LMFDB - Embedded newform 441.2.u.d.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			64.1
Character	$\chi$	$=$	441.64
Dual form			441.2.u.d.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.603790 + 2.64538i) q^{2} +(-4.83152 - 2.32674i) q^{4} +(0.940078 - 1.17882i) q^{5} +(2.57696 - 0.599410i) q^{7} +(5.68875 - 7.13347i) q^{8} +O(q^{10})$	\(q+(-0.603790 + 2.64538i) q^{2} +(-4.83152 - 2.32674i) q^{4} +(0.940078 - 1.17882i) q^{5} +(2.57696 - 0.599410i) q^{7} +(5.68875 - 7.13347i) q^{8} +(2.55081 + 3.19862i) q^{10} +(-0.818505 + 3.58610i) q^{11} +(-0.912735 + 3.99895i) q^{13} +(0.0297231 + 7.17894i) q^{14} +(8.74888 + 10.9707i) q^{16} +(-3.10771 + 1.49659i) q^{17} +5.74138 q^{19} +(-7.28481 + 3.50818i) q^{20} +(-8.99239 - 4.33051i) q^{22} +(3.61387 + 1.74035i) q^{23} +(0.606734 + 2.65827i) q^{25} +(-10.0276 - 4.82905i) q^{26} +(-13.8453 - 3.09984i) q^{28} +(5.37505 - 2.58849i) q^{29} -3.17733 q^{31} +(-17.8633 + 8.60250i) q^{32} +(-2.08265 - 9.12469i) q^{34} +(1.71594 - 3.60126i) q^{35} +(0.851904 - 0.410256i) q^{37} +(-3.46659 + 15.1881i) q^{38} +(-3.06121 - 13.4120i) q^{40} +(0.694334 - 0.870667i) q^{41} +(4.96092 + 6.22080i) q^{43} +(12.2985 - 15.4219i) q^{44} +(-6.78590 + 8.50925i) q^{46} +(0.237680 - 1.04134i) q^{47} +(6.28142 - 3.08931i) q^{49} -7.39848 q^{50} +(13.7144 - 17.1973i) q^{52} +(2.81909 + 1.35760i) q^{53} +(3.45791 + 4.33609i) q^{55} +(10.3838 - 21.7925i) q^{56} +(3.60213 + 15.7819i) q^{58} +(-4.89078 - 6.13285i) q^{59} +(-3.90279 + 1.87949i) q^{61} +(1.91844 - 8.40522i) q^{62} +(-5.72630 - 25.0886i) q^{64} +(3.85600 + 4.83528i) q^{65} -6.17301 q^{67} +18.4971 q^{68} +(8.49062 + 6.71372i) q^{70} +(-3.76309 - 1.81221i) q^{71} +(0.253225 + 1.10945i) q^{73} +(0.570909 + 2.50132i) q^{74} +(-27.7396 - 13.3587i) q^{76} +(0.0402930 + 9.73185i) q^{77} -15.6480 q^{79} +21.1572 q^{80} +(1.88401 + 2.36247i) q^{82} +(-2.63339 - 11.5376i) q^{83} +(-1.15727 + 5.07035i) q^{85} +(-19.4517 + 9.36745i) q^{86} +(20.9251 + 26.2392i) q^{88} +(2.12191 + 9.29669i) q^{89} +(0.0449317 + 10.8522i) q^{91} +(-13.4112 - 16.8171i) q^{92} +(2.61124 + 1.25751i) q^{94} +(5.39735 - 6.76806i) q^{95} -3.94450 q^{97} +(4.37972 + 18.4820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

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 $

$2$	−0.603790	+	2.64538i	−0.426944	+	1.87056i	0.0617228	+	0.998093i	$0.480341\pi$
$2$	−0.603790	+	2.64538i	−0.426944	+	1.87056i	−0.488667	+	0.872471i	$0.662517\pi$
$3$		0			0
$3$		0			0
$4$	−4.83152	−	2.32674i	−2.41576	−	1.16337i
$5$	0.940078	−	1.17882i	0.420416	−	0.527184i	−0.525849	−	0.850578i	$-0.676252\pi$
$5$	0.940078	−	1.17882i	0.420416	−	0.527184i	0.946265	+	0.323393i	$0.104824\pi$
$6$		0			0
$7$	2.57696	−	0.599410i	0.973998	−	0.226556i
$7$	2.57696	−	0.599410i	0.973998	−	0.226556i
$8$	5.68875	−	7.13347i	2.01128	−	2.52206i
$9$		0			0
$10$	2.55081	+	3.19862i	0.806638	+	1.01149i
$11$	−0.818505	+	3.58610i	−0.246788	+	1.08125i	0.687906	+	0.725799i	$0.258530\pi$
$11$	−0.818505	+	3.58610i	−0.246788	+	1.08125i	−0.934695	+	0.355451i	$0.884327\pi$
$12$		0			0
$13$	−0.912735	+	3.99895i	−0.253147	+	1.10911i	0.675270	+	0.737570i	$0.264027\pi$
$13$	−0.912735	+	3.99895i	−0.253147	+	1.10911i	−0.928417	+	0.371539i	$0.878830\pi$
$14$	0.0297231	+	7.17894i	0.00794383	+	1.91865i
$15$		0			0
$16$	8.74888	+	10.9707i	2.18722	+	2.74269i
$17$	−3.10771	+	1.49659i	−0.753731	+	0.362978i	−0.770968	−	0.636874i	$-0.780227\pi$
$17$	−3.10771	+	1.49659i	−0.753731	+	0.362978i	0.0172374	+	0.999851i	$0.494513\pi$
$18$		0			0
$19$	5.74138			1.31716			0.658582	−	0.752509i	$-0.271157\pi$
$19$	5.74138			1.31716			0.658582	+	0.752509i	$0.271157\pi$
$20$	−7.28481	+	3.50818i	−1.62893	+	0.784453i
$21$		0			0
$22$	−8.99239	−	4.33051i	−1.91718	−	0.923267i
$23$	3.61387	+	1.74035i	0.753544	+	0.362888i	0.770895	−	0.636962i	$-0.219809\pi$
$23$	3.61387	+	1.74035i	0.753544	+	0.362888i	−0.0173513	+	0.999849i	$0.505523\pi$
$24$		0			0
$25$	0.606734	+	2.65827i	0.121347	+	0.531655i
$26$	−10.0276	−	4.82905i	−1.96658	−	0.947055i
$27$		0			0
$28$	−13.8453	−	3.09984i	−2.61651	−	0.585815i
$29$	5.37505	−	2.58849i	0.998122	−	0.480670i	0.137822	−	0.990457i	$-0.455990\pi$
$29$	5.37505	−	2.58849i	0.998122	−	0.480670i	0.860301	+	0.509787i	$0.170276\pi$
$30$		0			0
$31$	−3.17733			−0.570665			−0.285332	−	0.958429i	$-0.592104\pi$
$31$	−3.17733			−0.570665			−0.285332	+	0.958429i	$0.592104\pi$
$32$	−17.8633	+	8.60250i	−3.15781	+	1.52072i
$33$		0			0
$34$	−2.08265	−	9.12469i	−0.357172	−	1.56487i
$35$	1.71594	−	3.60126i	0.290048	−	0.608724i
$36$		0			0
$37$	0.851904	−	0.410256i	0.140052	−	0.0674456i	−0.362545	−	0.931966i	$-0.618092\pi$
$37$	0.851904	−	0.410256i	0.140052	−	0.0674456i	0.502597	+	0.864521i	$0.332378\pi$
$38$	−3.46659	+	15.1881i	−0.562355	+	2.46384i
$39$		0			0
$40$	−3.06121	−	13.4120i	−0.484020	−	2.12063i
$41$	0.694334	−	0.870667i	0.108437	−	0.135975i	−0.724651	−	0.689116i	$-0.757999\pi$
$41$	0.694334	−	0.870667i	0.108437	−	0.135975i	0.833088	+	0.553140i	$0.186571\pi$
$42$		0			0
$43$	4.96092	+	6.22080i	0.756533	+	0.948663i	0.999773	−	0.0213036i	$-0.00678165\pi$
$43$	4.96092	+	6.22080i	0.756533	+	0.948663i	−0.243240	+	0.969966i	$0.578210\pi$
$44$	12.2985	−	15.4219i	1.85407	−	2.32494i
$45$		0			0
$46$	−6.78590	+	8.50925i	−1.00053	+	1.25462i
$47$	0.237680	−	1.04134i	0.0346692	−	0.151896i	−0.954631	−	0.297792i	$-0.903750\pi$
$47$	0.237680	−	1.04134i	0.0346692	−	0.151896i	0.989300	+	0.145897i	$0.0466068\pi$
$48$		0			0
$49$	6.28142	−	3.08931i	0.897345	−	0.441329i
$50$	−7.39848			−1.04630
$51$		0			0
$52$	13.7144	−	17.1973i	1.90185	−	2.38484i
$53$	2.81909	+	1.35760i	0.387231	+	0.186481i	0.617362	−	0.786679i	$-0.288201\pi$
$53$	2.81909	+	1.35760i	0.387231	+	0.186481i	−0.230131	+	0.973160i	$0.573916\pi$
$54$		0			0
$55$	3.45791	+	4.33609i	0.466265	+	0.584678i
$56$	10.3838	−	21.7925i	1.38759	−	2.91215i
$57$		0			0
$58$	3.60213	+	15.7819i	0.472982	+	2.07227i
$59$	−4.89078	−	6.13285i	−0.636726	−	0.798429i	0.353864	−	0.935297i	$-0.384868\pi$
$59$	−4.89078	−	6.13285i	−0.636726	−	0.798429i	−0.990589	+	0.136868i	$0.956296\pi$
$60$		0			0
$61$	−3.90279	+	1.87949i	−0.499702	+	0.240644i	−0.666717	−	0.745311i	$-0.732301\pi$
$61$	−3.90279	+	1.87949i	−0.499702	+	0.240644i	0.167016	+	0.985954i	$0.446587\pi$
$62$	1.91844	−	8.40522i	0.243642	−	1.06746i
$63$		0			0
$64$	−5.72630	−	25.0886i	−0.715788	−	3.13607i
$65$	3.85600	+	4.83528i	0.478278	+	0.599742i
$66$		0			0
$67$	−6.17301			−0.754153			−0.377077	−	0.926182i	$-0.623071\pi$
$67$	−6.17301			−0.754153			−0.377077	+	0.926182i	$0.623071\pi$
$68$	18.4971			2.24311
$69$		0			0
$70$	8.49062	+	6.71372i	1.01482	+	0.802444i
$71$	−3.76309	−	1.81221i	−0.446597	−	0.215070i	0.197048	−	0.980394i	$-0.436864\pi$
$71$	−3.76309	−	1.81221i	−0.446597	−	0.215070i	−0.643645	+	0.765324i	$0.722579\pi$
$72$		0			0
$73$	0.253225	+	1.10945i	0.0296378	+	0.129852i	0.987583	−	0.157101i	$-0.0502149\pi$
$73$	0.253225	+	1.10945i	0.0296378	+	0.129852i	−0.957945	+	0.286953i	$0.907358\pi$
$74$	0.570909	+	2.50132i	0.0663668	+	0.290772i
$75$		0			0
$76$	−27.7396	−	13.3587i	−3.18195	−	1.53235i
$77$	0.0402930	+	9.73185i	0.00459181	+	1.10905i
$78$		0			0
$79$	−15.6480			−1.76053			−0.880266	−	0.474480i	$-0.842636\pi$
$79$	−15.6480			−1.76053			−0.880266	+	0.474480i	$0.842636\pi$
$80$	21.1572			2.36544
$81$		0			0
