LMFDB - Embedded newform 775.2.o.e.149.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(149,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("775.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.o (of order $6$, degree $2$, 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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 88x^{12} - 301x^{10} + 739x^{8} - 825x^{6} + 664x^{4} - 279x^{2} + 81 $ x^16 - 11x^14 + 88x^12 - 301x^10 + 739x^8 - 825x^6 + 664x^4 - 279*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.3
Root			$-0.753430 - 0.434993i$ of defining polynomial
Character	$\chi$	$=$	775.149
Dual form			775.2.o.e.749.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.869986i q^{2} +(0.112596 - 0.0650072i) q^{3} +1.24312 q^{4} +(-0.0565553 - 0.0979567i) q^{6} +(2.74842 - 1.58680i) q^{7} -2.82147i q^{8} +(-1.49155 + 2.58344i) q^{9} +O(q^{10})$	\(q-0.869986i q^{2} +(0.112596 - 0.0650072i) q^{3} +1.24312 q^{4} +(-0.0565553 - 0.0979567i) q^{6} +(2.74842 - 1.58680i) q^{7} -2.82147i q^{8} +(-1.49155 + 2.58344i) q^{9} +(0.267382 - 0.463119i) q^{11} +(0.139971 - 0.0808121i) q^{12} +(-1.15634 - 0.667611i) q^{13} +(-1.38049 - 2.39108i) q^{14} +0.0316097 q^{16} +(5.53204 - 3.19392i) q^{17} +(2.24755 + 1.29763i) q^{18} +(-2.14335 - 3.71240i) q^{19} +(0.206307 - 0.357334i) q^{21} +(-0.402907 - 0.232618i) q^{22} +3.35624i q^{23} +(-0.183416 - 0.317686i) q^{24} +(-0.580812 + 1.00600i) q^{26} +0.777888i q^{27} +(3.41663 - 1.97259i) q^{28} -1.35624 q^{29} +(4.22417 + 3.62718i) q^{31} -5.67044i q^{32} -0.0695269i q^{33} +(-2.77867 - 4.81279i) q^{34} +(-1.85418 + 3.21154i) q^{36} +(-0.127235 + 0.0734590i) q^{37} +(-3.22973 + 1.86469i) q^{38} -0.173598 q^{39} +(-4.03230 + 6.98415i) q^{41} +(-0.310875 - 0.179484i) q^{42} +(7.51238 - 4.33728i) q^{43} +(0.332389 - 0.575714i) q^{44} +2.91988 q^{46} -1.02101i q^{47} +(0.00355912 - 0.00205486i) q^{48} +(1.53586 - 2.66019i) q^{49} +(0.415256 - 0.719244i) q^{51} +(-1.43747 - 0.829924i) q^{52} +(-9.10446 - 5.25646i) q^{53} +0.676752 q^{54} +(-4.47711 - 7.75458i) q^{56} +(-0.482665 - 0.278667i) q^{57} +1.17991i q^{58} +(0.0144388 + 0.0250088i) q^{59} +12.5276 q^{61} +(3.15559 - 3.67496i) q^{62} +9.46715i q^{63} -4.86999 q^{64} -0.0604874 q^{66} +(-4.69885 - 2.71288i) q^{67} +(6.87701 - 3.97045i) q^{68} +(0.218179 + 0.377898i) q^{69} +(2.88442 - 4.99597i) q^{71} +(7.28910 + 4.20836i) q^{72} +(1.00173 + 0.578347i) q^{73} +(0.0639083 + 0.110692i) q^{74} +(-2.66446 - 4.61498i) q^{76} -1.69712i q^{77} +0.151028i q^{78} +(4.86752 + 8.43079i) q^{79} +(-4.42408 - 7.66272i) q^{81} +(6.07611 + 3.50804i) q^{82} +(-8.97232 - 5.18017i) q^{83} +(0.256465 - 0.444210i) q^{84} +(-3.77337 - 6.53567i) q^{86} +(-0.152706 + 0.0881651i) q^{87} +(-1.30668 - 0.754410i) q^{88} -12.7519 q^{89} -4.23746 q^{91} +4.17222i q^{92} +(0.711416 + 0.133804i) q^{93} -0.888267 q^{94} +(-0.368620 - 0.638468i) q^{96} +13.7617i q^{97} +(-2.31433 - 1.33618i) q^{98} +(0.797625 + 1.38153i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4} + 20 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q - 12 * q^4 + 20 * q^6 + 2 * q^9	$ 16 q - 12 q^{4} + 20 q^{6} + 2 q^{9} + 8 q^{11} + 16 q^{14} + 20 q^{16} + 10 q^{19} + 18 q^{21} - 4 q^{24} - 24 q^{26} + 52 q^{29} + 38 q^{31} - 48 q^{34} - 10 q^{36} + 44 q^{39} - 8 q^{41} + 14 q^{44} - 44 q^{46} + 74 q^{49} - 24 q^{51} - 48 q^{54} - 58 q^{56} - 12 q^{59} - 4 q^{61} - 68 q^{64} + 4 q^{66} + 12 q^{69} + 24 q^{71} - 36 q^{74} - 46 q^{76} + 4 q^{79} + 24 q^{81} - 82 q^{84} - 26 q^{86} - 108 q^{89} - 88 q^{91} + 96 q^{94} + 26 q^{96} + 14 q^{99}+O(q^{100}) $ 16 * q - 12 * q^4 + 20 * q^6 + 2 * q^9 + 8 * q^11 + 16 * q^14 + 20 * q^16 + 10 * q^19 + 18 * q^21 - 4 * q^24 - 24 * q^26 + 52 * q^29 + 38 * q^31 - 48 * q^34 - 10 * q^36 + 44 * q^39 - 8 * q^41 + 14 * q^44 - 44 * q^46 + 74 * q^49 - 24 * q^51 - 48 * q^54 - 58 * q^56 - 12 * q^59 - 4 * q^61 - 68 * q^64 + 4 * q^66 + 12 * q^69 + 24 * q^71 - 36 * q^74 - 46 * q^76 + 4 * q^79 + 24 * q^81 - 82 * q^84 - 26 * q^86 - 108 * q^89 - 88 * q^91 + 96 * q^94 + 26 * q^96 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$		−	0.869986i		−	0.615173i	−0.951520	−	0.307586i	$-0.900479\pi$
$2$		−	0.869986i		−	0.615173i	0.951520	−	0.307586i	$-0.0995213\pi$
$3$	0.112596	−	0.0650072i	0.0650072	−	0.0375319i	−0.467144	−	0.884181i	$-0.654717\pi$
$3$	0.112596	−	0.0650072i	0.0650072	−	0.0375319i	0.532151	+	0.846649i	$0.321384\pi$
$4$	1.24312			0.621562
$5$		0			0
$5$		0			0
$6$	−0.0565553	−	0.0979567i	−0.0230886	−	0.0399906i
$7$	2.74842	−	1.58680i	1.03880	−	0.599754i	0.119310	−	0.992857i	$-0.461932\pi$
$7$	2.74842	−	1.58680i	1.03880	−	0.599754i	0.919494	+	0.393103i	$0.128599\pi$
$8$		−	2.82147i		−	0.997541i
$9$	−1.49155	+	2.58344i	−0.497183	+	0.861146i
$10$		0			0
$11$	0.267382	−	0.463119i	0.0806186	−	0.139636i	−0.822897	−	0.568190i	$-0.807644\pi$
$11$	0.267382	−	0.463119i	0.0806186	−	0.139636i	0.903516	+	0.428555i	$0.140977\pi$
$12$	0.139971	−	0.0808121i	0.0404060	−	0.0233284i
$13$	−1.15634	−	0.667611i	−0.320710	−	0.185162i	0.330999	−	0.943631i	$-0.392614\pi$
$13$	−1.15634	−	0.667611i	−0.320710	−	0.185162i	−0.651709	+	0.758469i	$0.725948\pi$
$14$	−1.38049	−	2.39108i	−0.368952	−	0.639044i
$15$		0			0
$16$	0.0316097			0.00790244
$17$	5.53204	−	3.19392i	1.34172	−	0.774640i	0.354657	−	0.934997i	$-0.384598\pi$
$17$	5.53204	−	3.19392i	1.34172	−	0.774640i	0.987059	+	0.160357i	$0.0512644\pi$
$18$	2.24755	+	1.29763i	0.529753	+	0.305853i
$19$	−2.14335	−	3.71240i	−0.491719	−	0.851683i	0.508235	−	0.861218i	$-0.330298\pi$
$19$	−2.14335	−	3.71240i	−0.491719	−	0.851683i	−0.999955	+	0.00953558i	$0.996965\pi$
$20$		0			0
$21$	0.206307	−	0.357334i	0.0450198	−	0.0779766i
$22$	−0.402907	−	0.232618i	−0.0859000	−	0.0495944i
$23$			3.35624i			0.699824i	0.936783	+	0.349912i	$0.113788\pi$
$23$			3.35624i			0.699824i	−0.936783	+	0.349912i	$0.886212\pi$
$24$	−0.183416	−	0.317686i	−0.0374396	−	0.0648473i
$25$		0			0
$26$	−0.580812	+	1.00600i	−0.113907	+	0.197292i
$27$			0.777888i			0.149705i
$28$	3.41663	−	1.97259i	0.645681	−	0.372784i
$29$	−1.35624			−0.251847			−0.125923	−	0.992040i	$-0.540189\pi$
$29$	−1.35624			−0.251847			−0.125923	+	0.992040i	$0.540189\pi$
$30$		0			0
$31$	4.22417	+	3.62718i	0.758683	+	0.651460i
$31$	4.22417	+	3.62718i	0.758683	+	0.651460i
$32$		−	5.67044i		−	1.00240i
$33$		−	0.0695269i		−	0.0121031i
$34$	−2.77867	−	4.81279i	−0.476537	−	0.825387i
$35$		0			0
$36$	−1.85418	+	3.21154i	−0.309030	+	0.535256i
$37$	−0.127235	+	0.0734590i	−0.0209173	+	0.0120766i	−0.510422	−	0.859924i	$-0.670511\pi$
$37$	−0.127235	+	0.0734590i	−0.0209173	+	0.0120766i	0.489505	+	0.872001i	$0.337178\pi$
$38$	−3.22973	+	1.86469i	−0.523932	+	0.302492i
$39$	−0.173598			−0.0277979
$40$		0			0
$41$	−4.03230	+	6.98415i	−0.629739	+	1.09074i	0.357865	+	0.933773i	$0.383505\pi$
$41$	−4.03230	+	6.98415i	−0.629739	+	1.09074i	−0.987604	+	0.156967i	$0.949828\pi$
$42$	−0.310875	−	0.179484i	−0.0479691	−	0.0276950i
$43$	7.51238	−	4.33728i	1.14563	−	0.661429i	0.197810	−	0.980240i	$-0.436617\pi$
$43$	7.51238	−	4.33728i	1.14563	−	0.661429i	0.947818	+	0.318812i	$0.103284\pi$
$44$	0.332389	−	0.575714i	0.0501095	−	0.0867922i
$45$		0			0
$46$	2.91988			0.430512
$47$		−	1.02101i		−	0.148930i	−0.997224	−	0.0744651i	$-0.976275\pi$
$47$		−	1.02101i		−	0.148930i	0.997224	−	0.0744651i	$-0.0237249\pi$
$48$	0.00355912	−	0.00205486i	0.000513715	−	0.000296594i
$49$	1.53586	−	2.66019i	0.219409	−	0.380027i
$50$		0			0
$51$	0.415256	−	0.719244i	0.0581474	−	0.100714i
$52$	−1.43747	−	0.829924i	−0.199341	−	0.115090i
$53$	−9.10446	−	5.25646i	−1.25059	−	0.722031i	−0.279367	−	0.960184i	$-0.590125\pi$
$53$	−9.10446	−	5.25646i	−1.25059	−	0.722031i	−0.971228	+	0.238153i	$0.923458\pi$
$54$	0.676752			0.0920943
$55$		0			0
$56$	−4.47711	−	7.75458i	−0.598279	−	1.03625i
$57$	−0.482665	−	0.278667i	−0.0639306	−	0.0369103i
$58$			1.17991i			0.154929i
$59$	0.0144388	+	0.0250088i	0.00187978	+	0.00325587i	0.866964	−	0.498371i	$-0.166068\pi$
