LMFDB - Embedded newform 930.2.br.a.761.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			761.11
Character	$\chi$	$=$	930.761
Dual form			930.2.br.a.11.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(1.51241 + 0.844159i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.17753 - 1.27020i) q^{6} +(0.00579634 - 0.0551485i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.57479 + 2.55344i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(1.51241 + 0.844159i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.17753 - 1.27020i) q^{6} +(0.00579634 - 0.0551485i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.57479 + 2.55344i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(-4.39351 + 1.95612i) q^{11} +(0.727384 + 1.57191i) q^{12} +(-1.17337 + 5.52027i) q^{13} +(-0.0225545 + 0.0506582i) q^{14} +(0.887709 + 1.48727i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.22241 - 1.87994i) q^{17} +(-0.708659 - 2.91510i) q^{18} +(-7.24514 + 1.54000i) q^{19} +(0.406737 + 0.913545i) q^{20} +(0.0553206 - 0.0785143i) q^{21} +(4.78295 - 0.502709i) q^{22} +(-1.07181 + 0.778717i) q^{23} +(-0.206035 - 1.71975i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.82180 - 4.88750i) q^{26} +(0.226225 + 5.19123i) q^{27} +(0.0371048 - 0.0412091i) q^{28} +(-0.765615 + 2.35632i) q^{29} +(-0.384669 - 1.68880i) q^{30} +(5.26534 - 1.81001i) q^{31} -1.00000i q^{32} +(-8.29608 - 0.750366i) q^{33} +(3.43482 + 3.09273i) q^{34} +(0.0325940 - 0.0448618i) q^{35} +(-0.226841 + 2.99141i) q^{36} +(4.18646 - 2.41705i) q^{37} +(7.36642 + 0.774242i) q^{38} +(-6.43461 + 7.35842i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(7.04768 - 6.34576i) q^{41} +(-0.0768752 + 0.0575765i) q^{42} +(0.517215 + 2.43330i) q^{43} +(-4.70420 - 0.999909i) q^{44} +(0.0870895 + 2.99874i) q^{45} +(1.25999 - 0.409396i) q^{46} +(-0.349977 + 0.113714i) q^{47} +(-0.335482 + 1.69925i) q^{48} +(6.84403 + 1.45474i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(-4.79907 - 6.40764i) q^{51} +(-4.19401 + 3.77630i) q^{52} +(0.476094 + 4.52973i) q^{53} +(1.38902 - 5.00706i) q^{54} +(-4.78295 - 0.502709i) q^{55} +(-0.0480231 + 0.0277261i) q^{56} +(-12.2577 - 3.78693i) q^{57} +(1.45629 - 2.00441i) q^{58} +(4.67634 + 4.21060i) q^{59} +(-0.156024 + 1.72501i) q^{60} -6.01788i q^{61} +(-5.56696 + 0.0943451i) q^{62} +(0.149946 - 0.0720467i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.77630 + 4.19401i) q^{65} +(7.65817 + 3.27727i) q^{66} +(-1.65285 + 2.86283i) q^{67} +(-2.31100 - 4.00278i) q^{68} +(-2.27839 + 0.272962i) q^{69} +(-0.0448618 + 0.0325940i) q^{70} +(-3.05457 + 0.321048i) q^{71} +(1.14014 - 2.77490i) q^{72} +(-2.89385 - 6.49970i) q^{73} +(-4.72847 + 1.00507i) q^{74} +(0.0251432 + 1.73187i) q^{75} +(-6.76663 - 3.01270i) q^{76} +(0.0824107 + 0.253634i) q^{77} +(8.39355 - 5.00987i) q^{78} +(5.28619 - 11.8730i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(-4.04008 + 8.04225i) q^{81} +(-8.66369 + 3.85732i) q^{82} +(1.77637 + 1.97286i) q^{83} +(0.0909048 - 0.0310028i) q^{84} +(-2.71675 - 3.73928i) q^{85} +(0.260032 - 2.47404i) q^{86} +(-3.14704 + 2.91743i) q^{87} +(4.16497 + 2.40465i) q^{88} +(6.09663 + 4.42946i) q^{89} +(0.843833 - 2.87888i) q^{90} +(0.297633 + 0.0967069i) q^{91} -1.32483 q^{92} +(9.49132 + 1.70730i) q^{93} +0.367987 q^{94} +(-7.04448 - 2.28889i) q^{95} +(0.844159 - 1.51241i) q^{96} +(1.98975 + 1.44564i) q^{97} +(-6.05951 - 3.49846i) q^{98} +(-11.9137 - 8.13808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{30}\right)$

Coefficient data

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

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

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

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	1.51241	+	0.844159i	0.873192	+	0.487376i
$3$	1.51241	+	0.844159i	0.873192	+	0.487376i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−1.17753	−	1.27020i	−0.480725	−	0.518559i
$7$	0.00579634	−	0.0551485i	0.00219081	−	0.0208442i	−0.993372	−	0.114945i	$-0.963331\pi$
$7$	0.00579634	−	0.0551485i	0.00219081	−	0.0208442i	0.995563	+	0.0941006i	$0.0299975\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	1.57479	+	2.55344i	0.524930	+	0.851145i
$10$	−0.669131	−	0.743145i	−0.211598	−	0.235003i
$11$	−4.39351	+	1.95612i	−1.32469	+	0.589792i	−0.942474	−	0.334280i	$-0.891507\pi$
$11$	−4.39351	+	1.95612i	−1.32469	+	0.589792i	−0.382220	+	0.924071i	$0.624840\pi$
$12$	0.727384	+	1.57191i	0.209978	+	0.453772i
$13$	−1.17337	+	5.52027i	−0.325434	+	1.53105i	0.446173	+	0.894947i	$0.352787\pi$
$13$	−1.17337	+	5.52027i	−0.325434	+	1.53105i	−0.771607	+	0.636100i	$0.780547\pi$
$14$	−0.0225545	+	0.0506582i	−0.00602793	+	0.0135390i
$15$	0.887709	+	1.48727i	0.229205	+	0.384012i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−4.22241	−	1.87994i	−1.02409	−	0.455952i	−0.175202	−	0.984532i	$-0.556058\pi$
$17$	−4.22241	−	1.87994i	−1.02409	−	0.455952i	−0.848883	+	0.528580i	$0.822725\pi$
$18$	−0.708659	−	2.91510i	−0.167032	−	0.687095i
$19$	−7.24514	+	1.54000i	−1.66215	+	0.353301i	−0.940719	−	0.339187i	$-0.889848\pi$
$19$	−7.24514	+	1.54000i	−1.66215	+	0.353301i	−0.721430	+	0.692487i	$0.756515\pi$
$20$	0.406737	+	0.913545i	0.0909491	+	0.204275i
$21$	0.0553206	−	0.0785143i	0.0120719	−	0.0171332i
$22$	4.78295	−	0.502709i	1.01973	−	0.107178i
$23$	−1.07181	+	0.778717i	−0.223488	+	0.162374i	−0.693896	−	0.720076i	$-0.744107\pi$
$23$	−1.07181	+	0.778717i	−0.223488	+	0.162374i	0.470407	+	0.882449i	$0.344107\pi$
$24$	−0.206035	−	1.71975i	−0.0420567	−	0.351043i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	2.82180	−	4.88750i	0.553400	−	0.958517i
$27$	0.226225	+	5.19123i	0.0435371	+	0.999052i
$28$	0.0371048	−	0.0412091i	0.00701215	−	0.00778778i
$29$	−0.765615	+	2.35632i	−0.142171	+	0.437558i	−0.996636	−	0.0819507i	$-0.973885\pi$
$29$	−0.765615	+	2.35632i	−0.142171	+	0.437558i	0.854465	+	0.519509i	$0.173885\pi$
$30$	−0.384669	−	1.68880i	−0.0702307	−	0.308330i
$31$	5.26534	−	1.81001i	0.945684	−	0.325088i
$31$	5.26534	−	1.81001i	0.945684	−	0.325088i
$32$		−	1.00000i		−	0.176777i
$33$	−8.29608	−	0.750366i	−1.44416	−	0.130622i
$34$	3.43482	+	3.09273i	0.589067	+	0.530398i
$35$	0.0325940	−	0.0448618i	0.00550940	−	0.00758303i
$36$	−0.226841	+	2.99141i	−0.0378068	+	0.498569i
$37$	4.18646	−	2.41705i	0.688249	−	0.397361i	−0.114707	−	0.993399i	$-0.536593\pi$
$37$	4.18646	−	2.41705i	0.688249	−	0.397361i	0.802956	+	0.596039i	$0.203259\pi$
$38$	7.36642	+	0.774242i	1.19499	+	0.125599i
$39$	−6.43461	+	7.35842i	−1.03036	+	1.17829i
$40$	−0.104528	−	0.994522i	−0.0165274	−	0.157248i
$41$	7.04768	−	6.34576i	1.10066	−	0.991041i	0.100670	−	0.994920i	$-0.467901\pi$
$41$	7.04768	−	6.34576i	1.10066	−	0.991041i	0.999992	+	0.00387861i	$0.00123460\pi$
$42$	−0.0768752	+	0.0575765i	−0.0118621	+	0.00888425i
$43$	0.517215	+	2.43330i	0.0788745	+	0.371075i	0.999827	−	0.0185995i	$-0.00592073\pi$
$43$	0.517215	+	2.43330i	0.0788745	+	0.371075i	−0.920953	+	0.389675i	$0.872587\pi$
$44$	−4.70420	−	0.999909i	−0.709185	−	0.150742i
$45$	0.0870895	+	2.99874i	0.0129825	+	0.447025i
$46$	1.25999	−	0.409396i	0.185776	−	0.0603621i
$47$	−0.349977	+	0.113714i	−0.0510494	+	0.0165869i	−0.334430	−	0.942420i	$-0.608544\pi$
$47$	−0.349977	+	0.113714i	−0.0510494	+	0.0165869i	0.283381	+	0.959007i	$0.408544\pi$
$48$	−0.335482	+	1.69925i	−0.0484226	+	0.245266i
$49$	6.84403	+	1.45474i	0.977718	+	0.207820i
$50$	−0.207912	−	0.978148i	−0.0294032	−	0.138331i
$51$	−4.79907	−	6.40764i	−0.672004	−	0.897249i
$52$	−4.19401	+	3.77630i	−0.581604	+	0.523679i
$53$	0.476094	+	4.52973i	0.0653965	+	0.622206i	0.977309	+	0.211820i	$0.0679392\pi$
$53$	0.476094	+	4.52973i	0.0653965	+	0.622206i	−0.911912	+	0.410386i	$0.865394\pi$
$54$	1.38902	−	5.00706i	0.189022	−	0.681374i
$55$	−4.78295	−	0.502709i	−0.644933	−	0.0677852i
$56$	−0.0480231	+	0.0277261i	−0.00641735	+	0.00370506i
$57$	−12.2577	−	3.78693i	−1.62357	−	0.501592i
$58$	1.45629	−	2.00441i	0.191220	−	0.263192i
$59$	4.67634	+	4.21060i	0.608808	+	0.548173i	0.914824	−	0.403853i	$-0.132329\pi$
$59$	4.67634	+	4.21060i	0.608808	+	0.548173i	−0.306016	+	0.952026i	$0.598996\pi$
$60$	−0.156024	+	1.72501i	−0.0201426	+	0.222698i
$61$		−	6.01788i		−	0.770511i	−0.922810	−	0.385256i	$-0.874113\pi$
$61$		−	6.01788i		−	0.770511i	0.922810	−	0.385256i	$-0.125887\pi$
$62$	−5.56696	+	0.0943451i	−0.707005	+	0.0119818i
$63$	0.149946	−	0.0720467i	0.0188914	−	0.00907703i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−3.77630	+	4.19401i	−0.468393	+	0.520203i
$66$	7.65817	+	3.27727i	0.942655	+	0.403404i
$67$	−1.65285	+	2.86283i	−0.201928	+	0.349750i	−0.949150	−	0.314825i	$-0.898054\pi$
$67$	−1.65285	+	2.86283i	−0.201928	+	0.349750i	0.747222	+	0.664575i	$0.231387\pi$
$68$	−2.31100	−	4.00278i	−0.280250	−	0.485408i
$69$	−2.27839	+	0.272962i	−0.274285	+	0.0328608i
$70$	−0.0448618	+	0.0325940i	−0.00536201	+	0.00389573i
$71$	−3.05457	+	0.321048i	−0.362511	+	0.0381014i	−0.284033	−	0.958814i	$-0.591673\pi$
$71$	−3.05457	+	0.321048i	−0.362511	+	0.0381014i	−0.0784776	+	0.996916i	$0.525006\pi$
$72$	1.14014	−	2.77490i	0.134366	−	0.327026i
$73$	−2.89385	−	6.49970i	−0.338700	−	0.760733i	−0.999944	−	0.0105619i	$-0.996638\pi$
$73$	−2.89385	−	6.49970i	−0.338700	−	0.760733i	0.661244	−	0.750171i	$-0.270029\pi$
$74$	−4.72847	+	1.00507i	−0.549673	+	0.116837i
$75$	0.0251432	+	1.73187i	0.00290329	+	0.199979i
$76$	−6.76663	−	3.01270i	−0.776186	−	0.345580i