$82$	1.88401	+	2.36247i	0.208054	+	0.260892i
$83$	−2.63339	−	11.5376i	−0.289052	−	1.26642i	−0.885829	−	0.464012i	$-0.846409\pi$
$83$	−2.63339	−	11.5376i	−0.289052	−	1.26642i	0.596777	−	0.802407i	$-0.296448\pi$
$84$		0			0
$85$	−1.15727	+	5.07035i	−0.125524	+	0.549956i
$86$	−19.4517	+	9.36745i	−2.09753	+	1.01012i
$87$		0			0
$88$	20.9251	+	26.2392i	2.23062	+	2.79711i
$89$	2.12191	+	9.29669i	0.224922	+	0.985447i	0.953715	+	0.300713i	$0.0972246\pi$
$89$	2.12191	+	9.29669i	0.224922	+	0.985447i	−0.728793	+	0.684734i	$0.759918\pi$
$90$		0			0
$91$	0.0449317	+	10.8522i	0.00471012	+	1.13762i
$92$	−13.4112	−	16.8171i	−1.39821	−	1.75330i
$93$		0			0
$94$	2.61124	+	1.25751i	0.269329	+	0.129702i
$95$	5.39735	−	6.76806i	0.553756	−	0.694388i
$96$		0			0
$97$	−3.94450			−0.400503			−0.200252	−	0.979745i	$-0.564176\pi$
$97$	−3.94450			−0.400503			−0.200252	+	0.979745i	$0.564176\pi$
$98$	4.37972	+	18.4820i	0.442419	+	1.86696i
$99$		0			0
$100$	3.25366	−	14.2552i	0.325366	−	1.42552i
$101$	10.1710	−	12.7540i	1.01205	−	1.26907i	0.0492742	−	0.998785i	$-0.484309\pi$
$101$	10.1710	−	12.7540i	1.01205	−	1.26907i	0.962779	−	0.270289i	$-0.0871194\pi$
$102$		0			0
$103$	11.7526	−	14.7373i	1.15802	−	1.45211i	0.288994	−	0.957331i	$-0.406679\pi$
$103$	11.7526	−	14.7373i	1.15802	−	1.45211i	0.869021	−	0.494774i	$-0.164749\pi$
$104$	23.3341	+	29.2600i	2.28810	+	2.86918i
$105$		0			0
$106$	−5.29350	+	6.63784i	−0.514150	+	0.644724i
$107$	1.15160	+	5.04550i	0.111330	+	0.487767i	0.999596	+	0.0284376i	$0.00905318\pi$
$107$	1.15160	+	5.04550i	0.111330	+	0.487767i	−0.888266	+	0.459330i	$0.848090\pi$
$108$		0			0
$109$	3.61924	−	15.8569i	0.346660	−	1.51882i	−0.438049	−	0.898951i	$-0.644330\pi$
$109$	3.61924	−	15.8569i	0.346660	−	1.51882i	0.784708	−	0.619865i	$-0.212813\pi$
$110$	−13.5584	+	6.52940i	−1.29275	+	0.622554i
$111$		0			0
$112$	29.1215	+	23.0270i	2.75172	+	2.17585i
$113$	2.72593	+	11.9431i	0.256434	+	1.12351i	0.925033	+	0.379888i	$0.124037\pi$
$113$	2.72593	+	11.9431i	0.256434	+	1.12351i	−0.668598	+	0.743624i	$0.733105\pi$
$114$		0			0
$115$	5.44888	−	2.62404i	0.508111	−	0.244693i
$116$	−31.9924			−2.97042
$117$		0			0
$118$	19.1767	−	9.23501i	1.76536	−	0.850152i
$119$	−7.11136	+	5.71945i	−0.651898	+	0.524301i
$120$		0			0
$121$	−2.27953	−	1.09776i	−0.207230	−	0.0997966i
$122$	−2.61548	−	11.4592i	−0.236795	−	1.03747i
$123$		0			0
$124$	15.3513	+	7.39280i	1.37859	+	0.663893i
$125$	10.4963	+	5.05473i	0.938814	+	0.452109i
$126$		0			0
$127$	−0.845435	+	0.407140i	−0.0750202	+	0.0361278i	−0.471018	−	0.882124i	$-0.656113\pi$
$127$	−0.845435	+	0.407140i	−0.0750202	+	0.0361278i	0.395997	+	0.918252i	$0.370399\pi$
$128$	30.1728			2.66692
$129$		0			0
$130$	−15.1193	+	7.28109i	−1.32605	+	0.638594i
$131$	−0.930986	−	1.16742i	−0.0813406	−	0.101998i	0.739496	−	0.673161i	$-0.235064\pi$
$131$	−0.930986	−	1.16742i	−0.0813406	−	0.101998i	−0.820837	+	0.571163i	$0.806492\pi$
$132$		0			0
$133$	14.7953	−	3.44144i	1.28292	−	0.298411i
$134$	3.72720	−	16.3299i	0.321981	−	1.41069i
$135$		0			0
$136$	−7.00309	+	30.6825i	−0.600510	+	2.63100i
$137$	6.71757	+	8.42357i	0.573921	+	0.719674i	0.981063	−	0.193691i	$-0.0620459\pi$
$137$	6.71757	+	8.42357i	0.573921	+	0.719674i	−0.407142	+	0.913365i	$0.633475\pi$
$138$		0			0
$139$	−7.52026	+	9.43011i	−0.637860	+	0.799852i	−0.990734	−	0.135820i	$-0.956633\pi$
$139$	−7.52026	+	9.43011i	−0.637860	+	0.799852i	0.352873	+	0.935671i	$0.385205\pi$
$140$	−16.6698	+	13.4070i	−1.40886	+	1.13310i
$141$		0			0
$142$	7.06610	−	8.86061i	0.592974	−	0.743566i
$143$	−13.5936	−	6.54632i	−1.13675	−	0.547431i
$144$		0			0
$145$	2.00160	−	8.76960i	0.166224	−	0.728276i
$146$	−3.08781			−0.255549
$147$		0			0
$148$	−5.07055			−0.416796
$149$	1.03745	−	4.54536i	0.0849911	−	0.372370i	−0.914489	−	0.404611i	$-0.867407\pi$
$149$	1.03745	−	4.54536i	0.0849911	−	0.372370i	0.999480	+	0.0322404i	$0.0102642\pi$
$150$		0			0
$151$	−6.32107	−	3.04407i	−0.514401	−	0.247723i	0.158628	−	0.987338i	$-0.449293\pi$
$151$	−6.32107	−	3.04407i	−0.514401	−	0.247723i	−0.673029	+	0.739616i	$0.735007\pi$
$152$	32.6613	−	40.9560i	2.64918	−	3.32197i
$153$		0			0
$154$	−25.7687	−	5.76941i	−2.07650	−	0.464912i
$155$	−2.98693	+	3.74550i	−0.239916	+	0.300846i
$156$		0			0
$157$	−6.17167	−	7.73903i	−0.492553	−	0.617642i	0.471978	−	0.881610i	$-0.343540\pi$
$157$	−6.17167	−	7.73903i	−0.492553	−	0.617642i	−0.964531	+	0.263968i	$0.914969\pi$
$158$	9.44808	−	41.3947i	0.751649	−	3.29319i
$159$		0			0
$160$	−6.65206	+	29.1446i	−0.525892	+	2.30408i
$161$	10.3560	+	2.31861i	0.816165	+	0.182732i
$162$		0			0
$163$	−7.03348	−	8.81971i	−0.550905	−	0.690813i	0.425943	−	0.904750i	$-0.359943\pi$
$163$	−7.03348	−	8.81971i	−0.550905	−	0.690813i	−0.976847	+	0.213937i	$0.931371\pi$
$164$	−5.38050	+	2.59111i	−0.420146	+	0.202332i
$165$		0			0
$166$	32.1114			2.49233
$167$	12.0470	−	5.80152i	0.932223	−	0.448935i	0.0948039	−	0.995496i	$-0.469778\pi$
$167$	12.0470	−	5.80152i	0.932223	−	0.448935i	0.837419	+	0.546561i	$0.184063\pi$
$168$		0			0
$169$	−3.44594	−	1.65948i	−0.265072	−	0.127652i
$170$	−12.7142	−	6.12285i	−0.975137	−	0.469601i
$171$		0			0
$172$	−9.49462	−	41.5986i	−0.723958	−	3.17187i
$173$	−10.0008	−	4.81615i	−0.760350	−	0.366165i	0.0131897	−	0.999913i	$-0.495801\pi$
$173$	−10.0008	−	4.81615i	−0.760350	−	0.366165i	−0.773540	+	0.633748i	$0.781516\pi$
$174$		0			0
$175$	3.15692	+	6.48658i	0.238641	+	0.490339i
$176$	−46.5032	+	22.3948i	−3.50531	+	1.68807i
$177$		0			0
$178$	−25.8744			−1.93937
$179$	1.33233	−	0.641618i	0.0995833	−	0.0479568i	−0.383429	−	0.923570i	$-0.625257\pi$
$179$	1.33233	−	0.641618i	0.0995833	−	0.0479568i	0.483012	+	0.875614i	$0.339543\pi$
$180$		0			0
$181$	−0.800597	−	3.50764i	−0.0595079	−	0.260721i	0.936419	−	0.350883i	$-0.114119\pi$
$181$	−0.800597	−	3.50764i	−0.0595079	−	0.260721i	−0.995927	+	0.0901622i	$0.971261\pi$
$182$	−28.7354	−	6.43361i	−2.13001	−	0.476891i
$183$		0			0
$184$	32.9731	−	15.8790i	2.43081	−	1.17062i
$185$	0.317239	−	1.38991i	0.0233239	−	0.102189i
$186$		0			0
$187$	−2.82327	−	12.3695i	−0.206458	−	0.904550i
$188$	−3.57129	+	4.47825i	−0.260463	+	0.326610i
$189$		0			0
$190$	14.6452	+	18.3645i	1.06247	+	1.33230i
$191$	−5.59057	+	7.01035i	−0.404519	+	0.507251i	−0.941810	−	0.336146i	$-0.890876\pi$
$191$	−5.59057	+	7.01035i	−0.404519	+	0.507251i	0.537291	+	0.843397i	$0.319448\pi$
$192$		0			0
$193$	11.2221	−	14.0721i	0.807784	−	1.01293i	−0.191720	−	0.981450i	$-0.561407\pi$
$193$	11.2221	−	14.0721i	0.807784	−	1.01293i	0.999504	−	0.0314797i	$-0.0100219\pi$
$194$	2.38165	−	10.4347i	0.170992	−	0.749167i
$195$		0			0
$196$	−37.5368	+	0.310834i	−2.68120	+	0.0222024i
$197$	−18.5560			−1.32206			−0.661030	−	0.750360i	$-0.729880\pi$
$197$	−18.5560			−1.32206			−0.661030	+	0.750360i	$0.729880\pi$
$198$		0			0
$199$	−2.74512	+	3.44227i	−0.194596	+	0.244016i	−0.869551	−	0.493843i	$-0.835592\pi$
$199$	−2.74512	+	3.44227i	−0.194596	+	0.244016i	0.674955	+	0.737859i	$0.264163\pi$
$200$	22.4143	+	10.7941i	1.58493	+	0.763261i
$201$		0			0
$202$	27.5981	+	34.6069i	1.94180	+	2.43493i
$203$	12.2997	−	9.89228i	0.863271	−	0.694302i
$204$		0			0
$205$	−0.373632	−	1.63699i	−0.0260956	−	0.114332i
$206$	31.8895	+	39.9882i	2.22185	+	2.78611i
$207$		0			0
$208$	−51.8569	+	24.9730i	−3.59563	+	1.73156i
$209$	−4.69935	+	20.5892i	−0.325061	+	1.42418i
$210$		0			0
