LMFDB - Embedded newform 228.2.v.a.23.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(23,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 2]))

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

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

chi := DirichletCharacter("228.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.v (of order $18$, degree $6$, 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:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.9
Character	$\chi$	$=$	228.23
Dual form			228.2.v.a.119.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09342 - 0.896904i) q^{2} +(-0.753513 - 1.55956i) q^{3} +(0.391126 + 1.96138i) q^{4} +(0.894860 + 1.06645i) q^{5} +(-0.574868 + 2.38108i) q^{6} +(3.30990 + 1.91097i) q^{7} +(1.33151 - 2.49541i) q^{8} +(-1.86444 + 2.35029i) q^{9} +O(q^{10})$	\(q+(-1.09342 - 0.896904i) q^{2} +(-0.753513 - 1.55956i) q^{3} +(0.391126 + 1.96138i) q^{4} +(0.894860 + 1.06645i) q^{5} +(-0.574868 + 2.38108i) q^{6} +(3.30990 + 1.91097i) q^{7} +(1.33151 - 2.49541i) q^{8} +(-1.86444 + 2.35029i) q^{9} +(-0.0219504 - 1.96868i) q^{10} +(1.86780 + 3.23513i) q^{11} +(2.76417 - 2.08791i) q^{12} +(0.211714 - 1.20069i) q^{13} +(-1.90515 - 5.05816i) q^{14} +(0.988905 - 2.19917i) q^{15} +(-3.69404 + 1.53430i) q^{16} +(0.651421 - 1.78976i) q^{17} +(4.14660 - 0.897634i) q^{18} +(4.35851 + 0.0585821i) q^{19} +(-1.74172 + 2.17228i) q^{20} +(0.486216 - 6.60193i) q^{21} +(0.859311 - 5.21259i) q^{22} +(-5.16396 - 4.33308i) q^{23} +(-4.89505 - 0.196234i) q^{24} +(0.531694 - 3.01539i) q^{25} +(-1.30840 + 1.12297i) q^{26} +(5.07029 + 1.13672i) q^{27} +(-2.45356 + 7.23942i) q^{28} +(1.92121 + 5.27848i) q^{29} +(-3.05373 + 1.51766i) q^{30} +(-3.36476 - 1.94264i) q^{31} +(5.41525 + 1.63557i) q^{32} +(3.63795 - 5.35066i) q^{33} +(-2.31752 + 1.37270i) q^{34} +(0.923938 + 5.23991i) q^{35} +(-5.33905 - 2.73761i) q^{36} +3.52532 q^{37} +(-4.71313 - 3.97322i) q^{38} +(-2.03208 + 0.574556i) q^{39} +(3.85275 - 0.813056i) q^{40} +(-4.50749 + 0.794791i) q^{41} +(-6.45293 + 6.78258i) q^{42} +(6.00767 + 7.15966i) q^{43} +(-5.61478 + 4.92882i) q^{44} +(-4.17489 + 0.114852i) q^{45} +(1.76001 + 9.36945i) q^{46} +(4.98106 - 1.81296i) q^{47} +(5.17633 + 4.60495i) q^{48} +(3.80364 + 6.58811i) q^{49} +(-3.28588 + 2.82020i) q^{50} +(-3.28209 + 0.332683i) q^{51} +(2.43782 - 0.0543693i) q^{52} +(-5.22663 + 6.22885i) q^{53} +(-4.52443 - 5.79047i) q^{54} +(-1.77869 + 4.88691i) q^{55} +(9.17583 - 5.71510i) q^{56} +(-3.19283 - 6.84148i) q^{57} +(2.63360 - 7.49472i) q^{58} +(1.45183 + 0.528424i) q^{59} +(4.70020 + 1.07947i) q^{60} +(-9.64491 - 8.09304i) q^{61} +(1.93672 + 5.14199i) q^{62} +(-10.6625 + 4.21636i) q^{63} +(-4.45418 - 6.64532i) q^{64} +(1.46993 - 0.848667i) q^{65} +(-8.77683 + 2.58761i) q^{66} +(-3.47539 - 9.54855i) q^{67} +(3.76520 + 0.577662i) q^{68} +(-2.86657 + 11.3185i) q^{69} +(3.68945 - 6.55810i) q^{70} +(2.30430 - 1.93354i) q^{71} +(3.38245 + 7.78197i) q^{72} +(0.820954 + 4.65586i) q^{73} +(-3.85465 - 3.16188i) q^{74} +(-5.10331 + 1.44293i) q^{75} +(1.58982 + 8.57161i) q^{76} +14.2773i q^{77} +(2.73723 + 1.19435i) q^{78} +(-15.1931 + 2.67896i) q^{79} +(-4.94190 - 2.56654i) q^{80} +(-2.04776 - 8.76394i) q^{81} +(5.64142 + 3.17374i) q^{82} +(7.18448 - 12.4439i) q^{83} +(13.1391 - 1.62853i) q^{84} +(2.49163 - 0.906879i) q^{85} +(-0.147365 - 13.2168i) q^{86} +(6.78443 - 6.97364i) q^{87} +(10.5600 - 0.353342i) q^{88} +(-0.594397 - 0.104808i) q^{89} +(4.66791 + 3.61889i) q^{90} +(2.99524 - 3.56959i) q^{91} +(6.47906 - 11.8233i) q^{92} +(-0.494274 + 6.71134i) q^{93} +(-7.07243 - 2.48521i) q^{94} +(3.83778 + 4.70056i) q^{95} +(-1.52969 - 9.67781i) q^{96} +(-7.87046 - 2.86461i) q^{97} +(1.74992 - 10.6151i) q^{98} +(-11.0859 - 1.64180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$	$-1$

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 $

$2$	−1.09342	−	0.896904i	−0.773163	−	0.634207i
$2$	−1.09342	−	0.896904i	−0.773163	−	0.634207i
$3$	−0.753513	−	1.55956i	−0.435041	−	0.900411i
$3$	−0.753513	−	1.55956i	−0.435041	−	0.900411i
$4$	0.391126	+	1.96138i	0.195563	+	0.980691i
$5$	0.894860	+	1.06645i	0.400194	+	0.476932i	0.928079	−	0.372384i	$-0.121459\pi$
$5$	0.894860	+	1.06645i	0.400194	+	0.476932i	−0.527885	+	0.849316i	$0.677015\pi$
$6$	−0.574868	+	2.38108i	−0.234689	+	0.972071i
$7$	3.30990	+	1.91097i	1.25103	+	0.722280i	0.971313	−	0.237803i	$-0.0764274\pi$
$7$	3.30990	+	1.91097i	1.25103	+	0.722280i	0.279713	+	0.960084i	$0.409761\pi$
$8$	1.33151	−	2.49541i	0.470759	−	0.882262i
$9$	−1.86444	+	2.35029i	−0.621478	+	0.783431i
$10$	−0.0219504	−	1.96868i	−0.00694134	−	0.622552i
$11$	1.86780	+	3.23513i	0.563164	+	0.975428i	0.997218	+	0.0745413i	$0.0237493\pi$
$11$	1.86780	+	3.23513i	0.563164	+	0.975428i	−0.434054	+	0.900887i	$0.642917\pi$
$12$	2.76417	−	2.08791i	0.797947	−	0.602728i
$13$	0.211714	−	1.20069i	0.0587190	−	0.333012i	−0.941270	−	0.337654i	$-0.890367\pi$
$13$	0.211714	−	1.20069i	0.0587190	−	0.333012i	0.999989	+	0.00464231i	$0.00147770\pi$
$14$	−1.90515	−	5.05816i	−0.509172	−	1.35185i
$15$	0.988905	−	2.19917i	0.255334	−	0.567824i
$16$	−3.69404	+	1.53430i	−0.923510	+	0.383574i
$17$	0.651421	−	1.78976i	0.157993	−	0.434082i	−0.835288	−	0.549813i	$-0.814699\pi$
$17$	0.651421	−	1.78976i	0.157993	−	0.434082i	0.993281	+	0.115731i	$0.0369212\pi$
$18$	4.14660	−	0.897634i	0.977362	−	0.211574i
$19$	4.35851	+	0.0585821i	0.999910	+	0.0134396i
$19$	4.35851	+	0.0585821i	0.999910	+	0.0134396i
$20$	−1.74172	+	2.17228i	−0.389460	+	0.485737i
$21$	0.486216	−	6.60193i	0.106101	−	1.44066i
$22$	0.859311	−	5.21259i	0.183206	−	1.11133i
$23$	−5.16396	−	4.33308i	−1.07676	−	0.903509i	−0.0811128	−	0.996705i	$-0.525847\pi$
$23$	−5.16396	−	4.33308i	−1.07676	−	0.903509i	−0.995648	+	0.0931955i	$0.970292\pi$
$24$	−4.89505	−	0.196234i	−0.999197	−	0.0400561i
$25$	0.531694	−	3.01539i	0.106339	−	0.603077i
$26$	−1.30840	+	1.12297i	−0.256598	+	0.220233i
$27$	5.07029	+	1.13672i	0.975778	+	0.218761i
$28$	−2.45356	+	7.23942i	−0.463679	+	1.36812i
$29$	1.92121	+	5.27848i	0.356759	+	0.980189i	0.980146	+	0.198275i	$0.0635339\pi$
$29$	1.92121	+	5.27848i	0.356759	+	0.980189i	−0.623387	+	0.781913i	$0.714244\pi$
$30$	−3.05373	+	1.51766i	−0.557533	+	0.277086i
$31$	−3.36476	−	1.94264i	−0.604328	−	0.348909i	0.166414	−	0.986056i	$-0.446781\pi$
$31$	−3.36476	−	1.94264i	−0.604328	−	0.348909i	−0.770742	+	0.637147i	$0.780114\pi$
$32$	5.41525	+	1.63557i	0.957289	+	0.289131i
$33$	3.63795	−	5.35066i	0.633286	−	0.931430i
$34$	−2.31752	+	1.37270i	−0.397452	+	0.235416i
$35$	0.923938	+	5.23991i	0.156174	+	0.885706i
$36$	−5.33905	−	2.73761i	−0.889842	−	0.456268i
$37$	3.52532			0.579559			0.289780	−	0.957093i	$-0.406418\pi$
$37$	3.52532			0.579559			0.289780	+	0.957093i	$0.406418\pi$
$38$	−4.71313	−	3.97322i	−0.764570	−	0.644541i
$39$	−2.03208	+	0.574556i	−0.325393	+	0.0920026i
$40$	3.85275	−	0.813056i	0.609174	−	0.128556i
$41$	−4.50749	+	0.794791i	−0.703951	+	0.124126i	−0.514154	−	0.857698i	$-0.671894\pi$
$41$	−4.50749	+	0.794791i	−0.703951	+	0.124126i	−0.189797	+	0.981823i	$0.560783\pi$
$42$	−6.45293	+	6.78258i	−0.995709	+	1.04657i
$43$	6.00767	+	7.15966i	0.916161	+	1.09184i	0.995478	+	0.0949886i	$0.0302815\pi$
$43$	6.00767	+	7.15966i	0.916161	+	1.09184i	−0.0793175	+	0.996849i	$0.525274\pi$
$44$	−5.61478	+	4.92882i	−0.846460	+	0.743047i
$45$	−4.17489	+	0.114852i	−0.622355	+	0.0171211i
$46$	1.76001	+	9.36945i	0.259500	+	1.38145i
$47$	4.98106	−	1.81296i	0.726563	−	0.264447i	0.0478536	−	0.998854i	$-0.484762\pi$
$47$	4.98106	−	1.81296i	0.726563	−	0.264447i	0.678709	+	0.734407i	$0.262540\pi$
$48$	5.17633	+	4.60495i	0.747139	+	0.664668i
$49$	3.80364	+	6.58811i	0.543378	+	0.941158i
$50$	−3.28588	+	2.82020i	−0.464693	+	0.398837i
$51$	−3.28209	+	0.332683i	−0.459585	+	0.0465850i
$52$	2.43782	−	0.0543693i	0.338065	−	0.00753966i
$53$	−5.22663	+	6.22885i	−0.717932	+	0.855598i	−0.994428	−	0.105417i	$-0.966382\pi$
$53$	−5.22663	+	6.22885i	−0.717932	+	0.855598i	0.276496	+	0.961015i	$0.410827\pi$
$54$	−4.52443	−	5.79047i	−0.615696	−	0.787983i
$55$	−1.77869	+	4.88691i	−0.239838	+	0.658951i
$56$	9.17583	−	5.71510i	1.22617	−	0.763713i
$57$	−3.19283	−	6.84148i	−0.422901	−	0.906176i
$58$	2.63360	−	7.49472i	0.345809	−	0.984105i
$59$	1.45183	+	0.528424i	0.189013	+	0.0687950i	0.434792	−	0.900531i	$-0.356822\pi$
$59$	1.45183	+	0.528424i	0.189013	+	0.0687950i	−0.245780	+	0.969326i	$0.579044\pi$
$60$	4.70020	+	1.07947i	0.606793	+	0.139358i
$61$	−9.64491	−	8.09304i	−1.23490	−	1.03621i	−0.997905	−	0.0646975i	$-0.979392\pi$
$61$	−9.64491	−	8.09304i	−1.23490	−	1.03621i	−0.236999	−	0.971510i	$-0.576164\pi$
$62$	1.93672	+	5.14199i	0.245964	+	0.653033i
$63$	−10.6625	+	4.21636i	−1.34334	+	0.531211i
$64$	−4.45418	−	6.64532i	−0.556772	−	0.830665i
$65$	1.46993	−	0.848667i	0.182323	−	0.105264i
$66$	−8.77683	+	2.58761i	−1.08035	+	0.318513i
$67$	−3.47539	−	9.54855i	−0.424586	−	1.16654i	−0.949055	−	0.315111i	$-0.897958\pi$
$67$	−3.47539	−	9.54855i	−0.424586	−	1.16654i	0.524469	−	0.851430i	$-0.324264\pi$
$68$	3.76520	+	0.577662i	0.456597	+	0.0700518i
$69$	−2.86657	+	11.3185i	−0.345094	+	1.36259i
$70$	3.68945	−	6.55810i	0.440973	−	0.783842i
$71$	2.30430	−	1.93354i	0.273470	−	0.229469i	−0.495730	−	0.868477i	$-0.665099\pi$
$71$	2.30430	−	1.93354i	0.273470	−	0.229469i	0.769200	+	0.639008i	$0.220655\pi$
$72$	3.38245	+	7.78197i	0.398625	+	0.917114i
