LMFDB - Embedded newform 77.2.n.a.17.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [77,2,Mod(17,77)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("77.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(77, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.n (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	77.17
Dual form			77.2.n.a.68.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.11268 - 1.00186i) q^{2} +(0.245339 + 0.551041i) q^{3} +(0.0252713 + 0.240440i) q^{4} +(-0.491349 - 2.31161i) q^{5} +(0.279082 - 0.858925i) q^{6} +(2.00635 - 1.72470i) q^{7} +(-1.54736 + 2.12976i) q^{8} +(1.76394 - 1.95905i) q^{9} +(-1.76920 + 3.06434i) q^{10} +(-3.23217 + 0.743693i) q^{11} +(-0.126292 + 0.0729149i) q^{12} +(0.304786 + 0.938034i) q^{13} +(-3.96031 - 0.0910454i) q^{14} +(1.15325 - 0.837884i) q^{15} +(4.32838 - 0.920026i) q^{16} +(4.87801 + 5.41758i) q^{17} +(-3.92538 + 0.412574i) q^{18} +(-0.511870 + 4.87012i) q^{19} +(0.543388 - 0.176557i) q^{20} +(1.44261 + 0.682444i) q^{21} +(4.34143 + 2.41068i) q^{22} +(-0.0581861 - 0.100781i) q^{23} +(-1.55321 - 0.330145i) q^{24} +(-0.534413 + 0.237936i) q^{25} +(0.600649 - 1.34908i) q^{26} +(3.23328 + 1.05056i) q^{27} +(0.465389 + 0.438820i) q^{28} +(-4.73419 - 6.51605i) q^{29} +(-2.12263 - 0.223098i) q^{30} +(-0.757301 + 3.56282i) q^{31} +(-1.17815 - 0.680207i) q^{32} +(-1.20278 - 1.59860i) q^{33} -10.9151i q^{34} +(-4.97265 - 3.79047i) q^{35} +(0.515611 + 0.374613i) q^{36} +(-3.37696 - 1.50352i) q^{37} +(5.44871 - 4.90604i) q^{38} +(-0.442120 + 0.398086i) q^{39} +(5.68347 + 2.53044i) q^{40} +(-3.09269 - 2.24697i) q^{41} +(-0.921451 - 2.20463i) q^{42} +5.00037i q^{43} +(-0.260494 - 0.758349i) q^{44} +(-5.39528 - 3.11497i) q^{45} +(-0.0362262 + 0.170431i) q^{46} +(7.99589 + 0.840402i) q^{47} +(1.56889 + 2.15940i) q^{48} +(1.05085 - 6.92067i) q^{49} +(0.833006 + 0.270660i) q^{50} +(-1.78854 + 4.01713i) q^{51} +(-0.217839 + 0.0969880i) q^{52} +(3.78179 + 0.803844i) q^{53} +(-2.54509 - 4.40822i) q^{54} +(3.30725 + 7.10612i) q^{55} +(0.568646 + 6.94175i) q^{56} +(-2.80922 + 0.912770i) q^{57} +(-1.26054 + 11.9932i) q^{58} +(1.41288 - 0.148500i) q^{59} +(0.230605 + 0.256113i) q^{60} +(-0.232071 + 0.0493282i) q^{61} +(4.41207 - 3.20555i) q^{62} +(0.160301 - 6.97279i) q^{63} +(-2.10542 - 6.47981i) q^{64} +(2.01862 - 1.16545i) q^{65} +(-0.263263 + 2.98374i) q^{66} +(-2.19586 + 3.80334i) q^{67} +(-1.17933 + 1.30978i) q^{68} +(0.0412593 - 0.0567886i) q^{69} +(1.73543 + 9.19945i) q^{70} +(-2.39057 + 7.35741i) q^{71} +(1.44286 + 6.78810i) q^{72} +(-0.168591 - 1.60403i) q^{73} +(2.25115 + 5.05616i) q^{74} +(-0.262225 - 0.236109i) q^{75} -1.18391 q^{76} +(-5.20221 + 7.06662i) q^{77} +0.890761 q^{78} +(-9.06956 - 8.16627i) q^{79} +(-4.25349 - 9.55349i) q^{80} +(-0.612311 - 5.82575i) q^{81} +(1.19001 + 5.59858i) q^{82} +(-1.29164 + 3.97526i) q^{83} +(-0.127630 + 0.364108i) q^{84} +(10.1266 - 13.9380i) q^{85} +(5.00966 - 5.56379i) q^{86} +(2.42913 - 4.20738i) q^{87} +(3.41744 - 8.03449i) q^{88} +(-11.4287 + 6.59836i) q^{89} +(2.88244 + 8.87124i) q^{90} +(2.22933 + 1.35636i) q^{91} +(0.0227614 - 0.0165371i) q^{92} +(-2.14906 + 0.456796i) q^{93} +(-8.05486 - 8.94583i) q^{94} +(11.5093 - 1.20968i) q^{95} +(0.0857748 - 0.816093i) q^{96} +(-16.5965 + 5.39254i) q^{97} +(-8.10278 + 6.64766i) q^{98} +(-4.24441 + 7.64381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26}+ \cdots - 12 q^{99}+O(q^{100}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	−1.11268	−	1.00186i	−0.786780	−	0.708420i	0.174299	−	0.984693i	$-0.444234\pi$
$2$	−1.11268	−	1.00186i	−0.786780	−	0.708420i	−0.961079	+	0.276273i	$0.910901\pi$
$3$	0.245339	+	0.551041i	0.141647	+	0.318144i	0.970413	−	0.241451i	$-0.0776233\pi$
$3$	0.245339	+	0.551041i	0.141647	+	0.318144i	−0.828766	+	0.559595i	$0.810957\pi$
$4$	0.0252713	+	0.240440i	0.0126356	+	0.120220i
$5$	−0.491349	−	2.31161i	−0.219738	−	1.03379i	−0.940287	−	0.340382i	$-0.889444\pi$
$5$	−0.491349	−	2.31161i	−0.219738	−	1.03379i	0.720549	−	0.693404i	$-0.243890\pi$
$6$	0.279082	−	0.858925i	0.113935	−	0.350655i
$7$	2.00635	−	1.72470i	0.758327	−	0.651874i
$7$	2.00635	−	1.72470i	0.758327	−	0.651874i
$8$	−1.54736	+	2.12976i	−0.547074	+	0.752982i
$9$	1.76394	−	1.95905i	0.587979	−	0.653017i
$10$	−1.76920	+	3.06434i	−0.559469	+	0.969029i
$11$	−3.23217	+	0.743693i	−0.974536	+	0.224232i
$11$	−3.23217	+	0.743693i	−0.974536	+	0.224232i
$12$	−0.126292	+	0.0729149i	−0.0364575	+	0.0210487i
$13$	0.304786	+	0.938034i	0.0845324	+	0.260164i	0.984385	−	0.176031i	$-0.0563259\pi$
$13$	0.304786	+	0.938034i	0.0845324	+	0.260164i	−0.899852	+	0.436195i	$0.856326\pi$
$14$	−3.96031	−	0.0910454i	−1.05844	−	0.0243329i
$15$	1.15325	−	0.837884i	0.297767	−	0.216341i
$16$	4.32838	−	0.920026i	1.08210	−	0.230006i
$17$	4.87801	+	5.41758i	1.18309	+	1.31396i	0.938884	+	0.344233i	$0.111861\pi$
$17$	4.87801	+	5.41758i	1.18309	+	1.31396i	0.244207	+	0.969723i	$0.421472\pi$
$18$	−3.92538	+	0.412574i	−0.925220	+	0.0972446i
$19$	−0.511870	+	4.87012i	−0.117431	+	1.11728i	0.764081	+	0.645120i	$0.223193\pi$
$19$	−0.511870	+	4.87012i	−0.117431	+	1.11728i	−0.881512	+	0.472161i	$0.843474\pi$
$20$	0.543388	−	0.176557i	0.121505	−	0.0394794i
$21$	1.44261	+	0.682444i	0.314804	+	0.148921i
$22$	4.34143	+	2.41068i	0.925596	+	0.513960i
$23$	−0.0581861	−	0.100781i	−0.0121326	−	0.0210144i	0.859895	−	0.510470i	$-0.170529\pi$
$23$	−0.0581861	−	0.100781i	−0.0121326	−	0.0210144i	−0.872028	+	0.489456i	$0.837195\pi$
$24$	−1.55321	−	0.330145i	−0.317048	−	0.0673906i
$25$	−0.534413	+	0.237936i	−0.106883	+	0.0475872i
$26$	0.600649	−	1.34908i	0.117797	−	0.264576i
$27$	3.23328	+	1.05056i	0.622246	+	0.202180i
$28$	0.465389	+	0.438820i	0.0879502	+	0.0829293i
$29$	−4.73419	−	6.51605i	−0.879116	−	1.21000i	−0.976665	−	0.214769i	$-0.931100\pi$
$29$	−4.73419	−	6.51605i	−0.879116	−	1.21000i	0.0975485	−	0.995231i	$-0.468900\pi$
$30$	−2.12263	−	0.223098i	−0.387538	−	0.0407318i
$31$	−0.757301	+	3.56282i	−0.136015	+	0.639901i	0.856332	+	0.516425i	$0.172738\pi$
$31$	−0.757301	+	3.56282i	−0.136015	+	0.639901i	−0.992348	+	0.123476i	$0.960596\pi$
$32$	−1.17815	−	0.680207i	−0.208270	−	0.120245i
$33$	−1.20278	−	1.59860i	−0.209378	−	0.278281i
$34$		−	10.9151i		−	1.87192i
$35$	−4.97265	−	3.79047i	−0.840531	−	0.640707i
$36$	0.515611	+	0.374613i	0.0859351	+	0.0624355i
$37$	−3.37696	−	1.50352i	−0.555169	−	0.247177i	0.109921	−	0.993940i	$-0.464940\pi$
$37$	−3.37696	−	1.50352i	−0.555169	−	0.247177i	−0.665090	+	0.746763i	$0.731607\pi$
$38$	5.44871	−	4.90604i	0.883897	−	0.795865i
$39$	−0.442120	+	0.398086i	−0.0707958	+	0.0637448i
$40$	5.68347	+	2.53044i	0.898635	+	0.400098i
$41$	−3.09269	−	2.24697i	−0.482996	−	0.350917i	0.319488	−	0.947590i	$-0.396489\pi$
$41$	−3.09269	−	2.24697i	−0.482996	−	0.350917i	−0.802485	+	0.596673i	$0.796489\pi$
$42$	−0.921451	−	2.20463i	−0.142183	−	0.340182i
$43$			5.00037i			0.762549i	0.924462	+	0.381275i	$0.124515\pi$
$43$			5.00037i			0.762549i	−0.924462	+	0.381275i	$0.875485\pi$
$44$	−0.260494	−	0.758349i	−0.0392710	−	0.114325i
$45$	−5.39528	−	3.11497i	−0.804281	−	0.464352i
$46$	−0.0362262	+	0.170431i	−0.00534127	+	0.0251287i
$47$	7.99589	+	0.840402i	1.16632	+	0.122585i	0.667832	−	0.744312i	$-0.267222\pi$
$47$	7.99589	+	0.840402i	1.16632	+	0.122585i	0.498488	+	0.866897i	$0.333889\pi$
$48$	1.56889	+	2.15940i	0.226450	+	0.311682i
$49$	1.05085	−	6.92067i	0.150121	−	0.988668i
$50$	0.833006	+	0.270660i	0.117805	+	0.0382771i
$51$	−1.78854	+	4.01713i	−0.250446	+	0.562511i
$52$	−0.217839	+	0.0969880i	−0.0302088	+	0.0134498i
$53$	3.78179	+	0.803844i	0.519469	+	0.110417i	0.460182	−	0.887824i	$-0.347784\pi$
$53$	3.78179	+	0.803844i	0.519469	+	0.110417i	0.0592866	+	0.998241i	$0.481117\pi$
$54$	−2.54509	−	4.40822i	−0.346342	−	0.599883i
$55$	3.30725	+	7.10612i	0.445950	+	0.958189i
$56$	0.568646	+	6.94175i	0.0759885	+	0.927630i
$57$	−2.80922	+	0.912770i	−0.372090	+	0.120899i
$58$	−1.26054	+	11.9932i	−0.165517	+	1.57479i
$59$	1.41288	−	0.148500i	0.183942	−	0.0193330i	−0.0121097	−	0.999927i	$-0.503855\pi$
$59$	1.41288	−	0.148500i	0.183942	−	0.0193330i	0.196051	+	0.980594i	$0.437188\pi$
$60$	0.230605	+	0.256113i	0.0297710	+	0.0330640i
$61$	−0.232071	+	0.0493282i	−0.0297136	+	0.00631583i	−0.222745	−	0.974877i	$-0.571502\pi$
$61$	−0.232071	+	0.0493282i	−0.0297136	+	0.00631583i	0.193031	+	0.981193i	$0.438168\pi$
$62$	4.41207	−	3.20555i	0.560333	−	0.407106i
$63$	0.160301	−	6.97279i	0.0201960	−	0.878489i
$64$	−2.10542	−	6.47981i	−0.263177	−	0.809976i
$65$	2.01862	−	1.16545i	0.250379	−	0.144556i
$66$	−0.263263	+	2.98374i	−0.0324054	+	0.367273i
$67$	−2.19586	+	3.80334i	−0.268267	+	0.464652i	−0.968414	−	0.249346i	$-0.919784\pi$
$67$	−2.19586	+	3.80334i	−0.268267	+	0.464652i	0.700147	+	0.713998i	$0.253118\pi$
$68$	−1.17933	+	1.30978i	−0.143015	+	0.158834i
$69$	0.0412593	−	0.0567886i	0.00496704	−	0.00683654i
$70$	1.73543	+	9.19945i	0.207424	+	1.09954i
$71$	−2.39057	+	7.35741i	−0.283708	+	0.873164i	0.703075	+	0.711116i	$0.251810\pi$
$71$	−2.39057	+	7.35741i	−0.283708	+	0.873164i	−0.986783	+	0.162048i	$0.948190\pi$
$72$	1.44286	+	6.78810i	0.170042	+	0.799986i
$73$	−0.168591	−	1.60403i	−0.0197321	−	0.187738i	0.980216	−	0.197931i	$-0.0634221\pi$
$73$	−0.168591	−	1.60403i	−0.0197321	−	0.187738i	−0.999948	+	0.0101928i	$0.996755\pi$
$74$	2.25115	+	5.05616i	0.261690	+	0.587766i
$75$	−0.262225	−	0.236109i	−0.0302791	−	0.0272635i
$76$	−1.18391			−0.135803
$77$	−5.20221	+	7.06662i	−0.592846	+	0.805316i
$78$	0.890761			0.100859
$79$	−9.06956	−	8.16627i	−1.02040	−	0.918777i	−0.0236862	−	0.999719i	$-0.507540\pi$
