LMFDB - Embedded newform 845.2.bg.a.621.54

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(36,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 47]))

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

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

chi := DirichletCharacter("845.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.bg (of order $78$, degree $24$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$1440$
Relative dimension:	$60$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			621.54
Character	$\chi$	$=$	845.621
Dual form			845.2.bg.a.381.54

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73956 + 1.42030i) q^{2} +(2.19184 + 0.176943i) q^{3} +(0.608741 + 2.98181i) q^{4} +(-0.992709 + 0.120537i) q^{5} +(3.56151 + 3.42087i) q^{6} +(-0.140312 - 0.221886i) q^{7} +(-1.08885 + 2.07463i) q^{8} +(1.81169 + 0.294427i) q^{9} +O(q^{10})$	\(q+(1.73956 + 1.42030i) q^{2} +(2.19184 + 0.176943i) q^{3} +(0.608741 + 2.98181i) q^{4} +(-0.992709 + 0.120537i) q^{5} +(3.56151 + 3.42087i) q^{6} +(-0.140312 - 0.221886i) q^{7} +(-1.08885 + 2.07463i) q^{8} +(1.81169 + 0.294427i) q^{9} +(-1.89807 - 1.20027i) q^{10} +(0.703714 + 4.33013i) q^{11} +(0.806649 + 6.64336i) q^{12} +(0.169822 + 3.60155i) q^{13} +(0.0710644 - 0.585268i) q^{14} +(-2.19718 + 0.0885435i) q^{15} +(0.758857 - 0.323319i) q^{16} +(4.64766 - 2.93900i) q^{17} +(2.73335 + 3.08532i) q^{18} +(-3.02747 - 1.74791i) q^{19} +(-0.963721 - 2.88670i) q^{20} +(-0.268280 - 0.511164i) q^{21} +(-4.92594 + 8.53199i) q^{22} +(-4.01018 - 6.94584i) q^{23} +(-2.75367 + 4.35458i) q^{24} +(0.970942 - 0.239316i) q^{25} +(-4.81988 + 6.50629i) q^{26} +(-2.48639 - 0.612839i) q^{27} +(0.576207 - 0.553455i) q^{28} +(0.602489 - 0.737915i) q^{29} +(-3.94788 - 2.96664i) q^{30} +(0.258120 - 1.04724i) q^{31} +(6.28029 + 1.81911i) q^{32} +(0.776239 + 9.61545i) q^{33} +(12.2591 + 1.48853i) q^{34} +(0.166034 + 0.203355i) q^{35} +(0.224920 + 5.58133i) q^{36} +(1.51763 - 0.439588i) q^{37} +(-2.78389 - 7.34051i) q^{38} +(-0.265049 + 7.92405i) q^{39} +(0.830842 - 2.19075i) q^{40} +(-0.847457 + 10.4976i) q^{41} +(0.259321 - 1.27024i) q^{42} +(2.41902 - 8.35142i) q^{43} +(-12.4832 + 4.73427i) q^{44} +(-1.83397 - 0.0739063i) q^{45} +(2.88926 - 17.7783i) q^{46} +(-5.22000 + 5.89216i) q^{47} +(1.72050 - 0.574387i) q^{48} +(2.97130 - 6.26189i) q^{49} +(2.02891 + 0.962729i) q^{50} +(10.7070 - 5.61944i) q^{51} +(-10.6358 + 2.69879i) q^{52} +(-4.50243 - 2.36306i) q^{53} +(-3.45479 - 4.59749i) q^{54} +(-1.22052 - 4.21373i) q^{55} +(0.613109 - 0.0494953i) q^{56} +(-6.32643 - 4.36682i) q^{57} +(2.09613 - 0.427927i) q^{58} +(5.40471 - 12.6853i) q^{59} +(-1.60154 - 6.49769i) q^{60} +(-0.308044 + 7.64404i) q^{61} +(1.93641 - 1.45512i) q^{62} +(-0.188872 - 0.443298i) q^{63} +(7.40407 + 10.7267i) q^{64} +(-0.602702 - 3.55482i) q^{65} +(-12.3065 + 17.8291i) q^{66} +(-14.5830 - 2.97714i) q^{67} +(11.5928 + 12.0694i) q^{68} +(-7.56064 - 15.9337i) q^{69} +0.589566i q^{70} +(1.81401 - 0.860761i) q^{71} +(-2.58348 + 3.43799i) q^{72} +(-0.512138 - 0.194228i) q^{73} +(3.26436 + 1.39081i) q^{74} +(2.17049 - 0.352739i) q^{75} +(3.36899 - 10.0914i) q^{76} +(0.862053 - 0.763712i) q^{77} +(-11.7156 + 13.4079i) q^{78} +(4.09224 + 3.62541i) q^{79} +(-0.714352 + 0.412431i) q^{80} +(-10.5643 - 3.52688i) q^{81} +(-16.3840 + 17.0576i) q^{82} +(10.0646 - 6.94706i) q^{83} +(1.36088 - 1.11113i) q^{84} +(-4.25952 + 3.47779i) q^{85} +(16.0696 - 11.0920i) q^{86} +(1.45113 - 1.51078i) q^{87} +(-9.74965 - 3.25491i) q^{88} +(3.57860 - 2.06611i) q^{89} +(-3.08532 - 2.73335i) q^{90} +(0.775304 - 0.543021i) q^{91} +(18.2700 - 16.1858i) q^{92} +(0.751059 - 2.24970i) q^{93} +(-17.4491 + 2.83576i) q^{94} +(3.21608 + 1.37024i) q^{95} +(13.4435 + 5.09844i) q^{96} +(7.23221 - 9.62432i) q^{97} +(14.0625 - 6.67275i) q^{98} +8.05202i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1440 q - 2 q^{3} - 58 q^{4} + 18 q^{6} + 6 q^{7} + 60 q^{9}+O(q^{10}) $ 1440 * q - 2 * q^3 - 58 * q^4 + 18 * q^6 + 6 * q^7 + 60 * q^9	$ 1440 q - 2 q^{3} - 58 q^{4} + 18 q^{6} + 6 q^{7} + 60 q^{9} + 2 q^{10} - 20 q^{12} + 26 q^{13} + 4 q^{14} + 6 q^{15} + 58 q^{16} + 6 q^{17} - 156 q^{18} - 12 q^{19} - 12 q^{20} + 60 q^{22} - 146 q^{23} - 144 q^{24} + 120 q^{25} - 10 q^{26} + 4 q^{27} + 18 q^{28} + 4 q^{29} - 4 q^{30} + 52 q^{31} + 20 q^{32} - 42 q^{33} + 130 q^{34} - 10 q^{35} - 56 q^{36} - 6 q^{37} - 162 q^{38} + 12 q^{40} - 12 q^{41} - 24 q^{42} + 2 q^{43} + 42 q^{46} - 156 q^{47} + 30 q^{48} + 18 q^{49} - 124 q^{52} + 48 q^{53} - 330 q^{54} - 4 q^{55} + 20 q^{56} + 78 q^{57} + 68 q^{58} - 196 q^{59} + 12 q^{61} - 118 q^{62} + 24 q^{63} + 96 q^{64} + 8 q^{65} + 44 q^{66} + 98 q^{67} + 120 q^{68} + 28 q^{69} - 156 q^{71} + 386 q^{72} - 30 q^{74} + 2 q^{75} - 392 q^{76} + 4 q^{77} - 204 q^{78} + 40 q^{79} + 40 q^{81} - 244 q^{82} + 30 q^{84} - 18 q^{85} - 30 q^{87} + 30 q^{88} - 24 q^{89} - 56 q^{90} + 76 q^{91} + 20 q^{92} - 130 q^{93} - 148 q^{94} + 16 q^{95} - 338 q^{96} + 30 q^{97} - 72 q^{98}+O(q^{100}) $ 1440 * q - 2 * q^3 - 58 * q^4 + 18 * q^6 + 6 * q^7 + 60 * q^9 + 2 * q^10 - 20 * q^12 + 26 * q^13 + 4 * q^14 + 6 * q^15 + 58 * q^16 + 6 * q^17 - 156 * q^18 - 12 * q^19 - 12 * q^20 + 60 * q^22 - 146 * q^23 - 144 * q^24 + 120 * q^25 - 10 * q^26 + 4 * q^27 + 18 * q^28 + 4 * q^29 - 4 * q^30 + 52 * q^31 + 20 * q^32 - 42 * q^33 + 130 * q^34 - 10 * q^35 - 56 * q^36 - 6 * q^37 - 162 * q^38 + 12 * q^40 - 12 * q^41 - 24 * q^42 + 2 * q^43 + 42 * q^46 - 156 * q^47 + 30 * q^48 + 18 * q^49 - 124 * q^52 + 48 * q^53 - 330 * q^54 - 4 * q^55 + 20 * q^56 + 78 * q^57 + 68 * q^58 - 196 * q^59 + 12 * q^61 - 118 * q^62 + 24 * q^63 + 96 * q^64 + 8 * q^65 + 44 * q^66 + 98 * q^67 + 120 * q^68 + 28 * q^69 - 156 * q^71 + 386 * q^72 - 30 * q^74 + 2 * q^75 - 392 * q^76 + 4 * q^77 - 204 * q^78 + 40 * q^79 + 40 * q^81 - 244 * q^82 + 30 * q^84 - 18 * q^85 - 30 * q^87 + 30 * q^88 - 24 * q^89 - 56 * q^90 + 76 * q^91 + 20 * q^92 - 130 * q^93 - 148 * q^94 + 16 * q^95 - 338 * q^96 + 30 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{17}{78}\right)$	$1$

Coefficient data

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

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

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

$2$	1.73956	+	1.42030i	1.23005	+	1.00431i	0.999512	+	0.0312432i	$0.00994663\pi$
$2$	1.73956	+	1.42030i	1.23005	+	1.00431i	0.230540	+	0.973063i	$0.425951\pi$
$3$	2.19184	+	0.176943i	1.26546	+	0.102158i	0.694904	−	0.719102i	$-0.255447\pi$
$3$	2.19184	+	0.176943i	1.26546	+	0.102158i	0.570553	+	0.821261i	$0.306729\pi$
$4$	0.608741	+	2.98181i	0.304371	+	1.49091i
$5$	−0.992709	+	0.120537i	−0.443953	+	0.0539056i
$5$	−0.992709	+	0.120537i	−0.443953	+	0.0539056i
$6$	3.56151	+	3.42087i	1.45398	+	1.39657i
$7$	−0.140312	−	0.221886i	−0.0530329	−	0.0838648i	0.817633	−	0.575740i	$-0.195286\pi$
$7$	−0.140312	−	0.221886i	−0.0530329	−	0.0838648i	−0.870666	+	0.491875i	$0.836312\pi$
$8$	−1.08885	+	2.07463i	−0.384967	+	0.733492i
$9$	1.81169	+	0.294427i	0.603895	+	0.0981425i
$10$	−1.89807	−	1.20027i	−0.600223	−	0.379558i
$11$	0.703714	+	4.33013i	0.212178	+	1.30558i	0.846448	+	0.532471i	$0.178737\pi$
$11$	0.703714	+	4.33013i	0.212178	+	1.30558i	−0.634270	+	0.773111i	$0.718699\pi$
$12$	0.806649	+	6.64336i	0.232860	+	1.91777i
$13$	0.169822	+	3.60155i	0.0471001	+	0.998890i
$13$	0.169822	+	3.60155i	0.0471001	+	0.998890i
$14$	0.0710644	−	0.585268i	0.0189927	−	0.156419i
$15$	−2.19718	+	0.0885435i	−0.567310	+	0.0228618i
$16$	0.758857	−	0.323319i	0.189714	−	0.0808297i
$17$	4.64766	−	2.93900i	1.12722	−	0.712813i	0.165330	−	0.986238i	$-0.447131\pi$
$17$	4.64766	−	2.93900i	1.12722	−	0.712813i	0.961893	+	0.273425i	$0.0881566\pi$
$18$	2.73335	+	3.08532i	0.644257	+	0.727216i
$19$	−3.02747	−	1.74791i	−0.694549	−	0.400998i	0.110765	−	0.993847i	$-0.464670\pi$
$19$	−3.02747	−	1.74791i	−0.694549	−	0.400998i	−0.805314	+	0.592849i	$0.798003\pi$
$20$	−0.963721	−	2.88670i	−0.215494	−	0.645485i
$21$	−0.268280	−	0.511164i	−0.0585434	−	0.111545i
$22$	−4.92594	+	8.53199i	−1.05021	+	1.81903i
$23$	−4.01018	−	6.94584i	−0.836180	−	1.44831i	−0.893066	−	0.449926i	$-0.851450\pi$
$23$	−4.01018	−	6.94584i	−0.836180	−	1.44831i	0.0568854	−	0.998381i	$-0.481883\pi$
$24$	−2.75367	+	4.35458i	−0.562091	+	0.888876i
$25$	0.970942	−	0.239316i	0.194188	−	0.0478631i
$26$	−4.81988	+	6.50629i	−0.945256	+	1.27599i
$27$	−2.48639	−	0.612839i	−0.478505	−	0.117941i
$28$	0.576207	−	0.553455i	0.108893	−	0.104593i
$29$	0.602489	−	0.737915i	0.111879	−	0.137027i	−0.715629	−	0.698480i	$-0.753860\pi$
$29$	0.602489	−	0.737915i	0.111879	−	0.137027i	0.827509	+	0.561453i	$0.189757\pi$
$30$	−3.94788	−	2.96664i	−0.720781	−	0.541632i
$31$	0.258120	−	1.04724i	0.0463598	−	0.188089i	−0.943197	−	0.332235i	$-0.892197\pi$
$31$	0.258120	−	1.04724i	0.0463598	−	0.188089i	0.989556	+	0.144146i	$0.0460435\pi$
$32$	6.28029	+	1.81911i	1.11021	+	0.321576i
$33$	0.776239	+	9.61545i	0.135126	+	1.67383i
$34$	12.2591	+	1.48853i	2.10243	+	0.255281i
$35$	0.166034	+	0.203355i	0.0280649	+	0.0343733i
$36$	0.224920	+	5.58133i	0.0374867	+	0.930222i
$37$	1.51763	−	0.439588i	0.249497	−	0.0722678i	−0.151112	−	0.988517i	$-0.548286\pi$
$37$	1.51763	−	0.439588i	0.249497	−	0.0722678i	0.400610	+	0.916249i	$0.368798\pi$
$38$	−2.78389	−	7.34051i	−0.451606	−	1.19079i
$39$	−0.265049	+	7.92405i	−0.0424417	+	1.26886i
$40$	0.830842	−	2.19075i	0.131368	−	0.346388i
$41$	−0.847457	+	10.4976i	−0.132351	+	1.63946i	0.500897	+	0.865507i	$0.333003\pi$
$41$	−0.847457	+	10.4976i	−0.132351	+	1.63946i	−0.633248	+	0.773949i	$0.718279\pi$
$42$	0.259321	−	1.27024i	0.0400140	−	0.196002i
$43$	2.41902	−	8.35142i	0.368897	−	1.27358i	−0.534644	−	0.845077i	$-0.679554\pi$
$43$	2.41902	−	8.35142i	0.368897	−	1.27358i	0.903541	−	0.428502i	$-0.140958\pi$
$44$	−12.4832	+	4.73427i	−1.88192	+	0.713718i
$45$	−1.83397	−	0.0739063i	−0.273391	−	0.0110173i
$46$	2.88926	−	17.7783i	0.425998	−	2.62127i
$47$	−5.22000	+	5.89216i	−0.761415	+	0.859460i	−0.993570	−	0.113219i	$-0.963884\pi$
