LMFDB - Embedded newform 225.2.m.b.154.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(19,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("225.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.m (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			154.2
Root			$1.35083i$ of defining polynomial
Character	$\chi$	$=$	225.154
Dual form			225.2.m.b.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28472 - 0.417429i) q^{2} +(-0.141788 - 0.103015i) q^{4} +(-1.34359 - 1.78739i) q^{5} -1.59580i q^{7} +(1.72715 + 2.37722i) q^{8} +O(q^{10})$	\(q+(-1.28472 - 0.417429i) q^{2} +(-0.141788 - 0.103015i) q^{4} +(-1.34359 - 1.78739i) q^{5} -1.59580i q^{7} +(1.72715 + 2.37722i) q^{8} +(0.980025 + 2.85714i) q^{10} +(-1.02988 + 3.16965i) q^{11} +(-6.70620 + 2.17898i) q^{13} +(-0.666132 + 2.05014i) q^{14} +(-1.11826 - 3.44165i) q^{16} +(-2.40771 - 3.31393i) q^{17} +(0.459145 - 0.333589i) q^{19} +(0.00637730 + 0.391840i) q^{20} +(2.64621 - 3.64220i) q^{22} +(-5.99546 - 1.94804i) q^{23} +(-1.38952 + 4.80304i) q^{25} +9.52513 q^{26} +(-0.164391 + 0.226264i) q^{28} +(2.25196 + 1.63614i) q^{29} +(0.805639 - 0.585331i) q^{31} -0.988473i q^{32} +(1.70989 + 5.26251i) q^{34} +(-2.85231 + 2.14410i) q^{35} +(-3.37943 + 1.09804i) q^{37} +(-0.729121 + 0.236906i) q^{38} +(1.92843 - 6.28110i) q^{40} +(-0.359364 - 1.10601i) q^{41} +0.117022i q^{43} +(0.472545 - 0.343324i) q^{44} +(6.88929 + 5.00536i) q^{46} +(4.49170 - 6.18229i) q^{47} +4.45343 q^{49} +(3.79007 - 5.59052i) q^{50} +(1.17532 + 0.381886i) q^{52} +(-0.307785 + 0.423629i) q^{53} +(7.04914 - 2.41792i) q^{55} +(3.79356 - 2.75618i) q^{56} +(-2.21015 - 3.04201i) q^{58} +(0.304072 + 0.935838i) q^{59} +(3.27982 - 10.0942i) q^{61} +(-1.27935 + 0.415686i) q^{62} +(-2.64914 + 8.15321i) q^{64} +(12.9051 + 9.05894i) q^{65} +(-8.94370 - 12.3099i) q^{67} +0.717905i q^{68} +(4.55942 - 1.56392i) q^{70} +(-8.62730 - 6.26810i) q^{71} +(5.28627 + 1.71761i) q^{73} +4.79996 q^{74} -0.0994657 q^{76} +(5.05812 + 1.64348i) q^{77} +(-11.8091 - 8.57982i) q^{79} +(-4.64908 + 6.62294i) q^{80} +1.57091i q^{82} +(2.95302 + 4.06448i) q^{83} +(-2.68830 + 8.75610i) q^{85} +(0.0488483 - 0.150339i) q^{86} +(-9.31372 + 3.02621i) q^{88} +(0.872511 - 2.68531i) q^{89} +(3.47720 + 10.7017i) q^{91} +(0.649405 + 0.893830i) q^{92} +(-8.35122 + 6.06752i) q^{94} +(-1.21316 - 0.372464i) q^{95} +(1.00271 - 1.38012i) q^{97} +(-5.72139 - 1.85899i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 30 q^{8}+O(q^{10}) $ 16 * q + 2 * q^4 + 30 * q^8	$ 16 q + 2 q^{4} + 30 q^{8} + 6 q^{11} + 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} - 20 q^{20} - 30 q^{22} + 20 q^{23} - 10 q^{25} - 12 q^{26} + 30 q^{28} - 16 q^{29} + 6 q^{31} - 36 q^{34} - 10 q^{35} - 10 q^{37} - 30 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 16 q^{46} - 40 q^{47} - 20 q^{50} + 40 q^{52} - 10 q^{53} + 10 q^{55} + 10 q^{58} - 12 q^{59} + 10 q^{62} + 8 q^{64} + 70 q^{65} - 40 q^{67} + 30 q^{70} + 8 q^{71} - 20 q^{73} + 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 10 q^{83} - 20 q^{85} + 36 q^{86} - 40 q^{88} - 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} + 40 q^{95} + 40 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 2 * q^4 + 30 * q^8 + 6 * q^11 + 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 - 20 * q^20 - 30 * q^22 + 20 * q^23 - 10 * q^25 - 12 * q^26 + 30 * q^28 - 16 * q^29 + 6 * q^31 - 36 * q^34 - 10 * q^35 - 10 * q^37 - 30 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 16 * q^46 - 40 * q^47 - 20 * q^50 + 40 * q^52 - 10 * q^53 + 10 * q^55 + 10 * q^58 - 12 * q^59 + 10 * q^62 + 8 * q^64 + 70 * q^65 - 40 * q^67 + 30 * q^70 + 8 * q^71 - 20 * q^73 + 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 10 * q^83 - 20 * q^85 + 36 * q^86 - 40 * q^88 - 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 + 40 * q^95 + 40 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.28472	−	0.417429i	−0.908431	−	0.295167i	−0.182719	−	0.983165i	$-0.558490\pi$
$2$	−1.28472	−	0.417429i	−0.908431	−	0.295167i	−0.725712	+	0.687998i	$0.758490\pi$
$3$		0			0
$3$		0			0
$4$	−0.141788	−	0.103015i	−0.0708938	−	0.0515074i
$5$	−1.34359	−	1.78739i	−0.600873	−	0.799345i
$5$	−1.34359	−	1.78739i	−0.600873	−	0.799345i
$6$		0			0
$7$		−	1.59580i		−	0.603155i	−0.953442	−	0.301577i	$-0.902487\pi$
$7$		−	1.59580i		−	0.603155i	0.953442	−	0.301577i	$-0.0975131\pi$
$8$	1.72715	+	2.37722i	0.610640	+	0.840474i
$9$		0			0
$10$	0.980025	+	2.85714i	0.309911	+	0.903507i
$11$	−1.02988	+	3.16965i	−0.310521	+	0.955686i	0.667038	+	0.745024i	$0.267562\pi$
$11$	−1.02988	+	3.16965i	−0.310521	+	0.955686i	−0.977559	+	0.210662i	$0.932438\pi$
$12$		0			0
$13$	−6.70620	+	2.17898i	−1.85997	+	0.604339i	−0.865292	+	0.501269i	$0.832867\pi$
$13$	−6.70620	+	2.17898i	−1.85997	+	0.604339i	−0.994674	+	0.103071i	$0.967133\pi$
$14$	−0.666132	+	2.05014i	−0.178031	+	0.547924i
$15$		0			0
$16$	−1.11826	−	3.44165i	−0.279565	−	0.860413i
$17$	−2.40771	−	3.31393i	−0.583957	−	0.803747i	0.410166	−	0.912011i	$-0.365471\pi$
$17$	−2.40771	−	3.31393i	−0.583957	−	0.803747i	−0.994122	+	0.108264i	$0.965471\pi$
$18$		0			0
$19$	0.459145	−	0.333589i	0.105335	−	0.0765305i	−0.533871	−	0.845566i	$-0.679263\pi$
$19$	0.459145	−	0.333589i	0.105335	−	0.0765305i	0.639206	+	0.769036i	$0.279263\pi$
$20$	0.00637730	+	0.391840i	0.00142601	+	0.0876180i
$21$		0			0
$22$	2.64621	−	3.64220i	0.564174	−	0.776519i
$23$	−5.99546	−	1.94804i	−1.25014	−	0.406195i	−0.392169	−	0.919893i	$-0.628275\pi$
$23$	−5.99546	−	1.94804i	−1.25014	−	0.406195i	−0.857971	+	0.513698i	$0.828275\pi$
$24$		0			0
$25$	−1.38952	+	4.80304i	−0.277904	+	0.960609i
$26$	9.52513			1.86803
$27$		0			0
$28$	−0.164391	+	0.226264i	−0.0310669	+	0.0427599i
$29$	2.25196	+	1.63614i	0.418178	+	0.303824i	0.776904	−	0.629619i	$-0.216789\pi$
$29$	2.25196	+	1.63614i	0.418178	+	0.303824i	−0.358726	+	0.933443i	$0.616789\pi$
$30$		0			0
$31$	0.805639	−	0.585331i	0.144697	−	0.105128i	−0.513082	−	0.858340i	$-0.671496\pi$
$31$	0.805639	−	0.585331i	0.144697	−	0.105128i	0.657779	+	0.753211i	$0.271496\pi$
$32$		−	0.988473i		−	0.174739i
$33$		0			0
$34$	1.70989	+	5.26251i	0.293244	+	0.902514i
$35$	−2.85231	+	2.14410i	−0.482128	+	0.362419i
$36$		0			0
$37$	−3.37943	+	1.09804i	−0.555574	+	0.180517i	−0.573329	−	0.819325i	$-0.694348\pi$
$37$	−3.37943	+	1.09804i	−0.555574	+	0.180517i	0.0177546	+	0.999842i	$0.494348\pi$
$38$	−0.729121	+	0.236906i	−0.118279	+	0.0384312i
$39$		0			0
$40$	1.92843	−	6.28110i	0.304912	−	0.993130i
$41$	−0.359364	−	1.10601i	−0.0561232	−	0.172729i	0.919065	−	0.394105i	$-0.128945\pi$
$41$	−0.359364	−	1.10601i	−0.0561232	−	0.172729i	−0.975189	+	0.221376i	$0.928945\pi$
$42$		0			0
$43$			0.117022i			0.0178456i	0.999960	+	0.00892281i	$0.00284026\pi$
$43$			0.117022i			0.0178456i	−0.999960	+	0.00892281i	$0.997160\pi$
$44$	0.472545	−	0.343324i	0.0712389	−	0.0517581i
$45$		0			0
$46$	6.88929	+	5.00536i	1.01577	+	0.738001i
$47$	4.49170	−	6.18229i	0.655182	−	0.901780i	−0.344128	−	0.938923i	$-0.611826\pi$
$47$	4.49170	−	6.18229i	0.655182	−	0.901780i	0.999310	+	0.0371425i	$0.0118256\pi$
$48$		0			0
$49$	4.45343			0.636205
$50$	3.79007	−	5.59052i	0.535997	−	0.790619i
$51$		0			0
$52$	1.17532	+	0.381886i	0.162988	+	0.0529580i
$53$	−0.307785	+	0.423629i	−0.0422775	+	0.0581900i	−0.829632	−	0.558310i	$-0.811450\pi$
$53$	−0.307785	+	0.423629i	−0.0422775	+	0.0581900i	0.787355	+	0.616500i	$0.211450\pi$
$54$		0			0
$55$	7.04914	−	2.41792i	0.950506	−	0.326032i
$56$	3.79356	−	2.75618i	0.506936	−	0.368310i
$57$		0			0
$58$	−2.21015	−	3.04201i	−0.290207	−	0.399436i
$59$	0.304072	+	0.935838i	0.0395868	+	0.121836i	0.968897	−	0.247465i	$-0.0795974\pi$
$59$	0.304072	+	0.935838i	0.0395868	+	0.121836i	−0.929310	+	0.369300i	$0.879597\pi$
$60$		0			0
$61$	3.27982	−	10.0942i	0.419937	−	1.29243i	−0.487822	−	0.872943i	$-0.662208\pi$
