LMFDB - Embedded newform 775.2.k.h.326.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(101,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(10))

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("775.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			326.14
Character	$\chi$	$=$	775.326
Dual form			775.2.k.h.126.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.19260 - 1.59301i) q^{2} +(-0.0871848 - 0.0633434i) q^{3} +(1.65175 - 5.08355i) q^{4} -0.292068 q^{6} +(-0.412403 + 1.26925i) q^{7} +(-2.80156 - 8.62233i) q^{8} +(-0.923462 - 2.84212i) q^{9} +O(q^{10})$	\(q+(2.19260 - 1.59301i) q^{2} +(-0.0871848 - 0.0633434i) q^{3} +(1.65175 - 5.08355i) q^{4} -0.292068 q^{6} +(-0.412403 + 1.26925i) q^{7} +(-2.80156 - 8.62233i) q^{8} +(-0.923462 - 2.84212i) q^{9} +(0.645600 - 1.98695i) q^{11} +(-0.466017 + 0.338581i) q^{12} +(4.27716 + 3.10754i) q^{13} +(1.11769 + 3.43991i) q^{14} +(-11.2295 - 8.15873i) q^{16} +(0.166005 + 0.510911i) q^{17} +(-6.55232 - 4.76054i) q^{18} +(-1.33255 + 0.968155i) q^{19} +(0.116354 - 0.0845360i) q^{21} +(-1.74970 - 5.38503i) q^{22} +(-1.57437 - 4.84540i) q^{23} +(-0.301914 + 0.929197i) q^{24} +14.3284 q^{26} +(-0.199423 + 0.613761i) q^{27} +(5.77110 + 4.19295i) q^{28} +(-5.49980 + 3.99584i) q^{29} +(-1.02157 + 5.47324i) q^{31} -19.4867 q^{32} +(-0.182147 + 0.132337i) q^{33} +(1.17787 + 0.855772i) q^{34} -15.9734 q^{36} +9.47746 q^{37} +(-1.37946 + 4.24554i) q^{38} +(-0.176061 - 0.541860i) q^{39} +(-4.83648 + 3.51391i) q^{41} +(0.120450 - 0.370706i) q^{42} +(7.66990 - 5.57251i) q^{43} +(-9.03441 - 6.56388i) q^{44} +(-11.1707 - 8.11602i) q^{46} +(-0.454274 - 0.330049i) q^{47} +(0.462242 + 1.42263i) q^{48} +(4.22221 + 3.06761i) q^{49} +(0.0178897 - 0.0550590i) q^{51} +(22.8621 - 16.6103i) q^{52} +(0.192906 + 0.593705i) q^{53} +(0.540475 + 1.66341i) q^{54} +12.0992 q^{56} +0.177504 q^{57} +(-5.69340 + 17.5225i) q^{58} +(8.23958 + 5.98641i) q^{59} +7.07355 q^{61} +(6.47905 + 13.6280i) q^{62} +3.98820 q^{63} +(-20.2673 + 14.7251i) q^{64} +(-0.188559 + 0.580325i) q^{66} +9.26497 q^{67} +2.87144 q^{68} +(-0.169664 + 0.522171i) q^{69} +(-1.57335 - 4.84227i) q^{71} +(-21.9186 + 15.9248i) q^{72} +(-1.37195 + 4.22244i) q^{73} +(20.7802 - 15.0977i) q^{74} +(2.72063 + 8.37324i) q^{76} +(2.25568 + 1.63885i) q^{77} +(-1.24922 - 0.907613i) q^{78} +(-2.81690 - 8.66952i) q^{79} +(-7.19670 + 5.22871i) q^{81} +(-5.00674 + 15.4091i) q^{82} +(-3.01847 + 2.19305i) q^{83} +(-0.237556 - 0.731123i) q^{84} +(7.93990 - 24.4365i) q^{86} +0.732608 q^{87} -18.9408 q^{88} +(-2.98913 + 9.19959i) q^{89} +(-5.70815 + 4.14722i) q^{91} -27.2323 q^{92} +(0.435760 - 0.412473i) q^{93} -1.52181 q^{94} +(1.69894 + 1.23435i) q^{96} +(-0.736960 + 2.26813i) q^{97} +14.1443 q^{98} -6.24335 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{4} - 4 q^{6} - 8 q^{9}+O(q^{10}) $ 56 * q - 2 * q^4 - 4 * q^6 - 8 * q^9	$ 56 q - 2 q^{4} - 4 q^{6} - 8 q^{9} - 14 q^{11} + 16 q^{14} - 22 q^{16} + 2 q^{19} - 38 q^{21} + 30 q^{24} + 12 q^{26} - 20 q^{29} + 26 q^{31} + 2 q^{34} - 44 q^{36} + 18 q^{39} - 20 q^{41} - 62 q^{44} - 70 q^{46} + 42 q^{49} + 10 q^{51} + 26 q^{54} + 208 q^{56} + 50 q^{59} + 56 q^{61} - 12 q^{64} + 60 q^{66} - 34 q^{69} - 8 q^{71} + 84 q^{74} - 20 q^{76} - 122 q^{79} + 42 q^{81} + 40 q^{84} + 78 q^{86} + 28 q^{89} - 20 q^{91} - 160 q^{94} - 70 q^{96} + 52 q^{99}+O(q^{100}) $ 56 * q - 2 * q^4 - 4 * q^6 - 8 * q^9 - 14 * q^11 + 16 * q^14 - 22 * q^16 + 2 * q^19 - 38 * q^21 + 30 * q^24 + 12 * q^26 - 20 * q^29 + 26 * q^31 + 2 * q^34 - 44 * q^36 + 18 * q^39 - 20 * q^41 - 62 * q^44 - 70 * q^46 + 42 * q^49 + 10 * q^51 + 26 * q^54 + 208 * q^56 + 50 * q^59 + 56 * q^61 - 12 * q^64 + 60 * q^66 - 34 * q^69 - 8 * q^71 + 84 * q^74 - 20 * q^76 - 122 * q^79 + 42 * q^81 + 40 * q^84 + 78 * q^86 + 28 * q^89 - 20 * q^91 - 160 * q^94 - 70 * q^96 + 52 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	2.19260	−	1.59301i	1.55040	−	1.12643i	0.607033	−	0.794677i	$-0.292360\pi$
$2$	2.19260	−	1.59301i	1.55040	−	1.12643i	0.943366	−	0.331754i	$-0.107640\pi$
$3$	−0.0871848	−	0.0633434i	−0.0503361	−	0.0365714i	0.562333	−	0.826911i	$-0.309904\pi$
$3$	−0.0871848	−	0.0633434i	−0.0503361	−	0.0365714i	−0.612669	+	0.790340i	$0.709904\pi$
$4$	1.65175	−	5.08355i	0.825873	−	2.54178i
$5$		0			0
$5$		0			0
$6$	−0.292068			−0.119236
$7$	−0.412403	+	1.26925i	−0.155874	+	0.479730i	−0.998248	−	0.0591622i	$-0.981157\pi$
$7$	−0.412403	+	1.26925i	−0.155874	+	0.479730i	0.842375	+	0.538892i	$0.181157\pi$
$8$	−2.80156	−	8.62233i	−0.990503	−	3.04845i
$9$	−0.923462	−	2.84212i	−0.307821	−	0.947375i
$10$		0			0
$11$	0.645600	−	1.98695i	0.194656	−	0.599088i	−0.805325	−	0.592834i	$-0.798009\pi$
$11$	0.645600	−	1.98695i	0.194656	−	0.599088i	0.999980	−	0.00625456i	$-0.00199090\pi$
$12$	−0.466017	+	0.338581i	−0.134528	+	0.0977400i
$13$	4.27716	+	3.10754i	1.18627	+	0.861877i	0.992865	−	0.119242i	$-0.0380464\pi$
$13$	4.27716	+	3.10754i	1.18627	+	0.861877i	0.193406	+	0.981119i	$0.438046\pi$
$14$	1.11769	+	3.43991i	0.298716	+	0.919354i
$15$		0			0
$16$	−11.2295	−	8.15873i	−2.80738	−	2.03968i
$17$	0.166005	+	0.510911i	0.0402621	+	0.123914i	0.969167	−	0.246404i	$-0.0792489\pi$
$17$	0.166005	+	0.510911i	0.0402621	+	0.123914i	−0.928905	+	0.370318i	$0.879249\pi$
$18$	−6.55232	−	4.76054i	−1.54440	−	1.12207i
$19$	−1.33255	+	0.968155i	−0.305708	+	0.222110i	−0.730053	−	0.683391i	$-0.760505\pi$
$19$	−1.33255	+	0.968155i	−0.305708	+	0.222110i	0.424345	+	0.905501i	$0.360505\pi$
$20$		0			0
$21$	0.116354	−	0.0845360i	0.0253905	−	0.0184473i
$22$	−1.74970	−	5.38503i	−0.373038	−	1.14809i
$23$	−1.57437	−	4.84540i	−0.328278	−	1.01034i	−0.969939	−	0.243348i	$-0.921754\pi$
$23$	−1.57437	−	4.84540i	−0.328278	−	1.01034i	0.641661	−	0.766988i	$-0.278246\pi$
$24$	−0.301914	+	0.929197i	−0.0616280	+	0.189671i
$25$		0			0
$26$	14.3284			2.81004
$27$	−0.199423	+	0.613761i	−0.0383790	+	0.118118i
$28$	5.77110	+	4.19295i	1.09064	+	0.792393i
$29$	−5.49980	+	3.99584i	−1.02129	+	0.742008i	−0.966546	−	0.256493i	$-0.917433\pi$
$29$	−5.49980	+	3.99584i	−1.02129	+	0.742008i	−0.0547401	+	0.998501i	$0.517433\pi$
$30$		0			0
$31$	−1.02157	+	5.47324i	−0.183480	+	0.983023i
$31$	−1.02157	+	5.47324i	−0.183480	+	0.983023i
$32$	−19.4867			−3.44479
$33$	−0.182147	+	0.132337i	−0.0317077	+	0.0230370i
$34$	1.17787	+	0.855772i	0.202003	+	0.146764i
$35$		0			0
$36$	−15.9734			−2.66224
$37$	9.47746			1.55808			0.779042	−	0.626972i	$-0.215706\pi$
$37$	9.47746			1.55808			0.779042	+	0.626972i	$0.215706\pi$
$38$	−1.37946	+	4.24554i	−0.223778	+	0.688718i
$39$	−0.176061	−	0.541860i	−0.0281923	−	0.0867671i
$40$		0			0
$41$	−4.83648	+	3.51391i	−0.755331	+	0.548780i	−0.897475	−	0.441066i	$-0.854600\pi$
$41$	−4.83648	+	3.51391i	−0.755331	+	0.548780i	0.142144	+	0.989846i	$0.454600\pi$
$42$	0.120450	−	0.370706i	0.0185858	−	0.0572012i
$43$	7.66990	−	5.57251i	1.16965	−	0.849799i	0.178682	−	0.983907i	$-0.442817\pi$
$43$	7.66990	−	5.57251i	1.16965	−	0.849799i	0.990967	+	0.134108i	$0.0428168\pi$
$44$	−9.03441	−	6.56388i	−1.36199	−	0.989542i
$45$		0			0
$46$	−11.1707	−	8.11602i	−1.64704	−	1.19664i
$47$	−0.454274	−	0.330049i	−0.0662626	−	0.0481426i	0.554161	−	0.832410i	$-0.313039\pi$
$47$	−0.454274	−	0.330049i	−0.0662626	−	0.0481426i	−0.620423	+	0.784267i	$0.713039\pi$
$48$	0.462242	+	1.42263i	0.0667188	+	0.205339i
$49$	4.22221	+	3.06761i	0.603172	+	0.438230i
$50$		0			0
$51$	0.0178897	−	0.0550590i	0.00250506	−	0.00770980i
$52$	22.8621	−	16.6103i	3.17041	−	2.30344i
$53$	0.192906	+	0.593705i	0.0264977	+	0.0815516i	0.963431	−	0.267957i	$-0.0863485\pi$
$53$	0.192906	+	0.593705i	0.0264977	+	0.0815516i	−0.936933	+	0.349509i	$0.886349\pi$
$54$	0.540475	+	1.66341i	0.0735494	+	0.226362i
$55$		0			0
$56$	12.0992			1.61683
$57$	0.177504			0.0235110
$58$	−5.69340	+	17.5225i	−0.747581	+	2.30082i
$59$	8.23958	+	5.98641i	1.07270	+	0.779364i	0.976396	−	0.215988i	$-0.0692972\pi$
$59$	8.23958	+	5.98641i	1.07270	+	0.779364i	0.0963061	+	0.995352i	$0.469297\pi$
$60$		0			0
$61$	7.07355			0.905675			0.452838	−	0.891593i	$-0.350412\pi$
$61$	7.07355			0.905675			0.452838	+	0.891593i	$0.350412\pi$
$62$	6.47905	+	13.6280i	0.822841	+	1.73076i
$63$	3.98820			0.502466
