LMFDB - Embedded newform 324.2.l.a.71.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(35,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("324.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, degree $6$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.4
Character	$\chi$	$=$	324.71
Dual form			324.2.l.a.251.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.940037 + 1.05657i) q^{2} +(-0.232661 - 1.98642i) q^{4} +(-0.546554 + 0.651358i) q^{5} +(-0.348909 + 0.958618i) q^{7} +(2.31749 + 1.62149i) q^{8} +O(q^{10})$	\(q+(-0.940037 + 1.05657i) q^{2} +(-0.232661 - 1.98642i) q^{4} +(-0.546554 + 0.651358i) q^{5} +(-0.348909 + 0.958618i) q^{7} +(2.31749 + 1.62149i) q^{8} +(-0.174421 - 1.18977i) q^{10} +(-1.57259 + 1.31956i) q^{11} +(-0.374417 + 2.12343i) q^{13} +(-0.684856 - 1.26978i) q^{14} +(-3.89174 + 0.924324i) q^{16} +(6.34902 + 3.66561i) q^{17} +(-4.39109 + 2.53520i) q^{19} +(1.42103 + 0.934141i) q^{20} +(0.0840920 - 2.90198i) q^{22} +(-5.20278 + 1.89366i) q^{23} +(0.742695 + 4.21203i) q^{25} +(-1.89157 - 2.39170i) q^{26} +(1.98540 + 0.470046i) q^{28} +(-3.64198 + 0.642180i) q^{29} +(1.60292 + 4.40400i) q^{31} +(2.68177 - 4.98077i) q^{32} +(-9.84127 + 3.26235i) q^{34} +(-0.433706 - 0.751201i) q^{35} +(5.33157 - 9.23455i) q^{37} +(1.44919 - 7.02265i) q^{38} +(-2.32280 + 0.623286i) q^{40} +(-4.00006 - 0.705319i) q^{41} +(-3.51843 - 4.19310i) q^{43} +(2.98709 + 2.81682i) q^{44} +(2.89003 - 7.27719i) q^{46} +(-4.10423 - 1.49382i) q^{47} +(4.56510 + 3.83057i) q^{49} +(-5.14845 - 3.17476i) q^{50} +(4.30513 + 0.249713i) q^{52} +5.55975i q^{53} -1.74553i q^{55} +(-2.36298 + 1.65584i) q^{56} +(2.74510 - 4.45167i) q^{58} +(9.24583 + 7.75817i) q^{59} +(-0.502750 - 0.182986i) q^{61} +(-6.15992 - 2.44633i) q^{62} +(2.74155 + 7.51558i) q^{64} +(-1.17847 - 1.40445i) q^{65} +(6.40223 + 1.12889i) q^{67} +(5.80427 - 13.4647i) q^{68} +(1.20139 + 0.247918i) q^{70} +(5.86015 - 10.1501i) q^{71} +(-0.769587 - 1.33296i) q^{73} +(4.74503 + 14.3140i) q^{74} +(6.05760 + 8.13271i) q^{76} +(-0.716265 - 1.96792i) q^{77} +(14.2516 - 2.51294i) q^{79} +(1.52498 - 3.04011i) q^{80} +(4.50542 - 3.56330i) q^{82} +(-0.916197 - 5.19601i) q^{83} +(-5.85770 + 2.13203i) q^{85} +(7.73773 + 0.224219i) q^{86} +(-5.78413 + 0.508136i) q^{88} +(3.41168 - 1.96973i) q^{89} +(-1.90492 - 1.09981i) q^{91} +(4.97208 + 9.89434i) q^{92} +(5.43644 - 2.93214i) q^{94} +(0.748647 - 4.24579i) q^{95} +(3.35056 - 2.81145i) q^{97} +(-8.33861 + 1.22245i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	−0.940037	+	1.05657i	−0.664707	+	0.747105i
$2$	−0.940037	+	1.05657i	−0.664707	+	0.747105i
$3$		0			0
$3$		0			0
$4$	−0.232661	−	1.98642i	−0.116330	−	0.993211i
$5$	−0.546554	+	0.651358i	−0.244426	+	0.291296i	−0.874284	−	0.485414i	$-0.838669\pi$
$5$	−0.546554	+	0.651358i	−0.244426	+	0.291296i	0.629858	+	0.776710i	$0.283113\pi$
$6$		0			0
$7$	−0.348909	+	0.958618i	−0.131875	+	0.362324i	−0.988002	−	0.154442i	$-0.950642\pi$
$7$	−0.348909	+	0.958618i	−0.131875	+	0.362324i	0.856127	+	0.516766i	$0.172864\pi$
$8$	2.31749	+	1.62149i	0.819358	+	0.573283i
$9$		0			0
$10$	−0.174421	−	1.18977i	−0.0551568	−	0.376238i
$11$	−1.57259	+	1.31956i	−0.474155	+	0.397863i	−0.848307	−	0.529504i	$-0.822378\pi$
$11$	−1.57259	+	1.31956i	−0.474155	+	0.397863i	0.374153	+	0.927367i	$0.377934\pi$
$12$		0			0
$13$	−0.374417	+	2.12343i	−0.103845	+	0.588933i	0.887831	+	0.460170i	$0.152212\pi$
$13$	−0.374417	+	2.12343i	−0.103845	+	0.588933i	−0.991675	+	0.128762i	$0.958900\pi$
$14$	−0.684856	−	1.26978i	−0.183035	−	0.339363i
$15$		0			0
$16$	−3.89174	+	0.924324i	−0.972934	+	0.231081i
$17$	6.34902	+	3.66561i	1.53986	+	0.889041i	0.998846	+	0.0480291i	$0.0152940\pi$
$17$	6.34902	+	3.66561i	1.53986	+	0.889041i	0.541017	+	0.841011i	$0.318039\pi$
$18$		0			0
$19$	−4.39109	+	2.53520i	−1.00738	+	0.581614i	−0.910425	−	0.413675i	$-0.864245\pi$
$19$	−4.39109	+	2.53520i	−1.00738	+	0.581614i	−0.0969597	+	0.995288i	$0.530912\pi$
$20$	1.42103	+	0.934141i	0.317753	+	0.208880i
$21$		0			0
$22$	0.0840920	−	2.90198i	0.0179285	−	0.618705i
$23$	−5.20278	+	1.89366i	−1.08486	+	0.394855i	−0.821713	−	0.569902i	$-0.806981\pi$
$23$	−5.20278	+	1.89366i	−1.08486	+	0.394855i	−0.263142	+	0.964757i	$0.584759\pi$
$24$		0			0
$25$	0.742695	+	4.21203i	0.148539	+	0.842407i
$26$	−1.89157	−	2.39170i	−0.370968	−	0.469050i
$27$		0			0
$28$	1.98540	+	0.470046i	0.375205	+	0.0888304i
$29$	−3.64198	+	0.642180i	−0.676300	+	0.119250i	−0.501240	−	0.865308i	$-0.667123\pi$
$29$	−3.64198	+	0.642180i	−0.676300	+	0.119250i	−0.175059	+	0.984558i	$0.556012\pi$
$30$		0			0
$31$	1.60292	+	4.40400i	0.287894	+	0.790981i	0.996361	+	0.0852374i	$0.0271649\pi$
$31$	1.60292	+	4.40400i	0.287894	+	0.790981i	−0.708467	+	0.705744i	$0.750613\pi$
$32$	2.68177	−	4.98077i	0.474074	−	0.880485i
$33$		0			0
$34$	−9.84127	+	3.26235i	−1.68776	+	0.559488i
$35$	−0.433706	−	0.751201i	−0.0733097	−	0.126976i
$36$		0			0
$37$	5.33157	−	9.23455i	0.876504	−	1.51815i	0.0213528	−	0.999772i	$-0.493203\pi$
$37$	5.33157	−	9.23455i	0.876504	−	1.51815i	0.855152	−	0.518378i	$-0.173464\pi$
$38$	1.44919	−	7.02265i	0.235089	−	1.13922i
$39$		0			0
$40$	−2.32280	+	0.623286i	−0.367268	+	0.0985502i
$41$	−4.00006	−	0.705319i	−0.624705	−	0.110152i	−0.147670	−	0.989037i	$-0.547177\pi$
$41$	−4.00006	−	0.705319i	−0.624705	−	0.110152i	−0.477035	+	0.878884i	$0.658288\pi$
$42$		0			0
$43$	−3.51843	−	4.19310i	−0.536555	−	0.639441i	0.427857	−	0.903847i	$-0.359269\pi$
$43$	−3.51843	−	4.19310i	−0.536555	−	0.639441i	−0.964412	+	0.264405i	$0.914824\pi$
$44$	2.98709	+	2.81682i	0.450320	+	0.424652i
$45$		0			0
$46$	2.89003	−	7.27719i	0.426112	−	1.07296i
$47$	−4.10423	−	1.49382i	−0.598663	−	0.217896i	0.0248724	−	0.999691i	$-0.492082\pi$
$47$	−4.10423	−	1.49382i	−0.598663	−	0.217896i	−0.623535	+	0.781795i	$0.714304\pi$
$48$		0			0
$49$	4.56510	+	3.83057i	0.652157	+	0.547225i
$50$	−5.14845	−	3.17476i	−0.728101	−	0.448979i
$51$		0			0
$52$	4.30513	+	0.249713i	0.597014	+	0.0346289i
$53$			5.55975i			0.763690i	0.924226	+	0.381845i	$0.124711\pi$
$53$			5.55975i			0.763690i	−0.924226	+	0.381845i	$0.875289\pi$
$54$		0			0
$55$		−	1.74553i		−	0.235368i
$56$	−2.36298	+	1.65584i	−0.315767	+	0.221271i
$57$		0			0
$58$	2.74510	−	4.45167i	0.360449	−	0.584533i
$59$	9.24583	+	7.75817i	1.20370	+	1.01003i	0.999516	+	0.0310964i	$0.00989987\pi$
$59$	9.24583	+	7.75817i	1.20370	+	1.01003i	0.204188	+	0.978932i	$0.434545\pi$
$60$		0			0
$61$	−0.502750	−	0.182986i	−0.0643705	−	0.0234290i	0.309634	−	0.950856i	$-0.399793\pi$
$61$	−0.502750	−	0.182986i	−0.0643705	−	0.0234290i	−0.374005	+	0.927427i	$0.622016\pi$
$62$	−6.15992	−	2.44633i	−0.782311	−	0.310684i
$63$		0			0
$64$	2.74155	+	7.51558i	0.342694	+	0.939447i
$65$	−1.17847	−	1.40445i	−0.146171	−	0.174200i
$66$		0			0
$67$	6.40223	+	1.12889i	0.782157	+	0.137915i	0.550448	−	0.834870i	$-0.314457\pi$
$67$	6.40223	+	1.12889i	0.782157	+	0.137915i	0.231709	+	0.972785i	$0.425568\pi$
$68$	5.80427	−	13.4647i	0.703872	−	1.63283i
$69$		0			0
$70$	1.20139	+	0.247918i	0.143594	+	0.0296319i
$71$	5.86015	−	10.1501i	0.695472	−	1.20459i	−0.274550	−	0.961573i	$-0.588529\pi$
$71$	5.86015	−	10.1501i	0.695472	−	1.20459i	0.970021	−	0.243019i	$-0.0781379\pi$
$72$		0			0
$73$	−0.769587	−	1.33296i	−0.0900734	−	0.156012i	0.817468	−	0.575973i	$-0.195377\pi$
$73$	−0.769587	−	1.33296i	−0.0900734	−	0.156012i	−0.907542	+	0.419962i	$0.862043\pi$
$74$	4.74503	+	14.3140i	0.551599	+	1.66396i
$75$		0			0
$76$	6.05760	+	8.13271i	0.694854	+	0.932886i
$77$	−0.716265	−	1.96792i	−0.0816260	−	0.224266i
$78$		0			0
$79$	14.2516	−	2.51294i	1.60343	−	0.282728i	0.700868	−	0.713291i	$-0.252796\pi$
$79$	14.2516	−	2.51294i	1.60343	−	0.282728i	0.902560	+	0.430563i	$0.141685\pi$