$73$	0.820954	+	4.65586i	0.0960855	+	0.544928i	0.994409	+	0.105594i	$0.0336744\pi$
$73$	0.820954	+	4.65586i	0.0960855	+	0.544928i	−0.898324	+	0.439334i	$0.855215\pi$
$74$	−3.85465	−	3.16188i	−0.448094	−	0.367561i
$75$	−5.10331	+	1.44293i	−0.589279	+	0.166615i
$76$	1.58982	+	8.57161i	0.182365	+	0.983231i
$77$			14.2773i			1.62705i
$78$	2.73723	+	1.19435i	0.309930	+	0.135233i
$79$	−15.1931	+	2.67896i	−1.70936	+	0.301407i	−0.940949	−	0.338548i	$-0.890064\pi$
$79$	−15.1931	+	2.67896i	−1.70936	+	0.301407i	−0.768413	+	0.639955i	$0.778953\pi$
$80$	−4.94190	−	2.56654i	−0.552522	−	0.286948i
$81$	−2.04776	−	8.76394i	−0.227529	−	0.973771i
$82$	5.64142	+	3.17374i	0.622991	+	0.350481i
$83$	7.18448	−	12.4439i	0.788599	−	1.36589i	−0.138226	−	0.990401i	$-0.544140\pi$
$83$	7.18448	−	12.4439i	0.788599	−	1.36589i	0.926825	−	0.375493i	$-0.122527\pi$
$84$	13.1391	−	1.62853i	1.43359	−	0.177687i
$85$	2.49163	−	0.906879i	0.270255	−	0.0983648i
$86$	−0.147365	−	13.2168i	−0.0158908	−	1.42520i
$87$	6.78443	−	6.97364i	0.727367	−	0.747652i
$88$	10.5600	−	0.353342i	1.12570	−	0.0376664i
$89$	−0.594397	−	0.104808i	−0.0630059	−	0.0111096i	0.142056	−	0.989859i	$-0.454629\pi$
$89$	−0.594397	−	0.104808i	−0.0630059	−	0.0111096i	−0.205062	+	0.978749i	$0.565740\pi$
$90$	4.66791	+	3.61889i	0.492041	+	0.381465i
$91$	2.99524	−	3.56959i	0.313987	−	0.374195i
$92$	6.47906	−	11.8233i	0.675489	−	1.23266i
$93$	−0.494274	+	6.71134i	−0.0512538	+	0.695933i
$94$	−7.07243	−	2.48521i	−0.729466	−	0.256330i
$95$	3.83778	+	4.70056i	0.393748	+	0.482267i
$96$	−1.52969	−	9.67781i	−0.156124	−	0.987738i
$97$	−7.87046	−	2.86461i	−0.799124	−	0.290857i	−0.0900006	−	0.995942i	$-0.528687\pi$
$97$	−7.87046	−	2.86461i	−0.799124	−	0.290857i	−0.709123	+	0.705084i	$0.750909\pi$
$98$	1.74992	−	10.6151i	0.176769	−	1.07228i
$99$	−11.0859	−	1.64180i	−1.11417	−	0.165008i
$100$	6.12229	−	0.136542i	0.612229	−	0.0136542i
$101$	15.1050	+	2.66342i	1.50300	+	0.265020i	0.863729	−	0.503957i	$-0.168123\pi$
$101$	15.1050	+	2.66342i	1.50300	+	0.265020i	0.639276	+	0.768977i	$0.279234\pi$
$102$	3.88709	+	2.57996i	0.384879	+	0.255454i
$103$	−5.24270	+	3.02688i	−0.516579	+	0.298247i	−0.735534	−	0.677488i	$-0.763069\pi$
$103$	−5.24270	+	3.02688i	−0.516579	+	0.298247i	0.218955	+	0.975735i	$0.429735\pi$
$104$	−2.71432	−	2.12704i	−0.266161	−	0.208574i
$105$	7.47574	−	5.38928i	0.729557	−	0.525939i
$106$	11.3016	−	2.12296i	1.09771	−	0.206200i
$107$	−5.99660	+	10.3864i	−0.579713	+	1.00409i	0.415799	+	0.909457i	$0.363502\pi$
$107$	−5.99660	+	10.3864i	−0.579713	+	1.00409i	−0.995512	+	0.0946359i	$0.969831\pi$
$108$	−0.246408	+	10.3894i	−0.0237107	+	0.999719i
$109$	−0.386755	+	0.324526i	−0.0370444	+	0.0310840i	−0.661122	−	0.750279i	$-0.729919\pi$
$109$	−0.386755	+	0.324526i	−0.0370444	+	0.0310840i	0.624077	+	0.781362i	$0.285475\pi$
$110$	6.32794	−	3.74812i	0.603345	−	0.357369i
$111$	−2.65638	−	5.49794i	−0.252132	−	0.521841i
$112$	−15.1589	−	1.98084i	−1.43238	−	0.187172i
$113$		−	9.15601i		−	0.861325i	−0.902513	−	0.430663i	$-0.858280\pi$
$113$		−	9.15601i		−	0.861325i	0.902513	−	0.430663i	$-0.141720\pi$
$114$	−2.64505	+	10.3443i	−0.247732	+	0.968829i
$115$		−	9.38462i		−	0.875120i
$116$	−9.60168	+	5.83277i	−0.891493	+	0.541560i
$117$	2.42725	+	2.73620i	0.224399	+	0.252962i
$118$	−1.11352	−	1.87994i	−0.102507	−	0.173063i
$119$	5.57633	−	4.67910i	0.511182	−	0.428932i
$120$	−4.17111	−	5.39594i	−0.380768	−	0.492579i
$121$	−1.47737	+	2.55888i	−0.134307	+	0.232626i
$122$	3.28724	+	17.4996i	0.297613	+	1.58434i
$123$	4.63597	+	6.43080i	0.418012	+	0.579845i
$124$	2.49422	−	7.35940i	0.223988	−	0.660893i
$125$	9.71977	−	5.61171i	0.869362	−	0.501927i
$126$	15.4402	+	4.95295i	1.37552	+	0.441244i
$127$	−1.33350	−	0.235132i	−0.118329	−	0.0208646i	0.114170	−	0.993461i	$-0.463579\pi$
$127$	−1.33350	−	0.235132i	−0.118329	−	0.0208646i	−0.232499	+	0.972597i	$0.574690\pi$
$128$	−1.08994	+	11.2611i	−0.0963378	+	0.995349i
$129$	6.63904	−	14.7642i	0.584535	−	1.29992i
$130$	−2.36843	−	0.390442i	−0.207725	−	0.0342441i
$131$	−15.1439	−	5.51194i	−1.32313	−	0.481581i	−0.418671	−	0.908138i	$-0.637504\pi$
$131$	−15.1439	−	5.51194i	−1.32313	−	0.481581i	−0.904460	+	0.426557i	$0.859726\pi$
$132$	11.9176	+	5.04263i	1.03729	+	0.438905i
$133$	14.3143	+	8.52289i	1.24121	+	0.739028i
$134$	−4.76408	+	13.5576i	−0.411554	+	1.17120i
$135$	3.32495	+	6.42443i	0.286166	+	0.552927i
$136$	−3.59883	−	4.00865i	−0.308597	−	0.343739i
$137$	−5.20212	+	6.19965i	−0.444447	+	0.529672i	−0.941032	−	0.338316i	$-0.890143\pi$
$137$	−5.20212	+	6.19965i	−0.444447	+	0.529672i	0.496585	+	0.867988i	$0.334587\pi$
$138$	13.2860	−	9.80484i	1.13098	−	0.834644i
$139$	−4.98426	−	0.878859i	−0.422759	−	0.0745439i	−0.0417786	−	0.999127i	$-0.513302\pi$
$139$	−4.98426	−	0.878859i	−0.422759	−	0.0745439i	−0.380981	+	0.924583i	$0.624414\pi$
$140$	−9.91609	+	3.86166i	−0.838063	+	0.326370i
$141$	−6.58071	−	6.40216i	−0.554196	−	0.539159i
$142$	−4.25376	+	0.0474287i	−0.356968	+	0.00398013i
$143$	4.27983	−	1.55773i	0.357897	−	0.130264i
$144$	3.28125	−	11.5427i	0.273438	−	0.961890i
$145$	−3.91003	+	6.77238i	−0.324711	+	0.562415i
$146$	3.27822	−	5.82712i	0.271307	−	0.482256i
$147$	7.40843	−	10.8962i	0.611037	−	0.898705i
$148$	1.37885	+	6.91450i	0.113340	+	0.568369i
$149$	−9.90946	+	1.74730i	−0.811814	+	0.143145i	−0.564119	−	0.825693i	$-0.690784\pi$
$149$	−9.90946	+	1.74730i	−0.811814	+	0.143145i	−0.247695	+	0.968838i	$0.579673\pi$
$150$	6.87422	+	2.99945i	0.561277	+	0.244904i
$151$		−	10.8984i		−	0.886903i	−0.896298	−	0.443451i	$-0.853754\pi$
$151$		−	10.8984i		−	0.886903i	0.896298	−	0.443451i	$-0.146246\pi$
$152$	5.94957	−	10.7983i	0.482574	−	0.875855i
$153$	2.99194	+	4.86793i	0.241884	+	0.393549i
$154$	12.8054	−	15.6110i	1.03189	−	1.25797i
$155$	−0.939250	−	5.32675i	−0.0754423	−	0.427855i
$156$	−1.92172	−	3.76095i	−0.153861	−	0.301117i
$157$	−18.5923	+	15.6008i	−1.48382	+	1.24508i	−0.581841	+	0.813303i	$0.697667\pi$
$157$	−18.5923	+	15.6008i	−1.48382	+	1.24508i	−0.901982	+	0.431773i	$0.857888\pi$
$158$	19.0152	+	10.6976i	1.51277	+	0.851053i
$159$	13.6526	+	3.45770i	1.08272	+	0.274213i
$160$	3.10163	+	7.23871i	0.245205	+	0.572270i
$161$	−8.81182	−	24.2103i	−0.694469	−	1.90804i
$162$	−5.62136	+	11.4193i	−0.441655	+	0.897185i
$163$	−2.76265	+	1.59501i	−0.216387	+	0.124931i	−0.604276	−	0.796775i	$-0.706538\pi$
$163$	−2.76265	+	1.59501i	−0.216387	+	0.124931i	0.387889	+	0.921706i	$0.373204\pi$
$164$	−3.32189	−	8.53004i	−0.259396	−	0.666084i
$165$	8.96168	−	0.908384i	0.697666	−	0.0707176i
$166$	−19.0166	+	7.16258i	−1.47597	+	0.555924i
$167$	−0.556567	−	0.467015i	−0.0430684	−	0.0361387i	0.620999	−	0.783811i	$-0.286727\pi$
$167$	−0.556567	−	0.467015i	−0.0430684	−	0.0361387i	−0.664068	+	0.747672i	$0.731171\pi$
$168$	−15.8271	−	10.0038i	−1.22109	−	0.771812i
$169$	10.8192	+	3.93786i	0.832244	+	0.302912i
$170$	−3.53778	−	1.24315i	−0.271335	−	0.0953456i
$171$	−8.26384	+	10.1345i	−0.631951	+	0.775008i
$172$	−11.6931	+	14.5837i	−0.891589	+	1.11199i
$173$	−1.03638	+	2.84742i	−0.0787942	+	0.216485i	−0.972835	−	0.231501i	$-0.925636\pi$
$173$	−1.03638	+	2.84742i	−0.0787942	+	0.216485i	0.894041	+	0.447986i	$0.147859\pi$
$174$	−13.6729	+	1.54012i	−1.03654	+	0.116756i
$175$	7.52218	−	8.96459i	0.568624	−	0.677659i
$176$	−11.8634	−	9.08493i	−0.894236	−	0.684803i
$177$	−0.269868	−	2.66239i	−0.0202846	−	0.200118i
$178$	0.555921	+	0.647716i	0.0416681	+	0.0485484i
$179$	−0.530225	−	0.918376i	−0.0396309	−	0.0686427i	0.845530	−	0.533929i	$-0.179285\pi$
$179$	−0.530225	−	0.918376i	−0.0396309	−	0.0686427i	−0.885160	+	0.465286i	$0.845952\pi$
$180$	−1.85818	−	8.14362i	−0.138500	−	0.606990i
$181$	9.93233	−	3.61507i	0.738264	−	0.268706i	0.0546055	−	0.998508i	$-0.482610\pi$
$181$	9.93233	−	3.61507i	0.738264	−	0.268706i	0.683659	+	0.729802i	$0.260388\pi$
$182$	−6.47664	+	1.21661i	−0.480080	+	0.0901812i
$183$	−5.35399	+	21.1400i	−0.395778	+	1.56271i
$184$	−17.6887	+	7.11670i	−1.30403	+	0.524650i
$185$	3.15467	+	3.75959i	0.231936	+	0.276410i
$186$	6.55988	−	6.89498i	0.480993	−	0.505565i
$187$	7.00684	−	1.23550i	0.512391	−	0.0903484i
$188$	5.50413	+	9.06067i	0.401430	+	0.660817i
$189$	14.6100	+	13.4516i	1.06272	+	0.978461i
$190$	0.0196584	−	8.58180i	0.00142617	−	0.622589i
$191$	−19.9650			−1.44462			−0.722309	−	0.691571i	$-0.756919\pi$
$191$	−19.9650			−1.44462			−0.722309	+	0.691571i	$0.756919\pi$
$192$	−7.00748	+	11.9539i	−0.505721	+	0.862697i
$193$	−3.89183	−	22.0716i	−0.280140	−	1.58875i	−0.722147	−	0.691740i	$-0.756844\pi$
$193$	−3.89183	−	22.0716i	−0.280140	−	1.58875i	0.442007	−	0.897012i	$-0.354267\pi$
$194$	6.03642	+	10.1913i	0.433390	+	0.731690i
$195$	−2.43116	−	1.65296i	−0.174099	−	0.118371i
$196$	−11.4341	+	10.0372i	−0.816721	+	0.716942i
$197$	−5.16680	−	2.98305i	−0.368119	−	0.212534i	0.304517	−	0.952507i	$-0.401505\pi$
$197$	−5.16680	−	2.98305i	−0.368119	−	0.212534i	−0.672636	+	0.739973i	$0.734838\pi$
$198$	10.6490	+	11.7382i	0.756790	+	0.834195i
$199$	3.38199	+	9.29193i	0.239743	+	0.658687i	0.999959	+	0.00901789i	$0.00287052\pi$
$199$	3.38199	+	9.29193i	0.239743	+	0.658687i	−0.760217	+	0.649670i	$0.774907\pi$
$200$	−6.81668	−	5.34181i	−0.482012	−	0.377723i
$201$	−12.2728	+	12.6150i	−0.865653	+	0.889795i
$202$	−14.1273	−	16.4600i	−0.993991	−	1.15812i
$203$	−3.72802	+	21.1426i	−0.261655	+	1.48392i
$204$	−1.93623	−	6.30732i	−0.135563	−	0.441601i
$205$	−4.88118	−	4.09579i	−0.340916	−	0.286063i
