LMFDB - Embedded newform 207.2.o.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.1
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.60132 + 0.123916i) q^{2} +(-1.41379 + 1.00061i) q^{3} +(4.76054 - 0.454577i) q^{4} +(2.77635 + 2.64725i) q^{5} +(3.55371 - 2.77808i) q^{6} +(-0.501364 - 2.60132i) q^{7} +(-7.17183 + 1.03115i) q^{8} +(0.997578 - 2.82928i) q^{9} +O(q^{10})$	\(q+(-2.60132 + 0.123916i) q^{2} +(-1.41379 + 1.00061i) q^{3} +(4.76054 - 0.454577i) q^{4} +(2.77635 + 2.64725i) q^{5} +(3.55371 - 2.77808i) q^{6} +(-0.501364 - 2.60132i) q^{7} +(-7.17183 + 1.03115i) q^{8} +(0.997578 - 2.82928i) q^{9} +(-7.55020 - 6.54229i) q^{10} +(1.59502 - 0.822292i) q^{11} +(-6.27553 + 5.40610i) q^{12} +(3.25272 + 0.626910i) q^{13} +(1.62655 + 6.70474i) q^{14} +(-6.57401 - 0.964605i) q^{15} +(9.13686 - 1.76099i) q^{16} +(0.919155 + 2.01267i) q^{17} +(-2.24442 + 7.48347i) q^{18} +(5.33902 + 2.43825i) q^{19} +(14.4203 + 11.3403i) q^{20} +(3.31172 + 3.17605i) q^{21} +(-4.04726 + 2.33669i) q^{22} +(-3.85812 - 2.84867i) q^{23} +(9.10765 - 8.63400i) q^{24} +(0.462308 + 9.70503i) q^{25} +(-8.53903 - 1.22773i) q^{26} +(1.42063 + 4.99818i) q^{27} +(-3.56927 - 12.1558i) q^{28} +(-0.0422940 + 0.442922i) q^{29} +(17.2206 + 1.69462i) q^{30} +(-3.26986 + 2.57144i) q^{31} +(-9.46697 + 2.29666i) q^{32} +(-1.43223 + 2.75853i) q^{33} +(-2.64041 - 5.12169i) q^{34} +(5.49438 - 8.54942i) q^{35} +(3.46289 - 13.9224i) q^{36} +(-2.15828 + 7.35043i) q^{37} +(-14.1906 - 5.68106i) q^{38} +(-5.22594 + 2.36837i) q^{39} +(-22.6412 - 16.1227i) q^{40} +(1.55771 - 1.63368i) q^{41} +(-9.00839 - 7.85152i) q^{42} +(0.495013 - 0.629460i) q^{43} +(7.21938 - 4.63962i) q^{44} +(10.2594 - 5.21425i) q^{45} +(10.3892 + 6.93222i) q^{46} +(2.64028 + 1.52437i) q^{47} +(-11.1555 + 11.6320i) q^{48} +(-0.0169429 + 0.00678290i) q^{49} +(-2.40522 - 25.1886i) q^{50} +(-3.31337 - 1.92577i) q^{51} +(15.7697 + 1.50582i) q^{52} +(-1.12878 - 1.30268i) q^{53} +(-4.31487 - 12.8258i) q^{54} +(6.60515 + 1.93945i) q^{55} +(6.27806 + 18.1393i) q^{56} +(-9.98795 + 1.89509i) q^{57} +(0.0551348 - 1.15742i) q^{58} +(-2.19825 + 11.4056i) q^{59} +(-31.7344 - 1.60365i) q^{60} +(1.58740 - 3.96512i) q^{61} +(8.18729 - 7.09433i) q^{62} +(-7.86003 - 1.17652i) q^{63} +(6.48578 - 1.90440i) q^{64} +(7.37111 + 10.3513i) q^{65} +(3.38386 - 7.35329i) q^{66} +(1.00004 - 1.93980i) q^{67} +(5.29059 + 9.16356i) q^{68} +(8.30495 + 0.166964i) q^{69} +(-13.2332 + 22.9206i) q^{70} +(-8.51253 - 13.2458i) q^{71} +(-4.23703 + 21.3198i) q^{72} +(1.67838 - 3.67515i) q^{73} +(4.70353 - 19.3882i) q^{74} +(-10.3645 - 13.2582i) q^{75} +(26.5250 + 9.18039i) q^{76} +(-2.93873 - 3.73690i) q^{77} +(13.3008 - 6.80846i) q^{78} +(-4.17826 + 1.44611i) q^{79} +(30.0289 + 19.2984i) q^{80} +(-7.00968 - 5.64486i) q^{81} +(-3.84966 + 4.44275i) q^{82} +(9.22137 - 8.79256i) q^{83} +(17.2093 + 13.6143i) q^{84} +(-2.77613 + 8.02110i) q^{85} +(-1.20968 + 1.69876i) q^{86} +(-0.383396 - 0.668517i) q^{87} +(-10.5913 + 7.54205i) q^{88} +(-0.218032 + 1.51645i) q^{89} +(-26.0419 + 14.8352i) q^{90} -8.77569i q^{91} +(-19.6617 - 11.8074i) q^{92} +(2.04988 - 6.90731i) q^{93} +(-7.05709 - 3.63818i) q^{94} +(8.36835 + 20.9031i) q^{95} +(11.0862 - 12.7197i) q^{96} +(-13.8812 - 3.36755i) q^{97} +(0.0432332 - 0.0197440i) q^{98} +(-0.735336 - 5.33307i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.60132	+	0.123916i	−1.83941	+	0.0876218i	−0.938268	−	0.345908i	$-0.887571\pi$
$2$	−2.60132	+	0.123916i	−1.83941	+	0.0876218i	−0.901139	+	0.433530i	$0.857268\pi$
$3$	−1.41379	+	1.00061i	−0.816249	+	0.577700i
$3$	−1.41379	+	1.00061i	−0.816249	+	0.577700i
$4$	4.76054	−	0.454577i	2.38027	−	0.227288i
$5$	2.77635	+	2.64725i	1.24162	+	1.18388i	0.975513	+	0.219941i	$0.0705866\pi$
$5$	2.77635	+	2.64725i	1.24162	+	1.18388i	0.266109	+	0.963943i	$0.414262\pi$
$6$	3.55371	−	2.77808i	1.45080	−	1.13415i
$7$	−0.501364	−	2.60132i	−0.189498	−	0.983208i	−0.944754	−	0.327779i	$-0.893700\pi$
$7$	−0.501364	−	2.60132i	−0.189498	−	0.983208i	0.755257	−	0.655429i	$-0.227512\pi$
$8$	−7.17183	+	1.03115i	−2.53562	+	0.364568i
$9$	0.997578	−	2.82928i	0.332526	−	0.943094i
$10$	−7.55020	−	6.54229i	−2.38758	−	2.06885i
$11$	1.59502	−	0.822292i	0.480918	−	0.247930i	−0.200681	−	0.979657i	$-0.564315\pi$
$11$	1.59502	−	0.822292i	0.480918	−	0.247930i	0.681598	+	0.731726i	$0.261285\pi$
$12$	−6.27553	+	5.40610i	−1.81159	+	1.56061i
$13$	3.25272	+	0.626910i	0.902142	+	0.173874i	0.619172	−	0.785255i	$-0.287468\pi$
$13$	3.25272	+	0.626910i	0.902142	+	0.173874i	0.282970	+	0.959129i	$0.408680\pi$
$14$	1.62655	+	6.70474i	0.434714	+	1.79192i
$15$	−6.57401	−	0.964605i	−1.69740	−	0.249060i
$16$	9.13686	−	1.76099i	2.28422	−	0.440246i
$17$	0.919155	+	2.01267i	0.222928	+	0.488144i	0.987740	−	0.156110i	$-0.0498954\pi$
$17$	0.919155	+	2.01267i	0.222928	+	0.488144i	−0.764812	+	0.644254i	$0.777168\pi$
$18$	−2.24442	+	7.48347i	−0.529015	+	1.76387i
$19$	5.33902	+	2.43825i	1.22486	+	0.559373i	0.919584	−	0.392893i	$-0.128526\pi$
$19$	5.33902	+	2.43825i	1.22486	+	0.559373i	0.305271	+	0.952266i	$0.401253\pi$
$20$	14.4203	+	11.3403i	3.22448	+	2.53576i
$21$	3.31172	+	3.17605i	0.722676	+	0.693070i
$22$	−4.04726	+	2.33669i	−0.862880	+	0.498184i
$23$	−3.85812	−	2.84867i	−0.804473	−	0.593990i
$23$	−3.85812	−	2.84867i	−0.804473	−	0.593990i
$24$	9.10765	−	8.63400i	1.85909	−	1.76241i
$25$	0.462308	+	9.70503i	0.0924615	+	1.94101i
$26$	−8.53903	−	1.22773i	−1.67464	−	0.240777i
$27$	1.42063	+	4.99818i	0.273401	+	0.961900i
$28$	−3.56927	−	12.1558i	−0.674528	−	2.29723i
$29$	−0.0422940	+	0.442922i	−0.00785379	+	0.0822486i	−0.998549	−	0.0538506i	$-0.982851\pi$
$29$	−0.0422940	+	0.442922i	−0.00785379	+	0.0822486i	0.990695	+	0.136099i	$0.0434566\pi$
$30$	17.2206	+	1.69462i	3.14404	+	0.309393i
$31$	−3.26986	+	2.57144i	−0.587284	+	0.461845i	−0.867049	−	0.498224i	$-0.833986\pi$
$31$	−3.26986	+	2.57144i	−0.587284	+	0.461845i	0.279765	+	0.960069i	$0.409743\pi$
$32$	−9.46697	+	2.29666i	−1.67354	+	0.405996i
$33$	−1.43223	+	2.75853i	−0.249319	+	0.480199i
$34$	−2.64041	−	5.12169i	−0.452827	−	0.878362i
$35$	5.49438	−	8.54942i	0.928720	−	1.44512i
$36$	3.46289	−	13.9224i	0.577148	−	2.32040i
$37$	−2.15828	+	7.35043i	−0.354819	+	1.20840i	0.567954	+	0.823060i	$0.307735\pi$
$37$	−2.15828	+	7.35043i	−0.354819	+	1.20840i	−0.922773	+	0.385343i	$0.874083\pi$
$38$	−14.1906	−	5.68106i	−2.30202	−	0.921590i
$39$	−5.22594	+	2.36837i	−0.836820	+	0.379243i
$40$	−22.6412	−	16.1227i	−3.57989	−	2.54923i
$41$	1.55771	−	1.63368i	0.243274	−	0.255138i	−0.590765	−	0.806843i	$-0.701174\pi$
$41$	1.55771	−	1.63368i	0.243274	−	0.255138i	0.834039	+	0.551705i	$0.186023\pi$
$42$	−9.00839	−	7.85152i	−1.39002	−	1.21152i
$43$	0.495013	−	0.629460i	0.0754887	−	0.0959917i	−0.746842	−	0.665001i	$-0.768431\pi$
$43$	0.495013	−	0.629460i	0.0754887	−	0.0959917i	0.822331	+	0.569010i	$0.192673\pi$
$44$	7.21938	−	4.63962i	1.08836	−	0.699448i
$45$	10.2594	−	5.21425i	1.52939	−	0.777294i
$46$	10.3892	+	6.93222i	1.53180	+	1.02210i
$47$	2.64028	+	1.52437i	0.385124	+	0.222352i	0.680045	−	0.733170i	$-0.261960\pi$
$47$	2.64028	+	1.52437i	0.385124	+	0.222352i	−0.294921	+	0.955522i	$0.595293\pi$
$48$	−11.1555	+	11.6320i	−1.61016	+	1.67894i
$49$	−0.0169429	+	0.00678290i	−0.00242041	+	0.000968986i
$50$	−2.40522	−	25.1886i	−0.340149	−	3.56220i
$51$	−3.31337	−	1.92577i	−0.463965	−	0.269662i
$52$	15.7697	+	1.50582i	2.18686	+	0.208820i
$53$	−1.12878	−	1.30268i	−0.155050	−	0.178937i	0.672910	−	0.739724i	$-0.265044\pi$
$53$	−1.12878	−	1.30268i	−0.155050	−	0.178937i	−0.827960	+	0.560787i	$0.810499\pi$
$54$	−4.31487	−	12.8258i	−0.587180	−	1.74537i
$55$	6.60515	+	1.93945i	0.890639	+	0.261515i
$56$	6.27806	+	18.1393i	0.838941	+	2.42396i
$57$	−9.98795	+	1.89509i	−1.32294	+	0.251011i
$58$	0.0551348	−	1.15742i	0.00723955	−	0.151977i
$59$	−2.19825	+	11.4056i	−0.286187	+	1.48488i	0.499531	+	0.866296i	$0.333506\pi$
$59$	−2.19825	+	11.4056i	−0.286187	+	1.48488i	−0.785718	+	0.618584i	$0.787706\pi$
$60$	−31.7344	−	1.60365i	−4.09689	−	0.207030i
$61$	1.58740	−	3.96512i	0.203245	−	0.507682i	−0.791368	−	0.611341i	$-0.790631\pi$
$61$	1.58740	−	3.96512i	0.203245	−	0.507682i	0.994613	+	0.103658i	$0.0330548\pi$
$62$	8.18729	−	7.09433i	1.03979	−	0.900980i
$63$	−7.86003	−	1.17652i	−0.990271	−	0.148228i
$64$	6.48578	−	1.90440i	0.810723	−	0.238050i
$65$	7.37111	+	10.3513i	0.914273	+	1.28392i
$66$	3.38386	−	7.35329i	0.416524	−	0.905128i
$67$	1.00004	−	1.93980i	0.122174	−	0.236985i	−0.819815	−	0.572629i	$-0.805924\pi$
$67$	1.00004	−	1.93980i	0.122174	−	0.236985i	0.941989	+	0.335644i	$0.108954\pi$
$68$	5.29059	+	9.16356i	0.641578	+	1.11125i
$69$	8.30495	+	0.166964i	0.999798	+	0.0201001i
$70$	−13.2332	+	22.9206i	−1.58167	+	2.73953i
$71$	−8.51253	−	13.2458i	−1.01025	−	1.57198i	−0.805002	−	0.593272i	$-0.797836\pi$
$71$	−8.51253	−	13.2458i	−1.01025	−	1.57198i	−0.205250	−	0.978710i	$-0.565801\pi$
$72$	−4.23703	+	21.3198i	−0.499339	+	2.51256i
$73$	1.67838	−	3.67515i	0.196440	−	0.430144i	−0.785621	−	0.618708i	$-0.787656\pi$
$73$	1.67838	−	3.67515i	0.196440	−	0.430144i	0.982061	+	0.188565i	$0.0603835\pi$
$74$	4.70353	−	19.3882i	0.546775	−	2.25384i
$75$	−10.3645	−	13.2582i	−1.19679	−	1.53093i
$76$	26.5250	+	9.18039i	3.04263	+	1.05306i
$77$	−2.93873	−	3.73690i	−0.334900	−	0.425860i
$78$	13.3008	−	6.80846i	1.50602	−	0.770906i
