LMFDB - Embedded newform 770.2.bv.a.157.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			157.5
Character	$\chi$	$=$	770.157
Dual form			770.2.bv.a.103.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.358368 - 0.933580i) q^{2} +(-1.20315 - 1.85269i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.76974 + 1.36676i) q^{5} +(-1.29847 + 1.78719i) q^{6} +(-2.10275 - 1.60576i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-0.764685 + 1.71751i) q^{9} +O(q^{10})$	\(q+(-0.358368 - 0.933580i) q^{2} +(-1.20315 - 1.85269i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.76974 + 1.36676i) q^{5} +(-1.29847 + 1.78719i) q^{6} +(-2.10275 - 1.60576i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-0.764685 + 1.71751i) q^{9} +(0.641764 - 2.14199i) q^{10} +(1.56086 - 2.92638i) q^{11} +(2.13381 + 0.571753i) q^{12} +(-2.41173 - 0.381981i) q^{13} +(-0.745547 + 2.53853i) q^{14} +(0.402924 - 4.92320i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-0.578715 + 1.50761i) q^{17} +(1.87747 + 0.0983942i) q^{18} +(2.01746 - 2.24061i) q^{19} +(-2.22971 + 0.168484i) q^{20} +(-0.445051 + 5.82772i) q^{21} +(-3.29138 - 0.408465i) q^{22} +(-8.98774 - 2.40826i) q^{23} +(-0.230912 - 2.19698i) q^{24} +(1.26393 + 4.83761i) q^{25} +(0.507678 + 2.38844i) q^{26} +(-2.44360 + 0.387029i) q^{27} +(2.63711 - 0.213701i) q^{28} +(-6.48616 - 2.10748i) q^{29} +(-4.74060 + 1.38816i) q^{30} +(5.72407 - 0.601624i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-7.29964 + 0.629096i) q^{33} +1.61486 q^{34} +(-1.52662 - 5.71572i) q^{35} +(-0.580967 - 1.78803i) q^{36} +(-3.42202 - 2.22229i) q^{37} +(-2.81479 - 1.08050i) q^{38} +(2.19399 + 4.92779i) q^{39} +(0.956350 + 2.02124i) q^{40} +(-1.53405 + 0.498443i) q^{41} +(5.60013 - 1.67298i) q^{42} +(-4.77141 + 4.77141i) q^{43} +(0.798189 + 3.21914i) q^{44} +(-3.70072 + 1.99440i) q^{45} +(0.972616 + 9.25382i) q^{46} +(-0.165558 - 3.15903i) q^{47} +(-1.96831 + 1.00290i) q^{48} +(1.84308 + 6.75300i) q^{49} +(4.06335 - 2.91363i) q^{50} +(3.48941 - 0.741698i) q^{51} +(2.04786 - 1.32990i) q^{52} +(9.74868 + 7.89433i) q^{53} +(1.23703 + 2.14260i) q^{54} +(6.76197 - 3.04561i) q^{55} +(-1.14456 - 2.38537i) q^{56} +(-6.57848 - 1.04193i) q^{57} +(0.356928 + 6.81060i) q^{58} +(-0.346252 - 0.384552i) q^{59} +(2.99483 + 3.92826i) q^{60} +(-6.65475 - 0.699442i) q^{61} +(-2.61299 - 5.12828i) q^{62} +(4.36585 - 2.38359i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-3.74606 - 3.97227i) q^{65} +(3.20327 + 6.58936i) q^{66} +(-3.51597 + 0.942102i) q^{67} +(-0.578715 - 1.50761i) q^{68} +(6.35186 + 19.5490i) q^{69} +(-4.78899 + 3.47355i) q^{70} +(0.855960 + 0.621891i) q^{71} +(-1.46107 + 1.18315i) q^{72} +(0.531945 - 10.1501i) q^{73} +(-0.848340 + 3.99113i) q^{74} +(7.44190 - 8.16207i) q^{75} +3.01504i q^{76} +(-7.98115 + 3.64708i) q^{77} +(3.81423 - 3.81423i) q^{78} +(-2.67025 + 5.99747i) q^{79} +(1.54426 - 1.61718i) q^{80} +(7.43107 + 8.25304i) q^{81} +(1.01509 + 1.25353i) q^{82} +(0.546687 + 3.45164i) q^{83} +(-3.56877 - 4.62863i) q^{84} +(-3.08471 + 1.87710i) q^{85} +(6.16442 + 2.74458i) q^{86} +(3.89932 + 14.5525i) q^{87} +(2.71929 - 1.89881i) q^{88} +(-5.21581 - 9.03406i) q^{89} +(3.18815 + 2.74019i) q^{90} +(4.45790 + 4.67587i) q^{91} +(8.29063 - 4.22429i) q^{92} +(-8.00156 - 9.88111i) q^{93} +(-2.88988 + 1.28666i) q^{94} +(6.63275 - 1.20791i) q^{95} +(1.64167 + 1.47817i) q^{96} +(0.833505 - 5.26254i) q^{97} +(5.64397 - 4.14073i) q^{98} +(3.83253 + 4.91855i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.358368	−	0.933580i	−0.253404	−	0.660141i
$2$	−0.358368	−	0.933580i	−0.253404	−	0.660141i
$3$	−1.20315	−	1.85269i	−0.694641	−	1.06965i	−0.993330	−	0.115303i	$-0.963216\pi$
$3$	−1.20315	−	1.85269i	−0.694641	−	1.06965i	0.298690	−	0.954350i	$-0.403450\pi$
$4$	−0.743145	+	0.669131i	−0.371572	+	0.334565i
$5$	1.76974	+	1.36676i	0.791450	+	0.611234i
$5$	1.76974	+	1.36676i	0.791450	+	0.611234i
$6$	−1.29847	+	1.78719i	−0.530097	+	0.729616i
$7$	−2.10275	−	1.60576i	−0.794763	−	0.606919i
$7$	−2.10275	−	1.60576i	−0.794763	−	0.606919i
$8$	0.891007	+	0.453990i	0.315018	+	0.160510i
$9$	−0.764685	+	1.71751i	−0.254895	+	0.572504i
$10$	0.641764	−	2.14199i	0.202944	−	0.677358i
$11$	1.56086	−	2.92638i	0.470617	−	0.882338i
$11$	1.56086	−	2.92638i	0.470617	−	0.882338i
$12$	2.13381	+	0.571753i	0.615978	+	0.165051i
$13$	−2.41173	−	0.381981i	−0.668895	−	0.105943i	−0.187254	−	0.982311i	$-0.559959\pi$
$13$	−2.41173	−	0.381981i	−0.668895	−	0.105943i	−0.481640	+	0.876369i	$0.659959\pi$
$14$	−0.745547	+	2.53853i	−0.199256	+	0.678452i
$15$	0.402924	−	4.92320i	0.104035	−	1.27116i
$16$	0.104528	−	0.994522i	0.0261321	−	0.248630i
$17$	−0.578715	+	1.50761i	−0.140359	+	0.365648i	−0.985684	−	0.168605i	$-0.946074\pi$
$17$	−0.578715	+	1.50761i	−0.140359	+	0.365648i	0.845325	+	0.534253i	$0.179407\pi$
$18$	1.87747	+	0.0983942i	0.442525	+	0.0231917i
$19$	2.01746	−	2.24061i	0.462837	−	0.514032i	−0.465867	−	0.884855i	$-0.654258\pi$
$19$	2.01746	−	2.24061i	0.462837	−	0.514032i	0.928704	+	0.370823i	$0.120924\pi$
$20$	−2.22971	+	0.168484i	−0.498579	+	0.0376741i
$21$	−0.445051	+	5.82772i	−0.0971181	+	1.27171i
$22$	−3.29138	−	0.408465i	−0.701724	−	0.0870850i
$23$	−8.98774	−	2.40826i	−1.87407	−	0.502156i	−0.999862	−	0.0166109i	$-0.994712\pi$
$23$	−8.98774	−	2.40826i	−1.87407	−	0.502156i	−0.874211	−	0.485546i	$-0.838621\pi$
$24$	−0.230912	−	2.19698i	−0.0471347	−	0.448457i
$25$	1.26393	+	4.83761i	0.252786	+	0.967522i
$26$	0.507678	+	2.38844i	0.0995639	+	0.468411i
$27$	−2.44360	+	0.387029i	−0.470272	+	0.0744837i
$28$	2.63711	−	0.213701i	0.498366	−	0.0403858i
$29$	−6.48616	−	2.10748i	−1.20445	−	0.391349i	−0.363053	−	0.931768i	$-0.618266\pi$
$29$	−6.48616	−	2.10748i	−1.20445	−	0.391349i	−0.841396	+	0.540419i	$0.818266\pi$
$30$	−4.74060	+	1.38816i	−0.865511	+	0.253441i
$31$	5.72407	−	0.601624i	1.02807	−	0.108055i	0.424554	−	0.905403i	$-0.360431\pi$
$31$	5.72407	−	0.601624i	1.02807	−	0.108055i	0.603520	+	0.797348i	$0.293764\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−7.29964	+	0.629096i	−1.27070	+	0.109512i
$34$	1.61486			0.276947
$35$	−1.52662	−	5.71572i	−0.258046	−	0.966133i
$36$	−0.580967	−	1.78803i	−0.0968279	−	0.298006i
$37$	−3.42202	−	2.22229i	−0.562577	−	0.365342i	0.231803	−	0.972763i	$-0.425537\pi$
$37$	−3.42202	−	2.22229i	−0.562577	−	0.365342i	−0.794380	+	0.607421i	$0.792204\pi$
$38$	−2.81479	−	1.08050i	−0.456619	−	0.175279i
$39$	2.19399	+	4.92779i	0.351320	+	0.789077i
$40$	0.956350	+	2.02124i	0.151212	+	0.319585i
$41$	−1.53405	+	0.498443i	−0.239578	+	0.0778437i	−0.426345	−	0.904561i	$-0.640199\pi$
$41$	−1.53405	+	0.498443i	−0.239578	+	0.0778437i	0.186767	+	0.982404i	$0.440199\pi$
$42$	5.60013	−	1.67298i	0.864119	−	0.258146i
$43$	−4.77141	+	4.77141i	−0.727634	+	0.727634i	−0.970148	−	0.242514i	$-0.922028\pi$
$43$	−4.77141	+	4.77141i	−0.727634	+	0.727634i	0.242514	+	0.970148i	$0.422028\pi$
$44$	0.798189	+	3.21914i	0.120332	+	0.485304i
$45$	−3.70072	+	1.99440i	−0.551670	+	0.297308i
$46$	0.972616	+	9.25382i	0.143404	+	1.36440i
$47$	−0.165558	−	3.15903i	−0.0241491	−	0.460792i	−0.983763	−	0.179472i	$-0.942561\pi$
$47$	−0.165558	−	3.15903i	−0.0241491	−	0.460792i	0.959614	−	0.281320i	$-0.0907723\pi$
$48$	−1.96831	+	1.00290i	−0.284101	+	0.144757i
$49$	1.84308	+	6.75300i	0.263298	+	0.964715i
$50$	4.06335	−	2.91363i	0.574644	−	0.412049i
$51$	3.48941	−	0.741698i	0.488616	−	0.103858i
$52$	2.04786	−	1.32990i	0.283988	−	0.184424i
$53$	9.74868	+	7.89433i	1.33908	+	1.08437i	0.989042	+	0.147636i	$0.0471663\pi$
$53$	9.74868	+	7.89433i	1.33908	+	1.08437i	0.350043	+	0.936734i	$0.386167\pi$
$54$	1.23703	+	2.14260i	0.168339	+	0.291571i
$55$	6.76197	−	3.04561i	0.911784	−	0.410670i
$56$	−1.14456	−	2.38537i	−0.152949	−	0.318758i
$57$	−6.57848	−	1.04193i	−0.871341	−	0.138007i
$58$	0.356928	+	6.81060i	0.0468670	+	0.894276i
$59$	−0.346252	−	0.384552i	−0.0450782	−	0.0500644i	0.720184	−	0.693783i	$-0.244057\pi$
$59$	−0.346252	−	0.384552i	−0.0450782	−	0.0500644i	−0.765262	+	0.643719i	$0.777391\pi$
$60$	2.99483	+	3.92826i	0.386631	+	0.507136i
$61$	−6.65475	−	0.699442i	−0.852053	−	0.0895544i	−0.331575	−	0.943429i	$-0.607580\pi$
$61$	−6.65475	−	0.699442i	−0.852053	−	0.0895544i	−0.520479	+	0.853875i	$0.674247\pi$
$62$	−2.61299	−	5.12828i	−0.331850	−	0.651292i
$63$	4.36585	−	2.38359i	0.550045	−	0.300304i
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	−3.74606	−	3.97227i	−0.464641	−	0.492699i
$66$	3.20327	+	6.58936i	0.394295	+	0.811094i
$67$	−3.51597	+	0.942102i	−0.429545	+	0.115096i	−0.467112	−	0.884198i	$-0.654706\pi$
$67$	−3.51597	+	0.942102i	−0.429545	+	0.115096i	0.0375678	+	0.999294i	$0.488039\pi$
$68$	−0.578715	−	1.50761i	−0.0701796	−	0.182824i
$69$	6.35186	+	19.5490i	0.764675	+	2.35343i
$70$	−4.78899	+	3.47355i	−0.572394	+	0.415169i
$71$	0.855960	+	0.621891i	0.101584	+	0.0738049i	0.637418	−	0.770519i	$-0.280003\pi$
$71$	0.855960	+	0.621891i	0.101584	+	0.0738049i	−0.535834	+	0.844323i	$0.680003\pi$
$72$	−1.46107	+	1.18315i	−0.172189	+	0.139436i
$73$	0.531945	−	10.1501i	0.0622595	−	1.18798i	−0.771638	−	0.636062i	$-0.780562\pi$
$73$	0.531945	−	10.1501i	0.0622595	−	1.18798i	0.833897	−	0.551920i	$-0.186105\pi$
$74$	−0.848340	+	3.99113i	−0.0986176	+	0.463959i
$75$	7.44190	−	8.16207i	0.859317	−	0.942474i
$76$			3.01504i			0.345849i
$77$	−7.98115	+	3.64708i	−0.909537	+	0.415624i
$78$	3.81423	−	3.81423i	0.431876	−	0.431876i
