LMFDB - Embedded newform 675.2.r.a.181.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			181.27
Character	$\chi$	$=$	675.181
Dual form			675.2.r.a.496.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.47708 + 0.526519i) q^{2} +(4.03160 + 1.79498i) q^{4} +(-1.67112 + 1.48572i) q^{5} +(-1.03406 + 1.79105i) q^{7} +(4.94396 + 3.59200i) q^{8} +O(q^{10})$	\(q+(2.47708 + 0.526519i) q^{2} +(4.03160 + 1.79498i) q^{4} +(-1.67112 + 1.48572i) q^{5} +(-1.03406 + 1.79105i) q^{7} +(4.94396 + 3.59200i) q^{8} +(-4.92175 + 2.80036i) q^{10} +(2.39587 + 0.509257i) q^{11} +(1.74601 - 0.371125i) q^{13} +(-3.50448 + 3.89212i) q^{14} +(4.44939 + 4.94155i) q^{16} +(-3.67466 - 2.66979i) q^{17} +(5.85004 + 4.25031i) q^{19} +(-9.40413 + 2.99019i) q^{20} +(5.66661 + 2.52294i) q^{22} +(-1.58401 + 1.75922i) q^{23} +(0.585285 - 4.96563i) q^{25} +4.52040 q^{26} +(-7.38384 + 5.36467i) q^{28} +(-0.855066 - 8.13541i) q^{29} +(-0.709441 + 6.74988i) q^{31} +(2.30859 + 3.99860i) q^{32} +(-7.69671 - 8.54806i) q^{34} +(-0.932951 - 4.52939i) q^{35} +(1.53985 - 4.73917i) q^{37} +(12.2531 + 13.6085i) q^{38} +(-13.5986 + 1.34267i) q^{40} +(-4.68289 + 0.995378i) q^{41} +(4.14034 - 7.17127i) q^{43} +(8.74507 + 6.35367i) q^{44} +(-4.84997 + 3.52371i) q^{46} +(-1.05889 - 10.0746i) q^{47} +(1.36143 + 2.35806i) q^{49} +(4.06429 - 11.9921i) q^{50} +(7.70536 + 1.63783i) q^{52} +(2.52356 - 1.83348i) q^{53} +(-4.76039 + 2.70855i) q^{55} +(-11.5458 + 5.14053i) q^{56} +(2.16538 - 20.6023i) q^{58} +(10.2183 - 2.17198i) q^{59} +(2.57932 + 0.548251i) q^{61} +(-5.31128 + 16.3465i) q^{62} +(-0.496397 - 1.52775i) q^{64} +(-2.36640 + 3.21427i) q^{65} +(0.170417 - 1.62141i) q^{67} +(-10.0225 - 17.3595i) q^{68} +(0.0738159 - 11.7109i) q^{70} +(-8.24169 + 5.98794i) q^{71} +(-0.608028 - 1.87132i) q^{73} +(6.30959 - 10.9285i) q^{74} +(15.9558 + 27.6363i) q^{76} +(-3.38958 + 3.76451i) q^{77} +(-1.55944 - 14.8370i) q^{79} +(-14.7772 - 1.64738i) q^{80} -12.1240 q^{82} +(-3.70931 + 1.65149i) q^{83} +(10.1074 - 0.997956i) q^{85} +(14.0318 - 15.5838i) q^{86} +(10.0158 + 11.1237i) q^{88} +(-0.105993 - 0.326212i) q^{89} +(-1.14078 + 3.51095i) q^{91} +(-9.54385 + 4.24919i) q^{92} +(2.68154 - 25.5132i) q^{94} +(-16.0909 + 1.58874i) q^{95} +(1.15152 + 10.9560i) q^{97} +(2.13079 + 6.55791i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	2.47708	+	0.526519i	1.75156	+	0.372305i	0.968378	−	0.249489i	$-0.0802625\pi$
$2$	2.47708	+	0.526519i	1.75156	+	0.372305i	0.783181	+	0.621794i	$0.213596\pi$
$3$		0			0
$3$		0			0
$4$	4.03160	+	1.79498i	2.01580	+	0.897492i
$5$	−1.67112	+	1.48572i	−0.747348	+	0.664433i
$5$	−1.67112	+	1.48572i	−0.747348	+	0.664433i
$6$		0			0
$7$	−1.03406	+	1.79105i	−0.390839	+	0.676953i	−0.992560	−	0.121753i	$-0.961148\pi$
$7$	−1.03406	+	1.79105i	−0.390839	+	0.676953i	0.601721	+	0.798706i	$0.294482\pi$
$8$	4.94396	+	3.59200i	1.74795	+	1.26996i
$9$		0			0
$10$	−4.92175	+	2.80036i	−1.55640	+	0.885552i
$11$	2.39587	+	0.509257i	0.722381	+	0.153547i	0.554408	−	0.832245i	$-0.312945\pi$
$11$	2.39587	+	0.509257i	0.722381	+	0.153547i	0.167973	+	0.985792i	$0.446278\pi$
$12$		0			0
$13$	1.74601	−	0.371125i	0.484255	−	0.102932i	0.0406862	−	0.999172i	$-0.487046\pi$
$13$	1.74601	−	0.371125i	0.484255	−	0.102932i	0.443569	+	0.896240i	$0.353712\pi$
$14$	−3.50448	+	3.89212i	−0.936611	+	1.04021i
$15$		0			0
$16$	4.44939	+	4.94155i	1.11235	+	1.23539i
$17$	−3.67466	−	2.66979i	−0.891235	−	0.647520i	0.0449649	−	0.998989i	$-0.485682\pi$
$17$	−3.67466	−	2.66979i	−0.891235	−	0.647520i	−0.936200	+	0.351469i	$0.885682\pi$
$18$		0			0
$19$	5.85004	+	4.25031i	1.34209	+	0.975087i	0.999364	+	0.0356524i	$0.0113509\pi$
$19$	5.85004	+	4.25031i	1.34209	+	0.975087i	0.342728	+	0.939435i	$0.388649\pi$
$20$	−9.40413	+	2.99019i	−2.10283	+	0.668626i
$21$		0			0
$22$	5.66661	+	2.52294i	1.20813	+	0.537892i
$23$	−1.58401	+	1.75922i	−0.330288	+	0.366822i	−0.885300	−	0.465020i	$-0.846047\pi$
$23$	−1.58401	+	1.75922i	−0.330288	+	0.366822i	0.555012	+	0.831842i	$0.312714\pi$
$24$		0			0
$25$	0.585285	−	4.96563i	0.117057	−	0.993125i
$26$	4.52040			0.886523
$27$		0			0
$28$	−7.38384	+	5.36467i	−1.39541	+	1.01383i
$29$	−0.855066	−	8.13541i	−0.158782	−	1.51071i	−0.726318	−	0.687359i	$-0.758770\pi$
$29$	−0.855066	−	8.13541i	−0.158782	−	1.51071i	0.567536	−	0.823349i	$-0.307897\pi$
$30$		0			0
$31$	−0.709441	+	6.74988i	−0.127419	+	1.21231i	0.724736	+	0.689026i	$0.241962\pi$
$31$	−0.709441	+	6.74988i	−0.127419	+	1.21231i	−0.852156	+	0.523288i	$0.824705\pi$
$32$	2.30859	+	3.99860i	0.408105	+	0.706859i
$33$		0			0
$34$	−7.69671	−	8.54806i	−1.31997	−	1.46598i
$35$	−0.932951	−	4.52939i	−0.157698	−	0.765606i
$36$		0			0
$37$	1.53985	−	4.73917i	0.253150	−	0.779115i	−0.741039	−	0.671462i	$-0.765667\pi$
$37$	1.53985	−	4.73917i	0.253150	−	0.779115i	0.994189	−	0.107653i	$-0.0343334\pi$
$38$	12.2531	+	13.6085i	1.98772	+	2.20759i
$39$		0			0
$40$	−13.5986	+	1.34267i	−2.15013	+	0.212295i
$41$	−4.68289	+	0.995378i	−0.731344	+	0.155452i	−0.558508	−	0.829499i	$-0.688626\pi$
$41$	−4.68289	+	0.995378i	−0.731344	+	0.155452i	−0.172835	+	0.984951i	$0.555293\pi$
$42$		0			0
$43$	4.14034	−	7.17127i	0.631395	−	1.09361i	−0.355871	−	0.934535i	$-0.615816\pi$
$43$	4.14034	−	7.17127i	0.631395	−	1.09361i	0.987267	−	0.159074i	$-0.0508508\pi$
$44$	8.74507	+	6.35367i	1.31837	+	0.957851i
$45$		0			0
$46$	−4.84997	+	3.52371i	−0.715088	+	0.519542i
$47$	−1.05889	−	10.0746i	−0.154455	−	1.46954i	−0.747443	−	0.664326i	$-0.768719\pi$
$47$	−1.05889	−	10.0746i	−0.154455	−	1.46954i	0.592988	−	0.805211i	$-0.297948\pi$
$48$		0			0
$49$	1.36143	+	2.35806i	0.194489	+	0.336866i
$50$	4.06429	−	11.9921i	0.574778	−	1.69594i
$51$		0			0
$52$	7.70536	+	1.63783i	1.06854	+	0.227125i
$53$	2.52356	−	1.83348i	0.346638	−	0.251847i	−0.400819	−	0.916157i	$-0.631274\pi$
$53$	2.52356	−	1.83348i	0.346638	−	0.251847i	0.747457	+	0.664310i	$0.231274\pi$
$54$		0			0
$55$	−4.76039	+	2.70855i	−0.641891	+	0.365221i
$56$	−11.5458	+	5.14053i	−1.54287	+	0.686932i
$57$		0			0
$58$	2.16538	−	20.6023i	0.284329	−	2.70521i
$59$	10.2183	−	2.17198i	1.33032	−	0.282767i	0.512718	−	0.858557i	$-0.328639\pi$
$59$	10.2183	−	2.17198i	1.33032	−	0.282767i	0.817598	+	0.575790i	$0.195305\pi$
$60$		0			0
$61$	2.57932	+	0.548251i	0.330248	+	0.0701964i	0.370052	−	0.929011i	$-0.379340\pi$
$61$	2.57932	+	0.548251i	0.330248	+	0.0701964i	−0.0398037	+	0.999208i	$0.512673\pi$
$62$	−5.31128	+	16.3465i	−0.674534	+	2.07600i
$63$		0			0
$64$	−0.496397	−	1.52775i	−0.0620496	−	0.190969i
$65$	−2.36640	+	3.21427i	−0.293516	+	0.398681i
$66$		0			0
$67$	0.170417	−	1.62141i	0.0208197	−	0.198086i	−0.979168	−	0.203052i	$-0.934914\pi$
$67$	0.170417	−	1.62141i	0.0208197	−	0.198086i	0.999988	+	0.00496571i	$0.00158064\pi$
$68$	−10.0225	−	17.3595i	−1.21541	−	2.10515i
$69$		0			0
$70$	0.0738159	−	11.7109i	0.00882269	−	1.39972i
$71$	−8.24169	+	5.98794i	−0.978109	+	0.710638i	−0.957285	−	0.289145i	$-0.906629\pi$
$71$	−8.24169	+	5.98794i	−0.978109	+	0.710638i	−0.0208238	+	0.999783i	$0.506629\pi$
$72$		0			0
$73$	−0.608028	−	1.87132i	−0.0711643	−	0.219021i	0.909148	−	0.416472i	$-0.136734\pi$
$73$	−0.608028	−	1.87132i	−0.0711643	−	0.219021i	−0.980313	+	0.197451i	$0.936734\pi$
$74$	6.30959	−	10.9285i	0.733475	−	1.27042i
$75$		0			0
$76$	15.9558	+	27.6363i	1.83026	+	3.17010i
$77$	−3.38958	+	3.76451i	−0.386279	+	0.429006i
$78$		0			0
$79$	−1.55944	−	14.8370i	−0.175450	−	1.66930i	−0.628499	−	0.777811i	$-0.716330\pi$
$79$	−1.55944	−	14.8370i	−0.175450	−	1.66930i	0.453048	−	0.891486i	$-0.350336\pi$
$80$	−14.7772	−	1.64738i	−1.65214	−	0.184183i
