LMFDB - Embedded newform 325.2.m.c.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(49,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("325.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.m (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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.4
Root			$1.20036 - 0.747754i$ of defining polynomial
Character	$\chi$	$=$	325.199
Dual form			325.2.m.c.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24775 - 2.16117i) q^{2} +(-2.44811 - 1.41342i) q^{3} +(-2.11378 - 3.66117i) q^{4} +(-6.10929 + 3.52720i) q^{6} +(-0.952606 - 1.64996i) q^{7} -5.55889 q^{8} +(2.49551 + 4.32235i) q^{9} +O(q^{10})$	\(q+(1.24775 - 2.16117i) q^{2} +(-2.44811 - 1.41342i) q^{3} +(-2.11378 - 3.66117i) q^{4} +(-6.10929 + 3.52720i) q^{6} +(-0.952606 - 1.64996i) q^{7} -5.55889 q^{8} +(2.49551 + 4.32235i) q^{9} +(0.926118 + 0.534695i) q^{11} +11.9506i q^{12} +(3.32235 - 1.40072i) q^{13} -4.75447 q^{14} +(-2.70857 + 4.69138i) q^{16} +(-0.551886 + 0.318632i) q^{17} +12.4551 q^{18} +(-4.96410 + 2.86603i) q^{19} +5.38573i q^{21} +(2.31114 - 1.33433i) q^{22} +(-3.30636 - 1.90893i) q^{23} +(13.6088 + 7.85704i) q^{24} +(1.11827 - 8.92792i) q^{26} -5.62828i q^{27} +(-4.02720 + 6.97531i) q^{28} +(4.72756 - 8.18837i) q^{29} -1.46410i q^{31} +(1.20036 + 2.07908i) q^{32} +(-1.51150 - 2.61799i) q^{33} +1.59030i q^{34} +(10.5499 - 18.2730i) q^{36} +(-0.378725 + 0.655970i) q^{37} +14.3044i q^{38} +(-10.1133 - 1.26675i) q^{39} +(-0.232051 - 0.133975i) q^{41} +(11.6395 + 6.72006i) q^{42} +(0.551886 - 0.318632i) q^{43} -4.52091i q^{44} +(-8.25104 + 4.76374i) q^{46} -9.44613 q^{47} +(13.2618 - 7.65668i) q^{48} +(1.68508 - 2.91865i) q^{49} +1.80144 q^{51} +(-12.1510 - 9.20287i) q^{52} +6.99102i q^{53} +(-12.1637 - 7.02271i) q^{54} +(5.29543 + 9.17196i) q^{56} +16.2036 q^{57} +(-11.7977 - 20.4341i) q^{58} +(0.641756 - 0.370518i) q^{59} +(-2.09928 - 3.63606i) q^{61} +(-3.16418 - 1.82684i) q^{62} +(4.75447 - 8.23499i) q^{63} -4.84325 q^{64} -7.54390 q^{66} +(4.04739 - 7.01029i) q^{67} +(2.33313 + 1.34703i) q^{68} +(5.39623 + 9.34654i) q^{69} +(8.45663 - 4.88244i) q^{71} +(-13.8723 - 24.0274i) q^{72} +3.71649 q^{73} +(0.945110 + 1.63698i) q^{74} +(20.9860 + 12.1163i) q^{76} -2.03741i q^{77} +(-15.3565 + 20.2760i) q^{78} +9.31937 q^{79} +(-0.468594 + 0.811629i) q^{81} +(-0.579085 + 0.334335i) q^{82} +5.11778 q^{83} +(19.7181 - 11.3842i) q^{84} -1.59030i q^{86} +(-23.1472 + 13.3640i) q^{87} +(-5.14819 - 2.97231i) q^{88} +(10.8932 + 6.28917i) q^{89} +(-5.47602 - 4.14741i) q^{91} +16.1402i q^{92} +(-2.06939 + 3.58429i) q^{93} +(-11.7864 + 20.4147i) q^{94} -6.78645i q^{96} +(-2.11078 - 3.65597i) q^{97} +(-4.20514 - 7.28351i) q^{98} +5.33734i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 6 q^{3} - 2 q^{4} - 18 q^{6} - 10 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 6 * q^3 - 2 * q^4 - 18 * q^6 - 10 * q^7 - 12 * q^8 + 4 * q^9	$ 8 q + 2 q^{2} - 6 q^{3} - 2 q^{4} - 18 q^{6} - 10 q^{7} - 12 q^{8} + 4 q^{9} - 8 q^{13} - 4 q^{14} - 2 q^{16} - 18 q^{17} + 40 q^{18} - 12 q^{19} - 6 q^{22} - 6 q^{23} + 12 q^{24} + 10 q^{26} - 8 q^{28} + 8 q^{29} + 4 q^{32} + 18 q^{33} + 20 q^{36} + 2 q^{37} + 12 q^{41} + 42 q^{42} + 18 q^{43} - 42 q^{46} + 16 q^{47} + 6 q^{48} - 12 q^{49} - 8 q^{51} - 16 q^{52} - 18 q^{54} + 12 q^{56} + 28 q^{57} - 22 q^{58} + 12 q^{59} - 28 q^{61} - 12 q^{62} + 4 q^{63} + 8 q^{64} + 12 q^{66} + 30 q^{67} - 12 q^{68} + 16 q^{69} - 12 q^{72} + 16 q^{73} - 10 q^{74} + 54 q^{76} - 18 q^{78} + 16 q^{79} + 8 q^{81} + 6 q^{82} - 24 q^{83} + 30 q^{84} - 54 q^{87} - 42 q^{88} - 24 q^{89} + 28 q^{91} - 8 q^{93} - 32 q^{94} + 2 q^{97} - 24 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 6 * q^3 - 2 * q^4 - 18 * q^6 - 10 * q^7 - 12 * q^8 + 4 * q^9 - 8 * q^13 - 4 * q^14 - 2 * q^16 - 18 * q^17 + 40 * q^18 - 12 * q^19 - 6 * q^22 - 6 * q^23 + 12 * q^24 + 10 * q^26 - 8 * q^28 + 8 * q^29 + 4 * q^32 + 18 * q^33 + 20 * q^36 + 2 * q^37 + 12 * q^41 + 42 * q^42 + 18 * q^43 - 42 * q^46 + 16 * q^47 + 6 * q^48 - 12 * q^49 - 8 * q^51 - 16 * q^52 - 18 * q^54 + 12 * q^56 + 28 * q^57 - 22 * q^58 + 12 * q^59 - 28 * q^61 - 12 * q^62 + 4 * q^63 + 8 * q^64 + 12 * q^66 + 30 * q^67 - 12 * q^68 + 16 * q^69 - 12 * q^72 + 16 * q^73 - 10 * q^74 + 54 * q^76 - 18 * q^78 + 16 * q^79 + 8 * q^81 + 6 * q^82 - 24 * q^83 + 30 * q^84 - 54 * q^87 - 42 * q^88 - 24 * q^89 + 28 * q^91 - 8 * q^93 - 32 * q^94 + 2 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.24775	−	2.16117i	0.882295	−	1.52818i	0.0335125	−	0.999438i	$-0.489331\pi$
$2$	1.24775	−	2.16117i	0.882295	−	1.52818i	0.848783	−	0.528742i	$-0.177336\pi$
$3$	−2.44811	−	1.41342i	−1.41342	−	0.816038i	−0.417710	−	0.908580i	$-0.637167\pi$
$3$	−2.44811	−	1.41342i	−1.41342	−	0.816038i	−0.995709	+	0.0925423i	$0.970501\pi$
$4$	−2.11378	−	3.66117i	−1.05689	−	1.83059i
$5$		0			0
$5$		0			0
$6$	−6.10929	+	3.52720i	−2.49411	+	1.43997i
$7$	−0.952606	−	1.64996i	−0.360051	−	0.623627i	0.627918	−	0.778280i	$-0.283907\pi$
$7$	−0.952606	−	1.64996i	−0.360051	−	0.623627i	−0.987969	+	0.154653i	$0.950574\pi$
$8$	−5.55889			−1.96536
$9$	2.49551	+	4.32235i	0.831836	+	1.44078i
$10$		0			0
$11$	0.926118	+	0.534695i	0.279235	+	0.161217i	0.633077	−	0.774089i	$-0.281792\pi$
$11$	0.926118	+	0.534695i	0.279235	+	0.161217i	−0.353842	+	0.935305i	$0.615125\pi$
$12$			11.9506i			3.44985i
$13$	3.32235	−	1.40072i	0.921453	−	0.388490i
$13$	3.32235	−	1.40072i	0.921453	−	0.388490i
$14$	−4.75447			−1.27069
$15$		0			0
$16$	−2.70857	+	4.69138i	−0.677142	+	1.17284i
$17$	−0.551886	+	0.318632i	−0.133852	+	0.0772795i	−0.565431	−	0.824796i	$-0.691290\pi$
$17$	−0.551886	+	0.318632i	−0.133852	+	0.0772795i	0.431579	+	0.902075i	$0.357957\pi$
$18$	12.4551			2.93570
$19$	−4.96410	+	2.86603i	−1.13884	+	0.657511i	−0.946144	−	0.323747i	$-0.895057\pi$
$19$	−4.96410	+	2.86603i	−1.13884	+	0.657511i	−0.192699	+	0.981258i	$0.561724\pi$
$20$		0			0
$21$			5.38573i			1.17526i
$22$	2.31114	−	1.33433i	0.492736	−	0.284481i
$23$	−3.30636	−	1.90893i	−0.689423	−	0.398039i	0.113973	−	0.993484i	$-0.463642\pi$
$23$	−3.30636	−	1.90893i	−0.689423	−	0.398039i	−0.803396	+	0.595445i	$0.796976\pi$
$24$	13.6088	+	7.85704i	2.77788	+	1.60381i
$25$		0			0
$26$	1.11827	−	8.92792i	0.219311	−	1.75091i
$27$		−	5.62828i		−	1.08316i
$28$	−4.02720	+	6.97531i	−0.761069	+	1.31821i
$29$	4.72756	−	8.18837i	0.877886	−	1.52054i	0.0242288	−	0.999706i	$-0.492287\pi$
$29$	4.72756	−	8.18837i	0.877886	−	1.52054i	0.853657	−	0.520836i	$-0.174380\pi$
$30$		0			0
$31$		−	1.46410i		−	0.262960i	−0.991319	−	0.131480i	$-0.958027\pi$
$31$		−	1.46410i		−	0.262960i	0.991319	−	0.131480i	$-0.0419730\pi$
$32$	1.20036	+	2.07908i	0.212196	+	0.367534i
$33$	−1.51150	−	2.61799i	−0.263118	−	0.455733i
$34$			1.59030i			0.272733i
$35$		0			0
$36$	10.5499	−	18.2730i	1.75832	−	3.04550i
$37$	−0.378725	+	0.655970i	−0.0622619	+	0.107841i	−0.895476	−	0.445110i	$-0.853165\pi$
$37$	−0.378725	+	0.655970i	−0.0622619	+	0.107841i	0.833214	+	0.552950i	$0.186498\pi$
$38$			14.3044i			2.32048i
$39$	−10.1133	−	1.26675i	−1.61942	−	0.202842i
$40$		0			0
$41$	−0.232051	−	0.133975i	−0.0362402	−	0.0209233i	0.481770	−	0.876297i	$-0.339994\pi$
$41$	−0.232051	−	0.133975i	−0.0362402	−	0.0209233i	−0.518011	+	0.855374i	$0.673327\pi$
$42$	11.6395	+	6.72006i	1.79601	+	1.03693i
$43$	0.551886	−	0.318632i	0.0841618	−	0.0485909i	−0.457328	−	0.889298i	$-0.651194\pi$
$43$	0.551886	−	0.318632i	0.0841618	−	0.0485909i	0.541490	+	0.840707i	$0.317860\pi$
$44$		−	4.52091i		−	0.681552i
$45$		0			0
$46$	−8.25104	+	4.76374i	−1.21655	+	0.702375i
$47$	−9.44613			−1.37786			−0.688930	−	0.724828i	$-0.741919\pi$
$47$	−9.44613			−1.37786			−0.688930	+	0.724828i	$0.741919\pi$
$48$	13.2618	−	7.65668i	1.91417	−	1.10515i
$49$	1.68508	−	2.91865i	0.240726	−	0.416950i
$50$		0			0
$51$	1.80144			0.252252
$52$	−12.1510	−	9.20287i	−1.68504	−	1.27621i
$53$			6.99102i			0.960290i	0.877189	+	0.480145i	$0.159416\pi$
$53$			6.99102i			0.960290i	−0.877189	+	0.480145i	$0.840584\pi$
$54$	−12.1637	−	7.02271i	−1.65527	−	0.955669i
$55$		0			0
$56$	5.29543	+	9.17196i	0.707632	+	1.22565i
$57$	16.2036			2.14622
$58$	−11.7977	−	20.4341i	−1.54911	−	2.68313i
