LMFDB - Embedded newform 297.2.t.a.62.10

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			62.10
Character	$\chi$	$=$	297.62
Dual form			297.2.t.a.206.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.46099 - 1.09570i) q^{2} +(3.51765 - 3.90675i) q^{4} +(-0.588502 + 1.32180i) q^{5} +(-0.300148 + 1.41209i) q^{7} +(2.71136 - 8.34470i) q^{8} +3.89775i q^{10} +(-3.03979 - 1.32654i) q^{11} +(2.96055 + 0.311167i) q^{13} +(0.808567 + 3.80401i) q^{14} +(-1.37167 - 13.0506i) q^{16} +(-3.35854 + 2.44012i) q^{17} +(-1.19136 - 0.387096i) q^{19} +(3.09378 + 6.94875i) q^{20} +(-8.93438 + 0.0661021i) q^{22} +(-5.02939 + 2.90372i) q^{23} +(1.94484 + 2.15996i) q^{25} +(7.62685 - 2.47811i) q^{26} +(4.46085 + 6.13983i) q^{28} +(0.0952306 + 0.0202419i) q^{29} +(-0.427327 + 4.06575i) q^{31} +(-8.90112 - 15.4172i) q^{32} +(-5.59169 + 9.68509i) q^{34} +(-1.68985 - 1.22775i) q^{35} +(-3.08635 - 9.49880i) q^{37} +(-3.35607 + 0.352737i) q^{38} +(9.43436 + 8.49473i) q^{40} +(4.47075 - 0.950287i) q^{41} +(1.84140 + 1.06313i) q^{43} +(-15.8754 + 7.20937i) q^{44} +(-9.19566 + 12.6567i) q^{46} +(5.39440 - 4.85714i) q^{47} +(4.49092 + 1.99949i) q^{49} +(7.15292 + 3.18469i) q^{50} +(11.6299 - 10.4716i) q^{52} +(-0.197492 + 0.271824i) q^{53} +(3.54233 - 3.23731i) q^{55} +(10.9696 + 6.33332i) q^{56} +(0.256541 - 0.0545294i) q^{58} +(2.24930 + 2.02528i) q^{59} +(-0.316566 + 0.0332724i) q^{61} +(3.40321 + 10.4740i) q^{62} +(-17.5657 - 12.7622i) q^{64} +(-2.15359 + 3.73013i) q^{65} +(-1.71828 - 2.97615i) q^{67} +(-2.28123 + 21.7045i) q^{68} +(-5.50397 - 1.16990i) q^{70} +(-5.38901 - 7.41734i) q^{71} +(-6.75113 + 2.19358i) q^{73} +(-18.0034 - 19.9948i) q^{74} +(-5.70308 + 3.29267i) q^{76} +(2.78557 - 3.89428i) q^{77} +(-4.07566 - 9.15408i) q^{79} +(18.0574 + 5.86722i) q^{80} +(9.96124 - 7.23727i) q^{82} +(-0.623446 - 5.93169i) q^{83} +(-1.24884 - 5.87533i) q^{85} +(5.69655 + 0.598731i) q^{86} +(-19.3115 + 21.7694i) q^{88} +5.11584i q^{89} +(-1.32800 + 4.08716i) q^{91} +(-6.34754 + 29.8628i) q^{92} +(7.95359 - 17.8641i) q^{94} +(1.21278 - 1.34693i) q^{95} +(5.51867 - 2.45707i) q^{97} +13.2430 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	2.46099	−	1.09570i	1.74018	−	0.774780i	0.746142	−	0.665787i	$-0.231904\pi$
$2$	2.46099	−	1.09570i	1.74018	−	0.774780i	0.994043	−	0.108993i	$-0.0347625\pi$
$3$		0			0
$3$		0			0
$4$	3.51765	−	3.90675i	1.75883	−	1.95337i
$5$	−0.588502	+	1.32180i	−0.263186	+	0.591125i	−0.996005	−	0.0892983i	$-0.971538\pi$
$5$	−0.588502	+	1.32180i	−0.263186	+	0.591125i	0.732819	+	0.680424i	$0.238204\pi$
$6$		0			0
$7$	−0.300148	+	1.41209i	−0.113445	+	0.533718i	0.884319	+	0.466884i	$0.154623\pi$
$7$	−0.300148	+	1.41209i	−0.113445	+	0.533718i	−0.997764	+	0.0668347i	$0.978710\pi$
$8$	2.71136	−	8.34470i	0.958610	−	2.95030i
$9$		0			0
$10$			3.89775i			1.23258i
$11$	−3.03979	−	1.32654i	−0.916530	−	0.399967i
$11$	−3.03979	−	1.32654i	−0.916530	−	0.399967i
$12$		0			0
$13$	2.96055	+	0.311167i	0.821110	+	0.0863022i	0.505761	−	0.862674i	$-0.331212\pi$
$13$	2.96055	+	0.311167i	0.821110	+	0.0863022i	0.315349	+	0.948976i	$0.397878\pi$
$14$	0.808567	+	3.80401i	0.216099	+	1.01666i
$15$		0			0
$16$	−1.37167	−	13.0506i	−0.342918	−	3.26265i
$17$	−3.35854	+	2.44012i	−0.814566	+	0.591817i	−0.915151	−	0.403112i	$-0.867929\pi$
$17$	−3.35854	+	2.44012i	−0.814566	+	0.591817i	0.100585	+	0.994928i	$0.467929\pi$
$18$		0			0
$19$	−1.19136	−	0.387096i	−0.273317	−	0.0888059i	0.169152	−	0.985590i	$-0.445897\pi$
$19$	−1.19136	−	0.387096i	−0.273317	−	0.0888059i	−0.442468	+	0.896784i	$0.645897\pi$
$20$	3.09378	+	6.94875i	0.691791	+	1.55379i
$21$		0			0
$22$	−8.93438	+	0.0661021i	−1.90482	+	0.0140930i
$23$	−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
$25$	1.94484	+	2.15996i	0.388968	+	0.431993i
$26$	7.62685	−	2.47811i	1.49575	−	0.485998i
$27$		0			0
$28$	4.46085	+	6.13983i	0.843021	+	1.16032i
$29$	0.0952306	+	0.0202419i	0.0176839	+	0.00375882i	0.216745	−	0.976228i	$-0.430456\pi$
$29$	0.0952306	+	0.0202419i	0.0176839	+	0.00375882i	−0.199061	+	0.979987i	$0.563789\pi$
$30$		0			0
$31$	−0.427327	+	4.06575i	−0.0767503	+	0.730230i	0.886700	+	0.462344i	$0.152992\pi$
$31$	−0.427327	+	4.06575i	−0.0767503	+	0.730230i	−0.963451	+	0.267886i	$0.913675\pi$
$32$	−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	−0.796711	−	0.604360i	$-0.793429\pi$
$37$	−3.08635	−	9.49880i	−0.507392	−	1.56159i	0.289319	−	0.957233i	$-0.406571\pi$
$38$	−3.35607	+	0.352737i	−0.544426	+	0.0572215i
$39$		0			0
$40$	9.43436	+	8.49473i	1.49170	+	1.34314i
$41$	4.47075	−	0.950287i	0.698214	−	0.148410i	0.154888	−	0.987932i	$-0.450498\pi$
$41$	4.47075	−	0.950287i	0.698214	−	0.148410i	0.543325	+	0.839522i	$0.317165\pi$
$42$		0			0
$43$	1.84140	+	1.06313i	0.280811	+	0.162126i	0.633790	−	0.773505i	$-0.281498\pi$
$43$	1.84140	+	1.06313i	0.280811	+	0.162126i	−0.352980	+	0.935631i	$0.614832\pi$
$44$	−15.8754	+	7.20937i	−2.39330	+	1.08685i
$45$		0			0
$46$	−9.19566	+	12.6567i	−1.35583	+	1.86614i
$47$	5.39440	−	4.85714i	0.786855	−	0.708487i	−0.174241	−	0.984703i	$-0.555747\pi$
$47$	5.39440	−	4.85714i	0.786855	−	0.708487i	0.961096	+	0.276216i	$0.0890805\pi$
$48$		0			0
$49$	4.49092	+	1.99949i	0.641560	+	0.285641i
$50$	7.15292	+	3.18469i	1.01158	+	0.450383i
$51$		0			0
$52$	11.6299	−	10.4716i	1.61277	−	1.45215i
$53$	−0.197492	+	0.271824i	−0.0271276	+	0.0373379i	−0.822365	−	0.568960i	$-0.807346\pi$
$53$	−0.197492	+	0.271824i	−0.0271276	+	0.0373379i	0.795238	+	0.606298i	$0.207346\pi$
$54$		0			0
$55$	3.54233	−	3.23731i	0.477648	−	0.436518i
$56$	10.9696	+	6.33332i	1.46588	+	0.846325i
$57$		0			0
$58$	0.256541	−	0.0545294i	0.0336855	−	0.00716006i
$59$	2.24930	+	2.02528i	0.292833	+	0.263668i	0.802432	−	0.596744i	$-0.203539\pi$
$59$	2.24930	+	2.02528i	0.292833	+	0.263668i	−0.509598	+	0.860413i	$0.670206\pi$
$60$		0			0
$61$	−0.316566	+	0.0332724i	−0.0405321	+	0.00426009i	−0.124773	−	0.992185i	$-0.539820\pi$
$61$	−0.316566	+	0.0332724i	−0.0405321	+	0.00426009i	0.0842407	+	0.996445i	$0.473154\pi$
$62$	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	$0.900654\pi$
$68$	−2.28123	+	21.7045i	−0.276640	+	2.63206i
$69$		0			0
$70$	−5.50397	−	1.16990i	−0.657850	−	0.139830i
$71$	−5.38901	−	7.41734i	−0.639558	−	0.880276i	0.359034	−	0.933325i	$-0.383106\pi$
$71$	−5.38901	−	7.41734i	−0.639558	−	0.880276i	−0.998592	+	0.0530483i	$0.983106\pi$
$72$		0			0
$73$	−6.75113	+	2.19358i	−0.790160	+	0.256739i	−0.676172	−	0.736743i	$-0.736363\pi$
$73$	−6.75113	+	2.19358i	−0.790160	+	0.256739i	−0.113988	+	0.993482i	$0.536363\pi$
$74$	−18.0034	−	19.9948i	−2.09285	−	2.32434i
$75$		0			0
$76$	−5.70308	+	3.29267i	−0.654188	+	0.377695i
$77$	2.78557	−	3.89428i	0.317446	−	0.443794i
$78$		0			0
$79$	−4.07566	−	9.15408i	−0.458547	−	1.02991i	−0.983849	−	0.178998i	$-0.942714\pi$
$79$	−4.07566	−	9.15408i	−0.458547	−	1.02991i	0.525302	−	0.850916i	$-0.323952\pi$
