LMFDB - Embedded newform 225.2.m.a.154.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("225.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			154.1
Root			$1.17421 + 0.0566033i$ of defining polynomial
Character	$\chi$	$=$	225.154
Dual form			225.2.m.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.174207 - 0.0566033i) q^{2} +(-1.59089 - 1.15585i) q^{4} +(-0.107666 + 2.23347i) q^{5} +3.26086i q^{7} +(0.427051 + 0.587785i) q^{8} +O(q^{10})$	\(q+(-0.174207 - 0.0566033i) q^{2} +(-1.59089 - 1.15585i) q^{4} +(-0.107666 + 2.23347i) q^{5} +3.26086i q^{7} +(0.427051 + 0.587785i) q^{8} +(0.145178 - 0.382993i) q^{10} +(-0.618034 + 1.90211i) q^{11} +(0.281873 - 0.0915860i) q^{13} +(0.184575 - 0.568064i) q^{14} +(1.17421 + 3.61384i) q^{16} +(3.03472 + 4.17693i) q^{17} +(1.39991 - 1.01709i) q^{19} +(2.75284 - 3.42877i) q^{20} +(0.215332 - 0.296379i) q^{22} +(-0.836161 - 0.271685i) q^{23} +(-4.97682 - 0.480938i) q^{25} -0.0542883 q^{26} +(3.76906 - 5.18766i) q^{28} +(-4.78304 - 3.47508i) q^{29} +(-4.93462 + 3.58521i) q^{31} -2.14910i q^{32} +(-0.292241 - 0.899425i) q^{34} +(-7.28304 - 0.351083i) q^{35} +(7.69215 - 2.49933i) q^{37} +(-0.301444 + 0.0979452i) q^{38} +(-1.35878 + 0.890523i) q^{40} +(0.313697 + 0.965461i) q^{41} -3.24199i q^{43} +(3.18178 - 2.31170i) q^{44} +(0.130287 + 0.0946589i) q^{46} +(2.48043 - 3.41402i) q^{47} -3.63318 q^{49} +(0.839774 + 0.365487i) q^{50} +(-0.554288 - 0.180099i) q^{52} +(4.76148 - 6.55362i) q^{53} +(-4.18178 - 1.58516i) q^{55} +(-1.91668 + 1.39255i) q^{56} +(0.636538 + 0.876119i) q^{58} +(1.83443 + 5.64581i) q^{59} +(0.282941 - 0.870802i) q^{61} +(1.06258 - 0.345253i) q^{62} +(2.22677 - 6.85329i) q^{64} +(0.174207 + 0.639416i) q^{65} +(4.04870 + 5.57255i) q^{67} -10.1527i q^{68} +(1.24888 + 0.473405i) q^{70} +(-4.82884 - 3.50836i) q^{71} +(8.40107 + 2.72967i) q^{73} -1.48150 q^{74} -3.40270 q^{76} +(-6.20252 - 2.01532i) q^{77} +(-6.27851 - 4.56161i) q^{79} +(-8.19784 + 2.23347i) q^{80} -0.185946i q^{82} +(8.53192 + 11.7432i) q^{83} +(-9.65580 + 6.32825i) q^{85} +(-0.183507 + 0.564778i) q^{86} +(-1.38197 + 0.449028i) q^{88} +(2.32579 - 7.15805i) q^{89} +(0.298649 + 0.919147i) q^{91} +(1.01621 + 1.39870i) q^{92} +(-0.625353 + 0.454345i) q^{94} +(2.12093 + 3.23616i) q^{95} +(3.95373 - 5.44184i) q^{97} +(0.632925 + 0.205650i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} - q^{4} - 10 q^{8}+O(q^{10}) $ 8 * q + 5 * q^2 - q^4 - 10 * q^8	$ 8 q + 5 q^{2} - q^{4} - 10 q^{8} - 5 q^{10} + 4 q^{11} - 5 q^{13} - 13 q^{14} + 3 q^{16} + 10 q^{17} - 5 q^{19} + 15 q^{20} - 5 q^{23} - 10 q^{25} - 6 q^{26} - 15 q^{28} + 5 q^{29} - 9 q^{31} + 13 q^{34} - 15 q^{35} + 30 q^{37} - 15 q^{38} + 10 q^{40} + 4 q^{41} + 2 q^{44} - 19 q^{46} + 14 q^{49} + 15 q^{50} - 10 q^{52} + 10 q^{53} - 10 q^{55} - 10 q^{56} + 20 q^{58} - 9 q^{61} + 30 q^{62} + 4 q^{64} - 5 q^{65} + 20 q^{67} + 30 q^{70} - 6 q^{71} + 15 q^{73} + 12 q^{74} - 20 q^{76} - 10 q^{77} + 15 q^{79} - 20 q^{80} + 45 q^{83} - 15 q^{85} + 9 q^{86} - 20 q^{88} + 25 q^{89} + 6 q^{91} - 30 q^{92} - 27 q^{94} - 15 q^{95} - 60 q^{97} + 10 q^{98}+O(q^{100}) $ 8 * q + 5 * q^2 - q^4 - 10 * q^8 - 5 * q^10 + 4 * q^11 - 5 * q^13 - 13 * q^14 + 3 * q^16 + 10 * q^17 - 5 * q^19 + 15 * q^20 - 5 * q^23 - 10 * q^25 - 6 * q^26 - 15 * q^28 + 5 * q^29 - 9 * q^31 + 13 * q^34 - 15 * q^35 + 30 * q^37 - 15 * q^38 + 10 * q^40 + 4 * q^41 + 2 * q^44 - 19 * q^46 + 14 * q^49 + 15 * q^50 - 10 * q^52 + 10 * q^53 - 10 * q^55 - 10 * q^56 + 20 * q^58 - 9 * q^61 + 30 * q^62 + 4 * q^64 - 5 * q^65 + 20 * q^67 + 30 * q^70 - 6 * q^71 + 15 * q^73 + 12 * q^74 - 20 * q^76 - 10 * q^77 + 15 * q^79 - 20 * q^80 + 45 * q^83 - 15 * q^85 + 9 * q^86 - 20 * q^88 + 25 * q^89 + 6 * q^91 - 30 * q^92 - 27 * q^94 - 15 * q^95 - 60 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.174207	−	0.0566033i	−0.123183	−	0.0400246i	0.246777	−	0.969072i	$-0.420629\pi$
$2$	−0.174207	−	0.0566033i	−0.123183	−	0.0400246i	−0.369960	+	0.929048i	$0.620629\pi$
$3$		0			0
$3$		0			0
$4$	−1.59089	−	1.15585i	−0.795445	−	0.577925i
$5$	−0.107666	+	2.23347i	−0.0481496	+	0.998840i
$5$	−0.107666	+	2.23347i	−0.0481496	+	0.998840i
$6$		0			0
$7$			3.26086i			1.23249i	0.787555	+	0.616244i	$0.211346\pi$
$7$			3.26086i			1.23249i	−0.787555	+	0.616244i	$0.788654\pi$
$8$	0.427051	+	0.587785i	0.150985	+	0.207813i
$9$		0			0
$10$	0.145178	−	0.382993i	0.0459094	−	0.121113i
$11$	−0.618034	+	1.90211i	−0.186344	+	0.573509i	−0.999969	−	0.00788181i	$-0.997491\pi$
$11$	−0.618034	+	1.90211i	−0.186344	+	0.573509i	0.813625	+	0.581390i	$0.197491\pi$
$12$		0			0
$13$	0.281873	−	0.0915860i	0.0781775	−	0.0254014i	−0.269667	−	0.962954i	$-0.586914\pi$
$13$	0.281873	−	0.0915860i	0.0781775	−	0.0254014i	0.347845	+	0.937552i	$0.386914\pi$
$14$	0.184575	−	0.568064i	0.0493298	−	0.151821i
$15$		0			0
$16$	1.17421	+	3.61384i	0.293552	+	0.903459i
$17$	3.03472	+	4.17693i	0.736027	+	1.01305i	0.998837	+	0.0482067i	$0.0153506\pi$
$17$	3.03472	+	4.17693i	0.736027	+	1.01305i	−0.262810	+	0.964847i	$0.584649\pi$
$18$		0			0
$19$	1.39991	−	1.01709i	0.321161	−	0.233337i	−0.415510	−	0.909589i	$-0.636397\pi$
$19$	1.39991	−	1.01709i	0.321161	−	0.233337i	0.736671	+	0.676252i	$0.236397\pi$
$20$	2.75284	−	3.42877i	0.615555	−	0.766695i
$21$		0			0
$22$	0.215332	−	0.296379i	0.0459089	−	0.0631881i
$23$	−0.836161	−	0.271685i	−0.174352	−	0.0566503i	0.220540	−	0.975378i	$-0.429218\pi$
$23$	−0.836161	−	0.271685i	−0.174352	−	0.0566503i	−0.394892	+	0.918728i	$0.629218\pi$
$24$		0			0
$25$	−4.97682	−	0.480938i	−0.995363	−	0.0961876i
$26$	−0.0542883			−0.0106468
$27$		0			0
$28$	3.76906	−	5.18766i	0.712285	−	0.980376i
$29$	−4.78304	−	3.47508i	−0.888188	−	0.645306i	0.0472171	−	0.998885i	$-0.484965\pi$
$29$	−4.78304	−	3.47508i	−0.888188	−	0.645306i	−0.935405	+	0.353578i	$0.884965\pi$
$30$		0			0
$31$	−4.93462	+	3.58521i	−0.886285	+	0.643923i	−0.934907	−	0.354894i	$-0.884517\pi$
$31$	−4.93462	+	3.58521i	−0.886285	+	0.643923i	0.0486220	+	0.998817i	$0.484517\pi$
$32$		−	2.14910i		−	0.379912i
$33$		0			0
$34$	−0.292241	−	0.899425i	−0.0501189	−	0.154250i
$35$	−7.28304	−	0.351083i	−1.23106	−	0.0593438i
$36$		0			0
$37$	7.69215	−	2.49933i	1.26458	−	0.410887i	0.401457	−	0.915878i	$-0.368504\pi$
$37$	7.69215	−	2.49933i	1.26458	−	0.410887i	0.863125	+	0.504991i	$0.168504\pi$
$38$	−0.301444	+	0.0979452i	−0.0489007	+	0.0158888i
$39$		0			0
$40$	−1.35878	+	0.890523i	−0.214842	+	0.140804i
$41$	0.313697	+	0.965461i	0.0489913	+	0.150780i	0.972559	−	0.232655i	$-0.0747412\pi$
$41$	0.313697	+	0.965461i	0.0489913	+	0.150780i	−0.923568	+	0.383434i	$0.874741\pi$
$42$		0			0
$43$		−	3.24199i		−	0.494399i	−0.968965	−	0.247200i	$-0.920490\pi$
$43$		−	3.24199i		−	0.494399i	0.968965	−	0.247200i	$-0.0795103\pi$
$44$	3.18178	−	2.31170i	0.479671	−	0.348502i
$45$		0			0
$46$	0.130287	+	0.0946589i	0.0192097	+	0.0139567i
$47$	2.48043	−	3.41402i	0.361808	−	0.497986i	−0.588844	−	0.808247i	$-0.700417\pi$
$47$	2.48043	−	3.41402i	0.361808	−	0.497986i	0.950651	+	0.310261i	$0.100417\pi$
$48$		0			0
$49$	−3.63318			−0.519026
$50$	0.839774	+	0.365487i	0.118762	+	0.0516877i
$51$		0			0
$52$	−0.554288	−	0.180099i	−0.0768660	−	0.0249753i
$53$	4.76148	−	6.55362i	0.654040	−	0.900209i	−0.345226	−	0.938520i	$-0.612198\pi$
$53$	4.76148	−	6.55362i	0.654040	−	0.900209i	0.999266	+	0.0383106i	$0.0121976\pi$
$54$		0			0
$55$	−4.18178	−	1.58516i	−0.563871	−	0.213742i
$56$	−1.91668	+	1.39255i	−0.256128	+	0.186088i
$57$		0			0
$58$	0.636538	+	0.876119i	0.0835815	+	0.115040i
$59$	1.83443	+	5.64581i	0.238823	+	0.735021i	0.996591	+	0.0824976i	$0.0262897\pi$
$59$	1.83443	+	5.64581i	0.238823	+	0.735021i	−0.757768	+	0.652524i	$0.773710\pi$
$60$		0			0
$61$	0.282941	−	0.870802i	0.0362268	−	0.111495i	−0.931308	−	0.364233i	$-0.881331\pi$
$61$	0.282941	−	0.870802i	0.0362268	−	0.111495i	0.967535	+	0.252738i	$0.0813312\pi$
$62$	1.06258	−	0.345253i	0.134948	−	0.0438472i
$63$		0			0
$64$	2.22677	−	6.85329i	0.278346	−	0.856661i