$81$		0			0
$82$	−12.1240			−1.33887
$83$	−3.70931	+	1.65149i	−0.407150	+	0.181275i	−0.600084	−	0.799937i	$-0.704866\pi$
$83$	−3.70931	+	1.65149i	−0.407150	+	0.181275i	0.192934	+	0.981212i	$0.438200\pi$
$84$		0			0
$85$	10.1074	−	0.997956i	1.09630	−	0.108243i
$86$	14.0318	−	15.5838i	1.51308	−	1.68045i
$87$		0			0
$88$	10.0158	+	11.1237i	1.06769	+	1.18579i
$89$	−0.105993	−	0.326212i	−0.0112352	−	0.0345784i	0.945282	−	0.326255i	$-0.105787\pi$
$89$	−0.105993	−	0.326212i	−0.0112352	−	0.0345784i	−0.956517	+	0.291677i	$0.905787\pi$
$90$		0			0
$91$	−1.14078	+	3.51095i	−0.119586	+	0.368048i
$92$	−9.54385	+	4.24919i	−0.995015	+	0.443009i
$93$		0			0
$94$	2.68154	−	25.5132i	0.276580	−	2.63148i
$95$	−16.0909	+	1.58874i	−1.65089	+	0.163002i
$96$		0			0
$97$	1.15152	+	10.9560i	0.116920	+	1.11242i	0.882903	+	0.469555i	$0.155586\pi$
$97$	1.15152	+	10.9560i	0.116920	+	1.11242i	−0.765983	+	0.642860i	$0.777748\pi$
$98$	2.13079	+	6.55791i	0.215243	+	0.662449i
$99$		0			0
$100$	11.2729	−	18.9688i	1.12729	−	1.89688i
$101$	−6.38861	+	11.0654i	−0.635691	+	1.10105i	0.350677	+	0.936496i	$0.385951\pi$
$101$	−6.38861	+	11.0654i	−0.635691	+	1.10105i	−0.986368	+	0.164553i	$0.947382\pi$
$102$		0			0
$103$	−8.38725	−	3.73425i	−0.826421	−	0.367946i	−0.0504589	−	0.998726i	$-0.516068\pi$
$103$	−8.38725	−	3.73425i	−0.826421	−	0.367946i	−0.775962	+	0.630780i	$0.782735\pi$
$104$	9.96526	+	4.43682i	0.977174	+	0.435066i
$105$		0			0
$106$	7.21643	−	3.21296i	0.700921	−	0.312070i
$107$	−0.980681			−0.0948061			−0.0474030	−	0.998876i	$-0.515095\pi$
$107$	−0.980681			−0.0948061			−0.0474030	+	0.998876i	$0.515095\pi$
$108$		0			0
$109$	−2.74384	+	8.44467i	−0.262812	+	0.808853i	0.729377	+	0.684112i	$0.239810\pi$
$109$	−2.74384	+	8.44467i	−0.262812	+	0.808853i	−0.992189	+	0.124741i	$0.960190\pi$
$110$	−13.2180	+	4.20286i	−1.26028	+	0.400727i
$111$		0			0
$112$	−13.4515	+	2.85921i	−1.27105	+	0.270170i
$113$	6.63465	−	1.41024i	0.624135	−	0.132664i	0.115021	−	0.993363i	$-0.463306\pi$
$113$	6.63465	−	1.41024i	0.624135	−	0.132664i	0.509114	+	0.860699i	$0.329973\pi$
$114$		0			0
$115$	0.0333644	−	5.29325i	0.00311125	−	0.493598i
$116$	11.1557	−	34.3336i	1.03578	−	3.18779i
$117$		0			0
$118$	26.4552			2.43540
$119$	8.58156	−	3.82076i	0.786670	−	0.350248i
$120$		0			0
$121$	−4.56817	−	2.03388i	−0.415288	−	0.184898i
$122$	6.10051	+	2.71612i	0.552314	+	0.245906i
$123$		0			0
$124$	−14.9761	+	25.9394i	−1.34490	+	2.32943i
$125$	6.39944	+	9.16773i	0.572383	+	0.819986i
$126$		0			0
$127$	3.08193	+	9.48521i	0.273477	+	0.841676i	0.989618	+	0.143721i	$0.0459067\pi$
$127$	3.08193	+	9.48521i	0.273477	+	0.841676i	−0.716141	+	0.697955i	$0.754093\pi$
$128$	−1.39048	−	13.2295i	−0.122902	−	1.16933i
$129$		0			0
$130$	−7.55412	+	6.71603i	−0.662541	+	0.589035i
$131$	−1.43811	+	13.6827i	−0.125648	+	1.19546i	0.732029	+	0.681274i	$0.238574\pi$
$131$	−1.43811	+	13.6827i	−0.125648	+	1.19546i	−0.857677	+	0.514189i	$0.828093\pi$
$132$		0			0
$133$	−13.6618	+	6.08264i	−1.18463	+	0.527432i
$134$	1.27584	−	3.92662i	0.110215	−	0.339208i
$135$		0			0
$136$	−8.57746	−	26.3987i	−0.735511	−	2.26367i
$137$	5.70711	+	6.33838i	0.487591	+	0.541525i	0.935859	−	0.352374i	$-0.114626\pi$
$137$	5.70711	+	6.33838i	0.487591	+	0.541525i	−0.448268	+	0.893899i	$0.647959\pi$
$138$		0			0
$139$	−6.24293	+	6.93348i	−0.529518	+	0.588090i	−0.947256	−	0.320478i	$-0.896157\pi$
$139$	−6.24293	+	6.93348i	−0.529518	+	0.588090i	0.417738	+	0.908568i	$0.362823\pi$
$140$	4.36889	−	19.9353i	0.369239	−	1.68484i
$141$		0			0
$142$	−23.5681	+	10.4932i	−1.97779	+	0.880569i
$143$	4.37219			0.365621
$144$		0			0
$145$	13.5158	+	12.3249i	1.12243	+	1.02352i
$146$	−0.520848	−	4.95554i	−0.0431057	−	0.410123i
$147$		0			0
$148$	14.7148	−	16.3424i	1.20955	−	1.34334i
$149$	3.47298	+	6.01538i	0.284518	+	0.492799i	0.972492	−	0.232936i	$-0.0748332\pi$
$149$	3.47298	+	6.01538i	0.284518	+	0.492799i	−0.687974	+	0.725735i	$0.741500\pi$
$150$		0			0
$151$	0.394205	−	0.682783i	0.0320800	−	0.0555641i	−0.849540	−	0.527525i	$-0.823120\pi$
$151$	0.394205	−	0.682783i	0.0320800	−	0.0555641i	0.881620	+	0.471961i	$0.156454\pi$
$152$	13.6553	+	42.0267i	1.10759	+	3.40881i
$153$		0			0
$154$	−10.3783	+	7.54031i	−0.836311	+	0.607616i
$155$	−8.84286	−	12.3339i	−0.710276	−	0.990682i
$156$		0			0
$157$	−1.94393	−	3.36698i	−0.155142	−	0.268714i	0.777969	−	0.628303i	$-0.216250\pi$
$157$	−1.94393	−	3.36698i	−0.155142	−	0.268714i	−0.933111	+	0.359589i	$0.882917\pi$
$158$	3.94914	−	37.5736i	0.314177	−	2.98919i
$159$		0			0
$160$	−9.79873	−	3.25222i	−0.774657	−	0.257111i
$161$	−1.51288	−	4.65617i	−0.119232	−	0.366958i
$162$		0			0
$163$	2.59370	−	7.98258i	0.203154	−	0.625244i	−0.796630	−	0.604467i	$-0.793386\pi$
$163$	2.59370	−	7.98258i	0.203154	−	0.625244i	0.999784	−	0.0207767i	$-0.00661392\pi$
$164$	−20.6662	−	4.39274i	−1.61376	−	0.343015i
$165$		0			0
$166$	−10.0578	+	2.13785i	−0.780637	+	0.165929i
$167$	1.12972	−	10.7486i	0.0874207	−	0.831753i	−0.859684	−	0.510827i	$-0.829339\pi$
$167$	1.12972	−	10.7486i	0.0874207	−	0.831753i	0.947104	−	0.320926i	$-0.103994\pi$
$168$		0			0
$169$	−8.96529	+	3.99160i	−0.689638	+	0.307046i
$170$	25.5621	+	2.84970i	1.96053	+	0.218562i
$171$		0			0
$172$	29.5645	−	21.4799i	2.25427	−	1.63783i
$173$	−16.1013	−	3.42244i	−1.22416	−	0.260203i	−0.449904	−	0.893077i	$-0.648542\pi$
$173$	−16.1013	−	3.42244i	−1.22416	−	0.260203i	−0.774255	+	0.632874i	$0.781875\pi$
$174$		0			0
$175$	8.28846	+	6.18305i	0.626549	+	0.467394i
$176$	8.14362	+	14.1052i	0.613849	+	1.06322i
$177$		0			0
$178$	−0.0907954	−	0.863860i	−0.00680540	−	0.0647491i
$179$	0.422707	−	0.307115i	0.0315946	−	0.0229548i	−0.571876	−	0.820340i	$-0.693784\pi$
$179$	0.422707	−	0.307115i	0.0315946	−	0.0229548i	0.603471	+	0.797385i	$0.293784\pi$
$180$		0			0
$181$	−18.6716	−	13.5657i	−1.38785	−	1.00833i	−0.996097	−	0.0882646i	$-0.971868\pi$
$181$	−18.6716	−	13.5657i	−1.38785	−	1.00833i	−0.391756	−	0.920069i	$-0.628132\pi$
$182$	−4.67438	+	8.09626i	−0.346488	+	0.600134i
$183$		0			0
$184$	−14.1504	+	3.00775i	−1.04318	+	0.221734i
$185$	4.46780	+	10.2075i	0.328479	+	0.750471i
$186$		0			0
$187$	−7.44437	−	8.26781i	−0.544386	−	0.604602i
$188$	13.8148	−	42.5176i	1.00755	−	3.10092i
$189$		0			0
$190$	−40.6949	−	4.53672i	−2.95232	−	0.329128i
$191$	0.671770	+	0.746076i	0.0486076	+	0.0539842i	0.766958	−	0.641697i	$-0.221769\pi$
$191$	0.671770	+	0.746076i	0.0486076	+	0.0539842i	−0.718351	+	0.695681i	$0.755103\pi$
$192$		0			0
$193$	6.92614	+	11.9964i	0.498554	+	0.863521i	0.999999	−	0.00166856i	$-0.000531120\pi$
$193$	6.92614	+	11.9964i	0.498554	+	0.863521i	−0.501444	+	0.865190i	$0.667198\pi$
$194$	−2.91614	+	27.7452i	−0.209367	+	1.99199i
$195$		0			0
$196$	1.25605	+	11.9505i	0.0897177	+	0.853607i
$197$	−6.40803	+	4.65571i	−0.456553	+	0.331705i	−0.792178	−	0.610291i	$-0.791053\pi$
$197$	−6.40803	+	4.65571i	−0.456553	+	0.331705i	0.335624	+	0.941996i	$0.391053\pi$
$198$		0			0
$199$	14.6161			1.03611			0.518053	−	0.855348i	$-0.326657\pi$
$199$	14.6161			1.03611			0.518053	+	0.855348i	$0.326657\pi$
$200$	20.7301	−	22.4475i	1.46584	−	1.58728i
$201$		0			0
$202$	−21.6512	+	24.0461i	−1.52338	+	1.69188i
$203$	15.4551	+	6.88107i	1.08474	+	0.482956i
$204$		0			0
$205$	6.34681	−	8.62084i	0.443281	−	0.602106i
$206$	−18.8097	−	13.6661i	−1.31054	−	0.952160i
$207$		0			0
$208$	9.60259	+	6.97669i	0.665820	+	0.483746i
$209$	11.8514	+	13.1623i	0.819780	+	0.910458i
$210$		0			0
$211$	8.91267	−	9.89852i	0.613574	−	0.681442i	−0.353647	−	0.935379i	$-0.615059\pi$
$211$	8.91267	−	9.89852i	0.613574	−	0.681442i	0.967221	+	0.253936i	$0.0817254\pi$