$79$	−9.06956	−	8.16627i	−1.02040	−	0.918777i	−0.996719	+	0.0809427i	$0.974207\pi$
$80$	−4.25349	−	9.55349i	−0.475555	−	1.06811i
$81$	−0.612311	−	5.82575i	−0.0680345	−	0.647305i
$82$	1.19001	+	5.59858i	0.131415	+	0.618259i
$83$	−1.29164	+	3.97526i	−0.141776	+	0.436341i	−0.996582	−	0.0826058i	$-0.973676\pi$
$83$	−1.29164	+	3.97526i	−0.141776	+	0.436341i	0.854806	+	0.518947i	$0.173676\pi$
$84$	−0.127630	+	0.364108i	−0.0139256	+	0.0397275i
$85$	10.1266	−	13.9380i	1.09838	−	1.51179i
$86$	5.00966	−	5.56379i	0.540205	−	0.599959i
$87$	2.42913	−	4.20738i	0.260430	−	0.451078i
$88$	3.41744	−	8.03449i	0.364300	−	0.856479i
$89$	−11.4287	+	6.59836i	−1.21144	+	0.699425i	−0.963073	−	0.269241i	$-0.913227\pi$
$89$	−11.4287	+	6.59836i	−1.21144	+	0.699425i	−0.248366	+	0.968666i	$0.579894\pi$
$90$	2.88244	+	8.87124i	0.303836	+	0.935111i
$91$	2.22933	+	1.35636i	0.233697	+	0.142185i
$92$	0.0227614	−	0.0165371i	0.00237304	−	0.00172412i
$93$	−2.14906	+	0.456796i	−0.222847	+	0.0473676i
$94$	−8.05486	−	8.94583i	−0.830796	−	0.922692i
$95$	11.5093	−	1.20968i	1.18083	−	0.124111i
$96$	0.0857748	−	0.816093i	0.00875436	−	0.0832921i
$97$	−16.5965	+	5.39254i	−1.68512	+	0.547529i	−0.985894	−	0.167370i	$-0.946473\pi$
$97$	−16.5965	+	5.39254i	−1.68512	+	0.547529i	−0.699227	+	0.714899i	$0.746473\pi$
$98$	−8.10278	+	6.64766i	−0.818504	+	0.671515i
$99$	−4.24441	+	7.64381i	−0.426579	+	0.768232i
$100$	−0.0707146	−	0.122481i	−0.00707146	−	0.0122481i
$101$	12.9630	+	2.75536i	1.28986	+	0.274169i	0.801248	−	0.598332i	$-0.204170\pi$
$101$	12.9630	+	2.75536i	1.28986	+	0.274169i	0.488613	+	0.872500i	$0.337503\pi$
$102$	6.01466	−	2.67790i	0.595540	−	0.265152i
$103$	0.133593	−	0.300054i	0.0131633	−	0.0295652i	−0.906844	−	0.421466i	$-0.861516\pi$
$103$	0.133593	−	0.300054i	0.0131633	−	0.0295652i	0.920007	+	0.391901i	$0.128182\pi$
$104$	−2.46940	−	0.802355i	−0.242144	−	0.0786774i
$105$	0.868720	−	3.67009i	0.0847784	−	0.358164i
$106$	−3.40257	−	4.68323i	−0.330487	−	0.454876i
$107$	1.63426	+	0.171768i	0.157990	+	0.0166054i	0.183193	−	0.983077i	$-0.441357\pi$
$107$	1.63426	+	0.171768i	0.157990	+	0.0166054i	−0.0252032	+	0.999682i	$0.508023\pi$
$108$	−0.170887	+	0.803960i	−0.0164436	+	0.0773610i
$109$	0.138154	+	0.0797633i	0.0132328	+	0.00763994i	0.506602	−	0.862180i	$-0.330901\pi$
$109$	0.138154	+	0.0797633i	0.0132328	+	0.00763994i	−0.493369	+	0.869820i	$0.664235\pi$
$110$	3.43942	−	11.2202i	0.327936	−	1.06980i
$111$		−	2.22972i		−	0.211635i
$112$	7.09746	−	9.31103i	0.670647	−	0.879810i
$113$	6.46936	+	4.70027i	0.608586	+	0.442164i	0.848916	−	0.528527i	$-0.177256\pi$
$113$	6.46936	+	4.70027i	0.608586	+	0.442164i	−0.240330	+	0.970691i	$0.577256\pi$
$114$	4.04021	+	1.79882i	0.378401	+	0.168475i
$115$	−0.204378	+	0.184023i	−0.0190583	+	0.0171602i
$116$	1.44708	−	1.30296i	0.134358	−	0.120976i
$117$	2.37528	+	1.05754i	0.219595	+	0.0977698i
$118$	−1.72086	−	1.25027i	−0.158418	−	0.115097i
$119$	19.1307	+	2.45645i	1.75370	+	0.225183i
$120$			3.75264i			0.342568i
$121$	9.89384	−	4.80748i	0.899440	−	0.437044i
$122$	0.307639	+	0.177616i	0.0278524	+	0.0160806i
$123$	0.479415	−	2.25547i	0.0432274	−	0.203369i
$124$	−0.875782	−	0.0920484i	−0.0786475	−	0.00826619i
$125$	−6.13284	−	8.44113i	−0.548538	−	0.754998i
$126$	−7.16410	+	7.59785i	−0.638229	+	0.676870i
$127$	−13.9300	−	4.52612i	−1.23608	−	0.401628i	−0.383169	−	0.923678i	$-0.625167\pi$
$127$	−13.9300	−	4.52612i	−1.23608	−	0.401628i	−0.852915	+	0.522050i	$0.825167\pi$
$128$	−5.25586	+	11.8049i	−0.464557	+	1.04341i
$129$	−2.75541	+	1.22679i	−0.242600	+	0.108013i
$130$	−3.41368	−	0.725600i	−0.299400	−	0.0636393i
$131$	−9.33814	−	16.1741i	−0.815877	−	1.41314i	−0.908696	−	0.417458i	$-0.862921\pi$
$131$	−9.33814	−	16.1741i	−0.815877	−	1.41314i	0.0928193	−	0.995683i	$-0.470412\pi$
$132$	0.353972	−	0.329596i	0.0308093	−	0.0286877i
$133$	7.37248	+	10.6540i	0.639275	+	0.923815i
$134$	6.25369	−	2.03195i	0.540236	−	0.175533i
$135$	0.839814	−	7.99030i	0.0722797	−	0.687695i
$136$	−19.0861	+	2.00603i	−1.63662	+	0.172016i
$137$	−0.250586	−	0.278304i	−0.0214090	−	0.0237771i	0.732345	−	0.680934i	$-0.238426\pi$
$137$	−0.250586	−	0.278304i	−0.0214090	−	0.0237771i	−0.753754	+	0.657156i	$0.771759\pi$
$138$	−0.102802	+	0.0218513i	−0.00875112	+	0.00186011i
$139$	−12.7105	+	9.23469i	−1.07809	+	0.783276i	−0.977348	−	0.211637i	$-0.932121\pi$
$139$	−12.7105	+	9.23469i	−1.07809	+	0.783276i	−0.100739	+	0.994913i	$0.532121\pi$
$140$	0.785716	−	1.29141i	0.0664051	−	0.109144i
$141$	1.49861	+	4.61225i	0.126206	+	0.388421i
$142$	10.0310	−	5.79140i	0.841782	−	0.486003i
$143$	−1.68273	−	2.80522i	−0.140717	−	0.234584i
$144$	5.83261	−	10.1024i	0.486051	−	0.841865i
$145$	−12.7365	+	14.1453i	−1.05771	+	1.17470i
$146$	−1.41943	+	1.95367i	−0.117473	+	0.161687i
$147$	4.07139	−	1.11885i	0.335803	−	0.0922816i
$148$	0.276166	−	0.849951i	0.0227007	−	0.0698656i
$149$	−2.07214	−	9.74867i	−0.169757	−	0.798642i	−0.977804	−	0.209524i	$-0.932809\pi$
$149$	−2.07214	−	9.74867i	−0.169757	−	0.798642i	0.808047	−	0.589118i	$-0.200525\pi$
$150$	0.0552243	+	0.525424i	0.00450905	+	0.0429007i
$151$	1.59669	+	3.58621i	0.129936	+	0.291842i	0.966784	−	0.255593i	$-0.0822709\pi$
$151$	1.59669	+	3.58621i	0.129936	+	0.291842i	−0.836848	+	0.547435i	$0.815604\pi$
$152$	−9.58011	−	8.62597i	−0.777050	−	0.699659i
$153$	19.2178			1.55367
$154$	12.8681	−	2.65098i	1.03694	−	0.213622i
$155$	8.60797			0.691408
$156$	−0.106889	−	0.0962431i	−0.00855795	−	0.00770561i
$157$	−3.09969	−	6.96203i	−0.247383	−	0.555630i	0.746587	−	0.665288i	$-0.231691\pi$
$157$	−3.09969	−	6.96203i	−0.247383	−	0.555630i	−0.993969	+	0.109658i	$0.965025\pi$
$158$	1.91004	+	18.1728i	0.151955	+	1.44575i
$159$	0.484871	+	2.28114i	0.0384528	+	0.180906i
$160$	−0.993493	+	3.05766i	−0.0785425	+	0.241729i
$161$	−0.290559	−	0.101849i	−0.0228992	−	0.00802681i
$162$	−5.15526	+	7.09561i	−0.405036	+	0.557484i
$163$	−4.66602	+	5.18214i	−0.365471	+	0.405897i	−0.897631	−	0.440747i	$-0.854714\pi$
$163$	−4.66602	+	5.18214i	−0.365471	+	0.405897i	0.532160	+	0.846643i	$0.321380\pi$
$164$	0.462105	−	0.800389i	0.0360843	−	0.0624999i
$165$	−3.10437	+	3.56585i	−0.241675	+	0.277601i
$166$	5.41981	−	3.12913i	0.420659	−	0.242868i
$167$	3.74083	+	11.5131i	0.289474	+	0.890909i	0.985022	+	0.172429i	$0.0551616\pi$
$167$	3.74083	+	11.5131i	0.289474	+	0.890909i	−0.695548	+	0.718479i	$0.744838\pi$
$168$	−3.68568	+	2.01643i	−0.284356	+	0.155571i
$169$	9.73021	−	7.06941i	0.748477	−	0.543801i
$170$	−25.2315	+	5.36311i	−1.93516	+	0.411332i
$171$	8.63790	+	9.59336i	0.660557	+	0.733622i
$172$	−1.20229	+	0.126366i	−0.0916736	+	0.00963529i
$173$	−0.339887	+	3.23381i	−0.0258411	+	0.245862i	0.973974	+	0.226658i	$0.0727799\pi$
$173$	−0.339887	+	3.23381i	−0.0258411	+	0.245862i	−0.999816	+	0.0192040i	$0.993887\pi$
$174$	−6.91802	+	2.24780i	−0.524454	+	0.170405i
$175$	−0.661850	+	1.39908i	−0.0500311	+	0.105761i
$176$	−13.3058	+	6.19266i	−1.00297	+	0.466790i
$177$	0.428466	+	0.742124i	0.0322054	+	0.0557815i
$178$	19.3270	+	4.10809i	1.44862	+	0.307914i
$179$	−9.24804	+	4.11749i	−0.691231	+	0.307756i	−0.722121	−	0.691767i	$-0.756833\pi$
$179$	−9.24804	+	4.11749i	−0.691231	+	0.307756i	0.0308897	+	0.999523i	$0.490166\pi$
$180$	0.612617	−	1.37596i	0.0456617	−	0.102558i
$181$	9.48074	+	3.08048i	0.704698	+	0.228970i	0.639376	−	0.768894i	$-0.279193\pi$
$181$	9.48074	+	3.08048i	0.704698	+	0.228970i	0.0653218	+	0.997864i	$0.479193\pi$
$182$	−1.12164	−	3.74266i	−0.0831417	−	0.277424i
$183$	−0.0841180	−	0.115778i	−0.00621818	−	0.00855859i
$184$	0.304674	+	0.0320226i	0.0224609	+	0.00236073i
$185$	−1.81629	+	8.54498i	−0.133536	+	0.628239i
$186$	2.84885	+	1.64478i	0.208888	+	0.120601i
$187$	−19.7956	−	13.8828i	−1.44760	−	1.01521i
$188$			1.94377i			0.141764i
$189$	8.29898	−	3.46865i	0.603662	−	0.252307i
$190$	−14.0181	−	10.1847i	−1.01698	−	0.738879i
$191$	19.3870	+	8.63163i	1.40279	+	0.624563i	0.962001	−	0.273047i	$-0.0880315\pi$
$191$	19.3870	+	8.63163i	1.40279	+	0.624563i	0.440791	+	0.897610i	$0.354698\pi$
$192$	3.05410	−	2.74992i	0.220411	−	0.198459i
$193$	7.76344	−	6.99023i	0.558825	−	0.503168i	−0.340621	−	0.940201i	$-0.610637\pi$
$193$	7.76344	−	6.99023i	0.558825	−	0.503168i	0.899446	+	0.437033i	$0.143971\pi$
$194$	23.8691	+	10.6272i	1.71370	+	0.762989i
$195$	1.13746	+	0.826411i	0.0814550	+	0.0591805i
$196$	1.69056	+	0.0777713i	0.120754	+	0.00555509i
$197$			6.57692i			0.468586i	0.972166	+	0.234293i	$0.0752776\pi$
$197$			6.57692i			0.468586i	−0.972166	+	0.234293i	$0.924722\pi$
$198$	12.3807	−	4.25278i	0.879855	−	0.302232i
$199$	0.834354	+	0.481715i	0.0591458	+	0.0341479i	0.529281	−	0.848446i	$-0.322462\pi$
$199$	0.834354	+	0.481715i	0.0591458	+	0.0341479i	−0.470135	+	0.882594i	$0.655795\pi$
$200$	0.320183	−	1.50634i	0.0226403	−	0.106514i
$201$	−2.63453	−	0.276900i	−0.185825	−	0.0195310i
$202$	−11.6631	−	16.0528i	−0.820611	−	1.12947i
$203$	−20.7366	−	4.90841i	−1.45543	−	0.344503i
$204$	−1.01108	−	0.328519i	−0.0707896	−	0.0230009i
$205$	−3.67454	+	8.25315i	−0.256641	+	0.576425i
$206$	−0.449257	+	0.200022i	−0.0313012	+	0.0139362i
$207$	−0.300072	−	0.0637823i	−0.0208565	−	0.00443318i
$208$	2.18224	+	3.77976i	0.151311	+	0.262079i
$209$	−1.96742	−	16.1217i	−0.136089	−	1.11516i
$210$	−4.64351	+	3.21328i	−0.320432	+	0.221738i
$211$	2.38877	−	0.776160i	0.164450	−	0.0534331i	−0.225635	−	0.974212i	$-0.572446\pi$
$211$	2.38877	−	0.776160i	0.164450	−	0.0534331i	0.390085	+	0.920779i	$0.372446\pi$
$212$	−0.0977057	+	0.929608i	−0.00671045	+	0.0638457i
$213$	−4.64074	+	0.487761i	−0.317978	+	0.0334208i
$214$	−1.64632	−	1.82842i	−0.112540	−	0.124988i
$215$	11.5589	−	2.45693i	0.788312	−	0.167561i
