LMFDB - Embedded newform 722.2.i.a.501.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(7,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(114))

chi = DirichletCharacter(H, H._module([50]))

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

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

chi := DirichletCharacter("722.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.i (of order $57$, degree $36$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$16$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			501.15
Character	$\chi$	$=$	722.501
Dual form			722.2.i.a.49.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.926494 + 0.376309i) q^{2} +(2.59216 + 0.580917i) q^{3} +(0.716783 + 0.697297i) q^{4} +(0.0939720 + 3.40913i) q^{5} +(2.18302 + 1.51367i) q^{6} +(-0.993714 - 3.92409i) q^{7} +(0.401695 + 0.915773i) q^{8} +(3.66875 + 1.73133i) q^{9} +O(q^{10})$	\(q+(0.926494 + 0.376309i) q^{2} +(2.59216 + 0.580917i) q^{3} +(0.716783 + 0.697297i) q^{4} +(0.0939720 + 3.40913i) q^{5} +(2.18302 + 1.51367i) q^{6} +(-0.993714 - 3.92409i) q^{7} +(0.401695 + 0.915773i) q^{8} +(3.66875 + 1.73133i) q^{9} +(-1.19582 + 3.19390i) q^{10} +(-0.317620 + 3.83311i) q^{11} +(1.45294 + 2.22390i) q^{12} +(-0.511441 - 1.63517i) q^{13} +(0.556001 - 4.00959i) q^{14} +(-1.73683 + 8.89160i) q^{15} +(0.0275543 + 0.999620i) q^{16} +(-0.772071 + 0.751082i) q^{17} +(2.74756 + 2.98465i) q^{18} +(-1.71182 - 4.00870i) q^{19} +(-2.30982 + 2.50913i) q^{20} +(-0.296298 - 10.7491i) q^{21} +(-1.73671 + 3.43183i) q^{22} +(4.20121 - 0.941513i) q^{23} +(0.509271 + 2.60718i) q^{24} +(-6.62093 + 0.365287i) q^{25} +(0.141482 - 1.70743i) q^{26} +(2.21529 + 1.72423i) q^{27} +(2.02398 - 3.50563i) q^{28} +(8.47533 + 2.39659i) q^{29} +(-4.95515 + 7.58443i) q^{30} +(-2.97614 - 2.31643i) q^{31} +(-0.350638 + 0.936511i) q^{32} +(-3.05004 + 9.75152i) q^{33} +(-0.997958 + 0.405336i) q^{34} +(13.2843 - 3.75645i) q^{35} +(1.42245 + 3.79920i) q^{36} +(0.233873 - 2.82243i) q^{37} +(-0.0774779 - 4.35821i) q^{38} +(-0.375840 - 4.53572i) q^{39} +(-3.08424 + 1.45549i) q^{40} +(-4.23521 - 3.68845i) q^{41} +(3.77048 - 10.0705i) q^{42} +(-0.539492 - 1.44092i) q^{43} +(-2.90048 + 2.52603i) q^{44} +(-5.55756 + 12.6700i) q^{45} +(4.24669 + 0.708648i) q^{46} +(-7.86107 - 5.45074i) q^{47} +(-0.509271 + 2.60718i) q^{48} +(-8.25467 + 4.46721i) q^{49} +(-6.27171 - 2.15308i) q^{50} +(-2.43765 + 1.49842i) q^{51} +(0.773605 - 1.52869i) q^{52} +(6.57136 + 4.55648i) q^{53} +(1.40361 + 2.43112i) q^{54} +(-13.0974 - 0.722605i) q^{55} +(3.19440 - 2.48630i) q^{56} +(-2.10859 - 11.3856i) q^{57} +(6.95048 + 5.40978i) q^{58} +(-5.59389 - 4.87173i) q^{59} +(-7.44501 + 5.16226i) q^{60} +(7.33195 + 9.97547i) q^{61} +(-1.88569 - 3.26611i) q^{62} +(3.14819 - 16.1170i) q^{63} +(-0.677282 + 0.735724i) q^{64} +(5.52644 - 1.89723i) q^{65} +(-6.49543 + 7.88697i) q^{66} +(-6.11192 - 0.676468i) q^{67} -1.07713 q^{68} +11.4371 q^{69} +(13.7215 + 1.51869i) q^{70} +(3.57203 - 4.85992i) q^{71} +(-0.111781 + 4.05521i) q^{72} +(6.45622 - 6.28071i) q^{73} +(1.27879 - 2.52695i) q^{74} +(-17.3747 - 2.89933i) q^{75} +(1.56825 - 4.06701i) q^{76} +(15.3571 - 2.56264i) q^{77} +(1.35862 - 4.34375i) q^{78} +(-0.745202 - 1.99035i) q^{79} +(-3.40525 + 0.187873i) q^{80} +(-2.99617 - 3.63805i) q^{81} +(-2.53590 - 5.01107i) q^{82} +(-8.84493 + 4.78663i) q^{83} +(7.28295 - 7.91139i) q^{84} +(-2.63309 - 2.56151i) q^{85} +(0.0423952 - 1.53802i) q^{86} +(20.5772 + 11.1358i) q^{87} +(-3.63785 + 1.24887i) q^{88} +(8.96686 + 8.72310i) q^{89} +(-9.91687 + 9.64728i) q^{90} +(-5.90831 + 3.63183i) q^{91} +(3.66787 + 2.25463i) q^{92} +(-6.36899 - 7.73344i) q^{93} +(-5.23207 - 8.00828i) q^{94} +(13.5053 - 6.21252i) q^{95} +(-1.45294 + 2.22390i) q^{96} +(-7.63650 + 0.845207i) q^{97} +(-9.32896 + 1.03253i) q^{98} +(-7.80164 + 13.5128i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9}+O(q^{10}) $ 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9} + q^{10} + 34 q^{11} - 2 q^{12} + 2 q^{13} - 14 q^{14} + 38 q^{15} + 16 q^{16} + 12 q^{17} + 26 q^{18} + 7 q^{19} + 2 q^{20} + 75 q^{21} + 36 q^{22} - 45 q^{23} - q^{24} + 9 q^{25} + 4 q^{26} - 110 q^{27} + 33 q^{28} - 36 q^{29} - 57 q^{30} - 4 q^{31} - 16 q^{32} + 81 q^{33} + 7 q^{34} - 2 q^{35} + 13 q^{36} + 14 q^{37} - 30 q^{38} + 40 q^{39} + q^{40} + 11 q^{41} + q^{42} - 9 q^{43} + 2 q^{44} - 85 q^{45} - 33 q^{46} - 213 q^{47} + q^{48} - 76 q^{49} - 20 q^{50} - 3 q^{51} + 2 q^{52} - 144 q^{53} + 78 q^{54} - 6 q^{55} - 29 q^{56} - 8 q^{57} + 4 q^{58} - 5 q^{59} + 69 q^{61} - 2 q^{62} - 95 q^{63} - 32 q^{64} - 84 q^{65} - 5 q^{66} - 5 q^{67} - 62 q^{68} + 2 q^{69} + 211 q^{70} + 129 q^{71} - 13 q^{72} - 8 q^{73} - 31 q^{74} - 36 q^{75} - 18 q^{76} - 10 q^{77} + q^{78} - 2 q^{79} - q^{80} - 64 q^{81} - 49 q^{82} - 72 q^{83} + 2 q^{84} - 6 q^{85} - 10 q^{86} - 81 q^{87} + 4 q^{88} - 7 q^{89} + 81 q^{90} + 35 q^{91} - 7 q^{92} - 80 q^{93} - 27 q^{94} + 285 q^{95} + 2 q^{96} + 38 q^{97} - 171 q^{98} + 84 q^{99}+O(q^{100}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9 + q^10 + 34 * q^11 - 2 * q^12 + 2 * q^13 - 14 * q^14 + 38 * q^15 + 16 * q^16 + 12 * q^17 + 26 * q^18 + 7 * q^19 + 2 * q^20 + 75 * q^21 + 36 * q^22 - 45 * q^23 - q^24 + 9 * q^25 + 4 * q^26 - 110 * q^27 + 33 * q^28 - 36 * q^29 - 57 * q^30 - 4 * q^31 - 16 * q^32 + 81 * q^33 + 7 * q^34 - 2 * q^35 + 13 * q^36 + 14 * q^37 - 30 * q^38 + 40 * q^39 + q^40 + 11 * q^41 + q^42 - 9 * q^43 + 2 * q^44 - 85 * q^45 - 33 * q^46 - 213 * q^47 + q^48 - 76 * q^49 - 20 * q^50 - 3 * q^51 + 2 * q^52 - 144 * q^53 + 78 * q^54 - 6 * q^55 - 29 * q^56 - 8 * q^57 + 4 * q^58 - 5 * q^59 + 69 * q^61 - 2 * q^62 - 95 * q^63 - 32 * q^64 - 84 * q^65 - 5 * q^66 - 5 * q^67 - 62 * q^68 + 2 * q^69 + 211 * q^70 + 129 * q^71 - 13 * q^72 - 8 * q^73 - 31 * q^74 - 36 * q^75 - 18 * q^76 - 10 * q^77 + q^78 - 2 * q^79 - q^80 - 64 * q^81 - 49 * q^82 - 72 * q^83 + 2 * q^84 - 6 * q^85 - 10 * q^86 - 81 * q^87 + 4 * q^88 - 7 * q^89 + 81 * q^90 + 35 * q^91 - 7 * q^92 - 80 * q^93 - 27 * q^94 + 285 * q^95 + 2 * q^96 + 38 * q^97 - 171 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{7}{57}\right)$

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 $