$212$	13.4651	−	2.86209i	0.924785	−	0.196569i
$213$		0			0
$214$	−2.42922	−	0.516348i	−0.166058	−	0.0352968i
$215$	3.73549	+	18.1354i	0.254758	+	1.23683i
$216$		0			0
$217$	−11.3558	−	8.25045i	−0.770880	−	0.560077i
$218$	−11.2430	+	19.4734i	−0.761471	+	1.31891i
$219$		0			0
$220$	−24.0538	+	2.37497i	−1.62171	+	0.160120i
$221$	−7.40679	−	3.29772i	−0.498235	−	0.221828i
$222$		0			0
$223$	−3.56890	−	0.758594i	−0.238991	−	0.0507992i	0.0868587	−	0.996221i	$-0.472317\pi$
$223$	−3.56890	−	0.758594i	−0.238991	−	0.0507992i	−0.325850	+	0.945421i	$0.605650\pi$
$224$	−9.54893			−0.638014
$225$		0			0
$226$	17.1771			1.14260
$227$	15.3712	+	3.26726i	1.02023	+	0.216856i	0.687513	−	0.726172i	$-0.258703\pi$
$227$	15.3712	+	3.26726i	1.02023	+	0.216856i	0.332713	+	0.943028i	$0.392036\pi$
$228$		0			0
$229$	5.48833	+	2.44356i	0.362679	+	0.161475i	0.579982	−	0.814629i	$-0.303059\pi$
$229$	5.48833	+	2.44356i	0.362679	+	0.161475i	−0.217303	+	0.976104i	$0.569726\pi$
$230$	2.86964	−	13.0942i	0.189219	−	0.863407i
$231$		0			0
$232$	24.9950	−	43.2926i	1.64100	−	2.84230i
$233$	0.484321	+	0.351880i	0.0317289	+	0.0230524i	0.603537	−	0.797335i	$-0.293758\pi$
$233$	0.484321	+	0.351880i	0.0317289	+	0.0230524i	−0.571808	+	0.820388i	$0.693758\pi$
$234$		0			0
$235$	16.7376	+	15.2627i	1.09184	+	0.995630i
$236$	45.0950	+	9.58523i	2.93543	+	0.623945i
$237$		0			0
$238$	23.2689	−	4.94596i	1.50830	−	0.320599i
$239$	−0.786263	+	0.873234i	−0.0508592	+	0.0564848i	−0.768038	−	0.640405i	$-0.778767\pi$
$239$	−0.786263	+	0.873234i	−0.0508592	+	0.0564848i	0.717178	+	0.696890i	$0.245433\pi$
$240$		0			0
$241$	12.0251	+	13.3552i	0.774604	+	0.860284i	0.993307	−	0.115507i	$-0.0368493\pi$
$241$	12.0251	+	13.3552i	0.774604	+	0.860284i	−0.218703	+	0.975791i	$0.570183\pi$
$242$	−10.2448	−	7.44331i	−0.658563	−	0.478474i
$243$		0			0
$244$	9.41469	+	6.84017i	0.602714	+	0.437897i
$245$	−5.77852	−	1.91790i	−0.369176	−	0.122530i
$246$		0			0
$247$	11.7916	+	5.24996i	0.750282	+	0.334047i
$248$	−27.7530	+	30.8228i	−1.76232	+	1.95725i
$249$		0			0
$250$	11.0249	+	26.0786i	0.697277	+	1.64936i
$251$	−0.313172			−0.0197673			−0.00988364	−	0.999951i	$-0.503146\pi$
$251$	−0.313172			−0.0197673			−0.00988364	+	0.999951i	$0.503146\pi$
$252$		0			0
$253$	−4.69096	+	3.40818i	−0.294918	+	0.214270i
$254$	2.64004	+	25.1183i	0.165651	+	1.57606i
$255$		0			0
$256$	3.18545	−	30.3075i	0.199090	−	1.89422i
$257$	−1.48530	−	2.57262i	−0.0926507	−	0.160476i	0.815975	−	0.578087i	$-0.196201\pi$
$257$	−1.48530	−	2.57262i	−0.0926507	−	0.160476i	−0.908626	+	0.417611i	$0.862867\pi$
$258$		0			0
$259$	6.89579	+	7.65855i	0.428484	+	0.475879i
$260$	−15.3099	+	8.71099i	−0.949482	+	0.540233i
$261$		0			0
$262$	−10.7665	+	33.1359i	−0.665158	+	2.04714i
$263$	5.43812	+	6.03964i	0.335329	+	0.372420i	0.887102	−	0.461574i	$-0.152715\pi$
$263$	5.43812	+	6.03964i	0.335329	+	0.372420i	−0.551773	+	0.833994i	$0.686048\pi$
$264$		0			0
$265$	−1.49315	+	6.81327i	−0.0917235	+	0.418536i
$266$	−37.0440	+	7.87395i	−2.27132	+	0.482783i
$267$		0			0
$268$	3.59745	−	6.23097i	0.219749	−	0.380617i
$269$	−18.6230	−	13.5304i	−1.13547	−	0.824965i	−0.148986	−	0.988839i	$-0.547601\pi$
$269$	−18.6230	−	13.5304i	−1.13547	−	0.824965i	−0.986481	+	0.163874i	$0.947601\pi$
$270$		0			0
$271$	−18.3049	+	13.2993i	−1.11194	+	0.807874i	−0.982969	−	0.183774i	$-0.941169\pi$
$271$	−18.3049	+	13.2993i	−1.11194	+	0.807874i	−0.128974	+	0.991648i	$0.541169\pi$
$272$	−3.15706	−	30.0374i	−0.191425	−	1.82129i
$273$		0			0
$274$	10.7997	+	18.7056i	0.652432	+	1.13005i
$275$	3.93104	−	11.5989i	0.237051	−	0.699441i
$276$		0			0
$277$	10.1292	+	2.15304i	0.608607	+	0.129363i	0.501898	−	0.864927i	$-0.332635\pi$
$277$	10.1292	+	2.15304i	0.608607	+	0.129363i	0.106709	+	0.994290i	$0.465969\pi$
$278$	−19.1148	+	13.8877i	−1.14643	+	0.832931i
$279$		0			0
$280$	11.6571	−	25.7443i	0.696643	−	1.53851i
$281$	23.2406	−	10.3474i	1.38642	−	0.617273i	0.428297	−	0.903638i	$-0.359114\pi$
$281$	23.2406	−	10.3474i	1.38642	−	0.617273i	0.958121	+	0.286365i	$0.0924470\pi$
$282$		0			0
$283$	1.73208	−	16.4797i	0.102962	−	0.979614i	−0.814061	−	0.580779i	$-0.802748\pi$
$283$	1.73208	−	16.4797i	0.102962	−	0.979614i	0.917023	−	0.398835i	$-0.130585\pi$
$284$	−43.9755	+	9.34728i	−2.60946	+	0.554659i
$285$		0			0
$286$	10.8303	+	2.30204i	0.640407	+	0.136123i
$287$	3.05963	−	9.41657i	0.180604	−	0.555842i
$288$		0			0
$289$	1.12201	+	3.45318i	0.0660004	+	0.203128i
$290$	26.9905	+	37.6460i	1.58494	+	2.21065i
$291$		0			0
$292$	0.907660	−	8.63581i	0.0531168	−	0.505373i
$293$	6.06420	+	10.5035i	0.354274	+	0.613621i	0.986993	−	0.160760i	$-0.0513946\pi$
$293$	6.06420	+	10.5035i	0.354274	+	0.613621i	−0.632719	+	0.774381i	$0.718061\pi$
$294$		0			0
$295$	−13.8491	+	18.8112i	−0.806328	+	1.09523i
$296$	24.6360	−	17.8991i	1.43194	−	1.04037i
$297$		0			0
$298$	5.43564	+	16.7292i	0.314878	+	0.969095i
$299$	−2.11279	+	3.65946i	−0.122186	+	0.211632i
$300$		0			0
$301$	8.56274	+	14.8311i	0.493548	+	0.854851i
$302$	1.33598	−	1.48375i	0.0768768	−	0.0853803i
$303$		0			0
$304$	5.02604	+	47.8195i	0.288263	+	2.74264i
$305$	−5.12490	+	2.91595i	−0.293451	+	0.166967i
$306$		0			0
$307$	−11.7705			−0.671776			−0.335888	−	0.941902i	$-0.609036\pi$
$307$	−11.7705			−0.671776			−0.335888	+	0.941902i	$0.609036\pi$
$308$	−20.4227	+	9.09277i	−1.16369	+	0.518109i
$309$		0			0
$310$	−15.4104	−	35.2080i	−0.875253	−	1.99968i
$311$	−6.61932	+	7.35150i	−0.375347	+	0.416865i	−0.900990	−	0.433840i	$-0.857158\pi$
$311$	−6.61932	+	7.35150i	−0.375347	+	0.416865i	0.525643	+	0.850705i	$0.323825\pi$
$312$		0			0
$313$	−23.0294	−	25.5767i	−1.30170	−	1.44568i	−0.823376	−	0.567497i	$-0.807912\pi$
$313$	−23.0294	−	25.5767i	−1.30170	−	1.44568i	−0.478322	−	0.878185i	$-0.658755\pi$
$314$	−3.04248	−	9.36378i	−0.171697	−	0.528429i
$315$		0			0
$316$	20.3452	−	62.6162i	1.14451	−	3.52243i
$317$	−20.3148	+	9.04473i	−1.14099	+	0.508003i	−0.888172	−	0.459510i	$-0.848025\pi$
$317$	−20.3148	+	9.04473i	−1.14099	+	0.508003i	−0.252821	+	0.967513i	$0.581358\pi$
$318$		0			0
$319$	2.09439	−	19.9268i	0.117263	−	1.11569i
$320$	3.09935	+	1.81555i	0.173259	+	0.101492i
$321$		0			0
$322$	−1.29596	−	12.3303i	−0.0722212	−	0.687139i
$323$	−10.1495	−	31.2368i	−0.564731	−	1.73806i
$324$		0			0
$325$	−0.820957	−	8.88722i	−0.0455385	−	0.492974i
$326$	10.6278	−	18.4078i	0.588618	−	1.01952i
$327$		0			0
$328$	−26.7274	−	11.8998i	−1.47577	−	0.657057i
$329$	19.1391	+	8.52130i	1.05518	+	0.469794i
$330$		0			0
$331$	−11.9559	+	5.32309i	−0.657154	+	0.292584i	−0.708094	−	0.706118i	$-0.750445\pi$
$331$	−11.9559	+	5.32309i	−0.657154	+	0.292584i	0.0509405	+	0.998702i	$0.483778\pi$
$332$	−17.9189			−0.983426
$333$		0			0
$334$	8.45777	−	26.0303i	0.462788	−	1.42432i
$335$	2.12416	+	2.96275i	0.116056	+	0.161873i
$336$		0			0
$337$	−14.2119	+	3.02084i	−0.774174	+	0.164556i	−0.578026	−	0.816019i	$-0.696177\pi$
$337$	−14.2119	+	3.02084i	−0.774174	+	0.164556i	−0.196148	+	0.980574i	$0.562843\pi$
$338$	−24.3094	+	5.16712i	−1.32226	+	0.281054i
$339$		0			0
$340$	42.5401	+	14.1192i	2.30706	+	0.765720i
$341$	−5.13715	+	15.8105i	−0.278192	+	0.856188i
$342$		0			0
$343$	−20.1081			−1.08573
$344$	46.2289	−	20.5824i	2.49249	−	1.10973i
$345$		0			0
$346$	−38.0822	−	16.9553i	−2.04731	−	0.911522i
$347$	−10.1994	−	4.54109i	−0.547535	−	0.243778i	0.114276	−	0.993449i	$-0.463545\pi$
$347$	−10.1994	−	4.54109i	−0.547535	−	0.243778i	−0.661811	+	0.749671i	$0.730212\pi$
$348$		0			0
$349$	4.08628	−	7.07765i	0.218734	−	0.378858i	−0.735687	−	0.677321i	$-0.763141\pi$
