LMFDB - Embedded newform 297.2.t.a.8.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(8,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("297.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.t (of order $30$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			8.10
Character	$\chi$	$=$	297.8
Dual form			297.2.t.a.260.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.281588 + 2.67913i) q^{2} +(-5.14217 + 1.09300i) q^{4} +(-1.43896 - 0.151241i) q^{5} +(-1.07283 + 0.965979i) q^{7} +(-2.71136 - 8.34470i) q^{8} -3.89775i q^{10} +(-2.66871 - 1.96926i) q^{11} +(-1.21080 + 2.71950i) q^{13} +(-2.89008 - 2.60224i) q^{14} +(11.9880 - 5.33739i) q^{16} +(3.35854 + 2.44012i) q^{17} +(-1.19136 + 0.387096i) q^{19} +(7.56469 - 0.795081i) q^{20} +(4.52444 - 7.70435i) q^{22} +(-5.02939 + 2.90372i) q^{23} +(-2.84300 - 0.604299i) q^{25} +(-7.62685 - 2.47811i) q^{26} +(4.46085 - 6.13983i) q^{28} +(0.0651453 + 0.0723511i) q^{29} +(3.73471 + 1.66280i) q^{31} +(8.90112 + 15.4172i) q^{32} +(-5.59169 + 9.68509i) q^{34} +(1.68985 - 1.22775i) q^{35} +(-3.08635 + 9.49880i) q^{37} +(-1.37255 - 3.08281i) q^{38} +(2.63948 + 12.4178i) q^{40} +(3.05835 - 3.39664i) q^{41} +(-1.84140 - 1.06313i) q^{43} +(15.8754 + 7.20937i) q^{44} +(-9.19566 - 12.6567i) q^{46} +(-1.50921 + 7.10026i) q^{47} +(-0.513854 + 4.88899i) q^{49} +(0.818442 - 7.78695i) q^{50} +(3.25372 - 15.3075i) q^{52} +(0.197492 + 0.271824i) q^{53} +(3.54233 + 3.23731i) q^{55} +(10.9696 + 6.33332i) q^{56} +(-0.175494 + 0.194906i) q^{58} +(-0.629292 - 2.96059i) q^{59} +(0.129468 + 0.290790i) q^{61} +(-3.40321 + 10.4740i) q^{62} +(-17.5657 + 12.7622i) q^{64} +(2.15359 - 3.73013i) q^{65} +(-1.71828 - 2.97615i) q^{67} +(-19.9373 - 8.87664i) q^{68} +(3.76515 + 4.18162i) q^{70} +(5.38901 - 7.41734i) q^{71} +(-6.75113 - 2.19358i) q^{73} +(-26.3176 - 5.59399i) q^{74} +(5.70308 - 3.29267i) q^{76} +(4.76533 - 0.465238i) q^{77} +(9.96549 - 1.04742i) q^{79} +(-18.0574 + 5.86722i) q^{80} +(9.96124 + 7.23727i) q^{82} +(-5.44872 + 2.42593i) q^{83} +(-4.46376 - 4.01919i) q^{85} +(2.32976 - 5.23272i) q^{86} +(-9.19707 + 27.6090i) q^{88} +5.11584i q^{89} +(-1.32800 - 4.08716i) q^{91} +(22.6882 - 20.4285i) q^{92} +(-19.4475 - 2.04402i) q^{94} +(1.77286 - 0.376834i) q^{95} +(-0.631450 - 6.00784i) q^{97} -13.2430 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) $ 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.281588	+	2.67913i	0.199113	+	1.89443i	0.402631	+	0.915362i	$0.368096\pi$
$2$	0.281588	+	2.67913i	0.199113	+	1.89443i	−0.203518	+	0.979071i	$0.565238\pi$
$3$		0			0
$3$		0			0
$4$	−5.14217	+	1.09300i	−2.57109	+	0.546501i
$5$	−1.43896	−	0.151241i	−0.643523	−	0.0676370i	−0.222855	−	0.974852i	$-0.571538\pi$
$5$	−1.43896	−	0.151241i	−0.643523	−	0.0676370i	−0.420668	+	0.907215i	$0.638204\pi$
$6$		0			0
$7$	−1.07283	+	0.965979i	−0.405491	+	0.365106i	−0.846493	−	0.532401i	$-0.821290\pi$
$7$	−1.07283	+	0.965979i	−0.405491	+	0.365106i	0.441001	+	0.897506i	$0.354623\pi$
$8$	−2.71136	−	8.34470i	−0.958610	−	2.95030i
$9$		0			0
$10$		−	3.89775i		−	1.23258i
$11$	−2.66871	−	1.96926i	−0.804646	−	0.593755i
$11$	−2.66871	−	1.96926i	−0.804646	−	0.593755i
$12$		0			0
$13$	−1.21080	+	2.71950i	−0.335815	+	0.754253i	0.664163	+	0.747588i	$0.268788\pi$
$13$	−1.21080	+	2.71950i	−0.335815	+	0.754253i	−0.999978	+	0.00666518i	$0.997878\pi$
$14$	−2.89008	−	2.60224i	−0.772407	−	0.695479i
$15$		0			0
$16$	11.9880	−	5.33739i	2.99699	−	1.33435i
$17$	3.35854	+	2.44012i	0.814566	+	0.591817i	0.915151	−	0.403112i	$-0.132071\pi$
$17$	3.35854	+	2.44012i	0.814566	+	0.591817i	−0.100585	+	0.994928i	$0.532071\pi$
$18$		0			0
$19$	−1.19136	+	0.387096i	−0.273317	+	0.0888059i	−0.442468	−	0.896784i	$-0.645897\pi$
$19$	−1.19136	+	0.387096i	−0.273317	+	0.0888059i	0.169152	+	0.985590i	$0.445897\pi$
$20$	7.56469	−	0.795081i	1.69152	−	0.177785i
$21$		0			0
$22$	4.52444	−	7.70435i	0.964613	−	1.64257i
$23$	−5.02939	+	2.90372i	−1.04870	+	0.605467i	−0.922285	−	0.386511i	$-0.873680\pi$
$23$	−5.02939	+	2.90372i	−1.04870	+	0.605467i	−0.126414	+	0.991978i	$0.540347\pi$
$24$		0			0
$25$	−2.84300	−	0.604299i	−0.568601	−	0.120860i
$26$	−7.62685	−	2.47811i	−1.49575	−	0.485998i
$27$		0			0
$28$	4.46085	−	6.13983i	0.843021	−	1.16032i
$29$	0.0651453	+	0.0723511i	0.0120972	+	0.0134353i	0.749163	−	0.662386i	$-0.230456\pi$
$29$	0.0651453	+	0.0723511i	0.0120972	+	0.0134353i	−0.737066	+	0.675821i	$0.763789\pi$
$30$		0			0
$31$	3.73471	+	1.66280i	0.670773	+	0.298647i	0.713721	−	0.700430i	$-0.247008\pi$
$31$	3.73471	+	1.66280i	0.670773	+	0.298647i	−0.0429482	+	0.999077i	$0.513675\pi$
$32$	8.90112	+	15.4172i	1.57351	+	2.72540i
$33$		0			0
$34$	−5.59169	+	9.68509i	−0.958967	+	1.66098i
$35$	1.68985	−	1.22775i	0.285637	−	0.207528i
$36$		0			0
$37$	−3.08635	+	9.49880i	−0.507392	+	1.56159i	0.289319	+	0.957233i	$0.406571\pi$
$37$	−3.08635	+	9.49880i	−0.507392	+	1.56159i	−0.796711	+	0.604360i	$0.793429\pi$
$38$	−1.37255	−	3.08281i	−0.222658	−	0.500098i
$39$		0			0
$40$	2.63948	+	12.4178i	0.417338	+	1.96342i
$41$	3.05835	−	3.39664i	0.477634	−	0.530466i	−0.455385	−	0.890295i	$-0.650498\pi$
$41$	3.05835	−	3.39664i	0.477634	−	0.530466i	0.933018	+	0.359829i	$0.117165\pi$
$42$		0			0
$43$	−1.84140	−	1.06313i	−0.280811	−	0.162126i	0.352980	−	0.935631i	$-0.385168\pi$
$43$	−1.84140	−	1.06313i	−0.280811	−	0.162126i	−0.633790	+	0.773505i	$0.718502\pi$
$44$	15.8754	+	7.20937i	2.39330	+	1.08685i
$45$		0			0
$46$	−9.19566	−	12.6567i	−1.35583	−	1.86614i
$47$	−1.50921	+	7.10026i	−0.220141	+	1.03568i	0.719758	+	0.694225i	$0.244253\pi$
$47$	−1.50921	+	7.10026i	−0.220141	+	1.03568i	−0.939898	+	0.341454i	$0.889080\pi$
$48$		0			0
$49$	−0.513854	+	4.88899i	−0.0734077	+	0.698428i
$50$	0.818442	−	7.78695i	0.115745	−	1.10124i
$51$		0			0
$52$	3.25372	−	15.3075i	0.451209	−	2.12277i
$53$	0.197492	+	0.271824i	0.0271276	+	0.0373379i	0.822365	−	0.568960i	$-0.192654\pi$
$53$	0.197492	+	0.271824i	0.0271276	+	0.0373379i	−0.795238	+	0.606298i	$0.792654\pi$
$54$		0			0
$55$	3.54233	+	3.23731i	0.477648	+	0.436518i
$56$	10.9696	+	6.33332i	1.46588	+	0.846325i
$57$		0			0
$58$	−0.175494	+	0.194906i	−0.0230435	+	0.0255924i
$59$	−0.629292	−	2.96059i	−0.0819268	−	0.385435i	0.918011	−	0.396554i	$-0.129794\pi$
$59$	−0.629292	−	2.96059i	−0.0819268	−	0.385435i	−0.999938	+	0.0111187i	$0.996461\pi$
$60$		0			0
$61$	0.129468	+	0.290790i	0.0165767	+	0.0372319i	0.921644	−	0.388036i	$-0.126846\pi$
$61$	0.129468	+	0.290790i	0.0165767	+	0.0372319i	−0.905067	+	0.425268i	$0.860180\pi$
$62$	−3.40321	+	10.4740i	−0.432208	+	1.33020i
$63$		0			0
$64$	−17.5657	+	12.7622i	−2.19571	+	1.59527i
$65$	2.15359	−	3.73013i	0.267120	−	0.462666i
$66$		0			0
$67$	−1.71828	−	2.97615i	−0.209922	−	0.363595i	0.741768	−	0.670657i	$-0.233988\pi$
$67$	−1.71828	−	2.97615i	−0.209922	−	0.363595i	−0.951690	+	0.307062i	$0.900654\pi$
$68$	−19.9373	−	8.87664i	−2.41775	−	1.07645i
$69$		0			0
$70$	3.76515	+	4.18162i	0.450021	+	0.499799i
$71$	5.38901	−	7.41734i	0.639558	−	0.880276i	−0.359034	−	0.933325i	$-0.616894\pi$
$71$	5.38901	−	7.41734i	0.639558	−	0.880276i	0.998592	+	0.0530483i	$0.0168937\pi$
$72$		0			0
$73$	−6.75113	−	2.19358i	−0.790160	−	0.256739i	−0.113988	−	0.993482i	$-0.536363\pi$
$73$	−6.75113	−	2.19358i	−0.790160	−	0.256739i	−0.676172	+	0.736743i	$0.736363\pi$
$74$	−26.3176	−	5.59399i	−3.05936	−	0.650288i
$75$		0			0
$76$	5.70308	−	3.29267i	0.654188	−	0.377695i
$77$	4.76533	−	0.465238i	0.543060	−	0.0530188i
$78$		0			0
$79$	9.96549	−	1.04742i	1.12121	−	0.117843i	0.474264	−	0.880383i	$-0.342714\pi$
$79$	9.96549	−	1.04742i	1.12121	−	0.117843i	0.646942	+	0.762539i	$0.276048\pi$
