LMFDB - Embedded newform 690.2.x.a.77.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(77,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 11, 12]))

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

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

chi := DirichletCharacter("690.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.x (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$48$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			77.8
Character	$\chi$	$=$	690.77
Dual form			690.2.x.a.233.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599278 - 0.800541i) q^{2} +(-0.987144 + 1.42322i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(1.97219 - 1.05378i) q^{5} +(1.73092 - 0.0626522i) q^{6} +(-0.0325198 - 0.149491i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-1.05109 - 2.80984i) q^{9} +O(q^{10})$	\(q+(-0.599278 - 0.800541i) q^{2} +(-0.987144 + 1.42322i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(1.97219 - 1.05378i) q^{5} +(1.73092 - 0.0626522i) q^{6} +(-0.0325198 - 0.149491i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-1.05109 - 2.80984i) q^{9} +(-2.02549 - 0.947313i) q^{10} +(-2.19661 + 0.315826i) q^{11} +(-1.08746 - 1.34812i) q^{12} +(1.46706 - 6.74396i) q^{13} +(-0.100185 + 0.115620i) q^{14} +(-0.447077 + 3.84709i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-2.72096 + 4.98307i) q^{17} +(-1.61950 + 2.52532i) q^{18} +(0.719218 - 2.44943i) q^{19} +(0.455466 + 2.18919i) q^{20} +(0.244860 + 0.101286i) q^{21} +(1.56921 + 1.56921i) q^{22} +(-4.67652 - 1.06311i) q^{23} +(-0.427541 + 1.67845i) q^{24} +(2.77908 - 4.15652i) q^{25} +(-6.27800 + 2.86707i) q^{26} +(5.03659 + 1.27779i) q^{27} +(0.152597 + 0.0109140i) q^{28} +(5.61240 - 1.64795i) q^{29} +(3.34768 - 1.94757i) q^{30} +(1.80592 - 3.95441i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(1.71889 - 3.43802i) q^{33} +(5.61977 - 0.808001i) q^{34} +(-0.221666 - 0.260556i) q^{35} +(2.99215 - 0.216891i) q^{36} +(-0.352744 + 0.0252287i) q^{37} +(-2.39188 + 0.892126i) q^{38} +(8.14992 + 8.74521i) q^{39} +(1.47959 - 1.67655i) q^{40} +(4.36902 - 3.78578i) q^{41} +(-0.0656549 - 0.256719i) q^{42} +(-8.27324 - 3.08576i) q^{43} +(0.315826 - 2.19661i) q^{44} +(-5.03392 - 4.43392i) q^{45} +(1.95147 + 4.38084i) q^{46} +(-1.73045 + 1.73045i) q^{47} +(1.59989 - 0.663596i) q^{48} +(6.34613 - 2.89818i) q^{49} +(-4.99291 + 0.266141i) q^{50} +(-4.40601 - 8.79154i) q^{51} +(6.05747 + 3.30763i) q^{52} +(-2.37083 - 10.8985i) q^{53} +(-1.99540 - 4.79775i) q^{54} +(-3.99933 + 2.93762i) q^{55} +(-0.0827111 - 0.128701i) q^{56} +(2.77610 + 3.44155i) q^{57} +(-4.68264 - 3.50538i) q^{58} +(-0.433919 + 0.278863i) q^{59} +(-3.56530 - 1.51282i) q^{60} +(1.54868 - 3.39114i) q^{61} +(-4.24791 + 0.924077i) q^{62} +(-0.385864 + 0.248504i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-4.21335 - 14.8464i) q^{65} +(-3.78237 + 0.684290i) q^{66} +(2.39255 - 1.79104i) q^{67} +(-4.01464 - 4.01464i) q^{68} +(6.12943 - 5.60626i) q^{69} +(-0.0757463 + 0.333598i) q^{70} +(14.1398 + 2.03300i) q^{71} +(-1.96676 - 2.26536i) q^{72} +(-1.61895 + 0.884013i) q^{73} +(0.231588 + 0.267267i) q^{74} +(3.17228 + 8.05833i) q^{75} +(2.14758 + 1.38017i) q^{76} +(0.118646 + 0.318103i) q^{77} +(2.11683 - 11.7652i) q^{78} +(-1.01028 - 1.57202i) q^{79} +(-2.22883 - 0.179749i) q^{80} +(-6.79041 + 5.90680i) q^{81} +(-5.64893 - 1.22885i) q^{82} +(-0.892063 + 0.0638016i) q^{83} +(-0.166169 + 0.206405i) q^{84} +(-0.115187 + 12.6949i) q^{85} +(2.48769 + 8.47230i) q^{86} +(-3.19486 + 9.61443i) q^{87} +(-1.94775 + 1.06355i) q^{88} +(-2.25617 - 4.94033i) q^{89} +(-0.532825 + 6.68701i) q^{90} -1.05587 q^{91} +(2.33757 - 4.18757i) q^{92} +(3.84528 + 6.47378i) q^{93} +(2.42232 + 0.348276i) q^{94} +(-1.16273 - 5.58865i) q^{95} +(-1.49001 - 0.883098i) q^{96} +(0.709377 - 9.91838i) q^{97} +(-6.12321 - 3.34353i) q^{98} +(3.19626 + 5.84018i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) $ 960 * q + 8 * q^3 + 8 * q^6	$ 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) $ 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$3$	−0.987144	+	1.42322i	−0.569928	+	0.821695i
$3$	−0.987144	+	1.42322i	−0.569928	+	0.821695i
$4$	−0.281733	+	0.959493i	−0.140866	+	0.479746i
$5$	1.97219	−	1.05378i	0.881991	−	0.471266i
$5$	1.97219	−	1.05378i	0.881991	−	0.471266i
$6$	1.73092	−	0.0626522i	0.706644	−	0.0255776i
$7$	−0.0325198	−	0.149491i	−0.0122913	−	0.0565023i	0.970593	−	0.240728i	$-0.0773860\pi$
$7$	−0.0325198	−	0.149491i	−0.0122913	−	0.0565023i	−0.982884	+	0.184225i	$0.941022\pi$
$8$	0.936950	−	0.349464i	0.331262	−	0.123554i
$9$	−1.05109	−	2.80984i	−0.350364	−	0.936614i
$10$	−2.02549	−	0.947313i	−0.640515	−	0.299567i
$11$	−2.19661	+	0.315826i	−0.662304	+	0.0952250i	−0.465266	−	0.885171i	$-0.654041\pi$
$11$	−2.19661	+	0.315826i	−0.662304	+	0.0952250i	−0.197038	+	0.980396i	$0.563132\pi$
$12$	−1.08746	−	1.34812i	−0.313921	−	0.389170i
$13$	1.46706	−	6.74396i	0.406889	−	1.87044i	−0.0797172	−	0.996818i	$-0.525402\pi$
$13$	1.46706	−	6.74396i	0.406889	−	1.87044i	0.486606	−	0.873621i	$-0.338235\pi$
$14$	−0.100185	+	0.115620i	−0.0267756	+	0.0309007i
$15$	−0.447077	+	3.84709i	−0.115435	+	0.993315i
$16$	−0.841254	−	0.540641i	−0.210313	−	0.135160i
$17$	−2.72096	+	4.98307i	−0.659931	+	1.20857i	0.306555	+	0.951853i	$0.400824\pi$
$17$	−2.72096	+	4.98307i	−0.659931	+	1.20857i	−0.966486	+	0.256720i	$0.917358\pi$
$18$	−1.61950	+	2.52532i	−0.381719	+	0.595223i
$19$	0.719218	−	2.44943i	0.165000	−	0.561938i	−0.834933	−	0.550352i	$-0.814494\pi$
$19$	0.719218	−	2.44943i	0.165000	−	0.561938i	0.999933	−	0.0115864i	$-0.00368815\pi$
$20$	0.455466	+	2.18919i	0.101845	+	0.489518i
$21$	0.244860	+	0.101286i	0.0534328	+	0.0221025i
$22$	1.56921	+	1.56921i	0.334557	+	0.334557i
$23$	−4.67652	−	1.06311i	−0.975121	−	0.221673i
$23$	−4.67652	−	1.06311i	−0.975121	−	0.221673i
$24$	−0.427541	+	1.67845i	−0.0872715	+	0.342613i
$25$	2.77908	−	4.15652i	0.555817	−	0.831305i
$26$	−6.27800	+	2.86707i	−1.23122	+	0.562278i
$27$	5.03659	+	1.27779i	0.969293	+	0.245910i
$28$	0.152597	+	0.0109140i	0.0288382	+	0.00206255i
$29$	5.61240	−	1.64795i	1.04220	−	0.306017i	0.284537	−	0.958665i	$-0.408160\pi$
$29$	5.61240	−	1.64795i	1.04220	−	0.306017i	0.757661	+	0.652648i	$0.226342\pi$
$30$	3.34768	−	1.94757i	0.611200	−	0.355577i
$31$	1.80592	−	3.95441i	0.324352	−	0.710232i	−0.675274	−	0.737567i	$-0.735975\pi$
$31$	1.80592	−	3.95441i	0.324352	−	0.710232i	0.999626	+	0.0273345i	$0.00870192\pi$
$32$	0.0713392	+	0.997452i	0.0126111	+	0.176326i
$33$	1.71889	−	3.43802i	0.299220	−	0.598483i
$34$	5.61977	−	0.808001i	0.963783	−	0.138571i
$35$	−0.221666	−	0.260556i	−0.0374684	−	0.0440420i
$36$	2.99215	−	0.216891i	0.498692	−	0.0361486i
$37$	−0.352744	+	0.0252287i	−0.0579907	+	0.00414758i	−0.100304	−	0.994957i	$-0.531982\pi$
$37$	−0.352744	+	0.0252287i	−0.0579907	+	0.00414758i	0.0423137	+	0.999104i	$0.486527\pi$
$38$	−2.39188	+	0.892126i	−0.388014	+	0.144722i
$39$	8.14992	+	8.74521i	1.30503	+	1.40035i
$40$	1.47959	−	1.67655i	0.233943	−	0.265086i
$41$	4.36902	−	3.78578i	0.682327	−	0.591240i	−0.243175	−	0.969982i	$-0.578189\pi$
$41$	4.36902	−	3.78578i	0.682327	−	0.591240i	0.925502	+	0.378743i	$0.123643\pi$
$42$	−0.0656549	−	0.256719i	−0.0101308	−	0.0396126i
$43$	−8.27324	−	3.08576i	−1.26166	−	0.470574i	−0.372439	−	0.928057i	$-0.621478\pi$
$43$	−8.27324	−	3.08576i	−1.26166	−	0.470574i	−0.889218	+	0.457483i	$0.848751\pi$
$44$	0.315826	−	2.19661i	0.0476125	−	0.331152i
$45$	−5.03392	−	4.43392i	−0.750412	−	0.660970i
$46$	1.95147	+	4.38084i	0.287729	+	0.645920i
$47$	−1.73045	+	1.73045i	−0.252412	+	0.252412i	−0.821959	−	0.569547i	$-0.807119\pi$
$47$	−1.73045	+	1.73045i	−0.252412	+	0.252412i	0.569547	+	0.821959i	$0.307119\pi$
$48$	1.59989	−	0.663596i	0.230924	−	0.0957818i
$49$	6.34613	−	2.89818i	0.906591	−	0.414026i
$50$	−4.99291	+	0.266141i	−0.706104	+	0.0376380i
$51$	−4.40601	−	8.79154i	−0.616965	−	1.23106i
$52$	6.05747	+	3.30763i	0.840020	+	0.458685i
$53$	−2.37083	−	10.8985i	−0.325659	−	1.49703i	−0.790955	−	0.611875i	$-0.790416\pi$
$53$	−2.37083	−	10.8985i	−0.325659	−	1.49703i	0.465296	−	0.885155i	$-0.345948\pi$
$54$	−1.99540	−	4.79775i	−0.271539	−	0.652891i
$55$	−3.99933	+	2.93762i	−0.539270	+	0.396109i
$56$	−0.0827111	−	0.128701i	−0.0110527	−	0.0171984i
$57$	2.77610	+	3.44155i	0.367703	+	0.455844i
$58$	−4.68264	−	3.50538i	−0.614861	−	0.460279i
$59$	−0.433919	+	0.278863i	−0.0564915	+	0.0363049i	−0.568582	−	0.822627i	$-0.692508\pi$
$59$	−0.433919	+	0.278863i	−0.0564915	+	0.0363049i	0.512090	+	0.858932i	$0.328871\pi$
$60$	−3.56530	−	1.51282i	−0.460279	−	0.195304i
$61$	1.54868	−	3.39114i	0.198288	−	0.434191i	−0.784202	−	0.620506i	$-0.786927\pi$
$61$	1.54868	−	3.39114i	0.198288	−	0.434191i	0.982490	+	0.186315i	$0.0596545\pi$
$62$	−4.24791	+	0.924077i	−0.539485	+	0.117358i
$63$	−0.385864	+	0.248504i	−0.0486143	+	0.0313086i
$64$	0.755750	−	0.654861i	0.0944687	−	0.0818576i
$65$	−4.21335	−	14.8464i	−0.522602	−	1.84146i
$66$	−3.78237	+	0.684290i	−0.465578	+	0.0842303i
$67$	2.39255	−	1.79104i	0.292296	−	0.218810i	−0.443058	−	0.896493i	$-0.646106\pi$
$67$	2.39255	−	1.79104i	0.292296	−	0.218810i	0.735355	+	0.677682i	$0.237016\pi$
$68$	−4.01464	−	4.01464i	−0.486847	−	0.486847i
$69$	6.12943	−	5.60626i	0.737896	−	0.674914i
$70$	−0.0757463	+	0.333598i	−0.00905341	+	0.0398726i
$71$	14.1398	+	2.03300i	1.67809	+	0.241273i	0.914545	−	0.404483i	$-0.132549\pi$
$71$	14.1398	+	2.03300i	1.67809	+	0.241273i	0.763544	+	0.645756i	$0.223458\pi$
$72$	−1.96676	−	2.26536i	−0.231785	−	0.266975i
