LMFDB - Embedded newform 250.2.g.b.231.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(11,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([38]))

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

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

chi := DirichletCharacter("250.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.g (of order $25$, 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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$7$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			231.6
Character	$\chi$	$=$	250.231
Dual form			250.2.g.b.171.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535827 - 0.844328i) q^{2} +(1.28815 - 1.20965i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-2.15875 - 0.582913i) q^{5} +(-0.331118 - 1.73578i) q^{6} +(3.35598 - 2.43826i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.00769630 - 0.122329i) q^{9} +O(q^{10})$	\(q+(0.535827 - 0.844328i) q^{2} +(1.28815 - 1.20965i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-2.15875 - 0.582913i) q^{5} +(-0.331118 - 1.73578i) q^{6} +(3.35598 - 2.43826i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.00769630 - 0.122329i) q^{9} +(-1.64889 + 1.51035i) q^{10} +(-2.53980 + 4.00208i) q^{11} +(-1.64299 - 0.650505i) q^{12} +(0.197700 - 3.14234i) q^{13} +(-0.260469 - 4.14003i) q^{14} +(-3.48591 + 1.86046i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(1.11135 - 2.36174i) q^{17} +(-0.0991620 - 0.0720454i) q^{18} +(2.31595 + 2.17482i) q^{19} +(0.391716 + 2.20149i) q^{20} +(1.37355 - 7.20039i) q^{21} +(2.01818 + 4.28884i) q^{22} +(-3.93272 - 1.00975i) q^{23} +(-1.42960 + 1.03866i) q^{24} +(4.32042 + 2.51673i) q^{25} +(-2.54724 - 1.85068i) q^{26} +(3.24108 + 3.91779i) q^{27} +(-3.63511 - 1.99842i) q^{28} +(7.05996 + 3.88124i) q^{29} +(-0.297008 + 3.94013i) q^{30} +(-0.0815496 + 0.173302i) q^{31} +(0.309017 + 0.951057i) q^{32} +(1.56948 + 8.22753i) q^{33} +(-1.39859 - 2.20383i) q^{34} +(-8.66602 + 3.30736i) q^{35} +(-0.113964 + 0.0451214i) q^{36} +(0.193687 - 0.234127i) q^{37} +(3.07721 - 0.790092i) q^{38} +(-3.54647 - 4.28694i) q^{39} +(2.06867 + 0.848880i) q^{40} +(-5.60937 + 1.44024i) q^{41} +(-5.34351 - 5.01789i) q^{42} +(0.158346 - 0.487340i) q^{43} +(4.70258 + 0.594074i) q^{44} +(-0.0879217 + 0.259592i) q^{45} +(-2.95982 + 2.77945i) q^{46} +(13.1694 - 1.66369i) q^{47} +(0.110956 + 1.76359i) q^{48} +(3.15435 - 9.70809i) q^{49} +(4.43995 - 2.29932i) q^{50} +(-1.42530 - 4.38661i) q^{51} +(-2.92745 + 1.15906i) q^{52} +(-2.32559 + 12.1912i) q^{53} +(5.04455 - 0.637275i) q^{54} +(7.81566 - 7.15902i) q^{55} +(-3.63511 + 1.99842i) q^{56} +5.61405 q^{57} +(7.05996 - 3.88124i) q^{58} +(-8.20944 - 3.25035i) q^{59} +(3.16762 + 2.36200i) q^{60} +(-4.63764 - 1.19074i) q^{61} +(0.102627 + 0.161714i) q^{62} +(-0.272442 - 0.429299i) q^{63} +(0.968583 + 0.248690i) q^{64} +(-2.25850 + 6.66830i) q^{65} +(7.78770 + 3.08337i) q^{66} +(-3.34298 + 1.83782i) q^{67} -2.61016 q^{68} +(-6.28736 + 3.45651i) q^{69} +(-1.85099 + 9.08913i) q^{70} +(6.03991 - 0.763018i) q^{71} +(-0.0229675 + 0.120400i) q^{72} +(-12.2094 + 4.83404i) q^{73} +(-0.0938975 - 0.288987i) q^{74} +(8.60970 - 1.98428i) q^{75} +(0.981753 - 3.02152i) q^{76} +(1.23461 + 19.6236i) q^{77} +(-5.51988 + 0.697323i) q^{78} +(-7.46915 + 7.01399i) q^{79} +(1.82518 - 1.29178i) q^{80} +(9.27894 + 1.17220i) q^{81} +(-1.78961 + 5.50787i) q^{82} +(-4.03833 - 3.79224i) q^{83} +(-7.09994 + 1.82295i) q^{84} +(-3.77582 + 4.45059i) q^{85} +(-0.326628 - 0.394826i) q^{86} +(13.7892 - 3.54046i) q^{87} +(3.02136 - 3.65220i) q^{88} +(10.8927 - 4.31272i) q^{89} +(0.172070 + 0.213331i) q^{90} +(-6.99838 - 11.0277i) q^{91} +(0.760821 + 3.98836i) q^{92} +(0.104587 + 0.321884i) q^{93} +(5.65184 - 12.0108i) q^{94} +(-3.73182 - 6.04489i) q^{95} +(1.54850 + 0.851297i) q^{96} +(4.71593 + 2.59261i) q^{97} +(-6.50663 - 7.86516i) q^{98} +(0.470024 + 0.341492i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9}+O(q^{10}) $ 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9	$ 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9} + 20 q^{10} - 10 q^{11} + 20 q^{12} + 20 q^{14} - 10 q^{15} - 5 q^{17} - 50 q^{18} + 40 q^{19} - 10 q^{20} - 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} - 5 q^{25} - 35 q^{26} + 30 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} + 35 q^{31} - 35 q^{32} - 55 q^{33} - 15 q^{34} - 25 q^{35} - 10 q^{36} - 25 q^{37} - 30 q^{39} + 25 q^{41} - 5 q^{42} - 45 q^{43} + 40 q^{44} - 5 q^{45} + 90 q^{47} - 5 q^{48} - 65 q^{49} + 30 q^{50} - 80 q^{51} - 50 q^{53} - 5 q^{54} - 35 q^{55} - 5 q^{56} + 40 q^{57} - 10 q^{58} + 45 q^{59} + 15 q^{60} + 45 q^{61} - 45 q^{62} - 75 q^{63} - 60 q^{65} + 15 q^{66} - 45 q^{67} + 10 q^{68} - 125 q^{69} - 15 q^{70} - 5 q^{71} - 5 q^{72} - 50 q^{73} + 20 q^{74} - 130 q^{75} - 5 q^{76} + 10 q^{77} + 10 q^{78} - 50 q^{79} - 5 q^{80} + 15 q^{81} + 40 q^{82} + 25 q^{83} - 50 q^{84} - 95 q^{85} - 10 q^{86} + 80 q^{87} - 10 q^{88} - 65 q^{89} - 10 q^{90} + 65 q^{91} - 25 q^{92} - 10 q^{93} - 35 q^{94} + 80 q^{95} - 40 q^{97} - 25 q^{98} + 90 q^{99}+O(q^{100}) $ 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9 + 20 * q^10 - 10 * q^11 + 20 * q^12 + 20 * q^14 - 10 * q^15 - 5 * q^17 - 50 * q^18 + 40 * q^19 - 10 * q^20 - 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 - 5 * q^25 - 35 * q^26 + 30 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 + 35 * q^31 - 35 * q^32 - 55 * q^33 - 15 * q^34 - 25 * q^35 - 10 * q^36 - 25 * q^37 - 30 * q^39 + 25 * q^41 - 5 * q^42 - 45 * q^43 + 40 * q^44 - 5 * q^45 + 90 * q^47 - 5 * q^48 - 65 * q^49 + 30 * q^50 - 80 * q^51 - 50 * q^53 - 5 * q^54 - 35 * q^55 - 5 * q^56 + 40 * q^57 - 10 * q^58 + 45 * q^59 + 15 * q^60 + 45 * q^61 - 45 * q^62 - 75 * q^63 - 60 * q^65 + 15 * q^66 - 45 * q^67 + 10 * q^68 - 125 * q^69 - 15 * q^70 - 5 * q^71 - 5 * q^72 - 50 * q^73 + 20 * q^74 - 130 * q^75 - 5 * q^76 + 10 * q^77 + 10 * q^78 - 50 * q^79 - 5 * q^80 + 15 * q^81 + 40 * q^82 + 25 * q^83 - 50 * q^84 - 95 * q^85 - 10 * q^86 + 80 * q^87 - 10 * q^88 - 65 * q^89 - 10 * q^90 + 65 * q^91 - 25 * q^92 - 10 * q^93 - 35 * q^94 + 80 * q^95 - 40 * q^97 - 25 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{17}{25}\right)$

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 $

$2$	0.535827	−	0.844328i	0.378887	−	0.597030i
$2$	0.535827	−	0.844328i	0.378887	−	0.597030i
$3$	1.28815	−	1.20965i	0.743711	−	0.698391i	−0.216929	−	0.976187i	$-0.569604\pi$
$3$	1.28815	−	1.20965i	0.743711	−	0.698391i	0.960640	+	0.277796i	$0.0896039\pi$
$4$	−0.425779	−	0.904827i	−0.212890	−	0.452414i
$5$	−2.15875	−	0.582913i	−0.965423	−	0.260687i
$5$	−2.15875	−	0.582913i	−0.965423	−	0.260687i
$6$	−0.331118	−	1.73578i	−0.135178	−	0.708629i
$7$	3.35598	−	2.43826i	1.26844	−	0.921576i	0.269301	−	0.963056i	$-0.413207\pi$
$7$	3.35598	−	2.43826i	1.26844	−	0.921576i	0.999139	+	0.0414805i	$0.0132075\pi$
$8$	−0.992115	−	0.125333i	−0.350766	−	0.0443120i
$9$	0.00769630	−	0.122329i	0.00256543	−	0.0407764i
$10$	−1.64889	+	1.51035i	−0.521424	+	0.477616i
$11$	−2.53980	+	4.00208i	−0.765778	+	1.20667i	0.207768	+	0.978178i	$0.433380\pi$
$11$	−2.53980	+	4.00208i	−0.765778	+	1.20667i	−0.973545	+	0.228494i	$0.926620\pi$
$12$	−1.64299	−	0.650505i	−0.474290	−	0.187785i
$13$	0.197700	−	3.14234i	0.0548320	−	0.871529i	−0.870452	−	0.492254i	$-0.836173\pi$
$13$	0.197700	−	3.14234i	0.0548320	−	0.871529i	0.925284	−	0.379276i	$-0.123827\pi$
$14$	−0.260469	−	4.14003i	−0.0696132	−	1.10647i
$15$	−3.48591	+	1.86046i	−0.900058	+	0.480368i
$16$	−0.637424	+	0.770513i	−0.159356	+	0.192628i
$17$	1.11135	−	2.36174i	0.269542	−	0.572806i	−0.723533	−	0.690290i	$-0.757483\pi$
$17$	1.11135	−	2.36174i	0.269542	−	0.572806i	0.993075	+	0.117484i	$0.0374829\pi$
$18$	−0.0991620	−	0.0720454i	−0.0233727	−	0.0169813i
$19$	2.31595	+	2.17482i	0.531315	+	0.498938i	0.903129	−	0.429369i	$-0.141264\pi$
$19$	2.31595	+	2.17482i	0.531315	+	0.498938i	−0.371814	+	0.928307i	$0.621264\pi$
$20$	0.391716	+	2.20149i	0.0875904	+	0.492268i
$21$	1.37355	−	7.20039i	0.299733	−	1.57125i
$22$	2.01818	+	4.28884i	0.430277	+	0.914384i
$23$	−3.93272	−	1.00975i	−0.820029	−	0.210548i	−0.184706	−	0.982794i	$-0.559133\pi$
$23$	−3.93272	−	1.00975i	−0.820029	−	0.210548i	−0.635323	+	0.772246i	$0.719133\pi$
$24$	−1.42960	+	1.03866i	−0.291815	+	0.212016i
$25$	4.32042	+	2.51673i	0.864085	+	0.503346i
$26$	−2.54724	−	1.85068i	−0.499554	−	0.362947i
$27$	3.24108	+	3.91779i	0.623745	+	0.753979i
$28$	−3.63511	−	1.99842i	−0.686971	−	0.377666i
$29$	7.05996	+	3.88124i	1.31100	+	0.720729i	0.975225	−	0.221213i	$-0.0710017\pi$
$29$	7.05996	+	3.88124i	1.31100	+	0.720729i	0.335775	+	0.941942i	$0.391002\pi$
$30$	−0.297008	+	3.94013i	−0.0542260	+	0.719366i
$31$	−0.0815496	+	0.173302i	−0.0146467	+	0.0311259i	−0.912017	−	0.410153i	$-0.865475\pi$
$31$	−0.0815496	+	0.173302i	−0.0146467	+	0.0311259i	0.897370	+	0.441279i	$0.145475\pi$
$32$	0.309017	+	0.951057i	0.0546270	+	0.168125i
$33$	1.56948	+	8.22753i	0.273212	+	1.43223i
$34$	−1.39859	−	2.20383i	−0.239857	−	0.377954i
$35$	−8.66602	+	3.30736i	−1.46482	+	0.559045i
$36$	−0.113964	+	0.0451214i	−0.0189939	+	0.00752023i
$37$	0.193687	−	0.234127i	0.0318419	−	0.0384903i	−0.754352	−	0.656470i	$-0.772049\pi$
$37$	0.193687	−	0.234127i	0.0318419	−	0.0384903i	0.786194	+	0.617980i	$0.212049\pi$
$38$	3.07721	−	0.790092i	0.499189	−	0.128170i
$39$	−3.54647	−	4.28694i	−0.567890	−	0.686460i
$40$	2.06867	+	0.848880i	0.327086	+	0.134220i
$41$	−5.60937	+	1.44024i	−0.876036	+	0.224928i	−0.659826	−	0.751419i	$-0.729370\pi$
$41$	−5.60937	+	1.44024i	−0.876036	+	0.224928i	−0.216211	+	0.976347i	$0.569370\pi$
$42$	−5.34351	−	5.01789i	−0.824521	−	0.774277i
$43$	0.158346	−	0.487340i	0.0241476	−	0.0743186i	−0.938257	−	0.345940i	$-0.887560\pi$
$43$	0.158346	−	0.487340i	0.0241476	−	0.0743186i	0.962404	+	0.271622i	$0.0875600\pi$
$44$	4.70258	+	0.594074i	0.708941	+	0.0895601i
$45$	−0.0879217	+	0.259592i	−0.0131066	+	0.0386977i
$46$	−2.95982	+	2.77945i	−0.436401	+	0.409808i