$77$	0.0824107	+	0.253634i	0.00939157	+	0.0289043i
$78$	8.39355	−	5.00987i	0.950382	−	0.567256i
$79$	5.28619	−	11.8730i	0.594743	−	1.33582i	−0.325898	−	0.945405i	$-0.605667\pi$
$79$	5.28619	−	11.8730i	0.594743	−	1.33582i	0.920641	−	0.390410i	$-0.127667\pi$
$80$	−0.207912	+	0.978148i	−0.0232452	+	0.109360i
$81$	−4.04008	+	8.04225i	−0.448897	+	0.893583i
$82$	−8.66369	+	3.85732i	−0.956745	+	0.425970i
$83$	1.77637	+	1.97286i	0.194982	+	0.216549i	0.832706	−	0.553716i	$-0.186791\pi$
$83$	1.77637	+	1.97286i	0.194982	+	0.216549i	−0.637724	+	0.770265i	$0.720124\pi$
$84$	0.0909048	−	0.0310028i	0.00991853	−	0.00338268i
$85$	−2.71675	−	3.73928i	−0.294673	−	0.405582i
$86$	0.260032	−	2.47404i	0.0280400	−	0.266782i
$87$	−3.14704	+	2.91743i	−0.337398	+	0.312781i
$88$	4.16497	+	2.40465i	0.443988	+	0.256336i
$89$	6.09663	+	4.42946i	0.646242	+	0.469522i	0.861989	−	0.506927i	$-0.169219\pi$
$89$	6.09663	+	4.42946i	0.646242	+	0.469522i	−0.215747	+	0.976449i	$0.569219\pi$
$90$	0.843833	−	2.87888i	0.0889478	−	0.303461i
$91$	0.297633	+	0.0967069i	0.0312004	+	0.0101376i
$92$	−1.32483			−0.138123
$93$	9.49132	+	1.70730i	0.984204	+	0.177039i
$94$	0.367987			0.0379550
$95$	−7.04448	−	2.28889i	−0.722748	−	0.234835i
$96$	0.844159	−	1.51241i	0.0861567	−	0.154360i
$97$	1.98975	+	1.44564i	0.202029	+	0.146782i	0.684200	−	0.729295i	$-0.260152\pi$
$97$	1.98975	+	1.44564i	0.202029	+	0.146782i	−0.482171	+	0.876077i	$0.660152\pi$
$98$	−6.05951	−	3.49846i	−0.612103	−	0.353398i
$99$	−11.9137	−	8.13808i	−1.19737	−	0.817908i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	10.3220	+	14.2070i	1.02708	+	1.41365i	0.907119	+	0.420874i	$0.138277\pi$
$101$	10.3220	+	14.2070i	1.02708	+	1.41365i	0.119960	+	0.992779i	$0.461723\pi$
$102$	2.58411	+	7.57702i	0.255865	+	0.750236i
$103$	4.35531	+	4.83706i	0.429141	+	0.476610i	0.918471	−	0.395489i	$-0.129425\pi$
$103$	4.35531	+	4.83706i	0.429141	+	0.476610i	−0.489329	+	0.872099i	$0.662758\pi$
$104$	5.15568	−	2.29546i	0.505556	−	0.225088i
$105$	0.0871662	−	0.0403351i	0.00850655	−	0.00393630i
$106$	0.946971	−	4.45515i	0.0919779	−	0.432722i
$107$	−8.15087	+	18.3072i	−0.787974	+	1.76982i	−0.167050	+	0.985948i	$0.553424\pi$
$107$	−8.15087	+	18.3072i	−0.787974	+	1.76982i	−0.620924	+	0.783871i	$0.713242\pi$
$108$	−2.86831	+	4.33276i	−0.276003	+	0.416920i
$109$	3.12570	+	9.61992i	0.299388	+	0.921421i	0.981712	+	0.190372i	$0.0609693\pi$
$109$	3.12570	+	9.61992i	0.299388	+	0.921421i	−0.682324	+	0.731050i	$0.739031\pi$
$110$	4.39351	+	1.95612i	0.418905	+	0.186509i
$111$	8.37203	−	0.121545i	0.794638	−	0.0115365i
$112$	0.0542405	−	0.0115292i	0.00512525	−	0.00108940i
$113$	−0.478150	−	1.07394i	−0.0449805	−	0.101028i	0.889658	−	0.456628i	$-0.150943\pi$
$113$	−0.478150	−	1.07394i	−0.0449805	−	0.101028i	−0.934638	+	0.355600i	$0.884276\pi$
$114$	10.4875	+	7.38941i	0.982244	+	0.692082i
$115$	−1.31758	+	0.138483i	−0.122865	+	0.0129136i
$116$	−2.00441	+	1.45629i	−0.186105	+	0.135213i
$117$	−15.9435	+	5.69714i	−1.47397	+	0.526700i
$118$	−3.14632	−	5.44959i	−0.289642	−	0.501675i
$119$	−0.128150	+	0.221963i	−0.0117475	+	0.0203473i
$120$	0.681445	−	1.59237i	0.0622071	−	0.145363i
$121$	8.11612	−	9.01387i	0.737829	−	0.819442i
$122$	−1.85963	+	5.72335i	−0.168363	+	0.518168i
$123$	16.0158	−	3.64805i	1.44410	−	0.328933i
$124$	5.32365	+	1.63056i	0.478078	+	0.146429i
$125$			1.00000i			0.0894427i
$126$	−0.164871	+	0.0221845i	−0.0146879	+	0.00197636i
$127$	2.52970	+	2.27775i	0.224475	+	0.202118i	0.773692	−	0.633561i	$-0.218408\pi$
$127$	2.52970	+	2.27775i	0.224475	+	0.202118i	−0.549218	+	0.835679i	$0.685074\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	−1.27185	+	4.11677i	−0.111981	+	0.362462i
$130$	4.88750	−	2.82180i	0.428662	−	0.247488i
$131$	−0.219272	−	0.0230464i	−0.0191579	−	0.00201357i	0.0949447	−	0.995483i	$-0.469733\pi$
$131$	−0.219272	−	0.0230464i	−0.0191579	−	0.00201357i	−0.114103	+	0.993469i	$0.536399\pi$
$132$	−6.27062	−	5.48337i	−0.545787	−	0.477267i
$133$	0.0429335	+	0.408485i	0.00372281	+	0.0354201i
$134$	2.45662	−	2.21195i	0.212219	−	0.191083i
$135$	−2.39970	+	4.60885i	−0.206533	+	0.396666i
$136$	0.960969	+	4.52100i	0.0824024	+	0.387673i
$137$	−7.90566	−	1.68040i	−0.675426	−	0.143566i	−0.142586	−	0.989782i	$-0.545542\pi$
$137$	−7.90566	−	1.68040i	−0.675426	−	0.143566i	−0.532840	+	0.846216i	$0.678875\pi$
$138$	2.25122	+	0.444458i	0.191637	+	0.0378347i
$139$	−2.87855	+	0.935296i	−0.244155	+	0.0793308i	−0.428538	−	0.903524i	$-0.640971\pi$
$139$	−2.87855	+	0.935296i	−0.244155	+	0.0793308i	0.184383	+	0.982854i	$0.440971\pi$
$140$	0.0527382	−	0.0171357i	0.00445719	−	0.00144823i
$141$	−0.625303	−	0.123453i	−0.0526600	−	0.0103966i
$142$	3.00428	+	0.638579i	0.252113	+	0.0535884i
$143$	−5.64308	−	26.5486i	−0.471898	−	2.22011i
$144$	−1.94183	+	2.28677i	−0.161819	+	0.190564i
$145$	−1.84120	+	1.65783i	−0.152904	+	0.137675i
$146$	0.743700	+	7.07583i	0.0615491	+	0.585600i
$147$	9.12296	+	7.97762i	0.752449	+	0.657983i
$148$	4.80762	+	0.505301i	0.395184	+	0.0415355i
$149$	7.38731	−	4.26507i	0.605192	−	0.349408i	−0.165889	−	0.986144i	$-0.553049\pi$
$149$	7.38731	−	4.26507i	0.605192	−	0.349408i	0.771081	+	0.636736i	$0.219716\pi$
$150$	0.511264	−	1.65487i	0.0417445	−	0.135120i
$151$	10.5873	−	14.5722i	0.861586	−	1.18587i	−0.119603	−	0.992822i	$-0.538162\pi$
$151$	10.5873	−	14.5722i	0.861586	−	1.18587i	0.981189	−	0.193050i	$-0.0618378\pi$
$152$	5.50447	+	4.95625i	0.446472	+	0.402005i
$153$	−1.84911	−	13.7422i	−0.149491	−	1.11099i
$154$		−	0.266686i		−	0.0214902i
$155$	5.46493	+	1.06515i	0.438954	+	0.0855552i
$156$	−9.53087	+	2.17092i	−0.763081	+	0.173813i
$157$	−2.87228	+	8.83996i	−0.229233	+	0.705506i	0.768602	+	0.639728i	$0.220953\pi$
$157$	−2.87228	+	8.83996i	−0.229233	+	0.705506i	−0.997834	+	0.0657780i	$0.979047\pi$
$158$	−8.69642	+	9.65836i	−0.691850	+	0.768378i
$159$	−3.10376	+	7.25272i	−0.246144	+	0.575178i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	0.0367325	+	0.0636226i	0.00289493	+	0.00501416i
$162$	6.32753	−	6.40018i	0.497138	−	0.502846i
$163$	16.4984	−	11.9868i	1.29225	−	0.938876i	0.292404	−	0.956295i	$-0.405545\pi$
$163$	16.4984	−	11.9868i	1.29225	−	0.938876i	0.999848	+	0.0174189i	$0.00554490\pi$
$164$	9.43164	−	0.991305i	0.736487	−	0.0774079i
$165$	−6.80944	−	4.79788i	−0.530114	−	0.373514i
$166$	−1.07978	−	2.42523i	−0.0838072	−	0.188234i
$167$	−19.9666	+	4.24403i	−1.54506	+	0.328413i	−0.900059	−	0.435768i	$-0.856477\pi$
$167$	−19.9666	+	4.24403i	−1.54506	+	0.328413i	−0.645002	+	0.764181i	$0.723143\pi$
$168$	−0.0960360	+	0.00139425i	−0.00740934	+	0.000107569i
$169$	−17.2205	−	7.66705i	−1.32465	−	0.589773i
$170$	1.42828	+	4.39579i	0.109544	+	0.337142i
$171$	−15.3419	−	16.0748i	−1.17322	−	1.22927i
$172$	−1.01182	+	2.27260i	−0.0771509	+	0.173284i
$173$	−2.83694	+	13.3467i	−0.215688	+	1.01473i	0.728428	+	0.685122i	$0.240251\pi$
$173$	−2.83694	+	13.3467i	−0.215688	+	1.01473i	−0.944117	+	0.329612i	$0.893082\pi$
$174$	3.89455	−	1.80215i	0.295245	−	0.136621i
$175$	0.0506582	−	0.0225545i	0.00382940	−	0.00170496i
$176$	−3.21805	−	3.57401i	−0.242570	−	0.269401i
$177$	3.51815	+	10.3157i	0.264440	+	0.775379i
$178$	−4.42946	−	6.09663i	−0.332002	−	0.456962i
$179$	1.42880	−	13.5941i	0.106793	−	1.01607i	−0.801573	−	0.597896i	$-0.796003\pi$
$179$	1.42880	−	13.5941i	0.106793	−	1.01607i	0.908367	−	0.418174i	$-0.137330\pi$
$180$	−1.69216	+	2.47722i	−0.126126	+	0.184641i
$181$	7.46802	+	4.31166i	0.555094	+	0.320483i	0.751174	−	0.660104i	$-0.229488\pi$
$181$	7.46802	+	4.31166i	0.555094	+	0.320483i	−0.196080	+	0.980588i	$0.562821\pi$
$182$	−0.253182	−	0.183947i	−0.0187671	−	0.0136351i
$183$	5.08005	−	9.10153i	0.375528	−	0.672804i
$184$	1.25999	+	0.409396i	0.0928878	+	0.0301811i
$185$	4.83410			0.355410
$186$	−8.49920	−	4.55672i	−0.623191	−	0.334115i
$187$	22.2286			1.62552
$188$	−0.349977	−	0.113714i	−0.0255247	−	0.00829347i
$189$	0.287600	+	0.0176141i	0.0209198	+	0.00128124i
$190$	5.99239	+	4.35373i	0.434734	+	0.315852i
$191$	6.80966	+	3.93156i	0.492730	+	0.284478i	0.725706	−	0.688005i	$-0.241513\pi$
$191$	6.80966	+	3.93156i	0.492730	+	0.284478i	−0.232976	+	0.972482i	$0.574846\pi$
$192$	−1.27020	+	1.17753i	−0.0916691	+	0.0849810i
$193$	−0.400990	+	3.81517i	−0.0288639	+	0.274622i	0.970565	+	0.240838i	$0.0774223\pi$
$193$	−0.400990	+	3.81517i	−0.0288639	+	0.274622i	−0.999429	+	0.0337835i	$0.989244\pi$
$194$	−1.44564	−	1.98975i	−0.103791	−	0.142856i
$195$	−9.25174	+	3.15527i	−0.662531	+	0.225954i
$196$	4.68186	+	5.19973i	0.334418	+	0.371409i
$197$	−12.2730	+	5.46427i	−0.874412	+	0.389313i	−0.794338	−	0.607476i	$-0.792182\pi$
$197$	−12.2730	+	5.46427i	−0.874412	+	0.389313i	−0.0800734	+	0.996789i	$0.525515\pi$
$198$	8.81578	+	11.4213i	0.626510	+	0.811677i
$199$	−4.60196	+	21.6505i	−0.326224	+	1.53476i	0.443434	+	0.896307i	$0.353760\pi$
$199$	−4.60196	+	21.6505i	−0.326224	+	1.53476i	−0.769658	+	0.638457i	$0.779573\pi$
$200$	0.406737	−	0.913545i	0.0287606	−	0.0645974i
$201$	−4.91648	+	2.93450i	−0.346782	+	0.206984i
$202$	−5.42660	−	16.7014i	−0.381815	−	1.17510i
$203$	0.125510	+	0.0558806i	0.00880906	+	0.00392205i
$204$	−0.116212	−	8.00471i	−0.00813648	−	0.560442i
$205$	9.27635	−	1.97175i	0.647888	−	0.137713i
$206$	−2.64741	−	5.94618i	−0.184454	−	0.414290i
$207$	−3.67628	−	1.51049i	−0.255519	−	0.104986i
$208$	−5.61268	+	0.589916i	−0.389169	+	0.0409033i
$209$	28.8192	−	20.9384i	1.99347	−	1.44834i