$65$	0.174207	+	0.639416i	0.0216077	+	0.0793099i
$66$		0			0
$67$	4.04870	+	5.57255i	0.494627	+	0.680796i	0.981233	−	0.192826i	$-0.0617652\pi$
$67$	4.04870	+	5.57255i	0.494627	+	0.680796i	−0.486606	+	0.873622i	$0.661765\pi$
$68$		−	10.1527i		−	1.23120i
$69$		0			0
$70$	1.24888	+	0.473405i	0.149270	+	0.0565827i
$71$	−4.82884	−	3.50836i	−0.573078	−	0.416366i	0.263144	−	0.964757i	$-0.415241\pi$
$71$	−4.82884	−	3.50836i	−0.573078	−	0.416366i	−0.836222	+	0.548391i	$0.815241\pi$
$72$		0			0
$73$	8.40107	+	2.72967i	0.983271	+	0.319484i	0.756161	−	0.654385i	$-0.227072\pi$
$73$	8.40107	+	2.72967i	0.983271	+	0.319484i	0.227110	+	0.973869i	$0.427072\pi$
$74$	−1.48150			−0.172220
$75$		0			0
$76$	−3.40270			−0.390317
$77$	−6.20252	−	2.01532i	−0.706842	−	0.229667i
$78$		0			0
$79$	−6.27851	−	4.56161i	−0.706388	−	0.513221i	0.175618	−	0.984458i	$-0.443808\pi$
$79$	−6.27851	−	4.56161i	−0.706388	−	0.513221i	−0.882006	+	0.471237i	$0.843808\pi$
$80$	−8.19784	+	2.23347i	−0.916546	+	0.249710i
$81$		0			0
$82$		−	0.185946i		−	0.0205343i
$83$	8.53192	+	11.7432i	0.936500	+	1.28898i	0.957269	+	0.289197i	$0.0933884\pi$
$83$	8.53192	+	11.7432i	0.936500	+	1.28898i	−0.0207694	+	0.999784i	$0.506612\pi$
$84$		0			0
$85$	−9.65580	+	6.32825i	−1.04732	+	0.686395i
$86$	−0.183507	+	0.564778i	−0.0197881	+	0.0609015i
$87$		0			0
$88$	−1.38197	+	0.449028i	−0.147318	+	0.0478665i
$89$	2.32579	−	7.15805i	0.246534	−	0.758752i	−0.748847	−	0.662743i	$-0.769392\pi$
$89$	2.32579	−	7.15805i	0.246534	−	0.758752i	0.995380	−	0.0960092i	$-0.0306078\pi$
$90$		0			0
$91$	0.298649	+	0.919147i	0.0313069	+	0.0963528i
$92$	1.01621	+	1.39870i	0.105948	+	0.145824i
$93$		0			0
$94$	−0.625353	+	0.454345i	−0.0645002	+	0.0468621i
$95$	2.12093	+	3.23616i	0.217602	+	0.332023i
$96$		0			0
$97$	3.95373	−	5.44184i	0.401440	−	0.552535i	−0.559664	−	0.828719i	$-0.689070\pi$
$97$	3.95373	−	5.44184i	0.401440	−	0.552535i	0.961105	+	0.276184i	$0.0890699\pi$
$98$	0.632925	+	0.205650i	0.0639351	+	0.0207738i
$99$		0			0
$100$	7.36167	+	6.51757i	0.736167	+	0.651757i
$101$	12.1955			1.21350			0.606748	−	0.794894i	$-0.292474\pi$
$101$	12.1955			1.21350			0.606748	+	0.794894i	$0.292474\pi$
$102$		0			0
$103$	0.811969	−	1.11758i	0.0800057	−	0.110118i	−0.767138	−	0.641482i	$-0.778320\pi$
$103$	0.811969	−	1.11758i	0.0800057	−	0.110118i	0.847144	+	0.531363i	$0.178320\pi$
$104$	0.174207	+	0.126569i	0.0170824	+	0.0124111i
$105$		0			0
$106$	−1.20044	+	0.872171i	−0.116597	+	0.0847127i
$107$			15.8285i			1.53020i	0.643911	+	0.765101i	$0.277311\pi$
$107$			15.8285i			1.53020i	−0.643911	+	0.765101i	$0.722689\pi$
$108$		0			0
$109$	0.619199	+	1.90570i	0.0593085	+	0.182533i	0.976322	−	0.216324i	$-0.0694069\pi$
$109$	0.619199	+	1.90570i	0.0593085	+	0.182533i	−0.917013	+	0.398857i	$0.869407\pi$
$110$	0.638770	+	0.512848i	0.0609044	+	0.0488981i
$111$		0			0
$112$	−11.7842	+	3.82892i	−1.11350	+	0.361799i
$113$	−9.91713	+	3.22227i	−0.932925	+	0.303126i	−0.735758	−	0.677244i	$-0.763174\pi$
$113$	−9.91713	+	3.22227i	−0.932925	+	0.303126i	−0.197167	+	0.980370i	$0.563174\pi$
$114$		0			0
$115$	0.696828	−	1.83829i	0.0649795	−	0.171422i
$116$	3.59262	+	11.0569i	0.333566	+	1.02661i
$117$		0			0
$118$		−	1.08737i		−	0.100101i
$119$	−13.6204	+	9.89577i	−1.24858	+	0.907144i
$120$		0			0
$121$	5.66312	+	4.11450i	0.514829	+	0.374045i
$122$	−0.0985805	+	0.135684i	−0.00892506	+	0.0122843i
$123$		0			0
$124$	11.9944			1.07713
$125$	1.61000	−	11.0638i	0.144002	−	0.989577i
$126$		0			0
$127$	5.56375	+	1.80777i	0.493703	+	0.160414i	0.545278	−	0.838255i	$-0.316424\pi$
$127$	5.56375	+	1.80777i	0.493703	+	0.160414i	−0.0515752	+	0.998669i	$0.516424\pi$
$128$	−3.30226	+	4.54517i	−0.291881	+	0.401740i
$129$		0			0
$130$	0.00584500	−	0.121252i	0.000512640	−	0.0106345i
$131$	−1.21081	+	0.879704i	−0.105789	+	0.0768601i	−0.639422	−	0.768856i	$-0.720826\pi$
$131$	−1.21081	+	0.879704i	−0.105789	+	0.0768601i	0.533633	+	0.845716i	$0.320826\pi$
$132$		0			0
$133$	3.31659	+	4.56489i	0.287585	+	0.395827i
$134$	−0.389887	−	1.19995i	−0.0336811	−	0.103660i
$135$		0			0
$136$	−1.15916	+	3.56752i	−0.0993970	+	0.305913i
$137$	7.46472	−	2.42543i	0.637754	−	0.207219i	0.0277472	−	0.999615i	$-0.491167\pi$
$137$	7.46472	−	2.42543i	0.637754	−	0.207219i	0.610007	+	0.792396i	$0.291167\pi$
$138$		0			0
$139$	−1.66607	+	5.12764i	−0.141314	+	0.434921i	−0.996519	−	0.0833702i	$-0.973432\pi$
$139$	−1.66607	+	5.12764i	−0.141314	+	0.434921i	0.855204	+	0.518291i	$0.173432\pi$
$140$	11.1807	+	8.97663i	0.944943	+	0.758663i
$141$		0			0
$142$	0.642634	+	0.884509i	0.0539286	+	0.0742264i
$143$			0.592757i			0.0495689i
$144$		0			0
$145$	8.27647	−	10.3086i	0.687324	−	0.856086i
$146$	−1.30902	−	0.951057i	−0.108335	−	0.0787100i
$147$		0			0
$148$	−15.1262	−	4.91480i	−1.24337	−	0.403994i
$149$	18.8229			1.54203			0.771015	−	0.636817i	$-0.219749\pi$
$149$	18.8229			1.54203			0.771015	+	0.636817i	$0.219749\pi$
$150$		0			0
$151$	−3.88797			−0.316398			−0.158199	−	0.987407i	$-0.550569\pi$
$151$	−3.88797			−0.316398			−0.158199	+	0.987407i	$0.550569\pi$
$152$	1.19566	+	0.388495i	0.0969811	+	0.0315111i
$153$		0			0
$154$	0.966448	+	0.702166i	0.0778786	+	0.0565821i
$155$	−7.47619	−	11.4074i	−0.600502	−	0.916261i
$156$		0			0
$157$		−	4.28378i		−	0.341883i	−0.985281	−	0.170941i	$-0.945319\pi$
$157$		−	4.28378i		−	0.341883i	0.985281	−	0.170941i	$-0.0546808\pi$
$158$	0.835559	+	1.15005i	0.0664735	+	0.0914930i
$159$		0			0
$160$	4.79997	+	0.231385i	0.379471	+	0.0182926i
$161$	0.885926	−	2.72660i	0.0698208	−	0.214886i
$162$		0			0
$163$	−14.9566	+	4.85970i	−1.17149	+	0.380641i	−0.829200	−	0.558952i	$-0.811204\pi$
$163$	−14.9566	+	4.85970i	−1.17149	+	0.380641i	−0.342293	+	0.939593i	$0.611204\pi$
$164$	0.616869	−	1.89853i	0.0481694	−	0.148250i
$165$		0			0
$166$	−0.821618	−	2.52868i	−0.0637699	−	0.196264i
$167$	−12.3629	−	17.0161i	−0.956670	−	1.31674i	−0.948500	−	0.316777i	$-0.897399\pi$
$167$	−12.3629	−	17.0161i	−0.956670	−	1.31674i	−0.00816967	−	0.999967i	$-0.502601\pi$
$168$		0			0
$169$	−10.4462	+	7.58958i	−0.803551	+	0.583814i
$170$	2.04031	−	0.555875i	0.156484	−	0.0426337i
$171$		0			0
$172$	−3.74725	+	5.15765i	−0.285725	+	0.393267i
$173$	−6.81587	−	2.21461i	−0.518201	−	0.168374i	0.0382277	−	0.999269i	$-0.487829\pi$
$173$	−6.81587	−	2.21461i	−0.518201	−	0.168374i	−0.556429	+	0.830895i	$0.687829\pi$
$174$		0			0
$175$	1.56827	−	16.2287i	0.118550	−	1.22677i
$176$	−7.59963			−0.572843
$177$		0			0
$178$	−0.810339	+	1.11534i	−0.0607375	+	0.0835979i
$179$	−6.50396	−	4.72540i	−0.486129	−	0.353193i	0.317565	−	0.948237i	$-0.397135\pi$
$179$	−6.50396	−	4.72540i	−0.486129	−	0.353193i	−0.803694	+	0.595043i	$0.797135\pi$
$180$		0			0
$181$	16.6796	−	12.1184i	1.23978	−	0.900756i	0.242200	−	0.970226i	$-0.422131\pi$
$181$	16.6796	−	12.1184i	1.23978	−	0.900756i	0.997584	+	0.0694707i	$0.0221310\pi$
$182$		−	0.177026i		−	0.0131221i
$183$		0			0
$184$	−0.197391	−	0.607507i	−0.0145518	−	0.0447860i
$185$	4.75401	+	17.4493i	0.349522	+	1.28290i
$186$		0			0
$187$	−9.82055	+	3.19089i	−0.718150	+	0.233341i
$188$	−7.89218	+	2.56432i	−0.575596	+	0.187023i
$189$		0			0
$190$	−0.186303	−	0.683814i	−0.0135158	−	0.0496090i
$191$	−5.57167	−	17.1478i	−0.403152	−	1.24077i	−0.922429	−	0.386167i	$-0.873799\pi$
$191$	−5.57167	−	17.1478i	−0.403152	−	1.24077i	0.519277	−	0.854606i	$-0.326201\pi$
$192$		0			0
$193$			6.78859i			0.488653i	0.969693	+	0.244327i	$0.0785669\pi$
$193$			6.78859i			0.488653i	−0.969693	+	0.244327i	$0.921433\pi$
$194$	−0.996793	+	0.724213i	−0.0715656	+	0.0519955i
$195$		0			0
$196$	5.77999	+	4.19941i	0.412856	+	0.299958i
$197$	4.69956	−	6.46839i	0.334830	−	0.460854i	−0.608092	−	0.793866i	$-0.708065\pi$
$197$	4.69956	−	6.46839i	0.334830	−	0.460854i	0.942923	+	0.333012i	$0.108065\pi$
$198$		0			0
$199$	5.20485			0.368962			0.184481	−	0.982836i	$-0.440940\pi$
$199$	5.20485			0.368962			0.184481	+	0.982836i	$0.440940\pi$
$200$	−1.84267	−	3.13068i	−0.130296	−	0.221373i
