LMFDB - Embedded newform 775.2.k.h.326.1

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			326.1
Character	$\chi$	$=$	775.326
Dual form			775.2.k.h.126.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.19260 + 1.59301i) q^{2} +(0.0871848 + 0.0633434i) q^{3} +(1.65175 - 5.08355i) q^{4} -0.292068 q^{6} +(0.412403 - 1.26925i) q^{7} +(2.80156 + 8.62233i) q^{8} +(-0.923462 - 2.84212i) q^{9} +O(q^{10})$	\(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	$0.707640\pi$
$2$	−2.19260	+	1.59301i	−1.55040	+	1.12643i	−0.943366	+	0.331754i	$0.892360\pi$
$3$	0.0871848	+	0.0633434i	0.0503361	+	0.0365714i	0.612669	−	0.790340i	$-0.290096\pi$
$3$	0.0871848	+	0.0633434i	0.0503361	+	0.0365714i	−0.562333	+	0.826911i	$0.690096\pi$
$4$	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	−0.842375	−	0.538892i	$-0.818843\pi$
$7$	0.412403	−	1.26925i	0.155874	−	0.479730i	0.998248	+	0.0591622i	$0.0188429\pi$
$8$	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	−0.193406	−	0.981119i	$-0.561954\pi$
$13$	−4.27716	−	3.10754i	−1.18627	−	0.861877i	−0.992865	+	0.119242i	$0.961954\pi$
$14$	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	0.928905	−	0.370318i	$-0.120751\pi$
$17$	−0.166005	−	0.510911i	−0.0402621	−	0.123914i	−0.969167	+	0.246404i	$0.920751\pi$
$18$	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	$0.0782456\pi$
$23$	1.57437	+	4.84540i	0.328278	+	1.01034i	−0.641661	+	0.766988i	$0.721754\pi$
$24$	−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	$-0.784294\pi$
$37$	−9.47746			−1.55808			−0.779042	+	0.626972i	$0.784294\pi$
$38$	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	−0.990967	−	0.134108i	$-0.957183\pi$
$43$	−7.66990	+	5.57251i	−1.16965	+	0.849799i	−0.178682	+	0.983907i	$0.557183\pi$
$44$	−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	0.620423	−	0.784267i	$-0.286961\pi$
$47$	0.454274	+	0.330049i	0.0662626	+	0.0481426i	−0.554161	+	0.832410i	$0.686961\pi$
$48$	−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	0.936933	−	0.349509i	$-0.113651\pi$
$53$	−0.192906	−	0.593705i	−0.0264977	−	0.0815516i	−0.963431	+	0.267957i	$0.913651\pi$
$54$	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	$-0.691490\pi$
$67$	−9.26497			−1.13190			−0.565948	+	0.824441i	$0.691490\pi$
$68$	−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	−0.838108	−	0.545504i	$-0.816338\pi$
$73$	1.37195	−	4.22244i	0.160575	−	0.494199i	0.998683	+	0.0513054i	$0.0163382\pi$
$74$	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	−0.409670	−	0.912234i	$-0.634356\pi$
$83$	3.01847	−	2.19305i	0.331321	−	0.240719i	0.740991	+	0.671515i	$0.234356\pi$
$84$	−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	−0.906647	−	0.421891i	$-0.861367\pi$
$97$	0.736960	−	2.26813i	0.0748269	−	0.230294i	0.981474	+	0.191597i	$0.0613666\pi$
$98$	−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	−0.0213655	−	0.999772i	$-0.506801\pi$
$103$	9.36612	−	6.80489i	0.922872	−	0.670506i	0.944237	+	0.329266i	$0.106801\pi$
$104$	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	$-0.959962\pi$
$107$	−2.72269	−	8.37958i	−0.263212	−	0.810084i	0.728888	−	0.684633i	$-0.240038\pi$
$108$	−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	$-0.704475\pi$
$113$	3.78653	−	11.6537i	0.356207	−	1.09629i	0.955306	−	0.295617i	$-0.0955254\pi$
$114$	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	0.0936480	−	0.995605i	$-0.470147\pi$
$127$	−9.28928	−	6.74906i	−0.824290	−	0.598882i	−0.917938	+	0.396724i	$0.870147\pi$
$128$	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	0.927961	−	0.372678i	$-0.121560\pi$
$137$	10.0693	+	7.31578i	0.860279	+	0.625029i	−0.0676817	+	0.997707i	$0.521560\pi$
$138$	−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	−0.560963	−	0.827841i	$-0.689569\pi$
$157$	0.664263	−	0.482615i	0.0530139	−	0.0385169i	0.613977	+	0.789324i	$0.289569\pi$
$158$	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	$0.0200540\pi$
$163$	2.90594	+	8.94357i	0.227611	+	0.700515i	−0.770405	+	0.637555i	$0.779946\pi$