$211$	−3.48021	−	15.2478i	−0.239588	−	1.04970i	−0.941387	−	0.337328i	$-0.890477\pi$
$211$	−3.48021	−	15.2478i	−0.239588	−	1.04970i	0.701800	−	0.712374i	$-0.252380\pi$
$212$	−10.4617	−	13.1185i	−0.718512	−	0.900985i
$213$		0			0
$214$	−14.0426			−0.959931
$215$	11.9969			0.818179
$216$		0			0
$217$	−8.18783	+	1.90452i	−0.555826	+	0.129287i
$218$	39.7622	+	19.1485i	2.69304	+	1.29690i
$219$		0			0
$220$	−6.61804	−	28.9955i	−0.446188	−	1.95488i
$221$	−3.14829	−	13.7936i	−0.211777	−	0.927857i
$222$		0			0
$223$	17.8407	+	8.59161i	1.19470	+	0.575337i	0.922160	−	0.386808i	$-0.126422\pi$
$223$	17.8407	+	8.59161i	1.19470	+	0.575337i	0.272539	+	0.962145i	$0.412137\pi$
$224$	−40.8765	+	32.8757i	−2.73117	+	2.19660i
$225$		0			0
$226$	−33.2399			−2.21108
$227$	−26.3247			−1.74723			−0.873617	−	0.486614i	$-0.838232\pi$
$227$	−26.3247			−1.74723			−0.873617	+	0.486614i	$0.838232\pi$
$228$		0			0
$229$	4.37598	+	5.48731i	0.289173	+	0.362611i	0.905105	−	0.425188i	$-0.139792\pi$
$229$	4.37598	+	5.48731i	0.289173	+	0.362611i	−0.615932	+	0.787799i	$0.711221\pi$
$230$	3.65160	+	15.9987i	0.240779	+	1.05492i
$231$		0			0
$232$	12.1124	−	53.0681i	0.795221	−	3.48409i
$233$	11.1777	−	5.38291i	0.732278	−	0.352646i	−0.0303019	−	0.999541i	$-0.509647\pi$
$233$	11.1777	−	5.38291i	0.732278	−	0.352646i	0.762580	+	0.646894i	$0.223933\pi$
$234$		0			0
$235$	−1.00412	−	1.25913i	−0.0655015	−	0.0821363i
$236$	9.36039	+	41.0105i	0.609309	+	2.66956i
$237$		0			0
$238$	−10.8363	−	22.2656i	−0.702415	−	1.44326i
$239$	−1.71031	−	2.14465i	−0.110630	−	0.138726i	0.723433	−	0.690394i	$-0.242563\pi$
$239$	−1.71031	−	2.14465i	−0.110630	−	0.138726i	−0.834064	+	0.551668i	$0.813992\pi$
$240$		0			0
$241$	−8.06716	−	3.88494i	−0.519652	−	0.250251i	0.155624	−	0.987816i	$-0.450261\pi$
$241$	−8.06716	−	3.88494i	−0.519652	−	0.250251i	−0.675276	+	0.737565i	$0.735975\pi$
$242$	4.28035	−	5.36739i	0.275151	−	0.345029i
$243$		0			0
$244$	23.2295			1.48712
$245$	2.26328	−	10.3088i	0.144596	−	0.658608i
$246$		0			0
$247$	−5.24036	+	22.9595i	−0.333436	+	1.46088i
$248$	−18.0750	+	22.6654i	−1.14777	+	1.43925i
$249$		0			0
$250$	−19.7092	+	24.7146i	−1.24652	+	1.56309i
$251$	−12.7176	−	15.9474i	−0.802731	−	1.00659i	−0.999657	−	0.0261741i	$-0.991668\pi$
$251$	−12.7176	−	15.9474i	−0.802731	−	1.00659i	0.196927	−	0.980418i	$-0.436904\pi$
$252$		0			0
$253$	−9.19904	+	11.5352i	−0.578339	+	0.725214i
$254$	−0.566574	−	2.48232i	−0.0355500	−	0.155755i
$255$		0			0
$256$	−6.76541	+	29.6412i	−0.422838	+	1.85257i
$257$	20.2719	−	9.76246i	1.26453	−	0.608965i	0.323160	−	0.946344i	$-0.395255\pi$
$257$	20.2719	−	9.76246i	1.26453	−	0.608965i	0.941369	+	0.337379i	$0.109540\pi$
$258$		0			0
$259$	1.94941	−	1.56785i	0.121130	−	0.0974215i
$260$	−7.37994	−	32.3336i	−0.457684	−	2.00525i
$261$		0			0
$262$	3.65038	−	1.75793i	0.225521	−	0.108605i
$263$	−26.8663			−1.65665			−0.828323	−	0.560251i	$-0.810705\pi$
$263$	−26.8663			−1.65665			−0.828323	+	0.560251i	$0.810705\pi$
$264$		0			0
$265$	4.25053	−	2.04695i	0.261108	−	0.125743i
$266$	0.170652	+	41.2171i	0.0104633	+	2.52718i
$267$		0			0
$268$	29.8250	+	14.3630i	1.82185	+	0.877358i
$269$	−4.57883	−	20.0612i	−0.279176	−	1.22315i	−0.898838	−	0.438282i	$-0.855587\pi$
$269$	−4.57883	−	20.0612i	−0.279176	−	1.22315i	0.619661	−	0.784869i	$-0.287270\pi$
$270$		0			0
$271$	−11.7303	−	5.64901i	−0.712564	−	0.343153i	0.0422358	−	0.999108i	$-0.486552\pi$
$271$	−11.7303	−	5.64901i	−0.712564	−	0.343153i	−0.754800	+	0.655955i	$0.772266\pi$
$272$	−43.6077	−	21.0004i	−2.64411	−	1.27334i
$273$		0			0
$274$	−26.3395	+	12.6844i	−1.59123	+	0.766295i
$275$	−10.0295			−0.604799
$276$		0			0
$277$	−9.34803	+	4.50177i	−0.561669	+	0.270485i	−0.693102	−	0.720840i	$-0.743756\pi$
$277$	−9.34803	+	4.50177i	−0.561669	+	0.270485i	0.131433	+	0.991325i	$0.458042\pi$
$278$	−20.4055	−	25.5877i	−1.22384	−	1.53465i
$279$		0			0
$280$	−15.9279	−	32.7273i	−0.951875	−	1.95583i
$281$	−2.36221	+	10.3495i	−0.140918	+	0.617401i	0.854305	+	0.519772i	$0.173983\pi$
$281$	−2.36221	+	10.3495i	−0.140918	+	0.617401i	−0.995223	+	0.0976292i	$0.968874\pi$
$282$		0			0
$283$	−1.64334	+	7.19992i	−0.0976862	+	0.427991i	−0.999995	−	0.00309871i	$-0.999014\pi$
$283$	−1.64334	+	7.19992i	−0.0976862	+	0.427991i	0.902309	+	0.431090i	$0.141871\pi$
$284$	13.9649	+	17.5115i	0.828666	+	1.03911i
$285$		0			0
$286$	25.5252	−	32.0075i	1.50933	−	1.89264i
$287$	1.26738	−	2.65986i	0.0748112	−	0.157007i
$288$		0			0
$289$	−3.18126	+	3.98917i	−0.187133	+	0.234657i
$290$	21.9904	+	10.5900i	1.29132	+	0.621866i
$291$		0			0
$292$	1.35794	−	5.94953i	0.0794675	−	0.348170i
$293$	18.2874			1.06836			0.534180	−	0.845371i	$-0.320620\pi$
$293$	18.2874			1.06836			0.534180	+	0.845371i	$0.320620\pi$
$294$		0			0
$295$	−11.8272			−0.688609
$296$	1.91973	−	8.41088i	0.111582	−	0.488872i
$297$		0			0
$298$	11.3978	+	5.48888i	0.660256	+	0.317962i
$299$	−10.2581	+	12.8632i	−0.593240	+	0.743899i
$300$		0			0
$301$	16.5129	+	13.0571i	0.951787	+	0.752599i
$302$	11.8693	−	14.8836i	0.683001	−	0.856456i
$303$		0			0
$304$	50.2307	+	62.9873i	2.88093	+	3.61257i
$305$	−1.45335	+	6.36756i	−0.0832188	+	0.364605i
$306$		0			0
$307$	5.08289	−	22.2696i	0.290096	−	1.27099i	−0.594295	−	0.804247i	$-0.702569\pi$
$307$	5.08289	−	22.2696i	0.290096	−	1.27099i	0.884391	−	0.466747i	$-0.154574\pi$
$308$	22.4488	−	47.1134i	1.27914	−	2.68453i
$309$		0			0
$310$	−8.10477	−	10.1631i	−0.460320	−	0.577223i
$311$	12.9585	−	6.24049i	0.734809	−	0.353865i	−0.0287644	−	0.999586i	$-0.509157\pi$
$311$	12.9585	−	6.24049i	0.734809	−	0.353865i	0.763574	+	0.645721i	$0.223443\pi$
$312$		0			0
$313$	1.09155			0.0616978			0.0308489	−	0.999524i	$-0.490179\pi$
$313$	1.09155			0.0616978			0.0308489	+	0.999524i	$0.490179\pi$
$314$	24.1990	−	11.6536i	1.36563	−	0.657653i
$315$		0			0
$316$	75.6034	+	36.4087i	4.25302	+	2.04815i
$317$	4.79637	+	2.30981i	0.269391	+	0.129732i	0.563703	−	0.825978i	$-0.309376\pi$
$317$	4.79637	+	2.30981i	0.269391	+	0.129732i	−0.294312	+	0.955709i	$0.595091\pi$
$318$		0			0
$319$	4.88308	+	21.3942i	0.273400	+	1.19784i
$320$	−34.9581	−	16.8349i	−1.95422	−	0.941101i
$321$		0			0
$322$	−12.3864	+	25.9955i	−0.690269	+	1.44867i
$323$	−17.8426	+	8.59253i	−0.992787	+	0.478101i
$324$		0			0
$325$	−11.1841			−0.620382
$326$	27.5782	−	13.2810i	1.52742	−	0.735564i
$327$		0			0
$328$	−2.26098	−	9.90602i	−0.124842	−	0.546968i
$329$	−0.0117004	−	2.82596i	−0.000645063	−	0.155800i
$330$		0			0
$331$	−9.86716	+	4.75178i	−0.542348	+	0.261181i	−0.684939	−	0.728601i	$-0.740171\pi$
$331$	−9.86716	+	4.75178i	−0.542348	+	0.261181i	0.142590	+	0.989782i	$0.454457\pi$
$332$	−14.1218	+	61.8714i	−0.775032	+	3.39564i
$333$		0			0
$334$	8.07336	+	35.3717i	0.441755	+	1.93545i
$335$	−5.80311	+	7.27687i	−0.317058	+	0.397578i
$336$		0			0
$337$	6.41022	+	8.03816i	0.349187	+	0.437867i	0.925146	−	0.379612i	$-0.123943\pi$
$337$	6.41022	+	8.03816i	0.349187	+	0.437867i	−0.575959	+	0.817479i	$0.695371\pi$
$338$	6.47056	−	8.11383i	0.351952	−	0.441334i
$339$		0			0
$340$	17.3888	−	21.8048i	0.943038	−	1.18253i
$341$	2.60066	−	11.3942i	0.140833	−	0.617032i
$342$		0			0
$343$	14.3352	−	11.7261i	0.774027	−	0.633152i
$344$	72.5973			3.91419
$345$		0			0
$346$	18.7789	−	23.5481i	1.00956	−	1.26595i
$347$	−1.92657	−	0.927785i	−0.103423	−	0.0498061i	0.381457	−	0.924387i	$-0.375423\pi$
$347$	−1.92657	−	0.927785i	−0.103423	−	0.0498061i	−0.484880	+	0.874581i	$0.661137\pi$