$201$		0			0
$202$	−2.12454	−	0.690305i	−0.149482	−	0.0485697i
$203$	11.3317	−	15.5968i	0.795332	−	1.09468i
$204$		0			0
$205$	−2.19011	+	0.596687i	−0.152964	+	0.0416745i
$206$	−0.204709	+	0.148730i	−0.0142628	+	0.0103625i
$207$		0			0
$208$	0.661954	+	0.911102i	0.0458983	+	0.0631735i
$209$	1.06943	+	3.29138i	0.0739743	+	0.227669i
$210$		0			0
$211$	5.13029	−	15.7894i	0.353184	−	1.08699i	−0.603872	−	0.797082i	$-0.706376\pi$
$211$	5.13029	−	15.7894i	0.353184	−	1.08699i	0.957055	−	0.289906i	$-0.0936239\pi$
$212$	−15.1500	+	4.92253i	−1.04051	+	0.338081i
$213$		0			0
$214$	0.895947	−	2.75744i	0.0612456	−	0.188495i
$215$	7.24091	+	0.349052i	0.493826	+	0.0238051i
$216$		0			0
$217$	−11.6909	−	16.0911i	−0.793628	−	1.09233i
$218$		−	0.367035i		−	0.0248587i
$219$		0			0
$220$	4.82055	+	7.35531i	0.325001	+	0.495895i
$221$	1.23795	+	0.899425i	0.0832737	+	0.0605019i
$222$		0			0
$223$	6.30368	+	2.04819i	0.422126	+	0.137157i	0.512374	−	0.858762i	$-0.328766\pi$
$223$	6.30368	+	2.04819i	0.422126	+	0.137157i	−0.0902485	+	0.995919i	$0.528766\pi$
$224$	7.00792			0.468236
$225$		0			0
$226$	1.91002			0.127053
$227$	12.7365	+	4.13833i	0.845350	+	0.274671i	0.699497	−	0.714636i	$-0.253407\pi$
$227$	12.7365	+	4.13833i	0.845350	+	0.274671i	0.145853	+	0.989306i	$0.453407\pi$
$228$		0			0
$229$	8.16032	+	5.92882i	0.539249	+	0.391788i	0.823806	−	0.566872i	$-0.191846\pi$
$229$	8.16032	+	5.92882i	0.539249	+	0.391788i	−0.284557	+	0.958659i	$0.591846\pi$
$230$	−0.225446	+	0.280801i	−0.0148655	+	0.0185155i
$231$		0			0
$232$		−	4.29544i		−	0.282009i
$233$	12.9345	+	17.8028i	0.847368	+	1.16630i	0.984437	+	0.175740i	$0.0562318\pi$
$233$	12.9345	+	17.8028i	0.847368	+	1.16630i	−0.137069	+	0.990562i	$0.543768\pi$
$234$		0			0
$235$	7.35806	+	5.90755i	0.479987	+	0.385366i
$236$	3.60732	−	11.1022i	0.234816	−	0.722691i
$237$		0			0
$238$	2.93290	−	0.952956i	0.190111	−	0.0617709i
$239$	2.33626	−	7.19026i	0.151120	−	0.465099i	−0.846627	−	0.532187i	$-0.821371\pi$
$239$	2.33626	−	7.19026i	0.151120	−	0.465099i	0.997747	+	0.0670870i	$0.0213705\pi$
$240$		0			0
$241$	−6.30226	−	19.3964i	−0.405964	−	1.24943i	−0.920087	−	0.391713i	$-0.871883\pi$
$241$	−6.30226	−	19.3964i	−0.405964	−	1.24943i	0.514123	−	0.857716i	$-0.328117\pi$
$242$	−0.753661	−	1.03733i	−0.0484472	−	0.0666818i
$243$		0			0
$244$	−1.45664	+	1.05831i	−0.0932520	+	0.0677515i
$245$	0.391169	−	8.11461i	0.0249909	−	0.518424i
$246$		0			0
$247$	0.301444	−	0.414902i	0.0191804	−	0.0263996i
$248$	−4.21467	−	1.36943i	−0.267632	−	0.0869589i
$249$		0			0
$250$	−0.906721	+	1.83626i	−0.0573460	+	0.116135i
$251$	−10.5717			−0.667278			−0.333639	−	0.942701i	$-0.608277\pi$
$251$	−10.5717			−0.667278			−0.333639	+	0.942701i	$0.608277\pi$
$252$		0			0
$253$	1.03355	−	1.42256i	0.0649789	−	0.0894357i
$254$	−0.866918	−	0.629853i	−0.0543953	−	0.0395205i
$255$		0			0
$256$	−10.8270	+	7.86625i	−0.676685	+	0.491640i
$257$		−	20.2700i		−	1.26441i	−0.774801	−	0.632205i	$-0.782150\pi$
$257$		−	20.2700i		−	1.26441i	0.774801	−	0.632205i	$-0.217850\pi$
$258$		0			0
$259$	8.14996	+	25.0830i	0.506414	+	1.55858i
$260$	0.461925	−	1.21860i	0.0286474	−	0.0755743i
$261$		0			0
$262$	0.260725	−	0.0847148i	0.0161077	−	0.00523370i
$263$	−26.7160	+	8.68056i	−1.64738	+	0.535267i	−0.978170	−	0.207806i	$-0.933368\pi$
$263$	−26.7160	+	8.68056i	−1.64738	+	0.535267i	−0.669211	+	0.743072i	$0.733368\pi$
$264$		0			0
$265$	14.1247	+	11.3403i	0.867673	+	0.696626i
$266$	−0.319385	−	0.982966i	−0.0195828	−	0.0602695i
$267$		0			0
$268$		−	13.5450i		−	0.827393i
$269$	−16.4416	+	11.9455i	−1.00246	+	0.728333i	−0.962615	−	0.270873i	$-0.912688\pi$
$269$	−16.4416	+	11.9455i	−1.00246	+	0.728333i	−0.0398490	+	0.999206i	$0.512688\pi$
$270$		0			0
$271$	−25.4409	−	18.4839i	−1.54543	−	1.12282i	−0.946816	−	0.321777i	$-0.895720\pi$
$271$	−25.4409	−	18.4839i	−1.54543	−	1.12282i	−0.598610	−	0.801041i	$-0.704280\pi$
$272$	−11.5314	+	15.8716i	−0.699191	+	0.962354i
$273$		0			0
$274$	−1.43769			−0.0868543
$275$	3.99064	−	9.16923i	0.240645	−	0.552925i
$276$		0			0
$277$	−13.2487	−	4.30475i	−0.796035	−	0.258648i	−0.117363	−	0.993089i	$-0.537444\pi$
$277$	−13.2487	−	4.30475i	−0.796035	−	0.258648i	−0.678672	+	0.734441i	$0.737444\pi$
$278$	0.580483	−	0.798966i	0.0348150	−	0.0479188i
$279$		0			0
$280$	−2.90387	−	4.43079i	−0.173539	−	0.264790i
$281$	20.9355	−	15.2105i	1.24891	−	0.907383i	0.250748	−	0.968052i	$-0.419323\pi$
$281$	20.9355	−	15.2105i	1.24891	−	0.907383i	0.998158	+	0.0606690i	$0.0193234\pi$
$282$		0			0
$283$	13.9491	+	19.1993i	0.829188	+	1.14128i	0.988074	+	0.153983i	$0.0492101\pi$
$283$	13.9491	+	19.1993i	0.829188	+	1.14128i	−0.158885	+	0.987297i	$0.550790\pi$
$284$	3.62702	+	11.1628i	0.215224	+	0.662392i
$285$		0			0
$286$	0.0335520	−	0.103262i	0.00198397	−	0.00610604i
$287$	−3.14823	+	1.02292i	−0.185834	+	0.0603811i
$288$		0			0
$289$	−2.98394	+	9.18363i	−0.175526	+	0.540214i
$290$	−2.02532	+	1.32736i	−0.118931	+	0.0779454i
$291$		0			0
$292$	−10.2101	−	14.0530i	−0.597500	−	0.822389i
$293$		−	12.3029i		−	0.718742i	−0.933195	−	0.359371i	$-0.882991\pi$
$293$		−	12.3029i		−	0.718742i	0.933195	−	0.359371i	$-0.117009\pi$
$294$		0			0
$295$	−12.8073	+	3.48930i	−0.745668	+	0.203155i
$296$	4.75401	+	3.45399i	0.276321	+	0.200759i
$297$		0			0
$298$	−3.27908	−	1.06544i	−0.189952	−	0.0617191i
$299$	−0.260574			−0.0150694
$300$		0			0
$301$	10.5717			0.609341
$302$	0.677311	+	0.220072i	0.0389749	+	0.0126637i
$303$		0			0
$304$	5.31939	+	3.86476i	0.305088	+	0.221659i
$305$	1.91445	+	0.725696i	0.109621	+	0.0415532i
$306$		0			0
$307$			4.28249i			0.244415i	0.992505	+	0.122207i	$0.0389973\pi$
$307$			4.28249i			0.244415i	−0.992505	+	0.122207i	$0.961003\pi$
$308$	7.53811	+	10.3753i	0.429524	+	0.591189i
$309$		0			0
$310$	0.656711	+	2.41042i	0.0372987	+	0.136903i
$311$	−7.92526	+	24.3915i	−0.449400	+	1.38311i	0.428185	+	0.903691i	$0.359153\pi$
$311$	−7.92526	+	24.3915i	−0.449400	+	1.38311i	−0.877585	+	0.479421i	$0.840847\pi$
$312$		0			0
$313$	−21.2573	+	6.90692i	−1.20153	+	0.390402i	−0.840325	−	0.542083i	$-0.817636\pi$
$313$	−21.2573	+	6.90692i	−1.20153	+	0.390402i	−0.361209	+	0.932485i	$0.617636\pi$
$314$	−0.242476	+	0.746264i	−0.0136837	+	0.0421141i
$315$		0			0
$316$	4.71589	+	14.5140i	0.265290	+	0.816478i
$317$	12.8859	+	17.7360i	0.723746	+	0.996151i	0.999391	+	0.0348911i	$0.0111084\pi$
$317$	12.8859	+	17.7360i	0.723746	+	0.996151i	−0.275645	+	0.961259i	$0.588892\pi$
$318$		0			0
$319$	9.56608	−	6.95016i	0.535597	−	0.389134i
$320$	15.0669	+	5.71129i	0.842265	+	0.319271i
$321$		0			0
$322$	−0.308669	+	0.424847i	−0.0172015	+	0.0236758i
$323$	8.49664	+	2.76073i	0.472766	+	0.153611i
$324$		0			0
$325$	−1.44688	+	0.320244i	−0.0802583	+	0.0177639i
$326$	2.88062			0.159543
$327$		0			0
$328$	−0.433519	+	0.596687i	−0.0239371	+	0.0329466i
$329$	11.1326	+	8.08832i	0.613761	+	0.445923i
$330$		0			0
$331$	7.25121	−	5.26831i	0.398563	−	0.289573i	−0.370393	−	0.928875i	$-0.620777\pi$
$331$	7.25121	−	5.26831i	0.398563	−	0.289573i	0.768955	+	0.639303i	$0.220777\pi$
$332$		−	28.5437i		−	1.56654i
$333$		0			0
$334$	1.19054	+	3.66410i	0.0651433	+	0.200491i
$335$	−12.8821	+	8.44269i	−0.703822	+	0.461273i
$336$		0			0
$337$	27.6601	−	8.98731i	1.50674	−	0.489570i	0.564766	−	0.825251i	$-0.308966\pi$
$337$	27.6601	−	8.98731i	1.50674	−	0.489570i	0.941976	+	0.335681i	$0.108966\pi$
$338$	2.24939	−	0.730871i	0.122351	−	0.0397541i
$339$		0			0
$340$	22.6758	+	1.09310i	1.22977	+	0.0592817i
$341$	−3.76972	−	11.6020i	−0.204142	−	0.628283i
$342$		0			0
$343$			10.9787i			0.592795i
$344$	1.90559	−	1.38450i	0.102743	−	0.0746470i
$345$		0			0
$346$	1.06202	+	0.771601i	0.0570944	+	0.0414815i
$347$	−8.40368	+	11.5667i	−0.451133	+	0.620931i	−0.972641	−	0.232315i	$-0.925370\pi$
$347$	−8.40368	+	11.5667i	−0.451133	+	0.620931i	0.521508	+	0.853247i	$0.325370\pi$
$348$		0			0
$349$	−5.62382			−0.301036			−0.150518	−	0.988607i	$-0.548094\pi$
$349$	−5.62382			−0.301036			−0.150518	+	0.988607i	$0.548094\pi$