$80$	−18.0574	+	5.86722i	−2.01888	+	0.655975i
$81$		0			0
$82$	9.96124	+	7.23727i	1.10004	+	0.799222i
$83$	−5.44872	+	2.42593i	−0.598075	+	0.266280i	−0.683366	−	0.730076i	$-0.739485\pi$
$83$	−5.44872	+	2.42593i	−0.598075	+	0.266280i	0.0852911	+	0.996356i	$0.472818\pi$
$84$		0			0
$85$	−4.46376	−	4.01919i	−0.484163	−	0.435942i
$86$	2.32976	−	5.23272i	0.251224	−	0.564259i
$87$		0			0
$88$	−9.19707	+	27.6090i	−0.980411	+	2.94312i
$89$			5.11584i			0.542278i	0.962540	+	0.271139i	$0.0874004\pi$
$89$			5.11584i			0.542278i	−0.962540	+	0.271139i	$0.912600\pi$
$90$		0			0
$91$	−1.32800	−	4.08716i	−0.139212	−	0.428451i
$92$	22.6882	−	20.4285i	2.36541	−	2.12982i
$93$		0			0
$94$	−19.4475	−	2.04402i	−2.00586	−	0.210824i
$95$	1.77286	−	0.376834i	0.181892	−	0.0386623i
$96$		0			0
$97$	−0.631450	−	6.00784i	−0.0641140	−	0.610004i	−0.978655	−	0.205511i	$-0.934114\pi$
$97$	−0.631450	−	6.00784i	−0.0641140	−	0.610004i	0.914541	−	0.404493i	$-0.132552\pi$
$98$	−13.2430			−1.33774
$99$		0			0
$100$	15.2797			1.52797
$101$	1.21696	+	11.5786i	0.121092	+	1.15211i	0.871246	+	0.490847i	$0.163313\pi$
$101$	1.21696	+	11.5786i	0.121092	+	1.15211i	−0.750154	+	0.661263i	$0.770021\pi$
$102$		0			0
$103$	3.27668	−	0.696481i	0.322861	−	0.0686263i	−0.0436300	−	0.999048i	$-0.513892\pi$
$103$	3.27668	−	0.696481i	0.322861	−	0.0686263i	0.366491	+	0.930421i	$0.380559\pi$
$104$	25.9763	+	2.73022i	2.54719	+	0.267720i
$105$		0			0
$106$	−0.672642	+	0.605650i	−0.0653328	+	0.0588259i
$107$	2.92166	+	8.99195i	0.282448	+	0.869285i	0.987152	+	0.159784i	$0.0510797\pi$
$107$	2.92166	+	8.99195i	0.282448	+	0.869285i	−0.704704	+	0.709501i	$0.748920\pi$
$108$		0			0
$109$		−	4.11325i		−	0.393978i	−0.980406	−	0.196989i	$-0.936884\pi$
$109$		−	4.11325i		−	0.393978i	0.980406	−	0.196989i	$-0.0631163\pi$
$110$	−7.67570	+	10.4020i	−0.731849	+	0.991789i
$111$		0			0
$112$	−7.70523	+	17.3062i	−0.728076	+	1.63529i
$113$	15.0282	+	13.5315i	1.41374	+	1.27293i	0.913377	+	0.407116i	$0.133465\pi$
$113$	15.0282	+	13.5315i	1.41374	+	1.27293i	0.500359	+	0.865818i	$0.333201\pi$
$114$		0			0
$115$	7.67625	−	3.41769i	0.715814	−	0.318701i
$116$	−0.414068	−	0.300838i	−0.0384452	−	0.0279321i
$117$		0			0
$118$	7.75460	−	2.51962i	0.713869	−	0.231950i
$119$	−5.96025	+	0.626447i	−0.546375	+	0.0574263i
$120$		0			0
$121$	3.24402	+	10.5108i	0.294911	+	0.955525i
$122$	−0.742609	+	0.428746i	−0.0672327	+	0.0388168i
$123$		0			0
$124$	−21.0219	−	4.46835i	−1.88783	−	0.401270i
$125$	10.8799	+	3.53510i	0.973131	+	0.316189i
$126$		0			0
$127$	−0.0604870	+	0.0832533i	−0.00536736	+	0.00738753i	−0.811692	−	0.584085i	$-0.801453\pi$
$127$	−0.0604870	+	0.0832533i	−0.00536736	+	0.00738753i	0.806325	+	0.591473i	$0.201453\pi$
$128$	−15.3139	−	17.0078i	−1.35357	−	1.50329i
$129$		0			0
$130$	10.5999	+	4.71940i	0.929676	+	0.413919i
$131$	−7.68267	−	13.3068i	−0.671238	−	1.16262i	−0.977553	−	0.210689i	$-0.932429\pi$
$131$	−7.68267	−	13.3068i	−0.671238	−	1.16262i	0.306315	−	0.951930i	$-0.400904\pi$
$132$		0			0
$133$	0.904197	−	1.56612i	0.0784039	−	0.135799i
$134$	7.48966	−	5.44156i	0.647008	−	0.470079i
$135$		0			0
$136$	11.2559	−	34.6421i	0.965185	−	2.97053i
$137$	1.51448	+	3.40157i	0.129391	+	0.290616i	0.966610	−	0.256250i	$-0.0824872\pi$
$137$	1.51448	+	3.40157i	0.129391	+	0.290616i	−0.837220	+	0.546867i	$0.815821\pi$
$138$		0			0
$139$	−3.53785	−	16.6443i	−0.300077	−	1.41175i	−0.827174	−	0.561945i	$-0.810053\pi$
$139$	−3.53785	−	16.6443i	−0.300077	−	1.41175i	0.527097	−	0.849805i	$-0.323280\pi$
$140$	−7.34758	+	8.16031i	−0.620984	+	0.689672i
$141$		0			0
$142$	21.3895	+	12.3492i	1.79497	+	1.03633i
$143$	8.58668	−	4.87317i	0.718054	−	0.407515i
$144$		0			0
$145$	−0.0827990	−	0.113963i	−0.00687608	−	0.00946412i
$146$	3.97584	−	18.7049i	0.329043	−	1.54803i
$147$		0			0
$148$	5.48832	−	52.2178i	0.451137	−	4.29228i
$149$	1.19705	−	11.3892i	0.0980665	−	0.933040i	−0.829279	−	0.558834i	$-0.811249\pi$
$149$	1.19705	−	11.3892i	0.0980665	−	0.933040i	0.927346	−	0.374206i	$-0.122085\pi$
$150$		0			0
$151$	−0.221010	+	1.03977i	−0.0179855	+	0.0846153i	−0.986225	−	0.165409i	$-0.947105\pi$
$151$	−0.221010	+	1.03977i	−0.0179855	+	0.0846153i	0.968239	+	0.250025i	$0.0804388\pi$
$152$	6.46040	+	8.89198i	0.524008	+	0.721235i
$153$		0			0
$154$	2.58830	+	12.6360i	0.208571	+	1.01823i
$155$	−5.12261	−	2.95754i	−0.411458	−	0.237555i
$156$		0			0
$157$	−0.0571368	+	0.0634569i	−0.00456002	+	0.00506441i	−0.745421	−	0.666595i	$-0.767751\pi$
$157$	−0.0571368	+	0.0634569i	−0.00456002	+	0.00506441i	0.740861	+	0.671659i	$0.234418\pi$
$158$	5.61233	+	26.4039i	0.446493	+	2.10058i
$159$		0			0
$160$	−10.4766	−	23.5309i	−0.828252	−	1.86028i
$161$	2.59074	−	7.97347i	0.204179	−	0.628398i
$162$		0			0
$163$	−2.37021	+	1.72206i	−0.185650	+	0.134882i	−0.676728	−	0.736233i	$-0.736603\pi$
$163$	−2.37021	+	1.72206i	−0.185650	+	0.134882i	0.491079	+	0.871115i	$0.336603\pi$
$164$	−12.0140	+	20.8089i	−0.938136	+	1.62490i
$165$		0			0
$166$	−8.03368	−	13.9147i	−0.623534	−	1.07999i
$167$	−4.06863	−	1.81147i	−0.314840	−	0.140176i	0.243233	−	0.969968i	$-0.421792\pi$
$167$	−4.06863	−	1.81147i	−0.314840	−	0.140176i	−0.558072	+	0.829792i	$0.688459\pi$
$168$		0			0
$169$	2.76906	+	3.07535i	0.213004	+	0.236565i
$170$	9.51100	−	13.0908i	0.729461	−	1.00402i
$171$		0			0
$172$	10.6308	+	3.45415i	0.810590	+	0.263377i
$173$	10.2220	+	2.17276i	0.777166	+	0.165192i	0.579384	−	0.815055i	$-0.303293\pi$
$173$	10.2220	+	2.17276i	0.777166	+	0.165192i	0.197781	+	0.980246i	$0.436626\pi$
$174$		0			0
$175$	3.63380	−	2.09797i	0.274689	−	0.158592i
$176$	−42.5031	−	9.36351i	−3.20379	−	0.705801i
$177$		0			0
$178$	−13.7060	+	1.44056i	−1.02731	+	0.107975i
$179$	−9.58188	+	3.11334i	−0.716183	+	0.232702i	−0.644368	−	0.764716i	$-0.722879\pi$
$179$	−9.58188	+	3.11334i	−0.716183	+	0.232702i	−0.0718157	+	0.997418i	$0.522879\pi$
$180$		0			0
$181$	12.5433	+	9.11327i	0.932339	+	0.677384i	0.946564	−	0.322515i	$-0.104528\pi$
$181$	12.5433	+	9.11327i	0.932339	+	0.677384i	−0.0142256	+	0.999899i	$0.504528\pi$
$182$	10.5761	−	4.70879i	0.783953	−	0.349038i
$183$		0			0
$184$	37.8671	+	34.0957i	2.79160	+	2.51357i
$185$	5.87774	−	13.2016i	0.432140	−	0.970602i
$186$		0			0
$187$	−4.15773	−	13.1258i	−0.304043	−	0.959855i
$188$		−	38.1603i		−	2.78313i
$189$		0			0
$190$	1.50881	+	4.64363i	0.109460	+	0.336884i
$191$	−2.76063	+	2.48568i	−0.199752	+	0.179857i	−0.762936	−	0.646474i	$-0.776243\pi$
$191$	−2.76063	+	2.48568i	−0.199752	+	0.179857i	0.563184	+	0.826331i	$0.309576\pi$
$192$		0			0
$193$	24.8007	+	2.60666i	1.78519	+	0.187631i	0.938692	−	0.344756i	$-0.112038\pi$
$193$	24.8007	+	2.60666i	1.78519	+	0.187631i	0.846501	+	0.532387i	$0.178705\pi$
$194$	15.9180	−	3.38348i	1.14285	−	0.242919i
$195$		0			0
$196$	−2.70136	−	25.7017i	−0.192954	−	1.83583i
$197$	−19.2214			−1.36947			−0.684733	−	0.728794i	$-0.740081\pi$
$197$	−19.2214			−1.36947			−0.684733	+	0.728794i	$0.740081\pi$
$198$		0			0
$199$	−26.0126			−1.84399			−0.921993	−	0.387206i	$-0.873440\pi$
$199$	−26.0126			−1.84399			−0.921993	+	0.387206i	$0.873440\pi$
$200$	2.66571	+	25.3625i	0.188494	+	1.79340i
$201$		0			0
$202$	−30.6778	+	6.52077i	−2.15848	+	0.458800i
$203$	−0.139779	−	0.0146914i	−0.00981059	−	0.00103113i
$204$		0			0
$205$	−4.91455	+	4.42508i	−0.343247	+	0.309061i
$206$	2.78864	+	8.58255i	0.194294	+	0.597975i
$207$		0			0
$208$			39.0638i			2.70859i
$209$	3.94168	+	1.31305i	0.272652	+	0.0908256i
$210$		0			0
$211$	−9.24806	+	20.7715i	−0.636663	+	1.42997i	0.250319	+	0.968163i	$0.419464\pi$
$211$	−9.24806	+	20.7715i	−0.636663	+	1.42997i	−0.886982	+	0.461804i	$0.847202\pi$