$64$	−20.2673	+	14.7251i	−2.53341	+	1.84063i
$65$		0			0
$66$	−0.188559	+	0.580325i	−0.0232100	+	0.0714330i
$67$	9.26497			1.13190			0.565948	−	0.824441i	$-0.308510\pi$
$67$	9.26497			1.13190			0.565948	+	0.824441i	$0.308510\pi$
$68$	2.87144			0.348213
$69$	−0.169664	+	0.522171i	−0.0204251	+	0.0628620i
$70$		0			0
$71$	−1.57335	−	4.84227i	−0.186722	−	0.574672i	0.813252	−	0.581912i	$-0.197695\pi$
$71$	−1.57335	−	4.84227i	−0.186722	−	0.574672i	−0.999974	+	0.00724037i	$0.997695\pi$
$72$	−21.9186	+	15.9248i	−2.58313	+	1.87675i
$73$	−1.37195	+	4.22244i	−0.160575	+	0.494199i	−0.998683	−	0.0513054i	$-0.983662\pi$
$73$	−1.37195	+	4.22244i	−0.160575	+	0.494199i	0.838108	+	0.545504i	$0.183662\pi$
$74$	20.7802	−	15.0977i	2.41565	−	1.75507i
$75$		0			0
$76$	2.72063	+	8.37324i	0.312078	+	0.960476i
$77$	2.25568	+	1.63885i	0.257059	+	0.186764i
$78$	−1.24922	−	0.907613i	−0.141447	−	0.102767i
$79$	−2.81690	−	8.66952i	−0.316926	−	0.975397i	−0.974955	−	0.222404i	$-0.928609\pi$
$79$	−2.81690	−	8.66952i	−0.316926	−	0.975397i	0.658029	−	0.752993i	$-0.271391\pi$
$80$		0			0
$81$	−7.19670	+	5.22871i	−0.799634	+	0.580968i
$82$	−5.00674	+	15.4091i	−0.552901	+	1.70166i
$83$	−3.01847	+	2.19305i	−0.331321	+	0.240719i	−0.740991	−	0.671515i	$-0.765644\pi$
$83$	−3.01847	+	2.19305i	−0.331321	+	0.240719i	0.409670	+	0.912234i	$0.365644\pi$
$84$	−0.237556	−	0.731123i	−0.0259195	−	0.0797720i
$85$		0			0
$86$	7.93990	−	24.4365i	0.856182	−	2.63506i
$87$	0.732608			0.0785439
$88$	−18.9408			−2.01910
$89$	−2.98913	+	9.19959i	−0.316847	+	0.975155i	0.658140	+	0.752895i	$0.271343\pi$
$89$	−2.98913	+	9.19959i	−0.316847	+	0.975155i	−0.974987	+	0.222260i	$0.928657\pi$
$90$		0			0
$91$	−5.70815	+	4.14722i	−0.598377	+	0.434746i
$92$	−27.2323			−2.83916
$93$	0.435760	−	0.412473i	0.0451862	−	0.0427715i
$94$	−1.52181			−0.156963
$95$		0			0
$96$	1.69894	+	1.23435i	0.173397	+	0.125981i
$97$	−0.736960	+	2.26813i	−0.0748269	+	0.230294i	−0.981474	−	0.191597i	$-0.938633\pi$
$97$	−0.736960	+	2.26813i	−0.0748269	+	0.230294i	0.906647	+	0.421891i	$0.138633\pi$
$98$	14.1443			1.42879
$99$	−6.24335			−0.627480
$100$		0			0
$101$	−2.70240	−	8.31714i	−0.268899	−	0.827586i	−0.990769	−	0.135558i	$-0.956717\pi$
$101$	−2.70240	−	8.31714i	−0.268899	−	0.827586i	0.721870	−	0.692028i	$-0.243283\pi$
$102$	−0.0484847	−	0.149221i	−0.00480070	−	0.0147750i
$103$	−9.36612	+	6.80489i	−0.922872	+	0.670506i	−0.944237	−	0.329266i	$-0.893199\pi$
$103$	−9.36612	+	6.80489i	−0.922872	+	0.670506i	0.0213655	+	0.999772i	$0.493199\pi$
$104$	14.8115	−	45.5851i	1.45239	−	4.46999i
$105$		0			0
$106$	1.36875	+	0.994452i	0.132944	+	0.0965897i
$107$	2.72269	+	8.37958i	0.263212	+	0.810084i	0.992100	+	0.125451i	$0.0400377\pi$
$107$	2.72269	+	8.37958i	0.263212	+	0.810084i	−0.728888	+	0.684633i	$0.759962\pi$
$108$	2.79069	+	2.02755i	0.268534	+	0.195102i
$109$	−4.59832	−	3.34088i	−0.440439	−	0.319998i	0.345370	−	0.938467i	$-0.387753\pi$
$109$	−4.59832	−	3.34088i	−0.440439	−	0.319998i	−0.785809	+	0.618469i	$0.787753\pi$
$110$		0			0
$111$	−0.826290	−	0.600335i	−0.0784280	−	0.0569812i
$112$	14.9865	−	10.8884i	1.41609	−	1.02885i
$113$	−3.78653	+	11.6537i	−0.356207	+	1.09629i	0.599100	+	0.800675i	$0.295525\pi$
$113$	−3.78653	+	11.6537i	−0.356207	+	1.09629i	−0.955306	+	0.295617i	$0.904475\pi$
$114$	0.389195	−	0.282767i	0.0364515	−	0.0264835i
$115$		0			0
$116$	11.2288	+	34.5586i	1.04257	+	3.20869i
$117$	4.88222	−	15.0259i	0.451361	−	1.38915i
$118$	27.6025			2.54102
$119$	−0.716933			−0.0657211
$120$		0			0
$121$	5.36801	+	3.90009i	0.488001	+	0.354553i
$122$	15.5094	−	11.2683i	1.40416	−	1.02018i
$123$	0.644250			0.0580901
$124$	26.1361	+	14.2336i	2.34710	+	1.27822i
$125$		0			0
$126$	8.74450	−	6.35325i	0.779022	−	0.565993i
$127$	9.28928	+	6.74906i	0.824290	+	0.598882i	0.917938	−	0.396724i	$-0.129853\pi$
$127$	9.28928	+	6.74906i	0.824290	+	0.598882i	−0.0936480	+	0.995605i	$0.529853\pi$
$128$	−8.93735	+	27.5063i	−0.789958	+	2.43124i
$129$	−1.02168			−0.0899539
$130$		0			0
$131$	0.953809	−	2.93552i	0.0833347	−	0.256478i	−0.900704	−	0.434434i	$-0.856948\pi$
$131$	0.953809	−	2.93552i	0.0833347	−	0.256478i	0.984038	+	0.177956i	$0.0569485\pi$
$132$	0.371884	+	1.14454i	0.0323683	+	0.0996195i
$133$	−0.679279	−	2.09061i	−0.0589010	−	0.181279i
$134$	20.3143	−	14.7592i	1.75489	−	1.27500i
$135$		0			0
$136$	3.94017	−	2.86270i	0.337867	−	0.245474i
$137$	−10.0693	−	7.31578i	−0.860279	−	0.625029i	0.0676817	−	0.997707i	$-0.478440\pi$
$137$	−10.0693	−	7.31578i	−0.860279	−	0.625029i	−0.927961	+	0.372678i	$0.878440\pi$
$138$	0.459822	+	1.41519i	0.0391426	+	0.120469i
$139$	−10.2849	−	7.47239i	−0.872351	−	0.633800i	0.0588660	−	0.998266i	$-0.481252\pi$
$139$	−10.2849	−	7.47239i	−0.872351	−	0.633800i	−0.931217	+	0.364466i	$0.881252\pi$
$140$		0			0
$141$	0.0186993	+	0.0575505i	0.00157476	+	0.00484663i
$142$	−11.1635	−	8.11077i	−0.936822	−	0.680641i
$143$	8.93587	−	6.49229i	0.747255	−	0.542912i
$144$	−12.8181	+	39.4500i	−1.06817	+	3.28750i
$145$		0			0
$146$	3.71826	+	11.4436i	0.307726	+	0.947082i
$147$	−0.173799	−	0.534898i	−0.0143347	−	0.0441177i
$148$	15.6544	−	48.1792i	1.28678	−	3.96030i
$149$	−16.7671			−1.37361			−0.686806	−	0.726840i	$-0.740988\pi$
$149$	−16.7671			−1.37361			−0.686806	+	0.726840i	$0.740988\pi$
$150$		0			0
$151$	3.04253	−	9.36393i	0.247597	−	0.762026i	−0.747601	−	0.664148i	$-0.768794\pi$
$151$	3.04253	−	9.36393i	0.247597	−	0.762026i	0.995198	−	0.0978781i	$-0.0312055\pi$
$152$	12.0810	+	8.77734i	0.979897	+	0.711937i
$153$	1.29877	−	0.943614i	0.105000	−	0.0762866i
$154$	7.55651			0.608921
$155$		0			0
$156$	−3.04539			−0.243826
$157$	−0.664263	+	0.482615i	−0.0530139	+	0.0385169i	−0.613977	−	0.789324i	$-0.710431\pi$
$157$	−0.664263	+	0.482615i	−0.0530139	+	0.0385169i	0.560963	+	0.827841i	$0.310431\pi$
$158$	−19.9870	−	14.5214i	−1.59008	−	1.15526i
$159$	0.0207888	−	0.0639814i	0.00164866	−	0.00507405i
$160$		0			0
$161$	6.79928			0.535859
$162$	−7.45005	+	22.9289i	−0.585331	+	1.80146i
$163$	−2.90594	−	8.94357i	−0.227611	−	0.700515i	−0.998016	−	0.0629599i	$-0.979946\pi$
$163$	−2.90594	−	8.94357i	−0.227611	−	0.700515i	0.770405	−	0.637555i	$-0.220054\pi$
$164$	9.87450	+	30.3906i	0.771069	+	2.37311i
$165$		0			0
$166$	−3.12473	+	9.61694i	−0.242526	+	0.746419i
$167$	12.5106	−	9.08947i	0.968098	−	0.703364i	0.0130807	−	0.999914i	$-0.495836\pi$
$167$	12.5106	−	9.08947i	0.968098	−	0.703364i	0.955017	+	0.296550i	$0.0958362\pi$
$168$	−1.05487	−	0.766408i	−0.0813850	−	0.0591296i
$169$	4.62009	+	14.2192i	0.355392	+	1.09378i
$170$		0			0
$171$	3.98218	+	2.89322i	0.304525	+	0.221250i
$172$	−15.6594	−	48.1947i	−1.19402	−	3.67481i
$173$	2.45735	+	1.78537i	0.186829	+	0.135739i	0.677268	−	0.735736i	$-0.263164\pi$
$173$	2.45735	+	1.78537i	0.186829	+	0.135739i	−0.490439	+	0.871475i	$0.663164\pi$
$174$	1.60631	−	1.16705i	0.121774	−	0.0884742i
$175$		0			0
$176$	−23.4608	+	17.0453i	−1.76842	+	1.28483i
$177$	−0.339166	−	1.04385i	−0.0254933	−	0.0784603i
$178$	8.10113	+	24.9327i	0.607205	+	1.86879i
$179$	−3.37706	+	10.3935i	−0.252413	+	0.776848i	0.741915	+	0.670494i	$0.233918\pi$
$179$	−3.37706	+	10.3935i	−0.252413	+	0.776848i	−0.994328	+	0.106354i	$0.966082\pi$
$180$		0			0
$181$	−11.4543			−0.851389			−0.425695	−	0.904867i	$-0.639970\pi$
$181$	−11.4543			−0.851389			−0.425695	+	0.904867i	$0.639970\pi$
$182$	−5.90910	+	18.1863i	−0.438011	+	1.34806i
$183$	−0.616706	−	0.448063i	−0.0455882	−	0.0331218i
$184$	−37.3680	+	27.1494i	−2.75480	+	2.00148i
$185$		0			0
$186$	0.298369	−	1.59856i	0.0218775	−	0.117212i
$187$	1.12233			0.0820727
$188$	−2.42817	+	1.76417i	−0.177092	+	0.128665i
$189$	−0.696771	−	0.506234i	−0.0506827	−	0.0368231i
$190$		0			0
$191$	8.87761			0.642361			0.321181	−	0.947018i	$-0.395920\pi$
$191$	8.87761			0.642361			0.321181	+	0.947018i	$0.395920\pi$
$192$	2.69974			0.194837
$193$	−0.686674	+	2.11337i	−0.0494279	+	0.152123i	−0.972724	−	0.231965i	$-0.925484\pi$
$193$	−0.686674	+	2.11337i	−0.0494279	+	0.152123i	0.923296	+	0.384089i	$0.125484\pi$
$194$	1.99731	+	6.14707i	0.143398	+	0.441334i
$195$		0			0
$196$	22.5684	−	16.3969i	1.61203	−	1.17121i
$197$	−1.83338	+	5.64256i	−0.130623	+	0.402016i	−0.994884	−	0.101029i	$-0.967787\pi$