$47$	13.1694	−	1.66369i	1.92096	−	0.242674i	0.929082	−	0.369873i	$-0.120599\pi$
$47$	13.1694	−	1.66369i	1.92096	−	0.242674i	0.991877	+	0.127200i	$0.0405989\pi$
$48$	0.110956	+	1.76359i	0.0160151	+	0.254553i
$49$	3.15435	−	9.70809i	0.450621	−	1.38687i
$50$	4.43995	−	2.29932i	0.627903	−	0.325173i
$51$	−1.42530	−	4.38661i	−0.199581	−	0.614248i
$52$	−2.92745	+	1.15906i	−0.405965	+	0.160733i
$53$	−2.32559	+	12.1912i	−0.319445	+	1.67459i	0.353919	+	0.935276i	$0.384849\pi$
$53$	−2.32559	+	12.1912i	−0.319445	+	1.67459i	−0.673364	+	0.739311i	$0.735151\pi$
$54$	5.04455	−	0.637275i	0.686477	−	0.0867222i
$55$	7.81566	−	7.15902i	1.05386	−	0.965322i
$56$	−3.63511	+	1.99842i	−0.485762	+	0.267050i
$57$	5.61405			0.743598
$58$	7.05996	−	3.88124i	0.927018	−	0.509632i
$59$	−8.20944	−	3.25035i	−1.06878	−	0.423159i	−0.233142	−	0.972443i	$-0.574901\pi$
$59$	−8.20944	−	3.25035i	−1.06878	−	0.423159i	−0.835636	+	0.549283i	$0.814901\pi$
$60$	3.16762	+	2.36200i	0.408938	+	0.304933i
$61$	−4.63764	−	1.19074i	−0.593789	−	0.152459i	−0.0601760	−	0.998188i	$-0.519166\pi$
$61$	−4.63764	−	1.19074i	−0.593789	−	0.152459i	−0.533613	+	0.845729i	$0.679166\pi$
$62$	0.102627	+	0.161714i	0.0130336	+	0.0205377i
$63$	−0.272442	−	0.429299i	−0.0343244	−	0.0540866i
$64$	0.968583	+	0.248690i	0.121073	+	0.0310862i
$65$	−2.25850	+	6.66830i	−0.280132	+	0.827101i
$66$	7.78770	+	3.08337i	0.958600	+	0.379537i
$67$	−3.34298	+	1.83782i	−0.408410	+	0.224525i	−0.672696	−	0.739919i	$-0.734864\pi$
$67$	−3.34298	+	1.83782i	−0.408410	+	0.224525i	0.264286	+	0.964444i	$0.414864\pi$
$68$	−2.61016			−0.316528
$69$	−6.28736	+	3.45651i	−0.756910	+	0.416115i
$70$	−1.85099	+	9.08913i	−0.221236	+	1.08636i
$71$	6.03991	−	0.763018i	0.716806	−	0.0905536i	0.241534	−	0.970392i	$-0.422350\pi$
$71$	6.03991	−	0.763018i	0.716806	−	0.0905536i	0.475272	+	0.879839i	$0.342350\pi$
$72$	−0.0229675	+	0.120400i	−0.00270675	+	0.0141893i
$73$	−12.2094	+	4.83404i	−1.42900	+	0.565781i	−0.950060	−	0.312067i	$-0.898979\pi$
$73$	−12.2094	+	4.83404i	−1.42900	+	0.565781i	−0.478940	+	0.877848i	$0.658979\pi$
$74$	−0.0938975	−	0.288987i	−0.0109154	−	0.0335940i
$75$	8.60970	−	1.98428i	0.994162	−	0.229125i
$76$	0.981753	−	3.02152i	0.112615	−	0.346593i
$77$	1.23461	+	19.6236i	0.140697	+	2.23631i
$78$	−5.51988	+	0.697323i	−0.625003	+	0.0789563i
$79$	−7.46915	+	7.01399i	−0.840345	+	0.789136i	−0.979566	−	0.201125i	$-0.935540\pi$
$79$	−7.46915	+	7.01399i	−0.840345	+	0.789136i	0.139221	+	0.990261i	$0.455540\pi$
$80$	1.82518	−	1.29178i	0.204062	−	0.144426i
$81$	9.27894	+	1.17220i	1.03099	+	0.130245i
$82$	−1.78961	+	5.50787i	−0.197630	+	0.608242i
$83$	−4.03833	−	3.79224i	−0.443264	−	0.416253i	0.430509	−	0.902586i	$-0.358334\pi$
$83$	−4.03833	−	3.79224i	−0.443264	−	0.416253i	−0.873773	+	0.486334i	$0.838334\pi$
$84$	−7.09994	+	1.82295i	−0.774666	+	0.198901i
$85$	−3.77582	+	4.45059i	−0.409545	+	0.482735i
$86$	−0.326628	−	0.394826i	−0.0352212	−	0.0425752i
$87$	13.7892	−	3.54046i	1.47836	−	0.379578i
$88$	3.02136	−	3.65220i	0.322078	−	0.389326i
$89$	10.8927	−	4.31272i	1.15462	−	0.457148i	0.288747	−	0.957406i	$-0.406761\pi$
$89$	10.8927	−	4.31272i	1.15462	−	0.457148i	0.865876	+	0.500258i	$0.166761\pi$
$90$	0.172070	+	0.213331i	0.0181378	+	0.0224871i
$91$	−6.99838	−	11.0277i	−0.733629	−	1.15601i
$92$	0.760821	+	3.98836i	0.0793211	+	0.415816i
$93$	0.104587	+	0.321884i	0.0108451	+	0.0333779i
$94$	5.65184	−	12.0108i	0.582943	−	1.23882i
$95$	−3.73182	−	6.04489i	−0.382877	−	0.620193i
$96$	1.54850	+	0.851297i	0.158044	+	0.0868852i
$97$	4.71593	+	2.59261i	0.478831	+	0.263239i	0.702840	−	0.711348i	$-0.251915\pi$
$97$	4.71593	+	2.59261i	0.478831	+	0.263239i	−0.224010	+	0.974587i	$0.571915\pi$
$98$	−6.50663	−	7.86516i	−0.657269	−	0.794501i
$99$	0.470024	+	0.341492i	0.0472392	+	0.0343213i
$100$	0.437660	−	4.98081i	0.0437660	−	0.498081i
$101$	−0.719273	+	0.522582i	−0.0715703	+	0.0519989i	−0.622995	−	0.782226i	$-0.714084\pi$
$101$	−0.719273	+	0.522582i	−0.0715703	+	0.0519989i	0.551425	+	0.834225i	$0.314084\pi$
$102$	−4.46745	−	1.14705i	−0.442344	−	0.113575i
$103$	−5.60569	−	11.9127i	−0.552345	−	1.17379i	−0.964841	−	0.262834i	$-0.915343\pi$
$103$	−5.60569	−	11.9127i	−0.552345	−	1.17379i	0.412496	−	0.910959i	$-0.364657\pi$
$104$	−0.589981	+	3.09279i	−0.0578524	+	0.303273i
$105$	−7.16235	+	14.7432i	−0.698974	+	1.43879i
$106$	9.04724	+	8.49592i	0.878746	+	0.825197i
$107$	−12.6143	−	9.16485i	−1.21947	−	0.885999i	−0.223417	−	0.974723i	$-0.571721\pi$
$107$	−12.6143	−	9.16485i	−1.21947	−	0.885999i	−0.996056	+	0.0887235i	$0.971721\pi$
$108$	2.16494	−	4.60073i	0.208321	−	0.442705i
$109$	1.81209	−	2.19044i	0.173567	−	0.209806i	−0.676555	−	0.736392i	$-0.736528\pi$
$109$	1.81209	−	2.19044i	0.173567	−	0.209806i	0.850122	+	0.526586i	$0.176528\pi$
$110$	−1.85672	−	10.4350i	−0.177031	−	0.994936i
$111$	−0.0337149	−	0.535883i	−0.00320008	−	0.0508638i
$112$	−0.260469	+	4.14003i	−0.0246120	+	0.391196i
$113$	−4.63573	−	1.83542i	−0.436093	−	0.172661i	0.139812	−	0.990178i	$-0.455350\pi$
$113$	−4.63573	−	1.83542i	−0.436093	−	0.172661i	−0.575905	+	0.817517i	$0.695350\pi$
$114$	3.00816	−	4.74010i	0.281740	−	0.443951i
$115$	7.90117	+	4.47224i	0.736788	+	0.417038i
$116$	0.505871	−	8.04059i	0.0469690	−	0.746550i
$117$	−0.382879	−	0.0483688i	−0.0353971	−	0.00447170i
$118$	−7.14320	+	5.18984i	−0.657585	+	0.477763i
$119$	−2.02887	−	10.6357i	−0.185986	−	0.974974i
$120$	3.69160	−	1.40889i	0.336995	−	0.128613i
$121$	−4.88250	−	10.3758i	−0.443864	−	0.943258i
$122$	−3.49035	+	3.27766i	−0.316002	+	0.296745i
$123$	−5.48350	+	8.64061i	−0.494430	+	0.779098i
$124$	0.191530			0.0171999
$125$	−7.85969	−	7.95143i	−0.702992	−	0.711198i
$126$	−0.508451			−0.0452964
$127$	0.354652	−	0.558842i	0.0314702	−	0.0495892i	−0.828229	−	0.560390i	$-0.810651\pi$
$127$	0.354652	−	0.558842i	0.0314702	−	0.0495892i	0.859699	+	0.510801i	$0.170651\pi$
$128$	0.728969	−	0.684547i	0.0644323	−	0.0605060i
$129$	−0.385537	−	0.819308i	−0.0339447	−	0.0721361i
$130$	4.42007	+	5.47997i	0.387666	+	0.480625i
$131$	1.33346	+	6.99025i	0.116505	+	0.610741i	0.991868	+	0.127274i	$0.0406228\pi$
$131$	1.33346	+	6.99025i	0.116505	+	0.610741i	−0.875362	+	0.483467i	$0.839377\pi$
$132$	6.77623	−	4.92322i	0.589795	−	0.428511i
$133$	13.0750	+	1.65176i	1.13375	+	0.143226i
$134$	−0.239537	+	3.80733i	−0.0206928	+	0.328903i
$135$	−4.71295	−	10.3468i	−0.405626	−	0.890511i
$136$	−1.39859	+	2.20383i	−0.119928	+	0.188977i
$137$	−14.6799	−	5.81218i	−1.25419	−	0.496568i	−0.355302	−	0.934751i	$-0.615622\pi$
$137$	−14.6799	−	5.81218i	−1.25419	−	0.496568i	−0.898886	+	0.438183i	$0.855622\pi$
$138$	−0.450512	+	7.16069i	−0.0383501	+	0.609558i
$139$	0.269136	+	4.27780i	0.0228279	+	0.362838i	0.992813	+	0.119675i	$0.0381852\pi$
$139$	0.269136	+	4.27780i	0.0228279	+	0.362838i	−0.969985	+	0.243164i	$0.921815\pi$
$140$	6.68240	+	6.43304i	0.564765	+	0.543691i
$141$	14.9517	−	18.0735i	1.25916	−	1.52206i
$142$	2.59211	−	5.50851i	0.217525	−	0.462264i
$143$	12.0738	+	8.77213i	1.00966	+	0.733562i
$144$	0.0893504	+	0.0839056i	0.00744587	+	0.00699214i
$145$	−12.9783	−	12.4940i	−1.07779	−	1.03757i
$146$	−2.46060	+	12.8989i	−0.203641	+	1.06752i
$147$	−7.68012	−	16.3211i	−0.633446	−	1.34614i
$148$	−0.294312	−	0.0755666i	−0.0241923	−	0.00621154i
$149$	−6.50086	+	4.72315i	−0.532571	+	0.386936i	−0.821319	−	0.570470i	$-0.806761\pi$
$149$	−6.50086	+	4.72315i	−0.532571	+	0.386936i	0.288747	+	0.957405i	$0.406761\pi$
$150$	2.93792	−	8.33264i	0.239880	−	0.680357i
$151$	−15.7346	−	11.4318i	−1.28046	−	0.930310i	−0.280895	−	0.959738i	$-0.590631\pi$
$151$	−15.7346	−	11.4318i	−1.28046	−	0.930310i	−0.999567	+	0.0294281i	$0.990631\pi$
$152$	−2.02511	−	2.44793i	−0.164258	−	0.198554i
$153$	−0.280356	−	0.154127i	−0.0226655	−	0.0124605i
$154$	17.2303	+	9.47242i	1.38845	+	0.763309i
$155$	0.277065	−	0.326579i	0.0222544	−	0.0262315i
$156$	−2.36893	+	5.03423i	−0.189666	+	0.403061i
$157$	5.94682	+	18.3024i	0.474608	+	1.46069i	0.846485	+	0.532412i	$0.178714\pi$
$157$	5.94682	+	18.3024i	0.474608	+	1.46069i	−0.371877	+	0.928282i	$0.621286\pi$
$158$	1.91994	+	10.0647i	0.152742	+	0.800704i
$159$	11.7514	+	18.5172i	0.931943	+	1.46851i
$160$	−0.112708	−	2.23323i	−0.00891032	−	0.176552i
$161$	−15.6602	+	6.20029i	−1.23419	+	0.488652i
$162$	5.96163	−	7.20637i	0.468390	−	0.566186i
$163$	−2.19504	+	0.563591i	−0.171929	+	0.0441438i	−0.333673	−	0.942689i	$-0.608288\pi$
$163$	−2.19504	+	0.563591i	−0.171929	+	0.0441438i	0.161744	+	0.986833i	$0.448288\pi$
$164$	3.69152	+	4.46228i	0.288260	+	0.348446i
$165$	1.40781	−	18.6761i	0.109598	−	1.45393i
$166$	−5.36574	+	1.37769i	−0.416462	+	0.106929i
$167$	−16.9907	−	15.9553i	−1.31478	−	1.23466i	−0.953208	−	0.302315i	$-0.902241\pi$
$167$	−16.9907	−	15.9553i	−1.31478	−	1.23466i	−0.361571	−	0.932345i	$-0.617759\pi$
$168$	−2.26516	+	6.97146i	−0.174761	+	0.537860i
$169$	3.06225	+	0.386852i	0.235558	+	0.0297578i
$170$	1.73457	+	5.57278i	0.133036	+	0.427413i
$171$	0.283868	−	0.266570i	0.0217079	−	0.0203851i
$172$	−0.508379	+	0.0642232i	−0.0387635	+	0.00489697i
$173$	0.646804	+	10.2807i	0.0491756	+	0.781624i	0.942914	+	0.333036i	$0.108073\pi$
$173$	0.646804	+	10.2807i	0.0491756	+	0.781624i	−0.893739	+	0.448588i	$0.851927\pi$
$174$	4.39931	−	13.5397i	0.333511	−	1.02644i
$175$	20.6357	−	2.08822i	1.55991	−	0.157855i
$176$	−1.46473	−	4.50797i	−0.110408	−	0.339801i
$177$	−14.5067	+	5.74363i	−1.09039	+	0.431717i
$178$	2.19524	−	11.5079i	0.164541	−	0.862552i
$179$	−25.4005	+	3.20883i	−1.89852	+	0.239839i	−0.985700	−	0.168512i	$-0.946104\pi$
$179$	−25.4005	+	3.20883i	−1.89852	+	0.239839i	−0.912825	+	0.408352i	$0.866104\pi$
$180$	0.272321	−	0.0309750i	0.0202976	−	0.00230874i
$181$	12.0724	−	6.63684i	0.897333	−	0.493313i	0.0348460	−	0.999393i	$-0.488906\pi$
$181$	12.0724	−	6.63684i	0.897333	−	0.493313i	0.862487	+	0.506080i	$0.168906\pi$
$182$	−13.0609			−0.968138
$183$	−7.41434	+	4.07607i	−0.548084	+	0.301312i
$184$	3.77516	+	1.49469i	0.278308	+	0.110190i
$185$	−0.554598	+	0.392520i	−0.0407748	+	0.0288586i
$186$	0.327816	+	0.0841689i	0.0240367	+	0.00617156i