$164$	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	−0.955017	−	0.296550i	$-0.904164\pi$
$167$	−12.5106	+	9.08947i	−0.968098	+	0.703364i	−0.0130807	+	0.999914i	$0.504164\pi$
$168$	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	0.490439	−	0.871475i	$-0.336836\pi$
$173$	−2.45735	−	1.78537i	−0.186829	−	0.135739i	−0.677268	+	0.735736i	$0.736836\pi$
$174$	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	−0.923296	−	0.384089i	$-0.874516\pi$
$193$	0.686674	−	2.11337i	0.0494279	−	0.152123i	0.972724	+	0.231965i	$0.0745156\pi$
$194$	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	−0.864261	−	0.503044i	$-0.832213\pi$
$197$	1.83338	−	5.64256i	0.130623	−	0.402016i	0.994884	+	0.101029i	$0.0322133\pi$
$198$	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	$-0.485155\pi$
$223$	1.39239			0.0932416			0.0466208	+	0.998913i	$0.485155\pi$
$224$	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	0.0508432	−	0.998707i	$-0.483809\pi$
$227$	15.3133	−	11.1258i	1.01638	−	0.738444i	0.965538	+	0.260263i	$0.0838091\pi$
$228$	−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	0.623885	−	0.781516i	$-0.285553\pi$
$233$	1.12057	+	0.814141i	0.0734109	+	0.0533362i	−0.550475	+	0.834852i	$0.685553\pi$
$234$	−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	$0.101701\pi$
$257$	5.86643	+	18.0550i	0.365938	+	1.12624i	−0.583453	+	0.812147i	$0.698299\pi$
$258$	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	0.447466	−	0.894301i	$-0.352327\pi$
$263$	−4.29418	−	3.11991i	−0.264791	−	0.192382i	−0.712256	+	0.701919i	$0.752327\pi$
$264$	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	−0.557327	−	0.830293i	$-0.688173\pi$
$277$	1.00034	−	0.726793i	0.0601049	−	0.0436688i	0.617432	+	0.786624i	$0.288173\pi$
$278$	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	$-0.742529\pi$
$283$	4.93621	−	15.1921i	0.293427	−	0.903076i	0.983745	−	0.179570i	$-0.0574706\pi$
$284$	−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	0.998761	−	0.0497562i	$-0.0158444\pi$
$293$	2.76444	+	8.50808i	0.161500	+	0.497047i	−0.837261	+	0.546804i	$0.815844\pi$
$294$	−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	0.418941	−	0.908014i	$-0.362402\pi$
$307$	−5.52226	−	4.01216i	−0.315172	−	0.228986i	−0.734113	+	0.679028i	$0.762402\pi$
$308$	−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	0.110790	−	0.993844i	$-0.464662\pi$
$313$	−14.1566	−	10.2853i	−0.800176	−	0.581362i	−0.910966	+	0.412482i	$0.864662\pi$
$314$	−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	−0.835417	−	0.549616i	$-0.814774\pi$
$317$	2.91114	−	8.95957i	0.163506	−	0.503219i	0.998923	+	0.0463970i	$0.0147739\pi$
$318$	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	$-0.727832\pi$
$337$	5.84176	−	17.9791i	0.318221	−	0.979383i	0.974408	−	0.224785i	$-0.0721680\pi$
$338$	−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	$-0.421358\pi$
$347$	9.11110			0.489110			0.244555	+	0.969635i	$0.421358\pi$
$348$	−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	−0.809706	−	0.586836i	$-0.800373\pi$
$353$	−9.42804	+	6.84987i	−0.501804	+	0.364582i	0.307902	+	0.951418i	$0.400373\pi$
$354$	−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	$-0.206247\pi$
$367$	30.5491			1.59465			0.797325	+	0.603550i	$0.206247\pi$
$368$	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	$-0.487587\pi$
$373$	1.50588			0.0779717			0.0389859	+	0.999240i	$0.487587\pi$
$374$	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	$0.290832\pi$
$383$	−6.82461	+	21.0040i	−0.348721	+	1.07325i	−0.959561	+	0.281500i	$0.909168\pi$
$384$	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	$-0.584178\pi$
$397$	−10.4160			−0.522763			−0.261381	+	0.965236i	$0.584178\pi$
$398$	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	$-0.792067\pi$
$433$	−33.0490			−1.58824			−0.794118	+	0.607764i	$0.792067\pi$
$434$	−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	$-0.980200\pi$