$348$		0			0
$349$	9.32327	+	11.6910i	0.499063	+	0.625805i	0.966018	−	0.258476i	$-0.0832203\pi$
$349$	9.32327	+	11.6910i	0.499063	+	0.625805i	−0.466955	+	0.884281i	$0.654649\pi$
$350$	−19.0656	+	4.43472i	−1.01910	+	0.237046i
$351$		0			0
$352$	−16.2283	−	71.1007i	−0.864970	−	3.78968i
$353$	−1.82786	−	2.29206i	−0.0972869	−	0.121994i	0.730805	−	0.682586i	$-0.239145\pi$
$353$	−1.82786	−	2.29206i	−0.0972869	−	0.121994i	−0.828092	+	0.560592i	$0.810573\pi$
$354$		0			0
$355$	−5.67387	+	2.73239i	−0.301138	+	0.145020i
$356$	11.3789	−	49.8542i	0.603081	−	2.64227i
$357$		0			0
$358$	0.892872	+	3.91193i	0.0471898	+	0.206752i
$359$	0.691991	+	0.867730i	0.0365219	+	0.0457970i	0.799757	−	0.600324i	$-0.204962\pi$
$359$	0.691991	+	0.867730i	0.0365219	+	0.0457970i	−0.763235	+	0.646121i	$0.776390\pi$
$360$		0			0
$361$	13.9635			0.734921
$362$	9.76243			0.513102
$363$		0			0
$364$	25.0332	−	52.5373i	1.31210	−	2.75370i
$365$	1.54590	+	0.744464i	0.0809159	+	0.0389670i
$366$		0			0
$367$	−5.12936	−	22.4732i	−0.267751	−	1.17309i	−0.912623	−	0.408802i	$-0.865947\pi$
$367$	−5.12936	−	22.4732i	−0.267751	−	1.17309i	0.644872	−	0.764290i	$-0.276910\pi$
$368$	12.5244	+	54.8730i	0.652879	+	2.86045i
$369$		0			0
$370$	3.48530	+	1.67843i	0.181192	+	0.0872576i
$371$	8.07842	+	1.80869i	0.419411	+	0.0939025i
$372$		0			0
$373$	29.5292			1.52896			0.764481	−	0.644646i	$-0.222995\pi$
$373$	29.5292			1.52896			0.764481	+	0.644646i	$0.222995\pi$
$374$	34.4268			1.78017
$375$		0			0
$376$	−6.07629	−	7.61943i	−0.313361	−	0.392942i
$377$	5.44525	+	23.8572i	0.280444	+	1.22871i
$378$		0			0
$379$	−5.78021	+	25.3248i	−0.296910	+	1.30085i	0.577792	+	0.816184i	$0.303915\pi$
$379$	−5.78021	+	25.3248i	−0.296910	+	1.30085i	−0.874701	+	0.484662i	$0.838943\pi$
$380$	−41.8249	+	20.1418i	−2.14557	+	1.03325i
$381$		0			0
$382$	−15.1695	−	19.0219i	−0.776139	−	0.973247i
$383$	−2.92683	−	12.8233i	−0.149554	−	0.655239i	−0.993009	−	0.118039i	$-0.962339\pi$
$383$	−2.92683	−	12.8233i	−0.149554	−	0.655239i	0.843455	−	0.537200i	$-0.180518\pi$
$384$		0			0
$385$	11.5100	+	9.10120i	0.586603	+	0.463840i
$386$	30.4501	+	38.1832i	1.54987	+	1.94348i
$387$		0			0
$388$	19.0579	+	9.17781i	0.967519	+	0.465933i
$389$	−7.15143	+	8.96761i	−0.362592	+	0.454676i	−0.929345	−	0.369212i	$-0.879628\pi$
$389$	−7.15143	+	8.96761i	−0.362592	+	0.454676i	0.566753	+	0.823887i	$0.308199\pi$
$390$		0			0
$391$	−13.8355			−0.699689
$392$	13.6960	−	62.3826i	0.691750	−	3.15080i
$393$		0			0
$394$	11.2039	−	49.0876i	0.564445	−	2.47300i
$395$	−14.7103	+	18.4461i	−0.740155	+	0.928125i
$396$		0			0
$397$	−15.1184	+	18.9578i	−0.758769	+	0.951466i	−0.999819	−	0.0190469i	$-0.993937\pi$
$397$	−15.1184	+	18.9578i	−0.758769	+	0.951466i	0.241050	+	0.970513i	$0.422508\pi$
$398$	−7.44862	−	9.34028i	−0.373366	−	0.468186i
$399$		0			0
$400$	−23.8550	+	29.9132i	−1.19275	+	1.49566i
$401$	−1.34562	−	5.89556i	−0.0671972	−	0.294410i	0.930152	−	0.367175i	$-0.119675\pi$
$401$	−1.34562	−	5.89556i	−0.0671972	−	0.294410i	−0.997349	+	0.0727647i	$0.976818\pi$
$402$		0			0
$403$	2.90006	−	12.7060i	0.144462	−	0.632930i
$404$	−78.8167	+	37.9561i	−3.92128	+	1.88839i
$405$		0			0
$406$	18.7424	+	38.5102i	0.930168	+	1.91123i
$407$	0.773931	+	3.39081i	0.0383623	+	0.168076i
$408$		0			0
$409$	−14.4128	+	6.94086i	−0.712669	+	0.343203i	−0.754842	−	0.655907i	$-0.772286\pi$
$409$	−14.4128	+	6.94086i	−0.712669	+	0.343203i	0.0421728	+	0.999110i	$0.486572\pi$
$410$	4.55605			0.225007
$411$		0			0
$412$	−91.0725	+	43.8582i	−4.48682	+	2.16074i
$413$	−16.2794	−	12.8725i	−0.801058	−	0.633415i
$414$		0			0
$415$	−16.0764	−	7.74198i	−0.789158	−	0.380039i
$416$	−18.0965	−	79.2861i	−0.887256	−	3.88732i
$417$		0			0
$418$	−51.6288	−	24.8631i	−2.52525	−	1.21609i
$419$	−15.8836	−	7.64912i	−0.775962	−	0.373684i	0.00361199	−	0.999993i	$-0.498850\pi$
$419$	−15.8836	−	7.64912i	−0.775962	−	0.373684i	−0.779574	+	0.626310i	$0.784565\pi$
$420$		0			0
$421$	−7.27554	+	3.50372i	−0.354588	+	0.170761i	−0.602694	−	0.797972i	$-0.705906\pi$
$421$	−7.27554	+	3.50372i	−0.354588	+	0.170761i	0.248106	+	0.968733i	$0.420192\pi$
$422$	42.4375			2.06582
$423$		0			0
$424$	25.7215	−	12.3868i	1.24915	−	0.601557i
$425$	−5.86391	−	7.35311i	−0.284441	−	0.356678i
$426$		0			0
$427$	−8.93075	+	7.18273i	−0.432189	+	0.347597i
$428$	6.17557	−	27.0569i	0.298507	−	1.30785i
$429$		0			0
$430$	−7.24358	+	31.7362i	−0.349316	+	1.53046i
$431$	15.7363	+	19.7327i	0.757992	+	0.950492i	0.999803	−	0.0198315i	$-0.00631296\pi$
$431$	15.7363	+	19.7327i	0.757992	+	0.950492i	−0.241811	+	0.970323i	$0.577742\pi$
$432$		0			0
$433$	21.8944	−	27.4547i	1.05218	−	1.31939i	0.106489	−	0.994314i	$-0.466039\pi$
$433$	21.8944	−	27.4547i	1.05218	−	1.31939i	0.945688	−	0.325074i	$-0.105389\pi$
$434$	−0.0944399	−	22.8098i	−0.00453326	−	1.09491i
$435$		0			0
$436$	−54.3812	+	68.1919i	−2.60439	+	3.26580i
$437$	20.7486	+	9.99201i	0.992541	+	0.477983i
$438$		0			0
$439$	5.60636	−	24.5631i	0.267577	−	1.17233i	−0.645245	−	0.763975i	$-0.723245\pi$
$439$	5.60636	−	24.5631i	0.267577	−	1.17233i	0.912822	−	0.408357i	$-0.133898\pi$
$440$	50.6026			2.41238
$441$		0			0
$442$	38.3901			1.82603
$443$	−3.11831	+	13.6622i	−0.148155	+	0.649111i	0.845242	+	0.534384i	$0.179456\pi$
$443$	−3.11831	+	13.6622i	−0.148155	+	0.649111i	−0.993397	+	0.114727i	$0.963401\pi$
$444$		0			0
$445$	12.9539	+	6.23826i	0.614073	+	0.295722i
$446$	−33.5001	+	42.0077i	−1.58627	+	1.98912i
$447$		0			0
$448$	−29.7948	−	61.2198i	−1.40767	−	2.89236i
$449$	−13.6981	+	17.1769i	−0.646455	+	0.810629i	−0.991794	−	0.127849i	$-0.959193\pi$
$449$	−13.6981	+	17.1769i	−0.646455	+	0.810629i	0.345338	+	0.938478i	$0.387764\pi$
$450$		0			0
$451$	2.55399	+	3.20260i	0.120262	+	0.150804i
$452$	14.6180	−	64.0458i	0.687575	−	3.01246i
$453$		0			0
$454$	15.8946	−	69.6388i	0.745971	−	3.26831i
$455$	12.8351	+	10.1490i	0.601717	+	0.475791i
$456$		0			0
$457$	10.3429	+	12.9696i	0.483820	+	0.606691i	0.962495	−	0.271301i	$-0.0874539\pi$
$457$	10.3429	+	12.9696i	0.483820	+	0.606691i	−0.478674	+	0.877993i	$0.658883\pi$
$458$	−17.1582	+	8.26294i	−0.801748	+	0.386102i
$459$		0			0
$460$	−32.4318			−1.51214
$461$	−11.6424	+	5.60666i	−0.542239	+	0.261128i	−0.684892	−	0.728644i	$-0.740151\pi$
$461$	−11.6424	+	5.60666i	−0.542239	+	0.261128i	0.142654	+	0.989773i	$0.454436\pi$
$462$		0			0
$463$	16.9694	+	8.17201i	0.788633	+	0.379786i	0.784439	−	0.620206i	$-0.212951\pi$
$463$	16.9694	+	8.17201i	0.788633	+	0.379786i	0.00419356	+	0.999991i	$0.498665\pi$
$464$	75.4233	+	36.3220i	3.50144	+	1.68620i
$465$		0			0
$466$	7.49083	+	32.8195i	0.347006	+	1.52033i
$467$	−7.03729	−	3.38898i	−0.325647	−	0.156823i	0.263916	−	0.964546i	$-0.414986\pi$
$467$	−7.03729	−	3.38898i	−0.325647	−	0.156823i	−0.589563	+	0.807722i	$0.700700\pi$
$468$		0			0
$469$	−15.9076	+	3.70016i	−0.734544	+	0.170858i
$470$	3.93714	−	1.89603i	0.181607	−	0.0874572i
$471$		0			0
$472$	−71.5710			−3.29432
$473$	−26.3690	+	12.6986i	−1.21245	+	0.583883i
$474$		0			0
$475$	3.48349	+	15.2622i	0.159834	+	0.700277i
$476$	47.6663	−	11.0874i	2.18478	−	0.508188i
$477$		0			0
$478$	6.70608	−	3.22948i	0.306729	−	0.147713i
$479$	0.383664	−	1.68094i	0.0175300	−	0.0768042i	−0.965406	−	0.260750i	$-0.916030\pi$
$479$	0.383664	−	1.68094i	0.0175300	−	0.0768042i	0.982936	+	0.183946i	$0.0588872\pi$
$480$		0			0