$80$	1.52498	−	3.04011i	0.170498	−	0.339894i
$81$		0			0
$82$	4.50542	−	3.56330i	0.497541	−	0.393501i
$83$	−0.916197	−	5.19601i	−0.100566	−	0.570337i	−0.992899	−	0.118960i	$-0.962044\pi$
$83$	−0.916197	−	5.19601i	−0.100566	−	0.570337i	0.892333	−	0.451377i	$-0.149067\pi$
$84$		0			0
$85$	−5.85770	+	2.13203i	−0.635357	+	0.231251i
$86$	7.73773	+	0.224219i	0.834381	+	0.0241782i
$87$		0			0
$88$	−5.78413	+	0.508136i	−0.616590	+	0.0541675i
$89$	3.41168	−	1.96973i	0.361637	−	0.208791i	−0.308162	−	0.951334i	$-0.599714\pi$
$89$	3.41168	−	1.96973i	0.361637	−	0.208791i	0.669799	+	0.742543i	$0.266380\pi$
$90$		0			0
$91$	−1.90492	−	1.09981i	−0.199690	−	0.115291i
$92$	4.97208	+	9.89434i	0.518376	+	1.03156i
$93$		0			0
$94$	5.43644	−	2.93214i	0.560726	−	0.302427i
$95$	0.748647	−	4.24579i	0.0768096	−	0.435609i
$96$		0			0
$97$	3.35056	−	2.81145i	0.340198	−	0.285460i	−0.456642	−	0.889651i	$-0.650948\pi$
$97$	3.35056	−	2.81145i	0.340198	−	0.285460i	0.796840	+	0.604191i	$0.206503\pi$
$98$	−8.33861	+	1.22245i	−0.842327	+	0.123486i
$99$		0			0
$100$	8.19408	−	2.45528i	0.819408	−	0.245528i
$101$	2.06720	−	5.67959i	0.205694	−	0.565140i	−0.793354	−	0.608760i	$-0.791667\pi$
$101$	2.06720	−	5.67959i	0.205694	−	0.565140i	0.999048	+	0.0436206i	$0.0138893\pi$
$102$		0			0
$103$	−0.110043	+	0.131145i	−0.0108429	+	0.0129221i	−0.771439	−	0.636304i	$-0.780463\pi$
$103$	−0.110043	+	0.131145i	−0.0108429	+	0.0129221i	0.760596	+	0.649226i	$0.224907\pi$
$104$	−4.31082	+	4.31391i	−0.422711	+	0.423014i
$105$		0			0
$106$	−5.87423	−	5.22637i	−0.570556	−	0.507630i
$107$	8.17263			0.790078			0.395039	−	0.918664i	$-0.370731\pi$
$107$	8.17263			0.790078			0.395039	+	0.918664i	$0.370731\pi$
$108$		0			0
$109$	−19.1819			−1.83729			−0.918646	−	0.395082i	$-0.870716\pi$
$109$	−19.1819			−1.83729			−0.918646	+	0.395082i	$0.870716\pi$
$110$	1.84427	+	1.64087i	0.175844	+	0.156450i
$111$		0			0
$112$	0.471786	−	4.05320i	0.0445796	−	0.382991i
$113$	3.19731	−	3.81040i	0.300777	−	0.358452i	−0.594395	−	0.804174i	$-0.702608\pi$
$113$	3.19731	−	3.81040i	0.300777	−	0.358452i	0.895172	+	0.445721i	$0.147053\pi$
$114$		0			0
$115$	1.61015	−	4.42386i	0.150148	−	0.412527i
$116$	2.12299	+	7.08511i	0.197114	+	0.657836i
$117$		0			0
$118$	−16.8884	+	2.47585i	−1.55471	+	0.227921i
$119$	−5.72915	+	4.80732i	−0.525190	+	0.440687i
$120$		0			0
$121$	−1.17833	+	6.68262i	−0.107121	+	0.607511i
$122$	0.665940	−	0.359175i	0.0602914	−	0.0325181i
$123$		0			0
$124$	8.37526	−	4.20872i	0.752120	−	0.377954i
$125$	−6.83132	−	3.94406i	−0.611011	−	0.352768i
$126$		0			0
$127$	−12.8653	+	7.42778i	−1.14161	+	0.659109i	−0.946829	−	0.321738i	$-0.895733\pi$
$127$	−12.8653	+	7.42778i	−1.14161	+	0.659109i	−0.194781	+	0.980847i	$0.562400\pi$
$128$	−10.5179	−	4.16829i	−0.929656	−	0.368428i
$129$		0			0
$130$	2.59170	+	0.0751006i	0.227307	+	0.00658676i
$131$	−2.94977	+	1.07363i	−0.257722	+	0.0938032i	−0.467650	−	0.883914i	$-0.654899\pi$
$131$	−2.94977	+	1.07363i	−0.257722	+	0.0938032i	0.209928	+	0.977717i	$0.432677\pi$
$132$		0			0
$133$	−0.898197	−	5.09393i	−0.0778836	−	0.441700i
$134$	−7.21108	+	5.70318i	−0.622942	+	0.492680i
$135$		0			0
$136$	8.77007	+	18.7899i	0.752027	+	1.61122i
$137$	11.8307	−	2.08607i	1.01077	−	0.178225i	0.356344	−	0.934355i	$-0.384023\pi$
$137$	11.8307	−	2.08607i	1.01077	−	0.178225i	0.654422	+	0.756130i	$0.272912\pi$
$138$		0			0
$139$	0.983129	+	2.70112i	0.0833879	+	0.229106i	0.974378	−	0.224916i	$-0.0722108\pi$
$139$	0.983129	+	2.70112i	0.0833879	+	0.229106i	−0.890990	+	0.454022i	$0.849989\pi$
$140$	−1.39130	+	1.03630i	−0.117586	+	0.0875832i
$141$		0			0
$142$	5.21546	+	15.7331i	0.437672	+	1.32029i
$143$	−2.21319	−	3.83335i	−0.185076	−	0.320561i
$144$		0			0
$145$	1.57225	−	2.72322i	0.130568	−	0.226151i
$146$	2.13180	+	0.439917i	0.176429	+	0.0364078i
$147$		0			0
$148$	−19.5841	−	8.44222i	−1.60981	−	0.693946i
$149$	−10.9239	−	1.92617i	−0.894918	−	0.157798i	−0.292770	−	0.956183i	$-0.594577\pi$
$149$	−10.9239	−	1.92617i	−0.894918	−	0.157798i	−0.602148	+	0.798385i	$0.705688\pi$
$150$		0			0
$151$	−3.78495	−	4.51073i	−0.308015	−	0.367078i	0.589725	−	0.807604i	$-0.299236\pi$
$151$	−3.78495	−	4.51073i	−0.308015	−	0.367078i	−0.897740	+	0.440527i	$0.854792\pi$
$152$	−14.2871	−	1.24480i	−1.15884	−	0.100966i
$153$		0			0
$154$	2.75256	+	1.09314i	0.221807	+	0.0880877i
$155$	−3.74466	−	1.36295i	−0.300779	−	0.109474i
$156$		0			0
$157$	−13.5896	−	11.4030i	−1.08456	−	0.910058i	−0.0882726	−	0.996096i	$-0.528135\pi$
$157$	−13.5896	−	11.4030i	−1.08456	−	0.910058i	−0.996292	+	0.0860388i	$0.972579\pi$
$158$	−10.7419	+	17.4200i	−0.854582	+	1.38586i
$159$		0			0
$160$	1.77853	+	4.46905i	0.140606	+	0.353310i
$161$		−	5.64820i		−	0.445140i
$162$		0			0
$163$		−	18.0395i		−	1.41296i	−0.707732	−	0.706481i	$-0.750282\pi$
$163$		−	18.0395i		−	1.41296i	0.707732	−	0.706481i	$-0.249718\pi$
$164$	−0.470403	+	8.10991i	−0.0367323	+	0.633277i
$165$		0			0
$166$	6.35119	+	3.91642i	0.492948	+	0.303973i
$167$	12.3127	+	10.3316i	0.952789	+	0.799485i	0.979765	−	0.200151i	$-0.0641433\pi$
$167$	12.3127	+	10.3316i	0.952789	+	0.799485i	−0.0269759	+	0.999636i	$0.508588\pi$
$168$		0			0
$169$	7.84725	+	2.85617i	0.603635	+	0.219705i
$170$	3.25383	−	8.19323i	0.249557	−	0.628392i
$171$		0			0
$172$	−7.51066	+	7.96465i	−0.572682	+	0.607299i
$173$	−3.51165	−	4.18502i	−0.266986	−	0.318181i	0.615850	−	0.787864i	$-0.288813\pi$
$173$	−3.51165	−	4.18502i	−0.266986	−	0.318181i	−0.882835	+	0.469683i	$0.844368\pi$
$174$		0			0
$175$	−4.29687	−	0.757653i	−0.324813	−	0.0572732i
$176$	4.90042	−	6.58898i	0.369383	−	0.496663i
$177$		0			0
$178$	−1.12595	+	5.45628i	−0.0843936	+	0.408965i
$179$	−6.73827	+	11.6710i	−0.503642	+	0.872333i	0.496349	+	0.868123i	$0.334674\pi$
$179$	−6.73827	+	11.6710i	−0.503642	+	0.872333i	−0.999991	+	0.00421032i	$0.998660\pi$
$180$		0			0
$181$	7.16955	+	12.4180i	0.532909	+	0.923025i	0.999261	+	0.0384262i	$0.0122345\pi$
$181$	7.16955	+	12.4180i	0.532909	+	0.923025i	−0.466353	+	0.884599i	$0.654432\pi$
$182$	2.95271	−	0.978813i	0.218869	−	0.0725545i
$183$		0			0
$184$	−15.1280	−	4.04771i	−1.11525	−	0.298401i
$185$	3.10100	+	8.51994i	0.227990	+	0.626398i
$186$		0			0
$187$	−14.8214	+	2.61342i	−1.08385	+	0.191112i
$188$	−2.01246	+	8.50028i	−0.146773	+	0.619946i
$189$		0			0
$190$	3.78220	+	4.78219i	0.274390	+	0.346937i
$191$	1.45788	+	8.26803i	0.105488	+	0.598254i	0.991024	+	0.133683i	$0.0426803\pi$
$191$	1.45788	+	8.26803i	0.105488	+	0.598254i	−0.885536	+	0.464571i	$0.846209\pi$
$192$		0			0
$193$	−1.16115	+	0.422623i	−0.0835812	+	0.0304211i	−0.383472	−	0.923552i	$-0.625272\pi$
$193$	−1.16115	+	0.422623i	−0.0835812	+	0.0304211i	0.299891	+	0.953973i	$0.403050\pi$
$194$	−0.179166	+	6.18296i	−0.0128634	+	0.443910i
$195$		0			0
$196$	6.54701	−	9.95943i	0.467644	−	0.711388i
$197$	−2.53158	+	1.46161i	−0.180368	+	0.104135i	−0.587466	−	0.809249i	$-0.699874\pi$
$197$	−2.53158	+	1.46161i	−0.180368	+	0.104135i	0.407098	+	0.913385i	$0.366541\pi$
$198$		0			0
$199$	12.5012	+	7.21757i	0.886186	+	0.511640i	0.872693	−	0.488269i	$-0.162372\pi$
$199$	12.5012	+	7.21757i	0.886186	+	0.511640i	0.0134930	+	0.999909i	$0.495705\pi$
$200$	−5.10857	+	10.9656i	−0.361231	+	0.775387i
$201$		0			0
$202$	4.05761	+	7.52315i	0.285492	+	0.529327i
$203$	0.655114	−	3.71534i	0.0459800	−	0.260765i
$204$		0			0
$205$	2.64567	−	2.21998i	0.184781	−	0.155050i
$206$	−0.0351180	−	0.239549i	−0.00244679	−	0.0166902i
$207$		0			0
$208$	−0.505601	−	8.60990i	−0.0350571	−	0.596989i
$209$	3.56005	−	9.78114i	0.246253	−	0.676576i
$210$		0			0
$211$	−3.58544	+	4.27296i	−0.246832	+	0.294163i	−0.875208	−	0.483747i	$-0.839276\pi$
$211$	−3.58544	+	4.27296i	−0.246832	+	0.294163i	0.628376	+	0.777910i	$0.283720\pi$
$212$	11.0440	−	1.29353i	0.758505	−	0.0888403i
