LMFDB - Embedded newform 616.2.bp.c.27.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(27,616)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 5, 4]))

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

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

chi := DirichletCharacter("616.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.bp (of order $10$, degree $4$, 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:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$352$
Relative dimension:	$88$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			27.5
Character	$\chi$	$=$	616.27
Dual form			616.2.bp.c.251.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37858 - 0.315464i) q^{2} +(-0.891388 + 1.22689i) q^{3} +(1.80096 + 0.869785i) q^{4} +(-0.0834388 + 0.256798i) q^{5} +(1.61589 - 1.41016i) q^{6} +(1.62621 - 2.08697i) q^{7} +(-2.20839 - 1.76721i) q^{8} +(0.216364 + 0.665900i) q^{9} +(0.196038 - 0.327695i) q^{10} +(-3.27175 + 0.543723i) q^{11} +(-2.67249 + 1.43427i) q^{12} +(-2.13341 - 6.56597i) q^{13} +(-2.90022 + 2.36404i) q^{14} +(-0.240687 - 0.331277i) q^{15} +(2.48695 + 3.13290i) q^{16} +(-3.21212 - 1.04368i) q^{17} +(-0.0882077 - 0.986252i) q^{18} +(-0.0370236 + 0.0509587i) q^{19} +(-0.373630 + 0.389911i) q^{20} +(1.11090 + 3.85548i) q^{21} +(4.68190 + 0.282554i) q^{22} +3.24436i q^{23} +(4.13670 - 1.13418i) q^{24} +(3.98610 + 2.89607i) q^{25} +(0.869753 + 9.72473i) q^{26} +(-5.33674 - 1.73401i) q^{27} +(4.74396 - 2.34411i) q^{28} +(-2.31211 - 3.18235i) q^{29} +(0.227300 + 0.532620i) q^{30} +(-0.974373 - 2.99881i) q^{31} +(-2.44014 - 5.10350i) q^{32} +(2.24931 - 4.49875i) q^{33} +(4.09892 + 2.45211i) q^{34} +(0.400241 + 0.591742i) q^{35} +(-0.189526 + 1.38745i) q^{36} +(-4.81529 - 6.62767i) q^{37} +(0.0671156 - 0.0585709i) q^{38} +(9.95742 + 3.23536i) q^{39} +(0.638081 - 0.419657i) q^{40} +(2.44596 - 3.36658i) q^{41} +(-0.315199 - 5.66553i) q^{42} -7.11479 q^{43} +(-6.36523 - 1.86649i) q^{44} -0.189055 q^{45} +(1.02348 - 4.47261i) q^{46} +(0.494132 + 0.359008i) q^{47} +(-6.06056 + 0.258582i) q^{48} +(-1.71089 - 6.78770i) q^{49} +(-4.58155 - 5.24994i) q^{50} +(4.14373 - 3.01060i) q^{51} +(1.86878 - 13.6807i) q^{52} +(11.7326 - 3.81214i) q^{53} +(6.81010 + 4.07402i) q^{54} +(0.133364 - 0.885548i) q^{55} +(-7.27941 + 1.73499i) q^{56} +(-0.0295182 - 0.0908478i) q^{57} +(2.18351 + 5.11651i) q^{58} +(-0.709701 - 0.976819i) q^{59} +(-0.145329 - 0.805964i) q^{60} +(2.29148 - 7.05244i) q^{61} +(0.397234 + 4.44148i) q^{62} +(1.74157 + 0.631348i) q^{63} +(1.75396 + 7.80536i) q^{64} +1.86414 q^{65} +(-4.52005 + 5.49231i) q^{66} +7.60314 q^{67} +(-4.87714 - 4.67349i) q^{68} +(-3.98047 - 2.89198i) q^{69} +(-0.365091 - 0.942025i) q^{70} +(-7.10243 - 2.30772i) q^{71} +(0.698968 - 1.85293i) q^{72} +(-7.13145 - 9.81560i) q^{73} +(4.54746 + 10.6558i) q^{74} +(-7.10632 + 2.30898i) q^{75} +(-0.111001 + 0.0595722i) q^{76} +(-4.18582 + 7.71226i) q^{77} +(-12.7065 - 7.60141i) q^{78} +(-9.50920 + 3.08973i) q^{79} +(-1.01203 + 0.377239i) q^{80} +(5.18520 - 3.76727i) q^{81} +(-4.43399 + 3.86949i) q^{82} +(-7.87395 - 2.55840i) q^{83} +(-1.35275 + 7.90983i) q^{84} +(0.536032 - 0.737784i) q^{85} +(9.80830 + 2.24446i) q^{86} +5.96537 q^{87} +(8.18617 + 4.58111i) q^{88} -6.36308i q^{89} +(0.260628 + 0.0596401i) q^{90} +(-17.1724 - 6.22527i) q^{91} +(-2.82189 + 5.84298i) q^{92} +(4.54776 + 1.47766i) q^{93} +(-0.567946 - 0.650802i) q^{94} +(-0.00999689 - 0.0137595i) q^{95} +(8.43654 + 1.55541i) q^{96} +(13.5188 - 4.39251i) q^{97} +(0.217319 + 9.89711i) q^{98} +(-1.06996 - 2.06102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 352 q - 2 q^{2} - 10 q^{4} - 14 q^{8} + 84 q^{9} - 28 q^{11} - 32 q^{14} + 14 q^{16} - 4 q^{18} - 62 q^{22} - 108 q^{25} - 44 q^{28} + 24 q^{30} - 112 q^{32} + 14 q^{35} + 20 q^{36} - 2 q^{42} + 8 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) $ 352 * q - 2 * q^2 - 10 * q^4 - 14 * q^8 + 84 * q^9 - 28 * q^11 - 32 * q^14 + 14 * q^16 - 4 * q^18 - 62 * q^22 - 108 * q^25 - 44 * q^28 + 24 * q^30 - 112 * q^32 + 14 * q^35 + 20 * q^36 - 2 * q^42 + 8 * q^43 + 22 * q^44 - 38 * q^46 - 34 * q^49 - 24 * q^50 - 36 * q^51 - 120 * q^56 - 36 * q^57 + 30 * q^58 - 136 * q^60 + 86 * q^64 + 8 * q^65 + 24 * q^67 + 52 * q^70 + 30 * q^72 + 94 * q^74 - 68 * q^78 - 60 * q^81 - 128 * q^84 + 34 * q^86 - 38 * q^88 + 78 * q^91 - 8 * q^92 - 100 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.37858	−	0.315464i	−0.974803	−	0.223067i
$2$	−1.37858	−	0.315464i	−0.974803	−	0.223067i
$3$	−0.891388	+	1.22689i	−0.514643	+	0.708345i	−0.984694	−	0.174294i	$-0.944236\pi$
$3$	−0.891388	+	1.22689i	−0.514643	+	0.708345i	0.470051	+	0.882639i	$0.344236\pi$
$4$	1.80096	+	0.869785i	0.900482	+	0.434892i
$5$	−0.0834388	+	0.256798i	−0.0373150	+	0.114844i	−0.967979	−	0.251031i	$-0.919230\pi$
$5$	−0.0834388	+	0.256798i	−0.0373150	+	0.114844i	0.930664	+	0.365875i	$0.119230\pi$
$6$	1.61589	−	1.41016i	0.659684	−	0.575697i
$7$	1.62621	−	2.08697i	0.614649	−	0.788800i
$7$	1.62621	−	2.08697i	0.614649	−	0.788800i
$8$	−2.20839	−	1.76721i	−0.780783	−	0.624802i
$9$	0.216364	+	0.665900i	0.0721214	+	0.221967i
$10$	0.196038	−	0.327695i	0.0619926	−	0.103626i
$11$	−3.27175	+	0.543723i	−0.986471	+	0.163939i
$11$	−3.27175	+	0.543723i	−0.986471	+	0.163939i
$12$	−2.67249	+	1.43427i	−0.771481	+	0.414038i
$13$	−2.13341	−	6.56597i	−0.591702	−	1.82107i	−0.570501	−	0.821297i	$-0.693251\pi$
$13$	−2.13341	−	6.56597i	−0.591702	−	1.82107i	−0.0212008	−	0.999775i	$-0.506749\pi$
$14$	−2.90022	+	2.36404i	−0.775117	+	0.631817i
$15$	−0.240687	−	0.331277i	−0.0621451	−	0.0855354i
$16$	2.48695	+	3.13290i	0.621737	+	0.783226i
$17$	−3.21212	−	1.04368i	−0.779054	−	0.253130i	−0.107618	−	0.994192i	$-0.534322\pi$
$17$	−3.21212	−	1.04368i	−0.779054	−	0.253130i	−0.671436	+	0.741062i	$0.734322\pi$
$18$	−0.0882077	−	0.986252i	−0.0207907	−	0.232462i
$19$	−0.0370236	+	0.0509587i	−0.00849380	+	0.0116907i	−0.813243	−	0.581925i	$-0.802300\pi$
$19$	−0.0370236	+	0.0509587i	−0.00849380	+	0.0116907i	0.804749	+	0.593615i	$0.202300\pi$
$20$	−0.373630	+	0.389911i	−0.0835461	+	0.0871867i
$21$	1.11090	+	3.85548i	0.242418	+	0.841335i
$22$	4.68190	+	0.282554i	0.998184	+	0.0602408i
$23$			3.24436i			0.676496i	0.941057	+	0.338248i	$0.109834\pi$
$23$			3.24436i			0.676496i	−0.941057	+	0.338248i	$0.890166\pi$
$24$	4.13670	−	1.13418i	0.844400	−	0.231514i
$25$	3.98610	+	2.89607i	0.797220	+	0.579214i
$26$	0.869753	+	9.72473i	0.170573	+	1.90718i
$27$	−5.33674	−	1.73401i	−1.02706	−	0.333711i
$28$	4.74396	−	2.34411i	0.896524	−	0.442995i
$29$	−2.31211	−	3.18235i	−0.429348	−	0.590947i	0.538455	−	0.842654i	$-0.319008\pi$
$29$	−2.31211	−	3.18235i	−0.429348	−	0.590947i	−0.967803	+	0.251707i	$0.919008\pi$
$30$	0.227300	+	0.532620i	0.0414991	+	0.0972427i
$31$	−0.974373	−	2.99881i	−0.175003	−	0.538603i	0.824631	−	0.565671i	$-0.191383\pi$
$31$	−0.974373	−	2.99881i	−0.175003	−	0.538603i	−0.999634	+	0.0270684i	$0.991383\pi$
$32$	−2.44014	−	5.10350i	−0.431360	−	0.902180i
$33$	2.24931	−	4.49875i	0.391555	−	0.783132i
$34$	4.09892	+	2.45211i	0.702960	+	0.420533i
$35$	0.400241	+	0.591742i	0.0676531	+	0.100023i
$36$	−0.189526	+	1.38745i	−0.0315876	+	0.231242i
$37$	−4.81529	−	6.62767i	−0.791628	−	1.08958i	−0.993903	−	0.110254i	$-0.964834\pi$
$37$	−4.81529	−	6.62767i	−0.791628	−	1.08958i	0.202275	−	0.979329i	$-0.435166\pi$
$38$	0.0671156	−	0.0585709i	0.0108876	−	0.00950146i
$39$	9.95742	+	3.23536i	1.59446	+	0.518072i
$40$	0.638081	−	0.419657i	0.100889	−	0.0663535i
$41$	2.44596	−	3.36658i	0.381995	−	0.525772i	−0.574116	−	0.818774i	$-0.694654\pi$
$41$	2.44596	−	3.36658i	0.381995	−	0.525772i	0.956112	+	0.293002i	$0.0946543\pi$
$42$	−0.315199	−	5.66553i	−0.0486362	−	0.874211i
$43$	−7.11479			−1.08500			−0.542498	−	0.840057i	$-0.682521\pi$
$43$	−7.11479			−1.08500			−0.542498	+	0.840057i	$0.682521\pi$
$44$	−6.36523	−	1.86649i	−0.959595	−	0.281385i
$45$	−0.189055			−0.0281827
$46$	1.02348	−	4.47261i	0.150904	−	0.659450i
$47$	0.494132	+	0.359008i	0.0720766	+	0.0523667i	0.623240	−	0.782031i	$-0.285816\pi$
$47$	0.494132	+	0.359008i	0.0720766	+	0.0523667i	−0.551163	+	0.834397i	$0.685816\pi$
$48$	−6.06056	+	0.258582i	−0.874767	+	0.0373230i
$49$	−1.71089	−	6.78770i	−0.244412	−	0.969671i
$50$	−4.58155	−	5.24994i	−0.647929	−	0.742453i
$51$	4.14373	−	3.01060i	0.580238	−	0.421568i
$52$	1.86878	−	13.6807i	0.259153	−	1.89717i
$53$	11.7326	−	3.81214i	1.61159	−	0.523638i	0.641654	−	0.766994i	$-0.278248\pi$
$53$	11.7326	−	3.81214i	1.61159	−	0.523638i	0.969937	+	0.243356i	$0.0782483\pi$
$54$	6.81010	+	4.07402i	0.926737	+	0.554404i
$55$	0.133364	−	0.885548i	0.0179828	−	0.119407i
$56$	−7.27941	+	1.73499i	−0.972752	+	0.231848i
$57$	−0.0295182	−	0.0908478i	−0.00390979	−	0.0120331i
$58$	2.18351	+	5.11651i	0.286709	+	0.671830i
$59$	−0.709701	−	0.976819i	−0.0923951	−	0.127171i	0.760317	−	0.649552i	$-0.225044\pi$
$59$	−0.709701	−	0.976819i	−0.0923951	−	0.127171i	−0.852712	+	0.522381i	$0.825044\pi$
$60$	−0.145329	−	0.805964i	−0.0187619	−	0.104050i
$61$	2.29148	−	7.05244i	0.293394	−	0.902973i	−0.690363	−	0.723464i	$-0.742549\pi$
$61$	2.29148	−	7.05244i	0.293394	−	0.902973i	0.983756	−	0.179509i	$-0.0574510\pi$
$62$	0.397234	+	4.44148i	0.0504488	+	0.564069i
$63$	1.74157	+	0.631348i	0.219417	+	0.0795424i
$64$	1.75396	+	7.80536i	0.219245	+	0.975670i
$65$	1.86414			0.231218
$66$	−4.52005	+	5.49231i	−0.556380	+	0.676056i
$67$	7.60314			0.928872			0.464436	−	0.885607i	$-0.346257\pi$