$481$	0.863029	+	3.78118i	0.0393508	+	0.172407i
$482$	15.1480	−	18.9950i	0.689973	−	0.865199i
$483$		0			0
$484$	8.45938	+	10.6077i	0.384517	+	0.482169i
$485$	−3.70813	+	4.64985i	−0.168378	+	0.211139i
$486$		0			0
$487$	16.3860	−	20.5473i	0.742518	−	0.931089i	−0.256856	−	0.966450i	$-0.582687\pi$
$487$	16.3860	−	20.5473i	0.742518	−	0.931089i	0.999375	+	0.0353610i	$0.0112581\pi$
$488$	−8.79477	+	38.5324i	−0.398121	+	1.74428i
$489$		0			0
$490$	25.9042	+	12.2116i	1.17023	+	0.551665i
$491$	9.26747			0.418235			0.209117	−	0.977891i	$-0.432941\pi$
$491$	9.26747			0.418235			0.209117	+	0.977891i	$0.432941\pi$
$492$		0			0
$493$	−12.8302	+	16.0886i	−0.577843	+	0.724592i
$494$	−57.5725	−	27.7255i	−2.59031	−	1.24743i
$495$		0			0
$496$	−27.7980	−	34.8576i	−1.24817	−	1.56515i
$497$	−10.7836	−	2.41435i	−0.483710	−	0.108299i
$498$		0			0
$499$	1.16740	+	5.11472i	0.0522600	+	0.228966i	0.994313	−	0.106498i	$-0.0339639\pi$
$499$	1.16740	+	5.11472i	0.0522600	+	0.228966i	−0.942053	+	0.335464i	$0.891107\pi$
$500$	−38.9519	−	48.8441i	−1.74198	−	2.18437i
$501$		0			0
$502$	49.8657	−	24.0141i	2.22562	−	1.07180i
$503$	−8.79906	+	38.5512i	−0.392330	+	1.71891i	0.264073	+	0.964503i	$0.414934\pi$
$503$	−8.79906	+	38.5512i	−0.392330	+	1.71891i	−0.656404	+	0.754410i	$0.727923\pi$
$504$		0			0
$505$	−5.47318	−	23.9796i	−0.243553	−	1.06708i
$506$	−24.9607	−	31.2998i	−1.10964	−	1.39145i
$507$		0			0
$508$	5.03204			0.223261
$509$	20.5473			0.910741			0.455371	−	0.890302i	$-0.349507\pi$
$509$	20.5473			0.910741			0.455371	+	0.890302i	$0.349507\pi$
$510$		0			0
$511$	1.31757	+	2.70723i	0.0582857	+	0.119761i
$512$	−19.9578	−	9.61115i	−0.882017	−	0.424757i
$513$		0			0
$514$	13.5854	+	59.5214i	0.599225	+	2.62538i
$515$	−6.32425	−	27.7083i	−0.278680	−	1.22098i
$516$		0			0
$517$	3.53982	+	1.70469i	0.155681	+	0.0749721i
$518$	2.97052	+	6.10358i	0.130517	+	0.268176i
$519$		0			0
$520$	56.4282			2.47454
$521$	21.7593			0.953293			0.476647	−	0.879095i	$-0.341852\pi$
$521$	21.7593			0.953293			0.476647	+	0.879095i	$0.341852\pi$
$522$		0			0
$523$	−18.3357	−	22.9922i	−0.801763	−	1.00538i	−0.999683	−	0.0251608i	$-0.991990\pi$
$523$	−18.3357	−	22.9922i	−0.801763	−	1.00538i	0.197921	−	0.980218i	$-0.436581\pi$
$524$	1.78180	+	7.80657i	0.0778382	+	0.341031i
$525$		0			0
$526$	16.2216	−	71.0715i	0.707295	−	3.09886i
$527$	9.87421	−	4.75517i	0.430127	−	0.207138i
$528$		0			0
$529$	−4.30901	−	5.40333i	−0.187348	−	0.234928i
$530$	2.84852	+	12.4802i	0.123732	+	0.542104i
$531$		0			0
$532$	−79.4911	−	17.7974i	−3.44638	−	0.771615i
$533$	2.84801	+	3.57129i	0.123361	+	0.154690i
$534$		0			0
$535$	7.03034	+	3.38563i	0.303948	+	0.146374i
$536$	−35.1167	+	44.0350i	−1.51681	+	1.90202i
$537$		0			0
$538$	55.8340			2.40717
$539$	5.93720	+	25.0544i	0.255733	+	1.07917i
$540$		0			0
$541$	−4.45349	+	19.5120i	−0.191470	+	0.838887i	0.784351	+	0.620317i	$0.212996\pi$
$541$	−4.45349	+	19.5120i	−0.191470	+	0.838887i	−0.975821	+	0.218569i	$0.929861\pi$
$542$	22.0264	−	27.6202i	0.946115	−	1.18639i
$543$		0			0
$544$	42.6394	−	53.4681i	1.82815	−	2.29243i
$545$	−15.2901	−	19.1732i	−0.654955	−	0.821288i
$546$		0			0
$547$	22.3408	−	28.0145i	0.955225	−	1.19781i	−0.0249515	−	0.999689i	$-0.507943\pi$
$547$	22.3408	−	28.0145i	0.955225	−	1.19781i	0.980177	−	0.198126i	$-0.0634854\pi$
$548$	−12.8566	−	56.3286i	−0.549209	−	2.40624i
$549$		0			0
$550$	6.05569	−	26.5317i	0.258215	−	1.13132i
$551$	30.8602	−	14.8615i	1.31469	−	0.633122i
$552$		0			0
$553$	−40.3241	+	9.37953i	−1.71476	+	0.398858i
$554$	−6.26464	−	27.4472i	−0.266159	−	1.16612i
$555$		0			0
$556$	58.2757	−	28.0641i	2.47144	−	1.19018i
$557$	−19.7254			−0.835792			−0.417896	−	0.908495i	$-0.637232\pi$
$557$	−19.7254			−0.835792			−0.417896	+	0.908495i	$0.637232\pi$
$558$		0			0
$559$	−29.4047	+	14.1605i	−1.24369	+	0.598927i
$560$	54.5211	−	12.6818i	2.30394	−	0.535904i
$561$		0			0
$562$	−25.9521	−	12.4979i	−1.09472	−	0.527191i
$563$	5.23698	+	22.9447i	0.220712	+	0.967004i	0.956944	+	0.290274i	$0.0937464\pi$
$563$	5.23698	+	22.9447i	0.220712	+	0.967004i	−0.736231	+	0.676730i	$0.763396\pi$
$564$		0			0
$565$	16.6414	+	8.01405i	0.700107	+	0.337154i
$566$	−18.0543	−	8.69448i	−0.758878	−	0.365456i
$567$		0			0
$568$	−34.3347	+	16.5347i	−1.44065	+	0.693781i
$569$	−23.9687			−1.00482			−0.502409	−	0.864630i	$-0.667553\pi$
$569$	−23.9687			−1.00482			−0.502409	+	0.864630i	$0.667553\pi$
$570$		0			0
$571$	−23.4648	+	11.3000i	−0.981971	+	0.472892i	−0.854783	−	0.518986i	$-0.826310\pi$
$571$	−23.4648	+	11.3000i	−0.981971	+	0.472892i	−0.127189	+	0.991879i	$0.540595\pi$
$572$	50.4460	+	63.2573i	2.10926	+	2.64492i
$573$		0			0
$574$	6.27110	+	4.95870i	0.261751	+	0.206972i
$575$	−2.43367	+	10.6626i	−0.101491	+	0.444661i
$576$		0			0
$577$	5.94586	−	26.0505i	0.247529	−	1.08450i	−0.686452	−	0.727175i	$-0.740833\pi$
$577$	5.94586	−	26.0505i	0.247529	−	1.08450i	0.933981	−	0.357321i	$-0.116310\pi$
$578$	−8.63204	−	10.8242i	−0.359046	−	0.450229i
$579$		0			0
$580$	−30.0753	+	37.7133i	−1.24881	+	1.56596i
$581$	−13.7019	−	28.1535i	−0.568450	−	1.16800i
$582$		0			0
$583$	−7.17593	+	8.99833i	−0.297197	+	0.372673i
$584$	9.35478	+	4.50503i	0.387104	+	0.186419i
$585$		0			0
$586$	−11.0417	+	48.3770i	−0.456130	+	1.99844i
$587$	15.5307			0.641020			0.320510	−	0.947245i	$-0.396146\pi$
$587$	15.5307			0.641020			0.320510	+	0.947245i	$0.396146\pi$
$588$		0			0
$589$	−18.2423			−0.751659
$590$	7.14117	−	31.2875i	0.293997	−	1.28809i
$591$		0			0
$592$	11.9540	+	5.75675i	0.491307	+	0.236601i
$593$	28.6983	−	35.9865i	1.17850	−	1.47779i	0.333718	−	0.942673i	$-0.391697\pi$
$593$	28.6983	−	35.9865i	1.17850	−	1.47779i	0.844779	−	0.535115i	$-0.179732\pi$
$594$		0			0
$595$	0.0569697	+	13.7598i	0.00233553	+	0.564095i
$596$	−15.5883	+	19.5471i	−0.638522	+	0.800681i
$597$		0			0
$598$	−27.8343	−	34.9032i	−1.13823	−	1.42730i
$599$	−1.29531	+	5.67514i	−0.0529250	+	0.231880i	−0.994472	−	0.105002i	$-0.966515\pi$
$599$	−1.29531	+	5.67514i	−0.0529250	+	0.231880i	0.941547	+	0.336882i	$0.109372\pi$
$600$		0			0
$601$	−5.08751	+	22.2898i	−0.207524	+	0.909222i	0.758684	+	0.651459i	$0.225843\pi$
$601$	−5.08751	+	22.2898i	−0.207524	+	0.909222i	−0.966208	+	0.257763i	$0.917015\pi$
$602$	−44.5113	+	35.7990i	−1.81414	+	1.45906i
$603$		0			0
$604$	23.4576	+	29.4149i	0.954477	+	1.19688i
$605$	−3.43700	+	1.65517i	−0.139734	+	0.0672923i
$606$		0			0
$607$	43.5963			1.76952			0.884759	−	0.466049i	$-0.154323\pi$
$607$	43.5963			1.76952			0.884759	+	0.466049i	$0.154323\pi$
$608$	−102.560	+	49.3902i	−4.15935	+	2.00304i
$609$		0			0
$610$	−15.9671	−	7.68933i	−0.646488	−	0.311332i
$611$	3.94734	+	1.90094i	0.159692	+	0.0769038i
$612$		0			0
$613$	4.38549	+	19.2141i	0.177128	+	0.776050i	0.982947	+	0.183888i	$0.0588683\pi$
$613$	4.38549	+	19.2141i	0.177128	+	0.776050i	−0.805819	+	0.592162i	$0.798275\pi$
$614$	55.8425	+	26.8923i	2.25362	+	1.08529i
$615$		0			0
$616$	69.6511	+	55.0747i	2.80632	+	2.21902i
$617$	37.0815	−	17.8575i	1.49285	−	0.718917i	0.503432	−	0.864035i	$-0.332071\pi$
$617$	37.0815	−	17.8575i	1.49285	−	0.718917i	0.989414	+	0.145118i	$0.0463563\pi$
$618$		0			0
$619$	−29.7010			−1.19378			−0.596891	−	0.802322i	$-0.703598\pi$
$619$	−29.7010			−1.19378			−0.596891	+	0.802322i	$0.703598\pi$
$620$	23.1462	−	11.1466i	0.929574	−	0.447659i
$621$		0			0
$622$	8.68422	+	38.0481i	0.348206	+	1.52559i