$61$	3.27982	−	10.0942i	0.419937	−	1.29243i	0.907759	−	0.419491i	$-0.137792\pi$
$62$	−1.27935	+	0.415686i	−0.162478	+	0.0527922i
$63$		0			0
$64$	−2.64914	+	8.15321i	−0.331142	+	1.01915i
$65$	12.9051	+	9.05894i	1.60068	+	1.12362i
$66$		0			0
$67$	−8.94370	−	12.3099i	−1.09265	−	1.50390i	−0.844786	−	0.535104i	$-0.820272\pi$
$67$	−8.94370	−	12.3099i	−1.09265	−	1.50390i	−0.247861	−	0.968796i	$-0.579728\pi$
$68$			0.717905i			0.0870588i
$69$		0			0
$70$	4.55942	−	1.56392i	0.544955	−	0.186924i
$71$	−8.62730	−	6.26810i	−1.02387	−	0.743887i	−0.0567995	−	0.998386i	$-0.518090\pi$
$71$	−8.62730	−	6.26810i	−1.02387	−	0.743887i	−0.967073	+	0.254499i	$0.918090\pi$
$72$		0			0
$73$	5.28627	+	1.71761i	0.618711	+	0.201032i	0.601568	−	0.798821i	$-0.294543\pi$
$73$	5.28627	+	1.71761i	0.618711	+	0.201032i	0.0171433	+	0.999853i	$0.494543\pi$
$74$	4.79996			0.557984
$75$		0			0
$76$	−0.0994657			−0.0114095
$77$	5.05812	+	1.64348i	0.576426	+	0.187292i
$78$		0			0
$79$	−11.8091	−	8.57982i	−1.32863	−	0.965305i	−0.999781	−	0.0209214i	$-0.993340\pi$
$79$	−11.8091	−	8.57982i	−1.32863	−	0.965305i	−0.328847	−	0.944383i	$-0.606660\pi$
$80$	−4.64908	+	6.62294i	−0.519783	+	0.740467i
$81$		0			0
$82$			1.57091i			0.173478i
$83$	2.95302	+	4.06448i	0.324136	+	0.446135i	0.939724	−	0.341933i	$-0.111082\pi$
$83$	2.95302	+	4.06448i	0.324136	+	0.446135i	−0.615588	+	0.788068i	$0.711082\pi$
$84$		0			0
$85$	−2.68830	+	8.75610i	−0.291588	+	0.949732i
$86$	0.0488483	−	0.150339i	0.00526744	−	0.0162115i
$87$		0			0
$88$	−9.31372	+	3.02621i	−0.992846	+	0.322595i
$89$	0.872511	−	2.68531i	0.0924859	−	0.284642i	−0.894104	−	0.447859i	$-0.852187\pi$
$89$	0.872511	−	2.68531i	0.0924859	−	0.284642i	0.986590	+	0.163216i	$0.0521868\pi$
$90$		0			0
$91$	3.47720	+	10.7017i	0.364510	+	1.12185i
$92$	0.649405	+	0.893830i	0.0677052	+	0.0931882i
$93$		0			0
$94$	−8.35122	+	6.06752i	−0.861363	+	0.625817i
$95$	−1.21316	−	0.372464i	−0.124467	−	0.0382140i
$96$		0			0
$97$	1.00271	−	1.38012i	0.101810	−	0.140130i	−0.755072	−	0.655642i	$-0.772398\pi$
$97$	1.00271	−	1.38012i	0.101810	−	0.140130i	0.856882	+	0.515512i	$0.172398\pi$
$98$	−5.72139	−	1.85899i	−0.577948	−	0.187787i
$99$		0			0
$100$	0.691801	−	0.537871i	0.0691801	−	0.0537871i
$101$	−13.1747			−1.31093			−0.655464	−	0.755226i	$-0.727527\pi$
$101$	−13.1747			−1.31093			−0.655464	+	0.755226i	$0.727527\pi$
$102$		0			0
$103$	6.39039	−	8.79562i	0.629664	−	0.866658i	−0.368347	−	0.929688i	$-0.620076\pi$
$103$	6.39039	−	8.79562i	0.629664	−	0.866658i	0.998012	+	0.0630298i	$0.0200763\pi$
$104$	−16.7625	−	12.1787i	−1.64370	−	1.19422i
$105$		0			0
$106$	0.572251	−	0.415765i	0.0555819	−	0.0403826i
$107$			9.37236i			0.906060i	0.891495	+	0.453030i	$0.149657\pi$
$107$			9.37236i			0.906060i	−0.891495	+	0.453030i	$0.850343\pi$
$108$		0			0
$109$	4.81755	+	14.8269i	0.461438	+	1.42016i	0.863408	+	0.504506i	$0.168326\pi$
$109$	4.81755	+	14.8269i	0.461438	+	1.42016i	−0.401970	+	0.915653i	$0.631674\pi$
$110$	−10.0655	+	0.163818i	−0.959703	+	0.0156194i
$111$		0			0
$112$	−5.49218	+	1.78452i	−0.518962	+	0.168621i
$113$	−9.55629	+	3.10503i	−0.898980	+	0.292096i	−0.721816	−	0.692085i	$-0.756692\pi$
$113$	−9.55629	+	3.10503i	−0.898980	+	0.292096i	−0.177164	+	0.984181i	$0.556692\pi$
$114$		0			0
$115$	4.57354	+	13.3336i	0.426485	+	1.24336i
$116$	−0.150753	−	0.463970i	−0.0139971	−	0.0430785i
$117$		0			0
$118$		−	1.32921i		−	0.122364i
$119$	−5.28837	+	3.84222i	−0.484784	+	0.352216i
$120$		0			0
$121$	−0.0868453	−	0.0630968i	−0.00789503	−	0.00573608i
$122$	−8.42726	+	11.5991i	−0.762968	+	1.05014i
$123$		0			0
$124$	−0.174527			−0.0156730
$125$	10.4519	−	3.96972i	0.934843	−	0.355062i
$126$		0			0
$127$	−0.928977	−	0.301843i	−0.0824334	−	0.0267842i	0.267510	−	0.963555i	$-0.413799\pi$
$127$	−0.928977	−	0.301843i	−0.0824334	−	0.0267842i	−0.349943	+	0.936771i	$0.613799\pi$
$128$	5.64476	−	7.76934i	0.498931	−	0.686719i
$129$		0			0
$130$	−12.7979	−	17.0251i	−1.12245	−	1.49320i
$131$	8.14001	−	5.91406i	0.711196	−	0.516714i	−0.172363	−	0.985033i	$-0.555140\pi$
$131$	8.14001	−	5.91406i	0.711196	−	0.516714i	0.883559	+	0.468319i	$0.155140\pi$
$132$		0			0
$133$	−0.532340	−	0.732703i	−0.0461597	−	0.0635334i
$134$	6.35158	+	19.5481i	0.548693	+	1.68870i
$135$		0			0
$136$	3.71946	−	11.4473i	0.318941	−	0.981600i
$137$	−4.63397	+	1.50567i	−0.395907	+	0.128638i	−0.500203	−	0.865908i	$-0.666741\pi$
$137$	−4.63397	+	1.50567i	−0.395907	+	0.128638i	0.104296	+	0.994546i	$0.466741\pi$
$138$		0			0
$139$	−0.0574103	+	0.176691i	−0.00486948	+	0.0149867i	−0.953462	−	0.301514i	$-0.902508\pi$
$139$	−0.0574103	+	0.176691i	−0.00486948	+	0.0149867i	0.948592	+	0.316501i	$0.102508\pi$
$140$	0.625296	−	0.0101769i	0.0528472	−	0.000860103i
$141$		0			0
$142$	8.46714	+	11.6540i	0.710547	+	0.977984i
$143$		−	23.5004i		−	1.96520i
$144$		0			0
$145$	−0.101288	−	6.22344i	−0.00841153	−	0.516828i
$146$	−6.07437	−	4.41329i	−0.502719	−	0.365247i
$147$		0			0
$148$	0.592276	+	0.192442i	0.0486847	+	0.0158186i
$149$	3.88889			0.318590			0.159295	−	0.987231i	$-0.449078\pi$
$149$	3.88889			0.318590			0.159295	+	0.987231i	$0.449078\pi$
$150$		0			0
$151$	−22.1146			−1.79966			−0.899829	−	0.436242i	$-0.856309\pi$
$151$	−22.1146			−1.79966			−0.899829	+	0.436242i	$0.856309\pi$
$152$	1.58603	+	0.515331i	0.128644	+	0.0417989i
$153$		0			0
$154$	−5.81221	−	4.22282i	−0.468361	−	0.340284i
$155$	−2.12866	−	0.653544i	−0.170978	−	0.0524939i
$156$		0			0
$157$			13.6058i			1.08586i	0.839777	+	0.542931i	$0.182686\pi$
$157$			13.6058i			1.08586i	−0.839777	+	0.542931i	$0.817314\pi$
$158$	11.5899	+	15.9521i	0.922041	+	1.26908i
$159$		0			0
$160$	−1.76679	+	1.32810i	−0.139677	+	0.104996i
$161$	−3.10868	+	9.56754i	−0.244999	+	0.754028i
$162$		0			0
$163$	8.20662	−	2.66649i	0.642792	−	0.208856i	0.0305587	−	0.999533i	$-0.490271\pi$
$163$	8.20662	−	2.66649i	0.642792	−	0.208856i	0.612233	+	0.790677i	$0.290271\pi$
$164$	−0.0629818	+	0.193838i	−0.00491805	+	0.0151362i
$165$		0			0
$166$	−2.09716	−	6.45438i	−0.162771	−	0.500957i
$167$	3.87874	+	5.33863i	0.300146	+	0.413116i	0.932277	−	0.361746i	$-0.117819\pi$
$167$	3.87874	+	5.33863i	0.300146	+	0.413116i	−0.632131	+	0.774862i	$0.717819\pi$
$168$		0			0
$169$	29.7080	−	21.5841i	2.28523	−	1.66032i
$170$	7.10876	−	10.1269i	0.545217	−	0.776699i
$171$		0			0
$172$	0.0120550	−	0.0165922i	0.000919182	−	0.00126514i
$173$	12.9910	+	4.22102i	0.987685	+	0.320918i	0.757934	−	0.652331i	$-0.226209\pi$
$173$	12.9910	+	4.22102i	0.987685	+	0.320918i	0.229751	+	0.973249i	$0.426209\pi$
$174$		0			0
$175$	7.66468	+	2.21739i	0.579396	+	0.167619i
$176$	12.0605			0.909095
$177$		0			0
$178$	−2.24186	+	3.08565i	−0.168034	+	0.231279i
$179$	−7.95167	−	5.77722i	−0.594336	−	0.431810i	0.249528	−	0.968368i	$-0.419724\pi$
$179$	−7.95167	−	5.77722i	−0.594336	−	0.431810i	−0.843864	+	0.536557i	$0.819724\pi$
$180$		0			0
$181$	−14.4561	+	10.5030i	−1.07451	+	0.780679i	−0.976718	−	0.214528i	$-0.931179\pi$
$181$	−14.4561	+	10.5030i	−1.07451	+	0.780679i	−0.0977940	+	0.995207i	$0.531179\pi$
$182$		−	15.2002i		−	1.12671i
$183$		0			0
$184$	−5.72414	−	17.6171i	−0.421989	−	1.29875i
$185$	6.50320	+	4.56503i	0.478125	+	0.335628i
$186$		0			0
$187$	12.9837	−	4.21865i	0.949461	−	0.308498i
$188$	−1.27373	+	0.413862i	−0.0928967	+	0.0301840i
$189$		0			0
$190$	1.40308	+	0.984918i	0.101790	+	0.0714535i
$191$	−0.100682	−	0.309867i	−0.00728509	−	0.0224212i	0.947348	−	0.320206i	$-0.103752\pi$
$191$	−0.100682	−	0.309867i	−0.00728509	−	0.0224212i	−0.954633	+	0.297785i	$0.903752\pi$
$192$		0			0
$193$			2.90187i			0.208881i	0.994531	+	0.104441i	$0.0333052\pi$
$193$			2.90187i			0.208881i	−0.994531	+	0.104441i	$0.966695\pi$
$194$	−1.86430	+	1.35450i	−0.133849	+	0.0972471i
$195$		0			0
$196$	−0.631442	−	0.458769i	−0.0451030	−	0.0327692i
$197$	10.6518	−	14.6610i	0.758911	−	1.04455i	−0.238393	−	0.971169i	$-0.576620\pi$