$79$	−2.67025	+	5.99747i	−0.300426	+	0.674768i	−0.999176	−	0.0405983i	$-0.987074\pi$
$79$	−2.67025	+	5.99747i	−0.300426	+	0.674768i	0.698749	+	0.715367i	$0.253740\pi$
$80$	1.54426	−	1.61718i	0.172654	−	0.180806i
$81$	7.43107	+	8.25304i	0.825675	+	0.917005i
$82$	1.01509	+	1.25353i	0.112098	+	0.138430i
$83$	0.546687	+	3.45164i	0.0600067	+	0.378867i	0.999355	+	0.0359033i	$0.0114308\pi$
$83$	0.546687	+	3.45164i	0.0600067	+	0.378867i	−0.939349	+	0.342964i	$0.888569\pi$
$84$	−3.56877	−	4.62863i	−0.389384	−	0.505025i
$85$	−3.08471	+	1.87710i	−0.334584	+	0.203600i
$86$	6.16442	+	2.74458i	0.664727	+	0.295955i
$87$	3.89932	+	14.5525i	0.418052	+	1.56019i
$88$	2.71929	−	1.89881i	0.289877	−	0.202414i
$89$	−5.21581	−	9.03406i	−0.552875	−	0.957608i	−0.998065	−	0.0621720i	$-0.980197\pi$
$89$	−5.21581	−	9.03406i	−0.552875	−	0.957608i	0.445190	−	0.895436i	$-0.353136\pi$
$90$	3.18815	+	2.74019i	0.336061	+	0.288841i
$91$	4.45790	+	4.67587i	0.467314	+	0.490164i
$92$	8.29063	−	4.22429i	0.864358	−	0.440412i
$93$	−8.00156	−	9.88111i	−0.829723	−	1.02462i
$94$	−2.88988	+	1.28666i	−0.298068	+	0.132709i
$95$	6.63275	−	1.20791i	0.680506	−	0.123929i
$96$	1.64167	+	1.47817i	0.167552	+	0.150865i
$97$	0.833505	−	5.26254i	0.0846296	−	0.534330i	−0.908554	−	0.417768i	$-0.862813\pi$
$97$	0.833505	−	5.26254i	0.0846296	−	0.534330i	0.993183	−	0.116562i	$-0.0371874\pi$
$98$	5.64397	−	4.14073i	0.570127	−	0.418277i
$99$	3.83253	+	4.91855i	0.385184	+	0.494333i
$100$	−4.17628	−	2.74931i	−0.417628	−	0.274931i
$101$	−4.56697	+	0.480008i	−0.454430	+	0.0477625i	−0.328979	−	0.944337i	$-0.606705\pi$
$101$	−4.56697	+	0.480008i	−0.454430	+	0.0477625i	−0.125451	+	0.992100i	$0.540038\pi$
$102$	−1.94293	−	2.99185i	−0.192379	−	0.296237i
$103$	0.123622	+	0.0802808i	0.0121808	+	0.00791030i	0.550715	−	0.834693i	$-0.314355\pi$
$103$	0.123622	+	0.0802808i	0.0121808	+	0.00791030i	−0.538534	+	0.842604i	$0.681022\pi$
$104$	−1.97546	−	1.43525i	−0.193709	−	0.140738i
$105$	−8.75271	+	9.70524i	−0.854177	+	0.947135i
$106$	3.87637	−	11.9303i	0.376507	−	1.15877i
$107$	−2.23852	+	0.117316i	−0.216406	+	0.0113413i	−0.160231	−	0.987080i	$-0.551224\pi$
$107$	−2.23852	+	0.117316i	−0.216406	+	0.0113413i	−0.0561750	+	0.998421i	$0.517890\pi$
$108$	1.55698	−	1.92271i	0.149820	−	0.185013i
$109$	−11.3283	−	6.54038i	−1.08505	−	0.626455i	−0.152797	−	0.988258i	$-0.548828\pi$
$109$	−11.3283	−	6.54038i	−1.08505	−	0.626455i	−0.932255	+	0.361803i	$0.882161\pi$
$110$	−5.26659	−	5.22140i	−0.502150	−	0.497841i
$111$			9.01371i			0.855543i
$112$	−1.81676	+	1.92338i	−0.171668	+	0.181742i
$113$	15.0599	+	7.67341i	1.41672	+	0.721854i	0.983748	−	0.179555i	$-0.0574657\pi$
$113$	15.0599	+	7.67341i	1.41672	+	0.721854i	0.432970	+	0.901408i	$0.357466\pi$
$114$	1.38479	+	6.51494i	0.129698	+	0.610180i
$115$	−12.6144	−	16.5461i	−1.17630	−	1.54293i
$116$	6.23033	−	2.77392i	0.578472	−	0.257552i
$117$	2.50027	−	3.85009i	0.231150	−	0.355941i
$118$	−0.234924	+	0.461065i	−0.0216266	+	0.0424445i
$119$	3.63774	−	2.24083i	0.333471	−	0.205417i
$120$	2.59409	−	4.20368i	0.236807	−	0.383742i
$121$	−6.12744	−	9.13534i	−0.557040	−	0.830486i
$122$	1.73186	+	6.46340i	0.156796	+	0.585169i
$123$	2.76916	+	2.24242i	0.249687	+	0.202192i
$124$	−3.85125	+	4.27725i	−0.345852	+	0.384108i
$125$	−4.37503	+	10.2888i	−0.391314	+	0.920257i
$126$	−3.78985	−	3.22167i	−0.337627	−	0.287009i
$127$	−3.25492	−	20.5508i	−0.288827	−	1.82358i	−0.524102	−	0.851656i	$-0.675599\pi$
$127$	−3.25492	−	20.5508i	−0.288827	−	1.82358i	0.235274	−	0.971929i	$-0.424401\pi$
$128$	0.544639	−	0.838671i	0.0481397	−	0.0741287i
$129$	14.5807	+	3.09923i	1.28376	+	0.272872i
$130$	−2.36597	+	4.92078i	−0.207509	+	0.431581i
$131$	10.2763	−	5.93300i	0.897841	−	0.518368i	0.0213416	−	0.999772i	$-0.493206\pi$
$131$	10.2763	−	5.93300i	0.897841	−	0.518368i	0.876499	+	0.481404i	$0.159873\pi$
$132$	5.00374	−	5.35192i	0.435520	−	0.465825i
$133$	−7.84009	+	1.47189i	−0.679822	+	0.127629i
$134$	2.13954	+	2.94483i	0.184828	+	0.254394i
$135$	−4.85351	−	2.65488i	−0.417723	−	0.228496i
$136$	−1.20008	+	1.08055i	−0.102906	+	0.0926568i
$137$	−9.85745	−	3.78392i	−0.842179	−	0.323282i	−0.101246	−	0.994861i	$-0.532283\pi$
$137$	−9.85745	−	3.78392i	−0.842179	−	0.323282i	−0.740933	+	0.671579i	$0.765616\pi$
$138$	15.9743	−	12.9357i	1.35982	−	1.10116i
$139$	5.44650	−	16.7626i	0.461966	−	1.42179i	−0.400792	−	0.916169i	$-0.631265\pi$
$139$	5.44650	−	16.7626i	0.461966	−	1.42179i	0.862758	−	0.505617i	$-0.168735\pi$
$140$	4.95906	+	3.22610i	0.419117	+	0.272655i
$141$	−5.65353	+	4.10753i	−0.476113	+	0.345916i
$142$	0.273837	−	1.02197i	0.0229799	−	0.0857621i
$143$	−4.88220	+	6.46144i	−0.408270	+	0.540333i
$144$	1.62817	+	0.940025i	0.135681	+	0.0783354i
$145$	−8.59837	−	12.5947i	−0.714055	−	1.04593i
$146$	−9.66659	+	3.14086i	−0.800013	+	0.259940i
$147$	10.2937	−	11.5396i	0.849013	−	0.951767i
$148$	4.03006	−	0.638298i	0.331269	−	0.0524678i
$149$	−9.86458	−	1.03681i	−0.808138	−	0.0849387i	−0.308557	−	0.951206i	$-0.599846\pi$
$149$	−9.86458	−	1.03681i	−0.808138	−	0.0849387i	−0.499581	+	0.866267i	$0.666513\pi$
$150$	−10.2869	−	4.02259i	−0.839921	−	0.328443i
$151$	−5.67649	−	1.20658i	−0.461947	−	0.0981898i	−0.0289412	−	0.999581i	$-0.509214\pi$
$151$	−5.67649	−	1.20658i	−0.461947	−	0.0981898i	−0.433005	+	0.901391i	$0.642547\pi$
$152$	2.81479	−	1.08050i	0.228309	−	0.0876397i
$153$	−2.14679	−	2.14679i	−0.173558	−	0.173558i
$154$	6.26503	+	6.14405i	0.504851	+	0.495102i
$155$	10.9524	+	6.75872i	0.879716	+	0.542873i
$156$	−4.92779	−	2.19399i	−0.394539	−	0.175660i
$157$	12.8868	−	8.36876i	1.02848	−	0.667900i	0.0839943	−	0.996466i	$-0.473232\pi$
$157$	12.8868	−	8.36876i	1.02848	−	0.667900i	0.944481	+	0.328567i	$0.106566\pi$
$158$	6.55605	+	0.343588i	0.521572	+	0.0273344i
$159$	2.89661	−	27.5594i	0.229716	−	2.18560i
$160$	−2.06318	−	0.862148i	−0.163109	−	0.0681588i
$161$	15.0319	+	19.4961i	1.18468	+	1.53651i
$162$	5.04182	−	9.89513i	0.396123	−	0.777435i
$163$	5.75463	−	2.20899i	0.450737	−	0.173022i	−0.122401	−	0.992481i	$-0.539059\pi$
$163$	5.75463	−	2.20899i	0.450737	−	0.173022i	0.573138	+	0.819459i	$0.305726\pi$
$164$	0.806498	−	1.39690i	0.0629769	−	0.109079i
$165$	−13.7783	−	8.86353i	−1.07264	−	0.690025i
$166$	3.02647	−	1.74733i	0.234900	−	0.135619i
$167$	3.20409	−	20.2298i	0.247940	−	1.56543i	−0.478431	−	0.878125i	$-0.658794\pi$
$167$	3.20409	−	20.2298i	0.247940	−	1.56543i	0.726370	−	0.687304i	$-0.241206\pi$
$168$	−3.04227	+	4.99048i	−0.234716	+	0.385024i
$169$	−6.69318	−	2.17475i	−0.514860	−	0.167288i
$170$	2.85788	+	2.20713i	0.219190	+	0.169279i
$171$	2.30556	+	5.17837i	0.176311	+	0.396000i
$172$	0.353152	−	6.73855i	0.0269276	−	0.513810i
$173$	12.9857	−	0.680551i	0.987284	−	0.0517414i	0.448147	−	0.893960i	$-0.352084\pi$
$173$	12.9857	−	0.680551i	0.987284	−	0.0517414i	0.539137	+	0.842218i	$0.318751\pi$
$174$	12.1885	−	8.85548i	0.924009	−	0.671332i
$175$	5.11030	−	12.2018i	0.386302	−	0.922372i
$176$	−2.74720	−	1.85820i	−0.207078	−	0.140067i
$177$	−0.295862	+	1.10417i	−0.0222384	+	0.0829948i
$178$	−6.56484	+	8.10690i	−0.492055	+	0.607638i
$179$	0.632912	−	2.97762i	0.0473061	−	0.222558i	−0.948144	−	0.317841i	$-0.897042\pi$
$179$	0.632912	−	2.97762i	0.0473061	−	0.222558i	0.995450	+	0.0952830i	$0.0303756\pi$
$180$	1.41565	−	3.95839i	0.105517	−	0.295041i
$181$	11.1944	−	15.4078i	0.832076	−	1.14525i	−0.155457	−	0.987843i	$-0.549685\pi$
$181$	11.1944	−	15.4078i	0.832076	−	1.14525i	0.987533	−	0.157412i	$-0.0503151\pi$
$182$	2.76773	−	5.83749i	0.205158	−	0.432703i
$183$	6.71083	+	13.1707i	0.496079	+	0.973610i
$184$	−6.91481	−	6.22612i	−0.509766	−	0.458996i
$185$	−3.01874	−	8.60994i	−0.221942	−	0.633016i
$186$	−6.35730	+	11.0112i	−0.466140	+	0.807378i
$187$	3.50854	+	4.04670i	0.256570	+	0.295924i
$188$	2.23684	+	2.23684i	0.163138	+	0.163138i
$189$	5.75975	+	3.11001i	0.418960	+	0.226220i
$190$	−3.50465	−	5.75933i	−0.254254	−	0.417826i
$191$	−7.40432	+	1.57384i	−0.535758	+	0.113879i	−0.467842	−	0.883812i	$-0.654968\pi$
$191$	−7.40432	+	1.57384i	−0.535758	+	0.113879i	−0.0679161	+	0.997691i	$0.521635\pi$
$192$	0.791665	−	2.06236i	0.0571335	−	0.148838i
$193$	−6.78601	+	17.6782i	−0.488468	+	1.27250i	0.438963	+	0.898505i	$0.355346\pi$
$193$	−6.78601	+	17.6782i	−0.488468	+	1.27250i	−0.927430	+	0.373996i	$0.877987\pi$
$194$	−5.21171	+	1.10778i	−0.374179	+	0.0795341i
$195$	−2.85232	+	11.7195i	−0.204259	+	0.839254i
$196$	−5.88832	−	3.78519i	−0.420594	−	0.270371i
$197$	3.72829	+	3.72829i	0.265630	+	0.265630i	0.827336	−	0.561707i	$-0.189855\pi$
$197$	3.72829	+	3.72829i	0.265630	+	0.265630i	−0.561707	+	0.827336i	$0.689855\pi$
$198$	3.21841	−	5.34063i	0.228722	−	0.379542i
$199$	−4.70328	+	8.14632i	−0.333407	+	0.577477i	−0.983177	−	0.182653i	$-0.941532\pi$
$199$	−4.70328	+	8.14632i	−0.333407	+	0.577477i	0.649771	+	0.760130i	$0.274865\pi$
$200$	−1.07006	+	4.88416i	−0.0756645	+	0.345362i
$201$	5.97568	+	5.38053i	0.421492	+	0.379513i
$202$	2.08478	+	4.09161i	0.146685	+	0.287885i
$203$	10.2546	+	14.8467i	0.719735	+	1.04203i
$204$	−2.09685	+	2.88606i	−0.146809	+	0.202065i
$205$	−3.39612	−	1.21457i	−0.237195	−	0.0848290i
$206$	0.0306466	−	0.144181i	0.00213525	−	0.0100455i
$207$	11.0090	−	13.5950i	0.765179	−	0.944917i
$208$	−0.631984	+	2.35859i	−0.0438202	+	0.163539i
$209$	−3.40793	−	9.40114i	−0.235732	−	0.650290i
$210$	12.1973	+	4.69332i	0.841695	+	0.323870i
$211$	−15.8095	+	11.4863i	−1.08837	+	0.790750i	−0.979124	−	0.203265i	$-0.934845\pi$
$211$	−15.8095	+	11.4863i	−1.08837	+	0.790750i	−0.109250	+	0.994014i	$0.534845\pi$
