LMFDB - Embedded newform 216.2.v.b.203.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			203.16
Character	$\chi$	$=$	216.203
Dual form			216.2.v.b.83.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.117471 - 1.40933i) q^{2} +(1.66179 - 0.488315i) q^{3} +(-1.97240 + 0.331111i) q^{4} +(-1.82990 - 1.53547i) q^{5} +(-0.883408 - 2.28464i) q^{6} +(0.455069 - 1.25029i) q^{7} +(0.698344 + 2.74086i) q^{8} +(2.52310 - 1.62295i) q^{9} +O(q^{10})$	\(q+(-0.117471 - 1.40933i) q^{2} +(1.66179 - 0.488315i) q^{3} +(-1.97240 + 0.331111i) q^{4} +(-1.82990 - 1.53547i) q^{5} +(-0.883408 - 2.28464i) q^{6} +(0.455069 - 1.25029i) q^{7} +(0.698344 + 2.74086i) q^{8} +(2.52310 - 1.62295i) q^{9} +(-1.94901 + 2.75930i) q^{10} +(-3.07907 - 3.66949i) q^{11} +(-3.11603 + 1.51339i) q^{12} +(0.552142 + 0.0973575i) q^{13} +(-1.81553 - 0.494467i) q^{14} +(-3.79070 - 1.65806i) q^{15} +(3.78073 - 1.30617i) q^{16} +(0.710885 + 0.410430i) q^{17} +(-2.58366 - 3.36522i) q^{18} +(3.02483 + 5.23916i) q^{19} +(4.11771 + 2.42266i) q^{20} +(0.145694 - 2.29994i) q^{21} +(-4.80981 + 4.77047i) q^{22} +(4.41436 - 1.60670i) q^{23} +(2.49890 + 4.21372i) q^{24} +(0.122629 + 0.695465i) q^{25} +(0.0723476 - 0.789585i) q^{26} +(3.40035 - 3.92907i) q^{27} +(-0.483593 + 2.61676i) q^{28} +(0.586451 + 3.32593i) q^{29} +(-1.89145 + 5.53711i) q^{30} +(3.71351 + 10.2028i) q^{31} +(-2.28494 - 5.17485i) q^{32} +(-6.90863 - 4.59437i) q^{33} +(0.494921 - 1.05008i) q^{34} +(-2.75251 + 1.58916i) q^{35} +(-4.43918 + 4.03654i) q^{36} +(-7.25187 - 4.18687i) q^{37} +(7.02835 - 4.87842i) q^{38} +(0.965085 - 0.107831i) q^{39} +(2.93060 - 6.08778i) q^{40} +(-4.16735 - 0.734815i) q^{41} +(-3.25848 + 0.0648473i) q^{42} +(2.38891 - 2.00453i) q^{43} +(7.28816 + 6.21819i) q^{44} +(-7.10901 - 0.904294i) q^{45} +(-2.78292 - 6.03253i) q^{46} +(10.7030 + 3.89558i) q^{47} +(5.64496 - 4.01676i) q^{48} +(4.00617 + 3.36158i) q^{49} +(0.965731 - 0.254522i) q^{50} +(1.38176 + 0.334913i) q^{51} +(-1.12128 - 0.00920769i) q^{52} -0.541186 q^{53} +(-5.93679 - 4.33065i) q^{54} +11.4426i q^{55} +(3.74467 + 0.374146i) q^{56} +(7.58499 + 7.22932i) q^{57} +(4.61843 - 1.21720i) q^{58} +(4.04416 - 4.81965i) q^{59} +(8.02579 + 2.01522i) q^{60} +(3.02063 - 8.29912i) q^{61} +(13.9428 - 6.43208i) q^{62} +(-0.880982 - 3.89316i) q^{63} +(-7.02463 + 3.82813i) q^{64} +(-0.860875 - 1.02595i) q^{65} +(-5.66340 + 10.2762i) q^{66} +(-0.850868 + 4.82551i) q^{67} +(-1.53805 - 0.574150i) q^{68} +(6.55117 - 4.82559i) q^{69} +(2.56299 + 3.69251i) q^{70} +(-2.20493 + 3.81906i) q^{71} +(6.21028 + 5.78208i) q^{72} +(-0.205251 - 0.355506i) q^{73} +(-5.04877 + 10.7121i) q^{74} +(0.543390 + 1.09584i) q^{75} +(-7.70092 - 9.33217i) q^{76} +(-5.98912 + 2.17986i) q^{77} +(-0.265339 - 1.34745i) q^{78} +(-4.56009 + 0.804066i) q^{79} +(-8.92394 - 3.41503i) q^{80} +(3.73204 - 8.18974i) q^{81} +(-0.546051 + 5.95947i) q^{82} +(-9.31771 + 1.64296i) q^{83} +(0.474169 + 4.58465i) q^{84} +(-0.670647 - 1.84259i) q^{85} +(-3.10567 - 3.13128i) q^{86} +(2.59866 + 5.24063i) q^{87} +(7.90731 - 11.0019i) q^{88} +(-8.67486 + 5.00843i) q^{89} +(-0.439340 + 10.1251i) q^{90} +(0.372988 - 0.646034i) q^{91} +(-8.17489 + 4.63069i) q^{92} +(11.1532 + 15.1415i) q^{93} +(4.23284 - 15.5417i) q^{94} +(2.50943 - 14.2317i) q^{95} +(-6.32405 - 7.48374i) q^{96} +(-6.77349 + 5.68363i) q^{97} +(4.26695 - 6.04089i) q^{98} +(-13.7242 - 4.26130i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	−0.117471	−	1.40933i	−0.0830649	−	0.996544i
$2$	−0.117471	−	1.40933i	−0.0830649	−	0.996544i
$3$	1.66179	−	0.488315i	0.959435	−	0.281929i
$3$	1.66179	−	0.488315i	0.959435	−	0.281929i
$4$	−1.97240	+	0.331111i	−0.986200	+	0.165556i
$5$	−1.82990	−	1.53547i	−0.818356	−	0.686682i	0.134231	−	0.990950i	$-0.457144\pi$
$5$	−1.82990	−	1.53547i	−0.818356	−	0.686682i	−0.952586	+	0.304268i	$0.901588\pi$
$6$	−0.883408	−	2.28464i	−0.360650	−	0.932701i
$7$	0.455069	−	1.25029i	0.172000	−	0.472566i	−0.823501	−	0.567314i	$-0.807982\pi$
$7$	0.455069	−	1.25029i	0.172000	−	0.472566i	0.995501	+	0.0947484i	$0.0302047\pi$
$8$	0.698344	+	2.74086i	0.246902	+	0.969040i
$9$	2.52310	−	1.62295i	0.841033	−	0.540984i
$10$	−1.94901	+	2.75930i	−0.616332	+	0.872567i
$11$	−3.07907	−	3.66949i	−0.928374	−	1.10639i	−0.994091	−	0.108554i	$-0.965378\pi$
$11$	−3.07907	−	3.66949i	−0.928374	−	1.10639i	0.0657167	−	0.997838i	$-0.479067\pi$
$12$	−3.11603	+	1.51339i	−0.899521	+	0.436878i
$13$	0.552142	+	0.0973575i	0.153137	+	0.0270021i	0.249691	−	0.968326i	$-0.419671\pi$
$13$	0.552142	+	0.0973575i	0.153137	+	0.0270021i	−0.0965542	+	0.995328i	$0.530782\pi$
$14$	−1.81553	−	0.494467i	−0.485220	−	0.132152i
$15$	−3.79070	−	1.65806i	−0.978755	−	0.428109i
$16$	3.78073	−	1.30617i	0.945183	−	0.326542i
$17$	0.710885	+	0.410430i	0.172415	+	0.0995438i	0.583724	−	0.811952i	$-0.301595\pi$
$17$	0.710885	+	0.410430i	0.172415	+	0.0995438i	−0.411309	+	0.911496i	$0.634928\pi$
$18$	−2.58366	−	3.36522i	−0.608975	−	0.793189i
$19$	3.02483	+	5.23916i	0.693944	+	1.20195i	0.970536	+	0.240958i	$0.0774617\pi$
$19$	3.02483	+	5.23916i	0.693944	+	1.20195i	−0.276592	+	0.960987i	$0.589205\pi$
$20$	4.11771	+	2.42266i	0.920747	+	0.541723i
$21$	0.145694	−	2.29994i	0.0317930	−	0.501888i
$22$	−4.80981	+	4.77047i	−1.02545	+	1.01707i
$23$	4.41436	−	1.60670i	0.920457	−	0.335019i	0.162037	−	0.986785i	$-0.448194\pi$
$23$	4.41436	−	1.60670i	0.920457	−	0.335019i	0.758420	+	0.651766i	$0.225971\pi$
$24$	2.49890	+	4.21372i	0.510087	+	0.860123i
$25$	0.122629	+	0.695465i	0.0245258	+	0.139093i
$26$	0.0723476	−	0.789585i	0.0141885	−	0.154850i
$27$	3.40035	−	3.92907i	0.654397	−	0.756151i
$28$	−0.483593	+	2.61676i	−0.0913905	+	0.494520i
$29$	0.586451	+	3.32593i	0.108901	+	0.617610i	0.989590	+	0.143915i	$0.0459691\pi$
$29$	0.586451	+	3.32593i	0.108901	+	0.617610i	−0.880689	+	0.473695i	$0.842920\pi$
$30$	−1.89145	+	5.53711i	−0.345330	+	1.01093i
$31$	3.71351	+	10.2028i	0.666966	+	1.83247i	0.542125	+	0.840298i	$0.317620\pi$
$31$	3.71351	+	10.2028i	0.666966	+	1.83247i	0.124841	+	0.992177i	$0.460158\pi$
$32$	−2.28494	−	5.17485i	−0.403925	−	0.914792i
$33$	−6.90863	−	4.59437i	−1.20264	−	0.799777i
$34$	0.494921	−	1.05008i	0.0848782	−	0.180088i
$35$	−2.75251	+	1.58916i	−0.465260	+	0.268618i
$36$	−4.43918	+	4.03654i	−0.739864	+	0.672757i
$37$	−7.25187	−	4.18687i	−1.19220	−	0.688317i	−0.233395	−	0.972382i	$-0.574983\pi$
$37$	−7.25187	−	4.18687i	−1.19220	−	0.688317i	−0.958805	+	0.284065i	$0.908317\pi$
$38$	7.02835	−	4.87842i	1.14015	−	0.791385i
$39$	0.965085	−	0.107831i	0.154537	−	0.0172668i
$40$	2.93060	−	6.08778i	0.463369	−	0.962563i
$41$	−4.16735	−	0.734815i	−0.650830	−	0.114759i	−0.161521	−	0.986869i	$-0.551640\pi$
$41$	−4.16735	−	0.734815i	−0.650830	−	0.114759i	−0.489309	+	0.872110i	$0.662751\pi$
$42$	−3.25848	+	0.0648473i	−0.502795	+	0.0100061i
$43$	2.38891	−	2.00453i	0.364305	−	0.305689i	−0.442199	−	0.896917i	$-0.645801\pi$
$43$	2.38891	−	2.00453i	0.364305	−	0.305689i	0.806504	+	0.591229i	$0.201357\pi$
$44$	7.28816	+	6.21819i	1.09873	+	0.937428i
$45$	−7.10901	−	0.904294i	−1.05975	−	0.134804i
$46$	−2.78292	−	6.03253i	−0.410319	−	0.889448i
$47$	10.7030	+	3.89558i	1.56119	+	0.568228i	0.971010	−	0.239039i	$-0.0768325\pi$
$47$	10.7030	+	3.89558i	1.56119	+	0.568228i	0.590185	+	0.807268i	$0.299055\pi$
$48$	5.64496	−	4.01676i	0.814780	−	0.579770i
$49$	4.00617	+	3.36158i	0.572310	+	0.480225i
$50$	0.965731	−	0.254522i	0.136575	−	0.0359948i
$51$	1.38176	+	0.334913i	0.193485	+	0.0468972i
$52$	−1.12128	−	0.00920769i	−0.155494	−	0.00127688i
$53$	−0.541186			−0.0743377			−0.0371688	−	0.999309i	$-0.511834\pi$
$53$	−0.541186			−0.0743377			−0.0371688	+	0.999309i	$0.511834\pi$
$54$	−5.93679	−	4.33065i	−0.807895	−	0.589326i
$55$			11.4426i			1.54292i
$56$	3.74467	+	0.374146i	0.500403	+	0.0499974i
$57$	7.58499	+	7.22932i	1.00466	+	0.957547i
$58$	4.61843	−	1.21720i	0.606430	−	0.159827i
$59$	4.04416	−	4.81965i	0.526505	−	0.627464i	−0.435601	−	0.900140i	$-0.643464\pi$
$59$	4.04416	−	4.81965i	0.526505	−	0.627464i	0.962106	+	0.272675i	$0.0879085\pi$
$60$	8.02579	+	2.01522i	1.03612	+	0.260163i
$61$	3.02063	−	8.29912i	0.386752	−	1.06259i	−0.581702	−	0.813402i	$-0.697613\pi$
$61$	3.02063	−	8.29912i	0.386752	−	1.06259i	0.968454	−	0.249191i	$-0.0801647\pi$
$62$	13.9428	−	6.43208i	1.77074	−	0.816875i
$63$	−0.880982	−	3.89316i	−0.110993	−	0.490493i
$64$	−7.02463	+	3.82813i	−0.878079	+	0.478516i
$65$	−0.860875	−	1.02595i	−0.106778	−	0.127253i
$66$	−5.66340	+	10.2762i	−0.697116	+	1.26492i
$67$	−0.850868	+	4.82551i	−0.103950	+	0.589530i	0.887684	+	0.460452i	$0.152313\pi$
$67$	−0.850868	+	4.82551i	−0.103950	+	0.589530i	−0.991634	+	0.129078i	$0.958798\pi$
$68$	−1.53805	−	0.574150i	−0.186516	−	0.0696259i
$69$	6.55117	−	4.82559i	0.788668	−	0.580932i
$70$	2.56299	+	3.69251i	0.306336	+	0.441339i
$71$	−2.20493	+	3.81906i	−0.261677	+	0.453239i	−0.966688	−	0.255958i	$-0.917609\pi$
$71$	−2.20493	+	3.81906i	−0.261677	+	0.453239i	0.705010	+	0.709197i	$0.250942\pi$
$72$	6.21028	+	5.78208i	0.731889	+	0.681424i
$73$	−0.205251	−	0.355506i	−0.0240229	−	0.0416088i	0.853764	−	0.520660i	$-0.174314\pi$
$73$	−0.205251	−	0.355506i	−0.0240229	−	0.0416088i	−0.877787	+	0.479051i	$0.840981\pi$
$74$	−5.04877	+	10.7121i	−0.586908	+	1.24525i
$75$	0.543390	+	1.09584i	0.0627452	+	0.126536i
$76$	−7.70092	−	9.33217i	−0.883356	−	1.07047i
$77$	−5.98912	+	2.17986i	−0.682524	+	0.248418i