$47$	−5.22000	+	5.89216i	−0.761415	+	0.859460i	0.232155	+	0.972679i	$0.425422\pi$
$48$	1.72050	−	0.574387i	0.248333	−	0.0829056i
$49$	2.97130	−	6.26189i	0.424472	−	0.894555i
$50$	2.02891	+	0.962729i	0.286931	+	0.136150i
$51$	10.7070	−	5.61944i	1.49927	−	0.786879i
$52$	−10.6358	+	2.69879i	−1.47492	+	0.374255i
$53$	−4.50243	−	2.36306i	−0.618456	−	0.324591i	0.126235	−	0.992000i	$-0.459711\pi$
$53$	−4.50243	−	2.36306i	−0.618456	−	0.324591i	−0.744691	+	0.667410i	$0.767403\pi$
$54$	−3.45479	−	4.59749i	−0.470137	−	0.625639i
$55$	−1.22052	−	4.21373i	−0.164575	−	0.568180i
$56$	0.613109	−	0.0494953i	0.0819301	−	0.00661408i
$57$	−6.32643	−	4.36682i	−0.837956	−	0.578400i
$58$	2.09613	−	0.427927i	0.275235	−	0.0561896i
$59$	5.40471	−	12.6853i	0.703633	−	1.65149i	−0.0537807	−	0.998553i	$-0.517127\pi$
$59$	5.40471	−	12.6853i	0.703633	−	1.65149i	0.757414	−	0.652935i	$-0.226463\pi$
$60$	−1.60154	−	6.49769i	−0.206757	−	0.838848i
$61$	−0.308044	+	7.64404i	−0.0394410	+	0.978719i	0.851432	+	0.524466i	$0.175735\pi$
$61$	−0.308044	+	7.64404i	−0.0394410	+	0.978719i	−0.890873	+	0.454253i	$0.849906\pi$
$62$	1.93641	−	1.45512i	0.245924	−	0.184800i
$63$	−0.188872	−	0.443298i	−0.0237956	−	0.0558503i
$64$	7.40407	+	10.7267i	0.925509	+	1.34083i
$65$	−0.602702	−	3.55482i	−0.0747560	−	0.440921i
$66$	−12.3065	+	17.8291i	−1.51483	+	2.19461i
$67$	−14.5830	−	2.97714i	−1.78160	−	0.363716i	−0.807505	−	0.589861i	$-0.799183\pi$
$67$	−14.5830	−	2.97714i	−1.78160	−	0.363716i	−0.974094	+	0.226145i	$0.927388\pi$
$68$	11.5928	+	12.0694i	1.40583	+	1.46363i
$69$	−7.56064	−	15.9337i	−0.910194	−	1.91819i
$70$			0.589566i			0.0704666i
$71$	1.81401	−	0.860761i	0.215284	−	0.102154i	−0.317997	−	0.948092i	$-0.603010\pi$
$71$	1.81401	−	0.860761i	0.215284	−	0.102154i	0.533281	+	0.845938i	$0.320959\pi$
$72$	−2.58348	+	3.43799i	−0.304466	+	0.405171i
$73$	−0.512138	−	0.194228i	−0.0599412	−	0.0227327i	0.324452	−	0.945902i	$-0.394820\pi$
$73$	−0.512138	−	0.194228i	−0.0599412	−	0.0227327i	−0.384393	+	0.923169i	$0.625589\pi$
$74$	3.26436	+	1.39081i	0.379474	+	0.161679i
$75$	2.17049	−	0.352739i	0.250627	−	0.0407308i
$76$	3.36899	−	10.0914i	0.386450	−	1.15756i
$77$	0.862053	−	0.763712i	0.0982401	−	0.0870331i
$78$	−11.7156	+	13.4079i	−1.32653	+	1.51814i
$79$	4.09224	+	3.62541i	0.460413	+	0.407891i	0.861188	−	0.508286i	$-0.169721\pi$
$79$	4.09224	+	3.62541i	0.460413	+	0.407891i	−0.400775	+	0.916177i	$0.631259\pi$
$80$	−0.714352	+	0.412431i	−0.0798670	+	0.0461112i
$81$	−10.5643	−	3.52688i	−1.17381	−	0.391876i
$82$	−16.3840	+	17.0576i	−1.80931	+	1.88369i
$83$	10.0646	−	6.94706i	1.10473	−	0.762539i	0.131257	−	0.991348i	$-0.458099\pi$
$83$	10.0646	−	6.94706i	1.10473	−	0.762539i	0.973471	+	0.228809i	$0.0734832\pi$
$84$	1.36088	−	1.11113i	0.148484	−	0.121234i
$85$	−4.25952	+	3.47779i	−0.462010	+	0.377219i
$86$	16.0696	−	11.0920i	1.73283	−	1.19608i
$87$	1.45113	−	1.51078i	0.155577	−	0.161973i
$88$	−9.74965	−	3.25491i	−1.03932	−	0.346975i
$89$	3.57860	−	2.06611i	0.379331	−	0.219007i	−0.298196	−	0.954505i	$-0.596385\pi$
$89$	3.57860	−	2.06611i	0.379331	−	0.219007i	0.677527	+	0.735498i	$0.263052\pi$
$90$	−3.08532	−	2.73335i	−0.325221	−	0.288120i
$91$	0.775304	−	0.543021i	0.0812739	−	0.0569241i
$92$	18.2700	−	16.1858i	1.90478	−	1.68749i
$93$	0.751059	−	2.24970i	0.0778812	−	0.233283i
$94$	−17.4491	+	2.83576i	−1.79974	+	0.292486i
$95$	3.21608	+	1.37024i	0.329963	+	0.140584i
$96$	13.4435	+	5.09844i	1.37207	+	0.520357i
$97$	7.23221	−	9.62432i	0.734319	−	0.977202i	−0.265594	−	0.964085i	$-0.585568\pi$
$97$	7.23221	−	9.62432i	0.734319	−	0.977202i	0.999914	−	0.0131169i	$-0.00417537\pi$
$98$	14.0625	−	6.67275i	1.42053	−	0.674050i
$99$			8.05202i			0.809258i
$100$	1.30465	+	2.74948i	0.130465	+	0.274948i
$101$	−10.0281	−	10.4403i	−0.997831	−	1.03885i	−0.999245	−	0.0388528i	$-0.987630\pi$
$101$	−10.0281	−	10.4403i	−0.997831	−	1.03885i	0.00141424	−	0.999999i	$-0.499550\pi$
$102$	26.6066	+	5.43179i	2.63445	+	0.537827i
$103$	0.854652	−	1.23818i	0.0842113	−	0.122001i	−0.778614	−	0.627503i	$-0.784077\pi$
$103$	0.854652	−	1.23818i	0.0842113	−	0.122001i	0.862826	+	0.505502i	$0.168693\pi$
$104$	−7.65679	−	3.56923i	−0.750810	−	0.349992i
$105$	0.327937	+	0.475099i	0.0320034	+	0.0463650i
$106$	−4.47597	−	10.5055i	−0.434744	−	1.02038i
$107$	−9.18719	+	6.90372i	−0.888159	+	0.667408i	−0.943612	−	0.331053i	$-0.892596\pi$
$107$	−9.18719	+	6.90372i	−0.888159	+	0.667408i	0.0554531	+	0.998461i	$0.482340\pi$
$108$	0.313805	−	7.78700i	0.0301959	−	0.749304i
$109$	−0.0921757	−	0.373972i	−0.00882883	−	0.0358200i	0.966362	−	0.257185i	$-0.0827950\pi$
$109$	−0.0921757	−	0.373972i	−0.00882883	−	0.0358200i	−0.975191	+	0.221365i	$0.928949\pi$
$110$	3.86161	−	9.06353i	0.368190	−	0.864174i
$111$	3.40418	−	0.694969i	0.323111	−	0.0659636i
$112$	−0.178216	−	0.123014i	−0.0168399	−	0.0116237i
$113$	4.65397	−	0.375707i	0.437809	−	0.0353436i	0.140402	−	0.990095i	$-0.455160\pi$
$113$	4.65397	−	0.375707i	0.437809	−	0.0353436i	0.297406	+	0.954751i	$0.403878\pi$
$114$	−4.80297	−	16.5818i	−0.449839	−	1.55303i
$115$	4.81817	+	6.41182i	0.449297	+	0.597905i
$116$	2.56708	+	1.34731i	0.238348	+	0.125095i
$117$	−0.752732	+	6.57487i	−0.0695901	+	0.607847i
$118$	27.4188	−	14.3905i	2.52410	−	1.32475i
$119$	−1.30424	−	0.618872i	−0.119560	−	0.0567319i
$120$	2.20871	−	4.65475i	0.201626	−	0.424919i
$121$	−7.82089	+	2.61100i	−0.710990	+	0.237363i
$122$	−11.3927	+	12.8597i	−1.03145	+	1.16426i
$123$	−3.71497	+	22.8592i	−0.334968	+	2.06114i
$124$	3.27979	+	0.132171i	0.294534	+	0.0118693i
$125$	−0.935016	+	0.354605i	−0.0836304	+	0.0317168i
$126$	0.301065	−	1.03940i	0.0268210	−	0.0925969i
$127$	−4.17128	+	20.4323i	−0.370141	+	1.81307i	0.186659	+	0.982425i	$0.440234\pi$
$127$	−4.17128	+	20.4323i	−0.370141	+	1.81307i	−0.556800	+	0.830646i	$0.687971\pi$
$128$	−1.30305	+	16.1412i	−0.115174	+	1.42669i
$129$	6.77982	−	17.8769i	0.596930	−	1.57397i
$130$	4.00049	−	7.03983i	0.350866	−	0.617434i
$131$	2.45704	+	6.47868i	0.214673	+	0.566045i	0.998489	−	0.0549473i	$-0.0174991\pi$
$131$	2.45704	+	6.47868i	0.214673	+	0.566045i	−0.783817	+	0.620992i	$0.786730\pi$
$132$	−28.1989	+	8.16792i	−2.45440	+	0.710926i
$133$	0.0369540	+	0.917004i	0.00320432	+	0.0795143i
$134$	−21.1395	−	25.8912i	−1.82618	−	2.23666i
$135$	2.54213	+	0.308670i	0.218791	+	0.0265661i
$136$	1.03674	+	12.8423i	0.0888996	+	1.10122i
$137$	−5.62858	−	1.63034i	−0.480882	−	0.139289i	0.0289188	−	0.999582i	$-0.490794\pi$
$137$	−5.62858	−	1.63034i	−0.480882	−	0.139289i	−0.509800	+	0.860293i	$0.670281\pi$
$138$	9.47854	−	38.4560i	0.806867	−	3.27359i
$139$	−4.76930	−	3.58389i	−0.404526	−	0.303982i	0.378934	−	0.925424i	$-0.376291\pi$
$139$	−4.76930	−	3.58389i	−0.404526	−	0.303982i	−0.783460	+	0.621442i	$0.786547\pi$
$140$	−0.505294	+	0.618873i	−0.0427052	+	0.0523043i
$141$	−12.4840	+	11.9910i	−1.05134	+	1.00982i
$142$	4.37812	+	1.07911i	0.367404	+	0.0905569i
$143$	−15.4757	+	3.26981i	−1.29414	+	0.273435i
$144$	1.47000	−	0.362323i	0.122500	−	0.0301936i
$145$	−0.509150	+	0.805157i	−0.0422826	+	0.0668646i
$146$	−0.615030	−	1.06526i	−0.0509002	−	0.0881618i
$147$	7.62061	−	13.1993i	0.628537	−	1.08866i
$148$	2.23461	+	4.25770i	0.183684	+	0.349981i
$149$	7.43953	+	22.2841i	0.609470	+	1.82558i	0.562672	+	0.826680i	$0.309773\pi$
$149$	7.43953	+	22.2841i	0.609470	+	1.82558i	0.0467978	+	0.998904i	$0.485098\pi$
$150$	4.27669	+	2.46915i	0.349190	+	0.201605i
$151$	−11.4217	−	12.8924i	−0.929485	−	1.04917i	−0.998669	−	0.0515679i	$-0.983578\pi$
$151$	−11.4217	−	12.8924i	−0.929485	−	1.04917i	0.0691844	−	0.997604i	$-0.477960\pi$
$152$	6.92272	−	4.37766i	0.561507	−	0.355076i
$153$	9.28542	−	3.95615i	0.750682	−	0.319836i
$154$	2.58429	−	0.104143i	0.208248	−	0.00839212i
$155$	−0.130008	+	1.07071i	−0.0104425	+	0.0860017i
$156$	−23.7894	+	4.03337i	−1.90468	+	0.322928i
$157$	0.744084	+	6.12808i	0.0593844	+	0.489074i	0.991811	+	0.127715i	$0.0407642\pi$
$157$	0.744084	+	6.12808i	0.0593844	+	0.489074i	−0.932427	+	0.361359i	$0.882313\pi$
$158$	1.96950	+	12.1188i	0.156685	+	0.964123i
$159$	−9.45045	−	5.97610i	−0.749470	−	0.473936i
$160$	−6.45376	−	1.04884i	−0.510215	−	0.0829180i
$161$	−0.978504	+	1.86438i	−0.0771170	+	0.146934i
$162$	−13.3679	−	21.1397i	−1.05028	−	1.66089i
$163$	6.61035	+	6.34933i	0.517763	+	0.497318i	0.905438	−	0.424478i	$-0.139542\pi$
$163$	6.61035	+	6.34933i	0.517763	+	0.497318i	−0.387676	+	0.921796i	$0.626722\pi$
$164$	−31.8179	+	3.86339i	−2.48456	+	0.301680i
$165$	−1.92959	−	9.45177i	−0.150219	−	0.735820i
$166$	27.3748	+	2.20992i	2.12470	+	0.171523i
$167$	13.2412	+	10.8111i	1.02464	+	0.836589i	0.986677	−	0.162691i	$-0.0520172\pi$
$167$	13.2412	+	10.8111i	1.02464	+	0.836589i	0.0379580	+	0.999279i	$0.487915\pi$
$168$	1.35259			0.104355
$169$	−12.9423	+	1.22324i	−0.995563	+	0.0940956i
$170$	−12.3492			−0.947139
$171$	−4.97019	−	4.05803i	−0.380080	−	0.310325i
$172$	26.3749	+	2.12920i	2.01107	+	0.162350i
$173$	−0.539984	−	2.64502i	−0.0410542	−	0.201097i	0.954091	−	0.299518i	$-0.0968259\pi$
$173$	−0.539984	−	2.64502i	−0.0410542	−	0.201097i	−0.995145	+	0.0984211i	$0.968621\pi$
$174$	4.67008	−	0.567051i	0.354038	−	0.0429880i
$175$	−0.189335	−	0.181859i	−0.0143124	−	0.0137473i
$176$	1.93403	+	3.05842i	0.145783	+	0.230537i
$177$	14.0908	−	26.8478i	1.05913	−	2.01800i
$178$	9.15967	+	1.48859i	0.686547	+	0.111575i
$179$	6.24106	+	3.94660i	0.466478	+	0.294983i	0.746951	−	0.664879i	$-0.231517\pi$
$179$	6.24106	+	3.94660i	0.466478	+	0.294983i	−0.280473	+	0.959862i	$0.590491\pi$
$180$	−0.896036	−	5.51353i	−0.0667866	−	0.410954i
$181$	0.883468	+	7.27602i	0.0656677	+	0.540822i	0.988003	+	0.154432i	$0.0493549\pi$
$181$	0.883468	+	7.27602i	0.0656677	+	0.540822i	−0.922336	+	0.386390i	$0.873722\pi$
$182$	2.11994	+	0.156551i	0.157140	+	0.0116043i
$183$	−2.02774	+	16.7000i	−0.149895	+	1.23450i
$184$	18.7765	−	0.756668i	1.38422	−	0.0557823i
$185$	−1.45358	+	0.619313i	−0.106869	+	0.0455328i
$186$	4.50176	−	2.84674i	0.330085	−	0.208733i
$187$	15.9969	+	18.0568i	1.16981	+	1.32044i