$59$	0.0144388	+	0.0250088i	0.00187978	+	0.00325587i	−0.865084	+	0.501627i	$0.832735\pi$
$60$		0			0
$61$	12.5276			1.60400			0.802000	−	0.597324i	$-0.203770\pi$
$61$	12.5276			1.60400			0.802000	+	0.597324i	$0.203770\pi$
$62$	3.15559	−	3.67496i	0.400761	−	0.466721i
$63$			9.46715i			1.19275i
$64$	−4.86999			−0.608748
$65$		0			0
$66$	−0.0604874			−0.00744549
$67$	−4.69885	−	2.71288i	−0.574056	−	0.331431i	0.184712	−	0.982793i	$-0.440865\pi$
$67$	−4.69885	−	2.71288i	−0.574056	−	0.331431i	−0.758768	+	0.651362i	$0.774198\pi$
$68$	6.87701	−	3.97045i	0.833960	−	0.481487i
$69$	0.218179	+	0.377898i	0.0262657	+	0.0454936i
$70$		0			0
$71$	2.88442	−	4.99597i	0.342318	−	0.592913i	−0.642545	−	0.766248i	$-0.722121\pi$
$71$	2.88442	−	4.99597i	0.342318	−	0.592913i	0.984863	+	0.173336i	$0.0554546\pi$
$72$	7.28910	+	4.20836i	0.859028	+	0.495960i
$73$	1.00173	+	0.578347i	0.117243	+	0.0676904i	0.557475	−	0.830194i	$-0.311770\pi$
$73$	1.00173	+	0.578347i	0.117243	+	0.0676904i	−0.440232	+	0.897884i	$0.645104\pi$
$74$	0.0639083	+	0.110692i	0.00742919	+	0.0128677i
$75$		0			0
$76$	−2.66446	−	4.61498i	−0.305634	−	0.529374i
$77$		−	1.69712i		−	0.193405i
$78$			0.151028i			0.0171005i
$79$	4.86752	+	8.43079i	0.547639	+	0.948538i	0.998436	+	0.0559118i	$0.0178066\pi$
$79$	4.86752	+	8.43079i	0.547639	+	0.948538i	−0.450797	+	0.892627i	$0.648860\pi$
$80$		0			0
$81$	−4.42408	−	7.66272i	−0.491564	−	0.851414i
$82$	6.07611	+	3.50804i	0.670994	+	0.387398i
$83$	−8.97232	−	5.18017i	−0.984840	−	0.568598i	−0.0811123	−	0.996705i	$-0.525847\pi$
$83$	−8.97232	−	5.18017i	−0.984840	−	0.568598i	−0.903728	+	0.428107i	$0.859181\pi$
$84$	0.256465	−	0.444210i	0.0279826	−	0.0484673i
$85$		0			0
$86$	−3.77337	−	6.53567i	−0.406893	−	0.704759i
$87$	−0.152706	+	0.0881651i	−0.0163718	+	0.00945229i
$88$	−1.30668	−	0.754410i	−0.139292	−	0.0804204i
$89$	−12.7519			−1.35170			−0.675852	−	0.737038i	$-0.736224\pi$
$89$	−12.7519			−1.35170			−0.675852	+	0.737038i	$0.736224\pi$
$90$		0			0
$91$	−4.23746			−0.444206
$92$			4.17222i			0.434984i
$93$	0.711416	+	0.133804i	0.0737704	+	0.0138748i
$94$	−0.888267			−0.0916177
$95$		0			0
$96$	−0.368620	−	0.638468i	−0.0376221	−	0.0651634i
$97$			13.7617i			1.39729i	0.715468	+	0.698646i	$0.246214\pi$
$97$			13.7617i			1.39729i	−0.715468	+	0.698646i	$0.753786\pi$
$98$	−2.31433	−	1.33618i	−0.233782	−	0.134974i
$99$	0.797625	+	1.38153i	0.0801644	+	0.138849i
$100$		0			0
$101$	−17.8432			−1.77547			−0.887733	−	0.460358i	$-0.847721\pi$
$101$	−17.8432			−1.77547			−0.887733	+	0.460358i	$0.847721\pi$
$102$	−0.625732	−	0.361267i	−0.0619567	−	0.0357707i
$103$	6.99332	+	4.03760i	0.689073	+	0.397836i	0.803265	−	0.595622i	$-0.203095\pi$
$103$	6.99332	+	4.03760i	0.689073	+	0.397836i	−0.114192	+	0.993459i	$0.536428\pi$
$104$	−1.88365	+	3.26257i	−0.184707	+	0.319921i
$105$		0			0
$106$	−4.57305	+	7.92075i	−0.444174	+	0.769332i
$107$	−12.6776	+	7.31942i	−1.22559	+	0.707595i	−0.966104	−	0.258152i	$-0.916886\pi$
$107$	−12.6776	+	7.31942i	−1.22559	+	0.707595i	−0.259486	+	0.965747i	$0.583553\pi$
$108$			0.967013i			0.0930508i
$109$	−0.165734			−0.0158744			−0.00793721	−	0.999968i	$-0.502527\pi$
$109$	−0.165734			−0.0158744			−0.00793721	+	0.999968i	$0.502527\pi$
$110$		0			0
$111$	−0.00955073	+	0.0165424i	−0.000906515	+	0.00157013i
$112$	0.0868767	−	0.0501583i	0.00820908	−	0.00473951i
$113$	5.14187	+	2.96866i	0.483706	+	0.279268i	0.721960	−	0.691935i	$-0.243242\pi$
$113$	5.14187	+	2.96866i	0.483706	+	0.279268i	−0.238254	+	0.971203i	$0.576575\pi$
$114$	−0.242436	+	0.419912i	−0.0227062	+	0.0393283i
$115$		0			0
$116$	−1.68597			−0.156538
$117$	3.44946	−	1.99155i	0.318903	−	0.184119i
$118$	0.0217573	−	0.0125616i	0.00200292	−	0.00115639i
$119$	10.1362	−	17.5565i	0.929186	−	1.60940i
$120$		0			0
$121$	5.35701	+	9.27862i	0.487001	+	0.843511i
$122$		−	10.8989i		−	0.986737i
$123$			1.04851i			0.0945413i
$124$	5.25117	+	4.50904i	0.471569	+	0.404923i
$125$		0			0
$126$	8.23628			0.733746
$127$	−16.0704	+	9.27826i	−1.42602	+	0.823312i	−0.996804	−	0.0798903i	$-0.974543\pi$
$127$	−16.0704	+	9.27826i	−1.42602	+	0.823312i	−0.429215	+	0.903202i	$0.641210\pi$
$128$		−	7.10407i		−	0.627917i
$129$	0.563908	−	0.976718i	0.0496494	−	0.0859952i
$130$		0			0
$131$	8.20480	+	14.2111i	0.716857	+	1.24163i	0.962239	+	0.272206i	$0.0877531\pi$
$131$	8.20480	+	14.2111i	0.716857	+	1.24163i	−0.245383	+	0.969426i	$0.578914\pi$
$132$		−	0.0864307i		−	0.00752282i
$133$	−11.7817	−	6.80215i	−1.02160	−	0.589821i
$134$	−2.36017	+	4.08793i	−0.203887	+	0.353143i
$135$		0			0
$136$	−9.01156	−	15.6085i	−0.772735	−	1.33842i
$137$	−3.98316	−	2.29968i	−0.340305	−	0.196475i	0.320102	−	0.947383i	$-0.396283\pi$
$137$	−3.98316	−	2.29968i	−0.340305	−	0.196475i	−0.660407	+	0.750908i	$0.729616\pi$
$138$	0.328766	−	0.189813i	0.0279864	−	0.0161580i
$139$	21.9951			1.86560			0.932799	−	0.360398i	$-0.117359\pi$
$139$	21.9951			1.86560			0.932799	+	0.360398i	$0.117359\pi$
$140$		0			0
$141$	−0.0663732	−	0.114962i	−0.00558963	−	0.00968153i
$142$	−4.34642	−	2.50941i	−0.364744	−	0.210585i
$143$	−0.618366	+	0.357014i	−0.0517104	+	0.0298550i
$144$	−0.0471475	+	0.0816618i	−0.00392895	+	0.00680515i
$145$		0			0
$146$	0.503154	−	0.871488i	0.0416413	−	0.0721248i
$147$		−	0.399368i		−	0.0329393i
$148$	−0.158169	+	0.0913188i	−0.0130014	+	0.00750636i
$149$	10.9019	+	18.8826i	0.893116	+	1.54692i	0.836119	+	0.548549i	$0.184819\pi$
$149$	10.9019	+	18.8826i	0.893116	+	1.54692i	0.0569976	+	0.998374i	$0.481847\pi$
$150$		0			0
$151$	8.96619			0.729658			0.364829	−	0.931074i	$-0.381127\pi$
$151$	8.96619			0.729658			0.364829	+	0.931074i	$0.381127\pi$
$152$	−10.4744	+	6.04741i	−0.849588	+	0.490510i
$153$			19.0556i			1.54055i
$154$	−1.47647			−0.118978
$155$		0			0
$156$	−0.215804			−0.0172782
$157$			7.32243i			0.584393i	0.956358	+	0.292197i	$0.0943862\pi$
$157$			7.32243i			0.584393i	−0.956358	+	0.292197i	$0.905614\pi$
$158$	7.33467	−	4.23467i	0.583515	−	0.336893i
$159$	−1.36683			−0.108397
$160$		0			0
$161$	5.32567	+	9.22433i	0.419722	+	0.726979i
$162$	−6.66646	+	3.84888i	−0.523767	+	0.302397i
$163$			3.24879i			0.254465i	0.991873	+	0.127232i	$0.0406094\pi$
$163$			3.24879i			0.254465i	−0.991873	+	0.127232i	$0.959391\pi$
$164$	−5.01265	+	8.68217i	−0.391422	+	0.677963i
$165$		0			0
$166$	−4.50668	+	7.80579i	−0.349786	+	0.605847i
$167$	1.32424	−	0.764548i	0.102473	−	0.0591625i	−0.447888	−	0.894090i	$-0.647824\pi$
$167$	1.32424	−	0.764548i	0.102473	−	0.0591625i	0.550360	+	0.834927i	$0.314490\pi$
$168$	−1.00821	−	0.582089i	−0.0777849	−	0.0449091i
$169$	−5.60859	−	9.71436i	−0.431430	−	0.747259i
$170$		0			0
$171$	12.7877			0.977897
$172$	9.33883	−	5.39178i	0.712079	−	0.411119i
$173$	2.47140	+	1.42686i	0.187897	+	0.108482i	0.590998	−	0.806673i	$-0.298734\pi$
$173$	2.47140	+	1.42686i	0.187897	+	0.108482i	−0.403101	+	0.915156i	$0.632068\pi$
$174$	0.0767023	+	0.132852i	0.00581479	+	0.0100715i
$175$		0			0
$176$	0.00845187	−	0.0146391i	0.000637083	−	0.00110346i
$177$	0.00325151	+	0.00187726i	0.000244398	+	0.000141103i
$178$			11.0940i			0.831531i
$179$	1.95925	+	3.39352i	0.146441	+	0.253644i	0.929910	−	0.367788i	$-0.119885\pi$
$179$	1.95925	+	3.39352i	0.146441	+	0.253644i	−0.783469	+	0.621431i	$0.786551\pi$
$180$		0			0
$181$	9.10297	−	15.7668i	0.676619	−	1.17194i	−0.299374	−	0.954136i	$-0.596778\pi$
$181$	9.10297	−	15.7668i	0.676619	−	1.17194i	0.975993	−	0.217802i	$-0.0698887\pi$
$182$			3.68653i			0.273264i
$183$	1.41056	−	0.814386i	0.104271	−	0.0602012i
$184$	9.46953			0.698103
$185$		0			0
$186$	0.116407	−	0.618921i	0.00853539	−	0.0453815i
$187$		−	3.41599i		−	0.249802i
$188$		−	1.26925i		−	0.0925694i
$189$	1.23435	+	2.13796i	0.0897859	+	0.155514i
$190$		0			0
$191$	−8.58570	+	14.8709i	−0.621239	+	1.07602i	0.368016	+	0.929820i	$0.380037\pi$
$191$	−8.58570	+	14.8709i	−0.621239	+	1.07602i	−0.989255	+	0.146199i	$0.953296\pi$
$192$	−0.548340	+	0.316584i	−0.0395730	+	0.0228475i
$193$	−14.7071	+	8.49114i	−1.05864	+	0.611205i	−0.925055	−	0.379832i	$-0.875982\pi$
$193$	−14.7071	+	8.49114i	−1.05864	+	0.611205i	−0.133584	+	0.991038i	$0.542648\pi$