$349$	4.08628	−	7.07765i	0.218734	−	0.378858i	0.954421	+	0.298463i	$0.0964740\pi$
$350$	17.2757	+	19.6799i	0.923424	+	1.05194i
$351$		0			0
$352$	3.49476	+	10.7558i	0.186272	+	0.573285i
$353$	−2.35701	−	22.4255i	−0.125451	−	1.19359i	−0.858283	−	0.513177i	$-0.828468\pi$
$353$	−2.35701	−	22.4255i	−0.125451	−	1.19359i	0.732832	−	0.680410i	$-0.238198\pi$
$354$		0			0
$355$	4.87647	−	22.2514i	0.258816	−	1.18098i
$356$	0.158225	−	1.50541i	0.00838592	−	0.0797867i
$357$		0			0
$358$	1.20878	−	0.538184i	0.0638861	−	0.0284439i
$359$	7.75846	−	23.8781i	0.409476	−	1.26024i	−0.507624	−	0.861579i	$-0.669476\pi$
$359$	7.75846	−	23.8781i	0.409476	−	1.26024i	0.917100	−	0.398658i	$-0.130524\pi$
$360$		0			0
$361$	10.2866	+	31.6589i	0.541400	+	1.66626i
$362$	−39.1085	−	43.4344i	−2.05550	−	2.28286i
$363$		0			0
$364$	−10.9013	+	12.1071i	−0.571381	+	0.634583i
$365$	3.79634	+	2.22384i	0.198709	+	0.116401i
$366$		0			0
$367$	−5.89638	+	2.62524i	−0.307788	+	0.137036i	−0.554818	−	0.831972i	$-0.687212\pi$
$367$	−5.89638	+	2.62524i	−0.307788	+	0.137036i	0.247030	+	0.969008i	$0.420545\pi$
$368$	−15.7411			−0.820562
$369$		0			0
$370$	5.69263	+	27.6372i	0.295946	+	1.43679i
$371$	0.674324	+	6.41576i	0.0350092	+	0.333090i
$372$		0			0
$373$	−16.1275	+	17.9114i	−0.835050	+	0.927417i	−0.998248	−	0.0591766i	$-0.981152\pi$
$373$	−16.1275	+	17.9114i	−0.835050	+	0.927417i	0.163198	+	0.986593i	$0.447819\pi$
$374$	−14.0871	−	24.3996i	−0.728428	−	1.26167i
$375$		0			0
$376$	30.9530	−	53.6121i	1.59628	−	2.76484i
$377$	−4.51220	−	13.8871i	−0.232390	−	0.715224i
$378$		0			0
$379$	−0.345496	+	0.251018i	−0.0177469	+	0.0128939i	−0.596623	−	0.802521i	$-0.703491\pi$
$379$	−0.345496	+	0.251018i	−0.0177469	+	0.0128939i	0.578876	+	0.815415i	$0.303491\pi$
$380$	−67.7238	−	22.4777i	−3.47416	−	1.15308i
$381$		0			0
$382$	1.27120	+	2.20179i	0.0650404	+	0.112653i
$383$	2.38455	−	22.6874i	0.121845	−	1.15927i	−0.747220	−	0.664576i	$-0.768612\pi$
$383$	2.38455	−	22.6874i	0.121845	−	1.15927i	0.869065	−	0.494698i	$-0.164721\pi$
$384$		0			0
$385$	0.0713958	−	11.3269i	0.00363867	−	0.577273i
$386$	10.8402	+	33.3628i	0.551753	+	1.69812i
$387$		0			0
$388$	−15.0234	+	46.2373i	−0.762698	+	2.34734i
$389$	12.1318	+	2.57870i	0.615108	+	0.130745i	0.504921	−	0.863166i	$-0.331522\pi$
$389$	12.1318	+	2.57870i	0.615108	+	0.130745i	0.110187	+	0.993911i	$0.464855\pi$
$390$		0			0
$391$	10.5174	−	2.23555i	0.531889	−	0.113056i
$392$	−1.73931	+	16.5484i	−0.0878482	+	0.835820i
$393$		0			0
$394$	−18.3245	+	8.15860i	−0.923175	+	0.411024i
$395$	24.6496	+	22.4776i	1.24026	+	1.13097i
$396$		0			0
$397$	−2.26012	+	1.64207i	−0.113432	+	0.0824133i	−0.643055	−	0.765820i	$-0.722333\pi$
$397$	−2.26012	+	1.64207i	−0.113432	+	0.0824133i	0.529623	+	0.848233i	$0.322333\pi$
$398$	36.2052	+	7.69565i	1.81480	+	0.385748i
$399$		0			0
$400$	27.1420	−	19.2018i	1.35710	−	0.960089i
$401$	18.1027	+	31.3549i	0.904008	+	1.56579i	0.822244	+	0.569136i	$0.192722\pi$
$401$	18.1027	+	31.3549i	0.904008	+	1.56579i	0.0817642	+	0.996652i	$0.473945\pi$
$402$		0			0
$403$	1.26636	+	12.0486i	0.0630820	+	0.600185i
$404$	−45.6186	+	33.1438i	−2.26961	+	1.64897i
$405$		0			0
$406$	34.6605	+	25.1824i	1.72017	+	1.24978i
$407$	6.10273	−	10.5702i	0.302501	−	0.523947i
$408$		0			0
$409$	21.7118	−	4.61499i	1.07358	−	0.228196i	0.362983	−	0.931796i	$-0.381758\pi$
$409$	21.7118	−	4.61499i	1.07358	−	0.228196i	0.710597	+	0.703599i	$0.248425\pi$
$410$	20.2606	−	18.0128i	1.00060	−	0.889588i
$411$		0			0
$412$	−27.1112	−	30.1100i	−1.33567	−	1.48341i
$413$	−6.67630	+	20.5475i	−0.328519	+	1.01108i
$414$		0			0
$415$	3.74506	−	8.27084i	0.183838	−	0.405999i
$416$	5.51480	+	6.12480i	0.270385	+	0.300293i
$417$		0			0
$418$	22.4267	+	38.8441i	1.09692	+	1.89993i
$419$	−3.34167	+	31.7939i	−0.163251	+	1.55323i	0.539617	+	0.841911i	$0.318569\pi$
$419$	−3.34167	+	31.7939i	−0.163251	+	1.55323i	−0.702868	+	0.711320i	$0.748097\pi$
$420$		0			0
$421$	0.145994	+	1.38904i	0.00711533	+	0.0676978i	0.997503	−	0.0706190i	$-0.0224974\pi$
$421$	0.145994	+	1.38904i	0.00711533	+	0.0676978i	−0.990388	+	0.138317i	$0.955831\pi$
$422$	27.2891	−	19.8267i	1.32841	−	0.965150i
$423$		0			0
$424$	19.0622			0.925745
$425$	−15.4079	+	16.6844i	−0.747394	+	0.809311i
$426$		0			0
$427$	−3.64913	+	4.05277i	−0.176594	+	0.196127i
$428$	−3.95372	−	1.76031i	−0.191110	−	0.0850877i
$429$		0			0
$430$	−0.295555	+	46.8897i	−0.0142529	+	2.26122i
$431$	0.506575	+	0.368048i	0.0244009	+	0.0177283i	0.599919	−	0.800061i	$-0.295200\pi$
$431$	0.506575	+	0.368048i	0.0244009	+	0.0177283i	−0.575518	+	0.817789i	$0.695200\pi$
$432$		0			0
$433$	−4.64257	−	3.37302i	−0.223108	−	0.162097i	0.470617	−	0.882338i	$-0.344031\pi$
$433$	−4.64257	−	3.37302i	−0.223108	−	0.162097i	−0.693724	+	0.720241i	$0.744031\pi$
$434$	−23.7851	−	26.4160i	−1.14172	−	1.26801i
$435$		0			0
$436$	−26.2201	+	29.1204i	−1.25572	+	1.39461i
$437$	−16.7437	+	3.55899i	−0.800960	+	0.170249i
$438$		0			0
$439$	22.6653	+	4.81766i	1.08176	+	0.229934i	0.714111	−	0.700032i	$-0.246831\pi$
$439$	22.6653	+	4.81766i	1.08176	+	0.229934i	0.367644	+	0.929966i	$0.380164\pi$
$440$	−33.2643	−	3.70835i	−1.58581	−	0.176789i
$441$		0			0
$442$	−16.6109	−	12.0685i	−0.790100	−	0.574041i
$443$	−10.9667	+	18.9950i	−0.521046	+	0.902477i	0.478655	+	0.878003i	$0.341125\pi$
$443$	−10.9667	+	18.9950i	−0.521046	+	0.902477i	−0.999700	+	0.0244742i	$0.992209\pi$
$444$		0			0
$445$	0.661786	+	0.387664i	0.0313717	+	0.0183771i
$446$	−8.44104	−	3.75819i	−0.399695	−	0.177956i
$447$		0			0
$448$	3.24959	+	0.690721i	0.153529	+	0.0326335i
$449$	12.6712			0.597990			0.298995	−	0.954255i	$-0.403349\pi$
$449$	12.6712			0.597990			0.298995	+	0.954255i	$0.403349\pi$
$450$		0			0
$451$	−11.7265			−0.552178
$452$	29.2796	+	6.22357i	1.37720	+	0.292732i
$453$		0			0
$454$	36.3555	+	16.1865i	1.70625	+	0.759671i
$455$	−3.30991	−	7.56209i	−0.155171	−	0.354516i
$456$		0			0
$457$	0.0638731	−	0.110631i	0.00298786	−	0.00517512i	−0.864528	−	0.502585i	$-0.832382\pi$
$457$	0.0638731	−	0.110631i	0.00298786	−	0.00517512i	0.867515	+	0.497410i	$0.165716\pi$
$458$	12.3084	+	8.94261i	0.575136	+	0.417861i
$459$		0			0
$460$	9.63581	−	21.2804i	0.449272	−	0.992203i
$461$	−7.08732	−	1.50646i	−0.330090	−	0.0701627i	0.0398858	−	0.999204i	$-0.487301\pi$
$461$	−7.08732	−	1.50646i	−0.330090	−	0.0701627i	−0.369975	+	0.929042i	$0.620634\pi$
$462$		0			0
$463$	−22.2769	+	4.73511i	−1.03530	+	0.220059i	−0.694059	−	0.719918i	$-0.744179\pi$
$463$	−22.2769	+	4.73511i	−1.03530	+	0.220059i	−0.341238	+	0.939977i	$0.610846\pi$
$464$	36.3970	−	40.4230i	1.68969	−	1.87659i
$465$		0			0
$466$	1.01443	+	1.12664i	0.0469925	+	0.0521905i
$467$	7.87672	+	5.72277i	0.364491	+	0.264818i	0.754923	−	0.655814i	$-0.227674\pi$
$467$	7.87672	+	5.72277i	0.364491	+	0.264818i	−0.390432	+	0.920632i	$0.627674\pi$
$468$		0			0
$469$	2.72780	+	1.98186i	0.125958	+	0.0915138i
$470$	33.4242	+	46.6196i	1.54174	+	2.15040i
$471$		0			0
$472$	58.3208	+	25.9661i	2.68443	+	1.19519i
$473$	13.5717	−	15.0729i	0.624028	−	0.693053i
$474$		0			0
$475$	24.5294	−	26.5615i	1.12548	−	1.21872i
$476$	41.4556			1.90012
$477$		0			0
$478$	−2.40741	+	1.74909i	−0.110112	+	0.0800013i
$479$	−1.17638	−	11.1925i	−0.0537503	−	0.511400i	−0.987964	−	0.154686i	$-0.950564\pi$
$479$	−1.17638	−	11.1925i	−0.0537503	−	0.511400i	0.934213	−	0.356715i	$-0.116103\pi$
$480$		0			0
$481$	0.929762	−	8.84609i	0.0423935	−	0.403347i
$482$	22.7553	+	39.4133i	1.03648	+	1.79523i
$483$		0			0
$484$	−14.7662	−	16.3996i	−0.671193	−	0.745436i
$485$	−18.2019	−	16.5980i	−0.826506	−	0.753676i