$206$	8.44729	+	1.39256i	0.588550	+	0.0970243i
$207$	19.8119	−	4.05808i	1.37702	−	0.282056i
$208$	1.06013	+	4.76023i	0.0735071	+	0.330063i
$209$	7.95131	+	14.2097i	0.550003	+	0.982909i
$210$	−13.0078	−	0.812289i	−0.897621	−	0.0560533i
$211$	−2.48841	+	6.83685i	−0.171309	+	0.470668i	−0.995402	−	0.0957868i	$-0.969463\pi$
$211$	−2.48841	+	6.83685i	−0.171309	+	0.470668i	0.824093	+	0.566455i	$0.191686\pi$
$212$	−14.2614	−	7.81514i	−0.979479	−	0.536746i
$213$	−4.75179	−	2.13674i	−0.325587	−	0.146407i
$214$	15.8724	−	5.97832i	1.08502	−	0.408669i
$215$	−2.25942	+	12.8138i	−0.154091	+	0.873893i
$216$	9.58771	−	11.1389i	0.652361	−	0.757909i
$217$	−7.42468	−	12.8599i	−0.504020	−	0.872989i
$218$	0.713954	−	0.00796045i	0.0483550	−	0.000539150i
$219$	6.64248	−	4.78858i	0.448858	−	0.323582i
$220$	−10.2808	−	1.57729i	−0.693131	−	0.106341i
$221$	−2.01104	−	1.16107i	−0.135277	−	0.0781023i
$222$	−2.02659	+	8.39406i	−0.136016	+	0.563373i
$223$	11.0821	+	13.2072i	0.742115	+	0.884418i	0.996577	−	0.0826645i	$-0.0263430\pi$
$223$	11.0821	+	13.2072i	0.742115	+	0.884418i	−0.254463	+	0.967083i	$0.581899\pi$
$224$	14.7984	+	15.7620i	0.988761	+	1.05314i
$225$	6.09574	+	6.87163i	0.406382	+	0.458109i
$226$	−8.21206	+	10.0113i	−0.546258	+	0.665945i
$227$	22.0677			1.46469			0.732343	−	0.680936i	$-0.238427\pi$
$227$	22.0677			1.46469			0.732343	+	0.680936i	$0.238427\pi$
$228$	12.1700	−	8.93824i	0.805975	−	0.591950i
$229$	−5.95034			−0.393210			−0.196605	−	0.980483i	$-0.562992\pi$
$229$	−5.95034			−0.393210			−0.196605	+	0.980483i	$0.562992\pi$
$230$	−8.41710	+	10.2613i	−0.555007	+	0.676611i
$231$	22.2662	−	10.7581i	1.46501	−	0.707833i
$232$	15.7301	+	2.23412i	1.03273	+	0.146677i
$233$	−17.4912	−	20.8452i	−1.14589	−	1.36562i	−0.920216	−	0.391412i	$-0.871987\pi$
$233$	−17.4912	−	20.8452i	−1.14589	−	1.36562i	−0.225672	−	0.974203i	$-0.572458\pi$
$234$	−0.199888	−	5.16882i	−0.0130671	−	0.337896i
$235$	6.39079	+	3.68972i	0.416889	+	0.240691i
$236$	−0.468592	+	3.05428i	−0.0305027	+	0.198817i
$237$	15.6262	+	21.6759i	1.01503	+	1.40800i
$238$	−10.2940	+	0.114776i	−0.667259	+	0.00743981i
$239$	4.86415	+	8.42496i	0.314636	+	0.544965i	0.979360	−	0.202124i	$-0.0647843\pi$
$239$	4.86415	+	8.42496i	0.314636	+	0.544965i	−0.664724	+	0.747089i	$0.731451\pi$
$240$	−0.278874	+	9.64110i	−0.0180012	+	0.622330i
$241$	−1.17388	+	6.65741i	−0.0756163	+	0.428842i	0.923373	+	0.383903i	$0.125420\pi$
$241$	−1.17388	+	6.65741i	−0.0756163	+	0.428842i	−0.998990	+	0.0449385i	$0.985691\pi$
$242$	3.91046	−	1.47287i	0.251374	−	0.0946796i
$243$	−12.1248	+	9.79735i	−0.777809	+	0.628500i
$244$	12.1012	−	22.0828i	0.774698	−	1.41370i
$245$	−3.62217	+	9.95184i	−0.231412	+	0.635800i
$246$	0.698749	−	11.1896i	0.0445506	−	0.713421i
$247$	0.993097	−	5.22082i	0.0631892	−	0.332193i
$248$	−9.32790	+	5.80982i	−0.592322	+	0.368924i
$249$	−24.8205	−	1.82797i	−1.57294	−	0.115843i
$250$	−15.6609	−	2.58175i	−0.990484	−	0.163284i
$251$	−7.68687	−	6.45005i	−0.485191	−	0.407124i	0.367108	−	0.930178i	$-0.380348\pi$
$251$	−7.68687	−	6.45005i	−0.485191	−	0.407124i	−0.852299	+	0.523055i	$0.824792\pi$
$252$	−12.4403	−	19.2640i	−0.783663	−	1.21352i
$253$	4.37281	−	24.7994i	0.274916	−	1.55913i
$254$	1.24718	+	1.45312i	0.0782551	+	0.0911767i
$255$	−3.29180	−	3.20249i	−0.206141	−	0.200548i
$256$	11.2919	−	11.3355i	0.705742	−	0.708469i
$257$	−0.952812	−	2.61783i	−0.0594348	−	0.163296i	0.906421	−	0.422375i	$-0.138803\pi$
$257$	−0.952812	−	2.61783i	−0.0594348	−	0.163296i	−0.965856	+	0.259079i	$0.916581\pi$
$258$	−20.5013	+	10.1889i	−1.27636	+	0.634331i
$259$	11.6685	+	6.73680i	0.725044	+	0.418604i
$260$	2.23949	+	2.55117i	0.138887	+	0.158217i
$261$	−15.9879	−	5.32597i	−0.989629	−	0.329670i
$262$	11.6150	+	19.6095i	0.717575	+	1.21148i
$263$	0.580523	+	3.29231i	0.0357966	+	0.203013i	0.997461	−	0.0712170i	$-0.0226883\pi$
$263$	0.580523	+	3.29231i	0.0357966	+	0.203013i	−0.961664	+	0.274230i	$0.911577\pi$
$264$	−8.50814	−	16.2026i	−0.523640	−	0.997203i
$265$	−11.3199			−0.695374
$266$	−8.00728	−	22.1576i	−0.490958	−	1.35857i
$267$	0.284432	+	1.00597i	0.0174069	+	0.0615644i
$268$	17.3690	−	10.5512i	1.06098	−	0.644520i
$269$	−2.75106	+	0.485087i	−0.167735	+	0.0295763i	−0.256885	−	0.966442i	$-0.582696\pi$
$269$	−2.75106	+	0.485087i	−0.167735	+	0.0295763i	0.0891496	+	0.996018i	$0.471585\pi$
$270$	2.12654	−	10.0067i	0.129417	−	0.608991i
$271$	−1.91359	−	2.28053i	−0.116242	−	0.138532i	0.704785	−	0.709421i	$-0.251043\pi$
$271$	−1.91359	−	2.28053i	−0.116242	−	0.138532i	−0.821028	+	0.570888i	$0.806599\pi$
$272$	0.339653	+	7.61093i	0.0205945	+	0.461481i
$273$	−7.82394	−	1.98152i	−0.473526	−	0.119927i
$274$	11.2486	−	2.11300i	0.679552	−	0.127651i
$275$	10.7483	−	3.91205i	0.648145	−	0.235905i
$276$	−23.3211	−	1.19546i	−1.40377	−	0.0719585i
$277$	−6.16664	−	10.6809i	−0.370518	−	0.641756i	0.619127	−	0.785290i	$-0.287486\pi$
$277$	−6.16664	−	10.6809i	−0.370518	−	0.641756i	−0.989645	+	0.143535i	$0.954153\pi$
$278$	4.66163	+	5.43136i	0.279586	+	0.325751i
$279$	10.8392	−	4.28624i	0.648923	−	0.256610i
$280$	14.3060	+	4.67137i	0.854945	+	0.279168i
$281$	8.33090	−	9.92838i	0.496980	−	0.592277i	−0.457999	−	0.888953i	$-0.651434\pi$
$281$	8.33090	−	9.92838i	0.496980	−	0.592277i	0.954978	+	0.296676i	$0.0958780\pi$
$282$	1.45334	+	12.9025i	0.0865452	+	0.768333i
$283$	7.96221	−	21.8760i	0.473304	−	1.30039i	−0.441777	−	0.897125i	$-0.645652\pi$
$283$	7.96221	−	21.8760i	0.473304	−	1.30039i	0.915082	−	0.403268i	$-0.132126\pi$
$284$	4.69368	+	3.76336i	0.278519	+	0.223314i
$285$	4.43898	−	9.52717i	0.262942	−	0.564341i
$286$	−6.07678	−	2.13535i	−0.359328	−	0.126266i
$287$	−16.4382	−	5.98301i	−0.970315	−	0.353166i
$288$	−13.9405	+	9.67800i	−0.821449	+	0.570282i
$289$	10.2438	+	8.59561i	0.602579	+	0.505624i
$290$	10.3495	−	3.89811i	0.607742	−	0.228905i
$291$	1.46297	+	14.4330i	0.0857608	+	0.846075i
$292$	−8.81083	+	3.43124i	−0.515615	+	0.200798i
$293$	27.4708	−	15.8603i	1.60486	−	0.926566i	0.614364	−	0.789023i	$-0.289413\pi$
$293$	27.4708	−	15.8603i	1.60486	−	0.926566i	0.990496	−	0.137544i	$-0.0439207\pi$
$294$	−17.8734	+	5.26948i	−1.04240	+	0.307322i
$295$	0.735649	+	2.02118i	0.0428311	+	0.117678i
$296$	4.69399	−	8.79714i	0.272833	−	0.511323i
$297$	5.79289	+	18.5262i	0.336137	+	1.07500i
$298$	12.4023	+	6.97730i	0.718448	+	0.404184i
$299$	−6.29597	+	5.28295i	−0.364106	+	0.305521i
$300$	−4.82617	−	9.44517i	−0.278639	−	0.545317i
$301$	6.20288	+	35.1783i	0.357528	+	2.02764i
$302$	−9.77486	+	11.9166i	−0.562480	+	0.685721i
$303$	−7.22807	−	25.5640i	−0.415242	−	1.46862i
$304$	−16.1904	+	6.47083i	−0.928582	+	0.371128i
$305$		−	17.5280i		−	1.00365i
$306$	1.09463	−	8.00617i	0.0625756	−	0.457682i
$307$	9.36719	−	1.65169i	0.534614	−	0.0942668i	0.100178	−	0.994970i	$-0.468059\pi$
$307$	9.36719	−	1.65169i	0.534614	−	0.0942668i	0.434436	+	0.900703i	$0.356948\pi$
$308$	−28.0032	+	5.58422i	−1.59563	+	0.318191i
$309$	8.67103	+	5.89550i	0.493278	+	0.335383i
$310$	−3.75059	+	6.66678i	−0.213019	+	0.378648i
$311$	2.46391	−	4.26763i	0.139716	−	0.241995i	−0.787673	−	0.616093i	$-0.788714\pi$
$311$	2.46391	−	4.26763i	0.139716	−	0.241995i	0.927389	+	0.374098i	$0.122048\pi$
$312$	−1.27197	+	5.83589i	−0.0720110	+	0.330392i
$313$	30.2105	−	10.9957i	1.70760	−	0.621516i	0.710946	−	0.703247i	$-0.248267\pi$
$313$	30.2105	−	10.9957i	1.70760	−	0.621516i	0.996654	+	0.0817311i	$0.0260449\pi$
$314$	34.3215	−	0.382678i	1.93687	−	0.0215958i
$315$	−14.0379	−	7.59795i	−0.790949	−	0.428096i
$316$	−11.1969	−	28.7517i	−0.629875	−	1.61741i
$317$	1.47393	+	0.259894i	0.0827843	+	0.0145971i	0.214887	−	0.976639i	$-0.431062\pi$
$317$	1.47393	+	0.259894i	0.0827843	+	0.0145971i	−0.132103	+	0.991236i	$0.542173\pi$
$318$	−11.8268	−	16.0258i	−0.663211	−	0.898680i
$319$	−13.4881	+	16.0745i	−0.755189	+	0.900000i
$320$	3.10106	−	10.6968i	0.173354	−	0.597969i
$321$	20.7167	+	1.52574i	1.15629	+	0.0851583i
$322$	−12.0793	+	34.3753i	−0.673153	+	1.91566i
$323$	2.94407	−	7.76253i	0.163812	−	0.431919i
$324$	16.3885	−	7.44425i	0.910473	−	0.413569i
$325$	−3.50798	−	1.27680i	−0.194588	−	0.0708242i
$326$	4.45130	+	0.733811i	0.246535	+	0.0406420i
$327$	0.797542	+	0.358632i	0.0441042	+	0.0198324i
$328$	−4.01842	+	12.3063i	−0.221880	+	0.679502i
$329$	19.9514	+	3.51796i	1.09995	+	0.193952i
$330$	−10.6136	−	7.04452i	−0.584259	−	0.387788i
$331$	−6.89423	+	3.98038i	−0.378941	+	0.218782i	−0.677357	−	0.735654i	$-0.736875\pi$
$331$	−6.89423	+	3.98038i	−0.378941	+	0.218782i	0.298416	+	0.954436i	$0.403542\pi$
$332$	27.2172	+	9.22438i	1.49374	+	0.506254i
$333$	−6.57274	+	8.28554i	−0.360184	+	0.454045i
$334$	0.189693	+	1.00983i	0.0103795	+	0.0552554i
$335$	7.07309	−	12.2509i	0.386444	−	0.669341i
$336$	8.33321	+	25.1338i	0.454614	+	1.37116i
$337$	22.5514	−	18.9228i	1.22845	−	1.03079i	0.230113	−	0.973164i	$-0.426091\pi$
$337$	22.5514	−	18.9228i	1.22845	−	1.03079i	0.998338	−	0.0576286i	$-0.0183539\pi$
$338$	−8.29800	−	14.0095i	−0.451351	−	0.762015i
$339$	−14.2793	+	6.89918i	−0.775546	+	0.374712i
$340$	2.75328	+	4.53233i	0.149317	+	0.245800i
$341$		−	14.5139i		−	0.785972i
$342$	18.1255	−	3.66943i	0.980117	−	0.198420i
$343$			2.32103i			0.125324i
$344$	25.8656	−	5.45848i	1.39458	−	0.294301i
$345$	−14.6358	+	7.07144i	−0.787968	+	0.380713i
$346$	3.68705	−	2.18389i	0.198217	−	0.117407i
$347$	18.5099	−	15.5316i	0.993662	−	0.833781i	0.00756787	−	0.999971i	$-0.497591\pi$