$187$	6.62927	+	10.4461i	0.484780	+	0.763891i
$188$	−7.11262	−	11.2077i	−0.518741	−	0.817405i
$189$	20.4296	+	5.24542i	1.48603	+	0.381548i
$190$	−7.10348	−	0.0881313i	−0.515341	−	0.00639371i
$191$	17.2612	+	6.83419i	1.24898	+	0.494505i	0.897219	−	0.441587i	$-0.145584\pi$
$191$	17.2612	+	6.83419i	1.24898	+	0.494505i	0.351757	+	0.936091i	$0.385584\pi$
$192$	1.54850	−	0.851297i	0.111754	−	0.0614371i
$193$	16.8863			1.21550			0.607750	−	0.794129i	$-0.292072\pi$
$193$	16.8863			1.21550			0.607750	+	0.794129i	$0.292072\pi$
$194$	4.71593	−	2.59261i	0.338584	−	0.186138i
$195$	5.15703	+	11.3217i	0.369303	+	0.810766i
$196$	−10.1272	+	1.27936i	−0.723371	+	0.0913831i
$197$	2.84621	−	14.9203i	0.202784	−	1.06303i	−0.724671	−	0.689095i	$-0.758008\pi$
$197$	2.84621	−	14.9203i	0.202784	−	1.06303i	0.927455	−	0.373935i	$-0.121992\pi$
$198$	0.540183	−	0.213874i	0.0383891	−	0.0151993i
$199$	−5.83735	−	17.9655i	−0.413799	−	1.27354i	−0.913321	−	0.407241i	$-0.866491\pi$
$199$	−5.83735	−	17.9655i	−0.413799	−	1.27354i	0.499522	−	0.866301i	$-0.333509\pi$
$200$	−3.97093	−	3.03838i	−0.280787	−	0.214846i
$201$	−2.08313	+	6.41121i	−0.146933	+	0.452212i
$202$	0.0558252	+	0.887316i	0.00392785	+	0.0624313i
$203$	33.1565	−	4.18864i	2.32713	−	0.293985i
$204$	−3.36226	+	3.15738i	−0.235405	+	0.221060i
$205$	12.9488	+	0.160652i	0.904382	+	0.0112205i
$206$	−13.0619	−	1.65010i	−0.910066	−	0.114968i
$207$	−0.153789	+	0.473315i	−0.0106891	+	0.0328977i
$208$	2.29520	+	2.15534i	0.159143	+	0.149446i
$209$	−14.5858	+	3.74501i	−1.00892	+	0.259047i
$210$	8.61031	+	13.9472i	0.594168	+	0.962447i
$211$	3.81425	+	4.61063i	0.262584	+	0.317409i	0.885283	−	0.465052i	$-0.153964\pi$
$211$	3.81425	+	4.61063i	0.262584	+	0.317409i	−0.622700	+	0.782461i	$0.713964\pi$
$212$	12.0211	−	3.08649i	0.825612	−	0.211981i
$213$	6.85730	−	8.28906i	0.469855	−	0.567957i
$214$	−14.4972	+	5.73986i	−0.991011	+	0.392369i
$215$	−0.625907	+	0.959744i	−0.0426865	+	0.0654540i
$216$	−2.72449	−	4.29311i	−0.185378	−	0.292109i
$217$	0.148876	+	0.780436i	0.0101064	+	0.0529794i
$218$	−0.878483	−	2.70369i	−0.0594984	−	0.183117i
$219$	−9.87997	+	20.9960i	−0.667627	+	1.41878i
$220$	−9.80542	−	4.02366i	−0.661081	−	0.271275i
$221$	−7.20169	−	3.95916i	−0.484438	−	0.266322i
$222$	−0.470526	−	0.258674i	−0.0315797	−	0.0173611i
$223$	13.0980	+	15.8327i	0.877106	+	1.06024i	0.997717	+	0.0675387i	$0.0215146\pi$
$223$	13.0980	+	15.8327i	0.877106	+	1.06024i	−0.120611	+	0.992700i	$0.538485\pi$
$224$	3.35598	+	2.43826i	0.224231	+	0.162913i
$225$	0.341121	−	0.509144i	0.0227414	−	0.0339429i
$226$	−4.03364	+	2.93061i	−0.268314	+	0.194941i
$227$	0.257763	+	0.0661823i	0.0171083	+	0.00439267i	0.257234	−	0.966349i	$-0.417189\pi$
$227$	0.257763	+	0.0661823i	0.0171083	+	0.00439267i	−0.240126	+	0.970742i	$0.577189\pi$
$228$	−2.39034	−	5.07974i	−0.158304	−	0.336414i
$229$	−4.48720	+	23.5227i	−0.296522	+	1.55442i	0.452429	+	0.891800i	$0.350557\pi$
$229$	−4.48720	+	23.5227i	−0.296522	+	1.55442i	−0.748952	+	0.662625i	$0.769443\pi$
$230$	8.00970	−	4.27484i	0.528144	−	0.281874i
$231$	25.3280	+	23.7846i	1.66646	+	1.56491i
$232$	−6.51784	−	4.73549i	−0.427917	−	0.310900i
$233$	−3.43974	+	7.30982i	−0.225345	+	0.478882i	−0.985243	−	0.171159i	$-0.945249\pi$
$233$	−3.43974	+	7.30982i	−0.225345	+	0.478882i	0.759898	+	0.650042i	$0.225249\pi$
$234$	−0.245996	+	0.297358i	−0.0160813	+	0.0194389i
$235$	−29.3993	−	4.08515i	−1.91780	−	0.266486i
$236$	0.554408	+	8.81206i	0.0360889	+	0.573616i
$237$	−1.13687	+	18.0701i	−0.0738479	+	1.17378i
$238$	−10.0672	−	3.98587i	−0.652556	−	0.258365i
$239$	10.3326	−	16.2815i	0.668358	−	1.05316i	−0.325822	−	0.945431i	$-0.605641\pi$
$239$	10.3326	−	16.2815i	0.668358	−	1.05316i	0.994180	−	0.107733i	$-0.0343591\pi$
$240$	0.788496	−	3.87184i	0.0508972	−	0.249926i
$241$	−0.400219	+	6.36130i	−0.0257804	+	0.409768i	0.963880	+	0.266337i	$0.0858134\pi$
$241$	−0.400219	+	6.36130i	−0.0257804	+	0.409768i	−0.989660	+	0.143431i	$0.954187\pi$
$242$	−11.3768	−	1.43722i	−0.731328	−	0.0923882i
$243$	1.02989	−	0.748256i	0.0660672	−	0.0480006i
$244$	0.897195	+	4.70326i	0.0574370	+	0.301095i
$245$	−12.4684	+	19.1187i	−0.796579	+	1.22145i
$246$	4.35730	+	9.25974i	0.277812	+	0.590380i
$247$	7.29189	−	6.84754i	0.463972	−	0.435699i
$248$	0.102627	−	0.161714i	0.00651682	−	0.0102689i
$249$	−9.78924			−0.620368
$250$	−10.9250	+	2.37556i	−0.690961	+	0.150244i
$251$	10.9339			0.690139			0.345069	−	0.938577i	$-0.387855\pi$
$251$	10.9339			0.690139			0.345069	+	0.938577i	$0.387855\pi$
$252$	−0.272442	+	0.429299i	−0.0171622	+	0.0270433i
$253$	14.0294	−	13.1745i	0.882022	−	0.828274i
$254$	−0.281814	−	0.598885i	−0.0176826	−	0.0375774i
$255$	0.519847	+	10.3004i	0.0325541	+	0.645038i
$256$	−0.187381	−	0.982287i	−0.0117113	−	0.0613930i
$257$	13.8340	−	10.0510i	0.862939	−	0.626962i	−0.0657438	−	0.997837i	$-0.520942\pi$
$257$	13.8340	−	10.0510i	0.862939	−	0.626962i	0.928683	+	0.370875i	$0.120942\pi$
$258$	−0.898346	−	0.113487i	−0.0559286	−	0.00706542i
$259$	0.0791457	−	1.25798i	0.00491787	−	0.0781673i
$260$	6.99528	−	0.795674i	0.433829	−	0.0493456i
$261$	0.529125	−	0.833767i	0.0327520	−	0.0516089i
$262$	6.61657	+	2.61969i	0.408773	+	0.161845i
$263$	1.12069	−	17.8128i	0.0691045	−	1.09839i	−0.798781	−	0.601622i	$-0.794522\pi$
$263$	1.12069	−	17.8128i	0.0691045	−	1.09839i	0.867886	−	0.496764i	$-0.165478\pi$
$264$	−0.525926	−	8.35936i	−0.0323685	−	0.514483i
$265$	12.1268	−	24.9621i	0.744942	−	1.53341i
$266$	8.40058	−	10.1546i	0.515073	−	0.622616i
$267$	8.81449	−	18.7318i	0.539438	−	1.14636i
$268$	3.08628	+	2.24231i	0.188525	+	0.136971i
$269$	17.2608	+	16.2090i	1.05241	+	0.988279i	0.999947	−	0.0103437i	$-0.00329258\pi$
$269$	17.2608	+	16.2090i	1.05241	+	0.988279i	0.0524638	+	0.998623i	$0.483293\pi$
$270$	−11.2614	−	1.56482i	−0.685348	−	0.0952318i
$271$	−0.396649	+	2.07930i	−0.0240947	+	0.126309i	−0.992302	−	0.123839i	$-0.960479\pi$
$271$	−0.396649	+	2.07930i	−0.0240947	+	0.126309i	0.968208	+	0.250148i	$0.0804793\pi$
$272$	1.11135	+	2.36174i	0.0673855	+	0.143202i
$273$	−22.3546	−	5.73967i	−1.35296	−	0.347381i
$274$	−12.7733	+	9.28032i	−0.771661	+	0.560645i
$275$	−21.0452	+	10.8987i	−1.26907	+	0.657216i
$276$	5.80457	+	4.21727i	0.349394	+	0.253850i
$277$	9.28247	+	11.2206i	0.557730	+	0.674179i	0.971729	−	0.236098i	$-0.0758685\pi$
$277$	9.28247	+	11.2206i	0.557730	+	0.674179i	−0.414000	+	0.910277i	$0.635869\pi$
$278$	3.75608	+	2.06492i	0.225275	+	0.123846i
$279$	0.0205722	+	0.0113097i	0.00123163	+	0.000677093i
$280$	9.01220	−	2.19514i	0.538582	−	0.131184i
$281$	−9.68582	+	20.5834i	−0.577807	+	1.22790i	0.375758	+	0.926718i	$0.377382\pi$
$281$	−9.68582	+	20.5834i	−0.577807	+	1.22790i	−0.953566	+	0.301185i	$0.902618\pi$
$282$	−7.24843	−	22.3084i	−0.431638	−	1.32844i
$283$	0.886779	+	4.64866i	0.0527135	+	0.276334i	0.998878	−	0.0473514i	$-0.0150780\pi$
$283$	0.886779	+	4.64866i	0.0527135	+	0.276334i	−0.946165	+	0.323685i	$0.895078\pi$
$284$	−3.26207	−	5.14020i	−0.193568	−	0.305015i
$285$	−12.1193	−	3.27250i	−0.717887	−	0.193846i
$286$	13.8760	−	5.49390i	0.820506	−	0.324861i
$287$	−15.3132	+	18.5105i	−0.903912	+	1.09264i
$288$	0.118720	−	0.0304822i	0.00699566	−	0.00179618i
$289$	6.49349	+	7.84928i	0.381970	+	0.461722i
$290$	−17.5031	+	4.26330i	−1.02782	+	0.250350i
$291$	9.21096	−	2.36497i	0.539956	−	0.138637i
$292$	9.57247	+	8.98915i	0.560186	+	0.526050i
$293$	10.2244	−	31.4676i	0.597318	−	1.83835i	0.0544836	−	0.998515i	$-0.482649\pi$
$293$	10.2244	−	31.4676i	0.597318	−	1.83835i	0.542834	−	0.839840i	$-0.317351\pi$
$294$	−17.8956	−	2.26074i	−1.04369	−	0.131849i
$295$	15.8275	+	11.8021i	0.921512	+	0.687144i
$296$	−0.221504	+	0.208006i	−0.0128746	+	0.0120901i
$297$	−23.9110	+	3.02066i	−1.38746	+	0.175276i
$298$	0.504554	+	8.01965i	0.0292280	+	0.464566i
$299$	−3.95048	+	12.1583i	−0.228462	+	0.703135i
$300$	−5.46126	−	6.94542i	−0.315306	−	0.400994i
$301$	−0.656855	−	2.02159i	−0.0378605	−	0.116523i
$302$	−18.0832	+	7.15966i	−1.04057	+	0.411992i
$303$	−0.294387	+	1.54323i	−0.0169121	+	0.0886563i
$304$	−3.15197	+	0.398186i	−0.180778	+	0.0228375i
$305$	9.31742	+	5.27387i	0.533514	+	0.301981i
$306$	−0.280356	+	0.154127i	−0.0160269	+	0.00881087i
$307$	16.7214			0.954338			0.477169	−	0.878811i	$-0.341663\pi$
$307$	16.7214			0.954338			0.477169	+	0.878811i	$0.341663\pi$
$308$	17.2303	−	9.47242i	0.981786	−	0.539741i
$309$	−21.6311	−	8.56437i	−1.23055	−	0.487210i
$310$	−0.127281	−	0.408924i	−0.00722907	−	0.0232253i
$311$	2.05732	+	0.528231i	0.116660	+	0.0299532i	0.306569	−	0.951849i	$-0.400819\pi$
$311$	2.05732	+	0.528231i	0.116660	+	0.0299532i	−0.189909	+	0.981802i	$0.560819\pi$
$312$	2.98121	+	4.69763i	0.168778	+	0.265951i
$313$	3.64472	+	5.74316i	0.206012	+	0.324623i	0.931586	−	0.363521i	$-0.118426\pi$
$313$	3.64472	+	5.74316i	0.206012	+	0.324623i	−0.725574	+	0.688144i	$0.758426\pi$
$314$	18.6397	+	4.78587i	1.05190	+	0.270082i
$315$	0.337890	+	1.08556i	0.0190379	+	0.0611644i
$316$	9.52666	+	3.77187i	0.535916	+	0.212184i
$317$	−9.52597	+	5.23695i	−0.535032	+	0.294136i	−0.726272	−	0.687407i	$-0.758749\pi$
$317$	−9.52597	+	5.23695i	−0.535032	+	0.294136i	0.191241	+	0.981543i	$0.438749\pi$
$318$	21.9312			1.22984
$319$	−33.4639	+	18.3969i	−1.87362	+	1.03003i
$320$	−1.94597	−	1.10146i	−0.108783	−	0.0615735i
$321$	−27.3354	+	3.45326i	−1.52571	+	0.192742i
$322$	−3.15605	+	16.5446i	−0.175880	+	0.921994i
$323$	7.71019	−	3.05268i	0.429006	−	0.169856i
$324$	−2.89014	−	8.89494i	−0.160563	−	0.494163i
$325$	8.76258	−	13.0787i	0.486061	−	0.725476i
$326$	−0.700306	+	2.15532i	−0.0387864	+	0.119372i
$327$	−0.315429	−	5.01360i	−0.0174432	−	0.277252i
$328$	5.74565	−	0.725844i	0.317250	−	0.0400780i
$329$	40.1398	−	37.6938i	2.21298	−	2.07813i
$330$	−15.0144	−	11.1958i	−0.826515	−	0.616308i
$331$	−9.99294	−	1.26240i	−0.549262	−	0.0693879i	−0.154195	−	0.988040i	$-0.549278\pi$
$331$	−9.99294	−	1.26240i	−0.549262	−	0.0693879i	−0.395066	+	0.918653i	$0.629278\pi$
$332$	−1.71189	+	5.26865i	−0.0939520	+	0.289154i
$333$	−0.0271499	−	0.0254955i	−0.00148781	−	0.00139714i