$73$	−1.61895	+	0.884013i	−0.189484	+	0.103466i	−0.571190	−	0.820818i	$-0.693518\pi$
$73$	−1.61895	+	0.884013i	−0.189484	+	0.103466i	0.381707	+	0.924283i	$0.375336\pi$
$74$	0.231588	+	0.267267i	0.0269216	+	0.0310691i
$75$	3.17228	+	8.05833i	0.366303	+	0.930496i
$76$	2.14758	+	1.38017i	0.246345	+	0.158316i
$77$	0.118646	+	0.318103i	0.0135210	+	0.0362512i
$78$	2.11683	−	11.7652i	0.239684	−	1.33214i
$79$	−1.01028	−	1.57202i	−0.113665	−	0.176867i	0.779760	−	0.626079i	$-0.215341\pi$
$79$	−1.01028	−	1.57202i	−0.113665	−	0.176867i	−0.893425	+	0.449212i	$0.851705\pi$
$80$	−2.22883	−	0.179749i	−0.249191	−	0.0200966i
$81$	−6.79041	+	5.90680i	−0.754490	+	0.656311i
$82$	−5.64893	−	1.22885i	−0.623820	−	0.135704i
$83$	−0.892063	+	0.0638016i	−0.0979166	+	0.00700314i	−0.120212	−	0.992748i	$-0.538357\pi$
$83$	−0.892063	+	0.0638016i	−0.0979166	+	0.00700314i	0.0222949	+	0.999751i	$0.492903\pi$
$84$	−0.166169	+	0.206405i	−0.0181305	+	0.0225207i
$85$	−0.115187	+	12.6949i	−0.0124938	+	1.37695i
$86$	2.48769	+	8.47230i	0.268255	+	0.913591i
$87$	−3.19486	+	9.61443i	−0.342525	+	1.03078i
$88$	−1.94775	+	1.06355i	−0.207631	+	0.113375i
$89$	−2.25617	−	4.94033i	−0.239154	−	0.523674i	0.751555	−	0.659670i	$-0.229304\pi$
$89$	−2.25617	−	4.94033i	−0.239154	−	0.523674i	−0.990709	+	0.135996i	$0.956577\pi$
$90$	−0.532825	+	6.68701i	−0.0561647	+	0.704873i
$91$	−1.05587			−0.110685
$92$	2.33757	−	4.18757i	0.243708	−	0.436585i
$93$	3.84528	+	6.47378i	0.398737	+	0.671300i
$94$	2.42232	+	0.348276i	0.249843	+	0.0359220i
$95$	−1.16273	−	5.58865i	−0.119294	−	0.573383i
$96$	−1.49001	−	0.883098i	−0.152074	−	0.0901308i
$97$	0.709377	−	9.91838i	0.0720263	−	1.00706i	−0.825015	−	0.565111i	$-0.808833\pi$
$97$	0.709377	−	9.91838i	0.0720263	−	1.00706i	0.897041	−	0.441948i	$-0.145712\pi$
$98$	−6.12321	−	3.34353i	−0.618538	−	0.337747i
$99$	3.19626	+	5.84018i	0.321236	+	0.586960i
$100$	3.20520	+	3.83754i	0.320520	+	0.383754i
$101$	−2.95043	−	2.55656i	−0.293579	−	0.254387i	0.495600	−	0.868551i	$-0.334948\pi$
$101$	−2.95043	−	2.55656i	−0.293579	−	0.254387i	−0.789179	+	0.614163i	$0.789494\pi$
$102$	−4.39756	+	8.79576i	−0.435424	+	0.870910i
$103$	10.4587	+	7.82932i	1.03053	+	0.771446i	0.973906	−	0.226950i	$-0.0728754\pi$
$103$	10.4587	+	7.82932i	1.03053	+	0.771446i	0.0566242	+	0.998396i	$0.481966\pi$
$104$	−0.982213	−	6.83144i	−0.0963139	−	0.669878i
$105$	0.589644	−	0.0582725i	0.0575434	−	0.00568682i
$106$	−7.30395	+	8.42920i	−0.709422	+	0.818716i
$107$	−0.399527	−	1.07117i	−0.0386237	−	0.103554i	0.916206	−	0.400707i	$-0.131236\pi$
$107$	−0.399527	−	1.07117i	−0.0386237	−	0.103554i	−0.954830	+	0.297153i	$0.903963\pi$
$108$	−2.64500	+	4.47258i	−0.254515	+	0.430374i
$109$	5.29245	+	18.0244i	0.506924	+	1.72643i	0.672378	+	0.740208i	$0.265273\pi$
$109$	5.29245	+	18.0244i	0.506924	+	1.72643i	−0.165453	+	0.986218i	$0.552909\pi$
$110$	4.74840	+	1.44118i	0.452742	+	0.137411i
$111$	0.312303	−	0.526935i	0.0296425	−	0.0500145i
$112$	−0.0534635	+	0.143341i	−0.00505183	+	0.0135445i
$113$	−8.43230	+	6.31234i	−0.793244	+	0.593815i	−0.917179	−	0.398475i	$-0.869539\pi$
$113$	−8.43230	+	6.31234i	−0.793244	+	0.593815i	0.123935	+	0.992290i	$0.460449\pi$
$114$	1.09144	−	4.28482i	0.102223	−	0.401310i
$115$	−10.3433	+	2.83138i	−0.964515	+	0.264028i
$116$			5.84934i			0.543098i
$117$	−20.4915	+	2.96632i	−1.89444	+	0.274236i
$118$	0.483279	+	0.180254i	0.0444895	+	0.0165937i
$119$	0.833409	+	0.244711i	0.0763985	+	0.0224326i
$120$	0.925532	+	3.76077i	0.0844891	+	0.343310i
$121$	−5.82905	+	1.71156i	−0.529914	+	0.155597i
$122$	−3.64284	+	0.792451i	−0.329807	+	0.0717451i
$123$	1.07513	+	9.95518i	0.0969411	+	0.897629i
$124$	3.28544	+	2.84685i	0.295041	+	0.255655i
$125$	1.10081	−	11.1260i	0.0984597	−	0.995141i
$126$	0.430178	+	0.159977i	0.0383233	+	0.0142519i
$127$	−4.18614	+	5.59202i	−0.371460	+	0.496212i	−0.946854	−	0.321664i	$-0.895758\pi$
$127$	−4.18614	+	5.59202i	−0.371460	+	0.496212i	0.575394	+	0.817876i	$0.304849\pi$
$128$	−0.977147	−	0.212565i	−0.0863684	−	0.0187883i
$129$	12.5586	−	8.72853i	1.10572	−	0.768504i
$130$	−9.36015	+	12.2700i	−0.820940	+	1.07615i
$131$	−0.564958	+	0.879091i	−0.0493606	+	0.0768066i	−0.865057	−	0.501674i	$-0.832718\pi$
$131$	−0.564958	+	0.879091i	−0.0493606	+	0.0768066i	0.815696	+	0.578480i	$0.196354\pi$
$132$	2.81449	+	2.61786i	0.244970	+	0.227856i
$133$	−0.389556	−	0.0278616i	−0.0337788	−	0.00241591i
$134$	−2.86760	−	0.842004i	−0.247723	−	0.0727381i
$135$	11.2796	−	2.78743i	0.970797	−	0.239904i
$136$	−0.808001	+	5.61977i	−0.0692855	+	0.481891i
$137$	−12.3521	+	12.3521i	−1.05531	+	1.05531i	−0.0569286	+	0.998378i	$0.518131\pi$
$137$	−12.3521	+	12.3521i	−1.05531	+	1.05531i	−0.998378	+	0.0569286i	$0.981869\pi$
$138$	−8.16127	−	1.54715i	−0.694733	−	0.131703i
$139$		−	4.02104i		−	0.341061i	−0.985352	−	0.170530i	$-0.945452\pi$
$139$		−	4.02104i		−	0.341061i	0.985352	−	0.170530i	$-0.0545481\pi$
$140$	0.312452	−	0.139280i	0.0264070	−	0.0117713i
$141$	−0.754601	−	4.17101i	−0.0635489	−	0.351262i
$142$	−6.84618	−	12.5378i	−0.574519	−	1.05215i
$143$	−1.09265	+	15.2772i	−0.0913719	+	1.27755i
$144$	−0.634880	+	2.93205i	−0.0529067	+	0.244338i
$145$	9.33216	−	9.16433i	0.774994	−	0.761056i
$146$	1.67789	+	0.766266i	0.138863	+	0.0634167i
$147$	−2.13981	+	11.8928i	−0.176489	+	0.980906i
$148$	0.0751726	−	0.345563i	0.00617915	−	0.0284051i
$149$	1.27290	+	8.85321i	0.104280	+	0.725283i	0.973138	+	0.230222i	$0.0739453\pi$
$149$	1.27290	+	8.85321i	0.104280	+	0.725283i	−0.868858	+	0.495061i	$0.835146\pi$
$150$	4.54995	−	7.36872i	0.371502	−	0.601653i
$151$	15.6069	−	10.0299i	1.27007	−	0.816223i	0.280439	−	0.959872i	$-0.409520\pi$
$151$	15.6069	−	10.0299i	1.27007	−	0.816223i	0.989629	+	0.143648i	$0.0458834\pi$
$152$	−0.182117	−	2.54633i	−0.0147717	−	0.206535i
$153$	16.8616	+	2.40781i	1.36318	+	0.194660i
$154$	0.183553	−	0.285614i	0.0147911	−	0.0230154i
$155$	−0.605470	−	9.70189i	−0.0486326	−	0.779275i
$156$	−10.6871	+	5.35598i	−0.855650	+	0.428822i
$157$	8.30785	+	15.2147i	0.663039	+	1.21426i	0.965326	+	0.261048i	$0.0840680\pi$
$157$	8.30785	+	15.2147i	0.663039	+	1.21426i	−0.302287	+	0.953217i	$0.597750\pi$
$158$	−0.653033	+	1.75085i	−0.0519525	+	0.139290i
$159$	17.8513	+	7.38423i	1.41570	+	0.585607i
$160$	1.19179	+	1.89199i	0.0942195	+	0.149575i
$161$	−0.00684549	+	0.733669i	−0.000539500	+	0.0578212i
$162$	8.79798	+	1.89619i	0.691235	+	0.148979i
$163$	5.11830	+	6.83724i	0.400896	+	0.535534i	0.954880	−	0.296993i	$-0.0959839\pi$
$163$	5.11830	+	6.83724i	0.400896	+	0.535534i	−0.553984	+	0.832528i	$0.686893\pi$
$164$	2.40153	+	5.25863i	0.187528	+	0.410630i
$165$	−0.232954	−	8.59178i	−0.0181354	−	0.668869i
$166$	0.585669	+	0.675898i	0.0454567	+	0.0524599i
$167$	0.758174	−	1.38849i	0.0586693	−	0.107445i	−0.846699	−	0.532073i	$-0.821413\pi$
$167$	0.758174	−	1.38849i	0.0586693	−	0.107445i	0.905368	+	0.424628i	$0.139595\pi$
$168$	0.264817	+	0.00933064i	0.0204311	+	0.000719874i
$169$	−31.5036	−	14.3872i	−2.42335	−	1.10671i
$170$	10.2318	−	7.51555i	0.784744	−	0.576416i
$171$	−7.63848	+	0.553689i	−0.584129	+	0.0423416i
$172$	5.29161	−	7.06876i	0.403481	−	0.538988i
$173$	9.73461	−	13.0039i	0.740109	−	0.988669i	−0.259628	−	0.965709i	$-0.583600\pi$
$173$	9.73461	−	13.0039i	0.740109	−	0.988669i	0.999736	−	0.0229606i	$-0.00730923\pi$
$174$	9.61136	−	3.20410i	0.728635	−	0.242902i
$175$	−0.711738	−	0.280279i	−0.0538023	−	0.0211871i
$176$	2.01866	+	0.921890i	0.152162	+	0.0694901i
$177$	0.0314585	−	0.892839i	0.00236457	−	0.0671099i
$178$	−2.60286	+	4.76679i	−0.195093	+	0.357286i
$179$	5.12676	+	5.91660i	0.383192	+	0.442228i	0.914276	−	0.405092i	$-0.132760\pi$
$179$	5.12676	+	5.91660i	0.383192	+	0.442228i	−0.531084	+	0.847319i	$0.678215\pi$
$180$	5.67254	−	3.58083i	0.422806	−	0.266899i
$181$	2.77302	+	6.07207i	0.206117	+	0.451333i	0.984254	−	0.176762i	$-0.0565622\pi$
$181$	2.77302	+	6.07207i	0.206117	+	0.451333i	−0.778137	+	0.628095i	$0.783835\pi$
$182$	0.632759	+	0.845267i	0.0469032	+	0.0626554i
$183$	3.29756	+	5.55166i	0.243762	+	0.410390i
$184$	−4.75318	+	0.638198i	−0.350409	+	0.0470486i
$185$	−0.669093	+	0.421471i	−0.0491927	+	0.0309872i
$186$	2.87814	−	6.95790i	0.211036	−	0.510178i
$187$	4.40313	−	11.8052i	0.321989	−	0.863285i
$188$	−1.17283	−	2.14788i	−0.0855374	−	0.156650i
$189$	0.0272289	−	0.794478i	0.00198061	−	0.0577898i
$190$	−3.77714	+	4.27997i	−0.274023	+	0.310501i
$191$	−13.6867	+	21.2970i	−0.990338	+	1.54100i	−0.157469	+	0.987524i	$0.550334\pi$
$191$	−13.6867	+	21.2970i	−0.990338	+	1.54100i	−0.832868	+	0.553471i	$0.813303\pi$
$192$	0.185975	+	1.72204i	0.0134216	+	0.124277i
$193$	1.42575	+	19.9346i	0.102628	+	1.43492i	0.744249	+	0.667902i	$0.232807\pi$
$193$	1.42575	+	19.9346i	0.102628	+	1.43492i	−0.641622	+	0.767021i	$0.721738\pi$
$194$	−8.36519	+	5.37598i	−0.600585	+	0.385973i
$195$	25.2888	+	8.65899i	1.81097	+	0.620083i
$196$	0.992873	+	6.90558i	0.0709195	+	0.493256i
$197$	1.48416	−	6.82257i	0.105742	−	0.486088i	−0.893567	−	0.448929i	$-0.851806\pi$
$197$	1.48416	−	6.82257i	0.105742	−	0.486088i	0.999309	−	0.0371590i	$-0.0118308\pi$
$198$	2.75985	−	6.05863i	0.196134	−	0.430568i
$199$	−22.2816	−	10.1757i	−1.57950	−	0.721333i	−0.583620	−	0.812027i	$-0.698364\pi$
$199$	−22.2816	−	10.1757i	−1.57950	−	0.721333i	−0.995879	+	0.0906944i	$0.971091\pi$
$200$	1.15131	−	4.86564i	0.0814096	−	0.344053i
$201$	0.187246	+	5.17313i	0.0132073	+	0.364885i
$202$	−0.278506	+	3.89403i	−0.0195956	+	0.273983i
$203$	−0.428868	−	0.785413i	−0.0301006	−	0.0551252i
$204$	9.67673	−	1.75067i	0.677507	−	0.122572i
$205$	4.62716	−	12.0703i	0.323175	−	0.843026i
$206$		−	13.0646i		−	0.910253i