$212$	−12.5270	+	0.656513i	−0.860359	+	0.0450895i
$213$	0.122323	−	2.33406i	0.00838143	−	0.159927i
$214$	0.911737	+	2.04779i	0.0623251	+	0.139984i
$215$	−14.9655	+	1.92276i	−1.02064	+	0.131131i
$216$	−2.35297	−	0.764527i	−0.160100	−	0.0520195i
$217$	−13.0023	−	7.92641i	−0.882656	−	0.538080i
$218$	−2.04628	+	12.9197i	−0.138592	+	0.875033i
$219$	−19.4451	+	11.2266i	−1.31398	+	0.758625i
$220$	−2.98722	+	6.78797i	−0.201398	+	0.457645i
$221$	1.97158	−	3.41488i	0.132623	−	0.229710i
$222$	8.41502	−	3.23022i	0.564779	−	0.216798i
$223$	−3.03767	+	5.96176i	−0.203417	+	0.399229i	−0.970067	−	0.242836i	$-0.921922\pi$
$223$	−3.03767	+	5.96176i	−0.203417	+	0.399229i	0.766650	+	0.642065i	$0.221922\pi$
$224$	2.44670	+	1.00681i	0.163477	+	0.0672705i
$225$	−9.27516	−	1.52843i	−0.618344	−	0.101895i
$226$	1.76675	−	16.8095i	0.117523	−	1.11815i
$227$	0.820833	+	0.0430180i	0.0544806	+	0.00285521i	0.0795568	−	0.996830i	$-0.474650\pi$
$227$	0.820833	+	0.0430180i	0.0544806	+	0.00285521i	−0.0250762	+	0.999686i	$0.507983\pi$
$228$	5.58595	−	3.62756i	0.369939	−	0.240241i
$229$	−13.4222	−	5.97597i	−0.886967	−	0.394903i	−0.0878886	−	0.996130i	$-0.528012\pi$
$229$	−13.4222	−	5.97597i	−0.886967	−	0.394903i	−0.799078	+	0.601227i	$0.794679\pi$
$230$	−10.9265	+	17.7062i	−0.720471	+	1.16751i
$231$	16.3595	+	10.3986i	1.07637	+	0.684180i
$232$	−4.82243	−	4.82243i	−0.316608	−	0.316608i
$233$	26.2011	−	10.0576i	1.71649	−	0.658899i	0.717210	−	0.696857i	$-0.245419\pi$
$233$	26.2011	−	10.0576i	1.71649	−	0.658899i	0.999279	+	0.0379585i	$0.0120855\pi$
$234$	−4.49038	−	0.954460i	−0.293546	−	0.0623950i
$235$	4.02465	−	5.81693i	0.262539	−	0.379455i
$236$	0.514631	+	0.0540899i	0.0334996	+	0.00352095i
$237$	14.3242	−	2.26873i	0.930456	−	0.147370i
$238$	−3.39565	−	2.59308i	−0.220107	−	0.168084i
$239$	6.39339	−	2.07734i	0.413554	−	0.134372i	−0.0948480	−	0.995492i	$-0.530237\pi$
$239$	6.39339	−	2.07734i	0.413554	−	0.134372i	0.508402	+	0.861120i	$0.330237\pi$
$240$	−4.85411	−	0.915331i	−0.313332	−	0.0590844i
$241$	18.5834	+	10.7291i	1.19706	+	0.691125i	0.959899	−	0.280345i	$-0.0904489\pi$
$241$	18.5834	+	10.7291i	1.19706	+	0.691125i	0.237164	+	0.971470i	$0.423782\pi$
$242$	−6.33270	+	8.99427i	−0.407081	+	0.578174i
$243$	4.42863	−	16.5279i	0.284097	−	1.06026i
$244$	5.41346	−	3.93311i	0.346561	−	0.251792i
$245$	−5.96796	+	14.4701i	−0.381279	+	0.924460i
$246$	1.10110	−	3.38885i	0.0702037	−	0.216065i
$247$	−5.72145	+	4.63314i	−0.364047	+	0.294799i
$248$	5.37332	+	2.06262i	0.341206	+	0.130977i
$249$	5.73709	−	5.16570i	0.363573	−	0.327363i
$250$	11.1733	+	0.397268i	0.706660	+	0.0251254i
$251$	9.80781	+	13.4993i	0.619063	+	0.852068i	0.997284	−	0.0736478i	$-0.0234641\pi$
$251$	9.80781	+	13.4993i	0.619063	+	0.852068i	−0.378221	+	0.925715i	$0.623464\pi$
$252$	−1.64952	+	4.69267i	−0.103910	+	0.295611i
$253$	−21.0761	+	22.5426i	−1.32504	+	1.41724i
$254$	−18.0193	+	10.4035i	−1.13063	+	0.652771i
$255$	7.18906	+	3.45658i	0.450197	+	0.216460i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	−1.80952	+	2.78641i	−0.112874	+	0.173811i	−0.890593	−	0.454801i	$-0.849710\pi$
$257$	−1.80952	+	2.78641i	−0.112874	+	0.173811i	0.777718	+	0.628613i	$0.216377\pi$
$258$	−2.33188	−	14.7229i	−0.145177	−	0.916609i
$259$	3.62719	+	10.1678i	0.225383	+	0.631799i
$260$	5.44183	+	0.445370i	0.337488	+	0.0276207i
$261$	8.57949	−	9.52849i	0.531057	−	0.589799i
$262$	−9.22161	−	7.46751i	−0.569713	−	0.461345i
$263$	−2.30511	−	8.60280i	−0.142139	−	0.530471i	−0.999866	−	0.0163655i	$-0.994790\pi$
$263$	−2.30511	−	8.60280i	−0.142139	−	0.530471i	0.857727	−	0.514106i	$-0.171876\pi$
$264$	−6.78963	−	2.75344i	−0.417873	−	0.169463i
$265$	6.46294	+	27.2950i	0.397015	+	1.67672i
$266$	4.18377	+	6.79187i	0.256523	+	0.416436i
$267$	−10.4619	+	20.5327i	−0.640259	+	1.25658i
$268$	1.98249	−	3.05276i	0.121100	−	0.186477i
$269$	24.7863	−	11.0356i	1.51125	−	0.672852i	0.527037	−	0.849842i	$-0.323303\pi$
$269$	24.7863	−	11.0356i	1.51125	−	0.672852i	0.984213	+	0.176990i	$0.0566361\pi$
$270$	−0.739203	+	5.48256i	−0.0449865	+	0.333658i
$271$	−1.99036	−	9.36391i	−0.120906	−	0.568817i	−0.996340	−	0.0854795i	$-0.972758\pi$
$271$	−1.99036	−	9.36391i	−0.120906	−	0.568817i	0.875434	−	0.483337i	$-0.160576\pi$
$272$	1.43885	+	0.733133i	0.0872434	+	0.0444527i
$273$	3.29942	−	13.8849i	0.199690	−	0.840353i
$274$			10.5588i			0.637878i
$275$	16.1295	+	3.85207i	0.972647	+	0.232289i
$276$	−17.8012	−	10.2775i	−1.07151	−	0.618635i
$277$	17.4068	−	21.4956i	1.04587	−	1.29155i	0.0905787	−	0.995889i	$-0.471128\pi$
$277$	17.4068	−	21.4956i	1.04587	−	1.29155i	0.955294	−	0.295656i	$-0.0955383\pi$
$278$	−17.6011	+	0.922434i	−1.05564	+	0.0553239i
$279$	−3.34382	+	10.2912i	−0.200189	+	0.616119i
$280$	1.23465	−	5.78581i	0.0737846	−	0.345768i
$281$	5.54245	+	4.02683i	0.330635	+	0.240220i	0.740700	−	0.671836i	$-0.234494\pi$
$281$	5.54245	+	4.02683i	0.330635	+	0.240220i	−0.410065	+	0.912056i	$0.634494\pi$
$282$	5.86075	+	3.80602i	0.349003	+	0.226645i
$283$	−9.18173	−	14.1386i	−0.545797	−	0.840454i	0.452896	−	0.891563i	$-0.350391\pi$
$283$	−9.18173	−	14.1386i	−0.545797	−	0.840454i	−0.998693	+	0.0511095i	$0.983724\pi$
$284$	−1.05223	+	0.110594i	−0.0624383	+	0.00656253i
$285$	−10.2181	−	10.8351i	−0.605269	−	0.641819i
$286$	7.78190	+	2.24235i	0.460153	+	0.132593i
$287$	4.02610	+	1.41521i	0.237653	+	0.0835374i
$288$	0.294105	−	1.85690i	0.0173303	−	0.109419i
$289$	10.6955	+	9.63027i	0.629147	+	0.566487i
$290$	−8.67679	+	12.5408i	−0.509519	+	0.736421i
$291$	−10.7527	+	4.78741i	−0.630335	+	0.280643i
$292$	6.39645	+	7.89895i	0.374324	+	0.462251i
$293$	7.80176	−	3.97520i	0.455784	−	0.232233i	−0.210998	−	0.977487i	$-0.567671\pi$
$293$	7.80176	−	3.97520i	0.455784	−	0.232233i	0.666782	+	0.745253i	$0.267671\pi$
$294$	−14.4621	−	5.47462i	−0.843444	−	0.319286i
$295$	−0.0871846	−	1.15380i	−0.00507608	−	0.0671768i
$296$	−2.04015	−	3.53364i	−0.118581	−	0.205388i
$297$	−2.68152	+	7.75502i	−0.155598	+	0.449992i
$298$	2.56720	+	9.58093i	0.148714	+	0.555009i
$299$	20.7561	+	9.24123i	1.20036	+	0.534434i
$300$	−0.0689250	+	11.0452i	−0.00397938	+	0.637695i
$301$	17.6948	−	2.37134i	1.01991	−	0.136682i
$302$	0.907838	+	5.73186i	0.0522402	+	0.329832i
$303$	6.38407	+	7.88367i	0.366755	+	0.452905i
$304$	−2.01746	−	2.24061i	−0.115709	−	0.128508i
$305$	−10.8212	−	10.3333i	−0.619619	−	0.591682i
$306$	−1.23486	+	2.77355i	−0.0705924	+	0.158553i
$307$	−3.67780	+	3.67780i	−0.209903	+	0.209903i	−0.804226	−	0.594323i	$-0.797420\pi$
$307$	−3.67780	+	3.67780i	−0.209903	+	0.209903i	0.594323	+	0.804226i	$0.297420\pi$
$308$	3.49078	−	8.05074i	0.198906	−	0.458734i
$309$		−	0.325623i		−	0.0185240i
$310$	2.38483	−	12.6470i	0.135449	−	0.718303i
$311$	−4.65992	+	21.9232i	−0.264240	+	1.24315i	0.623140	+	0.782111i	$0.285857\pi$
$311$	−4.65992	+	21.9232i	−0.264240	+	1.24315i	−0.887379	+	0.461040i	$0.847476\pi$
$312$	−0.282307	+	5.38674i	−0.0159825	+	0.304964i
$313$	4.44828	−	3.60214i	0.251432	−	0.203605i	−0.495316	−	0.868713i	$-0.664948\pi$
$313$	4.44828	−	3.60214i	0.251432	−	0.203605i	0.746747	+	0.665108i	$0.231614\pi$
$314$	−12.4311	−	9.03173i	−0.701528	−	0.509690i
$315$	10.9842	+	1.74874i	0.618889	+	0.0985302i
$316$	−2.02871	−	6.24373i	−0.114124	−	0.351237i
$317$	−1.64659	−	4.28952i	−0.0924819	−	0.240924i	0.879535	−	0.475834i	$-0.157854\pi$
$317$	−1.64659	−	4.28952i	−0.0924819	−	0.240924i	−0.972017	+	0.234910i	$0.924520\pi$
$318$	−26.7670	+	7.17219i	−1.50102	+	0.402196i
$319$	−16.2913	+	15.6915i	−0.912136	+	0.878556i
$320$	−0.0655075	+	2.23511i	−0.00366198	+	0.124946i
$321$	2.91063	+	4.00614i	0.162456	+	0.223601i
$322$	12.8142	−	21.0202i	0.714109	−	1.17141i
$323$	2.21043	+	4.33821i	0.122991	+	0.241384i
$324$	−11.0447	−	1.16085i	−0.613596	−	0.0644915i
$325$	−1.20039	−	12.1498i	−0.0665858	−	0.673951i
$326$	−4.12455	−	4.58077i	−0.228438	−	0.253706i
$327$	1.51233	+	28.8569i	0.0836318	+	1.59579i
$328$	−1.59314	−	0.252328i	−0.0879663	−	0.0139325i
$329$	−4.72451	+	6.90849i	−0.260471	+	0.380877i
$330$	−3.33713	+	16.0395i	−0.183703	+	0.882947i
$331$	−15.9992	−	27.7114i	−0.879396	−	1.52316i	−0.852005	−	0.523534i	$-0.824613\pi$
$331$	−15.9992	−	27.7114i	−0.879396	−	1.52316i	−0.0273910	−	0.999625i	$-0.508720\pi$
$332$	−2.71587	−	2.19927i	−0.149053	−	0.120700i
$333$	6.43357	−	4.17801i	0.352558	−	0.228954i
$334$	−20.0344	+	4.25844i	−1.09623	+	0.233012i
$335$	−7.50998	−	3.13822i	−0.410314	−	0.171459i
$336$	5.74927	+	1.05178i	0.313648	+	0.0573790i
$337$	−11.2312	+	5.72260i	−0.611805	+	0.311730i	−0.732298	−	0.680984i	$-0.761552\pi$
$337$	−11.2312	+	5.72260i	−0.611805	+	0.311730i	0.120494	+	0.992714i	$0.461552\pi$
$338$	0.368321	+	7.02798i	0.0200340	+	0.382272i
$339$	−3.90291	−	37.1337i	−0.211977	−	2.01683i
$340$	1.03636	−	3.45903i	0.0562046	−	0.187592i
$341$	7.17388	−	17.6899i	0.388488	−	0.957961i
$342$	4.00819	−	4.00819i	0.216738	−	0.216738i
$343$	6.96815	−	17.1594i	0.376245	−	0.926520i
$344$	−6.41754	+	2.08518i	−0.346010	+	0.112426i
$345$	−15.4777	+	43.2781i	−0.833292	+	2.33001i
$346$	−5.28901	−	11.8793i	−0.284339	−	0.638635i
$347$	25.0439	+	9.61344i	1.34443	+	0.516077i	0.920897	−	0.389806i	$-0.127458\pi$
$347$	25.0439	+	9.61344i	1.34443	+	0.516077i	0.423529	+	0.905883i	$0.360791\pi$
$348$	−12.6353	−	8.20544i	−0.677322	−	0.439858i
$349$	−9.25247	−	28.4762i	−0.495273	−	1.52429i	−0.816531	−	0.577302i	$-0.804106\pi$
$349$	−9.25247	−	28.4762i	−0.495273	−	1.52429i	0.321258	−	0.946992i	$-0.395894\pi$