$212$	−1.31264	−	1.18191i	−0.0901526	−	0.0811737i
$213$		0			0
$214$	−23.2679	+	10.3596i	−1.59056	+	0.708165i
$215$	2.48891	+	1.80830i	0.169742	+	0.123325i
$216$		0			0
$217$	−5.61293	+	1.82375i	−0.381030	+	0.123804i
$218$	11.0199	−	1.15824i	0.746365	−	0.0784461i
$219$		0			0
$220$	−21.7537	−	12.7750i	−1.46663	−	0.861291i
$221$	−10.7024	+	6.17905i	−0.719923	+	0.415648i
$222$		0			0
$223$	22.2512	+	4.72965i	1.49005	+	0.316721i	0.879746	−	0.475444i	$-0.157712\pi$
$223$	22.2512	+	4.72965i	1.49005	+	0.316721i	0.610308	+	0.792164i	$0.291046\pi$
$224$	−24.4421	−	7.94170i	−1.63310	−	0.530627i
$225$		0			0
$226$	−32.0208	+	44.0729i	−2.13000	+	2.93169i
$227$	−5.43847	−	6.04004i	−0.360964	−	0.400891i	0.535120	−	0.844776i	$-0.320267\pi$
$227$	−5.43847	−	6.04004i	−0.360964	−	0.400891i	−0.896084	+	0.443885i	$0.853600\pi$
$228$		0			0
$229$	12.4183	+	5.52899i	0.820625	+	0.365366i	0.773715	−	0.633533i	$-0.218396\pi$
$229$	12.4183	+	5.52899i	0.820625	+	0.365366i	0.0469095	+	0.998899i	$0.485063\pi$
$230$	11.3180	+	19.6033i	0.746285	+	1.29260i
$231$		0			0
$232$	0.427117	−	0.739788i	0.0280416	−	0.0485694i
$233$	−4.09157	+	2.97270i	−0.268048	+	0.194748i	−0.713687	−	0.700464i	$-0.752976\pi$
$233$	−4.09157	+	2.97270i	−0.268048	+	0.194748i	0.445640	+	0.895212i	$0.352976\pi$
$234$		0			0
$235$	3.24554	−	9.98874i	0.211716	−	0.651594i
$236$	6.47185	+	14.5360i	0.421282	+	0.946214i
$237$		0			0
$238$	−3.35667	−	15.7919i	−0.217581	−	1.02364i
$239$	−13.4937	+	14.9862i	−0.872832	+	0.969378i	−0.999746	−	0.0225358i	$-0.992826\pi$
$239$	−13.4937	+	14.9862i	−0.872832	+	0.969378i	0.126914	+	0.991914i	$0.459493\pi$
$240$		0			0
$241$	−24.5094	−	14.1505i	−1.57879	−	0.911516i	−0.995028	−	0.0995930i	$-0.968246\pi$
$241$	−24.5094	−	14.1505i	−1.57879	−	0.911516i	−0.583764	−	0.811923i	$-0.698421\pi$
$242$	−27.2463	+	11.6509i	−1.75146	+	0.748947i
$243$		0			0
$244$	−0.983581	−	1.35378i	−0.0629674	−	0.0866671i
$245$	1.47883	−	6.95735i	0.0944790	−	0.444489i
$246$		0			0
$247$	0.389789	−	3.70860i	0.0248017	−	0.235972i
$248$	3.74943	−	35.6734i	0.238089	−	2.26527i
$249$		0			0
$250$	−6.40735	+	30.1442i	−0.405237	+	1.90649i
$251$	−13.7475	−	18.9219i	−0.867737	−	1.19434i	−0.979669	−	0.200622i	$-0.935704\pi$
$251$	−13.7475	−	18.9219i	−0.867737	−	1.19434i	0.111931	−	0.993716i	$-0.464296\pi$
$252$		0			0
$253$	19.1401	+	2.15500i	1.20333	+	0.135483i
$254$	−0.240079	−	0.138610i	−0.0150639	−	0.00869715i
$255$		0			0
$256$	12.1971	−	13.5463i	0.762319	−	0.846641i
$257$	−0.0865878	−	0.407364i	−0.00540120	−	0.0254106i	0.975364	−	0.220599i	$-0.0708014\pi$
$257$	−0.0865878	−	0.407364i	−0.00540120	−	0.0254106i	−0.980766	+	0.195189i	$0.937468\pi$
$258$		0			0
$259$	−5.86452	−	13.1719i	−0.364404	−	0.818464i
$260$	−6.99709	+	21.5348i	−0.433941	+	1.33553i
$261$		0			0
$262$	33.4873	−	24.3299i	2.06885	−	1.50311i
$263$	14.0588	−	24.3505i	0.866902	−	1.50152i	0.00175644	−	0.999998i	$-0.499441\pi$
$263$	14.0588	−	24.3505i	0.866902	−	1.50152i	0.865146	−	0.501520i	$-0.167226\pi$
$264$		0			0
$265$	−0.243072	−	0.421013i	−0.0149318	−	0.0258626i
$266$	4.45045	+	1.98147i	0.272874	+	0.121491i
$267$		0			0
$268$	12.0886	+	13.4258i	0.738431	+	0.820111i
$269$	−7.97137	+	10.9716i	−0.486023	+	0.668953i	−0.979648	−	0.200721i	$-0.935671\pi$
$269$	−7.97137	+	10.9716i	−0.486023	+	0.668953i	0.493625	+	0.869675i	$0.335671\pi$
$270$		0			0
$271$	−10.5963	−	3.44294i	−0.643678	−	0.209144i	−0.0310533	−	0.999518i	$-0.509886\pi$
$271$	−10.5963	−	3.44294i	−0.643678	−	0.209144i	−0.612624	+	0.790374i	$0.709886\pi$
$272$	53.2860	+	11.3263i	3.23094	+	0.686757i
$273$		0			0
$274$	−8.68681	+	5.01533i	−0.524789	+	0.302987i
$275$	6.39713	+	7.21132i	0.385762	+	0.434859i
$276$		0			0
$277$	9.73067	−	1.02273i	0.584659	−	0.0614502i	0.192419	−	0.981313i	$-0.438367\pi$
$277$	9.73067	−	1.02273i	0.584659	−	0.0614502i	0.392240	+	0.919863i	$0.371700\pi$
$278$	43.5961	−	14.1652i	2.61472	−	0.849573i
$279$		0			0
$280$	−14.8270	−	10.7724i	−0.886083	−	0.643777i
$281$	−11.1314	+	4.95603i	−0.664046	+	0.295652i	−0.710945	−	0.703247i	$-0.751733\pi$
$281$	−11.1314	+	4.95603i	−0.664046	+	0.295652i	0.0468995	+	0.998900i	$0.485066\pi$
$282$		0			0
$283$	−11.4395	−	10.3001i	−0.680006	−	0.612280i	0.254988	−	0.966944i	$-0.417928\pi$
$283$	−11.4395	−	10.3001i	−0.680006	−	0.612280i	−0.934994	+	0.354664i	$0.884595\pi$
$284$	−19.6041	+	44.0314i	−1.16329	+	2.61278i
$285$		0			0
$286$	15.4738	+	21.6326i	0.914984	+	1.27916i
$287$			6.59831i			0.389486i
$288$		0			0
$289$	0.0723102	+	0.222548i	0.00425354	+	0.0130911i
$290$	0.282007	−	0.253920i	0.0165600	−	0.0149107i
$291$		0			0
$292$	37.1131	+	3.90074i	2.17188	+	0.228274i
$293$	−26.6244	+	5.65919i	−1.55541	+	0.330613i	−0.903806	−	0.427943i	$-0.859239\pi$
$293$	−26.6244	+	5.65919i	−1.55541	+	0.330613i	−0.651608	+	0.758556i	$0.725905\pi$
$294$		0			0
$295$	0.457765	+	4.35534i	0.0266521	+	0.253578i
$296$	87.6328			5.09356
$297$		0			0
$298$	30.8503			1.78711
$299$	−1.80708	−	17.1932i	−0.104506	−	0.994310i
$300$		0			0
$301$	3.00247	−	0.638194i	0.173059	−	0.0367849i
$302$	−2.84792	−	0.299328i	−0.163879	−	0.0172244i
$303$		0			0
$304$	−12.2159	+	10.9992i	−0.700630	+	0.630850i
$305$	−0.142320	−	0.438016i	−0.00814923	−	0.0250807i
$306$		0			0
$307$		−	31.0795i		−	1.77380i	−0.461960	−	0.886901i	$-0.652854\pi$
$307$		−	31.0795i		−	1.77380i	0.461960	−	0.886901i	$-0.347146\pi$
$308$	−23.9956	+	7.60085i	−1.36728	+	0.433099i
$309$		0			0
$310$	6.48118	−	14.5570i	0.368106	−	0.826780i
$311$	−4.24667	−	3.82372i	−0.240807	−	0.216823i	0.539886	−	0.841738i	$-0.318467\pi$
$311$	−4.24667	−	3.82372i	−0.240807	−	0.216823i	−0.780693	+	0.624914i	$0.785134\pi$
$312$		0			0
$313$	−24.1472	+	10.7510i	−1.36488	+	0.607685i	−0.952838	−	0.303479i	$-0.901852\pi$
$313$	−24.1472	+	10.7510i	−1.36488	+	0.607685i	−0.412044	+	0.911164i	$0.635185\pi$
$314$	−0.186099	−	0.135209i	−0.0105021	−	0.00763026i
$315$		0			0
$316$	−50.0994	+	16.2783i	−2.81831	+	0.915725i
$317$	1.96901	−	0.206952i	0.110591	−	0.0116236i	−0.0490713	−	0.998795i	$-0.515626\pi$
$317$	1.96901	−	0.206952i	0.110591	−	0.0116236i	0.159662	+	0.987172i	$0.448960\pi$
$318$		0			0
$319$	−0.0313755	−	0.321372i	−0.00175669	−	0.0179934i
$320$	27.2064	−	15.7076i	1.52089	−	0.878084i
$321$		0			0
$322$	22.0915	+	4.69570i	1.23111	+	0.261681i
$323$	−4.94579	−	1.60698i	−0.275191	−	0.0894150i
$324$		0			0
$325$	5.08570	−	6.99986i	0.282104	−	0.388283i
$326$	−5.28106	−	5.86521i	−0.292491	−	0.324844i
$327$		0			0
$328$	−36.6362	−	16.3115i	−2.02290	−	0.900651i
$329$	−5.23958	−	9.07523i	−0.288868	−	0.500333i
$330$		0			0
$331$	2.03858	−	3.53093i	0.112051	−	0.194078i	−0.804546	−	0.593890i	$-0.797591\pi$
$331$	2.03858	−	3.53093i	0.112051	−	0.194078i	0.916597	+	0.399812i	$0.130925\pi$
$332$	25.3667	−	18.4300i	1.39218	−	1.01148i
$333$		0			0
$334$	3.70749	−	11.4105i	0.202865	−	0.624354i
$335$	2.02242	+	4.54244i	0.110497	+	0.248180i
$336$		0			0
$337$	5.93123	+	27.9042i	0.323095	+	1.52004i	0.777292	+	0.629140i	$0.216593\pi$
$337$	5.93123	+	27.9042i	0.323095	+	1.52004i	−0.454198	+	0.890901i	$0.650074\pi$
$338$	−7.45954	+	8.28465i	−0.405745	+	0.450626i
$339$		0			0
$340$	27.3464	+	15.7885i	1.48307	+	0.856249i
$341$	−6.69236	−	11.7921i	−0.362412	−	0.638580i
$342$		0			0
$343$	−10.1112	−	13.9169i	−0.545954	−	0.751441i
$344$	−3.87883	+	18.2484i	−0.209132	+	0.983890i
$345$		0			0
$346$	−2.94271	+	27.9980i	−0.158201	+	1.50518i
$347$	−1.08070	+	10.2822i	−0.0580151	+	0.551976i	0.926453	+	0.376411i	$0.122842\pi$
$347$	−1.08070	+	10.2822i	−0.0580151	+	0.551976i	−0.984468	+	0.175565i	$0.943825\pi$
$348$		0			0
