LMFDB - Embedded newform 650.2.l.c.131.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(131,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("650.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.l (of order $5$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			131.4
Character	$\chi$	$=$	650.131
Dual form			650.2.l.c.521.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(0.859118 - 0.624186i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.70352 + 1.44845i) q^{5} +(0.859118 + 0.624186i) q^{6} +0.905410 q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.578575 + 1.78067i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(0.859118 - 0.624186i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.70352 + 1.44845i) q^{5} +(0.859118 + 0.624186i) q^{6} +0.905410 q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.578575 + 1.78067i) q^{9} +(-0.851143 + 2.06774i) q^{10} +(1.12437 + 3.46045i) q^{11} +(-0.328154 + 1.00995i) q^{12} +(0.309017 - 0.951057i) q^{13} +(0.279787 + 0.861096i) q^{14} +(2.36763 + 0.181078i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.10674 - 1.53064i) q^{17} -1.87231 q^{18} +(-0.976313 - 0.709333i) q^{19} +(-2.22956 - 0.170518i) q^{20} +(0.777854 - 0.565144i) q^{21} +(-2.94363 + 2.13867i) q^{22} +(-1.02042 - 3.14051i) q^{23} -1.06193 q^{24} +(0.803970 + 4.93494i) q^{25} +1.00000 q^{26} +(1.59887 + 4.92081i) q^{27} +(-0.732492 + 0.532187i) q^{28} +(2.76246 - 2.00704i) q^{29} +(0.559422 + 2.30770i) q^{30} +(6.05668 + 4.40044i) q^{31} +1.00000 q^{32} +(3.12593 + 2.27112i) q^{33} +(0.804705 - 2.47663i) q^{34} +(1.54239 + 1.31144i) q^{35} +(-0.578575 - 1.78067i) q^{36} +(-0.189703 + 0.583847i) q^{37} +(0.372918 - 1.14772i) q^{38} +(-0.328154 - 1.00995i) q^{39} +(-0.526799 - 2.17313i) q^{40} +(0.459848 - 1.41527i) q^{41} +(0.777854 + 0.565144i) q^{42} -5.24744 q^{43} +(-2.94363 - 2.13867i) q^{44} +(-3.56483 + 2.19537i) q^{45} +(2.67148 - 1.94094i) q^{46} +(3.99841 - 2.90501i) q^{47} +(-0.328154 - 1.00995i) q^{48} -6.18023 q^{49} +(-4.44497 + 2.28960i) q^{50} -2.76534 q^{51} +(0.309017 + 0.951057i) q^{52} +(7.47671 - 5.43215i) q^{53} +(-4.18589 + 3.04123i) q^{54} +(-3.09691 + 7.52354i) q^{55} +(-0.732492 - 0.532187i) q^{56} -1.28152 q^{57} +(2.76246 + 2.00704i) q^{58} +(0.0784786 - 0.241532i) q^{59} +(-2.02189 + 1.24516i) q^{60} +(-0.479129 - 1.47461i) q^{61} +(-2.31345 + 7.12006i) q^{62} +(-0.523848 + 1.61224i) q^{63} +(0.309017 + 0.951057i) q^{64} +(1.90398 - 1.17255i) q^{65} +(-1.19400 + 3.67475i) q^{66} +(6.20463 + 4.50793i) q^{67} +2.60408 q^{68} +(-2.83692 - 2.06114i) q^{69} +(-0.770634 + 1.87215i) q^{70} +(1.05895 - 0.769370i) q^{71} +(1.51473 - 1.10052i) q^{72} +(-3.54732 - 10.9175i) q^{73} -0.613893 q^{74} +(3.77102 + 3.73787i) q^{75} +1.20679 q^{76} +(1.01801 + 3.13312i) q^{77} +(0.859118 - 0.624186i) q^{78} +(-1.31847 + 0.957926i) q^{79} +(1.90398 - 1.17255i) q^{80} +(-0.0990782 - 0.0719846i) q^{81} +1.48810 q^{82} +(-1.44290 - 1.04833i) q^{83} +(-0.297114 + 0.914422i) q^{84} +(-1.37182 - 5.65899i) q^{85} +(-1.62155 - 4.99061i) q^{86} +(1.12051 - 3.44858i) q^{87} +(1.12437 - 3.46045i) q^{88} +(-2.30735 - 7.10130i) q^{89} +(-3.18952 - 2.71195i) q^{90} +(0.279787 - 0.861096i) q^{91} +(2.67148 + 1.94094i) q^{92} +7.95009 q^{93} +(3.99841 + 2.90501i) q^{94} +(-0.635735 - 2.62251i) q^{95} +(0.859118 - 0.624186i) q^{96} +(-0.299495 + 0.217596i) q^{97} +(-1.90980 - 5.87775i) q^{98} -6.81245 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	0.859118	−	0.624186i	0.496012	−	0.360374i	−0.311480	−	0.950253i	$-0.600825\pi$
$3$	0.859118	−	0.624186i	0.496012	−	0.360374i	0.807492	+	0.589879i	$0.200825\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	1.70352	+	1.44845i	0.761838	+	0.647768i
$5$	1.70352	+	1.44845i	0.761838	+	0.647768i
$6$	0.859118	+	0.624186i	0.350733	+	0.254823i
$7$	0.905410			0.342213			0.171106	−	0.985253i	$-0.445266\pi$
$7$	0.905410			0.342213			0.171106	+	0.985253i	$0.445266\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.578575	+	1.78067i	−0.192858	+	0.593557i
$10$	−0.851143	+	2.06774i	−0.269155	+	0.653877i
$11$	1.12437	+	3.46045i	0.339010	+	1.04336i	0.964713	+	0.263303i	$0.0848120\pi$
$11$	1.12437	+	3.46045i	0.339010	+	1.04336i	−0.625704	+	0.780061i	$0.715188\pi$
$12$	−0.328154	+	1.00995i	−0.0947298	+	0.291548i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$	0.279787	+	0.861096i	0.0747762	+	0.230138i
$15$	2.36763	+	0.181078i	0.611319	+	0.0467541i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.10674	−	1.53064i	−0.510960	−	0.371234i	0.302227	−	0.953236i	$-0.402270\pi$
$17$	−2.10674	−	1.53064i	−0.510960	−	0.371234i	−0.813188	+	0.582001i	$0.802270\pi$
$18$	−1.87231			−0.441307
$19$	−0.976313	−	0.709333i	−0.223982	−	0.162732i	0.470136	−	0.882594i	$-0.344205\pi$
$19$	−0.976313	−	0.709333i	−0.223982	−	0.162732i	−0.694117	+	0.719862i	$0.744205\pi$
$20$	−2.22956	−	0.170518i	−0.498544	−	0.0381290i
$21$	0.777854	−	0.565144i	0.169742	−	0.123325i
$22$	−2.94363	+	2.13867i	−0.627585	+	0.455967i
$23$	−1.02042	−	3.14051i	−0.212771	−	0.654843i	−0.999304	−	0.0372944i	$-0.988126\pi$
$23$	−1.02042	−	3.14051i	−0.212771	−	0.654843i	0.786533	−	0.617548i	$-0.211874\pi$
$24$	−1.06193			−0.216765
$25$	0.803970	+	4.93494i	0.160794	+	0.986988i
$26$	1.00000			0.196116
$27$	1.59887	+	4.92081i	0.307702	+	0.947009i
$28$	−0.732492	+	0.532187i	−0.138428	+	0.100574i
$29$	2.76246	−	2.00704i	0.512976	−	0.372699i	−0.300975	−	0.953632i	$-0.597312\pi$
$29$	2.76246	−	2.00704i	0.512976	−	0.372699i	0.813951	+	0.580933i	$0.197312\pi$
$30$	0.559422	+	2.30770i	0.102136	+	0.421327i
$31$	6.05668	+	4.40044i	1.08781	+	0.790342i	0.979028	−	0.203724i	$-0.0653044\pi$
$31$	6.05668	+	4.40044i	1.08781	+	0.790342i	0.108784	+	0.994065i	$0.465304\pi$
$32$	1.00000			0.176777
$33$	3.12593	+	2.27112i	0.544154	+	0.395351i
$34$	0.804705	−	2.47663i	0.138006	−	0.424738i
$35$	1.54239	+	1.31144i	0.260711	+	0.221674i
$36$	−0.578575	−	1.78067i	−0.0964292	−	0.296779i
$37$	−0.189703	+	0.583847i	−0.0311870	+	0.0959838i	−0.965438	−	0.260631i	$-0.916069\pi$
$37$	−0.189703	+	0.583847i	−0.0311870	+	0.0959838i	0.934251	+	0.356615i	$0.116069\pi$
$38$	0.372918	−	1.14772i	0.0604953	−	0.186186i
$39$	−0.328154	−	1.00995i	−0.0525467	−	0.161722i
$40$	−0.526799	−	2.17313i	−0.0832942	−	0.343602i
$41$	0.459848	−	1.41527i	0.0718161	−	0.221027i	−0.908706	−	0.417437i	$-0.862928\pi$
$41$	0.459848	−	1.41527i	0.0718161	−	0.221027i	0.980522	+	0.196410i	$0.0629283\pi$
$42$	0.777854	+	0.565144i	0.120025	+	0.0872036i
$43$	−5.24744			−0.800227			−0.400114	−	0.916466i	$-0.631029\pi$
$43$	−5.24744			−0.800227			−0.400114	+	0.916466i	$0.631029\pi$
$44$	−2.94363	−	2.13867i	−0.443769	−	0.322417i
$45$	−3.56483	+	2.19537i	−0.531414	+	0.327267i
$46$	2.67148	−	1.94094i	0.393888	−	0.286177i
$47$	3.99841	−	2.90501i	0.583227	−	0.423740i	−0.256659	−	0.966502i	$-0.582622\pi$
$47$	3.99841	−	2.90501i	0.583227	−	0.423740i	0.839886	+	0.542763i	$0.182622\pi$
$48$	−0.328154	−	1.00995i	−0.0473649	−	0.145774i
$49$	−6.18023			−0.882890
$50$	−4.44497	+	2.28960i	−0.628613	+	0.323798i
$51$	−2.76534			−0.387226
$52$	0.309017	+	0.951057i	0.0428529	+	0.131888i
$53$	7.47671	−	5.43215i	1.02701	−	0.746163i	0.0592982	−	0.998240i	$-0.481114\pi$
$53$	7.47671	−	5.43215i	1.02701	−	0.746163i	0.967707	+	0.252077i	$0.0811137\pi$
$54$	−4.18589	+	3.04123i	−0.569627	+	0.413858i
$55$	−3.09691	+	7.52354i	−0.417587	+	1.01447i
$56$	−0.732492	−	0.532187i	−0.0978834	−	0.0711164i
$57$	−1.28152			−0.169742
$58$	2.76246	+	2.00704i	0.362729	+	0.263538i
$59$	0.0784786	−	0.241532i	0.0102170	−	0.0314448i	−0.945818	−	0.324697i	$-0.894738\pi$
$59$	0.0784786	−	0.241532i	0.0102170	−	0.0314448i	0.956035	+	0.293252i	$0.0947376\pi$
$60$	−2.02189	+	1.24516i	−0.261024	+	0.160750i
$61$	−0.479129	−	1.47461i	−0.0613461	−	0.188804i	0.915687	−	0.401893i	$-0.131648\pi$
$61$	−0.479129	−	1.47461i	−0.0613461	−	0.188804i	−0.977033	+	0.213089i	$0.931648\pi$
$62$	−2.31345	+	7.12006i	−0.293808	+	0.904248i
$63$	−0.523848	+	1.61224i	−0.0659986	+	0.203123i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	1.90398	−	1.17255i	0.236159	−	0.145437i
$66$	−1.19400	+	3.67475i	−0.146971	+	0.452330i
$67$	6.20463	+	4.50793i	0.758017	+	0.550731i	0.898301	−	0.439380i	$-0.144802\pi$
$67$	6.20463	+	4.50793i	0.758017	+	0.550731i	−0.140285	+	0.990111i	$0.544802\pi$
$68$	2.60408			0.315791
$69$	−2.83692	−	2.06114i	−0.341525	−	0.248133i
$70$	−0.770634	+	1.87215i	−0.0921083	+	0.223765i
$71$	1.05895	−	0.769370i	0.125674	−	0.0913074i	−0.523173	−	0.852227i	$-0.675252\pi$
$71$	1.05895	−	0.769370i	0.125674	−	0.0913074i	0.648847	+	0.760919i	$0.275252\pi$
$72$	1.51473	−	1.10052i	0.178513	−	0.129697i
$73$	−3.54732	−	10.9175i	−0.415182	−	1.27780i	−0.912088	−	0.409995i	$-0.865530\pi$
$73$	−3.54732	−	10.9175i	−0.415182	−	1.27780i	0.496906	−	0.867805i	$-0.334470\pi$
$74$	−0.613893			−0.0713636
$75$	3.77102	+	3.73787i	0.435440	+	0.431612i