$334$	−22.5756	+	5.79643i	−1.23528	+	0.317166i
$335$	8.28796	−	2.01873i	0.452820	−	0.110295i
$336$	4.67246	+	5.64804i	0.254904	+	0.308126i
$337$	5.76500	−	1.48020i	0.314040	−	0.0806317i	−0.0883805	−	0.996087i	$-0.528169\pi$
$337$	5.76500	−	1.48020i	0.314040	−	0.0806317i	0.402420	+	0.915455i	$0.368169\pi$
$338$	1.96747	−	2.37826i	0.107016	−	0.129360i
$339$	−8.19171	+	3.24333i	−0.444913	+	0.176153i
$340$	5.63468	+	1.52150i	0.305584	+	0.0825147i
$341$	−0.486448	−	0.766519i	−0.0263426	−	0.0415094i
$342$	−0.0729682	−	0.382513i	−0.00394567	−	0.0206839i
$343$	−4.11184	−	12.6549i	−0.222019	−	0.683303i
$344$	−0.218178	+	0.463651i	−0.0117633	+	0.0249984i
$345$	15.5877	−	3.79675i	0.839214	−	0.204410i
$346$	9.02682	+	4.96254i	0.485285	+	0.266788i
$347$	7.25792	+	3.99007i	0.389625	+	0.214198i	0.664511	−	0.747279i	$-0.268640\pi$
$347$	7.25792	+	3.99007i	0.389625	+	0.214198i	−0.274885	+	0.961477i	$0.588640\pi$
$348$	−9.07466	−	10.9694i	−0.486453	−	0.588021i
$349$	−14.1411	−	10.2741i	−0.756958	−	0.549962i	0.141018	−	0.990007i	$-0.454963\pi$
$349$	−14.1411	−	10.2741i	−0.756958	−	0.549962i	−0.897976	+	0.440045i	$0.854963\pi$
$350$	9.29401	−	18.5422i	0.496786	−	0.991123i
$351$	12.9518	−	9.41003i	0.691316	−	0.502270i
$352$	−4.59104	−	1.17878i	−0.244703	−	0.0628292i
$353$	5.02433	+	10.6772i	0.267418	+	0.568292i	0.992763	−	0.120094i	$-0.0383195\pi$
$353$	5.02433	+	10.6772i	0.267418	+	0.568292i	−0.725345	+	0.688386i	$0.758320\pi$
$354$	−2.92360	+	15.3260i	−0.155387	+	0.814570i
$355$	−13.4835	−	1.87358i	−0.715627	−	0.0994392i
$356$	−8.54015	−	8.01974i	−0.452627	−	0.425045i
$357$	−15.4790	−	11.2461i	−0.819233	−	0.595208i
$358$	−10.9010	+	23.1658i	−0.576134	+	1.22435i
$359$	6.82622	−	8.25148i	0.360274	−	0.435497i	−0.558968	−	0.829189i	$-0.688803\pi$
$359$	6.82622	−	8.25148i	0.360274	−	0.435497i	0.919242	+	0.393693i	$0.128803\pi$
$360$	0.119764	−	0.246526i	0.00631211	−	0.0129930i
$361$	−0.559247	−	8.88898i	−0.0294341	−	0.467841i
$362$	0.865029	−	13.7492i	0.0454649	−	0.722644i
$363$	−18.8405	−	7.45948i	−0.988870	−	0.391521i
$364$	−6.99838	+	11.0277i	−0.366815	+	0.578007i
$365$	29.1749	−	3.31847i	1.52708	−	0.173697i
$366$	−0.531264	+	8.44420i	−0.0277696	+	0.441386i
$367$	−27.3309	−	3.45270i	−1.42666	−	0.180229i	−0.626223	−	0.779644i	$-0.715400\pi$
$367$	−27.3309	−	3.45270i	−1.42666	−	0.180229i	−0.800439	+	0.599414i	$0.795400\pi$
$368$	3.28484	−	2.38657i	0.171234	−	0.124409i
$369$	0.133012	+	0.697274i	0.00692433	+	0.0362986i
$370$	0.0342472	+	0.678585i	0.00178043	+	0.0352780i
$371$	21.9206	+	46.5837i	1.13806	+	2.41851i
$372$	0.246719	−	0.231684i	0.0127918	−	0.0120123i
$373$	7.60459	−	11.9829i	0.393751	−	0.620452i	−0.588395	−	0.808574i	$-0.700240\pi$
$373$	7.60459	−	11.9829i	0.393751	−	0.620452i	0.982146	+	0.188122i	$0.0602400\pi$
$374$	12.3720			0.639743
$375$	−19.7429	−	0.735137i	−1.01952	−	0.0379623i
$376$	−13.2741			−0.684560
$377$	13.5920	−	21.4175i	0.700021	−	1.10306i
$378$	15.3756	−	14.4386i	0.790833	−	0.742642i
$379$	−9.01562	−	19.1592i	−0.463101	−	0.984141i	−0.990879	−	0.134758i	$-0.956974\pi$
$379$	−9.01562	−	19.1592i	−0.463101	−	0.984141i	0.527777	−	0.849383i	$-0.323026\pi$
$380$	−3.88065	+	5.95045i	−0.199073	+	0.305251i
$381$	−0.219159	−	1.14887i	−0.0112279	−	0.0588586i
$382$	15.0193	−	10.9122i	0.768454	−	0.558315i
$383$	−18.3868	−	2.32279i	−0.939521	−	0.118689i	−0.359368	−	0.933196i	$-0.617008\pi$
$383$	−18.3868	−	2.32279i	−0.939521	−	0.118689i	−0.580154	+	0.814507i	$0.697008\pi$
$384$	0.110956	−	1.76359i	0.00566219	−	0.0899980i
$385$	8.77363	−	43.0821i	0.447145	−	2.19567i
$386$	9.04811	−	14.2575i	0.460537	−	0.725690i
$387$	−0.0583972	−	0.0231211i	−0.00296850	−	0.00117531i
$388$	0.337914	−	5.37098i	0.0171550	−	0.272670i
$389$	−1.90541	−	30.2856i	−0.0966080	−	1.53554i	−0.685946	−	0.727653i	$-0.740611\pi$
$389$	−1.90541	−	30.2856i	−0.0966080	−	1.53554i	0.589338	−	0.807887i	$-0.299389\pi$
$390$	12.3225	+	1.71226i	0.623976	+	0.0867039i
$391$	−6.75540	+	8.16588i	−0.341635	+	0.412966i
$392$	−4.34622	+	9.23620i	−0.219517	+	0.466498i
$393$	10.1735	+	7.39144i	0.513183	+	0.372849i
$394$	−11.0726	−	10.3978i	−0.557829	−	0.523836i
$395$	20.2126	−	10.7876i	1.01701	−	0.542784i
$396$	0.108865	−	0.570691i	0.00547068	−	0.0286783i
$397$	4.99707	+	10.6193i	0.250796	+	0.532968i	0.990093	−	0.140411i	$-0.0448424\pi$
$397$	4.99707	+	10.6193i	0.250796	+	0.532968i	−0.739298	+	0.673379i	$0.764842\pi$
$398$	−18.2966	−	4.69777i	−0.917126	−	0.235478i
$399$	18.8406	−	13.6885i	0.943210	−	0.685282i
$400$	−4.69312	+	1.72472i	−0.234656	+	0.0862359i
$401$	2.53734	+	1.84348i	0.126709	+	0.0920592i	0.649334	−	0.760503i	$-0.275048\pi$
$401$	2.53734	+	1.84348i	0.126709	+	0.0920592i	−0.522626	+	0.852562i	$0.675048\pi$
$402$	4.29697	+	5.19415i	0.214313	+	0.259060i
$403$	0.528452	+	0.290519i	0.0263240	+	0.0144718i
$404$	0.779098	+	0.428313i	0.0387616	+	0.0213094i
$405$	−19.3476	−	7.93931i	−0.961392	−	0.394508i
$406$	14.2296	−	30.2394i	0.706202	−	1.50075i
$407$	0.445070	+	1.36979i	0.0220613	+	0.0678978i
$408$	0.864269	+	4.53066i	0.0427877	+	0.224301i
$409$	10.6829	+	16.8336i	0.528237	+	0.832368i	0.998748	−	0.0500257i	$-0.0159303\pi$
$409$	10.6829	+	16.8336i	0.528237	+	0.832368i	−0.470511	+	0.882394i	$0.655930\pi$
$410$	7.07395	−	10.8469i	0.349357	−	0.535692i
$411$	−25.9405	+	10.2706i	−1.27955	+	0.506611i
$412$	−8.39215	+	10.1444i	−0.413451	+	0.499777i
$413$	−35.4759	+	9.10866i	−1.74565	+	0.448208i
$414$	0.317229	+	0.383464i	0.0155909	+	0.0188462i
$415$	6.50720	+	10.5405i	0.319426	+	0.517413i
$416$	3.04964	−	0.783014i	0.149521	−	0.0383904i
$417$	5.52133	+	5.18487i	0.270381	+	0.253904i
$418$	−4.65347	+	14.3219i	−0.227609	+	0.700507i
$419$	7.74269	+	0.978129i	0.378255	+	0.0477847i	0.312162	−	0.950029i	$-0.398947\pi$
$419$	7.74269	+	0.978129i	0.378255	+	0.0477847i	0.0660926	+	0.997813i	$0.478947\pi$
$420$	16.3896	+	0.203342i	0.799732	+	0.00992209i
$421$	1.27452	−	1.19686i	0.0621165	−	0.0583313i	−0.652867	−	0.757472i	$-0.726434\pi$
$421$	1.27452	−	1.19686i	0.0621165	−	0.0583313i	0.714984	+	0.699141i	$0.246434\pi$
$422$	5.93666	−	0.749975i	0.288992	−	0.0365082i
$423$	−0.102161	−	1.62381i	−0.00496726	−	0.0789523i
$424$	3.83521	−	11.8036i	0.186254	−	0.573232i
$425$	10.7454	−	7.40675i	0.521227	−	0.359280i
$426$	−3.32435	−	10.2313i	−0.161066	−	0.495709i
$427$	−18.4672	+	7.31167i	−0.893689	+	0.353836i
$428$	−2.92168	+	15.3160i	−0.141225	+	0.740326i
$429$	26.1640	−	3.30528i	1.26321	−	0.159581i
$430$	0.474961	+	1.04273i	0.0229046	+	0.0502848i
$431$	20.2606	−	11.1383i	0.975917	−	0.536515i	0.0878031	−	0.996138i	$-0.472015\pi$
$431$	20.2606	−	11.1383i	0.975917	−	0.536515i	0.888114	+	0.459623i	$0.152015\pi$
$432$	−5.08465			−0.244635
$433$	3.60630	−	1.98258i	0.173308	−	0.0952768i	−0.392739	−	0.919650i	$-0.628472\pi$
$433$	3.60630	−	1.98258i	0.173308	−	0.0952768i	0.566046	+	0.824373i	$0.308472\pi$
$434$	0.738716	+	0.292478i	0.0354595	+	0.0140394i
$435$	−31.8312	−	0.394923i	−1.52619	−	0.0189351i
$436$	−2.75352	−	0.706983i	−0.131870	−	0.0338584i
$437$	−6.91195	−	10.8915i	−0.330643	−	0.521010i
$438$	12.4336	+	19.5922i	0.594099	+	0.936150i
$439$	−7.91221	−	2.03151i	−0.377629	−	0.0969587i	0.0551042	−	0.998481i	$-0.482451\pi$
$439$	−7.91221	−	2.03151i	−0.377629	−	0.0969587i	−0.432733	+	0.901522i	$0.642451\pi$
$440$	−8.65129	+	6.12300i	−0.412434	+	0.291903i
$441$	−1.16331	−	0.460585i	−0.0553955	−	0.0219326i
$442$	−7.20169	+	3.95916i	−0.342549	+	0.188318i
$443$	−26.3559			−1.25221			−0.626103	−	0.779741i	$-0.715351\pi$
$443$	−26.3559			−1.25221			−0.626103	+	0.779741i	$0.715351\pi$
$444$	−0.470526	+	0.258674i	−0.0223302	+	0.0122761i
$445$	−26.0286	+	2.96060i	−1.23387	+	0.140346i
$446$	20.3863	−	2.57538i	0.965318	−	0.121948i
$447$	−2.66070	+	13.9479i	−0.125847	+	0.659712i
$448$	3.85691	−	1.52706i	0.182222	−	0.0721468i
$449$	1.43977	+	4.43116i	0.0679470	+	0.209119i	0.979265	−	0.202584i	$-0.0649340\pi$
$449$	1.43977	+	4.43116i	0.0679470	+	0.209119i	−0.911318	+	0.411703i	$0.864934\pi$
$450$	−0.247103	−	0.560831i	−0.0116485	−	0.0264378i
$451$	8.48270	−	26.1071i	0.399435	−	1.22933i
$452$	0.313065	+	4.97602i	0.0147253	+	0.234052i
$453$	−34.0970	+	4.30745i	−1.60201	+	0.202382i
$454$	0.193996	−	0.182174i	0.00910468	−	0.00854986i
$455$	8.67958	+	27.8855i	0.406905	+	1.30729i
$456$	−5.56978	−	0.703626i	−0.260829	−	0.0329503i
$457$	7.05217	−	21.7044i	0.329887	−	1.01529i	−0.639300	−	0.768958i	$-0.720776\pi$
$457$	7.05217	−	21.7044i	0.329887	−	1.01529i	0.969186	−	0.246329i	$-0.0792244\pi$
$458$	17.4565	+	16.3928i	0.815690	+	0.765984i
$459$	12.8548	−	3.30054i	0.600009	−	0.154056i
$460$	0.682446	−	9.05338i	0.0318192	−	0.422116i
$461$	−10.7390	−	12.9812i	−0.500164	−	0.604595i	0.458654	−	0.888615i	$-0.348332\pi$
$461$	−10.7390	−	12.9812i	−0.500164	−	0.604595i	−0.958818	+	0.284020i	$0.908332\pi$
$462$	33.6534	−	8.64072i	1.56570	−	0.402003i
$463$	15.2304	−	18.4104i	0.707817	−	0.855604i	−0.286932	−	0.957951i	$-0.592635\pi$
$463$	15.2304	−	18.4104i	0.707817	−	0.855604i	0.994749	+	0.102347i	$0.0326353\pi$
$464$	−7.49073	+	2.96579i	−0.347749	+	0.137683i
$465$	−0.0381458	−	0.755834i	−0.00176897	−	0.0350509i
$466$	4.32878	+	6.82107i	0.200527	+	0.315980i
$467$	−0.350921	−	1.83959i	−0.0162387	−	0.0851262i	0.973245	−	0.229768i	$-0.0737969\pi$
$467$	−0.350921	−	1.83959i	−0.0162387	−	0.0851262i	−0.989484	+	0.144642i	$0.953797\pi$
$468$	0.119256	+	0.367033i	0.00551263	+	0.0169661i
$469$	−6.73789	+	14.3187i	−0.311127	+	0.661178i
$470$	−19.2022	+	22.6337i	−0.885730	+	1.04402i
$471$	29.7999	+	16.3826i	1.37311	+	0.754872i
$472$	7.73733	+	4.25364i	0.356140	+	0.195789i
$473$	1.54821	+	1.87146i	0.0711866	+	0.0860498i
$474$	14.6479	+	10.6423i	0.672801	+	0.488819i
$475$	4.53244	+	15.2248i	0.207962	+	0.698560i
$476$	−8.75963	+	6.36424i	−0.401497	+	0.291705i
$477$	1.47344	+	0.378315i	0.0674641	+	0.0173218i
$478$	−8.21048	−	17.4482i	−0.375538	−	0.798060i
$479$	−0.140185	+	0.734875i	−0.00640521	+	0.0335773i	−0.985346	−	0.170565i	$-0.945441\pi$
$479$	−0.140185	+	0.734875i	−0.00640521	+	0.0335773i	0.978941	+	0.204143i	$0.0654406\pi$