$188$	−20.7469	−	11.9782i	−1.51313	−	0.873604i
$189$	0.212889	+	0.637682i	0.0154854	+	0.0463845i
$190$	3.64839	+	6.95143i	0.264682	+	0.504310i
$191$	−1.64078	+	2.84191i	−0.118722	+	0.205633i	−0.919262	−	0.393647i	$-0.871213\pi$
$191$	−1.64078	+	2.84191i	−0.118722	+	0.205633i	0.800539	+	0.599280i	$0.204547\pi$
$192$	14.3305	+	24.8212i	1.03421	+	1.79131i
$193$	−9.81490	+	15.5210i	−0.706492	+	1.11723i	0.281023	+	0.959701i	$0.409326\pi$
$193$	−9.81490	+	15.5210i	−0.706492	+	1.11723i	−0.987515	+	0.157526i	$0.949648\pi$
$194$	26.2503	−	6.47011i	1.88466	−	0.464527i
$195$	−0.692023	−	7.89823i	−0.0495568	−	0.565604i
$196$	20.4805	+	5.04800i	1.46289	+	0.360571i
$197$	−5.39843	+	5.18526i	−0.384622	+	0.369434i	−0.859954	−	0.510372i	$-0.829508\pi$
$197$	−5.39843	+	5.18526i	−0.384622	+	0.369434i	0.475332	+	0.879807i	$0.342328\pi$
$198$	−11.4363	+	14.0069i	−0.812743	+	0.995430i
$199$	−20.5874	−	15.4704i	−1.45940	−	1.09667i	−0.975100	−	0.221764i	$-0.928818\pi$
$199$	−20.5874	−	15.4704i	−1.45940	−	1.09667i	−0.484298	−	0.874903i	$-0.660925\pi$
$200$	−0.560718	+	2.27492i	−0.0396488	+	0.160861i
$201$	−31.4368	−	9.10578i	−2.21738	−	0.642272i
$202$	−2.61596	−	32.4044i	−0.184058	−	2.27997i
$203$	−0.248269	−	0.0301453i	−0.0174251	−	0.00211579i
$204$	23.2739	+	28.5053i	1.62950	+	1.99577i
$205$	−0.424072	−	10.5232i	−0.0296185	−	0.734976i
$206$	3.24530	−	0.940013i	0.226111	−	0.0654938i
$207$	−5.22014	−	13.7644i	−0.362825	−	0.956690i
$208$	1.29332	+	2.67815i	0.0896755	+	0.185697i
$209$	5.43820	−	14.3394i	0.376168	−	0.991874i
$210$	−0.104320	+	1.29223i	−0.00719875	+	0.0891725i
$211$	−4.04697	+	19.8234i	−0.278605	+	1.36470i	0.563826	+	0.825894i	$0.309329\pi$
$211$	−4.04697	+	19.8234i	−0.278605	+	1.36470i	−0.842431	+	0.538804i	$0.818876\pi$
$212$	4.30537	−	14.8639i	0.295694	−	1.02086i
$213$	4.12833	−	1.56567i	0.282868	−	0.107278i
$214$	−25.7870	−	1.03918i	−1.76276	−	0.0710369i
$215$	−1.39473	+	8.58211i	−0.0951197	+	0.585295i
$216$	3.97872	−	4.49104i	0.270717	−	0.305577i
$217$	−0.268584	+	0.0896664i	−0.0182327	+	0.00608695i
$218$	0.370808	−	0.781462i	0.0251143	−	0.0529273i
$219$	−1.08816	−	0.516336i	−0.0735307	−	0.0348908i
$220$	11.8216	−	6.20444i	0.797010	−	0.418303i
$221$	11.3742	+	16.2397i	0.765114	+	1.09240i
$222$	6.90884	+	3.62604i	0.463691	+	0.243364i
$223$	−0.0650169	−	0.0865218i	−0.00435385	−	0.00579393i	0.797261	−	0.603635i	$-0.206282\pi$
$223$	−0.0650169	−	0.0865218i	−0.00435385	−	0.00579393i	−0.801614	+	0.597841i	$0.796025\pi$
$224$	−0.477565	−	1.64875i	−0.0319087	−	0.110162i
$225$	1.82950	−	0.147693i	0.121967	−	0.00984618i
$226$	8.62946	+	5.95648i	0.574023	+	0.396219i
$227$	25.6887	−	5.24439i	1.70502	−	0.348082i	0.753920	−	0.656966i	$-0.228160\pi$
$227$	25.6887	−	5.24439i	1.70502	−	0.348082i	0.951100	+	0.308883i	$0.0999553\pi$
$228$	9.16988	−	21.5225i	0.607290	−	1.42536i
$229$	2.45521	+	9.96120i	0.162245	+	0.658254i	0.994579	+	0.103980i	$0.0331579\pi$
$229$	2.45521	+	9.96120i	0.162245	+	0.658254i	−0.832334	+	0.554274i	$0.812996\pi$
$230$	−0.725253	+	17.9970i	−0.0478218	+	1.18669i
$231$	2.02461	−	1.52140i	0.133210	−	0.100101i
$232$	0.874880	+	2.05342i	0.0574387	+	0.134814i
$233$	−11.1530	−	16.1579i	−0.730657	−	1.05854i	−0.995547	−	0.0942612i	$-0.969951\pi$
$233$	−11.1530	−	16.1579i	−0.730657	−	1.05854i	0.264890	−	0.964279i	$-0.414664\pi$
$234$	−10.6477	+	10.3683i	−0.696064	+	0.677794i
$235$	4.47172	−	6.47840i	0.291703	−	0.422604i
$236$	41.1153	+	8.39375i	2.67638	+	0.546387i
$237$	8.32804	+	8.67040i	0.540964	+	0.563203i
$238$	−1.38982	−	2.92898i	−0.0900887	−	0.189858i
$239$			2.57437i			0.166522i	0.996528	+	0.0832611i	$0.0265335\pi$
$239$			2.57437i			0.166522i	−0.996528	+	0.0832611i	$0.973466\pi$
$240$	−1.63872	+	0.777582i	−0.105779	+	0.0501927i
$241$	−0.767583	+	1.02147i	−0.0494444	+	0.0657985i	−0.823488	−	0.567334i	$-0.807975\pi$
$241$	−0.767583	+	1.02147i	−0.0494444	+	0.0657985i	0.774043	+	0.633133i	$0.218231\pi$
$242$	−17.3133	−	6.56606i	−1.11294	−	0.422082i
$243$	−15.4635	−	6.58838i	−0.991984	−	0.422645i
$244$	−22.9806	+	3.73471i	−1.47118	+	0.239090i
$245$	−2.19485	+	6.57438i	−0.140224	+	0.420022i
$246$	−38.9293	+	34.4884i	−2.48204	+	2.19890i
$247$	5.78105	−	11.2004i	0.367840	−	0.712665i
$248$	1.89157	+	1.67579i	0.120115	+	0.106413i
$249$	23.2891	−	13.4460i	1.47589	−	0.852103i
$250$	−2.13016	−	0.711152i	−0.134723	−	0.0449772i
$251$	−4.58411	+	4.77257i	−0.289347	+	0.301242i	−0.849972	−	0.526828i	$-0.823381\pi$
$251$	−4.58411	+	4.77257i	−0.289347	+	0.301242i	0.560625	+	0.828069i	$0.310561\pi$
$252$	1.20686	−	0.833034i	0.0760249	−	0.0524762i
$253$	27.2543	−	22.2525i	1.71347	−	1.39900i
$254$	−36.2762	+	29.6186i	−2.27617	+	1.85844i
$255$	−9.95154	+	6.86905i	−0.623189	+	0.430157i
$256$	−7.13435	+	7.42764i	−0.445897	+	0.464228i
$257$	−9.52681	−	3.18052i	−0.594266	−	0.198395i	0.00359684	−	0.999994i	$-0.498855\pi$
$257$	−9.52681	−	3.18052i	−0.594266	−	0.198395i	−0.597863	+	0.801598i	$0.703983\pi$
$258$	37.1845	−	21.4685i	2.31501	−	1.33657i
$259$	−0.310480	−	0.275061i	−0.0192923	−	0.0170915i
$260$	10.2329	−	3.96111i	0.634619	−	0.245658i
$261$	1.30878	−	1.15948i	0.0810116	−	0.0717700i
$262$	−4.92753	+	14.7598i	−0.304424	+	0.911861i
$263$	−7.03040	+	1.14255i	−0.433513	+	0.0704527i	−0.373252	−	0.927730i	$-0.621757\pi$
$263$	−7.03040	+	1.14255i	−0.433513	+	0.0704527i	−0.0602609	+	0.998183i	$0.519193\pi$
$264$	−20.7937	−	8.85937i	−1.27976	−	0.545256i
$265$	4.75443	+	1.80312i	0.292063	+	0.110765i
$266$	−1.23814	+	1.64767i	−0.0759152	+	0.101025i
$267$	8.20929	−	3.89536i	0.502400	−	0.238392i
$268$		−	45.2961i		−	2.76690i
$269$	4.81014	+	10.1372i	0.293279	+	0.618073i	0.995591	−	0.0937961i	$-0.0299002\pi$
$269$	4.81014	+	10.1372i	0.293279	+	0.618073i	−0.702312	+	0.711869i	$0.747849\pi$
$270$	3.98377	+	4.14754i	0.242444	+	0.252411i
$271$	−30.4009	−	6.20639i	−1.84672	−	0.377011i	−0.856459	−	0.516214i	$-0.827341\pi$
$271$	−30.4009	−	6.20639i	−1.84672	−	0.377011i	−0.990264	+	0.139203i	$0.955546\pi$
$272$	2.57668	−	3.73296i	0.156234	−	0.226344i
$273$	1.79542	−	1.05303i	0.108664	−	0.0637322i
$274$	−7.47565	−	10.8303i	−0.451620	−	0.654285i
$275$	1.71953	+	4.03589i	0.103692	+	0.243373i
$276$	42.9088	−	32.2439i	2.58281	−	1.94085i
$277$	−0.615075	+	15.2629i	−0.0369563	+	0.917060i	0.869288	+	0.494306i	$0.164578\pi$
$277$	−0.615075	+	15.2629i	−0.0369563	+	0.917060i	−0.906244	+	0.422754i	$0.861063\pi$
$278$	−3.20624	−	13.0082i	−0.192298	−	0.780182i
$279$	0.775968	−	1.82126i	0.0464560	−	0.109036i
$280$	−0.602673	+	0.123037i	−0.0360166	+	0.00735284i
$281$	19.8697	+	13.7151i	1.18533	+	0.818172i	0.986803	−	0.161925i	$-0.0517701\pi$
$281$	19.8697	+	13.7151i	1.18533	+	0.818172i	0.198523	+	0.980096i	$0.436386\pi$
$282$	−38.7474	+	3.12801i	−2.30737	+	0.186270i
$283$	−5.58362	−	19.2769i	−0.331912	−	1.14589i	−0.936883	−	0.349644i	$-0.886302\pi$
$283$	−5.58362	−	19.2769i	−0.331912	−	1.14589i	0.604971	−	0.796248i	$-0.293185\pi$
$284$	3.67089	+	4.88507i	0.217827	+	0.289876i
$285$	6.80667	+	3.57241i	0.403192	+	0.211612i
$286$	−31.5649	−	16.2921i	−1.86647	−	0.963373i
$287$	2.44818	−	1.28491i	0.144512	−	0.0758456i
$288$	10.8423	+	5.14474i	0.638889	+	0.303157i
$289$	5.67525	−	11.9603i	0.333838	−	0.703549i
$290$	−2.02926	+	0.677467i	−0.119162	+	0.0397822i
$291$	17.5548	−	19.8152i	1.02908	−	1.16159i
$292$	0.267393	−	1.64533i	0.0156480	−	0.0962859i
$293$	−6.65250	−	0.268087i	−0.388643	−	0.0156618i	−0.154825	−	0.987942i	$-0.549481\pi$
$293$	−6.65250	−	0.268087i	−0.388643	−	0.0156618i	−0.233819	+	0.972280i	$0.575122\pi$
$294$	32.0034	−	12.1373i	1.86648	−	0.707862i
$295$	−3.83626	+	13.2443i	−0.223355	+	0.771113i
$296$	−0.740492	+	3.62717i	−0.0430403	+	0.210825i
$297$	0.903966	−	11.1976i	0.0524534	−	0.649753i
$298$	−18.7087	+	49.3308i	−1.08377	+	2.85766i
$299$	24.3348	−	15.6224i	1.40732	−	0.903468i
$300$	2.37307	+	6.25727i	0.137009	+	0.361264i
$301$	−2.19248	+	0.635058i	−0.126372	+	0.0366041i
$302$	−1.55752	−	38.6494i	−0.0896251	−	2.22402i
$303$	−20.1325	−	24.6579i	−1.15658	−	1.41656i
$304$	−2.86255	−	0.347576i	−0.164178	−	0.0199349i
$305$	−0.615589	−	7.62544i	−0.0352485	−	0.436631i
$306$	21.7714	+	6.30618i	1.24459	+	0.360500i
$307$	−4.57304	+	18.5535i	−0.260997	+	1.05891i	0.683386	+	0.730057i	$0.260507\pi$
$307$	−4.57304	+	18.5535i	−0.260997	+	1.05891i	−0.944383	+	0.328849i	$0.893339\pi$
$308$	2.80201	+	2.10558i	0.159660	+	0.119976i
$309$	2.09234	−	2.56266i	0.119029	−	0.145784i
$310$	−1.74689	+	1.67791i	−0.0992169	+	0.0952991i
$311$	24.8916	+	6.13523i	1.41147	+	0.347897i	0.870096	−	0.492883i	$-0.164057\pi$
$311$	24.8916	+	6.13523i	1.41147	+	0.347897i	0.541378	+	0.840780i	$0.317903\pi$
$312$	−16.1509	−	9.17798i	−0.914364	−	0.519601i
$313$	−18.3997	+	4.53512i	−1.04001	+	0.256340i	−0.722106	−	0.691782i	$-0.756826\pi$
$313$	−18.3997	+	4.53512i	−1.04001	+	0.256340i	−0.317906	+	0.948122i	$0.602980\pi$
$314$	−7.40936	+	11.7170i	−0.418134	+	0.661227i
$315$	0.240928	+	0.417300i	0.0135748	+	0.0235122i
$316$	−8.31918	+	14.4092i	−0.467990	+	0.810583i
$317$	1.33624	+	2.54599i	0.0750507	+	0.142997i	0.920090	−	0.391707i	$-0.128115\pi$
$317$	1.33624	+	2.54599i	0.0750507	+	0.142997i	−0.845039	+	0.534704i	$0.820423\pi$
$318$	−7.95171	−	23.8183i	−0.445910	−	1.33566i
$319$	3.61925	+	2.08957i	0.202639	+	0.116994i
$320$	−8.64304	−	9.75598i	−0.483161	−	0.545376i
$321$	−21.3584	+	13.5062i	−1.19211	+	0.753844i
$322$	−4.35015	+	1.85343i	−0.242425	+	0.103287i
$323$	−19.2078	+	0.774046i	−1.06875	+	0.0430691i
$324$	4.08557	−	33.6477i	0.226976	−	1.86932i
$325$	1.02679	+	3.45625i	0.0569563	+	0.191718i
$326$	2.48110	+	20.4337i	0.137416	+	1.13172i
$327$	−0.135862	−	0.835994i	−0.00751320	−	0.0462306i
$328$	−20.8560	−	13.1885i	−1.15158	−	0.728214i
$329$	2.03981	+	0.331502i	0.112459	+	0.0182763i
$330$	10.0677	−	19.1825i	0.554211	−	1.05596i
$331$	13.3225	+	21.0679i	0.732273	+	1.15800i	0.981853	+	0.189643i	$0.0607331\pi$
$331$	13.3225	+	21.0679i	0.732273	+	1.15800i	−0.249580	+	0.968354i	$0.580293\pi$
$332$	26.8415	+	25.7816i	1.47312	+	1.41495i