$78$	−0.265339	−	1.34745i	−0.0300437	−	0.152569i
$79$	−4.56009	+	0.804066i	−0.513050	+	0.0904645i	−0.424179	−	0.905579i	$-0.639437\pi$
$79$	−4.56009	+	0.804066i	−0.513050	+	0.0904645i	−0.0888713	+	0.996043i	$0.528326\pi$
$80$	−8.92394	−	3.41503i	−0.997726	−	0.381812i
$81$	3.73204	−	8.18974i	0.414672	−	0.909971i
$82$	−0.546051	+	5.95947i	−0.0603012	+	0.658113i
$83$	−9.31771	+	1.64296i	−1.02275	+	0.180339i	−0.659778	−	0.751461i	$-0.729350\pi$
$83$	−9.31771	+	1.64296i	−1.02275	+	0.180339i	−0.362974	+	0.931799i	$0.618239\pi$
$84$	0.474169	+	4.58465i	0.0517361	+	0.500226i
$85$	−0.670647	−	1.84259i	−0.0727418	−	0.199857i
$86$	−3.10567	−	3.13128i	−0.334893	−	0.337655i
$87$	2.59866	+	5.24063i	0.278606	+	0.561854i
$88$	7.90731	−	11.0019i	0.842922	−	1.17280i
$89$	−8.67486	+	5.00843i	−0.919533	+	0.530893i	−0.883486	−	0.468457i	$-0.844810\pi$
$89$	−8.67486	+	5.00843i	−0.919533	+	0.530893i	−0.0360470	+	0.999350i	$0.511477\pi$
$90$	−0.439340	+	10.1251i	−0.0463105	+	1.06728i
$91$	0.372988	−	0.646034i	0.0390998	−	0.0677228i
$92$	−8.17489	+	4.63069i	−0.852291	+	0.482783i
$93$	11.1532	+	15.1415i	1.15654	+	1.57010i
$94$	4.23284	−	15.5417i	0.436584	−	1.60300i
$95$	2.50943	−	14.2317i	0.257462	−	1.46014i
$96$	−6.32405	−	7.48374i	−0.645446	−	0.763806i
$97$	−6.77349	+	5.68363i	−0.687744	+	0.577085i	−0.918258	−	0.395984i	$-0.870404\pi$
$97$	−6.77349	+	5.68363i	−0.687744	+	0.577085i	0.230514	+	0.973069i	$0.425959\pi$
$98$	4.26695	−	6.04089i	0.431027	−	0.610222i
$99$	−13.7242	−	4.26130i	−1.37933	−	0.428277i
$100$	−0.472150	−	1.33113i	−0.0472150	−	0.133113i
$101$	−13.1186	−	4.77480i	−1.30535	−	0.475110i	−0.406617	−	0.913599i	$-0.633292\pi$
$101$	−13.1186	−	4.77480i	−1.30535	−	0.475110i	−0.898737	+	0.438488i	$0.855514\pi$
$102$	0.309684	−	1.98670i	0.0306633	−	0.196712i
$103$	9.86004	−	11.7507i	0.971538	−	1.15783i	−0.0159072	−	0.999873i	$-0.505064\pi$
$103$	9.86004	−	11.7507i	0.971538	−	1.15783i	0.987445	−	0.157961i	$-0.0504919\pi$
$104$	0.118742	+	1.58133i	0.0116436	+	0.155062i
$105$	−3.79809	+	3.98495i	−0.370656	+	0.388891i
$106$	0.0635739	+	0.762708i	0.00617485	+	0.0740808i
$107$			16.9514i			1.63875i	0.573257	+	0.819375i	$0.305679\pi$
$107$			16.9514i			1.63875i	−0.573257	+	0.819375i	$0.694321\pi$
$108$	−5.40589	+	8.87560i	−0.520182	+	0.854055i
$109$		−	8.61539i		−	0.825205i	−0.910911	−	0.412602i	$-0.864620\pi$
$109$		−	8.61539i		−	0.825205i	0.910911	−	0.412602i	$-0.135380\pi$
$110$	16.1264	−	1.34418i	1.53759	−	0.128162i
$111$	−14.0956	−	3.41651i	−1.33789	−	0.324280i
$112$	0.0874022	−	5.32141i	0.00825874	−	0.502826i
$113$	3.34008	−	3.98056i	0.314209	−	0.374459i	−0.585707	−	0.810523i	$-0.699183\pi$
$113$	3.34008	−	3.98056i	0.314209	−	0.374459i	0.899916	+	0.436063i	$0.143628\pi$
$114$	9.29745	−	11.5390i	0.870786	−	1.08072i
$115$	−10.5449	−	3.83802i	−0.983313	−	0.357897i
$116$	−2.25797	−	6.36589i	−0.209647	−	0.591058i
$117$	1.55111	−	0.650458i	0.143401	−	0.0601349i
$118$	−7.26753	−	5.13337i	−0.669030	−	0.472565i
$119$	0.836659	−	0.702040i	0.0766964	−	0.0643559i
$120$	1.89730	−	11.5477i	0.173199	−	1.05415i
$121$	−2.07437	+	11.7643i	−0.188579	+	1.06948i
$122$	−12.0510	−	3.28215i	−1.09105	−	0.297152i
$123$	−7.28408	+	0.813866i	−0.656783	+	0.0733838i
$124$	−10.7028	−	18.8944i	−0.961139	−	1.69677i
$125$	−5.12845	+	8.88273i	−0.458702	+	0.794495i
$126$	−5.38325	+	1.69893i	−0.479578	+	0.151352i
$127$	−4.00356	+	2.31146i	−0.355259	+	0.205109i	−0.666999	−	0.745059i	$-0.732421\pi$
$127$	−4.00356	+	2.31146i	−0.355259	+	0.205109i	0.311740	+	0.950167i	$0.399088\pi$
$128$	6.22028	+	9.45030i	0.549800	+	0.835296i
$129$	2.99103	−	4.49766i	0.263345	−	0.395997i
$130$	−1.34477	+	1.33377i	−0.117944	+	0.116980i
$131$	3.93615	+	10.8145i	0.343903	+	0.944865i	0.984250	+	0.176780i	$0.0565680\pi$
$131$	3.93615	+	10.8145i	0.343903	+	0.944865i	−0.640348	+	0.768085i	$0.721210\pi$
$132$	15.1478	+	6.77442i	1.31845	+	0.589637i
$133$	7.92698	−	1.39774i	0.687357	−	0.121200i
$134$	6.90067	+	0.632291i	0.596127	+	0.0546216i
$135$	−12.2553	+	1.96868i	−1.05477	+	0.169437i
$136$	−0.628488	+	2.23506i	−0.0538924	+	0.191655i
$137$	−8.30956	+	1.46520i	−0.709933	+	0.125180i	−0.516943	−	0.856020i	$-0.672930\pi$
$137$	−8.30956	+	1.46520i	−0.709933	+	0.125180i	−0.192991	+	0.981201i	$0.561819\pi$
$138$	−7.57040	−	8.66586i	−0.644435	−	0.737687i
$139$	−3.15230	+	1.14734i	−0.267375	+	0.0973165i	−0.472229	−	0.881476i	$-0.656550\pi$
$139$	−3.15230	+	1.14734i	−0.267375	+	0.0973165i	0.204854	+	0.978793i	$0.434328\pi$
$140$	4.90287	−	4.04586i	0.414368	−	0.341937i
$141$	19.6884	+	1.24720i	1.65807	+	0.105033i
$142$	5.64131	+	2.65884i	0.473409	+	0.223125i
$143$	−1.34283	−	2.32585i	−0.112293	−	0.194497i
$144$	7.41930	−	9.43154i	0.618275	−	0.785962i
$145$	4.03371	−	6.98660i	0.334982	−	0.580205i
$146$	−0.476913	+	0.331028i	−0.0394696	+	0.0273961i
$147$	8.29892	+	3.62996i	0.684484	+	0.299394i
$148$	15.6899	+	5.85701i	1.28970	+	0.481443i
$149$	−2.96736	+	16.8288i	−0.243096	+	1.37867i	0.581777	+	0.813348i	$0.302358\pi$
$149$	−2.96736	+	16.8288i	−0.243096	+	1.37867i	−0.824873	+	0.565318i	$0.808754\pi$
$150$	1.48056	−	0.894543i	0.120887	−	0.0730391i
$151$	−2.38057	−	2.83705i	−0.193728	−	0.230876i	0.660433	−	0.750885i	$-0.270373\pi$
$151$	−2.38057	−	2.83705i	−0.193728	−	0.230876i	−0.854161	+	0.520009i	$0.825929\pi$
$152$	−12.2474	+	11.9494i	−0.993398	+	0.969222i
$153$	2.45974	−	0.118179i	0.198858	−	0.00955422i
$154$	3.77569	+	8.18455i	0.304254	+	0.659530i
$155$	8.87070	−	24.3720i	0.712512	−	1.95761i
$156$	−1.86783	+	0.532237i	−0.149546	+	0.0426130i
$157$	−4.95438	+	5.90440i	−0.395402	+	0.471222i	−0.926612	−	0.376018i	$-0.877293\pi$
$157$	−4.95438	+	5.90440i	−0.395402	+	0.471222i	0.531210	+	0.847240i	$0.321738\pi$
$158$	1.66887	+	6.33219i	0.132768	+	0.503762i
$159$	−0.899338	+	0.264269i	−0.0713222	+	0.0209579i
$160$	−3.76459	+	12.9779i	−0.297617	+	1.02599i
$161$		−	6.25039i		−	0.492600i
$162$	−11.9804	−	4.29761i	−0.941271	−	0.337652i
$163$	20.1482			1.57813			0.789066	−	0.614309i	$-0.210565\pi$
$163$	20.1482			1.57813			0.789066	+	0.614309i	$0.210565\pi$
$164$	8.46298	+	0.0694960i	0.660848	+	0.00542672i
$165$	5.58759	+	19.0152i	0.434993	+	1.48033i
$166$	3.41004	+	12.9387i	0.264670	+	1.00424i
$167$	−11.7203	−	9.83453i	−0.906946	−	0.761018i	0.0645892	−	0.997912i	$-0.479426\pi$
$167$	−11.7203	−	9.83453i	−0.906946	−	0.761018i	−0.971536	+	0.236894i	$0.923871\pi$
$168$	6.40556	−	1.20682i	0.494200	−	0.0931085i
$169$	−11.9206	−	4.33875i	−0.916971	−	0.333750i
$170$	−2.51802	+	1.16161i	−0.193124	+	0.0890915i
$171$	16.1349	+	8.30975i	1.23386	+	0.635463i
$172$	−4.04817	+	4.74474i	−0.308670	+	0.361783i
$173$	4.70819	−	3.95064i	0.357957	−	0.300362i	−0.446019	−	0.895024i	$-0.647159\pi$
$173$	4.70819	−	3.95064i	0.357957	−	0.300362i	0.803976	+	0.594662i	$0.202714\pi$
$174$	7.08049	−	4.27798i	0.536770	−	0.324313i
$175$	0.925339	+	0.163162i	0.0699490	+	0.0123339i
$176$	−16.4341	−	9.85157i	−1.23877	−	0.742590i
$177$	4.36705	−	9.98407i	0.328248	−	0.750448i
$178$	8.07756	+	11.6374i	0.605439	+	0.872257i
$179$	−15.0820	−	8.70758i	−1.12728	−	0.650835i	−0.184030	−	0.982921i	$-0.558914\pi$
$179$	−15.0820	−	8.70758i	−1.12728	−	0.650835i	−0.943249	+	0.332086i	$0.892248\pi$
$180$	14.3212	−	0.570242i	1.06744	−	0.0425033i
$181$	20.6704	−	11.9341i	1.53642	−	0.887051i	0.537373	−	0.843345i	$-0.319417\pi$
$181$	20.6704	−	11.9341i	1.53642	−	0.887051i	0.999044	−	0.0437065i	$-0.0139167\pi$
$182$	−0.954288	−	0.449771i	−0.0707365	−	0.0333392i
$183$	0.967078	−	15.2664i	0.0714885	−	1.12853i
$184$	7.48647	+	10.9771i	0.551910	+	0.809244i
$185$	6.84139	+	18.7966i	0.502989	+	1.38195i
$186$	20.0292	−	17.4973i	1.46861	−	1.28296i
$187$	−0.682796	−	3.87233i	−0.0499310	−	0.283173i
$188$	−22.4005	−	4.13975i	−1.63372	−	0.301923i
$189$	−3.36510	−	6.03943i	−0.244775	−	0.439304i
$190$	−20.3518	−	1.86479i	−1.47648	−	0.135286i
$191$	0.751494	+	4.26194i	0.0543762	+	0.308383i	0.999850	−	0.0173151i	$-0.00551185\pi$
$191$	0.751494	+	4.26194i	0.0543762	+	0.308383i	−0.945474	+	0.325698i	$0.894401\pi$
$192$	−9.80413	+	9.79178i	−0.707552	+	0.706661i
$193$	2.14782	−	0.781743i	0.154604	−	0.0562711i	−0.263559	−	0.964643i	$-0.584896\pi$
$193$	2.14782	−	0.781743i	0.154604	−	0.0562711i	0.418163	+	0.908372i	$0.362674\pi$
$194$	8.80578	+	8.87839i	0.632218	+	0.637431i
$195$	−1.93158	−	1.28454i	−0.138323	−	0.0919876i
$196$	−9.01483	−	5.30389i	−0.643916	−	0.378849i
$197$	7.00375	+	12.1308i	0.498996	+	0.864287i	0.999999	−	0.00115839i	$-0.000368727\pi$
$197$	7.00375	+	12.1308i	0.498996	+	0.864287i	−0.501003	+	0.865446i	$0.667035\pi$
$198$	−4.39336	+	19.8425i	−0.312222	+	1.41014i
$199$	−8.97113	−	5.17949i	−0.635947	−	0.367164i	0.147105	−	0.989121i	$-0.453005\pi$
$199$	−8.97113	−	5.17949i	−0.635947	−	0.367164i	−0.783051	+	0.621957i	$0.786338\pi$
$200$	−1.82053	+	0.821783i	−0.128731	+	0.0581089i
$201$	0.942403	+	8.43448i	0.0664720	+	0.594922i
$202$	−5.18818	+	19.0494i	−0.365039	+	1.34031i
$203$	4.42526	+	0.780293i	0.310592	+	0.0547658i
$204$	−2.83628	−	0.203066i	−0.198579	−	0.0142174i
$205$	6.49754	+	7.74346i	0.453808	+	0.540827i
$206$	−17.7189	−	12.5156i	−1.23453	−	0.872005i
$207$	8.53027	−	11.2181i	0.592895	−	0.779715i
$208$	2.21466	−	0.353107i	0.153559	−	0.0244836i
$209$	9.91139	−	27.2313i	0.685585	−	1.88363i
$210$	6.06226	+	4.88463i	0.418336	+	0.337071i