$350$	−1.19180	+	2.73838i	−0.0637044	+	0.146373i
$351$		0			0
$352$	4.08784	+	1.32822i	0.217883	+	0.0707944i
$353$	1.12265	−	1.54520i	0.0597529	−	0.0822427i	−0.778095	−	0.628147i	$-0.783814\pi$
$353$	1.12265	−	1.54520i	0.0597529	−	0.0822427i	0.837848	+	0.545904i	$0.183814\pi$
$354$		0			0
$355$	8.35573	−	10.4074i	0.443476	−	0.552366i
$356$	−11.9737	+	8.69941i	−0.634605	+	0.461068i
$357$		0			0
$358$	0.865562	+	1.19134i	0.0457464	+	0.0629645i
$359$	6.86161	+	21.1179i	0.362142	+	1.11456i	0.951751	+	0.306870i	$0.0992818\pi$
$359$	6.86161	+	21.1179i	0.362142	+	1.11456i	−0.589609	+	0.807689i	$0.700718\pi$
$360$		0			0
$361$	−4.94606	+	15.2224i	−0.260319	+	0.801179i
$362$	−3.59164	+	1.16700i	−0.188773	+	0.0613359i
$363$		0			0
$364$	0.587277	−	1.80745i	0.0307817	−	0.0947363i
$365$	−7.00116	+	18.4697i	−0.366458	+	0.966748i
$366$		0			0
$367$	12.6050	+	17.3493i	0.657978	+	0.905629i	0.999412	−	0.0342768i	$-0.0109128\pi$
$367$	12.6050	+	17.3493i	0.657978	+	0.905629i	−0.341435	+	0.939906i	$0.610913\pi$
$368$		−	3.34077i		−	0.174149i
$369$		0			0
$370$	0.159507	−	3.30888i	0.00829235	−	0.172021i
$371$	21.3704	+	15.5265i	1.10950	+	0.806096i
$372$		0			0
$373$	−22.0074	−	7.15063i	−1.13950	−	0.370245i	−0.322320	−	0.946631i	$-0.604463\pi$
$373$	−22.0074	−	7.15063i	−1.13950	−	0.370245i	−0.817178	+	0.576385i	$0.804463\pi$
$374$	1.89142			0.0978032
$375$		0			0
$376$	3.06598			0.158116
$377$	−1.66648	−	0.541471i	−0.0858279	−	0.0278872i
$378$		0			0
$379$	−17.5153	−	12.7256i	−0.899702	−	0.653672i	0.0386872	−	0.999251i	$-0.487682\pi$
$379$	−17.5153	−	12.7256i	−0.899702	−	0.653672i	−0.938390	+	0.345579i	$0.887682\pi$
$380$	0.366355	−	7.59985i	0.0187936	−	0.389864i
$381$		0			0
$382$			3.30265i			0.168978i
$383$	−3.32381	−	4.57484i	−0.169839	−	0.233763i	0.715610	−	0.698500i	$-0.246149\pi$
$383$	−3.32381	−	4.57484i	−0.169839	−	0.233763i	−0.885449	+	0.464737i	$0.846149\pi$
$384$		0			0
$385$	5.16896	−	13.6362i	0.263435	−	0.694964i
$386$	0.384257	−	1.18262i	0.0195581	−	0.0601938i
$387$		0			0
$388$	−12.5799	+	4.08746i	−0.638647	+	0.207509i
$389$	−2.51109	+	7.72833i	−0.127317	+	0.391842i	−0.994316	−	0.106468i	$-0.966046\pi$
$389$	−2.51109	+	7.72833i	−0.127317	+	0.391842i	0.866999	+	0.498310i	$0.166046\pi$
$390$		0			0
$391$	−1.40270	−	4.31707i	−0.0709377	−	0.218324i
$392$	−1.55155	−	2.13553i	−0.0783653	−	0.107861i
$393$		0			0
$394$	−1.18483	+	0.860829i	−0.0596908	+	0.0433679i
$395$	10.8642	−	13.5318i	0.546638	−	0.680857i
$396$		0			0
$397$	−12.2076	+	16.8024i	−0.612684	+	0.843287i	−0.996795	−	0.0799998i	$-0.974508\pi$
$397$	−12.2076	+	16.8024i	−0.612684	+	0.843287i	0.384111	+	0.923287i	$0.374508\pi$
$398$	−0.906721	−	0.294611i	−0.0454498	−	0.0147675i
$399$		0			0
$400$	−4.10578	−	18.5501i	−0.205289	−	0.927506i
$401$	−30.1195			−1.50410			−0.752049	−	0.659107i	$-0.770934\pi$
$401$	−30.1195			−1.50410			−0.752049	+	0.659107i	$0.770934\pi$
$402$		0			0
$403$	−1.06258	+	1.46252i	−0.0529309	+	0.0728532i
$404$	−19.4017	−	14.0961i	−0.965269	−	0.701309i
$405$		0			0
$406$	−2.85690	+	2.07566i	−0.141785	+	0.103013i
$407$			16.1760i			0.801815i
$408$		0			0
$409$	−3.41317	−	10.5046i	−0.168770	−	0.519421i	0.830524	−	0.556983i	$-0.188041\pi$
$409$	−3.41317	−	10.5046i	−0.168770	−	0.519421i	−0.999294	+	0.0375613i	$0.988041\pi$
$410$	0.415306	+	0.0200201i	0.0205105	+	0.000988721i
$411$		0			0
$412$	−2.58351	+	0.839433i	−0.127280	+	0.0413559i
$413$	−18.4102	+	5.98182i	−0.905905	+	0.294346i
$414$		0			0
$415$	−27.1467	+	17.7915i	−1.33258	+	0.873350i
$416$	−0.196828	−	0.605774i	−0.00965029	−	0.0297005i
$417$		0			0
$418$		−	0.633915i		−	0.0310058i
$419$	26.6338	−	19.3506i	1.30115	−	0.945337i	0.301179	−	0.953568i	$-0.402620\pi$
$419$	26.6338	−	19.3506i	1.30115	−	0.945337i	0.999966	+	0.00823011i	$0.00261975\pi$
$420$		0			0
$421$	16.3945	+	11.9113i	0.799019	+	0.580522i	0.910626	−	0.413231i	$-0.135600\pi$
$421$	16.3945	+	11.9113i	0.799019	+	0.580522i	−0.111607	+	0.993752i	$0.535600\pi$
$422$	−1.78746	+	2.46023i	−0.0870124	+	0.119762i
$423$		0			0
$424$	5.88552			0.285826
$425$	−13.0944	−	22.2473i	−0.635171	−	1.07915i
$426$		0			0
$427$	2.83956	+	0.922629i	0.137416	+	0.0446491i
$428$	18.2954	−	25.1814i	0.884341	−	1.21719i
$429$		0			0
$430$	−1.24166	−	0.470666i	−0.0598781	−	0.0226975i
$431$	5.78873	−	4.20576i	0.278833	−	0.202584i	−0.439575	−	0.898206i	$-0.644871\pi$
$431$	5.78873	−	4.20576i	0.278833	−	0.202584i	0.718408	+	0.695622i	$0.244871\pi$
$432$		0			0
$433$	−3.22262	−	4.43555i	−0.154869	−	0.213159i	0.724531	−	0.689242i	$-0.242056\pi$
$433$	−3.22262	−	4.43555i	−0.154869	−	0.213159i	−0.879400	+	0.476083i	$0.842056\pi$
$434$	1.12582	+	3.46492i	0.0540412	+	0.166322i
$435$		0			0
$436$	1.21762	−	3.74746i	0.0583135	−	0.179471i
$437$	−1.44688	+	0.470119i	−0.0692135	+	0.0224888i
$438$		0			0
$439$	9.50415	−	29.2508i	0.453609	−	1.39606i	−0.419153	−	0.907916i	$-0.637673\pi$
$439$	9.50415	−	29.2508i	0.453609	−	1.39606i	0.872761	−	0.488148i	$-0.162327\pi$
$440$	−0.854102	−	3.13493i	−0.0407177	−	0.149452i
$441$		0			0
$442$	−0.164750	−	0.226758i	−0.00783634	−	0.0107858i
$443$			11.3527i			0.539381i	0.962947	+	0.269691i	$0.0869214\pi$
$443$			11.3527i			0.539381i	−0.962947	+	0.269691i	$0.913079\pi$
$444$		0			0
$445$	15.7369	+	5.96528i	0.746002	+	0.282781i
$446$	−0.982211	−	0.713618i	−0.0465090	−	0.0337908i
$447$		0			0
$448$	22.3476	+	7.26117i	1.05582	+	0.343058i
$449$	−15.7661			−0.744050			−0.372025	−	0.928223i	$-0.621336\pi$
$449$	−15.7661			−0.744050			−0.372025	+	0.928223i	$0.621336\pi$
$450$		0			0
$451$	−2.03029			−0.0956027
$452$	19.5015	+	6.33643i	0.917274	+	0.298040i
$453$		0			0
$454$	−1.98454	−	1.44185i	−0.0931391	−	0.0676695i
$455$	−2.08504	+	0.568064i	−0.0977484	+	0.0266312i
$456$		0			0
$457$		−	4.16714i		−	0.194931i	−0.995239	−	0.0974653i	$-0.968926\pi$
$457$		−	4.16714i		−	0.194931i	0.995239	−	0.0974653i	$-0.0310735\pi$
$458$	−1.08599	−	1.49474i	−0.0507452	−	0.0698448i
$459$		0			0
$460$	−3.23337	+	2.11909i	−0.150756	+	0.0988033i
$461$	7.40758	−	22.7982i	0.345005	−	1.06182i	−0.616576	−	0.787296i	$-0.711481\pi$
$461$	7.40758	−	22.7982i	0.345005	−	1.06182i	0.961581	−	0.274521i	$-0.0885194\pi$
$462$		0			0
$463$	39.3021	−	12.7700i	1.82652	−	0.593473i	0.827013	−	0.562183i	$-0.190038\pi$
$463$	39.3021	−	12.7700i	1.82652	−	0.593473i	0.999510	−	0.0312899i	$-0.00996151\pi$
$464$	6.94210	−	21.3656i	0.322279	−	0.991872i
$465$		0			0
$466$	−1.24558	−	3.83351i	−0.0577005	−	0.177584i
$467$	−6.11096	−	8.41102i	−0.282782	−	0.389216i	0.643871	−	0.765134i	$-0.277327\pi$
$467$	−6.11096	−	8.41102i	−0.282782	−	0.389216i	−0.926653	+	0.375918i	$0.877327\pi$
$468$		0			0
$469$	−18.1713	+	13.2022i	−0.839072	+	0.609622i
$470$	−0.947439	−	1.44563i	−0.0437021	−	0.0666818i
$471$		0			0
$472$	−2.53512	+	3.48930i	−0.116689	+	0.160608i
$473$	6.16663	+	2.00366i	0.283542	+	0.0921284i
$474$		0			0
$475$	−7.45624	+	4.38861i	−0.342116	+	0.201363i
$476$	33.1065			1.51743
$477$		0			0
$478$	−0.813985	+	1.12035i	−0.0372308	+	0.0512438i
$479$	−29.1312	−	21.1650i	−1.33104	−	0.967055i	−0.999723	−	0.0235349i	$-0.992508\pi$
$479$	−29.1312	−	21.1650i	−1.33104	−	0.967055i	−0.331314	−	0.943520i	$-0.607492\pi$
$480$		0			0
$481$	1.93930	−	1.40899i	0.0884246	−	0.0642443i
$482$			3.73571i			0.170157i
$483$		0			0
$484$	−4.25366	−	13.0914i	−0.193348	−	0.595065i
$485$	11.7285	+	9.41645i	0.532565	+	0.427579i
$486$		0			0
$487$	−10.1172	+	3.28726i	−0.458452	+	0.148960i	−0.529133	−	0.848539i	$-0.677483\pi$
$487$	−10.1172	+	3.28726i	−0.458452	+	0.148960i	0.0706809	+	0.997499i	$0.477483\pi$
$488$	0.632674	−	0.205568i	0.0286398	−	0.00930564i
$489$		0			0
$490$	−0.527458	+	1.39148i	−0.0238281	+	0.0628607i
$491$	5.46010	+	16.8045i	0.246411	+	0.758375i	0.995401	+	0.0957938i	$0.0305389\pi$
$491$	5.46010	+	16.8045i	0.246411	+	0.758375i	−0.748990	+	0.662581i	$0.769461\pi$
$492$		0			0
$493$		−	30.5243i		−	1.37475i
$494$	−0.0759986	+	0.0552162i	−0.00341934	+	0.00248429i