$333$	2.87890	−	0.349562i	0.157763	−	0.0191559i
$334$	7.67876	+	37.6131i	0.420163	+	2.05809i
$335$	14.8355	+	1.19765i	0.810552	+	0.0654345i
$336$	−0.368855	−	0.301160i	−0.0201227	−	0.0164296i
$337$	25.7407			1.40218			0.701091	−	0.713071i	$-0.252696\pi$
$337$	25.7407			1.40218			0.701091	+	0.713071i	$0.252696\pi$
$338$	−24.2513	−	16.2541i	−1.31909	−	0.884108i
$339$	10.2672			0.557639
$340$	−12.9631	−	10.5840i	−0.703020	−	0.573998i
$341$	4.71631	+	0.380740i	0.255402	+	0.0206182i
$342$	−2.88228	−	14.1183i	−0.155856	−	0.763433i
$343$	−3.63062	+	0.440838i	−0.196035	+	0.0238030i
$344$	14.6922	+	14.1120i	0.792148	+	0.760868i
$345$	9.42611	+	14.9062i	0.507485	+	0.802523i
$346$	2.81739	−	5.36810i	0.151464	−	0.288591i
$347$	14.9380	+	2.42766i	0.801912	+	0.130323i	0.547536	−	0.836782i	$-0.315566\pi$
$347$	14.9380	+	2.42766i	0.801912	+	0.130323i	0.254376	+	0.967105i	$0.418130\pi$
$348$	5.38823	+	3.40731i	0.288839	+	0.182651i
$349$	−0.895557	−	5.51059i	−0.0479381	−	0.294975i	0.952000	−	0.306098i	$-0.0990235\pi$
$349$	−0.895557	−	5.51059i	−0.0479381	−	0.294975i	−0.999938	+	0.0111229i	$0.996459\pi$
$350$	−0.0710644	−	0.585268i	−0.00379855	−	0.0312839i
$351$	1.78493	−	9.05892i	0.0952724	−	0.483529i
$352$	−3.45744	+	28.4746i	−0.184282	+	1.51770i
$353$	11.0364	−	0.444753i	0.587410	−	0.0236718i	0.255218	−	0.966884i	$-0.417853\pi$
$353$	11.0364	−	0.444753i	0.587410	−	0.0236718i	0.332192	+	0.943212i	$0.392212\pi$
$354$	62.6438	−	26.6900i	3.32948	−	1.41856i
$355$	−1.69704	+	1.07314i	−0.0900693	+	0.0569564i
$356$	8.33918	+	9.41299i	0.441976	+	0.498887i
$357$	−2.74919	−	1.58724i	−0.145502	−	0.0840058i
$358$	5.25129	+	15.7295i	0.277539	+	0.831332i
$359$	−0.226898	−	0.432317i	−0.0119752	−	0.0228168i	0.879395	−	0.476093i	$-0.157947\pi$
$359$	−0.226898	−	0.432317i	−0.0119752	−	0.0228168i	−0.891370	+	0.453276i	$0.850255\pi$
$360$	2.15024	−	3.72433i	0.113328	−	0.196289i
$361$	−3.38962	−	5.87100i	−0.178401	−	0.309000i
$362$	−8.79731	+	13.9118i	−0.462376	+	0.731189i
$363$	−17.6041	+	4.33902i	−0.923976	+	0.227740i
$364$	2.09115	+	1.98125i	0.109606	+	0.103846i
$365$	0.531816	+	0.131081i	0.0278365	+	0.00686108i
$366$	−27.2464	+	26.1705i	−1.42419	+	1.36796i
$367$	18.7022	−	22.9061i	0.976248	−	1.19569i	−0.00441658	−	0.999990i	$-0.501406\pi$
$367$	18.7022	−	22.9061i	0.976248	−	1.19569i	0.980665	−	0.195696i	$-0.0626967\pi$
$368$	−5.28887	−	3.97433i	−0.275701	−	0.207176i
$369$	−4.62612	+	18.7689i	−0.240826	+	0.977070i
$370$	−3.40820	−	0.987197i	−0.177184	−	0.0513219i
$371$	0.107416	+	1.33059i	0.00557677	+	0.0690807i
$372$	7.16537	+	0.870033i	0.371507	+	0.0451091i
$373$	−10.8880	−	13.3353i	−0.563757	−	0.690478i	0.411535	−	0.911394i	$-0.364993\pi$
$373$	−10.8880	−	13.3353i	−0.563757	−	0.690478i	−0.975293	+	0.220916i	$0.929095\pi$
$374$	2.18141	+	54.1312i	0.112798	+	2.79906i
$375$	−2.11215	+	0.611791i	−0.109071	+	0.0315927i
$376$	−6.54026	−	17.2452i	−0.337288	−	0.889355i
$377$	2.75995	+	2.04458i	0.142145	+	0.105301i
$378$	−0.535368	+	1.41165i	−0.0275364	+	0.0726075i
$379$	−0.957296	+	11.8582i	−0.0491730	+	0.609117i	0.924502	+	0.381177i	$0.124481\pi$
$379$	−0.957296	+	11.8582i	−0.0491730	+	0.609117i	−0.973675	+	0.227940i	$0.926801\pi$
$380$	−2.12805	+	10.4239i	−0.109167	+	0.534733i
$381$	−12.7581	+	44.0461i	−0.653618	+	2.25655i
$382$	−6.89059	+	2.61326i	−0.352553	+	0.133706i
$383$	−7.65264	−	0.308391i	−0.391032	−	0.0157580i	−0.156028	−	0.987753i	$-0.549869\pi$
$383$	−7.65264	−	0.308391i	−0.391032	−	0.0157580i	−0.235003	+	0.971995i	$0.575510\pi$
$384$	−5.71214	+	35.1482i	−0.291497	+	1.79365i
$385$	−0.763712	+	0.862053i	−0.0389224	+	0.0439343i
$386$	−39.1181	+	13.0595i	−1.99106	+	0.664713i
$387$	6.84138	−	14.4179i	0.347767	−	0.732904i
$388$	33.1005	+	15.7064i	1.68042	+	0.797370i
$389$	−12.1606	+	6.38240i	−0.616569	+	0.323601i	−0.743932	−	0.668256i	$-0.767041\pi$
$389$	−12.1606	+	6.38240i	−0.616569	+	0.323601i	0.127362	+	0.991856i	$0.459349\pi$
$390$	10.0141	−	14.7223i	0.507082	−	0.745492i
$391$	−39.0518	−	20.4960i	−1.97493	−	1.03653i
$392$	9.75580	+	12.9826i	0.492742	+	0.655721i
$393$	4.23907	+	14.6350i	0.213833	+	0.738236i
$394$	−16.7555	+	1.35264i	−0.844130	+	0.0681452i
$395$	−4.49940	−	3.10571i	−0.226389	−	0.156265i
$396$	−24.0096	+	4.90160i	−1.20653	+	0.246314i
$397$	5.20169	−	12.2088i	0.261066	−	0.612743i	−0.736934	−	0.675965i	$-0.763727\pi$
$397$	5.20169	−	12.2088i	0.261066	−	0.612743i	0.998000	+	0.0632214i	$0.0201374\pi$
$398$	−13.8402	−	56.1519i	−0.693746	−	2.81464i
$399$	−0.0812606	+	2.01646i	−0.00406812	+	0.100949i
$400$	0.659431	−	0.495530i	0.0329715	−	0.0247765i
$401$	3.87642	+	9.09829i	0.193579	+	0.454347i	0.988280	−	0.152655i	$-0.0487823\pi$
$401$	3.87642	+	9.09829i	0.193579	+	0.454347i	−0.794700	+	0.607002i	$0.792372\pi$
$402$	−41.7531	−	60.4898i	−2.08245	−	3.01696i
$403$	3.81551	+	0.751790i	0.190064	+	0.0374493i
$404$	25.0266	−	36.2573i	1.24512	−	1.80387i
$405$	10.9124	+	2.22778i	0.542241	+	0.110699i
$406$	−0.389062	−	0.405057i	−0.0193088	−	0.0201026i
$407$	2.97145	+	6.26220i	0.147289	+	0.310406i
$408$			28.3317i			1.40263i
$409$	−31.9734	+	15.1716i	−1.58099	+	0.750187i	−0.998055	−	0.0623358i	$-0.980145\pi$
$409$	−31.9734	+	15.1716i	−1.58099	+	0.750187i	−0.582930	+	0.812522i	$0.698094\pi$
$410$	14.2085	−	18.9081i	0.701708	−	0.933804i
$411$	−12.0484	−	4.56937i	−0.594306	−	0.225390i
$412$	4.21227	+	1.79468i	0.207524	+	0.0884176i
$413$	−3.57303	+	0.580674i	−0.175817	+	0.0285731i
$414$	10.4689	−	31.3581i	0.514517	−	1.54117i
$415$	−9.15380	+	8.10956i	−0.449342	+	0.398083i
$416$	−5.48507	+	22.9277i	−0.268928	+	1.12412i
$417$	−9.81937	−	8.69920i	−0.480857	−	0.426002i
$418$	29.8263	−	17.2202i	1.45885	−	0.842268i
$419$	−4.96456	−	1.65741i	−0.242535	−	0.0809700i	0.192802	−	0.981238i	$-0.438242\pi$
$419$	−4.96456	−	1.65741i	−0.242535	−	0.0809700i	−0.435337	+	0.900268i	$0.643371\pi$
$420$	−1.21703	+	1.26706i	−0.0593849	+	0.0618262i
$421$	−0.819899	+	0.565935i	−0.0399594	+	0.0275820i	−0.587877	−	0.808950i	$-0.700036\pi$
$421$	−0.819899	+	0.565935i	−0.0399594	+	0.0275820i	0.547918	+	0.836532i	$0.315421\pi$
$422$	−35.1952	+	28.7360i	−1.71327	+	1.39884i
$423$	−11.1918	+	9.13783i	−0.544164	+	0.444296i
$424$	9.80493	−	6.76786i	0.476170	−	0.328676i
$425$	3.80926	−	3.96586i	0.184776	−	0.192372i
$426$	9.40518	+	3.13991i	0.455683	+	0.152129i
$427$	1.73932	−	1.00420i	0.0841718	−	0.0485966i
$428$	−26.1782	−	23.1919i	−1.26537	−	1.12102i
$429$	−34.4987	+	4.42858i	−1.66561	+	0.213814i
$430$	−14.6154	+	12.9481i	−0.704817	+	0.624414i
$431$	8.42076	−	25.2232i	0.405614	−	1.21496i	−0.525677	−	0.850684i	$-0.676188\pi$
$431$	8.42076	−	25.2232i	0.405614	−	1.21496i	0.931291	−	0.364277i	$-0.118684\pi$
$432$	−2.08495	+	0.338838i	−0.100312	+	0.0163023i
$433$	0.114404	+	0.0487430i	0.00549790	+	0.00234244i	0.394714	−	0.918804i	$-0.370844\pi$
$433$	0.114404	+	0.0487430i	0.00549790	+	0.00234244i	−0.389216	+	0.921147i	$0.627254\pi$
$434$	−0.594570	−	0.225491i	−0.0285403	−	0.0108239i
$435$	−1.25844	+	1.67468i	−0.0603376	+	0.0802948i
$436$	1.05900	−	0.502503i	0.0507170	−	0.0240655i
$437$			28.0377i			1.34123i
$438$	−1.15955	−	2.44371i	−0.0554056	−	0.116765i
$439$	−1.05863	−	1.10215i	−0.0505256	−	0.0526027i	0.695460	−	0.718565i	$-0.255201\pi$
$439$	−1.05863	−	1.10215i	−0.0505256	−	0.0526027i	−0.745985	+	0.665962i	$0.768021\pi$
$440$	10.0709	+	2.05599i	0.480111	+	0.0980154i
$441$	7.22674	−	10.4697i	0.344130	−	0.498559i
$442$	−3.27914	+	44.4047i	−0.155973	+	2.11212i
$443$	2.63547	+	3.81814i	0.125215	+	0.181405i	0.880578	−	0.473902i	$-0.157155\pi$
$443$	2.63547	+	3.81814i	0.125215	+	0.181405i	−0.755363	+	0.655307i	$0.772539\pi$
$444$	4.14454	+	9.72758i	0.196691	+	0.461651i
$445$	−3.30347	+	2.48239i	−0.156599	+	0.117677i
$446$	0.00978664	−	0.242853i	0.000463411	−	0.0114994i
$447$	12.3632	+	50.1595i	0.584759	+	2.37246i
$448$	1.34121	−	3.14793i	0.0633662	−	0.148726i
$449$	22.1559	−	4.52316i	1.04560	−	0.213461i	0.353629	−	0.935386i	$-0.384947\pi$
$449$	22.1559	−	4.52316i	1.04560	−	0.213461i	0.691972	+	0.721925i	$0.256742\pi$
$450$	3.39229	+	2.34153i	0.159914	+	0.110381i
$451$	−46.0525	+	3.71774i	−2.16853	+	0.175062i
$452$	3.95335	+	13.6486i	0.185950	+	0.641974i
$453$	−22.7533	−	30.2791i	−1.06904	−	1.42264i
$454$	52.1356	+	27.3629i	2.44684	+	1.28420i
$455$	−0.704197	+	0.632515i	−0.0330133	+	0.0296527i
$456$	15.9481	−	8.37019i	0.746837	−	0.391970i
$457$	−21.0553	−	9.99086i	−0.984925	−	0.467353i	−0.133057	−	0.991108i	$-0.542479\pi$
$457$	−21.0553	−	9.99086i	−0.984925	−	0.467353i	−0.851869	+	0.523756i	$0.824530\pi$
$458$	−9.87694	+	20.8152i	−0.461519	+	0.972631i
$459$	−13.3570	+	4.45923i	−0.623452	+	0.208139i
$460$	−16.1858	+	18.2700i	−0.754668	+	0.851844i
$461$	−2.05767	+	12.6613i	−0.0958352	+	0.589697i	0.894066	+	0.447936i	$0.147841\pi$
$461$	−2.05767	+	12.6613i	−0.0958352	+	0.589697i	−0.989901	+	0.141762i	$0.954723\pi$
$462$	5.68277	+	0.229008i	0.264387	+	0.0106544i
$463$	−27.8097	+	10.5468i	−1.29243	+	0.490153i	−0.902499	−	0.430693i	$-0.858269\pi$
$463$	−27.8097	+	10.5468i	−1.29243	+	0.490153i	−0.389928	+	0.920845i	$0.627500\pi$
$464$	0.218621	−	0.754768i	0.0101492	−	0.0350392i
$465$	−0.474412	+	2.32382i	−0.0220003	+	0.107765i
$466$	3.54787	−	43.9482i	0.164352	−	2.03586i
$467$	12.0239	−	31.7044i	0.556400	−	1.46711i	−0.301589	−	0.953438i	$-0.597517\pi$
$467$	12.0239	−	31.7044i	0.556400	−	1.46711i	0.857989	−	0.513668i	$-0.171714\pi$
$468$	−20.0633	+	1.75789i	−0.927424	+	0.0812586i
$469$	1.38559	+	3.65349i	0.0639804	+	0.168702i
$470$	16.9801	−	4.91834i	0.783233	−	0.226866i
$471$	0.546587	+	13.5634i	0.0251854	+	0.624969i
$472$	20.4324	+	25.0252i	0.940479	+	1.15188i
$473$	37.8650	+	4.59764i	1.74103	+	0.211400i
$474$	2.17248	+	26.9110i	0.0997853	+	1.23606i
$475$	−3.35780	−	0.972598i	−0.154066	−	0.0446259i
$476$	1.05141	−	4.26575i	0.0481914	−	0.195520i
$477$	−7.46123	−	5.60675i	−0.341626	−	0.256715i
$478$	−3.65639	+	4.47826i	−0.167239	+	0.204831i
$479$	−1.15454	+	1.10895i	−0.0527522	+	0.0506692i	−0.718637	−	0.695385i	$-0.755234\pi$
