LMFDB - Embedded newform 224.2.be.a.115.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(3,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("224.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.be (of order $24$, degree $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			115.12
Character	$\chi$	$=$	224.115
Dual form			224.2.be.a.187.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.449803 - 1.34077i) q^{2} +(0.100927 + 0.131530i) q^{3} +(-1.59535 + 1.20617i) q^{4} +(-0.463954 + 0.604637i) q^{5} +(0.130955 - 0.194483i) q^{6} +(2.49637 - 0.876446i) q^{7} +(2.33480 + 1.59647i) q^{8} +(0.769343 - 2.87123i) q^{9} +O(q^{10})$	\(q+(-0.449803 - 1.34077i) q^{2} +(0.100927 + 0.131530i) q^{3} +(-1.59535 + 1.20617i) q^{4} +(-0.463954 + 0.604637i) q^{5} +(0.130955 - 0.194483i) q^{6} +(2.49637 - 0.876446i) q^{7} +(2.33480 + 1.59647i) q^{8} +(0.769343 - 2.87123i) q^{9} +(1.01937 + 0.350091i) q^{10} +(0.485906 - 3.69082i) q^{11} +(-0.319662 - 0.0881027i) q^{12} +(1.74960 - 4.22391i) q^{13} +(-2.29799 - 2.95284i) q^{14} -0.126354 q^{15} +(1.09031 - 3.84854i) q^{16} +(-3.44670 + 5.96986i) q^{17} +(-4.19572 + 0.259971i) q^{18} +(-0.167475 - 1.27210i) q^{19} +(0.0108768 - 1.52422i) q^{20} +(0.367230 + 0.239891i) q^{21} +(-5.16712 + 1.00865i) q^{22} +(6.09119 + 1.63213i) q^{23} +(0.0256590 + 0.468224i) q^{24} +(1.14376 + 4.26858i) q^{25} +(-6.45029 - 0.445893i) q^{26} +(0.914812 - 0.378928i) q^{27} +(-2.92545 + 4.40928i) q^{28} +(-0.478719 + 1.15573i) q^{29} +(0.0568342 + 0.169412i) q^{30} +(1.64276 - 2.84535i) q^{31} +(-5.65044 + 0.269222i) q^{32} +(0.534496 - 0.308592i) q^{33} +(9.55457 + 1.93599i) q^{34} +(-0.628268 + 1.91603i) q^{35} +(2.23581 + 5.50858i) q^{36} +(-7.53920 - 5.78504i) q^{37} +(-1.63027 + 0.796740i) q^{38} +(0.732154 - 0.196180i) q^{39} +(-2.04852 + 0.671014i) q^{40} +(-7.52016 + 7.52016i) q^{41} +(0.156459 - 0.600276i) q^{42} +(5.35637 - 2.21868i) q^{43} +(3.67656 + 6.47425i) q^{44} +(1.37911 + 1.79729i) q^{45} +(-0.551519 - 8.90106i) q^{46} +(4.87523 - 2.81471i) q^{47} +(0.616241 - 0.245011i) q^{48} +(5.46368 - 4.37586i) q^{49} +(5.20874 - 3.45355i) q^{50} +(-1.13308 + 0.149173i) q^{51} +(2.30352 + 8.84895i) q^{52} +(-2.64212 - 0.347842i) q^{53} +(-0.919542 - 1.05611i) q^{54} +(2.00617 + 2.00617i) q^{55} +(7.22773 + 1.93906i) q^{56} +(0.150417 - 0.150417i) q^{57} +(1.76490 + 0.122004i) q^{58} +(-1.73785 + 13.2002i) q^{59} +(0.201579 - 0.152404i) q^{60} +(1.44512 + 10.9768i) q^{61} +(-4.55390 - 0.922729i) q^{62} +(-0.595914 - 7.84192i) q^{63} +(2.90255 + 7.45488i) q^{64} +(1.74220 + 3.01757i) q^{65} +(-0.654170 - 0.577834i) q^{66} +(-7.37852 + 5.66174i) q^{67} +(-1.70195 - 13.6813i) q^{68} +(0.400090 + 0.965903i) q^{69} +(2.85156 - 0.0194686i) q^{70} +(-5.31630 - 5.31630i) q^{71} +(6.38009 - 5.47550i) q^{72} +(1.33462 + 4.98088i) q^{73} +(-4.36527 + 12.7105i) q^{74} +(-0.446012 + 0.581254i) q^{75} +(1.80155 + 1.82744i) q^{76} +(-2.02181 - 9.63951i) q^{77} +(-0.592359 - 0.893411i) q^{78} +(3.13677 + 5.43304i) q^{79} +(1.82111 + 2.44479i) q^{80} +(-7.58065 - 4.37669i) q^{81} +(13.4654 + 6.70025i) q^{82} +(-6.31332 - 2.61506i) q^{83} +(-0.875210 + 0.0602298i) q^{84} +(-2.01049 - 4.85374i) q^{85} +(-5.38407 - 6.18372i) q^{86} +(-0.200329 + 0.0536781i) q^{87} +(7.02679 - 7.84159i) q^{88} +(-3.01639 + 11.2573i) q^{89} +(1.78944 - 2.65750i) q^{90} +(0.665615 - 12.0779i) q^{91} +(-11.6862 + 4.74319i) q^{92} +(0.540049 - 0.0710988i) q^{93} +(-5.96679 - 5.27052i) q^{94} +(0.846859 + 0.488934i) q^{95} +(-0.605692 - 0.716033i) q^{96} -0.918957i q^{97} +(-8.32462 - 5.35730i) q^{98} +(-10.2234 - 4.23466i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−0.449803	−	1.34077i	−0.318059	−	0.948071i
$2$	−0.449803	−	1.34077i	−0.318059	−	0.948071i
$3$	0.100927	+	0.131530i	0.0582701	+	0.0759391i	0.821579	−	0.570094i	$-0.193093\pi$
$3$	0.100927	+	0.131530i	0.0582701	+	0.0759391i	−0.763309	+	0.646033i	$0.776427\pi$
$4$	−1.59535	+	1.20617i	−0.797677	+	0.603085i
$5$	−0.463954	+	0.604637i	−0.207487	+	0.270402i	−0.885492	−	0.464656i	$-0.846178\pi$
$5$	−0.463954	+	0.604637i	−0.207487	+	0.270402i	0.678005	+	0.735057i	$0.262845\pi$
$6$	0.130955	−	0.194483i	0.0534623	−	0.0793973i
$7$	2.49637	−	0.876446i	0.943538	−	0.331265i
$7$	2.49637	−	0.876446i	0.943538	−	0.331265i
$8$	2.33480	+	1.59647i	0.825475	+	0.564438i
$9$	0.769343	−	2.87123i	0.256448	−	0.957076i
$10$	1.01937	+	0.350091i	0.322353	+	0.110708i
$11$	0.485906	−	3.69082i	0.146506	−	1.11282i	−0.747337	−	0.664445i	$-0.768668\pi$
$11$	0.485906	−	3.69082i	0.146506	−	1.11282i	0.893843	−	0.448380i	$-0.147999\pi$
$12$	−0.319662	−	0.0881027i	−0.0922785	−	0.0254331i
$13$	1.74960	−	4.22391i	0.485252	−	1.17150i	−0.471831	−	0.881689i	$-0.656407\pi$
$13$	1.74960	−	4.22391i	0.485252	−	1.17150i	0.957083	−	0.289813i	$-0.0935931\pi$
$14$	−2.29799	−	2.95284i	−0.614164	−	0.789179i
$15$	−0.126354			−0.0326243
$16$	1.09031	−	3.84854i	0.272578	−	0.962134i
$17$	−3.44670	+	5.96986i	−0.835947	+	1.44790i	0.0573094	+	0.998356i	$0.481748\pi$
$17$	−3.44670	+	5.96986i	−0.835947	+	1.44790i	−0.893257	+	0.449547i	$0.851585\pi$
$18$	−4.19572	+	0.259971i	−0.988941	+	0.0612758i
$19$	−0.167475	−	1.27210i	−0.0384214	−	0.291839i	−0.999859	−	0.0168150i	$-0.994647\pi$
$19$	−0.167475	−	1.27210i	−0.0384214	−	0.291839i	0.961437	−	0.275024i	$-0.0886860\pi$
$20$	0.0108768	−	1.52422i	0.00243213	−	0.340825i
$21$	0.367230	+	0.239891i	0.0801361	+	0.0523485i
$22$	−5.16712	+	1.00865i	−1.10163	+	0.215046i
$23$	6.09119	+	1.63213i	1.27010	+	0.340323i	0.830070	−	0.557659i	$-0.188300\pi$
$23$	6.09119	+	1.63213i	1.27010	+	0.340323i	0.440032	+	0.897982i	$0.354967\pi$
$24$	0.0256590	+	0.468224i	0.00523762	+	0.0955757i
$25$	1.14376	+	4.26858i	0.228753	+	0.853716i
$26$	−6.45029	−	0.445893i	−1.26501	−	0.0874468i
$27$	0.914812	−	0.378928i	0.176056	−	0.0729246i
$28$	−2.92545	+	4.40928i	−0.552857	+	0.833276i
$29$	−0.478719	+	1.15573i	−0.0888959	+	0.214614i	−0.962075	−	0.272787i	$-0.912055\pi$
$29$	−0.478719	+	1.15573i	−0.0888959	+	0.214614i	0.873179	+	0.487400i	$0.162055\pi$
$30$	0.0568342	+	0.169412i	0.0103765	+	0.0309302i
$31$	1.64276	−	2.84535i	0.295049	−	0.511040i	−0.679947	−	0.733261i	$-0.737997\pi$
$31$	1.64276	−	2.84535i	0.295049	−	0.511040i	0.974996	+	0.222221i	$0.0713306\pi$
$32$	−5.65044	+	0.269222i	−0.998867	+	0.0475921i
$33$	0.534496	−	0.308592i	0.0930439	−	0.0537189i
$34$	9.55457	+	1.93599i	1.63860	+	0.332019i
$35$	−0.628268	+	1.91603i	−0.106197	+	0.323867i
$36$	2.23581	+	5.50858i	0.372635	+	0.918097i
$37$	−7.53920	−	5.78504i	−1.23944	−	0.951054i	−0.239634	−	0.970863i	$-0.577027\pi$
$37$	−7.53920	−	5.78504i	−1.23944	−	0.951054i	−0.999804	+	0.0198094i	$0.993694\pi$
$38$	−1.63027	+	0.796740i	−0.264464	+	0.129248i
$39$	0.732154	−	0.196180i	0.117238	−	0.0314140i
$40$	−2.04852	+	0.671014i	−0.323900	+	0.106097i
$41$	−7.52016	+	7.52016i	−1.17445	+	1.17445i	−0.193315	+	0.981137i	$0.561924\pi$
$41$	−7.52016	+	7.52016i	−1.17445	+	1.17445i	−0.981137	+	0.193315i	$0.938076\pi$
$42$	0.156459	−	0.600276i	0.0241421	−	0.0926246i
$43$	5.35637	−	2.21868i	0.816839	−	0.338346i	0.0651601	−	0.997875i	$-0.479244\pi$
$43$	5.35637	−	2.21868i	0.816839	−	0.338346i	0.751679	+	0.659529i	$0.229244\pi$
$44$	3.67656	+	6.47425i	0.554263	+	0.976031i
$45$	1.37911	+	1.79729i	0.205586	+	0.267924i
$46$	−0.551519	−	8.90106i	−0.0813170	−	1.31239i
$47$	4.87523	−	2.81471i	0.711125	−	0.410568i	−0.100352	−	0.994952i	$-0.531997\pi$
$47$	4.87523	−	2.81471i	0.711125	−	0.410568i	0.811478	+	0.584384i	$0.198664\pi$
$48$	0.616241	−	0.245011i	0.0889467	−	0.0353643i
$49$	5.46368	−	4.37586i	0.780526	−	0.625123i
$50$	5.20874	−	3.45355i	0.736627	−	0.488406i
$51$	−1.13308	+	0.149173i	−0.158663	+	0.0208884i
$52$	2.30352	+	8.84895i	0.319440	+	1.22713i
$53$	−2.64212	−	0.347842i	−0.362923	−	0.0477798i	−0.0531403	−	0.998587i	$-0.516923\pi$
$53$	−2.64212	−	0.347842i	−0.362923	−	0.0477798i	−0.309783	+	0.950807i	$0.600256\pi$
$54$	−0.919542	−	1.05611i	−0.125134	−	0.143719i
$55$	2.00617	+	2.00617i	0.270512	+	0.270512i
$56$	7.22773	+	1.93906i	0.965846	+	0.259117i
$57$	0.150417	−	0.150417i	0.0199232	−	0.0199232i
$58$	1.76490	+	0.122004i	0.231743	+	0.0160198i
$59$	−1.73785	+	13.2002i	−0.226248	+	1.71853i	0.381477	+	0.924378i	$0.375415\pi$
$59$	−1.73785	+	13.2002i	−0.226248	+	1.71853i	−0.607725	+	0.794147i	$0.707918\pi$
$60$	0.201579	−	0.152404i	0.0260237	−	0.0196752i
$61$	1.44512	+	10.9768i	0.185028	+	1.40543i	0.791910	+	0.610638i	$0.209087\pi$
$61$	1.44512	+	10.9768i	0.185028	+	1.40543i	−0.606881	+	0.794793i	$0.707580\pi$
$62$	−4.55390	−	0.922729i	−0.578345	−	0.117187i
$63$	−0.595914	−	7.84192i	−0.0750781	−	0.987989i
$64$	2.90255	+	7.45488i	0.362819	+	0.931860i
$65$	1.74220	+	3.01757i	0.216093	+	0.374284i
$66$	−0.654170	−	0.577834i	−0.0805227	−	0.0711264i
$67$	−7.37852	+	5.66174i	−0.901429	+	0.691691i	−0.951695	−	0.307045i	$-0.900660\pi$
$67$	−7.37852	+	5.66174i	−0.901429	+	0.691691i	0.0502656	+	0.998736i	$0.483993\pi$
$68$	−1.70195	−	13.6813i	−0.206392	−	1.65911i
$69$	0.400090	+	0.965903i	0.0481652	+	0.116281i
$70$	2.85156	−	0.0194686i	0.340826	−	0.00232694i
$71$	−5.31630	−	5.31630i	−0.630929	−	0.630929i	0.317372	−	0.948301i	$-0.397200\pi$
$71$	−5.31630	−	5.31630i	−0.630929	−	0.630929i	−0.948301	+	0.317372i	$0.897200\pi$
$72$	6.38009	−	5.47550i	0.751901	−	0.645294i
$73$	1.33462	+	4.98088i	0.156206	+	0.582968i	0.998999	+	0.0447307i	$0.0142430\pi$
$73$	1.33462	+	4.98088i	0.156206	+	0.582968i	−0.842793	+	0.538237i	$0.819090\pi$