$2$	0.926494	+	0.376309i	0.655130	+	0.266091i
$2$	0.926494	+	0.376309i	0.655130	+	0.266091i
$3$	2.59216	+	0.580917i	1.49658	+	0.335392i	0.888647	−	0.458593i	$-0.151646\pi$
$3$	2.59216	+	0.580917i	1.49658	+	0.335392i	0.607937	+	0.793985i	$0.291997\pi$
$4$	0.716783	+	0.697297i	0.358391	+	0.348648i
$5$	0.0939720	+	3.40913i	0.0420256	+	1.52461i	0.667644	+	0.744480i	$0.267303\pi$
$5$	0.0939720	+	3.40913i	0.0420256	+	1.52461i	−0.625619	+	0.780129i	$0.715153\pi$
$6$	2.18302	+	1.51367i	0.891213	+	0.617953i
$7$	−0.993714	−	3.92409i	−0.375588	−	1.48317i	−0.812128	−	0.583480i	$-0.801691\pi$
$7$	−0.993714	−	3.92409i	−0.375588	−	1.48317i	0.436539	−	0.899685i	$-0.356204\pi$
$8$	0.401695	+	0.915773i	0.142021	+	0.323775i
$9$	3.66875	+	1.73133i	1.22292	+	0.577109i
$10$	−1.19582	+	3.19390i	−0.378152	+	1.01000i
$11$	−0.317620	+	3.83311i	−0.0957662	+	1.15573i	0.764062	+	0.645143i	$0.223202\pi$
$11$	−0.317620	+	3.83311i	−0.0957662	+	1.15573i	−0.859828	+	0.510583i	$0.829430\pi$
$12$	1.45294	+	2.22390i	0.419429	+	0.641983i
$13$	−0.511441	−	1.63517i	−0.141848	−	0.453514i	0.856152	−	0.516724i	$-0.172849\pi$
$13$	−0.511441	−	1.63517i	−0.141848	−	0.453514i	−0.998000	+	0.0632101i	$0.979866\pi$
$14$	0.556001	−	4.00959i	0.148597	−	1.07161i
$15$	−1.73683	+	8.89160i	−0.448447	+	2.29580i
$16$	0.0275543	+	0.999620i	0.00688859	+	0.249905i
$17$	−0.772071	+	0.751082i	−0.187255	+	0.182164i	−0.784950	−	0.619559i	$-0.787311\pi$
$17$	−0.772071	+	0.751082i	−0.187255	+	0.182164i	0.597695	+	0.801723i	$0.296083\pi$
$18$	2.74756	+	2.98465i	0.647607	+	0.703489i
$19$	−1.71182	−	4.00870i	−0.392718	−	0.919659i
$19$	−1.71182	−	4.00870i	−0.392718	−	0.919659i
$20$	−2.30982	+	2.50913i	−0.516491	+	0.561059i
$21$	−0.296298	−	10.7491i	−0.0646574	−	2.34565i
$22$	−1.73671	+	3.43183i	−0.370267	+	0.731668i
$23$	4.20121	−	0.941513i	0.876012	−	0.196319i	0.242593	−	0.970128i	$-0.422002\pi$
$23$	4.20121	−	0.941513i	0.876012	−	0.196319i	0.633419	+	0.773809i	$0.281651\pi$
$24$	0.509271	+	2.60718i	0.103954	+	0.532189i
$25$	−6.62093	+	0.365287i	−1.32419	+	0.0730574i
$26$	0.141482	−	1.70743i	0.0277469	−	0.334855i
$27$	2.21529	+	1.72423i	0.426333	+	0.331828i
$28$	2.02398	−	3.50563i	0.382496	−	0.662502i
$29$	8.47533	+	2.39659i	1.57383	+	0.445036i	0.943522	−	0.331309i	$-0.107490\pi$
$29$	8.47533	+	2.39659i	1.57383	+	0.445036i	0.630307	+	0.776346i	$0.282929\pi$
$30$	−4.95515	+	7.58443i	−0.904683	+	1.38472i
$31$	−2.97614	−	2.31643i	−0.534531	−	0.416042i	0.310648	−	0.950525i	$-0.399454\pi$
$31$	−2.97614	−	2.31643i	−0.534531	−	0.416042i	−0.845180	+	0.534483i	$0.820507\pi$
$32$	−0.350638	+	0.936511i	−0.0619845	+	0.165553i
$33$	−3.05004	+	9.75152i	−0.530944	+	1.69752i
$34$	−0.997958	+	0.405336i	−0.171148	+	0.0695145i
$35$	13.2843	−	3.75645i	2.24546	−	0.634957i
$36$	1.42245	+	3.79920i	0.237075	+	0.633199i
$37$	0.233873	−	2.82243i	0.0384485	−	0.464004i	−0.949979	−	0.312313i	$-0.898896\pi$
$37$	0.233873	−	2.82243i	0.0384485	−	0.464004i	0.988428	−	0.151692i	$-0.0484721\pi$
$38$	−0.0774779	−	4.35821i	−0.0125686	−	0.706995i
$39$	−0.375840	−	4.53572i	−0.0601826	−	0.726296i
$40$	−3.08424	+	1.45549i	−0.487662	+	0.230133i
$41$	−4.23521	−	3.68845i	−0.661429	−	0.576039i	0.259513	−	0.965740i	$-0.416438\pi$
$41$	−4.23521	−	3.68845i	−0.661429	−	0.576039i	−0.920941	+	0.389701i	$0.872578\pi$
$42$	3.77048	−	10.0705i	0.581797	−	1.55391i
$43$	−0.539492	−	1.44092i	−0.0822718	−	0.219738i	0.888908	−	0.458085i	$-0.151465\pi$
$43$	−0.539492	−	1.44092i	−0.0822718	−	0.219738i	−0.971180	+	0.238347i	$0.923394\pi$
$44$	−2.90048	+	2.52603i	−0.437264	+	0.380813i
$45$	−5.55756	+	12.6700i	−0.828472	+	1.88873i
$46$	4.24669	+	0.708648i	0.626141	+	0.104484i
$47$	−7.86107	−	5.45074i	−1.14665	−	0.795073i	−0.165104	−	0.986276i	$-0.552796\pi$
$47$	−7.86107	−	5.45074i	−1.14665	−	0.795073i	−0.981550	+	0.191203i	$0.938761\pi$
$48$	−0.509271	+	2.60718i	−0.0735069	+	0.376314i
$49$	−8.25467	+	4.46721i	−1.17924	+	0.638172i
$50$	−6.27171	−	2.15308i	−0.886954	−	0.304492i
$51$	−2.43765	+	1.49842i	−0.341339	+	0.209820i
$52$	0.773605	−	1.52869i	0.107280	−	0.211991i
$53$	6.57136	+	4.55648i	0.902645	+	0.625880i	0.927505	−	0.373811i	$-0.121949\pi$
$53$	6.57136	+	4.55648i	0.902645	+	0.625880i	−0.0248599	+	0.999691i	$0.507914\pi$
$54$	1.40361	+	2.43112i	0.191007	+	0.330834i
$55$	−13.0974	−	0.722605i	−1.76606	−	0.0974360i
$56$	3.19440	−	2.48630i	0.426870	−	0.332246i
$57$	−2.10859	−	11.3856i	−0.279289	−	1.50806i
$58$	6.95048	+	5.40978i	0.912643	+	0.710338i
$59$	−5.59389	−	4.87173i	−0.728263	−	0.634245i	0.210983	−	0.977490i	$-0.432334\pi$
$59$	−5.59389	−	4.87173i	−0.728263	−	0.634245i	−0.939246	+	0.343245i	$0.888474\pi$
$60$	−7.44501	+	5.16226i	−0.961147	+	0.666445i
$61$	7.33195	+	9.97547i	0.938759	+	1.27723i	0.960734	+	0.277470i	$0.0894958\pi$
$61$	7.33195	+	9.97547i	0.938759	+	1.27723i	−0.0219750	+	0.999759i	$0.506995\pi$
$62$	−1.88569	−	3.26611i	−0.239483	−	0.414796i
$63$	3.14819	−	16.1170i	0.396634	−	2.03055i
$64$	−0.677282	+	0.735724i	−0.0846602	+	0.0919655i
$65$	5.52644	−	1.89723i	0.685470	−	0.235322i
$66$	−6.49543	+	7.88697i	−0.799532	+	0.970818i
$67$	−6.11192	−	0.676468i	−0.746690	−	0.0826437i	−0.271393	−	0.962469i	$-0.587484\pi$
$67$	−6.11192	−	0.676468i	−0.746690	−	0.0826437i	−0.475298	+	0.879825i	$0.657660\pi$
$68$	−1.07713			−0.130622
$69$	11.4371			1.37687
$70$	13.7215	+	1.51869i	1.64003	+	0.181518i
$71$	3.57203	−	4.85992i	0.423922	−	0.576766i	−0.540431	−	0.841389i	$-0.681739\pi$
$71$	3.57203	−	4.85992i	0.423922	−	0.576766i	0.964352	+	0.264623i	$0.0852474\pi$
$72$	−0.111781	+	4.05521i	−0.0131735	+	0.477912i
$73$	6.45622	−	6.28071i	0.755643	−	0.735101i	−0.214740	−	0.976671i	$-0.568890\pi$
$73$	6.45622	−	6.28071i	0.755643	−	0.735101i	0.970383	+	0.241570i	$0.0776624\pi$
$74$	1.27879	−	2.52695i	0.148656	−	0.293753i
$75$	−17.3747	−	2.89933i	−2.00626	−	0.334785i
$76$	1.56825	−	4.06701i	0.179891	−	0.466518i
$77$	15.3571	−	2.56264i	1.75010	−	0.292040i
$78$	1.35862	−	4.34375i	0.153833	−	0.491833i
$79$	−0.745202	−	1.99035i	−0.0838417	−	0.223931i	0.887873	−	0.460088i	$-0.152182\pi$
$79$	−0.745202	−	1.99035i	−0.0838417	−	0.223931i	−0.971715	+	0.236157i	$0.924112\pi$
$80$	−3.40525	+	0.187873i	−0.380718	+	0.0210048i
