LMFDB - Embedded newform 405.2.r.a.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

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

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

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			8.2
Character	$\chi$	$=$	405.8
Dual form			405.2.r.a.152.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94894 + 1.36466i) q^{2} +(1.25203 - 3.43992i) q^{4} +(-0.278496 - 2.21866i) q^{5} +(-1.02475 + 2.19758i) q^{7} +(1.02263 + 3.81650i) q^{8} +O(q^{10})$	\(q+(-1.94894 + 1.36466i) q^{2} +(1.25203 - 3.43992i) q^{4} +(-0.278496 - 2.21866i) q^{5} +(-1.02475 + 2.19758i) q^{7} +(1.02263 + 3.81650i) q^{8} +(3.57049 + 3.94398i) q^{10} +(-0.00275056 + 0.00327799i) q^{11} +(0.792678 - 1.13206i) q^{13} +(-1.00178 - 5.68139i) q^{14} +(-1.59279 - 1.33651i) q^{16} +(-0.510074 + 1.90362i) q^{17} +(-6.69182 - 3.86352i) q^{19} +(-7.98068 - 1.81982i) q^{20} +(0.000887327 - 0.0101422i) q^{22} +(-6.70002 + 3.12427i) q^{23} +(-4.84488 + 1.23578i) q^{25} +3.28806i q^{26} +(6.27648 + 6.27648i) q^{28} +(1.74110 - 9.87424i) q^{29} +(-5.62932 - 2.04890i) q^{31} +(-2.94406 - 0.257571i) q^{32} +(-1.60370 - 4.40613i) q^{34} +(5.16106 + 1.66155i) q^{35} +(1.68417 + 0.451272i) q^{37} +(18.3144 - 1.60230i) q^{38} +(8.18270 - 3.33174i) q^{40} +(2.95191 - 0.520501i) q^{41} +(-0.628957 - 7.18901i) q^{43} +(0.00783223 + 0.0135658i) q^{44} +(8.79437 - 15.2323i) q^{46} +(-1.86865 - 0.871367i) q^{47} +(0.720271 + 0.858385i) q^{49} +(7.75597 - 9.02009i) q^{50} +(-2.90174 - 4.14412i) q^{52} +(-1.25315 + 1.25315i) q^{53} +(0.00803875 + 0.00518964i) q^{55} +(-9.43499 - 1.66364i) q^{56} +(10.0817 + 21.6203i) q^{58} +(-0.763311 + 0.640494i) q^{59} +(-6.39745 + 2.32848i) q^{61} +(13.7673 - 3.68893i) q^{62} +(9.69063 - 5.59489i) q^{64} +(-2.73241 - 1.44340i) q^{65} +(-7.45442 - 5.21964i) q^{67} +(5.90968 + 4.13800i) q^{68} +(-12.3261 + 3.80486i) q^{70} +(-8.32564 + 4.80681i) q^{71} +(-2.77741 + 0.744204i) q^{73} +(-3.89819 + 1.41882i) q^{74} +(-21.6685 + 18.1821i) q^{76} +(-0.00438501 - 0.00940367i) q^{77} +(6.95996 + 1.22723i) q^{79} +(-2.52167 + 3.90606i) q^{80} +(-5.04279 + 5.04279i) q^{82} +(-5.84421 - 8.34640i) q^{83} +(4.36554 + 0.601528i) q^{85} +(11.0364 + 13.1527i) q^{86} +(-0.0153232 - 0.00714534i) q^{88} +(-3.03785 + 5.26171i) q^{89} +(1.67550 + 2.90205i) q^{91} +(2.35862 + 26.9592i) q^{92} +(4.83102 - 0.851839i) q^{94} +(-6.70819 + 15.9228i) q^{95} +(12.5529 - 1.09824i) q^{97} +(-2.57517 - 0.690016i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−1.94894	+	1.36466i	−1.37811	+	0.964963i	−0.378892	+	0.925441i	$0.623695\pi$
$2$	−1.94894	+	1.36466i	−1.37811	+	0.964963i	−0.999219	+	0.0395221i	$0.987416\pi$
$3$		0			0
$3$		0			0
$4$	1.25203	−	3.43992i	0.626014	−	1.71996i
$5$	−0.278496	−	2.21866i	−0.124547	−	0.992214i
$5$	−0.278496	−	2.21866i	−0.124547	−	0.992214i
$6$		0			0
$7$	−1.02475	+	2.19758i	−0.387318	+	0.830607i	0.611895	+	0.790939i	$0.290408\pi$
$7$	−1.02475	+	2.19758i	−0.387318	+	0.830607i	−0.999213	+	0.0396673i	$0.987370\pi$
$8$	1.02263	+	3.81650i	0.361553	+	1.34934i
$9$		0			0
$10$	3.57049	+	3.94398i	1.12909	+	1.24720i
$11$	−0.00275056	+	0.00327799i	−0.000829324	+	0.000988350i	−0.766459	−	0.642293i	$-0.777983\pi$
$11$	−0.00275056	+	0.00327799i	−0.000829324	+	0.000988350i	0.765630	+	0.643282i	$0.222428\pi$
$12$		0			0
$13$	0.792678	−	1.13206i	0.219849	−	0.313977i	−0.694043	−	0.719933i	$-0.744172\pi$
$13$	0.792678	−	1.13206i	0.219849	−	0.313977i	0.913893	+	0.405956i	$0.133061\pi$
$14$	−1.00178	−	5.68139i	−0.267738	−	1.51842i
$15$		0			0
$16$	−1.59279	−	1.33651i	−0.398197	−	0.334127i
$17$	−0.510074	+	1.90362i	−0.123711	+	0.461696i	−0.999790	−	0.0204707i	$-0.993484\pi$
$17$	−0.510074	+	1.90362i	−0.123711	+	0.461696i	0.876079	+	0.482167i	$0.160150\pi$
$18$		0			0
$19$	−6.69182	−	3.86352i	−1.53521	−	0.886353i	−0.999109	−	0.0421981i	$-0.986564\pi$
$19$	−6.69182	−	3.86352i	−1.53521	−	0.886353i	−0.536099	−	0.844155i	$-0.680103\pi$
$20$	−7.98068	−	1.81982i	−1.78453	−	0.406923i
$21$		0			0
$22$	0.000887327	−	0.0101422i	0.000189179	−	0.00216232i
$23$	−6.70002	+	3.12427i	−1.39705	+	0.651456i	−0.967798	−	0.251729i	$-0.919001\pi$
$23$	−6.70002	+	3.12427i	−1.39705	+	0.651456i	−0.429253	+	0.903184i	$0.641223\pi$
$24$		0			0
$25$	−4.84488	+	1.23578i	−0.968976	+	0.247155i
$26$			3.28806i			0.644842i
$27$		0			0
$28$	6.27648	+	6.27648i	1.18614	+	1.18614i
$29$	1.74110	−	9.87424i	0.323313	−	1.83360i	−0.197959	−	0.980210i	$-0.563431\pi$
$29$	1.74110	−	9.87424i	0.323313	−	1.83360i	0.521272	−	0.853391i	$-0.325458\pi$
$30$		0			0
$31$	−5.62932	−	2.04890i	−1.01106	−	0.367994i	−0.217217	−	0.976123i	$-0.569698\pi$
$31$	−5.62932	−	2.04890i	−1.01106	−	0.367994i	−0.793838	+	0.608129i	$0.791920\pi$
$32$	−2.94406	−	0.257571i	−0.520440	−	0.0455326i
$33$		0			0
$34$	−1.60370	−	4.40613i	−0.275032	−	0.755645i
$35$	5.16106	+	1.66155i	0.872379	+	0.280853i
$36$		0			0
$37$	1.68417	+	0.451272i	0.276876	+	0.0741887i	0.394585	−	0.918859i	$-0.370888\pi$
$37$	1.68417	+	0.451272i	0.276876	+	0.0741887i	−0.117709	+	0.993048i	$0.537555\pi$
$38$	18.3144	−	1.60230i	2.97098	−	0.259927i
$39$		0			0
$40$	8.18270	−	3.33174i	1.29380	−	0.526795i
$41$	2.95191	−	0.520501i	0.461011	−	0.0812887i	0.0616809	−	0.998096i	$-0.480354\pi$
$41$	2.95191	−	0.520501i	0.461011	−	0.0812887i	0.399330	+	0.916807i	$0.369243\pi$
$42$		0			0
$43$	−0.628957	−	7.18901i	−0.0959151	−	1.09631i	−0.879779	−	0.475382i	$-0.842310\pi$
$43$	−0.628957	−	7.18901i	−0.0959151	−	1.09631i	0.783864	−	0.620932i	$-0.213246\pi$
$44$	0.00783223	+	0.0135658i	0.00118075	+	0.00204512i
$45$		0			0
$46$	8.79437	−	15.2323i	1.29666	−	2.24588i
$47$	−1.86865	−	0.871367i	−0.272571	−	0.127102i	0.281527	−	0.959553i	$-0.409159\pi$
$47$	−1.86865	−	0.871367i	−0.272571	−	0.127102i	−0.554098	+	0.832451i	$0.686937\pi$
$48$		0			0
$49$	0.720271	+	0.858385i	0.102896	+	0.122626i
$50$	7.75597	−	9.02009i	1.09686	−	1.27563i
$51$		0			0
$52$	−2.90174	−	4.14412i	−0.402399	−	0.574686i
$53$	−1.25315	+	1.25315i	−0.172134	+	0.172134i	−0.787916	−	0.615782i	$-0.788840\pi$
$53$	−1.25315	+	1.25315i	−0.172134	+	0.172134i	0.615782	+	0.787916i	$0.288840\pi$
$54$		0			0
$55$	0.00803875	+	0.00518964i	0.00108394	+	0.000699770i
$56$	−9.43499	−	1.66364i	−1.26080	−	0.222314i
$57$		0			0
$58$	10.0817	+	21.6203i	1.32380	+	2.83889i
$59$	−0.763311	+	0.640494i	−0.0993747	+	0.0833853i	−0.691121	−	0.722739i	$-0.742883\pi$
$59$	−0.763311	+	0.640494i	−0.0993747	+	0.0833853i	0.591747	+	0.806124i	$0.298439\pi$
$60$		0			0
$61$	−6.39745	+	2.32848i	−0.819109	+	0.298131i	−0.717381	−	0.696681i	$-0.754659\pi$
$61$	−6.39745	+	2.32848i	−0.819109	+	0.298131i	−0.101728	+	0.994812i	$0.532437\pi$
$62$	13.7673	−	3.68893i	1.74845	−	0.468495i
$63$		0			0
$64$	9.69063	−	5.59489i	1.21133	−	0.699361i
$65$	−2.73241	−	1.44340i	−0.338914	−	0.179032i
$66$		0			0
$67$	−7.45442	−	5.21964i	−0.910702	−	0.637680i	0.0214414	−	0.999770i	$-0.493174\pi$
$67$	−7.45442	−	5.21964i	−0.910702	−	0.637680i	−0.932143	+	0.362090i	$0.882063\pi$
$68$	5.90968	+	4.13800i	0.716654	+	0.501806i
$69$		0			0
$70$	−12.3261	+	3.80486i	−1.47325	+	0.454767i
$71$	−8.32564	+	4.80681i	−0.988072	+	0.570464i	−0.904697	−	0.426055i	$-0.859903\pi$
$71$	−8.32564	+	4.80681i	−0.988072	+	0.570464i	−0.0833745	+	0.996518i	$0.526570\pi$
$72$		0			0
$73$	−2.77741	+	0.744204i	−0.325071	+	0.0871025i	−0.417664	−	0.908602i	$-0.637151\pi$
$73$	−2.77741	+	0.744204i	−0.325071	+	0.0871025i	0.0925931	+	0.995704i	$0.470484\pi$
$74$	−3.89819	+	1.41882i	−0.453155	+	0.164935i
$75$		0			0
$76$	−21.6685	+	18.1821i	−2.48555	+	2.08563i
$77$	−0.00438501	−	0.00940367i	−0.000499718	−	0.00107165i
$78$		0			0
$79$	6.95996	+	1.22723i	0.783057	+	0.138074i	0.550863	−	0.834595i	$-0.314299\pi$