$443$	−4.78101	−	14.7144i	−0.227153	−	0.699104i	0.770913	−	0.636940i	$-0.219800\pi$
$444$	−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	$-0.945638\pi$
$457$	−6.15890	−	18.9551i	−0.288101	−	0.886684i	0.697351	−	0.716730i	$-0.254362\pi$
$458$	−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	−0.732897	−	0.680339i	$-0.761832\pi$
$463$	−6.72063	+	4.88282i	−0.312334	+	0.226924i	0.420563	+	0.907263i	$0.361832\pi$
$464$	94.3610			4.38060
$465$		0			0
$466$	−3.75389			−0.173896
$467$	−11.5832	+	8.41565i	−0.536004	+	0.389430i	−0.822599	−	0.568622i	$-0.807477\pi$
$467$	−11.5832	+	8.41565i	−0.536004	+	0.389430i	0.286595	+	0.958052i	$0.407477\pi$
$468$	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	$0.0926946\pi$
$487$	7.76137	+	23.8870i	0.351701	+	1.08243i	−0.606196	+	0.795315i	$0.707305\pi$
$488$	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	−0.929469	−	0.368899i	$-0.879735\pi$
$503$	0.881868	−	2.71411i	0.0393206	−	0.121016i	0.968790	+	0.247883i	$0.0797348\pi$
$504$	−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	$-0.779608\pi$
$523$	5.21923	−	16.0631i	0.228221	−	0.702392i	0.997949	−	0.0640196i	$-0.0203920\pi$
$524$	−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	$0.351588\pi$
$547$	−10.2718	+	31.6133i	−0.439190	+	1.35169i	−0.888731	+	0.458429i	$0.848412\pi$
$548$	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	$-0.850844\pi$
$557$	−42.1137			−1.78441			−0.892207	+	0.451627i	$0.850844\pi$
$558$	−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	$-0.548410\pi$
$563$	−7.18940			−0.302997			−0.151498	+	0.988457i	$0.548410\pi$
$564$	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	0.0504414	−	0.998727i	$-0.483937\pi$
$577$	24.4021	−	17.7292i	1.01587	−	0.738076i	0.965433	+	0.260651i	$0.0839372\pi$
$578$	−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	−0.100344	−	0.994953i	$-0.531994\pi$
$587$	19.7436	−	14.3445i	0.814904	−	0.592063i	0.915248	+	0.402890i	$0.131994\pi$
$588$	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	−0.982601	−	0.185729i	$-0.940535\pi$
$593$	−1.91139	+	5.88265i	−0.0784914	+	0.241572i	0.904110	+	0.427301i	$0.140535\pi$
$594$	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	$-0.907108\pi$
$607$	−37.6285	−	27.3387i	−1.52729	−	1.10964i	−0.569575	−	0.821940i	$-0.692892\pi$
$608$	−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	−0.954293	−	0.298874i	$-0.903389\pi$
$613$	−0.162908	+	0.501379i	−0.00657979	+	0.0202505i	0.947713	+	0.319125i	$0.103389\pi$
$614$	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	0.684498	−	0.729015i	$-0.260021\pi$
$617$	5.03461	+	3.65786i	0.202686	+	0.147260i	−0.481813	+	0.876274i	$0.660021\pi$
$618$	−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	$-0.755469\pi$
$643$	−13.8393	−	42.5931i	−0.545770	−	1.67971i	0.173381	−	0.984855i	$-0.444531\pi$
$644$	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	$0.457218\pi$
$647$	−14.1652	+	43.5961i	−0.556893	+	1.71394i	−0.690891	+	0.722959i	$0.742782\pi$
$648$	−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	−0.0912677	−	0.995826i	$-0.529092\pi$
$653$	21.1488	−	15.3655i	0.827616	−	0.601298i	0.918884	+	0.394528i	$0.129092\pi$
$654$	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	$0.148453\pi$
$673$	11.2820	+	34.7223i	0.434887	+	1.33845i	−0.458315	+	0.888790i	$0.651547\pi$
$674$	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	$-0.743225\pi$
$677$	−36.0053			−1.38379			−0.691897	+	0.721996i	$0.743225\pi$
$678$	−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	$-0.669476\pi$
$683$	−26.5328			−1.01525			−0.507625	+	0.861578i	$0.669476\pi$
$684$	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	$0.0435852\pi$
$727$	7.26457	+	22.3580i	0.269428	+	0.829214i	−0.721212	+	0.692714i	$0.756415\pi$
$728$	−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	−0.848909	−	0.528538i	$-0.822740\pi$
$733$	4.02156	−	12.3771i	0.148540	−	0.457158i	0.997449	+	0.0713800i	$0.0227403\pi$