$350$	−13.2228	−	0.398130i	−0.706786	−	0.0212809i
$351$	6.04116			0.322453
$352$	−0.750270	+	3.23065i	−0.0399895	+	0.172194i
$353$	35.0991	−	9.40478i	1.86814	−	0.500566i	0.868146	−	0.496308i	$-0.165311\pi$
$353$	35.0991	−	9.40478i	1.86814	−	0.500566i	0.999991	−	0.00425756i	$-0.00135523\pi$
$354$	1.13686	−	0.119489i	0.0604236	−	0.00635077i
$355$	0.664847	+	2.27047i	0.0352864	+	0.120504i
$356$	9.92107	+	3.22355i	0.525816	+	0.170848i
$357$	−8.52834	−	4.04355i	−0.451368	−	0.214007i
$358$	−3.00666	+	0.476209i	−0.158907	+	0.0251684i
$359$	−0.623429	−	2.93300i	−0.0329033	−	0.154798i	0.958629	−	0.284659i	$-0.0918803\pi$
$359$	−0.623429	−	2.93300i	−0.0329033	−	0.154798i	−0.991532	+	0.129861i	$0.958547\pi$
$360$	−4.20280	+	0.0969332i	−0.221507	+	0.00510883i
$361$	1.03583	+	9.85522i	0.0545171	+	0.518696i
$362$	−18.3962	−	4.92924i	−0.966881	−	0.259075i
$363$	−9.55273	+	22.3435i	−0.501388	+	1.17273i
$364$	−6.44163	−	0.491934i	−0.337633	−	0.0257844i
$365$	14.8142	−	17.2360i	0.775410	−	0.902173i
$366$	9.89100	−	10.9851i	0.517011	−	0.574199i
$367$	29.9548	+	1.56986i	1.56363	+	0.0819462i	0.814375	−	0.580339i	$-0.197080\pi$
$367$	29.9548	+	1.56986i	1.56363	+	0.0819462i	0.749252	+	0.662285i	$0.230413\pi$
$368$	−3.33454	+	8.68677i	−0.173825	+	0.452829i
$369$	0.316984	−	3.01590i	0.0165015	−	0.157002i
$370$	−6.95625	+	5.90377i	−0.361638	+	0.306922i
$371$	−7.82263	−	32.2538i	−0.406131	−	1.67453i
$372$	12.5581	+	1.98900i	0.651106	+	0.103125i
$373$	−28.5301	−	7.64463i	−1.47723	−	0.395824i	−0.571830	−	0.820372i	$-0.693766\pi$
$373$	−28.5301	−	7.64463i	−1.47723	−	0.395824i	−0.905405	+	0.424548i	$0.860433\pi$
$374$	2.52057	−	4.72571i	0.130336	−	0.244361i
$375$	24.3258	−	4.27340i	1.25618	−	0.220678i
$376$	1.28666	−	2.88988i	0.0663543	−	0.149034i
$377$	14.8379	+	7.56027i	0.764189	+	0.389374i
$378$	0.839335	−	6.49172i	0.0431708	−	0.333898i
$379$	14.5959	−	20.0895i	0.749740	−	1.03193i	−0.248259	−	0.968694i	$-0.579858\pi$
$379$	14.5959	−	20.0895i	0.749740	−	1.03193i	0.997999	−	0.0632350i	$-0.0201418\pi$
$380$	−4.12084	+	5.33583i	−0.211395	+	0.273722i
$381$	−34.1581	+	30.7561i	−1.74997	+	1.57568i
$382$	4.12278	+	6.34852i	0.210940	+	0.324818i
$383$	1.47149	+	3.83336i	0.0751895	+	0.195875i	0.966024	−	0.258453i	$-0.0832127\pi$
$383$	1.47149	+	3.83336i	0.0751895	+	0.195875i	−0.890834	+	0.454328i	$0.849879\pi$
$384$	−2.20908			−0.112732
$385$	−19.1092	−	4.45395i	−0.973896	−	0.226994i
$386$	18.9359			0.963810
$387$	−4.54633	−	11.8436i	−0.231103	−	0.602043i
$388$	2.90191	+	4.46855i	0.147322	+	0.226856i
$389$	−20.1226	+	18.1184i	−1.02025	+	0.918642i	−0.996708	−	0.0810812i	$-0.974163\pi$
$389$	−20.1226	+	18.1184i	−1.02025	+	0.918642i	−0.0235473	+	0.999723i	$0.507496\pi$
$390$	11.9633	−	1.53704i	0.605786	−	0.0778311i
$391$	8.83205	−	12.1563i	0.446656	−	0.614769i
$392$	−1.42360	+	6.85371i	−0.0719026	+	0.346165i
$393$	−23.3559	−	11.9004i	−1.17815	−	0.600298i
$394$	2.14456	−	4.81676i	0.108041	−	0.242665i
$395$	−12.9227	+	6.96436i	−0.650214	+	0.350415i
$396$	−6.13928	−	1.09073i	−0.308510	−	0.0548115i
$397$	−25.1651	−	6.74298i	−1.26300	−	0.338420i	−0.435656	−	0.900113i	$-0.643484\pi$
$397$	−25.1651	−	6.74298i	−1.26300	−	0.338420i	−0.827346	+	0.561693i	$0.810150\pi$
$398$	9.29075	+	1.47151i	0.465703	+	0.0737601i
$399$	12.1598	+	12.7544i	0.608751	+	0.638517i
$400$	4.94323	−	0.751341i	0.247161	−	0.0375670i
$401$	−1.78752	+	17.0071i	−0.0892644	+	0.849294i	0.854672	+	0.519168i	$0.173758\pi$
$401$	−1.78752	+	17.0071i	−0.0892644	+	0.849294i	−0.943937	+	0.330126i	$0.892909\pi$
$402$	2.88166	−	7.50699i	0.143724	−	0.374415i
$403$	−14.0348	−	0.735530i	−0.699121	−	0.0366394i
$404$	3.07273	−	3.41261i	0.152874	−	0.169784i
$405$	1.87111	+	24.7622i	0.0929761	+	1.23044i
$406$	10.1856	−	14.8941i	0.505505	−	0.739182i
$407$	−11.8446	+	6.54547i	−0.587113	+	0.324447i
$408$	3.44581	+	0.923303i	0.170593	+	0.0457103i
$409$	3.10056	+	29.4999i	0.153313	+	1.45867i	0.752779	+	0.658274i	$0.228713\pi$
$409$	3.10056	+	29.4999i	0.153313	+	1.45867i	−0.599466	+	0.800400i	$0.704620\pi$
$410$	0.0831642	+	3.60581i	0.00410719	+	0.178078i
$411$	4.84958	+	22.8155i	0.239212	+	1.12540i
$412$	−0.145587	+	0.0230587i	−0.00717256	+	0.00113602i
$413$	0.110583	+	1.36461i	0.00544144	+	0.0671482i
$414$	−16.6373	−	5.40578i	−0.817678	−	0.265680i
$415$	−3.75008	+	6.85569i	−0.184084	+	0.336533i
$416$	2.42842	−	0.255237i	0.119063	−	0.0125140i
$417$	−37.6089	+	10.0773i	−1.84172	+	0.493487i
$418$	−7.55543	+	6.55064i	−0.369548	+	0.320402i
$419$	11.4461			0.559178			0.279589	−	0.960120i	$-0.409802\pi$
$419$	11.4461			0.559178			0.279589	+	0.960120i	$0.409802\pi$
$420$	0.0104595	−	13.0691i	0.000510369	−	0.637707i
$421$	5.95618	+	18.3312i	0.290286	+	0.893409i	0.984764	+	0.173895i	$0.0556354\pi$
$421$	5.95618	+	18.3312i	0.290286	+	0.893409i	−0.694478	+	0.719514i	$0.744365\pi$
$422$	16.3890	+	10.6432i	0.797805	+	0.518101i
$423$	5.55227	+	2.13132i	0.269961	+	0.103628i
$424$	5.10219	+	11.4597i	0.247784	+	0.556533i
$425$	−8.02466	−	0.894089i	−0.389253	−	0.0433697i
$426$	−2.22287	+	0.722254i	−0.107698	+	0.0349933i
$427$	12.8701	+	12.1567i	0.622828	+	0.588302i
$428$	1.58504	−	1.58504i	0.0766160	−	0.0766160i
$429$	17.8451	+	1.27111i	0.861570	+	0.0613700i
$430$	7.15822	+	13.2825i	0.345200	+	0.640537i
$431$	−3.26143	−	31.0305i	−0.157098	−	1.49468i	−0.734714	−	0.678377i	$-0.762684\pi$
$431$	−3.26143	−	31.0305i	−0.157098	−	1.49468i	0.577617	−	0.816308i	$-0.303983\pi$
$432$	0.129482	+	2.47067i	0.00622973	+	0.118870i
$433$	11.6636	−	5.94290i	0.560517	−	0.285598i	−0.150689	−	0.988581i	$-0.548149\pi$
$433$	11.6636	−	5.94290i	0.560517	−	0.285598i	0.711206	+	0.702984i	$0.248149\pi$
$434$	−2.74032	+	14.9793i	−0.131540	+	0.719029i
$435$	−12.9890	+	31.0835i	−0.622774	+	1.49034i
$436$	12.7949	−	2.71964i	0.612765	−	0.130247i
$437$	−23.5284	+	15.2795i	−1.12551	+	0.730918i
$438$	17.4494	+	14.1303i	0.833767	+	0.675171i
$439$	3.32166	+	5.75328i	0.158534	+	0.274589i	0.934340	−	0.356382i	$-0.115990\pi$
$439$	3.32166	+	5.75328i	0.158534	+	0.274589i	−0.775806	+	0.630971i	$0.782657\pi$
$440$	7.40764	+	0.356215i	0.353145	+	0.0169819i
$441$	−13.0077	−	1.99840i	−0.619416	−	0.0951621i
$442$	−3.89462	−	0.616848i	−0.185248	−	0.0293404i
$443$	−1.71425	−	32.7099i	−0.0814466	−	1.55409i	−0.667986	−	0.744173i	$-0.732844\pi$
$443$	−1.71425	−	32.7099i	−0.0814466	−	1.55409i	0.586540	−	0.809920i	$-0.300490\pi$
$444$	−6.03135	−	6.69849i	−0.286235	−	0.317896i
$445$	3.11677	−	23.1167i	0.147749	−	1.09584i
$446$	6.65439	+	0.699404i	0.315094	+	0.0331178i
$447$	9.94771	+	19.5235i	0.470510	+	0.923429i
$448$	0.0631221	−	2.64500i	0.00298224	−	0.124964i
$449$	4.03646	+	5.55572i	0.190493	+	0.262191i	0.893571	−	0.448922i	$-0.148192\pi$
$449$	4.03646	+	5.55572i	0.190493	+	0.262191i	−0.703079	+	0.711112i	$0.748192\pi$
$450$	1.89701	+	9.20685i	0.0894258	+	0.434015i
$451$	−0.935799	+	5.26722i	−0.0440651	+	0.248024i
$452$	−16.3262	+	4.37460i	−0.767920	+	0.205764i
$453$	4.59428	+	11.9685i	0.215858	+	0.562329i
$454$	−0.253999	−	0.781730i	−0.0119208	−	0.0366884i
$455$	1.49851	+	14.3679i	0.0702510	+	0.673579i
$456$	−5.38845	−	3.91493i	−0.252337	−	0.183334i
$457$	−9.75952	+	7.90310i	−0.456531	+	0.369691i	−0.829827	−	0.558021i	$-0.811561\pi$
$457$	−9.75952	+	7.90310i	−0.456531	+	0.369691i	0.373296	+	0.927712i	$0.378228\pi$
$458$	−0.768945	+	14.6723i	−0.0359304	+	0.685593i
$459$	0.830664	−	3.90797i	0.0387721	−	0.182408i
$460$	20.4458	+	3.85543i	0.953291	+	0.179760i
$461$		−	29.2861i		−	1.36399i	−0.731356	−	0.681996i	$-0.761112\pi$
$461$		−	29.2861i		−	1.36399i	0.731356	−	0.681996i	$-0.238888\pi$
$462$	3.84525	−	18.9994i	0.178897	−	0.883933i
$463$	−22.8396	+	22.8396i	−1.06145	+	1.06145i	−0.0634636	+	0.997984i	$0.520215\pi$
$463$	−22.8396	+	22.8396i	−1.06145	+	1.06145i	−0.997984	+	0.0634636i	$0.979785\pi$
$464$	−2.77392	+	6.23033i	−0.128776	+	0.289236i
$465$	−0.655550	−	28.4232i	−0.0304004	−	1.31809i
$466$	−18.7792	−	20.8565i	−0.869932	−	0.966157i
$467$	22.9715	+	28.3674i	1.06299	+	1.31269i	0.947633	+	0.319362i	$0.103469\pi$
$467$	22.9715	+	28.3674i	1.06299	+	1.31269i	0.115359	+	0.993324i	$0.463198\pi$
$468$	0.718144	+	4.53418i	0.0331962	+	0.209593i
$469$	8.90599	+	3.66480i	0.411240	+	0.169225i
$470$	−6.87288	−	1.67273i	−0.317022	−	0.0771572i
$471$	−31.0095	−	13.8063i	−1.42884	−	0.636161i
$472$	−0.133930	−	0.499833i	−0.00616463	−	0.0230067i
$473$	6.51549	+	21.4105i	0.299582	+	0.984455i
$474$	−7.25137	−	12.5597i	−0.333067	−	0.576888i
$475$	13.3892	+	6.92769i	0.614336	+	0.317864i
$476$	−1.20396	+	4.09939i	−0.0551833	+	0.187895i
$477$	−21.0133	+	10.7068i	−0.962132	+	0.490231i
$478$	−4.23055	−	5.22429i	−0.193501	−	0.238953i
$479$	−34.0158	+	15.1448i	−1.55422	+	0.691983i	−0.990943	−	0.134284i	$-0.957126\pi$
$479$	−34.0158	+	15.1448i	−1.55422	+	0.691983i	−0.563277	+	0.826268i	$0.690460\pi$
$480$	0.885023	+	4.85973i	0.0403956	+	0.221815i
$481$	7.40413	+	6.66671i	0.337599	+	0.303976i
$482$	3.35681	−	21.1941i	0.152899	−	0.965364i
$483$	18.0346	−	51.3062i	0.820605	−	2.33451i
$484$	10.6663	+	2.68882i	0.484832	+	0.122219i
$485$	8.66772	−	8.17411i	0.393581	−	0.371167i
$486$	−17.0172	+	1.78858i	−0.771915	+	0.0811316i
$487$	2.19508	+	3.38012i	0.0994685	+	0.153168i	0.884901	−	0.465779i	$-0.154226\pi$
$487$	2.19508	+	3.38012i	0.0994685	+	0.153168i	−0.785432	+	0.618948i	$0.787559\pi$
$488$	−5.61188	−	3.64440i	−0.254038	−	0.164974i
$489$	−11.0163	−	8.00380i	−0.498174	−	0.361944i