$79$	6.95996	+	1.22723i	0.783057	+	0.138074i	0.232194	+	0.972670i	$0.425410\pi$
$80$	−2.52167	+	3.90606i	−0.281931	+	0.436711i
$81$		0			0
$82$	−5.04279	+	5.04279i	−0.556883	+	0.556883i
$83$	−5.84421	−	8.34640i	−0.641485	−	0.916136i	0.358363	−	0.933582i	$-0.383335\pi$
$83$	−5.84421	−	8.34640i	−0.641485	−	0.916136i	−0.999848	+	0.0174466i	$0.994446\pi$
$84$		0			0
$85$	4.36554	+	0.601528i	0.473509	+	0.0652448i
$86$	11.0364	+	13.1527i	1.19008	+	1.41829i
$87$		0			0
$88$	−0.0153232	−	0.00714534i	−0.00163346	−	0.000761696i
$89$	−3.03785	+	5.26171i	−0.322012	+	0.557741i	−0.980903	−	0.194498i	$-0.937692\pi$
$89$	−3.03785	+	5.26171i	−0.322012	+	0.557741i	0.658891	+	0.752238i	$0.271026\pi$
$90$		0			0
$91$	1.67550	+	2.90205i	0.175640	+	0.304217i
$92$	2.35862	+	26.9592i	0.245904	+	2.81069i
$93$		0			0
$94$	4.83102	−	0.851839i	0.498281	−	0.0878604i
$95$	−6.70819	+	15.9228i	−0.688245	+	1.63365i
$96$		0			0
$97$	12.5529	−	1.09824i	1.27456	−	0.111509i	0.570289	−	0.821444i	$-0.306831\pi$
$97$	12.5529	−	1.09824i	1.27456	−	0.111509i	0.704267	+	0.709935i	$0.251276\pi$
$98$	−2.57517	−	0.690016i	−0.260132	−	0.0697021i
$99$		0			0
$100$	−1.81496	+	18.2132i	−0.181496	+	1.82132i
$101$	1.67645	+	4.60600i	0.166813	+	0.458314i	0.994729	−	0.102537i	$-0.0326961\pi$
$101$	1.67645	+	4.60600i	0.166813	+	0.458314i	−0.827916	+	0.560852i	$0.810474\pi$
$102$		0			0
$103$	−11.5458	−	1.01013i	−1.13764	−	0.0995307i	−0.497269	−	0.867596i	$-0.665664\pi$
$103$	−11.5458	−	1.01013i	−1.13764	−	0.0995307i	−0.640371	+	0.768066i	$0.721219\pi$
$104$	5.13112	+	1.86758i	0.503148	+	0.183131i
$105$		0			0
$106$	0.732191	−	4.15246i	0.0711167	−	0.403323i
$107$	3.31844	+	3.31844i	0.320806	+	0.320806i	0.849076	−	0.528270i	$-0.177159\pi$
$107$	3.31844	+	3.31844i	0.320806	+	0.320806i	−0.528270	+	0.849076i	$0.677159\pi$
$108$		0			0
$109$		−	11.2538i		−	1.07792i	−0.842332	−	0.538960i	$-0.818818\pi$
$109$		−	11.2538i		−	1.07792i	0.842332	−	0.538960i	$-0.181182\pi$
$110$	−0.0227492		0.000855890i	−0.00216905		8.16059e-5i
$111$		0			0
$112$	4.56928	−	2.13069i	0.431757	−	0.201331i
$113$	0.164272	−	1.87764i	0.0154535	−	0.176634i	−0.984545	−	0.175129i	$-0.943966\pi$
$113$	0.164272	−	1.87764i	0.0154535	−	0.176634i	0.999999	−	0.00150433i	$-0.000478843\pi$
$114$		0			0
$115$	8.79762	+	13.9950i	0.820382	+	1.30504i
$116$	−31.7867	−	18.3520i	−2.95132	−	1.70394i
$117$		0			0
$118$	0.613590	−	2.28995i	0.0564856	−	0.210807i
$119$	−3.66066	−	3.07166i	−0.335572	−	0.281579i
$120$		0			0
$121$	1.91013	+	10.8329i	0.173648	+	0.984806i
$122$	9.29066	−	13.2684i	0.841137	−	1.20127i
$123$		0			0
$124$	−14.0961	+	16.7991i	−1.26587	+	1.50860i
$125$	4.09104	+	10.4050i	0.365914	+	0.930649i
$126$		0			0
$127$	1.52603	+	5.69522i	0.135413	+	0.505369i	0.999996	+	0.00287859i	$0.000916284\pi$
$127$	1.52603	+	5.69522i	0.135413	+	0.505369i	−0.864583	+	0.502491i	$0.832417\pi$
$128$	−8.75341	+	18.7718i	−0.773700	+	1.65920i
$129$		0			0
$130$	7.29508	−	0.915713i	0.639821	−	0.0803133i
$131$	5.29212	−	14.5400i	0.462375	−	1.27036i	−0.461320	−	0.887234i	$-0.652624\pi$
$131$	5.29212	−	14.5400i	0.462375	−	1.27036i	0.923694	−	0.383130i	$-0.125154\pi$
$132$		0			0
$133$	15.3478	−	10.7467i	1.33082	−	0.931854i
$134$	21.6513			1.87039
$135$		0			0
$136$	−7.78679			−0.667712
$137$	3.20087	−	2.24127i	0.273468	−	0.191485i	−0.428795	−	0.903402i	$-0.641062\pi$
$137$	3.20087	−	2.24127i	0.273468	−	0.191485i	0.702263	+	0.711917i	$0.252173\pi$
$138$		0			0
$139$	−1.85959	+	5.10917i	−0.157728	+	0.433354i	−0.993234	−	0.116126i	$-0.962952\pi$
$139$	−1.85959	+	5.10917i	−0.157728	+	0.433354i	0.835506	+	0.549481i	$0.185174\pi$
$140$	12.1774	−	15.6733i	1.02918	−	1.32464i
$141$		0			0
$142$	9.66651	−	20.7299i	0.811196	−	1.73961i
$143$	0.00153058	+	0.00571218i	0.000127993	+	0.000477677i
$144$		0			0
$145$	−22.3924	−	1.11295i	−1.85959	−	0.0924257i
$146$	4.39742	−	5.24064i	0.363933	−	0.433718i
$147$		0			0
$148$	3.66097	−	5.22840i	0.300930	−	0.429772i
$149$	−1.59684	−	9.05612i	−0.130818	−	0.741907i	−0.977681	−	0.210095i	$-0.932623\pi$
$149$	−1.59684	−	9.05612i	−0.130818	−	0.741907i	0.846863	−	0.531811i	$-0.178488\pi$
$150$		0			0
$151$	8.68937	+	7.29124i	0.707131	+	0.593353i	0.923792	−	0.382894i	$-0.125072\pi$
$151$	8.68937	+	7.29124i	0.707131	+	0.593353i	−0.216662	+	0.976247i	$0.569517\pi$
$152$	7.90189	−	29.4903i	0.640928	−	2.39198i
$153$		0			0
$154$	0.0213790	+	0.0123432i	0.00172277	+	0.000994640i
$155$	−2.97807	+	13.0601i	−0.239204	+	1.04902i
$156$		0			0
$157$	−0.0766881	+	0.876549i	−0.00612037	+	0.0699562i	−0.998641	−	0.0521239i	$-0.983401\pi$
$157$	−0.0766881	+	0.876549i	−0.00612037	+	0.0699562i	0.992520	+	0.122080i	$0.0389565\pi$
$158$	−15.2393	+	7.10621i	−1.21238	+	0.565340i
$159$		0			0
$160$	0.248446	+	6.60358i	0.0196414	+	0.522059i
$161$		−	17.9254i		−	1.41272i
$162$		0			0
$163$	4.75545	+	4.75545i	0.372476	+	0.372476i	0.868378	−	0.495902i	$-0.165163\pi$
$163$	4.75545	+	4.75545i	0.372476	+	0.372476i	−0.495902	+	0.868378i	$0.665163\pi$
$164$	1.90539	−	10.8060i	0.148786	−	0.843808i
$165$		0			0
$166$	22.7800	+	8.29126i	1.76807	+	0.643527i
$167$	−7.21152	−	0.630926i	−0.558044	−	0.0488226i	−0.195355	−	0.980733i	$-0.562586\pi$
$167$	−7.21152	−	0.630926i	−0.558044	−	0.0488226i	−0.362689	+	0.931910i	$0.618141\pi$
$168$		0			0
$169$	3.79304	+	10.4213i	0.291772	+	0.801637i
$170$	−9.32907	+	4.78515i	−0.715507	+	0.367004i
$171$		0			0
$172$	−25.5171	−	6.83728i	−1.94566	−	0.521338i
$173$	−2.37946	+	0.208175i	−0.180907	+	0.0158273i	−0.177249	−	0.984166i	$-0.556720\pi$
$173$	−2.37946	+	0.208175i	−0.180907	+	0.0158273i	−0.00365760	+	0.999993i	$0.501164\pi$
$174$		0			0
$175$	2.24906	−	11.9134i	0.170013	−	0.900565i
$176$	0.00876211	−	0.00154500i	0.000660469	−	0.000116458i
$177$		0			0
$178$	−1.25987	−	14.4004i	−0.0944315	−	1.07936i
$179$	8.41245	+	14.5708i	0.628776	+	1.08907i	0.987798	+	0.155743i	$0.0497772\pi$
$179$	8.41245	+	14.5708i	0.628776	+	1.08907i	−0.359021	+	0.933329i	$0.616889\pi$
$180$		0			0
$181$	3.54419	−	6.13871i	0.263437	−	0.456287i	−0.703716	−	0.710482i	$-0.748477\pi$
$181$	3.54419	−	6.13871i	0.263437	−	0.456287i	0.967153	+	0.254195i	$0.0818105\pi$
$182$	−7.22577	−	3.36943i	−0.535610	−	0.249759i
$183$		0			0
$184$	−18.7754	−	22.3757i	−1.38414	−	1.64955i
$185$	0.532183	−	3.86228i	0.0391269	−	0.283960i
$186$		0			0
$187$	−0.00483706	−	0.00690804i	−0.000353721	−	0.000505166i
$188$	−5.33703	+	5.33703i	−0.389243	+	0.389243i
$189$		0			0
$190$	−8.65544	−	40.1871i	−0.627932	−	2.91548i
$191$	7.71793	+	1.36088i	0.558450	+	0.0984697i	0.445747	−	0.895159i	$-0.352938\pi$
$191$	7.71793	+	1.36088i	0.558450	+	0.0984697i	0.112703	+	0.993629i	$0.464049\pi$
$192$		0			0
$193$	−7.85219	−	16.8391i	−0.565213	−	1.21210i	−0.956472	−	0.291823i	$-0.905738\pi$
$193$	−7.85219	−	16.8391i	−0.565213	−	1.21210i	0.391259	−	0.920280i	$-0.372040\pi$
$194$	−22.9662	+	19.2709i	−1.64888	+	1.38357i
$195$		0			0
$196$	3.85457	−	1.40295i	0.275327	−	0.100211i
$197$	6.50660	−	1.74344i	0.463576	−	0.124215i	−0.0194688	−	0.999810i	$-0.506198\pi$
$197$	6.50660	−	1.74344i	0.463576	−	0.124215i	0.483045	+	0.875596i	$0.339531\pi$
$198$		0			0
$199$	7.81601	−	4.51257i	0.554062	−	0.319888i	−0.196697	−	0.980464i	$-0.563021\pi$
$199$	7.81601	−	4.51257i	0.554062	−	0.319888i	0.750759	+	0.660576i	$0.229688\pi$
$200$	−9.67084	−	17.2267i	−0.683832	−	1.21811i
$201$		0			0
$202$	−9.55295	−	6.68904i	−0.672143	−	0.470640i
$203$	19.9152	+	13.9448i	1.39778	+	0.978733i
$204$		0			0
$205$	−1.97691	−	6.40432i	−0.138073	−	0.447297i
$206$	23.8806	−	13.7874i	1.66384	−	0.960617i
$207$		0			0
$208$	−2.77557	+	0.743713i	−0.192451	+	0.0515672i
$209$	0.0310708	−	0.0113089i	0.00214921	−	0.000782250i
$210$		0			0