$67$	7.60314			0.928872			0.464436	+	0.885607i	$0.346257\pi$
$68$	−4.87714	−	4.67349i	−0.591440	−	0.566744i
$69$	−3.98047	−	2.89198i	−0.479192	−	0.348154i
$70$	−0.365091	−	0.942025i	−0.0436368	−	0.112594i
$71$	−7.10243	−	2.30772i	−0.842903	−	0.273876i	−0.144433	−	0.989515i	$-0.546136\pi$
$71$	−7.10243	−	2.30772i	−0.842903	−	0.273876i	−0.698471	+	0.715639i	$0.746136\pi$
$72$	0.698968	−	1.85293i	0.0823742	−	0.218370i
$73$	−7.13145	−	9.81560i	−0.834673	−	1.14883i	−0.987035	−	0.160504i	$-0.948688\pi$
$73$	−7.13145	−	9.81560i	−0.834673	−	1.14883i	0.152362	−	0.988325i	$-0.451312\pi$
$74$	4.54746	+	10.6558i	0.528632	+	1.23871i
$75$	−7.10632	+	2.30898i	−0.820568	+	0.266619i
$76$	−0.111001	+	0.0595722i	−0.0127327	+	0.00683340i
$77$	−4.18582	+	7.71226i	−0.477019	+	0.878893i
$78$	−12.7065	−	7.60141i	−1.43872	−	0.860690i
$79$	−9.50920	+	3.08973i	−1.06987	+	0.347621i	−0.790436	−	0.612544i	$-0.790146\pi$
$79$	−9.50920	+	3.08973i	−1.06987	+	0.347621i	−0.279432	+	0.960165i	$0.590146\pi$
$80$	−1.01203	+	0.377239i	−0.113149	+	0.0421766i
$81$	5.18520	−	3.76727i	0.576133	−	0.418585i
$82$	−4.43399	+	3.86949i	−0.489652	+	0.427313i
$83$	−7.87395	−	2.55840i	−0.864278	−	0.280821i	−0.156864	−	0.987620i	$-0.550138\pi$
$83$	−7.87395	−	2.55840i	−0.864278	−	0.280821i	−0.707414	+	0.706799i	$0.750138\pi$
$84$	−1.35275	+	7.90983i	−0.147597	+	0.863033i
$85$	0.536032	−	0.737784i	0.0581408	−	0.0800239i
$86$	9.80830	+	2.24446i	1.05766	+	0.242026i
$87$	5.96537			0.639555
$88$	8.18617	+	4.58111i	0.872649	+	0.488348i
$89$		−	6.36308i		−	0.674485i	−0.941418	−	0.337243i	$-0.890506\pi$
$89$		−	6.36308i		−	0.674485i	0.941418	−	0.337243i	$-0.109494\pi$
$90$	0.260628	+	0.0596401i	0.0274726	+	0.00628662i
$91$	−17.1724	−	6.22527i	−1.80015	−	0.652586i
$92$	−2.82189	+	5.84298i	−0.294203	+	0.609172i
$93$	4.54776	+	1.47766i	0.471580	+	0.153226i
$94$	−0.567946	−	0.650802i	−0.0585792	−	0.0671251i
$95$	−0.00999689	−	0.0137595i	−0.00102566	−	0.00141170i
$96$	8.43654	+	1.55541i	0.861051	+	0.158749i
$97$	13.5188	−	4.39251i	1.37262	−	0.445992i	0.472385	−	0.881392i	$-0.343393\pi$
$97$	13.5188	−	4.39251i	1.37262	−	0.445992i	0.900237	+	0.435400i	$0.143393\pi$
$98$	0.217319	+	9.89711i	0.0219525	+	0.999759i
$99$	−1.06996	−	2.06102i	−0.107535	−	0.207140i
$100$	4.65987	+	8.68277i	0.465987	+	0.868277i
$101$	2.70662	+	8.33012i	0.269319	+	0.828878i	0.990667	+	0.136305i	$0.0435228\pi$
$101$	2.70662	+	8.33012i	0.269319	+	0.828878i	−0.721348	+	0.692573i	$0.756477\pi$
$102$	−6.66220	+	2.84315i	−0.659656	+	0.281514i
$103$	0.506106	−	0.367708i	0.0498681	−	0.0362313i	−0.562572	−	0.826748i	$-0.690188\pi$
$103$	0.506106	−	0.367708i	0.0498681	−	0.0362313i	0.612440	+	0.790517i	$0.290188\pi$
$104$	−6.89202	+	18.2704i	−0.675819	+	1.79156i
$105$	−1.08277	−	0.0364196i	−0.105668	−	0.00355419i
$106$	−17.3769	+	1.55414i	−1.68779	+	0.150951i
$107$	6.95435	+	5.05263i	0.672302	+	0.488456i	0.870795	−	0.491646i	$-0.163605\pi$
$107$	6.95435	+	5.05263i	0.672302	+	0.488456i	−0.198493	+	0.980102i	$0.563605\pi$
$108$	−8.10306	−	7.76471i	−0.779717	−	0.747159i
$109$			11.4190i			1.09375i	0.837215	+	0.546873i	$0.184182\pi$
$109$			11.4190i			1.09375i	−0.837215	+	0.546873i	$0.815818\pi$
$110$	−0.463211	+	1.17873i	−0.0441655	+	0.112387i
$111$	12.4237			1.17921
$112$	10.5826	−	0.0954318i	0.999959	−	0.00901746i
$113$	−6.33099	−	4.59973i	−0.595569	−	0.432706i	0.248734	−	0.968572i	$-0.419985\pi$
$113$	−6.33099	−	4.59973i	−0.595569	−	0.432706i	−0.844303	+	0.535865i	$0.819985\pi$
$114$	0.0120340	+	0.134553i	0.00112709	+	0.0126020i
$115$	−0.833146	−	0.270705i	−0.0776913	−	0.0252434i
$116$	−1.39607	−	7.74233i	−0.129622	−	0.718857i
$117$	3.91069	−	2.84128i	0.361543	−	0.262676i
$118$	0.670228	+	1.57051i	0.0616995	+	0.144577i
$119$	−7.40172	+	5.00636i	−0.678514	+	0.458932i
$120$	−0.0539051	+	1.15693i	−0.00492084	+	0.105613i
$121$	10.4087	−	3.55786i	0.946248	−	0.323441i
$122$	−5.38378	+	8.99948i	−0.487424	+	0.814774i
$123$	1.95012	+	6.00186i	0.175837	+	0.541169i
$124$	0.853509	−	6.24825i	0.0766474	−	0.561110i
$125$	−2.16853	+	1.57553i	−0.193959	+	0.140920i
$126$	−2.20172	−	1.41977i	−0.196145	−	0.126483i
$127$	10.0620	+	3.26935i	0.892859	+	0.290108i	0.719287	−	0.694713i	$-0.244469\pi$
$127$	10.0620	+	3.26935i	0.892859	+	0.290108i	0.173573	+	0.984821i	$0.444469\pi$
$128$	0.0443396	−	11.3136i	0.00391910	−	0.999992i
$129$	6.34203	−	8.72906i	0.558385	−	0.768551i
$130$	−2.56986	−	0.588069i	−0.225392	−	0.0515770i
$131$			18.9540i			1.65602i	0.560714	+	0.828009i	$0.310527\pi$
$131$			18.9540i			1.65602i	−0.560714	+	0.828009i	$0.689473\pi$
$132$	7.96387	−	6.14567i	0.693166	−	0.534912i
$133$	0.0461410	+	0.160137i	0.00400093	+	0.0138856i
$134$	−10.4815	−	2.39852i	−0.905467	−	0.207200i
$135$	0.890582	−	1.22578i	0.0766491	−	0.105498i
$136$	5.24921	+	7.98134i	0.450116	+	0.684394i
$137$	−1.45708	+	4.48444i	−0.124487	+	0.383132i	−0.993807	−	0.111117i	$-0.964557\pi$
$137$	−1.45708	+	4.48444i	−0.124487	+	0.383132i	0.869320	+	0.494249i	$0.164557\pi$
$138$	4.57508	+	5.24252i	0.389457	+	0.446273i
$139$	6.72472	+	9.25579i	0.570384	+	0.785066i	0.992600	−	0.121429i	$-0.0387478\pi$
$139$	6.72472	+	9.25579i	0.570384	+	0.785066i	−0.422216	+	0.906495i	$0.638748\pi$
$140$	0.206132	+	1.41383i	0.0174214	+	0.119490i
$141$	−0.880927	+	0.286230i	−0.0741874	+	0.0241049i
$142$	9.06326	+	5.42193i	0.760572	+	0.454999i
$143$	10.5501	+	20.3222i	0.882241	+	1.69943i
$144$	−1.54811	+	2.33391i	−0.129010	+	0.194492i
$145$	1.01014	−	0.328215i	0.0838876	−	0.0272567i
$146$	6.73480	+	15.7813i	0.557376	+	1.30607i
$147$	9.85282	+	3.95140i	0.812647	+	0.325906i
$148$	−2.90751	−	16.1245i	−0.238996	−	1.32542i
$149$	−11.0892	−	3.60311i	−0.908466	−	0.295178i	−0.182739	−	0.983161i	$-0.558496\pi$
$149$	−11.0892	−	3.60311i	−0.908466	−	0.295178i	−0.725727	+	0.687983i	$0.758496\pi$
$150$	10.5250	−	0.941330i	0.859366	−	0.0768593i
$151$	4.45382	−	6.13015i	0.362446	−	0.498865i	−0.588382	−	0.808583i	$-0.700235\pi$
$151$	4.45382	−	6.13015i	0.362446	−	0.498865i	0.950828	+	0.309719i	$0.100235\pi$
$152$	0.171817	−	0.0471081i	0.0139362	−	0.00382097i
$153$		−	2.36477i		−	0.191180i
$154$	8.20343	−	9.31149i	0.661051	−	0.750341i
$155$	0.851391			0.0683853
$156$	15.1189	+	14.4876i	1.21048	+	1.15993i
$157$	−6.43336	−	4.67411i	−0.513438	−	0.373034i	0.300688	−	0.953722i	$-0.402784\pi$
$157$	−6.43336	−	4.67411i	−0.513438	−	0.373034i	−0.814126	+	0.580688i	$0.802784\pi$
$158$	14.0839	−	1.25962i	1.12045	−	0.100210i
$159$	−5.78119	+	17.7927i	−0.458478	+	1.41105i
$160$	1.51417	−	0.200794i	0.119706	−	0.0158741i
$161$	6.77088	+	5.27601i	0.533620	+	0.415808i
$162$	−8.33664	+	3.55773i	−0.654989	+	0.279522i
$163$	0.953361	+	2.93414i	0.0746730	+	0.229820i	0.981426	−	0.191843i	$-0.0614465\pi$
$163$	0.953361	+	2.93414i	0.0746730	+	0.229820i	−0.906753	+	0.421663i	$0.861446\pi$
$164$	7.33330	−	3.93563i	0.572634	−	0.307321i
$165$	0.967591	+	0.952990i	0.0753269	+	0.0741901i
$166$	10.0478	+	6.01091i	0.779859	+	0.466537i
$167$	−4.35966	−	13.4177i	−0.337361	−	1.03829i	−0.965547	−	0.260227i	$-0.916203\pi$
$167$	−4.35966	−	13.4177i	−0.337361	−	1.03829i	0.628187	−	0.778063i	$-0.283797\pi$
$168$	4.36013	−	10.4776i	0.336392	−	0.808363i
$169$	−28.0433	+	20.3746i	−2.15717	+	1.56728i
$170$	−0.971707	+	0.847996i	−0.0745265	+	0.0650383i
$171$	−0.0419440	−	0.0136284i	−0.00320754	−	0.00104219i
$172$	−12.8135	−	6.18833i	−0.977019	−	0.471856i
$173$	−5.07769	−	3.68916i	−0.386050	−	0.280482i	0.377785	−	0.925893i	$-0.376686\pi$
$173$	−5.07769	−	3.68916i	−0.386050	−	0.280482i	−0.763835	+	0.645412i	$0.776686\pi$
$174$	−8.22375	−	1.88186i	−0.623441	−	0.142664i
$175$	12.5263	−	3.60925i	0.946896	−	0.272834i
$176$	−9.84012	−	8.89787i	−0.741727	−	0.670702i
$177$	1.83107			0.137631
$178$	−2.00732	+	8.77202i	−0.150455	+	0.657490i
$179$	−10.3540	−	7.52262i	−0.773894	−	0.562267i	0.129246	−	0.991613i	$-0.458744\pi$
$179$	−10.3540	−	7.52262i	−0.773894	−	0.562267i	−0.903140	+	0.429345i	$0.858744\pi$
$180$	−0.340482	−	0.164437i	−0.0253780	−	0.0122564i
$181$	−6.20519	+	19.0976i	−0.461228	+	1.41951i	0.402436	+	0.915448i	$0.368163\pi$
$181$	−6.20519	+	19.0976i	−0.461228	+	1.41951i	−0.863665	+	0.504067i	$0.831837\pi$
$182$	21.7096	+	13.9993i	1.60922	+	1.03770i
$183$	6.60998	+	9.09785i	0.488624	+	0.672533i
$184$	5.73345	−	7.16480i	0.422676	−	0.528196i
$185$	2.10376	−	0.683552i	0.154671	−	0.0502557i
$186$	−5.80330	−	3.47172i	−0.425519	−	0.254559i
$187$	11.0767	+	1.66816i	0.810012	+	0.121988i
$188$	0.577655	+	1.07635i	0.0421298	+	0.0785008i
$189$	−12.2975	+	8.31775i	−0.894510	+	0.605027i
$190$	0.00944087	+	0.0221223i	0.000684913	+	0.00160492i
$191$	−4.03868	−	5.55877i	−0.292229	−	0.402218i	0.637508	−	0.770444i	$-0.279965\pi$
$191$	−4.03868	−	5.55877i	−0.292229	−	0.402218i	−0.929736	+	0.368226i	$0.879965\pi$
$192$	−11.1398	−	4.80569i	−0.803944	−	0.346821i
$193$	−4.06283	+	12.5041i	−0.292449	+	0.900066i	0.691617	+	0.722264i	$0.256899\pi$
$193$	−4.06283	+	12.5041i	−0.292449	+	0.900066i	−0.984066	+	0.177802i	$0.943101\pi$
$194$	−20.0224	+	1.79075i	−1.43752	+	0.128568i
$195$	−1.66167	+	2.28709i	−0.118995	+	0.163782i
$196$	2.82259	−	13.7125i	0.201614	−	0.979465i
$197$		−	17.0577i		−	1.21531i	−0.794200	−	0.607657i	$-0.792110\pi$
$197$		−	17.0577i		−	1.21531i	0.794200	−	0.607657i	$-0.207890\pi$
$198$	0.824842	+	3.17881i	0.0586190	+	0.225908i
$199$	−4.45836			−0.316044			−0.158022	−	0.987436i	$-0.550512\pi$
$199$	−4.45836			−0.316044			−0.158022	+	0.987436i	$0.550512\pi$