$486$		0			0
$487$	−2.45081	+	7.54283i	−0.111057	+	0.341798i	−0.991104	−	0.133088i	$-0.957511\pi$
$487$	−2.45081	+	7.54283i	−0.111057	+	0.341798i	0.880047	+	0.474886i	$0.157511\pi$
$488$	10.7827	+	11.9754i	0.488112	+	0.542103i
$489$		0			0
$490$	−13.3040	−	7.79330i	−0.601014	−	0.352065i
$491$	14.3906	−	3.05881i	0.649438	−	0.138042i	0.128598	−	0.991697i	$-0.458952\pi$
$491$	14.3906	−	3.05881i	0.649438	−	0.138042i	0.520840	+	0.853654i	$0.325619\pi$
$492$		0			0
$493$	−18.5778	+	32.1777i	−0.836702	+	1.44921i
$494$	26.4445	+	19.2131i	1.18980	+	0.864437i
$495$		0			0
$496$	−36.5114	+	26.5271i	−1.63941	+	1.19110i
$497$	−2.20227	−	20.9532i	−0.0987853	−	0.939879i
$498$		0			0
$499$	−11.7212	−	20.3017i	−0.524714	−	0.908831i	−0.999586	−	0.0287762i	$-0.990839\pi$
$499$	−11.7212	−	20.3017i	−0.524714	−	0.908831i	0.474872	−	0.880055i	$-0.342494\pi$
$500$	9.34406	+	48.4475i	0.417879	+	2.16664i
$501$		0			0
$502$	−0.775753	−	0.164891i	−0.0346235	−	0.00735946i
$503$	11.6643	−	8.47463i	0.520087	−	0.377865i	−0.296550	−	0.955017i	$-0.595836\pi$
$503$	11.6643	−	8.47463i	0.520087	−	0.377865i	0.816637	+	0.577152i	$0.195836\pi$
$504$		0			0
$505$	−5.76393	−	27.9833i	−0.256491	−	1.24524i
$506$	−13.4143	+	5.97245i	−0.596340	+	0.265508i
$507$		0			0
$508$	−4.60069	+	43.7726i	−0.204122	+	1.94209i
$509$	0.377856	−	0.0803159i	0.0167482	−	0.00355994i	−0.199530	−	0.979892i	$-0.563942\pi$
$509$	0.377856	−	0.0803159i	0.0167482	−	0.00355994i	0.216278	+	0.976332i	$0.430608\pi$
$510$		0			0
$511$	3.98037	+	0.846053i	0.176081	+	0.0374272i
$512$	15.6267	−	48.0942i	0.690611	−	2.12548i
$513$		0			0
$514$	−2.32468	−	7.15462i	−0.102537	−	0.315577i
$515$	19.5641	−	6.22072i	0.862099	−	0.274118i
$516$		0			0
$517$	2.59363	−	24.6767i	0.114068	−	1.08528i
$518$	13.0490	+	22.6016i	0.573342	+	0.993057i
$519$		0			0
$520$	−23.2450	+	7.39111i	−1.01936	+	0.324121i
$521$	−35.3256	+	25.6656i	−1.54764	+	1.12443i	−0.602340	+	0.798240i	$0.705765\pi$
$521$	−35.3256	+	25.6656i	−1.54764	+	1.12443i	−0.945304	+	0.326190i	$0.894235\pi$
$522$		0			0
$523$	−6.03504	−	18.5739i	−0.263894	−	0.812182i	−0.991946	−	0.126660i	$-0.959574\pi$
$523$	−6.03504	−	18.5739i	−0.263894	−	0.812182i	0.728052	−	0.685522i	$-0.240426\pi$
$524$	−30.3581	+	52.5818i	−1.32620	+	2.29705i
$525$		0			0
$526$	10.2907	+	17.8239i	0.448694	+	0.777161i
$527$	20.6277	−	22.9094i	0.898559	−	0.997950i
$528$		0			0
$529$	1.81839	+	17.3008i	0.0790603	+	0.752208i
$530$	−7.28596	+	16.0908i	−0.316482	+	0.698940i
$531$		0			0
$532$	−65.9973			−2.86135
$533$	−7.80693	+	3.47587i	−0.338156	+	0.150557i
$534$		0			0
$535$	1.63884	−	1.45702i	0.0708531	−	0.0629923i
$536$	6.66662	−	7.40403i	0.287954	−	0.319805i
$537$		0			0
$538$	−39.0067	−	43.3213i	−1.68170	−	1.86771i
$539$	2.06094	+	6.34291i	0.0887708	+	0.273208i
$540$		0			0
$541$	−5.67479	+	17.4652i	−0.243978	+	0.750888i	0.751824	+	0.659363i	$0.229174\pi$
$541$	−5.67479	+	17.4652i	−0.243978	+	0.750888i	−0.995803	+	0.0915249i	$0.970826\pi$
$542$	−52.3450	+	23.3055i	−2.24841	+	1.00106i
$543$		0			0
$544$	2.19215	−	20.8569i	0.0939878	−	0.894234i
$545$	−7.96111	−	18.1886i	−0.341017	−	0.779115i
$546$		0			0
$547$	−4.02229	−	38.2695i	−0.171981	−	1.63629i	−0.651425	−	0.758713i	$-0.725828\pi$
$547$	−4.02229	−	38.2695i	−0.171981	−	1.63629i	0.479444	−	0.877572i	$-0.340838\pi$
$548$	11.6315	+	35.7980i	0.496872	+	1.52922i
$549$		0			0
$550$	15.8446	−	26.6616i	0.675614	−	1.13686i
$551$	29.5758	−	51.2268i	1.25997	−	2.18234i
$552$		0			0
$553$	28.1864	+	12.5494i	1.19861	+	0.533655i
$554$	23.9573	+	10.6665i	1.01785	+	0.453175i
$555$		0			0
$556$	−37.6145	+	16.7471i	−1.59521	+	0.710233i
$557$	−34.0992			−1.44483			−0.722414	−	0.691461i	$-0.756968\pi$
$557$	−34.0992			−1.44483			−0.722414	+	0.691461i	$0.756968\pi$
$558$		0			0
$559$	4.56761	−	14.0577i	0.193189	−	0.594576i
$560$	18.2311	−	24.7632i	0.770405	−	1.04644i
$561$		0			0
$562$	63.0169	−	13.3946i	2.65821	−	0.565019i
$563$	−24.2833	+	5.16157i	−1.02342	+	0.217534i	−0.688901	−	0.724855i	$-0.741907\pi$
$563$	−24.2833	+	5.16157i	−1.02342	+	0.217534i	−0.334518	+	0.942390i	$0.608573\pi$
$564$		0			0
$565$	−8.99208	+	12.2139i	−0.378300	+	0.513842i
$566$	12.9674	−	39.9094i	0.545058	−	1.67752i
$567$		0			0
$568$	−62.2553			−2.61217
$569$	25.8779	−	11.5216i	1.08486	−	0.483011i	0.215153	−	0.976580i	$-0.430975\pi$
$569$	25.8779	−	11.5216i	1.08486	−	0.483011i	0.869706	+	0.493570i	$0.164308\pi$
$570$		0			0
$571$	29.1809	+	12.9922i	1.22118	+	0.543706i	0.913132	−	0.407663i	$-0.133656\pi$
$571$	29.1809	+	12.9922i	1.22118	+	0.543706i	0.308052	+	0.951370i	$0.400323\pi$
$572$	17.6269	+	7.84802i	0.737020	+	0.328142i
$573$		0			0
$574$	12.5369	−	21.7146i	0.523282	−	0.906351i
$575$	7.80852	+	8.89522i	0.325638	+	0.370956i
$576$		0			0
$577$	−4.21265	−	12.9652i	−0.175375	−	0.539748i	0.824276	−	0.566189i	$-0.191583\pi$
$577$	−4.21265	−	12.9652i	−0.175375	−	0.539748i	−0.999650	+	0.0264408i	$0.991583\pi$
$578$	0.961131	+	9.14455i	0.0399778	+	0.380363i
$579$		0			0
$580$	32.3676	+	73.9497i	1.34399	+	3.07059i
$581$	0.877759	−	8.35132i	0.0364156	−	0.346471i
$582$		0			0
$583$	6.97983	−	3.10762i	0.289075	−	0.128705i
$584$	3.71570	−	11.4358i	0.153757	−	0.473215i
$585$		0			0
$586$	9.49120	+	29.2109i	0.392078	+	1.20669i
$587$	26.5805	+	29.5207i	1.09710	+	1.21845i	0.974118	+	0.226039i	$0.0725777\pi$
$587$	26.5805	+	29.5207i	1.09710	+	1.21845i	0.122978	+	0.992409i	$0.460756\pi$
$588$		0			0
$589$	−32.8393	+	36.4718i	−1.35312	+	1.50279i
$590$	−44.2099	+	39.3050i	−1.82009	+	1.61816i
$591$		0			0
$592$	30.2702	−	13.4772i	1.24410	−	0.553908i
$593$	−16.9892			−0.697663			−0.348832	−	0.937185i	$-0.613421\pi$
$593$	−16.9892			−0.697663			−0.348832	+	0.937185i	$0.613421\pi$
$594$		0			0
$595$	−8.66425	+	19.1347i	−0.355200	+	0.784447i
$596$	3.20416	+	30.4856i	0.131248	+	1.24874i
$597$		0			0
$598$	−7.16033	+	7.95235i	−0.292808	+	0.325196i
$599$	7.81800	+	13.5412i	0.319435	+	0.553277i	0.980370	−	0.197166i	$-0.0631736\pi$
$599$	7.81800	+	13.5412i	0.319435	+	0.553277i	−0.660935	+	0.750443i	$0.729840\pi$
$600$		0			0
$601$	−0.702116	+	1.21610i	−0.0286399	+	0.0496058i	−0.879990	−	0.474992i	$-0.842451\pi$
$601$	−0.702116	+	1.21610i	−0.0286399	+	0.0496058i	0.851350	+	0.524598i	$0.175784\pi$
$602$	13.4017	+	41.2462i	0.546213	+	1.68107i
$603$		0			0
$604$	2.81486	−	2.04512i	0.114535	−	0.0832147i
$605$	10.6557	−	3.38815i	0.433217	−	0.137748i
$606$		0			0
$607$	−3.79337	−	6.57031i	−0.153968	−	0.266681i	0.778715	−	0.627378i	$-0.215872\pi$
$607$	−3.79337	−	6.57031i	−0.153968	−	0.266681i	−0.932683	+	0.360698i	$0.882539\pi$
$608$	−3.48990	+	33.2042i	−0.141534	+	1.34661i
$609$		0			0
$610$	−14.2301	+	4.52467i	−0.576159	+	0.183199i
$611$	−5.58777	−	17.1974i	−0.226057	−	0.695732i
$612$		0			0
$613$	9.44377	−	29.0649i	0.381430	−	1.17392i	−0.557607	−	0.830105i	$-0.688280\pi$
$613$	9.44377	−	29.0649i	0.381430	−	1.17392i	0.939037	−	0.343816i	$-0.111720\pi$
$614$	−29.1564	−	6.19737i	−1.17665	−	0.250106i
$615$		0			0
$616$	−30.2801	+	6.43623i	−1.22002	+	0.259323i
$617$	0.105946	−	1.00801i	0.00426524	−	0.0405811i	−0.992182	−	0.124797i	$-0.960172\pi$
$617$	0.105946	−	1.00801i	0.00426524	−	0.0405811i	0.996448	+	0.0842162i	$0.0268386\pi$
$618$		0			0
$619$	42.0648	−	18.7285i	1.69073	−	0.752761i	0.691181	−	0.722681i	$-0.257091\pi$
$619$	42.0648	−	18.7285i	1.69073	−	0.752761i	0.999548	−	0.0300796i	$-0.00957609\pi$
$620$	−13.5117	−	65.5981i	−0.542644	−	2.63448i
$621$		0			0
$622$	−20.2673	+	14.7250i	−0.812644	+	0.590420i
$623$	0.693866	+	0.147486i	0.0277991	+	0.00590889i
$624$		0			0
