LMFDB - Embedded newform 250.2.g.b.231.2

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			231.2
Character	$\chi$	$=$	250.231
Dual form			250.2.g.b.171.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535827 - 0.844328i) q^{2} +(-2.24293 + 2.10625i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-2.18511 - 0.474634i) q^{5} +(0.576544 + 3.02235i) q^{6} +(2.32290 - 1.68768i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.406067 - 6.45425i) q^{9} +O(q^{10})$	\(q+(0.535827 - 0.844328i) q^{2} +(-2.24293 + 2.10625i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-2.18511 - 0.474634i) q^{5} +(0.576544 + 3.02235i) q^{6} +(2.32290 - 1.68768i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.406067 - 6.45425i) q^{9} +(-1.57159 + 1.59063i) q^{10} +(2.65953 - 4.19075i) q^{11} +(2.86078 + 1.13266i) q^{12} +(0.256974 - 4.08448i) q^{13} +(-0.180288 - 2.86559i) q^{14} +(5.90075 - 3.53782i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(-2.52907 + 5.37454i) q^{17} +(-5.23192 - 3.80121i) q^{18} +(-2.66600 - 2.50355i) q^{19} +(0.500914 + 2.17924i) q^{20} +(-1.65541 + 8.67795i) q^{21} +(-2.11332 - 4.49104i) q^{22} +(-0.110139 - 0.0282788i) q^{23} +(2.48922 - 1.80853i) q^{24} +(4.54944 + 2.07426i) q^{25} +(-3.31095 - 2.40554i) q^{26} +(6.79970 + 8.21943i) q^{27} +(-2.51610 - 1.38324i) q^{28} +(-8.24718 - 4.53392i) q^{29} +(0.174697 - 6.87783i) q^{30} +(2.32598 - 4.94296i) q^{31} +(0.309017 + 0.951057i) q^{32} +(2.86163 + 15.0012i) q^{33} +(3.18273 + 5.01519i) q^{34} +(-5.87683 + 2.58525i) q^{35} +(-6.01287 + 2.38066i) q^{36} +(-2.01600 + 2.43692i) q^{37} +(-3.54233 + 0.909516i) q^{38} +(8.02656 + 9.70245i) q^{39} +(2.10840 + 0.744759i) q^{40} +(5.71733 - 1.46796i) q^{41} +(6.44002 + 6.04758i) q^{42} +(2.59037 - 7.97234i) q^{43} +(-4.92428 - 0.622081i) q^{44} +(-3.95071 + 13.9105i) q^{45} +(-0.0828918 + 0.0778406i) q^{46} +(-4.61577 + 0.583107i) q^{47} +(-0.193197 - 3.07078i) q^{48} +(0.384455 - 1.18323i) q^{49} +(4.18907 - 2.72978i) q^{50} +(-5.64761 - 17.3816i) q^{51} +(-3.80516 + 1.50657i) q^{52} +(-0.611671 + 3.20649i) q^{53} +(10.5834 - 1.33699i) q^{54} +(-7.80046 + 7.89497i) q^{55} +(-2.51610 + 1.38324i) q^{56} +11.2527 q^{57} +(-8.24718 + 4.53392i) q^{58} +(3.41110 + 1.35055i) q^{59} +(-5.71354 - 3.83283i) q^{60} +(1.96466 + 0.504438i) q^{61} +(-2.92715 - 4.61246i) q^{62} +(-9.94947 - 15.6779i) q^{63} +(0.968583 + 0.248690i) q^{64} +(-2.50015 + 8.80309i) q^{65} +(14.1993 + 5.62189i) q^{66} +(0.709563 - 0.390085i) q^{67} +5.93986 q^{68} +(0.306595 - 0.168552i) q^{69} +(-0.966159 + 6.34722i) q^{70} +(3.82270 - 0.482919i) q^{71} +(-1.21180 + 6.35246i) q^{72} +(0.275244 - 0.108977i) q^{73} +(0.977336 + 3.00793i) q^{74} +(-14.5730 + 4.92985i) q^{75} +(-1.13015 + 3.47823i) q^{76} +(-0.894844 - 14.2231i) q^{77} +(12.4929 - 1.57822i) q^{78} +(5.93151 - 5.57006i) q^{79} +(1.75856 - 1.38112i) q^{80} +(-13.3153 - 1.68212i) q^{81} +(1.82406 - 5.61387i) q^{82} +(11.9706 + 11.2411i) q^{83} +(8.55688 - 2.19703i) q^{84} +(8.07724 - 10.5436i) q^{85} +(-5.34328 - 6.45892i) q^{86} +(28.0474 - 7.20135i) q^{87} +(-3.16380 + 3.82438i) q^{88} +(-0.259618 + 0.102790i) q^{89} +(9.62816 + 10.7893i) q^{90} +(-6.29639 - 9.92152i) q^{91} +(0.0213073 + 0.111697i) q^{92} +(5.19410 + 15.9858i) q^{93} +(-1.98092 + 4.20967i) q^{94} +(4.63726 + 6.73591i) q^{95} +(-2.69626 - 1.48228i) q^{96} +(6.67955 + 3.67211i) q^{97} +(-0.793034 - 0.958613i) q^{98} +(-25.9682 - 18.8670i) 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
$3$	−2.24293	+	2.10625i	−1.29495	+	1.21604i	−0.332971	+	0.942937i	$0.608051\pi$
$3$	−2.24293	+	2.10625i	−1.29495	+	1.21604i	−0.961984	+	0.273106i	$0.911949\pi$
$4$	−0.425779	−	0.904827i	−0.212890	−	0.452414i
$5$	−2.18511	−	0.474634i	−0.977213	−	0.212263i
$5$	−2.18511	−	0.474634i	−0.977213	−	0.212263i
$6$	0.576544	+	3.02235i	0.235373	+	1.23387i
$7$	2.32290	−	1.68768i	0.877972	−	0.637884i	−0.0547419	−	0.998501i	$-0.517434\pi$
$7$	2.32290	−	1.68768i	0.877972	−	0.637884i	0.932714	+	0.360616i	$0.117434\pi$
$8$	−0.992115	−	0.125333i	−0.350766	−	0.0443120i
$9$	0.406067	−	6.45425i	0.135356	−	2.15142i
$10$	−1.57159	+	1.59063i	−0.496980	+	0.503002i
$11$	2.65953	−	4.19075i	0.801879	−	1.26356i	−0.159189	−	0.987248i	$-0.550888\pi$
$11$	2.65953	−	4.19075i	0.801879	−	1.26356i	0.961068	−	0.276312i	$-0.0891122\pi$
$12$	2.86078	+	1.13266i	0.825837	+	0.326972i
$13$	0.256974	−	4.08448i	0.0712717	−	1.13283i	−0.786088	−	0.618114i	$-0.787897\pi$
$13$	0.256974	−	4.08448i	0.0712717	−	1.13283i	0.857360	−	0.514717i	$-0.172103\pi$
$14$	−0.180288	−	2.86559i	−0.0481839	−	0.765862i
$15$	5.90075	−	3.53782i	1.52357	−	0.913462i
$16$	−0.637424	+	0.770513i	−0.159356	+	0.192628i
$17$	−2.52907	+	5.37454i	−0.613389	+	1.30352i	0.320938	+	0.947100i	$0.396002\pi$
$17$	−2.52907	+	5.37454i	−0.613389	+	1.30352i	−0.934327	+	0.356418i	$0.883998\pi$
$18$	−5.23192	−	3.80121i	−1.23318	−	0.895954i
$19$	−2.66600	−	2.50355i	−0.611623	−	0.574353i	0.315586	−	0.948897i	$-0.397799\pi$
$19$	−2.66600	−	2.50355i	−0.611623	−	0.574353i	−0.927209	+	0.374545i	$0.877799\pi$
$20$	0.500914	+	2.17924i	0.112008	+	0.487293i
$21$	−1.65541	+	8.67795i	−0.361240	+	1.89368i
$22$	−2.11332	−	4.49104i	−0.450562	−	0.957492i
$23$	−0.110139	−	0.0282788i	−0.0229655	−	0.00589654i	0.237190	−	0.971463i	$-0.423774\pi$
$23$	−0.110139	−	0.0282788i	−0.0229655	−	0.00589654i	−0.260155	+	0.965567i	$0.583774\pi$
$24$	2.48922	−	1.80853i	0.508111	−	0.369164i
$25$	4.54944	+	2.07426i	0.909889	+	0.414852i
$26$	−3.31095	−	2.40554i	−0.649330	−	0.471766i
$27$	6.79970	+	8.21943i	1.30860	+	1.58183i
$28$	−2.51610	−	1.38324i	−0.475499	−	0.261408i
$29$	−8.24718	−	4.53392i	−1.53146	−	0.841929i	−0.531476	−	0.847074i	$-0.678362\pi$
$29$	−8.24718	−	4.53392i	−1.53146	−	0.841929i	−0.999987	+	0.00514512i	$0.998362\pi$
$30$	0.174697	−	6.87783i	0.0318951	−	1.25571i
$31$	2.32598	−	4.94296i	0.417758	−	0.887781i	−0.579583	−	0.814913i	$-0.696785\pi$
$31$	2.32598	−	4.94296i	0.417758	−	0.887781i	0.997342	−	0.0728683i	$-0.0232153\pi$
$32$	0.309017	+	0.951057i	0.0546270	+	0.168125i
$33$	2.86163	+	15.0012i	0.498146	+	2.61137i
$34$	3.18273	+	5.01519i	0.545834	+	0.860097i
$35$	−5.87683	+	2.58525i	−0.993365	+	0.436988i
$36$	−6.01287	+	2.38066i	−1.00215	+	0.396777i
$37$	−2.01600	+	2.43692i	−0.331428	+	0.400628i	−0.909734	−	0.415193i	$-0.863714\pi$
$37$	−2.01600	+	2.43692i	−0.331428	+	0.400628i	0.578305	+	0.815820i	$0.303714\pi$
$38$	−3.54233	+	0.909516i	−0.574642	+	0.147543i
$39$	8.02656	+	9.70245i	1.28528	+	1.55363i
$40$	2.10840	+	0.744759i	0.333367	+	0.117757i
$41$	5.71733	−	1.46796i	0.892897	−	0.229257i	0.225752	−	0.974185i	$-0.427516\pi$
$41$	5.71733	−	1.46796i	0.892897	−	0.229257i	0.667145	+	0.744928i	$0.267516\pi$
$42$	6.44002	+	6.04758i	0.993717	+	0.933163i
$43$	2.59037	−	7.97234i	0.395028	−	1.21577i	−0.533912	−	0.845540i	$-0.679279\pi$
$43$	2.59037	−	7.97234i	0.395028	−	1.21577i	0.928940	−	0.370231i	$-0.120721\pi$
$44$	−4.92428	−	0.622081i	−0.742363	−	0.0937823i
$45$	−3.95071	+	13.9105i	−0.588937	+	2.07366i
$46$	−0.0828918	+	0.0778406i	−0.0122217	+	0.0114770i
$47$	−4.61577	+	0.583107i	−0.673279	+	0.0850549i	−0.454537	−	0.890728i	$-0.650195\pi$
$47$	−4.61577	+	0.583107i	−0.673279	+	0.0850549i	−0.218742	+	0.975783i	$0.570195\pi$
$48$	−0.193197	−	3.07078i	−0.0278856	−	0.443229i
$49$	0.384455	−	1.18323i	0.0549222	−	0.169033i
$50$	4.18907	−	2.72978i	0.592424	−	0.386049i
$51$	−5.64761	−	17.3816i	−0.790823	−	2.43390i
$52$	−3.80516	+	1.50657i	−0.527681	+	0.208924i
$53$	−0.611671	+	3.20649i	−0.0840194	+	0.440445i	0.915273	+	0.402834i	$0.131975\pi$
$53$	−0.611671	+	3.20649i	−0.0840194	+	0.440445i	−0.999292	+	0.0376112i	$0.988025\pi$
$54$	10.5834	−	1.33699i	1.44021	−	0.181941i
$55$	−7.80046	+	7.89497i	−1.05181	+	1.06456i
$56$	−2.51610	+	1.38324i	−0.336228	+	0.184843i
$57$	11.2527			1.49046
$58$	−8.24718	+	4.53392i	−1.08291	+	0.595333i
$59$	3.41110	+	1.35055i	0.444087	+	0.175826i	0.579517	−	0.814960i	$-0.303241\pi$
$59$	3.41110	+	1.35055i	0.444087	+	0.175826i	−0.135429	+	0.990787i	$0.543241\pi$
$60$	−5.71354	−	3.83283i	−0.737614	−	0.494816i
$61$	1.96466	+	0.504438i	0.251549	+	0.0645867i	0.372359	−	0.928089i	$-0.378549\pi$
$61$	1.96466	+	0.504438i	0.251549	+	0.0645867i	−0.120810	+	0.992676i	$0.538549\pi$
$62$	−2.92715	−	4.61246i	−0.371749	−	0.585783i
$63$	−9.94947	−	15.6779i	−1.25352	−	1.97523i
$64$	0.968583	+	0.248690i	0.121073	+	0.0310862i
$65$	−2.50015	+	8.80309i	−0.310106	+	1.09189i
$66$	14.1993	+	5.62189i	1.74781	+	0.692007i
$67$	0.709563	−	0.390085i	0.0866869	−	0.0476565i	−0.437821	−	0.899062i	$-0.644249\pi$
$67$	0.709563	−	0.390085i	0.0866869	−	0.0476565i	0.524507	+	0.851406i	$0.324249\pi$
$68$	5.93986			0.720313
$69$	0.306595	−	0.168552i	0.0369097	−	0.0202913i
$70$	−0.966159	+	6.34722i	−0.115478	+	0.758637i
$71$	3.82270	−	0.482919i	0.453671	−	0.0573120i	0.104822	−	0.994491i	$-0.466573\pi$
$71$	3.82270	−	0.482919i	0.453671	−	0.0573120i	0.348849	+	0.937179i	$0.386573\pi$
$72$	−1.21180	+	6.35246i	−0.142812	+	0.748645i
$73$	0.275244	−	0.108977i	0.0322148	−	0.0127548i	−0.351962	−	0.936014i	$-0.614485\pi$
$73$	0.275244	−	0.108977i	0.0322148	−	0.0127548i	0.384177	+	0.923260i	$0.374485\pi$
$74$	0.977336	+	3.00793i	0.113613	+	0.349665i
$75$	−14.5730	+	4.92985i	−1.68274	+	0.569250i
$76$	−1.13015	+	3.47823i	−0.129637	+	0.398980i