$79$	−4.17826	+	1.44611i	−0.470091	+	0.162700i	−0.551835	−	0.833953i	$-0.686072\pi$
$79$	−4.17826	+	1.44611i	−0.470091	+	0.162700i	0.0817440	+	0.996653i	$0.473951\pi$
$80$	30.0289	+	19.2984i	3.35733	+	2.15763i
$81$	−7.00968	−	5.64486i	−0.778853	−	0.627206i
$82$	−3.84966	+	4.44275i	−0.425124	+	0.490619i
$83$	9.22137	−	8.79256i	1.01218	−	0.965108i	0.0127827	−	0.999918i	$-0.495931\pi$
$83$	9.22137	−	8.79256i	1.01218	−	0.965108i	0.999394	+	0.0348098i	$0.0110825\pi$
$84$	17.2093	+	13.6143i	1.87769	+	1.48544i
$85$	−2.77613	+	8.02110i	−0.301114	+	0.870010i
$86$	−1.20968	+	1.69876i	−0.130444	+	0.183182i
$87$	−0.383396	−	0.668517i	−0.0411044	−	0.0716725i
$88$	−10.5913	+	7.54205i	−1.12904	+	0.803985i
$89$	−0.218032	+	1.51645i	−0.0231114	+	0.160743i	−0.998109	−	0.0614733i	$-0.980420\pi$
$89$	−0.218032	+	1.51645i	−0.0231114	+	0.160743i	0.974997	+	0.222217i	$0.0713292\pi$
$90$	−26.0419	+	14.8352i	−2.74506	+	1.56377i
$91$		−	8.77569i		−	0.919942i
$92$	−19.6617	−	11.8074i	−2.04987	−	1.23101i
$93$	2.04988	−	6.90731i	0.212562	−	0.716254i
$94$	−7.05709	−	3.63818i	−0.727883	−	0.375250i
$95$	8.36835	+	20.9031i	0.858575	+	2.14462i
$96$	11.0862	−	12.7197i	1.13148	−	1.29820i
$97$	−13.8812	−	3.36755i	−1.40943	−	0.341923i	−0.542373	−	0.840138i	$-0.682474\pi$
$97$	−13.8812	−	3.36755i	−1.40943	−	0.341923i	−0.867054	+	0.498215i	$0.833989\pi$
$98$	0.0432332	−	0.0197440i	0.00436722	−	0.00199444i
$99$	−0.735336	−	5.33307i	−0.0739040	−	0.535994i
$100$	6.61252	+	45.9911i	0.661252	+	4.59911i
$101$	5.27287	+	5.53002i	0.524670	+	0.550258i	0.931734	−	0.363142i	$-0.118296\pi$
$101$	5.27287	+	5.53002i	0.524670	+	0.550258i	−0.407064	+	0.913400i	$0.633447\pi$
$102$	8.85776	+	4.59895i	0.877049	+	0.455364i
$103$	14.7721	+	0.703681i	1.45554	+	0.0693357i	0.760359	−	0.649503i	$-0.225023\pi$
$103$	14.7721	+	0.703681i	1.45554	+	0.0693357i	0.695177	+	0.718839i	$0.255326\pi$
$104$	−23.9744	−	1.14204i	−2.35088	−	0.111986i
$105$	0.786724	+	17.5848i	0.0767764	+	1.71610i
$106$	3.09773	+	3.24881i	0.300878	+	0.315552i
$107$	0.219990	+	1.53007i	0.0212673	+	0.147917i	0.997688	−	0.0679585i	$-0.0216485\pi$
$107$	0.219990	+	1.53007i	0.0212673	+	0.147917i	−0.976421	+	0.215876i	$0.930739\pi$
$108$	9.03505	+	23.1483i	0.869398	+	2.22744i
$109$	8.60283	−	3.92878i	0.824001	−	0.376309i	0.0416393	−	0.999133i	$-0.486742\pi$
$109$	8.60283	−	3.92878i	0.824001	−	0.376309i	0.782362	+	0.622824i	$0.214015\pi$
$110$	−17.4224	−	4.22663i	−1.66116	−	0.402994i
$111$	−4.30353	−	12.5515i	−0.408473	−	1.19134i
$112$	−9.16179	−	22.8850i	−0.865707	−	2.16243i
$113$	2.82708	+	1.45746i	0.265949	+	0.137106i	0.586044	−	0.810279i	$-0.300685\pi$
$113$	2.82708	+	1.45746i	0.265949	+	0.137106i	−0.320095	+	0.947385i	$0.603715\pi$
$114$	25.7470	−	6.16740i	2.41143	−	0.577630i
$115$	−3.17034	−	18.1223i	−0.295636	−	1.68991i
$116$			2.12778i			0.197559i
$117$	5.01855	−	8.57747i	0.463965	−	0.792987i
$118$	4.30500	−	29.9419i	0.396307	−	2.75638i
$119$	4.77477	−	3.40010i	0.437702	−	0.311686i
$120$	48.1424	+	0.139166i	4.39478	+	0.0127040i
$121$	−4.51269	+	6.33719i	−0.410245	+	0.576108i
$122$	−3.63798	+	10.5112i	−0.329367	+	0.951643i
$123$	−0.567600	+	3.86833i	−0.0511788	+	0.348796i
$124$	−14.3974	+	13.7279i	−1.29292	+	1.23280i
$125$	−11.8474	+	13.6726i	−1.05966	+	1.22291i
$126$	20.5922	+	2.08652i	1.83450	+	0.185882i
$127$	0.209143	+	0.134408i	0.0185585	+	0.0119268i	0.549887	−	0.835239i	$-0.314671\pi$
$127$	0.209143	+	0.134408i	0.0185585	+	0.0119268i	−0.531329	+	0.847166i	$0.678307\pi$
$128$	1.77599	−	0.614678i	0.156977	−	0.0543304i
$129$	−0.0700008	+	1.38523i	−0.00616322	+	0.121963i
$130$	−20.4573	−	26.0135i	−1.79422	−	2.28154i
$131$	−0.169201	−	0.0585609i	−0.0147831	−	0.00511649i	0.319666	−	0.947530i	$-0.396429\pi$
$131$	−0.169201	−	0.0585609i	−0.0147831	−	0.00511649i	−0.334450	+	0.942414i	$0.608550\pi$
$132$	−5.56423	+	13.7832i	−0.484304	+	1.19967i
$133$	3.66588	−	15.1110i	0.317872	−	1.31029i
$134$	−2.36104	+	5.16996i	−0.203963	+	0.446617i
$135$	−9.28723	+	17.6375i	−0.799317	+	1.51799i
$136$	−8.66739	−	13.4867i	−0.743222	−	1.15648i
$137$	3.65084	−	6.32345i	0.311913	−	0.540249i	−0.666864	−	0.745180i	$-0.732364\pi$
$137$	3.65084	−	6.32345i	0.311913	−	0.540249i	0.978776	+	0.204931i	$0.0656970\pi$
$138$	−21.6245	+	0.594789i	−1.84080	+	0.0506318i
$139$	−10.6526	−	18.4508i	−0.903542	−	1.56498i	−0.822863	−	0.568240i	$-0.807625\pi$
$139$	−10.6526	−	18.4508i	−0.903542	−	1.56498i	−0.0806786	−	0.996740i	$-0.525709\pi$
$140$	22.2699	−	43.1975i	1.88215	−	3.65086i
$141$	−5.25807	+	0.486751i	−0.442810	+	0.0409919i
$142$	23.7851	+	33.4015i	1.99600	+	2.80300i
$143$	5.70367	−	1.67475i	0.476965	−	0.140049i
$144$	4.13240	−	27.6075i	0.344367	−	2.30062i
$145$	−1.28995	+	1.11775i	−0.107124	+	0.0928237i
$146$	−3.91060	+	9.76820i	−0.323643	+	0.808422i
$147$	0.0171666	−	0.0265427i	0.00141588	−	0.00218920i
$148$	−6.93325	+	35.9731i	−0.569910	+	2.95697i
$149$	0.584862	−	12.2778i	0.0479137	−	1.00583i	−0.839068	−	0.544027i	$-0.816899\pi$
$149$	0.584862	−	12.2778i	0.0479137	−	1.00583i	0.886981	−	0.461805i	$-0.152798\pi$
$150$	28.6043	+	33.2045i	2.33553	+	2.71114i
$151$	0.842930	+	2.43549i	0.0685967	+	0.198197i	0.974089	−	0.226166i	$-0.0726192\pi$
$151$	0.842930	+	2.43549i	0.0685967	+	0.198197i	−0.905492	+	0.424363i	$0.860498\pi$
$152$	−40.8047	−	11.9814i	−3.30970	−	0.971816i
$153$	6.61133	−	0.592755i	0.534495	−	0.0479214i
$154$	8.10764	+	9.35671i	0.653332	+	0.753985i
$155$	−15.8855	−	1.51688i	−1.27596	−	0.121839i
$156$	−23.8017	+	13.6503i	−1.90566	+	1.09290i
$157$	1.39676	+	14.6275i	0.111474	+	1.16740i	0.862121	+	0.506702i	$0.169135\pi$
$157$	1.39676	+	14.6275i	0.111474	+	1.16740i	−0.750648	+	0.660702i	$0.770258\pi$
$158$	10.6898	−	4.27954i	0.850433	−	0.340462i
$159$	2.89932	+	0.712248i	0.229931	+	0.0564849i
$160$	−32.3635	−	18.6850i	−2.55856	−	1.47718i
$161$	−5.47601	+	11.4644i	−0.431570	+	0.903524i
$162$	18.9339	+	13.8154i	1.48759	+	1.08544i
$163$	−9.01920	+	5.79629i	−0.706438	+	0.454000i	−0.843896	−	0.536507i	$-0.819743\pi$
$163$	−9.01920	+	5.79629i	−0.706438	+	0.454000i	0.137457	+	0.990508i	$0.456107\pi$
$164$	6.67292	−	8.48531i	0.521068	−	0.662592i
$165$	−11.2789	+	3.86719i	−0.878060	+	0.301060i
$166$	−22.8981	+	24.0149i	−1.77724	+	1.86392i
$167$	−4.22967	−	3.01193i	−0.327302	−	0.233070i	0.404579	−	0.914503i	$-0.367418\pi$
$167$	−4.22967	−	3.01193i	−0.327302	−	0.233070i	−0.731881	+	0.681432i	$0.761357\pi$
$168$	−27.0261	−	19.3632i	−2.08511	−	1.49390i
$169$	−1.88162	−	0.753285i	−0.144740	−	0.0579450i
$170$	6.22765	−	21.2094i	0.477639	−	1.62669i
$171$	12.2246	−	12.6733i	0.934837	−	0.969148i
$172$	2.07039	−	3.22159i	0.157866	−	0.245644i
$173$	−4.29673	−	8.33450i	−0.326674	−	0.633660i	0.667113	−	0.744957i	$-0.267530\pi$
$173$	−4.29673	−	8.33450i	−0.326674	−	0.633660i	−0.993787	+	0.111297i	$0.964500\pi$
$174$	1.08017	+	1.69151i	0.0818877	+	0.128233i
$175$	25.0141	−	6.06836i	1.89089	−	0.458725i
$176$	13.1255	−	10.3220i	0.989369	−	0.778048i
$177$	−8.30464	−	18.3246i	−0.624215	−	1.37736i
$178$	0.379259	−	3.97178i	0.0284266	−	0.297697i
$179$	2.41548	+	8.22638i	0.180542	+	0.614869i	0.999177	+	0.0405554i	$0.0129127\pi$
$179$	2.41548	+	8.22638i	0.180542	+	0.614869i	−0.818636	+	0.574313i	$0.805269\pi$
$180$	46.4702	−	29.4864i	3.46368	−	2.19778i
$181$	−21.5546	−	3.09908i	−1.60214	−	0.230353i	−0.717476	−	0.696583i	$-0.754703\pi$
$181$	−21.5546	−	3.09908i	−1.60214	−	0.230353i	−0.884663	+	0.466231i	$0.845612\pi$
$182$	1.08745	+	22.8283i	0.0806070	+	1.69215i
$183$	1.72329	+	7.19419i	0.127389	+	0.531810i
$184$	30.6072	+	16.4519i	2.25639	+	1.21285i
$185$	−25.4505	+	14.6939i	−1.87116	+	1.08032i
$186$	−4.47645	+	18.2221i	−0.328229	+	1.33611i
$187$	3.12107	+	2.45444i	0.228235	+	0.179486i
$188$	13.2621	+	6.05660i	0.967238	+	0.441723i
$189$	12.2896	−	6.20144i	0.893939	−	0.451088i
$190$	−24.3590	−	53.3387i	−1.76718	−	3.86959i
$191$	−2.61658	+	0.504304i	−0.189329	+	0.0364902i	−0.283034	−	0.959110i	$-0.591341\pi$
$191$	−2.61658	+	0.504304i	−0.189329	+	0.0364902i	0.0937052	+	0.995600i	$0.470129\pi$
$192$	−7.26395	+	9.18212i	−0.524231	+	0.662662i
$193$	−3.76740	−	15.5294i	−0.271184	−	1.11783i	−0.930595	−	0.366051i	$-0.880709\pi$
$193$	−3.76740	−	15.5294i	−0.271184	−	1.11783i	0.659411	−	0.751783i	$-0.270806\pi$
$194$	36.5268	+	7.03996i	2.62247	+	0.505440i
$195$	−20.7787	−	7.25891i	−1.48799	−	0.519821i
$196$	−0.0775739	+	0.0399921i	−0.00554099	+	0.00285658i
$197$	−10.8321	−	9.38607i	−0.771755	−	0.668730i	0.177188	−	0.984177i	$-0.443300\pi$
$197$	−10.8321	−	9.38607i	−0.771755	−	0.668730i	−0.948943	+	0.315447i	$0.897845\pi$
$198$	2.57369	+	13.7819i	0.182904	+	0.979436i
$199$	14.1618	−	2.03616i	1.00390	−	0.144339i	0.379293	−	0.925277i	$-0.376167\pi$
$199$	14.1618	−	2.03616i	1.00390	−	0.144339i	0.624610	+	0.780937i	$0.285258\pi$
$200$	−13.3230	−	69.1261i	−0.942076	−	4.88795i
$201$	0.527138	+	3.74311i	0.0371815	+	0.264019i
$202$	−14.4016	−	13.7319i	−1.01330	−	0.966176i
$203$	1.17339	−	0.112045i	0.0823558	−	0.00786402i
$204$	−16.6489	−	7.66152i	−1.16565	−	0.536414i
$205$	8.64952	−	0.412027i	0.604108	−	0.0287772i
$206$	−38.5140			−2.68340
$207$	−11.9085	+	8.07392i	−0.827696	+	0.561176i
$208$	30.8236			2.13723
$209$	10.5208	−	0.501168i	0.727740	−	0.0346665i
$210$	−4.22555	−	45.6460i	−0.291591	−	3.14987i
$211$	−9.46780	+	0.904066i	−0.651790	+	0.0622384i	−0.415713	−	0.909496i	$-0.636468\pi$