$211$	4.86924	−	4.08578i	0.335213	−	0.281277i	−0.459607	−	0.888122i	$-0.652010\pi$
$211$	4.86924	−	4.08578i	0.335213	−	0.281277i	0.794820	+	0.606846i	$0.207565\pi$
$212$	2.74176	+	5.87973i	0.188305	+	0.403822i
$213$		0			0
$214$	−10.9960	−	1.93889i	−0.751672	−	0.132540i
$215$	−15.7748	+	3.39755i	−1.07583	+	0.231711i
$216$		0			0
$217$	10.2713	−	10.2713i	0.697258	−	0.697258i
$218$	15.3577	+	21.9330i	1.04015	+	1.48549i
$219$		0			0
$220$	0.0279167	−	0.0211551i	0.00188214	−	0.00142627i
$221$	1.75069	+	2.08639i	0.117764	+	0.140346i
$222$		0			0
$223$	3.40610	+	1.58829i	0.228089	+	0.106360i	0.533304	−	0.845924i	$-0.320950\pi$
$223$	3.40610	+	1.58829i	0.228089	+	0.106360i	−0.305214	+	0.952284i	$0.598728\pi$
$224$	3.58295	−	6.20585i	0.239396	−	0.414646i
$225$		0			0
$226$	2.24219	+	3.88359i	0.149149	+	0.258333i
$227$	0.568200	+	6.49455i	0.0377127	+	0.431059i	0.991456	+	0.130438i	$0.0416383\pi$
$227$	0.568200	+	6.49455i	0.0377127	+	0.431059i	−0.953744	+	0.300621i	$0.902806\pi$
$228$		0			0
$229$	−4.26742	+	0.752462i	−0.281999	+	0.0497241i	−0.312859	−	0.949800i	$-0.601287\pi$
$229$	−4.26742	+	0.752462i	−0.281999	+	0.0497241i	0.0308595	+	0.999524i	$0.490176\pi$
$230$	−36.2445	−	15.2696i	−2.38989	−	1.00684i
$231$		0			0
$232$	39.4655	−	3.45279i	2.59104	−	0.226687i
$233$	−25.2831	−	6.77460i	−1.65635	−	0.443818i	−0.694972	−	0.719037i	$-0.744583\pi$
$233$	−25.2831	−	6.77460i	−1.65635	−	0.443818i	−0.961382	+	0.275219i	$0.911250\pi$
$234$		0			0
$235$	−1.41285	+	4.38857i	−0.0921642	+	0.286279i
$236$	1.24756	+	3.42764i	0.0812093	+	0.223121i
$237$		0			0
$238$	11.3262	+	0.990915i	0.734169	+	0.0642314i
$239$	17.2215	+	6.26813i	1.11397	+	0.405452i	0.832448	−	0.554103i	$-0.186939\pi$
$239$	17.2215	+	6.26813i	1.11397	+	0.405452i	0.281521	+	0.959555i	$0.409161\pi$
$240$		0			0
$241$	−1.09892	+	6.23226i	−0.0707874	+	0.401455i	0.928740	+	0.370731i	$0.120893\pi$
$241$	−1.09892	+	6.23226i	−0.0707874	+	0.401455i	−0.999528	+	0.0307248i	$0.990218\pi$
$242$	−18.5060	−	18.5060i	−1.18961	−	1.18961i
$243$		0			0
$244$			24.9220i			1.59547i
$245$	1.70387	−	1.83709i	0.108856	−	0.117367i
$246$		0			0
$247$	−9.67820	+	4.51302i	−0.615809	+	0.287156i
$248$	2.06294	−	23.5795i	0.130997	−	1.49730i
$249$		0			0
$250$	−22.1725	−	14.6958i	−1.40231	−	0.929443i
$251$	23.1604	+	13.3717i	1.46187	+	0.844013i	0.999098	−	0.0424628i	$-0.0135204\pi$
$251$	23.1604	+	13.3717i	1.46187	+	0.844013i	0.462775	+	0.886476i	$0.346854\pi$
$252$		0			0
$253$	0.00818747	−	0.0305561i	0.000514742	−	0.00192104i
$254$	−10.7462	−	9.01714i	−0.674277	−	0.565786i
$255$		0			0
$256$	−4.67107	−	26.4910i	−0.291942	−	1.65569i
$257$	2.24834	−	3.21096i	0.140248	−	0.200294i	−0.742883	−	0.669421i	$-0.766542\pi$
$257$	2.24834	−	3.21096i	0.140248	−	0.200294i	0.883131	+	0.469127i	$0.155431\pi$
$258$		0			0
$259$	−2.71756	+	3.23866i	−0.168861	+	0.201240i
$260$	−8.38625	+	7.59209i	−0.520093	+	0.470841i
$261$		0			0
$262$	9.52815	+	35.5596i	0.588651	+	2.19688i
$263$	13.0357	−	27.9551i	0.803815	−	1.72379i	0.121669	−	0.992571i	$-0.461176\pi$
$263$	13.0357	−	27.9551i	0.803815	−	1.72379i	0.682146	−	0.731216i	$-0.261047\pi$
$264$		0			0
$265$	3.12932	+	2.43132i	0.192233	+	0.149355i
$266$	−15.2464	+	41.8892i	−0.934819	+	2.56839i
$267$		0			0
$268$	−27.2883	+	19.1074i	−1.66690	+	1.16717i
$269$	−11.5179			−0.702257			−0.351128	−	0.936327i	$-0.614202\pi$
$269$	−11.5179			−0.702257			−0.351128	+	0.936327i	$0.614202\pi$
$270$		0			0
$271$	−6.78072			−0.411899			−0.205950	−	0.978563i	$-0.566028\pi$
$271$	−6.78072			−0.411899			−0.205950	+	0.978563i	$0.566028\pi$
$272$	3.35665	−	2.35035i	0.203527	−	0.142511i
$273$		0			0
$274$	−3.17972	+	8.73621i	−0.192094	+	0.527774i
$275$	0.00927526	−	0.0192805i	0.000559319	−	0.00116266i
$276$		0			0
$277$	4.19864	−	9.00402i	0.252272	−	0.540999i	−0.738863	−	0.673855i	$-0.764637\pi$
$277$	4.19864	−	9.00402i	0.252272	−	0.540999i	0.991135	+	0.132856i	$0.0424149\pi$
$278$	−3.34808	−	12.4952i	−0.200804	−	0.749412i
$279$		0			0
$280$	−1.06344	+	21.3963i	−0.0635529	+	1.27867i
$281$	16.7510	−	19.9630i	0.999280	−	1.19090i	0.0177003	−	0.999843i	$-0.494366\pi$
$281$	16.7510	−	19.9630i	0.999280	−	1.19090i	0.981580	−	0.191052i	$-0.0611900\pi$
$282$		0			0
$283$	4.26583	−	6.09224i	0.253577	−	0.362146i	−0.672100	−	0.740461i	$-0.734607\pi$
$283$	4.26583	−	6.09224i	0.253577	−	0.362146i	0.925677	+	0.378315i	$0.123496\pi$
$284$	6.11110	+	34.6578i	0.362627	+	2.05656i
$285$		0			0
$286$	−0.0107782	−	0.00904400i	−0.000637329	−	0.000534783i
$287$	−1.88112	+	7.02044i	−0.111039	+	0.414403i
$288$		0			0
$289$	11.3588	+	6.55802i	0.668166	+	0.385766i
$290$	45.1604	−	28.3891i	2.65191	−	1.66706i
$291$		0			0
$292$	−0.917390	+	10.4858i	−0.0536862	+	0.613636i
$293$	−7.55448	+	3.52271i	−0.441337	+	0.205799i	−0.630568	−	0.776134i	$-0.717178\pi$
$293$	−7.55448	+	3.52271i	−0.441337	+	0.205799i	0.189231	+	0.981933i	$0.439400\pi$
$294$		0			0
$295$	1.63362	+	1.51515i	0.0951128	+	0.0882155i
$296$			6.88912i			0.400422i
$297$		0			0
$298$	15.4707	+	15.4707i	0.896194	+	0.896194i
$299$	−1.77409	+	10.0614i	−0.102598	+	0.581864i
$300$		0			0
$301$	16.4429	+	5.98474i	0.947755	+	0.344955i
$302$	−26.8852	−	2.35215i	−1.54707	−	0.135351i
$303$		0			0
$304$	5.49502	+	15.0974i	0.315161	+	0.865897i
$305$	6.94777	+	13.5453i	0.397828	+	0.775600i
$306$		0			0
$307$	−11.7737	−	3.15476i	−0.671962	−	0.180052i	−0.0933234	−	0.995636i	$-0.529749\pi$
$307$	−11.7737	−	3.15476i	−0.671962	−	0.180052i	−0.578638	+	0.815584i	$0.696416\pi$
$308$	−0.0378380	+	0.00331040i	−0.00215602	+	0.000188627i
$309$		0			0
$310$	−12.0186	−	29.5175i	−0.682611	−	1.67648i
$311$	−19.9366	+	3.51536i	−1.13050	+	0.199338i	−0.707447	−	0.706767i	$-0.750153\pi$
$311$	−19.9366	+	3.51536i	−1.13050	+	0.199338i	−0.423054	+	0.906104i	$0.639042\pi$
$312$		0			0
$313$	0.631317	+	7.21599i	0.0356842	+	0.407872i	0.992939	+	0.118626i	$0.0378489\pi$
$313$	0.631317	+	7.21599i	0.0356842	+	0.407872i	−0.957255	+	0.289246i	$0.906596\pi$
$314$	−1.04673	−	1.81300i	−0.0590706	−	0.102313i
$315$		0			0
$316$	12.9356	−	22.4052i	0.727686	−	1.26039i
$317$	4.44794	+	2.07411i	0.249821	+	0.116493i	0.543496	−	0.839412i	$-0.317100\pi$
$317$	4.44794	+	2.07411i	0.249821	+	0.116493i	−0.293675	+	0.955905i	$0.594878\pi$
$318$		0			0
$319$	0.0275787	+	0.0328670i	0.00154411	+	0.00184020i
$320$	−15.1120	−	19.9420i	−0.844784	−	1.11479i
$321$		0			0
$322$	24.4622	+	34.9356i	1.36322	+	1.94688i
$323$	10.7680	−	10.7680i	0.599148	−	0.599148i
$324$		0			0
$325$	−2.44145	+	6.46427i	−0.135427	+	0.358573i
$326$	−15.7577	−	2.77851i	−0.872739	−	0.153887i
$327$		0			0
$328$	5.00520	+	10.7337i	0.276366	+	0.592668i
$329$	3.82979	−	3.21358i	0.211143	−	0.177170i
$330$		0			0
$331$	−4.66635	+	1.69841i	−0.256486	+	0.0933531i	−0.467063	−	0.884224i	$-0.654688\pi$
$331$	−4.66635	+	1.69841i	−0.256486	+	0.0933531i	0.210577	+	0.977577i	$0.432466\pi$
$332$	−36.0280	+	9.65368i	−1.97729	+	0.529814i
$333$		0			0
$334$	14.9158	−	8.61167i	0.816159	−	0.471209i
$335$	−9.50456	+	17.9924i	−0.519290	+	0.983032i
$336$		0			0
$337$	17.9831	+	12.5919i	0.979602	+	0.685925i	0.949547	−	0.313624i	$-0.101543\pi$
$337$	17.9831	+	12.5919i	0.979602	+	0.685925i	0.0300546	+	0.999548i	$0.490432\pi$
$338$	−21.6140	−	15.1343i	−1.17564	−	0.823195i
$339$		0			0
$340$	7.53498	−	14.2640i	0.408642	−	0.773572i
$341$	0.0222000	−	0.0128172i	0.00120220	−	0.000694090i
$342$		0			0
$343$	−19.0194	+	5.09624i	−1.02695	+	0.275171i
$344$	26.7937	−	9.75210i	1.44462	−	0.525798i
$345$		0			0
$346$	4.35333	−	3.65288i	0.234037	−	0.196380i
$347$	6.59670	+	14.1467i	0.354129	+	0.759433i	0.999992	−	0.00402090i	$-0.00127990\pi$
$347$	6.59670	+	14.1467i	0.354129	+	0.759433i	−0.645863	+	0.763454i	$0.723502\pi$
$348$		0			0