$80$	18.0574	+	5.86722i	2.01888	+	0.655975i
$81$		0			0
$82$	9.96124	−	7.23727i	1.10004	−	0.799222i
$83$	−0.623446	−	5.93169i	−0.0684321	−	0.651088i	−0.973947	−	0.226774i	$-0.927182\pi$
$83$	−0.623446	−	5.93169i	−0.0684321	−	0.651088i	0.905515	−	0.424314i	$-0.139485\pi$
$84$		0			0
$85$	−1.24884	−	5.87533i	−0.135456	−	0.637269i
$86$	5.69655	+	0.598731i	0.614274	+	0.0645628i
$87$		0			0
$88$	−19.3115	+	21.7694i	−2.05861	+	2.32062i
$89$			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
$92$	−6.34754	+	29.8628i	−0.661777	+	3.11341i
$93$		0			0
$94$	7.95359	−	17.8641i	0.820350	−	1.84254i
$95$	1.21278	−	1.34693i	0.124429	−	0.138192i
$96$		0			0
$97$	5.51867	−	2.45707i	0.560336	−	0.249478i	−0.106969	−	0.994262i	$-0.534114\pi$
$97$	5.51867	−	2.45707i	0.560336	−	0.249478i	0.667305	+	0.744785i	$0.267448\pi$
$98$	13.2430			1.33774
$99$		0			0
$100$	15.2797			1.52797
$101$	10.6358	−	4.73537i	1.05830	−	0.471187i	0.197593	−	0.980284i	$-0.436687\pi$
$101$	10.6358	−	4.73537i	1.05830	−	0.471187i	0.860709	+	0.509098i	$0.170021\pi$
$102$		0			0
$103$	−2.24151	+	2.48945i	−0.220863	+	0.245293i	−0.843386	−	0.537309i	$-0.819441\pi$
$103$	−2.24151	+	2.48945i	−0.220863	+	0.245293i	0.622523	+	0.782602i	$0.286108\pi$
$104$	10.6237	−	23.8613i	1.04174	−	2.33979i
$105$		0			0
$106$	−0.188187	+	0.885350i	−0.0182783	+	0.0859928i
$107$	−2.92166	+	8.99195i	−0.282448	+	0.869285i	0.704704	+	0.709501i	$0.251080\pi$
$107$	−2.92166	+	8.99195i	−0.282448	+	0.869285i	−0.987152	+	0.159784i	$0.948920\pi$
$108$		0			0
$109$			4.11325i			0.393978i	0.980406	+	0.196989i	$0.0631163\pi$
$109$			4.11325i			0.393978i	−0.980406	+	0.196989i	$0.936884\pi$
$110$	5.17053	−	11.8483i	0.492990	−	1.12969i
$111$		0			0
$112$	18.8403	+	1.98019i	1.78024	+	0.187110i
$113$	−4.20449	−	19.7806i	−0.395525	−	1.86080i	−0.499640	−	0.866233i	$-0.666535\pi$
$113$	−4.20449	−	19.7806i	−0.395525	−	1.86080i	0.104116	−	0.994565i	$-0.466799\pi$
$114$		0			0
$115$	−0.878321	−	8.35667i	−0.0819039	−	0.779263i
$116$	0.414068	−	0.300838i	0.0384452	−	0.0279321i
$117$		0			0
$118$	7.75460	+	2.51962i	0.713869	+	0.231950i
$119$	−2.43760	−	5.47495i	−0.223455	−	0.501888i
$120$		0			0
$121$	7.48059	+	8.06479i	0.680053	+	0.733163i
$122$	−0.742609	+	0.428746i	−0.0672327	+	0.0388168i
$123$		0			0
$124$	14.3807	+	15.9714i	1.29142	+	1.43427i
$125$	−10.8799	+	3.53510i	−0.973131	+	0.316189i
$126$		0			0
$127$	−0.0604870	−	0.0832533i	−0.00536736	−	0.00738753i	0.806325	−	0.591473i	$-0.201453\pi$
$127$	−0.0604870	−	0.0832533i	−0.00536736	−	0.00738753i	−0.811692	+	0.584085i	$0.801453\pi$
$128$	−22.3861	−	4.75831i	−1.97867	−	0.420579i
$129$		0			0
$130$	−1.21285	+	11.5395i	−0.106374	+	1.01208i
$131$	7.68267	+	13.3068i	0.671238	+	1.16262i	0.977553	+	0.210689i	$0.0675706\pi$
$131$	7.68267	+	13.3068i	0.671238	+	1.16262i	−0.306315	+	0.951930i	$0.599096\pi$
$132$		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
$137$	3.70309	−	0.389210i	0.316376	−	0.0332525i	0.0549904	−	0.998487i	$-0.482487\pi$
$137$	3.70309	−	0.389210i	0.316376	−	0.0332525i	0.261386	+	0.965234i	$0.415821\pi$
$138$		0			0
$139$	−12.6455	−	11.3860i	−1.07257	−	0.965749i	−0.0730719	−	0.997327i	$-0.523280\pi$
$139$	−12.6455	−	11.3860i	−1.07257	−	0.965749i	−0.999501	+	0.0315774i	$0.989947\pi$
$140$	−10.7408	+	2.28303i	−0.907766	+	0.192952i
$141$		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
$146$	−14.2110	+	12.7956i	−1.17611	+	1.05897i
$147$		0			0
$148$	−47.9661	−	21.3559i	−3.94279	−	1.75544i
$149$	10.4619	+	4.65792i	0.857070	+	0.381592i	0.787744	−	0.616002i	$-0.211249\pi$
$149$	10.4619	+	4.65792i	0.857070	+	0.381592i	0.0693251	+	0.997594i	$0.477915\pi$
$150$		0			0
$151$	−0.789963	+	0.711286i	−0.0642863	+	0.0578836i	−0.700648	−	0.713508i	$-0.747105\pi$
$151$	−0.789963	+	0.711286i	−0.0642863	+	0.0578836i	0.636361	+	0.771391i	$0.280439\pi$
$152$	−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
$157$	0.0835237	−	0.0177535i	0.00666592	−	0.00141688i	−0.204578	−	0.978850i	$-0.565582\pi$
$157$	0.0835237	−	0.0177535i	0.00666592	−	0.00141688i	0.211243	+	0.977433i	$0.432249\pi$
$158$	−20.0603	−	18.0624i	−1.59591	−	1.43697i
$159$		0			0
$160$	25.6167	−	2.69242i	2.02518	−	0.212855i
$161$	−2.59074	−	7.97347i	−0.204179	−	0.628398i
$162$		0			0
$163$	−2.37021	−	1.72206i	−0.185650	−	0.134882i	0.491079	−	0.871115i	$-0.336603\pi$
$163$	−2.37021	−	1.72206i	−0.185650	−	0.134882i	−0.676728	+	0.736233i	$0.736603\pi$
$164$	12.0140	−	20.8089i	0.938136	−	1.62490i
$165$		0			0
$166$	−8.03368	−	13.9147i	−0.623534	−	1.07999i
$167$	−0.465535	+	4.42927i	−0.0360242	+	0.342747i	0.961633	+	0.274338i	$0.0884588\pi$
$167$	−0.465535	+	4.42927i	−0.0360242	+	0.342747i	−0.997657	+	0.0684086i	$0.978208\pi$
$168$		0			0
$169$	−4.04786	−	0.860399i	−0.311374	−	0.0661845i
$170$	−9.51100	−	13.0908i	−0.729461	−	1.00402i
$171$		0			0
$172$	10.6308	−	3.45415i	0.810590	−	0.263377i
$173$	6.99267	+	7.76615i	0.531643	+	0.590449i	0.947809	−	0.318839i	$-0.103293\pi$
$173$	6.99267	+	7.76615i	0.531643	+	0.590449i	−0.416166	+	0.909289i	$0.636626\pi$
$174$		0			0
$175$	−3.63380	+	2.09797i	−0.274689	+	0.158592i
$176$	−13.1425	+	41.4905i	−0.990655	+	3.12747i
$177$		0			0
$178$	5.60545	+	12.5901i	0.420146	+	0.943664i
$179$	9.58188	+	3.11334i	0.716183	+	0.232702i	0.644368	−	0.764716i	$-0.277121\pi$
$179$	9.58188	+	3.11334i	0.716183	+	0.232702i	0.0718157	+	0.997418i	$0.477121\pi$
$180$		0			0
$181$	12.5433	−	9.11327i	0.932339	−	0.677384i	−0.0142256	−	0.999899i	$-0.504528\pi$
$181$	12.5433	−	9.11327i	0.932339	−	0.677384i	0.946564	+	0.322515i	$0.104528\pi$
$182$	1.21012	+	11.5136i	0.0897004	+	0.853443i
$183$		0			0
$184$	10.5942	+	49.8417i	0.781014	+	3.67438i
$185$	14.3718	+	1.51054i	1.05664	+	0.111057i
$186$		0			0
$187$	13.4462	−	2.96221i	0.983281	−	0.216618i
$188$		−	38.1603i		−	2.78313i
$189$		0			0
$190$	1.50881	−	4.64363i	0.109460	−	0.336884i
$191$	0.772348	−	3.63361i	0.0558851	−	0.262919i	−0.941331	−	0.337485i	$-0.890424\pi$
$191$	0.772348	−	3.63361i	0.0558851	−	0.262919i	0.997216	+	0.0745660i	$0.0237572\pi$
$192$		0			0
$193$	−10.1429	+	22.7814i	−0.730103	+	1.63984i	0.0378104	+	0.999285i	$0.487962\pi$
$193$	−10.1429	+	22.7814i	−0.730103	+	1.63984i	−0.767914	+	0.640554i	$0.778705\pi$
$194$	10.8892	−	12.0937i	0.781798	−	0.868274i
$195$		0			0
$196$	23.6090	−	10.5114i	1.68636	−	0.750814i
$197$	19.2214			1.36947			0.684733	−	0.728794i	$-0.259919\pi$
$197$	19.2214			1.36947			0.684733	+	0.728794i	$0.259919\pi$
$198$		0			0
$199$	−26.0126			−1.84399			−0.921993	−	0.387206i	$-0.873440\pi$
$199$	−26.0126			−1.84399			−0.921993	+	0.387206i	$0.873440\pi$
$200$	23.2974	−	10.3727i	1.64738	−	0.733459i
$201$		0			0
$202$	20.9861	−	23.3074i	1.47657	−	1.63990i
$203$	−0.0571666	+	0.128398i	−0.00401231	+	0.00901179i
$204$		0			0
$205$	−1.37496	+	6.46867i	−0.0960312	+	0.451791i
$206$	−2.78864	+	8.58255i	−0.194294	+	0.597975i
$207$		0			0