$625$	−24.3149	−	5.81261i	−0.972595	−	0.232505i
$626$	−43.5789	−	75.4809i	−1.74176	−	3.01682i
$627$		0			0
$628$	−1.79346	−	17.0636i	−0.0715668	−	0.680913i
$629$	−18.3110	+	13.3037i	−0.730108	+	0.530455i
$630$		0			0
$631$	−6.24556	−	4.53767i	−0.248632	−	0.180642i	0.456488	−	0.889729i	$-0.349107\pi$
$631$	−6.24556	−	4.53767i	−0.248632	−	0.180642i	−0.705120	+	0.709088i	$0.749107\pi$
$632$	45.5848	−	78.9552i	1.81327	−	3.14067i
$633$		0			0
$634$	−55.0836	+	11.7084i	−2.18765	+	0.464999i
$635$	−19.2426	−	11.2720i	−0.763620	−	0.447317i
$636$		0			0
$637$	3.25219	+	3.61192i	0.128857	+	0.143110i
$638$	15.6798	−	48.2575i	0.620770	−	1.91053i
$639$		0			0
$640$	21.9790	+	20.0422i	0.868795	+	0.792239i
$641$	−18.6755	−	20.7412i	−0.737637	−	0.819229i	0.251246	−	0.967923i	$-0.419160\pi$
$641$	−18.6755	−	20.7412i	−0.737637	−	0.819229i	−0.988883	+	0.148694i	$0.952493\pi$
$642$		0			0
$643$	−3.87285	−	6.70797i	−0.152730	−	0.264537i	0.779500	−	0.626402i	$-0.215473\pi$
$643$	−3.87285	−	6.70797i	−0.152730	−	0.264537i	−0.932230	+	0.361866i	$0.882140\pi$
$644$	2.25842	−	21.4874i	0.0889943	−	0.846724i
$645$		0			0
$646$	−8.69421	−	82.7199i	−0.342069	−	3.25457i
$647$	27.8778	−	20.2544i	1.09599	−	0.796283i	0.115588	−	0.993297i	$-0.463125\pi$
$647$	27.8778	−	20.2544i	1.09599	−	0.796283i	0.980401	+	0.197015i	$0.0631246\pi$
$648$		0			0
$649$	25.5879			1.00441
$650$	2.64572	−	22.4466i	0.103774	−	0.880428i
$651$		0			0
$652$	24.7854	−	27.5269i	0.970670	−	1.07804i
$653$	10.9336	+	4.86796i	0.427866	+	0.190498i	0.609360	−	0.792894i	$-0.291427\pi$
$653$	10.9336	+	4.86796i	0.427866	+	0.190498i	−0.181494	+	0.983392i	$0.558093\pi$
$654$		0			0
$655$	−17.9254	−	25.0021i	−0.700403	−	0.976911i
$656$	−25.7547	−	18.7119i	−1.00555	−	0.730576i
$657$		0			0
$658$	42.9225	+	31.1850i	1.67329	+	1.21572i
$659$	−6.24538	−	6.93619i	−0.243285	−	0.270196i	0.609119	−	0.793079i	$-0.291523\pi$
$659$	−6.24538	−	6.93619i	−0.243285	−	0.270196i	−0.852404	+	0.522883i	$0.824856\pi$
$660$		0			0
$661$	3.22292	−	3.57941i	0.125357	−	0.139223i	−0.677199	−	0.735800i	$-0.736806\pi$
$661$	3.22292	−	3.57941i	0.125357	−	0.139223i	0.802556	+	0.596577i	$0.203473\pi$
$662$	−32.4183	+	6.89073i	−1.25997	+	0.267816i
$663$		0			0
$664$	−24.2709	−	5.15893i	−0.941892	−	0.200205i
$665$	13.7935	−	30.4624i	0.534888	−	1.18128i
$666$		0			0
$667$	15.6664	+	11.3823i	0.606605	+	0.440724i
$668$	23.8482	−	41.3063i	0.922714	−	1.59819i
$669$		0			0
$670$	3.70177	+	8.45739i	0.143012	+	0.326737i
$671$	5.90050	+	2.62707i	0.227786	+	0.101417i
$672$		0			0
$673$	17.4410	+	3.70720i	0.672301	+	0.142902i	0.531399	−	0.847122i	$-0.321666\pi$
$673$	17.4410	+	3.70720i	0.672301	+	0.142902i	0.140902	+	0.990024i	$0.455000\pi$
$674$	−36.7946			−1.41728
$675$		0			0
$676$	−43.3093			−1.66574
$677$	14.9861	+	3.18540i	0.575963	+	0.122425i	0.486678	−	0.873581i	$-0.338208\pi$
$677$	14.9861	+	3.18540i	0.575963	+	0.122425i	0.0892851	+	0.996006i	$0.471542\pi$
$678$		0			0
$679$	−20.8135	−	9.26678i	−0.798750	−	0.355627i
$680$	53.5550	+	31.3717i	2.05374	+	1.20305i
$681$		0			0
$682$	−21.0497	+	36.4591i	−0.806034	+	1.39609i
$683$	22.9889	+	16.7024i	0.879645	+	0.639100i	0.933158	−	0.359468i	$-0.117042\pi$
$683$	22.9889	+	16.7024i	0.879645	+	0.639100i	−0.0535124	+	0.998567i	$0.517042\pi$
$684$		0			0
$685$	−18.9543	−	2.11305i	−0.724207	−	0.0807355i
$686$	−49.8093	−	10.5873i	−1.90173	−	0.404225i
$687$		0			0
$688$	53.8592	−	11.4481i	2.05336	−	0.436455i
$689$	3.72571	−	4.13782i	0.141938	−	0.157638i
$690$		0			0
$691$	14.7072	+	16.3340i	0.559488	+	0.621374i	0.954827	−	0.297161i	$-0.0960397\pi$
$691$	14.7072	+	16.3340i	0.559488	+	0.621374i	−0.395340	+	0.918535i	$0.629373\pi$
$692$	−58.7708	−	42.6995i	−2.23413	−	1.62319i
$693$		0			0
$694$	−22.8739	−	16.6188i	−0.868280	−	0.630842i
$695$	0.131497	−	20.8619i	0.00498796	−	0.791337i
$696$		0			0
$697$	19.8654	+	8.84466i	0.752457	+	0.335016i
$698$	13.8486	−	15.3804i	0.524176	−	0.582156i
$699$		0			0
$700$	22.3173	+	39.8052i	0.843515	+	1.50450i
$701$	−6.44692			−0.243497			−0.121748	−	0.992561i	$-0.538850\pi$
$701$	−6.44692			−0.243497			−0.121748	+	0.992561i	$0.538850\pi$
$702$		0			0
$703$	29.1511	−	21.1795i	1.09946	−	0.798801i
$704$	−0.411282	−	3.91309i	−0.0155008	−	0.147480i
$705$		0			0
$706$	5.96893	−	56.7906i	0.224644	−	2.13734i
$707$	−13.2125	−	22.8847i	−0.496906	−	0.860666i
$708$		0			0
$709$	−3.28572	−	3.64916i	−0.123398	−	0.137047i	0.678280	−	0.734804i	$-0.262726\pi$
$709$	−3.28572	−	3.64916i	−0.123398	−	0.137047i	−0.801678	+	0.597756i	$0.796059\pi$
$710$	23.7952	−	52.5509i	0.893017	−	1.97220i
$711$		0			0
$712$	0.647729	−	1.99351i	0.0242747	−	0.0747098i
$713$	−10.7507	−	11.9399i	−0.402619	−	0.447153i
$714$		0			0
$715$	−7.30646	+	6.49585i	−0.273246	+	0.242931i
$716$	2.25545	−	0.479412i	0.0842903	−	0.0179165i
$717$		0			0
$718$	31.7906	−	55.0629i	1.18641	−	2.05493i
$719$	−38.7957	−	28.1867i	−1.44683	−	1.05119i	−0.986558	−	0.163412i	$-0.947750\pi$
$719$	−38.7957	−	28.1867i	−1.44683	−	1.05119i	−0.460277	−	0.887775i	$-0.652250\pi$
$720$		0			0
$721$	15.3612	−	11.1605i	0.572080	−	0.415640i
$722$	8.81169	+	83.8376i	0.327937	+	3.12011i
$723$		0			0
$724$	−50.9263	−	88.2070i	−1.89266	−	3.27819i
$725$	−40.8979	−	0.515595i	−1.51891	−	0.0191487i
$726$		0			0
$727$	−10.1485	−	2.15714i	−0.376389	−	0.0800039i	0.0158329	−	0.999875i	$-0.494960\pi$
$727$	−10.1485	−	2.15714i	−0.376389	−	0.0800039i	−0.392222	+	0.919871i	$0.628293\pi$
$728$	−18.2513	+	13.2603i	−0.676437	+	0.491461i
$729$		0			0
$730$	8.23293	+	7.50747i	0.304715	+	0.277864i
$731$	−34.3601	+	15.2981i	−1.27086	+	0.565821i
$732$		0			0
$733$	1.00624	−	9.57373i	0.0371663	−	0.353614i	−0.960096	−	0.279670i	$-0.909775\pi$
$733$	1.00624	−	9.57373i	0.0371663	−	0.353614i	0.997262	−	0.0739435i	$-0.0235584\pi$
$734$	−15.9880	+	3.39836i	−0.590129	+	0.125436i
$735$		0			0
$736$	−10.6912	−	2.27249i	−0.394084	−	0.0837651i
$737$	1.23401	−	3.79789i	0.0454553	−	0.139897i
$738$		0			0
$739$	−10.9628	−	33.7400i	−0.403273	−	1.24115i	−0.922329	−	0.386406i	$-0.873716\pi$
$739$	−10.9628	−	33.7400i	−0.403273	−	1.24115i	0.519056	−	0.854740i	$-0.326284\pi$
$740$	−0.309942	+	49.1722i	−0.0113937	+	1.80761i
$741$		0			0
$742$	−1.70767	+	16.2474i	−0.0626905	+	0.596460i
$743$	−1.41943	−	2.45852i	−0.0520738	−	0.0901944i	0.838814	−	0.544419i	$-0.183250\pi$
$743$	−1.41943	−	2.45852i	−0.0520738	−	0.0901944i	−0.890887	+	0.454224i	$0.849916\pi$
$744$		0			0
$745$	−14.7409	−	4.89255i	−0.540066	−	0.179249i
$746$	−49.3797	+	35.8765i	−1.80792	+	1.31353i
$747$		0			0
$748$	−15.1721	−	46.6951i	−0.554749	−	1.70734i
$749$	1.01409	−	1.75645i	0.0370539	−	0.0641793i
$750$		0			0
$751$	−19.4018	−	33.6049i	−0.707983	−	1.22626i	−0.965604	−	0.260016i	$-0.916272\pi$
$751$	−19.4018	−	33.6049i	−0.707983	−	1.22626i	0.257622	−	0.966246i	$-0.417061\pi$
$752$	45.0729	−	50.0585i	1.64364	−	1.82545i
$753$		0			0
$754$	−3.86524	−	36.7753i	−0.140764	−	1.33928i
$755$	0.355659	+	1.72669i	0.0129438	+	0.0628407i
$756$		0			0
$757$	32.7437			1.19009			0.595046	−	0.803692i	$-0.297134\pi$
$757$	32.7437			1.19009			0.595046	+	0.803692i	$0.297134\pi$
$758$	−0.987987	+	0.439880i	−0.0358853	+	0.0159772i
$759$		0			0
$760$	−85.2594	−	49.9437i	−3.09269	−	1.81165i
$761$	0.299221	−	0.332319i	0.0108468	−	0.0120465i	−0.737697	−	0.675132i	$-0.764087\pi$
$761$	0.299221	−	0.332319i	0.0108468	−	0.0120465i	0.748544	+	0.663085i	$0.230753\pi$
$762$		0			0
$763$	−12.2875	−	13.6467i	−0.444838	−	0.494043i
$764$	1.36911	+	4.21370i	0.0495328	+	0.152446i
$765$		0			0
$766$	17.8521	−	54.9431i	0.645022	−	1.98517i