$59$	0.641756	−	0.370518i	0.0835495	−	0.0482373i	−0.457643	−	0.889136i	$-0.651306\pi$
$59$	0.641756	−	0.370518i	0.0835495	−	0.0482373i	0.541193	+	0.840899i	$0.317973\pi$
$60$		0			0
$61$	−2.09928	−	3.63606i	−0.268785	−	0.465550i	0.699763	−	0.714375i	$-0.253289\pi$
$61$	−2.09928	−	3.63606i	−0.268785	−	0.465550i	−0.968548	+	0.248825i	$0.919956\pi$
$62$	−3.16418	−	1.82684i	−0.401851	−	0.232009i
$63$	4.75447	−	8.23499i	0.599007	−	1.03751i
$64$	−4.84325			−0.605406
$65$		0			0
$66$	−7.54390			−0.928589
$67$	4.04739	−	7.01029i	0.494468	−	0.856443i	−0.505512	−	0.862820i	$-0.668696\pi$
$67$	4.04739	−	7.01029i	0.494468	−	0.856443i	0.999980	+	0.00637624i	$0.00202963\pi$
$68$	2.33313	+	1.34703i	0.282934	+	0.163352i
$69$	5.39623	+	9.34654i	0.649629	+	1.12519i
$70$		0			0
$71$	8.45663	−	4.88244i	1.00362	−	0.579439i	0.0943010	−	0.995544i	$-0.469938\pi$
$71$	8.45663	−	4.88244i	1.00362	−	0.579439i	0.909317	+	0.416105i	$0.136605\pi$
$72$	−13.8723	−	24.0274i	−1.63486	−	2.83166i
$73$	3.71649			0.434982			0.217491	−	0.976062i	$-0.430213\pi$
$73$	3.71649			0.434982			0.217491	+	0.976062i	$0.430213\pi$
$74$	0.945110	+	1.63698i	0.109867	+	0.190295i
$75$		0			0
$76$	20.9860	+	12.1163i	2.40726	+	1.38983i
$77$		−	2.03741i		−	0.232185i
$78$	−15.3565	+	20.2760i	−1.73879	+	2.29580i
$79$	9.31937			1.04851			0.524255	−	0.851561i	$-0.324344\pi$
$79$	9.31937			1.04851			0.524255	+	0.851561i	$0.324344\pi$
$80$		0			0
$81$	−0.468594	+	0.811629i	−0.0520660	+	0.0901809i
$82$	−0.579085	+	0.334335i	−0.0639492	+	0.0369211i
$83$	5.11778			0.561749			0.280875	−	0.959744i	$-0.409376\pi$
$83$	5.11778			0.561749			0.280875	+	0.959744i	$0.409376\pi$
$84$	19.7181	−	11.3842i	2.15142	−	1.24212i
$85$		0			0
$86$		−	1.59030i		−	0.171486i
$87$	−23.1472	+	13.3640i	−2.48164	+	1.43278i
$88$	−5.14819	−	2.97231i	−0.548799	−	0.316849i
$89$	10.8932	+	6.28917i	1.15467	+	0.666650i	0.950021	−	0.312185i	$-0.101061\pi$
$89$	10.8932	+	6.28917i	1.15467	+	0.666650i	0.204651	+	0.978835i	$0.434394\pi$
$90$		0			0
$91$	−5.47602	−	4.14741i	−0.574043	−	0.434767i
$92$			16.1402i			1.68273i
$93$	−2.06939	+	3.58429i	−0.214586	+	0.371673i
$94$	−11.7864	+	20.4147i	−1.21568	+	2.10562i
$95$		0			0
$96$		−	6.78645i		−	0.692639i
$97$	−2.11078	−	3.65597i	−0.214317	−	0.371208i	0.738744	−	0.673986i	$-0.235419\pi$
$97$	−2.11078	−	3.65597i	−0.214317	−	0.371208i	−0.953061	+	0.302778i	$0.902086\pi$
$98$	−4.20514	−	7.28351i	−0.424783	−	0.735746i
$99$			5.33734i			0.536423i
$100$		0			0
$101$	−7.62379	+	13.2048i	−0.758595	+	1.31393i	0.184972	+	0.982744i	$0.440781\pi$
$101$	−7.62379	+	13.2048i	−0.758595	+	1.31393i	−0.943567	+	0.331181i	$0.892553\pi$
$102$	2.24775	−	3.89322i	0.222561	−	0.385487i
$103$		−	13.5269i		−	1.33285i	−0.745574	−	0.666423i	$-0.767824\pi$
$103$		−	13.5269i		−	1.33285i	0.745574	−	0.666423i	$-0.232176\pi$
$104$	−18.4686	+	7.78645i	−1.81099	+	0.763524i
$105$		0			0
$106$	15.1088	+	8.72307i	1.46750	+	0.847259i
$107$	6.37632	+	3.68137i	0.616422	+	0.355891i	0.775475	−	0.631379i	$-0.217511\pi$
$107$	6.37632	+	3.68137i	0.616422	+	0.355891i	−0.159053	+	0.987270i	$0.550844\pi$
$108$	−20.6061	+	11.8969i	−1.98282	+	1.14478i
$109$		−	10.0760i		−	0.965103i	−0.875868	−	0.482551i	$-0.839710\pi$
$109$		−	10.0760i		−	0.965103i	0.875868	−	0.482551i	$-0.160290\pi$
$110$		0			0
$111$	1.85432	−	1.07059i	0.176004	−	0.101616i
$112$	10.3208			0.975223
$113$	5.79203	−	3.34403i	0.544868	−	0.314580i	−0.202181	−	0.979348i	$-0.564803\pi$
$113$	5.79203	−	3.34403i	0.544868	−	0.314580i	0.747050	+	0.664768i	$0.231470\pi$
$114$	20.2181	−	35.0187i	1.89360	−	3.27981i
$115$		0			0
$116$	−39.9721			−3.71131
$117$	14.3453	+	10.8648i	1.32623	+	1.00445i
$118$		−	1.84926i		−	0.170238i
$119$	1.05146	+	0.607061i	0.0963872	+	0.0556492i
$120$		0			0
$121$	−4.92820	−	8.53590i	−0.448018	−	0.775991i
$122$	−10.4775			−0.948592
$123$	0.378725	+	0.655970i	0.0341484	+	0.0591468i
$124$	−5.36033	+	3.09479i	−0.481372	+	0.277920i
$125$		0			0
$126$	−11.8648	−	20.5505i	−1.05700	−	1.83078i
$127$	1.28994	+	0.744750i	0.114464	+	0.0660859i	0.556139	−	0.831089i	$-0.312282\pi$
$127$	1.28994	+	0.744750i	0.114464	+	0.0660859i	−0.441675	+	0.897175i	$0.645616\pi$
$128$	−8.44391	+	14.6253i	−0.746343	+	1.29270i
$129$	−1.80144			−0.158608
$130$		0			0
$131$	4.12676			0.360557			0.180278	−	0.983616i	$-0.442300\pi$
$131$	4.12676			0.360557			0.180278	+	0.983616i	$0.442300\pi$
$132$	−6.38994	+	11.0677i	−0.556172	+	0.963319i
$133$	9.45767	+	5.46039i	0.820084	+	0.473476i
$134$	−10.1003	−	17.4942i	−0.872533	−	1.51127i
$135$		0			0
$136$	3.06787	−	1.77124i	0.263068	−	0.151882i
$137$	10.0548	+	17.4155i	0.859041	+	1.48790i	0.872844	+	0.487999i	$0.162273\pi$
$137$	10.0548	+	17.4155i	0.859041	+	1.48790i	−0.0138029	+	0.999905i	$0.504394\pi$
$138$	26.9327			2.29266
$139$	10.4126	+	18.0352i	0.883189	+	1.52973i	0.847776	+	0.530355i	$0.177941\pi$
$139$	10.4126	+	18.0352i	0.883189	+	1.52973i	0.0354130	+	0.999373i	$0.488725\pi$
$140$		0			0
$141$	23.1252	+	13.3513i	1.94749	+	1.12439i
$142$		−	24.3683i		−	2.04494i
$143$	3.82584	+	0.479208i	0.319933	+	0.0400734i
$144$	−27.0370			−2.25308
$145$		0			0
$146$	4.63726	−	8.03198i	0.383783	−	0.664731i
$147$	−8.25055	+	4.76346i	−0.680494	+	0.392883i
$148$	3.20216			0.263216
$149$	−11.5768	+	6.68388i	−0.948410	+	0.547565i	−0.892587	−	0.450876i	$-0.851112\pi$
$149$	−11.5768	+	6.68388i	−0.948410	+	0.547565i	−0.0558233	+	0.998441i	$0.517778\pi$
$150$		0			0
$151$		−	18.2984i		−	1.48910i	−0.667567	−	0.744550i	$-0.732664\pi$
$151$		−	18.2984i		−	1.48910i	0.667567	−	0.744550i	$-0.267336\pi$
$152$	27.5949	−	15.9319i	2.23824	−	1.29225i
$153$	−2.75447	−	1.59030i	−0.222686	−	0.128568i
$154$	−4.40320	−	2.54219i	−0.354820	−	0.204856i
$155$		0			0
$156$	16.7395	+	39.7041i	1.34023	+	3.17887i
$157$			2.42229i			0.193320i	0.995317	+	0.0966599i	$0.0308159\pi$
$157$			2.42229i			0.193320i	−0.995317	+	0.0966599i	$0.969184\pi$
$158$	11.6283	−	20.1408i	0.925096	−	1.60231i
$159$	9.88124	−	17.1148i	0.783633	−	1.35729i
$160$		0			0
$161$			7.27382i			0.573258i
$162$	1.16938	+	2.02543i	0.0918752	+	0.159132i
$163$	7.99144	+	13.8416i	0.625938	+	1.08416i	0.988359	+	0.152142i	$0.0486170\pi$
$163$	7.99144	+	13.8416i	0.625938	+	1.08416i	−0.362421	+	0.932015i	$0.618050\pi$
$164$			1.13277i			0.0884545i
$165$		0			0
$166$	6.38573	−	11.0604i	0.495629	−	0.858454i
$167$	7.19658	−	12.4648i	0.556888	−	0.964558i	−0.440866	−	0.897573i	$-0.645329\pi$
$167$	7.19658	−	12.4648i	0.556888	−	0.964558i	0.997754	−	0.0669853i	$-0.0213381\pi$
$168$		−	29.9387i		−	2.30982i
$169$	9.07597	−	9.30735i	0.698151	−	0.715950i
$170$		0			0
$171$	−24.7759	−	14.3044i	−1.89466	−	1.09388i
$172$	−2.33313	−	1.34703i	−0.177900	−	0.102710i
$173$	−21.0868	+	12.1745i	−1.60320	+	0.925608i	−0.612358	+	0.790581i	$0.709779\pi$
$173$	−21.0868	+	12.1745i	−1.60320	+	0.925608i	−0.990842	+	0.135027i	$0.956888\pi$
$174$			66.7001i			5.05653i
$175$		0			0
$176$	−5.01691	+	2.89651i	−0.378164	+	0.218333i
$177$	−2.09479			−0.157454
$178$	27.1840	−	15.6947i	2.03752	−	1.17636i
$179$	−1.89414	+	3.28075i	−0.141575	+	0.245215i	−0.928090	−	0.372356i	$-0.878550\pi$
$179$	−1.89414	+	3.28075i	−0.141575	+	0.245215i	0.786515	+	0.617571i	$0.211883\pi$
$180$		0			0
$181$	8.48794			0.630904			0.315452	−	0.948942i	$-0.397844\pi$
$181$	8.48794			0.630904			0.315452	+	0.948942i	$0.397844\pi$
$182$	−15.7960	+	6.65968i	−1.17088	+	0.493649i
$183$			11.8687i			0.877356i
$184$	18.3797	+	10.6115i	1.35497	+	0.782291i
$185$		0			0
$186$	5.16418	+	8.94462i	0.378656	+	0.655851i
$187$	−0.681482			−0.0498349
$188$	19.9670	+	34.5839i	1.45625	+	2.52229i
$189$	−9.28645	+	5.36153i	−0.675490	+	0.389994i
$190$		0			0
$191$	2.72155	+	4.71386i	0.196924	+	0.341083i	0.947530	−	0.319668i	$-0.103571\pi$
$191$	2.72155	+	4.71386i	0.196924	+	0.341083i	−0.750605	+	0.660751i	$0.770238\pi$
$192$	11.8568	+	6.84555i	0.855693	+	0.494035i
$193$	6.07880	−	10.5288i	0.437562	−	0.757879i	−0.559939	−	0.828534i	$-0.689176\pi$
$193$	6.07880	−	10.5288i	0.437562	−	0.757879i	0.997501	+	0.0706548i	$0.0225089\pi$
$194$	−10.5349			−0.756363
$195$		0			0
$196$	−14.2476			−1.01768
$197$	−2.18915	+	3.79172i	−0.155970	+	0.270149i	−0.933412	−	0.358807i	$-0.883184\pi$