$208$		−	39.0638i		−	2.70859i
$209$	3.10798	+	2.75707i	0.214983	+	0.190711i
$210$		0			0
$211$	22.6127	+	2.37669i	1.55672	+	0.163618i	0.843425	−	0.537247i	$-0.180536\pi$
$211$	22.6127	+	2.37669i	1.55672	+	0.163618i	0.713294	+	0.700865i	$0.247202\pi$
$212$	0.367241	+	1.72773i	0.0252222	+	0.118661i
$213$		0			0
$214$	2.66233	+	25.3304i	0.181993	+	1.73155i
$215$	−2.48891	+	1.80830i	−0.169742	+	0.123325i
$216$		0			0
$217$	−5.61293	−	1.82375i	−0.381030	−	0.123804i
$218$	4.50691	+	10.1227i	0.305246	+	0.685594i
$219$		0			0
$220$	−0.186643	−	25.2267i	−0.0125835	−	1.70079i
$221$	−10.7024	+	6.17905i	−0.719923	+	0.415648i
$222$		0			0
$223$	−15.2216	−	16.9053i	−1.01932	−	1.13206i	−0.991188	−	0.132460i	$-0.957712\pi$
$223$	−15.2216	−	16.9053i	−1.01932	−	1.13206i	−0.0281268	−	0.999604i	$-0.508954\pi$
$224$	24.4421	−	7.94170i	1.63310	−	0.530627i
$225$		0			0
$226$	−32.0208	−	44.0729i	−2.13000	−	2.93169i
$227$	−7.95006	−	1.68984i	−0.527664	−	0.112158i	−0.0636262	−	0.997974i	$-0.520267\pi$
$227$	−7.95006	−	1.68984i	−0.527664	−	0.112158i	−0.464038	+	0.885815i	$0.653600\pi$
$228$		0			0
$229$	−1.42091	+	13.5191i	−0.0938964	+	0.893365i	0.841617	+	0.540074i	$0.181604\pi$
$229$	−1.42091	+	13.5191i	−0.0938964	+	0.893365i	−0.935514	+	0.353290i	$0.885063\pi$
$230$	−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	$-0.247024\pi$
$233$	4.09157	+	2.97270i	0.268048	+	0.194748i	−0.445640	+	0.895212i	$0.647024\pi$
$234$		0			0
$235$	3.24554	+	9.98874i	0.211716	+	0.651594i
$236$	15.8245	−	1.66322i	1.03009	−	0.108266i
$237$		0			0
$238$	−11.9978	−	10.8029i	−0.777705	−	0.700249i
$239$	−19.7253	+	4.19274i	−1.27592	+	0.271206i	−0.795565	−	0.605868i	$-0.792826\pi$
$239$	−19.7253	+	4.19274i	−1.27592	+	0.271206i	−0.480356	+	0.877073i	$0.659493\pi$
$240$		0			0
$241$	24.5094	+	14.1505i	1.57879	+	0.911516i	0.995028	+	0.0995930i	$0.0317541\pi$
$241$	24.5094	+	14.1505i	1.57879	+	0.911516i	0.583764	+	0.811923i	$0.301579\pi$
$242$	27.2463	+	11.6509i	1.75146	+	0.748947i
$243$		0			0
$244$	−0.983581	+	1.35378i	−0.0629674	+	0.0866671i
$245$	−5.28583	+	4.75938i	−0.337699	+	0.304066i
$246$		0			0
$247$	−3.40663	−	1.51673i	−0.216759	−	0.0965073i
$248$	32.7688	+	14.5896i	2.08082	+	0.926442i
$249$		0			0
$250$	−22.9020	+	20.6210i	−1.44845	+	1.30419i
$251$	13.7475	−	18.9219i	0.867737	−	1.19434i	−0.111931	−	0.993716i	$-0.535704\pi$
$251$	13.7475	−	18.9219i	0.867737	−	1.19434i	0.979669	−	0.200622i	$-0.0642964\pi$
$252$		0			0
$253$	19.1401	−	2.15500i	1.20333	−	0.135483i
$254$	−0.240079	−	0.138610i	−0.0150639	−	0.00869715i
$255$		0			0
$256$	−17.8299	+	3.78987i	−1.11437	+	0.236867i
$257$	0.309493	+	0.278669i	0.0193057	+	0.0173829i	0.678727	−	0.734391i	$-0.262532\pi$
$257$	0.309493	+	0.278669i	0.0193057	+	0.0173829i	−0.659421	+	0.751774i	$0.729199\pi$
$258$		0			0
$259$	14.3395	−	1.50714i	0.891012	−	0.0936492i
$260$	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	$0.500559\pi$
$263$	−14.0588	+	24.3505i	−0.866902	+	1.50152i	−0.865146	+	0.501520i	$0.832774\pi$
$264$		0			0
$265$	−0.243072	−	0.421013i	−0.0149318	−	0.0258626i
$266$	0.509223	−	4.84493i	0.0312225	−	0.297062i
$267$		0			0
$268$	−17.6714	−	3.75617i	−1.07945	−	0.229445i
$269$	7.97137	+	10.9716i	0.486023	+	0.668953i	0.979648	−	0.200721i	$-0.0643286\pi$
$269$	7.97137	+	10.9716i	0.486023	+	0.668953i	−0.493625	+	0.869675i	$0.664329\pi$
$270$		0			0
$271$	−10.5963	+	3.44294i	−0.643678	+	0.209144i	−0.612624	−	0.790374i	$-0.709886\pi$
$271$	−10.5963	+	3.44294i	−0.643678	+	0.209144i	−0.0310533	+	0.999518i	$0.509886\pi$
$272$	36.4518	+	40.4839i	2.21022	+	2.45470i
$273$		0			0
$274$	8.68681	−	5.01533i	0.524789	−	0.302987i
$275$	−3.04662	−	9.14574i	−0.183718	−	0.551509i
$276$		0			0
$277$	−3.97962	−	8.93837i	−0.239112	−	0.537055i	0.753633	−	0.657296i	$-0.228300\pi$
$277$	−3.97962	−	8.93837i	−0.239112	−	0.537055i	−0.992745	+	0.120241i	$0.961633\pi$
$278$	−43.5961	−	14.1652i	−2.61472	−	0.849573i
$279$		0			0
$280$	−14.8270	+	10.7724i	−0.886083	+	0.643777i
$281$	−1.27367	−	12.1181i	−0.0759805	−	0.722906i	−0.964503	−	0.264073i	$-0.914934\pi$
$281$	−1.27367	−	12.1181i	−0.0759805	−	0.722906i	0.888522	−	0.458834i	$-0.151733\pi$
$282$		0			0
$283$	−3.20045	−	15.0569i	−0.190247	−	0.895042i	−0.964892	−	0.262646i	$-0.915405\pi$
$283$	−3.20045	−	15.0569i	−0.190247	−	0.895042i	0.774645	−	0.632396i	$-0.217928\pi$
$284$	−47.9344	−	5.03810i	−2.84438	−	0.298956i
$285$		0			0
$286$	−26.4713	−	2.58438i	−1.56528	−	0.152818i
$287$			6.59831i			0.389486i
$288$		0			0
$289$	0.0723102	−	0.222548i	0.00425354	−	0.0130911i
$290$	−0.0788979	+	0.371185i	−0.00463304	+	0.0217968i
$291$		0			0
$292$	−15.1784	+	34.0912i	−0.888248	+	1.99504i
$293$	−18.2132	+	20.2278i	−1.06403	+	1.18172i	−0.0812937	+	0.996690i	$0.525905\pi$
$293$	−18.2132	+	20.2278i	−1.06403	+	1.18172i	−0.982733	+	0.185031i	$0.940761\pi$
$294$		0			0
$295$	−4.00072	+	1.78123i	−0.232931	+	0.103707i
$296$	−87.6328			−5.09356
$297$		0			0
$298$	30.8503			1.78711
$299$	−15.7933	+	7.03164i	−0.913351	+	0.406650i
$300$		0			0
$301$	−2.05393	+	2.28112i	−0.118386	+	0.131481i
$302$	−1.16473	+	2.61603i	−0.0670229	+	0.150536i
$303$		0			0
$304$	−3.41768	+	16.0789i	−0.196017	+	0.922188i
$305$	0.142320	−	0.438016i	0.00814923	−	0.0250807i
$306$		0			0
$307$			31.0795i			1.77380i	0.461960	+	0.886901i	$0.347146\pi$
$307$			31.0795i			1.77380i	−0.461960	+	0.886901i	$0.652854\pi$
$308$	−5.41529	−	24.5813i	−0.308565	−	1.40065i
$309$		0			0
$310$	−15.8473	−	1.66562i	−0.900066	−	0.0946007i
$311$	1.18810	+	5.58959i	0.0673712	+	0.316956i	0.998910	−	0.0466865i	$-0.0148662\pi$
$311$	1.18810	+	5.58959i	0.0673712	+	0.316956i	−0.931538	+	0.363643i	$0.881533\pi$
$312$		0			0
$313$	2.76294	+	26.2876i	0.156171	+	1.48587i	0.739240	+	0.673442i	$0.235185\pi$
$313$	2.76294	+	26.2876i	0.156171	+	1.48587i	−0.583069	+	0.812423i	$0.698148\pi$
$314$	0.186099	−	0.135209i	0.0105021	−	0.00763026i
$315$		0			0
$316$	−50.0994	−	16.2783i	−2.81831	−	0.915725i
$317$	0.805282	+	1.80869i	0.0452291	+	0.101586i	0.934747	−	0.355314i	$-0.115626\pi$
$317$	0.805282	+	1.80869i	0.0452291	+	0.101586i	−0.889518	+	0.456901i	$0.848960\pi$
$318$		0			0
$319$	−0.262629	−	0.187858i	−0.0147044	−	0.0105180i
$320$	27.2064	−	15.7076i	1.52089	−	0.878084i
$321$		0			0
$322$	−15.1124	−	16.7840i	−0.842178	−	0.935334i
$323$	4.94579	−	1.60698i	0.275191	−	0.0894150i
$324$		0			0
$325$	5.08570	+	6.99986i	0.282104	+	0.388283i
$326$	−7.71995	−	1.64093i	−0.427569	−	0.0908825i
$327$		0			0
$328$	4.19194	−	39.8836i	0.231461	−	2.20220i
$329$	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
$335$	4.94508	−	0.519749i	0.270179	−	0.0283969i
$336$		0			0
$337$	21.2002	+	19.0887i	1.15485	+	1.03983i	0.998642	+	0.0521039i	$0.0165927\pi$
$337$	21.2002	+	19.0887i	1.15485	+	1.03983i	0.156205	+	0.987725i	$0.450074\pi$
$338$	−10.9045	+	2.31782i	−0.593126	+	0.126073i
$339$		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