$76$	1.20679			0.138428
$77$	1.01801	+	3.13312i	0.116013	+	0.357053i
$78$	0.859118	−	0.624186i	0.0972759	−	0.0706751i
$79$	−1.31847	+	0.957926i	−0.148340	+	0.107775i	−0.659480	−	0.751722i	$-0.729223\pi$
$79$	−1.31847	+	0.957926i	−0.148340	+	0.107775i	0.511140	+	0.859497i	$0.329223\pi$
$80$	1.90398	−	1.17255i	0.212871	−	0.131095i
$81$	−0.0990782	−	0.0719846i	−0.0110087	−	0.00799828i
$82$	1.48810			0.164333
$83$	−1.44290	−	1.04833i	−0.158379	−	0.115069i	0.505773	−	0.862667i	$-0.331207\pi$
$83$	−1.44290	−	1.04833i	−0.158379	−	0.115069i	−0.664152	+	0.747597i	$0.731207\pi$
$84$	−0.297114	+	0.914422i	−0.0324178	+	0.0997716i
$85$	−1.37182	−	5.65899i	−0.148795	−	0.613804i
$86$	−1.62155	−	4.99061i	−0.174856	−	0.538152i
$87$	1.12051	−	3.44858i	0.120131	−	0.369726i
$88$	1.12437	−	3.46045i	0.119858	−	0.368885i
$89$	−2.30735	−	7.10130i	−0.244579	−	0.752736i	−0.995705	−	0.0925782i	$-0.970489\pi$
$89$	−2.30735	−	7.10130i	−0.244579	−	0.752736i	0.751127	−	0.660158i	$-0.229511\pi$
$90$	−3.18952	−	2.71195i	−0.336205	−	0.285865i
$91$	0.279787	−	0.861096i	0.0293297	−	0.0902674i
$92$	2.67148	+	1.94094i	0.278521	+	0.202357i
$93$	7.95009			0.824386
$94$	3.99841	+	2.90501i	0.412404	+	0.299629i
$95$	−0.635735	−	2.62251i	−0.0652250	−	0.269063i
$96$	0.859118	−	0.624186i	0.0876833	−	0.0637057i
$97$	−0.299495	+	0.217596i	−0.0304091	+	0.0220935i	−0.602886	−	0.797827i	$-0.705983\pi$
$97$	−0.299495	+	0.217596i	−0.0304091	+	0.0220935i	0.572477	+	0.819921i	$0.305983\pi$
$98$	−1.90980	−	5.87775i	−0.192919	−	0.593742i
$99$	−6.81245			−0.684677
$100$	−3.55111	−	3.51989i	−0.355111	−	0.351989i
$101$	−7.33867			−0.730225			−0.365113	−	0.930963i	$-0.618970\pi$
$101$	−7.33867			−0.730225			−0.365113	+	0.930963i	$0.618970\pi$
$102$	−0.854538	−	2.63000i	−0.0846119	−	0.260409i
$103$	−5.14141	+	3.73545i	−0.506598	+	0.368065i	−0.811531	−	0.584309i	$-0.801366\pi$
$103$	−5.14141	+	3.73545i	−0.506598	+	0.368065i	0.304934	+	0.952374i	$0.401366\pi$
$104$	−0.809017	+	0.587785i	−0.0793306	+	0.0576371i
$105$	2.14367	+	0.163950i	0.209201	+	0.0159999i
$106$	7.47671	+	5.43215i	0.726202	+	0.527617i
$107$	3.05252			0.295098			0.147549	−	0.989055i	$-0.452862\pi$
$107$	3.05252			0.295098			0.147549	+	0.989055i	$0.452862\pi$
$108$	−4.18589	−	3.04123i	−0.402787	−	0.292642i
$109$	4.69475	−	14.4490i	0.449676	−	1.38396i	−0.427597	−	0.903969i	$-0.640640\pi$
$109$	4.69475	−	14.4490i	0.449676	−	1.38396i	0.877273	−	0.479991i	$-0.159360\pi$
$110$	−8.11231	−	0.620435i	−0.773478	−	0.0591562i
$111$	0.201451	+	0.620003i	0.0191209	+	0.0588481i
$112$	0.279787	−	0.861096i	0.0264374	−	0.0813659i
$113$	1.99438	−	6.13806i	0.187615	−	0.577421i	−0.812368	−	0.583145i	$-0.801822\pi$
$113$	1.99438	−	6.13806i	0.187615	−	0.577421i	0.999984	+	0.00572415i	$0.00182206\pi$
$114$	−0.396012	−	1.21880i	−0.0370900	−	0.114151i
$115$	2.81059	−	6.82796i	0.262089	−	0.636710i
$116$	−1.05517	+	3.24747i	−0.0979697	+	0.301520i
$117$	1.51473	+	1.10052i	0.140037	+	0.101743i
$118$	0.253962			0.0233791
$119$	−1.90747	−	1.38586i	−0.174857	−	0.127041i
$120$	−1.80902	−	1.53815i	−0.165140	−	0.140413i
$121$	−1.81131	+	1.31599i	−0.164664	+	0.119636i
$122$	1.25438	−	0.911357i	0.113566	−	0.0825104i
$123$	−0.488325	−	1.50291i	−0.0440308	−	0.135513i
$124$	−7.48647			−0.672305
$125$	−5.77845	+	9.57129i	−0.516840	+	0.856082i
$126$	−1.69521			−0.151021
$127$	−2.64586	−	8.14311i	−0.234782	−	0.722584i	−0.997150	−	0.0754409i	$-0.975964\pi$
$127$	−2.64586	−	8.14311i	−0.234782	−	0.722584i	0.762368	−	0.647143i	$-0.224036\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−4.50817	+	3.27538i	−0.396922	+	0.288381i
$130$	1.70352	+	1.44845i	0.149409	+	0.127038i
$131$	−2.84280	−	2.06541i	−0.248376	−	0.180456i	0.456631	−	0.889656i	$-0.349056\pi$
$131$	−2.84280	−	2.06541i	−0.248376	−	0.180456i	−0.705007	+	0.709200i	$0.749056\pi$
$132$	−3.86386			−0.336306
$133$	−0.883963	−	0.642237i	−0.0766494	−	0.0556890i
$134$	−2.36996	+	7.29398i	−0.204733	+	0.630104i
$135$	−4.40385	+	10.6986i	−0.379023	+	0.920787i
$136$	0.804705	+	2.47663i	0.0690028	+	0.212369i
$137$	6.53289	−	20.1062i	0.558142	−	1.71779i	−0.129355	−	0.991598i	$-0.541291\pi$
$137$	6.53289	−	20.1062i	0.558142	−	1.71779i	0.687497	−	0.726187i	$-0.258709\pi$
$138$	1.08361	−	3.33500i	0.0922428	−	0.283894i
$139$	1.26731	+	3.90039i	0.107492	+	0.330827i	0.990307	−	0.138894i	$-0.0443547\pi$
$139$	1.26731	+	3.90039i	0.107492	+	0.330827i	−0.882815	+	0.469721i	$0.844355\pi$
$140$	−2.01866	−	0.154389i	−0.170608	−	0.0130482i
$141$	1.62183	−	4.99149i	0.136583	−	0.420360i
$142$	1.05895	+	0.769370i	0.0888648	+	0.0645641i
$143$	3.63853			0.304269
$144$	1.51473	+	1.10052i	0.126227	+	0.0917096i
$145$	7.61302	+	0.582249i	0.632227	+	0.0483532i
$146$	9.28700	−	6.74740i	0.768598	−	0.558419i
$147$	−5.30955	+	3.85761i	−0.437924	+	0.318170i
$148$	−0.189703	−	0.583847i	−0.0155935	−	0.0479919i
$149$	−17.4931			−1.43309			−0.716545	−	0.697541i	$-0.754278\pi$
$149$	−17.4931			−1.43309			−0.716545	+	0.697541i	$0.754278\pi$
$150$	−2.38961	+	4.74152i	−0.195111	+	0.387144i
$151$	−4.65028			−0.378435			−0.189217	−	0.981935i	$-0.560595\pi$
$151$	−4.65028			−0.378435			−0.189217	+	0.981935i	$0.560595\pi$
$152$	0.372918	+	1.14772i	0.0302477	+	0.0930928i
$153$	3.94448	−	2.86583i	0.318892	−	0.231689i
$154$	−2.66519	+	1.93638i	−0.214768	+	0.156038i
$155$	3.94386	+	16.2691i	0.316779	+	1.30676i
$156$	0.859118	+	0.624186i	0.0687845	+	0.0499748i
$157$	19.4524			1.55247			0.776235	−	0.630443i	$-0.217127\pi$
$157$	19.4524			1.55247			0.776235	+	0.630443i	$0.217127\pi$
$158$	−1.31847	−	0.957926i	−0.104892	−	0.0762085i
$159$	3.03271	−	9.33371i	0.240509	−	0.740211i
$160$	1.70352	+	1.44845i	0.134675	+	0.114510i
$161$	−0.923894	−	2.84345i	−0.0728131	−	0.224096i
$162$	0.0378445	−	0.116473i	0.00297335	−	0.00915102i
$163$	0.771268	−	2.37372i	0.0604103	−	0.185924i	−0.916297	−	0.400499i	$-0.868837\pi$
$163$	0.771268	−	2.37372i	0.0604103	−	0.185924i	0.976707	+	0.214575i	$0.0688367\pi$
$164$	0.459848	+	1.41527i	0.0359081	+	0.110514i
$165$	2.03547	+	8.39665i	0.158461	+	0.653679i
$166$	0.551140	−	1.69623i	0.0427768	−	0.131653i
$167$	−4.90916	−	3.56671i	−0.379882	−	0.276001i	0.381415	−	0.924404i	$-0.375437\pi$
$167$	−4.90916	−	3.56671i	−0.379882	−	0.276001i	−0.761297	+	0.648403i	$0.775437\pi$
$168$	−0.961480			−0.0741798
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	4.95811	−	3.05341i	0.380269	−	0.234186i
$171$	1.82796	−	1.32809i	0.139788	−	0.101562i
$172$	4.24527	−	3.08437i	0.323699	−	0.235181i
$173$	−3.11283	−	9.58032i	−0.236664	−	0.728378i	−0.996896	−	0.0787262i	$-0.974915\pi$
$173$	−3.11283	−	9.58032i	−0.236664	−	0.728378i	0.760232	−	0.649652i	$-0.225085\pi$
$174$	3.62605			0.274890
$175$	0.727922	+	4.46814i	0.0550258	+	0.337760i
$176$	3.63853			0.274265
$177$	−0.0833386	−	0.256490i	−0.00626411	−	0.0192790i
$178$	6.04073	−	4.38885i	0.452772	−	0.328958i
$179$	13.8098	−	10.0334i	1.03219	−	0.749932i	0.0634462	−	0.997985i	$-0.479791\pi$
$179$	13.8098	−	10.0334i	1.03219	−	0.749932i	0.968746	+	0.248053i	$0.0797909\pi$
$180$	1.59360	−	3.87145i	0.118780	−	0.288561i
$181$	10.8458	+	7.87993i	0.806162	+	0.585711i	0.912715	−	0.408596i	$-0.133982\pi$
$181$	10.8458	+	7.87993i	0.806162	+	0.585711i	−0.106554	+	0.994307i	$0.533982\pi$
$182$	0.905410			0.0671135
$183$	−1.33206	−	0.967795i	−0.0984684	−	0.0715415i
$184$	−1.02042	+	3.14051i	−0.0752260	+	0.231522i
$185$	−1.16884	+	0.719819i	−0.0859347	+	0.0529221i
$186$	2.45671	+	7.56099i	0.180135	+	0.554399i
$187$	2.92794	−	9.01128i	0.214112	−	0.658970i
$188$	−1.52726	+	4.70041i	−0.111387	+	0.342812i
$189$	1.44763	+	4.45535i	0.105300	+	0.324079i
$190$	2.29770	−	1.41502i	0.166693	−	0.102656i
$191$	−0.758805	+	2.33536i	−0.0549052	+	0.168981i	−0.974749	−	0.223305i	$-0.928315\pi$
$191$	−0.758805	+	2.33536i	−0.0549052	+	0.168981i	0.919843	+	0.392286i	$0.128315\pi$
$192$	0.859118	+	0.624186i	0.0620015	+	0.0450467i
$193$	10.8093			0.778074			0.389037	−	0.921222i	$-0.372808\pi$
$193$	10.8093			0.778074			0.389037	+	0.921222i	$0.372808\pi$
$194$	−0.299495	−	0.217596i	−0.0215025	−	0.0156225i
$195$	0.903853	−	2.19579i	0.0647263	−	0.157244i
$196$	4.99991	−	3.63265i	0.357137	−	0.259475i
$197$	−1.17297	+	0.852216i	−0.0835710	+	0.0607179i	−0.628786	−	0.777578i	$-0.716448\pi$
$197$	−1.17297	+	0.852216i	−0.0835710	+	0.0607179i	0.545215	+	0.838296i	$0.316448\pi$
$198$	−2.10516	−	6.47903i	−0.149607	−	0.460444i
$199$	−18.9612			−1.34413			−0.672063	−	0.740494i	$-0.734591\pi$
$199$	−18.9612			−1.34413			−0.672063	+	0.740494i	$0.734591\pi$
$200$	2.25026	−	4.46501i	0.159117	−	0.315724i
$201$	8.14430			0.574454
$202$	−2.26778	−	6.97949i	−0.159560	−	0.491076i
$203$	2.50116	−	1.81720i	0.175547	−	0.127542i
$204$	2.23721	−	1.62543i	0.156636	−	0.113803i
$205$	2.83331	−	1.74487i	0.197887	−	0.121867i
$206$	−5.14141	−	3.73545i	−0.358219	−	0.260261i
$207$	6.18261			0.429721
$208$	−0.809017	−	0.587785i	−0.0560952	−	0.0407556i
$209$	1.35687	−	4.17603i	0.0938570	−	0.288862i