$767$	17.0352	−	7.58457i	0.615106	−	0.273863i
$768$		0			0
$769$	0.783090	−	7.45061i	0.0282390	−	0.268676i	−0.971288	−	0.237908i	$-0.923538\pi$
$769$	0.783090	−	7.45061i	0.0282390	−	0.268676i	0.999527	−	0.0307674i	$-0.00979512\pi$
$770$	6.14069	−	28.0201i	0.221295	−	1.00977i
$771$		0			0
$772$	6.39003	+	60.7971i	0.229982	+	2.18814i
$773$	5.48853	+	16.8920i	0.197409	+	0.607562i	0.999940	+	0.0109516i	$0.00348607\pi$
$773$	5.48853	+	16.8920i	0.197409	+	0.607562i	−0.802531	+	0.596610i	$0.796514\pi$
$774$		0			0
$775$	33.1022	+	7.47343i	1.18906	+	0.268453i
$776$	−33.6609	+	58.3024i	−1.20836	+	2.09293i
$777$		0			0
$778$	28.6937	+	12.7753i	1.02872	+	0.458016i
$779$	−31.6257	−	14.0807i	−1.13311	−	0.504493i
$780$		0			0
$781$	−22.7954	+	10.1492i	−0.815683	+	0.363166i
$782$	27.2295			0.973726
$783$		0			0
$784$	−5.59494	+	17.2195i	−0.199819	+	0.614981i
$785$	8.25091	+	2.73850i	0.294488	+	0.0977412i
$786$		0			0
$787$	−13.4663	+	2.86235i	−0.480022	+	0.102032i	−0.441567	−	0.897228i	$-0.645577\pi$
$787$	−13.4663	+	2.86235i	−0.480022	+	0.102032i	−0.0384555	+	0.999260i	$0.512244\pi$
$788$	−34.1915	+	7.26764i	−1.21802	+	0.258899i
$789$		0			0
$790$	49.2242	+	68.6572i	1.75132	+	2.44272i
$791$	−4.33484	+	13.3413i	−0.154129	+	0.474361i
$792$		0			0
$793$	4.70698			0.167150
$794$	−6.46308	+	2.87755i	−0.229366	+	0.102120i
$795$		0			0
$796$	58.9262	+	26.2357i	2.08859	+	0.929898i
$797$	−21.3588	−	9.50955i	−0.756567	−	0.336846i	−0.00805616	−	0.999968i	$-0.502564\pi$
$797$	−21.3588	−	9.50955i	−0.756567	−	0.336846i	−0.748511	+	0.663122i	$0.769231\pi$
$798$		0			0
$799$	−23.0062	+	39.8478i	−0.813899	+	1.40972i
$800$	21.2067	−	9.12329i	0.749771	−	0.322557i
$801$		0			0
$802$	28.3330	+	87.1999i	1.00047	+	3.07914i
$803$	−0.503772	−	4.79307i	−0.0177777	−	0.169144i
$804$		0			0
$805$	9.44597	+	5.53331i	0.332927	+	0.195024i
$806$	−3.20696	+	30.5121i	−0.112960	+	1.07474i
$807$		0			0
$808$	−71.3320	+	31.7590i	−2.50945	+	1.11728i
$809$	3.98567	−	12.2666i	0.140129	−	0.431272i	−0.856224	−	0.516605i	$-0.827195\pi$
$809$	3.98567	−	12.2666i	0.140129	−	0.431272i	0.996352	+	0.0853332i	$0.0271955\pi$
$810$		0			0
$811$	−5.74344	−	17.6765i	−0.201679	−	0.620705i	−0.999833	−	0.0182520i	$-0.994190\pi$
$811$	−5.74344	−	17.6765i	−0.201679	−	0.620705i	0.798154	−	0.602454i	$-0.205810\pi$
$812$	49.9575	+	55.4834i	1.75316	+	1.94709i
$813$		0			0
$814$	20.6824	−	22.9701i	0.724917	−	0.805102i
$815$	7.52548	+	17.1934i	0.263606	+	0.602257i
$816$		0			0
$817$	54.7013	−	24.3546i	1.91375	−	0.852059i
$818$	56.2117			1.96540
$819$		0			0
$820$	41.0621	−	23.3634i	1.43395	−	0.815884i
$821$	3.64312	+	34.6620i	0.127146	+	1.20971i	0.853018	+	0.521882i	$0.174770\pi$
$821$	3.64312	+	34.6620i	0.127146	+	1.20971i	−0.725872	+	0.687830i	$0.758563\pi$
$822$		0			0
$823$	17.3963	−	19.3206i	0.606398	−	0.673473i	−0.359276	−	0.933231i	$-0.616976\pi$
$823$	17.3963	−	19.3206i	0.606398	−	0.673473i	0.965674	+	0.259758i	$0.0836429\pi$
$824$	−28.0528	−	48.5890i	−0.977267	−	1.69268i
$825$		0			0
$826$	−27.3564	+	47.3826i	−0.951850	+	1.64865i
$827$	10.5951	+	32.6084i	0.368428	+	1.13390i	0.947807	+	0.318846i	$0.103295\pi$
$827$	10.5951	+	32.6084i	0.368428	+	1.13390i	−0.579379	+	0.815058i	$0.696705\pi$
$828$		0			0
$829$	−11.1943	+	8.13310i	−0.388792	+	0.282474i	−0.764960	−	0.644077i	$-0.777242\pi$
$829$	−11.1943	+	8.13310i	−0.388792	+	0.282474i	0.376168	+	0.926551i	$0.377242\pi$
$830$	13.6316	−	18.5157i	0.473158	−	0.642688i
$831$		0			0
$832$	−1.43370	−	2.48324i	−0.0497046	−	0.0860908i
$833$	1.29276	−	12.2998i	0.0447914	−	0.426162i
$834$		0			0
$835$	14.0815	+	19.6407i	0.487310	+	0.679694i
$836$	24.1540	+	74.3384i	0.835384	+	2.57105i
$837$		0			0
$838$	−25.0176	+	76.9964i	−0.864220	+	2.65980i
$839$	35.4174	+	7.52820i	1.22274	+	0.259902i	0.773668	−	0.633591i	$-0.218420\pi$
$839$	35.4174	+	7.52820i	1.22274	+	0.259902i	0.449077	+	0.893493i	$0.351753\pi$
$840$		0			0
$841$	−37.0875	+	7.88319i	−1.27888	+	0.271834i
$842$	−0.369719	+	3.51764i	−0.0127413	+	0.121226i
$843$		0			0
$844$	53.7000	−	23.9088i	1.84843	−	0.822975i
$845$	9.05168	−	19.9903i	0.311387	−	0.687689i
$846$		0			0
$847$	8.36655	−	6.07866i	0.287478	−	0.208865i
$848$	20.2885	+	4.31246i	0.696711	+	0.148091i
$849$		0			0
$850$	−46.9513	+	33.2159i	−1.61041	+	1.13930i
$851$	5.89809	+	10.2158i	0.202184	+	0.350193i
$852$		0			0
$853$	3.27183	+	31.1294i	0.112025	+	1.06585i	0.895694	+	0.444671i	$0.146679\pi$
$853$	3.27183	+	31.1294i	0.112025	+	1.06585i	−0.783669	+	0.621179i	$0.786654\pi$
$854$	−11.1730	+	8.11768i	−0.382333	+	0.277781i
$855$		0			0
$856$	−4.84845	−	3.52261i	−0.165717	−	0.120400i
$857$	−6.62700	+	11.4783i	−0.226374	+	0.392091i	−0.956731	−	0.290975i	$-0.906021\pi$
$857$	−6.62700	+	11.4783i	−0.226374	+	0.392091i	0.730357	+	0.683066i	$0.239354\pi$
$858$		0			0
$859$	26.5737	−	5.64842i	0.906685	−	0.192722i	0.269109	−	0.963110i	$-0.413271\pi$
$859$	26.5737	−	5.64842i	0.906685	−	0.192722i	0.637575	+	0.770388i	$0.279937\pi$
$860$	−17.4928	+	79.8200i	−0.596500	+	2.72184i
$861$		0			0
$862$	1.06104	+	1.17841i	0.0361392	+	0.0401367i
$863$	−17.1394	+	52.7496i	−0.583431	+	1.79562i	0.0220503	+	0.999757i	$0.492981\pi$
$863$	−17.1394	+	52.7496i	−0.583431	+	1.79562i	−0.605481	+	0.795859i	$0.707019\pi$
$864$		0			0
$865$	31.9920	−	18.2027i	1.08776	−	0.618910i
$866$	−9.72404	−	10.7996i	−0.330436	−	0.366987i
$867$		0			0
$868$	−30.9725	−	53.6460i	−1.05128	−	1.82086i
$869$	3.81967	−	36.3417i	0.129573	−	1.23281i
$870$		0			0
$871$	−0.304196	−	2.89423i	−0.0103073	−	0.0980672i
$872$	−43.8987	+	31.8943i	−1.48660	+	1.08008i
$873$		0			0
$874$	−43.3493			−1.46631
$875$	−23.0373	+	1.98170i	−0.778802	+	0.0669939i
$876$		0			0
$877$	−30.2841	+	33.6339i	−1.02262	+	1.13574i	−0.0319477	+	0.999490i	$0.510171\pi$
$877$	−30.2841	+	33.6339i	−1.02262	+	1.13574i	−0.990675	+	0.136248i	$0.956496\pi$
$878$	53.6071	+	23.8674i	1.80915	+	0.805487i
$879$		0			0
$880$	−34.5653	−	11.4723i	−1.16520	−	0.386731i
$881$	−3.25840	−	2.36737i	−0.109778	−	0.0797587i	0.531542	−	0.847032i	$-0.321613\pi$
$881$	−3.25840	−	2.36737i	−0.109778	−	0.0797587i	−0.641320	+	0.767273i	$0.721613\pi$
$882$		0			0
$883$	−23.5316	−	17.0967i	−0.791900	−	0.575349i	0.116626	−	0.993176i	$-0.462792\pi$
$883$	−23.5316	−	17.0967i	−0.791900	−	0.575349i	−0.908527	+	0.417827i	$0.862792\pi$
$884$	−23.9419	−	26.5902i	−0.805253	−	0.894324i
$885$		0			0
$886$	−37.1667	+	41.2778i	−1.24864	+	1.38675i
$887$	12.3394	−	2.62282i	0.414317	−	0.0880658i	0.00396318	−	0.999992i	$-0.498738\pi$
$887$	12.3394	−	2.62282i	0.414317	−	0.0880658i	0.410354	+	0.911926i	$0.365405\pi$
$888$		0			0
$889$	−20.1754	−	4.28841i	−0.676661	−	0.143829i
$890$	1.43518	+	1.30872i	0.0481074	+	0.0438683i
$891$		0			0
$892$	−13.0267	−	9.46448i	−0.436167	−	0.316894i
$893$	36.6258	−	63.4377i	1.22563	−	2.12286i
$894$		0			0
$895$	−0.250109	+	1.14125i	−0.00836022	+	0.0381478i
$896$	25.1326	+	11.1897i	0.839620	+	0.373823i
$897$		0			0
$898$	31.3875	+	6.67162i	1.04741	+	0.222635i
$899$	55.5197			1.85169
$900$		0			0
$901$	−14.1682			−0.472012
$902$	−29.0474	−	6.17421i	−0.967172	−	0.205579i
$903$		0			0
$904$	37.8670	+	16.8595i	1.25944	+	0.560738i
$905$	51.3574	−	5.07081i	1.70718	−	0.168559i
$906$		0			0
$907$	3.40353	−	5.89509i	0.113012	−	0.195743i	−0.803971	−	0.594668i	$-0.797283\pi$
$907$	3.40353	−	5.89509i	0.113012	−	0.195743i	0.916983	+	0.398925i	$0.130617\pi$
$908$	56.1061	+	40.7634i	1.86195	+	1.35278i
$909$		0			0
$910$	−4.21731	−	20.4746i	−0.139802	−	0.678727i
$911$	−25.3692	−	5.39238i	−0.840518	−	0.178658i	−0.232515	−	0.972593i	$-0.574696\pi$