$210$	−0.0953642	+	0.0114251i	−0.00658075	+	0.000788407i
$211$	−2.10081	−	3.63872i	−0.144626	−	0.250500i	0.784607	−	0.619993i	$-0.212865\pi$
$211$	−2.10081	−	3.63872i	−0.144626	−	0.250500i	−0.929233	+	0.369493i	$0.879531\pi$
$212$	−2.27734	+	3.94447i	−0.156408	+	0.270907i
$213$	−4.89079	−	2.09299i	−0.335111	−	0.143409i
$214$	13.4092	−	14.8924i	0.916631	−	1.01802i
$215$	−0.768731	+	2.36591i	−0.0524270	+	0.161354i
$216$	4.06682	−	3.23435i	0.276712	−	0.220069i
$217$	−0.0692998	−	0.300867i	−0.00470438	−	0.0204242i
$218$		−	10.1150i		−	0.685073i
$219$	1.11008	−	12.2731i	0.0750123	−	0.829340i
$220$	−3.57401	−	3.21805i	−0.240959	−	0.216961i
$221$	15.3322	−	21.1030i	1.03136	−	1.41954i
$222$	−7.99983	−	2.47150i	−0.536914	−	0.165876i
$223$	−17.2637	+	9.96720i	−1.15606	+	0.667453i	−0.950357	−	0.311161i	$-0.899282\pi$
$223$	−17.2637	+	9.96720i	−1.15606	+	0.667453i	−0.205706	+	0.978614i	$0.565949\pi$
$224$	−0.0551485	−	0.00579634i	−0.00368476	−	0.000387284i
$225$	−1.42395	+	2.64053i	−0.0949297	+	0.176035i
$226$	0.122881	+	1.16914i	0.00817393	+	0.0777697i
$227$	−4.17651	+	3.76054i	−0.277204	+	0.249596i	−0.795992	−	0.605307i	$-0.793050\pi$
$227$	−4.17651	+	3.76054i	−0.277204	+	0.249596i	0.518788	+	0.854903i	$0.326384\pi$
$228$	−7.69075	−	10.2686i	−0.509332	−	0.680052i
$229$	−4.76991	−	22.4407i	−0.315205	−	1.48292i	−0.795575	−	0.605855i	$-0.792831\pi$
$229$	−4.76991	−	22.4407i	−0.315205	−	1.48292i	0.480370	−	0.877066i	$-0.340502\pi$
$230$	1.29588	+	0.275448i	0.0854480	+	0.0181625i
$231$	−0.0894685	+	0.453167i	−0.00588659	+	0.0298162i
$232$	2.35632	−	0.765615i	0.154700	−	0.0502651i
$233$	16.5162	−	5.36645i	1.08202	−	0.351568i	0.286859	−	0.957973i	$-0.407389\pi$
$233$	16.5162	−	5.36645i	1.08202	−	0.351568i	0.795156	+	0.606405i	$0.207389\pi$
$234$	16.9236	−	0.491498i	1.10633	−	0.0321302i
$235$	−0.359946	−	0.0765089i	−0.0234803	−	0.00499089i
$236$	1.30831	+	6.15513i	0.0851639	+	0.400665i
$237$	18.0176	−	13.4945i	1.17037	−	0.876560i
$238$	0.190469	−	0.171499i	0.0123462	−	0.0111166i
$239$	−0.710742	−	6.76226i	−0.0459741	−	0.437414i	−0.993163	−	0.116737i	$-0.962756\pi$
$239$	−0.710742	−	6.76226i	−0.0459741	−	0.437414i	0.947189	−	0.320677i	$-0.103910\pi$
$240$	−1.14016	+	1.30385i	−0.0735971	+	0.0841634i
$241$	23.6259	+	2.48318i	1.52188	+	0.159956i	0.828242	−	0.560371i	$-0.189342\pi$
$241$	23.6259	+	2.48318i	1.52188	+	0.159956i	0.693635	+	0.720327i	$0.256008\pi$
$242$	−10.5043	+	6.06468i	−0.675244	+	0.389852i
$243$	−12.8992	+	8.75274i	−0.827485	+	0.561489i
$244$	3.53722	−	4.86857i	0.226448	−	0.311678i
$245$	5.19973	+	4.68186i	0.332198	+	0.299113i
$246$	−16.3593	−	1.47967i	−1.04303	−	0.0943402i
$247$		−	41.8021i		−	2.65980i
$248$	−4.55922	−	3.19585i	−0.289511	−	0.202937i
$249$	1.02120	+	4.48331i	0.0647157	+	0.284118i
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	12.5247	−	13.9101i	0.790554	−	0.877999i	−0.204343	−	0.978899i	$-0.565506\pi$
$251$	12.5247	−	13.9101i	0.790554	−	0.877999i	0.994897	+	0.100901i	$0.0321724\pi$
$252$	0.163657	+	0.0298492i	0.0103094	+	0.00188032i
$253$	3.18576	−	5.51790i	0.200287	−	0.346907i
$254$	−1.70202	−	2.94799i	−0.106795	−	0.184974i
$255$	−0.952295	−	7.94871i	−0.0596350	−	0.497767i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	13.9544	−	1.46667i	0.870454	−	0.0914884i	0.341240	−	0.939976i	$-0.389153\pi$
$257$	13.9544	−	1.46667i	0.870454	−	0.0914884i	0.529215	+	0.848488i	$0.322487\pi$
$258$	2.48176	−	3.52226i	0.154508	−	0.219286i
$259$	−0.109031	−	0.244887i	−0.00677483	−	0.0152165i
$260$	−5.52027	+	1.17337i	−0.342352	+	0.0727693i
$261$	−7.22240	+	1.75576i	−0.447055	+	0.108679i
$262$	0.201418	+	0.0896771i	0.0124436	+	0.00554027i
$263$	−1.19730	−	3.68491i	−0.0738287	−	0.227221i	0.907332	−	0.420415i	$-0.138115\pi$
$263$	−1.19730	−	3.68491i	−0.0738287	−	0.227221i	−0.981161	+	0.193194i	$0.938115\pi$
$264$	4.26926	+	7.15273i	0.262755	+	0.440220i
$265$	−1.85255	+	4.16091i	−0.113802	+	0.255602i
$266$	0.0853966	−	0.401759i	0.00523600	−	0.0246335i
$267$	5.48145	+	11.8457i	0.335460	+	0.724945i
$268$	−3.01991	+	1.34455i	−0.184471	+	0.0821316i
$269$	−16.7866	−	18.6434i	−1.02349	−	1.13671i	−0.990537	−	0.137249i	$-0.956174\pi$
$269$	−16.7866	−	18.6434i	−1.02349	−	1.13671i	−0.0329584	−	0.999457i	$-0.510493\pi$
$270$	3.70646	−	3.64173i	0.225568	−	0.221628i
$271$	−14.5086	−	19.9693i	−0.881333	−	1.21305i	−0.976050	−	0.217547i	$-0.930195\pi$
$271$	−14.5086	−	19.9693i	−0.881333	−	1.21305i	0.0947168	−	0.995504i	$-0.469805\pi$
$272$	0.483131	−	4.59669i	0.0292941	−	0.278715i
$273$	0.368508	+	0.397511i	0.0223031	+	0.0240584i
$274$	6.99946	+	4.04114i	0.422853	+	0.244134i
$275$	−3.89080	−	2.82683i	−0.234624	−	0.170465i
$276$	−2.00370	−	1.11837i	−0.120608	−	0.0673180i
$277$	−18.1270	−	5.88982i	−1.08915	−	0.353885i	−0.291230	−	0.956653i	$-0.594064\pi$
$277$	−18.1270	−	5.88982i	−1.08915	−	0.353885i	−0.797917	+	0.602768i	$0.794064\pi$
$278$	3.02668			0.181528
$279$	12.9136	+	10.5943i	0.773115	+	0.634266i
$280$	−0.0554523			−0.00331391
$281$	31.1820	+	10.1317i	1.86016	+	0.604404i	0.994623	+	0.103564i	$0.0330248\pi$
$281$	31.1820	+	10.1317i	1.86016	+	0.604404i	0.865540	+	0.500839i	$0.166975\pi$
$282$	0.556549	+	0.310640i	0.0331420	+	0.0184983i
$283$	−15.1384	−	10.9987i	−0.899885	−	0.653805i	0.0385517	−	0.999257i	$-0.487726\pi$
$283$	−15.1384	−	10.9987i	−0.899885	−	0.653805i	−0.938436	+	0.345452i	$0.887726\pi$
$284$	−2.65991	−	1.53570i	−0.157836	−	0.0911269i
$285$	−8.72197	−	9.40841i	−0.516645	−	0.557306i
$286$	−2.83708	+	26.9930i	−0.167760	+	1.59613i
$287$	−0.309108	−	0.425451i	−0.0182461	−	0.0251136i
$288$	2.55344	−	1.57479i	0.150463	−	0.0927954i
$289$	2.91938	+	3.24230i	0.171728	+	0.190724i
$290$	2.26338	−	1.00772i	0.132911	−	0.0591756i
$291$	1.78898	+	3.86607i	0.104872	+	0.226633i
$292$	1.47925	−	6.95933i	0.0865667	−	0.407264i
$293$	−0.942288	+	2.11641i	−0.0550491	+	0.123642i	−0.938976	−	0.343983i	$-0.888224\pi$
$293$	−0.942288	+	2.11641i	−0.0550491	+	0.123642i	0.883927	+	0.467625i	$0.154890\pi$
$294$	−6.21123	−	10.4063i	−0.362246	−	0.606909i
$295$	1.94453	+	5.98466i	0.113215	+	0.348440i
$296$	−4.41617	−	1.96621i	−0.256685	−	0.114283i
$297$	−11.1486	−	22.3652i	−0.646906	−	1.29776i
$298$	−8.34373	+	1.77351i	−0.483339	+	0.102737i
$299$	−3.04110	−	6.83041i	−0.175871	−	0.395013i
$300$	−0.997625	+	1.41589i	−0.0575979	+	0.0817464i
$301$	0.137191	−	0.0144194i	0.00790756	−	0.000831118i
$302$	−14.5722	+	10.5873i	−0.838538	+	0.609233i
$303$	3.61815	+	30.2003i	0.207857	+	1.73496i
$304$	−3.70350	−	6.41465i	−0.212410	−	0.367905i
$305$	3.00894	−	5.21164i	0.172292	−	0.298418i
$306$	−2.48796	+	13.6410i	−0.142227	+	0.779803i
$307$	8.41836	−	9.34953i	0.480461	−	0.533606i	−0.453369	−	0.891323i	$-0.649778\pi$
$307$	8.41836	−	9.34953i	0.480461	−	0.533606i	0.933830	+	0.357717i	$0.116445\pi$
$308$	−0.0824107	+	0.253634i	−0.00469578	+	0.0144521i
$309$	2.50378	+	10.9922i	0.142435	+	0.625325i
$310$	−4.86831	−	2.70178i	−0.276501	−	0.153451i
$311$			7.04247i			0.399342i	0.979863	+	0.199671i	$0.0639873\pi$
$311$			7.04247i			0.399342i	−0.979863	+	0.199671i	$0.936013\pi$
$312$	9.73525	+	0.880536i	0.551150	+	0.0498505i
$313$	11.4480	+	10.3078i	0.647081	+	0.582634i	0.925927	−	0.377702i	$-0.123286\pi$
$313$	11.4480	+	10.3078i	0.647081	+	0.582634i	−0.278847	+	0.960336i	$0.589952\pi$
$314$	5.46340	−	7.51972i	0.308317	−	0.424362i
$315$	0.165881	+	0.0125788i	0.00934631	+	0.000708737i
$316$	11.2554	−	6.49830i	0.633165	−	0.365558i
$317$	0.195632	+	0.0205617i	0.0109878	+	0.00115486i	0.110021	−	0.993929i	$-0.464908\pi$
$317$	0.195632	+	0.0205617i	0.0109878	+	0.00115486i	−0.0990330	+	0.995084i	$0.531575\pi$
$318$	5.19307	−	5.93863i	0.291213	−	0.333022i
$319$	−1.24550	−	11.8502i	−0.0697347	−	0.663482i
$320$	−0.743145	+	0.669131i	−0.0415431	+	0.0374055i
$321$	−27.7816	+	20.8074i	−1.55062	+	1.16135i
$322$	−0.0152742	−	0.0718596i	−0.000851200	−	0.00400458i
$323$	33.4871	+	7.11790i	1.86327	+	0.396051i
$324$	−7.99561	+	4.13162i	−0.444200	+	0.229534i
$325$	−5.36738	+	1.74397i	−0.297728	+	0.0967378i
$326$	−19.3950	+	6.30182i	−1.07419	+	0.349025i
$327$	−3.39339	+	17.1879i	−0.187655	+	0.950492i
$328$	−9.27635	−	1.97175i	−0.512201	−	0.108872i
$329$	0.00424259	+	0.0199598i	0.000233902	+	0.00110042i
$330$	4.99353	+	6.66728i	0.274885	+	0.367022i
$331$	−22.7083	+	20.4467i	−1.24816	+	1.12385i	−0.260798	+	0.965393i	$0.583986\pi$
$331$	−22.7083	+	20.4467i	−1.24816	+	1.12385i	−0.987366	+	0.158458i	$0.949348\pi$
$332$	0.277496	+	2.64020i	0.0152296	+	0.144900i
$333$	12.7646	+	6.88350i	0.699494	+	0.377214i
$334$	20.3008	+	2.13370i	1.11081	+	0.116751i
$335$	−2.86283	+	1.65285i	−0.156413	+	0.0903050i
$336$	0.0917665	+	0.0283508i	0.00500627	+	0.00154666i
$337$	−18.0451	+	24.8370i	−0.982980	+	1.35296i	−0.0477716	+	0.998858i	$0.515212\pi$
$337$	−18.0451	+	24.8370i	−0.982980	+	1.35296i	−0.935208	+	0.354098i	$0.884788\pi$
$338$	14.0084	+	12.6132i	0.761956	+	0.686068i
$339$	0.183418	−	2.02788i	0.00996190	−	0.110139i
$340$		−	4.62201i		−	0.250664i
$341$	−19.5928	+	18.2520i	−1.06101	+	0.988399i
$342$	9.62359	+	20.0290i	0.520384	+	1.08304i
$343$	0.239847	−	0.738173i	0.0129505	−	0.0398576i
$344$	1.66457	−	1.84870i	0.0897478	−	0.0996750i
$345$	−2.10962	−	0.902801i	−0.113578	−	0.0486052i
$346$	6.82245	−	11.8168i	0.366777	−	0.635277i
$347$	10.9628	+	18.9881i	0.588514	+	1.01934i	0.994427	+	0.105424i	$0.0336201\pi$
$347$	10.9628	+	18.9881i	0.588514	+	1.01934i	−0.405914	+	0.913911i	$0.633047\pi$