$197$	−1.83338	+	5.64256i	−0.130623	+	0.402016i	0.864261	+	0.503044i	$0.167787\pi$
$198$	−13.6891	+	9.94574i	−0.972845	+	0.706813i
$199$	−18.9512	−	13.7688i	−1.34341	−	0.976047i	−0.999311	−	0.0371153i	$-0.988183\pi$
$199$	−18.9512	−	13.7688i	−1.34341	−	0.976047i	−0.344103	−	0.938932i	$-0.611817\pi$
$200$		0			0
$201$	−0.807765	−	0.586875i	−0.0569753	−	0.0413950i
$202$	−19.1746	−	13.9311i	−1.34912	−	0.980192i
$203$	−2.80357	−	8.62849i	−0.196772	−	0.605602i
$204$	−0.250346	−	0.181887i	−0.0175277	−	0.0127346i
$205$		0			0
$206$	−9.69584	+	29.8407i	−0.675541	+	2.07910i
$207$	−12.3174	+	8.94909i	−0.856116	+	0.622005i
$208$	−22.6769	−	69.7924i	−1.57236	−	4.83923i
$209$	1.06338	+	3.27275i	0.0735557	+	0.226381i
$210$		0			0
$211$	−6.65520			−0.458163			−0.229081	−	0.973407i	$-0.573572\pi$
$211$	−6.65520			−0.458163			−0.229081	+	0.973407i	$0.573572\pi$
$212$	3.33676			0.229170
$213$	−0.169554	+	0.521834i	−0.0116177	+	0.0357555i
$214$	19.3185	+	14.0357i	1.32059	+	0.959463i
$215$		0			0
$216$	5.85074			0.398093
$217$	−6.52560	−	3.55381i	−0.442986	−	0.241249i
$218$	−15.4043			−1.04331
$219$	0.387077	−	0.281228i	0.0261562	−	0.0190036i
$220$		0			0
$221$	−0.877646	+	2.70112i	−0.0590368	+	0.181697i
$222$	−2.76806			−0.185780
$223$	−1.39239			−0.0932416			−0.0466208	−	0.998913i	$-0.514845\pi$
$223$	−1.39239			−0.0932416			−0.0466208	+	0.998913i	$0.514845\pi$
$224$	8.03637	−	24.7334i	0.536952	−	1.65257i
$225$		0			0
$226$	10.2622	+	31.5839i	0.682634	+	2.10093i
$227$	−15.3133	+	11.1258i	−1.01638	+	0.738444i	−0.965538	−	0.260263i	$-0.916191\pi$
$227$	−15.3133	+	11.1258i	−1.01638	+	0.738444i	−0.0508432	+	0.998707i	$0.516191\pi$
$228$	0.293192	−	0.902353i	0.0194171	−	0.0597598i
$229$	11.0186	−	8.00552i	0.728133	−	0.529019i	−0.160839	−	0.986981i	$-0.551420\pi$
$229$	11.0186	−	8.00552i	0.728133	−	0.529019i	0.888972	+	0.457961i	$0.151420\pi$
$230$		0			0
$231$	−0.0928509	−	0.285766i	−0.00610914	−	0.0188020i
$232$	49.8614	+	36.2265i	3.27356	+	2.37838i
$233$	−1.12057	−	0.814141i	−0.0734109	−	0.0533362i	0.550475	−	0.834852i	$-0.314447\pi$
$233$	−1.12057	−	0.814141i	−0.0734109	−	0.0533362i	−0.623885	+	0.781516i	$0.714447\pi$
$234$	−13.2318	−	40.7232i	−0.864988	−	2.66216i
$235$		0			0
$236$	44.0419	−	31.9983i	2.86688	−	2.08291i
$237$	−0.303567	+	0.934282i	−0.0197188	+	0.0606881i
$238$	−1.57194	+	1.14208i	−0.101894	+	0.0740303i
$239$	4.24494	+	13.0646i	0.274583	+	0.845078i	0.989330	+	0.145695i	$0.0465419\pi$
$239$	4.24494	+	13.0646i	0.274583	+	0.845078i	−0.714747	+	0.699383i	$0.753458\pi$
$240$		0			0
$241$	−4.08426	+	12.5701i	−0.263090	+	0.809709i	0.729037	+	0.684474i	$0.239968\pi$
$241$	−4.08426	+	12.5701i	−0.263090	+	0.809709i	−0.992127	+	0.125234i	$0.960032\pi$
$242$	17.9828			1.15598
$243$	2.89469			0.185694
$244$	11.6837	−	35.9588i	0.747973	−	2.30202i
$245$		0			0
$246$	1.41258	−	1.02630i	0.0900628	−	0.0654344i
$247$	−8.70812			−0.554084
$248$	50.0541	−	6.52530i	3.17844	−	0.414357i
$249$	0.402080			0.0254808
$250$		0			0
$251$	−19.8280	−	14.4059i	−1.25153	−	0.909289i	−0.253220	−	0.967409i	$-0.581490\pi$
$251$	−19.8280	−	14.4059i	−1.25153	−	0.909289i	−0.998310	+	0.0581195i	$0.981490\pi$
$252$	6.58749	−	20.2742i	0.414973	−	1.27716i
$253$	−10.6440			−0.669182
$254$	31.1190			1.95258
$255$		0			0
$256$	8.73914	+	26.8963i	0.546196	+	1.68102i
$257$	−5.86643	−	18.0550i	−0.365938	−	1.12624i	−0.949392	−	0.314095i	$-0.898299\pi$
$257$	−5.86643	−	18.0550i	−0.365938	−	1.12624i	0.583453	−	0.812147i	$-0.301701\pi$
$258$	−2.24013	+	1.62755i	−0.139464	+	0.101327i
$259$	−3.90854	+	12.0292i	−0.242865	+	0.747460i
$260$		0			0
$261$	16.4355	+	11.9411i	1.01733	+	0.739135i
$262$	−2.58501	−	7.95585i	−0.159702	−	0.491514i
$263$	4.29418	+	3.11991i	0.264791	+	0.192382i	0.712256	−	0.701919i	$-0.247673\pi$
$263$	4.29418	+	3.11991i	0.264791	+	0.192382i	−0.447466	+	0.894301i	$0.647673\pi$
$264$	1.65135	+	1.19978i	0.101634	+	0.0738412i
$265$		0			0
$266$	−4.81975	−	3.50175i	−0.295518	−	0.214706i
$267$	0.843340	−	0.612723i	0.0516116	−	0.0374980i
$268$	15.3034	−	47.0990i	0.934803	−	2.87703i
$269$	−7.16253	+	5.20388i	−0.436707	+	0.317286i	−0.784325	−	0.620350i	$-0.786991\pi$
$269$	−7.16253	+	5.20388i	−0.436707	+	0.317286i	0.347618	+	0.937636i	$0.386991\pi$
$270$		0			0
$271$	−6.72218	−	20.6887i	−0.408343	−	1.25675i	−0.918071	−	0.396416i	$-0.870254\pi$
$271$	−6.72218	−	20.6887i	−0.408343	−	1.25675i	0.509728	−	0.860336i	$-0.329746\pi$
$272$	2.30423	−	7.09168i	0.139714	−	0.429996i
$273$	0.760363			0.0460193
$274$	−33.7321			−2.03783
$275$		0			0
$276$	2.37424	+	1.72499i	0.142913	+	0.103832i
$277$	−1.00034	+	0.726793i	−0.0601049	+	0.0436688i	−0.617432	−	0.786624i	$-0.711827\pi$
$277$	−1.00034	+	0.726793i	−0.0601049	+	0.0436688i	0.557327	+	0.830293i	$0.311827\pi$
$278$	−34.4542			−2.06642
$279$	16.4990	−	2.15090i	0.987771	−	0.128771i
$280$		0			0
$281$	−20.4586	+	14.8641i	−1.22046	+	0.886716i	−0.996138	−	0.0877996i	$-0.972016\pi$
$281$	−20.4586	+	14.8641i	−1.22046	+	0.886716i	−0.224321	+	0.974515i	$0.572016\pi$
$282$	0.132679	+	0.0963967i	0.00790090	+	0.00574034i
$283$	−4.93621	+	15.1921i	−0.293427	+	0.903076i	0.690318	+	0.723506i	$0.257471\pi$
$283$	−4.93621	+	15.1921i	−0.293427	+	0.903076i	−0.983745	+	0.179570i	$0.942529\pi$
$284$	−27.2147			−1.61490
$285$		0			0
$286$	9.25044	−	28.4699i	0.546990	−	1.68346i
$287$	−2.46544	−	7.58783i	−0.145530	−	0.447896i
$288$	17.9952	+	55.3835i	1.06038	+	3.26351i
$289$	13.5198	−	9.82272i	0.795283	−	0.577807i
$290$		0			0
$291$	0.207923	−	0.151065i	0.0121886	−	0.00885557i
$292$	19.1989	+	13.9488i	1.12353	+	0.816291i
$293$	−2.76444	−	8.50808i	−0.161500	−	0.497047i	0.837261	−	0.546804i	$-0.184156\pi$
$293$	−2.76444	−	8.50808i	−0.161500	−	0.497047i	−0.998761	+	0.0497562i	$0.984156\pi$
$294$	−1.23317	−	0.895951i	−0.0719200	−	0.0522529i
$295$		0			0
$296$	−26.5517	−	81.7178i	−1.54329	−	4.74975i
$297$	1.09077	+	0.792487i	0.0632926	+	0.0459848i
$298$	−36.7634	+	26.7102i	−2.12965	+	1.54728i
$299$	8.32346	−	25.6170i	0.481358	−	1.48147i
$300$		0			0
$301$	3.90980	+	12.0331i	0.225357	+	0.693577i
$302$	−8.24584	−	25.3781i	−0.474495	−	1.46035i
$303$	−0.291228	+	0.896307i	−0.0167306	+	0.0514915i
$304$	22.8628			1.31127
$305$		0			0
$306$	1.34449	−	4.13793i	0.0768596	−	0.236549i
$307$	5.52226	+	4.01216i	0.315172	+	0.228986i	0.734113	−	0.679028i	$-0.237598\pi$
$307$	5.52226	+	4.01216i	0.315172	+	0.228986i	−0.418941	+	0.908014i	$0.637598\pi$
$308$	12.0570	−	8.75993i	0.687012	−	0.499143i
$309$	1.24763			0.0709751
$310$		0			0
$311$	−12.7928			−0.725412			−0.362706	−	0.931904i	$-0.618147\pi$
$311$	−12.7928			−0.725412			−0.362706	+	0.931904i	$0.618147\pi$
$312$	−4.17885	+	3.03611i	−0.236581	+	0.171886i
$313$	14.1566	+	10.2853i	0.800176	+	0.581362i	0.910966	−	0.412482i	$-0.135338\pi$
$313$	14.1566	+	10.2853i	0.800176	+	0.581362i	−0.110790	+	0.993844i	$0.535338\pi$
$314$	−0.687647	+	2.11636i	−0.0388061	+	0.119433i
$315$		0			0
$316$	−48.7248			−2.74098
$317$	−2.91114	+	8.95957i	−0.163506	+	0.503219i	−0.998923	−	0.0463970i	$-0.985226\pi$
$317$	−2.91114	+	8.95957i	−0.163506	+	0.503219i	0.835417	+	0.549616i	$0.185226\pi$
$318$	−0.0563418	−	0.173402i	−0.00315949	−	0.00972391i
$319$	4.38886	+	13.5075i	0.245729	+	0.756277i
$320$		0			0
$321$	0.293414	−	0.903036i	0.0163768	−	0.0504025i
$322$	14.9081	−	10.8314i	0.830795	−	0.603608i
$323$	−0.715851	−	0.520096i	−0.0398310	−	0.0289389i
$324$	14.6933	+	45.2213i	0.816294	+	2.51230i
$325$		0			0
$326$	−20.6188	−	14.9804i	−1.14197	−	0.829689i
$327$	0.189281	+	0.582547i	0.0104673	+	0.0322149i
$328$	43.8478	+	31.8573i	2.42109	+	1.75902i
$329$	0.606258	−	0.440472i	0.0334241	−	0.0242840i
$330$		0			0
$331$	27.6279	−	20.0728i	1.51857	−	1.10330i	0.556373	−	0.830933i	$-0.312193\pi$
$331$	27.6279	−	20.0728i	1.51857	−	1.10330i	0.962193	−	0.272370i	$-0.0878073\pi$
$332$	6.16273	+	18.9669i	0.338224	+	1.04095i
$333$	−8.75207	−	26.9361i	−0.479611	−	1.47609i
$334$	12.9510	−	39.8591i	0.708647	−	2.18099i
$335$		0			0
$336$	−1.99630			−0.108907
$337$	−5.84176	+	17.9791i	−0.318221	+	0.979383i	0.656188	+	0.754598i	$0.272168\pi$
$337$	−5.84176	+	17.9791i	−0.318221	+	0.979383i	−0.974408	+	0.224785i	$0.927832\pi$
$338$	32.7813	+	23.8170i	1.78307	+	1.29548i
$339$	1.06832	−	0.776177i	0.0580230	−	0.0421561i