$347$	18.5099	−	15.5316i	0.993662	−	0.833781i	0.986094	+	0.166190i	$0.0531466\pi$
$348$	16.3315	+	10.5793i	0.875462	+	0.567109i
$349$	−7.22664	+	12.5169i	−0.386833	+	0.670015i	−0.992022	−	0.126067i	$-0.959764\pi$
$349$	−7.22664	+	12.5169i	−0.386833	+	0.670015i	0.605188	+	0.796082i	$0.293098\pi$
$350$	−16.2653	+	3.05537i	−0.869415	+	0.163316i
$351$	2.43830	−	5.84720i	0.130147	−	0.312100i
$352$	4.82332	+	20.5739i	0.257084	+	1.09660i
$353$	−13.1263	+	7.57847i	−0.698642	+	0.403361i	−0.806842	−	0.590768i	$-0.798825\pi$
$353$	−13.1263	+	7.57847i	−0.698642	+	0.403361i	0.108199	+	0.994129i	$0.465492\pi$
$354$	−2.09283	+	3.15315i	−0.111233	+	0.167588i
$355$	4.12406	+	0.727182i	0.218882	+	0.0385948i
$356$	−0.0269153	−	1.20683i	−0.00142651	−	0.0639620i
$357$	−11.4992	−	5.17085i	−0.608600	−	0.273670i
$358$	−0.243938	+	1.47973i	−0.0128925	+	0.0782062i
$359$	−6.90602	−	2.51359i	−0.364486	−	0.132662i	0.153283	−	0.988182i	$-0.451015\pi$
$359$	−6.90602	−	2.51359i	−0.364486	−	0.132662i	−0.517769	+	0.855520i	$0.673237\pi$
$360$	−5.27229	+	10.5710i	−0.277874	+	0.557140i
$361$	18.9931	+	0.510660i	0.999639	+	0.0268769i
$362$	−14.1026	−	4.95556i	−0.741214	−	0.260459i
$363$	5.10394	+	0.375893i	0.267888	+	0.0197293i
$364$	8.17285	+	4.47866i	0.428374	+	0.234745i
$365$	−4.23062	+	5.04186i	−0.221441	+	0.263903i
$366$	24.8147	−	18.3128i	1.29708	−	0.957227i
$367$	−13.0305	−	2.29762i	−0.680184	−	0.119935i	−0.177127	−	0.984188i	$-0.556680\pi$
$367$	−13.0305	−	2.29762i	−0.680184	−	0.119935i	−0.503057	+	0.864253i	$0.667792\pi$
$368$	25.7241	+	8.08352i	1.34096	+	0.421383i
$369$	6.53592	−	12.0758i	0.340247	−	0.628639i
$370$	−0.0773824	−	6.94024i	−0.00402292	−	0.360806i
$371$	−29.2028	+	10.6289i	−1.51613	+	0.551828i
$372$	−13.3568	+	1.65552i	−0.692519	+	0.0858348i
$373$	−16.1032	+	27.8915i	−0.833790	+	1.44417i	0.0612224	+	0.998124i	$0.480500\pi$
$373$	−16.1032	+	27.8915i	−0.833790	+	1.44417i	−0.895012	+	0.446042i	$0.852833\pi$
$374$	−8.76953	−	4.93355i	−0.453462	−	0.255108i
$375$	−16.0758	−	10.9300i	−0.830148	−	0.564424i
$376$	2.10824	−	14.8438i	0.108724	−	0.765509i
$377$	6.74457	−	1.18925i	0.347363	−	0.0612495i
$378$	−3.90998	−	27.8120i	−0.201107	−	1.43049i
$379$			32.4145i			1.66502i	0.554010	+	0.832510i	$0.313097\pi$
$379$			32.4145i			1.66502i	−0.554010	+	0.832510i	$0.686903\pi$
$380$	−7.71854	+	9.36586i	−0.395953	+	0.480458i
$381$	0.638107	+	2.25684i	0.0326912	+	0.115621i
$382$	21.8301	+	17.9067i	1.11693	+	0.916187i
$383$	0.739335	+	4.19298i	0.0377782	+	0.214251i	0.997853	−	0.0654922i	$-0.0208618\pi$
$383$	0.739335	+	4.19298i	0.0377782	+	0.214251i	−0.960075	+	0.279743i	$0.909751\pi$
$384$	18.3836	−	6.78556i	0.938133	−	0.346274i
$385$	−15.2261	+	12.7762i	−0.775991	+	0.651134i
$386$	−15.5408	+	27.6241i	−0.791003	+	1.40603i
$387$	−28.0282	+	0.771061i	−1.42475	+	0.0391953i
$388$	2.54026	−	16.5574i	0.128962	−	0.840575i
$389$	−0.925852	−	2.54376i	−0.0469426	−	0.128974i	0.914006	−	0.405701i	$-0.132972\pi$
$389$	−0.925852	−	2.54376i	−0.0469426	−	0.128974i	−0.960949	+	0.276727i	$0.910750\pi$
$390$	1.17572	+	3.98790i	0.0595351	+	0.201935i
$391$	−11.1191	+	6.41962i	−0.562317	+	0.324654i
$392$	21.5046	−	0.719556i	1.08615	−	0.0363431i
$393$	2.81497	+	27.7711i	0.141996	+	1.40087i
$394$	2.97396	+	7.89585i	0.149826	+	0.397787i
$395$	−16.4527	−	13.8055i	−0.827826	−	0.694628i
$396$	−1.11578	−	22.3858i	−0.0560701	−	1.12493i
$397$	−8.37983	−	3.05001i	−0.420572	−	0.153076i	0.123061	−	0.992399i	$-0.460729\pi$
$397$	−8.37983	−	3.05001i	−0.420572	−	0.153076i	−0.543632	+	0.839324i	$0.682951\pi$
$398$	4.63605	−	13.1933i	0.232384	−	0.661319i
$399$	2.50593	−	28.7461i	0.125453	−	1.43910i
$400$	2.66240	+	11.9547i	0.133120	+	0.597737i
$401$	0.689475	−	1.89432i	0.0344308	−	0.0945977i	−0.921286	−	0.388885i	$-0.872860\pi$
$401$	0.689475	−	1.89432i	0.0344308	−	0.0945977i	0.955717	+	0.294288i	$0.0950824\pi$
$402$	24.7337	−	2.78601i	1.23361	−	0.138954i
$403$	−3.04488	+	3.62875i	−0.151676	+	0.180761i
$404$	0.683980	+	30.6684i	0.0340293	+	1.52581i
$405$	7.51387	−	10.0263i	0.373367	−	0.498213i
$406$	23.0392	−	19.7741i	1.14342	−	0.981370i
$407$	6.58461	+	11.4049i	0.326387	+	0.565318i
$408$	−3.53995	+	8.63315i	−0.175254	+	0.427405i
$409$	8.09198	−	2.94524i	0.400123	−	0.145633i	−0.134118	−	0.990965i	$-0.542820\pi$
$409$	8.09198	−	2.94524i	0.400123	−	0.145633i	0.534240	+	0.845333i	$0.320598\pi$
$410$	1.66363	+	8.85636i	0.0821610	+	0.437385i
$411$	13.5886	+	3.44149i	0.670275	+	0.169756i
$412$	−7.98742	−	9.09906i	−0.393512	−	0.448278i
$413$	3.79563	+	4.52345i	0.186771	+	0.222584i
$414$	−25.3024	−	13.3322i	−1.24354	−	0.655241i
$415$	19.6999	−	3.47363i	0.967031	−	0.170514i
$416$	3.11030	−	6.15577i	0.152495	−	0.301811i
$417$	2.38507	+	8.43547i	0.116798	+	0.413087i
$418$	4.05068	−	22.6688i	0.198125	−	1.10876i
$419$	3.42935			0.167535			0.0837674	−	0.996485i	$-0.473305\pi$
$419$	3.42935			0.167535			0.0837674	+	0.996485i	$0.473305\pi$
$420$	13.4944	+	12.5549i	0.658459	+	0.612616i
$421$	0.345644	+	1.96024i	0.0168456	+	0.0955364i	0.992071	−	0.125676i	$-0.0401098\pi$
$421$	0.345644	+	1.96024i	0.0168456	+	0.0955364i	−0.975226	+	0.221212i	$0.928999\pi$
$422$	8.85287	−	5.24367i	0.430951	−	0.255258i
$423$	−5.02588	+	15.0871i	−0.244367	+	0.733560i
$424$	8.58427	+	21.3363i	0.416889	+	1.03618i
$425$	−5.05048	−	2.91589i	−0.244984	−	0.141442i
$426$	3.27924	+	6.59825i	0.158880	+	0.319686i
$427$	−16.4581	−	45.2184i	−0.796465	−	2.18827i
$428$	−22.7172	−	7.69922i	−1.09808	−	0.372156i
$429$	−5.65428	−	5.50087i	−0.272991	−	0.265584i
$430$	13.9632	−	11.9843i	0.673366	−	0.577937i
$431$	0.968075	−	5.49023i	0.0466305	−	0.264455i	−0.952575	−	0.304303i	$-0.901576\pi$
$431$	0.968075	−	5.49023i	0.0466305	−	0.264455i	0.999206	+	0.0398484i	$0.0126875\pi$
$432$	−20.4739	+	3.58026i	−0.985052	+	0.172255i
$433$	−8.91930	−	7.48418i	−0.428634	−	0.359667i	0.402802	−	0.915287i	$-0.368036\pi$
$433$	−8.91930	−	7.48418i	−0.428634	−	0.359667i	−0.831436	+	0.555620i	$0.812481\pi$
$434$	−3.41584	+	20.7205i	−0.163966	+	0.994616i
$435$	13.5082	+	0.994843i	0.647667	+	0.0476991i
$436$	−0.787790	−	0.631644i	−0.0377283	−	0.0302502i
$437$	−22.2533	−	19.1883i	−1.06452	−	0.917899i
$438$	−11.5579	−	0.721751i	−0.552258	−	0.0344866i
$439$	−8.99427	+	24.7115i	−0.429273	+	1.17942i	0.516982	+	0.855996i	$0.327055\pi$
$439$	−8.99427	+	24.7115i	−0.429273	+	1.17942i	−0.946255	+	0.323422i	$0.895167\pi$
$440$	9.82652	+	10.9455i	0.468461	+	0.521807i
$441$	−22.5756	−	3.34341i	−1.07503	−	0.159210i
$442$	1.15753	+	3.07325i	0.0550583	+	0.146180i
$443$	5.28840	−	29.9920i	0.251260	−	1.42496i	−0.554235	−	0.832361i	$-0.686989\pi$
$443$	5.28840	−	29.9920i	0.251260	−	1.42496i	0.805494	−	0.592604i	$-0.201900\pi$
$444$	9.74458	−	7.36056i	0.462457	−	0.349317i
$445$	−0.420129	−	0.727684i	−0.0199160	−	0.0344956i
$446$	−0.271839	−	24.3806i	−0.0128719	−	1.15445i
$447$	10.1919	+	14.1377i	0.482062	+	0.668692i
$448$	−2.04386	−	30.5072i	−0.0965634	−	1.44133i
$449$	−16.5407	−	9.54980i	−0.780605	−	0.450683i	0.0560393	−	0.998429i	$-0.482153\pi$
$449$	−16.5407	−	9.54980i	−0.780605	−	0.450683i	−0.836645	+	0.547746i	$0.815486\pi$
$450$	−0.501994	−	12.9809i	−0.0236642	−	0.611924i
$451$	−10.9903	−	13.0978i	−0.517515	−	0.616751i
$452$	17.9584	−	3.58116i	0.844694	−	0.168443i
$453$	−16.9967	+	8.21212i	−0.798577	+	0.385839i
$454$	−24.1292	−	19.7926i	−1.13244	−	0.928914i
$455$	6.48712			0.304121
$456$	−21.3236	−	1.14205i	−0.998569	−	0.0534813i
$457$	−15.0149			−0.702368			−0.351184	−	0.936307i	$-0.614221\pi$
$457$	−15.0149			−0.702368			−0.351184	+	0.936307i	$0.614221\pi$
$458$	6.50621	+	5.33688i	0.304015	+	0.249376i
$459$	5.33735	−	8.33415i	0.249126	−	0.389005i
$460$	18.4068	−	3.67057i	0.858223	−	0.171141i
$461$	17.1425	+	20.4296i	0.798405	+	0.951502i	0.999607	−	0.0280475i	$-0.00892896\pi$
$461$	17.1425	+	20.4296i	0.798405	+	0.951502i	−0.201201	+	0.979550i	$0.564485\pi$
$462$	−33.9953	−	8.20755i	−1.58161	−	0.381850i
$463$	−7.17015	−	4.13969i	−0.333225	−	0.192387i	0.324047	−	0.946041i	$-0.394956\pi$
$463$	−7.17015	−	4.13969i	−0.333225	−	0.192387i	−0.657272	+	0.753653i	$0.728290\pi$
$464$	−15.1958	−	16.5512i	−0.705446	−	0.768370i
$465$	−7.59963	+	5.47859i	−0.352424	+	0.254063i
$466$	0.429050	+	38.4805i	0.0198754	+	1.78257i
$467$	5.66423	+	9.81073i	0.262109	+	0.453986i	0.966802	−	0.255526i	$-0.0822486\pi$
$467$	5.66423	+	9.81073i	0.262109	+	0.453986i	−0.704693	+	0.709512i	$0.748915\pi$
$468$	−4.41738	+	5.83096i	−0.204193	+	0.269536i
$469$	6.74383	−	38.2461i	0.311401	−	1.76604i
$470$	−3.67848	−	9.76633i	−0.169675	−	0.450487i
$471$	38.3398	+	17.2403i	1.76660	+	0.794391i
$472$	3.25176	−	2.91933i	0.149675	−	0.134373i
$473$	−11.9413	+	32.8084i	−0.549061	+	1.50853i
$474$	2.35524	−	37.7161i	0.108180	−	1.73236i
$475$	2.49404	−	13.1114i	0.114434	−	0.601594i
$476$	11.3586	+	9.10720i	0.520618	+	0.417428i
$477$	−4.89492	−	23.8974i	−0.224123	−	1.09419i
$478$	2.23783	−	13.5747i	0.102356	−	0.620891i
$479$	14.0355	+	11.7772i	0.641299	+	0.538114i	0.904417	−	0.426650i	$-0.140306\pi$
$479$	14.0355	+	11.7772i	0.641299	+	0.538114i	−0.263118	+	0.964764i	$0.584751\pi$
$480$	8.95207	−	10.2916i	0.408604	−	0.469746i
$481$	0.746361	−	4.23282i	0.0340311	−	0.193000i
$482$	7.25460	−	6.22648i	0.330438	−	0.283608i
$483$	−31.1175	+	31.9853i	−1.41589	+	1.45538i
$484$	−5.59679	−	1.89685i	−0.254399	−	0.0862202i
$485$	−3.98798	−	10.9569i	−0.181085	−	0.497527i
