LMFDB - Embedded newform 775.2.e.g.501.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(501,775)]

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([0, 4]))

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

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

chi := DirichletCharacter("775.501");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.e (of order $3$, degree $2$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} + 3x^{5} + 23x^{4} + x^{3} + 16x^{2} + 3x + 9 $ x^8 - x^7 + 6x^6 + 3x^5 + 23x^4 + x^3 + 16x^2 + 3*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.3
Root			$0.434993 + 0.753430i$ of defining polynomial
Character	$\chi$	$=$	775.501
Dual form			775.2.e.g.676.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.869986 q^{2} +(-0.0650072 + 0.112596i) q^{3} -1.24312 q^{4} +(-0.0565553 + 0.0979567i) q^{6} +(1.58680 - 2.74842i) q^{7} -2.82147 q^{8} +(1.49155 + 2.58344i) q^{9} +O(q^{10})$	\(q+0.869986 q^{2} +(-0.0650072 + 0.112596i) q^{3} -1.24312 q^{4} +(-0.0565553 + 0.0979567i) q^{6} +(1.58680 - 2.74842i) q^{7} -2.82147 q^{8} +(1.49155 + 2.58344i) q^{9} +(0.267382 + 0.463119i) q^{11} +(0.0808121 - 0.139971i) q^{12} +(-0.667611 - 1.15634i) q^{13} +(1.38049 - 2.39108i) q^{14} +0.0316097 q^{16} +(3.19392 - 5.53204i) q^{17} +(1.29763 + 2.24755i) q^{18} +(2.14335 - 3.71240i) q^{19} +(0.206307 + 0.357334i) q^{21} +(0.232618 + 0.402907i) q^{22} +3.35624 q^{23} +(0.183416 - 0.317686i) q^{24} +(-0.580812 - 1.00600i) q^{26} -0.777888 q^{27} +(-1.97259 + 3.41663i) q^{28} +1.35624 q^{29} +(4.22417 - 3.62718i) q^{31} +5.67044 q^{32} -0.0695269 q^{33} +(2.77867 - 4.81279i) q^{34} +(-1.85418 - 3.21154i) q^{36} +(-0.0734590 + 0.127235i) q^{37} +(1.86469 - 3.22973i) q^{38} +0.173598 q^{39} +(-4.03230 - 6.98415i) q^{41} +(0.179484 + 0.310875i) q^{42} +(-4.33728 + 7.51238i) q^{43} +(-0.332389 - 0.575714i) q^{44} +2.91988 q^{46} +1.02101 q^{47} +(-0.00205486 + 0.00355912i) q^{48} +(-1.53586 - 2.66019i) q^{49} +(0.415256 + 0.719244i) q^{51} +(0.829924 + 1.43747i) q^{52} +(-5.25646 - 9.10446i) q^{53} -0.676752 q^{54} +(-4.47711 + 7.75458i) q^{56} +(0.278667 + 0.482665i) q^{57} +1.17991 q^{58} +(-0.0144388 + 0.0250088i) q^{59} +12.5276 q^{61} +(3.67496 - 3.15559i) q^{62} +9.46715 q^{63} +4.86999 q^{64} -0.0604874 q^{66} +(2.71288 + 4.69885i) q^{67} +(-3.97045 + 6.87701i) q^{68} +(-0.218179 + 0.377898i) q^{69} +(2.88442 + 4.99597i) q^{71} +(-4.20836 - 7.28910i) q^{72} +(0.578347 + 1.00173i) q^{73} +(-0.0639083 + 0.110692i) q^{74} +(-2.66446 + 4.61498i) q^{76} +1.69712 q^{77} +0.151028 q^{78} +(-4.86752 + 8.43079i) q^{79} +(-4.42408 + 7.66272i) q^{81} +(-3.50804 - 6.07611i) q^{82} +(-5.18017 - 8.97232i) q^{83} +(-0.256465 - 0.444210i) q^{84} +(-3.77337 + 6.53567i) q^{86} +(-0.0881651 + 0.152706i) q^{87} +(-0.754410 - 1.30668i) q^{88} +12.7519 q^{89} -4.23746 q^{91} -4.17222 q^{92} +(0.133804 + 0.711416i) q^{93} +0.888267 q^{94} +(-0.368620 + 0.638468i) q^{96} -13.7617 q^{97} +(-1.33618 - 2.31433i) q^{98} +(-0.797625 + 1.38153i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 10 q^{6} + q^{7} + 18 q^{8} - q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 10 * q^6 + q^7 + 18 * q^8 - q^9	$ 8 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 10 q^{6} + q^{7} + 18 q^{8} - q^{9} + 4 q^{11} + 8 q^{12} - q^{13} - 8 q^{14} + 10 q^{16} + 12 q^{17} + 11 q^{18} - 5 q^{19} + 9 q^{21} - 10 q^{23} + 2 q^{24} - 12 q^{26} + 6 q^{27} - 4 q^{28} - 26 q^{29} + 19 q^{31} + 28 q^{32} - 8 q^{33} + 24 q^{34} - 5 q^{36} - 16 q^{37} - 9 q^{38} - 22 q^{39} - 4 q^{41} - 6 q^{42} + q^{43} - 7 q^{44} - 22 q^{46} - 20 q^{47} + 27 q^{48} - 37 q^{49} - 12 q^{51} - 21 q^{52} + q^{53} + 24 q^{54} - 29 q^{56} + 4 q^{57} - 26 q^{58} + 6 q^{59} - 2 q^{61} + 17 q^{62} - 24 q^{63} + 34 q^{64} + 2 q^{66} + 7 q^{67} + 5 q^{68} - 6 q^{69} + 12 q^{71} - 14 q^{72} - 20 q^{73} + 18 q^{74} - 23 q^{76} - 58 q^{77} - 22 q^{78} - 2 q^{79} + 12 q^{81} + 18 q^{82} + 4 q^{83} + 41 q^{84} - 13 q^{86} + 10 q^{88} + 54 q^{89} - 44 q^{91} - 86 q^{92} - 55 q^{93} - 48 q^{94} + 13 q^{96} + 18 q^{97} + 46 q^{98} - 7 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 10 * q^6 + q^7 + 18 * q^8 - q^9 + 4 * q^11 + 8 * q^12 - q^13 - 8 * q^14 + 10 * q^16 + 12 * q^17 + 11 * q^18 - 5 * q^19 + 9 * q^21 - 10 * q^23 + 2 * q^24 - 12 * q^26 + 6 * q^27 - 4 * q^28 - 26 * q^29 + 19 * q^31 + 28 * q^32 - 8 * q^33 + 24 * q^34 - 5 * q^36 - 16 * q^37 - 9 * q^38 - 22 * q^39 - 4 * q^41 - 6 * q^42 + q^43 - 7 * q^44 - 22 * q^46 - 20 * q^47 + 27 * q^48 - 37 * q^49 - 12 * q^51 - 21 * q^52 + q^53 + 24 * q^54 - 29 * q^56 + 4 * q^57 - 26 * q^58 + 6 * q^59 - 2 * q^61 + 17 * q^62 - 24 * q^63 + 34 * q^64 + 2 * q^66 + 7 * q^67 + 5 * q^68 - 6 * q^69 + 12 * q^71 - 14 * q^72 - 20 * q^73 + 18 * q^74 - 23 * q^76 - 58 * q^77 - 22 * q^78 - 2 * q^79 + 12 * q^81 + 18 * q^82 + 4 * q^83 + 41 * q^84 - 13 * q^86 + 10 * q^88 + 54 * q^89 - 44 * q^91 - 86 * q^92 - 55 * q^93 - 48 * q^94 + 13 * q^96 + 18 * q^97 + 46 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.869986			0.615173			0.307586	−	0.951520i	$-0.400479\pi$
$2$	0.869986			0.615173			0.307586	+	0.951520i	$0.400479\pi$
$3$	−0.0650072	+	0.112596i	−0.0375319	+	0.0650072i	−0.884181	−	0.467144i	$-0.845283\pi$
$3$	−0.0650072	+	0.112596i	−0.0375319	+	0.0650072i	0.846649	+	0.532151i	$0.178616\pi$
$4$	−1.24312			−0.621562
$5$		0			0
$5$		0			0
$6$	−0.0565553	+	0.0979567i	−0.0230886	+	0.0399906i
$7$	1.58680	−	2.74842i	0.599754	−	1.03880i	−0.393103	−	0.919494i	$-0.628599\pi$
$7$	1.58680	−	2.74842i	0.599754	−	1.03880i	0.992857	−	0.119310i	$-0.0380681\pi$
$8$	−2.82147			−0.997541
$9$	1.49155	+	2.58344i	0.497183	+	0.861146i
$10$		0			0
$11$	0.267382	+	0.463119i	0.0806186	+	0.139636i	0.903516	−	0.428555i	$-0.140977\pi$
$11$	0.267382	+	0.463119i	0.0806186	+	0.139636i	−0.822897	+	0.568190i	$0.807644\pi$
$12$	0.0808121	−	0.139971i	0.0233284	−	0.0404060i
$13$	−0.667611	−	1.15634i	−0.185162	−	0.320710i	0.758469	−	0.651709i	$-0.225948\pi$
$13$	−0.667611	−	1.15634i	−0.185162	−	0.320710i	−0.943631	+	0.330999i	$0.892614\pi$
$14$	1.38049	−	2.39108i	0.368952	−	0.639044i
$15$		0			0
$16$	0.0316097			0.00790244
$17$	3.19392	−	5.53204i	0.774640	−	1.34172i	−0.160357	−	0.987059i	$-0.551264\pi$
$17$	3.19392	−	5.53204i	0.774640	−	1.34172i	0.934997	−	0.354657i	$-0.115402\pi$
$18$	1.29763	+	2.24755i	0.305853	+	0.529753i
$19$	2.14335	−	3.71240i	0.491719	−	0.851683i	−0.508235	−	0.861218i	$-0.669702\pi$
$19$	2.14335	−	3.71240i	0.491719	−	0.851683i	0.999955	+	0.00953558i	$0.00303532\pi$
$20$		0			0
$21$	0.206307	+	0.357334i	0.0450198	+	0.0779766i
$22$	0.232618	+	0.402907i	0.0495944	+	0.0859000i
$23$	3.35624			0.699824			0.349912	−	0.936783i	$-0.386212\pi$
$23$	3.35624			0.699824			0.349912	+	0.936783i	$0.386212\pi$
$24$	0.183416	−	0.317686i	0.0374396	−	0.0648473i
$25$		0			0
$26$	−0.580812	−	1.00600i	−0.113907	−	0.197292i
$27$	−0.777888			−0.149705
$28$	−1.97259	+	3.41663i	−0.372784	+	0.645681i
$29$	1.35624			0.251847			0.125923	−	0.992040i	$-0.459811\pi$
$29$	1.35624			0.251847			0.125923	+	0.992040i	$0.459811\pi$
$30$		0			0
$31$	4.22417	−	3.62718i	0.758683	−	0.651460i
$31$	4.22417	−	3.62718i	0.758683	−	0.651460i
$32$	5.67044			1.00240
$33$	−0.0695269			−0.0121031
$34$	2.77867	−	4.81279i	0.476537	−	0.825387i
$35$		0			0
$36$	−1.85418	−	3.21154i	−0.309030	−	0.535256i
$37$	−0.0734590	+	0.127235i	−0.0120766	+	0.0209173i	−0.872001	−	0.489505i	$-0.837178\pi$
$37$	−0.0734590	+	0.127235i	−0.0120766	+	0.0209173i	0.859924	+	0.510422i	$0.170511\pi$
$38$	1.86469	−	3.22973i	0.302492	−	0.523932i
$39$	0.173598			0.0277979
$40$		0			0
$41$	−4.03230	−	6.98415i	−0.629739	−	1.09074i	−0.987604	−	0.156967i	$-0.949828\pi$
$41$	−4.03230	−	6.98415i	−0.629739	−	1.09074i	0.357865	−	0.933773i	$-0.383505\pi$
$42$	0.179484	+	0.310875i	0.0276950	+	0.0479691i
$43$	−4.33728	+	7.51238i	−0.661429	+	1.14563i	0.318812	+	0.947818i	$0.396716\pi$
$43$	−4.33728	+	7.51238i	−0.661429	+	1.14563i	−0.980240	+	0.197810i	$0.936617\pi$
$44$	−0.332389	−	0.575714i	−0.0501095	−	0.0867922i
$45$		0			0
$46$	2.91988			0.430512