$340$		0			0
$341$	10.2155	+	5.56334i	0.553203	+	0.301272i
$342$	13.3402			0.721357
$343$	−13.1926	+	9.58500i	−0.712334	+	0.517541i
$344$	−69.5357	−	50.5207i	−3.74911	−	2.72389i
$345$		0			0
$346$	8.23209			0.442560
$347$	−9.11110			−0.489110			−0.244555	−	0.969635i	$-0.578642\pi$
$347$	−9.11110			−0.489110			−0.244555	+	0.969635i	$0.578642\pi$
$348$	1.21008	−	3.72425i	0.0648673	−	0.199641i
$349$	4.33123	+	13.3301i	0.231845	+	0.713546i	0.997524	+	0.0703233i	$0.0224031\pi$
$349$	4.33123	+	13.3301i	0.231845	+	0.713546i	−0.765679	+	0.643223i	$0.777597\pi$
$350$		0			0
$351$	−2.76025	+	2.00544i	−0.147331	+	0.107042i
$352$	−12.5806	+	38.7191i	−0.670547	+	2.06373i
$353$	9.42804	−	6.84987i	0.501804	−	0.364582i	−0.307902	−	0.951418i	$-0.599627\pi$
$353$	9.42804	−	6.84987i	0.501804	−	0.364582i	0.809706	+	0.586836i	$0.199627\pi$
$354$	−2.40652	−	1.74844i	−0.127905	−	0.0929284i
$355$		0			0
$356$	41.8293	+	30.3908i	2.21695	+	1.61071i
$357$	0.0625056	+	0.0454130i	0.00330815	+	0.00240351i
$358$	9.15249	+	28.1685i	0.483724	+	1.48875i
$359$	−5.44025	−	3.95258i	−0.287126	−	0.208609i	0.434894	−	0.900482i	$-0.356786\pi$
$359$	−5.44025	−	3.95258i	−0.287126	−	0.208609i	−0.722019	+	0.691873i	$0.756786\pi$
$360$		0			0
$361$	−5.03296	+	15.4898i	−0.264892	+	0.815255i
$362$	−25.1146	+	18.2468i	−1.31999	+	0.959031i
$363$	−0.220964	−	0.680056i	−0.0115976	−	0.0356937i
$364$	11.6542	+	35.8679i	0.610845	+	1.87999i
$365$		0			0
$366$	−2.06596			−0.107989
$367$	−30.5491			−1.59465			−0.797325	−	0.603550i	$-0.793753\pi$
$367$	−30.5491			−1.59465			−0.797325	+	0.603550i	$0.793753\pi$
$368$	−21.8529	+	67.2564i	−1.13916	+	3.50598i
$369$	14.4533	+	10.5009i	0.752407	+	0.546656i
$370$		0			0
$371$	−0.833113			−0.0432531
$372$	−1.37707	−	2.89651i	−0.0713976	−	0.150177i
$373$	−1.50588			−0.0779717			−0.0389859	−	0.999240i	$-0.512413\pi$
$373$	−1.50588			−0.0779717			−0.0389859	+	0.999240i	$0.512413\pi$
$374$	2.46081	−	1.78788i	0.127245	−	0.0924492i
$375$		0			0
$376$	−1.57312	+	4.84155i	−0.0811272	+	0.249684i
$377$	−35.9407			−1.85104
$378$	−2.33417			−0.120057
$379$	5.17692	−	15.9329i	0.265921	−	0.818420i	−0.725559	−	0.688160i	$-0.758419\pi$
$379$	5.17692	−	15.9329i	0.265921	−	0.818420i	0.991480	−	0.130260i	$-0.0415812\pi$
$380$		0			0
$381$	−0.382375	−	1.17683i	−0.0195897	−	0.0602908i
$382$	19.4650	−	14.1422i	0.995916	−	0.723575i
$383$	6.82461	−	21.0040i	0.348721	−	1.07325i	−0.610840	−	0.791754i	$-0.709168\pi$
$383$	6.82461	−	21.0040i	0.348721	−	1.07325i	0.959561	−	0.281500i	$-0.0908319\pi$
$384$	2.52155	−	1.83201i	0.128677	−	0.0934895i
$385$		0			0
$386$	1.86102	+	5.72764i	0.0947235	+	0.291529i
$387$	−22.9206	−	16.6528i	−1.16512	−	0.846510i
$388$	10.3129	+	7.49275i	0.523557	+	0.380387i
$389$	−0.121316	−	0.373372i	−0.00615096	−	0.0189307i	0.947934	−	0.318467i	$-0.103168\pi$
$389$	−0.121316	−	0.373372i	−0.00615096	−	0.0189307i	−0.954085	+	0.299536i	$0.903168\pi$
$390$		0			0
$391$	2.21422	−	1.60872i	0.111978	−	0.0813565i
$392$	14.6212	−	44.9994i	0.738481	−	2.27281i
$393$	−0.269104	+	0.195515i	−0.0135745	+	0.00986244i
$394$	4.96881	+	15.2924i	0.250325	+	0.770422i
$395$		0			0
$396$	−10.3124	+	31.7384i	−0.518219	+	1.59491i
$397$	10.4160			0.522763			0.261381	−	0.965236i	$-0.415822\pi$
$397$	10.4160			0.522763			0.261381	+	0.965236i	$0.415822\pi$
$398$	−63.4862			−3.18228
$399$	−0.0732034	+	0.225297i	−0.00366475	+	0.0112790i
$400$		0			0
$401$	−1.51296	+	1.09923i	−0.0755536	+	0.0548929i	−0.624921	−	0.780688i	$-0.714869\pi$
$401$	−1.51296	+	1.09923i	−0.0755536	+	0.0548929i	0.549367	+	0.835581i	$0.314869\pi$
$402$	−2.70600			−0.134963
$403$	−21.3778	+	20.2354i	−1.06490	+	1.00800i
$404$	−46.7443			−2.32562
$405$		0			0
$406$	−19.8924	−	14.4527i	−0.987243	−	0.717274i
$407$	6.11864	−	18.8312i	0.303290	−	0.933430i
$408$	−0.524856			−0.0259842
$409$	−8.08301			−0.399679			−0.199839	−	0.979829i	$-0.564042\pi$
$409$	−8.08301			−0.399679			−0.199839	+	0.979829i	$0.564042\pi$
$410$		0			0
$411$	0.414484	+	1.27565i	0.0204450	+	0.0629231i
$412$	19.1225	+	58.8532i	0.942100	+	2.89949i
$413$	−10.9963	+	7.98925i	−0.541091	+	0.393125i
$414$	−12.7510	+	39.2435i	−0.626676	+	1.92871i
$415$		0			0
$416$	−83.3476	−	60.5556i	−4.08645	−	2.96898i
$417$	0.423356	+	1.30296i	0.0207319	+	0.0638061i
$418$	7.54511	+	5.48184i	0.369043	+	0.268126i
$419$	−21.8909	−	15.9047i	−1.06944	−	0.776994i	−0.0936291	−	0.995607i	$-0.529847\pi$
$419$	−21.8909	−	15.9047i	−1.06944	−	0.776994i	−0.975812	+	0.218613i	$0.929847\pi$
$420$		0			0
$421$	7.32537	+	5.32219i	0.357017	+	0.259388i	0.751807	−	0.659384i	$-0.229183\pi$
$421$	7.32537	+	5.32219i	0.357017	+	0.259388i	−0.394790	+	0.918771i	$0.629183\pi$
$422$	−14.5922	+	10.6018i	−0.710335	+	0.516088i
$423$	−0.518536	+	1.59589i	−0.0252121	+	0.0775948i
$424$	4.57868	−	3.32661i	0.222360	−	0.161554i
$425$		0			0
$426$	0.459525	+	1.41427i	0.0222640	+	0.0685217i
$427$	−2.91716	+	8.97808i	−0.141171	+	0.434480i
$428$	47.0952			2.27643
$429$	−1.19032			−0.0574690
$430$		0			0
$431$	−3.49993	−	2.54285i	−0.168586	−	0.122485i	0.500293	−	0.865856i	$-0.333226\pi$
$431$	−3.49993	−	2.54285i	−0.168586	−	0.122485i	−0.668879	+	0.743371i	$0.733226\pi$
$432$	7.24693	−	5.26521i	0.348668	−	0.253322i
$433$	33.0490			1.58824			0.794118	−	0.607764i	$-0.207933\pi$
$433$	33.0490			1.58824			0.794118	+	0.607764i	$0.207933\pi$
$434$	−19.9693	+	2.60329i	−0.958555	+	0.124962i
$435$		0			0
$436$	−24.5788	+	17.8575i	−1.17711	+	0.855221i
$437$	6.78902	+	4.93251i	0.324763	+	0.235954i
$438$	0.400703	−	1.23324i	0.0191463	−	0.0589264i
$439$	−37.9067			−1.80919			−0.904595	−	0.426272i	$-0.859827\pi$
$439$	−37.9067			−1.80919			−0.904595	+	0.426272i	$0.859827\pi$
$440$		0			0
$441$	4.81949	−	14.8329i	0.229499	−	0.706327i
$442$	2.37859	+	7.32056i	0.113138	+	0.348203i
$443$	4.78101	+	14.7144i	0.227153	+	0.699104i	0.998066	+	0.0621638i	$0.0198001\pi$
$443$	4.78101	+	14.7144i	0.227153	+	0.699104i	−0.770913	+	0.636940i	$0.780200\pi$
$444$	−4.41666	+	3.20889i	−0.209605	+	0.152287i
$445$		0			0
$446$	−3.05296	+	2.21810i	−0.144562	+	0.105030i
$447$	1.46183	+	1.06208i	0.0691424	+	0.0502349i
$448$	−10.3314	−	31.7969i	−0.488114	−	1.50226i
$449$	15.7030	+	11.4089i	0.741068	+	0.538417i	0.893045	−	0.449966i	$-0.148564\pi$
$449$	15.7030	+	11.4089i	0.741068	+	0.538417i	−0.151977	+	0.988384i	$0.548564\pi$
$450$		0			0
$451$	3.85953	+	11.8784i	0.181738	+	0.559333i
$452$	52.9880	+	38.4981i	2.49235	+	1.81080i
$453$	−0.858406	+	0.623668i	−0.0403314	+	0.0293025i
$454$	−15.8524	+	48.7887i	−0.743990	+	2.28977i
$455$		0			0
$456$	−0.497290	−	1.53050i	−0.0232877	−	0.0716723i
$457$	6.15890	+	18.9551i	0.288101	+	0.886684i	0.985452	+	0.169954i	$0.0543620\pi$
$457$	6.15890	+	18.9551i	0.288101	+	0.886684i	−0.697351	+	0.716730i	$0.745638\pi$
$458$	11.4065	−	35.1057i	0.532992	−	1.64038i
$459$	−0.346682			−0.0161817
$460$		0			0
$461$	3.23942	−	9.96990i	0.150875	−	0.464344i	−0.846845	−	0.531840i	$-0.821501\pi$
$461$	3.23942	−	9.96990i	0.150875	−	0.464344i	0.997720	+	0.0674955i	$0.0215008\pi$
$462$	−0.658813	−	0.478656i	−0.0306508	−	0.0222691i
$463$	6.72063	−	4.88282i	0.312334	−	0.226924i	−0.420563	−	0.907263i	$-0.638168\pi$
$463$	6.72063	−	4.88282i	0.312334	−	0.226924i	0.732897	+	0.680339i	$0.238168\pi$
$464$	94.3610			4.38060
$465$		0			0
$466$	−3.75389			−0.173896
$467$	11.5832	−	8.41565i	0.536004	−	0.389430i	−0.286595	−	0.958052i	$-0.592523\pi$
$467$	11.5832	−	8.41565i	0.536004	−	0.389430i	0.822599	+	0.568622i	$0.192523\pi$
$468$	−68.3209	−	49.6381i	−3.15814	−	2.29452i
$469$	−3.82091	+	11.7595i	−0.176433	+	0.543005i
$470$		0			0
$471$	0.0884841			0.00407713
$472$	28.5330	−	87.8157i	1.31334	−	4.04204i
$473$	−6.12062	−	18.8373i	−0.281426	−	0.866141i
$474$	0.822725	+	2.53209i	0.0377890	+	0.116303i
$475$		0			0
$476$	−1.18419	+	3.64457i	−0.0542773	+	0.167049i
$477$	1.50924	−	1.09653i	0.0691034	−	0.0502066i
$478$	30.1195	+	21.8831i	1.37763	+	1.00091i
$479$	−4.31549	−	13.2817i	−0.197180	−	0.606857i	−0.999944	−	0.0105609i	$-0.996638\pi$
$479$	−4.31549	−	13.2817i	−0.197180	−	0.606857i	0.802764	−	0.596296i	$-0.203362\pi$
$480$		0			0
$481$	40.5366	+	29.4516i	1.84831	+	1.34288i
$482$	11.0691	+	34.0673i	0.504186	+	1.55172i