$197$	10.6518	−	14.6610i	0.758911	−	1.04455i	0.997304	−	0.0733829i	$-0.0233795\pi$
$198$		0			0
$199$	−1.53256			−0.108640			−0.0543201	−	0.998524i	$-0.517299\pi$
$199$	−1.53256			−0.108640			−0.0543201	+	0.998524i	$0.517299\pi$
$200$	−13.8178	+	4.99239i	−0.977066	+	0.353015i
$201$		0			0
$202$	16.9257	+	5.49949i	1.19089	+	0.386943i
$203$	2.61095	−	3.59367i	0.183253	−	0.252226i
$204$		0			0
$205$	−1.49403	+	2.12835i	−0.104347	+	0.148650i
$206$	−11.8814	+	8.63233i	−0.827816	+	0.601443i
$207$		0			0
$208$	14.9986	+	20.6437i	1.03996	+	1.43139i
$209$	0.584494	+	1.79889i	0.0404303	+	0.124432i
$210$		0			0
$211$	−3.51345	+	10.8133i	−0.241876	+	0.744418i	0.754259	+	0.656577i	$0.227996\pi$
$211$	−3.51345	+	10.8133i	−0.241876	+	0.744418i	−0.996135	+	0.0878402i	$0.972004\pi$
$212$	0.0872802	−	0.0283590i	0.00599443	−	0.00194771i
$213$		0			0
$214$	3.91230	−	12.0408i	0.267439	−	0.823093i
$215$	0.209163	−	0.157229i	0.0142648	−	0.0107229i
$216$		0			0
$217$	−0.934069	−	1.28564i	−0.0634087	−	0.0872746i
$218$		−	21.0593i		−	1.42632i
$219$		0			0
$220$	−1.24856	−	0.383335i	−0.0841781	−	0.0258444i
$221$	23.3676	+	16.9776i	1.57188	+	1.14203i
$222$		0			0
$223$	−16.1210	−	5.23804i	−1.07954	−	0.350765i	−0.285347	−	0.958424i	$-0.592109\pi$
$223$	−16.1210	−	5.23804i	−1.07954	−	0.350765i	−0.794198	+	0.607659i	$0.792109\pi$
$224$	−1.57740			−0.105395
$225$		0			0
$226$	13.5732			0.902878
$227$	−13.4210	−	4.36076i	−0.890785	−	0.289434i	−0.172357	−	0.985035i	$-0.555138\pi$
$227$	−13.4210	−	4.36076i	−0.890785	−	0.289434i	−0.718428	+	0.695601i	$0.755138\pi$
$228$		0			0
$229$	0.0501546	+	0.0364394i	0.00331431	+	0.00240799i	0.589441	−	0.807811i	$-0.299348\pi$
$229$	0.0501546	+	0.0364394i	0.00331431	+	0.00240799i	−0.586127	+	0.810219i	$0.699348\pi$
$230$	−0.309865	−	19.0390i	−0.0204319	−	1.25540i
$231$		0			0
$232$			8.17927i			0.536995i
$233$	15.2936	+	21.0499i	1.00192	+	1.37902i	0.924141	+	0.382052i	$0.124782\pi$
$233$	15.2936	+	21.0499i	1.00192	+	1.37902i	0.0777775	+	0.996971i	$0.475218\pi$
$234$		0			0
$235$	−17.0852	+	0.278066i	−1.11451	+	0.0181390i
$236$	0.0532914	−	0.164014i	0.00346898	−	0.0106764i
$237$		0			0
$238$	8.39790	−	2.72864i	0.544355	−	0.176872i
$239$	6.02491	−	18.5428i	0.389719	−	1.19943i	−0.543279	−	0.839552i	$-0.682817\pi$
$239$	6.02491	−	18.5428i	0.389719	−	1.19943i	0.932998	−	0.359881i	$-0.117183\pi$
$240$		0			0
$241$	−1.26654	−	3.89800i	−0.0815848	−	0.251092i	0.901941	−	0.431859i	$-0.142142\pi$
$241$	−1.26654	−	3.89800i	−0.0815848	−	0.251092i	−0.983526	+	0.180767i	$0.942142\pi$
$242$	0.0852331	+	0.117313i	0.00547899	+	0.00754118i
$243$		0			0
$244$	−1.50489	+	1.09337i	−0.0963409	+	0.0699957i
$245$	−5.98360	−	7.96002i	−0.382278	−	0.508547i
$246$		0			0
$247$	−2.35224	+	3.23758i	−0.149669	+	0.206002i
$248$	2.78292	+	0.904225i	0.176716	+	0.0574184i
$249$		0			0
$250$	−15.0847	+	0.737046i	−0.954043	+	0.0466149i
$251$	1.02933			0.0649704			0.0324852	−	0.999472i	$-0.489658\pi$
$251$	1.02933			0.0649704			0.0324852	+	0.999472i	$0.489658\pi$
$252$		0			0
$253$	12.3492	−	16.9973i	0.776390	−	1.06861i
$254$	1.06747	+	0.775565i	0.0669792	+	0.0486633i
$255$		0			0
$256$	3.37601	−	2.45281i	0.211001	−	0.153301i
$257$			18.5597i			1.15772i	0.815426	+	0.578862i	$0.196503\pi$
$257$			18.5597i			1.15772i	−0.815426	+	0.578862i	$0.803497\pi$
$258$		0			0
$259$	1.75225	+	5.39288i	0.108880	+	0.335097i
$260$	−0.896577	−	2.61386i	−0.0556033	−	0.162105i
$261$		0			0
$262$	−12.9263	+	4.20001i	−0.798589	+	0.259477i
$263$	−11.7872	+	3.82988i	−0.726827	+	0.236161i	−0.648981	−	0.760805i	$-0.724804\pi$
$263$	−11.7872	+	3.82988i	−0.726827	+	0.236161i	−0.0778466	+	0.996965i	$0.524804\pi$
$264$		0			0
$265$	1.17073	−	0.0190539i	0.0719172	−	0.00117047i
$266$	0.378053	+	1.16353i	0.0231799	+	0.0713405i
$267$		0			0
$268$			2.66673i			0.162897i
$269$	4.28805	−	3.11545i	0.261447	−	0.189952i	−0.449338	−	0.893362i	$-0.648340\pi$
$269$	4.28805	−	3.11545i	0.261447	−	0.189952i	0.710785	+	0.703410i	$0.248340\pi$
$270$		0			0
$271$	−0.645132	−	0.468716i	−0.0391890	−	0.0284725i	0.568018	−	0.823016i	$-0.307710\pi$
$271$	−0.645132	−	0.468716i	−0.0391890	−	0.0284725i	−0.607207	+	0.794543i	$0.707710\pi$
$272$	−8.71295	+	11.9924i	−0.528300	+	0.727143i
$273$		0			0
$274$	6.58184			0.397624
$275$	−13.7929	−	9.35086i	−0.831745	−	0.563878i
$276$		0			0
$277$	−4.51205	−	1.46605i	−0.271103	−	0.0880867i	0.170311	−	0.985390i	$-0.445523\pi$
$277$	−4.51205	−	1.46605i	−0.271103	−	0.0880867i	−0.441414	+	0.897304i	$0.645523\pi$
$278$	0.147512	−	0.203033i	0.00884717	−	0.0121771i
$279$		0			0
$280$	−10.0234	−	3.07738i	−0.599011	−	0.183909i
$281$	−15.1608	+	11.0150i	−0.904418	+	0.657098i	−0.939597	−	0.342283i	$-0.888800\pi$
$281$	−15.1608	+	11.0150i	−0.904418	+	0.657098i	0.0351791	+	0.999381i	$0.488800\pi$
$282$		0			0
$283$	6.91306	+	9.51501i	0.410939	+	0.565608i	0.963447	−	0.267899i	$-0.0863293\pi$
$283$	6.91306	+	9.51501i	0.410939	+	0.565608i	−0.552508	+	0.833507i	$0.686329\pi$
$284$	0.577538	+	1.77748i	0.0342706	+	0.105474i
$285$		0			0
$286$	−9.80976	+	30.1913i	−0.580063	+	1.78525i
$287$	−1.76496	+	0.573471i	−0.104182	+	0.0338509i
$288$		0			0
$289$	0.0682154	−	0.209945i	0.00401267	−	0.0123497i
$290$	−2.46772	+	8.03762i	−0.144909	+	0.471986i
$291$		0			0
$292$	−0.572589	−	0.788101i	−0.0335082	−	0.0461201i
$293$			22.2819i			1.30172i	0.759198	+	0.650860i	$0.225592\pi$
$293$			22.2819i			1.30172i	−0.759198	+	0.650860i	$0.774408\pi$
$294$		0			0
$295$	1.26416	−	1.80088i	0.0736021	−	0.104851i
$296$	−8.44707	−	6.13715i	−0.490976	−	0.356715i
$297$		0			0
$298$	−4.99611	−	1.62333i	−0.289417	−	0.0940373i
$299$	44.4515			2.57070
$300$		0			0
$301$	0.186743			0.0107637
$302$	28.4109	+	9.23127i	1.63487	+	0.531200i
$303$		0			0
$304$	−1.66154	−	1.20718i	−0.0952958	−	0.0692365i
$305$	−22.4491	+	7.70023i	−1.28543	+	0.440914i
$306$		0			0
$307$		−	15.3063i		−	0.873574i	−0.899565	−	0.436787i	$-0.856116\pi$
$307$		−	15.3063i		−	0.873574i	0.899565	−	0.436787i	$-0.143884\pi$
$308$	−0.547876	−	0.754087i	−0.0312181	−	0.0429681i
$309$		0			0
$310$	2.46192	+	1.72818i	0.139828	+	0.0981543i
$311$	3.97226	−	12.2254i	0.225246	−	0.693237i	−0.773020	−	0.634382i	$-0.781255\pi$
$311$	3.97226	−	12.2254i	0.225246	−	0.693237i	0.998267	−	0.0588556i	$-0.0187452\pi$
$312$		0			0
$313$	−9.99293	+	3.24690i	−0.564834	+	0.183526i	−0.577495	−	0.816394i	$-0.695970\pi$
$313$	−9.99293	+	3.24690i	−0.564834	+	0.183526i	0.0126612	+	0.999920i	$0.495970\pi$
$314$	5.67947	−	17.4796i	0.320511	−	0.986431i
$315$		0			0
$316$	0.790537	+	2.43302i	0.0444712	+	0.136868i
$317$	−11.4504	−	15.7602i	−0.643120	−	0.885179i	0.355657	−	0.934617i	$-0.384257\pi$
$317$	−11.4504	−	15.7602i	−0.643120	−	0.885179i	−0.998777	+	0.0494374i	$0.984257\pi$
$318$		0			0
$319$	−7.50526	+	5.45289i	−0.420214	+	0.305303i
$320$	18.1323	−	6.21955i	1.01363	−	0.347683i
$321$		0			0
$322$	7.98754	−	10.9939i	0.445128	−	0.612667i
$323$	−2.21098	−	0.718392i	−0.123022	−	0.0399724i
$324$		0			0
$325$	−1.14732	−	35.2379i	−0.0636418	−	1.95465i
$326$	−11.6562			−0.645579
$327$		0			0
$328$	2.00855	−	2.76453i	0.110903	−	0.152646i
$329$	−9.86568	−	7.16784i	−0.543913	−	0.395176i
$330$		0			0
$331$	11.7247	−	8.51846i	0.644446	−	0.468217i	−0.216929	−	0.976187i	$-0.569604\pi$
$331$	11.7247	−	8.51846i	0.644446	−	0.468217i	0.861375	+	0.507970i	$0.169604\pi$
$332$		−	0.880498i		−	0.0483236i
$333$		0			0
$334$	−2.75458	−	8.47772i	−0.150724	−	0.463880i
$335$	−9.98598	+	32.5254i	−0.545593	+	1.77705i
$336$		0			0
$337$	−8.87550	+	2.88382i	−0.483479	+	0.157092i	−0.540608	−	0.841275i	$-0.681806\pi$
$337$	−8.87550	+	2.88382i	−0.483479	+	0.157092i	0.0571283	+	0.998367i	$0.481806\pi$
$338$	−47.1761	+	15.3285i	−2.56604	+	0.833758i
$339$		0			0
$340$	1.28318	−	0.964572i	0.0695900	−	0.0523112i
$341$	1.02558	+	3.15641i	0.0555383	+	0.170929i
$342$		0			0
$343$		−	18.2774i		−	0.986884i