$211$	5.48774	+	4.60476i	0.377792	+	0.317005i	0.811835	−	0.583887i	$-0.198469\pi$
$211$	5.48774	+	4.60476i	0.377792	+	0.317005i	−0.434043	+	0.900892i	$0.642913\pi$
$212$	1.06744	−	0.179193i	0.0733118	−	0.0123070i
$213$	−1.79924	+	7.42318i	−0.123282	+	0.508628i
$214$	23.8900	−	1.99130i	1.63309	−	0.136123i
$215$	−7.44936			−0.508042
$216$	13.1437	+	6.57603i	0.894313	+	0.447442i
$217$	14.4464			0.980683
$218$	−12.1419	+	1.01206i	−0.822353	+	0.0685455i
$219$	−0.514684	−	0.490549i	−0.0347791	−	0.0331482i
$220$	−3.78877	−	22.5694i	−0.255439	−	1.52163i
$221$	0.352551	+	0.295825i	0.0237151	+	0.0198994i
$222$	−3.15914	+	20.2666i	−0.212028	+	1.36021i
$223$	−3.21157	+	8.82372i	−0.215063	+	0.590880i	−0.999573	−	0.0292366i	$-0.990692\pi$
$223$	−3.21157	+	8.82372i	−0.215063	+	0.590880i	0.784510	+	0.620116i	$0.212915\pi$
$224$	−7.50987	+	0.501936i	−0.501775	+	0.0335370i
$225$	1.43811	+	1.55570i	0.0958742	+	0.103714i
$226$	−6.00227	−	4.23967i	−0.399265	−	0.282018i
$227$	9.60066	+	11.4416i	0.637218	+	0.759407i	0.983928	−	0.178566i	$-0.0571456\pi$
$227$	9.60066	+	11.4416i	0.637218	+	0.759407i	−0.346710	+	0.937972i	$0.612701\pi$
$228$	−17.3544	−	11.7476i	−1.14932	−	0.778006i
$229$	−9.18182	−	1.61900i	−0.606752	−	0.106987i	−0.138173	−	0.990408i	$-0.544123\pi$
$229$	−9.18182	−	1.61900i	−0.606752	−	0.106987i	−0.468579	+	0.883421i	$0.655234\pi$
$230$	−4.17030	+	15.3120i	−0.274981	+	1.00964i
$231$	−8.88821	+	6.54705i	−0.584801	+	0.430764i
$232$	−8.70637	+	3.93003i	−0.571601	+	0.258019i
$233$	13.7940	+	7.96400i	0.903678	+	0.521739i	0.878392	−	0.477941i	$-0.158617\pi$
$233$	13.7940	+	7.96400i	0.903678	+	0.521739i	0.0252864	+	0.999680i	$0.491950\pi$
$234$	−1.09892	−	2.10962i	−0.0718386	−	0.137910i
$235$	−13.6039	−	23.5626i	−0.887421	−	1.53706i
$236$	−6.38087	+	10.8453i	−0.415359	+	0.705972i
$237$	−7.18527	+	3.56295i	−0.466734	+	0.231438i
$238$	−1.08769	−	1.09666i	−0.0705043	−	0.0710856i
$239$	16.3896	−	5.96534i	1.06016	−	0.385866i	0.247670	−	0.968845i	$-0.420335\pi$
$239$	16.3896	−	5.96534i	1.06016	−	0.385866i	0.812487	+	0.582979i	$0.198113\pi$
$240$	−16.4973	−	1.31739i	−1.06490	−	0.0850369i
$241$	−4.67757	−	26.5278i	−0.301309	−	1.70881i	−0.640391	−	0.768049i	$-0.721228\pi$
$241$	−4.67757	−	26.5278i	−0.301309	−	1.70881i	0.339082	−	0.940757i	$-0.389884\pi$
$242$	16.8235	+	1.54149i	1.08145	+	0.0990907i
$243$	2.20271	−	15.4320i	0.141304	−	0.989966i
$244$	−3.20997	+	17.3694i	−0.205497	+	1.11196i
$245$	−2.16930	−	12.3027i	−0.138591	−	0.785990i
$246$	2.00267	+	10.1700i	0.127686	+	0.648418i
$247$	1.16006	+	3.18725i	0.0738131	+	0.202800i
$248$	−25.3711	+	17.3033i	−1.61107	+	1.09876i
$249$	−14.6818	+	7.28024i	−0.930421	+	0.461366i
$250$	13.1211	+	6.18419i	0.829852	+	0.391122i
$251$	11.6387	−	6.71960i	0.734628	−	0.424138i	−0.0854849	−	0.996339i	$-0.527244\pi$
$251$	11.6387	−	6.71960i	0.734628	−	0.424138i	0.820113	+	0.572202i	$0.193911\pi$
$252$	3.02672	+	7.38718i	0.190665	+	0.465348i
$253$	−19.4879	−	11.2513i	−1.22519	−	0.707364i
$254$	3.72790	+	5.37080i	0.233910	+	0.336994i
$255$	−2.01424	−	2.73451i	−0.126136	−	0.171241i
$256$	12.5879	−	9.87654i	0.786741	−	0.617284i
$257$	27.3502	+	4.82258i	1.70606	+	0.300824i	0.939804	−	0.341713i	$-0.111007\pi$
$257$	27.3502	+	4.82258i	1.70606	+	0.300824i	0.766254	+	0.642537i	$0.222118\pi$
$258$	−6.69003	−	3.68699i	−0.416503	−	0.229542i
$259$	−8.53491	+	7.16164i	−0.530333	+	0.445002i
$260$	2.03769	+	1.73854i	0.126372	+	0.107820i
$261$	6.87751	+	7.43987i	0.425707	+	0.460516i
$262$	14.7787	−	6.81770i	0.913033	−	0.421199i
$263$	2.74946	+	1.00072i	0.169539	+	0.0617071i	0.425395	−	0.905008i	$-0.360135\pi$
$263$	2.74946	+	1.00072i	0.169539	+	0.0617071i	−0.255856	+	0.966715i	$0.582357\pi$
$264$	7.76792	−	22.1440i	0.478083	−	1.36287i
$265$	0.990316	+	0.830974i	0.0608347	+	0.0510463i
$266$	−2.90107	−	11.0075i	−0.177876	−	0.674914i
$267$	−11.9701	+	12.5590i	−0.732559	+	0.768600i
$268$	0.0804718	−	9.79957i	0.00491560	−	0.598604i
$269$	19.3788			1.18155			0.590773	−	0.806838i	$-0.298823\pi$
$269$	19.3788			1.18155			0.590773	+	0.806838i	$0.298823\pi$
$270$	4.21416	+	17.0404i	0.256466	+	1.03705i
$271$			25.2492i			1.53378i	0.641779	+	0.766890i	$0.278197\pi$
$271$			25.2492i			1.53378i	−0.641779	+	0.766890i	$0.721803\pi$
$272$	3.22376	+	0.623189i	0.195469	+	0.0377864i
$273$	0.304360	−	1.25571i	0.0184207	−	0.0759990i
$274$	3.04108	+	11.5388i	0.183718	+	0.697082i
$275$	2.17442	−	2.59137i	0.131122	−	0.156265i
$276$	−11.3237	+	11.6872i	−0.681608	+	0.703484i
$277$	−8.11046	+	22.2833i	−0.487310	+	1.33887i	0.415796	+	0.909458i	$0.363503\pi$
$277$	−8.11046	+	22.2833i	−0.487310	+	1.33887i	−0.903107	+	0.429416i	$0.858719\pi$
$278$	1.98729	+	4.30784i	0.119190	+	0.258367i
$279$	25.9282	+	19.7158i	1.55228	+	1.18035i
$280$	−6.27788	−	6.43447i	−0.375175	−	0.384533i
$281$	8.55970	+	10.2011i	0.510629	+	0.608544i	0.958338	−	0.285635i	$-0.0922046\pi$
$281$	8.55970	+	10.2011i	0.510629	+	0.608544i	−0.447709	+	0.894179i	$0.647760\pi$
$282$	−0.555119	−	27.8939i	−0.0330569	−	1.66106i
$283$	−2.09329	+	11.8716i	−0.124433	+	0.705696i	0.857210	+	0.514968i	$0.172196\pi$
$283$	−2.09329	+	11.8716i	−0.124433	+	0.705696i	−0.981643	+	0.190728i	$0.938915\pi$
$284$	3.08448	−	8.26279i	0.183030	−	0.490306i
$285$	−2.77939	−	24.8754i	−0.164637	−	1.47349i
$286$	−3.12014	+	2.16571i	−0.184497	+	0.128061i
$287$	−2.81516	+	4.87601i	−0.166174	+	0.287822i
$288$	−14.1637	−	9.34828i	−0.834602	−	0.550853i
$289$	−8.16309	−	14.1389i	−0.480182	−	0.831700i
$290$	−10.3202	−	4.86409i	−0.606025	−	0.285629i
$291$	−8.48072	+	12.7526i	−0.497149	+	0.747571i
$292$	0.522550	+	0.633239i	0.0305799	+	0.0370575i
$293$	−6.00209	+	2.18458i	−0.350646	+	0.127625i	−0.511338	−	0.859380i	$-0.670850\pi$
$293$	−6.00209	+	2.18458i	−0.350646	+	0.127625i	0.160692	+	0.987005i	$0.448628\pi$
$294$	4.14092	−	12.1223i	0.241503	−	0.706987i
$295$	−14.8008	+	2.60978i	−0.861737	+	0.151948i
$296$	6.41132	−	22.8002i	0.372650	−	1.32524i
$297$	−24.8876	−	0.379659i	−1.44413	−	0.0220301i
$298$	24.0658	+	2.20509i	1.39409	+	0.127737i
$299$	2.59378	−	0.457353i	0.150002	−	0.0264494i
$300$	−1.43463	−	1.98150i	−0.0828281	−	0.114402i
$301$	−1.41913	−	3.89904i	−0.0817975	−	0.224737i
$302$	−3.71869	+	3.68827i	−0.213986	+	0.212236i
$303$	−24.1321	−	1.52869i	−1.38635	−	0.0878208i
$304$	18.2793	+	15.8569i	1.04839	+	0.909456i
$305$	−18.2705	+	10.5485i	−1.04616	+	0.604003i
$306$	−0.455502	−	3.45270i	−0.0260393	−	0.197377i
$307$	7.56813	−	13.1084i	0.431936	−	0.748136i	−0.565104	−	0.825020i	$-0.691164\pi$
$307$	7.56813	−	13.1084i	0.431936	−	0.748136i	0.997040	+	0.0768843i	$0.0244972\pi$
$308$	11.0912	−	6.28263i	0.631978	−	0.357986i
$309$	10.6473	−	24.3421i	0.605702	−	1.38477i
$310$	−35.3902	−	9.63869i	−2.01003	−	0.547441i
$311$	1.04978	−	5.95361i	0.0595277	−	0.337598i	−0.940470	−	0.339878i	$-0.889614\pi$
$311$	1.04978	−	5.95361i	0.0595277	−	0.337598i	0.999997	+	0.00227916i	$0.000725481\pi$
$312$	0.969512	+	2.56986i	0.0548878	+	0.145490i
$313$	8.82704	−	7.40677i	0.498934	−	0.418655i	−0.358281	−	0.933614i	$-0.616637\pi$
$313$	8.82704	−	7.40677i	0.498934	−	0.418655i	0.857215	+	0.514958i	$0.172193\pi$
$314$	8.90322	+	6.28873i	0.502438	+	0.354894i
$315$	−4.36572	+	8.47682i	−0.245980	+	0.477615i
$316$	8.72808	−	3.09584i	0.490993	−	0.174154i
$317$	−11.9885	−	4.36344i	−0.673339	−	0.245075i	−0.0173540	−	0.999849i	$-0.505524\pi$
$317$	−11.9885	−	4.36344i	−0.673339	−	0.245075i	−0.655985	+	0.754774i	$0.727746\pi$
$318$	0.478088	+	1.23642i	0.0268098	+	0.0693348i
$319$	10.3987	−	12.3927i	0.582218	−	0.693861i
$320$	18.7323	+	3.78100i	1.04717	+	0.211364i
$321$	8.27760	+	28.1696i	0.462011	+	1.57228i
$322$	−8.80884	+	0.734243i	−0.490898	+	0.0409177i
$323$			4.96592i			0.276311i
$324$	−4.64937	+	17.3892i	−0.258298	+	0.966065i
$325$			0.395934i			0.0219625i
$326$	−2.36684	−	28.3954i	−0.131087	−	1.57268i
$327$	−4.20702	−	14.3170i	−0.232649	−	0.791731i
$328$	−0.896216	−	11.9353i	−0.0494853	−	0.659015i
$329$	9.74122	−	11.6091i	0.537051	−	0.640032i
$330$	26.1423	−	10.1085i	1.43908	−	0.556454i
$331$	−8.23367	−	2.99681i	−0.452563	−	0.164720i	0.105674	−	0.994401i	$-0.466300\pi$
$331$	−8.23367	−	2.99681i	−0.452563	−	0.164720i	−0.558237	+	0.829681i	$0.688522\pi$
$332$	17.8343	−	6.32578i	0.978782	−	0.347172i
$333$	−25.0923	+	1.20557i	−1.37505	+	0.0660647i
$334$	−12.4833	+	17.6730i	−0.683053	+	0.967026i
$335$	8.96642	−	7.52372i	0.489888	−	0.411065i
$336$	−2.45328	−	8.88576i	−0.133837	−	0.484758i
$337$	2.10804	−	11.9553i	0.114832	−	0.651245i	−0.872001	−	0.489504i	$-0.837178\pi$
$337$	2.10804	−	11.9553i	0.114832	−	0.651245i	0.986833	−	0.161741i	$-0.0517110\pi$
$338$	−4.71438	+	17.3097i	−0.256429	+	0.941525i
$339$	3.60676	−	8.24587i	0.195892	−	0.447854i
$340$	1.93289	+	3.41226i	0.104825	+	0.185056i
$341$	26.0049	−	45.0418i	1.40824	−	2.43915i
$342$	9.81577	−	23.7154i	0.530776	−	1.28238i
$343$	14.0920	−	8.13600i	0.760894	−	0.439303i
$344$	7.16243	+	5.14782i	0.386172	+	0.277552i
$345$	−19.3975	−	1.22877i	−1.04433	−	0.0661547i
$346$	−6.12082	−	6.17129i	−0.329057	−	0.331771i
$347$	−3.14976	−	8.65389i	−0.169088	−	0.464565i	0.825987	−	0.563689i	$-0.190618\pi$
$347$	−3.14976	−	8.65389i	−0.169088	−	0.464565i	−0.995075	+	0.0991236i	$0.968396\pi$
$348$	−6.86083	−	9.47618i	−0.367779	−	0.507976i
$349$	13.3909	−	2.36117i	0.716798	−	0.126391i	0.196658	−	0.980472i	$-0.436991\pi$
$349$	13.3909	−	2.36117i	0.716798	−	0.126391i	0.520139	+	0.854081i	$0.325880\pi$