$47$	1.02101			0.148930			0.0744651	−	0.997224i	$-0.476275\pi$
$47$	1.02101			0.148930			0.0744651	+	0.997224i	$0.476275\pi$
$48$	−0.00205486	+	0.00355912i	−0.000296594	+	0.000513715i
$49$	−1.53586	−	2.66019i	−0.219409	−	0.380027i
$50$		0			0
$51$	0.415256	+	0.719244i	0.0581474	+	0.100714i
$52$	0.829924	+	1.43747i	0.115090	+	0.199341i
$53$	−5.25646	−	9.10446i	−0.722031	−	1.25059i	−0.960184	−	0.279367i	$-0.909875\pi$
$53$	−5.25646	−	9.10446i	−0.722031	−	1.25059i	0.238153	−	0.971228i	$-0.423458\pi$
$54$	−0.676752			−0.0920943
$55$		0			0
$56$	−4.47711	+	7.75458i	−0.598279	+	1.03625i
$57$	0.278667	+	0.482665i	0.0369103	+	0.0639306i
$58$	1.17991			0.154929
$59$	−0.0144388	+	0.0250088i	−0.00187978	+	0.00325587i	−0.866964	−	0.498371i	$-0.833932\pi$
$59$	−0.0144388	+	0.0250088i	−0.00187978	+	0.00325587i	0.865084	+	0.501627i	$0.167265\pi$
$60$		0			0
$61$	12.5276			1.60400			0.802000	−	0.597324i	$-0.203770\pi$
$61$	12.5276			1.60400			0.802000	+	0.597324i	$0.203770\pi$
$62$	3.67496	−	3.15559i	0.466721	−	0.400761i
$63$	9.46715			1.19275
$64$	4.86999			0.608748
$65$		0			0
$66$	−0.0604874			−0.00744549
$67$	2.71288	+	4.69885i	0.331431	+	0.574056i	0.982793	−	0.184712i	$-0.0591352\pi$
$67$	2.71288	+	4.69885i	0.331431	+	0.574056i	−0.651362	+	0.758768i	$0.725802\pi$
$68$	−3.97045	+	6.87701i	−0.481487	+	0.833960i
$69$	−0.218179	+	0.377898i	−0.0262657	+	0.0454936i
$70$		0			0
$71$	2.88442	+	4.99597i	0.342318	+	0.592913i	0.984863	−	0.173336i	$-0.0554546\pi$
$71$	2.88442	+	4.99597i	0.342318	+	0.592913i	−0.642545	+	0.766248i	$0.722121\pi$
$72$	−4.20836	−	7.28910i	−0.495960	−	0.859028i
$73$	0.578347	+	1.00173i	0.0676904	+	0.117243i	0.897884	−	0.440232i	$-0.145104\pi$
$73$	0.578347	+	1.00173i	0.0676904	+	0.117243i	−0.830194	+	0.557475i	$0.811770\pi$
$74$	−0.0639083	+	0.110692i	−0.00742919	+	0.0128677i
$75$		0			0
$76$	−2.66446	+	4.61498i	−0.305634	+	0.529374i
$77$	1.69712			0.193405
$78$	0.151028			0.0171005
$79$	−4.86752	+	8.43079i	−0.547639	+	0.948538i	0.450797	+	0.892627i	$0.351140\pi$
$79$	−4.86752	+	8.43079i	−0.547639	+	0.948538i	−0.998436	+	0.0559118i	$0.982193\pi$
$80$		0			0
$81$	−4.42408	+	7.66272i	−0.491564	+	0.851414i
$82$	−3.50804	−	6.07611i	−0.387398	−	0.670994i
$83$	−5.18017	−	8.97232i	−0.568598	−	0.984840i	−0.996705	−	0.0811123i	$-0.974153\pi$
$83$	−5.18017	−	8.97232i	−0.568598	−	0.984840i	0.428107	−	0.903728i	$-0.359181\pi$
$84$	−0.256465	−	0.444210i	−0.0279826	−	0.0484673i
$85$		0			0
$86$	−3.77337	+	6.53567i	−0.406893	+	0.704759i
$87$	−0.0881651	+	0.152706i	−0.00945229	+	0.0163718i
$88$	−0.754410	−	1.30668i	−0.0804204	−	0.139292i
$89$	12.7519			1.35170			0.675852	−	0.737038i	$-0.263776\pi$
$89$	12.7519			1.35170			0.675852	+	0.737038i	$0.263776\pi$
$90$		0			0
$91$	−4.23746			−0.444206
$92$	−4.17222			−0.434984
$93$	0.133804	+	0.711416i	0.0138748	+	0.0737704i
$94$	0.888267			0.0916177
$95$		0			0
$96$	−0.368620	+	0.638468i	−0.0376221	+	0.0651634i
$97$	−13.7617			−1.39729			−0.698646	−	0.715468i	$-0.746214\pi$
$97$	−13.7617			−1.39729			−0.698646	+	0.715468i	$0.746214\pi$
$98$	−1.33618	−	2.31433i	−0.134974	−	0.233782i
$99$	−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	$0.847721\pi$
$102$	0.361267	+	0.625732i	0.0357707	+	0.0619567i
$103$	4.03760	+	6.99332i	0.397836	+	0.689073i	0.993459	−	0.114192i	$-0.0364279\pi$
$103$	4.03760	+	6.99332i	0.397836	+	0.689073i	−0.595622	+	0.803265i	$0.703095\pi$
$104$	1.88365	+	3.26257i	0.184707	+	0.319921i
$105$		0			0
$106$	−4.57305	−	7.92075i	−0.444174	−	0.769332i
$107$	−7.31942	+	12.6776i	−0.707595	+	1.22559i	0.258152	+	0.966104i	$0.416886\pi$
$107$	−7.31942	+	12.6776i	−0.707595	+	1.22559i	−0.965747	+	0.259486i	$0.916447\pi$
$108$	0.967013			0.0930508
$109$	0.165734			0.0158744			0.00793721	−	0.999968i	$-0.497473\pi$
$109$	0.165734			0.0158744			0.00793721	+	0.999968i	$0.497473\pi$
$110$		0			0
$111$	−0.00955073	−	0.0165424i	−0.000906515	−	0.00157013i
$112$	0.0501583	−	0.0868767i	0.00473951	−	0.00820908i
$113$	2.96866	+	5.14187i	0.279268	+	0.483706i	0.971203	−	0.238254i	$-0.0765749\pi$
$113$	2.96866	+	5.14187i	0.279268	+	0.483706i	−0.691935	+	0.721960i	$0.743242\pi$
$114$	0.242436	+	0.419912i	0.0227062	+	0.0393283i
$115$		0			0
$116$	−1.68597			−0.156538
$117$	1.99155	−	3.44946i	0.184119	−	0.318903i
$118$	−0.0125616	+	0.0217573i	−0.00115639	+	0.00200292i
$119$	−10.1362	−	17.5565i	−0.929186	−	1.60940i
$120$		0			0
$121$	5.35701	−	9.27862i	0.487001	−	0.843511i
$122$	10.8989			0.986737
$123$	1.04851			0.0945413
$124$	−5.25117	+	4.50904i	−0.471569	+	0.404923i
$125$		0			0
$126$	8.23628			0.733746
$127$	−9.27826	+	16.0704i	−0.823312	+	1.42602i	0.0798903	+	0.996804i	$0.474543\pi$
$127$	−9.27826	+	16.0704i	−0.823312	+	1.42602i	−0.903202	+	0.429215i	$0.858790\pi$
$128$	−7.10407			−0.627917
$129$	−0.563908	−	0.976718i	−0.0496494	−	0.0859952i
$130$		0			0
$131$	8.20480	−	14.2111i	0.716857	−	1.24163i	−0.245383	−	0.969426i	$-0.578914\pi$
$131$	8.20480	−	14.2111i	0.716857	−	1.24163i	0.962239	−	0.272206i	$-0.0877531\pi$
$132$	0.0864307			0.00752282
$133$	−6.80215	−	11.7817i	−0.589821	−	1.02160i
$134$	2.36017	+	4.08793i	0.203887	+	0.353143i
$135$		0			0
$136$	−9.01156	+	15.6085i	−0.772735	+	1.33842i
$137$	2.29968	+	3.98316i	0.196475	+	0.340305i	0.947383	−	0.320102i	$-0.103717\pi$
$137$	2.29968	+	3.98316i	0.196475	+	0.340305i	−0.750908	+	0.660407i	$0.770384\pi$
$138$	−0.189813	+	0.328766i	−0.0161580	+	0.0279864i
$139$	−21.9951			−1.86560			−0.932799	−	0.360398i	$-0.882641\pi$
$139$	−21.9951			−1.86560			−0.932799	+	0.360398i	$0.882641\pi$
$140$		0			0
$141$	−0.0663732	+	0.114962i	−0.00558963	+	0.00968153i
$142$	2.50941	+	4.34642i	0.210585	+	0.364744i
$143$	0.357014	−	0.618366i	0.0298550	−	0.0517104i
$144$	0.0471475	+	0.0816618i	0.00392895	+	0.00680515i
$145$		0			0
$146$	0.503154	+	0.871488i	0.0416413	+	0.0721248i
$147$	0.399368			0.0329393
$148$	0.0913188	−	0.158169i	0.00750636	−	0.0130014i
$149$	−10.9019	+	18.8826i	−0.893116	+	1.54692i	−0.0569976	+	0.998374i	$0.518153\pi$
$149$	−10.9019	+	18.8826i	−0.893116	+	1.54692i	−0.836119	+	0.548549i	$0.815181\pi$
$150$		0			0
$151$	8.96619			0.729658			0.364829	−	0.931074i	$-0.381127\pi$
$151$	8.96619			0.729658			0.364829	+	0.931074i	$0.381127\pi$
$152$	−6.04741	+	10.4744i	−0.490510	+	0.849588i
$153$	19.0556			1.54055
$154$	1.47647			0.118978
$155$		0			0
$156$	−0.215804			−0.0172782
$157$	−7.32243			−0.584393			−0.292197	−	0.956358i	$-0.594386\pi$
$157$	−7.32243			−0.584393			−0.292197	+	0.956358i	$0.594386\pi$
$158$	−4.23467	+	7.33467i	−0.336893	+	0.583515i
$159$	1.36683			0.108397
$160$		0			0
$161$	5.32567	−	9.22433i	0.419722	−	0.726979i
$162$	−3.84888	+	6.66646i	−0.302397	+	0.523767i
$163$	3.24879			0.254465			0.127232	−	0.991873i	$-0.459391\pi$
$163$	3.24879			0.254465			0.127232	+	0.991873i	$0.459391\pi$
$164$	5.01265	+	8.68217i	0.391422	+	0.677963i
$165$		0			0
$166$	−4.50668	−	7.80579i	−0.349786	−	0.605847i
$167$	0.764548	−	1.32424i	0.0591625	−	0.102473i	−0.834927	−	0.550360i	$-0.814490\pi$
$167$	0.764548	−	1.32424i	0.0591625	−	0.102473i	0.894090	+	0.447888i	$0.147824\pi$
$168$	−0.582089	−	1.00821i	−0.0449091	−	0.0777849i
$169$	5.60859	−	9.71436i	0.431430	−	0.747259i
$170$		0			0
$171$	12.7877			0.977897
$172$	5.39178	−	9.33883i	0.411119	−	0.712079i
$173$	1.42686	+	2.47140i	0.108482	+	0.187897i	0.915156	−	0.403101i	$-0.132068\pi$
$173$	1.42686	+	2.47140i	0.108482	+	0.187897i	−0.806673	+	0.590998i	$0.798734\pi$
$174$	−0.0767023	+	0.132852i	−0.00581479	+	0.0100715i
$175$		0			0
$176$	0.00845187	+	0.0146391i	0.000637083	+	0.00110346i
$177$	−0.00187726	−	0.00325151i	−0.000141103	−	0.000244398i
$178$	11.0940			0.831531
$179$	−1.95925	+	3.39352i	−0.146441	+	0.253644i	−0.929910	−	0.367788i	$-0.880115\pi$
$179$	−1.95925	+	3.39352i	−0.146441	+	0.253644i	0.783469	+	0.621431i	$0.213449\pi$
$180$		0			0
$181$	9.10297	+	15.7668i	0.676619	+	1.17194i	0.975993	+	0.217802i	$0.0698887\pi$
$181$	9.10297	+	15.7668i	0.676619	+	1.17194i	−0.299374	+	0.954136i	$0.596778\pi$
$182$	−3.68653			−0.273264
$183$	−0.814386	+	1.41056i	−0.0602012	+	0.104271i