$348$	−4.26083	+	0.510469i	−0.228405	+	0.0273640i
$349$	9.43959	−	6.85826i	0.505289	−	0.367114i	−0.305744	−	0.952114i	$-0.598905\pi$
$349$	9.43959	−	6.85826i	0.505289	−	0.367114i	0.811034	+	0.584999i	$0.198905\pi$
$350$	−0.0551485	+	0.00579634i	−0.00294781	+	0.000309827i
$351$	−28.9224	−	4.84240i	−1.54376	−	0.258468i
$352$	1.95612	+	4.39351i	0.104261	+	0.234175i
$353$	33.0664	−	7.02849i	1.75995	−	0.374089i	0.789191	−	0.614148i	$-0.210500\pi$
$353$	33.0664	−	7.02849i	1.75995	−	0.374089i	0.970758	+	0.240059i	$0.0771669\pi$
$354$	−0.158217	−	10.8980i	−0.00840915	−	0.579223i
$355$	−2.80586	−	1.24925i	−0.148920	−	0.0663033i
$356$	2.32871	+	7.16702i	0.123421	+	0.379851i
$357$	−0.381188	+	0.227520i	−0.0201746	+	0.0120417i
$358$	−5.55968	+	12.4872i	−0.293838	+	0.659971i
$359$	5.26772	−	24.7827i	0.278020	−	1.30798i	−0.588362	−	0.808598i	$-0.700227\pi$
$359$	5.26772	−	24.7827i	0.278020	−	1.30798i	0.866382	−	0.499383i	$-0.166440\pi$
$360$	2.37484	−	1.83307i	0.125165	−	0.0966112i
$361$	32.7631	−	14.5871i	1.72437	−	0.767740i
$362$	−5.77013	−	6.40838i	−0.303271	−	0.336817i
$363$	19.8841	−	6.78139i	1.04364	−	0.355931i
$364$	0.183947	+	0.253182i	0.00964146	+	0.0132703i
$365$	0.743700	−	7.07583i	0.0389270	−	0.370366i
$366$	−7.64395	+	7.08625i	−0.399555	+	0.370404i
$367$	−5.69923	−	3.29045i	−0.297497	−	0.171760i	0.343821	−	0.939035i	$-0.388279\pi$
$367$	−5.69923	−	3.29045i	−0.297497	−	0.171760i	−0.641318	+	0.767275i	$0.721612\pi$
$368$	−1.07181	−	0.778717i	−0.0558721	−	0.0405934i
$369$	27.3021	+	8.00257i	1.42129	+	0.416597i
$370$	−4.59751	−	1.49382i	−0.239013	−	0.0776600i
$371$	0.252567			0.0131126
$372$	6.67511	+	6.96009i	0.346088	+	0.360864i
$373$	4.24372			0.219732			0.109866	−	0.993946i	$-0.464958\pi$
$373$	4.24372			0.219732			0.109866	+	0.993946i	$0.464958\pi$
$374$	−21.1407	−	6.86902i	−1.09316	−	0.355188i
$375$	−0.844159	+	1.51241i	−0.0435922	+	0.0781007i
$376$	0.297708	+	0.216298i	0.0153531	+	0.0111547i
$377$	−12.1092	−	6.99124i	−0.623654	−	0.360067i
$378$	−0.268080	−	0.105625i	−0.0137886	−	0.00543277i
$379$	−3.46762	+	32.9922i	−0.178120	+	1.69469i	0.431590	+	0.902070i	$0.357953\pi$
$379$	−3.46762	+	32.9922i	−0.178120	+	1.69469i	−0.609710	+	0.792625i	$0.708714\pi$
$380$	−4.35373	−	5.99239i	−0.223341	−	0.307403i
$381$	1.90317	+	5.58038i	0.0975022	+	0.285891i
$382$	−5.26145	−	5.84344i	−0.269199	−	0.298976i
$383$	−24.9969	+	11.1293i	−1.27728	+	0.568682i	−0.929475	−	0.368885i	$-0.879740\pi$
$383$	−24.9969	+	11.1293i	−1.27728	+	0.568682i	−0.347805	+	0.937567i	$0.613073\pi$
$384$	1.57191	−	0.727384i	0.0802164	−	0.0371191i
$385$	−0.0554472	+	0.260859i	−0.00282585	+	0.0132946i
$386$	1.56032	−	3.50453i	0.0794180	−	0.178376i
$387$	−5.39878	+	5.15262i	−0.274436	+	0.261922i
$388$	0.760017	+	2.33909i	0.0385840	+	0.118749i
$389$	−30.3902	−	13.5306i	−1.54084	−	0.686027i	−0.551843	−	0.833948i	$-0.686075\pi$
$389$	−30.3902	−	13.5306i	−1.54084	−	0.686027i	−0.988999	+	0.147921i	$0.952742\pi$
$390$	9.77396	−	0.141898i	0.494924	−	0.00718529i
$391$	5.98958	−	1.27312i	0.302906	−	0.0643846i
$392$	−2.84591	−	6.39201i	−0.143740	−	0.322845i
$393$	−0.312175	−	0.219956i	−0.0157471	−	0.0110953i
$394$	13.3608	−	1.40428i	0.673108	−	0.0707466i
$395$	10.5145	−	7.63921i	0.529040	−	0.384370i
$396$	−4.85493	−	13.5865i	−0.243969	−	0.682749i
$397$	−2.60107	−	4.50518i	−0.130544	−	0.226109i	0.793342	−	0.608776i	$-0.208339\pi$
$397$	−2.60107	−	4.50518i	−0.130544	−	0.226109i	−0.923886	+	0.382667i	$0.875006\pi$
$398$	11.0671	−	19.1688i	0.554743	−	0.960844i
$399$	−0.279893	+	0.654041i	−0.0140122	+	0.0327430i
$400$	−0.669131	+	0.743145i	−0.0334565	+	0.0371572i
$401$	10.2012	−	31.3960i	0.509423	−	1.56784i	−0.283783	−	0.958889i	$-0.591589\pi$
$401$	10.2012	−	31.3960i	0.509423	−	1.56784i	0.793206	−	0.608954i	$-0.208411\pi$
$402$	5.58266	−	1.27160i	0.278438	−	0.0634218i
$403$	3.81357	+	31.1899i	0.189968	+	1.55368i
$404$			17.5609i			0.873685i
$405$	−7.51993	+	4.94476i	−0.373668	+	0.245707i
$406$	−0.102099	−	0.0919302i	−0.00506708	−	0.00456242i
$407$	−13.6652	+	18.8085i	−0.677359	+	0.932305i
$408$	−2.36307	+	7.64884i	−0.116989	+	0.378674i
$409$	−16.0188	+	9.24846i	−0.792079	+	0.457307i	−0.840694	−	0.541511i	$-0.817853\pi$
$409$	−16.0188	+	9.24846i	−0.792079	+	0.457307i	0.0486150	+	0.998818i	$0.484519\pi$
$410$	−9.43164	−	0.991305i	−0.465795	−	0.0489571i
$411$	−10.5381	−	9.21510i	−0.519806	−	0.454547i
$412$	0.680366	+	6.47325i	0.0335192	+	0.318914i
$413$	0.259314	−	0.233487i	0.0127600	−	0.0114892i
$414$	3.02959	+	2.57259i	0.148896	+	0.126436i
$415$	0.551951	+	2.59673i	0.0270942	+	0.127468i
$416$	5.52027	+	1.17337i	0.270653	+	0.0575292i
$417$	−5.14309	−	1.01540i	−0.251858	−	0.0497242i
$418$	−33.8790	+	11.0080i	−1.65708	+	0.538417i
$419$	−1.99398	+	0.647883i	−0.0974123	+	0.0316512i	−0.357318	−	0.933983i	$-0.616309\pi$
$419$	−1.99398	+	0.647883i	−0.0974123	+	0.0316512i	0.259905	+	0.965634i	$0.416309\pi$
$420$	0.0942273	+	0.0186032i	0.00459782	+	0.000907745i
$421$	−9.89485	−	2.10321i	−0.482245	−	0.102504i	−0.0396271	−	0.999215i	$-0.512617\pi$
$421$	−9.89485	−	2.10321i	−0.482245	−	0.102504i	−0.442618	+	0.896710i	$0.645950\pi$
$422$	0.873567	+	4.10981i	0.0425246	+	0.200063i
$423$	−0.841502	−	0.714567i	−0.0409152	−	0.0347434i
$424$	3.38479	−	3.04767i	0.164380	−	0.148008i
$425$	−0.483131	−	4.59669i	−0.0234353	−	0.222972i
$426$	4.00465	+	3.50189i	0.194026	+	0.169667i
$427$	−0.331877	−	0.0348817i	−0.0160607	−	0.00168804i
$428$	−17.3549	+	10.0198i	−0.838879	+	0.484327i
$429$	13.8766	−	44.9161i	0.669968	−	2.16857i
$430$	1.46221	−	2.01256i	0.0705142	−	0.0970544i
$431$	3.40460	+	3.06551i	0.163994	+	0.147661i	0.747042	−	0.664777i	$-0.231473\pi$
$431$	3.40460	+	3.06551i	0.163994	+	0.147661i	−0.583048	+	0.812438i	$0.698140\pi$
$432$	−4.86724	+	1.81933i	−0.234175	+	0.0875326i
$433$			0.0498821i			0.00239718i	0.999999	+	0.00119859i	$0.000381523\pi$
$433$			0.0498821i			0.00239718i	−0.999999	+	0.00119859i	$0.999618\pi$
$434$	−0.0270650	+	0.307557i	−0.00129916	+	0.0147632i
$435$	−4.18413	+	0.953051i	−0.200614	+	0.0456953i
$436$	−3.12570	+	9.61992i	−0.149694	+	0.460711i
$437$	6.56621	−	7.29251i	0.314104	−	0.348848i
$438$	−4.84835	+	11.3294i	−0.231663	+	0.541339i
$439$	−14.9447	+	25.8850i	−0.713273	+	1.23543i	0.250349	+	0.968156i	$0.419455\pi$
$439$	−14.9447	+	25.8850i	−0.713273	+	1.23543i	−0.963622	+	0.267269i	$0.913879\pi$
$440$	2.40465	+	4.16497i	0.114637	+	0.198557i
$441$	7.06331	+	19.7667i	0.336348	+	0.941271i
$442$	−21.1030	+	15.3322i	−1.00377	+	0.729279i
$443$	−32.6130	+	3.42777i	−1.54949	+	0.162858i	−0.840286	−	0.542144i	$-0.817613\pi$
$443$	−32.6130	+	3.42777i	−1.54949	+	0.162858i	−0.709205	+	0.705002i	$0.750946\pi$
$444$	6.84456	+	4.82262i	0.324828	+	0.228872i
$445$	3.06511	+	6.88434i	0.145300	+	0.326349i
$446$	19.4988	−	4.14460i	0.923294	−	0.196252i
$447$	14.7731	−	0.214475i	0.698742	−	0.0101443i
$448$	0.0506582	+	0.0225545i	0.00239337	+	0.00106560i
$449$	7.83440	+	24.1118i	0.369728	+	1.13791i	0.946967	+	0.321331i	$0.104130\pi$
$449$	7.83440	+	24.1118i	0.369728	+	1.13791i	−0.577239	+	0.816575i	$0.695870\pi$
$450$	2.17022	−	2.07127i	0.102305	−	0.0976404i
$451$	−18.5510	+	41.6663i	−0.873533	+	1.96199i
$452$	0.244416	−	1.14989i	0.0114964	−	0.0540861i
$453$	28.3137	−	13.1018i	1.33030	−	0.615578i
$454$	5.13416	−	2.28588i	0.240958	−	0.107282i
$455$	0.209404	+	0.232567i	0.00981703	+	0.0109029i
$456$	4.14118	+	12.1426i	0.193928	+	0.568627i
$457$	3.62253	+	4.98599i	0.169455	+	0.233235i	0.885295	−	0.465029i	$-0.153956\pi$
$457$	3.62253	+	4.98599i	0.169455	+	0.233235i	−0.715840	+	0.698264i	$0.753956\pi$
$458$	−2.39809	+	22.8163i	−0.112056	+	1.06614i
$459$	8.80397	−	22.3448i	0.410934	−	1.04297i
$460$	−1.14734	−	0.662417i	−0.0534950	−	0.0308853i
$461$	20.8915	+	15.1785i	0.973013	+	0.706935i	0.956136	−	0.292922i	$-0.0946278\pi$
$461$	20.8915	+	15.1785i	0.973013	+	0.706935i	0.0168765	+	0.999858i	$0.494628\pi$
$462$	0.225126	−	0.403340i	0.0104738	−	0.0187651i
$463$	−11.9045	−	3.86802i	−0.553251	−	0.179762i	0.0190314	−	0.999819i	$-0.493942\pi$
$463$	−11.9045	−	3.86802i	−0.553251	−	0.179762i	−0.572282	+	0.820057i	$0.693942\pi$
$464$	−2.47758			−0.115019
$465$	7.36607	+	6.22422i	0.341593	+	0.288641i
$466$	−17.3662			−0.804474
$467$	3.68440	+	1.19713i	0.170494	+	0.0553968i	0.393020	−	0.919530i	$-0.371430\pi$
$467$	3.68440	+	1.19713i	0.170494	+	0.0553968i	−0.222526	+	0.974927i	$0.571430\pi$
$468$	−16.2472	−	4.76225i	−0.751028	−	0.220135i
$469$	0.148300	+	0.107746i	0.00684786	+	0.00497526i
$470$	0.318686	+	0.183994i	0.0146999	+	0.00848699i
$471$	−11.8064	+	10.9450i	−0.544011	+	0.504320i
$472$	0.657760	−	6.25817i	0.0302759	−	0.288056i
$473$	−7.03222	−	9.67902i	−0.323342	−	0.445042i
$474$	−21.3058	+	7.26626i	−0.978607	+	0.333750i
$475$	−4.95625	−	5.50447i	−0.227408	−	0.252563i
$476$	−0.234142	+	0.104247i	−0.0107319	+	0.00477815i
$477$	−10.8166	+	8.34904i	−0.495259	+	0.382276i
$478$	−1.41370	+	6.65092i	−0.0646610	+	0.304206i
$479$	−3.37512	+	7.58063i	−0.154213	+	0.346368i	−0.974086	−	0.226177i	$-0.927377\pi$
$479$	−3.37512	+	7.58063i	−0.154213	+	0.346368i	0.819873	+	0.572545i	$0.194044\pi$
$480$	1.48727	−	0.887709i	0.0678843	−	0.0405182i
$481$	8.43051	+	25.9464i	0.384398	+	1.18306i
$482$	−21.7022	−	9.66244i	−0.988508	−	0.440112i
$483$	0.00184715	+	0.127232i	8.40481e−5	+	0.00578924i
$484$	11.8643	−	2.52183i	0.539286	−	0.114629i
$485$	1.00036	+	2.24684i	0.0454238	+	0.102024i
$486$	14.9726	−	4.33828i	0.679172	−	0.196788i