$350$	0.121248	−	1.32327i	0.00648097	−	0.0707318i
$351$	2.26000	−	1.83836i	0.120630	−	0.0981242i
$352$	−11.9535	+	24.3183i	−0.637126	+	1.29617i
$353$	−21.6804	+	3.82285i	−1.15393	+	0.203470i	−0.717692	−	0.696360i	$-0.754802\pi$
$353$	−21.6804	+	3.82285i	−1.15393	+	0.203470i	−0.436241	+	0.899830i	$0.643690\pi$
$354$	−14.5838	−	4.98175i	−0.775121	−	0.264777i
$355$	9.89885	−	3.60289i	0.525376	−	0.191221i
$356$	15.4519	−	12.7510i	0.818952	−	0.675800i
$357$	1.04754	−	1.57520i	0.0554415	−	0.0833682i
$358$	−10.5001	+	22.2783i	−0.554948	+	1.17744i
$359$	−3.83216	−	6.63749i	−0.202253	−	0.350313i	0.747001	−	0.664823i	$-0.231493\pi$
$359$	−3.83216	−	6.63749i	−0.202253	−	0.350313i	−0.949254	+	0.314510i	$0.898160\pi$
$360$	−2.48599	−	20.1163i	−0.131023	−	1.06022i
$361$	−8.79919	+	15.2407i	−0.463115	+	0.802140i
$362$	−19.2472	−	27.7294i	−1.01161	−	1.45743i
$363$	2.29753	+	20.5628i	0.120589	+	1.07927i
$364$	−0.521773	+	1.39774i	−0.0273483	+	0.0732614i
$365$	−0.170278	+	0.965697i	−0.00891278	+	0.0505469i
$366$	−21.6290	+	0.430440i	−1.13056	+	0.0224994i
$367$	−19.4285	−	23.1540i	−1.01416	−	1.20863i	−0.977854	−	0.209290i	$-0.932885\pi$
$367$	−19.4285	−	23.1540i	−1.01416	−	1.20863i	−0.0363077	−	0.999341i	$-0.511560\pi$
$368$	14.5909	−	11.8404i	0.760603	−	0.617222i
$369$	−11.7072	+	4.90940i	−0.609452	+	0.255573i
$370$	25.6868	−	11.8498i	1.33539	−	0.616042i
$371$	−0.246277	+	0.676641i	−0.0127861	+	0.0351294i
$372$	−27.0122	−	26.1722i	−1.40052	−	1.35697i
$373$	−24.0563	+	28.6692i	−1.24559	+	1.48444i	−0.433224	+	0.901286i	$0.642624\pi$
$373$	−24.0563	+	28.6692i	−1.24559	+	1.48444i	−0.812365	+	0.583149i	$0.801820\pi$
$374$	−5.37716	+	1.41717i	−0.278046	+	0.0732801i
$375$	−4.18484	+	17.2655i	−0.216104	+	0.891588i
$376$	−3.20285	+	32.0559i	−0.165174	+	1.65316i
$377$			1.89348i			0.0975192i
$378$	−8.11622	+	5.45198i	−0.417453	+	0.280420i
$379$	−16.6417			−0.854828			−0.427414	−	0.904056i	$-0.640575\pi$
$379$	−16.6417			−0.854828			−0.427414	+	0.904056i	$0.640575\pi$
$380$	−0.237332	+	28.9014i	−0.0121749	+	1.48261i
$381$	−5.52437	+	5.79616i	−0.283022	+	0.296946i
$382$	5.91818	−	1.55976i	0.302800	−	0.0798041i
$383$	17.0762	+	14.3286i	0.872552	+	0.732158i	0.964634	−	0.263594i	$-0.0849078\pi$
$383$	17.0762	+	14.3286i	0.872552	+	0.732158i	−0.0920820	+	0.995751i	$0.529352\pi$
$384$	14.9515	+	12.6670i	0.762991	+	0.646409i
$385$	14.3066	+	5.20718i	0.729132	+	0.265382i
$386$	−1.35404	−	2.93515i	−0.0689188	−	0.149395i
$387$	2.77419	−	8.93473i	0.141020	−	0.454178i
$388$	11.4781	−	13.4532i	0.582713	−	0.682982i
$389$	−19.8343	+	16.6429i	−1.00564	+	0.843830i	−0.987755	−	0.156010i	$-0.950137\pi$
$389$	−19.8343	+	16.6429i	−1.00564	+	0.843830i	−0.0178816	+	0.999840i	$0.505692\pi$
$390$	−1.58343	+	2.87312i	−0.0801799	+	0.145486i
$391$	3.79754	+	0.669608i	0.192050	+	0.0338636i
$392$	−6.41592	+	13.3279i	−0.324053	+	0.673160i
$393$	11.8219	+	16.0493i	0.596337	+	0.809581i
$394$	16.2736	−	11.2956i	0.819851	−	0.569064i
$395$	9.57912	+	5.53051i	0.481978	+	0.278270i
$396$	28.4806	+	3.86075i	1.43120	+	0.194010i
$397$	−3.38256	+	1.95292i	−0.169766	+	0.0980145i	−0.582476	−	0.812848i	$-0.697916\pi$
$397$	−3.38256	+	1.95292i	−0.169766	+	0.0980145i	0.412709	+	0.910863i	$0.364582\pi$
$398$	−6.24573	+	13.2517i	−0.313070	+	0.664247i
$399$	12.4905	−	6.19362i	0.625305	−	0.310069i
$400$	1.37202	+	2.46919i	0.0686011	+	0.123460i
$401$	−5.64844	−	15.5190i	−0.282070	−	0.774980i	−0.997115	−	0.0759022i	$-0.975816\pi$
$401$	−5.64844	−	15.5190i	−0.282070	−	0.774980i	0.715046	−	0.699078i	$-0.246406\pi$
$402$	11.7762	−	2.31896i	0.587345	−	0.115659i
$403$	1.05707	+	5.99492i	0.0526562	+	0.298628i
$404$	27.4562	+	5.07408i	1.36600	+	0.252445i
$405$	−19.4043	+	9.25597i	−0.964210	+	0.459933i
$406$	0.579845	−	6.32830i	0.0287772	−	0.314068i
$407$	6.96532	+	39.5023i	0.345258	+	1.95806i
$408$	0.0469962	+	4.02110i	0.00232666	+	0.199074i
$409$	−27.3270	+	9.94621i	−1.35123	+	0.491808i	−0.913332	−	0.407215i	$-0.866500\pi$
$409$	−27.3270	+	9.94621i	−1.35123	+	0.491808i	−0.437900	+	0.899024i	$0.644278\pi$
$410$	10.1498	−	10.0668i	0.501262	−	0.497163i
$411$	−13.0933	+	6.49253i	−0.645843	+	0.320253i
$412$	−15.5571	+	26.4419i	−0.766445	+	1.30270i
$413$	−4.18559	−	7.24966i	−0.205959	−	0.356732i
$414$	−16.8121	−	10.7041i	−0.826269	−	0.526079i
$415$	19.5732	+	11.3006i	0.960810	+	0.554724i
$416$	−0.757803	−	3.07970i	−0.0371544	−	0.150995i
$417$	−4.67820	+	3.44596i	−0.229093	+	0.168749i
$418$	−39.5421	−	10.7695i	−1.93407	−	0.526752i
$419$	−2.77065	−	0.488540i	−0.135355	−	0.0238667i	0.105560	−	0.994413i	$-0.466336\pi$
$419$	−2.77065	−	0.488540i	−0.135355	−	0.0238667i	−0.240915	+	0.970546i	$0.577448\pi$
$420$	6.17189	−	9.11751i	0.301158	−	0.444889i
$421$	13.5423	+	16.1391i	0.660013	+	0.786573i	0.987388	−	0.158322i	$-0.0506084\pi$
$421$	13.5423	+	16.1391i	0.660013	+	0.786573i	−0.327375	+	0.944895i	$0.606164\pi$
$422$	5.84496	−	8.27495i	0.284528	−	0.402818i
$423$	33.3271	−	7.54157i	1.62042	−	0.366684i
$424$	−0.377934	−	1.48332i	−0.0183541	−	0.0720362i
$425$	−0.198264	+	0.544726i	−0.00961722	+	0.0264231i
$426$	10.6730	+	1.66370i	0.517110	+	0.0806066i
$427$	−9.00172	−	7.55334i	−0.435624	−	0.365532i
$428$	−5.61279	−	33.4349i	−0.271304	−	1.61614i
$429$	−3.36725	−	3.20935i	−0.162572	−	0.154949i
$430$	0.875088	+	10.4986i	0.0422005	+	0.506287i
$431$	−29.2337			−1.40814			−0.704070	−	0.710131i	$-0.748636\pi$
$431$	−29.2337			−1.40814			−0.704070	+	0.710131i	$0.748636\pi$
$432$	7.72377	−	19.2962i	0.371610	−	0.928389i
$433$	−3.83819			−0.184451			−0.0922257	−	0.995738i	$-0.529398\pi$
$433$	−3.83819			−0.184451			−0.0922257	+	0.995738i	$0.529398\pi$
$434$	−1.69704	−	20.3596i	−0.0814603	−	0.977294i
$435$	3.29153	−	13.5800i	0.157817	−	0.651110i
$436$	2.85265	+	16.9930i	0.136617	+	0.813817i
$437$	21.7704	+	18.2675i	1.04142	+	0.873855i
$438$	−0.630883	+	0.782983i	−0.0301448	+	0.0374124i
$439$	1.73144	−	4.75709i	0.0826370	−	0.227043i	−0.891492	−	0.453037i	$-0.850341\pi$
$439$	1.73144	−	4.75709i	0.0826370	−	0.227043i	0.974129	+	0.225993i	$0.0725628\pi$
$440$	−31.3626	+	7.99088i	−1.49515	+	0.380950i
$441$	15.5636	+	1.97976i	0.741126	+	0.0942741i
$442$	0.375500	−	0.531610i	0.0178607	−	0.0252861i
$443$	17.8169	+	21.2333i	0.846506	+	1.00883i	0.999787	+	0.0206439i	$0.00657164\pi$
$443$	17.8169	+	21.2333i	0.846506	+	1.00883i	−0.153281	+	0.988183i	$0.548984\pi$
$444$	28.9334	+	2.07151i	1.37312	+	0.0983095i
$445$	23.5644	+	4.15504i	1.11706	+	0.196968i
$446$	12.8128	+	3.48961i	0.606702	+	0.165238i
$447$	3.28659	+	29.4149i	0.155450	+	1.39128i
$448$	1.58959	+	10.5249i	0.0751009	+	0.497255i
$449$	−7.77540	−	4.48913i	−0.366944	−	0.211855i	0.305179	−	0.952295i	$-0.401284\pi$
$449$	−7.77540	−	4.48913i	−0.366944	−	0.211855i	−0.672122	+	0.740440i	$0.734617\pi$
$450$	2.02356	−	2.20952i	0.0953914	−	0.104158i
$451$	10.1351	+	17.5546i	0.477245	+	0.826613i
$452$	−5.26998	+	8.95719i	−0.247879	+	0.421311i
$453$	−5.34139	−	3.55212i	−0.250960	−	0.166893i
$454$	14.9972	−	14.8745i	0.703852	−	0.698096i
$455$	−1.67449	+	0.609466i	−0.0785015	+	0.0285722i
$456$	−14.5176	+	25.8380i	−0.679850	+	1.20997i
$457$	3.37381	+	19.1338i	0.157820	+	0.895042i	0.956162	+	0.292838i	$0.0945996\pi$
$457$	3.37381	+	19.1338i	0.157820	+	0.895042i	−0.798342	+	0.602204i	$0.794289\pi$
$458$	−1.20310	+	13.1304i	−0.0562172	+	0.613542i
$459$	4.02987	−	1.39752i	0.188098	−	0.0652305i
$460$	22.0695	+	4.07858i	1.02900	+	0.190165i
$461$	−3.92114	−	22.2379i	−0.182626	−	1.03572i	−0.928968	−	0.370159i	$-0.879303\pi$
$461$	−3.92114	−	22.2379i	−0.182626	−	1.03572i	0.746343	−	0.665562i	$-0.231808\pi$
$462$	10.2710	+	11.7573i	0.477852	+	0.546999i
$463$	−2.63844	−	7.24905i	−0.122619	−	0.336892i	0.863163	−	0.504926i	$-0.168480\pi$
$463$	−2.63844	−	7.24905i	−0.122619	−	0.336892i	−0.985781	+	0.168034i	$0.946258\pi$
$464$	6.56144	+	11.8084i	0.304607	+	0.548193i
$465$	2.84002	−	44.8329i	0.131703	−	2.07908i
$466$	9.60346	−	20.3759i	0.444872	−	0.943893i
$467$	−5.54719	+	3.20267i	−0.256694	+	0.148202i	−0.622825	−	0.782361i	$-0.714015\pi$
$467$	−5.54719	+	3.20267i	−0.256694	+	0.148202i	0.366132	+	0.930563i	$0.380682\pi$
$468$	−2.84405	+	1.79656i	−0.131466	+	0.0830458i
$469$	5.64609	+	3.25977i	0.260712	+	0.150522i
$470$	−31.6094	+	21.9403i	−1.45803	+	1.01203i
$471$	−5.34993	+	12.2312i	−0.246512	+	0.563582i
$472$	16.0342	+	7.71871i	0.738034	+	0.355283i
$473$	−14.7112	−	2.59399i	−0.676423	−	0.119272i
$474$	5.86542	+	9.70785i	0.269408	+	0.445896i
$475$	−3.27272	+	2.74614i	−0.150163	+	0.126001i
$476$	−1.41777	+	1.66173i	−0.0649835	+	0.0761653i
$477$	−1.36547	+	0.878320i	−0.0625204	+	0.0402155i
$478$	−10.3324	−	22.3976i	−0.472594	−	1.02444i
$479$	−21.6559	−	7.88212i	−0.989485	−	0.360143i	−0.203964	−	0.978978i	$-0.565383\pi$
$479$	−21.6559	−	7.88212i	−0.989485	−	0.360143i	−0.785521	+	0.618835i	$0.787605\pi$
$480$	0.0813390	+	23.4049i	0.00371260	+	1.06828i
$481$	−3.59644	−	3.01777i	−0.163983	−	0.137598i
$482$	−36.8368	+	9.70848i	−1.67787	+	0.442209i
$483$	−3.05216	−	10.3868i	−0.138878	−	0.472618i
$484$	0.196186	−	23.8908i	0.00891753	−	1.08595i
$485$	21.1218			0.959093
$486$	−22.0075	−	1.29151i	−0.998282	−	0.0585840i
$487$			13.8956i			0.629672i	0.949146	+	0.314836i	$0.101949\pi$
$487$			13.8956i			0.629672i	−0.949146	+	0.314836i	$0.898051\pi$
$488$	24.8562	+	2.48349i	1.12519	+	0.112422i
$489$	33.4822	−	9.83868i	1.51412	−	0.444920i