$213$		0			0
$214$	−7.68258	+	8.63492i	−0.525170	+	0.590271i
$215$	4.65422			0.317415
$216$		0			0
$217$	−4.78103			−0.324557
$218$	18.0317	−	20.2669i	1.22126	−	1.37265i
$219$		0			0
$220$	−3.46736	+	0.406117i	−0.233770	+	0.0273804i
$221$	−10.1608	+	12.1092i	−0.683492	+	0.814554i
$222$		0			0
$223$	4.64768	−	12.7694i	0.311231	−	0.855102i	−0.681177	−	0.732119i	$-0.738532\pi$
$223$	4.64768	−	12.7694i	0.311231	−	0.855102i	0.992409	−	0.122983i	$-0.0392461\pi$
$224$	3.83897	+	4.30863i	0.256502	+	0.287882i
$225$		0			0
$226$	1.02035	+	6.96008i	0.0678728	+	0.462978i
$227$	13.7746	−	11.5582i	0.914249	−	0.767146i	−0.0586732	−	0.998277i	$-0.518687\pi$
$227$	13.7746	−	11.5582i	0.914249	−	0.767146i	0.972923	+	0.231131i	$0.0742426\pi$
$228$		0			0
$229$	2.41193	−	13.6787i	0.159385	−	0.903916i	−0.795282	−	0.606240i	$-0.792677\pi$
$229$	2.41193	−	13.6787i	0.159385	−	0.903916i	0.954667	−	0.297676i	$-0.0962117\pi$
$230$	3.16049	+	5.85982i	0.208397	+	0.386385i
$231$		0			0
$232$	−9.48156	−	4.41719i	−0.622495	−	0.290003i
$233$	−2.12007	−	1.22403i	−0.138891	−	0.0801886i	0.428945	−	0.903331i	$-0.358886\pi$
$233$	−2.12007	−	1.22403i	−0.138891	−	0.0801886i	−0.567835	+	0.823142i	$0.692219\pi$
$234$		0			0
$235$	3.21619	−	1.85687i	0.209801	−	0.121129i
$236$	13.2599	−	20.1711i	0.863143	−	1.31303i
$237$		0			0
$238$	0.306357	−	10.5723i	0.0198582	−	0.685299i
$239$	−14.4768	+	5.26911i	−0.936424	+	0.340831i	−0.764753	−	0.644324i	$-0.777139\pi$
$239$	−14.4768	+	5.26911i	−0.936424	+	0.340831i	−0.171671	+	0.985154i	$0.554917\pi$
$240$		0			0
$241$	2.02973	+	11.5112i	0.130747	+	0.741501i	0.977728	+	0.209878i	$0.0673067\pi$
$241$	2.02973	+	11.5112i	0.130747	+	0.741501i	−0.846981	+	0.531623i	$0.821582\pi$
$242$	−5.95295	−	7.52688i	−0.382670	−	0.483846i
$243$		0			0
$244$	−0.246517	+	1.04125i	−0.0157816	+	0.0666590i
$245$	−4.99015	+	0.879897i	−0.318809	+	0.0562146i
$246$		0			0
$247$	−3.73920	−	10.2734i	−0.237920	−	0.653679i
$248$	−3.42626	+	12.8054i	−0.217568	+	0.813141i
$249$		0			0
$250$	10.5888	−	3.51017i	0.669698	−	0.222002i
$251$	1.74376	+	3.02028i	0.110065	+	0.190639i	0.915796	−	0.401643i	$-0.131561\pi$
$251$	1.74376	+	3.02028i	0.110065	+	0.190639i	−0.805731	+	0.592281i	$0.798227\pi$
$252$		0			0
$253$	5.68306	−	9.84335i	0.357291	−	0.618846i
$254$	4.24591	−	20.5754i	0.266412	−	1.29102i
$255$		0			0
$256$	14.2912	−	7.19446i	0.893203	−	0.449654i
$257$	17.5820	+	3.10019i	1.09674	+	0.193385i	0.692606	−	0.721316i	$-0.256463\pi$
$257$	17.5820	+	3.10019i	1.09674	+	0.193385i	0.404132	+	0.914701i	$0.367574\pi$
$258$		0			0
$259$	6.99218	+	8.33295i	0.434473	+	0.517784i
$260$	−2.51564	+	2.66770i	−0.156013	+	0.165444i
$261$		0			0
$262$	1.63853	−	4.12587i	0.101229	−	0.254897i
$263$	6.92028	+	2.51878i	0.426723	+	0.155314i	0.546449	−	0.837493i	$-0.315979\pi$
$263$	6.92028	+	2.51878i	0.426723	+	0.155314i	−0.119726	+	0.992807i	$0.538202\pi$
$264$		0			0
$265$	−3.62138	−	3.03870i	−0.222460	−	0.186666i
$266$	6.22641	+	3.83948i	0.381765	+	0.235413i
$267$		0			0
$268$	0.752896	−	12.9802i	0.0459904	−	0.792891i
$269$			0.906912i			0.0552954i	0.999618	+	0.0276477i	$0.00880165\pi$
$269$			0.906912i			0.0552954i	−0.999618	+	0.0276477i	$0.991198\pi$
$270$		0			0
$271$			6.71551i			0.407938i	0.978977	+	0.203969i	$0.0653842\pi$
$271$			6.71551i			0.407938i	−0.978977	+	0.203969i	$0.934616\pi$
$272$	−28.0969	−	8.39703i	−1.70363	−	0.509145i
$273$		0			0
$274$	−8.91723	+	14.4609i	−0.538709	+	0.873615i
$275$	−6.72600	−	5.64378i	−0.405593	−	0.340333i
$276$		0			0
$277$	1.68312	+	0.612607i	0.101129	+	0.0368080i	0.392089	−	0.919927i	$-0.371752\pi$
$277$	1.68312	+	0.612607i	0.101129	+	0.0368080i	−0.290960	+	0.956735i	$0.593975\pi$
$278$	−3.77809	−	1.50042i	−0.226595	−	0.0899890i
$279$		0			0
$280$	0.212953	−	2.44415i	0.0127263	−	0.146066i
$281$	3.69638	+	4.40517i	0.220508	+	0.262791i	0.864945	−	0.501866i	$-0.167353\pi$
$281$	3.69638	+	4.40517i	0.220508	+	0.262791i	−0.644438	+	0.764657i	$0.722909\pi$
$282$		0			0
$283$	10.1948	+	1.79762i	0.606019	+	0.106858i	0.468234	−	0.883605i	$-0.344890\pi$
$283$	10.1948	+	1.79762i	0.606019	+	0.106858i	0.137785	+	0.990462i	$0.456002\pi$
$284$	−21.5258	−	9.27920i	−1.27732	−	0.550619i
$285$		0			0
$286$	6.13067	+	1.26512i	0.362514	+	0.0748079i
$287$	2.07179	−	3.58844i	0.122294	−	0.211819i
$288$		0			0
$289$	18.3734	+	31.8236i	1.08079	+	1.87198i
$290$	1.39929	+	4.22112i	0.0821689	+	0.247872i
$291$		0			0
$292$	−2.46878	+	1.83885i	−0.144474	+	0.107611i
$293$	4.28880	+	11.7834i	0.250555	+	0.688393i	0.999663	+	0.0259461i	$0.00825984\pi$
$293$	4.28880	+	11.7834i	0.250555	+	0.688393i	−0.749109	+	0.662447i	$0.769518\pi$
$294$		0			0
$295$	−10.1067	+	1.78208i	−0.588434	+	0.103757i
$296$	27.3296	−	12.7559i	1.58850	−	0.741423i
$297$		0			0
$298$	12.3040	−	9.73111i	0.712750	−	0.563708i
$299$	−2.07303	−	11.7567i	−0.119886	−	0.679910i
$300$		0			0
$301$	5.24719	−	1.90982i	0.302443	−	0.110080i
$302$	8.32387	+	0.241204i	0.478985	+	0.0138797i
$303$		0			0
$304$	14.7456	−	13.9251i	0.845719	−	0.798660i
$305$	0.393969	−	0.227458i	0.0225586	−	0.0130242i
$306$		0			0
$307$	23.0184	+	13.2897i	1.31373	+	0.758482i	0.982712	−	0.185143i	$-0.0592749\pi$
$307$	23.0184	+	13.2897i	1.31373	+	0.758482i	0.331017	+	0.943625i	$0.392608\pi$
$308$	−3.74248	+	1.88066i	−0.213247	+	0.107161i
$309$		0			0
$310$	4.96016	−	2.67526i	0.281718	−	0.151945i
$311$	3.84093	−	21.7830i	0.217799	−	1.23520i	−0.658184	−	0.752857i	$-0.728675\pi$
$311$	3.84093	−	21.7830i	0.217799	−	1.23520i	0.875983	−	0.482342i	$-0.160214\pi$
$312$		0			0
$313$	−4.20542	+	3.52877i	−0.237705	+	0.199458i	−0.753856	−	0.657039i	$-0.771809\pi$
$313$	−4.20542	+	3.52877i	−0.237705	+	0.199458i	0.516152	+	0.856497i	$0.327364\pi$
$314$	24.8227	−	3.63902i	1.40083	−	0.205362i
$315$		0			0
$316$	−8.30754	−	27.7250i	−0.467336	−	1.55965i
$317$	−6.85935	+	18.8459i	−0.385260	+	1.05849i	0.583850	+	0.811862i	$0.301546\pi$
$317$	−6.85935	+	18.8459i	−0.385260	+	1.05849i	−0.969110	+	0.246631i	$0.920677\pi$
$318$		0			0
$319$	4.87996	−	5.81571i	0.273225	−	0.325617i
$320$	−6.39374	−	2.32194i	−0.357421	−	0.129800i
$321$		0			0
$322$	5.96769	+	5.30951i	0.332566	+	0.295888i
$323$	−37.1721			−2.06831
$324$		0			0
$325$	−9.22202			−0.511546
$326$	19.0599	+	16.9578i	1.05563	+	0.939204i
$327$		0			0
$328$	−8.12645	−	8.12063i	−0.448708	−	0.448387i
$329$	2.86400	−	3.41318i	0.157897	−	0.188175i
$330$		0			0
$331$	−7.99263	+	21.9596i	−0.439315	+	1.20701i	0.500624	+	0.865665i	$0.333104\pi$
$331$	−7.99263	+	21.9596i	−0.439315	+	1.20701i	−0.939939	+	0.341343i	$0.889118\pi$
$332$	−10.1083	+	3.02886i	−0.554766	+	0.166230i
$333$		0			0
$334$	−22.4905	+	3.29712i	−1.23062	+	0.180410i
$335$	−4.23448	+	3.55315i	−0.231354	+	0.194129i
$336$		0			0
$337$	1.10728	−	6.27969i	0.0603173	−	0.342076i	−0.939683	−	0.342047i	$-0.888880\pi$
$337$	1.10728	−	6.27969i	0.0603173	−	0.342076i	1.00000		2.90332e-5i	$-9.24155e-6\pi$
$338$	−10.3944	+	5.60623i	−0.565383	+	0.304939i
$339$		0			0
$340$	5.59797	+	11.1398i	0.303592	+	0.604142i
$341$	−8.33210	−	4.81054i	−0.451208	−	0.260505i
$342$		0			0
$343$	−11.4491	+	6.61016i	−0.618195	+	0.356915i
$344$	−1.35487	−	15.4226i	−0.0730498	−	0.831529i
$345$		0			0
$346$	7.72282	+	0.223787i	0.415182	+	0.0120309i
$347$	15.1793	−	5.52480i	0.814866	−	0.296587i	0.0992334	−	0.995064i	$-0.468361\pi$
$347$	15.1793	−	5.52480i	0.814866	−	0.296587i	0.715632	+	0.698477i	$0.246139\pi$
$348$		0			0
$349$	−3.65392	−	20.7224i	−0.195590	−	1.10925i	−0.911576	−	0.411132i	$-0.865134\pi$
$349$	−3.65392	−	20.7224i	−0.195590	−	1.10925i	0.715986	−	0.698115i	$-0.245978\pi$
$350$	4.83972	−	3.82770i	0.258694	−	0.204599i
$351$		0			0
$352$	2.35511	+	11.3715i	0.125528	+	0.606103i
$353$	9.47086	−	1.66997i	0.504083	−	0.0888834i	0.0841766	−	0.996451i	$-0.473174\pi$