$74$	−4.36527	+	12.7105i	−0.507453	+	1.47757i
$75$	−0.446012	+	0.581254i	−0.0515010	+	0.0671174i
$76$	1.80155	+	1.82744i	0.206652	+	0.209622i
$77$	−2.02181	−	9.63951i	−0.230406	−	1.09852i
$78$	−0.592359	−	0.893411i	−0.0670714	−	0.101159i
$79$	3.13677	+	5.43304i	0.352914	+	0.611265i	0.986759	−	0.162195i	$-0.0518575\pi$
$79$	3.13677	+	5.43304i	0.352914	+	0.611265i	−0.633845	+	0.773460i	$0.718524\pi$
$80$	1.82111	+	2.44479i	0.203607	+	0.273335i
$81$	−7.58065	−	4.37669i	−0.842294	−	0.486299i
$82$	13.4654	+	6.70025i	1.48701	+	0.739919i
$83$	−6.31332	−	2.61506i	−0.692977	−	0.287040i	0.00826298	−	0.999966i	$-0.497370\pi$
$83$	−6.31332	−	2.61506i	−0.692977	−	0.287040i	−0.701240	+	0.712925i	$0.747370\pi$
$84$	−0.875210	+	0.0602298i	−0.0954933	+	0.00657161i
$85$	−2.01049	−	4.85374i	−0.218068	−	0.526462i
$86$	−5.38407	−	6.18372i	−0.580579	−	0.666808i
$87$	−0.200329	+	0.0536781i	−0.0214775	+	0.00575489i
$88$	7.02679	−	7.84159i	0.749058	−	0.835916i
$89$	−3.01639	+	11.2573i	−0.319736	+	1.19327i	0.599762	+	0.800178i	$0.295262\pi$
$89$	−3.01639	+	11.2573i	−0.319736	+	1.19327i	−0.919498	+	0.393094i	$0.871405\pi$
$90$	1.78944	−	2.65750i	0.188623	−	0.280125i
$91$	0.665615	−	12.0779i	0.0697754	−	1.26610i
$92$	−11.6862	+	4.74319i	−1.21837	+	0.494511i
$93$	0.540049	−	0.0710988i	0.0560005	−	0.00737260i
$94$	−5.96679	−	5.27052i	−0.615428	−	0.543612i
$95$	0.846859	+	0.488934i	0.0868859	+	0.0501636i
$96$	−0.605692	−	0.716033i	−0.0618182	−	0.0730799i
$97$		−	0.918957i		−	0.0933060i	−0.998911	−	0.0466530i	$-0.985145\pi$
$97$		−	0.918957i		−	0.0933060i	0.998911	−	0.0466530i	$-0.0148555\pi$
$98$	−8.32462	−	5.35730i	−0.840914	−	0.541169i
$99$	−10.2234	−	4.23466i	−1.02749	−	0.425599i
$100$	−6.97334	−	5.43033i	−0.697334	−	0.543033i
$101$	5.14716	+	0.677636i	0.512161	+	0.0674273i	0.382178	−	0.924089i	$-0.375174\pi$
$101$	5.14716	+	0.677636i	0.512161	+	0.0674273i	0.129984	+	0.991516i	$0.458508\pi$
$102$	0.709671	+	1.45211i	0.0702679	+	0.143780i
$103$	11.7156	+	3.13918i	1.15437	+	0.309312i	0.784715	−	0.619857i	$-0.212809\pi$
$103$	11.7156	+	3.13918i	1.15437	+	0.309312i	0.369654	+	0.929169i	$0.379476\pi$
$104$	10.8283	−	7.06878i	1.06180	−	0.693151i
$105$	−0.315425	+	0.110742i	−0.0307823	+	0.0108073i
$106$	0.722057	+	3.69895i	0.0701324	+	0.359274i
$107$	−5.31242	−	4.07636i	−0.513571	−	0.394077i	0.319206	−	0.947685i	$-0.396584\pi$
$107$	−5.31242	−	4.07636i	−0.513571	−	0.394077i	−0.832777	+	0.553608i	$0.813250\pi$
$108$	−1.00240	+	1.70794i	−0.0964559	+	0.164347i
$109$	3.03629	−	2.32983i	0.290824	−	0.223157i	−0.453037	−	0.891492i	$-0.649659\pi$
$109$	3.03629	−	2.32983i	0.290824	−	0.223157i	0.743861	+	0.668335i	$0.232993\pi$
$110$	1.78744	−	3.59220i	0.170426	−	0.342503i
$111$		−	1.57550i		−	0.149540i
$112$	−0.651219	−	10.5630i	−0.0615344	−	0.998105i
$113$		−	5.43512i		−	0.511293i	−0.966770	−	0.255647i	$-0.917712\pi$
$113$		−	5.43512i		−	0.511293i	0.966770	−	0.255647i	$-0.0822884\pi$
$114$	−0.269333	−	0.134017i	−0.0252254	−	0.0125519i
$115$	−3.81288	+	2.92573i	−0.355553	+	0.272825i
$116$	−0.630280	−	2.42122i	−0.0585200	−	0.224804i
$117$	−10.7818	−	8.27314i	−0.996774	−	0.764852i
$118$	18.4802	−	3.60745i	1.70124	−	0.332093i
$119$	−3.37196	+	17.9238i	−0.309107	+	1.64307i
$120$	−0.295010	−	0.201720i	−0.0269306	−	0.0184144i
$121$	−2.76088	−	0.739776i	−0.250989	−	0.0672524i
$122$	14.0674	−	6.87496i	1.27360	−	0.622430i
$123$	−1.74812	−	0.230144i	−0.157622	−	0.0207514i
$124$	0.811185	+	6.52080i	0.0728465	+	0.585585i
$125$	−6.63217	−	2.74713i	−0.593199	−	0.245711i
$126$	−10.2462	+	4.32631i	−0.912805	+	0.385418i
$127$		−	8.82945i		−	0.783487i	−0.920074	−	0.391744i	$-0.871872\pi$
$127$		−	8.82945i		−	0.783487i	0.920074	−	0.391744i	$-0.128128\pi$
$128$	8.68973	−	7.24490i	0.768071	−	0.640364i
$129$	0.832426	+	0.480601i	0.0732910	+	0.0423146i
$130$	3.26224	−	3.69321i	0.286118	−	0.323916i
$131$	4.66132	−	0.613674i	0.407261	−	0.0536170i	0.0758872	−	0.997116i	$-0.475821\pi$
$131$	4.66132	−	0.613674i	0.407261	−	0.0536170i	0.331374	+	0.943499i	$0.392488\pi$
$132$	−0.480497	+	1.13701i	−0.0418219	+	0.0989637i
$133$	−1.53300	−	3.02884i	−0.132928	−	0.262634i
$134$	10.9100	+	7.34627i	0.942480	+	0.634621i
$135$	−0.195317	+	0.728934i	−0.0168102	+	0.0627367i
$136$	−17.5781	+	8.43585i	−1.50731	+	0.723368i
$137$	−2.10939	+	0.565209i	−0.180217	+	0.0482891i	−0.347799	−	0.937569i	$-0.613071\pi$
$137$	−2.10939	+	0.565209i	−0.180217	+	0.0482891i	0.167582	+	0.985858i	$0.446404\pi$
$138$	1.11510	−	0.970897i	0.0949233	−	0.0826482i
$139$	−4.95117	−	11.9532i	−0.419953	−	1.01386i	−0.982361	−	0.186996i	$-0.940125\pi$
$139$	−4.95117	−	11.9532i	−0.419953	−	1.01386i	0.562407	−	0.826860i	$-0.309875\pi$
$140$	−1.30874	−	3.81454i	−0.110609	−	0.322387i
$141$	0.862262	+	0.357161i	0.0726155	+	0.0300783i
$142$	−4.73667	+	9.51925i	−0.397493	+	0.798838i
$143$	−14.7396	−	8.50989i	−1.23258	−	0.711633i
$144$	−10.2112	−	6.09137i	−0.850933	−	0.507615i
$145$	−0.476693	−	0.825657i	−0.0395872	−	0.0685671i
$146$	6.07792	−	4.02985i	0.503013	−	0.333512i
$147$	1.12699	+	0.276999i	0.0929526	+	0.0228465i
$148$	19.0054	+	0.135623i	1.56224	+	0.0111481i
$149$	2.32379	−	3.02842i	0.190372	−	0.248098i	−0.688409	−	0.725323i	$-0.741691\pi$
$149$	2.32379	−	3.02842i	0.190372	−	0.248098i	0.878781	+	0.477225i	$0.158357\pi$
$150$	0.979948	+	0.336552i	0.0800124	+	0.0274793i
$151$	2.60497	+	9.72187i	0.211989	+	0.791154i	0.987205	+	0.159458i	$0.0509745\pi$
$151$	2.60497	+	9.72187i	0.211989	+	0.791154i	−0.775216	+	0.631697i	$0.782359\pi$
$152$	1.63985	−	3.23746i	0.133009	−	0.262593i
$153$	14.4891	+	14.4891i	1.17138	+	1.17138i
$154$	−12.0150	+	7.04667i	−0.968196	+	0.567837i
$155$	0.958237	+	2.31339i	0.0769675	+	0.185816i
$156$	−0.931419	+	1.19608i	−0.0745732	+	0.0957629i
$157$	4.32395	−	3.31788i	0.345089	−	0.264796i	−0.421645	−	0.906761i	$-0.638547\pi$
$157$	4.32395	−	3.31788i	0.345089	−	0.264796i	0.766734	+	0.641965i	$0.221881\pi$
$158$	5.87356	−	6.64950i	0.467275	−	0.529006i
$159$	−0.220909	−	0.382626i	−0.0175192	−	0.0303442i
$160$	2.45877	−	3.54137i	0.194383	−	0.279970i
$161$	16.6363	−	1.26421i	1.31113	−	0.0996335i
$162$	−2.45836	+	12.1326i	−0.193147	+	0.953226i
$163$	2.89751	+	22.0087i	0.226950	+	1.72386i	0.603416	+	0.797427i	$0.293806\pi$
$163$	2.89751	+	22.0087i	0.226950	+	1.72386i	−0.376465	+	0.926431i	$0.622861\pi$
$164$	2.92673	−	21.0679i	0.228539	−	1.64513i
$165$	−0.0613959	+	0.466349i	−0.00477967	+	0.0363052i
$166$	−0.666459	+	9.64100i	−0.0517273	+	0.748287i
$167$	−2.28366	+	2.28366i	−0.176715	+	0.176715i	−0.789922	−	0.613207i	$-0.789879\pi$
$167$	−2.28366	+	2.28366i	−0.176715	+	0.176715i	0.613207	+	0.789922i	$0.289879\pi$
$168$	0.474427	+	1.14637i	0.0366028	+	0.0884443i
$169$	−5.58792	−	5.58792i	−0.429840	−	0.429840i
$170$	−5.60345	+	4.87884i	−0.429765	+	0.374190i
$171$	−3.78133	−	0.497822i	−0.289166	−	0.0380694i
$172$	−5.86921	+	10.0003i	−0.447523	+	0.762514i
$173$	17.8137	−	2.34522i	1.35435	−	0.178304i	0.581839	−	0.813304i	$-0.302333\pi$
$173$	17.8137	−	2.34522i	1.35435	−	0.178304i	0.772512	+	0.635001i	$0.219000\pi$
$174$	0.162079	+	0.244452i	0.0122872	+	0.0185318i
$175$	6.59643	+	9.65349i	0.498643	+	0.729736i
$176$	−13.6745	−	5.89417i	−1.03075	−	0.444290i
$177$	−1.91163	+	1.10368i	−0.143687	+	0.0829576i
$178$	16.4503	−	1.01928i	1.23300	−	0.0763980i
$179$	−3.07134	−	4.00265i	−0.229563	−	0.299172i	0.664342	−	0.747429i	$-0.268712\pi$
$179$	−3.07134	−	4.00265i	−0.229563	−	0.299172i	−0.893905	+	0.448256i	$0.852045\pi$
$180$	−4.36801	−	1.20388i	−0.325572	−	0.0897316i
$181$	−10.4866	+	4.34370i	−0.779465	+	0.322865i	−0.736699	−	0.676220i	$-0.763617\pi$
$181$	−10.4866	+	4.34370i	−0.779465	+	0.322865i	−0.0427652	+	0.999085i	$0.513617\pi$
$182$	−16.4931	+	4.54022i	−1.22255	+	0.336543i
$183$	−1.29793	+	1.29793i	−0.0959455	+	0.0959455i
$184$	11.6161	+	13.5351i	0.856347	+	0.997822i
$185$	6.99569	−	1.87449i	0.514334	−	0.137815i
$186$	−0.338243	−	0.692104i	−0.0248012	−	0.0507475i
$187$	20.3589	+	15.6219i	1.48879	+	1.14239i
$188$	−4.38269	+	10.3708i	−0.319641	+	0.756370i
$189$	1.95160	−	1.74773i	0.141958	−	0.127128i
$190$	0.274631	−	1.35537i	0.0199238	−	0.0983289i
$191$	−5.30380	+	3.06215i	−0.383769	+	0.221569i	−0.679457	−	0.733715i	$-0.737785\pi$
$191$	−5.30380	+	3.06215i	−0.383769	+	0.221569i	0.295688	+	0.955285i	$0.404451\pi$
$192$	−0.687597	+	1.13417i	−0.0496231	+	0.0818517i
$193$	8.12985	−	14.0813i	0.585199	−	1.01359i	−0.409651	−	0.912242i	$-0.634350\pi$
$193$	8.12985	−	14.0813i	0.585199	−	1.01359i	0.994851	−	0.101353i	$-0.0323171\pi$
$194$	−1.23211	+	0.413350i	−0.0884607	+	0.0296768i
$195$	−0.221068	+	0.533706i	−0.0158310	+	0.0382195i
$196$	−3.43849	+	13.5712i	−0.245606	+	0.969370i
$197$	7.20307	−	2.98361i	0.513197	−	0.212573i	−0.111029	−	0.993817i	$-0.535415\pi$
$197$	7.20307	−	2.98361i	0.513197	−	0.212573i	0.624226	+	0.781244i	$0.285415\pi$
$198$	−1.07922	+	15.6120i	−0.0766968	+	1.10950i
$199$	−0.895286	−	3.34125i	−0.0634651	−	0.236855i	0.926906	−	0.375294i	$-0.122458\pi$
$199$	−0.895286	−	3.34125i	−0.0634651	−	0.236855i	−0.990371	+	0.138439i	$0.955792\pi$
$200$	−4.14422	+	11.7923i	−0.293040	+	0.833838i
$201$	−1.48938	−	0.399078i	−0.105053	−	0.0281488i
$202$	−1.40665	−	7.20598i	−0.0989715	−	0.507011i
$203$	−0.182123	+	3.30470i	−0.0127825	+	0.231944i
$204$	1.62774	−	1.60467i	0.113965	−	0.112350i
$205$	−1.05796	−	8.03598i	−0.0738909	−	0.561257i
$206$	−1.06077	−	17.1199i	−0.0739073	−	1.19280i
$207$	9.37244	−	16.2335i	0.651429	−	1.12831i