$487$	38.4362	−	4.03981i	1.74171	−	0.183061i	0.820374	−	0.571827i	$-0.193765\pi$
$487$	38.4362	−	4.03981i	1.74171	−	0.183061i	0.921337	+	0.388766i	$0.127099\pi$
$488$	−4.86857	+	3.53722i	−0.220390	+	0.160123i
$489$	35.0711	−	4.20169i	1.58597	−	0.190007i
$490$	−3.49846	−	6.05951i	−0.158044	−	0.273741i
$491$	1.15064	−	1.99297i	0.0519277	−	0.0899415i	−0.838893	−	0.544296i	$-0.816797\pi$
$491$	1.15064	−	1.99297i	0.0519277	−	0.0899415i	0.890821	+	0.454355i	$0.150130\pi$
$492$	15.1014	+	6.46254i	0.680822	+	0.291354i
$493$	7.66249	−	8.51005i	0.345101	−	0.383274i
$494$	−12.9176	+	39.7562i	−0.581189	+	1.78871i
$495$	−6.24851	−	13.0046i	−0.280850	−	0.584514i
$496$	3.34851	+	4.44831i	0.150352	+	0.199735i
$497$			0.170316i			0.00763971i
$498$	0.414203	−	4.57945i	0.0185609	−	0.205210i
$499$	10.8749	+	9.79176i	0.486825	+	0.438339i	0.875631	−	0.482980i	$-0.160446\pi$
$499$	10.8749	+	9.79176i	0.486825	+	0.438339i	−0.388806	+	0.921320i	$0.627112\pi$
$500$	−0.587785	+	0.809017i	−0.0262866	+	0.0361803i
$501$	−33.7804	−	10.4363i	−1.50920	−	0.466258i
$502$	−16.2102	+	9.35895i	−0.723496	+	0.417711i
$503$	−22.0793	−	2.32063i	−0.984466	−	0.103472i	−0.401406	−	0.915900i	$-0.631478\pi$
$503$	−22.0793	−	2.32063i	−0.984466	−	0.103472i	−0.583060	+	0.812429i	$0.698145\pi$
$504$	−0.146423	−	0.0789610i	−0.00652221	−	0.00351720i
$505$	1.83561	+	17.4647i	0.0816836	+	0.777167i
$506$	−4.73496	+	4.26338i	−0.210495	+	0.189530i
$507$	−19.5723	−	26.1326i	−0.869234	−	1.16059i
$508$	0.707742	+	3.32966i	0.0314010	+	0.147730i
$509$	42.6201	+	9.05919i	1.88910	+	0.401542i	0.998574	−	0.0533821i	$-0.0170001\pi$
$509$	42.6201	+	9.05919i	1.88910	+	0.401542i	0.890530	+	0.454924i	$0.150333\pi$
$510$	−1.55060	+	7.85395i	−0.0686617	+	0.347779i
$511$	−0.375223	+	0.121917i	−0.0165989	+	0.00539330i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−9.63353	−	37.2628i	−0.425331	−	1.64519i
$514$	−13.7247	−	2.91727i	−0.605370	−	0.128675i
$515$	1.35328	+	6.36667i	0.0596326	+	0.280549i
$516$	−3.44873	+	2.58296i	−0.151822	+	0.113709i
$517$	1.31519	−	1.18420i	0.0578419	−	0.0520811i
$518$	0.0280201	+	0.266593i	0.00123113	+	0.0117134i
$519$	−15.5574	+	17.7910i	−0.682894	+	0.780936i
$520$	5.61268	+	0.589916i	0.246132	+	0.0258695i
$521$	6.88015	−	3.97226i	0.301425	−	0.174028i	−0.341658	−	0.939824i	$-0.610988\pi$
$521$	6.88015	−	3.97226i	0.301425	−	0.174028i	0.643083	+	0.765797i	$0.277655\pi$
$522$	7.41147	+	0.562017i	0.324391	+	0.0245988i
$523$	16.0130	−	22.0400i	0.700198	−	0.963741i	−0.299754	−	0.954016i	$-0.596905\pi$
$523$	16.0130	−	22.0400i	0.700198	−	0.963741i	0.999953	−	0.00972406i	$-0.00309531\pi$
$524$	−0.163848	−	0.147530i	−0.00715774	−	0.00644486i
$525$	0.0956557	+	0.00865189i	0.00417476	+	0.000377599i
$526$			3.87455i			0.168938i
$527$	−25.6352	−	2.25590i	−1.11669	−	0.0982685i
$528$	−1.84999	−	8.12192i	−0.0805105	−	0.353461i
$529$	−6.56501	+	20.2050i	−0.285435	+	0.878479i
$530$	3.04767	−	3.38479i	0.132383	−	0.147026i
$531$	−3.38724	+	18.5715i	−0.146994	+	0.805937i
$532$	−0.205367	+	0.355707i	−0.00890381	+	0.0154219i
$533$	26.7608	+	46.3510i	1.15914	+	2.00768i
$534$	−1.55265	−	12.9598i	−0.0671897	−	0.560825i
$535$	−16.2124	+	11.7790i	−0.700925	+	0.509252i
$536$	3.28760	−	0.345540i	0.142003	−	0.0149251i
$537$	13.6365	−	19.3538i	0.588459	−	0.835177i
$538$	10.2039	+	22.9182i	0.439919	+	0.988075i
$539$	−32.9150	+	6.99629i	−1.41775	+	0.301352i
$540$	−4.65041	+	2.31813i	−0.200122	+	0.0997564i
$541$	−30.9134	−	13.7635i	−1.32907	−	0.591740i	−0.385436	−	0.922734i	$-0.625949\pi$
$541$	−30.9134	−	13.7635i	−1.32907	−	0.591740i	−0.943633	+	0.330995i	$0.892616\pi$
$542$	7.62761	+	23.4754i	0.327634	+	1.00835i
$543$	7.65500	+	12.8252i	0.328508	+	0.550383i
$544$	−1.87994	+	4.22241i	−0.0806017	+	0.181034i
$545$	−2.10302	+	9.89395i	−0.0900836	+	0.423810i
$546$	−0.227635	−	0.491930i	−0.00974187	−	0.0210527i
$547$	13.8563	−	6.16924i	0.592454	−	0.263778i	−0.0885327	−	0.996073i	$-0.528218\pi$
$547$	13.8563	−	6.16924i	0.592454	−	0.263778i	0.680987	+	0.732296i	$0.261551\pi$
$548$	−5.40810	−	6.00630i	−0.231023	−	0.256577i
$549$	15.3663	−	9.47690i	0.655817	−	0.404464i
$550$	2.82683	+	3.89080i	0.120537	+	0.165904i
$551$	1.91825	−	18.2509i	0.0817202	−	0.777516i
$552$	1.56003	+	1.68281i	0.0663994	+	0.0716251i
$553$	−0.624137	−	0.360345i	−0.0265410	−	0.0153234i
$554$	15.4198	+	11.2031i	0.655123	+	0.475974i
$555$	7.31116	+	4.08075i	0.310342	+	0.173218i
$556$	−2.87855	−	0.935296i	−0.122078	−	0.0396654i
$557$	−2.66733			−0.113018			−0.0565092	−	0.998402i	$-0.517997\pi$
$557$	−2.66733			−0.113018			−0.0565092	+	0.998402i	$0.517997\pi$
$558$	−9.00770	−	14.0663i	−0.381326	−	0.595475i
$559$	−14.0394			−0.593802
$560$	0.0527382	+	0.0171357i	0.00222860	+	0.000724115i
$561$	33.6189	+	18.7645i	1.41939	+	0.792237i
$562$	−26.5250	−	19.2715i	−1.11889	−	0.812921i
$563$	−34.4344	−	19.8807i	−1.45124	−	0.837873i	−0.452687	−	0.891670i	$-0.649534\pi$
$563$	−34.4344	−	19.8807i	−1.45124	−	0.837873i	−0.998552	+	0.0537967i	$0.982868\pi$
$564$	−0.433317	−	0.467419i	−0.0182459	−	0.0196819i
$565$	0.122881	−	1.16914i	0.00516965	−	0.0491859i
$566$	10.9987	+	15.1384i	0.462310	+	0.636315i
$567$	0.420100	+	0.269420i	0.0176426	+	0.0113146i
$568$	2.05516	+	2.28249i	0.0862328	+	0.0957712i
$569$	36.6236	−	16.3059i	1.53534	−	0.683578i	0.547182	−	0.837013i	$-0.315700\pi$
$569$	36.6236	−	16.3059i	1.53534	−	0.683578i	0.988159	+	0.153436i	$0.0490337\pi$
$570$	5.38773	+	11.6432i	0.225667	+	0.487679i
$571$	−4.26990	+	20.0883i	−0.178690	+	0.840670i	0.793883	+	0.608071i	$0.208056\pi$
$571$	−4.26990	+	20.0883i	−0.178690	+	0.840670i	−0.972573	+	0.232599i	$0.925277\pi$
$572$	11.0395	−	24.7952i	0.461586	−	1.03674i
$573$	6.98016	+	11.6946i	0.291600	+	0.488548i
$574$	0.162508	+	0.500148i	0.00678295	+	0.0208758i
$575$	−1.21030	−	0.538858i	−0.0504728	−	0.0224719i
$576$	−2.91510	+	0.708659i	−0.121462	+	0.0295274i
$577$	33.4289	−	7.10553i	1.39166	−	0.295807i	0.549708	−	0.835357i	$-0.314739\pi$
$577$	33.4289	−	7.10553i	1.39166	−	0.295807i	0.841954	+	0.539550i	$0.181405\pi$
$578$	−1.77457	−	3.98575i	−0.0738124	−	0.165785i
$579$	−3.82707	+	5.43161i	−0.159048	+	0.225730i
$580$	−2.46401	+	0.258978i	−0.102312	+	0.0107535i
$581$	0.119096	−	0.0865286i	0.00494095	−	0.00358981i
$582$	−0.506737	−	4.22968i	−0.0210049	−	0.175326i
$583$	−10.9524	−	18.9701i	−0.453602	−	0.785662i
$584$	−3.55740	+	6.16161i	−0.147206	+	0.254969i
$585$	−16.6560	−	3.03787i	−0.688641	−	0.125600i
$586$	1.55018	−	1.72165i	0.0640372	−	0.0711206i
$587$	13.4062	−	41.2600i	0.553332	−	1.70298i	−0.146975	−	0.989140i	$-0.546954\pi$
$587$	13.4062	−	41.2600i	0.553332	−	1.70298i	0.700308	−	0.713841i	$-0.253046\pi$
$588$	2.69150	+	11.8164i	0.110996	+	0.487299i
$589$	−35.3607	+	21.2224i	−1.45701	+	0.874456i
$590$		−	6.29264i		−	0.259064i
$591$	−23.1745	−	2.09609i	−0.953271	−	0.0862217i
$592$	3.59244	+	3.23465i	0.147648	+	0.132943i
$593$	24.0691	−	33.1283i	0.988401	−	1.36042i	0.0562229	−	0.998418i	$-0.482094\pi$
$593$	24.0691	−	33.1283i	0.988401	−	1.36042i	0.932178	−	0.361999i	$-0.117906\pi$
$594$	3.69170	+	24.7157i	0.151472	+	1.01410i
$595$	−0.221963	+	0.128150i	−0.00909959	+	0.00525365i
$596$	8.48341	+	0.891642i	0.347494	+	0.0365231i
$597$	−25.2365	+	28.8597i	−1.03286	+	1.18115i
$598$	0.781540	+	7.43586i	0.0319596	+	0.304075i
$599$	−25.6952	+	23.1361i	−1.04988	+	0.945316i	−0.998575	−	0.0533675i	$-0.983005\pi$
$599$	−25.6952	+	23.1361i	−1.04988	+	0.945316i	−0.0513043	+	0.998683i	$0.516338\pi$
$600$	1.38633	−	1.03831i	0.0565968	−	0.0423887i
$601$	1.15150	+	5.41737i	0.0469706	+	0.220979i	0.995373	−	0.0960914i	$-0.0306341\pi$
$601$	1.15150	+	5.41737i	0.0469706	+	0.220979i	−0.948402	+	0.317071i	$0.897301\pi$
$602$	−0.134932	−	0.0286807i	−0.00549943	−	0.00116894i
$603$	−9.91294	+	0.287892i	−0.403686	+	0.0117239i
$604$	17.1307	−	5.56610i	0.697038	−	0.226481i
$605$	11.5357	−	3.74818i	0.468993	−	0.152385i
$606$	5.89135	−	29.8403i	0.239320	−	1.21218i
$607$	41.6095	+	8.84438i	1.68888	+	0.358982i	0.949369	−	0.314163i	$-0.101724\pi$
$607$	41.6095	+	8.84438i	1.68888	+	0.358982i	0.739510	+	0.673145i	$0.235057\pi$
$608$	1.54000	+	7.24514i	0.0624553	+	0.293829i
$609$	0.142651	+	0.190465i	0.00578050	+	0.00771802i
$610$	−4.47216	+	4.02675i	−0.181072	+	0.163038i
$611$	−0.217082	−	2.06539i	−0.00878218	−	0.0835569i
$612$	6.58149	−	12.2045i	0.266041	−	0.493339i
$613$	−38.4636	−	4.04269i	−1.55353	−	0.163283i	−0.711489	−	0.702697i	$-0.751979\pi$
$613$	−38.4636	−	4.04269i	−1.55353	−	0.163283i	−0.842041	+	0.539414i	$0.818646\pi$
$614$	−10.8955	+	6.29052i	−0.439707	+	0.253865i
$615$	15.6941	+	4.84862i	0.632849	+	0.195515i
$616$	0.156754	−	0.215754i	0.00631581	−	0.00869297i
$617$	5.69407	+	5.12696i	0.229235	+	0.206404i	0.775741	−	0.631051i	$-0.217376\pi$
$617$	5.69407	+	5.12696i	0.229235	+	0.206404i	−0.546507	+	0.837455i	$0.684043\pi$
$618$	1.01555	−	11.2279i	0.0408513	−	0.451653i
$619$		−	18.7668i		−	0.754300i	−0.926152	−	0.377150i	$-0.876904\pi$
$619$		−	18.7668i		−	0.754300i	0.926152	−	0.377150i	$-0.123096\pi$
$620$	3.79514	+	4.07393i	0.152416	+	0.163613i
$621$	−4.28497	−	5.38785i	−0.171950	−	0.216207i
$622$	2.17624	−	6.69779i	0.0872594	−	0.268557i
$623$	0.279616	−	0.310545i	0.0112026	−	0.0124417i
$624$	−8.98667	−	3.84580i	−0.359755	−	0.153955i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−7.70242	−	13.3410i	−0.307851	−	0.533213i
$627$	61.2619	−	7.33948i	2.44656	−	0.293111i