$210$	0.506506	+	2.08942i	0.0349523	+	0.144184i
$211$	7.18400	+	22.1101i	0.494567	+	1.52212i	0.817631	+	0.575743i	$0.195287\pi$
$211$	7.18400	+	22.1101i	0.494567	+	1.52212i	−0.323064	+	0.946377i	$0.604713\pi$
$212$	−2.85585	+	8.78940i	−0.196141	+	0.603659i
$213$	0.429530	−	1.32196i	0.0294309	−	0.0905791i
$214$	0.943280	+	2.90312i	0.0644813	+	0.198453i
$215$	−8.93913	−	7.60067i	−0.609643	−	0.518361i
$216$	1.59887	−	4.92081i	0.108789	−	0.334818i
$217$	5.48378	+	3.98420i	0.372263	+	0.270465i
$218$	15.1925			1.02897
$219$	−9.86213	−	7.16525i	−0.666421	−	0.484183i
$220$	−1.91677	−	7.90699i	−0.129229	−	0.533089i
$221$	−2.10674	+	1.53064i	−0.141715	+	0.102962i
$222$	−0.527406	+	0.383183i	−0.0353972	+	0.0257176i
$223$	4.91864	+	15.1380i	0.329376	+	1.01372i	0.969426	+	0.245383i	$0.0789136\pi$
$223$	4.91864	+	15.1380i	0.329376	+	1.01372i	−0.640050	+	0.768333i	$0.721086\pi$
$224$	0.905410			0.0604953
$225$	−9.25266	−	1.42363i	−0.616844	−	0.0949085i
$226$	6.45394			0.429310
$227$	−8.48410	−	26.1114i	−0.563110	−	1.73307i	−0.673502	−	0.739185i	$-0.735211\pi$
$227$	−8.48410	−	26.1114i	−0.563110	−	1.73307i	0.110393	−	0.993888i	$-0.464789\pi$
$228$	1.03677	−	0.753260i	0.0686620	−	0.0498859i
$229$	−13.1720	+	9.57004i	−0.870432	+	0.632406i	−0.930703	−	0.365776i	$-0.880804\pi$
$229$	−13.1720	+	9.57004i	−0.870432	+	0.632406i	0.0602708	+	0.998182i	$0.480804\pi$
$230$	7.36229	+	0.563073i	0.485455	+	0.0371280i
$231$	2.83024	+	2.05629i	0.186216	+	0.135294i
$232$	−3.41459			−0.224179
$233$	−0.478971	−	0.347993i	−0.0313784	−	0.0227978i	0.571985	−	0.820264i	$-0.306173\pi$
$233$	−0.478971	−	0.347993i	−0.0313784	−	0.0227978i	−0.603364	+	0.797466i	$0.706173\pi$
$234$	−0.578575	+	1.78067i	−0.0378226	+	0.116406i
$235$	11.0191	+	0.842752i	0.718810	+	0.0549751i
$236$	0.0784786	+	0.241532i	0.00510852	+	0.0157224i
$237$	−0.534799	+	1.64594i	−0.0347389	+	0.106915i
$238$	0.728588	−	2.24236i	0.0472273	−	0.145351i
$239$	−3.15010	−	9.69500i	−0.203763	−	0.627117i	−0.999762	−	0.0218195i	$-0.993054\pi$
$239$	−3.15010	−	9.69500i	−0.203763	−	0.627117i	0.795999	−	0.605298i	$-0.206946\pi$
$240$	0.903853	−	2.19579i	0.0583435	−	0.141738i
$241$	−7.73082	+	23.7930i	−0.497986	+	1.53264i	0.314266	+	0.949335i	$0.398242\pi$
$241$	−7.73082	+	23.7930i	−0.497986	+	1.53264i	−0.812252	+	0.583307i	$0.801758\pi$
$242$	−1.81131	−	1.31599i	−0.116435	−	0.0845952i
$243$	−15.6522			−1.00409
$244$	1.25438	+	0.911357i	0.0803031	+	0.0583436i
$245$	−10.5282	−	8.95177i	−0.672619	−	0.571908i
$246$	1.27845	−	0.928850i	0.0815111	−	0.0592213i
$247$	−0.976313	+	0.709333i	−0.0621213	+	0.0451338i
$248$	−2.31345	−	7.12006i	−0.146904	−	0.452124i
$249$	−1.89398			−0.120026
$250$	−10.8885	−	2.53794i	−0.688648	−	0.160513i
$251$	−30.7235			−1.93925			−0.969626	−	0.244592i	$-0.921346\pi$
$251$	−30.7235			−1.93925			−0.969626	+	0.244592i	$0.921346\pi$
$252$	−0.523848	−	1.61224i	−0.0329993	−	0.101561i
$253$	9.72027	−	7.06219i	0.611108	−	0.443996i
$254$	6.92694	−	5.03272i	0.434635	−	0.315781i
$255$	−4.71082	−	4.00547i	−0.295003	−	0.250832i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	30.8494			1.92433			0.962167	−	0.272460i	$-0.0878373\pi$
$257$	30.8494			1.92433			0.962167	+	0.272460i	$0.0878373\pi$
$258$	−4.50817	−	3.27538i	−0.280666	−	0.203916i
$259$	−0.171759	+	0.528621i	−0.0106726	+	0.0328469i
$260$	−0.851143	+	2.06774i	−0.0527857	+	0.128236i
$261$	1.97560	+	6.08026i	0.122286	+	0.376359i
$262$	1.08585	−	3.34191i	0.0670842	−	0.206464i
$263$	−8.01534	+	24.6687i	−0.494247	+	1.52114i	0.323880	+	0.946098i	$0.395013\pi$
$263$	−8.01534	+	24.6687i	−0.494247	+	1.52114i	−0.818127	+	0.575038i	$0.804987\pi$
$264$	−1.19400	−	3.67475i	−0.0734855	−	0.226165i
$265$	20.6049	+	1.57588i	1.26575	+	0.0968056i
$266$	0.337644	−	1.03916i	0.0207023	−	0.0637151i
$267$	−6.41482	−	4.66064i	−0.392580	−	0.285226i
$268$	−7.66935			−0.468480
$269$	4.73784	+	3.44224i	0.288871	+	0.209877i	0.722778	−	0.691081i	$-0.242865\pi$
$269$	4.73784	+	3.44224i	0.288871	+	0.209877i	−0.433906	+	0.900958i	$0.642865\pi$
$270$	−11.5358	−	0.882268i	−0.702048	−	0.0536931i
$271$	−7.84739	+	5.70146i	−0.476695	+	0.346339i	−0.800045	−	0.599940i	$-0.795191\pi$
$271$	−7.84739	+	5.70146i	−0.476695	+	0.346339i	0.323350	+	0.946279i	$0.395191\pi$
$272$	−2.10674	+	1.53064i	−0.127740	+	0.0928086i
$273$	−0.297114	−	0.914422i	−0.0179821	−	0.0553433i
$274$	21.1409			1.27717
$275$	−16.1731	+	8.33078i	−0.975277	+	0.502365i
$276$	3.50663			0.211074
$277$	−0.759104	−	2.33628i	−0.0456102	−	0.140374i	0.925658	−	0.378361i	$-0.123512\pi$
$277$	−0.759104	−	2.33628i	−0.0456102	−	0.140374i	−0.971268	+	0.237988i	$0.923512\pi$
$278$	−3.31787	+	2.41057i	−0.198993	+	0.144577i
$279$	−11.3400	+	8.23898i	−0.678907	+	0.493255i
$280$	−0.476969	−	1.96757i	−0.0285043	−	0.117585i
$281$	−9.09131	−	6.60522i	−0.542342	−	0.394034i	0.282612	−	0.959234i	$-0.408799\pi$
$281$	−9.09131	−	6.60522i	−0.542342	−	0.394034i	−0.824954	+	0.565200i	$0.808799\pi$
$282$	5.24837			0.312536
$283$	19.7363	+	14.3392i	1.17320	+	0.852380i	0.991388	−	0.130954i	$-0.0418040\pi$
$283$	19.7363	+	14.3392i	1.17320	+	0.852380i	0.181811	+	0.983333i	$0.441804\pi$
$284$	−0.404482	+	1.24487i	−0.0240016	+	0.0738692i
$285$	−2.18310	−	1.85623i	−0.129316	−	0.109953i
$286$	1.12437	+	3.46045i	0.0664853	+	0.204621i
$287$	0.416351	−	1.28140i	0.0245764	−	0.0756384i
$288$	−0.578575	+	1.78067i	−0.0340929	+	0.104927i
$289$	−3.15778	−	9.71863i	−0.185751	−	0.571684i
$290$	1.79880	+	7.42034i	0.105629	+	0.435737i
$291$	−0.121481	+	0.373881i	−0.00712136	+	0.0219173i
$292$	9.28700	+	6.74740i	0.543481	+	0.394862i
$293$	−20.3134			−1.18672			−0.593362	−	0.804936i	$-0.702200\pi$
$293$	−20.3134			−1.18672			−0.593362	+	0.804936i	$0.702200\pi$
$294$	−5.30955	−	3.85761i	−0.309659	−	0.224981i
$295$	0.483538	−	0.297783i	0.0281527	−	0.0173376i
$296$	0.496650	−	0.360837i	0.0288672	−	0.0209732i
$297$	−15.2305	+	11.0656i	−0.883762	+	0.642091i
$298$	−5.40567	−	16.6369i	−0.313142	−	0.963751i
$299$	−3.30213			−0.190967
$300$	−5.24789	−	0.807447i	−0.302987	−	0.0466180i
$301$	−4.75109			−0.273848
$302$	−1.43702	−	4.42268i	−0.0826910	−	0.254497i
$303$	−6.30479	+	4.58070i	−0.362201	+	0.263154i
$304$	−0.976313	+	0.709333i	−0.0559954	+	0.0406830i
$305$	1.31969	−	3.20602i	0.0755653	−	0.183576i
$306$	3.94448	+	2.86583i	0.225491	+	0.163829i
$307$	19.3497			1.10434			0.552171	−	0.833731i	$-0.313799\pi$
$307$	19.3497			1.10434			0.552171	+	0.833731i	$0.313799\pi$
$308$	−2.66519	−	1.93638i	−0.151864	−	0.110335i
$309$	−2.08546	+	6.41838i	−0.118638	+	0.365129i
$310$	−14.2541	+	8.77825i	−0.809577	+	0.498571i
$311$	10.3390	+	31.8203i	0.586273	+	1.80436i	0.594097	+	0.804393i	$0.297509\pi$
$311$	10.3390	+	31.8203i	0.586273	+	1.80436i	−0.00782433	+	0.999969i	$0.502491\pi$
$312$	−0.328154	+	1.00995i	−0.0185781	+	0.0571774i
$313$	−7.89149	+	24.2875i	−0.446054	+	1.37281i	0.435271	+	0.900300i	$0.356653\pi$
$313$	−7.89149	+	24.2875i	−0.446054	+	1.37281i	−0.881324	+	0.472512i	$0.843347\pi$
$314$	6.01112	+	18.5003i	0.339227	+	1.04403i
$315$	−3.22764	+	1.98771i	−0.181857	+	0.111995i
$316$	0.503611	−	1.54996i	0.0283304	−	0.0871919i
$317$	4.47634	+	3.25225i	0.251416	+	0.182664i	0.706354	−	0.707859i	$-0.250339\pi$
$317$	4.47634	+	3.25225i	0.251416	+	0.182664i	−0.454938	+	0.890523i	$0.650339\pi$
$318$	9.81405			0.550344
$319$	10.0513	+	7.30269i	0.562764	+	0.408872i
$320$	−0.851143	+	2.06774i	−0.0475804	+	0.115590i
$321$	2.62247	−	1.90534i	0.146372	−	0.106346i
$322$	2.41879	−	1.75735i	0.134794	−	0.0979333i
$323$	0.971109	+	2.98876i	0.0540339	+	0.166299i
$324$	0.122467			0.00680375
$325$	4.94185	+	0.760360i	0.274124	+	0.0421772i
$326$	2.49587			0.138234
$327$	−4.98549	−	15.3438i	−0.275698	−	0.848512i
$328$	−1.20390	+	0.874682i	−0.0664741	+	0.0482963i
$329$	3.62020	−	2.63023i	0.199588	−	0.145009i
$330$	−7.35670	+	4.53056i	−0.404973	+	0.249399i
$331$	1.57857	+	1.14690i	0.0867660	+	0.0630392i	0.630323	−	0.776333i	$-0.282923\pi$
$331$	1.57857	+	1.14690i	0.0867660	+	0.0630392i	−0.543557	+	0.839373i	$0.682923\pi$
$332$	1.78353			0.0978837
$333$	−0.929881	−	0.675598i	−0.0509572	−	0.0370226i
$334$	1.87513	−	5.77106i	0.102603	−	0.315779i
$335$	4.04020	+	16.6665i	0.220740	+	0.910587i
$336$	−0.297114	−	0.914422i	−0.0162089	−	0.0498858i
$337$	5.75506	−	17.7123i	0.313498	−	0.964848i	−0.662870	−	0.748735i	$-0.730662\pi$
$337$	5.75506	−	17.7123i	0.313498	−	0.964848i	0.976368	−	0.216114i	$-0.0693382\pi$
$338$	0.309017	−	0.951057i	0.0168083	−	0.0517307i
$339$	−2.11789	−	6.51818i	−0.115028	−	0.354019i
$340$	4.43610	+	3.77188i	0.240581	+	0.204559i
$341$	−8.41755	+	25.9065i	−0.455836	+	1.40292i
$342$	1.82796	+	1.32809i	0.0988447	+	0.0718149i
$343$	−11.9335			−0.644349
$344$	4.24527	+	3.08437i	0.228890	+	0.166298i
$345$	−1.84729	−	7.62035i	−0.0994545	−	0.410266i
$346$	8.14950	−	5.92096i	0.438120	−	0.318313i
$347$	−28.1318	+	20.4389i	−1.51019	+	1.09722i	−0.544102	+	0.839019i	$0.683129\pi$