$207$	1.92829	+	14.2577i	0.134025	+	0.990978i
$208$	−4.88023	+	4.88023i	−0.338383	+	0.338383i
$209$	−0.806252	+	5.60760i	−0.0557696	+	0.387886i
$210$	−0.400010	−	0.437113i	−0.0276033	−	0.0301637i
$211$	−18.3039	−	5.37452i	−1.26010	−	0.369997i	−0.417565	−	0.908647i	$-0.637117\pi$
$211$	−18.3039	−	5.37452i	−1.26010	−	0.369997i	−0.842530	+	0.538649i	$0.818935\pi$
$212$	11.1250	+	0.795677i	0.764069	+	0.0546473i
$213$	−16.8515	+	18.1172i	−1.15464	+	1.24137i
$214$	−0.618091	+	0.961768i	−0.0422518	+	0.0657451i
$215$	−19.5681	+	2.63249i	−1.33454	+	0.179534i
$216$	5.16557	−	0.562886i	0.351473	−	0.0382995i
$217$	−0.649876	−	0.141372i	−0.0441164	−	0.00959695i
$218$	11.2576	−	15.0385i	0.762464	−	1.01853i
$219$	0.339994	−	3.17676i	0.0229747	−	0.214666i
$220$	−1.69189	−	4.66496i	−0.114067	−	0.314511i
$221$	29.6139	+	25.6606i	1.99204	+	1.72612i
$222$	−0.608990	+	0.0657690i	−0.0408727	+	0.00441413i
$223$	−3.04469	+	0.662333i	−0.203888	+	0.0443531i	−0.313349	−	0.949638i	$-0.601451\pi$
$223$	−3.04469	+	0.662333i	−0.203888	+	0.0443531i	0.109461	+	0.993991i	$0.465087\pi$
$224$	0.146790	−	0.0431015i	0.00980783	−	0.00287984i
$225$	−14.6002	−	3.43989i	−0.973350	−	0.229326i
$226$	10.1066	+	2.96756i	0.672280	+	0.197399i
$227$	9.26014	+	3.45386i	0.614617	+	0.229240i	0.637441	−	0.770499i	$-0.279993\pi$
$227$	9.26014	+	3.45386i	0.614617	+	0.229240i	−0.0228237	+	0.999740i	$0.507266\pi$
$228$	−4.08426	+	1.69405i	−0.270486	+	0.112191i
$229$		−	10.5155i		−	0.694886i	−0.937701	−	0.347443i	$-0.887050\pi$
$229$		−	10.5155i		−	0.694886i	0.937701	−	0.347443i	$-0.112950\pi$
$230$	8.46513	+	6.58343i	0.558174	+	0.434099i
$231$	−0.569851	−	0.145154i	−0.0374935	−	0.00955046i
$232$	4.68264	−	3.50538i	0.307430	−	0.230140i
$233$	8.30940	−	22.2784i	0.544367	−	1.45950i	−0.315471	−	0.948935i	$-0.602162\pi$
$233$	8.30940	−	22.2784i	0.544367	−	1.45950i	0.859837	−	0.510568i	$-0.170565\pi$
$234$	14.6547	+	14.6266i	0.958011	+	0.956172i
$235$	−1.58926	+	5.23630i	−0.103672	+	0.341578i
$236$	−0.145318	−	0.494907i	−0.00945939	−	0.0322157i
$237$	3.23462	+	0.113970i	0.210111	+	0.00740312i
$238$	−0.303542	−	0.813828i	−0.0196757	−	0.0527527i
$239$	15.9623	−	18.4215i	1.03252	−	1.19159i	0.0513007	−	0.998683i	$-0.483663\pi$
$239$	15.9623	−	18.4215i	1.03252	−	1.19159i	0.981217	−	0.192906i	$-0.0617912\pi$
$240$	2.45600	−	2.99467i	0.158534	−	0.193305i
$241$	−0.634890	−	4.41576i	−0.0408969	−	0.284444i	−0.999999	−	0.00138384i	$-0.999560\pi$
$241$	−0.634890	−	4.41576i	−0.0408969	−	0.284444i	0.959102	−	0.283060i	$-0.0913496\pi$
$242$	4.86340	+	3.64069i	0.312631	+	0.234033i
$243$	−1.70354	−	15.4951i	−0.109282	−	0.994011i
$244$	2.81746	+	2.44134i	0.180369	+	0.156291i
$245$	9.46174	−	12.4032i	0.604488	−	0.792413i
$246$	7.32523	−	6.82660i	0.467040	−	0.435248i
$247$	−15.4637	−	8.44384i	−0.983934	−	0.537269i
$248$	0.310130	−	4.33618i	0.0196933	−	0.275348i
$249$	0.789791	−	1.33258i	0.0500510	−	0.0844488i
$250$	−9.56653	+	5.78633i	−0.605040	+	0.365959i
$251$	−9.87211	−	1.41940i	−0.623122	−	0.0895915i	−0.176480	−	0.984304i	$-0.556471\pi$
$251$	−9.87211	−	1.41940i	−0.623122	−	0.0895915i	−0.446642	+	0.894713i	$0.647380\pi$
$252$	−0.129727	−	0.440246i	−0.00817205	−	0.0277329i
$253$	10.6083	+	0.858271i	0.666936	+	0.0539590i
$254$	6.98530			0.438297
$255$	−17.9539	−	12.6956i	−1.12431	−	0.795031i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−17.6736	+	9.65051i	−1.10245	+	0.601983i	−0.924164	−	0.381996i	$-0.875237\pi$
$257$	−17.6736	+	9.65051i	−1.10245	+	0.601983i	−0.178285	+	0.983979i	$0.557055\pi$
$258$	−14.5136	−	4.82286i	−0.903579	−	0.300258i
$259$	0.0152426	+	0.0519116i	0.000947129	+	0.00322563i
$260$	15.4320	+	0.140022i	0.957053	+	0.00868379i
$261$	−10.5296	−	14.0378i	−0.651768	−	0.868919i
$262$	1.04232	−	0.0745479i	0.0643945	−	0.00460558i
$263$	−28.7546	−	6.25518i	−1.77308	−	0.385711i	−0.797151	−	0.603780i	$-0.793661\pi$
$263$	−28.7546	−	6.25518i	−1.77308	−	0.385711i	−0.975933	+	0.218069i	$0.930024\pi$
$264$	0.409045	−	3.82195i	0.0251750	−	0.235224i
$265$	−16.1604	−	18.9957i	−0.992728	−	1.16690i
$266$	0.211148	+	0.328553i	0.0129463	+	0.0201449i
$267$	9.25833	+	1.66580i	0.566601	+	0.101945i
$268$	1.04443	+	2.80023i	0.0637988	+	0.171051i
$269$	14.7217	+	9.46106i	0.897598	+	0.576851i	0.906077	−	0.423113i	$-0.139063\pi$
$269$	14.7217	+	9.46106i	0.897598	+	0.576851i	−0.00847916	+	0.999964i	$0.502699\pi$
$270$	−8.99109	−	7.35937i	−0.547180	−	0.447877i
$271$	18.9396	+	21.8575i	1.15050	+	1.32775i	0.936400	+	0.350936i	$0.114136\pi$
$271$	18.9396	+	21.8575i	1.15050	+	1.32775i	0.214100	+	0.976812i	$0.431318\pi$
$272$	4.98307	−	2.72096i	0.302143	−	0.164983i
$273$	1.04230	−	1.50273i	0.0630826	−	0.0909494i
$274$	17.2906	+	2.48602i	1.04457	+	0.150186i
$275$	−4.79184	+	10.0080i	−0.288959	+	0.603504i
$276$	3.65231	+	7.46061i	0.219843	+	0.449076i
$277$	−1.76871	−	1.76871i	−0.106271	−	0.106271i	0.651972	−	0.758243i	$-0.273942\pi$
$277$	−1.76871	−	1.76871i	−0.106271	−	0.106271i	−0.758243	+	0.651972i	$0.773942\pi$
$278$	−3.21901	+	2.40972i	−0.193064	+	0.144526i
$279$	−13.0094	−	0.917896i	−0.778855	−	0.0549530i
$280$	−0.298745	−	0.166664i	−0.0178534	−	0.00996005i
$281$	−14.8900	+	12.9023i	−0.888265	+	0.769686i	−0.973980	−	0.226633i	$-0.927228\pi$
$281$	−14.8900	+	12.9023i	−0.888265	+	0.769686i	0.0857147	+	0.996320i	$0.472683\pi$
$282$	−2.88685	+	3.10368i	−0.171909	+	0.184821i
$283$	22.4514	−	4.88401i	1.33460	−	0.290324i	0.512020	−	0.858974i	$-0.328898\pi$
$283$	22.4514	−	4.88401i	1.33460	−	0.290324i	0.822580	+	0.568649i	$0.192534\pi$
$284$	−5.93430	+	12.9943i	−0.352136	+	0.771070i
$285$	9.10164	+	3.86198i	0.539135	+	0.228764i
$286$	12.8848	−	8.28059i	0.761897	−	0.489641i
$287$	−0.708020	−	0.530017i	−0.0417931	−	0.0312859i
$288$	2.72770	−	1.24887i	0.160731	−	0.0735901i
$289$	−8.23649	−	12.8162i	−0.484499	−	0.753896i
$290$	−12.9290	−	1.97880i	−0.759216	−	0.116199i
$291$	13.4157	+	10.8005i	0.786445	+	0.633135i
$292$	−0.392094	−	1.80243i	−0.0229456	−	0.105479i
$293$	−4.90858	−	2.68029i	−0.286762	−	0.156584i	0.329429	−	0.944180i	$-0.393144\pi$
$293$	−4.90858	−	2.68029i	−0.286762	−	0.156584i	−0.616192	+	0.787596i	$0.711325\pi$
$294$	10.8031	−	5.41411i	0.630047	−	0.315757i
$295$	−0.561911	+	1.00723i	−0.0327157	+	0.0586431i
$296$	−0.321687	+	0.146909i	−0.0186977	+	0.00853893i
$297$	−11.4670	−	1.21612i	−0.665383	−	0.0705666i
$298$	6.32454	−	6.32454i	0.366371	−	0.366371i
$299$	−14.0303	+	29.9786i	−0.811392	+	1.73371i
$300$	−8.62564	+	0.773485i	−0.498002	+	0.0446572i
$301$	−0.192249	+	1.33712i	−0.0110811	+	0.0770705i
$302$	−17.3822	−	6.48323i	−1.00023	−	0.373068i
$303$	6.55104	−	1.67540i	0.376347	−	0.0962494i
$304$	−1.92931	+	1.67175i	−0.110653	+	0.0958817i
$305$	−0.519227	−	8.31996i	−0.0297309	−	0.476399i
$306$	−8.17725	−	14.9414i	−0.467462	−	0.854142i
$307$	−14.2892	+	5.32960i	−0.815528	+	0.304176i	−0.722398	−	0.691478i	$-0.756960\pi$
$307$	−14.2892	+	5.32960i	−0.815528	+	0.304176i	−0.0931302	+	0.995654i	$0.529687\pi$
$308$	−0.338644	+	0.0242203i	−0.0192961	+	0.00138008i
$309$	−21.4671	+	7.15639i	−1.22122	+	0.407113i
$310$	−7.40392	+	6.29883i	−0.420514	+	0.357750i
$311$	−16.4001	+	2.35798i	−0.929963	+	0.133709i	−0.590616	−	0.806953i	$-0.701115\pi$
$311$	−16.4001	+	2.35798i	−0.929963	+	0.133709i	−0.339347	+	0.940661i	$0.610206\pi$
$312$	10.6922	+	5.34572i	0.605327	+	0.302642i
$313$	0.351354	+	4.91258i	0.0198597	+	0.277675i	0.997672	+	0.0681929i	$0.0217233\pi$
$313$	0.351354	+	4.91258i	0.0198597	+	0.277675i	−0.977812	+	0.209482i	$0.932822\pi$
$314$	7.20128	−	15.7686i	0.406392	−	0.889874i
$315$	−0.499130	+	0.896715i	−0.0281228	+	0.0505242i
$316$	1.79297	−	0.526465i	0.100863	−	0.0296160i
$317$	−21.6728	−	1.55007i	−1.21727	−	0.0870607i	−0.552115	−	0.833768i	$-0.686179\pi$
$317$	−21.6728	−	1.55007i	−1.21727	−	0.0870607i	−0.665153	+	0.746707i	$0.731634\pi$
$318$	−4.78653	−	18.7159i	−0.268415	−	1.04954i
$319$	−11.8078	+	5.39245i	−0.661111	+	0.301919i
$320$	0.800402	−	2.08791i	0.0447439	−	0.116718i
$321$	1.91890	+	0.488789i	0.107103	+	0.0272816i
$322$	0.591434	−	0.434191i	0.0329593	−	0.0241965i
$323$	10.2487	+	10.2487i	0.570255	+	0.570255i
$324$	−3.75445	−	8.17949i	−0.208581	−	0.454416i
$325$	−23.9544	−	24.8399i	−1.32875	−	1.37787i
$326$	2.40622	−	8.19482i	0.133268	−	0.453869i
$327$	−30.8771	−	10.2604i	−1.70751	−	0.567402i
$328$	2.77056	−	5.07390i	0.152979	−	0.280160i
$329$	0.314960	+	0.202413i	0.0173643	+	0.0111594i
$330$	−6.73847	+	5.33535i	−0.370941	+	0.293701i
$331$	−2.63802	+	3.04444i	−0.144999	+	0.167337i	−0.823603	−	0.567166i	$-0.808040\pi$
$331$	−2.63802	+	3.04444i	−0.144999	+	0.167337i	0.678605	+	0.734504i	$0.262585\pi$
$332$	0.190106	−	0.873903i	0.0104334	−	0.0479617i
$333$	0.441655	+	0.964636i	0.0242025	+	0.0528617i
$334$	−1.56590	+	0.225143i	−0.0856824	+	0.0123193i
$335$	2.83120	−	6.05350i	0.154685	−	0.330738i
$336$	−0.151229	−	0.217589i	−0.00825024	−	0.0118704i
$337$	20.5483	−	7.66412i	1.11934	−	0.417491i	0.279400	−	0.960175i	$-0.409864\pi$
$337$	20.5483	−	7.66412i	1.11934	−	0.417491i	0.839937	+	0.542683i	$0.182592\pi$
$338$	7.36184	+	33.8418i	0.400431	+	1.84075i
$339$	−0.659931	−	18.2322i	−0.0358425	−	0.990236i
$340$	−12.1482	−	3.68708i	−0.658829	−	0.199960i
$341$	−2.71800	+	9.25666i	−0.147188	+	0.501276i
$342$	5.02082	+	5.78310i	0.271495	+	0.312714i
$343$	−1.28140	−	1.71175i	−0.0691890	−	0.0924257i
$344$	−8.82997			−0.476080
$345$	6.18063	−	17.5157i	0.332754	−	0.943014i
$346$	−16.2439			−0.873278
$347$	14.3770	+	19.2054i	0.771797	+	1.03100i	0.998374	+	0.0570069i	$0.0181557\pi$
$347$	14.3770	+	19.2054i	0.771797	+	1.03100i	−0.226577	+	0.973993i	$0.572753\pi$
