i	0.606850	−	2.26480i
$203$	0.902929	−	0.390675i	0.0633732	−	0.0274200i
$204$		0			0
$205$	−7.35842	−	4.24839i	−0.513935	−	0.296720i
$206$	39.1020	−	10.4773i	2.72436	−	0.729991i
$207$		0			0
$208$	13.1978	−	8.19756i	0.915102	−	0.568398i
$209$			2.39821i			0.165888i
$210$		0			0
$211$	−4.61920	+	8.00070i	−0.317999	+	0.550791i	−0.980070	−	0.198650i	$-0.936344\pi$
$211$	−4.61920	+	8.00070i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$212$	17.4614	−	10.0813i	1.19925	−	0.692389i
$213$		0			0
$214$	10.6430	−	39.7201i	0.727539	−	2.71521i
$215$	−1.34508	+	5.01991i	−0.0917338	+	0.342355i
$216$		0			0
$217$	13.1033	−	1.93420i	0.889507	−	0.131302i
$218$	−5.35570	−	3.09212i	−0.362734	−	0.209425i
$219$		0			0
$220$	2.03534			0.137223
$221$	−0.527913	−	16.3823i	−0.0355112	−	1.10200i
$222$		0			0
$223$	−0.482353	−	1.80016i	−0.0323007	−	0.120548i	0.947893	−	0.318589i	$-0.103209\pi$
$223$	−0.482353	−	1.80016i	−0.0323007	−	0.120548i	−0.980194	+	0.198041i	$0.936542\pi$
$224$	1.05531	−	0.836340i	0.0705112	−	0.0558803i
$225$		0			0
$226$	−10.3061	−	10.3061i	−0.685549	−	0.685549i
$227$	5.38143	+	1.44195i	0.357178	+	0.0957056i	0.432946	−	0.901420i	$-0.357474\pi$
$227$	5.38143	+	1.44195i	0.357178	+	0.0957056i	−0.0757678	+	0.997125i	$0.524141\pi$
$228$		0			0
$229$	−0.153144	−	0.153144i	−0.0101200	−	0.0101200i	0.702029	−	0.712149i	$-0.252278\pi$
$229$	−0.153144	−	0.153144i	−0.0101200	−	0.0101200i	−0.712149	+	0.702029i	$0.752278\pi$
$230$	2.89615	−	1.67209i	0.190966	−	0.110254i
$231$		0			0
$232$	−0.485580	−	1.81221i	−0.0318799	−	0.118977i
$233$		−	19.7822i		−	1.29598i	−0.761650	−	0.647989i	$-0.775610\pi$
$233$		−	19.7822i		−	1.29598i	0.761650	−	0.647989i	$-0.224390\pi$
$234$		0			0
$235$	3.54781			0.231434
$236$	4.18944	+	15.6352i	0.272710	+	1.01777i
$237$		0			0
$238$	−4.32053	−	29.2694i	−0.280058	−	1.89726i
$239$	0.636908	+	0.636908i	0.0411982	+	0.0411982i	0.727406	−	0.686208i	$-0.240726\pi$
$239$	0.636908	+	0.636908i	0.0411982	+	0.0411982i	−0.686208	+	0.727406i	$0.740726\pi$
$240$		0			0
$241$	5.16499	−	19.2760i	0.332706	−	1.24168i	−0.573629	−	0.819116i	$-0.694465\pi$
$241$	5.16499	−	19.2760i	0.332706	−	1.24168i	0.906335	−	0.422561i	$-0.138869\pi$
$242$	−18.2498	+	18.2498i	−1.17314	+	1.17314i
$243$		0			0
$244$	−23.5574	+	40.8025i	−1.50811	+	2.61212i
$245$	−4.34828	−	2.33213i	−0.277802	−	0.148994i
$246$		0			0
$247$	−8.85003	−	8.29746i	−0.563114	−	0.527955i
$248$		−	25.2585i		−	1.60392i
$249$		0			0
$250$	14.2703	+	8.23896i	0.902533	+	0.521078i
$251$	−14.0053	−	24.2580i	−0.884010	−	1.53115i	−0.846845	−	0.531840i	$-0.821501\pi$
$251$	−14.0053	−	24.2580i	−0.884010	−	1.53115i	−0.0371651	−	0.999309i	$-0.511833\pi$
$252$		0			0
$253$	0.355793	−	1.32784i	0.0223685	−	0.0834805i
$254$	47.7858	+	12.8042i	2.99835	+	0.803405i
$255$		0			0
$256$	16.1723	+	28.0113i	1.01077	+	1.75070i
$257$	4.51978	−	7.82849i	0.281936	−	0.488328i	−0.689925	−	0.723880i	$-0.742357\pi$
$257$	4.51978	−	7.82849i	0.281936	−	0.488328i	0.971862	+	0.235553i	$0.0756900\pi$
$258$		0			0
$259$	−2.05391	+	5.18677i	−0.127624	+	0.322290i
$260$	−7.04199	+	7.51095i	−0.436726	+	0.465809i
$261$		0			0
$262$	7.69071	+	28.7021i	0.475134	+	1.77322i
$263$	11.6573	−	20.1910i	0.718819	−	1.24503i	−0.242649	−	0.970114i	$-0.578016\pi$
$263$	11.6573	−	20.1910i	0.718819	−	1.24503i	0.961468	−	0.274917i	$-0.0886503\pi$
$264$		0			0
$265$	−2.48075	+	2.48075i	−0.152391	+	0.152391i
$266$	−17.5794	−	13.0571i	−1.07786	−	0.800581i
$267$		0			0
$268$	−37.3278	+	37.3278i	−2.28016	+	2.28016i
$269$	−24.9574	+	14.4092i	−1.52168	+	0.878543i	−0.522010	+	0.852939i	$0.674818\pi$
$269$	−24.9574	+	14.4092i	−1.52168	+	0.878543i	−0.999672	+	0.0256040i	$0.991849\pi$
$270$		0			0
$271$	11.9008	−	3.18880i	0.722920	−	0.193706i	0.121446	−	0.992598i	$-0.461247\pi$
$271$	11.9008	−	3.18880i	0.722920	−	0.193706i	0.601474	+	0.798892i	$0.294580\pi$
$272$	−19.5889			−1.18775
$273$		0			0
$274$	−35.6236			−2.15210
$275$	3.10032	−	0.830728i	0.186956	−	0.0500948i
$276$		0			0
$277$	−12.3959	+	7.15677i	−0.744797	+	0.430009i	−0.823811	−	0.566865i	$-0.808156\pi$
$277$	−12.3959	+	7.15677i	−0.744797	+	0.430009i	0.0790140	+	0.996874i	$0.474823\pi$
$278$	−13.9720	+	13.9720i	−0.837987	+	0.837987i
$279$		0			0
$280$	−5.61057	+	7.55379i	−0.335296	+	0.451425i
$281$	10.7886	−	10.7886i	0.643591	−	0.643591i	−0.307845	−	0.951437i	$-0.599608\pi$
$281$	10.7886	−	10.7886i	0.643591	−	0.643591i	0.951437	+	0.307845i	$0.0996078\pi$
$282$		0			0
$283$	6.96923	−	12.0711i	0.414278	−	0.717550i	−0.581075	−	0.813850i	$-0.697368\pi$
$283$	6.96923	−	12.0711i	0.414278	−	0.717550i	0.995352	+	0.0963004i	$0.0307009\pi$
$284$	8.53485	+	31.8525i	0.506450	+	1.89010i
$285$		0			0
$286$	0.203609	+	6.31844i	0.0120396	+	0.373617i
$287$	11.7419	−	29.6519i	0.693101	−	1.75030i
$288$		0			0
$289$	−1.83307	+	3.17497i	−0.107828	+	0.186763i
$290$	0.322384	+	0.558385i	0.0189310	+	0.0327895i
$291$		0			0
$292$	−3.36957	−	0.902873i	−0.197189	−	0.0528367i
$293$	−4.49081	+	16.7599i	−0.262356	+	0.979126i	0.701493	+	0.712677i	$0.252517\pi$
$293$	−4.49081	+	16.7599i	−0.262356	+	0.979126i	−0.963849	+	0.266450i	$0.914149\pi$
$294$		0			0
$295$	−1.40825	−	2.43916i	−0.0819915	−	0.142013i
$296$	9.21312	+	5.31920i	0.535502	+	0.309172i
$297$		0			0
$298$			20.2750i			1.17450i
$299$	3.66909	+	5.90711i	0.212189	+	0.341617i
$300$		0			0
$301$	−19.3772	−	2.24308i	−1.11688	−	0.129289i
$302$	7.22375	−	12.5119i	0.415680	−	0.719980i
$303$		0			0
$304$	−10.2519	+	10.2519i	−0.587988	+	0.587988i
$305$	2.12179	−	7.91863i	0.121493	−	0.453419i
$306$		0			0
$307$	14.5281	+	14.5281i	0.829164	+	0.829164i	0.987401	−	0.158237i	$-0.0505810\pi$