$628$	−7.51972	+	5.46340i	−0.300070	+	0.218013i
$629$	−22.2209	+	2.33551i	−0.886004	+	0.0931227i
$630$	−0.153875	−	0.0632231i	−0.00613051	−	0.00251887i
$631$	4.65845	+	10.4631i	0.185450	+	0.416528i	0.982214	−	0.187762i	$-0.0601235\pi$
$631$	4.65845	+	10.4631i	0.185450	+	0.416528i	−0.796764	+	0.604290i	$0.793457\pi$
$632$	−12.7126	+	2.70215i	−0.505680	+	0.107486i
$633$	−0.105642	−	7.27667i	−0.00419891	−	0.289221i
$634$	−0.179703	−	0.0800088i	−0.00713691	−	0.00317756i
$635$	1.05191	+	3.23744i	0.0417437	+	0.128474i
$636$	−6.77404	+	4.04323i	−0.268608	+	0.160324i
$637$	−16.0611	+	36.0739i	−0.636365	+	1.42930i
$638$	−2.47736	+	11.6551i	−0.0980796	+	0.461428i
$639$	−5.63008	−	7.29407i	−0.222723	−	0.288549i
$640$	0.913545	−	0.406737i	0.0361111	−	0.0160777i
$641$	−14.4259	−	16.0216i	−0.569790	−	0.632816i	0.387526	−	0.921859i	$-0.373330\pi$
$641$	−14.4259	−	16.0216i	−0.569790	−	0.632816i	−0.957316	+	0.289043i	$0.906663\pi$
$642$	32.8517	−	11.2040i	1.29655	−	0.442185i
$643$	−23.9445	−	32.9568i	−0.944280	−	1.29969i	−0.954022	−	0.299738i	$-0.903101\pi$
$643$	−23.9445	−	32.9568i	−0.944280	−	1.29969i	0.00974134	−	0.999953i	$-0.496899\pi$
$644$	−0.00767918	+	0.0730625i	−0.000302602	+	0.00287907i
$645$	−3.15984	+	2.92930i	−0.124419	+	0.115341i
$646$	−29.6486	−	17.1176i	−1.16651	−	0.673483i
$647$	−18.8482	−	13.6940i	−0.740998	−	0.538367i	0.152025	−	0.988377i	$-0.451420\pi$
$647$	−18.8482	−	13.6940i	−0.740998	−	0.538367i	−0.893024	+	0.450010i	$0.851420\pi$
$648$	8.88101	−	1.45863i	0.348879	−	0.0573002i
$649$	−28.7820	−	9.35184i	−1.12979	−	0.367092i
$650$	5.64359			0.221360
$651$	0.149170	−	0.513536i	0.00584643	−	0.0201271i
$652$	20.3931			0.798656
$653$	23.6532	+	7.68539i	0.925622	+	0.300753i	0.732771	−	0.680475i	$-0.238227\pi$
$653$	23.6532	+	7.68539i	0.925622	+	0.300753i	0.192851	+	0.981228i	$0.438227\pi$
$654$	8.53866	−	15.2980i	0.333888	−	0.598201i
$655$	−0.178372	−	0.129595i	−0.00696956	−	0.00506368i
$656$	8.21303	+	4.74179i	0.320665	+	0.185136i
$657$	12.0394	−	17.6249i	0.469700	−	0.687614i
$658$	0.00213298	−	0.0202939i	8.31522e−5	−	0.000791140i
$659$	6.52985	+	8.98756i	0.254367	+	0.350106i	0.917035	−	0.398808i	$-0.130576\pi$
$659$	6.52985	+	8.98756i	0.254367	+	0.350106i	−0.662668	+	0.748913i	$0.730576\pi$
$660$	−2.68883	−	7.88405i	−0.104662	−	0.306886i
$661$	−11.8590	−	13.1707i	−0.461260	−	0.512281i	0.466978	−	0.884269i	$-0.345343\pi$
$661$	−11.8590	−	13.1707i	−0.461260	−	0.512281i	−0.928238	+	0.371988i	$0.878676\pi$
$662$	27.9153	−	12.4287i	1.08496	−	0.483055i
$663$	41.0029	−	18.9736i	1.59242	−	0.736874i
$664$	0.551951	−	2.59673i	0.0214199	−	0.100773i
$665$	−0.167061	+	0.375225i	−0.00647835	+	0.0145506i
$666$	−10.0127	−	10.4911i	−0.387985	−	0.406521i
$667$	−1.01431	−	3.12173i	−0.0392743	−	0.120874i
$668$	−18.6479	−	8.30257i	−0.721508	−	0.321236i
$669$	−34.5238	+	0.501215i	−1.33477	+	0.0193781i
$670$	3.23347	−	0.687295i	0.124920	−	0.0265525i
$671$	11.7717	+	26.4397i	0.454441	+	1.02069i
$672$	−0.0785143	−	0.0553206i	−0.00302875	−	0.00213404i
$673$	20.7893	−	2.18504i	0.801367	−	0.0842271i	0.305014	−	0.952348i	$-0.401339\pi$
$673$	20.7893	−	2.18504i	0.801367	−	0.0842271i	0.496353	+	0.868121i	$0.334672\pi$
$674$	24.8370	−	18.0451i	0.956684	−	0.695072i
$675$	−4.38262	+	2.79153i	−0.168687	+	0.107446i
$676$	−9.42507	−	16.3247i	−0.362503	−	0.627873i
$677$	16.8300	−	29.1503i	0.646828	−	1.12034i	−0.337048	−	0.941487i	$-0.609429\pi$
$677$	16.8300	−	29.1503i	0.646828	−	1.12034i	0.983876	−	0.178851i	$-0.0572381\pi$
$678$	−0.801090	+	1.87195i	−0.0307657	+	0.0718917i
$679$	0.0912581	−	0.101352i	0.00350216	−	0.00388955i
$680$	−1.42828	+	4.39579i	−0.0547720	+	0.168571i
$681$	−9.49110	+	2.16186i	−0.363700	+	0.0828426i
$682$	24.2740	−	11.3041i	0.929499	−	0.432858i
$683$		−	3.06638i		−	0.117332i	−0.998278	−	0.0586659i	$-0.981315\pi$
$683$		−	3.06638i		−	0.117332i	0.998278	−	0.0586659i	$-0.0186847\pi$
$684$	−2.96329	−	22.0225i	−0.113304	−	0.842053i
$685$	−6.00630	−	5.40810i	−0.229489	−	0.206633i
$686$	−0.456216	+	0.627928i	−0.0174184	+	0.0239744i
$687$	11.7294	−	37.9661i	0.447506	−	1.44850i
$688$	−2.15438	+	1.24383i	−0.0821350	+	0.0474207i
$689$	−25.5639	−	2.68688i	−0.973909	−	0.102362i
$690$	1.72739	+	1.51052i	0.0657605	+	0.0575046i
$691$	3.20024	+	30.4483i	0.121743	+	1.15831i	0.869361	+	0.494178i	$0.164531\pi$
$691$	3.20024	+	30.4483i	0.121743	+	1.15831i	−0.747618	+	0.664129i	$0.768803\pi$
$692$	−10.1401	+	9.13023i	−0.385470	+	0.347079i
$693$	−0.517859	+	0.609850i	−0.0196718	+	0.0231663i
$694$	−4.55859	−	21.4465i	−0.173042	−	0.814097i
$695$	−2.96054	−	0.629283i	−0.112300	−	0.0238700i
$696$	4.21003	+	0.831184i	0.159581	+	0.0315060i
$697$	−41.6879	+	13.5452i	−1.57904	+	0.513061i
$698$	−11.0969	+	3.60560i	−0.420024	+	0.136474i
$699$	29.5095	+	5.82605i	1.11615	+	0.220361i
$700$	0.0542405	+	0.0115292i	0.00205010	+	0.000435762i
$701$	−2.85404	−	13.4272i	−0.107796	−	0.507138i	−0.998607	−	0.0527651i	$-0.983197\pi$
$701$	−2.85404	−	13.4272i	−0.107796	−	0.507138i	0.890811	−	0.454373i	$-0.150137\pi$
$702$	26.0105	+	13.5429i	0.981701	+	0.511144i
$703$	−26.6092	+	23.9590i	−1.00358	+	0.903632i
$704$	−0.502709	−	4.78295i	−0.0189465	−	0.180264i
$705$	−0.479801	−	0.419565i	−0.0180704	−	0.0158017i
$706$	−33.6200	−	3.53360i	−1.26530	−	0.132989i
$707$	0.843326	−	0.486895i	0.0317166	−	0.0183116i
$708$	−3.21720	+	10.4135i	−0.120910	+	0.391364i
$709$	17.2317	−	23.7174i	0.647151	−	0.890727i	−0.351821	−	0.936067i	$-0.614437\pi$
$709$	17.2317	−	23.7174i	0.647151	−	0.890727i	0.998972	+	0.0453406i	$0.0144373\pi$
$710$	2.28249	+	2.05516i	0.0856604	+	0.0771290i
$711$	38.6416	−	5.19949i	1.44917	−	0.194996i
$712$		−	7.53585i		−	0.282418i
$713$	−4.23397	+	6.04021i	−0.158563	+	0.226208i
$714$	0.432839	−	0.0985911i	0.0161986	−	0.00368968i
$715$	8.38725	−	25.8133i	0.313666	−	0.965363i
$716$	9.14633	−	10.1580i	0.341815	−	0.379623i
$717$	4.63349	−	10.8273i	0.173041	−	0.404353i
$718$	−12.6682	+	21.9419i	−0.472772	+	0.818865i
$719$	−10.8375	−	18.7710i	−0.404169	−	0.700041i	0.590055	−	0.807363i	$-0.299106\pi$
$719$	−10.8375	−	18.7710i	−0.404169	−	0.700041i	−0.994224	+	0.107321i	$0.965773\pi$
$720$	−2.82505	+	1.00949i	−0.105284	+	0.0376214i
$721$	0.292002	−	0.212152i	0.0108747	−	0.00790094i
$722$	−35.6672	+	3.74877i	−1.32740	+	0.139515i
$723$	33.6359	+	23.6996i	1.25093	+	0.881398i
$724$	3.50742	+	7.87780i	0.130352	+	0.292776i
$725$	−2.42344	+	0.515119i	−0.0900044	+	0.0191310i
$726$	−21.0064	+	0.304971i	−0.779622	+	0.0113185i
$727$	27.8518	+	12.4004i	1.03297	+	0.459906i	0.851977	−	0.523579i	$-0.175404\pi$
$727$	27.8518	+	12.4004i	1.03297	+	0.459906i	0.180988	+	0.983485i	$0.442070\pi$
$728$	−0.0967069	−	0.297633i	−0.00358420	−	0.0110310i
$729$	−26.8976	+	2.34877i	−0.996209	+	0.0869917i
$730$	−2.89385	+	6.49970i	−0.107106	+	0.240565i
$731$	2.39057	−	11.2467i	0.0884184	−	0.415976i
$732$	9.45960	−	4.37731i	0.349637	−	0.161790i
$733$	9.20971	−	4.10043i	0.340168	−	0.151453i	−0.229541	−	0.973299i	$-0.573722\pi$
$733$	9.20971	−	4.10043i	0.340168	−	0.151453i	0.569709	+	0.821846i	$0.307056\pi$
$734$	4.40348	+	4.89056i	0.162535	+	0.180514i
$735$	3.91191	+	11.4703i	0.144293	+	0.423089i
$736$	0.778717	+	1.07181i	0.0287039	+	0.0395075i
$737$	1.66181	−	15.8110i	0.0612134	−	0.582407i
$738$	−23.4929	−	16.0477i	−0.864786	−	0.590724i
$739$	−15.8869	−	9.17233i	−0.584410	−	0.337409i	0.178474	−	0.983945i	$-0.442884\pi$
$739$	−15.8869	−	9.17233i	−0.584410	−	0.337409i	−0.762884	+	0.646535i	$0.776217\pi$
$740$	3.91087	+	2.84141i	0.143766	+	0.104452i
$741$	35.2876	−	63.2221i	1.29632	−	2.32252i
$742$	−0.240206	−	0.0780476i	−0.00881823	−	0.00286522i
$743$	−9.74870			−0.357645			−0.178823	−	0.983881i	$-0.557229\pi$
$743$	−9.74870			−0.357645			−0.178823	+	0.983881i	$0.557229\pi$
$744$	−4.19762	−	8.68216i	−0.153892	−	0.318304i
$745$	8.53013			0.312520
$746$	−4.03602	−	1.31138i	−0.147769	−	0.0480131i
$747$	−2.24016	+	7.64267i	−0.0819631	+	0.279631i
$748$	17.9833	+	13.0656i	0.657535	+	0.477727i
$749$	0.962367	+	0.555623i	0.0351641	+	0.0203020i
$750$	1.27020	−	1.17753i	0.0463813	−	0.0429974i
$751$	3.83030	−	36.4428i	0.139770	−	1.32982i	−0.669689	−	0.742641i	$-0.733573\pi$
$751$	3.83030	−	36.4428i	0.139770	−	1.32982i	0.809459	−	0.587177i	$-0.199761\pi$
$752$	−0.216298	−	0.297708i	−0.00788756	−	0.0108563i
$753$	30.6849	−	10.4650i	1.11822	−	0.381365i
$754$	9.35610	+	10.3910i	0.340729	+	0.378418i
$755$	16.4550	−	7.32625i	0.598860	−	0.266630i
$756$	0.222320	+	0.183297i	0.00808569	+	0.00666644i
$757$	−5.82549	+	27.4068i	−0.211731	+	0.996116i	0.735984	+	0.676998i	$0.236720\pi$
$757$	−5.82549	+	27.4068i	−0.211731	+	0.996116i	−0.947715	+	0.319117i	$0.896614\pi$
$758$	13.4930	−	30.3059i	0.490089	−	1.10076i
$759$	9.47617	−	5.65605i	0.343963	−	0.205302i
$760$	2.28889	+	7.04448i	0.0830267	+	0.255530i
$761$	−7.18615	−	3.19948i	−0.260498	−	0.115981i	0.272332	−	0.962203i	$-0.412205\pi$
$761$	−7.18615	−	3.19948i	−0.260498	−	0.115981i	−0.532830	+	0.846222i	$0.678872\pi$
$762$	−0.0855888	−	5.89537i	−0.00310055	−	0.213567i
$763$	0.548642	−	0.116617i	0.0198622	−	0.00422183i
$764$	3.19822	+	7.18332i	0.115708	+	0.259883i
$765$	5.26971	−	12.8256i	0.190527	−	0.463711i
$766$	27.2126	−	2.86016i	0.983231	−	0.103342i
$767$	−28.7307	+	20.8741i	−1.03741	+	0.753719i
$768$	−1.71975	+	0.206035i	−0.0620562	+	0.00743465i
$769$	−20.1776	−	34.9486i	−0.727623	−	1.26028i	−0.957885	−	0.287151i	$-0.907292\pi$