$483$	−0.592794	−	0.430690i	−0.0269731	−	0.0195971i
$484$	28.6929	−	20.8466i	1.30422	−	0.947573i
$485$		0			0
$486$	6.34687	−	4.61127i	0.287900	−	0.209172i
$487$	−7.76137	−	23.8870i	−0.351701	−	1.08243i	−0.957898	−	0.287110i	$-0.907305\pi$
$487$	−7.76137	−	23.8870i	−0.351701	−	1.08243i	0.606196	−	0.795315i	$-0.292695\pi$
$488$	−19.8170	−	60.9905i	−0.897074	−	2.76091i
$489$	−0.313163	+	0.963816i	−0.0141617	+	0.0435852i
$490$		0			0
$491$	−4.83315			−0.218117			−0.109058	−	0.994035i	$-0.534784\pi$
$491$	−4.83315			−0.218117			−0.109058	+	0.994035i	$0.534784\pi$
$492$	1.06414	−	3.27508i	0.0479750	−	0.147652i
$493$	−2.95451	−	2.14658i	−0.133064	−	0.0966769i
$494$	−19.0934	+	13.8721i	−0.859051	+	0.624137i
$495$		0			0
$496$	56.1265	−	53.1272i	2.52015	−	2.38548i
$497$	6.79489			0.304793
$498$	0.881599	−	0.640519i	0.0395054	−	0.0287024i
$499$	32.4987	+	23.6117i	1.45484	+	1.05700i	0.984670	+	0.174427i	$0.0558072\pi$
$499$	32.4987	+	23.6117i	1.45484	+	1.05700i	0.470169	+	0.882576i	$0.344193\pi$
$500$		0			0
$501$	−1.66649			−0.0744533
$502$	−66.4234			−2.96462
$503$	−0.881868	+	2.71411i	−0.0393206	+	0.121016i	−0.968790	−	0.247883i	$-0.920265\pi$
$503$	−0.881868	+	2.71411i	−0.0393206	+	0.121016i	0.929469	+	0.368899i	$0.120265\pi$
$504$	−11.1732	−	34.3876i	−0.497694	−	1.53174i
$505$		0			0
$506$	−23.3380	+	16.9560i	−1.03750	+	0.753787i
$507$	0.497890	−	1.53235i	0.0221121	−	0.0680540i
$508$	49.6527	−	36.0748i	2.20298	−	1.60056i
$509$	−9.59797	−	6.97333i	−0.425423	−	0.309088i	0.354393	−	0.935096i	$-0.384687\pi$
$509$	−9.59797	−	6.97333i	−0.425423	−	0.309088i	−0.779816	+	0.626009i	$0.784687\pi$
$510$		0			0
$511$	−4.79352	−	3.48269i	−0.212053	−	0.154065i
$512$	15.2110	+	11.0514i	0.672237	+	0.488409i
$513$	−0.328474	−	1.01094i	−0.0145025	−	0.0446341i
$514$	−41.6246	−	30.2421i	−1.83598	−	1.33392i
$515$		0			0
$516$	−1.68756	+	5.19377i	−0.0742905	+	0.228643i
$517$	−0.949070	+	0.689540i	−0.0417401	+	0.0303259i
$518$	10.5929	+	32.6016i	0.465425	+	1.43243i
$519$	−0.101152	−	0.311314i	−0.00444008	−	0.0136652i
$520$		0			0
$521$	5.98088			0.262027			0.131013	−	0.991381i	$-0.458177\pi$
$521$	5.98088			0.262027			0.131013	+	0.991381i	$0.458177\pi$
$522$	55.0588			2.40986
$523$	−5.21923	+	16.0631i	−0.228221	+	0.702392i	0.769728	+	0.638372i	$0.220392\pi$
$523$	−5.21923	+	16.0631i	−0.228221	+	0.702392i	−0.997949	+	0.0640196i	$0.979608\pi$
$524$	−13.3474	−	9.69748i	−0.583086	−	0.423637i
$525$		0			0
$526$	14.3855			0.627236
$527$	−2.96593	+	0.386653i	−0.129198	+	0.0168429i
$528$	3.12513			0.136004
$529$	−2.39189	+	1.73781i	−0.103995	+	0.0755569i
$530$		0			0
$531$	9.40517	−	28.9461i	0.408150	−	1.25616i
$532$	−11.7497			−0.509414
$533$	−31.6060			−1.36901
$534$	0.873028	−	2.68691i	0.0377796	−	0.116274i
$535$		0			0
$536$	−25.9564	−	79.8857i	−1.12115	−	3.45054i
$537$	0.952789	−	0.692242i	0.0411159	−	0.0298724i
$538$	−7.41467	+	22.8200i	−0.319669	+	0.983840i
$539$	8.82105	−	6.40887i	0.379950	−	0.276050i
$540$		0			0
$541$	3.33455	+	10.2627i	0.143363	+	0.441227i	0.996797	−	0.0799745i	$-0.0254839\pi$
$541$	3.33455	+	10.2627i	0.143363	+	0.441227i	−0.853433	+	0.521202i	$0.825484\pi$
$542$	−47.6965	−	34.6535i	−2.04874	−	1.48850i
$543$	0.998638	+	0.725553i	0.0428556	+	0.0311364i
$544$	−3.23488	−	9.95595i	−0.138694	−	0.426858i
$545$		0			0
$546$	1.66717	−	1.21127i	0.0713482	−	0.0518375i
$547$	10.2718	−	31.6133i	0.439190	−	1.35169i	−0.449541	−	0.893260i	$-0.648412\pi$
$547$	10.2718	−	31.6133i	0.439190	−	1.35169i	0.888731	−	0.458429i	$-0.151588\pi$
$548$	−53.8221	+	39.1041i	−2.29917	+	1.67044i
$549$	−6.53216	−	20.1039i	−0.278786	−	0.858014i
$550$		0			0
$551$	3.46017	−	10.6493i	0.147408	−	0.453676i
$552$	4.97765			0.211863
$553$	12.1655			0.517328
$554$	−1.03556	+	3.18713i	−0.0439967	+	0.135408i
$555$		0			0
$556$	−54.9743	+	39.9412i	−2.33143	+	1.69388i
$557$	42.1137			1.78441			0.892207	−	0.451627i	$-0.149156\pi$
$557$	42.1137			1.78441			0.892207	+	0.451627i	$0.149156\pi$
$558$	32.7493	−	30.9992i	1.38639	−	1.31230i
$559$	50.1222			2.11994
$560$		0			0
$561$	−0.0978499	−	0.0710921i	−0.00413122	−	0.00300151i
$562$	−21.1788	+	65.1817i	−0.893375	+	2.74953i
$563$	7.18940			0.302997			0.151498	−	0.988457i	$-0.451590\pi$
$563$	7.18940			0.302997			0.151498	+	0.988457i	$0.451590\pi$
$564$	0.323448			0.0136196
$565$		0			0
$566$	13.3781	+	41.1736i	0.562323	+	1.73065i
$567$	−3.66858	−	11.2907i	−0.154066	−	0.474166i
$568$	−37.3438	+	27.1319i	−1.56691	+	1.13843i
$569$	9.46601	−	29.1334i	0.396836	−	1.22133i	−0.530687	−	0.847568i	$-0.678066\pi$
$569$	9.46601	−	29.1334i	0.396836	−	1.22133i	0.927523	−	0.373767i	$-0.121934\pi$
$570$		0			0
$571$	−13.2096	−	9.59731i	−0.552803	−	0.401635i	0.276015	−	0.961153i	$-0.410986\pi$
$571$	−13.2096	−	9.59731i	−0.552803	−	0.401635i	−0.828818	+	0.559518i	$0.810986\pi$
$572$	−18.2441	−	56.1496i	−0.762824	−	2.34773i
$573$	−0.773992	−	0.562338i	−0.0323340	−	0.0234920i
$574$	−17.4932	−	12.7096i	−0.730153	−	0.530487i
$575$		0			0
$576$	60.5665	+	44.0042i	2.52361	+	1.83351i
$577$	−24.4021	+	17.7292i	−1.01587	+	0.738076i	−0.965433	−	0.260651i	$-0.916063\pi$
$577$	−24.4021	+	17.7292i	−1.01587	+	0.738076i	−0.0504414	+	0.998727i	$0.516063\pi$
$578$	13.9958	−	43.0745i	0.582147	−	1.79166i
$579$	0.193735	−	0.140757i	0.00805137	−	0.00584966i
$580$		0			0
$581$	−1.53869	−	4.73561i	−0.0638358	−	0.196466i
$582$	0.215242	−	0.662447i	0.00892208	−	0.0274593i
$583$	1.30420			0.0540146
$584$	40.2509			1.66559
$585$		0			0
$586$	−19.6148	−	14.2510i	−0.810280	−	0.588703i
$587$	−19.7436	+	14.3445i	−0.814904	+	0.592063i	−0.915248	−	0.402890i	$-0.868006\pi$
$587$	−19.7436	+	14.3445i	−0.814904	+	0.592063i	0.100344	+	0.994953i	$0.468006\pi$
$588$	−3.00626			−0.123976
$589$	−3.93765	−	8.28241i	−0.162248	−	0.341271i
$590$		0			0
$591$	0.517262	−	0.375813i	0.0212773	−	0.0154589i
$592$	−106.427	−	77.3240i	−4.37414	−	3.17800i
$593$	1.91139	−	5.88265i	0.0784914	−	0.241572i	−0.904110	−	0.427301i	$-0.859465\pi$
$593$	1.91139	−	5.88265i	0.0784914	−	0.241572i	0.982601	+	0.185729i	$0.0594646\pi$
$594$	3.65405			0.149927
$595$		0			0
$596$	−27.6950	+	85.2364i	−1.13443	+	3.49142i
$597$	0.780089	+	2.40087i	0.0319269	+	0.0982609i
$598$	−22.5582	−	69.4270i	−0.922474	−	2.83908i
$599$	32.3808	−	23.5260i	1.32304	−	0.961247i	0.323154	−	0.946346i	$-0.395257\pi$
$599$	32.3808	−	23.5260i	1.32304	−	0.961247i	0.999889	−	0.0149005i	$-0.00474315\pi$
$600$		0			0
$601$	−6.64819	+	4.83019i	−0.271185	+	0.197028i	−0.715064	−	0.699060i	$-0.753602\pi$
$601$	−6.64819	+	4.83019i	−0.271185	+	0.197028i	0.443878	+	0.896087i	$0.353602\pi$
$602$	27.7415	+	20.1554i	1.13066	+	0.821472i
$603$	−8.55585	−	26.3322i	−0.348421	−	1.07233i
$604$	−42.5766	−	30.9337i	−1.73242	−	1.25867i
$605$		0			0
$606$	0.789284	+	2.42917i	0.0320625	+	0.0986782i
$607$	37.6285	+	27.3387i	1.52729	+	1.10964i	0.957719	+	0.287704i	$0.0928920\pi$
$607$	37.6285	+	27.3387i	1.52729	+	1.10964i	0.569575	+	0.821940i	$0.307108\pi$
$608$	25.9670	−	18.8661i	1.05310	−	0.765122i
$609$	−0.302130	+	0.929861i	−0.0122429	+	0.0376799i
$610$		0			0
$611$	−0.917361	−	2.82335i	−0.0371125	−	0.114220i
$612$	−2.65167	−	8.16099i	−0.107187	−	0.329889i
$613$	0.162908	−	0.501379i	0.00657979	−	0.0202505i	−0.947713	−	0.319125i	$-0.896611\pi$
$613$	0.162908	−	0.501379i	0.00657979	−	0.0202505i	0.954293	+	0.298874i	$0.0966111\pi$
$614$	18.4995			0.746579
$615$		0			0
$616$	7.81127	−	24.0406i	0.314725	−	0.968624i
$617$	−5.03461	−	3.65786i	−0.202686	−	0.147260i	0.481813	−	0.876274i	$-0.339979\pi$
$617$	−5.03461	−	3.65786i	−0.202686	−	0.147260i	−0.684498	+	0.729015i	$0.739979\pi$
$618$	2.73554	−	1.98749i	0.110040	−	0.0799485i
$619$	−14.0030			−0.562827			−0.281413	−	0.959587i	$-0.590803\pi$
$619$	−14.0030			−0.562827			−0.281413	+	0.959587i	$0.590803\pi$
$620$		0			0
$621$	3.28788			0.131938
$622$	−28.0494	+	20.3791i	−1.12468	+	0.817126i
$623$	−10.4438	−	7.58789i	−0.418423	−	0.304002i
$624$	−2.44381	+	7.52127i	−0.0978307	+	0.301092i
$625$		0			0
$626$	47.4243			1.89546
$627$	0.114597	−	0.352693i	0.00457655	−	0.0140852i
$628$	1.35621	+	4.17397i	0.0541185	+	0.166560i
$629$	1.57331	+	4.84214i	0.0627318	+	0.193069i
$630$		0			0
$631$	12.6547	−	38.9473i	0.503777	−	1.55047i	−0.299040	−	0.954241i	$-0.596666\pi$