$197$	−2.18915	+	3.79172i	−0.155970	+	0.270149i	0.777442	+	0.628955i	$0.216517\pi$
$198$	11.5349	+	6.65968i	0.819751	+	0.473283i
$199$	−10.4186	−	18.0456i	−0.738558	−	1.27922i	−0.953144	−	0.302516i	$-0.902174\pi$
$199$	−10.4186	−	18.0456i	−0.738558	−	1.27922i	0.214586	−	0.976705i	$-0.431160\pi$
$200$		0			0
$201$	−19.8170	+	11.4413i	−1.39778	+	0.807009i
$202$	19.0252	+	32.9526i	1.33861	+	2.31854i
$203$	−18.0140			−1.26434
$204$	−3.80785	−	6.59538i	−0.266603	−	0.461769i
$205$		0			0
$206$	−29.2340	−	16.8783i	−2.03683	−	1.17596i
$207$		−	19.0550i		−	1.32441i
$208$	−2.42749	+	19.3803i	−0.168316	+	1.34378i
$209$	−6.12979			−0.424007
$210$		0			0
$211$	5.32684	−	9.22635i	0.366715	−	0.635168i	−0.622335	−	0.782751i	$-0.713816\pi$
$211$	5.32684	−	9.22635i	0.366715	−	0.635168i	0.989050	+	0.147583i	$0.0471492\pi$
$212$	25.5953	−	14.7775i	1.75789	−	1.01492i
$213$	−27.6037			−1.89138
$214$	15.9121	−	9.18688i	1.08773	−	0.628002i
$215$		0			0
$216$			31.2870i			2.12881i
$217$	−2.41571	+	1.39471i	−0.163989	+	0.0946792i
$218$	−21.7759	−	12.5723i	−1.47485	−	0.851505i
$219$	−9.09839	−	5.25296i	−0.614812	−	0.354962i
$220$		0			0
$221$	−1.38724	+	1.83164i	−0.0933161	+	0.123210i
$222$		−	5.34335i		−	0.358622i
$223$	−10.6697	+	18.4804i	−0.714494	+	1.23754i	0.248661	+	0.968591i	$0.420010\pi$
$223$	−10.6697	+	18.4804i	−0.714494	+	1.23754i	−0.963155	+	0.268949i	$0.913324\pi$
$224$	2.28694	−	3.96110i	0.152803	−	0.264662i
$225$		0			0
$226$		−	16.6901i		−	1.11021i
$227$	7.84283	+	13.5842i	0.520547	+	0.901613i	0.999715	+	0.0238900i	$0.00760515\pi$
$227$	7.84283	+	13.5842i	0.520547	+	0.901613i	−0.479168	+	0.877723i	$0.659062\pi$
$228$	−34.2508	−	59.3241i	−2.26831	−	3.92884i
$229$		−	7.62085i		−	0.503600i	−0.967779	−	0.251800i	$-0.918977\pi$
$229$		−	7.62085i		−	0.503600i	0.967779	−	0.251800i	$-0.0810225\pi$
$230$		0			0
$231$	−2.87972	+	4.98782i	−0.189472	+	0.328175i
$232$	−26.2800	+	45.5182i	−1.72536	+	2.98842i
$233$		−	19.0550i		−	1.24833i	−0.781292	−	0.624166i	$-0.785439\pi$
$233$		−	19.0550i		−	1.24833i	0.781292	−	0.624166i	$-0.214561\pi$
$234$	41.3802	−	17.4461i	2.70511	−	1.14049i
$235$		0			0
$236$	−2.71306	−	1.56639i	−0.176605	−	0.101963i
$237$	−22.8149	−	13.1722i	−1.48199	−	0.855625i
$238$	2.62393	−	1.51493i	0.170084	−	0.0981980i
$239$		−	12.7535i		−	0.824954i	−0.910968	−	0.412477i	$-0.864664\pi$
$239$		−	12.7535i		−	0.824954i	0.910968	−	0.412477i	$-0.135336\pi$
$240$		0			0
$241$	−22.4550	+	12.9644i	−1.44646	+	0.835111i	−0.998268	−	0.0588285i	$-0.981263\pi$
$241$	−22.4550	+	12.9644i	−1.44646	+	0.835111i	−0.448187	+	0.893940i	$0.647930\pi$
$242$	−24.5967			−1.58114
$243$	−12.3284	+	7.11778i	−0.790864	+	0.456606i
$244$	−8.87483	+	15.3717i	−0.568153	+	0.984069i
$245$		0			0
$246$	1.89022			0.120516
$247$	−12.4780	+	16.4752i	−0.793954	+	1.04829i
$248$			8.13878i			0.516813i
$249$	−12.5289	−	7.23357i	−0.793987	−	0.458409i
$250$		0			0
$251$	3.80593	+	6.59207i	0.240228	+	0.416088i	0.960779	−	0.277314i	$-0.0894444\pi$
$251$	3.80593	+	6.59207i	0.240228	+	0.416088i	−0.720551	+	0.693402i	$0.756111\pi$
$252$	−40.1996			−2.53234
$253$	−2.04139	−	3.53578i	−0.128341	−	0.222293i
$254$	3.21907	−	1.85853i	0.201982	−	0.116614i
$255$		0			0
$256$	16.2286	+	28.1087i	1.01429	+	1.75680i
$257$	0.290796	+	0.167891i	0.0181394	+	0.0104728i	0.509042	−	0.860742i	$-0.330000\pi$
$257$	0.290796	+	0.167891i	0.0181394	+	0.0104728i	−0.490903	+	0.871214i	$0.663333\pi$
$258$	−2.24775	+	3.89322i	−0.139939	+	0.242382i
$259$	1.44310			0.0896700
$260$		0			0
$261$	47.1906			2.92103
$262$	5.14918	−	8.91865i	0.318118	−	0.550996i
$263$	−4.65566	−	2.68795i	−0.287080	−	0.165746i	0.349544	−	0.936920i	$-0.386336\pi$
$263$	−4.65566	−	2.68795i	−0.287080	−	0.165746i	−0.636624	+	0.771174i	$0.719670\pi$
$264$	8.40224	+	14.5531i	0.517122	+	0.895681i
$265$		0			0
$266$	23.6017	−	13.6264i	1.44711	−	0.835491i
$267$	−17.7785	−	30.7932i	−1.08802	−	1.88451i
$268$	−34.2212			−2.09039
$269$	−0.655192	−	1.13483i	−0.0399478	−	0.0691916i	0.845360	−	0.534197i	$-0.179386\pi$
$269$	−0.655192	−	1.13483i	−0.0399478	−	0.0691916i	−0.885308	+	0.465005i	$0.846052\pi$
$270$		0			0
$271$	−10.0851	−	5.82266i	−0.612629	−	0.353701i	0.161365	−	0.986895i	$-0.448410\pi$
$271$	−10.0851	−	5.82266i	−0.612629	−	0.353701i	−0.773994	+	0.633194i	$0.781744\pi$
$272$		−	3.45214i		−	0.209317i
$273$	7.54390	+	17.8933i	0.456577	+	1.08295i
$274$	50.1838			3.03171
$275$		0			0
$276$	22.8129	−	39.5130i	1.37317	−	2.37841i
$277$	17.5943	−	10.1581i	1.05714	−	0.610338i	0.132498	−	0.991183i	$-0.457700\pi$
$277$	17.5943	−	10.1581i	1.05714	−	0.610338i	0.924639	+	0.380845i	$0.124367\pi$
$278$	51.9697			3.11693
$279$	6.32835	−	3.65368i	0.378869	−	0.218740i
$280$		0			0
$281$			11.8744i			0.708366i	0.935176	+	0.354183i	$0.115241\pi$
$281$			11.8744i			0.708366i	−0.935176	+	0.354183i	$0.884759\pi$
$282$	57.7091	−	33.3184i	3.43653	−	1.98408i
$283$	19.6173	+	11.3261i	1.16613	+	0.673264i	0.952765	−	0.303709i	$-0.0982249\pi$
$283$	19.6173	+	11.3261i	1.16613	+	0.673264i	0.213363	+	0.976973i	$0.431558\pi$
$284$	−35.7509	−	20.6408i	−2.12143	−	1.22481i
$285$		0			0
$286$	5.80936	−	7.67038i	0.343515	−	0.453559i
$287$			0.510500i			0.0301339i
$288$	−5.99102	+	10.3767i	−0.353024	+	0.611455i
$289$	−8.29695	+	14.3707i	−0.488056	+	0.845337i
$290$		0			0
$291$			11.9336i			0.699562i
$292$	−7.85584	−	13.6067i	−0.459728	−	0.796272i
$293$	9.30636	+	16.1191i	0.543683	+	0.941687i	0.998689	+	0.0511983i	$0.0163040\pi$
$293$	9.30636	+	16.1191i	0.543683	+	0.941687i	−0.455005	+	0.890489i	$0.650363\pi$
$294$			23.7745i			1.38656i
$295$		0			0
$296$	2.10529	−	3.64647i	0.122367	−	0.211946i
$297$	3.00941	−	5.21245i	0.174624	−	0.302457i
$298$			33.3593i			1.93245i
$299$	−13.6587	−	1.71083i	−0.789905	−	0.0989400i
$300$		0			0
$301$	−1.05146	−	0.607061i	−0.0606052	−	0.0349904i
$302$	−39.5459	−	22.8319i	−2.27561	−	1.31383i
$303$	37.3278	−	21.5512i	2.14443	−	1.23808i
$304$		−	31.0513i		−	1.78091i
$305$		0			0
$306$	−6.87381	+	3.96859i	−0.392949	+	0.226869i
$307$	3.14776			0.179652			0.0898262	−	0.995957i	$-0.471369\pi$
$307$	3.14776			0.179652			0.0898262	+	0.995957i	$0.471369\pi$
$308$	−7.45932	+	4.30664i	−0.425034	+	0.245394i
$309$	−19.1192	+	33.1154i	−1.08765	+	1.88387i
$310$		0			0
$311$	3.18059			0.180355			0.0901774	−	0.995926i	$-0.471257\pi$
$311$	3.18059			0.180355			0.0901774	+	0.995926i	$0.471257\pi$
$312$	56.2186	+	7.04170i	3.18275	+	0.398658i
$313$		−	35.3533i		−	1.99829i	−0.0413596	−	0.999144i	$-0.513169\pi$
$313$		−	35.3533i		−	1.99829i	0.0413596	−	0.999144i	$-0.486831\pi$
$314$	5.23499	+	3.02242i	0.295427	+	0.170565i
$315$		0			0
$316$	−19.6991	−	34.1198i	−1.10816	−	1.91939i
$317$	13.6357			0.765858			0.382929	−	0.923778i	$-0.374915\pi$
$317$	13.6357			0.765858			0.382929	+	0.923778i	$0.374915\pi$
$318$	−24.6587	−	42.7101i	−1.38279	−	2.39506i
$319$	8.75656	−	5.05560i	0.490273	−	0.283059i
$320$		0			0
$321$	−10.4066	−	18.0248i	−0.580842	−	1.00605i
$322$	15.7200	+	9.07594i	0.876041	+	0.505782i
$323$	1.82641	−	3.16344i	0.101624	−	0.176018i
$324$	3.96202			0.220112
$325$		0			0
$326$	39.8854			2.20905
$327$	−14.2416	+	24.6671i	−0.787560	+	1.36409i
$328$	1.28994	+	0.744750i	0.0712253	+	0.0411219i
$329$	8.99844	+	15.5858i	0.496100	+	0.859271i
$330$		0			0
$331$	−24.9380	+	14.3980i	−1.37072	+	0.791383i	−0.991018	−	0.133727i	$-0.957305\pi$
$331$	−24.9380	+	14.3980i	−1.37072	+	0.791383i	−0.379698	+	0.925110i	$0.623972\pi$
$332$	−10.8179	−	18.7371i	−0.593707	−	1.02833i
$333$	−3.78044			−0.207167
$334$	−17.9591	−	31.1061i	−0.982679	−	1.70205i
$335$		0			0
$336$	−25.2665	−	14.5876i	−1.37840	−	0.795819i
$337$		−	11.7493i		−	0.640026i	−0.947413	−	0.320013i	$-0.896313\pi$
$337$		−	11.7493i		−	0.640026i	0.947413	−	0.320013i	$-0.103687\pi$
$338$	−8.79023	−	31.2280i	−0.478125	−	1.69858i
$339$	−18.9061			−1.02684
$340$		0			0
$341$	0.782847	−	1.35593i	0.0423936	−	0.0734278i
$342$	−61.8285	+	35.6967i	−3.34330	+	1.93026i
$343$	−19.7574			−1.06680
$344$	−3.06787	+	1.77124i	−0.165409	+	0.0954987i
$345$		0			0
$346$			60.7630i			3.26664i
$347$	1.64525	−	0.949887i	0.0883218	−	0.0509926i	−0.455189	−	0.890395i	$-0.650428\pi$