$479$	−1.15454	+	1.10895i	−0.0527522	+	0.0506692i	0.665885	+	0.746055i	$0.268054\pi$
$480$	−13.9600	−	3.44083i	−0.637184	−	0.157052i
$481$	1.84092	+	5.39118i	0.0839389	+	0.245817i
$482$	−2.78605	+	0.686699i	−0.126901	+	0.0312783i
$483$	−2.47461	+	3.91328i	−0.112599	+	0.178061i
$484$	−12.5464	−	21.7310i	−0.570291	−	0.987773i
$485$	−6.01939	+	10.4259i	−0.273327	+	0.473416i
$486$	−17.5421	−	33.4237i	−0.795727	−	1.51613i
$487$	−11.0183	−	33.0039i	−0.499288	−	1.49555i	−0.833214	−	0.552951i	$-0.813502\pi$
$487$	−11.0183	−	33.0039i	−0.499288	−	1.49555i	0.333926	−	0.942599i	$-0.391627\pi$
$488$	−15.5231	−	8.96229i	−0.702700	−	0.405704i
$489$	13.3653	+	15.0863i	0.604401	+	0.682228i
$490$	−13.1557	+	8.31915i	−0.594313	+	0.375821i
$491$	30.5095	−	12.9989i	1.37687	−	0.586631i	0.428430	−	0.903575i	$-0.359067\pi$
$491$	30.5095	−	12.9989i	1.37687	−	0.586631i	0.948444	+	0.316944i	$0.102657\pi$
$492$	−70.4231	+	2.83796i	−3.17492	+	0.127945i
$493$	0.631430	−	5.20030i	0.0284382	−	0.234210i
$494$	25.9644	−	11.2729i	1.16820	−	0.507191i
$495$	−0.970564	−	7.99331i	−0.0436236	−	0.359273i
$496$	−0.142714	−	0.878157i	−0.00640806	−	0.0394304i
$497$	−0.445518	−	0.281729i	−0.0199842	−	0.0126373i
$498$	59.6100	+	9.68757i	2.67119	+	0.434110i
$499$	−11.9934	+	22.8515i	−0.536898	+	1.02297i	0.454333	+	0.890832i	$0.349877\pi$
$499$	−11.9934	+	22.8515i	−0.536898	+	1.02297i	−0.991231	+	0.132141i	$0.957815\pi$
$500$	−1.62655	−	2.57218i	−0.0727414	−	0.115031i
$501$	27.1096	+	26.0391i	1.21117	+	1.16334i
$502$	−14.7528	+	1.79132i	−0.658450	+	0.0799503i
$503$	−0.297064	−	1.45512i	−0.0132454	−	0.0648805i	0.972631	−	0.232356i	$-0.0746435\pi$
$503$	−0.297064	−	1.45512i	−0.0132454	−	0.0648805i	−0.985876	+	0.167476i	$0.946438\pi$
$504$	1.12533	+	0.0908463i	0.0501263	+	0.00404661i
$505$	11.2134	+	9.15546i	0.498990	+	0.407413i
$506$	79.0157			3.51268
$507$	−28.5839	+	0.391092i	−1.26946	+	0.0173690i
$508$	−63.4644			−2.81578
$509$	−8.08766	−	6.60337i	−0.358479	−	0.292689i	0.436041	−	0.899927i	$-0.356380\pi$
$509$	−8.08766	−	6.60337i	−0.358479	−	0.292689i	−0.794520	+	0.607237i	$0.792278\pi$
$510$	−27.0674	−	2.18511i	−1.19856	−	0.0967581i
$511$	0.0287626	+	0.140889i	0.00127238	+	0.00623255i
$512$	9.19112	−	1.11600i	0.406194	−	0.0493209i
$513$	6.45627	+	6.20133i	0.285051	+	0.273795i
$514$	−12.0551	−	19.0636i	−0.531728	−	0.840861i
$515$	−0.699175	+	1.33217i	−0.0308093	+	0.0587022i
$516$	57.4327	+	9.33373i	2.52833	+	0.410894i
$517$	−29.1872	−	18.4569i	−1.28365	−	0.811732i
$518$	−0.149427	−	0.919461i	−0.00656544	−	0.0403988i
$519$	−0.715539	−	5.89299i	−0.0314087	−	0.258674i
$520$	8.03119	+	2.62028i	0.352191	+	0.114907i
$521$	0.905489	−	7.45738i	0.0396702	−	0.326714i	−0.959341	−	0.282250i	$-0.908919\pi$
$521$	0.905489	−	7.45738i	0.0396702	−	0.326714i	0.999011	−	0.0444633i	$-0.0141578\pi$
$522$	3.92351	−	0.158112i	0.171728	−	0.00692038i
$523$	41.8218	−	17.8186i	1.82874	−	0.779154i	0.871156	−	0.491007i	$-0.163371\pi$
$523$	41.8218	−	17.8186i	1.82874	−	0.779154i	0.957586	−	0.288147i	$-0.0930391\pi$
$524$	−17.8225	+	11.2703i	−0.778580	+	0.492344i
$525$	−0.382813	−	0.432107i	−0.0167073	−	0.0188587i
$526$	−13.8525	−	7.99777i	−0.604000	−	0.348719i
$527$	−1.87817	−	5.62581i	−0.0818145	−	0.245064i
$528$	3.69791	+	7.04577i	0.160931	+	0.306628i
$529$	−20.6631	+	35.7895i	−0.898395	+	1.55607i
$530$	5.70963	+	9.88936i	0.248010	+	0.429566i
$531$	13.5265	−	21.3905i	0.587002	−	0.928269i
$532$	−2.71184	+	0.668408i	−0.117573	+	0.0289792i
$533$	−37.9517	−	1.26943i	−1.64387	−	0.0549852i
$534$	19.8131	+	4.88349i	0.857397	+	0.211329i
$535$	8.28805	−	7.96078i	0.358324	−	0.344175i
$536$	22.0552	−	27.0127i	0.952639	−	1.16677i
$537$	12.9810	+	9.75462i	0.560173	+	0.420943i
$538$	−6.03033	+	24.4660i	−0.259986	+	1.05480i
$539$	29.2057	+	8.45954i	1.25798	+	0.364378i
$540$	0.627101	+	7.76805i	0.0269862	+	0.334283i
$541$	−19.1025	−	2.31946i	−0.821281	−	0.0997216i	−0.300900	−	0.953656i	$-0.597287\pi$
$541$	−19.1025	−	2.31946i	−0.821281	−	0.0997216i	−0.520381	+	0.853934i	$0.674210\pi$
$542$	−44.0691	−	53.9749i	−1.89293	−	2.31842i
$543$	0.648975	+	16.1042i	0.0278502	+	0.691096i
$544$	34.5350	−	10.0032i	1.48068	−	0.428883i
$545$	0.136581	+	0.360134i	0.00585048	+	0.0154265i
$546$	4.61886	+	0.718242i	0.197669	+	0.0307379i
$547$	1.92309	−	5.07077i	0.0822254	−	0.216810i	−0.887598	−	0.460619i	$-0.847628\pi$
$547$	1.92309	−	5.07077i	0.0822254	−	0.216810i	0.969823	+	0.243808i	$0.0783968\pi$
$548$	1.43501	−	17.7758i	0.0613007	−	0.759345i
$549$	−2.80869	+	13.7579i	−0.119872	+	0.587173i
$550$	−2.74097	+	9.46292i	−0.116875	+	0.403500i
$551$	−3.11382	+	1.18092i	−0.132653	+	0.0503088i
$552$	41.2889	+	1.66389i	1.75737	+	0.0708198i
$553$	0.230236	−	1.41670i	0.00979062	−	0.0602441i
$554$	−22.7479	+	25.6771i	−0.966467	+	1.09092i
$555$	−3.29560	+	1.10023i	−0.139890	+	0.0467022i
$556$	7.78323	−	16.4028i	0.330082	−	0.695634i
$557$	−14.9095	−	7.07464i	−0.631735	−	0.299762i	0.0857702	−	0.996315i	$-0.472665\pi$
$557$	−14.9095	−	7.07464i	−0.631735	−	0.299762i	−0.717506	+	0.696553i	$0.754716\pi$
$558$	3.93658	−	2.06608i	0.166649	−	0.0874641i
$559$	30.4888	+	7.29396i	1.28954	+	0.308502i
$560$	0.191745	+	0.100635i	0.00810269	+	0.00425262i
$561$	31.8675	+	42.4080i	1.34545	+	1.79047i
$562$	15.0849	+	52.0791i	0.636318	+	2.19682i
$563$	40.3804	−	3.25984i	1.70183	−	0.137386i	0.809010	−	0.587795i	$-0.200004\pi$
$563$	40.3804	−	3.25984i	1.70183	−	0.137386i	0.892822	+	0.450409i	$0.148722\pi$
$564$	−43.3544	−	29.9254i	−1.82555	−	1.26009i
$565$	−4.57475	+	0.933942i	−0.192461	+	0.0392912i
$566$	17.6660	−	41.4636i	0.742558	−	1.74285i
$567$	0.699733	+	2.83893i	0.0293860	+	0.119224i
$568$	−0.189430	+	4.70065i	−0.00794829	+	0.197235i
$569$	−3.01552	+	2.26602i	−0.126417	+	0.0949963i	−0.662070	−	0.749442i	$-0.730322\pi$
$569$	−3.01552	+	2.26602i	−0.126417	+	0.0949963i	0.535653	+	0.844438i	$0.320066\pi$
$570$	6.76667	+	15.8819i	0.283424	+	0.665222i
$571$	−6.98243	−	10.1158i	−0.292206	−	0.423333i	0.649196	−	0.760621i	$-0.275106\pi$
$571$	−6.98243	−	10.1158i	−0.292206	−	0.423333i	−0.941401	+	0.337288i	$0.890490\pi$
$572$	−19.1706	−	44.1550i	−0.801565	−	1.84622i
$573$	−4.09917	+	5.93867i	−0.171245	+	0.248091i
$574$	6.08371	+	1.24200i	0.253929	+	0.0518400i
$575$	−5.55590	−	5.78430i	−0.231697	−	0.241222i
$576$	10.2556	+	21.6133i	0.427318	+	0.900553i
$577$			8.69526i			0.361988i	0.983484	+	0.180994i	$0.0579315\pi$
$577$			8.69526i			0.361988i	−0.983484	+	0.180994i	$0.942068\pi$
$578$	26.8597	−	12.7451i	1.11722	−	0.530126i
$579$	−24.2590	+	32.2828i	−1.00817	+	1.34163i
$580$	−2.71077	−	1.02806i	−0.112558	−	0.0426878i
$581$	−2.95363	−	1.25842i	−0.122537	−	0.0522082i
$582$	58.6812	−	9.53662i	2.43241	−	0.395305i
$583$	7.06391	−	21.1590i	0.292557	−	0.876316i
$584$	0.960594	−	0.851012i	0.0397496	−	0.0352151i
$585$	−0.0452701	−	6.61767i	−0.00187169	−	0.273607i
$586$	−11.1916	−	9.91492i	−0.462322	−	0.409582i
$587$	0.0376802	−	0.0217547i	0.00155523	−	0.000897912i	−0.499222	−	0.866474i	$-0.666381\pi$
$587$	0.0376802	−	0.0217547i	0.00155523	−	0.000897912i	0.500777	+	0.865576i	$0.333048\pi$
$588$	43.9967	+	14.6883i	1.81439	+	0.605734i
$589$	−2.61192	+	2.71930i	−0.107622	+	0.112047i
$590$	−25.4843	+	17.5905i	−1.04917	+	0.724191i
$591$	−12.7500	+	10.4100i	−0.524463	+	0.428211i
$592$	1.00954	−	0.824263i	0.0414918	−	0.0338770i
$593$	−1.30847	+	0.903168i	−0.0537322	+	0.0370887i	−0.594628	−	0.804001i	$-0.702701\pi$
$593$	−1.30847	+	0.903168i	−0.0537322	+	0.0370887i	0.540896	+	0.841090i	$0.318085\pi$
$594$	17.4765	−	18.1950i	0.717071	−	0.746550i
$595$	1.36933	+	0.457150i	0.0561371	+	0.0187413i
$596$	−61.9183	+	35.7485i	−2.53627	+	1.46432i
$597$	−42.3867	−	37.5514i	−1.73477	−	1.53687i
$598$	64.5202	+	7.38667i	2.63843	+	0.302063i
$599$	−17.7678	+	15.7409i	−0.725971	+	0.643154i	−0.942916	−	0.333029i	$-0.891929\pi$
$599$	−17.7678	+	15.7409i	−0.725971	+	0.643154i	0.216945	+	0.976184i	$0.430391\pi$
$600$	−1.63154	+	4.88704i	−0.0666071	+	0.199513i
$601$	15.3377	−	2.49262i	0.625638	−	0.101676i	0.160677	−	0.987007i	$-0.448632\pi$
$601$	15.3377	−	2.49262i	0.625638	−	0.101676i	0.464961	+	0.885331i	$0.346068\pi$
$602$	−4.71591	−	2.00926i	−0.192206	−	0.0818914i
$603$	−25.5433	−	9.68729i	−1.04020	−	0.394497i
$604$	31.4900	−	41.9055i	1.28131	−	1.70511i
$605$	7.44914	−	3.53466i	0.302851	−	0.143704i
$606$		−	71.4881i		−	2.90401i
$607$	−8.93155	−	18.8228i	−0.362521	−	0.763996i	0.637458	−	0.770485i	$-0.279986\pi$
$607$	−8.93155	−	18.8228i	−0.362521	−	0.763996i	−0.999979	+	0.00648895i	$0.997934\pi$
$608$	−15.8337	−	16.4847i	−0.642143	−	0.668541i
$609$	−0.538831	−	0.110003i	−0.0218345	−	0.00445755i
$610$	9.75958	−	14.1392i	0.395154	−	0.572479i
$611$	−22.1074	−	17.7995i	−0.894369	−	0.720089i
$612$	17.4489	+	25.2791i	0.705330	+	1.02185i
$613$	5.21822	+	12.2476i	0.210762	+	0.494676i	0.991488	−	0.130197i	$-0.0415610\pi$
$613$	5.21822	+	12.2476i	0.210762	+	0.494676i	−0.780726	+	0.624873i	$0.785151\pi$
$614$	−34.3067	+	25.7798i	−1.38451	+	1.04039i
$615$	0.932521	−	23.1403i	0.0376029	−	0.933106i
$616$	0.645774	+	2.62001i	0.0260190	+	0.105563i
$617$	8.19340	−	19.2306i	0.329854	−	0.774195i	−0.669649	−	0.742677i	$-0.733556\pi$
$617$	8.19340	−	19.2306i	0.329854	−	0.774195i	0.999503	−	0.0315178i	$-0.0100341\pi$
$618$	7.27950	−	1.48612i	0.292824	−	0.0597805i
$619$	4.02812	+	2.78041i	0.161904	+	0.111754i	0.646262	−	0.763116i	$-0.276331\pi$
$619$	4.02812	+	2.78041i	0.161904	+	0.111754i	−0.484358	+	0.874870i	$0.660947\pi$
$620$	−3.27181	+	0.264127i	−0.131399	+	0.0106076i
$621$	5.71418	+	19.7276i	0.229302	+	0.791642i
$622$	34.5864	+	46.0262i	1.38679	+	1.84548i
$623$	−0.960559	−	0.504140i	−0.0384840	−	0.0201980i
$624$	2.36086	+	6.09892i	0.0945101	+	0.244152i
$625$	0.885456	−	0.464723i	0.0354182	−	0.0185889i
$626$	−38.4486	−	18.2441i	−1.53671	−	0.729180i
$627$	14.4569	−	30.4673i	0.577353	−	1.21674i
$628$	−17.8198	+	5.94913i	−0.711089	+	0.237396i
$629$	5.76150	−	6.50338i	0.229726	−	0.259307i
$630$	−0.173585	+	1.06811i	−0.00691577	+	0.0425545i
$631$	−23.9947	−	0.966955i	−0.955216	−	0.0384939i	−0.442240	−	0.896897i	$-0.645816\pi$