$631$	12.6547	−	38.9473i	0.503777	−	1.55047i	0.802817	−	0.596225i	$-0.203334\pi$
$632$	−66.8597	+	48.5764i	−2.65954	+	1.93227i
$633$	0.580232	+	0.421563i	0.0230621	+	0.0167556i
$634$	7.88976	+	24.2822i	0.313342	+	0.964369i
$635$		0			0
$636$	−0.290915	−	0.211362i	−0.0115355	−	0.00838105i
$637$	8.52634	+	26.2414i	0.337826	+	1.03972i
$638$	31.1407	+	22.6250i	1.23287	+	0.895734i
$639$	−12.3094	+	8.94331i	−0.486953	+	0.353792i
$640$		0			0
$641$	−1.52149	+	1.10543i	−0.0600953	+	0.0436618i	−0.617427	−	0.786628i	$-0.711825\pi$
$641$	−1.52149	+	1.10543i	−0.0600953	+	0.0436618i	0.557332	+	0.830290i	$0.311825\pi$
$642$	−0.795210	−	2.44740i	−0.0313844	−	0.0965914i
$643$	13.8393	+	42.5931i	0.545770	+	1.67971i	0.719151	+	0.694853i	$0.244531\pi$
$643$	13.8393	+	42.5931i	0.545770	+	1.67971i	−0.173381	+	0.984855i	$0.555469\pi$
$644$	11.2307	−	34.5645i	0.442551	−	1.36203i
$645$		0			0
$646$	−2.39809			−0.0943516
$647$	14.1652	−	43.5961i	0.556893	−	1.71394i	−0.133998	−	0.990982i	$-0.542782\pi$
$647$	14.1652	−	43.5961i	0.556893	−	1.71394i	0.690891	−	0.722959i	$-0.257218\pi$
$648$	65.2457	+	47.4038i	2.56309	+	1.86220i
$649$	17.2142	−	12.5068i	0.675715	−	0.490936i
$650$		0			0
$651$	0.343822	+	0.723192i	0.0134754	+	0.0283441i
$652$	−50.2650			−1.96853
$653$	−21.1488	+	15.3655i	−0.827616	+	0.601298i	−0.918884	−	0.394528i	$-0.870908\pi$
$653$	−21.1488	+	15.3655i	−0.827616	+	0.601298i	0.0912677	+	0.995826i	$0.470908\pi$
$654$	1.34302	+	0.975763i	0.0525163	+	0.0381553i
$655$		0			0
$656$	82.9804			3.23984
$657$	13.2676			0.517620
$658$	0.627600	−	1.93155i	0.0244664	−	0.0752998i
$659$	10.3168	+	31.7517i	0.401884	+	1.23687i	0.923469	+	0.383672i	$0.125341\pi$
$659$	10.3168	+	31.7517i	0.401884	+	1.23687i	−0.521586	+	0.853199i	$0.674659\pi$
$660$		0			0
$661$	−17.1253	+	12.4423i	−0.666097	+	0.483948i	−0.868716	−	0.495310i	$-0.835055\pi$
$661$	−17.1253	+	12.4423i	−0.666097	+	0.483948i	0.202619	+	0.979258i	$0.435055\pi$
$662$	28.6005	−	88.0232i	1.11159	−	3.42112i
$663$	0.247615	−	0.179903i	0.00961658	−	0.00698686i
$664$	27.3657	+	19.8823i	1.06199	+	0.771583i
$665$		0			0
$666$	−62.0993	−	45.1178i	−2.40630	−	1.74828i
$667$	28.0201	+	20.3578i	1.08494	+	0.788257i
$668$	−25.5425	−	78.6117i	−0.988269	−	3.04158i
$669$	0.121396	+	0.0881991i	0.00469342	+	0.00340997i
$670$		0			0
$671$	4.56668	−	14.0548i	0.176295	−	0.542579i
$672$	−2.26735	+	1.64732i	−0.0874648	+	0.0635469i
$673$	−11.2820	−	34.7223i	−0.434887	−	1.33845i	−0.893202	−	0.449655i	$-0.851547\pi$
$673$	−11.2820	−	34.7223i	−0.434887	−	1.33845i	0.458315	−	0.888790i	$-0.348453\pi$
$674$	15.8323	+	48.7268i	0.609838	+	1.87689i
$675$		0			0
$676$	79.9152			3.07366
$677$	36.0053			1.38379			0.691897	−	0.721996i	$-0.256775\pi$
$677$	36.0053			1.38379			0.691897	+	0.721996i	$0.256775\pi$
$678$	1.10592	−	3.40368i	0.0424728	−	0.130718i
$679$	−2.57489	−	1.87077i	−0.0988153	−	0.0717935i
$680$		0			0
$681$	2.03983			0.0781666
$682$	31.2610	−	4.07534i	1.19705	−	0.156053i
$683$	26.5328			1.01525			0.507625	−	0.861578i	$-0.330524\pi$
$683$	26.5328			1.01525			0.507625	+	0.861578i	$0.330524\pi$
$684$	21.2854	−	15.4647i	0.813867	−	0.591309i
$685$		0			0
$686$	−13.6570	+	42.0320i	−0.521428	+	1.60479i
$687$	−1.46776			−0.0559983
$688$	−131.594			−5.01697
$689$	−1.01987	+	3.13884i	−0.0388540	+	0.119580i
$690$		0			0
$691$	−3.21088	−	9.88208i	−0.122148	−	0.375932i	0.871223	−	0.490888i	$-0.163327\pi$
$691$	−3.21088	−	9.88208i	−0.122148	−	0.375932i	−0.993371	+	0.114956i	$0.963327\pi$
$692$	13.1349	−	9.54310i	0.499316	−	0.362774i
$693$	2.57478	−	7.92435i	0.0978077	−	0.301021i
$694$	−19.9770	+	14.5141i	−0.758315	+	0.550948i
$695$		0			0
$696$	−2.05245	−	6.31679i	−0.0777979	−	0.239437i
$697$	−2.59817	−	1.88768i	−0.0984128	−	0.0715011i
$698$	30.7317	+	22.3279i	1.16321	+	0.845124i
$699$	0.0461261	+	0.141961i	0.00174465	+	0.00536947i
$700$		0			0
$701$	−35.7691	+	25.9878i	−1.35098	+	0.981544i	−0.352018	+	0.935993i	$0.614504\pi$
$701$	−35.7691	+	25.9878i	−1.35098	+	0.981544i	−0.998962	+	0.0455507i	$0.985496\pi$
$702$	−2.85742	+	8.79423i	−0.107846	+	0.331917i
$703$	−12.6292	+	9.17564i	−0.476319	+	0.346066i
$704$	16.1734	+	49.7766i	0.609558	+	1.87603i
$705$		0			0
$706$	9.75994	−	30.0380i	0.367320	−	1.13049i
$707$	11.6710			0.438932
$708$	−5.86667			−0.220483
$709$	−2.60037	+	8.00312i	−0.0976590	+	0.300563i	−0.987938	−	0.154853i	$-0.950510\pi$
$709$	−2.60037	+	8.00312i	−0.0976590	+	0.300563i	0.890279	+	0.455416i	$0.150510\pi$
$710$		0			0
$711$	−22.0386	+	16.0119i	−0.826510	+	0.600495i
$712$	87.6962			3.28655
$713$	28.1284	−	3.66696i	1.05342	−	0.137329i
$714$	0.209393			0.00783634
$715$		0			0
$716$	47.2580	+	34.3349i	1.76611	+	1.28316i
$717$	0.457462	−	1.40792i	0.0170842	−	0.0525798i
$718$	−18.2248			−0.680143
$719$	−6.12721			−0.228506			−0.114253	−	0.993452i	$-0.536447\pi$
$719$	−6.12721			−0.228506			−0.114253	+	0.993452i	$0.536447\pi$
$720$		0			0
$721$	−4.77446	−	14.6943i	−0.177810	−	0.547244i
$722$	13.6403	+	41.9805i	0.507639	+	1.56235i
$723$	1.15232	−	0.837207i	0.0428551	−	0.0311360i
$724$	−18.9196	+	58.2284i	−0.703140	+	2.16404i
$725$		0			0
$726$	−1.56782	−	1.13909i	−0.0581874	−	0.0422756i
$727$	−7.26457	−	22.3580i	−0.269428	−	0.829214i	−0.990640	−	0.136500i	$-0.956415\pi$
$727$	−7.26457	−	22.3580i	−0.269428	−	0.829214i	0.721212	−	0.692714i	$-0.243585\pi$
$728$	51.7504	+	37.5989i	1.91800	+	1.39351i
$729$	21.3377	+	15.5028i	0.790286	+	0.574177i
$730$		0			0
$731$	4.12030	+	2.99357i	0.152395	+	0.110721i
$732$	−3.29639	+	2.39497i	−0.121838	+	0.0885207i
$733$	−4.02156	+	12.3771i	−0.148540	+	0.457158i	−0.997449	−	0.0713800i	$-0.977260\pi$
$733$	−4.02156	+	12.3771i	−0.148540	+	0.457158i	0.848909	+	0.528538i	$0.177260\pi$
$734$	−66.9818	+	48.6652i	−2.47234	+	1.79626i
$735$		0			0
$736$	30.6791	+	94.4207i	1.13085	+	3.48039i
$737$	5.98146	−	18.4091i	0.220330	−	0.678106i
$738$	48.4182			1.78230
$739$	−2.17120			−0.0798688			−0.0399344	−	0.999202i	$-0.512715\pi$
$739$	−2.17120			−0.0798688			−0.0399344	+	0.999202i	$0.512715\pi$
$740$		0			0
$741$	0.759215	+	0.551602i	0.0278905	+	0.0202636i
$742$	−1.82668	+	1.32716i	−0.0670595	+	0.0487216i
$743$	−2.92421			−0.107279			−0.0536394	−	0.998560i	$-0.517082\pi$
$743$	−2.92421			−0.107279			−0.0536394	+	0.998560i	$0.517082\pi$
$744$	−4.77729	−	2.60169i	−0.175144	−	0.0953827i
$745$		0			0
$746$	−3.30179	+	2.39889i	−0.120887	+	0.0878297i
$747$	9.02037	+	6.55368i	0.330038	+	0.239787i
$748$	1.85380	−	5.70541i	0.0677817	−	0.208611i
$749$	−11.7586			−0.429650
$750$		0			0
$751$	−1.80296	+	5.54894i	−0.0657909	+	0.202484i	−0.978548	−	0.206019i	$-0.933949\pi$
$751$	−1.80296	+	5.54894i	−0.0657909	+	0.202484i	0.912757	+	0.408503i	$0.133949\pi$
$752$	2.40850	+	7.41259i	0.0878288	+	0.270309i
$753$	0.816179	+	2.51194i	0.0297432	+	0.0915402i
$754$	−78.8035	+	57.2541i	−2.86985	+	2.08507i
$755$		0			0
$756$	−3.72436	+	2.70590i	−0.135454	+	0.0984128i
$757$	−4.44738	−	3.23121i	−0.161643	−	0.117440i	0.504023	−	0.863690i	$-0.331853\pi$
$757$	−4.44738	−	3.23121i	−0.161643	−	0.117440i	−0.665666	+	0.746250i	$0.731853\pi$
$758$	−14.0305	−	43.1814i	−0.509610	−	1.56842i
$759$	0.927993	+	0.674227i	0.0336840	+	0.0244729i
$760$		0			0
$761$	6.83742	+	21.0434i	0.247856	+	0.762824i	0.995154	+	0.0983335i	$0.0313512\pi$
$761$	6.83742	+	21.0434i	0.247856	+	0.762824i	−0.747297	+	0.664490i	$0.768649\pi$
$762$	−2.71310	−	1.97118i	−0.0982852	−	0.0714084i
$763$	6.13676	−	4.45862i	0.222166	−	0.161413i
$764$	14.6636	−	45.1298i	0.530509	−	1.63274i
$765$		0			0
$766$	−18.4960	−	56.9249i	−0.668289	−	2.05678i
$767$	16.6390	+	51.2097i	0.600801	+	1.84907i
$768$	0.941785	−	2.89852i	0.0339837	−	0.104591i
$769$	35.4868			1.27969			0.639844	−	0.768505i	$-0.278999\pi$
$769$	35.4868			1.27969			0.639844	+	0.768505i	$0.278999\pi$
$770$		0			0
$771$	−0.632204	+	1.94572i	−0.0227683	+	0.0700735i
$772$	9.60920	+	6.98149i	0.345843	+	0.251269i
$773$	−12.6038	+	9.15722i	−0.453328	+	0.329362i	−0.790908	−	0.611934i	$-0.790392\pi$
$773$	−12.6038	+	9.15722i	−0.453328	+	0.329362i	0.337580	+	0.941297i	$0.390392\pi$
$774$	−76.7838			−2.75994
$775$		0			0
$776$	21.6212			0.776156
$777$	1.10274	−	0.801186i	0.0395605	−	0.0287424i
$778$	−0.860783	−	0.625396i	−0.0308606	−	0.0224215i