$490$	15.6477	+	0.385959i	0.706892	+	0.0174358i
$491$	−3.05984	+	9.41720i	−0.138088	+	0.424992i	−0.996058	−	0.0887087i	$-0.971726\pi$
$491$	−3.05984	+	9.41720i	−0.138088	+	0.424992i	0.857969	+	0.513701i	$0.171726\pi$
$492$	−3.55836	+	0.186486i	−0.160423	+	0.00840743i
$493$	6.93089	−	8.55893i	0.312151	−	0.385475i
$494$	6.37579	+	3.68106i	0.286860	+	0.165619i
$495$	0.0600848	+	13.9427i	0.00270061	+	0.626678i
$496$		−	5.75560i		−	0.258434i
$497$	−0.801259	−	2.68214i	−0.0359414	−	0.120311i
$498$	−6.87859	−	3.50481i	−0.308237	−	0.157054i
$499$	−1.01470	−	4.77379i	−0.0454242	−	0.213704i	0.949582	−	0.313520i	$-0.101508\pi$
$499$	−1.01470	−	4.77379i	−0.0454242	−	0.213704i	−0.995006	+	0.0998154i	$0.968175\pi$
$500$	−3.63326	−	10.5735i	−0.162484	−	0.472862i
$501$	−41.3346	+	18.4034i	−1.84669	+	0.822202i
$502$	9.08787	−	13.9941i	0.405611	−	0.624587i
$503$	−13.1153	+	25.7402i	−0.584782	+	1.14770i	0.389217	+	0.921146i	$0.372745\pi$
$503$	−13.1153	+	25.7402i	−0.584782	+	1.14770i	−0.973999	+	0.226553i	$0.927255\pi$
$504$	4.97213	−	0.141743i	0.221476	−	0.00631371i
$505$	−8.73838	−	5.39246i	−0.388853	−	0.239961i
$506$	28.5983	+	11.5977i	1.27135	+	0.515579i
$507$	4.02378	+	15.0170i	0.178703	+	0.666927i
$508$	16.1700	+	13.0942i	0.717428	+	0.580962i
$509$	−8.26555	+	9.17982i	−0.366364	+	0.406888i	−0.897937	−	0.440124i	$-0.854934\pi$
$509$	−8.26555	+	9.17982i	−0.366364	+	0.406888i	0.531573	+	0.847012i	$0.321601\pi$
$510$	0.650668	−	7.95030i	0.0288120	−	0.352045i
$511$	−17.4172	+	20.4890i	−0.770491	+	0.906378i
$512$	0.156434	+	0.987688i	0.00691349	+	0.0436501i
$513$	−4.06268	+	6.25599i	−0.179372	+	0.276209i
$514$	3.24981	+	0.690768i	0.143343	+	0.0304685i
$515$	0.109053	+	0.311037i	0.00480545	+	0.0137059i
$516$	−12.9094	+	7.45323i	−0.568303	+	0.328110i
$517$	−9.50295	−	4.44632i	−0.417939	−	0.195549i
$518$	8.19263	−	7.03010i	0.359963	−	0.308885i
$519$	−16.8846	−	23.2397i	−0.741153	−	1.02011i
$520$	−1.53439	−	5.23999i	−0.0672874	−	0.229789i
$521$	17.5582	−	15.8094i	0.769237	−	0.692624i	−0.187923	−	0.982184i	$-0.560176\pi$
$521$	17.5582	−	15.8094i	0.769237	−	0.692624i	0.957160	+	0.289560i	$0.0935089\pi$
$522$	−11.9702	−	4.59494i	−0.523922	−	0.201115i
$523$	−1.45015	+	1.17430i	−0.0634104	+	0.0513488i	−0.660502	−	0.750825i	$-0.729656\pi$
$523$	−1.45015	+	1.17430i	−0.0634104	+	0.0513488i	0.597091	+	0.802173i	$0.296323\pi$
$524$	−3.66679	+	11.2852i	−0.160185	+	0.492998i
$525$	−28.7547	+	5.21286i	−1.25496	+	0.227508i
$526$	−7.20533	+	5.23498i	−0.314167	+	0.228256i
$527$	−2.40560	+	8.97781i	−0.104789	+	0.391080i
$528$	−0.137371	+	7.32541i	−0.00597831	+	0.318798i
$529$	55.0612	+	31.7896i	2.39396	+	1.38216i
$530$	23.1660	−	15.8153i	1.00626	−	0.686974i
$531$	0.925246	−	0.300631i	0.0401523	−	0.0130463i
$532$	4.84143	−	6.33987i	0.209903	−	0.274868i
$533$	3.89012	−	0.616134i	0.168500	−	0.0266877i
$534$	22.9181	+	2.40879i	0.991763	+	0.104239i
$535$	−4.12193	−	2.85190i	−0.178207	−	0.123298i
$536$	−3.56046	−	0.756799i	−0.153789	−	0.0326888i
$537$	−6.27811	+	2.40994i	−0.270920	+	0.103997i
$538$	−19.1852	−	19.1852i	−0.827134	−	0.827134i
$539$	22.6387	+	5.14691i	0.975116	+	0.221693i
$540$	5.38332	−	1.27467i	0.231661	−	0.0548531i
$541$	−26.0041	−	11.5778i	−1.11800	−	0.497767i	−0.237300	−	0.971436i	$-0.576262\pi$
$541$	−26.0041	−	11.5778i	−1.11800	−	0.497767i	−0.880703	+	0.473670i	$0.842929\pi$
$542$	−8.02868	+	5.21389i	−0.344861	+	0.223956i
$543$	−42.0146	−	2.20189i	−1.80302	−	0.0944922i
$544$	0.168799	−	1.60602i	0.00723721	−	0.0688574i
$545$	−11.1089	−	27.0578i	−0.475854	−	1.15903i
$546$	−14.1451	+	1.89563i	−0.605354	+	0.0811254i
$547$	12.7539	−	25.0310i	0.545318	−	1.07025i	−0.439756	−	0.898117i	$-0.644935\pi$
$547$	12.7539	−	25.0310i	0.545318	−	1.07025i	0.985074	−	0.172130i	$-0.0550648\pi$
$548$	9.85745	−	3.78392i	0.421089	−	0.161641i
$549$	6.29009	−	10.8948i	0.268454	−	0.464977i
$550$	−2.18408	−	16.4387i	−0.0931297	−	0.700947i
$551$	−17.8076	+	10.2812i	−0.758629	+	0.437995i
$552$	−3.21552	+	20.3020i	−0.136862	+	0.864110i
$553$	15.2453	−	8.32339i	0.648298	−	0.353947i
$554$	−26.3059	−	8.54731i	−1.11763	−	0.363140i
$555$	−12.3196	+	15.9519i	−0.522937	+	0.677120i
$556$	7.16883	+	16.1015i	0.304026	+	0.682854i
$557$	1.40649	−	26.8373i	0.0595947	−	1.13713i	−0.791173	−	0.611593i	$-0.790529\pi$
$557$	1.40649	−	26.8373i	0.0595947	−	1.13713i	0.850768	−	0.525542i	$-0.176137\pi$
$558$	10.8060	−	0.566318i	0.457454	−	0.0239742i
$559$	13.3300	−	9.68479i	0.563798	−	0.409623i
$560$	−5.84398	+	0.920802i	−0.246953	+	0.0389110i
$561$	3.27599	−	11.3690i	0.138312	−	0.480002i
$562$	1.77313	−	6.61741i	0.0747950	−	0.279139i
$563$	−19.6537	+	24.2703i	−0.828304	+	1.02287i	0.170989	+	0.985273i	$0.445304\pi$
$563$	−19.6537	+	24.2703i	−0.828304	+	1.02287i	−0.999293	+	0.0375977i	$0.988029\pi$
$564$	1.45292	−	6.83544i	0.0611788	−	0.287824i
$565$	16.1644	+	34.1632i	0.680040	+	1.43726i
$566$	−9.90910	+	13.6387i	−0.416511	+	0.573278i
$567$	−2.37327	−	29.2866i	−0.0996681	−	1.22992i
$568$	0.480333	+	0.942706i	0.0201543	+	0.0395551i
$569$	−1.22186	−	1.10017i	−0.0512230	−	0.0461214i	0.643122	−	0.765764i	$-0.277639\pi$
$569$	−1.22186	−	1.10017i	−0.0512230	−	0.0461214i	−0.694345	+	0.719643i	$0.744306\pi$
$570$	−6.45364	+	13.4224i	−0.270313	+	0.562202i
$571$	−1.56983	+	2.71903i	−0.0656955	+	0.113788i	−0.897002	−	0.442026i	$-0.854260\pi$
$571$	−1.56983	+	2.71903i	−0.0656955	+	0.113788i	0.831307	+	0.555814i	$0.187593\pi$
$572$	−0.695367	−	8.06862i	−0.0290748	−	0.337366i
$573$	11.8244	+	11.8244i	0.493970	+	0.493970i
$574$	−0.121609	−	4.26585i	−0.00507584	−	0.178053i
$575$	0.290316	−	46.5231i	0.0121070	−	1.94015i
$576$	−1.83897	+	0.390884i	−0.0766236	+	0.0162869i
$577$	−5.01395	+	13.0618i	−0.208733	+	0.543769i	−0.997480	−	0.0709495i	$-0.977397\pi$
$577$	−5.01395	+	13.0618i	−0.208733	+	0.543769i	0.788747	+	0.614719i	$0.210730\pi$
$578$	5.15771	−	13.4363i	0.214532	−	0.558876i
$579$	40.9168	−	8.69714i	1.70044	−	0.361441i
$580$	14.8173	+	3.60626i	0.615256	+	0.149742i
$581$	4.39296	−	8.13578i	0.182251	−	0.337529i
$582$	8.32286	+	8.32286i	0.344994	+	0.344994i
$583$	38.3181	−	16.2065i	1.58698	−	0.671203i
$584$	5.08203	−	8.80233i	0.210296	−	0.364243i
$585$	9.68697	−	3.39636i	0.400507	−	0.140422i
$586$	−6.50707	−	5.85899i	−0.268804	−	0.242033i
$587$	−6.61377	−	12.9803i	−0.272980	−	0.535753i	0.713295	−	0.700863i	$-0.247202\pi$
$587$	−6.61377	−	12.9803i	−0.272980	−	0.535753i	−0.986275	+	0.165111i	$0.947202\pi$
$588$	0.0717437	+	15.4634i	0.00295866	+	0.637701i
$589$	10.2001	−	14.0392i	0.420287	−	0.578475i
$590$	−1.04592	+	0.494878i	−0.0430598	+	0.0203738i
$591$	2.42168	−	11.3931i	0.0996144	−	0.468649i
$592$	−2.56781	+	3.17098i	−0.105536	+	0.130327i
$593$	−5.53183	+	20.6451i	−0.227165	+	0.847791i	0.754361	+	0.656460i	$0.227947\pi$
$593$	−5.53183	+	20.6451i	−0.227165	+	0.847791i	−0.981526	+	0.191331i	$0.938720\pi$
$594$	8.20090	−	0.275731i	0.336487	−	0.0113134i
$595$	9.50053	+	1.00623i	0.389484	+	0.0412516i
$596$	8.02457	−	5.83019i	0.328699	−	0.238814i
$597$	20.7514	−	1.08753i	0.849298	−	0.0445098i
$598$	1.18909	−	22.6893i	0.0486257	−	0.927834i
$599$	5.64275	+	12.6738i	0.230556	+	0.517838i	0.991364	−	0.131139i	$-0.0418635\pi$
$599$	5.64275	+	12.6738i	0.230556	+	0.517838i	−0.760807	+	0.648978i	$0.775197\pi$
$600$	10.3363	−	3.89390i	0.421977	−	0.158968i
$601$	−26.0711	−	8.47103i	−1.06346	−	0.345540i	−0.275525	−	0.961294i	$-0.588852\pi$
$601$	−26.0711	−	8.47103i	−1.06346	−	0.345540i	−0.787939	+	0.615753i	$0.788852\pi$
$602$	−8.55509	−	15.6697i	−0.348679	−	0.638650i
$603$	1.07054	−	6.75914i	0.0435958	−	0.275253i
$604$	5.02581	−	2.90166i	0.204497	−	0.118067i
$605$	1.64186	−	24.5419i	0.0667513	−	0.997770i
$606$	5.07219	−	8.78530i	0.206044	−	0.356878i
$607$	−5.94118	+	2.28061i	−0.241145	+	0.0925670i	−0.475939	−	0.879478i	$-0.657892\pi$
$607$	−5.94118	+	2.28061i	−0.241145	+	0.0925670i	0.234794	+	0.972045i	$0.424558\pi$
$608$	−1.36880	+	2.68642i	−0.0555122	+	0.108949i
$609$	15.1685	−	36.8615i	0.614657	−	1.49371i
$610$	−5.76898	+	13.8056i	−0.233579	+	0.558971i
$611$	−0.807409	+	7.68199i	−0.0326643	+	0.310780i
$612$	3.03186	+	0.158893i	0.122556	+	0.00642288i
$613$	25.8858	−	16.8104i	1.04552	−	0.678967i	0.0968687	−	0.995297i	$-0.469117\pi$
$613$	25.8858	−	16.8104i	1.04552	−	0.678967i	0.948649	+	0.316330i	$0.102451\pi$
$614$	4.75153	+	2.11552i	0.191756	+	0.0853754i
$615$	1.83583	+	7.75327i	0.0740278	+	0.312642i
$616$	−8.76700	−	0.373794i	−0.353232	−	0.0150606i
$617$	−8.66713	−	8.66713i	−0.348926	−	0.348926i	0.510784	−	0.859709i	$-0.329355\pi$
$617$	−8.66713	−	8.66713i	−0.348926	−	0.348926i	−0.859709	+	0.510784i	$0.829355\pi$
$618$	−0.303995	+	0.116693i	−0.0122285	+	0.00469407i
$619$	12.0302	+	2.55709i	0.483534	+	0.102778i	0.443228	−	0.896409i	$-0.353833\pi$
$619$	12.0302	+	2.55709i	0.483534	+	0.102778i	0.0403060	+	0.999187i	$0.487167\pi$
$620$	−12.6617	+	2.30586i	−0.508505	+	0.0926057i
$621$	22.8945	+	2.40631i	0.918726	+	0.0965620i
$622$	22.1370	−	3.50616i	0.887614	−	0.140584i
$623$	−3.53897	+	27.3717i	−0.141786	+	1.09662i
$624$	5.13013	−	1.66688i	0.205369	−	0.0667286i
$625$	−21.8049	+	12.2288i	−0.872198	+	0.489153i
$626$	−4.95701	−	2.86193i	−0.198122	−	0.114386i
$627$	−13.3172	+	17.6249i	−0.531836	+	0.703869i
$628$	−3.97693	+	14.8421i	−0.158697	+	0.592265i
$629$	5.33071	−	3.87299i	0.212549	−	0.154426i
$630$	−2.30380	−	10.8813i	−0.0917854	−	0.433522i
$631$	11.5337	−	35.4971i	0.459150	−	1.41312i	−0.407043	−	0.913409i	$-0.633440\pi$