$480$	−2.84660	−	2.74038i	−0.129929	−	0.125081i
$481$	−0.697416	−	0.654918i	−0.0317995	−	0.0298617i
$482$	5.15658	+	3.74647i	0.234876	+	0.170647i
$483$	−12.6724	+	26.9302i	−0.576613	+	1.22537i
$484$	−7.30948	+	8.83564i	−0.332249	+	0.401620i
$485$	−8.66927	−	8.34578i	−0.393651	−	0.378962i
$486$	−0.0799329	−	1.27050i	−0.00362583	−	0.0576309i
$487$	−0.125026	+	1.98724i	−0.00566549	+	0.0900504i	−0.999843	−	0.0177014i	$-0.994365\pi$
$487$	−0.125026	+	1.98724i	−0.00566549	+	0.0900504i	0.994178	+	0.107752i	$0.0343652\pi$
$488$	4.45183	+	1.76261i	0.201525	+	0.0797894i
$489$	−2.14579	+	3.38122i	−0.0970358	+	0.152904i
$490$	9.46149	+	20.7717i	0.427427	+	0.938371i
$491$	−0.149269	+	2.37257i	−0.00673643	+	0.107073i	−0.999958	−	0.00916385i	$-0.997083\pi$
$491$	−0.149269	+	2.37257i	−0.00673643	+	0.107073i	0.993222	+	0.116236i	$0.0370830\pi$
$492$	10.1530	+	1.28262i	0.457733	+	0.0578252i
$493$	17.0126	−	12.3604i	0.766208	−	0.556683i
$494$	−1.87438	−	9.82584i	−0.0843323	−	0.442086i
$495$	−0.815605	−	1.01118i	−0.0366587	−	0.0454492i
$496$	−0.0815496	−	0.173302i	−0.00366169	−	0.00778148i
$497$	18.4094	−	17.2876i	0.825773	−	0.775453i
$498$	−5.24533	+	8.26533i	−0.235049	+	0.370378i
$499$	−34.7153			−1.55407			−0.777034	−	0.629458i	$-0.783277\pi$
$499$	−34.7153			−1.55407			−0.777034	+	0.629458i	$0.783277\pi$
$500$	−3.84818	+	10.4972i	−0.172096	+	0.469450i
$501$	−41.1868			−1.84009
$502$	5.85865	−	9.23176i	0.261484	−	0.412034i
$503$	−6.84274	+	6.42576i	−0.305103	+	0.286511i	−0.821941	−	0.569572i	$-0.807109\pi$
$503$	−6.84274	+	6.42576i	−0.305103	+	0.286511i	0.516838	+	0.856083i	$0.327109\pi$
$504$	0.216488	+	0.460060i	0.00964314	+	0.0204927i
$505$	1.85735	−	0.708852i	0.0826511	−	0.0315435i
$506$	−3.60626	−	18.9047i	−0.160318	−	0.840416i
$507$	4.41258	−	3.20593i	0.195969	−	0.142380i
$508$	−0.656658	−	0.0829552i	−0.0291345	−	0.00368054i
$509$	0.712530	−	11.3253i	0.0315823	−	0.501987i	−0.950159	−	0.311766i	$-0.899080\pi$
$509$	0.712530	−	11.3253i	0.0315823	−	0.501987i	0.981741	−	0.190221i	$-0.0609204\pi$
$510$	8.97549	+	5.08033i	0.397441	+	0.224961i
$511$	−29.1878	+	45.9926i	−1.29119	+	2.03459i
$512$	−0.929776	−	0.368125i	−0.0410907	−	0.0162690i
$513$	−1.01432	+	16.1221i	−0.0447833	+	0.711810i
$514$	−1.07370	−	17.0660i	−0.0473589	−	0.752748i
$515$	5.15723	+	28.9842i	0.227255	+	1.27720i
$516$	−0.577178	+	0.697689i	−0.0254089	+	0.0307140i
$517$	−26.7895	+	56.9305i	−1.17820	+	2.50380i
$518$	−1.01974	−	0.740887i	−0.0448049	−	0.0325527i
$519$	13.2692	+	12.4606i	0.582452	+	0.546959i
$520$	3.07645	−	6.33265i	0.134911	−	0.277705i
$521$	−3.36745	+	17.6528i	−0.147531	+	0.773382i	0.829207	+	0.558942i	$0.188793\pi$
$521$	−3.36745	+	17.6528i	−0.147531	+	0.773382i	−0.976737	+	0.214440i	$0.931207\pi$
$522$	−0.420454	−	0.893510i	−0.0184028	−	0.0391078i
$523$	−6.32653	−	1.62438i	−0.276640	−	0.0710290i	0.107821	−	0.994170i	$-0.465613\pi$
$523$	−6.32653	−	1.62438i	−0.276640	−	0.0710290i	−0.384461	+	0.923141i	$0.625613\pi$
$524$	5.75721	−	4.18286i	0.251505	−	0.182729i
$525$	24.0558	−	27.6519i	1.04988	−	1.20683i
$526$	−14.4394	−	10.4908i	−0.629586	−	0.457421i
$527$	0.318664	+	0.385198i	0.0138812	+	0.0167795i
$528$	−7.33984	−	4.03511i	−0.319426	−	0.175606i
$529$	−5.70835	−	3.13819i	−0.248189	−	0.136443i
$530$	−14.5784	−	23.6144i	−0.633244	−	1.02574i
$531$	−0.460795	+	0.979239i	−0.0199968	+	0.0424953i
$532$	−4.07252	−	12.5339i	−0.176566	−	0.543415i
$533$	3.41676	+	17.9113i	0.147996	+	0.775825i
$534$	−11.0927	−	17.4793i	−0.480028	−	0.756403i
$535$	21.8889	+	27.1377i	0.946340	+	1.17327i
$536$	3.54696	−	1.40434i	0.153205	−	0.0606583i
$537$	−28.8380	+	34.8592i	−1.24445	+	1.50428i
$538$	22.9345	−	5.88858i	0.988777	−	0.253875i
$539$	30.8411	+	37.2805i	1.32842	+	1.60579i
$540$	−7.35539	+	8.66986i	−0.316526	+	0.373091i
$541$	10.5070	−	2.69773i	0.451730	−	0.115985i	−0.0159686	−	0.999872i	$-0.505083\pi$
$541$	10.5070	−	2.69773i	0.451730	−	0.115985i	0.467699	+	0.883888i	$0.345083\pi$
$542$	1.54308	+	1.44905i	0.0662810	+	0.0622420i
$543$	7.52272	−	23.1526i	0.322831	−	0.993572i
$544$	2.58958	+	0.327139i	0.111027	+	0.0140260i
$545$	−5.18869	+	3.67232i	−0.222259	+	0.157305i
$546$	−16.8243	+	15.7991i	−0.720015	+	0.676139i
$547$	31.3533	−	3.96085i	1.34057	−	0.169354i	0.577883	−	0.816119i	$-0.303879\pi$
$547$	31.3533	−	3.96085i	1.34057	−	0.169354i	0.762689	+	0.646766i	$0.223879\pi$
$548$	0.991376	+	15.7575i	0.0423495	+	0.673126i
$549$	−0.181355	+	0.558155i	−0.00774006	+	0.0238215i
$550$	−2.07449	+	23.6088i	−0.0884565	+	1.00668i
$551$	7.90948	+	24.3429i	0.336955	+	1.03704i
$552$	6.67100	−	2.64124i	0.283937	−	0.112418i
$553$	−7.96434	+	41.7505i	−0.338678	+	1.77541i
$554$	14.4476	−	1.82516i	0.613822	−	0.0775437i
$555$	−0.239591	+	1.17649i	−0.0101701	+	0.0499393i
$556$	3.75608	−	2.06492i	0.159293	−	0.0875722i
$557$	−20.2961			−0.859975			−0.429987	−	0.902835i	$-0.641482\pi$
$557$	−20.2961			−0.859975			−0.429987	+	0.902835i	$0.641482\pi$
$558$	0.0205722	−	0.0113097i	0.000870892	−	0.000478777i
$559$	−1.50008	−	0.593925i	−0.0634468	−	0.0251204i
$560$	2.97557	−	8.78547i	0.125741	−	0.371254i
$561$	21.1755	+	5.43695i	0.894032	+	0.229548i
$562$	12.1892	+	19.2071i	0.514171	+	0.810205i
$563$	−2.75662	−	4.34374i	−0.116178	−	0.183067i	0.781263	−	0.624202i	$-0.214576\pi$
$563$	−2.75662	−	4.34374i	−0.116178	−	0.183067i	−0.897441	+	0.441135i	$0.854576\pi$
$564$	−22.7195	−	5.83337i	−0.956662	−	0.245629i
$565$	8.93751	+	6.66444i	0.376004	+	0.280375i
$566$	4.40015	+	1.74214i	0.184952	+	0.0732278i
$567$	33.9980	−	18.6906i	1.42778	−	0.784931i
$568$	−6.08792			−0.255443
$569$	−28.7260	+	15.7922i	−1.20425	+	0.662045i	−0.952143	−	0.305654i	$-0.901125\pi$
$569$	−28.7260	+	15.7922i	−1.20425	+	0.662045i	−0.252112	+	0.967698i	$0.581125\pi$
$570$	−9.25693	+	8.47920i	−0.387730	+	0.355155i
$571$	−14.6716	+	1.85345i	−0.613986	+	0.0775644i	−0.426175	−	0.904641i	$-0.640139\pi$
$571$	−14.6716	+	1.85345i	−0.613986	+	0.0775644i	−0.187811	+	0.982205i	$0.560139\pi$
$572$	2.79648	−	14.6597i	0.116927	−	0.612952i
$573$	30.5019	−	12.0766i	1.27424	−	0.504505i
$574$	7.42371	+	22.8478i	0.309860	+	0.953650i
$575$	−14.4498	−	14.2602i	−0.602596	−	0.594690i
$576$	0.0378765	−	0.116572i	0.00157819	−	0.00485716i
$577$	−1.45018	−	23.0500i	−0.0603718	−	0.959582i	−0.905319	−	0.424732i	$-0.860368\pi$
$577$	−1.45018	−	23.0500i	−0.0603718	−	0.959582i	0.844947	−	0.534850i	$-0.179632\pi$
$578$	10.1068	−	1.27678i	0.420385	−	0.0531070i
$579$	21.7520	−	20.4265i	0.903981	−	0.848894i
$580$	−5.77902	+	17.0628i	−0.239961	+	0.708493i
$581$	−22.7990	−	2.88018i	−0.945862	−	0.119490i
$582$	2.93867	−	9.04428i	0.121812	−	0.374898i
$583$	−42.8835	−	40.2703i	−1.77605	−	1.66783i
$584$	12.7190	−	3.26568i	0.526315	−	0.135135i
$585$	0.798345	+	0.327601i	0.0330075	+	0.0135447i
$586$	−21.0904	−	25.4939i	−0.871237	−	1.05314i
$587$	44.3468	−	11.3863i	1.83039	−	0.469964i	0.833770	−	0.552112i	$-0.186178\pi$
$587$	44.3468	−	11.3863i	1.83039	−	0.469964i	0.996620	+	0.0821480i	$0.0261780\pi$
$588$	−11.4977	+	13.8984i	−0.474158	+	0.573159i
$589$	−0.565765	+	0.224002i	−0.0233119	+	0.00922984i
$590$	18.4456	−	7.03971i	0.759395	−	0.289820i
$591$	−14.3820	−	22.6625i	−0.591598	−	0.932210i
$592$	0.0569375	+	0.298477i	0.00234012	+	0.0122673i
$593$	−0.934590	−	2.87637i	−0.0383790	−	0.118118i	0.930031	−	0.367480i	$-0.119779\pi$
$593$	−0.934590	−	2.87637i	−0.0383790	−	0.118118i	−0.968411	+	0.249361i	$0.919779\pi$
$594$	−10.2617	+	21.8073i	−0.421043	+	0.894762i
$595$	−1.81987	+	24.1425i	−0.0746074	+	0.989747i
$596$	7.04157	+	3.87114i	0.288434	+	0.158568i
$597$	−29.2513	−	16.0811i	−1.19718	−	0.658154i
$598$	8.14885	+	9.85027i	0.333231	+	0.402807i
$599$	8.59191	+	6.24239i	0.351056	+	0.255057i	0.749312	−	0.662217i	$-0.230384\pi$
$599$	8.59191	+	6.24239i	0.351056	+	0.255057i	−0.398256	+	0.917274i	$0.630384\pi$
$600$	−8.79050	+	0.889553i	−0.358871	+	0.0363158i
$601$	35.7193	−	25.9516i	1.45702	−	1.05859i	0.472894	−	0.881120i	$-0.343209\pi$
$601$	35.7193	−	25.9516i	1.45702	−	1.05859i	0.984127	−	0.177468i	$-0.0567905\pi$
$602$	−2.05885	−	0.528622i	−0.0839123	−	0.0215450i
$603$	0.199090	+	0.423088i	0.00810758	+	0.0172295i
$604$	−3.64438	+	19.1045i	−0.148288	+	0.777352i
$605$	4.49189	+	25.2449i	0.182621	+	1.02635i
$606$	1.14525	+	1.07546i	0.0465227	+	0.0436877i
$607$	−7.10818	−	5.16439i	−0.288512	−	0.209616i	0.434110	−	0.900860i	$-0.357063\pi$
$607$	−7.10818	−	5.16439i	−0.288512	−	0.209616i	−0.722622	+	0.691244i	$0.757063\pi$
$608$	−1.35271	+	2.87465i	−0.0548596	+	0.116583i
$609$	37.6437	−	45.5034i	1.52540	−	1.84389i
$610$	9.44540	−	5.04108i	0.382433	−	0.204107i
$611$	−2.62428	−	41.7118i	−0.106167	−	1.68748i
$612$	−0.0200885	+	0.319298i	−0.000812031	+	0.0129069i
$613$	−17.7252	−	7.01792i	−0.715915	−	0.283451i	−0.0182085	−	0.999834i	$-0.505796\pi$
$613$	−17.7252	−	7.01792i	−0.715915	−	0.283451i	−0.697707	+	0.716383i	$0.745796\pi$
$614$	8.95975	−	14.1183i	0.361586	−	0.569769i
$615$	16.8742	−	15.4565i	0.680435	−	0.623268i
$616$	1.23461	−	19.6236i	0.0497439	−	0.790656i
$617$	3.89441	+	0.491978i	0.156783	+	0.0198063i	0.203333	−	0.979110i	$-0.434823\pi$
$617$	3.89441	+	0.491978i	0.156783	+	0.0198063i	−0.0465499	+	0.998916i	$0.514823\pi$
$618$	−18.8217	+	13.6748i	−0.757119	+	0.550079i
$619$	1.72255	+	9.02993i	0.0692352	+	0.362944i	0.999996	−	0.00268411i	$-0.000854378\pi$
$619$	1.72255	+	9.02993i	0.0692352	+	0.362944i	−0.930761	+	0.365628i	$0.880854\pi$
$620$	−0.413466	−	0.111646i	−0.0166052	−	0.00448379i
$621$	−8.79026	−	18.6802i	−0.352741	−	0.749612i
$622$	1.54837	−	1.45401i	0.0620839	−	0.0583007i
$623$	26.0401	−	41.0326i	1.04327	−	1.64394i
$624$	5.56375			0.222728
$625$	12.3321	+	21.7467i	0.493285	+	0.869868i
$626$	6.80205			0.271865
$627$	−14.2585	+	22.4679i	−0.569431	+	0.897280i
$628$	14.0285	−	13.1736i	0.559798	−	0.525686i
$629$	−0.337694	−	0.717636i	−0.0134647	−	0.0286140i
$630$	1.09762	+	0.296383i	0.0437302	+	0.0118082i
$631$	−6.17304	−	32.3602i	−0.245745	−	1.28824i	−0.864491	−	0.502649i	$-0.832359\pi$