$208$	−14.3483	−	11.3388i	−0.994873	−	0.786203i
$209$	−4.77647			−0.330395
$210$	0.290359	+	0.373101i	0.0200367	+	0.0257464i
$211$	−5.19732	+	12.5474i	−0.357798	+	0.863801i	0.637811	+	0.770193i	$0.279840\pi$
$211$	−5.19732	+	12.5474i	−0.357798	+	0.863801i	−0.995609	+	0.0936084i	$0.970160\pi$
$212$	4.63468	−	2.63191i	0.318311	−	0.180761i
$213$	0.162698	−	1.23581i	0.0111479	−	0.0846765i
$214$	−3.07594	+	8.95632i	−0.210267	+	0.612242i
$215$	−1.14361	+	4.26803i	−0.0779939	+	0.291077i
$216$	2.74085	+	0.575753i	0.186491	+	0.0391750i
$217$	1.60714	−	8.54283i	0.109100	−	0.579925i
$218$	−4.48951	−	3.02302i	−0.304068	−	0.204745i
$219$	−0.520438	+	0.678248i	−0.0351679	+	0.0458318i
$220$	−5.62033	−	0.780771i	−0.378923	−	0.0526396i
$221$	19.1858	+	25.0034i	1.29058	+	1.68191i
$222$	−2.11239	+	0.708665i	−0.141774	+	0.0475625i
$223$	−18.0910			−1.21146			−0.605731	−	0.795669i	$-0.707119\pi$
$223$	−18.0910			−1.21146			−0.605731	+	0.795669i	$0.707119\pi$
$224$	−13.8696	+	5.62439i	−0.926703	+	0.375795i
$225$	13.1360			0.875734
$226$	−7.28728	+	2.44474i	−0.484742	+	0.162621i
$227$	−10.5180	−	13.7073i	−0.698102	−	0.909784i	0.300936	−	0.953644i	$-0.402701\pi$
$227$	−10.5180	−	13.7073i	−0.698102	−	0.909784i	−0.999038	+	0.0438601i	$0.986034\pi$
$228$	−0.0585400	+	0.421397i	−0.00387691	+	0.0279077i
$229$	−5.61518	+	7.31784i	−0.371061	+	0.483577i	−0.941142	−	0.338012i	$-0.890245\pi$
$229$	−5.61518	+	7.31784i	−0.371061	+	0.483577i	0.570080	+	0.821589i	$0.306912\pi$
$230$	5.63779	+	3.79622i	0.371745	+	0.250315i
$231$	1.06383	−	1.23881i	0.0699952	−	0.0815080i
$232$	−2.96280	+	1.93413i	−0.194518	+	0.126982i
$233$	−0.832350	+	3.10637i	−0.0545291	+	0.203505i	−0.987816	−	0.155626i	$-0.950260\pi$
$233$	−0.832350	+	3.10637i	−0.0545291	+	0.203505i	0.933287	+	0.359132i	$0.116927\pi$
$234$	−6.24274	+	18.1772i	−0.408101	+	1.18828i
$235$	−0.560003	+	4.25364i	−0.0365305	+	0.277477i
$236$	−13.1493	−	23.1552i	−0.855943	−	1.50728i
$237$	−0.398026	+	0.960920i	−0.0258546	+	0.0624184i
$238$	25.5485	−	3.54113i	1.65606	−	0.229538i
$239$	9.57247			0.619192			0.309596	−	0.950868i	$-0.399806\pi$
$239$	9.57247			0.619192			0.309596	+	0.950868i	$0.399806\pi$
$240$	−0.137765	+	0.486276i	−0.00889267	+	0.0313890i
$241$	2.51104	−	4.34925i	0.161750	−	0.280160i	−0.773746	−	0.633496i	$-0.781619\pi$
$241$	2.51104	−	4.34925i	0.161750	−	0.280160i	0.935497	+	0.353336i	$0.114953\pi$
$242$	0.249980	+	4.03447i	0.0160693	+	0.259346i
$243$	−0.577158	−	4.38395i	−0.0370247	−	0.281231i
$244$	−15.5453	−	15.7688i	−0.995187	−	1.00949i
$245$	0.110907	+	5.33374i	0.00708556	+	0.340760i
$246$	0.477737	+	2.44735i	0.0304594	+	0.156037i
$247$	−5.66624	−	1.51827i	−0.360534	−	0.0966049i
$248$	8.37805	−	4.02069i	0.532006	−	0.255314i
$249$	−0.293223	−	1.09432i	−0.0185823	−	0.0693499i
$250$	−0.700118	+	10.1279i	−0.0442794	+	0.640546i
$251$	3.85388	−	1.59633i	0.243255	−	0.100759i	−0.257725	−	0.966218i	$-0.582973\pi$
$251$	3.85388	−	1.59633i	0.243255	−	0.100759i	0.500980	+	0.865459i	$0.332973\pi$
$252$	10.4094	+	11.7919i	0.655729	+	0.742818i
$253$	8.98365	−	21.6885i	0.564797	−	1.36354i
$254$	−11.8383	+	3.97152i	−0.742802	+	0.249195i
$255$	0.435503	−	0.754313i	0.0272722	−	0.0472369i
$256$	−13.6224	−	8.39220i	−0.851403	−	0.524512i
$257$	−8.95509	+	5.17022i	−0.558603	+	0.322510i	−0.752585	−	0.658495i	$-0.771193\pi$
$257$	−8.95509	+	5.17022i	−0.558603	+	0.322510i	0.193981	+	0.981005i	$0.437860\pi$
$258$	0.269950	−	1.33227i	0.0168064	−	0.0829436i
$259$	−23.8909	−	7.83386i	−1.48451	−	0.486772i
$260$	−6.41913	−	2.71271i	−0.398097	−	0.168235i
$261$	2.95007	+	2.26366i	0.182604	+	0.140117i
$262$	−2.91947	−	5.97375i	−0.180366	−	0.369059i
$263$	23.7101	−	6.35310i	1.46203	−	0.391749i	0.561837	−	0.827248i	$-0.310095\pi$
$263$	23.7101	−	6.35310i	1.46203	−	0.391749i	0.900189	+	0.435499i	$0.143428\pi$
$264$	1.74060	+	0.132810i	0.107126	+	0.00817388i
$265$	1.43614	−	1.43614i	0.0882215	−	0.0882215i
$266$	−3.37144	+	3.41780i	−0.206716	+	0.209559i
$267$	−1.78511	+	0.739418i	−0.109247	+	0.0452516i
$268$	4.94234	−	17.9322i	0.301901	−	1.09538i
$269$	17.1893	+	22.4015i	1.04805	+	1.36584i	0.927791	+	0.373101i	$0.121705\pi$
$269$	17.1893	+	22.4015i	1.04805	+	1.36584i	0.120258	+	0.992743i	$0.461628\pi$
$270$	1.06519	−	0.0660003i	0.0648255	−	0.00401665i
$271$	−13.7220	+	7.92238i	−0.833550	+	0.481250i	−0.855066	−	0.518518i	$-0.826484\pi$
$271$	−13.7220	+	7.92238i	−0.833550	+	0.481250i	0.0215168	+	0.999768i	$0.493150\pi$
$272$	19.2172	+	19.7737i	1.16522	+	1.19896i
$273$	1.65578	−	1.13143i	0.100213	−	0.0684773i
$274$	1.70663	+	2.57398i	0.103101	+	0.155500i
$275$	16.3103	−	2.14730i	0.983550	−	0.129487i
$276$	−1.80333	−	1.05838i	−0.108548	−	0.0637071i
$277$	−2.78527	−	0.366687i	−0.167350	−	0.0220321i	0.0463853	−	0.998924i	$-0.485230\pi$
$277$	−2.78527	−	0.366687i	−0.167350	−	0.0220321i	−0.213736	+	0.976892i	$0.568563\pi$
$278$	−13.7995	+	12.0150i	−0.827638	+	0.720611i
$279$	−6.90580	−	6.90580i	−0.413440	−	0.413440i
$280$	−4.52576	+	3.47052i	−0.270466	+	0.207403i
$281$	−13.2850	+	13.2850i	−0.792516	+	0.792516i	−0.981903	−	0.189387i	$-0.939350\pi$
$281$	−13.2850	+	13.2850i	−0.792516	+	0.792516i	0.189387	+	0.981903i	$0.439350\pi$
$282$	0.0910238	−	1.31675i	0.00542039	−	0.0784114i
$283$	0.0395696	−	0.300561i	0.00235217	−	0.0178665i	−0.990229	−	0.139454i	$-0.955465\pi$
$283$	0.0395696	−	0.300561i	0.00235217	−	0.0178665i	0.992581	+	0.121588i	$0.0387986\pi$
$284$	14.8937	+	2.06902i	0.883781	+	0.122774i
$285$	0.0211611	+	0.160734i	0.00125347	+	0.00952107i
$286$	−4.77994	+	23.5902i	−0.282644	+	1.39492i
$287$	−12.1821	+	25.3641i	−0.719084	+	1.49719i
$288$	−3.57413	+	16.4308i	−0.210608	+	0.968196i
$289$	−15.2595	−	26.4302i	−0.897616	−	1.55472i
$290$	−0.892602	+	1.01052i	−0.0524154	+	0.0593399i
$291$	0.120871	−	0.0927474i	0.00708557	−	0.00543695i
$292$	−8.13698	−	6.33649i	−0.476181	−	0.370815i
$293$	−2.40867	−	5.81504i	−0.140716	−	0.339718i	0.837773	−	0.546019i	$-0.183857\pi$
$293$	−2.40867	−	5.81504i	−0.140716	−	0.339718i	−0.978489	+	0.206301i	$0.933857\pi$
$294$	−0.135531	−	1.63564i	−0.00790431	−	0.0953922i
$295$	−7.17507	−	7.17507i	−0.417749	−	0.417749i
$296$	−8.36686	−	25.5430i	−0.486314	−	1.48466i
$297$	−0.954042	−	3.56053i	−0.0553591	−	0.206603i
$298$	−5.10568	−	1.75349i	−0.295764	−	0.101577i
$299$	17.5511	−	22.8731i	1.01501	−	1.32278i
$300$	0.0104562	−	1.46527i	0.000603689	−	0.0845975i
$301$	11.4269	−	10.2332i	0.658636	−	0.589833i
$302$	11.8631	−	7.86560i	0.682645	−	0.452614i
$303$	0.430356	+	0.745399i	0.0247233	+	0.0428221i
$304$	−5.07832	−	0.742450i	−0.291261	−	0.0425824i
$305$	−7.30743	−	4.21894i	−0.418422	−	0.241576i
$306$	12.9094	−	25.9439i	0.737981	−	1.48311i
$307$	23.6025	+	9.77646i	1.34706	+	0.557972i	0.935474	−	0.353397i	$-0.114973\pi$
$307$	23.6025	+	9.77646i	1.34706	+	0.557972i	0.411590	+	0.911369i	$0.364973\pi$
$308$	14.8524	+	12.9398i	0.846293	+	0.737313i
$309$	0.769518	+	1.85778i	0.0437763	+	0.105685i
$310$	2.67072	−	2.32535i	0.151686	−	0.132071i
$311$	0.686962	−	0.184071i	0.0389540	−	0.0104377i	−0.239289	−	0.970948i	$-0.576914\pi$
$311$	0.686962	−	0.184071i	0.0389540	−	0.0104377i	0.278243	+	0.960511i	$0.410248\pi$
$312$	2.02263	+	0.710823i	0.114509	+	0.0402424i
$313$	1.75489	−	6.54934i	0.0991923	−	0.370191i	−0.898429	−	0.439118i	$-0.855291\pi$
$313$	1.75489	−	6.54934i	0.0991923	−	0.370191i	0.997622	+	0.0689272i	$0.0219576\pi$
$314$	−6.39346	−	4.30505i	−0.360804	−	0.242948i
$315$	5.01799	+	3.27798i	0.282732	+	0.184693i
$316$	−11.5574	−	4.88415i	−0.650156	−	0.274755i
$317$	−16.4382	+	2.16413i	−0.923263	+	0.121550i	−0.577146	−	0.816641i	$-0.695833\pi$
$317$	−16.4382	+	2.16413i	−0.923263	+	0.121550i	−0.346118	+	0.938191i	$0.612500\pi$
$318$	−0.413649	+	0.468296i	−0.0231963	+	0.0262607i
$319$	4.03298	+	2.32844i	0.225804	+	0.130368i
$320$	−5.85415	−	1.70373i	−0.327257	−	0.0952414i
$321$		−	1.11016i		−	0.0619630i
$322$	−9.17809	−	21.7369i	−0.511475	−	1.21135i
$323$	8.17148	+	3.38474i	0.454674	+	0.188332i
$324$	17.3728	−	2.16118i	0.965158	−	0.120065i
$325$	20.0312	+	2.63716i	1.11113	+	0.146283i
$326$	28.2055	−	13.7845i	1.56216	−	0.763453i
$327$	0.612887	+	0.164222i	0.0338927	+	0.00908152i
$328$	−29.5638	+	5.55232i	−1.63239	+	0.306576i
$329$	9.70341	−	11.2994i	0.534966	−	0.622958i
$330$	0.652884	−	0.127447i	0.0359401	−	0.00701572i
$331$	17.8756	+	13.7164i	0.982533	+	0.753924i	0.969273	−	0.245988i	$-0.0791124\pi$
$331$	17.8756	+	13.7164i	0.982533	+	0.753924i	0.0132601	+	0.999912i	$0.495779\pi$
$332$	13.2262	−	3.44298i	0.725881	−	0.188958i
$333$	−22.4104	+	17.1961i	−1.22808	+	0.942340i
$334$	4.08906	+	2.03467i	0.223744	+	0.111332i
$335$		−	7.08811i		−	0.387265i
$336$	1.32362	−	1.15174i	0.0722096	−	0.0628326i
$337$		−	0.915967i		−	0.0498959i	−0.999689	−	0.0249479i	$-0.992058\pi$
$337$		−	0.915967i		−	0.0498959i	0.999689	−	0.0249479i	$-0.00794200\pi$
$338$	−4.97868	+	10.0056i	−0.270805	+	0.544233i
$339$	0.714884	−	0.548550i	0.0388272	−	0.0297931i
$340$	9.06187	+	5.31845i	0.491449	+	0.288434i
$341$	−9.70346	−	7.44573i	−0.525472	−	0.403209i
$342$	1.03339	+	5.29383i	0.0558792	+	0.286258i
$343$	9.80415	−	15.7124i	0.529374	−	0.848388i
$344$	16.0481	+	3.37113i	0.865256	+	0.181759i
$345$	−0.769644	−	0.206226i	−0.0414362	−	0.0111028i
$346$	−11.1571	−	22.8293i	−0.599808	−	1.22731i
$347$	9.58899	+	1.26241i	0.514764	+	0.0677699i	0.383433	−	0.923569i	$-0.374742\pi$
$347$	9.58899	+	1.26241i	0.514764	+	0.0677699i	0.131331	+	0.991339i	$0.458075\pi$
$348$	0.254851	−	0.327267i	0.0136615	−	0.0175433i