$349$	−3.83672	+	18.0504i	−0.205375	+	0.966213i	0.747830	+	0.663890i	$0.231096\pi$
$349$	−3.83672	+	18.0504i	−0.205375	+	0.966213i	−0.953205	+	0.302324i	$0.902238\pi$
$350$	6.64399	+	9.14466i	0.355136	+	0.488803i
$351$		0			0
$352$	6.60597	−	58.6726i	0.352100	−	3.12726i
$353$	11.5976	+	6.69588i	0.617279	+	0.356386i	0.775809	−	0.630968i	$-0.217342\pi$
$353$	11.5976	+	6.69588i	0.617279	+	0.356386i	−0.158530	+	0.987354i	$0.550676\pi$
$354$		0			0
$355$	−8.87638	+	9.85822i	−0.471109	+	0.523220i
$356$	−5.59163	−	26.3065i	−0.296356	−	1.39424i
$357$		0			0
$358$	−11.0392	−	24.7945i	−0.583440	−	1.31043i
$359$	−1.92854	+	5.93545i	−0.101785	+	0.313261i	−0.988962	−	0.148167i	$-0.952663\pi$
$359$	−1.92854	+	5.93545i	−0.101785	+	0.313261i	0.887178	+	0.461428i	$0.152663\pi$
$360$		0			0
$361$	−14.1018	+	10.2456i	−0.742202	+	0.539241i
$362$	−20.8836	+	36.1715i	−1.09762	+	1.90113i
$363$		0			0
$364$	11.2961	+	19.5654i	0.592075	+	1.02550i
$365$	9.38285	+	4.17752i	0.491121	+	0.218661i
$366$		0			0
$367$	−5.15250	−	5.72243i	−0.268958	−	0.298708i	0.593503	−	0.804832i	$-0.297745\pi$
$367$	−5.15250	−	5.72243i	−0.268958	−	0.298708i	−0.862461	+	0.506124i	$0.831078\pi$
$368$	−44.7939	+	61.6535i	−2.33504	+	3.21391i
$369$		0			0
$370$	37.0240	+	12.0298i	1.92479	+	0.625401i
$371$	−0.474451	−	0.100848i	−0.0246323	−	0.00523575i
$372$		0			0
$373$	18.2379	−	10.5296i	0.944321	−	0.545204i	0.0530086	−	0.998594i	$-0.483119\pi$
$373$	18.2379	−	10.5296i	0.944321	−	0.545204i	0.891312	+	0.453390i	$0.149786\pi$
$374$	33.9951	−	14.8352i	1.75784	−	0.767110i
$375$		0			0
$376$	63.3416	−	6.65747i	3.26659	−	0.343333i
$377$	−0.275637	+	0.0895598i	−0.0141960	+	0.00461256i
$378$		0			0
$379$	24.0003	+	17.4372i	1.23281	+	0.895691i	0.997098	−	0.0761314i	$-0.0242568\pi$
$379$	24.0003	+	17.4372i	1.23281	+	0.895691i	0.235715	+	0.971822i	$0.424257\pi$
$380$	−8.70449	+	3.87549i	−0.446531	+	0.198808i
$381$		0			0
$382$	−7.43682	−	6.69615i	−0.380501	−	0.342605i
$383$	−1.08521	+	2.43741i	−0.0554515	+	0.124546i	−0.939146	−	0.343518i	$-0.888382\pi$
$383$	−1.08521	+	2.43741i	−0.0554515	+	0.124546i	0.883695	+	0.468064i	$0.155048\pi$
$384$		0			0
$385$	−6.92749	−	0.0512539i	−0.353057	−	0.00261214i
$386$			67.1784i			3.41929i
$387$		0			0
$388$	9.81361	+	30.2032i	0.498210	+	1.53333i
$389$	0.473711	−	0.426531i	0.0240181	−	0.0216260i	−0.657034	−	0.753861i	$-0.728189\pi$
$389$	0.473711	−	0.426531i	0.0240181	−	0.0216260i	0.681052	+	0.732235i	$0.261523\pi$
$390$		0			0
$391$	−23.9768	−	2.52007i	−1.21256	−	0.127445i
$392$	42.1904	−	8.96785i	2.13094	−	0.452945i
$393$		0			0
$394$	−5.41251	−	51.4966i	−0.272678	−	2.59436i
$395$	−14.4984			−0.729492
$396$		0			0
$397$	−25.2145			−1.26548			−0.632741	−	0.774364i	$-0.718070\pi$
$397$	−25.2145			−1.26548			−0.632741	+	0.774364i	$0.718070\pi$
$398$	−7.32485	−	69.6913i	−0.367162	−	3.49331i
$399$		0			0
$400$	−37.3072	+	7.92990i	−1.86536	+	0.396495i
$401$	29.0104	+	3.04912i	1.44871	+	0.152266i	0.795979	−	0.605324i	$-0.206956\pi$
$401$	29.0104	+	3.04912i	1.44871	+	0.152266i	0.652731	+	0.757590i	$0.273623\pi$
$402$		0			0
$403$	−9.04396	+	8.14322i	−0.450512	+	0.405642i
$404$	−18.9132	−	58.2088i	−0.940966	−	2.89600i
$405$		0			0
$406$		−	0.378625i		−	0.0187908i
$407$	26.9422	−	19.2717i	1.33547	−	0.955263i
$408$		0			0
$409$	6.75518	−	15.1724i	0.334022	−	0.750226i	−0.665969	−	0.745979i	$-0.731982\pi$
$409$	6.75518	−	15.1724i	0.334022	−	0.750226i	0.999991	−	0.00424629i	$-0.00135164\pi$
$410$	−13.2393	−	11.9207i	−0.653841	−	0.588721i
$411$		0			0
$412$	−16.0880	+	7.16284i	−0.792599	+	0.352888i
$413$	3.53499	+	2.56832i	0.173945	+	0.126379i
$414$		0			0
$415$	8.20739	−	2.66674i	0.402885	−	0.130905i
$416$	−52.7045	+	5.53947i	−2.58405	+	0.271595i
$417$		0			0
$418$	−2.40791	+	10.9300i	−0.117775	+	0.534606i
$419$	8.11793	−	4.68689i	0.396587	−	0.228969i	−0.288423	−	0.957503i	$-0.593131\pi$
$419$	8.11793	−	4.68689i	0.396587	−	0.228969i	0.685010	+	0.728534i	$0.259798\pi$
$420$		0			0
$421$	3.23871	+	0.688408i	0.157845	+	0.0335510i	0.286156	−	0.958183i	$-0.407622\pi$
$421$	3.23871	+	0.688408i	0.157845	+	0.0335510i	−0.128311	+	0.991734i	$0.540956\pi$
$422$	−58.2537	−	18.9278i	−2.83575	−	0.921390i
$423$		0			0
$424$	1.73282	−	2.38502i	0.0841532	−	0.115827i
$425$	−8.07378	−	8.96685i	−0.391636	−	0.434956i
$426$		0			0
$427$	−0.419794	−	0.186904i	−0.0203153	−	0.00904494i
$428$	−24.8519	−	43.0448i	−1.20126	−	2.08065i
$429$		0			0
$430$	−4.14383	+	7.17732i	−0.199833	+	0.346121i
$431$	1.72195	−	1.25107i	0.0829434	−	0.0602619i	−0.545541	−	0.838084i	$-0.683676\pi$
$431$	1.72195	−	1.25107i	0.0829434	−	0.0602619i	0.628484	+	0.777822i	$0.283676\pi$
$432$		0			0
$433$	−4.76068	+	14.6519i	−0.228784	+	0.704124i	0.769102	+	0.639126i	$0.220704\pi$
$433$	−4.76068	+	14.6519i	−0.228784	+	0.704124i	−0.997885	+	0.0649975i	$0.979296\pi$
$434$	−6.46661	−	14.5242i	−0.310407	−	0.697186i
$435$		0			0
$436$	4.49579	+	21.1510i	0.215309	+	1.01295i
$437$	4.86779	−	5.40623i	0.232858	−	0.258615i
$438$		0			0
$439$	31.0083	+	17.9026i	1.47995	+	0.854447i	0.999742	−	0.0227105i	$-0.00722958\pi$
$439$	31.0083	+	17.9026i	1.47995	+	0.854447i	0.480203	+	0.877157i	$0.340563\pi$
$440$	17.4098	−	38.3372i	0.829981	−	1.82765i
$441$		0			0
$442$	−19.5682	−	26.9333i	−0.930764	−	1.28109i
$443$	−2.49445	+	11.7354i	−0.118515	+	0.557568i	0.878321	+	0.478072i	$0.158664\pi$
$443$	−2.49445	+	11.7354i	−0.118515	+	0.557568i	−0.996835	+	0.0794956i	$0.974669\pi$
$444$		0			0
$445$	0.773725	−	7.36150i	0.0366781	−	0.348968i
$446$	−6.40567	+	60.9459i	−0.303317	+	2.88587i
$447$		0			0
$448$	6.51692	−	30.6597i	0.307896	−	1.44853i
$449$	−15.0088	−	20.6578i	−0.708307	−	0.974901i	−0.999832	−	0.0183378i	$-0.994163\pi$
$449$	−15.0088	−	20.6578i	−0.708307	−	0.974901i	0.291525	−	0.956563i	$-0.405837\pi$
$450$		0			0
$451$	−14.8507	+	3.04196i	−0.699292	+	0.143240i
$452$	−92.0676	−	53.1552i	−4.33050	−	2.50021i
$453$		0			0
$454$	14.6507	−	16.2712i	0.687589	−	0.763645i
$455$	1.29279	+	6.08211i	0.0606071	+	0.285134i
$456$		0			0
$457$	0.414845	+	0.931757i	0.0194056	+	0.0435857i	0.922988	−	0.384828i	$-0.125739\pi$
$457$	0.414845	+	0.931757i	0.0194056	+	0.0435857i	−0.903583	+	0.428414i	$0.859073\pi$
$458$	−11.3160	+	34.8272i	−0.528764	+	1.62737i
$459$		0			0
$460$	−35.7370	+	25.9645i	−1.66625	+	1.21060i
$461$	−2.26202	+	3.91794i	−0.105353	+	0.182477i	−0.913882	−	0.405979i	$-0.866931\pi$
$461$	−2.26202	+	3.91794i	−0.105353	+	0.182477i	0.808529	+	0.588456i	$0.200264\pi$
$462$		0			0
$463$	4.22594	+	7.31953i	0.196396	+	0.340168i	0.947357	−	0.320179i	$-0.103743\pi$
$463$	4.22594	+	7.31953i	0.196396	+	0.340168i	−0.750961	+	0.660346i	$0.770410\pi$
$464$	1.16713	+	0.519638i	0.0541825	+	0.0241236i
$465$		0			0
$466$	−9.11640	−	10.1248i	−0.422309	−	0.469022i
$467$	−3.64591	+	5.01817i	−0.168713	+	0.232213i	−0.884998	−	0.465594i	$-0.845841\pi$
$467$	−3.64591	+	5.01817i	−0.168713	+	0.232213i	0.716286	+	0.697807i	$0.245841\pi$
$468$		0			0
$469$	4.71832	+	1.53308i	0.217872	+	0.0707909i
$470$	27.6751	+	5.88252i	1.27656	+	0.271340i
$471$		0			0
$472$	−22.9990	+	13.2785i	−1.05861	+	0.611191i
$473$	2.82057	+	6.46338i	0.129690	+	0.297187i
$474$		0			0
$475$	3.62096	−	0.380578i	0.166141	−	0.0174621i
$476$	29.9639	−	9.73586i	1.37339	−	0.446242i
$477$		0			0
$478$	−43.9497	−	31.9314i	−2.01021	−	1.46051i
$479$	20.3778	−	9.07278i	0.931085	−	0.414546i	0.115582	−	0.993298i	$-0.463127\pi$
$479$	20.3778	−	9.07278i	0.931085	−	0.414546i	0.815504	+	0.578752i	$0.196460\pi$
$480$		0			0
$481$	−22.0950	−	19.8945i	−1.00745	−	0.907109i
$482$	31.0096	−	69.6487i	1.41245	−	3.17241i
$483$		0			0
$484$	−28.1696	−	50.5025i	−1.28044	−	2.29557i