$631$	−6.17304	−	32.3602i	−0.245745	−	1.28824i	0.618746	−	0.785591i	$-0.287641\pi$
$632$	8.28934	−	6.02256i	0.329732	−	0.239564i
$633$	10.4906	+	1.32526i	0.416962	+	0.0526745i
$634$	−0.682570	+	10.8491i	−0.0271083	+	0.430874i
$635$	−1.09136	+	0.999670i	−0.0433094	+	0.0396707i
$636$	11.7514	−	18.5172i	0.465971	−	0.734253i
$637$	−29.8826	−	11.8313i	−1.18399	−	0.468775i
$638$	−2.39781	+	38.1121i	−0.0949302	+	1.50887i
$639$	−0.0468544	−	0.744730i	−0.00185353	−	0.0294611i
$640$	−1.97269	+	1.05284i	−0.0779776	+	0.0416172i
$641$	−5.04779	+	6.10173i	−0.199376	+	0.241004i	−0.860720	−	0.509079i	$-0.829986\pi$
$641$	−5.04779	+	6.10173i	−0.199376	+	0.241004i	0.661344	+	0.750083i	$0.269986\pi$
$642$	−11.7313	+	24.9303i	−0.462999	+	0.983922i
$643$	1.40470	+	1.02058i	0.0553961	+	0.0402476i	0.615139	−	0.788419i	$-0.289100\pi$
$643$	1.40470	+	1.02058i	0.0553961	+	0.0402476i	−0.559743	+	0.828667i	$0.689100\pi$
$644$	12.2780	+	11.5298i	0.483820	+	0.454337i
$645$	0.354694	+	1.99342i	0.0139660	+	0.0784908i
$646$	1.55386	−	8.14563i	0.0611359	−	0.320486i
$647$	4.88134	+	10.3734i	0.191905	+	0.407819i	0.977504	−	0.210917i	$-0.0676449\pi$
$647$	4.88134	+	10.3734i	0.191905	+	0.407819i	−0.785599	+	0.618736i	$0.787645\pi$
$648$	−9.05886	−	2.32592i	−0.355866	−	0.0913707i
$649$	33.8585	−	24.5996i	1.32906	−	0.965620i
$650$	−6.34749	−	14.4064i	−0.248969	−	0.565066i
$651$	1.13583	+	0.825227i	0.0445166	+	0.0323432i
$652$	1.44455	+	1.74617i	0.0565731	+	0.0683852i
$653$	1.98926	+	1.09361i	0.0778459	+	0.0427961i	0.520201	−	0.854044i	$-0.325857\pi$
$653$	1.98926	+	1.09361i	0.0778459	+	0.0427961i	−0.442355	+	0.896840i	$0.645857\pi$
$654$	−4.40213	−	2.42009i	−0.172137	−	0.0946332i
$655$	1.19610	−	15.8675i	0.0467354	−	0.619995i
$656$	2.46582	−	5.24014i	0.0962742	−	0.204593i
$657$	0.497376	+	1.53077i	0.0194045	+	0.0597209i
$658$	−10.3179	−	54.0885i	−0.402235	−	2.10859i
$659$	−4.48517	−	7.06749i	−0.174717	−	0.275310i	0.745672	−	0.666313i	$-0.232128\pi$
$659$	−4.48517	−	7.06749i	−0.174717	−	0.275310i	−0.920390	+	0.391002i	$0.872128\pi$
$660$	−17.4980	+	6.67806i	−0.681110	+	0.259943i
$661$	−23.3619	+	9.24963i	−0.908673	+	0.359769i	−0.775517	−	0.631326i	$-0.782511\pi$
$661$	−23.3619	+	9.24963i	−0.908673	+	0.359769i	−0.133155	+	0.991095i	$0.542511\pi$
$662$	−6.42037	+	7.76089i	−0.249535	+	0.301636i
$663$	−14.0660	+	3.61154i	−0.546279	+	0.140261i
$664$	3.53119	+	4.26847i	0.137037	+	0.165649i
$665$	−27.2629	−	11.1874i	−1.05721	−	0.433827i
$666$	−0.0360742	+	0.00926227i	−0.00139785	+	0.000358906i
$667$	−23.8457	−	22.3926i	−0.923311	−	0.867047i
$668$	−7.20252	+	22.1671i	−0.278674	+	0.857670i
$669$	36.0242	+	4.55091i	1.39277	+	0.175948i
$670$	2.73644	−	8.07944i	0.105718	−	0.312136i
$671$	16.5441	−	15.5360i	0.638679	−	0.599759i
$672$	7.27243	−	0.918721i	0.280540	−	0.0354404i
$673$	1.51629	+	24.1007i	0.0584485	+	0.929012i	0.912565	+	0.408931i	$0.134098\pi$
$673$	1.51629	+	24.1007i	0.0584485	+	0.929012i	−0.854117	+	0.520081i	$0.825902\pi$
$674$	1.83927	−	5.66068i	0.0708459	−	0.218041i
$675$	4.14280	+	25.0834i	0.159457	+	0.965461i
$676$	−0.953808	−	2.93552i	−0.0366849	−	0.112905i
$677$	8.93330	−	3.53695i	0.343335	−	0.135936i	−0.190128	−	0.981759i	$-0.560890\pi$
$677$	8.93330	−	3.53695i	0.343335	−	0.135936i	0.533463	+	0.845823i	$0.320890\pi$
$678$	−1.65091	+	8.65435i	−0.0634026	+	0.332368i
$679$	22.1480	−	2.79795i	0.849963	−	0.107375i
$680$	4.30386	−	3.94226i	0.165045	−	0.151179i
$681$	0.412094	−	0.226550i	0.0157915	−	0.00868143i
$682$	−0.907846			−0.0347632
$683$	−1.96345	+	1.07941i	−0.0751291	+	0.0413026i	−0.518875	−	0.854850i	$-0.673649\pi$
$683$	−1.96345	+	1.07941i	−0.0751291	+	0.0413026i	0.443746	+	0.896152i	$0.353649\pi$
$684$	−0.362065	−	0.143352i	−0.0138439	−	0.00548118i
$685$	28.3023	+	21.1042i	1.08137	+	0.806349i
$686$	−12.8882	−	3.30912i	−0.492072	−	0.126343i
$687$	22.6741	+	35.7286i	0.865070	+	1.36313i
$688$	0.274568	+	0.432650i	0.0104678	+	0.0164946i
$689$	37.8491	+	9.71800i	1.44194	+	0.370226i
$690$	5.14660	−	15.1955i	0.195928	−	0.578484i
$691$	−44.2791	−	17.5314i	−1.68446	−	0.666924i	−0.686284	−	0.727333i	$-0.740759\pi$
$691$	−44.2791	−	17.5314i	−1.68446	−	0.666924i	−0.998174	+	0.0604091i	$0.980759\pi$
$692$	9.02682	−	4.96254i	0.343148	−	0.188647i
$693$	2.41004			0.0915497
$694$	7.25792	−	3.99007i	0.275507	−	0.151461i
$695$	1.91259	−	9.39160i	0.0725486	−	0.356244i
$696$	−14.1242	+	1.78430i	−0.535376	+	0.0676338i
$697$	−2.83250	+	14.8485i	−0.107289	+	0.562427i
$698$	−16.2519	+	6.43460i	−0.615145	+	0.243553i
$699$	4.41143	+	13.5770i	0.166856	+	0.513529i
$700$	−10.6757	−	17.7826i	−0.403505	−	0.672119i
$701$	−5.54351	+	17.0612i	−0.209375	+	0.644392i	0.790130	+	0.612940i	$0.210013\pi$
$701$	−5.54351	+	17.0612i	−0.209375	+	0.644392i	−0.999505	+	0.0314519i	$0.989987\pi$
$702$	−1.00523	−	15.9777i	−0.0379400	−	0.603040i
$703$	0.957753	−	0.120992i	0.0361223	−	0.00456331i
$704$	−3.45528	+	3.24473i	−0.130226	+	0.122290i
$705$	−42.8122	+	30.3006i	−1.61240	+	1.14119i
$706$	11.7073	+	1.47897i	0.440609	+	0.0556618i
$707$	−1.13967	+	3.50755i	−0.0428618	+	0.131915i
$708$	11.3737	+	10.6806i	0.427448	+	0.401401i
$709$	−0.232145	+	0.0596048i	−0.00871840	+	0.00223851i	−0.253047	−	0.967454i	$-0.581433\pi$
$709$	−0.232145	+	0.0596048i	−0.00871840	+	0.00223851i	0.244328	+	0.969693i	$0.421433\pi$
$710$	−8.80671	+	10.3805i	−0.330510	+	0.389575i
$711$	0.800531	+	0.967676i	0.0300223	+	0.0362907i
$712$	−11.3473	+	2.91350i	−0.425259	+	0.109188i
$713$	0.495704	−	0.599203i	0.0185642	−	0.0224403i
$714$	−17.7895	+	7.04334i	−0.665754	+	0.263591i
$715$	−20.9509	−	25.9748i	−0.783521	−	0.971403i
$716$	13.7185	+	21.6168i	0.512683	+	0.807859i
$717$	−6.38508	−	33.4718i	−0.238455	−	1.25003i
$718$	−3.30929	−	10.1849i	−0.123501	−	0.380098i
$719$	13.2948	−	28.2529i	0.495812	−	1.05365i	−0.487733	−	0.872993i	$-0.662176\pi$
$719$	13.2948	−	28.2529i	0.495812	−	1.05365i	0.983545	−	0.180662i	$-0.0578239\pi$
$720$	−0.143976	−	0.233215i	−0.00536566	−	0.00869141i
$721$	−47.8588	−	26.3106i	−1.78236	−	0.979859i
$722$	−7.80487	−	4.29076i	−0.290467	−	0.159686i
$723$	7.17941	+	8.67841i	0.267005	+	0.322754i
$724$	−11.1454	−	8.09758i	−0.414214	−	0.300944i
$725$	20.7340	+	34.5366i	0.770040	+	1.28266i
$726$	−16.3935	+	11.9106i	−0.608420	+	0.442043i
$727$	34.2040	+	8.78209i	1.26856	+	0.325710i	0.822227	−	0.569160i	$-0.192731\pi$
$727$	34.2040	+	8.78209i	1.26856	+	0.325710i	0.446328	+	0.894869i	$0.352731\pi$
$728$	5.56106	+	11.8178i	0.206107	+	0.437999i
$729$	−4.83604	+	25.3514i	−0.179113	+	0.938941i
$730$	12.8308	−	26.4113i	0.474889	−	0.977525i
$731$	−0.974992	−	0.915578i	−0.0360614	−	0.0338639i
$732$	6.84501	+	4.97319i	0.252999	+	0.183814i
$733$	−7.60399	+	16.1593i	−0.280860	+	0.596858i	−0.994627	−	0.103526i	$-0.966988\pi$
$733$	−7.60399	+	16.1593i	−0.280860	+	0.596858i	0.713767	+	0.700383i	$0.246988\pi$
$734$	−17.5598	+	21.2262i	−0.648146	+	0.783474i
$735$	7.06570	+	39.7100i	0.260622	+	1.46473i
$736$	−0.254947	−	4.05227i	−0.00939748	−	0.149369i
$737$	1.13539	−	18.0466i	0.0418228	−	0.664754i
$738$	0.659999	+	0.261312i	0.0242949	+	0.00961904i
$739$	−11.0069	+	17.3441i	−0.404895	+	0.638012i	−0.984192	−	0.177104i	$-0.943327\pi$
$739$	−11.0069	+	17.3441i	−0.404895	+	0.638012i	0.579297	+	0.815116i	$0.303327\pi$
$740$	0.591299	+	0.334688i	0.0217366	+	0.0123034i
$741$	1.10989	−	17.6413i	0.0407730	−	0.648068i
$742$	51.0776	+	6.45260i	1.87512	+	0.236882i
$743$	−31.9269	+	23.1963i	−1.17128	+	0.850988i	−0.991162	−	0.132656i	$-0.957649\pi$
$743$	−31.9269	+	23.1963i	−1.17128	+	0.850988i	−0.180123	+	0.983644i	$0.557649\pi$
$744$	−0.0634191	−	0.332454i	−0.00232506	−	0.0121884i
$745$	16.7869	−	6.40668i	0.615026	−	0.234723i
$746$	−6.04276	−	12.8415i	−0.221241	−	0.470162i
$747$	−0.494982	+	0.464819i	−0.0181104	+	0.0170068i
$748$	6.62927	−	10.4461i	0.242390	−	0.381946i
$749$	−64.6797			−2.36334
$750$	−11.1995	+	16.2756i	−0.408946	+	0.594299i
$751$	11.3650			0.414713			0.207357	−	0.978265i	$-0.433514\pi$
$751$	11.3650			0.414713			0.207357	+	0.978265i	$0.433514\pi$
$752$	−7.11262	+	11.2077i	−0.259371	+	0.408703i
$753$	14.0844	−	13.2261i	0.513264	−	0.481987i
$754$	−10.8005	−	22.9521i	−0.393329	−	0.835867i
$755$	27.3033	+	33.8504i	0.993669	+	1.23194i
$756$	−3.95229	−	20.7186i	−0.143743	−	0.753529i
$757$	−36.9915	+	26.8759i	−1.34448	+	0.976820i	−0.345211	+	0.938525i	$0.612193\pi$
$757$	−36.9915	+	26.8759i	−1.34448	+	0.976820i	−0.999266	+	0.0382947i	$0.987807\pi$
$758$	−21.0074	−	2.65386i	−0.763025	−	0.0963924i
$759$	2.13541	−	33.9414i	0.0775104	−	1.23199i
$760$	2.94477	+	6.46495i	0.106818	+	0.234508i
$761$	18.3639	−	28.9368i	0.665690	−	1.04896i	−0.328827	−	0.944390i	$-0.606653\pi$
$761$	18.3639	−	28.9368i	0.665690	−	1.04896i	0.994518	−	0.104570i	$-0.0333466\pi$
$762$	−1.08746	−	0.430555i	−0.0393944	−	0.0155974i
$763$	0.740468	−	11.7694i	0.0268067	−	0.426081i
$764$	−1.16570	−	18.5282i	−0.0421735	−	0.670328i
$765$	0.515377	+	0.496146i	0.0186335	+	0.0179382i
$766$	−11.8133	+	14.2799i	−0.426833	+	0.515953i
$767$	−11.8367	+	25.1543i	−0.427399	+	0.908269i
$768$	−1.42960	−	1.03866i	−0.0515862	−	0.0374795i
$769$	−19.4585	−	18.2728i	−0.701693	−	0.658934i	0.249200	−	0.968452i	$-0.419832\pi$
$769$	−19.4585	−	18.2728i	−0.701693	−	0.658934i	−0.950893	+	0.309518i	$0.899832\pi$
$770$	−31.6743	−	30.4924i	−1.14146	−	1.09887i
$771$	5.66202	−	29.6814i	0.203913	−	1.06895i
$772$	−7.18982	−	15.2791i	−0.258767	−	0.549908i
$773$	32.9732	+	8.46607i	1.18596	+	0.304503i	0.789618	−	0.613599i	$-0.210279\pi$
$773$	32.9732	+	8.46607i	1.18596	+	0.304503i	0.396344	+	0.918102i	$0.370279\pi$
$774$	−0.0508125	+	0.0369175i	−0.00182642	+	0.00132697i
$775$	−0.788483	+	0.543499i	−0.0283231	+	0.0195230i
$776$	−4.35381	−	3.16323i	−0.156293	−	0.113553i
$777$	−1.41977	−	1.71621i	−0.0509339	−	0.0615685i
$778$	−26.5919	−	14.6190i	−0.953367	−	0.524118i
$779$	−16.1233	−	8.86384i	−0.577676	−	0.317580i
$780$	8.04846	−	9.48678i	0.288181	−	0.339681i
$781$	−12.2865	+	26.1101i	−0.439645	+	0.934294i
$782$	3.27495	+	10.0793i	0.117112	+	0.360434i
$783$	7.67596	+	40.2388i	0.274317	+	1.43802i