$353$	9.47086	−	1.66997i	0.504083	−	0.0888834i	0.419906	+	0.907567i	$0.362063\pi$
$354$		0			0
$355$	3.40844	+	9.36462i	0.180901	+	0.497022i
$356$	−4.70648	−	6.31875i	−0.249443	−	0.334893i
$357$		0			0
$358$	−5.99698	−	18.0906i	−0.316950	−	0.956119i
$359$	7.01604	+	12.1521i	0.370292	+	0.641365i	0.989610	−	0.143775i	$-0.0459242\pi$
$359$	7.01604	+	12.1521i	0.370292	+	0.641365i	−0.619318	+	0.785140i	$0.712591\pi$
$360$		0			0
$361$	3.35443	−	5.81005i	0.176549	−	0.305792i
$362$	−19.8601	−	4.09831i	−1.04382	−	0.215402i
$363$		0			0
$364$	−1.74148	+	4.03985i	−0.0912782	+	0.211746i
$365$	1.28886	+	0.227260i	0.0674619	+	0.0118954i
$366$		0			0
$367$	23.8419	+	28.4137i	1.24454	+	1.48318i	0.814276	+	0.580478i	$0.197134\pi$
$367$	23.8419	+	28.4137i	1.24454	+	1.48318i	0.430261	+	0.902704i	$0.358421\pi$
$368$	18.4975	−	12.1787i	0.964249	−	0.634857i
$369$		0			0
$370$	−11.9169	−	4.73264i	−0.619532	−	0.246038i
$371$	−5.32967	−	1.93984i	−0.276703	−	0.100712i
$372$		0			0
$373$	21.7187	+	18.2242i	1.12455	+	0.943611i	0.998825	−	0.0484536i	$-0.0154293\pi$
$373$	21.7187	+	18.2242i	1.12455	+	0.943611i	0.125727	+	0.992065i	$0.459874\pi$
$374$	11.1714	−	18.1165i	0.577661	−	0.936782i
$375$		0			0
$376$	−7.08931	−	10.1169i	−0.365603	−	0.521737i
$377$		−	7.97393i		−	0.410678i
$378$		0			0
$379$		−	15.3245i		−	0.787168i	−0.919289	−	0.393584i	$-0.871235\pi$
$379$		−	15.3245i		−	0.787168i	0.919289	−	0.393584i	$-0.128765\pi$
$380$	−8.60811	−	0.499300i	−0.441587	−	0.0256136i
$381$		0			0
$382$	−10.1062	−	6.23191i	−0.517077	−	0.318852i
$383$	−28.1952	−	23.6586i	−1.44071	−	1.20890i	−0.939028	−	0.343841i	$-0.888272\pi$
$383$	−28.1952	−	23.6586i	−1.44071	−	1.20890i	−0.501678	−	0.865055i	$-0.667284\pi$
$384$		0			0
$385$	1.67330	+	0.609031i	0.0852792	+	0.0310391i
$386$	0.644992	−	1.62411i	0.0328292	−	0.0826650i
$387$		0			0
$388$	−6.36428	−	6.00151i	−0.323097	−	0.304681i
$389$	5.77806	+	6.88602i	0.292959	+	0.349135i	0.892369	−	0.451307i	$-0.149042\pi$
$389$	5.77806	+	6.88602i	0.292959	+	0.349135i	−0.599409	+	0.800443i	$0.704598\pi$
$390$		0			0
$391$	−39.9740	−	7.04849i	−2.02157	−	0.356457i
$392$	4.36836	+	16.2796i	0.220635	+	0.822243i
$393$		0			0
$394$	0.835495	−	4.04875i	0.0420917	−	0.203973i
$395$	−6.15244	+	10.6563i	−0.309563	+	0.536178i
$396$		0			0
$397$	−2.35735	−	4.08305i	−0.118312	−	0.204922i	0.800787	−	0.598949i	$-0.204415\pi$
$397$	−2.35735	−	4.08305i	−0.118312	−	0.204922i	−0.919099	+	0.394027i	$0.871082\pi$
$398$	−19.3774	+	6.42355i	−0.971302	+	0.321983i
$399$		0			0
$400$	−6.78366	−	15.7056i	−0.339183	−	0.785282i
$401$	−5.87724	−	16.1476i	−0.293495	−	0.806372i	−0.995549	−	0.0942475i	$-0.969955\pi$
$401$	−5.87724	−	16.1476i	−0.293495	−	0.806372i	0.702053	−	0.712124i	$-0.252267\pi$
$402$		0			0
$403$	−9.95173	+	1.75476i	−0.495731	+	0.0874107i
$404$	−11.7630	−	2.78491i	−0.585231	−	0.138555i
$405$		0			0
$406$	3.30966	+	4.18472i	0.164256	+	0.207684i
$407$	3.80117	+	21.5575i	0.188417	+	1.06857i
$408$		0			0
$409$	18.1511	−	6.60646i	0.897514	−	0.326668i	0.148258	−	0.988949i	$-0.452633\pi$
$409$	18.1511	−	6.60646i	0.897514	−	0.326668i	0.749256	+	0.662280i	$0.230411\pi$
$410$	−0.141473	+	4.88218i	−0.00698684	+	0.241114i
$411$		0			0
$412$	0.286111	+	0.188080i	0.0140957	+	0.00926605i
$413$	−10.6631	+	6.15633i	−0.524696	+	0.302933i
$414$		0			0
$415$	3.88522	+	2.24313i	0.190718	+	0.110111i
$416$	9.57221	+	7.55943i	0.469316	+	0.370631i
$417$		0			0
$418$	6.98784	+	12.9561i	0.341787	+	0.633702i
$419$	−2.66451	+	15.1112i	−0.130170	+	0.738230i	0.847932	+	0.530105i	$0.177847\pi$
$419$	−2.66451	+	15.1112i	−0.130170	+	0.738230i	−0.978102	+	0.208126i	$0.933264\pi$
$420$		0			0
$421$	−17.8213	+	14.9539i	−0.868558	+	0.728807i	−0.963794	−	0.266648i	$-0.914084\pi$
$421$	−17.8213	+	14.9539i	−0.868558	+	0.728807i	0.0952359	+	0.995455i	$0.469639\pi$
$422$	−1.14422	−	7.80500i	−0.0556996	−	0.379941i
$423$		0			0
$424$	−9.01506	+	12.8847i	−0.437810	+	0.625735i
$425$	−10.7243	+	29.4647i	−0.520204	+	1.42925i
$426$		0			0
$427$	0.350828	−	0.418100i	0.0169777	−	0.0202333i
$428$	−1.90145	−	16.2343i	−0.0919101	−	0.784714i
$429$		0			0
$430$	−4.37514	+	4.91748i	−0.210988	+	0.237142i
$431$	16.8732			0.812754			0.406377	−	0.913706i	$-0.366792\pi$
$431$	16.8732			0.812754			0.406377	+	0.913706i	$0.366792\pi$
$432$		0			0
$433$	−2.79450			−0.134295			−0.0671475	−	0.997743i	$-0.521390\pi$
$433$	−2.79450			−0.134295			−0.0671475	+	0.997743i	$0.521390\pi$
$434$	4.49434	−	5.05147i	0.215735	−	0.242478i
$435$		0			0
$436$	4.46287	+	38.1033i	0.213733	+	1.82482i
$437$	18.0451	−	21.5053i	0.863213	−	1.02874i
$438$		0			0
$439$	1.92679	−	5.29380i	0.0919605	−	0.252659i	−0.885182	−	0.465245i	$-0.845966\pi$
$439$	1.92679	−	5.29380i	0.0919605	−	0.252659i	0.977142	+	0.212586i	$0.0681884\pi$
$440$	2.83036	−	4.04526i	0.134932	−	0.192850i
$441$		0			0
$442$	−3.24261	−	22.1187i	−0.154235	−	1.05208i
$443$	−4.19281	+	3.51819i	−0.199206	+	0.167154i	−0.736934	−	0.675964i	$-0.763727\pi$
$443$	−4.19281	+	3.51819i	−0.199206	+	0.167154i	0.537728	+	0.843119i	$0.319283\pi$
$444$		0			0
$445$	−0.581665	+	3.29879i	−0.0275736	+	0.156377i
$446$	9.12270	+	16.9143i	0.431973	+	0.800914i
$447$		0			0
$448$	−8.16112	+	0.00585318i	−0.385577	+	0.000276537i
$449$	21.3460	+	12.3241i	1.00738	+	0.581612i	0.910424	−	0.413676i	$-0.135755\pi$
$449$	21.3460	+	12.3241i	1.00738	+	0.581612i	0.0969581	+	0.995288i	$0.469089\pi$
$450$		0			0
$451$	7.22118	−	4.16915i	0.340032	−	0.196318i
$452$	−8.31295	−	5.46467i	−0.391008	−	0.257036i
$453$		0			0
$454$	−0.736573	+	25.4189i	−0.0345691	+	1.19297i
$455$	1.75751	−	0.639680i	0.0823932	−	0.0299887i
$456$		0			0
$457$	−1.98007	−	11.2295i	−0.0926236	−	0.525294i	−0.995450	−	0.0952886i	$-0.969623\pi$
$457$	−1.98007	−	11.2295i	−0.0926236	−	0.525294i	0.902826	−	0.430006i	$-0.141489\pi$
$458$	12.1852	+	15.4069i	0.569376	+	0.719916i
$459$		0			0
$460$	−9.16227	−	2.16918i	−0.427193	−	0.101139i
$461$	−18.4150	+	3.24705i	−0.857670	+	0.151230i	−0.585155	−	0.810921i	$-0.698966\pi$
$461$	−18.4150	+	3.24705i	−0.857670	+	0.151230i	−0.272515	+	0.962152i	$0.587855\pi$
$462$		0			0
$463$	−12.1162	−	33.2889i	−0.563086	−	1.54707i	−0.815086	−	0.579340i	$-0.803310\pi$
$463$	−12.1162	−	33.2889i	−0.563086	−	1.54707i	0.252000	−	0.967727i	$-0.418912\pi$
$464$	13.5801	−	5.86557i	0.630439	−	0.272302i
$465$		0			0
$466$	3.28621	−	1.08937i	0.152231	−	0.0504640i
$467$	−1.62531	−	2.81512i	−0.0752103	−	0.130268i	0.825967	−	0.563718i	$-0.190629\pi$
$467$	−1.62531	−	2.81512i	−0.0752103	−	0.130268i	−0.901178	+	0.433450i	$0.857296\pi$
$468$		0			0
$469$	−3.31596	+	5.74342i	−0.153117	+	0.265206i
$470$	−1.06144	+	5.14364i	−0.0489604	+	0.237258i
$471$		0			0
$472$	8.84737	+	32.9715i	0.407233	+	1.51764i
$473$	11.0661	+	1.95125i	0.508820	+	0.0897187i
$474$		0			0
$475$	−13.9396	−	16.6125i	−0.639591	−	0.762235i
$476$	10.8823	+	10.2620i	0.498790	+	0.470359i
$477$		0			0
$478$	8.04154	−	20.2488i	0.367811	−	0.926159i
$479$	36.5463	+	13.3018i	1.66984	+	0.607774i	0.991864	−	0.127306i	$-0.0406329\pi$
$479$	36.5463	+	13.3018i	1.66984	+	0.607774i	0.677981	+	0.735079i	$0.262855\pi$
$480$		0			0
$481$	17.6126	+	14.7788i	0.803068	+	0.673854i
$482$	−14.0704	−	8.67640i	−0.640887	−	0.395199i
$483$		0			0
$484$	13.5486	+	0.785868i	0.615847	+	0.0357213i
$485$			3.71903i			0.168872i
$486$		0			0
$487$		−	14.4854i		−	0.656395i	−0.944609	−	0.328198i	$-0.893559\pi$
$487$		−	14.4854i		−	0.656395i	0.944609	−	0.328198i	$-0.106441\pi$
$488$	−0.868410	−	1.23927i	−0.0393111	−	0.0560992i
$489$		0			0
$490$	3.76125	−	6.09955i	0.169916	−	0.275550i
$491$	5.58619	+	4.68737i	0.252101	+	0.211538i	0.760076	−	0.649834i	$-0.225161\pi$
$491$	5.58619	+	4.68737i	0.252101	+	0.211538i	−0.507975	+	0.861372i	$0.669606\pi$