$485$			8.74055i			0.396888i
$486$		0			0
$487$	10.5290	+	32.4051i	0.477117	+	1.46841i	0.843082	+	0.537786i	$0.180739\pi$
$487$	10.5290	+	32.4051i	0.477117	+	1.46841i	−0.365965	+	0.930629i	$0.619261\pi$
$488$	2.07552	−	1.86881i	0.0939545	−	0.0845970i
$489$		0			0
$490$	19.0561	+	2.00288i	0.860867	+	0.0904807i
$491$	−18.4134	+	3.91389i	−0.830985	+	0.176631i	−0.603715	−	0.797201i	$-0.706313\pi$
$491$	−18.4134	+	3.91389i	−0.830985	+	0.176631i	−0.227270	+	0.973832i	$0.572980\pi$
$492$		0			0
$493$	0.0422474	+	0.401957i	0.00190273	+	0.0181032i
$494$	10.0456			0.451972
$495$		0			0
$496$	53.6466			2.40880
$497$	1.38351	+	13.1632i	0.0620588	+	0.590450i
$498$		0			0
$499$	−7.43187	+	1.57969i	−0.332696	+	0.0707167i	−0.371231	−	0.928541i	$-0.621064\pi$
$499$	−7.43187	+	1.57969i	−0.332696	+	0.0707167i	0.0385350	+	0.999257i	$0.487731\pi$
$500$	−59.8103	−	6.28632i	−2.67480	−	0.281133i
$501$		0			0
$502$	46.8231	−	42.1597i	2.08982	−	1.88168i
$503$	8.18033	+	25.1765i	0.364743	+	1.12256i	0.950142	+	0.311818i	$0.100938\pi$
$503$	8.18033	+	25.1765i	0.364743	+	1.12256i	−0.585399	+	0.810745i	$0.699062\pi$
$504$		0			0
$505$		−	16.8451i		−	0.749599i
$506$	−0.383884	+	51.8858i	−0.0170657	+	2.30661i
$507$		0			0
$508$	0.220039	−	0.494215i	0.00976264	−	0.0219272i
$509$	9.47468	+	8.53104i	0.419958	+	0.378132i	0.851843	−	0.523797i	$-0.175485\pi$
$509$	9.47468	+	8.53104i	0.419958	+	0.378132i	−0.431885	+	0.901929i	$0.642151\pi$
$510$		0			0
$511$	9.36176	−	4.16812i	0.414140	−	0.184387i
$512$	2.69612	+	1.95884i	0.119153	+	0.0865695i
$513$		0			0
$514$	1.06700	−	0.346689i	0.0470633	−	0.0152918i
$515$	−4.82035	+	0.506640i	−0.212410	+	0.0223252i
$516$		0			0
$517$	18.0099	−	15.9765i	0.792075	−	0.702646i
$518$	33.6380	−	19.4209i	1.47797	−	0.853305i
$519$		0			0
$520$	−36.9660	−	7.85736i	−1.62106	−	0.344568i
$521$	6.80629	+	2.21150i	0.298189	+	0.0968875i	0.454291	−	0.890854i	$-0.349893\pi$
$521$	6.80629	+	2.21150i	0.298189	+	0.0968875i	−0.156102	+	0.987741i	$0.549893\pi$
$522$		0			0
$523$	18.1933	−	25.0410i	0.795539	−	1.09497i	−0.197857	−	0.980231i	$-0.563398\pi$
$523$	18.1933	−	25.0410i	0.795539	−	1.09497i	0.993396	−	0.114734i	$-0.0366017\pi$
$524$	54.0500	+	60.0286i	2.36118	+	2.62236i
$525$		0			0
$526$	69.1972	+	30.8086i	3.01714	+	1.34332i
$527$	8.48573	+	14.6977i	0.369644	+	0.640243i
$528$		0			0
$529$	5.36315	−	9.28924i	0.233180	−	0.403880i
$530$	1.05950	−	0.769775i	0.0460219	−	0.0334369i
$531$		0			0
$532$	−2.93777	+	9.04152i	−0.127368	+	0.392000i
$533$	5.53411	+	12.4298i	0.239709	+	0.538395i
$534$		0			0
$535$	−2.84421	−	13.3809i	−0.122966	−	0.578508i
$536$	−20.1762	+	22.4080i	−0.871480	+	0.967876i
$537$		0			0
$538$	−31.6392	−	18.2669i	−1.36406	−	0.787541i
$539$	10.9990	−	12.0354i	0.473762	−	0.518401i
$540$		0			0
$541$	25.5272	+	35.1352i	1.09750	+	1.51058i	0.838656	+	0.544661i	$0.183342\pi$
$541$	25.5272	+	35.1352i	1.09750	+	1.51058i	0.258845	+	0.965919i	$0.416658\pi$
$542$	6.24030	−	29.3583i	0.268044	−	1.26105i
$543$		0			0
$544$	−7.72506	+	73.4991i	−0.331209	+	3.15125i
$545$	−0.622091	+	5.91881i	−0.0266475	+	0.253534i
$546$		0			0
$547$	−1.55388	+	7.31045i	−0.0664392	+	0.312572i	−0.998801	−	0.0489546i	$-0.984411\pi$
$547$	−1.55388	+	7.31045i	−0.0664392	+	0.312572i	0.932362	+	0.361527i	$0.117744\pi$
$548$	−11.5056	−	15.8361i	−0.491496	−	0.676487i
$549$		0			0
$550$	−17.5187	+	19.1694i	−0.747001	+	0.817386i
$551$	−0.105618	−	0.0609787i	−0.00449949	−	0.00259778i
$552$		0			0
$553$	−9.67948	+	10.7502i	−0.411613	+	0.457143i
$554$	5.48008	+	25.7818i	0.232826	+	1.09536i
$555$		0			0
$556$	36.3845	+	81.7209i	1.54305	+	3.46574i
$557$	8.26967	−	25.4514i	0.350397	−	1.07841i	−0.608233	−	0.793758i	$-0.708121\pi$
$557$	8.26967	−	25.4514i	0.350397	−	1.07841i	0.958631	−	0.284653i	$-0.0918785\pi$
$558$		0			0
$559$	5.12075	−	3.72044i	0.216585	−	0.157358i
$560$	13.7049	−	23.7376i	0.579139	−	1.00310i
$561$		0			0
$562$	−16.4124	−	28.4270i	−0.692314	−	1.19912i
$563$	21.3311	+	9.49724i	0.899000	+	0.400261i	0.803594	−	0.595178i	$-0.202918\pi$
$563$	21.3311	+	9.49724i	0.899000	+	0.400261i	0.0954063	+	0.995438i	$0.469585\pi$
$564$		0			0
$565$	−19.5785	−	21.7441i	−0.823674	−	0.914782i
$566$	24.3742	−	33.5483i	1.02453	−	1.41014i
$567$		0			0
$568$	−76.5070	−	24.8586i	−3.21016	−	1.04305i
$569$	−5.31206	−	1.12911i	−0.222693	−	0.0473349i	0.0952135	−	0.995457i	$-0.469647\pi$
$569$	−5.31206	−	1.12911i	−0.222693	−	0.0473349i	−0.317907	+	0.948122i	$0.602980\pi$
$570$		0			0
$571$	8.79380	−	5.07710i	0.368009	−	0.212470i	−0.304579	−	0.952487i	$-0.598516\pi$
$571$	8.79380	−	5.07710i	0.368009	−	0.212470i	0.672588	+	0.740017i	$0.265183\pi$
$572$	−38.8278	+	34.4439i	−1.62347	+	1.44017i
$573$		0			0
$574$	−17.6778	+	1.85801i	−0.737855	+	0.0775517i
$575$	16.0533	−	5.21603i	0.669468	−	0.217523i
$576$		0			0
$577$	17.0075	+	12.3566i	0.708029	+	0.514414i	0.882537	−	0.470242i	$-0.155833\pi$
$577$	17.0075	+	12.3566i	0.708029	+	0.514414i	−0.174508	+	0.984656i	$0.555833\pi$
$578$	−0.575874	+	0.256396i	−0.0239532	+	0.0106647i
$579$		0			0
$580$	0.550328	+	0.495518i	0.0228511	+	0.0205753i
$581$	3.50215	−	7.86595i	0.145294	−	0.326335i
$582$		0			0
$583$	0.00824453	−	1.11433i	0.000341453	−	0.0461510i
$584$			62.2837i			2.57732i
$585$		0			0
$586$	−22.6588	−	69.7367i	−0.936028	−	2.88080i
$587$	−32.4155	+	29.1870i	−1.33793	+	1.20468i	−0.377550	+	0.925989i	$0.623233\pi$
$587$	−32.4155	+	29.1870i	−1.33793	+	1.20468i	−0.960381	+	0.278689i	$0.910100\pi$
$588$		0			0
$589$	−5.09304	−	0.535300i	−0.209855	−	0.0220567i
$590$	−11.5396	+	2.45283i	−0.475079	+	0.100981i
$591$		0			0
$592$	13.6998	+	130.344i	0.563056	+	5.35712i
$593$	37.0300			1.52064			0.760319	−	0.649549i	$-0.225042\pi$
$593$	37.0300			1.52064			0.760319	+	0.649549i	$0.225042\pi$
$594$		0			0
$595$	8.67130			0.355489
$596$	6.29297	+	59.8736i	0.257770	+	2.45252i
$597$		0			0
$598$	45.5541	−	9.68282i	1.86285	−	0.395960i
$599$	23.9622	+	2.51853i	0.979068	+	0.102904i	0.580522	−	0.814244i	$-0.302848\pi$
$599$	23.9622	+	2.51853i	0.979068	+	0.102904i	0.398546	+	0.917148i	$0.369515\pi$
$600$		0			0
$601$	13.8822	−	12.4996i	0.566268	−	0.509870i	−0.335529	−	0.942030i	$-0.608915\pi$
$601$	13.8822	−	12.4996i	0.566268	−	0.509870i	0.901797	+	0.432160i	$0.142248\pi$
$602$	2.55527	+	7.86431i	0.104145	+	0.320525i
$603$		0			0
$604$		−	5.58824i		−	0.227382i
$605$	−3.07836	−	15.6152i	−0.125153	−	0.634849i
$606$		0			0
$607$	−10.0075	+	22.4773i	−0.406193	+	0.912324i	0.588409	+	0.808563i	$0.299754\pi$
$607$	−10.0075	+	22.4773i	−0.406193	+	0.912324i	−0.994602	+	0.103761i	$0.966912\pi$
$608$	−16.5724	−	14.9218i	−0.672098	−	0.605160i
$609$		0			0
$610$	1.13343	−	0.504635i	0.0458912	−	0.0204321i
$611$	−17.4818	−	12.7013i	−0.707238	−	0.513839i
$612$		0			0
$613$	21.4976	−	6.98501i	0.868282	−	0.282122i	0.159199	−	0.987247i	$-0.449109\pi$
$613$	21.4976	−	6.98501i	0.868282	−	0.282122i	0.709083	+	0.705125i	$0.249109\pi$
$614$	83.2662	−	8.75163i	3.36035	−	0.353187i
$615$		0			0
$616$	−16.8028	−	38.5038i	−0.677004	−	1.55136i
$617$	−8.17258	+	4.71844i	−0.329016	+	0.189957i	−0.655404	−	0.755278i	$-0.727502\pi$
$617$	−8.17258	+	4.71844i	−0.329016	+	0.189957i	0.326388	+	0.945236i	$0.394168\pi$
$618$		0			0
$619$	13.0960	+	2.78364i	0.526373	+	0.111884i	0.463431	−	0.886133i	$-0.346618\pi$
$619$	13.0960	+	2.78364i	0.526373	+	0.111884i	0.0629422	+	0.998017i	$0.479952\pi$
$620$	29.5739	+	9.60915i	1.18772	+	0.385913i
$621$		0			0
$622$	9.04845	−	12.4541i	0.362810	−	0.499365i
$623$	−4.94180	−	5.48842i	−0.197989	−	0.219889i
$624$		0			0
$625$	−1.84495	−	0.821424i	−0.0737980	−	0.0328570i