$347$	−28.1318	+	20.4389i	−1.51019	+	1.09722i	−0.966091	+	0.258200i	$0.916871\pi$
$348$	1.12051	+	3.44858i	0.0600657	+	0.184863i
$349$	−11.1603			−0.597396			−0.298698	−	0.954348i	$-0.596552\pi$
$349$	−11.1603			−0.597396			−0.298698	+	0.954348i	$0.596552\pi$
$350$	−4.02452	+	2.07303i	−0.215120	+	0.110808i
$351$	5.17404			0.276170
$352$	1.12437	+	3.46045i	0.0599290	+	0.184442i
$353$	3.52353	−	2.56000i	0.187539	−	0.136255i	−0.490054	−	0.871692i	$-0.663023\pi$
$353$	3.52353	−	2.56000i	0.187539	−	0.136255i	0.677593	+	0.735437i	$0.263023\pi$
$354$	0.218183	−	0.158519i	0.0115963	−	0.00842521i
$355$	2.91833	+	0.223196i	0.154889	+	0.0118460i
$356$	6.04073	+	4.38885i	0.320158	+	0.232608i
$357$	−2.50377			−0.132514
$358$	13.8098	+	10.0334i	0.729870	+	0.530282i
$359$	−4.67823	+	14.3981i	−0.246908	+	0.759904i	0.748409	+	0.663237i	$0.230818\pi$
$359$	−4.67823	+	14.3981i	−0.246908	+	0.759904i	−0.995317	+	0.0966666i	$0.969182\pi$
$360$	4.17442	+	0.319263i	0.220011	+	0.0168266i
$361$	−5.42129	−	16.6850i	−0.285331	−	0.878159i
$362$	−4.14273	+	12.7500i	−0.217737	+	0.670125i
$363$	−0.734704	+	2.26119i	−0.0385619	+	0.118681i
$364$	0.279787	+	0.861096i	0.0146648	+	0.0451337i
$365$	9.77058	−	23.7364i	0.511416	−	1.24242i
$366$	0.508800	−	1.56593i	0.0265954	−	0.0818523i
$367$	12.1921	+	8.85807i	0.636422	+	0.462387i	0.858619	−	0.512614i	$-0.171323\pi$
$367$	12.1921	+	8.85807i	0.636422	+	0.462387i	−0.222197	+	0.975002i	$0.571323\pi$
$368$	−3.30213			−0.172136
$369$	2.25407	+	1.63768i	0.117342	+	0.0852540i
$370$	−1.04578	−	0.889194i	−0.0543675	−	0.0462270i
$371$	6.76949	−	4.91832i	0.351454	−	0.255347i
$372$	−6.43176	+	4.67295i	−0.333471	+	0.242281i
$373$	6.97501	+	21.4669i	0.361152	+	1.11151i	0.952356	+	0.304990i	$0.0986531\pi$
$373$	6.97501	+	21.4669i	0.361152	+	1.11151i	−0.591203	+	0.806523i	$0.701347\pi$
$374$	9.47502			0.489942
$375$	1.00989	+	11.8297i	0.0521507	+	0.610882i
$376$	−4.94230			−0.254880
$377$	−1.05517	−	3.24747i	−0.0543438	−	0.167253i
$378$	−3.78994	+	2.75356i	−0.194934	+	0.141628i
$379$	−7.30560	+	5.30783i	−0.375264	+	0.272645i	−0.759390	−	0.650635i	$-0.774503\pi$
$379$	−7.30560	+	5.30783i	−0.375264	+	0.272645i	0.384127	+	0.923280i	$0.374503\pi$
$380$	2.05579	+	1.74798i	0.105460	+	0.0896693i
$381$	−7.35591	−	5.34438i	−0.376855	−	0.273801i
$382$	−2.45554			−0.125637
$383$	−17.3575	−	12.6109i	−0.886925	−	0.644389i	0.0481493	−	0.998840i	$-0.484668\pi$
$383$	−17.3575	−	12.6109i	−0.886925	−	0.644389i	−0.935074	+	0.354451i	$0.884668\pi$
$384$	−0.328154	+	1.00995i	−0.0167460	+	0.0515390i
$385$	−2.80397	+	6.81189i	−0.142904	+	0.347166i
$386$	3.34027	+	10.2803i	0.170015	+	0.523253i
$387$	3.03604	−	9.34397i	0.154331	−	0.474981i
$388$	0.114397	−	0.352078i	0.00580763	−	0.0178740i
$389$	−2.84733	−	8.76318i	−0.144365	−	0.444311i	0.852564	−	0.522624i	$-0.175047\pi$
$389$	−2.84733	−	8.76318i	−0.144365	−	0.444311i	−0.996929	+	0.0783129i	$0.975047\pi$
$390$	2.36763	+	0.181078i	0.119890	+	0.00916924i
$391$	−2.65724	+	8.17815i	−0.134382	+	0.413587i
$392$	4.99991	+	3.63265i	0.252534	+	0.183477i
$393$	−3.73150			−0.188229
$394$	−1.17297	−	0.852216i	−0.0590936	−	0.0429340i
$395$	−3.63356	−	0.277897i	−0.182824	−	0.0139825i
$396$	5.51139	−	4.00426i	0.276958	−	0.201222i
$397$	1.04387	−	0.758418i	0.0523905	−	0.0380639i	−0.561282	−	0.827625i	$-0.689692\pi$
$397$	1.04387	−	0.758418i	0.0523905	−	0.0380639i	0.613672	+	0.789561i	$0.289692\pi$
$398$	−5.85934	−	18.0332i	−0.293702	−	0.903922i
$399$	−1.16030			−0.0580878
$400$	4.94185	+	0.760360i	0.247092	+	0.0380180i
$401$	−36.5286			−1.82415			−0.912075	−	0.410023i	$-0.865521\pi$
$401$	−36.5286			−1.82415			−0.912075	+	0.410023i	$0.865521\pi$
$402$	2.51673	+	7.74569i	0.125523	+	0.386320i
$403$	6.05668	−	4.40044i	0.301705	−	0.219201i
$404$	5.93711	−	4.31356i	0.295382	−	0.214608i
$405$	−0.0645157	−	0.266137i	−0.00320581	−	0.0132245i
$406$	2.50116	+	1.81720i	0.124130	+	0.0901861i
$407$	−2.23367			−0.110719
$408$	2.23721	+	1.62543i	0.110758	+	0.0804707i
$409$	−0.629780	+	1.93826i	−0.0311406	+	0.0958409i	−0.965419	−	0.260704i	$-0.916045\pi$
$409$	−0.629780	+	1.93826i	−0.0311406	+	0.0958409i	0.934278	+	0.356545i	$0.116045\pi$
$410$	2.53501	+	2.15544i	0.125195	+	0.106450i
$411$	−6.93746	−	21.3513i	−0.342199	−	1.05318i
$412$	1.96384	−	6.04408i	0.0967516	−	0.297771i
$413$	0.0710553	−	0.218686i	0.00349640	−	0.0107608i
$414$	1.91053	+	5.88001i	0.0938975	+	0.288987i
$415$	−0.939559	−	3.87583i	−0.0461211	−	0.190257i
$416$	0.309017	−	0.951057i	0.0151508	−	0.0466294i
$417$	3.52334	+	2.55986i	0.172539	+	0.125357i
$418$	4.39094			0.214768
$419$	28.9369	+	21.0239i	1.41366	+	1.02709i	0.992777	+	0.119972i	$0.0382805\pi$
$419$	28.9369	+	21.0239i	1.41366	+	1.02709i	0.420885	+	0.907114i	$0.361720\pi$
$420$	−1.83064	+	1.12738i	−0.0893259	+	0.0550106i
$421$	17.0061	−	12.3557i	0.828827	−	0.602178i	−0.0904005	−	0.995905i	$-0.528815\pi$
$421$	17.0061	−	12.3557i	0.828827	−	0.602178i	0.919227	+	0.393728i	$0.128815\pi$
$422$	−18.8080	+	13.6648i	−0.915557	+	0.665191i
$423$	2.85949	+	8.80062i	0.139033	+	0.427901i
$424$	−9.24172			−0.448818
$425$	5.85985	−	11.6272i	0.284245	−	0.564004i
$426$	1.38999			0.0673452
$427$	−0.433808	−	1.33512i	−0.0209934	−	0.0646112i
$428$	−2.46954	+	1.79422i	−0.119370	+	0.0867271i
$429$	3.12593	−	2.27112i	0.150921	−	0.109651i
$430$	4.46632	−	10.8504i	0.215385	−	0.523250i
$431$	14.0471	+	10.2058i	0.676624	+	0.491596i	0.872236	−	0.489085i	$-0.162669\pi$
$431$	14.0471	+	10.2058i	0.676624	+	0.491596i	−0.195612	+	0.980681i	$0.562669\pi$
$432$	5.17404			0.248936
$433$	−5.55787	−	4.03803i	−0.267094	−	0.194055i	0.446174	−	0.894946i	$-0.352786\pi$
$433$	−5.55787	−	4.03803i	−0.267094	−	0.194055i	−0.713269	+	0.700891i	$0.752786\pi$
$434$	−2.09462	+	6.44657i	−0.100545	+	0.309445i
$435$	6.90391	−	4.25172i	0.331017	−	0.203854i
$436$	4.69475	+	14.4490i	0.224838	+	0.691980i
$437$	−1.23143	+	3.78994i	−0.0589071	+	0.181297i
$438$	3.76700	−	11.5936i	0.179994	−	0.553965i
$439$	7.43339	+	22.8776i	0.354776	+	1.09189i	0.956139	+	0.292913i	$0.0946248\pi$
$439$	7.43339	+	22.8776i	0.354776	+	1.09189i	−0.601363	+	0.798976i	$0.705375\pi$
$440$	6.92768	−	4.26635i	0.330264	−	0.203390i
$441$	3.57573	−	11.0050i	0.170273	−	0.524046i
$442$	−2.10674	−	1.53064i	−0.100208	−	0.0728051i
$443$	−18.0961			−0.859773			−0.429887	−	0.902883i	$-0.641446\pi$
$443$	−18.0961			−0.859773			−0.429887	+	0.902883i	$0.641446\pi$
$444$	−0.527406	−	0.383183i	−0.0250296	−	0.0181851i
$445$	6.35527	−	15.4393i	0.301269	−	0.731893i
$446$	−12.8772	+	9.35580i	−0.609751	+	0.443010i
$447$	−15.0286	+	10.9189i	−0.710830	+	0.516448i
$448$	0.279787	+	0.861096i	0.0132187	+	0.0406830i
$449$	30.9792			1.46200			0.731000	−	0.682377i	$-0.239054\pi$
$449$	30.9792			1.46200			0.731000	+	0.682377i	$0.239054\pi$
$450$	−1.50528	−	9.23973i	−0.0709596	−	0.435565i
$451$	5.41449			0.254958
$452$	1.99438	+	6.13806i	0.0938077	+	0.288710i
$453$	−3.99514	+	2.90264i	−0.187708	+	0.136378i
$454$	22.2117	−	16.1377i	1.04245	−	0.757381i
$455$	1.72388	−	1.06164i	0.0808168	−	0.0497703i
$456$	1.03677	+	0.753260i	0.0485514	+	0.0352746i
$457$	25.8229			1.20794			0.603971	−	0.797006i	$-0.293584\pi$
$457$	25.8229			1.20794			0.603971	+	0.797006i	$0.293584\pi$
$458$	−13.1720	−	9.57004i	−0.615488	−	0.447179i
$459$	4.16357	−	12.8142i	0.194339	−	0.598114i
$460$	1.73956	+	7.17596i	0.0811074	+	0.334581i
$461$	1.36897	+	4.21327i	0.0637595	+	0.196232i	0.977862	−	0.209252i	$-0.0671030\pi$
$461$	1.36897	+	4.21327i	0.0637595	+	0.196232i	−0.914102	+	0.405484i	$0.867103\pi$
$462$	−1.08106	+	3.32715i	−0.0502953	+	0.154793i
$463$	−9.52775	+	29.3234i	−0.442792	+	1.36277i	0.442094	+	0.896968i	$0.354236\pi$
$463$	−9.52775	+	29.3234i	−0.442792	+	1.36277i	−0.884887	+	0.465806i	$0.845764\pi$
$464$	−1.05517	−	3.24747i	−0.0489849	−	0.150760i
$465$	13.5432	+	11.5153i	0.628049	+	0.534011i
$466$	0.182951	−	0.563064i	0.00847503	−	0.0260835i
$467$	1.24299	+	0.903084i	0.0575187	+	0.0417898i	0.616173	−	0.787611i	$-0.288682\pi$
$467$	1.24299	+	0.903084i	0.0575187	+	0.0417898i	−0.558654	+	0.829401i	$0.688682\pi$
$468$	−1.87231			−0.0865475
$469$	5.61774	+	4.08153i	0.259403	+	0.188467i
$470$	2.60360	+	10.7403i	0.120095	+	0.495411i
$471$	16.7119	−	12.1419i	0.770044	−	0.559470i
$472$	−0.205460	+	0.149275i	−0.00945705	+	0.00687095i
$473$	−5.90005	−	18.1585i	−0.271285	−	0.834929i
$474$	−1.73065			−0.0794912
$475$	2.71559	−	5.38833i	0.124600	−	0.247233i
$476$	2.35776			0.108068
$477$	5.34703	+	16.4565i	0.244824	+	0.753490i
$478$	8.24706	−	5.99184i	0.377212	−	0.274060i
$479$	9.47621	−	6.88487i	0.432979	−	0.314578i	−0.349860	−	0.936802i	$-0.613771\pi$
$479$	9.47621	−	6.88487i	0.432979	−	0.314578i	0.782839	+	0.622224i	$0.213771\pi$
$480$	2.36763	+	0.181078i	0.108067	+	0.00826504i
$481$	0.496650	+	0.360837i	0.0226453	+	0.0164528i
$482$	−25.0174			−1.13951
$483$	−2.56858	−	1.86618i	−0.116874	−	0.0849141i
$484$	0.691858	−	2.12932i	0.0314481	−	0.0967873i