$492$		0			0
$493$	−25.4770	−	9.27287i	−1.14743	−	0.417629i
$494$	14.3695	+	5.70664i	0.646513	+	0.256754i
$495$		0			0
$496$	−10.3089	−	15.6576i	−0.462882	−	0.703046i
$497$	7.68539	+	9.15909i	0.344737	+	0.410842i
$498$		0			0
$499$	14.1578	+	2.49639i	0.633788	+	0.111754i	0.481307	−	0.876552i	$-0.340162\pi$
$499$	14.1578	+	2.49639i	0.633788	+	0.111754i	0.152482	+	0.988306i	$0.451274\pi$
$500$	−6.24519	+	14.4875i	−0.279293	+	0.647901i
$501$		0			0
$502$	−4.83033	−	0.996780i	−0.215588	−	0.0444885i
$503$	−9.08769	+	15.7403i	−0.405200	+	0.701827i	−0.994345	−	0.106200i	$-0.966132\pi$
$503$	−9.08769	+	15.7403i	−0.405200	+	0.701827i	0.589145	+	0.808028i	$0.299465\pi$
$504$		0			0
$505$	2.56961	+	4.45069i	0.114346	+	0.198053i
$506$	5.05785	+	15.2576i	0.224849	+	0.678285i
$507$		0			0
$508$	17.7479	+	23.8277i	0.787437	+	1.05718i
$509$	−6.60337	−	18.1426i	−0.292689	−	0.804157i	−0.995671	−	0.0929491i	$-0.970371\pi$
$509$	−6.60337	−	18.1426i	−0.292689	−	0.804157i	0.702982	−	0.711208i	$-0.251852\pi$
$510$		0			0
$511$	1.54632	−	0.272658i	0.0684052	−	0.0120617i
$512$	−5.83289	+	21.8627i	−0.257780	+	0.966204i
$513$		0			0
$514$	−19.8033	+	15.6623i	−0.873487	+	0.690834i
$515$	−0.0252774	−	0.143355i	−0.00111386	−	0.00631699i
$516$		0			0
$517$	8.42546	−	3.06662i	0.370551	−	0.134870i
$518$	−15.3772	−	0.445592i	−0.675636	−	0.0195782i
$519$		0			0
$520$	−0.453805	−	5.16567i	−0.0199006	−	0.226530i
$521$	−24.7853	+	14.3098i	−1.08586	+	0.626924i	−0.932472	−	0.361241i	$-0.882353\pi$
$521$	−24.7853	+	14.3098i	−1.08586	+	0.626924i	−0.153392	+	0.988165i	$0.549020\pi$
$522$		0			0
$523$	−10.5509	−	6.09156i	−0.461359	−	0.266365i	0.251257	−	0.967920i	$-0.419156\pi$
$523$	−10.5509	−	6.09156i	−0.461359	−	0.266365i	−0.712615	+	0.701555i	$0.752489\pi$
$524$	2.81897	+	5.60969i	0.123147	+	0.245060i
$525$		0			0
$526$	−9.16657	+	4.94399i	−0.399682	+	0.215568i
$527$	−5.96633	+	33.8368i	−0.259898	+	1.47395i
$528$		0			0
$529$	5.86398	−	4.92046i	0.254956	−	0.213933i
$530$	6.61482	−	0.969736i	0.287329	−	0.0421227i
$531$		0			0
$532$	−9.90971	+	2.96935i	−0.429641	+	0.128738i
$533$	2.99539	−	8.22975i	0.129745	−	0.356470i
$534$		0			0
$535$	−4.46679	+	5.32331i	−0.193116	+	0.230147i
$536$	13.0067	+	12.9973i	0.561802	+	0.561399i
$537$		0			0
$538$	−0.958211	−	0.852531i	−0.0413114	−	0.0367552i
$539$	−12.2337			−0.526944
$540$		0			0
$541$	6.27951			0.269977			0.134989	−	0.990847i	$-0.456900\pi$
$541$	6.27951			0.269977			0.134989	+	0.990847i	$0.456900\pi$
$542$	−7.09538	−	6.31283i	−0.304773	−	0.271159i
$543$		0			0
$544$	35.2842	−	21.7927i	1.51280	−	0.934355i
$545$	10.4839	−	12.4943i	0.449083	−	0.535196i
$546$		0			0
$547$	−8.59471	+	23.6138i	−0.367483	+	1.00965i	0.608832	+	0.793299i	$0.291638\pi$
$547$	−8.59471	+	23.6138i	−0.367483	+	1.00965i	−0.976315	+	0.216353i	$0.930584\pi$
$548$	−6.89636	−	23.0154i	−0.294598	−	0.983170i
$549$		0			0
$550$	12.2857	−	1.80109i	0.523865	−	0.0767988i
$551$	14.3642	−	12.0530i	0.611936	−	0.513476i
$552$		0			0
$553$	−2.56355	+	14.5386i	−0.109013	+	0.618245i
$554$	−2.22946	+	1.20246i	−0.0947206	+	0.0510875i
$555$		0			0
$556$	5.13683	−	2.58135i	0.217850	−	0.109474i
$557$	−17.6052	−	10.1644i	−0.745958	−	0.430679i	0.0782737	−	0.996932i	$-0.475059\pi$
$557$	−17.6052	−	10.1644i	−0.745958	−	0.430679i	−0.824232	+	0.566253i	$0.808393\pi$
$558$		0			0
$559$	10.2211	−	5.90115i	0.432306	−	0.249592i
$560$	2.38222	+	2.52259i	0.100667	+	0.106599i
$561$		0			0
$562$	−8.12909	−	0.235560i	−0.342905	−	0.00993649i
$563$	33.7274	−	12.2758i	1.42144	−	0.517362i	0.486976	−	0.873416i	$-0.338100\pi$
$563$	33.7274	−	12.2758i	1.42144	−	0.517362i	0.934466	+	0.356053i	$0.115878\pi$
$564$		0			0
$565$	0.734434	+	4.16518i	0.0308979	+	0.175230i
$566$	−11.4828	+	9.08166i	−0.482659	+	0.381731i
$567$		0			0
$568$	30.0391	−	14.0206i	1.26041	−	0.588290i
$569$	−37.1364	+	6.54816i	−1.55684	+	0.274513i	−0.884789	−	0.465992i	$-0.845698\pi$
$569$	−37.1364	+	6.54816i	−1.55684	+	0.274513i	−0.672051	+	0.740505i	$0.734587\pi$
$570$		0			0
$571$	4.67247	+	12.8375i	0.195537	+	0.537233i	0.998250	−	0.0591320i	$-0.0188333\pi$
$571$	4.67247	+	12.8375i	0.195537	+	0.537233i	−0.802713	+	0.596365i	$0.796611\pi$
$572$	−7.09973	+	5.28819i	−0.296855	+	0.221110i
$573$		0			0
$574$	1.84387	+	5.56225i	0.0769615	+	0.232164i
$575$	−11.8402	−	20.5079i	−0.493772	−	0.855238i
$576$		0			0
$577$	8.52845	−	14.7717i	0.355044	−	0.614954i	−0.632082	−	0.774902i	$-0.717799\pi$
$577$	8.52845	−	14.7717i	0.355044	−	0.614954i	0.987125	+	0.159948i	$0.0511326\pi$
$578$	−50.8954	−	10.5027i	−2.11697	−	0.436855i
$579$		0			0
$580$	−5.77527	−	2.48957i	−0.239805	−	0.103374i
$581$	5.30066	+	0.934650i	0.219909	+	0.0387758i
$582$		0			0
$583$	−7.33643	−	8.74322i	−0.303844	−	0.362107i
$584$	0.377872	−	4.33701i	0.0156365	−	0.179467i
$585$		0			0
$586$	−16.4816	−	6.54542i	−0.680847	−	0.270389i
$587$	−5.94463	−	2.16367i	−0.245361	−	0.0893041i	0.216412	−	0.976302i	$-0.430564\pi$
$587$	−5.94463	−	2.16367i	−0.245361	−	0.0893041i	−0.461773	+	0.886998i	$0.652787\pi$
$588$		0			0
$589$	−18.2036	−	15.2746i	−0.750065	−	0.629379i
$590$	7.61778	−	12.3536i	0.313619	−	0.508590i
$591$		0			0
$592$	−12.2133	+	40.8665i	−0.501966	+	1.67960i
$593$		−	28.7935i		−	1.18241i	−0.806523	−	0.591203i	$-0.798653\pi$
$593$		−	28.7935i		−	1.18241i	0.806523	−	0.591203i	$-0.201347\pi$
$594$		0			0
$595$		−	6.35919i		−	0.260701i
$596$	−1.28464	+	22.1476i	−0.0526207	+	0.907199i
$597$		0			0
$598$	14.3705	+	8.86148i	0.587653	+	0.362373i
$599$	−36.9656	−	31.0178i	−1.51037	−	1.26735i	−0.863024	−	0.505163i	$-0.831433\pi$
$599$	−36.9656	−	31.0178i	−1.51037	−	1.26735i	−0.647351	−	0.762192i	$-0.724123\pi$
$600$		0			0
$601$	−41.1432	−	14.9749i	−1.67827	−	0.610839i	−0.685196	−	0.728358i	$-0.740284\pi$
$601$	−41.1432	−	14.9749i	−1.67827	−	0.610839i	−0.993071	+	0.117519i	$0.962506\pi$
$602$	−2.91470	+	7.33930i	−0.118794	+	0.299128i
$603$		0			0
$604$	−8.07959	+	8.56797i	−0.328754	+	0.348626i
$605$	−3.70876	−	4.41992i	−0.150782	−	0.179695i
$606$		0			0
$607$	−1.37632	−	0.242682i	−0.0558630	−	0.00985015i	0.145647	−	0.989337i	$-0.453474\pi$
$607$	−1.37632	−	0.242682i	−0.0558630	−	0.00985015i	−0.201510	+	0.979486i	$0.564585\pi$
$608$	0.851357	+	28.6698i	0.0345271	+	1.16271i
$609$		0			0
$610$	−0.130021	+	0.630074i	−0.00526441	+	0.0255109i
$611$	4.70870	−	8.15571i	0.190494	−	0.329945i
$612$		0			0
$613$	−9.57422	−	16.5830i	−0.386699	−	0.669782i	0.605304	−	0.795994i	$-0.293051\pi$
$613$	−9.57422	−	16.5830i	−0.386699	−	0.669782i	−0.992003	+	0.126212i	$0.959718\pi$
$614$	−35.6795	+	11.8276i	−1.43991	+	0.477325i
$615$		0			0
$616$	1.53102	−	5.72206i	0.0616867	−	0.230549i
$617$	−2.45052	−	6.73275i	−0.0986543	−	0.271050i	0.880541	−	0.473970i	$-0.157179\pi$
$617$	−2.45052	−	6.73275i	−0.0986543	−	0.271050i	−0.979195	+	0.202919i	$0.934957\pi$
$618$		0			0
$619$	0.559347	−	0.0986280i	0.0224821	−	0.00396419i	−0.162396	−	0.986726i	$-0.551922\pi$
$619$	0.559347	−	0.0986280i	0.0224821	−	0.00396419i	0.184878	+	0.982761i	$0.440811\pi$
$620$	−1.83615	+	7.75558i	−0.0737415	+	0.311472i
$621$		0			0
$622$	19.4045	+	24.5350i	0.778051	+	0.983764i
$623$	0.697858	+	3.95775i	0.0279591	+	0.158564i
$624$		0			0
$625$	−13.7927	+	5.02013i	−0.551708	+	0.200805i
$626$	0.224878	−	7.76048i	0.00898795	−	0.310171i
$627$		0			0
$628$	−19.4894	+	29.6476i	−0.777711	+	1.18307i
$629$	67.7005	−	39.0869i	2.69939	−	1.55850i
$630$		0			0
$631$	16.0510	+	9.26705i	0.638980	+	0.368915i	0.784222	−	0.620481i	$-0.213063\pi$
$631$	16.0510	+	9.26705i	0.638980	+	0.368915i	−0.145242	+	0.989396i	$0.546396\pi$
$632$	37.1027	+	17.2851i	1.47586	+	0.687563i
$633$		0			0
$634$	−13.4639	−	24.9632i	−0.534720	−	0.991416i
$635$	2.19343	−	12.4396i	0.0870438	−	0.493650i
$636$		0			0