$486$	22.0448	+	0.162230i	0.999973	+	0.00735892i
$487$	−20.0666	−	11.5855i	−0.909305	−	0.524987i	−0.0290974	−	0.999577i	$-0.509263\pi$
$487$	−20.0666	−	11.5855i	−0.909305	−	0.524987i	−0.880207	+	0.474589i	$0.842597\pi$
$488$	−33.0377	+	13.2921i	−1.49555	+	0.601705i
$489$	4.56921	+	3.10664i	0.206627	+	0.140487i
$490$	12.8864	−	7.63278i	0.582148	−	0.344814i
$491$	2.84650	+	16.1433i	0.128461	+	0.728536i	0.979192	+	0.202935i	$0.0650482\pi$
$491$	2.84650	+	16.1433i	0.128461	+	0.728536i	−0.850732	+	0.525600i	$0.823841\pi$
$492$	−10.8000	+	11.6082i	−0.486901	+	0.523337i
$493$	10.6987			0.481847
$494$	−5.76844	+	4.81782i	−0.259534	+	0.216764i
$495$	−8.16942	−	13.2918i	−0.367188	−	0.597421i
$496$	15.4101	+	2.01367i	0.691936	+	0.0904165i
$497$	11.3220	−	1.99637i	0.507859	−	0.0895493i
$498$	25.4997	+	24.2604i	1.14267	+	1.08713i
$499$	−0.220363	−	0.262618i	−0.00986478	−	0.0117564i	0.761089	−	0.648647i	$-0.224665\pi$
$499$	−0.220363	−	0.262618i	−0.00986478	−	0.0117564i	−0.770954	+	0.636890i	$0.780220\pi$
$500$	14.8084	+	16.8693i	0.662250	+	0.754418i
$501$	−0.308956	+	1.21990i	−0.0138031	+	0.0545011i
$502$	2.61989	+	13.9470i	0.116931	+	0.622485i
$503$	−10.9632	+	3.99027i	−0.488824	+	0.177917i	−0.574661	−	0.818392i	$-0.694866\pi$
$503$	−10.9632	+	3.99027i	−0.488824	+	0.177917i	0.0858365	+	0.996309i	$0.472644\pi$
$504$	−3.67557	+	32.2213i	−0.163723	+	1.43525i
$505$	10.6765	+	18.4922i	0.475096	+	0.822891i
$506$	−27.0240	+	23.1941i	−1.20136	+	1.03111i
$507$	−2.01108	−	19.8403i	−0.0893151	−	0.881140i
$508$	−0.0603830	−	2.70747i	−0.00267906	−	0.120124i
$509$	−19.8631	+	23.6719i	−0.880415	+	1.04924i	0.118003	+	0.993013i	$0.462351\pi$
$509$	−19.8631	+	23.6719i	−0.880415	+	1.04924i	−0.998418	+	0.0562243i	$0.982094\pi$
$510$	0.726991	+	6.45410i	0.0321917	+	0.285792i
$511$	−6.17996	+	16.9793i	−0.273385	+	0.751119i
$512$	−22.5136	+	2.26672i	−0.994970	+	0.100176i
$513$	22.0323	+	5.25141i	0.972750	+	0.231855i
$514$	−1.30612	+	3.71696i	−0.0576105	+	0.163948i
$515$	−7.91951	−	2.88246i	−0.348975	−	0.127017i
$516$	31.5549	+	7.24703i	1.38913	+	0.319033i
$517$	15.1688	+	12.7281i	0.667123	+	0.559783i
$518$	−6.71626	−	17.8316i	−0.295096	−	0.783477i
$519$	5.22164	−	0.529281i	0.229204	−	0.0232329i
$520$	−0.160547	−	4.79810i	−0.00704045	−	0.210411i
$521$	−14.8704	+	8.58542i	−0.651483	+	0.376134i	−0.789024	−	0.614362i	$-0.789413\pi$
$521$	−14.8704	+	8.58542i	−0.651483	+	0.376134i	0.137541	+	0.990496i	$0.456080\pi$
$522$	12.7046	+	20.1632i	0.556066	+	0.882518i
$523$	6.38353	+	17.5386i	0.279132	+	0.766910i	0.997462	+	0.0712064i	$0.0226849\pi$
$523$	6.38353	+	17.5386i	0.279132	+	0.766910i	−0.718329	+	0.695703i	$0.755093\pi$
$524$	4.88783	−	31.8589i	0.213526	−	1.39176i
$525$	−19.6489	−	4.97634i	−0.857546	−	0.217185i
$526$	2.31813	−	4.12055i	0.101075	−	0.179664i
$527$	−5.66875	+	4.75664i	−0.246935	+	0.207203i
$528$	−5.22926	+	25.3472i	−0.227574	+	1.10310i
$529$	3.89703	+	22.1011i	0.169436	+	0.960919i
$530$	12.3773	+	10.1528i	0.537638	+	0.441011i
$531$	−3.94880	+	2.42702i	−0.171363	+	0.105324i
$532$	−11.1180	+	31.4093i	−0.482025	+	1.36177i
$533$			5.58037i			0.241713i
$534$	0.591256	−	1.35505i	0.0255861	−	0.0586389i
$535$	−16.4427	+	2.89930i	−0.710881	+	0.125348i
$536$	−28.4551	−	4.04143i	−1.22907	−	0.174563i
$537$	−1.03273	+	1.51892i	−0.0445655	+	0.0655464i
$538$	3.44314	+	1.93704i	0.148444	+	0.0835117i
$539$	−14.2089	+	24.6106i	−0.612021	+	1.06005i
$540$	−11.3003	+	9.03426i	−0.486287	+	0.388773i
$541$	15.4414	−	5.62020i	0.663877	−	0.241631i	0.0119675	−	0.999928i	$-0.496191\pi$
$541$	15.4414	−	5.62020i	0.663877	−	0.241631i	0.651909	+	0.758297i	$0.273968\pi$
$542$	0.0469393	+	4.20988i	0.00201622	+	0.180830i
$543$	−13.1221	−	12.7660i	−0.563121	−	0.547843i
$544$	6.45489	−	8.62657i	0.276751	−	0.369861i
$545$	−0.692183	−	0.122051i	−0.0296499	−	0.00522807i
$546$	6.77760	+	9.18395i	0.290055	+	0.393037i
$547$	26.5167	−	31.6013i	1.13377	−	1.35118i	0.205769	−	0.978601i	$-0.434030\pi$
$547$	26.5167	−	31.6013i	1.13377	−	1.35118i	0.928002	−	0.372575i	$-0.121525\pi$
$548$	−14.1946	−	7.77851i	−0.606362	−	0.332281i
$549$	37.0033	−	7.57942i	1.57926	−	0.323482i
$550$	−15.2611	−	5.36266i	−0.650735	−	0.228665i
$551$	8.06437	+	23.1188i	0.343554	+	0.984895i
$552$	24.4275	+	22.2240i	1.03971	+	0.945915i
$553$	−55.4073	−	20.1666i	−2.35616	−	0.857571i
$554$	−2.83706	+	17.2096i	−0.120535	+	0.731167i
$555$	3.48621	−	7.75279i	0.147981	−	0.329087i
$556$	−0.225695	−	10.1198i	−0.00957162	−	0.429174i
$557$	−35.4027	−	6.24245i	−1.50006	−	0.264501i	−0.637499	−	0.770451i	$-0.720031\pi$
$557$	−35.4027	−	6.24245i	−1.50006	−	0.264501i	−0.862563	+	0.505950i	$0.831142\pi$
$558$	−15.6961	−	5.03504i	−0.664468	−	0.213150i
$559$	9.86845	−	5.69755i	0.417391	−	0.240981i
$560$	−11.4526	−	17.9388i	−0.483962	−	0.758055i
$561$	−7.20658	−	9.99661i	−0.304262	−	0.422057i
$562$	−18.0140	+	3.38385i	−0.759873	+	0.142739i
$563$	8.48791	−	14.7015i	0.357723	−	0.619594i	−0.629857	−	0.776711i	$-0.716887\pi$
$563$	8.48791	−	14.7015i	0.357723	−	0.619594i	0.987580	+	0.157117i	$0.0502200\pi$
$564$	9.98320	−	15.4113i	0.420369	−	0.648934i
$565$	9.76445	−	8.19335i	0.410794	−	0.344697i
$566$	−28.3267	+	16.7783i	−1.19066	+	0.705243i
$567$	9.96977	−	32.9210i	0.418691	−	1.38255i
$568$	−1.75678	−	8.32471i	−0.0737130	−	0.349297i
$569$		−	4.31942i		−	0.181080i	−0.995893	−	0.0905398i	$-0.971141\pi$
$569$		−	4.31942i		−	0.181080i	0.995893	−	0.0905398i	$-0.0288592\pi$
$570$	−13.3986	+	6.43584i	−0.561206	+	0.269568i
$571$			31.4506i			1.31617i	0.752945	+	0.658084i	$0.228633\pi$
$571$			31.4506i			1.31617i	−0.752945	+	0.658084i	$0.771367\pi$
$572$	4.72926	+	7.78511i	0.197740	+	0.325512i
$573$	15.0439	+	31.1366i	0.628468	+	1.30075i
$574$	12.6076	+	21.2854i	0.526232	+	0.888435i
$575$	−15.8116	+	13.2675i	−0.659388	+	0.553292i
$576$	23.9230	+	1.92115i	0.996791	+	0.0800478i
$577$	−15.0209	+	26.0170i	−0.625329	+	1.08310i	0.363149	+	0.931731i	$0.381702\pi$
$577$	−15.0209	+	26.0170i	−0.625329	+	1.08310i	−0.988477	+	0.151370i	$0.951632\pi$
$578$	−3.49137	−	18.5863i	−0.145222	−	0.773090i
$579$	−31.4894	+	22.7008i	−1.30866	+	0.943413i
$580$	−14.8125	−	5.02021i	−0.615057	−	0.208453i
$581$	47.5599	−	27.4587i	1.97312	−	1.13918i
$582$	11.3453	−	17.0934i	0.470279	−	0.708544i
$583$	−29.9134	−	5.27455i	−1.23889	−	0.218449i
$584$	12.7114	+	4.15070i	0.526002	+	0.171757i
$585$	−0.745981	+	5.03706i	−0.0308425	+	0.208257i
$586$	−44.2622	−	7.29675i	−1.82845	−	0.301426i
$587$	−8.89614	−	3.23793i	−0.367183	−	0.133644i	0.151837	−	0.988405i	$-0.451481\pi$
$587$	−8.89614	−	3.23793i	−0.367183	−	0.133644i	−0.519021	+	0.854762i	$0.673703\pi$
$588$	24.2693	+	10.2690i	1.00085	+	0.423485i
$589$	−14.5515	−	8.66414i	−0.599585	−	0.357000i
$590$	1.00843	−	2.86980i	0.0415165	−	0.118148i
$591$	−0.758989	+	10.3057i	−0.0312206	+	0.423919i
$592$	−13.0227	+	5.40889i	−0.535229	+	0.222304i
$593$	24.1703	−	28.8050i	0.992555	−	1.18288i	0.00942808	−	0.999956i	$-0.496999\pi$
$593$	24.1703	−	28.8050i	0.992555	−	1.18288i	0.983127	−	0.182925i	$-0.0585567\pi$
$594$	10.2822	−	25.4526i	0.421883	−	1.04433i
$595$	9.98008	+	1.75976i	0.409143	+	0.0721430i
$596$	−7.30298	−	18.7528i	−0.299142	−	0.768145i
$597$	11.9429	−	12.2760i	0.488791	−	0.502423i
$598$	11.6224	−	0.129588i	0.475277	−	0.00529924i
$599$	18.2661	−	6.64831i	0.746332	−	0.271642i	0.0592703	−	0.998242i	$-0.481123\pi$
$599$	18.2661	−	6.64831i	0.746332	−	0.271642i	0.687061	+	0.726599i	$0.258900\pi$
$600$	−3.19439	+	14.6561i	−0.130410	+	0.598334i
$601$	9.82681	−	17.0205i	0.400844	−	0.694282i	−0.592984	−	0.805214i	$-0.702050\pi$
$601$	9.82681	−	17.0205i	0.400844	−	0.694282i	0.993828	+	0.110932i	$0.0353836\pi$
$602$	24.7692	−	44.0280i	1.00952	−	1.79445i
$603$	28.9215	+	9.63447i	1.17778	+	0.392346i
$604$	21.3760	−	4.26267i	0.869778	−	0.173445i
$605$	−4.05097	+	0.714295i	−0.164695	+	0.0290402i
$606$	−15.0252	+	34.4351i	−0.610357	+	1.39883i
$607$			28.9741i			1.17602i	0.808853	+	0.588011i	$0.200089\pi$
$607$			28.9741i			1.17602i	−0.808853	+	0.588011i	$0.799911\pi$
$608$	23.5066	+	7.44589i	0.953317	+	0.301971i
$609$	35.7822	−	10.1172i	1.44997	−	0.409970i
$610$	−15.7209	+	19.1654i	−0.636521	+	0.775984i
$611$	−1.12224	−	6.36455i	−0.0454010	−	0.257482i
$612$	−8.37765	+	7.77231i	−0.338646	+	0.314177i
$613$	−10.4108	+	8.73571i	−0.420489	+	0.352832i	−0.828349	−	0.560212i	$-0.810720\pi$
$613$	−10.4108	+	8.73571i	−0.420489	+	0.352832i	0.407860	+	0.913044i	$0.366275\pi$
$614$	−11.7237	−	6.59548i	−0.473128	−	0.266172i
$615$	−2.70959	+	10.6987i	−0.109261	+	0.431414i
$616$	35.6277	+	19.0103i	1.43548	+	0.765947i
$617$	14.7558	+	40.5412i	0.594046	+	1.63213i	0.762922	+	0.646491i	$0.223764\pi$
$617$	14.7558	+	40.5412i	0.594046	+	1.63213i	−0.168876	+	0.985637i	$0.554014\pi$
$618$	−4.19336	−	14.2233i	−0.168682	−	0.572146i
$619$	30.5271	−	17.6249i	1.22699	−	0.708403i	0.260591	−	0.965449i	$-0.416083\pi$
$619$	30.5271	−	17.6249i	1.22699	−	0.708403i	0.966399	+	0.257047i	$0.0827494\pi$
$620$	10.0804	−	3.92566i	0.404840	−	0.157658i
$621$	−21.2573	−	27.8399i	−0.853027	−	1.11718i
$622$	−6.52174	+	2.45640i	−0.261498	+	0.0984928i
$623$	−1.76711	−	1.48278i	−0.0707978	−	0.0594064i
$624$	6.62503	−	5.24024i	0.265213	−	0.209777i
$625$	0.296207	+	0.107810i	0.0118483	+	0.00431242i
$626$	−42.8949	−	15.0730i	−1.71442	−	0.602439i
$627$	16.1695	−	23.1077i	0.645747	−	0.922835i
$628$	−37.8710	−	30.3646i	−1.51122	−	1.21168i