$194$	11.9725			0.859575
$195$		0			0
$196$	1.90927	−	3.30695i	0.136376	−	0.236211i
$197$	6.21252	+	3.58680i	0.442624	+	0.255549i	0.704710	−	0.709496i	$-0.251077\pi$
$197$	6.21252	+	3.58680i	0.442624	+	0.255549i	−0.262086	+	0.965044i	$0.584411\pi$
$198$	1.20191	−	0.693923i	0.0854160	−	0.0493149i
$199$	−6.23919	+	10.8066i	−0.442285	+	0.766059i	−0.997859	−	0.0654076i	$-0.979165\pi$
$199$	−6.23919	+	10.8066i	−0.442285	+	0.766059i	0.555574	+	0.831467i	$0.312499\pi$
$200$		0			0
$201$	−0.705427			−0.0497570
$202$			15.5233i			1.09222i
$203$	−3.72750	+	2.15207i	−0.261619	+	0.151046i
$204$	0.516215	−	0.894110i	0.0361423	−	0.0626003i
$205$		0			0
$206$	3.51265	−	6.08409i	0.244738	−	0.423899i
$207$	−8.67062	−	5.00599i	−0.602650	−	0.347940i
$208$	−0.0365515	−	0.0211030i	−0.00253439	−	0.00146323i
$209$	−2.29238			−0.158567
$210$		0			0
$211$	−0.940980	−	1.62982i	−0.0647797	−	0.112202i	0.831817	−	0.555051i	$-0.187301\pi$
$211$	−0.940980	−	1.62982i	−0.0647797	−	0.112202i	−0.896596	+	0.442849i	$0.853968\pi$
$212$	−11.3180	−	6.53444i	−0.777323	−	0.448787i
$213$		−	0.750033i		−	0.0513914i
$214$	6.36779	+	11.0293i	0.435293	+	0.753950i
$215$		0			0
$216$	2.19479			0.149337
$217$	17.3654	+	3.26609i	1.17884	+	0.221717i
$218$			0.144186i			0.00976551i
$219$	0.150387			0.0101622
$220$		0			0
$221$	−8.52919			−0.573736
$222$	0.0143916	+	0.00830900i	0.000965902	+	0.000557664i
$223$	−11.4415	+	6.60576i	−0.766180	+	0.442354i	−0.831510	−	0.555509i	$-0.812523\pi$
$223$	−11.4415	+	6.60576i	−0.766180	+	0.442354i	0.0653302	+	0.997864i	$0.479190\pi$
$224$	−8.99786	−	15.5847i	−0.601195	−	1.04130i
$225$		0			0
$226$	2.58269	−	4.47335i	0.171798	−	0.297563i
$227$	−1.07658	−	0.621562i	−0.0714550	−	0.0412546i	0.463847	−	0.885915i	$-0.346469\pi$
$227$	−1.07658	−	0.621562i	−0.0714550	−	0.0412546i	−0.535302	+	0.844661i	$0.679802\pi$
$228$	−0.600013	−	0.346418i	−0.0397368	−	0.0229421i
$229$	−7.61106	−	13.1827i	−0.502953	−	0.871140i	−0.999994	−	0.00341287i	$-0.998914\pi$
$229$	−7.61106	−	13.1827i	−0.502953	−	0.871140i	0.497041	−	0.867727i	$-0.334420\pi$
$230$		0			0
$231$	−0.110325	−	0.191089i	−0.00725887	−	0.0125727i
$232$			3.82658i			0.251227i
$233$		−	1.60649i		−	0.105245i	−0.998614	−	0.0526223i	$-0.983242\pi$
$233$		−	1.60649i		−	0.105245i	0.998614	−	0.0526223i	$-0.0167579\pi$
$234$	−1.73262	−	3.00098i	−0.113265	−	0.196180i
$235$		0			0
$236$	0.0179493	+	0.0310891i	0.00116840	+	0.00202373i
$237$	1.09612	+	0.632848i	0.0712009	+	0.0411079i
$238$	−15.2739	−	8.81837i	−0.990058	−	0.571610i
$239$	−10.3667	+	17.9557i	−0.670569	+	1.16146i	0.307174	+	0.951653i	$0.400617\pi$
$239$	−10.3667	+	17.9557i	−0.670569	+	1.16146i	−0.977743	+	0.209806i	$0.932717\pi$
$240$		0			0
$241$	7.43988	+	12.8863i	0.479245	+	0.830076i	0.999717	−	0.0238024i	$-0.00757725\pi$
$241$	7.43988	+	12.8863i	0.479245	+	0.830076i	−0.520472	+	0.853879i	$0.674244\pi$
$242$	8.07227	−	4.66053i	0.518905	−	0.299590i
$243$	−3.01728	−	1.74203i	−0.193558	−	0.111751i
$244$	15.5734			0.996986
$245$		0			0
$246$	0.912192			0.0581592
$247$			5.72371i			0.364191i
$248$	10.2340	−	11.9184i	0.649858	−	0.756817i
$249$	−1.34699			−0.0853623
$250$		0			0
$251$	−1.86752	−	3.23464i	−0.117877	−	0.204169i	0.801049	−	0.598598i	$-0.204275\pi$
$251$	−1.86752	−	3.23464i	−0.117877	−	0.204169i	−0.918926	+	0.394430i	$0.870942\pi$
$252$			11.7688i			0.741368i
$253$	1.55434	+	0.897396i	0.0977202	+	0.0564188i
$254$	8.07195	+	13.9810i	0.506479	+	0.877248i
$255$		0			0
$256$	−15.9204			−0.995026
$257$	−4.09576	−	2.36469i	−0.255486	−	0.147505i	0.366787	−	0.930305i	$-0.380458\pi$
$257$	−4.09576	−	2.36469i	−0.255486	−	0.147505i	−0.622274	+	0.782800i	$0.713791\pi$
$258$	−0.849731	−	0.490592i	−0.0529019	−	0.0305429i
$259$	−0.233129	+	0.403792i	−0.0144860	+	0.0250904i
$260$		0			0
$261$	2.02289	−	3.50375i	0.125214	−	0.216877i
$262$	12.3635	−	7.13806i	0.763818	−	0.440991i
$263$			7.58401i			0.467650i	0.972279	+	0.233825i	$0.0751243\pi$
$263$			7.58401i			0.467650i	−0.972279	+	0.233825i	$0.924876\pi$
$264$	−0.196168			−0.0120733
$265$		0			0
$266$	−5.91777	+	10.2499i	−0.362842	+	0.628460i
$267$	−1.43581	+	0.828968i	−0.0878704	+	0.0507320i
$268$	−5.84126	−	3.37245i	−0.356811	−	0.206005i
$269$	−6.92408	+	11.9929i	−0.422168	+	0.731217i	−0.996151	−	0.0876502i	$-0.972064\pi$
$269$	−6.92408	+	11.9929i	−0.422168	+	0.731217i	0.573983	+	0.818867i	$0.305398\pi$
$270$		0			0
$271$	−21.2796			−1.29264			−0.646321	−	0.763065i	$-0.723693\pi$
$271$	−21.2796			−1.29264			−0.646321	+	0.763065i	$0.723693\pi$
$272$	0.174866	−	0.100959i	0.0106028	−	0.00612154i
$273$	−0.477120	+	0.275465i	−0.0288766	+	0.0166719i
$274$	−2.00069	+	3.46529i	−0.120866	+	0.209346i
$275$		0			0
$276$	0.271224	+	0.469774i	0.0163258	+	0.0282771i
$277$		−	29.0763i		−	1.74702i	−0.486802	−	0.873512i	$-0.661837\pi$
$277$		−	29.0763i		−	1.74702i	0.486802	−	0.873512i	$-0.338163\pi$
$278$		−	19.1354i		−	1.14766i
$279$	−15.6711	+	5.50276i	−0.938206	+	0.329442i
$280$		0			0
$281$	4.36938			0.260656			0.130328	−	0.991471i	$-0.458397\pi$
$281$	4.36938			0.260656			0.130328	+	0.991471i	$0.458397\pi$
$282$	−0.100015	+	0.0577437i	−0.00595581	+	0.00343859i
$283$			16.9233i			1.00599i	0.864290	+	0.502994i	$0.167768\pi$
$283$			16.9233i			1.00599i	−0.864290	+	0.502994i	$0.832232\pi$
$284$	3.58570	−	6.21061i	0.212772	−	0.368532i
$285$		0			0
$286$	0.310597	+	0.537970i	0.0183660	+	0.0318108i
$287$			25.5938i			1.51075i
$288$	14.6492	+	8.45774i	0.863215	+	0.498377i
$289$	11.9023	−	20.6154i	0.700134	−	1.21267i
$290$		0			0
$291$	0.894611	+	1.54951i	0.0524430	+	0.0908340i
$292$	1.24527	+	0.718958i	0.0728740	+	0.0420738i
$293$	12.6939	−	7.32883i	0.741585	−	0.428155i	−0.0810601	−	0.996709i	$-0.525831\pi$
$293$	12.6939	−	7.32883i	0.741585	−	0.428155i	0.822645	+	0.568555i	$0.192497\pi$
$294$	−0.347445			−0.0202634
$295$		0			0
$296$	0.207263	+	0.358989i	0.0120469	+	0.0208658i
$297$	0.360255	+	0.207993i	0.0209041	+	0.0120690i
$298$	16.4276	−	9.48447i	0.951625	−	0.549421i
$299$	2.24066	−	3.88094i	0.129581	−	0.224440i
$300$		0			0
$301$	13.7648	−	23.8413i	0.793388	−	1.37419i
$302$		−	7.80046i		−	0.448866i
$303$	−2.00907	+	1.15994i	−0.115418	+	0.0666367i
$304$	−0.0677509	−	0.117348i	−0.00388578	−	0.00673037i
$305$		0			0
$306$	16.5781			0.947705
$307$	−23.0284	+	13.2954i	−1.31430	+	0.758810i	−0.982805	−	0.184648i	$-0.940886\pi$
$307$	−23.0284	+	13.2954i	−1.31430	+	0.758810i	−0.331493	+	0.943458i	$0.607552\pi$
$308$		−	2.10974i		−	0.120213i
$309$	1.04989			0.0597262
$310$		0			0
$311$	−12.9169			−0.732453			−0.366226	−	0.930526i	$-0.619350\pi$
$311$	−12.9169			−0.732453			−0.366226	+	0.930526i	$0.619350\pi$
$312$			0.489802i			0.0277296i
$313$	22.7789	−	13.1514i	1.28754	−	0.743361i	0.309324	−	0.950957i	$-0.399897\pi$
$313$	22.7789	−	13.1514i	1.28754	−	0.743361i	0.978215	+	0.207596i	$0.0665639\pi$
$314$	6.37041			0.359503
$315$		0			0
$316$	6.05094	+	10.4805i	0.340392	+	0.589576i
$317$	16.1922	−	9.34856i	0.909444	−	0.525068i	0.0291916	−	0.999574i	$-0.490707\pi$
$317$	16.1922	−	9.34856i	0.909444	−	0.525068i	0.880252	+	0.474506i	$0.157373\pi$
$318$			1.18912i			0.0666828i
$319$	−0.362633	+	0.628098i	−0.0203035	+	0.0351667i
$320$		0			0
$321$	−0.951629	+	1.64827i	−0.0531148	+	0.0919975i
$322$	8.02504	−	4.63326i	0.447218	−	0.258201i
$323$	−23.7142	−	13.6914i	−1.31949	−	0.761811i
$324$	−5.49968	−	9.52572i	−0.305538	−	0.529207i
$325$		0			0
$326$	2.82640			0.156540
$327$	−0.0186609	+	0.0107739i	−0.00103195	+	0.000595797i
$328$	19.7056	+	11.3770i	1.08806	+	0.628191i
$329$	−1.62014	−	2.80617i	−0.0893214	−	0.154709i
$330$		0			0
$331$	11.5085	−	19.9332i	0.632562	−	1.09563i	−0.354464	−	0.935069i	$-0.615337\pi$
$331$	11.5085	−	19.9332i	0.632562	−	1.09563i	0.987026	−	0.160560i	$-0.0513299\pi$
$332$	−11.1537	−	6.43960i	−0.612140	−	0.353419i
$333$		−	0.438271i		−	0.0240171i
$334$	−0.665146	−	1.15207i	−0.0363952	−	0.0630383i
$335$		0			0
$336$	0.00652130	−	0.0112952i	0.000355766	−	0.000616205i
$337$		−	35.6562i		−	1.94232i	−0.238436	−	0.971158i	$-0.576635\pi$