$81$	−2.99617	−	3.63805i	−0.332908	−	0.404228i
$82$	−2.53590	−	5.01107i	−0.280043	−	0.553381i
$83$	−8.84493	+	4.78663i	−0.970857	+	0.525401i	−0.882309	−	0.470671i	$-0.844012\pi$
$83$	−8.84493	+	4.78663i	−0.970857	+	0.525401i	−0.0885477	+	0.996072i	$0.528223\pi$
$84$	7.28295	−	7.91139i	0.794635	−	0.863203i
$85$	−2.63309	−	2.56151i	−0.285599	−	0.277835i
$86$	0.0423952	−	1.53802i	0.00457159	−	0.165849i
$87$	20.5772	+	11.1358i	2.20611	+	1.19388i
$88$	−3.63785	+	1.24887i	−0.387796	+	0.133130i
$89$	8.96686	+	8.72310i	0.950485	+	0.924646i	0.997239	−	0.0742600i	$-0.0236595\pi$
$89$	8.96686	+	8.72310i	0.950485	+	0.924646i	−0.0467535	+	0.998906i	$0.514888\pi$
$90$	−9.91687	+	9.64728i	−1.04533	+	1.01691i
$91$	−5.90831	+	3.63183i	−0.619360	+	0.380719i
$92$	3.66787	+	2.25463i	0.382401	+	0.235061i
$93$	−6.36899	−	7.73344i	−0.660434	−	0.801920i
$94$	−5.23207	−	8.00828i	−0.539647	−	0.825991i
$95$	13.5053	−	6.21252i	1.38562	−	0.637391i
$96$	−1.45294	+	2.22390i	−0.148290	+	0.226975i
$97$	−7.63650	+	0.845207i	−0.775369	+	0.0858178i	−0.488979	−	0.872295i	$-0.662631\pi$
$97$	−7.63650	+	0.845207i	−0.775369	+	0.0858178i	−0.286390	+	0.958113i	$0.592455\pi$
$98$	−9.32896	+	1.03253i	−0.942367	+	0.104301i
$99$	−7.80164	+	13.5128i	−0.784094	+	1.35809i
$100$	−5.00048	−	4.35492i	−0.500048	−	0.435492i
$101$	−6.71927	−	3.17090i	−0.668593	−	0.315516i	0.0622518	−	0.998060i	$-0.480172\pi$
$101$	−6.71927	−	3.17090i	−0.668593	−	0.315516i	−0.730845	+	0.682544i	$0.760874\pi$
$102$	−2.82233	+	0.470964i	−0.279453	+	0.0466324i
$103$	0.726660	−	2.86952i	0.0716000	−	0.282742i	−0.923237	−	0.384232i	$-0.874466\pi$
$103$	0.726660	−	2.86952i	0.0716000	−	0.282742i	0.994837	+	0.101490i	$0.0323610\pi$
$104$	1.29200	−	1.12520i	0.126691	−	0.110335i
$105$	36.6173	−	2.02023i	3.57348	−	0.197155i
$106$	4.37368	+	6.69441i	0.424809	+	0.650219i
$107$	9.59650	−	7.46925i	0.927728	−	0.722080i	−0.0330335	−	0.999454i	$-0.510517\pi$
$107$	9.59650	−	7.46925i	0.927728	−	0.722080i	0.960762	+	0.277374i	$0.0894642\pi$
$108$	0.385582	+	2.78061i	0.0371026	+	0.267565i
$109$	13.0733	−	9.06485i	1.25220	−	0.868255i	0.257027	−	0.966404i	$-0.417257\pi$
$109$	13.0733	−	9.06485i	1.25220	−	0.868255i	0.995172	+	0.0981489i	$0.0312922\pi$
$110$	−11.8628	−	5.59817i	−1.13107	−	0.533764i
$111$	2.24583	−	7.18032i	0.213165	−	0.681526i
$112$	3.89522	−	1.10146i	0.368063	−	0.104078i
$113$	−4.39035	+	17.3371i	−0.413010	+	1.63094i	0.317659	+	0.948205i	$0.397103\pi$
$113$	−4.39035	+	17.3371i	−0.413010	+	1.63094i	−0.730668	+	0.682733i	$0.760791\pi$
$114$	2.33092	−	11.3422i	0.218311	−	1.06229i
$115$	3.60454	+	14.2340i	0.336125	+	1.32733i
$116$	4.40383	+	7.62766i	0.408885	+	0.708210i
$117$	0.954659	−	6.88450i	0.0882582	−	0.636472i
$118$	−3.34943	−	6.61866i	−0.308340	−	0.609297i
$119$	3.71453	+	2.28331i	0.340510	+	0.209311i
$120$	−8.84037	+	1.98117i	−0.807011	+	0.180855i
$121$	−3.74187	−	0.624407i	−0.340170	−	0.0567643i
$122$	3.03914	+	12.0013i	0.275151	+	1.08655i
$123$	−8.83566	−	12.0213i	−0.796685	−	1.08393i
$124$	−0.518012	−	3.73563i	−0.0465188	−	0.335469i
$125$	−0.459340	−	5.54341i	−0.0410846	−	0.495817i
$126$	8.98174	−	13.7476i	0.800157	−	1.22473i
$127$	−5.82256	+	10.0850i	−0.516669	+	0.894896i	0.483144	+	0.875541i	$0.339495\pi$
$127$	−5.82256	+	10.0850i	−0.516669	+	0.894896i	−0.999813	+	0.0193555i	$0.993839\pi$
$128$	−0.904357	+	0.426776i	−0.0799346	+	0.0377221i
$129$	−0.561396	−	4.04849i	−0.0494282	−	0.356450i
$130$	5.83416	+	0.321879i	0.511689	+	0.0282307i
$131$	−2.44955	+	17.6649i	−0.214019	+	1.54339i	0.513974	+	0.857806i	$0.328173\pi$
$131$	−2.44955	+	17.6649i	−0.214019	+	1.54339i	−0.727993	+	0.685585i	$0.759547\pi$
$132$	−8.98592	+	4.86294i	−0.782124	+	0.423264i
$133$	−14.0294	+	10.7008i	−1.21651	+	0.927879i
$134$	−5.40810	−	2.92672i	−0.467189	−	0.252830i
$135$	−5.66995	+	7.71425i	−0.487992	+	0.663937i
$136$	−0.997958	−	0.405336i	−0.0855742	−	0.0347572i
$137$	−20.6733	−	2.28812i	−1.76624	−	0.195487i	−0.832642	−	0.553812i	$-0.813173\pi$
$137$	−20.6733	−	2.28812i	−1.76624	−	0.195487i	−0.933597	+	0.358325i	$0.883348\pi$
$138$	10.5964	+	4.30390i	0.902029	+	0.366373i
$139$	13.0558	−	15.8528i	1.10738	−	1.34462i	0.174405	−	0.984674i	$-0.444200\pi$
$139$	13.0558	−	15.8528i	1.10738	−	1.34462i	0.932975	−	0.359942i	$-0.117204\pi$
$140$	12.1413	+	6.57057i	1.02613	+	0.555314i
$141$	−17.2107	−	18.6958i	−1.44940	−	1.57447i
$142$	5.13829	−	3.15850i	0.431196	−	0.265055i
$143$	6.43022	−	1.44105i	0.537722	−	0.120506i
$144$	−1.62958	+	3.71507i	−0.135798	+	0.309589i
$145$	−7.37386	+	29.1187i	−0.612366	+	2.41818i
$146$	8.34514	−	3.38950i	0.690648	−	0.280517i
$147$	−23.9925	+	6.78443i	−1.97887	+	0.559571i
$148$	2.13571	−	1.85999i	0.175554	−	0.152890i
$149$	3.36692	+	17.2368i	0.275829	+	1.41209i	0.819638	+	0.572882i	$0.194175\pi$
$149$	3.36692	+	17.2368i	0.275829	+	1.41209i	−0.543809	+	0.839209i	$0.683018\pi$
$150$	−15.0065	−	9.22448i	−1.22528	−	0.753175i
$151$	6.34822	+	2.17934i	0.516610	+	0.177353i	0.570661	−	0.821186i	$-0.306687\pi$
$151$	6.34822	+	2.17934i	0.516610	+	0.177353i	−0.0540508	+	0.998538i	$0.517213\pi$
$152$	2.98343	−	3.17791i	0.241988	−	0.257763i
$153$	−4.13291	+	1.41883i	−0.334126	+	0.114705i
$154$	15.1926	+	3.40474i	1.22425	+	0.274362i
$155$	7.61733	−	10.3637i	0.611838	−	0.832436i
$156$	2.89335	−	3.51320i	0.231653	−	0.281281i
$157$	−18.8585	−	4.22630i	−1.50508	−	0.337295i	−0.613328	−	0.789829i	$-0.710169\pi$
$157$	−18.8585	−	4.22630i	−1.50508	−	0.337295i	−0.891747	+	0.452533i	$0.850520\pi$
$158$	0.0585606	−	2.12447i	0.00465883	−	0.169014i
$159$	14.3871	+	15.6285i	1.14097	+	1.23942i
$160$	−3.22564	−	1.10736i	−0.255009	−	0.0875448i
$161$	−7.86938	−	15.5503i	−0.620194	−	1.22554i
$162$	−1.40690	−	4.49812i	−0.110537	−	0.353406i
$163$	−3.24430	+	2.52514i	−0.254113	+	0.197784i	−0.733256	−	0.679953i	$-0.762000\pi$
$163$	−3.24430	+	2.52514i	−0.254113	+	0.197784i	0.479143	+	0.877737i	$0.340948\pi$
$164$	−0.463782	−	5.59701i	−0.0362153	−	0.437053i
$165$	−33.5308	−	9.48161i	−2.61037	−	0.738142i
$166$	−9.99603	+	1.10636i	−0.775842	+	0.0858702i
$167$	−19.9677	−	5.64633i	−1.54515	−	0.436926i	−0.610357	−	0.792127i	$-0.708974\pi$
$167$	−19.9677	−	5.64633i	−1.54515	−	0.436926i	−0.934790	+	0.355201i	$0.884412\pi$