$307$	14.5281	+	14.5281i	0.829164	+	0.829164i	−0.158237	+	0.987401i	$0.550581\pi$
$308$	1.11560	+	7.55763i	0.0635672	+	0.430636i
$309$		0			0
$310$	2.24669	+	8.38475i	0.127603	+	0.476222i
$311$	7.52888			0.426924			0.213462	−	0.976951i	$-0.431526\pi$
$311$	7.52888			0.426924			0.213462	+	0.976951i	$0.431526\pi$
$312$		0			0
$313$			7.90713i			0.446938i	0.974711	+	0.223469i	$0.0717381\pi$
$313$			7.90713i			0.446938i	−0.974711	+	0.223469i	$0.928262\pi$
$314$	−9.30570	−	34.7293i	−0.525151	−	1.95989i
$315$		0			0
$316$	34.4356	−	19.8814i	1.93715	−	1.11842i
$317$	−12.2598	−	12.2598i	−0.688580	−	0.688580i	0.273338	−	0.961918i	$-0.411872\pi$
$317$	−12.2598	−	12.2598i	−0.688580	−	0.688580i	−0.961918	+	0.273338i	$0.911872\pi$
$318$		0			0
$319$	0.256011	+	0.0685980i	0.0143339	+	0.00384075i
$320$	−3.67151	−	3.67151i	−0.205243	−	0.205243i
$321$		0			0
$322$	7.79623	+	9.83748i	0.434467	+	0.548221i
$323$	3.95882	+	14.7745i	0.220274	+	0.822075i
$324$		0			0
$325$	−7.66105	+	14.3152i	−0.424959	+	0.794065i
$326$	−18.7230			−1.03697
$327$		0			0
$328$	−52.6699	−	30.4090i	−2.90821	−	1.67905i
$329$	1.94461	+	13.1737i	0.107210	+	0.726292i
$330$		0			0
$331$	1.27846	−	4.77126i	0.0702703	−	0.262252i	−0.921849	−	0.387549i	$-0.873322\pi$
$331$	1.27846	−	4.77126i	0.0702703	−	0.262252i	0.992119	+	0.125297i	$0.0399884\pi$
$332$	−3.34299	+	12.4762i	−0.183470	+	0.684720i
$333$		0			0
$334$	−16.7634	+	9.67835i	−0.917252	+	0.529576i
$335$	4.59269	−	7.95477i	0.250925	−	0.434615i
$336$		0			0
$337$		−	7.35624i		−	0.400720i	−0.979722	−	0.200360i	$-0.935789\pi$
$337$		−	7.35624i		−	0.400720i	0.979722	−	0.200360i	$-0.0642112\pi$
$338$	−24.0212	−	21.1095i	−1.30658	−	1.14821i
$339$		0			0
$340$	12.5390	−	3.35982i	0.680023	−	0.182212i
$341$	3.09022	+	1.78414i	0.167345	+	0.0966165i
$342$		0			0
$343$	6.27632	−	17.4243i	0.338890	−	0.940826i
$344$	−9.62778	+	35.9314i	−0.519095	+	1.93729i
$345$		0			0
$346$	−18.6471	−	18.6471i	−1.00247	−	1.00247i
$347$	−1.58494	−	2.74519i	−0.0850839	−	0.147370i	0.820343	−	0.571872i	$-0.193782\pi$
$347$	−1.58494	−	2.74519i	−0.0850839	−	0.147370i	−0.905427	+	0.424502i	$0.860449\pi$
$348$		0			0
$349$	26.0697	−	6.98534i	1.39548	−	0.373917i	0.518758	−	0.854921i	$-0.326395\pi$
$349$	26.0697	−	6.98534i	1.39548	−	0.373917i	0.876718	+	0.481004i	$0.159728\pi$
$350$	−10.7903	+	27.2489i	−0.576766	+	1.45652i
$351$		0			0
$352$	0.362757			0.0193350
$353$	−1.36374	−	5.08954i	−0.0725845	−	0.270889i	0.920090	−	0.391706i	$-0.128115\pi$
$353$	−1.36374	−	5.08954i	−0.0725845	−	0.270889i	−0.992675	+	0.120817i	$0.961448\pi$
$354$		0			0
$355$	−2.86893	−	4.96913i	−0.152267	−	0.263734i
$356$	−52.0533	+	52.0533i	−2.75882	+	2.75882i
$357$		0			0
$358$	23.6824	+	6.34567i	1.25165	+	0.335379i
$359$	−17.8470	+	17.8470i	−0.941927	+	0.941927i	−0.998404	−	0.0564767i	$-0.982013\pi$
$359$	−17.8470	+	17.8470i	−0.941927	+	0.941927i	0.0564767	+	0.998404i	$0.482013\pi$
$360$		0			0
$361$	−6.65034	−	3.83958i	−0.350018	−	0.202083i
$362$	−9.42133	+	2.52444i	−0.495174	+	0.132682i
$363$		0			0
$364$	−31.7495	−	22.0315i	−1.66413	−	1.15476i
$365$	0.606988			0.0317712
$366$		0			0
$367$	−28.6206	−	16.5241i	−1.49398	−	0.862551i	−0.494006	−	0.869458i	$-0.664468\pi$
$367$	−28.6206	−	16.5241i	−1.49398	−	0.862551i	−0.999976	+	0.00690739i	$0.997801\pi$
$368$	7.19723	−	4.15532i	0.375181	−	0.216611i
$369$		0			0
$370$	−3.53149	−	0.946261i	−0.183594	−	0.0491938i
$371$	−10.5713	−	7.85179i	−0.548832	−	0.407645i
$372$		0			0
$373$	13.8983	+	24.0726i	0.719627	+	1.24643i	0.961148	+	0.276035i	$0.0890204\pi$
$373$	13.8983	+	24.0726i	0.719627	+	1.24643i	−0.241521	+	0.970396i	$0.577646\pi$
$374$	3.98532	−	6.90278i	0.206076	−	0.356934i
$375$		0			0
$376$	25.3944			1.30962
$377$	−1.13891	+	0.707411i	−0.0586567	+	0.0364335i
$378$		0			0
$379$	14.6943	−	3.93733i	0.754797	−	0.202247i	0.139152	−	0.990271i	$-0.455562\pi$
$379$	14.6943	−	3.93733i	0.754797	−	0.202247i	0.615645	+	0.788024i	$0.288896\pi$
$380$	4.80395	−	8.32069i	0.246438	−	0.426843i
$381$		0			0
$382$	−31.9314	−	31.9314i	−1.63375	−	1.63375i
$383$	8.30637	+	2.22568i	0.424436	+	0.113727i	0.464713	−	0.885461i	$-0.346158\pi$
$383$	8.30637	+	2.22568i	0.424436	+	0.113727i	−0.0402774	+	0.999189i	$0.512824\pi$
$384$		0			0
$385$	−0.527855	−	1.21998i	−0.0269020	−	0.0621759i
$386$	−20.1864	−	34.9639i	−1.02746	−	1.77962i
$387$		0			0
$388$	−35.3987	+	9.48505i	−1.79710	+	0.481530i
$389$			11.3461i			0.575268i	0.957740	+	0.287634i	$0.0928686\pi$
$389$			11.3461i			0.575268i	−0.957740	+	0.287634i	$0.907131\pi$
$390$		0			0
$391$		−	8.76766i		−	0.443400i
$392$	−31.1240	−	16.6929i	−1.57200	−	0.843116i
$393$		0			0
$394$	12.5614	−	7.25232i	0.632833	−	0.365366i
$395$	−4.89228	+	4.89228i	−0.246157	+	0.246157i
$396$		0			0
$397$	4.16966	−	15.5614i	0.209269	−	0.781003i	−0.778836	−	0.627227i	$-0.784190\pi$
$397$	4.16966	−	15.5614i	0.209269	−	0.781003i	0.988106	−	0.153776i	$-0.0491435\pi$
$398$	−33.4482	−	33.4482i	−1.67661	−	1.67661i
$399$		0			0
$400$	16.8045	+	9.70209i	0.840226	+	0.485105i
$401$	9.35796	+	34.9244i	0.467314	+	1.74404i	0.649101	+	0.760702i	$0.275145\pi$
$401$	9.35796	+	34.9244i	0.467314	+	1.74404i	−0.181787	+	0.983338i	$0.558188\pi$
$402$		0			0
$403$	−17.2757	+	5.23087i	−0.860562	+	0.260568i
$404$			54.8801i			2.73039i
$405$		0			0
$406$	−1.89670	+	1.50314i	−0.0941314	+	0.0745994i
$407$	−1.30154	+	0.751444i	−0.0645149	+	0.0372477i
$408$		0			0
$409$	−13.9857	−	3.74745i	−0.691547	−	0.185300i	−0.104106	−	0.994566i	$-0.533198\pi$
$409$	−13.9857	−	3.74745i	−0.691547	−	0.185300i	−0.587441	+	0.809267i	$0.699865\pi$