$337$		−	35.6562i		−	1.94232i	0.238436	−	0.971158i	$-0.423365\pi$
$338$	−8.45136	+	4.87939i	−0.459693	+	0.265404i
$339$	0.771936			0.0419258
$340$		0			0
$341$	2.80928	−	0.986450i	0.152131	−	0.0534192i
$342$		−	11.1251i		−	0.601576i
$343$			12.4668i			0.673142i
$344$	−12.2375	−	21.1960i	−0.659802	−	1.14281i
$345$		0			0
$346$	1.24135	−	2.15008i	0.0667353	−	0.115589i
$347$	14.7071	−	8.49114i	0.789518	−	0.455828i	−0.0502751	−	0.998735i	$-0.516010\pi$
$347$	14.7071	−	8.49114i	0.789518	−	0.455828i	0.839793	+	0.542907i	$0.182676\pi$
$348$	−0.189833	+	0.109600i	−0.0101761	+	0.00587519i
$349$	−17.4728			−0.935298			−0.467649	−	0.883914i	$-0.654899\pi$
$349$	−17.4728			−0.935298			−0.467649	+	0.883914i	$0.654899\pi$
$350$		0			0
$351$	0.519327	−	0.899501i	0.0277196	−	0.0480118i
$352$	−2.62609	−	1.51617i	−0.139971	−	0.0808123i
$353$	10.3880	−	5.99754i	0.552899	−	0.319217i	−0.197391	−	0.980325i	$-0.563247\pi$
$353$	10.3880	−	5.99754i	0.552899	−	0.319217i	0.750291	+	0.661108i	$0.229914\pi$
$354$	0.00163319	−	0.00282876i	8.68029e−5	−	0.000150347i
$355$		0			0
$356$	−15.8523			−0.840168
$357$		−	2.63571i		−	0.139497i
$358$	2.95231	−	1.70452i	0.156035	−	0.0900866i
$359$	12.5819	−	21.7924i	0.664046	−	1.15016i	−0.315497	−	0.948926i	$-0.602171\pi$
$359$	12.5819	−	21.7924i	0.664046	−	1.15016i	0.979543	−	0.201234i	$-0.0644953\pi$
$360$		0			0
$361$	0.312064	−	0.540511i	0.0164244	−	0.0284480i
$362$	−13.7169	−	7.91946i	−0.720944	−	0.416237i
$363$	1.20635	+	0.696489i	0.0633172	+	0.0365562i
$364$	−5.26769			−0.276102
$365$		0			0
$366$	−0.708504	−	1.22717i	−0.0370341	−	0.0641450i
$367$	10.3321	+	5.96524i	0.539331	+	0.311383i	0.744808	−	0.667279i	$-0.232541\pi$
$367$	10.3321	+	5.96524i	0.539331	+	0.311383i	−0.205477	+	0.978662i	$0.565875\pi$
$368$			0.106090i			0.00553031i
$369$	−12.0287	−	20.8344i	−0.626191	−	1.08459i
$370$		0			0
$371$	−33.3638			−1.73216
$372$	0.884379	+	0.166335i	0.0458529	+	0.00862405i
$373$		−	9.20712i		−	0.476727i	−0.971176	−	0.238363i	$-0.923389\pi$
$373$		−	9.20712i		−	0.476727i	0.971176	−	0.238363i	$-0.0766109\pi$
$374$	−2.97186			−0.153671
$375$		0			0
$376$	−2.88076			−0.148564
$377$	1.56826	+	0.905438i	0.0807697	+	0.0466324i
$378$	1.86000	−	1.07387i	0.0956679	−	0.0552339i
$379$	2.28639	+	3.96014i	0.117444	+	0.203419i	0.918754	−	0.394830i	$-0.129197\pi$
$379$	2.28639	+	3.96014i	0.117444	+	0.203419i	−0.801310	+	0.598249i	$0.795863\pi$
$380$		0			0
$381$	−1.20631	+	2.08938i	−0.0618010	+	0.107042i
$382$	12.9374	+	7.46944i	0.661937	+	0.382170i
$383$	−10.6753	−	6.16336i	−0.545480	−	0.314933i	0.201817	−	0.979423i	$-0.435315\pi$
$383$	−10.6753	−	6.16336i	−0.545480	−	0.314933i	−0.747297	+	0.664490i	$0.768649\pi$
$384$	−0.461816	−	0.799888i	−0.0235669	−	0.0408191i
$385$		0			0
$386$	7.38717	+	12.7950i	0.375997	+	0.651246i
$387$			25.8770i			1.31540i
$388$			17.1075i			0.868504i
$389$	−3.24518	−	5.62082i	−0.164537	−	0.284987i	0.771954	−	0.635679i	$-0.219280\pi$
$389$	−3.24518	−	5.62082i	−0.164537	−	0.284987i	−0.936491	+	0.350692i	$0.885946\pi$
$390$		0			0
$391$	10.7196	+	18.5668i	0.542111	+	0.938964i
$392$	−7.50566	−	4.33339i	−0.379093	−	0.218869i
$393$	1.84765	+	1.06674i	0.0932016	+	0.0538100i
$394$	3.12046	−	5.40480i	0.157207	−	0.272290i
$395$		0			0
$396$	0.991548	+	1.71741i	0.0498272	+	0.0863032i
$397$	−22.6389	+	13.0706i	−1.13621	+	0.655994i	−0.945490	−	0.325650i	$-0.894417\pi$
$397$	−22.6389	+	13.0706i	−1.13621	+	0.655994i	−0.190724	+	0.981644i	$0.561084\pi$
$398$	9.40159	+	5.42801i	0.471259	+	0.272081i
$399$	−1.76875			−0.0885484
$400$		0			0
$401$	−4.58685			−0.229056			−0.114528	−	0.993420i	$-0.536536\pi$
$401$	−4.58685			−0.229056			−0.114528	+	0.993420i	$0.536536\pi$
$402$			0.613711i			0.0306091i
$403$	−2.46301	−	7.01434i	−0.122691	−	0.349409i
$404$	−22.1814			−1.10356
$405$		0			0
$406$	1.87227	+	3.24287i	0.0929193	+	0.160941i
$407$			0.0785664i			0.00389439i
$408$	−2.02933	−	1.17163i	−0.100467	−	0.0580045i
$409$	−12.0171	−	20.8143i	−0.594209	−	1.02920i	−0.993658	−	0.112445i	$-0.964132\pi$
$409$	−12.0171	−	20.8143i	−0.594209	−	1.02920i	0.399449	−	0.916755i	$-0.369201\pi$
$410$		0			0
$411$	−0.597983			−0.0294963
$412$	8.69357	+	5.01924i	0.428302	+	0.247280i
$413$	0.0793679	+	0.0458231i	0.00390544	+	0.00225481i
$414$	−4.35514	+	7.54332i	−0.214043	+	0.370734i
$415$		0			0
$416$	−3.78565	+	6.55694i	−0.185607	+	0.321480i
$417$	2.47655	−	1.42984i	0.121277	−	0.0700194i
$418$			1.99433i			0.0975460i
$419$	16.9894			0.829987			0.414993	−	0.909824i	$-0.363784\pi$
$419$	16.9894			0.829987			0.414993	+	0.909824i	$0.363784\pi$
$420$		0			0
$421$	3.87172	−	6.70602i	0.188696	−	0.326831i	−0.756120	−	0.654433i	$-0.772907\pi$
$421$	3.87172	−	6.70602i	0.188696	−	0.326831i	0.944816	+	0.327602i	$0.106241\pi$
$422$	−1.41792	+	0.818639i	−0.0690235	+	0.0398507i
$423$	2.63772	+	1.52289i	0.128251	+	0.0740455i
$424$	−14.8310	+	25.6880i	−0.720256	+	1.24752i
$425$		0			0
$426$	−0.652518			−0.0316146
$427$	34.4312	−	19.8788i	1.66624	−	0.962005i
$428$	−15.7598	+	9.09895i	−0.761781	+	0.439814i
$429$	−0.0464170	+	0.0803965i	−0.00224103	+	0.00388158i
$430$		0			0
$431$	−16.7947	−	29.0893i	−0.808972	−	1.40118i	−0.913577	−	0.406667i	$-0.866691\pi$
$431$	−16.7947	−	29.0893i	−0.808972	−	1.40118i	0.104604	−	0.994514i	$-0.466642\pi$
$432$			0.0245889i			0.00118303i
$433$			0.313472i			0.0150645i	0.999972	+	0.00753225i	$0.00239761\pi$
$433$			0.313472i			0.0150645i	−0.999972	+	0.00753225i	$0.997602\pi$
$434$	2.84145	−	15.1076i	0.136394	−	0.725189i
$435$		0			0
$436$	−0.206028			−0.00986695
$437$	12.4597	−	7.19360i	0.596028	−	0.344117i
$438$		−	0.130834i		−	0.00625151i
$439$	−17.1980	+	29.7879i	−0.820817	+	1.42170i	0.0842571	+	0.996444i	$0.473148\pi$
$439$	−17.1980	+	29.7879i	−0.820817	+	1.42170i	−0.905074	+	0.425253i	$0.860185\pi$
$440$		0			0
$441$	4.58163	+	7.93561i	0.218173	+	0.377886i
$442$			7.42028i			0.352946i
$443$	−23.9114	−	13.8053i	−1.13607	−	0.655908i	−0.190612	−	0.981665i	$-0.561047\pi$
$443$	−23.9114	−	13.8053i	−1.13607	−	0.655908i	−0.945453	+	0.325758i	$0.894381\pi$
$444$	−0.0118728	+	0.0205642i	−0.000563456	+	0.000975934i
$445$		0			0
$446$	5.74691	+	9.95395i	0.272124	+	0.471333i
$447$	2.45501	+	1.41740i	0.116118	+	0.0670407i
$448$	−13.3847	+	7.72769i	−0.632370	+	0.365099i
$449$	8.50075			0.401175			0.200588	−	0.979676i	$-0.435715\pi$
$449$	8.50075			0.401175			0.200588	+	0.979676i	$0.435715\pi$
$450$		0			0
$451$	2.15633	+	3.73487i	0.101537	+	0.175868i
$452$	6.39198	+	3.69041i	0.300654	+	0.173582i
$453$	1.00956	−	0.582867i	0.0474330	−	0.0273855i
$454$	−0.540750	+	0.936607i	−0.0253787	+	0.0439572i
$455$		0			0
$456$	−0.786251	+	1.36183i	−0.0368196	+	0.0637734i
$457$		−	22.9281i		−	1.07253i	−0.844049	−	0.536266i	$-0.819835\pi$
$457$		−	22.9281i		−	1.07253i	0.844049	−	0.536266i	$-0.180165\pi$
$458$	−11.4688	+	6.62151i	−0.535901	+	0.309403i
$459$	2.48452	+	4.30331i	0.115967	+	0.200861i
$460$		0			0
$461$	10.1595			0.473177			0.236588	−	0.971610i	$-0.423971\pi$
$461$	10.1595			0.473177			0.236588	+	0.971610i	$0.423971\pi$
$462$	−0.166245	+	0.0959814i	−0.00773440	+	0.00446546i
$463$		−	25.2596i		−	1.17391i	−0.809619	−	0.586956i	$-0.800326\pi$
$463$		−	25.2596i		−	1.17391i	0.809619	−	0.586956i	$-0.199674\pi$
$464$	−0.0428703			−0.00199020
$465$		0			0
$466$	−1.39762			−0.0647436
$467$			32.0270i			1.48203i	0.671486	+	0.741017i	$0.265656\pi$
$467$			32.0270i			1.48203i	−0.671486	+	0.741017i	$0.734344\pi$
$468$	4.28811	−	2.47574i	0.198218	−	0.114441i
$469$	−17.2192			−0.795108
$470$		0			0
$471$	0.476010	+	0.824474i	0.0219334	+	0.0379898i
$472$	0.0705617	−	0.0407388i	0.00324786	−	0.00187516i
$473$		−	4.63883i		−	0.213294i
$474$	0.550568	−	0.953612i	0.0252884	−	0.0438009i
$475$		0			0
$476$	12.6006	−	21.8249i	0.577547	−	1.00034i
$477$	27.1595	−	15.6805i	1.24355	−	0.717963i
$478$	15.6212	+	9.01892i	0.714498	+	0.412516i
$479$	−6.47633	−	11.2173i	−0.295911	−	0.512533i	0.679285	−	0.733874i	$-0.262290\pi$
$479$	−6.47633	−	11.2173i	−0.295911	−	0.512533i	−0.975196	+	0.221341i	$0.928957\pi$
$480$		0			0
$481$	0.196168			0.00894450