$626$	−35.6031	−	61.6663i	−1.42298	−	2.46468i
$627$		0			0
$628$	0.224449	−	0.388757i	0.00895648	−	0.0155131i
$629$	−33.5439	+	24.3710i	−1.33748	+	0.971737i
$630$		0			0
$631$	−3.99811	+	12.3049i	−0.159162	+	0.489851i	−0.998559	−	0.0536685i	$-0.982909\pi$
$631$	−3.99811	+	12.3049i	−0.159162	+	0.489851i	0.839397	+	0.543519i	$0.182909\pi$
$632$	−35.7604	−	80.3191i	−1.42247	−	3.19492i
$633$		0			0
$634$	1.10890	+	5.21698i	0.0440402	+	0.207193i
$635$	0.0996297	−	0.110650i	0.00395369	−	0.00439101i
$636$		0			0
$637$	−12.6734	−	7.31701i	−0.502140	−	0.289911i
$638$	0.852164	−	0.174554i	0.0337375	−	0.00691065i
$639$		0			0
$640$	19.4638	+	26.7896i	0.769373	+	1.05895i
$641$	2.07714	−	9.77218i	0.0820421	−	0.385978i	−0.917899	−	0.396814i	$-0.870116\pi$
$641$	2.07714	−	9.77218i	0.0820421	−	0.385978i	0.999941	+	0.0108359i	$0.00344924\pi$
$642$		0			0
$643$	1.32573	−	12.6135i	0.0522817	−	0.497428i	−0.936779	−	0.349921i	$-0.886209\pi$
$643$	1.32573	−	12.6135i	0.0522817	−	0.497428i	0.989061	−	0.147507i	$-0.0471248\pi$
$644$	−4.60700	+	43.8326i	−0.181541	+	1.72725i
$645$		0			0
$646$	2.91265	−	13.7029i	0.114597	−	0.539135i
$647$	19.3401	+	26.6193i	0.760337	+	1.04651i	0.997186	+	0.0749678i	$0.0238854\pi$
$647$	19.3401	+	26.6193i	0.760337	+	1.04651i	−0.236849	+	0.971547i	$0.576115\pi$
$648$		0			0
$649$	−4.15077	+	9.14018i	−0.162932	+	0.358784i
$650$	20.1856	+	11.6542i	0.791746	+	0.457115i
$651$		0			0
$652$	10.3058	−	11.4458i	0.403608	−	0.448252i
$653$	4.44155	+	20.8959i	0.173811	+	0.817718i	0.975504	+	0.219982i	$0.0705998\pi$
$653$	4.44155	+	20.8959i	0.173811	+	0.817718i	−0.801693	+	0.597736i	$0.796067\pi$
$654$		0			0
$655$	9.04253	+	20.3099i	0.353321	+	0.793572i
$656$	18.5342	−	57.0424i	0.723639	−	2.22713i
$657$		0			0
$658$	22.8383	−	16.5930i	0.890331	−	0.646863i
$659$	−5.34609	+	9.25969i	−0.208254	+	0.360706i	−0.951165	−	0.308684i	$-0.900111\pi$
$659$	−5.34609	+	9.25969i	−0.208254	+	0.360706i	0.742911	+	0.669391i	$0.233445\pi$
$660$		0			0
$661$	−14.6301	−	25.3401i	−0.569045	−	0.985615i	−0.996661	−	0.0816544i	$-0.973980\pi$
$661$	−14.6301	−	25.3401i	−0.569045	−	0.985615i	0.427616	−	0.903961i	$-0.359354\pi$
$662$	10.0339	+	4.46737i	0.389978	+	0.173629i
$663$		0			0
$664$	35.0171	+	38.8904i	1.35893	+	1.50924i
$665$	−1.53796	+	2.11683i	−0.0596397	+	0.0820870i
$666$		0			0
$667$	−0.537728	−	0.174718i	−0.0208209	−	0.00676512i
$668$	22.9015	+	4.86786i	0.886086	+	0.188343i
$669$		0			0
$670$	−11.6003	+	6.69744i	−0.448159	+	0.258745i
$671$	0.227129	−	1.03099i	0.00876822	−	0.0398010i
$672$		0			0
$673$	41.5078	−	4.36264i	1.60001	−	0.168168i	0.737906	−	0.674904i	$-0.235815\pi$
$673$	41.5078	−	4.36264i	1.60001	−	0.168168i	0.862101	+	0.506736i	$0.169148\pi$
$674$	−73.0890	+	23.7481i	−2.81528	+	0.914741i
$675$		0			0
$676$	−17.6003	−	12.7874i	−0.676935	−	0.491822i
$677$	27.1757	−	12.0994i	1.04445	−	0.465017i	0.188495	−	0.982074i	$-0.439639\pi$
$677$	27.1757	−	12.0994i	1.04445	−	0.465017i	0.855951	+	0.517057i	$0.172972\pi$
$678$		0			0
$679$	6.48089	+	5.83542i	0.248714	+	0.223943i
$680$	−21.4361	+	48.1462i	−0.822036	+	1.84632i
$681$		0			0
$682$	29.7082	−	21.2503i	1.13759	−	0.813714i
$683$		−	27.9122i		−	1.06803i	−0.845475	−	0.534015i	$-0.820683\pi$
$683$		−	27.9122i		−	1.06803i	0.845475	−	0.534015i	$-0.179317\pi$
$684$		0			0
$685$	−1.66482	−	5.12378i	−0.0636094	−	0.195770i
$686$	34.4380	−	31.0081i	1.31485	−	1.18390i
$687$		0			0
$688$	−27.7490	−	2.91654i	−1.05792	−	0.111192i
$689$	−0.978349	+	0.207954i	−0.0372721	+	0.00792243i
$690$		0			0
$691$	−0.134166	−	1.27650i	−0.00510390	−	0.0485604i	0.991674	−	0.128777i	$-0.0411053\pi$
$691$	−0.134166	−	1.27650i	−0.00510390	−	0.0485604i	−0.996777	+	0.0802171i	$0.974439\pi$
$692$	−54.9382			−2.08844
$693$		0			0
$694$	−27.8516			−1.05723
$695$	2.57353	+	24.4855i	0.0976197	+	0.928790i
$696$		0			0
$697$	18.5598	−	3.94501i	0.703003	−	0.149428i
$698$	−49.4397	−	5.19632i	−1.87132	−	0.196684i
$699$		0			0
$700$	−16.3925	+	14.7599i	−0.619579	+	0.557871i
$701$	−9.82030	−	30.2238i	−0.370908	−	1.14154i	−0.946198	−	0.323588i	$-0.895111\pi$
$701$	−9.82030	−	30.2238i	−0.370908	−	1.14154i	0.575290	−	0.817949i	$-0.304889\pi$
$702$		0			0
$703$		−	12.5112i		−	0.471869i
$704$	72.0097	+	0.532773i	2.71397	+	0.0200796i
$705$		0			0
$706$	−14.6734	+	32.9570i	−0.552241	+	1.24035i
$707$	−12.4902	−	11.2463i	−0.469744	−	0.422959i
$708$		0			0
$709$	0.437717	−	0.194884i	0.0164388	−	0.00731903i	−0.398501	−	0.917168i	$-0.630469\pi$
$709$	0.437717	−	0.194884i	0.0164388	−	0.00731903i	0.414940	+	0.909849i	$0.363803\pi$
$710$	−28.9110	−	21.0050i	−1.08501	−	0.788305i
$711$		0			0
$712$	42.6902	−	13.8709i	1.59988	−	0.519833i
$713$	−23.6116	+	2.48168i	−0.884260	+	0.0929395i
$714$		0			0
$715$	−13.0929	+	5.71365i	−0.489647	+	0.213678i
$716$	45.8688	−	26.4823i	1.71420	−	0.989692i
$717$		0			0
$718$	−16.4449	−	3.49548i	−0.613719	−	0.130450i
$719$	22.0526	+	7.16534i	0.822425	+	0.267222i	0.689851	−	0.723951i	$-0.257676\pi$
$719$	22.0526	+	7.16534i	0.822425	+	0.267222i	0.132574	+	0.991173i	$0.457676\pi$
$720$		0			0
$721$	−2.84253	+	3.91241i	−0.105862	+	0.145706i
$722$	−31.4202	−	34.8957i	−1.16934	−	1.29868i
$723$		0			0
$724$	−74.4608	−	33.1521i	−2.76731	−	1.23209i
$725$	−0.141487	−	0.245062i	−0.00525468	−	0.00910137i
$726$		0			0
$727$	−19.7219	+	34.1593i	−0.731444	+	1.26690i	0.224822	+	0.974400i	$0.427820\pi$
$727$	−19.7219	+	34.1593i	−0.731444	+	1.26690i	−0.956266	+	0.292498i	$0.905513\pi$
$728$	−30.5055	+	22.1635i	−1.13061	+	0.821435i
$729$		0			0
$730$	−8.55002	+	26.3143i	−0.316450	+	0.973934i
$731$	−3.59024	−	8.06381i	−0.132790	−	0.298251i
$732$		0			0
$733$	−2.03269	−	9.56304i	−0.0750790	−	0.353219i	0.924532	−	0.381104i	$-0.124456\pi$
$733$	−2.03269	−	9.56304i	−0.0750790	−	0.353219i	−0.999611	+	0.0278852i	$0.991123\pi$
$734$	13.8803	−	15.4156i	0.512330	−	0.569000i
$735$		0			0
$736$	−89.5343	−	51.6927i	−3.30028	−	1.90542i
$737$	−1.27523	+	11.3262i	−0.0469735	+	0.417207i
$738$		0			0
$739$	−14.0478	−	19.3351i	−0.516757	−	0.711255i	0.468284	−	0.883578i	$-0.344873\pi$
$739$	−14.0478	−	19.3351i	−0.516757	−	0.711255i	−0.985040	+	0.172324i	$0.944873\pi$
$740$	−15.7949	+	74.3093i	−0.580633	+	2.73167i
$741$		0			0
$742$	0.136585	−	1.29952i	0.00501418	−	0.0477067i
$743$	3.84917	−	36.6224i	0.141212	−	1.34355i	−0.662738	−	0.748851i	$-0.730606\pi$
$743$	3.84917	−	36.6224i	0.141212	−	1.34355i	0.803951	−	0.594696i	$-0.202727\pi$
$744$		0			0
$745$	−3.44503	+	16.2076i	−0.126216	+	0.593799i
$746$	33.3459	+	45.8967i	1.22088	+	1.68040i
$747$		0			0
$748$	35.7263	+	62.9508i	1.30628	+	2.30171i
$749$	−11.8205	−	6.82456i	−0.431911	−	0.249364i
$750$		0			0
$751$	−20.5430	+	22.8153i	−0.749625	+	0.832543i	−0.990428	−	0.138031i	$-0.955923\pi$
$751$	−20.5430	+	22.8153i	−0.749625	+	0.832543i	0.240803	+	0.970574i	$0.422589\pi$
$752$	19.8045	+	93.1730i	0.722197	+	3.39767i
$753$		0			0
$754$	−0.317559	−	0.713249i	−0.0115648	−	0.0259750i
$755$	0.475281	−	1.46276i	0.0172972	−	0.0532354i
$756$		0			0
$757$	−34.5971	+	25.1362i	−1.25745	+	0.913592i	−0.998630	−	0.0523331i	$-0.983334\pi$
$757$	−34.5971	+	25.1362i	−1.25745	+	0.913592i	−0.258822	+	0.965925i	$0.583334\pi$
$758$	−39.9585	+	69.2101i	−1.45136	+	2.51383i
$759$		0			0
$760$	−7.95143	−	13.7723i	−0.288429	−	0.499573i
$761$	−24.6757	−	10.9863i	−0.894493	−	0.398254i	−0.0925874	−	0.995705i	$-0.529514\pi$
$761$	−24.6757	−	10.9863i	−0.894493	−	0.398254i	−0.801906	+	0.597451i	$0.796180\pi$
$762$		0			0
$763$	3.97331	+	4.41281i	0.143844	+	0.159755i
$764$	11.4788	−	15.7991i	0.415287	−	0.571593i
$765$		0			0
$766$	−6.83574	−	2.22107i	−0.246985	−	0.0802504i