$485$	−0.825374	−	0.0631252i	−0.0374783	−	0.00286637i
$486$	−4.83679	−	14.8861i	−0.219401	−	0.675247i
$487$	5.38557	−	16.5751i	0.244044	−	0.751089i	−0.751749	−	0.659450i	$-0.770789\pi$
$487$	5.38557	−	16.5751i	0.244044	−	0.751089i	0.995792	−	0.0916392i	$-0.0292106\pi$
$488$	−0.479129	+	1.47461i	−0.0216891	+	0.0667523i
$489$	−0.819031	−	2.52072i	−0.0370378	−	0.113991i
$490$	5.26026	−	12.7791i	0.237634	−	0.577302i
$491$	10.9735	−	33.7729i	0.495226	−	1.52415i	−0.321379	−	0.946951i	$-0.604146\pi$
$491$	10.9735	−	33.7729i	0.495226	−	1.52415i	0.816605	−	0.577197i	$-0.195854\pi$
$492$	1.27845	+	0.928850i	0.0576371	+	0.0418758i
$493$	−8.89186			−0.400469
$494$	−0.976313	−	0.709333i	−0.0439264	−	0.0319144i
$495$	−11.6052	−	9.86751i	−0.521613	−	0.443512i
$496$	6.05668	−	4.40044i	0.271953	−	0.197585i
$497$	0.958781	−	0.696595i	0.0430072	−	0.0312466i
$498$	−0.585271	−	1.80128i	−0.0262266	−	0.0807172i
$499$	−16.3888			−0.733663			−0.366831	−	0.930287i	$-0.619557\pi$
$499$	−16.3888			−0.733663			−0.366831	+	0.930287i	$0.619557\pi$
$500$	−0.951000	−	11.1398i	−0.0425300	−	0.498188i
$501$	−6.44384			−0.287890
$502$	−9.49409	−	29.2198i	−0.423742	−	1.30414i
$503$	−4.42914	+	3.21796i	−0.197486	+	0.143482i	−0.682134	−	0.731228i	$-0.738948\pi$
$503$	−4.42914	+	3.21796i	−0.197486	+	0.143482i	0.484648	+	0.874709i	$0.338948\pi$
$504$	1.37145	−	0.996418i	0.0610893	−	0.0443840i
$505$	−12.5016	−	10.6297i	−0.556313	−	0.473016i
$506$	9.72027	+	7.06219i	0.432119	+	0.313952i
$507$	−1.06193			−0.0471619
$508$	6.92694	+	5.03272i	0.307333	+	0.223291i
$509$	5.48476	−	16.8804i	0.243108	−	0.748209i	−0.752834	−	0.658210i	$-0.771314\pi$
$509$	5.48476	−	16.8804i	0.243108	−	0.748209i	0.995942	−	0.0899987i	$-0.0286863\pi$
$510$	2.35370	−	5.71802i	0.104224	−	0.253198i
$511$	−3.21178	−	9.88484i	−0.142081	−	0.437279i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	1.92949	−	5.93837i	0.0851893	−	0.262186i
$514$	9.53300	+	29.3395i	0.420482	+	1.29411i
$515$	−14.1691	−	1.08366i	−0.624366	−	0.0477519i
$516$	1.72197	−	5.29967i	0.0758054	−	0.233305i
$517$	14.5483	+	10.5700i	0.639834	+	0.464867i
$518$	−0.555825			−0.0244215
$519$	−8.65419	−	6.28763i	−0.379877	−	0.275997i
$520$	−2.22956	−	0.170518i	−0.0977725	−	0.00747771i
$521$	−1.25092	+	0.908847i	−0.0548038	+	0.0398173i	−0.614850	−	0.788644i	$-0.710783\pi$
$521$	−1.25092	+	0.908847i	−0.0548038	+	0.0398173i	0.560046	+	0.828461i	$0.310783\pi$
$522$	−5.17218	+	3.75781i	−0.226380	+	0.164475i
$523$	1.21012	+	3.72436i	0.0529148	+	0.162855i	0.974022	−	0.226455i	$-0.0727136\pi$
$523$	1.21012	+	3.72436i	0.0529148	+	0.162855i	−0.921107	+	0.389310i	$0.872714\pi$
$524$	3.51389			0.153505
$525$	3.41432	+	3.38430i	0.149013	+	0.147703i
$526$	−25.9382			−1.13096
$527$	−6.02440	−	18.5412i	−0.262427	−	0.807667i
$528$	3.12593	−	2.27112i	0.136038	−	0.0988377i
$529$	9.78580	−	7.10980i	0.425470	−	0.309122i
$530$	4.86853	+	20.0834i	0.211475	+	0.872369i
$531$	0.384684	+	0.279489i	0.0166939	+	0.0121288i
$532$	1.09264			0.0473719
$533$	−1.20390	−	0.874682i	−0.0521466	−	0.0378867i
$534$	2.45024	−	7.54107i	0.106032	−	0.326334i
$535$	5.20003	+	4.42143i	0.224817	+	0.191155i
$536$	−2.36996	−	7.29398i	−0.102367	−	0.315052i
$537$	5.60153	−	17.2398i	0.241724	−	0.743950i
$538$	−1.80969	+	5.56967i	−0.0780215	+	0.240125i
$539$	−6.94885	−	21.3864i	−0.299308	−	0.921176i
$540$	−2.72568	−	11.2439i	−0.117294	−	0.483858i
$541$	−9.67021	+	29.7619i	−0.415755	+	1.27956i	0.495819	+	0.868426i	$0.334868\pi$
$541$	−9.67021	+	29.7619i	−0.415755	+	1.27956i	−0.911574	+	0.411136i	$0.865132\pi$
$542$	−7.84739	−	5.70146i	−0.337074	−	0.244899i
$543$	14.2364			0.610941
$544$	−2.10674	−	1.53064i	−0.0903259	−	0.0656256i
$545$	28.9263	−	17.8140i	1.23907	−	0.763068i
$546$	0.777854	−	0.565144i	0.0332891	−	0.0241859i
$547$	8.52230	−	6.19181i	0.364387	−	0.264743i	−0.390492	−	0.920606i	$-0.627695\pi$
$547$	8.52230	−	6.19181i	0.364387	−	0.264743i	0.754880	+	0.655863i	$0.227695\pi$
$548$	6.53289	+	20.1062i	0.279071	+	0.858893i
$549$	2.90300			0.123897
$550$	−12.9208	−	12.8072i	−0.550946	−	0.546102i
$551$	−4.12069			−0.175547
$552$	1.08361	+	3.33500i	0.0461214	+	0.141947i
$553$	−1.19376	+	0.867316i	−0.0507637	+	0.0368820i
$554$	1.98736	−	1.44390i	0.0844349	−	0.0613455i
$555$	−0.554869	+	1.34798i	−0.0235529	+	0.0572186i
$556$	−3.31787	−	2.41057i	−0.140709	−	0.102231i
$557$	−33.5252			−1.42051			−0.710253	−	0.703946i	$-0.751420\pi$
$557$	−33.5252			−1.42051			−0.710253	+	0.703946i	$0.751420\pi$
$558$	−11.3400	−	8.23898i	−0.480060	−	0.348784i
$559$	−1.62155	+	4.99061i	−0.0685842	+	0.211080i
$560$	1.72388	−	1.06164i	0.0728472	−	0.0448624i
$561$	−3.10926	−	9.56933i	−0.131273	−	0.404017i
$562$	3.47257	−	10.6875i	0.146482	−	0.450824i
$563$	−4.61704	+	14.2098i	−0.194585	+	0.598872i	0.805396	+	0.592737i	$0.201953\pi$
$563$	−4.61704	+	14.2098i	−0.194585	+	0.598872i	−0.999981	+	0.00613444i	$0.998047\pi$
$564$	1.62183	+	4.99149i	0.0682916	+	0.210180i
$565$	12.2882	−	7.56756i	0.516967	−	0.318370i
$566$	−7.53859	+	23.2014i	−0.316870	+	0.975227i
$567$	−0.0897064	−	0.0651755i	−0.00376732	−	0.00273712i
$568$	−1.30893			−0.0549215
$569$	4.77000	+	3.46561i	0.199969	+	0.145286i	0.683263	−	0.730172i	$-0.260560\pi$
$569$	4.77000	+	3.46561i	0.199969	+	0.145286i	−0.483295	+	0.875458i	$0.660560\pi$
$570$	1.09076	−	2.64986i	0.0456869	−	0.110990i
$571$	16.5669	−	12.0365i	0.693301	−	0.503713i	−0.184443	−	0.982843i	$-0.559048\pi$
$571$	16.5669	−	12.0365i	0.693301	−	0.503713i	0.877744	+	0.479131i	$0.159048\pi$
$572$	−2.94363	+	2.13867i	−0.123079	+	0.0894225i
$573$	0.805796	+	2.47999i	0.0336626	+	0.103603i
$574$	1.34734			0.0562369
$575$	14.6779	−	7.56057i	0.612109	−	0.315297i
$576$	−1.87231			−0.0780129
$577$	4.68358	+	14.4146i	0.194980	+	0.600087i	0.999977	+	0.00680762i	$0.00216695\pi$
$577$	4.68358	+	14.4146i	0.194980	+	0.600087i	−0.804997	+	0.593279i	$0.797833\pi$
$578$	8.26716	−	6.00645i	0.343869	−	0.249835i
$579$	9.28650	−	6.74704i	0.385934	−	0.280397i
$580$	−6.50130	+	4.00377i	−0.269952	+	0.166248i
$581$	−1.30642	−	0.949169i	−0.0541994	−	0.0393782i
$582$	−0.393122			−0.0162954
$583$	27.2042	+	19.7650i	1.12668	+	0.818584i
$584$	−3.54732	+	10.9175i	−0.146789	+	0.451770i
$585$	0.986330	+	4.06877i	0.0407797	+	0.168223i
$586$	−6.27720	−	19.3192i	−0.259309	−	0.798070i
$587$	−8.81817	+	27.1395i	−0.363965	+	1.12017i	0.586662	+	0.809832i	$0.300442\pi$
$587$	−8.81817	+	27.1395i	−0.363965	+	1.12017i	−0.950627	+	0.310336i	$0.899558\pi$
$588$	2.02807	−	6.24175i	0.0836361	−	0.257405i
$589$	−2.79184	−	8.59241i	−0.115036	−	0.354044i
$590$	0.432630	+	0.367852i	0.0178111	+	0.0151442i
$591$	−0.475782	+	1.46431i	−0.0195711	+	0.0602336i
$592$	0.496650	+	0.360837i	0.0204122	+	0.0148303i
$593$	10.6573			0.437642			0.218821	−	0.975765i	$-0.429779\pi$
$593$	10.6573			0.437642			0.218821	+	0.975765i	$0.429779\pi$
$594$	−15.2305	−	11.0656i	−0.624914	−	0.454027i
$595$	−1.24206	−	5.12371i	−0.0509197	−	0.210052i
$596$	14.1522	−	10.2822i	0.579697	−	0.421175i
$597$	−16.2899	+	11.8353i	−0.666702	+	0.484387i
$598$	−1.02042	−	3.14051i	−0.0417279	−	0.128425i
$599$	37.3695			1.52688			0.763438	−	0.645881i	$-0.223510\pi$
$599$	37.3695			1.52688			0.763438	+	0.645881i	$0.223510\pi$
$600$	−0.853758	−	5.24055i	−0.0348545	−	0.213945i
$601$	−44.1417			−1.80058			−0.900289	−	0.435292i	$-0.856645\pi$
$601$	−44.1417			−1.80058			−0.900289	+	0.435292i	$0.856645\pi$
$602$	−1.46817	−	4.51855i	−0.0598380	−	0.184162i
$603$	−11.6170	+	8.44024i	−0.473080	+	0.343713i
$604$	3.76216	−	2.73337i	0.153080	−	0.111219i
$605$	−4.99176	−	0.381773i	−0.202944	−	0.0155213i
$606$	−6.30479	−	4.58070i	−0.256114	−	0.186078i
$607$	−27.2583			−1.10638			−0.553190	−	0.833055i	$-0.686590\pi$
$607$	−27.2583			−1.10638			−0.553190	+	0.833055i	$0.686590\pi$
$608$	−0.976313	−	0.709333i	−0.0395947	−	0.0287672i
$609$	1.01452	−	3.12238i	0.0411105	−	0.126525i
$610$	3.45691	+	0.264387i	0.139966	+	0.0107047i
$611$	−1.52726	−	4.70041i	−0.0617861	−	0.190158i
$612$	−1.50666	+	4.63701i	−0.0609029	+	0.187440i
$613$	14.3153	−	44.0579i	0.578189	−	1.77948i	−0.0468647	−	0.998901i	$-0.514923\pi$
$613$	14.3153	−	44.0579i	0.578189	−	1.77948i	0.625054	−	0.780582i	$-0.285077\pi$
$614$	5.97937	+	18.4026i	0.241308	+	0.742669i
$615$	1.34502	−	3.26756i	0.0542365	−	0.131761i
$616$	1.01801	−	3.13312i	0.0410169	−	0.126237i
$617$	14.7727	+	10.7330i	0.594726	+	0.432094i	0.844003	−	0.536338i	$-0.180193\pi$
$617$	14.7727	+	10.7330i	0.594726	+	0.432094i	−0.249277	+	0.968432i	$0.580193\pi$
$618$	−6.74869			−0.271472
$619$	13.3679	+	9.71232i	0.537300	+	0.390371i	0.823081	−	0.567924i	$-0.192253\pi$
$619$	13.3679	+	9.71232i	0.537300	+	0.390371i	−0.285781	+	0.958295i	$0.592253\pi$
$620$	−12.7534	−	10.8438i	−0.512187	−	0.435497i
$621$	13.8224	−	10.0425i	0.554672	−	0.402993i
$622$	−27.0679	+	19.6660i	−1.08533	+	0.788535i
$623$	−2.08910	−	6.42959i	−0.0836980	−	0.257596i
$624$	−1.06193			−0.0425111
$625$	−23.7073	+	7.93509i	−0.948291	+	0.317403i