$631$	11.5337	−	35.4971i	0.459150	−	1.41312i	0.866193	−	0.499710i	$-0.166560\pi$
$632$	−5.10200	+	4.13152i	−0.202947	+	0.164343i
$633$	40.3019	+	15.4704i	1.60186	+	0.614895i
$634$	−3.41453	+	3.07445i	−0.135608	+	0.122102i
$635$	22.3276	−	40.8181i	0.886044	−	1.61982i
$636$	16.2882	+	22.4188i	0.645871	+	0.888965i
$637$	−1.86551	−	16.9905i	−0.0739141	−	0.673187i
$638$	20.4875	+	9.58587i	0.811110	+	0.379508i
$639$	−1.72264	+	0.994569i	−0.0681468	+	0.0393446i
$640$	2.11013	−	0.739835i	0.0834102	−	0.0292445i
$641$	8.95874	+	1.90424i	0.353849	+	0.0752129i	0.381407	−	0.924407i	$-0.375440\pi$
$641$	8.95874	+	1.90424i	0.353849	+	0.0752129i	−0.0275579	+	0.999620i	$0.508773\pi$
$642$	2.69698	−	4.15298i	0.106441	−	0.163905i
$643$	−5.95200	−	37.5795i	−0.234724	−	1.48199i	−0.770397	−	0.637564i	$-0.779942\pi$
$643$	−5.95200	−	37.5795i	−0.234724	−	1.48199i	0.535673	−	0.844425i	$-0.320058\pi$
$644$	−24.2163	−	4.43014i	−0.954255	−	0.174572i
$645$	21.5681	+	25.4131i	0.849244	+	1.00064i
$646$	3.25792	−	3.61829i	0.128181	−	0.142360i
$647$	1.09322	+	0.885276i	0.0429791	+	0.0348038i	0.650569	−	0.759447i	$-0.274530\pi$
$647$	1.09322	+	0.885276i	0.0429791	+	0.0348038i	−0.607590	+	0.794251i	$0.707864\pi$
$648$	2.87433	+	10.7271i	0.112914	+	0.421402i
$649$	−1.66580	+	0.413035i	−0.0653882	+	0.0162131i
$650$	−10.9127	+	5.47477i	−0.428030	+	0.214738i
$651$	0.958592	+	33.6260i	0.0375702	+	1.31791i
$652$	−2.79842	+	5.49220i	−0.109594	+	0.215091i
$653$	−23.2183	+	35.7531i	−0.908602	+	1.39913i	0.00827917	+	0.999966i	$0.497365\pi$
$653$	−23.2183	+	35.7531i	−0.908602	+	1.39913i	−0.916882	+	0.399159i	$0.869302\pi$
$654$	26.3983	−	11.7533i	1.03225	−	0.459589i
$655$	26.2952	+	3.54533i	1.02744	+	0.138528i
$656$	0.335361	+	1.57775i	0.0130936	+	0.0616007i
$657$	17.0262	+	8.67527i	0.664255	+	0.338455i
$658$	8.14274	+	1.93493i	0.317437	+	0.0754315i
$659$			1.15344i			0.0449318i	0.999748	+	0.0224659i	$0.00715171\pi$
$659$			1.15344i			0.0449318i	−0.999748	+	0.0224659i	$0.992848\pi$
$660$	16.1701	−	2.63257i	0.629421	−	0.102473i
$661$	25.8858	+	14.9452i	1.00684	+	0.581301i	0.910266	−	0.414025i	$-0.135877\pi$
$661$	25.8858	+	14.9452i	1.00684	+	0.581301i	0.0965766	+	0.995326i	$0.469211\pi$
$662$	−20.1373	+	24.8674i	−0.782657	+	0.966500i
$663$	−8.69885	+	0.455888i	−0.337835	+	0.0177052i
$664$	−1.07991	+	3.32363i	−0.0419087	+	0.128982i
$665$	−15.8866	−	8.11066i	−0.616056	−	0.314518i
$666$	−6.20609	−	4.50899i	−0.240481	−	0.174720i
$667$	53.2205	+	34.5618i	2.06071	+	1.33824i
$668$	11.1553	+	17.1776i	0.431611	+	0.664622i
$669$	14.7001	−	1.54504i	0.568339	−	0.0597348i
$670$	−0.238448	+	8.13580i	−0.00921203	+	0.314314i
$671$	−12.4340	+	18.3826i	−0.480008	+	0.709653i
$672$	−1.07844	−	5.74433i	−0.0416016	−	0.221592i
$673$	0.597261	−	3.77096i	0.0230227	−	0.145360i	−0.973499	−	0.228690i	$-0.926556\pi$
$673$	0.597261	−	3.77096i	0.0230227	−	0.145360i	0.996522	+	0.0833305i	$0.0265557\pi$
$674$	9.36743	+	8.43447i	0.360820	+	0.324884i
$675$	−4.96084	−	11.3320i	−0.190943	−	0.436170i
$676$	6.42919	−	2.86246i	0.247277	−	0.110095i
$677$	−0.556164	−	0.686805i	−0.0213751	−	0.0263961i	0.766346	−	0.642428i	$-0.222073\pi$
$677$	−0.556164	−	0.686805i	−0.0213751	−	0.0263961i	−0.787721	+	0.616032i	$0.788739\pi$
$678$	−33.2686	+	16.9512i	−1.27767	+	0.651007i
$679$	−10.2030	+	9.72738i	−0.391556	+	0.373303i
$680$	−3.60068	+	0.272078i	−0.138080	+	0.0104337i
$681$	−0.907888	−	1.57251i	−0.0347904	−	0.0602587i
$682$	−19.0858	−	0.357910i	−0.730834	−	0.0137051i
$683$	−11.2364	−	41.9349i	−0.429950	−	1.60460i	−0.752870	−	0.658169i	$-0.771331\pi$
$683$	−11.2364	−	41.9349i	−0.429950	−	1.60460i	0.322920	−	0.946426i	$-0.395336\pi$
$684$	−5.17837	−	2.30556i	−0.198000	−	0.0881553i
$685$	−12.2734	−	20.1693i	−0.468941	−	0.770630i
$686$	−18.5168	−	0.355949i	−0.706976	−	0.0135902i
$687$	5.07738	+	32.0573i	0.193714	+	1.22306i
$688$	4.24653	+	5.24402i	0.161897	+	0.199927i
$689$	−20.4957	−	22.7628i	−0.780826	−	0.867195i
$690$	45.9503	−	1.05979i	1.74930	−	0.0403457i
$691$	6.30105	−	14.1524i	0.239703	−	0.538382i	−0.753133	−	0.657869i	$-0.771458\pi$
$691$	6.30105	−	14.1524i	0.239703	−	0.538382i	0.992836	+	0.119486i	$0.0381248\pi$
$692$	−9.19487	+	9.19487i	−0.349537	+	0.349537i
$693$	−0.160834	−	16.4966i	−0.00610959	−	0.626654i
$694$		−	26.8256i		−	1.01829i
$695$	32.5493	−	22.2213i	1.23467	−	0.842903i
$696$	−3.13236	+	14.7366i	−0.118732	+	0.558590i
$697$	0.136323	−	2.60120i	0.00516360	−	0.0985274i
$698$	−23.2690	+	18.8429i	−0.880745	+	0.713213i
$699$	−50.1576	−	36.4417i	−1.89714	−	1.37835i
$700$	4.36693	+	12.4872i	0.165054	+	0.471971i
$701$	−0.121897	−	0.375161i	−0.00460399	−	0.0141696i	0.948728	−	0.316093i	$-0.102371\pi$
$701$	−0.121897	−	0.375161i	−0.00460399	−	0.0141696i	−0.953332	+	0.301924i	$0.902371\pi$
$702$	−2.16496	−	5.63991i	−0.0817111	−	0.212865i
$703$	−11.8831	+	3.18406i	−0.448179	+	0.120089i
$704$	3.28494	−	0.457324i	0.123806	−	0.0172361i
$705$	−15.6193	−	0.457776i	−0.588255	−	0.0172408i
$706$	−21.3585	−	29.3975i	−0.803838	−	1.10639i
$707$	10.3740	+	6.32411i	0.390153	+	0.237843i
$708$	−0.518968	−	1.01853i	−0.0195040	−	0.0382788i
$709$	10.7691	+	1.13188i	0.404444	+	0.0425088i	0.304567	−	0.952491i	$-0.401488\pi$
$709$	10.7691	+	1.13188i	0.404444	+	0.0425088i	0.0998772	+	0.995000i	$0.468155\pi$
$710$	1.88141	−	1.43435i	0.0706081	−	0.0538303i
$711$	−8.25883	−	9.17236i	−0.309730	−	0.343990i
$712$	−0.545949	−	10.4173i	−0.0204603	−	0.390406i
$713$	−52.8954	−	8.37780i	−1.98095	−	0.313751i
$714$	−0.718697	+	9.41097i	−0.0268966	+	0.352197i
$715$	−17.4714	+	4.76225i	−0.653395	+	0.178098i
$716$	1.52207	+	2.63630i	0.0568824	+	0.0985233i
$717$	−11.5409	−	9.34563i	−0.431002	−	0.349019i
$718$	−2.51478	+	1.63312i	−0.0938507	+	0.0609473i
$719$	19.4250	−	4.12891i	0.724429	−	0.153982i	0.169083	−	0.985602i	$-0.445919\pi$
$719$	19.4250	−	4.12891i	0.724429	−	0.153982i	0.555346	+	0.831620i	$0.312586\pi$
$720$	1.59664	+	3.88892i	0.0595034	+	0.144931i
$721$	−0.131033	−	0.367316i	−0.00487994	−	0.0136796i
$722$	8.82944	−	4.49882i	0.328598	−	0.167429i
$723$	−2.48089	−	47.3382i	−0.0922652	−	1.76053i
$724$	1.99076	+	18.9408i	0.0739859	+	0.703929i
$725$	1.99710	−	34.0412i	0.0741706	−	1.26426i
$726$	24.2828	+	0.911056i	0.901221	+	0.0338125i
$727$	−21.6326	+	21.6326i	−0.802309	+	0.802309i	−0.983456	−	0.181147i	$-0.942019\pi$
$727$	−21.6326	+	21.6326i	−0.802309	+	0.802309i	0.181147	+	0.983456i	$0.442019\pi$
$728$	1.84921	+	6.19007i	0.0685364	+	0.229419i
$729$	−4.26338	+	1.38526i	−0.157903	+	0.0513057i
$730$	−21.4001	−	7.65341i	−0.792054	−	0.283265i
$731$	−4.43212	−	9.95470i	−0.163928	−	0.368188i
$732$	−13.8001	−	5.29735i	−0.510065	−	0.195796i
$733$	−30.8373	−	20.0260i	−1.13900	−	0.739677i	−0.169687	−	0.985498i	$-0.554276\pi$
$733$	−30.8373	−	20.0260i	−1.13900	−	0.739677i	−0.969315	+	0.245821i	$0.920942\pi$
$734$	−9.26924	−	28.5278i	−0.342134	−	1.05298i
$735$	33.9890	−	6.35292i	1.25370	−	0.234331i
$736$	9.30479			0.342979
$737$	−2.73098	+	11.7596i	−0.100597	+	0.433170i
$738$	−2.92918	+	0.784872i	−0.107825	+	0.0288915i
$739$	5.82972	−	0.612728i	0.214450	−	0.0225396i	0.00330562	−	0.999995i	$-0.498948\pi$
$739$	5.82972	−	0.612728i	0.214450	−	0.0225396i	0.211144	+	0.977455i	$0.432281\pi$
$740$	8.00454	+	4.37850i	0.294253	+	0.160957i
$741$	15.4676	+	5.02571i	0.568215	+	0.184624i
$742$	−27.3081	+	18.8618i	−1.00251	+	0.692438i
$743$	4.62614	−	0.732708i	0.169717	−	0.0268805i	−0.0709977	−	0.997476i	$-0.522618\pi$
$743$	4.62614	−	0.732708i	0.169717	−	0.0268805i	0.240714	+	0.970596i	$0.422618\pi$
$744$	−2.64352	−	12.4368i	−0.0969160	−	0.455954i
$745$	−16.0406	−	15.3174i	−0.587683	−	0.561186i
$746$	3.08741	+	29.3748i	0.113038	+	1.07549i
$747$	−6.34628	−	1.70048i	−0.232198	−	0.0622173i
$748$	−5.31512	−	0.659615i	−0.194340	−	0.0241179i
$749$	4.89542	+	3.34783i	0.178875	+	0.122327i
$750$	−12.7072	−	21.1786i	−0.464000	−	0.773334i
$751$	−36.6072	+	40.6564i	−1.33582	+	1.48357i	−0.623008	+	0.782215i	$0.714090\pi$
$751$	−36.6072	+	40.6564i	−1.33582	+	1.48357i	−0.712808	+	0.701359i	$0.752577\pi$
$752$	−3.15903	−	0.165558i	−0.115198	−	0.00603727i
$753$	13.2097	−	34.4126i	0.481390	−	1.25406i
$754$	1.74070	−	16.5617i	0.0633927	−	0.603142i
$755$	−8.39680	−	9.89373i	−0.305591	−	0.360070i
$756$	−6.36133	+	1.54284i	−0.231359	+	0.0561124i
$757$	6.89601	+	1.09222i	0.250640	+	0.0396974i	0.280490	−	0.959857i	$-0.409503\pi$
$757$	6.89601	+	1.09222i	0.250640	+	0.0396974i	−0.0298503	+	0.999554i	$0.509503\pi$
$758$	−23.9859	−	6.42699i	−0.871206	−	0.233439i
$759$	67.1223	+	11.9253i	2.43639	+	0.432860i
$760$	6.45821	+	1.93495i	0.234264	+	0.0701879i
$761$	12.7428	−	28.6207i	0.461924	−	1.03750i	−0.521011	−	0.853550i	$-0.674445\pi$
$761$	12.7428	−	28.6207i	0.461924	−	1.03750i	0.982936	−	0.183950i	$-0.0588883\pi$
$762$	40.9544	+	20.8673i	1.48362	+	0.755943i
$763$	13.3182	+	31.9432i	0.482152	+	1.15642i
$764$	4.44938	−	6.12405i	0.160973	−	0.221560i
$765$	−0.865106	−	6.73341i	−0.0312780	−	0.243447i
$766$	3.05141	−	2.74750i	0.110252	−	0.0992713i
$767$	0.688176	+	1.05970i	0.0248486	+	0.0382635i
$768$	0.791665	+	2.06236i	0.0285667	+	0.0744189i
$769$	−41.6715			−1.50271			−0.751356	−	0.659897i	$-0.770600\pi$
$769$	−41.6715			−1.50271			−0.751356	+	0.659897i	$0.770600\pi$
$770$	2.69001	+	19.4361i	0.0969413	+	0.700430i
$771$	7.33949			0.264325
$772$	−6.78601	−	17.6782i	−0.244234	−	0.636251i
$773$	−26.5155	−	40.8303i	−0.953696	−	1.46856i	−0.882063	−	0.471132i	$-0.843846\pi$