$168$	9.72474	−	4.58921i	0.750280	−	0.354066i
$169$	8.27091	−	5.73492i	0.636224	−	0.441148i
$170$	−1.47562	−	3.36408i	−0.113175	−	0.258013i
$171$	0.660130	−	17.6707i	0.0504814	−	1.35131i
$172$	0.618050	−	1.40901i	0.0471259	−	0.107436i
$173$	−1.59600	−	8.17061i	−0.121341	−	0.621200i	−0.991678	−	0.128743i	$-0.958906\pi$
$173$	−1.59600	−	8.17061i	−0.121341	−	0.621200i	0.870337	−	0.492457i	$-0.163901\pi$
$174$	14.8741	+	18.0607i	1.12760	+	1.36917i
$175$	8.01273	+	25.6181i	0.605705	+	1.93655i
$176$	−3.84041	−	0.211881i	−0.289481	−	0.0159711i
$177$	−11.6702	−	15.8779i	−0.877186	−	1.19345i
$178$	5.02516	+	11.4562i	0.376652	+	0.858679i
$179$	−16.2186	+	2.70641i	−1.21224	+	0.202287i	−0.735970	−	0.677014i	$-0.763274\pi$
$179$	−16.2186	+	2.70641i	−1.21224	+	0.202287i	−0.476267	+	0.879301i	$0.658010\pi$
$180$	−12.8183	+	5.20634i	−0.955418	+	0.388057i
$181$	20.9859	−	8.52372i	1.55987	−	0.633563i	0.576812	−	0.816877i	$-0.304296\pi$
$181$	20.9859	−	8.52372i	1.55987	−	0.633563i	0.983054	+	0.183314i	$0.0586824\pi$
$182$	−6.84071	+	1.14151i	−0.507067	+	0.0846145i
$183$	13.2107	+	30.1173i	0.976560	+	2.22633i
$184$	2.54982	+	3.46915i	0.187975	+	0.255749i
$185$	9.64400	+	0.532075i	0.709041	+	0.0391189i
$186$	−2.99067	−	9.56170i	−0.219286	−	0.701098i
$187$	−2.63375	−	3.19799i	−0.192599	−	0.233860i
$188$	−1.83389	−	9.38850i	−0.133750	−	0.684727i
$189$	4.56466	−	10.4064i	0.332030	−	0.756953i
$190$	14.8504	−	0.673682i	1.07736	−	0.0488740i
$191$	0.376549	+	0.858444i	0.0272461	+	0.0621148i	0.928870	−	0.370407i	$-0.120782\pi$
$191$	0.376549	+	0.858444i	0.0272461	+	0.0621148i	−0.901623	+	0.432522i	$0.857624\pi$
$192$	−2.18302	+	1.51367i	−0.157546	+	0.109240i
$193$	2.06574	−	0.974845i	0.148695	−	0.0701709i	−0.350984	−	0.936381i	$-0.614153\pi$
$193$	2.06574	−	0.974845i	0.148695	−	0.0701709i	0.499679	+	0.866210i	$0.333451\pi$
$194$	−7.39323	−	2.09061i	−0.530803	−	0.150097i
$195$	15.4275	−	1.70752i	1.10479	−	0.122278i
$196$	−9.03177	−	2.55394i	−0.645127	−	0.182424i
$197$	0.0644780	+	0.778134i	0.00459387	+	0.0554398i	0.998496	−	0.0548275i	$-0.0174609\pi$
$197$	0.0644780	+	0.778134i	0.00459387	+	0.0554398i	−0.993902	+	0.110267i	$0.964829\pi$
$198$	−12.3132	+	9.58373i	−0.875059	+	0.681086i
$199$	2.51253	+	8.03301i	0.178109	+	0.569445i	1.00000		0.000199400i	$-6.34708e-5\pi$
$199$	2.51253	+	8.03301i	0.178109	+	0.569445i	−0.821891	+	0.569644i	$0.807081\pi$
$200$	−2.99412	−	5.91654i	−0.211716	−	0.418362i
$201$	−15.4501	−	5.30403i	−1.08977	−	0.374117i
$202$	−5.03213	−	5.46635i	−0.354059	−	0.384611i
$203$	0.982395	−	35.6395i	0.0689506	−	2.50140i
$204$	−2.79210	−	0.625725i	−0.195486	−	0.0438095i
$205$	12.1764	−	14.7850i	0.850437	−	1.03263i
$206$	1.75307	−	2.38514i	0.122142	−	0.166181i
$207$	17.0433	+	3.81949i	1.18459	+	0.265473i
$208$	1.62045	−	0.556303i	0.112358	−	0.0385727i
$209$	15.9095	−	5.28834i	1.10048	−	0.365802i
$210$	34.6860	+	11.9077i	2.39356	+	0.821710i
$211$	1.93603	+	1.19008i	0.133282	+	0.0819282i	0.588709	−	0.808345i	$-0.299636\pi$
$211$	1.93603	+	1.19008i	0.133282	+	0.0819282i	−0.455427	+	0.890273i	$0.650513\pi$
$212$	1.53302	+	7.84819i	0.105288	+	0.539016i
$213$	12.0825	−	10.5226i	0.827877	−	0.720999i
$214$	11.7018	−	3.30897i	0.799922	−	0.226196i
$215$	4.86159	−	1.97461i	0.331558	−	0.134667i
$216$	−0.689132	+	2.72132i	−0.0468895	+	0.185162i
$217$	−6.13242	+	13.9805i	−0.416296	+	0.949059i
$218$	15.5236	−	3.47891i	1.05139	−	0.235622i
$219$	20.3841	−	12.5301i	1.37743	−	0.846703i
$220$	−8.88413	−	9.65074i	−0.598968	−	0.650653i
$221$	1.62301	+	0.878331i	0.109176	+	0.0590829i
$222$	4.78277	−	5.80740i	0.320999	−	0.389767i
$223$	−7.44999	−	3.02593i	−0.498889	−	0.202631i	0.112970	−	0.993598i	$-0.463964\pi$
$223$	−7.44999	−	3.02593i	−0.498889	−	0.202631i	−0.611858	+	0.790967i	$0.709578\pi$
$224$	4.02338	+	0.445308i	0.268824	+	0.0297534i
$225$	−24.9230	−	10.1229i	−1.66153	−	0.674857i
$226$	−10.5917	+	14.4106i	−0.704553	+	0.958579i
$227$	12.2999	+	6.65635i	0.816371	+	0.441798i	0.829765	−	0.558113i	$-0.188474\pi$
$227$	12.2999	+	6.65635i	0.816371	+	0.441798i	−0.0133946	+	0.999910i	$0.504264\pi$
$228$	6.42775	−	9.63132i	0.425688	−	0.637850i
$229$	19.7709	−	10.6995i	1.30650	−	0.707040i	0.334579	−	0.942368i	$-0.391406\pi$
$229$	19.7709	−	10.6995i	1.30650	−	0.707040i	0.971916	+	0.235328i	$0.0756163\pi$
$230$	−2.01680	+	14.5441i	−0.132984	+	0.959011i
$231$	41.2967	+	2.27840i	2.71712	+	0.149908i
$232$	1.20976	+	8.72418i	0.0794249	+	0.572771i
$233$	−20.6640	+	9.75157i	−1.35374	+	0.638846i	−0.959903	−	0.280333i	$-0.909555\pi$
$233$	−20.6640	+	9.75157i	−1.35374	+	0.638846i	−0.393839	+	0.919179i	$0.628853\pi$
$234$	3.47519	−	6.01920i	0.227180	−	0.393488i
$235$	17.8436	−	27.3116i	1.16399	−	1.78161i
$236$	−0.612566	−	7.39257i	−0.0398747	−	0.481216i
$237$	−0.775457	−	5.59219i	−0.0503714	−	0.363252i
$238$	2.58226	+	3.51329i	0.167383	+	0.227733i
$239$	4.34816	+	17.1705i	0.281259	+	1.11067i	0.935199	+	0.354121i	$0.115220\pi$
$239$	4.34816	+	17.1705i	0.281259	+	1.11067i	−0.653940	+	0.756546i	$0.726885\pi$
$240$	−8.93608	−	1.49117i	−0.576822	−	0.0962545i
$241$	−2.74540	+	0.615259i	−0.176847	+	0.0396323i	−0.306205	−	0.951966i	$-0.599059\pi$
$241$	−2.74540	+	0.615259i	−0.176847	+	0.0396323i	0.129358	+	0.991598i	$0.458708\pi$
$242$	−3.23185	−	1.98661i	−0.207751	−	0.127704i
$243$	−9.45581	−	18.6852i	−0.606591	−	1.19866i
$244$	−1.70045	+	12.2628i	−0.108860	+	0.785044i
$245$	−16.0050	−	27.7215i	−1.02252	−	1.77106i
$246$	−3.66244	−	14.4627i	−0.233509	−	0.922105i
$247$	−5.67940	+	4.84932i	−0.361372	+	0.308555i
$248$	0.925818	−	3.65597i	0.0587895	−	0.232154i
$249$	−25.7081	+	7.26956i	−1.62918	+	0.460689i
$250$	1.66046	−	5.30879i	0.105017	−	0.335757i
$251$	−21.0545	−	9.93586i	−1.32895	−	0.627146i	−0.374974	−	0.927035i	$-0.622349\pi$
$251$	−21.0545	−	9.93586i	−1.32895	−	0.627146i	−0.953974	+	0.299889i	$0.903050\pi$
$252$	13.4949	−	9.35713i	0.850097	−	0.589444i
$253$	2.27453	+	16.4027i	0.142999	+	1.03123i
$254$	−9.18964	+	7.15258i	−0.576609	+	0.448793i
$255$	−5.33736	−	8.16944i	−0.334239	−	0.511590i
$256$	−0.998482	+	0.0550878i	−0.0624051	+	0.00344299i
$257$	−14.9190	+	12.9930i	−0.930624	+	0.810481i	−0.982132	−	0.188191i	$-0.939737\pi$