$349$	−23.5190	−	4.14704i	−1.25895	−	0.221986i	−0.495928	−	0.868364i	$-0.665172\pi$
$349$	−23.5190	−	4.14704i	−1.25895	−	0.221986i	−0.763017	+	0.646378i	$0.776283\pi$
$350$	11.8744	+	26.2877i	0.634715	+	1.40513i
$351$		0			0
$352$	0.00894211	−	0.00894211i	0.000476616	−	0.000476616i
$353$	−0.184497	−	0.263489i	−0.00981980	−	0.0140241i	0.814212	−	0.580567i	$-0.197169\pi$
$353$	−0.184497	−	0.263489i	−0.00981980	−	0.0140241i	−0.824032	+	0.566543i	$0.808280\pi$
$354$		0			0
$355$	12.9833	+	17.1331i	0.689084	+	0.909329i
$356$	14.2964	+	17.0378i	0.757707	+	0.903000i
$357$		0			0
$358$	−36.2796	−	16.9175i	−1.91744	−	0.894116i
$359$	−2.09252	+	3.62435i	−0.110439	+	0.191286i	−0.915947	−	0.401298i	$-0.868559\pi$
$359$	−2.09252	+	3.62435i	−0.110439	+	0.191286i	0.805508	+	0.592585i	$0.201892\pi$
$360$		0			0
$361$	20.3536	+	35.2535i	1.07124	+	1.85545i
$362$	1.46986	+	16.8006i	0.0772543	+	0.883021i
$363$		0			0
$364$	12.0806	−	2.13013i	0.633194	−	0.111649i
$365$	2.42463	+	5.95486i	0.126911	+	0.311691i
$366$		0			0
$367$	−13.3335	+	1.16653i	−0.696004	+	0.0608924i	−0.429667	−	0.902988i	$-0.641369\pi$
$367$	−13.3335	+	1.16653i	−0.696004	+	0.0608924i	−0.266337	+	0.963880i	$0.585813\pi$
$368$	14.8473	+	3.97833i	0.773970	+	0.207385i
$369$		0			0
$370$	4.23351	+	8.25360i	0.220090	+	0.429084i
$371$	−1.46974	−	4.03807i	−0.0763050	−	0.209646i
$372$		0			0
$373$	−15.6366	−	1.36803i	−0.809634	−	0.0708338i	−0.325182	−	0.945652i	$-0.605425\pi$
$373$	−15.6366	−	1.36803i	−0.809634	−	0.0708338i	−0.484452	+	0.874818i	$0.660981\pi$
$374$	0.0188543	+	0.00686241i	0.000974933	+	0.000354847i
$375$		0			0
$376$	1.41463	−	8.02279i	0.0729542	−	0.413744i
$377$	−9.79812	−	9.79812i	−0.504629	−	0.504629i
$378$		0			0
$379$			26.4477i			1.35853i	0.733894	+	0.679264i	$0.237701\pi$
$379$			26.4477i			1.35853i	−0.733894	+	0.679264i	$0.762299\pi$
$380$	46.3744	+	43.0114i	2.37896	+	2.20644i
$381$		0			0
$382$	−16.8989	+	7.88010i	−0.864625	+	0.403181i
$383$	1.62124	−	18.5309i	0.0828415	−	0.946883i	−0.835082	−	0.550126i	$-0.814580\pi$
$383$	1.62124	−	18.5309i	0.0828415	−	0.946883i	0.917923	−	0.396758i	$-0.129865\pi$
$384$		0			0
$385$	−0.0196423	+	0.0123477i	−0.00100107	+	0.000629298i
$386$	38.2831	+	22.1028i	1.94856	+	1.12500i
$387$		0			0
$388$	11.9388	−	44.5560i	0.606098	−	2.26199i
$389$	−25.4642	−	21.3670i	−1.29108	−	1.08335i	−0.991613	−	0.129243i	$-0.958745\pi$
$389$	−25.4642	−	21.3670i	−1.29108	−	1.08335i	−0.299472	−	0.954105i	$-0.596810\pi$
$390$		0			0
$391$	−2.52993	−	14.3479i	−0.127944	−	0.725606i
$392$	−2.53946	+	3.62672i	−0.128262	+	0.183177i
$393$		0			0
$394$	−10.3018	+	12.2772i	−0.518996	+	0.618515i
$395$	0.784477	−	15.7836i	0.0394713	−	0.794157i
$396$		0			0
$397$	−8.84314	−	33.0030i	−0.443824	−	1.65637i	−0.719022	−	0.694987i	$-0.755410\pi$
$397$	−8.84314	−	33.0030i	−0.443824	−	1.65637i	0.275198	−	0.961388i	$-0.411257\pi$
$398$	−9.07480	+	19.4610i	−0.454879	+	0.975490i
$399$		0			0
$400$	9.36849	+	4.50689i	0.468424	+	0.225344i
$401$	3.56868	−	9.80487i	0.178211	−	0.489632i	−0.818136	−	0.575025i	$-0.804992\pi$
$401$	3.56868	−	9.80487i	0.178211	−	0.489632i	0.996347	+	0.0853930i	$0.0272146\pi$
$402$		0			0
$403$	−6.78172	+	4.74861i	−0.337821	+	0.236545i
$404$	17.9432			0.892709
$405$		0			0
$406$	−57.8436			−2.87073
$407$	−0.00611167	+	0.00427944i	−0.000302944	+	0.000212124i
$408$		0			0
$409$	13.0223	−	35.7785i	0.643911	−	1.76913i	0.00483335	−	0.999988i	$-0.498461\pi$
$409$	13.0223	−	35.7785i	0.643911	−	1.76913i	0.639078	−	0.769142i	$-0.279316\pi$
$410$	12.5926	+	9.78383i	0.621906	+	0.483189i
$411$		0			0
$412$	−17.9304	+	38.4519i	−0.883367	+	1.89439i
$413$	−0.625335	−	2.33378i	−0.0307707	−	0.114838i
$414$		0			0
$415$	−16.8902	+	15.2907i	−0.829107	+	0.750593i
$416$	−2.62527	+	3.12868i	−0.128715	+	0.153396i
$417$		0			0
$418$	−0.0451224	+	0.0644415i	−0.00220701	+	0.00315194i
$419$	−4.45593	−	25.2708i	−0.217686	−	1.23456i	−0.876184	−	0.481978i	$-0.839919\pi$
$419$	−4.45593	−	25.2708i	−0.217686	−	1.23456i	0.658497	−	0.752583i	$-0.271192\pi$
$420$		0			0
$421$	−18.3149	−	15.3680i	−0.892611	−	0.748990i	0.0761208	−	0.997099i	$-0.475747\pi$
$421$	−18.3149	−	15.3680i	−0.892611	−	0.748990i	−0.968732	+	0.248109i	$0.920191\pi$
$422$	−3.91416	+	14.6078i	−0.190538	+	0.711098i
$423$		0			0
$424$	−6.06417	−	3.50115i	−0.294502	−	0.170031i
$425$	0.118797	−	9.85316i	0.00576248	−	0.477948i
$426$		0			0
$427$	1.43875	−	16.4450i	0.0696260	−	0.795829i
$428$	15.5699	−	7.26039i	0.752602	−	0.350944i
$429$		0			0
$430$	26.1076	−	28.1489i	1.25902	−	1.35746i
$431$		−	15.6671i		−	0.754660i	−0.926079	−	0.377330i	$-0.876842\pi$
$431$		−	15.6671i		−	0.754660i	0.926079	−	0.377330i	$-0.123158\pi$
$432$		0			0
$433$	10.5845	+	10.5845i	0.508657	+	0.508657i	0.914114	−	0.405457i	$-0.132888\pi$
$433$	10.5845	+	10.5845i	0.508657	+	0.508657i	−0.405457	+	0.914114i	$0.632888\pi$
$434$	−6.00127	+	34.0349i	−0.288070	+	1.63373i
$435$		0			0
$436$	−38.7122	−	14.0901i	−1.85398	−	0.674792i
$437$	56.9060	+	4.97863i	2.72218	+	0.238160i
$438$		0			0
$439$	7.09912	+	19.5047i	0.338823	+	0.930907i	0.985729	+	0.168338i	$0.0538401\pi$
$439$	7.09912	+	19.5047i	0.338823	+	0.930907i	−0.646907	+	0.762569i	$0.723938\pi$
$440$	−0.0115856	+	0.0359869i	−0.000552321	+	0.00171561i
$441$		0			0
$442$	−6.25923	−	1.67715i	−0.297721	−	0.0797741i
$443$	7.49047	−	0.655331i	0.355883	−	0.0311357i	0.0921874	−	0.995742i	$-0.470614\pi$
$443$	7.49047	−	0.655331i	0.355883	−	0.0311357i	0.263696	+	0.964606i	$0.415059\pi$
$444$		0			0
$445$	12.5200	+	5.27458i	0.593504	+	0.250039i
$446$	−8.80576	+	1.55269i	−0.416965	+	0.0735222i
$447$		0			0
$448$	2.36476	+	27.0293i	0.111724	+	1.27701i
$449$	2.66419	+	4.61452i	0.125731	+	0.217773i	0.922018	−	0.387146i	$-0.126539\pi$
$449$	2.66419	+	4.61452i	0.125731	+	0.217773i	−0.796287	+	0.604918i	$0.793206\pi$
$450$		0			0
$451$	−0.00641320	+	0.0111080i	−0.000301986	+	0.000523055i
$452$	−6.25326	−	2.91594i	−0.294129	−	0.137154i
$453$		0			0
$454$	−9.97027	−	11.8821i	−0.467928	−	0.557655i
$455$	5.97203	−	4.52557i	0.279973	−	0.212162i
$456$		0			0
$457$	−13.4866	−	19.2609i	−0.630879	−	0.900988i	0.368714	−	0.929543i	$-0.379798\pi$
$457$	−13.4866	−	19.2609i	−0.630879	−	0.900988i	−0.999592	+	0.0285551i	$0.990909\pi$
$458$	7.29010	−	7.29010i	0.340644	−	0.340644i
$459$		0			0
$460$	59.1563	−	12.7410i	2.75818	−	0.594053i
$461$	−15.8701	−	2.79833i	−0.739145	−	0.130331i	−0.208615	−	0.977998i	$-0.566896\pi$
$461$	−15.8701	−	2.79833i	−0.739145	−	0.130331i	−0.530529	+	0.847667i	$0.678007\pi$
$462$		0			0
$463$	−6.30838	−	13.5284i	−0.293175	−	0.628716i	0.703455	−	0.710740i	$-0.251640\pi$
$463$	−6.30838	−	13.5284i	−0.293175	−	0.628716i	−0.996630	+	0.0820233i	$0.973862\pi$
$464$	−15.9702	+	13.4006i	−0.741398	+	0.622106i
$465$		0			0
$466$	58.5204	−	21.2997i	2.71091	−	0.986689i
$467$	6.07179	−	1.62693i	0.280969	−	0.0752854i	−0.115583	−	0.993298i	$-0.536873\pi$
$467$	6.07179	−	1.62693i	0.280969	−	0.0752854i	0.396552	+	0.918012i	$0.370207\pi$
$468$		0			0
$469$	19.1095	−	11.0329i	0.882393	−	0.509450i
$470$	−3.23536	−	10.4811i	−0.149236	−	0.483459i
$471$		0			0
$472$	−3.22503	−	2.25819i	−0.148444	−	0.103942i
$473$	0.0252955	+	0.0177121i	0.00116309	+	0.000814402i
$474$		0			0
$475$	37.1955	+	10.4487i	1.70665	+	0.479420i
$476$	−15.1495	+	8.74657i	−0.694377	+	0.400899i
$477$		0			0
$478$	−42.1177	+	11.2854i	−1.92642	+	0.516182i
$479$	−6.42357	+	2.33799i	−0.293501	+	0.106825i	−0.484574	−	0.874750i	$-0.661025\pi$
$479$	−6.42357	+	2.33799i	−0.293501	+	0.106825i	0.191073	+	0.981576i	$0.438803\pi$
$480$		0			0
$481$	1.84587	−	1.54887i	0.0841645	−	0.0706224i
$482$	−6.36322	−	13.6460i	−0.289837	−	0.621557i
$483$		0			0
$484$	39.6557	+	6.99237i	1.80253	+	0.317835i
$485$	−5.93256	−	27.5448i	−0.269384	−	1.25074i