$200$	−3.68490	−	13.4399i	−0.260562	−	0.950346i
$201$	−6.77735	+	9.32822i	−0.478037	+	0.657962i
$202$	−1.10344	−	12.3376i	−0.0776377	−	0.868069i
$203$	−10.4014	−	0.349857i	−0.730038	−	0.0245552i
$204$	10.0813	−	1.81783i	0.705831	−	0.127273i
$205$	0.660444	+	0.909023i	0.0461274	+	0.0634889i
$206$	−0.813707	+	0.347256i	−0.0566936	+	0.0241945i
$207$	−2.16042	+	0.701963i	−0.150160	+	0.0487898i
$208$	15.2649	−	23.0130i	1.05843	−	1.59566i
$209$	0.0934247	−	0.186855i	0.00646232	−	0.0129250i
$210$	1.48120	+	0.391783i	0.102212	+	0.0270356i
$211$	−0.0411581	−	0.126672i	−0.00283344	−	0.00872044i	0.949630	−	0.313374i	$-0.101459\pi$
$211$	−0.0411581	−	0.126672i	−0.00283344	−	0.00872044i	−0.952463	+	0.304654i	$0.901459\pi$
$212$	24.4457	+	3.33927i	1.67894	+	0.229342i
$213$	9.16233	−	6.65682i	0.627793	−	0.456118i
$214$	−7.99320	−	9.15930i	−0.546404	−	0.626117i
$215$	0.593650	−	1.82707i	0.0404866	−	0.124605i
$216$	8.72123	+	13.2605i	0.593405	+	0.902262i
$217$	−7.84297	−	2.84321i	−0.532415	−	0.193010i
$218$	3.60230	−	15.7421i	0.243978	−	1.06619i
$219$	18.3995			1.24333
$220$	1.01042	−	1.47884i	0.0681225	−	0.0997036i
$221$			23.3173i			1.56849i
$222$	−17.1271	−	3.91923i	−1.14949	−	0.263042i
$223$	−7.67963	−	5.57958i	−0.514266	−	0.373636i	0.300174	−	0.953885i	$-0.402955\pi$
$223$	−7.67963	−	5.57958i	−0.514266	−	0.373636i	−0.814439	+	0.580249i	$0.802955\pi$
$224$	−14.6190	−	3.20686i	−0.976775	−	0.214267i
$225$	−1.06605	+	3.28095i	−0.0710698	+	0.218730i
$226$	7.27672	+	8.33830i	0.484040	+	0.554655i
$227$	6.66401	+	9.17223i	0.442306	+	0.608782i	0.970723	−	0.240203i	$-0.0772140\pi$
$227$	6.66401	+	9.17223i	0.442306	+	0.608782i	−0.528417	+	0.848985i	$0.677214\pi$
$228$	0.0258567	−	0.189288i	0.00171240	−	0.0125359i
$229$	−4.37810	−	13.4744i	−0.289313	−	0.890414i	−0.985073	−	0.172139i	$-0.944932\pi$
$229$	−4.37810	−	13.4744i	−0.289313	−	0.890414i	0.695760	−	0.718275i	$-0.255068\pi$
$230$	1.06316	+	0.636017i	0.0701027	+	0.0419377i
$231$	−5.73090	−	12.0102i	−0.377066	−	0.790210i
$232$	−0.517829	+	11.1138i	−0.0339971	+	0.729659i
$233$	6.00356	+	18.4771i	0.393307	+	1.21047i	0.930272	+	0.366869i	$0.119570\pi$
$233$	6.00356	+	18.4771i	0.393307	+	1.21047i	−0.536966	+	0.843604i	$0.680430\pi$
$234$	−6.28752	+	2.68325i	−0.411028	+	0.175410i
$235$	−0.133422	+	0.0969371i	−0.00870352	+	0.00632348i
$236$	−0.428524	−	2.37650i	−0.0278945	−	0.154697i
$237$	4.68563	−	14.4209i	0.304364	−	0.936737i
$238$	11.7832	−	4.56669i	0.763790	−	0.296015i
$239$	−4.72648	+	6.50545i	−0.305731	+	0.420802i	−0.934044	−	0.357158i	$-0.883746\pi$
$239$	−4.72648	+	6.50545i	−0.305731	+	0.420802i	0.628313	+	0.777961i	$0.283746\pi$
$240$	0.439283	−	1.57792i	0.0283556	−	0.101854i
$241$			25.4494i			1.63934i	0.572836	+	0.819670i	$0.305843\pi$
$241$			25.4494i			1.63934i	−0.572836	+	0.819670i	$0.694157\pi$
$242$	−15.4716	+	1.62121i	−0.994555	+	0.104215i
$243$		−	7.11437i		−	0.456387i
$244$	10.2610	−	10.7081i	0.656892	−	0.685517i
$245$	1.88582	+	0.127005i	0.120481	+	0.00811405i
$246$	−0.795029	−	8.88923i	−0.0506892	−	0.566757i
$247$	0.413580	+	0.134380i	0.0263154	+	0.00855040i
$248$	−3.14773	+	8.34446i	−0.199881	+	0.529874i
$249$	10.1576	−	7.37994i	0.643713	−	0.467685i
$250$	3.48652	−	1.48790i	0.220507	−	0.0941031i
$251$	23.7962	−	7.73187i	1.50201	−	0.488031i	0.561403	−	0.827542i	$-0.310262\pi$
$251$	23.7962	−	7.73187i	1.50201	−	0.488031i	0.940602	+	0.339511i	$0.110262\pi$
$252$	2.58737	+	2.65182i	0.162989	+	0.167049i
$253$	−1.76403	−	10.6147i	−0.110904	−	0.667343i
$254$	−12.8399	−	7.68126i	−0.805649	−	0.481965i
$255$	0.427368	+	1.31530i	0.0267628	+	0.0823675i
$256$	−3.63017	+	15.5827i	−0.226885	+	0.973921i
$257$	−17.9782	−	24.7448i	−1.12145	−	1.54354i	−0.803375	−	0.595473i	$-0.796965\pi$
$257$	−17.9782	−	24.7448i	−1.12145	−	1.54354i	−0.318072	−	0.948067i	$-0.603035\pi$
$258$	−11.4967	+	10.0330i	−0.715754	+	0.624629i
$259$	−21.6624	−	0.728626i	−1.34604	−	0.0452746i
$260$	3.35725	+	1.62140i	0.208208	+	0.100555i
$261$	1.61887	−	2.22818i	0.100205	−	0.137921i
$262$	5.97931	−	26.1296i	0.369403	−	1.61429i
$263$		−	17.4129i		−	1.07373i	−0.843669	−	0.536864i	$-0.819609\pi$
$263$		−	17.4129i		−	1.07373i	0.843669	−	0.536864i	$-0.180391\pi$
$264$	−12.9176	+	5.95998i	−0.795022	+	0.366812i
$265$			3.33098i			0.204621i
$266$	−0.0130917	−	0.235317i	−0.000802705	−	0.0144282i
$267$	7.80680	+	5.67197i	0.477768	+	0.347119i
$268$	13.6930	+	6.61310i	0.836433	+	0.403959i
$269$	−4.70769	+	14.4888i	−0.287033	+	0.883397i	0.698749	+	0.715367i	$0.253741\pi$
$269$	−4.70769	+	14.4888i	−0.287033	+	0.883397i	−0.985782	+	0.168030i	$0.946259\pi$
$270$	−1.61443	+	1.40889i	−0.0982510	+	0.0857424i
$271$	−3.05407	+	2.21892i	−0.185522	+	0.134790i	−0.676670	−	0.736287i	$-0.736577\pi$
$271$	−3.05407	+	2.21892i	−0.185522	+	0.134790i	0.491148	+	0.871076i	$0.336577\pi$
$272$	−4.71863	−	12.6589i	−0.286109	−	0.767556i
$273$	22.9449	−	15.5195i	1.38869	−	0.939280i
$274$	3.42339	−	5.72251i	0.206814	−	0.345709i
$275$	−14.6162	−	7.30790i	−0.881390	−	0.440683i
$276$	−4.65329	−	8.67051i	−0.280095	−	0.521903i
$277$	21.4668	−	6.97498i	1.28981	−	0.419086i	0.417788	−	0.908545i	$-0.362806\pi$
$277$	21.4668	−	6.97498i	1.28981	−	0.419086i	0.872027	+	0.489459i	$0.162806\pi$
$278$	−6.35070	−	14.8813i	−0.380890	−	0.892518i
$279$	1.78609	−	1.29767i	0.106930	−	0.0776895i
$280$	0.161843	−	2.01411i	0.00967195	−	0.120366i
$281$	6.60588	−	20.3308i	0.394074	−	1.21283i	−0.535607	−	0.844468i	$-0.679917\pi$
$281$	6.60588	−	20.3308i	0.394074	−	1.21283i	0.929680	−	0.368367i	$-0.120083\pi$
$282$	1.30472	−	0.116691i	0.0776951	−	0.00694884i
$283$	−16.6529	+	22.9207i	−0.989911	+	1.36250i	−0.0585952	+	0.998282i	$0.518662\pi$
$283$	−16.6529	+	22.9207i	−0.989911	+	1.36250i	−0.931316	+	0.364213i	$0.881338\pi$
$284$	−10.7840	−	10.3337i	−0.639913	−	0.613192i
$285$	0.0257925			0.00152782
$286$	−8.13318	−	31.3440i	−0.480925	−	1.85341i
$287$	−3.04830	−	10.5794i	−0.179936	−	0.624483i
$288$	2.87046	−	2.72910i	0.169144	−	0.160814i
$289$	−4.52483	−	3.28748i	−0.266166	−	0.193381i
$290$	−1.49610	+	0.133807i	−0.0878540	+	0.00785742i
$291$	−6.66133	+	20.5015i	−0.390494	+	1.20182i
$292$	−4.30603	−	23.8804i	−0.251992	−	1.39749i
$293$	−25.5031	+	18.5291i	−1.48991	+	1.08248i	−0.515717	+	0.856759i	$0.672474\pi$
$293$	−25.5031	+	18.5291i	−1.48991	+	1.08248i	−0.974192	+	0.225723i	$0.927526\pi$
$294$	−12.3364	−	8.55554i	−0.719472	−	0.498969i
$295$	0.310062	−	0.100745i	0.0180525	−	0.00586562i
$296$	−1.07845	+	23.1461i	−0.0626836	+	1.34534i
$297$	18.4033	+	2.77155i	1.06787	+	0.160821i
$298$	14.1507	+	8.46543i	0.819731	+	0.490389i
$299$	21.3024	−	6.92156i	1.23195	−	0.400284i
$300$	−14.8066	−	2.02257i	−0.854857	−	0.116773i
$301$	−11.5701	+	14.8483i	−0.666892	+	0.855845i
$302$	−8.07378	+	7.04588i	−0.464594	+	0.405445i
$303$	−12.6328	−	4.10464i	−0.725735	−	0.235805i
$304$	−0.251724	+	0.0107401i	−0.0144374	+	0.000615989i
$305$	1.61986	+	1.17690i	0.0927527	+	0.0673888i
$306$	−0.746000	+	3.26002i	−0.0426460	+	0.186363i
$307$			4.09109i			0.233491i	0.993162	+	0.116746i	$0.0372462\pi$
$307$			4.09109i			0.233491i	−0.993162	+	0.116746i	$0.962754\pi$
$308$	−14.2465	+	10.2487i	−0.811771	+	0.583976i
$309$			0.948707i			0.0539701i
$310$	−1.17371	−	0.268583i	−0.0666622	−	0.0152545i
$311$	−19.7077	−	14.3185i	−1.11752	−	0.811928i	−0.133691	−	0.991023i	$-0.542683\pi$
$311$	−19.7077	−	14.3185i	−1.11752	−	0.811928i	−0.983832	+	0.179095i	$0.942683\pi$
$312$	−16.2723	−	24.7418i	−0.921237	−	1.40073i
$313$	25.0321	+	8.13341i	1.41490	+	0.459728i	0.913977	−	0.405766i	$-0.132995\pi$
$313$	25.0321	+	8.13341i	1.41490	+	0.459728i	0.500919	+	0.865494i	$0.332995\pi$
$314$	7.39438	+	8.47312i	0.417289	+	0.478166i
$315$	−0.307443	+	0.394553i	−0.0173225	+	0.0222305i
$316$	−19.8131	−	2.70647i	−1.11458	−	0.152251i
$317$	−8.51045	+	2.76521i	−0.477994	+	0.155310i	−0.538098	−	0.842882i	$-0.680857\pi$
$317$	−8.51045	+	2.76521i	−0.477994	+	0.155310i	0.0601035	+	0.998192i	$0.480857\pi$
$318$	13.5828	−	22.7048i	0.761684	−	1.27322i
$319$	9.29497	+	9.15470i	0.520418	+	0.512565i
$320$	−2.15075	−	0.200857i	−0.120231	−	0.0112282i
$321$	−12.3980	+	4.02837i	−0.691991	+	0.224842i
$322$	−7.66981	−	9.40937i	−0.427422	−	0.524363i
$323$	0.172109	−	0.125045i	0.00957641	−	0.00695767i
$324$	12.6151	−	2.27471i	0.700837	−	0.126373i
$325$	10.5115	−	32.3511i	0.583074	−	1.79452i
$326$	−0.388668	−	4.34570i	−0.0215263	−	0.240686i
$327$	−14.0099	−	10.1788i	−0.774750	−	0.562889i
$328$	−11.3511	+	3.11219i	−0.626759	+	0.171842i
$329$	1.55280	−	0.447417i	0.0856087	−	0.0246669i
$330$	−1.03327	−	1.61901i	−0.0568795	−	0.0891237i
$331$	6.16504			0.338861			0.169431	−	0.985542i	$-0.445807\pi$
$331$	6.16504			0.338861			0.169431	+	0.985542i	$0.445807\pi$
$332$	−11.9555	−	11.4562i	−0.656141	−	0.628743i
$333$	3.37151	−	4.64049i	0.184758	−	0.254297i
$334$	1.77735	+	19.8726i	0.0972525	+	1.08738i
$335$	−0.634397	+	1.95247i	−0.0346608	+	0.106675i
$336$	−9.31609	+	13.0687i	−0.508235	+	0.712957i
$337$	5.63501	−	4.09407i	0.306958	−	0.223018i	−0.423632	−	0.905834i	$-0.639245\pi$
$337$	5.63501	−	4.09407i	0.306958	−	0.223018i	0.730590	+	0.682816i	$0.239245\pi$
$338$	45.0873	−	19.2414i	2.45243	−	1.04659i
$339$	11.2867	−	3.66728i	0.613011	−	0.199179i
$340$	1.60709	−	0.862491i	0.0871565	−	0.0467752i
$341$	4.81843	+	9.28158i	0.260933	+	0.502626i
$342$	0.0535238	+	0.0320197i	0.00289424	+	0.00173143i
$343$	−16.9480	−	7.46765i	−0.915105	−	0.403215i
$344$	15.7122	+	12.5733i	0.847146	+	0.677907i