$348$	−8.32488	−	5.77415i	−0.446261	−	0.309527i
$349$	−9.24576	+	31.4882i	−0.494914	+	1.68552i	0.211214	+	0.977440i	$0.432258\pi$
$349$	−9.24576	+	31.4882i	−0.494914	+	1.68552i	−0.706128	+	0.708084i	$0.749560\pi$
$350$	0.202154	+	0.737740i	0.0108056	+	0.0394339i
$351$	16.0063	−	32.0920i	0.854355	−	1.71294i
$352$	−0.471726	−	2.16849i	−0.0251431	−	0.115581i
$353$	−12.8858	+	4.80616i	−0.685843	+	0.255806i	−0.668138	−	0.744037i	$-0.732909\pi$
$353$	−12.8858	+	4.80616i	−0.685843	+	0.255806i	−0.0177047	+	0.999843i	$0.505636\pi$
$354$	−0.733607	+	0.509875i	−0.0389908	+	0.0270995i
$355$	30.0288	−	10.8908i	1.59376	−	0.578026i
$356$	5.37585	−	0.772931i	0.284920	−	0.0409652i
$357$	−1.17097	+	0.944557i	−0.0619744	+	0.0499913i
$358$	1.66413	−	7.64987i	0.0879519	−	0.404308i
$359$	14.8414	−	17.1279i	0.783299	−	0.903975i	−0.214044	−	0.976824i	$-0.568664\pi$
$359$	14.8414	−	17.1279i	0.783299	−	0.903975i	0.997343	+	0.0728488i	$0.0232090\pi$
$360$	−6.26602	−	2.39519i	−0.330248	−	0.126238i
$361$	10.5014	+	6.74883i	0.552704	+	0.355201i
$362$	3.19913	−	5.85877i	0.168143	−	0.307930i
$363$	3.31819	−	9.98557i	0.174160	−	0.524106i
$364$	0.297473	−	1.01310i	0.0155918	−	0.0531008i
$365$	−2.26132	+	3.44947i	−0.118363	+	0.180553i
$366$	2.46818	−	5.96681i	0.129014	−	0.311890i
$367$	−6.24128	−	6.24128i	−0.325792	−	0.325792i	0.525192	−	0.850984i	$-0.323994\pi$
$367$	−6.24128	−	6.24128i	−0.325792	−	0.325792i	−0.850984	+	0.525192i	$0.823994\pi$
$368$	3.35938	+	3.42266i	0.175120	+	0.178418i
$369$	−15.2297	−	8.29706i	−0.792826	−	0.431928i
$370$	0.738377	+	0.283058i	0.0383864	+	0.0147155i
$371$	−1.55213	+	0.708836i	−0.0805828	+	0.0368009i
$372$	−7.29489	+	1.86564i	−0.378222	+	0.0967290i
$373$	12.6488	+	0.904661i	0.654931	+	0.0468416i	0.394850	−	0.918745i	$-0.370796\pi$
$373$	12.6488	+	0.904661i	0.654931	+	0.0468416i	0.260080	+	0.965587i	$0.416251\pi$
$374$	−12.0893	+	3.54973i	−0.625122	+	0.183552i
$375$	14.7481	+	12.5497i	0.761587	+	0.648063i
$376$	−1.01661	+	2.22607i	−0.0524278	+	0.114801i
$377$	−2.87999	−	40.2675i	−0.148327	−	2.07388i
$378$	−0.652330	+	0.454315i	−0.0335522	+	0.0233674i
$379$	4.70056	−	0.675838i	0.241452	−	0.0347155i	−0.0205266	−	0.999789i	$-0.506534\pi$
$379$	4.70056	−	0.675838i	0.241452	−	0.0347155i	0.261978	+	0.965074i	$0.415625\pi$
$380$	5.68985	+	0.458870i	0.291883	+	0.0235396i
$381$	−3.82634	−	11.4779i	−0.196029	−	0.588031i
$382$	25.2513	−	1.80601i	1.29197	−	0.0924033i
$383$	18.6622	−	6.96064i	0.953594	−	0.355672i	0.175965	−	0.984396i	$-0.443695\pi$
$383$	18.6622	−	6.96064i	0.953594	−	0.355672i	0.777628	+	0.628724i	$0.216423\pi$
$384$	1.26711	−	1.18086i	0.0646620	−	0.0602605i
$385$	0.569205	+	0.502333i	0.0290094	+	0.0256013i
$386$	15.1040	−	13.0877i	0.768776	−	0.666148i
$387$	0.0254419	+	26.4899i	0.00129328	+	1.34656i
$388$	9.31676	+	3.47497i	0.472987	+	0.176415i
$389$	1.93034	−	13.4258i	0.0978723	−	0.680717i	−0.880527	−	0.473995i	$-0.842811\pi$
$389$	1.93034	−	13.4258i	0.0978723	−	0.680717i	0.978400	−	0.206722i	$-0.0662795\pi$
$390$	−8.22312	−	25.4338i	−0.416394	−	1.28789i
$391$	18.0222	−	20.4108i	0.911420	−	1.03222i
$392$	4.93320	−	4.93320i	0.249164	−	0.249164i
$393$	−0.693443	−	1.67185i	−0.0349796	−	0.0843335i
$394$	−6.35117	+	2.90048i	−0.319967	+	0.146124i
$395$	−3.64904	−	2.03572i	−0.183603	−	0.102428i
$396$	−6.50410	+	1.42142i	−0.326843	+	0.0714292i
$397$	30.0117	+	16.3876i	1.50624	+	0.822471i	0.999221	−	0.0394628i	$-0.0125647\pi$
$397$	30.0117	+	16.3876i	1.50624	+	0.822471i	0.507021	+	0.861933i	$0.330746\pi$
$398$	5.20682	+	23.9354i	0.260994	+	1.19977i
$399$	0.424202	−	0.526920i	0.0212366	−	0.0263790i
$400$	−4.58510	+	1.99420i	−0.229255	+	0.0997102i
$401$	−3.14409	−	4.89230i	−0.157009	−	0.244310i	0.753833	−	0.657066i	$-0.228203\pi$
$401$	−3.14409	−	4.89230i	−0.157009	−	0.244310i	−0.910842	+	0.412756i	$0.864566\pi$
$402$	4.02909	−	3.25004i	0.200953	−	0.162097i
$403$	−24.0190	−	17.9804i	−1.19647	−	0.895667i
$404$	3.28423	−	2.11065i	0.163397	−	0.105009i
$405$	−7.16751	+	18.8050i	−0.356157	+	0.934426i
$406$	−0.371744	+	0.814006i	−0.0184494	+	0.0403985i
$407$	0.766874	−	0.166823i	0.0380125	−	0.00826912i
$408$	−7.20054	−	6.69748i	−0.356480	−	0.331575i
$409$	1.48148	−	1.28371i	0.0732543	−	0.0634752i	−0.617464	−	0.786599i	$-0.711840\pi$
$409$	1.48148	−	1.28371i	0.0732543	−	0.0634752i	0.690718	+	0.723124i	$0.257294\pi$
$410$	−12.4357	+	3.52922i	−0.614157	+	0.174296i
$411$	−5.38639	−	29.7729i	−0.265691	−	1.46859i
$412$	−10.4587	+	7.82932i	−0.515265	+	0.385723i
$413$	0.0557984	+	0.0557984i	0.00274566	+	0.00274566i
$414$	10.2583	−	10.0880i	0.504167	−	0.495798i
$415$	−1.69209	+	1.06587i	−0.0830613	+	0.0523215i
$416$	6.83144	+	0.982213i	0.334939	+	0.0481569i
$417$	5.72282	+	3.96935i	0.280248	+	0.194380i
$418$	4.97229	−	2.71507i	0.243202	−	0.132799i
$419$	−0.677330	−	0.781681i	−0.0330897	−	0.0381876i	0.738963	−	0.673746i	$-0.235316\pi$
$419$	−0.677330	−	0.781681i	−0.0330897	−	0.0381876i	−0.772053	+	0.635558i	$0.780770\pi$
$420$	−0.110210	+	0.582177i	−0.00537769	+	0.0284073i
$421$	16.6461	+	10.6978i	0.811281	+	0.521378i	0.879279	−	0.476307i	$-0.158025\pi$
$421$	16.6461	+	10.6978i	0.811281	+	0.521378i	−0.0679984	+	0.997685i	$0.521661\pi$
$422$	6.66662	+	17.8739i	0.324526	+	0.870087i
$423$	6.68115	+	3.04343i	0.324848	+	0.147976i
$424$	−6.03000	−	9.38286i	−0.292843	−	0.455672i
$425$	13.1505	+	25.1581i	0.637892	+	1.22035i
$426$	24.6022	+	2.63307i	1.19198	+	0.127572i
$427$	−0.557307	−	0.121235i	−0.0269700	−	0.00586696i
$428$	1.14034	−	0.0815590i	0.0551206	−	0.00394230i
$429$	−20.6642	−	16.6359i	−0.997677	−	0.803189i
$430$	13.8342	+	14.0875i	0.667143	+	0.679360i
$431$	−8.89186	−	30.2829i	−0.428306	−	1.45868i	−0.837605	−	0.546276i	$-0.816045\pi$
$431$	−8.89186	−	30.2829i	−0.428306	−	1.45868i	0.409299	−	0.912400i	$-0.365773\pi$
$432$	−3.54623	−	3.79793i	−0.170618	−	0.182728i
$433$	−3.77919	+	2.06360i	−0.181616	+	0.0991701i	−0.567485	−	0.823384i	$-0.692084\pi$
$433$	−3.77919	+	2.06360i	−0.181616	+	0.0991701i	0.385869	+	0.922554i	$0.373902\pi$
$434$	0.276282	+	0.604973i	0.0132620	+	0.0290397i
$435$	3.83064	+	22.3282i	0.183665	+	1.07056i
$436$	−18.7854			−0.899655
$437$	−5.96744	+	10.6902i	−0.285461	+	0.511382i
$438$	−2.74688	+	1.63158i	−0.131251	+	0.0779601i
$439$	26.1969	+	3.76654i	1.25031	+	0.179767i	0.735492	−	0.677533i	$-0.236951\pi$
$439$	26.1969	+	3.76654i	1.25031	+	0.179767i	0.514817	+	0.857300i	$0.327860\pi$
$440$	−2.72058	+	4.15003i	−0.129699	+	0.197845i
$441$	−14.8138	−	14.7854i	−0.705419	−	0.704065i
$442$	2.79541	−	39.0849i	0.132964	−	1.85908i
$443$	12.9445	+	7.06824i	0.615012	+	0.335822i	0.756377	−	0.654135i	$-0.226967\pi$
$443$	12.9445	+	7.06824i	0.615012	+	0.335822i	−0.141365	+	0.989958i	$0.545149\pi$
$444$	0.417605	+	0.448107i	0.0198186	+	0.0212662i
$445$	−9.65564	−	7.36577i	−0.457721	−	0.349171i
$446$	2.35484	+	2.04048i	0.111505	+	0.0966196i
$447$	−13.8566	−	6.92779i	−0.655393	−	0.327673i
$448$	−0.122473	−	0.0916818i	−0.00578628	−	0.00433156i
$449$	−2.09976	−	14.6041i	−0.0990936	−	0.689211i	−0.977444	−	0.211194i	$-0.932265\pi$
$449$	−2.09976	−	14.6041i	−0.0990936	−	0.689211i	0.878351	−	0.478017i	$-0.158644\pi$
$450$	5.99582	+	13.7495i	0.282646	+	0.648160i
$451$	−8.40142	+	9.69575i	−0.395607	+	0.456555i
$452$	−3.68099	−	9.86912i	−0.173139	−	0.464205i
$453$	−1.13148	+	32.1129i	−0.0531614	+	1.50880i
$454$	−2.78444	−	9.48295i	−0.130680	−	0.445057i
$455$	−2.08238	+	1.11266i	−0.0976234	+	0.0521622i
$456$	3.80376	+	2.25441i	0.178127	+	0.105572i
$457$	6.08056	−	16.3026i	0.284437	−	0.762604i	−0.713634	−	0.700518i	$-0.752952\pi$
$457$	6.08056	−	16.3026i	0.284437	−	0.762604i	0.998071	−	0.0620854i	$-0.0197751\pi$
$458$	−8.41811	+	6.30172i	−0.393353	+	0.294460i
$459$	−20.0717	+	21.6209i	−0.936867	+	1.00918i
$460$	0.197344	−	10.7220i	0.00920120	−	0.499915i
$461$			1.70651i			0.0794803i	0.999210	+	0.0397401i	$0.0126530\pi$
$461$			1.70651i			0.0794803i	−0.999210	+	0.0397401i	$0.987347\pi$
$462$	0.225297	+	0.543177i	0.0104818	+	0.0252709i
$463$	27.4225	+	10.2281i	1.27443	+	0.475339i	0.893417	−	0.449229i	$-0.148301\pi$
$463$	27.4225	+	10.2281i	1.27443	+	0.475339i	0.381017	+	0.924568i	$0.375574\pi$
$464$	−5.61240	−	1.64795i	−0.260549	−	0.0765042i
$465$	14.4056	+	8.71546i	0.668043	+	0.404170i
$466$	−22.8144	+	6.69890i	−1.05686	+	0.310321i
$467$	39.9143	−	8.68282i	1.84701	−	0.401793i	0.854046	−	0.520197i	$-0.174141\pi$
$467$	39.9143	−	8.68282i	1.84701	−	0.401793i	0.992965	+	0.118404i	$0.0377778\pi$
$468$	2.92695	−	20.4971i	0.135298	−	0.947481i
$469$	−0.345549	−	0.299420i	−0.0159560	−	0.0138259i
$470$	5.14428	−	1.86573i	0.237288	−	0.0860595i
$471$	−29.8549	−	3.19523i	−1.37564	−	0.147228i
$472$	−0.309108	+	0.412920i	−0.0142278	+	0.0190062i
$473$	19.1477	+	4.16532i	0.880411	+	0.191522i
$474$	−1.84720	−	2.65775i	−0.0848447	−	0.122074i
$475$	−8.18235	−	9.79662i	−0.375432	−	0.449500i
$476$	−0.469597	+	0.730707i	−0.0215239	+	0.0334919i
$477$	−28.1312	+	18.1170i	−1.28804	+	0.829522i
$478$	−24.3131	−	1.73890i	−1.11205	−	0.0795356i
$479$	1.63598	+	0.480368i	0.0747499	+	0.0219486i	0.318894	−	0.947790i	$-0.396689\pi$
$479$	1.63598	+	0.480368i	0.0747499	+	0.0219486i	−0.244144	+	0.969739i	$0.578507\pi$
$480$	−3.86918	−	0.171490i	−0.176603	−	0.00782740i
$481$	−0.347354	+	2.41590i	−0.0158380	+	0.110156i
$482$	−3.15452	+	3.15452i	−0.143684	+	0.143684i
$483$	−1.03741	−	0.733980i	−0.0472039	−	0.0333972i
$484$		−	6.07514i		−	0.276143i
$485$	−9.05279	−	20.3085i	−0.411066	−	0.922161i
$486$	−11.3836	+	10.6496i	−0.516369	+	0.483076i
$487$	−8.37139	−	15.3311i	−0.379344	−	0.694717i	0.616345	−	0.787477i	$-0.288613\pi$