$773$	−26.5155	−	40.8303i	−0.953696	−	1.46856i	−0.0716333	−	0.997431i	$-0.522821\pi$
$774$	−9.42768	+	8.48872i	−0.338871	+	0.305121i
$775$	10.1453	+	26.9304i	0.364429	+	0.967369i
$776$	3.13180	−	4.31055i	0.112425	−	0.154740i
$777$	14.4738	−	18.9535i	0.519246	−	0.679954i
$778$	24.1263	+	12.2930i	0.864970	+	0.440724i
$779$	−1.97806	+	4.44280i	−0.0708715	+	0.159180i
$780$	−5.72222	−	10.6179i	−0.204888	−	0.380181i
$781$	3.15592	−	1.53418i	0.112928	−	0.0548974i
$782$	−14.5140	−	3.88901i	−0.519019	−	0.139071i
$783$	16.6652	+	2.63952i	0.595567	+	0.0943286i
$784$	6.90866	−	1.12711i	0.246738	−	0.0402538i
$785$	34.2442	+	2.80261i	1.22223	+	0.100030i
$786$	−2.74000	+	26.0694i	−0.0977326	+	0.929864i
$787$	3.09600	−	8.06536i	0.110360	−	0.287499i	−0.867267	−	0.497844i	$-0.834125\pi$
$787$	3.09600	−	8.06536i	0.110360	−	0.287499i	0.977627	+	0.210345i	$0.0674587\pi$
$788$	−5.26538	−	0.275947i	−0.187571	−	0.00983019i
$789$	−13.1649	+	14.6212i	−0.468685	+	0.520527i
$790$	11.1329	+	9.56861i	0.396090	+	0.340436i
$791$	−19.3455	−	40.3178i	−0.687848	−	1.43354i
$792$	1.18183	+	6.12240i	0.0419946	+	0.217550i
$793$	15.7823	+	4.22886i	0.560446	+	0.150171i
$794$	2.72327	+	25.9101i	0.0966451	+	0.919517i
$795$	42.7933	−	44.8139i	1.51772	−	1.58939i
$796$	−1.95573	−	9.20100i	−0.0693192	−	0.326121i
$797$	−2.10841	+	0.333939i	−0.0746836	+	0.0118287i	−0.193664	−	0.981068i	$-0.562037\pi$
$797$	−2.10841	+	0.333939i	−0.0746836	+	0.0118287i	0.118981	+	0.992897i	$0.462037\pi$
$798$	7.54954	−	15.9229i	0.267251	−	0.563665i
$799$	4.85838	+	1.57858i	0.171877	+	0.0558463i
$800$	−2.47293	−	4.34564i	−0.0874313	−	0.153642i
$801$	19.5046	−	2.05001i	0.689159	−	0.0724336i
$802$	16.5181	−	4.42601i	0.583274	−	0.156288i
$803$	−28.8729	−	17.3996i	−1.01890	−	0.614018i
$804$	−8.04107			−0.283587
$805$	−0.0440559	+	55.0479i	−0.00155277	+	1.94018i
$806$	4.34293	+	13.3662i	0.152973	+	0.470803i
$807$	−50.2673	−	32.6440i	−1.76949	−	1.14912i
$808$	−4.28712	−	1.64567i	−0.150820	−	0.0578945i
$809$	18.2390	+	40.9655i	0.641250	+	1.44027i	0.882737	+	0.469867i	$0.155698\pi$
$809$	18.2390	+	40.9655i	0.641250	+	1.44027i	−0.241487	+	0.970404i	$0.577635\pi$
$810$	22.4470	−	10.6208i	0.788706	−	0.373177i
$811$	−21.1627	+	6.87618i	−0.743124	+	0.241455i	−0.656020	−	0.754744i	$-0.727761\pi$
$811$	−21.1627	+	6.87618i	−0.743124	+	0.241455i	−0.0871038	+	0.996199i	$0.527761\pi$
$812$	−17.5551	−	4.17155i	−0.616062	−	0.146393i
$813$	−14.9537	+	14.9537i	−0.524451	+	0.524451i
$814$	10.3554	+	8.71216i	0.362958	+	0.305361i
$815$	13.2033	+	3.95586i	0.462493	+	0.138568i
$816$	−0.372892	−	3.54783i	−0.0130538	−	0.124199i
$817$	1.06477	+	20.3170i	0.0372516	+	0.710803i
$818$	26.4293	−	13.4664i	0.924080	−	0.470842i
$819$	−11.4397	+	4.08092i	−0.399737	+	0.142599i
$820$	3.33651	−	1.36985i	0.116516	−	0.0478371i
$821$	36.6852	−	7.79768i	1.28032	−	0.272141i	0.482960	−	0.875642i	$-0.339562\pi$
$821$	36.6852	−	7.79768i	1.28032	−	0.272141i	0.797362	+	0.603502i	$0.206228\pi$
$822$	19.5621	−	12.7038i	0.682308	−	0.443096i
$823$	−40.4786	−	32.7789i	−1.41100	−	1.14260i	−0.969429	−	0.245373i	$-0.921089\pi$
$823$	−40.4786	−	32.7789i	−1.41100	−	1.14260i	−0.441567	−	0.897228i	$-0.645577\pi$
$824$	0.0737009	+	0.127654i	0.00256749	+	0.00444703i
$825$	−12.2696	−	34.5177i	−0.427172	−	1.20175i
$826$	1.23435	−	0.592271i	0.0429484	−	0.0206078i
$827$	−10.0847	−	1.59726i	−0.350679	−	0.0555420i	−0.0213896	−	0.999771i	$-0.506809\pi$
$827$	−10.0847	−	1.59726i	−0.350679	−	0.0555420i	−0.329289	+	0.944229i	$0.606809\pi$
$828$	0.915538	+	17.4695i	0.0318171	+	0.607107i
$829$	22.5247	+	25.0162i	0.782315	+	0.868849i	0.994100	−	0.108467i	$-0.0345942\pi$
$829$	22.5247	+	25.0162i	0.782315	+	0.868849i	−0.211785	+	0.977316i	$0.567928\pi$
$830$	7.74425	+	1.04414i	0.268807	+	0.0362427i
$831$	−60.7678	−	6.38695i	−2.10801	−	0.221561i
$832$	−1.10855	−	2.17566i	−0.0384321	−	0.0754273i
$833$	−11.2475	−	1.12942i	−0.389702	−	0.0391322i
$834$	22.8858	+	31.4996i	0.792470	+	1.09074i
$835$	33.3197	−	31.4222i	1.15308	−	1.08741i
$836$	8.82318	+	4.70606i	0.305156	+	0.162762i
$837$	−13.7545	+	3.68551i	−0.475426	+	0.127390i
$838$	−4.10191	−	10.6858i	−0.141698	−	0.369136i
$839$	−0.0130560	−	0.0401822i	−0.000450743	−	0.00138724i	0.950831	−	0.309711i	$-0.100232\pi$
$839$	−0.0130560	−	0.0401822i	−0.000450743	−	0.00138724i	−0.951282	+	0.308323i	$0.900232\pi$
$840$	−12.2048	+	4.67379i	−0.421106	+	0.161261i
$841$	14.1673	+	10.2931i	0.488526	+	0.354935i
$842$	14.9792	−	12.1299i	0.516216	−	0.418024i
$843$	0.792058	−	15.1134i	0.0272799	−	0.520532i
$844$	4.06294	−	19.1146i	0.139852	−	0.657953i
$845$	−8.87281	−	12.9967i	−0.305234	−	0.447100i
$846$		−	5.94729i		−	0.204472i
$847$	−1.78469	+	29.0485i	−0.0613226	+	0.998118i
$848$	8.87010	−	8.87010i	0.304600	−	0.304600i
$849$	−15.1475	+	34.0219i	−0.519861	+	1.16763i
$850$	2.04108	+	7.81208i	0.0700084	+	0.267952i
$851$	25.4044	+	28.2144i	0.870852	+	0.967179i
$852$	1.47089	+	1.81640i	0.0503918	+	0.0622287i
$853$	0.900538	+	5.68577i	0.0308338	+	0.194677i	0.998297	−	0.0583343i	$-0.0185789\pi$
$853$	0.900538	+	5.68577i	0.0308338	+	0.194677i	−0.967463	+	0.253012i	$0.918579\pi$
$854$	6.73699	−	16.3718i	0.230535	−	0.560233i
$855$	−2.99736	+	12.3155i	−0.102508	+	0.421181i
$856$	−2.04779	−	0.911737i	−0.0699922	−	0.0311625i
$857$	8.78354	+	32.7806i	0.300040	+	1.11976i	0.937132	+	0.348976i	$0.113471\pi$
$857$	8.78354	+	32.7806i	0.300040	+	1.11976i	−0.637092	+	0.770788i	$0.719863\pi$
$858$	−5.20843	−	17.1154i	−0.177813	−	0.584309i
$859$	−8.16034	−	14.1341i	−0.278427	−	0.482250i	0.692567	−	0.721354i	$-0.256480\pi$
$859$	−8.16034	−	14.1341i	−0.278427	−	0.482250i	−0.970994	+	0.239104i	$0.923146\pi$
$860$	9.83497	−	11.4428i	0.335370	−	0.390196i
$861$	−2.22206	−	9.16184i	−0.0757274	−	0.312235i
$862$	−27.8006	+	14.1651i	−0.946893	+	0.482466i
$863$	20.7858	+	25.6683i	0.707557	+	0.873761i	0.996501	−	0.0835856i	$-0.0266372\pi$
$863$	20.7858	+	25.6683i	0.707557	+	0.873761i	−0.288943	+	0.957346i	$0.593304\pi$
$864$	2.26017	−	1.00629i	0.0768925	−	0.0342347i
$865$	23.9114	+	16.5439i	0.813012	+	0.562511i
$866$	−9.72804	−	8.75916i	−0.330572	−	0.297649i
$867$	4.97362	−	31.4022i	0.168913	−	1.06647i
$868$	14.9664	−	2.80979i	0.507994	−	0.0953705i
$869$	13.3830	+	17.1754i	0.453988	+	0.582635i
$870$	33.6738	+	0.986925i	1.14165	+	0.0334599i
$871$	8.83946	−	0.929065i	0.299514	−	0.0314802i
$872$	−7.12429	−	10.9704i	−0.241259	−	0.371506i
$873$	8.40110	+	5.45574i	0.284334	+	0.184649i
$874$	22.6965	+	16.4899i	0.767719	+	0.557781i
$875$	25.7209	−	14.6095i	0.869524	−	0.493890i
$876$	6.93843	−	21.3543i	0.234428	−	0.721495i
$877$	−5.69326	+	0.298371i	−0.192248	+	0.0100753i	−0.148217	−	0.988955i	$-0.547353\pi$
$877$	−5.69326	+	0.298371i	−0.192248	+	0.0100753i	−0.0440310	+	0.999030i	$0.514020\pi$
$878$	4.18077	−	5.16282i	0.141094	−	0.174237i
$879$	−16.7515	−	9.67150i	−0.565015	−	0.326212i
$880$	−2.32211	−	7.04328i	−0.0782781	−	0.237429i
$881$		−	32.1143i		−	1.08196i	−0.841036	−	0.540979i	$-0.818054\pi$
$881$		−	32.1143i		−	1.08196i	0.841036	−	0.540979i	$-0.181946\pi$
$882$	2.79588	+	12.8599i	0.0941423	+	0.433016i
$883$	−24.6249	−	12.5470i	−0.828693	−	0.422240i	−0.0124313	−	0.999923i	$-0.503957\pi$
$883$	−24.6249	−	12.5470i	−0.828693	−	0.422240i	−0.816261	+	0.577683i	$0.803957\pi$
$884$	0.819831	+	3.85700i	0.0275739	+	0.129725i
$885$	−2.03274	+	1.54972i	−0.0683298	+	0.0520934i
$886$	−29.9230	+	13.3226i	−1.00528	+	0.447580i
$887$	−26.9218	+	41.4559i	−0.903945	+	1.39195i	0.0159855	+	0.999872i	$0.494911\pi$
$887$	−26.9218	+	41.4559i	−0.903945	+	1.39195i	−0.919931	+	0.392081i	$0.871755\pi$
$888$	−4.09214	+	8.03127i	−0.137323	+	0.269512i
$889$	−26.1553	+	48.4396i	−0.877219	+	1.62461i
$890$	−22.6982	+	5.37451i	−0.760846	+	0.180154i
$891$	35.7504	−	8.86434i	1.19768	−	0.296966i
$892$	−1.73177	−	6.46305i	−0.0579839	−	0.216399i
$893$	−7.41218	−	6.00226i	−0.248039	−	0.200858i
$894$	14.6618	−	16.2836i	0.490364	−	0.544604i
$895$	5.18978	−	4.40456i	0.173475	−	0.147228i
$896$	−2.49194	+	0.888953i	−0.0832499	+	0.0296978i
$897$	−7.85165	−	49.5734i	−0.262159	−	1.65521i
$898$	3.74017	−	5.75936i	0.124811	−	0.192192i
$899$	−38.3951	−	8.16114i	−1.28055	−	0.272189i
$900$	7.91551	−	5.07045i	0.263850	−	0.169015i
$901$	−17.5432	+	10.1286i	−0.584450	+	0.337432i
$902$	5.25273	−	1.01396i	0.174897	−	0.0337611i
$903$	−25.6829	−	29.9300i	−0.854674	−	0.996007i
$904$	9.93483	+	13.6741i	0.330427	+	0.454794i
$905$	40.8700	−	11.9677i	1.35857	−	0.397819i
$906$	9.52711	−	8.57825i	0.316517	−	0.284993i
$907$	7.77608	+	2.98496i	0.258200	+	0.0991139i	0.484025	−	0.875054i	$-0.339174\pi$
$907$	7.77608	+	2.98496i	0.258200	+	0.0991139i	−0.225825	+	0.974168i	$0.572508\pi$
$908$	−0.638782	+	0.517276i	−0.0211987	+	0.0171664i
$909$	2.66787	−	8.21087i	0.0884878	−	0.272338i
$910$	12.8766	−	6.54798i	0.426855	−	0.217064i
$911$	−10.4296	+	7.57758i	−0.345549	+	0.251056i	−0.747000	−	0.664825i	$-0.768506\pi$
$911$	−10.4296	+	7.57758i	−0.345549	+	0.251056i	0.401450	+	0.915881i	$0.368506\pi$
$912$	−1.72386	+	6.43353i	−0.0570827	+	0.213036i
$913$	10.9541	+	3.78771i	0.362529	+	0.125355i
$914$	10.8757	+	6.27908i	0.359735	+	0.207693i
$915$	−6.12485	+	32.4808i	−0.202481	+	1.07378i
$916$	13.9734	−	4.54022i	0.461693	−	0.150013i
$917$	−31.1353	−	4.02559i	−1.02818	−	0.132937i
$918$	−3.94609	+	0.624999i	−0.130240	+	0.0206280i
$919$	−3.92141	−	0.412157i	−0.129355	−	0.0135958i	0.0396295	−	0.999214i	$-0.487382\pi$
$919$	−3.92141	−	0.412157i	−0.129355	−	0.0135958i	−0.168985	+	0.985619i	$0.554049\pi$