$623$	11.0406	+	22.6853i	0.442332	+	0.908867i
$624$		0			0
$625$	3.54285	−	1.70615i	0.141714	−	0.0682460i
$626$	−0.659064	+	2.88755i	−0.0263415	+	0.115410i
$627$		0			0
$628$	11.8119	+	51.7511i	0.471344	+	2.06509i
$629$	−2.03349	+	2.54991i	−0.0810804	+	0.101672i
$630$		0			0
$631$	−2.42517	−	3.04107i	−0.0965445	−	0.121063i	0.731212	−	0.682150i	$-0.238955\pi$
$631$	−2.42517	−	3.04107i	−0.0965445	−	0.121063i	−0.827757	+	0.561087i	$0.810383\pi$
$632$	−89.0173	+	111.624i	−3.54092	+	4.44017i
$633$		0			0
$634$	−9.00631	+	11.2936i	−0.357686	+	0.448524i
$635$	−0.314830	+	1.37936i	−0.0124936	+	0.0547382i
$636$		0			0
$637$	6.62072	+	27.9388i	0.262322	+	1.10698i
$638$	−59.5440			−2.35737
$639$		0			0
$640$	28.3647	−	35.5683i	1.12122	−	1.40596i
$641$	41.0215	+	19.7549i	1.62025	+	0.780272i	0.999991	−	0.00412390i	$-0.00131268\pi$
$641$	41.0215	+	19.7549i	1.62025	+	0.780272i	0.620260	+	0.784396i	$0.287027\pi$
$642$		0			0
$643$	11.2353	+	14.0886i	0.443077	+	0.555601i	0.952351	−	0.305003i	$-0.0986575\pi$
$643$	11.2353	+	14.0886i	0.443077	+	0.555601i	−0.509274	+	0.860604i	$0.670086\pi$
$644$	−44.6403	−	35.2980i	−1.75907	−	1.39094i
$645$		0			0
$646$	−11.9573	−	52.3884i	−0.470454	−	2.06119i
$647$	−4.12104	−	5.16762i	−0.162015	−	0.203160i	0.694197	−	0.719785i	$-0.255760\pi$
$647$	−4.12104	−	5.16762i	−0.162015	−	0.203160i	−0.856212	+	0.516625i	$0.827188\pi$
$648$		0			0
$649$	25.9962	−	12.5191i	1.02044	−	0.491417i
$650$	6.75285	−	29.5861i	0.264868	−	1.16046i
$651$		0			0
$652$	13.4613	+	58.9776i	0.527184	+	2.30974i
$653$	0.820121	+	1.02840i	0.0320938	+	0.0402444i	0.797619	−	0.603161i	$-0.206092\pi$
$653$	0.820121	+	1.02840i	0.0320938	+	0.0402444i	−0.765526	+	0.643405i	$0.777521\pi$
$654$		0			0
$655$	−2.25138			−0.0879686
$656$	15.6265			0.610112
$657$		0			0
$658$	7.48281	+	1.67534i	0.291710	+	0.0653114i
$659$	−20.1704	−	9.71354i	−0.785726	−	0.378386i	−0.00240026	−	0.999997i	$-0.500764\pi$
$659$	−20.1704	−	9.71354i	−0.785726	−	0.378386i	−0.783326	+	0.621611i	$0.786478\pi$
$660$		0			0
$661$	−5.67565	−	24.8667i	−0.220757	−	0.967201i	−0.956910	−	0.290385i	$-0.906217\pi$
$661$	−5.67565	−	24.8667i	−0.220757	−	0.967201i	0.736153	−	0.676816i	$-0.236641\pi$
$662$	−6.61254	−	28.9714i	−0.257004	−	1.12601i
$663$		0			0
$664$	−97.2840	−	46.8495i	−3.77535	−	1.81811i
$665$	9.85190	−	20.6762i	0.382040	−	0.801790i
$666$		0			0
$667$	23.9296			0.926559
$668$	−71.7038			−2.77430
$669$		0			0
$670$	−15.7462	−	19.7451i	−0.608329	−	0.762820i
$671$	−3.54558	−	15.5342i	−0.136876	−	0.599691i
$672$		0			0
$673$	−3.85795	+	16.9028i	−0.148713	+	0.651554i	0.844531	+	0.535507i	$0.179879\pi$
$673$	−3.85795	+	16.9028i	−0.148713	+	0.651554i	−0.993244	+	0.116047i	$0.962978\pi$
$674$	−25.1344	+	12.1041i	−0.968141	+	0.466232i
$675$		0			0
$676$	12.7879	+	16.0356i	0.491844	+	0.616753i
$677$	5.27932	+	23.1302i	0.202901	+	0.888967i	0.969159	+	0.246434i	$0.0792590\pi$
$677$	5.27932	+	23.1302i	0.202901	+	0.888967i	−0.766259	+	0.642532i	$0.777884\pi$
$678$		0			0
$679$	−10.1648	+	2.36437i	−0.390089	+	0.0907362i
$680$	29.5857	+	37.0993i	1.13456	+	1.42269i
$681$		0			0
$682$	28.5718	+	13.7594i	1.09407	+	0.526876i
$683$	21.1301	−	26.4963i	0.808521	−	1.01385i	−0.190959	−	0.981598i	$-0.561160\pi$
$683$	21.1301	−	26.4963i	0.808521	−	1.01385i	0.999480	−	0.0322550i	$-0.0102689\pi$
$684$		0			0
$685$	16.2449			0.620686
$686$	22.3646	+	45.0021i	0.853886	+	1.71819i
$687$		0			0
$688$	−24.8443	+	108.850i	−0.947180	+	4.14987i
$689$	−8.00205	+	10.0343i	−0.304854	+	0.382275i
$690$		0			0
$691$	−16.1228	+	20.2174i	−0.613341	+	0.769106i	−0.987391	−	0.158303i	$-0.949398\pi$
$691$	−16.1228	+	20.2174i	−0.613341	+	0.769106i	0.374049	+	0.927409i	$0.377969\pi$
$692$	37.1133	+	46.5387i	1.41084	+	1.76913i
$693$		0			0
$694$	3.61758	−	4.53631i	0.137322	−	0.172196i
$695$	4.04677	+	17.7301i	0.153503	+	0.672540i
$696$		0			0
$697$	−0.854753	+	3.74492i	−0.0323761	+	0.141849i
$698$	−36.5564	+	17.6046i	−1.38368	+	0.666345i
$699$		0			0
$700$	−0.160170	−	38.6853i	−0.00605384	−	1.46217i
$701$	−1.38971	−	6.08872i	−0.0524887	−	0.229968i	0.941879	−	0.335952i	$-0.109058\pi$
$701$	−1.38971	−	6.08872i	−0.0524887	−	0.229968i	−0.994368	+	0.105984i	$0.966201\pi$
$702$		0			0
$703$	4.89111	−	2.35543i	0.184472	−	0.0888369i
$704$	94.6572			3.56753
$705$		0			0
$706$	7.16700	−	3.45144i	0.269734	−	0.129897i
$707$	18.5654	−	38.9632i	0.698222	−	1.46536i
$708$		0			0
$709$	22.3307	+	10.7539i	0.838646	+	0.403871i	0.803351	−	0.595506i	$-0.203049\pi$
$709$	22.3307	+	10.7539i	0.838646	+	0.403871i	0.0352954	+	0.999377i	$0.488763\pi$
$710$	−3.80238	−	16.6593i	−0.142701	−	0.625213i
$711$		0			0
$712$	78.3887	+	37.7500i	2.93774	+	1.41474i
$713$	−11.4824	−	5.52965i	−0.430021	−	0.207087i
$714$		0			0
$715$	−20.4960	+	9.87033i	−0.766505	+	0.369129i
$716$	−7.93007			−0.296361
$717$		0			0
$718$	−2.71329	+	1.30665i	−0.101259	+	0.0487638i
$719$	−30.9154	−	38.7667i	−1.15295	−	1.44575i	−0.874316	−	0.485358i	$-0.838689\pi$
$719$	−30.9154	−	38.7667i	−1.15295	−	1.44575i	−0.278635	−	0.960397i	$-0.589882\pi$
$720$		0			0
$721$	21.4522	−	45.0219i	0.798922	−	1.67670i
$722$	−8.43102	+	36.9387i	−0.313770	+	1.37472i
$723$		0			0
$724$	−4.29326	+	18.8100i	−0.159558	+	0.699069i
$725$	10.1421	+	12.7178i	0.376670	+	0.472329i
$726$		0			0
$727$	29.8883	−	37.4787i	1.10850	−	1.39001i	0.196156	−	0.980573i	$-0.437154\pi$
$727$	29.8883	−	37.4787i	1.10850	−	1.39001i	0.912339	−	0.409436i	$-0.134275\pi$
$728$	77.6697	+	61.4151i	2.87863	+	2.27620i
$729$		0			0
$730$	−2.90279	+	3.63998i	−0.107437	+	0.134722i
$731$	−24.7271	−	11.9080i	−0.914565	−	0.440431i
$732$		0			0
$733$	2.38514	−	10.4500i	0.0880973	−	0.385979i	−0.911587	−	0.411107i	$-0.865142\pi$
$733$	2.38514	−	10.4500i	0.0880973	−	0.385979i	0.999684	+	0.0251279i	$0.00799931\pi$
$734$	62.5472			2.30866
$735$		0			0
$736$	−79.5269			−2.93140
$737$	5.05264	−	22.1371i	0.186116	−	0.815429i
$738$		0			0
$739$	−39.5145	−	19.0292i	−1.45356	−	0.699999i	−0.470354	−	0.882478i	$-0.655874\pi$
$739$	−39.5145	−	19.0292i	−1.45356	−	0.699999i	−0.983210	+	0.182479i	$0.941588\pi$
$740$	−4.76671	+	5.97726i	−0.175228	+	0.219729i
$741$		0			0
$742$	−9.66234	+	20.2784i	−0.354716	+	0.744443i
$743$	−9.95055	+	12.4776i	−0.365050	+	0.457758i	−0.930104	−	0.367295i	$-0.880284\pi$
$743$	−9.95055	+	12.4776i	−0.365050	+	0.457758i	0.565054	+	0.825054i	$0.308855\pi$
$744$		0			0
$745$	−4.38288	−	5.49596i	−0.160576	−	0.201356i
$746$	−17.8294	+	78.1158i	−0.652782	+	2.86002i
$747$		0			0
$748$	−15.1400	+	66.3327i	−0.553573	+	2.42536i
$749$	5.99195	+	12.3118i	0.218941	+	0.449862i
$750$		0			0
$751$	−10.2080	−	12.8005i	−0.372497	−	0.467096i	0.559886	−	0.828570i	$-0.310845\pi$
$751$	−10.2080	−	12.8005i	−0.372497	−	0.467096i	−0.932382	+	0.361474i	$0.882274\pi$
$752$	13.5037	−	6.50306i	0.492431	−	0.237142i
$753$		0			0
$754$	−66.3990			−2.41811
$755$	−9.53070	+	4.58974i	−0.346858	+	0.167038i
$756$		0			0
$757$	−44.8425	−	21.5950i	−1.62983	−	0.784884i	−0.999967	−	0.00817759i	$-0.997397\pi$
$757$	−44.8425	−	21.5950i	−1.62983	−	0.784884i	−0.629862	−	0.776707i	$-0.716889\pi$
$758$	−63.5035	−	30.5817i	−2.30655	−	1.11078i
$759$		0			0
$760$	−17.5756	−	77.0037i	−0.637533	−	2.79322i
$761$	−24.4290	−	11.7644i	−0.885550	−	0.426458i	−0.0649015	−	0.997892i	$-0.520673\pi$
$761$	−24.4290	−	11.7644i	−0.885550	−	0.426458i	−0.820649	+	0.571433i	$0.806388\pi$
$762$		0			0