$487$	−8.37139	−	15.3311i	−0.379344	−	0.694717i	−0.995688	+	0.0927600i	$0.970431\pi$
$488$	0.265955	−	3.71854i	0.0120392	−	0.168330i
$489$	−14.7834	+	0.535098i	−0.668528	+	0.0241980i
$490$	−15.5995	−	0.141542i	−0.704714	−	0.00639420i
$491$	33.1400	+	15.1345i	1.49559	+	0.683012i	0.984317	−	0.176408i	$-0.0564480\pi$
$491$	33.1400	+	15.1345i	1.49559	+	0.683012i	0.511270	+	0.859420i	$0.329175\pi$
$492$	−9.85483	−	1.77312i	−0.444290	−	0.0799384i
$493$	−7.05929	+	32.4510i	−0.317935	+	1.46152i
$494$	2.50743	+	17.4396i	0.112815	+	0.784643i
$495$	12.4579	+	8.14978i	0.559942	+	0.366305i
$496$	−3.65715	+	2.35031i	−0.164211	+	0.105532i
$497$	−0.155909	−	2.17989i	−0.00699346	−	0.0977814i
$498$	−1.54009	+	0.166325i	−0.0690131	+	0.00745320i
$499$	5.80855	−	9.03828i	0.260026	−	0.404609i	−0.686553	−	0.727080i	$-0.740877\pi$
$499$	5.80855	−	9.03828i	0.260026	−	0.404609i	0.946579	+	0.322471i	$0.104513\pi$
$500$	10.3652	+	4.19078i	0.463546	+	0.187418i
$501$	1.22770	+	2.44969i	0.0548495	+	0.109444i
$502$	4.77985	+	8.75365i	0.213335	+	0.390694i
$503$	−8.33756	+	22.3539i	−0.371754	+	0.996710i	0.607544	+	0.794286i	$0.292155\pi$
$503$	−8.33756	+	22.3539i	−0.371754	+	0.996710i	−0.979298	+	0.202424i	$0.935118\pi$
$504$	−0.274692	+	0.367682i	−0.0122358	+	0.0163778i
$505$	−8.51287	−	1.93292i	−0.378818	−	0.0860137i
$506$	−5.67021	−	9.00669i	−0.252072	−	0.400396i
$507$	51.5747	−	30.6342i	2.29051	−	1.36051i
$508$	−4.18614	−	5.59202i	−0.185730	−	0.248106i
$509$	13.4214	+	29.3887i	0.594891	+	1.30263i	0.932441	+	0.361322i	$0.117675\pi$
$509$	13.4214	+	29.3887i	0.594891	+	1.30263i	−0.337550	+	0.941308i	$0.609598\pi$
$510$	0.595983	+	21.9810i	0.0263906	+	0.973336i
$511$	0.184800	+	0.213270i	0.00817506	+	0.00943452i
$512$	0.479249	−	0.877679i	0.0211800	−	0.0387883i
$513$	6.75226	−	11.4178i	0.298120	−	0.504107i
$514$	18.3170	+	8.36511i	0.807929	+	0.368969i
$515$	28.8771	+	4.41967i	1.27247	+	0.194754i
$516$	4.83680	+	14.5090i	0.212928	+	0.638723i
$517$	3.25461	−	4.34765i	0.143138	−	0.191209i
$518$	0.0324228	−	0.0433118i	0.00142458	−	0.00190301i
$519$	8.89792	+	26.6912i	0.390576	+	1.17161i
$520$	−9.13597	−	12.4379i	−0.400639	−	0.545437i
$521$	1.86544	+	0.851916i	0.0817263	+	0.0373231i	0.455859	−	0.890052i	$-0.349332\pi$
$521$	1.86544	+	0.851916i	0.0817263	+	0.0373231i	−0.374133	+	0.927375i	$0.622059\pi$
$522$	−4.92768	+	16.8420i	−0.215679	+	0.737152i
$523$	17.7922	−	32.5840i	0.777999	−	1.42480i	−0.123648	−	0.992326i	$-0.539459\pi$
$523$	17.7922	−	32.5840i	0.777999	−	1.42480i	0.901647	−	0.432473i	$-0.142359\pi$
$524$	−0.684315	−	0.789742i	−0.0298944	−	0.0345000i
$525$	1.10149	−	0.736282i	0.0480728	−	0.0321340i
$526$	12.2245	+	26.7678i	0.533012	+	1.16713i
$527$	14.7913	+	19.7588i	0.644318	+	0.860708i
$528$	−3.30476	+	1.96295i	−0.143821	+	0.0854264i
$529$	20.7396	+	9.94326i	0.901722	+	0.432316i
$530$	−5.52224	+	24.3208i	−0.239871	+	1.05643i
$531$	1.23965	+	0.926134i	0.0537962	+	0.0401908i
$532$	0.136484	−	0.365927i	0.00591732	−	0.0158650i
$533$	−19.1216	−	35.0185i	−0.828246	−	1.51682i
$534$	−4.21477	−	8.40995i	−0.182391	−	0.363934i
$535$	−1.91673	−	1.69155i	−0.0828674	−	0.0731319i
$536$	1.61579	−	2.51423i	0.0697917	−	0.108598i
$537$	−13.4815	+	1.45596i	−0.581768	+	0.0628292i
$538$	−1.24842	−	17.4551i	−0.0538230	−	0.752544i
$539$	−13.0247	+	8.37046i	−0.561013	+	0.360541i
$540$	−0.503320	+	11.6080i	−0.0216595	+	0.499531i
$541$	0.720564	+	5.01164i	0.0309795	+	0.215467i	0.999431	−	0.0337358i	$-0.0107405\pi$
$541$	0.720564	+	5.01164i	0.0309795	+	0.215467i	−0.968451	+	0.249203i	$0.919831\pi$
$542$	6.14773	−	28.2606i	0.264067	−	1.21390i
$543$	−11.3792	−	2.04740i	−0.488330	−	0.0878623i
$544$	−5.16449	−	2.35854i	−0.221426	−	0.101122i
$545$	29.4315	+	29.9705i	1.26071	+	1.28380i
$546$	−1.82762	+	0.0661525i	−0.0782150	+	0.00283107i
$547$	1.29801	−	18.1485i	0.0554988	−	0.775974i	−0.891150	−	0.453708i	$-0.850101\pi$
$547$	1.29801	−	18.1485i	0.0554988	−	0.775974i	0.946649	−	0.322266i	$-0.104445\pi$
$548$	−8.37173	−	15.3317i	−0.357623	−	0.654937i
$549$	−11.1564	−	0.787150i	−0.476142	−	0.0335948i
$550$	10.8834	−	2.16150i	0.464072	−	0.0921666i
$551$		−	14.9324i		−	0.636143i
$552$	3.78378	−	7.39480i	0.161048	−	0.314743i
$553$	−0.202149	+	0.202149i	−0.00859626	+	0.00859626i
$554$	−0.355977	+	2.47587i	−0.0151240	+	0.105190i
$555$	0.0606464	−	1.36832i	0.00257430	−	0.0580818i
$556$	3.85816	+	1.13286i	0.163623	+	0.0480439i
$557$	31.3639	+	2.24319i	1.32893	+	0.0950469i	0.717670	−	0.696383i	$-0.245209\pi$
$557$	31.3639	+	2.24319i	1.32893	+	0.0950469i	0.611260	+	0.791430i	$0.290663\pi$
$558$	7.06145	+	10.9647i	0.298935	+	0.464171i
$559$	−32.9476	+	51.2674i	−1.39353	+	2.16838i
$560$	0.0456102	+	0.339035i	0.00192738	+	0.0143269i
$561$	12.4549	+	17.9201i	0.525846	+	0.756587i
$562$	19.2521	+	4.18804i	0.812100	+	0.176662i
$563$	−18.6632	+	24.9312i	−0.786562	+	1.05072i	0.210756	+	0.977539i	$0.432407\pi$
$563$	−18.6632	+	24.9312i	−0.786562	+	1.05072i	−0.997318	+	0.0731853i	$0.976684\pi$
$564$	4.21465	+	0.451074i	0.177469	+	0.0189937i
$565$	−9.97828	+	21.3350i	−0.419789	+	0.897569i
$566$	−17.3645	−	15.0464i	−0.729884	−	0.632448i
$567$	1.10384	+	0.823017i	0.0463567	+	0.0345635i
$568$	13.9588	−	3.03654i	0.585697	−	0.127411i
$569$	33.9943	−	9.98163i	1.42512	−	0.418452i	0.523884	−	0.851790i	$-0.324483\pi$
$569$	33.9943	−	9.98163i	1.42512	−	0.418452i	0.901232	+	0.433338i	$0.142664\pi$
$570$	−2.36273	−	9.60064i	−0.0989641	−	0.402127i
$571$	3.27718	+	0.962266i	0.137146	+	0.0402696i	0.349585	−	0.936905i	$-0.386323\pi$
$571$	3.27718	+	0.962266i	0.137146	+	0.0402696i	−0.212439	+	0.977174i	$0.568141\pi$
$572$	−14.3506	−	5.35248i	−0.600027	−	0.223798i
$573$	−16.7994	−	40.5024i	−0.701806	−	1.69201i
$574$			0.884426i			0.0369152i
$575$	−17.4153	+	16.4836i	−0.726266	+	0.687413i
$576$	−2.63442	−	1.43522i	−0.109767	−	0.0598007i
$577$	27.8338	−	20.8361i	1.15874	−	0.867419i	0.165810	−	0.986158i	$-0.446976\pi$
$577$	27.8338	−	20.8361i	1.15874	−	0.867419i	0.992925	+	0.118739i	$0.0378852\pi$
$578$	−5.32397	+	14.2741i	−0.221448	+	0.593725i
$579$	−29.7787	−	17.6492i	−1.23756	−	0.733474i
$580$	6.16394	+	11.5360i	0.255944	+	0.479008i
$581$	0.0385474	+	0.131280i	0.00159922	+	0.00544643i
$582$	0.606464	−	17.2123i	0.0251388	−	0.713475i
$583$	8.64984	+	23.1911i	0.358240	+	0.960478i
$584$	−1.20794	+	1.39404i	−0.0499850	+	0.0576858i
$585$	−37.2873	+	27.4437i	−1.54164	+	1.13466i
$586$	0.795922	+	5.53576i	0.0328792	+	0.228680i
$587$	−3.79753	−	2.84280i	−0.156741	−	0.117335i	0.518029	−	0.855363i	$-0.326666\pi$
$587$	−3.79753	−	2.84280i	−0.156741	−	0.117335i	−0.674770	+	0.738028i	$0.735757\pi$
$588$	−10.8083	−	5.40373i	−0.445725	−	0.222846i
$589$	−8.38720	−	7.26755i	−0.345589	−	0.299454i
$590$	1.14307	−	0.153776i	0.0470594	−	0.00633087i
$591$	8.24492	+	8.84714i	0.339151	+	0.363923i
$592$	0.310387	+	0.169484i	0.0127568	+	0.00696575i
$593$	1.33598	−	18.6794i	0.0548621	−	0.767072i	−0.893335	−	0.449390i	$-0.851641\pi$
$593$	1.33598	−	18.6794i	0.0548621	−	0.767072i	0.948198	−	0.317681i	$-0.102904\pi$
$594$	5.89837	+	9.90861i	0.242013	+	0.406555i
$595$	1.90152	−	0.395615i	0.0779545	−	0.0162186i
$596$	−8.85321	−	1.27290i	−0.362642	−	0.0521400i
$597$	36.4773	−	21.6667i	1.49292	−	0.886757i
$598$	32.4071	−	6.73370i	1.32523	−	0.275362i
$599$	6.98806			0.285524			0.142762	−	0.989757i	$-0.454402\pi$
$599$	6.98806			0.285524			0.142762	+	0.989757i	$0.454402\pi$
$600$	5.78836	+	6.44165i	0.236309	+	0.262979i
$601$	9.14944	+	20.0345i	0.373214	+	0.817224i	0.999298	+	0.0374683i	$0.0119293\pi$
$601$	9.14944	+	20.0345i	0.373214	+	0.817224i	−0.626084	+	0.779755i	$0.715343\pi$
$602$	1.18563	−	0.647404i	0.0483228	−	0.0263862i
$603$	−7.54733	−	4.84014i	−0.307351	−	0.197106i
$604$	5.22668	+	17.8004i	0.212670	+	0.724289i
$605$	−9.69239	+	9.51809i	−0.394052	+	0.386965i
$606$	−5.26712	−	4.24034i	−0.213962	−	0.172252i
$607$	−36.0903	+	2.58123i	−1.46486	+	0.104769i	−0.780857	−	0.624709i	$-0.785217\pi$
$607$	−36.0903	+	2.58123i	−1.46486	+	0.104769i	−0.684004	+	0.729478i	$0.739763\pi$
$608$	2.49450	+	0.542645i	0.101165	+	0.0220072i
$609$	1.54117	+	0.164944i	0.0624512	+	0.00668387i
$610$	−6.34931	+	5.40163i	−0.257076	+	0.218705i
$611$	9.13141	+	14.2088i	0.369417	+	0.574825i
$612$	−7.06075	+	15.5003i	−0.285414	+	0.626561i
$613$	9.25559	+	24.8152i	0.373830	+	1.00228i	0.978581	+	0.205862i	$0.0659997\pi$
$613$	9.25559	+	24.8152i	0.373830	+	1.00228i	−0.604751	+	0.796414i	$0.706728\pi$
$614$	12.8298	+	8.24519i	0.517767	+	0.332749i
$615$	12.6110	+	18.5006i	0.508523	+	0.746015i
$616$	0.222331	+	0.256584i	0.00895799	+	0.0103381i
$617$	−12.7977	+	6.98807i	−0.515216	+	0.281329i	−0.715749	−	0.698358i	$-0.753914\pi$
$617$	−12.7977	+	6.98807i	−0.515216	+	0.281329i	0.200533	+	0.979687i	$0.435733\pi$
$618$	18.5937	+	12.8966i	0.747950	+	0.518779i
$619$	−6.31359	−	0.907757i	−0.253765	−	0.0364858i	0.0142585	−	0.999898i	$-0.495461\pi$
$619$	−6.31359	−	0.907757i	−0.253765	−	0.0364858i	−0.268023	+	0.963413i	$0.586370\pi$
$620$	9.47948	+	2.15239i	0.380705	+	0.0864423i
$621$	−22.1953	−	11.3300i	−0.890666	−	0.454658i
$622$	11.7159	+	11.7159i	0.469763	+	0.469763i
$623$	−0.665164	+	0.497936i	−0.0266492	+	0.0199494i
$624$	−2.12813	−	11.7631i	−0.0851935	−	0.470902i
$625$	−9.55339	−	23.1027i	−0.382136	−	0.924106i
$626$	3.72216	−	3.22527i	0.148767	−	0.128908i
$627$	−7.18495	−	6.68299i	−0.286939	−	0.266893i
$628$	−16.9390	+	3.68485i	−0.675939	+	0.147042i
$629$	0.834087	−	1.82639i	0.0332572	−	0.0728231i
$630$	1.01697	−	0.137807i	0.0405172	−	0.00549038i