$349$	−11.5729	−	4.79365i	−0.619482	−	0.256598i	0.0507946	−	0.998709i	$-0.483825\pi$
$349$	−11.5729	−	4.79365i	−0.619482	−	0.256598i	−0.670277	+	0.742111i	$0.733825\pi$
$350$	9.97607	−	13.1865i	0.533243	−	0.704848i
$351$		−	4.52706i		−	0.241636i
$352$	−1.75193	+	20.9856i	−0.0933784	+	1.11854i
$353$	−11.5041	−	6.64190i	−0.612302	−	0.353513i	0.161564	−	0.986862i	$-0.448346\pi$
$353$	−11.5041	−	6.64190i	−0.612302	−	0.353513i	−0.773866	+	0.633350i	$0.781680\pi$
$354$	2.33964	+	2.06662i	0.124351	+	0.109840i
$355$	5.68095	−	0.747912i	0.301514	−	0.0396950i
$356$	−8.76601	−	21.5977i	−0.464598	−	1.14467i
$357$	−2.69785	+	1.36548i	−0.142785	+	0.0722686i
$358$	−3.98515	+	5.91838i	−0.210622	+	0.312796i
$359$	−5.49807	+	20.5191i	−0.290177	+	1.08296i	0.654796	+	0.755806i	$0.272755\pi$
$359$	−5.49807	+	20.5191i	−0.290177	+	1.08296i	−0.944973	+	0.327149i	$0.893912\pi$
$360$	0.350617	+	6.39802i	0.0184791	+	0.337205i
$361$	16.7624	−	4.49147i	0.882232	−	0.236393i
$362$	10.5408	+	12.1064i	0.554014	+	0.636298i
$363$	−0.181344	−	0.437803i	−0.00951809	−	0.0229787i
$364$	13.5060	+	20.0713i	0.707909	+	1.05202i
$365$	−3.63083	−	1.50394i	−0.190046	−	0.0787198i
$366$	2.32404	+	1.15642i	0.121479	+	0.0604468i
$367$	−11.2214	−	6.47865i	−0.585750	−	0.338183i	0.177665	−	0.984091i	$-0.443146\pi$
$367$	−11.2214	−	6.47865i	−0.585750	−	0.338183i	−0.763415	+	0.645908i	$0.776479\pi$
$368$	12.9226	−	21.6626i	0.673638	−	1.12924i
$369$	15.8065	+	27.3777i	0.822854	+	1.42523i
$370$	−5.65995	−	8.53650i	−0.294247	−	0.443791i
$371$	−6.90057	+	1.44734i	−0.358260	+	0.0751419i
$372$	−0.775813	+	0.764819i	−0.0402240	+	0.0396540i
$373$	−1.87472	+	2.44318i	−0.0970692	+	0.126503i	−0.839362	−	0.543572i	$-0.817071\pi$
$373$	−1.87472	+	2.44318i	−0.0970692	+	0.126503i	0.742293	+	0.670075i	$0.233738\pi$
$374$	11.7880	−	34.3235i	0.609543	−	1.77483i
$375$	−0.308032	−	1.14959i	−0.0159067	−	0.0593646i
$376$	15.8763	+	1.21138i	0.818757	+	0.0624722i
$377$	4.04413	+	4.04413i	0.208283	+	0.208283i
$378$	−3.22114	−	1.83052i	−0.165678	−	0.0941517i
$379$	−13.4966	−	32.5837i	−0.693275	−	1.67371i	−0.738076	−	0.674718i	$-0.764265\pi$
$379$	−13.4966	−	32.5837i	−0.693275	−	1.67371i	0.0448006	−	0.998996i	$-0.485735\pi$
$380$	−1.94078	+	0.241432i	−0.0995597	+	0.0123852i
$381$	1.16134	−	0.891129i	0.0594973	−	0.0456539i
$382$	6.49131	+	5.73383i	0.332125	+	0.293368i
$383$	−15.8005	−	27.3673i	−0.807370	−	1.39841i	−0.914680	−	0.404179i	$-0.867557\pi$
$383$	−15.8005	−	27.3673i	−0.807370	−	1.39841i	0.107310	−	0.994226i	$-0.465776\pi$
$384$	1.82995	+	0.411760i	0.0933843	+	0.0210125i
$385$	6.76643	+	3.24983i	0.344849	+	0.165627i
$386$	−22.5367	−	4.56648i	−1.14709	−	0.232428i
$387$	−2.24945	−	17.0863i	−0.114346	−	0.868545i
$388$	1.10842	+	1.46606i	0.0562714	+	0.0744280i
$389$	−2.45833	+	18.6728i	−0.124642	+	0.946750i	0.808816	+	0.588062i	$0.200109\pi$
$389$	−2.45833	+	18.6728i	−0.124642	+	0.946750i	−0.933458	+	0.358688i	$0.883224\pi$
$390$	0.815017	+	0.0563401i	0.0412700	+	0.00285289i
$391$	−30.7381	+	30.7381i	−1.55449	+	1.55449i
$392$	19.7425	−	1.49412i	0.997148	−	0.0754646i
$393$	0.551169	+	0.551169i	0.0278028	+	0.0278028i
$394$	−7.24031	−	8.31565i	−0.364761	−	0.418937i
$395$	−4.74033	−	0.624077i	−0.238512	−	0.0314007i
$396$	21.4176	−	5.57533i	1.07627	−	0.280171i
$397$	−26.0615	+	3.43106i	−1.30799	+	0.172200i	−0.752096	−	0.659054i	$-0.770957\pi$
$397$	−26.0615	+	3.43106i	−1.30799	+	0.172200i	−0.555893	+	0.831254i	$0.687624\pi$
$398$	−4.07716	+	2.70328i	−0.204370	+	0.135503i
$399$	0.243663	−	0.507328i	0.0121984	−	0.0253982i
$400$	17.6748	+	0.252269i	0.883742	+	0.0126134i
$401$	12.2322	−	7.06227i	0.610847	−	0.352673i	−0.162450	−	0.986717i	$-0.551940\pi$
$401$	12.2322	−	7.06227i	0.610847	−	0.352673i	0.773297	+	0.634044i	$0.218606\pi$
$402$	0.134854	+	2.17643i	0.00672590	+	0.108551i
$403$	−9.14433	−	11.9171i	−0.455511	−	0.593634i
$404$	−9.02888	+	5.12727i	−0.449204	+	0.255091i
$405$	6.16338	−	2.55296i	0.306261	−	0.126857i
$406$	4.51277	−	1.24228i	0.223965	−	0.0616532i
$407$	−25.0149	+	25.0149i	−1.23994	+	1.23994i
$408$	−2.88367	−	1.46065i	−0.142763	−	0.0723127i
$409$	−29.4963	+	7.90351i	−1.45850	+	0.390803i	−0.898971	−	0.438009i	$-0.855684\pi$
$409$	−29.4963	+	7.90351i	−1.45850	+	0.390803i	−0.559527	+	0.828812i	$0.689017\pi$
$410$	−10.2986	+	5.03309i	−0.508610	+	0.248567i
$411$	−0.287236	−	0.220404i	−0.0141683	−	0.0108717i
$412$	−22.4769	+	9.12286i	−1.10736	+	0.449451i
$413$	7.23100	+	34.4758i	0.355814	+	1.69644i
$414$	−25.9813	−	5.26443i	−1.27691	−	0.258733i
$415$	4.51025	−	2.60400i	0.221400	−	0.127825i
$416$	−8.74885	+	24.3380i	−0.428948	+	1.19327i
$417$	1.07250	−	1.85763i	0.0525206	−	0.0909684i
$418$	2.14847	+	6.40417i	0.105085	+	0.313238i
$419$	1.09590	−	2.64573i	0.0535381	−	0.129252i	−0.894847	−	0.446372i	$-0.852716\pi$
$419$	1.09590	−	2.64573i	0.0535381	−	0.129252i	0.948385	+	0.317120i	$0.102716\pi$
$420$	0.369640	−	0.557128i	0.0180366	−	0.0271851i
$421$	−10.0359	+	4.15701i	−0.489120	+	0.202600i	−0.613592	−	0.789623i	$-0.710276\pi$
$421$	−10.0359	+	4.15701i	−0.489120	+	0.202600i	0.124473	+	0.992223i	$0.460276\pi$
$422$	19.1611	+	1.32456i	0.932746	+	0.0644785i
$423$	−4.33096	−	16.1634i	−0.210579	−	0.785890i
$424$	−5.61350	−	5.03021i	−0.272616	−	0.244289i
$425$	−29.4250	−	7.88441i	−1.42732	−	0.382450i
$426$	−1.73013	+	0.337731i	−0.0838250	+	0.0163631i
$427$	13.2281	+	26.1355i	0.640152	+	1.26478i
$428$	13.3920	+	0.0955653i	0.647326	+	0.00461932i
$429$	−0.368308	−	2.79758i	−0.0177821	−	0.135068i
$430$	6.23687	−	0.386443i	0.300768	−	0.0186359i
$431$	−8.83029	+	15.2945i	−0.425340	+	0.736711i	−0.996452	−	0.0841614i	$-0.973179\pi$
$431$	−8.83029	+	15.2945i	−0.425340	+	0.736711i	0.571112	+	0.820872i	$0.306512\pi$
$432$	−0.460887	−	3.93384i	−0.0221744	−	0.189267i
$433$	−5.56633			−0.267501			−0.133750	−	0.991015i	$-0.542702\pi$
$433$	−5.56633			−0.267501			−0.133750	+	0.991015i	$0.542702\pi$
$434$	−12.1769	+	1.68777i	−0.584511	+	0.0810158i
$435$	0.0604879	−	0.146031i	0.00290017	−	0.00700163i
$436$	−2.03379	+	7.37919i	−0.0974011	+	0.353399i
$437$	1.05611	−	8.02194i	0.0505205	−	0.383742i
$438$	1.14347	+	0.392712i	0.0546372	+	0.0187645i
$439$	8.28467	−	30.9188i	0.395406	−	1.47567i	−0.425683	−	0.904873i	$-0.639966\pi$
$439$	8.28467	−	30.9188i	0.395406	−	1.47567i	0.821088	−	0.570801i	$-0.193367\pi$
$440$	1.48120	+	7.88679i	0.0706137	+	0.375988i
$441$	−8.36064	−	19.0540i	−0.398126	−	0.907334i
$442$	24.8941	−	36.9704i	1.18409	−	1.75850i
$443$	6.23607	−	8.12701i	0.296285	−	0.386126i	−0.621361	−	0.783524i	$-0.713420\pi$
$443$	6.23607	−	8.12701i	0.296285	−	0.386126i	0.917646	+	0.397398i	$0.130087\pi$
$444$	1.90032	+	2.51348i	0.0901852	+	0.119284i
$445$	−5.40712	−	7.04669i	−0.256322	−	0.334045i
$446$	8.13739	+	24.2560i	0.385316	+	1.14855i
$447$	0.632863			0.0299334
$448$	13.7796	+	16.0662i	0.651026	+	0.759055i
$449$	14.2000			0.670138			0.335069	−	0.942194i	$-0.391240\pi$
$449$	14.2000			0.670138			0.335069	+	0.942194i	$0.391240\pi$
$450$	−5.90862	−	17.6124i	−0.278535	−	0.830258i
$451$	24.1015	+	31.4097i	1.13489	+	1.47902i
$452$	6.55568	+	8.67095i	0.308353	+	0.407847i
$453$	−1.01581	+	1.32383i	−0.0477269	+	0.0621989i
$454$	−13.6474	+	20.2678i	−0.640503	+	0.951215i
$455$	6.99390	+	6.00603i	0.327879	+	0.281567i
$456$	0.591329	−	0.111057i	0.0276915	−	0.00520070i
$457$	1.15982	−	4.32849i	0.0542539	−	0.202478i	−0.933479	−	0.358633i	$-0.883243\pi$
$457$	1.15982	−	4.32849i	0.0542539	−	0.202478i	0.987733	+	0.156154i	$0.0499097\pi$
$458$	12.3373	+	4.23710i	0.576484	+	0.197987i
$459$	−0.890938	+	6.76735i	−0.0415854	+	0.315873i
$460$	2.55398	−	9.26655i	0.119080	−	0.432055i
$461$	−15.0926	+	36.4369i	−0.702934	+	1.69703i	0.0140091	+	0.999902i	$0.495541\pi$
$461$	−15.0926	+	36.4369i	−0.702934	+	1.69703i	−0.716943	+	0.697131i	$0.754459\pi$
$462$	−2.13949	−	0.869140i	−0.0995380	−	0.0404360i
$463$	14.3306			0.666001			0.333001	−	0.942927i	$-0.391939\pi$
$463$	14.3306			0.666001			0.333001	+	0.942927i	$0.391939\pi$
$464$	3.92592	+	3.10247i	0.182256	+	0.144029i
$465$	−0.207569	+	0.359520i	−0.00962579	+	0.0166724i
$466$	4.53934	−	0.281262i	0.210281	−	0.0130292i
$467$	−1.85627	−	14.0998i	−0.0858979	−	0.652459i	−0.979185	−	0.202972i	$-0.934940\pi$
$467$	−1.85627	−	14.0998i	−0.0858979	−	0.652459i	0.893287	−	0.449487i	$-0.148393\pi$
$468$	27.1795	+	0.193953i	1.25637	+	0.00896550i
$469$	−13.4573	+	20.6006i	−0.621399	+	0.951249i
$470$	5.95507	−	1.16246i	0.274687	−	0.0536205i
$471$	0.872805	+	0.233867i	0.0402167	+	0.0107760i
$472$	−25.1313	+	28.0455i	−1.15676	+	1.29090i
$473$	−5.58607	−	20.8475i	−0.256848	−	0.958569i
$474$	1.46741	+	0.101439i	0.0674004	+	0.00465923i
$475$	5.23851	−	2.16986i	0.240359	−	0.0995600i
$476$	−16.2397	−	32.6620i	−0.744343	−	1.49706i
$477$	−3.03143	+	7.31852i	−0.138800	+	0.335092i
$478$	−4.30573	−	12.8345i	−0.196939	−	0.587038i
$479$	11.1648	−	19.3380i	0.510133	−	0.883576i	−0.489798	−	0.871836i	$-0.662930\pi$
$479$	11.1648	−	19.3380i	0.510133	−	0.883576i	0.999931	−	0.0117402i	$-0.00373711\pi$
$480$	0.713954	−	0.0340171i	0.0325874	−	0.00155266i
$481$	−37.6261	+	21.7234i	−1.71560	+	0.990503i
$482$	−6.96084	−	1.41043i	−0.317058	−	0.0642435i
$483$	1.84533	+	2.06059i	0.0839656	+	0.0937601i
$484$	5.29688	−	2.14989i	0.240767	−	0.0977221i
$485$	0.555635	+	0.426354i	0.0252301	+	0.0193597i
$486$	−5.61829	+	2.74576i	−0.254851	+	0.124550i
$487$	7.99926	−	2.14340i	0.362481	−	0.0971266i	−0.0729815	−	0.997333i	$-0.523251\pi$