$211$	−9.46780	+	0.904066i	−0.651790	+	0.0622384i	−0.236077	+	0.971734i	$0.575862\pi$
$212$	−5.96577	−	5.68835i	−0.409731	−	0.390677i
$213$	25.2887	+	10.2090i	1.73275	+	0.699507i
$214$	−0.761863	−	3.95292i	−0.0520799	−	0.270216i
$215$	3.04066	−	0.437181i	0.207372	−	0.0298155i
$216$	−15.3424	−	34.3812i	−1.04392	−	2.33934i
$217$	8.32855	+	7.21673i	0.565379	+	0.489903i
$218$	−21.8918	+	11.2860i	−1.48270	+	0.764386i
$219$	1.30450	+	6.87527i	0.0881498	+	0.464588i
$220$	32.3257	+	6.23028i	2.17940	+	0.420045i
$221$	1.72799	+	7.12287i	0.116237	+	0.479136i
$222$	12.7502	+	32.1172i	0.855736	+	2.15556i
$223$	6.64322	−	1.28037i	0.444863	−	0.0857402i	0.0380996	−	0.999274i	$-0.487870\pi$
$223$	6.64322	−	1.28037i	0.444863	−	0.0857402i	0.406763	+	0.913534i	$0.366657\pi$
$224$	10.7208	+	23.4752i	0.716311	+	1.56850i
$225$	27.9195	+	8.37352i	1.86130	+	0.558235i
$226$	−7.53472	−	3.44099i	−0.501202	−	0.228891i
$227$	0.940402	+	0.739540i	0.0624166	+	0.0490850i	0.648880	−	0.760891i	$-0.275238\pi$
$227$	0.940402	+	0.739540i	0.0624166	+	0.0490850i	−0.586463	+	0.809976i	$0.699480\pi$
$228$	−46.6866	+	13.5620i	−3.09190	+	0.898163i
$229$	9.02087	−	5.20820i	0.596116	−	0.344168i	−0.171396	−	0.985202i	$-0.554828\pi$
$229$	9.02087	−	5.20820i	0.596116	−	0.344168i	0.767512	+	0.641035i	$0.221494\pi$
$230$	10.4927	+	46.7490i	0.691868	+	3.08254i
$231$	7.89391	+	2.34267i	0.519381	+	0.154136i
$232$	−0.153396	−	3.22017i	−0.0100709	−	0.211415i
$233$	26.8065	+	3.85420i	1.75615	+	0.252497i	0.943765	−	0.330618i	$-0.107257\pi$
$233$	26.8065	+	3.85420i	1.75615	+	0.252497i	0.812390	+	0.583115i	$0.198166\pi$
$234$	−11.9919	+	22.9346i	−0.783937	+	1.49928i
$235$	3.29497	+	11.2216i	0.214940	+	0.732019i
$236$	−5.28013	+	55.2960i	−0.343707	+	3.59947i
$237$	4.46018	−	6.22528i	0.289720	−	0.404375i
$238$	−11.9994	+	9.43640i	−0.777803	+	0.611671i
$239$	−12.4963	+	3.03157i	−0.808320	+	0.196096i	−0.618563	−	0.785735i	$-0.712285\pi$
$239$	−12.4963	+	3.03157i	−0.808320	+	0.196096i	−0.189756	+	0.981831i	$0.560770\pi$
$240$	−61.7645	+	2.76328i	−3.98688	+	0.178369i
$241$	5.84694	+	11.3415i	0.376635	+	0.730569i	0.998623	−	0.0524572i	$-0.0167053\pi$
$241$	5.84694	+	11.3415i	0.376635	+	0.730569i	−0.621989	+	0.783026i	$0.713675\pi$
$242$	10.9537	−	17.0442i	0.704127	−	1.09564i
$243$	15.5585	+	0.966696i	0.998075	+	0.0620136i
$244$	5.75442	−	19.5977i	0.368389	−	1.25462i
$245$	−0.0649954	−	0.0260202i	−0.00415240	−	0.00166237i
$246$	0.997159	−	10.1331i	0.0635766	−	0.646062i
$247$	15.8378	+	11.2780i	1.00773	+	0.717604i
$248$	20.7993	−	21.8137i	1.32076	−	1.38517i
$249$	−4.23915	+	21.6577i	−0.268646	+	1.37250i
$250$	29.1245	−	37.0348i	1.84199	−	2.34228i
$251$	−15.2592	+	9.80651i	−0.963154	+	0.618982i	−0.924869	−	0.380285i	$-0.875826\pi$
$251$	−15.2592	+	9.80651i	−0.963154	+	0.618982i	−0.0382851	+	0.999267i	$0.512189\pi$
$252$	−37.9528	−	2.02790i	−2.39080	−	0.127746i
$253$	−8.49623	−	1.37121i	−0.534153	−	0.0862071i
$254$	−0.560703	−	0.323722i	−0.0351816	−	0.0203121i
$255$	−4.10110	−	14.1179i	−0.256821	−	0.884099i
$256$	−17.0945	+	6.84362i	−1.06841	+	0.427726i
$257$	−2.23609	−	23.4174i	−0.139483	−	1.46073i	−0.746150	−	0.665778i	$-0.768100\pi$
$257$	−2.23609	−	23.4174i	−0.139483	−	1.46073i	0.606666	−	0.794956i	$-0.292506\pi$
$258$	0.0104415	−	3.61210i	0.000650062	−	0.224880i
$259$	20.2029	+	1.92915i	1.25535	+	0.119871i
$260$	39.7959	+	45.9269i	2.46804	+	2.84827i
$261$	1.21096	+	0.561511i	0.0749566	+	0.0347567i
$262$	0.447401	+	0.131369i	0.0276405	+	0.00811599i
$263$	1.02073	+	2.94920i	0.0629407	+	0.181855i	0.972086	−	0.234623i	$-0.0753855\pi$
$263$	1.02073	+	2.94920i	0.0629407	+	0.181855i	−0.909146	+	0.416478i	$0.863264\pi$
$264$	7.42725	−	21.2606i	0.457115	−	1.30850i
$265$	0.314628	−	6.60485i	0.0193274	−	0.405733i
$266$	−7.66362	+	39.7627i	−0.469887	+	2.43800i
$267$	−1.20912	−	2.36210i	−0.0739967	−	0.144558i
$268$	3.87893	−	9.68911i	0.236944	−	0.591857i
$269$	−20.5579	+	17.8135i	−1.25344	+	1.08611i	−0.260749	+	0.965407i	$0.583969\pi$
$269$	−20.5579	+	17.8135i	−1.25344	+	1.08611i	−0.992689	+	0.120703i	$0.961485\pi$
$270$	21.9734	−	47.0315i	1.33726	−	2.86224i
$271$	−28.1936	+	8.27839i	−1.71264	+	0.502876i	−0.983410	−	0.181394i	$-0.941939\pi$
$271$	−28.1936	+	8.27839i	−1.71264	+	0.502876i	−0.729229	+	0.684270i	$0.760121\pi$
$272$	11.9425	+	16.7708i	0.724118	+	1.01688i
$273$	8.78100	+	12.4069i	0.531450	+	0.750902i
$274$	−8.71342	+	16.9017i	−0.526397	+	1.02107i
$275$	8.71776	+	15.0996i	0.525701	+	0.910540i
$276$	39.6119	−	2.98040i	2.38436	−	0.179399i
$277$	7.61253	−	13.1853i	0.457393	−	0.792227i	−0.541430	−	0.840746i	$-0.682117\pi$
$277$	7.61253	−	13.1853i	0.457393	−	0.792227i	0.998822	+	0.0485189i	$0.0154501\pi$
$278$	29.9971	+	46.6764i	1.79911	+	2.79947i
$279$	4.01341	+	11.8166i	0.240276	+	0.707439i
$280$	−30.5890	+	66.9805i	−1.82804	+	4.00285i
$281$	2.55991	−	10.5521i	0.152712	−	0.629486i	−0.843076	−	0.537795i	$-0.819258\pi$
$281$	2.55991	−	10.5521i	0.152712	−	0.629486i	0.995787	−	0.0916913i	$-0.0292273\pi$
$282$	13.6176	−	1.91775i	0.810916	−	0.114201i
$283$	−14.4221	−	4.99155i	−0.857307	−	0.296717i	−0.137169	−	0.990548i	$-0.543800\pi$
$283$	−14.4221	−	4.99155i	−0.857307	−	0.296717i	−0.720138	+	0.693831i	$0.755922\pi$
$284$	−46.5455	−	59.1874i	−2.76197	−	3.51213i
$285$	−32.7468	−	21.1791i	−1.93976	−	1.25454i
$286$	−14.6295	+	5.06332i	−0.865061	+	0.299401i
$287$	−5.03072	−	3.23305i	−0.296954	−	0.190841i
$288$	−2.94613	+	29.0758i	−0.173602	+	1.71331i
$289$	7.92665	−	9.14784i	0.466273	−	0.538108i
$290$	3.21705	−	3.06745i	0.188912	−	0.180127i
$291$	22.9947	−	9.12865i	1.34797	−	0.535131i
$292$	6.31938	−	18.2587i	0.369814	−	1.06851i
$293$	12.0782	−	16.9615i	0.705617	−	0.990900i	−0.293769	−	0.955876i	$-0.594910\pi$
$293$	12.0782	−	16.9615i	0.705617	−	0.990900i	0.999386	−	0.0350242i	$-0.0111508\pi$
$294$	−0.0413666	+	0.0711731i	−0.00241255	+	0.00415090i
$295$	−36.2965	+	25.8466i	−2.11326	+	1.50485i
$296$	7.89940	−	54.9415i	0.459143	−	3.19341i
$297$	6.37591	+	6.80404i	0.369968	+	0.394810i
$298$			32.0108i			1.85433i
$299$	−10.7635	−	11.6846i	−0.622469	−	0.675740i
$300$	−55.3676	−	58.4050i	−3.19665	−	3.37201i
$301$	−1.88561	−	0.972100i	−0.108685	−	0.0560309i
$302$	−2.49452	−	6.23102i	−0.143544	−	0.358555i
$303$	−12.9881	−	2.54221i	−0.746145	−	0.146046i
$304$	53.0756	+	12.8760i	3.04409	+	0.738489i
$305$	14.9038	−	6.80635i	0.853391	−	0.389731i
$306$	−17.1247	+	2.36119i	−0.978955	+	0.134980i
$307$	−0.243859	−	1.69608i	−0.0139178	−	0.0968002i	0.981679	−	0.190545i	$-0.0610254\pi$
$307$	−0.243859	−	1.69608i	−0.0139178	−	0.0968002i	−0.995596	+	0.0937445i	$0.970116\pi$
$308$	−15.6887	−	16.4538i	−0.893946	−	0.937543i
$309$	−21.5887	+	13.7862i	−1.22814	+	0.784268i
$310$	41.5112	+	1.97742i	2.35768	+	0.112310i
$311$	18.6893	+	0.890283i	1.05978	+	0.0504833i	0.570222	−	0.821490i	$-0.306857\pi$
$311$	18.6893	+	0.890283i	1.05978	+	0.0504833i	0.489553	+	0.871974i	$0.337160\pi$
$312$	35.0374	−	22.3743i	1.98360	−	1.26670i
$313$	2.61979	+	2.74756i	0.148079	+	0.155301i	0.793596	−	0.608445i	$-0.208206\pi$
$313$	2.61979	+	2.74756i	0.148079	+	0.155301i	−0.645517	+	0.763746i	$0.723358\pi$
$314$	−5.44600	−	37.8777i	−0.307335	−	2.13756i
$315$	−18.7077	−	24.0739i	−1.05406	−	1.35641i
$316$	−19.2334	+	8.78361i	−1.08196	+	0.494117i
$317$	−5.75160	−	1.39532i	−0.323042	−	0.0783692i	0.0709587	−	0.997479i	$-0.477394\pi$
$317$	−5.75160	−	1.39532i	−0.323042	−	0.0783692i	−0.394001	+	0.919110i	$0.628909\pi$
$318$	−7.63030	−	1.49351i	−0.427886	−	0.0837519i
$319$	0.296752	+	0.741249i	0.0166149	+	0.0415020i
$320$	23.0482	+	11.8822i	1.28843	+	0.664234i
$321$	−1.84201	−	1.94306i	−0.102811	−	0.108451i
$322$	12.8242	−	30.5012i	0.714664	−	1.69976i
$323$			12.9868i			0.722605i
$324$	−35.9359	−	23.6862i	−1.99644	−	1.31590i
$325$	−4.58043	+	31.8576i	−0.254076	+	1.76714i
$326$	22.7435	−	16.1956i	1.25965	−	0.896991i
$327$	−8.23139	+	14.1625i	−0.455197	+	0.783187i
$328$	−9.48707	+	13.3227i	−0.523836	+	0.735625i
$329$	2.64163	−	7.63248i	0.145638	−	0.420792i
$330$	28.8607	−	11.4574i	1.58873	−	0.630710i
$331$	2.74717	−	2.61942i	0.150998	−	0.143976i	−0.610815	−	0.791773i	$-0.709158\pi$
$331$	2.74717	−	2.61942i	0.150998	−	0.143976i	0.761813	+	0.647797i	$0.224310\pi$
$332$	39.9018	−	46.0492i	2.18990	−	2.52728i
$333$	18.6434	+	13.4390i	1.02165	+	0.736453i
$334$	11.3759	+	7.31087i	0.622463	+	0.400033i
$335$	7.91159	−	2.73823i	0.432256	−	0.149605i
$336$	35.8517	+	23.1872i	1.95587	+	1.26497i
$337$	−8.05353	−	10.2409i	−0.438704	−	0.557857i	0.515548	−	0.856861i	$-0.327588\pi$
$337$	−8.05353	−	10.2409i	−0.438704	−	0.557857i	−0.954252	+	0.299003i	$0.903346\pi$
$338$	4.98802	+	1.72637i	0.271313	+	0.0939022i
$339$	−5.45522	+	0.768254i	−0.296287	+	0.0417258i
$340$	−9.56968	+	39.4468i	−0.518989	+	2.13930i
$341$	−3.10102	+	6.79029i	−0.167930	+	0.367715i
$342$	−30.2296	+	34.4819i	−1.63463	+	1.86457i
$343$	−9.99971	−	15.5599i	−0.539934	−	0.840153i
$344$	−2.90108	+	5.02481i	−0.156416	+	0.270920i
$345$	22.6155	+	22.4488i	1.21757	+	1.20860i
$346$	12.2099	+	21.1482i	0.656410	+	1.13694i
$347$	−16.0108	+	31.0565i	−0.859502	+	1.66720i	−0.121307	+	0.992615i	$0.538709\pi$
$347$	−16.0108	+	31.0565i	−0.859502	+	1.66720i	−0.738195	+	0.674587i	$0.764322\pi$
$348$	−2.12906	−	3.00822i	−0.114130	−	0.161257i
$349$	−9.50996	−	13.3549i	−0.509056	−	0.714869i	0.477438	−	0.878665i	$-0.341566\pi$
$349$	−9.50996	−	13.3549i	−0.509056	−	0.714869i	−0.986494	+	0.163796i	$0.947626\pi$