$495$		0			0
$496$	−18.7507	−	13.6231i	−0.841929	−	0.611697i
$497$	11.4403	−	15.7462i	0.513166	−	0.706312i
$498$		0			0
$499$	9.41734			0.421578			0.210789	−	0.977532i	$-0.432397\pi$
$499$	9.41734			0.421578			0.210789	+	0.977532i	$0.432397\pi$
$500$	−15.3494	+	15.7404i	−0.686447	+	0.703932i
$501$		0			0
$502$	1.84166	+	0.598391i	0.0821972	+	0.0267075i
$503$	−10.5879	+	14.5730i	−0.472093	+	0.649780i	−0.976961	−	0.213416i	$-0.931541\pi$
$503$	−10.5879	+	14.5730i	−0.472093	+	0.649780i	0.504869	+	0.863196i	$0.331541\pi$
$504$		0			0
$505$	−1.31304	+	27.2383i	−0.0584294	+	1.21209i
$506$	−0.260574	+	0.189318i	−0.0115839	+	0.00841621i
$507$		0			0
$508$	−6.76180	−	9.30681i	−0.300006	−	0.412923i
$509$	−4.95926	−	15.2630i	−0.219815	−	0.676522i	−0.998777	−	0.0494500i	$-0.984253\pi$
$509$	−4.95926	−	15.2630i	−0.219815	−	0.676522i	0.778961	−	0.627072i	$-0.215747\pi$
$510$		0			0
$511$	−8.90107	+	27.3947i	−0.393760	+	1.21187i
$512$	13.0177	−	4.22972i	0.575308	−	0.186929i
$513$		0			0
$514$	−1.14735	+	3.53118i	−0.0506075	+	0.155754i
$515$	2.40867	+	1.93384i	0.106138	+	0.0852151i
$516$		0			0
$517$	4.96086	+	6.82803i	0.218178	+	0.300297i
$518$		−	4.83095i		−	0.212260i
$519$		0			0
$520$	−0.301444	+	0.375460i	−0.0132192	+	0.0164650i
$521$	−1.78040	−	1.29354i	−0.0780007	−	0.0566708i	0.548102	−	0.836412i	$-0.315351\pi$
$521$	−1.78040	−	1.29354i	−0.0780007	−	0.0566708i	−0.626102	+	0.779741i	$0.715351\pi$
$522$		0			0
$523$	7.07194	+	2.29781i	0.309234	+	0.100476i	0.459523	−	0.888166i	$-0.348020\pi$
$523$	7.07194	+	2.29781i	0.309234	+	0.100476i	−0.150289	+	0.988642i	$0.548020\pi$
$524$	2.94307			0.128569
$525$		0			0
$526$	5.14547			0.224353
$527$	−29.9504	−	9.73147i	−1.30466	−	0.423909i
$528$		0			0
$529$	−17.9820	−	13.0647i	−0.781828	−	0.568031i
$530$	−1.81873	−	2.77506i	−0.0790004	−	0.120541i
$531$		0			0
$532$		−	11.0957i		−	0.481061i
$533$	0.176845	+	0.243407i	0.00766003	+	0.0105431i
$534$		0			0
$535$	−35.3526	−	1.70419i	−1.52843	−	0.0736786i
$536$	−1.54646	+	4.75953i	−0.0667971	+	0.205580i
$537$		0			0
$538$	3.54040	−	1.15035i	0.152638	−	0.0495950i
$539$	2.24543	−	6.91072i	0.0967174	−	0.297666i
$540$		0			0
$541$	6.38040	+	19.6368i	0.274315	+	0.844254i	0.989400	+	0.145216i	$0.0463878\pi$
$541$	6.38040	+	19.6368i	0.274315	+	0.844254i	−0.715085	+	0.699037i	$0.753612\pi$
$542$	3.38574	+	4.66007i	0.145430	+	0.200167i
$543$		0			0
$544$	8.97666	−	6.52192i	0.384871	−	0.279625i
$545$	−4.32299	+	1.17779i	−0.185177	+	0.0504508i
$546$		0			0
$547$	18.4424	−	25.3839i	0.788542	−	1.08534i	−0.205746	−	0.978605i	$-0.565962\pi$
$547$	18.4424	−	25.3839i	0.788542	−	1.08534i	0.994288	−	0.106730i	$-0.0340379\pi$
$548$	−14.6790	−	4.76949i	−0.627055	−	0.203743i
$549$		0			0
$550$	−1.21421	+	1.37146i	−0.0517739	+	0.0584793i
$551$	−10.2303			−0.435825
$552$		0			0
$553$	14.8747	−	20.4733i	0.632538	−	0.870615i
$554$	2.06435	+	1.49984i	0.0877057	+	0.0637219i
$555$		0			0
$556$	8.57732	−	6.23178i	0.363759	−	0.264287i
$557$			22.3515i			0.947064i	0.880776	+	0.473532i	$0.157021\pi$
$557$			22.3515i			0.947064i	−0.880776	+	0.473532i	$0.842979\pi$
$558$		0			0
$559$	−0.296921	−	0.913829i	−0.0125584	−	0.0386509i
$560$	−7.28304	−	26.7320i	−0.307765	−	1.12963i
$561$		0			0
$562$	−4.50807	+	1.46476i	−0.190162	+	0.0617872i
$563$	32.6843	−	10.6198i	1.37748	−	0.447570i	0.475639	−	0.879640i	$-0.342217\pi$
$563$	32.6843	−	10.6198i	1.37748	−	0.447570i	0.901840	+	0.432070i	$0.142217\pi$
$564$		0			0
$565$	−6.12912	−	22.4966i	−0.257854	−	0.946438i
$566$	−1.34329	−	4.13422i	−0.0564626	−	0.173774i
$567$		0			0
$568$		−	4.33657i		−	0.181958i
$569$	−26.0230	+	18.9068i	−1.09094	+	0.792615i	−0.979558	−	0.201162i	$-0.935528\pi$
$569$	−26.0230	+	18.9068i	−1.09094	+	0.792615i	−0.111383	+	0.993778i	$0.535528\pi$
$570$		0			0
$571$	21.9784	+	15.9683i	0.919768	+	0.668251i	0.943466	−	0.331468i	$-0.107544\pi$
$571$	21.9784	+	15.9683i	0.919768	+	0.668251i	−0.0236979	+	0.999719i	$0.507544\pi$
$572$	0.685138	−	0.943012i	0.0286471	−	0.0394293i
$573$		0			0
$574$	0.606344			0.0253083
$575$	4.03076	+	1.75427i	0.168094	+	0.0731581i
$576$		0			0
$577$	13.1724	+	4.27998i	0.548375	+	0.178178i	0.570084	−	0.821586i	$-0.306911\pi$
$577$	13.1724	+	4.27998i	0.548375	+	0.178178i	−0.0217089	+	0.999764i	$0.506911\pi$
$578$	1.03965	−	1.43095i	0.0432436	−	0.0595198i
$579$		0			0
$580$	−25.0822	+	6.83356i	−1.04148	+	0.283748i
$581$	−38.2928	+	27.8214i	−1.58865	+	1.15422i
$582$		0			0
$583$	9.52297	+	13.1072i	0.394401	+	0.542847i
$584$	1.98322	+	6.10374i	0.0820664	+	0.252574i
$585$		0			0
$586$	−0.696383	+	2.14325i	−0.0287673	+	0.0885367i
$587$	41.9890	−	13.6431i	1.73307	−	0.563110i	0.739185	−	0.673502i	$-0.235211\pi$
$587$	41.9890	−	13.6431i	1.73307	−	0.563110i	0.993888	+	0.110392i	$0.0352107\pi$
$588$		0			0
$589$	−3.26152	+	10.0379i	−0.134389	+	0.413606i
$590$	2.42862	+	0.117073i	0.0999848	+	0.00481982i
$591$		0			0
$592$	18.0643	+	24.8634i	0.742440	+	1.02188i
$593$		−	16.2531i		−	0.667437i	−0.942673	−	0.333718i	$-0.891697\pi$
$593$		−	16.2531i		−	0.667437i	0.942673	−	0.333718i	$-0.108303\pi$
$594$		0			0
$595$	−20.6355	−	31.4862i	−0.845973	−	1.29081i
$596$	−29.9451	−	21.7564i	−1.22660	−	0.891177i
$597$		0			0
$598$	0.0453938	+	0.0147493i	0.00185629	+	0.000603145i
$599$	30.4822			1.24547			0.622734	−	0.782433i	$-0.286022\pi$
$599$	30.4822			1.24547			0.622734	+	0.782433i	$0.286022\pi$
$600$		0			0
$601$	−28.9162			−1.17952			−0.589758	−	0.807580i	$-0.700777\pi$
$601$	−28.9162			−1.17952			−0.589758	+	0.807580i	$0.700777\pi$
$602$	−1.84166	−	0.598391i	−0.0750604	−	0.0243886i
$603$		0			0
$604$	6.18533	+	4.49390i	0.251677	+	0.182854i
$605$	−9.79935	+	12.2054i	−0.398400	+	0.496222i
$606$		0			0
$607$			8.23276i			0.334157i	0.985944	+	0.167079i	$0.0534334\pi$
$607$			8.23276i			0.334157i	−0.985944	+	0.167079i	$0.946567\pi$
$608$	−2.18584	−	3.00855i	−0.0886474	−	0.122013i
$609$		0			0
$610$	−0.292434	−	0.234786i	−0.0118403	−	0.00950619i
$611$	0.386489	−	1.18949i	0.0156357	−	0.0481217i
$612$		0			0
$613$	4.56327	−	1.48270i	0.184309	−	0.0598856i	−0.215408	−	0.976524i	$-0.569108\pi$
$613$	4.56327	−	1.48270i	0.184309	−	0.0598856i	0.399717	+	0.916638i	$0.369108\pi$
$614$	0.242403	−	0.746040i	0.00978259	−	0.0301077i
$615$		0			0
$616$	−1.46422	−	4.50639i	−0.0589949	−	0.181568i
$617$	−1.19428	−	1.64379i	−0.0480800	−	0.0661765i	0.784300	−	0.620382i	$-0.213022\pi$
$617$	−1.19428	−	1.64379i	−0.0480800	−	0.0661765i	−0.832380	+	0.554205i	$0.813022\pi$
$618$		0			0
$619$	6.58621	−	4.78516i	0.264722	−	0.192332i	−0.447504	−	0.894282i	$-0.647687\pi$
$619$	6.58621	−	4.78516i	0.264722	−	0.192332i	0.712226	+	0.701950i	$0.247687\pi$
$620$	−1.29139	+	26.7892i	−0.0518634	+	1.07588i
$621$		0			0
$622$	2.76127	−	3.80057i	0.110717	−	0.152389i
$623$	23.3414	+	7.58408i	0.935153	+	0.303850i
$624$		0			0
$625$	24.5374	+	4.78708i	0.981496	+	0.191483i
$626$	4.09413			0.163634
$627$		0			0
$628$	−4.95140	+	6.81502i	−0.197582	+	0.271949i
$629$	33.7830	+	24.5448i	1.34702	+	0.978665i
$630$		0			0
$631$	−26.9279	+	19.5643i	−1.07198	+	0.778841i	−0.976268	−	0.216567i	$-0.930514\pi$
$631$	−26.9279	+	19.5643i	−1.07198	+	0.778841i	−0.0957154	+	0.995409i	$0.530514\pi$
$632$		−	5.63846i		−	0.224286i
$633$		0			0
$634$	−1.24091	−	3.81911i	−0.0492826	−	0.151676i
$635$	−4.63663	+	12.2318i	−0.183999	+	0.485406i
$636$		0			0
$637$	−1.02409	+	0.332749i	−0.0405761	+	0.0131840i
$638$	−2.05988	+	0.669295i	−0.0815514	+	0.0264977i
$639$		0			0
$640$	−9.79599	−	7.86488i	−0.387220	−	0.310887i
$641$	12.3755	+	38.0880i	0.488804	+	1.50439i	0.826394	+	0.563092i	$0.190388\pi$
$641$	12.3755	+	38.0880i	0.488804	+	1.50439i	−0.337590	+	0.941293i	$0.609612\pi$
$642$		0			0
$643$			11.6870i			0.460890i	0.973085	+	0.230445i	$0.0740182\pi$
$643$			11.6870i			0.460890i	−0.973085	+	0.230445i	$0.925982\pi$
$644$	−4.56095	+	3.31372i	−0.179727	+	0.130579i
$645$		0			0
$646$	−1.32391	−	0.961876i	−0.0520885	−	0.0378445i