$637$	−9.84319	+	8.25942i	−0.390002	+	0.327250i
$638$	1.55734	+	10.6230i	0.0616555	+	0.420568i
$639$		0			0
$640$	8.46363	−	4.57269i	0.334554	−	0.180752i
$641$	8.67287	−	23.8285i	0.342558	−	0.941170i	−0.642092	−	0.766628i	$-0.721933\pi$
$641$	8.67287	−	23.8285i	0.342558	−	0.941170i	0.984650	−	0.174542i	$-0.0558446\pi$
$642$		0			0
$643$	18.0729	−	21.5384i	0.712725	−	0.849392i	−0.281178	−	0.959656i	$-0.590725\pi$
$643$	18.0729	−	21.5384i	0.712725	−	0.849392i	0.993902	+	0.110263i	$0.0351694\pi$
$644$	−11.2197	+	1.31411i	−0.442118	+	0.0517833i
$645$		0			0
$646$	34.9432	−	39.2748i	1.37482	−	1.54525i
$647$	26.2892			1.03353			0.516767	−	0.856126i	$-0.327135\pi$
$647$	26.2892			1.03353			0.516767	+	0.856126i	$0.327135\pi$
$648$		0			0
$649$	−24.7773			−0.972595
$650$	8.66904	−	9.74367i	0.340028	−	0.382178i
$651$		0			0
$652$	−35.8340	+	4.19708i	−1.40337	+	0.164370i
$653$	−3.30137	+	3.93442i	−0.129193	+	0.153966i	−0.826763	−	0.562551i	$-0.809820\pi$
$653$	−3.30137	+	3.93442i	−0.129193	+	0.153966i	0.697570	+	0.716516i	$0.254265\pi$
$654$		0			0
$655$	0.912891	−	2.50815i	0.0356696	−	0.0980014i
$656$	16.2191	−	0.952439i	0.633251	−	0.0371865i
$657$		0			0
$658$	0.913984	+	6.23452i	0.0356308	+	0.243047i
$659$	6.33669	−	5.31712i	0.246842	−	0.207125i	−0.510969	−	0.859599i	$-0.670713\pi$
$659$	6.33669	−	5.31712i	0.246842	−	0.207125i	0.757811	+	0.652474i	$0.226269\pi$
$660$		0			0
$661$	0.914795	−	5.18806i	0.0355814	−	0.201792i	−0.961835	−	0.273630i	$-0.911775\pi$
$661$	0.914795	−	5.18806i	0.0355814	−	0.201792i	0.997416	+	0.0718384i	$0.0228866\pi$
$662$	−15.6884	−	29.0876i	−0.609745	−	1.13052i
$663$		0			0
$664$	6.30199	−	13.5273i	0.244565	−	0.524962i
$665$	3.80888	+	2.19906i	0.147702	+	0.0852759i
$666$		0			0
$667$	17.7324	−	10.2378i	0.686601	−	0.396409i
$668$	17.6583	−	26.8621i	0.683219	−	1.03932i
$669$		0			0
$670$	0.226432	−	7.81409i	0.00874783	−	0.301885i
$671$	1.03208	−	0.375647i	0.0398431	−	0.0145017i
$672$		0			0
$673$	2.65489	+	15.0566i	0.102338	+	0.580390i	0.992250	+	0.124257i	$0.0396547\pi$
$673$	2.65489	+	15.0566i	0.102338	+	0.580390i	−0.889912	+	0.456133i	$0.849234\pi$
$674$	5.59402	+	7.07305i	0.215474	+	0.272444i
$675$		0			0
$676$	3.84780	−	16.2525i	0.147992	−	0.625095i
$677$	24.0011	−	4.23205i	0.922439	−	0.162651i	0.307792	−	0.951454i	$-0.400410\pi$
$677$	24.0011	−	4.23205i	0.922439	−	0.162651i	0.614647	+	0.788803i	$0.289299\pi$
$678$		0			0
$679$	1.52607	+	4.19285i	0.0585653	+	0.160907i
$680$	−17.0323	−	4.55723i	−0.653157	−	0.174762i
$681$		0			0
$682$	12.9151	−	4.28132i	0.494546	−	0.163940i
$683$	12.9096	+	22.3600i	0.493971	+	0.855582i	0.999976	−	0.00694804i	$-0.00221165\pi$
$683$	12.9096	+	22.3600i	0.493971	+	0.855582i	−0.506005	+	0.862530i	$0.668878\pi$
$684$		0			0
$685$	−5.10734	+	8.84617i	−0.195141	+	0.337995i
$686$	3.77854	−	18.3106i	0.144265	−	0.699100i
$687$		0			0
$688$	17.5686	+	13.0663i	0.669796	+	0.498147i
$689$	−11.8057	−	2.08167i	−0.449762	−	0.0793051i
$690$		0			0
$691$	6.26030	+	7.46074i	0.238153	+	0.283820i	0.871862	−	0.489752i	$-0.162913\pi$
$691$	6.26030	+	7.46074i	0.238153	+	0.283820i	−0.633709	+	0.773572i	$0.718468\pi$
$692$	−7.49619	+	7.94930i	−0.284962	+	0.302187i
$693$		0			0
$694$	−8.43176	+	21.2314i	−0.320065	+	0.805933i
$695$	−2.29673	−	0.835942i	−0.0871200	−	0.0317091i
$696$		0			0
$697$	−22.8110	−	19.1407i	−0.864030	−	0.725007i
$698$	25.3294	+	15.6192i	0.958733	+	0.591197i
$699$		0			0
$700$	−0.505307	+	8.71166i	−0.0190988	+	0.329270i
$701$			46.8518i			1.76957i	0.466000	+	0.884785i	$0.345695\pi$
$701$			46.8518i			1.76957i	−0.466000	+	0.884785i	$0.654305\pi$
$702$		0			0
$703$			54.0663i			2.03915i
$704$	−14.2286	−	8.20130i	−0.536261	−	0.309098i
$705$		0			0
$706$	−7.13853	+	11.5764i	−0.268662	+	0.435684i
$707$	4.72329	+	3.96331i	0.177638	+	0.149056i
$708$		0			0
$709$	25.0301	+	9.11022i	0.940026	+	0.342142i	0.766176	−	0.642631i	$-0.222157\pi$
$709$	25.0301	+	9.11022i	0.940026	+	0.342142i	0.173850	+	0.984772i	$0.444379\pi$
$710$	−13.0984	−	5.20185i	−0.491574	−	0.195222i
$711$		0			0
$712$	11.1004	+	0.967151i	0.416006	+	0.0362455i
$713$	−16.6793	−	19.8776i	−0.624646	−	0.744424i
$714$		0			0
$715$	3.70651	+	0.653558i	0.138616	+	0.0244417i
$716$	24.7513	+	10.6696i	0.924999	+	0.398744i
$717$		0			0
$718$	−19.4349	−	4.01055i	−0.725303	−	0.149673i
$719$	19.9787	−	34.6042i	0.745081	−	1.29052i	−0.205076	−	0.978746i	$-0.565744\pi$
$719$	19.9787	−	34.6042i	0.745081	−	1.29052i	0.950157	−	0.311772i	$-0.100922\pi$
$720$		0			0
$721$	−0.0873226	−	0.151247i	−0.00325206	−	0.00563274i
$722$	2.98540	+	9.00584i	0.111105	+	0.335163i
$723$		0			0
$724$	22.9994	−	17.1309i	0.854765	−	0.636666i
$725$	−5.40977	−	14.8632i	−0.200914	−	0.552006i
$726$		0			0
$727$	46.3051	−	8.16484i	1.71736	−	0.302817i	0.773657	−	0.633605i	$-0.218426\pi$
$727$	46.3051	−	8.16484i	1.71736	−	0.302817i	0.943705	+	0.330788i	$0.107314\pi$
$728$	−2.63131	−	5.63759i	−0.0975230	−	0.208943i
$729$		0			0
$730$	−1.45169	+	1.14813i	−0.0537294	+	0.0424942i
$731$	−6.96831	−	39.5192i	−0.257732	−	1.46167i
$732$		0			0
$733$	−10.6192	+	3.86508i	−0.392230	+	0.142760i	−0.530604	−	0.847620i	$-0.678035\pi$
$733$	−10.6192	+	3.86508i	−0.392230	+	0.142760i	0.138374	+	0.990380i	$0.455812\pi$
$734$	−52.4332	−	1.51938i	−1.93534	−	0.0560812i
$735$		0			0
$736$	−4.52078	+	30.9922i	−0.166638	+	1.14239i
$737$	−11.5577	+	6.67287i	−0.425735	+	0.245798i
$738$		0			0
$739$	−27.1693	−	15.6862i	−0.999438	−	0.577026i	−0.0913557	−	0.995818i	$-0.529120\pi$
$739$	−27.1693	−	15.6862i	−0.999438	−	0.577026i	−0.908082	+	0.418793i	$0.862453\pi$
$740$	16.2027	−	8.14215i	0.595623	−	0.299311i
$741$		0			0
$742$	7.05966	−	3.80762i	0.259168	−	0.139782i
$743$	1.81455	−	10.2908i	0.0665695	−	0.377535i	−0.933262	−	0.359196i	$-0.883051\pi$
$743$	1.81455	−	10.2908i	0.0665695	−	0.377535i	0.999832	−	0.0183390i	$-0.00583781\pi$
$744$		0			0
$745$	7.22511	−	6.06259i	0.264708	−	0.222116i
$746$	−39.6714	+	5.81585i	−1.45247	+	0.212933i
$747$		0			0
$748$	8.63971	+	28.8335i	0.315899	+	1.05426i
$749$	−2.85150	+	7.83444i	−0.104192	+	0.286264i
$750$		0			0
$751$	6.54549	−	7.80061i	0.238848	−	0.284648i	−0.633283	−	0.773920i	$-0.718293\pi$
$751$	6.54549	−	7.80061i	0.238848	−	0.284648i	0.872131	+	0.489272i	$0.162737\pi$
$752$	17.3533	+	2.01991i	0.632811	+	0.0736584i
$753$		0			0
$754$	8.42498	+	7.49579i	0.306820	+	0.272981i
$755$	5.00678			0.182215
$756$		0			0
$757$	46.4748			1.68916			0.844578	−	0.535433i	$-0.179851\pi$
$757$	46.4748			1.68916			0.844578	+	0.535433i	$0.179851\pi$
$758$	16.1914	+	14.4056i	0.588097	+	0.523236i
$759$		0			0
$760$	8.61948	−	8.62567i	0.312662	−	0.312886i
$761$	−34.3388	+	40.9234i	−1.24478	+	1.48347i	−0.430942	+	0.902380i	$0.641819\pi$
$761$	−34.3388	+	40.9234i	−1.24478	+	1.48347i	−0.813838	+	0.581092i	$0.802626\pi$
$762$		0			0
$763$	6.69273	−	18.3881i	0.242293	−	0.665694i
$764$	16.0846	−	4.81960i	0.581921	−	0.174367i
$765$		0			0
$766$	51.5013	−	7.55012i	1.86082	−	0.272797i
$767$	−19.9357	+	16.7280i	−0.719837	+	0.604015i
$768$		0			0
$769$	4.11818	−	23.3554i	0.148506	−	0.842217i	−0.815980	−	0.578080i	$-0.803802\pi$
$769$	4.11818	−	23.3554i	0.148506	−	0.842217i	0.964485	−	0.264136i	$-0.0850869\pi$
$770$	−2.21645	+	1.19544i	−0.0798751	+	0.0430806i
$771$		0			0
$772$	1.10966	+	2.20820i	0.0399376	+	0.0794748i
$773$	−24.4917	−	14.1403i	−0.880907	−	0.508592i	−0.00994940	−	0.999951i	$-0.503167\pi$
$773$	−24.4917	−	14.1403i	−0.880907	−	0.508592i	−0.870957	+	0.491359i	$0.836500\pi$
$774$		0			0
$775$	−17.3593	+	10.0224i	−0.623565	+	0.360015i
$776$	12.3236	−	1.08263i	0.442393	−	0.0388642i
$777$		0			0
$778$	−12.7071	−	0.368219i	−0.455572	−	0.0132013i
$779$	19.3527	−	7.04382i	0.693384	−	0.252371i
$780$		0			0
$781$	4.17803	+	23.6948i	0.149502	+	0.847866i