$344$	−0.278186	+	0.202114i	−0.0149988	+	0.0108973i
$345$		0			0
$346$	−14.9277	−	10.8456i	−0.802519	−	0.583064i
$347$	0.619178	−	0.852225i	0.0332392	−	0.0457498i	−0.792074	−	0.610425i	$-0.790999\pi$
$347$	0.619178	−	0.852225i	0.0332392	−	0.0457498i	0.825313	+	0.564675i	$0.190999\pi$
$348$		0			0
$349$	13.0715			0.699700			0.349850	−	0.936806i	$-0.386233\pi$
$349$	13.0715			0.699700			0.349850	+	0.936806i	$0.386233\pi$
$350$	−8.92133	−	6.04818i	−0.476865	−	0.323289i
$351$		0			0
$352$	3.13311	+	1.01801i	0.166996	+	0.0542602i
$353$	19.9537	−	27.4639i	1.06203	−	1.46176i	0.184134	−	0.982901i	$-0.441052\pi$
$353$	19.9537	−	27.4639i	1.06203	−	1.46176i	0.877894	−	0.478855i	$-0.158948\pi$
$354$		0			0
$355$	0.388037	+	23.8421i	0.0205949	+	1.26541i
$356$	−0.400338	+	0.290863i	−0.0212179	+	0.0154157i
$357$		0			0
$358$	7.80405	+	10.7413i	0.412457	+	0.567698i
$359$	−1.88331	−	5.79622i	−0.0993971	−	0.305913i	0.888978	−	0.457951i	$-0.151416\pi$
$359$	−1.88331	−	5.79622i	−0.0993971	−	0.305913i	−0.988375	+	0.152038i	$0.951416\pi$
$360$		0			0
$361$	−5.77179	+	17.7637i	−0.303778	+	0.934934i
$362$	22.9562	−	7.45892i	1.20655	−	0.392032i
$363$		0			0
$364$	0.609412	−	1.87558i	0.0319419	−	0.0983070i
$365$	−4.03255	−	11.7564i	−0.211073	−	0.615358i
$366$		0			0
$367$	12.8511	+	17.6881i	0.670823	+	0.923309i	0.999779	−	0.0210364i	$-0.00669658\pi$
$367$	12.8511	+	17.6881i	0.670823	+	0.923309i	−0.328955	+	0.944345i	$0.606697\pi$
$368$			22.8127i			1.18919i
$369$		0			0
$370$	−6.44918	−	8.57939i	−0.335277	−	0.446021i
$371$	0.676026	+	0.491162i	0.0350975	+	0.0254999i
$372$		0			0
$373$	23.2590	+	7.55730i	1.20430	+	0.391302i	0.841343	−	0.540502i	$-0.181766\pi$
$373$	23.2590	+	7.55730i	1.20430	+	0.391302i	0.362961	+	0.931804i	$0.381766\pi$
$374$	−18.4413			−0.953578
$375$		0			0
$376$	22.4545			1.15800
$377$	−18.6672	−	6.06534i	−0.961410	−	0.312381i
$378$		0			0
$379$	−5.07918	−	3.69024i	−0.260900	−	0.189555i	0.449644	−	0.893208i	$-0.351551\pi$
$379$	−5.07918	−	3.69024i	−0.260900	−	0.189555i	−0.710544	+	0.703653i	$0.751551\pi$
$380$	0.133641	+	0.177784i	0.00685566	+	0.00912012i
$381$		0			0
$382$			0.440118i			0.0225184i
$383$	−14.5110	−	19.9727i	−0.741477	−	1.02056i	−0.998532	−	0.0541589i	$-0.982752\pi$
$383$	−14.5110	−	19.9727i	−0.741477	−	1.02056i	0.257055	−	0.966397i	$-0.417248\pi$
$384$		0			0
$385$	−3.85851	−	11.2490i	−0.196648	−	0.573302i
$386$	1.21133	−	3.72808i	0.0616549	−	0.189754i
$387$		0			0
$388$	−0.284345	+	0.0923892i	−0.0144354	+	0.00469035i
$389$	−3.99360	+	12.2910i	−0.202484	+	0.623181i	0.797324	+	0.603552i	$0.206248\pi$
$389$	−3.99360	+	12.2910i	−0.202484	+	0.623181i	−0.999807	+	0.0196288i	$0.993752\pi$
$390$		0			0
$391$	7.97967	+	24.5589i	0.403549	+	1.24200i
$392$	7.69175	+	10.5868i	0.388492	+	0.534713i
$393$		0			0
$394$	−19.8045	+	14.3888i	−0.997736	+	0.724897i
$395$	0.531148	+	32.6352i	0.0267249	+	1.64206i
$396$		0			0
$397$	−17.0584	+	23.4788i	−0.856135	+	1.17837i	0.126342	+	0.991987i	$0.459676\pi$
$397$	−17.0584	+	23.4788i	−0.856135	+	1.17837i	−0.982477	+	0.186383i	$0.940324\pi$
$398$	1.96890	+	0.639734i	0.0986921	+	0.0320670i
$399$		0			0
$400$	18.0842	−	0.588809i	0.904212	−	0.0294404i
$401$	−23.3926			−1.16817			−0.584084	−	0.811693i	$-0.698546\pi$
$401$	−23.3926			−1.16817			−0.584084	+	0.811693i	$0.698546\pi$
$402$		0			0
$403$	−4.12735	+	5.68081i	−0.205598	+	0.282981i
$404$	1.86800	+	1.35719i	0.0929367	+	0.0675225i
$405$		0			0
$406$	−4.85443	+	3.52695i	−0.240921	+	0.175040i
$407$		−	11.8425i		−	0.587009i
$408$		0			0
$409$	4.94173	+	15.2091i	0.244353	+	0.752040i	0.995742	+	0.0921815i	$0.0293840\pi$
$409$	4.94173	+	15.2091i	0.244353	+	0.752040i	−0.751389	+	0.659859i	$0.770616\pi$
$410$	2.80783	−	2.11067i	0.138669	−	0.104238i
$411$		0			0
$412$	−1.81216	+	0.588806i	−0.0892786	+	0.0290084i
$413$	1.49341	−	0.485237i	0.0734858	−	0.0238770i
$414$		0			0
$415$	3.29716	−	10.7392i	0.161851	−	0.527167i
$416$	2.15386	+	6.62890i	0.105602	+	0.325008i
$417$		0			0
$418$		−	2.55504i		−	0.124971i
$419$	−26.1935	+	19.0307i	−1.27964	+	0.929710i	−0.999542	−	0.0302627i	$-0.990366\pi$
$419$	−26.1935	+	19.0307i	−1.27964	+	0.929710i	−0.280094	+	0.959973i	$0.590366\pi$
$420$		0			0
$421$	−14.6044	−	10.6107i	−0.711774	−	0.517134i	0.171972	−	0.985102i	$-0.444986\pi$
$421$	−14.6044	−	10.6107i	−0.711774	−	0.517134i	−0.883745	+	0.467968i	$0.844986\pi$
$422$	9.02757	−	12.4254i	0.439455	−	0.604858i
$423$		0			0
$424$	−1.53865			−0.0747235
$425$	19.2625	−	6.95958i	0.934371	−	0.337589i
$426$		0			0
$427$	−16.1084	−	5.23392i	−0.779538	−	0.253287i
$428$	0.965491	−	1.32888i	0.0466688	−	0.0642340i
$429$		0			0
$430$	−0.334347	+	0.114684i	−0.0161237	+	0.00553056i
$431$	26.8070	−	19.4764i	1.29125	−	0.938146i	0.291417	−	0.956596i	$-0.405873\pi$
$431$	26.8070	−	19.4764i	1.29125	−	0.938146i	0.999830	+	0.0184500i	$0.00587314\pi$
$432$		0			0
$433$	−13.3223	−	18.3366i	−0.640230	−	0.881201i	0.358398	−	0.933569i	$-0.383323\pi$
$433$	−13.3223	−	18.3366i	−0.640230	−	0.881201i	−0.998628	+	0.0523682i	$0.983323\pi$
$434$	0.663351	+	2.04158i	0.0318419	+	0.0979991i
$435$		0			0
$436$	0.844320	−	2.59855i	0.0404356	−	0.124448i
$437$	−3.40263	+	1.10558i	−0.162770	+	0.0528872i
$438$		0			0
$439$	2.62799	−	8.08812i	0.125427	−	0.386025i	−0.868551	−	0.495599i	$-0.834949\pi$
$439$	2.62799	−	8.08812i	0.125427	−	0.386025i	0.993979	+	0.109574i	$0.0349486\pi$
$440$	17.9229	+	12.5812i	0.854439	+	0.599787i
$441$		0			0
$442$	−22.9338	−	31.5657i	−1.09085	−	1.50142i
$443$			6.35768i			0.302063i	0.988529	+	0.151031i	$0.0482594\pi$
$443$			6.35768i			0.302063i	−0.988529	+	0.151031i	$0.951741\pi$
$444$		0			0
$445$	−5.97200	+	2.04845i	−0.283100	+	0.0971057i
$446$	18.5244	+	13.4588i	0.877157	+	0.637292i
$447$		0			0
$448$	13.0109	+	4.22749i	0.614706	+	0.199730i
$449$	−6.25726			−0.295298			−0.147649	−	0.989040i	$-0.547171\pi$
$449$	−6.25726			−0.295298			−0.147649	+	0.989040i	$0.547171\pi$
$450$		0			0
$451$	3.87576			0.182502
$452$	1.67483	+	0.544184i	0.0787772	+	0.0255963i
$453$		0			0
$454$	15.4219	+	11.2047i	0.723786	+	0.525861i
$455$	14.4562	−	20.5939i	0.677718	−	0.965456i
$456$		0			0
$457$		−	11.0441i		−	0.516620i	−0.966062	−	0.258310i	$-0.916834\pi$
$457$		−	11.0441i		−	0.516620i	0.966062	−	0.258310i	$-0.0831657\pi$
$458$	−0.0492235	−	0.0677503i	−0.00230006	−	0.00316576i
$459$		0			0
$460$	0.725086	−	2.36168i	0.0338073	−	0.110114i
$461$	7.31202	−	22.5041i	0.340555	−	1.04812i	−0.623366	−	0.781930i	$-0.714235\pi$
$461$	7.31202	−	22.5041i	0.340555	−	1.04812i	0.963921	−	0.266189i	$-0.0857646\pi$
$462$		0			0
$463$	−5.91977	+	1.92345i	−0.275115	+	0.0893903i	−0.443325	−	0.896361i	$-0.646201\pi$
$463$	−5.91977	+	1.92345i	−0.275115	+	0.0893903i	0.168210	+	0.985751i	$0.446201\pi$
$464$	3.11276	−	9.58009i	0.144506	−	0.444744i
$465$		0			0
$466$	−10.8611	−	33.4271i	−0.503132	−	1.54848i
$467$	2.90765	+	4.00204i	0.134550	+	0.185192i	0.870976	−	0.491326i	$-0.163488\pi$
$467$	2.90765	+	4.00204i	0.134550	+	0.185192i	−0.736425	+	0.676519i	$0.763488\pi$
$468$		0			0
$469$	−19.6442	+	14.2723i	−0.907084	+	0.659035i
$470$	22.0657	+	6.77462i	1.01781	+	0.312490i
$471$		0			0
$472$	−1.69951	+	2.33918i	−0.0782264	+	0.107669i
$473$	−0.370918	−	0.120518i	−0.0170548	−	0.00554144i
$474$		0			0
$475$	0.964249	+	2.66882i	0.0442428	+	0.122454i
$476$	1.14563			0.0525099
$477$		0			0
$478$	−15.4806	+	21.3072i	−0.708066	+	0.974569i
$479$	24.3432	+	17.6863i	1.11227	+	0.808109i	0.983019	−	0.183503i	$-0.0587436\pi$
$479$	24.3432	+	17.6863i	1.11227	+	0.808109i	0.129248	+	0.991612i	$0.458744\pi$
$480$		0			0
$481$	20.2705	−	14.7274i	0.924256	−	0.671511i
$482$			5.53651i			0.252181i
$483$		0			0
$484$	0.00581369	+	0.0178927i	0.000264259	+	0.000813305i
$485$	−3.81404	+	0.0620747i	−0.173187	+	0.00281867i
$486$		0			0
$487$	32.5736	−	10.5838i	1.47605	−	0.479598i	0.543120	−	0.839655i	$-0.317243\pi$