$626$	−25.5374			−1.02068
$627$	−1.44090	−	4.43464i	−0.0575441	−	0.177103i
$628$	−15.7373	+	11.4338i	−0.627987	+	0.456260i
$629$	1.29331	−	0.939648i	0.0515678	−	0.0374662i
$630$	−2.88782	−	2.45543i	−0.115054	−	0.0978266i
$631$	11.0647	+	8.03898i	0.440479	+	0.320027i	0.785825	−	0.618449i	$-0.212238\pi$
$631$	11.0647	+	8.03898i	0.440479	+	0.320027i	−0.345346	+	0.938475i	$0.612238\pi$
$632$	1.62972			0.0648268
$633$	19.9727	+	14.5110i	0.793843	+	0.576761i
$634$	−1.70981	+	5.26225i	−0.0679051	+	0.208991i
$635$	7.28764	−	17.7044i	0.289201	−	0.702576i
$636$	3.03271	+	9.33371i	0.120255	+	0.370106i
$637$	−1.90980	+	5.87775i	−0.0756689	+	0.232885i
$638$	−3.83925	+	11.8160i	−0.151997	+	0.467800i
$639$	0.757315	+	2.33077i	0.0299589	+	0.0922040i
$640$	−2.22956	−	0.170518i	−0.0881310	−	0.00674032i
$641$	2.48765	−	7.65621i	0.0982565	−	0.302402i	−0.889832	−	0.456288i	$-0.849179\pi$
$641$	2.48765	−	7.65621i	0.0982565	−	0.302402i	0.988089	+	0.153886i	$0.0491787\pi$
$642$	2.62247	+	1.90534i	0.103501	+	0.0751977i
$643$	−4.98552			−0.196610			−0.0983049	−	0.995156i	$-0.531342\pi$
$643$	−4.98552			−0.196610			−0.0983049	+	0.995156i	$0.531342\pi$
$644$	2.41879	+	1.75735i	0.0953135	+	0.0692493i
$645$	−12.4240	−	0.950196i	−0.489194	−	0.0374139i
$646$	−2.54240	+	1.84716i	−0.100029	+	0.0726755i
$647$	−36.3034	+	26.3760i	−1.42723	+	1.03695i	−0.436711	+	0.899602i	$0.643857\pi$
$647$	−36.3034	+	26.3760i	−1.42723	+	1.03695i	−0.990523	+	0.137344i	$0.956143\pi$
$648$	0.0378445	+	0.116473i	0.00148667	+	0.00457551i
$649$	0.924049			0.0362721
$650$	0.803970	+	4.93494i	0.0315343	+	0.193564i
$651$	7.19810			0.282116
$652$	0.771268	+	2.37372i	0.0302052	+	0.0929619i
$653$	6.24257	−	4.53549i	0.244290	−	0.177487i	−0.458902	−	0.888487i	$-0.651757\pi$
$653$	6.24257	−	4.53549i	0.244290	−	0.177487i	0.703193	+	0.710999i	$0.251757\pi$
$654$	13.0522	−	9.48297i	0.510381	−	0.370813i
$655$	−1.85111	−	7.63614i	−0.0723290	−	0.298369i
$656$	−1.20390	−	0.874682i	−0.0470043	−	0.0341506i
$657$	21.4929			0.838518
$658$	3.62020	+	2.63023i	0.141130	+	0.102537i
$659$	7.60182	−	23.3960i	0.296125	−	0.911378i	−0.686717	−	0.726925i	$-0.740949\pi$
$659$	7.60182	−	23.3960i	0.296125	−	0.911378i	0.982841	−	0.184453i	$-0.0590514\pi$
$660$	−6.58216	−	5.59661i	−0.256210	−	0.217848i
$661$	−11.0515	−	34.0131i	−0.429855	−	1.32296i	−0.898268	−	0.439448i	$-0.855174\pi$
$661$	−11.0515	−	34.0131i	−0.429855	−	1.32296i	0.468413	−	0.883510i	$-0.344826\pi$
$662$	−0.602960	+	1.85572i	−0.0234347	+	0.0721246i
$663$	−0.854538	+	2.63000i	−0.0331875	+	0.102141i
$664$	0.551140	+	1.69623i	0.0213884	+	0.0658267i
$665$	−0.575601	−	2.37444i	−0.0223208	−	0.0920770i
$666$	0.355183	−	1.09314i	0.0137631	−	0.0423584i
$667$	−9.12201	−	6.62753i	−0.353206	−	0.256619i
$668$	6.06806			0.234780
$669$	13.6746	+	9.93519i	0.528691	+	0.384117i
$670$	−14.6023	+	8.99268i	−0.564135	+	0.347418i
$671$	4.56408	−	3.31600i	0.176194	−	0.128013i
$672$	0.777854	−	0.565144i	0.0300064	−	0.0218009i
$673$	12.2642	+	37.7454i	0.472751	+	1.45498i	0.848966	+	0.528447i	$0.177225\pi$
$673$	12.2642	+	37.7454i	0.472751	+	1.45498i	−0.376215	+	0.926532i	$0.622775\pi$
$674$	18.6238			0.717361
$675$	−22.9984	+	11.8465i	−0.885210	+	0.455972i
$676$	1.00000			0.0384615
$677$	−6.21056	−	19.1141i	−0.238691	−	0.734616i	−0.996610	−	0.0822676i	$-0.973784\pi$
$677$	−6.21056	−	19.1141i	−0.238691	−	0.734616i	0.757919	−	0.652349i	$-0.226216\pi$
$678$	5.54470	−	4.02846i	0.212943	−	0.154712i
$679$	−0.271166	+	0.197014i	−0.0104064	+	0.00756069i
$680$	−2.21644	+	5.38456i	−0.0849967	+	0.206489i
$681$	−23.5872	−	17.1371i	−0.903863	−	0.656695i
$682$	−27.2398			−1.04306
$683$	−0.521533	−	0.378916i	−0.0199559	−	0.0144988i	0.577763	−	0.816205i	$-0.303926\pi$
$683$	−0.521533	−	0.378916i	−0.0199559	−	0.0144988i	−0.597718	+	0.801706i	$0.703926\pi$
$684$	−0.698218	+	2.14889i	−0.0266970	+	0.0821650i
$685$	40.2517	−	24.7887i	1.53794	−	0.947127i
$686$	−3.68766	−	11.3494i	−0.140795	−	0.433324i
$687$	−5.34284	+	16.4436i	−0.203842	+	0.627362i
$688$	−1.62155	+	4.99061i	−0.0618210	+	0.190265i
$689$	−2.85585	−	8.78940i	−0.108799	−	0.334850i
$690$	6.67654	−	4.11169i	0.254171	−	0.156529i
$691$	14.0878	−	43.3579i	0.535927	−	1.64941i	−0.205711	−	0.978613i	$-0.565951\pi$
$691$	14.0878	−	43.3579i	0.535927	−	1.64941i	0.741638	−	0.670801i	$-0.234049\pi$
$692$	8.14950	+	5.92096i	0.309798	+	0.225081i
$693$	−6.16806			−0.234305
$694$	−28.1318	−	20.4389i	−1.06787	−	0.775851i
$695$	−3.49064	+	8.48004i	−0.132407	+	0.321666i
$696$	−2.93353	+	2.13134i	−0.111195	+	0.0807881i
$697$	−3.13504	+	2.27774i	−0.118748	+	0.0862756i
$698$	−3.44872	−	10.6141i	−0.130536	−	0.401748i
$699$	−0.628705			−0.0237798
$700$	−3.21521	−	3.18694i	−0.121524	−	0.120455i
$701$	−4.60883			−0.174073			−0.0870365	−	0.996205i	$-0.527740\pi$
$701$	−4.60883			−0.174073			−0.0870365	+	0.996205i	$0.527740\pi$
$702$	1.59887	+	4.92081i	0.0603453	+	0.185724i
$703$	0.599351	−	0.435454i	0.0226050	−	0.0164235i
$704$	−2.94363	+	2.13867i	−0.110942	+	0.0806043i
$705$	9.99277	−	6.15397i	0.376350	−	0.231772i
$706$	3.52353	+	2.56000i	0.132610	+	0.0963467i
$707$	−6.64451			−0.249893
$708$	0.218183	+	0.158519i	0.00819983	+	0.00595753i
$709$	−11.5493	+	35.5451i	−0.433743	+	1.33492i	0.460627	+	0.887594i	$0.347625\pi$
$709$	−11.5493	+	35.5451i	−0.433743	+	1.33492i	−0.894369	+	0.447329i	$0.852375\pi$
$710$	0.689543	+	2.84447i	0.0258781	+	0.106751i
$711$	−0.942916	−	2.90200i	−0.0353621	−	0.108833i
$712$	−2.30735	+	7.10130i	−0.0864717	+	0.266133i
$713$	7.63931	−	23.5114i	0.286094	−	0.880508i
$714$	−0.773708	−	2.38123i	−0.0289553	−	0.0891152i
$715$	6.19831	+	5.27024i	0.231804	+	0.197096i
$716$	−5.27487	+	16.2344i	−0.197131	+	0.606708i
$717$	−8.75778	−	6.36290i	−0.327065	−	0.237627i
$718$	−15.1391			−0.564986
$719$	8.96302	+	6.51202i	0.334264	+	0.242857i	0.742238	−	0.670137i	$-0.233764\pi$
$719$	8.96302	+	6.51202i	0.334264	+	0.242857i	−0.407974	+	0.912994i	$0.633764\pi$
$720$	0.986330	+	4.06877i	0.0367583	+	0.151634i
$721$	−4.65508	+	3.38211i	−0.173364	+	0.125957i
$722$	14.1931	−	10.3119i	0.528213	−	0.383769i
$723$	8.20957	+	25.2665i	0.305317	+	0.939670i
$724$	−13.4061			−0.498235
$725$	12.1256	+	12.0190i	0.450333	+	0.446373i
$726$	−2.37755			−0.0882392
$727$	−6.03721	−	18.5806i	−0.223908	−	0.689117i	−0.998401	−	0.0565345i	$-0.981995\pi$
$727$	−6.03721	−	18.5806i	−0.223908	−	0.689117i	0.774493	−	0.632583i	$-0.218005\pi$
$728$	−0.732492	+	0.532187i	−0.0271480	+	0.0197242i
$729$	−13.1498	+	9.55391i	−0.487031	+	0.353848i
$730$	25.5939	+	1.95744i	0.947272	+	0.0724481i
$731$	11.0550	+	8.03194i	0.408884	+	0.297072i
$732$	1.64651			0.0608568
$733$	−16.8649	−	12.2531i	−0.622919	−	0.452577i	0.231021	−	0.972949i	$-0.425794\pi$
$733$	−16.8649	−	12.2531i	−0.622919	−	0.452577i	−0.853940	+	0.520371i	$0.825794\pi$
$734$	−4.65696	+	14.3327i	−0.171892	+	0.529028i
$735$	−14.6325	−	1.11910i	−0.539728	−	0.0412788i
$736$	−1.02042	−	3.14051i	−0.0376130	−	0.115761i
$737$	−8.62317	+	26.5394i	−0.317638	+	0.977591i
$738$	−0.860977	+	2.64981i	−0.0316930	+	0.0975410i
$739$	−8.11241	−	24.9674i	−0.298420	−	0.918442i	−0.982051	−	0.188614i	$-0.939600\pi$
$739$	−8.11241	−	24.9674i	−0.298420	−	0.918442i	0.683631	−	0.729828i	$-0.260400\pi$
$740$	0.522511	−	1.26937i	0.0192079	−	0.0466630i
$741$	−0.396012	+	1.21880i	−0.0145479	+	0.0447738i
$742$	6.76949	+	4.91832i	0.248516	+	0.180557i
$743$	44.2243			1.62243			0.811216	−	0.584747i	$-0.198806\pi$
$743$	44.2243			1.62243			0.811216	+	0.584747i	$0.198806\pi$
$744$	−6.43176	−	4.67295i	−0.235800	−	0.171319i
$745$	−29.7999	−	25.3379i	−1.09178	−	0.928310i
$746$	−18.2608	+	13.2673i	−0.668576	+	0.485749i
$747$	2.70156	−	1.96280i	0.0988449	−	0.0718150i
$748$	2.92794	+	9.01128i	0.107056	+	0.329485i
$749$	2.76378			0.100986
$750$	−10.9386	+	4.61604i	−0.399422	+	0.168554i
$751$	−27.2600			−0.994731			−0.497365	−	0.867541i	$-0.665699\pi$
$751$	−27.2600			−0.994731			−0.497365	+	0.867541i	$0.665699\pi$
$752$	−1.52726	−	4.70041i	−0.0556933	−	0.171406i
$753$	−26.3951	+	19.1772i	−0.961892	+	0.698855i
$754$	2.76246	−	2.00704i	0.100603	−	0.0730923i
$755$	−7.92186	−	6.73571i	−0.288306	−	0.245138i
$756$	−3.78994	−	2.75356i	−0.137839	−	0.100146i
$757$	2.13885			0.0777378			0.0388689	−	0.999244i	$-0.487625\pi$
$757$	2.13885			0.0777378			0.0388689	+	0.999244i	$0.487625\pi$
$758$	−7.30560	−	5.30783i	−0.265351	−	0.192789i
$759$	3.94274	−	12.1345i	0.143112	−	0.440454i
$760$	−1.02715	+	2.49533i	−0.0372587	+	0.0905151i
$761$	−14.0220	−	43.1552i	−0.508296	−	1.56437i	−0.795158	−	0.606402i	$-0.792612\pi$
$761$	−14.0220	−	43.1552i	−0.508296	−	1.56437i	0.286862	−	0.957972i	$-0.407388\pi$
$762$	2.80971	−	8.64740i	0.101785	−	0.313262i
$763$	4.25068	−	13.0822i	0.153885	−	0.473609i
$764$	−0.758805	−	2.33536i	−0.0274526	−	0.0844904i
$765$	10.8705	+	0.831385i	0.393024	+	0.0300588i
$766$	6.62996	−	20.4049i	0.239550	−	0.737260i
$767$	−0.205460	−	0.149275i	−0.00741872	−	0.00539001i