$784$	5.46955	+	8.61864i	0.195341	+	0.307809i
$785$	−2.16898	−	42.9769i	−0.0774143	−	1.53391i
$786$	11.6920	−	4.62919i	0.417040	−	0.165118i
$787$	−18.5883	+	22.4694i	−0.662603	+	0.800949i	−0.989565	−	0.144088i	$-0.953975\pi$
$787$	−18.5883	+	22.4694i	−0.662603	+	0.800949i	0.326962	+	0.945037i	$0.393975\pi$
$788$	−14.7122	+	3.77745i	−0.524100	+	0.134566i
$789$	−20.1037	−	24.3011i	−0.715709	−	0.865144i
$790$	1.72216	−	22.8463i	0.0612718	−	0.812836i
$791$	−20.0326	+	5.14351i	−0.712278	+	0.182882i
$792$	−0.423517	−	0.397709i	−0.0150490	−	0.0141320i
$793$	−4.65859	+	14.3377i	−0.165431	+	0.509145i
$794$	11.6437	+	1.47095i	0.413221	+	0.0522019i
$795$	−14.5744	−	46.8240i	−0.516899	−	1.66068i
$796$	−13.7703	+	12.9311i	−0.488074	+	0.458332i
$797$	52.5795	−	6.64234i	1.86246	−	0.235284i	0.888001	−	0.459841i	$-0.152094\pi$
$797$	52.5795	−	6.64234i	1.86246	−	0.235284i	0.974461	+	0.224557i	$0.0720936\pi$
$798$	−1.46228	−	23.2423i	−0.0517642	−	0.822769i
$799$	10.7067	−	32.9517i	0.378775	−	1.16575i
$800$	−1.05847	+	4.88668i	−0.0374225	+	0.172770i
$801$	−0.443738	−	1.36569i	−0.0156787	−	0.0482541i
$802$	2.91608	−	1.15456i	0.102970	−	0.0407688i
$803$	11.6632	−	61.1404i	0.411584	−	2.15760i
$804$	6.68799	−	0.844890i	0.235867	−	0.0297970i
$805$	37.4206	−	4.25639i	1.31890	−	0.150018i
$806$	0.528452	−	0.290519i	0.0186139	−	0.0102331i
$807$	41.8416			1.47290
$808$	0.779098	−	0.428313i	0.0274086	−	0.0150680i
$809$	6.06819	+	2.40257i	0.213346	+	0.0844698i	0.472367	−	0.881402i	$-0.343400\pi$
$809$	6.06819	+	2.40257i	0.213346	+	0.0844698i	−0.259021	+	0.965872i	$0.583400\pi$
$810$	−17.0704	+	12.0817i	−0.599792	+	0.424506i
$811$	−2.31293	−	0.593860i	−0.0812181	−	0.0208533i	0.207862	−	0.978158i	$-0.433349\pi$
$811$	−2.31293	−	0.593860i	−0.0812181	−	0.0208533i	−0.289080	+	0.957305i	$0.593349\pi$
$812$	−17.9074	−	28.2175i	−0.628425	−	0.990240i
$813$	2.00429	+	3.15825i	0.0702935	+	0.110765i
$814$	1.39503	+	0.358183i	0.0488957	+	0.0125543i
$815$	5.06707	+	0.0628660i	0.177492	+	0.00220210i
$816$	4.28846	+	1.69792i	0.150126	+	0.0594391i
$817$	1.42660	−	0.784279i	0.0499103	−	0.0274384i
$818$	19.9373			0.697091
$819$	−1.40287	+	0.771233i	−0.0490202	+	0.0269491i
$820$	−5.36796	−	11.7848i	−0.187457	−	0.411543i
$821$	43.0387	−	5.43706i	1.50206	−	0.189755i	0.669136	−	0.743140i	$-0.266664\pi$
$821$	43.0387	−	5.43706i	1.50206	−	0.189755i	0.832926	+	0.553385i	$0.186664\pi$
$822$	−5.22790	+	27.4056i	−0.182344	+	0.955880i
$823$	−38.0572	+	15.0679i	−1.32659	+	0.525234i	−0.921264	−	0.388938i	$-0.872842\pi$
$823$	−38.0572	+	15.0679i	−1.32659	+	0.525234i	−0.405326	+	0.914172i	$0.632842\pi$
$824$	4.06843	+	12.5213i	0.141731	+	0.436202i
$825$	−13.9256	+	39.4964i	−0.484828	+	1.37509i
$826$	−11.3182	+	34.8340i	−0.393812	+	1.21203i
$827$	−2.73230	−	43.4286i	−0.0950113	−	1.51016i	−0.700124	−	0.714021i	$-0.746872\pi$
$827$	−2.73230	−	43.4286i	−0.0950113	−	1.51016i	0.605113	−	0.796140i	$-0.293128\pi$
$828$	0.493749	−	0.0623750i	0.0171590	−	0.00216768i
$829$	10.1223	−	9.50548i	0.351562	−	0.330139i	−0.488566	−	0.872527i	$-0.662480\pi$
$829$	10.1223	−	9.50548i	0.351562	−	0.330139i	0.840128	+	0.542388i	$0.182480\pi$
$830$	12.3864	+	0.153675i	0.429937	+	0.00533413i
$831$	25.5301	+	3.22521i	0.885631	+	0.111881i
$832$	0.972958	−	2.99446i	0.0337312	−	0.103814i
$833$	−19.4224	−	18.2389i	−0.672947	−	0.631939i
$834$	7.33621	−	1.88362i	0.254032	−	0.0652243i
$835$	27.3781	+	44.3477i	0.947459	+	1.53471i
$836$	9.59893	+	11.6031i	0.331986	+	0.401302i
$837$	−0.943268	+	0.242190i	−0.0326041	+	0.00837131i
$838$	4.97460	−	6.01326i	0.171845	−	0.207725i
$839$	−41.4623	+	16.4161i	−1.43144	+	0.566747i	−0.950699	−	0.310117i	$-0.899632\pi$
$839$	−41.4623	+	16.4161i	−1.43144	+	0.566747i	−0.480740	+	0.876863i	$0.659632\pi$
$840$	8.95369	−	13.7293i	0.308932	−	0.473705i
$841$	19.2399	+	30.3173i	0.663446	+	1.04542i
$842$	−0.327616	−	1.71742i	−0.0112904	−	0.0591864i
$843$	12.4220	+	38.2309i	0.427835	+	1.31674i
$844$	2.54780	−	5.41434i	0.0876988	−	0.186369i
$845$	−6.38514	−	2.62014i	−0.219655	−	0.0901357i
$846$	−1.42577	−	0.783823i	−0.0490189	−	0.0269484i
$847$	−41.6846	−	22.9163i	−1.43230	−	0.787413i
$848$	−7.91108	−	9.56285i	−0.271668	−	0.328390i
$849$	6.76555	+	4.91546i	0.232193	+	0.168698i
$850$	−0.496066	−	13.0414i	−0.0170149	−	0.447315i
$851$	−0.998127	+	0.725182i	−0.0342153	+	0.0248589i
$852$	−10.4199	−	2.67537i	−0.356979	−	0.0916565i
$853$	−9.37689	−	19.9269i	−0.321058	−	0.682284i	0.677525	−	0.735500i	$-0.263053\pi$
$853$	−9.37689	−	19.9269i	−0.321058	−	0.682284i	−0.998583	+	0.0532162i	$0.983053\pi$
$854$	−3.72176	+	19.5101i	−0.127356	+	0.667623i
$855$	−0.768188	+	0.409988i	−0.0262715	+	0.0140213i
$856$	11.3662	+	10.6736i	0.388489	+	0.364815i
$857$	29.6062	+	21.5102i	1.01133	+	0.734773i	0.964487	−	0.264129i	$-0.0850845\pi$
$857$	29.6062	+	21.5102i	1.01133	+	0.734773i	0.0468413	+	0.998902i	$0.485084\pi$
$858$	11.2286	−	23.8621i	0.383339	−	0.814637i
$859$	−8.89364	+	10.7506i	−0.303447	+	0.366805i	−0.900091	−	0.435701i	$-0.856500\pi$
$859$	−8.89364	+	10.7506i	−0.303447	+	0.366805i	0.596644	+	0.802506i	$0.296500\pi$
$860$	1.13490	+	0.157699i	0.0386998	+	0.00537749i
$861$	2.66556	+	42.3679i	0.0908421	+	1.44389i
$862$	1.45174	−	23.0748i	0.0494466	−	0.785930i
$863$	−43.9427	−	17.3982i	−1.49583	−	0.592240i	−0.529216	−	0.848487i	$-0.677514\pi$
$863$	−43.9427	−	17.3982i	−1.49583	−	0.592240i	−0.966611	+	0.256247i	$0.917514\pi$
$864$	−2.72449	+	4.29311i	−0.0926890	+	0.146055i
$865$	4.59644	−	22.5704i	0.156284	−	0.767418i
$866$	0.258404	−	4.10722i	0.00878094	−	0.139569i
$867$	17.8594	+	2.25617i	0.606538	+	0.0766236i
$868$	0.642771	−	0.467001i	0.0218171	−	0.0158510i
$869$	−9.10045	−	47.7062i	−0.308712	−	1.61832i
$870$	−17.3895	+	26.6644i	−0.589559	+	0.904008i
$871$	5.11416	+	10.8681i	0.173287	+	0.368253i
$872$	−2.07233	+	1.94605i	−0.0701781	+	0.0659016i
$873$	0.353447	−	0.556943i	0.0119624	−	0.0188497i
$874$	−12.8996			−0.436335
$875$	−45.7646	−	7.52086i	−1.54713	−	0.254252i
$876$	23.2044			0.784006
$877$	15.0626	−	23.7349i	0.508629	−	0.801472i	−0.488854	−	0.872365i	$-0.662585\pi$
$877$	15.0626	−	23.7349i	0.508629	−	0.801472i	0.997484	+	0.0708936i	$0.0225851\pi$
$878$	−5.95484	+	5.59196i	−0.200966	+	0.188720i
$879$	−24.8942	−	52.9028i	−0.839659	−	1.78437i
$880$	0.534229	+	10.5854i	0.0180089	+	0.356834i
$881$	9.12925	+	47.8572i	0.307572	+	1.61235i	0.715008	+	0.699117i	$0.246423\pi$
$881$	9.12925	+	47.8572i	0.307572	+	1.61235i	−0.407435	+	0.913234i	$0.633577\pi$
$882$	−1.01222	+	0.735418i	−0.0340831	+	0.0247628i
$883$	7.13986	+	0.901974i	0.240275	+	0.0303539i	0.244549	−	0.969637i	$-0.421360\pi$
$883$	7.13986	+	0.901974i	0.240275	+	0.0303539i	−0.00427320	+	0.999991i	$0.501360\pi$
$884$	−0.516027	+	8.20201i	−0.0173559	+	0.275864i
$885$	34.6645	−	3.94289i	1.16523	−	0.132539i
$886$	−14.1222	+	22.2530i	−0.474444	+	0.747604i
$887$	9.49365	+	3.75880i	0.318766	+	0.126208i	0.522058	−	0.852910i	$-0.325164\pi$
$887$	9.49365	+	3.75880i	0.318766	+	0.126208i	−0.203293	+	0.979118i	$0.565164\pi$
$888$	−0.0337149	+	0.535883i	−0.00113140	+	0.0179831i
$889$	−0.172398	−	2.74019i	−0.00578205	−	0.0919031i
$890$	−11.4471	+	23.5630i	−0.383707	+	0.789834i
$891$	−28.2579	+	34.1579i	−0.946674	+	1.14433i
$892$	8.74904	−	18.5927i	0.292940	−	0.622528i
$893$	34.1179	+	24.7881i	1.14171	+	0.829503i
$894$	10.3509	+	9.72015i	0.346186	+	0.325090i
$895$	56.7039	+	7.87923i	1.89540	+	0.263374i
$896$	0.777298	−	4.07474i	0.0259677	−	0.136127i
$897$	9.61853	+	20.4404i	0.321153	+	0.682485i
$898$	4.51282	+	1.15869i	0.150595	+	0.0386661i
$899$	−1.24836	+	0.906989i	−0.0416352	+	0.0302498i
$900$	−0.605930	−	0.0918723i	−0.0201977	−	0.00306241i
$901$	26.2079	+	19.0411i	0.873110	+	0.634352i
$902$	−17.4977	−	21.1510i	−0.582609	−	0.704253i
$903$	−3.29154	−	1.80954i	−0.109536	−	0.0602177i
$904$	4.36914	+	2.40195i	0.145315	+	0.0798878i
$905$	−29.9300	+	7.29015i	−0.994906	+	0.242333i
$906$	−14.6332	+	31.0971i	−0.486154	+	1.03313i
$907$	13.6741	+	42.0846i	0.454042	+	1.39740i	0.872257	+	0.489049i	$0.162656\pi$
$907$	13.6741	+	42.0846i	0.454042	+	1.39740i	−0.418215	+	0.908348i	$0.637344\pi$
$908$	−0.0498666	−	0.261410i	−0.00165488	−	0.00867519i
$909$	0.0583913	+	0.0920100i	0.00193672	+	0.00305178i
$910$	28.1952	+	7.61337i	0.934663	+	0.252381i
$911$	47.7784	−	18.9168i	1.58297	−	0.626742i	0.598316	−	0.801260i	$-0.295837\pi$
$911$	47.7784	−	18.9168i	1.58297	−	0.626742i	0.984654	+	0.174518i	$0.0558369\pi$
$912$	−3.57853	+	4.32570i	−0.118497	+	0.143238i
$913$	25.4334	−	6.53018i	0.841722	−	0.216118i
$914$	−14.5468	−	17.5841i	−0.481167	−	0.581631i
$915$	18.3817	−	4.47730i	0.607681	−	0.148015i
$916$	23.1945	−	5.95535i	0.766369	−	0.196770i
$917$	21.5191	+	20.2078i	0.710624	+	0.667320i
$918$	4.10119	−	12.6222i	0.135359	−	0.416593i
$919$	29.3069	+	3.70232i	0.966744	+	0.122128i	0.592823	−	0.805332i	$-0.298013\pi$
$919$	29.3069	+	3.70232i	0.966744	+	0.122128i	0.373921	+	0.927461i	$0.378013\pi$
$920$	−7.27835	−	5.42725i	−0.239960	−	0.178931i
$921$	21.5395	−	20.2270i	0.709752	−	0.666502i
$922$	−16.7146	+	2.11155i	−0.550467	+	0.0695401i
$923$	−1.20358	−	19.1303i	−0.0396163	−	0.629683i
$924$	10.7368	−	33.0444i	0.353214	−	1.08708i
$925$	1.42604	−	0.524071i	0.0468881	−	0.0172313i
$926$	−7.38356	−	22.7242i	−0.242639	−	0.746765i
$927$	−1.50041	+	0.594056i	−0.0492800	+	0.0195114i
$928$	−1.50964	+	7.91379i	−0.0495562	+	0.259783i
$929$	−20.1184	+	2.54155i	−0.660064	+	0.0833855i	−0.448227	−	0.893920i	$-0.647945\pi$
$929$	−20.1184	+	2.54155i	−0.660064	+	0.0833855i	−0.211837	+	0.977305i	$0.567945\pi$
$930$	−0.658611	−	0.372788i	−0.0215967	−	0.0122242i
$931$	28.4186	−	15.6233i	0.931384	−	0.512032i
$932$	8.07870			0.264627
$933$	3.28910	−	1.80820i	0.107680	−	0.0591978i
$934$	−1.74125	−	0.689410i	−0.0569755	−	0.0225582i
$935$	−8.22180	−	26.4147i	−0.268882	−	0.863854i
$936$	0.373797	+	0.0959749i	0.0122179	+	0.00313704i
$937$	9.62276	+	15.1630i	0.314362	+	0.495355i	0.964365	−	0.264577i	$-0.0852323\pi$
$937$	9.62276	+	15.1630i	0.314362	+	0.495355i	−0.650003	+	0.759932i	$0.725232\pi$