$257$	−14.9190	+	12.9930i	−0.930624	+	0.810481i	0.0515085	+	0.998673i	$0.483597\pi$
$258$	1.00336	−	3.96216i	0.0624662	−	0.246674i
$259$	−11.3079	+	1.88695i	−0.702636	+	0.117249i
$260$	5.28419	+	2.49367i	0.327711	+	0.154651i
$261$	26.9446	+	23.4661i	1.66783	+	1.45251i
$262$	−8.91697	+	15.4446i	−0.550892	+	0.954173i
$263$	4.62578	−	0.511982i	0.285238	−	0.0315701i	0.0337492	−	0.999430i	$-0.489255\pi$
$263$	4.62578	−	0.511982i	0.285238	−	0.0315701i	0.251489	+	0.967860i	$0.419080\pi$
$264$	−10.1554	+	1.12400i	−0.625020	+	0.0691772i
$265$	−14.9161	+	22.8308i	−0.916289	+	1.40248i
$266$	−17.0250	+	4.63484i	−1.04387	+	0.284180i
$267$	18.1761	+	27.8207i	1.11236	+	1.70260i
$268$	−3.90922	−	4.74671i	−0.238794	−	0.289951i
$269$	−11.6559	−	7.16488i	−0.710676	−	0.436851i	0.120607	−	0.992700i	$-0.461516\pi$
$269$	−11.6559	−	7.16488i	−0.710676	−	0.436851i	−0.831283	+	0.555850i	$0.812393\pi$
$270$	−8.15612	+	5.01355i	−0.496366	+	0.305115i
$271$	−5.56498	+	5.41370i	−0.338049	+	0.328859i	−0.846657	−	0.532139i	$-0.821388\pi$
$271$	−5.56498	+	5.41370i	−0.338049	+	0.328859i	0.508608	+	0.860998i	$0.330160\pi$
$272$	−0.772071	−	0.751082i	−0.0468137	−	0.0455410i
$273$	−17.4251	+	5.98204i	−1.05461	+	0.362049i
$274$	−18.2926	−	9.89948i	−1.10510	−	0.598050i
$275$	0.702759	−	25.4948i	0.0423779	−	1.53739i
$276$	8.19794	+	7.97508i	0.493458	+	0.480044i
$277$	−14.4365	+	15.6822i	−0.867403	+	0.942250i	−0.998795	−	0.0490800i	$-0.984371\pi$
$277$	−14.4365	+	15.6822i	−0.867403	+	0.942250i	0.131392	+	0.991330i	$0.458055\pi$
$278$	18.0617	−	9.77449i	1.08327	−	0.586235i
$279$	−6.90825	−	13.6511i	−0.413586	−	0.817269i
$280$	8.77632	+	10.6565i	0.524485	+	0.636847i
$281$	−5.11990	+	0.282473i	−0.305427	+	0.0168509i	−0.207153	−	0.978308i	$-0.566420\pi$
$281$	−5.11990	+	0.282473i	−0.305427	+	0.0168509i	−0.0982741	+	0.995159i	$0.531332\pi$
$282$	−8.91021	−	23.7981i	−0.530596	−	1.41716i
$283$	−2.80184	+	8.95798i	−0.166552	+	0.532497i	−0.999792	−	0.0204155i	$-0.993501\pi$
$283$	−2.80184	+	8.95798i	−0.166552	+	0.532497i	0.833239	+	0.552912i	$0.186484\pi$
$284$	5.94917	−	0.992741i	0.353018	−	0.0589083i
$285$	38.6169	−	8.25837i	2.28747	−	0.489184i
$286$	6.49984	+	1.08463i	0.384344	+	0.0641356i
$287$	−10.2652	+	20.2846i	−0.605936	+	1.19736i
$288$	−2.90781	+	2.82876i	−0.171344	+	0.166686i
$289$	−0.436455	+	15.8338i	−0.0256738	+	0.931398i
$290$	−17.7895	+	24.2035i	−1.04463	+	1.42128i
$291$	−20.2860	−	2.24526i	−1.18919	−	0.131619i
$292$	9.00722			0.527108
$293$	11.9049			0.695491			0.347746	−	0.937589i	$-0.386947\pi$
$293$	11.9049			0.695491			0.347746	+	0.937589i	$0.386947\pi$
$294$	−24.7820	−	2.74287i	−1.44531	−	0.159967i
$295$	16.0827	−	19.5281i	0.936370	−	1.13697i
$296$	2.67865	−	0.919582i	0.155693	−	0.0534496i
$297$	−7.31279	+	7.94380i	−0.424331	+	0.460946i
$298$	−3.36692	+	17.2368i	−0.195041	+	0.998499i
$299$	−3.68820	−	6.38815i	−0.213294	−	0.369436i
$300$	−10.4322	−	14.1935i	−0.602303	−	0.819463i
$301$	−5.11819	+	3.54888i	−0.295008	+	0.204554i
$302$	5.06148	+	4.40804i	0.291255	+	0.253654i
$303$	−15.5754	−	12.1228i	−0.894783	−	0.696438i
$304$	3.96001	−	1.82163i	0.227122	−	0.104477i
$305$	−33.3187	+	25.9330i	−1.90782	+	1.48492i
$306$	−4.36303	−	0.240715i	−0.249418	−	0.0137608i
$307$	−3.63956	−	6.30390i	−0.207721	−	0.359783i	0.743276	−	0.668985i	$-0.233271\pi$
$307$	−3.63956	−	6.30390i	−0.207721	−	0.359783i	−0.950996	+	0.309203i	$0.899938\pi$
$308$	12.7946	+	8.87158i	0.729040	+	0.505505i
$309$	3.55057	−	7.01612i	0.201985	−	0.399133i
$310$	10.9574	−	6.73548i	0.622337	−	0.382549i
$311$	3.20237	+	1.09938i	0.181590	+	0.0623399i	0.413995	−	0.910279i	$-0.364133\pi$
$311$	3.20237	+	1.09938i	0.181590	+	0.0623399i	−0.232405	+	0.972619i	$0.574659\pi$
$312$	4.00272	−	2.16616i	0.226609	−	0.122635i
$313$	4.11830	−	21.0834i	0.232780	−	1.19171i	−0.663486	−	0.748189i	$-0.730924\pi$
$313$	4.11830	−	21.0834i	0.232780	−	1.19171i	0.896266	−	0.443516i	$-0.146269\pi$
$314$	−15.8819	−	11.0123i	−0.896269	−	0.621459i
$315$	55.2406	+	9.21803i	3.11246	+	0.519377i
$316$	0.853714	−	1.94627i	0.0480251	−	0.109486i
$317$	−18.7699	+	16.3467i	−1.05422	+	0.918121i	−0.996777	−	0.0802278i	$-0.974435\pi$
$317$	−18.7699	+	16.3467i	−1.05422	+	0.918121i	−0.0574434	+	0.998349i	$0.518295\pi$
$318$	7.44837	+	19.8937i	0.417684	+	1.11558i
$319$	−11.8783	+	31.7257i	−0.665060	+	1.77630i
$320$	−2.57182	−	2.23980i	−0.143769	−	0.125209i
$321$	29.2147	−	13.7867i	1.63060	−	0.769500i
$322$	−1.43920	−	17.3686i	−0.0802036	−	0.967914i
$323$	4.33251	+	1.80928i	0.241067	+	0.100671i
$324$	0.389197	−	4.69691i	0.0216221	−	0.260939i
$325$	3.98352	+	10.6395i	0.220966	+	0.590174i
$326$	−3.95606	+	1.11867i	−0.219106	+	0.0619572i
$327$	39.1541	−	15.9030i	2.16523	−	0.879439i
$328$	1.67652	−	5.36013i	0.0925702	−	0.295963i
$329$	−13.5775	+	36.2640i	−0.748554	+	1.99930i
$330$	−27.4981	−	21.4026i	−1.51372	−	1.17818i
$331$	4.85193	−	7.42644i	0.266686	−	0.408194i	−0.678563	−	0.734542i	$-0.737397\pi$
$331$	4.85193	−	7.42644i	0.266686	−	0.408194i	0.945250	+	0.326348i	$0.105818\pi$
$332$	−9.67759	−	2.73656i	−0.531127	−	0.150188i
$333$	5.74457	−	9.94989i	0.314801	−	0.545250i
$334$	−16.3752	−	12.7453i	−0.896010	−	0.697393i
$335$	1.73182	−	20.8999i	0.0946192	−	1.14188i
$336$	10.7369	−	0.592370i	0.585745	−	0.0323164i
$337$	−3.44054	−	17.6136i	−0.187418	−	0.959475i	−0.949921	−	0.312491i	$-0.898837\pi$
$337$	−3.44054	−	17.6136i	−0.187418	−	0.959475i	0.762503	−	0.646985i	$-0.223970\pi$
$338$	9.82105	−	2.20095i	0.534195	−	0.119716i
$339$	−21.4519	+	42.3901i	−1.16511	+	2.30231i
$340$	−0.101220	−	3.67209i	−0.00548945	−	0.199147i
$341$	9.82440	−	10.6721i	0.532021	−	0.577929i
$342$	7.26124	−	16.1233i	0.392643	−	0.871851i
$343$	6.54125	+	7.10569i	0.353194	+	0.383671i
$344$	1.10284	−	1.07286i	0.0594614	−	0.0578449i
$345$	1.07477	+	38.9907i	0.0578637	+	2.09919i
$346$	1.59600	−	8.17061i	0.0858013	−	0.439255i
$347$	−2.58961	+	18.6749i	−0.139018	+	1.00252i	0.784816	+	0.619728i	$0.212757\pi$
$347$	−2.58961	+	18.6749i	−0.139018	+	1.00252i	−0.923834	+	0.382793i	$0.874962\pi$
$348$	6.98440	+	22.3304i	0.374403	+	1.19703i
$349$	10.6910	+	16.3638i	0.572276	+	0.875934i	0.999603	−	0.0281632i	$-0.00896581\pi$
$349$	10.6910	+	16.3638i	0.572276	+	0.875934i	−0.427327	+	0.904097i	$0.640545\pi$