$920$	−3.72777	−	20.4695i	−0.122901	−	0.674859i
$921$	11.2388	+	2.38888i	0.370331	+	0.0787163i
$922$	−27.3410	+	10.4952i	−0.900427	+	0.345642i
$923$	−1.82680	−	1.82680i	−0.0601297	−	0.0601297i
$924$	−19.1155	+	3.21894i	−0.628854	+	0.105895i
$925$	6.42535	−	19.3632i	0.211264	−	0.636659i
$926$	29.5076	+	13.1376i	0.969681	+	0.431730i
$927$	−0.232415	+	0.150932i	−0.00763350	+	0.00495726i
$928$	6.81060	+	0.356928i	0.223569	+	0.0117168i
$929$	−0.575435	+	5.47490i	−0.0188794	+	0.179626i	−0.999898	−	0.0142885i	$-0.995452\pi$
$929$	−0.575435	+	5.47490i	−0.0188794	+	0.179626i	0.981018	+	0.193914i	$0.0621183\pi$
$930$	−26.3004	+	10.7980i	−0.862424	+	0.354079i
$931$	18.8492	+	9.49426i	0.617758	+	0.311162i
$932$	−12.7413	+	25.0062i	−0.417356	+	0.819106i
$933$	46.2236	−	17.7436i	1.51329	−	0.580898i
$934$	18.2510	−	31.6117i	0.597191	−	1.03436i
$935$	0.678316	+	11.9569i	0.0221833	+	0.391033i
$936$	3.97566	−	2.29535i	0.129949	−	0.0750259i
$937$	2.34189	−	14.7861i	0.0765064	−	0.483042i	−0.919450	−	0.393206i	$-0.871366\pi$
$937$	2.34189	−	14.7861i	0.0765064	−	0.483042i	0.995957	−	0.0898357i	$-0.0286342\pi$
$938$	0.229765	−	9.62781i	0.00750208	−	0.314359i
$939$	−12.0256	−	3.90736i	−0.392442	−	0.127512i
$940$	0.901392	+	7.01584i	0.0294002	+	0.228831i
$941$	−10.9428	−	24.5780i	−0.356726	−	0.801221i	−0.999385	−	0.0350679i	$-0.988835\pi$
$941$	−10.9428	−	24.5780i	−0.356726	−	0.801221i	0.642659	−	0.766153i	$-0.277831\pi$
$942$	−1.77650	+	33.8976i	−0.0578814	+	1.10444i
$943$	14.9880	−	0.785489i	0.488077	−	0.0255790i
$944$	−0.418638	+	0.304159i	−0.0136255	+	0.00989952i
$945$	5.94260	+	13.3761i	0.193313	+	0.435125i
$946$	17.6535	−	13.7556i	0.573964	−	0.447232i
$947$	−8.95511	+	33.4209i	−0.291002	+	1.08603i	0.653339	+	0.757066i	$0.273368\pi$
$947$	−8.95511	+	33.4209i	−0.291002	+	1.08603i	−0.944341	+	0.328969i	$0.893299\pi$
$948$	−9.12687	+	11.2707i	−0.296427	+	0.366057i
$949$	−5.16007	+	24.2762i	−0.167503	+	0.788039i
$950$	1.66932	−	14.9825i	0.0541597	−	0.486097i
$951$	−5.96606	+	8.21158i	−0.193463	+	0.266279i
$952$	4.25857	−	0.345099i	0.138021	−	0.0111847i
$953$	26.9099	+	52.8136i	0.871697	+	1.71080i	0.685213	+	0.728343i	$0.259709\pi$
$953$	26.9099	+	52.8136i	0.871697	+	1.71080i	0.186484	+	0.982458i	$0.440291\pi$
$954$	17.5261	+	15.7806i	0.567430	+	0.510916i
$955$	−15.2548	−	7.33466i	−0.493632	−	0.237344i
$956$	−3.36120	+	5.82177i	−0.108709	+	0.188290i
$957$	48.6724	+	11.3034i	1.57336	+	0.365388i
$958$	26.3290	+	26.3290i	0.850653	+	0.850653i
$959$	14.6517	+	23.7853i	0.473127	+	0.768067i
$960$	4.21979	−	2.56781i	0.136193	−	0.0828758i
$961$	2.08049	−	0.442221i	0.0671125	−	0.0142652i
$962$	3.57051	−	9.30149i	0.115118	−	0.299892i
$963$	1.51027	−	3.93439i	0.0486678	−	0.126784i
$964$	−20.9894	+	4.46143i	−0.676022	+	0.143693i
$965$	−36.1712	+	22.0108i	−1.16439	+	0.708554i
$966$	−54.3615	+	1.54971i	−1.74905	+	0.0498610i
$967$	−1.48498	−	1.48498i	−0.0477538	−	0.0477538i	0.682827	−	0.730580i	$-0.260750\pi$
$967$	−1.48498	−	1.48498i	−0.0477538	−	0.0477538i	−0.730580	+	0.682827i	$0.760750\pi$
$968$	−1.31223	−	10.9214i	−0.0421768	−	0.351029i
$969$	5.37789	−	9.31477i	0.172763	−	0.299234i
$970$	−10.7374	−	5.16267i	−0.344758	−	0.165763i
$971$	−35.2237	−	31.7156i	−1.13038	−	1.01780i	−0.999652	−	0.0263828i	$-0.991601\pi$
$971$	−35.2237	−	31.7156i	−1.13038	−	1.01780i	−0.130730	−	0.991418i	$-0.541732\pi$
$972$	7.76820	+	15.2459i	0.249165	+	0.489014i
$973$	−38.3693	+	26.5017i	−1.23006	+	0.849607i
$974$	2.36897	−	3.26061i	0.0759068	−	0.104477i
$975$	−21.0657	+	16.8421i	−0.674641	+	0.539378i
$976$	−1.39122	+	6.54518i	−0.0445319	+	0.209506i
$977$	−5.71311	+	7.05510i	−0.182779	+	0.225713i	−0.860297	−	0.509793i	$-0.829722\pi$
$977$	−5.71311	+	7.05510i	−0.182779	+	0.225713i	0.677519	+	0.735506i	$0.263055\pi$
$978$	−3.52431	+	13.1529i	−0.112695	+	0.420583i
$979$	−34.5783	+	1.16259i	−1.10513	+	0.0371566i
$980$	−5.24732	−	14.7467i	−0.167619	−	0.471067i
$981$	19.8957	−	14.4551i	0.635222	−	0.461516i
$982$	9.88826	−	0.518222i	0.315547	−	0.0165371i
$983$	−0.314113	+	5.99364i	−0.0100187	+	0.191168i	0.989035	+	0.147679i	$0.0471804\pi$
$983$	−0.314113	+	5.99364i	−0.0100187	+	0.191168i	−0.999054	+	0.0434881i	$0.986153\pi$
$984$	1.44930	+	3.25518i	0.0462020	+	0.103771i
$985$	1.50241	+	11.6938i	0.0478708	+	0.372595i
$986$	−10.4743	−	3.40329i	−0.333568	−	0.108383i
$987$	18.4836	+	0.441106i	0.588340	+	0.0140406i
$988$	1.15169	−	7.27149i	0.0366401	−	0.231337i
$989$	54.3750	−	31.3934i	1.72903	−	0.998253i
$990$	12.9951	−	5.05271i	0.413011	−	0.160586i
$991$	−23.9164	+	41.4244i	−0.759729	+	1.31589i	0.183260	+	0.983064i	$0.441335\pi$
$991$	−23.9164	+	41.4244i	−0.759729	+	1.31589i	−0.942989	+	0.332824i	$0.891998\pi$
$992$	−5.37332	+	2.06262i	−0.170603	+	0.0654884i
$993$	−32.0913	+	62.9827i	−1.01839	+	1.99870i
$994$	−2.21685	+	1.70923i	−0.0703142	+	0.0542136i
$995$	−19.4576	+	7.98858i	−0.616848	+	0.253255i
$996$	−0.806962	+	7.67773i	−0.0255696	+	0.243278i
$997$	51.5881	+	2.70362i	1.63381	+	0.0856244i	0.847008	−	0.531580i	$-0.178401\pi$
$997$	51.5881	+	2.70362i	1.63381	+	0.0856244i	0.786803	+	0.617204i	$0.211735\pi$
$998$	−4.09308	+	2.65808i	−0.129564	+	0.0841400i
$999$	9.22215	+	4.10597i	0.291776	+	0.129907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.157.5	yes	768
5.3	odd	4	inner	770.2.bv.a.3.20	✓	768
7.5	odd	6	inner	770.2.bv.a.47.5	yes	768
11.4	even	5	inner	770.2.bv.a.367.29	yes	768
35.33	even	12	inner	770.2.bv.a.663.29	yes	768
55.48	odd	20	inner	770.2.bv.a.213.5	yes	768
77.26	odd	30	inner	770.2.bv.a.257.20	yes	768
385.103	even	60	inner	770.2.bv.a.103.5	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.20	✓	768	5.3	odd	4	inner
770.2.bv.a.47.5	yes	768	7.5	odd	6	inner
770.2.bv.a.103.5	yes	768	385.103	even	60	inner
770.2.bv.a.157.5	yes	768	1.1	even	1	trivial
770.2.bv.a.213.5	yes	768	55.48	odd	20	inner
770.2.bv.a.257.20	yes	768	77.26	odd	30	inner
770.2.bv.a.367.29	yes	768	11.4	even	5	inner
770.2.bv.a.663.29	yes	768	35.33	even	12	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.358368 - 0.933580i) q^{2} +(-1.20315 - 1.85269i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.76974 + 1.36676i) q^{5} +(-1.29847 + 1.78719i) q^{6} +(-2.10275 - 1.60576i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-0.764685 + 1.71751i) q^{9} +O(q^{10})\)	\(q+(-0.358368 - 0.933580i) q^{2} +(-1.20315 - 1.85269i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.76974 + 1.36676i) q^{5} +(-1.29847 + 1.78719i) q^{6} +(-2.10275 - 1.60576i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-0.764685 + 1.71751i) q^{9} +(0.641764 - 2.14199i) q^{10} +(1.56086 - 2.92638i) q^{11} +(2.13381 + 0.571753i) q^{12} +(-2.41173 - 0.381981i) q^{13} +(-0.745547 + 2.53853i) q^{14} +(0.402924 - 4.92320i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-0.578715 + 1.50761i) q^{17} +(1.87747 + 0.0983942i) q^{18} +(2.01746 - 2.24061i) q^{19} +(-2.22971 + 0.168484i) q^{20} +(-0.445051 + 5.82772i) q^{21} +(-3.29138 - 0.408465i) q^{22} +(-8.98774 - 2.40826i) q^{23} +(-0.230912 - 2.19698i) q^{24} +(1.26393 + 4.83761i) q^{25} +(0.507678 + 2.38844i) q^{26} +(-2.44360 + 0.387029i) q^{27} +(2.63711 - 0.213701i) q^{28} +(-6.48616 - 2.10748i) q^{29} +(-4.74060 + 1.38816i) q^{30} +(5.72407 - 0.601624i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-7.29964 + 0.629096i) q^{33} +1.61486 q^{34} +(-1.52662 - 5.71572i) q^{35} +(-0.580967 - 1.78803i) q^{36} +(-3.42202 - 2.22229i) q^{37} +(-2.81479 - 1.08050i) q^{38} +(2.19399 + 4.92779i) q^{39} +(0.956350 + 2.02124i) q^{40} +(-1.53405 + 0.498443i) q^{41} +(5.60013 - 1.67298i) q^{42} +(-4.77141 + 4.77141i) q^{43} +(0.798189 + 3.21914i) q^{44} +(-3.70072 + 1.99440i) q^{45} +(0.972616 + 9.25382i) q^{46} +(-0.165558 - 3.15903i) q^{47} +(-1.96831 + 1.00290i) q^{48} +(1.84308 + 6.75300i) q^{49} +(4.06335 - 2.91363i) q^{50} +(3.48941 - 0.741698i) q^{51} +(2.04786 - 1.32990i) q^{52} +(9.74868 + 7.89433i) q^{53} +(1.23703 + 2.14260i) q^{54} +(6.76197 - 3.04561i) q^{55} +(-1.14456 - 2.38537i) q^{56} +(-6.57848 - 1.04193i) q^{57} +(0.356928 + 6.81060i) q^{58} +(-0.346252 - 0.384552i) q^{59} +(2.99483 + 3.92826i) q^{60} +(-6.65475 - 0.699442i) q^{61} +(-2.61299 - 5.12828i) q^{62} +(4.36585 - 2.38359i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-3.74606 - 3.97227i) q^{65} +(3.20327 + 6.58936i) q^{66} +(-3.51597 + 0.942102i) q^{67} +(-0.578715 - 1.50761i) q^{68} +(6.35186 + 19.5490i) q^{69} +(-4.78899 + 3.47355i) q^{70} +(0.855960 + 0.621891i) q^{71} +(-1.46107 + 1.18315i) q^{72} +(0.531945 - 10.1501i) q^{73} +(-0.848340 + 3.99113i) q^{74} +(7.44190 - 8.16207i) q^{75} +3.01504i q^{76} +(-7.98115 + 3.64708i) q^{77} +(3.81423 - 3.81423i) q^{78} +(-2.67025 + 5.99747i) q^{79} +(1.54426 - 1.61718i) q^{80} +(7.43107 + 8.25304i) q^{81} +(1.01509 + 1.25353i) q^{82} +(0.546687 + 3.45164i) q^{83} +(-3.56877 - 4.62863i) q^{84} +(-3.08471 + 1.87710i) q^{85} +(6.16442 + 2.74458i) q^{86} +(3.89932 + 14.5525i) q^{87} +(2.71929 - 1.89881i) q^{88} +(-5.21581 - 9.03406i) q^{89} +(3.18815 + 2.74019i) q^{90} +(4.45790 + 4.67587i) q^{91} +(8.29063 - 4.22429i) q^{92} +(-8.00156 - 9.88111i) q^{93} +(-2.88988 + 1.28666i) q^{94} +(6.63275 - 1.20791i) q^{95} +(1.64167 + 1.47817i) q^{96} +(0.833505 - 5.26254i) q^{97} +(5.64397 - 4.14073i) q^{98} +(3.83253 + 4.91855i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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