$487$	32.5736	−	10.5838i	1.47605	−	0.479598i	0.932930	+	0.360057i	$0.117243\pi$
$488$	29.6609	−	9.63743i	1.34269	−	0.436266i
$489$		0			0
$490$	4.36447	+	12.7241i	0.197167	+	0.574816i
$491$	3.21975	+	9.90938i	0.145305	+	0.447204i	0.997050	−	0.0767530i	$-0.0244553\pi$
$491$	3.21975	+	9.90938i	0.145305	+	0.447204i	−0.851745	+	0.523957i	$0.824455\pi$
$492$		0			0
$493$		−	11.4022i		−	0.513530i
$494$	4.37342	−	3.17747i	0.196769	−	0.142961i
$495$		0			0
$496$	−2.91542	−	2.11817i	−0.130906	−	0.0951088i
$497$	−10.0026	+	13.7674i	−0.448679	+	0.617553i
$498$		0			0
$499$	−8.83514			−0.395515			−0.197757	−	0.980251i	$-0.563366\pi$
$499$	−8.83514			−0.395515			−0.197757	+	0.980251i	$0.563366\pi$
$500$	−1.89088	−	0.513839i	−0.0845629	−	0.0229796i
$501$		0			0
$502$	−1.32239	−	0.429671i	−0.0590211	−	0.0191771i
$503$	12.5630	−	17.2915i	0.560156	−	0.770988i	−0.431190	−	0.902261i	$-0.641906\pi$
$503$	12.5630	−	17.2915i	0.560156	−	0.770988i	0.991346	+	0.131273i	$0.0419063\pi$
$504$		0			0
$505$	17.7014	+	23.5483i	0.787701	+	1.04788i
$506$	−22.9604	+	16.6817i	−1.02072	+	0.741593i
$507$		0			0
$508$	0.100623	+	0.138496i	0.00446443	+	0.00614477i
$509$	−5.18529	−	15.9587i	−0.229834	−	0.707356i	−0.997765	−	0.0668236i	$-0.978714\pi$
$509$	−5.18529	−	15.9587i	−0.229834	−	0.707356i	0.767931	−	0.640533i	$-0.221286\pi$
$510$		0			0
$511$	2.74096	−	8.43582i	0.121253	−	0.373179i
$512$	−23.6279	+	7.67717i	−1.04422	+	0.339286i
$513$		0			0
$514$	7.74737	−	23.8440i	0.341722	−	1.05171i
$515$	−24.3073	+	0.395608i	−1.07111	+	0.0174326i
$516$		0			0
$517$	14.9698	+	20.6042i	0.658371	+	0.906170i
$518$		−	7.65976i		−	0.336550i
$519$		0			0
$520$	0.753942	+	46.3244i	0.0330625	+	2.03146i
$521$	−3.72559	−	2.70680i	−0.163221	−	0.118587i	0.503176	−	0.864184i	$-0.332165\pi$
$521$	−3.72559	−	2.70680i	−0.163221	−	0.118587i	−0.666397	+	0.745597i	$0.732165\pi$
$522$		0			0
$523$	−12.3290	−	4.00592i	−0.539108	−	0.175167i	0.0267915	−	0.999641i	$-0.491471\pi$
$523$	−12.3290	−	4.00592i	−0.539108	−	0.175167i	−0.565899	+	0.824474i	$0.691471\pi$
$524$	−1.76339			−0.0770340
$525$		0			0
$526$	16.7418			0.729979
$527$	−3.87949	−	1.26052i	−0.168993	−	0.0549093i
$528$		0			0
$529$	13.5433	+	9.83979i	0.588840	+	0.427817i
$530$	−1.51201	−	0.464217i	−0.0656773	−	0.0201643i
$531$		0			0
$532$			0.158727i			0.00688169i
$533$	4.81993	+	6.63406i	0.208774	+	0.287353i
$534$		0			0
$535$	16.7520	−	12.5926i	0.724254	−	0.544427i
$536$	13.8163	−	42.5223i	0.596774	−	1.83668i
$537$		0			0
$538$	−6.80940	+	2.21251i	−0.293574	+	0.0953880i
$539$	−4.58651	+	14.1158i	−0.197555	+	0.608012i
$540$		0			0
$541$	−8.45597	−	26.0248i	−0.363551	−	1.11889i	−0.950884	−	0.309548i	$-0.899822\pi$
$541$	−8.45597	−	26.0248i	−0.363551	−	1.11889i	0.587333	−	0.809345i	$-0.300178\pi$
$542$	0.633156	+	0.871464i	0.0271964	+	0.0374326i
$543$		0			0
$544$	−3.27573	+	2.37996i	−0.140446	+	0.102040i
$545$	20.0286	−	28.5321i	0.857931	−	1.22218i
$546$		0			0
$547$	16.2495	−	22.3656i	0.694779	−	0.956282i	−0.305213	−	0.952284i	$-0.598728\pi$
$547$	16.2495	−	22.3656i	0.694779	−	0.956282i	0.999992	−	0.00399765i	$-0.00127250\pi$
$548$	0.812146	+	0.263882i	0.0346931	+	0.0112725i
$549$		0			0
$550$	13.8167	+	17.7708i	0.589145	+	0.757748i
$551$	1.57978			0.0673007
$552$		0			0
$553$	−13.6916	+	18.8449i	−0.582228	+	0.801368i
$554$	5.18473	+	3.76692i	0.220278	+	0.160041i
$555$		0			0
$556$	0.0263418	−	0.0191385i	0.00111714	−	0.000811652i
$557$			6.17333i			0.261572i	0.991411	+	0.130786i	$0.0417501\pi$
$557$			6.17333i			0.261572i	−0.991411	+	0.130786i	$0.958250\pi$
$558$		0			0
$559$	−0.254987	−	0.784770i	−0.0107848	−	0.0331923i
$560$	10.5689	+	7.41899i	0.446616	+	0.313510i
$561$		0			0
$562$	24.0753	−	7.82254i	1.01555	−	0.329974i
$563$	−5.42039	+	1.76119i	−0.228442	+	0.0742254i	−0.421001	−	0.907060i	$-0.638321\pi$
$563$	−5.42039	+	1.76119i	−0.228442	+	0.0742254i	0.192559	+	0.981285i	$0.438321\pi$
$564$		0			0
$565$	18.3896	+	12.9089i	0.773658	+	0.543082i
$566$	−4.90947	−	15.1098i	−0.206360	−	0.635112i
$567$		0			0
$568$		−	31.3350i		−	1.31479i
$569$	−16.3185	+	11.8561i	−0.684109	+	0.497034i	−0.874718	−	0.484632i	$-0.838954\pi$
$569$	−16.3185	+	11.8561i	−0.684109	+	0.497034i	0.190610	+	0.981666i	$0.438954\pi$
$570$		0			0
$571$	12.7464	+	9.26077i	0.533418	+	0.387551i	0.821635	−	0.570014i	$-0.193062\pi$
$571$	12.7464	+	9.26077i	0.533418	+	0.387551i	−0.288217	+	0.957565i	$0.593062\pi$
$572$	−2.42089	+	3.33207i	−0.101222	+	0.139321i
$573$		0			0
$574$	2.50686			0.104634
$575$	17.6874	−	26.0896i	0.737614	−	1.08801i
$576$		0			0
$577$	−15.3179	−	4.97709i	−0.637692	−	0.207199i	−0.0277128	−	0.999616i	$-0.508822\pi$
$577$	−15.3179	−	4.97709i	−0.637692	−	0.207199i	−0.609980	+	0.792417i	$0.708822\pi$
$578$	−0.175275	+	0.241245i	−0.00729047	+	0.0100345i
$579$		0			0
$580$	−0.626744	+	0.892840i	−0.0260241	+	0.0370732i
$581$	6.48609	−	4.71242i	0.269088	−	0.195504i
$582$		0			0
$583$	−1.02578	−	1.41186i	−0.0424833	−	0.0584732i
$584$	5.04705	+	15.5332i	0.208848	+	0.642769i
$585$		0			0
$586$	9.30110	−	28.6258i	0.384225	−	1.18252i
$587$	1.90280	−	0.618257i	0.0785369	−	0.0255182i	−0.269485	−	0.963005i	$-0.586853\pi$
$587$	1.90280	−	0.618257i	0.0785369	−	0.0255182i	0.348022	+	0.937486i	$0.386853\pi$
$588$		0			0
$589$	0.174646	−	0.537504i	0.00719614	−	0.0221475i
$590$	−2.37582	+	1.78592i	−0.0978111	+	0.0735252i
$591$		0			0
$592$	7.55816	+	10.4029i	0.310638	+	0.427557i
$593$		−	26.8231i		−	1.10149i	−0.834672	−	0.550747i	$-0.814343\pi$
$593$		−	26.8231i		−	1.10149i	0.834672	−	0.550747i	$-0.185657\pi$
$594$		0			0
$595$	13.9730	+	4.28999i	0.572835	+	0.175872i
$596$	−0.551396	−	0.400613i	−0.0225861	−	0.0164097i
$597$		0			0
$598$	−57.1076	−	18.5554i	−2.33530	−	0.758786i
$599$	−44.8025			−1.83058			−0.915290	−	0.402796i	$-0.868038\pi$
$599$	−44.8025			−1.83058			−0.915290	+	0.402796i	$0.868038\pi$
$600$		0			0
$601$	−14.2298			−0.580446			−0.290223	−	0.956959i	$-0.593729\pi$
$601$	−14.2298			−0.580446			−0.290223	+	0.956959i	$0.593729\pi$
$602$	−0.239911	−	0.0779519i	−0.00977805	−	0.00317708i
$603$		0			0
$604$	3.13557	+	2.27813i	0.127585	+	0.0926957i
$605$	0.00390612	+	0.240003i	0.000158806	+	0.00975750i
$606$		0			0
$607$		−	20.3346i		−	0.825356i	−0.910877	−	0.412678i	$-0.864594\pi$
$607$		−	20.3346i		−	0.825356i	0.910877	−	0.412678i	$-0.135406\pi$
$608$	−0.329743	−	0.453853i	−0.0133729	−	0.0184062i
$609$		0			0
$610$	32.0550	−	0.521704i	1.29787	−	0.0211232i
$611$	−16.6512	+	51.2470i	−0.673634	+	2.07323i
$612$		0			0
$613$	−19.7744	+	6.42510i	−0.798681	+	0.259507i	−0.679797	−	0.733401i	$-0.737932\pi$
$613$	−19.7744	+	6.42510i	−0.798681	+	0.259507i	−0.118885	+	0.992908i	$0.537932\pi$
$614$	−6.38928	+	19.6642i	−0.257850	+	0.793582i
$615$		0			0
$616$	4.82922	+	14.8628i	0.194575	+	0.598839i
$617$	2.90738	+	4.00167i	0.117047	+	0.161101i	0.863520	−	0.504314i	$-0.168255\pi$
$617$	2.90738	+	4.00167i	0.117047	+	0.161101i	−0.746474	+	0.665415i	$0.768255\pi$
$618$		0			0
$619$	−37.1765	+	27.0103i	−1.49425	+	1.08564i	−0.521650	+	0.853160i	$0.674683\pi$
$619$	−37.1765	+	27.0103i	−1.49425	+	1.08564i	−0.972602	+	0.232477i	$0.925317\pi$
$620$	0.234493	+	0.311948i	0.00941749	+	0.0125281i
$621$		0			0
$622$	−10.2065	+	14.0480i	−0.409242	+	0.563273i
$623$	−4.28521	−	1.39235i	−0.171683	−	0.0557833i
$624$		0			0
$625$	−21.1385	−	13.3479i	−0.845539	−	0.533914i
$626$	14.1934			0.567283
$627$		0			0
$628$	1.40160	−	1.92914i	0.0559299	−	0.0769810i
$629$	11.7755	+	8.55543i	0.469521	+	0.341127i
$630$		0			0
$631$	17.5262	−	12.7335i	0.697707	−	0.506914i	−0.181477	−	0.983395i	$-0.558088\pi$
$631$	17.5262	−	12.7335i	0.697707	−	0.506914i	0.879185	+	0.476481i	$0.158088\pi$
$632$		−	42.8915i		−	1.70613i
$633$		0			0
$634$	8.13179	+	25.0271i	0.322955	+	0.993952i
$635$	0.708656	+	2.06600i	0.0281221	+	0.0819866i
$636$		0			0
$637$	−29.8656	+	9.70393i	−1.18332	+	0.384484i