$763$	−0.178166	−	43.0320i	−0.00645004	−	1.55786i
$764$	43.3222	−	20.8629i	1.56734	−	0.754792i
$765$		0			0
$766$	35.6896			1.28952
$767$	28.9890	−	13.9603i	1.04673	−	0.504079i
$768$		0			0
$769$	−6.86557	−	30.0800i	−0.247579	−	1.08471i	−0.933933	−	0.357447i	$-0.883647\pi$
$769$	−6.86557	−	30.0800i	−0.247579	−	1.08471i	0.686355	−	0.727267i	$-0.259210\pi$
$770$	−31.0257	+	24.9530i	−1.11809	+	0.899245i
$771$		0			0
$772$	−86.9617	+	41.8786i	−3.12982	+	1.50724i
$773$	10.3639	−	45.4071i	0.372762	−	1.63318i	−0.346222	−	0.938153i	$-0.612536\pi$
$773$	10.3639	−	45.4071i	0.372762	−	1.63318i	0.718984	−	0.695026i	$-0.244607\pi$
$774$		0			0
$775$	−1.92779	−	8.44620i	−0.0692483	−	0.303397i
$776$	−22.4393	+	28.1380i	−0.805523	+	1.01009i
$777$		0			0
$778$	−19.4047	−	24.3328i	−0.695694	−	0.872373i
$779$	3.98644	−	4.99883i	0.142829	−	0.179102i
$780$		0			0
$781$	9.57888	−	12.0115i	0.342759	−	0.429807i
$782$	8.35371	−	36.6000i	0.298728	−	1.30881i
$783$		0			0
$784$	88.8473	+	41.8839i	3.17312	+	1.49585i
$785$	−14.9248			−0.532688
$786$		0			0
$787$	−5.71394	+	7.16505i	−0.203680	+	0.255407i	−0.873172	−	0.487413i	$-0.837941\pi$
$787$	−5.71394	+	7.16505i	−0.203680	+	0.255407i	0.669492	+	0.742820i	$0.266512\pi$
$788$	89.6536	+	43.1749i	3.19378	+	1.53804i
$789$		0			0
$790$	−39.9150	−	50.0518i	−1.42011	−	1.78076i
$791$	14.1834	+	29.1429i	0.504304	+	1.03620i
$792$		0			0
$793$	−3.95376	−	17.3226i	−0.140402	−	0.615142i
$794$	−41.0223	−	51.4403i	−1.45583	−	1.82555i
$795$		0			0
$796$	21.2723	−	10.2442i	0.753978	−	0.363097i
$797$	−10.3933	+	45.5361i	−0.368150	+	1.61297i	0.363708	+	0.931513i	$0.381511\pi$
$797$	−10.3933	+	45.5361i	−0.368150	+	1.61297i	−0.731858	+	0.681457i	$0.761347\pi$
$798$		0			0
$799$	0.819829	+	3.59190i	0.0290035	+	0.127072i
$800$	−33.7060	−	42.2660i	−1.19169	−	1.49433i
$801$		0			0
$802$	16.4084			0.579403
$803$	−4.18588			−0.147716
$804$		0			0
$805$	12.4687	−	10.0282i	0.439462	−	0.353446i
$806$	31.8611	+	15.3435i	1.12226	+	0.540451i
$807$		0			0
$808$	−33.1202	−	145.109i	−1.16517	−	5.10492i
$809$	11.0567	+	48.4426i	0.388733	+	1.70315i	0.669027	+	0.743238i	$0.266711\pi$
$809$	11.0567	+	48.4426i	0.388733	+	1.70315i	−0.280294	+	0.959914i	$0.590432\pi$
$810$		0			0
$811$	−8.60197	−	4.14249i	−0.302056	−	0.145462i	0.276716	−	0.960952i	$-0.410754\pi$
$811$	−8.60197	−	4.14249i	−0.302056	−	0.145462i	−0.578772	+	0.815489i	$0.696468\pi$
$812$	−82.4430	+	19.1765i	−2.89318	+	0.672965i
$813$		0			0
$814$	−9.43727			−0.330776
$815$	−17.0089			−0.595795
$816$		0			0
$817$	28.4825	+	35.7160i	0.996478	+	1.24954i
$818$	−9.65885	−	42.3182i	−0.337714	−	1.47962i
$819$		0			0
$820$	−2.00363	+	8.77849i	−0.0699699	+	0.306558i
$821$	20.9014	−	10.0656i	0.729462	−	0.351291i	−0.0320103	−	0.999488i	$-0.510191\pi$
$821$	20.9014	−	10.0656i	0.729462	−	0.351291i	0.761473	+	0.648197i	$0.224477\pi$
$822$		0			0
$823$	27.0786	+	33.9555i	0.943902	+	1.18362i	0.982856	+	0.184375i	$0.0590260\pi$
$823$	27.0786	+	33.9555i	0.943902	+	1.18362i	−0.0389539	+	0.999241i	$0.512403\pi$
$824$	−38.2703	−	167.673i	−1.33321	−	5.84117i
$825$		0			0
$826$	43.8820	−	35.2929i	1.52685	−	1.22800i
$827$	−30.3528	−	38.0612i	−1.05547	−	1.32352i	−0.944071	−	0.329742i	$-0.893038\pi$
$827$	−30.3528	−	38.0612i	−1.05547	−	1.32352i	−0.111399	−	0.993776i	$-0.535533\pi$
$828$		0			0
$829$	26.6355	+	12.8270i	0.925087	+	0.445499i	0.834885	−	0.550425i	$-0.185534\pi$
$829$	26.6355	+	12.8270i	0.925087	+	0.445499i	0.0902027	+	0.995923i	$0.471249\pi$
$830$	30.1872	−	37.8535i	1.04781	−	1.31392i
$831$		0			0
$832$	105.555			3.65945
$833$	−14.8974	+	19.0014i	−0.516164	+	0.658360i
$834$		0			0
$835$	4.48615	−	19.6551i	0.155250	−	0.680193i
$836$	70.6106	−	88.5429i	2.44212	−	3.06232i
$837$		0			0
$838$	29.8251	−	37.3995i	1.03029	−	1.29195i
$839$	5.79797	+	7.27043i	0.200168	+	0.251003i	0.871777	−	0.489903i	$-0.162968\pi$
$839$	5.79797	+	7.27043i	0.200168	+	0.251003i	−0.671609	+	0.740906i	$0.734396\pi$
$840$		0			0
$841$	4.10972	−	5.15342i	0.141714	−	0.177704i
$842$	−4.87575	−	21.3621i	−0.168029	−	0.736185i
$843$		0			0
$844$	−18.6629	+	81.7675i	−0.642404	+	2.81456i
$845$	−5.19567	+	2.50210i	−0.178737	+	0.0860750i
$846$		0			0
$847$	−6.53226	−	1.46252i	−0.224451	−	0.0502527i
$848$	9.76995	+	42.8049i	0.335501	+	1.46993i
$849$		0			0
$850$	22.9923	−	11.0725i	0.788630	−	0.379784i
$851$	3.79266			0.130011
$852$		0			0
$853$	−31.2640	+	15.0559i	−1.07046	+	0.515505i	−0.884254	−	0.467006i	$-0.845333\pi$
$853$	−31.2640	+	15.0559i	−1.07046	+	0.515505i	−0.186203	+	0.982511i	$0.559618\pi$
$854$	−13.6087	−	27.9621i	−0.465681	−	0.956842i
$855$		0			0
$856$	42.5431	+	20.4877i	1.45409	+	0.700255i
$857$	0.646317	+	2.83170i	0.0220778	+	0.0967290i	0.984766	−	0.173882i	$-0.0556313\pi$
$857$	0.646317	+	2.83170i	0.0220778	+	0.0967290i	−0.962689	+	0.270611i	$0.912774\pi$
$858$		0			0
$859$	−34.0970	−	16.4203i	−1.16338	−	0.560252i	−0.250350	−	0.968155i	$-0.580546\pi$
$859$	−34.0970	−	16.4203i	−1.16338	−	0.560252i	−0.913025	+	0.407903i	$0.866260\pi$
$860$	−57.9630	−	27.9135i	−1.97652	−	0.951843i
$861$		0			0
$862$	−61.7019	+	29.7141i	−2.10158	+	1.01207i
$863$	43.9292			1.49537			0.747684	−	0.664055i	$-0.231166\pi$
$863$	43.9292			1.49537			0.747684	+	0.664055i	$0.231166\pi$
$864$		0			0
$865$	−15.0789	+	7.26164i	−0.512700	+	0.246903i
$866$	59.4084	+	74.4958i	2.01878	+	2.53147i
$867$		0			0
$868$	43.9910	+	9.84921i	1.49315	+	0.334304i
$869$	12.8079	−	56.1152i	0.434479	−	1.90358i
$870$		0			0
$871$	5.63432	−	24.6856i	0.190912	−	0.836439i
$872$	−92.5259	−	116.024i	−3.13332	−	3.92906i
$873$		0			0
$874$	−38.9604	+	48.8549i	−1.31786	+	1.65254i
$875$	30.0783	+	6.73427i	1.01683	+	0.227660i
$876$		0			0
$877$	15.7441	−	19.7425i	0.531641	−	0.666656i	−0.441394	−	0.897313i	$-0.645516\pi$
$877$	15.7441	−	19.7425i	0.531641	−	0.666656i	0.973035	+	0.230657i	$0.0740874\pi$
$878$	61.5935	+	29.6619i	2.07868	+	1.00104i
$879$		0			0
$880$	−17.3172	+	75.8718i	−0.583764	+	2.55764i
$881$	−8.16550			−0.275103			−0.137551	−	0.990495i	$-0.543923\pi$
$881$	−8.16550			−0.275103			−0.137551	+	0.990495i	$0.543923\pi$
$882$		0			0
$883$	35.9017			1.20819			0.604095	−	0.796912i	$-0.293535\pi$
$883$	35.9017			1.20819			0.604095	+	0.796912i	$0.293535\pi$
$884$	−16.8830	+	73.9692i	−0.567836	+	2.48785i
$885$		0			0
$886$	−34.2589	−	16.4982i	−1.15095	−	0.554268i
$887$	−29.8176	+	37.3901i	−1.00118	+	1.25544i	−0.0345076	+	0.999404i	$0.510986\pi$
$887$	−29.8176	+	37.3901i	−1.00118	+	1.25544i	−0.966669	+	0.256031i	$0.917585\pi$
$888$		0			0
$889$	−1.93461	+	1.55594i	−0.0648846	+	0.0521847i
$890$	−24.3240	+	30.5013i	−0.815342	+	1.02241i
$891$		0			0
$892$	−66.2071	−	83.0210i	−2.21678	−	2.77975i
$893$	1.36461	−	5.97875i	0.0456650	−	0.200071i
$894$		0			0
$895$	0.496145	−	2.17375i	0.0165843	−	0.0726606i
$896$	77.7539	−	18.0858i	2.59758	−	0.604206i
$897$		0			0
$898$	−37.1686	−	46.6080i	−1.24033	−	1.55533i
$899$	−17.0783	+	8.22447i	−0.569593	+	0.274302i
$900$		0			0
$901$	−10.7927			−0.359556
$902$	−10.0141	+	4.82256i	−0.333435	+	0.160574i
$903$		0			0
$904$	100.703	+	48.4959i	3.34933	+	1.61295i
$905$	−4.88750	−	2.35370i	−0.162466	−	0.0782396i
$906$		0			0
$907$	3.20749	+	14.0529i	0.106503	+	0.466619i	0.999851	+	0.0172545i	$0.00549256\pi$
$907$	3.20749	+	14.0529i	0.106503	+	0.466619i	−0.893348	+	0.449365i	$0.851650\pi$
$908$	127.188	+	61.2507i	4.22090	+	2.03268i