$629$	2.29647	−	6.30950i	0.0915662	−	0.251576i
$630$	8.53472	+	20.8984i	0.340031	+	0.832613i
$631$	0.912507	−	1.08748i	0.0363263	−	0.0432920i	−0.747575	−	0.664177i	$-0.768782\pi$
$631$	0.912507	−	1.08748i	0.0363263	−	0.0432920i	0.783902	+	0.620885i	$0.213227\pi$
$632$	−13.5447	+	41.4802i	−0.538778	+	1.64999i
$633$	12.5375	−	1.27084i	0.498321	−	0.0505114i
$634$	−1.37852	−	1.60615i	−0.0547482	−	0.0637883i
$635$	−0.942537	−	1.63252i	−0.0374035	−	0.0647847i
$636$	−1.44199	+	28.1303i	−0.0571785	+	1.11544i
$637$	8.71556	−	3.17221i	0.345323	−	0.125687i
$638$	29.1654	−	5.47861i	1.15467	−	0.216900i
$639$	0.248162	+	9.02075i	0.00981715	+	0.356855i
$640$	−12.9848	+	8.91473i	−0.513267	+	0.352386i
$641$	27.3351	+	32.5767i	1.07967	+	1.28670i	0.955677	+	0.294417i	$0.0951256\pi$
$641$	27.3351	+	32.5767i	1.07967	+	1.28670i	0.123993	+	0.992283i	$0.460430\pi$
$642$	−21.2836	−	20.2492i	−0.839997	−	0.799171i
$643$	42.2474	−	7.44936i	1.66608	−	0.293774i	0.740421	−	0.672143i	$-0.234626\pi$
$643$	42.2474	−	7.44936i	1.66608	−	0.293774i	0.925655	+	0.378369i	$0.123515\pi$
$644$	44.0391	−	26.7526i	1.73538	−	1.05420i
$645$	21.6863	−	6.13167i	0.853898	−	0.241434i
$646$	−10.1813	+	5.84715i	−0.400580	+	0.230053i
$647$	12.3149			0.484147			0.242074	−	0.970258i	$-0.422172\pi$
$647$	12.3149			0.484147			0.242074	+	0.970258i	$0.422172\pi$
$648$	−24.5963	−	6.55924i	−0.966233	−	0.257671i
$649$	1.00222	+	5.68386i	0.0393405	+	0.223111i
$650$	2.69052	+	4.54240i	0.105531	+	0.178168i
$651$	−14.4612	+	21.2693i	−0.566779	+	0.833611i
$652$	−4.20898	−	4.79475i	−0.164836	−	0.187777i
$653$	−4.41759	−	2.55049i	−0.172874	−	0.0998086i	0.411067	−	0.911605i	$-0.365156\pi$
$653$	−4.41759	−	2.55049i	−0.172874	−	0.0998086i	−0.583940	+	0.811797i	$0.698490\pi$
$654$	−0.550388	−	1.10745i	−0.0215219	−	0.0433048i
$655$	−7.67348	−	21.0827i	−0.299828	−	0.823769i
$656$	15.4314	−	9.85181i	0.602495	−	0.384649i
$657$	−12.4733	−	6.75107i	−0.486628	−	0.263384i
$658$	−18.6599	−	21.7411i	−0.727439	−	0.847555i
$659$	−1.68121	+	9.53462i	−0.0654907	+	0.371416i	0.934394	+	0.356241i	$0.115942\pi$
$659$	−1.68121	+	9.53462i	−0.0654907	+	0.371416i	−0.999885	+	0.0151752i	$0.995169\pi$
$660$	5.28684	+	17.2220i	0.205790	+	0.670365i
$661$	7.62780	+	6.40048i	0.296687	+	0.248950i	0.778964	−	0.627069i	$-0.215746\pi$
$661$	7.62780	+	6.40048i	0.296687	+	0.248950i	−0.482277	+	0.876019i	$0.660190\pi$
$662$	11.1083	+	1.83124i	0.431736	+	0.0711730i
$663$	−0.295416	+	4.01121i	−0.0114730	+	0.155783i
$664$	−21.4864	−	34.4974i	−0.833836	−	1.33876i
$665$	3.72002	+	22.8923i	0.144256	+	0.887725i
$666$	14.6181	−	3.16445i	0.566439	−	0.122620i
$667$	12.9510	−	35.5826i	0.501465	−	1.37776i
$668$	0.698307	−	1.27430i	0.0270183	−	0.0493042i
$669$	12.2468	−	27.2350i	0.473489	−	1.05297i
$670$	−18.7218	+	7.05153i	−0.723285	+	0.272424i
$671$	8.16724	−	46.3187i	0.315293	−	1.78811i
$672$	13.4309	−	34.9558i	0.518109	−	1.34845i
$673$	−7.14046	−	12.3676i	−0.275244	−	0.476737i	0.694952	−	0.719056i	$-0.255425\pi$
$673$	−7.14046	−	12.3676i	−0.275244	−	0.476737i	−0.970197	+	0.242318i	$0.922092\pi$
$674$	−41.6300	+	0.464167i	−1.60353	+	0.0178790i
$675$	6.12348	−	14.6845i	0.235693	−	0.565207i
$676$	−3.49198	+	22.7607i	−0.134307	+	0.875412i
$677$	−15.3043	−	8.83595i	−0.588192	−	0.339593i	0.176190	−	0.984356i	$-0.443623\pi$
$677$	−15.3043	−	8.83595i	−0.588192	−	0.339593i	−0.764382	+	0.644763i	$0.776956\pi$
$678$	21.8012	+	5.26350i	0.837269	+	0.202143i
$679$	−20.5763	−	24.5218i	−0.789645	−	0.941062i
$680$	1.05458	−	7.42516i	0.0404415	−	0.284742i
$681$	−16.6283	−	34.4159i	−0.637199	−	1.31882i
$682$	−13.0176	+	15.8698i	−0.498469	+	0.607685i
$683$	27.7201			1.06068			0.530340	−	0.847785i	$-0.322064\pi$
$683$	27.7201			1.06068			0.530340	+	0.847785i	$0.322064\pi$
$684$	−23.1099	−	12.2447i	−0.883630	−	0.468186i
$685$	−11.2668			−0.430482
$686$	2.08174	−	2.53785i	0.0794811	−	0.0968956i
$687$	4.48366	+	9.27989i	0.171062	+	0.354050i
$688$	−33.1776	−	17.2305i	−1.26488	−	0.656908i
$689$	6.37237	+	7.59430i	0.242768	+	0.289320i
$690$	22.3455	+	5.39492i	0.850679	+	0.205381i
$691$	11.7322	+	6.77358i	0.446313	+	0.257679i	0.706272	−	0.707941i	$-0.250376\pi$
$691$	11.7322	+	6.77358i	0.446313	+	0.257679i	−0.259959	+	0.965620i	$0.583709\pi$
$692$	−5.99023	−	0.919029i	−0.227714	−	0.0349362i
$693$	−33.5558	−	26.6191i	−1.27468	−	1.01118i
$694$	−34.1694	+	0.380982i	−1.29705	+	0.0144619i
$695$	−3.52295	−	6.10193i	−0.133633	−	0.231459i
$696$	−8.36859	−	26.2154i	−0.317211	−	0.993692i
$697$	−1.51378	+	8.58508i	−0.0573386	+	0.325183i
$698$	19.1282	−	7.20462i	0.724014	−	0.272699i
$699$	−19.3294	+	42.9857i	−0.731106	+	1.62587i
$700$	20.5251	+	11.2476i	0.775776	+	0.425119i
$701$	0.769575	−	2.11439i	0.0290664	−	0.0798594i	−0.924311	−	0.381641i	$-0.875359\pi$
$701$	0.769575	−	2.11439i	0.0290664	−	0.0798594i	0.953377	+	0.301782i	$0.0975813\pi$
$702$	−7.91045	+	4.20651i	−0.298561	+	0.158765i
$703$	15.3651	+	0.206521i	0.579507	+	0.00778907i
$704$	13.1789	−	26.8220i	0.496700	−	1.01089i
$705$	0.938789	−	12.7471i	0.0353569	−	0.480082i
$706$	21.1497	+	3.48659i	0.795979	+	0.131220i
$707$	44.9064	+	37.6810i	1.68888	+	1.41714i
$708$	5.11642	−	1.57065i	0.192287	−	0.0590285i
$709$	4.29335	−	24.3488i	0.161240	−	0.914438i	−0.791617	−	0.611018i	$-0.790760\pi$
$709$	4.29335	−	24.3488i	0.161240	−	0.914438i	0.952857	−	0.303420i	$-0.0981286\pi$
$710$	−3.85710	−	4.49400i	−0.144755	−	0.168657i
$711$	22.0303	−	40.7031i	0.826200	−	1.52649i
$712$	−1.05298	+	1.34371i	−0.0394622	+	0.0503578i
$713$	8.95785	+	24.6115i	0.335474	+	0.921708i
$714$	7.93564	+	15.9675i	0.296984	+	0.597570i
$715$	5.49110	+	3.17029i	0.205355	+	0.118562i
$716$	1.59390	−	1.39917i	0.0595669	−	0.0522896i
$717$	9.47400	−	13.9342i	0.353813	−	0.520384i
$718$	5.29673	+	8.94244i	0.197672	+	0.333729i
$719$	−2.86184	−	16.2303i	−0.106728	−	0.605287i	−0.990516	−	0.137398i	$-0.956126\pi$
$719$	−2.86184	−	16.2303i	−0.106728	−	0.605287i	0.883787	−	0.467889i	$-0.154985\pi$
$720$	15.2460	−	6.82978i	0.568184	−	0.254531i
$721$	−23.1371			−0.861672
$722$	−20.3094	−	17.5934i	−0.755839	−	0.654758i
$723$	11.2671	−	3.18571i	0.419030	−	0.118478i
$724$	10.9753	+	18.0671i	0.407895	+	0.671460i
$725$	16.9381	−	2.98665i	0.629067	−	0.110921i
$726$	−5.24361	−	4.98876i	−0.194608	−	0.185150i
$727$	26.3438	+	31.3953i	0.977038	+	1.16439i	0.986388	+	0.164433i	$0.0525793\pi$
$727$	26.3438	+	31.3953i	0.977038	+	1.16439i	−0.00934990	+	0.999956i	$0.502976\pi$
$728$	−4.91942	−	12.2273i	−0.182326	−	0.453174i
$729$	24.4158	+	11.5270i	0.904287	+	0.426925i
$730$	9.14790	−	1.71840i	0.338579	−	0.0636007i
$731$	16.7276	−	6.08836i	0.618694	−	0.225186i
$732$	−43.5577	−	2.23281i	−1.60994	−	0.0825270i
$733$	7.24488	+	12.5485i	0.267596	+	0.463489i	0.968240	−	0.250021i	$-0.0804375\pi$
$733$	7.24488	+	12.5485i	0.267596	+	0.463489i	−0.700645	+	0.713510i	$0.747104\pi$
$734$	12.1870	+	14.1993i	0.449830	+	0.524107i
$735$	18.2498	−	1.84986i	0.673154	−	0.0682330i
$736$	−20.8771	−	31.9107i	−0.769539	−	1.17625i
$737$	24.3994	−	29.0781i	0.898765	−	1.07111i
$738$	−17.9773	+	7.34175i	−0.661753	+	0.270254i
$739$	−6.97751	+	19.1706i	−0.256672	+	0.705200i	0.742695	+	0.669630i	$0.233547\pi$
$739$	−6.97751	+	19.1706i	−0.256672	+	0.705200i	−0.999367	+	0.0355708i	$0.988675\pi$
$740$	−6.14012	+	7.65799i	−0.225715	+	0.281513i
$741$	−8.89047	+	2.38516i	−0.326600	+	0.0876212i
$742$	41.4640	+	14.5702i	1.52219	+	0.534890i
$743$	−49.2850	−	17.9383i	−1.80809	−	0.658091i	−0.997355	−	0.0726788i	$-0.976845\pi$
$743$	−49.2850	−	17.9383i	−1.80809	−	0.658091i	−0.810736	−	0.585412i	$-0.800933\pi$
$744$	16.0894	+	10.1696i	0.589867	+	0.372836i
$745$	−10.7310	−	9.00437i	−0.393153	−	0.329895i
$746$	42.6235	−	16.0541i	1.56056	−	0.587781i
$747$	15.8518	+	40.0864i	0.579986	+	1.46669i
$748$	5.16384	+	13.2599i	0.188809	+	0.484829i
$749$	−39.6963	+	22.9187i	−1.45047	+	0.837431i
$750$	7.77433	+	26.3695i	0.283878	+	0.962878i
$751$	−5.35675	−	14.7176i	−0.195471	−	0.537051i	0.802773	−	0.596284i	$-0.203357\pi$
$751$	−5.35675	−	14.7176i	−0.195471	−	0.537051i	−0.998244	+	0.0592327i	$0.981135\pi$
$752$	−15.6186	+	14.3396i	−0.569553	+	0.522910i
$753$	−4.26706	+	16.8483i	−0.155500	+	0.613987i
$754$	−8.44127	−	4.74888i	−0.307413	−	0.172944i
$755$	11.6227	−	9.75258i	0.422992	−	0.354933i
$756$	−20.6694	+	33.9170i	−0.751740	+	1.23355i
$757$	1.42932	+	8.10610i	0.0519496	+	0.294621i	0.999703	−	0.0243840i	$-0.00776243\pi$
$757$	1.42932	+	8.10610i	0.0519496	+	0.294621i	−0.947753	+	0.319005i	$0.896651\pi$
$758$	29.0727	−	35.4426i	1.05597	−	1.28733i
$759$	−41.9711	+	11.8671i	−1.52345	+	0.430747i
$760$	16.8399	−	3.31801i	0.610846	−	0.120357i
$761$			41.7287i			1.51266i	0.654189	+	0.756331i	$0.273010\pi$
$761$			41.7287i			1.51266i	−0.654189	+	0.756331i	$0.726990\pi$
$762$	1.32645	−	3.03999i	0.0480523	−	0.110127i
$763$	−1.90028	+	0.335071i	−0.0687949	+	0.0121304i
$764$	−7.80884	−	39.1590i	−0.282514	−	1.41672i
$765$	−2.51405	+	7.54688i	−0.0908957	+	0.272858i
$766$	2.95230	−	5.24779i	0.106671	−	0.189610i
$767$	0.941848	−	1.63133i	0.0340082	−	0.0589039i
$768$	−26.1869	−	9.06886i	−0.944940	−	0.327244i
$769$	−10.8209	+	3.93850i	−0.390213	+	0.142026i	−0.529673	−	0.848202i	$-0.677685\pi$
$769$	−10.8209	+	3.93850i	−0.390213	+	0.142026i	0.139460	+	0.990228i	$0.455463\pi$
$770$	28.1074	−	0.313393i	1.01292	−	0.0112939i
$771$	−3.36470	+	3.45854i	−0.121177	+	0.124556i
$772$	41.7687	−	16.2662i	1.50329	−	0.585432i