$486$		0			0
$487$	−11.7403	+	11.7403i	−0.532002	+	0.532002i	−0.921168	−	0.389165i	$-0.872763\pi$
$487$	−11.7403	+	11.7403i	−0.532002	+	0.532002i	0.389165	+	0.921168i	$0.372763\pi$
$488$	−15.4289	−	22.0347i	−0.698431	−	0.997463i
$489$		0			0
$490$	−0.813732	+	5.90559i	−0.0367606	+	0.266788i
$491$	−10.6951	−	12.7459i	−0.482663	−	0.575215i	0.468673	−	0.883372i	$-0.344732\pi$
$491$	−10.6951	−	12.7459i	−0.482663	−	0.575215i	−0.951336	+	0.308157i	$0.900288\pi$
$492$		0			0
$493$	17.9087	+	8.35099i	0.806569	+	0.376109i
$494$	12.7035	−	22.0031i	0.571557	−	0.989966i
$495$		0			0
$496$	6.22793	+	10.7871i	0.279642	+	0.484355i
$497$	−2.03166	−	23.2220i	−0.0911326	−	1.04165i
$498$		0			0
$499$	−27.4365	+	4.83779i	−1.22823	+	0.216569i	−0.749863	−	0.661593i	$-0.769881\pi$
$499$	−27.4365	+	4.83779i	−1.22823	+	0.216569i	−0.478363	+	0.878162i	$0.658770\pi$
$500$	40.9143	−	1.04555i	1.82974	−	0.0467584i
$501$		0			0
$502$	−63.3862	+	5.54557i	−2.82906	+	0.247511i
$503$	14.4253	+	3.86525i	0.643192	+	0.172343i	0.565649	−	0.824646i	$-0.308626\pi$
$503$	14.4253	+	3.86525i	0.643192	+	0.172343i	0.0775431	+	0.996989i	$0.475292\pi$
$504$		0			0
$505$	9.75226	−	5.00222i	0.433970	−	0.222596i
$506$	0.0257419	+	0.0707252i	0.00114436	+	0.00314412i
$507$		0			0
$508$	21.5017	+	1.88116i	0.953985	+	0.0834629i
$509$	−5.75433	−	2.09440i	−0.255056	−	0.0928328i	0.211328	−	0.977415i	$-0.432221\pi$
$509$	−5.75433	−	2.09440i	−0.255056	−	0.0928328i	−0.466384	+	0.884582i	$0.654443\pi$
$510$		0			0
$511$	1.21069	−	6.86619i	0.0535580	−	0.303742i
$512$	15.9632	+	15.9632i	0.705482	+	0.705482i
$513$		0			0
$514$			9.32621i			0.411361i
$515$	0.974338	+	25.8975i	0.0429345	+	1.14118i
$516$		0			0
$517$	0.00799616	−	0.00372867i	0.000351671	−	0.000163987i
$518$	0.876681	−	10.0205i	0.0385191	−	0.440276i
$519$		0			0
$520$	2.71451	−	11.9043i	0.119039	−	0.522039i
$521$	−19.3541	−	11.1741i	−0.847920	−	0.489547i	0.0120282	−	0.999928i	$-0.496171\pi$
$521$	−19.3541	−	11.1741i	−0.847920	−	0.489547i	−0.859949	+	0.510381i	$0.829505\pi$
$522$		0			0
$523$	−0.878392	+	3.27820i	−0.0384094	+	0.143346i	−0.982468	−	0.186433i	$-0.940307\pi$
$523$	−0.878392	+	3.27820i	−0.0384094	+	0.143346i	0.944058	+	0.329778i	$0.106974\pi$
$524$	−43.3905	−	36.4089i	−1.89552	−	1.59053i
$525$		0			0
$526$	12.7435	+	72.2722i	0.555645	+	3.15122i
$527$	6.77171	−	9.67101i	0.294980	−	0.421276i
$528$		0			0
$529$	20.3451	−	24.2463i	0.884569	−	1.05419i
$530$	−9.41680	−	0.468035i	−0.409040	−	0.0203302i
$531$		0			0
$532$	−17.7517	−	66.2503i	−0.769635	−	2.87232i
$533$	1.75067	−	3.75433i	0.0758301	−	0.162618i
$534$		0			0
$535$	6.43831	−	8.28666i	0.278353	−	0.358264i
$536$	12.2976	−	33.7875i	0.531178	−	1.45940i
$537$		0			0
$538$	22.4477	−	15.7180i	0.967787	−	0.677652i
$539$	−0.00479492			−0.000206532
$540$		0			0
$541$	−32.7244			−1.40693			−0.703466	−	0.710729i	$-0.748365\pi$
$541$	−32.7244			−1.40693			−0.703466	+	0.710729i	$0.748365\pi$
$542$	13.2152	−	9.25340i	0.567642	−	0.397467i
$543$		0			0
$544$	1.99201	−	5.47299i	0.0854065	−	0.234653i
$545$	−24.9683	+	3.13414i	−1.06953	+	0.134252i
$546$		0			0
$547$	12.0993	−	25.9469i	0.517327	−	1.10941i	−0.458063	−	0.888920i	$-0.651456\pi$
$547$	12.0993	−	25.9469i	0.517327	−	1.10941i	0.975389	−	0.220491i	$-0.0707658\pi$
$548$	−3.70221	−	13.8168i	−0.158151	−	0.590226i
$549$		0			0
$550$	0.00823449	+	0.0502342i	0.000351120	+	0.00214200i
$551$	−49.8005	+	59.3499i	−2.12157	+	2.52839i
$552$		0			0
$553$	−9.82914	+	14.0375i	−0.417977	+	0.596934i
$554$	4.10455	+	23.2780i	0.174385	+	0.988989i
$555$		0			0
$556$	15.2469	+	12.7937i	0.646612	+	0.542572i
$557$	−5.67171	+	21.1671i	−0.240318	+	0.896879i	0.735361	+	0.677675i	$0.237012\pi$
$557$	−5.67171	+	21.1671i	−0.240318	+	0.896879i	−0.975679	+	0.219203i	$0.929654\pi$
$558$		0			0
$559$	−8.63696	−	4.98655i	−0.365304	−	0.210909i
$560$	−5.99980	−	9.54429i	−0.253538	−	0.403320i
$561$		0			0
$562$	−5.40385	+	61.7663i	−0.227948	+	2.60545i
$563$	9.80704	−	4.57310i	0.413317	−	0.192733i	−0.204826	−	0.978798i	$-0.565663\pi$
$563$	9.80704	−	4.57310i	0.413317	−	0.192733i	0.618143	+	0.786065i	$0.287885\pi$
$564$		0			0
$565$	−4.21160	+	0.158452i	−0.177183	+	0.00666614i
$566$			17.6948i			0.743770i
$567$		0			0
$568$	−26.8592	−	26.8592i	−1.12699	−	1.12699i
$569$	−2.29260	+	13.0020i	−0.0961109	+	0.545072i	0.898290	+	0.439402i	$0.144810\pi$
$569$	−2.29260	+	13.0020i	−0.0961109	+	0.545072i	−0.994401	+	0.105670i	$0.966301\pi$
$570$		0			0
$571$	−7.42564	−	2.70271i	−0.310753	−	0.113105i	0.181936	−	0.983310i	$-0.441764\pi$
$571$	−7.42564	−	2.70271i	−0.310753	−	0.113105i	−0.492689	+	0.870206i	$0.663986\pi$
$572$	0.0215658	+	0.00188676i	0.000901710	+	7.88894e-5i
$573$		0			0
$574$	−5.91434	−	16.2495i	−0.246860	−	0.678242i
$575$	28.5999	−	23.4164i	1.19270	−	0.976533i
$576$		0			0
$577$	25.1985	+	6.75192i	1.04903	+	0.281086i	0.741850	−	0.670566i	$-0.233949\pi$
$577$	25.1985	+	6.75192i	1.04903	+	0.281086i	0.307178	+	0.951652i	$0.400615\pi$
$578$	−31.0872	+	2.71978i	−1.29306	+	0.113128i
$579$		0			0
$580$	−31.8644	+	75.6347i	−1.32310	+	3.14056i
$581$	24.3307	−	4.29016i	1.00941	−	0.177986i
$582$		0			0
$583$	−0.000660950	−	0.00755470i	−2.73738e−5	−	0.000312884i
$584$	−5.68051	−	9.83893i	−0.235061	−	0.407138i
$585$		0			0
$586$	9.91592	−	17.1749i	0.409623	−	0.709488i
$587$	−13.7926	−	6.43160i	−0.569282	−	0.265460i	0.116593	−	0.993180i	$-0.462803\pi$
$587$	−13.7926	−	6.43160i	−0.569282	−	0.265460i	−0.685875	+	0.727719i	$0.740580\pi$
$588$		0			0
$589$	29.7544	+	35.4599i	1.22601	+	1.46110i
$590$	−5.25150	−	0.723604i	−0.216201	−	0.0297903i
$591$		0			0
$592$	−2.07940	−	2.96969i	−0.0854627	−	0.122053i
$593$	−30.1991	+	30.1991i	−1.24013	+	1.24013i	−0.280181	+	0.959947i	$0.590395\pi$
$593$	−30.1991	+	30.1991i	−1.24013	+	1.24013i	−0.959947	+	0.280181i	$0.909605\pi$
$594$		0			0
$595$	−5.79548	+	8.97720i	−0.237592	+	0.368029i
$596$	−33.1516	−	5.84552i	−1.35794	−	0.239442i
$597$		0			0
$598$	−10.2728	−	22.0301i	−0.420086	−	0.900876i
$599$	−13.7064	+	11.5010i	−0.560028	+	0.469920i	−0.878320	−	0.478073i	$-0.841335\pi$
$599$	−13.7064	+	11.5010i	−0.560028	+	0.469920i	0.318292	+	0.947993i	$0.396891\pi$
$600$		0			0
$601$	−34.7520	+	12.6487i	−1.41757	+	0.515952i	−0.933341	−	0.358992i	$-0.883121\pi$
$601$	−34.7520	+	12.6487i	−1.41757	+	0.515952i	−0.484225	+	0.874944i	$0.660898\pi$
$602$	−40.2135	+	10.7752i	−1.63898	+	0.439163i
$603$		0			0
$604$	35.9606	−	20.7619i	1.46322	−	0.844788i
$605$	23.5025	−	7.25483i	0.955511	−	0.294951i
$606$		0			0
$607$	35.5036	+	24.8599i	1.44105	+	1.00903i	0.993385	+	0.114830i	$0.0366323\pi$
$607$	35.5036	+	24.8599i	1.44105	+	1.00903i	0.447663	+	0.894203i	$0.352257\pi$
$608$	18.7059	+	13.0980i	0.758626	+	0.531196i
$609$		0			0
$610$	−32.0255	−	16.9176i	−1.29668	−	0.684973i
$611$	−2.46768	+	1.42471i	−0.0998316	+	0.0576378i
$612$		0			0
$613$	0.212147	−	0.0568446i	0.00856854	−	0.00229593i	−0.254532	−	0.967064i	$-0.581921\pi$
$613$	0.212147	−	0.0568446i	0.00856854	−	0.00229593i	0.263101	+	0.964768i	$0.415255\pi$
$614$	27.2515	−	9.91873i	1.09978	−	0.400287i
$615$		0			0
$616$	0.0314049	−	0.0263518i	0.00126534	−	0.00106175i
$617$	11.5791	+	24.8316i	0.466159	+	0.999681i	0.989091	+	0.147307i	$0.0470604\pi$
$617$	11.5791	+	24.8316i	0.466159	+	0.999681i	−0.522932	+	0.852374i	$0.675162\pi$
$618$		0			0
$619$	−40.1687	−	7.08283i	−1.61452	−	0.284683i	−0.707797	−	0.706416i	$-0.750311\pi$
$619$	−40.1687	−	7.08283i	−1.61452	−	0.284683i	−0.906720	+	0.421733i	$0.861422\pi$
$620$	41.1972	+	26.5960i	1.65452	+	1.06812i
$621$		0			0
$622$	34.0580	−	34.0580i	1.36560	−	1.36560i
$623$	−8.45000	−	12.0678i	−0.338542	−	0.483488i
$624$		0			0
$625$	21.9457	−	11.9744i	0.877829	−	0.478975i