$638$	11.9183	−	3.87249i	0.471851	−	0.153314i
$639$		0			0
$640$	−21.4711	+	0.349448i	−0.848719	+	0.0138131i
$641$	−11.2442	−	34.6061i	−0.444119	−	1.36686i	−0.883447	−	0.468531i	$-0.844783\pi$
$641$	−11.2442	−	34.6061i	−0.444119	−	1.36686i	0.439328	−	0.898327i	$-0.355217\pi$
$642$		0			0
$643$			1.01349i			0.0399682i	0.999800	+	0.0199841i	$0.00636156\pi$
$643$			1.01349i			0.0399682i	−0.999800	+	0.0199841i	$0.993638\pi$
$644$	1.42637	−	1.03632i	0.0562069	−	0.0408367i
$645$		0			0
$646$	2.54060	+	1.84586i	0.0999587	+	0.0726243i
$647$	−8.05306	+	11.0841i	−0.316598	+	0.435760i	−0.937425	−	0.348188i	$-0.886797\pi$
$647$	−8.05306	+	11.0841i	−0.316598	+	0.435760i	0.620826	+	0.783948i	$0.286797\pi$
$648$		0			0
$649$	−3.27944			−0.128729
$650$	−13.2354	+	45.7496i	−0.519134	+	1.79445i
$651$		0			0
$652$	−1.43829	−	0.467327i	−0.0563276	−	0.0183019i
$653$	−14.0112	+	19.2847i	−0.548299	+	0.754669i	−0.989780	−	0.142601i	$-0.954453\pi$
$653$	−14.0112	+	19.2847i	−0.548299	+	0.754669i	0.441481	+	0.897271i	$0.354453\pi$
$654$		0			0
$655$	−21.5076	−	6.60327i	−0.840371	−	0.258011i
$656$	−3.40463	+	2.47361i	−0.132928	+	0.0965782i
$657$		0			0
$658$	9.68253	+	13.3269i	0.377464	+	0.519535i
$659$	4.56597	+	14.0526i	0.177865	+	0.547412i	0.999753	−	0.0222376i	$-0.00707903\pi$
$659$	4.56597	+	14.0526i	0.177865	+	0.547412i	−0.821888	+	0.569649i	$0.807079\pi$
$660$		0			0
$661$	2.33453	−	7.18496i	0.0908029	−	0.279463i	−0.895334	−	0.445395i	$-0.853063\pi$
$661$	2.33453	−	7.18496i	0.0908029	−	0.279463i	0.986137	+	0.165932i	$0.0530633\pi$
$662$	−18.6187	+	6.04958i	−0.723637	+	0.235124i
$663$		0			0
$664$	−4.56186	+	14.0399i	−0.177034	+	0.544856i
$665$	−0.594378	+	1.93595i	−0.0230490	+	0.0750730i
$666$		0			0
$667$	−10.3143	−	14.1964i	−0.399369	−	0.549685i
$668$		−	1.15652i		−	0.0447471i
$669$		0			0
$670$	26.4062	−	37.6175i	1.02016	−	1.45329i
$671$	28.6174	+	20.7917i	1.10476	+	0.802656i
$672$		0			0
$673$	11.5978	+	3.76836i	0.447063	+	0.145259i	0.523892	−	0.851785i	$-0.324480\pi$
$673$	11.5978	+	3.76836i	0.447063	+	0.145259i	−0.0768292	+	0.997044i	$0.524480\pi$
$674$	12.6063			0.485576
$675$		0			0
$676$	−6.43571			−0.247527
$677$	−17.0721	−	5.54706i	−0.656134	−	0.213191i	−0.0380172	−	0.999277i	$-0.512104\pi$
$677$	−17.0721	−	5.54706i	−0.656134	−	0.213191i	−0.618117	+	0.786086i	$0.712104\pi$
$678$		0			0
$679$	−2.20239	−	1.60013i	−0.0845198	−	0.0614073i
$680$	−25.4583	+	8.73241i	−0.976280	+	0.334873i
$681$		0			0
$682$		−	4.48320i		−	0.171671i
$683$	−5.89391	−	8.11227i	−0.225524	−	0.310407i	0.681228	−	0.732071i	$-0.261446\pi$
$683$	−5.89391	−	8.11227i	−0.225524	−	0.310407i	−0.906752	+	0.421664i	$0.861446\pi$
$684$		0			0
$685$	8.91738	+	6.25970i	0.340716	+	0.239171i
$686$	−7.62950	+	23.4812i	−0.291296	+	0.896516i
$687$		0			0
$688$	0.402748	−	0.130861i	0.0153546	−	0.00498901i
$689$	1.14099	−	3.51160i	0.0434682	−	0.133781i
$690$		0			0
$691$	5.91136	+	18.1933i	0.224879	+	0.692105i	0.998304	+	0.0582177i	$0.0185418\pi$
$691$	5.91136	+	18.1933i	0.224879	+	0.692105i	−0.773425	+	0.633887i	$0.781458\pi$
$692$	−1.40713	−	1.93675i	−0.0534911	−	0.0736242i
$693$		0			0
$694$	−1.15121	+	0.836404i	−0.0436994	+	0.0317494i
$695$	0.392951	−	0.134786i	0.0149055	−	0.00511272i
$696$		0			0
$697$	−2.79999	+	3.85386i	−0.106057	+	0.145975i
$698$	−16.7931	−	5.45642i	−0.635629	−	0.206528i
$699$		0			0
$700$	−0.858333	−	1.10397i	−0.0324419	−	0.0417263i
$701$	3.81920			0.144249			0.0721246	−	0.997396i	$-0.477022\pi$
$701$	3.81920			0.144249			0.0721246	+	0.997396i	$0.477022\pi$
$702$		0			0
$703$	−1.18535	+	1.63150i	−0.0447065	+	0.0615332i
$704$	−23.1145	−	16.7937i	−0.871162	−	0.632936i
$705$		0			0
$706$	−37.0991	+	26.9540i	−1.39624	+	1.01443i
$707$			21.0241i			0.790692i
$708$		0			0
$709$	−11.7592	−	36.1911i	−0.441626	−	1.35918i	−0.886142	−	0.463413i	$-0.846625\pi$
$709$	−11.7592	−	36.1911i	−0.441626	−	1.35918i	0.444517	−	0.895771i	$-0.353375\pi$
$710$	9.45388	−	30.7923i	0.354798	−	1.15562i
$711$		0			0
$712$	7.89053	−	2.56379i	0.295710	−	0.0960821i
$713$	−5.97043	+	1.93991i	−0.223594	+	0.0726502i
$714$		0			0
$715$	−42.0044	+	31.5750i	−1.57087	+	1.18084i
$716$	0.532309	+	1.63828i	0.0198933	+	0.0612253i
$717$		0			0
$718$			8.23264i			0.307239i
$719$	−15.7224	+	11.4230i	−0.586348	+	0.426007i	−0.841007	−	0.541024i	$-0.818037\pi$
$719$	−15.7224	+	11.4230i	−0.586348	+	0.426007i	0.254659	+	0.967031i	$0.418037\pi$
$720$		0			0
$721$	−14.0360	−	10.1978i	−0.522729	−	0.379785i
$722$	14.8302	−	20.4120i	0.551923	−	0.759657i
$723$		0			0
$724$	3.13165			0.116387
$725$	−10.9876	+	8.54280i	−0.408070	+	0.317272i
$726$		0			0
$727$	−36.2104	−	11.7655i	−1.34297	−	0.436358i	−0.452649	−	0.891689i	$-0.649521\pi$
$727$	−36.2104	−	11.7655i	−1.34297	−	0.436358i	−0.890322	+	0.455331i	$0.849521\pi$
$728$	−19.4347	+	26.7496i	−0.720298	+	0.991406i
$729$		0			0
$730$	0.273212	+	16.7869i	0.0101120	+	0.621312i
$731$	0.387802	−	0.281755i	0.0143434	−	0.0104211i
$732$		0			0
$733$	9.96833	+	13.7202i	0.368189	+	0.506768i	0.952407	−	0.304828i	$-0.0985990\pi$
$733$	9.96833	+	13.7202i	0.368189	+	0.506768i	−0.584219	+	0.811596i	$0.698599\pi$
$734$	−9.12653	−	28.0886i	−0.336866	−	1.03677i
$735$		0			0
$736$	−1.92559	+	5.92635i	−0.0709781	+	0.218448i
$737$	48.2292	−	15.6706i	1.77655	−	0.577235i
$738$		0			0
$739$	−4.08025	+	12.5577i	−0.150095	+	0.461944i	−0.997631	−	0.0687937i	$-0.978085\pi$
$739$	−4.08025	+	12.5577i	−0.150095	+	0.461944i	0.847536	+	0.530737i	$0.178085\pi$
$740$	−0.451808	−	1.31719i	−0.0166088	−	0.0484209i
$741$		0			0
$742$	−0.663476	−	0.913197i	−0.0243570	−	0.0335245i
$743$			42.2364i			1.54950i	0.632265	+	0.774752i	$0.282125\pi$
$743$			42.2364i			1.54950i	−0.632265	+	0.774752i	$0.717875\pi$
$744$		0			0
$745$	−5.22508	−	6.95095i	−0.191432	−	0.254663i
$746$	−26.7265	−	19.4180i	−0.978528	−	0.710942i
$747$		0			0
$748$	−2.27551	−	0.739358i	−0.0832008	−	0.0270336i
$749$	14.9564			0.546494
$750$		0			0
$751$	−1.04801			−0.0382426			−0.0191213	−	0.999817i	$-0.506087\pi$
$751$	−1.04801			−0.0382426			−0.0191213	+	0.999817i	$0.506087\pi$
$752$	−26.3002	−	8.54545i	−0.959069	−	0.311620i
$753$		0			0
$754$	21.4502	+	15.5845i	0.781170	+	0.567553i
$755$	29.7130	+	39.5274i	1.08137	+	1.43855i
$756$		0			0
$757$			17.0074i			0.618146i	0.951038	+	0.309073i	$0.100019\pi$
$757$			17.0074i			0.618146i	−0.951038	+	0.309073i	$0.899981\pi$
$758$	4.98488	+	6.86110i	0.181059	+	0.249207i
$759$		0			0
$760$	−1.20988	−	3.52724i	−0.0438868	−	0.127947i
$761$	7.45484	−	22.9436i	0.270238	−	0.831706i	−0.720203	−	0.693764i	$-0.755951\pi$
$761$	7.45484	−	22.9436i	0.270238	−	0.831706i	0.990440	−	0.137942i	$-0.0440489\pi$
$762$		0			0
$763$	23.6607	−	7.68783i	0.856575	−	0.278318i
$764$	−0.0176454	+	0.0543070i	−0.000638389	+	0.00196476i
$765$		0			0
$766$	10.3053	+	31.7165i	0.372346	+	1.14596i
$767$	−4.07834	−	5.61335i	−0.147260	−	0.202686i
$768$		0			0
$769$	40.2744	−	29.2611i	1.45233	−	1.05518i	0.467053	−	0.884230i	$-0.345316\pi$
$769$	40.2744	−	29.2611i	1.45233	−	1.05518i	0.985279	−	0.170952i	$-0.0546841\pi$
$770$	0.261420	+	16.0624i	0.00942094	+	0.578849i
$771$		0			0
$772$	0.298936	−	0.411450i	0.0107589	−	0.0148084i
$773$	−29.9338	−	9.72608i	−1.07664	−	0.349823i	−0.283572	−	0.958951i	$-0.591520\pi$
$773$	−29.9338	−	9.72608i	−1.07664	−	0.349823i	−0.793072	+	0.609128i	$0.791520\pi$
$774$		0			0
$775$	1.69192	+	4.68285i	0.0607755	+	0.168213i
$776$	5.01268			0.179945
$777$		0			0
$778$	10.2613	−	14.1235i	0.367885	−	0.506350i
$779$	−0.533952	−	0.387939i	−0.0191308	−	0.0138993i
$780$		0			0
$781$	28.7528	−	20.8901i	1.02886	−	0.747508i
$782$		−	34.8822i		−	1.24738i
$783$		0			0
$784$	−4.98010	−	15.3272i	−0.177861	−	0.547399i
$785$	24.3189	−	18.2807i	0.867979	−	0.652465i
$786$		0			0
$787$	18.2047	−	5.91505i	0.648926	−	0.210849i	0.0339855	−	0.999422i	$-0.489180\pi$