$773$	28.1432	+	4.96240i	1.01224	+	0.178485i	0.655081	−	0.755558i	$-0.272634\pi$
$773$	28.1432	+	4.96240i	1.01224	+	0.178485i	0.357159	+	0.934044i	$0.383745\pi$
$774$	31.3381	+	24.2955i	1.12643	+	0.873285i
$775$	−7.64685	+	9.11316i	−0.274683	+	0.327354i
$776$	−17.6280	+	15.8258i	−0.632807	+	0.568113i
$777$	1.71407	−	23.2739i	0.0614918	−	0.834947i
$778$	−1.26916	+	3.61179i	−0.0455017	+	0.129489i
$779$	−19.6925	+	3.20005i	−0.705556	+	0.114654i
$780$	2.29121	−	5.41495i	0.0820383	−	0.193886i
$781$	10.5592	+	3.84325i	0.377839	+	0.137522i
$782$	17.9156	+	2.95344i	0.640661	+	0.105615i
$783$	3.74097	+	28.9473i	0.133691	+	1.03449i
$784$	−24.1589	−	18.5008i	−0.862819	−	0.660743i
$785$	−33.2749	−	5.86727i	−1.18763	−	0.209412i
$786$	21.8301	−	32.8902i	0.778654	−	1.17316i
$787$	13.2113	−	7.62757i	0.470933	−	0.271893i	−0.245697	−	0.969347i	$-0.579017\pi$
$787$	13.2113	−	7.62757i	0.470933	−	0.271893i	0.716630	+	0.697453i	$0.245684\pi$
$788$	3.83004	−	11.3008i	0.136439	−	0.402575i
$789$	4.69712	−	3.38616i	0.167222	−	0.120550i
$790$	5.60752	+	29.8517i	0.199507	+	1.06207i
$791$	17.4969	−	30.3055i	0.622118	−	1.07754i
$792$	−18.8579	+	25.4778i	−0.670088	+	0.905315i
$793$	−11.7592	+	9.86714i	−0.417582	+	0.350393i
$794$	6.42709	+	10.8508i	0.228089	+	0.385082i
$795$	8.52967	+	17.6540i	0.302516	+	0.626122i
$796$	−16.9022	+	10.2677i	−0.599084	+	0.363928i
$797$			31.0422i			1.09957i	0.835306	+	0.549785i	$0.185291\pi$
$797$			31.0422i			1.09957i	−0.835306	+	0.549785i	$0.814709\pi$
$798$	−28.5225	+	29.1839i	−1.00968	+	1.03310i
$799$		−	10.0959i		−	0.357168i
$800$	7.81114	−	15.4594i	0.276166	−	0.546574i
$801$	1.35454	−	1.20160i	0.0478605	−	0.0424564i
$802$	−2.45291	+	1.45289i	−0.0866151	+	0.0513033i
$803$	−13.5289	+	11.3521i	−0.477426	+	0.400608i
$804$	−29.5431	−	19.1375i	−1.04190	−	0.674927i
$805$	17.9338	−	31.0622i	0.632082	−	1.09480i
$806$	6.58397	−	1.23677i	0.231910	−	0.0435635i
$807$	2.82948	+	3.92492i	0.0996026	+	0.138164i
$808$	26.7588	−	34.1469i	0.941370	−	1.20128i
$809$	−37.0420	+	21.3862i	−1.30233	+	0.751899i	−0.980803	−	0.195002i	$-0.937529\pi$
$809$	−37.0420	+	21.3862i	−1.30233	+	0.751899i	−0.321524	+	0.946901i	$0.604195\pi$
$810$	−17.2085	+	4.22376i	−0.604644	+	0.148408i
$811$	−17.7988	−	3.13841i	−0.625001	−	0.110205i	−0.147827	−	0.989013i	$-0.547228\pi$
$811$	−17.7988	−	3.13841i	−0.625001	−	0.110205i	−0.477174	+	0.878809i	$0.658339\pi$
$812$	−42.9269	+	0.957373i	−1.50644	+	0.0335972i
$813$	−2.11470	+	4.70276i	−0.0741657	+	0.164933i
$814$	3.02935	−	18.3761i	0.106179	−	0.644080i
$815$	−4.17319	−	1.51892i	−0.146180	−	0.0532053i
$816$	11.6138	−	6.26465i	0.406563	−	0.219307i
$817$	25.7650	+	31.5574i	0.901404	+	1.10405i
$818$	−11.4895	−	4.03735i	−0.401722	−	0.141163i
$819$	2.80515	+	13.6950i	0.0980200	+	0.478541i
$820$	6.12426	−	11.1758i	0.213868	−	0.390277i
$821$	−3.02414	+	3.60402i	−0.105543	+	0.125781i	−0.816230	−	0.577727i	$-0.803940\pi$
$821$	−3.02414	+	3.60402i	−0.105543	+	0.125781i	0.710687	+	0.703508i	$0.248384\pi$
$822$	−11.7713	−	15.9506i	−0.410571	−	0.556342i
$823$	−7.08823	−	1.24985i	−0.247080	−	0.0435669i	0.0487364	−	0.998812i	$-0.484481\pi$
$823$	−7.08823	−	1.24985i	−0.247080	−	0.0435669i	−0.295816	+	0.955245i	$0.595592\pi$
$824$	0.572611	+	17.1130i	0.0199478	+	0.596160i
$825$	−14.2000	−	13.8148i	−0.494381	−	0.480968i
$826$	−0.0931047	−	8.35034i	−0.00323953	−	0.290545i
$827$	−40.6769	+	14.8052i	−1.41448	+	0.514827i	−0.932440	−	0.361324i	$-0.882325\pi$
$827$	−40.6769	+	14.8052i	−1.41448	+	0.514827i	−0.482036	+	0.876152i	$0.660102\pi$
$828$	15.7084	+	37.2715i	0.545905	+	1.29527i
$829$	−0.364165	+	0.630753i	−0.0126480	+	0.0219069i	−0.872280	−	0.489007i	$-0.837359\pi$
$829$	−0.364165	+	0.630753i	−0.0126480	+	0.0219069i	0.859632	+	0.510913i	$0.170693\pi$
$830$	−24.6557	−	13.8708i	−0.855814	−	0.481463i
$831$	−12.0109	+	17.6655i	−0.416653	+	0.612808i
$832$	−8.92199	+	3.94118i	−0.309314	+	0.136636i
$833$	14.2689	−	2.51600i	0.494389	−	0.0871741i
$834$	4.95792	−	11.3627i	0.171679	−	0.393457i
$835$		−	1.01147i		−	0.0350032i
$836$	−24.7608	+	21.1534i	−0.856369	+	0.731604i
$837$	−14.8521	−	13.6745i	−0.513363	−	0.472661i
$838$	−3.74972	−	3.07580i	−0.129532	−	0.106252i
$839$	7.68499	+	43.5837i	0.265315	+	1.50468i	0.768136	+	0.640286i	$0.221184\pi$
$839$	7.68499	+	43.5837i	0.265315	+	1.50468i	−0.502821	+	0.864391i	$0.667705\pi$
$840$	−3.49447	−	25.8309i	−0.120571	−	0.891251i
$841$	−1.95599	+	1.64127i	−0.0674478	+	0.0565954i
$842$	1.38022	−	2.45337i	0.0475654	−	0.0845488i
$843$	−21.7613	−	5.51135i	−0.749499	−	0.189821i
$844$	−14.3830	−	2.20665i	−0.495082	−	0.0759561i
$845$	5.48210	+	15.0620i	0.188590	+	0.518147i
$846$	19.0271	−	11.9888i	0.654164	−	0.412183i
$847$	−9.77992	+	5.64644i	−0.336042	+	0.194014i
$848$	9.75047	−	31.0288i	0.334832	−	1.06553i
$849$	−40.1165	+	4.06633i	−1.37679	+	0.139556i
$850$	2.90700	+	7.71808i	0.0997094	+	0.264728i
$851$	−18.2046	−	15.2755i	−0.624047	−	0.523637i
$852$	2.33242	−	10.1558i	0.0799074	−	0.347932i
$853$	15.3423	+	5.58414i	0.525310	+	0.191197i	0.591043	−	0.806640i	$-0.298716\pi$
$853$	15.3423	+	5.58414i	0.525310	+	0.191197i	−0.0657331	+	0.997837i	$0.520939\pi$
$854$	−22.5609	+	64.2039i	−0.772018	+	2.19701i
$855$	−18.2030	+	0.256009i	−0.622529	+	0.00875533i
$856$	17.9339	+	28.7936i	0.612967	+	0.984144i
$857$	−5.25626	+	14.4415i	−0.179550	+	0.493311i	−0.996518	−	0.0833721i	$-0.973431\pi$
$857$	−5.25626	+	14.4415i	−0.179550	+	0.493311i	0.816968	+	0.576683i	$0.195653\pi$
$858$	1.24874	+	11.0861i	0.0426313	+	0.378473i
$859$	−23.0869	+	27.5139i	−0.787715	+	0.938762i	−0.999254	−	0.0386074i	$-0.987708\pi$
$859$	−23.0869	+	27.5139i	−0.787715	+	0.938762i	0.211540	+	0.977369i	$0.432152\pi$
$860$	−26.0165	+	0.580229i	−0.887154	+	0.0197857i
$861$	3.05554	+	30.1445i	0.104133	+	1.02732i
$862$	−5.98272	+	5.13484i	−0.203772	+	0.174893i
$863$	15.9715	+	27.6634i	0.543676	+	0.941674i	0.998689	+	0.0511895i	$0.0163012\pi$
$863$	15.9715	+	27.6634i	0.543676	+	0.941674i	−0.455013	+	0.890485i	$0.650365\pi$
$864$	25.5977	+	14.4484i	0.870852	+	0.491546i
$865$	−3.96405	+	1.44280i	−0.134782	+	0.0490565i
$866$	3.03993	+	16.1831i	0.103301	+	0.549924i
$867$	5.68647	−	22.4528i	0.193123	−	0.762536i
$868$	22.3192	−	19.5925i	0.757565	−	0.665013i
$869$	−37.0446	−	44.1480i	−1.25665	−	1.49762i
$870$	−13.8778	−	13.2033i	−0.470501	−	0.447634i
$871$	−12.2006	+	2.15130i	−0.413403	+	0.0728941i
$872$	0.294859	+	1.39722i	0.00998520	+	0.0473159i
$873$	21.4066	−	13.1570i	0.724505	−	0.445297i
$874$	7.12215	+	40.9399i	0.240910	+	1.38481i
$875$	42.8953			1.45013
$876$	11.9903	+	11.1555i	0.405114	+	0.376910i
$877$	−6.89313	−	39.0929i	−0.232765	−	1.32007i	−0.847271	−	0.531161i	$-0.821756\pi$
$877$	−6.89313	−	39.0929i	−0.232765	−	1.32007i	0.614506	−	0.788912i	$-0.289355\pi$
$878$	31.9984	−	18.9531i	1.07989	−	0.639635i
$879$	−45.4346	−	30.8913i	−1.53247	−	1.04194i
$880$	−0.927415	−	20.7815i	−0.0312632	−	0.700544i
$881$	12.1844	+	7.03468i	0.410504	+	0.237005i	0.691006	−	0.722849i	$-0.257168\pi$
$881$	12.1844	+	7.03468i	0.410504	+	0.237005i	−0.280502	+	0.959853i	$0.590501\pi$
$882$	21.6859	+	23.9039i	0.730202	+	0.804887i
$883$	1.31675	+	3.61775i	0.0443123	+	0.121747i	0.959875	−	0.280428i	$-0.0904765\pi$
$883$	1.31675	+	3.61775i	0.0443123	+	0.121747i	−0.915563	+	0.402175i	$0.868254\pi$
$884$	1.49074	−	4.39854i	0.0501390	−	0.147939i
$885$	2.59782	−	2.67027i	0.0873248	−	0.0897602i
$886$	−32.6824	+	28.0506i	−1.09799	+	0.942379i
$887$	3.21767	−	18.2483i	0.108039	−	0.612719i	−0.881924	−	0.471391i	$-0.843752\pi$
$887$	3.21767	−	18.2483i	0.108039	−	0.612719i	0.989963	−	0.141327i	$-0.0451370\pi$
$888$	−17.2566	−	0.691788i	−0.579094	−	0.0232149i
$889$	−3.96442	−	3.32654i	−0.132962	−	0.111569i
$890$	−0.193287	+	1.17248i	−0.00647898	+	0.0393016i
$891$	24.5277	−	22.9941i	0.821708	−	0.770331i
$892$	−21.5698	+	26.9020i	−0.722211	+	0.900745i
$893$	21.8162	−	7.60999i	0.730051	−	0.254659i
$894$	1.53616	−	24.5996i	0.0513769	−	0.822735i
$895$	0.504928	−	1.38728i	0.0168779	−	0.0463716i
$896$	−25.1272	+	35.1903i	−0.839442	+	1.17562i
$897$	12.9832	+	5.83816i	0.433495	+	0.194930i
$898$	9.52069	+	25.2774i	0.317709	+	0.843517i
$899$	3.78980	−	21.4930i	0.126397	−	0.716832i
$900$	−11.0937	+	14.6437i	−0.369790	+	0.488125i
$901$	7.74344	+	13.4120i	0.257971	+	0.446819i
$902$	0.269587	+	24.1786i	0.00897628	+	0.805061i
$903$	50.1886	−	36.1811i	1.67017	−	1.20403i
$904$	−22.8480	−	12.1913i	−0.759914	−	0.405476i
$905$	12.7433	+	7.35737i	0.423603	+	0.244567i
$906$	25.9500	+	6.26516i	0.862132	+	0.208146i
$907$	−19.5866	−	23.3424i	−0.650362	−	0.775071i	0.335607	−	0.942002i	$-0.391059\pi$
$907$	−19.5866	−	23.3424i	−0.650362	−	0.775071i	−0.985969	+	0.166931i	$0.946614\pi$
$908$	8.63126	+	43.2832i	0.286439	+	1.43640i
$909$	−34.4221	+	30.5354i	−1.14171	+	1.01280i
$910$	−7.09314	−	5.81833i	−0.235135	−	0.192876i
$911$	25.3718			0.840606			0.420303	−	0.907384i	$-0.361924\pi$
$911$	25.3718			0.840606			0.420303	+	0.907384i	$0.361924\pi$
$912$	22.2913	+	20.3740i	0.738139	+	0.674649i
$913$	53.6767			1.77644
$914$	16.4176	+	13.4669i	0.543045	+	0.445446i
$915$	−27.3359	+	13.2076i	−0.903696	+	0.436628i
$916$	−2.32733	−	11.6709i	−0.0768973	−	0.385617i
$917$	−39.5918	−	47.1837i	−1.30744	−	1.55814i
$918$	−13.3109	+	4.32562i	−0.439325	+	0.142767i
$919$	−5.35216	−	3.09007i	−0.176551	−	0.101932i	0.409120	−	0.912481i	$-0.365836\pi$