$350$	−64.3177	+	18.8854i	−3.43793	+	1.00947i
$351$	1.48752	+	17.1483i	0.0793977	+	0.915308i
$352$	−13.2115	+	11.4478i	−0.704176	+	0.610172i
$353$	11.7240	−	29.2850i	0.624003	−	1.55868i	−0.192471	−	0.981303i	$-0.561650\pi$
$353$	11.7240	−	29.2850i	0.624003	−	1.55868i	0.816474	−	0.577382i	$-0.195926\pi$
$354$	23.8737	+	46.6390i	1.26887	+	2.47884i
$355$	11.4310	−	59.3096i	0.606694	−	3.14783i
$356$	−0.348610	+	7.31823i	−0.0184763	+	0.387865i
$357$	−3.34834	+	9.58467i	−0.177213	+	0.507274i
$358$	−7.30282	−	21.1001i	−0.385966	−	1.11517i
$359$	−24.3292	−	7.14369i	−1.28404	−	0.377030i	−0.432653	−	0.901560i	$-0.642423\pi$
$359$	−24.3292	−	7.14369i	−1.28404	−	0.377030i	−0.851391	+	0.524531i	$0.824241\pi$
$360$	−68.2022	+	47.9747i	−3.59457	+	2.52849i
$361$	10.1177	+	11.6765i	0.532512	+	0.614551i
$362$	56.4543	+	5.39073i	2.96717	+	0.283330i
$363$	0.0389519	−	13.4748i	0.00204444	−	0.707246i
$364$	−3.98922	−	41.7770i	−0.209092	−	2.18971i
$365$	14.3888	−	5.76041i	0.753144	−	0.301514i
$366$	−5.37429	−	18.5008i	−0.280919	−	0.967053i
$367$	−22.8849	−	13.2126i	−1.19458	−	0.689694i	−0.235242	−	0.971937i	$-0.575588\pi$
$367$	−22.8849	−	13.2126i	−1.19458	−	0.689694i	−0.959343	+	0.282243i	$0.908921\pi$
$368$	−40.2675	−	19.2339i	−2.09909	−	1.00263i
$369$	−3.06821	−	6.03693i	−0.159725	−	0.314270i
$370$	64.3841	−	41.3771i	3.34717	−	2.15109i
$371$	−2.82276	+	3.58944i	−0.146551	+	0.186354i
$372$	6.61862	−	33.8144i	0.343159	−	1.75319i
$373$	−19.5499	+	20.5034i	−1.01226	+	1.06162i	−0.0141632	+	0.999900i	$0.504508\pi$
$373$	−19.5499	+	20.5034i	−1.01226	+	1.06162i	−0.998093	+	0.0617243i	$0.980340\pi$
$374$	−8.42304	−	5.99802i	−0.435545	−	0.310150i
$375$	3.06876	−	31.1846i	0.158470	−	1.61037i
$376$	−20.5075	−	8.20996i	−1.05759	−	0.423396i
$377$	−0.415243	+	1.41419i	−0.0213861	+	0.0728344i
$378$	−31.2007	+	17.6548i	−1.60479	+	0.908064i
$379$	10.7760	−	16.7677i	0.553524	−	0.861300i	−0.445905	−	0.895080i	$-0.647118\pi$
$379$	10.7760	−	16.7677i	0.553524	−	0.861300i	0.999429	+	0.0337799i	$0.0107545\pi$
$380$	49.3400	+	95.7062i	2.53109	+	4.90962i
$381$	−0.430173	+	0.0192455i	−0.0220385	+	0.000985978i
$382$	6.74405	−	1.63609i	0.345056	−	0.0837096i
$383$	−13.6138	+	10.7060i	−0.695633	+	0.547052i	−0.902167	−	0.431388i	$-0.858024\pi$
$383$	−13.6138	+	10.7060i	−0.695633	+	0.547052i	0.206534	+	0.978439i	$0.433782\pi$
$384$	−1.89583	+	2.64609i	−0.0967459	+	0.135033i
$385$	1.73355	−	18.1545i	0.0883497	−	0.925240i
$386$	11.7246	+	39.9302i	0.596764	+	2.03239i
$387$	−1.28711	−	2.02847i	−0.0654273	−	0.103113i
$388$	−67.6130	−	9.72129i	−3.43253	−	0.493524i
$389$	−0.269883	−	5.66554i	−0.0136836	−	0.287254i	−0.995329	−	0.0965398i	$-0.969223\pi$
$389$	−0.269883	−	5.66554i	−0.0136836	−	0.287254i	0.981646	−	0.190715i	$-0.0610805\pi$
$390$	54.9514	+	16.3079i	2.78257	+	0.825782i
$391$	2.18723	−	10.3835i	0.110613	−	0.525115i
$392$	0.114517	−	0.0661165i	0.00578399	−	0.00333939i
$393$	0.297810	−	0.0865106i	0.0150225	−	0.00436388i
$394$	29.3408	+	23.0739i	1.47817	+	1.16244i
$395$	−15.4285	−	7.04597i	−0.776293	−	0.354521i
$396$	−5.92489	−	25.0540i	−0.297737	−	1.25901i
$397$	6.66528	+	14.5949i	0.334521	+	0.732499i	0.999902	−	0.0140053i	$-0.00445816\pi$
$397$	6.66528	+	14.5949i	0.334521	+	0.732499i	−0.665381	+	0.746504i	$0.731731\pi$
$398$	−36.5870	+	7.05156i	−1.83394	+	0.353463i
$399$	9.93735	+	25.0318i	0.497490	+	1.25316i
$400$	21.3145	+	87.8594i	1.06572	+	4.39297i
$401$	−6.02913	−	1.16202i	−0.301080	−	0.0580285i	0.0364738	−	0.999335i	$-0.488387\pi$
$401$	−6.02913	−	1.16202i	−0.301080	−	0.0580285i	−0.337554	+	0.941306i	$0.609600\pi$
$402$	−1.83508	−	9.67169i	−0.0915257	−	0.482380i
$403$	−12.2480	+	6.31428i	−0.610116	+	0.314537i
$404$	27.6155	+	23.9290i	1.37392	+	1.19051i
$405$	−4.51800	−	34.2284i	−0.224501	−	1.70083i
$406$	−3.03847	+	0.436866i	−0.150797	+	0.0216813i
$407$	2.60169	+	13.4988i	0.128961	+	0.669113i
$408$	25.7487	+	10.3947i	1.27475	+	0.514614i
$409$	15.4991	+	14.7783i	0.766380	+	0.730742i	0.968607	−	0.248597i	$-0.0799695\pi$
$409$	15.4991	+	14.7783i	0.766380	+	0.730742i	−0.202227	+	0.979339i	$0.564818\pi$
$410$	−22.4491	+	2.14363i	−1.10868	+	0.105866i
$411$	1.16577	+	12.5931i	0.0575030	+	0.621169i
$412$	70.6430	−	3.36514i	3.48033	−	0.165789i
$413$	30.7717			1.51418
$414$	29.9772	−	22.4785i	1.47330	−	1.10476i
$415$	48.8778			2.39932
$416$	−32.2332	+	1.53546i	−1.58036	+	0.0752819i
$417$	33.5225	+	15.4265i	1.64160	+	0.755438i
$418$	−27.3059	+	2.60739i	−1.33557	+	0.127532i
$419$	10.0160	+	9.55028i	0.489316	+	0.466562i	0.894111	−	0.447846i	$-0.147809\pi$
$419$	10.0160	+	9.55028i	0.489316	+	0.466562i	−0.404795	+	0.914407i	$0.632657\pi$
$420$	11.7389	+	83.3553i	0.572797	+	4.06732i
$421$	−3.84170	−	19.9326i	−0.187233	−	0.971456i	−0.946993	−	0.321253i	$-0.895896\pi$
$421$	−3.84170	−	19.9326i	−0.187233	−	0.971456i	0.759761	−	0.650203i	$-0.225316\pi$
$422$	24.5167	−	3.52497i	1.19345	−	0.171593i
$423$	6.94674	−	5.94942i	0.337762	−	0.289271i
$424$	9.43867	+	8.17866i	0.458382	+	0.397191i
$425$	−19.1081	+	9.85089i	−0.926877	+	0.477839i
$426$	−67.0488	−	23.4231i	−3.24853	−	1.13485i
$427$	−11.1104	−	2.14136i	−0.537672	−	0.103628i
$428$	1.74281	+	7.18394i	0.0842417	+	0.347249i
$429$	−6.38800	+	8.07485i	−0.308415	+	0.389858i
$430$	−7.85555	+	1.51403i	−0.378828	+	0.0730132i
$431$	−7.12729	−	15.6066i	−0.343309	−	0.751743i	0.656688	−	0.754163i	$-0.271957\pi$
$431$	−7.12729	−	15.6066i	−0.343309	−	0.751743i	−0.999997	+	0.00241981i	$0.999230\pi$
$432$	21.7819	+	43.1660i	1.04798	+	2.07682i
$433$	−21.2797	−	9.71810i	−1.02264	−	0.467022i	−0.167745	−	0.985830i	$-0.553649\pi$
$433$	−21.2797	−	9.71810i	−1.02264	−	0.467022i	−0.854891	+	0.518808i	$0.826376\pi$
$434$	−22.5594	−	17.7409i	−1.08289	−	0.851593i
$435$	0.705286	−	2.87098i	0.0338159	−	0.137653i
$436$	39.1682	−	22.6138i	1.87582	−	1.08300i
$437$	−13.6528	−	24.6162i	−0.653101	−	1.17755i
$438$	−4.24537	−	17.7231i	−0.202852	−	0.846842i
$439$	−0.0541803	−	1.13738i	−0.00258588	−	0.0542844i	0.997206	−	0.0747065i	$-0.0238020\pi$
$439$	−0.0541803	−	1.13738i	−0.00258588	−	0.0542844i	−0.999791	+	0.0204222i	$0.993499\pi$
$440$	−49.3709	−	7.09846i	−2.35367	−	0.338406i
$441$	0.00228892	+	0.0547026i	0.000108996	+	0.00260489i
$442$	−5.37768	−	18.3147i	−0.255790	−	0.871142i
$443$	−2.69389	+	28.2117i	−0.127991	+	1.34038i	0.672082	+	0.740477i	$0.265400\pi$
$443$	−2.69389	+	28.2117i	−0.127991	+	1.34038i	−0.800073	+	0.599903i	$0.795206\pi$
$444$	−26.1928	−	57.7957i	−1.24305	−	2.74286i
$445$	−4.61974	+	3.63301i	−0.218997	+	0.172221i
$446$	−17.1224	+	4.15386i	−0.810771	+	0.196691i
$447$	11.4583	+	17.9433i	0.541960	+	0.848690i
$448$	−8.20569	−	15.9168i	−0.387683	−	0.751999i
$449$	17.8738	−	27.8121i	0.843516	−	1.31254i	−0.104569	−	0.994518i	$-0.533346\pi$
$449$	17.8738	−	27.8121i	0.843516	−	1.31254i	0.948085	−	0.318018i	$-0.103017\pi$
$450$	−73.6649	−	18.3225i	−3.47260	−	0.863731i
$451$	1.14123	−	3.88666i	0.0537382	−	0.183015i
$452$	14.1210	+	5.65318i	0.664194	+	0.265903i
$453$	−3.62868	−	2.59981i	−0.170490	−	0.122150i
$454$	−2.53792	−	1.80725i	−0.119111	−	0.0848183i
$455$	23.2314	−	24.3644i	1.08910	−	1.14222i
$456$	69.6778	−	23.8904i	3.26296	−	1.11877i
$457$	−14.5218	+	18.4660i	−0.679303	+	0.863804i	−0.996416	−	0.0845834i	$-0.973044\pi$
$457$	−14.5218	+	18.4660i	−0.679303	+	0.863804i	0.317113	+	0.948388i	$0.397286\pi$
$458$	−22.8208	+	14.6660i	−1.06634	+	0.685297i
$459$	−8.75389	+	7.45336i	−0.408597	+	0.347893i
$460$	−23.3305	−	84.8308i	−1.08779	−	3.95526i
$461$	−2.99383	−	1.72849i	−0.139437	−	0.0805038i	0.428659	−	0.903466i	$-0.358986\pi$
$461$	−2.99383	−	1.72849i	−0.139437	−	0.0805038i	−0.568095	+	0.822963i	$0.692320\pi$
$462$	−20.8248	−	5.11584i	−0.968859	−	0.238010i
$463$	35.4634	−	14.1974i	1.64812	−	0.659809i	0.652901	−	0.757443i	$-0.273552\pi$
$463$	35.4634	−	14.1974i	1.64812	−	0.659809i	0.995222	+	0.0976343i	$0.0311275\pi$
$464$	0.393546	+	4.12140i	0.0182699	+	0.191331i
$465$	23.9765	−	13.7506i	1.11188	−	0.637668i
$466$	−70.2098	−	6.70423i	−3.25241	−	0.310567i
$467$	22.8932	+	26.4201i	1.05937	+	1.22258i	0.974076	+	0.226222i	$0.0726375\pi$
$467$	22.8932	+	26.4201i	1.05937	+	1.22258i	0.0852940	+	0.996356i	$0.472817\pi$
$468$	19.9919	−	43.1147i	0.924125	−	1.99298i
$469$	−5.54744	−	1.62887i	−0.256157	−	0.0752145i
$470$	−9.96180	−	28.7827i	−0.459503	−	1.32765i
$471$	−16.6111	−	19.2826i	−0.765399	−	0.888495i
$472$	4.00454	−	84.0656i	0.184324	−	3.86943i
$473$	0.271957	−	1.41105i	0.0125046	−	0.0648801i
$474$	−10.8309	+	16.7466i	−0.497481	+	0.769197i
$475$	−21.1950	+	52.9426i	−0.972494	+	2.42917i
$476$	21.1849	−	18.3568i	0.971008	−	0.841383i
$477$	−4.81170	+	1.89411i	−0.220312	+	0.0867253i
$478$	32.1312	−	9.43457i	1.46965	−	0.431527i
$479$	−11.8538	−	16.6463i	−0.541614	−	0.760590i	0.449547	−	0.893257i	$-0.351585\pi$
$479$	−11.8538	−	16.6463i	−0.541614	−	0.760590i	−0.991161	+	0.132667i	$0.957646\pi$
$480$	64.4513	−	5.96640i	2.94179	−	0.272328i
$481$	−11.6283	+	22.5558i	−0.530207	+	1.02846i
$482$	−16.6151	−	28.7782i	−0.756798	−	1.31081i
$483$	−3.72947	−	21.6876i	−0.169697	−	0.986818i
$484$	−18.6021	+	32.2198i	−0.845551	+	1.46454i
$485$	−29.6245	−	46.0966i	−1.34518	−	2.09314i
$486$	−40.5922	−	0.586741i	−1.84130	−	0.0266151i
$487$	−0.0167778	+	0.0367382i	−0.000760273	+	0.00166477i	−0.910012	−	0.414582i	$-0.863928\pi$