$345$	1.07478	−	0.780875i	0.0578643	−	0.0420409i
$346$	5.83621	+	6.68763i	0.313757	+	0.359529i
$347$	−2.83827	+	8.73529i	−0.152366	+	0.468935i	−0.997885	−	0.0650113i	$-0.979292\pi$
$347$	−2.83827	+	8.73529i	−0.152366	+	0.468935i	0.845518	+	0.533947i	$0.179292\pi$
$348$	10.7434	+	5.18859i	0.575908	+	0.278138i
$349$	0.718241	+	0.521833i	0.0384466	+	0.0279331i	0.606843	−	0.794822i	$-0.292436\pi$
$349$	0.718241	+	0.521833i	0.0384466	+	0.0279331i	−0.568396	+	0.822755i	$0.692436\pi$
$350$	−18.4070	+	1.02406i	−0.983897	+	0.0547385i
$351$			38.7402i			2.06780i
$352$	10.7584	+	15.3706i	0.573426	+	0.819257i
$353$			11.6057i			0.617708i	0.951110	+	0.308854i	$0.0999454\pi$
$353$			11.6057i			0.617708i	−0.951110	+	0.308854i	$0.900055\pi$
$354$	−2.52427	−	0.577636i	−0.134164	−	0.0307010i
$355$	1.18524	−	1.63134i	0.0629058	−	0.0865824i
$356$	5.53451	−	11.4597i	0.293328	−	0.607362i
$357$	0.455549	−	13.5437i	0.0241102	−	0.716809i
$358$	11.9007	+	13.6368i	0.628972	+	0.720730i
$359$	1.49820	+	2.06209i	0.0790718	+	0.108833i	0.846721	−	0.532038i	$-0.178574\pi$
$359$	1.49820	+	2.06209i	0.0790718	+	0.108833i	−0.767649	+	0.640871i	$0.778574\pi$
$360$	0.417507	+	0.334100i	0.0220046	+	0.0176086i
$361$	5.87010	+	18.0663i	0.308952	+	0.950858i
$362$	14.5790	−	24.3701i	0.766253	−	1.28086i
$363$	−4.91312	+	15.9418i	−0.257872	+	0.836727i
$364$	−25.5122	−	26.1477i	−1.33720	−	1.37051i
$365$	3.11567	−	1.01234i	0.163082	−	0.0529884i
$366$	−6.24234	−	14.6273i	−0.326292	−	0.764583i
$367$	−15.8256	+	11.4980i	−0.826089	+	0.600189i	−0.918450	−	0.395537i	$-0.870559\pi$
$367$	−15.8256	+	11.4980i	−0.826089	+	0.600189i	0.0923609	+	0.995726i	$0.470559\pi$
$368$	−10.1643	+	8.06856i	−0.529849	+	0.420603i
$369$	2.77103	+	0.900361i	0.144254	+	0.0468709i
$370$	−3.11583	+	0.278671i	−0.161984	+	0.0144874i
$371$	11.1238	−	30.6848i	0.577518	−	1.59308i
$372$	6.90511	+	6.61678i	0.358013	+	0.343064i
$373$		−	0.194032i		−	0.0100466i	−0.999987	−	0.00502331i	$-0.998401\pi$
$373$		−	0.194032i		−	0.0100466i	0.999987	−	0.00502331i	$-0.00159898\pi$
$374$	−14.7439	−	5.79401i	−0.762391	−	0.299601i
$375$		−	4.06496i		−	0.209913i
$376$	−0.456794	−	1.66606i	−0.0235574	−	0.0859206i
$377$	−15.9625	+	21.9705i	−0.822111	+	1.13154i
$378$	19.5770	−	7.58726i	1.00693	−	0.390247i
$379$	8.52362	−	26.2330i	0.437829	−	1.34750i	−0.452331	−	0.891850i	$-0.649407\pi$
$379$	8.52362	−	26.2330i	0.437829	−	1.34750i	0.890160	−	0.455649i	$-0.150593\pi$
$380$	−0.00603621	−	0.0334756i	−0.000309651	−	0.00171726i
$381$	−12.9803	+	9.43073i	−0.665000	+	0.483151i
$382$	3.81405	+	8.93726i	0.195144	+	0.457270i
$383$	6.14397	+	18.9092i	0.313942	+	0.966215i	0.976188	+	0.216928i	$0.0696036\pi$
$383$	6.14397	+	18.9092i	0.313942	+	0.966215i	−0.662245	+	0.749287i	$0.730396\pi$
$384$	13.8410	+	10.1392i	0.706323	+	0.517415i
$385$	−1.63123	−	1.71841i	−0.0831354	−	0.0875784i
$386$	9.54554	−	15.9562i	0.485855	−	0.812152i
$387$	−1.53939	−	4.73774i	−0.0782514	−	0.240833i
$388$	28.1673	+	3.84765i	1.42998	+	0.195335i
$389$	6.60110	+	9.08564i	0.334689	+	0.460660i	0.942881	−	0.333130i	$-0.108105\pi$
$389$	6.60110	+	9.08564i	0.334689	+	0.460660i	−0.608192	+	0.793790i	$0.708105\pi$
$390$	3.01224	−	2.62874i	0.152531	−	0.133112i
$391$	3.38608	−	10.4213i	0.171241	−	0.527027i
$392$	−8.21697	+	18.0134i	−0.415020	+	0.909812i
$393$	−23.2545	−	16.8954i	−1.17303	−	0.852258i
$394$	−5.38110	+	23.5154i	−0.271096	+	1.18469i
$395$		−	2.69975i		−	0.135839i
$396$	−0.134309	−	4.64245i	−0.00674931	−	0.233292i
$397$	23.4894			1.17890			0.589450	−	0.807805i	$-0.299345\pi$
$397$	23.4894			1.17890			0.589450	+	0.807805i	$0.299345\pi$
$398$	6.14620	+	1.40645i	0.308081	+	0.0704990i
$399$	−0.237600	−	0.0861339i	−0.0118949	−	0.00431209i
$400$	0.840118	+	19.6905i	0.0420059	+	0.984523i
$401$	2.40972	−	7.41635i	0.120336	−	0.370355i	−0.872687	−	0.488280i	$-0.837624\pi$
$401$	2.40972	−	7.41635i	0.120336	−	0.370355i	0.993022	+	0.117925i	$0.0376243\pi$
$402$	12.2858	−	10.7217i	0.612761	−	0.534749i
$403$	−17.6114	+	12.7954i	−0.877285	+	0.637385i
$404$	−2.37088	+	17.3564i	−0.117956	+	0.863515i
$405$	0.534781	+	1.64589i	0.0265735	+	0.0817847i
$406$	14.2288	+	3.76358i	0.706166	+	0.186784i
$407$	19.3580	+	19.0659i	0.959543	+	0.945063i
$408$	−14.4713	−	0.674265i	−0.716437	−	0.0333811i
$409$	−11.8275	+	3.84300i	−0.584834	+	0.190024i	−0.586465	−	0.809974i	$-0.699481\pi$
$409$	−11.8275	+	3.84300i	−0.584834	+	0.190024i	0.00163074	+	0.999999i	$0.499481\pi$
$410$	−0.623711	−	1.46151i	−0.0308029	−	0.0721787i
$411$	−4.20309	−	5.78506i	−0.207323	−	0.285356i
$412$	1.23131	−	0.222025i	0.0606621	−	0.0109384i
$413$	−3.19271	−	0.107389i	−0.157103	−	0.00528424i
$414$	3.19976	−	0.286177i	0.157259	−	0.0140648i
$415$	1.31399	−	1.80855i	0.0645011	−	0.0887781i
$416$	−28.3036	+	26.9098i	−1.38770	+	1.31936i
$417$	−17.3502			−0.849642
$418$	−0.187739	+	0.228122i	−0.00918263	+	0.0111578i
$419$		−	34.5803i		−	1.68936i	−0.535272	−	0.844680i	$-0.679791\pi$
$419$		−	34.5803i		−	1.68936i	0.535272	−	0.844680i	$-0.320209\pi$
$420$	−1.91836	−	1.00737i	−0.0936063	−	0.0491546i
$421$	21.8061	−	30.0135i	1.06276	−	1.46277i	0.185573	−	0.982631i	$-0.440586\pi$
$421$	21.8061	−	30.0135i	1.06276	−	1.46277i	0.877192	−	0.480140i	$-0.159414\pi$
$422$	0.0167794	+	0.187611i	0.000816809	+	0.00913276i
$423$	−0.132151	+	0.406719i	−0.00642541	+	0.0197754i
$424$	−32.6469	−	12.3152i	−1.58547	−	0.598078i
$425$	−9.78127	−	13.4628i	−0.474461	−	0.653040i
$426$	−14.7310	+	6.28658i	−0.713719	+	0.304586i
$427$	−10.9918	−	16.2510i	−0.531931	−	0.786441i
$428$	8.12984	+	15.1484i	0.392970	+	0.732225i
$429$	−34.3373	−	5.17122i	−1.65782	−	0.249669i
$430$	−1.39477	+	2.33148i	−0.0672616	+	0.112434i
$431$	25.2643	−	8.20888i	1.21694	−	0.395408i	0.370973	−	0.928643i	$-0.379024\pi$
$431$	25.2643	−	8.20888i	1.21694	−	0.395408i	0.845967	+	0.533236i	$0.179024\pi$
$432$	−7.83971	−	21.0319i	−0.377188	−	1.01190i
$433$	10.9566	+	15.0804i	0.526539	+	0.724719i	0.986598	−	0.163169i	$-0.0521717\pi$
$433$	10.9566	+	15.0804i	0.526539	+	0.724719i	−0.460059	+	0.887888i	$0.652172\pi$
$434$	9.91523	+	6.39377i	0.475946	+	0.306911i
$435$	−0.497744	+	1.53190i	−0.0238650	+	0.0734489i
$436$	−9.93211	+	20.5653i	−0.475662	+	0.984899i
$437$	−0.165328	−	0.120118i	−0.00790872	−	0.00574602i
$438$	−25.3652	−	5.80439i	−1.21200	−	0.277345i
$439$	−16.2986			−0.777889			−0.388945	−	0.921261i	$-0.627160\pi$
$439$	−16.2986			−0.777889			−0.388945	+	0.921261i	$0.627160\pi$
$440$	−1.85947	+	1.71995i	−0.0886466	+	0.0819955i
$441$	4.14976	−	2.60790i	0.197608	−	0.124185i
$442$	7.35577	−	32.1448i	0.349878	−	1.52897i
$443$	0.100487	+	0.0730078i	0.00477426	+	0.00346870i	0.590170	−	0.807279i	$-0.299061\pi$
$443$	0.100487	+	0.0730078i	0.00477426	+	0.00346870i	−0.585396	+	0.810748i	$0.699061\pi$
$444$	22.3747	+	10.8060i	1.06185	+	0.512828i
$445$	1.63403	+	0.530928i	0.0774604	+	0.0251684i
$446$	8.82683	+	10.1145i	0.417962	+	0.478937i
$447$	14.3054	−	10.3935i	0.676624	−	0.491596i
$448$	19.1419	+	9.03269i	0.904367	+	0.426755i
$449$	7.89960	+	24.3125i	0.372805	+	1.14738i	0.944947	+	0.327222i	$0.106113\pi$
$449$	7.89960	+	24.3125i	0.372805	+	1.14738i	−0.572142	+	0.820155i	$0.693887\pi$
$450$	2.50465	−	4.18676i	0.118070	−	0.197366i
$451$	−6.17210	+	12.3445i	−0.290633	+	0.581282i
$452$	−7.40111	−	13.7905i	−0.348119	−	0.648653i
$453$	3.55094	+	10.9287i	0.166838	+	0.513474i
$454$	−6.29337	−	14.7469i	−0.295362	−	0.692107i
$455$	3.03148	−	3.89040i	0.142118	−	0.182385i
$456$	−0.0953592	+	0.252792i	−0.00446560	+	0.0118381i
$457$	10.2107	−	31.4254i	0.477638	−	1.47002i	−0.364729	−	0.931114i	$-0.618838\pi$
$457$	10.2107	−	31.4254i	0.477638	−	1.47002i	0.842367	−	0.538905i	$-0.181162\pi$
$458$	1.78487	+	19.9567i	0.0834015	+	0.932515i
$459$	15.3325	+	11.1397i	0.715660	+	0.519957i
$460$	−1.26501	−	1.21219i	−0.0589814	−	0.0565186i
$461$	37.4098			1.74235			0.871174	−	0.490974i	$-0.163359\pi$
$461$	37.4098			1.74235			0.871174	+	0.490974i	$0.163359\pi$
$462$	4.11173	+	18.3648i	0.191295	+	0.854410i
$463$		−	7.02019i		−	0.326256i	−0.986605	−	0.163128i	$-0.947842\pi$
$463$		−	7.02019i		−	0.326256i	0.986605	−	0.163128i	$-0.0521583\pi$
$464$	4.21988	−	15.1580i	0.195903	−	0.703690i
$465$	−0.758919	+	1.04456i	−0.0351940	+	0.0484404i
$466$	−2.44754	−	27.3660i	−0.113380	−	1.26771i
$467$	26.0139	+	8.45242i	1.20378	+	0.391131i	0.841150	−	0.540803i	$-0.181879\pi$
$467$	26.0139	+	8.45242i	1.20378	+	0.391131i	0.362628	+	0.931934i	$0.381879\pi$
$468$	9.51431	−	1.71559i	0.439799	−	0.0793032i
$469$	12.3643	−	15.8675i	0.570930	−	0.732694i
$470$	0.214514	−	0.0915455i	0.00989478	−	0.00422268i
$471$	11.4692	−	3.72658i	0.528474	−	0.171712i
$472$	−0.158947	+	3.41138i	−0.00731614	+	0.157022i
$473$	23.2778	−	3.86848i	1.07032	−	0.177873i
$474$	−11.0088	+	18.4022i	−0.505650	+	0.845241i
$475$	−0.295160	+	0.0959033i	−0.0135429	+	0.00440034i
$476$	−17.6847	+	2.57838i	−0.810576	+	0.118180i
$477$	5.07701	+	6.98791i	0.232460	+	0.319954i
$478$	8.56807	−	7.47724i	0.391894	−	0.342001i
$479$	5.93557	−	18.2678i	0.271203	−	0.834678i	−0.718996	−	0.695014i	$-0.755398\pi$
$479$	5.93557	−	18.2678i	0.271203	−	0.834678i	0.990199	−	0.139663i	$-0.0446020\pi$
$480$	−1.10336	+	2.03671i	−0.0503614	+	0.0929626i
$481$	−33.2441	+	45.7566i	−1.51580	+	2.08632i
$482$	8.02837	−	35.0840i	0.365682	−	1.59803i
$483$	−12.5086	+	3.60416i	−0.569159	+	0.163995i
$484$	21.8403	+	2.64578i	0.992742	+	0.120263i
$485$			3.83810i			0.174279i
$486$	−2.24433	+	9.80773i	−0.101805	+	0.444888i