$490$	−17.0837	+	4.50246i	−0.771762	+	0.203400i
$491$	−8.62398	+	10.2777i	−0.389195	+	0.463824i	−0.924694	−	0.380711i	$-0.875679\pi$
$491$	−8.62398	+	10.2777i	−0.389195	+	0.463824i	0.535499	+	0.844536i	$0.320124\pi$
$492$	14.0976	−	4.01711i	0.635571	−	0.181105i
$493$	−0.948162	+	2.60505i	−0.0427031	+	0.117326i
$494$	4.35560	−	2.00932i	0.195968	−	0.0904035i
$495$	18.5708	+	28.8708i	0.834696	+	1.29765i
$496$	27.3663	+	33.7235i	1.22878	+	1.51423i
$497$	3.77154	+	4.49474i	0.169177	+	0.201617i
$498$	11.9849	+	19.8362i	0.537057	+	0.888883i
$499$	4.93870	−	28.0088i	0.221087	−	1.25384i	−0.648940	−	0.760840i	$-0.724787\pi$
$499$	4.93870	−	28.0088i	0.221087	−	1.25384i	0.870027	−	0.493005i	$-0.164102\pi$
$500$	7.17418	−	19.2184i	0.320839	−	0.859472i
$501$	−24.2791	−	10.6197i	−1.08471	−	0.474454i
$502$	−10.8373	−	15.6134i	−0.483694	−	0.696858i
$503$	−0.398330	+	0.689928i	−0.0177607	+	0.0307624i	−0.874769	−	0.484540i	$-0.838987\pi$
$503$	−0.398330	+	0.689928i	−0.0177607	+	0.0307624i	0.857008	+	0.515302i	$0.172320\pi$
$504$	10.0554	−	5.13342i	0.447903	−	0.228661i
$505$	16.6743	+	28.8807i	0.741995	+	1.28517i
$506$	−13.5675	+	28.7865i	−0.603150	+	1.27971i
$507$	−21.9283	−	1.38908i	−0.973868	−	0.0616914i
$508$	7.13128	−	5.88475i	0.316400	−	0.261093i
$509$	−1.21052	+	0.440593i	−0.0536553	+	0.0195289i	−0.368708	−	0.929545i	$-0.620200\pi$
$509$	−1.21052	+	0.440593i	−0.0536553	+	0.0195289i	0.315053	+	0.949074i	$0.397978\pi$
$510$	−3.61720	+	3.15994i	−0.160172	+	0.139925i
$511$	−0.537890	+	0.0948445i	−0.0237948	+	0.00419567i
$512$	−15.3980	−	16.5802i	−0.680501	−	0.732747i
$513$	30.8705	+	5.93019i	1.36297	+	0.261824i
$514$	3.58372	−	39.1119i	0.158071	−	1.72515i
$515$	−36.0857	+	6.36289i	−1.59013	+	0.280382i
$516$	−4.41028	+	9.86154i	−0.194152	+	0.434130i
$517$	−18.6605	−	51.2693i	−0.820689	−	2.25482i
$518$	11.0957	+	11.1872i	0.487517	+	0.491536i
$519$	5.89488	−	8.86422i	0.258756	−	0.389096i
$520$	2.21080	−	3.07600i	0.0969500	−	0.134892i
$521$	20.9324	−	12.0854i	0.917067	−	0.529469i	0.0343687	−	0.999409i	$-0.489058\pi$
$521$	20.9324	−	12.0854i	0.917067	−	0.529469i	0.882698	+	0.469940i	$0.155725\pi$
$522$	9.67729	−	10.5666i	0.423563	−	0.462488i
$523$	−4.01413	+	6.95268i	−0.175526	+	0.304019i	−0.940343	−	0.340228i	$-0.889496\pi$
$523$	−4.01413	+	6.95268i	−0.175526	+	0.304019i	0.764817	+	0.644247i	$0.222829\pi$
$524$	−11.3444	−	20.0272i	−0.495585	−	0.874891i
$525$	1.61739	−	0.180715i	0.0705889	−	0.00788705i
$526$	1.08736	−	3.99244i	0.0474111	−	0.174079i
$527$	−1.54765	+	8.77715i	−0.0674166	+	0.382338i
$528$	−32.1207	−	8.34625i	−1.39787	−	0.363224i
$529$	−0.713930	+	0.599059i	−0.0310404	+	0.0260460i
$530$	1.05478	−	1.49329i	0.0458167	−	0.0648646i
$531$	2.38176	−	18.7239i	0.103359	−	0.812549i
$532$	−15.1724	+	5.38162i	−0.657806	+	0.233323i
$533$	−2.22943	−	0.811445i	−0.0965671	−	0.0351476i
$534$	19.1059	+	15.3945i	0.826794	+	0.666183i
$535$	26.0283	−	31.0193i	1.12530	−	1.34108i
$536$	−13.8203	+	1.03776i	−0.596944	+	0.0448244i
$537$	−29.3151	−	7.10543i	−1.26504	−	0.306622i
$538$	−2.27645	−	27.3110i	−0.0981449	−	1.17746i
$539$		−	25.0511i		−	1.07903i
$540$	23.5204	−	7.94089i	1.01216	−	0.341722i
$541$			1.64488i			0.0707187i	0.999375	+	0.0353594i	$0.0112576\pi$
$541$			1.64488i			0.0707187i	−0.999375	+	0.0353594i	$0.988742\pi$
$542$	35.5844	−	2.96606i	1.52848	−	0.127403i
$543$	28.5223	−	29.9255i	1.22401	−	1.28423i
$544$	0.499577	−	4.61653i	0.0214192	−	0.197932i
$545$	−13.2287	+	15.7653i	−0.566653	+	0.675311i
$546$	−1.80546	−	0.281433i	−0.0772664	−	0.0120442i
$547$	35.6199	+	12.9646i	1.52300	+	0.554325i	0.961894	−	0.273422i	$-0.0881555\pi$
$547$	35.6199	+	12.9646i	1.52300	+	0.554325i	0.561102	+	0.827747i	$0.310378\pi$
$548$	15.9046	−	5.64135i	0.679412	−	0.240986i
$549$	−5.84773	−	25.8418i	−0.249575	−	1.10290i
$550$	−3.90752	−	2.76005i	−0.166617	−	0.117689i
$551$	−15.6512	+	13.1329i	−0.666762	+	0.559480i
$552$	17.8012	+	14.5859i	0.757671	+	0.620818i
$553$	−1.06984	+	6.06734i	−0.0454941	+	0.258010i
$554$	32.3572	+	8.81263i	1.37473	+	0.374413i
$555$	20.5476	+	27.8952i	0.872196	+	1.18408i
$556$	5.83771	−	3.30679i	0.247574	−	0.140239i
$557$	−3.28402	+	5.68809i	−0.139148	+	0.241012i	−0.927174	−	0.374630i	$-0.877770\pi$
$557$	−3.28402	+	5.68809i	−0.139148	+	0.241012i	0.788026	+	0.615642i	$0.211103\pi$
$558$	24.7401	−	38.8573i	1.04733	−	1.64496i
$559$	1.51417	−	0.874209i	0.0640427	−	0.0369751i
$560$	−8.33080	+	9.60345i	−0.352040	+	0.405820i
$561$	−3.02558	−	6.10158i	−0.127740	−	0.257609i
$562$	13.3711	−	13.2617i	0.564026	−	0.559413i
$563$	−3.45245	−	9.48552i	−0.145503	−	0.399767i	0.845436	−	0.534077i	$-0.179341\pi$
$563$	−3.45245	−	9.48552i	−0.145503	−	0.399767i	−0.990939	+	0.134309i	$0.957118\pi$
$564$	−39.2465	+	4.05909i	−1.65257	+	0.170918i
$565$	−12.2240	+	2.15543i	−0.514269	+	0.0906795i
$566$	16.9769	+	1.55555i	0.713593	+	0.0653847i
$567$	−8.54123	−	8.39304i	−0.358698	−	0.352475i
$568$	−12.0073	−	3.37640i	−0.503815	−	0.141670i
$569$	−21.9875	+	3.87699i	−0.921765	+	0.162532i	−0.614341	−	0.789041i	$-0.710578\pi$
$569$	−21.9875	+	3.87699i	−0.921765	+	0.162532i	−0.307424	+	0.951573i	$0.599467\pi$
$570$	−34.7311	+	6.83922i	−1.45473	+	0.286463i
$571$	−16.6507	+	6.06035i	−0.696809	+	0.253618i	−0.666048	−	0.745909i	$-0.732015\pi$
$571$	−16.6507	+	6.06035i	−0.696809	+	0.253618i	−0.0307612	+	0.999527i	$0.509793\pi$
$572$	3.41871	+	4.14288i	0.142944	+	0.173223i
$573$	3.32999	+	6.71548i	0.139112	+	0.280543i
$574$	7.20258	+	3.39469i	0.300630	+	0.141692i
$575$	1.65873	+	2.87300i	0.0691738	+	0.119813i
$576$	−11.5110	+	21.0594i	−0.479623	+	0.877475i
$577$	5.85438	−	10.1401i	0.243721	−	0.422137i	−0.718050	−	0.695991i	$-0.754965\pi$
$577$	5.85438	−	10.1401i	0.243721	−	0.422137i	0.961771	+	0.273854i	$0.0882986\pi$
$578$	−18.9674	+	13.1654i	−0.788939	+	0.547608i
$579$	3.18749	−	2.34791i	0.132468	−	0.0975757i
$580$	−5.64276	+	15.1160i	−0.234303	+	0.627657i
$581$	−2.18602	+	12.3975i	−0.0906913	+	0.514336i
$582$	18.9688	+	10.4540i	0.786283	+	0.433334i
$583$	1.66635	+	1.98588i	0.0690131	+	0.0822466i
$584$	0.831056	−	0.810831i	0.0343893	−	0.0335524i
$585$	−3.83714	−	1.19141i	−0.158646	−	0.0492589i
$586$	3.78386	+	8.20228i	0.156310	+	0.338833i
$587$	2.01611	−	5.53922i	0.0832138	−	0.228628i	−0.891107	−	0.453794i	$-0.850070\pi$
$587$	2.01611	−	5.53922i	0.0832138	−	0.228628i	0.974320	+	0.225166i	$0.0722924\pi$
$588$	−17.5707	−	4.41188i	−0.724604	−	0.181943i
$589$	−42.2213	+	50.3174i	−1.73970	+	2.07329i
$590$	5.41671	+	20.5526i	0.223002	+	0.846138i
$591$	17.5624	+	16.7389i	0.722422	+	0.688546i
$592$	−32.8861	−	6.35726i	−1.35161	−	0.261282i
$593$			5.17543i			0.212530i	0.994338	+	0.106265i	$0.0338891\pi$
$593$			5.17543i			0.212530i	−0.994338	+	0.106265i	$0.966111\pi$
$594$	2.38852	+	35.1194i	0.0980021	+	1.44096i
$595$	−2.60896			−0.106957
$596$	0.280642	−	34.1756i	0.0114955	−	1.39989i
$597$	−17.4374	−	4.22649i	−0.713664	−	0.172979i
$598$	−0.949254	−	3.60175i	−0.0388179	−	0.147287i
$599$	−3.88449	−	3.25948i	−0.158716	−	0.133179i	0.559971	−	0.828512i	$-0.310812\pi$
$599$	−3.88449	−	3.25948i	−0.158716	−	0.133179i	−0.718687	+	0.695334i	$0.755257\pi$
$600$	−2.62406	+	2.25463i	−0.107127	+	0.0920447i
$601$	2.56491	+	0.933552i	0.104625	+	0.0380804i	0.393802	−	0.919195i	$-0.371159\pi$
$601$	2.56491	+	0.933552i	0.104625	+	0.0380804i	−0.289177	+	0.957276i	$0.593382\pi$
$602$	−5.32831	+	2.45805i	−0.217166	+	0.100183i
$603$	5.68476	+	13.5562i	0.231501	+	0.552049i
$604$	5.63482	+	4.80757i	0.229278	+	0.195617i
$605$	21.8596	−	18.3424i	0.888720	−	0.745725i
$606$	0.680408	+	34.1895i	0.0276397	+	1.38885i
$607$	−32.1776	−	5.67378i	−1.30605	−	0.230292i	−0.523043	−	0.852306i	$-0.675203\pi$
$607$	−32.1776	−	5.67378i	−1.30605	−	0.230292i	−0.783006	+	0.622015i	$0.786314\pi$
$608$	20.2003	−	27.6242i	0.819229	−	1.12031i
$609$	7.73489	−	0.864236i	0.313433	−	0.0350206i
$610$	17.0125	+	24.5099i	0.688816	+	0.992378i
$611$	5.53032	+	3.19293i	0.223733	+	0.129172i
$612$	−4.81247	+	1.04754i	−0.194532	+	0.0423445i
$613$	28.4007	−	16.3971i	1.14709	−	0.662274i	0.198915	−	0.980017i	$-0.436258\pi$
$613$	28.4007	−	16.3971i	1.14709	−	0.662274i	0.948177	+	0.317743i	$0.102925\pi$
$614$	−19.3630	−	9.12611i	−0.781429	−	0.368300i
$615$	14.5788	+	9.69517i	0.587874	+	0.390947i
$616$	−10.1572	−	14.8931i	−0.409244	−	0.600058i
$617$	−9.77386	−	26.8534i	−0.393481	−	1.08108i	−0.965401	−	0.260770i	$-0.916024\pi$
$617$	−9.77386	−	26.8534i	−0.393481	−	1.08108i	0.571920	−	0.820309i	$-0.306199\pi$
$618$	−35.5567	−	12.1460i	−1.43030	−	0.488583i
$619$	−1.65174	−	9.36748i	−0.0663890	−	0.376511i	−0.999841	−	0.0178096i	$-0.994331\pi$
$619$	−1.65174	−	9.36748i	−0.0663890	−	0.376511i	0.933452	−	0.358701i	$-0.116780\pi$
$620$	−9.42672	+	51.0086i	−0.378586	+	2.04856i
$621$	8.69753	−	22.8077i	0.349020	−	0.915240i
$622$	−8.51390	−	0.780107i	−0.341376	−	0.0312794i
$623$	2.31434	+	13.1253i	0.0927221	+	0.525853i
$624$	3.50788	−	1.66824i	0.140428	−	0.0667832i
$625$	26.3417	−	9.58760i	1.05367	−	0.383504i
$626$	−11.4755	−	11.5701i	−0.458652	−	0.462434i
$627$	3.17320	−	50.0926i	0.126726	−	2.00051i
$628$	7.81701	−	13.2863i	0.311932	−	0.530181i
$629$	−3.43683	−	5.95276i	−0.137035	−	0.237352i
$630$	12.4595	+	5.15694i	0.496396	+	0.205457i
$631$	−19.9443	−	11.5149i	−0.793970	−	0.458399i	0.0473880	−	0.998877i	$-0.484910\pi$