$482$	11.2109	−	6.47259i	0.510640	−	0.294818i
$483$	1.19930	+	0.692414i	0.0545699	+	0.0315059i
$484$	6.65944	+	11.5345i	0.302702	+	0.524295i
$485$		0			0
$486$	−1.51554	+	2.62499i	−0.0687462	+	0.119072i
$487$	−23.4187	−	13.5208i	−1.06120	−	0.612686i	−0.135438	−	0.990786i	$-0.543244\pi$
$487$	−23.4187	−	13.5208i	−1.06120	−	0.612686i	−0.925765	+	0.378100i	$0.876577\pi$
$488$		−	35.3464i		−	1.60006i
$489$	0.211195	+	0.365800i	0.00955056	+	0.0165421i
$490$		0			0
$491$	5.64719	−	9.78121i	0.254854	−	0.441420i	−0.710002	−	0.704200i	$-0.751306\pi$
$491$	5.64719	−	9.78121i	0.254854	−	0.441420i	0.964856	+	0.262780i	$0.0846393\pi$
$492$			1.30343i			0.0587633i
$493$	−7.50274	+	4.33171i	−0.337907	+	0.195090i
$494$	4.97954			0.224040
$495$		0			0
$496$	0.133525	+	0.114654i	0.00599544	+	0.00514812i
$497$		−	18.3080i		−	0.821226i
$498$			1.17187i			0.0525125i
$499$	8.38428	+	14.5220i	0.375332	+	0.650094i	0.990377	−	0.138398i	$-0.0441954\pi$
$499$	8.38428	+	14.5220i	0.375332	+	0.650094i	−0.615045	+	0.788492i	$0.710862\pi$
$500$		0			0
$501$	0.0994023	−	0.172170i	0.00444097	−	0.00769198i
$502$	−2.81409	+	1.62472i	−0.125599	+	0.0725146i
$503$	34.3767	−	19.8474i	1.53278	−	0.884953i	0.533551	−	0.845768i	$-0.320857\pi$
$503$	34.3767	−	19.8474i	1.53278	−	0.884953i	0.999232	−	0.0391850i	$-0.0124762\pi$
$504$	26.7113			1.18982
$505$		0			0
$506$	0.780722	−	1.35225i	0.0347073	−	0.0601148i
$507$	−1.26301	−	0.729197i	−0.0560921	−	0.0323848i
$508$	−19.9775	+	11.5340i	−0.886360	+	0.511740i
$509$	8.56890	−	14.8418i	0.379810	−	0.657850i	−0.611225	−	0.791457i	$-0.709323\pi$
$509$	8.56890	−	14.8418i	0.379810	−	0.657850i	0.991034	+	0.133607i	$0.0426561\pi$
$510$		0			0
$511$	3.67088			0.162390
$512$		−	0.357613i		−	0.0158044i
$513$	2.88783	−	1.66729i	0.127501	−	0.0736127i
$514$	−2.05724	+	3.56325i	−0.0907411	+	0.157168i
$515$		0			0
$516$	0.701009	−	1.21418i	0.0308602	−	0.0534514i
$517$	−0.472850	−	0.273000i	−0.0207959	−	0.0120065i
$518$	0.351293	+	0.202819i	0.0154349	+	0.00891137i
$519$	0.371025			0.0162862
$520$		0			0
$521$	4.11183	+	7.12191i	0.180143	+	0.312016i	0.941929	−	0.335812i	$-0.109011\pi$
$521$	4.11183	+	7.12191i	0.180143	+	0.312016i	−0.761786	+	0.647828i	$0.775677\pi$
$522$	−3.04821	−	1.75989i	−0.133417	−	0.0770281i
$523$			19.7062i			0.861690i	0.902426	+	0.430845i	$0.141784\pi$
$523$			19.7062i			0.861690i	−0.902426	+	0.430845i	$0.858216\pi$
$524$	10.1996	+	17.6662i	0.445571	+	0.771752i
$525$		0			0
$526$	6.59798			0.287686
$527$	34.9532	+	6.57402i	1.52258	+	0.286369i
$528$		−	0.00219773i		−	9.56439e-5i
$529$	11.7357			0.510247
$530$		0			0
$531$	−0.0861449			−0.00373837
$532$	−14.6461	−	8.45592i	−0.634988	−	0.366610i
$533$	9.32539	−	5.38401i	0.403927	−	0.233208i
$534$	0.721190	+	1.24914i	0.0312090	+	0.0540555i
$535$		0			0
$536$	−7.65432	+	13.2577i	−0.330616	+	0.572644i
$537$	0.441206	+	0.254731i	0.0190395	+	0.0109924i
$538$	10.4336	+	6.02385i	0.449825	+	0.259706i
$539$	−0.821323	−	1.42257i	−0.0353769	−	0.0612746i
$540$		0			0
$541$	−8.19068	−	14.1867i	−0.352145	−	0.609933i	0.634480	−	0.772939i	$-0.281214\pi$
$541$	−8.19068	−	14.1867i	−0.352145	−	0.609933i	−0.986625	+	0.163006i	$0.947881\pi$
$542$			18.5129i			0.795198i
$543$		−	2.36703i		−	0.101579i
$544$	−18.1110	−	31.3691i	−0.776501	−	1.34494i
$545$		0			0
$546$	0.239651	+	0.415087i	0.0102561	+	0.0177641i
$547$	4.08603	+	2.35907i	0.174706	+	0.100867i	0.584803	−	0.811175i	$-0.301172\pi$
$547$	4.08603	+	2.35907i	0.174706	+	0.100867i	−0.410097	+	0.912042i	$0.634505\pi$
$548$	−4.95157	−	2.85879i	−0.211521	−	0.122121i
$549$	−18.6856	+	32.3644i	−0.797481	+	1.38128i
$550$		0			0
$551$	2.90689	+	5.03489i	0.123838	+	0.214493i
$552$	1.06623	−	0.615587i	0.0453817	−	0.0262011i
$553$	26.7559	+	15.4476i	1.13778	+	0.656897i
$554$	−25.2960			−1.07472
$555$		0			0
$556$	27.3426			1.15959
$557$		−	32.9280i		−	1.39520i	−0.716486	−	0.697602i	$-0.754250\pi$
$557$		−	32.9280i		−	1.39520i	0.716486	−	0.697602i	$-0.245750\pi$
$558$	4.78732	+	13.6337i	0.202663	+	0.577159i
$559$	−11.5825			−0.489886
$560$		0			0
$561$	−0.222064	−	0.384626i	−0.00937553	−	0.0162389i
$562$		−	3.80130i		−	0.160348i
$563$	31.9583	+	18.4511i	1.34688	+	0.777622i	0.987806	−	0.155687i	$-0.0497590\pi$
$563$	31.9583	+	18.4511i	1.34688	+	0.777622i	0.359075	+	0.933309i	$0.383092\pi$
$564$	−0.0825102	−	0.142912i	−0.00347431	−	0.00601767i
$565$		0			0
$566$	14.7231			0.618857
$567$	−24.3184	−	14.0402i	−1.02128	−	0.589635i
$568$	−14.0960	−	8.13832i	−0.591455	−	0.341476i
$569$	18.3707	−	31.8190i	0.770141	−	1.33392i	−0.167345	−	0.985898i	$-0.553519\pi$
$569$	18.3707	−	31.8190i	0.770141	−	1.33392i	0.937485	−	0.348024i	$-0.113147\pi$
$570$		0			0
$571$	−11.2222	+	19.4375i	−0.469636	+	0.813434i	−0.999397	−	0.0347129i	$-0.988948\pi$
$571$	−11.2222	+	19.4375i	−0.469636	+	0.813434i	0.529761	+	0.848147i	$0.322282\pi$
$572$	−0.768707	+	0.443813i	−0.0321412	+	0.0185568i
$573$			2.23253i			0.0932652i
$574$	22.2662			0.929374
$575$		0			0
$576$	7.26382	−	12.5813i	0.302659	−	0.524221i
$577$	1.28375	−	0.741171i	0.0534431	−	0.0308554i	−0.473040	−	0.881041i	$-0.656844\pi$
$577$	1.28375	−	0.741171i	0.0534431	−	0.0308554i	0.526483	+	0.850185i	$0.323510\pi$
$578$	−17.9351	−	10.3548i	−0.746000	−	0.430704i
$579$	−1.10397	+	1.91213i	−0.0458794	+	0.0794655i
$580$		0			0
$581$	−32.8796			−1.36407
$582$	1.34805	−	0.778298i	0.0558786	−	0.0322615i
$583$	−4.86873	+	2.81097i	−0.201642	+	0.116418i
$584$	1.63179	−	2.82634i	0.0675240	−	0.116955i
$585$		0			0
$586$	−6.37597	−	11.0435i	−0.263389	−	0.456203i
$587$			24.4284i			1.00827i	0.863625	+	0.504134i	$0.168188\pi$
$587$			24.4284i			1.00827i	−0.863625	+	0.504134i	$0.831812\pi$
$588$		−	0.496465i		−	0.0204739i
$589$	4.41164	−	23.4561i	0.181779	−	0.966492i
$590$		0			0
$591$	0.932671			0.0383650
$592$	−0.00402186	+	0.00232202i	−0.000165297	+	9.54345e-5i
$593$			10.3694i			0.425820i	0.977072	+	0.212910i	$0.0682940\pi$
$593$			10.3694i			0.425820i	−0.977072	+	0.212910i	$0.931706\pi$
$594$	0.180951	−	0.313416i	0.00742451	−	0.0128596i
$595$		0			0
$596$	13.5524	+	23.4734i	0.555128	+	0.961509i
$597$			1.62237i			0.0663992i
$598$	−3.37636	−	1.94934i	−0.138070	−	0.0797145i
$599$	3.96208	−	6.86253i	0.161886	−	0.280395i	−0.773659	−	0.633602i	$-0.781576\pi$
$599$	3.96208	−	6.86253i	0.161886	−	0.280395i	0.935545	+	0.353207i	$0.114909\pi$
$600$		0			0
$601$	16.5481	+	28.6622i	0.675011	+	1.16915i	0.976466	+	0.215673i	$0.0691946\pi$
$601$	16.5481	+	28.6622i	0.675011	+	1.16915i	−0.301454	+	0.953481i	$0.597472\pi$
$602$	−20.7416	−	11.9752i	−0.845364	−	0.488071i
$603$	14.0171	−	8.09279i	0.570821	−	0.329564i
$604$	11.1461			0.453528
$605$		0			0
$606$	1.00913	+	1.74786i	0.0409931	+	0.0710021i
$607$	−19.3615	−	11.1784i	−0.785860	−	0.453717i	0.0526429	−	0.998613i	$-0.483236\pi$
$607$	−19.3615	−	11.1784i	−0.785860	−	0.453717i	−0.838503	+	0.544897i	$0.816569\pi$
$608$	−21.0509	+	12.1538i	−0.853729	+	0.492901i
$609$	−0.279800	+	0.484629i	−0.0113381	+	0.0196381i
$610$		0			0
$611$	−0.681640	+	1.18063i	−0.0275762	+	0.0477634i
$612$			23.6884i			0.957548i
$613$	26.0567	−	15.0439i	1.05242	−	0.607615i	0.129095	−	0.991632i	$-0.458793\pi$
$613$	26.0567	−	15.0439i	1.05242	−	0.607615i	0.923326	+	0.384017i	$0.125460\pi$
$614$	11.5668	+	20.0343i	0.466799	+	0.808520i
$615$		0			0
$616$	−4.78839			−0.192930
$617$	−33.6776	+	19.4438i	−1.35581	+	0.782777i	−0.989056	−	0.147541i	$-0.952864\pi$
$617$	−33.6776	+	19.4438i	−1.35581	+	0.782777i	−0.366753	+	0.930318i	$0.619531\pi$
$618$		−	0.913390i		−	0.0367419i
$619$	4.63033			0.186109			0.0930543	−	0.995661i	$-0.470337\pi$
$619$	4.63033			0.186109			0.0930543	+	0.995661i	$0.470337\pi$
$620$		0			0
$621$	−2.61078			−0.104767
$622$			11.2376i			0.450585i
$623$	−35.0477	+	20.2348i	−1.40415	+	0.810689i
$624$	−0.00548739			−0.000219671
$625$		0			0
$626$	−11.4415	−	19.8173i	−0.457295	−	0.792059i
$627$	−0.258112	+	0.149021i	−0.0103080	+	0.00595132i
$628$			9.10269i			0.363237i
$629$	−0.469245	+	0.812756i	−0.0187100	+	0.0324067i
$630$		0			0