$344$	13.8642	−	12.4834i	0.747508	−	0.673059i
$345$		0			0
$346$	25.7183	+	11.4505i	1.38262	+	0.615584i
$347$	−9.44498	−	4.20518i	−0.507033	−	0.225746i	0.137245	−	0.990537i	$-0.456175\pi$
$347$	−9.44498	−	4.20518i	−0.507033	−	0.225746i	−0.644278	+	0.764791i	$0.722842\pi$
$348$		0			0
$349$	−13.7137	+	12.3479i	−0.734078	+	0.660967i	−0.948861	−	0.315695i	$-0.897762\pi$
$349$	−13.7137	+	12.3479i	−0.734078	+	0.660967i	0.214783	+	0.976662i	$0.431096\pi$
$350$	−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
$355$	12.9757	−	2.75806i	0.688676	−	0.146383i
$356$	19.9863	+	17.9958i	1.05927	+	0.953774i
$357$		0			0
$358$	26.9922	−	2.83700i	1.42658	−	0.149940i
$359$	1.92854	+	5.93545i	0.101785	+	0.313261i	0.988962	−	0.148167i	$-0.0473373\pi$
$359$	1.92854	+	5.93545i	0.101785	+	0.313261i	−0.887178	+	0.461428i	$0.847337\pi$
$360$		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
$365$	1.07359	−	10.2145i	0.0561944	−	0.534654i
$366$		0			0
$367$	7.53202	+	1.60098i	0.393168	+	0.0835705i	0.400254	−	0.916404i	$-0.368922\pi$
$367$	7.53202	+	1.60098i	0.393168	+	0.0835705i	−0.00708542	+	0.999975i	$0.502255\pi$
$368$	44.7939	+	61.6535i	2.33504	+	3.21391i
$369$		0			0
$370$	37.0240	−	12.0298i	1.92479	−	0.625401i
$371$	−0.324562	−	0.360463i	−0.0168504	−	0.0187143i
$372$		0			0
$373$	−18.2379	+	10.5296i	−0.944321	+	0.545204i	−0.891312	−	0.453390i	$-0.850214\pi$
$373$	−18.2379	+	10.5296i	−0.944321	+	0.545204i	−0.0530086	+	0.998594i	$0.516881\pi$
$374$	29.8452	−	22.0230i	1.54326	−	1.13878i
$375$		0			0
$376$	−25.9052	−	58.1841i	−1.33596	−	3.00062i
$377$	0.275637	+	0.0895598i	0.0141960	+	0.00461256i
$378$		0			0
$379$	24.0003	−	17.4372i	1.23281	−	0.895691i	0.235715	−	0.971822i	$-0.424257\pi$
$379$	24.0003	−	17.4372i	1.23281	−	0.895691i	0.997098	+	0.0761314i	$0.0242568\pi$
$380$	−0.995973	−	9.47605i	−0.0510923	−	0.486111i
$381$		0			0
$382$	−2.08062	−	9.78855i	−0.106454	−	0.500826i
$383$	−2.65347	−	0.278891i	−0.135586	−	0.0142506i	0.0364924	−	0.999334i	$-0.488382\pi$
$383$	−2.65347	−	0.278891i	−0.135586	−	0.0142506i	−0.172078	+	0.985083i	$0.555048\pi$
$384$		0			0
$385$	3.50813	+	5.97375i	0.178791	+	0.304451i
$386$			67.1784i			3.41929i
$387$		0			0
$388$	9.81361	−	30.2032i	0.498210	−	1.53333i
$389$	−0.132531	+	0.623511i	−0.00671961	+	0.0316133i	−0.981380	−	0.192078i	$-0.938477\pi$
$389$	−0.132531	+	0.623511i	−0.00671961	+	0.0316133i	0.974660	+	0.223691i	$0.0718107\pi$
$390$		0			0
$391$	9.80597	−	22.0246i	0.495909	−	1.11383i
$392$	28.8616	−	32.0541i	1.45773	−	1.61897i
$393$		0			0
$394$	47.3036	−	21.0609i	2.38312	−	1.06103i
$395$	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	$0.718070\pi$
$398$	−64.0169	+	28.5021i	−3.20888	+	1.42868i
$399$		0			0
$400$	25.5211	−	28.3441i	1.27606	−	1.41720i
$401$	11.8646	−	26.6483i	0.592489	−	1.33075i	−0.329726	−	0.944077i	$-0.606956\pi$
$401$	11.8646	−	26.6483i	0.592489	−	1.33075i	0.922216	−	0.386676i	$-0.126377\pi$
$402$		0			0
$403$	−2.53025	+	11.9039i	−0.126041	+	0.592976i
$404$	18.9132	−	58.2088i	0.940966	−	2.89600i
$405$		0			0
$406$			0.378625i			0.0187908i
$407$	−3.21870	+	32.9685i	−0.159545	+	1.63419i
$408$		0			0
$409$	−16.5173	−	1.73603i	−0.816726	−	0.0858413i	−0.313053	−	0.949736i	$-0.601352\pi$
$409$	−16.5173	−	1.73603i	−0.816726	−	0.0858413i	−0.503673	+	0.863894i	$0.668018\pi$
$410$	3.70399	+	17.4259i	0.182927	+	0.860603i
$411$		0			0
$412$	1.84080	+	17.5140i	0.0906897	+	0.862855i
$413$	−3.53499	+	2.56832i	−0.173945	+	0.126379i
$414$		0			0
$415$	8.20739	+	2.66674i	0.402885	+	0.130905i
$416$	−21.5549	−	48.4132i	−1.05682	−	2.37365i
$417$		0			0
$418$	10.6696	+	3.37971i	0.521869	+	0.165307i
$419$	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
$421$	−2.21553	−	2.46060i	−0.107978	−	0.119922i	0.686733	−	0.726910i	$-0.259044\pi$
$421$	−2.21553	−	2.46060i	−0.107978	−	0.119922i	−0.794711	+	0.606988i	$0.792378\pi$
$422$	58.2537	−	18.9278i	2.83575	−	0.921390i
$423$		0			0
$424$	1.73282	+	2.38502i	0.0841532	+	0.115827i
$425$	−11.8024	−	2.50868i	−0.572501	−	0.121689i
$426$		0			0
$427$	0.0480331	−	0.457005i	0.00232449	−	0.0221160i
$428$	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	$-0.316324\pi$
$431$	−1.72195	−	1.25107i	−0.0829434	−	0.0602619i	−0.628484	+	0.777822i	$0.716324\pi$
$432$		0			0
$433$	−4.76068	−	14.6519i	−0.228784	−	0.704124i	−0.997885	−	0.0649975i	$-0.979296\pi$
$433$	−4.76068	−	14.6519i	−0.228784	−	0.704124i	0.769102	−	0.639126i	$-0.220704\pi$
$434$	−15.8117	+	1.66187i	−0.758984	+	0.0797724i
$435$		0			0
$436$	16.0694	+	14.4690i	0.769587	+	0.692939i
$437$	7.11582	−	1.51251i	0.340396	−	0.0723534i
$438$		0			0
$439$	−31.0083	−	17.9026i	−1.47995	−	0.854447i	−0.480203	−	0.877157i	$-0.659437\pi$
$439$	−31.0083	−	17.9026i	−1.47995	−	0.854447i	−0.999742	+	0.0227105i	$0.992770\pi$
$440$	−17.4098	−	38.3372i	−0.829981	−	1.82765i
$441$		0			0
$442$	−19.5682	+	26.9333i	−0.930764	+	1.28109i
$443$	8.91597	−	8.02798i	0.423611	−	0.381421i	−0.429572	−	0.903032i	$-0.641336\pi$
$443$	8.91597	−	8.02798i	0.423611	−	0.381421i	0.853183	+	0.521612i	$0.174669\pi$
$444$		0			0
$445$	−6.76211	−	3.01068i	−0.320555	−	0.142720i
$446$	−55.9835	−	24.9255i	−2.65090	−	1.18026i
$447$		0			0
$448$	23.2936	−	20.9737i	1.10052	−	0.990913i
$449$	15.0088	−	20.6578i	0.708307	−	0.974901i	−0.291525	−	0.956563i	$-0.594163\pi$
$449$	15.0088	−	20.6578i	0.708307	−	0.974901i	0.999832	−	0.0183378i	$-0.00583742\pi$
$450$		0			0
$451$	−14.8507	−	3.04196i	−0.699292	−	0.143240i
$452$	−92.0676	−	53.1552i	−4.33050	−	2.50021i
$453$		0			0
$454$	−21.4166	+	4.55224i	−1.00513	+	0.213647i
$455$	−4.62087	−	4.16065i	−0.216630	−	0.195054i
$456$		0			0
$457$	−1.01435	+	0.106612i	−0.0474492	+	0.00498711i	−0.128223	−	0.991745i	$-0.540927\pi$
$457$	−1.01435	+	0.106612i	−0.0474492	+	0.00498711i	0.0807741	+	0.996732i	$0.474261\pi$
$458$	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	−0.808529	−	0.588456i	$-0.799736\pi$
$461$	2.26202	−	3.91794i	0.105353	−	0.182477i	0.913882	+	0.405979i	$0.133069\pi$
$462$		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	$0.770410\pi$
$464$	0.133543	−	1.27058i	0.00619959	−	0.0589852i
$465$		0			0
$466$	13.3265	+	2.83264i	0.617339	+	0.131219i
$467$	3.64591	+	5.01817i	0.168713	+	0.232213i	0.884998	−	0.465594i	$-0.154159\pi$
$467$	3.64591	+	5.01817i	0.168713	+	0.232213i	−0.716286	+	0.697807i	$0.754159\pi$
$468$		0			0
$469$	4.71832	−	1.53308i	0.217872	−	0.0707909i
$470$	18.9320	+	21.0261i	0.873266	+	0.969860i
$471$		0			0
$472$	22.9990	−	13.2785i	1.05861	−	0.611191i
$473$	−4.18717	−	5.67438i	−0.192526	−	0.260908i
$474$		0			0
$475$	−1.48089	−	3.32613i	−0.0679479	−	0.152614i
$476$	−29.9639	−	9.73586i	−1.37339	−	0.446242i
$477$		0			0
$478$	−43.9497	+	31.9314i	−2.01021	+	1.46051i
$479$	2.33164	+	22.1841i	0.106535	+	1.01362i	0.908966	+	0.416871i	$0.136873\pi$
$479$	2.33164	+	22.1841i	0.106535	+	1.01362i	−0.802430	+	0.596746i	$0.796460\pi$