$347$	1.64525	−	0.949887i	0.0883218	−	0.0509926i	0.543510	+	0.839402i	$0.317095\pi$
$348$	97.8562	+	56.4973i	5.24564	+	3.02857i
$349$	8.89329	+	5.13454i	0.476047	+	0.274846i	0.718768	−	0.695250i	$-0.244707\pi$
$349$	8.89329	+	5.13454i	0.476047	+	0.274846i	−0.242721	+	0.970096i	$0.578040\pi$
$350$		0			0
$351$	−7.88364	−	18.6991i	−0.420798	−	0.998084i
$352$			2.56730i			0.136838i
$353$	−0.400294	+	0.693330i	−0.0213055	+	0.0369022i	−0.876482	−	0.481435i	$-0.840116\pi$
$353$	−0.400294	+	0.693330i	−0.0213055	+	0.0369022i	0.855176	+	0.518338i	$0.173449\pi$
$354$	−2.61378	+	4.52720i	−0.138921	+	0.240618i
$355$		0			0
$356$		−	53.1756i		−	2.81830i
$357$	−1.71606	−	2.97231i	−0.0908237	−	0.157311i
$358$	4.72685	+	8.18714i	0.249822	+	0.432704i
$359$			8.13272i			0.429228i	0.976699	+	0.214614i	$0.0688494\pi$
$359$			8.13272i			0.429228i	−0.976699	+	0.214614i	$0.931151\pi$
$360$		0			0
$361$	6.92820	−	12.0000i	0.364642	−	0.631579i
$362$	10.5909	−	18.3439i	0.556643	−	0.964135i
$363$			27.8625i			1.46240i
$364$	−3.60929	+	28.8154i	−0.189178	+	1.51034i
$365$		0			0
$366$	25.6502	+	14.8092i	1.34076	+	0.774087i
$367$	17.7765	+	10.2632i	0.927924	+	0.535737i	0.886154	−	0.463390i	$-0.153367\pi$
$367$	17.7765	+	10.2632i	0.927924	+	0.535737i	0.0417696	+	0.999127i	$0.486700\pi$
$368$	17.9110	−	10.3409i	0.933675	−	0.539057i
$369$		−	1.33734i		−	0.0696191i
$370$		0			0
$371$	11.5349	−	6.65968i	0.598863	−	0.345754i
$372$	17.4969			0.907173
$373$	15.4203	−	8.90292i	0.798433	−	0.460976i	−0.0444897	−	0.999010i	$-0.514166\pi$
$373$	15.4203	−	8.90292i	0.798433	−	0.460976i	0.842923	+	0.538034i	$0.180833\pi$
$374$	−0.850322	+	1.47280i	−0.0439691	+	0.0761568i
$375$		0			0
$376$	52.5100			2.70800
$377$	4.23697	−	33.8266i	0.218215	−	1.74216i
$378$			26.7595i			1.37636i
$379$	1.77150	+	1.02277i	0.0909956	+	0.0525363i	0.544807	−	0.838561i	$-0.316603\pi$
$379$	1.77150	+	1.02277i	0.0909956	+	0.0525363i	−0.453812	+	0.891098i	$0.649936\pi$
$380$		0			0
$381$	−2.10529	−	3.64647i	−0.107857	−	0.186814i
$382$	13.5833			0.694982
$383$	3.95261	+	6.84611i	0.201969	+	0.349820i	0.949163	−	0.314786i	$-0.101933\pi$
$383$	3.95261	+	6.84611i	0.201969	+	0.349820i	−0.747194	+	0.664606i	$0.768599\pi$
$384$	41.3433	−	23.8696i	2.10979	−	1.21809i
$385$		0			0
$386$	−15.1697	−	26.2747i	−0.772117	−	1.33735i
$387$	2.75447	+	1.59030i	0.140018	+	0.0808393i
$388$	−8.92343	+	15.4558i	−0.453018	+	0.784651i
$389$	−9.21171			−0.467052			−0.233526	−	0.972351i	$-0.575026\pi$
$389$	−9.21171			−0.467052			−0.233526	+	0.972351i	$0.575026\pi$
$390$		0			0
$391$	2.43298			0.123041
$392$	−9.36719	+	16.2244i	−0.473114	+	0.819458i
$393$	−10.1028	−	5.83285i	−0.509618	−	0.294228i
$394$	5.46304	+	9.46226i	0.275224	+	0.476702i
$395$		0			0
$396$	19.5409	−	11.2820i	0.981968	−	0.566940i
$397$	3.17719	+	5.50305i	0.159458	+	0.276190i	0.934674	−	0.355507i	$-0.115692\pi$
$397$	3.17719	+	5.50305i	0.159458	+	0.276190i	−0.775215	+	0.631697i	$0.782359\pi$
$398$	−51.9996			−2.60651
$399$	−15.4356	−	26.7353i	−0.772748	−	1.33844i
$400$		0			0
$401$	3.61063	+	2.08460i	0.180306	+	0.104100i	0.587437	−	0.809270i	$-0.300137\pi$
$401$	3.61063	+	2.08460i	0.180306	+	0.104100i	−0.407130	+	0.913370i	$0.633470\pi$
$402$			57.1038i			2.84808i
$403$	−2.05080	−	4.86425i	−0.102157	−	0.242306i
$404$	64.4600			3.20701
$405$		0			0
$406$	−22.4770	+	38.9314i	−1.11552	+	1.93213i
$407$	−0.701487	+	0.405004i	−0.0347714	+	0.0200753i
$408$	−10.0140			−0.495767
$409$	−8.80580	+	5.08403i	−0.435419	+	0.251389i	−0.701652	−	0.712519i	$-0.747554\pi$
$409$	−8.80580	+	5.08403i	−0.435419	+	0.251389i	0.266234	+	0.963909i	$0.414221\pi$
$410$		0			0
$411$		−	56.8467i		−	2.80404i
$412$	−49.5244	+	28.5929i	−2.43989	+	1.40867i
$413$	−1.22268	−	0.705915i	−0.0601642	−	0.0347358i
$414$	−41.1811	−	23.7759i	−2.02394	−	1.16852i
$415$		0			0
$416$	6.90023	+	5.22607i	0.338311	+	0.256229i
$417$		−	58.8697i		−	2.88286i
$418$	−7.64847	+	13.2475i	−0.374099	+	0.647959i
$419$	14.2954	−	24.7604i	0.698378	−	1.20963i	−0.270651	−	0.962677i	$-0.587239\pi$
$419$	14.2954	−	24.7604i	0.698378	−	1.20963i	0.969029	−	0.246948i	$-0.0794277\pi$
$420$		0			0
$421$			2.01797i			0.0983498i	0.998790	+	0.0491749i	$0.0156592\pi$
$421$			2.01797i			0.0983498i	−0.998790	+	0.0491749i	$0.984341\pi$
$422$	−13.2932	−	23.0244i	−0.647101	−	1.12081i
$423$	−23.5729	−	40.8295i	−1.14615	−	1.98520i
$424$		−	38.8623i		−	1.88732i
$425$		0			0
$426$	−34.4427	+	59.6564i	−1.66875	+	2.89036i
$427$	−3.99957	+	6.92747i	−0.193553	+	0.335244i
$428$		−	31.1264i		−	1.50455i
$429$	−8.68878	−	6.58068i	−0.419498	−	0.317718i
$430$		0			0
$431$	17.8508	+	10.3061i	0.859842	+	0.496430i	0.863959	−	0.503562i	$-0.167977\pi$
$431$	17.8508	+	10.3061i	0.859842	+	0.496430i	−0.00411765	+	0.999992i	$0.501311\pi$
$432$	26.4044	+	15.2446i	1.27038	+	0.733455i
$433$	25.4920	−	14.7178i	1.22507	−	0.707292i	0.259072	−	0.965858i	$-0.416583\pi$
$433$	25.4920	−	14.7178i	1.22507	−	0.707292i	0.965994	+	0.258566i	$0.0832499\pi$
$434$			6.96103i			0.334140i
$435$		0			0
$436$	−36.8899	+	21.2984i	−1.76670	+	1.02001i
$437$	21.8841			1.04686
$438$	−22.7051	+	13.1088i	−1.08489	+	0.626362i
$439$	−8.47602	+	14.6809i	−0.404538	+	0.700681i	−0.994268	−	0.106920i	$-0.965901\pi$
$439$	−8.47602	+	14.6809i	−0.404538	+	0.700681i	0.589729	+	0.807601i	$0.299235\pi$
$440$		0			0
$441$	16.8205			0.800978
$442$	2.22756	+	5.28351i	0.105954	+	0.251311i
$443$			24.1399i			1.14692i	0.819233	+	0.573461i	$0.194400\pi$
$443$			24.1399i			1.14692i	−0.819233	+	0.573461i	$0.805600\pi$
$444$	−7.83925	−	4.52599i	−0.372034	−	0.214794i
$445$		0			0
$446$	26.6262	+	46.1180i	1.26079	+	2.18375i
$447$	37.7885			1.78733
$448$	4.61371	+	7.99118i	0.217977	+	0.377548i
$449$	−18.0679	+	10.4315i	−0.852676	+	0.492293i	−0.861553	−	0.507668i	$-0.830508\pi$
$449$	−18.0679	+	10.4315i	−0.852676	+	0.492293i	0.00887706	+	0.999961i	$0.497174\pi$
$450$		0			0
$451$	−0.143271	−	0.248153i	−0.00674637	−	0.0116851i
$452$	−24.4861	−	14.1371i	−1.15173	−	0.664952i
$453$	−25.8633	+	44.7965i	−1.21516	+	2.10472i
$454$	39.1437			1.83710
$455$		0			0
$456$	−90.0739			−4.21810
$457$	−15.2830	+	26.4708i	−0.714906	+	1.23825i	0.248089	+	0.968737i	$0.420197\pi$
$457$	−15.2830	+	26.4708i	−0.714906	+	1.23825i	−0.962996	+	0.269517i	$0.913136\pi$
$458$	−16.4700	−	9.50894i	−0.769591	−	0.444324i
$459$	1.79335	+	3.10617i	0.0837063	+	0.144984i
$460$		0			0
$461$	4.05146	−	2.33911i	0.188695	−	0.108943i	−0.402676	−	0.915342i	$-0.631920\pi$
$461$	4.05146	−	2.33911i	0.188695	−	0.108943i	0.591372	+	0.806399i	$0.298587\pi$
$462$	7.18636	+	12.4471i	0.334340	+	0.579094i
$463$	14.0011			0.650688			0.325344	−	0.945596i	$-0.394520\pi$
$463$	14.0011			0.650688			0.325344	+	0.945596i	$0.394520\pi$
$464$	25.6098	+	44.3575i	1.18891	+	2.05925i
$465$		0			0
$466$	−41.1811	−	23.7759i	−1.90768	−	1.10140i
$467$			6.98506i			0.323230i	0.986854	+	0.161615i	$0.0516703\pi$
$467$			6.98506i			0.323230i	−0.986854	+	0.161615i	$0.948330\pi$
$468$	9.45512	−	75.4866i	0.437063	−	3.48937i
$469$	−15.4223			−0.712135
$470$		0			0
$471$	3.42371	−	5.93004i	0.157756	−	0.273242i
$472$	−3.56745	+	2.05967i	−0.164205	+	0.0948039i
$473$	0.681482			0.0313346
$474$	−56.9347	+	32.8713i	−2.61510	+	1.50983i
$475$		0			0
$476$		−	5.13277i		−	0.235260i
$477$	−30.2176	+	17.4461i	−1.38357	+	0.798804i
$478$	−27.5625	−	15.9132i	−1.26068	−	0.727853i
$479$	14.1065	+	8.14438i	0.644542	+	0.372126i	0.786362	−	0.617766i	$-0.211962\pi$
$479$	14.1065	+	8.14438i	0.644542	+	0.372126i	−0.141820	+	0.989892i	$0.545296\pi$
$480$		0			0
$481$	−0.339423	+	2.70985i	−0.0154764	+	0.123558i
$482$			64.7056i			2.94726i
$483$	10.2810	−	17.8071i	0.467800	−	0.810253i
$484$	−20.8343	+	36.0860i	−0.947012	+	1.64027i
$485$		0			0
$486$			35.5249i			1.61144i
$487$	10.0204	+	17.3559i	0.454069	+	0.786471i	0.998634	−	0.0522474i	$-0.0166385\pi$
$487$	10.0204	+	17.3559i	0.454069	+	0.786471i	−0.544565	+	0.838719i	$0.683305\pi$
$488$	11.6697	+	20.2125i	0.528261	+	0.914975i
$489$		−	45.1810i		−	2.04316i
$490$		0			0
$491$	−7.89916	+	13.6818i	−0.356484	+	0.617449i	−0.987371	−	0.158426i	$-0.949358\pi$
$491$	−7.89916	+	13.6818i	−0.356484	+	0.617449i	0.630887	+	0.775875i	$0.282691\pi$
$492$	1.60108	−	2.77315i	0.0721823	−	0.125023i