$911$	−25.3692	−	5.39238i	−0.840518	−	0.178658i	−0.608003	+	0.793935i	$0.708029\pi$
$912$		0			0
$913$	−9.72805	+	2.06776i	−0.321952	+	0.0684329i
$914$	0.216468	−	0.240412i	0.00716013	−	0.00795213i
$915$		0			0
$916$	17.7406	+	19.7029i	0.586166	+	0.651004i
$917$	−23.0193	−	16.7245i	−0.760165	−	0.552292i
$918$		0			0
$919$	1.07405	+	0.780342i	0.0354296	+	0.0257411i	0.605359	−	0.795952i	$-0.293030\pi$
$919$	1.07405	+	0.780342i	0.0354296	+	0.0257411i	−0.569930	+	0.821694i	$0.693030\pi$
$920$	19.1783	−	26.0498i	0.632289	−	0.858835i
$921$		0			0
$922$	−16.7627	−	7.46322i	−0.552049	−	0.245788i
$923$	−12.1678	+	13.5137i	−0.400507	+	0.444808i
$924$		0			0
$925$	−22.6317	−	10.4201i	−0.744126	−	0.342610i
$926$	−57.6748			−1.89531
$927$		0			0
$928$	30.5563	−	22.2004i	1.00306	−	0.728765i
$929$	3.51432	+	33.4365i	0.115301	+	1.09702i	0.887236	+	0.461316i	$0.152623\pi$
$929$	3.51432	+	33.4365i	0.115301	+	1.09702i	−0.771935	+	0.635702i	$0.780711\pi$
$930$		0			0
$931$	−2.05807	+	19.5812i	−0.0674505	+	0.641749i
$932$	1.32097	+	2.28799i	0.0432698	+	0.0749455i
$933$		0			0
$934$	16.4981	+	18.3230i	0.539834	+	0.599547i
$935$	24.7241	+	2.75627i	0.808564	+	0.0901397i
$936$		0			0
$937$	5.34347	−	16.4455i	0.174563	−	0.537251i	−0.825050	−	0.565060i	$-0.808853\pi$
$937$	5.34347	−	16.4455i	0.174563	−	0.537251i	0.999613	+	0.0278089i	$0.00885300\pi$
$938$	5.71348	+	6.34546i	0.186552	+	0.207187i
$939$		0			0
$940$	40.0830	+	91.5770i	1.30736	+	2.98691i
$941$	35.4844	−	7.54245i	1.15676	−	0.245877i	0.410709	−	0.911766i	$-0.365281\pi$
$941$	35.4844	−	7.54245i	1.15676	−	0.245877i	0.746050	+	0.665889i	$0.231948\pi$
$942$		0			0
$943$	5.66663	−	9.81489i	0.184531	−	0.319617i
$944$	56.1983	+	40.8305i	1.82910	+	1.32892i
$945$		0			0
$946$	41.5544	−	30.1910i	1.35105	−	0.981595i
$947$	1.22544	+	11.6593i	0.0398216	+	0.378877i	0.996224	+	0.0868238i	$0.0276717\pi$
$947$	1.22544	+	11.6593i	0.0398216	+	0.378877i	−0.956402	+	0.292053i	$0.905662\pi$
$948$		0			0
$949$	−1.75611	−	3.04168i	−0.0570059	−	0.0987370i
$950$	74.7463	−	52.8797i	2.42509	−	1.71564i
$951$		0			0
$952$	56.1510	+	11.9353i	1.81987	+	0.386824i
$953$	−0.574496	+	0.417395i	−0.0186097	+	0.0135208i	−0.597051	−	0.802203i	$-0.703661\pi$
$953$	−0.574496	+	0.417395i	−0.0186097	+	0.0135208i	0.578442	+	0.815724i	$0.303661\pi$
$954$		0			0
$955$	−2.23107	−	0.248722i	−0.0721957	−	0.00804847i
$956$	−4.73734	+	2.10920i	−0.153217	+	0.0682164i
$957$		0			0
$958$	2.97909	−	28.3442i	0.0962501	−	0.915759i
$959$	−17.2539	+	3.66742i	−0.557157	+	0.118427i
$960$		0			0
$961$	−14.7350	−	3.13203i	−0.475324	−	0.101033i
$962$	6.96073	−	21.4229i	0.224423	−	0.690703i
$963$		0			0
$964$	24.5079	+	75.4277i	0.789348	+	2.42936i
$965$	−29.3977	−	9.75718i	−0.946346	−	0.314095i
$966$		0			0
$967$	−2.91903	+	27.7728i	−0.0938698	+	0.893112i	0.841694	+	0.539955i	$0.181559\pi$
$967$	−2.91903	+	27.7728i	−0.0938698	+	0.893112i	−0.935564	+	0.353157i	$0.885108\pi$
$968$	−15.2792	−	26.4643i	−0.491090	−	0.850594i
$969$		0			0
$970$	−36.3484	−	50.6982i	−1.16708	−	1.62782i
$971$	24.9120	−	18.0996i	0.799465	−	0.580845i	−0.111292	−	0.993788i	$-0.535499\pi$
$971$	24.9120	−	18.0996i	0.799465	−	0.580845i	0.910757	+	0.412942i	$0.135499\pi$
$972$		0			0
$973$	−5.96262	−	18.3511i	−0.191153	−	0.588308i
$974$	−10.0423	+	17.3938i	−0.321776	+	0.557333i
$975$		0			0
$976$	8.76719	+	15.1852i	0.280631	+	0.486067i
$977$	−16.8170	+	18.6771i	−0.538022	+	0.597534i	−0.949454	−	0.313907i	$-0.898362\pi$
$977$	−16.8170	+	18.6771i	−0.538022	+	0.597534i	0.411432	+	0.911441i	$0.365029\pi$
$978$		0			0
$979$	−0.0878186	−	0.835538i	−0.00280669	−	0.0267039i
$980$	−19.8541	−	18.1046i	−0.634215	−	0.578329i
$981$		0			0
$982$	37.2571			1.18892
$983$	−43.2866	+	19.2725i	−1.38063	+	0.614696i	−0.956720	−	0.291009i	$-0.906009\pi$
$983$	−43.2866	+	19.2725i	−1.38063	+	0.614696i	−0.423909	+	0.905705i	$0.639342\pi$
$984$		0			0
$985$	3.79152	−	17.3008i	0.120808	−	0.551248i
$986$	−62.9608	+	69.9251i	−2.00508	+	2.22687i
$987$		0			0
$988$	38.1155	+	42.3315i	1.21261	+	1.34674i
$989$	6.05751	+	18.6431i	0.192617	+	0.592816i
$990$		0			0
$991$	14.2923	−	43.9872i	0.454010	−	1.39730i	−0.418284	−	0.908316i	$-0.637368\pi$
$991$	14.2923	−	43.9872i	0.454010	−	1.39730i	0.872294	−	0.488982i	$-0.162632\pi$
$992$	−28.6279	+	12.7460i	−0.908936	+	0.404685i
$993$		0			0
$994$	5.57707	−	53.0622i	0.176894	−	1.68303i
$995$	−24.4252	+	21.7154i	−0.774332	+	0.688424i
$996$		0			0
$997$	5.40789	+	51.4526i	0.171269	+	1.62952i	0.655933	+	0.754819i	$0.272275\pi$
$997$	5.40789	+	51.4526i	0.171269	+	1.62952i	−0.484663	+	0.874701i	$0.661058\pi$
$998$	−18.3451	−	56.4605i	−0.580705	−	1.78722i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.181.27		224
3.2	odd	2		225.2.q.a.106.2	yes	224
9.4	even	3	inner	675.2.r.a.631.2		224
9.5	odd	6		225.2.q.a.31.27	✓	224
25.21	even	5	inner	675.2.r.a.46.2		224
75.71	odd	10		225.2.q.a.196.27	yes	224
225.121	even	15	inner	675.2.r.a.496.27		224
225.221	odd	30		225.2.q.a.121.2	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.27	✓	224	9.5	odd	6
225.2.q.a.106.2	yes	224	3.2	odd	2
225.2.q.a.121.2	yes	224	225.221	odd	30
225.2.q.a.196.27	yes	224	75.71	odd	10
675.2.r.a.46.2		224	25.21	even	5	inner
675.2.r.a.181.27		224	1.1	even	1	trivial
675.2.r.a.496.27		224	225.121	even	15	inner
675.2.r.a.631.2		224	9.4	even	3	inner

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.47708 + 0.526519i) q^{2} +(4.03160 + 1.79498i) q^{4} +(-1.67112 + 1.48572i) q^{5} +(-1.03406 + 1.79105i) q^{7} +(4.94396 + 3.59200i) q^{8} +O(q^{10})\)	\(q+(2.47708 + 0.526519i) q^{2} +(4.03160 + 1.79498i) q^{4} +(-1.67112 + 1.48572i) q^{5} +(-1.03406 + 1.79105i) q^{7} +(4.94396 + 3.59200i) q^{8} +(-4.92175 + 2.80036i) q^{10} +(2.39587 + 0.509257i) q^{11} +(1.74601 - 0.371125i) q^{13} +(-3.50448 + 3.89212i) q^{14} +(4.44939 + 4.94155i) q^{16} +(-3.67466 - 2.66979i) q^{17} +(5.85004 + 4.25031i) q^{19} +(-9.40413 + 2.99019i) q^{20} +(5.66661 + 2.52294i) q^{22} +(-1.58401 + 1.75922i) q^{23} +(0.585285 - 4.96563i) q^{25} +4.52040 q^{26} +(-7.38384 + 5.36467i) q^{28} +(-0.855066 - 8.13541i) q^{29} +(-0.709441 + 6.74988i) q^{31} +(2.30859 + 3.99860i) q^{32} +(-7.69671 - 8.54806i) q^{34} +(-0.932951 - 4.52939i) q^{35} +(1.53985 - 4.73917i) q^{37} +(12.2531 + 13.6085i) q^{38} +(-13.5986 + 1.34267i) q^{40} +(-4.68289 + 0.995378i) q^{41} +(4.14034 - 7.17127i) q^{43} +(8.74507 + 6.35367i) q^{44} +(-4.84997 + 3.52371i) q^{46} +(-1.05889 - 10.0746i) q^{47} +(1.36143 + 2.35806i) q^{49} +(4.06429 - 11.9921i) q^{50} +(7.70536 + 1.63783i) q^{52} +(2.52356 - 1.83348i) q^{53} +(-4.76039 + 2.70855i) q^{55} +(-11.5458 + 5.14053i) q^{56} +(2.16538 - 20.6023i) q^{58} +(10.2183 - 2.17198i) q^{59} +(2.57932 + 0.548251i) q^{61} +(-5.31128 + 16.3465i) q^{62} +(-0.496397 - 1.52775i) q^{64} +(-2.36640 + 3.21427i) q^{65} +(0.170417 - 1.62141i) q^{67} +(-10.0225 - 17.3595i) q^{68} +(0.0738159 - 11.7109i) q^{70} +(-8.24169 + 5.98794i) q^{71} +(-0.608028 - 1.87132i) q^{73} +(6.30959 - 10.9285i) q^{74} +(15.9558 + 27.6363i) q^{76} +(-3.38958 + 3.76451i) q^{77} +(-1.55944 - 14.8370i) q^{79} +(-14.7772 - 1.64738i) q^{80} -12.1240 q^{82} +(-3.70931 + 1.65149i) q^{83} +(10.1074 - 0.997956i) q^{85} +(14.0318 - 15.5838i) q^{86} +(10.0158 + 11.1237i) q^{88} +(-0.105993 - 0.326212i) q^{89} +(-1.14078 + 3.51095i) q^{91} +(-9.54385 + 4.24919i) q^{92} +(2.68154 - 25.5132i) q^{94} +(-16.0909 + 1.58874i) q^{95} +(1.15152 + 10.9560i) q^{97} +(2.13079 + 6.55791i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

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