$480$		0			0
$481$	−6.18159	−	29.0821i	−0.281856	−	1.32603i
$482$	75.8224	+	7.96925i	3.45361	+	0.362989i
$483$		0			0
$484$	57.8212	−	0.855641i	2.62824	−	0.0388928i
$485$			8.74055i			0.396888i
$486$		0			0
$487$	10.5290	−	32.4051i	0.477117	−	1.46841i	−0.365965	−	0.930629i	$-0.619261\pi$
$487$	10.5290	−	32.4051i	0.477117	−	1.46841i	0.843082	−	0.537786i	$-0.180739\pi$
$488$	−0.580675	+	2.73186i	−0.0262859	+	0.123665i
$489$		0			0
$490$	−7.79351	+	17.5045i	−0.352075	+	0.790773i
$491$	−12.5962	+	13.9895i	−0.568460	+	0.631338i	−0.956998	−	0.290094i	$-0.906313\pi$
$491$	−12.5962	+	13.9895i	−0.568460	+	0.631338i	0.388539	+	0.921432i	$0.372980\pi$
$492$		0			0
$493$	−0.369228	+	0.164391i	−0.0166292	+	0.00740380i
$494$	−10.0456			−0.451972
$495$		0			0
$496$	53.6466			2.40880
$497$	12.0914	−	5.38345i	0.542375	−	0.241481i
$498$		0			0
$499$	5.08399	−	5.64634i	0.227591	−	0.252765i	−0.618524	−	0.785766i	$-0.712269\pi$
$499$	5.08399	−	5.64634i	0.227591	−	0.252765i	0.846115	+	0.533001i	$0.178936\pi$
$500$	−24.4611	+	54.9404i	−1.09393	+	2.45701i
$501$		0			0
$502$	13.0998	−	61.6298i	0.584674	−	2.75067i
$503$	−8.18033	+	25.1765i	−0.364743	+	1.12256i	0.585399	+	0.810745i	$0.300938\pi$
$503$	−8.18033	+	25.1765i	−0.364743	+	1.12256i	−0.950142	+	0.311818i	$0.899062\pi$
$504$		0			0
$505$			16.8451i			0.749599i
$506$	44.7425	−	26.2754i	1.98905	−	1.16808i
$507$		0			0
$508$	−0.538022	−	0.0565484i	−0.0238709	−	0.00250893i
$509$	−2.65076	−	12.4708i	−0.117493	−	0.552760i	−0.997036	−	0.0769406i	$-0.975485\pi$
$509$	−2.65076	−	12.4708i	−0.117493	−	0.552760i	0.879543	−	0.475820i	$-0.157849\pi$
$510$		0			0
$511$	−1.07118	−	10.1916i	−0.0473861	−	0.450849i
$512$	−2.69612	+	1.95884i	−0.119153	+	0.0865695i
$513$		0			0
$514$	1.06700	+	0.346689i	0.0470633	+	0.0152918i
$515$	−1.97141	−	4.42787i	−0.0868709	−	0.195115i
$516$		0			0
$517$	−22.8410	+	7.60878i	−1.00455	+	0.334634i
$518$	33.6380	−	19.4209i	1.47797	−	0.853305i
$519$		0			0
$520$	25.2877	+	28.0848i	1.10894	+	1.23160i
$521$	−6.80629	+	2.21150i	−0.298189	+	0.0968875i	−0.454291	−	0.890854i	$-0.650107\pi$
$521$	−6.80629	+	2.21150i	−0.298189	+	0.0968875i	0.156102	+	0.987741i	$0.450107\pi$
$522$		0			0
$523$	18.1933	+	25.0410i	0.795539	+	1.09497i	0.993396	+	0.114734i	$0.0366017\pi$
$523$	18.1933	+	25.0410i	0.795539	+	1.09497i	−0.197857	+	0.980231i	$0.563398\pi$
$524$	79.0112	+	16.7944i	3.45162	+	0.733665i
$525$		0			0
$526$	−7.91758	+	75.3308i	−0.345223	+	3.28458i
$527$	−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
$533$	13.5316	−	1.42223i	0.586118	−	0.0616035i
$534$		0			0
$535$	−10.1661	−	9.15362i	−0.439520	−	0.395746i
$536$	−29.4940	+	6.26914i	−1.27395	+	0.270785i
$537$		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	0.258845	−	0.965919i	$-0.416658\pi$
$541$	25.5272	−	35.1352i	1.09750	−	1.51058i	0.838656	−	0.544661i	$-0.183342\pi$
$542$	−22.3049	+	20.0834i	−0.958077	+	0.862657i
$543$		0			0
$544$	67.5146	+	30.0594i	2.89466	+	1.28879i
$545$	−5.43688	−	2.42066i	−0.232890	−	0.103689i
$546$		0			0
$547$	−5.55409	+	5.00092i	−0.237476	+	0.213824i	−0.779272	−	0.626686i	$-0.784411\pi$
$547$	−5.55409	+	5.00092i	−0.237476	+	0.213824i	0.541796	+	0.840510i	$0.317744\pi$
$548$	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
$553$	14.1496	−	3.00760i	0.601704	−	0.127896i
$554$	−19.5876	−	17.6368i	−0.832199	−	0.749315i
$555$		0			0
$556$	−88.9646	+	9.35056i	−3.77294	+	0.396552i
$557$	−8.26967	−	25.4514i	−0.350397	−	1.07841i	−0.958631	−	0.284653i	$-0.908121\pi$
$557$	−8.26967	−	25.4514i	−0.350397	−	1.07841i	0.608233	−	0.793758i	$-0.291879\pi$
$558$		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
$563$	2.44072	−	23.2219i	0.102864	−	0.978688i	−0.814372	−	0.580343i	$-0.802918\pi$
$563$	2.44072	−	23.2219i	0.102864	−	0.978688i	0.917236	−	0.398344i	$-0.130415\pi$
$564$		0			0
$565$	28.6202	+	6.08342i	1.20406	+	0.255931i
$566$	−24.3742	−	33.5483i	−1.02453	−	1.41014i
$567$		0			0
$568$	−76.5070	+	24.8586i	−3.21016	+	1.04305i
$569$	−3.63387	−	4.03583i	−0.152340	−	0.169191i	0.662144	−	0.749376i	$-0.269647\pi$
$569$	−3.63387	−	4.03583i	−0.152340	−	0.169191i	−0.814484	+	0.580186i	$0.802980\pi$
$570$		0			0
$571$	−8.79380	+	5.07710i	−0.368009	+	0.212470i	−0.672588	−	0.740017i	$-0.734817\pi$
$571$	−8.79380	+	5.07710i	−0.368009	+	0.212470i	0.304579	+	0.952487i	$0.401484\pi$
$572$	−49.2432	+	16.4039i	−2.05896	+	0.685880i
$573$		0			0
$574$	7.22980	+	16.2384i	0.301766	+	0.677777i
$575$	−16.0533	−	5.21603i	−0.669468	−	0.217523i
$576$		0			0
$577$	17.0075	−	12.3566i	0.708029	−	0.514414i	−0.174508	−	0.984656i	$-0.555833\pi$
$577$	17.0075	−	12.3566i	0.708029	−	0.514414i	0.882537	+	0.470242i	$0.155833\pi$
$578$	−0.0658919	−	0.626919i	−0.00274074	−	0.0260764i
$579$		0			0
$580$	0.153967	+	0.724357i	0.00639313	+	0.0300773i
$581$	8.56319	+	0.900028i	0.355261	+	0.0373394i
$582$		0			0
$583$	0.960918	−	0.564306i	0.0397972	−	0.0233712i
$584$			62.2837i			2.57732i
$585$		0			0
$586$	−22.6588	+	69.7367i	−0.936028	+	2.88080i
$587$	9.06898	−	42.6662i	0.374317	−	1.76102i	−0.238839	−	0.971059i	$-0.576767\pi$
$587$	9.06898	−	42.6662i	0.374317	−	1.76102i	0.613155	−	0.789962i	$-0.289900\pi$
$588$		0			0
$589$	2.08294	−	4.67835i	0.0858259	−	0.192768i
$590$	−7.89403	+	8.76721i	−0.324992	+	0.360940i
$591$		0			0
$592$	−119.731	+	53.3079i	−4.92093	+	2.19094i
$593$	−37.0300			−1.52064			−0.760319	−	0.649549i	$-0.774958\pi$
$593$	−37.0300			−1.52064			−0.760319	+	0.649549i	$0.774958\pi$
$594$		0			0
$595$	8.67130			0.355489
$596$	54.9986	−	24.4869i	2.25283	−	1.00302i
$597$		0			0
$598$	−31.1626	+	34.6096i	−1.27433	+	1.41529i
$599$	9.79998	−	22.0111i	0.400416	−	0.899350i	−0.595001	−	0.803725i	$-0.702848\pi$
$599$	9.79998	−	22.0111i	0.400416	−	0.899350i	0.995417	−	0.0956251i	$-0.0304850\pi$
$600$		0			0
$601$	3.88387	−	18.2722i	0.158426	−	0.745337i	−0.825160	−	0.564899i	$-0.808915\pi$
$601$	3.88387	−	18.2722i	0.158426	−	0.745337i	0.983586	−	0.180438i	$-0.0577516\pi$
$602$	−2.55527	+	7.86431i	−0.104145	+	0.320525i
$603$		0			0
$604$			5.58824i			0.227382i
$605$	−15.0624	+	5.14167i	−0.612372	+	0.209039i
$606$		0			0
$607$	24.4696	+	2.57186i	0.993192	+	0.104389i	0.587161	−	0.809470i	$-0.300246\pi$
$607$	24.4696	+	2.57186i	0.993192	+	0.104389i	0.406032	+	0.913859i	$0.366912\pi$
$608$	4.63650	+	21.8130i	0.188035	+	0.884634i
$609$		0			0
$610$	−0.129688	−	1.23390i	−0.00525090	−	0.0499590i
$611$	17.4818	−	12.7013i	0.707238	−	0.513839i
$612$		0			0
$613$	21.4976	+	6.98501i	0.868282	+	0.282122i	0.709083	−	0.705125i	$-0.249109\pi$
$613$	21.4976	+	6.98501i	0.868282	+	0.282122i	0.159199	+	0.987247i	$0.449109\pi$
$614$	34.0539	+	76.4864i	1.37431	+	3.08674i
$615$		0			0
$616$	−24.9439	−	33.8036i	−1.00502	−	1.36198i
$617$	−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
$619$	−8.95871	−	9.94965i	−0.360081	−	0.399910i	0.535698	−	0.844409i	$-0.320048\pi$