$77$	−0.894844	−	14.2231i	−0.101977	−	1.62088i
$78$	12.4929	−	1.57822i	1.41454	−	0.178698i
$79$	5.93151	−	5.57006i	0.667347	−	0.626680i	−0.274950	−	0.961458i	$-0.588661\pi$
$79$	5.93151	−	5.57006i	0.667347	−	0.626680i	0.942297	+	0.334778i	$0.108661\pi$
$80$	1.75856	−	1.38112i	0.196613	−	0.154413i
$81$	−13.3153	−	1.68212i	−1.47948	−	0.186902i
$82$	1.82406	−	5.61387i	0.201433	−	0.619948i
$83$	11.9706	+	11.2411i	1.31394	+	1.23387i	0.953609	+	0.301047i	$0.0973360\pi$
$83$	11.9706	+	11.2411i	1.31394	+	1.23387i	0.360330	+	0.932825i	$0.382664\pi$
$84$	8.55688	−	2.19703i	0.933632	−	0.239716i
$85$	8.07724	−	10.5436i	0.876100	−	1.14361i
$86$	−5.34328	−	6.45892i	−0.576181	−	0.696483i
$87$	28.0474	−	7.20135i	3.00700	−	0.772065i
$88$	−3.16380	+	3.82438i	−0.337262	+	0.407680i
$89$	−0.259618	+	0.102790i	−0.0275194	+	0.0108957i	−0.381844	−	0.924227i	$-0.624711\pi$
$89$	−0.259618	+	0.102790i	−0.0275194	+	0.0108957i	0.354325	+	0.935123i	$0.384711\pi$
$90$	9.62816	+	10.7893i	1.01490	+	1.13730i
$91$	−6.29639	−	9.92152i	−0.660041	−	1.04006i
$92$	0.0213073	+	0.111697i	0.00222144	+	0.0116452i
$93$	5.19410	+	15.9858i	0.538603	+	1.65765i
$94$	−1.98092	+	4.20967i	−0.204316	+	0.434194i
$95$	4.63726	+	6.73591i	0.475772	+	0.691090i
$96$	−2.69626	−	1.48228i	−0.275186	−	0.151285i
$97$	6.67955	+	3.67211i	0.678205	+	0.372847i	0.783324	−	0.621613i	$-0.213522\pi$
$97$	6.67955	+	3.67211i	0.678205	+	0.372847i	−0.105119	+	0.994460i	$0.533522\pi$
$98$	−0.793034	−	0.958613i	−0.0801085	−	0.0968346i
$99$	−25.9682	−	18.8670i	−2.60990	−	1.89621i
$100$	−0.0602127	−	4.99964i	−0.00602127	−	0.499964i
$101$	−12.7250	+	9.24528i	−1.26619	+	0.919939i	−0.999044	−	0.0437171i	$-0.986080\pi$
$101$	−12.7250	+	9.24528i	−1.26619	+	0.919939i	−0.267144	+	0.963657i	$0.586080\pi$
$102$	−17.7019	−	4.54507i	−1.75275	−	0.450029i
$103$	−1.26132	−	2.68044i	−0.124282	−	0.264112i	0.832998	−	0.553276i	$-0.186623\pi$
$103$	−1.26132	−	2.68044i	−0.124282	−	0.264112i	−0.957279	+	0.289164i	$0.906623\pi$
$104$	−0.766869	+	4.02007i	−0.0751977	+	0.394200i
$105$	7.73611	−	18.1766i	0.754967	−	1.77385i
$106$	2.37958	+	2.23457i	0.231125	+	0.217041i
$107$	−1.97805	−	1.43714i	−0.191226	−	0.138934i	0.488053	−	0.872814i	$-0.337707\pi$
$107$	−1.97805	−	1.43714i	−0.191226	−	0.138934i	−0.679279	+	0.733880i	$0.737707\pi$
$108$	4.54199	−	9.65221i	0.437053	−	0.928785i
$109$	−1.64784	+	1.99189i	−0.157834	+	0.190789i	−0.843502	−	0.537125i	$-0.819510\pi$
$109$	−1.64784	+	1.99189i	−0.157834	+	0.190789i	0.685668	+	0.727914i	$0.259510\pi$
$110$	2.48625	+	10.8165i	0.237054	+	1.03131i
$111$	−0.611030	−	9.71204i	−0.0579964	−	0.921826i
$112$	−0.180288	+	2.86559i	−0.0170356	+	0.270773i
$113$	−9.12464	−	3.61270i	−0.858374	−	0.339854i	−0.102628	−	0.994720i	$-0.532725\pi$
$113$	−9.12464	−	3.61270i	−0.858374	−	0.339854i	−0.755745	+	0.654866i	$0.772725\pi$
$114$	6.02952	−	9.50101i	0.564716	−	0.889851i
$115$	0.227243	+	0.114068i	0.0211906	+	0.0106369i
$116$	−0.590940	+	9.39272i	−0.0548674	+	0.872092i
$117$	−26.2579	−	3.31714i	−2.42754	−	0.306670i
$118$	2.96806	−	2.15642i	0.273232	−	0.198515i
$119$	3.19576	+	16.7528i	0.292955	+	1.53572i
$120$	−6.29763	+	2.77037i	−0.574892	+	0.252899i
$121$	−5.80573	−	12.3378i	−0.527793	−	1.12162i
$122$	1.47863	−	1.38852i	0.133869	−	0.125711i
$123$	−9.73166	+	15.3346i	−0.877474	+	1.38268i
$124$	−5.46287			−0.490581
$125$	−8.95654	−	6.69182i	−0.801097	−	0.598534i
$126$	−18.5685			−1.65421
$127$	0.721412	−	1.13676i	0.0640150	−	0.100872i	−0.810813	−	0.585306i	$-0.800975\pi$
$127$	0.721412	−	1.13676i	0.0640150	−	0.100872i	0.874828	+	0.484434i	$0.160975\pi$
$128$	0.728969	−	0.684547i	0.0644323	−	0.0605060i
$129$	10.9817	+	23.3374i	0.966887	+	2.05474i
$130$	6.09304	+	6.82788i	0.534395	+	0.598845i
$131$	0.294139	+	1.54193i	0.0256990	+	0.134719i	0.992824	−	0.119581i	$-0.0381550\pi$
$131$	0.294139	+	1.54193i	0.0256990	+	0.134719i	−0.967125	+	0.254300i	$0.918155\pi$
$132$	12.3551	−	8.97648i	1.07537	−	0.781302i
$133$	−10.4180	−	1.31611i	−0.903359	−	0.114121i
$134$	0.0508427	−	0.808122i	0.00439214	−	0.0698111i
$135$	−10.9569	−	21.1878i	−0.943020	−	1.82355i
$136$	3.18273	−	5.01519i	0.272917	−	0.430049i
$137$	1.91682	+	0.758924i	0.163765	+	0.0648392i	0.448577	−	0.893744i	$-0.351931\pi$
$137$	1.91682	+	0.758924i	0.163765	+	0.0648392i	−0.284812	+	0.958584i	$0.591931\pi$
$138$	0.0219686	−	0.349182i	0.00187010	−	0.0297243i
$139$	0.918021	+	14.5915i	0.0778655	+	1.23764i	0.821953	+	0.569555i	$0.192884\pi$
$139$	0.918021	+	14.5915i	0.0778655	+	1.23764i	−0.744088	+	0.668082i	$0.767116\pi$
$140$	4.84144	+	4.21676i	0.409176	+	0.356382i
$141$	9.12466	−	11.0298i	0.768435	−	0.928879i
$142$	1.64056	−	3.48637i	0.137673	−	0.292570i
$143$	−16.4336	−	11.9397i	−1.37425	−	0.998450i
$144$	4.71425	+	4.42697i	0.392854	+	0.368914i
$145$	15.8691	+	13.8215i	1.31785	+	1.14782i
$146$	0.0554709	−	0.290789i	0.00459080	−	0.0240658i
$147$	1.62987	+	3.46366i	0.134430	+	0.285678i
$148$	3.06336	+	0.786538i	0.251807	+	0.0646530i
$149$	1.13375	−	0.823716i	0.0928803	−	0.0674815i	−0.540376	−	0.841424i	$-0.681718\pi$
$149$	1.13375	−	0.823716i	0.0928803	−	0.0674815i	0.633256	+	0.773942i	$0.281718\pi$
$150$	−3.64619	+	14.9459i	−0.297710	+	1.22033i
$151$	6.49213	+	4.71681i	0.528322	+	0.383848i	0.819730	−	0.572751i	$-0.194124\pi$
$151$	6.49213	+	4.71681i	0.528322	+	0.383848i	−0.291408	+	0.956599i	$0.594124\pi$
$152$	2.33121	+	2.81794i	0.189086	+	0.228565i
$153$	33.6617	+	18.5057i	2.72138	+	1.49609i
$154$	−12.4885	−	6.86560i	−1.00635	−	0.553245i
$155$	−7.42862	+	9.69693i	−0.596682	+	0.778876i
$156$	5.36149	−	11.3938i	0.429263	−	0.912230i
$157$	0.563663	+	1.73478i	0.0449852	+	0.138450i	0.971026	−	0.238972i	$-0.0768105\pi$
$157$	0.563663	+	1.73478i	0.0449852	+	0.138450i	−0.926041	+	0.377422i	$0.876810\pi$
$158$	−1.52469	−	7.99273i	−0.121298	−	0.635867i
$159$	−5.38173	−	8.48026i	−0.426799	−	0.672528i
$160$	−0.223833	−	2.22484i	−0.0176956	−	0.175889i
$161$	−0.303566	+	0.120190i	−0.0239244	+	0.00947233i
$162$	−8.55498	+	10.3412i	−0.672143	+	0.812481i
$163$	0.473794	−	0.121650i	0.0371104	−	0.00952833i	−0.230089	−	0.973170i	$-0.573902\pi$
$163$	0.473794	−	0.121650i	0.0371104	−	0.00952833i	0.267199	+	0.963641i	$0.413902\pi$
$164$	−3.76257	−	4.54817i	−0.293807	−	0.355152i
$165$	0.867093	−	34.1375i	0.0675031	−	2.65760i
$166$	15.9053	−	4.08379i	1.23449	−	0.316964i
$167$	−12.9775	−	12.1866i	−1.00423	−	0.943031i	−0.00584898	−	0.999983i	$-0.501862\pi$
$167$	−12.9775	−	12.1866i	−1.00423	−	0.943031i	−0.998377	+	0.0569520i	$0.981862\pi$
$168$	2.72999	−	8.40204i	0.210623	−	0.648232i
$169$	−3.71946	−	0.469877i	−0.286112	−	0.0361444i
$170$	−4.57426	−	12.4694i	−0.350829	−	0.956358i
$171$	−17.2411	+	16.1904i	−1.31846	+	1.23811i
$172$	−8.31652	+	1.05062i	−0.634129	+	0.0801091i
$173$	−1.23680	−	19.6584i	−0.0940322	−	1.49460i	−0.708530	−	0.705680i	$-0.750641\pi$
$173$	−1.23680	−	19.6584i	−0.0940322	−	1.49460i	0.614498	−	0.788918i	$-0.289359\pi$
$174$	8.94825	−	27.5399i	0.678365	−	2.08779i
$175$	14.0686	−	2.85973i	1.06348	−	0.216175i
$176$	1.53378	+	4.72049i	0.115613	+	0.355820i
$177$	−10.4954	+	4.15544i	−0.788885	+	0.312342i
$178$	−0.0523217	+	0.274280i	−0.00392168	+	0.0205582i
$179$	24.3977	−	3.08215i	1.82357	−	0.230371i	0.862382	−	0.506257i	$-0.168971\pi$
$179$	24.3977	−	3.08215i	1.82357	−	0.230371i	0.961190	+	0.275887i	$0.0889714\pi$
$180$	14.2688	−	2.34811i	1.06353	−	0.175018i
$181$	8.31227	−	4.56971i	0.617846	−	0.339664i	−0.141902	−	0.989881i	$-0.545322\pi$
$181$	8.31227	−	4.56971i	0.617846	−	0.339664i	0.759749	+	0.650217i	$0.225322\pi$
$182$	−11.7508			−0.871026
$183$	−5.46906	+	3.00664i	−0.404284	+	0.222257i
$184$	0.105726	+	0.0418599i	0.00779422	+	0.00308595i
$185$	5.56183	−	4.36809i	0.408914	−	0.321149i
$186$	16.2804	+	4.18009i	1.19374	+	0.306499i
$187$	15.7972	+	24.8925i	1.15521	+	1.82032i
$188$	2.49291	+	3.92820i	0.181814	+	0.286493i
$189$	29.6668	+	7.61714i	2.15794	+	0.554065i
$190$	8.17208	−	0.306084i	0.592865	−	0.0222057i
$191$	21.9028	+	8.67193i	1.58483	+	0.627479i	0.984986	−	0.172636i	$-0.0552286\pi$
$191$	21.9028	+	8.67193i	1.58483	+	0.627479i	0.599846	+	0.800116i	$0.295229\pi$
$192$	−2.69626	+	1.48228i	−0.194586	+	0.106975i
$193$	17.0425			1.22674			0.613372	−	0.789794i	$-0.289812\pi$
$193$	17.0425			1.22674			0.613372	+	0.789794i	$0.289812\pi$
$194$	6.67955	−	3.67211i	0.479564	−	0.263642i
$195$	−12.9338	−	25.0106i	−0.926211	−	1.79105i
$196$	−1.23431	+	0.155930i	−0.0881652	+	0.0111379i
$197$	3.08810	−	16.1884i	0.220018	−	1.15338i	−0.685176	−	0.728378i	$-0.740275\pi$
$197$	3.08810	−	16.1884i	0.220018	−	1.15338i	0.905194	−	0.424998i	$-0.139725\pi$
$198$	−29.8444	+	11.8162i	−2.12095	+	0.839743i
$199$	−0.934531	−	2.87619i	−0.0662471	−	0.203888i	0.912453	−	0.409180i	$-0.134185\pi$
$199$	−0.934531	−	2.87619i	−0.0662471	−	0.203888i	−0.978701	+	0.205293i	$0.934185\pi$
$200$	−4.25360	−	2.62810i	−0.300775	−	0.185835i
$201$	−0.769881	+	2.36945i	−0.0543032	+	0.167128i
$202$	0.987632	+	15.6980i	0.0694896	+	1.10451i
$203$	−26.8092	+	3.38679i	−1.88163	+	0.237706i
$204$	−13.3227	+	12.5108i	−0.932773	+	0.875932i
$205$	−13.1898	+	0.494020i	−0.921213	+	0.0345039i
$206$	−2.93902	−	0.371285i	−0.204771	−	0.0258686i
$207$	−0.227242	+	0.699379i	−0.0157944	+	0.0486102i
$208$	2.98335	+	2.80155i	0.206858	+	0.194252i
$209$	−17.5821	+	4.51431i	−1.21618	+	0.312261i