$938$	8.47937	+	13.3613i	0.276861	+	0.436263i
$939$	11.6421	+	2.98919i	0.379927	+	0.0975487i
$940$	8.82127	+	28.3407i	0.287718	+	0.924371i
$941$	−46.6766	−	18.4806i	−1.52161	−	0.602449i	−0.549194	−	0.835695i	$-0.685065\pi$
$941$	−46.6766	−	18.4806i	−1.52161	−	0.602449i	−0.972418	+	0.233246i	$0.925065\pi$
$942$	29.7999	−	16.3826i	0.970934	−	0.533775i
$943$	23.5144			0.765733
$944$	7.73733	−	4.25364i	0.251829	−	0.138444i
$945$	−41.0447	−	23.2322i	−1.33519	−	0.755744i
$946$	2.40969	−	0.304415i	0.0783459	−	0.00989739i
$947$	2.69891	−	14.1482i	0.0877029	−	0.459755i	−0.911159	−	0.412055i	$-0.864811\pi$
$947$	2.69891	−	14.1482i	0.0877029	−	0.459755i	0.998862	−	0.0476994i	$-0.0151890\pi$
$948$	16.8344	−	6.66520i	0.546755	−	0.216476i
$949$	12.7764	+	39.3218i	0.414740	+	1.27644i
$950$	15.2833	+	4.33097i	0.495855	+	0.140515i
$951$	−5.93597	+	18.2690i	−0.192487	+	0.592414i
$952$	0.679864	+	10.8061i	0.0220345	+	0.350229i
$953$	−33.6197	+	4.24716i	−1.08905	+	0.137579i	−0.649293	−	0.760538i	$-0.724935\pi$
$953$	−33.6197	+	4.24716i	−1.08905	+	0.137579i	−0.439756	+	0.898117i	$0.644935\pi$
$954$	1.10893	−	1.04135i	0.0359029	−	0.0337151i
$955$	−33.2789	−	24.8151i	−1.07688	−	0.802998i
$956$	−19.1314	−	2.41685i	−0.618752	−	0.0781666i
$957$	−20.8525	+	64.1775i	−0.674067	+	2.07456i
$958$	0.545360	+	0.512127i	0.0176198	+	0.0165461i
$959$	−63.4370	+	16.2879i	−2.04849	+	0.525962i
$960$	−3.83907	+	0.935096i	−0.123905	+	0.0301801i
$961$	19.7368	+	23.8576i	0.636670	+	0.769601i
$962$	−0.926660	+	0.237926i	−0.0298767	+	0.00767103i
$963$	−1.21821	+	1.47257i	−0.0392563	+	0.0474527i
$964$	5.92629	−	2.34638i	0.190873	−	0.0755719i
$965$	−36.4533	−	9.84323i	−1.17347	−	0.316865i
$966$	15.9477	+	25.1296i	0.513109	+	0.808530i
$967$	−0.870213	−	4.56182i	−0.0279842	−	0.146698i	0.965553	−	0.260207i	$-0.0837909\pi$
$967$	−0.870213	−	4.56182i	−0.0279842	−	0.146698i	−0.993537	+	0.113509i	$0.963791\pi$
$968$	3.54356	+	10.9060i	0.113894	+	0.350531i
$969$	6.23917	−	13.2589i	0.200431	−	0.425938i
$970$	−11.6918	+	2.84782i	−0.375401	+	0.0914378i
$971$	−11.8489	−	6.51401i	−0.380250	−	0.209044i	0.280153	−	0.959955i	$-0.409615\pi$
$971$	−11.8489	−	6.51401i	−0.380250	−	0.209044i	−0.660404	+	0.750911i	$0.729615\pi$
$972$	−1.11555	−	0.613277i	−0.0357811	−	0.0196709i
$973$	11.3336	+	13.7000i	0.363339	+	0.439201i
$974$	1.61089	+	1.17038i	0.0516162	+	0.0375014i
$975$	−4.53316	−	27.4469i	−0.145177	−	0.879005i
$976$	3.87363	−	2.81436i	0.123992	−	0.0900854i
$977$	−17.0833	−	4.38624i	−0.546542	−	0.140328i	−0.0346845	−	0.999398i	$-0.511043\pi$
$977$	−17.0833	−	4.38624i	−0.546542	−	0.140328i	−0.511858	+	0.859070i	$0.671043\pi$
$978$	1.70509	+	3.62349i	0.0545226	+	0.115867i
$979$	−10.4054	+	54.5469i	−0.332557	+	1.74333i
$980$	22.6079	+	3.14145i	0.722182	+	0.100350i
$981$	−0.254008	−	0.238529i	−0.00810985	−	0.00761566i
$982$	1.92324	+	1.39732i	0.0613732	+	0.0445902i
$983$	23.6982	−	50.3612i	0.755855	−	1.60627i	−0.0388264	−	0.999246i	$-0.512362\pi$
$983$	23.6982	−	50.3612i	0.755855	−	1.60627i	0.794681	−	0.607027i	$-0.207638\pi$
$984$	6.52322	−	7.88521i	0.207953	−	0.251371i
$985$	−14.8415	+	30.5502i	−0.472890	+	0.973411i
$986$	−1.32040	−	20.9872i	−0.0420502	−	0.668369i
$987$	6.10966	−	97.1102i	0.194472	−	3.09105i
$988$	−9.30058	−	3.68236i	−0.295891	−	0.117151i
$989$	−1.11482	+	1.75668i	−0.0354493	+	0.0558592i
$990$	−1.29079	+	0.146820i	−0.0410240	+	0.00466625i
$991$	0.775663	−	12.3288i	0.0246398	−	0.391638i	−0.966308	−	0.257389i	$-0.917138\pi$
$991$	0.775663	−	12.3288i	0.0246398	−	0.391638i	0.990948	−	0.134249i	$-0.0428621\pi$
$992$	−0.190020	−	0.0240051i	−0.00603314	−	0.000762163i
$993$	−14.3994	+	10.4618i	−0.456952	+	0.331995i
$994$	−4.73213	−	24.8067i	−0.150094	−	0.786820i
$995$	2.12905	+	42.1858i	0.0674955	+	1.33738i
$996$	4.16805	+	8.85757i	0.132070	+	0.280663i
$997$	32.4770	−	30.4979i	1.02856	−	0.965880i	0.0291253	−	0.999576i	$-0.490728\pi$
$997$	32.4770	−	30.4979i	1.02856	−	0.965880i	0.999432	+	0.0336960i	$0.0107278\pi$
$998$	−18.6014	+	29.3111i	−0.588816	+	0.927826i
$999$	1.54501			0.0488821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.g.b.231.6	yes	140
125.46	even	25	inner	250.2.g.b.171.6	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.g.b.171.6	✓	140	125.46	even	25	inner
250.2.g.b.231.6	yes	140	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.535827 - 0.844328i) q^{2} +(1.28815 - 1.20965i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-2.15875 - 0.582913i) q^{5} +(-0.331118 - 1.73578i) q^{6} +(3.35598 - 2.43826i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.00769630 - 0.122329i) q^{9} +O(q^{10})\)	\(q+(0.535827 - 0.844328i) q^{2} +(1.28815 - 1.20965i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-2.15875 - 0.582913i) q^{5} +(-0.331118 - 1.73578i) q^{6} +(3.35598 - 2.43826i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.00769630 - 0.122329i) q^{9} +(-1.64889 + 1.51035i) q^{10} +(-2.53980 + 4.00208i) q^{11} +(-1.64299 - 0.650505i) q^{12} +(0.197700 - 3.14234i) q^{13} +(-0.260469 - 4.14003i) q^{14} +(-3.48591 + 1.86046i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(1.11135 - 2.36174i) q^{17} +(-0.0991620 - 0.0720454i) q^{18} +(2.31595 + 2.17482i) q^{19} +(0.391716 + 2.20149i) q^{20} +(1.37355 - 7.20039i) q^{21} +(2.01818 + 4.28884i) q^{22} +(-3.93272 - 1.00975i) q^{23} +(-1.42960 + 1.03866i) q^{24} +(4.32042 + 2.51673i) q^{25} +(-2.54724 - 1.85068i) q^{26} +(3.24108 + 3.91779i) q^{27} +(-3.63511 - 1.99842i) q^{28} +(7.05996 + 3.88124i) q^{29} +(-0.297008 + 3.94013i) q^{30} +(-0.0815496 + 0.173302i) q^{31} +(0.309017 + 0.951057i) q^{32} +(1.56948 + 8.22753i) q^{33} +(-1.39859 - 2.20383i) q^{34} +(-8.66602 + 3.30736i) q^{35} +(-0.113964 + 0.0451214i) q^{36} +(0.193687 - 0.234127i) q^{37} +(3.07721 - 0.790092i) q^{38} +(-3.54647 - 4.28694i) q^{39} +(2.06867 + 0.848880i) q^{40} +(-5.60937 + 1.44024i) q^{41} +(-5.34351 - 5.01789i) q^{42} +(0.158346 - 0.487340i) q^{43} +(4.70258 + 0.594074i) q^{44} +(-0.0879217 + 0.259592i) q^{45} +(-2.95982 + 2.77945i) q^{46} +(13.1694 - 1.66369i) q^{47} +(0.110956 + 1.76359i) q^{48} +(3.15435 - 9.70809i) q^{49} +(4.43995 - 2.29932i) q^{50} +(-1.42530 - 4.38661i) q^{51} +(-2.92745 + 1.15906i) q^{52} +(-2.32559 + 12.1912i) q^{53} +(5.04455 - 0.637275i) q^{54} +(7.81566 - 7.15902i) q^{55} +(-3.63511 + 1.99842i) q^{56} +5.61405 q^{57} +(7.05996 - 3.88124i) q^{58} +(-8.20944 - 3.25035i) q^{59} +(3.16762 + 2.36200i) q^{60} +(-4.63764 - 1.19074i) q^{61} +(0.102627 + 0.161714i) q^{62} +(-0.272442 - 0.429299i) q^{63} +(0.968583 + 0.248690i) q^{64} +(-2.25850 + 6.66830i) q^{65} +(7.78770 + 3.08337i) q^{66} +(-3.34298 + 1.83782i) q^{67} -2.61016 q^{68} +(-6.28736 + 3.45651i) q^{69} +(-1.85099 + 9.08913i) q^{70} +(6.03991 - 0.763018i) q^{71} +(-0.0229675 + 0.120400i) q^{72} +(-12.2094 + 4.83404i) q^{73} +(-0.0938975 - 0.288987i) q^{74} +(8.60970 - 1.98428i) q^{75} +(0.981753 - 3.02152i) q^{76} +(1.23461 + 19.6236i) q^{77} +(-5.51988 + 0.697323i) q^{78} +(-7.46915 + 7.01399i) q^{79} +(1.82518 - 1.29178i) q^{80} +(9.27894 + 1.17220i) q^{81} +(-1.78961 + 5.50787i) q^{82} +(-4.03833 - 3.79224i) q^{83} +(-7.09994 + 1.82295i) q^{84} +(-3.77582 + 4.45059i) q^{85} +(-0.326628 - 0.394826i) q^{86} +(13.7892 - 3.54046i) q^{87} +(3.02136 - 3.65220i) q^{88} +(10.8927 - 4.31272i) q^{89} +(0.172070 + 0.213331i) q^{90} +(-6.99838 - 11.0277i) q^{91} +(0.760821 + 3.98836i) q^{92} +(0.104587 + 0.321884i) q^{93} +(5.65184 - 12.0108i) q^{94} +(-3.73182 - 6.04489i) q^{95} +(1.54850 + 0.851297i) q^{96} +(4.71593 + 2.59261i) q^{97} +(-6.50663 - 7.86516i) q^{98} +(0.470024 + 0.341492i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9}+O(q^{10}) \) 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9	\( 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9} + 20 q^{10} - 10 q^{11} + 20 q^{12} + 20 q^{14} - 10 q^{15} - 5 q^{17} - 50 q^{18} + 40 q^{19} - 10 q^{20} - 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} - 5 q^{25} - 35 q^{26} + 30 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} + 35 q^{31} - 35 q^{32} - 55 q^{33} - 15 q^{34} - 25 q^{35} - 10 q^{36} - 25 q^{37} - 30 q^{39} + 25 q^{41} - 5 q^{42} - 45 q^{43} + 40 q^{44} - 5 q^{45} + 90 q^{47} - 5 q^{48} - 65 q^{49} + 30 q^{50} - 80 q^{51} - 50 q^{53} - 5 q^{54} - 35 q^{55} - 5 q^{56} + 40 q^{57} - 10 q^{58} + 45 q^{59} + 15 q^{60} + 45 q^{61} - 45 q^{62} - 75 q^{63} - 60 q^{65} + 15 q^{66} - 45 q^{67} + 10 q^{68} - 125 q^{69} - 15 q^{70} - 5 q^{71} - 5 q^{72} - 50 q^{73} + 20 q^{74} - 130 q^{75} - 5 q^{76} + 10 q^{77} + 10 q^{78} - 50 q^{79} - 5 q^{80} + 15 q^{81} + 40 q^{82} + 25 q^{83} - 50 q^{84} - 95 q^{85} - 10 q^{86} + 80 q^{87} - 10 q^{88} - 65 q^{89} - 10 q^{90} + 65 q^{91} - 25 q^{92} - 10 q^{93} - 35 q^{94} + 80 q^{95} - 40 q^{97} - 25 q^{98} + 90 q^{99}+O(q^{100}) \) 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9 + 20 * q^10 - 10 * q^11 + 20 * q^12 + 20 * q^14 - 10 * q^15 - 5 * q^17 - 50 * q^18 + 40 * q^19 - 10 * q^20 - 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 - 5 * q^25 - 35 * q^26 + 30 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 + 35 * q^31 - 35 * q^32 - 55 * q^33 - 15 * q^34 - 25 * q^35 - 10 * q^36 - 25 * q^37 - 30 * q^39 + 25 * q^41 - 5 * q^42 - 45 * q^43 + 40 * q^44 - 5 * q^45 + 90 * q^47 - 5 * q^48 - 65 * q^49 + 30 * q^50 - 80 * q^51 - 50 * q^53 - 5 * q^54 - 35 * q^55 - 5 * q^56 + 40 * q^57 - 10 * q^58 + 45 * q^59 + 15 * q^60 + 45 * q^61 - 45 * q^62 - 75 * q^63 - 60 * q^65 + 15 * q^66 - 45 * q^67 + 10 * q^68 - 125 * q^69 - 15 * q^70 - 5 * q^71 - 5 * q^72 - 50 * q^73 + 20 * q^74 - 130 * q^75 - 5 * q^76 + 10 * q^77 + 10 * q^78 - 50 * q^79 - 5 * q^80 + 15 * q^81 + 40 * q^82 + 25 * q^83 - 50 * q^84 - 95 * q^85 - 10 * q^86 + 80 * q^87 - 10 * q^88 - 65 * q^89 - 10 * q^90 + 65 * q^91 - 25 * q^92 - 10 * q^93 - 35 * q^94 + 80 * q^95 - 40 * q^97 - 25 * q^98 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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