$493$			6.02540i			0.271370i
$494$	20.0364	+	47.5241i	0.901481	+	2.13821i
$495$		0			0
$496$	6.86865	+	3.96562i	0.308411	+	0.178061i
$497$	−16.1117	−	9.30208i	−0.722708	−	0.417255i
$498$	−31.2660	+	18.0514i	−1.40106	+	0.808903i
$499$		−	1.24651i		−	0.0558016i	−0.999611	−	0.0279008i	$-0.991118\pi$
$499$		−	1.24651i		−	0.0558016i	0.999611	−	0.0279008i	$-0.00888226\pi$
$500$		0			0
$501$	−35.2361	+	20.3436i	−1.57423	+	0.908883i
$502$	18.9955			0.847809
$503$	6.62808	−	3.82672i	0.295532	−	0.170625i	−0.344902	−	0.938639i	$-0.612088\pi$
$503$	6.62808	−	3.82672i	0.295532	−	0.170625i	0.640434	+	0.768013i	$0.278755\pi$
$504$	−26.4296	+	45.7774i	−1.17727	+	2.03909i
$505$		0			0
$506$	−10.1886			−0.452938
$507$	−35.3742	+	9.95732i	−1.57102	+	0.442220i
$508$		−	6.29695i		−	0.279382i
$509$	22.2777	+	12.8621i	0.987444	+	0.570101i	0.904509	−	0.426454i	$-0.140237\pi$
$509$	22.2777	+	12.8621i	0.987444	+	0.570101i	0.0829345	+	0.996555i	$0.473571\pi$
$510$		0			0
$511$	−3.54035	−	6.13207i	−0.156616	−	0.271267i
$512$	47.2215			2.08691
$513$	16.1308	+	27.9393i	0.712192	+	1.23355i
$514$	0.725685	−	0.418974i	0.0320086	−	0.0184802i
$515$		0			0
$516$	3.80785	+	6.59538i	0.167631	+	0.290346i
$517$	−8.74824	−	5.05080i	−0.384747	−	0.222134i
$518$	1.80064	−	3.11879i	0.0791154	−	0.137032i
$519$	68.8305			3.02132
$520$		0			0
$521$	−30.1519			−1.32098			−0.660490	−	0.750835i	$-0.729651\pi$
$521$	−30.1519			−1.32098			−0.660490	+	0.750835i	$0.729651\pi$
$522$	58.8823	−	101.987i	2.57721	−	4.46386i
$523$	3.41000	+	1.96876i	0.149109	+	0.0860880i	0.572698	−	0.819766i	$-0.305897\pi$
$523$	3.41000	+	1.96876i	0.149109	+	0.0860880i	−0.423589	+	0.905854i	$0.639230\pi$
$524$	−8.72307	−	15.1088i	−0.381069	−	0.660031i
$525$		0			0
$526$	−11.6182	+	6.70779i	−0.506579	+	0.292473i
$527$	0.466509	+	0.808017i	0.0203215	+	0.0351978i
$528$	16.3759			0.712672
$529$	−4.21200	−	7.29539i	−0.183130	−	0.317191i
$530$		0			0
$531$	3.20301	+	1.84926i	0.138999	+	0.0802510i
$532$		−	46.1682i		−	2.00165i
$533$	−0.958614	−	0.120072i	−0.0415222	−	0.00520088i
$534$	−88.7326			−3.83983
$535$		0			0
$536$	−22.4990	+	38.9694i	−0.971809	+	1.68322i
$537$	9.27415	−	5.35444i	0.400209	−	0.231061i
$538$	−3.27007			−0.140983
$539$	3.12117	−	1.80201i	0.134438	−	0.0776180i
$540$		0			0
$541$			15.8881i			0.683083i	0.939867	+	0.341541i	$0.110949\pi$
$541$			15.8881i			0.683083i	−0.939867	+	0.341541i	$0.889051\pi$
$542$	−25.1675	+	14.5305i	−1.08104	+	0.624138i
$543$	−20.7795	−	11.9970i	−0.891732	−	0.514842i
$544$	−1.32492	−	0.764945i	−0.0568057	−	0.0327968i
$545$		0			0
$546$	48.0833	+	6.02271i	2.05778	+	0.257748i
$547$		−	6.56107i		−	0.280531i	−0.990114	−	0.140266i	$-0.955204\pi$
$547$		−	6.56107i		−	0.280531i	0.990114	−	0.140266i	$-0.0447956\pi$
$548$	42.5074	−	73.6249i	1.81582	−	3.14510i
$549$	10.4775	−	18.1476i	0.447170	−	0.774522i
$550$		0			0
$551$			54.1972i			2.30888i
$552$	−29.9970	−	51.9564i	−1.27676	−	2.21141i
$553$	−8.87769	−	15.3766i	−0.377518	−	0.653880i
$554$		−	50.6990i		−	2.15399i
$555$		0			0
$556$	44.0200	−	76.2450i	1.86687	−	3.23351i
$557$	−3.92503	+	6.79835i	−0.166309	+	0.288055i	−0.937119	−	0.349009i	$-0.886518\pi$
$557$	−3.92503	+	6.79835i	−0.166309	+	0.288055i	0.770810	+	0.637065i	$0.219852\pi$
$558$		−	18.2356i		−	0.771973i
$559$	1.38724	−	1.83164i	0.0586741	−	0.0774702i
$560$		0			0
$561$	1.66835	+	0.963220i	0.0704377	+	0.0406672i
$562$	25.6626	+	14.8163i	1.08251	+	0.624988i
$563$	−13.4749	+	7.77976i	−0.567901	+	0.327878i	−0.756310	−	0.654213i	$-0.773000\pi$
$563$	−13.4749	+	7.77976i	−0.567901	+	0.327878i	0.188410	+	0.982091i	$0.439667\pi$
$564$		−	112.887i		−	4.75341i
$565$		0			0
$566$	48.9552	−	28.2643i	2.05774	−	1.18804i
$567$	1.78554			0.0749857
$568$	−47.0095	+	27.1409i	−1.97247	+	1.13881i
$569$	−1.73957	+	3.01303i	−0.0729267	+	0.126313i	−0.900183	−	0.435512i	$-0.856567\pi$
$569$	−1.73957	+	3.01303i	−0.0729267	+	0.126313i	0.827256	+	0.561825i	$0.189901\pi$
$570$		0			0
$571$	21.5118			0.900240			0.450120	−	0.892968i	$-0.351381\pi$
$571$	21.5118			0.900240			0.450120	+	0.892968i	$0.351381\pi$
$572$	−6.33252	−	15.0200i	−0.264776	−	0.628018i
$573$		−	15.3868i		−	0.642791i
$574$	1.10328	+	0.636978i	0.0460500	+	0.0265870i
$575$		0			0
$576$	−12.0864	−	20.9342i	−0.503599	−	0.872259i
$577$	−9.97608			−0.415310			−0.207655	−	0.978202i	$-0.566583\pi$
$577$	−9.97608			−0.415310			−0.207655	+	0.978202i	$0.566583\pi$
$578$	20.7051	+	35.8623i	0.861218	+	1.49167i
$579$	−29.7632	+	17.1838i	−1.23692	+	0.714134i
$580$		0			0
$581$	−4.87523	−	8.44414i	−0.202259	−	0.350322i
$582$	25.7907	+	14.8902i	1.06906	+	0.617221i
$583$	−3.73806	+	6.47451i	−0.154815	+	0.268147i
$584$	−20.6595			−0.854898
$585$		0			0
$586$	46.4482			1.91876
$587$	−12.0286	+	20.8341i	−0.496472	+	0.859915i	−0.999992	−	0.00406862i	$-0.998705\pi$
$587$	−12.0286	+	20.8341i	−0.496472	+	0.859915i	0.503519	+	0.863984i	$0.332038\pi$
$588$	34.8797	+	20.1378i	1.43841	+	0.830469i
$589$	4.19615	+	7.26795i	0.172899	+	0.299471i
$590$		0			0
$591$	10.7186	−	6.18837i	0.440903	−	0.254556i
$592$	−2.05160	−	3.55348i	−0.0843203	−	0.146047i
$593$	−0.940219			−0.0386102			−0.0193051	−	0.999814i	$-0.506145\pi$
$593$	−0.940219			−0.0386102			−0.0193051	+	0.999814i	$0.506145\pi$
$594$	−7.51001	−	13.0077i	−0.308139	−	0.533713i
$595$		0			0
$596$	48.9417	+	28.2565i	2.00473	+	1.15743i
$597$			58.9037i			2.41077i
$598$	−20.7401	+	27.3842i	−0.848128	+	1.11982i
$599$	11.4270			0.466896			0.233448	−	0.972369i	$-0.424999\pi$
$599$	11.4270			0.466896			0.233448	+	0.972369i	$0.424999\pi$
$600$		0			0
$601$	18.0215	−	31.2142i	0.735114	−	1.27325i	−0.219560	−	0.975599i	$-0.570462\pi$
$601$	18.0215	−	31.2142i	0.735114	−	1.27325i	0.954674	−	0.297655i	$-0.0962045\pi$
$602$	−2.62393	+	1.51493i	−0.106943	+	0.0617437i
$603$	40.4012			1.64526
$604$	−66.9935	+	38.6787i	−2.72593	+	1.57381i
$605$		0			0
$606$		−	107.562i		−	4.36942i
$607$	34.5464	−	19.9454i	1.40219	−	0.809557i	0.407576	−	0.913171i	$-0.366374\pi$
$607$	34.5464	−	19.9454i	1.40219	−	0.809557i	0.994618	+	0.103614i	$0.0330407\pi$
$608$	−11.9174	−	6.88052i	−0.483315	−	0.279042i
$609$	44.1003	+	25.4613i	1.78704	+	1.03175i
$610$		0			0
$611$	−31.3833	+	13.2314i	−1.26963	+	0.535285i
$612$			13.4461i			0.543528i
$613$	0.172736	−	0.299187i	0.00697673	−	0.0120841i	−0.862516	−	0.506030i	$-0.831113\pi$
$613$	0.172736	−	0.299187i	0.00697673	−	0.0120841i	0.869493	+	0.493946i	$0.164446\pi$
$614$	3.92763	−	6.80286i	0.158506	−	0.274541i
$615$		0			0
$616$			11.3258i			0.456328i
$617$	19.3425	+	33.5022i	0.778700	+	1.34875i	0.932691	+	0.360676i	$0.117454\pi$
$617$	19.3425	+	33.5022i	0.778700	+	1.34875i	−0.153991	+	0.988072i	$0.549213\pi$
$618$	47.7121	+	82.6398i	1.91926	+	3.32426i
$619$			14.8971i			0.598764i	0.954133	+	0.299382i	$0.0967805\pi$
$619$			14.8971i			0.598764i	−0.954133	+	0.299382i	$0.903219\pi$
$620$		0			0
$621$	−10.7440	+	18.6091i	−0.431141	+	0.746758i
$622$	3.96859	−	6.87381i	0.159126	−	0.275615i
$623$		−	23.9644i		−	0.960113i
$624$	33.3353	−	44.0142i	1.33448	−	1.76198i
$625$		0			0
$626$	−76.4047	−	44.1123i	−3.05374	−	1.76308i
$627$	15.0064	+	8.66397i	0.599299	+	0.346006i
$628$	8.86842	−	5.12019i	0.353889	−	0.204318i
$629$		−	0.482694i		−	0.0192463i
$630$		0			0
$631$	33.6408	−	19.4225i	1.33922	−	0.773198i	0.352526	−	0.935802i	$-0.385323\pi$
$631$	33.6408	−	19.4225i	1.33922	−	0.773198i	0.986691	+	0.162604i	$0.0519893\pi$
$632$	−51.8053			−2.06071
$633$	−26.0814	+	15.0581i	−1.03664	+	0.598506i
$634$	17.0140	−	29.4691i	0.675713	−	1.17037i
$635$		0			0
$636$	−83.5470			−3.31285
$637$	1.51022	−	12.0571i	0.0598370	−	0.477719i
$638$		−	25.2326i		−	0.998967i
$639$	42.2072	+	24.3683i	1.66969	+	0.963996i
$640$		0			0
$641$	18.5908	+	32.2003i	0.734293	+	1.27183i	0.955033	+	0.296501i	$0.0958197\pi$
$641$	18.5908	+	32.2003i	0.734293	+	1.27183i	−0.220739	+	0.975333i	$0.570847\pi$
$642$	−51.9397			−2.04990
$643$	−4.55189	−	7.88410i	−0.179509	−	0.310918i	0.762204	−	0.647337i	$-0.224118\pi$
$643$	−4.55189	−	7.88410i	−0.179509	−	0.310918i	−0.941712	+	0.336419i	$0.890784\pi$
$644$	26.6307	−	15.3753i	1.04940	−	0.605870i
$645$		0			0
$646$	−4.55783	−	7.89439i	−0.179325	−	0.310601i