$647$	4.67252	−	6.43117i	0.183696	−	0.252835i	−0.707231	−	0.706982i	$-0.750056\pi$
$647$	4.67252	−	6.43117i	0.183696	−	0.252835i	0.890927	+	0.454147i	$0.150056\pi$
$648$		0			0
$649$	−11.8727			−0.466044
$650$	0.270183	+	0.0261093i	0.0105974	+	0.00102409i
$651$		0			0
$652$	29.4114	+	9.55635i	1.15184	+	0.374256i
$653$	1.96165	−	2.69998i	0.0767653	−	0.105658i	−0.768908	−	0.639360i	$-0.779199\pi$
$653$	1.96165	−	2.69998i	0.0767653	−	0.105658i	0.845673	+	0.533702i	$0.179199\pi$
$654$		0			0
$655$	−1.83443	−	2.79902i	−0.0716772	−	0.109367i
$656$	−3.12067	+	2.26730i	−0.121842	+	0.0885232i
$657$		0			0
$658$	−1.48155	−	2.03918i	−0.0577570	−	0.0794957i
$659$	−9.28621	−	28.5800i	−0.361739	−	1.11332i	−0.951998	−	0.306105i	$-0.900974\pi$
$659$	−9.28621	−	28.5800i	−0.361739	−	1.11332i	0.590259	−	0.807214i	$-0.299026\pi$
$660$		0			0
$661$	−2.03462	+	6.26192i	−0.0791375	+	0.243560i	−0.982796	−	0.184693i	$-0.940871\pi$
$661$	−2.03462	+	6.26192i	−0.0791375	+	0.243560i	0.903659	+	0.428253i	$0.140871\pi$
$662$	−1.56142	+	0.507335i	−0.0606862	+	0.0197181i
$663$		0			0
$664$	−3.25890	+	10.0299i	−0.126470	+	0.389235i
$665$	−10.5527	+	6.91604i	−0.409215	+	0.268192i
$666$		0			0
$667$	3.05526	+	4.20521i	0.118300	+	0.162826i
$668$			41.3603i			1.60028i
$669$		0			0
$670$	2.72203	−	0.741608i	0.105161	−	0.0286508i
$671$	1.48150	+	1.07637i	0.0571925	+	0.0415528i
$672$		0			0
$673$	−6.40194	−	2.08012i	−0.246777	−	0.0801826i	0.183017	−	0.983110i	$-0.441414\pi$
$673$	−6.40194	−	2.08012i	−0.246777	−	0.0801826i	−0.429794	+	0.902927i	$0.641414\pi$
$674$	−5.32730			−0.205200
$675$		0			0
$676$	25.3911			0.976580
$677$	−12.9799	−	4.21741i	−0.498857	−	0.162088i	0.0487718	−	0.998810i	$-0.484469\pi$
$677$	−12.9799	−	4.21741i	−0.498857	−	0.162088i	−0.547629	+	0.836722i	$0.684469\pi$
$678$		0			0
$679$	17.7451	+	12.8925i	0.680993	+	0.494770i
$680$	−7.84317	−	2.97305i	−0.300772	−	0.114011i
$681$		0			0
$682$			2.23453i			0.0855645i
$683$	−0.689001	−	0.948329i	−0.0263639	−	0.0362868i	0.795632	−	0.605781i	$-0.207139\pi$
$683$	−0.689001	−	0.948329i	−0.0263639	−	0.0362868i	−0.821995	+	0.569494i	$0.807139\pi$
$684$		0			0
$685$	4.61345	+	16.9334i	0.176271	+	0.646992i
$686$	0.621431	−	1.91257i	0.0237264	−	0.0730222i
$687$		0			0
$688$	11.7160	−	3.80677i	0.446669	−	0.145132i
$689$	0.741913	−	2.28337i	0.0282646	−	0.0869896i
$690$		0			0
$691$	3.79083	+	11.6670i	0.144210	+	0.443832i	0.996909	−	0.0785709i	$-0.0250357\pi$
$691$	3.79083	+	11.6670i	0.144210	+	0.443832i	−0.852699	+	0.522403i	$0.825036\pi$
$692$	8.28354	+	11.4013i	0.314893	+	0.433413i
$693$		0			0
$694$	2.11869	−	1.53932i	0.0804244	−	0.0584317i
$695$	−11.2731	−	4.27320i	−0.427612	−	0.162092i
$696$		0			0
$697$	−3.08068	+	4.24019i	−0.116689	+	0.160609i
$698$	0.979709	+	0.318327i	0.0370825	+	0.0120488i
$699$		0			0
$700$	−21.2528	+	24.0054i	−0.803282	+	0.907317i
$701$	20.0271			0.756415			0.378207	−	0.925721i	$-0.376541\pi$
$701$	20.0271			0.756415			0.378207	+	0.925721i	$0.376541\pi$
$702$		0			0
$703$	8.22624	−	11.3225i	0.310259	−	0.427034i
$704$	11.6595	+	8.47113i	0.439434	+	0.319268i
$705$		0			0
$706$	−0.283038	+	0.205639i	−0.0106523	+	0.00773932i
$707$			39.7677i			1.49562i
$708$		0			0
$709$	1.35816	+	4.17998i	0.0510067	+	0.156983i	0.973315	−	0.229471i	$-0.0736998\pi$
$709$	1.35816	+	4.17998i	0.0510067	+	0.156983i	−0.922309	+	0.386454i	$0.873700\pi$
$710$	−2.04472	+	1.34007i	−0.0767369	+	0.0502921i
$711$		0			0
$712$	5.20063	−	1.68979i	0.194902	−	0.0633275i
$713$	5.10019	−	1.65715i	0.191004	−	0.0620608i
$714$		0			0
$715$	−1.32391	−	0.0638197i	−0.0495114	−	0.00238672i
$716$	4.88523	+	15.0352i	0.182570	+	0.561892i
$717$		0			0
$718$		−	4.06727i		−	0.151789i
$719$	8.84119	−	6.42350i	0.329721	−	0.239556i	−0.410591	−	0.911819i	$-0.634678\pi$
$719$	8.84119	−	6.42350i	0.329721	−	0.239556i	0.740312	+	0.672263i	$0.234678\pi$
$720$		0			0
$721$	3.64427	+	2.64772i	0.135720	+	0.0986061i
$722$	1.72328	−	2.37189i	0.0641337	−	0.0882725i
$723$		0			0
$724$	−40.5425			−1.50675
$725$	22.1330	+	19.5952i	0.821999	+	0.727747i
$726$		0			0
$727$	−31.2928	−	10.1677i	−1.16059	−	0.377097i	−0.335465	−	0.942053i	$-0.608893\pi$
$727$	−31.2928	−	10.1677i	−1.16059	−	0.377097i	−0.825122	+	0.564955i	$0.808893\pi$
$728$	−0.412723	+	0.568064i	−0.0152965	+	0.0210538i
$729$		0			0
$730$	2.26510	−	2.82126i	0.0838350	−	0.104420i
$731$	13.5416	−	9.83853i	0.500853	−	0.363891i
$732$		0			0
$733$	−8.08190	−	11.1238i	−0.298512	−	0.410866i	0.633244	−	0.773952i	$-0.281723\pi$
$733$	−8.08190	−	11.1238i	−0.298512	−	0.410866i	−0.931756	+	0.363086i	$0.881723\pi$
$734$	−1.21386	−	3.73586i	−0.0448042	−	0.137893i
$735$		0			0
$736$	−0.583880	+	1.79700i	−0.0215221	+	0.0662382i
$737$	−13.1019	+	4.25705i	−0.482613	+	0.156811i
$738$		0			0
$739$	13.3462	−	41.0754i	0.490949	−	1.51098i	−0.332228	−	0.943199i	$-0.607800\pi$
$739$	13.3462	−	41.0754i	0.490949	−	1.51098i	0.823177	−	0.567785i	$-0.192200\pi$
$740$	12.6057	−	33.2548i	0.463393	−	1.22247i
$741$		0			0
$742$	−2.84402	−	3.91446i	−0.104407	−	0.143704i
$743$		−	31.8479i		−	1.16838i	−0.811615	−	0.584192i	$-0.801411\pi$
$743$		−	31.8479i		−	1.16838i	0.811615	−	0.584192i	$-0.198589\pi$
$744$		0			0
$745$	−2.02658	+	42.0404i	−0.0742482	+	1.54024i
$746$	3.42909	+	2.49138i	0.125548	+	0.0912158i
$747$		0			0
$748$	19.3116	+	6.27472i	0.706102	+	0.229426i
$749$	−51.6145			−1.88595
$750$		0			0
$751$	−29.5952			−1.07995			−0.539973	−	0.841682i	$-0.681565\pi$
$751$	−29.5952			−1.07995			−0.539973	+	0.841682i	$0.681565\pi$
$752$	15.2502	+	4.95510i	0.556119	+	0.180694i
$753$		0			0
$754$	0.259663	+	0.188656i	0.00945637	+	0.00687045i
$755$	0.418601	−	8.68368i	0.0152345	−	0.316031i
$756$		0			0
$757$			0.0984401i			0.00357786i	0.999998	+	0.00178893i	$0.000569435\pi$
$757$			0.0984401i			0.00357786i	−0.999998	+	0.00178893i	$0.999431\pi$
$758$	2.33098	+	3.20832i	0.0846651	+	0.116531i
$759$		0			0
$760$	−0.996425	+	2.62866i	−0.0361441	+	0.0953514i
$761$	1.09516	−	3.37056i	0.0396996	−	0.122183i	−0.929243	−	0.369470i	$-0.879539\pi$
$761$	1.09516	−	3.37056i	0.0396996	−	0.122183i	0.968942	+	0.247287i	$0.0795392\pi$
$762$		0			0
$763$	−6.21421	+	2.01912i	−0.224969	+	0.0730970i
$764$	−10.9564	+	33.7203i	−0.396388	+	1.21996i
$765$		0			0
$766$	0.320081	+	0.985108i	0.0115650	+	0.0355934i
$767$	1.03415	+	1.42339i	0.0373411	+	0.0513957i
$768$		0			0
$769$	1.15494	−	0.839116i	0.0416484	−	0.0302593i	−0.566766	−	0.823879i	$-0.691806\pi$
$769$	1.15494	−	0.839116i	0.0416484	−	0.0302593i	0.608415	+	0.793619i	$0.291806\pi$
$770$	−1.67232	+	2.08294i	−0.0602663	+	0.0750639i
$771$		0			0
$772$	7.84659	−	10.7999i	0.282405	−	0.388697i
$773$	−32.1274	−	10.4388i	−1.15554	−	0.375458i	−0.332313	−	0.943169i	$-0.607829\pi$
$773$	−32.1274	−	10.4388i	−1.15554	−	0.375458i	−0.823228	+	0.567711i	$0.807829\pi$
$774$		0			0
$775$	26.2830	−	15.4697i	0.944113	−	0.555688i
$776$	4.88708			0.175436
$777$		0			0
$778$	0.874898	−	1.20419i	0.0313666	−	0.0431725i
$779$	1.42111	+	1.03250i	0.0509165	+	0.0369930i
$780$		0			0
$781$	9.65769	−	7.01672i	0.345579	−	0.251078i
$782$			0.831462i			0.0297330i
$783$		0			0
$784$	−4.26610	−	13.1297i	−0.152361	−	0.468919i
$785$	9.56771	+	0.461216i	0.341486	+	0.0164615i
$786$		0			0
$787$	2.07358	−	0.673749i	0.0739153	−	0.0240165i	−0.271826	−	0.962346i	$-0.587627\pi$
$787$	2.07358	−	0.673749i	0.0739153	−	0.0240165i	0.345741	+	0.938330i	$0.387627\pi$
$788$	−14.9530	+	4.85852i	−0.532678	+	0.173077i
$789$		0			0
$790$	−2.65857	+	1.74238i	−0.0945875	+	0.0619911i
$791$	−10.5074	−	32.3383i	−0.373599	−	1.14982i
$792$		0			0
$793$		−	0.271369i		−	0.00963659i
$794$	3.07773	−	2.23610i	0.109224	−	0.0793562i
$795$		0			0
$796$	−8.28034	−	6.01602i	−0.293489	−	0.213232i
$797$	13.8082	−	19.0053i	0.489110	−	0.673203i	−0.491113	−	0.871096i	$-0.663410\pi$
$797$	13.8082	−	19.0053i	0.489110	−	0.673203i	0.980224	+	0.197893i	$0.0634099\pi$
$798$		0			0
$799$	21.7875			0.770787
$800$	−1.03359	+	10.6957i	−0.0365428	+	0.378150i
$801$		0			0