$779$	3.04285	−	9.36492i	0.109021	−	0.335533i
$780$		0			0
$781$	−10.6371			−0.380626
$782$	2.29216	−	7.05455i	0.0819675	−	0.252270i
$783$	−1.35570	−	4.17242i	−0.0484488	−	0.149110i
$784$	−22.3856	−	68.8957i	−0.799485	−	2.46056i
$785$		0			0
$786$	−0.278577	+	0.857372i	−0.00993651	+	0.0305814i
$787$	14.5644	−	10.5817i	0.519165	−	0.377196i	−0.297124	−	0.954839i	$-0.596027\pi$
$787$	14.5644	−	10.5817i	0.519165	−	0.377196i	0.816289	+	0.577643i	$0.196027\pi$
$788$	25.6560	+	18.6402i	0.913956	+	0.664028i
$789$	−0.176762	−	0.544017i	−0.00629288	−	0.0193675i
$790$		0			0
$791$	−13.2299	−	9.61209i	−0.470401	−	0.341766i
$792$	17.4911	+	53.8322i	0.621521	+	1.91284i
$793$	30.2547	+	21.9813i	1.07438	+	0.780580i
$794$	22.8380	−	16.5928i	0.810491	−	0.588856i
$795$		0			0
$796$	−101.297	+	73.5967i	−3.59038	+	2.60857i
$797$	6.38341	+	19.6461i	0.226112	+	0.695901i	0.998177	+	0.0603574i	$0.0192241\pi$
$797$	6.38341	+	19.6461i	0.226112	+	0.695901i	−0.772065	+	0.635544i	$0.780776\pi$
$798$	0.198396	+	0.610599i	0.00702313	+	0.0216150i
$799$	0.0932140	−	0.286883i	0.00329767	−	0.0101492i
$800$		0			0
$801$	28.9067			1.02137
$802$	−1.56622	+	4.82033i	−0.0553051	+	0.170212i
$803$	7.50404	+	5.45201i	0.264812	+	0.192397i
$804$	−4.31763	+	3.13695i	−0.152271	+	0.110632i
$805$		0			0
$806$	−14.6376	+	78.4230i	−0.515586	+	2.76233i
$807$	0.954095			0.0335857
$808$	−64.1421	+	46.6020i	−2.25651	+	1.63945i
$809$	−1.59122	−	1.15609i	−0.0559443	−	0.0406459i	0.559462	−	0.828856i	$-0.311008\pi$
$809$	−1.59122	−	1.15609i	−0.0559443	−	0.0406459i	−0.615406	+	0.788210i	$0.711008\pi$
$810$		0			0
$811$	2.74083			0.0962437			0.0481219	−	0.998841i	$-0.484676\pi$
$811$	2.74083			0.0962437			0.0481219	+	0.998841i	$0.484676\pi$
$812$	−48.4942			−1.70181
$813$	−0.724425	+	2.22955i	−0.0254067	+	0.0781937i
$814$	−16.5827	−	51.0364i	−0.581224	−	1.78882i
$815$		0			0
$816$	−0.650105	+	0.472329i	−0.0227582	+	0.0165348i
$817$	−4.82548	+	14.8513i	−0.168822	+	0.519581i
$818$	−17.7228	+	12.8763i	−0.619662	+	0.450211i
$819$	17.0582	+	12.3935i	0.596061	+	0.433063i
$820$		0			0
$821$	22.0359	+	16.0100i	0.769058	+	0.558753i	0.901675	−	0.432414i	$-0.142338\pi$
$821$	22.0359	+	16.0100i	0.769058	+	0.558753i	−0.132617	+	0.991167i	$0.542338\pi$
$822$	2.94092	+	2.13670i	0.102576	+	0.0745261i
$823$	9.23593	+	28.4253i	0.321944	+	0.990843i	0.972801	+	0.231642i	$0.0744098\pi$
$823$	9.23593	+	28.4253i	0.321944	+	0.990843i	−0.650857	+	0.759201i	$0.725590\pi$
$824$	84.9138	+	61.6935i	2.95811	+	2.14919i
$825$		0			0
$826$	−11.3834	+	35.0344i	−0.396078	+	1.21900i
$827$	−20.5628	+	14.9398i	−0.715040	+	0.519507i	−0.884796	−	0.465979i	$-0.845702\pi$
$827$	−20.5628	+	14.9398i	−0.715040	+	0.519507i	0.169756	+	0.985486i	$0.445702\pi$
$828$	25.1480	+	77.3976i	0.873954	+	2.68975i
$829$	−7.01528	−	21.5908i	−0.243651	−	0.749880i	−0.995855	−	0.0909503i	$-0.971010\pi$
$829$	−7.01528	−	21.5908i	−0.243651	−	0.749880i	0.752205	−	0.658930i	$-0.228990\pi$
$830$		0			0
$831$	0.133252			0.00462247
$832$	−132.445			−4.59171
$833$	−0.866369	+	2.66641i	−0.0300179	+	0.0923856i
$834$	3.00388	+	2.18245i	0.104016	+	0.0755719i
$835$		0			0
$836$	18.3937			0.636158
$837$	−3.15554	−	1.71849i	−0.109071	−	0.0593998i
$838$	−73.3343			−2.53329
$839$	4.22481	−	3.06951i	0.145857	−	0.105971i	−0.512464	−	0.858709i	$-0.671267\pi$
$839$	4.22481	−	3.06951i	0.145857	−	0.105971i	0.658321	+	0.752738i	$0.271267\pi$
$840$		0			0
$841$	5.31956	−	16.3719i	0.183433	−	0.564549i
$842$	24.5399			0.845701
$843$	2.72522			0.0938616
$844$	−10.9927	+	33.8320i	−0.378384	+	1.16455i
$845$		0			0
$846$	1.40533	+	4.32517i	0.0483164	+	0.148703i
$847$	−7.16396	+	5.20492i	−0.246157	+	0.178843i
$848$	2.67763	−	8.24090i	0.0919502	−	0.282994i
$849$	1.39268	−	1.01184i	0.0477967	−	0.0347263i
$850$		0			0
$851$	−14.9210	−	45.9221i	−0.511485	−	1.57419i
$852$	2.37271	+	1.72387i	0.0812877	+	0.0590590i
$853$	−4.92287	−	3.57668i	−0.168556	−	0.122463i	0.500309	−	0.865847i	$-0.333220\pi$
$853$	−4.92287	−	3.57668i	−0.168556	−	0.122463i	−0.668865	+	0.743384i	$0.733220\pi$
$854$	7.90607	+	24.3324i	0.270540	+	0.832636i
$855$		0			0
$856$	64.6237	−	46.9519i	2.20879	−	1.60478i
$857$	13.0682	−	40.2197i	0.446400	−	1.37388i	−0.434541	−	0.900652i	$-0.643089\pi$
$857$	13.0682	−	40.2197i	0.446400	−	1.37388i	0.880941	−	0.473227i	$-0.156911\pi$
$858$	−2.60988	+	1.89619i	−0.0890998	+	0.0647348i
$859$	−9.37619	−	28.8569i	−0.319911	−	0.984586i	−0.973685	−	0.227896i	$-0.926815\pi$
$859$	−9.37619	−	28.8569i	−0.319911	−	0.984586i	0.653774	−	0.756690i	$-0.273185\pi$
$860$		0			0
$861$	−0.265691	+	0.817712i	−0.00905472	+	0.0278676i
$862$	−11.7247			−0.399345
$863$	38.5374			1.31183			0.655914	−	0.754836i	$-0.272284\pi$
$863$	38.5374			1.31183			0.655914	+	0.754836i	$0.272284\pi$
$864$	3.88609	−	11.9601i	0.132207	−	0.406893i
$865$		0			0
$866$	72.4631	−	52.6476i	2.46240	−	1.78904i
$867$	−1.80093			−0.0611627
$868$	−28.8446	+	27.3032i	−0.979051	+	0.926732i
$869$	−19.0445			−0.646040
$870$		0			0
$871$	39.6278	+	28.7913i	1.34274	+	0.975556i
$872$	−15.9236	+	49.0079i	−0.539243	+	1.65962i
$873$	7.12686			0.241208
$874$	22.7431			0.769298
$875$		0			0
$876$	−0.790284	−	2.43224i	−0.0267012	−	0.0821779i
$877$	−13.9785	−	43.0213i	−0.472019	−	1.45272i	−0.849936	−	0.526886i	$-0.823360\pi$
$877$	−13.9785	−	43.0213i	−0.472019	−	1.45272i	0.377917	−	0.925839i	$-0.376640\pi$
$878$	−83.1141	+	60.3859i	−2.80497	+	2.03793i
$879$	−0.297914	+	0.916884i	−0.0100484	+	0.0309257i
$880$		0			0
$881$	17.2648	+	12.5436i	0.581665	+	0.422604i	0.839324	−	0.543632i	$-0.182951\pi$
$881$	17.2648	+	12.5436i	0.581665	+	0.422604i	−0.257659	+	0.966236i	$0.582951\pi$
$882$	−13.0618	−	40.2000i	−0.439812	−	1.35360i
$883$	−35.3363	−	25.6733i	−1.18916	−	0.863977i	−0.195987	−	0.980607i	$-0.562791\pi$
$883$	−35.3363	−	25.6733i	−1.18916	−	0.863977i	−0.993175	+	0.116630i	$0.962791\pi$
$884$	12.2816	+	8.92312i	0.413076	+	0.300117i
$885$		0			0
$886$	33.9231	+	24.6466i	1.13967	+	0.828018i
$887$	−28.6208	+	20.7942i	−0.960991	+	0.698201i	−0.953381	−	0.301770i	$-0.902422\pi$
$887$	−28.6208	+	20.7942i	−0.960991	+	0.698201i	−0.00761018	+	0.999971i	$0.502422\pi$
$888$	−2.86138	+	8.80642i	−0.0960216	+	0.295524i
$889$	−12.3971	+	9.00706i	−0.415787	+	0.302087i
$890$		0			0
$891$	5.74300	+	17.6751i	0.192398	+	0.592140i
$892$	−2.29988	+	7.07831i	−0.0770058	+	0.236999i
$893$	0.924881			0.0309500
$894$	4.89713			0.163784
$895$		0			0
$896$	−31.2266	−	22.6874i	−1.04321	−	0.757934i
$897$	−2.34835	+	1.70617i	−0.0784090	+	0.0569675i
$898$	52.6047			1.75544
$899$	−16.2517	−	34.1838i	−0.542026	−	1.14009i
$900$		0			0
$901$	−0.271307	+	0.197116i	−0.00903854	+	0.00656688i
$902$	27.3849	+	19.8963i	0.911817	+	0.662474i
$903$	0.421344	−	1.29676i	0.0140215	−	0.0431536i
$904$	111.091			3.69482
$905$		0			0
$906$	−0.888624	+	2.73490i	−0.0295226	+	0.0908611i
$907$	7.17084	+	22.0696i	0.238104	+	0.732808i	0.996695	+	0.0812406i	$0.0258882\pi$
$907$	7.17084	+	22.0696i	0.238104	+	0.732808i	−0.758591	+	0.651567i	$0.774112\pi$
$908$	31.2648	+	96.2231i	1.03756	+	3.19328i
$909$	−21.1428	+	15.3611i	−0.701261	+	0.509496i
$910$		0			0
$911$	22.2060	−	16.1336i	0.735718	−	0.534531i	−0.155649	−	0.987812i	$-0.549747\pi$
$911$	22.2060	−	16.1336i	0.735718	−	0.534531i	0.891367	+	0.453282i	$0.149747\pi$
$912$	−1.99329	−	1.44821i	−0.0660044	−	0.0479550i
$913$	2.40876	+	7.41339i	0.0797182	+	0.245348i
$914$	43.6998	+	31.7497i	1.44546	+	1.05019i
$915$		0			0
$916$	−22.4965	−	69.2370i	−0.743304	−	2.28765i
$917$	3.33255	+	2.42124i	0.110051	+	0.0799564i
$918$	−0.760134	+	0.552269i	−0.0250881	+	0.0182276i
$919$	4.19517	−	12.9114i	0.138386	−	0.425908i	−0.857715	−	0.514125i	$-0.828117\pi$
$919$	4.19517	−	12.9114i	0.138386	−	0.425908i	0.996101	+	0.0882169i	$0.0281169\pi$
$920$		0			0
$921$	−0.227313	−	0.699598i	−0.00749022	−	0.0230525i
$922$	−8.77945	−	27.0204i	−0.289136	−	0.889869i
$923$	8.31808	−	25.6004i	0.273793	−	0.842649i
$924$	−1.60607			−0.0528359
$925$		0			0
$926$	6.95721	−	21.4121i	0.228628	−	0.703645i
$927$	27.9896	+	20.3356i	0.919299	+	0.667910i
$928$	107.173	−	77.8655i	3.51811	−	2.55606i
$929$	27.4806			0.901608			0.450804	−	0.892623i	$-0.351137\pi$