$619$	−8.95871	−	9.94965i	−0.360081	−	0.399910i	−0.895779	+	0.444499i	$0.853382\pi$
$620$	−29.5739	+	9.60915i	−1.18772	+	0.385913i
$621$		0			0
$622$	9.04845	+	12.4541i	0.362810	+	0.499365i
$623$	−7.22401	−	1.53551i	−0.289424	−	0.0615190i
$624$		0			0
$625$	0.211100	−	2.00849i	0.00844401	−	0.0803394i
$626$	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	0.839397	−	0.543519i	$-0.182909\pi$
$631$	−3.99811	−	12.3049i	−0.159162	−	0.489851i	−0.998559	+	0.0536685i	$0.982909\pi$
$632$	−87.4386	+	9.19017i	−3.47812	+	0.365565i
$633$		0			0
$634$	3.96358	+	3.56883i	0.157414	+	0.141736i
$635$	0.145641	−	0.0309569i	0.00577957	−	0.00122849i
$636$		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
$641$	−7.42438	+	6.68494i	−0.293245	+	0.264039i	−0.802600	−	0.596517i	$-0.796551\pi$
$641$	−7.42438	+	6.68494i	−0.293245	+	0.264039i	0.509355	+	0.860557i	$0.329884\pi$
$642$		0			0
$643$	−11.5865	−	5.15863i	−0.456926	−	0.203436i	0.165349	−	0.986235i	$-0.447125\pi$
$643$	−11.5865	−	5.15863i	−0.456926	−	0.203436i	−0.622275	+	0.782799i	$0.713791\pi$
$644$	−40.2637	−	17.9265i	−1.58661	−	0.706405i
$645$		0			0
$646$	10.4108	−	9.37390i	0.409606	−	0.368811i
$647$	−19.3401	+	26.6193i	−0.760337	+	1.04651i	0.236849	+	0.971547i	$0.423885\pi$
$647$	−19.3401	+	26.6193i	−0.760337	+	1.04651i	−0.997186	+	0.0749678i	$0.976115\pi$
$648$		0			0
$649$	−4.15077	−	9.14018i	−0.162932	−	0.358784i
$650$	20.1856	+	11.6542i	0.791746	+	0.457115i
$651$		0			0
$652$	−15.0653	+	3.20222i	−0.590001	+	0.125409i
$653$	−15.8756	−	14.2944i	−0.621259	−	0.559384i	0.297242	−	0.954802i	$-0.403933\pi$
$653$	−15.8756	−	14.2944i	−0.621259	−	0.559384i	−0.918501	+	0.395418i	$0.870600\pi$
$654$		0			0
$655$	−22.1101	+	2.32387i	−0.863914	+	0.0908010i
$656$	−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	−0.742911	−	0.669391i	$-0.766555\pi$
$659$	5.34609	−	9.25969i	0.208254	−	0.360706i	0.951165	+	0.308684i	$0.0998886\pi$
$660$		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	$-0.359354\pi$
$662$	1.14808	−	10.9233i	0.0446215	−	0.424545i
$663$		0			0
$664$	−51.1886	−	10.8805i	−1.98650	−	0.422244i
$665$	1.53796	+	2.11683i	0.0596397	+	0.0820870i
$666$		0			0
$667$	−0.537728	+	0.174718i	−0.0208209	+	0.00676512i
$668$	15.6664	+	17.3994i	0.606153	+	0.673201i
$669$		0			0
$670$	11.6003	−	6.69744i	0.448159	−	0.258745i
$671$	1.00643	+	0.318796i	0.0388528	+	0.0123070i
$672$		0			0
$673$	−16.9757	−	38.1281i	−0.654366	−	1.46973i	−0.869897	−	0.493233i	$-0.835815\pi$
$673$	−16.9757	−	38.1281i	−0.654366	−	1.46973i	0.215531	−	0.976497i	$-0.430852\pi$
$674$	73.0890	+	23.7481i	2.81528	+	0.914741i
$675$		0			0
$676$	−17.6003	+	12.7874i	−0.676935	+	0.491822i
$677$	3.10946	+	29.5845i	0.119506	+	1.13703i	0.875760	+	0.482747i	$0.160361\pi$
$677$	3.10946	+	29.5845i	0.119506	+	1.13703i	−0.756254	+	0.654278i	$0.772972\pi$
$678$		0			0
$679$	1.81318	+	8.53032i	0.0695833	+	0.327364i
$680$	−52.4139	−	5.50892i	−2.00998	−	0.211257i
$681$		0			0
$682$	3.54915	−	36.3532i	0.135904	−	1.39204i
$683$		−	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
$686$	−9.63482	+	45.3283i	−0.367859	+	1.73064i
$687$		0			0
$688$	11.3487	−	25.4896i	0.432665	−	0.971782i
$689$	−0.669268	+	0.743298i	−0.0254971	+	0.0283174i
$690$		0			0
$691$	1.17256	−	0.522059i	0.0446064	−	0.0198601i	−0.384312	−	0.923203i	$-0.625561\pi$
$691$	1.17256	−	0.522059i	0.0446064	−	0.0198601i	0.428919	+	0.903343i	$0.358895\pi$
$692$	54.9382			2.08844
$693$		0			0
$694$	−27.8516			−1.05723
$695$	22.4919	−	10.0140i	0.853165	−	0.379854i
$696$		0			0
$697$	−12.6964	+	14.1008i	−0.480910	+	0.534104i
$698$	−20.2197	+	45.4142i	−0.765327	+	1.71895i
$699$		0			0
$700$	−4.58618	+	21.5763i	−0.173341	+	0.815507i
$701$	9.82030	−	30.2238i	0.370908	−	1.14154i	−0.575290	−	0.817949i	$-0.695111\pi$
$701$	9.82030	−	30.2238i	0.370908	−	1.14154i	0.946198	−	0.323588i	$-0.104889\pi$
$702$		0			0
$703$			12.5112i			0.471869i
$704$	36.4662	+	62.0959i	1.37437	+	2.34033i
$705$		0			0
$706$	35.8783	+	3.77097i	1.35030	+	0.141922i
$707$	3.49443	+	16.4400i	0.131421	+	0.618289i
$708$		0			0
$709$	−0.0500839	−	0.476516i	−0.00188094	−	0.0178959i	0.993541	−	0.113472i	$-0.0361973\pi$
$709$	−0.0500839	−	0.476516i	−0.00188094	−	0.0178959i	−0.995422	+	0.0955763i	$0.969531\pi$
$710$	28.9110	−	21.0050i	1.08501	−	0.788305i
$711$		0			0
$712$	42.6902	+	13.8709i	1.59988	+	0.519833i
$713$	−9.65659	−	21.6891i	−0.361642	−	0.812262i
$714$		0			0
$715$	11.4946	−	8.48197i	0.429874	−	0.317208i
$716$	45.8688	−	26.4823i	1.71420	−	0.989692i
$717$		0			0
$718$	11.2496	+	12.4940i	0.419833	+	0.466271i
$719$	−22.0526	+	7.16534i	−0.822425	+	0.267222i	−0.689851	−	0.723951i	$-0.742324\pi$
$719$	−22.0526	+	7.16534i	−0.822425	+	0.267222i	−0.132574	+	0.991173i	$0.542324\pi$
$720$		0			0
$721$	−2.84253	−	3.91241i	−0.105862	−	0.145706i
$722$	−45.9306	−	9.76285i	−1.70936	−	0.363336i
$723$		0			0
$724$	8.51985	−	81.0610i	0.316638	−	3.01261i
$725$	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
$731$	−8.77859	+	0.922667i	−0.324688	+	0.0341261i
$732$		0			0
$733$	−7.26549	−	6.54188i	−0.268357	−	0.241630i	0.523955	−	0.851746i	$-0.324456\pi$
$733$	−7.26549	−	6.54188i	−0.268357	−	0.241630i	−0.792312	+	0.610116i	$0.791123\pi$
$734$	20.2904	−	4.31287i	0.748934	−	0.159191i
$735$		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	−0.985040	−	0.172324i	$-0.944873\pi$
$739$	−14.0478	+	19.3351i	−0.516757	+	0.711255i	0.468284	+	0.883578i	$0.344873\pi$
$740$	56.4563	−	50.8335i	2.07538	−	1.86868i
$741$		0			0
$742$	−1.19371	−	0.531472i	−0.0438223	−	0.0195110i
$743$	33.6405	+	14.9777i	1.23415	+	0.549480i	0.916997	−	0.398894i	$-0.130606\pi$
$743$	33.6405	+	14.9777i	1.23415	+	0.549480i	0.317155	+	0.948374i	$0.397273\pi$
$744$		0			0
$745$	−12.3137	+	11.0873i	−0.451137	+	0.406206i
$746$	−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
$751$	30.0301	−	6.38311i	1.09582	−	0.232923i	0.375675	−	0.926751i	$-0.377411\pi$
$751$	30.0301	−	6.38311i	1.09582	−	0.232923i	0.720140	+	0.693828i	$0.244077\pi$
$752$	−70.7879	−	63.7377i	−2.58137	−	2.32428i
$753$		0			0
$754$	0.776471	−	0.0816104i	0.0282774	−	0.00297207i
$755$	−0.475281	−	1.46276i	−0.0172972	−	0.0532354i
$756$		0			0
$757$	−34.5971	−	25.1362i	−1.25745	−	0.913592i	−0.258822	−	0.965925i	$-0.583334\pi$
$757$	−34.5971	−	25.1362i	−1.25745	−	0.913592i	−0.998630	+	0.0523331i	$0.983334\pi$
$758$	39.9585	−	69.2101i	1.45136	−	2.51383i
$759$		0			0
$760$	−7.95143	−	13.7723i	−0.288429	−	0.499573i
$761$	−2.82341	+	26.8629i	−0.102348	+	0.973781i	0.816012	+	0.578035i	$0.196180\pi$
$761$	−2.82341	+	26.8629i	−0.102348	+	0.973781i	−0.918360	+	0.395746i	$0.870486\pi$
$762$		0			0
$763$	−5.80827	−	1.23458i	−0.210273	−	0.0446950i
$764$	−11.4788	−	15.7991i	−0.415287	−	0.571593i
$765$		0			0
$766$	−6.83574	+	2.22107i	−0.246985	+	0.0802504i
$767$	6.02897	+	6.69585i	0.217693	+	0.241773i
$768$		0			0