$410$	20.1890	+	5.40962i	0.997062	+	0.267162i
$411$		0			0
$412$	−57.7350	+	33.3333i	−2.84440	+	1.64221i
$413$	8.28522	−	6.56606i	0.407689	−	0.323095i
$414$		0			0
$415$		−	2.24744i		−	0.110322i
$416$	−1.25509	+	1.33867i	−0.0615357	+	0.0656337i
$417$		0			0
$418$	−1.52686	−	5.69832i	−0.0746812	−	0.278714i
$419$	19.0889	+	11.0210i	0.932553	+	0.538410i	0.887618	−	0.460580i	$-0.152359\pi$
$419$	19.0889	+	11.0210i	0.932553	+	0.538410i	0.0449347	+	0.998990i	$0.485692\pi$
$420$		0			0
$421$	−7.69603	−	7.69603i	−0.375082	−	0.375082i	0.494243	−	0.869324i	$-0.335445\pi$
$421$	−7.69603	−	7.69603i	−0.375082	−	0.375082i	−0.869324	+	0.494243i	$0.835445\pi$
$422$	5.88179	−	21.9511i	0.286321	−	1.06856i
$423$		0			0
$424$	−17.7566	+	17.7566i	−0.862338	+	0.862338i
$425$	17.7286	−	10.2356i	0.859965	−	0.496501i
$426$		0			0
$427$	30.5665	+	3.53832i	1.47921	+	0.171232i
$428$			67.7206i			3.27340i
$429$		0			0
$430$		−	12.7840i		−	0.616502i
$431$	26.2932	−	7.04525i	1.26650	−	0.339358i	0.437812	−	0.899067i	$-0.355754\pi$
$431$	26.2932	−	7.04525i	1.26650	−	0.339358i	0.828689	+	0.559709i	$0.189087\pi$
$432$		0			0
$433$	6.55214	+	11.3486i	0.314876	+	0.545381i	0.979411	−	0.201876i	$-0.0647038\pi$
$433$	6.55214	+	11.3486i	0.314876	+	0.545381i	−0.664535	+	0.747257i	$0.731371\pi$
$434$	−29.9029	+	12.9382i	−1.43538	+	0.621054i
$435$		0			0
$436$	9.83747	+	2.63594i	0.471129	+	0.126239i
$437$	−4.58858	−	4.58858i	−0.219502	−	0.219502i
$438$		0			0
$439$	−19.9333	+	34.5255i	−0.951364	+	1.64781i	−0.208887	+	0.977940i	$0.566984\pi$
$439$	−19.9333	+	34.5255i	−0.951364	+	1.64781i	−0.742477	+	0.669872i	$0.766349\pi$
$440$	−2.44854	+	0.656085i	−0.116730	+	0.0312776i
$441$		0			0
$442$	11.6845	+	38.5896i	0.555773	+	1.83552i
$443$	−23.0066			−1.09308			−0.546539	−	0.837433i	$-0.684055\pi$
$443$	−23.0066			−1.09308			−0.546539	+	0.837433i	$0.684055\pi$
$444$		0			0
$445$	6.40446	−	11.0928i	0.303600	−	0.525851i
$446$	2.29221	+	3.97023i	0.108539	+	0.187996i
$447$		0			0
$448$	11.6206	−	15.6455i	0.549024	−	0.739178i
$449$	−15.6281	−	4.18754i	−0.737536	−	0.197622i	−0.129553	−	0.991572i	$-0.541354\pi$
$449$	−15.6281	−	4.18754i	−0.737536	−	0.197622i	−0.607983	+	0.793950i	$0.708021\pi$
$450$		0			0
$451$	7.44068	−	4.29588i	0.350368	−	0.202285i
$452$	20.7870	+	12.0014i	0.977739	+	0.564498i
$453$		0			0
$454$	−13.7047			−0.643194
$455$	6.32836	+	2.27303i	0.296678	+	0.106561i
$456$		0			0
$457$	0.658952	−	0.176566i	0.0308245	−	0.00825939i	−0.243374	−	0.969933i	$-0.578254\pi$
$457$	0.658952	−	0.176566i	0.0308245	−	0.00825939i	0.274198	+	0.961673i	$0.411588\pi$
$458$	0.461383	+	0.266380i	0.0215590	+	0.0124471i
$459$		0			0
$460$	−3.89429	+	3.89429i	−0.181572	+	0.181572i
$461$	8.08252	+	2.16570i	0.376440	+	0.100867i	0.442078	−	0.896977i	$-0.354241\pi$
$461$	8.08252	+	2.16570i	0.376440	+	0.100867i	−0.0656375	+	0.997844i	$0.520908\pi$
$462$		0			0
$463$	22.3879	−	22.3879i	1.04045	−	1.04045i	0.0413082	−	0.999146i	$-0.486847\pi$
$463$	22.3879	−	22.3879i	1.04045	−	1.04045i	0.999146	−	0.0413082i	$-0.0131525\pi$
$464$	0.801158	+	1.38765i	0.0371928	+	0.0644199i
$465$		0			0
$466$	12.5947	+	47.0041i	0.583438	+	2.17742i
$467$	−13.5832			−0.628554			−0.314277	−	0.949331i	$-0.601762\pi$
$467$	−13.5832			−0.628554			−0.314277	+	0.949331i	$0.601762\pi$
$468$		0			0
$469$	32.0550	+	12.6935i	1.48016	+	0.586130i
$470$	−8.42986	+	2.25877i	−0.388840	+	0.104189i
$471$		0			0
$472$	−10.0799	−	17.4589i	−0.463966	−	0.803613i
$473$	−3.71591	−	3.71591i	−0.170858	−	0.170858i
$474$		0			0
$475$	3.92148	−	14.6352i	0.179930	−	0.671508i
$476$	19.3485	+	44.7183i	0.886836	+	2.04966i
$477$		0			0
$478$	−1.91884	−	1.10784i	−0.0877656	−	0.0506715i
$479$	−4.03229	+	1.08045i	−0.184240	+	0.0493669i	−0.349759	−	0.936840i	$-0.613737\pi$
$479$	−4.03229	+	1.08045i	−0.184240	+	0.0493669i	0.165519	+	0.986207i	$0.447070\pi$
$480$		0			0
$481$	1.73011	−	7.40292i	0.0788863	−	0.337544i
$482$			49.0896i			2.23597i
$483$		0			0
$484$	21.2518	−	36.8093i	0.965993	−	1.67315i
$485$	5.52235	−	3.18833i	0.250757	−	0.144775i
$486$		0			0
$487$	4.28159	−	15.9791i	0.194018	−	0.724083i	−0.798501	−	0.601993i	$-0.794374\pi$
$487$	4.28159	−	15.9791i	0.194018	−	0.724083i	0.992519	−	0.122090i	$-0.0389598\pi$
$488$	15.1873	−	56.6797i	0.687496	−	2.56577i
$489$		0			0
$490$	11.8166	+	2.77291i	0.533821	+	0.125267i
$491$	−27.7156	−	16.0016i	−1.25079	−	0.722143i	−0.279523	−	0.960139i	$-0.590176\pi$
$491$	−27.7156	−	16.0016i	−1.25079	−	0.722143i	−0.971266	+	0.237996i	$0.923510\pi$
$492$		0			0
$493$	1.69043			0.0761332
$494$	26.3111	+	14.0809i	1.18379	+	0.633528i
$495$		0			0
$496$	5.58326	+	20.8370i	0.250696	+	0.935609i
$497$	16.8789	−	13.3766i	0.757121	−	0.600021i
$498$		0			0
$499$	−14.4246	−	14.4246i	−0.645734	−	0.645734i	0.306225	−	0.951959i	$-0.400934\pi$
$499$	−14.4246	−	14.4246i	−0.645734	−	0.645734i	−0.951959	+	0.306225i	$0.900934\pi$
$500$	−26.2120	−	7.02348i	−1.17224	−	0.314100i
$501$		0			0
$502$	48.7220	+	48.7220i	2.17457	+	2.17457i
$503$	23.6349	−	13.6456i	1.05383	−	0.608427i	0.130109	−	0.991500i	$-0.458467\pi$
$503$	23.6349	−	13.6456i	1.05383	−	0.608427i	0.923718	+	0.383072i	$0.125134\pi$
$504$		0			0
$505$	−2.47150	−	9.22376i	−0.109980	−	0.410452i
$506$			3.38157i			0.150329i
$507$		0			0
$508$	−81.4721			−3.61474
$509$	8.17110	+	30.4949i	0.362177	+	1.35166i	0.871207	+	0.490916i	$0.163338\pi$
$509$	8.17110	+	30.4949i	0.362177	+	1.35166i	−0.509030	+	0.860749i	$0.669996\pi$
$510$		0			0
$511$	0.332699	+	2.25387i	0.0147177	+	0.0997054i
$512$	−29.1956	−	29.1956i	−1.29027	−	1.29027i
$513$		0			0
$514$	−5.75519	+	21.4787i	−0.253851	+	0.947383i