$767$	8.81326	+	1.87332i	0.318228	+	0.0676415i
$768$		0			0
$769$	−41.9099	+	24.1967i	−1.51131	+	0.872555i	−0.511396	+	0.859345i	$0.670871\pi$
$769$	−41.9099	+	24.1967i	−1.51131	+	0.872555i	−0.999913	+	0.0132095i	$0.995795\pi$
$770$	−1.81338	−	18.5741i	−0.0653498	−	0.669364i
$771$		0			0
$772$	−130.379	+	13.7033i	−4.69242	+	0.493194i
$773$	33.6456	−	10.9321i	1.21015	−	0.393201i	0.366664	−	0.930354i	$-0.380500\pi$
$773$	33.6456	−	10.9321i	1.21015	−	0.393201i	0.843485	+	0.537152i	$0.180500\pi$
$774$		0			0
$775$	−9.61296	−	6.98422i	−0.345308	−	0.250881i
$776$	−48.4216	+	21.5587i	−1.73823	+	0.773911i
$777$		0			0
$778$	1.27613	+	1.14903i	0.0457513	+	0.0411947i
$779$	−2.32876	+	5.23049i	−0.0834366	+	0.187402i
$780$		0			0
$781$	−28.9884	+	9.18235i	−1.03729	+	0.328570i
$782$		−	64.9467i		−	2.32249i
$783$		0			0
$784$	19.9344	+	61.3518i	0.711943	+	2.19113i
$785$	0.0918149	−	0.0826705i	0.00327701	−	0.00295064i
$786$		0			0
$787$	−25.6484	−	2.69576i	−0.914267	−	0.0960933i	−0.364302	−	0.931281i	$-0.618692\pi$
$787$	−25.6484	−	2.69576i	−0.914267	−	0.0960933i	−0.549965	+	0.835188i	$0.685359\pi$
$788$	98.8396	−	21.0090i	3.52101	−	0.748415i
$789$		0			0
$790$	−4.08257	−	38.8430i	−0.145251	−	1.38197i
$791$	−29.1938			−1.03801
$792$		0			0
$793$	−0.947564			−0.0336490
$794$	−7.10012	−	67.5531i	−0.251974	−	2.39737i
$795$		0			0
$796$	133.761	−	28.4319i	4.74105	−	1.00774i
$797$	−16.9653	−	1.78313i	−0.600943	−	0.0631617i	−0.200828	−	0.979627i	$-0.564363\pi$
$797$	−16.9653	−	1.78313i	−0.600943	−	0.0631617i	−0.400115	+	0.916465i	$0.631030\pi$
$798$		0			0
$799$	−22.3943	+	20.1639i	−0.792252	+	0.713347i
$800$	−15.9893	−	49.2101i	−0.565308	−	1.73984i
$801$		0			0
$802$			78.5813i			2.77480i
$803$	13.6971	+	19.1488i	0.483360	+	0.675745i
$804$		0			0
$805$	−4.93388	+	11.0817i	−0.173897	+	0.390578i
$806$	−24.3634	−	21.9369i	−0.858165	−	0.772696i
$807$		0			0
$808$	93.3200	−	41.5487i	3.28299	−	1.46168i
$809$	38.7684	+	28.1669i	1.36302	+	0.990295i	0.998246	+	0.0592001i	$0.0188550\pi$
$809$	38.7684	+	28.1669i	1.36302	+	0.990295i	0.364778	+	0.931095i	$0.381145\pi$
$810$		0			0
$811$	45.0299	−	14.6311i	1.58121	−	0.513768i	0.618845	−	0.785513i	$-0.287601\pi$
$811$	45.0299	−	14.6311i	1.58121	−	0.513768i	0.962369	+	0.271745i	$0.0876009\pi$
$812$	0.734827	−	0.0772334i	0.0257874	−	0.00271036i
$813$		0			0
$814$	59.2181	+	66.7550i	2.07559	+	2.33976i
$815$	3.67109	−	2.11951i	0.128593	−	0.0742430i
$816$		0			0
$817$	2.60530	+	0.553774i	0.0911480	+	0.0193741i
$818$	42.5510	+	13.8257i	1.48776	+	0.483403i
$819$		0			0
$820$	20.4348	−	28.1261i	0.713615	−	0.982207i
$821$	11.7622	+	13.0632i	0.410503	+	0.455910i	0.912571	−	0.408918i	$-0.134094\pi$
$821$	11.7622	+	13.0632i	0.410503	+	0.455910i	−0.502068	+	0.864828i	$0.667427\pi$
$822$		0			0
$823$	26.1285	+	11.6332i	0.910784	+	0.405507i	0.807990	−	0.589196i	$-0.200555\pi$
$823$	26.1285	+	11.6332i	0.910784	+	0.405507i	0.102793	+	0.994703i	$0.467222\pi$
$824$	−14.6962	−	25.4545i	−0.511966	−	0.886751i
$825$		0			0
$826$	−5.88546	+	10.1939i	−0.204781	+	0.354691i
$827$	13.0031	−	9.44733i	0.452163	−	0.328516i	−0.338286	−	0.941043i	$-0.609847\pi$
$827$	13.0031	−	9.44733i	0.452163	−	0.328516i	0.790449	+	0.612527i	$0.209847\pi$
$828$		0			0
$829$	0.324003	−	0.997179i	0.0112531	−	0.0346335i	−0.945272	−	0.326282i	$-0.894204\pi$
$829$	0.324003	−	0.997179i	0.0112531	−	0.0346335i	0.956525	+	0.291649i	$0.0942039\pi$
$830$	9.45567	+	21.2378i	0.328211	+	0.737174i
$831$		0			0
$832$	−13.4383	−	63.2222i	−0.465889	−	2.19184i
$833$	−13.6555	+	15.1660i	−0.473137	+	0.525471i
$834$		0			0
$835$	5.58062	+	3.22197i	0.193125	+	0.111501i
$836$	−21.7040	−	2.44366i	−0.750648	−	0.0845158i
$837$		0			0
$838$	14.8427	+	20.4292i	0.512733	+	0.705716i
$839$	−4.36460	+	20.5338i	−0.150683	+	0.708907i	0.836325	+	0.548234i	$0.184700\pi$
$839$	−4.36460	+	20.5338i	−0.150683	+	0.708907i	−0.987008	+	0.160673i	$0.948634\pi$
$840$		0			0
$841$	3.03033	−	28.8317i	0.104494	−	0.994197i
$842$	−0.932356	+	8.87077i	−0.0321311	+	0.305707i
$843$		0			0
$844$	24.8518	−	116.919i	0.855435	−	4.02451i
$845$	−3.51944	−	4.84410i	−0.121073	−	0.166642i
$846$		0			0
$847$	−13.6335	−	8.14260i	−0.468451	−	0.279783i
$848$	3.81836	+	2.20453i	0.131123	+	0.0757039i
$849$		0			0
$850$	21.7499	−	24.1557i	0.746015	−	0.828534i
$851$	−12.0594	−	56.7350i	−0.413391	−	1.94485i
$852$		0			0
$853$	−2.15268	−	4.83501i	−0.0737065	−	0.165547i	0.872935	−	0.487837i	$-0.162214\pi$
$853$	−2.15268	−	4.83501i	−0.0737065	−	0.165547i	−0.946641	+	0.322290i	$0.895547\pi$
$854$	0.382533	−	1.17732i	0.0130900	−	0.0402869i
$855$		0			0
$856$	67.1135	−	48.7608i	2.29389	−	1.66661i
$857$	3.88021	−	6.72072i	0.132545	−	0.229575i	−0.792112	−	0.610376i	$-0.791018\pi$
$857$	3.88021	−	6.72072i	0.132545	−	0.229575i	0.924657	+	0.380801i	$0.124352\pi$
$858$		0			0
$859$	24.3358	+	42.1508i	0.830326	+	1.43817i	0.897780	+	0.440445i	$0.145179\pi$
$859$	24.3358	+	42.1508i	0.830326	+	1.43817i	−0.0674537	+	0.997722i	$0.521488\pi$
$860$	−14.7749	−	6.57820i	−0.503819	−	0.224315i
$861$		0			0
$862$	3.83666	+	4.26105i	0.130677	+	0.145132i
$863$	−8.87079	+	12.2096i	−0.301965	+	0.415619i	−0.932854	−	0.360253i	$-0.882690\pi$
$863$	−8.87079	+	12.2096i	−0.301965	+	0.415619i	0.630889	+	0.775873i	$0.282690\pi$
$864$		0			0
$865$	−14.3805	−	4.67250i	−0.488951	−	0.158870i
$866$	−40.5949	−	8.62871i	−1.37947	−	0.293215i
$867$		0			0
$868$	26.8693	−	15.5130i	0.912002	−	0.526545i
$869$	−28.6576	−	16.8294i	−0.972144	−	0.570899i
$870$		0			0
$871$	10.1741	−	1.06934i	0.344737	−	0.0362334i
$872$	−34.3238	+	11.1525i	−1.16235	+	0.377671i
$873$		0			0
$874$	15.8547	+	11.5191i	0.536294	+	0.389640i
$875$	−15.0871	+	6.71723i	−0.510038	+	0.227084i
$876$		0			0
$877$	−16.4615	−	14.8220i	−0.555866	−	0.500504i	0.342639	−	0.939467i	$-0.388679\pi$
$877$	−16.4615	−	14.8220i	−0.555866	−	0.500504i	−0.898505	+	0.438963i	$0.855346\pi$
$878$	−39.2320	+	88.1166i	−1.32402	+	2.97379i
$879$		0			0
$880$	59.7442	+	19.9019i	2.01398	+	0.670894i
$881$			18.8235i			0.634180i	0.948395	+	0.317090i	$0.102706\pi$
$881$			18.8235i			0.634180i	−0.948395	+	0.317090i	$0.897294\pi$
$882$		0			0
$883$	−11.7223	−	36.0776i	−0.394488	−	1.21411i	−0.929360	−	0.369175i	$-0.879640\pi$
$883$	−11.7223	−	36.0776i	−0.394488	−	1.21411i	0.534872	−	0.844933i	$-0.320360\pi$
$884$	48.2800	−	43.4715i	1.62383	−	1.46211i
$885$		0			0
$886$	−32.1432	−	3.37839i	−1.07987	−	0.113499i
$887$	28.4769	−	6.05295i	0.956161	−	0.203238i	0.296694	−	0.954972i	$-0.404116\pi$
$887$	28.4769	−	6.05295i	0.956161	−	0.203238i	0.659466	+	0.751734i	$0.270782\pi$
$888$		0			0
$889$	−0.0155287	−	0.147746i	−0.000520816	−	0.00495523i
$890$	19.9403			0.668401
$891$		0			0
$892$	−119.589			−4.00414
$893$	−0.950476	−	9.04317i	−0.0318065	−	0.302618i
$894$		0			0
$895$	14.2588	−	3.03080i	0.476619	−	0.101309i
$896$	32.8583	+	3.45355i	1.09772	+	0.115375i
$897$		0			0
$898$	51.1187	−	46.0275i	1.70585	−	1.53596i
$899$	0.122993	+	0.378534i	0.00410205	+	0.0126248i
$900$		0			0
$901$			1.39484i			0.0464688i
$902$	−12.3316	−	38.9305i	−0.410597	−	1.29624i
$903$		0			0
$904$	72.1692	−	162.095i	2.40031	−	5.39119i
$905$	−16.6711	−	15.0107i	−0.554165	−	0.498972i
$906$		0			0
$907$	−16.9502	+	7.54671i	−0.562822	+	0.250584i	−0.668369	−	0.743830i	$-0.733007\pi$
$907$	−16.9502	+	7.54671i	−0.562822	+	0.250584i	0.105547	+	0.994414i	$0.466341\pi$
$908$	34.5673	+	25.1146i	1.14716	+	0.833458i
$909$		0			0
$910$	−15.9308	+	5.17622i	−0.528100	+	0.171590i
$911$	−33.0374	+	3.47238i	−1.09458	+	0.115045i	−0.634567	−	0.772868i	$-0.718822\pi$
$911$	−33.0374	+	3.47238i	−1.09458	+	0.115045i	−0.460012	+	0.887913i	$0.652155\pi$