$769$	41.9099	−	24.1967i	1.51131	−	0.872555i	0.511396	−	0.859345i	$-0.329129\pi$
$769$	41.9099	−	24.1967i	1.51131	−	0.872555i	0.999913	−	0.0132095i	$-0.00420483\pi$
$770$	15.1789	+	10.8575i	0.547011	+	0.391277i
$771$		0			0
$772$	53.3218	+	119.763i	1.91909	+	4.31036i
$773$	−33.6456	−	10.9321i	−1.21015	−	0.393201i	−0.366664	−	0.930354i	$-0.619500\pi$
$773$	−33.6456	−	10.9321i	−1.21015	−	0.393201i	−0.843485	+	0.537152i	$0.819500\pi$
$774$		0			0
$775$	−9.61296	+	6.98422i	−0.345308	+	0.250881i
$776$	−5.54043	−	52.7136i	−0.198890	−	1.89231i
$777$		0			0
$778$	0.357025	+	1.67967i	0.0128000	+	0.0602192i
$779$	−5.69412	−	0.598476i	−0.204013	−	0.0214426i
$780$		0			0
$781$	6.54205	+	29.6959i	0.234093	+	1.06260i
$782$		−	64.9467i		−	2.32249i
$783$		0			0
$784$	19.9344	−	61.3518i	0.711943	−	2.19113i
$785$	−0.0256873	+	0.120849i	−0.000916819	+	0.00431330i
$786$		0			0
$787$	10.4896	−	23.5601i	0.373914	−	0.839825i	−0.624362	−	0.781135i	$-0.714641\pi$
$787$	10.4896	−	23.5601i	0.373914	−	0.839825i	0.998276	−	0.0586900i	$-0.0186924\pi$
$788$	67.6141	−	75.0931i	2.40865	−	2.67508i
$789$		0			0
$790$	35.6803	−	15.8859i	1.26945	−	0.565195i
$791$	29.1938			1.03801
$792$		0			0
$793$	−0.947564			−0.0336490
$794$	−62.0528	+	27.6277i	−2.20217	+	0.980470i
$795$		0			0
$796$	−91.5034	+	101.625i	−3.24325	+	3.60200i
$797$	−6.93844	+	15.5840i	−0.245772	+	0.552013i	−0.993739	−	0.111722i	$-0.964363\pi$
$797$	−6.93844	+	15.5840i	−0.245772	+	0.552013i	0.747967	+	0.663735i	$0.231030\pi$
$798$		0			0
$799$	−6.26530	+	29.4759i	−0.221650	+	1.04278i
$800$	15.9893	−	49.2101i	0.565308	−	1.73984i
$801$		0			0
$802$		−	78.5813i		−	2.77480i
$803$	23.4319	+	2.28764i	0.826892	+	0.0807292i
$804$		0			0
$805$	12.0640	+	1.26797i	0.425199	+	0.0446902i
$806$	6.81623	+	32.0678i	0.240091	+	1.12954i
$807$		0			0
$808$	−10.6777	−	101.592i	−0.375641	−	3.57399i
$809$	−38.7684	+	28.1669i	−1.36302	+	0.990295i	−0.364778	+	0.931095i	$0.618855\pi$
$809$	−38.7684	+	28.1669i	−1.36302	+	0.990295i	−0.998246	+	0.0592001i	$0.981145\pi$
$810$		0			0
$811$	45.0299	+	14.6311i	1.58121	+	0.513768i	0.962369	−	0.271745i	$-0.0876009\pi$
$811$	45.0299	+	14.6311i	1.58121	+	0.513768i	0.618845	+	0.785513i	$0.287601\pi$
$812$	0.300527	+	0.674996i	0.0105464	+	0.0236877i
$813$		0			0
$814$	28.2025	+	84.6619i	0.988497	+	2.96740i
$815$	3.67109	−	2.11951i	0.128593	−	0.0742430i
$816$		0			0
$817$	−1.78223	−	1.97937i	−0.0623524	−	0.0692494i
$818$	−42.5510	+	13.8257i	−1.48776	+	0.483403i
$819$		0			0
$820$	20.4348	+	28.1261i	0.713615	+	0.982207i
$821$	17.1942	+	3.65474i	0.600081	+	0.127551i	0.497929	−	0.867218i	$-0.334094\pi$
$821$	17.1942	+	3.65474i	0.600081	+	0.127551i	0.102152	+	0.994769i	$0.467427\pi$
$822$		0			0
$823$	−2.98965	+	28.4446i	−0.104212	+	0.991516i	0.810041	+	0.586373i	$0.199445\pi$
$823$	−2.98965	+	28.4446i	−0.104212	+	0.991516i	−0.914254	+	0.405142i	$0.867222\pi$
$824$	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	$-0.390153\pi$
$827$	−13.0031	−	9.44733i	−0.452163	−	0.328516i	−0.790449	+	0.612527i	$0.790153\pi$
$828$		0			0
$829$	0.324003	+	0.997179i	0.0112531	+	0.0346335i	0.956525	−	0.291649i	$-0.0942039\pi$
$829$	0.324003	+	0.997179i	0.0112531	+	0.0346335i	−0.945272	+	0.326282i	$0.894204\pi$
$830$	23.1203	−	2.43004i	0.802517	−	0.0843479i
$831$		0			0
$832$	−48.0329	−	43.2490i	−1.66524	−	1.49939i
$833$	−19.9619	+	4.24304i	−0.691640	+	0.147013i
$834$		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
$839$	15.6005	−	14.0468i	0.538590	−	0.484949i	−0.354357	−	0.935110i	$-0.615300\pi$
$839$	15.6005	−	14.0468i	0.538590	−	0.484949i	0.892947	+	0.450161i	$0.148634\pi$
$840$		0			0
$841$	−26.4842	−	11.7915i	−0.913247	−	0.406604i
$842$	−8.14849	−	3.62794i	−0.280816	−	0.125027i
$843$		0			0
$844$	88.8286	−	79.9816i	3.05761	−	2.75308i
$845$	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
$850$	−31.7944	+	6.75811i	−1.09054	+	0.231801i
$851$	43.1043	+	38.8113i	1.47760	+	1.33043i
$852$		0			0
$853$	5.26358	−	0.553224i	0.180222	−	0.0189420i	−0.0139877	−	0.999902i	$-0.504453\pi$
$853$	5.26358	−	0.553224i	0.180222	−	0.0189420i	0.194209	+	0.980960i	$0.437786\pi$
$854$	−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	−0.924657	−	0.380801i	$-0.875648\pi$
$857$	−3.88021	+	6.72072i	−0.132545	+	0.229575i	0.792112	+	0.610376i	$0.208982\pi$
$858$		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	$0.521488\pi$
$860$	−1.69055	+	16.0845i	−0.0576473	+	0.548478i
$861$		0			0
$862$	−5.60851	−	1.19213i	−0.191027	−	0.0406039i
$863$	8.87079	+	12.2096i	0.301965	+	0.415619i	0.932854	−	0.360253i	$-0.117310\pi$
$863$	8.87079	+	12.2096i	0.301965	+	0.415619i	−0.630889	+	0.775873i	$0.717310\pi$
$864$		0			0
$865$	−14.3805	+	4.67250i	−0.488951	+	0.158870i
$866$	−27.7701	−	30.8418i	−0.943667	−	1.04805i
$867$		0			0
$868$	−26.8693	+	15.5130i	−0.912002	+	0.526545i
$869$	0.245878	+	33.2329i	0.00834084	+	1.12735i
$870$		0			0
$871$	−4.16099	−	9.34573i	−0.140990	−	0.316668i
$872$	34.3238	+	11.1525i	1.16235	+	0.377671i
$873$		0			0
$874$	15.8547	−	11.5191i	0.536294	−	0.389640i
$875$	−1.72628	−	16.4245i	−0.0583589	−	0.555248i
$876$		0			0
$877$	−4.60549	−	21.6671i	−0.155516	−	0.731646i	−0.984922	−	0.172999i	$-0.944654\pi$
$877$	−4.60549	−	21.6671i	−0.155516	−	0.731646i	0.829406	−	0.558647i	$-0.188679\pi$
$878$	−95.9272	−	10.0824i	−3.23739	−	0.340263i
$879$		0			0
$880$	−47.1077	−	41.7890i	−1.58800	−	1.40871i
$881$			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	0.534872	+	0.844933i	$0.320360\pi$
$883$	−11.7223	+	36.0776i	−0.394488	+	1.21411i	−0.929360	+	0.369175i	$0.879640\pi$
$884$	−13.5074	+	63.5475i	−0.454304	+	2.13733i
$885$		0			0
$886$	13.1458	−	29.5260i	0.441643	−	0.991947i
$887$	19.4805	−	21.6352i	0.654090	−	0.726440i	−0.321288	−	0.946982i	$-0.604116\pi$
$887$	19.4805	−	21.6352i	0.654090	−	0.726440i	0.975378	+	0.220541i	$0.0707824\pi$
$888$		0			0
$889$	0.135716	−	0.0604246i	0.00455176	−	0.00202658i
$890$	−19.9403			−0.668401
$891$		0			0
$892$	−119.589			−4.00414
$893$	−8.30685	+	3.69845i	−0.277978	+	0.123764i
$894$		0			0
$895$	−9.75416	+	10.8331i	−0.326046	+	0.362110i
$896$	13.4383	−	30.1829i	0.448942	−	1.00834i
$897$		0			0
$898$	14.3016	−	67.2838i	0.477251	−	2.24529i
$899$	−0.122993	+	0.378534i	−0.00410205	+	0.0126248i
$900$		0			0
$901$		−	1.39484i		−	0.0464688i
$902$	−39.8806	+	8.78575i	−1.32788	+	0.292534i
$903$		0			0
$904$	−176.463	−	18.5470i	−5.86906	−	0.616863i
$905$	4.66411	+	21.9429i	0.155040	+	0.729407i
$906$		0			0
$907$	1.93945	+	18.4526i	0.0643984	+	0.612710i	0.978360	+	0.206910i	$0.0663406\pi$
$907$	1.93945	+	18.4526i	0.0643984	+	0.612710i	−0.913962	+	0.405801i	$0.866993\pi$
$908$	−34.5673	+	25.1146i	−1.14716	+	0.833458i
$909$		0			0
$910$	−15.9308	−	5.17622i	−0.528100	−	0.171590i
$911$	−13.5116	−	30.3475i	−0.447658	−	1.00546i	−0.986607	−	0.163118i	$-0.947845\pi$
$911$	−13.5116	−	30.3475i	−0.447658	−	1.00546i	0.538949	−	0.842339i	$-0.318822\pi$