$515$	8.20244	−	8.20244i	0.361443	−	0.361443i
$516$		0			0
$517$	−1.79374	+	3.10684i	−0.0788884	+	0.136639i
$518$	1.57800	−	13.6318i	0.0693332	−	0.598948i
$519$		0			0
$520$	6.05048	−	11.3057i	0.265331	−	0.495790i
$521$		−	13.1042i		−	0.574107i	−0.957915	−	0.287054i	$-0.907324\pi$
$521$		−	13.1042i		−	0.574107i	0.957915	−	0.287054i	$-0.0926758\pi$
$522$		0			0
$523$	−7.44365	−	4.29760i	−0.325488	−	0.187921i	0.328348	−	0.944557i	$-0.393508\pi$
$523$	−7.44365	−	4.29760i	−0.325488	−	0.187921i	−0.653836	+	0.756636i	$0.726841\pi$
$524$	−24.4678	−	42.3794i	−1.06888	−	1.85135i
$525$		0			0
$526$	−14.8436	+	55.3971i	−0.647212	+	2.41543i
$527$	21.9829	+	5.89029i	0.957589	+	0.256585i
$528$		0			0
$529$	−9.64015	−	16.6972i	−0.419137	−	0.725966i
$530$	4.31503	−	7.47385i	0.187433	−	0.324643i
$531$		0			0
$532$	33.5295	+	13.2774i	1.45369	+	0.575647i
$533$	−9.89076	+	42.3213i	−0.428417	+	1.83314i
$534$		0			0
$535$	−3.04977	−	11.3819i	−0.131853	−	0.492082i
$536$	32.8734	−	56.9384i	1.41991	−	2.45936i
$537$		0			0
$538$	50.1269	−	50.1269i	2.16112	−	2.16112i
$539$	4.24071	−	2.62872i	0.182660	−	0.113227i
$540$		0			0
$541$	6.09190	−	6.09190i	0.261911	−	0.261911i	−0.563919	−	0.825830i	$-0.690707\pi$
$541$	6.09190	−	6.09190i	0.261911	−	0.261911i	0.825830	+	0.563919i	$0.190707\pi$
$542$	−26.2469	+	15.1537i	−1.12740	+	0.650905i
$543$		0			0
$544$	2.23482	−	0.598817i	0.0958169	−	0.0256741i
$545$	−1.77210			−0.0759086
$546$		0			0
$547$	30.2438			1.29313			0.646566	−	0.762858i	$-0.276205\pi$
$547$	30.2438			1.29313			0.646566	+	0.762858i	$0.276205\pi$
$548$	56.6677	−	15.1841i	2.42072	−	0.648631i
$549$		0			0
$550$	−6.83769	+	3.94774i	−0.291560	+	0.168332i
$551$	0.884692	−	0.884692i	0.0376892	−	0.0376892i
$552$		0			0
$553$	−20.8476	−	15.4845i	−0.886528	−	0.658468i
$554$	24.8971	−	24.8971i	1.05778	−	1.05778i
$555$		0			0
$556$	16.2704	−	28.1812i	0.690019	−	1.19515i
$557$	11.7586	+	43.8837i	0.498228	+	1.85941i	0.511141	+	0.859497i	$0.329223\pi$
$557$	11.7586	+	43.8837i	0.498228	+	1.85941i	−0.0129131	+	0.999917i	$0.504110\pi$
$558$		0			0
$559$	26.5692	−	0.856180i	1.12376	−	0.0362126i
$560$	2.95871	−	7.47168i	0.125028	−	0.315736i
$561$		0			0
$562$	−18.7657	+	32.5031i	−0.791583	+	1.37106i
$563$	−12.5992	−	21.8224i	−0.530992	−	0.919704i	−0.999346	−	0.0361636i	$-0.988486\pi$
$563$	−12.5992	−	21.8224i	−0.530992	−	0.919704i	0.468354	−	0.883541i	$-0.344847\pi$
$564$		0			0
$565$	−4.03418	−	1.08095i	−0.169719	−	0.0454761i
$566$	−8.87415	+	33.1188i	−0.373009	+	1.39209i
$567$		0			0
$568$	−20.5351	−	35.5679i	−0.861634	−	1.49239i
$569$	−13.9572	−	8.05819i	−0.585116	−	0.337817i	0.178048	−	0.984022i	$-0.443022\pi$
$569$	−13.9572	−	8.05819i	−0.585116	−	0.337817i	−0.763164	+	0.646205i	$0.776355\pi$
$570$		0			0
$571$			13.5825i			0.568409i	0.958764	+	0.284204i	$0.0917294\pi$
$571$			13.5825i			0.568409i	−0.958764	+	0.284204i	$0.908271\pi$
$572$	−3.01703	−	9.96418i	−0.126149	−	0.416623i
$573$		0			0
$574$	−9.02115	+	77.9308i	−0.376535	+	3.25277i
$575$	−4.34249	+	7.52142i	−0.181094	+	0.313665i
$576$		0			0
$577$	−33.5657	+	33.5657i	−1.39736	+	1.39736i	−0.589829	+	0.807528i	$0.700805\pi$
$577$	−33.5657	+	33.5657i	−1.39736	+	1.39736i	−0.807528	+	0.589829i	$0.799195\pi$
$578$	2.33411	−	8.71103i	0.0970863	−	0.362331i
$579$		0			0
$580$	−0.750831	−	0.750831i	−0.0311766	−	0.0311766i
$581$	8.34520	−	1.23185i	0.346217	−	0.0511059i
$582$		0			0
$583$	−0.918168	−	3.42665i	−0.0380266	−	0.141917i
$584$	4.34468			0.179784
$585$		0			0
$586$		−	42.6820i		−	1.76318i
$587$	−6.29368	−	23.4883i	−0.259768	−	0.969467i	−0.965375	−	0.260864i	$-0.915992\pi$
$587$	−6.29368	−	23.4883i	−0.259768	−	0.969467i	0.705607	−	0.708603i	$-0.250674\pi$
$588$		0			0
$589$	14.5875	−	8.42210i	0.601067	−	0.347026i
$590$	4.89904	+	4.89904i	0.201690	+	0.201690i
$591$		0			0
$592$	−8.77613	−	2.35156i	−0.360697	−	0.0966484i
$593$	−10.0628	−	10.0628i	−0.413231	−	0.413231i	0.469631	−	0.882863i	$-0.344387\pi$
$593$	−10.0628	−	10.0628i	−0.413231	−	0.413231i	−0.882863	+	0.469631i	$0.844387\pi$
$594$		0			0
$595$	−5.26579	−	6.64451i	−0.215876	−	0.272398i
$596$	−8.64195	−	32.2522i	−0.353988	−	1.32110i
$597$		0			0
$598$	−12.4789	−	11.6997i	−0.510299	−	0.478438i
$599$	−15.7719			−0.644422			−0.322211	−	0.946668i	$-0.604426\pi$
$599$	−15.7719			−0.644422			−0.322211	+	0.946668i	$0.604426\pi$
$600$		0			0
$601$	−18.2565	−	10.5404i	−0.744698	−	0.429952i	0.0790767	−	0.996869i	$-0.474803\pi$
$601$	−18.2565	−	10.5404i	−0.744698	−	0.429952i	−0.823775	+	0.566917i	$0.808136\pi$
$602$	47.4698	−	7.00712i	1.93472	−	0.285589i
$603$		0			0
$604$	−6.15805	+	22.9821i	−0.250567	+	0.935130i
$605$	−1.91413	+	7.14365i	−0.0778206	+	0.290431i
$606$		0			0
$607$	14.6360	−	8.45008i	0.594056	−	0.342978i	−0.172644	−	0.984984i	$-0.555231\pi$
$607$	14.6360	−	8.45008i	0.594056	−	0.342978i	0.766700	+	0.642006i	$0.221898\pi$
$608$	0.856205	−	1.48299i	0.0347237	−	0.0601432i
$609$		0			0
$610$			20.1661i			0.816502i
$611$	−5.25901	−	17.3686i	−0.212757	−	0.702658i
$612$		0			0
$613$	17.4644	−	4.67958i	0.705381	−	0.189006i	0.111742	−	0.993737i	$-0.464357\pi$
$613$	17.4644	−	4.67958i	0.705381	−	0.189006i	0.593640	+	0.804731i	$0.297690\pi$
$614$	−43.7695	−	25.2703i	−1.76639	−	1.01983i
$615$		0			0
$616$	−3.77826	−	8.73233i	−0.152230	−	0.351836i
$617$	−5.54500	+	20.6942i	−0.223233	+	0.833118i	0.759871	+	0.650074i	$0.225262\pi$
$617$	−5.54500	+	20.6942i	−0.223233	+	0.833118i	−0.983105	+	0.183045i	$0.941405\pi$
$618$		0			0
$619$	−19.4756	−	19.4756i	−0.782790	−	0.782790i	0.197511	−	0.980301i	$-0.436714\pi$
$619$	−19.4756	−	19.4756i	−0.782790	−	0.782790i	−0.980301	+	0.197511i	$0.936714\pi$