$631$	−25.8403	+	16.6066i	−1.02869	+	0.661096i	−0.942164	−	0.335153i	$-0.891212\pi$
$631$	−25.8403	+	16.6066i	−1.02869	+	0.661096i	−0.0865225	+	0.996250i	$0.527575\pi$
$632$	−1.49595	−	1.11985i	−0.0595055	−	0.0445453i
$633$	25.7177	−	20.7450i	1.02219	−	0.824542i
$634$	11.7472	+	18.2789i	0.466539	+	0.725949i
$635$	−2.36309	+	15.4398i	−0.0937763	+	0.612711i
$636$	−12.1144	+	15.0479i	−0.480368	+	0.596686i
$637$	−10.2351	−	47.0499i	−0.405529	−	1.86418i
$638$	11.3930	+	6.22107i	0.451055	+	0.246295i
$639$	−9.14985	−	41.8675i	−0.361962	−	1.65625i
$640$	−2.15112	+	0.610481i	−0.0850304	+	0.0241314i
$641$	−8.11178	+	3.70453i	−0.320396	+	0.146320i	−0.569120	−	0.822254i	$-0.692716\pi$
$641$	−8.11178	+	3.70453i	−0.320396	+	0.146320i	0.248724	+	0.968574i	$0.419989\pi$
$642$	−0.758660	−	1.82908i	−0.0299419	−	0.0721881i
$643$	−12.1752	+	12.1752i	−0.480142	+	0.480142i	−0.905177	−	0.425035i	$-0.860262\pi$
$643$	−12.1752	+	12.1752i	−0.480142	+	0.480142i	0.425035	+	0.905177i	$0.360262\pi$
$644$	−0.702021	−	0.213267i	−0.0276635	−	0.00840388i
$645$	15.5700	−	30.4484i	0.613067	−	1.19890i
$646$	2.06270	−	14.3464i	0.0811557	−	0.564450i
$647$	−18.1530	−	6.77072i	−0.713668	−	0.266185i	−0.0337062	−	0.999432i	$-0.510731\pi$
$647$	−18.1530	−	6.77072i	−0.713668	−	0.266185i	−0.679962	+	0.733247i	$0.738004\pi$
$648$	−4.29806	+	7.90738i	−0.168844	+	0.310631i
$649$	0.865081	−	0.749597i	0.0339574	−	0.0294243i
$650$	−5.53005	+	34.0625i	−0.216907	+	1.33604i
$651$	0.842724	−	0.785360i	0.0330290	−	0.0307807i
$652$	−8.00228	+	2.98470i	−0.313393	+	0.116890i
$653$	34.8363	−	2.49154i	1.36325	−	0.0975014i	0.629541	−	0.776967i	$-0.283243\pi$
$653$	34.8363	−	2.49154i	1.36325	−	0.0975014i	0.733707	+	0.679466i	$0.237788\pi$
$654$	10.2901	+	30.8672i	0.402373	+	1.20700i
$655$	−0.187834	+	2.32908i	−0.00733927	+	0.0910047i
$656$	−5.72221	+	0.822729i	−0.223415	+	0.0321222i
$657$	4.18560	+	3.61981i	0.163296	+	0.141222i
$658$	−0.0267090	−	0.373440i	−0.00104122	−	0.0145582i
$659$	15.6678	−	34.3078i	0.610333	−	1.33644i	−0.312014	−	0.950078i	$-0.601003\pi$
$659$	15.6678	−	34.3078i	0.610333	−	1.33644i	0.922346	−	0.386364i	$-0.126269\pi$
$660$	8.30938	+	2.19707i	0.323442	+	0.0855207i
$661$	−39.2504	+	11.5250i	−1.52667	+	0.448269i	−0.934028	−	0.357200i	$-0.883731\pi$
$661$	−39.2504	+	11.5250i	−1.52667	+	0.448269i	−0.592637	+	0.805470i	$0.701913\pi$
$662$	4.01810	+	0.287380i	0.156168	+	0.0111694i
$663$	−65.7537	+	16.8163i	−2.55366	+	0.653090i
$664$	−0.813522	+	0.371523i	−0.0315708	+	0.0144179i
$665$	−0.797640	+	0.355559i	−0.0309312	+	0.0137880i
$666$	0.507557	−	0.931648i	0.0196674	−	0.0361006i
$667$	−27.9984	+	1.74009i	−1.08410	+	0.0673765i
$668$	1.11865	+	1.11865i	0.0432817	+	0.0432817i
$669$	2.06291	−	4.98708i	0.0797567	−	0.192812i
$670$	−6.54275	+	1.36124i	−0.252769	+	0.0525892i
$671$	−2.33085	+	7.93814i	−0.0899814	+	0.306449i
$672$	−0.0835603	+	0.251461i	−0.00322341	+	0.00970034i
$673$	11.9414	−	21.8690i	0.460305	−	0.842987i	−0.539694	−	0.841861i	$-0.681460\pi$
$673$	11.9414	−	21.8690i	0.460305	−	0.842987i	0.999999	−	0.00112521i	$-0.000358165\pi$
$674$	−18.4496	−	11.8568i	−0.710652	−	0.456708i
$675$	19.3083	−	17.3836i	0.743175	−	0.669097i
$676$	22.6800	−	26.1741i	0.872307	−	1.00670i
$677$	7.19900	−	33.0933i	0.276680	−	1.27188i	−0.603548	−	0.797327i	$-0.706247\pi$
$677$	7.19900	−	33.0933i	0.276680	−	1.27188i	0.880228	−	0.474551i	$-0.157390\pi$
$678$	−14.2001	+	11.4544i	−0.545353	+	0.439905i
$679$	−1.50578	+	0.216498i	−0.0577864	+	0.00830843i
$680$	4.32848	+	11.9347i	0.165990	+	0.457676i
$681$	−14.0567	+	9.76974i	−0.538653	+	0.374377i
$682$	9.03918	−	3.37144i	0.346128	−	0.129099i
$683$	4.53085	+	20.8280i	0.173368	+	0.796961i	0.978889	+	0.204393i	$0.0655222\pi$
$683$	4.53085	+	20.8280i	0.173368	+	0.796961i	−0.805521	+	0.592568i	$0.798114\pi$
$684$	1.62075	−	7.48506i	0.0619708	−	0.286198i
$685$	−11.3442	+	37.3770i	−0.433441	+	1.42810i
$686$	−0.602412	+	2.05163i	−0.0230002	+	0.0783314i
$687$	14.9659	+	10.3803i	0.570984	+	0.396035i
$688$	5.29161	+	7.06876i	0.201741	+	0.269494i
$689$	−76.9775			−2.93261
$690$	−17.7260	+	5.54892i	−0.674816	+	0.211244i
$691$	3.01869			0.114837			0.0574183	−	0.998350i	$-0.481713\pi$
$691$	3.01869			0.114837			0.0574183	+	0.998350i	$0.481713\pi$
$692$	9.73461	+	13.0039i	0.370054	+	0.494335i
$693$	0.769112	−	0.667733i	0.0292161	−	0.0253651i
$694$	6.75891	−	23.0187i	0.256565	−	0.873780i
$695$	−4.23731	−	7.93027i	−0.160730	−	0.300812i
$696$	0.366474	+	10.1247i	0.0138912	+	0.383777i
$697$	6.97687	+	32.0722i	0.264268	+	1.21482i
$698$	30.7484	−	11.4685i	1.16384	−	0.434091i
$699$	23.5043	+	33.8180i	0.889016	+	1.27912i
$700$	0.469445	−	0.603944i	0.0177434	−	0.0228269i
$701$	8.51991	−	1.22498i	0.321792	−	0.0462668i	0.0204741	−	0.999790i	$-0.493482\pi$
$701$	8.51991	−	1.22498i	0.321792	−	0.0462668i	0.301318	+	0.953524i	$0.402573\pi$
$702$	−35.2832	+	6.41829i	−1.33168	+	0.242243i
$703$	−0.191904	+	0.882166i	−0.00723778	+	0.0332715i
$704$	−1.45327	+	1.67716i	−0.0547721	+	0.0632104i
$705$	−5.88355	−	7.43084i	−0.221587	−	0.279862i
$706$	11.5697	+	7.43540i	0.435432	+	0.279835i
$707$	−0.286235	+	0.524201i	−0.0107650	+	0.0197146i
$708$	0.847810	+	0.281726i	0.0318627	+	0.0105879i
$709$	6.78684	−	23.1138i	0.254885	−	0.868059i	−0.728271	−	0.685290i	$-0.759676\pi$
$709$	6.78684	−	23.1138i	0.254885	−	0.868059i	0.983156	−	0.182769i	$-0.0585062\pi$
$710$	−26.7142	−	17.5127i	−1.00256	−	0.657238i
$711$	−3.35524	+	4.49106i	−0.125831	+	0.168428i
$712$	−3.84039	−	3.84039i	−0.143925	−	0.143925i
$713$	−12.6494	+	16.5730i	−0.473722	+	0.620662i
$714$	1.45789	+	0.371360i	0.0545603	+	0.0138978i
$715$	13.9440	+	31.2810i	0.521475	+	1.16984i
$716$	−7.12131	+	3.25219i	−0.266136	+	0.121540i
$717$	10.4607	+	40.9026i	0.390661	+	1.52753i
$718$	−22.6057	−	1.61679i	−0.843637	−	0.0603381i
$719$	−47.8066	+	14.0373i	−1.78288	+	0.523502i	−0.995652	−	0.0931543i	$-0.970305\pi$
$719$	−47.8066	+	14.0373i	−1.78288	+	0.523502i	−0.787232	+	0.616656i	$0.788487\pi$
$720$	1.83764	+	6.45160i	0.0684848	+	0.240437i
$721$	0.830296	−	1.81809i	0.0309218	−	0.0677094i
$722$	−0.890528	−	12.4512i	−0.0331420	−	0.463386i
$723$	6.91131	+	3.45540i	0.257034	+	0.128508i
$724$	−6.60736	+	0.949994i	−0.245560	+	0.0353063i
$725$	8.74759	−	27.9079i	0.324878	−	1.03647i
$726$	−9.98238	+	3.32778i	−0.370481	+	0.123505i
$727$	−8.14639	+	0.582641i	−0.302133	+	0.0216090i	−0.221583	−	0.975142i	$-0.571122\pi$
$727$	−8.14639	+	0.582641i	−0.302133	+	0.0216090i	−0.0805501	+	0.996751i	$0.525668\pi$
$728$	−0.989297	+	0.368989i	−0.0366658	+	0.0136756i
$729$	23.7345	+	12.8714i	0.879056	+	0.476718i
$730$	4.11660	−	0.256906i	0.152362	−	0.00950853i
$731$	37.8878	−	32.8299i	1.40133	−	1.21426i
$732$	−6.25580	+	1.59990i	−0.231221	+	0.0591340i
$733$	25.9073	+	9.66291i	0.956907	+	0.356908i	0.778919	−	0.627125i	$-0.215768\pi$
$733$	25.9073	+	9.66291i	0.956907	+	0.356908i	0.177988	+	0.984033i	$0.443041\pi$
$734$	−1.25614	+	8.73667i	−0.0463651	+	0.322476i
$735$	8.31236	+	25.7099i	0.306606	+	0.948323i
$736$	0.726778	−	4.74044i	0.0267894	−	0.174735i
$737$	−4.68985	+	4.68985i	−0.172753	+	0.172753i
$738$	2.48467	+	17.1642i	0.0914621	+	0.631824i
$739$	−3.31190	+	1.51249i	−0.121830	+	0.0556380i	−0.475398	−	0.879771i	$-0.657696\pi$
$739$	−3.31190	+	1.51249i	−0.121830	+	0.0556380i	0.353567	+	0.935409i	$0.384969\pi$
$740$	−0.215893	−	0.760732i	−0.00793640	−	0.0279651i
$741$	27.2824	−	13.6730i	1.00224	−	0.502289i
$742$	1.49761	+	0.817758i	0.0549791	+	0.0300208i
$743$	0.581003	+	2.67083i	0.0213149	+	0.0979831i	0.986575	−	0.163306i	$-0.0522159\pi$
$743$	0.581003	+	2.67083i	0.0213149	+	0.0979831i	−0.965260	+	0.261290i	$0.915852\pi$
$744$	5.86519	+	4.72182i	0.215028	+	0.173110i
$745$	11.8398	+	16.1189i	0.433775	+	0.590550i
$746$	−6.85593	−	10.6680i	−0.251013	−	0.390585i
$747$	1.11691	+	2.43949i	0.0408657	+	0.0892564i
$748$	10.0865	+	7.55069i	0.368801	+	0.276081i
$749$	−0.147138	+	0.0945600i	−0.00537631	+	0.00345515i
$750$	1.20835	−	19.3272i	0.0441226	−	0.705729i
$751$	4.66748	−	10.2203i	0.170319	−	0.372946i	−0.805154	−	0.593065i	$-0.797918\pi$
$751$	4.66748	−	10.2203i	0.170319	−	0.372946i	0.975473	+	0.220120i	$0.0706448\pi$
$752$	2.39130	−	0.520195i	0.0872017	−	0.0189696i
$753$	11.7653	−	12.6490i	0.428752	−	0.460956i
$754$	−30.5099	+	26.4370i	−1.11110	+	0.962777i
$755$	20.2104	−	36.2272i	0.735531	−	1.31844i
$756$	0.754625	+	0.249956i	0.0274454	+	0.00909082i
$757$	33.4996	−	25.0775i	1.21756	−	0.911456i	0.219621	−	0.975585i	$-0.429518\pi$
$757$	33.4996	−	25.0775i	1.21756	−	0.911456i	0.997942	+	0.0641295i	$0.0204271\pi$
$758$	−3.35798	−	3.35798i	−0.121967	−	0.121967i
$759$	−11.6934	+	14.2506i	−0.424443	+	0.517265i
$760$	−3.04245	−	4.82995i	−0.110361	−	0.175201i
$761$	−8.08455	−	1.16238i	−0.293065	−	0.0421363i	−0.00578562	−	0.999983i	$-0.501842\pi$
$761$	−8.08455	−	1.16238i	−0.293065	−	0.0421363i	−0.287279	+	0.957847i	$0.592751\pi$
$762$	−6.89550	+	9.94160i	−0.249798	+	0.360146i
$763$	2.52238	−	1.37732i	0.0913162	−	0.0498624i
$764$	−16.5783	−	19.1324i	−0.599782	−	0.692185i
$765$	35.7917	−	13.0198i	1.29405	−	0.470733i
$766$	−16.7561	−	10.7685i	−0.605423	−	0.389082i
$767$	1.24406	+	3.33544i	0.0449203	+	0.120436i
$768$	−1.70468	−	0.306713i	−0.0615123	−	0.0110675i
$769$	16.5205	+	25.7063i	0.595743	+	0.926994i	0.999924	+	0.0123149i	$0.00392007\pi$
$769$	16.5205	+	25.7063i	0.595743	+	0.926994i	−0.404181	+	0.914679i	$0.632444\pi$
$770$	0.0610265	−	0.756710i	0.00219924	−	0.0272699i
$771$	3.71162	−	34.6798i	0.133671	−	1.24896i
$772$	−19.5288	−	4.24823i	−0.702856	−	0.152897i
$773$	−17.6353	+	1.26130i	−0.634296	+	0.0453658i	−0.384785	−	0.923006i	$-0.625724\pi$