$912$		0			0
$913$	−5.97348	+	18.8581i	−0.197693	+	0.624112i
$914$	−2.37949	+	1.37380i	−0.0787064	+	0.0454411i
$915$		0			0
$916$	47.8173	+	53.1065i	1.57993	+	1.75469i
$917$	−21.0963	+	6.85459i	−0.696660	+	0.226359i
$918$		0			0
$919$	−10.8277	−	14.9031i	−0.357173	−	0.491606i	0.592185	−	0.805802i	$-0.298265\pi$
$919$	−10.8277	−	14.9031i	−0.357173	−	0.491606i	−0.949358	+	0.314195i	$0.898265\pi$
$920$	−72.1153	−	15.3286i	−2.37757	−	0.505369i
$921$		0			0
$922$	1.27392	−	12.1205i	0.0419543	−	0.399168i
$923$	−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
$929$	−29.1247	+	3.06113i	−0.955551	+	0.100432i	−0.569452	−	0.822025i	$-0.692844\pi$
$929$	−29.1247	+	3.06113i	−0.955551	+	0.100432i	−0.386099	+	0.922457i	$0.626178\pi$
$930$		0			0
$931$	−4.57631	−	4.12052i	−0.149982	−	0.135045i
$932$	26.0063	−	5.52781i	0.851865	−	0.181070i
$933$		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	−0.933312	−	0.359066i	$-0.883095\pi$
$937$	−9.28756	+	12.7832i	−0.303411	+	0.417610i	0.629901	+	0.776675i	$0.283095\pi$
$938$	9.93196	−	8.94277i	0.324290	−	0.291992i
$939$		0			0
$940$	50.4402	+	22.4574i	1.64518	+	0.732480i
$941$	7.56700	+	3.36905i	0.246677	+	0.109828i	0.526351	−	0.850267i	$-0.323560\pi$
$941$	7.56700	+	3.36905i	0.246677	+	0.109828i	−0.279674	+	0.960095i	$0.590226\pi$
$942$		0			0
$943$	−19.7258	+	17.7611i	−0.642359	+	0.578383i
$944$	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
$949$	−20.6697	+	4.39347i	−0.670966	+	0.142618i
$950$	−7.28892	−	6.56297i	−0.236484	−	0.212931i
$951$		0			0
$952$	−52.2960	+	5.49653i	−1.69492	+	0.178144i
$953$	1.81366	+	5.58186i	0.0587501	+	0.180814i	0.976125	−	0.217211i	$-0.0696958\pi$
$953$	1.81366	+	5.58186i	0.0587501	+	0.180814i	−0.917375	+	0.398025i	$0.869696\pi$
$954$		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
$959$	−0.561877	+	5.34590i	−0.0181439	+	0.172628i
$960$		0			0
$961$	13.9749	+	2.97045i	0.450802	+	0.0958210i
$962$	−47.0782	−	64.7976i	−1.51786	−	2.08916i
$963$		0			0
$964$	141.498	−	45.9756i	4.55735	−	1.48077i
$965$	−24.1432	−	26.8137i	−0.777197	−	0.863165i
$966$		0			0
$967$	15.1909	−	8.77049i	0.488507	−	0.282040i	−0.235448	−	0.971887i	$-0.575656\pi$
$967$	15.1909	−	8.77049i	0.488507	−	0.282040i	0.723955	+	0.689847i	$0.242322\pi$
$968$	87.5808	−	40.5567i	2.81495	−	1.30354i
$969$		0			0
$970$	9.57706	+	21.5104i	0.307501	+	0.690658i
$971$	46.6836	+	15.1684i	1.49815	+	0.486778i	0.939478	−	0.342610i	$-0.111311\pi$
$971$	46.6836	+	15.1684i	1.49815	+	0.486778i	0.558672	+	0.829389i	$0.311311\pi$
$972$		0			0
$973$	19.8735	−	14.4390i	0.637117	−	0.462892i
$974$	−9.59448	−	91.2854i	−0.307427	−	2.92497i
$975$		0			0
$976$	0.868449	+	4.08573i	0.0277984	+	0.130781i
$977$	−12.4796	−	1.31166i	−0.399258	−	0.0419637i	−0.0972278	−	0.995262i	$-0.530998\pi$
$977$	−12.4796	−	1.31166i	−0.399258	−	0.0419637i	−0.302030	+	0.953298i	$0.597664\pi$
$978$		0			0
$979$	6.78637	−	15.5511i	0.216893	−	0.497014i
$980$			37.3923i			1.19445i
$981$		0			0
$982$	−15.6708	+	48.2298i	−0.500076	+	1.53908i
$983$	−4.38228	+	20.6170i	−0.139773	+	0.657580i	0.851346	+	0.524604i	$0.175787\pi$
$983$	−4.38228	+	20.6170i	−0.139773	+	0.657580i	−0.991119	+	0.132976i	$0.957547\pi$
$984$		0			0
$985$	−11.3118	+	25.4067i	−0.360424	+	0.809526i
$986$	−0.728544	+	0.809130i	−0.0232016	+	0.0257680i
$987$		0			0
$988$	−17.9088	+	7.97353i	−0.569756	+	0.253672i
$989$	−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	$0.0927826\pi$
$992$	66.4861	−	29.6015i	2.11094	−	0.939849i
$993$		0			0
$994$	23.8582	−	26.4973i	0.756737	−	0.840442i
$995$	15.3085	−	34.3834i	0.485311	−	1.09003i
$996$		0			0
$997$	−11.6859	+	54.9777i	−0.370096	+	1.74116i	0.260890	+	0.965368i	$0.415984\pi$
$997$	−11.6859	+	54.9777i	−0.370096	+	1.74116i	−0.630986	+	0.775794i	$0.717349\pi$
$998$	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.62.10		80
3.2	odd	2		99.2.p.a.29.1	✓	80
9.2	odd	6		891.2.k.a.161.20		80
9.4	even	3		99.2.p.a.95.1	yes	80
9.5	odd	6	inner	297.2.t.a.260.10		80
9.7	even	3		891.2.k.a.161.1		80
11.8	odd	10	inner	297.2.t.a.8.10		80
33.8	even	10		99.2.p.a.74.1	yes	80
99.41	even	30	inner	297.2.t.a.206.10		80
99.52	odd	30		891.2.k.a.404.20		80
99.74	even	30		891.2.k.a.404.1		80
99.85	odd	30		99.2.p.a.41.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.1	✓	80	3.2	odd	2
99.2.p.a.41.1	yes	80	99.85	odd	30
99.2.p.a.74.1	yes	80	33.8	even	10
99.2.p.a.95.1	yes	80	9.4	even	3
297.2.t.a.8.10		80	11.8	odd	10	inner
297.2.t.a.62.10		80	1.1	even	1	trivial
297.2.t.a.206.10		80	99.41	even	30	inner
297.2.t.a.260.10		80	9.5	odd	6	inner
891.2.k.a.161.1		80	9.7	even	3
891.2.k.a.161.20		80	9.2	odd	6
891.2.k.a.404.1		80	99.74	even	30
891.2.k.a.404.20		80	99.52	odd	30

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)

\(f(q)\)	\(=\)	\(q+(2.46099 - 1.09570i) q^{2} +(3.51765 - 3.90675i) q^{4} +(-0.588502 + 1.32180i) q^{5} +(-0.300148 + 1.41209i) q^{7} +(2.71136 - 8.34470i) q^{8} +3.89775i q^{10} +(-3.03979 - 1.32654i) q^{11} +(2.96055 + 0.311167i) q^{13} +(0.808567 + 3.80401i) q^{14} +(-1.37167 - 13.0506i) q^{16} +(-3.35854 + 2.44012i) q^{17} +(-1.19136 - 0.387096i) q^{19} +(3.09378 + 6.94875i) q^{20} +(-8.93438 + 0.0661021i) q^{22} +(-5.02939 + 2.90372i) q^{23} +(1.94484 + 2.15996i) q^{25} +(7.62685 - 2.47811i) q^{26} +(4.46085 + 6.13983i) q^{28} +(0.0952306 + 0.0202419i) q^{29} +(-0.427327 + 4.06575i) q^{31} +(-8.90112 - 15.4172i) q^{32} +(-5.59169 + 9.68509i) q^{34} +(-1.68985 - 1.22775i) q^{35} +(-3.08635 - 9.49880i) q^{37} +(-3.35607 + 0.352737i) q^{38} +(9.43436 + 8.49473i) q^{40} +(4.47075 - 0.950287i) q^{41} +(1.84140 + 1.06313i) q^{43} +(-15.8754 + 7.20937i) q^{44} +(-9.19566 + 12.6567i) q^{46} +(5.39440 - 4.85714i) q^{47} +(4.49092 + 1.99949i) q^{49} +(7.15292 + 3.18469i) q^{50} +(11.6299 - 10.4716i) q^{52} +(-0.197492 + 0.271824i) q^{53} +(3.54233 - 3.23731i) q^{55} +(10.9696 + 6.33332i) q^{56} +(0.256541 - 0.0545294i) q^{58} +(2.24930 + 2.02528i) q^{59} +(-0.316566 + 0.0332724i) q^{61} +(3.40321 + 10.4740i) q^{62} +(-17.5657 - 12.7622i) q^{64} +(-2.15359 + 3.73013i) q^{65} +(-1.71828 - 2.97615i) q^{67} +(-2.28123 + 21.7045i) q^{68} +(-5.50397 - 1.16990i) q^{70} +(-5.38901 - 7.41734i) q^{71} +(-6.75113 + 2.19358i) q^{73} +(-18.0034 - 19.9948i) q^{74} +(-5.70308 + 3.29267i) q^{76} +(2.78557 - 3.89428i) q^{77} +(-4.07566 - 9.15408i) q^{79} +(18.0574 + 5.86722i) q^{80} +(9.96124 - 7.23727i) q^{82} +(-0.623446 - 5.93169i) q^{83} +(-1.24884 - 5.87533i) q^{85} +(5.69655 + 0.598731i) q^{86} +(-19.3115 + 21.7694i) q^{88} +5.11584i q^{89} +(-1.32800 + 4.08716i) q^{91} +(-6.34754 + 29.8628i) q^{92} +(7.95359 - 17.8641i) q^{94} +(1.21278 - 1.34693i) q^{95} +(5.51867 - 2.45707i) q^{97} +13.2430 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 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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