$912$		0			0
$913$	19.3183	+	4.25586i	0.639344	+	0.140848i
$914$	−2.37949	+	1.37380i	−0.0787064	+	0.0454411i
$915$		0			0
$916$	−69.9002	−	14.8578i	−2.30957	−	0.490914i
$917$	21.0963	+	6.85459i	0.696660	+	0.226359i
$918$		0			0
$919$	−10.8277	+	14.9031i	−0.357173	+	0.491606i	−0.949358	−	0.314195i	$-0.898265\pi$
$919$	−10.8277	+	14.9031i	−0.357173	+	0.491606i	0.592185	+	0.805802i	$0.298265\pi$
$920$	−49.3326	−	54.7894i	−1.62645	−	1.80635i
$921$		0			0
$922$	−11.1336	−	4.95702i	−0.366667	−	0.163251i
$923$	13.6464	+	23.6363i	0.449178	+	0.777999i
$924$		0			0
$925$	14.5146	−	25.1401i	0.477238	−	0.826600i
$926$	−18.4200	+	13.3829i	−0.605320	+	0.439791i
$927$		0			0
$928$	−0.535586	+	1.64836i	−0.0175815	+	0.0541102i
$929$	−11.9113	−	26.7533i	−0.390798	−	0.877747i	−0.996620	−	0.0821472i	$-0.973822\pi$
$929$	−11.9113	−	26.7533i	−0.390798	−	0.877747i	0.605822	−	0.795600i	$-0.292844\pi$
$930$		0			0
$931$	−1.28033	−	6.02346i	−0.0419610	−	0.197411i
$932$	17.7904	−	19.7582i	0.582743	−	0.647202i
$933$		0			0
$934$	−14.4710	−	8.35483i	−0.473505	−	0.273378i
$935$	3.99765	+	19.5164i	0.130737	+	0.638253i
$936$		0			0
$937$	−9.28756	−	12.7832i	−0.303411	−	0.417610i	0.629901	−	0.776675i	$-0.283095\pi$
$937$	−9.28756	−	12.7832i	−0.303411	−	0.417610i	−0.933312	+	0.359066i	$0.883095\pi$
$938$	−2.77869	+	13.0727i	−0.0907275	+	0.426839i
$939$		0			0
$940$	−5.77140	+	54.9112i	−0.188242	+	1.79101i
$941$	0.865821	−	8.23774i	0.0282250	−	0.268543i	−0.971304	−	0.237843i	$-0.923560\pi$
$941$	0.865821	−	8.23774i	0.0282250	−	0.268543i	0.999529	−	0.0306999i	$-0.00977362\pi$
$942$		0			0
$943$	−5.51873	+	25.9636i	−0.179715	+	0.845490i
$944$	−23.3457	−	32.1326i	−0.759839	−	1.04583i
$945$		0			0
$946$	−16.5220	+	9.37671i	−0.537178	+	0.304863i
$947$	4.25424	+	2.45619i	0.138244	+	0.0798154i	0.567527	−	0.823355i	$-0.307900\pi$
$947$	4.25424	+	2.45619i	0.138244	+	0.0798154i	−0.429283	+	0.903170i	$0.641234\pi$
$948$		0			0
$949$	14.1397	−	15.7037i	0.458994	−	0.509764i
$950$	2.03924	+	9.59388i	0.0661617	+	0.311266i
$951$		0			0
$952$	21.3879	+	48.0379i	0.693185	+	1.55692i
$953$	−1.81366	+	5.58186i	−0.0587501	+	0.180814i	−0.976125	−	0.217211i	$-0.930304\pi$
$953$	−1.81366	+	5.58186i	−0.0587501	+	0.180814i	0.917375	+	0.398025i	$0.130304\pi$
$954$		0			0
$955$	4.34837	−	3.15927i	0.140710	−	0.102232i
$956$	53.0067	−	91.8103i	1.71436	−	2.96936i
$957$		0			0
$958$	30.0453	+	52.0401i	0.970721	+	1.68134i
$959$	−4.91062	−	2.18635i	−0.158572	−	0.0706009i
$960$		0			0
$961$	−9.55992	−	10.6174i	−0.308384	−	0.342496i
$962$	47.0782	−	64.7976i	1.51786	−	2.08916i
$963$		0			0
$964$	141.498	+	45.9756i	4.55735	+	1.48077i
$965$	−35.2930	−	7.50176i	−1.13612	−	0.241490i
$966$		0			0
$967$	−15.1909	+	8.77049i	−0.488507	+	0.282040i	−0.723955	−	0.689847i	$-0.757678\pi$
$967$	−15.1909	+	8.77049i	−0.488507	+	0.282040i	0.235448	+	0.971887i	$0.424344\pi$
$968$	78.9135	−	55.5688i	2.53638	−	1.78605i
$969$		0			0
$970$	−23.4171	+	2.46124i	−0.751878	+	0.0790255i
$971$	−46.6836	+	15.1684i	−1.49815	+	0.486778i	−0.939478	−	0.342610i	$-0.888689\pi$
$971$	−46.6836	+	15.1684i	−1.49815	+	0.486778i	−0.558672	+	0.829389i	$0.688689\pi$
$972$		0			0
$973$	19.8735	+	14.4390i	0.637117	+	0.462892i
$974$	−83.8527	+	37.3336i	−2.68681	+	1.19625i
$975$		0			0
$976$	3.10412	+	2.79496i	0.0993605	+	0.0894646i
$977$	−5.10387	+	11.4635i	−0.163287	+	0.366749i	−0.976596	−	0.215084i	$-0.930998\pi$
$977$	−5.10387	+	11.4635i	−0.163287	+	0.366749i	0.813308	+	0.581833i	$0.197664\pi$
$978$		0			0
$979$	10.0744	−	13.6527i	0.321980	−	0.436342i
$980$			37.3923i			1.19445i
$981$		0			0
$982$	−15.6708	−	48.2298i	−0.500076	−	1.53908i
$983$	15.6637	−	14.1037i	0.499594	−	0.449837i	−0.380399	−	0.924822i	$-0.624213\pi$
$983$	15.6637	−	14.1037i	0.499594	−	0.449837i	0.879994	+	0.474986i	$0.157547\pi$
$984$		0			0
$985$	27.6588	+	2.90706i	0.881282	+	0.0926265i
$986$	−1.06500	+	0.226373i	−0.0339165	+	0.00720917i
$987$		0			0
$988$	2.04914	+	19.4963i	0.0651919	+	0.620259i
$989$	12.3481			0.392648
$990$		0			0
$991$	60.3045			1.91564			0.957818	−	0.287375i	$-0.0927826\pi$
$991$	60.3045			1.91564			0.957818	+	0.287375i	$0.0927826\pi$
$992$	7.60738	+	72.3794i	0.241535	+	2.29805i
$993$		0			0
$994$	−34.8764	+	7.41321i	−1.10621	+	0.235133i
$995$	37.4311	+	3.93417i	1.18665	+	0.124722i
$996$		0			0
$997$	−41.7692	+	37.6091i	−1.32284	+	1.19109i	−0.356365	+	0.934347i	$0.615984\pi$
$997$	−41.7692	+	37.6091i	−1.32284	+	1.19109i	−0.966479	+	0.256747i	$0.917349\pi$
$998$	−6.32493	−	19.4661i	−0.200212	−	0.616190i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.8.10		80
3.2	odd	2		99.2.p.a.74.1	yes	80
9.2	odd	6		891.2.k.a.404.1		80
9.4	even	3		99.2.p.a.41.1	yes	80
9.5	odd	6	inner	297.2.t.a.206.10		80
9.7	even	3		891.2.k.a.404.20		80
11.7	odd	10	inner	297.2.t.a.62.10		80
33.29	even	10		99.2.p.a.29.1	✓	80
99.7	odd	30		891.2.k.a.161.1		80
99.29	even	30		891.2.k.a.161.20		80
99.40	odd	30		99.2.p.a.95.1	yes	80
99.95	even	30	inner	297.2.t.a.260.10		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.1	✓	80	33.29	even	10
99.2.p.a.41.1	yes	80	9.4	even	3
99.2.p.a.74.1	yes	80	3.2	odd	2
99.2.p.a.95.1	yes	80	99.40	odd	30
297.2.t.a.8.10		80	1.1	even	1	trivial
297.2.t.a.62.10		80	11.7	odd	10	inner
297.2.t.a.206.10		80	9.5	odd	6	inner
297.2.t.a.260.10		80	99.95	even	30	inner
891.2.k.a.161.1		80	99.7	odd	30
891.2.k.a.161.20		80	99.29	even	30
891.2.k.a.404.1		80	9.2	odd	6
891.2.k.a.404.20		80	9.7	even	3

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.t (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.281588 + 2.67913i) q^{2} +(-5.14217 + 1.09300i) q^{4} +(-1.43896 - 0.151241i) q^{5} +(-1.07283 + 0.965979i) q^{7} +(-2.71136 - 8.34470i) q^{8} -3.89775i q^{10} +(-2.66871 - 1.96926i) q^{11} +(-1.21080 + 2.71950i) q^{13} +(-2.89008 - 2.60224i) q^{14} +(11.9880 - 5.33739i) q^{16} +(3.35854 + 2.44012i) q^{17} +(-1.19136 + 0.387096i) q^{19} +(7.56469 - 0.795081i) q^{20} +(4.52444 - 7.70435i) q^{22} +(-5.02939 + 2.90372i) q^{23} +(-2.84300 - 0.604299i) q^{25} +(-7.62685 - 2.47811i) q^{26} +(4.46085 - 6.13983i) q^{28} +(0.0651453 + 0.0723511i) q^{29} +(3.73471 + 1.66280i) q^{31} +(8.90112 + 15.4172i) q^{32} +(-5.59169 + 9.68509i) q^{34} +(1.68985 - 1.22775i) q^{35} +(-3.08635 + 9.49880i) q^{37} +(-1.37255 - 3.08281i) q^{38} +(2.63948 + 12.4178i) q^{40} +(3.05835 - 3.39664i) q^{41} +(-1.84140 - 1.06313i) q^{43} +(15.8754 + 7.20937i) q^{44} +(-9.19566 - 12.6567i) q^{46} +(-1.50921 + 7.10026i) q^{47} +(-0.513854 + 4.88899i) q^{49} +(0.818442 - 7.78695i) q^{50} +(3.25372 - 15.3075i) q^{52} +(0.197492 + 0.271824i) q^{53} +(3.54233 + 3.23731i) q^{55} +(10.9696 + 6.33332i) q^{56} +(-0.175494 + 0.194906i) q^{58} +(-0.629292 - 2.96059i) q^{59} +(0.129468 + 0.290790i) q^{61} +(-3.40321 + 10.4740i) q^{62} +(-17.5657 + 12.7622i) q^{64} +(2.15359 - 3.73013i) q^{65} +(-1.71828 - 2.97615i) q^{67} +(-19.9373 - 8.87664i) q^{68} +(3.76515 + 4.18162i) q^{70} +(5.38901 - 7.41734i) q^{71} +(-6.75113 - 2.19358i) q^{73} +(-26.3176 - 5.59399i) q^{74} +(5.70308 - 3.29267i) q^{76} +(4.76533 - 0.465238i) q^{77} +(9.96549 - 1.04742i) q^{79} +(-18.0574 + 5.86722i) q^{80} +(9.96124 + 7.23727i) q^{82} +(-5.44872 + 2.42593i) q^{83} +(-4.46376 - 4.01919i) q^{85} +(2.32976 - 5.23272i) q^{86} +(-9.19707 + 27.6090i) q^{88} +5.11584i q^{89} +(-1.32800 - 4.08716i) q^{91} +(22.6882 - 20.4285i) q^{92} +(-19.4475 - 2.04402i) q^{94} +(1.77286 - 0.376834i) q^{95} +(-0.631450 - 6.00784i) q^{97} -13.2430 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

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