$626$	−11.0778	−	13.2020i	−0.442758	−	0.527658i
$627$		0			0
$628$	2.91924	+	1.36126i	0.116490	+	0.0543203i
$629$	−1.71810	+	2.97584i	−0.0685053	+	0.118655i
$630$		0			0
$631$	−21.0645	−	36.4848i	−0.838565	−	1.45244i	−0.891095	−	0.453817i	$-0.850062\pi$
$631$	−21.0645	−	36.4848i	−0.838565	−	1.45244i	0.0525304	−	0.998619i	$-0.483271\pi$
$632$	2.43373	+	27.8177i	0.0968087	+	1.10653i
$633$		0			0
$634$	−11.4992	+	2.02762i	−0.456693	+	0.0805272i
$635$	12.2108	−	4.97184i	0.484569	−	0.197301i
$636$		0			0
$637$	1.54269	−	0.134968i	0.0611235	−	0.00534761i
$638$	−0.0986016	−	0.0264202i	−0.00390367	−	0.00104599i
$639$		0			0
$640$	44.0859	+	14.1930i	1.74265	+	0.561026i
$641$	8.97472	+	24.6578i	0.354480	+	0.973926i	0.980912	+	0.194450i	$0.0622922\pi$
$641$	8.97472	+	24.6578i	0.354480	+	0.973926i	−0.626432	+	0.779476i	$0.715486\pi$
$642$		0			0
$643$	−29.4868	−	2.57976i	−1.16284	−	0.101736i	−0.510651	−	0.859788i	$-0.670596\pi$
$643$	−29.4868	−	2.57976i	−1.16284	−	0.101736i	−0.652194	+	0.758052i	$0.726151\pi$
$644$	−61.6619	−	22.4431i	−2.42982	−	0.884382i
$645$		0			0
$646$	−6.29152	+	35.6810i	−0.247536	+	1.40385i
$647$	−3.41329	−	3.41329i	−0.134190	−	0.134190i	0.636821	−	0.771012i	$-0.280249\pi$
$647$	−3.41329	−	3.41329i	−0.134190	−	0.134190i	−0.771012	+	0.636821i	$0.780249\pi$
$648$		0			0
$649$		−	0.00426384i		−	0.000167370i
$650$	−4.06331	−	15.9303i	−0.159376	−	0.624836i
$651$		0			0
$652$	22.3123	−	10.4044i	0.873818	−	0.407468i
$653$	−3.91945	+	44.7996i	−0.153380	+	1.75314i	0.396625	+	0.917981i	$0.370181\pi$
$653$	−3.91945	+	44.7996i	−0.153380	+	1.75314i	−0.550005	+	0.835161i	$0.685374\pi$
$654$		0			0
$655$	−33.7331	−	7.69207i	−1.31806	−	0.300554i
$656$	−5.39742	−	3.11620i	−0.210734	−	0.121667i
$657$		0			0
$658$	−3.07859	+	11.4895i	−0.120016	+	0.447906i
$659$	31.0081	+	26.0189i	1.20790	+	1.01355i	0.999368	+	0.0355365i	$0.0113140\pi$
$659$	31.0081	+	26.0189i	1.20790	+	1.01355i	0.208535	+	0.978015i	$0.433130\pi$
$660$		0			0
$661$	−2.96480	−	16.8142i	−0.115318	−	0.653998i	−0.986593	−	0.163203i	$-0.947817\pi$
$661$	−2.96480	−	16.8142i	−0.115318	−	0.653998i	0.871275	−	0.490795i	$-0.163294\pi$
$662$	6.77668	−	9.67810i	0.263383	−	0.376150i
$663$		0			0
$664$	25.8776	−	30.8397i	1.00424	−	1.19681i
$665$	−28.1175	−	31.0586i	−1.09035	−	1.20440i
$666$		0			0
$667$	19.1844	+	71.5973i	0.742824	+	2.77226i
$668$	−11.1994	+	24.0171i	−0.433316	+	0.929250i
$669$		0			0
$670$	−6.02980	−	48.0368i	−0.232952	−	1.85582i
$671$	0.00996382	−	0.0273754i	0.000384649	−	0.00105681i
$672$		0			0
$673$	25.0337	−	17.5288i	0.964978	−	0.675685i	0.0189672	−	0.999820i	$-0.493962\pi$
$673$	25.0337	−	17.5288i	0.964978	−	0.675685i	0.946011	+	0.324135i	$0.105073\pi$
$674$	−52.2317			−2.01189
$675$		0			0
$676$	40.5973			1.56144
$677$	−17.6437	+	12.3542i	−0.678102	+	0.474812i	−0.861189	−	0.508284i	$-0.830280\pi$
$677$	−17.6437	+	12.3542i	−0.678102	+	0.474812i	0.183087	+	0.983097i	$0.441391\pi$
$678$		0			0
$679$	−10.4501	+	28.7114i	−0.401038	+	1.10184i
$680$	2.16859	+	17.2762i	0.0831617	+	0.662513i
$681$		0			0
$682$	−0.0257754	+	0.0552756i	−0.000986992	+	0.00211661i
$683$	2.39311	+	8.93120i	0.0915697	+	0.341743i	0.996477	−	0.0838658i	$-0.0267267\pi$
$683$	2.39311	+	8.93120i	0.0915697	+	0.341743i	−0.904907	+	0.425609i	$0.860060\pi$
$684$		0			0
$685$	−5.86404	−	6.47744i	−0.224053	−	0.247490i
$686$	30.1131	−	35.8874i	1.14972	−	1.37019i
$687$		0			0
$688$	−8.60637	+	12.2912i	−0.328115	+	0.468597i
$689$	0.425300	+	2.41199i	0.0162026	+	0.0918897i
$690$		0			0
$691$	15.9016	+	13.3430i	0.604925	+	0.507592i	0.893024	−	0.450008i	$-0.148579\pi$
$691$	15.9016	+	13.3430i	0.604925	+	0.507592i	−0.288099	+	0.957601i	$0.593023\pi$
$692$	−2.26304	+	8.44577i	−0.0860278	+	0.321060i
$693$		0			0
$694$	−32.1620	−	18.5688i	−1.22085	−	0.704860i
$695$	11.8534	+	2.70290i	0.449625	+	0.102527i
$696$		0			0
$697$	−0.514855	+	5.88482i	−0.0195015	+	0.222903i
$698$	51.4966	−	24.0132i	1.94917	−	0.908915i
$699$		0			0
$700$	−38.1651	−	22.6524i	−1.44250	−	0.856182i
$701$		−	5.94733i		−	0.224627i	−0.993673	−	0.112314i	$-0.964174\pi$
$701$		−	5.94733i		−	0.224627i	0.993673	−	0.112314i	$-0.0358262\pi$
$702$		0			0
$703$	−9.52667	−	9.52667i	−0.359305	−	0.359305i
$704$	−0.00831467	+	0.0471548i	−0.000313371	+	0.00177721i
$705$		0			0
$706$	0.719149	+	0.261749i	0.0270655	+	0.00985105i
$707$	−11.8400	−	1.03586i	−0.445289	−	0.0389577i
$708$		0			0
$709$	0.0976022	+	0.268160i	0.00366553	+	0.0100710i	0.941512	−	0.336980i	$-0.109405\pi$
$709$	0.0976022	+	0.268160i	0.00366553	+	0.0100710i	−0.937846	+	0.347051i	$0.887183\pi$
$710$	−48.6846	−	15.6735i	−1.82710	−	0.588215i
$711$		0			0
$712$	−23.1879	−	6.21318i	−0.869004	−	0.232849i
$713$	44.1179	−	3.85981i	1.65223	−	0.144551i
$714$		0			0
$715$	0.0122471	−	0.00498664i	0.000458016	−	0.000186490i
$716$	60.6550	−	10.6951i	2.26678	−	0.399695i
$717$		0			0
$718$	−0.867822	−	9.91925i	−0.0323868	−	0.370183i
$719$	−13.3454	−	23.1148i	−0.497698	−	0.862038i	0.502299	−	0.864694i	$-0.332488\pi$
$719$	−13.3454	−	23.1148i	−0.497698	−	0.862038i	−0.999996	+	0.00265626i	$0.999154\pi$
$720$		0			0
$721$	14.0514	−	24.3377i	0.523300	−	0.906382i
$722$	−87.7772	−	40.9312i	−3.26673	−	1.52330i
$723$		0			0
$724$	−16.6792	−	19.8775i	−0.619879	−	0.738743i
$725$	3.76695	+	49.9911i	0.139901	+	1.85662i
$726$		0			0
$727$	−28.9346	−	41.3229i	−1.07313	−	1.53258i	−0.826059	−	0.563584i	$-0.809422\pi$
$727$	−28.9346	−	41.3229i	−1.07313	−	1.53258i	−0.247067	−	0.968998i	$-0.579467\pi$
$728$	−9.36225	+	9.36225i	−0.346988	+	0.346988i
$729$		0			0
$730$	−12.8518	−	8.29686i	−0.475668	−	0.307081i
$731$	14.0060	+	2.46963i	0.518030	+	0.0913427i
$732$		0			0
$733$	16.9546	+	36.3592i	0.626231	+	1.34296i	0.921811	+	0.387639i	$0.126709\pi$
$733$	16.9546	+	36.3592i	0.626231	+	1.34296i	−0.295580	+	0.955318i	$0.595513\pi$
$734$	24.3943	−	20.4693i	0.900411	−	0.755535i
$735$		0			0
$736$	20.5300	−	7.47229i	0.756744	−	0.275432i
$737$	0.0376137	−	0.0100786i	0.00138552	−	0.000371249i
$738$		0			0
$739$	18.7080	−	10.8011i	0.688186	−	0.397324i	−0.114746	−	0.993395i	$-0.536605\pi$
$739$	18.7080	−	10.8011i	0.688186	−	0.397324i	0.802932	+	0.596070i	$0.203272\pi$
$740$	−12.6196	−	6.66634i	−0.463906	−	0.245060i
$741$		0			0
$742$	8.37505	+	5.86427i	0.307458	+	0.215284i
$743$	−22.4982	−	15.7534i	−0.825380	−	0.577937i	0.0827765	−	0.996568i	$-0.473621\pi$
$743$	−22.4982	−	15.7534i	−0.825380	−	0.577937i	−0.908156	+	0.418631i	$0.862510\pi$
$744$		0			0
$745$	−19.6477	+	6.06494i	−0.719837	+	0.222202i
$746$	32.3418	−	18.6725i	1.18412	−	0.683650i
$747$		0			0
$748$	−0.0298192	+	0.00799004i	−0.00109030	+	0.000292145i
$749$	−10.6931	+	3.89197i	−0.390717	+	0.142210i
$750$		0			0
$751$	36.9715	−	31.0228i	1.34911	−	1.13204i	0.369926	−	0.929061i	$-0.379383\pi$
$751$	36.9715	−	31.0228i	1.34911	−	1.13204i	0.979184	−	0.202976i	$-0.0650615\pi$
$752$	1.81178	+	3.88537i	0.0660687	+	0.141685i
$753$		0			0
$754$	32.4671	+	5.72483i	1.18238	+	0.208486i
$755$	13.7568	−	21.3093i	0.500662	−	0.775525i
$756$		0			0
$757$	25.7438	−	25.7438i	0.935673	−	0.935673i	−0.0623799	−	0.998052i	$-0.519869\pi$
$757$	25.7438	−	25.7438i	0.935673	−	0.935673i	0.998052	+	0.0623799i	$0.0198691\pi$
$758$	−36.0923	−	51.5451i	−1.31093	−	1.87220i
$759$		0			0
$760$	−67.6294	−	9.31866i	−2.45318	−	0.338023i
$761$	−8.43284	−	10.0499i	−0.305690	−	0.364308i	0.591227	−	0.806505i	$-0.298644\pi$
$761$	−8.43284	−	10.0499i	−0.305690	−	0.364308i	−0.896918	+	0.442197i	$0.854199\pi$
$762$		0			0
$763$	24.7311	+	11.5323i	0.895327	+	0.417498i
$764$	14.3444	−	24.8452i	0.518961	−	0.898867i
$765$		0			0
$766$	22.1287	+	38.3280i	0.799543	+	1.38485i
$767$	0.120019	+	1.37182i	0.00433362	+	0.0495336i
$768$		0			0