$350$	−2.21659	+	26.7503i	−0.118482	+	1.42986i
$351$	1.68642	−	4.50421i	0.0900142	−	0.240417i
$352$	−3.47838	−	1.64149i	−0.185398	−	0.0874916i
$353$	4.63520	+	10.5672i	0.246707	+	0.562434i	0.994879	−	0.101070i	$-0.0322265\pi$
$353$	4.63520	+	10.5672i	0.246707	+	0.562434i	−0.748173	+	0.663504i	$0.769069\pi$
$354$	−4.83738	−	19.1024i	−0.257104	−	1.01528i
$355$	16.9038	+	11.7208i	0.897159	+	0.622076i
$356$	0.344701	+	12.5051i	0.0182691	+	0.662770i
$357$	8.30223	+	8.07654i	0.439401	+	0.427456i
$358$	−16.0449	−	3.59575i	−0.848000	−	0.190041i
$359$	13.4375	+	5.45786i	0.709206	+	0.288055i	0.702259	−	0.711921i	$-0.252175\pi$
$359$	13.4375	+	5.45786i	0.709206	+	0.288055i	0.00694694	+	0.999976i	$0.497789\pi$
$360$	−13.8353			−0.729182
$361$	−13.1394	+	13.7243i	−0.691545	+	0.722333i
$362$	22.6508			1.19050
$363$	−9.33679	−	3.79228i	−0.490054	−	0.199043i
$364$	−6.76744	−	1.51662i	−0.354710	−	0.0794924i
$365$	22.0184	+	21.4199i	1.15250	+	1.12117i
$366$	0.906186	+	32.8748i	0.0473671	+	1.71839i
$367$	29.0173	+	20.1201i	1.51469	+	1.05026i	0.978520	+	0.206150i	$0.0660936\pi$
$367$	29.0173	+	20.1201i	1.51469	+	1.05026i	0.536168	+	0.844111i	$0.319871\pi$
$368$	1.05692	+	4.17367i	0.0550956	+	0.217568i
$369$	−9.15204	−	20.8645i	−0.476436	−	1.08616i
$370$	8.73489	+	4.12209i	0.454105	+	0.214297i
$371$	11.3500	−	30.3144i	0.589261	−	1.57385i
$372$	0.827320	−	9.98427i	0.0428946	−	0.517660i
$373$	−5.27780	−	8.07827i	−0.273274	−	0.418277i	0.673986	−	0.738745i	$-0.264581\pi$
$373$	−5.27780	−	8.07827i	−0.273274	−	0.418277i	−0.947259	+	0.320468i	$0.896160\pi$
$374$	−1.23672	−	3.95402i	−0.0639494	−	0.204458i
$375$	2.02957	−	14.6362i	0.104807	−	0.755812i
$376$	1.83389	−	9.38850i	0.0945757	−	0.484175i
$377$	−0.415796	−	15.0843i	−0.0214146	−	0.776881i
$378$	8.14516	−	7.92373i	0.418942	−	0.407553i
$379$	−6.80192	−	7.38886i	−0.349391	−	0.379540i	0.536133	−	0.844134i	$-0.319885\pi$
$379$	−6.80192	−	7.38886i	−0.349391	−	0.379540i	−0.885524	+	0.464594i	$0.846200\pi$
$380$	14.0123	+	4.96419i	0.718818	+	0.254658i
$381$	−20.9515	+	22.7594i	−1.07338	+	1.16600i
$382$	0.0258294	+	0.937042i	0.00132155	+	0.0479433i
$383$	9.63792	−	19.0451i	0.492475	−	0.973157i	−0.501666	−	0.865062i	$-0.667279\pi$
$383$	9.63792	−	19.0451i	0.492475	−	0.973157i	0.994141	−	0.108095i	$-0.0344751\pi$
$384$	−2.59216	+	0.580917i	−0.132281	+	0.0296448i
$385$	10.1795	+	52.1135i	0.518796	+	2.65595i
$386$	2.28074	−	0.125832i	0.116086	−	0.00640467i
$387$	0.515439	−	6.22042i	0.0262012	−	0.316202i
$388$	−6.06307	−	4.71908i	−0.307806	−	0.239575i
$389$	−8.91304	+	15.4378i	−0.451909	+	0.782729i	−0.998505	−	0.0546675i	$-0.982590\pi$
$389$	−8.91304	+	15.4378i	−0.451909	+	0.782729i	0.546596	+	0.837397i	$0.315923\pi$
$390$	14.9361	+	4.22352i	0.756318	+	0.213866i
$391$	−2.53648	+	3.88237i	−0.128275	+	0.196340i
$392$	−7.40681	−	5.76495i	−0.374100	−	0.291174i
$393$	−16.6115	+	44.3673i	−0.837938	+	2.23803i
$394$	−0.233081	+	0.745200i	−0.0117424	+	0.0375426i
$395$	6.71532	−	2.72753i	0.337884	−	0.137237i
$396$	−15.0145	+	4.24571i	−0.754509	+	0.213355i
$397$	3.11737	+	8.32612i	0.156456	+	0.417876i	0.991135	−	0.132862i	$-0.0424166\pi$
$397$	3.11737	+	8.32612i	0.156456	+	0.417876i	−0.834678	+	0.550738i	$0.814346\pi$
$398$	−0.695051	+	8.38802i	−0.0348398	+	0.420454i
$399$	−42.5828	+	19.5883i	−2.13181	+	0.980642i
$400$	−0.547584	−	6.60835i	−0.0273792	−	0.330418i
$401$	34.9260	−	16.4820i	1.74412	−	0.823071i	0.759028	−	0.651058i	$-0.225675\pi$
$401$	34.9260	−	16.4820i	1.74412	−	0.823071i	0.985095	−	0.172013i	$-0.0550270\pi$
$402$	−12.3185	−	10.7282i	−0.614390	−	0.535073i
$403$	−2.26562	+	6.05121i	−0.112859	+	0.301432i
$404$	−2.60520	−	6.95817i	−0.129613	−	0.346182i
$405$	12.1210	−	10.5562i	0.602299	−	0.524542i
$406$	14.3216	−	32.6501i	0.710771	−	1.62040i
$407$	10.7444	+	1.79292i	0.532580	+	0.0888719i
$408$	−2.35140	−	1.63042i	−0.116412	−	0.0807180i
$409$	−1.82704	+	9.35343i	−0.0903413	+	0.462497i	0.908649	+	0.417562i	$0.137115\pi$
$409$	−1.82704	+	9.35343i	−0.0903413	+	0.462497i	−0.998990	+	0.0449355i	$0.985692\pi$
$410$	16.8451	−	9.11611i	0.831920	−	0.450213i
$411$	−52.2593	−	17.9406i	−2.57776	−	0.884946i
$412$	2.52176	−	1.55012i	0.124238	−	0.0763690i
$413$	−13.5583	+	26.7920i	−0.667163	+	1.31835i
$414$	14.3532	+	9.95227i	0.705420	+	0.489128i
$415$	−17.1494	−	29.7037i	−0.841833	−	1.45810i
$416$	1.71068	+	0.0943810i	0.0838731	+	0.00462741i
$417$	43.0519	−	33.5086i	2.10826	−	1.64092i
$418$	16.7301	+	1.08728i	0.818296	+	0.0531804i
$419$	15.0812	+	11.7381i	0.736763	+	0.573446i	0.911564	−	0.411158i	$-0.134876\pi$
$419$	15.0812	+	11.7381i	0.736763	+	0.573446i	−0.174801	+	0.984604i	$0.555928\pi$
$420$	27.6554	+	24.0851i	1.34944	+	1.17523i
$421$	−18.5854	+	12.8868i	−0.905795	+	0.628064i	−0.928361	−	0.371681i	$-0.878782\pi$
$421$	−18.5854	+	12.8868i	−0.905795	+	0.628064i	0.0225653	+	0.999745i	$0.492817\pi$
$422$	1.34589	+	1.83115i	0.0655168	+	0.0891388i
$423$	−19.4033	−	33.6075i	−0.943421	−	1.63405i
$424$	−1.53302	+	7.84819i	−0.0744498	+	0.381142i
$425$	4.83747	−	5.25489i	0.234652	−	0.254900i
$426$	15.1541	−	5.20241i	0.734219	−	0.252058i
$427$	31.8588	−	38.6840i	1.54175	−	1.87205i
$428$	12.0869	+	1.33778i	0.584242	+	0.0646639i
$429$	17.5053			0.845163
$430$	5.24729			0.253047
$431$	33.2394	+	3.67894i	1.60109	+	0.177208i	0.865744	−	0.500487i	$-0.166846\pi$
$431$	33.2394	+	3.67894i	1.60109	+	0.177208i	0.735343	+	0.677696i	$0.237021\pi$
$432$	−1.66253	+	2.26196i	−0.0799888	+	0.108829i
$433$	−0.856376	+	31.0677i	−0.0411548	+	1.49302i	0.644226	+	0.764835i	$0.277180\pi$
$433$	−0.856376	+	31.0677i	−0.0411548	+	1.49302i	−0.685381	+	0.728185i	$0.740364\pi$
$434$	−10.9427	+	10.6452i	−0.525264	+	0.510985i
$435$	−36.0298	+	71.1968i	−1.72749	+	3.41362i
$436$	15.6916	+	2.61847i	0.751493	+	0.125402i
$437$	−10.9659	−	15.2297i	−0.524572	−	0.728535i
$438$	23.6009	−	3.93830i	1.12770	−	0.188179i
$439$	−3.59795	+	11.5033i	−0.171721	+	0.549022i	−0.999935	−	0.0113895i	$-0.996375\pi$
$439$	−3.59795	+	11.5033i	−0.171721	+	0.549022i	0.828214	+	0.560411i	$0.189357\pi$
$440$	−4.59943	−	12.2845i	−0.219269	−	0.585642i
$441$	−38.0186	+	2.09754i	−1.81041	+	0.0998830i
$442$	1.17319	+	1.42452i	0.0558029	+	0.0677577i