$768$	−1.06193			−0.0383190
$769$	2.48978	+	1.80893i	0.0897837	+	0.0652317i	0.631771	−	0.775155i	$-0.282328\pi$
$769$	2.48978	+	1.80893i	0.0897837	+	0.0652317i	−0.541988	+	0.840386i	$0.682328\pi$
$770$	−7.34497	−	0.561748i	−0.264694	−	0.0202440i
$771$	26.5033	−	19.2558i	0.954493	−	0.693480i
$772$	−8.74494	+	6.35357i	−0.314737	+	0.228670i
$773$	−5.56103	−	17.1151i	−0.200016	−	0.615587i	−0.999881	−	0.0154072i	$-0.995096\pi$
$773$	−5.56103	−	17.1151i	−0.200016	−	0.615587i	0.799865	−	0.600180i	$-0.204904\pi$
$774$	9.82483			0.353146
$775$	−16.8465	+	33.4272i	−0.605144	+	1.20074i
$776$	0.370196			0.0132893
$777$	0.182396	+	0.561357i	0.00654342	+	0.0201386i
$778$	7.45440	−	5.41594i	0.267253	−	0.194171i
$779$	−1.45285	+	1.05556i	−0.0520537	+	0.0378193i
$780$	0.559422	+	2.30770i	0.0200305	+	0.0826291i
$781$	3.85301	+	2.79938i	0.137872	+	0.100170i
$782$	−8.59901			−0.307500
$783$	14.2931	+	10.3845i	0.510793	+	0.371113i
$784$	−1.90980	+	5.87775i	−0.0682070	+	0.209920i
$785$	33.1376	+	28.1759i	1.18273	+	1.00564i
$786$	−1.15310	−	3.54887i	−0.0411296	−	0.126584i
$787$	13.7409	−	42.2902i	0.489811	−	1.50748i	−0.335080	−	0.942190i	$-0.608763\pi$
$787$	13.7409	−	42.2902i	0.489811	−	1.50748i	0.824890	−	0.565293i	$-0.191237\pi$
$788$	0.448036	−	1.37891i	0.0159606	−	0.0491218i
$789$	8.51172	+	26.1964i	0.303025	+	0.932615i
$790$	−0.858535	−	3.54159i	−0.0305453	−	0.126004i
$791$	1.80573	−	5.55747i	0.0642044	−	0.197601i
$792$	5.51139	+	4.00426i	0.195839	+	0.142285i
$793$	−1.55049			−0.0550596
$794$	1.04387	+	0.758418i	0.0370457	+	0.0269153i
$795$	18.6857	−	11.5074i	0.662714	−	0.408127i
$796$	15.3399	−	11.1451i	0.543710	−	0.395028i
$797$	4.59238	−	3.33656i	0.162670	−	0.118187i	−0.503472	−	0.864012i	$-0.667944\pi$
$797$	4.59238	−	3.33656i	0.162670	−	0.118187i	0.666142	+	0.745825i	$0.267944\pi$
$798$	−0.358554	−	1.10351i	−0.0126927	−	0.0390640i
$799$	−12.8701			−0.455313
$800$	0.803970	+	4.93494i	0.0284246	+	0.174476i
$801$	13.9801			0.493961
$802$	−11.2880	−	34.7408i	−0.398592	−	1.22674i
$803$	33.7910	−	24.5506i	1.19246	−	0.866373i
$804$	−6.58887	+	4.78710i	−0.232372	+	0.168828i
$805$	2.54473	−	6.18210i	0.0896901	−	0.217890i
$806$	6.05668	+	4.40044i	0.213338	+	0.154999i
$807$	6.21896			0.218918
$808$	5.93711	+	4.31356i	0.208867	+	0.151751i
$809$	−6.99284	+	21.5218i	−0.245855	+	0.756665i	0.749639	+	0.661847i	$0.230227\pi$
$809$	−6.99284	+	21.5218i	−0.245855	+	0.756665i	−0.995495	+	0.0948181i	$0.969773\pi$
$810$	0.233175	−	0.143599i	0.00819294	−	0.00504556i
$811$	−9.64170	−	29.6741i	−0.338566	−	1.04200i	−0.964939	−	0.262475i	$-0.915461\pi$
$811$	−9.64170	−	29.6741i	−0.338566	−	1.04200i	0.626373	−	0.779523i	$-0.284539\pi$
$812$	−0.955358	+	2.94029i	−0.0335265	+	0.103184i
$813$	−3.18306	+	9.79645i	−0.111635	+	0.343577i
$814$	−0.690241	−	2.12434i	−0.0241929	−	0.0744582i
$815$	4.75209	−	2.92653i	0.166458	−	0.102512i
$816$	−0.854538	+	2.63000i	−0.0299148	+	0.0920684i
$817$	5.12314	+	3.72218i	0.179236	+	0.130223i
$818$	−2.03801			−0.0712574
$819$	1.37145	+	0.996418i	0.0479224	+	0.0348177i
$820$	−1.26659	+	3.07700i	−0.0442311	+	0.107454i
$821$	18.5628	−	13.4867i	0.647846	−	0.470687i	−0.214691	−	0.976682i	$-0.568874\pi$
$821$	18.5628	−	13.4867i	0.647846	−	0.470687i	0.862537	+	0.505995i	$0.168874\pi$
$822$	18.1625	−	13.1958i	0.633490	−	0.460257i
$823$	8.10921	+	24.9576i	0.282669	+	0.869967i	0.987088	+	0.160182i	$0.0512080\pi$
$823$	8.10921	+	24.9576i	0.282669	+	0.869967i	−0.704418	+	0.709785i	$0.748792\pi$
$824$	6.35513			0.221391
$825$	−8.69468	+	17.2522i	−0.302710	+	0.600643i
$826$	0.229940			0.00800063
$827$	−4.76707	−	14.6715i	−0.165767	−	0.510180i	0.833325	−	0.552784i	$-0.186435\pi$
$827$	−4.76707	−	14.6715i	−0.165767	−	0.510180i	−0.999092	+	0.0426043i	$0.986435\pi$
$828$	−5.00184	+	3.63405i	−0.173826	+	0.126292i
$829$	−43.0099	+	31.2485i	−1.49380	+	1.08531i	−0.521025	+	0.853541i	$0.674450\pi$
$829$	−43.0099	+	31.2485i	−1.49380	+	1.08531i	−0.972772	+	0.231765i	$0.925550\pi$
$830$	3.39579	−	2.09127i	0.117870	−	0.0725891i
$831$	−2.11043	−	1.53332i	−0.0732102	−	0.0531903i
$832$	1.00000			0.0346688
$833$	13.0202	+	9.45970i	0.451122	+	0.327759i
$834$	−1.34580	+	4.14193i	−0.0466011	+	0.143423i
$835$	−3.19664	−	13.1867i	−0.110624	−	0.456343i
$836$	1.35687	+	4.17603i	0.0469285	+	0.144431i
$837$	−11.9699	+	36.8395i	−0.413739	+	1.27336i
$838$	−11.0529	+	34.0174i	−0.381817	+	1.17511i
$839$	2.60824	+	8.02734i	0.0900465	+	0.277135i	0.985931	−	0.167152i	$-0.0534571\pi$
$839$	2.60824	+	8.02734i	0.0900465	+	0.277135i	−0.895885	+	0.444287i	$0.853457\pi$
$840$	−1.63790	−	1.39266i	−0.0565130	−	0.0480513i
$841$	−5.35853	+	16.4919i	−0.184777	+	0.568685i
$842$	17.0061	+	12.3557i	0.586069	+	0.425804i
$843$	−11.9334			−0.411008
$844$	−18.8080	−	13.6648i	−0.647397	−	0.470361i
$845$	−0.526799	−	2.17313i	−0.0181224	−	0.0747579i
$846$	−7.48625	+	5.43908i	−0.257383	+	0.186999i
$847$	−1.63998	+	1.19151i	−0.0563503	+	0.0409409i
$848$	−2.85585	−	8.78940i	−0.0980703	−	0.301829i
$849$	25.9061			0.889096
$850$	12.8690	+	1.98004i	0.441402	+	0.0679147i
$851$	2.02715			0.0694900
$852$	0.429530	+	1.32196i	0.0147155	+	0.0452896i
$853$	16.4462	−	11.9489i	0.563107	−	0.409121i	−0.269488	−	0.963004i	$-0.586854\pi$
$853$	16.4462	−	11.9489i	0.563107	−	0.409121i	0.832595	+	0.553883i	$0.186854\pi$
$854$	1.13572	−	0.825152i	0.0388637	−	0.0282361i
$855$	5.03764	+	0.385283i	0.172284	+	0.0131764i
$856$	−2.46954	−	1.79422i	−0.0844071	−	0.0613253i
$857$	−20.0366			−0.684436			−0.342218	−	0.939621i	$-0.611178\pi$
$857$	−20.0366			−0.684436			−0.342218	+	0.939621i	$0.611178\pi$
$858$	3.12593	+	2.27112i	0.106717	+	0.0775347i
$859$	14.1919	−	43.6782i	0.484222	−	1.49028i	−0.348883	−	0.937166i	$-0.613439\pi$
$859$	14.1919	−	43.6782i	0.484222	−	1.49028i	0.833105	−	0.553115i	$-0.186561\pi$
$860$	11.6995	+	0.894784i	0.398949	+	0.0305119i
$861$	−0.442135	−	1.36075i	−0.0150679	−	0.0463742i
$862$	−5.36551	+	16.5133i	−0.182750	+	0.562446i
$863$	2.62440	−	8.07706i	0.0893355	−	0.274946i	−0.896401	−	0.443245i	$-0.853827\pi$
$863$	2.62440	−	8.07706i	0.0893355	−	0.274946i	0.985736	+	0.168298i	$0.0538272\pi$
$864$	1.59887	+	4.92081i	0.0543945	+	0.167409i
$865$	8.57386	−	20.8291i	0.291520	−	0.708209i
$866$	2.12292	−	6.53367i	0.0721397	−	0.222023i
$867$	−8.77913	−	6.37841i	−0.298155	−	0.216622i
$868$	−6.77833			−0.230071
$869$	−4.79730	−	3.48544i	−0.162737	−	0.118236i
$870$	6.17705	+	5.25216i	0.209422	+	0.178065i
$871$	6.20463	−	4.50793i	0.210236	−	0.152745i
$872$	−12.2910	+	8.92995i	−0.416227	+	0.302406i
$873$	−0.214187	−	0.659198i	−0.00724912	−	0.0223105i
$874$	−3.98498			−0.134794
$875$	−5.23186	+	8.66594i	−0.176869	+	0.292962i
$876$	12.1903			0.411871
$877$	7.65588	+	23.5624i	0.258521	+	0.795645i	0.993116	+	0.117139i	$0.0373723\pi$
$877$	7.65588	+	23.5624i	0.258521	+	0.795645i	−0.734595	+	0.678506i	$0.762628\pi$
$878$	−19.4609	+	14.1392i	−0.656773	+	0.477173i
$879$	−17.4516	+	12.6794i	−0.588629	+	0.427664i
$880$	6.19831	+	5.27024i	0.208945	+	0.177660i
$881$	−32.7000	−	23.7579i	−1.10169	−	0.800425i	−0.120355	−	0.992731i	$-0.538403\pi$
$881$	−32.7000	−	23.7579i	−1.10169	−	0.800425i	−0.981335	+	0.192306i	$0.938403\pi$
$882$	11.5713			0.389626
$883$	−9.97106	−	7.24440i	−0.335553	−	0.243794i	0.407230	−	0.913326i	$-0.366495\pi$
$883$	−9.97106	−	7.24440i	−0.335553	−	0.243794i	−0.742783	+	0.669532i	$0.766495\pi$
$884$	0.804705	−	2.47663i	0.0270651	−	0.0832979i
$885$	0.229544	−	0.557648i	0.00771605	−	0.0187451i
$886$	−5.59201	−	17.2104i	−0.187867	−	0.578196i
$887$	15.2409	−	46.9068i	0.511741	−	1.57498i	−0.277395	−	0.960756i	$-0.589471\pi$
$887$	15.2409	−	46.9068i	0.511741	−	1.57498i	0.789135	−	0.614219i	$-0.210529\pi$
$888$	0.201451	−	0.620003i	0.00676026	−	0.0208059i
$889$	−2.39559	−	7.37285i	−0.0803454	−	0.247278i
$890$	16.6475	+	1.27322i	0.558027	+	0.0426783i
$891$	0.137698	−	0.423792i	0.00461307	−	0.0141976i
$892$	−12.8772	−	9.35580i	−0.431159	−	0.313255i
$893$	−5.96431			−0.199588
$894$	−15.0286	−	10.9189i	−0.502633	−	0.365184i
$895$	38.0582	+	2.91072i	1.27215	+	0.0972946i
$896$	−0.732492	+	0.532187i	−0.0244708	+	0.0177791i
$897$	−2.83692	+	2.06114i	−0.0947220	+	0.0688196i
$898$	9.57311	+	29.4630i	0.319459	+	0.983193i
$899$	25.5632			0.852581
$900$	8.32235	−	4.28684i	0.277412	−	0.142895i
$901$	−24.0662			−0.801761
$902$	1.67317	+	5.14949i	0.0557105	+	0.171459i
$903$	−4.08174	+	2.96556i	−0.135832	+	0.0986876i
$904$	−5.22135	+	3.79353i	−0.173660	+	0.126171i
$905$	7.06234	+	29.1333i	0.234760	+	0.968422i
$906$	−3.99514	−	2.90264i	−0.132730	−	0.0964337i
$907$	−27.1484			−0.901449			−0.450724	−	0.892663i	$-0.648834\pi$
$907$	−27.1484			−0.901449			−0.450724	+	0.892663i	$0.648834\pi$
$908$	22.2117	+	16.1377i	0.737120	+	0.535549i
$909$	4.24598	−	13.0678i	0.140830	−	0.433431i
$910$	1.54239	+	1.31144i	0.0511296	+	0.0434739i
$911$	12.0831	+	37.1879i	0.400331	+	1.23209i	0.924732	+	0.380619i	$0.124289\pi$
$911$	12.0831	+	37.1879i	0.400331	+	1.23209i	−0.524401	+	0.851471i	$0.675711\pi$