$909$		0			0
$910$	−34.5975	+	27.8257i	−1.14690	+	0.922414i
$911$	−6.07789	+	2.92696i	−0.201369	+	0.0969744i	−0.531851	−	0.846838i	$-0.678503\pi$
$911$	−6.07789	+	2.92696i	−0.201369	+	0.0969744i	0.330481	+	0.943813i	$0.392789\pi$
$912$		0			0
$913$	43.5306			1.44065
$914$	−40.5544	+	19.5300i	−1.34142	+	0.645993i
$915$		0			0
$916$	−8.37511	−	36.6938i	−0.276722	−	1.21240i
$917$	−3.09887	−	2.45035i	−0.102334	−	0.0809176i
$918$		0			0
$919$	−0.201770	+	0.0971674i	−0.00665579	+	0.00320526i	−0.437209	−	0.899360i	$-0.644033\pi$
$919$	−0.201770	+	0.0971674i	−0.00665579	+	0.00320526i	0.430553	+	0.902565i	$0.358319\pi$
$920$	12.2788	−	53.7969i	0.404820	−	1.77363i
$921$		0			0
$922$	−7.80220	−	34.1837i	−0.256952	−	1.12578i
$923$	10.6817	−	13.3944i	0.351591	−	0.440881i
$924$		0			0
$925$	1.60745	+	2.01568i	0.0528526	+	0.0662751i
$926$	−31.8640	+	39.9562i	−1.04712	+	1.31304i
$927$		0			0
$928$	−73.7485	+	92.4777i	−2.42091	+	3.03573i
$929$	0.445181	−	1.95047i	0.0146059	−	0.0639927i	−0.967100	−	0.254397i	$-0.918123\pi$
$929$	0.445181	−	1.95047i	0.0146059	−	0.0639927i	0.981706	+	0.190405i	$0.0609800\pi$
$930$		0			0
$931$	36.0640	−	17.7369i	1.18195	−	0.581303i
$932$	−66.5300			−2.17926
$933$		0			0
$934$	13.2142	−	16.5701i	0.432381	−	0.542189i
$935$	−17.2356	−	8.30021i	−0.563663	−	0.271446i
$936$		0			0
$937$	−14.0731	−	17.6471i	−0.459749	−	0.576507i	0.496879	−	0.867820i	$-0.334479\pi$
$937$	−14.0731	−	17.6471i	−0.459749	−	0.576507i	−0.956628	+	0.291313i	$0.905908\pi$
$938$	−0.183481	−	44.3157i	−0.00599086	−	1.44696i
$939$		0			0
$940$	1.92177	+	8.41981i	0.0626811	+	0.274624i
$941$	18.3832	+	23.0518i	0.599275	+	0.751467i	0.985265	−	0.171036i	$-0.0547115\pi$
$941$	18.3832	+	23.0518i	0.599275	+	0.751467i	−0.385990	+	0.922503i	$0.626140\pi$
$942$		0			0
$943$	4.02450	−	1.93809i	0.131056	−	0.0631131i
$944$	24.4931	−	107.311i	0.797181	−	3.49268i
$945$		0			0
$946$	−17.6713	−	77.4231i	−0.574544	−	2.51724i
$947$	−16.1963	−	20.3095i	−0.526309	−	0.659971i	0.445626	−	0.895219i	$-0.352981\pi$
$947$	−16.1963	−	20.3095i	−0.526309	−	0.659971i	−0.971935	+	0.235248i	$0.924410\pi$
$948$		0			0
$949$	−4.66777			−0.151522
$950$	−42.4775			−1.37815
$951$		0			0
$952$	0.344745	+	83.2653i	0.0111732	+	2.69864i
$953$	−17.7722	−	8.55866i	−0.575699	−	0.277242i	0.123294	−	0.992370i	$-0.460654\pi$
$953$	−17.7722	−	8.55866i	−0.575699	−	0.277242i	−0.698994	+	0.715128i	$0.746368\pi$
$954$		0			0
$955$	3.00838	+	13.1806i	0.0973487	+	0.426513i
$956$	3.27332	+	14.3414i	0.105867	+	0.463833i
$957$		0			0
$958$	4.21507	+	2.02987i	0.136183	+	0.0655821i
$959$	22.3601	+	17.6806i	0.722044	+	0.570936i
$960$		0			0
$961$	−20.9046			−0.674342
$962$	−10.5237			−0.339299
$963$		0			0
$964$	29.9374	+	37.5403i	0.964219	+	1.20909i
$965$	−6.03879	−	26.4577i	−0.194396	−	0.851703i
$966$		0			0
$967$	−7.26565	+	31.8329i	−0.233647	+	1.02368i	0.712939	+	0.701226i	$0.247364\pi$
$967$	−7.26565	+	31.8329i	−0.233647	+	1.02368i	−0.946586	+	0.322450i	$0.895494\pi$
$968$	−20.7985	+	10.0160i	−0.668490	+	0.321928i
$969$		0			0
$970$	−10.0617	−	12.6169i	−0.323061	−	0.405106i
$971$	−9.75499	−	42.7394i	−0.313053	−	1.37157i	−0.849477	−	0.527625i	$-0.823083\pi$
$971$	−9.75499	−	42.7394i	−0.313053	−	1.37157i	0.536425	−	0.843948i	$-0.319775\pi$
$972$		0			0
$973$	−13.7269	+	28.8087i	−0.440064	+	0.923565i
$974$	44.4618	+	55.7533i	1.42465	+	1.78645i
$975$		0			0
$976$	−54.7644	−	26.3732i	−1.75297	−	0.844184i
$977$	−23.3634	+	29.2968i	−0.747463	+	0.937289i	−0.999537	−	0.0304192i	$-0.990316\pi$
$977$	−23.3634	+	29.2968i	−0.747463	+	0.937289i	0.252074	+	0.967708i	$0.418887\pi$
$978$		0			0
$979$	−35.0757			−1.12102
$980$	−34.9211	+	44.5413i	−1.11551	+	1.42282i
$981$		0			0
$982$	−5.59560	+	24.5159i	−0.178563	+	0.782335i
$983$	−23.8469	+	29.9031i	−0.760598	+	0.953760i	−0.999852	−	0.0171971i	$-0.994526\pi$
$983$	−23.8469	+	29.9031i	−0.760598	+	0.953760i	0.239254	+	0.970957i	$0.423097\pi$
$984$		0			0
$985$	−17.4441	+	21.8742i	−0.555814	+	0.696969i
$986$	−34.8135	−	43.6548i	−1.10869	−	1.39025i
$987$		0			0
$988$	78.7397	−	98.7364i	2.50504	−	3.14122i
$989$	7.10177	+	31.1149i	0.225823	+	0.989396i
$990$		0			0
$991$	−2.77380	+	12.1528i	−0.0881127	+	0.386047i	−0.999685	−	0.0250925i	$-0.992012\pi$
$991$	−2.77380	+	12.1528i	−0.0881127	+	0.386047i	0.911572	+	0.411140i	$0.134869\pi$
$992$	56.7574	−	27.3329i	1.80205	−	0.867821i
$993$		0			0
$994$	12.8979	−	27.0689i	0.409097	−	0.858573i
$995$	1.47719	+	6.47200i	0.0468301	+	0.205176i
$996$		0			0
$997$	12.9762	−	6.24901i	0.410961	−	0.197908i	−0.216969	−	0.976179i	$-0.569617\pi$
$997$	12.9762	−	6.24901i	0.410961	−	0.197908i	0.627929	+	0.778270i	$0.283903\pi$
$998$	−14.2352			−0.450608
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.d.64.1		36
3.2	odd	2		147.2.i.b.64.6	✓	36
49.36	even	7	inner	441.2.u.d.379.1		36
147.92	odd	14		7203.2.a.h.1.1		18
147.104	even	14		7203.2.a.g.1.1		18
147.134	odd	14		147.2.i.b.85.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.64.6	✓	36	3.2	odd	2
147.2.i.b.85.6	yes	36	147.134	odd	14
441.2.u.d.64.1		36	1.1	even	1	trivial
441.2.u.d.379.1		36	49.36	even	7	inner
7203.2.a.g.1.1		18	147.104	even	14
7203.2.a.h.1.1		18	147.92	odd	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.603790 + 2.64538i) q^{2} +(-4.83152 - 2.32674i) q^{4} +(0.940078 - 1.17882i) q^{5} +(2.57696 - 0.599410i) q^{7} +(5.68875 - 7.13347i) q^{8} +O(q^{10})\)	\(q+(-0.603790 + 2.64538i) q^{2} +(-4.83152 - 2.32674i) q^{4} +(0.940078 - 1.17882i) q^{5} +(2.57696 - 0.599410i) q^{7} +(5.68875 - 7.13347i) q^{8} +(2.55081 + 3.19862i) q^{10} +(-0.818505 + 3.58610i) q^{11} +(-0.912735 + 3.99895i) q^{13} +(0.0297231 + 7.17894i) q^{14} +(8.74888 + 10.9707i) q^{16} +(-3.10771 + 1.49659i) q^{17} +5.74138 q^{19} +(-7.28481 + 3.50818i) q^{20} +(-8.99239 - 4.33051i) q^{22} +(3.61387 + 1.74035i) q^{23} +(0.606734 + 2.65827i) q^{25} +(-10.0276 - 4.82905i) q^{26} +(-13.8453 - 3.09984i) q^{28} +(5.37505 - 2.58849i) q^{29} -3.17733 q^{31} +(-17.8633 + 8.60250i) q^{32} +(-2.08265 - 9.12469i) q^{34} +(1.71594 - 3.60126i) q^{35} +(0.851904 - 0.410256i) q^{37} +(-3.46659 + 15.1881i) q^{38} +(-3.06121 - 13.4120i) q^{40} +(0.694334 - 0.870667i) q^{41} +(4.96092 + 6.22080i) q^{43} +(12.2985 - 15.4219i) q^{44} +(-6.78590 + 8.50925i) q^{46} +(0.237680 - 1.04134i) q^{47} +(6.28142 - 3.08931i) q^{49} -7.39848 q^{50} +(13.7144 - 17.1973i) q^{52} +(2.81909 + 1.35760i) q^{53} +(3.45791 + 4.33609i) q^{55} +(10.3838 - 21.7925i) q^{56} +(3.60213 + 15.7819i) q^{58} +(-4.89078 - 6.13285i) q^{59} +(-3.90279 + 1.87949i) q^{61} +(1.91844 - 8.40522i) q^{62} +(-5.72630 - 25.0886i) q^{64} +(3.85600 + 4.83528i) q^{65} -6.17301 q^{67} +18.4971 q^{68} +(8.49062 + 6.71372i) q^{70} +(-3.76309 - 1.81221i) q^{71} +(0.253225 + 1.10945i) q^{73} +(0.570909 + 2.50132i) q^{74} +(-27.7396 - 13.3587i) q^{76} +(0.0402930 + 9.73185i) q^{77} -15.6480 q^{79} +21.1572 q^{80} +(1.88401 + 2.36247i) q^{82} +(-2.63339 - 11.5376i) q^{83} +(-1.15727 + 5.07035i) q^{85} +(-19.4517 + 9.36745i) q^{86} +(20.9251 + 26.2392i) q^{88} +(2.12191 + 9.29669i) q^{89} +(0.0449317 + 10.8522i) q^{91} +(-13.4112 - 16.8171i) q^{92} +(2.61124 + 1.25751i) q^{94} +(5.39735 - 6.76806i) q^{95} -3.94450 q^{97} +(4.37972 + 18.4820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

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