$647$	−16.5605	−	9.56118i	−0.651059	−	0.375889i	0.137803	−	0.990460i	$-0.455996\pi$
$647$	−16.5605	−	9.56118i	−0.651059	−	0.375889i	−0.788862	+	0.614571i	$0.789329\pi$
$648$	2.60486	−	4.51175i	0.102329	−	0.177238i
$649$	0.792455			0.0311066
$650$		0			0
$651$	7.88525			0.309047
$652$	33.7843	−	58.5161i	1.32309	−	2.29167i
$653$	29.9926	+	17.3162i	1.17370	+	0.677636i	0.954549	−	0.298055i	$-0.0963378\pi$
$653$	29.9926	+	17.3162i	1.17370	+	0.677636i	0.219152	+	0.975691i	$0.429671\pi$
$654$	35.5399	+	61.5570i	1.38972	+	2.40707i
$655$		0			0
$656$	1.25705	−	0.725758i	0.0490796	−	0.0283361i
$657$	9.27453	+	16.0640i	0.361834	+	0.626714i
$658$	44.9114			1.75083
$659$	−3.34926	−	5.80109i	−0.130469	−	0.225978i	0.793389	−	0.608715i	$-0.208315\pi$
$659$	−3.34926	−	5.80109i	−0.130469	−	0.225978i	−0.923857	+	0.382737i	$0.874982\pi$
$660$		0			0
$661$	5.22004	+	3.01379i	0.203036	+	0.117223i	0.598071	−	0.801443i	$-0.295934\pi$
$661$	5.22004	+	3.01379i	0.203036	+	0.117223i	−0.395035	+	0.918666i	$0.629268\pi$
$662$			71.8604i			2.79294i
$663$	5.98501	−	2.52331i	0.232438	−	0.0979974i
$664$	−28.4492			−1.10404
$665$		0			0
$666$	−4.71706	+	8.17018i	−0.182782	+	0.316588i
$667$	−31.2620	+	18.0491i	−1.21047	+	0.698865i
$668$	−60.8479			−2.35428
$669$	52.2411	−	30.1614i	2.01976	−	1.16611i
$670$		0			0
$671$		−	4.48990i		−	0.173330i
$672$	−11.1974	+	6.46481i	−0.431948	+	0.249386i
$673$	−20.2276	−	11.6784i	−0.779715	−	0.450169i	0.0566140	−	0.998396i	$-0.481970\pi$
$673$	−20.2276	−	11.6784i	−0.779715	−	0.450169i	−0.836329	+	0.548227i	$0.815303\pi$
$674$	−25.3923	−	14.6603i	−0.978075	−	0.564692i
$675$		0			0
$676$	−53.2604	−	13.5550i	−2.04848	−	0.521346i
$677$		−	45.4042i		−	1.74503i	−0.488590	−	0.872513i	$-0.662489\pi$
$677$		−	45.4042i		−	1.74503i	0.488590	−	0.872513i	$-0.337511\pi$
$678$	−23.5901	+	40.8593i	−0.905973	+	1.56919i
$679$	−4.02148	+	6.96540i	−0.154330	+	0.267308i
$680$		0			0
$681$		−	44.3408i		−	1.69914i
$682$	−1.95360	−	3.38374i	−0.0748073	−	0.129570i
$683$	−12.7489	−	22.0817i	−0.487823	−	0.844934i	0.512079	−	0.858938i	$-0.328875\pi$
$683$	−12.7489	−	22.0817i	−0.487823	−	0.844934i	−0.999902	+	0.0140045i	$0.995542\pi$
$684$			120.945i			4.62445i
$685$		0			0
$686$	−24.6523	+	42.6991i	−0.941230	+	1.63026i
$687$	−10.7715	+	18.6567i	−0.410957	+	0.711798i
$688$			3.45214i			0.131612i
$689$	9.79246	+	23.2266i	0.373063	+	0.884862i
$690$		0			0
$691$	5.71257	+	3.29815i	0.217316	+	0.125468i	0.604707	−	0.796448i	$-0.293290\pi$
$691$	5.71257	+	3.29815i	0.217316	+	0.125468i	−0.387391	+	0.921916i	$0.626624\pi$
$692$	89.1457	+	51.4683i	3.38881	+	1.95653i
$693$	8.80641	−	5.08438i	0.334528	−	0.193140i
$694$		−	4.74090i		−	0.179962i
$695$		0			0
$696$	128.673	−	74.2892i	4.87733	−	2.81593i
$697$	0.170754			0.00646778
$698$	22.1933	−	12.8133i	0.840028	−	0.484990i
$699$	−26.9327	+	46.6487i	−1.01869	+	1.76442i
$700$		0			0
$701$	−29.2474			−1.10466			−0.552329	−	0.833626i	$-0.686261\pi$
$701$	−29.2474			−1.10466			−0.552329	+	0.833626i	$0.686261\pi$
$702$	−50.2488	−	6.29394i	−1.89652	−	0.237550i
$703$		−	4.34174i		−	0.163752i
$704$	−4.48542	−	2.58966i	−0.169051	−	0.0976015i
$705$		0			0
$706$	0.998937	+	1.73021i	0.0375955	+	0.0651173i
$707$	29.0499			1.09253
$708$	4.42792	+	7.66938i	0.166411	+	0.288233i
$709$	9.46865	−	5.46673i	0.355603	−	0.205307i	−0.311548	−	0.950231i	$-0.600847\pi$
$709$	9.46865	−	5.46673i	0.355603	−	0.205307i	0.667150	+	0.744923i	$0.267514\pi$
$710$		0			0
$711$	23.2566	+	40.2815i	0.872189	+	1.51068i
$712$	−60.5538	−	34.9608i	−2.26935	−	1.31021i
$713$	−2.79486	+	4.84084i	−0.104668	+	0.181291i
$714$	−8.56490			−0.320533
$715$		0			0
$716$	16.0152			0.598516
$717$	−18.0260	+	31.2220i	−0.673194	+	1.16601i
$718$	17.5762	+	10.1476i	0.655938	+	0.378706i
$719$	−8.02989	−	13.9082i	−0.299464	−	0.518688i	0.676549	−	0.736398i	$-0.263475\pi$
$719$	−8.02989	−	13.9082i	−0.299464	−	0.518688i	−0.976014	+	0.217710i	$0.930141\pi$
$720$		0			0
$721$	−22.3189	+	12.8858i	−0.831199	+	0.479893i
$722$	−17.2894	−	29.9461i	−0.643444	−	1.11448i
$723$	73.2966			2.72593
$724$	−17.9416	−	31.0758i	−0.666796	−	1.15492i
$725$		0			0
$726$	60.2156	+	34.7655i	2.23481	+	1.29027i
$727$		−	51.3754i		−	1.90541i	−0.303900	−	0.952704i	$-0.598289\pi$
$727$		−	51.3754i		−	1.90541i	0.303900	−	0.952704i	$-0.401711\pi$
$728$	30.4406	+	23.0550i	1.12820	+	0.854475i
$729$	43.0532			1.59456
$730$		0			0
$731$	−0.203052	+	0.351697i	−0.00751016	+	0.0130080i
$732$	43.4532	−	25.0877i	1.60608	−	0.927268i
$733$	−9.82358			−0.362842			−0.181421	−	0.983406i	$-0.558070\pi$
$733$	−9.82358			−0.362842			−0.181421	+	0.983406i	$0.558070\pi$
$734$	44.3613	−	25.6120i	1.63741	−	0.945357i
$735$		0			0
$736$		−	9.16560i		−	0.337848i
$737$	7.49673	−	4.32824i	0.276146	−	0.159433i
$738$	−2.89022	−	1.66867i	−0.106390	−	0.0614246i
$739$	−42.5082	−	24.5421i	−1.56369	−	0.902797i	−0.996879	−	0.0789487i	$-0.974844\pi$
$739$	−42.5082	−	24.5421i	−1.56369	−	0.902797i	−0.566811	−	0.823848i	$-0.691823\pi$
$740$		0			0
$741$	53.8339	−	22.6967i	1.97764	−	0.833783i
$742$		−	33.2386i		−	1.22023i
$743$	−20.4188	+	35.3663i	−0.749091	+	1.29746i	0.199167	+	0.979966i	$0.436176\pi$
$743$	−20.4188	+	35.3663i	−0.749091	+	1.29746i	−0.948259	+	0.317499i	$0.897157\pi$
$744$	11.5035	−	19.9247i	0.421739	−	0.730473i
$745$		0			0
$746$		−	44.4346i		−	1.62687i
$747$	12.7715	+	22.1208i	0.467283	+	0.809358i
$748$	1.44050	+	2.49503i	0.0526700	+	0.0912272i
$749$		−	14.0276i		−	0.512557i
$750$		0			0
$751$	−1.36340	+	2.36148i	−0.0497512	+	0.0861716i	−0.889829	−	0.456295i	$-0.849176\pi$
$751$	−1.36340	+	2.36148i	−0.0497512	+	0.0861716i	0.840077	+	0.542467i	$0.182510\pi$
$752$	25.5855	−	44.3154i	0.933006	−	1.61601i
$753$		−	21.5175i		−	0.784142i
$754$	−67.8184	−	51.3641i	−2.46980	−	1.87057i
$755$		0			0
$756$	39.2590	+	22.6662i	1.42784	+	0.824362i
$757$	−12.8224	−	7.40301i	−0.466038	−	0.269067i	0.248542	−	0.968621i	$-0.420049\pi$
$757$	−12.8224	−	7.40301i	−0.466038	−	0.269067i	−0.714580	+	0.699554i	$0.753382\pi$
$758$	4.42078	−	2.55234i	0.160570	−	0.0927051i
$759$			11.5413i			0.418924i
$760$		0			0
$761$	9.84575	−	5.68445i	0.356908	−	0.206061i	−0.310815	−	0.950470i	$-0.600602\pi$
$761$	9.84575	−	5.68445i	0.356908	−	0.206061i	0.667724	+	0.744409i	$0.267269\pi$
$762$	−10.5075			−0.380647
$763$	−16.6250	+	9.59843i	−0.601864	+	0.347486i
$764$	11.5055	−	19.9281i	0.416255	−	0.720975i
$765$		0			0
$766$	19.7275			0.712784
$767$	1.61314	−	2.12991i	0.0582472	−	0.0769065i
$768$		−	91.7512i		−	3.31078i
$769$	−18.2352	−	10.5281i	−0.657579	−	0.379654i	0.133775	−	0.991012i	$-0.457290\pi$
$769$	−18.2352	−	10.5281i	−0.657579	−	0.379654i	−0.791354	+	0.611358i	$0.790623\pi$
$770$		0			0
$771$	−0.474602	−	0.822034i	−0.0170924	−	0.0296048i
$772$	−51.3970			−1.84982
$773$	−7.04144	−	12.1961i	−0.253263	−	0.438664i	0.711159	−	0.703031i	$-0.248170\pi$
$773$	−7.04144	−	12.1961i	−0.253263	−	0.438664i	−0.964422	+	0.264367i	$0.914837\pi$
$774$	6.87381	−	3.96859i	0.247074	−	0.142648i
$775$		0			0
$776$	11.7336	+	20.3231i	0.421210	+	0.729558i
$777$	−3.53288	−	2.03971i	−0.126741	−	0.0731741i
$778$	−11.4940	+	19.9081i	−0.412078	+	0.713740i
$779$	1.53590			0.0550293
$780$		0			0
$781$	10.4425			0.373660
$782$	3.03576	−	5.25809i	0.108558	−	0.188029i
$783$	−46.0864	−	26.6080i	−1.64699	−	0.950893i
$784$	9.12832	+	15.8107i	0.326011	+	0.564668i
$785$		0			0
$786$	−25.2116	+	14.5559i	−0.899267	+	0.519192i
$787$	−16.5121	−	28.5998i	−0.588593	−	1.01947i	−0.994417	−	0.105522i	$-0.966349\pi$
$787$	−16.5121	−	28.5998i	−0.588593	−	1.01947i	0.405823	−	0.913951i	$-0.366985\pi$
$788$	18.5095			0.659374
$789$	7.59839	+	13.1608i	0.270510	+	0.468537i
$790$		0			0
$791$	−11.0350	−	6.37109i	−0.392361	−	0.226530i
$792$		−	29.6697i		−	1.05427i
$793$	−12.0676	−	9.13974i	−0.428534	−	0.324562i
$794$	15.8574			0.562758
$795$		0			0
$796$	−44.0454	+	76.2890i	−1.56115	+	2.70399i
$797$	14.6718	−	8.47079i	0.519703	−	0.300051i	−0.217110	−	0.976147i	$-0.569663\pi$
$797$	14.6718	−	8.47079i	0.519703	−	0.300051i	0.736813	+	0.676096i	$0.236330\pi$
$798$	−77.0395			−2.72717
$799$	5.21319	−	3.00984i	0.184429	−	0.106480i
$800$		0			0
$801$			62.7787i			2.21817i