$184$	−9.46953			−0.698103
$185$		0			0
$186$	0.116407	+	0.618921i	0.00853539	+	0.0453815i
$187$	3.41599			0.249802
$188$	−1.26925			−0.0925694
$189$	−1.23435	+	2.13796i	−0.0897859	+	0.155514i
$190$		0			0
$191$	−8.58570	−	14.8709i	−0.621239	−	1.07602i	−0.989255	−	0.146199i	$-0.953296\pi$
$191$	−8.58570	−	14.8709i	−0.621239	−	1.07602i	0.368016	−	0.929820i	$-0.380037\pi$
$192$	−0.316584	+	0.548340i	−0.0228475	+	0.0395730i
$193$	8.49114	−	14.7071i	0.611205	−	1.05864i	−0.379832	−	0.925055i	$-0.624018\pi$
$193$	8.49114	−	14.7071i	0.611205	−	1.05864i	0.991038	−	0.133584i	$-0.0426484\pi$
$194$	−11.9725			−0.859575
$195$		0			0
$196$	1.90927	+	3.30695i	0.136376	+	0.236211i
$197$	−3.58680	−	6.21252i	−0.255549	−	0.442624i	0.709496	−	0.704710i	$-0.248923\pi$
$197$	−3.58680	−	6.21252i	−0.255549	−	0.442624i	−0.965044	+	0.262086i	$0.915589\pi$
$198$	−0.693923	+	1.20191i	−0.0493149	+	0.0854160i
$199$	6.23919	+	10.8066i	0.442285	+	0.766059i	0.997859	−	0.0654076i	$-0.0208348\pi$
$199$	6.23919	+	10.8066i	0.442285	+	0.766059i	−0.555574	+	0.831467i	$0.687501\pi$
$200$		0			0
$201$	−0.705427			−0.0497570
$202$	−15.5233			−1.09222
$203$	2.15207	−	3.72750i	0.151046	−	0.261619i
$204$	−0.516215	−	0.894110i	−0.0361423	−	0.0626003i
$205$		0			0
$206$	3.51265	+	6.08409i	0.244738	+	0.423899i
$207$	5.00599	+	8.67062i	0.347940	+	0.602650i
$208$	−0.0211030	−	0.0365515i	−0.00146323	−	0.00253439i
$209$	2.29238			0.158567
$210$		0			0
$211$	−0.940980	+	1.62982i	−0.0647797	+	0.112202i	−0.896596	−	0.442849i	$-0.853968\pi$
$211$	−0.940980	+	1.62982i	−0.0647797	+	0.112202i	0.831817	+	0.555051i	$0.187301\pi$
$212$	6.53444	+	11.3180i	0.448787	+	0.777323i
$213$	−0.750033			−0.0513914
$214$	−6.36779	+	11.0293i	−0.435293	+	0.753950i
$215$		0			0
$216$	2.19479			0.149337
$217$	−3.26609	−	17.3654i	−0.221717	−	1.17884i
$218$	0.144186			0.00976551
$219$	−0.150387			−0.0101622
$220$		0			0
$221$	−8.52919			−0.573736
$222$	−0.00830900	−	0.0143916i	−0.000557664	−	0.000965902i
$223$	6.60576	−	11.4415i	0.442354	−	0.766180i	−0.555509	−	0.831510i	$-0.687477\pi$
$223$	6.60576	−	11.4415i	0.442354	−	0.766180i	0.997864	+	0.0653302i	$0.0208101\pi$
$224$	8.99786	−	15.5847i	0.601195	−	1.04130i
$225$		0			0
$226$	2.58269	+	4.47335i	0.171798	+	0.297563i
$227$	0.621562	+	1.07658i	0.0412546	+	0.0714550i	0.885915	−	0.463847i	$-0.153531\pi$
$227$	0.621562	+	1.07658i	0.0412546	+	0.0714550i	−0.844661	+	0.535302i	$0.820198\pi$
$228$	−0.346418	−	0.600013i	−0.0229421	−	0.0397368i
$229$	7.61106	−	13.1827i	0.502953	−	0.871140i	−0.497041	−	0.867727i	$-0.665580\pi$
$229$	7.61106	−	13.1827i	0.502953	−	0.871140i	0.999994	−	0.00341287i	$-0.00108635\pi$
$230$		0			0
$231$	−0.110325	+	0.191089i	−0.00725887	+	0.0125727i
$232$	−3.82658			−0.251227
$233$	−1.60649			−0.105245			−0.0526223	−	0.998614i	$-0.516758\pi$
$233$	−1.60649			−0.105245			−0.0526223	+	0.998614i	$0.516758\pi$
$234$	1.73262	−	3.00098i	0.113265	−	0.196180i
$235$		0			0
$236$	0.0179493	−	0.0310891i	0.00116840	−	0.00202373i
$237$	−0.632848	−	1.09612i	−0.0411079	−	0.0712009i
$238$	−8.81837	−	15.2739i	−0.571610	−	0.990058i
$239$	10.3667	+	17.9557i	0.670569	+	1.16146i	0.977743	+	0.209806i	$0.0672832\pi$
$239$	10.3667	+	17.9557i	0.670569	+	1.16146i	−0.307174	+	0.951653i	$0.599383\pi$
$240$		0			0
$241$	7.43988	−	12.8863i	0.479245	−	0.830076i	−0.520472	−	0.853879i	$-0.674244\pi$
$241$	7.43988	−	12.8863i	0.479245	−	0.830076i	0.999717	+	0.0238024i	$0.00757725\pi$
$242$	4.66053	−	8.07227i	0.299590	−	0.518905i
$243$	−1.74203	−	3.01728i	−0.111751	−	0.193558i
$244$	−15.5734			−0.996986
$245$		0			0
$246$	0.912192			0.0581592
$247$	−5.72371			−0.364191
$248$	−11.9184	+	10.2340i	−0.756817	+	0.649858i
$249$	1.34699			0.0853623
$250$		0			0
$251$	−1.86752	+	3.23464i	−0.117877	+	0.204169i	−0.918926	−	0.394430i	$-0.870942\pi$
$251$	−1.86752	+	3.23464i	−0.117877	+	0.204169i	0.801049	+	0.598598i	$0.204275\pi$
$252$	−11.7688			−0.741368
$253$	0.897396	+	1.55434i	0.0564188	+	0.0977202i
$254$	−8.07195	+	13.9810i	−0.506479	+	0.877248i
$255$		0			0
$256$	−15.9204			−0.995026
$257$	2.36469	+	4.09576i	0.147505	+	0.255486i	0.930305	−	0.366787i	$-0.119542\pi$
$257$	2.36469	+	4.09576i	0.147505	+	0.255486i	−0.782800	+	0.622274i	$0.786209\pi$
$258$	−0.490592	−	0.849731i	−0.0305429	−	0.0529019i
$259$	0.233129	+	0.403792i	0.0144860	+	0.0250904i
$260$		0			0
$261$	2.02289	+	3.50375i	0.125214	+	0.216877i
$262$	7.13806	−	12.3635i	0.440991	−	0.763818i
$263$	7.58401			0.467650			0.233825	−	0.972279i	$-0.424876\pi$
$263$	7.58401			0.467650			0.233825	+	0.972279i	$0.424876\pi$
$264$	0.196168			0.0120733
$265$		0			0
$266$	−5.91777	−	10.2499i	−0.362842	−	0.628460i
$267$	−0.828968	+	1.43581i	−0.0507320	+	0.0878704i
$268$	−3.37245	−	5.84126i	−0.206005	−	0.356811i
$269$	6.92408	+	11.9929i	0.422168	+	0.731217i	0.996151	−	0.0876502i	$-0.0279358\pi$
$269$	6.92408	+	11.9929i	0.422168	+	0.731217i	−0.573983	+	0.818867i	$0.694602\pi$
$270$		0			0
$271$	−21.2796			−1.29264			−0.646321	−	0.763065i	$-0.723693\pi$
$271$	−21.2796			−1.29264			−0.646321	+	0.763065i	$0.723693\pi$
$272$	0.100959	−	0.174866i	0.00612154	−	0.0106028i
$273$	0.275465	−	0.477120i	0.0166719	−	0.0288766i
$274$	2.00069	+	3.46529i	0.120866	+	0.209346i
$275$		0			0
$276$	0.271224	−	0.469774i	0.0163258	−	0.0282771i
$277$	29.0763			1.74702			0.873512	−	0.486802i	$-0.161837\pi$
$277$	29.0763			1.74702			0.873512	+	0.486802i	$0.161837\pi$
$278$	−19.1354			−1.14766
$279$	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	$0.458397\pi$
$282$	−0.0577437	+	0.100015i	−0.00343859	+	0.00595581i
$283$	16.9233			1.00599			0.502994	−	0.864290i	$-0.332232\pi$
$283$	16.9233			1.00599			0.502994	+	0.864290i	$0.332232\pi$
$284$	−3.58570	−	6.21061i	−0.212772	−	0.368532i
$285$		0			0
$286$	0.310597	−	0.537970i	0.0183660	−	0.0318108i
$287$	−25.5938			−1.51075
$288$	8.45774	+	14.6492i	0.498377	+	0.863215i
$289$	−11.9023	−	20.6154i	−0.700134	−	1.21267i
$290$		0			0
$291$	0.894611	−	1.54951i	0.0524430	−	0.0908340i
$292$	−0.718958	−	1.24527i	−0.0420738	−	0.0728740i
$293$	−7.32883	+	12.6939i	−0.428155	+	0.741585i	−0.996709	−	0.0810601i	$-0.974169\pi$
$293$	−7.32883	+	12.6939i	−0.428155	+	0.741585i	0.568555	+	0.822645i	$0.307503\pi$
$294$	0.347445			0.0202634
$295$		0			0
$296$	0.207263	−	0.358989i	0.0120469	−	0.0208658i
$297$	−0.207993	−	0.360255i	−0.0120690	−	0.0209041i
$298$	−9.48447	+	16.4276i	−0.549421	+	0.951625i
$299$	−2.24066	−	3.88094i	−0.129581	−	0.224440i
$300$		0			0
$301$	13.7648	+	23.8413i	0.793388	+	1.37419i
$302$	7.80046			0.448866
$303$	1.15994	−	2.00907i	0.0666367	−	0.115418i
$304$	0.0677509	−	0.117348i	0.00388578	−	0.00673037i
$305$		0			0
$306$	16.5781			0.947705
$307$	−13.2954	+	23.0284i	−0.758810	+	1.31430i	0.184648	+	0.982805i	$0.440886\pi$
$307$	−13.2954	+	23.0284i	−0.758810	+	1.31430i	−0.943458	+	0.331493i	$0.892448\pi$
$308$	−2.10974			−0.120213
$309$	−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	$0.619350\pi$
$312$	−0.489802			−0.0277296
$313$	−13.1514	+	22.7789i	−0.743361	+	1.28754i	0.207596	+	0.978215i	$0.433436\pi$
$313$	−13.1514	+	22.7789i	−0.743361	+	1.28754i	−0.950957	+	0.309324i	$0.899897\pi$
$314$	−6.37041			−0.359503
$315$		0			0
$316$	6.05094	−	10.4805i	0.340392	−	0.589576i
$317$	9.34856	−	16.1922i	0.525068	−	0.909444i	−0.474506	−	0.880252i	$-0.657373\pi$
$317$	9.34856	−	16.1922i	0.525068	−	0.909444i	0.999574	−	0.0291916i	$-0.00929329\pi$
$318$	1.18912			0.0666828
$319$	0.362633	+	0.628098i	0.0203035	+	0.0351667i
$320$		0			0
$321$	−0.951629	−	1.64827i	−0.0531148	−	0.0919975i
$322$	4.63326	−	8.02504i	0.258201	−	0.447218i
$323$	−13.6914	−	23.7142i	−0.761811	−	1.31949i
$324$	5.49968	−	9.52572i	0.305538	−	0.529207i
$325$		0			0
$326$	2.82640			0.156540
$327$	−0.0107739	+	0.0186609i	−0.000595797	+	0.00103195i
$328$	11.3770	+	19.7056i	0.628191	+	1.08806i
$329$	1.62014	−	2.80617i	0.0893214	−	0.154709i
$330$		0			0
$331$	11.5085	+	19.9332i	0.632562	+	1.09563i	0.987026	+	0.160560i	$0.0513299\pi$
$331$	11.5085	+	19.9332i	0.632562	+	1.09563i	−0.354464	+	0.935069i	$0.615337\pi$
$332$	6.43960	+	11.1537i	0.353419	+	0.612140i