$487$	−0.0167778	+	0.0367382i	−0.000760273	+	0.00166477i	0.909251	+	0.416247i	$0.136655\pi$
$488$	−7.29589	+	30.0740i	−0.330269	+	1.36139i
$489$	6.95141	−	17.2194i	0.314354	−	0.778687i
$490$	0.172298	+	0.0596328i	0.00778362	+	0.00269394i
$491$	19.0606	+	24.2375i	0.860192	+	1.09382i	0.994691	+	0.102909i	$0.0328151\pi$
$491$	19.0606	+	24.2375i	0.860192	+	1.09382i	−0.134499	+	0.990914i	$0.542942\pi$
$492$	−0.943632	+	18.6734i	−0.0425422	+	0.841861i
$493$	−0.930330	+	0.321990i	−0.0419000	+	0.0145017i
$494$	−42.5966	−	27.3752i	−1.91651	−	1.23167i
$495$	12.0764	−	16.7531i	0.542794	−	0.752996i
$496$	−25.3480	+	29.2531i	−1.13816	+	1.31350i
$497$	−30.1886	+	28.7848i	−1.35414	+	1.29117i
$498$	8.34364	−	56.8639i	0.373887	−	2.54813i
$499$	2.06124	−	5.95558i	0.0922740	−	0.266608i	−0.889414	−	0.457102i	$-0.848888\pi$
$499$	2.06124	−	5.95558i	0.0922740	−	0.266608i	0.981688	+	0.190493i	$0.0610088\pi$
$500$	−50.1846	+	70.4744i	−2.24432	+	3.15171i
$501$	8.99360	+	0.0259979i	0.401805	+	0.00116150i
$502$	38.4789	−	27.4007i	1.71740	−	1.22295i
$503$	−1.47746	+	10.2760i	−0.0658768	+	0.458183i	0.930007	+	0.367542i	$0.119801\pi$
$503$	−1.47746	+	10.2760i	−0.0658768	+	0.458183i	−0.995884	+	0.0906409i	$0.971108\pi$
$504$	57.5840	+	0.332920i	2.56499	+	0.0148294i
$505$			29.3119i			1.30436i
$506$	22.2713	+	2.51412i	0.990079	+	0.111766i
$507$	3.41394	−	0.817771i	0.151618	−	0.0363185i
$508$	1.05673	+	0.544785i	0.0468850	+	0.0241709i
$509$	−4.11138	−	10.2697i	−0.182234	−	0.455198i	0.808920	−	0.587919i	$-0.200053\pi$
$509$	−4.11138	−	10.2697i	−0.182234	−	0.455198i	−0.991153	+	0.132721i	$0.957628\pi$
$510$	12.4177	+	36.2170i	0.549865	+	1.60371i
$511$	−10.4017	−	2.52343i	−0.460145	−	0.111630i
$512$	40.2012	−	18.3593i	1.77666	−	0.811373i
$513$	−4.60201	+	30.1492i	−0.203184	+	1.33112i
$514$	8.71855	+	60.6388i	0.384559	+	2.67466i
$515$	39.1497	+	41.0590i	1.72514	+	1.80928i
$516$	0.296453	+	6.62628i	0.0130506	+	0.291706i
$517$	5.46478	+	0.260320i	0.240341	+	0.0114488i
$518$	−52.7932	−	2.51485i	−2.31960	−	0.110496i
$519$	14.4142	+	7.48386i	0.632713	+	0.328505i
$520$	−63.5381	−	66.6368i	−2.78633	−	2.92222i
$521$	−0.289337	−	2.01239i	−0.0126761	−	0.0881642i	0.982501	−	0.186256i	$-0.0596353\pi$
$521$	−0.289337	−	2.01239i	−0.0126761	−	0.0881642i	−0.995177	+	0.0980915i	$0.968726\pi$
$522$	−3.21967	−	1.31061i	−0.140921	−	0.0573638i
$523$	−11.5481	+	5.27386i	−0.504965	+	0.230610i	−0.651574	−	0.758585i	$-0.725891\pi$
$523$	−11.5481	+	5.27386i	−0.504965	+	0.230610i	0.146610	+	0.989194i	$0.453164\pi$
$524$	−0.832108	−	0.201867i	−0.0363508	−	0.00881861i
$525$	−29.2926	+	33.6086i	−1.27843	+	1.46680i
$526$	−3.02069	−	7.54531i	−0.131708	−	0.328991i
$527$	−8.18097	−	4.21758i	−0.356369	−	0.183721i
$528$	−8.22836	+	27.7265i	−0.358093	+	1.20664i
$529$	6.77010	+	21.9810i	0.294352	+	0.955697i
$530$			17.2203i			0.748002i
$531$	30.0767	+	17.5974i	1.30522	+	0.763663i
$532$	10.5825	−	73.6028i	0.458809	−	3.19109i
$533$	6.09097	−	4.33736i	0.263829	−	0.187872i
$534$	3.43799	+	5.99473i	0.148776	+	0.259417i
$535$	−3.43969	+	4.83037i	−0.148711	+	0.208835i
$536$	−5.17187	+	14.9431i	−0.223391	+	0.645445i
$537$	−11.6463	−	9.21339i	−0.502577	−	0.397587i
$538$	51.2702	−	48.8860i	2.21042	−	2.10763i
$539$	−0.0214468	+	0.0247509i	−0.000923777	+	0.00106610i
$540$	−36.1947	+	88.1857i	−1.55757	+	3.79491i
$541$	4.54887	+	2.92338i	0.195571	+	0.125686i	0.634762	−	0.772708i	$-0.281098\pi$
$541$	4.54887	+	2.92338i	0.195571	+	0.125686i	−0.439190	+	0.898394i	$0.644735\pi$
$542$	72.3146	−	25.0283i	3.10618	−	1.07506i
$543$	33.5745	−	17.1862i	1.44082	−	0.737530i
$544$	−13.3240	−	16.9429i	−0.571263	−	0.726420i
$545$	34.2849	+	11.8661i	1.46860	+	0.508289i
$546$	−24.3796	−	31.1862i	−1.04335	−	1.33465i
$547$	3.45353	−	14.2356i	0.147662	−	0.608672i	−0.849098	−	0.528236i	$-0.822854\pi$
$547$	3.45353	−	14.2356i	0.147662	−	0.608672i	0.996760	−	0.0804359i	$-0.0256312\pi$
$548$	14.5055	−	31.7626i	0.619645	−	1.35683i
$549$	−9.63491	−	8.44671i	−0.411208	−	0.360497i
$550$	−24.5487	−	38.1985i	−1.04676	−	1.62879i
$551$	−1.30576	+	2.26165i	−0.0556274	+	0.0963494i
$552$	−59.7338	+	7.36624i	−2.54244	+	0.313528i
$553$	5.85663	+	10.1440i	0.249049	+	0.431366i
$554$	−18.1687	+	35.2424i	−0.771915	+	1.49731i
$555$	21.2788	−	46.2399i	0.903236	−	1.96278i
$556$	−59.0995	−	82.9936i	−2.50638	−	3.51971i
$557$	−29.7304	+	8.72965i	−1.25972	+	0.369887i	−0.842390	−	0.538868i	$-0.818852\pi$
$557$	−29.7304	+	8.72965i	−1.25972	+	0.369887i	−0.417329	+	0.908755i	$0.637034\pi$
$558$	−11.9044	−	30.2413i	−0.503953	−	1.28022i
$559$	2.00475	−	1.73713i	0.0847920	−	0.0734727i
$560$	35.1460	−	87.7904i	1.48519	−	3.70982i
$561$	−6.86845	−	0.347087i	−0.289986	−	0.0146540i
$562$	−5.35157	+	27.7666i	−0.225742	+	1.17126i
$563$	−0.505822	+	10.6185i	−0.0213178	+	0.447517i	0.962824	+	0.270131i	$0.0870670\pi$
$563$	−0.505822	+	10.6185i	−0.0213178	+	0.447517i	−0.984141	+	0.177386i	$0.943236\pi$
$564$	−24.8100	+	4.70740i	−1.04469	+	0.198217i
$565$	3.99071	+	11.5304i	0.167890	+	0.485087i
$566$	38.1351	+	11.1975i	1.60294	+	0.470665i
$567$	−11.1697	+	21.0646i	−0.469083	+	0.884629i
$568$	74.7088	+	86.2186i	3.13471	+	3.61765i
$569$	−23.6529	−	2.25858i	−0.991581	−	0.0946845i	−0.413363	−	0.910567i	$-0.635646\pi$
$569$	−23.6529	−	2.25858i	−0.991581	−	0.0946845i	−0.578218	+	0.815882i	$0.696252\pi$
$570$	87.8093	+	51.0357i	3.67793	+	2.13765i
$571$	−0.839046	−	8.78688i	−0.0351130	−	0.367720i	−0.995902	−	0.0904391i	$-0.971173\pi$
$571$	−0.839046	−	8.78688i	−0.0351130	−	0.367720i	0.960789	−	0.277280i	$-0.0894331\pi$
$572$	26.3912	−	10.5655i	1.10347	−	0.441764i
$573$	3.19467	−	3.33114i	0.133459	−	0.139160i
$574$	13.4871	+	7.78679i	0.562941	+	0.325014i
$575$	25.8628	−	38.7601i	1.07855	−	1.61641i
$576$	1.08199	−	20.2499i	0.0450831	−	0.843746i
$577$	−30.3039	+	19.4751i	−1.26157	+	0.810760i	−0.988498	−	0.151235i	$-0.951675\pi$
$577$	−30.3039	+	19.4751i	−1.26157	+	0.810760i	−0.273069	+	0.961994i	$0.588039\pi$
$578$	−19.4861	+	24.7786i	−0.810517	+	1.03066i
$579$	20.8651	+	18.1856i	0.867126	+	0.755769i
$580$	−5.63275	+	5.90745i	−0.233887	+	0.245294i
$581$	−27.4955	−	19.5795i	−1.14071	−	0.812294i
$582$	−58.6852	+	26.5959i	−2.43258	+	1.10244i
$583$	−2.87161	−	1.14962i	−0.118930	−	0.0476124i
$584$	−8.24744	+	28.0882i	−0.341282	+	1.16230i
$585$	36.6399	−	10.5287i	1.51487	−	0.435310i
$586$	−29.3175	+	45.6189i	−1.21109	+	1.88450i
$587$	2.96507	+	5.75144i	0.122382	+	0.237387i	0.942066	−	0.335429i	$-0.108881\pi$
$587$	2.96507	+	5.75144i	0.122382	+	0.237387i	−0.819684	+	0.572816i	$0.805851\pi$
$588$	0.0696565	−	0.134161i	0.00287259	−	0.00553271i
$589$	−23.7277	+	5.75627i	−0.977681	+	0.237183i
$590$	91.2158	−	71.7329i	3.75529	−	2.95320i
$591$	24.7060	+	2.43123i	1.01627	+	0.100007i
$592$	−6.77591	+	70.9606i	−0.278488	+	2.91646i
$593$	−3.77109	−	12.8432i	−0.154860	−	0.527405i	0.845114	−	0.534586i	$-0.179532\pi$
$593$	−3.77109	−	12.8432i	−0.154860	−	0.527405i	−0.999974	+	0.00718076i	$0.997714\pi$
$594$	−17.4289	−	16.9094i	−0.715115	−	0.693800i
$595$	22.2573	+	3.20012i	0.912461	+	0.131192i
$596$	−2.79692	−	58.7146i	−0.114566	−	2.40505i
$597$	−17.9843	+	17.0491i	−0.736050	+	0.697771i
$598$	29.4472	+	29.0616i	1.20418	+	1.18842i
$599$	1.02406	−	0.591240i	0.0418419	−	0.0241574i	−0.478933	−	0.877851i	$-0.658976\pi$
$599$	1.02406	−	0.591240i	0.0418419	−	0.0241574i	0.520775	+	0.853694i	$0.325643\pi$
$600$	88.0038	+	84.3984i	3.59274	+	3.44555i
$601$	25.6034	+	20.1347i	1.04438	+	0.821312i	0.984233	−	0.176877i	$-0.0565995\pi$
$601$	25.6034	+	20.1347i	1.04438	+	0.821312i	0.0601507	+	0.998189i	$0.480842\pi$
$602$	5.02553	+	2.29508i	0.204825	+	0.0935405i
$603$	−4.49064	−	4.76449i	−0.182873	−	0.194025i
$604$	5.11992	+	11.2111i	0.208327	+	0.456172i
$605$	−29.3049	+	5.64806i	−1.19141	+	0.229626i
$606$	34.1011	+	5.00365i	1.38526	+	0.203260i
$607$	5.84955	+	24.1122i	0.237426	+	0.978682i	0.958334	+	0.285651i	$0.0922099\pi$
$607$	5.84955	+	24.1122i	0.237426	+	0.978682i	−0.720908	+	0.693031i	$0.756275\pi$
$608$	−56.1442	−	10.8209i	−2.27695	−	0.438845i
$609$	−1.54681	+	1.33251i	−0.0626798	+	0.0539959i
$610$	−37.9261	+	19.5523i	−1.53558	+	0.791649i
$611$	7.63244	+	6.61355i	0.308776	+	0.267556i
$612$	31.2041	−	5.82720i	1.26135	−	0.235550i
$613$	−26.4982	+	3.80986i	−1.07025	+	0.153879i	−0.654849	−	0.755760i	$-0.727268\pi$
$613$	−26.4982	+	3.80986i	−1.07025	+	0.153879i	−0.415401	+	0.909638i	$0.636359\pi$
$614$	0.844525	+	4.38181i	0.0340823	+	0.176836i
$615$	−11.8163	+	9.23727i	−0.476478	+	0.372483i
$616$	24.9294	+	23.7702i	1.00444	+	0.957727i
$617$	−13.2768	+	1.26778i	−0.534505	+	0.0510391i	−0.358819	−	0.933407i	$-0.616820\pi$
$617$	−13.2768	+	1.26778i	−0.534505	+	0.0510391i	−0.175686	+	0.984446i	$0.556214\pi$
$618$	54.4506	−	38.5374i	2.19032	−	1.55020i
$619$	−0.881907	+	0.0420104i	−0.0354468	+	0.00168854i	−0.0652978	−	0.997866i	$-0.520800\pi$
$619$	−0.881907	+	0.0420104i	−0.0354468	+	0.00168854i	0.0298510	+	0.999554i	$0.490497\pi$
$620$	−76.3132			−3.06481
$621$	8.75722	−	23.3305i	0.351415	−	0.936220i
$622$	−48.7272			−1.95378
$623$	4.05409	−	0.193120i	0.162424	−	0.00773719i
$624$	−43.5780	+	30.8423i	−1.74452	+	1.23468i
$625$	−20.7269	+	1.97918i	−0.829075	+	0.0791671i
$626$	−7.15537	−	6.82263i	−0.285986	−	0.272687i
$627$	−14.3727	+	11.2357i	−0.573990	+	0.448712i
$628$	13.2987	+	69.0001i	0.530675	+	2.75340i
$629$	−16.7778	+	2.41228i	−0.668973	+	0.0961838i