$631$	−19.9443	−	11.5149i	−0.793970	−	0.458399i	−0.841358	+	0.540477i	$0.818244\pi$
$632$	−5.38834	−	11.9370i	−0.214337	−	0.474830i
$633$	11.3681	+	4.97241i	0.451840	+	0.197636i
$634$	−4.74121	+	17.4082i	−0.188298	+	0.691369i
$635$	10.8753	+	1.91761i	0.431573	+	0.0760979i
$636$	1.68635	−	0.819026i	0.0668683	−	0.0324765i
$637$	1.88470	+	2.24610i	0.0746745	+	0.0889936i
$638$	−18.6870	−	13.1994i	−0.739824	−	0.522571i
$639$	0.634889	+	13.2144i	0.0251158	+	0.522752i
$640$	3.12815	−	26.8441i	0.123651	−	1.06111i
$641$	2.38888	−	6.56340i	0.0943552	−	0.259239i	−0.883532	−	0.468370i	$-0.844841\pi$
$641$	2.38888	−	6.56340i	0.0943552	−	0.259239i	0.977888	+	0.209131i	$0.0670636\pi$
$642$	38.7278	−	14.9750i	1.52846	−	0.591015i
$643$	8.55274	+	7.17660i	0.337287	+	0.283018i	0.795661	−	0.605742i	$-0.207124\pi$
$643$	8.55274	+	7.17660i	0.337287	+	0.283018i	−0.458374	+	0.888759i	$0.651568\pi$
$644$	2.06958	+	12.3283i	0.0815527	+	0.485802i
$645$	−12.3793	+	3.63763i	−0.487434	+	0.143232i
$646$	6.99860	−	0.583354i	0.275356	−	0.0229518i
$647$	2.90752			0.114306			0.0571532	−	0.998365i	$-0.481798\pi$
$647$	2.90752			0.114306			0.0571532	+	0.998365i	$0.481798\pi$
$648$	25.0532	+	4.50975i	0.984182	+	0.177160i
$649$	−30.1379			−1.18302
$650$	0.558000	−	0.0465109i	0.0218866	−	0.00182431i
$651$	24.0068	−	7.05437i	0.940902	−	0.276483i
$652$	−39.7404	+	6.67131i	−1.55635	+	0.261269i
$653$	−11.8399	−	9.93486i	−0.463331	−	0.388781i	0.381024	−	0.924565i	$-0.375572\pi$
$653$	−11.8399	−	9.93486i	−0.463331	−	0.388781i	−0.844355	+	0.535784i	$0.820016\pi$
$654$	−19.6831	+	7.61090i	−0.769670	+	0.297610i
$655$	9.40252	−	25.8332i	0.367387	−	1.00939i
$656$	−16.7154	+	2.66511i	−0.652627	+	0.104055i
$657$	−1.09484	−	0.563863i	−0.0427137	−	0.0219984i
$658$	−17.5054	−	12.3648i	−0.682430	−	0.482031i
$659$	−3.67612	−	4.38103i	−0.143201	−	0.170661i	0.689676	−	0.724118i	$-0.257753\pi$
$659$	−3.67612	−	4.38103i	−0.143201	−	0.170661i	−0.832878	+	0.553457i	$0.813308\pi$
$660$	−17.3171	−	35.6555i	−0.674068	−	1.38789i
$661$	22.9903	+	4.05381i	0.894220	+	0.157675i	0.601830	−	0.798624i	$-0.294438\pi$
$661$	22.9903	+	4.05381i	0.894220	+	0.157675i	0.292390	+	0.956299i	$0.405550\pi$
$662$	−3.25626	+	11.9560i	−0.126558	+	0.464682i
$663$	0.730322	+	0.319444i	0.0283634	+	0.0124062i
$664$	−11.0101	−	24.3912i	−0.427275	−	0.946562i
$665$	−16.6518	−	9.61390i	−0.645728	−	0.372811i
$666$	4.64666	+	35.2216i	0.180054	+	1.36481i
$667$	7.93256	+	13.7396i	0.307150	+	0.532000i
$668$	26.3735	+	15.5169i	1.02042	+	0.600367i
$669$	−1.02821	+	16.2314i	−0.0397528	+	0.627543i
$670$	−11.6567	−	11.7528i	−0.450337	−	0.454050i
$671$	−39.7543	+	14.4694i	−1.53470	+	0.558584i
$672$	−12.2347	+	4.50129i	−0.471965	+	0.173641i
$673$	5.99277	+	33.9867i	0.231004	+	1.31009i	0.850867	+	0.525381i	$0.176077\pi$
$673$	5.99277	+	33.9867i	0.231004	+	1.31009i	−0.619863	+	0.784710i	$0.712812\pi$
$674$	−17.0965	−	1.56651i	−0.658533	−	0.0603397i
$675$	3.14951	+	1.88300i	0.121225	+	0.0724768i
$676$	24.9489	+	4.61071i	0.959571	+	0.177335i
$677$	−5.44766	−	30.8952i	−0.209370	−	1.18740i	−0.890412	−	0.455155i	$-0.849584\pi$
$677$	−5.44766	−	30.8952i	−0.209370	−	1.18740i	0.681042	−	0.732244i	$-0.261527\pi$
$678$	−12.0448	−	4.11444i	−0.462578	−	0.158014i
$679$	4.02379	+	11.0553i	0.154419	+	0.424263i
$680$	4.58193	−	3.12491i	0.175709	−	0.119835i
$681$	21.5414	+	14.3254i	0.825468	+	0.548952i
$682$	−66.5334	−	31.3582i	−2.54769	−	1.20077i
$683$	7.51680	−	4.33983i	0.287622	−	0.166059i	−0.349247	−	0.937031i	$-0.613562\pi$
$683$	7.51680	−	4.33983i	0.287622	−	0.166059i	0.636869	+	0.770972i	$0.280229\pi$
$684$	−34.5759	−	11.0477i	−1.32204	−	0.422421i
$685$	17.4554	+	10.0779i	0.666937	+	0.385056i
$686$	−13.1217	−	18.9044i	−0.500988	−	0.721774i
$687$	−16.0489	+	1.79317i	−0.612302	+	0.0684138i
$688$	6.41357	−	10.6989i	0.244515	−	0.407893i
$689$	−0.298812	−	0.0526885i	−0.0113838	−	0.00200727i
$690$	0.546917	+	27.4818i	0.0208208	+	1.04621i
$691$	20.4210	−	17.1353i	0.776853	−	0.651857i	−0.165601	−	0.986193i	$-0.552956\pi$
$691$	20.4210	−	17.1353i	0.776853	−	0.651857i	0.942454	+	0.334336i	$0.108512\pi$
$692$	−7.97834	+	9.35119i	−0.303291	+	0.355479i
$693$	−11.5733	+	15.2201i	−0.439634	+	0.578163i
$694$	−11.8262	+	5.45562i	−0.448915	+	0.207093i
$695$	7.53011	+	2.74074i	0.285633	+	0.103962i
$696$	−12.5491	+	10.7823i	−0.475671	+	0.408703i
$697$	−2.66091	−	2.23277i	−0.100789	−	0.0845723i
$698$	−4.90071	−	18.5948i	−0.185495	−	0.703822i
$699$	26.8118	+	6.49866i	1.01411	+	0.245802i
$700$	−1.87916	−	0.0154312i	−0.0710257	−	0.000583246i
$701$	−2.75968			−0.104232			−0.0521159	−	0.998641i	$-0.516597\pi$
$701$	−2.75968			−0.104232			−0.0521159	+	0.998641i	$0.516597\pi$
$702$	−2.85633	−	2.96912i	−0.107805	−	0.112062i
$703$		−	50.6582i		−	1.91061i
$704$	35.6766	+	13.9897i	1.34461	+	0.527258i
$705$	−34.1128	−	32.5132i	−1.28476	−	1.22452i
$706$	7.93447	+	30.1057i	0.298618	+	1.13304i
$707$	−11.9398	+	14.2293i	−0.449042	+	0.535147i
$708$	−5.30774	+	21.1386i	−0.199477	+	0.794436i
$709$	1.60307	−	4.40439i	0.0602044	−	0.165410i	−0.905944	−	0.423398i	$-0.860837\pi$
$709$	1.60307	−	4.40439i	0.0602044	−	0.165410i	0.966148	+	0.257988i	$0.0830594\pi$
$710$	−6.24047	−	13.5275i	−0.234201	−	0.507677i
$711$	−10.2006	+	9.42955i	−0.382552	+	0.353636i
$712$	−19.7854	−	20.2790i	−0.741491	−	0.759986i
$713$	32.7855	+	39.0723i	1.22783	+	1.46327i
$714$	−2.34302	−	1.29128i	−0.0876854	−	0.0483249i
$715$	−1.11402	+	6.31794i	−0.0416621	+	0.236278i
$716$	32.6309	+	12.1810i	1.21947	+	0.455226i
$717$	24.3232	−	17.9164i	0.908366	−	0.669102i
$718$	−8.90422	+	6.18047i	−0.332302	+	0.230653i
$719$	−12.9939	+	22.5060i	−0.484589	+	0.839333i	−0.999843	−	0.0177047i	$-0.994364\pi$
$719$	−12.9939	+	22.5060i	−0.484589	+	0.839333i	0.515254	+	0.857037i	$0.327697\pi$
$720$	−28.0584	+	5.86667i	−1.04568	+	0.218638i
$721$	−10.2048	−	17.6753i	−0.380048	−	0.658263i
$722$	22.5127	+	10.6106i	0.837836	+	0.394885i
$723$	−20.7271	−	41.7995i	−0.770847	−	1.55454i
$724$	−36.8188	+	30.3829i	−1.36836	+	1.12917i
$725$	−2.24115	+	0.815713i	−0.0832343	+	0.0302948i
$726$	28.7098	−	5.65351i	1.06552	−	0.209821i
$727$	−1.66409	+	0.293423i	−0.0617175	+	0.0108825i	−0.204422	−	0.978883i	$-0.565531\pi$
$727$	−1.66409	+	0.293423i	−0.0617175	+	0.0108825i	0.142704	+	0.989765i	$0.454420\pi$
$728$	2.03116	+	0.571153i	0.0752799	+	0.0211684i
$729$	−3.87526	−	26.7204i	−0.143528	−	0.989646i
$730$	1.38099	+	0.126536i	0.0511126	+	0.00468331i
$731$	2.52096	−	0.444514i	0.0932411	−	0.0164409i
$732$	3.14742	+	30.4317i	0.116332	+	1.12479i
$733$	2.90306	+	7.97608i	0.107227	+	0.294603i	0.981689	−	0.190490i	$-0.0610078\pi$
$733$	2.90306	+	7.97608i	0.107227	+	0.294603i	−0.874462	+	0.485094i	$0.838786\pi$
$734$	−30.3493	+	30.1011i	−1.12021	+	1.11105i
$735$	−9.61250	−	19.3852i	−0.354562	−	0.715034i
$736$	−18.4010	−	19.1724i	−0.678269	−	0.706705i
$737$	20.3270	−	11.7358i	0.748756	−	0.432295i
$738$	8.29420	+	15.9225i	0.305314	+	0.586117i
$739$	−25.0132	+	43.3241i	−0.920125	+	1.59370i	−0.120907	+	0.992664i	$0.538580\pi$
$739$	−25.0132	+	43.3241i	−0.920125	+	1.59370i	−0.799219	+	0.601040i	$0.794753\pi$
$740$	−19.7177	−	34.8091i	−0.724837	−	1.27961i
$741$	3.48416	+	4.73006i	0.127994	+	0.173763i
$742$	0.982538	+	0.267599i	0.0360701	+	0.00982386i
$743$	3.59368	−	20.3808i	0.131839	−	0.747699i	−0.845169	−	0.534499i	$-0.820500\pi$
$743$	3.59368	−	20.3808i	0.131839	−	0.747699i	0.977009	−	0.213200i	$-0.0683885\pi$
$744$	−33.7120	+	41.1435i	−1.23594	+	1.50839i
$745$	31.2700	−	26.2386i	1.14564	−	0.961310i
$746$	43.2302	+	30.5354i	1.58277	+	1.11798i
$747$	−20.8430	+	19.2676i	−0.762607	+	0.704963i
$748$	2.62892	+	7.41170i	0.0961227	+	0.270999i
$749$	21.1942	+	7.71404i	0.774418	+	0.281865i
$750$	24.8244	+	3.86960i	0.906458	+	0.141298i
$751$	29.7395	−	35.4421i	1.08521	−	1.29330i	0.131913	−	0.991261i	$-0.457888\pi$
$751$	29.7395	−	35.4421i	1.08521	−	1.29330i	0.953295	−	0.302039i	$-0.0976674\pi$
$752$	45.5535	+	0.748199i	1.66116	+	0.0272840i
$753$	16.0598	−	16.8499i	0.585252	−	0.614045i
$754$	2.66853	−	0.222430i	0.0971822	−	0.00810042i
$755$			8.84681i			0.321969i
$756$	8.63704	+	10.7980i	0.314126	+	0.392718i
$757$		−	3.04806i		−	0.110784i	−0.998465	−	0.0553919i	$-0.982359\pi$
$757$		−	3.04806i		−	0.110784i	0.998465	−	0.0553919i	$-0.0176408\pi$
$758$	1.95493	+	23.4536i	0.0710061	+	0.851874i
$759$	−37.8789	−	9.18114i	−1.37492	−	0.333254i
$760$	40.7594	−	3.06062i	1.47850	−	0.111020i
$761$	−21.3392	+	25.4310i	−0.773544	+	0.921873i	−0.998623	−	0.0524671i	$-0.983292\pi$
$761$	−21.3392	+	25.4310i	−0.773544	+	0.921873i	0.225079	+	0.974341i	$0.427736\pi$
$762$	8.81764	+	7.10475i	0.319429	+	0.257378i
$763$	−10.7718	−	3.92060i	−0.389964	−	0.141935i
$764$	−2.89342	−	8.15742i	−0.104680	−	0.295125i
$765$	−4.68254	−	3.56060i	−0.169298	−	0.128734i
$766$	18.1877	−	25.7491i	0.657149	−	0.930353i
$767$	2.70218	−	2.26740i	0.0975701	−	0.0818710i
$768$	16.0955	−	22.5596i	0.580797	−	0.814048i
$769$	2.85202	−	16.1746i	0.102847	−	0.583272i	−0.889212	−	0.457495i	$-0.848747\pi$
$769$	2.85202	−	16.1746i	0.102847	−	0.583272i	0.992059	−	0.125777i	$-0.0401423\pi$
$770$	5.65799	−	20.7744i	0.203900	−	0.748656i
$771$	47.8053	−	5.34139i	1.72166	−	0.192365i
$772$	−3.97752	+	2.25308i	−0.143154	+	0.0810901i
$773$	−12.1498	+	21.0441i	−0.436998	+	0.756902i	−0.997456	−	0.0712802i	$-0.977292\pi$
$773$	−12.1498	+	21.0441i	−0.436998	+	0.756902i	0.560459	+	0.828182i	$0.310625\pi$