$631$	−23.9947	−	0.966955i	−0.955216	−	0.0384939i	−0.512976	+	0.858403i	$0.671457\pi$
$632$	−11.9772	+	4.54236i	−0.476428	+	0.180685i
$633$	−12.3779	+	42.7335i	−0.491978	+	1.69850i
$634$	−1.29162	+	6.32676i	−0.0512967	+	0.251268i
$635$	1.67803	−	20.7861i	0.0665905	−	0.824871i
$636$	12.0667	−	31.8174i	0.478477	−	1.26164i
$637$	23.0571	+	9.63789i	0.913555	+	0.381867i
$638$	3.32805	+	8.77535i	0.131759	+	0.347420i
$639$	3.53986	−	1.02533i	0.140035	−	0.0405615i
$640$	−0.652054	−	16.1805i	−0.0257747	−	0.639592i
$641$	−7.53624	−	9.23022i	−0.297664	−	0.364572i	0.604019	−	0.796970i	$-0.293565\pi$
$641$	−7.53624	−	9.23022i	−0.297664	−	0.364572i	−0.901683	+	0.432398i	$0.857668\pi$
$642$	−56.3370	−	6.84055i	−2.22344	−	0.269975i
$643$	3.26923	+	40.4967i	0.128926	+	1.59703i	0.661034	+	0.750356i	$0.270118\pi$
$643$	3.26923	+	40.4967i	0.128926	+	1.59703i	−0.532108	+	0.846677i	$0.678600\pi$
$644$	−6.15490	−	1.78279i	−0.242537	−	0.0702517i
$645$	−4.57556	+	18.5638i	−0.180163	+	0.730948i
$646$	−34.5124	−	25.9343i	−1.35787	−	1.02037i
$647$	15.7607	−	19.3034i	0.619619	−	0.758895i	−0.365492	−	0.930814i	$-0.619099\pi$
$647$	15.7607	−	19.3034i	0.619619	−	0.758895i	0.985111	+	0.171919i	$0.0549968\pi$
$648$	18.8199	−	18.0768i	0.739316	−	0.710122i
$649$	58.7324	+	14.4762i	2.30545	+	0.568242i
$650$	−3.12276	+	7.47071i	−0.122485	+	0.293025i
$651$	−0.604557	+	0.149010i	−0.0236945	+	0.00584016i
$652$	−14.9085	+	23.5759i	−0.583862	+	0.923304i
$653$	0.0306876	+	0.0531524i	0.00120090	+	0.00208001i	0.866625	−	0.498960i	$-0.166284\pi$
$653$	0.0306876	+	0.0531524i	0.00120090	+	0.00208001i	−0.865424	+	0.501040i	$0.832951\pi$
$654$	0.951025	−	1.64722i	0.0371880	−	0.0644116i
$655$	−3.22004	−	6.13528i	−0.125818	−	0.239725i
$656$	2.75098	+	8.24020i	0.107408	+	0.321726i
$657$	−0.870647	−	0.502668i	−0.0339672	−	0.0196110i
$658$	3.07753	+	3.47382i	0.119975	+	0.135424i
$659$	2.67169	−	1.68947i	0.104074	−	0.0658125i	−0.481415	−	0.876493i	$-0.659877\pi$
$659$	2.67169	−	1.68947i	0.104074	−	0.0658125i	0.585489	+	0.810680i	$0.300903\pi$
$660$	27.0088	−	11.5074i	1.05132	−	0.447924i
$661$	8.28603	−	0.333916i	0.322289	−	0.0129878i	0.121406	−	0.992603i	$-0.461260\pi$
$661$	8.28603	−	0.333916i	0.322289	−	0.0129878i	0.200884	+	0.979615i	$0.435619\pi$
$662$	−6.74752	+	55.5709i	−0.262250	+	2.15982i
$663$	22.0570	+	37.6073i	0.856622	+	1.46055i
$664$	3.45379	+	28.4445i	0.134033	+	1.10386i
$665$	−0.147217	−	0.905864i	−0.00570884	−	0.0351279i
$666$	5.50449	+	3.48083i	0.213295	+	0.134879i
$667$	−7.54152	−	1.22562i	−0.292009	−	0.0474561i
$668$	−24.1762	+	46.0639i	−0.935406	+	1.78227i
$669$	−0.127197	−	0.201146i	−0.00491772	−	0.00777675i
$670$	24.1062	+	23.1543i	0.931305	+	0.894530i
$671$	−33.3164	+	4.04535i	−1.28617	+	0.156169i
$672$	−0.755010	−	3.69828i	−0.0291252	−	0.142664i
$673$	−22.4685	−	1.81384i	−0.866096	−	0.0699185i	−0.360572	−	0.932731i	$-0.617419\pi$
$673$	−22.4685	−	1.81384i	−0.866096	−	0.0699185i	−0.505524	+	0.862813i	$0.668701\pi$
$674$	44.7773	+	36.5595i	1.72476	+	1.40822i
$675$	−2.56080			−0.0985652
$676$	−11.5260	−	37.8469i	−0.443308	−	1.45565i
$677$	29.4821			1.13309			0.566545	−	0.824030i	$-0.308280\pi$
$677$	29.4821			1.13309			0.566545	+	0.824030i	$0.308280\pi$
$678$	17.8604	+	14.5826i	0.685924	+	0.560040i
$679$	−3.15026	−	0.254315i	−0.120896	−	0.00975973i
$680$	−2.57715	−	12.6237i	−0.0988292	−	0.484097i
$681$	57.2334	−	6.94940i	2.19319	−	0.266301i
$682$	7.66351	+	7.36090i	0.293451	+	0.281864i
$683$	−4.95102	−	7.82940i	−0.189445	−	0.299584i	0.737088	−	0.675797i	$-0.236200\pi$
$683$	−4.95102	−	7.82940i	−0.189445	−	0.299584i	−0.926533	+	0.376213i	$0.877226\pi$
$684$	9.07473	−	17.2905i	0.346981	−	0.661117i
$685$	5.78405	+	0.940000i	0.220997	+	0.0359156i
$686$	−6.94180	−	4.38973i	−0.265039	−	0.167600i
$687$	3.61886	+	22.2677i	0.138068	+	0.849567i
$688$	−0.864481	−	7.11964i	−0.0329580	−	0.271434i
$689$	7.74605	−	16.6170i	0.295101	−	0.633058i
$690$	−4.77408	+	39.3181i	−0.181746	+	1.49681i
$691$	28.7392	−	1.15815i	1.09329	−	0.0440580i	0.512939	−	0.858425i	$-0.328557\pi$
$691$	28.7392	−	1.15815i	1.09329	−	0.0440580i	0.580350	+	0.814367i	$0.302916\pi$
$692$	7.55823	−	3.22026i	0.287321	−	0.122416i
$693$	1.78663	−	1.12979i	0.0678683	−	0.0429173i
$694$	22.5374	+	25.4395i	0.855509	+	0.965670i
$695$	5.16651	+	2.98289i	0.195977	+	0.113147i
$696$	1.55426	+	4.65556i	0.0589139	+	0.176469i
$697$	26.9139	+	51.2802i	1.01944	+	1.94237i
$698$	6.26883	−	10.8579i	0.237279	−	0.410979i
$699$	−21.5865	−	37.3889i	−0.816477	−	1.41418i
$700$	0.427013	−	0.675268i	0.0161396	−	0.0255227i
$701$	−34.2329	+	8.43765i	−1.29296	+	0.318686i	−0.825034	−	0.565083i	$-0.808844\pi$
$701$	−34.2329	+	8.43765i	−1.29296	+	0.318686i	−0.467924	+	0.883769i	$0.654998\pi$
$702$	15.9714	−	13.2234i	0.602801	−	0.499083i
$703$	−5.36295	−	1.32185i	−0.202267	−	0.0498544i
$704$	−41.2374	+	39.6091i	−1.55419	+	1.49282i
$705$	10.9476	−	13.4083i	0.412310	−	0.504988i
$706$	19.8302	+	14.9014i	0.746319	+	0.560822i
$707$	−0.909500	+	3.68999i	−0.0342053	+	0.138776i
$708$	88.6328	+	25.6728i	3.33102	+	0.964843i
$709$	0.299951	+	3.71556i	0.0112649	+	0.139541i	0.999945	−	0.0104988i	$-0.00334192\pi$
$709$	0.299951	+	3.71556i	0.0112649	+	0.139541i	−0.988680	+	0.150040i	$0.952060\pi$
$710$	−4.47627	−	0.543518i	−0.167991	−	0.0203979i
$711$	6.34644	+	7.77297i	0.238010	+	0.291509i
$712$	0.389847	+	9.67395i	0.0146101	+	0.362547i
$713$	−8.30903	+	2.40674i	−0.311176	+	0.0901332i
$714$	−2.52799	−	6.66577i	−0.0946078	−	0.249460i
$715$	14.9687	−	5.11136i	0.559797	−	0.191154i
$716$	−7.96884	+	21.0121i	−0.297810	+	0.785260i
$717$	−0.455517	+	5.64260i	−0.0170116	+	0.210727i
$718$	0.219321	−	1.07430i	0.00818497	−	0.0400926i
$719$	2.84072	−	9.80730i	0.105941	−	0.365751i	−0.889978	−	0.456004i	$-0.849280\pi$
$719$	2.84072	−	9.80730i	0.105941	−	0.365751i	0.995919	+	0.0902530i	$0.0287676\pi$
$720$	−1.41561	+	0.536871i	−0.0527567	+	0.0200080i
$721$	−0.394651	−	0.0159039i	−0.0146976	−	0.000592292i
$722$	2.44216	−	15.0272i	0.0908879	−	0.559256i
$723$	−1.86316	+	2.10307i	−0.0692916	+	0.0782141i
$724$	−21.1579	+	7.06355i	−0.786327	+	0.262515i
$725$	0.408387	−	0.860658i	0.0151671	−	0.0319640i
$726$	−36.7860	−	17.4552i	−1.36526	−	0.647823i
$727$	20.6009	−	10.8122i	0.764047	−	0.401003i	−0.0372223	−	0.999307i	$-0.511851\pi$
$727$	20.6009	−	10.8122i	0.764047	−	0.401003i	0.801269	+	0.598304i	$0.204159\pi$
$728$	0.282379	+	2.19974i	0.0104657	+	0.0815277i
$729$	−3.14247	−	1.64929i	−0.116388	−	0.0610850i
$730$	0.738949	+	0.983362i	0.0273497	+	0.0363959i
$731$	−13.3021	−	45.9241i	−0.491995	−	1.69856i
$732$	−51.0306	+	4.11961i	−1.88614	+	0.152265i
$733$	33.9792	+	23.4541i	1.25505	+	0.866298i	0.995056	−	0.0993123i	$-0.0316643\pi$
$733$	33.9792	+	23.4541i	1.25505	+	0.866298i	0.259993	+	0.965610i	$0.416280\pi$
$734$	65.0671	−	13.2835i	2.40167	−	0.490305i
$735$	−5.97405	+	14.0216i	−0.220356	+	0.517195i
$736$	−12.5499	−	50.9168i	−0.462594	−	1.87682i
$737$	2.62914	−	65.2414i	0.0968455	−	2.40320i
$738$	−34.7049	+	26.0791i	−1.27751	+	0.959983i
$739$	−10.3889	−	24.3836i	−0.382162	−	0.896966i	−0.994340	−	0.106246i	$-0.966117\pi$
$739$	−10.3889	−	24.3836i	−0.382162	−	0.896966i	0.612178	−	0.790720i	$-0.290294\pi$
$740$	−2.73153	−	3.95730i	−0.100413	−	0.145473i
$741$	14.6530	−	23.5265i	0.538290	−	0.864269i
$742$	−1.70298	+	2.46720i	−0.0625184	+	0.0905736i
$743$	42.1276	+	8.60040i	1.54551	+	0.315518i	0.895728	−	0.444602i	$-0.146655\pi$
$743$	42.1276	+	8.60040i	1.54551	+	0.315518i	0.649782	+	0.760120i	$0.274860\pi$
$744$	3.84950	+	4.00775i	0.141129	+	0.146931i
$745$	−10.0713	−	21.2249i	−0.368985	−	0.777620i
$746$		−	38.6618i		−	1.41551i
$747$	20.2792	−	9.62260i	0.741978	−	0.352073i
$748$	−44.1039	+	58.6916i	−1.61260	+	2.14598i
$749$	2.82091	+	1.06983i	0.103074	+	0.0390907i
$750$	−4.54313	−	1.93565i	−0.165892	−	0.0706798i
$751$	−28.3437	+	4.60631i	−1.03428	+	0.168087i	−0.653772	−	0.756692i	$-0.726814\pi$
$751$	−28.3437	+	4.60631i	−1.03428	+	0.168087i	−0.380506	+	0.924778i	$0.624250\pi$
$752$	−2.05619	+	6.15903i	−0.0749814	+	0.224597i
$753$	−10.8921	+	9.64955i	−0.396930	+	0.351649i
$754$	1.89717	+	7.47663i	0.0690908	+	0.272283i
$755$	12.8924	+	11.4217i	0.469204	+	0.415678i
$756$	−1.77185	+	1.02298i	−0.0644416	+	0.0372054i
$757$	45.4538	+	15.1747i	1.65205	+	0.551534i	0.981687	−	0.190503i	$-0.0610118\pi$
$757$	45.4538	+	15.1747i	1.65205	+	0.551534i	0.670359	+	0.742037i	$0.266140\pi$
$758$	−18.5076	+	19.2684i	−0.672225	+	0.699860i
$759$	63.6745	−	43.9513i	2.31124	−	1.59533i
$760$	−6.34458	+	5.18019i	−0.230142	+	0.187905i
$761$	8.87007	−	7.24218i	0.321540	−	0.262529i	−0.457904	−	0.889002i	$-0.651400\pi$
$761$	8.87007	−	7.24218i	0.321540	−	0.262529i	0.779443	+	0.626473i	$0.215502\pi$
$762$	−84.7523	+	58.5003i	−3.07025	+	2.11924i
$763$	−0.0700455	+	0.0729251i	−0.00253582	+	0.00264007i
$764$	−9.47284	−	3.16250i	−0.342715	−	0.114415i
$765$	−8.74086	+	5.04654i	−0.316027	+	0.182458i
$766$	−12.8742	−	11.4055i	−0.465163	−	0.412099i
$767$	46.6046	+	17.3111i	1.68280	+	0.625067i
$768$	−16.9516	+	15.0178i	−0.611688	+	0.541908i
$769$	0.968280	−	2.90035i	0.0349171	−	0.104589i	−0.929635	−	0.368481i	$-0.879878\pi$
$769$	0.968280	−	2.90035i	0.0349171	−	0.104589i	0.964552	+	0.263892i	$0.0850061\pi$
$770$	−2.55290	+	0.414886i	−0.0920000	+	0.0149515i
$771$	−20.3184	−	8.65688i	−0.731751	−	0.311770i
$772$	−52.2555	−	19.8179i	−1.88072	−	0.713261i
$773$	−2.71584	+	3.61412i	−0.0976818	+	0.129991i	−0.845637	−	0.533758i	$-0.820779\pi$
$773$	−2.71584	+	3.61412i	−0.0976818	+	0.129991i	0.747955	+	0.663749i	$0.231036\pi$
$774$	32.3788	−	15.3639i	1.16383	−	0.552245i
$775$		−	1.07858i		−	0.0387436i
$776$	12.0921	+	25.4836i	0.434082	+	0.914808i
$777$	−0.631851	−	0.657827i	−0.0226675	−	0.0235994i
$778$	−30.2191	−	6.16927i	−1.08341	−	0.221179i
$779$	20.9146	−	30.3000i	0.749342	−	1.08561i
$780$	23.1298	−	6.87146i	0.828178	−	0.246038i
$781$	5.00375	+	7.24919i	0.179048	+	0.259396i
$782$	−38.8223	−	91.1193i	−1.38828	−	3.25842i