$773$	−17.6353	+	1.26130i	−0.634296	+	0.0453658i	−0.249511	+	0.968372i	$0.580270\pi$
$774$	21.1910	−	15.8952i	0.761695	−	0.571340i
$775$	−11.4178	−	18.4960i	−0.410139	−	0.664395i
$776$	−2.80147	−	9.54093i	−0.100567	−	0.342499i
$777$	−0.0889280	−	0.0295507i	−0.00319028	−	0.00106012i
$778$	−11.9047	+	6.50049i	−0.426806	+	0.233054i
$779$	−6.13073	−	13.4244i	−0.219656	−	0.480980i
$780$	−15.4329	+	21.8249i	−0.552587	+	0.781456i
$781$	−31.7018			−1.13438
$782$	−27.1399	−	2.19578i	−0.970522	−	0.0785210i
$783$	30.3731	−	1.12859i	1.08545	−	0.0403327i
$784$	−6.90558	−	0.992873i	−0.246628	−	0.0354597i
$785$	32.4177	+	21.2516i	1.15704	+	0.758503i
$786$	−0.922818	+	1.55703i	−0.0329158	+	0.0555374i
$787$	−2.38629	+	33.3648i	−0.0850622	+	1.18932i	0.758273	+	0.651937i	$0.226043\pi$
$787$	−2.38629	+	33.3648i	−0.0850622	+	1.18932i	−0.843335	+	0.537388i	$0.819411\pi$
$788$	6.12807	+	3.34618i	0.218304	+	0.119203i
$789$	37.2874	−	34.7493i	1.32747	−	1.23711i
$790$	0.557108	+	4.14116i	0.0198210	+	0.147336i
$791$	1.21785	+	1.05528i	0.0433019	+	0.0375213i
$792$	5.03567	+	4.35497i	0.178935	+	0.154747i
$793$	−20.5977	−	15.4193i	−0.731446	−	0.547554i
$794$	−4.86636	−	33.8463i	−0.172701	−	1.20116i
$795$	42.9876	−	4.24832i	1.52461	−	0.150672i
$796$	16.0409	−	18.5122i	0.568555	−	0.656147i
$797$	8.51096	+	22.8188i	0.301474	+	0.808282i	0.996044	+	0.0888576i	$0.0283216\pi$
$797$	8.51096	+	22.8188i	0.301474	+	0.808282i	−0.694571	+	0.719424i	$0.744406\pi$
$798$	−0.676036	−	0.0238196i	−0.0239314	−	0.000843205i
$799$	−3.91447	−	13.3314i	−0.138484	−	0.471633i
$800$	4.34419	+	2.47548i	0.153590	+	0.0875214i
$801$	−11.5101	+	11.5322i	−0.406689	+	0.407471i
$802$	−2.03231	+	5.44883i	−0.0717633	+	0.192405i
$803$	3.27701	−	2.45314i	0.115643	−	0.0865695i
$804$	−5.01634	−	1.27778i	−0.176913	−	0.0450638i
$805$	0.759627	+	1.45415i	0.0267733	+	0.0512520i
$806$			30.0034i			1.05683i
$807$	−27.9976	+	11.6127i	−0.985562	+	0.408788i
$808$	−3.65783	−	1.36430i	−0.128682	−	0.0479959i
$809$	−6.76871	−	1.98747i	−0.237975	−	0.0698758i	0.160570	−	0.987024i	$-0.448667\pi$
$809$	−6.76871	−	1.98747i	−0.237975	−	0.0698758i	−0.398545	+	0.917149i	$0.630485\pi$
$810$	19.3495	−	5.53151i	0.679871	−	0.194357i
$811$	−27.2127	+	7.99038i	−0.955569	+	0.280580i	−0.722104	−	0.691785i	$-0.756825\pi$
$811$	−27.2127	+	7.99038i	−0.955569	+	0.280580i	−0.233465	+	0.972365i	$0.575006\pi$
$812$	0.874424	−	0.190219i	0.0306863	−	0.00667539i
$813$	−49.8041	+	5.37869i	−1.74671	+	0.188639i
$814$	−0.593119	−	0.513941i	−0.0207888	−	0.0180136i
$815$	17.2992	+	8.09079i	0.605966	+	0.283408i
$816$	−1.04649	+	9.77798i	−0.0366345	+	0.342298i
$817$	−13.5086	+	18.0454i	−0.472607	+	0.631329i
$818$	−1.91548	−	0.416686i	−0.0669730	−	0.0145691i
$819$	1.10982	+	2.96683i	0.0387801	+	0.103669i
$820$	10.2777	+	7.84033i	0.358914	+	0.273796i
$821$	15.2525	−	23.7334i	0.532317	−	0.828302i	−0.466089	−	0.884738i	$-0.654337\pi$
$821$	15.2525	−	23.7334i	0.532317	−	0.828302i	0.998406	+	0.0564360i	$0.0179737\pi$
$822$	−20.6065	+	22.1543i	−0.718734	+	0.772719i
$823$	3.77865	+	0.270254i	0.131715	+	0.00942047i	0.137041	−	0.990565i	$-0.456241\pi$
$823$	3.77865	+	0.270254i	0.131715	+	0.00942047i	−0.00532584	+	0.999986i	$0.501695\pi$
$824$	12.5354	+	3.68072i	0.436691	+	0.128224i
$825$	−9.51330	−	16.6992i	−0.331211	−	0.581390i
$826$	0.0112302	−	0.0781077i	0.000390748	−	0.00271771i
$827$	−0.969336	+	0.969336i	−0.0337071	+	0.0337071i	−0.723759	−	0.690052i	$-0.757587\pi$
$827$	−0.969336	+	0.969336i	−0.0337071	+	0.0337071i	0.690052	+	0.723759i	$0.257587\pi$
$828$	−14.2234	−	2.16668i	−0.494298	−	0.0752972i
$829$			18.9894i			0.659528i	0.944063	+	0.329764i	$0.106969\pi$
$829$			18.9894i			0.659528i	−0.944063	+	0.329764i	$0.893031\pi$
$830$	1.86730	+	0.715833i	0.0648150	+	0.0248469i
$831$	4.26323	−	0.771285i	0.147890	−	0.0267556i
$832$	−3.30763	−	6.05747i	−0.114671	−	0.210005i
$833$	−2.82575	+	39.5091i	−0.0979063	+	1.36891i
$834$	−0.251927	−	6.96010i	−0.00872352	−	0.241008i
$835$	0.0320958	−	3.53732i	0.00111072	−	0.122414i
$836$	−5.15331	−	2.35344i	−0.178231	−	0.0813953i
$837$	14.1486	−	17.6092i	0.489046	−	0.608661i
$838$	−0.219859	+	1.01067i	−0.00759490	+	0.0349132i
$839$	0.137044	+	0.953160i	0.00473127	+	0.0329067i	0.992050	−	0.125842i	$-0.0401632\pi$
$839$	0.137044	+	0.953160i	0.00473127	+	0.0329067i	−0.987319	+	0.158749i	$0.949254\pi$
$840$	0.532103	−	0.260658i	0.0183593	−	0.00899355i
$841$	4.38699	−	2.81935i	0.151276	−	0.0972189i
$842$	−1.41161	−	19.7368i	−0.0486471	−	0.680176i
$843$	−3.66414	−	33.9282i	−0.126200	−	1.16855i
$844$	10.3136	−	16.0483i	0.355010	−	0.552406i
$845$	−77.2921	+	4.82360i	−2.65893	+	0.165937i
$846$	−1.56747	−	7.17239i	−0.0538909	−	0.246592i
$847$	0.445423	+	0.815731i	0.0153049	+	0.0280288i
$848$	−3.89773	+	10.4502i	−0.133848	+	0.358862i
$849$	−15.2118	+	36.7745i	−0.522068	+	1.26210i
$850$	12.2593	−	25.6042i	0.420492	−	0.878217i
$851$	1.67643	+	0.257021i	0.0574674	+	0.00881058i
$852$	−12.6357	−	21.2731i	−0.432892	−	0.728803i
$853$	13.7781	+	18.4053i	0.471752	+	0.630187i	0.971799	−	0.235811i	$-0.0757747\pi$
$853$	13.7781	+	18.4053i	0.471752	+	0.630187i	−0.500047	+	0.865998i	$0.666684\pi$
$854$	0.236928	+	0.518801i	0.00810752	+	0.0177530i
$855$	−14.4811	+	9.14128i	−0.495242	+	0.312625i
$856$	−0.748674	−	0.864016i	−0.0255891	−	0.0295314i
$857$	16.0761	−	29.4411i	0.549148	−	1.00569i	−0.444778	−	0.895641i	$-0.646717\pi$
$857$	16.0761	−	29.4411i	0.549148	−	1.00569i	0.993926	−	0.110049i	$-0.0351008\pi$
$858$	−0.934133	+	26.5121i	−0.0318908	+	0.905107i
$859$	−21.1590	−	9.66299i	−0.721936	−	0.329697i	0.0203384	−	0.999793i	$-0.493526\pi$
$859$	−21.1590	−	9.66299i	−0.721936	−	0.329697i	−0.742274	+	0.670096i	$0.766253\pi$
$860$	2.98713	−	19.5172i	0.101860	−	0.665529i
$861$	1.45325	−	0.484462i	0.0495265	−	0.0165104i
$862$	−18.9140	+	25.2662i	−0.644214	+	0.860569i
$863$	−3.24474	+	4.33446i	−0.110452	+	0.147547i	−0.852361	−	0.522954i	$-0.824830\pi$
$863$	−3.24474	+	4.33446i	−0.110452	+	0.147547i	0.741909	+	0.670501i	$0.233921\pi$
$864$	−0.915226	+	5.11492i	−0.0311366	+	0.174013i
$865$	5.49522	−	35.9044i	0.186843	−	1.22079i
$866$	3.91678	+	1.78873i	0.133098	+	0.0607836i
$867$	26.3709	+	0.929158i	0.895602	+	0.0315559i
$868$	0.318736	−	0.583722i	0.0108186	−	0.0198128i
$869$	2.71568	+	3.13406i	0.0921231	+	0.106316i
$870$	15.5790	−	16.4474i	0.528179	−	0.557618i
$871$	−8.56870	−	18.7628i	−0.290339	−	0.635754i
$872$	11.2576	+	15.0385i	0.381232	+	0.509266i
$873$	−28.6147	+	8.43189i	−0.968461	+	0.285376i
$874$	12.1341	−	1.62922i	0.410442	−	0.0551091i
$875$	−1.69904	+	0.197254i	−0.0574379	+	0.00666839i
$876$	2.95230	+	1.22122i	0.0997488	+	0.0412612i
$877$	−2.54562	+	6.82508i	−0.0859596	+	0.230467i	−0.972816	−	0.231578i	$-0.925611\pi$
$877$	−2.54562	+	6.82508i	−0.0859596	+	0.230467i	0.886857	+	0.462044i	$0.152884\pi$
$878$	−12.6839	−	23.2289i	−0.428062	−	0.783937i
$879$	8.66011	−	4.34014i	0.292098	−	0.146389i
$880$	4.95265	−	0.309082i	0.166954	−	0.0104192i
$881$	−13.6161	+	21.1871i	−0.458739	+	0.713811i	−0.991161	−	0.132668i	$-0.957646\pi$
$881$	−13.6161	+	21.1871i	−0.458739	+	0.713811i	0.532422	+	0.846479i	$0.321282\pi$
$882$	−2.95872	+	20.7196i	−0.0996253	+	0.697665i
$883$	−2.87379	−	40.1808i	−0.0967107	−	1.35219i	−0.781707	−	0.623646i	$-0.785651\pi$
$883$	−2.87379	−	40.1808i	−0.0967107	−	1.35219i	0.684996	−	0.728546i	$-0.259804\pi$
$884$	−32.9643	+	21.1849i	−1.10871	+	0.712524i
$885$	−0.878816	−	1.79400i	−0.0295411	−	0.0603047i
$886$	−2.09894	−	14.5984i	−0.0705153	−	0.490444i
$887$	−2.46190	+	11.3172i	−0.0826626	+	0.379994i	−0.999829	−	0.0185115i	$-0.994107\pi$
$887$	−2.46190	+	11.3172i	−0.0826626	+	0.379994i	0.917166	+	0.398505i	$0.130471\pi$
$888$	0.108467	−	0.602851i	0.00363992	−	0.0202303i
$889$	0.972089	+	0.443938i	0.0326028	+	0.0148892i
$890$	−0.110187	+	12.1439i	−0.00369348	+	0.407064i
$891$	13.0504	−	15.1196i	0.437205	−	0.506524i
$892$	0.222286	−	3.10796i	0.00744268	−	0.104062i
$893$	2.99405	+	5.48319i	0.100192	+	0.183488i
$894$	2.75796	+	15.2444i	0.0922399	+	0.509850i
$895$	16.3458	+	6.26618i	0.546379	+	0.209455i
$896$			0.152987i			0.00511094i
$897$	−28.8162	−	49.5613i	−0.962144	−	1.65481i
$898$	−10.4329	+	10.4329i	−0.348149	+	0.348149i
$899$	3.61887	−	25.1698i	0.120696	−	0.839460i
$900$	7.41392	−	13.0397i	0.247131	−	0.434657i
$901$	60.7592	+	17.8405i	2.02418	+	0.594354i
$902$	12.7966	+	0.915233i	0.426081	+	0.0304739i
$903$	−1.71324	−	1.59355i	−0.0570130	−	0.0530299i
$904$	−5.69470	+	8.86113i	−0.189403	+	0.294717i
$905$	11.8676	+	9.05312i	0.394491	+	0.300936i
$906$	26.3858	−	18.3388i	0.876609	−	0.609265i
$907$	15.7299	+	3.42184i	0.522304	+	0.113620i	0.465985	−	0.884793i	$-0.345700\pi$
$907$	15.7299	+	3.42184i	0.522304	+	0.113620i	0.0563187	+	0.998413i	$0.482064\pi$
$908$	−5.92283	+	7.91198i	−0.196556	+	0.262568i
$909$	−4.08236	+	10.9774i	−0.135403	+	0.364098i
$910$	2.13865	+	1.00024i	0.0708956	+	0.0331576i
$911$	−23.0069	−	19.9356i	−0.762253	−	0.660496i	0.184363	−	0.982858i	$-0.440978\pi$
$911$	−23.0069	−	19.9356i	−0.762253	−	0.660496i	−0.946617	+	0.322362i	$0.895523\pi$
$912$	−0.474764	−	4.39608i	−0.0157210	−	0.145569i
$913$	1.93937	−	0.421884i	0.0641837	−	0.0139623i
$914$	−16.6949	+	4.90205i	−0.552217	+	0.162145i
$915$	12.3537	+	7.47402i	0.408399	+	0.247084i
$916$	10.0896	+	2.96257i	0.333369	+	0.0978860i
$917$	0.149788	+	0.0558682i	0.00494645	+	0.00184493i
$918$	29.3369	+	3.11130i	0.968263	+	0.102688i
$919$		−	0.766494i		−	0.0252843i	−0.999920	−	0.0126422i	$-0.995976\pi$
$919$		−	0.766494i		−	0.0252843i	0.999920	−	0.0126422i	$-0.00402423\pi$