$802$	5.24703	+	1.70486i	0.185279	+	0.0602009i
$803$	−10.3843	+	14.2928i	−0.366454	+	0.504380i
$804$		0			0
$805$	5.99441	+	2.27226i	0.211275	+	0.0800865i
$806$	0.267892	−	0.194635i	0.00943610	−	0.00685573i
$807$		0			0
$808$	5.20809	+	7.16833i	0.183220	+	0.252181i
$809$	−11.7893	−	36.2837i	−0.414489	−	1.27567i	−0.912707	−	0.408615i	$-0.866012\pi$
$809$	−11.7893	−	36.2837i	−0.414489	−	1.27567i	0.498217	−	0.867052i	$-0.333988\pi$
$810$		0			0
$811$	14.8040	−	45.5622i	0.519840	−	1.59990i	−0.254458	−	0.967084i	$-0.581897\pi$
$811$	14.8040	−	45.5622i	0.519840	−	1.59990i	0.774298	−	0.632821i	$-0.218103\pi$
$812$	−36.0551	+	11.7150i	−1.26529	+	0.411116i
$813$		0			0
$814$	0.915615	−	2.81797i	0.0320923	−	0.0987699i
$815$	−9.24370	−	33.9285i	−0.323793	−	1.18846i
$816$		0			0
$817$	−3.29740	−	4.53849i	−0.115362	−	0.158782i
$818$			2.02318i			0.0707388i
$819$		0			0
$820$	4.17390	+	1.58217i	0.145759	+	0.0552517i
$821$	15.3558	+	11.1566i	0.535920	+	0.389369i	0.822568	−	0.568667i	$-0.192541\pi$
$821$	15.3558	+	11.1566i	0.535920	+	0.389369i	−0.286647	+	0.958036i	$0.592541\pi$
$822$		0			0
$823$	−21.0831	−	6.85033i	−0.734912	−	0.238787i	−0.0824356	−	0.996596i	$-0.526270\pi$
$823$	−21.0831	−	6.85033i	−0.734912	−	0.238787i	−0.652476	+	0.757809i	$0.726270\pi$
$824$	1.00365			0.0349638
$825$		0			0
$826$	3.54577			0.123373
$827$	−4.49790	−	1.46146i	−0.156407	−	0.0508199i	0.229767	−	0.973246i	$-0.426204\pi$
$827$	−4.49790	−	1.46146i	−0.156407	−	0.0508199i	−0.386174	+	0.922426i	$0.626204\pi$
$828$		0			0
$829$	13.3003	+	9.66320i	0.461937	+	0.335617i	0.794291	−	0.607538i	$-0.207843\pi$
$829$	13.3003	+	9.66320i	0.461937	+	0.335617i	−0.332354	+	0.943155i	$0.607843\pi$
$830$	5.73620	−	1.56281i	0.199106	−	0.0542459i
$831$		0			0
$832$		−	2.13570i		−	0.0740419i
$833$	−11.0257	−	15.1755i	−0.382017	−	0.525801i
$834$		0			0
$835$	39.3360	−	25.7802i	1.36128	−	0.892160i
$836$	2.10299	−	6.47232i	0.0727333	−	0.223850i
$837$		0			0
$838$	−5.73510	+	1.86345i	−0.198116	+	0.0643717i
$839$	−1.73075	+	5.32671i	−0.0597522	+	0.183898i	−0.976477	−	0.215620i	$-0.930823\pi$
$839$	−1.73075	+	5.32671i	−0.0597522	+	0.183898i	0.916725	+	0.399519i	$0.130823\pi$
$840$		0			0
$841$	1.83977	+	5.66224i	0.0634405	+	0.195250i
$842$	−2.18182	−	3.00302i	−0.0751904	−	0.103491i
$843$		0			0
$844$	−26.4119	+	19.1894i	−0.909135	+	0.660525i
$845$	−15.8264	−	24.1484i	−0.544446	−	0.830729i
$846$		0			0
$847$	−13.4168	+	18.4666i	−0.461006	+	0.634520i
$848$	29.2747	+	9.51192i	1.00530	+	0.326641i
$849$		0			0
$850$	1.02186	+	4.61682i	0.0350496	+	0.158356i
$851$	−7.11091			−0.243759
$852$		0			0
$853$	−10.5158	+	14.4737i	−0.360053	+	0.495571i	−0.950164	−	0.311752i	$-0.899084\pi$
$853$	−10.5158	+	14.4737i	−0.360053	+	0.495571i	0.590110	+	0.807323i	$0.299084\pi$
$854$	−0.442447	−	0.321457i	−0.0151402	−	0.0110000i
$855$		0			0
$856$	−9.30377	+	6.75959i	−0.317996	+	0.231038i
$857$			3.19536i			0.109151i	0.998510	+	0.0545757i	$0.0173806\pi$
$857$			3.19536i			0.109151i	−0.998510	+	0.0545757i	$0.982619\pi$
$858$		0			0
$859$	−13.4174	−	41.2945i	−0.457795	−	1.40895i	−0.867822	−	0.496875i	$-0.834481\pi$
$859$	−13.4174	−	41.2945i	−0.457795	−	1.40895i	0.410027	−	0.912073i	$-0.365519\pi$
$860$	−11.1160	−	8.92470i	−0.379054	−	0.304330i
$861$		0			0
$862$	−1.24650	+	0.405011i	−0.0424558	+	0.0137947i
$863$	41.1545	−	13.3719i	1.40091	−	0.455185i	0.491428	−	0.870918i	$-0.336475\pi$
$863$	41.1545	−	13.3719i	1.40091	−	0.455185i	0.909486	+	0.415734i	$0.136475\pi$
$864$		0			0
$865$	5.68011	−	14.9846i	0.193130	−	0.509493i
$866$	0.310336	+	0.955115i	0.0105456	+	0.0324561i
$867$		0			0
$868$			39.1120i			1.32755i
$869$	12.5570	−	9.12322i	0.425968	−	0.309484i
$870$		0			0
$871$	1.65159	+	1.19995i	0.0559619	+	0.0406587i
$872$	−0.855712	+	1.17779i	−0.0289781	+	0.0398849i
$873$		0			0
$874$	0.278666			0.00942603
$875$	36.0775	+	5.24996i	1.21964	+	0.177481i
$876$		0			0
$877$	−32.5584	−	10.5789i	−1.09942	−	0.357223i	−0.297540	−	0.954709i	$-0.596166\pi$
$877$	−32.5584	−	10.5789i	−1.09942	−	0.357223i	−0.801879	+	0.597487i	$0.796166\pi$
$878$	−3.31138	+	4.55772i	−0.111754	+	0.153816i
$879$		0			0
$880$	0.818220	−	16.9736i	0.0275822	−	0.572179i
$881$	22.3507	−	16.2388i	0.753016	−	0.547098i	−0.143744	−	0.989615i	$-0.545914\pi$
$881$	22.3507	−	16.2388i	0.753016	−	0.547098i	0.896760	+	0.442517i	$0.145914\pi$
$882$		0			0
$883$	−15.2231	−	20.9527i	−0.512297	−	0.705116i	0.472008	−	0.881594i	$-0.343529\pi$
$883$	−15.2231	−	20.9527i	−0.512297	−	0.705116i	−0.984305	+	0.176478i	$0.943529\pi$
$884$	−0.929846	−	2.86177i	−0.0312741	−	0.0962518i
$885$		0			0
$886$	0.642598	−	1.97771i	0.0215885	−	0.0664425i
$887$	−16.4009	+	5.32897i	−0.550688	+	0.178929i	−0.571127	−	0.820862i	$-0.693494\pi$
$887$	−16.4009	+	5.32897i	−0.550688	+	0.178929i	0.0204392	+	0.999791i	$0.493494\pi$
$888$		0			0
$889$	−5.89488	+	18.1426i	−0.197708	+	0.608482i
$890$	−2.40383	−	1.92995i	−0.0805765	−	0.0646922i
$891$		0			0
$892$	−7.66106	−	10.5445i	−0.256511	−	0.353058i
$893$		−	7.30213i		−	0.244356i
$894$		0			0
$895$	11.2543	−	14.0177i	0.376191	−	0.468559i
$896$	−14.8212	−	10.7682i	−0.495140	−	0.359740i
$897$		0			0
$898$	2.74657	+	0.892415i	0.0916543	+	0.0297803i
$899$	36.0614			1.20271
$900$		0			0
$901$	41.8238			1.39335
$902$	0.353691	+	0.114921i	0.0117766	+	0.00382645i
$903$		0			0
$904$	−6.12912	−	4.45307i	−0.203852	−	0.148107i
$905$	25.2704	+	38.5582i	0.840016	+	1.28172i
$906$		0			0
$907$			57.0465i			1.89420i	0.320940	+	0.947099i	$0.396001\pi$
$907$			57.0465i			1.89420i	−0.320940	+	0.947099i	$0.603999\pi$
$908$	−15.4790	−	21.3051i	−0.513690	−	0.707034i
$909$		0			0
$910$	0.395384	+	0.0190597i	0.0131068	+	0.000631822i
$911$	−6.13965	+	18.8959i	−0.203416	+	0.626049i	0.796359	+	0.604824i	$0.206757\pi$
$911$	−6.13965	+	18.8959i	−0.203416	+	0.626049i	−0.999775	+	0.0212248i	$0.993243\pi$
$912$		0			0
$913$	−27.6099	+	8.97099i	−0.913754	+	0.296897i
$914$	−0.235874	+	0.725945i	−0.00780201	+	0.0240121i
$915$		0			0
$916$	−6.12935	−	18.8642i	−0.202519	−	0.623291i
$917$	−2.86859	−	3.94827i	−0.0947291	−	0.130383i
$918$		0			0
$919$	22.6350	−	16.4453i	0.746661	−	0.542481i	−0.148129	−	0.988968i	$-0.547325\pi$
$919$	22.6350	−	16.4453i	0.746661	−	0.542481i	0.894790	+	0.446487i	$0.147325\pi$
$920$	1.37810	−	0.375460i	0.0454347	−	0.0123785i
$921$		0			0
$922$	−2.58090	+	3.55231i	−0.0849975	+	0.116989i
$923$	−1.68244	−	0.546657i	−0.0553781	−	0.0179934i
$924$		0			0
$925$	−39.4844	+	8.73926i	−1.29824	+	0.287345i
$926$	−7.56952			−0.248750
$927$		0			0
$928$	−7.46831	+	10.2792i	−0.245159	+	0.337433i
$929$	11.4273	+	8.30242i	0.374918	+	0.272394i	0.759247	−	0.650802i	$-0.225567\pi$
$929$	11.4273	+	8.30242i	0.374918	+	0.272394i	−0.384329	+	0.923196i	$0.625567\pi$
$930$		0			0
$931$	−5.08611	+	3.69528i	−0.166691	+	0.121108i
$932$		−	43.2727i		−	1.41744i
$933$		0			0
$934$	0.588481	+	1.81116i	0.0192557	+	0.0592629i
$935$	−6.06943	−	22.2775i	−0.198492	−	0.728552i
$936$		0			0
$937$	34.1949	−	11.1106i	1.11710	−	0.362967i	0.308438	−	0.951244i	$-0.400194\pi$
$937$	34.1949	−	11.1106i	1.11710	−	0.362967i	0.808659	+	0.588277i	$0.200194\pi$
$938$	3.91286	−	1.27136i	0.127759	−	0.0415115i
$939$		0			0
$940$	−4.87763	−	17.9031i	−0.159091	−	0.583934i
$941$	−8.25011	−	25.3912i	−0.268946	−	0.827730i	−0.990758	−	0.135641i	$-0.956691\pi$
$941$	−8.25011	−	25.3912i	−0.268946	−	0.827730i	0.721812	−	0.692089i	$-0.243309\pi$
$942$		0			0
$943$		−	0.892508i		−	0.0290640i
$944$	−18.2490	+	13.2587i	−0.593955	+	0.431534i
$945$		0			0
$946$	−0.960857	−	0.698104i	−0.0312402	−	0.0226973i
$947$	10.1747	−	14.0042i	0.330633	−	0.455077i	−0.611044	−	0.791597i	$-0.709250\pi$
$947$	10.1747	−	14.0042i	0.330633	−	0.455077i	0.941676	+	0.336520i	$0.109250\pi$
$948$		0			0
$949$	2.61803			0.0849850
$950$	1.54734	−	0.342479i	0.0502023	−	0.0111115i
$951$		0			0
$952$	−11.6332	−	3.77985i	−0.377034	−	0.122506i
$953$	−14.2610	+	19.6286i	−0.461959	+	0.635831i	−0.974913	−	0.222584i	$-0.928551\pi$