$630$	51.6477	+	60.3055i	2.05769	+	2.40263i
$631$	−5.95890	−	5.16342i	−0.237220	−	0.205552i	0.528135	−	0.849160i	$-0.322891\pi$
$631$	−5.95890	−	5.16342i	−0.237220	−	0.205552i	−0.765356	+	0.643608i	$0.777437\pi$
$632$	28.4746	−	14.6797i	1.13266	−	0.583926i
$633$	12.4808	−	10.7517i	0.496068	−	0.427341i
$634$	15.1346	+	2.91696i	0.601073	+	0.115847i
$635$	0.224844	+	0.926818i	0.00892265	+	0.0367797i
$636$	14.1261	+	2.07272i	0.560137	+	0.0821888i
$637$	−0.0593627	+	0.0114412i	−0.00235204	+	0.000453318i
$638$	−0.863797	−	1.89145i	−0.0341980	−	0.0748833i
$639$	−45.9679	+	10.8707i	−1.81846	+	0.430037i
$640$	6.55799	+	2.99493i	0.259227	+	0.118385i
$641$	31.8232	+	25.0261i	1.25694	+	0.988470i	0.999756	+	0.0221082i	$0.00703782\pi$
$641$	31.8232	+	25.0261i	1.25694	+	0.988470i	0.257186	+	0.966362i	$0.417205\pi$
$642$	5.03243	+	4.82626i	0.198614	+	0.190477i
$643$	6.46771	−	3.73413i	0.255061	−	0.147260i	−0.367018	−	0.930214i	$-0.619621\pi$
$643$	6.46771	−	3.73413i	0.255061	−	0.147260i	0.622080	+	0.782954i	$0.286288\pi$
$644$	−20.8573	+	57.0662i	−0.821893	+	2.24872i
$645$	−3.86140	+	3.66059i	−0.152042	+	0.144135i
$646$	−1.60927	−	33.7828i	−0.0633159	−	1.32917i
$647$	32.7053	+	4.70232i	1.28578	+	0.184867i	0.751100	−	0.660188i	$-0.229524\pi$
$647$	32.7053	+	4.70232i	1.28578	+	0.184867i	0.534679	+	0.845055i	$0.320433\pi$
$648$	56.0929	+	33.2559i	2.20354	+	1.30642i
$649$	5.87246	+	19.9998i	0.230514	+	0.785060i
$650$	7.96747	−	83.4392i	0.312510	−	3.27275i
$651$	−18.9959	−	1.86931i	−0.744507	−	0.0732642i
$652$	−40.3014	+	31.6934i	−1.57833	+	1.24121i
$653$	31.0828	−	7.54060i	1.21636	−	0.295086i	0.424298	−	0.905523i	$-0.360521\pi$
$653$	31.0828	−	7.54060i	1.21636	−	0.295086i	0.792065	+	0.610436i	$0.209006\pi$
$654$	19.6575	−	37.8611i	0.768669	−	1.48049i
$655$	−0.314735	−	0.610502i	−0.0122977	−	0.0238543i
$656$	11.3557	−	17.6698i	0.443366	−	0.689891i
$657$	−8.72371	−	8.41487i	−0.340344	−	0.328295i
$658$	−5.92592	+	20.1818i	−0.231016	+	0.786770i
$659$	−10.3720	−	4.15231i	−0.404035	−	0.161751i	0.160739	−	0.986997i	$-0.448612\pi$
$659$	−10.3720	−	4.15231i	−0.404035	−	0.161751i	−0.564774	+	0.825246i	$0.691037\pi$
$660$	−51.9357	+	23.5370i	−2.02159	+	0.916178i
$661$	24.2613	+	17.2764i	0.943653	+	0.671973i	0.944668	−	0.328027i	$-0.106384\pi$
$661$	24.2613	+	17.2764i	0.943653	+	0.671973i	−0.00101489	+	0.999999i	$0.500323\pi$
$662$	−6.82166	+	7.15435i	−0.265131	+	0.278062i
$663$	−9.57019	−	8.34117i	−0.371675	−	0.323944i
$664$	−57.0676	+	72.5674i	−2.21465	+	2.81616i
$665$	50.1802	−	32.2489i	1.94591	−	1.25056i
$666$	−50.1626	−	32.6489i	−1.94376	−	1.26512i
$667$	1.42492	−	1.58836i	0.0551730	−	0.0615017i
$668$	−21.5047	−	12.4157i	−0.832041	−	0.480379i
$669$	−8.11093	+	8.45741i	−0.313587	+	0.326982i
$670$	−20.2412	+	8.10337i	−0.781987	+	0.313060i
$671$	−0.728555	−	7.62977i	−0.0281255	−	0.294544i
$672$	−38.6462	−	22.4616i	−1.49081	−	0.866476i
$673$	24.0708	+	2.29848i	0.927859	+	0.0885998i	0.548032	−	0.836458i	$-0.315377\pi$
$673$	24.0708	+	2.29848i	0.927859	+	0.0885998i	0.379828	+	0.925057i	$0.375983\pi$
$674$	22.2188	+	25.6418i	0.855836	+	0.987687i
$675$	−47.8507	+	16.0980i	−1.84177	+	0.619612i
$676$	−9.29994	−	2.73071i	−0.357690	−	0.105027i
$677$	−15.0560	−	43.5016i	−0.578651	−	1.67190i	−0.730021	−	0.683424i	$-0.760490\pi$
$677$	−15.0560	−	43.5016i	−0.578651	−	1.67190i	0.151371	−	0.988477i	$-0.451631\pi$
$678$	14.0956	−	2.67446i	0.541337	−	0.102712i
$679$	−1.80054	+	37.7980i	−0.0690983	+	1.45055i
$680$	11.6389	−	60.3886i	0.446333	−	2.31580i
$681$	−2.06951	−	0.104580i	−0.0793039	−	0.00400751i
$682$	7.22531	−	18.0480i	0.276671	−	0.691092i
$683$	0.675703	−	0.585500i	0.0258551	−	0.0224035i	−0.641837	−	0.766841i	$-0.721828\pi$
$683$	0.675703	−	0.585500i	0.0258551	−	0.0224035i	0.667692	+	0.744437i	$0.267282\pi$
$684$	52.4347	−	65.8886i	2.00489	−	2.51931i
$685$	26.8757	−	7.89143i	1.02687	−	0.301516i
$686$	27.9405	+	39.2370i	1.06677	+	1.49807i
$687$	−7.54222	+	16.3896i	−0.287754	+	0.625303i
$688$	3.41439	−	6.62300i	0.130172	−	0.252499i
$689$	−2.85494	−	4.94490i	−0.108764	−	0.188386i
$690$	−61.6117	−	55.5939i	−2.34552	−	2.11643i
$691$	−5.62405	+	9.74115i	−0.213949	+	0.370571i	−0.952947	−	0.303137i	$-0.901966\pi$
$691$	−5.62405	+	9.74115i	−0.213949	+	0.370571i	0.738998	+	0.673708i	$0.235299\pi$
$692$	−24.2434	−	37.7235i	−0.921597	−	1.43403i
$693$	−13.5044	+	4.58666i	−0.512989	+	0.174233i
$694$	37.8006	−	82.7718i	1.43489	−	3.14198i
$695$	19.2686	−	79.4261i	0.730898	−	3.01280i
$696$	3.43899	+	4.39915i	0.130355	+	0.166749i
$697$	4.71984	+	1.63355i	0.178777	+	0.0618752i
$698$	26.3933	+	33.5618i	0.999000	+	1.27033i
$699$	−41.7552	+	21.3737i	−1.57933	+	0.808429i
$700$	116.322	−	40.2596i	4.39657	−	1.52167i
$701$	19.2081	+	12.3443i	0.725479	+	0.466237i	0.850539	−	0.525912i	$-0.176276\pi$
$701$	19.2081	+	12.3443i	0.725479	+	0.466237i	−0.125060	+	0.992149i	$0.539912\pi$
$702$	−5.99444	−	44.4238i	−0.226246	−	1.67667i
$703$	−29.4453	+	33.9817i	−1.11055	+	1.28164i
$704$	8.77901	−	8.37076i	0.330871	−	0.315485i
$705$	−15.8868	−	12.5680i	−0.598332	−	0.473339i
$706$	−26.8688	+	77.6324i	−1.01122	+	2.92173i
$707$	11.7418	−	16.4890i	0.441594	−	0.620132i
$708$	−47.8645	−	83.4601i	−1.79886	−	3.13662i
$709$	2.58471	−	1.84056i	0.0970708	−	0.0691238i	−0.530491	−	0.847691i	$-0.677992\pi$
$709$	2.58471	−	1.84056i	0.0970708	−	0.0691238i	0.627562	+	0.778567i	$0.284053\pi$
$710$	−22.3862	+	155.700i	−0.840140	+	5.84330i
$711$	−0.0766859	+	13.2641i	−0.00287595	+	0.497442i
$712$		−	11.1005i		−	0.416010i
$713$	19.9407	−	0.606167i	0.746785	−	0.0227011i
$714$	7.52240	−	25.3477i	0.281519	−	0.948612i
$715$	20.2689	+	10.4493i	0.758012	+	0.390782i
$716$	15.2385	+	38.0640i	0.569491	+	1.42252i
$717$	14.6337	−	16.7899i	0.546506	−	0.627029i
$718$	64.1731	+	15.5682i	2.39492	+	0.581001i
$719$	7.99664	−	3.65194i	0.298224	−	0.136194i	−0.260683	−	0.965424i	$-0.583948\pi$
$719$	7.99664	−	3.65194i	0.298224	−	0.136194i	0.558908	+	0.829230i	$0.311221\pi$
$720$	84.5568	−	65.7086i	3.15124	−	2.44881i
$721$	−5.57569	−	38.7798i	−0.207649	−	1.44423i
$722$	−27.7663	−	29.1205i	−1.03335	−	1.08375i
$723$	−19.6147	−	10.1839i	−0.729477	−	0.378745i
$724$	−104.020	−	4.95510i	−3.86588	−	0.184155i
$725$	−4.31813	−	0.205698i	−0.160371	−	0.00763942i
$726$	1.56842	+	35.0571i	0.0582096	+	1.30109i
$727$	30.2768	+	31.7534i	1.12290	+	1.17767i	0.982244	+	0.187609i	$0.0600737\pi$
$727$	30.2768	+	31.7534i	1.12290	+	1.17767i	0.140659	+	0.990058i	$0.455078\pi$
$728$	9.04908	+	62.9377i	0.335381	+	2.33263i
$729$	−22.9636	+	14.2012i	−0.850504	+	0.525969i
$730$	−36.7160	+	16.7676i	−1.35892	+	0.620598i
$731$	1.72189	+	0.417725i	0.0636863	+	0.0154501i
$732$	11.4741	+	33.4649i	0.424095	+	1.23690i
$733$	−12.9091	−	32.2455i	−0.476810	−	1.19101i	−0.950612	−	0.310382i	$-0.899543\pi$
$733$	−12.9091	−	32.2455i	−0.476810	−	1.19101i	0.473802	−	0.880632i	$-0.342881\pi$
$734$	61.1682	+	31.5344i	2.25776	+	1.16396i
$735$	0.117925	−	0.0282477i	0.00434975	−	0.00104193i
$736$	43.0671	+	18.1075i	1.58747	+	0.667452i
$737$		−	3.91635i		−	0.144261i
$738$	8.72945	+	15.3238i	0.321336	+	0.564076i
$739$	5.64224	−	39.2426i	0.207553	−	1.44356i	−0.573555	−	0.819167i	$-0.694436\pi$
$739$	5.64224	−	39.2426i	0.207553	−	1.44356i	0.781108	−	0.624396i	$-0.214655\pi$
$740$	−114.479	+	81.5200i	−4.20833	+	2.99674i
$741$	−33.6761	−	0.0973477i	−1.23712	−	0.00357616i
$742$	6.89811	−	9.68704i	0.253238	−	0.355622i
$743$	12.4772	−	36.0506i	0.457746	−	1.32257i	−0.446204	−	0.894931i	$-0.647224\pi$
$743$	12.4772	−	36.0506i	0.457746	−	1.32257i	0.903950	−	0.427638i	$-0.140654\pi$
$744$	−7.57886	+	51.6518i	−0.277855	+	1.89365i
$745$	34.1260	−	32.5391i	1.25028	−	1.19214i
$746$	48.3148	−	55.7583i	1.76893	−	2.04146i
$747$	−15.6776	−	34.8611i	−0.573613	−	1.27550i
$748$	15.9737	+	10.2657i	0.584057	+	0.375351i
$749$	3.86990	−	1.33939i	0.141403	−	0.0489401i
$750$	−4.11855	+	81.5013i	−0.150388	+	2.97601i
$751$	4.94949	+	6.29379i	0.180610	+	0.229664i	0.867925	−	0.496695i	$-0.165453\pi$
$751$	4.94949	+	6.29379i	0.180610	+	0.229664i	−0.687315	+	0.726359i	$0.741211\pi$
$752$	26.8082	+	9.27842i	0.977596	+	0.338349i
$753$	11.7608	−	29.1328i	0.428588	−	1.06166i
$754$	0.904937	−	3.73020i	0.0329559	−	0.135846i
$755$	−4.10706	+	8.99321i	−0.149471	+	0.327296i
$756$	55.6863	−	35.1088i	2.02529	−	1.27689i
$757$	−23.3456	−	36.3264i	−0.848509	−	1.32031i	−0.945700	−	0.325040i	$-0.894622\pi$
$757$	−23.3456	−	36.3264i	−0.848509	−	1.32031i	0.0971909	−	0.995266i	$-0.469014\pi$
$758$	−25.9539	+	44.9535i	−0.942688	+	1.63278i
$759$	13.3839	−	6.56278i	0.485804	−	0.238214i
$760$	−81.5707	−	141.285i	−2.95888	−	5.12493i
$761$	−2.47085	+	4.79279i	−0.0895684	+	0.173738i	−0.929364	−	0.369164i	$-0.879644\pi$
$761$	−2.47085	+	4.79279i	−0.0895684	+	0.173738i	0.839796	+	0.542902i	$0.182674\pi$
$762$	1.11663	−	0.103369i	0.0404513	−	0.00374467i
$763$	−14.5332	−	20.4090i	−0.526136	−	0.738855i
$764$	−12.2271	+	3.59020i	−0.442361	+	0.129889i
$765$	19.9246	+	15.8561i	0.720374	+	0.573279i
$766$	34.0871	−	29.5367i	1.23162	−	1.06720i
$767$	−14.3006	+	35.7211i	−0.516363	+	1.28981i
$768$	17.3202	−	26.7803i	0.624990	−	0.966351i
$769$	−5.73588	+	29.7606i	−0.206841	+	1.07319i	0.718922	+	0.695090i	$0.244636\pi$
$769$	−5.73588	+	29.7606i	−0.206841	+	1.07319i	−0.925763	+	0.378103i	$0.876576\pi$
$770$	−2.25987	+	47.4404i	−0.0814399	+	1.70963i