$920$	−8.70166	+	6.26747i	−0.286885	+	0.206632i
$921$	6.52034	−	25.5977i	0.214852	−	0.843474i
$922$	1.36613	−	1.02268i	0.0449912	−	0.0336800i
$923$	34.4545	−	92.3760i	1.13408	−	3.04059i
$924$	0.299820	−	0.505873i	0.00986336	−	0.0166420i
$925$	−0.875441	+	1.53630i	−0.0287843	+	0.0505133i
$926$	−8.24572	−	28.0823i	−0.270971	−	0.922843i
$927$	11.0060	−	37.6167i	0.361486	−	1.23550i
$928$	2.04414	+	5.48054i	0.0671021	+	0.179908i
$929$	−8.97978	+	10.3632i	−0.294617	+	0.340006i	−0.883689	−	0.468074i	$-0.844948\pi$
$929$	−8.97978	+	10.3632i	−0.294617	+	0.340006i	0.589072	+	0.808081i	$0.299493\pi$
$930$	−1.65586	−	16.7552i	−0.0542979	−	0.549426i
$931$	−2.53464	−	17.6288i	−0.0830696	−	0.577762i
$932$	19.0349	+	14.2493i	0.623509	+	0.466753i
$933$	12.8333	−	25.6685i	0.420145	−	0.840350i
$934$	−30.8707	−	26.7496i	−1.01012	−	0.875274i
$935$	−3.75635	−	27.9221i	−0.122846	−	0.913152i
$936$	−18.1629	+	9.94033i	−0.593672	+	0.324910i
$937$	40.5537	+	22.1440i	1.32483	+	0.723412i	0.976817	−	0.214077i	$-0.0686745\pi$
$937$	40.5537	+	22.1440i	1.32483	+	0.723412i	0.348014	+	0.937489i	$0.386856\pi$
$938$	−0.0326182	+	0.456062i	−0.00106502	+	0.0148910i
$939$	−7.33850	−	4.34937i	−0.239483	−	0.141936i
$940$	−4.57644	−	3.00012i	−0.149267	−	0.0978531i
$941$	−43.1449	−	6.20331i	−1.40648	−	0.202222i	−0.603092	−	0.797672i	$-0.706065\pi$
$941$	−43.1449	−	6.20331i	−1.40648	−	0.202222i	−0.803393	+	0.595450i	$0.796974\pi$
$942$	15.3334	+	25.8149i	0.499590	+	0.841094i
$943$	−24.4565	+	13.0595i	−0.796413	+	0.425277i
$944$	0.515801			0.0167879
$945$	−0.783507	−	1.59556i	−0.0254875	−	0.0519035i
$946$	−8.14027	−	17.8247i	−0.264663	−	0.579531i
$947$	3.16172	−	1.72643i	0.102742	−	0.0561015i	−0.427056	−	0.904225i	$-0.640449\pi$
$947$	3.16172	−	1.72643i	0.102742	−	0.0561015i	0.529798	+	0.848124i	$0.322268\pi$
$948$	−1.02065	+	3.07149i	−0.0331492	+	0.0997573i
$949$	3.58666	+	12.2150i	0.116428	+	0.396517i
$950$	−2.93910	+	12.4212i	−0.0953569	+	0.402997i
$951$	23.6003	−	29.3150i	0.765293	−	0.950604i
$952$	0.866380	−	0.0619648i	0.0280796	−	0.00200829i
$953$	−4.05417	−	0.881932i	−0.131328	−	0.0285686i	0.146421	−	0.989222i	$-0.453225\pi$
$953$	−4.05417	−	0.881932i	−0.131328	−	0.0285686i	−0.277749	+	0.960654i	$0.589588\pi$
$954$	31.3618	+	11.6631i	1.01538	+	0.377606i
$955$	−4.55049	+	56.4246i	−0.147250	+	1.82586i
$956$	13.1782	+	20.5057i	0.426214	+	0.663202i
$957$	3.98140	−	22.1282i	0.128700	−	0.715304i
$958$	−0.595853	−	1.59755i	−0.0192512	−	0.0516143i
$959$	2.24820	+	1.44483i	0.0725983	+	0.0466561i
$960$	2.18143	+	3.20021i	0.0704054	+	0.103286i
$961$	7.92469	+	9.14558i	0.255635	+	0.295019i
$962$	2.14219	−	1.16973i	0.0690670	−	0.0377135i
$963$	−2.58989	+	2.24851i	−0.0834580	+	0.0724572i
$964$	4.41576	+	0.634890i	0.142222	+	0.0204484i
$965$	23.8186	+	37.8124i	0.766747	+	1.21722i
$966$	0.0341169	+	1.27035i	0.00109769	+	0.0408728i
$967$	−8.99416	−	8.99416i	−0.289233	−	0.289233i	0.547544	−	0.836777i	$-0.315563\pi$
$967$	−8.99416	−	8.99416i	−0.289233	−	0.289233i	−0.836777	+	0.547544i	$0.815563\pi$
$968$	−4.86340	+	3.64069i	−0.156316	+	0.117016i
$969$	−24.7031	+	4.46919i	−0.793579	+	0.143571i
$970$	−10.8326	+	19.4176i	−0.347815	+	0.623460i
$971$	12.0174	−	10.4132i	0.385658	−	0.334174i	−0.440357	−	0.897823i	$-0.645148\pi$
$971$	12.0174	−	10.4132i	0.385658	−	0.334174i	0.826015	+	0.563648i	$0.190603\pi$
$972$	15.3474	+	2.73094i	0.492267	+	0.0875949i
$973$	−0.601110	+	0.130763i	−0.0192707	+	0.00419208i
$974$	−7.25636	+	15.8892i	−0.232509	+	0.509123i
$975$	58.9990	−	9.57168i	1.88948	−	0.306539i
$976$	−3.13622	+	2.01553i	−0.100388	+	0.0645155i
$977$	14.4093	+	10.7866i	0.460993	+	0.345095i	0.804396	−	0.594093i	$-0.202489\pi$
$977$	14.4093	+	10.7866i	0.460993	+	0.345095i	−0.343403	+	0.939188i	$0.611580\pi$
$978$	9.28772	+	11.5140i	0.296988	+	0.368178i
$979$	6.51623	+	10.1394i	0.208260	+	0.324058i
$980$	9.23512	+	12.5729i	0.295005	+	0.401625i
$981$	45.0829	−	33.8162i	1.43939	−	1.07967i
$982$	−7.74424	−	35.5997i	−0.247129	−	1.13603i
$983$	29.0536	+	15.8645i	0.926667	+	0.505999i	0.870361	−	0.492415i	$-0.163886\pi$
$983$	29.0536	+	15.8645i	0.926667	+	0.505999i	0.0563066	+	0.998414i	$0.482068\pi$
$984$	4.48632	+	8.95179i	0.143019	+	0.285373i
$985$	−4.26246	−	15.0194i	−0.135813	−	0.478558i
$986$	30.2089	−	13.7959i	0.962047	−	0.439352i
$987$	−0.598988	+	0.248446i	−0.0190660	+	0.00790813i
$988$	12.4584	−	12.4584i	0.396356	−	0.396356i
$989$	35.4095	+	23.2259i	1.12596	+	0.738542i
$990$	−0.941517	−	14.8571i	−0.0299234	−	0.472188i
$991$	6.09339	−	42.3804i	0.193563	−	1.34626i	−0.628920	−	0.777470i	$-0.716503\pi$
$991$	6.09339	−	42.3804i	0.193563	−	1.34626i	0.822483	−	0.568789i	$-0.192588\pi$
$992$	4.07316	+	1.51921i	0.129323	+	0.0482350i
$993$	−1.72879	−	6.75977i	−0.0548614	−	0.214515i
$994$	−1.65166	+	1.43117i	−0.0523874	+	0.0453940i
$995$	−54.6665	+	3.41159i	−1.73304	+	0.108155i
$996$	1.05609	+	1.13323i	0.0334635	+	0.0359078i
$997$	15.6896	−	5.85193i	0.496896	−	0.185333i	−0.0885063	−	0.996076i	$-0.528209\pi$
$997$	15.6896	−	5.85193i	0.496896	−	0.185333i	0.585402	+	0.810743i	$0.300937\pi$
$998$	−10.7164	+	0.766456i	−0.339223	+	0.0242617i
$999$	−1.80886	−	0.323665i	−0.0572299	−	0.0102403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.x.a.77.8	✓	960
3.2	odd	2	inner	690.2.x.a.77.39	yes	960
5.3	odd	4	inner	690.2.x.a.353.5	yes	960
15.8	even	4	inner	690.2.x.a.353.47	yes	960
23.3	even	11	inner	690.2.x.a.647.47	yes	960
69.26	odd	22	inner	690.2.x.a.647.5	yes	960
115.3	odd	44	inner	690.2.x.a.233.39	yes	960
345.233	even	44	inner	690.2.x.a.233.8	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.x.a.77.8	✓	960	1.1	even	1	trivial
690.2.x.a.77.39	yes	960	3.2	odd	2	inner
690.2.x.a.233.8	yes	960	345.233	even	44	inner
690.2.x.a.233.39	yes	960	115.3	odd	44	inner
690.2.x.a.353.5	yes	960	5.3	odd	4	inner
690.2.x.a.353.47	yes	960	15.8	even	4	inner
690.2.x.a.647.5	yes	960	69.26	odd	22	inner
690.2.x.a.647.47	yes	960	23.3	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599278 - 0.800541i) q^{2} +(-0.987144 + 1.42322i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(1.97219 - 1.05378i) q^{5} +(1.73092 - 0.0626522i) q^{6} +(-0.0325198 - 0.149491i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-1.05109 - 2.80984i) q^{9} +O(q^{10})\)	\(q+(-0.599278 - 0.800541i) q^{2} +(-0.987144 + 1.42322i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(1.97219 - 1.05378i) q^{5} +(1.73092 - 0.0626522i) q^{6} +(-0.0325198 - 0.149491i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-1.05109 - 2.80984i) q^{9} +(-2.02549 - 0.947313i) q^{10} +(-2.19661 + 0.315826i) q^{11} +(-1.08746 - 1.34812i) q^{12} +(1.46706 - 6.74396i) q^{13} +(-0.100185 + 0.115620i) q^{14} +(-0.447077 + 3.84709i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-2.72096 + 4.98307i) q^{17} +(-1.61950 + 2.52532i) q^{18} +(0.719218 - 2.44943i) q^{19} +(0.455466 + 2.18919i) q^{20} +(0.244860 + 0.101286i) q^{21} +(1.56921 + 1.56921i) q^{22} +(-4.67652 - 1.06311i) q^{23} +(-0.427541 + 1.67845i) q^{24} +(2.77908 - 4.15652i) q^{25} +(-6.27800 + 2.86707i) q^{26} +(5.03659 + 1.27779i) q^{27} +(0.152597 + 0.0109140i) q^{28} +(5.61240 - 1.64795i) q^{29} +(3.34768 - 1.94757i) q^{30} +(1.80592 - 3.95441i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(1.71889 - 3.43802i) q^{33} +(5.61977 - 0.808001i) q^{34} +(-0.221666 - 0.260556i) q^{35} +(2.99215 - 0.216891i) q^{36} +(-0.352744 + 0.0252287i) q^{37} +(-2.39188 + 0.892126i) q^{38} +(8.14992 + 8.74521i) q^{39} +(1.47959 - 1.67655i) q^{40} +(4.36902 - 3.78578i) q^{41} +(-0.0656549 - 0.256719i) q^{42} +(-8.27324 - 3.08576i) q^{43} +(0.315826 - 2.19661i) q^{44} +(-5.03392 - 4.43392i) q^{45} +(1.95147 + 4.38084i) q^{46} +(-1.73045 + 1.73045i) q^{47} +(1.59989 - 0.663596i) q^{48} +(6.34613 - 2.89818i) q^{49} +(-4.99291 + 0.266141i) q^{50} +(-4.40601 - 8.79154i) q^{51} +(6.05747 + 3.30763i) q^{52} +(-2.37083 - 10.8985i) q^{53} +(-1.99540 - 4.79775i) q^{54} +(-3.99933 + 2.93762i) q^{55} +(-0.0827111 - 0.128701i) q^{56} +(2.77610 + 3.44155i) q^{57} +(-4.68264 - 3.50538i) q^{58} +(-0.433919 + 0.278863i) q^{59} +(-3.56530 - 1.51282i) q^{60} +(1.54868 - 3.39114i) q^{61} +(-4.24791 + 0.924077i) q^{62} +(-0.385864 + 0.248504i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-4.21335 - 14.8464i) q^{65} +(-3.78237 + 0.684290i) q^{66} +(2.39255 - 1.79104i) q^{67} +(-4.01464 - 4.01464i) q^{68} +(6.12943 - 5.60626i) q^{69} +(-0.0757463 + 0.333598i) q^{70} +(14.1398 + 2.03300i) q^{71} +(-1.96676 - 2.26536i) q^{72} +(-1.61895 + 0.884013i) q^{73} +(0.231588 + 0.267267i) q^{74} +(3.17228 + 8.05833i) q^{75} +(2.14758 + 1.38017i) q^{76} +(0.118646 + 0.318103i) q^{77} +(2.11683 - 11.7652i) q^{78} +(-1.01028 - 1.57202i) q^{79} +(-2.22883 - 0.179749i) q^{80} +(-6.79041 + 5.90680i) q^{81} +(-5.64893 - 1.22885i) q^{82} +(-0.892063 + 0.0638016i) q^{83} +(-0.166169 + 0.206405i) q^{84} +(-0.115187 + 12.6949i) q^{85} +(2.48769 + 8.47230i) q^{86} +(-3.19486 + 9.61443i) q^{87} +(-1.94775 + 1.06355i) q^{88} +(-2.25617 - 4.94033i) q^{89} +(-0.532825 + 6.68701i) q^{90} -1.05587 q^{91} +(2.33757 - 4.18757i) q^{92} +(3.84528 + 6.47378i) q^{93} +(2.42232 + 0.348276i) q^{94} +(-1.16273 - 5.58865i) q^{95} +(-1.49001 - 0.883098i) q^{96} +(0.709377 - 9.91838i) q^{97} +(-6.12321 - 3.34353i) q^{98} +(3.19626 + 5.84018i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) \) 960 * q + 8 * q^3 + 8 * q^6	\( 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) \) 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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