$620$	−7.14777	−	12.3803i	−0.287061	−	0.497205i
$621$		0			0
$622$	−17.8892	+	4.79339i	−0.717291	+	0.192197i
$623$	44.7004	+	17.7009i	1.79088	+	0.709172i
$624$		0			0
$625$	−17.7939			−0.711756
$626$	−5.03421	−	18.7879i	−0.201208	−	0.750917i
$627$		0			0
$628$	29.6058	+	51.2787i	1.18140	+	2.04624i
$629$	−6.77788	+	6.77788i	−0.270252	+	0.270252i
$630$		0			0
$631$	−20.8332	−	5.58224i	−0.829356	−	0.222225i	−0.180923	−	0.983497i	$-0.557909\pi$
$631$	−20.8332	−	5.58224i	−0.829356	−	0.222225i	−0.648433	+	0.761272i	$0.724575\pi$
$632$	−35.0178	+	35.0178i	−1.39293	+	1.39293i
$633$		0			0
$634$	36.9357	+	21.3248i	1.46690	+	0.846916i
$635$	13.6931	−	3.66906i	0.543395	−	0.145602i
$636$		0			0
$637$	−4.97157	+	24.7444i	−0.196981	+	0.980407i
$638$	−0.651976			−0.0258120
$639$		0			0
$640$	11.6827	+	6.74499i	0.461798	+	0.266619i
$641$	−25.3468	+	14.6340i	−1.00114	+	0.578006i	−0.908584	−	0.417701i	$-0.862836\pi$
$641$	−25.3468	+	14.6340i	−1.00114	+	0.578006i	−0.0925521	+	0.995708i	$0.529502\pi$
$642$		0			0
$643$	−12.4873	−	3.34595i	−0.492449	−	0.131951i	0.00404423	−	0.999992i	$-0.498713\pi$
$643$	−12.4873	−	3.34595i	−0.492449	−	0.131951i	−0.496494	+	0.868040i	$0.665379\pi$
$644$	−16.5948	−	12.3258i	−0.653927	−	0.485704i
$645$		0			0
$646$	−18.8129	−	32.5849i	−0.740183	−	1.28203i
$647$	−18.8428	+	32.6368i	−0.740788	+	1.28308i	0.211348	+	0.977411i	$0.432215\pi$
$647$	−18.8428	+	32.6368i	−0.740788	+	1.28308i	−0.952137	+	0.305672i	$0.901119\pi$
$648$		0			0
$649$	2.84798			0.111793
$650$	9.08921	−	38.8915i	0.356508	−	1.52545i
$651$		0			0
$652$	29.7833	−	7.98041i	1.16640	−	0.312537i
$653$	20.0158	−	34.6685i	0.783280	−	1.35668i	−0.146740	−	0.989175i	$-0.546878\pi$
$653$	20.0158	−	34.6685i	0.783280	−	1.35668i	0.930021	−	0.367507i	$-0.119788\pi$
$654$		0			0
$655$	6.02086	+	6.02086i	0.235255	+	0.235255i
$656$	50.1717	+	13.4435i	1.95888	+	0.524879i
$657$		0			0
$658$	−13.0078	−	30.0637i	−0.507097	−	1.17201i
$659$	−15.0023	−	25.9848i	−0.584407	−	1.01222i	−0.994949	−	0.100381i	$-0.967994\pi$
$659$	−15.0023	−	25.9848i	−0.584407	−	1.01222i	0.410542	−	0.911842i	$-0.365340\pi$
$660$		0			0
$661$	19.0751	−	5.11115i	0.741934	−	0.198801i	0.131996	−	0.991250i	$-0.457861\pi$
$661$	19.0751	−	5.11115i	0.741934	−	0.198801i	0.609937	+	0.792450i	$0.291195\pi$
$662$			12.1508i			0.472255i
$663$		0			0
$664$		−	16.0866i		−	0.624283i
$665$	−6.23329	−	0.721556i	−0.241717	−	0.0279807i
$666$		0			0
$667$	−0.621087	+	0.358585i	−0.0240486	+	0.0138845i
$668$	22.5408	−	22.5408i	0.872131	−	0.872131i
$669$		0			0
$670$	−5.84803	+	21.8251i	−0.225929	+	0.843178i
$671$	5.86164	+	5.86164i	0.226286	+	0.226286i
$672$		0			0
$673$	−39.4906	−	22.7999i	−1.52225	−	0.878872i	−0.999654	−	0.0262924i	$-0.991630\pi$
$673$	−39.4906	−	22.7999i	−1.52225	−	0.878872i	−0.522597	−	0.852580i	$-0.675037\pi$
$674$	4.68348	+	17.4790i	0.180401	+	0.673265i
$675$		0			0
$676$	47.2090	+	23.3410i	1.81573	+	0.897730i
$677$		−	6.55217i		−	0.251821i	−0.992042	−	0.125910i	$-0.959815\pi$
$677$		−	6.55217i		−	0.251821i	0.992042	−	0.125910i	$-0.0401851\pi$
$678$		0			0
$679$	14.8658	+	18.7580i	0.570497	+	0.719867i
$680$	−14.0016	+	8.08381i	−0.536936	+	0.310000i
$681$		0			0
$682$	−8.47849	−	2.27180i	−0.324658	−	0.0869919i
$683$	−42.6432	−	11.4262i	−1.63170	−	0.437212i	−0.677290	−	0.735716i	$-0.736846\pi$
$683$	−42.6432	−	11.4262i	−1.63170	−	0.437212i	−0.954408	+	0.298504i	$0.903512\pi$
$684$		0			0
$685$	−8.84040	+	5.10401i	−0.337774	+	0.195014i
$686$	−3.81950	+	45.3975i	−0.145829	+	1.73328i
$687$		0			0
$688$		−	31.7697i		−	1.21121i
$689$	15.8220	+	8.46743i	0.602769	+	0.322584i
$690$		0			0
$691$	−8.50701	−	31.7486i	−0.323622	−	1.20777i	−0.915690	−	0.401885i	$-0.868355\pi$
$691$	−8.50701	−	31.7486i	−0.323622	−	1.20777i	0.592068	−	0.805888i	$-0.298312\pi$
$692$	37.6106	+	21.7145i	1.42974	+	0.825462i
$693$		0			0
$694$	5.51370	+	5.51370i	0.209297	+	0.209297i
$695$	−1.46546	+	5.46917i	−0.0555881	+	0.207457i
$696$		0			0
$697$	38.7480	−	38.7480i	1.46769	−	1.46769i
$698$	−57.4961	+	33.1954i	−2.17626	+	1.25646i
$699$		0			0
$700$	5.55004	−	47.9450i	0.209772	−	1.81215i
$701$			8.83206i			0.333582i	0.985992	+	0.166791i	$0.0533406\pi$
$701$			8.83206i			0.333582i	−0.985992	+	0.166791i	$0.946659\pi$
$702$		0			0
$703$			7.09444i			0.267572i
$704$	5.07144	−	1.35889i	0.191137	−	0.0512150i
$705$		0			0
$706$	6.48069	+	11.2249i	0.243904	+	0.422454i
$707$	32.8950	−	14.2329i	1.23715	−	0.535282i
$708$		0			0
$709$	28.7065	+	7.69188i	1.07809	+	0.288874i	0.753815	−	0.657087i	$-0.228212\pi$
$709$	28.7065	+	7.69188i	1.07809	+	0.288874i	0.324279	+	0.945961i	$0.394878\pi$
$710$	9.98046	+	9.98046i	0.374560	+	0.374560i
$711$		0			0
$712$	45.8416	−	79.4000i	1.71799	−	2.97564i
$713$	−9.32628	+	2.49897i	−0.349272	+	0.0935872i
$714$		0			0
$715$	0.955809	+	1.53882i	0.0357452	+	0.0575486i
$716$	−40.3771			−1.50896
$717$		0			0
$718$	31.0431	−	53.7683i	1.15852	−	2.00662i
$719$	−18.6597	−	32.3196i	−0.695890	−	1.20532i	−0.969880	−	0.243584i	$-0.921677\pi$
$719$	−18.6597	−	32.3196i	−0.695890	−	1.20532i	0.273990	−	0.961733i	$-0.411657\pi$
$720$		0			0
$721$	34.9532	+	25.9615i	1.30173	+	0.966855i
$722$	18.2462	+	4.88907i	0.679055	+	0.181952i
$723$		0			0
$724$	13.9108	−	8.03142i	0.516992	−	0.298485i
$725$	−1.45015	−	0.837245i	−0.0538573	−	0.0310945i
$726$		0			0
$727$	9.88660			0.366674			0.183337	−	0.983050i	$-0.441310\pi$
$727$	9.88660			0.366674			0.183337	+	0.983050i	$0.441310\pi$
$728$	45.2969	+	16.2698i	1.67881	+	0.603001i
$729$		0			0
$730$	−1.44225	+	0.386449i	−0.0533800	+	0.0143031i