$487$	15.3832	−	21.1731i	0.697078	−	0.959445i	−0.302901	−	0.953022i	$-0.597955\pi$
$487$	15.3832	−	21.1731i	0.697078	−	0.959445i	0.999979	−	0.00642354i	$-0.00204469\pi$
$488$	−17.5236	+	11.5250i	−0.793256	+	0.521713i
$489$	−4.44969	−	1.44579i	−0.201222	−	0.0653809i
$490$	−2.55969	−	0.769996i	−0.115635	−	0.0347849i
$491$	2.89984	−	2.10685i	0.130868	−	0.0950810i	−0.520426	−	0.853907i	$-0.674227\pi$
$491$	2.89984	−	2.10685i	0.130868	−	0.0950810i	0.651293	+	0.758826i	$0.274227\pi$
$492$	−1.70822	+	12.5053i	−0.0770126	+	0.563783i
$493$	4.10542	+	12.6352i	0.184899	+	0.569061i
$494$	−0.527760	−	0.315723i	−0.0237451	−	0.0142051i
$495$	0.618542	−	0.102794i	0.0278014	−	0.00462023i
$496$	6.97177	−	10.5105i	0.313042	−	0.471936i
$497$	−16.3662	+	11.0697i	−0.734123	+	0.496545i
$498$	−16.3312	+	6.96948i	−0.731818	+	0.312310i
$499$	13.7916	−	10.0202i	0.617398	−	0.448566i	−0.234614	−	0.972089i	$-0.575383\pi$
$499$	13.7916	−	10.0202i	0.617398	−	0.448566i	0.852012	+	0.523523i	$0.175383\pi$
$500$	−5.27582	+	0.951319i	−0.235942	+	0.0425443i
$501$	20.3481	+	6.61151i	0.909088	+	0.295381i
$502$	−35.2441	+	3.15214i	−1.57302	+	0.140687i
$503$	−8.76124	−	6.36542i	−0.390645	−	0.283820i	0.375075	−	0.926994i	$-0.377617\pi$
$503$	−8.76124	−	6.36542i	−0.390645	−	0.283820i	−0.765720	+	0.643175i	$0.777617\pi$
$504$	−2.73033	−	4.47197i	−0.121619	−	0.199197i
$505$	−2.36500			−0.105241
$506$	−0.916708	+	15.1898i	−0.0407526	+	0.675267i
$507$		−	52.5677i		−	2.33461i
$508$	15.2777	+	14.6398i	0.677839	+	0.649534i
$509$	5.47446	+	3.97743i	0.242651	+	0.176296i	0.702464	−	0.711720i	$-0.252083\pi$
$509$	5.47446	+	3.97743i	0.242651	+	0.176296i	−0.459812	+	0.888016i	$0.652083\pi$
$510$	−0.174230	−	1.94807i	−0.00771503	−	0.0862620i
$511$	−32.0821	−	1.07910i	−1.41923	−	0.0477364i
$512$	9.92027	−	20.3369i	0.438418	−	0.898771i
$513$	0.285948	−	0.207754i	0.0126249	−	0.00917254i
$514$	16.9782	+	39.7842i	0.748878	+	1.75480i
$515$	0.0521978	+	0.160648i	0.00230011	+	0.00707901i
$516$	19.0142	−	10.2045i	0.837053	−	0.449229i
$517$	−1.81188	−	0.905914i	−0.0796863	−	0.0398421i
$518$	29.6335	+	7.83818i	1.30202	+	0.344390i
$519$	9.05239	−	2.94130i	0.397356	−	0.129109i
$520$	−4.11674	−	3.29432i	−0.180531	−	0.144465i
$521$	2.06910	+	2.84787i	0.0906488	+	0.124767i	0.851933	−	0.523651i	$-0.175431\pi$
$521$	2.06910	+	2.84787i	0.0906488	+	0.124767i	−0.761284	+	0.648419i	$0.775431\pi$
$522$	−2.93465	+	2.56103i	−0.128446	+	0.112093i
$523$	−29.9080	−	9.71771i	−1.30779	−	0.424926i	−0.429503	−	0.903065i	$-0.641311\pi$
$523$	−29.9080	−	9.71771i	−1.30779	−	0.424926i	−0.878284	+	0.478140i	$0.841311\pi$
$524$	−16.4859	+	34.1355i	−0.720190	+	1.49122i
$525$	−6.73759	+	18.5856i	−0.294052	+	0.811141i
$526$	−5.49315	+	24.0051i	−0.239513	+	1.04667i
$527$			10.6495i			0.463899i
$528$	19.6881	−	4.14128i	0.856813	−	0.180226i
$529$	12.4741			0.542354
$530$	1.05081	−	4.59203i	0.0456441	−	0.199465i
$531$	0.496910	−	0.683939i	0.0215641	−	0.0296804i
$532$	−0.0561861	+	0.328533i	−0.00243597	+	0.0142437i
$533$	−27.3231	−	8.87782i	−1.18350	−	0.384541i
$534$	−8.97299	−	10.2820i	−0.388299	−	0.444947i
$535$	−1.87777	+	1.36428i	−0.0811830	+	0.0589829i
$536$	−16.7907	−	13.4363i	−0.725247	−	0.580361i
$537$	18.4589	−	5.99765i	0.796558	−	0.258818i
$538$	11.0606	−	18.4888i	0.476857	−	0.797111i
$539$	9.28823	+	21.2774i	0.400072	+	0.916484i
$540$	2.67007	−	1.43297i	0.114902	−	0.0616654i
$541$	−2.63155	+	0.855043i	−0.113139	+	0.0367612i	−0.365039	−	0.930992i	$-0.618945\pi$
$541$	−2.63155	+	0.855043i	−0.113139	+	0.0367612i	0.251900	+	0.967753i	$0.418945\pi$
$542$	4.91027	−	2.09550i	0.210914	−	0.0900095i
$543$	−17.8994	−	24.6365i	−0.768139	−	1.05725i
$544$	2.51160	+	18.9398i	0.107684	+	0.812037i
$545$	−2.93239	−	0.952792i	−0.125610	−	0.0408131i
$546$	−36.5273	+	14.1565i	−1.56322	+	0.605842i
$547$	26.0211	+	18.9055i	1.11258	+	0.808339i	0.983068	−	0.183239i	$-0.0586581\pi$
$547$	26.0211	+	18.9055i	1.11258	+	0.808339i	0.129515	+	0.991578i	$0.458658\pi$
$548$	−6.52466	+	6.80898i	−0.278720	+	0.290865i
$549$	5.19202			0.221590
$550$	17.8442	+	14.6854i	0.760880	+	0.626188i
$551$	0.247771			0.0105554
$552$	3.67970	+	13.4209i	0.156618	+	0.571233i
$553$	−9.01578	+	24.8700i	−0.383390	+	1.05758i
$554$	−31.7940	+	2.84357i	−1.35080	+	0.120812i
$555$	−1.03662	+	3.19039i	−0.0440021	+	0.135424i
$556$	4.06045	+	22.5184i	0.172201	+	0.954994i
$557$	12.7594	+	17.5618i	0.540634	+	0.744119i	0.988704	−	0.149879i	$-0.0478884\pi$
$557$	12.7594	+	17.5618i	0.540634	+	0.744119i	−0.448070	+	0.893999i	$0.647888\pi$
$558$	−2.87164	+	1.22550i	−0.121566	+	0.0518794i
$559$	15.1788	+	46.7155i	0.641994	+	1.97585i
$560$	−0.858491	+	2.72555i	−0.0362779	+	0.115176i
$561$	−11.9203	+	12.1030i	−0.503277	+	0.510988i
$562$	−15.5204	+	25.9437i	−0.654688	+	1.09437i
$563$	27.7125	−	9.00434i	1.16794	−	0.379488i	0.340068	−	0.940401i	$-0.389550\pi$
$563$	27.7125	−	9.00434i	1.16794	−	0.379488i	0.827875	+	0.560913i	$0.189550\pi$
$564$	−1.83548	−	0.250725i	−0.0772875	−	0.0105574i
$565$	1.70945	−	1.24199i	0.0719172	−	0.0522509i
$566$	30.1880	−	26.3447i	1.26890	−	1.10735i
$567$	0.570045	−	16.9477i	0.0239396	−	0.711737i
$568$	11.6067	+	17.6478i	0.487006	+	0.740485i
$569$	−14.1324	−	10.2678i	−0.592460	−	0.430448i	0.250734	−	0.968056i	$-0.419328\pi$
$569$	−14.1324	−	10.2678i	−0.592460	−	0.430448i	−0.843195	+	0.537608i	$0.819328\pi$
$570$	−0.0355571	−	0.00813662i	−0.00148932	−	0.000340805i
$571$	−40.3181			−1.68726			−0.843630	−	0.536924i	$-0.819586\pi$
$571$	−40.3181			−1.68726			−0.843630	+	0.536924i	$0.819586\pi$
$572$	1.32433	+	45.7759i	0.0553730	+	1.91399i
$573$	10.4200			0.435303
$574$	0.864903	+	15.5462i	0.0361004	+	0.648886i
$575$	−9.39590	+	12.9323i	−0.391836	+	0.539316i
$576$	−4.81810	+	2.85676i	−0.200754	+	0.119032i
$577$	−4.80211	−	1.56030i	−0.199914	−	0.0649561i	0.207348	−	0.978267i	$-0.433517\pi$
$577$	−4.80211	−	1.56030i	−0.199914	−	0.0649561i	−0.407263	+	0.913311i	$0.633517\pi$
$578$	5.20075	+	5.95947i	0.216323	+	0.247881i
$579$	−11.7196	−	16.1307i	−0.487051	−	0.670368i
$580$	2.10470	+	0.287502i	0.0873931	+	0.0119379i
$581$	−18.1440	+	12.2722i	−0.752740	+	0.509137i
$582$	15.6506	−	26.1615i	0.648740	−	1.08443i
$583$	−36.3133	+	18.8516i	−1.50394	+	0.780756i
$584$	−1.59719	+	34.2794i	−0.0660920	+	1.41849i
$585$	0.403333	+	1.24133i	0.0166758	+	0.0513227i
$586$	41.0034	−	17.4985i	1.69383	−	0.722858i
$587$	−10.0471	−	13.8287i	−0.414690	−	0.570772i	0.549664	−	0.835386i	$-0.314756\pi$
$587$	−10.0471	−	13.8287i	−0.414690	−	0.570772i	−0.964355	+	0.264614i	$0.914756\pi$
$588$	14.3077	+	15.6862i	0.590040	+	0.646887i
$589$	0.188890	+	0.0613742i	0.00778309	+	0.00252888i
$590$	−0.459227	+	0.0410720i	−0.0189061	+	0.00169091i
$591$	20.9280	+	15.2051i	0.860861	+	0.625452i
$592$	8.78848	−	31.5685i	0.361204	−	1.29746i
$593$		−	5.20740i		−	0.213842i	−0.994268	−	0.106921i	$-0.965901\pi$
$593$		−	5.20740i		−	0.213842i	0.994268	−	0.106921i	$-0.0340992\pi$
$594$	−24.4961	−	9.62638i	−1.00509	−	0.394975i
$595$	−0.668034	−	2.31847i	−0.0273867	−	0.0950481i
$596$	−16.8374	−	16.1343i	−0.689687	−	0.660888i
$597$	3.97412	−	5.46991i	0.162650	−	0.223869i
$598$	−31.5505	+	2.82179i	−1.29020	+	0.115392i
$599$	5.50064	+	1.78727i	0.224750	+	0.0730257i	0.419227	−	0.907881i	$-0.362301\pi$
$599$	5.50064	+	1.78727i	0.224750	+	0.0730257i	−0.194477	+	0.980907i	$0.562301\pi$
$600$	19.7740	+	7.45921i	0.807269	+	0.304521i
$601$	−5.92855	−	8.15995i	−0.241831	−	0.332851i	0.670799	−	0.741640i	$-0.265952\pi$
$601$	−5.92855	−	8.15995i	−0.241831	−	0.332851i	−0.912629	+	0.408788i	$0.865952\pi$
$602$	20.6345	−	16.8197i	0.840998	−	0.685519i
$603$	1.64505	+	5.06293i	0.0669915	+	0.206179i
$604$	13.3531	−	7.16633i	0.543329	−	0.291594i
$605$	0.0451590	+	2.96981i	0.00183598	+	0.120740i
$606$	16.1204	+	9.64376i	0.654848	+	0.391751i
$607$	1.58571	+	4.88032i	0.0643621	+	0.198086i	0.978066	−	0.208294i	$-0.0667910\pi$
$607$	1.58571	+	4.88032i	0.0643621	+	0.198086i	−0.913704	+	0.406380i	$0.866791\pi$
$608$	0.350410	+	0.0646038i	0.0142110	+	0.00262003i
$609$	9.70095	−	12.4496i	0.393102	−	0.504482i
$610$	−1.86183	−	2.13345i	−0.0753835	−	0.0863809i
$611$	1.30305	−	4.01037i	0.0527157	−	0.162242i
$612$	2.05684	−	4.25887i	0.0831428	−	0.172154i
$613$	−16.3107	+	22.4497i	−0.658783	+	0.906737i	−0.999440	−	0.0334508i	$-0.989350\pi$
$613$	−16.3107	+	22.4497i	−0.658783	+	0.906737i	0.340658	+	0.940187i	$0.389350\pi$
$614$	1.29059	−	5.63990i	0.0520841	−	0.227608i
$615$	−1.70398			−0.0687112
$616$	22.8731	−	9.63444i	0.921582	−	0.388183i
$617$	−20.0028			−0.805282			−0.402641	−	0.915358i	$-0.631908\pi$
$617$	−20.0028			−0.805282			−0.402641	+	0.915358i	$0.631908\pi$
$618$	0.299283	−	1.30787i	0.0120389	−	0.0526102i
$619$	12.5351	−	17.2531i	0.503827	−	0.693459i	−0.479036	−	0.877795i	$-0.659014\pi$
$619$	12.5351	−	17.2531i	0.503827	−	0.693459i	0.982863	+	0.184337i	$0.0590136\pi$
$620$	1.53332	+	0.740526i	0.0615798	+	0.0297403i
$621$	5.62575	−	17.3143i	0.225754	−	0.694799i
$622$	22.6517	+	25.9563i	0.908251	+	1.04075i
$623$	−13.2796	−	10.3477i	−0.532034	−	0.414572i
$624$	14.6275	+	39.2418i	0.585569	+	1.57093i
$625$	7.38912	+	22.7414i	0.295565	+	0.909655i
$626$	−31.9429	−	19.1093i	−1.27670	−	0.763760i
$627$	0.145972	+	0.281182i	0.00582958	+	0.0112293i
$628$	−7.52078	−	14.0135i	−0.300112	−	0.559201i
$629$	8.55011	+	26.3145i	0.340915	+	1.04923i
$630$	0.548302	−	0.446935i	0.0218449	−	0.0178063i
$631$	25.6043	+	35.2413i	1.01929	+	1.40293i	0.912699	+	0.408632i	$0.133994\pi$