$774$	−12.9178	−	2.86016i	−0.464322	−	0.102806i
$775$	−6.64029	+	3.83378i	−0.238526	+	0.137713i
$776$	−20.3083	−	14.5961i	−0.729024	−	0.523968i
$777$	−10.6861	+	16.0689i	−0.383362	+	0.576467i
$778$	25.7853	+	25.9979i	0.924447	+	0.932069i
$779$	−8.75570	−	24.0561i	−0.313705	−	0.861898i
$780$	4.23517	+	1.89405i	0.151644	+	0.0678180i
$781$	20.8031	−	3.66815i	0.744394	−	0.131257i
$782$	0.497594	−	5.43063i	0.0177939	−	0.194199i
$783$	15.0620	+	9.00512i	0.538271	+	0.321817i
$784$	19.5370	+	7.47648i	0.697751	+	0.267017i
$785$	18.1320	−	3.19716i	0.647160	−	0.114112i
$786$	21.2300	−	18.5463i	0.757248	−	0.661524i
$787$	20.2994	−	7.38838i	0.723595	−	0.263367i	0.0461441	−	0.998935i	$-0.485307\pi$
$787$	20.2994	−	7.38838i	0.723595	−	0.263367i	0.677451	+	0.735568i	$0.263084\pi$
$788$	−17.8309	−	21.6079i	−0.635198	−	0.769749i
$789$	5.05769	+	0.320388i	0.180058	+	0.0114061i
$790$	6.66901	−	14.1498i	0.237273	−	0.503426i
$791$	−3.45689	−	5.98751i	−0.122913	−	0.212891i
$792$	2.09540	−	40.5920i	0.0744569	−	1.44237i
$793$	2.47580	−	4.28821i	0.0879182	−	0.152279i
$794$	3.14966	+	4.53772i	0.111777	+	0.161038i
$795$	2.05148	+	0.897319i	0.0727583	+	0.0318246i
$796$	19.4097	+	7.24558i	0.687957	+	0.256813i
$797$	−0.278613	+	1.58009i	−0.00986897	+	0.0559697i	−0.989345	−	0.145593i	$-0.953491\pi$
$797$	−0.278613	+	1.58009i	−0.00986897	+	0.0559697i	0.979476	+	0.201563i	$0.0646021\pi$
$798$	−10.1961	−	16.8756i	−0.360938	−	0.597388i
$799$	6.00975	+	7.16214i	0.212610	+	0.253378i
$800$	3.31872	−	2.22369i	0.117335	−	0.0786192i
$801$	−13.7591	+	26.7157i	−0.486153	+	0.943951i
$802$	−21.2078	+	9.78353i	−0.748872	+	0.345468i
$803$	−0.672542	+	1.84779i	−0.0237335	+	0.0652073i
$804$	−4.65155	−	16.3241i	−0.164047	−	0.575708i
$805$	−9.59728	+	11.4376i	−0.338260	+	0.403122i
$806$	8.32463	−	2.19398i	0.293222	−	0.0772798i
$807$	32.2035	−	9.46294i	1.13362	−	0.333111i
$808$	3.92572	−	39.2908i	0.138106	−	1.38225i
$809$		−	20.4558i		−	0.719187i	−0.933109	−	0.359593i	$-0.882915\pi$
$809$		−	20.4558i		−	0.719187i	0.933109	−	0.359593i	$-0.117085\pi$
$810$	15.3241	+	26.2597i	0.538435	+	0.922673i
$811$	−5.49673			−0.193016			−0.0965081	−	0.995332i	$-0.530767\pi$
$811$	−5.49673			−0.193016			−0.0965081	+	0.995332i	$0.530767\pi$
$812$	−8.98675	−	0.0737971i	−0.315373	−	0.00258977i
$813$	12.3296	+	41.9589i	0.432416	+	1.47156i
$814$	54.8534	−	14.4568i	1.92261	−	0.506711i
$815$	−36.8692	−	30.9370i	−1.29147	−	1.08367i
$816$	5.66152	−	0.538597i	0.198193	−	0.0188547i
$817$	17.7281	+	6.45251i	0.620229	+	0.225745i
$818$	17.2276	+	37.3442i	0.602349	+	1.30571i
$819$	−0.107398	−	2.23535i	−0.00375280	−	0.0781094i
$820$	−15.3797	−	13.1218i	−0.537082	−	0.458233i
$821$	18.3310	−	15.3815i	0.639756	−	0.536819i	−0.264187	−	0.964471i	$-0.585104\pi$
$821$	18.3310	−	15.3815i	0.639756	−	0.536819i	0.903943	+	0.427653i	$0.140659\pi$
$822$	10.6882	+	17.6900i	0.372793	+	0.617010i
$823$	−41.8956	−	7.38732i	−1.46039	−	0.257506i	−0.613676	−	0.789558i	$-0.710310\pi$
$823$	−41.8956	−	7.38732i	−1.46039	−	0.257506i	−0.846711	+	0.532053i	$0.821421\pi$
$824$	39.0928	+	18.8189i	1.36186	+	0.655588i
$825$	2.34802	−	5.36811i	0.0817477	−	0.186894i
$826$	−9.72544	+	6.75049i	−0.338391	+	0.234880i
$827$	1.29000	+	0.744779i	0.0448575	+	0.0258985i	0.522261	−	0.852786i	$-0.325089\pi$
$827$	1.29000	+	0.744779i	0.0448575	+	0.0258985i	−0.477404	+	0.878684i	$0.658422\pi$
$828$	−13.1107	+	24.9512i	−0.455627	+	0.867112i
$829$	−29.6403	+	17.1128i	−1.02945	+	0.594353i	−0.916827	−	0.399284i	$-0.869259\pi$
$829$	−29.6403	+	17.1128i	−1.02945	+	0.594353i	−0.112623	+	0.993638i	$0.535925\pi$
$830$	13.6269	−	28.9125i	0.472997	−	1.00357i
$831$	−2.59663	+	40.9907i	−0.0900759	+	1.42195i
$832$	−4.25129	+	1.42977i	−0.147387	+	0.0495683i
$833$	1.46824	+	4.03395i	0.0508714	+	0.139768i
$834$	5.40604	+	6.18831i	0.187196	+	0.214284i
$835$	6.34643	+	35.9924i	0.219627	+	1.24557i
$836$	−10.5326	+	56.9928i	−0.364279	+	1.97114i
$837$	52.7147	+	20.1024i	1.82209	+	0.694840i
$838$	−0.363040	+	3.96213i	−0.0125410	+	0.136870i
$839$	−5.25860	−	29.8230i	−0.181547	−	1.02960i	−0.930312	−	0.366769i	$-0.880464\pi$
$839$	−5.25860	−	29.8230i	−0.181547	−	1.02960i	0.748765	−	0.662835i	$-0.230647\pi$
$840$	−13.5746	−	7.62716i	−0.468367	−	0.263162i
$841$	16.5332	−	6.01759i	0.570110	−	0.207503i
$842$	21.1544	−	20.9814i	0.729030	−	0.723068i
$843$	19.2058	+	12.7722i	0.661481	+	0.439898i
$844$	−12.3487	−	7.26539i	−0.425060	−	0.250085i
$845$	15.1515	+	26.2432i	0.521228	+	0.902794i
$846$	−14.5435	−	46.0828i	−0.500016	−	1.58436i
$847$	13.7649	+	7.94715i	0.472966	+	0.273067i
$848$	−2.04608	+	0.706880i	−0.0702627	+	0.0242744i
$849$	2.31849	+	20.7504i	0.0795702	+	0.712151i
$850$	0.790987	+	0.215429i	0.0271306	+	0.00738916i
$851$	−38.7394	−	6.83079i	−1.32797	−	0.234157i
$852$	1.09092	−	15.2372i	0.0373743	−	0.522019i
$853$	19.1696	+	22.8454i	0.656353	+	0.782211i	0.986857	−	0.161593i	$-0.0516633\pi$
$853$	19.1696	+	22.8454i	0.656353	+	0.782211i	−0.330504	+	0.943804i	$0.607219\pi$
$854$	−9.58768	+	13.5737i	−0.328084	+	0.464481i
$855$	−16.7658	−	39.9806i	−0.573378	−	1.36731i
$856$	−46.4613	+	11.8379i	−1.58802	+	0.404611i
$857$	−8.70467	+	23.9159i	−0.297346	+	0.816951i	0.697595	+	0.716492i	$0.254253\pi$
$857$	−8.70467	+	23.9159i	−0.297346	+	0.816951i	−0.994941	+	0.100459i	$0.967969\pi$
$858$	−4.12747	+	5.12256i	−0.140909	+	0.174881i
$859$	−35.6942	−	29.9510i	−1.21787	−	1.02191i	−0.998933	−	0.0461739i	$-0.985297\pi$
$859$	−35.6942	−	29.9510i	−1.21787	−	1.02191i	−0.218935	−	0.975739i	$-0.570258\pi$
$860$	14.6931	−	2.46657i	0.501032	−	0.0841093i
$861$	−2.29719	+	9.47759i	−0.0782880	+	0.322995i
$862$	3.43413	+	41.1999i	0.116967	+	1.40327i
$863$	4.01789			0.136771			0.0683853	−	0.997659i	$-0.478215\pi$
$863$	4.01789			0.136771			0.0683853	+	0.997659i	$0.478215\pi$
$864$	−28.1020	−	8.61856i	−0.956048	−	0.293209i
$865$	−14.6816			−0.499190
$866$	0.450877	+	5.40926i	0.0153214	+	0.183814i
$867$	−20.4696	−	19.5097i	−0.695184	−	0.662585i
$868$	−28.4940	+	4.78335i	−0.967150	+	0.162358i
$869$	16.9913	+	14.2574i	0.576391	+	0.483650i
$870$	−19.5253	−	3.04358i	−0.661969	−	0.103187i
$871$	−0.939599	+	2.58153i	−0.0318371	+	0.0874717i
$872$	23.6136	−	6.01651i	0.799657	−	0.203745i
$873$	−7.86590	+	25.3334i	−0.266221	+	0.857406i
$874$	23.1875	−	32.8275i	0.784330	−	1.11041i
$875$	8.77221	+	10.4543i	0.296555	+	0.353420i
$876$	1.17759	+	0.797142i	0.0397870	+	0.0269329i
$877$	35.2007	+	6.20683i	1.18864	+	0.209590i	0.732784	−	0.680462i	$-0.238221\pi$
$877$	35.2007	+	6.20683i	1.18864	+	0.209590i	0.455860	+	0.890052i	$0.349332\pi$
$878$	−6.90768	−	1.88134i	−0.233123	−	0.0634921i
$879$	−8.90746	+	6.56123i	−0.300441	+	0.221305i
$880$	14.9460	+	43.2614i	0.503828	+	1.45834i
$881$	−11.3067	−	6.52790i	−0.380931	−	0.219931i	0.297292	−	0.954787i	$-0.403916\pi$
$881$	−11.3067	−	6.52790i	−0.380931	−	0.219931i	−0.678223	+	0.734856i	$0.737250\pi$
$882$	0.961840	−	22.1668i	0.0323868	−	0.746395i
$883$	−6.74255	−	11.6784i	−0.226905	−	0.393011i	0.729984	−	0.683464i	$-0.239527\pi$
$883$	−6.74255	−	11.6784i	−0.226905	−	0.393011i	−0.956889	+	0.290453i	$0.906194\pi$
$884$	−0.793323	−	0.466753i	−0.0266823	−	0.0156986i
$885$	−23.3215	+	11.5644i	−0.783943	+	0.388732i
$886$	27.8317	−	27.6041i	0.935025	−	0.927379i
$887$	9.99335	−	3.63728i	0.335544	−	0.122128i	−0.168753	−	0.985658i	$-0.553974\pi$
$887$	9.99335	−	3.63728i	0.335544	−	0.122128i	0.504297	+	0.863530i	$0.331752\pi$
$888$	−0.479416	−	41.0199i	−0.0160882	−	1.37654i
$889$	1.06810	+	6.05750i	0.0358229	+	0.203162i
$890$	3.08766	−	33.6980i	0.103499	−	1.12956i
$891$	−41.5434	+	11.5221i	−1.39176	+	0.386004i
$892$	3.41287	−	18.4673i	0.114271	−	0.618331i
$893$	11.9652	+	67.8583i	0.400402	+	2.27079i
$894$	41.0691	−	8.08729i	1.37356	−	0.270479i
$895$	14.2283	+	39.0919i	0.475599	+	1.30670i
$896$	14.6463	−	3.47662i	0.489298	−	0.116146i
$897$	4.08698	−	2.02660i	0.136460	−	0.0676663i
$898$	−5.41326	+	11.4854i	−0.180643	+	0.383273i
$899$	−31.7560	+	18.3343i	−1.05912	+	0.611484i
$900$	−3.35165	−	2.59230i	−0.111722	−	0.0864099i
$901$	−0.384721	−	0.222119i	−0.0128169	−	0.00739986i
$902$	23.5495	−	16.3459i	0.784114	−	0.544258i
$903$	−4.26226	−	5.78640i	−0.141839	−	0.192559i
$904$	13.2427	+	6.37490i	0.440445	+	0.212026i
$905$	−56.1491	−	9.90060i	−1.86646	−	0.329107i
$906$	−4.37864	+	7.94503i	−0.145471	+	0.263956i
$907$	−20.2985	+	17.0325i	−0.674002	+	0.565555i	−0.914247	−	0.405157i	$-0.867217\pi$
$907$	−20.2985	+	17.0325i	−0.674002	+	0.565555i	0.240245	+	0.970712i	$0.422772\pi$
$908$	−22.7248	−	19.3886i	−0.754149	−	0.643432i
$909$	−40.8489	+	9.24367i	−1.35487	+	0.306593i
$910$	1.05564	+	2.28831i	0.0349942	+	0.0758569i
$911$	15.1149	+	5.50138i	0.500780	+	0.182269i	0.580045	−	0.814585i	$-0.303035\pi$
$911$	15.1149	+	5.50138i	0.500780	+	0.182269i	−0.0792648	+	0.996854i	$0.525257\pi$
$912$	38.1195	+	17.4248i	1.26226	+	0.576994i
$913$	34.7187	+	29.1324i	1.14902	+	0.964143i
$914$	26.5695	−	7.00247i	0.878839	−	0.231621i
$915$	−25.2107	+	26.4511i	−0.833442	+	0.874446i
$916$	18.6463	+	0.153119i	0.616091	+	0.00505919i
$917$	15.3125			0.505662
$918$	−2.44295	−	5.51523i	−0.0806294	−	0.182030i
$919$			31.3508i			1.03417i	0.855935	+	0.517084i	$0.172983\pi$
$919$			31.3508i			1.03417i	−0.855935	+	0.517084i	$0.827017\pi$
$920$	3.15552	−	31.5822i	0.104034	−	1.04124i
$921$	6.17564	−	25.4790i	0.203494	−	0.839563i