$769$	−3.71767	+	0.655525i	−0.134062	+	0.0236388i	−0.240277	−	0.970704i	$-0.577238\pi$
$769$	−3.71767	+	0.655525i	−0.134062	+	0.0236388i	0.106214	+	0.994343i	$0.466127\pi$
$770$	0.0214313	−	0.0508701i	0.000772329	−	0.00183323i
$771$		0			0
$772$	−67.7562	+	5.92790i	−2.43860	+	0.213350i
$773$	22.9201	+	6.14142i	0.824379	+	0.220892i	0.646260	−	0.763117i	$-0.276332\pi$
$773$	22.9201	+	6.14142i	0.824379	+	0.220892i	0.178119	+	0.984009i	$0.442999\pi$
$774$		0			0
$775$	29.8054	+	2.97012i	1.07064	+	0.106690i
$776$	17.0284	+	46.7851i	0.611284	+	1.67949i
$777$		0			0
$778$	78.7869	+	6.89296i	2.82465	+	0.247125i
$779$	−21.7646	−	7.92167i	−0.779798	−	0.283823i
$780$		0			0
$781$	0.00714349	−	0.0405128i	0.000255614	−	0.00144966i
$782$	24.5108	+	24.5108i	0.876503	+	0.876503i
$783$		0			0
$784$		−	2.32987i		−	0.0832097i
$785$	1.96612	−	0.0739711i	0.0701738	−	0.00264014i
$786$		0			0
$787$	−2.14886	+	1.00203i	−0.0765987	+	0.0357185i	−0.460540	−	0.887639i	$-0.652344\pi$
$787$	−2.14886	+	1.00203i	−0.0765987	+	0.0357185i	0.383941	+	0.923357i	$0.374566\pi$
$788$	2.14916	−	24.5650i	0.0765606	−	0.875092i
$789$		0			0
$790$	20.0103	+	31.8318i	0.711936	+	1.13252i
$791$	3.95793	+	2.28511i	0.140728	+	0.0812492i
$792$		0			0
$793$	−2.43513	+	9.08804i	−0.0864741	+	0.322726i
$794$	62.2728	+	52.2531i	2.20998	+	1.85439i
$795$		0			0
$796$	−5.73703	−	32.5363i	−0.203343	−	1.15322i
$797$	−11.0535	+	15.7860i	−0.391534	+	0.559169i	−0.965730	−	0.259549i	$-0.916426\pi$
$797$	−11.0535	+	15.7860i	−0.391534	+	0.559169i	0.574196	+	0.818718i	$0.305315\pi$
$798$		0			0
$799$	2.61190	−	3.11275i	0.0924025	−	0.110121i
$800$	14.5819	−	2.39029i	0.515548	−	0.0845095i
$801$		0			0
$802$	6.42520	+	23.9792i	0.226882	+	0.846734i
$803$	0.00519993	−	0.0111513i	0.000183501	−	0.000393520i
$804$		0			0
$805$	−39.7703	+	4.99216i	−1.40172	+	0.175951i
$806$	6.73692	−	18.5095i	0.237298	−	0.651971i
$807$		0			0
$808$	−15.8644	+	11.1084i	−0.558108	+	0.390792i
$809$	48.9190			1.71990			0.859951	−	0.510377i	$-0.170494\pi$
$809$	48.9190			1.71990			0.859951	+	0.510377i	$0.170494\pi$
$810$		0			0
$811$	11.0352			0.387500			0.193750	−	0.981051i	$-0.437935\pi$
$811$	11.0352			0.387500			0.193750	+	0.981051i	$0.437935\pi$
$812$	72.9034	−	51.0475i	2.55841	−	1.79142i
$813$		0			0
$814$	0.00607130	−	0.0166808i	0.000212799	−	0.000584660i
$815$	9.22635	−	11.8751i	0.323185	−	0.415967i
$816$		0			0
$817$	−23.5661	+	50.5376i	−0.824472	+	1.76809i
$818$	23.4459	+	87.5012i	0.819766	+	3.05941i
$819$		0			0
$820$	−24.5055	−	1.21798i	−0.855768	−	0.0425335i
$821$	7.94924	−	9.47354i	0.277431	−	0.330629i	−0.609279	−	0.792956i	$-0.708541\pi$
$821$	7.94924	−	9.47354i	0.277431	−	0.330629i	0.886709	+	0.462327i	$0.152985\pi$
$822$		0			0
$823$	22.1538	−	31.6390i	0.772234	−	1.10286i	−0.219632	−	0.975583i	$-0.570486\pi$
$823$	22.1538	−	31.6390i	0.772234	−	1.10286i	0.991867	−	0.127282i	$-0.0406253\pi$
$824$	−7.95190	−	45.0975i	−0.277018	−	1.57104i
$825$		0			0
$826$	4.40357	+	3.69503i	0.153220	+	0.128567i
$827$	4.58916	−	17.1270i	0.159581	−	0.595563i	−0.839089	−	0.543994i	$-0.816911\pi$
$827$	4.58916	−	17.1270i	0.159581	−	0.595563i	0.998669	−	0.0515685i	$-0.0164220\pi$
$828$		0			0
$829$	20.1611	+	11.6400i	0.700224	+	0.404275i	0.807431	−	0.589962i	$-0.200857\pi$
$829$	20.1611	+	11.6400i	0.700224	+	0.404275i	−0.107207	+	0.994237i	$0.534191\pi$
$830$	12.0513	−	52.8502i	0.418307	−	1.83446i
$831$		0			0
$832$	1.34779	−	15.4053i	0.0467263	−	0.534084i
$833$	−2.00143	+	0.933284i	−0.0693455	+	0.0323364i
$834$		0			0
$835$	0.608573	+	16.1756i	0.0210605	+	0.559780i
$836$		−	0.121040i		−	0.00418626i
$837$		0			0
$838$	43.1705	+	43.1705i	1.49130	+	1.49130i
$839$	0.280939	−	1.59329i	0.00969910	−	0.0550063i	−0.979574	−	0.201084i	$-0.935554\pi$
$839$	0.280939	−	1.59329i	0.00969910	−	0.0550063i	0.989273	+	0.146077i	$0.0466648\pi$
$840$		0			0
$841$	−67.2182	−	24.4654i	−2.31787	−	0.843635i
$842$	56.6667	+	4.95770i	1.95286	+	0.170854i
$843$		0			0
$844$	−7.95832	−	21.8653i	−0.273937	−	0.752635i
$845$	22.0649	−	11.3177i	0.759056	−	0.389342i
$846$		0			0
$847$	−25.7635	−	6.90330i	−0.885243	−	0.237200i
$848$	3.67086	−	0.321159i	0.126058	−	0.0110286i
$849$		0			0
$850$	13.2147	+	19.3654i	0.453261	+	0.664226i
$851$	−12.6939	+	2.23827i	−0.435141	+	0.0767270i
$852$		0			0
$853$	−1.96923	−	22.5084i	−0.0674252	−	0.770674i	−0.952363	−	0.304965i	$-0.901355\pi$
$853$	−1.96923	−	22.5084i	−0.0674252	−	0.770674i	0.884938	−	0.465708i	$-0.154200\pi$
$854$	19.6379	+	34.0138i	0.671994	+	1.16393i
$855$		0			0
$856$	−9.27130	+	16.0584i	−0.316886	+	0.548863i
$857$	−28.0044	−	13.0587i	−0.956612	−	0.446076i	−0.119335	−	0.992854i	$-0.538076\pi$
$857$	−28.0044	−	13.0587i	−0.956612	−	0.446076i	−0.837277	+	0.546778i	$0.815854\pi$
$858$		0			0
$859$	17.7378	+	21.1391i	0.605205	+	0.721256i	0.978452	−	0.206477i	$-0.0661997\pi$
$859$	17.7378	+	21.1391i	0.605205	+	0.721256i	−0.373246	+	0.927732i	$0.621755\pi$
$860$	−8.06317	+	58.5178i	−0.274952	+	1.99544i
$861$		0			0
$862$	21.3804	+	30.5344i	0.728219	+	1.04000i
$863$	−15.5004	+	15.5004i	−0.527641	+	0.527641i	−0.919868	−	0.392228i	$-0.871705\pi$
$863$	−15.5004	+	15.5004i	−0.527641	+	0.527641i	0.392228	+	0.919868i	$0.371705\pi$
$864$		0			0
$865$	1.12454	+	5.22122i	0.0382355	+	0.177527i
$866$	−35.0727	−	6.18427i	−1.19182	−	0.210150i
$867$		0			0
$868$	−22.4724	−	48.1922i	−0.762762	−	1.63575i
$869$	−0.0231666	+	0.0194391i	−0.000785874	+	0.000659426i
$870$		0			0
$871$	−11.8179	+	4.30136i	−0.400434	+	0.145746i
$872$	42.9501	−	11.5085i	1.45448	−	0.389725i
$873$		0			0
$874$	−117.701	+	67.9545i	−3.98129	+	2.29860i
$875$	−27.0580	−	1.67207i	−0.914728	−	0.0565264i
$876$		0			0
$877$	2.23967	+	1.56824i	0.0756283	+	0.0529555i	0.610779	−	0.791801i	$-0.290856\pi$
$877$	2.23967	+	1.56824i	0.0756283	+	0.0529555i	−0.535151	+	0.844757i	$0.679745\pi$
$878$	−40.4531	−	28.3256i	−1.36523	−	0.955942i
$879$		0			0
$880$	−0.00586803	−	0.0190098i	−0.000197811	−	0.000640821i
$881$	−38.0975	+	21.9956i	−1.28354	+	0.741051i	−0.977493	−	0.210966i	$-0.932339\pi$
$881$	−38.0975	+	21.9956i	−1.28354	+	0.741051i	−0.306045	+	0.952017i	$0.599006\pi$
$882$		0			0
$883$	−26.2915	+	7.04478i	−0.884779	+	0.237076i	−0.672468	−	0.740126i	$-0.734766\pi$
$883$	−26.2915	+	7.04478i	−0.884779	+	0.237076i	−0.212311	+	0.977202i	$0.568099\pi$
$884$	9.36894	−	3.41001i	0.315111	−	0.114691i
$885$		0			0
$886$	−13.7042	+	11.4992i	−0.460401	+	0.386322i
$887$	−22.6131	−	48.4940i	−0.759274	−	1.62827i	−0.777856	−	0.628442i	$-0.783693\pi$
$887$	−22.6131	−	48.4940i	−0.759274	−	1.62827i	0.0185820	−	0.999827i	$-0.494085\pi$
$888$		0			0
$889$	−14.0795	−	2.48260i	−0.472211	−	0.0832636i
$890$	−31.5987	+	6.80569i	−1.05919	+	0.228127i
$891$		0			0
$892$	9.72811	−	9.72811i	0.325721	−	0.325721i
$893$	9.13813	+	13.0506i	0.305796	+	0.436722i
$894$		0			0
$895$	29.9848	−	22.7223i	1.00228	−	0.759522i
$896$	−32.2824	−	38.4726i	−1.07848	−	1.28528i
$897$		0			0
$898$	−11.4896	−	5.35770i	−0.383414	−	0.178789i
$899$	−30.0326	+	52.0179i	−1.00164	+	1.73489i
$900$		0			0
$901$	−1.74633	−	3.02474i	−0.0581788	−	0.100769i
$902$	−0.00265972	−	0.0304007i	−8.85589e−5	−	0.00101223i
$903$		0			0
$904$	7.33401	−	1.29318i	0.243926	−	0.0430107i
$905$	−14.6067	−	6.15373i	−0.485544	−	0.204557i
$906$		0			0
$907$	48.1046	−	4.20861i	1.59729	−	0.139745i	0.746548	−	0.665332i	$-0.231710\pi$
$907$	48.1046	−	4.20861i	1.59729	−	0.139745i	0.850740	+	0.525587i	$0.176154\pi$
$908$	23.0521	+	6.17680i	0.765011	+	0.204984i
$909$		0			0
$910$	−5.46326	+	16.9699i	−0.181105	+	0.562546i
$911$	14.5674	+	40.0237i	0.482640	+	1.32604i	0.907221	+	0.420653i	$0.138199\pi$
$911$	14.5674	+	40.0237i	0.482640	+	1.32604i	−0.424581	+	0.905390i	$0.639579\pi$
$912$		0			0
$913$	0.0434342	+	0.00380000i	0.00143746	+	0.000125762i