$210$	−11.2018	−	16.2713i	−0.772997	−	1.12283i
$211$	10.9459	+	13.2313i	0.753548	+	0.910882i	0.998275	−	0.0587094i	$-0.0186985\pi$
$211$	10.9459	+	13.2313i	0.753548	+	0.910882i	−0.244728	+	0.969592i	$0.578699\pi$
$212$	3.16176	−	0.811801i	0.217150	−	0.0557547i
$213$	−7.55689	+	9.13471i	−0.517789	+	0.625900i
$214$	−2.27331	+	0.900067i	−0.155400	+	0.0615273i
$215$	−9.44420	+	16.1910i	−0.644089	+	1.10422i
$216$	−5.71592	−	9.00684i	−0.388919	−	0.612838i
$217$	−2.93914	−	15.4075i	−0.199522	−	1.04593i
$218$	0.798856	+	2.45863i	0.0541054	+	0.166519i
$219$	−0.387820	+	0.824159i	−0.0262064	+	0.0556915i
$220$	10.4649	+	3.69655i	0.705540	+	0.249221i
$221$	21.3023	+	11.7110i	1.43295	+	0.787770i
$222$	−8.52755	−	4.68806i	−0.572332	−	0.314642i
$223$	2.29214	+	2.77072i	0.153493	+	0.185541i	0.841655	−	0.540016i	$-0.181582\pi$
$223$	2.29214	+	2.77072i	0.153493	+	0.185541i	−0.688162	+	0.725558i	$0.741582\pi$
$224$	2.32290	+	1.68768i	0.155205	+	0.112763i
$225$	15.2352	−	28.5210i	1.01568	−	1.90140i
$226$	−7.93953	+	5.76840i	−0.528129	+	0.383709i
$227$	−13.2005	−	3.38932i	−0.876150	−	0.224957i	−0.216275	−	0.976332i	$-0.569391\pi$
$227$	−13.2005	−	3.38932i	−0.876150	−	0.224957i	−0.659875	+	0.751375i	$0.729391\pi$
$228$	−4.79119	−	10.1818i	−0.317304	−	0.674305i
$229$	−1.17330	+	6.15063i	−0.0775336	+	0.406445i	0.922269	+	0.386550i	$0.126333\pi$
$229$	−1.17330	+	6.15063i	−0.0775336	+	0.406445i	−0.999802	+	0.0198953i	$0.993667\pi$
$230$	0.218074	−	0.130747i	0.0143794	−	0.00862122i
$231$	31.9645	+	30.0167i	2.10311	+	1.97495i
$232$	7.61389	+	5.53182i	0.499877	+	0.363182i
$233$	−8.01746	+	17.0380i	−0.525242	+	1.11620i	0.449586	+	0.893237i	$0.351571\pi$
$233$	−8.01746	+	17.0380i	−0.525242	+	1.11620i	−0.974828	+	0.222958i	$0.928429\pi$
$234$	−16.8704	+	20.3929i	−1.10286	+	1.33312i
$235$	10.3627	+	0.916646i	0.675991	+	0.0597954i
$236$	−0.230361	−	3.66149i	−0.0149952	−	0.238343i
$237$	−1.57202	+	24.9865i	−0.102113	+	1.62305i
$238$	15.8572	+	6.27831i	1.02787	+	0.406963i
$239$	4.34154	−	6.84117i	0.280831	−	0.442519i	−0.674406	−	0.738361i	$-0.735600\pi$
$239$	4.34154	−	6.84117i	0.280831	−	0.442519i	0.955237	+	0.295842i	$0.0956002\pi$
$240$	−1.03534	+	6.80170i	−0.0668309	+	0.439048i
$241$	1.54775	−	24.6009i	0.0996996	−	1.58468i	−0.556990	−	0.830519i	$-0.688044\pi$
$241$	1.54775	−	24.6009i	0.0996996	−	1.58468i	0.656690	−	0.754161i	$-0.271956\pi$
$242$	−13.5280	−	1.70899i	−0.869613	−	0.109858i
$243$	7.51783	−	5.46203i	0.482269	−	0.350389i
$244$	−0.380081	−	1.99245i	−0.0243322	−	0.127554i
$245$	−1.40168	+	2.40302i	−0.0895501	+	0.153523i
$246$	7.73298	+	16.4334i	0.493037	+	1.04776i
$247$	−10.9108	+	10.2459i	−0.694236	+	0.651931i
$248$	−2.92715	+	4.61246i	−0.185874	+	0.292891i
$249$	−50.5257			−3.20193
$250$	−10.4492	+	3.97660i	−0.660868	+	0.251502i
$251$	11.6261			0.733834			0.366917	−	0.930254i	$-0.380413\pi$
$251$	11.6261			0.733834			0.366917	+	0.930254i	$0.380413\pi$
$252$	−9.94947	+	15.6779i	−0.626758	+	0.987613i
$253$	−0.411427	+	0.386356i	−0.0258662	+	0.0242900i
$254$	−0.573250	−	1.21822i	−0.0359689	−	0.0764378i
$255$	4.09079	+	40.6612i	0.256175	+	2.54630i
$256$	−0.187381	−	0.982287i	−0.0117113	−	0.0613930i
$257$	−3.30077	+	2.39815i	−0.205896	+	0.149593i	−0.685955	−	0.727644i	$-0.740615\pi$
$257$	−3.30077	+	2.39815i	−0.205896	+	0.149593i	0.480059	+	0.877236i	$0.340615\pi$
$258$	25.5887	+	3.23260i	1.59308	+	0.201253i
$259$	−0.570201	+	9.06309i	−0.0354306	+	0.563153i
$260$	9.02978	−	1.48597i	0.560003	−	0.0921558i
$261$	−32.6120	+	51.3882i	−2.01863	+	3.18085i
$262$	1.45950	+	0.577857i	0.0901682	+	0.0357001i
$263$	1.65577	−	26.3178i	0.102099	−	1.62282i	−0.530042	−	0.847971i	$-0.677824\pi$
$263$	1.65577	−	26.3178i	0.102099	−	1.62282i	0.632142	−	0.774853i	$-0.282176\pi$
$264$	−0.958918	−	15.2416i	−0.0590173	−	0.938053i
$265$	2.85848	−	6.71623i	0.175595	−	0.412575i
$266$	−6.69349	+	8.09104i	−0.410404	+	0.496094i
$267$	0.365803	−	0.777370i	0.0223868	−	0.0475743i
$268$	−0.655077	−	0.475941i	−0.0400152	−	0.0290727i
$269$	5.65073	+	5.30639i	0.344531	+	0.323536i	0.837424	−	0.546554i	$-0.184061\pi$
$269$	5.65073	+	5.30639i	0.344531	+	0.323536i	−0.492893	+	0.870090i	$0.664061\pi$
$270$	−23.7604	−	2.10175i	−1.44601	−	0.127908i
$271$	1.42600	−	7.47535i	0.0866233	−	0.454095i	−0.912375	−	0.409355i	$-0.865754\pi$
$271$	1.42600	−	7.47535i	0.0866233	−	0.454095i	0.998999	−	0.0447407i	$-0.0142462\pi$
$272$	−2.52907	−	5.37454i	−0.153347	−	0.325879i
$273$	35.0195	+	8.99149i	2.11948	+	0.544190i
$274$	1.66787	−	1.21177i	0.100759	−	0.0732060i
$275$	20.7921	−	13.5490i	1.25381	−	0.817038i
$276$	−0.283052	−	0.205650i	−0.0170378	−	0.0123787i
$277$	11.3117	+	13.6735i	0.679653	+	0.821559i	0.991709	−	0.128505i	$-0.0410177\pi$
$277$	11.3117	+	13.6735i	0.679653	+	0.821559i	−0.312056	+	0.950064i	$0.601018\pi$
$278$	12.8119	+	7.04342i	0.768409	+	0.422436i
$279$	−30.9586	−	17.0196i	−1.85344	−	1.01894i
$280$	6.15450	−	1.82831i	0.367802	−	0.109262i
$281$	−12.4170	+	26.3875i	−0.740738	+	1.57415i	0.0759782	+	0.997109i	$0.475792\pi$
$281$	−12.4170	+	26.3875i	−0.740738	+	1.57415i	−0.816716	+	0.577039i	$0.804208\pi$
$282$	−4.42355	−	13.6143i	−0.263418	−	0.810719i
$283$	−4.09224	−	21.4523i	−0.243259	−	1.27521i	−0.868858	−	0.495062i	$-0.835145\pi$
$283$	−4.09224	−	21.4523i	−0.243259	−	1.27521i	0.625599	−	0.780145i	$-0.284855\pi$
$284$	−2.06458	−	3.25326i	−0.122511	−	0.193046i
$285$	−24.5885	−	5.34094i	−1.45650	−	0.316370i
$286$	−18.8866	+	7.47774i	−1.11679	+	0.442168i
$287$	10.8033	−	13.0590i	0.637699	−	0.770846i
$288$	6.26384	−	1.60828i	0.369100	−	0.0947688i
$289$	−11.6533	−	14.0864i	−0.685489	−	0.828614i
$290$	20.1730	−	5.99275i	1.18460	−	0.351906i
$291$	−22.7161	+	5.83251i	−1.33164	+	0.341908i
$292$	−0.215798	−	0.202648i	−0.0126286	−	0.0118591i
$293$	−2.34827	+	7.22725i	−0.137188	+	0.422220i	−0.995924	−	0.0901977i	$-0.971250\pi$
$293$	−2.34827	+	7.22725i	−0.137188	+	0.422220i	0.858736	+	0.512418i	$0.171250\pi$
$294$	3.79780	+	0.479773i	0.221492	+	0.0279809i
$295$	−6.81262	−	4.57013i	−0.396646	−	0.266083i
$296$	2.30553	−	2.16504i	0.134006	−	0.125840i
$297$	52.5296	−	6.63603i	3.04808	−	0.385062i
$298$	−0.0879940	−	1.39862i	−0.00509735	−	0.0810201i
$299$	−0.143807	+	0.442592i	−0.00831657	+	0.0255958i
$300$	10.6655	+	11.0870i	0.615775	+	0.640108i
$301$	−7.43762	−	22.8907i	−0.428698	−	1.31940i
$302$	7.46119	−	2.95409i	0.429343	−	0.169989i
$303$	9.06847	−	47.5386i	0.520970	−	2.73102i
$304$	3.62839	−	0.458372i	0.208102	−	0.0262895i
$305$	−4.05358	−	2.03475i	−0.232107	−	0.116509i
$306$	33.6617	−	18.5057i	1.92431	−	1.05790i
$307$	−3.32472			−0.189752			−0.0948759	−	0.995489i	$-0.530245\pi$
$307$	−3.32472			−0.189752			−0.0948759	+	0.995489i	$0.530245\pi$
$308$	−12.4885	+	6.86560i	−0.711597	+	0.391204i
$309$	8.47473	+	3.35538i	0.482111	+	0.190881i
$310$	4.20693	+	11.4681i	0.238938	+	0.651343i
$311$	4.05295	+	1.04062i	0.229821	+	0.0590081i	0.361844	−	0.932239i	$-0.382147\pi$
$311$	4.05295	+	1.04062i	0.229821	+	0.0590081i	−0.132023	+	0.991247i	$0.542147\pi$
$312$	−6.74723	−	10.6319i	−0.381987	−	0.601915i
$313$	−12.1128	−	19.0867i	−0.684657	−	1.07885i	−0.991876	−	0.127208i	$-0.959399\pi$
$313$	−12.1128	−	19.0867i	−0.684657	−	1.07885i	0.307219	−	0.951639i	$-0.400601\pi$
$314$	1.76675	+	0.453623i	0.0997032	+	0.0255994i
$315$	14.2995	+	38.9803i	0.805685	+	2.19629i
$316$	−7.56545	−	2.99537i	−0.425590	−	0.168503i
$317$	15.1260	−	8.31562i	0.849564	−	0.467052i	0.00341220	−	0.999994i	$-0.498914\pi$
$317$	15.1260	−	8.31562i	0.849564	−	0.467052i	0.846151	+	0.532943i	$0.178914\pi$
$318$	−10.0438			−0.563228
$319$	−40.9342	+	22.5038i	−2.29188	+	1.25997i
$320$	−1.99843	−	1.00314i	−0.111716	−	0.0560771i
$321$	7.46360	−	0.942872i	0.416578	−	0.0526260i
$322$	−0.0611789	+	0.320711i	−0.00340936	+	0.0178725i
$323$	20.1979	−	7.99692i	1.12384	−	0.444961i
$324$	4.14737	+	12.7643i	0.230410	+	0.709128i
$325$	9.64136	−	18.0491i	0.534807	−	1.00118i
$326$	0.151159	−	0.465221i	0.00837194	−	0.0257662i
$327$	−0.499444	−	7.93843i	−0.0276193	−	0.438996i
$328$	−5.85623	+	0.739814i	−0.323356	+	0.0408494i
$329$	−9.73785	+	9.14445i	−0.536865	+	0.504150i
$330$	−28.3587	−	19.0239i	−1.56109	−	1.04723i
$331$	−3.04740	−	0.384976i	−0.167500	−	0.0211602i	0.0411359	−	0.999154i	$-0.486902\pi$
$331$	−3.04740	−	0.384976i	−0.167500	−	0.0211602i	−0.208636	+	0.977993i	$0.566902\pi$
$332$	5.07444	−	15.6175i	0.278496	−	0.857123i
$333$	14.9099	+	14.0013i	0.817056	+	0.767267i
$334$	−17.2432	+	4.42730i	−0.943506	+	0.242251i
$335$	−1.73562	+	0.515598i	−0.0948272	+	0.0281701i
$336$	−5.63128	−	6.80705i	−0.307211	−	0.371355i
$337$	−22.2316	+	5.70810i	−1.21103	+	0.310940i	−0.799618	−	0.600509i	$-0.794965\pi$
$337$	−22.2316	+	5.70810i	−1.21103	+	0.310940i	−0.411413	+	0.911449i	$0.634965\pi$
$338$	−2.38972	+	2.88867i	−0.129983	+	0.157123i
$339$	28.0751	−	11.1157i	1.52483	−	0.603724i
$340$	−12.9793	−	2.81926i	−0.703899	−	0.152896i
$341$	−14.5287	−	22.8936i	−0.786773	−	1.23976i
$342$	4.43182	+	23.2324i	0.239645	+	1.25626i
$343$	5.10700	+	15.7177i	0.275752	+	0.848678i
$344$	−3.56915	+	7.58482i	−0.192435	+	0.408946i
$345$	−0.749946	+	0.222785i	−0.0403757	+	0.0119943i
$346$	−17.2608	−	9.48922i	−0.927948	−	0.510144i
$347$	2.60283	+	1.43092i	0.139727	+	0.0768158i	0.550084	−	0.835109i	$-0.314596\pi$
$347$	2.60283	+	1.43092i	0.139727	+	0.0768158i	−0.410357	+	0.911925i	$0.634596\pi$