$487$	7.99926	−	2.14340i	0.362481	−	0.0971266i	0.435463	+	0.900207i	$0.356585\pi$
$488$	−14.1500	+	27.9356i	−0.640542	+	1.26459i
$489$	−2.60238	+	2.60238i	−0.117684	+	0.117684i
$490$	7.10146	−	2.54784i	0.320811	−	0.115099i
$491$	3.23599	−	1.34039i	0.146038	−	0.0604910i	−0.308467	−	0.951235i	$-0.599816\pi$
$491$	3.23599	−	1.34039i	0.146038	−	0.0604910i	0.454505	+	0.890744i	$0.349816\pi$
$492$	3.06646	−	1.74136i	0.138247	−	0.0785067i
$493$	−5.24955	−	6.84134i	−0.236428	−	0.308118i
$494$	0.513042	+	8.28008i	0.0230829	+	0.372538i
$495$	7.30360	−	4.21674i	0.328272	−	0.189528i
$496$	−9.15931	−	9.42456i	−0.411265	−	0.423175i
$497$	−17.9309	−	8.61198i	−0.804310	−	0.386300i
$498$	−1.33535	+	0.885376i	−0.0598384	+	0.0396747i
$499$	2.60182	−	0.342537i	0.116474	−	0.0153340i	−0.0720640	−	0.997400i	$-0.522959\pi$
$499$	2.60182	−	0.342537i	0.116474	−	0.0153340i	0.188538	+	0.982066i	$0.439625\pi$
$500$	13.8942	−	3.61687i	0.621366	−	0.161751i
$501$	−0.530852	−	0.0698880i	−0.0237167	−	0.00312237i
$502$	−3.87381	−	4.44915i	−0.172897	−	0.198575i
$503$	6.94204	+	6.94204i	0.309530	+	0.309530i	0.844727	−	0.535197i	$-0.179763\pi$
$503$	6.94204	+	6.94204i	0.309530	+	0.309530i	−0.535197	+	0.844727i	$0.679763\pi$
$504$	11.1281	−	19.2607i	0.495684	−	0.857938i
$505$	−2.79777	+	2.79777i	−0.124499	+	0.124499i
$506$	−33.1202	−	2.28952i	−1.47237	−	0.101782i
$507$	0.171010	−	1.29895i	0.00759484	−	0.0576885i
$508$	10.6498	+	14.0861i	0.472509	+	0.624970i
$509$	−2.43311	−	18.4813i	−0.107846	−	0.819169i	−0.956809	−	0.290717i	$-0.906106\pi$
$509$	−2.43311	−	18.4813i	−0.107846	−	0.819169i	0.848963	−	0.528452i	$-0.177227\pi$
$510$	−1.20725	−	0.244619i	−0.0534581	−	0.0108319i
$511$	7.69718	+	11.2644i	0.340503	+	0.498307i
$512$	−5.12463	+	22.0395i	−0.226479	+	0.974016i
$513$	−0.635241	−	1.10027i	−0.0280466	−	0.0485781i
$514$	10.9601	+	9.68118i	0.483431	+	0.427019i
$515$	−7.33355	+	5.62723i	−0.323155	+	0.247965i
$516$	−1.90770	+	0.237317i	−0.0839819	+	0.0104473i
$517$	−8.01971	−	19.3613i	−0.352706	−	0.851509i
$518$	0.242753	+	35.5560i	0.0106660	+	1.56224i
$519$	2.10635	+	2.10635i	0.0924584	+	0.0924584i
$520$	−0.749796	+	9.82679i	−0.0328807	+	0.430933i
$521$	2.02450	+	7.55554i	0.0886950	+	0.331014i	0.995988	−	0.0894842i	$-0.0285218\pi$
$521$	2.02450	+	7.55554i	0.0886950	+	0.331014i	−0.907293	+	0.420499i	$0.861855\pi$
$522$	1.70812	−	4.97358i	0.0747622	−	0.217688i
$523$	−19.3048	+	25.1584i	−0.844138	+	1.10010i	0.149642	+	0.988740i	$0.452188\pi$
$523$	−19.3048	+	25.1584i	−0.844138	+	1.10010i	−0.993780	+	0.111362i	$0.964479\pi$
$524$	−6.69626	+	6.60137i	−0.292527	+	0.288382i
$525$	−0.603971	+	1.84193i	−0.0263595	+	0.0803883i
$526$	−19.1829	−	28.9322i	−0.836416	−	1.26151i
$527$	11.3242	+	19.6141i	0.493291	+	0.854406i
$528$	−0.604858	−	2.39349i	−0.0263231	−	0.104163i
$529$	14.5202	+	8.38325i	0.631314	+	0.364489i
$530$	−2.57152	−	1.27956i	−0.111700	−	0.0555806i
$531$	36.5639	+	15.1453i	1.58674	+	0.657249i
$532$	6.09898	+	2.98301i	0.264424	+	0.129330i
$533$	18.6072	+	44.9218i	0.805967	+	1.94578i
$534$	1.79434	+	2.06084i	0.0776488	+	0.0891813i
$535$	4.92944	−	1.32084i	0.213118	−	0.0571049i
$536$	−26.2661	+	1.43941i	−1.13452	+	0.0621728i
$537$	0.216489	−	0.807949i	0.00934221	−	0.0348656i
$538$	22.3036	−	33.1232i	0.961575	−	1.42804i
$539$	−13.4957	−	22.2917i	−0.581300	−	0.960174i
$540$	−0.567618	−	1.39849i	−0.0244264	−	0.0601816i
$541$	3.40898	−	0.448801i	0.146563	−	0.0192954i	−0.0568874	−	0.998381i	$-0.518118\pi$
$541$	3.40898	−	0.448801i	0.146563	−	0.0192954i	0.203451	+	0.979085i	$0.434784\pi$
$542$	16.7943	+	14.8345i	0.721377	+	0.637198i
$543$	−1.62971	−	0.940914i	−0.0699376	−	0.0403785i
$544$	17.8682	−	34.6603i	0.766091	−	1.48605i
$545$			2.91679i			0.124942i
$546$	−2.26177	−	1.71111i	−0.0967948	−	0.0732288i
$547$	21.7445	+	9.00687i	0.929728	+	0.385106i	0.795575	−	0.605855i	$-0.207169\pi$
$547$	21.7445	+	9.00687i	0.929728	+	0.385106i	0.134153	+	0.990961i	$0.457169\pi$
$548$	2.68349	−	3.44599i	0.114633	−	0.147205i
$549$	32.6286	+	4.29563i	1.39255	+	0.183333i
$550$	−10.2155	−	20.9026i	−0.435590	−	0.891291i
$551$	1.55038	+	0.415422i	0.0660483	+	0.0176976i
$552$	−0.607908	+	2.89392i	−0.0258743	+	0.123173i
$553$	12.5923	+	10.8136i	0.535478	+	0.459843i
$554$	0.761176	+	3.89935i	0.0323393	+	0.165668i
$555$	0.952605	+	0.730960i	0.0404358	+	0.0310275i
$556$	22.3165	+	13.0976i	0.946428	+	0.555463i
$557$	25.9441	−	19.9076i	1.09929	−	0.843513i	0.110654	−	0.993859i	$-0.464705\pi$
$557$	25.9441	−	19.9076i	1.09929	−	0.843513i	0.988633	+	0.150346i	$0.0480388\pi$
$558$	−6.15288	+	12.3654i	−0.260472	+	0.523468i
$559$		−	26.5066i		−	1.12111i
$560$	6.68889	+	4.50697i	0.282657	+	0.190454i
$561$			4.25449i			0.179625i
$562$	23.7878	+	11.8365i	1.00343	+	0.499294i
$563$	17.1249	−	13.1404i	0.721728	−	0.553802i	−0.181276	−	0.983432i	$-0.558023\pi$
$563$	17.1249	−	13.1404i	0.721728	−	0.553802i	0.903005	+	0.429631i	$0.141356\pi$
$564$	−1.80641	+	0.470236i	−0.0760635	+	0.0198005i
$565$	3.28628	+	2.52165i	0.138255	+	0.106087i
$566$	−0.420783	+	0.0821393i	−0.0176868	+	0.00345257i
$567$	−22.7600	−	4.28179i	−0.955830	−	0.179818i
$568$	−3.92516	−	20.8998i	−0.164696	−	0.876937i
$569$	3.46806	+	0.929263i	0.145389	+	0.0389567i	0.330779	−	0.943708i	$-0.392688\pi$
$569$	3.46806	+	0.929263i	0.145389	+	0.0389567i	−0.185391	+	0.982665i	$0.559355\pi$
$570$	0.205990	−	0.100671i	0.00862797	−	0.00421664i
$571$	−35.0047	−	4.60845i	−1.46490	−	0.192858i	−0.644480	−	0.764621i	$-0.722926\pi$
$571$	−35.0047	−	4.60845i	−1.46490	−	0.192858i	−0.820419	+	0.571763i	$0.806260\pi$
$572$	33.7792	−	4.20212i	1.41238	−	0.175699i
$573$	−0.938061	−	0.388557i	−0.0391880	−	0.0162322i
$574$	39.4871	+	4.92455i	1.64816	+	0.205547i
$575$			27.8675i			1.16216i
$576$	23.6377	−	2.59853i	0.984904	−	0.108272i
$577$	−27.3948	−	15.8164i	−1.14046	−	0.658444i	−0.193915	−	0.981018i	$-0.562119\pi$
$577$	−27.3948	−	15.8164i	−1.14046	−	0.658444i	−0.946544	+	0.322574i	$0.895452\pi$
$578$	−28.5732	+	32.3479i	−1.18849	+	1.34549i
$579$	2.67264	−	0.351860i	0.111071	−	0.0146228i
$580$	1.75638	+	0.742243i	0.0729296	+	0.0308200i
$581$	−18.0523	−	0.994869i	−0.748936	−	0.0412741i
$582$	−0.178721	−	0.120342i	−0.00740824	−	0.00498835i
$583$	−2.56765	+	9.58258i	−0.106341	+	0.396870i
$584$	−4.83577	+	13.7600i	−0.200105	+	0.569394i
$585$	10.0045	−	2.68069i	0.413635	−	0.110833i
$586$	−6.71323	+	5.84510i	−0.277321	+	0.241459i
$587$	−17.2902	−	41.7421i	−0.713641	−	1.72288i	−0.690696	−	0.723145i	$-0.742696\pi$
$587$	−17.2902	−	41.7421i	−0.713641	−	1.72288i	−0.0229454	−	0.999737i	$-0.507304\pi$
$588$	−2.13206	+	0.917430i	−0.0879246	+	0.0378342i
$589$	−3.89469	−	1.61323i	−0.160478	−	0.0664721i
$590$	−6.39279	+	12.8475i	−0.263187	+	0.528924i
$591$	1.11942	+	0.646296i	0.0460467	+	0.0265851i
$592$	−30.4840	+	22.7074i	−1.25288	+	0.933269i
$593$	−7.13623	−	12.3603i	−0.293050	−	0.507577i	0.681480	−	0.731837i	$-0.261337\pi$
$593$	−7.13623	−	12.3603i	−0.293050	−	0.507577i	−0.974529	+	0.224260i	$0.928003\pi$
$594$	−4.34474	+	2.88069i	−0.178267	+	0.118196i
$595$	−9.27295	−	10.3546i	−0.380154	−	0.424499i
$596$	−0.0544784	+	7.63430i	−0.00223152	+	0.312713i
$597$	0.349118	−	0.454979i	0.0142884	−	0.0186211i
$598$	−38.5622	−	13.2437i	−1.57693	−	0.541577i
$599$	−9.41520	−	35.1380i	−0.384695	−	1.43570i	−0.838647	−	0.544675i	$-0.816653\pi$
$599$	−9.41520	−	35.1380i	−0.384695	−	1.43570i	0.453953	−	0.891026i	$-0.350014\pi$
$600$	−1.96930	+	0.645064i	−0.0803964	+	0.0263346i
$601$	28.1564	+	28.1564i	1.14852	+	1.14852i	0.986844	+	0.161678i	$0.0516907\pi$
$601$	28.1564	+	28.1564i	1.14852	+	1.14852i	0.161678	+	0.986844i	$0.448309\pi$
$602$	−18.8603	−	10.7180i	−0.768688	−	0.436832i
$603$	10.5795	+	25.5412i	0.430831	+	1.04012i
$604$	−15.8821	−	12.3678i	−0.646232	−	0.503238i
$605$	1.72822	−	1.32611i	0.0702621	−	0.0539140i
$606$	0.805837	−	0.912294i	0.0327349	−	0.0370594i
$607$	1.97544	+	3.42156i	0.0801806	+	0.138877i	0.903327	−	0.428952i	$-0.141117\pi$
$607$	1.97544	+	3.42156i	0.0801806	+	0.138877i	−0.823147	+	0.567829i	$0.807784\pi$
$608$	1.28878	+	7.14283i	0.0522671	+	0.289680i
$609$	−0.453049	+	0.309578i	−0.0183585	+	0.0125447i
$610$	−2.36975	+	11.6953i	−0.0959484	+	0.473529i
$611$	−3.35940	−	25.5172i	−0.135907	−	1.03231i
$612$	−40.5916	−	5.63895i	−1.64082	−	0.227941i
$613$	−5.27854	+	40.0945i	−0.213198	+	1.61940i	0.465544	+	0.885025i	$0.345859\pi$
$613$	−5.27854	+	40.0945i	−0.213198	+	1.61940i	−0.678742	+	0.734377i	$0.737474\pi$
$614$	2.49157	−	36.0431i	0.100552	−	1.45458i
$615$	0.950199	−	0.950199i	0.0383157	−	0.0383157i
$616$	10.6687	−	25.7341i	0.429854	−	1.03686i
$617$	−11.3927	−	11.3927i	−0.458653	−	0.458653i	0.439560	−	0.898213i	$-0.355134\pi$
$617$	−11.3927	−	11.3927i	−0.458653	−	0.458653i	−0.898213	+	0.439560i	$0.855134\pi$
$618$	2.14473	−	1.86738i	0.0862738	−	0.0751172i
$619$	−8.57203	−	1.12853i	−0.344539	−	0.0453594i	−0.0437287	−	0.999043i	$-0.513924\pi$
$619$	−8.57203	−	1.12853i	−0.344539	−	0.0453594i	−0.300810	+	0.953684i	$0.597257\pi$
$620$	−4.31907	−	2.53488i	−0.173458	−	0.101803i
$621$	6.19076	−	0.815029i	0.248427	−	0.0327060i
$622$	−0.555795	−	0.838266i	−0.0222854	−	0.0336114i
$623$	2.33642	+	30.7461i	0.0936066	+	1.23181i
$624$	0.0432695	−	3.03162i	0.00173217	−	0.121362i
$625$	−14.3975	+	8.31239i	−0.575899	+	0.332496i
$626$	−9.57055	+	0.593001i	−0.382516	+	0.0237011i
$627$	−0.482074	−	0.628251i	−0.0192522	−	0.0250899i
$628$	−2.89630	+	10.5086i	−0.115575	+	0.419339i
$629$	60.5212	−	25.0687i	2.41314	−	0.999555i