$631$	25.6043	+	35.2413i	1.01929	+	1.40293i	0.106593	+	0.994303i	$0.466006\pi$
$632$	26.4602	+	9.98141i	1.05253	+	0.397039i
$633$	0.192100	+	0.0624171i	0.00763529	+	0.00248086i
$634$	12.6047	−	1.12733i	0.500595	−	0.0447718i
$635$	−1.67913	+	2.31112i	−0.0666340	+	0.0917139i
$636$	−25.8875	+	27.0156i	−1.02651	+	1.07124i
$637$	−40.9178	+	25.7146i	−1.62122	+	1.01885i
$638$	−9.92588	−	15.5527i	−0.392969	−	0.615738i
$639$		−	5.22882i		−	0.206849i
$640$	2.90162	+	0.955382i	0.114697	+	0.0377648i
$641$	−2.53543	−	1.84210i	−0.100144	−	0.0727586i	0.536587	−	0.843845i	$-0.319713\pi$
$641$	−2.53543	−	1.84210i	−0.100144	−	0.0727586i	−0.636730	+	0.771087i	$0.719713\pi$
$642$	18.3625	−	1.64229i	0.724710	−	0.0648160i
$643$	−26.0731	−	8.47166i	−1.02822	−	0.334090i	−0.254135	−	0.967169i	$-0.581791\pi$
$643$	−26.0731	−	8.47166i	−1.02822	−	0.334090i	−0.774087	+	0.633079i	$0.781791\pi$
$644$	7.60513	+	15.3911i	0.299684	+	0.606495i
$645$	1.71244	+	2.35697i	0.0674271	+	0.0928055i
$646$	−0.276713	+	0.118090i	−0.0108871	+	0.00464618i
$647$	−12.6139	−	38.8215i	−0.495903	−	1.52623i	−0.815545	−	0.578694i	$-0.803563\pi$
$647$	−12.6139	−	38.8215i	−0.495903	−	1.52623i	0.319642	−	0.947538i	$-0.396437\pi$
$648$	−18.1085	−	0.843731i	−0.711368	−	0.0331449i
$649$	2.85308	+	2.81003i	0.111993	+	0.110303i
$650$	−24.6966	+	41.2826i	−0.968680	+	1.61924i
$651$	10.4794	−	7.08806i	0.410721	−	0.277803i
$652$	−0.835104	+	6.11351i	−0.0327052	+	0.239424i
$653$	−3.15151	−	4.33769i	−0.123328	−	0.169747i	0.742889	−	0.669415i	$-0.233455\pi$
$653$	−3.15151	−	4.33769i	−0.123328	−	0.169747i	−0.866217	+	0.499668i	$0.833455\pi$
$654$	16.1027	+	18.4519i	0.629667	+	0.721527i
$655$	−4.86736	−	1.58150i	−0.190183	−	0.0617943i
$656$	16.6302	−	0.709547i	0.649299	−	0.0277031i
$657$	4.99322	−	6.87258i	0.194804	−	0.268125i
$658$	−2.28180	+	0.126947i	−0.0889540	+	0.00494890i
$659$	48.0909			1.87336			0.936678	−	0.350193i	$-0.113884\pi$
$659$	48.0909			1.87336			0.936678	+	0.350193i	$0.113884\pi$
$660$	0.913702	+	2.55790i	0.0355658	+	0.0995660i
$661$	32.0893			1.24813			0.624064	−	0.781374i	$-0.285481\pi$
$661$	32.0893			1.24813			0.624064	+	0.781374i	$0.285481\pi$
$662$	−8.49899	−	1.94485i	−0.330323	−	0.0755886i
$663$	−28.6078	−	20.7848i	−1.11103	−	0.807213i
$664$	12.8675	+	19.5648i	0.499356	+	0.759263i
$665$	−0.0449728	−	0.00151268i	−0.00174397	−	5.86593e-5i
$666$	−6.11181	+	5.33370i	−0.236828	+	0.206677i
$667$	10.3247	−	7.50131i	0.399773	−	0.290452i
$668$	3.81888	−	27.9567i	0.147757	−	1.08168i
$669$	13.6911	−	4.44849i	0.529327	−	0.171989i
$670$	1.49050	−	2.49151i	0.0575831	−	0.0962555i
$671$	−3.66257	+	24.3198i	−0.141392	+	0.938855i
$672$	16.9657	−	15.0774i	0.654466	−	0.581623i
$673$	−7.55370	−	23.2479i	−0.291174	−	0.896140i	−0.984480	−	0.175497i	$-0.943847\pi$
$673$	−7.55370	−	23.2479i	−0.291174	−	0.896140i	0.693306	−	0.720643i	$-0.256153\pi$
$674$	−9.05984	+	3.86636i	−0.348972	+	0.148927i
$675$	−16.2510	−	22.3675i	−0.625500	−	0.860926i
$676$	−68.2265	+	12.3024i	−2.62410	+	0.473169i
$677$	−0.877490	+	2.70064i	−0.0337247	+	0.103794i	−0.966502	−	0.256660i	$-0.917378\pi$
$677$	−0.877490	+	2.70064i	−0.0337247	+	0.103794i	0.932777	+	0.360454i	$0.117378\pi$
$678$	−16.7165	+	1.49508i	−0.641995	+	0.0574183i
$679$	12.8173	−	35.3564i	0.491883	−	1.35685i
$680$	−2.48758	+	0.682035i	−0.0953945	+	0.0261548i
$681$	−17.1935			−0.658858
$682$	−3.71459	−	14.3154i	−0.142239	−	0.548167i
$683$	15.7082			0.601058			0.300529	−	0.953773i	$-0.402837\pi$
$683$	15.7082			0.601058			0.300529	+	0.953773i	$0.402837\pi$
$684$	−0.0636858	−	0.0610265i	−0.00243509	−	0.00233341i
$685$	−1.03002	−	0.748353i	−0.0393550	−	0.0285931i
$686$	21.0084	+	15.6412i	0.802103	+	0.597185i
$687$	20.4342	+	6.63948i	0.779614	+	0.253312i
$688$	−17.6941	−	22.2899i	−0.674582	−	0.849796i
$689$	−50.0608	−	68.9028i	−1.90716	−	2.62499i
$690$	−1.72801	+	0.737443i	−0.0657842	+	0.0280740i
$691$	−34.7853	+	11.3024i	−1.32330	+	0.429965i	−0.883626	−	0.468194i	$-0.844905\pi$
$691$	−34.7853	+	11.3024i	−1.32330	+	0.429965i	−0.439671	+	0.898159i	$0.644905\pi$
$692$	−5.93597	−	11.0605i	−0.225652	−	0.420459i
$693$	−6.04126	−	1.11868i	−0.229488	−	0.0424953i
$694$	6.66845	−	11.1469i	0.253131	−	0.423132i
$695$	−2.93797	+	0.954606i	−0.111444	+	0.0362103i
$696$	−13.1739	−	10.5421i	−0.499354	−	0.399595i
$697$	−11.3704	+	8.26106i	−0.430684	+	0.312910i
$698$	−0.825533	−	0.945967i	−0.0312469	−	0.0358054i
$699$	−28.0208	−	9.10452i	−1.05985	−	0.344365i
$700$	25.6986	+	4.39500i	0.971316	+	0.166115i
$701$	12.0117	−	16.5326i	0.453674	−	0.624429i	−0.519508	−	0.854466i	$-0.673885\pi$
$701$	12.0117	−	16.5326i	0.453674	−	0.624429i	0.973182	+	0.230037i	$0.0738847\pi$
$702$	12.2211	−	53.4065i	0.461257	−	2.01570i
$703$	0.516017			0.0194619
$704$	−9.98247	−	24.5835i	−0.376228	−	0.926527i
$705$		−	0.250103i		−	0.00941943i
$706$	3.66117	−	15.9993i	0.137790	−	0.602143i
$707$	21.7862	+	7.89788i	0.819356	+	0.297030i
$708$	3.29769	+	1.59263i	0.123935	+	0.0598549i
$709$	12.8086	+	4.16176i	0.481036	+	0.156298i	0.539490	−	0.841992i	$-0.318617\pi$
$709$	12.8086	+	4.16176i	0.481036	+	0.156298i	−0.0584538	+	0.998290i	$0.518617\pi$
$710$	−2.14857	+	1.87503i	−0.0806345	+	0.0703686i
$711$	−4.11490	−	5.66367i	−0.154321	−	0.212404i
$712$	−11.2449	+	14.0522i	−0.421420	+	0.526627i
$713$	9.72923	−	3.16122i	0.364362	−	0.118389i
$714$	−4.90056	+	18.5274i	−0.183399	+	0.693369i
$715$	−6.09900	+	1.01358i	−0.228090	+	0.0379056i
$716$	−12.1041	−	22.5537i	−0.452353	−	0.842872i
$717$	−3.76834	−	11.5978i	−0.140731	−	0.433126i
$718$	−1.41487	−	3.31539i	−0.0528024	−	0.123729i
$719$	36.2494	−	26.3367i	1.35187	−	0.982194i	0.352958	−	0.935639i	$-0.385176\pi$
$719$	36.2494	−	26.3367i	1.35187	−	0.982194i	0.998916	−	0.0465550i	$-0.0148243\pi$
$720$	−0.470171	−	0.592292i	−0.0175222	−	0.0220734i
$721$	0.0556398	−	1.65420i	0.00207213	−	0.0616056i
$722$	−2.39313	−	26.7576i	−0.0890631	−	0.995816i
$723$	−31.2236	−	22.6853i	−1.16122	−	0.843675i
$724$	−27.7861	+	28.9970i	−1.03266	+	1.07766i
$725$		−	19.3812i		−	0.719799i
$726$	11.8022	−	20.4271i	0.438020	−	0.758122i
$727$	−19.8703			−0.736950			−0.368475	−	0.929638i	$-0.620120\pi$
$727$	−19.8703			−0.736950			−0.368475	+	0.929638i	$0.620120\pi$
$728$	26.9219	+	44.0949i	0.997791	+	1.63427i
$729$	24.2841	+	17.6435i	0.899413	+	0.653462i
$730$	−4.61455	+	0.412713i	−0.170792	+	0.0152752i
$731$	22.8536	+	7.42558i	0.845270	+	0.274645i
$732$	3.99116	+	22.1342i	0.147518	+	0.818102i
$733$	−7.51197	+	5.45776i	−0.277461	+	0.201587i	−0.717809	−	0.696240i	$-0.754855\pi$
$733$	−7.51197	+	5.45776i	−0.277461	+	0.201587i	0.440348	+	0.897827i	$0.354855\pi$
$734$	25.4440	−	10.8585i	0.939157	−	0.400793i
$735$	−1.83682	+	2.20049i	−0.0677522	+	0.0811662i
$736$	16.5576	−	7.91669i	0.610321	−	0.291813i
$737$	−24.8756	+	4.13400i	−0.916304	+	0.152278i
$738$	−3.53605	−	2.11538i	−0.130164	−	0.0778682i
$739$	−1.02995	−	3.16987i	−0.0378874	−	0.116605i	0.930324	−	0.366738i	$-0.119526\pi$
$739$	−1.02995	−	3.16987i	−0.0378874	−	0.116605i	−0.968211	+	0.250133i	$0.919526\pi$
$740$	4.38333	+	0.598762i	0.161135	+	0.0220109i
$741$	−0.533529	+	0.387632i	−0.0195997	+	0.0142400i
$742$	−25.0150	+	38.7924i	−0.918329	+	1.42411i
$743$	6.64140	+	2.15792i	0.243649	+	0.0791665i	0.428296	−	0.903638i	$-0.359114\pi$
$743$	6.64140	+	2.15792i	0.243649	+	0.0791665i	−0.184647	+	0.982805i	$0.559114\pi$
$744$	−7.43189	−	11.3001i	−0.272466	−	0.414281i
$745$	1.85055	−	2.54706i	0.0677987	−	0.0933170i
$746$	−0.0612102	+	0.267489i	−0.00224107	+	0.00979347i
$747$		−	5.79681i		−	0.212094i
$748$	18.4979	+	12.6387i	0.676350	+	0.462116i
$749$	21.8539	−	6.29688i	0.798524	−	0.230083i
$750$	−1.28235	+	5.60387i	−0.0468247	+	0.204624i
$751$	−11.8999	+	16.3788i	−0.434234	+	0.597672i	−0.968919	−	0.247380i	$-0.920430\pi$
$751$	−11.8999	+	16.3788i	−0.434234	+	0.597672i	0.534684	+	0.845052i	$0.320430\pi$
$752$	0.104144	+	2.44090i	0.00379775	+	0.0890106i
$753$	−11.7255	+	36.0875i	−0.427302	+	1.31510i
$754$	28.9365	−	25.2525i	1.05380	−	0.919641i
$755$	1.20259	+	1.65522i	0.0437668	+	0.0602398i
$756$	−29.3820	+	4.28381i	−1.06861	+	0.155801i
$757$	−16.0415	+	5.21221i	−0.583040	+	0.189441i	−0.585662	−	0.810555i	$-0.699165\pi$
$757$	−16.0415	+	5.21221i	−0.583040	+	0.189441i	0.00262211	+	0.999997i	$0.499165\pi$
$758$	−20.0261	+	33.4754i	−0.727379	+	1.21588i
$759$	14.5956	+	7.29757i	0.529785	+	0.264885i
$760$	−0.00223894	+	0.0480530i	−8.12149e−5	+	0.00174306i
$761$	−33.2165	+	10.7927i	−1.20410	+	0.391235i	−0.841267	−	0.540620i	$-0.818190\pi$
$761$	−33.2165	+	10.7927i	−1.20410	+	0.391235i	−0.362831	+	0.931855i	$0.618190\pi$
$762$	20.8694	−	8.90620i	0.756019	−	0.322638i
$763$	23.8312	+	18.5698i	0.862748	+	0.672271i
$764$	−2.43859	−	13.5239i	−0.0882251	−	0.489278i
$765$	0.607269	+	0.197314i	0.0219558	+	0.00713389i
$766$	−2.50478	−	28.0060i	−0.0905015	−	1.01190i
$767$	−4.89968	+	6.74383i	−0.176917	+	0.243506i
$768$	−15.8824	−	18.3441i	−0.573108	−	0.661935i
$769$			3.66026i			0.131992i	0.997820	+	0.0659961i	$0.0210225\pi$
$769$			3.66026i			0.131992i	−0.997820	+	0.0659961i	$0.978978\pi$
$770$	1.70669	+	2.88357i	0.0615048	+	0.103916i
$771$	46.3847			1.67050
$772$	−18.1929	+	18.9857i	−0.654777	+	0.683310i
$773$	−17.0099	−	12.3584i	−0.611802	−	0.444500i	0.238246	−	0.971205i	$-0.423427\pi$
$773$	−17.0099	−	12.3584i	−0.611802	−	0.444500i	−0.850049	+	0.526704i	$0.823427\pi$
$774$	0.627579	+	7.01697i	0.0225579	+	0.252220i
$775$	4.80083	−	14.7754i	0.172451	−	0.530749i
$776$	−37.6171	−	14.1901i	−1.35038	−	0.509394i