$348$	−18.4580	−	22.3119i	−0.989451	−	1.19604i
$349$	29.4764	+	21.4159i	1.57784	+	1.14636i	0.919123	+	0.393970i	$0.128899\pi$
$349$	29.4764	+	21.4159i	1.57784	+	1.14636i	0.658713	+	0.752395i	$0.271101\pi$
$350$	5.12377	−	13.4108i	0.273877	−	0.716838i
$351$	35.3194	−	25.6611i	1.88521	−	1.36969i
$352$	4.80748	+	1.23435i	0.256240	+	0.0657912i
$353$	3.98497	+	8.46849i	0.212098	+	0.450732i	0.982361	−	0.186995i	$-0.0598748\pi$
$353$	3.98497	+	8.46849i	0.212098	+	0.450732i	−0.770262	+	0.637727i	$0.779875\pi$
$354$	−2.11518	+	11.0882i	−0.112421	+	0.589330i
$355$	−8.58224	−	0.759151i	−0.455498	−	0.0402915i
$356$	0.203547	+	0.191143i	0.0107880	+	0.0101306i
$357$	−42.4534	−	30.8442i	−2.24687	−	1.63245i
$358$	10.4706	−	22.2512i	0.553389	−	1.17601i
$359$	6.77399	−	8.18835i	0.357518	−	0.432165i	−0.560835	−	0.827928i	$-0.689520\pi$
$359$	6.77399	−	8.18835i	0.357518	−	0.432165i	0.918353	+	0.395763i	$0.129520\pi$
$360$	5.66301	−	13.3057i	0.298467	−	0.701271i
$361$	−0.353177	−	5.61358i	−0.0185882	−	0.295452i
$362$	0.595604	−	9.46686i	0.0313043	−	0.497567i
$363$	39.0083	+	15.4445i	2.04740	+	0.810625i
$364$	−6.29639	+	9.92152i	−0.330020	+	0.520029i
$365$	−0.653163	+	0.107486i	−0.0341881	+	0.00562609i
$366$	−0.391878	+	6.22872i	−0.0204838	+	0.325580i
$367$	23.7853	+	3.00478i	1.24158	+	0.156848i	0.718556	−	0.695469i	$-0.244803\pi$
$367$	23.7853	+	3.00478i	1.24158	+	0.156848i	0.523025	+	0.852317i	$0.324803\pi$
$368$	0.0919942	−	0.0668377i	0.00479553	−	0.00348416i
$369$	−7.15296	−	37.4971i	−0.372368	−	1.95202i
$370$	−0.707923	−	7.03655i	−0.0368032	−	0.365813i
$371$	3.99069	+	8.48065i	0.207186	+	0.440294i
$372$	12.2528	−	11.5062i	0.635280	−	0.596567i
$373$	−9.13693	+	14.3975i	−0.473092	+	0.745474i	−0.994145	−	0.108050i	$-0.965539\pi$
$373$	−9.13693	+	14.3975i	−0.473092	+	0.745474i	0.521053	+	0.853524i	$0.325539\pi$
$374$	29.4820			1.52448
$375$	34.1835	−	3.85544i	1.76523	−	0.199094i
$376$	4.65245			0.239932
$377$	−20.6380	+	32.5203i	−1.06291	+	1.67488i
$378$	22.3276	−	20.9670i	1.14841	−	1.07843i
$379$	11.4683	+	24.3714i	0.589087	+	1.25187i	0.947931	+	0.318475i	$0.103171\pi$
$379$	11.4683	+	24.3714i	0.589087	+	1.25187i	−0.358845	+	0.933397i	$0.616829\pi$
$380$	4.12038	−	7.06392i	0.211371	−	0.362372i
$381$	0.776233	+	4.06915i	0.0397676	+	0.208469i
$382$	19.0581	−	13.8465i	0.975096	−	0.708448i
$383$	5.53004	+	0.698606i	0.282572	+	0.0356971i	0.265342	−	0.964154i	$-0.414515\pi$
$383$	5.53004	+	0.698606i	0.282572	+	0.0356971i	0.0172301	+	0.999852i	$0.494515\pi$
$384$	−0.193197	+	3.07078i	−0.00985905	+	0.156705i
$385$	−4.79545	+	31.5039i	−0.244399	+	1.60559i
$386$	9.13182	−	14.3894i	0.464797	−	0.732404i
$387$	−50.4036	−	19.9562i	−2.56216	−	1.01443i
$388$	0.478614	−	7.60734i	0.0242979	−	0.386204i
$389$	−1.14823	−	18.2507i	−0.0582178	−	0.925345i	−0.913412	−	0.407037i	$-0.866562\pi$
$389$	−1.14823	−	18.2507i	−0.0582178	−	0.925345i	0.855194	−	0.518308i	$-0.173438\pi$
$390$	−28.0475	−	2.48097i	−1.42024	−	0.125629i
$391$	0.430534	−	0.520426i	0.0217730	−	0.0263191i
$392$	−0.529722	+	1.12572i	−0.0267550	+	0.0568573i
$393$	−3.90742	−	2.83890i	−0.197103	−	0.143204i
$394$	−12.0136	−	11.2816i	−0.605238	−	0.568356i
$395$	−15.6048	+	9.35591i	−0.785161	+	0.470747i
$396$	−6.01465	+	31.5299i	−0.302248	+	1.58444i
$397$	−8.27022	−	17.5751i	−0.415071	−	0.882070i	−0.997599	−	0.0692594i	$-0.977936\pi$
$397$	−8.27022	−	17.5751i	−0.415071	−	0.882070i	0.582528	−	0.812811i	$-0.302064\pi$
$398$	−2.92919	−	0.752089i	−0.146827	−	0.0376988i
$399$	26.1390	−	18.9911i	1.30858	−	0.950743i
$400$	−4.49817	+	2.18322i	−0.224908	+	0.109161i
$401$	−27.2064	−	19.7666i	−1.35862	−	0.987098i	−0.998531	−	0.0541819i	$-0.982745\pi$
$401$	−27.2064	−	19.7666i	−1.35862	−	0.987098i	−0.360093	−	0.932916i	$-0.617255\pi$
$402$	1.58807	+	1.91965i	0.0792057	+	0.0957433i
$403$	−19.5917	−	10.7706i	−0.975932	−	0.536523i
$404$	13.7834	+	7.57751i	0.685751	+	0.376995i
$405$	28.2972	+	9.99554i	1.40610	+	0.496683i
$406$	−11.5055	+	24.4505i	−0.571009	+	1.21346i
$407$	4.85093	+	14.9296i	0.240452	+	0.740034i
$408$	3.42459	+	17.9523i	0.169542	+	0.888773i
$409$	1.89041	+	2.97881i	0.0934749	+	0.147293i	0.887847	−	0.460138i	$-0.152200\pi$
$409$	1.89041	+	2.97881i	0.0934749	+	0.147293i	−0.794372	+	0.607431i	$0.792200\pi$
$410$	−6.65031	+	11.4012i	−0.328435	+	0.563065i
$411$	−5.89778	+	2.33509i	−0.290916	+	0.115182i
$412$	−1.88829	+	2.28255i	−0.0930295	+	0.112453i
$413$	10.2029	−	2.61967i	0.502053	−	0.128905i
$414$	0.468743	+	0.566613i	0.0230375	+	0.0278475i
$415$	−20.8216	−	30.2447i	−1.02209	−	1.48466i
$416$	3.96398	−	1.01778i	0.194350	−	0.0499006i
$417$	−32.7924	−	30.7942i	−1.60585	−	1.50800i
$418$	−5.60939	+	17.2639i	−0.274364	+	0.844406i
$419$	7.40191	+	0.935079i	0.361607	+	0.0456816i	0.304038	−	0.952660i	$-0.401665\pi$
$419$	7.40191	+	0.935079i	0.361607	+	0.0456816i	0.0575692	+	0.998342i	$0.481665\pi$
$420$	−19.7405	+	0.739379i	−0.963240	+	0.0360780i
$421$	−3.12612	+	2.93562i	−0.152358	+	0.143074i	−0.756978	−	0.653440i	$-0.773325\pi$
$421$	−3.12612	+	2.93562i	−0.152358	+	0.143074i	0.604620	+	0.796514i	$0.293325\pi$
$422$	17.0367	−	2.15224i	0.829333	−	0.104769i
$423$	1.88921	+	30.0281i	0.0918564	+	1.46002i
$424$	1.00873	−	3.10454i	0.0489881	−	0.150770i
$425$	−22.6541	+	19.2052i	−1.09888	+	0.931591i
$426$	3.66351	+	11.2751i	0.177497	+	0.546281i
$427$	5.41503	−	2.14396i	0.262052	−	0.103754i
$428$	−0.458149	+	2.40170i	−0.0221455	+	0.116091i
$429$	62.0075	−	7.83336i	2.99375	−	0.378198i
$430$	8.61005	+	16.6496i	0.415214	+	0.802914i
$431$	−32.3235	+	17.7700i	−1.55697	+	0.855952i	−0.557299	+	0.830312i	$0.688162\pi$
$431$	−32.3235	+	17.7700i	−1.55697	+	0.855952i	−0.999671	+	0.0256400i	$0.991838\pi$
$432$	−10.6675			−0.513239
$433$	11.4563	−	6.29813i	0.550553	−	0.302669i	−0.182091	−	0.983282i	$-0.558286\pi$
$433$	11.4563	−	6.29813i	0.550553	−	0.302669i	0.732643	+	0.680613i	$0.238286\pi$
$434$	−14.5838	−	5.77415i	−0.700047	−	0.277168i
$435$	−64.7048	+	2.42351i	−3.10236	+	0.116198i
$436$	2.50394	+	0.642901i	0.119917	+	0.0307894i
$437$	0.222833	+	0.351129i	0.0106595	+	0.0167968i
$438$	0.488056	+	0.769053i	0.0233202	+	0.0367468i
$439$	−28.4117	−	7.29489i	−1.35602	−	0.348166i	−0.500409	−	0.865789i	$-0.666817\pi$
$439$	−28.4117	−	7.29489i	−1.35602	−	0.348166i	−0.855609	+	0.517623i	$0.826817\pi$
$440$	8.72845	−	6.85506i	0.416113	−	0.326802i
$441$	−7.48075	−	2.96184i	−0.356226	−	0.141040i
$442$	21.3023	−	11.7110i	1.01325	−	0.557038i
$443$	23.0776			1.09645			0.548225	−	0.836331i	$-0.315304\pi$
$443$	23.0776			1.09645			0.548225	+	0.836331i	$0.315304\pi$
$444$	−8.52755	+	4.68806i	−0.404700	+	0.222485i
$445$	0.616082	−	0.101384i	0.0292051	−	0.00480607i
$446$	3.56759	−	0.450691i	0.168930	−	0.0213408i
$447$	−0.807963	+	4.23549i	−0.0382153	+	0.200332i
$448$	2.66963	−	1.05698i	0.126128	−	0.0499376i
$449$	11.6818	+	35.9529i	0.551298	+	1.69672i	0.705524	+	0.708686i	$0.250712\pi$
$449$	11.6818	+	35.9529i	0.551298	+	1.69672i	−0.154226	+	0.988036i	$0.549288\pi$
$450$	−15.9176	−	28.1458i	−0.750364	−	1.32680i
$451$	9.05356	−	27.8640i	0.426316	−	1.31206i
$452$	0.616213	+	9.79443i	0.0289842	+	0.460691i
$453$	−24.4961	+	3.09458i	−1.15093	+	0.145396i
$454$	−9.93490	+	9.32949i	−0.466268	+	0.437855i
$455$	9.04923	+	24.6681i	0.424234	+	1.15646i
$456$	−11.1640	−	1.41034i	−0.522803	−	0.0660454i
$457$	−9.30914	+	28.6506i	−0.435463	+	1.34022i	0.457148	+	0.889391i	$0.348871\pi$
$457$	−9.30914	+	28.6506i	−0.435463	+	1.34022i	−0.892611	+	0.450827i	$0.851129\pi$
$458$	4.56447	+	4.28632i	0.213284	+	0.200287i
$459$	−61.3726	+	15.7578i	−2.86463	+	0.735511i
$460$	0.00645626	−	0.254184i	0.000301025	−	0.0118514i
$461$	4.14277	+	5.00775i	0.192948	+	0.233234i	0.858111	−	0.513464i	$-0.171638\pi$
$461$	4.14277	+	5.00775i	0.192948	+	0.233234i	−0.665163	+	0.746698i	$0.731638\pi$
$462$	42.4714	−	10.9048i	1.97595	−	0.507337i
$463$	−23.6118	+	28.5418i	−1.09733	+	1.32645i	−0.156463	+	0.987684i	$0.550009\pi$
$463$	−23.6118	+	28.5418i	−1.09733	+	1.32645i	−0.940871	+	0.338765i	$0.889991\pi$
$464$	8.75040	−	3.46453i	0.406227	−	0.160837i
$465$	−3.76229	−	37.3961i	−0.174472	−	1.73420i
$466$	10.0897	+	15.8988i	0.467395	+	0.736496i
$467$	−4.67365	−	24.5001i	−0.216271	−	1.13373i	−0.910352	−	0.413834i	$-0.864189\pi$
$467$	−4.67365	−	24.5001i	−0.216271	−	1.13373i	0.694081	−	0.719896i	$-0.255811\pi$
$468$	8.17863	+	25.1712i	0.378057	+	1.16354i
$469$	0.989900	−	2.10365i	0.0457094	−	0.0971373i
$470$	6.32658	−	8.25839i	0.291824	−	0.380931i
$471$	−4.91812	−	2.70376i	−0.226615	−	0.124583i
$472$	−3.21493	−	1.76742i	−0.147979	−	0.0813523i
$473$	−26.5209	−	32.0583i	−1.21943	−	1.47404i
$474$	20.2544	+	14.7157i	0.930318	+	0.675915i
$475$	−6.93584	−	16.9197i	−0.318238	−	0.776330i
$476$	13.7977	−	10.0246i	0.632415	−	0.459477i
$477$	20.4471	+	5.24992i	0.936209	+	0.240378i
$478$	−3.44988	−	7.33137i	−0.157794	−	0.335329i
$479$	4.71092	−	24.6955i	0.215247	−	1.12837i	−0.696482	−	0.717574i	$-0.745252\pi$
$479$	4.71092	−	24.6955i	0.215247	−	1.12837i	0.911729	−	0.410791i	$-0.134748\pi$
$480$	5.18810	+	4.51870i	0.236803	+	0.206249i
$481$	9.43551	+	8.86053i	0.430222	+	0.404005i
$482$	−19.9419	−	14.4886i	−0.908327	−	0.659938i
$483$	0.427726	−	0.908965i	0.0194622	−	0.0413593i
$484$	−8.69161	+	10.5064i	−0.395073	+	0.477562i
$485$	−12.8527	−	11.1943i	−0.583609	−	0.508308i