$443$	1.16020	+	2.29263i	0.0551230	+	0.108926i	0.918152	−	0.396228i	$-0.129681\pi$
$443$	1.16020	+	2.29263i	0.0551230	+	0.108926i	−0.863029	+	0.505154i	$0.831436\pi$
$444$	6.61659	−	3.58072i	0.314009	−	0.169933i
$445$	−28.8955	+	31.3889i	−1.36978	+	1.48798i
$446$	−5.76369	−	5.60701i	−0.272919	−	0.265499i
$447$	−1.28552	+	46.6364i	−0.0608031	+	2.20582i
$448$	3.56007	+	1.92661i	0.168197	+	0.0910239i
$449$	10.9914	−	3.77337i	0.518718	−	0.178076i	−0.0528939	−	0.998600i	$-0.516845\pi$
$449$	10.9914	−	3.77337i	0.518718	−	0.178076i	0.571612	+	0.820524i	$0.306318\pi$
$450$	−19.2817	−	18.7575i	−0.908948	−	0.884238i
$451$	15.4834	−	15.0625i	0.729085	−	0.709265i
$452$	−15.2360	+	9.36556i	−0.716643	+	0.440519i
$453$	15.1896	+	9.33699i	0.713668	+	0.438690i
$454$	8.89090	+	10.7956i	0.417271	+	0.506664i
$455$	−12.9366	−	19.8009i	−0.606477	−	0.928281i
$456$	9.57963	−	6.50454i	0.448607	−	0.304603i
$457$	3.68699	−	5.64336i	0.172470	−	0.263985i	−0.740461	−	0.672100i	$-0.765393\pi$
$457$	3.68699	−	5.64336i	0.172470	−	0.263985i	0.912931	+	0.408115i	$0.133814\pi$
$458$	22.3439	−	2.47302i	1.04406	−	0.115557i
$459$	−3.00540	+	0.332638i	−0.140280	+	0.0155262i
$460$	−7.34165	+	12.7161i	−0.342306	+	0.592892i
$461$	−24.4656	−	21.3071i	−1.13948	−	0.992372i	−0.999998	−	0.00214742i	$-0.999316\pi$
$461$	−24.4656	−	21.3071i	−1.13948	−	0.992372i	−0.139480	−	0.990225i	$-0.544543\pi$
$462$	37.4037	+	17.6512i	1.74018	+	0.821210i
$463$	17.5450	−	2.92774i	0.815386	−	0.136064i	0.257816	−	0.966194i	$-0.416997\pi$
$463$	17.5450	−	2.92774i	0.815386	−	0.136064i	0.557570	+	0.830130i	$0.311734\pi$
$464$	−2.16215	+	8.53815i	−0.100375	+	0.396374i
$465$	25.7658	−	22.4394i	1.19486	−	1.04060i
$466$	−22.8147	+	1.25872i	−1.05687	+	0.0583091i
$467$	−2.35980	−	3.61194i	−0.109198	−	0.167141i	0.778386	−	0.627786i	$-0.216039\pi$
$467$	−2.35980	−	3.61194i	−0.109198	−	0.167141i	−0.887584	+	0.460646i	$0.847618\pi$
$468$	5.48482	−	4.26901i	0.253536	−	0.197335i
$469$	3.41899	+	24.6559i	0.157874	+	1.13851i
$470$	26.8096	−	18.5894i	1.23663	−	0.857463i
$471$	−46.4292	−	21.9105i	−2.13934	−	1.00958i
$472$	2.21436	−	7.07969i	0.101924	−	0.325869i
$473$	5.69456	−	1.61027i	0.261836	−	0.0740402i
$474$	1.38594	−	5.47294i	0.0636582	−	0.251381i
$475$	12.7982	+	25.9160i	0.587220	+	1.18911i
$476$	1.07036	+	4.22677i	0.0490600	+	0.193734i
$477$	16.2199	+	28.0938i	0.742660	+	1.28632i
$478$	−2.43288	+	17.5446i	−0.111277	+	0.802473i
$479$	−9.22136	−	18.2219i	−0.421335	−	0.832580i	−0.999857	−	0.0169135i	$-0.994616\pi$
$479$	−9.22136	−	18.2219i	−0.421335	−	0.832580i	0.578522	−	0.815667i	$-0.303630\pi$
$480$	−7.71808	−	4.74429i	−0.352281	−	0.216546i
$481$	−4.73476	+	1.06108i	−0.215886	+	0.0483813i
$482$	−2.77512	−	0.463086i	−0.126403	−	0.0210930i
$483$	−11.3652	−	44.8803i	−0.517136	−	2.04213i
$484$	−2.24671	−	3.05676i	−0.102123	−	0.138943i
$485$	−3.59904	−	25.9544i	−0.163424	−	1.17853i
$486$	−1.72934	−	20.8700i	−0.0784444	−	0.946684i
$487$	−12.7907	+	19.5776i	−0.579601	+	0.887145i	−0.999794	−	0.0202896i	$-0.993541\pi$
$487$	−12.7907	+	19.5776i	−0.579601	+	0.887145i	0.420193	+	0.907435i	$0.361962\pi$
$488$	−6.19006	+	10.7215i	−0.280211	+	0.485340i
$489$	−9.87664	+	4.66090i	−0.446637	+	0.210773i
$490$	−4.39669	−	31.7066i	−0.198622	−	1.43236i
$491$	15.1358	+	0.835066i	0.683070	+	0.0376860i	0.393300	−	0.919410i	$-0.371333\pi$
$491$	15.1358	+	0.835066i	0.683070	+	0.0376860i	0.289770	+	0.957096i	$0.406421\pi$
$492$	2.04920	−	14.7778i	0.0923851	−	0.666233i
$493$	−8.34359	+	4.51533i	−0.375776	+	0.203360i
$494$	−7.08678	+	2.35566i	−0.318849	+	0.105986i
$495$	−46.8001	−	25.3270i	−2.10351	−	1.13836i
$496$	2.23354	−	3.03884i	0.100289	−	0.136448i
$497$	−22.6203	−	9.18757i	−1.01466	−	0.412119i
$498$	−26.5540	−	2.93900i	−1.18991	−	0.131700i
$499$	−8.04111	−	3.26602i	−0.359969	−	0.146207i	0.189156	−	0.981947i	$-0.439425\pi$
$499$	−8.04111	−	3.26602i	−0.359969	−	0.146207i	−0.549125	+	0.835740i	$0.685039\pi$
$500$	3.53615	−	4.29371i	0.158142	−	0.192021i
$501$	−48.4794	−	26.2357i	−2.16590	−	1.17213i
$502$	−15.7679	−	17.1285i	−0.703756	−	0.764483i
$503$	17.8105	−	10.9481i	0.794133	−	0.488152i	−0.0662481	−	0.997803i	$-0.521103\pi$
$503$	17.8105	−	10.9481i	0.794133	−	0.488152i	0.860381	+	0.509652i	$0.170226\pi$
$504$	16.0241	−	3.59108i	0.713770	−	0.159960i
$505$	10.1786	−	23.2049i	0.452941	−	1.03260i
$506$	−4.06516	+	16.0530i	−0.180718	+	0.713641i
$507$	24.7710	−	10.0611i	1.10012	−	0.446830i
$508$	−11.2057	+	3.16868i	−0.497174	+	0.140587i
$509$	27.5610	−	24.0029i	1.22162	−	1.06391i	0.225652	−	0.974208i	$-0.427549\pi$
$509$	27.5610	−	24.0029i	1.22162	−	1.06391i	0.995969	−	0.0897026i	$-0.0285917\pi$
$510$	−1.87080	−	9.57744i	−0.0828403	−	0.424096i
$511$	−31.0617	−	19.0935i	−1.37409	−	0.844648i
$512$	−0.945817	−	0.324699i	−0.0417996	−	0.0143498i
$513$	3.11975	−	11.8320i	0.137740	−	0.522396i
$514$	−18.7118	+	6.42376i	−0.825341	+	0.283340i
$515$	9.85084	+	2.20763i	0.434080	+	0.0972796i
$516$	2.42060	−	3.29335i	0.106561	−	0.144982i
$517$	23.3901	−	28.4011i	1.02870	−	1.24908i
$518$	−11.1867	−	2.50701i	−0.491517	−	0.110152i
$519$	0.609366	−	22.1067i	0.0267482	−	0.970375i
$520$	3.95738	+	4.29886i	0.173542	+	0.188517i
$521$	18.6845	+	6.41441i	0.818584	+	0.281020i	0.702015	−	0.712162i	$-0.252284\pi$
$521$	18.6845	+	6.41441i	0.818584	+	0.281020i	0.116569	+	0.993183i	$0.462810\pi$
$522$	16.1335	+	31.8807i	0.706145	+	1.39538i
$523$	−3.69927	−	11.8272i	−0.161758	−	0.517168i	0.837828	−	0.545934i	$-0.183825\pi$
$523$	−3.69927	−	11.8272i	−0.161758	−	0.517168i	−0.999586	+	0.0287653i	$0.990842\pi$
$524$	−14.0735	+	10.9538i	−0.614803	+	0.478520i
$525$	5.88828	+	71.0610i	0.256986	+	3.10135i
$526$	4.47842	+	1.26638i	0.195269	+	0.0552167i
$527$	4.03762	−	0.446884i	0.175881	−	0.0194666i
$528$	−9.83186	−	2.78018i	−0.427877	−	0.120992i
$529$	−4.03651	+	1.90488i	−0.175501	+	0.0828207i
$530$	−22.4111	+	15.5395i	−0.973477	+	0.674994i
$531$	−12.0881	−	27.5580i	−0.524578	−	1.19592i
$532$	−17.5177	−	2.11251i	−0.759489	−	0.0915891i
$533$	−3.86517	+	8.81170i	−0.167419	+	0.381677i
$534$	6.37091	+	32.6155i	0.275696	+	1.41141i
$535$	26.3655	+	32.0138i	1.13988	+	1.38408i
$536$	−1.83564	−	5.86887i	−0.0792876	−	0.253497i