$731$	−29.0264	−	16.7584i	−1.07358	−	0.619832i
$732$		0			0
$733$	−14.5543	+	14.5543i	−0.537577	+	0.537577i	−0.922817	−	0.385240i	$-0.874119\pi$
$733$	−14.5543	+	14.5543i	−0.537577	+	0.537577i	0.385240	+	0.922817i	$0.374119\pi$
$734$	78.5250	+	21.0407i	2.89841	+	0.776626i
$735$		0			0
$736$	−0.694076	+	0.694076i	−0.0255840	+	0.0255840i
$737$	4.64403	+	8.04370i	0.171065	+	0.296293i
$738$		0			0
$739$	13.1964	+	49.2497i	0.485438	+	1.81168i	0.578079	+	0.815981i	$0.303803\pi$
$739$	13.1964	+	49.2497i	0.485438	+	1.81168i	−0.0926405	+	0.995700i	$0.529531\pi$
$740$	6.02100			0.221336
$741$		0			0
$742$	30.1171	+	11.9261i	1.10563	+	0.437820i
$743$	13.4007	−	3.59070i	0.491623	−	0.131730i	−0.00448658	−	0.999990i	$-0.501428\pi$
$743$	13.4007	−	3.59070i	0.491623	−	0.131730i	0.496109	+	0.868260i	$0.334761\pi$
$744$		0			0
$745$	2.90493	+	5.03148i	0.106428	+	0.184339i
$746$	−48.3496	−	48.3496i	−1.77020	−	1.77020i
$747$		0			0
$748$	−3.39737	+	12.6792i	−0.124220	+	0.463597i
$749$	40.5916	−	17.5630i	1.48319	−	0.641737i
$750$		0			0
$751$	−7.39608	−	4.27013i	−0.269887	−	0.155819i	0.358949	−	0.933357i	$-0.383135\pi$
$751$	−7.39608	−	4.27013i	−0.269887	−	0.155819i	−0.628836	+	0.777538i	$0.716468\pi$
$752$	−20.9491	+	5.61329i	−0.763935	+	0.204696i
$753$		0			0
$754$	2.25574	−	2.40597i	0.0821494	−	0.0876201i
$755$		−	4.13996i		−	0.150669i
$756$		0			0
$757$	−5.08375	+	8.80531i	−0.184772	+	0.320034i	−0.943500	−	0.331374i	$-0.892488\pi$
$757$	−5.08375	+	8.80531i	−0.184772	+	0.320034i	0.758728	+	0.651408i	$0.225821\pi$
$758$	−32.4080	+	18.7108i	−1.17711	+	0.679606i
$759$		0			0
$760$	−3.09708	+	11.5585i	−0.112343	+	0.419269i
$761$	0.975866	−	3.64198i	0.0353751	−	0.132022i	−0.945980	−	0.324225i	$-0.894897\pi$
$761$	0.975866	−	3.64198i	0.0353751	−	0.132022i	0.981355	+	0.192203i	$0.0615632\pi$
$762$		0			0
$763$	−0.971316	−	6.58019i	−0.0351640	−	0.238219i
$764$	64.4046	+	37.1840i	2.33008	+	1.34527i
$765$		0			0
$766$	−21.1536			−0.764309
$767$	−9.85363	+	10.5098i	−0.355794	+	0.379488i
$768$		0			0
$769$	1.12134	+	4.18491i	0.0404367	+	0.150912i	0.983192	−	0.182572i	$-0.0584424\pi$
$769$	1.12134	+	4.18491i	0.0404367	+	0.150912i	−0.942756	+	0.333484i	$0.891776\pi$
$770$	2.03094	+	2.56270i	0.0731901	+	0.0923531i
$771$		0			0
$772$	47.0142	+	47.0142i	1.69208	+	1.69208i
$773$	14.9644	+	4.00970i	0.538233	+	0.144219i	0.517687	−	0.855570i	$-0.326793\pi$
$773$	14.9644	+	4.00970i	0.538233	+	0.144219i	0.0205453	+	0.999789i	$0.493460\pi$
$774$		0			0
$775$	−15.9408	−	15.9408i	−0.572611	−	0.572611i
$776$	39.5277	−	22.8213i	1.41896	−	0.819237i
$777$		0			0
$778$	−7.22366	−	26.9591i	−0.258981	−	0.966529i
$779$		−	40.5578i		−	1.45313i
$780$		0			0
$781$	5.80200			0.207612
$782$	5.58208	+	20.8326i	0.199615	+	0.744973i
$783$		0			0
$784$	29.3656	+	6.89097i	1.04877	+	0.246106i
$785$	−7.28519	−	7.28519i	−0.260020	−	0.260020i
$786$		0			0
$787$	−11.1122	+	41.4712i	−0.396106	+	1.47829i	0.423782	+	0.905764i	$0.360702\pi$
$787$	−11.1122	+	41.4712i	−0.396106	+	1.47829i	−0.819888	+	0.572524i	$0.805964\pi$
$788$	−16.8906	+	16.8906i	−0.601703	+	0.601703i
$789$		0			0
$790$	8.50966	−	14.7392i	0.302760	−	0.524396i
$791$	1.80261	−	15.5722i	0.0640936	−	0.553684i
$792$		0			0
$793$	−41.9115	+	1.35058i	−1.48832	+	0.0479604i
$794$			39.6297i			1.40640i
$795$		0			0
$796$	67.4641	+	38.9504i	2.39120	+	1.38056i
$797$	23.6527	+	40.9678i	0.837823	+	1.45115i	0.891711	+	0.452606i	$0.149505\pi$
$797$	23.6527	+	40.9678i	0.837823	+	1.45115i	−0.0538875	+	0.998547i	$0.517161\pi$
$798$		0			0
$799$	−5.92198	+	22.1011i	−0.209505	+	0.781882i
$800$	−2.21374	−	0.593170i	−0.0782676	−	0.0209717i
$801$		0			0
$802$	−44.4704	−	77.0250i	−1.57030	−	2.71985i
$803$	−0.306887	+	0.531543i	−0.0108298	+	0.0187578i
$804$		0			0
$805$	3.34420	+	1.32427i	0.117867	+	0.0466744i
$806$	37.7179	−	23.4278i	1.32856	−	0.825208i
$807$		0			0
$808$	−17.6904	−	66.0215i	−0.622347	−	2.32263i
$809$	−9.15672	+	15.8599i	−0.321933	+	0.557604i	−0.980887	−	0.194579i	$-0.937666\pi$
$809$	−9.15672	+	15.8599i	−0.321933	+	0.557604i	0.658954	+	0.752183i	$0.270999\pi$
$810$		0			0
$811$	7.95198	−	7.95198i	0.279232	−	0.279232i	−0.553571	−	0.832802i	$-0.686735\pi$
$811$	7.95198	−	7.95198i	0.279232	−	0.279232i	0.832802	+	0.553571i	$0.186735\pi$
$812$	2.37645	−	3.19953i	0.0833970	−	0.112282i
$813$		0			0
$814$	2.61413	−	2.61413i	0.0916253	−	0.0916253i
$815$	−4.64632	+	2.68255i	−0.162753	+	0.0939658i
$816$		0			0
$817$	−23.9616	+	6.42049i	−0.838311	+	0.224625i
$818$	35.6169			1.24532
$819$		0			0
$820$	−34.4210			−1.20204
$821$	35.4162	−	9.48973i	1.23603	−	0.331194i	0.419107	−	0.907937i	$-0.362343\pi$
$821$	35.4162	−	9.48973i	1.23603	−	0.331194i	0.816926	+	0.576743i	$0.195677\pi$
$822$		0			0
$823$	−14.5778	+	8.41649i	−0.508150	+	0.293380i	−0.732073	−	0.681226i	$-0.761447\pi$
$823$	−14.5778	+	8.41649i	−0.508150	+	0.293380i	0.223923	+	0.974607i	$0.428114\pi$
$824$	58.7112	−	58.7112i	2.04530	−	2.04530i
$825$		0			0
$826$	−15.5059	+	20.8764i	−0.539519	+	0.726381i
$827$	20.4920	−	20.4920i	0.712578	−	0.712578i	−0.254496	−	0.967074i	$-0.581910\pi$
$827$	20.4920	−	20.4920i	0.712578	−	0.712578i	0.967074	+	0.254496i	$0.0819096\pi$
$828$		0			0
$829$	2.04801	−	3.54725i	0.0711302	−	0.123201i	−0.828267	−	0.560334i	$-0.810673\pi$
$829$	2.04801	−	3.54725i	0.0711302	−	0.123201i	0.899397	+	0.437133i	$0.144006\pi$
$830$	1.43087	+	5.34008i	0.0496662	+	0.185357i
$831$		0			0
$832$	−12.5318	+	23.4165i	−0.434462	+	0.811822i
$833$	21.7862	−	23.1949i	0.754846	−	0.803656i
$834$		0			0
$835$	−2.77335	+	4.80358i	−0.0959757	+	0.166235i
$836$	4.85766	+	8.41371i	0.168006	+	0.290994i
$837$		0			0