$631$	24.9423	−	43.2013i	0.992936	−	1.71982i	0.393711	−	0.919234i	$-0.371191\pi$
$631$	24.9423	−	43.2013i	0.992936	−	1.71982i	0.599224	−	0.800581i	$-0.295476\pi$
$632$	23.7872	−	13.7336i	0.946206	−	0.546292i
$633$	−0.211901	−	0.122341i	−0.00842229	−	0.00486261i
$634$	−8.13311	−	14.0870i	−0.323007	−	0.559465i
$635$		0			0
$636$	−1.69914			−0.0673754
$637$	−3.55195	+	2.05072i	−0.140733	+	0.0812524i
$638$	0.546436	+	0.315485i	0.0216336	+	0.0124902i
$639$	8.60452	+	14.9035i	0.340389	+	0.589572i
$640$		0			0
$641$	−23.5393	+	40.7712i	−0.929746	+	1.61037i	−0.146001	+	0.989284i	$0.546640\pi$
$641$	−23.5393	+	40.7712i	−0.929746	+	1.61037i	−0.783745	+	0.621083i	$0.786693\pi$
$642$	1.43397	+	0.827904i	0.0565943	+	0.0326748i
$643$		−	5.84458i		−	0.230488i	−0.993337	−	0.115244i	$-0.963235\pi$
$643$		−	5.84458i		−	0.230488i	0.993337	−	0.115244i	$-0.0367649\pi$
$644$	6.62048	+	11.4670i	0.260883	+	0.451863i
$645$		0			0
$646$	−11.9113	+	20.6310i	−0.468645	+	0.811717i
$647$		−	9.58090i		−	0.376664i	−0.982105	−	0.188332i	$-0.939692\pi$
$647$		−	9.58090i		−	0.376664i	0.982105	−	0.188332i	$-0.0603081\pi$
$648$	−21.6202	+	12.4824i	−0.849320	+	0.490355i
$649$	0.0154427			0.000606180
$650$		0			0
$651$	2.16759	−	0.761126i	0.0849544	−	0.0298309i
$652$			4.03865i			0.158166i
$653$		−	26.2744i		−	1.02820i	−0.857731	−	0.514099i	$-0.828126\pi$
$653$		−	26.2744i		−	1.02820i	0.857731	−	0.514099i	$-0.171874\pi$
$654$	0.00937313	+	0.0162347i	0.000366518	+	0.000634828i
$655$		0			0
$656$	−0.127460	+	0.220767i	−0.00497647	+	0.00861951i
$657$	−2.98825	+	1.72527i	−0.116583	+	0.0673090i
$658$	−2.44133	+	1.40950i	−0.0951729	+	0.0549481i
$659$	23.5445			0.917165			0.458583	−	0.888652i	$-0.348357\pi$
$659$	23.5445			0.917165			0.458583	+	0.888652i	$0.348357\pi$
$660$		0			0
$661$	−15.2692	+	26.4470i	−0.593903	+	1.02867i	0.399797	+	0.916604i	$0.369080\pi$
$661$	−15.2692	+	26.4470i	−0.593903	+	1.02867i	−0.993701	+	0.112067i	$0.964253\pi$
$662$	−17.3416	−	10.0122i	−0.674001	−	0.389135i
$663$	−0.960351	+	0.554459i	−0.0372969	+	0.0215334i
$664$	−14.6157	+	25.3152i	−0.567200	+	0.982419i
$665$		0			0
$666$	−0.381289			−0.0147747
$667$		−	4.55185i		−	0.176248i
$668$	1.64619	−	0.950429i	0.0636931	−	0.0367732i
$669$	−0.858843	+	1.48756i	−0.0332048	+	0.0575124i
$670$		0			0
$671$	3.34966	−	5.80178i	0.129312	−	0.223975i
$672$	−2.02624	−	1.16985i	−0.0781639	−	0.0451280i
$673$	6.00126	+	3.46483i	0.231331	+	0.133559i	0.611186	−	0.791487i	$-0.290693\pi$
$673$	6.00126	+	3.46483i	0.231331	+	0.133559i	−0.379855	+	0.925046i	$0.624026\pi$
$674$	−31.0204			−1.19486
$675$		0			0
$676$	−6.97218	−	12.0762i	−0.268161	−	0.464468i
$677$	29.4789	+	17.0196i	1.13297	+	0.654118i	0.944679	−	0.327996i	$-0.106373\pi$
$677$	29.4789	+	17.0196i	1.13297	+	0.654118i	0.188287	+	0.982114i	$0.439707\pi$
$678$		−	0.671573i		−	0.0257916i
$679$	21.8371	+	37.8229i	0.838030	+	1.45151i
$680$		0			0
$681$	−0.161624			−0.00619345
$682$	−0.858197	−	2.44403i	−0.0328621	−	0.0935868i
$683$		−	45.5911i		−	1.74449i	−0.489066	−	0.872247i	$-0.662662\pi$
$683$		−	45.5911i		−	1.74449i	0.489066	−	0.872247i	$-0.337338\pi$
$684$	15.8967			0.607824
$685$		0			0
$686$	10.8459			0.414099
$687$	−1.71394	−	0.989547i	−0.0653911	−	0.0377536i
$688$	0.237465	−	0.137100i	0.00905325	−	0.00522690i
$689$	7.01855	+	12.1565i	0.267385	+	0.463125i
$690$		0			0
$691$	−17.2635	+	29.9012i	−0.656733	+	1.13749i	0.324724	+	0.945809i	$0.394729\pi$
$691$	−17.2635	+	29.9012i	−0.656733	+	1.13749i	−0.981456	+	0.191686i	$0.938605\pi$
$692$	3.07225	+	1.77377i	0.116790	+	0.0674285i
$693$	4.38441	+	2.53134i	0.166550	+	0.0961578i
$694$	−7.38717	−	12.7950i	−0.280413	−	0.485690i
$695$		0			0
$696$	0.248755	+	0.430857i	0.00942904	+	0.0163316i
$697$			51.5154i			1.95128i
$698$			15.2011i			0.575370i
$699$	−0.104433	−	0.180884i	−0.00395003	−	0.00684165i
$700$		0			0
$701$	−7.50205	−	12.9939i	−0.283349	−	0.490774i	0.688859	−	0.724896i	$-0.258112\pi$
$701$	−7.50205	−	12.9939i	−0.283349	−	0.490774i	−0.972207	+	0.234121i	$0.924779\pi$
$702$	−0.782553	−	0.451807i	−0.0295355	−	0.0170524i
$703$	0.545419	+	0.314898i	0.0205709	+	0.0118766i
$704$	−1.30215	+	2.25538i	−0.0490764	+	0.0850029i
$705$		0			0
$706$	−5.21777	−	9.03744i	−0.196373	−	0.340129i
$707$	−49.0406	+	28.3136i	−1.84436	+	1.06484i
$708$	0.00404203	+	0.00233367i	0.000151909	+	8.77045e-5i
$709$	−0.373139			−0.0140135			−0.00700677	−	0.999975i	$-0.502230\pi$
$709$	−0.373139			−0.0140135			−0.00700677	+	0.999975i	$0.502230\pi$
$710$		0			0
$711$	−29.0406			−1.08911
$712$			35.9793i			1.34838i
$713$	−12.1737	+	14.1773i	−0.455907	+	0.530944i
$714$	−2.29303			−0.0858145
$715$		0			0
$716$	2.43559	+	4.21857i	0.0910224	+	0.157655i
$717$			2.69565i			0.100671i
$718$	−18.9591	−	10.9460i	−0.707548	−	0.408503i
$719$	15.2527	+	26.4185i	0.568831	+	0.985244i	0.996682	+	0.0813944i	$0.0259373\pi$
$719$	15.2527	+	26.4185i	0.568831	+	0.985244i	−0.427851	+	0.903849i	$0.640729\pi$
$720$		0			0
$721$	25.6274			0.954415
$722$	−0.470237	−	0.271491i	−0.0175004	−	0.0101039i
$723$	1.67540	+	0.967291i	0.0623087	+	0.0359740i
$724$	11.3161	−	19.6001i	0.420561	−	0.728433i
$725$		0			0
$726$	0.605935	−	1.04951i	0.0224884	−	0.0389510i
$727$	−13.3517	+	7.70859i	−0.495186	+	0.285896i	−0.726723	−	0.686930i	$-0.758958\pi$
$727$	−13.3517	+	7.70859i	−0.495186	+	0.285896i	0.231537	+	0.972826i	$0.425624\pi$
$728$			11.9559i			0.443114i
$729$	26.0915			0.966351
$730$		0			0
$731$	27.7059	−	47.9879i	1.02474	−	1.77490i
$732$	1.75350	−	1.01238i	0.0648112	−	0.0374188i
$733$	5.74164	+	3.31494i	0.212072	+	0.122440i	0.602274	−	0.798289i	$-0.294261\pi$
$733$	5.74164	+	3.31494i	0.212072	+	0.122440i	−0.390202	+	0.920729i	$0.627595\pi$
$734$	5.18967	−	8.98877i	0.191554	−	0.331782i
$735$		0			0
$736$	19.0313			0.701505
$737$	−2.51277	+	1.45075i	−0.0925592	+	0.0534391i
$738$	−18.1256	+	10.4648i	−0.667213	+	0.385216i
$739$	−10.5788	+	18.3231i	−0.389149	+	0.674026i	−0.992335	−	0.123574i	$-0.960564\pi$
$739$	−10.5788	+	18.3231i	−0.389149	+	0.674026i	0.603186	+	0.797600i	$0.293898\pi$
$740$		0			0
$741$	0.372082	+	0.644465i	0.0136688	+	0.0236750i
$742$			29.0260i			1.06558i
$743$			52.4521i			1.92428i	0.272556	+	0.962140i	$0.412131\pi$
$743$			52.4521i			1.92428i	−0.272556	+	0.962140i	$0.587869\pi$
$744$	0.377523	−	2.00724i	0.0138407	−	0.0735890i
$745$		0			0
$746$	−8.01006			−0.293269
$747$	26.7653	−	15.4530i	0.979291	−	0.565394i
$748$		−	4.24650i		−	0.155267i
$749$	−23.2289	+	40.2336i	−0.848765	+	1.47010i
$750$		0			0
$751$	−20.3114	−	35.1804i	−0.741174	−	1.28375i	−0.951961	−	0.306219i	$-0.900936\pi$
$751$	−20.3114	−	35.1804i	−0.741174	−	1.28375i	0.210787	−	0.977532i	$-0.432397\pi$
$752$		−	0.0322740i		−	0.00117691i
$753$	−0.420550	−	0.242805i	−0.0153257	−	0.00884829i
$754$	0.787718	−	1.36437i	0.0286870	−	0.0496873i
$755$		0			0
$756$	1.53445	+	2.65775i	0.0558076	+	0.0966616i
$757$	21.0345	+	12.1443i	0.764512	+	0.441391i	0.830913	−	0.556402i	$-0.187819\pi$
$757$	21.0345	+	12.1443i	0.764512	+	0.441391i	−0.0664017	+	0.997793i	$0.521152\pi$
$758$	3.44527	−	1.98912i	0.125138	−	0.0722483i
$759$	0.233349			0.00847002
$760$		0			0
$761$	−5.24537	−	9.08525i	−0.190145	−	0.329340i	0.755153	−	0.655548i	$-0.227562\pi$
$761$	−5.24537	−	9.08525i	−0.190145	−	0.329340i	−0.945298	+	0.326208i	$0.894229\pi$
$762$	1.81773	+	1.04947i	0.0658496	+	0.0380183i
$763$	−0.455506	+	0.262986i	−0.0164904	+	0.00952074i
$764$	−10.6731	+	18.4863i	−0.386139	+	0.668813i
$765$		0			0
$766$	−5.36203	+	9.28731i	−0.193738	+	0.335564i
$767$		−	0.0385581i		−	0.00139225i
$768$	−1.79257	+	1.03494i	−0.0646838	+	0.0373452i
$769$	−19.2155	−	33.2823i	−0.692930	−	1.20019i	−0.970874	−	0.239592i	$-0.922986\pi$
$769$	−19.2155	−	33.2823i	−0.692930	−	1.20019i	0.277944	−	0.960597i	$-0.410347\pi$
$770$		0			0
$771$	−0.614887			−0.0221446
$772$	−18.2827	+	10.5555i	−0.658010	+	0.379902i
$773$		−	29.3184i		−	1.05451i	−0.849707	−	0.527255i	$-0.823221\pi$
$773$		−	29.3184i		−	1.05451i	0.849707	−	0.527255i	$-0.176779\pi$
$774$	22.5126			0.809200
$775$		0			0
$776$	38.8283			1.39386