$783$	−1.95024	+	1.46551i	−0.0696960	+	0.0523732i
$784$	0.230208	−	5.71255i	0.00822171	−	0.204020i
$785$	−1.47732	−	5.99371i	−0.0527277	−	0.213925i
$786$	−13.4120	+	31.4791i	−0.478390	+	1.12282i
$787$	18.2259	−	3.72084i	0.649682	−	0.132633i	0.136128	−	0.990691i	$-0.456534\pi$
$787$	18.2259	−	3.72084i	0.649682	−	0.132633i	0.513553	+	0.858058i	$0.328329\pi$
$788$	−18.7477	−	12.9406i	−0.667859	−	0.460990i
$789$	−15.6117	+	1.26030i	−0.555789	+	0.0448680i
$790$	−3.41591	−	11.7931i	−0.121532	−	0.419579i
$791$	−0.736371	−	0.979932i	−0.0261823	−	0.0348424i
$792$	−16.7050	−	8.76744i	−0.593585	−	0.311537i
$793$	−27.5827	+	0.188688i	−0.979491	+	0.00670050i
$794$	26.3889	−	13.8499i	0.936506	−	0.491516i
$795$	10.1019	+	4.79341i	0.358277	+	0.170005i
$796$	33.5974	−	70.8051i	1.19083	−	2.50962i
$797$	51.1497	−	17.0763i	1.81181	−	0.604872i	0.812040	−	0.583601i	$-0.198357\pi$
$797$	51.1497	−	17.0763i	1.81181	−	0.604872i	0.999774	−	0.0212711i	$-0.00677131\pi$
$798$	−3.00534	+	3.39233i	−0.106388	+	0.120087i
$799$	−6.94371	+	42.7264i	−0.245651	+	1.51155i
$800$	6.53313	+	0.263276i	0.230981	+	0.00930822i
$801$	7.09162	−	2.68950i	0.250570	−	0.0950286i
$802$	−6.17908	+	21.3327i	−0.218191	+	0.753282i
$803$	0.480635	−	2.35431i	0.0169612	−	0.0830816i
$804$	8.01484	−	99.2816i	0.282662	−	3.50139i
$805$	0.746643	−	1.96874i	0.0263157	−	0.0693888i
$806$	5.56951	+	6.72695i	0.196178	+	0.236947i
$807$	8.74933	+	23.0701i	0.307991	+	0.812106i
$808$	32.5789	−	9.43659i	1.14612	−	0.331978i
$809$	1.06471	+	26.4206i	0.0374334	+	0.928899i	0.903400	+	0.428798i	$0.141063\pi$
$809$	1.06471	+	26.4206i	0.0374334	+	0.928899i	−0.865967	+	0.500101i	$0.833296\pi$
$810$	15.8186	+	19.3743i	0.555808	+	0.680742i
$811$	−34.2345	−	4.15682i	−1.20213	−	0.145966i	−0.505137	−	0.863039i	$-0.668558\pi$
$811$	−34.2345	−	4.15682i	−1.20213	−	0.145966i	−0.696997	+	0.717074i	$0.745481\pi$
$812$	−0.0612439	−	0.758642i	−0.00214924	−	0.0266231i
$813$	−65.5356	−	18.9826i	−2.29843	−	0.665750i
$814$	−3.72522	+	15.1138i	−0.130569	+	0.529739i
$815$	−7.32748	−	5.50624i	−0.256670	−	0.192875i
$816$	6.30817	−	7.72611i	0.220830	−	0.270468i
$817$	−21.9210	+	21.0554i	−0.766919	+	0.736636i
$818$	−77.1678	−	19.0202i	−2.69811	−	0.665024i
$819$	1.56449	−	0.755513i	0.0546676	−	0.0263998i
$820$	31.1202	−	7.67044i	1.08676	−	0.267863i
$821$	16.9944	−	26.8744i	0.593107	−	0.937924i	−0.406597	−	0.913607i	$-0.633285\pi$
$821$	16.9944	−	26.8744i	0.593107	−	0.937924i	0.999704	−	0.0243161i	$-0.00774083\pi$
$822$	−14.4690	−	25.0611i	−0.504666	−	0.874107i
$823$	−3.45524	+	5.98465i	−0.120442	+	0.208612i	−0.919942	−	0.392054i	$-0.871765\pi$
$823$	−3.45524	+	5.98465i	−0.120442	+	0.208612i	0.799500	+	0.600666i	$0.205098\pi$
$824$	1.63817	+	3.12127i	0.0570684	+	0.108735i
$825$	3.05481	+	9.15027i	0.106355	+	0.318572i
$826$	−7.04022	−	4.06468i	−0.244961	−	0.141428i
$827$	−8.35008	−	9.42529i	−0.290361	−	0.327749i	0.585171	−	0.810910i	$-0.301027\pi$
$827$	−8.35008	−	9.42529i	−0.290361	−	0.327749i	−0.875532	+	0.483160i	$0.839489\pi$
$828$	37.8651	−	23.9444i	1.31590	−	0.832126i
$829$	−30.2714	+	12.8974i	−1.05137	+	0.447946i	−0.847358	−	0.531022i	$-0.821808\pi$
$829$	−30.2714	+	12.8974i	−1.05137	+	0.447946i	−0.204011	+	0.978969i	$0.565398\pi$
$830$	−27.4416	+	1.10586i	−0.952511	+	0.0383849i
$831$	−4.04882	+	33.3450i	−0.140452	+	1.15673i
$832$	−37.3752	+	28.4878i	−1.29575	+	0.987635i
$833$	−4.59410	−	37.8358i	−0.159176	−	1.31093i
$834$	−4.72583	−	29.0792i	−0.163642	−	1.00693i
$835$	−14.4478	−	9.13623i	−0.499987	−	0.316172i
$836$	46.0677	+	7.48673i	1.59328	+	0.258934i
$837$	−1.28357	+	2.44565i	−0.0443668	+	0.0845339i
$838$	−6.28210	−	9.93435i	−0.217012	−	0.343176i
$839$	−28.3312	−	27.2125i	−0.978101	−	0.939479i	0.0200783	−	0.999798i	$-0.493608\pi$
$839$	−28.3312	−	27.2125i	−0.978101	−	0.939479i	−0.998179	+	0.0603198i	$0.980788\pi$
$840$	−1.34273	+	0.163037i	−0.0463286	+	0.00562531i
$841$	5.61922	+	27.5248i	0.193766	+	0.949130i
$842$	−2.23006	−	0.180029i	−0.0768529	−	0.00620421i
$843$	41.1243	+	33.5770i	1.41640	+	1.15645i
$844$	−61.5732			−2.11944
$845$	12.7005	−	2.77435i	0.436911	−	0.0954405i
$846$	−32.4472			−1.11556
$847$	1.67671	+	1.36899i	0.0576123	+	0.0470390i
$848$	−4.18072	−	0.337502i	−0.143566	−	0.0115899i
$849$	−8.82746	−	43.2398i	−0.302958	−	1.48398i
$850$	12.2591	−	1.48853i	0.420485	−	0.0510561i
$851$	−9.13929	−	8.77840i	−0.313291	−	0.300920i
$852$	7.18161	+	11.3568i	0.246038	+	0.389078i
$853$	5.67779	−	10.8181i	0.194404	−	0.370405i	−0.768669	−	0.639647i	$-0.779081\pi$
$853$	5.67779	−	10.8181i	0.194404	−	0.370405i	0.963073	+	0.269241i	$0.0867729\pi$
$854$	4.45192	+	0.723507i	0.152342	+	0.0247579i
$855$	5.42309	+	3.42935i	0.185466	+	0.117281i
$856$	−4.31920	−	26.5771i	−0.147627	−	0.908388i
$857$	−2.77805	−	22.8793i	−0.0948965	−	0.781543i	−0.960010	−	0.279967i	$-0.909677\pi$
$857$	−2.77805	−	22.8793i	−0.0948965	−	0.781543i	0.865113	−	0.501577i	$-0.167246\pi$
$858$	−66.3023	−	41.2948i	−2.26352	−	1.40978i
$859$	7.05864	−	58.1331i	0.240838	−	1.98348i	0.0765245	−	0.997068i	$-0.475618\pi$
$859$	7.05864	−	58.1331i	0.240838	−	1.98348i	0.164313	−	0.986408i	$-0.447459\pi$
$860$	−26.4393	+	1.06547i	−0.901571	+	0.0363321i
$861$	5.59337	−	2.38311i	0.190622	−	0.0812162i
$862$	50.4730	−	31.9172i	1.71912	−	1.08710i
$863$	8.60951	+	9.71813i	0.293071	+	0.330809i	0.876542	−	0.481325i	$-0.159844\pi$
$863$	8.60951	+	9.71813i	0.293071	+	0.330809i	−0.583471	+	0.812134i	$0.698306\pi$
$864$	−14.5004	−	8.37181i	−0.493313	−	0.284815i
$865$	0.854869	+	2.56064i	0.0290664	+	0.0870645i
$866$	0.129782	+	0.247279i	0.00441018	+	0.00840290i
$867$	14.5555	−	25.2109i	0.494331	−	0.856207i
$868$	−0.430866	−	0.746283i	−0.0146246	−	0.0253305i
$869$	−12.8187	+	20.2712i	−0.434845	+	0.687653i
$870$	−4.56768	+	1.12583i	−0.154859	+	0.0381693i
$871$	8.24582	−	53.0270i	0.279399	−	1.79675i
$872$	0.876218	+	0.215968i	0.0296725	+	0.00731361i
$873$	15.9361	−	15.3069i	0.539357	−	0.518059i
$874$	−39.8221	+	48.7732i	−1.34700	+	1.64978i
$875$	0.209876	+	0.157711i	0.00709509	+	0.00533161i
$876$	0.877212	−	3.55899i	0.0296383	−	0.120247i
$877$	20.5302	+	5.94664i	0.693255	+	0.200804i	0.606097	−	0.795391i	$-0.292734\pi$
$877$	20.5302	+	5.94664i	0.693255	+	0.200804i	0.0871582	+	0.996194i	$0.472221\pi$
$878$	−0.276157	−	3.42082i	−0.00931986	−	0.115447i
$879$	−14.5338	−	1.76472i	−0.490211	−	0.0595224i
$880$	−2.28858	−	2.80300i	−0.0771480	−	0.0944892i
$881$	1.35039	+	33.5097i	0.0454959	+	1.12897i	0.847209	+	0.531260i	$0.178281\pi$
$881$	1.35039	+	33.5097i	0.0454959	+	1.12897i	−0.801713	+	0.597710i	$0.796078\pi$
$882$	27.4415	−	7.94853i	0.924004	−	0.267641i
$883$	−15.9996	−	42.1876i	−0.538431	−	1.41973i	−0.877780	−	0.479065i	$-0.840976\pi$
$883$	−15.9996	−	42.1876i	−0.538431	−	1.41973i	0.339349	−	0.940661i	$-0.389793\pi$
$884$	−41.4997	+	43.8016i	−1.39579	+	1.47321i
$885$	−10.7519	+	28.3505i	−0.361422	+	0.952992i
$886$	−0.838367	+	10.3850i	−0.0281655	+	0.348892i
$887$	5.54150	−	27.1441i	0.186065	−	0.911408i	−0.774333	−	0.632778i	$-0.781915\pi$
$887$	5.54150	−	27.1441i	0.186065	−	0.911408i	0.960398	−	0.278630i	$-0.0898803\pi$
$888$	−2.26484	+	7.81914i	−0.0760031	+	0.262393i
$889$	5.11891	−	1.94134i	0.171683	−	0.0651106i
$890$	−9.27232	−	0.373662i	−0.310809	−	0.0125252i
$891$	7.83760	−	48.2267i	0.262569	−	1.61565i
$892$	0.218413	−	0.246537i	0.00731301	−	0.00825468i
$893$	26.1023	−	8.71424i	0.873481	−	0.291611i
$894$	−49.7352	+	104.815i	−1.66339	+	3.50553i
$895$	−6.67126	−	3.16555i	−0.222996	−	0.105813i
$896$	3.76432	−	1.97567i	0.125757	−	0.0660025i
$897$	56.1021	−	29.9359i	1.87319	−	0.999531i
$898$	44.9656	+	23.5998i	1.50052	+	0.787535i
$899$	−0.617256	−	0.821419i	−0.0205866	−	0.0273958i
$900$	1.55408	+	5.36532i	0.0518028	+	0.178844i
$901$	−27.8708	+	2.24996i	−0.928510	+	0.0749571i
$902$	−85.3912	−	58.9413i	−2.84322	−	1.96253i
$903$	−4.91792	+	1.00400i	−0.163658	+	0.0334110i
$904$	−4.28802	+	10.0644i	−0.142617	+	0.334735i
$905$	−1.75405	−	7.11648i	−0.0583067	−	0.236560i
$906$	3.42493	−	84.9887i	0.113786	−	2.82356i
$907$	2.80136	−	2.10509i	0.0930176	−	0.0698982i	−0.553216	−	0.833038i	$-0.686600\pi$
$907$	2.80136	−	2.10509i	0.0930176	−	0.0698982i	0.646234	+	0.763140i	$0.276343\pi$
$908$	31.2756	+	73.4065i	1.03792	+	2.43608i
$909$	−15.0938	−	21.8671i	−0.500629	−	0.725287i
$910$	−2.12335	+	0.100121i	−0.0703884	+	0.00331899i
$911$	−9.19037	+	13.3146i	−0.304491	+	0.441131i	−0.945122	−	0.326718i	$-0.894057\pi$
$911$	−9.19037	+	13.3146i	−0.304491	+	0.441131i	0.640631	+	0.767849i	$0.278673\pi$
$912$	−6.21273	−	1.26834i	−0.205724	−	0.0419989i
$913$	37.1642	+	38.6921i	1.22996	+	1.28052i
$914$	−22.4368	−	47.2846i	−0.742144	−	1.56403i
$915$		−	16.8226i		−	0.556139i
$916$	−28.2078	+	13.3848i	−0.932013	+	0.442246i
$917$	1.09277	−	1.45422i	0.0360866	−	0.0480225i
$918$	−29.5687	−	11.2139i	−0.975914	−	0.370115i
$919$	−26.7844	−	11.4118i	−0.883535	−	0.376439i	−0.0979490	−	0.995191i	$-0.531228\pi$
$919$	−26.7844	−	11.4118i	−0.883535	−	0.376439i	−0.785586	+	0.618752i	$0.787638\pi$
$920$	−18.5484	+	3.01441i	−0.611523	+	0.0993822i
$921$	−13.3063	+	39.8571i	−0.438456	+	1.31334i
$922$	−21.5624	+	19.1026i	−0.710119	+	0.629110i
$923$	3.40813	+	6.38709i	0.112180	+	0.210234i
$924$	5.76899	+	5.11088i	0.189786	+	0.168135i
$925$	1.36833	−	0.790008i	0.0449905	−	0.0259753i
$926$	−63.3562	−	21.1514i	−2.08201	−	0.695078i
$927$	1.91291	−	1.99155i	0.0628283	−	0.0654112i
$928$	5.12615	−	3.53832i	0.168274	−	0.116151i
$929$	0.879312	−	0.717936i	0.0288493	−	0.0235547i	−0.617911	−	0.786248i	$-0.712021\pi$
$929$	0.879312	−	0.717936i	0.0288493	−	0.0235547i	0.646760	+	0.762693i	$0.276123\pi$
$930$	−4.12580	+	3.36861i	−0.135290	+	0.110461i
$931$	−19.9407	+	13.7641i	−0.653531	+	0.451100i
$932$	41.3906	−	43.0921i	1.35579	−	1.41153i
$933$	53.4727	+	17.8518i	1.75062	+	0.584442i
$934$	65.9462	−	38.0740i	2.15782	−	1.24582i
$935$	−18.0568	−	15.9969i	−0.590519	−	0.523154i
$936$	−12.8208	−	8.72069i	−0.419062	−	0.285045i
$937$	−15.3567	+	13.6049i	−0.501683	+	0.444452i	−0.875619	−	0.483002i	$-0.839546\pi$