$216$	−7.24048	+	5.26052i	−0.492652	+	0.357933i
$217$	4.62537	+	8.45436i	0.313991	+	0.573919i
$218$	−0.0738092	−	0.227161i	−0.00499899	−	0.0153853i
$219$	0.842527	−	0.486433i	0.0569327	−	0.0328701i
$220$	−1.62502	+	0.974777i	−0.109559	+	0.0657194i
$221$	−3.59513	+	6.22694i	−0.241834	+	0.418869i
$222$	−2.23386	+	2.48095i	−0.149927	+	0.166510i
$223$	15.0520	−	20.7173i	1.00796	−	1.38733i	0.0876440	−	0.996152i	$-0.472066\pi$
$223$	15.0520	−	20.7173i	1.00796	−	1.38733i	0.920313	−	0.391182i	$-0.127934\pi$
$224$	−3.53693	+	0.667226i	−0.236321	+	0.0445809i
$225$	−0.476542	+	1.46665i	−0.0317695	+	0.0977764i
$226$	−2.48930	−	11.7112i	−0.165586	−	0.779020i
$227$	−2.03291	−	19.3419i	−0.134929	−	1.28376i	−0.827110	−	0.562041i	$-0.810016\pi$
$227$	−2.03291	−	19.3419i	−0.134929	−	1.28376i	0.692181	−	0.721724i	$-0.256650\pi$
$228$	−0.290459	−	0.652381i	−0.0192361	−	0.0432050i
$229$	15.5655	+	14.0153i	1.02860	+	0.926155i	0.997306	−	0.0733555i	$-0.0233708\pi$
$229$	15.5655	+	14.0153i	1.02860	+	0.926155i	0.0312932	+	0.999510i	$0.490037\pi$
$230$	0.411771			0.0271514
$231$	−5.17030	−	1.13291i	−0.340181	−	0.0745401i
$232$	21.2031			1.39205
$233$	−11.3080	−	10.1817i	−0.740810	−	0.667028i	0.209685	−	0.977769i	$-0.432756\pi$
$233$	−11.3080	−	10.1817i	−0.740810	−	0.667028i	−0.950495	+	0.310741i	$0.899423\pi$
$234$	−1.58341	−	3.55639i	−0.103511	−	0.232489i
$235$	−1.98609	−	18.8963i	−0.129558	−	1.23266i
$236$	0.0714106	+	0.335961i	0.00464844	+	0.0218692i
$237$	2.27483	−	7.00121i	0.147766	−	0.454777i
$238$	−18.8252	−	21.8994i	−1.22026	−	1.41953i
$239$	5.56179	−	7.65514i	0.359762	−	0.495170i	−0.590320	−	0.807169i	$-0.700999\pi$
$239$	5.56179	−	7.65514i	0.359762	−	0.495170i	0.950082	+	0.311999i	$0.100999\pi$
$240$	4.22082	−	4.68770i	0.272453	−	0.302590i
$241$	−3.47748	+	6.02317i	−0.224004	+	0.387987i	−0.956020	−	0.293301i	$-0.905246\pi$
$241$	−3.47748	+	6.02317i	−0.224004	+	0.387987i	0.732016	+	0.681287i	$0.238580\pi$
$242$	−15.8250	−	4.56305i	−1.01727	−	0.293324i
$243$	11.8926	−	6.86621i	0.762912	−	0.440467i
$244$	−0.0177252	−	0.0545525i	−0.00113474	−	0.00349237i
$245$	−16.5143	+	0.971314i	−1.05506	+	0.0620549i
$246$	−2.79309	+	2.02930i	−0.178081	+	0.129383i
$247$	−4.72435	+	1.00419i	−0.300603	+	0.0638951i
$248$	−6.41612	−	7.12582i	−0.407424	−	0.452490i
$249$	−2.50742	+	0.263541i	−0.158901	+	0.0167012i
$250$	−1.63295	+	15.5365i	−0.103277	+	0.982613i
$251$	9.44333	−	3.06832i	0.596058	−	0.193671i	0.00457626	−	0.999990i	$-0.498543\pi$
$251$	9.44333	−	3.06832i	0.596058	−	0.193671i	0.591481	+	0.806319i	$0.298543\pi$
$252$	1.68059	−	0.137668i	0.105867	−	0.00867229i
$253$	0.263018	+	0.282470i	0.0165358	+	0.0177587i
$254$	10.9650	+	18.9919i	0.688005	+	1.19166i
$255$	10.1649	+	2.16061i	0.636548	+	0.135303i
$256$	5.22637	−	2.32693i	0.326648	−	0.145433i
$257$	−1.59069	+	3.57276i	−0.0992247	+	0.222862i	−0.956336	−	0.292268i	$-0.905590\pi$
$257$	−1.59069	+	3.57276i	−0.0992247	+	0.222862i	0.857112	+	0.515131i	$0.172257\pi$
$258$	4.29494	+	1.39551i	0.267392	+	0.0868808i
$259$	−9.36846	+	2.80765i	−0.582128	+	0.174459i
$260$	0.331234	+	0.455904i	0.0205422	+	0.0282740i
$261$	−21.1161	−	2.21939i	−1.30705	−	0.137377i
$262$	−5.81386	+	27.3520i	−0.359181	+	1.68981i
$263$	−14.0065	−	8.08668i	−0.863680	−	0.498646i	0.00156274	−	0.999999i	$-0.499503\pi$
$263$	−14.0065	−	8.08668i	−0.863680	−	0.498646i	−0.865243	+	0.501353i	$0.832836\pi$
$264$	5.26577	−	0.0880265i	0.324086	−	0.00541765i
$265$		−	9.13701i		−	0.561282i
$266$	2.47057	−	19.2406i	0.151480	−	1.17972i
$267$	−6.43988	−	4.67885i	−0.394114	−	0.286341i
$268$	−0.969968	−	0.431857i	−0.0592502	−	0.0263799i
$269$	−7.13969	+	6.42860i	−0.435315	+	0.391959i	−0.857445	−	0.514576i	$-0.827949\pi$
$269$	−7.13969	+	6.42860i	−0.435315	+	0.391959i	0.422130	+	0.906535i	$0.361283\pi$
$270$	−8.93958	+	8.04923i	−0.544045	+	0.489861i
$271$	0.113237	+	0.0504164i	0.00687866	+	0.00306258i	0.410173	−	0.912008i	$-0.365468\pi$
$271$	0.113237	+	0.0504164i	0.00687866	+	0.00306258i	−0.403294	+	0.915070i	$0.632135\pi$
$272$	26.0982	+	18.9614i	1.58244	+	1.14971i
$273$	−0.200467	+	1.56122i	−0.0121328	+	0.0944894i
$274$			0.560713i			0.0338739i
$275$	1.55036	−	1.16649i	0.0934903	−	0.0703419i
$276$	0.0146969	+	0.00848527i	0.000884651	+	0.000510753i
$277$	−6.13243	+	28.8508i	−0.368462	+	1.73348i	0.269130	+	0.963104i	$0.413264\pi$
$277$	−6.13243	+	28.8508i	−0.368462	+	1.73348i	−0.637592	+	0.770374i	$0.720070\pi$
$278$	23.3945	+	2.45886i	1.40311	+	0.147472i
$279$	5.64391	+	7.76818i	0.337892	+	0.465069i
$280$	15.7672	−	4.72531i	0.942273	−	0.282391i
$281$	12.9022	+	4.19217i	0.769679	+	0.250084i	0.667428	−	0.744675i	$-0.267395\pi$
$281$	12.9022	+	4.19217i	0.769679	+	0.250084i	0.102252	+	0.994759i	$0.467395\pi$
$282$	2.95335	−	6.63333i	0.175869	−	0.395009i
$283$	11.1202	−	4.95103i	0.661026	−	0.294308i	−0.0486706	−	0.998815i	$-0.515498\pi$
$283$	11.1202	−	4.95103i	0.661026	−	0.294308i	0.709697	+	0.704507i	$0.248832\pi$
$284$	−1.82943	−	0.388857i	−0.108557	−	0.0230744i
$285$	3.49028	+	6.04534i	0.206746	+	0.358095i
$286$	−0.938098	+	4.80715i	−0.0554709	+	0.284253i
$287$	−10.0803	+	0.825749i	−0.595023	+	0.0487424i
$288$	−3.41075	+	1.10822i	−0.200980	+	0.0653024i
$289$	−3.77820	+	35.9471i	−0.222247	+	2.11454i
$290$	28.3431	−	2.97898i	1.66436	−	0.174932i
$291$	−7.04329	−	7.82237i	−0.412885	−	0.458555i
$292$	0.381413	−	0.0810719i	0.0223205	−	0.00474438i
$293$	5.74034	−	4.17060i	0.335354	−	0.243649i	−0.407345	−	0.913274i	$-0.633545\pi$
$293$	5.74034	−	4.17060i	0.335354	−	0.243649i	0.742699	+	0.669625i	$0.233545\pi$
$294$	−5.65107	−	2.83403i	−0.329577	−	0.165284i
$295$	−1.03749	−	3.19308i	−0.0604052	−	0.185908i
$296$	8.42749	−	4.86561i	0.489838	−	0.282808i
$297$	−11.2318	−	0.991011i	−0.651736	−	0.0575043i
$298$	−7.46115	+	12.9231i	−0.432213	+	0.748615i
$299$	0.0768020	−	0.0852973i	0.00444158	−	0.00493287i
$300$	0.0501432	−	0.0690161i	0.00289502	−	0.00398465i
$301$	8.62412	+	10.0325i	0.497086	+	0.578262i
$302$	1.81628	−	5.58994i	0.104515	−	0.321665i
$303$	1.66201	+	7.81912i	0.0954797	+	0.449197i
$304$	2.26506	+	21.5507i	0.129910	+	1.23601i
$305$	0.228056	+	0.512221i	0.0130584	+	0.0293297i
$306$	−21.3832	−	19.2535i	−1.22240	−	1.10065i
$307$	−22.2280			−1.26862			−0.634309	−	0.773080i	$-0.718715\pi$
$307$	−22.2280			−1.26862			−0.634309	+	0.773080i	$0.718715\pi$
$308$	−1.83056	−	1.07224i	−0.104306	−	0.0610963i
$309$	0.198118			0.0112705
$310$	−9.57787	−	8.62395i	−0.543986	−	0.489808i
$311$	1.41263	+	3.17283i	0.0801032	+	0.179915i	0.949157	−	0.314803i	$-0.101938\pi$
$311$	1.41263	+	3.17283i	0.0801032	+	0.179915i	−0.869054	+	0.494717i	$0.835272\pi$
$312$	−0.163709	−	1.55759i	−0.00926821	−	0.0881811i
$313$	2.07731	+	9.77295i	0.117416	+	0.552400i	0.997050	+	0.0767492i	$0.0244541\pi$
$313$	2.07731	+	9.77295i	0.117416	+	0.552400i	−0.879634	+	0.475651i	$0.842213\pi$
$314$	−3.52600	+	10.8519i	−0.198984	+	0.612410i
$315$	−16.1972	+	3.05552i	−0.912607	+	0.172159i
$316$	1.73430	−	2.38706i	0.0975618	−	0.134282i
$317$	14.1186	−	15.6803i	0.792979	−	0.880692i	−0.202142	−	0.979356i	$-0.564790\pi$
$317$	14.1186	−	15.6803i	0.792979	−	0.880692i	0.995121	+	0.0986639i	$0.0314569\pi$
$318$	1.74587	−	3.02394i	0.0979036	−	0.169574i
$319$	20.1476	+	17.5402i	1.12805	+	0.982062i
$320$	−13.9443	+	8.05076i	−0.779512	+	0.450051i
$321$	0.306298	+	0.942687i	0.0170959	+	0.0526157i
$322$	0.221259	+	0.404423i	0.0123303	+	0.0225376i
$323$	−28.8812	+	20.9834i	−1.60699	+	1.16755i
$324$	1.38527	−	0.294448i	0.0769593	−	0.0163582i
$325$	−0.386073	−	0.428778i	−0.0214155	−	0.0237843i
$326$	10.3835	−	1.09135i	0.575091	−	0.0604445i
$327$	−0.0100582	+	0.0956978i	−0.000556222	+	0.00529210i
$328$	9.57099	−	3.10980i	0.528469	−	0.171710i
$329$	17.4920	−	12.1043i	0.964363	−	0.667334i
$330$	7.02662	−	0.857496i	0.386803	−	0.0472036i
$331$	−10.1074	−	17.5066i	−0.555554	−	0.962249i	−0.997860	−	0.0653842i	$-0.979173\pi$
$331$	−10.1074	−	17.5066i	−0.555554	−	0.962249i	0.442306	−	0.896864i	$-0.354161\pi$
$332$	−0.988452	−	0.210102i	−0.0542483	−	0.0115308i
$333$	−8.90221	+	3.96352i	−0.487838	+	0.217199i
$334$	7.37214	−	16.5581i	0.403385	−	0.906018i
$335$	9.87080	+	3.20722i	0.539299	+	0.175229i
$336$	6.87205	+	1.62663i	0.374901	+	0.0887401i
$337$	7.87101	+	10.8335i	0.428761	+	0.590139i	0.967668	−	0.252226i	$-0.0811626\pi$
$337$	7.87101	+	10.8335i	0.428761	+	0.590139i	−0.538907	+	0.842365i	$0.681163\pi$
$338$	−17.9091	−	1.88232i	−0.974127	−	0.102385i
$339$	−1.00285	+	4.71805i	−0.0544674	+	0.256249i
$340$	3.60716	+	2.08260i	0.195626	+	0.112945i
$341$	−0.201919	−	12.0788i	−0.0109345	−	0.654106i
$342$		−	19.3282i		−	1.04515i
$343$	−9.82770	−	15.6977i	−0.530646	−	0.847594i
$344$	−10.6496	−	7.73736i	−0.574186	−	0.417170i
$345$	−0.151546	−	0.0674727i	−0.00815897	−	0.00363261i
$346$	3.61800	−	3.25766i	0.194505	−	0.175133i
$347$	−0.262090	+	0.235986i	−0.0140697	+	0.0126684i	−0.676135	−	0.736777i	$-0.736347\pi$
$347$	−0.262090	+	0.235986i	−0.0140697	+	0.0126684i	0.662066	+	0.749446i	$0.269680\pi$
$348$	1.07301	+	0.477734i	0.0575193	+	0.0256092i
$349$	−28.5886	−	20.7709i	−1.53032	−	1.11184i	−0.956063	−	0.293160i	$-0.905293\pi$
$349$	−28.5886	−	20.7709i	−1.53032	−	1.11184i	−0.574252	−	0.818679i	$-0.694707\pi$
$350$	2.13810	−	0.893644i	0.114286	−	0.0477673i
$351$			3.35313i			0.178977i
$352$	4.31386	+	1.32236i	0.229929	+	0.0704821i
$353$	−17.0258	−	9.82986i	−0.906193	−	0.523191i	−0.0269887	−	0.999636i	$-0.508592\pi$
$353$	−17.0258	−	9.82986i	−0.906193	−	0.523191i	−0.879204	+	0.476445i	$0.841925\pi$
$354$	0.266759	−	1.25500i	0.0141781	−	0.0667027i
$355$	18.1821	+	1.91102i	0.965005	+	0.101426i