$333$	−0.438271			−0.0240171
$334$	0.665146	−	1.15207i	0.0363952	−	0.0630383i
$335$		0			0
$336$	0.00652130	+	0.0112952i	0.000355766	+	0.000616205i
$337$	35.6562			1.94232			0.971158	−	0.238436i	$-0.0766347\pi$
$337$	35.6562			1.94232			0.971158	+	0.238436i	$0.0766347\pi$
$338$	4.87939	−	8.45136i	0.265404	−	0.459693i
$339$	−0.771936			−0.0419258
$340$		0			0
$341$	2.80928	+	0.986450i	0.152131	+	0.0534192i
$342$	11.1251			0.601576
$343$	12.4668			0.673142
$344$	12.2375	−	21.1960i	0.659802	−	1.14281i
$345$		0			0
$346$	1.24135	+	2.15008i	0.0667353	+	0.115589i
$347$	8.49114	−	14.7071i	0.455828	−	0.789518i	−0.542907	−	0.839793i	$-0.682676\pi$
$347$	8.49114	−	14.7071i	0.455828	−	0.789518i	0.998735	+	0.0502751i	$0.0160098\pi$
$348$	0.109600	−	0.189833i	0.00587519	−	0.0101761i
$349$	17.4728			0.935298			0.467649	−	0.883914i	$-0.345101\pi$
$349$	17.4728			0.935298			0.467649	+	0.883914i	$0.345101\pi$
$350$		0			0
$351$	0.519327	+	0.899501i	0.0277196	+	0.0480118i
$352$	1.51617	+	2.62609i	0.0808123	+	0.139971i
$353$	−5.99754	+	10.3880i	−0.319217	+	0.552899i	−0.980325	−	0.197391i	$-0.936753\pi$
$353$	−5.99754	+	10.3880i	−0.319217	+	0.552899i	0.661108	+	0.750291i	$0.270086\pi$
$354$	−0.00163319	−	0.00282876i	−8.68029e−5	−	0.000150347i
$355$		0			0
$356$	−15.8523			−0.840168
$357$	2.63571			0.139497
$358$	−1.70452	+	2.95231i	−0.0900866	+	0.156035i
$359$	−12.5819	−	21.7924i	−0.664046	−	1.15016i	−0.979543	−	0.201234i	$-0.935505\pi$
$359$	−12.5819	−	21.7924i	−0.664046	−	1.15016i	0.315497	−	0.948926i	$-0.397829\pi$
$360$		0			0
$361$	0.312064	+	0.540511i	0.0164244	+	0.0284480i
$362$	7.91946	+	13.7169i	0.416237	+	0.720944i
$363$	0.696489	+	1.20635i	0.0365562	+	0.0633172i
$364$	5.26769			0.276102
$365$		0			0
$366$	−0.708504	+	1.22717i	−0.0370341	+	0.0641450i
$367$	−5.96524	−	10.3321i	−0.311383	−	0.539331i	0.667279	−	0.744808i	$-0.267459\pi$
$367$	−5.96524	−	10.3321i	−0.311383	−	0.539331i	−0.978662	+	0.205477i	$0.934125\pi$
$368$	0.106090			0.00553031
$369$	12.0287	−	20.8344i	0.626191	−	1.08459i
$370$		0			0
$371$	−33.3638			−1.73216
$372$	−0.166335	−	0.884379i	−0.00862405	−	0.0458529i
$373$	−9.20712			−0.476727			−0.238363	−	0.971176i	$-0.576611\pi$
$373$	−9.20712			−0.476727			−0.238363	+	0.971176i	$0.576611\pi$
$374$	2.97186			0.153671
$375$		0			0
$376$	−2.88076			−0.148564
$377$	−0.905438	−	1.56826i	−0.0466324	−	0.0807697i
$378$	−1.07387	+	1.86000i	−0.0552339	+	0.0956679i
$379$	−2.28639	+	3.96014i	−0.117444	+	0.203419i	−0.918754	−	0.394830i	$-0.870803\pi$
$379$	−2.28639	+	3.96014i	−0.117444	+	0.203419i	0.801310	+	0.598249i	$0.204137\pi$
$380$		0			0
$381$	−1.20631	−	2.08938i	−0.0618010	−	0.107042i
$382$	−7.46944	−	12.9374i	−0.382170	−	0.661937i
$383$	−6.16336	−	10.6753i	−0.314933	−	0.545480i	0.664490	−	0.747297i	$-0.268649\pi$
$383$	−6.16336	−	10.6753i	−0.314933	−	0.545480i	−0.979423	+	0.201817i	$0.935315\pi$
$384$	0.461816	−	0.799888i	0.0235669	−	0.0408191i
$385$		0			0
$386$	7.38717	−	12.7950i	0.375997	−	0.651246i
$387$	−25.8770			−1.31540
$388$	17.1075			0.868504
$389$	3.24518	−	5.62082i	0.164537	−	0.284987i	−0.771954	−	0.635679i	$-0.780720\pi$
$389$	3.24518	−	5.62082i	0.164537	−	0.284987i	0.936491	+	0.350692i	$0.114054\pi$
$390$		0			0
$391$	10.7196	−	18.5668i	0.542111	−	0.938964i
$392$	4.33339	+	7.50566i	0.218869	+	0.379093i
$393$	1.06674	+	1.84765i	0.0538100	+	0.0932016i
$394$	−3.12046	−	5.40480i	−0.157207	−	0.272290i
$395$		0			0
$396$	0.991548	−	1.71741i	0.0498272	−	0.0863032i
$397$	−13.0706	+	22.6389i	−0.655994	+	1.13621i	0.325650	+	0.945490i	$0.394417\pi$
$397$	−13.0706	+	22.6389i	−0.655994	+	1.13621i	−0.981644	+	0.190724i	$0.938916\pi$
$398$	5.42801	+	9.40159i	0.272081	+	0.471259i
$399$	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	$0.536536\pi$
$402$	−0.613711			−0.0306091
$403$	−7.01434	−	2.46301i	−0.349409	−	0.122691i
$404$	22.1814			1.10356
$405$		0			0
$406$	1.87227	−	3.24287i	0.0929193	−	0.160941i
$407$	−0.0785664			−0.00389439
$408$	−1.17163	−	2.02933i	−0.0580045	−	0.100467i
$409$	12.0171	−	20.8143i	0.594209	−	1.02920i	−0.399449	−	0.916755i	$-0.630799\pi$
$409$	12.0171	−	20.8143i	0.594209	−	1.02920i	0.993658	−	0.112445i	$-0.0358681\pi$
$410$		0			0
$411$	−0.597983			−0.0294963
$412$	−5.01924	−	8.69357i	−0.247280	−	0.428302i
$413$	0.0458231	+	0.0793679i	0.00225481	+	0.00390544i
$414$	4.35514	+	7.54332i	0.214043	+	0.370734i
$415$		0			0
$416$	−3.78565	−	6.55694i	−0.185607	−	0.321480i
$417$	1.42984	−	2.47655i	0.0700194	−	0.121277i
$418$	1.99433			0.0975460
$419$	−16.9894			−0.829987			−0.414993	−	0.909824i	$-0.636216\pi$
$419$	−16.9894			−0.829987			−0.414993	+	0.909824i	$0.636216\pi$
$420$		0			0
$421$	3.87172	+	6.70602i	0.188696	+	0.326831i	0.944816	−	0.327602i	$-0.106241\pi$
$421$	3.87172	+	6.70602i	0.188696	+	0.326831i	−0.756120	+	0.654433i	$0.772907\pi$
$422$	−0.818639	+	1.41792i	−0.0398507	+	0.0690235i
$423$	1.52289	+	2.63772i	0.0740455	+	0.128251i
$424$	14.8310	+	25.6880i	0.720256	+	1.24752i
$425$		0			0
$426$	−0.652518			−0.0316146
$427$	19.8788	−	34.4312i	0.962005	−	1.66624i
$428$	9.09895	−	15.7598i	0.439814	−	0.761781i
$429$	0.0464170	+	0.0803965i	0.00224103	+	0.00388158i
$430$		0			0
$431$	−16.7947	+	29.0893i	−0.808972	+	1.40118i	0.104604	+	0.994514i	$0.466642\pi$
$431$	−16.7947	+	29.0893i	−0.808972	+	1.40118i	−0.913577	+	0.406667i	$0.866691\pi$
$432$	−0.0245889			−0.00118303
$433$	0.313472			0.0150645			0.00753225	−	0.999972i	$-0.497602\pi$
$433$	0.313472			0.0150645			0.00753225	+	0.999972i	$0.497602\pi$
$434$	−2.84145	−	15.1076i	−0.136394	−	0.725189i
$435$		0			0
$436$	−0.206028			−0.00986695
$437$	7.19360	−	12.4597i	0.344117	−	0.596028i
$438$	−0.130834			−0.00625151
$439$	17.1980	+	29.7879i	0.820817	+	1.42170i	0.905074	+	0.425253i	$0.139815\pi$
$439$	17.1980	+	29.7879i	0.820817	+	1.42170i	−0.0842571	+	0.996444i	$0.526852\pi$
$440$		0			0
$441$	4.58163	−	7.93561i	0.218173	−	0.377886i
$442$	−7.42028			−0.352946
$443$	−13.8053	−	23.9114i	−0.655908	−	1.13607i	−0.981665	−	0.190612i	$-0.938953\pi$
$443$	−13.8053	−	23.9114i	−0.655908	−	1.13607i	0.325758	−	0.945453i	$-0.394381\pi$
$444$	0.0118728	+	0.0205642i	0.000563456	+	0.000975934i
$445$		0			0
$446$	5.74691	−	9.95395i	0.272124	−	0.471333i
$447$	−1.41740	−	2.45501i	−0.0670407	−	0.116118i
$448$	7.72769	−	13.3847i	0.365099	−	0.632370i
$449$	−8.50075			−0.401175			−0.200588	−	0.979676i	$-0.564285\pi$
$449$	−8.50075			−0.401175			−0.200588	+	0.979676i	$0.564285\pi$
$450$		0			0
$451$	2.15633	−	3.73487i	0.101537	−	0.175868i
$452$	−3.69041	−	6.39198i	−0.173582	−	0.300654i
$453$	−0.582867	+	1.00956i	−0.0273855	+	0.0474330i
$454$	0.540750	+	0.936607i	0.0253787	+	0.0439572i
$455$		0			0
$456$	−0.786251	−	1.36183i	−0.0368196	−	0.0637734i
$457$	22.9281			1.07253			0.536266	−	0.844049i	$-0.319835\pi$
$457$	22.9281			1.07253			0.536266	+	0.844049i	$0.319835\pi$
$458$	6.62151	−	11.4688i	0.309403	−	0.535901i
$459$	−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	$0.423971\pi$
$462$	−0.0959814	+	0.166245i	−0.00446546	+	0.00773440i
$463$	−25.2596			−1.17391			−0.586956	−	0.809619i	$-0.699674\pi$
$463$	−25.2596			−1.17391			−0.586956	+	0.809619i	$0.699674\pi$
$464$	0.0428703			0.00199020
$465$		0			0
$466$	−1.39762			−0.0647436
$467$	−32.0270			−1.48203			−0.741017	−	0.671486i	$-0.765656\pi$
$467$	−32.0270			−1.48203			−0.741017	+	0.671486i	$0.765656\pi$
$468$	−2.47574	+	4.28811i	−0.114441	+	0.198218i
$469$	17.2192			0.795108
$470$		0			0
$471$	0.476010	−	0.824474i	0.0219334	−	0.0379898i
$472$	0.0407388	−	0.0705617i	0.00187516	−	0.00324786i
$473$	−4.63883			−0.213294
$474$	−0.550568	−	0.953612i	−0.0252884	−	0.0438009i
$475$		0			0
$476$	12.6006	+	21.8249i	0.577547	+	1.00034i
$477$	15.6805	−	27.1595i	0.717963	−	1.24355i
$478$	9.01892	+	15.6212i	0.412516	+	0.714498i
$479$	6.47633	−	11.2173i	0.295911	−	0.512533i	−0.679285	−	0.733874i	$-0.737710\pi$
$479$	6.47633	−	11.2173i	0.295911	−	0.512533i	0.975196	+	0.221341i	$0.0710434\pi$
$480$		0			0
$481$	0.196168			0.00894450
$482$	6.47259	−	11.2109i	0.294818	−	0.510640i
$483$	0.692414	+	1.19930i	0.0315059	+	0.0545699i