$777$			0.0606204i			0.00217474i
$778$	−4.89003	+	2.82326i	−0.175316	+	0.101219i
$779$	34.5706			1.23862
$780$		0			0
$781$	−1.54248	−	2.67166i	−0.0551944	−	0.0955996i
$782$	16.1529	−	9.32586i	0.577625	−	0.333492i
$783$		−	1.05500i		−	0.0377026i
$784$	0.0485482	−	0.0840880i	0.00173386	−	0.00300314i
$785$		0			0
$786$	0.928050	−	1.60743i	0.0331024	−	0.0573351i
$787$	−0.318951	+	0.184146i	−0.0113694	+	0.00656411i	−0.505674	−	0.862725i	$-0.668756\pi$
$787$	−0.318951	+	0.184146i	−0.0113694	+	0.00656411i	0.494305	+	0.869289i	$0.335423\pi$
$788$	7.72294	+	4.45884i	0.275118	+	0.158840i
$789$	0.493015	+	0.853928i	0.0175518	+	0.0304006i
$790$		0			0
$791$	18.8427			0.669968
$792$	3.89794	−	2.25048i	0.138507	−	0.0799673i
$793$	−14.4862	−	8.36359i	−0.514419	−	0.297000i
$794$	11.3712	+	19.6955i	0.403550	+	0.698968i
$795$		0			0
$796$	−7.75610	+	13.4340i	−0.274908	+	0.476154i
$797$	−27.3241	−	15.7756i	−0.967871	−	0.558800i	−0.0692843	−	0.997597i	$-0.522072\pi$
$797$	−27.3241	−	15.7756i	−0.967871	−	0.558800i	−0.898586	+	0.438796i	$0.855405\pi$
$798$			1.53879i			0.0544726i
$799$	−3.26104	−	5.64828i	−0.115367	−	0.199822i
$800$		0			0
$801$	19.0201	−	32.9438i	0.672044	−	1.16401i
$802$			3.99050i			0.140909i
$803$	0.535687	−	0.309279i	0.0189040	−	0.0109142i
$804$	−0.876934			−0.0309271
$805$		0			0
$806$	−6.10237	+	2.14279i	−0.214947	+	0.0754764i
$807$			1.80046i			0.0633791i
$808$			50.3442i			1.77110i
$809$	7.86117	+	13.6159i	0.276384	+	0.478711i	0.970483	−	0.241168i	$-0.0775306\pi$
$809$	7.86117	+	13.6159i	0.276384	+	0.478711i	−0.694099	+	0.719879i	$0.744197\pi$
$810$		0			0
$811$	10.4033	−	18.0191i	0.365311	−	0.632737i	−0.623515	−	0.781811i	$-0.714296\pi$
$811$	10.4033	−	18.0191i	0.365311	−	0.632737i	0.988826	+	0.149074i	$0.0476294\pi$
$812$	−4.63375	+	2.67530i	−0.162613	+	0.0938845i
$813$	−2.39599	+	1.38333i	−0.0840310	+	0.0485153i
$814$	0.0683517			0.00239572
$815$		0			0
$816$	0.0131261	−	0.0227351i	0.000459506	−	0.000795889i
$817$	−32.2034	−	18.5926i	−1.12665	−	0.650474i
$818$	−18.1081	+	10.4547i	−0.633136	+	0.365541i
$819$	6.32037	−	10.9472i	0.220852	−	0.382526i
$820$		0			0
$821$	−24.8522			−0.867346			−0.433673	−	0.901070i	$-0.642783\pi$
$821$	−24.8522			−0.867346			−0.433673	+	0.901070i	$0.642783\pi$
$822$			0.520237i			0.0181453i
$823$	21.0231	−	12.1377i	0.732819	−	0.423093i	−0.0866336	−	0.996240i	$-0.527611\pi$
$823$	21.0231	−	12.1377i	0.732819	−	0.423093i	0.819453	+	0.573147i	$0.194278\pi$
$824$	11.3920	−	19.7315i	0.396858	−	0.687378i
$825$		0			0
$826$	0.0398654	−	0.0690490i	0.00138710	−	0.00240252i
$827$	−42.9371	−	24.7898i	−1.49307	−	0.862025i	−0.493102	−	0.869971i	$-0.664137\pi$
$827$	−42.9371	−	24.7898i	−1.49307	−	0.862025i	−0.999968	+	0.00794639i	$0.997471\pi$
$828$	−10.7787	−	6.22307i	−0.374585	−	0.216267i
$829$	−33.8998			−1.17739			−0.588694	−	0.808356i	$-0.700358\pi$
$829$	−33.8998			−1.17739			−0.588694	+	0.808356i	$0.700358\pi$
$830$		0			0
$831$	−1.89017	−	3.27387i	−0.0655692	−	0.113569i
$832$	5.63134	+	3.25126i	0.195232	+	0.112717i
$833$		−	19.6217i		−	0.679852i
$834$	−1.24394	−	2.15456i	−0.0430741	−	0.0746065i
$835$		0			0
$836$	−2.84971			−0.0985592
$837$	−2.82154	+	3.28593i	−0.0975267	+	0.113578i
$838$		−	14.7805i		−	0.510585i
$839$	19.6413			0.678092			0.339046	−	0.940770i	$-0.389896\pi$
$839$	19.6413			0.678092			0.339046	+	0.940770i	$0.389896\pi$
$840$		0			0
$841$	−27.1606			−0.936573
$842$	−5.83414	−	3.36834i	−0.201058	−	0.116081i
$843$	0.491974	−	0.284041i	0.0169445	−	0.00978291i
$844$	−1.16976	−	2.02608i	−0.0402646	−	0.0697404i
$845$		0			0
$846$	1.32489	−	2.29478i	0.0455508	−	0.0788962i
$847$	29.4466	+	17.0010i	1.01180	+	0.584162i
$848$	−0.287790	−	0.166156i	−0.00988274	−	0.00570580i
$849$	1.10014	+	1.90550i	0.0377567	+	0.0653965i
$850$		0			0
$851$	−0.246546	−	0.427030i	−0.00845148	−	0.0146384i
$852$		−	0.932385i		−	0.0319430i
$853$		−	8.69028i		−	0.297550i	−0.988871	−	0.148775i	$-0.952467\pi$
$853$		−	8.69028i		−	0.297550i	0.988871	−	0.148775i	$-0.0475330\pi$
$854$	−17.2943	−	29.9546i	−0.591799	−	1.02503i
$855$		0			0
$856$	20.6515	+	35.7695i	0.705855	+	1.22258i
$857$	−30.8770	−	17.8268i	−1.05474	−	0.608953i	−0.130765	−	0.991413i	$-0.541743\pi$
$857$	−30.8770	−	17.8268i	−1.05474	−	0.608953i	−0.923972	+	0.382460i	$0.875077\pi$
$858$	0.0699438	+	0.0403821i	0.00238784	+	0.00137862i
$859$	−15.7067	+	27.2048i	−0.535905	+	0.928214i	0.463214	+	0.886246i	$0.346696\pi$
$859$	−15.7067	+	27.2048i	−0.535905	+	0.928214i	−0.999119	+	0.0419680i	$0.986637\pi$
$860$		0			0
$861$	1.66378	+	2.88175i	0.0567015	+	0.0982098i
$862$	−25.3072	+	14.6111i	−0.861968	+	0.497658i
$863$	1.87660	+	1.08345i	0.0638801	+	0.0368812i	0.531600	−	0.846996i	$-0.321591\pi$
$863$	1.87660	+	1.08345i	0.0638801	+	0.0368812i	−0.467720	+	0.883877i	$0.654924\pi$
$864$	4.41097			0.150064
$865$		0			0
$866$	0.272716			0.00926727
$867$		−	3.09494i		−	0.105110i
$868$	21.5873	+	4.06016i	0.732722	+	0.137811i
$869$	5.20594			0.176600
$870$		0			0
$871$	3.62230	+	6.27401i	0.122737	+	0.212587i
$872$			0.467613i			0.0158354i
$873$	−35.5525	−	20.5263i	−1.20327	−	0.694709i
$874$	−6.25833	−	10.8397i	−0.211691	−	0.366660i
$875$		0			0
$876$	0.186950			0.00631644
$877$	20.3231	+	11.7336i	0.686264	+	0.396215i	0.802211	−	0.597041i	$-0.203657\pi$
$877$	20.3231	+	11.7336i	0.686264	+	0.396215i	−0.115947	+	0.993255i	$0.536990\pi$
$878$	25.9150	+	14.9620i	0.874589	+	0.504944i
$879$	0.952853	−	1.65039i	0.0321389	−	0.0556662i
$880$		0			0
$881$	15.1116	−	26.1741i	0.509123	−	0.881827i	−0.490821	−	0.871260i	$-0.663303\pi$
$881$	15.1116	−	26.1741i	0.509123	−	0.881827i	0.999944	−	0.0105663i	$-0.00336343\pi$
$882$	6.90386	−	3.98595i	0.232465	−	0.134214i
$883$			26.1830i			0.881128i	0.897721	+	0.440564i	$0.145221\pi$
$883$			26.1830i			0.881128i	−0.897721	+	0.440564i	$0.854779\pi$
$884$	−10.6029			−0.356613
$885$		0			0
$886$	−12.0104	+	20.8026i	−0.403496	+	0.698876i
$887$	−13.3748	+	7.72193i	−0.449081	+	0.259277i	−0.707442	−	0.706771i	$-0.750151\pi$
$887$	−13.3748	+	7.72193i	−0.449081	+	0.259277i	0.258361	+	0.966048i	$0.416818\pi$
$888$	0.0466738	+	0.0269471i	0.00156627	+	0.000904286i
$889$	−29.4455	+	51.0010i	−0.987569	+	1.71052i
$890$		0			0
$891$	−4.73167			−0.158517
$892$	−14.2232	+	8.21178i	−0.476229	+	0.274951i
$893$	−3.79041	+	2.18839i	−0.126841	+	0.0732318i
$894$	1.23312	−	2.13582i	0.0412416	−	0.0714326i
$895$		0			0
$896$	−11.2727	−	19.5249i	−0.376596	−	0.652283i
$897$		−	0.582636i		−	0.0194536i
$898$		−	7.39553i		−	0.246792i
$899$	−5.72896	−	4.91931i	−0.191072	−	0.164068i
$900$		0			0
$901$	−67.1550			−2.23726
$902$	3.24928	−	1.87597i	0.108189	−	0.0624631i
$903$		−	3.57924i		−	0.119110i
$904$	8.37598	−	14.5076i	0.278581	−	0.482517i
$905$		0			0
$906$	−0.507086	−	0.878298i	−0.0168468	−	0.0291795i
$907$			31.5594i			1.04791i	0.851746	+	0.523956i	$0.175544\pi$
$907$			31.5594i			1.04791i	−0.851746	+	0.523956i	$0.824456\pi$
$908$	−1.33832	−	0.772680i	−0.0444137	−	0.0256423i
$909$	26.6140	−	46.0968i	0.882731	−	1.52894i
$910$		0			0
$911$	21.0506	+	36.4608i	0.697438	+	1.20800i	0.969352	+	0.245677i	$0.0790103\pi$
$911$	21.0506	+	36.4608i	0.697438	+	1.20800i	−0.271913	+	0.962322i	$0.587656\pi$
$912$	−0.0152569	−	0.00880859i	−0.000505207	−	0.000291681i
$913$	−4.79807	+	2.77017i	−0.158793	+	0.0916791i
$914$	−19.9471			−0.659792
$915$		0			0
$916$	−9.46149	−	16.3878i	−0.312617	−	0.541468i
$917$	45.1004	+	26.0387i	1.48935	+	0.859875i
$918$	3.74382	−	2.16149i	0.123564	−	0.0713399i
$919$	18.3891	−	31.8509i	0.606601	−	1.05066i	−0.385195	−	0.922835i	$-0.625866\pi$
$919$	18.3891	−	31.8509i	0.606601	−	1.05066i	0.991796	−	0.127829i	$-0.0408008\pi$
$920$		0			0
$921$	−1.72860	+	2.99402i	−0.0569592	+	0.0986562i
$922$		−	8.83865i		−	0.291085i
$923$	−6.67073	+	3.85135i	−0.219570	+	0.126769i
$924$	−0.137148	−	0.237547i	−0.00451184	−	0.00781474i
$925$		0			0
$926$	−21.9755			−0.722158
$927$	−20.8618	+	12.0445i	−0.685190	+	0.395595i
$928$			7.69046i			0.252452i
$929$	−7.61636			−0.249885			−0.124942	−	0.992164i	$-0.539875\pi$