$356$	−1.87533	−	2.58117i	−0.0993921	−	0.136802i
$357$	3.33990	+	11.1444i	0.176766	+	0.589827i
$358$	14.4152	+	4.68379i	0.761868	+	0.247546i
$359$	2.46420	−	5.53469i	0.130056	−	0.292110i	−0.836767	−	0.547560i	$-0.815557\pi$
$359$	2.46420	−	5.53469i	0.130056	−	0.292110i	0.966822	+	0.255450i	$0.0822236\pi$
$360$	14.9825	−	6.67066i	0.789649	−	0.351574i
$361$	−4.87123	−	1.03541i	−0.256380	−	0.0544953i
$362$	−7.46279	−	12.9259i	−0.392235	−	0.679372i
$363$	5.07647	+	4.27245i	0.266446	+	0.224246i
$364$	−0.269785	+	0.570297i	−0.0141406	+	0.0298917i
$365$	−3.62507	+	1.17786i	−0.189745	+	0.0616519i
$366$	−0.0223975	+	0.213098i	−0.00117074	+	0.0111388i
$367$	−15.2333	+	1.60108i	−0.795169	+	0.0835757i	−0.493397	−	0.869804i	$-0.664245\pi$
$367$	−15.2333	+	1.60108i	−0.795169	+	0.0835757i	−0.301772	+	0.953380i	$0.597578\pi$
$368$	−0.344573	−	0.382687i	−0.0179621	−	0.0199489i
$369$	−9.85723	+	2.09522i	−0.513147	+	0.109073i
$370$	10.5818	−	7.68812i	0.550121	−	0.399686i
$371$	8.97397	−	4.90965i	0.465905	−	0.254896i
$372$	−0.164141	−	0.505175i	−0.00851033	−	0.0261921i
$373$	4.60679	−	2.65973i	0.238530	−	0.137716i	−0.375971	−	0.926632i	$-0.622691\pi$
$373$	4.60679	−	2.65973i	0.238530	−	0.137716i	0.614501	+	0.788916i	$0.289357\pi$
$374$	8.11746	+	35.2794i	0.419744	+	1.82425i
$375$	3.14679	−	5.45039i	0.162499	−	0.281457i
$376$	−14.1623	+	15.7289i	−0.730367	+	0.811155i
$377$	4.66936	−	6.42683i	0.240484	−	0.330998i
$378$	−12.7092	−	4.45491i	−0.653689	−	0.229136i
$379$	5.21419	−	16.0476i	0.267835	−	0.824312i	−0.723191	−	0.690648i	$-0.757326\pi$
$379$	5.21419	−	16.0476i	0.267835	−	0.824312i	0.991027	−	0.133664i	$-0.0426744\pi$
$380$	0.581711	+	2.73674i	0.0298411	+	0.140392i
$381$	−0.923490	−	8.78642i	−0.0473118	−	0.450142i
$382$	−12.9237	−	29.0272i	−0.661235	−	1.48516i
$383$	−16.2192	−	14.6038i	−0.828760	−	0.746219i	0.141070	−	0.990000i	$-0.454946\pi$
$383$	−16.2192	−	14.6038i	−0.828760	−	0.746219i	−0.969830	+	0.243780i	$0.921612\pi$
$384$	−7.79443			−0.397758
$385$	18.8914	+	8.55332i	0.962795	+	0.435918i
$386$	−15.6414			−0.796127
$387$	9.79597	+	8.82033i	0.497957	+	0.448363i
$388$	−1.71600	−	3.85419i	−0.0871165	−	0.195667i
$389$	−0.757958	−	7.21148i	−0.0384300	−	0.365637i	−0.996789	−	0.0800712i	$-0.974485\pi$
$389$	−0.757958	−	7.21148i	−0.0384300	−	0.365637i	0.958359	−	0.285566i	$-0.0921814\pi$
$390$	−0.437675	−	2.05910i	−0.0221625	−	0.104266i
$391$	0.262158	−	0.806840i	0.0132579	−	0.0408037i
$392$	13.1133	+	12.9468i	0.662322	+	0.653912i
$393$	6.62160	−	9.11386i	0.334016	−	0.459733i
$394$	6.58914	−	7.31798i	0.331956	−	0.368675i
$395$	−14.4209	+	24.9778i	−0.725597	+	1.25677i
$396$	−1.94514	−	0.827357i	−0.0977469	−	0.0415763i
$397$	19.0789	−	11.0152i	0.957545	−	0.552839i	0.0621284	−	0.998068i	$-0.480211\pi$
$397$	19.0789	−	11.0152i	0.957545	−	0.552839i	0.895417	+	0.445229i	$0.146878\pi$
$398$	−0.445756	−	1.37190i	−0.0223437	−	0.0687669i
$399$	−4.06201	+	6.67638i	−0.203355	+	0.334237i
$400$	−2.09423	+	1.52155i	−0.104712	+	0.0760775i
$401$	28.0949	−	5.97175i	1.40299	−	0.298215i	0.556601	−	0.830780i	$-0.312105\pi$
$401$	28.0949	−	5.97175i	1.40299	−	0.298215i	0.846389	+	0.532565i	$0.178772\pi$
$402$	2.65396	+	2.94752i	0.132368	+	0.147009i
$403$	−3.57286	+	0.375523i	−0.177977	+	0.0187061i
$404$	−0.334909	+	3.18644i	−0.0166623	+	0.158531i
$405$	−13.1660	+	4.27790i	−0.654225	+	0.212571i
$406$	18.1556	+	26.2366i	0.901047	+	1.30210i
$407$	12.0331	+	2.34821i	0.596457	+	0.116396i
$408$	−5.78799	−	10.0251i	−0.286548	−	0.496316i
$409$	−1.40295	−	0.298206i	−0.0693713	−	0.0147453i	0.173095	−	0.984905i	$-0.444623\pi$
$409$	−1.40295	−	0.298206i	−0.0693713	−	0.0147453i	−0.242467	+	0.970160i	$0.577956\pi$
$410$	12.3570	−	5.50171i	0.610271	−	0.271710i
$411$	0.0918783	−	0.206362i	0.00453202	−	0.0101791i
$412$	0.0755211	+	0.0245383i	0.00372066	+	0.00120892i
$413$	2.57861	−	2.73474i	0.126885	−	0.134568i
$414$	0.269982	+	0.371599i	0.0132689	+	0.0182631i
$415$	9.82391	+	1.03253i	0.482237	+	0.0506851i
$416$	0.278973	−	1.31247i	0.0136778	−	0.0643489i
$417$	−8.20708	−	4.73836i	−0.401902	−	0.232038i
$418$	−13.9626	+	19.9093i	−0.682931	+	0.973796i
$419$			27.7505i			1.35570i	0.735199	+	0.677851i	$0.237089\pi$
$419$			27.7505i			1.35570i	−0.735199	+	0.677851i	$0.762911\pi$
$420$	0.904389	+	0.116127i	0.0441297	+	0.00566643i
$421$	16.9889	+	12.3432i	0.827989	+	0.601569i	0.918990	−	0.394282i	$-0.129007\pi$
$421$	16.9889	+	12.3432i	0.827989	+	0.601569i	−0.0910006	+	0.995851i	$0.529007\pi$
$422$	−3.43553	−	1.52960i	−0.167239	−	0.0744596i
$423$	15.7506	−	14.1819i	0.765822	−	0.689549i
$424$	−7.56377	+	6.81045i	−0.367329	+	0.330745i
$425$	−3.89591	−	1.73457i	−0.188979	−	0.0841390i
$426$	5.65230	+	4.10664i	0.273855	+	0.198967i
$427$	−0.380538	+	0.499221i	−0.0184155	+	0.0241590i
$428$			0.397283i			0.0192034i
$429$	1.13295	−	1.61548i	0.0546994	−	0.0779963i
$430$	−15.3228	−	8.84664i	−0.738932	−	0.426623i
$431$	5.62998	−	26.4870i	0.271187	−	1.27583i	−0.605915	−	0.795529i	$-0.707193\pi$
$431$	5.62998	−	26.4870i	0.271187	−	1.27583i	0.877102	−	0.480304i	$-0.159474\pi$
$432$	14.9614	+	1.57251i	0.719832	+	0.0756574i
$433$	13.1270	+	18.0677i	0.630843	+	0.868280i	0.998086	−	0.0618445i	$-0.0196983\pi$
$433$	13.1270	+	18.0677i	0.630843	+	0.868280i	−0.367243	+	0.930125i	$0.619698\pi$
$434$	3.32352	−	14.0409i	0.159534	−	0.673986i
$435$	−10.9194	−	3.54792i	−0.523544	−	0.170110i
$436$	−0.0156870	+	0.0352335i	−0.000751269	+	0.00168738i
$437$	0.520601	−	0.231786i	0.0249037	−	0.0110878i
$438$	−1.42480	−	0.302850i	−0.0680794	−	0.0144707i
$439$	−3.78492	−	6.55567i	−0.180644	−	0.312885i	0.761456	−	0.648217i	$-0.224485\pi$
$439$	−3.78492	−	6.55567i	−0.180644	−	0.312885i	−0.942100	+	0.335332i	$0.891152\pi$
$440$	−20.2518	−	3.95207i	−0.965467	−	0.188407i
$441$	−11.7043	−	14.2663i	−0.557349	−	0.679347i
$442$	10.2387	−	3.32676i	0.487006	−	0.158238i
$443$	−0.810767	+	7.71393i	−0.0385207	+	0.366500i	0.958233	+	0.285989i	$0.0923220\pi$
$443$	−0.810767	+	7.71393i	−0.0385207	+	0.366500i	−0.996754	+	0.0805113i	$0.974345\pi$
$444$	0.536113	−	0.0563477i	0.0254428	−	0.00267414i
$445$	20.8683	+	23.1766i	0.989254	+	1.09868i
$446$	−37.5038	+	7.97168i	−1.77586	+	0.377470i
$447$	4.86354	−	3.53357i	0.230038	−	0.167132i
$448$	−15.3999	−	9.36953i	−0.727577	−	0.442669i
$449$	0.951113	+	2.92722i	0.0448858	+	0.138144i	0.970988	−	0.239129i	$-0.0768618\pi$
$449$	0.951113	+	2.92722i	0.0448858	+	0.138144i	−0.926102	+	0.377273i	$0.876862\pi$
$450$	1.99961	−	1.15447i	0.0942623	−	0.0544224i
$451$	11.6671	+	4.96257i	0.549384	+	0.233679i
$452$	−0.966643	+	1.67427i	−0.0454670	+	0.0787512i
$453$	−1.58442	+	1.75968i	−0.0744427	+	0.0826770i
$454$	−17.1158	+	23.5579i	−0.803285	+	1.10563i
$455$	2.04000	−	5.81980i	0.0956366	−	0.272836i
$456$	2.40289	−	7.39533i	0.112526	−	0.346318i
$457$	0.803669	+	3.78097i	0.0375940	+	0.176866i	0.992939	−	0.118627i	$-0.0378493\pi$
$457$	0.803669	+	3.78097i	0.0375940	+	0.176866i	−0.955345	+	0.295493i	$0.904516\pi$
$458$	−3.27808	−	31.1889i	−0.153175	−	1.45736i
$459$	10.0805	+	22.6412i	0.470518	+	1.05680i
$460$	−0.0494113	−	0.0444901i	−0.00230381	−	0.00207436i
$461$	−21.6189			−1.00689			−0.503446	−	0.864027i	$-0.667935\pi$
$461$	−21.6189			−1.00689			−0.503446	+	0.864027i	$0.667935\pi$
$462$	4.61785	+	6.44047i	0.214842	+	0.299638i
$463$	−38.1528			−1.77311			−0.886555	−	0.462623i	$-0.846908\pi$
$463$	−38.1528			−1.77311			−0.886555	+	0.462623i	$0.846908\pi$
$464$	−26.4863	−	23.8484i	−1.22960	−	1.10713i
$465$	2.11187	+	4.74335i	0.0979358	+	0.219967i
$466$	2.38145	+	22.6580i	0.110318	+	1.04961i
$467$	0.00576608	+	0.0271273i	0.000266822	+	0.00125530i	0.978281	−	0.207284i	$-0.0664624\pi$
$467$	0.00576608	+	0.0271273i	0.000266822	+	0.00125530i	−0.978014	+	0.208539i	$0.933129\pi$
$468$	−0.194249	+	0.597837i	−0.00897917	+	0.0276350i
$469$	2.15395	+	11.4180i	0.0994604	+	0.527235i
$470$	−16.7216	+	23.0153i	−0.771309	+	1.06162i
$471$	3.07589	−	3.41612i	0.141729	−	0.157407i
$472$	−1.86997	+	3.23888i	−0.0860722	+	0.149081i
$473$	−3.71874	−	16.1620i	−0.170988	−	0.743131i
$474$	−9.54536	+	5.51102i	−0.438433	+	0.253129i
$475$	−0.885226	−	2.72445i	−0.0406170	−	0.125006i
$476$	−0.107173	+	4.66185i	−0.00491228	+	0.213676i
$477$	8.24561	−	5.99079i	0.377541	−	0.274299i
$478$	−13.8578	+	2.94557i	−0.633842	+	0.134727i
$479$	4.27360	+	4.74632i	0.195266	+	0.216865i	0.832824	−	0.553537i	$-0.186722\pi$
$479$	4.27360	+	4.74632i	0.195266	+	0.216865i	−0.637559	+	0.770402i	$0.720056\pi$
$480$	−1.92864	+	0.202708i	−0.0880299	+	0.00925231i
$481$	0.381103	−	3.62595i	0.0173768	−	0.165329i
$482$	9.90367	−	3.21790i	0.451100	−	0.146571i
$483$	−0.0151626	−	0.185097i	−0.000689922	−	0.00842222i
$484$	1.40594	+	2.25738i	0.0639064	+	0.102608i
$485$	20.6202	+	35.7152i	0.936313	+	1.62174i
$486$	−20.1116	−	4.27485i	−0.912280	−	0.193911i
$487$	32.2806	−	14.3722i	1.46277	−	0.651269i	0.487672	−	0.873027i	$-0.337846\pi$
$487$	32.2806	−	14.3722i	1.46277	−	0.651269i	0.975102	+	0.221758i	$0.0711797\pi$
$488$	0.254040	−	0.570582i	0.0114998	−	0.0258291i
$489$	−4.00033	−	1.29979i	−0.180901	−	0.0587784i
$490$	19.3481	+	15.4642i	0.874059	+	0.698600i
$491$	−6.84289	−	9.41843i	−0.308815	−	0.425048i	0.626196	−	0.779666i	$-0.284611\pi$
$491$	−6.84289	−	9.41843i	−0.308815	−	0.425048i	−0.935011	+	0.354618i	$0.884611\pi$
$492$	0.554420	+	0.0582719i	0.0249952	+	0.00262710i
$493$	12.2078	−	57.4332i	0.549812	−	2.58666i
$494$	6.26272	+	3.61578i	0.281773	+	0.162682i
$495$	19.7550	+	6.05567i	0.887923	+	0.272182i
$496$			16.1180i			0.723718i
$497$	7.89299	+	18.8845i	0.354049	+	0.847086i
$498$	3.05398	+	2.21884i	0.136852	+	0.0994287i