$802$	9.01036	−	5.20213i	0.318167	−	0.183694i
$803$	3.44191	+	1.98719i	0.121462	+	0.0701263i
$804$	83.7774	+	48.3689i	2.95460	+	1.70584i
$805$		0			0
$806$	−13.0714	−	1.63726i	−0.460420	−	0.0576701i
$807$			3.70425i			0.130396i
$808$	42.3798	−	73.4039i	1.49092	−	2.58234i
$809$	−25.8818	+	44.8285i	−0.909954	+	1.57609i	−0.0958292	+	0.995398i	$0.530550\pi$
$809$	−25.8818	+	44.8285i	−0.909954	+	1.57609i	−0.814125	+	0.580689i	$0.802783\pi$
$810$		0			0
$811$			22.6699i			0.796047i	0.917375	+	0.398023i	$0.130304\pi$
$811$			22.6699i			0.796047i	−0.917375	+	0.398023i	$0.869696\pi$
$812$	38.0776	+	65.9524i	1.33626	+	2.31448i
$813$	16.4597	+	28.5091i	0.577267	+	0.999856i
$814$			2.02138i			0.0708494i
$815$		0			0
$816$	−4.87932	+	8.45123i	−0.170810	+	0.295852i
$817$	−1.82641	+	3.16344i	−0.0638981	+	0.110675i
$818$			25.3745i			0.887198i
$819$	4.26109	−	34.0192i	0.148895	−	1.18873i
$820$		0			0
$821$	−24.8230	−	14.3315i	−0.866328	−	0.500174i	−0.000201482	−	1.00000i	$-0.500064\pi$
$821$	−24.8230	−	14.3315i	−0.866328	−	0.500174i	−0.866126	+	0.499826i	$0.833397\pi$
$822$	−122.856	−	70.9307i	−4.28508	−	2.47399i
$823$	−22.3718	+	12.9164i	−0.779831	+	0.450236i	−0.836371	−	0.548165i	$-0.815327\pi$
$823$	−22.3718	+	12.9164i	−0.779831	+	0.450236i	0.0565391	+	0.998400i	$0.481993\pi$
$824$			75.1946i			2.61953i
$825$		0			0
$826$	−3.05121	+	1.76162i	−0.106165	+	0.0612945i
$827$	−16.0820			−0.559227			−0.279613	−	0.960113i	$-0.590206\pi$
$827$	−16.0820			−0.559227			−0.279613	+	0.960113i	$0.590206\pi$
$828$	−69.7635	+	40.2780i	−2.42445	+	1.39976i
$829$	11.2909	−	19.5564i	0.392149	−	0.679222i	−0.600584	−	0.799562i	$-0.705065\pi$
$829$	11.2909	−	19.5564i	0.392149	−	0.679222i	0.992733	+	0.120340i	$0.0383984\pi$
$830$		0			0
$831$	−57.4304			−1.99224
$832$	−16.0910	+	6.78404i	−0.557854	+	0.235194i
$833$			2.14768i			0.0744128i
$834$	−127.228	−	73.4549i	−4.40553	−	2.54354i
$835$		0			0
$836$	12.9570	+	22.4422i	0.448128	+	0.776181i
$837$	−8.24037			−0.284829
$838$	−35.6744	−	61.7898i	−1.23235	−	2.13449i
$839$	−15.4533	+	8.92198i	−0.533508	+	0.308021i	−0.742444	−	0.669908i	$-0.766333\pi$
$839$	−15.4533	+	8.92198i	−0.533508	+	0.308021i	0.208936	+	0.977929i	$0.433000\pi$
$840$		0			0
$841$	−30.1996	−	52.3073i	−1.04137	−	1.80370i
$842$	4.36118	+	2.51793i	0.150296	+	0.0867736i
$843$	16.7835	−	29.0698i	0.578053	−	1.00122i
$844$	−45.0390			−1.55031
$845$		0			0
$846$	−117.653			−4.04498
$847$	−9.38927	+	16.2627i	−0.322619	+	0.558793i
$848$	−32.7975	−	18.9356i	−1.12627	−	0.650252i
$849$	−32.0169	−	55.4550i	−1.09882	−	1.90321i
$850$		0			0
$851$	2.50440	−	1.44591i	0.0858497	−	0.0495653i
$852$	58.3482	+	101.062i	1.99898	+	3.46233i
$853$	−19.7936			−0.677720			−0.338860	−	0.940837i	$-0.610041\pi$
$853$	−19.7936			−0.677720			−0.338860	+	0.940837i	$0.610041\pi$
$854$	9.98097	+	17.2875i	0.341542	+	0.591568i
$855$		0			0
$856$	−35.4452	−	20.4643i	−1.21149	−	0.699456i
$857$			11.7302i			0.400696i	0.979725	+	0.200348i	$0.0642073\pi$
$857$			11.7302i			0.400696i	−0.979725	+	0.200348i	$0.935793\pi$
$858$	−25.0634	+	10.5669i	−0.855652	+	0.360748i
$859$	−5.37452			−0.183376			−0.0916882	−	0.995788i	$-0.529226\pi$
$859$	−5.37452			−0.183376			−0.0916882	+	0.995788i	$0.529226\pi$
$860$		0			0
$861$	0.721551	−	1.24976i	0.0245904	−	0.0425918i
$862$	44.5467	−	25.7191i	1.51727	−	0.875995i
$863$	−25.3234			−0.862017			−0.431008	−	0.902348i	$-0.641842\pi$
$863$	−25.3234			−0.862017			−0.431008	+	0.902348i	$0.641842\pi$
$864$	11.7017	−	6.75596i	0.398099	−	0.229842i
$865$		0			0
$866$		−	73.4567i		−	2.49616i
$867$	40.6237	−	23.4541i	1.37965	−	0.796544i
$868$	10.2126	+	5.89623i	0.346637	+	0.200131i
$869$	8.63084	+	4.98302i	0.292781	+	0.169037i
$870$		0			0
$871$	3.62739	−	28.9599i	0.122909	−	0.981268i
$872$			56.0112i			1.89678i
$873$	10.5349	−	18.2470i	0.356553	−	0.617567i
$874$	27.3060	−	47.2954i	0.923640	−	1.59979i
$875$		0			0
$876$			44.4144i			1.50062i
$877$	10.3458	+	17.9194i	0.349352	+	0.605095i	0.986134	−	0.165949i	$-0.0530686\pi$
$877$	10.3458	+	17.9194i	0.349352	+	0.605095i	−0.636783	+	0.771043i	$0.719735\pi$
$878$	21.1520	+	36.6363i	0.713845	+	1.23642i
$879$		−	52.6151i		−	1.77466i
$880$		0			0
$881$	24.1997	−	41.9150i	0.815307	−	1.41215i	−0.0937999	−	0.995591i	$-0.529901\pi$
$881$	24.1997	−	41.9150i	0.815307	−	1.41215i	0.909107	−	0.416562i	$-0.136765\pi$
$882$	20.9879	−	36.3521i	0.706699	−	1.22404i
$883$			45.8550i			1.54314i	0.636142	+	0.771572i	$0.280529\pi$
$883$			45.8550i			1.54314i	−0.636142	+	0.771572i	$0.719471\pi$
$884$	9.63829	+	1.20725i	0.324171	+	0.0406042i
$885$		0			0
$886$	52.1705	+	30.1207i	1.75270	+	1.01192i
$887$	0.937332	+	0.541169i	0.0314725	+	0.0181707i	0.515654	−	0.856797i	$-0.327549\pi$
$887$	0.937332	+	0.541169i	0.0314725	+	0.0181707i	−0.484181	+	0.874968i	$0.660882\pi$
$888$	−10.3080	+	5.95131i	−0.345913	+	0.199713i
$889$		−	2.83781i		−	0.0951772i
$890$		0			0
$891$	−0.867947	+	0.501109i	−0.0290773	+	0.0167878i
$892$	90.2133			3.02056
$893$	46.8916	−	27.0729i	1.56917	−	0.905959i
$894$	47.1507	−	81.6675i	1.57696	−	2.73137i
$895$		0			0
$896$	32.1749			1.07489
$897$	31.0200	+	23.4938i	1.03573	+	0.784436i
$898$			52.0637i			1.73739i
$899$	−11.9886	−	6.92163i	−0.399842	−	0.230849i
$900$		0			0
$901$	−2.22756	−	3.85824i	−0.0742107	−	0.128537i
$902$	−0.715068			−0.0238092
$903$	1.71606	+	2.97231i	0.0571070	+	0.0989122i
$904$	−32.1973	+	18.5891i	−1.07086	+	0.618264i
$905$		0			0
$906$	64.5420	+	111.790i	2.14426	+	3.71397i
$907$	−39.4307	−	22.7653i	−1.30928	−	0.755910i	−0.327300	−	0.944920i	$-0.606139\pi$
$907$	−39.4307	−	22.7653i	−1.30928	−	0.755910i	−0.981975	+	0.189010i	$0.939472\pi$
$908$	33.1560	−	57.4279i	1.10032	−	1.90581i
$909$	−76.1009			−2.52411
$910$		0			0
$911$	39.7417			1.31670			0.658350	−	0.752712i	$-0.271255\pi$
$911$	39.7417			1.31670			0.658350	+	0.752712i	$0.271255\pi$
$912$	−43.8885	+	76.0171i	−1.45329	+	2.51718i
$913$	4.73967	+	2.73645i	0.156860	+	0.0905632i
$914$	38.1387	+	66.0582i	1.26152	+	2.18501i
$915$		0			0
$916$	−27.9012	+	16.1088i	−0.921883	+	0.532250i
$917$	−3.93118	−	6.80900i	−0.129819	−	0.224853i
$918$	8.95062			0.295415
$919$	23.4969	+	40.6978i	0.775091	+	1.34250i	0.934743	+	0.355323i	$0.115629\pi$
$919$	23.4969	+	40.6978i	0.775091	+	1.34250i	−0.159653	+	0.987173i	$0.551037\pi$
$920$		0			0
$921$	−7.70608	−	4.44911i	−0.253924	−	0.146603i
$922$		−	11.6745i		−	0.384481i
$923$	21.2569	−	28.0665i	0.699680	−	0.923821i
$924$	24.3484			0.801002
$925$		0			0
$926$	17.4700	−	30.2589i	0.574099	−	0.994369i
$927$	58.4680	−	33.7565i	1.92034	−	1.10871i
$928$	22.6991			0.745134
$929$	13.1821	−	7.61066i	0.432489	−	0.249698i	−0.267917	−	0.963442i	$-0.586335\pi$
$929$	13.1821	−	7.61066i	0.432489	−	0.249698i	0.700406	+	0.713744i	$0.253002\pi$
$930$		0			0
$931$			19.3180i			0.633121i
$932$	−69.7635	+	40.2780i	−2.28518	+	1.31935i
$933$	−7.78645	−	4.49551i	−0.254917	−	0.147176i
$934$	15.0959	+	8.71564i	0.493954	+	0.285184i
$935$		0			0
$936$	−79.7441	−	60.3963i	−2.60652	−	1.97412i
$937$			6.07285i			0.198392i	0.995068	+	0.0991958i	$0.0316270\pi$
$937$			6.07285i			0.198392i	−0.995068	+	0.0991958i	$0.968373\pi$
$938$	−19.2432	+	33.3302i	−0.628313	+	1.08827i
$939$	−49.9691	+	86.5490i	−1.63068	+	2.82442i
$940$		0			0
$941$		−	0.0496576i		−	0.00161879i	−1.00000		0.000809396i	$-0.999742\pi$
$941$		−	0.0496576i		−	0.00161879i	1.00000		0.000809396i	$-0.000257639\pi$
$942$	−8.54390	−	14.7985i	−0.278375	−	0.482160i
$943$	0.511495	+	0.885936i	0.0166566	+	0.0288500i
$944$			4.01429i			0.130654i
$945$		0			0
$946$	0.850322	−	1.47280i	0.0276464	−	0.0478849i
$947$	9.32907	−	16.1584i	0.303154	−	0.525078i	−0.673695	−	0.739010i	$-0.735294\pi$
$947$	9.32907	−	16.1584i	0.303154	−	0.525078i	0.976849	+	0.213932i	$0.0686270\pi$
$948$			111.372i			3.61720i
$949$	12.3475	−	5.20576i	0.400816	−	0.168986i
$950$		0			0
$951$	−33.3818	−	19.2730i	−1.08248	−	0.624969i
$952$	−5.84495	−	3.37458i	−0.189436	−	0.109371i
$953$	−1.32461	+	0.764764i	−0.0429083	+	0.0247731i	−0.521301	−	0.853373i	$-0.674553\pi$
$953$	−1.32461	+	0.764764i	−0.0429083	+	0.0247731i	0.478392	+	0.878146i	$0.341220\pi$
$954$			87.0739i			2.81912i
$955$		0			0
$956$	−46.6927	+	26.9581i	−1.51015	+	0.871886i