$484$	−6.65944	+	11.5345i	−0.302702	+	0.524295i
$485$		0			0
$486$	−1.51554	−	2.62499i	−0.0687462	−	0.119072i
$487$	13.5208	+	23.4187i	0.612686	+	1.06120i	0.990786	+	0.135438i	$0.0432442\pi$
$487$	13.5208	+	23.4187i	0.612686	+	1.06120i	−0.378100	+	0.925765i	$0.623423\pi$
$488$	−35.3464			−1.60006
$489$	−0.211195	+	0.365800i	−0.00955056	+	0.0165421i
$490$		0			0
$491$	5.64719	+	9.78121i	0.254854	+	0.441420i	0.964856	−	0.262780i	$-0.0846393\pi$
$491$	5.64719	+	9.78121i	0.254854	+	0.441420i	−0.710002	+	0.704200i	$0.751306\pi$
$492$	−1.30343			−0.0587633
$493$	4.33171	−	7.50274i	0.195090	−	0.337907i
$494$	−4.97954			−0.224040
$495$		0			0
$496$	0.133525	−	0.114654i	0.00599544	−	0.00514812i
$497$	18.3080			0.821226
$498$	1.17187			0.0525125
$499$	−8.38428	+	14.5220i	−0.375332	+	0.650094i	−0.990377	−	0.138398i	$-0.955805\pi$
$499$	−8.38428	+	14.5220i	−0.375332	+	0.650094i	0.615045	+	0.788492i	$0.289138\pi$
$500$		0			0
$501$	0.0994023	+	0.172170i	0.00444097	+	0.00769198i
$502$	−1.62472	+	2.81409i	−0.0725146	+	0.125599i
$503$	−19.8474	+	34.3767i	−0.884953	+	1.53278i	−0.0391850	+	0.999232i	$0.512476\pi$
$503$	−19.8474	+	34.3767i	−0.884953	+	1.53278i	−0.845768	+	0.533551i	$0.820857\pi$
$504$	−26.7113			−1.18982
$505$		0			0
$506$	0.780722	+	1.35225i	0.0347073	+	0.0601148i
$507$	0.729197	+	1.26301i	0.0323848	+	0.0560921i
$508$	11.5340	−	19.9775i	0.511740	−	0.886360i
$509$	−8.56890	−	14.8418i	−0.379810	−	0.657850i	0.611225	−	0.791457i	$-0.290677\pi$
$509$	−8.56890	−	14.8418i	−0.379810	−	0.657850i	−0.991034	+	0.133607i	$0.957344\pi$
$510$		0			0
$511$	3.67088			0.162390
$512$	0.357613			0.0158044
$513$	−1.66729	+	2.88783i	−0.0736127	+	0.127501i
$514$	2.05724	+	3.56325i	0.0907411	+	0.157168i
$515$		0			0
$516$	0.701009	+	1.21418i	0.0308602	+	0.0534514i
$517$	0.273000	+	0.472850i	0.0120065	+	0.0207959i
$518$	0.202819	+	0.351293i	0.00891137	+	0.0154349i
$519$	−0.371025			−0.0162862
$520$		0			0
$521$	4.11183	−	7.12191i	0.180143	−	0.312016i	−0.761786	−	0.647828i	$-0.775677\pi$
$521$	4.11183	−	7.12191i	0.180143	−	0.312016i	0.941929	+	0.335812i	$0.109011\pi$
$522$	1.75989	+	3.04821i	0.0770281	+	0.133417i
$523$	19.7062			0.861690			0.430845	−	0.902426i	$-0.358216\pi$
$523$	19.7062			0.861690			0.430845	+	0.902426i	$0.358216\pi$
$524$	−10.1996	+	17.6662i	−0.445571	+	0.771752i
$525$		0			0
$526$	6.59798			0.287686
$527$	−6.57402	−	34.9532i	−0.286369	−	1.52258i
$528$	−0.00219773			−9.56439e−5
$529$	−11.7357			−0.510247
$530$		0			0
$531$	−0.0861449			−0.00373837
$532$	8.45592	+	14.6461i	0.366610	+	0.634988i
$533$	−5.38401	+	9.32539i	−0.233208	+	0.403927i
$534$	−0.721190	+	1.24914i	−0.0312090	+	0.0540555i
$535$		0			0
$536$	−7.65432	−	13.2577i	−0.330616	−	0.572644i
$537$	−0.254731	−	0.441206i	−0.0109924	−	0.0190395i
$538$	6.02385	+	10.4336i	0.259706	+	0.449825i
$539$	0.821323	−	1.42257i	0.0353769	−	0.0612746i
$540$		0			0
$541$	−8.19068	+	14.1867i	−0.352145	+	0.609933i	−0.986625	−	0.163006i	$-0.947881\pi$
$541$	−8.19068	+	14.1867i	−0.352145	+	0.609933i	0.634480	+	0.772939i	$0.281214\pi$
$542$	−18.5129			−0.795198
$543$	−2.36703			−0.101579
$544$	18.1110	−	31.3691i	0.776501	−	1.34494i
$545$		0			0
$546$	0.239651	−	0.415087i	0.0102561	−	0.0177641i
$547$	−2.35907	−	4.08603i	−0.100867	−	0.174706i	0.811175	−	0.584803i	$-0.198828\pi$
$547$	−2.35907	−	4.08603i	−0.100867	−	0.174706i	−0.912042	+	0.410097i	$0.865495\pi$
$548$	−2.85879	−	4.95157i	−0.122121	−	0.211521i
$549$	18.6856	+	32.3644i	0.797481	+	1.38128i
$550$		0			0
$551$	2.90689	−	5.03489i	0.123838	−	0.214493i
$552$	0.615587	−	1.06623i	0.0262011	−	0.0453817i
$553$	15.4476	+	26.7559i	0.656897	+	1.13778i
$554$	25.2960			1.07472
$555$		0			0
$556$	27.3426			1.15959
$557$	32.9280			1.39520			0.697602	−	0.716486i	$-0.254250\pi$
$557$	32.9280			1.39520			0.697602	+	0.716486i	$0.254250\pi$
$558$	13.6337	+	4.78732i	0.577159	+	0.202663i
$559$	11.5825			0.489886
$560$		0			0
$561$	−0.222064	+	0.384626i	−0.00937553	+	0.0162389i
$562$	3.80130			0.160348
$563$	18.4511	+	31.9583i	0.777622	+	1.34688i	0.933309	+	0.359075i	$0.116908\pi$
$563$	18.4511	+	31.9583i	0.777622	+	1.34688i	−0.155687	+	0.987806i	$0.549759\pi$
$564$	0.0825102	−	0.142912i	0.00347431	−	0.00601767i
$565$		0			0
$566$	14.7231			0.618857
$567$	14.0402	+	24.3184i	0.589635	+	1.02128i
$568$	−8.13832	−	14.0960i	−0.341476	−	0.591455i
$569$	−18.3707	−	31.8190i	−0.770141	−	1.33392i	−0.937485	−	0.348024i	$-0.886853\pi$
$569$	−18.3707	−	31.8190i	−0.770141	−	1.33392i	0.167345	−	0.985898i	$-0.446481\pi$
$570$		0			0
$571$	−11.2222	−	19.4375i	−0.469636	−	0.813434i	0.529761	−	0.848147i	$-0.322282\pi$
$571$	−11.2222	−	19.4375i	−0.469636	−	0.813434i	−0.999397	+	0.0347129i	$0.988948\pi$
$572$	−0.443813	+	0.768707i	−0.0185568	+	0.0321412i
$573$	2.23253			0.0932652
$574$	−22.2662			−0.929374
$575$		0			0
$576$	7.26382	+	12.5813i	0.302659	+	0.524221i
$577$	0.741171	−	1.28375i	0.0308554	−	0.0534431i	−0.850185	−	0.526483i	$-0.823510\pi$
$577$	0.741171	−	1.28375i	0.0308554	−	0.0534431i	0.881041	+	0.473040i	$0.156844\pi$
$578$	−10.3548	−	17.9351i	−0.430704	−	0.746000i
$579$	1.10397	+	1.91213i	0.0458794	+	0.0794655i
$580$		0			0
$581$	−32.8796			−1.36407
$582$	0.778298	−	1.34805i	0.0322615	−	0.0558786i
$583$	2.81097	−	4.86873i	0.116418	−	0.201642i
$584$	−1.63179	−	2.82634i	−0.0675240	−	0.116955i
$585$		0			0
$586$	−6.37597	+	11.0435i	−0.263389	+	0.456203i
$587$	−24.4284			−1.00827			−0.504134	−	0.863625i	$-0.668188\pi$
$587$	−24.4284			−1.00827			−0.504134	+	0.863625i	$0.668188\pi$
$588$	−0.496465			−0.0204739
$589$	−4.41164	−	23.4561i	−0.181779	−	0.966492i
$590$		0			0
$591$	0.932671			0.0383650
$592$	−0.00232202	+	0.00402186i	−9.54345e−5	+	0.000165297i
$593$	10.3694			0.425820			0.212910	−	0.977072i	$-0.431706\pi$
$593$	10.3694			0.425820			0.212910	+	0.977072i	$0.431706\pi$
$594$	−0.180951	−	0.313416i	−0.00742451	−	0.0128596i
$595$		0			0
$596$	13.5524	−	23.4734i	0.555128	−	0.961509i
$597$	−1.62237			−0.0663992
$598$	−1.94934	−	3.37636i	−0.0797145	−	0.138070i
$599$	−3.96208	−	6.86253i	−0.161886	−	0.280395i	0.773659	−	0.633602i	$-0.218424\pi$
$599$	−3.96208	−	6.86253i	−0.161886	−	0.280395i	−0.935545	+	0.353207i	$0.885091\pi$
$600$		0			0
$601$	16.5481	−	28.6622i	0.675011	−	1.16915i	−0.301454	−	0.953481i	$-0.597472\pi$
$601$	16.5481	−	28.6622i	0.675011	−	1.16915i	0.976466	−	0.215673i	$-0.0691946\pi$
$602$	11.9752	+	20.7416i	0.488071	+	0.845364i
$603$	−8.09279	+	14.0171i	−0.329564	+	0.570821i
$604$	−11.1461			−0.453528
$605$		0			0
$606$	1.00913	−	1.74786i	0.0409931	−	0.0710021i
$607$	11.1784	+	19.3615i	0.453717	+	0.785860i	0.998613	−	0.0526429i	$-0.0167645\pi$
$607$	11.1784	+	19.3615i	0.453717	+	0.785860i	−0.544897	+	0.838503i	$0.683431\pi$
$608$	12.1538	−	21.0509i	0.492901	−	0.853729i
$609$	0.279800	+	0.484629i	0.0113381	+	0.0196381i
$610$		0			0
$611$	−0.681640	−	1.18063i	−0.0275762	−	0.0477634i
$612$	−23.6884			−0.957548
$613$	−15.0439	+	26.0567i	−0.607615	+	1.05242i	0.384017	+	0.923326i	$0.374540\pi$
$613$	−15.0439	+	26.0567i	−0.607615	+	1.05242i	−0.991632	+	0.129095i	$0.958793\pi$
$614$	−11.5668	+	20.0343i	−0.466799	+	0.808520i
$615$		0			0
$616$	−4.78839			−0.192930
$617$	−19.4438	+	33.6776i	−0.782777	+	1.35581i	0.147541	+	0.989056i	$0.452864\pi$
$617$	−19.4438	+	33.6776i	−0.782777	+	1.35581i	−0.930318	+	0.366753i	$0.880469\pi$
$618$	−0.913390			−0.0367419
$619$	−4.63033			−0.186109			−0.0930543	−	0.995661i	$-0.529663\pi$
$619$	−4.63033			−0.186109			−0.0930543	+	0.995661i	$0.529663\pi$
$620$		0			0
$621$	−2.61078			−0.104767
$622$	−11.2376			−0.450585
$623$	20.2348	−	35.0477i	0.810689	−	1.40415i
$624$	0.00548739			0.000219671
$625$		0			0
$626$	−11.4415	+	19.8173i	−0.457295	+	0.792059i
$627$	−0.149021	+	0.258112i	−0.00595132	+	0.0103080i
$628$	9.10269			0.363237
$629$	0.469245	+	0.812756i	0.0187100	+	0.0324067i
$630$		0			0
$631$	24.9423	+	43.2013i	0.992936	+	1.71982i	0.599224	+	0.800581i	$0.295476\pi$
$631$	24.9423	+	43.2013i	0.992936	+	1.71982i	0.393711	+	0.919234i	$0.371191\pi$
$632$	13.7336	−	23.7872i	0.546292	−	0.946206i