$486$	−0.583484	−	9.27422i	−0.0264674	−	0.420687i
$487$	1.68834	−	26.8354i	0.0765061	−	1.21603i	−0.753186	−	0.657808i	$-0.771484\pi$
$487$	1.68834	−	26.8354i	0.0765061	−	1.21603i	0.829692	−	0.558222i	$-0.188516\pi$
$488$	−1.88594	−	0.746698i	−0.0853726	−	0.0338014i
$489$	−0.806461	+	1.27078i	−0.0364694	+	0.0574666i
$490$	1.27788	+	2.47108i	0.0577287	+	0.111632i
$491$	−0.278678	+	4.42946i	−0.0125766	+	0.199899i	0.986721	+	0.162424i	$0.0519313\pi$
$491$	−0.278678	+	4.42946i	−0.0125766	+	0.199899i	−0.999298	+	0.0374745i	$0.988069\pi$
$492$	18.0187	+	2.27630i	0.812348	+	0.102623i
$493$	45.2254	−	32.8582i	2.03685	−	1.47986i
$494$	2.80461	+	14.7023i	0.126186	+	0.661488i
$495$	47.7886	+	53.5520i	2.14794	+	2.40698i
$496$	2.32598	+	4.94296i	0.104440	+	0.221945i
$497$	8.06472	−	7.57327i	0.361752	−	0.339708i
$498$	−27.0730	+	42.6602i	−1.21317	+	1.91165i
$499$	−0.901190			−0.0403428			−0.0201714	−	0.999797i	$-0.506421\pi$
$499$	−0.901190			−0.0403428			−0.0201714	+	0.999797i	$0.506421\pi$
$500$	−2.24143	+	10.9534i	−0.100240	+	0.489849i
$501$	54.7756			2.44719
$502$	6.22959	−	9.81626i	0.278040	−	0.438121i
$503$	0.448492	−	0.421162i	0.0199973	−	0.0187787i	−0.674484	−	0.738289i	$-0.735634\pi$
$503$	0.448492	−	0.421162i	0.0199973	−	0.0187787i	0.694481	+	0.719511i	$0.255634\pi$
$504$	7.90606	+	16.8012i	0.352164	+	0.748387i
$505$	32.1938	−	14.1622i	1.43260	−	0.630212i
$506$	0.105757	+	0.554399i	0.00470148	+	0.0246460i
$507$	9.33216	−	6.78021i	0.414456	−	0.301120i
$508$	−1.33574	−	0.168743i	−0.0592638	−	0.00748675i
$509$	2.11765	−	33.6590i	0.0938630	−	1.49191i	−0.616099	−	0.787669i	$-0.711288\pi$
$509$	2.11765	−	33.6590i	0.0938630	−	1.49191i	0.709962	−	0.704240i	$-0.248712\pi$
$510$	36.5234	+	18.3334i	1.61728	+	0.811817i
$511$	0.455445	−	0.717666i	0.0201477	−	0.0317477i
$512$	−0.929776	−	0.368125i	−0.0410907	−	0.0162690i
$513$	2.44967	−	38.9364i	0.108156	−	1.71908i
$514$	0.256184	+	4.07193i	0.0112998	+	0.179605i
$515$	1.48390	+	6.45574i	0.0653884	+	0.284474i
$516$	16.4405	−	19.8731i	0.723752	−	0.874866i
$517$	−9.83213	+	20.8943i	−0.432416	+	0.918932i
$518$	7.34669	+	5.33768i	0.322795	+	0.234524i
$519$	44.1795	+	41.4873i	1.93926	+	1.82109i
$520$	3.58376	−	8.42032i	0.157158	−	0.369255i
$521$	5.93420	−	31.1081i	0.259982	−	1.36287i	−0.577493	−	0.816396i	$-0.695969\pi$
$521$	5.93420	−	31.1081i	0.259982	−	1.36287i	0.837474	−	0.546477i	$-0.184031\pi$
$522$	25.9142	+	55.0704i	1.13423	+	2.41037i
$523$	−33.4795	−	8.59608i	−1.46396	−	0.375880i	−0.569114	−	0.822259i	$-0.692714\pi$
$523$	−33.4795	−	8.59608i	−1.46396	−	0.375880i	−0.894844	+	0.446378i	$0.852714\pi$
$524$	1.26994	−	0.922666i	0.0554776	−	0.0403068i
$525$	−25.5315	+	36.0461i	−1.11429	+	1.57318i
$526$	−21.3336	−	15.4998i	−0.930190	−	0.675823i
$527$	20.6836	+	25.0021i	0.900990	+	1.08911i
$528$	−13.3827	−	7.35720i	−0.582407	−	0.320181i
$529$	−20.1437	−	11.0741i	−0.875814	−	0.481483i
$530$	−4.13905	−	6.01223i	−0.179789	−	0.261155i
$531$	10.1019	−	21.4677i	0.438386	−	0.931617i
$532$	3.24494	+	9.98690i	0.140686	+	0.432987i
$533$	−4.52665	−	23.7295i	−0.196071	−	1.02784i
$534$	−0.460348	−	0.725393i	−0.0199212	−	0.0313908i
$535$	3.64015	+	4.07917i	0.157378	+	0.176358i
$536$	−0.752858	+	0.298078i	−0.0325185	+	0.0128750i
$537$	−48.2306	+	58.3008i	−2.08130	+	2.51586i
$538$	7.50815	−	1.92776i	0.323699	−	0.0831118i
$539$	−3.93616	−	4.75800i	−0.169542	−	0.204942i
$540$	−14.5060	+	18.9354i	−0.624240	+	0.814850i
$541$	−23.1708	+	5.94925i	−0.996191	+	0.255778i	−0.711382	−	0.702806i	$-0.751930\pi$
$541$	−23.1708	+	5.94925i	−0.996191	+	0.255778i	−0.284809	+	0.958584i	$0.591930\pi$
$542$	−5.54756	−	5.20951i	−0.238288	−	0.223767i
$543$	−9.01888	+	27.7572i	−0.387037	+	1.19118i
$544$	−5.89302	−	0.744461i	−0.252661	−	0.0319185i
$545$	4.54614	−	3.57040i	0.194735	−	0.152939i
$546$	26.3562	−	24.7501i	1.12794	−	1.05921i
$547$	−16.1369	+	2.03856i	−0.689962	+	0.0871625i	−0.462493	−	0.886623i	$-0.653045\pi$
$547$	−16.1369	+	2.03856i	−0.689962	+	0.0871625i	−0.227469	+	0.973785i	$0.573045\pi$
$548$	−0.129449	−	2.05753i	−0.00552977	−	0.0878932i
$549$	4.05355	−	12.4756i	0.173001	−	0.532444i
$550$	−0.298861	−	24.8153i	−0.0127435	−	1.05813i
$551$	10.6361	+	32.7346i	0.453114	+	1.39454i
$552$	−0.325303	+	0.128797i	−0.0138458	+	0.00548194i
$553$	4.37779	−	22.9492i	0.186163	−	0.975898i
$554$	17.6060	−	2.22415i	0.748007	−	0.0944952i
$555$	−3.27450	+	21.5119i	−0.138995	+	0.913130i
$556$	12.8119	−	7.04342i	0.543347	−	0.298708i
$557$	27.6879			1.17317			0.586587	−	0.809886i	$-0.300471\pi$
$557$	27.6879			1.17317			0.586587	+	0.809886i	$0.300471\pi$
$558$	−30.9586	+	17.0196i	−1.31058	+	0.720498i
$559$	−31.8972	−	12.6290i	−1.34911	−	0.534150i
$560$	1.75406	−	6.17607i	0.0741225	−	0.260987i
$561$	−87.8618	−	22.5591i	−3.70953	−	0.952445i
$562$	15.6264	+	24.6232i	0.659158	+	1.03867i
$563$	−8.52061	−	13.4263i	−0.359101	−	0.565853i	0.615963	−	0.787775i	$-0.288767\pi$
$563$	−8.52061	−	13.4263i	−0.359101	−	0.565853i	−0.975064	+	0.221922i	$0.928767\pi$
$564$	−13.8652	−	3.55997i	−0.583829	−	0.149902i
$565$	18.2237	+	12.2250i	0.766675	+	0.514311i
$566$	−20.3055	−	8.03952i	−0.853504	−	0.337926i
$567$	−33.7691	+	18.5647i	−1.41817	+	0.779644i
$568$	−3.85308			−0.161672
$569$	30.0959	−	16.5454i	1.26169	−	0.693617i	0.296462	−	0.955045i	$-0.404193\pi$
$569$	30.0959	−	16.5454i	1.26169	−	0.693617i	0.965223	+	0.261427i	$0.0841932\pi$
$570$	−17.6847	+	17.8990i	−0.740730	+	0.749705i
$571$	−39.1617	+	4.94727i	−1.63886	+	0.207037i	−0.890089	−	0.455787i	$-0.849358\pi$
$571$	−39.1617	+	4.94727i	−1.63886	+	0.207037i	−0.748776	+	0.662824i	$0.769358\pi$
$572$	−3.80629	+	19.9533i	−0.159149	+	0.834288i
$573$	−67.3917	+	26.6822i	−2.81533	+	1.11467i
$574$	−5.23734	−	16.1189i	−0.218602	−	0.672789i
$575$	−0.442412	−	0.357109i	−0.0184499	−	0.0148925i
$576$	1.99842	−	6.15049i	0.0832673	−	0.256270i
$577$	0.431785	+	6.86303i	0.0179755	+	0.285712i	0.996737	+	0.0807119i	$0.0257194\pi$
$577$	0.431785	+	6.86303i	0.0179755	+	0.285712i	−0.978762	+	0.205000i	$0.934281\pi$
$578$	−18.1377	+	2.29133i	−0.754430	+	0.0953067i
$579$	−38.2251	+	35.8957i	−1.58858	+	1.49178i
$580$	5.74938	−	20.2437i	0.238730	−	0.840573i
$581$	46.7778	+	5.90941i	1.94067	+	0.245164i
$582$	−7.24736	+	22.3051i	−0.300413	+	0.924575i
$583$	11.8109	+	11.0911i	0.489156	+	0.459348i
$584$	−0.286732	+	0.0736202i	−0.0118650	+	0.00304643i
$585$	55.8021	+	19.7112i	2.30713	+	0.814960i
$586$	4.84390	+	5.85527i	0.200100	+	0.241879i
$587$	11.4689	−	2.94472i	0.473374	−	0.121542i	−0.00446358	−	0.999990i	$-0.501421\pi$
$587$	11.4689	−	2.94472i	0.473374	−	0.121542i	0.477837	+	0.878448i	$0.341421\pi$
$588$	2.44005	−	2.94951i	0.100626	−	0.121636i
$589$	−18.5760	+	7.35475i	−0.765410	+	0.303047i
$590$	−7.50907	+	3.30329i	−0.309143	+	0.135994i
$591$	27.1704	+	42.8137i	1.11764	+	1.76112i
$592$	−0.592636	−	3.10671i	−0.0243572	−	0.127685i
$593$	10.3986	+	32.0036i	0.427020	+	1.31423i	0.901047	+	0.433722i	$0.142800\pi$
$593$	10.3986	+	32.0036i	0.427020	+	1.31423i	−0.474027	+	0.880510i	$0.657200\pi$
$594$	22.5438	−	47.9080i	0.924983	−	1.96569i
$595$	0.968337	−	38.1235i	0.0396979	−	1.56291i
$596$	−1.22805	−	0.675125i	−0.0503028	−	0.0276542i
$597$	8.15406	+	4.48273i	0.333723	+	0.183466i
$598$	0.296637	+	0.358573i	0.0121304	+	0.0146631i
$599$	3.77318	+	2.74138i	0.154168	+	0.112010i	0.662195	−	0.749331i	$-0.269625\pi$
$599$	3.77318	+	2.74138i	0.154168	+	0.112010i	−0.508027	+	0.861341i	$0.669625\pi$
$600$	15.0759	−	3.06450i	0.615473	−	0.125108i
$601$	−22.5334	+	16.3715i	−0.919156	+	0.667806i	−0.943314	−	0.331902i	$-0.892310\pi$
$601$	−22.5334	+	16.3715i	−0.919156	+	0.667806i	0.0241576	+	0.999708i	$0.492310\pi$
$602$	−23.3125	−	5.98563i	−0.950147	−	0.243956i
$603$	−2.22958	−	4.73810i	−0.0907954	−	0.192950i
$604$	1.50368	−	7.88257i	0.0611839	−	0.320737i
$605$	6.83023	+	29.7151i	0.277688	+	1.20809i
$606$	−35.2790	−	33.1292i	−1.43311	−	1.34578i
$607$	5.65369	+	4.10765i	0.229476	+	0.166724i	0.696582	−	0.717477i	$-0.254703\pi$
$607$	5.65369	+	4.10765i	0.229476	+	0.166724i	−0.467106	+	0.884202i	$0.654703\pi$
$608$	1.55717	−	3.30916i	0.0631517	−	0.134204i
$609$	52.9976	−	64.0631i	2.14757	−	2.59597i
$610$	−3.89001	+	2.33227i	−0.157502	+	0.0944310i
$611$	1.19556	+	19.0029i	0.0483671	+	0.768773i
$612$	2.41198	−	38.3373i	0.0974985	−	1.54969i
$613$	24.9323	+	9.87141i	1.00701	+	0.398702i	0.812979	−	0.582293i	$-0.197844\pi$
$613$	24.9323	+	9.87141i	1.00701	+	0.398702i	0.194029	+	0.980996i	$0.437844\pi$
$614$	−1.78147	+	2.80715i	−0.0718944	+	0.113287i
$615$	28.5431	−	28.8890i	1.15097	−	1.16492i
$616$	−0.894844	+	14.2231i	−0.0360543	+	0.573066i
$617$	29.6621	+	3.74720i	1.19415	+	0.150856i	0.697171	−	0.716905i	$-0.254442\pi$
$617$	29.6621	+	3.74720i	1.19415	+	0.150856i	0.496981	+	0.867762i	$0.334442\pi$
$618$	7.37403	−	5.35755i	0.296627	−	0.215512i
$619$	4.49921	+	23.5857i	0.180839	+	0.947989i	0.950778	+	0.309873i	$0.100286\pi$
$619$	4.49921	+	23.5857i	0.180839	+	0.947989i	−0.769939	+	0.638117i	$0.779714\pi$
$620$	11.9370	+	2.59287i	0.479402	+	0.104132i
$621$	−0.516474	−	1.09756i	−0.0207254	−	0.0440437i
$622$	3.05030	−	2.86442i	0.122306	−	0.114853i
$623$	−0.429588	+	0.676923i	−0.0172111	+	0.0271203i
$624$	−12.5922			−0.504091
$625$	16.3949	+	18.8735i	0.655796	+	0.754938i
$626$	−22.6058			−0.903511
$627$	29.9270	−	47.1575i	1.19517	−	1.88329i