$630$	2.13793	−	8.20244i	0.0851770	−	0.326793i
$631$	22.3250	−	22.3250i	0.888745	−	0.888745i	−0.105657	−	0.994403i	$-0.533695\pi$
$631$	22.3250	−	22.3250i	0.888745	−	0.888745i	0.994403	+	0.105657i	$0.0336947\pi$
$632$	−1.34998	+	17.6928i	−0.0536994	+	0.703782i
$633$	−2.17492	+	0.582768i	−0.0864453	+	0.0231629i
$634$	10.2956	+	21.0665i	0.408890	+	0.836659i
$635$	5.33861	+	4.09646i	0.211856	+	0.162563i
$636$	0.813940	+	0.343970i	0.0322748	+	0.0136393i
$637$	−8.92397	−	30.7341i	−0.353581	−	1.21773i
$638$	1.30787	−	6.45466i	0.0517791	−	0.255543i
$639$	−19.3544	+	11.1743i	−0.765647	+	0.442047i
$640$	0.348894	+	8.61543i	0.0137912	+	0.340555i
$641$	−8.31636	+	14.4044i	−0.328477	+	0.568938i	−0.982210	−	0.187787i	$-0.939869\pi$
$641$	−8.31636	+	14.4044i	−0.328477	+	0.568938i	0.653733	+	0.756725i	$0.273202\pi$
$642$	−1.48847	+	0.499353i	−0.0587454	+	0.0197079i
$643$	18.4617	−	44.5706i	0.728060	−	1.75769i	0.0791019	−	0.996867i	$-0.474795\pi$
$643$	18.4617	−	44.5706i	0.728060	−	1.75769i	0.648958	−	0.760825i	$-0.275205\pi$
$644$	−25.0160	+	22.0831i	−0.985768	+	0.870195i
$645$	−0.676797	+	0.280338i	−0.0266489	+	0.0110383i
$646$	0.862615	−	12.4786i	0.0339391	−	0.490963i
$647$	−8.85575	−	33.0501i	−0.348155	−	1.29933i	−0.888883	−	0.458135i	$-0.848518\pi$
$647$	−8.85575	−	33.0501i	−0.348155	−	1.29933i	0.540727	−	0.841198i	$-0.318149\pi$
$648$	−10.7120	−	22.3210i	−0.420807	−	0.876851i
$649$	47.8753	+	12.8282i	1.87927	+	0.503549i
$650$	−5.47427	−	28.0436i	−0.214719	−	1.09996i
$651$	1.28585	−	0.650813i	0.0503963	−	0.0255074i
$652$	−31.1688	−	31.6169i	−1.22067	−	1.23821i
$653$	−1.84414	−	14.0076i	−0.0721666	−	0.548160i	−0.988891	−	0.148641i	$-0.952510\pi$
$653$	−1.84414	−	14.0076i	−0.0721666	−	0.548160i	0.916725	−	0.399520i	$-0.130823\pi$
$654$	−0.0554930	−	0.895611i	−0.00216995	−	0.0350212i
$655$	−1.79159	+	3.10312i	−0.0700032	+	0.121249i
$656$	20.7423	+	37.1409i	0.809850	+	1.45011i
$657$	15.3280			0.598003
$658$	−19.5146	−	7.92757i	−0.760759	−	0.309049i
$659$	−9.75158	+	23.5424i	−0.379868	+	0.917081i	0.612122	+	0.790763i	$0.290316\pi$
$659$	−9.75158	+	23.5424i	−0.379868	+	0.917081i	−0.991990	+	0.126318i	$0.959684\pi$
$660$	−0.464547	−	0.818045i	−0.0180825	−	0.0318424i
$661$	2.55942	−	19.4407i	0.0995499	−	0.756157i	−0.866751	−	0.498741i	$-0.833796\pi$
$661$	2.55942	−	19.4407i	0.0995499	−	0.756157i	0.966301	−	0.257415i	$-0.0828709\pi$
$662$	10.3502	−	30.1369i	0.402270	−	1.17130i
$663$	−1.35235	+	5.04703i	−0.0525208	+	0.196010i
$664$	−10.5654	−	16.1847i	−0.410019	−	0.628087i
$665$	2.54259	+	0.478332i	0.0985975	+	0.0185489i
$666$	33.1364	+	22.3124i	1.28401	+	0.864589i
$667$	−4.80227	+	6.25845i	−0.185945	+	0.242328i
$668$	0.888764	−	6.39771i	0.0343873	−	0.247535i
$669$	−1.82587	−	2.37952i	−0.0705921	−	0.0919974i
$670$	−9.50356	+	3.18825i	−0.367155	+	0.123173i
$671$	41.2155			1.59111
$672$	−2.13959	−	1.25662i	−0.0825366	−	0.0484754i
$673$	4.92340			0.189783			0.0948915	−	0.995488i	$-0.469750\pi$
$673$	4.92340			0.189783			0.0948915	+	0.995488i	$0.469750\pi$
$674$	−1.22811	+	0.412005i	−0.0473048	+	0.0158698i
$675$	2.66381	+	3.47155i	0.102530	+	0.133620i
$676$	15.6547	+	2.17474i	0.602104	+	0.0836437i
$677$	23.6205	−	30.7828i	0.907810	−	1.18308i	−0.0747628	−	0.997201i	$-0.523820\pi$
$677$	23.6205	−	30.7828i	0.907810	−	1.18308i	0.982573	−	0.185879i	$-0.0595134\pi$
$678$	−1.05704	−	0.711759i	−0.0405953	−	0.0273349i
$679$	−0.805416	−	2.29405i	−0.0309090	−	0.0880377i
$680$	3.05479	−	14.5422i	0.117146	−	0.557667i
$681$	0.741379	−	2.76687i	0.0284097	−	0.106026i
$682$	−5.61840	+	16.3593i	−0.215139	+	0.626429i
$683$	−1.11245	+	8.44987i	−0.0425666	+	0.323325i	0.956893	+	0.290442i	$0.0938023\pi$
$683$	−1.11245	+	8.44987i	−0.0425666	+	0.323325i	−0.999459	+	0.0328833i	$0.989531\pi$
$684$	6.63302	−	3.76672i	0.253620	−	0.144024i
$685$	0.636914	−	1.53765i	0.0243352	−	0.0587504i
$686$	−25.4767	−	6.07769i	−0.972705	−	0.232047i
$687$	−1.52924			−0.0583442
$688$	−2.69857	−	23.0332i	−0.102882	−	0.878134i
$689$	−6.09191	+	10.5515i	−0.232083	+	0.401980i
$690$	0.0696863	+	1.12468i	0.00265291	+	0.0428158i
$691$	0.465346	+	3.53466i	0.0177026	+	0.134465i	0.998014	−	0.0629934i	$-0.0200647\pi$
$691$	0.465346	+	3.53466i	0.0177026	+	0.134465i	−0.980311	+	0.197458i	$0.936731\pi$
$692$	−25.5904	+	25.2278i	−0.972802	+	0.959017i
$693$	−29.2327	−	1.61102i	−1.11046	−	0.0611977i
$694$	−2.62054	−	13.4245i	−0.0994744	−	0.509587i
$695$	9.52446	+	2.55207i	0.361283	+	0.0968056i
$696$	−0.553424	−	0.194493i	−0.0209775	−	0.00737223i
$697$	−18.9746	−	70.8140i	−0.718713	−	2.68227i
$698$	−1.22168	+	17.6728i	−0.0462413	+	0.668926i
$699$	−0.492589	+	0.204037i	−0.0186314	+	0.00771739i
$700$	−22.1674	−	7.44433i	−0.837849	−	0.281369i
$701$	4.49496	−	10.8518i	0.169772	−	0.409867i	−0.815978	−	0.578083i	$-0.803801\pi$
$701$	4.49496	−	10.8518i	0.169772	−	0.409867i	0.985750	+	0.168217i	$0.0538009\pi$
$702$	−6.06976	+	2.03628i	−0.229088	+	0.0768546i
$703$	−6.09651	+	10.5595i	−0.229934	+	0.398258i
$704$	28.9250	−	7.09044i	1.09015	−	0.267231i
$705$	−0.616002	+	0.355649i	−0.0232000	+	0.0133945i
$706$	−3.73071	+	18.4120i	−0.140407	+	0.692944i
$707$	13.4431	−	2.81958i	0.505580	−	0.106041i
$708$	1.71850	−	4.06651i	0.0645852	−	0.152829i
$709$	−31.9399	−	24.5084i	−1.19953	−	0.920431i	−0.201277	−	0.979534i	$-0.564509\pi$
$709$	−31.9399	−	24.5084i	−1.19953	−	0.920431i	−0.998252	+	0.0591038i	$0.981176\pi$
$710$	−3.55809	−	7.28047i	−0.133533	−	0.273231i
$711$	18.0127	−	4.82650i	0.675531	−	0.181008i
$712$	−25.0146	+	21.4679i	−0.937463	+	0.804545i
$713$	14.6504	−	14.6504i	0.548661	−	0.548661i
$714$	3.04429	+	3.00301i	0.113930	+	0.112385i
$715$	11.9839	−	4.96388i	0.448171	−	0.185639i
$716$	9.72775	+	2.68109i	0.363543	+	0.100197i
$717$	0.966119	+	1.25907i	0.0360804	+	0.0470209i
$718$	29.9845	−	1.85787i	1.11901	−	0.0693351i
$719$	−11.2169	+	6.47606i	−0.418319	+	0.241516i	−0.694358	−	0.719630i	$-0.744311\pi$
$719$	−11.2169	+	6.47606i	−0.418319	+	0.241516i	0.276039	+	0.961146i	$0.410978\pi$
$720$	8.42060	−	3.34795i	0.313817	−	0.124771i
$721$	31.9977	−	2.43153i	1.19165	−	0.0905548i
$722$	−13.5618	−	20.4543i	−0.504719	−	0.761231i
$723$	0.825490	−	0.108678i	0.0307003	−	0.00404177i
$724$	11.4906	−	19.5784i	0.427046	−	0.727625i
$725$	−5.48087	−	0.721570i	−0.203554	−	0.0267984i
$726$	−0.505426	+	0.440067i	−0.0187581	+	0.0163324i
$727$	9.58470	+	9.58470i	0.355477	+	0.355477i	0.862143	−	0.506666i	$-0.169122\pi$
$727$	9.58470	+	9.58470i	0.355477	+	0.355477i	−0.506666	+	0.862143i	$0.669122\pi$
$728$	20.8360	−	27.1367i	0.772235	−	1.00575i
$729$	−18.0503	+	18.0503i	−0.668531	+	0.668531i
$730$	−0.383285	+	5.54460i	−0.0141860	+	0.205215i
$731$	−5.21659	+	39.6239i	−0.192943	+	1.46554i
$732$	0.505134	−	3.63617i	0.0186703	−	0.134397i
$733$	2.15566	+	16.3739i	0.0796212	+	0.604783i	0.984015	+	0.178085i	$0.0569901\pi$
$733$	2.15566	+	16.3739i	0.0796212	+	0.604783i	−0.904394	+	0.426698i	$0.859677\pi$
$734$	−3.63901	+	17.9594i	−0.134318	+	0.662895i
$735$	−0.690356	+	0.552905i	−0.0254642	+	0.0203942i
$736$	−34.8574	−	7.58238i	−1.28486	−	0.279490i
$737$	17.3112	+	29.9839i	0.637666	+	1.10447i
$738$	29.5975	−	33.5075i	1.08950	−	1.23343i
$739$	−10.6529	+	8.17427i	−0.391874	+	0.300695i	−0.785840	−	0.618429i	$-0.787769\pi$
$739$	−10.6529	+	8.17427i	−0.391874	+	0.300695i	0.393966	+	0.919125i	$0.371103\pi$
$740$	−8.89965	+	11.4285i	−0.327158	+	0.420119i
$741$	−0.372178	−	0.898517i	−0.0136723	−	0.0330078i
$742$	5.04445	+	8.60109i	0.185188	+	0.315756i
$743$	−37.8565	−	37.8565i	−1.38882	−	1.38882i	−0.827803	−	0.561018i	$-0.810410\pi$
$743$	−37.8565	−	37.8565i	−1.38882	−	1.38882i	−0.561018	−	0.827803i	$-0.689590\pi$
$744$	1.37441	+	0.696172i	0.0503884	+	0.0255229i
$745$	0.752964	+	2.81010i	0.0275865	+	0.102954i
$746$	4.11901	+	1.41462i	0.150808	+	0.0517931i
$747$	−12.3655	+	16.1151i	−0.452432	+	0.589621i
$748$	−51.3224	−	0.366237i	−1.87653	−	0.0133910i
$749$	−16.8345	−	5.52005i	−0.615118	−	0.201698i
$750$	−1.40279	+	0.930091i	−0.0512226	+	0.0339621i
$751$	−17.6776	−	30.6185i	−0.645064	−	1.11728i	−0.984287	−	0.176578i	$-0.943497\pi$
$751$	−17.6776	−	30.6185i	−0.645064	−	1.11728i	0.339222	−	0.940706i	$-0.389836\pi$
$752$	−5.51701	−	21.8314i	−0.201185	−	0.796109i
$753$	0.598926	+	0.345790i	0.0218261	+	0.0126013i
$754$	3.60321	−	7.24134i	0.131221	−	0.263714i
$755$	−7.08679	−	2.93544i	−0.257915	−	0.106832i
$756$	−1.00543	+	5.14220i	−0.0365673	+	0.187020i
$757$	13.5015	+	32.5954i	0.490719	+	1.18470i	0.954355	+	0.298675i	$0.0965447\pi$
$757$	13.5015	+	32.5954i	0.490719	+	1.18470i	−0.463635	+	0.886026i	$0.653455\pi$
$758$	−37.6166	+	32.7522i	−1.36630	+	1.18961i
$759$	3.75938	−	1.00732i	0.136457	−	0.0365635i
$760$	1.19667	+	2.49355i	0.0434079	+	0.0904505i
$761$	13.9793	−	52.1715i	0.506750	−	1.89122i	0.0562987	−	0.998414i	$-0.482070\pi$
$761$	13.9793	−	52.1715i	0.506750	−	1.89122i	0.450451	−	0.892801i	$-0.351263\pi$
$762$	−1.71718	−	1.15627i	−0.0622068	−	0.0418871i
$763$	5.53773	−	8.47725i	0.200479	−	0.306897i
$764$	4.76796	−	11.2825i	0.172499	−	0.408186i
$765$	−15.4830	+	2.03837i	−0.559787	+	0.0736974i
$766$	−29.5863	+	33.4949i	−1.06900	+	1.21022i
$767$	52.7161	+	30.4357i	1.90347	+	1.09897i
$768$	−0.271041	−	2.63876i	−0.00978034	−	0.0952182i
$769$		−	12.5480i		−	0.452494i	−0.974070	−	0.226247i	$-0.927354\pi$
$769$		−	12.5480i		−	0.452494i	0.974070	−	0.226247i	$-0.0726457\pi$
$770$	1.31373	−	10.5340i	0.0473437	−	0.379621i
$771$	−1.58385	−	0.656052i	−0.0570410	−	0.0236271i