$633$	−0.122341	−	0.211901i	−0.00486261	−	0.00842229i
$634$	8.13311	−	14.0870i	0.323007	−	0.559465i
$635$		0			0
$636$	−1.69914			−0.0673754
$637$	−2.05072	+	3.55195i	−0.0812524	+	0.140733i
$638$	0.315485	+	0.546436i	0.0124902	+	0.0216336i
$639$	−8.60452	+	14.9035i	−0.340389	+	0.589572i
$640$		0			0
$641$	−23.5393	−	40.7712i	−0.929746	−	1.61037i	−0.783745	−	0.621083i	$-0.786693\pi$
$641$	−23.5393	−	40.7712i	−0.929746	−	1.61037i	−0.146001	−	0.989284i	$-0.546640\pi$
$642$	−0.827904	−	1.43397i	−0.0326748	−	0.0565943i
$643$	−5.84458			−0.230488			−0.115244	−	0.993337i	$-0.536765\pi$
$643$	−5.84458			−0.230488			−0.115244	+	0.993337i	$0.536765\pi$
$644$	−6.62048	+	11.4670i	−0.260883	+	0.451863i
$645$		0			0
$646$	−11.9113	−	20.6310i	−0.468645	−	0.811717i
$647$	9.58090			0.376664			0.188332	−	0.982105i	$-0.439692\pi$
$647$	9.58090			0.376664			0.188332	+	0.982105i	$0.439692\pi$
$648$	12.4824	−	21.6202i	0.490355	−	0.849320i
$649$	−0.0154427			−0.000606180
$650$		0			0
$651$	2.16759	+	0.761126i	0.0849544	+	0.0298309i
$652$	−4.03865			−0.158166
$653$	−26.2744			−1.02820			−0.514099	−	0.857731i	$-0.671874\pi$
$653$	−26.2744			−1.02820			−0.514099	+	0.857731i	$0.671874\pi$
$654$	−0.00937313	+	0.0162347i	−0.000366518	+	0.000634828i
$655$		0			0
$656$	−0.127460	−	0.220767i	−0.00497647	−	0.00861951i
$657$	−1.72527	+	2.98825i	−0.0673090	+	0.116583i
$658$	1.40950	−	2.44133i	0.0549481	−	0.0951729i
$659$	−23.5445			−0.917165			−0.458583	−	0.888652i	$-0.651643\pi$
$659$	−23.5445			−0.917165			−0.458583	+	0.888652i	$0.651643\pi$
$660$		0			0
$661$	−15.2692	−	26.4470i	−0.593903	−	1.02867i	−0.993701	−	0.112067i	$-0.964253\pi$
$661$	−15.2692	−	26.4470i	−0.593903	−	1.02867i	0.399797	−	0.916604i	$-0.369080\pi$
$662$	10.0122	+	17.3416i	0.389135	+	0.674001i
$663$	0.554459	−	0.960351i	0.0215334	−	0.0372969i
$664$	14.6157	+	25.3152i	0.567200	+	0.982419i
$665$		0			0
$666$	−0.381289			−0.0147747
$667$	4.55185			0.176248
$668$	−0.950429	+	1.64619i	−0.0367732	+	0.0636931i
$669$	0.858843	+	1.48756i	0.0332048	+	0.0575124i
$670$		0			0
$671$	3.34966	+	5.80178i	0.129312	+	0.223975i
$672$	1.16985	+	2.02624i	0.0451280	+	0.0781639i
$673$	3.46483	+	6.00126i	0.133559	+	0.231331i	0.925046	−	0.379855i	$-0.124026\pi$
$673$	3.46483	+	6.00126i	0.133559	+	0.231331i	−0.791487	+	0.611186i	$0.790693\pi$
$674$	31.0204			1.19486
$675$		0			0
$676$	−6.97218	+	12.0762i	−0.268161	+	0.464468i
$677$	−17.0196	−	29.4789i	−0.654118	−	1.13297i	−0.982114	−	0.188287i	$-0.939707\pi$
$677$	−17.0196	−	29.4789i	−0.654118	−	1.13297i	0.327996	−	0.944679i	$-0.393627\pi$
$678$	−0.671573			−0.0257916
$679$	−21.8371	+	37.8229i	−0.838030	+	1.45151i
$680$		0			0
$681$	−0.161624			−0.00619345
$682$	2.44403	+	0.858197i	0.0935868	+	0.0328621i
$683$	−45.5911			−1.74449			−0.872247	−	0.489066i	$-0.837338\pi$
$683$	−45.5911			−1.74449			−0.872247	+	0.489066i	$0.837338\pi$
$684$	−15.8967			−0.607824
$685$		0			0
$686$	10.8459			0.414099
$687$	0.989547	+	1.71394i	0.0377536	+	0.0653911i
$688$	−0.137100	+	0.237465i	−0.00522690	+	0.00905325i
$689$	−7.01855	+	12.1565i	−0.267385	+	0.463125i
$690$		0			0
$691$	−17.2635	−	29.9012i	−0.656733	−	1.13749i	−0.981456	−	0.191686i	$-0.938605\pi$
$691$	−17.2635	−	29.9012i	−0.656733	−	1.13749i	0.324724	−	0.945809i	$-0.394729\pi$
$692$	−1.77377	−	3.07225i	−0.0674285	−	0.116790i
$693$	2.53134	+	4.38441i	0.0961578	+	0.166550i
$694$	7.38717	−	12.7950i	0.280413	−	0.485690i
$695$		0			0
$696$	0.248755	−	0.430857i	0.00942904	−	0.0163316i
$697$	−51.5154			−1.95128
$698$	15.2011			0.575370
$699$	0.104433	−	0.180884i	0.00395003	−	0.00684165i
$700$		0			0
$701$	−7.50205	+	12.9939i	−0.283349	+	0.490774i	−0.972207	−	0.234121i	$-0.924779\pi$
$701$	−7.50205	+	12.9939i	−0.283349	+	0.490774i	0.688859	+	0.724896i	$0.258112\pi$
$702$	0.451807	+	0.782553i	0.0170524	+	0.0295355i
$703$	0.314898	+	0.545419i	0.0118766	+	0.0205709i
$704$	1.30215	+	2.25538i	0.0490764	+	0.0850029i
$705$		0			0
$706$	−5.21777	+	9.03744i	−0.196373	+	0.340129i
$707$	−28.3136	+	49.0406i	−1.06484	+	1.84436i
$708$	0.00233367	+	0.00404203i	8.77045e−5	+	0.000151909i
$709$	0.373139			0.0140135			0.00700677	−	0.999975i	$-0.497770\pi$
$709$	0.373139			0.0140135			0.00700677	+	0.999975i	$0.497770\pi$
$710$		0			0
$711$	−29.0406			−1.08911
$712$	−35.9793			−1.34838
$713$	14.1773	−	12.1737i	0.530944	−	0.455907i
$714$	2.29303			0.0858145
$715$		0			0
$716$	2.43559	−	4.21857i	0.0910224	−	0.157655i
$717$	−2.69565			−0.100671
$718$	−10.9460	−	18.9591i	−0.408503	−	0.707548i
$719$	−15.2527	+	26.4185i	−0.568831	+	0.985244i	0.427851	+	0.903849i	$0.359271\pi$
$719$	−15.2527	+	26.4185i	−0.568831	+	0.985244i	−0.996682	+	0.0813944i	$0.974063\pi$
$720$		0			0
$721$	25.6274			0.954415
$722$	0.271491	+	0.470237i	0.0101039	+	0.0175004i
$723$	0.967291	+	1.67540i	0.0359740	+	0.0623087i
$724$	−11.3161	−	19.6001i	−0.420561	−	0.728433i
$725$		0			0
$726$	0.605935	+	1.04951i	0.0224884	+	0.0389510i
$727$	−7.70859	+	13.3517i	−0.285896	+	0.495186i	−0.972826	−	0.231537i	$-0.925624\pi$
$727$	−7.70859	+	13.3517i	−0.285896	+	0.495186i	0.686930	+	0.726723i	$0.258958\pi$
$728$	11.9559			0.443114
$729$	−26.0915			−0.966351
$730$		0			0
$731$	27.7059	+	47.9879i	1.02474	+	1.77490i
$732$	1.01238	−	1.75350i	0.0374188	−	0.0648112i
$733$	3.31494	+	5.74164i	0.122440	+	0.212072i	0.920729	−	0.390202i	$-0.127595\pi$
$733$	3.31494	+	5.74164i	0.122440	+	0.212072i	−0.798289	+	0.602274i	$0.794261\pi$
$734$	−5.18967	−	8.98877i	−0.191554	−	0.331782i
$735$		0			0
$736$	19.0313			0.701505
$737$	−1.45075	+	2.51277i	−0.0534391	+	0.0925592i
$738$	10.4648	−	18.1256i	0.385216	−	0.667213i
$739$	10.5788	+	18.3231i	0.389149	+	0.674026i	0.992335	−	0.123574i	$-0.0394357\pi$
$739$	10.5788	+	18.3231i	0.389149	+	0.674026i	−0.603186	+	0.797600i	$0.706102\pi$
$740$		0			0
$741$	0.372082	−	0.644465i	0.0136688	−	0.0236750i
$742$	−29.0260			−1.06558
$743$	52.4521			1.92428			0.962140	−	0.272556i	$-0.0878689\pi$
$743$	52.4521			1.92428			0.962140	+	0.272556i	$0.0878689\pi$
$744$	−0.377523	−	2.00724i	−0.0138407	−	0.0735890i
$745$		0			0
$746$	−8.01006			−0.293269
$747$	15.4530	−	26.7653i	0.565394	−	0.979291i
$748$	−4.24650			−0.155267
$749$	23.2289	+	40.2336i	0.848765	+	1.47010i
$750$		0			0
$751$	−20.3114	+	35.1804i	−0.741174	+	1.28375i	0.210787	+	0.977532i	$0.432397\pi$
$751$	−20.3114	+	35.1804i	−0.741174	+	1.28375i	−0.951961	+	0.306219i	$0.900936\pi$
$752$	0.0322740			0.00117691
$753$	−0.242805	−	0.420550i	−0.00884829	−	0.0153257i
$754$	−0.787718	−	1.36437i	−0.0286870	−	0.0496873i
$755$		0			0
$756$	1.53445	−	2.65775i	0.0558076	−	0.0966616i
$757$	−12.1443	−	21.0345i	−0.441391	−	0.764512i	0.556402	−	0.830913i	$-0.312181\pi$
$757$	−12.1443	−	21.0345i	−0.441391	−	0.764512i	−0.997793	+	0.0664017i	$0.978848\pi$
$758$	−1.98912	+	3.44527i	−0.0722483	+	0.125138i
$759$	−0.233349			−0.00847002
$760$		0			0
$761$	−5.24537	+	9.08525i	−0.190145	+	0.329340i	−0.945298	−	0.326208i	$-0.894229\pi$
$761$	−5.24537	+	9.08525i	−0.190145	+	0.329340i	0.755153	+	0.655548i	$0.227562\pi$
$762$	−1.04947	−	1.81773i	−0.0380183	−	0.0658496i
$763$	0.262986	−	0.455506i	0.00952074	−	0.0164904i
$764$	10.6731	+	18.4863i	0.386139	+	0.668813i
$765$		0			0
$766$	−5.36203	−	9.28731i	−0.193738	−	0.335564i
$767$	0.0385581			0.00139225
$768$	1.03494	−	1.79257i	0.0373452	−	0.0646838i
$769$	19.2155	−	33.2823i	0.692930	−	1.20019i	−0.277944	−	0.960597i	$-0.589653\pi$
$769$	19.2155	−	33.2823i	0.692930	−	1.20019i	0.970874	−	0.239592i	$-0.0770137\pi$
$770$		0			0
$771$	−0.614887			−0.0221446
$772$	−10.5555	+	18.2827i	−0.379902	+	0.658010i
$773$	−29.3184			−1.05451			−0.527255	−	0.849707i	$-0.676779\pi$
$773$	−29.3184			−1.05451			−0.527255	+	0.849707i	$0.676779\pi$
$774$	−22.5126			−0.809200
$775$		0			0
$776$	38.8283			1.39386
$777$	−0.0606204			−0.00217474
$778$	2.82326	−	4.89003i	0.101219	−	0.175316i
$779$	−34.5706			−1.23862
$780$		0			0
$781$	−1.54248	+	2.67166i	−0.0551944	+	0.0955996i
$782$	9.32586	−	16.1529i	0.333492	−	0.577625i
$783$	−1.05500			−0.0377026
$784$	−0.0485482	−	0.0840880i	−0.00173386	−	0.00300314i
$785$		0			0
$786$	0.928050	+	1.60743i	0.0331024	+	0.0573351i