$929$	27.4806			0.901608			0.450804	+	0.892623i	$0.351137\pi$
$930$		0			0
$931$	−8.59623			−0.281730
$932$	−5.98963	+	4.35172i	−0.196197	+	0.142545i
$933$	1.11533	+	0.810338i	0.0365144	+	0.0265293i
$934$	11.9909	−	36.9042i	0.392355	−	1.20754i
$935$		0			0
$936$	−143.236			−4.68183
$937$	−9.66675	+	29.7512i	−0.315799	+	0.971929i	0.659625	+	0.751595i	$0.270715\pi$
$937$	−9.66675	+	29.7512i	−0.315799	+	0.971929i	−0.975424	+	0.220335i	$0.929285\pi$
$938$	10.3554	+	31.8707i	0.338116	+	1.04061i
$939$	−0.582728	−	1.79345i	−0.0190166	−	0.0585271i
$940$		0			0
$941$	1.06514	−	3.27816i	0.0347225	−	0.106865i	−0.932193	−	0.361961i	$-0.882107\pi$
$941$	1.06514	−	3.27816i	0.0347225	−	0.106865i	0.966916	+	0.255096i	$0.0821072\pi$
$942$	0.194010	−	0.140956i	0.00632118	−	0.00459261i
$943$	24.6407	+	17.9025i	0.802411	+	0.582985i
$944$	−43.6851	−	134.449i	−1.42183	−	4.37594i
$945$		0			0
$946$	−43.4281	−	31.5524i	−1.41197	−	1.02586i
$947$	−2.43080	−	7.48122i	−0.0789903	−	0.243107i	0.903762	−	0.428036i	$-0.140794\pi$
$947$	−2.43080	−	7.48122i	−0.0789903	−	0.243107i	−0.982752	+	0.184929i	$0.940794\pi$
$948$	4.24806	+	3.08639i	0.137970	+	0.100241i
$949$	−18.9895	+	13.7967i	−0.616424	+	0.447858i
$950$		0			0
$951$	0.821337	−	0.596736i	0.0266337	−	0.0193505i
$952$	2.00853	+	6.18163i	0.0650970	+	0.200348i
$953$	−3.61754	−	11.1336i	−0.117183	−	0.360654i	0.875213	−	0.483738i	$-0.160721\pi$
$953$	−3.61754	−	11.1336i	−0.117183	−	0.360654i	−0.992396	+	0.123085i	$0.960721\pi$
$954$	1.56237	−	4.80848i	0.0505836	−	0.155680i
$955$		0			0
$956$	73.4261			2.37477
$957$	0.472972	−	1.45566i	0.0152890	−	0.0470547i
$958$	−30.6201	−	22.2468i	−0.989290	−	0.718761i
$959$	13.4382	−	9.76339i	0.433941	−	0.315276i
$960$		0			0
$961$	−28.9128	−	11.1826i	−0.932670	−	0.360730i
$962$	135.797			4.37828
$963$	21.3015	−	15.4764i	0.686431	−	0.498721i
$964$	57.1544	+	41.5251i	1.84082	+	1.33743i
$965$		0			0
$966$	−1.98585			−0.0638938
$967$	34.0728			1.09571			0.547854	−	0.836574i	$-0.315445\pi$
$967$	34.0728			1.09571			0.547854	+	0.836574i	$0.315445\pi$
$968$	18.5890	−	57.2111i	0.597474	−	1.83883i
$969$	0.0294666	+	0.0906889i	0.000946604	+	0.00291335i
$970$		0			0
$971$	0.0104742	−	0.00760998i	0.000336134	−	0.000244216i	−0.587617	−	0.809139i	$-0.699934\pi$
$971$	0.0104742	−	0.00760998i	0.000336134	−	0.000244216i	0.587953	+	0.808895i	$0.299934\pi$
$972$	4.78129	−	14.7153i	0.153360	−	0.471993i
$973$	13.7258	−	9.97239i	0.440030	−	0.319700i
$974$	−55.0699	−	40.0106i	−1.76455	−	1.28202i
$975$		0			0
$976$	−79.4326	−	57.7112i	−2.54258	−	1.84729i
$977$	−22.6123	−	16.4288i	−0.723433	−	0.525605i	0.164046	−	0.986453i	$-0.447545\pi$
$977$	−22.6123	−	16.4288i	−0.723433	−	0.525605i	−0.887479	+	0.460848i	$0.847545\pi$
$978$	0.848732	+	2.61213i	0.0271395	+	0.0835267i
$979$	16.3494	+	11.8785i	0.522528	+	0.379639i
$980$		0			0
$981$	−5.24881	+	16.1542i	−0.167582	+	0.515763i
$982$	−10.5971	+	7.69927i	−0.338168	+	0.245694i
$983$	−9.92878	−	30.5577i	−0.316679	−	0.974638i	−0.975058	−	0.221951i	$-0.928757\pi$
$983$	−9.92878	−	30.5577i	−0.316679	−	0.974638i	0.658379	−	0.752687i	$-0.271243\pi$
$984$	−1.80491	−	5.55494i	−0.0575384	−	0.177085i
$985$		0			0
$986$	−9.89757			−0.315203
$987$	−0.0807575			−0.00257054
$988$	−14.3836	+	44.2682i	−0.457603	+	1.40836i
$989$	−39.0763	−	28.3906i	−1.24255	−	0.902767i
$990$		0			0
$991$	−6.77806			−0.215312			−0.107656	−	0.994188i	$-0.534335\pi$
$991$	−6.77806			−0.215312			−0.107656	+	0.994188i	$0.534335\pi$
$992$	19.9071	−	106.655i	0.632050	−	3.38631i
$993$	−3.68021			−0.116788
$994$	14.8984	−	10.8244i	0.472550	−	0.343328i
$995$		0			0
$996$	0.664135	−	2.04400i	0.0210439	−	0.0647665i
$997$	−44.2590			−1.40170			−0.700848	−	0.713311i	$-0.747195\pi$
$997$	−44.2590			−1.40170			−0.700848	+	0.713311i	$0.747195\pi$
$998$	108.870			3.44622
$999$	−1.89002	+	5.81689i	−0.0597977	+	0.184038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.k.h.326.14		56
5.2	odd	4		155.2.n.a.109.14	yes	56
5.3	odd	4		155.2.n.a.109.1	yes	56
5.4	even	2	inner	775.2.k.h.326.1		56
31.2	even	5	inner	775.2.k.h.126.14		56
155.2	odd	20		155.2.n.a.64.1	✓	56
155.33	odd	20		155.2.n.a.64.14	yes	56
155.64	even	10	inner	775.2.k.h.126.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.n.a.64.1	✓	56	155.2	odd	20
155.2.n.a.64.14	yes	56	155.33	odd	20
155.2.n.a.109.1	yes	56	5.3	odd	4
155.2.n.a.109.14	yes	56	5.2	odd	4
775.2.k.h.126.1		56	155.64	even	10	inner
775.2.k.h.126.14		56	31.2	even	5	inner
775.2.k.h.326.1		56	5.4	even	2	inner
775.2.k.h.326.14		56	1.1	even	1	trivial

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.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.19260 - 1.59301i) q^{2} +(-0.0871848 - 0.0633434i) q^{3} +(1.65175 - 5.08355i) q^{4} -0.292068 q^{6} +(-0.412403 + 1.26925i) q^{7} +(-2.80156 - 8.62233i) q^{8} +(-0.923462 - 2.84212i) q^{9} +O(q^{10})\)	\(q+(2.19260 - 1.59301i) q^{2} +(-0.0871848 - 0.0633434i) q^{3} +(1.65175 - 5.08355i) q^{4} -0.292068 q^{6} +(-0.412403 + 1.26925i) q^{7} +(-2.80156 - 8.62233i) q^{8} +(-0.923462 - 2.84212i) q^{9} +(0.645600 - 1.98695i) q^{11} +(-0.466017 + 0.338581i) q^{12} +(4.27716 + 3.10754i) q^{13} +(1.11769 + 3.43991i) q^{14} +(-11.2295 - 8.15873i) q^{16} +(0.166005 + 0.510911i) q^{17} +(-6.55232 - 4.76054i) q^{18} +(-1.33255 + 0.968155i) q^{19} +(0.116354 - 0.0845360i) q^{21} +(-1.74970 - 5.38503i) q^{22} +(-1.57437 - 4.84540i) q^{23} +(-0.301914 + 0.929197i) q^{24} +14.3284 q^{26} +(-0.199423 + 0.613761i) q^{27} +(5.77110 + 4.19295i) q^{28} +(-5.49980 + 3.99584i) q^{29} +(-1.02157 + 5.47324i) q^{31} -19.4867 q^{32} +(-0.182147 + 0.132337i) q^{33} +(1.17787 + 0.855772i) q^{34} -15.9734 q^{36} +9.47746 q^{37} +(-1.37946 + 4.24554i) q^{38} +(-0.176061 - 0.541860i) q^{39} +(-4.83648 + 3.51391i) q^{41} +(0.120450 - 0.370706i) q^{42} +(7.66990 - 5.57251i) q^{43} +(-9.03441 - 6.56388i) q^{44} +(-11.1707 - 8.11602i) q^{46} +(-0.454274 - 0.330049i) q^{47} +(0.462242 + 1.42263i) q^{48} +(4.22221 + 3.06761i) q^{49} +(0.0178897 - 0.0550590i) q^{51} +(22.8621 - 16.6103i) q^{52} +(0.192906 + 0.593705i) q^{53} +(0.540475 + 1.66341i) q^{54} +12.0992 q^{56} +0.177504 q^{57} +(-5.69340 + 17.5225i) q^{58} +(8.23958 + 5.98641i) q^{59} +7.07355 q^{61} +(6.47905 + 13.6280i) q^{62} +3.98820 q^{63} +(-20.2673 + 14.7251i) q^{64} +(-0.188559 + 0.580325i) q^{66} +9.26497 q^{67} +2.87144 q^{68} +(-0.169664 + 0.522171i) q^{69} +(-1.57335 - 4.84227i) q^{71} +(-21.9186 + 15.9248i) q^{72} +(-1.37195 + 4.22244i) q^{73} +(20.7802 - 15.0977i) q^{74} +(2.72063 + 8.37324i) q^{76} +(2.25568 + 1.63885i) q^{77} +(-1.24922 - 0.907613i) q^{78} +(-2.81690 - 8.66952i) q^{79} +(-7.19670 + 5.22871i) q^{81} +(-5.00674 + 15.4091i) q^{82} +(-3.01847 + 2.19305i) q^{83} +(-0.237556 - 0.731123i) q^{84} +(7.93990 - 24.4365i) q^{86} +0.732608 q^{87} -18.9408 q^{88} +(-2.98913 + 9.19959i) q^{89} +(-5.70815 + 4.14722i) q^{91} -27.2323 q^{92} +(0.435760 - 0.412473i) q^{93} -1.52181 q^{94} +(1.69894 + 1.23435i) q^{96} +(-0.736960 + 2.26813i) q^{97} +14.1443 q^{98} -6.24335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{4} - 4 q^{6} - 8 q^{9}+O(q^{10}) \) 56 * q - 2 * q^4 - 4 * q^6 - 8 * q^9	\( 56 q - 2 q^{4} - 4 q^{6} - 8 q^{9} - 14 q^{11} + 16 q^{14} - 22 q^{16} + 2 q^{19} - 38 q^{21} + 30 q^{24} + 12 q^{26} - 20 q^{29} + 26 q^{31} + 2 q^{34} - 44 q^{36} + 18 q^{39} - 20 q^{41} - 62 q^{44} - 70 q^{46} + 42 q^{49} + 10 q^{51} + 26 q^{54} + 208 q^{56} + 50 q^{59} + 56 q^{61} - 12 q^{64} + 60 q^{66} - 34 q^{69} - 8 q^{71} + 84 q^{74} - 20 q^{76} - 122 q^{79} + 42 q^{81} + 40 q^{84} + 78 q^{86} + 28 q^{89} - 20 q^{91} - 160 q^{94} - 70 q^{96} + 52 q^{99}+O(q^{100}) \) 56 * q - 2 * q^4 - 4 * q^6 - 8 * q^9 - 14 * q^11 + 16 * q^14 - 22 * q^16 + 2 * q^19 - 38 * q^21 + 30 * q^24 + 12 * q^26 - 20 * q^29 + 26 * q^31 + 2 * q^34 - 44 * q^36 + 18 * q^39 - 20 * q^41 - 62 * q^44 - 70 * q^46 + 42 * q^49 + 10 * q^51 + 26 * q^54 + 208 * q^56 + 50 * q^59 + 56 * q^61 - 12 * q^64 + 60 * q^66 - 34 * q^69 - 8 * q^71 + 84 * q^74 - 20 * q^76 - 122 * q^79 + 42 * q^81 + 40 * q^84 + 78 * q^86 + 28 * q^89 - 20 * q^91 - 160 * q^94 - 70 * q^96 + 52 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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