$628$	1.32968	−	1.24865i	0.0530599	−	0.0498265i
$629$	−7.99875	−	16.9982i	−0.318931	−	0.677763i
$630$	40.5742	+	8.81322i	1.61651	+	0.351127i
$631$	−0.979367	−	5.13402i	−0.0389880	−	0.204382i	0.957463	−	0.288556i	$-0.0931750\pi$
$631$	−0.979367	−	5.13402i	−0.0389880	−	0.204382i	−0.996451	+	0.0841734i	$0.973175\pi$
$632$	−6.58285	+	4.78272i	−0.261852	+	0.190246i
$633$	−52.4194	−	6.62211i	−2.08348	−	0.263205i
$634$	1.08384	−	17.2271i	0.0430446	−	0.684175i
$635$	−2.11592	+	2.14155i	−0.0839675	+	0.0849849i
$636$	−5.38173	+	8.48026i	−0.213400	+	0.336264i
$637$	−4.73409	−	1.87436i	−0.187572	−	0.0742648i
$638$	−2.93308	+	46.6200i	−0.116122	+	1.84570i
$639$	−1.56461	−	24.8687i	−0.0618950	−	0.983792i
$640$	−1.91779	+	1.14982i	−0.0758073	+	0.0454506i
$641$	4.99288	−	6.03536i	0.197207	−	0.238382i	−0.662635	−	0.748942i	$-0.730562\pi$
$641$	4.99288	−	6.03536i	0.197207	−	0.238382i	0.859842	+	0.510560i	$0.170562\pi$
$642$	3.20311	−	6.80694i	0.126416	−	0.268649i
$643$	11.1393	+	8.09315i	0.439290	+	0.319163i	0.785353	−	0.619049i	$-0.212482\pi$
$643$	11.1393	+	8.09315i	0.439290	+	0.319163i	−0.346063	+	0.938211i	$0.612482\pi$
$644$	0.238004	+	0.223500i	0.00937867	+	0.00880715i
$645$	−12.9196	−	56.2071i	−0.508709	−	2.21315i
$646$	4.07056	−	21.3386i	0.160154	−	0.839557i
$647$	2.42371	+	5.15065i	0.0952860	+	0.202493i	0.946788	−	0.321859i	$-0.104308\pi$
$647$	2.42371	+	5.15065i	0.0952860	+	0.202493i	−0.851502	+	0.524352i	$0.824308\pi$
$648$	12.9995	+	3.33771i	0.510670	+	0.131118i
$649$	14.7317	−	10.7032i	0.578272	−	0.420139i
$650$	−10.0732	−	17.8117i	−0.395105	−	0.698631i
$651$	39.0443	+	28.3673i	1.53027	+	1.11180i
$652$	−0.311804	−	0.376906i	−0.0122112	−	0.0147608i
$653$	37.6029	+	20.6724i	1.47151	+	0.808972i	0.997440	−	0.0715133i	$-0.0227828\pi$
$653$	37.6029	+	20.6724i	1.47151	+	0.808972i	0.474074	+	0.880485i	$0.342783\pi$
$654$	−6.97026	−	3.83193i	−0.272559	−	0.149840i
$655$	0.0891259	−	3.50890i	0.00348244	−	0.137104i
$656$	−2.51328	+	5.34099i	−0.0981271	+	0.208531i
$657$	−0.591595	−	1.82074i	−0.0230803	−	0.0710339i
$658$	2.50311	+	13.1218i	0.0975815	+	0.511540i
$659$	19.5041	+	30.7335i	0.759772	+	1.19721i	0.975337	+	0.220719i	$0.0708404\pi$
$659$	19.5041	+	30.7335i	0.759772	+	1.19721i	−0.215566	+	0.976489i	$0.569160\pi$
$660$	−31.2578	+	13.7505i	−1.21671	+	0.535237i
$661$	9.06998	−	3.59106i	0.352781	−	0.139676i	−0.185049	−	0.982729i	$-0.559244\pi$
$661$	9.06998	−	3.59106i	0.352781	−	0.139676i	0.537830	+	0.843053i	$0.319244\pi$
$662$	−1.95792	+	2.36672i	−0.0760968	+	0.0919852i
$663$	−72.4459	+	18.6010i	−2.81357	+	0.722401i
$664$	−10.4673	−	12.6528i	−0.406209	−	0.491023i
$665$	22.1399	+	7.82060i	0.858550	+	0.303270i
$666$	19.8108	−	5.08655i	0.767653	−	0.197100i
$667$	0.780119	+	0.732581i	0.0302063	+	0.0283656i
$668$	−5.50127	+	16.9312i	−0.212851	+	0.655087i
$669$	−10.9769	−	1.38671i	−0.424393	−	0.0536133i
$670$	−0.494660	+	1.74171i	−0.0191104	+	0.0672880i
$671$	7.33905	−	6.89182i	0.283321	−	0.266056i
$672$	−8.76477	+	1.10725i	−0.338108	+	0.0427130i
$673$	−2.50425	−	39.8040i	−0.0965319	−	1.53433i	−0.686635	−	0.727003i	$-0.740913\pi$
$673$	−2.50425	−	39.8040i	−0.0965319	−	1.53433i	0.590103	−	0.807328i	$-0.299087\pi$
$674$	−7.09276	+	21.8293i	−0.273203	+	0.840833i
$675$	13.8856	+	51.4982i	0.534458	+	1.98217i
$676$	1.15851	+	3.56553i	0.0445581	+	0.137136i
$677$	−7.38061	+	2.92219i	−0.283660	+	0.112309i	−0.505646	−	0.862741i	$-0.668746\pi$
$677$	−7.38061	+	2.92219i	−0.283660	+	0.112309i	0.221987	+	0.975050i	$0.428746\pi$
$678$	5.65809	−	29.6607i	0.217298	−	1.13911i
$679$	21.7133	−	2.74302i	0.833278	−	0.105268i
$680$	−9.33501	+	9.44812i	−0.357981	+	0.362319i
$681$	36.7466	−	20.2016i	1.40813	−	0.774128i
$682$	−27.1145			−1.03827
$683$	−22.0524	+	12.1234i	−0.843813	+	0.463890i	−0.844148	−	0.536110i	$-0.819893\pi$
$683$	−22.0524	+	12.1234i	−0.843813	+	0.463890i	0.000335296		1.00000i	$0.499893\pi$
$684$	21.9904	+	8.70663i	0.840826	+	0.332907i
$685$	−3.82826	−	2.56812i	−0.146270	−	0.0981230i
$686$	16.0074	+	4.11000i	0.611165	+	0.156921i
$687$	−10.3231	−	16.2667i	−0.393853	−	0.620612i
$688$	4.49163	+	7.07768i	0.171242	+	0.269834i
$689$	12.9397	+	3.32234i	0.492962	+	0.126571i
$690$	−0.213738	+	0.752575i	−0.00813685	+	0.0286500i
$691$	−30.8354	−	12.2086i	−1.17303	−	0.464437i	−0.300877	−	0.953663i	$-0.597279\pi$
$691$	−30.8354	−	12.2086i	−1.17303	−	0.464437i	−0.872157	+	0.489226i	$0.837279\pi$
$692$	−17.2608	+	9.48922i	−0.656158	+	0.360726i
$693$	−92.1630			−3.50098
$694$	2.60283	−	1.43092i	0.0988022	−	0.0543170i
$695$	4.91966	−	32.3199i	0.186613	−	1.22596i
$696$	−28.7288	+	3.62929i	−1.08896	+	0.137568i
$697$	−6.56989	+	34.4406i	−0.248852	+	1.30453i
$698$	33.8763	−	13.4126i	1.28224	−	0.507673i
$699$	−17.9036	−	55.1017i	−0.677178	−	2.08414i
$700$	−8.57767	−	11.5120i	−0.324206	−	0.435113i
$701$	−4.45543	+	13.7124i	−0.168279	+	0.517910i	−0.999263	−	0.0383867i	$-0.987778\pi$
$701$	−4.45543	+	13.7124i	−0.168279	+	0.517910i	0.830984	+	0.556297i	$0.187778\pi$
$702$	−2.74126	−	43.5711i	−0.103462	−	1.64448i
$703$	11.4756	−	1.44971i	0.432811	−	0.0546767i
$704$	3.61818	−	3.39769i	0.136365	−	0.128055i
$705$	−25.1736	+	19.7705i	−0.948091	+	0.744602i
$706$	9.28543	+	1.17302i	0.349462	+	0.0441473i
$707$	−13.9558	+	42.9516i	−0.524863	+	1.61536i
$708$	8.22869	+	7.72726i	0.309253	+	0.290408i
$709$	45.4138	−	11.6603i	1.70555	−	0.437911i	0.734856	−	0.678224i	$-0.237250\pi$
$709$	45.4138	−	11.6603i	1.70555	−	0.437911i	0.970696	+	0.240312i	$0.0772499\pi$
$710$	−5.23957	+	6.83945i	−0.196637	+	0.256680i
$711$	−33.5419	−	40.5452i	−1.25792	−	1.52057i
$712$	0.270454	−	0.0694407i	0.0101357	−	0.00260240i
$713$	−0.395961	+	0.478635i	−0.0148289	+	0.0179250i
$714$	−48.7903	+	19.3174i	−1.82593	+	0.722937i
$715$	30.2423	+	33.8896i	1.13100	+	1.26740i
$716$	−13.1769	−	20.7634i	−0.492443	−	0.775965i
$717$	4.67145	+	24.4886i	0.174459	+	0.914544i
$718$	−3.28397	−	10.1070i	−0.122557	−	0.377190i
$719$	4.62802	−	9.83504i	0.172596	−	0.366785i	−0.799749	−	0.600335i	$-0.795034\pi$
$719$	4.62802	−	9.83504i	0.172596	−	0.366785i	0.972345	+	0.233550i	$0.0750341\pi$
$720$	−8.19997	−	11.9110i	−0.305595	−	0.443896i
$721$	−7.45366	−	4.09768i	−0.277589	−	0.152606i
$722$	−4.92895	−	2.70971i	−0.183436	−	0.100845i
$723$	48.3440	+	58.4379i	1.79793	+	2.17333i
$724$	−7.67399	−	5.57548i	−0.285202	−	0.207211i
$725$	−28.1155	−	37.7336i	−1.04418	−	1.40139i
$726$	33.9419	−	24.6602i	1.25970	−	0.915227i
$727$	32.6867	+	8.39253i	1.21228	+	0.311262i	0.800115	−	0.599846i	$-0.204771\pi$
$727$	32.6867	+	8.39253i	1.21228	+	0.311262i	0.412169	+	0.911108i	$0.364771\pi$
$728$	5.00324	+	10.6324i	0.185432	+	0.394064i
$729$	2.18706	−	11.4650i	0.0810024	−	0.424629i
$730$	−0.259228	+	0.609078i	−0.00959448	+	0.0225430i
$731$	36.2965	+	34.0847i	1.34247	+	1.26067i
$732$	5.04910	+	3.66839i	0.186620	+	0.135587i
$733$	−19.1133	+	40.6178i	−0.705966	+	1.50025i	0.153002	+	0.988226i	$0.451106\pi$
$733$	−19.1133	+	40.6178i	−0.705966	+	1.50025i	−0.858968	+	0.512028i	$0.828894\pi$
$734$	15.2818	−	18.4725i	0.564062	−	0.681833i
$735$	−1.91749	−	8.34209i	−0.0707277	−	0.307702i
$736$	−0.00713998	−	0.113487i	−0.000263183	−	0.00418318i
$737$	0.252354	−	4.01105i	0.00929557	−	0.147749i
$738$	−35.4926	−	14.0525i	−1.30650	−	0.517281i
$739$	−1.72916	+	2.72471i	−0.0636080	+	0.100230i	−0.874643	−	0.484767i	$-0.838904\pi$
$739$	−1.72916	+	2.72471i	−0.0636080	+	0.100230i	0.811035	+	0.584997i	$0.198904\pi$
$740$	−6.32048	−	3.17265i	−0.232346	−	0.116629i
$741$	2.89166	−	45.9616i	0.106228	−	1.68844i
$742$	9.29877	+	1.17471i	0.341369	+	0.0431249i
$743$	41.4957	−	30.1484i	1.52233	−	1.10604i	0.562010	−	0.827130i	$-0.310028\pi$
$743$	41.4957	−	30.1484i	1.52233	−	1.10604i	0.960318	−	0.278906i	$-0.0899719\pi$
$744$	−3.14959	−	16.5107i	−0.115470	−	0.605312i
$745$	−2.86833	+	1.26180i	−0.105088	+	0.0462287i
$746$	7.26040	+	15.4291i	0.265822	+	0.564901i
$747$	77.4137	−	72.6963i	2.83242	−	2.65982i
$748$	15.7972	−	24.8925i	0.577604	−	0.910159i
$749$	−7.02025			−0.256514
$750$	15.0612	−	30.9279i	0.549956	−	1.12933i
$751$	−36.5710			−1.33449			−0.667247	−	0.744836i	$-0.732528\pi$
$751$	−36.5710			−1.33449			−0.667247	+	0.744836i	$0.732528\pi$
$752$	2.49291	−	3.92820i	0.0909070	−	0.143247i
$753$	−26.0765	+	24.4875i	−0.950282	+	0.892374i
$754$	16.3994	+	34.8505i	0.597232	+	1.26918i
$755$	−11.9473	−	13.3881i	−0.434806	−	0.487244i
$756$	−5.73931	−	30.0865i	−0.208737	−	1.09424i
$757$	−1.05906	+	0.769452i	−0.0384922	+	0.0279662i	−0.606865	−	0.794805i	$-0.707573\pi$
$757$	−1.05906	+	0.769452i	−0.0384922	+	0.0279662i	0.568373	+	0.822771i	$0.307573\pi$
$758$	26.7224	+	3.37583i	0.970603	+	0.122616i
$759$	0.109040	−	1.73314i	0.00395789	−	0.0629088i
$760$	−3.75646	−	7.26400i	−0.136261	−	0.263493i
$761$	19.2962	−	30.4059i	0.699485	−	1.10221i	−0.289922	−	0.957050i	$-0.593629\pi$
$761$	19.2962	−	30.4059i	0.699485	−	1.10221i	0.989408	−	0.145163i	$-0.0463705\pi$
$762$	3.85163	+	1.52497i	0.139530	+	0.0552437i
$763$	−0.466071	+	7.40799i	−0.0168729	+	0.268187i
$764$	−1.47916	−	23.5106i	−0.0535141	−	0.850583i
$765$	−64.7711	−	56.4139i	−2.34181	−	2.03965i
$766$	3.55300	−	4.29483i	0.128375	−	0.155179i
$767$	6.39285	−	13.5855i	0.230833	−	0.490544i
$768$	2.48922	+	1.80853i	0.0898221	+	0.0652596i
$769$	20.2562	+	19.0218i	0.730456	+	0.685943i	0.957659	−	0.287904i	$-0.0929584\pi$