$782$	45.0242	−	35.6093i	1.61006	−	1.27338i
$783$		0			0
$784$	−21.3069	−	10.6880i	−0.760959	−	0.381713i
$785$	14.8548	−	2.61931i	0.530192	−	0.0934872i
$786$		0			0
$787$	−2.69409	−	7.40195i	−0.0960339	−	0.263851i	0.882369	−	0.470558i	$-0.155947\pi$
$787$	−2.69409	−	7.40195i	−0.0960339	−	0.263851i	−0.978403	+	0.206707i	$0.933725\pi$
$788$	3.49237	+	4.68873i	0.124411	+	0.167029i
$789$		0			0
$790$	−5.47560	−	16.5178i	−0.194813	−	0.587677i
$791$	2.53715	+	4.39448i	0.0902108	+	0.156250i
$792$		0			0
$793$	0.576796	−	0.999040i	0.0204826	−	0.0354769i
$794$	6.53000	+	1.34752i	0.231741	+	0.0478218i
$795$		0			0
$796$	11.4286	−	26.5119i	0.405076	−	0.939689i
$797$	−1.80271	−	0.317867i	−0.0638553	−	0.0112594i	0.141629	−	0.989920i	$-0.454766\pi$
$797$	−1.80271	−	0.317867i	−0.0638553	−	0.0112594i	−0.205485	+	0.978660i	$0.565877\pi$
$798$		0			0
$799$	−20.5821	−	24.5288i	−0.728141	−	0.867765i
$800$	22.9709	+	7.59650i	0.812145	+	0.268577i
$801$		0			0
$802$	22.5858	+	8.96964i	0.797532	+	0.316729i
$803$	2.96918	+	1.08069i	0.104780	+	0.0381368i
$804$		0			0
$805$	3.67900	+	3.08704i	0.129668	+	0.108804i
$806$	7.50098	−	12.1642i	0.264211	−	0.428465i
$807$		0			0
$808$	14.0001	−	9.81046i	0.492522	−	0.345131i
$809$			0.784403i			0.0275781i	0.999905	+	0.0137891i	$0.00438933\pi$
$809$			0.784403i			0.0275781i	−0.999905	+	0.0137891i	$0.995611\pi$
$810$		0			0
$811$		−	41.4637i		−	1.45599i	−0.685584	−	0.727994i	$-0.740453\pi$
$811$		−	41.4637i		−	1.45599i	0.685584	−	0.727994i	$-0.259547\pi$
$812$	−7.53264	−	0.436919i	−0.264344	−	0.0153329i
$813$		0			0
$814$	−26.3502	−	16.2487i	−0.923573	−	0.569516i
$815$	11.7502	+	9.85955i	0.411590	+	0.345365i
$816$		0			0
$817$	26.0800	+	9.49236i	0.912425	+	0.332096i
$818$	−10.0825	+	25.3881i	−0.352528	+	0.887675i
$819$		0			0
$820$	−5.02535	−	4.73890i	−0.175493	−	0.165490i
$821$	1.49518	+	1.78189i	0.0521823	+	0.0621884i	0.791504	−	0.611164i	$-0.209298\pi$
$821$	1.49518	+	1.78189i	0.0521823	+	0.0621884i	−0.739322	+	0.673352i	$0.764854\pi$
$822$		0			0
$823$	44.3729	+	7.82414i	1.54674	+	0.272732i	0.880879	−	0.473341i	$-0.156952\pi$
$823$	44.3729	+	7.82414i	1.54674	+	0.272732i	0.665863	+	0.746074i	$0.268063\pi$
$824$	−0.467674	+	0.125493i	−0.0162922	+	0.00437175i
$825$		0			0
$826$	3.51912	−	17.0534i	0.122446	−	0.593364i
$827$	−20.6443	+	35.7571i	−0.717874	+	1.24339i	0.243966	+	0.969784i	$0.421551\pi$
$827$	−20.6443	+	35.7571i	−0.717874	+	1.24339i	−0.961840	+	0.273611i	$0.911782\pi$
$828$		0			0
$829$	−2.75417	−	4.77037i	−0.0956564	−	0.165682i	0.814226	−	0.580548i	$-0.197162\pi$
$829$	−2.75417	−	4.77037i	−0.0956564	−	0.165682i	−0.909882	+	0.414866i	$0.863828\pi$
$830$	−6.02226	+	1.99636i	−0.209036	+	0.0692946i
$831$		0			0
$832$	−16.9853	+	3.00752i	−0.588858	+	0.104267i
$833$	14.9425	+	41.0542i	0.517728	+	1.42245i
$834$		0			0
$835$	−13.4592	+	2.37321i	−0.465774	+	0.0821285i
$836$	−20.2578	−	4.79606i	−0.700629	−	0.165875i
$837$		0			0
$838$	−13.4612	−	17.0203i	−0.465011	−	0.587957i
$839$	4.43317	+	25.1418i	0.153050	+	0.867990i	0.960547	+	0.278118i	$0.0897107\pi$
$839$	4.43317	+	25.1418i	0.153050	+	0.867990i	−0.807497	+	0.589872i	$0.799178\pi$
$840$		0			0
$841$	−14.3994	+	5.24096i	−0.496532	+	0.180723i
$842$	0.952967	−	32.8866i	0.0328414	−	1.13335i
$843$		0			0
$844$	9.32209	+	6.12805i	0.320880	+	0.210936i
$845$	−6.14933	+	3.55032i	−0.211543	+	0.122135i
$846$		0			0
$847$	−5.99495	−	3.46119i	−0.205989	−	0.118928i
$848$	−5.13901	−	21.6371i	−0.176474	−	0.743020i
$849$		0			0
$850$	−21.0502	−	39.0288i	−0.722015	−	1.33868i
$851$	−10.2519	+	58.1415i	−0.351431	+	1.99306i
$852$		0			0
$853$	35.0320	−	29.3953i	1.19947	−	1.00648i	0.199827	−	0.979831i	$-0.435962\pi$
$853$	35.0320	−	29.3953i	1.19947	−	1.00648i	0.999645	−	0.0266448i	$-0.00848230\pi$
$854$	0.111959	+	0.763702i	0.00383116	+	0.0261333i
$855$		0			0
$856$	18.9400	+	13.2518i	0.647357	+	0.452938i
$857$	14.1429	−	38.8574i	0.483113	−	1.32734i	−0.423697	−	0.905804i	$-0.639268\pi$
$857$	14.1429	−	38.8574i	0.483113	−	1.32734i	0.906810	−	0.421539i	$-0.138510\pi$
$858$		0			0
$859$	−36.1399	+	43.0699i	−1.23308	+	1.46953i	−0.399866	+	0.916574i	$0.630943\pi$
$859$	−36.1399	+	43.0699i	−1.23308	+	1.46953i	−0.833213	+	0.552952i	$0.813501\pi$
$860$	−1.08285	−	9.24524i	−0.0369250	−	0.315260i
$861$		0			0
$862$	−15.8614	+	17.8276i	−0.540243	+	0.607212i
$863$	−12.4602			−0.424150			−0.212075	−	0.977253i	$-0.568022\pi$
$863$	−12.4602			−0.424150			−0.212075	+	0.977253i	$0.568022\pi$
$864$		0			0
$865$	4.64525			0.157943
$866$	2.62693	−	2.95257i	0.0892668	−	0.100332i
$867$		0			0
$868$	1.11236	+	9.49713i	0.0377559	+	0.322354i
$869$	−19.0960	+	22.7577i	−0.647786	+	0.772002i
$870$		0			0
$871$	−4.79421	+	13.1720i	−0.162446	+	0.446316i
$872$	−44.4539	−	31.1032i	−1.50540	−	1.05329i
$873$		0			0
$874$	5.75870	+	39.2816i	0.194791	+	1.32872i
$875$	6.16435	−	5.17251i	0.208393	−	0.174863i
$876$		0			0
$877$	−3.26229	+	18.5014i	−0.110160	+	0.624747i	0.878873	+	0.477055i	$0.158296\pi$
$877$	−3.26229	+	18.5014i	−0.110160	+	0.624747i	−0.989033	+	0.147693i	$0.952815\pi$
$878$	3.78200	+	7.01215i	0.127636	+	0.236649i
$879$		0			0
$880$	1.61344	+	6.79316i	0.0543890	+	0.228997i
$881$	13.9892	+	8.07667i	0.471308	+	0.272110i	0.716787	−	0.697292i	$-0.245612\pi$
$881$	13.9892	+	8.07667i	0.471308	+	0.272110i	−0.245479	+	0.969402i	$0.578945\pi$
$882$		0			0
$883$	−1.99218	+	1.15019i	−0.0670423	+	0.0387069i	−0.533146	−	0.846023i	$-0.678991\pi$
$883$	−1.99218	+	1.15019i	−0.0670423	+	0.0387069i	0.466104	+	0.884730i	$0.345657\pi$
$884$	26.4180	+	17.3664i	0.888534	+	0.584094i
$885$		0			0
$886$	0.224204	−	7.73720i	0.00753228	−	0.259936i
$887$	−9.36820	+	3.40975i	−0.314553	+	0.114488i	−0.494472	−	0.869193i	$-0.664639\pi$
$887$	−9.36820	+	3.40975i	−0.314553	+	0.114488i	0.179919	+	0.983681i	$0.442416\pi$
$888$		0			0
$889$	−2.63159	−	14.9245i	−0.0882608	−	0.500552i
$890$	−2.93860	−	3.71555i	−0.0985020	−	0.124545i
$891$		0			0
$892$	−26.4467	−	6.26131i	−0.885502	−	0.209644i
$893$	21.8091	−	3.84554i	0.729815	−	0.128686i
$894$		0			0
$895$	−3.91918	−	10.7679i	−0.131004	−	0.359930i
$896$	7.66557	−	8.62826i	0.256089	−	0.288250i
$897$		0			0
$898$	−33.0873	+	10.9683i	−1.10414	+	0.366018i
$899$	−8.66598	−	15.0099i	−0.289027	−	0.500609i
$900$		0			0
$901$	−20.3798	+	35.2989i	−0.678951	+	1.17598i
$902$	−2.38320	+	11.5488i	−0.0793518	+	0.384533i
$903$		0			0
$904$	13.5883	−	3.64618i	0.451939	−	0.121270i
$905$	−12.0071	−	2.11718i	−0.399131	−	0.0703775i
$906$		0			0
$907$	−17.6103	−	20.9872i	−0.584741	−	0.696868i	0.389845	−	0.920881i	$-0.372529\pi$
$907$	−17.6103	−	20.9872i	−0.584741	−	0.696868i	−0.974586	+	0.224013i	$0.928084\pi$
$908$	−26.1643	−	24.6729i	−0.868293	−	0.818800i
$909$		0			0
$910$	−0.976258	+	2.45824i	−0.0323626	+	0.0814900i
$911$	−43.0029	−	15.6518i	−1.42475	−	0.518566i	−0.489327	−	0.872100i	$-0.662758\pi$
$911$	−43.0029	−	15.6518i	−1.42475	−	0.518566i	−0.935422	+	0.353534i	$0.884980\pi$
$912$		0			0
$913$	8.29727	+	6.96224i	0.274600	+	0.230416i
$914$	13.7260	+	8.46409i	0.454017	+	0.279967i
$915$		0			0
$916$	−27.7329	−	1.60860i	−0.916320	−	0.0531498i
$917$		−	3.20230i		−	0.105749i
$918$		0			0
$919$			35.8178i			1.18152i	0.806847	+	0.590760i	$0.201172\pi$
$919$			35.8178i			1.18152i	−0.806847	+	0.590760i	$0.798828\pi$
$920$	10.9048	−	7.64142i	0.359519	−	0.251930i
$921$		0			0
$922$	13.8800	−	22.5090i	0.457114	−	0.741293i
$923$	19.3588	+	16.2440i	0.637203	+	0.534676i
$924$		0			0
$925$	42.8560	+	15.5983i	1.40910	+	0.512869i
$926$	46.5616	+	18.4913i	1.53011	+	0.607661i
$927$		0			0
$928$	−6.56841	+	19.8621i	−0.215618	+	0.652005i
$929$	9.73496	+	11.6017i	0.319394	+	0.380639i	0.901723	−	0.432314i	$-0.142303\pi$