$922$	−30.8798	+	8.13848i	−1.01697	+	0.268026i
$923$	−1.58925	+	1.89399i	−0.0523108	+	0.0623416i
$924$	15.3633	−	15.8564i	0.505416	−	0.521637i
$925$	2.02253	−	5.55685i	0.0665003	−	0.182708i
$926$	−9.90633	+	4.56998i	−0.325542	+	0.150179i
$927$	5.80694	−	45.6506i	0.190725	−	1.49936i
$928$	15.8712	−	10.6344i	0.520997	−	0.349090i
$929$	−3.84272	−	4.57958i	−0.126076	−	0.150251i	0.699314	−	0.714815i	$-0.253489\pi$
$929$	−3.84272	−	4.57958i	−0.126076	−	0.150251i	−0.825390	+	0.564564i	$0.809045\pi$
$930$	−63.5179	+	1.26407i	−2.08283	+	0.0414506i
$931$	−5.49385	+	31.1572i	−0.180054	+	1.02113i
$932$	−29.8444	−	11.1408i	−0.977584	−	0.364930i
$933$	−1.16272	−	10.4063i	−0.0380656	−	0.340686i
$934$	5.16525	+	7.44158i	0.169012	+	0.243496i
$935$	−4.69639	+	8.13438i	−0.153588	+	0.266023i
$936$	2.86603	+	3.79714i	0.0936790	+	0.124114i
$937$	−5.04870	−	8.74460i	−0.164934	−	0.285674i	0.771698	−	0.635989i	$-0.219408\pi$
$937$	−5.04870	−	8.74460i	−0.164934	−	0.285674i	−0.936632	+	0.350315i	$0.886074\pi$
$938$	3.93083	−	8.34012i	0.128346	−	0.272315i
$939$	11.0519	−	16.6189i	0.360664	−	0.542336i
$940$	34.6342	+	41.9706i	1.12964	+	1.36893i
$941$	14.5701	−	5.30310i	0.474973	−	0.172876i	−0.0934309	−	0.995626i	$-0.529783\pi$
$941$	14.5701	−	5.30310i	0.474973	−	0.172876i	0.568404	+	0.822750i	$0.307561\pi$
$942$	17.8662	+	6.10299i	0.582111	+	0.198846i
$943$	−19.5768	+	3.45191i	−0.637508	+	0.112410i
$944$	8.99462	−	23.5041i	0.292750	−	0.764995i
$945$	−3.11556	+	16.2185i	−0.101349	+	0.527589i
$946$	−1.92762	+	21.0377i	−0.0626725	+	0.683993i
$947$	−18.1746	+	3.20467i	−0.590594	+	0.104138i	−0.460955	−	0.887424i	$-0.652493\pi$
$947$	−18.1746	+	3.20467i	−0.590594	+	0.104138i	−0.129639	+	0.991561i	$0.541382\pi$
$948$	12.9925	−	9.40668i	0.421977	−	0.305515i
$949$	−0.0787167	−	0.216272i	−0.00255525	−	0.00702050i
$950$	4.25465	+	4.28973i	0.138039	+	0.139177i
$951$	−22.0530	−	1.39699i	−0.715119	−	0.0453005i
$952$	2.50847	+	1.80290i	0.0813000	+	0.0584323i
$953$	33.4092	−	19.2888i	1.08223	−	0.624825i	0.150732	−	0.988575i	$-0.451837\pi$
$953$	33.4092	−	19.2888i	1.08223	−	0.624825i	0.931497	+	0.363749i	$0.118504\pi$
$954$	1.39824	+	1.82121i	0.0452698	+	0.0589638i
$955$	5.16891	−	8.95281i	0.167262	−	0.289706i
$956$	−30.3517	+	17.1928i	−0.981645	+	0.556056i
$957$	11.2290	−	25.6720i	0.362982	−	0.829858i
$958$	−8.56452	+	31.4462i	−0.276707	+	1.01598i
$959$	−1.94950	+	11.0561i	−0.0629525	+	0.357021i
$960$	32.9755	−	2.86404i	1.06428	−	0.0924364i
$961$	−66.5593	+	55.8499i	−2.14707	+	1.80161i
$962$	−3.83054	+	5.42305i	−0.123502	+	0.174846i
$963$	27.5113	+	42.7700i	0.886539	+	1.37824i
$964$	18.0097	+	50.7747i	0.580053	+	1.63534i
$965$	−5.13064	−	1.86740i	−0.165161	−	0.0601137i
$966$	−14.2799	+	5.52164i	−0.459449	+	0.177656i
$967$	−18.7329	+	22.3250i	−0.602409	+	0.717923i	−0.977940	−	0.208887i	$-0.933016\pi$
$967$	−18.7329	+	22.3250i	−0.602409	+	0.717923i	0.375531	+	0.926810i	$0.377460\pi$
$968$	−33.6930	+	2.53000i	−1.08293	+	0.0813173i
$969$	2.42493	+	8.25232i	0.0779000	+	0.265103i
$970$	−2.48121	−	29.7676i	−0.0796669	−	0.955779i
$971$		−	49.1955i		−	1.57876i	−0.613906	−	0.789379i	$-0.710403\pi$
$971$		−	49.1955i		−	1.57876i	0.613906	−	0.789379i	$-0.289597\pi$
$972$	0.765102	+	31.1675i	0.0245407	+	0.999699i
$973$			4.46342i			0.143091i
$974$	19.5835	−	1.63234i	0.627496	−	0.0523036i
$975$	0.193340	+	0.657959i	0.00619185	+	0.0210716i
$976$	0.580154	−	35.3222i	0.0185703	−	1.13064i
$977$	−11.8068	+	14.0708i	−0.377733	+	0.450164i	−0.921097	−	0.389333i	$-0.872706\pi$
$977$	−11.8068	+	14.0708i	−0.377733	+	0.450164i	0.543365	+	0.839497i	$0.317150\pi$
$978$	−17.7991	−	46.0315i	−0.569153	−	1.47193i
$979$	45.0889	+	16.4110i	1.44105	+	0.524498i
$980$	8.35228	+	23.5476i	0.266804	+	0.752199i
$981$	−13.9824	−	21.7375i	−0.446423	−	0.694024i
$982$	15.4977	+	10.9467i	0.494550	+	0.349322i
$983$	27.2316	−	22.8500i	0.868553	−	0.728803i	−0.0952398	−	0.995454i	$-0.530362\pi$
$983$	27.2316	−	22.8500i	0.868553	−	0.728803i	0.963793	+	0.266652i	$0.0859174\pi$
$984$	−7.31749	−	19.3963i	−0.233273	−	0.618331i
$985$	5.81037	−	32.9523i	0.185134	−	1.04995i
$986$	3.78275	+	1.03025i	0.120467	+	0.0328098i
$987$	10.5190	−	24.0487i	0.334822	−	0.765480i
$988$	−3.34344	−	5.90242i	−0.106369	−	0.187781i
$989$	7.32483	−	12.6870i	0.232916	−	0.403423i
$990$	38.5069	−	29.5638i	1.22383	−	0.939600i
$991$	−34.1795	+	19.7335i	−1.08575	+	0.626857i	−0.932441	−	0.361322i	$-0.882326\pi$
$991$	−34.1795	+	19.7335i	−1.08575	+	0.626857i	−0.153307	+	0.988179i	$0.548992\pi$
$992$	44.3127	−	42.5296i	1.40693	−	1.35032i
$993$	−15.1460	−	0.959452i	−0.480645	−	0.0304473i
$994$	5.89151	−	5.84333i	0.186867	−	0.185339i
$995$	8.46334	+	23.2528i	0.268306	+	0.737164i
$996$	26.5478	−	19.2209i	0.841200	−	0.609036i
$997$	−12.4794	+	2.20045i	−0.395226	+	0.0696889i	−0.367729	−	0.929933i	$-0.619865\pi$
$997$	−12.4794	+	2.20045i	−0.395226	+	0.0696889i	−0.0274965	+	0.999622i	$0.508754\pi$
$998$	−40.0536	−	3.67001i	−1.26788	−	0.116172i
$999$	−41.1094	+	14.2563i	−1.30064	+	0.451050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.203.16	yes	192
3.2	odd	2		648.2.v.b.395.17		192
4.3	odd	2		864.2.bh.b.527.1		192
8.3	odd	2	inner	216.2.v.b.203.20	yes	192
8.5	even	2		864.2.bh.b.527.2		192
24.11	even	2		648.2.v.b.395.13		192
27.2	odd	18	inner	216.2.v.b.83.20	yes	192
27.25	even	9		648.2.v.b.251.13		192
108.83	even	18		864.2.bh.b.623.2		192
216.29	odd	18		864.2.bh.b.623.1		192
216.83	even	18	inner	216.2.v.b.83.16	✓	192
216.187	odd	18		648.2.v.b.251.17		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.83.16	✓	192	216.83	even	18	inner
216.2.v.b.83.20	yes	192	27.2	odd	18	inner
216.2.v.b.203.16	yes	192	1.1	even	1	trivial
216.2.v.b.203.20	yes	192	8.3	odd	2	inner
648.2.v.b.251.13		192	27.25	even	9
648.2.v.b.251.17		192	216.187	odd	18
648.2.v.b.395.13		192	24.11	even	2
648.2.v.b.395.17		192	3.2	odd	2
864.2.bh.b.527.1		192	4.3	odd	2
864.2.bh.b.527.2		192	8.5	even	2
864.2.bh.b.623.1		192	216.29	odd	18
864.2.bh.b.623.2		192	108.83	even	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.117471 - 1.40933i) q^{2} +(1.66179 - 0.488315i) q^{3} +(-1.97240 + 0.331111i) q^{4} +(-1.82990 - 1.53547i) q^{5} +(-0.883408 - 2.28464i) q^{6} +(0.455069 - 1.25029i) q^{7} +(0.698344 + 2.74086i) q^{8} +(2.52310 - 1.62295i) q^{9} +O(q^{10})\)	\(q+(-0.117471 - 1.40933i) q^{2} +(1.66179 - 0.488315i) q^{3} +(-1.97240 + 0.331111i) q^{4} +(-1.82990 - 1.53547i) q^{5} +(-0.883408 - 2.28464i) q^{6} +(0.455069 - 1.25029i) q^{7} +(0.698344 + 2.74086i) q^{8} +(2.52310 - 1.62295i) q^{9} +(-1.94901 + 2.75930i) q^{10} +(-3.07907 - 3.66949i) q^{11} +(-3.11603 + 1.51339i) q^{12} +(0.552142 + 0.0973575i) q^{13} +(-1.81553 - 0.494467i) q^{14} +(-3.79070 - 1.65806i) q^{15} +(3.78073 - 1.30617i) q^{16} +(0.710885 + 0.410430i) q^{17} +(-2.58366 - 3.36522i) q^{18} +(3.02483 + 5.23916i) q^{19} +(4.11771 + 2.42266i) q^{20} +(0.145694 - 2.29994i) q^{21} +(-4.80981 + 4.77047i) q^{22} +(4.41436 - 1.60670i) q^{23} +(2.49890 + 4.21372i) q^{24} +(0.122629 + 0.695465i) q^{25} +(0.0723476 - 0.789585i) q^{26} +(3.40035 - 3.92907i) q^{27} +(-0.483593 + 2.61676i) q^{28} +(0.586451 + 3.32593i) q^{29} +(-1.89145 + 5.53711i) q^{30} +(3.71351 + 10.2028i) q^{31} +(-2.28494 - 5.17485i) q^{32} +(-6.90863 - 4.59437i) q^{33} +(0.494921 - 1.05008i) q^{34} +(-2.75251 + 1.58916i) q^{35} +(-4.43918 + 4.03654i) q^{36} +(-7.25187 - 4.18687i) q^{37} +(7.02835 - 4.87842i) q^{38} +(0.965085 - 0.107831i) q^{39} +(2.93060 - 6.08778i) q^{40} +(-4.16735 - 0.734815i) q^{41} +(-3.25848 + 0.0648473i) q^{42} +(2.38891 - 2.00453i) q^{43} +(7.28816 + 6.21819i) q^{44} +(-7.10901 - 0.904294i) q^{45} +(-2.78292 - 6.03253i) q^{46} +(10.7030 + 3.89558i) q^{47} +(5.64496 - 4.01676i) q^{48} +(4.00617 + 3.36158i) q^{49} +(0.965731 - 0.254522i) q^{50} +(1.38176 + 0.334913i) q^{51} +(-1.12128 - 0.00920769i) q^{52} -0.541186 q^{53} +(-5.93679 - 4.33065i) q^{54} +11.4426i q^{55} +(3.74467 + 0.374146i) q^{56} +(7.58499 + 7.22932i) q^{57} +(4.61843 - 1.21720i) q^{58} +(4.04416 - 4.81965i) q^{59} +(8.02579 + 2.01522i) q^{60} +(3.02063 - 8.29912i) q^{61} +(13.9428 - 6.43208i) q^{62} +(-0.880982 - 3.89316i) q^{63} +(-7.02463 + 3.82813i) q^{64} +(-0.860875 - 1.02595i) q^{65} +(-5.66340 + 10.2762i) q^{66} +(-0.850868 + 4.82551i) q^{67} +(-1.53805 - 0.574150i) q^{68} +(6.55117 - 4.82559i) q^{69} +(2.56299 + 3.69251i) q^{70} +(-2.20493 + 3.81906i) q^{71} +(6.21028 + 5.78208i) q^{72} +(-0.205251 - 0.355506i) q^{73} +(-5.04877 + 10.7121i) q^{74} +(0.543390 + 1.09584i) q^{75} +(-7.70092 - 9.33217i) q^{76} +(-5.98912 + 2.17986i) q^{77} +(-0.265339 - 1.34745i) q^{78} +(-4.56009 + 0.804066i) q^{79} +(-8.92394 - 3.41503i) q^{80} +(3.73204 - 8.18974i) q^{81} +(-0.546051 + 5.95947i) q^{82} +(-9.31771 + 1.64296i) q^{83} +(0.474169 + 4.58465i) q^{84} +(-0.670647 - 1.84259i) q^{85} +(-3.10567 - 3.13128i) q^{86} +(2.59866 + 5.24063i) q^{87} +(7.90731 - 11.0019i) q^{88} +(-8.67486 + 5.00843i) q^{89} +(-0.439340 + 10.1251i) q^{90} +(0.372988 - 0.646034i) q^{91} +(-8.17489 + 4.63069i) q^{92} +(11.1532 + 15.1415i) q^{93} +(4.23284 - 15.5417i) q^{94} +(2.50943 - 14.2317i) q^{95} +(-6.32405 - 7.48374i) q^{96} +(-6.77349 + 5.68363i) q^{97} +(4.26695 - 6.04089i) q^{98} +(-13.7242 - 4.26130i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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