$499$	18.5016	+	8.23746i	0.828247	+	0.368759i	0.776669	−	0.629909i	$-0.216908\pi$
$499$	18.5016	+	8.23746i	0.828247	+	0.368759i	0.0515788	+	0.998669i	$0.483575\pi$
$500$	1.87460	−	1.68790i	0.0838347	−	0.0754851i
$501$	−5.42641	+	4.88596i	−0.242434	+	0.218289i
$502$	−13.5814	−	6.04682i	−0.606167	−	0.269883i
$503$	12.1336	+	8.81555i	0.541009	+	0.393066i	0.824460	−	0.565921i	$-0.191479\pi$
$503$	12.1336	+	8.81555i	0.541009	+	0.393066i	−0.283451	+	0.958987i	$0.591479\pi$
$504$	14.6023	+	11.1308i	0.650438	+	0.495805i
$505$		−	31.3192i		−	1.39369i
$506$	−0.00965899	−	0.577803i	−0.000429394	−	0.0256865i
$507$	6.28274	+	3.62734i	0.279026	+	0.161096i
$508$	0.736232	−	3.46370i	0.0326650	−	0.153677i
$509$	−24.4105	−	2.56564i	−1.08197	−	0.113720i	−0.453277	−	0.891370i	$-0.649745\pi$
$509$	−24.4105	−	2.56564i	−1.08197	−	0.113720i	−0.628698	+	0.777650i	$0.716412\pi$
$510$	−9.14557	−	12.5878i	−0.404973	−	0.557397i
$511$	−3.10472	−	2.92748i	−0.137345	−	0.129504i
$512$	16.4326	+	5.33929i	0.726227	+	0.235965i
$513$	−6.77136	+	15.2087i	−0.298963	+	0.671482i
$514$	5.34932	−	2.38167i	0.235948	−	0.105051i
$515$	−0.759251	−	0.161384i	−0.0334566	−	0.00711142i
$516$	−0.364601	−	0.631508i	−0.0160507	−	0.0278006i
$517$	−26.4691	+	3.23016i	−1.16411	+	0.142062i
$518$	13.2369	+	6.26186i	0.581597	+	0.275130i
$519$	−1.86535	+	0.606089i	−0.0818797	+	0.0266043i
$520$	−0.641402	+	6.10253i	−0.0281273	+	0.267614i
$521$	−28.5400	+	2.99967i	−1.25036	+	0.131418i	−0.706473	−	0.707740i	$-0.749715\pi$
$521$	−28.5400	+	2.99967i	−1.25036	+	0.131418i	−0.543887	+	0.839159i	$0.683048\pi$
$522$	21.2718	+	23.6247i	0.931042	+	1.03403i
$523$	35.2614	−	7.49504i	1.54187	−	0.327735i	0.642972	−	0.765889i	$-0.277701\pi$
$523$	35.2614	−	7.49504i	1.54187	−	0.327735i	0.898900	+	0.438154i	$0.144368\pi$
$524$	3.65292	−	2.65400i	0.159579	−	0.115941i
$525$	−0.933330	−	0.0214567i	−0.0407338	−	0.000936449i
$526$	7.48303	+	23.0304i	0.326276	+	1.00417i
$527$	−22.9960	+	13.2767i	−1.00172	+	0.578344i
$528$	−6.67686	−	5.81277i	−0.290573	−	0.252968i
$529$	11.4932	−	19.9069i	0.499706	−	0.865515i
$530$	−9.15398	+	10.1665i	−0.397624	+	0.441606i
$531$	2.20132	−	3.02985i	0.0955290	−	0.131484i
$532$	−2.37533	+	2.04188i	−0.102983	+	0.0885267i
$533$	1.16513	−	3.58589i	0.0504672	−	0.155322i
$534$	2.47796	+	11.6579i	0.107232	+	0.504486i
$535$	−0.405932	−	3.86218i	−0.0175500	−	0.166977i
$536$	−4.70241	−	10.5618i	−0.203113	−	0.456199i
$537$	−4.53782	−	4.08587i	−0.195821	−	0.176318i
$538$	14.3847			0.620168
$539$	1.75034	+	23.1503i	0.0753925	+	0.997154i
$540$	1.94241			0.0835880
$541$	−14.3212	−	12.8949i	−0.615717	−	0.554394i	0.301155	−	0.953575i	$-0.402628\pi$
$541$	−14.3212	−	12.8949i	−0.615717	−	0.554394i	−0.916872	+	0.399181i	$0.869294\pi$
$542$	−0.0754861	−	0.169545i	−0.00324240	−	0.00728256i
$543$	0.628528	+	5.98005i	0.0269727	+	0.256628i
$544$	−2.06197	−	9.70080i	−0.0884062	−	0.415918i
$545$	0.116500	−	0.358551i	0.00499032	−	0.0153586i
$546$	1.78718	−	1.53629i	0.0764840	−	0.0657473i
$547$	−15.2932	+	21.0493i	−0.653891	+	0.900003i	−0.999260	−	0.0384635i	$-0.987754\pi$
$547$	−15.2932	+	21.0493i	−0.653891	+	0.900003i	0.345369	+	0.938467i	$0.387754\pi$
$548$	0.0605827	−	0.0672839i	0.00258796	−	0.00287423i
$549$	−0.312722	+	0.541650i	−0.0133466	+	0.0231171i
$550$	−2.89370	−	0.255319i	−0.123388	−	0.0108868i
$551$	34.1572	−	19.7207i	1.45515	−	0.840129i
$552$	0.0571029	+	0.175745i	0.00243046	+	0.00748019i
$553$	−32.2810	−	0.742122i	−1.37273	−	0.0315583i
$554$	35.7278	−	25.9578i	1.51793	−	1.10284i
$555$	−5.15425	+	1.09557i	−0.218786	+	0.0465043i
$556$	−2.54160	−	2.82273i	−0.107788	−	0.119710i
$557$	24.3514	−	2.55944i	1.03180	−	0.108447i	0.426537	−	0.904470i	$-0.359733\pi$
$557$	24.3514	−	2.55944i	1.03180	−	0.108447i	0.605266	+	0.796023i	$0.293067\pi$
$558$	1.50276	−	14.2979i	0.0636171	−	0.605276i
$559$	−4.69052	+	1.52404i	−0.198388	+	0.0644601i
$560$	−25.0108	−	11.8316i	−1.05690	−	0.499978i
$561$	2.79336	−	14.3142i	0.117936	−	0.604345i
$562$	−10.1560	−	17.5907i	−0.428404	−	0.742017i
$563$	−3.97817	−	0.845586i	−0.167660	−	0.0356372i	0.123317	−	0.992367i	$-0.460647\pi$
$563$	−3.97817	−	0.845586i	−0.167660	−	0.0356372i	−0.290977	+	0.956730i	$0.593980\pi$
$564$	−1.07110	+	0.476883i	−0.0451013	+	0.0200804i
$565$	7.68649	−	17.2641i	0.323373	−	0.726308i
$566$	−17.3334	−	5.63196i	−0.728576	−	0.236729i
$567$	−11.2761	−	10.6324i	−0.473554	−	0.446519i
$568$	−11.9704	−	16.4759i	−0.502267	−	0.691312i
$569$	−14.4474	−	1.51848i	−0.605667	−	0.0636582i	−0.203269	−	0.979123i	$-0.565157\pi$
$569$	−14.4474	−	1.51848i	−0.605667	−	0.0636582i	−0.402398	+	0.915465i	$0.631823\pi$
$570$	2.17302	−	10.2233i	0.0910179	−	0.428205i
$571$	15.6855	+	9.05601i	0.656416	+	0.378982i	0.790910	−	0.611932i	$-0.209608\pi$
$571$	15.6855	+	9.05601i	0.656416	+	0.378982i	−0.134494	+	0.990914i	$0.542941\pi$
$572$	0.631962	−	0.475486i	0.0264237	−	0.0198811i
$573$			12.8007i			0.534757i
$574$	12.0434	+	9.18027i	0.502683	+	0.383177i
$575$	0.0550749	+	0.0400143i	0.00229678	+	0.00166871i
$576$	−16.4081	−	7.30535i	−0.683670	−	0.304390i
$577$	3.53341	−	3.18149i	0.147098	−	0.132447i	−0.592297	−	0.805720i	$-0.701779\pi$
$577$	3.53341	−	3.18149i	0.147098	−	0.132447i	0.739394	+	0.673273i	$0.235112\pi$
$578$	40.2178	−	36.2123i	1.67284	−	1.50623i
$579$	5.75659	+	2.56300i	0.239236	+	0.106515i
$580$	−3.72295	−	2.70488i	−0.154587	−	0.112314i
$581$	4.26463	+	10.2034i	0.176927	+	0.423309i
$582$			15.7601i			0.653278i
$583$	−12.8212	+	0.214329i	−0.531000	+	0.00887658i
$584$	3.67707	+	2.12296i	0.152158	+	0.0878486i
$585$	1.27754	−	6.01035i	0.0528198	−	0.248497i
$586$	−10.5655	−	1.11048i	−0.436456	−	0.0458734i
$587$	21.3316	+	29.3605i	0.880451	+	1.21184i	0.976296	+	0.216441i	$0.0694449\pi$
$587$	21.3316	+	29.3605i	0.880451	+	1.21184i	−0.0958445	+	0.995396i	$0.530555\pi$
$588$	0.371906	+	0.950650i	0.0153372	+	0.0392042i
$589$	−16.9637	−	5.51184i	−0.698977	−	0.227112i
$590$	−2.04461	+	4.59228i	−0.0841754	+	0.189061i
$591$	−3.62416	+	1.61358i	−0.149078	+	0.0663738i
$592$	−16.0000	−	3.40091i	−0.657597	−	0.139777i
$593$	22.1014	+	38.2808i	0.907596	+	1.57200i	0.817394	+	0.576079i	$0.195418\pi$
$593$	22.1014	+	38.2808i	0.907596	+	1.57200i	0.0902024	+	0.995923i	$0.471249\pi$
$594$	11.5045	+	12.3553i	0.472036	+	0.506946i
$595$	−3.72146	−	45.4297i	−0.152565	−	1.86244i
$596$	2.29160	−	0.744587i	0.0938678	−	0.0304995i
$597$	−0.0607447	+	0.577947i	−0.00248612	+	0.0236538i
$598$	−0.170911	+	0.0179635i	−0.00698909	+	0.000734583i
$599$	−27.6849	−	30.7472i	−1.13117	−	1.25630i	−0.962694	−	0.270592i	$-0.912781\pi$
$599$	−27.6849	−	30.7472i	−1.13117	−	1.25630i	−0.168481	−	0.985705i	$-0.553886\pi$
$600$	0.908609	−	0.193131i	0.0370938	−	0.00788454i
$601$	29.8418	−	21.6813i	1.21727	−	0.884400i	0.221401	−	0.975183i	$-0.428937\pi$
$601$	29.8418	−	21.6813i	1.21727	−	0.884400i	0.995871	+	0.0907828i	$0.0289369\pi$
$602$	0.455260	−	19.8030i	0.0185550	−	0.807111i
$603$	3.57758	+	11.0107i	0.145690	+	0.448389i
$604$	−0.821919	+	0.474535i	−0.0334434	+	0.0193086i
$605$	−15.9744	−	20.5086i	−0.649451	−	0.833793i
$606$	5.98437	−	10.3652i	0.243098	−	0.421059i
$607$	−18.4948	+	20.5406i	−0.750681	+	0.833716i	−0.990559	−	0.137087i	$-0.956226\pi$
$607$	−18.4948	+	20.5406i	−0.750681	+	0.833716i	0.239878	+	0.970803i	$0.422893\pi$
$608$	3.91575	−	5.38957i	0.158805	−	0.218576i
$609$	−2.38277	−	12.6310i	−0.0965548	−	0.511832i
$610$	0.259421	−	0.798415i	0.0105036	−	0.0323269i
$611$	1.64871	+	7.75656i	0.0666996	+	0.313797i
$612$	0.485658	+	4.62073i	0.0196316	+	0.186782i
$613$	5.56874	+	12.5076i	0.224919	+	0.505177i	0.990392	−	0.138292i	$-0.0441612\pi$
$613$	5.56874	+	12.5076i	0.224919	+	0.505177i	−0.765472	+	0.643469i	$0.777494\pi$
$614$	24.7325	+	22.2693i	0.998123	+	0.898714i
$615$	−5.44933			−0.219738
$616$	−7.00049	−	22.0140i	−0.282058	−	0.886970i
$617$	−34.9288			−1.40618			−0.703090	−	0.711100i	$-0.748197\pi$
$617$	−34.9288			−1.40618			−0.703090	+	0.711100i	$0.748197\pi$
$618$	−0.220441	−	0.198486i	−0.00886744	−	0.00798428i
$619$	−16.1125	−	36.1892i	−0.647614	−	1.45457i	−0.876641	−	0.481146i	$-0.840221\pi$
$619$	−16.1125	−	36.1892i	−0.647614	−	1.45457i	0.229026	−	0.973420i	$-0.426446\pi$
$620$	0.217534	+	2.06970i	0.00873638	+	0.0831211i
$621$	−0.0822557	−	0.386983i	−0.00330081	−	0.0155291i
$622$	1.60692	−	4.94559i	0.0644316	−	0.198300i
$623$	−11.5497	+	32.9496i	−0.462731	+	1.32010i
$624$	−1.54741	+	2.12983i	−0.0619461	+	0.0852615i
$625$	−18.4564	+	20.4980i	−0.738258	+	0.819918i
$626$	7.47974	−	12.9553i	0.298950	−	0.517797i
$627$	8.40105	−	5.03942i	0.335506	−	0.201255i
$628$	1.59562	−	0.921229i	0.0636720	−	0.0367611i
$629$	−8.32741	−	25.6291i	−0.332035	−	1.02190i
$630$	21.0834	+	12.8274i	0.839982	+	0.511058i
$631$	−13.4804	+	9.79409i	−0.536647	+	0.389897i	−0.822838	−	0.568276i	$-0.807611\pi$
$631$	−13.4804	+	9.79409i	−0.536647	+	0.389897i	0.286191	+	0.958172i	$0.407611\pi$
$632$	31.4260	−	6.67980i	1.25006	−	0.265708i
$633$	1.01376	+	1.12589i	0.0402932	+	0.0447502i
$634$	−31.4188	+	3.30225i	−1.24780	+	0.131149i
$635$	−3.61817	+	34.4246i	−0.143583	+	1.36610i
$636$	−0.536223	+	0.174230i	−0.0212626	+	0.00690865i
$637$	6.81211	−	1.12359i	0.269906	−	0.0445184i
$638$	−4.84500	−	39.7016i	−0.191815	−	1.57180i
$639$	10.1967	+	17.6612i	0.403376	+	0.698668i
$640$	29.8707	+	6.34922i	1.18074	+	0.250975i
$641$	−35.6199	+	15.8590i	−1.40690	+	0.626394i	−0.962956	−	0.269659i	$-0.913089\pi$
$641$	−35.6199	+	15.8590i	−1.40690	+	0.626394i	−0.443947	+	0.896053i	$0.646422\pi$
$642$	0.603628	−	1.35577i	0.0238233	−	0.0535080i
$643$	−13.6671	−	4.44072i	−0.538979	−	0.175125i	0.0268622	−	0.999639i	$-0.491448\pi$