$772$	4.01446	+	32.2707i	0.144483	+	1.16145i
$773$	−5.81490	−	0.765546i	−0.209148	−	0.0275348i	0.0252243	−	0.999682i	$-0.491970\pi$
$773$	−5.81490	−	0.765546i	−0.209148	−	0.0275348i	−0.234372	+	0.972147i	$0.575303\pi$
$774$	−21.8971	+	10.7015i	−0.787074	+	0.384657i
$775$	14.0245	+	3.75787i	0.503777	+	0.134987i
$776$	1.46709	−	2.14558i	0.0526654	−	0.0770218i
$777$	−1.38084	−	3.93302i	−0.0495374	−	0.141096i
$778$	26.1418	−	5.10304i	0.937230	−	0.182953i
$779$	10.8258	+	8.30695i	0.387875	+	0.297627i
$780$	−0.291058	−	1.11810i	−0.0104215	−	0.0400343i
$781$	−22.2047	+	17.0383i	−0.794548	+	0.609678i
$782$	55.0390	+	27.3868i	1.96819	+	0.979349i
$783$			1.23868i			0.0442667i
$784$	−10.8835	−	25.7982i	−0.388698	−	0.921365i
$785$			4.15377i			0.148254i
$786$	0.491076	−	0.986911i	0.0175161	−	0.0352019i
$787$	−27.2313	+	20.8953i	−0.970692	+	0.744838i	−0.966900	−	0.255154i	$-0.917874\pi$
$787$	−27.2313	+	20.8953i	−0.970692	+	0.744838i	−0.00379200	+	0.999993i	$0.501207\pi$
$788$	−7.89271	+	13.4480i	−0.281166	+	0.479066i
$789$	3.22861	+	2.47740i	0.114942	+	0.0881977i
$790$	1.29547	+	6.63643i	0.0460908	+	0.236114i
$791$	−4.76359	−	13.5681i	−0.169374	−	0.482424i
$792$	−17.1090	−	26.2084i	−0.607941	−	0.931274i
$793$	48.8932	+	13.1009i	1.73625	+	0.465227i
$794$	16.3228	+	33.3993i	0.579275	+	1.18530i
$795$	0.333841	+	0.0439511i	0.0118401	+	0.00155878i
$796$	5.45841	+	4.25061i	0.193468	+	0.150659i
$797$	−24.9001	−	10.3139i	−0.882006	−	0.365339i	−0.104731	−	0.994501i	$-0.533398\pi$
$797$	−24.9001	−	10.3139i	−0.882006	−	0.365339i	−0.777274	+	0.629162i	$0.783398\pi$
$798$	−0.789813	−	0.0985000i	−0.0279591	−	0.00348686i
$799$			38.8059i			1.37285i
$800$	−7.61196	−	23.8115i	−0.269124	−	0.841862i
$801$	30.0017	+	17.3215i	1.06006	+	0.612024i
$802$	−14.9710	−	13.2240i	−0.528644	−	0.466956i
$803$	19.0321	−	2.50562i	0.671627	−	0.0884213i
$804$	2.85745	−	1.15977i	0.100774	−	0.0409021i
$805$	−6.95411	+	10.6455i	−0.245100	+	0.375204i
$806$	−11.8650	+	17.6208i	−0.417928	+	0.620668i
$807$	−1.21162	+	4.52182i	−0.0426510	+	0.159176i
$808$	10.9357	+	9.79943i	0.384718	+	0.344743i
$809$	−51.7619	+	13.8695i	−1.81985	+	0.487627i	−0.996771	−	0.0802991i	$-0.974412\pi$
$809$	−51.7619	+	13.8695i	−1.81985	+	0.487627i	−0.823079	+	0.567926i	$0.807746\pi$
$810$	−6.19525	−	7.11538i	−0.217679	−	0.250009i
$811$	12.0724	+	29.1453i	0.423919	+	1.02343i	0.981180	+	0.193093i	$0.0618519\pi$
$811$	12.0724	+	29.1453i	0.423919	+	1.02343i	−0.557262	+	0.830337i	$0.688148\pi$
$812$	−3.69547	−	5.49183i	−0.129686	−	0.192726i
$813$	−2.42695	−	1.00527i	−0.0851167	−	0.0352565i
$814$	44.7911	+	22.2876i	1.56993	+	0.781178i
$815$	−14.6516	−	8.45911i	−0.513223	−	0.296310i
$816$	−0.661314	+	4.52335i	−0.0231506	+	0.158349i
$817$	−3.71944	−	6.44226i	−0.130127	−	0.225386i
$818$	23.8643	+	35.9929i	0.834397	+	1.25846i
$819$	−34.1662	−	11.2031i	−1.19386	−	0.391470i
$820$	11.3806	+	11.5442i	0.397427	+	0.403139i
$821$	15.0833	−	19.6569i	0.526411	−	0.686032i	−0.452161	−	0.891936i	$-0.649347\pi$
$821$	15.0833	−	19.6569i	0.526411	−	0.686032i	0.978572	+	0.205904i	$0.0660135\pi$
$822$	−0.166312	+	0.484257i	−0.00580081	+	0.0168904i
$823$	0.551127	+	2.05683i	0.0192111	+	0.0716967i	0.974866	−	0.222792i	$-0.0715172\pi$
$823$	0.551127	+	2.05683i	0.0192111	+	0.0716967i	−0.955655	+	0.294489i	$0.904851\pi$
$824$	22.3419	+	26.0329i	0.778315	+	0.906899i
$825$	1.92859	+	1.92859i	0.0671447	+	0.0671447i
$826$	42.9717	−	25.2025i	1.49518	−	0.876906i
$827$	−11.4984	−	27.7596i	−0.399839	−	0.965297i	−0.987704	−	0.156338i	$-0.950031\pi$
$827$	−11.4984	−	27.7596i	−0.399839	−	0.965297i	0.587865	−	0.808959i	$-0.299969\pi$
$828$	4.62804	+	37.2030i	0.160835	+	1.29289i
$829$	34.6421	−	26.5818i	1.20317	−	0.923226i	0.204718	−	0.978821i	$-0.434372\pi$
$829$	34.6421	−	26.5818i	1.20317	−	0.923226i	0.998453	+	0.0555956i	$0.0177057\pi$
$830$	−5.52010	−	4.87595i	−0.191605	−	0.169247i
$831$	−0.232878	−	0.403356i	−0.00807843	−	0.0139923i
$832$	36.5670	+	0.782934i	1.26773	+	0.0271434i
$833$	7.29158	+	47.6997i	0.252638	+	1.65270i
$834$	−2.97307	−	0.602417i	−0.102949	−	0.0208600i
$835$	−0.321271	−	2.44029i	−0.0111180	−	0.0844498i
$836$	7.62016	−	5.76123i	0.263549	−	0.199256i
$837$	0.424639	−	3.22545i	0.0146777	−	0.111488i
$838$	−4.04027	−	0.279294i	−0.139569	−	0.00964805i
$839$	−24.7653	+	24.7653i	−0.854993	+	0.854993i	−0.990743	−	0.135750i	$-0.956655\pi$
$839$	−24.7653	+	24.7653i	−0.854993	+	0.854993i	0.135750	+	0.990743i	$0.456655\pi$
$840$	−0.913249	−	0.245007i	−0.0315101	−	0.00845353i
$841$	19.3996	+	19.3996i	0.668950	+	0.668950i
$842$	10.0878	+	11.5860i	0.347648	+	0.399282i
$843$	−3.08819	−	0.406568i	−0.106363	−	0.0140029i
$844$	−6.84277	−	26.2865i	−0.235538	−	0.904817i
$845$	5.97120	−	0.786124i	0.205416	−	0.0270435i
$846$	−19.7234	+	13.0772i	−0.678103	+	0.449603i
$847$	−7.54054	+	0.573012i	−0.259096	+	0.0196889i
$848$	−4.21942	+	9.78904i	−0.144895	+	0.336157i
$849$	0.0435265	−	0.0251301i	0.00149383	−	0.000862461i
$850$	2.66425	+	42.9988i	0.0913829	+	1.47485i
$851$	−36.4808	−	47.5427i	−1.25055	−	1.62974i
$852$	1.23104	+	2.16780i	0.0421747	+	0.0742676i
$853$	28.4368	−	11.7789i	0.973656	−	0.403302i	0.161584	−	0.986859i	$-0.448340\pi$
$853$	28.4368	−	11.7789i	0.973656	−	0.403302i	0.812072	+	0.583557i	$0.198340\pi$
$854$	29.0917	−	29.4917i	0.995498	−	1.00918i
$855$	2.05537	−	2.05537i	0.0702920	−	0.0702920i
$856$	−5.89562	−	17.9986i	−0.201508	−	0.615180i
$857$	11.1457	−	2.98648i	0.380730	−	0.102016i	−0.0633778	−	0.997990i	$-0.520187\pi$
$857$	11.1457	−	2.98648i	0.380730	−	0.102016i	0.444108	+	0.895973i	$0.353521\pi$
$858$	−3.58525	+	1.75218i	−0.122399	+	0.0598183i
$859$	−16.7224	−	12.8316i	−0.570562	−	0.437807i	0.282761	−	0.959190i	$-0.408750\pi$
$859$	−16.7224	−	12.8316i	−0.570562	−	0.437807i	−0.853323	+	0.521383i	$0.825416\pi$
$860$	−3.32349	−	8.18841i	−0.113330	−	0.279223i
$861$	−4.56564	+	0.957606i	−0.155597	+	0.0326351i
$862$	24.4784	+	4.95991i	0.833737	+	0.168935i
$863$	25.2885	−	14.6003i	0.860830	−	0.497000i	−0.00346028	−	0.999994i	$-0.501101\pi$
$863$	25.2885	−	14.6003i	0.860830	−	0.497000i	0.864290	+	0.502994i	$0.167768\pi$
$864$	−5.06708	+	2.38740i	−0.172386	+	0.0812209i
$865$	−6.84674	+	11.8589i	−0.232796	+	0.403214i
$866$	2.50375	+	7.46320i	0.0850810	+	0.253610i
$867$	1.93628	−	4.67460i	0.0657596	−	0.158758i
$868$	7.74014	+	15.5673i	0.262717	+	0.528390i
$869$	21.5766	−	8.93730i	0.731935	−	0.303177i
$870$	−0.223002	−	0.0154156i	−0.00756047	−	0.000522637i
$871$	11.0052	+	41.0720i	0.372897	+	1.39167i
$872$	10.8086	−	0.592321i	0.366027	−	0.0200585i
$873$	−2.63854	−	0.706993i	−0.0893009	−	0.0239281i
$874$	−11.2307	+	2.19229i	−0.379883	+	0.0741553i
$875$	−18.9640	−	1.04511i	−0.641101	−	0.0353313i
$876$	0.0122010	−	1.70978i	0.000412234	−	0.0577682i
$877$	5.57549	+	42.3501i	0.188271	+	1.43006i	0.780936	+	0.624611i	$0.214743\pi$
$877$	5.57549	+	42.3501i	0.188271	+	1.43006i	−0.592665	+	0.805449i	$0.701924\pi$
$878$	−45.1816	+	2.79950i	−1.52481	+	0.0944785i
$879$	0.521755	−	0.903706i	0.0175984	−	0.0304812i
$880$	9.90816	−	5.53347i	0.334004	−	0.186533i
$881$	21.7004			0.731104			0.365552	−	0.930791i	$-0.380880\pi$
$881$	21.7004			0.731104			0.365552	+	0.930791i	$0.380880\pi$
$882$	−21.7865	+	19.7803i	−0.733590	+	0.666037i
$883$	−20.5104	+	49.5165i	−0.690230	+	1.66636i	0.0540868	+	0.998536i	$0.482775\pi$
$883$	−20.5104	+	49.5165i	−0.690230	+	1.66636i	−0.744317	+	0.667827i	$0.767225\pi$
$884$	−60.7665	−	16.7480i	−2.04380	−	0.563296i
$885$	0.219583	−	1.66790i	0.00738120	−	0.0560658i
$886$	−13.7015	−	4.70562i	−0.460311	−	0.158088i
$887$	0.424519	−	1.58433i	0.0142539	−	0.0531965i	−0.958433	−	0.285319i	$-0.907900\pi$
$887$	0.424519	−	1.58433i	0.0142539	−	0.0531965i	0.972687	+	0.232123i	$0.0745671\pi$
$888$	2.51524	−	3.67847i	0.0844060	−	0.123441i
$889$	−7.73854	−	22.0415i	−0.259542	−	0.739250i
$890$	−7.01589	+	10.4194i	−0.235173	+	0.349258i
$891$	−19.8371	+	25.8522i	−0.664567	+	0.866080i
$892$	28.8615	−	21.8208i	0.966356	−	0.730615i
$893$	−4.39707	−	5.73038i	−0.147142	−	0.191760i
$894$	−0.284664	−	0.848526i	−0.00952058	−	0.0283790i
$895$	3.84511			0.128528
$896$	15.3430	−	25.7020i	0.512573	−	0.858643i
$897$	4.77988			0.159596
$898$	−6.38719	−	19.0390i	−0.213143	−	0.635338i
$899$	2.50204	+	3.26072i	0.0834476	+	0.108751i
$900$	−20.9566	+	15.8443i	−0.698553	+	0.528142i
$901$	11.1832	−	14.5742i	0.372565	−	0.485536i
$902$	31.2724	−	46.4428i	1.04126	−	1.54638i
$903$	2.49926	+	0.470180i	0.0831702	+	0.0156466i
$904$	8.67702	−	12.6899i	0.288593	−	0.422060i
$905$	2.23895	−	8.35588i	0.0744253	−	0.277759i
$906$	2.23187	+	0.766510i	0.0741490	+	0.0254656i
$907$	−2.89851	+	22.0164i	−0.0962434	+	0.731041i	0.873484	+	0.486852i	$0.161855\pi$
$907$	−2.89851	+	22.0164i	−0.0962434	+	0.731041i	−0.969728	+	0.244189i	$0.921478\pi$
$908$	33.3132	+	9.18152i	1.10554	+	0.304700i
$909$	5.90558	−	14.2573i	0.195876	−	0.472886i
$910$	4.90685	−	12.0788i	0.162661	−	0.400408i
$911$	19.3134			0.639882			0.319941	−	0.947438i	$-0.396337\pi$
$911$	19.3134			0.639882			0.319941	+	0.947438i	$0.396337\pi$
$912$	−0.414884	−	0.742886i	−0.0137382	−	0.0245994i
$913$	−12.7194	+	22.0307i	−0.420951	+	0.729109i
$914$	−6.32522	+	0.391917i	−0.209220	+	0.0129635i
$915$	−0.182596	−	1.38695i	−0.00603643	−	0.0458513i
$916$	0.131641	−	18.4474i	0.00434954	−	0.609520i
$917$	11.0985	−	5.61735i	0.366505	−	0.185501i
$918$	9.47424	−	1.84943i	0.312696	−	0.0610402i
$919$	9.82917	+	2.63372i	0.324235	+	0.0868784i	0.417265	−	0.908785i	$-0.362989\pi$