$734$	−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	$-0.482918\pi$
$743$	2.92421			0.107279			0.0536394	+	0.998560i	$0.482918\pi$
$744$	−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	0.665666	−	0.746250i	$-0.268147\pi$
$757$	4.44738	+	3.23121i	0.161643	+	0.117440i	−0.504023	+	0.863690i	$0.668147\pi$
$758$	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	−0.337580	−	0.941297i	$-0.609608\pi$
$773$	12.6038	−	9.15722i	0.453328	−	0.329362i	0.790908	+	0.611934i	$0.209608\pi$
$774$	−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	−0.816289	−	0.577643i	$-0.803973\pi$
$787$	−14.5644	+	10.5817i	−0.519165	+	0.377196i	0.297124	+	0.954839i	$0.403973\pi$
$788$	−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	$-0.980776\pi$
$797$	−6.38341	−	19.6461i	−0.226112	−	0.695901i	0.772065	−	0.635544i	$-0.219224\pi$
$798$	−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	$-0.925590\pi$
$823$	−9.23593	−	28.4253i	−0.321944	−	0.990843i	0.650857	−	0.759201i	$-0.274410\pi$
$824$	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	−0.169756	−	0.985486i	$-0.554298\pi$
$827$	20.5628	−	14.9398i	0.715040	−	0.519507i	0.884796	+	0.465979i	$0.154298\pi$
$828$	−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	0.668865	−	0.743384i	$-0.266780\pi$
$853$	4.92287	+	3.57668i	0.168556	+	0.122463i	−0.500309	+	0.865847i	$0.666780\pi$
$854$	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	$0.356911\pi$
$857$	−13.0682	+	40.2197i	−0.446400	+	1.37388i	−0.880941	+	0.473227i	$0.843089\pi$
$858$	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	$-0.727716\pi$
$863$	−38.5374			−1.31183			−0.655914	+	0.754836i	$0.727716\pi$
$864$	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	$0.176640\pi$
$877$	13.9785	+	43.0213i	0.472019	+	1.45272i	−0.377917	+	0.925839i	$0.623360\pi$
$878$	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	0.993175	−	0.116630i	$-0.0372090\pi$
$883$	35.3363	+	25.6733i	1.18916	+	0.863977i	0.195987	+	0.980607i	$0.437209\pi$
$884$	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	0.00761018	−	0.999971i	$-0.497578\pi$
$887$	28.6208	−	20.7942i	0.960991	−	0.698201i	0.953381	+	0.301770i	$0.0975776\pi$
$888$	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	$-0.974112\pi$
$907$	−7.17084	−	22.0696i	−0.238104	−	0.732808i	0.758591	−	0.651567i	$-0.225888\pi$
$908$	−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	$-0.729285\pi$
$937$	9.66675	−	29.7512i	0.315799	−	0.971929i	0.975424	−	0.220335i	$-0.0707150\pi$
$938$	−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	0.982752	−	0.184929i	$-0.0592056\pi$
$947$	2.43080	+	7.48122i	0.0789903	+	0.243107i	−0.903762	+	0.428036i	$0.859206\pi$
$948$	−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	0.992396	−	0.123085i	$-0.0392787\pi$
$953$	3.61754	+	11.1336i	0.117183	+	0.360654i	−0.875213	+	0.483738i	$0.839279\pi$
$954$	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	$-0.684555\pi$
$967$	−34.0728			−1.09571			−0.547854	+	0.836574i	$0.684555\pi$
$968$	−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	0.887479	−	0.460848i	$-0.152455\pi$
$977$	22.6123	+	16.4288i	0.723433	+	0.525605i	−0.164046	+	0.986453i	$0.552455\pi$
$978$	−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	$0.0712425\pi$
$983$	9.92878	+	30.5577i	0.316679	+	0.974638i	−0.658379	+	0.752687i	$0.728757\pi$
$984$	−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	$-0.252805\pi$
$997$	44.2590			1.40170			0.700848	+	0.713311i	$0.252805\pi$
$998$	−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.326.1		56
5.2	odd	4		155.2.n.a.109.1	yes	56
5.3	odd	4		155.2.n.a.109.14	yes	56
5.4	even	2	inner	775.2.k.h.326.14		56
31.2	even	5	inner	775.2.k.h.126.1		56
155.2	odd	20		155.2.n.a.64.14	yes	56
155.33	odd	20		155.2.n.a.64.1	✓	56
155.64	even	10	inner	775.2.k.h.126.14		56

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

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

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