$937$	−15.3567	+	13.6049i	−0.501683	+	0.444452i	0.373936	+	0.927454i	$0.378008\pi$
$938$	−2.77876	+	8.32340i	−0.0907297	+	0.271769i
$939$	−41.1316	+	6.68453i	−1.34228	+	0.218142i
$940$	22.0395	+	9.39015i	0.718849	+	0.306273i
$941$	0.696438	+	0.264124i	0.0227032	+	0.00861020i	0.365930	−	0.930642i	$-0.380751\pi$
$941$	0.696438	+	0.264124i	0.0227032	+	0.00861020i	−0.343227	+	0.939252i	$0.611520\pi$
$942$	−18.3133	+	24.3706i	−0.596681	+	0.794038i
$943$	76.3133	−	36.2111i	2.48510	−	1.17920i
$944$		−	11.3738i		−	0.370185i
$945$	−0.288201	−	0.607371i	−0.00937519	−	0.0197578i
$946$	59.3382	+	61.7776i	1.92925	+	2.00856i
$947$	−23.4351	−	4.78432i	−0.761539	−	0.155469i	−0.196467	−	0.980510i	$-0.562947\pi$
$947$	−23.4351	−	4.78432i	−0.761539	−	0.155469i	−0.565073	+	0.825041i	$0.691152\pi$
$948$	−20.7839	+	30.1107i	−0.675029	+	0.977949i
$949$	0.612551	−	1.87748i	0.0198842	−	0.0609454i
$950$	−4.45969	−	6.46098i	−0.144692	−	0.209622i
$951$	2.47832	+	5.81684i	0.0803651	+	0.188624i
$952$	2.70406	−	2.03197i	0.0876390	−	0.0658564i
$953$	−0.0251089	+	0.623070i	−0.000813355	+	0.0201832i	−0.999545	−	0.0301723i	$-0.990394\pi$
$953$	−0.0251089	+	0.623070i	−0.000813355	+	0.0201832i	0.998731	+	0.0503555i	$0.0160354\pi$
$954$	−5.01594	−	20.3505i	−0.162397	−	0.658871i
$955$	1.28626	−	3.01896i	0.0416223	−	0.0976912i
$956$	−7.67628	+	1.56712i	−0.248269	+	0.0506844i
$957$	7.56306	+	5.22040i	0.244479	+	0.168752i
$958$	−3.58343	+	0.289284i	−0.115775	+	0.00934635i
$959$	0.428008	+	1.47766i	0.0138211	+	0.0477160i
$960$	−17.2179	−	22.9128i	−0.555705	−	0.739509i
$961$	26.4191	+	13.8658i	0.852228	+	0.447284i
$962$	−4.45472	+	11.9929i	−0.143626	+	0.386668i
$963$	−18.6769	+	9.80241i	−0.601856	+	0.315878i
$964$	−3.51308	−	1.66698i	−0.113149	−	0.0536898i
$965$	7.87248	−	16.5909i	0.253424	−	0.534080i
$966$	−9.86278	+	3.29268i	−0.317330	+	0.105940i
$967$	−31.9959	+	36.1159i	−1.02892	+	1.16141i	−0.0421771	+	0.999110i	$0.513429\pi$
$967$	−31.9959	+	36.1159i	−1.02892	+	1.16141i	−0.986742	+	0.162299i	$0.948109\pi$
$968$	3.09892	−	19.0684i	0.0996031	−	0.612883i
$969$	−42.2372	−	1.70210i	−1.35686	−	0.0546794i
$970$	−25.2790	+	9.58706i	−0.811660	+	0.307822i
$971$	12.2841	−	42.4097i	0.394216	−	1.36099i	−0.480772	−	0.876846i	$-0.659644\pi$
$971$	12.2841	−	42.4097i	0.394216	−	1.36099i	0.874988	−	0.484145i	$-0.160869\pi$
$972$	10.2320	−	50.1199i	0.328193	−	1.60760i
$973$	−0.126025	+	1.56110i	−0.00404018	+	0.0500466i
$974$	27.7086	−	73.0615i	0.887840	−	2.34104i
$975$	1.63900	+	7.75723i	0.0524901	+	0.248430i
$976$	2.23770	+	5.90033i	0.0716270	+	0.188865i
$977$	−16.2650	+	4.71122i	−0.520364	+	0.150725i	−0.527998	−	0.849246i	$-0.677057\pi$
$977$	−16.2650	+	4.71122i	−0.520364	+	0.150725i	0.00763399	+	0.999971i	$0.497570\pi$
$978$	1.82256	+	45.2264i	0.0582790	+	1.44618i
$979$	11.4648	+	14.0418i	0.366417	+	0.448779i
$980$	−20.9397	−	2.54254i	−0.668893	−	0.0812183i
$981$	−0.0568859	−	0.704658i	−0.00181623	−	0.0224980i
$982$	71.5353	+	20.7205i	2.28278	+	0.661216i
$983$	4.37048	−	17.7317i	0.139397	−	0.565554i	−0.859153	−	0.511718i	$-0.829009\pi$
$983$	4.37048	−	17.7317i	0.139397	−	0.565554i	0.998550	−	0.0538358i	$-0.0171448\pi$
$984$	−43.3792	−	32.5974i	−1.38288	−	1.03917i
$985$	4.73405	−	5.79816i	0.150839	−	0.184745i
$986$	8.48441	−	8.14938i	0.270199	−	0.259529i
$987$	4.41228	+	1.08753i	0.140444	+	0.0346164i
$988$	36.9167	+	10.4199i	1.17448	+	0.331500i
$989$	−67.7083	+	16.6886i	−2.15300	+	0.530666i
$990$	9.66458	−	15.2833i	0.307160	−	0.485735i
$991$	1.37558	+	2.38257i	0.0436967	+	0.0756850i	0.887047	−	0.461680i	$-0.152753\pi$
$991$	1.37558	+	2.38257i	0.0436967	+	0.0756850i	−0.843350	+	0.537365i	$0.819420\pi$
$992$	3.52610	−	6.10739i	0.111954	−	0.193910i
$993$	25.4730	+	48.5348i	0.808361	+	1.54020i
$994$	−0.374864	−	1.12285i	−0.0118900	−	0.0356148i
$995$	22.3020	+	12.8761i	0.707021	+	0.408199i
$996$	54.2704	+	61.2586i	1.71962	+	1.94105i
$997$	33.5808	−	21.2352i	1.06351	−	0.672526i	0.116328	−	0.993211i	$-0.462888\pi$
$997$	33.5808	−	21.2352i	1.06351	−	0.672526i	0.947186	+	0.320685i	$0.103913\pi$
$998$	−53.3192	+	22.7172i	−1.68779	+	0.719100i
$999$	−4.04282	+	0.162920i	−0.127909	+	0.00515456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.bg.a.621.54	yes	1440
169.43	even	78	inner	845.2.bg.a.381.54	✓	1440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.bg.a.381.54	✓	1440	169.43	even	78	inner
845.2.bg.a.621.54	yes	1440	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.bg (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73956 + 1.42030i) q^{2} +(2.19184 + 0.176943i) q^{3} +(0.608741 + 2.98181i) q^{4} +(-0.992709 + 0.120537i) q^{5} +(3.56151 + 3.42087i) q^{6} +(-0.140312 - 0.221886i) q^{7} +(-1.08885 + 2.07463i) q^{8} +(1.81169 + 0.294427i) q^{9} +O(q^{10})\)	\(q+(1.73956 + 1.42030i) q^{2} +(2.19184 + 0.176943i) q^{3} +(0.608741 + 2.98181i) q^{4} +(-0.992709 + 0.120537i) q^{5} +(3.56151 + 3.42087i) q^{6} +(-0.140312 - 0.221886i) q^{7} +(-1.08885 + 2.07463i) q^{8} +(1.81169 + 0.294427i) q^{9} +(-1.89807 - 1.20027i) q^{10} +(0.703714 + 4.33013i) q^{11} +(0.806649 + 6.64336i) q^{12} +(0.169822 + 3.60155i) q^{13} +(0.0710644 - 0.585268i) q^{14} +(-2.19718 + 0.0885435i) q^{15} +(0.758857 - 0.323319i) q^{16} +(4.64766 - 2.93900i) q^{17} +(2.73335 + 3.08532i) q^{18} +(-3.02747 - 1.74791i) q^{19} +(-0.963721 - 2.88670i) q^{20} +(-0.268280 - 0.511164i) q^{21} +(-4.92594 + 8.53199i) q^{22} +(-4.01018 - 6.94584i) q^{23} +(-2.75367 + 4.35458i) q^{24} +(0.970942 - 0.239316i) q^{25} +(-4.81988 + 6.50629i) q^{26} +(-2.48639 - 0.612839i) q^{27} +(0.576207 - 0.553455i) q^{28} +(0.602489 - 0.737915i) q^{29} +(-3.94788 - 2.96664i) q^{30} +(0.258120 - 1.04724i) q^{31} +(6.28029 + 1.81911i) q^{32} +(0.776239 + 9.61545i) q^{33} +(12.2591 + 1.48853i) q^{34} +(0.166034 + 0.203355i) q^{35} +(0.224920 + 5.58133i) q^{36} +(1.51763 - 0.439588i) q^{37} +(-2.78389 - 7.34051i) q^{38} +(-0.265049 + 7.92405i) q^{39} +(0.830842 - 2.19075i) q^{40} +(-0.847457 + 10.4976i) q^{41} +(0.259321 - 1.27024i) q^{42} +(2.41902 - 8.35142i) q^{43} +(-12.4832 + 4.73427i) q^{44} +(-1.83397 - 0.0739063i) q^{45} +(2.88926 - 17.7783i) q^{46} +(-5.22000 + 5.89216i) q^{47} +(1.72050 - 0.574387i) q^{48} +(2.97130 - 6.26189i) q^{49} +(2.02891 + 0.962729i) q^{50} +(10.7070 - 5.61944i) q^{51} +(-10.6358 + 2.69879i) q^{52} +(-4.50243 - 2.36306i) q^{53} +(-3.45479 - 4.59749i) q^{54} +(-1.22052 - 4.21373i) q^{55} +(0.613109 - 0.0494953i) q^{56} +(-6.32643 - 4.36682i) q^{57} +(2.09613 - 0.427927i) q^{58} +(5.40471 - 12.6853i) q^{59} +(-1.60154 - 6.49769i) q^{60} +(-0.308044 + 7.64404i) q^{61} +(1.93641 - 1.45512i) q^{62} +(-0.188872 - 0.443298i) q^{63} +(7.40407 + 10.7267i) q^{64} +(-0.602702 - 3.55482i) q^{65} +(-12.3065 + 17.8291i) q^{66} +(-14.5830 - 2.97714i) q^{67} +(11.5928 + 12.0694i) q^{68} +(-7.56064 - 15.9337i) q^{69} +0.589566i q^{70} +(1.81401 - 0.860761i) q^{71} +(-2.58348 + 3.43799i) q^{72} +(-0.512138 - 0.194228i) q^{73} +(3.26436 + 1.39081i) q^{74} +(2.17049 - 0.352739i) q^{75} +(3.36899 - 10.0914i) q^{76} +(0.862053 - 0.763712i) q^{77} +(-11.7156 + 13.4079i) q^{78} +(4.09224 + 3.62541i) q^{79} +(-0.714352 + 0.412431i) q^{80} +(-10.5643 - 3.52688i) q^{81} +(-16.3840 + 17.0576i) q^{82} +(10.0646 - 6.94706i) q^{83} +(1.36088 - 1.11113i) q^{84} +(-4.25952 + 3.47779i) q^{85} +(16.0696 - 11.0920i) q^{86} +(1.45113 - 1.51078i) q^{87} +(-9.74965 - 3.25491i) q^{88} +(3.57860 - 2.06611i) q^{89} +(-3.08532 - 2.73335i) q^{90} +(0.775304 - 0.543021i) q^{91} +(18.2700 - 16.1858i) q^{92} +(0.751059 - 2.24970i) q^{93} +(-17.4491 + 2.83576i) q^{94} +(3.21608 + 1.37024i) q^{95} +(13.4435 + 5.09844i) q^{96} +(7.23221 - 9.62432i) q^{97} +(14.0625 - 6.67275i) q^{98} +8.05202i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1440 q - 2 q^{3} - 58 q^{4} + 18 q^{6} + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 1440 * q - 2 * q^3 - 58 * q^4 + 18 * q^6 + 6 * q^7 + 60 * q^9	\( 1440 q - 2 q^{3} - 58 q^{4} + 18 q^{6} + 6 q^{7} + 60 q^{9} + 2 q^{10} - 20 q^{12} + 26 q^{13} + 4 q^{14} + 6 q^{15} + 58 q^{16} + 6 q^{17} - 156 q^{18} - 12 q^{19} - 12 q^{20} + 60 q^{22} - 146 q^{23} - 144 q^{24} + 120 q^{25} - 10 q^{26} + 4 q^{27} + 18 q^{28} + 4 q^{29} - 4 q^{30} + 52 q^{31} + 20 q^{32} - 42 q^{33} + 130 q^{34} - 10 q^{35} - 56 q^{36} - 6 q^{37} - 162 q^{38} + 12 q^{40} - 12 q^{41} - 24 q^{42} + 2 q^{43} + 42 q^{46} - 156 q^{47} + 30 q^{48} + 18 q^{49} - 124 q^{52} + 48 q^{53} - 330 q^{54} - 4 q^{55} + 20 q^{56} + 78 q^{57} + 68 q^{58} - 196 q^{59} + 12 q^{61} - 118 q^{62} + 24 q^{63} + 96 q^{64} + 8 q^{65} + 44 q^{66} + 98 q^{67} + 120 q^{68} + 28 q^{69} - 156 q^{71} + 386 q^{72} - 30 q^{74} + 2 q^{75} - 392 q^{76} + 4 q^{77} - 204 q^{78} + 40 q^{79} + 40 q^{81} - 244 q^{82} + 30 q^{84} - 18 q^{85} - 30 q^{87} + 30 q^{88} - 24 q^{89} - 56 q^{90} + 76 q^{91} + 20 q^{92} - 130 q^{93} - 148 q^{94} + 16 q^{95} - 338 q^{96} + 30 q^{97} - 72 q^{98}+O(q^{100}) \) 1440 * q - 2 * q^3 - 58 * q^4 + 18 * q^6 + 6 * q^7 + 60 * q^9 + 2 * q^10 - 20 * q^12 + 26 * q^13 + 4 * q^14 + 6 * q^15 + 58 * q^16 + 6 * q^17 - 156 * q^18 - 12 * q^19 - 12 * q^20 + 60 * q^22 - 146 * q^23 - 144 * q^24 + 120 * q^25 - 10 * q^26 + 4 * q^27 + 18 * q^28 + 4 * q^29 - 4 * q^30 + 52 * q^31 + 20 * q^32 - 42 * q^33 + 130 * q^34 - 10 * q^35 - 56 * q^36 - 6 * q^37 - 162 * q^38 + 12 * q^40 - 12 * q^41 - 24 * q^42 + 2 * q^43 + 42 * q^46 - 156 * q^47 + 30 * q^48 + 18 * q^49 - 124 * q^52 + 48 * q^53 - 330 * q^54 - 4 * q^55 + 20 * q^56 + 78 * q^57 + 68 * q^58 - 196 * q^59 + 12 * q^61 - 118 * q^62 + 24 * q^63 + 96 * q^64 + 8 * q^65 + 44 * q^66 + 98 * q^67 + 120 * q^68 + 28 * q^69 - 156 * q^71 + 386 * q^72 - 30 * q^74 + 2 * q^75 - 392 * q^76 + 4 * q^77 - 204 * q^78 + 40 * q^79 + 40 * q^81 - 244 * q^82 + 30 * q^84 - 18 * q^85 - 30 * q^87 + 30 * q^88 - 24 * q^89 - 56 * q^90 + 76 * q^91 + 20 * q^92 - 130 * q^93 - 148 * q^94 + 16 * q^95 - 338 * q^96 + 30 * q^97 - 72 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more