$919$	9.82917	+	2.63372i	0.324235	+	0.0868784i	−0.0930304	+	0.995663i	$0.529655\pi$
$920$	−13.5731	+	0.743819i	−0.447493	+	0.0245230i
$921$	1.09622	+	4.09115i	0.0361217	+	0.134808i
$922$	55.6423	+	3.84642i	1.83248	+	0.126675i
$923$	−31.7570	+	13.1542i	−1.04529	+	0.432975i
$924$	−0.202973	+	3.25951i	−0.00667731	+	0.107230i
$925$	16.0708	−	38.7984i	0.528406	−	1.27568i
$926$	−6.44597	−	19.2142i	−0.211828	−	0.631417i
$927$	18.0266	−	31.2229i	0.592070	−	1.02550i
$928$	2.39383	−	6.65927i	0.0785813	−	0.218601i
$929$	−33.6366	+	19.4201i	−1.10358	+	0.637153i	−0.937159	−	0.348901i	$-0.886555\pi$
$929$	−33.6366	+	19.4201i	−1.10358	+	0.637153i	−0.166422	+	0.986055i	$0.553221\pi$
$930$	0.575401	+	0.116590i	0.0188681	+	0.00382314i
$931$	−6.48156	−	6.21750i	−0.212424	−	0.203770i
$932$	−2.41892	−	5.95972i	−0.0792343	−	0.195217i
$933$	0.0935438	+	0.0717787i	0.00306249	+	0.00234993i
$934$	−18.0697	+	8.83096i	−0.591257	+	0.288958i
$935$	−18.8912	+	5.06188i	−0.617809	+	0.165541i
$936$	−11.9654	−	36.5289i	−0.391101	−	1.19398i
$937$	−31.5427	+	31.5427i	−1.03045	+	1.03045i	−0.0309321	+	0.999521i	$0.509848\pi$
$937$	−31.5427	+	31.5427i	−1.03045	+	1.03045i	−0.999521	+	0.0309321i	$0.990152\pi$
$938$	33.6739	+	8.77694i	1.09949	+	0.286577i
$939$	1.03855	−	0.430183i	0.0338919	−	0.0140385i
$940$	−4.23721	−	7.46152i	−0.138203	−	0.243368i
$941$	8.20086	+	10.6876i	0.267341	+	0.348405i	0.907662	−	0.419702i	$-0.137865\pi$
$941$	8.20086	+	10.6876i	0.267341	+	0.348405i	−0.640321	+	0.768107i	$0.721199\pi$
$942$	−0.0790269	−	1.27543i	−0.00257483	−	0.0415557i
$943$	−58.0807	+	33.5329i	−1.89137	+	1.09198i
$944$	48.9068	+	21.0805i	1.59178	+	0.686113i
$945$	0.151288	+	1.99087i	0.00492140	+	0.0647631i
$946$	−25.4392	+	16.8669i	−0.827099	+	0.548391i
$947$	5.83197	−	0.767793i	0.189513	−	0.0249499i	−0.0351720	−	0.999381i	$-0.511198\pi$
$947$	5.83197	−	0.767793i	0.189513	−	0.0249499i	0.224685	+	0.974431i	$0.427865\pi$
$948$	−0.524039	−	2.01309i	−0.0170200	−	0.0653823i
$949$	23.3739	+	3.07723i	0.758747	+	0.0998910i
$950$	−5.26559	−	6.04765i	−0.170838	−	0.196212i
$951$	−1.94371	−	1.94371i	−0.0630290	−	0.0630290i
$952$	−36.4877	+	36.4652i	−1.18257	+	1.18184i
$953$	−7.07749	+	7.07749i	−0.229263	+	0.229263i	−0.812385	−	0.583122i	$-0.801831\pi$
$953$	−7.07749	+	7.07749i	−0.229263	+	0.229263i	0.583122	+	0.812385i	$0.301831\pi$
$954$	11.1760	+	0.772573i	0.361838	+	0.0250130i
$955$	0.609231	−	4.62757i	0.0197142	−	0.149745i
$956$	−15.2715	+	11.5460i	−0.493915	+	0.373425i
$957$	0.100775	+	0.765462i	0.00325759	+	0.0247439i
$958$	−30.9499	−	6.27119i	−0.999945	−	0.202613i
$959$	−4.77043	+	3.25973i	−0.154045	+	0.105262i
$960$	−0.366748	−	0.941950i	−0.0118367	−	0.0304013i
$961$	10.1026	+	17.4983i	0.325892	+	0.564461i
$962$	46.0505	+	40.6768i	1.48473	+	1.31147i
$963$	−15.7912	+	12.1170i	−0.508866	+	0.390466i
$964$	1.23993	+	9.96734i	0.0399355	+	0.321026i
$965$	4.74220	+	11.4487i	0.152657	+	0.368546i
$966$	1.93275	−	3.40104i	0.0621852	−	0.109427i
$967$	−2.01214	−	2.01214i	−0.0647061	−	0.0647061i	0.674013	−	0.738719i	$-0.264569\pi$
$967$	−2.01214	−	2.01214i	−0.0647061	−	0.0647061i	−0.738719	+	0.674013i	$0.764569\pi$
$968$	−5.26507	−	6.13490i	−0.169226	−	0.197183i
$969$	0.379526	+	1.41641i	0.0121921	+	0.0455016i
$970$	0.321718	−	0.936757i	0.0103298	−	0.0300775i
$971$	−19.5250	+	25.4455i	−0.626589	+	0.816586i	−0.993519	−	0.113662i	$-0.963742\pi$
$971$	−19.5250	+	25.4455i	−0.626589	+	0.816586i	0.366931	+	0.930248i	$0.380409\pi$
$972$	6.20856	+	6.29781i	0.199140	+	0.202002i
$973$	−22.8363	−	25.5001i	−0.732097	−	0.817496i
$974$	−6.47191	−	9.76111i	−0.207373	−	0.312766i
$975$	1.67482	+	2.90088i	0.0536372	+	0.0929024i
$976$	43.8201	+	6.40650i	1.40265	+	0.205067i
$977$	−20.5849	−	11.8847i	−0.658570	−	0.380225i	0.133162	−	0.991094i	$-0.457487\pi$
$977$	−20.5849	−	11.8847i	−0.658570	−	0.380225i	−0.791732	+	0.610869i	$0.790820\pi$
$978$	4.65977	+	2.31865i	0.149003	+	0.0741422i
$979$	40.0830	+	16.6029i	1.28106	+	0.530632i
$980$	−6.61033	−	8.37544i	−0.211159	−	0.267544i
$981$	−4.35352	−	10.5103i	−0.138997	−	0.335569i
$982$	−3.25272	−	3.73582i	−0.103799	−	0.119215i
$983$	−12.6986	+	3.40257i	−0.405022	+	0.108525i	−0.455578	−	0.890196i	$-0.650567\pi$
$983$	−12.6986	+	3.40257i	−0.405022	+	0.108525i	0.0505560	+	0.998721i	$0.483901\pi$
$984$	−3.71408	−	3.32816i	−0.118400	−	0.106098i
$985$	−1.53789	+	5.73950i	−0.0490014	+	0.182876i
$986$	−6.81144	+	10.1157i	−0.216920	+	0.322150i
$987$	2.46555	+	0.135877i	0.0784794	+	0.00432503i
$988$	10.8710	−	4.41228i	0.345851	−	0.140373i
$989$	36.2479	−	4.77213i	1.15262	−	0.151745i
$990$	−8.93888	−	7.89578i	−0.284096	−	0.250944i
$991$	−7.99556	−	4.61624i	−0.253987	−	0.146640i	0.367601	−	0.929984i	$-0.380179\pi$
$991$	−7.99556	−	4.61624i	−0.253987	−	0.146640i	−0.621589	+	0.783344i	$0.713512\pi$
$992$	−8.51632	+	16.5198i	−0.270393	+	0.524503i
$993$			3.73554i			0.118544i
$994$	−3.48136	+	27.9150i	−0.110422	+	0.885409i
$995$	2.43562	+	1.00886i	0.0772142	+	0.0319832i
$996$	1.78773	+	1.39216i	0.0566465	+	0.0441122i
$997$	−49.3355	−	6.49515i	−1.56247	−	0.205703i	−0.700870	−	0.713289i	$-0.747205\pi$
$997$	−49.3355	−	6.49515i	−1.56247	−	0.205703i	−0.861601	+	0.507585i	$0.830538\pi$
$998$	−1.62957	−	3.33439i	−0.0515832	−	0.105548i
$999$	−9.08907	−	2.43541i	−0.287565	−	0.0770529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.be.a.115.12	yes	240
4.3	odd	2		896.2.bi.a.367.15		240
7.5	odd	6	inner	224.2.be.a.19.9	✓	240
28.19	even	6		896.2.bi.a.495.15		240
32.5	even	8		896.2.bi.a.143.15		240
32.27	odd	8	inner	224.2.be.a.59.9	yes	240
224.5	odd	24		896.2.bi.a.271.15		240
224.187	even	24	inner	224.2.be.a.187.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.be.a.19.9	✓	240	7.5	odd	6	inner
224.2.be.a.59.9	yes	240	32.27	odd	8	inner
224.2.be.a.115.12	yes	240	1.1	even	1	trivial
224.2.be.a.187.12	yes	240	224.187	even	24	inner
896.2.bi.a.143.15		240	32.5	even	8
896.2.bi.a.271.15		240	224.5	odd	24
896.2.bi.a.367.15		240	4.3	odd	2
896.2.bi.a.495.15		240	28.19	even	6

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.be (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.449803 - 1.34077i) q^{2} +(0.100927 + 0.131530i) q^{3} +(-1.59535 + 1.20617i) q^{4} +(-0.463954 + 0.604637i) q^{5} +(0.130955 - 0.194483i) q^{6} +(2.49637 - 0.876446i) q^{7} +(2.33480 + 1.59647i) q^{8} +(0.769343 - 2.87123i) q^{9} +O(q^{10})\)	\(q+(-0.449803 - 1.34077i) q^{2} +(0.100927 + 0.131530i) q^{3} +(-1.59535 + 1.20617i) q^{4} +(-0.463954 + 0.604637i) q^{5} +(0.130955 - 0.194483i) q^{6} +(2.49637 - 0.876446i) q^{7} +(2.33480 + 1.59647i) q^{8} +(0.769343 - 2.87123i) q^{9} +(1.01937 + 0.350091i) q^{10} +(0.485906 - 3.69082i) q^{11} +(-0.319662 - 0.0881027i) q^{12} +(1.74960 - 4.22391i) q^{13} +(-2.29799 - 2.95284i) q^{14} -0.126354 q^{15} +(1.09031 - 3.84854i) q^{16} +(-3.44670 + 5.96986i) q^{17} +(-4.19572 + 0.259971i) q^{18} +(-0.167475 - 1.27210i) q^{19} +(0.0108768 - 1.52422i) q^{20} +(0.367230 + 0.239891i) q^{21} +(-5.16712 + 1.00865i) q^{22} +(6.09119 + 1.63213i) q^{23} +(0.0256590 + 0.468224i) q^{24} +(1.14376 + 4.26858i) q^{25} +(-6.45029 - 0.445893i) q^{26} +(0.914812 - 0.378928i) q^{27} +(-2.92545 + 4.40928i) q^{28} +(-0.478719 + 1.15573i) q^{29} +(0.0568342 + 0.169412i) q^{30} +(1.64276 - 2.84535i) q^{31} +(-5.65044 + 0.269222i) q^{32} +(0.534496 - 0.308592i) q^{33} +(9.55457 + 1.93599i) q^{34} +(-0.628268 + 1.91603i) q^{35} +(2.23581 + 5.50858i) q^{36} +(-7.53920 - 5.78504i) q^{37} +(-1.63027 + 0.796740i) q^{38} +(0.732154 - 0.196180i) q^{39} +(-2.04852 + 0.671014i) q^{40} +(-7.52016 + 7.52016i) q^{41} +(0.156459 - 0.600276i) q^{42} +(5.35637 - 2.21868i) q^{43} +(3.67656 + 6.47425i) q^{44} +(1.37911 + 1.79729i) q^{45} +(-0.551519 - 8.90106i) q^{46} +(4.87523 - 2.81471i) q^{47} +(0.616241 - 0.245011i) q^{48} +(5.46368 - 4.37586i) q^{49} +(5.20874 - 3.45355i) q^{50} +(-1.13308 + 0.149173i) q^{51} +(2.30352 + 8.84895i) q^{52} +(-2.64212 - 0.347842i) q^{53} +(-0.919542 - 1.05611i) q^{54} +(2.00617 + 2.00617i) q^{55} +(7.22773 + 1.93906i) q^{56} +(0.150417 - 0.150417i) q^{57} +(1.76490 + 0.122004i) q^{58} +(-1.73785 + 13.2002i) q^{59} +(0.201579 - 0.152404i) q^{60} +(1.44512 + 10.9768i) q^{61} +(-4.55390 - 0.922729i) q^{62} +(-0.595914 - 7.84192i) q^{63} +(2.90255 + 7.45488i) q^{64} +(1.74220 + 3.01757i) q^{65} +(-0.654170 - 0.577834i) q^{66} +(-7.37852 + 5.66174i) q^{67} +(-1.70195 - 13.6813i) q^{68} +(0.400090 + 0.965903i) q^{69} +(2.85156 - 0.0194686i) q^{70} +(-5.31630 - 5.31630i) q^{71} +(6.38009 - 5.47550i) q^{72} +(1.33462 + 4.98088i) q^{73} +(-4.36527 + 12.7105i) q^{74} +(-0.446012 + 0.581254i) q^{75} +(1.80155 + 1.82744i) q^{76} +(-2.02181 - 9.63951i) q^{77} +(-0.592359 - 0.893411i) q^{78} +(3.13677 + 5.43304i) q^{79} +(1.82111 + 2.44479i) q^{80} +(-7.58065 - 4.37669i) q^{81} +(13.4654 + 6.70025i) q^{82} +(-6.31332 - 2.61506i) q^{83} +(-0.875210 + 0.0602298i) q^{84} +(-2.01049 - 4.85374i) q^{85} +(-5.38407 - 6.18372i) q^{86} +(-0.200329 + 0.0536781i) q^{87} +(7.02679 - 7.84159i) q^{88} +(-3.01639 + 11.2573i) q^{89} +(1.78944 - 2.65750i) q^{90} +(0.665615 - 12.0779i) q^{91} +(-11.6862 + 4.74319i) q^{92} +(0.540049 - 0.0710988i) q^{93} +(-5.96679 - 5.27052i) q^{94} +(0.846859 + 0.488934i) q^{95} +(-0.605692 - 0.716033i) q^{96} -0.918957i q^{97} +(-8.32462 - 5.35730i) q^{98} +(-10.2234 - 4.23466i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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