$787$	18.2047	−	5.91505i	0.648926	−	0.210849i	0.614941	+	0.788573i	$0.289180\pi$
$788$	−3.02060	+	0.981451i	−0.107604	+	0.0349627i
$789$		0			0
$790$	12.9405	−	42.1487i	0.460403	−	1.49958i
$791$	4.95499	+	15.2499i	0.176179	+	0.542224i
$792$		0			0
$793$			74.8406i			2.65767i
$794$	31.7159	−	23.0430i	1.12556	−	0.817764i
$795$		0			0
$796$	0.217298	+	0.157876i	0.00770191	+	0.00559577i
$797$	4.24050	−	5.83655i	0.150206	−	0.206741i	−0.727283	−	0.686338i	$-0.759217\pi$
$797$	4.24050	−	5.83655i	0.150206	−	0.206741i	0.877489	+	0.479597i	$0.159217\pi$
$798$		0			0
$799$	−31.3024			−1.10740
$800$	4.74768	+	1.37350i	0.167856	+	0.0485607i
$801$		0			0
$802$	30.0528	+	9.76474i	1.06120	+	0.344805i
$803$	−10.8885	+	14.9867i	−0.384246	+	0.528869i
$804$		0			0
$805$	21.2777	−	7.29845i	0.749941	−	0.257236i
$806$	7.67381	−	5.57535i	0.270298	−	0.196383i
$807$		0			0
$808$	−22.7546	−	31.3191i	−0.800505	−	1.10180i
$809$	0.327376	+	1.00756i	0.0115099	+	0.0354239i	0.956647	−	0.291251i	$-0.0940716\pi$
$809$	0.327376	+	1.00756i	0.0115099	+	0.0354239i	−0.945137	+	0.326675i	$0.894072\pi$
$810$		0			0
$811$	6.68712	−	20.5808i	0.234817	−	0.722691i	−0.762329	−	0.647190i	$-0.775944\pi$
$811$	6.68712	−	20.5808i	0.234817	−	0.722691i	0.997146	−	0.0755016i	$-0.0240558\pi$
$812$	−0.740402	+	0.240571i	−0.0259830	+	0.00844239i
$813$		0			0
$814$	−4.94339	+	15.2142i	−0.173266	+	0.533257i
$815$	−15.7924	−	11.0857i	−0.553184	−	0.388317i
$816$		0			0
$817$	0.0390371	+	0.0537299i	0.00136573	+	0.00187977i
$818$		−	21.6022i		−	0.755302i
$819$		0			0
$820$	0.431086	−	0.147866i	0.0150542	−	0.00516371i
$821$	−18.7553	−	13.6265i	−0.654564	−	0.475568i	0.210259	−	0.977646i	$-0.432569\pi$
$821$	−18.7553	−	13.6265i	−0.654564	−	0.475568i	−0.864823	+	0.502077i	$0.832569\pi$
$822$		0			0
$823$	26.6076	+	8.64534i	0.927483	+	0.301358i	0.733533	−	0.679654i	$-0.237870\pi$
$823$	26.6076	+	8.64534i	0.927483	+	0.301358i	0.193950	+	0.981011i	$0.437870\pi$
$824$	31.9463			1.11290
$825$		0			0
$826$	−2.12116			−0.0738044
$827$	39.2829	+	12.7638i	1.36600	+	0.443841i	0.898042	−	0.439909i	$-0.144989\pi$
$827$	39.2829	+	12.7638i	1.36600	+	0.443841i	0.467959	+	0.883750i	$0.344989\pi$
$828$		0			0
$829$	38.4838	+	27.9602i	1.33660	+	0.971096i	0.999562	+	0.0296051i	$0.00942497\pi$
$829$	38.4838	+	27.9602i	1.33660	+	0.971096i	0.337038	+	0.941491i	$0.390575\pi$
$830$	−8.71877	+	12.4205i	−0.302633	+	0.431121i
$831$		0			0
$832$		−	60.4495i		−	2.09571i
$833$	−10.7226	−	14.7584i	−0.371516	−	0.511348i
$834$		0			0
$835$	4.33076	−	14.1058i	0.149872	−	0.488150i
$836$	0.102438	−	0.315272i	0.00354289	−	0.0109039i
$837$		0			0
$838$	41.5951	−	13.5151i	1.43688	−	0.466871i
$839$	15.1518	−	46.6324i	0.523097	−	1.60993i	−0.244950	−	0.969536i	$-0.578772\pi$
$839$	15.1518	−	46.6324i	0.523097	−	1.60993i	0.768048	−	0.640393i	$-0.221228\pi$
$840$		0			0
$841$	−6.56714	−	20.2116i	−0.226453	−	0.696951i
$842$	14.3332	+	19.7280i	0.493956	+	0.679872i
$843$		0			0
$844$	1.61209	−	1.17125i	0.0554905	−	0.0403162i
$845$	−78.4946	−	24.0995i	−2.70030	−	0.829047i
$846$		0			0
$847$	−0.100690	+	0.138588i	−0.00345974	+	0.00476192i
$848$	1.80217	+	0.585560i	0.0618867	+	0.0201082i
$849$		0			0
$850$	−27.6520	+	0.900327i	−0.948456	+	0.0308810i
$851$	22.4003			0.767871
$852$		0			0
$853$	19.1251	−	26.3235i	0.654832	−	0.901299i	−0.344464	−	0.938799i	$-0.611939\pi$
$853$	19.1251	−	26.3235i	0.654832	−	0.901299i	0.999297	+	0.0375002i	$0.0119395\pi$
$854$	18.5099	+	13.4482i	0.633394	+	0.460188i
$855$		0			0
$856$	−22.2801	+	16.1875i	−0.761520	+	0.553276i
$857$			30.4813i			1.04122i	0.853794	+	0.520610i	$0.174296\pi$
$857$			30.4813i			1.04122i	−0.853794	+	0.520610i	$0.825704\pi$
$858$		0			0
$859$	−1.27382	−	3.92040i	−0.0434620	−	0.133762i	0.926971	−	0.375133i	$-0.122403\pi$
$859$	−1.27382	−	3.92040i	−0.0434620	−	0.133762i	−0.970433	+	0.241371i	$0.922403\pi$
$860$	−0.0458537		0.000746282i	−0.00156360		2.54480e-5i
$861$		0			0
$862$	−42.5694	+	13.8316i	−1.44992	+	0.471107i
$863$	17.5169	−	5.69159i	0.596283	−	0.193744i	0.00470109	−	0.999989i	$-0.498504\pi$
$863$	17.5169	−	5.69159i	0.596283	−	0.193744i	0.591582	+	0.806245i	$0.298504\pi$
$864$		0			0
$865$	−9.90996	−	28.8913i	−0.336949	−	0.982332i
$866$	9.46115	+	29.1184i	0.321503	+	0.989485i
$867$		0			0
$868$			0.278510i			0.00945325i
$869$	39.3570	−	28.5945i	1.33510	−	0.970003i
$870$		0			0
$871$	86.8013	+	63.0649i	2.94115	+	2.13687i
$872$	−26.9261	+	37.0607i	−0.911834	+	1.25503i
$873$		0			0
$874$	4.83292			0.163476
$875$	−6.33486	−	16.6790i	−0.214158	−	0.563855i
$876$		0			0
$877$	−17.9870	−	5.84432i	−0.607377	−	0.197349i	−0.0108490	−	0.999941i	$-0.503453\pi$
$877$	−17.9870	−	5.84432i	−0.607377	−	0.197349i	−0.596528	+	0.802593i	$0.703453\pi$
$878$	−6.75244	+	9.29394i	−0.227884	+	0.313655i
$879$		0			0
$880$	−16.2044	−	21.5568i	−0.546250	−	0.726680i
$881$	28.0192	−	20.3571i	0.943990	−	0.685849i	−0.00538802	−	0.999985i	$-0.501715\pi$
$881$	28.0192	−	20.3571i	0.943990	−	0.685849i	0.949378	+	0.314137i	$0.101715\pi$
$882$		0			0
$883$	−19.2132	−	26.4447i	−0.646575	−	0.889934i	0.352370	−	0.935861i	$-0.385376\pi$
$883$	−19.2132	−	26.4447i	−0.646575	−	0.889934i	−0.998945	+	0.0459269i	$0.985376\pi$
$884$	−1.56430	−	4.81442i	−0.0526131	−	0.161926i
$885$		0			0
$886$	2.65388	−	8.16781i	0.0891589	−	0.274403i
$887$	46.4037	−	15.0775i	1.55809	−	0.506253i	0.601790	−	0.798655i	$-0.294455\pi$
$887$	46.4037	−	15.0775i	1.55809	−	0.506253i	0.956296	+	0.292402i	$0.0944545\pi$
$888$		0			0
$889$	−0.481680	+	1.48246i	−0.0161550	+	0.0497201i
$890$	8.52740	−	0.138786i	0.285839	−	0.00465211i
$891$		0			0
$892$	1.74617	+	2.40340i	0.0584661	+	0.0804716i
$893$		−	4.33695i		−	0.145131i
$894$		0			0
$895$	0.357649	+	21.9750i	0.0119549	+	0.734542i
$896$	−12.3983	−	9.00789i	−0.414198	−	0.300932i
$897$		0			0
$898$	8.03879	+	2.61196i	0.268258	+	0.0871623i
$899$	2.77195			0.0924497
$900$		0			0
$901$	2.14494			0.0714582
$902$	−4.97925	−	1.61786i	−0.165791	−	0.0538687i
$903$		0			0
$904$	−23.8865	−	17.3545i	−0.794452	−	0.577203i
$905$	38.1959	+	11.7269i	1.26968	+	0.389817i
$906$		0			0
$907$			45.0367i			1.49542i	0.664025	+	0.747710i	$0.268847\pi$
$907$			45.0367i			1.49542i	−0.664025	+	0.747710i	$0.731153\pi$
$908$	1.45371	+	2.00087i	0.0482432	+	0.0664011i
$909$		0			0
$910$	−27.1686	+	20.4228i	−0.900631	+	0.677010i
$911$	−4.00018	+	12.3113i	−0.132532	+	0.407891i	−0.995198	−	0.0978826i	$-0.968793\pi$
$911$	−4.00018	+	12.3113i	−0.132532	+	0.407891i	0.862666	+	0.505774i	$0.168793\pi$
$912$		0			0
$913$	−15.9243	+	5.17410i	−0.527016	+	0.171238i
$914$	−4.61012	+	14.1885i	−0.152489	+	0.469314i
$915$		0			0
$916$	−0.00335750	−	0.0103333i	−0.000110935	−	0.000341423i
$917$	−9.43764	−	12.9898i	−0.311658	−	0.428961i
$918$		0			0
$919$	11.7889	−	8.56513i	0.388880	−	0.282538i	−0.376117	−	0.926572i	$-0.622741\pi$
$919$	11.7889	−	8.56513i	0.388880	−	0.282538i	0.764996	+	0.644035i	$0.222741\pi$
$920$	−23.7977	+	33.9015i	−0.784587	+	1.11770i
$921$		0			0
$922$	−18.7877	+	25.8591i	−0.618741	+	0.851623i
$923$	71.5145	+	23.2365i	2.35393	+	0.764838i
$924$		0			0
$925$	−0.578163	−	17.7573i	−0.0190099	−	0.583856i
$926$	8.40813			0.276308
$927$		0			0
$928$	1.61728	−	2.22600i	0.0530899	−	0.0730720i
$929$	25.3701	+	18.4324i	0.832365	+	0.604749i	0.920227	−	0.391384i	$-0.128004\pi$
$929$	25.3701	+	18.4324i	0.832365	+	0.604749i	−0.0878623	+	0.996133i	$0.528004\pi$
$930$		0			0
$931$	2.04477	−	1.48561i	0.0670147	−	0.0486890i
$932$		−	4.56008i		−	0.149370i
$933$		0			0
$934$	−2.06494	−	6.35522i	−0.0675668	−	0.207949i
$935$	−24.9851	−	17.5387i	−0.817102	−	0.573578i
$936$		0			0
$937$	46.3855	−	15.0716i	1.51535	−	0.492367i	0.570898	−	0.821021i	$-0.306595\pi$
$937$	46.3855	−	15.0716i	1.51535	−	0.492367i	0.944450	+	0.328654i	$0.106595\pi$
$938$	31.1949	−	10.1358i	1.01855	−	0.330946i
$939$		0			0
$940$	2.45111	+	1.72060i	0.0799464	+	0.0561197i