$771$	26.5929	+	30.8697i	0.957719	+	1.11174i
$772$	−24.9942	−	72.2160i	−0.899561	−	2.59911i
$773$	−5.06971	−	1.48860i	−0.182345	−	0.0535413i	0.189285	−	0.981922i	$-0.439383\pi$
$773$	−5.06971	−	1.48860i	−0.182345	−	0.0535413i	−0.371630	+	0.928381i	$0.621201\pi$
$774$	3.59953	+	5.11719i	0.129382	+	0.183933i
$775$	−26.4676	−	30.5453i	−0.950745	−	1.09722i
$776$	103.026	+	9.83782i	3.69843	+	0.353157i
$777$	−30.4929	+	17.4878i	−1.09393	+	0.627370i
$778$	1.40410	+	14.7044i	0.0503395	+	0.527179i
$779$	12.3000	−	4.92417i	0.440693	−	0.176427i
$780$	−102.218	−	25.1108i	−3.65998	−	0.899111i
$781$	−24.4696	−	14.1275i	−0.875590	−	0.505522i
$782$	−4.40300	+	27.2817i	−0.157451	+	0.975593i
$783$	−2.27389	+	0.417838i	−0.0812622	+	0.0149323i
$784$	−0.142860	+	0.0918106i	−0.00510215	+	0.00327895i
$785$	−34.8448	+	44.3087i	−1.24366	+	1.58145i
$786$	−0.763978	+	0.261945i	−0.0272502	+	0.00934326i
$787$	2.72570	−	2.85863i	0.0971606	−	0.101899i	−0.673358	−	0.739316i	$-0.735149\pi$
$787$	2.72570	−	2.85863i	0.0971606	−	0.101899i	0.770519	+	0.637417i	$0.219997\pi$
$788$	−55.8334	−	39.7588i	−1.98898	−	1.41635i
$789$	−4.39407	−	3.14819i	−0.156433	−	0.112078i
$790$	41.0076	+	16.4170i	1.45898	+	0.584089i
$791$	2.37393	−	8.08486i	0.0844072	−	0.287465i
$792$	10.7729	+	37.4896i	0.382799	+	1.33214i
$793$	7.64913	−	11.9023i	0.271629	−	0.422662i
$794$	−19.1470	−	37.1401i	−0.679503	−	1.31805i
$795$	6.16404	+	9.65266i	0.218616	+	0.342345i
$796$	66.4922	−	16.1308i	2.35675	−	0.571743i
$797$	−7.28332	+	5.72767i	−0.257989	+	0.202884i	−0.738773	−	0.673954i	$-0.764594\pi$
$797$	−7.28332	+	5.72767i	−0.257989	+	0.202884i	0.480784	+	0.876839i	$0.340352\pi$
$798$	−28.9520	−	63.8841i	−1.02489	−	2.26147i
$799$	−0.641217	+	6.71513i	−0.0226846	+	0.237564i
$800$	−26.6658	−	90.8154i	−0.942779	−	3.21081i
$801$	4.07296	+	2.12965i	0.143911	+	0.0752475i
$802$	15.8277	+	2.27567i	0.558894	+	0.0803568i
$803$	−0.344982	−	7.24207i	−0.0121742	−	0.255567i
$804$	4.21100	+	17.5796i	0.148510	+	0.619985i
$805$	−45.5525	+	17.3330i	−1.60551	+	0.610906i
$806$	31.0785	−	17.9432i	1.09469	−	0.632021i
$807$	11.2402	−	45.7548i	0.395672	−	1.61065i
$808$	−43.5184	−	34.2232i	−1.53097	−	1.20397i
$809$	26.5830	+	12.1401i	0.934610	+	0.426822i	0.823711	−	0.567010i	$-0.191900\pi$
$809$	26.5830	+	12.1401i	0.934610	+	0.426822i	0.110899	+	0.993832i	$0.464627\pi$
$810$	15.9942	+	88.4791i	0.561979	+	3.10884i
$811$	8.15328	+	17.8532i	0.286300	+	0.626910i	0.997068	−	0.0765163i	$-0.0243797\pi$
$811$	8.15328	+	17.8532i	0.286300	+	0.626910i	−0.710768	+	0.703426i	$0.751652\pi$
$812$	5.53504	−	1.06679i	0.194242	−	0.0374370i
$813$	31.5763	−	39.9145i	1.10743	−	1.39986i
$814$	−8.44054	−	34.7924i	−0.295841	−	1.21947i
$815$	−40.3847	−	7.78350i	−1.41461	−	0.272644i
$816$	−33.6651	−	11.7607i	−1.17851	−	0.411706i
$817$	4.17766	−	2.15373i	0.146158	−	0.0753496i
$818$	−42.1492	−	36.5225i	−1.47371	−	1.27698i
$819$	−24.8289	−	8.75443i	−0.867592	−	0.305904i
$820$	40.9891	−	5.89334i	1.43140	−	0.205804i
$821$	−2.20425	−	11.4368i	−0.0769290	−	0.399145i	−0.999898	−	0.0142716i	$-0.995457\pi$
$821$	−2.20425	−	11.4368i	−0.0769290	−	0.399145i	0.922969	−	0.384874i	$-0.125755\pi$
$822$	−4.59300	−	32.6140i	−0.160199	−	1.13755i
$823$	3.32901	+	3.17420i	0.116042	+	0.110646i	0.745879	−	0.666082i	$-0.232030\pi$
$823$	3.32901	+	3.17420i	0.116042	+	0.110646i	−0.629837	+	0.776727i	$0.716878\pi$
$824$	−106.668	+	10.1856i	−3.71597	+	0.354832i
$825$	−27.4338	−	12.6246i	−0.955122	−	0.439531i
$826$	−80.0470	+	3.81311i	−2.78519	+	0.132675i
$827$	15.7706			0.548398			0.274199	−	0.961673i	$-0.411587\pi$
$827$	15.7706			0.548398			0.274199	+	0.961673i	$0.411587\pi$
$828$	−53.0206	+	43.8496i	−1.84259	+	1.52388i
$829$	−22.6475			−0.786580			−0.393290	−	0.919414i	$-0.628663\pi$
$829$	−22.6475			−0.786580			−0.393290	+	0.919414i	$0.628663\pi$
$830$	−127.147	+	6.05674i	−4.41332	+	0.210232i
$831$	2.43079	+	26.2583i	0.0843231	+	0.910890i
$832$	22.2903	−	2.12847i	0.772778	−	0.0737913i
$833$	−0.0292248	−	0.0278658i	−0.00101258	−	0.000965494i
$834$	−89.1142	−	35.9752i	−3.08577	−	1.24572i
$835$	−3.76972	−	19.5592i	−0.130457	−	0.676873i
$836$	49.8570	−	7.16835i	1.72434	−	0.247923i
$837$	−17.4978	−	12.6903i	−0.604813	−	0.438639i
$838$	−27.2383	−	23.6021i	−0.940933	−	0.815323i
$839$	−30.7874	+	15.8720i	−1.06290	+	0.547962i	−0.898745	−	0.438472i	$-0.855520\pi$
$839$	−30.7874	+	15.8720i	−1.06290	+	0.547962i	−0.164154	+	0.986435i	$0.552489\pi$
$840$	−23.7748	−	125.304i	−0.820309	−	4.32339i
$841$	28.2815	+	5.45082i	0.975226	+	0.187959i
$842$	12.4634	+	51.3750i	0.429518	+	1.77050i
$843$	6.93933	+	17.4799i	0.239003	+	0.602039i
$844$	−44.6609	+	8.60769i	−1.53729	+	0.296289i
$845$	−3.22989	−	7.07248i	−0.111112	−	0.243301i
$846$	−17.3334	+	16.3371i	−0.595936	+	0.561682i
$847$	18.7476	+	8.56173i	0.644174	+	0.294185i
$848$	−12.6075	−	9.91464i	−0.432943	−	0.340470i
$849$	25.3844	−	7.37389i	0.871190	−	0.253071i
$850$	48.4854	−	27.9931i	1.66304	−	0.960155i
$851$	29.2659	−	22.2106i	1.00322	−	0.761368i
$852$	125.029	+	37.1046i	4.28341	+	1.27118i
$853$	0.277107	+	5.81718i	0.00948795	+	0.199177i	0.998634	+	0.0522435i	$0.0166372\pi$
$853$	0.277107	+	5.81718i	0.00948795	+	0.199177i	−0.989146	+	0.146933i	$0.953060\pi$
$854$	29.1671	+	4.19360i	0.998078	+	0.143502i
$855$	67.4889	−	2.82393i	2.30807	−	0.0965764i
$856$	−3.15546	−	10.7465i	−0.107852	−	0.367309i
$857$	1.43634	−	15.0420i	0.0490644	−	0.513826i	−0.937216	−	0.348749i	$-0.886607\pi$
$857$	1.43634	−	15.0420i	0.0490644	−	0.513826i	0.986281	−	0.165077i	$-0.0527873\pi$
$858$	15.6166	−	21.7968i	0.533142	−	0.744131i
$859$	20.7088	−	16.2856i	0.706575	−	0.555657i	−0.198919	−	0.980016i	$-0.563743\pi$
$859$	20.7088	−	16.2856i	0.706575	−	0.555657i	0.905494	+	0.424359i	$0.139501\pi$
$860$	14.2765	−	3.46344i	0.486824	−	0.118102i
$861$	10.3474	−	0.462930i	0.352637	−	0.0157766i
$862$	20.4742	+	39.7145i	0.697355	+	1.35268i
$863$	−26.3014	+	40.9258i	−0.895312	+	1.39313i	0.0240467	+	0.999711i	$0.492345\pi$
$863$	−26.3014	+	40.9258i	−0.895312	+	1.39313i	−0.919358	+	0.393421i	$0.871291\pi$
$864$	−24.9282	−	44.0549i	−0.848075	−	1.49878i
$865$	10.1342	−	34.5140i	0.344574	−	1.17351i
$866$	56.5594	+	22.6430i	1.92197	+	0.769439i
$867$	−2.05320	+	20.8645i	−0.0697303	+	0.708596i
$868$	42.9290	+	30.5696i	1.45710	+	1.03760i
$869$	−5.47530	+	5.74233i	−0.185737	+	0.194795i
$870$	−1.47891	+	7.55572i	−0.0501398	+	0.256163i
$871$	4.46893	−	5.68270i	0.151424	−	0.192551i
$872$	−57.6468	+	37.0474i	−1.95217	+	1.25458i
$873$	−23.3754	+	35.9145i	−0.791136	+	1.21552i
$874$	38.5655	+	62.3426i	1.30450	+	2.10877i
$875$	41.5066	+	23.9639i	1.40318	+	0.810126i
$876$	9.33546	+	32.1370i	0.315416	+	1.08581i
$877$	18.3512	−	7.34669i	0.619675	−	0.248080i	−0.0405155	−	0.999179i	$-0.512900\pi$
$877$	18.3512	−	7.34669i	0.619675	−	0.248080i	0.660190	+	0.751099i	$0.270476\pi$
$878$	0.281880	+	2.95198i	0.00951299	+	0.0996246i
$879$	−0.104255	+	36.0654i	−0.00351642	+	1.21646i
$880$	63.7657	+	6.08889i	2.14954	+	0.205256i
$881$	−19.6113	−	22.6326i	−0.660721	−	0.762512i	0.322174	−	0.946680i	$-0.395586\pi$
$881$	−19.6113	−	22.6326i	−0.660721	−	0.762512i	−0.982895	+	0.184168i	$0.941041\pi$
$882$	−0.0127327	−	0.142015i	−0.000428733	−	0.00478190i
$883$	48.1840	+	14.1481i	1.62152	+	0.476121i	0.961426	−	0.275062i	$-0.0886985\pi$
$883$	48.1840	+	14.1481i	1.62152	+	0.476121i	0.660093	+	0.751184i	$0.270517\pi$
$884$	11.4641	+	33.1232i	0.385578	+	1.11405i
$885$	25.4532	−	72.8600i	0.855599	−	2.44916i
$886$	3.51178	−	73.7214i	0.117981	−	2.47672i
$887$	1.02523	−	5.31941i	0.0344239	−	0.178608i	−0.960647	−	0.277771i	$-0.910404\pi$
$887$	1.02523	−	5.31941i	0.0344239	−	0.178608i	0.995071	+	0.0991628i	$0.0316165\pi$
$888$	43.8067	+	85.5797i	1.47006	+	2.87187i
$889$	0.244782	−	0.611437i	0.00820974	−	0.0205069i
$890$	11.5672	−	10.0231i	0.387734	−	0.335974i
$891$	−15.8223	−	3.23968i	−0.530068	−	0.108533i
$892$	31.0433	−	9.11513i	1.03941	−	0.305197i
$893$	10.3797	+	14.5763i	0.347344	+	0.487776i
$894$	−32.0302	−	45.2564i	−1.07125	−	1.51360i
$895$	−15.0710	+	29.2337i	−0.503769	+	0.977175i
$896$	−2.48940	−	4.31176i	−0.0831649	−	0.144046i
$897$	26.9090	+	5.74954i	0.898465	+	0.191972i
$898$	−43.0490	+	74.5630i	−1.43656	+	2.48820i
$899$	−1.00065	−	1.55705i	−0.0333737	−	0.0519305i
$900$	136.718	+	27.1710i	4.55727	+	0.905699i
$901$	1.58434	−	3.46922i	0.0527820	−	0.115577i
$902$	−2.48707	+	10.2518i	−0.0828103	+	0.341349i
$903$	3.63854	−	0.512412i	0.121083	−	0.0170520i
$904$	−21.7782	−	7.53750i	−0.724332	−	0.250694i
$905$	−51.6391	−	65.6644i	−1.71654	−	2.18276i
$906$	9.76151	+	6.31329i	0.324304	+	0.209745i
$907$	−15.6279	+	5.40886i	−0.518915	+	0.179598i	−0.573957	−	0.818886i	$-0.694592\pi$
$907$	−15.6279	+	5.40886i	−0.518915	+	0.179598i	0.0550413	+	0.998484i	$0.482471\pi$
$908$	4.81300	+	3.09313i	0.159725	+	0.102649i
$909$	20.9061	−	9.40180i	0.693411	−	0.311838i
$910$	−57.4131	+	66.2582i	−1.90322	+	2.19644i
$911$	−21.0629	+	20.0834i	−0.697844	+	0.665393i	−0.953506	−	0.301373i	$-0.902555\pi$
$911$	−21.0629	+	20.0834i	−0.697844	+	0.665393i	0.255662	+	0.966766i	$0.417706\pi$
$912$	−87.9213	+	34.9038i	−2.91137	+	1.15578i
$913$	7.47825	−	21.6070i	0.247494	−	0.715087i
$914$	35.4877	−	49.8354i	1.17383	−	1.64841i
$915$	−14.2603	+	24.5356i	−0.471432	+	0.811121i
$916$	40.5767	−	28.8945i	1.34069	−	0.954703i
$917$	−0.0675048	+	0.469506i	−0.00222921	+	0.0155045i