$914$	52.5694	+	19.1337i	1.73884	+	0.632886i
$915$		0			0
$916$	−2.75452	+	15.6217i	−0.0910121	+	0.516155i
$917$	26.5297	+	26.5297i	0.876087	+	0.876087i
$918$		0			0
$919$		−	29.7860i		−	0.982549i	−0.871005	−	0.491274i	$-0.836531\pi$
$919$		−	29.7860i		−	0.982549i	0.871005	−	0.491274i	$-0.163469\pi$
$920$	−44.4150	+	47.8877i	−1.46432	+	1.57881i
$921$		0			0
$922$	34.7487	−	16.2036i	1.14439	−	0.533637i
$923$	−1.15795	+	13.2354i	−0.0381143	+	0.435648i
$924$		0			0
$925$	−8.71728	−	0.105102i	−0.286622	−	0.00345572i
$926$	30.7563	+	17.7572i	1.01072	+	0.583537i
$927$		0			0
$928$	−7.66920	+	28.6219i	−0.251754	+	0.939559i
$929$	6.65219	+	5.58185i	0.218251	+	0.183135i	0.745358	−	0.666665i	$-0.232279\pi$
$929$	6.65219	+	5.58185i	0.218251	+	0.183135i	−0.527106	+	0.849799i	$0.676723\pi$
$930$		0			0
$931$	−1.50353	−	8.52694i	−0.0492762	−	0.279459i
$932$	−54.9592	+	78.4899i	−1.80025	+	2.57102i
$933$		0			0
$934$	−9.61335	+	11.4567i	−0.314559	+	0.374876i
$935$	−0.0139795	+	0.0126556i	−0.000457178	+	0.000413884i
$936$		0			0
$937$	−8.64443	−	32.2615i	−0.282401	−	1.05394i	−0.950717	−	0.310059i	$-0.899651\pi$
$937$	−8.64443	−	32.2615i	−0.282401	−	1.05394i	0.668316	−	0.743877i	$-0.267015\pi$
$938$	−22.1871	+	47.5804i	−0.724434	+	1.55355i
$939$		0			0
$940$	13.3274	+	10.3547i	0.434692	+	0.337733i
$941$	2.59435	−	7.12792i	0.0845735	−	0.232364i	−0.890196	−	0.455578i	$-0.849433\pi$
$941$	2.59435	−	7.12792i	0.0845735	−	0.232364i	0.974769	+	0.223214i	$0.0716549\pi$
$942$		0			0
$943$	−18.1517	+	12.7099i	−0.591100	+	0.413893i
$944$	2.07182			0.0674319
$945$		0			0
$946$	−0.0734704			−0.00238873
$947$	16.9682	−	11.8813i	0.551393	−	0.386089i	−0.264418	−	0.964408i	$-0.585180\pi$
$947$	16.9682	−	11.8813i	0.551393	−	0.386089i	0.815811	+	0.578319i	$0.196291\pi$
$948$		0			0
$949$	−1.35910	+	3.73411i	−0.0441184	+	0.121214i
$950$	−86.7509	+	30.3954i	−2.81457	+	0.986158i
$951$		0			0
$952$	7.97949	−	17.1121i	0.258617	−	0.554606i
$953$	−8.62530	−	32.1900i	−0.279401	−	1.04274i	−0.952835	−	0.303490i	$-0.901848\pi$
$953$	−8.62530	−	32.1900i	−0.279401	−	1.04274i	0.673434	−	0.739248i	$-0.264819\pi$
$954$		0			0
$955$	0.869909	−	17.5024i	0.0281496	−	0.566366i
$956$	43.1237	−	51.3928i	1.39472	−	1.66216i
$957$		0			0
$958$	9.32860	−	13.3226i	0.301394	−	0.430435i
$959$	1.64529	+	9.33089i	0.0531291	+	0.301310i
$960$		0			0
$961$	3.74384	+	3.14145i	0.120769	+	0.101337i
$962$	−1.48381	+	5.53765i	−0.0478400	+	0.178541i
$963$		0			0
$964$	20.0626	+	11.5831i	0.646173	+	0.373068i
$965$	−35.1733	+	22.1109i	−1.13227	+	0.711776i
$966$		0			0
$967$	−1.31002	+	14.9736i	−0.0421275	+	0.481519i	0.945600	+	0.325332i	$0.105476\pi$
$967$	−1.31002	+	14.9736i	−0.0421275	+	0.481519i	−0.987727	+	0.156188i	$0.950080\pi$
$968$	−39.3903	+	18.3680i	−1.26605	+	0.590369i
$969$		0			0
$970$	49.1516	+	45.5872i	1.57816	+	1.46372i
$971$			29.8876i			0.959139i	0.877504	+	0.479570i	$0.159207\pi$
$971$			29.8876i			0.959139i	−0.877504	+	0.479570i	$0.840793\pi$
$972$		0			0
$973$	−9.32220	−	9.32220i	−0.298856	−	0.298856i
$974$	6.85958	−	38.9026i	0.219795	−	1.24652i
$975$		0			0
$976$	13.3018	+	4.84146i	0.425780	+	0.154971i
$977$	38.8342	+	3.39755i	1.24242	+	0.108697i	0.689343	−	0.724435i	$-0.257899\pi$
$977$	38.8342	+	3.39755i	1.24242	+	0.108697i	0.553074	+	0.833132i	$0.313455\pi$
$978$		0			0
$979$	−0.00889204	−	0.0244307i	−0.000284191	−	0.000780808i
$980$	−4.18615	−	8.16126i	−0.133722	−	0.260702i
$981$		0			0
$982$	38.2380	+	10.2458i	1.22022	+	0.326958i
$983$	27.8303	−	2.43483i	0.887648	−	0.0776592i	0.365796	−	0.930695i	$-0.380797\pi$
$983$	27.8303	−	2.43483i	0.887648	−	0.0776592i	0.521852	+	0.853036i	$0.325241\pi$
$984$		0			0
$985$	−5.68015	−	13.9504i	−0.180985	−	0.444496i
$986$	−46.2994	+	8.16383i	−1.47447	+	0.259989i
$987$		0			0
$988$	3.40704	+	38.9426i	0.108392	+	1.23893i
$989$	26.6744	+	46.2015i	0.848198	+	1.46912i
$990$		0			0
$991$	−19.0981	+	33.0789i	−0.606672	+	1.05079i	0.385113	+	0.922870i	$0.374163\pi$
$991$	−19.0981	+	33.0789i	−0.606672	+	1.05079i	−0.991785	+	0.127917i	$0.959171\pi$
$992$	16.0453	+	7.48204i	0.509438	+	0.237555i
$993$		0			0
$994$	35.6498	+	42.4858i	1.13074	+	1.34757i
$995$	−12.1886	−	16.0843i	−0.386404	−	0.509907i
$996$		0			0
$997$	−4.38139	−	6.25727i	−0.138760	−	0.198170i	0.743757	−	0.668450i	$-0.233042\pi$
$997$	−4.38139	−	6.25727i	−0.138760	−	0.198170i	−0.882517	+	0.470280i	$0.844153\pi$
$998$	46.8702	−	46.8702i	1.48365	−	1.48365i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.8.2		192
3.2	odd	2		135.2.q.a.83.15	yes	192
5.2	odd	4	inner	405.2.r.a.332.2		192
15.2	even	4		135.2.q.a.2.15	✓	192
15.8	even	4		675.2.ba.b.407.2		192
15.14	odd	2		675.2.ba.b.218.2		192
27.13	even	9		135.2.q.a.68.15	yes	192
27.14	odd	18	inner	405.2.r.a.233.2		192
135.13	odd	36		675.2.ba.b.257.2		192
135.67	odd	36		135.2.q.a.122.15	yes	192
135.94	even	18		675.2.ba.b.68.2		192
135.122	even	36	inner	405.2.r.a.152.2		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.15	✓	192	15.2	even	4
135.2.q.a.68.15	yes	192	27.13	even	9
135.2.q.a.83.15	yes	192	3.2	odd	2
135.2.q.a.122.15	yes	192	135.67	odd	36
405.2.r.a.8.2		192	1.1	even	1	trivial
405.2.r.a.152.2		192	135.122	even	36	inner
405.2.r.a.233.2		192	27.14	odd	18	inner
405.2.r.a.332.2		192	5.2	odd	4	inner
675.2.ba.b.68.2		192	135.94	even	18
675.2.ba.b.218.2		192	15.14	odd	2
675.2.ba.b.257.2		192	135.13	odd	36
675.2.ba.b.407.2		192	15.8	even	4

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.94894 + 1.36466i) q^{2} +(1.25203 - 3.43992i) q^{4} +(-0.278496 - 2.21866i) q^{5} +(-1.02475 + 2.19758i) q^{7} +(1.02263 + 3.81650i) q^{8} +O(q^{10})\)	\(q+(-1.94894 + 1.36466i) q^{2} +(1.25203 - 3.43992i) q^{4} +(-0.278496 - 2.21866i) q^{5} +(-1.02475 + 2.19758i) q^{7} +(1.02263 + 3.81650i) q^{8} +(3.57049 + 3.94398i) q^{10} +(-0.00275056 + 0.00327799i) q^{11} +(0.792678 - 1.13206i) q^{13} +(-1.00178 - 5.68139i) q^{14} +(-1.59279 - 1.33651i) q^{16} +(-0.510074 + 1.90362i) q^{17} +(-6.69182 - 3.86352i) q^{19} +(-7.98068 - 1.81982i) q^{20} +(0.000887327 - 0.0101422i) q^{22} +(-6.70002 + 3.12427i) q^{23} +(-4.84488 + 1.23578i) q^{25} +3.28806i q^{26} +(6.27648 + 6.27648i) q^{28} +(1.74110 - 9.87424i) q^{29} +(-5.62932 - 2.04890i) q^{31} +(-2.94406 - 0.257571i) q^{32} +(-1.60370 - 4.40613i) q^{34} +(5.16106 + 1.66155i) q^{35} +(1.68417 + 0.451272i) q^{37} +(18.3144 - 1.60230i) q^{38} +(8.18270 - 3.33174i) q^{40} +(2.95191 - 0.520501i) q^{41} +(-0.628957 - 7.18901i) q^{43} +(0.00783223 + 0.0135658i) q^{44} +(8.79437 - 15.2323i) q^{46} +(-1.86865 - 0.871367i) q^{47} +(0.720271 + 0.858385i) q^{49} +(7.75597 - 9.02009i) q^{50} +(-2.90174 - 4.14412i) q^{52} +(-1.25315 + 1.25315i) q^{53} +(0.00803875 + 0.00518964i) q^{55} +(-9.43499 - 1.66364i) q^{56} +(10.0817 + 21.6203i) q^{58} +(-0.763311 + 0.640494i) q^{59} +(-6.39745 + 2.32848i) q^{61} +(13.7673 - 3.68893i) q^{62} +(9.69063 - 5.59489i) q^{64} +(-2.73241 - 1.44340i) q^{65} +(-7.45442 - 5.21964i) q^{67} +(5.90968 + 4.13800i) q^{68} +(-12.3261 + 3.80486i) q^{70} +(-8.32564 + 4.80681i) q^{71} +(-2.77741 + 0.744204i) q^{73} +(-3.89819 + 1.41882i) q^{74} +(-21.6685 + 18.1821i) q^{76} +(-0.00438501 - 0.00940367i) q^{77} +(6.95996 + 1.22723i) q^{79} +(-2.52167 + 3.90606i) q^{80} +(-5.04279 + 5.04279i) q^{82} +(-5.84421 - 8.34640i) q^{83} +(4.36554 + 0.601528i) q^{85} +(11.0364 + 13.1527i) q^{86} +(-0.0153232 - 0.00714534i) q^{88} +(-3.03785 + 5.26171i) q^{89} +(1.67550 + 2.90205i) q^{91} +(2.35862 + 26.9592i) q^{92} +(4.83102 - 0.851839i) q^{94} +(-6.70819 + 15.9228i) q^{95} +(12.5529 - 1.09824i) q^{97} +(-2.57517 - 0.690016i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

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