$957$	−28.5827			−0.923948
$958$	35.2028	−	20.3244i	1.13735	−	0.656650i
$959$	19.1566	−	33.1802i	0.618598	−	1.07144i
$960$		0			0
$961$	28.8564			0.930852
$962$	5.43293	+	4.11477i	0.175165	+	0.132666i
$963$			36.7475i			1.18417i
$964$	94.9299	+	54.8078i	3.05749	+	1.76524i
$965$		0			0
$966$	−25.6562	−	44.4379i	−0.825475	−	1.42976i
$967$	−32.1716			−1.03457			−0.517285	−	0.855813i	$-0.673057\pi$
$967$	−32.1716			−1.03457			−0.517285	+	0.855813i	$0.673057\pi$
$968$	27.3953	+	47.4501i	0.880519	+	1.52510i
$969$	−8.94253	+	5.16297i	−0.287276	+	0.165859i
$970$		0			0
$971$	8.62705	+	14.9425i	0.276855	+	0.479527i	0.970601	−	0.240692i	$-0.0773745\pi$
$971$	8.62705	+	14.9425i	0.276855	+	0.479527i	−0.693746	+	0.720219i	$0.744041\pi$
$972$	52.1188	+	30.0908i	1.67171	+	0.965164i
$973$	19.8383	−	34.3609i	0.635986	−	1.10156i
$974$	50.0122			1.60249
$975$		0			0
$976$	22.7442			0.728023
$977$	7.86142	−	13.6164i	0.251509	−	0.435626i	−0.712432	−	0.701741i	$-0.752407\pi$
$977$	7.86142	−	13.6164i	0.251509	−	0.435626i	0.963942	+	0.266114i	$0.0857398\pi$
$978$	−97.6440	−	56.3748i	−3.12231	−	1.80267i
$979$	6.72557	+	11.6490i	0.214950	+	0.372304i
$980$		0			0
$981$	43.5518	−	25.1447i	1.39050	−	0.802807i
$982$	19.7124	+	34.1429i	0.629049	+	1.08954i
$983$	−38.5356			−1.22910			−0.614548	−	0.788880i	$-0.710662\pi$
$983$	−38.5356			−1.22910			−0.614548	+	0.788880i	$0.710662\pi$
$984$	−2.10529	−	3.64647i	−0.0671141	−	0.116245i
$985$		0			0
$986$	13.0219	+	7.51821i	0.414703	+	0.239429i
$987$		−	50.8743i		−	1.61935i
$988$	86.6944	+	10.8590i	2.75812	+	0.345469i
$989$	−2.43298			−0.0773642
$990$		0			0
$991$	−4.29571	+	7.44040i	−0.136458	+	0.236352i	−0.926153	−	0.377147i	$-0.876905\pi$
$991$	−4.29571	+	7.44040i	−0.136458	+	0.236352i	0.789696	+	0.613499i	$0.210238\pi$
$992$	3.04399	−	1.75745i	0.0966468	−	0.0557991i
$993$	81.4014			2.58320
$994$	−40.2068	+	23.2134i	−1.27528	+	0.736285i
$995$		0			0
$996$			61.1606i			1.93795i
$997$	−17.7859	+	10.2687i	−0.563285	+	0.325213i	−0.754463	−	0.656343i	$-0.772103\pi$
$997$	−17.7859	+	10.2687i	−0.563285	+	0.325213i	0.191178	+	0.981555i	$0.438769\pi$
$998$	−2.69393	−	1.55534i	−0.0852750	−	0.0492335i
$999$	3.69198	+	2.13157i	0.116809	+	0.0674398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.m.c.199.4		8
5.2	odd	4		325.2.n.d.251.4		8
5.3	odd	4		65.2.m.a.56.1	yes	8
5.4	even	2		325.2.m.b.199.1		8
13.10	even	6		325.2.m.b.49.1		8
15.8	even	4		585.2.bu.c.316.4		8
20.3	even	4		1040.2.da.b.641.1		8
65.3	odd	12		845.2.m.g.361.4		8
65.7	even	12		4225.2.a.bl.1.4		4
65.8	even	4		845.2.e.n.191.4		8
65.18	even	4		845.2.e.m.191.1		8
65.23	odd	12		65.2.m.a.36.1	✓	8
65.28	even	12		845.2.e.m.146.1		8
65.32	even	12		4225.2.a.bi.1.1		4
65.33	even	12		845.2.a.l.1.1		4
65.38	odd	4		845.2.m.g.316.4		8
65.43	odd	12		845.2.c.g.506.1		8
65.48	odd	12		845.2.c.g.506.8		8
65.49	even	6	inner	325.2.m.c.49.4		8
65.58	even	12		845.2.a.m.1.4		4
65.62	odd	12		325.2.n.d.101.4		8
65.63	even	12		845.2.e.n.146.4		8
195.23	even	12		585.2.bu.c.361.4		8
195.98	odd	12		7605.2.a.cj.1.4		4
195.188	odd	12		7605.2.a.cf.1.1		4
260.23	even	12		1040.2.da.b.881.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.1	✓	8	65.23	odd	12
65.2.m.a.56.1	yes	8	5.3	odd	4
325.2.m.b.49.1		8	13.10	even	6
325.2.m.b.199.1		8	5.4	even	2
325.2.m.c.49.4		8	65.49	even	6	inner
325.2.m.c.199.4		8	1.1	even	1	trivial
325.2.n.d.101.4		8	65.62	odd	12
325.2.n.d.251.4		8	5.2	odd	4
585.2.bu.c.316.4		8	15.8	even	4
585.2.bu.c.361.4		8	195.23	even	12
845.2.a.l.1.1		4	65.33	even	12
845.2.a.m.1.4		4	65.58	even	12
845.2.c.g.506.1		8	65.43	odd	12
845.2.c.g.506.8		8	65.48	odd	12
845.2.e.m.146.1		8	65.28	even	12
845.2.e.m.191.1		8	65.18	even	4
845.2.e.n.146.4		8	65.63	even	12
845.2.e.n.191.4		8	65.8	even	4
845.2.m.g.316.4		8	65.38	odd	4
845.2.m.g.361.4		8	65.3	odd	12
1040.2.da.b.641.1		8	20.3	even	4
1040.2.da.b.881.1		8	260.23	even	12
4225.2.a.bi.1.1		4	65.32	even	12
4225.2.a.bl.1.4		4	65.7	even	12
7605.2.a.cf.1.1		4	195.188	odd	12
7605.2.a.cj.1.4		4	195.98	odd	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.24775 - 2.16117i) q^{2} +(-2.44811 - 1.41342i) q^{3} +(-2.11378 - 3.66117i) q^{4} +(-6.10929 + 3.52720i) q^{6} +(-0.952606 - 1.64996i) q^{7} -5.55889 q^{8} +(2.49551 + 4.32235i) q^{9} +O(q^{10})\)	\(q+(1.24775 - 2.16117i) q^{2} +(-2.44811 - 1.41342i) q^{3} +(-2.11378 - 3.66117i) q^{4} +(-6.10929 + 3.52720i) q^{6} +(-0.952606 - 1.64996i) q^{7} -5.55889 q^{8} +(2.49551 + 4.32235i) q^{9} +(0.926118 + 0.534695i) q^{11} +11.9506i q^{12} +(3.32235 - 1.40072i) q^{13} -4.75447 q^{14} +(-2.70857 + 4.69138i) q^{16} +(-0.551886 + 0.318632i) q^{17} +12.4551 q^{18} +(-4.96410 + 2.86603i) q^{19} +5.38573i q^{21} +(2.31114 - 1.33433i) q^{22} +(-3.30636 - 1.90893i) q^{23} +(13.6088 + 7.85704i) q^{24} +(1.11827 - 8.92792i) q^{26} -5.62828i q^{27} +(-4.02720 + 6.97531i) q^{28} +(4.72756 - 8.18837i) q^{29} -1.46410i q^{31} +(1.20036 + 2.07908i) q^{32} +(-1.51150 - 2.61799i) q^{33} +1.59030i q^{34} +(10.5499 - 18.2730i) q^{36} +(-0.378725 + 0.655970i) q^{37} +14.3044i q^{38} +(-10.1133 - 1.26675i) q^{39} +(-0.232051 - 0.133975i) q^{41} +(11.6395 + 6.72006i) q^{42} +(0.551886 - 0.318632i) q^{43} -4.52091i q^{44} +(-8.25104 + 4.76374i) q^{46} -9.44613 q^{47} +(13.2618 - 7.65668i) q^{48} +(1.68508 - 2.91865i) q^{49} +1.80144 q^{51} +(-12.1510 - 9.20287i) q^{52} +6.99102i q^{53} +(-12.1637 - 7.02271i) q^{54} +(5.29543 + 9.17196i) q^{56} +16.2036 q^{57} +(-11.7977 - 20.4341i) q^{58} +(0.641756 - 0.370518i) q^{59} +(-2.09928 - 3.63606i) q^{61} +(-3.16418 - 1.82684i) q^{62} +(4.75447 - 8.23499i) q^{63} -4.84325 q^{64} -7.54390 q^{66} +(4.04739 - 7.01029i) q^{67} +(2.33313 + 1.34703i) q^{68} +(5.39623 + 9.34654i) q^{69} +(8.45663 - 4.88244i) q^{71} +(-13.8723 - 24.0274i) q^{72} +3.71649 q^{73} +(0.945110 + 1.63698i) q^{74} +(20.9860 + 12.1163i) q^{76} -2.03741i q^{77} +(-15.3565 + 20.2760i) q^{78} +9.31937 q^{79} +(-0.468594 + 0.811629i) q^{81} +(-0.579085 + 0.334335i) q^{82} +5.11778 q^{83} +(19.7181 - 11.3842i) q^{84} -1.59030i q^{86} +(-23.1472 + 13.3640i) q^{87} +(-5.14819 - 2.97231i) q^{88} +(10.8932 + 6.28917i) q^{89} +(-5.47602 - 4.14741i) q^{91} +16.1402i q^{92} +(-2.06939 + 3.58429i) q^{93} +(-11.7864 + 20.4147i) q^{94} -6.78645i q^{96} +(-2.11078 - 3.65597i) q^{97} +(-4.20514 - 7.28351i) q^{98} +5.33734i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 6 q^{3} - 2 q^{4} - 18 q^{6} - 10 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 6 * q^3 - 2 * q^4 - 18 * q^6 - 10 * q^7 - 12 * q^8 + 4 * q^9	\( 8 q + 2 q^{2} - 6 q^{3} - 2 q^{4} - 18 q^{6} - 10 q^{7} - 12 q^{8} + 4 q^{9} - 8 q^{13} - 4 q^{14} - 2 q^{16} - 18 q^{17} + 40 q^{18} - 12 q^{19} - 6 q^{22} - 6 q^{23} + 12 q^{24} + 10 q^{26} - 8 q^{28} + 8 q^{29} + 4 q^{32} + 18 q^{33} + 20 q^{36} + 2 q^{37} + 12 q^{41} + 42 q^{42} + 18 q^{43} - 42 q^{46} + 16 q^{47} + 6 q^{48} - 12 q^{49} - 8 q^{51} - 16 q^{52} - 18 q^{54} + 12 q^{56} + 28 q^{57} - 22 q^{58} + 12 q^{59} - 28 q^{61} - 12 q^{62} + 4 q^{63} + 8 q^{64} + 12 q^{66} + 30 q^{67} - 12 q^{68} + 16 q^{69} - 12 q^{72} + 16 q^{73} - 10 q^{74} + 54 q^{76} - 18 q^{78} + 16 q^{79} + 8 q^{81} + 6 q^{82} - 24 q^{83} + 30 q^{84} - 54 q^{87} - 42 q^{88} - 24 q^{89} + 28 q^{91} - 8 q^{93} - 32 q^{94} + 2 q^{97} - 24 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 6 * q^3 - 2 * q^4 - 18 * q^6 - 10 * q^7 - 12 * q^8 + 4 * q^9 - 8 * q^13 - 4 * q^14 - 2 * q^16 - 18 * q^17 + 40 * q^18 - 12 * q^19 - 6 * q^22 - 6 * q^23 + 12 * q^24 + 10 * q^26 - 8 * q^28 + 8 * q^29 + 4 * q^32 + 18 * q^33 + 20 * q^36 + 2 * q^37 + 12 * q^41 + 42 * q^42 + 18 * q^43 - 42 * q^46 + 16 * q^47 + 6 * q^48 - 12 * q^49 - 8 * q^51 - 16 * q^52 - 18 * q^54 + 12 * q^56 + 28 * q^57 - 22 * q^58 + 12 * q^59 - 28 * q^61 - 12 * q^62 + 4 * q^63 + 8 * q^64 + 12 * q^66 + 30 * q^67 - 12 * q^68 + 16 * q^69 - 12 * q^72 + 16 * q^73 - 10 * q^74 + 54 * q^76 - 18 * q^78 + 16 * q^79 + 8 * q^81 + 6 * q^82 - 24 * q^83 + 30 * q^84 - 54 * q^87 - 42 * q^88 - 24 * q^89 + 28 * q^91 - 8 * q^93 - 32 * q^94 + 2 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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