$777$	20.2036	−	25.9279i	0.724798	−	0.930159i
$778$	−6.23396	−	14.6077i	−0.223498	−	0.523711i
$779$	0.0809979	+	0.249286i	0.00290205	+	0.00893160i
$780$	−4.98189	+	2.67368i	−0.178380	+	0.0957331i
$781$	24.4921	+	3.68853i	0.876398	+	0.131986i
$782$	−7.95552	+	13.2984i	−0.284489	+	0.475549i
$783$	6.82090	+	20.9926i	0.243759	+	0.750213i
$784$	17.0103	−	22.2407i	0.607511	−	0.794311i
$785$	1.73709	−	1.26207i	0.0619996	−	0.0450453i
$786$	26.7283	+	30.6276i	0.953366	+	1.09245i
$787$	−25.5846	−	8.31295i	−0.911993	−	0.296325i	−0.184815	−	0.982773i	$-0.559169\pi$
$787$	−25.5846	−	8.31295i	−0.911993	−	0.296325i	−0.727178	+	0.686449i	$0.759169\pi$
$788$	14.8366	−	30.7204i	0.528530	−	1.09437i
$789$	21.3638	+	15.5217i	0.760570	+	0.552586i
$790$	−0.851674	+	3.72182i	−0.0303012	+	0.132416i
$791$	−19.8950	+	5.73245i	−0.707385	+	0.203823i
$792$	−1.27937	+	6.44236i	−0.0454605	+	0.228919i
$793$	−51.1948			−1.81798
$794$	−32.3820	−	7.41006i	−1.14920	−	0.262973i
$795$	−4.08675	−	2.96920i	−0.144942	−	0.105307i
$796$	−8.02934	−	3.87781i	−0.284593	−	0.137445i
$797$	8.57659	−	26.3960i	0.303798	−	0.934995i	−0.676325	−	0.736604i	$-0.736428\pi$
$797$	8.57659	−	26.3960i	0.303798	−	0.934995i	0.980123	−	0.198391i	$-0.0635717\pi$
$798$	0.300378	+	0.193697i	0.0106333	+	0.00685678i
$799$	−1.21252	−	1.66889i	−0.0428960	−	0.0590412i
$800$	5.05346	−	27.4099i	0.178667	−	0.969086i
$801$	4.23718	−	1.37674i	0.149713	−	0.0486448i
$802$	−5.66158	+	9.46386i	−0.199917	+	0.334180i
$803$	28.6693	+	28.2367i	1.01172	+	0.996450i
$804$	−20.3193	+	10.9050i	−0.716607	+	0.384588i
$805$	−1.91982	+	1.29853i	−0.0676649	+	0.0457670i
$806$	28.3152	−	12.0837i	0.997359	−	0.425632i
$807$	−13.5798	−	18.6909i	−0.478030	−	0.657953i
$808$	8.74378	−	23.1793i	0.307605	−	0.815445i
$809$	11.4219	−	35.1530i	0.401572	−	1.23591i	−0.522151	−	0.852853i	$-0.674870\pi$
$809$	11.4219	−	35.1530i	0.401572	−	1.23591i	0.923724	−	0.383060i	$-0.125130\pi$
$810$	−0.218020	−	2.43769i	−0.00766045	−	0.0856517i
$811$	1.24680	−	1.71607i	0.0437810	−	0.0602593i	−0.786565	−	0.617507i	$-0.788143\pi$
$811$	1.24680	−	1.71607i	0.0437810	−	0.0602593i	0.830346	+	0.557248i	$0.188143\pi$
$812$	−18.4283	−	9.67709i	−0.646707	−	0.339599i
$813$		−	5.72493i		−	0.200782i
$814$	−20.6720	−	32.3907i	−0.724553	−	1.13529i
$815$	−0.833031			−0.0291798
$816$	19.7372	+	5.49471i	0.690939	+	0.192353i
$817$	0.263415	−	0.362560i	0.00921573	−	0.0126844i
$818$	17.5175	−	1.56672i	0.612487	−	0.0547791i
$819$	0.429929	−	12.7820i	0.0150229	−	0.446639i
$820$	0.398782	+	2.21156i	0.0139261	+	0.0772311i
$821$	−16.5368	−	22.7610i	−0.577140	−	0.794365i	0.416238	−	0.909256i	$-0.363348\pi$
$821$	−16.5368	−	22.7610i	−0.577140	−	0.794365i	−0.993378	+	0.114891i	$0.963348\pi$
$822$	3.96932	+	9.30109i	0.138446	+	0.324413i
$823$	7.30480	−	2.37347i	0.254629	−	0.0827340i	−0.178921	−	0.983863i	$-0.557261\pi$
$823$	7.30480	−	2.37347i	0.254629	−	0.0827340i	0.433550	+	0.901129i	$0.357261\pi$
$824$	−1.76750	−	0.0823532i	−0.0615736	−	0.00286891i
$825$	21.9947	−	11.4183i	0.765757	−	0.397534i
$826$	4.36753	+	1.15523i	0.151966	+	0.0401956i
$827$	−3.34248	−	10.2871i	−0.116229	−	0.357718i	0.875972	−	0.482362i	$-0.160221\pi$
$827$	−3.34248	−	10.2871i	−0.116229	−	0.357718i	−0.992201	+	0.124644i	$0.960221\pi$
$828$	−4.50140	−	0.614889i	−0.156434	−	0.0213689i
$829$	−8.10175	+	5.88626i	−0.281385	+	0.204438i	−0.719521	−	0.694470i	$-0.755639\pi$
$829$	−8.10175	+	5.88626i	−0.281385	+	0.204438i	0.438136	+	0.898909i	$0.355639\pi$
$830$	−2.38197	+	2.07871i	−0.0826793	+	0.0721531i
$831$	−10.5777	+	32.5548i	−0.366936	+	1.12931i
$832$	47.5078	−	28.1685i	1.64704	−	0.976566i
$833$	−1.58862	+	23.5885i	−0.0550425	+	0.817295i
$834$	23.9186	+	5.47335i	0.828233	+	0.189527i
$835$	3.80940			0.131830
$836$	0.330778	−	0.255259i	0.0114402	−	0.00882833i
$837$			17.6935i			0.611575i
$838$	−10.9089	+	47.6718i	−0.376840	+	1.64679i
$839$	−15.0576	−	10.9400i	−0.519848	−	0.377691i	0.296699	−	0.954971i	$-0.404114\pi$
$839$	−15.0576	−	10.9400i	−0.519848	−	0.377691i	−0.816546	+	0.577280i	$0.804114\pi$
$840$	2.32682	+	1.99391i	0.0802830	+	0.0687965i
$841$	4.18002	−	12.8648i	0.144139	−	0.443613i
$842$	−39.5297	+	34.4970i	−1.36228	+	1.18885i
$843$	19.0553	+	26.2273i	0.656298	+	0.903317i
$844$	0.0360528	−	0.263930i	0.00124099	−	0.00908485i
$845$	−2.89227	−	8.90150i	−0.0994972	−	0.306221i
$846$	0.310486	−	0.519006i	0.0106747	−	0.0178438i
$847$	9.50164	−	27.5085i	0.326480	−	0.945204i
$848$	41.1214	+	27.2764i	1.41211	+	0.936675i
$849$	−13.2770	−	40.8625i	−0.455666	−	1.40240i
$850$	9.23725	+	21.6451i	0.316835	+	0.742422i
$851$	21.5025	−	15.6225i	0.737098	−	0.535533i
$852$	22.2910	−	4.01945i	0.763679	−	0.137704i
$853$	1.69449	−	5.21512i	0.0580184	−	0.178562i	−0.917847	−	0.396933i	$-0.870074\pi$
$853$	1.69449	−	5.21512i	0.0580184	−	0.178562i	0.975866	+	0.218371i	$0.0700744\pi$
$854$	10.0265	+	25.8708i	0.343099	+	0.885281i
$855$	0.00699951	−	0.00963400i	0.000239378	−	0.000329476i
$856$	−6.42886	−	23.4479i	−0.219734	−	0.801434i
$857$			36.0251i			1.23059i	0.788296	+	0.615297i	$0.210964\pi$
$857$			36.0251i			1.23059i	−0.788296	+	0.615297i	$0.789036\pi$
$858$	45.7054	+	17.9611i	1.56036	+	0.613183i
$859$		−	46.4331i		−	1.58428i	−0.610341	−	0.792139i	$-0.708967\pi$
$859$		−	46.4331i		−	1.58428i	0.610341	−	0.792139i	$-0.291033\pi$
$860$	2.65830	−	2.77413i	0.0906471	−	0.0945972i
$861$	15.6970	+	5.69043i	0.534952	+	0.193929i
$862$	−37.4185	+	3.34661i	−1.27448	+	0.113986i
$863$	37.1283	+	12.0637i	1.26386	+	0.410654i	0.862869	−	0.505427i	$-0.168665\pi$
$863$	37.1283	+	12.0637i	1.26386	+	0.410654i	0.400993	+	0.916081i	$0.368665\pi$
$864$	4.17286	+	31.4673i	0.141964	+	1.07054i
$865$	1.37105	−	0.996124i	0.0466170	−	0.0338692i
$866$	−10.3472	−	24.2460i	−0.351611	−	0.823912i
$867$	8.06675	−	2.62105i	0.273961	−	0.0890154i
$868$	−11.6519	−	11.9422i	−0.395492	−	0.405345i
$869$	29.4318	−	15.2792i	0.998405	−	0.518311i
$870$	1.16944	−	1.95482i	0.0396477	−	0.0662747i
$871$	−16.2206	−	49.9220i	−0.549615	−	1.69154i
$872$	20.1798	−	25.2177i	0.683375	−	0.853979i
$873$	5.84995	+	8.05176i	0.197991	+	0.272511i
$874$	0.190025	+	0.217747i	0.00642770	+	0.00736541i
$875$	−0.238402	+	7.08780i	−0.00805945	+	0.239611i
$876$	33.1369	+	16.0036i	1.11959	+	0.540713i
$877$	−7.99167	+	10.9996i	−0.269860	+	0.371430i	−0.922342	−	0.386374i	$-0.873727\pi$
$877$	−7.99167	+	10.9996i	−0.269860	+	0.371430i	0.652483	+	0.757804i	$0.273727\pi$
$878$	22.4689	+	5.14162i	0.758289	+	0.173521i
$879$		−	47.8061i		−	1.61246i
$880$	3.10601	−	1.78450i	0.104703	−	0.0601554i
$881$			15.0890i			0.508361i	0.967157	+	0.254180i	$0.0818057\pi$
$881$			15.0890i			0.508361i	−0.967157	+	0.254180i	$0.918194\pi$
$882$	−6.54347	+	2.28609i	−0.220330	+	0.0769767i
$883$	−7.81538	−	5.67821i	−0.263009	−	0.191087i	0.448464	−	0.893801i	$-0.351971\pi$
$883$	−7.81538	−	5.67821i	−0.263009	−	0.191087i	−0.711472	+	0.702714i	$0.751971\pi$
$884$	−20.2810	+	41.9936i	−0.682125	+	1.41240i
$885$	−0.152782	+	0.470215i	−0.00513572	+	0.0158061i
$886$	−0.115497	−	0.132347i	−0.00388021	−	0.00444628i
$887$	34.5974	−	25.1365i	1.16167	−	0.843999i	0.171678	−	0.985153i	$-0.445081\pi$
$887$	34.5974	−	25.1365i	1.16167	−	0.843999i	0.989988	+	0.141154i	$0.0450812\pi$
$888$	−27.4364	−	21.9553i	−0.920705	−	0.736771i
$889$	23.1860	−	15.6825i	0.777632	−	0.525973i
$890$	−2.08515	−	1.24740i	−0.0698944	−	0.0418131i
$891$	−14.9163	+	15.1449i	−0.499716	+	0.507372i
$892$	−8.97771	−	16.7282i	−0.300596	−	0.560103i
$893$	−0.0365891	+	0.0118885i	−0.00122441	+	0.000397834i
$894$	−23.0000	+	9.81543i	−0.769234	+	0.328277i
$895$	2.79572	−	2.03121i	0.0934507	−	0.0678959i
$896$	−23.5391	−	18.4909i	−0.786386	−	0.617736i
$897$	−10.4967	+	32.3054i	−0.350474	+	1.07865i
$898$	−3.22052	−	36.0087i	−0.107470	−	1.20163i
$899$	−7.29040	+	10.0344i	−0.243149	+	0.334665i
$900$	−4.77363	+	4.98165i	−0.159121	+	0.166055i
$901$	−41.6651			−1.38807
$902$	12.4030	−	15.0709i	0.412975	−	0.501805i
$903$	−7.90381	−	27.4309i	−0.263022	−	0.912844i
$904$	5.85260	+	21.3462i	0.194655	+	0.709963i
$905$	−4.38648	−	3.18697i	−0.145812	−	0.105938i
$906$	−1.44765	−	16.1863i	−0.0480951	−	0.537752i
$907$	−2.32434	+	7.15357i	−0.0771783	+	0.237530i	−0.982201	−	0.187833i	$-0.939854\pi$
$907$	−2.32434	+	7.15357i	−0.0771783	+	0.237530i	0.905023	+	0.425363i	$0.139854\pi$
$908$	4.02379	+	22.3151i	0.133534	+	0.740553i
$909$	−4.96141	+	3.60468i	−0.164560	+	0.119560i
$910$	−5.40642	+	4.40691i	−0.179221	+	0.146088i
$911$	−36.1543	+	11.7472i	−1.19784	+	0.389203i	−0.838968	−	0.544181i	$-0.816840\pi$
$911$	−36.1543	+	11.7472i	−1.19784	+	0.389203i	−0.358877	+	0.933385i	$0.616840\pi$
$912$	0.211207	−	0.318412i	0.00699376	−	0.0105437i
$913$	27.1527	+	4.08921i	0.898623	+	0.135333i
$914$	−23.9899	+	40.1013i	−0.793515	+	1.32643i
$915$	−2.88784	+	0.938317i	−0.0954691	+	0.0310198i
$916$	3.83503	−	28.0749i	0.126713	−	0.927622i
$917$	39.5564	+	30.8232i	1.30627	+	1.01787i
$918$	−17.6229	−	20.1938i	−0.581642	−	0.666496i
$919$	11.5734	+	3.76044i	0.381773	+	0.124045i	0.493615	−	0.869680i	$-0.335675\pi$
$919$	11.5734	+	3.76044i	0.381773	+	0.124045i	−0.111842	+	0.993726i	$0.535675\pi$
$920$	1.36152	+	2.07016i	0.0448879	+	0.0682513i
$921$	−5.01932	−	3.64675i	−0.165392	−	0.120165i
$922$	−51.5724	−	11.8014i	−1.69845	−	0.388660i
$923$			51.5576i			1.69704i
$924$	0.125094	−	26.6145i	0.00411529	−	0.875553i
$925$		−	40.3640i		−	1.32716i
$926$	−2.21462	+	9.67789i	−0.0727768	+	0.318035i