$769$	−20.1776	−	34.9486i	−0.727623	−	1.26028i	0.230262	−	0.973129i	$-0.426042\pi$
$770$	0.133343	−	0.230957i	0.00480536	−	0.00832312i
$771$	22.3430	+	9.56156i	0.804663	+	0.344351i
$772$	−2.56691	+	2.85084i	−0.0923850	+	0.102604i
$773$	−7.06065	+	21.7304i	−0.253954	+	0.781589i	0.740080	+	0.672519i	$0.234788\pi$
$773$	−7.06065	+	21.7304i	−0.253954	+	0.781589i	−0.994034	+	0.109071i	$0.965212\pi$
$774$	6.72679	−	3.23211i	0.241790	−	0.116176i
$775$	4.20019	+	3.65491i	0.150875	+	0.131288i
$776$		−	2.45947i		−	0.0882898i
$777$	0.0418241	−	0.462409i	0.00150043	−	0.0165888i
$778$	24.7216	+	22.2594i	0.886312	+	0.798038i
$779$	−41.2890	+	56.8294i	−1.47933	+	2.03612i
$780$	−9.33944	−	2.88537i	−0.334406	−	0.103313i
$781$	12.7923	−	7.38563i	0.457744	−	0.264279i
$782$	−6.08984	−	0.640068i	−0.217772	−	0.0228888i
$783$	−12.4054	−	3.44142i	−0.443333	−	0.122986i
$784$	0.731378	+	6.95860i	0.0261206	+	0.248521i
$785$	−6.90745	+	6.21949i	−0.246537	+	0.221983i
$786$	0.228926	+	0.305658i	0.00816551	+	0.0109025i
$787$	−0.105509	−	0.496378i	−0.00376097	−	0.0176940i	0.976227	−	0.216750i	$-0.0695457\pi$
$787$	−0.105509	−	0.496378i	−0.00376097	−	0.0176940i	−0.979988	+	0.199056i	$0.936212\pi$
$788$	−13.1408	−	2.79317i	−0.468123	−	0.0995026i
$789$	1.29984	−	6.58382i	0.0462755	−	0.234390i
$790$	−12.3605	+	4.01617i	−0.439767	+	0.142889i
$791$	−0.0619978	+	0.0201443i	−0.00220439	+	0.000716249i
$792$	0.418839	+	14.4218i	0.0148828	+	0.512457i
$793$	33.2203	+	7.06120i	1.17969	+	0.250751i
$794$	1.08159	+	5.08846i	0.0383840	+	0.180583i
$795$	−6.31430	+	4.72916i	−0.223945	+	0.167726i
$796$	−16.4489	+	14.8107i	−0.583016	+	0.524950i
$797$	−1.29483	−	12.3195i	−0.0458653	−	0.436380i	−0.993225	−	0.116208i	$-0.962926\pi$
$797$	−1.29483	−	12.3195i	−0.0458653	−	0.436380i	0.947360	−	0.320172i	$-0.103741\pi$
$798$	0.468304	−	0.535538i	0.0165778	−	0.0189578i
$799$	1.69152	+	0.177786i	0.0598418	+	0.00628962i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−1.70944	+	22.5428i	−0.0604000	+	0.796512i
$802$	−19.4038	+	26.7071i	−0.685172	+	0.943059i
$803$	25.4284	+	22.8958i	0.897348	+	0.807975i
$804$	−5.70237	−	0.515770i	−0.201107	−	0.0181898i
$805$			0.0734650i			0.00258930i
$806$	6.01129	−	30.8418i	0.211739	−	1.08636i
$807$	−9.65025	−	42.3670i	−0.339705	−	1.49139i
$808$	5.42660	−	16.7014i	0.190907	−	0.587552i
$809$	−20.0230	+	22.2378i	−0.703972	+	0.781840i	−0.984003	−	0.178151i	$-0.942989\pi$
$809$	−20.0230	+	22.2378i	−0.703972	+	0.781840i	0.280031	+	0.959991i	$0.409655\pi$
$810$	8.67989	−	2.37895i	0.304980	−	0.0835879i
$811$	−5.49777	+	9.52242i	−0.193053	+	0.334377i	−0.946260	−	0.323406i	$-0.895172\pi$
$811$	−5.49777	+	9.52242i	−0.193053	+	0.334377i	0.753208	+	0.657783i	$0.228506\pi$
$812$	0.0686938	+	0.118981i	0.00241068	+	0.00417542i
$813$	−5.08566	−	42.4494i	−0.178362	−	1.48877i
$814$	18.8085	−	13.6652i	0.659239	−	0.478965i
$815$	20.2814	−	2.13166i	0.710426	−	0.0746688i
$816$	4.61103	−	6.54425i	0.161418	−	0.229095i
$817$	−7.49459	−	16.8331i	−0.262202	−	0.588916i
$818$	18.0927	−	3.84573i	0.632597	−	0.134463i
$819$	0.221775	+	0.912280i	0.00774944	+	0.0318777i
$820$	8.66369	+	3.85732i	0.302549	+	0.134704i
$821$	7.30538	+	22.4836i	0.254959	+	0.784684i	0.993838	+	0.110845i	$0.0353558\pi$
$821$	7.30538	+	22.4836i	0.254959	+	0.784684i	−0.738878	+	0.673839i	$0.764644\pi$
$822$	7.17471	+	12.0205i	0.250247	+	0.419264i
$823$	12.5934	−	28.2853i	0.438979	−	0.985964i	−0.549623	−	0.835413i	$-0.685229\pi$
$823$	12.5934	−	28.2853i	0.438979	−	0.985964i	0.988602	−	0.150551i	$-0.0481048\pi$
$824$	1.35328	−	6.36667i	0.0471437	−	0.221794i
$825$	−3.49821	−	7.55980i	−0.121792	−	0.263199i
$826$	−0.318774	+	0.141927i	−0.0110916	+	0.00493828i
$827$	−14.8064	−	16.4442i	−0.514870	−	0.571821i	0.428509	−	0.903537i	$-0.359039\pi$
$827$	−14.8064	−	16.4442i	−0.514870	−	0.571821i	−0.943379	+	0.331716i	$0.892372\pi$
$828$	−2.08633	−	3.38288i	−0.0725051	−	0.117563i
$829$	4.39246	+	6.04570i	0.152556	+	0.209976i	0.878454	−	0.477827i	$-0.158575\pi$
$829$	4.39246	+	6.04570i	0.152556	+	0.209976i	−0.725898	+	0.687803i	$0.758575\pi$
$830$	0.277496	−	2.64020i	0.00963202	−	0.0916426i
$831$	−22.4436	−	24.2099i	−0.778559	−	0.839833i
$832$	−4.88750	−	2.82180i	−0.169443	−	0.0978282i
$833$	−26.1635	−	19.0089i	−0.906511	−	0.658619i
$834$	4.57759	+	2.55500i	0.158509	+	0.0884725i
$835$	−19.4136	−	6.30786i	−0.671835	−	0.218292i
$836$	35.6225			1.23203
$837$	10.5873	+	26.9241i	0.365952	+	0.930634i
$838$	2.09659			0.0724256
$839$	−35.8569	−	11.6506i	−1.23792	−	0.402224i	−0.384342	−	0.923191i	$-0.625572\pi$
$839$	−35.8569	−	11.6506i	−1.23792	−	0.402224i	−0.853577	+	0.520967i	$0.825572\pi$
$840$	−0.0838668	−	0.0468106i	−0.00289368	−	0.00161512i
$841$	18.4954	+	13.4377i	0.637773	+	0.463369i
$842$	8.76063	+	5.05795i	0.301911	+	0.174309i
$843$	38.6074	+	41.6458i	1.32971	+	1.43436i
$844$	0.439190	−	4.17861i	0.0151175	−	0.143834i
$845$	−11.0798	−	15.2501i	−0.381158	−	0.524619i
$846$	0.579503	+	0.939632i	0.0199237	+	0.0323052i
$847$	−0.450057	−	0.499839i	−0.0154641	−	0.0171747i
$848$	−4.16091	+	1.85255i	−0.142886	+	0.0636170i
$849$	−13.6109	−	29.4138i	−0.467124	−	1.00948i
$850$	−0.960969	+	4.52100i	−0.0329610	+	0.155069i
$851$	−2.60490	+	5.85069i	−0.0892947	+	0.200559i
$852$	−2.72651	−	4.56800i	−0.0934085	−	0.156497i
$853$	−0.811071	−	2.49622i	−0.0277705	−	0.0854689i	0.936211	−	0.351439i	$-0.114308\pi$
$853$	−0.811071	−	2.49622i	−0.0277705	−	0.0854689i	−0.963981	+	0.265970i	$0.914308\pi$
$854$	0.304855	+	0.135730i	0.0104319	+	0.00464459i
$855$	−5.24904	−	21.5921i	−0.179513	−	0.738436i
$856$	19.6018	−	4.16648i	0.669974	−	0.142407i
$857$	18.8426	+	42.3211i	0.643650	+	1.44566i	0.880467	+	0.474108i	$0.157229\pi$
$857$	18.8426	+	42.3211i	0.643650	+	1.44566i	−0.236816	+	0.971554i	$0.576104\pi$
$858$	−27.0773	+	38.4297i	−0.924403	+	1.31197i
$859$	−18.5082	+	1.94530i	−0.631493	+	0.0663726i	−0.414867	−	0.909882i	$-0.636172\pi$
$859$	−18.5082	+	1.94530i	−0.631493	+	0.0663726i	−0.216626	+	0.976255i	$0.569505\pi$
$860$	−2.01256	+	1.46221i	−0.0686278	+	0.0498611i
$861$	−0.108351	−	0.904395i	−0.00369259	−	0.0308217i
$862$	−2.29067	−	3.96755i	−0.0780205	−	0.135135i
$863$	6.44495	−	11.1630i	0.219389	−	0.379993i	−0.735232	−	0.677815i	$-0.762927\pi$
$863$	6.44495	−	11.1630i	0.219389	−	0.379993i	0.954621	+	0.297822i	$0.0962604\pi$
$864$	5.19123	−	0.226225i	0.176609	−	0.00769635i
$865$	−9.13023	+	10.1401i	−0.310437	+	0.344775i
$866$	0.0154144	−	0.0474407i	0.000523803	−	0.00161210i
$867$	1.67829	+	7.36812i	0.0569978	+	0.250235i
$868$	0.120781	−	0.284140i	0.00409956	−	0.00964434i
$869$			62.5045i			2.12032i
$870$	4.27385	+	0.386563i	0.144897	+	0.0131057i
$871$	−13.8642	−	12.4833i	−0.469769	−	0.422982i
$872$	5.94544	−	8.18319i	0.201338	−	0.277118i
$873$	−0.557908	+	7.35728i	−0.0188823	+	0.249006i
$874$	−8.49834	+	4.90652i	−0.287461	+	0.165966i
$875$	0.0551485	+	0.00579634i	0.00186436	+	0.000195952i
$876$	8.11203	−	9.27667i	0.274080	−	0.313430i
$877$	−4.56922	−	43.4732i	−0.154292	−	1.46799i	−0.748211	−	0.663461i	$-0.769087\pi$
$877$	−4.56922	−	43.4732i	−0.154292	−	1.46799i	0.593919	−	0.804525i	$-0.297580\pi$
$878$	22.2122	−	20.0000i	0.749625	−	0.674966i
$879$	−3.21172	+	2.40545i	−0.108329	+	0.0811339i
$880$	−0.999909	−	4.70420i	−0.0337069	−	0.158579i
$881$	1.69509	+	0.360302i	0.0571089	+	0.0121389i	0.236378	−	0.971661i	$-0.424040\pi$
$881$	1.69509	+	0.360302i	0.0571089	+	0.0121389i	−0.179269	+	0.983800i	$0.557373\pi$
$882$	−0.609359	−	20.9819i	−0.0205182	−	0.706498i
$883$	48.4255	−	15.7344i	1.62965	−	0.529505i	0.655458	−	0.755231i	$-0.272476\pi$
$883$	48.4255	−	15.7344i	1.62965	−	0.529505i	0.974191	+	0.225726i	$0.0724756\pi$
$884$	24.8080	−	8.06062i	0.834385	−	0.271108i
$885$	−2.11107	+	10.6928i	−0.0709627	+	0.359434i
$886$	32.0761	+	6.81798i	1.07762	+	0.229054i
$887$	2.64089	+	12.4244i	0.0886724	+	0.417171i	0.999985	+	0.00545591i	$0.00173668\pi$
$887$	2.64089	+	12.4244i	0.0886724	+	0.417171i	−0.911313	+	0.411715i	$0.864930\pi$
$888$	−5.01929	−	6.70167i	−0.168436	−	0.224893i
$889$	0.140278	−	0.126307i	0.00470476	−	0.00423619i
$890$	−0.787711	−	7.49457i	−0.0264041	−	0.251218i
$891$	2.01853	−	43.2366i	0.0676235	−	1.44848i
$892$	−19.8252	−	2.08371i	−0.663797	−	0.0697679i
$893$	2.36051	−	1.36284i	0.0789915	−	0.0456057i
$894$	−14.1163	−	4.36115i	−0.472120	−	0.145859i
$895$	8.03443	−	11.0584i	0.268561	−	0.369643i
$896$	−0.0412091	−	0.0371048i	−0.00137670	−	0.00123958i
$897$	1.16656	−	12.8976i	0.0389504	−	0.430638i
$898$		−	25.3526i		−	0.846029i
$899$	0.233748	+	13.7926i	0.00779593	+	0.460010i
$900$	−2.70406	+	1.29926i	−0.0901353	+	0.0433085i
$901$	6.50535	−	20.0214i	0.216725	−	0.667010i
$902$	30.5187	−	33.8944i	1.01616	−	1.12856i
$903$	0.219662	+	0.0940030i	0.00730989	+	0.00312823i
$904$	−0.587788	+	1.01808i	−0.0195495	+	0.0338608i
$905$	4.31166	+	7.46802i	0.143325	+	0.248245i
$906$	−30.9767	+	3.71116i	−1.02913	+	0.123295i
$907$	−8.01607	+	5.82401i	−0.266169	+	0.193383i	−0.712862	−	0.701304i	$-0.752602\pi$
$907$	−8.01607	+	5.82401i	−0.266169	+	0.193383i	0.446693	+	0.894687i	$0.352602\pi$
$908$	−5.58926	+	0.587454i	−0.185486	+	0.0194954i
$909$	−20.0218	+	48.7297i	−0.664080	+	1.61626i
$910$	−0.127288	−	0.285894i	−0.00421956	−	0.00947730i
$911$	−4.29245	+	0.912388i	−0.142215	+	0.0302288i	−0.278469	−	0.960445i	$-0.589827\pi$
$911$	−4.29245	+	0.912388i	−0.142215	+	0.0302288i	0.136254	+	0.990674i	$0.456494\pi$
$912$	−0.186236	−	12.8280i	−0.00616689	−	0.424776i