$918$	21.8480	−	20.4733i	0.721093	−	0.675720i
$919$			30.9735i			1.02172i	0.859663	+	0.510861i	$0.170673\pi$
$919$			30.9735i			1.02172i	−0.859663	+	0.510861i	$0.829327\pi$
$920$	41.4240	+	126.701i	1.36571	+	4.17721i
$921$	2.04187	+	2.15388i	0.0672818	+	0.0709728i
$922$	8.00209	+	4.12536i	0.263535	+	0.135862i
$923$	−19.3850	−	48.4213i	−0.638064	−	1.59381i
$924$	38.6442	+	7.56398i	1.27130	+	0.248837i
$925$	−72.3339	−	17.5480i	−2.37833	−	0.576975i
$926$	−90.4922	+	41.3264i	−2.97376	+	1.35807i
$927$	16.7272	−	41.0924i	0.549394	−	1.34965i
$928$	−0.616847	−	4.29027i	−0.0202490	−	0.140835i
$929$	7.12666	+	7.47423i	0.233818	+	0.245222i	0.830182	−	0.557493i	$-0.188237\pi$
$929$	7.12666	+	7.47423i	0.233818	+	0.245222i	−0.596363	+	0.802715i	$0.703388\pi$
$930$	−60.6666	+	38.7407i	−1.98933	+	1.27036i
$931$	−0.106997	−	0.00509688i	−0.00350668	−	0.000167044i
$932$	129.366	+	6.16245i	4.23751	+	0.201858i
$933$	−27.3135	+	17.4420i	−0.894205	+	0.571025i
$934$	−62.8262	−	65.8903i	−2.05574	−	2.15600i
$935$	2.16769	+	15.0766i	0.0708911	+	0.493059i
$936$	−27.1475	+	66.6910i	−0.887343	+	2.17986i
$937$	−49.8660	+	22.7730i	−1.62905	+	0.743962i	−0.999457	−	0.0329618i	$-0.989506\pi$
$937$	−49.8660	+	22.7730i	−1.62905	+	0.743962i	−0.629594	+	0.776924i	$0.716779\pi$
$938$	14.6325	+	3.54980i	0.477767	+	0.115905i
$939$	−6.45304	−	1.26308i	−0.210587	−	0.0412190i
$940$	20.7869	+	51.9233i	0.677995	+	1.69355i
$941$	42.7887	+	22.0591i	1.39487	+	0.719106i	0.981501	−	0.191457i	$-0.0613212\pi$
$941$	42.7887	+	22.0591i	1.39487	+	0.719106i	0.413370	+	0.910563i	$0.364352\pi$
$942$	45.6001	+	48.1017i	1.48573	+	1.56724i
$943$	−10.6637	+	1.86552i	−0.347257	+	0.0607496i
$944$			108.082i			3.51778i
$945$	50.5370	+	15.3163i	1.64397	+	0.498239i
$946$	−0.532595	+	3.70428i	−0.0173162	+	0.120437i
$947$	−27.3453	+	19.4725i	−0.888602	+	0.632771i	−0.930476	−	0.366352i	$-0.880607\pi$
$947$	−27.3453	+	19.4725i	−0.888602	+	0.632771i	0.0418740	+	0.999123i	$0.486667\pi$
$948$	18.4030	−	31.6632i	0.597702	−	1.02837i
$949$	7.76330	−	10.9020i	0.252007	−	0.353895i
$950$	48.5745	−	140.347i	1.57596	−	4.55345i
$951$	9.52770	−	3.78240i	0.308957	−	0.122653i
$952$	−30.7378	+	29.3084i	−0.996218	+	0.949892i
$953$	−39.2866	+	45.3391i	−1.27262	+	1.46868i	−0.457693	+	0.889110i	$0.651324\pi$
$953$	−39.2866	+	45.3391i	−1.27262	+	1.46868i	−0.814924	+	0.579568i	$0.803221\pi$
$954$	12.2820	−	5.52342i	0.397645	−	0.178827i
$955$	−8.59956	−	5.52660i	−0.278275	−	0.178837i
$956$	−58.1112	+	20.1125i	−1.87945	+	0.650484i
$957$	−1.16124	−	0.751036i	−0.0375376	−	0.0242776i
$958$	32.8982	+	41.8335i	1.06289	+	1.35158i
$959$	−18.2797	−	6.32668i	−0.590283	−	0.204299i
$960$	−44.4746	+	6.26332i	−1.43541	+	0.202148i
$961$	−3.22889	+	13.3096i	−0.104158	+	0.429343i
$962$	27.4540	−	60.1158i	0.885151	−	1.93821i
$963$	4.54845	+	0.903945i	0.146572	+	0.0291292i
$964$	32.9902	+	51.3337i	1.06254	+	1.65335i
$965$	30.6506	−	53.0884i	0.986679	−	1.70898i
$966$	12.3890	+	55.9540i	0.398609	+	1.80029i
$967$	−8.46492	−	14.6617i	−0.272213	−	0.471487i	0.697215	−	0.716862i	$-0.254422\pi$
$967$	−8.46492	−	14.6617i	−0.272213	−	0.471487i	−0.969428	+	0.245375i	$0.921089\pi$
$968$	25.8296	−	50.1025i	0.830196	−	1.61036i
$969$	−12.9947	−	18.3605i	−0.417449	−	0.589826i
$970$	82.7747	+	116.241i	2.65773	+	3.73227i
$971$	15.3885	−	4.51848i	0.493842	−	0.145005i	−0.0253229	−	0.999679i	$-0.508061\pi$
$971$	15.3885	−	4.51848i	0.493842	−	0.145005i	0.519164	+	0.854674i	$0.326243\pi$
$972$	74.5061	−	2.47051i	2.38979	−	0.0792417i
$973$	−42.6558	+	36.9614i	−1.36748	+	1.18493i
$974$	0.0390918	−	0.0976466i	0.00125258	−	0.00312880i
$975$	−25.4011	−	49.6230i	−0.813487	−	1.58921i
$976$	7.52129	−	39.0242i	0.240751	−	1.24913i
$977$	0.217856	−	4.57337i	0.00696984	−	0.146315i	−0.992700	−	0.120612i	$-0.961514\pi$
$977$	0.217856	−	4.57337i	0.00696984	−	0.146315i	0.999670	−	0.0257034i	$-0.00818255\pi$
$978$	−15.9491	+	45.6544i	−0.509995	+	1.45987i
$979$	0.899196	+	2.59806i	0.0287384	+	0.0830342i
$980$	−0.321241	−	0.0943250i	−0.0102617	−	0.00301310i
$981$	−2.53364	−	28.2591i	−0.0808928	−	0.902243i
$982$	−52.5860	−	60.6875i	−1.67809	−	1.93661i
$983$	−25.9320	−	2.47621i	−0.827103	−	0.0789788i	−0.327086	−	0.944994i	$-0.606067\pi$
$983$	−25.9320	−	2.47621i	−0.827103	−	0.0789788i	−0.500017	+	0.866016i	$0.666673\pi$
$984$	0.0818889	−	28.3283i	0.00261052	−	0.903073i
$985$	−5.22649	−	54.7343i	−0.166530	−	1.74398i
$986$	2.38018	−	0.952881i	0.0758004	−	0.0303459i
$987$	3.90241	+	13.4339i	0.124215	+	0.427606i
$988$	80.5231	+	46.4900i	2.56178	+	1.47905i
$989$	−3.70294	+	1.01840i	−0.117747	+	0.0323832i
$990$	−29.3385	+	45.0765i	−0.932440	+	1.43263i
$991$	31.6171	−	20.3191i	1.00435	−	0.645456i	0.0684244	−	0.997656i	$-0.478203\pi$
$991$	31.6171	−	20.3191i	1.00435	−	0.645456i	0.935925	+	0.352200i	$0.114566\pi$
$992$	25.0499	−	31.8535i	0.795335	−	1.01135i
$993$	−1.26290	+	6.45213i	−0.0400769	+	0.204752i
$994$	74.9632	−	78.6192i	2.37769	−	2.49365i
$995$	44.7083	+	31.8367i	1.41735	+	1.00929i
$996$	−10.3356	+	105.030i	−0.327495	+	3.32799i
$997$	−3.42741	−	1.37213i	−0.108547	−	0.0434558i	0.316753	−	0.948508i	$-0.397407\pi$
$997$	−3.42741	−	1.37213i	−0.108547	−	0.0434558i	−0.425300	+	0.905052i	$0.639832\pi$
$998$	−4.62396	+	15.7478i	−0.146369	+	0.498486i
$999$	−39.8049	−	0.345201i	−1.25937	−	0.0109217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.11.1	✓	440
3.2	odd	2		621.2.s.a.494.22		440
9.4	even	3		621.2.s.a.287.22		440
9.5	odd	6	inner	207.2.o.a.149.1	yes	440
23.21	odd	22	inner	207.2.o.a.182.1	yes	440
69.44	even	22		621.2.s.a.251.22		440
207.67	odd	66		621.2.s.a.44.22		440
207.113	even	66	inner	207.2.o.a.113.1	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.1	✓	440	1.1	even	1	trivial
207.2.o.a.113.1	yes	440	207.113	even	66	inner
207.2.o.a.149.1	yes	440	9.5	odd	6	inner
207.2.o.a.182.1	yes	440	23.21	odd	22	inner
621.2.s.a.44.22		440	207.67	odd	66
621.2.s.a.251.22		440	69.44	even	22
621.2.s.a.287.22		440	9.4	even	3
621.2.s.a.494.22		440	3.2	odd	2

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.60132 + 0.123916i) q^{2} +(-1.41379 + 1.00061i) q^{3} +(4.76054 - 0.454577i) q^{4} +(2.77635 + 2.64725i) q^{5} +(3.55371 - 2.77808i) q^{6} +(-0.501364 - 2.60132i) q^{7} +(-7.17183 + 1.03115i) q^{8} +(0.997578 - 2.82928i) q^{9} +O(q^{10})\)	\(q+(-2.60132 + 0.123916i) q^{2} +(-1.41379 + 1.00061i) q^{3} +(4.76054 - 0.454577i) q^{4} +(2.77635 + 2.64725i) q^{5} +(3.55371 - 2.77808i) q^{6} +(-0.501364 - 2.60132i) q^{7} +(-7.17183 + 1.03115i) q^{8} +(0.997578 - 2.82928i) q^{9} +(-7.55020 - 6.54229i) q^{10} +(1.59502 - 0.822292i) q^{11} +(-6.27553 + 5.40610i) q^{12} +(3.25272 + 0.626910i) q^{13} +(1.62655 + 6.70474i) q^{14} +(-6.57401 - 0.964605i) q^{15} +(9.13686 - 1.76099i) q^{16} +(0.919155 + 2.01267i) q^{17} +(-2.24442 + 7.48347i) q^{18} +(5.33902 + 2.43825i) q^{19} +(14.4203 + 11.3403i) q^{20} +(3.31172 + 3.17605i) q^{21} +(-4.04726 + 2.33669i) q^{22} +(-3.85812 - 2.84867i) q^{23} +(9.10765 - 8.63400i) q^{24} +(0.462308 + 9.70503i) q^{25} +(-8.53903 - 1.22773i) q^{26} +(1.42063 + 4.99818i) q^{27} +(-3.56927 - 12.1558i) q^{28} +(-0.0422940 + 0.442922i) q^{29} +(17.2206 + 1.69462i) q^{30} +(-3.26986 + 2.57144i) q^{31} +(-9.46697 + 2.29666i) q^{32} +(-1.43223 + 2.75853i) q^{33} +(-2.64041 - 5.12169i) q^{34} +(5.49438 - 8.54942i) q^{35} +(3.46289 - 13.9224i) q^{36} +(-2.15828 + 7.35043i) q^{37} +(-14.1906 - 5.68106i) q^{38} +(-5.22594 + 2.36837i) q^{39} +(-22.6412 - 16.1227i) q^{40} +(1.55771 - 1.63368i) q^{41} +(-9.00839 - 7.85152i) q^{42} +(0.495013 - 0.629460i) q^{43} +(7.21938 - 4.63962i) q^{44} +(10.2594 - 5.21425i) q^{45} +(10.3892 + 6.93222i) q^{46} +(2.64028 + 1.52437i) q^{47} +(-11.1555 + 11.6320i) q^{48} +(-0.0169429 + 0.00678290i) q^{49} +(-2.40522 - 25.1886i) q^{50} +(-3.31337 - 1.92577i) q^{51} +(15.7697 + 1.50582i) q^{52} +(-1.12878 - 1.30268i) q^{53} +(-4.31487 - 12.8258i) q^{54} +(6.60515 + 1.93945i) q^{55} +(6.27806 + 18.1393i) q^{56} +(-9.98795 + 1.89509i) q^{57} +(0.0551348 - 1.15742i) q^{58} +(-2.19825 + 11.4056i) q^{59} +(-31.7344 - 1.60365i) q^{60} +(1.58740 - 3.96512i) q^{61} +(8.18729 - 7.09433i) q^{62} +(-7.86003 - 1.17652i) q^{63} +(6.48578 - 1.90440i) q^{64} +(7.37111 + 10.3513i) q^{65} +(3.38386 - 7.35329i) q^{66} +(1.00004 - 1.93980i) q^{67} +(5.29059 + 9.16356i) q^{68} +(8.30495 + 0.166964i) q^{69} +(-13.2332 + 22.9206i) q^{70} +(-8.51253 - 13.2458i) q^{71} +(-4.23703 + 21.3198i) q^{72} +(1.67838 - 3.67515i) q^{73} +(4.70353 - 19.3882i) q^{74} +(-10.3645 - 13.2582i) q^{75} +(26.5250 + 9.18039i) q^{76} +(-2.93873 - 3.73690i) q^{77} +(13.3008 - 6.80846i) q^{78} +(-4.17826 + 1.44611i) q^{79} +(30.0289 + 19.2984i) q^{80} +(-7.00968 - 5.64486i) q^{81} +(-3.84966 + 4.44275i) q^{82} +(9.22137 - 8.79256i) q^{83} +(17.2093 + 13.6143i) q^{84} +(-2.77613 + 8.02110i) q^{85} +(-1.20968 + 1.69876i) q^{86} +(-0.383396 - 0.668517i) q^{87} +(-10.5913 + 7.54205i) q^{88} +(-0.218032 + 1.51645i) q^{89} +(-26.0419 + 14.8352i) q^{90} -8.77569i q^{91} +(-19.6617 - 11.8074i) q^{92} +(2.04988 - 6.90731i) q^{93} +(-7.05709 - 3.63818i) q^{94} +(8.36835 + 20.9031i) q^{95} +(11.0862 - 12.7197i) q^{96} +(-13.8812 - 3.36755i) q^{97} +(0.0432332 - 0.0197440i) q^{98} +(-0.735336 - 5.33307i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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