$838$	−52.3733	−	14.0334i	−1.80920	−	0.484775i
$839$	8.69536	−	32.4515i	0.300197	−	1.12035i	−0.636804	−	0.771026i	$-0.719744\pi$
$839$	8.69536	−	32.4515i	0.300197	−	1.12035i	0.937001	−	0.349326i	$-0.113589\pi$
$840$		0			0
$841$	14.4309	+	24.9950i	0.497616	+	0.861896i
$842$	23.1861	+	13.3865i	0.799047	+	0.461330i
$843$		0			0
$844$			37.4255i			1.28824i
$845$	−8.98562	−	1.79691i	−0.309115	−	0.0618156i
$846$		0			0
$847$	−27.5750	−	3.19204i	−0.947488	−	0.109680i
$848$	10.7233	−	18.5733i	0.368240	−	0.637810i
$849$		0			0
$850$	−35.6079	+	35.6079i	−1.22134	+	1.22134i
$851$	1.05252	−	3.92805i	0.0360798	−	0.134652i
$852$		0			0
$853$	−6.65000	−	6.65000i	−0.227692	−	0.227692i	0.584036	−	0.811728i	$-0.301473\pi$
$853$	−6.65000	−	6.65000i	−0.227692	−	0.227692i	−0.811728	+	0.584036i	$0.801473\pi$
$854$	−74.8809	+	11.0533i	−2.56237	+	0.378237i
$855$		0			0
$856$	−21.8295	−	81.4688i	−0.746117	−	2.78455i
$857$	−38.2819			−1.30768			−0.653842	−	0.756631i	$-0.726844\pi$
$857$	−38.2819			−1.30768			−0.653842	+	0.756631i	$0.726844\pi$
$858$		0			0
$859$			16.5870i			0.565942i	0.959128	+	0.282971i	$0.0913201\pi$
$859$			16.5870i			0.565942i	−0.959128	+	0.282971i	$0.908680\pi$
$860$	5.44902	+	20.3360i	0.185810	+	0.693453i
$861$		0			0
$862$	−57.9892	+	33.4801i	−1.97512	+	1.14034i
$863$	11.6109	+	11.6109i	0.395240	+	0.395240i	0.876550	−	0.481310i	$-0.159839\pi$
$863$	11.6109	+	11.6109i	0.395240	+	0.395240i	−0.481310	+	0.876550i	$0.659839\pi$
$864$		0			0
$865$	−7.29917	−	1.95581i	−0.248179	−	0.0664994i
$866$	−22.7937	−	22.7937i	−0.774560	−	0.774560i
$867$		0			0
$868$	42.0528	−	33.3269i	1.42736	−	1.13119i
$869$	−1.81072	−	6.75769i	−0.0614244	−	0.229239i
$870$		0			0
$871$	−45.7511	−	10.6923i	−1.55022	−	0.362296i
$872$	−12.6843			−0.429545
$873$		0			0
$874$	13.8242	+	7.98141i	0.467611	+	0.269975i
$875$	2.58808	+	17.5329i	0.0874929	+	0.592721i
$876$		0			0
$877$	−5.37931	+	20.0759i	−0.181646	+	0.677914i	0.813677	+	0.581317i	$0.197462\pi$
$877$	−5.37931	+	20.0759i	−0.181646	+	0.677914i	−0.995324	+	0.0965967i	$0.969204\pi$
$878$	25.3817	−	94.7260i	0.856592	−	3.19685i
$879$		0			0
$880$	1.87490	−	1.08247i	0.0632029	−	0.0364902i
$881$	−6.22366	+	10.7797i	−0.209680	+	0.363177i	−0.951614	−	0.307297i	$-0.900576\pi$
$881$	−6.22366	+	10.7797i	−0.209680	+	0.363177i	0.741934	+	0.670473i	$0.233909\pi$
$882$		0			0
$883$			28.9456i			0.974097i	0.873375	+	0.487049i	$0.161927\pi$
$883$			28.9456i			0.974097i	−0.873375	+	0.487049i	$0.838073\pi$
$884$	−35.0351	−	56.4054i	−1.17836	−	1.89712i
$885$		0			0
$886$	54.6655	−	14.6476i	1.83652	−	0.492095i
$887$	−6.26961	−	3.61976i	−0.210513	−	0.121540i	0.391037	−	0.920375i	$-0.372117\pi$
$887$	−6.26961	−	3.61976i	−0.210513	−	0.121540i	−0.601550	+	0.798835i	$0.705450\pi$
$888$		0			0
$889$	21.1294	+	48.8343i	0.708656	+	1.63785i
$890$	−8.15502	+	30.4349i	−0.273357	+	1.02018i
$891$		0			0
$892$	−5.33855	−	5.33855i	−0.178748	−	0.178748i
$893$	8.46740	+	14.6660i	0.283351	+	0.490778i
$894$		0			0
$895$	6.78623	−	1.81836i	0.226839	−	0.0607812i
$896$	−18.6421	+	47.0771i	−0.622788	+	1.57274i
$897$		0			0
$898$	39.7996			1.32813
$899$	−0.481809	−	1.79814i	−0.0160692	−	0.0599712i
$900$		0			0
$901$	−11.3130	−	19.5947i	−0.376891	−	0.652794i
$902$	−14.9446	+	14.9446i	−0.497600	+	0.497600i
$903$		0			0
$904$	−28.8757	−	7.73722i	−0.960391	−	0.257336i
$905$	−1.97632	+	1.97632i	−0.0656950	+	0.0656950i
$906$		0			0
$907$	0.515467	+	0.297605i	0.0171158	+	0.00988182i	0.508533	−	0.861042i	$-0.330188\pi$
$907$	0.515467	+	0.297605i	0.0171158	+	0.00988182i	−0.491418	+	0.870924i	$0.663521\pi$
$908$	21.8006	−	5.84144i	0.723477	−	0.193855i
$909$		0			0
$910$	−16.4838	−	1.37184i	−0.546433	−	0.0454760i
$911$	23.8117			0.788915			0.394458	−	0.918914i	$-0.370932\pi$
$911$	23.8117			0.788915			0.394458	+	0.918914i	$0.370932\pi$
$912$		0			0
$913$	1.96810	+	1.13628i	0.0651345	+	0.0376054i
$914$	−1.45331	+	0.839066i	−0.0480711	+	0.0277538i
$915$		0			0
$916$	−0.847479	−	0.227081i	−0.0280015	−	0.00750297i
$917$	−19.0566	+	25.6568i	−0.629303	+	0.847263i
$918$		0			0
$919$	−2.86358	−	4.95987i	−0.0944609	−	0.163611i	0.814923	−	0.579570i	$-0.196779\pi$
$919$	−2.86358	−	4.95987i	−0.0944609	−	0.163611i	−0.909383	+	0.415959i	$0.863446\pi$
$920$	3.42958	−	5.94020i	0.113070	−	0.195843i
$921$		0			0
$922$	−20.5835			−0.677881
$923$	−20.0741	+	21.4109i	−0.660747	+	0.704749i
$924$		0			0
$925$	9.17144	−	2.45748i	0.301555	−	0.0808015i
$926$	−38.9417	+	67.4490i	−1.27970	+	2.21651i
$927$		0			0
$928$	−0.133820	−	0.133820i	−0.00439286	−	0.00439286i
$929$	−23.7758	−	6.37070i	−0.780058	−	0.209016i	−0.153247	−	0.988188i	$-0.548973\pi$
$929$	−23.7758	−	6.37070i	−0.780058	−	0.209016i	−0.626810	+	0.779172i	$0.715640\pi$
$930$		0			0
$931$	−0.737273	−	23.5410i	−0.0241631	−	0.771524i
$932$	−40.0696	−	69.4026i	−1.31252	−	2.27336i
$933$		0			0
$934$	32.2746	−	8.64795i	1.05606	−	0.282970i
$935$		−	2.28400i		−	0.0746949i
$936$		0			0
$937$		−	26.2867i		−	0.858749i	−0.903127	−	0.429374i	$-0.858734\pi$
$937$		−	26.2867i		−	0.858749i	0.903127	−	0.429374i	$-0.141266\pi$
$938$	−84.2466	−	9.75225i	−2.75075	−	0.318422i
$939$		0			0
$940$	12.4469	−	7.18622i	0.405973	−	0.234389i
$941$	−2.11330	+	2.11330i	−0.0688916	+	0.0688916i	−0.740713	−	0.671821i	$-0.765512\pi$
$941$	−2.11330	+	2.11330i	−0.0688916	+	0.0688916i	0.671821	+	0.740713i	$0.265512\pi$
$942$		0			0
$943$	−6.01707	+	22.4560i	−0.195943	+	0.731268i
$944$	12.1746	+	12.1746i	0.396250	+	0.396250i
$945$		0			0
$946$	11.1951	+	6.46348i	0.363983	+	0.210146i
$947$	0.631600	+	2.35716i	0.0205243	+	0.0765976i	0.975428	−	0.220317i	$-0.0707091\pi$