$643$	−13.6671	−	4.44072i	−0.538979	−	0.175125i	−0.565841	+	0.824514i	$0.691448\pi$
$644$	0.0171457	−	0.0724358i	0.000675637	−	0.00285437i
$645$	4.18973	+	5.76667i	0.164970	+	0.227062i
$646$	53.1577	+	5.58710i	2.09146	+	0.219822i
$647$	−5.47446	+	25.7553i	−0.215223	+	1.01255i	0.729324	+	0.684169i	$0.239835\pi$
$647$	−5.47446	+	25.7553i	−0.215223	+	1.01255i	−0.944547	+	0.328377i	$0.893499\pi$
$648$	13.3549	+	7.71044i	0.524629	+	0.302895i
$649$	−4.45624	+	1.53073i	−0.174923	+	0.0600863i
$650$			0.863881i			0.0338842i
$651$	−3.52392	+	4.62296i	−0.138113	+	0.181188i
$652$	−1.36391	−	0.990938i	−0.0534148	−	0.0388081i
$653$	−13.4642	−	5.99465i	−0.526895	−	0.234589i	0.126009	−	0.992029i	$-0.459783\pi$
$653$	−13.4642	−	5.99465i	−0.526895	−	0.234589i	−0.652905	+	0.757440i	$0.726450\pi$
$654$	0.107067	−	0.0964036i	0.00418665	−	0.00376968i
$655$	−32.8001	+	29.5333i	−1.28161	+	1.15396i
$656$	−15.4536	−	6.88038i	−0.603361	−	0.268634i
$657$	−3.43977	−	2.49914i	−0.134198	−	0.0975006i
$658$	−31.5897	−	4.05624i	−1.23149	−	0.158129i
$659$		−	8.67875i		−	0.338076i	−0.985610	−	0.169038i	$-0.945934\pi$
$659$		−	8.67875i		−	0.338076i	0.985610	−	0.169038i	$-0.0540661\pi$
$660$	−0.935823	−	0.656300i	−0.0364269	−	0.0255465i
$661$	42.8215	+	24.7230i	1.66556	+	0.961613i	0.969986	+	0.243160i	$0.0781841\pi$
$661$	42.8215	+	24.7230i	1.66556	+	0.961613i	0.695576	+	0.718452i	$0.255149\pi$
$662$	−6.29281	+	29.6053i	−0.244577	+	1.15064i
$663$	−4.31333	−	0.453349i	−0.167516	−	0.0176066i
$664$	−6.46770	−	8.90202i	−0.250995	−	0.345465i
$665$	21.0054	−	22.2772i	0.814554	−	0.863871i
$666$	13.8761	+	4.50863i	0.537690	+	0.174706i
$667$	−0.381232	+	0.856261i	−0.0147614	+	0.0331546i
$668$	−2.67367	+	1.19039i	−0.103447	+	0.0460577i
$669$	15.1090	+	3.21151i	0.584146	+	0.124164i
$670$	−7.76982	−	13.4577i	−0.300174	−	0.519917i
$671$	0.713407	−	0.332026i	0.0275408	−	0.0128177i
$672$	−1.23542	−	1.78530i	−0.0476573	−	0.0688695i
$673$	43.1998	−	14.0365i	1.66523	−	0.541066i	0.683273	−	0.730163i	$-0.260556\pi$
$673$	43.1998	−	14.0365i	1.66523	−	0.541066i	0.981958	+	0.189097i	$0.0605560\pi$
$674$	2.09576	−	19.9398i	0.0807256	−	0.768053i
$675$	−1.97787	+	0.207883i	−0.0761284	+	0.00800142i
$676$	1.94566	+	2.16088i	0.0748332	+	0.0831107i
$677$	6.65241	−	1.41401i	0.255673	−	0.0543449i	−0.0782920	−	0.996930i	$-0.524947\pi$
$677$	6.65241	−	1.41401i	0.255673	−	0.0543449i	0.333965	+	0.942586i	$0.391613\pi$
$678$	5.84266	−	4.24494i	0.224386	−	0.163026i
$679$	−23.9979	+	39.4433i	−0.920954	+	1.51369i
$680$	14.0151	+	43.1342i	0.537456	+	1.65412i
$681$	10.1594	−	5.86554i	0.389310	−	0.224768i
$682$	−11.8766	+	13.6421i	−0.454779	+	0.522384i
$683$	4.76061	−	8.24562i	0.182160	−	0.315510i	−0.760456	−	0.649389i	$-0.775025\pi$
$683$	4.76061	−	8.24562i	0.182160	−	0.315510i	0.942616	+	0.333880i	$0.108358\pi$
$684$	−2.08834	+	2.31933i	−0.0798495	+	0.0886819i
$685$	−0.520206	+	0.716002i	−0.0198760	+	0.0273570i
$686$	−4.79177	+	27.3123i	−0.182951	+	1.04279i
$687$	−3.90415	+	12.0157i	−0.148953	+	0.458429i
$688$	4.60047	+	21.6435i	0.175391	+	0.825151i
$689$	0.398602	+	3.79245i	0.0151855	+	0.144481i
$690$	0.101024	+	0.226903i	0.00384590	+	0.00863804i
$691$	−10.5081	−	9.46154i	−0.399747	−	0.359934i	0.444601	−	0.895729i	$-0.353345\pi$
$691$	−10.5081	−	9.46154i	−0.399747	−	0.359934i	−0.844348	+	0.535795i	$0.820012\pi$
$692$	−0.786126			−0.0298840
$693$	4.66749	+	22.6564i	0.177303	+	0.860647i
$694$	0.528045			0.0200443
$695$	27.5923	+	24.8442i	1.04664	+	0.942396i
$696$	5.20195	+	11.6838i	0.197179	+	0.442872i
$697$	−2.91303	−	27.7156i	−0.110339	−	1.04980i
$698$	11.0004	+	51.7530i	0.416373	+	1.95888i
$699$	2.83627	−	8.72915i	0.107278	−	0.330167i
$700$	−0.353121	−	0.123779i	−0.0133467	−	0.00467839i
$701$	−0.0985827	+	0.135687i	−0.00372342	+	0.00512485i	−0.810875	−	0.585220i	$-0.801008\pi$
$701$	−0.0985827	+	0.135687i	−0.00372342	+	0.00512485i	0.807151	+	0.590345i	$0.201008\pi$
$702$	3.35935	−	3.73094i	0.126791	−	0.140815i
$703$	9.05088	−	15.6766i	0.341360	−	0.591253i
$704$	11.6241	+	19.3781i	0.438098	+	0.730338i
$705$	9.92540	−	5.73043i	0.373812	−	0.215821i
$706$	9.09609	+	27.9949i	0.342336	+	1.05360i
$707$	30.7603	−	16.8289i	1.15686	−	0.632918i
$708$	−0.167608	+	0.121775i	−0.00629911	+	0.00457657i
$709$	−26.5063	+	5.63410i	−0.995467	+	0.211593i	−0.676715	−	0.736245i	$-0.736597\pi$
$709$	−26.5063	+	5.63410i	−0.995467	+	0.211593i	−0.318752	+	0.947838i	$0.603264\pi$
$710$	−18.3162	−	20.3422i	−0.687395	−	0.763429i
$711$	−31.9962	+	3.36294i	−1.19995	+	0.126120i
$712$	3.63139	−	34.5503i	0.136092	−	1.29483i
$713$	0.403130	−	0.130985i	0.0150973	−	0.00490542i
$714$	7.44892	−	15.7463i	0.278769	−	0.589289i
$715$	−5.65778	+	5.26816i	−0.211589	+	0.197018i
$716$	−1.22372	−	2.11954i	−0.0457326	−	0.0792111i
$717$	5.58283	+	1.18667i	0.208494	+	0.0443169i
$718$	−8.28682	+	3.68953i	−0.309262	+	0.137692i
$719$	3.73942	−	8.39887i	0.139457	−	0.313225i	−0.830293	−	0.557328i	$-0.811827\pi$
$719$	3.73942	−	8.39887i	0.139457	−	0.313225i	0.969749	+	0.244103i	$0.0784934\pi$
$720$	−26.2187	−	8.51896i	−0.977112	−	0.317483i
$721$	−0.249469	−	0.832420i	−0.00929072	−	0.0310009i
$722$	4.38276	+	6.03235i	0.163109	+	0.224501i
$723$	−4.17218	−	0.438514i	−0.155165	−	0.0163085i
$724$	−0.501080	+	2.35740i	−0.0186225	+	0.0876120i
$725$	4.08041	+	2.35583i	0.151543	+	0.0874932i
$726$	−1.36808	−	9.83975i	−0.0507741	−	0.365187i
$727$			12.8249i			0.475647i	0.971308	+	0.237824i	$0.0764341\pi$
$727$			12.8249i			0.475647i	−0.971308	+	0.237824i	$0.923566\pi$
$728$	−6.33828	+	2.64916i	−0.234912	+	0.0981842i
$729$	−7.51597	−	5.46067i	−0.278369	−	0.202247i
$730$	5.21357	+	2.32123i	0.192963	+	0.0859127i
$731$	−27.0899	+	24.3919i	−1.00196	+	0.902165i
$732$	0.0257120	−	0.0231512i	0.000950343	−	0.000855693i
$733$	−29.2783	−	13.0355i	−1.08142	−	0.481479i	−0.212869	−	0.977081i	$-0.568281\pi$
$733$	−29.2783	−	13.0355i	−1.08142	−	0.481479i	−0.868550	+	0.495602i	$0.834947\pi$
$734$	18.5537	+	13.4801i	0.684830	+	0.497558i
$735$	−4.58683	−	8.86174i	−0.169188	−	0.326870i
$736$			0.158315i			0.00583555i
$737$	4.26888	−	13.9261i	0.157246	−	0.512974i
$738$	13.0670	+	7.54424i	0.481003	+	0.277707i
$739$	2.31380	−	10.8856i	0.0851147	−	0.400433i	−0.914880	−	0.403726i	$-0.867715\pi$
$739$	2.31380	−	10.8856i	0.0851147	−	0.400433i	0.999995	+	0.00329308i	$0.00104822\pi$
$740$	−2.10045	−	0.220767i	−0.0772142	−	0.00811554i
$741$	−1.71242	−	2.35694i	−0.0629073	−	0.0865845i
$742$	−14.9039	−	3.52779i	−0.547139	−	0.129509i
$743$	−3.50271	−	1.13810i	−0.128502	−	0.0417528i	0.244060	−	0.969760i	$-0.421521\pi$
$743$	−3.50271	−	1.13810i	−0.128502	−	0.0417528i	−0.372562	+	0.928007i	$0.621521\pi$
$744$	2.35250	−	5.28379i	0.0862467	−	0.193713i
$745$	−21.5170	+	9.58000i	−0.788323	+	0.350984i
$746$	−7.79053	−	1.65593i	−0.285231	−	0.0606278i
$747$	5.50936	+	9.54249i	0.201577	+	0.349141i
$748$	2.83772	−	5.11048i	0.103757	−	0.186858i
$749$	3.57514	−	2.47398i	0.130633	−	0.0903972i
$750$	−8.96187	+	2.91189i	−0.327241	+	0.106327i
$751$	5.05066	−	48.0539i	0.184301	−	1.75351i	−0.377290	−	0.926095i	$-0.623144\pi$
$751$	5.05066	−	48.0539i	0.184301	−	1.75351i	0.561591	−	0.827415i	$-0.310189\pi$
$752$	35.3824	−	3.71884i	1.29026	−	0.135612i
$753$	4.00759	+	4.45088i	0.146045	+	0.162199i
$754$	−11.6342	+	2.47294i	−0.423694	+	0.0900590i
$755$	7.50542	−	5.45300i	0.273150	−	0.198455i
$756$	1.04373	+	1.90775i	0.0379600	+	0.0693841i
$757$	−16.6580	−	51.2680i	−0.605444	−	1.86337i	−0.493708	−	0.869628i	$-0.664359\pi$
$757$	−16.6580	−	51.2680i	−0.605444	−	1.86337i	−0.111736	−	0.993738i	$-0.535641\pi$
$758$	−21.8792	+	12.6319i	−0.794687	+	0.458813i
$759$	−0.0911239	+	0.214235i	−0.00330759	+	0.00777623i
$760$	−15.2327	+	26.3839i	−0.552550	+	0.957044i
$761$	31.2597	−	34.7175i	1.13316	−	1.25851i	0.171229	−	0.985231i	$-0.445226\pi$
$761$	31.2597	−	34.7175i	1.13316	−	1.25851i	0.961936	−	0.273276i	$-0.0881072\pi$
$762$	−7.77519	+	10.7016i	−0.281665	+	0.387679i
$763$	0.414753	−	0.0782411i	0.0150150	−	0.00283252i
$764$	−1.58546	+	4.87953i	−0.0573598	+	0.176535i
$765$	−9.44265	−	44.4242i	−0.341400	−	1.60616i
$766$	3.41574	+	32.4986i	0.123416	+	1.17422i
$767$	0.569925	+	1.28007i	0.0205788	+	0.0462207i
$768$	2.56447	+	2.30906i	0.0925373	+	0.0833210i
$769$	23.0259			0.830334			0.415167	−	0.909745i	$-0.363723\pi$
$769$	23.0259			0.830334			0.415167	+	0.909745i	$0.363723\pi$
$770$	−12.4508	−	28.4436i	−0.448695	−	1.02503i
$771$	−2.35900			−0.0849572
$772$	1.87692	+	1.68999i	0.0675520	+	0.0608240i
$773$	18.8562	+	42.3518i	0.678212	+	1.52329i	0.843550	+	0.537051i	$0.180462\pi$
$773$	18.8562	+	42.3518i	0.678212	+	1.52329i	−0.165338	+	0.986237i	$0.552872\pi$
$774$	−2.06302	−	19.6283i	−0.0741538	−	0.705526i
$775$	−0.443012	−	2.08421i	−0.0159134	−	0.0748669i
$776$	14.1960	−	43.6907i	0.509606	−	1.56841i
$777$	−3.84558	−	4.47358i	−0.137960	−	0.160489i
$778$	−6.38152	+	8.78341i	−0.228788	+	0.314900i
$779$	12.5261	−	13.9116i	0.448792	−	0.498434i
$780$	−0.169957	+	0.294375i	−0.00608545	+	0.0105403i
$781$	2.25507	−	25.5582i	0.0806926	−	0.914546i
$782$	−1.10004	+	0.635106i	−0.0393372	+	0.0227113i
$783$	−8.46149	−	26.0418i	−0.302389	−	0.930657i
$784$	−1.81873	−	30.9221i	−0.0649548	−	1.10436i
$785$	−14.5705	+	10.5861i	−0.520043	+	0.377834i
$786$	−16.4985	+	3.50686i	−0.588481	+	0.125086i
$787$	5.54534	+	6.15872i	0.197670	+	0.219535i	0.833828	−	0.552024i	$-0.186144\pi$
$787$	5.54534	+	6.15872i	0.197670	+	0.219535i	−0.636158	+	0.771558i	$0.719478\pi$
$788$	−1.58136	+	0.166207i	−0.0563334	+	0.00592088i
$789$	1.01974	−	9.70217i	0.0363037	−	0.345406i
$790$	41.0700	−	13.3445i	1.46121	−	0.474775i