$913$	−11.6636	−	5.19298i	−0.386010	−	0.171863i
$914$	−1.90448	−	5.86138i	−0.0629945	−	0.193877i
$915$	8.95022	−	5.34213i	0.295885	−	0.176605i
$916$	9.33136	−	20.9586i	0.308317	−	0.692491i
$917$	−0.00254195	+	0.0119589i	−8.39425e−5	+	0.000394918i
$918$	−15.2780	+	18.5306i	−0.504249	+	0.611600i
$919$	17.3152	−	7.70922i	0.571176	−	0.254304i	−0.100763	−	0.994910i	$-0.532128\pi$
$919$	17.3152	−	7.70922i	0.571176	−	0.254304i	0.671939	+	0.740607i	$0.265462\pi$
$920$	0.886486	+	0.984543i	0.0292266	+	0.0324594i
$921$	20.6245	−	7.03392i	0.679602	−	0.231776i
$922$	−15.1785	−	20.8915i	−0.499879	−	0.688024i
$923$	1.81187	−	17.2388i	0.0596383	−	0.567420i
$924$	−0.338746	+	0.314032i	−0.0111439	+	0.0103309i
$925$	4.18646	+	2.41705i	0.137650	+	0.0794722i
$926$	10.1266	+	7.35741i	0.332781	+	0.241779i
$927$	−5.49243	+	18.7384i	−0.180395	+	0.615449i
$928$	2.35632	+	0.765615i	0.0773501	+	0.0251326i
$929$	−31.2383			−1.02490			−0.512448	−	0.858718i	$-0.671261\pi$
$929$	−31.2383			−1.02490			−0.512448	+	0.858718i	$0.671261\pi$
$930$	−5.08216	−	8.19583i	−0.166651	−	0.268752i
$931$	−51.8262			−1.69854
$932$	16.5162	+	5.36645i	0.541008	+	0.175784i
$933$	−5.94497	+	10.6511i	−0.194629	+	0.348702i
$934$	−3.13414	−	2.27708i	−0.102552	−	0.0745085i
$935$	19.2505	+	11.1143i	0.629560	+	0.363477i
$936$	13.9804	+	9.54984i	0.456964	+	0.312146i
$937$	−3.73734	+	35.5584i	−0.122094	+	1.16164i	0.746245	+	0.665671i	$0.231855\pi$
$937$	−3.73734	+	35.5584i	−0.122094	+	1.16164i	−0.868339	+	0.495971i	$0.834812\pi$
$938$	−0.107746	−	0.148300i	−0.00351804	−	0.00484217i
$939$	8.61268	+	25.2537i	0.281064	+	0.824123i
$940$	−0.246232	−	0.273468i	−0.00803119	−	0.00891954i
$941$	−6.66892	+	2.96920i	−0.217401	+	0.0967930i	−0.512547	−	0.858659i	$-0.671298\pi$
$941$	−6.66892	+	2.96920i	−0.217401	+	0.0967930i	0.295147	+	0.955452i	$0.404631\pi$
$942$	14.6108	−	6.76095i	0.476044	−	0.220284i
$943$	−2.61224	+	12.2896i	−0.0850662	+	0.400205i
$944$	−2.55945	+	5.74861i	−0.0833029	+	0.187101i
$945$	0.240261	+	0.159054i	0.00781571	+	0.00517403i
$946$	3.69706	+	11.3784i	0.120202	+	0.369943i
$947$	45.3997	+	20.2132i	1.47529	+	0.656842i	0.977592	−	0.210508i	$-0.0675117\pi$
$947$	45.3997	+	20.2132i	1.47529	+	0.656842i	0.497699	+	0.867350i	$0.334178\pi$
$948$	22.5084	−	0.326776i	0.731039	−	0.0106132i
$949$	39.2757	−	8.34830i	1.27494	−	0.270997i
$950$	3.01270	+	6.76663i	0.0977449	+	0.219539i
$951$	0.278518	+	0.196242i	0.00903158	+	0.00636358i
$952$	0.254897	−	0.0267907i	0.00826125	−	0.000868292i
$953$	−27.2531	+	19.8005i	−0.882814	+	0.641402i	−0.933995	−	0.357287i	$-0.883702\pi$
$953$	−27.2531	+	19.8005i	−0.882814	+	0.641402i	0.0511801	+	0.998689i	$0.483702\pi$
$954$	12.8672	−	4.59789i	0.416592	−	0.148862i
$955$	3.93156	+	6.80966i	0.127222	+	0.220355i
$956$	3.39975	−	5.88854i	0.109956	−	0.190449i
$957$	8.11971	−	18.9738i	0.262473	−	0.613334i
$958$	5.55247	−	6.16664i	0.179392	−	0.199235i
$959$	−0.138495	+	0.426245i	−0.00447225	+	0.0137642i
$960$	−1.68880	+	0.384669i	−0.0545056	+	0.0124152i
$961$	24.4477	−	19.0607i	0.788635	−	0.614861i
$962$		−	27.2817i		−	0.879598i
$963$	−59.5821	+	8.01718i	−1.92000	+	0.258350i
$964$	17.6542	+	15.8959i	0.568602	+	0.511972i
$965$	−2.25485	+	3.10354i	−0.0725863	+	0.0999064i
$966$	0.0375600	−	0.121575i	0.00120847	−	0.00391162i
$967$	−20.6970	+	11.9494i	−0.665569	+	0.384267i	−0.794396	−	0.607400i	$-0.792212\pi$
$967$	−20.6970	+	11.9494i	−0.665569	+	0.384267i	0.128826	+	0.991667i	$0.458879\pi$
$968$	−12.0629	−	1.26786i	−0.387716	−	0.0407506i
$969$	44.6377	+	39.0337i	1.43397	+	1.25394i
$970$	−0.257084	−	2.44599i	−0.00825448	−	0.0785362i
$971$	−1.21162	+	1.09095i	−0.0388828	+	0.0350103i	−0.688343	−	0.725385i	$-0.741662\pi$
$971$	−1.21162	+	1.09095i	−0.0388828	+	0.0350103i	0.649460	+	0.760396i	$0.274995\pi$
$972$	−15.5804	−	0.500848i	−0.499742	−	0.0160647i
$973$	0.0348951	+	0.164169i	0.00111869	+	0.00526301i
$974$	−37.8034	−	8.03536i	−1.21130	−	0.257469i
$975$	−9.58988	−	1.89332i	−0.307122	−	0.0606349i
$976$	5.72335	−	1.85963i	0.183200	−	0.0595253i
$977$	22.8662	−	7.42969i	0.731555	−	0.237697i	0.0805293	−	0.996752i	$-0.474339\pi$
$977$	22.8662	−	7.42969i	0.731555	−	0.237697i	0.651026	+	0.759056i	$0.274339\pi$
$978$	−34.6530	−	6.84152i	−1.10808	−	0.218768i
$979$	−35.4502	−	7.53517i	−1.13299	−	0.240825i
$980$	1.45474	+	6.84403i	0.0464700	+	0.218624i
$981$	−19.6415	+	23.1306i	−0.627106	+	0.738504i
$982$	−1.71019	+	1.53986i	−0.0545743	+	0.0491389i
$983$	4.23128	+	40.2579i	0.134957	+	1.28403i	0.827012	+	0.562184i	$0.190039\pi$
$983$	4.23128	+	40.2579i	0.134957	+	1.28403i	−0.692055	+	0.721845i	$0.743295\pi$
$984$	−12.3652	−	10.8128i	−0.394188	−	0.344700i
$985$	−13.3608	−	1.40428i	−0.425711	−	0.0447440i
$986$	−9.91721	+	5.72570i	−0.315828	+	0.182344i
$987$	−0.0104327	+	0.0337689i	−0.000332077	+	0.00107488i
$988$	24.5707	−	33.8186i	0.781697	−	1.07591i
$989$	−2.44921	−	2.20528i	−0.0778804	−	0.0701239i
$990$	1.92404	+	14.2990i	0.0611499	+	0.454453i
$991$			13.0496i			0.414535i	0.978284	+	0.207268i	$0.0664571\pi$
$991$			13.0496i			0.414535i	−0.978284	+	0.207268i	$0.933543\pi$
$992$	−1.81001	−	5.26534i	−0.0574680	−	0.167175i
$993$	−51.6047	+	11.7544i	−1.63762	+	0.373014i
$994$	0.0526305	−	0.161980i	0.00166934	−	0.00513769i
$995$	−14.8107	+	16.4489i	−0.469530	+	0.521466i
$996$	−1.80906	+	4.22732i	−0.0573222	+	0.133948i
$997$	−5.10071	+	8.83469i	−0.161541	+	0.279797i	−0.935422	−	0.353534i	$-0.884980\pi$
$997$	−5.10071	+	8.83469i	−0.161541	+	0.279797i	0.773880	+	0.633332i	$0.218313\pi$
$998$	−7.31678	−	12.6730i	−0.231609	−	0.401158i
$999$	13.4945	+	21.1860i	0.426948	+	0.670297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.761.11	yes	176
3.2	odd	2	inner	930.2.br.a.761.19	yes	176
31.11	odd	30	inner	930.2.br.a.11.19	yes	176
93.11	even	30	inner	930.2.br.a.11.11	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.11	✓	176	93.11	even	30	inner
930.2.br.a.11.19	yes	176	31.11	odd	30	inner
930.2.br.a.761.11	yes	176	1.1	even	1	trivial
930.2.br.a.761.19	yes	176	3.2	odd	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.51241 + 0.844159i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.17753 - 1.27020i) q^{6} +(0.00579634 - 0.0551485i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.57479 + 2.55344i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.51241 + 0.844159i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.17753 - 1.27020i) q^{6} +(0.00579634 - 0.0551485i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.57479 + 2.55344i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(-4.39351 + 1.95612i) q^{11} +(0.727384 + 1.57191i) q^{12} +(-1.17337 + 5.52027i) q^{13} +(-0.0225545 + 0.0506582i) q^{14} +(0.887709 + 1.48727i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.22241 - 1.87994i) q^{17} +(-0.708659 - 2.91510i) q^{18} +(-7.24514 + 1.54000i) q^{19} +(0.406737 + 0.913545i) q^{20} +(0.0553206 - 0.0785143i) q^{21} +(4.78295 - 0.502709i) q^{22} +(-1.07181 + 0.778717i) q^{23} +(-0.206035 - 1.71975i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.82180 - 4.88750i) q^{26} +(0.226225 + 5.19123i) q^{27} +(0.0371048 - 0.0412091i) q^{28} +(-0.765615 + 2.35632i) q^{29} +(-0.384669 - 1.68880i) q^{30} +(5.26534 - 1.81001i) q^{31} -1.00000i q^{32} +(-8.29608 - 0.750366i) q^{33} +(3.43482 + 3.09273i) q^{34} +(0.0325940 - 0.0448618i) q^{35} +(-0.226841 + 2.99141i) q^{36} +(4.18646 - 2.41705i) q^{37} +(7.36642 + 0.774242i) q^{38} +(-6.43461 + 7.35842i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(7.04768 - 6.34576i) q^{41} +(-0.0768752 + 0.0575765i) q^{42} +(0.517215 + 2.43330i) q^{43} +(-4.70420 - 0.999909i) q^{44} +(0.0870895 + 2.99874i) q^{45} +(1.25999 - 0.409396i) q^{46} +(-0.349977 + 0.113714i) q^{47} +(-0.335482 + 1.69925i) q^{48} +(6.84403 + 1.45474i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(-4.79907 - 6.40764i) q^{51} +(-4.19401 + 3.77630i) q^{52} +(0.476094 + 4.52973i) q^{53} +(1.38902 - 5.00706i) q^{54} +(-4.78295 - 0.502709i) q^{55} +(-0.0480231 + 0.0277261i) q^{56} +(-12.2577 - 3.78693i) q^{57} +(1.45629 - 2.00441i) q^{58} +(4.67634 + 4.21060i) q^{59} +(-0.156024 + 1.72501i) q^{60} -6.01788i q^{61} +(-5.56696 + 0.0943451i) q^{62} +(0.149946 - 0.0720467i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.77630 + 4.19401i) q^{65} +(7.65817 + 3.27727i) q^{66} +(-1.65285 + 2.86283i) q^{67} +(-2.31100 - 4.00278i) q^{68} +(-2.27839 + 0.272962i) q^{69} +(-0.0448618 + 0.0325940i) q^{70} +(-3.05457 + 0.321048i) q^{71} +(1.14014 - 2.77490i) q^{72} +(-2.89385 - 6.49970i) q^{73} +(-4.72847 + 1.00507i) q^{74} +(0.0251432 + 1.73187i) q^{75} +(-6.76663 - 3.01270i) q^{76} +(0.0824107 + 0.253634i) q^{77} +(8.39355 - 5.00987i) q^{78} +(5.28619 - 11.8730i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(-4.04008 + 8.04225i) q^{81} +(-8.66369 + 3.85732i) q^{82} +(1.77637 + 1.97286i) q^{83} +(0.0909048 - 0.0310028i) q^{84} +(-2.71675 - 3.73928i) q^{85} +(0.260032 - 2.47404i) q^{86} +(-3.14704 + 2.91743i) q^{87} +(4.16497 + 2.40465i) q^{88} +(6.09663 + 4.42946i) q^{89} +(0.843833 - 2.87888i) q^{90} +(0.297633 + 0.0967069i) q^{91} -1.32483 q^{92} +(9.49132 + 1.70730i) q^{93} +0.367987 q^{94} +(-7.04448 - 2.28889i) q^{95} +(0.844159 - 1.51241i) q^{96} +(1.98975 + 1.44564i) q^{97} +(-6.05951 - 3.49846i) q^{98} +(-11.9137 - 8.13808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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