$941$	9.96145	+	30.6582i	0.324734	+	0.999429i	0.971561	+	0.236791i	$0.0760958\pi$
$941$	9.96145	+	30.6582i	0.324734	+	0.999429i	−0.646827	+	0.762637i	$0.723904\pi$
$942$		0			0
$943$			7.33108i			0.238733i
$944$	2.88080	−	2.09302i	0.0937619	−	0.0681220i
$945$		0			0
$946$	0.426216	+	0.309664i	0.0138575	+	0.0100680i
$947$	30.5199	−	42.0070i	0.991763	−	1.36505i	0.0615183	−	0.998106i	$-0.480406\pi$
$947$	30.5199	−	42.0070i	0.991763	−	1.36505i	0.930245	−	0.366939i	$-0.119594\pi$
$948$		0			0
$949$	−39.1935			−1.27227
$950$	−0.124740	−	3.83118i	−0.00404711	−	0.124300i
$951$		0			0
$952$	−18.2676	−	5.93551i	−0.592057	−	0.192371i
$953$	−23.3814	+	32.1817i	−0.757398	+	1.04247i	0.240028	+	0.970766i	$0.422843\pi$
$953$	−23.3814	+	32.1817i	−0.757398	+	1.04247i	−0.997426	+	0.0717028i	$0.977157\pi$
$954$		0			0
$955$	−0.418578	+	0.596293i	−0.0135449	+	0.0192956i
$956$	−2.76444	+	2.00848i	−0.0894083	+	0.0649590i
$957$		0			0
$958$	−23.8912	−	32.8835i	−0.771891	−	1.06242i
$959$	2.40274	+	7.39487i	0.0775885	+	0.238793i
$960$		0			0
$961$	−9.27309	+	28.5396i	−0.299132	+	0.920633i
$962$	−32.1895	+	10.4590i	−1.03783	+	0.337211i
$963$		0			0
$964$	−0.221972	+	0.683160i	−0.00714924	+	0.0220031i
$965$	5.18677	−	3.89893i	0.166968	−	0.125511i
$966$		0			0
$967$	11.6862	+	16.0847i	0.375802	+	0.517248i	0.954466	−	0.298318i	$-0.0964257\pi$
$967$	11.6862	+	16.0847i	0.375802	+	0.517248i	−0.578664	+	0.815566i	$0.696426\pi$
$968$		−	0.315428i		−	0.0101382i
$969$		0			0
$970$	4.92587	+	1.51235i	0.158160	+	0.0485585i
$971$	−33.4804	−	24.3250i	−1.07444	−	0.780625i	−0.0977335	−	0.995213i	$-0.531159\pi$
$971$	−33.4804	−	24.3250i	−1.07444	−	0.780625i	−0.976705	+	0.214588i	$0.931159\pi$
$972$		0			0
$973$	0.281963	+	0.0916152i	0.00903931	+	0.00293705i
$974$	−46.2658			−1.48245
$975$		0			0
$976$	−38.4085			−1.22943
$977$	3.44274	+	1.11861i	0.110143	+	0.0357876i	0.363570	−	0.931567i	$-0.381558\pi$
$977$	3.44274	+	1.11861i	0.110143	+	0.0357876i	−0.253427	+	0.967355i	$0.581558\pi$
$978$		0			0
$979$	7.61292	+	5.53111i	0.243310	+	0.176775i
$980$	0.0284009	+	1.74503i	0.000907233	+	0.0557430i
$981$		0			0
$982$		−	14.0747i		−	0.449143i
$983$	−11.8203	−	16.2692i	−0.377008	−	0.518907i	0.577781	−	0.816192i	$-0.303919\pi$
$983$	−11.8203	−	16.2692i	−0.377008	−	0.518907i	−0.954789	+	0.297285i	$0.903919\pi$
$984$		0			0
$985$	−40.5166	+	0.659419i	−1.29097	+	0.0210108i
$986$	−4.75962	+	14.6486i	−0.151577	+	0.466506i
$987$		0			0
$988$	0.667037	−	0.216733i	0.0212213	−	0.00689521i
$989$	0.227963	−	0.701599i	0.00724881	−	0.0223095i
$990$		0			0
$991$	2.29905	+	7.07576i	0.0730319	+	0.224769i	0.980909	−	0.194467i	$-0.0622978\pi$
$991$	2.29905	+	7.07576i	0.0730319	+	0.224769i	−0.907877	+	0.419236i	$0.862298\pi$
$992$	−0.578584	−	0.796352i	−0.0183700	−	0.0252842i
$993$		0			0
$994$	18.5974	−	13.5118i	0.589875	−	0.428569i
$995$	2.05913	+	2.73928i	0.0652789	+	0.0868409i
$996$		0			0
$997$	27.1246	−	37.3338i	0.859045	−	1.18237i	−0.122751	−	0.992438i	$-0.539172\pi$
$997$	27.1246	−	37.3338i	0.859045	−	1.18237i	0.981796	−	0.189937i	$-0.0608284\pi$
$998$	11.3506	+	3.68804i	0.359298	+	0.116743i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.m.b.154.2		16
3.2	odd	2		75.2.i.a.4.3	✓	16
15.2	even	4		375.2.g.d.226.1		16
15.8	even	4		375.2.g.e.226.4		16
15.14	odd	2		375.2.i.c.274.2		16
25.12	odd	20		5625.2.a.t.1.7		8
25.13	odd	20		5625.2.a.bd.1.2		8
25.19	even	10	inner	225.2.m.b.19.2		16
75.8	even	20		375.2.g.e.151.4		16
75.17	even	20		375.2.g.d.151.1		16
75.38	even	20		1875.2.a.m.1.7		8
75.41	odd	10		1875.2.b.h.1249.12		16
75.44	odd	10		75.2.i.a.19.3	yes	16
75.56	odd	10		375.2.i.c.349.2		16
75.59	odd	10		1875.2.b.h.1249.5		16
75.62	even	20		1875.2.a.p.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.3	✓	16	3.2	odd	2
75.2.i.a.19.3	yes	16	75.44	odd	10
225.2.m.b.19.2		16	25.19	even	10	inner
225.2.m.b.154.2		16	1.1	even	1	trivial
375.2.g.d.151.1		16	75.17	even	20
375.2.g.d.226.1		16	15.2	even	4
375.2.g.e.151.4		16	75.8	even	20
375.2.g.e.226.4		16	15.8	even	4
375.2.i.c.274.2		16	15.14	odd	2
375.2.i.c.349.2		16	75.56	odd	10
1875.2.a.m.1.7		8	75.38	even	20
1875.2.a.p.1.2		8	75.62	even	20
1875.2.b.h.1249.5		16	75.59	odd	10
1875.2.b.h.1249.12		16	75.41	odd	10
5625.2.a.t.1.7		8	25.12	odd	20
5625.2.a.bd.1.2		8	25.13	odd	20

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28472 - 0.417429i) q^{2} +(-0.141788 - 0.103015i) q^{4} +(-1.34359 - 1.78739i) q^{5} -1.59580i q^{7} +(1.72715 + 2.37722i) q^{8} +O(q^{10})\)	\(q+(-1.28472 - 0.417429i) q^{2} +(-0.141788 - 0.103015i) q^{4} +(-1.34359 - 1.78739i) q^{5} -1.59580i q^{7} +(1.72715 + 2.37722i) q^{8} +(0.980025 + 2.85714i) q^{10} +(-1.02988 + 3.16965i) q^{11} +(-6.70620 + 2.17898i) q^{13} +(-0.666132 + 2.05014i) q^{14} +(-1.11826 - 3.44165i) q^{16} +(-2.40771 - 3.31393i) q^{17} +(0.459145 - 0.333589i) q^{19} +(0.00637730 + 0.391840i) q^{20} +(2.64621 - 3.64220i) q^{22} +(-5.99546 - 1.94804i) q^{23} +(-1.38952 + 4.80304i) q^{25} +9.52513 q^{26} +(-0.164391 + 0.226264i) q^{28} +(2.25196 + 1.63614i) q^{29} +(0.805639 - 0.585331i) q^{31} -0.988473i q^{32} +(1.70989 + 5.26251i) q^{34} +(-2.85231 + 2.14410i) q^{35} +(-3.37943 + 1.09804i) q^{37} +(-0.729121 + 0.236906i) q^{38} +(1.92843 - 6.28110i) q^{40} +(-0.359364 - 1.10601i) q^{41} +0.117022i q^{43} +(0.472545 - 0.343324i) q^{44} +(6.88929 + 5.00536i) q^{46} +(4.49170 - 6.18229i) q^{47} +4.45343 q^{49} +(3.79007 - 5.59052i) q^{50} +(1.17532 + 0.381886i) q^{52} +(-0.307785 + 0.423629i) q^{53} +(7.04914 - 2.41792i) q^{55} +(3.79356 - 2.75618i) q^{56} +(-2.21015 - 3.04201i) q^{58} +(0.304072 + 0.935838i) q^{59} +(3.27982 - 10.0942i) q^{61} +(-1.27935 + 0.415686i) q^{62} +(-2.64914 + 8.15321i) q^{64} +(12.9051 + 9.05894i) q^{65} +(-8.94370 - 12.3099i) q^{67} +0.717905i q^{68} +(4.55942 - 1.56392i) q^{70} +(-8.62730 - 6.26810i) q^{71} +(5.28627 + 1.71761i) q^{73} +4.79996 q^{74} -0.0994657 q^{76} +(5.05812 + 1.64348i) q^{77} +(-11.8091 - 8.57982i) q^{79} +(-4.64908 + 6.62294i) q^{80} +1.57091i q^{82} +(2.95302 + 4.06448i) q^{83} +(-2.68830 + 8.75610i) q^{85} +(0.0488483 - 0.150339i) q^{86} +(-9.31372 + 3.02621i) q^{88} +(0.872511 - 2.68531i) q^{89} +(3.47720 + 10.7017i) q^{91} +(0.649405 + 0.893830i) q^{92} +(-8.35122 + 6.06752i) q^{94} +(-1.21316 - 0.372464i) q^{95} +(1.00271 - 1.38012i) q^{97} +(-5.72139 - 1.85899i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 30 q^{8}+O(q^{10}) \) 16 * q + 2 * q^4 + 30 * q^8	\( 16 q + 2 q^{4} + 30 q^{8} + 6 q^{11} + 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} - 20 q^{20} - 30 q^{22} + 20 q^{23} - 10 q^{25} - 12 q^{26} + 30 q^{28} - 16 q^{29} + 6 q^{31} - 36 q^{34} - 10 q^{35} - 10 q^{37} - 30 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 16 q^{46} - 40 q^{47} - 20 q^{50} + 40 q^{52} - 10 q^{53} + 10 q^{55} + 10 q^{58} - 12 q^{59} + 10 q^{62} + 8 q^{64} + 70 q^{65} - 40 q^{67} + 30 q^{70} + 8 q^{71} - 20 q^{73} + 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 10 q^{83} - 20 q^{85} + 36 q^{86} - 40 q^{88} - 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} + 40 q^{95} + 40 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 2 * q^4 + 30 * q^8 + 6 * q^11 + 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 - 20 * q^20 - 30 * q^22 + 20 * q^23 - 10 * q^25 - 12 * q^26 + 30 * q^28 - 16 * q^29 + 6 * q^31 - 36 * q^34 - 10 * q^35 - 10 * q^37 - 30 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 16 * q^46 - 40 * q^47 - 20 * q^50 + 40 * q^52 - 10 * q^53 + 10 * q^55 + 10 * q^58 - 12 * q^59 + 10 * q^62 + 8 * q^64 + 70 * q^65 - 40 * q^67 + 30 * q^70 + 8 * q^71 - 20 * q^73 + 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 10 * q^83 - 20 * q^85 + 36 * q^86 - 40 * q^88 - 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 + 40 * q^95 + 40 * q^97 - 60 * q^98

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