$791$	21.0863	−	1.72732i	0.749743	−	0.0614166i
$792$	−9.71182	−	20.8673i	−0.345095	−	0.741486i
$793$	−0.117003	−	0.202656i	−0.00415491	−	0.00719652i
$794$	−32.2644	−	6.85800i	−1.14502	−	0.243381i
$795$	5.03487	−	2.24167i	0.178569	−	0.0795038i
$796$	−0.0947383	+	0.212786i	−0.00335791	+	0.00754199i
$797$	−3.02147	−	0.981734i	−0.107026	−	0.0347748i	0.255014	−	0.966937i	$-0.417920\pi$
$797$	−3.02147	−	0.981734i	−0.107026	−	0.0347748i	−0.362040	+	0.932162i	$0.617920\pi$
$798$	11.2085	−	3.35909i	0.396776	−	0.118910i
$799$	34.4511	+	47.4178i	1.21879	+	1.67752i
$800$	0.791466	+	0.0831864i	0.0279826	+	0.00294108i
$801$	−7.23298	+	34.0285i	−0.255565	+	1.20234i
$802$	−37.2433	−	21.5024i	−1.31511	−	0.759277i
$803$	1.73782	+	5.05913i	0.0613264	+	0.178533i
$804$		−	0.640444i		−	0.0225867i
$805$	−0.0926695	+	0.721703i	−0.00326617	+	0.0254367i
$806$	4.35165	+	3.16166i	0.153280	+	0.111365i
$807$	−5.29408	−	2.35707i	−0.186360	−	0.0829729i
$808$	−25.9266	+	23.3444i	−0.912093	+	0.821253i
$809$	−19.9750	+	17.9855i	−0.702283	+	0.632338i	−0.940864	−	0.338784i	$-0.889984\pi$
$809$	−19.9750	+	17.9855i	−0.702283	+	0.632338i	0.238581	+	0.971123i	$0.423318\pi$
$810$	18.9354	+	8.43056i	0.665320	+	0.296220i
$811$	−14.9220	−	10.8414i	−0.523981	−	0.380695i	0.294120	−	0.955768i	$-0.404973\pi$
$811$	−14.9220	−	10.8414i	−0.523981	−	0.380695i	−0.818102	+	0.575074i	$0.804973\pi$
$812$	0.656138	−	5.10995i	0.0230259	−	0.179324i
$813$			0.0747675i			0.00262221i
$814$	−11.0363	−	14.6682i	−0.386823	−	0.514120i
$815$	14.2718	+	8.23980i	0.499918	+	0.288628i
$816$	−4.04563	+	19.0332i	−0.141625	+	0.666294i
$817$	−24.3524	−	2.55954i	−0.851982	−	0.0895469i
$818$	1.26227	+	1.73736i	0.0441341	+	0.0607454i
$819$	6.58957	−	1.97484i	0.230258	−	0.0690064i
$820$	−2.07725	−	0.674938i	−0.0725406	−	0.0235699i
$821$	4.77936	−	10.7346i	0.166801	−	0.374641i	−0.810734	−	0.585415i	$-0.800932\pi$
$821$	4.77936	−	10.7346i	0.166801	−	0.374641i	0.977535	+	0.210774i	$0.0675984\pi$
$822$	−0.308976	+	0.137565i	−0.0107768	+	0.00479813i
$823$	9.07144	+	1.92819i	0.316211	+	0.0672126i	0.363283	−	0.931679i	$-0.381656\pi$
$823$	9.07144	+	1.92819i	0.316211	+	0.0672126i	−0.0470724	+	0.998891i	$0.514989\pi$
$824$	0.432327	+	0.748812i	0.0150608	+	0.0260861i
$825$	1.02315	+	0.568128i	0.0356215	+	0.0197797i
$826$	−5.60898	+	0.459470i	−0.195161	+	0.0159870i
$827$	20.9538	−	6.80830i	0.728635	−	0.236748i	0.0788720	−	0.996885i	$-0.474868\pi$
$827$	20.9538	−	6.80830i	0.728635	−	0.236748i	0.649763	+	0.760137i	$0.274868\pi$
$828$	0.00775262	−	0.0737612i	0.000269422	−	0.00256338i
$829$	26.4863	−	2.78382i	0.919906	−	0.0966860i	0.367275	−	0.930112i	$-0.380291\pi$
$829$	26.4863	−	2.78382i	0.919906	−	0.0966860i	0.552631	+	0.833426i	$0.313624\pi$
$830$	−9.89637	−	10.9910i	−0.343508	−	0.381504i
$831$	−17.4025	+	3.69902i	−0.603687	+	0.128318i
$832$	5.43658	−	3.94991i	0.188479	−	0.136938i
$833$	42.6193	−	28.0661i	1.47667	−	0.972432i
$834$	4.38465	+	13.4946i	0.151828	+	0.467279i
$835$	24.7758	−	14.3043i	0.857400	−	0.495020i
$836$	3.82659	−	0.880462i	0.132345	−	0.0304514i
$837$	−6.19152	+	10.7240i	−0.214010	+	0.370676i
$838$	27.8021	−	30.8773i	0.960407	−	1.06664i
$839$	1.29965	−	1.78881i	0.0448689	−	0.0617567i	−0.785993	−	0.618235i	$-0.787848\pi$
$839$	1.29965	−	1.78881i	0.0448689	−	0.0617567i	0.830862	+	0.556479i	$0.187848\pi$
$840$	6.47217	+	7.52910i	0.223311	+	0.259779i
$841$	−11.0849	+	34.1157i	−0.382237	+	1.17640i
$842$	−6.53705	−	30.7544i	−0.225282	−	1.05987i
$843$	0.855353	+	8.13814i	0.0294599	+	0.280292i
$844$	0.246987	+	0.554742i	0.00850165	+	0.0190950i
$845$	−21.1227	−	19.0189i	−0.726642	−	0.654272i
$846$	−31.7336			−1.09102
$847$	11.5590	−	26.7093i	0.397173	−	0.917744i
$848$	17.1086			0.587511
$849$	5.45644	+	4.91300i	0.187265	+	0.168614i
$850$	2.59709	+	5.83316i	0.0890794	+	0.200076i
$851$	0.0449655	+	0.427818i	0.00154140	+	0.0146654i
$852$	−0.234554	−	1.10349i	−0.00803570	−	0.0378050i
$853$	−2.49530	+	7.67974i	−0.0854374	+	0.262949i	−0.984644	−	0.174575i	$-0.944145\pi$
$853$	−2.49530	+	7.67974i	−0.0854374	+	0.262949i	0.899206	+	0.437525i	$0.144145\pi$
$854$	0.923564	−	0.174226i	0.0316037	−	0.00596189i
$855$	17.9319	−	24.6812i	0.613259	−	0.844079i
$856$	−2.89461	+	3.21479i	−0.0989358	+	0.109879i
$857$	−6.55177	+	11.3480i	−0.223804	+	0.387640i	−0.955960	−	0.293497i	$-0.905181\pi$
$857$	−6.55177	+	11.3480i	−0.223804	+	0.387640i	0.732156	+	0.681137i	$0.238514\pi$
$858$	−2.87909	+	0.662453i	−0.0982906	+	0.0226158i
$859$	−5.96487	+	3.44382i	−0.203519	+	0.117502i	−0.598296	−	0.801275i	$-0.704155\pi$
$859$	−5.96487	+	3.44382i	−0.203519	+	0.117502i	0.394777	+	0.918777i	$0.370822\pi$
$860$	0.882852	+	2.71714i	0.0301050	+	0.0926536i
$861$	−2.92813	−	5.35209i	−0.0997903	−	0.182399i
$862$	−32.8005	+	23.8310i	−1.11719	+	0.811686i
$863$	−20.8945	+	4.44127i	−0.711258	+	0.151183i	−0.549312	−	0.835617i	$-0.685110\pi$
$863$	−20.8945	+	4.44127i	−0.711258	+	0.151183i	−0.161946	+	0.986800i	$0.551777\pi$
$864$	−3.09471	−	3.43702i	−0.105284	−	0.116930i
$865$	7.64232	−	0.803240i	0.259847	−	0.0273110i
$866$	3.49523	−	33.2549i	0.118773	−	1.13005i
$867$	−20.7353	+	6.73731i	−0.704208	+	0.228811i
$868$	−1.91588	+	1.32578i	−0.0650291	+	0.0449998i
$869$	35.3875	+	19.6498i	1.20044	+	0.666574i
$870$	8.59522	+	14.8874i	0.291405	+	0.504729i
$871$	−4.23693	−	0.900588i	−0.143563	−	0.0305153i
$872$	−0.383650	+	0.170812i	−0.0129920	+	0.00578443i
$873$	−18.7110	+	42.0255i	−0.633270	+	1.42235i
$874$	−0.811476	−	0.263665i	−0.0274486	−	0.00891859i
$875$	−26.8630	−	6.35854i	−0.908135	−	0.214958i
$876$	0.138250	+	0.190284i	0.00467103	+	0.00642912i
$877$	23.3188	+	2.45091i	0.787421	+	0.0827613i	0.489699	−	0.871891i	$-0.337107\pi$
$877$	23.3188	+	2.45091i	0.787421	+	0.0827613i	0.297722	+	0.954653i	$0.403773\pi$
$878$	−2.35646	+	11.0863i	−0.0795267	+	0.374144i
$879$	3.70651	+	2.13995i	0.125017	+	0.0721788i
$880$	20.8529	+	27.7152i	0.702950	+	0.934280i
$881$			39.3172i			1.32463i	0.749225	+	0.662315i	$0.230426\pi$
$881$			39.3172i			1.32463i	−0.749225	+	0.662315i	$0.769574\pi$
$882$	−1.26968	+	27.5998i	−0.0427523	+	0.929334i
$883$	21.9250	+	15.9295i	0.737836	+	0.536069i	0.892033	−	0.451971i	$-0.149279\pi$
$883$	21.9250	+	15.9295i	0.737836	+	0.536069i	−0.154196	+	0.988040i	$0.549279\pi$
$884$	−1.58806	−	0.707049i	−0.0534122	−	0.0237806i
$885$	1.50498	−	1.35509i	0.0505893	−	0.0455508i
$886$	8.63038	−	7.77083i	0.289943	−	0.261066i
$887$	−14.5417	−	6.47436i	−0.488261	−	0.217388i	0.147814	−	0.989015i	$-0.452776\pi$
$887$	−14.5417	−	6.47436i	−0.488261	−	0.217388i	−0.636075	+	0.771627i	$0.719443\pi$
$888$	4.74875	+	3.45017i	0.159358	+	0.115780i
$889$	−35.7545	+	14.9440i	−1.19917	+	0.501205i
$890$		−	46.6952i		−	1.56523i
$891$	6.31166	+	18.3744i	0.211448	+	0.615566i
$892$	5.36165	+	3.09555i	0.179521	+	0.103647i
$893$	−8.18571	+	38.5107i	−0.273924	+	1.28871i
$894$	−8.95168	−	0.940859i	−0.299389	−	0.0314670i
$895$	14.0621	+	19.3548i	0.470043	+	0.646959i
$896$	9.81471	+	32.7494i	0.327887	+	1.09408i
$897$	0.0658449	+	0.0213943i	0.00219850	+	0.000714335i
$898$	1.87438	−	4.20993i	0.0625489	−	0.140487i
$899$	26.8007	−	11.9324i	0.893854	−	0.397969i
$900$	−0.364683	−	0.0775157i	−0.0121561	−	0.00258386i
$901$	14.0927	+	24.4093i	0.469497	+	0.813192i
$902$	−8.00995	−	17.2105i	−0.266702	−	0.573048i
$903$	−3.41247	+	7.21361i	−0.113560	+	0.240054i
$904$	−20.0208	+	6.50516i	−0.665883	+	0.216358i
$905$	2.46253	−	23.4294i	0.0818573	−	0.778820i
$906$	3.52590	−	0.370587i	0.117140	−	0.0123119i
$907$	−8.63348	−	9.58845i	−0.286670	−	0.318379i	0.582560	−	0.812788i	$-0.302051\pi$
$907$	−8.63348	−	9.58845i	−0.286670	−	0.318379i	−0.869230	+	0.494409i	$0.835385\pi$
$908$	4.59918	−	0.977587i	0.152629	−	0.0324424i
$909$	28.2637	−	20.5348i	0.937448	−	0.681096i
$910$	−8.10046	+	4.43176i	−0.268528	+	0.146911i
$911$	−6.23228	−	19.1810i	−0.206485	−	0.635494i	−0.999649	−	0.0264869i	$-0.991568\pi$
$911$	−6.23228	−	19.1810i	−0.206485	−	0.635494i	0.793165	−	0.609007i	$-0.208432\pi$
$912$	−11.3196	+	6.53537i	−0.374829	+	0.216408i
$913$	1.21843	−	13.8093i	0.0403241	−	0.457021i
$914$	2.89377	−	5.01215i	0.0957172	−	0.165787i
$915$	−0.226304	+	0.251336i	−0.00748138	+	0.00830891i
$916$	−2.97647	+	4.09676i	−0.0983453	+	0.135361i
$917$	−46.6310	−	16.3454i	−1.53989	−	0.539774i
$918$	11.4669	−	35.2915i	0.378465	−	1.16479i
$919$	−0.231466	−	1.08896i	−0.00763537	−	0.0359216i	0.974165	−	0.225837i	$-0.0725118\pi$
$919$	−0.231466	−	1.08896i	−0.00763537	−	0.0359216i	−0.981800	+	0.189916i	$0.939178\pi$
$920$	−0.0756776	−	0.720024i	−0.00249502	−	0.0237385i
$921$	−5.45340	−	12.2485i	−0.179696	−	0.403603i
$922$	24.0548	+	21.6590i	0.792203	+	0.713302i
$923$	−7.63011			−0.251148
$924$	0.141737	−	1.27178i	0.00466281	−	0.0418384i
$925$	2.16243			0.0711003
$926$	42.4517	+	38.2236i	1.39505	+	1.25611i
$927$	−0.352172	−	0.790992i	−0.0115669	−	0.0259796i
$928$	1.14533	+	10.8971i	0.0375975	+	0.357716i
$929$	−1.92251	−	9.04471i	−0.0630756	−	0.296747i	0.935291	−	0.353879i	$-0.115138\pi$
$929$	−1.92251	−	9.04471i	−0.0630756	−	0.296747i	−0.998367	+	0.0571322i	$0.981804\pi$
$930$	2.40233	−	7.39360i	0.0787754	−	0.242446i
$931$	33.1666	+	8.66023i	1.08699	+	0.283828i
$932$	2.16233	−	2.97619i	0.0708295	−	0.0974885i
$933$	−1.40179	+	1.55684i	−0.0458924	+	0.0509687i
$934$	0.0207619	−	0.0359606i	0.000679350	−	0.00117667i
$935$	−22.3651	+	52.5810i	−0.731418	+	1.71958i
$936$	−5.92771	+	3.42237i	−0.193753	+	0.111864i
$937$	7.01380	+	21.5862i	0.229131	+	0.705192i	0.997846	+	0.0656008i	$0.0208964\pi$
$937$	7.01380	+	21.5862i	0.229131	+	0.705192i	−0.768715	+	0.639591i	$0.779104\pi$