$787$	−0.184146	+	0.318951i	−0.00656411	+	0.0113694i	−0.869289	−	0.494305i	$-0.835423\pi$
$787$	−0.184146	+	0.318951i	−0.00656411	+	0.0113694i	0.862725	+	0.505674i	$0.168756\pi$
$788$	4.45884	+	7.72294i	0.158840	+	0.275118i
$789$	−0.493015	+	0.853928i	−0.0175518	+	0.0304006i
$790$		0			0
$791$	18.8427			0.669968
$792$	2.25048	−	3.89794i	0.0799673	−	0.138507i
$793$	−8.36359	−	14.4862i	−0.297000	−	0.514419i
$794$	−11.3712	+	19.6955i	−0.403550	+	0.698968i
$795$		0			0
$796$	−7.75610	−	13.4340i	−0.274908	−	0.476154i
$797$	15.7756	+	27.3241i	0.558800	+	0.967871i	0.997597	+	0.0692843i	$0.0220716\pi$
$797$	15.7756	+	27.3241i	0.558800	+	0.967871i	−0.438796	+	0.898586i	$0.644595\pi$
$798$	1.53879			0.0544726
$799$	3.26104	−	5.64828i	0.115367	−	0.199822i
$800$		0			0
$801$	19.0201	+	32.9438i	0.672044	+	1.16401i
$802$	−3.99050			−0.140909
$803$	−0.309279	+	0.535687i	−0.0109142	+	0.0189040i
$804$	0.876934			0.0309271
$805$		0			0
$806$	−6.10237	−	2.14279i	−0.214947	−	0.0754764i
$807$	−1.80046			−0.0633791
$808$	50.3442			1.77110
$809$	−7.86117	+	13.6159i	−0.276384	+	0.478711i	−0.970483	−	0.241168i	$-0.922469\pi$
$809$	−7.86117	+	13.6159i	−0.276384	+	0.478711i	0.694099	+	0.719879i	$0.255803\pi$
$810$		0			0
$811$	10.4033	+	18.0191i	0.365311	+	0.632737i	0.988826	−	0.149074i	$-0.0476294\pi$
$811$	10.4033	+	18.0191i	0.365311	+	0.632737i	−0.623515	+	0.781811i	$0.714296\pi$
$812$	−2.67530	+	4.63375i	−0.0938845	+	0.162613i
$813$	1.38333	−	2.39599i	0.0485153	−	0.0840310i
$814$	−0.0683517			−0.00239572
$815$		0			0
$816$	0.0131261	+	0.0227351i	0.000459506	+	0.000795889i
$817$	18.5926	+	32.2034i	0.650474	+	1.12665i
$818$	10.4547	−	18.1081i	0.365541	−	0.633136i
$819$	−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	$0.642783\pi$
$822$	−0.520237			−0.0181453
$823$	−12.1377	+	21.0231i	−0.423093	+	0.732819i	−0.996240	−	0.0866336i	$-0.972389\pi$
$823$	−12.1377	+	21.0231i	−0.423093	+	0.732819i	0.573147	+	0.819453i	$0.305722\pi$
$824$	−11.3920	−	19.7315i	−0.396858	−	0.687378i
$825$		0			0
$826$	0.0398654	+	0.0690490i	0.00138710	+	0.00240252i
$827$	24.7898	+	42.9371i	0.862025	+	1.49307i	0.869971	+	0.493102i	$0.164137\pi$
$827$	24.7898	+	42.9371i	0.862025	+	1.49307i	−0.00794639	+	0.999968i	$0.502529\pi$
$828$	−6.22307	−	10.7787i	−0.216267	−	0.374585i
$829$	33.8998			1.17739			0.588694	−	0.808356i	$-0.299642\pi$
$829$	33.8998			1.17739			0.588694	+	0.808356i	$0.299642\pi$
$830$		0			0
$831$	−1.89017	+	3.27387i	−0.0655692	+	0.113569i
$832$	−3.25126	−	5.63134i	−0.112717	−	0.195232i
$833$	−19.6217			−0.679852
$834$	1.24394	−	2.15456i	0.0430741	−	0.0746065i
$835$		0			0
$836$	−2.84971			−0.0985592
$837$	−3.28593	+	2.82154i	−0.113578	+	0.0975267i
$838$	−14.7805			−0.510585
$839$	−19.6413			−0.678092			−0.339046	−	0.940770i	$-0.610104\pi$
$839$	−19.6413			−0.678092			−0.339046	+	0.940770i	$0.610104\pi$
$840$		0			0
$841$	−27.1606			−0.936573
$842$	3.36834	+	5.83414i	0.116081	+	0.201058i
$843$	−0.284041	+	0.491974i	−0.00978291	+	0.0169445i
$844$	1.16976	−	2.02608i	0.0402646	−	0.0697404i
$845$		0			0
$846$	1.32489	+	2.29478i	0.0455508	+	0.0788962i
$847$	−17.0010	−	29.4466i	−0.584162	−	1.01180i
$848$	−0.166156	−	0.287790i	−0.00570580	−	0.00988274i
$849$	−1.10014	+	1.90550i	−0.0377567	+	0.0653965i
$850$		0			0
$851$	−0.246546	+	0.427030i	−0.00845148	+	0.0146384i
$852$	0.932385			0.0319430
$853$	−8.69028			−0.297550			−0.148775	−	0.988871i	$-0.547533\pi$
$853$	−8.69028			−0.297550			−0.148775	+	0.988871i	$0.547533\pi$
$854$	17.2943	−	29.9546i	0.591799	−	1.02503i
$855$		0			0
$856$	20.6515	−	35.7695i	0.705855	−	1.22258i
$857$	17.8268	+	30.8770i	0.608953	+	1.05474i	0.991413	+	0.130765i	$0.0417435\pi$
$857$	17.8268	+	30.8770i	0.608953	+	1.05474i	−0.382460	+	0.923972i	$0.624923\pi$
$858$	0.0403821	+	0.0699438i	0.00137862	+	0.00238784i
$859$	15.7067	+	27.2048i	0.535905	+	0.928214i	0.999119	+	0.0419680i	$0.0133628\pi$
$859$	15.7067	+	27.2048i	0.535905	+	0.928214i	−0.463214	+	0.886246i	$0.653304\pi$
$860$		0			0
$861$	1.66378	−	2.88175i	0.0567015	−	0.0982098i
$862$	−14.6111	+	25.3072i	−0.497658	+	0.861968i
$863$	1.08345	+	1.87660i	0.0368812	+	0.0638801i	0.883877	−	0.467720i	$-0.154924\pi$
$863$	1.08345	+	1.87660i	0.0368812	+	0.0638801i	−0.846996	+	0.531600i	$0.821591\pi$
$864$	−4.41097			−0.150064
$865$		0			0
$866$	0.272716			0.00926727
$867$	3.09494			0.105110
$868$	4.06016	+	21.5873i	0.137811	+	0.732722i
$869$	−5.20594			−0.176600
$870$		0			0
$871$	3.62230	−	6.27401i	0.122737	−	0.212587i
$872$	−0.467613			−0.0158354
$873$	−20.5263	−	35.5525i	−0.694709	−	1.20327i
$874$	6.25833	−	10.8397i	0.211691	−	0.366660i
$875$		0			0
$876$	0.186950			0.00631644
$877$	−11.7336	−	20.3231i	−0.396215	−	0.686264i	0.597041	−	0.802211i	$-0.296343\pi$
$877$	−11.7336	−	20.3231i	−0.396215	−	0.686264i	−0.993255	+	0.115947i	$0.963010\pi$
$878$	14.9620	+	25.9150i	0.504944	+	0.874589i
$879$	−0.952853	−	1.65039i	−0.0321389	−	0.0556662i
$880$		0			0
$881$	15.1116	+	26.1741i	0.509123	+	0.881827i	0.999944	+	0.0105663i	$0.00336343\pi$
$881$	15.1116	+	26.1741i	0.509123	+	0.881827i	−0.490821	+	0.871260i	$0.663303\pi$
$882$	3.98595	−	6.90386i	0.134214	−	0.232465i
$883$	26.1830			0.881128			0.440564	−	0.897721i	$-0.354779\pi$
$883$	26.1830			0.881128			0.440564	+	0.897721i	$0.354779\pi$
$884$	10.6029			0.356613
$885$		0			0
$886$	−12.0104	−	20.8026i	−0.403496	−	0.698876i
$887$	−7.72193	+	13.3748i	−0.259277	+	0.449081i	−0.966048	−	0.258361i	$-0.916818\pi$
$887$	−7.72193	+	13.3748i	−0.259277	+	0.449081i	0.706771	+	0.707442i	$0.250151\pi$
$888$	0.0269471	+	0.0466738i	0.000904286	+	0.00156627i
$889$	29.4455	+	51.0010i	0.987569	+	1.71052i
$890$		0			0
$891$	−4.73167			−0.158517
$892$	−8.21178	+	14.2232i	−0.274951	+	0.476229i
$893$	2.18839	−	3.79041i	0.0732318	−	0.126841i
$894$	−1.23312	−	2.13582i	−0.0412416	−	0.0714326i
$895$		0			0
$896$	−11.2727	+	19.5249i	−0.376596	+	0.652283i
$897$	0.582636			0.0194536
$898$	−7.39553			−0.246792
$899$	5.72896	−	4.91931i	0.191072	−	0.164068i
$900$		0			0
$901$	−67.1550			−2.23726
$902$	1.87597	−	3.24928i	0.0624631	−	0.108189i
$903$	−3.57924			−0.119110
$904$	−8.37598	−	14.5076i	−0.278581	−	0.482517i
$905$		0			0
$906$	−0.507086	+	0.878298i	−0.0168468	+	0.0291795i
$907$	−31.5594			−1.04791			−0.523956	−	0.851746i	$-0.675544\pi$
$907$	−31.5594			−1.04791			−0.523956	+	0.851746i	$0.675544\pi$
$908$	−0.772680	−	1.33832i	−0.0256423	−	0.0444137i
$909$	−26.6140	−	46.0968i	−0.882731	−	1.52894i
$910$		0			0
$911$	21.0506	−	36.4608i	0.697438	−	1.20800i	−0.271913	−	0.962322i	$-0.587656\pi$
$911$	21.0506	−	36.4608i	0.697438	−	1.20800i	0.969352	−	0.245677i	$-0.0790103\pi$
$912$	0.00880859	+	0.0152569i	0.000291681	+	0.000505207i
$913$	2.77017	−	4.79807i	0.0916791	−	0.158793i
$914$	19.9471			0.659792
$915$		0			0
$916$	−9.46149	+	16.3878i	−0.312617	+	0.541468i
$917$	−26.0387	−	45.1004i	−0.859875	−	1.48935i
$918$	−2.16149	+	3.74382i	−0.0713399	+	0.123564i
$919$	−18.3891	−	31.8509i	−0.606601	−	1.05066i	−0.991796	−	0.127829i	$-0.959199\pi$
$919$	−18.3891	−	31.8509i	−0.606601	−	1.05066i	0.385195	−	0.922835i	$-0.374134\pi$
$920$		0			0
$921$	−1.72860	−	2.99402i	−0.0569592	−	0.0986562i
$922$	8.83865			0.291085
$923$	3.85135	−	6.67073i	0.126769	−	0.219570i
$924$	0.137148	−	0.237547i	0.00451184	−	0.00781474i
$925$		0			0
$926$	−21.9755			−0.722158
$927$	−12.0445	+	20.8618i	−0.395595	+	0.685190i
$928$	7.69046			0.252452
$929$	7.61636			0.249885			0.124942	−	0.992164i	$-0.460125\pi$
$929$	7.61636			0.249885			0.124942	+	0.992164i	$0.460125\pi$
$930$		0			0
$931$	−13.1676			−0.431550
$932$	1.99707			0.0654161
$933$	0.839694	−	1.45439i	0.0274903	−	0.0476147i
$934$	−27.8631			−0.911707
$935$		0			0
$936$	−5.61910	+	9.73256i	−0.183666	+	0.318119i
$937$	23.0654	−	39.9504i	0.753513	−	1.30512i	−0.192597	−	0.981278i	$-0.561691\pi$
$937$	23.0654	−	39.9504i	0.753513	−	1.30512i	0.946110	−	0.323845i	$-0.104976\pi$
$938$	14.9804			0.489129
$939$	−1.70987	−	2.96158i	−0.0557995	−	0.0966476i
$940$		0			0
$941$	8.86885	+	15.3613i	0.289116	+	0.500764i	0.973599	−	0.228265i	$-0.0733053\pi$