$929$	−7.61636			−0.249885			−0.124942	+	0.992164i	$0.539875\pi$
$930$		0			0
$931$	−13.1676			−0.431550
$932$		−	1.99707i		−	0.0654161i
$933$	−1.45439	+	0.839694i	−0.0476147	+	0.0274903i
$934$	27.8631			0.911707
$935$		0			0
$936$	−5.61910	−	9.73256i	−0.183666	−	0.318119i
$937$	39.9504	−	23.0654i	1.30512	−	0.753513i	0.323845	−	0.946110i	$-0.395024\pi$
$937$	39.9504	−	23.0654i	1.30512	−	0.753513i	0.981278	+	0.192597i	$0.0616911\pi$
$938$			14.9804i			0.489129i
$939$	1.70987	−	2.96158i	0.0557995	−	0.0966476i
$940$		0			0
$941$	8.86885	−	15.3613i	0.289116	−	0.500764i	−0.684483	−	0.729029i	$-0.739972\pi$
$941$	8.86885	−	15.3613i	0.289116	−	0.500764i	0.973599	+	0.228265i	$0.0733053\pi$
$942$	0.717281	−	0.414122i	0.0233703	−	0.0134928i
$943$	−23.4404	−	13.5333i	−0.763326	−	0.440706i
$944$	0.000456408	0	0.000790522i	1.48548e−5	0	2.57293e-5i
$945$		0			0
$946$	−4.03572			−0.131213
$947$	22.9943	−	13.2758i	0.747216	−	0.431405i	−0.0774712	−	0.996995i	$-0.524685\pi$
$947$	22.9943	−	13.2758i	0.747216	−	0.431405i	0.824687	+	0.565589i	$0.191351\pi$
$948$	1.36262	+	0.786709i	0.0442558	+	0.0255511i
$949$	−0.772222	−	1.33753i	−0.0250674	−	0.0434180i
$950$		0			0
$951$	1.21545	−	2.10522i	0.0394136	−	0.0682663i
$952$	−49.5351	−	28.5991i	−1.60544	−	0.926902i
$953$			0.448226i			0.0145195i	0.999974	+	0.00725974i	$0.00231087\pi$
$953$			0.448226i			0.0145195i	−0.999974	+	0.00725974i	$0.997689\pi$
$954$	−13.6418	−	23.6284i	−0.441671	−	0.764997i
$955$		0			0
$956$	−12.8872	+	22.3212i	−0.416800	+	0.721920i
$957$			0.0942949i			0.00304812i
$958$	−9.75892	+	5.63431i	−0.315296	+	0.182036i
$959$	−14.5965			−0.471346
$960$		0			0
$961$	4.68716	+	30.6436i	0.151199	+	0.988503i
$962$		−	0.170664i		−	0.00550242i
$963$		−	43.6691i		−	1.40722i
$964$	9.24870	+	16.0192i	0.297881	+	0.515944i
$965$		0			0
$966$	0.602390	−	1.04337i	0.0193816	−	0.0335699i
$967$	29.4776	−	17.0189i	0.947937	−	0.547291i	0.0554973	−	0.998459i	$-0.482326\pi$
$967$	29.4776	−	17.0189i	0.947937	−	0.547291i	0.892439	+	0.451167i	$0.148992\pi$
$968$	26.1794	−	15.1147i	0.841437	−	0.485804i
$969$	−3.56016			−0.114369
$970$		0			0
$971$	8.99114	−	15.5731i	0.288539	−	0.499765i	−0.684922	−	0.728616i	$-0.740164\pi$
$971$	8.99114	−	15.5731i	0.288539	−	0.499765i	0.973461	+	0.228852i	$0.0734971\pi$
$972$	−3.75085	−	2.16556i	−0.120309	−	0.0694602i
$973$	60.4516	−	34.9018i	1.93799	−	1.11890i
$974$	−11.7629	+	20.3739i	−0.376908	+	0.652823i
$975$		0			0
$976$	0.395995			0.0126755
$977$			24.3612i			0.779383i	0.920946	+	0.389691i	$0.127418\pi$
$977$			24.3612i			0.779383i	−0.920946	+	0.389691i	$0.872582\pi$
$978$	0.318241	−	0.183736i	0.0101762	−	0.00587524i
$979$	−3.40964	+	5.90566i	−0.108972	+	0.188746i
$980$		0			0
$981$	0.247200	−	0.428163i	0.00789249	−	0.0136702i
$982$	−8.50951	−	4.91297i	−0.271549	−	0.156779i
$983$	28.3603	+	16.3738i	0.904553	+	0.522244i	0.878675	−	0.477421i	$-0.158428\pi$
$983$	28.3603	+	16.3738i	0.904553	+	0.522244i	0.0258783	+	0.999665i	$0.491762\pi$
$984$	2.95835			0.0943088
$985$		0			0
$986$	3.76853	+	6.52728i	0.120014	+	0.207871i
$987$	−0.364842	−	0.210642i	−0.0116131	−	0.00670481i
$988$			7.11529i			0.226367i
$989$	14.5569	+	25.2133i	0.462883	+	0.801737i
$990$		0			0
$991$	−10.9383			−0.347468			−0.173734	−	0.984793i	$-0.555583\pi$
$991$	−10.9383			−0.347468			−0.173734	+	0.984793i	$0.555583\pi$
$992$	20.5677	−	23.9529i	0.653025	−	0.760505i
$993$		−	2.99253i		−	0.0949650i
$994$	−15.9277			−0.505196
$995$		0			0
$996$	−1.67448			−0.0530580
$997$	−22.2694	−	12.8572i	−0.705279	−	0.407193i	0.104032	−	0.994574i	$-0.466826\pi$
$997$	−22.2694	−	12.8572i	−0.705279	−	0.407193i	−0.809310	+	0.587381i	$0.800159\pi$
$998$	12.6339	−	7.29420i	0.399920	−	0.230894i
$999$	−0.0571429	−	0.0989745i	−0.00180792	−	0.00313141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.o.e.149.3		16
5.2	odd	4		775.2.e.g.676.3		8
5.3	odd	4		155.2.e.c.56.2	yes	8
5.4	even	2	inner	775.2.o.e.149.6		16
31.5	even	3	inner	775.2.o.e.749.3		16
155.67	odd	12		775.2.e.g.501.3		8
155.68	even	12		4805.2.a.k.1.2		4
155.98	odd	12		155.2.e.c.36.2	✓	8
155.118	odd	12		4805.2.a.i.1.2		4
155.129	even	6	inner	775.2.o.e.749.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.e.c.36.2	✓	8	155.98	odd	12
155.2.e.c.56.2	yes	8	5.3	odd	4
775.2.e.g.501.3		8	155.67	odd	12
775.2.e.g.676.3		8	5.2	odd	4
775.2.o.e.149.3		16	1.1	even	1	trivial
775.2.o.e.149.6		16	5.4	even	2	inner
775.2.o.e.749.3		16	31.5	even	3	inner
775.2.o.e.749.6		16	155.129	even	6	inner
4805.2.a.i.1.2		4	155.118	odd	12
4805.2.a.k.1.2		4	155.68	even	12

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.869986i q^{2} +(0.112596 - 0.0650072i) q^{3} +1.24312 q^{4} +(-0.0565553 - 0.0979567i) q^{6} +(2.74842 - 1.58680i) q^{7} -2.82147i q^{8} +(-1.49155 + 2.58344i) q^{9} +O(q^{10})\)	\(q-0.869986i q^{2} +(0.112596 - 0.0650072i) q^{3} +1.24312 q^{4} +(-0.0565553 - 0.0979567i) q^{6} +(2.74842 - 1.58680i) q^{7} -2.82147i q^{8} +(-1.49155 + 2.58344i) q^{9} +(0.267382 - 0.463119i) q^{11} +(0.139971 - 0.0808121i) q^{12} +(-1.15634 - 0.667611i) q^{13} +(-1.38049 - 2.39108i) q^{14} +0.0316097 q^{16} +(5.53204 - 3.19392i) q^{17} +(2.24755 + 1.29763i) q^{18} +(-2.14335 - 3.71240i) q^{19} +(0.206307 - 0.357334i) q^{21} +(-0.402907 - 0.232618i) q^{22} +3.35624i q^{23} +(-0.183416 - 0.317686i) q^{24} +(-0.580812 + 1.00600i) q^{26} +0.777888i q^{27} +(3.41663 - 1.97259i) q^{28} -1.35624 q^{29} +(4.22417 + 3.62718i) q^{31} -5.67044i q^{32} -0.0695269i q^{33} +(-2.77867 - 4.81279i) q^{34} +(-1.85418 + 3.21154i) q^{36} +(-0.127235 + 0.0734590i) q^{37} +(-3.22973 + 1.86469i) q^{38} -0.173598 q^{39} +(-4.03230 + 6.98415i) q^{41} +(-0.310875 - 0.179484i) q^{42} +(7.51238 - 4.33728i) q^{43} +(0.332389 - 0.575714i) q^{44} +2.91988 q^{46} -1.02101i q^{47} +(0.00355912 - 0.00205486i) q^{48} +(1.53586 - 2.66019i) q^{49} +(0.415256 - 0.719244i) q^{51} +(-1.43747 - 0.829924i) q^{52} +(-9.10446 - 5.25646i) q^{53} +0.676752 q^{54} +(-4.47711 - 7.75458i) q^{56} +(-0.482665 - 0.278667i) q^{57} +1.17991i q^{58} +(0.0144388 + 0.0250088i) q^{59} +12.5276 q^{61} +(3.15559 - 3.67496i) q^{62} +9.46715i q^{63} -4.86999 q^{64} -0.0604874 q^{66} +(-4.69885 - 2.71288i) q^{67} +(6.87701 - 3.97045i) q^{68} +(0.218179 + 0.377898i) q^{69} +(2.88442 - 4.99597i) q^{71} +(7.28910 + 4.20836i) q^{72} +(1.00173 + 0.578347i) q^{73} +(0.0639083 + 0.110692i) q^{74} +(-2.66446 - 4.61498i) q^{76} -1.69712i q^{77} +0.151028i q^{78} +(4.86752 + 8.43079i) q^{79} +(-4.42408 - 7.66272i) q^{81} +(6.07611 + 3.50804i) q^{82} +(-8.97232 - 5.18017i) q^{83} +(0.256465 - 0.444210i) q^{84} +(-3.77337 - 6.53567i) q^{86} +(-0.152706 + 0.0881651i) q^{87} +(-1.30668 - 0.754410i) q^{88} -12.7519 q^{89} -4.23746 q^{91} +4.17222i q^{92} +(0.711416 + 0.133804i) q^{93} -0.888267 q^{94} +(-0.368620 - 0.638468i) q^{96} +13.7617i q^{97} +(-2.31433 - 1.33618i) q^{98} +(0.797625 + 1.38153i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} + 20 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q - 12 * q^4 + 20 * q^6 + 2 * q^9	\( 16 q - 12 q^{4} + 20 q^{6} + 2 q^{9} + 8 q^{11} + 16 q^{14} + 20 q^{16} + 10 q^{19} + 18 q^{21} - 4 q^{24} - 24 q^{26} + 52 q^{29} + 38 q^{31} - 48 q^{34} - 10 q^{36} + 44 q^{39} - 8 q^{41} + 14 q^{44} - 44 q^{46} + 74 q^{49} - 24 q^{51} - 48 q^{54} - 58 q^{56} - 12 q^{59} - 4 q^{61} - 68 q^{64} + 4 q^{66} + 12 q^{69} + 24 q^{71} - 36 q^{74} - 46 q^{76} + 4 q^{79} + 24 q^{81} - 82 q^{84} - 26 q^{86} - 108 q^{89} - 88 q^{91} + 96 q^{94} + 26 q^{96} + 14 q^{99}+O(q^{100}) \) 16 * q - 12 * q^4 + 20 * q^6 + 2 * q^9 + 8 * q^11 + 16 * q^14 + 20 * q^16 + 10 * q^19 + 18 * q^21 - 4 * q^24 - 24 * q^26 + 52 * q^29 + 38 * q^31 - 48 * q^34 - 10 * q^36 + 44 * q^39 - 8 * q^41 + 14 * q^44 - 44 * q^46 + 74 * q^49 - 24 * q^51 - 48 * q^54 - 58 * q^56 - 12 * q^59 - 4 * q^61 - 68 * q^64 + 4 * q^66 + 12 * q^69 + 24 * q^71 - 36 * q^74 - 46 * q^76 + 4 * q^79 + 24 * q^81 - 82 * q^84 - 26 * q^86 - 108 * q^89 - 88 * q^91 + 96 * q^94 + 26 * q^96 + 14 * q^99

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