$938$	9.04257	−	14.8625i	0.295250	−	0.485278i
$939$	−4.87566	+	3.54237i	−0.159111	+	0.115601i
$940$	4.49324	−	0.955069i	0.146553	−	0.0311509i
$941$	−4.62320	−	5.13459i	−0.150712	−	0.167383i	0.663061	−	0.748565i	$-0.269257\pi$
$941$	−4.62320	−	5.13459i	−0.150712	−	0.167383i	−0.813773	+	0.581182i	$0.802590\pi$
$942$	−6.84493	+	0.719431i	−0.223020	+	0.0234403i
$943$	−0.0465010	+	0.442427i	−0.00151428	+	0.0144074i
$944$	5.97887	−	1.94265i	0.194596	−	0.0632280i
$945$	−12.0959	−	17.4797i	−0.393479	−	0.568616i
$946$	−12.0543	+	21.7087i	−0.391919	+	0.705812i
$947$	−12.4130	−	21.4999i	−0.403368	−	0.698654i	0.590762	−	0.806846i	$-0.298827\pi$
$947$	−12.4130	−	21.4999i	−0.403368	−	0.698654i	−0.994130	+	0.108192i	$0.965494\pi$
$948$	1.74086	+	0.370031i	0.0565404	+	0.0120180i
$949$	1.45325	−	0.647031i	0.0471746	−	0.0210035i
$950$	−1.74454	+	3.91829i	−0.0566002	+	0.127126i
$951$	12.1043	+	3.93294i	0.392510	+	0.127534i
$952$	−34.8336	+	36.9426i	−1.12896	+	1.19732i
$953$	12.1732	+	16.7550i	0.394328	+	0.542747i	0.959309	−	0.282357i	$-0.0911164\pi$
$953$	12.1732	+	16.7550i	0.394328	+	0.542747i	−0.564981	+	0.825104i	$0.691116\pi$
$954$	−15.1766	−	1.59512i	−0.491361	−	0.0516441i
$955$	10.4272	−	49.0563i	0.337418	−	1.58743i
$956$	1.98116	+	1.14382i	0.0640751	+	0.0369938i
$957$	−4.72237	+	15.4055i	−0.152652	+	0.497989i
$958$		−	9.56265i		−	0.308955i
$959$	−0.982751	−	0.126189i	−0.0317347	−	0.00407486i
$960$	−7.85740	−	5.70873i	−0.253596	−	0.184249i
$961$	16.1997	+	7.21259i	0.522572	+	0.232664i
$962$	−4.05673	+	3.65270i	−0.130794	+	0.117768i
$963$	3.21924	−	2.89861i	0.103738	−	0.0934065i
$964$	−1.53609	−	0.683912i	−0.0494742	−	0.0220273i
$965$	−19.9733	−	14.5114i	−0.642963	−	0.467140i
$966$	−0.168570	+	0.221144i	−0.00542366	+	0.00711519i
$967$		−	19.7404i		−	0.634809i	−0.948290	−	0.317404i	$-0.897189\pi$
$967$		−	19.7404i		−	0.634809i	0.948290	−	0.317404i	$-0.102811\pi$
$968$	−5.07055	+	28.5104i	−0.162974	+	0.916358i
$969$	−18.6484	−	10.7667i	−0.599073	−	0.345875i
$970$	12.8380	−	60.3978i	0.412202	−	1.93926i
$971$	18.3572	+	1.92941i	0.589109	+	0.0619179i	0.394393	−	0.918942i	$-0.370955\pi$
$971$	18.3572	+	1.92941i	0.589109	+	0.0619179i	0.194716	+	0.980860i	$0.437621\pi$
$972$	1.95145	+	2.68594i	0.0625929	+	0.0861517i
$973$	−9.57454	+	40.4497i	−0.306946	+	1.29676i
$974$	−50.3168	−	16.3489i	−1.61225	−	0.523853i
$975$	0.141555	−	0.317939i	0.00453340	−	0.0101822i
$976$	−0.959108	+	0.427022i	−0.0307003	+	0.0136686i
$977$	−9.76888	−	2.07644i	−0.312534	−	0.0664312i	0.0489742	−	0.998800i	$-0.484405\pi$
$977$	−9.76888	−	2.07644i	−0.312534	−	0.0664312i	−0.361508	+	0.932369i	$0.617738\pi$
$978$	3.14887	+	5.45400i	0.100690	+	0.174400i
$979$	32.0323	−	29.8265i	1.02376	−	0.953258i
$980$	−0.650879	−	3.94614i	−0.0207916	−	0.126055i
$981$	0.399956	−	0.129953i	0.0127696	−	0.00414909i
$982$	−1.82201	+	17.3353i	−0.0581426	+	0.553190i
$983$	−18.3690	+	1.93066i	−0.585880	+	0.0615785i	−0.392831	−	0.919611i	$-0.628504\pi$
$983$	−18.3690	+	1.93066i	−0.585880	+	0.0615785i	−0.193049	+	0.981189i	$0.561838\pi$
$984$	4.06177	+	4.51105i	0.129484	+	0.143807i
$985$	15.2033	−	3.23156i	0.484418	−	0.102966i
$986$	−71.1232	+	51.6740i	−2.26502	+	1.64564i
$987$	10.9615	+	6.66912i	0.348907	+	0.212280i
$988$	−0.360838	−	1.11054i	−0.0114798	−	0.0353311i
$989$	0.503944	−	0.290952i	0.0160245	−	0.00925174i
$990$	−15.9140	−	26.5297i	−0.505781	−	0.843170i
$991$	−3.23393	+	5.60134i	−0.102729	+	0.177932i	−0.912808	−	0.408388i	$-0.866091\pi$
$991$	−3.23393	+	5.60134i	−0.102729	+	0.177932i	0.810079	+	0.586321i	$0.199424\pi$
$992$	3.31567	−	3.68243i	0.105273	−	0.116917i
$993$	7.16710	−	9.86467i	0.227441	−	0.313046i
$994$	10.1372	−	28.9200i	0.321534	−	0.917286i
$995$	0.703580	−	2.16540i	0.0223050	−	0.0686477i
$996$	−0.126731	−	0.596224i	−0.00401564	−	0.0188921i
$997$	−0.580979	−	5.52765i	−0.0183998	−	0.175062i	0.981463	−	0.191654i	$-0.0613851\pi$
$997$	−0.580979	−	5.52765i	−0.0183998	−	0.175062i	−0.999862	+	0.0165917i	$0.994718\pi$
$998$	−12.3336	−	27.7016i	−0.390412	−	0.876880i
$999$	−9.33913	−	8.40899i	−0.295477	−	0.266049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.n.a.17.3	✓	48
3.2	odd	2		693.2.cg.a.325.4		48
7.2	even	3		539.2.s.d.215.3		48
7.3	odd	6		539.2.m.a.391.7		48
7.4	even	3		539.2.m.a.391.8		48
7.5	odd	6	inner	77.2.n.a.61.3	yes	48
7.6	odd	2		539.2.s.d.325.3		48
11.2	odd	10	inner	77.2.n.a.24.3	yes	48
11.3	even	5		847.2.i.b.241.6		48
11.4	even	5		847.2.r.a.360.4		48
11.5	even	5		847.2.r.d.766.4		48
11.6	odd	10		847.2.r.a.766.3		48
11.7	odd	10		847.2.r.d.360.3		48
11.8	odd	10		847.2.i.b.241.19		48
11.9	even	5		847.2.r.c.717.4		48
11.10	odd	2		847.2.r.c.94.4		48
21.5	even	6		693.2.cg.a.523.4		48
33.2	even	10		693.2.cg.a.640.4		48
77.2	odd	30		539.2.s.d.68.3		48
77.5	odd	30		847.2.r.d.40.3		48
77.13	even	10		539.2.s.d.178.3		48
77.19	even	30		847.2.i.b.362.6		48
77.24	even	30		539.2.m.a.244.8		48
77.26	odd	30		847.2.r.a.481.3		48
77.40	even	30		847.2.r.d.481.4		48
77.46	odd	30		539.2.m.a.244.7		48
77.47	odd	30		847.2.i.b.362.19		48
77.54	even	6		847.2.r.c.215.4		48
77.61	even	30		847.2.r.a.40.4		48
77.68	even	30	inner	77.2.n.a.68.3	yes	48
77.75	odd	30		847.2.r.c.838.4		48
231.68	odd	30		693.2.cg.a.145.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.17.3	✓	48	1.1	even	1	trivial
77.2.n.a.24.3	yes	48	11.2	odd	10	inner
77.2.n.a.61.3	yes	48	7.5	odd	6	inner
77.2.n.a.68.3	yes	48	77.68	even	30	inner
539.2.m.a.244.7		48	77.46	odd	30
539.2.m.a.244.8		48	77.24	even	30
539.2.m.a.391.7		48	7.3	odd	6
539.2.m.a.391.8		48	7.4	even	3
539.2.s.d.68.3		48	77.2	odd	30
539.2.s.d.178.3		48	77.13	even	10
539.2.s.d.215.3		48	7.2	even	3
539.2.s.d.325.3		48	7.6	odd	2
693.2.cg.a.145.4		48	231.68	odd	30
693.2.cg.a.325.4		48	3.2	odd	2
693.2.cg.a.523.4		48	21.5	even	6
693.2.cg.a.640.4		48	33.2	even	10
847.2.i.b.241.6		48	11.3	even	5
847.2.i.b.241.19		48	11.8	odd	10
847.2.i.b.362.6		48	77.19	even	30
847.2.i.b.362.19		48	77.47	odd	30
847.2.r.a.40.4		48	77.61	even	30
847.2.r.a.360.4		48	11.4	even	5
847.2.r.a.481.3		48	77.26	odd	30
847.2.r.a.766.3		48	11.6	odd	10
847.2.r.c.94.4		48	11.10	odd	2
847.2.r.c.215.4		48	77.54	even	6
847.2.r.c.717.4		48	11.9	even	5
847.2.r.c.838.4		48	77.75	odd	30
847.2.r.d.40.3		48	77.5	odd	30
847.2.r.d.360.3		48	11.7	odd	10
847.2.r.d.481.4		48	77.40	even	30
847.2.r.d.766.4		48	11.5	even	5

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.n (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11268 - 1.00186i) q^{2} +(0.245339 + 0.551041i) q^{3} +(0.0252713 + 0.240440i) q^{4} +(-0.491349 - 2.31161i) q^{5} +(0.279082 - 0.858925i) q^{6} +(2.00635 - 1.72470i) q^{7} +(-1.54736 + 2.12976i) q^{8} +(1.76394 - 1.95905i) q^{9} +(-1.76920 + 3.06434i) q^{10} +(-3.23217 + 0.743693i) q^{11} +(-0.126292 + 0.0729149i) q^{12} +(0.304786 + 0.938034i) q^{13} +(-3.96031 - 0.0910454i) q^{14} +(1.15325 - 0.837884i) q^{15} +(4.32838 - 0.920026i) q^{16} +(4.87801 + 5.41758i) q^{17} +(-3.92538 + 0.412574i) q^{18} +(-0.511870 + 4.87012i) q^{19} +(0.543388 - 0.176557i) q^{20} +(1.44261 + 0.682444i) q^{21} +(4.34143 + 2.41068i) q^{22} +(-0.0581861 - 0.100781i) q^{23} +(-1.55321 - 0.330145i) q^{24} +(-0.534413 + 0.237936i) q^{25} +(0.600649 - 1.34908i) q^{26} +(3.23328 + 1.05056i) q^{27} +(0.465389 + 0.438820i) q^{28} +(-4.73419 - 6.51605i) q^{29} +(-2.12263 - 0.223098i) q^{30} +(-0.757301 + 3.56282i) q^{31} +(-1.17815 - 0.680207i) q^{32} +(-1.20278 - 1.59860i) q^{33} -10.9151i q^{34} +(-4.97265 - 3.79047i) q^{35} +(0.515611 + 0.374613i) q^{36} +(-3.37696 - 1.50352i) q^{37} +(5.44871 - 4.90604i) q^{38} +(-0.442120 + 0.398086i) q^{39} +(5.68347 + 2.53044i) q^{40} +(-3.09269 - 2.24697i) q^{41} +(-0.921451 - 2.20463i) q^{42} +5.00037i q^{43} +(-0.260494 - 0.758349i) q^{44} +(-5.39528 - 3.11497i) q^{45} +(-0.0362262 + 0.170431i) q^{46} +(7.99589 + 0.840402i) q^{47} +(1.56889 + 2.15940i) q^{48} +(1.05085 - 6.92067i) q^{49} +(0.833006 + 0.270660i) q^{50} +(-1.78854 + 4.01713i) q^{51} +(-0.217839 + 0.0969880i) q^{52} +(3.78179 + 0.803844i) q^{53} +(-2.54509 - 4.40822i) q^{54} +(3.30725 + 7.10612i) q^{55} +(0.568646 + 6.94175i) q^{56} +(-2.80922 + 0.912770i) q^{57} +(-1.26054 + 11.9932i) q^{58} +(1.41288 - 0.148500i) q^{59} +(0.230605 + 0.256113i) q^{60} +(-0.232071 + 0.0493282i) q^{61} +(4.41207 - 3.20555i) q^{62} +(0.160301 - 6.97279i) q^{63} +(-2.10542 - 6.47981i) q^{64} +(2.01862 - 1.16545i) q^{65} +(-0.263263 + 2.98374i) q^{66} +(-2.19586 + 3.80334i) q^{67} +(-1.17933 + 1.30978i) q^{68} +(0.0412593 - 0.0567886i) q^{69} +(1.73543 + 9.19945i) q^{70} +(-2.39057 + 7.35741i) q^{71} +(1.44286 + 6.78810i) q^{72} +(-0.168591 - 1.60403i) q^{73} +(2.25115 + 5.05616i) q^{74} +(-0.262225 - 0.236109i) q^{75} -1.18391 q^{76} +(-5.20221 + 7.06662i) q^{77} +0.890761 q^{78} +(-9.06956 - 8.16627i) q^{79} +(-4.25349 - 9.55349i) q^{80} +(-0.612311 - 5.82575i) q^{81} +(1.19001 + 5.59858i) q^{82} +(-1.29164 + 3.97526i) q^{83} +(-0.127630 + 0.364108i) q^{84} +(10.1266 - 13.9380i) q^{85} +(5.00966 - 5.56379i) q^{86} +(2.42913 - 4.20738i) q^{87} +(3.41744 - 8.03449i) q^{88} +(-11.4287 + 6.59836i) q^{89} +(2.88244 + 8.87124i) q^{90} +(2.22933 + 1.35636i) q^{91} +(0.0227614 - 0.0165371i) q^{92} +(-2.14906 + 0.456796i) q^{93} +(-8.05486 - 8.94583i) q^{94} +(11.5093 - 1.20968i) q^{95} +(0.0857748 - 0.816093i) q^{96} +(-16.5965 + 5.39254i) q^{97} +(-8.10278 + 6.64766i) q^{98} +(-4.24441 + 7.64381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26}+ \cdots - 12 q^{99}+O(q^{100}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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