$929$	9.73496	+	11.6017i	0.319394	+	0.380639i	−0.582329	+	0.812953i	$0.697859\pi$
$930$		0			0
$931$	−29.7570	−	5.24696i	−0.975246	−	0.171962i
$932$	−1.93817	+	4.49614i	−0.0634869	+	0.147276i
$933$		0			0
$934$	4.50221	+	0.929069i	0.147317	+	0.0304001i
$935$	6.39844	−	11.0824i	0.209251	−	0.362434i
$936$		0			0
$937$	−20.1768	−	34.9472i	−0.659147	−	1.14168i	−0.980837	−	0.194831i	$-0.937584\pi$
$937$	−20.1768	−	34.9472i	−0.659147	−	1.14168i	0.321690	−	0.946845i	$-0.395749\pi$
$938$	−2.95117	−	8.90256i	−0.0963591	−	0.290679i
$939$		0			0
$940$	−4.43680	−	5.95669i	−0.144713	−	0.194286i
$941$	12.8302	+	35.2506i	0.418252	+	1.14914i	0.952694	+	0.303932i	$0.0982995\pi$
$941$	12.8302	+	35.2506i	0.418252	+	1.14914i	−0.534442	+	0.845205i	$0.679478\pi$
$942$		0			0
$943$	22.1471	−	3.90513i	0.721208	−	0.127168i
$944$	−43.1534	−	21.6466i	−1.40452	−	0.704538i
$945$		0			0
$946$	−12.4642	+	9.85782i	−0.405245	+	0.320505i
$947$	−1.96803	−	11.1613i	−0.0639525	−	0.362693i	−0.999943	−	0.0106676i	$-0.996604\pi$
$947$	−1.96803	−	11.1613i	−0.0639525	−	0.362693i	0.935991	−	0.352025i	$-0.114507\pi$
$948$		0			0
$949$	3.11860	−	1.13508i	0.101234	−	0.0368462i
$950$	30.6559	+	0.888329i	0.994610	+	0.0288212i
$951$		0			0
$952$	−21.0723	+	1.85120i	−0.682956	+	0.0599977i
$953$	−34.5149	+	19.9272i	−1.11805	+	0.645505i	−0.940902	−	0.338680i	$-0.890020\pi$
$953$	−34.5149	+	19.9272i	−1.11805	+	0.645505i	−0.177145	+	0.984185i	$0.556686\pi$
$954$		0			0
$955$	−6.18226	−	3.56933i	−0.200053	−	0.115501i
$956$	13.8349	+	27.5310i	0.447451	+	0.890418i
$957$		0			0
$958$	−48.4091	+	26.1094i	−1.56403	+	0.843557i
$959$	−2.12809	+	12.0690i	−0.0687195	+	0.389728i
$960$		0			0
$961$	6.92155	−	5.80787i	0.223276	−	0.187351i
$962$	−32.1713	+	4.71633i	−1.03724	+	0.152060i
$963$		0			0
$964$	22.3938	−	6.71011i	0.721257	−	0.216118i
$965$	0.359351	−	0.987308i	0.0115679	−	0.0317826i
$966$		0			0
$967$	−12.8413	+	15.3037i	−0.412948	+	0.492132i	−0.931923	−	0.362657i	$-0.881870\pi$
$967$	−12.8413	+	15.3037i	−0.412948	+	0.492132i	0.518974	+	0.854790i	$0.326314\pi$
$968$	−13.5665	+	13.5763i	−0.436045	+	0.436358i
$969$		0			0
$970$	−3.92939	−	3.49602i	−0.126165	−	0.112250i
$971$	−7.27802			−0.233563			−0.116781	−	0.993158i	$-0.537258\pi$
$971$	−7.27802			−0.233563			−0.116781	+	0.993158i	$0.537258\pi$
$972$		0			0
$973$	−2.93237			−0.0940074
$974$	15.3048	+	13.6168i	0.490396	+	0.436310i
$975$		0			0
$976$	2.12571	+	0.247430i	0.0680423	+	0.00792003i
$977$	11.3127	−	13.4819i	0.361925	−	0.431325i	−0.554098	−	0.832451i	$-0.686937\pi$
$977$	11.3127	−	13.4819i	0.361925	−	0.431325i	0.916023	+	0.401126i	$0.131381\pi$
$978$		0			0
$979$	−2.76599	+	7.59951i	−0.0884015	+	0.242881i
$980$	2.90886	+	9.70782i	0.0929201	+	0.310105i
$981$		0			0
$982$	−10.2037	+	1.49587i	−0.325614	+	0.0477352i
$983$	−30.8633	+	25.8973i	−0.984385	+	0.825997i	−0.984745	−	0.174003i	$-0.944330\pi$
$983$	−30.8633	+	25.8973i	−0.984385	+	0.825997i	0.000360257		1.00000i	$0.499885\pi$
$984$		0			0
$985$	0.431616	−	2.44782i	0.0137524	−	0.0779939i
$986$	33.7467	−	18.2013i	1.07471	−	0.579647i
$987$		0			0
$988$	−19.5373	+	9.81784i	−0.621564	+	0.312347i
$989$	26.2459	+	15.1531i	0.834571	+	0.481840i
$990$		0			0
$991$	−34.6152	+	19.9851i	−1.09959	+	0.634848i	−0.936113	−	0.351700i	$-0.885604\pi$
$991$	−34.6152	+	19.9851i	−1.09959	+	0.634848i	−0.163476	+	0.986547i	$0.552271\pi$
$992$	26.2340	+	3.82670i	0.832930	+	0.121498i
$993$		0			0
$994$	−16.9017	−	0.489768i	−0.536091	−	0.0155345i
$995$	−11.5338	+	4.19796i	−0.365646	+	0.133084i
$996$		0			0
$997$	4.92799	+	27.9480i	0.156071	+	0.885123i	0.957800	+	0.287435i	$0.0928026\pi$
$997$	4.92799	+	27.9480i	0.156071	+	0.885123i	−0.801729	+	0.597688i	$0.796086\pi$
$998$	−15.9464	+	12.6119i	−0.504775	+	0.399222i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.71.4		96
3.2	odd	2		108.2.l.a.95.13	yes	96
4.3	odd	2	inner	324.2.l.a.71.3		96
9.2	odd	6		972.2.l.c.863.1		96
9.4	even	3		972.2.l.a.539.7		96
9.5	odd	6		972.2.l.d.539.10		96
9.7	even	3		972.2.l.b.863.16		96
12.11	even	2		108.2.l.a.95.14	yes	96
27.2	odd	18	inner	324.2.l.a.251.3		96
27.7	even	9		972.2.l.c.107.8		96
27.11	odd	18		972.2.l.a.431.14		96
27.16	even	9		972.2.l.d.431.3		96
27.20	odd	18		972.2.l.b.107.9		96
27.25	even	9		108.2.l.a.83.14	yes	96
36.7	odd	6		972.2.l.b.863.9		96
36.11	even	6		972.2.l.c.863.8		96
36.23	even	6		972.2.l.d.539.3		96
36.31	odd	6		972.2.l.a.539.14		96
108.7	odd	18		972.2.l.c.107.1		96
108.11	even	18		972.2.l.a.431.7		96
108.43	odd	18		972.2.l.d.431.10		96
108.47	even	18		972.2.l.b.107.16		96
108.79	odd	18		108.2.l.a.83.13	✓	96
108.83	even	18	inner	324.2.l.a.251.4		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.83.13	✓	96	108.79	odd	18
108.2.l.a.83.14	yes	96	27.25	even	9
108.2.l.a.95.13	yes	96	3.2	odd	2
108.2.l.a.95.14	yes	96	12.11	even	2
324.2.l.a.71.3		96	4.3	odd	2	inner
324.2.l.a.71.4		96	1.1	even	1	trivial
324.2.l.a.251.3		96	27.2	odd	18	inner
324.2.l.a.251.4		96	108.83	even	18	inner
972.2.l.a.431.7		96	108.11	even	18
972.2.l.a.431.14		96	27.11	odd	18
972.2.l.a.539.7		96	9.4	even	3
972.2.l.a.539.14		96	36.31	odd	6
972.2.l.b.107.9		96	27.20	odd	18
972.2.l.b.107.16		96	108.47	even	18
972.2.l.b.863.9		96	36.7	odd	6
972.2.l.b.863.16		96	9.7	even	3
972.2.l.c.107.1		96	108.7	odd	18
972.2.l.c.107.8		96	27.7	even	9
972.2.l.c.863.1		96	9.2	odd	6
972.2.l.c.863.8		96	36.11	even	6
972.2.l.d.431.3		96	27.16	even	9
972.2.l.d.431.10		96	108.43	odd	18
972.2.l.d.539.3		96	36.23	even	6
972.2.l.d.539.10		96	9.5	odd	6

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.940037 + 1.05657i) q^{2} +(-0.232661 - 1.98642i) q^{4} +(-0.546554 + 0.651358i) q^{5} +(-0.348909 + 0.958618i) q^{7} +(2.31749 + 1.62149i) q^{8} +O(q^{10})\)	\(q+(-0.940037 + 1.05657i) q^{2} +(-0.232661 - 1.98642i) q^{4} +(-0.546554 + 0.651358i) q^{5} +(-0.348909 + 0.958618i) q^{7} +(2.31749 + 1.62149i) q^{8} +(-0.174421 - 1.18977i) q^{10} +(-1.57259 + 1.31956i) q^{11} +(-0.374417 + 2.12343i) q^{13} +(-0.684856 - 1.26978i) q^{14} +(-3.89174 + 0.924324i) q^{16} +(6.34902 + 3.66561i) q^{17} +(-4.39109 + 2.53520i) q^{19} +(1.42103 + 0.934141i) q^{20} +(0.0840920 - 2.90198i) q^{22} +(-5.20278 + 1.89366i) q^{23} +(0.742695 + 4.21203i) q^{25} +(-1.89157 - 2.39170i) q^{26} +(1.98540 + 0.470046i) q^{28} +(-3.64198 + 0.642180i) q^{29} +(1.60292 + 4.40400i) q^{31} +(2.68177 - 4.98077i) q^{32} +(-9.84127 + 3.26235i) q^{34} +(-0.433706 - 0.751201i) q^{35} +(5.33157 - 9.23455i) q^{37} +(1.44919 - 7.02265i) q^{38} +(-2.32280 + 0.623286i) q^{40} +(-4.00006 - 0.705319i) q^{41} +(-3.51843 - 4.19310i) q^{43} +(2.98709 + 2.81682i) q^{44} +(2.89003 - 7.27719i) q^{46} +(-4.10423 - 1.49382i) q^{47} +(4.56510 + 3.83057i) q^{49} +(-5.14845 - 3.17476i) q^{50} +(4.30513 + 0.249713i) q^{52} +5.55975i q^{53} -1.74553i q^{55} +(-2.36298 + 1.65584i) q^{56} +(2.74510 - 4.45167i) q^{58} +(9.24583 + 7.75817i) q^{59} +(-0.502750 - 0.182986i) q^{61} +(-6.15992 - 2.44633i) q^{62} +(2.74155 + 7.51558i) q^{64} +(-1.17847 - 1.40445i) q^{65} +(6.40223 + 1.12889i) q^{67} +(5.80427 - 13.4647i) q^{68} +(1.20139 + 0.247918i) q^{70} +(5.86015 - 10.1501i) q^{71} +(-0.769587 - 1.33296i) q^{73} +(4.74503 + 14.3140i) q^{74} +(6.05760 + 8.13271i) q^{76} +(-0.716265 - 1.96792i) q^{77} +(14.2516 - 2.51294i) q^{79} +(1.52498 - 3.04011i) q^{80} +(4.50542 - 3.56330i) q^{82} +(-0.916197 - 5.19601i) q^{83} +(-5.85770 + 2.13203i) q^{85} +(7.73773 + 0.224219i) q^{86} +(-5.78413 + 0.508136i) q^{88} +(3.41168 - 1.96973i) q^{89} +(-1.90492 - 1.09981i) q^{91} +(4.97208 + 9.89434i) q^{92} +(5.43644 - 2.93214i) q^{94} +(0.748647 - 4.24579i) q^{95} +(3.35056 - 2.81145i) q^{97} +(-8.33861 + 1.22245i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

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