$919$	−5.35216	−	3.09007i	−0.176551	−	0.101932i	−0.585671	+	0.810549i	$0.699169\pi$
$920$	−23.4185	−	12.4957i	−0.772085	−	0.411971i
$921$	−9.63420	−	13.3641i	−0.317458	−	0.440362i
$922$	−0.420496	−	37.7133i	−0.0138483	−	1.24202i
$923$	−1.83373	−	3.17611i	−0.0603579	−	0.104543i
$924$	29.8097	+	39.4648i	0.980668	+	1.29830i
$925$	1.87439	−	10.6302i	0.0616297	−	0.349519i
$926$	4.12707	+	10.9573i	0.135624	+	0.360081i
$927$	2.66063	−	17.9653i	0.0873867	−	0.590058i
$928$	1.77049	+	31.7265i	0.0581190	+	1.04147i
$929$	5.12892	−	14.0916i	0.168274	−	0.462330i	−0.826678	−	0.562675i	$-0.809772\pi$
$929$	5.12892	−	14.0916i	0.168274	−	0.462330i	0.994953	+	0.100345i	$0.0319946\pi$
$930$	13.2233	+	0.825751i	0.433610	+	0.0270774i
$931$	16.1923	+	28.9371i	0.530680	+	0.948376i
$932$	34.0442	−	42.4601i	1.11515	−	1.39083i
$933$	−8.51220	−	0.626902i	−0.278677	−	0.0205239i
$934$	2.60591	−	15.8075i	0.0852681	−	0.517237i
$935$	7.58774	+	6.36687i	0.248146	+	0.208219i
$936$	10.0599	−	2.41372i	0.328817	−	0.0788949i
$937$	−3.31743	+	18.8141i	−0.108376	+	0.614629i	0.881442	+	0.472291i	$0.156573\pi$
$937$	−3.31743	+	18.8141i	−0.108376	+	0.614629i	−0.989818	+	0.142338i	$0.954538\pi$
$938$	−41.6770	+	35.7705i	−1.36080	+	1.16795i
$939$	−39.9125	−	38.8296i	−1.30250	−	1.26716i
$940$	−4.73735	+	13.9779i	−0.154515	+	0.455910i
$941$	6.70157	+	18.4124i	0.218465	+	0.600228i	0.999712	−	0.0239943i	$-0.00763836\pi$
$941$	6.70157	+	18.4124i	0.218465	+	0.600228i	−0.781247	+	0.624222i	$0.785416\pi$
$942$	−26.4585	−	53.2380i	−0.862065	−	1.73459i
$943$	26.7204	+	15.4270i	0.870135	+	0.502373i
$944$	−6.17389	+	0.275522i	−0.200943	+	0.00896749i
$945$	−1.27165	+	27.6181i	−0.0413668	+	0.898418i
$946$	42.4828	−	25.1631i	1.38124	−	0.818124i
$947$	1.78162	+	10.1041i	0.0578949	+	0.328338i	0.999975	−	0.00704929i	$-0.00224388\pi$
$947$	1.78162	+	10.1041i	0.0578949	+	0.328338i	−0.942080	+	0.335387i	$0.891133\pi$
$948$	−36.4030	+	39.1270i	−1.18231	+	1.27079i
$949$	5.76406			0.187109
$950$	−14.4867	+	12.0994i	−0.470011	+	0.392555i
$951$	−0.705308	−	2.49452i	−0.0228712	−	0.0808902i
$952$	−4.25136	−	20.1455i	−0.137787	−	0.652920i
$953$	−24.0515	+	4.24093i	−0.779106	+	0.137377i	−0.549038	−	0.835797i	$-0.685006\pi$
$953$	−24.0515	+	4.24093i	−0.779106	+	0.137377i	−0.230068	+	0.973175i	$0.573895\pi$
$954$	−16.0815	+	30.5201i	−0.520657	+	0.988125i
$955$	−17.8659	−	21.2917i	−0.578127	−	0.688985i
$956$	−14.6221	+	12.8357i	−0.472911	+	0.415136i
$957$	35.2326	+	8.92313i	1.13891	+	0.288444i
$958$	−4.78367	−	25.4659i	−0.154553	−	0.822766i
$959$	−29.0659	+	10.5791i	−0.938587	+	0.341618i
$960$	−19.0190	+	3.22391i	−0.613834	+	0.104051i
$961$	−7.95227	−	13.7737i	−0.256525	−	0.444314i
$962$	−4.61252	+	3.95883i	−0.148714	+	0.127638i
$963$	−13.2309	−	33.4586i	−0.426358	−	1.07819i
$964$	−13.5169	+	0.301458i	−0.435349	+	0.00970932i
$965$	20.0557	−	23.9015i	0.645616	−	0.769416i
$966$	62.7122	−	7.06391i	2.01773	−	0.227278i
$967$	−3.35236	+	9.21055i	−0.107805	+	0.296191i	−0.981852	−	0.189650i	$-0.939265\pi$
$967$	−3.35236	+	9.21055i	−0.107805	+	0.296191i	0.874047	+	0.485842i	$0.161487\pi$
$968$	4.41834	+	7.09383i	0.142011	+	0.228004i
$969$	−14.3245	+	1.25773i	−0.460170	+	0.0404041i
$970$	−5.46675	+	15.5573i	−0.175527	+	0.499515i
$971$	38.0587	+	13.8522i	1.22136	+	0.444539i	0.870631	−	0.491937i	$-0.163711\pi$
$971$	38.0587	+	13.8522i	1.22136	+	0.444539i	0.350730	+	0.936476i	$0.385933\pi$
$972$	−23.9587	−	19.9495i	−0.768475	−	0.639879i
$973$	−14.8179	−	12.4337i	−0.475041	−	0.398607i
$974$	11.5501	+	30.6656i	0.370090	+	0.982588i
$975$	0.652067	+	6.43298i	0.0208829	+	0.206020i
$976$	48.0458	+	15.0979i	1.53791	+	0.483271i
$977$	−0.179209	+	0.103467i	−0.00573342	+	0.00331019i	−0.502864	−	0.864366i	$-0.667720\pi$
$977$	−0.179209	+	0.103467i	−0.00573342	+	0.00331019i	0.497131	+	0.867676i	$0.334387\pi$
$978$	−2.20970	−	7.49500i	−0.0706583	−	0.239664i
$979$	−0.771148	−	2.11871i	−0.0246460	−	0.0677143i
$980$	−20.9361	−	3.21204i	−0.668779	−	0.102605i
$981$	−0.0416517	−	1.51405i	−0.00132984	−	0.0483398i
$982$	11.3666	−	20.2044i	0.362722	−	0.644748i
$983$	−36.7287	+	30.8190i	−1.17146	+	0.982974i	−0.999998	−	0.00221620i	$-0.999295\pi$
$983$	−36.7287	+	30.8190i	−1.17146	+	0.982974i	−0.171465	+	0.985190i	$0.554850\pi$
$984$	22.2203	−	3.00602i	0.708358	−	0.0958284i
$985$	−1.44228	−	8.17956i	−0.0459548	−	0.260622i
$986$	−11.6982	−	9.59575i	−0.372547	−	0.305591i
$987$	−9.54715	−	33.7661i	−0.303889	−	1.07479i
$988$	10.6284	−	0.0941561i	0.338136	−	0.00299551i
$989$		−	63.0039i		−	2.00341i
$990$	−2.98885	+	21.8607i	−0.0949919	+	0.694777i
$991$	−23.7733	+	4.19188i	−0.755184	+	0.133159i	−0.537969	−	0.842964i	$-0.680808\pi$
$991$	−23.7733	+	4.19188i	−0.755184	+	0.133159i	−0.217215	+	0.976124i	$0.569697\pi$
$992$	−15.0437	−	16.0232i	−0.477637	−	0.508737i
$993$	11.4025	+	7.75267i	0.361848	+	0.246023i
$994$	−14.1702	−	7.97185i	−0.449451	−	0.252852i
$995$	−6.88300	+	11.9217i	−0.218206	+	0.377943i
$996$	−6.12261	−	49.3975i	−0.194002	−	1.56522i
$997$	−24.2528	+	8.82730i	−0.768094	+	0.279563i	−0.696199	−	0.717849i	$-0.745127\pi$
$997$	−24.2528	+	8.82730i	−0.768094	+	0.279563i	−0.0718951	+	0.997412i	$0.522905\pi$
$998$	0.00540538	+	0.484795i	0.000171104	+	0.0153459i
$999$	17.8744	+	4.00729i	0.565522	+	0.126785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.v.a.23.9	yes	216
3.2	odd	2	inner	228.2.v.a.23.28	yes	216
4.3	odd	2	inner	228.2.v.a.23.36	yes	216
12.11	even	2	inner	228.2.v.a.23.1	✓	216
19.5	even	9	inner	228.2.v.a.119.1	yes	216
57.5	odd	18	inner	228.2.v.a.119.36	yes	216
76.43	odd	18	inner	228.2.v.a.119.28	yes	216
228.119	even	18	inner	228.2.v.a.119.9	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.v.a.23.1	✓	216	12.11	even	2	inner
228.2.v.a.23.9	yes	216	1.1	even	1	trivial
228.2.v.a.23.28	yes	216	3.2	odd	2	inner
228.2.v.a.23.36	yes	216	4.3	odd	2	inner
228.2.v.a.119.1	yes	216	19.5	even	9	inner
228.2.v.a.119.9	yes	216	228.119	even	18	inner
228.2.v.a.119.28	yes	216	76.43	odd	18	inner
228.2.v.a.119.36	yes	216	57.5	odd	18	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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09342 - 0.896904i) q^{2} +(-0.753513 - 1.55956i) q^{3} +(0.391126 + 1.96138i) q^{4} +(0.894860 + 1.06645i) q^{5} +(-0.574868 + 2.38108i) q^{6} +(3.30990 + 1.91097i) q^{7} +(1.33151 - 2.49541i) q^{8} +(-1.86444 + 2.35029i) q^{9} +O(q^{10})\)	\(q+(-1.09342 - 0.896904i) q^{2} +(-0.753513 - 1.55956i) q^{3} +(0.391126 + 1.96138i) q^{4} +(0.894860 + 1.06645i) q^{5} +(-0.574868 + 2.38108i) q^{6} +(3.30990 + 1.91097i) q^{7} +(1.33151 - 2.49541i) q^{8} +(-1.86444 + 2.35029i) q^{9} +(-0.0219504 - 1.96868i) q^{10} +(1.86780 + 3.23513i) q^{11} +(2.76417 - 2.08791i) q^{12} +(0.211714 - 1.20069i) q^{13} +(-1.90515 - 5.05816i) q^{14} +(0.988905 - 2.19917i) q^{15} +(-3.69404 + 1.53430i) q^{16} +(0.651421 - 1.78976i) q^{17} +(4.14660 - 0.897634i) q^{18} +(4.35851 + 0.0585821i) q^{19} +(-1.74172 + 2.17228i) q^{20} +(0.486216 - 6.60193i) q^{21} +(0.859311 - 5.21259i) q^{22} +(-5.16396 - 4.33308i) q^{23} +(-4.89505 - 0.196234i) q^{24} +(0.531694 - 3.01539i) q^{25} +(-1.30840 + 1.12297i) q^{26} +(5.07029 + 1.13672i) q^{27} +(-2.45356 + 7.23942i) q^{28} +(1.92121 + 5.27848i) q^{29} +(-3.05373 + 1.51766i) q^{30} +(-3.36476 - 1.94264i) q^{31} +(5.41525 + 1.63557i) q^{32} +(3.63795 - 5.35066i) q^{33} +(-2.31752 + 1.37270i) q^{34} +(0.923938 + 5.23991i) q^{35} +(-5.33905 - 2.73761i) q^{36} +3.52532 q^{37} +(-4.71313 - 3.97322i) q^{38} +(-2.03208 + 0.574556i) q^{39} +(3.85275 - 0.813056i) q^{40} +(-4.50749 + 0.794791i) q^{41} +(-6.45293 + 6.78258i) q^{42} +(6.00767 + 7.15966i) q^{43} +(-5.61478 + 4.92882i) q^{44} +(-4.17489 + 0.114852i) q^{45} +(1.76001 + 9.36945i) q^{46} +(4.98106 - 1.81296i) q^{47} +(5.17633 + 4.60495i) q^{48} +(3.80364 + 6.58811i) q^{49} +(-3.28588 + 2.82020i) q^{50} +(-3.28209 + 0.332683i) q^{51} +(2.43782 - 0.0543693i) q^{52} +(-5.22663 + 6.22885i) q^{53} +(-4.52443 - 5.79047i) q^{54} +(-1.77869 + 4.88691i) q^{55} +(9.17583 - 5.71510i) q^{56} +(-3.19283 - 6.84148i) q^{57} +(2.63360 - 7.49472i) q^{58} +(1.45183 + 0.528424i) q^{59} +(4.70020 + 1.07947i) q^{60} +(-9.64491 - 8.09304i) q^{61} +(1.93672 + 5.14199i) q^{62} +(-10.6625 + 4.21636i) q^{63} +(-4.45418 - 6.64532i) q^{64} +(1.46993 - 0.848667i) q^{65} +(-8.77683 + 2.58761i) q^{66} +(-3.47539 - 9.54855i) q^{67} +(3.76520 + 0.577662i) q^{68} +(-2.86657 + 11.3185i) q^{69} +(3.68945 - 6.55810i) q^{70} +(2.30430 - 1.93354i) q^{71} +(3.38245 + 7.78197i) q^{72} +(0.820954 + 4.65586i) q^{73} +(-3.85465 - 3.16188i) q^{74} +(-5.10331 + 1.44293i) q^{75} +(1.58982 + 8.57161i) q^{76} +14.2773i q^{77} +(2.73723 + 1.19435i) q^{78} +(-15.1931 + 2.67896i) q^{79} +(-4.94190 - 2.56654i) q^{80} +(-2.04776 - 8.76394i) q^{81} +(5.64142 + 3.17374i) q^{82} +(7.18448 - 12.4439i) q^{83} +(13.1391 - 1.62853i) q^{84} +(2.49163 - 0.906879i) q^{85} +(-0.147365 - 13.2168i) q^{86} +(6.78443 - 6.97364i) q^{87} +(10.5600 - 0.353342i) q^{88} +(-0.594397 - 0.104808i) q^{89} +(4.66791 + 3.61889i) q^{90} +(2.99524 - 3.56959i) q^{91} +(6.47906 - 11.8233i) q^{92} +(-0.494274 + 6.71134i) q^{93} +(-7.07243 - 2.48521i) q^{94} +(3.83778 + 4.70056i) q^{95} +(-1.52969 - 9.67781i) q^{96} +(-7.87046 - 2.86461i) q^{97} +(1.74992 - 10.6151i) q^{98} +(-11.0859 - 1.64180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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