$912$	−0.396012	+	1.21880i	−0.0131133	+	0.0403585i
$913$	2.00534	−	6.17180i	0.0663670	−	0.204257i
$914$	7.97971	+	24.5590i	0.263945	+	0.812340i
$915$	−0.867380	−	3.57808i	−0.0286747	−	0.118288i
$916$	5.03127	−	15.4846i	0.166238	−	0.511627i
$917$	−2.57390	−	1.87005i	−0.0849976	−	0.0617544i
$918$	13.4736			0.444695
$919$	27.1875	+	19.7529i	0.896832	+	0.651587i	0.937650	−	0.347580i	$-0.112997\pi$
$919$	27.1875	+	19.7529i	0.896832	+	0.651587i	−0.0408184	+	0.999167i	$0.512997\pi$
$920$	−6.28719	+	3.87191i	−0.207282	+	0.127653i
$921$	16.6236	−	12.0778i	0.547767	−	0.397976i
$922$	−3.58402	+	2.60394i	−0.118033	+	0.0857563i
$923$	−0.404482	−	1.24487i	−0.0133137	−	0.0409753i
$924$	−3.49837			−0.115088
$925$	−3.03376	−	0.466779i	−0.0997495	−	0.0153476i
$926$	−30.8325			−1.01322
$927$	−3.67692	−	11.3164i	−0.120766	−	0.371679i
$928$	2.76246	−	2.00704i	0.0906822	−	0.0658845i
$929$	−29.9283	+	21.7442i	−0.981916	+	0.713404i	−0.958136	−	0.286313i	$-0.907570\pi$
$929$	−29.9283	+	21.7442i	−0.981916	+	0.713404i	−0.0237801	+	0.999717i	$0.507570\pi$
$930$	−6.76667	+	16.4387i	−0.221888	+	0.539047i
$931$	6.03384	+	4.38384i	0.197751	+	0.143675i
$932$	0.592041			0.0193929
$933$	28.7442	+	20.8839i	0.941043	+	0.683708i
$934$	−0.474779	+	1.46122i	−0.0155353	+	0.0478126i
$935$	18.0402	−	11.1099i	0.589978	−	0.363333i
$936$	−0.578575	−	1.78067i	−0.0189113	−	0.0582031i
$937$	−6.71367	+	20.6625i	−0.219326	+	0.675016i	0.779492	+	0.626412i	$0.215477\pi$
$937$	−6.71367	+	20.6625i	−0.219326	+	0.675016i	−0.998818	+	0.0486039i	$0.984523\pi$
$938$	−2.14579	+	6.60405i	−0.0700624	+	0.215630i
$939$	8.38020	+	25.7916i	0.273477	+	0.841677i
$940$	−9.41003	+	5.79509i	−0.306921	+	0.189015i
$941$	−14.1427	+	43.5266i	−0.461037	+	1.41893i	0.402861	+	0.915261i	$0.368016\pi$
$941$	−14.1427	+	43.5266i	−0.461037	+	1.41893i	−0.863899	+	0.503666i	$0.831984\pi$
$942$	16.7119	+	12.1419i	0.544503	+	0.395605i
$943$	−4.91390			−0.160019
$944$	−0.205460	−	0.149275i	−0.00668714	−	0.00485849i
$945$	−3.98729	+	9.68660i	−0.129707	+	0.315105i
$946$	15.4465	−	11.2226i	0.502210	−	0.364877i
$947$	−24.0993	+	17.5091i	−0.783121	+	0.568971i	−0.905914	−	0.423462i	$-0.860815\pi$
$947$	−24.0993	+	17.5091i	−0.783121	+	0.568971i	0.122793	+	0.992432i	$0.460815\pi$
$948$	−0.534799	−	1.64594i	−0.0173695	−	0.0534577i
$949$	−11.4794			−0.372636
$950$	5.96377	+	0.917594i	0.193490	+	0.0297707i
$951$	5.87571			0.190533
$952$	0.728588	+	2.24236i	0.0236137	+	0.0726754i
$953$	−28.9172	+	21.0095i	−0.936719	+	0.680566i	−0.947629	−	0.319375i	$-0.896527\pi$
$953$	−28.9172	+	21.0095i	−0.936719	+	0.680566i	0.0109100	+	0.999940i	$0.496527\pi$
$954$	−13.9987	+	10.1707i	−0.453225	+	0.329287i
$955$	−4.67530	+	2.87925i	−0.151289	+	0.0931702i
$956$	8.24706	+	5.99184i	0.266729	+	0.193790i
$957$	13.1935			0.426485
$958$	9.47621	+	6.88487i	0.306162	+	0.222440i
$959$	5.91494	−	18.2043i	0.191003	−	0.587848i
$960$	0.559422	+	2.30770i	0.0180553	+	0.0744809i
$961$	7.74003	+	23.8214i	0.249678	+	0.768431i
$962$	−0.189703	+	0.583847i	−0.00611628	+	0.0188240i
$963$	−1.76611	+	5.43553i	−0.0569121	+	0.175157i
$964$	−7.73082	−	23.7930i	−0.248993	−	0.766321i
$965$	18.4139	+	15.6568i	0.592766	+	0.504011i
$966$	0.981109	−	3.01954i	0.0315667	−	0.0971522i
$967$	38.2849	+	27.8156i	1.23116	+	0.894489i	0.996977	−	0.0777032i	$-0.0247586\pi$
$967$	38.2849	+	27.8156i	1.23116	+	0.894489i	0.234183	+	0.972193i	$0.424759\pi$
$968$	2.23890			0.0719610
$969$	2.69984	+	1.96155i	0.0867314	+	0.0630140i
$970$	−0.195019	−	0.804484i	−0.00626168	−	0.0258304i
$971$	−15.6102	+	11.3415i	−0.500954	+	0.363965i	−0.809381	−	0.587283i	$-0.800197\pi$
$971$	−15.6102	+	11.3415i	−0.500954	+	0.363965i	0.308427	+	0.951248i	$0.400197\pi$
$972$	12.6629	−	9.20012i	0.406162	−	0.295094i
$973$	1.14744	+	3.53145i	0.0367852	+	0.113213i
$974$	17.4281			0.558432
$975$	4.72023	−	2.43139i	0.151168	−	0.0778668i
$976$	−1.55049			−0.0496301
$977$	−1.06392	−	3.27441i	−0.0340378	−	0.104758i	0.932594	−	0.360927i	$-0.117540\pi$
$977$	−1.06392	−	3.27441i	−0.0340378	−	0.104758i	−0.966632	+	0.256169i	$0.917540\pi$
$978$	2.14425	−	1.55789i	0.0685656	−	0.0498158i
$979$	21.9794	−	15.9689i	0.702464	−	0.510370i
$980$	13.7792	+	1.05384i	0.440160	+	0.0336637i
$981$	23.0126	+	16.7196i	0.734736	+	0.533817i
$982$	35.5109			1.13320
$983$	21.9844	+	15.9726i	0.701193	+	0.509447i	0.880321	−	0.474379i	$-0.157327\pi$
$983$	21.9844	+	15.9726i	0.701193	+	0.509447i	−0.179127	+	0.983826i	$0.557327\pi$
$984$	−0.488325	+	1.50291i	−0.0155672	+	0.0479110i
$985$	−3.23258	−	0.247230i	−0.102999	−	0.00787741i
$986$	−2.74774	−	8.45666i	−0.0875057	−	0.269315i
$987$	1.46843	−	4.51935i	0.0467405	−	0.143852i
$988$	0.372918	−	1.14772i	0.0118641	−	0.0365140i
$989$	5.35457	+	16.4797i	0.170265	+	0.524023i
$990$	5.79837	−	14.0864i	0.184284	−	0.447695i
$991$	−10.9092	+	33.5750i	−0.346542	+	1.06655i	0.614212	+	0.789141i	$0.289474\pi$
$991$	−10.9092	+	33.5750i	−0.346542	+	1.06655i	−0.960753	+	0.277404i	$0.910526\pi$
$992$	6.05668	+	4.40044i	0.192300	+	0.139714i
$993$	2.07205			0.0657546
$994$	0.958781	+	0.696595i	0.0304107	+	0.0220947i
$995$	−32.3008	−	27.4644i	−1.02401	−	0.870681i
$996$	1.53226	−	1.11325i	0.0485515	−	0.0352747i
$997$	−25.1978	+	18.3073i	−0.798022	+	0.579797i	−0.910333	−	0.413876i	$-0.864175\pi$
$997$	−25.1978	+	18.3073i	−0.798022	+	0.579797i	0.112311	+	0.993673i	$0.464175\pi$
$998$	−5.06441	−	15.5867i	−0.160311	−	0.493387i
$999$	−3.17631			−0.100494

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.l.c.131.4	✓	24
25.21	even	5	inner	650.2.l.c.521.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.l.c.131.4	✓	24	1.1	even	1	trivial
650.2.l.c.521.4	yes	24	25.21	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.859118 - 0.624186i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.70352 + 1.44845i) q^{5} +(0.859118 + 0.624186i) q^{6} +0.905410 q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.578575 + 1.78067i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.859118 - 0.624186i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.70352 + 1.44845i) q^{5} +(0.859118 + 0.624186i) q^{6} +0.905410 q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.578575 + 1.78067i) q^{9} +(-0.851143 + 2.06774i) q^{10} +(1.12437 + 3.46045i) q^{11} +(-0.328154 + 1.00995i) q^{12} +(0.309017 - 0.951057i) q^{13} +(0.279787 + 0.861096i) q^{14} +(2.36763 + 0.181078i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.10674 - 1.53064i) q^{17} -1.87231 q^{18} +(-0.976313 - 0.709333i) q^{19} +(-2.22956 - 0.170518i) q^{20} +(0.777854 - 0.565144i) q^{21} +(-2.94363 + 2.13867i) q^{22} +(-1.02042 - 3.14051i) q^{23} -1.06193 q^{24} +(0.803970 + 4.93494i) q^{25} +1.00000 q^{26} +(1.59887 + 4.92081i) q^{27} +(-0.732492 + 0.532187i) q^{28} +(2.76246 - 2.00704i) q^{29} +(0.559422 + 2.30770i) q^{30} +(6.05668 + 4.40044i) q^{31} +1.00000 q^{32} +(3.12593 + 2.27112i) q^{33} +(0.804705 - 2.47663i) q^{34} +(1.54239 + 1.31144i) q^{35} +(-0.578575 - 1.78067i) q^{36} +(-0.189703 + 0.583847i) q^{37} +(0.372918 - 1.14772i) q^{38} +(-0.328154 - 1.00995i) q^{39} +(-0.526799 - 2.17313i) q^{40} +(0.459848 - 1.41527i) q^{41} +(0.777854 + 0.565144i) q^{42} -5.24744 q^{43} +(-2.94363 - 2.13867i) q^{44} +(-3.56483 + 2.19537i) q^{45} +(2.67148 - 1.94094i) q^{46} +(3.99841 - 2.90501i) q^{47} +(-0.328154 - 1.00995i) q^{48} -6.18023 q^{49} +(-4.44497 + 2.28960i) q^{50} -2.76534 q^{51} +(0.309017 + 0.951057i) q^{52} +(7.47671 - 5.43215i) q^{53} +(-4.18589 + 3.04123i) q^{54} +(-3.09691 + 7.52354i) q^{55} +(-0.732492 - 0.532187i) q^{56} -1.28152 q^{57} +(2.76246 + 2.00704i) q^{58} +(0.0784786 - 0.241532i) q^{59} +(-2.02189 + 1.24516i) q^{60} +(-0.479129 - 1.47461i) q^{61} +(-2.31345 + 7.12006i) q^{62} +(-0.523848 + 1.61224i) q^{63} +(0.309017 + 0.951057i) q^{64} +(1.90398 - 1.17255i) q^{65} +(-1.19400 + 3.67475i) q^{66} +(6.20463 + 4.50793i) q^{67} +2.60408 q^{68} +(-2.83692 - 2.06114i) q^{69} +(-0.770634 + 1.87215i) q^{70} +(1.05895 - 0.769370i) q^{71} +(1.51473 - 1.10052i) q^{72} +(-3.54732 - 10.9175i) q^{73} -0.613893 q^{74} +(3.77102 + 3.73787i) q^{75} +1.20679 q^{76} +(1.01801 + 3.13312i) q^{77} +(0.859118 - 0.624186i) q^{78} +(-1.31847 + 0.957926i) q^{79} +(1.90398 - 1.17255i) q^{80} +(-0.0990782 - 0.0719846i) q^{81} +1.48810 q^{82} +(-1.44290 - 1.04833i) q^{83} +(-0.297114 + 0.914422i) q^{84} +(-1.37182 - 5.65899i) q^{85} +(-1.62155 - 4.99061i) q^{86} +(1.12051 - 3.44858i) q^{87} +(1.12437 - 3.46045i) q^{88} +(-2.30735 - 7.10130i) q^{89} +(-3.18952 - 2.71195i) q^{90} +(0.279787 - 0.861096i) q^{91} +(2.67148 + 1.94094i) q^{92} +7.95009 q^{93} +(3.99841 + 2.90501i) q^{94} +(-0.635735 - 2.62251i) q^{95} +(0.859118 - 0.624186i) q^{96} +(-0.299495 + 0.217596i) q^{97} +(-1.90980 - 5.87775i) q^{98} -6.81245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

Introduction

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