$947$	0.631600	+	2.35716i	0.0205243	+	0.0765976i	−0.954904	+	0.296914i	$0.904042\pi$
$948$		0			0
$949$	−0.899753	−	2.97156i	−0.0292072	−	0.0964609i
$950$			37.2709i			1.20923i
$951$		0			0
$952$	−37.6913	−	47.5599i	−1.22158	−	1.54142i
$953$	11.0082	−	6.35559i	0.356591	−	0.205878i	−0.310994	−	0.950412i	$-0.600662\pi$
$953$	11.0082	−	6.35559i	0.356591	−	0.205878i	0.667584	+	0.744534i	$0.267328\pi$
$954$		0			0
$955$	−12.4991	−	3.34913i	−0.404462	−	0.108375i
$956$	3.52456	+	0.944404i	0.113993	+	0.0305442i
$957$		0			0
$958$	8.89312	−	5.13445i	0.287324	−	0.165886i
$959$	−23.7978	−	30.0286i	−0.768470	−	0.969675i
$960$		0			0
$961$			5.93766i			0.191537i
$962$	0.602320	+	18.6914i	0.0194196	+	0.602634i
$963$		0			0
$964$	−20.9237	−	78.0885i	−0.673908	−	2.51506i
$965$	−10.0190	−	5.78446i	−0.322523	−	0.186209i
$966$		0			0
$967$	−12.3880	−	12.3880i	−0.398371	−	0.398371i	0.479287	−	0.877658i	$-0.340895\pi$
$967$	−12.3880	−	12.3880i	−0.398371	−	0.398371i	−0.877658	+	0.479287i	$0.840895\pi$
$968$	−13.7009	+	51.1326i	−0.440365	+	1.64346i
$969$		0			0
$970$	−11.0916	+	11.0916i	−0.356130	+	0.356130i
$971$	6.20175	−	3.58058i	0.199024	−	0.114906i	−0.397176	−	0.917742i	$-0.630010\pi$
$971$	6.20175	−	3.58058i	0.199024	−	0.114906i	0.596200	+	0.802836i	$0.296677\pi$
$972$		0			0
$973$	−21.1114	−	2.44382i	−0.676800	−	0.0783453i
$974$			40.6935i			1.30390i
$975$		0			0
$976$			50.1149i			1.60414i
$977$	3.17102	−	0.849671i	0.101450	−	0.0271834i	−0.207737	−	0.978185i	$-0.566610\pi$
$977$	3.17102	−	0.849671i	0.101450	−	0.0271834i	0.309187	+	0.951001i	$0.399943\pi$
$978$		0			0
$979$	6.47605	+	11.2169i	0.206976	+	0.358492i
$980$	−19.9790	+	0.625717i	−0.638207	+	0.0199878i
$981$		0			0
$982$	76.0421	+	20.3754i	2.42660	+	0.650206i
$983$	−10.1688	−	10.1688i	−0.324335	−	0.324335i	0.526092	−	0.850428i	$-0.323657\pi$
$983$	−10.1688	−	10.1688i	−0.324335	−	0.324335i	−0.850428	+	0.526092i	$0.823657\pi$
$984$		0			0
$985$	2.07817	−	3.59949i	0.0662159	−	0.114689i
$986$	−4.01659	+	1.07624i	−0.127914	+	0.0342745i
$987$		0			0
$988$	−47.8557	−	11.1842i	−1.52249	−	0.355816i
$989$	14.2196			0.452156
$990$		0			0
$991$	−4.87954	+	8.45161i	−0.155004	+	0.268474i	−0.933060	−	0.359720i	$-0.882872\pi$
$991$	−4.87954	+	8.45161i	−0.155004	+	0.268474i	0.778057	+	0.628194i	$0.216206\pi$
$992$	−1.27394	−	2.20653i	−0.0404476	−	0.0700574i
$993$		0			0
$994$	−31.5891	+	42.5299i	−1.00194	+	1.34897i
$995$	−13.0929	−	3.50823i	−0.415072	−	0.111218i
$996$		0			0
$997$	−27.8354	+	16.0708i	−0.881555	+	0.508966i	−0.871171	−	0.490980i	$-0.836639\pi$
$997$	−27.8354	+	16.0708i	−0.881555	+	0.508966i	−0.0103840	+	0.999946i	$0.503305\pi$
$998$	43.4576	+	25.0903i	1.37563	+	0.794218i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.f.748.1		32
3.2	odd	2		273.2.by.c.202.8	✓	32
7.6	odd	2		819.2.fm.e.748.1		32
13.2	odd	12		819.2.fm.e.496.1		32
21.20	even	2		273.2.by.d.202.8	yes	32
39.2	even	12		273.2.by.d.223.8	yes	32
91.41	even	12	inner	819.2.fm.f.496.1		32
273.41	odd	12		273.2.by.c.223.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.8	✓	32	3.2	odd	2
273.2.by.c.223.8	yes	32	273.41	odd	12
273.2.by.d.202.8	yes	32	21.20	even	2
273.2.by.d.223.8	yes	32	39.2	even	12
819.2.fm.e.496.1		32	13.2	odd	12
819.2.fm.e.748.1		32	7.6	odd	2
819.2.fm.f.496.1		32	91.41	even	12	inner
819.2.fm.f.748.1		32	1.1	even	1	trivial

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.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.37607 + 0.636667i) q^{2} +(3.50833 - 2.02554i) q^{4} +(-0.498430 + 0.498430i) q^{5} +(-2.12397 - 1.57758i) q^{7} +(-3.56765 + 3.56765i) q^{8} +O(q^{10})\)	\(q+(-2.37607 + 0.636667i) q^{2} +(3.50833 - 2.02554i) q^{4} +(-0.498430 + 0.498430i) q^{5} +(-2.12397 - 1.57758i) q^{7} +(-3.56765 + 3.56765i) q^{8} +(0.866973 - 1.50164i) q^{10} +(-0.184478 - 0.688480i) q^{11} +(3.17894 + 1.70127i) q^{13} +(6.05110 + 2.39618i) q^{14} +(2.15452 - 3.73174i) q^{16} +(-2.27300 - 3.93695i) q^{17} +(-3.25000 - 0.870835i) q^{19} +(-0.739070 + 2.75825i) q^{20} +(0.876665 + 1.51843i) q^{22} +(1.67026 + 0.964326i) q^{23} +4.50313i q^{25} +(-8.63655 - 2.01842i) q^{26} +(-10.6470 - 1.23248i) q^{28} +(-0.185925 + 0.322032i) q^{29} +(-3.53994 + 3.53994i) q^{31} +(-0.131724 + 0.491600i) q^{32} +(7.90735 + 7.90735i) q^{34} +(1.84496 - 0.272339i) q^{35} +(-0.545727 - 2.03668i) q^{37} +8.27667 q^{38} -3.55645i q^{40} +(3.11983 + 11.6434i) q^{41} +(6.38504 - 3.68640i) q^{43} +(-2.04175 - 2.04175i) q^{44} +(-4.58262 - 1.22791i) q^{46} +(-3.55898 - 3.55898i) q^{47} +(2.02250 + 6.70145i) q^{49} +(-2.86700 - 10.6998i) q^{50} +(14.5988 - 0.470438i) q^{52} +4.97712 q^{53} +(0.435109 + 0.251210i) q^{55} +(13.2058 - 1.94934i) q^{56} +(0.236745 - 0.883543i) q^{58} +(-1.03416 + 3.85953i) q^{59} +(-10.0720 + 5.81509i) q^{61} +(6.15739 - 10.6649i) q^{62} +7.36614i q^{64} +(-2.43245 + 0.736516i) q^{65} +(-12.5870 + 3.37267i) q^{67} +(-15.9489 - 9.20809i) q^{68} +(-4.21038 + 1.82173i) q^{70} +(-2.10681 + 7.86274i) q^{71} +(-0.608899 - 0.608899i) q^{73} +(2.59337 + 4.49186i) q^{74} +(-13.1660 + 3.52781i) q^{76} +(-0.694305 + 1.75334i) q^{77} +9.81537 q^{79} +(0.786133 + 2.93389i) q^{80} +(-14.8259 - 25.6792i) q^{82} +(-2.25452 + 2.25452i) q^{83} +(3.09523 + 0.829364i) q^{85} +(-12.8243 + 12.8243i) q^{86} +(3.11441 + 1.79810i) q^{88} +(-17.5524 + 4.70315i) q^{89} +(-4.06809 - 8.62848i) q^{91} +7.81311 q^{92} +(10.7223 + 6.19052i) q^{94} +(2.05395 - 1.18585i) q^{95} +(-8.73810 - 2.34137i) q^{97} +(-9.07221 - 14.6355i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

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