$941$	8.86885	+	15.3613i	0.289116	+	0.500764i	−0.684483	+	0.729029i	$0.739972\pi$
$942$	0.414122	−	0.717281i	0.0134928	−	0.0233703i
$943$	−13.5333	−	23.4404i	−0.440706	−	0.763326i
$944$	−0.000456408	0	0.000790522i	−1.48548e−5	0	2.57293e-5i
$945$		0			0
$946$	−4.03572			−0.131213
$947$	13.2758	−	22.9943i	0.431405	−	0.747216i	−0.565589	−	0.824687i	$-0.691351\pi$
$947$	13.2758	−	22.9943i	0.431405	−	0.747216i	0.996995	+	0.0774712i	$0.0246846\pi$
$948$	0.786709	+	1.36262i	0.0255511	+	0.0442558i
$949$	0.772222	−	1.33753i	0.0250674	−	0.0434180i
$950$		0			0
$951$	1.21545	+	2.10522i	0.0394136	+	0.0682663i
$952$	28.5991	+	49.5351i	0.926902	+	1.60544i
$953$	0.448226			0.0145195			0.00725974	−	0.999974i	$-0.497689\pi$
$953$	0.448226			0.0145195			0.00725974	+	0.999974i	$0.497689\pi$
$954$	13.6418	−	23.6284i	0.441671	−	0.764997i
$955$		0			0
$956$	−12.8872	−	22.3212i	−0.416800	−	0.721920i
$957$	−0.0942949			−0.00304812
$958$	5.63431	−	9.75892i	0.182036	−	0.315296i
$959$	14.5965			0.471346
$960$		0			0
$961$	4.68716	−	30.6436i	0.151199	−	0.988503i
$962$	0.170664			0.00550242
$963$	−43.6691			−1.40722
$964$	−9.24870	+	16.0192i	−0.297881	+	0.515944i
$965$		0			0
$966$	0.602390	+	1.04337i	0.0193816	+	0.0335699i
$967$	17.0189	−	29.4776i	0.547291	−	0.947937i	−0.451167	−	0.892439i	$-0.648992\pi$
$967$	17.0189	−	29.4776i	0.547291	−	0.947937i	0.998459	−	0.0554973i	$-0.0176744\pi$
$968$	−15.1147	+	26.1794i	−0.485804	+	0.841437i
$969$	3.56016			0.114369
$970$		0			0
$971$	8.99114	+	15.5731i	0.288539	+	0.499765i	0.973461	−	0.228852i	$-0.0734971\pi$
$971$	8.99114	+	15.5731i	0.288539	+	0.499765i	−0.684922	+	0.728616i	$0.740164\pi$
$972$	2.16556	+	3.75085i	0.0694602	+	0.120309i
$973$	−34.9018	+	60.4516i	−1.11890	+	1.93799i
$974$	11.7629	+	20.3739i	0.376908	+	0.652823i
$975$		0			0
$976$	0.395995			0.0126755
$977$	−24.3612			−0.779383			−0.389691	−	0.920946i	$-0.627418\pi$
$977$	−24.3612			−0.779383			−0.389691	+	0.920946i	$0.627418\pi$
$978$	−0.183736	+	0.318241i	−0.00587524	+	0.0101762i
$979$	3.40964	+	5.90566i	0.108972	+	0.188746i
$980$		0			0
$981$	0.247200	+	0.428163i	0.00789249	+	0.0136702i
$982$	4.91297	+	8.50951i	0.156779	+	0.271549i
$983$	16.3738	+	28.3603i	0.522244	+	0.904553i	0.999665	+	0.0258783i	$0.00823825\pi$
$983$	16.3738	+	28.3603i	0.522244	+	0.904553i	−0.477421	+	0.878675i	$0.658428\pi$
$984$	−2.95835			−0.0943088
$985$		0			0
$986$	3.76853	−	6.52728i	0.120014	−	0.207871i
$987$	0.210642	+	0.364842i	0.00670481	+	0.0116131i
$988$	7.11529			0.226367
$989$	−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	$0.555583\pi$
$992$	23.9529	−	20.5677i	0.760505	−	0.653025i
$993$	−2.99253			−0.0949650
$994$	15.9277			0.505196
$995$		0			0
$996$	−1.67448			−0.0530580
$997$	12.8572	+	22.2694i	0.407193	+	0.705279i	0.994574	−	0.104032i	$-0.0331744\pi$
$997$	12.8572	+	22.2694i	0.407193	+	0.705279i	−0.587381	+	0.809310i	$0.699841\pi$
$998$	−7.29420	+	12.6339i	−0.230894	+	0.399920i
$999$	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.e.g.501.3		8
5.2	odd	4		775.2.o.e.749.6		16
5.3	odd	4		775.2.o.e.749.3		16
5.4	even	2		155.2.e.c.36.2	✓	8
31.25	even	3	inner	775.2.e.g.676.3		8
155.87	odd	12		775.2.o.e.149.6		16
155.118	odd	12		775.2.o.e.149.3		16
155.119	odd	6		4805.2.a.k.1.2		4
155.129	even	6		4805.2.a.i.1.2		4
155.149	even	6		155.2.e.c.56.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.e.c.36.2	✓	8	5.4	even	2
155.2.e.c.56.2	yes	8	155.149	even	6
775.2.e.g.501.3		8	1.1	even	1	trivial
775.2.e.g.676.3		8	31.25	even	3	inner
775.2.o.e.149.3		16	155.118	odd	12
775.2.o.e.149.6		16	155.87	odd	12
775.2.o.e.749.3		16	5.3	odd	4
775.2.o.e.749.6		16	5.2	odd	4
4805.2.a.i.1.2		4	155.129	even	6
4805.2.a.k.1.2		4	155.119	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.869986 q^{2} +(-0.0650072 + 0.112596i) q^{3} -1.24312 q^{4} +(-0.0565553 + 0.0979567i) q^{6} +(1.58680 - 2.74842i) q^{7} -2.82147 q^{8} +(1.49155 + 2.58344i) q^{9} +O(q^{10})\)	\(q+0.869986 q^{2} +(-0.0650072 + 0.112596i) q^{3} -1.24312 q^{4} +(-0.0565553 + 0.0979567i) q^{6} +(1.58680 - 2.74842i) q^{7} -2.82147 q^{8} +(1.49155 + 2.58344i) q^{9} +(0.267382 + 0.463119i) q^{11} +(0.0808121 - 0.139971i) q^{12} +(-0.667611 - 1.15634i) q^{13} +(1.38049 - 2.39108i) q^{14} +0.0316097 q^{16} +(3.19392 - 5.53204i) q^{17} +(1.29763 + 2.24755i) q^{18} +(2.14335 - 3.71240i) q^{19} +(0.206307 + 0.357334i) q^{21} +(0.232618 + 0.402907i) q^{22} +3.35624 q^{23} +(0.183416 - 0.317686i) q^{24} +(-0.580812 - 1.00600i) q^{26} -0.777888 q^{27} +(-1.97259 + 3.41663i) q^{28} +1.35624 q^{29} +(4.22417 - 3.62718i) q^{31} +5.67044 q^{32} -0.0695269 q^{33} +(2.77867 - 4.81279i) q^{34} +(-1.85418 - 3.21154i) q^{36} +(-0.0734590 + 0.127235i) q^{37} +(1.86469 - 3.22973i) q^{38} +0.173598 q^{39} +(-4.03230 - 6.98415i) q^{41} +(0.179484 + 0.310875i) q^{42} +(-4.33728 + 7.51238i) q^{43} +(-0.332389 - 0.575714i) q^{44} +2.91988 q^{46} +1.02101 q^{47} +(-0.00205486 + 0.00355912i) q^{48} +(-1.53586 - 2.66019i) q^{49} +(0.415256 + 0.719244i) q^{51} +(0.829924 + 1.43747i) q^{52} +(-5.25646 - 9.10446i) q^{53} -0.676752 q^{54} +(-4.47711 + 7.75458i) q^{56} +(0.278667 + 0.482665i) q^{57} +1.17991 q^{58} +(-0.0144388 + 0.0250088i) q^{59} +12.5276 q^{61} +(3.67496 - 3.15559i) q^{62} +9.46715 q^{63} +4.86999 q^{64} -0.0604874 q^{66} +(2.71288 + 4.69885i) q^{67} +(-3.97045 + 6.87701i) q^{68} +(-0.218179 + 0.377898i) q^{69} +(2.88442 + 4.99597i) q^{71} +(-4.20836 - 7.28910i) q^{72} +(0.578347 + 1.00173i) q^{73} +(-0.0639083 + 0.110692i) q^{74} +(-2.66446 + 4.61498i) q^{76} +1.69712 q^{77} +0.151028 q^{78} +(-4.86752 + 8.43079i) q^{79} +(-4.42408 + 7.66272i) q^{81} +(-3.50804 - 6.07611i) q^{82} +(-5.18017 - 8.97232i) q^{83} +(-0.256465 - 0.444210i) q^{84} +(-3.77337 + 6.53567i) q^{86} +(-0.0881651 + 0.152706i) q^{87} +(-0.754410 - 1.30668i) q^{88} +12.7519 q^{89} -4.23746 q^{91} -4.17222 q^{92} +(0.133804 + 0.711416i) q^{93} +0.888267 q^{94} +(-0.368620 + 0.638468i) q^{96} -13.7617 q^{97} +(-1.33618 - 2.31433i) q^{98} +(-0.797625 + 1.38153i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 10 q^{6} + q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 10 * q^6 + q^7 + 18 * q^8 - q^9	\( 8 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 10 q^{6} + q^{7} + 18 q^{8} - q^{9} + 4 q^{11} + 8 q^{12} - q^{13} - 8 q^{14} + 10 q^{16} + 12 q^{17} + 11 q^{18} - 5 q^{19} + 9 q^{21} - 10 q^{23} + 2 q^{24} - 12 q^{26} + 6 q^{27} - 4 q^{28} - 26 q^{29} + 19 q^{31} + 28 q^{32} - 8 q^{33} + 24 q^{34} - 5 q^{36} - 16 q^{37} - 9 q^{38} - 22 q^{39} - 4 q^{41} - 6 q^{42} + q^{43} - 7 q^{44} - 22 q^{46} - 20 q^{47} + 27 q^{48} - 37 q^{49} - 12 q^{51} - 21 q^{52} + q^{53} + 24 q^{54} - 29 q^{56} + 4 q^{57} - 26 q^{58} + 6 q^{59} - 2 q^{61} + 17 q^{62} - 24 q^{63} + 34 q^{64} + 2 q^{66} + 7 q^{67} + 5 q^{68} - 6 q^{69} + 12 q^{71} - 14 q^{72} - 20 q^{73} + 18 q^{74} - 23 q^{76} - 58 q^{77} - 22 q^{78} - 2 q^{79} + 12 q^{81} + 18 q^{82} + 4 q^{83} + 41 q^{84} - 13 q^{86} + 10 q^{88} + 54 q^{89} - 44 q^{91} - 86 q^{92} - 55 q^{93} - 48 q^{94} + 13 q^{96} + 18 q^{97} + 46 q^{98} - 7 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 10 * q^6 + q^7 + 18 * q^8 - q^9 + 4 * q^11 + 8 * q^12 - q^13 - 8 * q^14 + 10 * q^16 + 12 * q^17 + 11 * q^18 - 5 * q^19 + 9 * q^21 - 10 * q^23 + 2 * q^24 - 12 * q^26 + 6 * q^27 - 4 * q^28 - 26 * q^29 + 19 * q^31 + 28 * q^32 - 8 * q^33 + 24 * q^34 - 5 * q^36 - 16 * q^37 - 9 * q^38 - 22 * q^39 - 4 * q^41 - 6 * q^42 + q^43 - 7 * q^44 - 22 * q^46 - 20 * q^47 + 27 * q^48 - 37 * q^49 - 12 * q^51 - 21 * q^52 + q^53 + 24 * q^54 - 29 * q^56 + 4 * q^57 - 26 * q^58 + 6 * q^59 - 2 * q^61 + 17 * q^62 - 24 * q^63 + 34 * q^64 + 2 * q^66 + 7 * q^67 + 5 * q^68 - 6 * q^69 + 12 * q^71 - 14 * q^72 - 20 * q^73 + 18 * q^74 - 23 * q^76 - 58 * q^77 - 22 * q^78 - 2 * q^79 + 12 * q^81 + 18 * q^82 + 4 * q^83 + 41 * q^84 - 13 * q^86 + 10 * q^88 + 54 * q^89 - 44 * q^91 - 86 * q^92 - 55 * q^93 - 48 * q^94 + 13 * q^96 + 18 * q^97 + 46 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

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