$927$	0.354360	+	0.257458i	0.0116387	+	0.00845602i
$928$	−10.5992	+	19.5652i	−0.347937	+	0.642260i
$929$	39.1710	+	12.7274i	1.28516	+	0.417573i	0.870394	−	0.492356i	$-0.163864\pi$
$929$	39.1710	+	12.7274i	1.28516	+	0.417573i	0.414764	+	0.909929i	$0.363864\pi$
$930$	1.37575	−	1.20060i	0.0451127	−	0.0393693i
$931$	0.409235	+	0.164121i	0.0134121	+	0.00537884i
$932$	−5.25886	+	38.4984i	−0.172260	+	1.26106i
$933$	35.1345	−	11.4159i	1.15025	−	0.373739i
$934$	−33.1958	−	19.8588i	−1.08620	−	0.649799i
$935$	−1.35261	+	2.70530i	−0.0442351	+	0.0884728i
$936$	−13.6574	−	0.636344i	−0.446408	−	0.0207996i
$937$	−17.5046	+	5.68758i	−0.571850	+	0.185805i	−0.580646	−	0.814156i	$-0.697200\pi$
$937$	−17.5046	+	5.68758i	−0.571850	+	0.185805i	0.00879636	+	0.999961i	$0.497200\pi$
$938$	−22.0508	+	17.9742i	−0.719984	+	0.586877i
$939$	−32.2921	+	23.4616i	−1.05381	+	0.765639i
$940$	−0.324604	+	0.0585315i	−0.0105874	+	0.00190909i
$941$	2.19790	−	6.76444i	0.0716495	−	0.220515i	−0.908819	−	0.417191i	$-0.863015\pi$
$941$	2.19790	−	6.76444i	0.0716495	−	0.220515i	0.980469	+	0.196676i	$0.0630147\pi$
$942$	−16.9869	+	1.51926i	−0.553462	+	0.0495001i
$943$	10.9224	+	7.93559i	0.355682	+	0.258418i
$944$	1.29529	−	4.65272i	0.0421581	−	0.151433i
$945$	−1.10990	−	3.85200i	−0.0361049	−	0.125305i
$946$	−33.3107	−	2.01031i	−1.08302	−	0.0653609i
$947$	−1.57810			−0.0512814			−0.0256407	−	0.999671i	$-0.508163\pi$
$947$	−1.57810			−0.0512814			−0.0256407	+	0.999671i	$0.508163\pi$
$948$	20.9817	−	21.8960i	0.681454	−	0.711150i
$949$	−49.2346	+	67.7656i	−1.59822	+	2.19976i
$950$	0.437155	−	0.0390980i	0.0141832	−	0.00126851i
$951$	4.19350	−	12.9063i	0.135983	−	0.418514i
$952$	25.1931	+	2.02439i	0.816514	+	0.0656107i
$953$	−19.1279	+	13.8972i	−0.619612	+	0.450175i	−0.852786	−	0.522260i	$-0.825089\pi$
$953$	−19.1279	+	13.8972i	−0.619612	+	0.450175i	0.233174	+	0.972435i	$0.425089\pi$
$954$	−4.79463	−	11.2350i	−0.155232	−	0.363747i
$955$	1.76446	−	0.573309i	0.0570967	−	0.0185518i
$956$	−14.1706	+	7.60506i	−0.458309	+	0.245965i
$957$	−19.5172	+	3.24351i	−0.630902	+	0.104848i
$958$	−13.9455	+	23.3112i	−0.450559	+	0.753150i
$959$	6.98938	+	10.3335i	0.225699	+	0.333687i
$960$	2.16358	−	2.45969i	0.0698293	−	0.0793863i
$961$	17.0361	−	12.3774i	0.549550	−	0.399271i
$962$	60.2642	−	52.5918i	1.94300	−	1.69563i
$963$	−1.85988	+	5.72411i	−0.0599337	+	0.184457i
$964$	−22.1355	+	45.8335i	−0.712936	+	1.47620i
$965$	−2.87204	−	2.08666i	−0.0924542	−	0.0671719i
$966$	18.3810	−	1.02262i	0.591400	−	0.0329022i
$967$		−	57.3670i		−	1.84480i	−0.386238	−	0.922399i	$-0.626226\pi$
$967$		−	57.3670i		−	1.84480i	0.386238	−	0.922399i	$-0.373774\pi$
$968$	−29.2740	−	10.5373i	−0.940902	−	0.338680i
$969$			0.322622i			0.0103641i
$970$	1.21078	−	5.29113i	0.0388759	−	0.169888i
$971$	15.2697	−	21.0169i	0.490027	−	0.674464i	−0.490366	−	0.871516i	$-0.663137\pi$
$971$	15.2697	−	21.0169i	0.490027	−	0.674464i	0.980393	+	0.197053i	$0.0631370\pi$
$972$	6.18797	−	12.8127i	0.198479	−	0.410969i
$973$	30.2524	+	1.01755i	0.969846	+	0.0326213i
$974$	−27.8863	+	24.3360i	−0.893534	+	0.779776i
$975$	30.3214	+	41.7339i	0.971063	+	1.33655i
$976$	27.7934	−	10.3601i	0.889645	−	0.331618i
$977$	−16.2790	−	50.1015i	−0.520810	−	1.60289i	−0.772455	−	0.635069i	$-0.780972\pi$
$977$	−16.2790	−	50.1015i	−0.520810	−	1.60289i	0.251645	−	0.967819i	$-0.419028\pi$
$978$	5.67815	+	3.39685i	0.181567	+	0.108619i
$979$	3.45976	+	20.8184i	0.110574	+	0.665360i
$980$	3.28584	+	1.86899i	0.104962	+	0.0597028i
$981$	−7.60395	+	2.47067i	−0.242775	+	0.0788825i
$982$	−4.66229	+	1.98967i	−0.148780	+	0.0634930i
$983$	−20.0304	+	14.5529i	−0.638869	+	0.464166i	−0.859462	−	0.511200i	$-0.829201\pi$
$983$	−20.0304	+	14.5529i	−0.638869	+	0.464166i	0.220592	+	0.975366i	$0.429201\pi$
$984$	6.29990	−	16.7007i	0.200833	−	0.532399i
$985$	4.38040	+	1.42328i	0.139571	+	0.0453494i
$986$	−1.67371	−	18.7137i	−0.0533016	−	0.595967i
$987$	−0.835217	+	2.30394i	−0.0265852	+	0.0733351i
$988$	0.627960	+	0.601739i	0.0199781	+	0.0191439i
$989$		−	23.0829i		−	0.733994i
$990$	−0.885137	−	0.0534184i	−0.0281315	−	0.00169775i
$991$			38.2433i			1.21484i	0.794382	+	0.607419i	$0.207795\pi$
$991$			38.2433i			1.21484i	−0.794382	+	0.607419i	$0.792205\pi$
$992$	−12.9268	+	12.2902i	−0.410427	+	0.390215i
$993$	−5.49544	+	7.56382i	−0.174392	+	0.240031i
$994$	26.0542	−	10.0976i	0.826388	−	0.320275i
$995$	0.372000	−	1.14490i	0.0117932	−	0.0362957i
$996$	24.7125	−	4.45608i	0.783045	−	0.141196i
$997$	−22.8031	+	16.5674i	−0.722181	+	0.524696i	−0.887080	−	0.461615i	$-0.847270\pi$
$997$	−22.8031	+	16.5674i	−0.722181	+	0.524696i	0.164899	+	0.986310i	$0.447270\pi$
$998$	−22.1739	+	9.46289i	−0.701901	+	0.299542i
$999$	14.2055	+	43.7199i	0.449441	+	1.38324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.bp.c.27.5	✓	352
7.6	odd	2	inner	616.2.bp.c.27.6	yes	352
8.3	odd	2	inner	616.2.bp.c.27.65	yes	352
11.9	even	5	inner	616.2.bp.c.251.66	yes	352
56.27	even	2	inner	616.2.bp.c.27.66	yes	352
77.20	odd	10	inner	616.2.bp.c.251.65	yes	352
88.75	odd	10	inner	616.2.bp.c.251.6	yes	352
616.251	even	10	inner	616.2.bp.c.251.5	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bp.c.27.5	✓	352	1.1	even	1	trivial
616.2.bp.c.27.6	yes	352	7.6	odd	2	inner
616.2.bp.c.27.65	yes	352	8.3	odd	2	inner
616.2.bp.c.27.66	yes	352	56.27	even	2	inner
616.2.bp.c.251.5	yes	352	616.251	even	10	inner
616.2.bp.c.251.6	yes	352	88.75	odd	10	inner
616.2.bp.c.251.65	yes	352	77.20	odd	10	inner
616.2.bp.c.251.66	yes	352	11.9	even	5	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:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.bp (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37858 - 0.315464i) q^{2} +(-0.891388 + 1.22689i) q^{3} +(1.80096 + 0.869785i) q^{4} +(-0.0834388 + 0.256798i) q^{5} +(1.61589 - 1.41016i) q^{6} +(1.62621 - 2.08697i) q^{7} +(-2.20839 - 1.76721i) q^{8} +(0.216364 + 0.665900i) q^{9} +(0.196038 - 0.327695i) q^{10} +(-3.27175 + 0.543723i) q^{11} +(-2.67249 + 1.43427i) q^{12} +(-2.13341 - 6.56597i) q^{13} +(-2.90022 + 2.36404i) q^{14} +(-0.240687 - 0.331277i) q^{15} +(2.48695 + 3.13290i) q^{16} +(-3.21212 - 1.04368i) q^{17} +(-0.0882077 - 0.986252i) q^{18} +(-0.0370236 + 0.0509587i) q^{19} +(-0.373630 + 0.389911i) q^{20} +(1.11090 + 3.85548i) q^{21} +(4.68190 + 0.282554i) q^{22} +3.24436i q^{23} +(4.13670 - 1.13418i) q^{24} +(3.98610 + 2.89607i) q^{25} +(0.869753 + 9.72473i) q^{26} +(-5.33674 - 1.73401i) q^{27} +(4.74396 - 2.34411i) q^{28} +(-2.31211 - 3.18235i) q^{29} +(0.227300 + 0.532620i) q^{30} +(-0.974373 - 2.99881i) q^{31} +(-2.44014 - 5.10350i) q^{32} +(2.24931 - 4.49875i) q^{33} +(4.09892 + 2.45211i) q^{34} +(0.400241 + 0.591742i) q^{35} +(-0.189526 + 1.38745i) q^{36} +(-4.81529 - 6.62767i) q^{37} +(0.0671156 - 0.0585709i) q^{38} +(9.95742 + 3.23536i) q^{39} +(0.638081 - 0.419657i) q^{40} +(2.44596 - 3.36658i) q^{41} +(-0.315199 - 5.66553i) q^{42} -7.11479 q^{43} +(-6.36523 - 1.86649i) q^{44} -0.189055 q^{45} +(1.02348 - 4.47261i) q^{46} +(0.494132 + 0.359008i) q^{47} +(-6.06056 + 0.258582i) q^{48} +(-1.71089 - 6.78770i) q^{49} +(-4.58155 - 5.24994i) q^{50} +(4.14373 - 3.01060i) q^{51} +(1.86878 - 13.6807i) q^{52} +(11.7326 - 3.81214i) q^{53} +(6.81010 + 4.07402i) q^{54} +(0.133364 - 0.885548i) q^{55} +(-7.27941 + 1.73499i) q^{56} +(-0.0295182 - 0.0908478i) q^{57} +(2.18351 + 5.11651i) q^{58} +(-0.709701 - 0.976819i) q^{59} +(-0.145329 - 0.805964i) q^{60} +(2.29148 - 7.05244i) q^{61} +(0.397234 + 4.44148i) q^{62} +(1.74157 + 0.631348i) q^{63} +(1.75396 + 7.80536i) q^{64} +1.86414 q^{65} +(-4.52005 + 5.49231i) q^{66} +7.60314 q^{67} +(-4.87714 - 4.67349i) q^{68} +(-3.98047 - 2.89198i) q^{69} +(-0.365091 - 0.942025i) q^{70} +(-7.10243 - 2.30772i) q^{71} +(0.698968 - 1.85293i) q^{72} +(-7.13145 - 9.81560i) q^{73} +(4.54746 + 10.6558i) q^{74} +(-7.10632 + 2.30898i) q^{75} +(-0.111001 + 0.0595722i) q^{76} +(-4.18582 + 7.71226i) q^{77} +(-12.7065 - 7.60141i) q^{78} +(-9.50920 + 3.08973i) q^{79} +(-1.01203 + 0.377239i) q^{80} +(5.18520 - 3.76727i) q^{81} +(-4.43399 + 3.86949i) q^{82} +(-7.87395 - 2.55840i) q^{83} +(-1.35275 + 7.90983i) q^{84} +(0.536032 - 0.737784i) q^{85} +(9.80830 + 2.24446i) q^{86} +5.96537 q^{87} +(8.18617 + 4.58111i) q^{88} -6.36308i q^{89} +(0.260628 + 0.0596401i) q^{90} +(-17.1724 - 6.22527i) q^{91} +(-2.82189 + 5.84298i) q^{92} +(4.54776 + 1.47766i) q^{93} +(-0.567946 - 0.650802i) q^{94} +(-0.00999689 - 0.0137595i) q^{95} +(8.43654 + 1.55541i) q^{96} +(13.5188 - 4.39251i) q^{97} +(0.217319 + 9.89711i) q^{98} +(-1.06996 - 2.06102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 352 q - 2 q^{2} - 10 q^{4} - 14 q^{8} + 84 q^{9} - 28 q^{11} - 32 q^{14} + 14 q^{16} - 4 q^{18} - 62 q^{22} - 108 q^{25} - 44 q^{28} + 24 q^{30} - 112 q^{32} + 14 q^{35} + 20 q^{36} - 2 q^{42} + 8 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) \) 352 * q - 2 * q^2 - 10 * q^4 - 14 * q^8 + 84 * q^9 - 28 * q^11 - 32 * q^14 + 14 * q^16 - 4 * q^18 - 62 * q^22 - 108 * q^25 - 44 * q^28 + 24 * q^30 - 112 * q^32 + 14 * q^35 + 20 * q^36 - 2 * q^42 + 8 * q^43 + 22 * q^44 - 38 * q^46 - 34 * q^49 - 24 * q^50 - 36 * q^51 - 120 * q^56 - 36 * q^57 + 30 * q^58 - 136 * q^60 + 86 * q^64 + 8 * q^65 + 24 * q^67 + 52 * q^70 + 30 * q^72 + 94 * q^74 - 68 * q^78 - 60 * q^81 - 128 * q^84 + 34 * q^86 - 38 * q^88 + 78 * q^91 - 8 * q^92 - 100 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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