$953$	−14.2610	+	19.6286i	−0.461959	+	0.635831i	0.512955	+	0.858416i	$0.328551\pi$
$954$		0			0
$955$	38.8991	−	10.5979i	1.25875	−	0.342941i
$956$	−12.0276	+	8.73855i	−0.389000	+	0.282625i
$957$		0			0
$958$	3.87684	+	5.33602i	0.125255	+	0.172399i
$959$	7.90899	+	24.3414i	0.255395	+	0.786024i
$960$		0			0
$961$	1.91722	−	5.90061i	0.0618460	−	0.190342i
$962$	−0.417594	+	0.135684i	−0.0134638	+	0.00437464i
$963$		0			0
$964$	−12.3931	+	38.1419i	−0.399154	+	1.22847i
$965$	−15.1621	−	0.730899i	−0.488087	−	0.0235285i
$966$		0			0
$967$	−18.2885	−	25.1720i	−0.588120	−	0.809477i	0.406437	−	0.913679i	$-0.366771\pi$
$967$	−18.2885	−	25.1720i	−0.588120	−	0.809477i	−0.994556	+	0.104202i	$0.966771\pi$
$968$			5.08580i			0.163464i
$969$		0			0
$970$	−1.51019	−	2.30429i	−0.0484893	−	0.0739862i
$971$	−14.0543	−	10.2111i	−0.451025	−	0.327689i	0.338975	−	0.940795i	$-0.389920\pi$
$971$	−14.0543	−	10.2111i	−0.451025	−	0.327689i	−0.790000	+	0.613106i	$0.789920\pi$
$972$		0			0
$973$	−16.7205	−	5.43282i	−0.536034	−	0.174168i
$974$	1.94855			0.0624356
$975$		0			0
$976$	3.47917			0.111365
$977$	−40.7936	−	13.2546i	−1.30510	−	0.424054i	−0.427749	−	0.903898i	$-0.640693\pi$
$977$	−40.7936	−	13.2546i	−1.30510	−	0.424054i	−0.877354	+	0.479844i	$0.840693\pi$
$978$		0			0
$979$	12.1780	+	8.84784i	0.389211	+	0.282778i
$980$	−10.0016	+	12.4573i	−0.319489	+	0.397935i
$981$		0			0
$982$		−	3.23651i		−	0.103281i
$983$	−22.0145	−	30.3003i	−0.702153	−	0.966431i	−0.999930	−	0.0117954i	$-0.996245\pi$
$983$	−22.0145	−	30.3003i	−0.702153	−	0.966431i	0.297777	−	0.954635i	$-0.403755\pi$
$984$		0			0
$985$	13.9410	+	11.1928i	0.444198	+	0.356632i
$986$	−1.72778	+	5.31755i	−0.0550236	+	0.169345i
$987$		0			0
$988$	−0.959129	+	0.311640i	−0.0305140	+	0.00991459i
$989$	−0.880801	+	2.71083i	−0.0280078	+	0.0861993i
$990$		0			0
$991$	5.17987	+	15.9420i	0.164544	+	0.506415i	0.999002	−	0.0446564i	$-0.0142193\pi$
$991$	5.17987	+	15.9420i	0.164544	+	0.506415i	−0.834458	+	0.551071i	$0.814219\pi$
$992$	7.70500	+	10.6050i	0.244634	+	0.336710i
$993$		0			0
$994$	−2.88426	+	2.09554i	−0.0914831	+	0.0664663i
$995$	−0.560384	+	11.6249i	−0.0177654	+	0.368534i
$996$		0			0
$997$	35.1845	−	48.4273i	1.11430	−	1.53371i	0.299388	−	0.954132i	$-0.403218\pi$
$997$	35.1845	−	48.4273i	1.11430	−	1.53371i	0.814917	−	0.579577i	$-0.196782\pi$
$998$	−1.64057	−	0.533052i	−0.0519312	−	0.0168735i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.m.a.154.1		8
3.2	odd	2		25.2.e.a.4.2	✓	8
12.11	even	2		400.2.y.c.129.2		8
15.2	even	4		125.2.d.b.101.2		16
15.8	even	4		125.2.d.b.101.3		16
15.14	odd	2		125.2.e.b.24.1		8
25.12	odd	20		5625.2.a.x.1.5		8
25.13	odd	20		5625.2.a.x.1.4		8
25.19	even	10	inner	225.2.m.a.19.1		8
75.2	even	20		625.2.d.o.376.3		16
75.8	even	20		125.2.d.b.26.3		16
75.11	odd	10		625.2.e.a.249.2		8
75.14	odd	10		625.2.e.i.249.1		8
75.17	even	20		125.2.d.b.26.2		16
75.23	even	20		625.2.d.o.376.2		16
75.29	odd	10		625.2.e.a.374.2		8
75.38	even	20		625.2.a.f.1.5		8
75.41	odd	10		625.2.b.c.624.5		8
75.44	odd	10		25.2.e.a.19.2	yes	8
75.47	even	20		625.2.d.o.251.3		16
75.53	even	20		625.2.d.o.251.2		16
75.56	odd	10		125.2.e.b.99.1		8
75.59	odd	10		625.2.b.c.624.4		8
75.62	even	20		625.2.a.f.1.4		8
75.71	odd	10		625.2.e.i.374.1		8
300.119	even	10		400.2.y.c.369.2		8
300.263	odd	20		10000.2.a.bj.1.3		8
300.287	odd	20		10000.2.a.bj.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.4.2	✓	8	3.2	odd	2
25.2.e.a.19.2	yes	8	75.44	odd	10
125.2.d.b.26.2		16	75.17	even	20
125.2.d.b.26.3		16	75.8	even	20
125.2.d.b.101.2		16	15.2	even	4
125.2.d.b.101.3		16	15.8	even	4
125.2.e.b.24.1		8	15.14	odd	2
125.2.e.b.99.1		8	75.56	odd	10
225.2.m.a.19.1		8	25.19	even	10	inner
225.2.m.a.154.1		8	1.1	even	1	trivial
400.2.y.c.129.2		8	12.11	even	2
400.2.y.c.369.2		8	300.119	even	10
625.2.a.f.1.4		8	75.62	even	20
625.2.a.f.1.5		8	75.38	even	20
625.2.b.c.624.4		8	75.59	odd	10
625.2.b.c.624.5		8	75.41	odd	10
625.2.d.o.251.2		16	75.53	even	20
625.2.d.o.251.3		16	75.47	even	20
625.2.d.o.376.2		16	75.23	even	20
625.2.d.o.376.3		16	75.2	even	20
625.2.e.a.249.2		8	75.11	odd	10
625.2.e.a.374.2		8	75.29	odd	10
625.2.e.i.249.1		8	75.14	odd	10
625.2.e.i.374.1		8	75.71	odd	10
5625.2.a.x.1.4		8	25.13	odd	20
5625.2.a.x.1.5		8	25.12	odd	20
10000.2.a.bj.1.3		8	300.263	odd	20
10000.2.a.bj.1.6		8	300.287	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.174207 - 0.0566033i) q^{2} +(-1.59089 - 1.15585i) q^{4} +(-0.107666 + 2.23347i) q^{5} +3.26086i q^{7} +(0.427051 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(-0.174207 - 0.0566033i) q^{2} +(-1.59089 - 1.15585i) q^{4} +(-0.107666 + 2.23347i) q^{5} +3.26086i q^{7} +(0.427051 + 0.587785i) q^{8} +(0.145178 - 0.382993i) q^{10} +(-0.618034 + 1.90211i) q^{11} +(0.281873 - 0.0915860i) q^{13} +(0.184575 - 0.568064i) q^{14} +(1.17421 + 3.61384i) q^{16} +(3.03472 + 4.17693i) q^{17} +(1.39991 - 1.01709i) q^{19} +(2.75284 - 3.42877i) q^{20} +(0.215332 - 0.296379i) q^{22} +(-0.836161 - 0.271685i) q^{23} +(-4.97682 - 0.480938i) q^{25} -0.0542883 q^{26} +(3.76906 - 5.18766i) q^{28} +(-4.78304 - 3.47508i) q^{29} +(-4.93462 + 3.58521i) q^{31} -2.14910i q^{32} +(-0.292241 - 0.899425i) q^{34} +(-7.28304 - 0.351083i) q^{35} +(7.69215 - 2.49933i) q^{37} +(-0.301444 + 0.0979452i) q^{38} +(-1.35878 + 0.890523i) q^{40} +(0.313697 + 0.965461i) q^{41} -3.24199i q^{43} +(3.18178 - 2.31170i) q^{44} +(0.130287 + 0.0946589i) q^{46} +(2.48043 - 3.41402i) q^{47} -3.63318 q^{49} +(0.839774 + 0.365487i) q^{50} +(-0.554288 - 0.180099i) q^{52} +(4.76148 - 6.55362i) q^{53} +(-4.18178 - 1.58516i) q^{55} +(-1.91668 + 1.39255i) q^{56} +(0.636538 + 0.876119i) q^{58} +(1.83443 + 5.64581i) q^{59} +(0.282941 - 0.870802i) q^{61} +(1.06258 - 0.345253i) q^{62} +(2.22677 - 6.85329i) q^{64} +(0.174207 + 0.639416i) q^{65} +(4.04870 + 5.57255i) q^{67} -10.1527i q^{68} +(1.24888 + 0.473405i) q^{70} +(-4.82884 - 3.50836i) q^{71} +(8.40107 + 2.72967i) q^{73} -1.48150 q^{74} -3.40270 q^{76} +(-6.20252 - 2.01532i) q^{77} +(-6.27851 - 4.56161i) q^{79} +(-8.19784 + 2.23347i) q^{80} -0.185946i q^{82} +(8.53192 + 11.7432i) q^{83} +(-9.65580 + 6.32825i) q^{85} +(-0.183507 + 0.564778i) q^{86} +(-1.38197 + 0.449028i) q^{88} +(2.32579 - 7.15805i) q^{89} +(0.298649 + 0.919147i) q^{91} +(1.01621 + 1.39870i) q^{92} +(-0.625353 + 0.454345i) q^{94} +(2.12093 + 3.23616i) q^{95} +(3.95373 - 5.44184i) q^{97} +(0.632925 + 0.205650i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} - q^{4} - 10 q^{8}+O(q^{10}) \) 8 * q + 5 * q^2 - q^4 - 10 * q^8	\( 8 q + 5 q^{2} - q^{4} - 10 q^{8} - 5 q^{10} + 4 q^{11} - 5 q^{13} - 13 q^{14} + 3 q^{16} + 10 q^{17} - 5 q^{19} + 15 q^{20} - 5 q^{23} - 10 q^{25} - 6 q^{26} - 15 q^{28} + 5 q^{29} - 9 q^{31} + 13 q^{34} - 15 q^{35} + 30 q^{37} - 15 q^{38} + 10 q^{40} + 4 q^{41} + 2 q^{44} - 19 q^{46} + 14 q^{49} + 15 q^{50} - 10 q^{52} + 10 q^{53} - 10 q^{55} - 10 q^{56} + 20 q^{58} - 9 q^{61} + 30 q^{62} + 4 q^{64} - 5 q^{65} + 20 q^{67} + 30 q^{70} - 6 q^{71} + 15 q^{73} + 12 q^{74} - 20 q^{76} - 10 q^{77} + 15 q^{79} - 20 q^{80} + 45 q^{83} - 15 q^{85} + 9 q^{86} - 20 q^{88} + 25 q^{89} + 6 q^{91} - 30 q^{92} - 27 q^{94} - 15 q^{95} - 60 q^{97} + 10 q^{98}+O(q^{100}) \) 8 * q + 5 * q^2 - q^4 - 10 * q^8 - 5 * q^10 + 4 * q^11 - 5 * q^13 - 13 * q^14 + 3 * q^16 + 10 * q^17 - 5 * q^19 + 15 * q^20 - 5 * q^23 - 10 * q^25 - 6 * q^26 - 15 * q^28 + 5 * q^29 - 9 * q^31 + 13 * q^34 - 15 * q^35 + 30 * q^37 - 15 * q^38 + 10 * q^40 + 4 * q^41 + 2 * q^44 - 19 * q^46 + 14 * q^49 + 15 * q^50 - 10 * q^52 + 10 * q^53 - 10 * q^55 - 10 * q^56 + 20 * q^58 - 9 * q^61 + 30 * q^62 + 4 * q^64 - 5 * q^65 + 20 * q^67 + 30 * q^70 - 6 * q^71 + 15 * q^73 + 12 * q^74 - 20 * q^76 - 10 * q^77 + 15 * q^79 - 20 * q^80 + 45 * q^83 - 15 * q^85 + 9 * q^86 - 20 * q^88 + 25 * q^89 + 6 * q^91 - 30 * q^92 - 27 * q^94 - 15 * q^95 - 60 * q^97 + 10 * q^98

Introduction

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