$769$	20.2562	+	19.0218i	0.730456	+	0.685943i	−0.227204	+	0.973847i	$0.572958\pi$
$770$	24.0301	+	20.9296i	0.865984	+	0.754249i
$771$	2.35229	−	12.3311i	0.0847156	−	0.444095i
$772$	−7.25634	−	15.4205i	−0.261161	−	0.554996i
$773$	3.11438	+	0.799637i	0.112017	+	0.0287610i	0.304282	−	0.952582i	$-0.401583\pi$
$773$	3.11438	+	0.799637i	0.112017	+	0.0287610i	−0.192266	+	0.981343i	$0.561583\pi$
$774$	−43.8572	+	31.8641i	−1.57641	+	1.14533i
$775$	20.8349	−	17.6630i	0.748411	−	0.634474i
$776$	−6.16664	−	4.48033i	−0.221369	−	0.160834i
$777$	−17.8102	−	21.5288i	−0.638937	−	0.772343i
$778$	−16.0248	−	8.80971i	−0.574517	−	0.315843i
$779$	−18.9175	−	10.4000i	−0.677791	−	0.372619i
$780$	−17.1233	+	22.3519i	−0.613114	+	0.800326i
$781$	8.14280	−	17.3043i	0.291372	−	0.619197i
$782$	−0.208719	−	0.642370i	−0.00746376	−	0.0229711i
$783$	−18.8121	−	98.6164i	−0.672289	−	3.52426i
$784$	0.666634	+	1.05045i	0.0238084	+	0.0375160i
$785$	−0.408283	−	4.05822i	−0.0145723	−	0.144844i
$786$	−4.49066	+	1.77798i	−0.160177	+	0.0634184i
$787$	−17.1138	+	20.6870i	−0.610041	+	0.737413i	−0.981590	−	0.191000i	$-0.938827\pi$
$787$	−17.1138	+	20.6870i	−0.610041	+	0.737413i	0.371549	+	0.928413i	$0.378827\pi$
$788$	−15.9626	+	4.09849i	−0.568642	+	0.146003i
$789$	51.7180	+	62.5163i	1.84121	+	2.22564i
$790$	−0.461992	+	18.1887i	−0.0164369	+	0.647124i
$791$	−27.2927	+	7.00757i	−0.970416	+	0.249160i
$792$	23.3988	+	21.9729i	0.831440	+	0.780774i
$793$	2.56523	−	7.89498i	0.0910941	−	0.280359i
$794$	−19.2706	−	2.43444i	−0.683887	−	0.0863950i
$795$	7.73468	+	21.0847i	0.274321	+	0.747797i
$796$	−2.20455	+	2.07021i	−0.0781382	+	0.0733767i
$797$	−4.04914	+	0.511525i	−0.143428	+	0.0181192i	−0.196719	−	0.980460i	$-0.563029\pi$
$797$	−4.04914	+	0.511525i	−0.143428	+	0.0181192i	0.0532914	+	0.998579i	$0.483029\pi$
$798$	−2.02873	−	32.2458i	−0.0718164	−	1.14149i
$799$	8.53965	−	26.2824i	0.302111	−	0.929803i
$800$	−0.566883	+	4.96776i	−0.0200423	+	0.175637i
$801$	0.558010	+	1.71738i	0.0197163	+	0.0606805i
$802$	−31.2674	+	12.3797i	−1.10409	+	0.437141i
$803$	0.275325	−	1.44331i	0.00971602	−	0.0509332i
$804$	2.47174	−	0.312254i	0.0871716	−	0.0110123i
$805$	0.720374	−	0.118547i	0.0253898	−	0.00417822i
$806$	−19.5917	+	10.7706i	−0.690088	+	0.379379i
$807$	−23.8508			−0.839586
$808$	13.7834	−	7.57751i	0.484899	−	0.266576i
$809$	−3.67417	−	1.45471i	−0.129177	−	0.0511448i	0.302647	−	0.953103i	$-0.402130\pi$
$809$	−3.67417	−	1.45471i	−0.129177	−	0.0511448i	−0.431824	+	0.901958i	$0.642130\pi$
$810$	23.6019	−	18.5362i	0.829286	−	0.651296i
$811$	−19.4781	−	5.00112i	−0.683967	−	0.175613i	−0.109311	−	0.994008i	$-0.534864\pi$
$811$	−19.4781	−	5.00112i	−0.683967	−	0.175613i	−0.574657	+	0.818395i	$0.694864\pi$
$812$	14.4792	+	22.8156i	0.508122	+	0.800672i
$813$	12.5465	+	19.7702i	0.440027	+	0.693371i
$814$	15.2048	+	3.90392i	0.532927	+	0.136832i
$815$	−1.09303	+	0.0409394i	−0.0382873	+	0.00143404i
$816$	16.9926	+	6.72786i	0.594861	+	0.235522i
$817$	−26.8651	+	14.7692i	−0.939890	+	0.516709i
$818$	3.52803			0.123355
$819$	−66.5927	+	36.6096i	−2.32694	+	1.27924i
$820$	6.06293	+	11.7241i	0.211727	+	0.409423i
$821$	−18.3375	+	2.31656i	−0.639982	+	0.0808485i	−0.438626	−	0.898670i	$-0.644535\pi$
$821$	−18.3375	+	2.31656i	−0.639982	+	0.0808485i	−0.201356	+	0.979518i	$0.564535\pi$
$822$	−1.18860	+	6.23086i	−0.0414572	+	0.217326i
$823$	13.7179	−	5.43130i	0.478175	−	0.189323i	−0.116658	−	0.993172i	$-0.537218\pi$
$823$	13.7179	−	5.43130i	0.478175	−	0.189323i	0.594833	+	0.803849i	$0.297218\pi$
$824$	0.915426	+	2.81739i	0.0318904	+	0.0981485i
$825$	−18.0975	+	74.1829i	−0.630076	+	2.58272i
$826$	3.25514	−	10.0183i	0.113261	−	0.348581i
$827$	−0.606868	−	9.64588i	−0.0211029	−	0.335420i	−0.994386	−	0.105813i	$-0.966256\pi$
$827$	−0.606868	−	9.64588i	−0.0211029	−	0.335420i	0.973283	−	0.229608i	$-0.0737443\pi$
$828$	0.729572	−	0.0921664i	0.0253544	−	0.00320300i
$829$	9.51582	−	8.93595i	0.330498	−	0.310358i	−0.501478	−	0.865171i	$-0.667210\pi$
$829$	9.51582	−	8.93595i	0.330498	−	0.310358i	0.831975	+	0.554812i	$0.187210\pi$
$830$	−36.6933	+	1.37434i	−1.27364	+	0.0477040i
$831$	−54.1710	−	6.84339i	−1.87917	−	0.237395i
$832$	1.26467	−	3.89225i	0.0438445	−	0.134940i
$833$	5.38701	+	5.05874i	0.186649	+	0.175275i
$834$	−43.5714	+	11.1872i	−1.50876	+	0.387383i
$835$	22.5730	+	32.7888i	0.781172	+	1.13470i
$836$	11.5707	+	13.9866i	0.400183	+	0.483738i
$837$	56.4442	−	14.4924i	1.95100	−	0.500931i
$838$	4.75566	−	5.74860i	0.164281	−	0.198582i
$839$	−7.95201	+	3.14842i	−0.274534	+	0.108696i	−0.501358	−	0.865240i	$-0.667166\pi$
$839$	−7.95201	+	3.14842i	−0.274534	+	0.108696i	0.226824	+	0.973936i	$0.427166\pi$
$840$	−9.95324	+	17.0637i	−0.343419	+	0.588753i
$841$	31.9205	+	50.2986i	1.10071	+	1.73444i
$842$	0.803569	+	4.21246i	0.0276928	+	0.145171i
$843$	−27.7282	−	85.3387i	−0.955011	−	2.93922i
$844$	7.31153	−	15.5378i	0.251673	−	0.534833i
$845$	7.90443	+	2.79212i	0.271921	+	0.0960518i
$846$	26.3658	+	14.4947i	0.906476	+	0.498339i
$847$	−34.3084	−	18.8612i	−1.17885	−	0.648079i
$848$	−2.08075	−	2.51519i	−0.0714532	−	0.0863721i
$849$	54.3625	+	39.4966i	1.86571	+	1.35552i
$850$	4.07687	+	29.4181i	0.139836	+	1.00903i
$851$	0.290953	−	0.211389i	0.00997373	−	0.00724634i
$852$	11.4829	+	2.94831i	0.393398	+	0.101007i
$853$	−0.451671	−	0.959851i	−0.0154649	−	0.0328647i	0.896945	−	0.442141i	$-0.145781\pi$
$853$	−0.451671	−	0.959851i	−0.0154649	−	0.0328647i	−0.912410	+	0.409277i	$0.865781\pi$
$854$	1.09131	−	5.72085i	0.0373439	−	0.195763i
$855$	45.3583	−	27.1948i	1.55122	−	0.930041i
$856$	1.78233	+	1.67372i	0.0609189	+	0.0572067i
$857$	7.44441	+	5.40868i	0.254296	+	0.184757i	0.707629	−	0.706585i	$-0.249765\pi$
$857$	7.44441	+	5.40868i	0.254296	+	0.184757i	−0.453333	+	0.891341i	$0.649765\pi$
$858$	26.6113	−	56.5520i	0.908496	−	1.93065i
$859$	0.192723	−	0.232962i	0.00657562	−	0.00794856i	−0.767215	−	0.641390i	$-0.778358\pi$
$859$	0.192723	−	0.232962i	0.00657562	−	0.00794856i	0.773791	+	0.633441i	$0.218358\pi$
$860$	18.6712	+	1.65158i	0.636683	+	0.0563184i
$861$	3.27438	+	52.0448i	0.111591	+	1.77368i
$862$	−2.31610	+	36.8133i	−0.0788866	+	1.25387i
$863$	−15.6519	−	6.19703i	−0.532798	−	0.210949i	0.0862920	−	0.996270i	$-0.472498\pi$
$863$	−15.6519	−	6.19703i	−0.532798	−	0.210949i	−0.619090	+	0.785320i	$0.712498\pi$
$864$	−5.71592	+	9.00684i	−0.194459	+	0.306419i
$865$	−6.62799	+	43.5428i	−0.225358	+	1.48050i
$866$	0.820882	−	13.0475i	0.0278947	−	0.443374i
$867$	55.8071	+	7.05007i	1.89531	+	0.239433i
$868$	−12.6897	+	9.21960i	−0.430716	+	0.312934i
$869$	−7.56769	−	39.6712i	−0.256716	−	1.34575i
$870$	−32.6243	+	55.9306i	−1.10607	+	1.89623i
$871$	−1.41096	−	2.99844i	−0.0478085	−	0.101598i
$872$	1.88450	−	1.76966i	0.0638171	−	0.0599282i
$873$	26.4131	−	41.6203i	0.893947	−	1.40863i
$874$	0.415867			0.0140669
$875$	−32.0988	−	0.428598i	−1.08514	−	0.0144893i
$876$	0.910847			0.0307747
$877$	−11.5484	+	18.1974i	−0.389962	+	0.614482i	−0.981424	−	0.191851i	$-0.938551\pi$
$877$	−11.5484	+	18.1974i	−0.389962	+	0.614482i	0.591462	+	0.806333i	$0.298551\pi$
$878$	−21.3830	+	20.0800i	−0.721642	+	0.677667i
$879$	−9.95537	−	21.1562i	−0.335786	−	0.713582i
$880$	−1.11098	−	11.0428i	−0.0374511	−	0.372253i
$881$	−9.07180	−	47.5561i	−0.305637	−	1.60220i	−0.721258	−	0.692667i	$-0.756436\pi$
$881$	−9.07180	−	47.5561i	−0.305637	−	1.60220i	0.415621	−	0.909538i	$-0.363564\pi$
$882$	−6.50915	+	4.72918i	−0.219175	+	0.159240i
$883$	1.35373	+	0.171016i	0.0455568	+	0.00575516i	0.148079	−	0.988976i	$-0.452691\pi$
$883$	1.35373	+	0.171016i	0.0455568	+	0.00575516i	−0.102522	+	0.994731i	$0.532691\pi$
$884$	1.52639	−	24.2612i	0.0513380	−	0.815993i
$885$	24.9060	−	4.09861i	0.837207	−	0.137773i
$886$	12.3656	−	19.4851i	0.415430	−	0.654613i
$887$	15.9661	+	6.32143i	0.536089	+	0.212253i	0.620540	−	0.784175i	$-0.286913\pi$
$887$	15.9661	+	6.32143i	0.536089	+	0.212253i	−0.0844505	+	0.996428i	$0.526913\pi$
$888$	−0.611030	+	9.71204i	−0.0205048	+	0.325915i
$889$	−0.242731	−	3.85810i	−0.00814094	−	0.129397i
$890$	0.244512	−	0.574500i	0.00819605	−	0.0192573i
$891$	−42.4620	+	51.3277i	−1.42253	+	1.71954i
$892$	1.53108	−	3.25371i	0.0512643	−	0.108942i
$893$	13.7655	+	10.0012i	0.460645	+	0.334678i
$894$	3.14322	+	2.95168i	0.105125	+	0.0987188i
$895$	−54.7747	−	4.84515i	−1.83092	−	0.161956i
$896$	0.538020	−	2.82040i	0.0179740	−	0.0942230i
$897$	−0.609661	−	1.29560i	−0.0203560	−	0.0432587i
$898$	36.6154	+	9.40125i	1.22187	+	0.313724i
$899$	−41.5937	+	30.2196i	−1.38723	+	1.00788i
$900$	−32.2933	−	1.64156i	−1.07644	−	0.0547186i
$901$	−15.6865	−	11.3969i	−0.522592	−	0.379685i
$902$	−18.6752	−	22.5745i	−0.621817	−	0.751647i
$903$	64.8955	+	35.6766i	2.15959	+	1.18724i
$904$	8.59989	+	4.72783i	0.286028	+	0.157245i
$905$	−20.3322	+	6.04005i	−0.675865	+	0.200778i
$906$	−10.5128	+	22.3409i	−0.349266	+	0.742228i
$907$	6.63211	+	20.4115i	0.220216	+	0.677754i	0.998742	+	0.0501421i	$0.0159674\pi$
$907$	6.63211	+	20.4115i	0.220216	+	0.677754i	−0.778527	+	0.627612i	$0.784033\pi$
$908$	2.55376	+	13.3873i	0.0847497	+	0.444273i
$909$	54.5041	+	85.8847i	1.80779	+	2.84862i
$910$	25.6768	+	5.57733i	0.851178	+	0.184887i
$911$	20.0987	−	7.95765i	0.665901	−	0.263649i	−0.0107616	−	0.999942i	$-0.503426\pi$
$911$	20.0987	−	7.95765i	0.665901	−	0.263649i	0.676663	+	0.736293i	$0.263426\pi$
$912$	−7.17277	+	8.67039i	−0.237514	+	0.287105i
$913$	78.9448	−	20.2696i	2.61269	−	0.670825i
$914$	19.2024	+	23.2117i	0.635159	+	0.767775i
$915$	13.3776	−	3.97405i	0.442249	−	0.131378i
$916$	6.06482	−	1.55718i	0.200387	−	0.0514507i
$917$	3.28554	+	3.08533i	0.108498	+	0.101886i
$918$	−19.5803	+	60.2620i	−0.646247	+	1.98894i
$919$	43.6490	+	5.51415i	1.43985	+	0.181895i	0.806162	−	0.591695i	$-0.201541\pi$
$919$	43.6490	+	5.51415i	1.43985	+	0.181895i	0.633686	+	0.773590i	$0.281541\pi$
$920$	−0.211155	−	0.141650i	−0.00696158	−	0.00467005i
$921$	7.45710	−	7.00269i	0.245720	−	0.230746i
$922$	6.44799	−	0.814570i	0.212353	−	0.0268264i
$923$	−0.990141	−	15.7378i	−0.0325909	−	0.518017i
$924$	13.5501	−	41.7029i	0.445765	−	1.37192i
$925$	−14.2265	+	6.90494i	−0.467764	+	0.227033i
$926$	11.4468	+	35.2296i	0.376164	+	1.15772i
$927$	−17.8124	+	7.05244i	−0.585037	+	0.231632i
$928$	1.76350	−	9.24459i	0.0578897	−	0.303469i
$929$	−48.1005	+	6.07651i	−1.57813	+	0.199364i	−0.865036	−	0.501709i	$-0.832705\pi$
$929$	−48.1005	+	6.07651i	−1.57813	+	0.199364i	−0.713090	+	0.701073i	$0.752705\pi$
$930$	−33.5905	−	16.8612i	−1.10147	−	0.552901i
$931$	−3.98723	+	2.19200i	−0.130676	+	0.0718399i
$932$	18.8301			0.616800
$933$	−11.2823	+	6.20248i	−0.369365	+	0.203060i
$934$	−23.1904	−	9.18173i	−0.758813	−	0.300435i
$935$	−22.7040	−	61.8908i	−0.742499	−	2.02405i
$936$	25.6351	+	6.58198i	0.837910	+	0.215139i
$937$	13.7316	+	21.6376i	0.448593	+	0.706870i	0.991091	−	0.133188i	$-0.0425213\pi$
$937$	13.7316	+	21.6376i	0.448593	+	0.706870i	−0.542498	+	0.840057i	$0.682521\pi$
$938$	−1.24575	−	1.96299i	−0.0406752	−	0.0640939i
$939$	67.3696	+	17.2976i	2.19852	+	0.564485i
$940$	−3.58283	−	9.76678i	−0.116859	−	0.318557i
$941$	−7.37916	−	2.92162i	−0.240554	−	0.0952420i	0.244755	−	0.969585i	$-0.421293\pi$
$941$	−7.37916	−	2.92162i	−0.240554	−	0.0952420i	−0.485308	+	0.874343i	$0.661293\pi$
$942$	−4.91812	+	2.70376i	−0.160241	+	0.0880933i
$943$	−0.671211			−0.0218576
$944$	−3.21493	+	1.76742i	−0.104637	+	0.0575247i
$945$	−61.2100	−	30.7252i	−1.99116	−	0.999490i
$946$	−41.2784	+	5.21467i	−1.34208	+	0.169544i
$947$	10.0700	−	52.7890i	0.327232	−	1.71541i	−0.315163	−	0.949037i	$-0.602059\pi$
$947$	10.0700	−	52.7890i	0.327232	−	1.71541i	0.642396	−	0.766373i	$-0.277941\pi$
$948$	23.2778	−	9.21632i	0.756027	−	0.299332i
$949$	−0.374383	−	1.15223i	−0.0121530	−	0.0374030i
$950$	−18.0022	−	3.20992i	−0.584069	−	0.104144i
$951$	−16.4119	+	50.5106i	−0.532191	+	1.63792i
$952$	−1.07088	−	17.0212i	−0.0347075	−	0.551660i
$953$	−49.5264	+	6.25663i	−1.60432	+	0.202672i	−0.875910	−	0.482474i	$-0.839738\pi$
$953$	−49.5264	+	6.25663i	−1.60432	+	0.202672i	−0.728406	+	0.685146i	$0.759738\pi$
$954$	15.3888	−	14.4510i	0.498230	−	0.467869i
$955$	−43.7441	−	29.3450i	−1.41553	−	0.949581i
$956$	−8.03862	−	1.01551i	−0.259987	−	0.0328440i
$957$	44.4139	−	136.692i	1.43570	−	4.41862i
$958$	−18.3269	−	17.2101i	−0.592114	−	0.556032i
$959$	5.73340	−	1.47209i	0.185141	−	0.0475362i
$960$	6.59519	−	1.95922i	0.212859	−	0.0632335i
$961$	0.737503	+	0.891488i	0.0237904	+	0.0287577i
$962$	12.5370	−	3.21895i	0.404209	−	0.103783i
$963$	−10.0789	+	12.1833i	−0.324787	+	0.392600i
$964$	−22.9185	+	9.07408i	−0.738156	+	0.292257i
$965$	−37.2398	−	8.08895i	−1.19879	−	0.260392i
$966$	−0.538277	−	0.848189i	−0.0173188	−	0.0272900i
$967$	−0.281376	−	1.47503i	−0.00904846	−	0.0474337i	0.977477	−	0.211044i	$-0.0676862\pi$
$967$	−0.281376	−	1.47503i	−0.00904846	−	0.0474337i	−0.986525	+	0.163610i	$0.947686\pi$
$968$	4.21361	+	12.9682i	0.135431	+	0.416812i
$969$	−28.4590	+	60.4784i	−0.914233	+	1.94284i
$970$	−16.3385	+	4.85364i	−0.524597	+	0.155841i
$971$	48.4408	+	26.6305i	1.55454	+	0.854615i	0.999744	+	0.0226278i	$0.00720327\pi$
$971$	48.4408	+	26.6305i	1.55454	+	0.854615i	0.554795	+	0.831987i	$0.312797\pi$
$972$	−8.14313	−	4.47672i	−0.261191	−	0.143591i
$973$	26.7583	+	32.3453i	0.857833	+	1.03694i
$974$	−21.7532	−	15.8047i	−0.697019	−	0.506414i
$975$	16.3910	+	60.7899i	0.524932	+	1.94684i
$976$	−1.64100	+	1.19225i	−0.0525270	+	0.0381631i
$977$	8.37151	+	2.14944i	0.267828	+	0.0687667i	0.380216	−	0.924898i	$-0.375850\pi$
$977$	8.37151	+	2.14944i	0.267828	+	0.0687667i	−0.112387	+	0.993664i	$0.535850\pi$
$978$	0.640831	+	1.36184i	0.0204915	+	0.0435467i
$979$	−0.259695	+	1.36137i	−0.00829988	+	0.0435095i
$980$	2.77112	+	0.245122i	0.0885203	+	0.00783015i
$981$	12.1870	+	11.4444i	0.389103	+	0.365392i
$982$	3.59059	+	2.60872i	0.114580	+	0.0832475i
$983$	2.55358	−	5.42664i	0.0814466	−	0.173083i	−0.859956	−	0.510369i	$-0.829509\pi$
$983$	2.55358	−	5.42664i	0.0814466	−	0.173083i	0.941402	+	0.337286i	$0.109509\pi$
$984$	11.5769	−	13.9940i	0.369057	−	0.446113i
$985$	−14.4314	+	33.9078i	−0.459824	+	1.08039i
$986$	−3.51010	−	55.7914i	−0.111784	−	1.77676i
$987$	2.58080	−	41.0207i	0.0821478	−	1.30570i
$988$	13.9164	+	5.50987i	0.442738	+	0.175292i
$989$	−0.510748	+	0.804811i	−0.0162409	+	0.0255915i
$990$	70.8218	−	11.6546i	2.25087	−	0.370409i
$991$	0.680111	−	10.8101i	0.0216044	−	0.343393i	−0.972345	−	0.233551i	$-0.924965\pi$
$991$	0.680111	−	10.8101i	0.0216044	−	0.343393i	0.993949	−	0.109842i	$-0.0350345\pi$
$992$	5.41980	+	0.684680i	0.172079	+	0.0217386i
$993$	7.64594	−	5.55510i	0.242637	−	0.176286i
$994$	−2.07304	−	10.8672i	−0.0657527	−	0.344688i
$995$	0.676917	+	6.72836i	0.0214597	+	0.213303i
$996$	21.5128	+	45.7170i	0.681659	+	1.44860i
$997$	5.16105	−	4.84654i	0.163452	−	0.153492i	−0.598505	−	0.801119i	$-0.704239\pi$
$997$	5.16105	−	4.84654i	0.163452	−	0.153492i	0.761957	+	0.647627i	$0.224239\pi$
$998$	−0.482882	+	0.760900i	−0.0152854	+	0.0240859i
$999$	−33.7383			−1.06743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.g.b.231.2	yes	140
125.46	even	25	inner	250.2.g.b.171.2	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.g.b.171.2	✓	140	125.46	even	25	inner
250.2.g.b.231.2	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)

\(f(q)\)	\(=\)	\(q+(0.535827 - 0.844328i) q^{2} +(-2.24293 + 2.10625i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-2.18511 - 0.474634i) q^{5} +(0.576544 + 3.02235i) q^{6} +(2.32290 - 1.68768i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.406067 - 6.45425i) q^{9} +O(q^{10})\)	\(q+(0.535827 - 0.844328i) q^{2} +(-2.24293 + 2.10625i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-2.18511 - 0.474634i) q^{5} +(0.576544 + 3.02235i) q^{6} +(2.32290 - 1.68768i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.406067 - 6.45425i) q^{9} +(-1.57159 + 1.59063i) q^{10} +(2.65953 - 4.19075i) q^{11} +(2.86078 + 1.13266i) q^{12} +(0.256974 - 4.08448i) q^{13} +(-0.180288 - 2.86559i) q^{14} +(5.90075 - 3.53782i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(-2.52907 + 5.37454i) q^{17} +(-5.23192 - 3.80121i) q^{18} +(-2.66600 - 2.50355i) q^{19} +(0.500914 + 2.17924i) q^{20} +(-1.65541 + 8.67795i) q^{21} +(-2.11332 - 4.49104i) q^{22} +(-0.110139 - 0.0282788i) q^{23} +(2.48922 - 1.80853i) q^{24} +(4.54944 + 2.07426i) q^{25} +(-3.31095 - 2.40554i) q^{26} +(6.79970 + 8.21943i) q^{27} +(-2.51610 - 1.38324i) q^{28} +(-8.24718 - 4.53392i) q^{29} +(0.174697 - 6.87783i) q^{30} +(2.32598 - 4.94296i) q^{31} +(0.309017 + 0.951057i) q^{32} +(2.86163 + 15.0012i) q^{33} +(3.18273 + 5.01519i) q^{34} +(-5.87683 + 2.58525i) q^{35} +(-6.01287 + 2.38066i) q^{36} +(-2.01600 + 2.43692i) q^{37} +(-3.54233 + 0.909516i) q^{38} +(8.02656 + 9.70245i) q^{39} +(2.10840 + 0.744759i) q^{40} +(5.71733 - 1.46796i) q^{41} +(6.44002 + 6.04758i) q^{42} +(2.59037 - 7.97234i) q^{43} +(-4.92428 - 0.622081i) q^{44} +(-3.95071 + 13.9105i) q^{45} +(-0.0828918 + 0.0778406i) q^{46} +(-4.61577 + 0.583107i) q^{47} +(-0.193197 - 3.07078i) q^{48} +(0.384455 - 1.18323i) q^{49} +(4.18907 - 2.72978i) q^{50} +(-5.64761 - 17.3816i) q^{51} +(-3.80516 + 1.50657i) q^{52} +(-0.611671 + 3.20649i) q^{53} +(10.5834 - 1.33699i) q^{54} +(-7.80046 + 7.89497i) q^{55} +(-2.51610 + 1.38324i) q^{56} +11.2527 q^{57} +(-8.24718 + 4.53392i) q^{58} +(3.41110 + 1.35055i) q^{59} +(-5.71354 - 3.83283i) q^{60} +(1.96466 + 0.504438i) q^{61} +(-2.92715 - 4.61246i) q^{62} +(-9.94947 - 15.6779i) q^{63} +(0.968583 + 0.248690i) q^{64} +(-2.50015 + 8.80309i) q^{65} +(14.1993 + 5.62189i) q^{66} +(0.709563 - 0.390085i) q^{67} +5.93986 q^{68} +(0.306595 - 0.168552i) q^{69} +(-0.966159 + 6.34722i) q^{70} +(3.82270 - 0.482919i) q^{71} +(-1.21180 + 6.35246i) q^{72} +(0.275244 - 0.108977i) q^{73} +(0.977336 + 3.00793i) q^{74} +(-14.5730 + 4.92985i) q^{75} +(-1.13015 + 3.47823i) q^{76} +(-0.894844 - 14.2231i) q^{77} +(12.4929 - 1.57822i) q^{78} +(5.93151 - 5.57006i) q^{79} +(1.75856 - 1.38112i) q^{80} +(-13.3153 - 1.68212i) q^{81} +(1.82406 - 5.61387i) q^{82} +(11.9706 + 11.2411i) q^{83} +(8.55688 - 2.19703i) q^{84} +(8.07724 - 10.5436i) q^{85} +(-5.34328 - 6.45892i) q^{86} +(28.0474 - 7.20135i) q^{87} +(-3.16380 + 3.82438i) q^{88} +(-0.259618 + 0.102790i) q^{89} +(9.62816 + 10.7893i) q^{90} +(-6.29639 - 9.92152i) q^{91} +(0.0213073 + 0.111697i) q^{92} +(5.19410 + 15.9858i) q^{93} +(-1.98092 + 4.20967i) q^{94} +(4.63726 + 6.73591i) q^{95} +(-2.69626 - 1.48228i) q^{96} +(6.67955 + 3.67211i) q^{97} +(-0.793034 - 0.958613i) q^{98} +(-25.9682 - 18.8670i) 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

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Representations

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