$537$	−43.6135	−	2.40622i	−1.88206	−	0.103836i
$538$	−8.10295	−	11.0245i	−0.349343	−	0.475298i
$539$	−14.5014	−	33.0599i	−0.624621	−	1.42399i
$540$	−9.44324	+	1.57580i	−0.406372	+	0.0678116i
$541$	29.5185	−	11.9894i	1.26910	−	0.515464i	0.360355	−	0.932815i	$-0.382656\pi$
$541$	29.5185	−	11.9894i	1.26910	−	0.515464i	0.908745	+	0.417351i	$0.137041\pi$
$542$	−7.19315	+	2.92161i	−0.308972	+	0.125494i
$543$	59.3503	−	9.90381i	2.54696	−	0.425013i
$544$	−0.432680	−	0.986410i	−0.0185510	−	0.0422920i
$545$	32.1318	+	43.7169i	1.37637	+	1.87263i
$546$	−18.3953	−	1.01490i	−0.787247	−	0.0434336i
$547$	2.81593	+	9.00303i	0.120400	+	0.384942i	0.994996	−	0.0999107i	$-0.0318557\pi$
$547$	2.81593	+	9.00303i	0.120400	+	0.384942i	−0.874596	+	0.484853i	$0.838873\pi$
$548$	−13.2228	−	16.0555i	−0.564848	−	0.685857i
$549$	9.62831	+	49.2916i	0.410926	+	2.10371i
$550$	10.2450	−	23.3563i	0.436849	−	0.995916i
$551$	−4.90099	−	38.0776i	−0.208789	−	1.62216i
$552$	4.59425	+	10.4738i	0.195544	+	0.445796i
$553$	−7.06977	+	4.90207i	−0.300637	+	0.208457i
$554$	−19.2766	+	9.09687i	−0.818986	+	0.386489i
$555$	24.6897	+	6.98158i	1.04802	+	0.296352i
$556$	20.4123	−	2.25923i	0.865673	−	0.0958127i
$557$	0.853926	+	0.241467i	0.0361820	+	0.0102313i	0.290146	−	0.956982i	$-0.406296\pi$
$557$	0.853926	+	0.241467i	0.0361820	+	0.0102313i	−0.253964	+	0.967214i	$0.581735\pi$
$558$	−1.26343	−	15.2473i	−0.0534851	−	0.645469i
$559$	−2.08023	+	1.61911i	−0.0879842	+	0.0684809i
$560$	4.12107	+	13.1758i	0.174147	+	0.556779i
$561$	−4.96934	−	9.81969i	−0.209806	−	0.414588i
$562$	−4.84985	−	1.66496i	−0.204579	−	0.0702319i
$563$	28.0611	+	30.4825i	1.18263	+	1.28468i	0.950046	+	0.312108i	$0.101035\pi$
$563$	28.0611	+	30.4825i	1.18263	+	1.28468i	0.232588	+	0.972575i	$0.425281\pi$
$564$	0.700196	−	25.4018i	0.0294836	−	1.06961i
$565$	−59.5170	−	13.3381i	−2.50390	−	0.561137i
$566$	−5.96686	+	7.24516i	−0.250806	+	0.304537i
$567$	−11.2987	+	15.3724i	−0.474500	+	0.645581i
$568$	5.88545	+	1.31896i	0.246948	+	0.0553423i
$569$	−39.2149	+	13.4625i	−1.64398	+	0.564378i	−0.982609	−	0.185685i	$-0.940549\pi$
$569$	−39.2149	+	13.4625i	−1.64398	+	0.564378i	−0.661366	+	0.750063i	$0.730023\pi$
$570$	38.8860	+	6.88057i	1.62876	+	0.288195i
$571$	−10.5969	−	3.63794i	−0.443468	−	0.152243i	0.0939164	−	0.995580i	$-0.470061\pi$
$571$	−10.5969	−	3.63794i	−0.443468	−	0.152243i	−0.537385	+	0.843337i	$0.680588\pi$
$572$	5.61391	+	3.45086i	0.234729	+	0.144288i
$573$	0.477389	+	2.44397i	0.0199432	+	0.102098i
$574$	−17.1439	+	14.9307i	−0.715574	+	0.623194i
$575$	−27.4720	+	7.76834i	−1.14566	+	0.323962i
$576$	−3.75856	+	1.52659i	−0.156607	+	0.0636081i
$577$	−3.39737	+	13.4159i	−0.141434	+	0.558512i	0.857589	+	0.514335i	$0.171961\pi$
$577$	−3.39737	+	13.4159i	−0.141434	+	0.558512i	−0.999024	+	0.0441769i	$0.985933\pi$
$578$	−6.36277	+	14.5057i	−0.264656	+	0.603356i
$579$	5.92102	−	1.32693i	0.246069	−	0.0551454i
$580$	−25.5898	+	15.7300i	−1.06256	+	0.653153i
$581$	27.5725	+	29.9517i	1.14390	+	1.24261i
$582$	−17.9500	−	9.71403i	−0.744050	−	0.402660i
$583$	−19.5527	+	23.7415i	−0.809789	+	0.983272i
$584$	8.34514	+	3.38950i	0.345324	+	0.140259i
$585$	23.5599	+	2.60761i	0.974081	+	0.107811i
$586$	11.0298	+	4.47992i	0.455637	+	0.185064i
$587$	9.08715	−	12.3635i	0.375067	−	0.510297i	−0.576768	−	0.816908i	$-0.695686\pi$
$587$	9.08715	−	12.3635i	0.375067	−	0.510297i	0.951835	+	0.306611i	$0.0991951\pi$
$588$	−21.9282	−	11.8669i	−0.904302	−	0.489384i
$589$	−4.19124	+	15.8958i	−0.172697	+	0.654974i
$590$	22.2491	−	12.0406i	0.915982	−	0.495705i
$591$	−0.284894	+	2.05450i	−0.0117190	+	0.0845110i
$592$	2.82780	+	0.156014i	0.116222	+	0.00641214i
$593$	−0.669773	−	4.83005i	−0.0275043	−	0.198346i	0.971793	−	0.235837i	$-0.0757830\pi$
$593$	−0.669773	−	4.83005i	−0.0275043	−	0.198346i	−0.999297	+	0.0374901i	$0.988064\pi$
$594$	−9.76458	+	4.60802i	−0.400646	+	0.189069i
$595$	−7.43505	+	12.8779i	−0.304807	+	0.527941i
$596$	−9.60579	+	14.7028i	−0.393469	+	0.602249i
$597$	1.84637	+	22.2824i	0.0755670	+	0.911958i
$598$	−1.01318	−	7.30649i	−0.0414318	−	0.298785i
$599$	13.8013	+	18.7773i	0.563905	+	0.767221i	0.990543	−	0.137202i	$-0.0438108\pi$
$599$	13.8013	+	18.7773i	0.563905	+	0.767221i	−0.426638	+	0.904423i	$0.640302\pi$
$600$	−4.32422	−	17.0759i	−0.176535	−	0.697122i
$601$	−15.3304	−	2.55819i	−0.625340	−	0.104351i	−0.156564	−	0.987668i	$-0.550042\pi$
$601$	−15.3304	−	2.55819i	−0.625340	−	0.104351i	−0.468776	+	0.883317i	$0.655305\pi$
$602$	−6.07745	+	1.36199i	−0.247698	+	0.0555105i
$603$	−21.2520	−	13.0635i	−0.865447	−	0.531988i
$604$	3.03064	+	5.98871i	0.123315	+	0.243677i
$605$	1.77705	−	12.8152i	0.0722475	−	0.521012i
$606$	−9.86858	−	17.0929i	−0.400884	−	0.694351i
$607$	3.18080	+	12.5607i	0.129105	+	0.509823i	0.999837	+	0.0180656i	$0.00575076\pi$
$607$	3.18080	+	12.5607i	0.129105	+	0.509823i	−0.870732	+	0.491758i	$0.836355\pi$
$608$	4.35442	−	0.197536i	0.176595	−	0.00801115i
$609$	23.2501	−	91.8125i	0.942140	−	3.72043i
$610$	−40.6284	+	11.4886i	−1.64500	+	0.465160i
$611$	−4.89241	+	15.6419i	−0.197926	+	0.632804i
$612$	−3.95174	−	1.86487i	−0.159740	−	0.0753829i
$613$	35.7174	−	24.7659i	1.44261	−	1.00028i	0.448288	−	0.893889i	$-0.352034\pi$
$613$	35.7174	−	24.7659i	1.44261	−	1.00028i	0.994324	−	0.106395i	$-0.0339309\pi$
$614$	−0.999813	−	7.21013i	−0.0403492	−	0.290977i
$615$	40.1520	−	31.2516i	1.61909	−	1.26019i
$616$	8.51567	+	13.0342i	0.343106	+	0.525163i
$617$	16.4622	−	0.908243i	0.662742	−	0.0365645i	0.279406	−	0.960173i	$-0.409863\pi$
$617$	16.4622	−	0.908243i	0.662742	−	0.0365645i	0.383337	+	0.923609i	$0.374775\pi$
$618$	5.92981	−	5.16428i	0.238532	−	0.207738i
$619$	−4.83925	+	19.1098i	−0.194506	+	0.768087i	0.792830	+	0.609443i	$0.208607\pi$
$619$	−4.83925	+	19.1098i	−0.194506	+	0.768087i	−0.987336	+	0.158644i	$0.949288\pi$
$620$	12.6866	−	2.11701i	0.509505	−	0.0850213i
$621$	10.9303	+	5.15813i	0.438617	+	0.206988i
$622$	2.55328	+	2.22365i	0.102377	+	0.0891602i
$623$	25.3197	−	43.8550i	1.01441	−	1.75701i
$624$	4.52364	−	0.500677i	0.181091	−	0.0200431i
$625$	−14.0987	+	1.56045i	−0.563950	+	0.0624179i
$626$	11.7495	−	17.9839i	0.469603	−	0.718781i
$627$	44.3120	−	4.46613i	1.76965	−	0.178360i
$628$	−10.5705	−	16.1793i	−0.421808	−	0.645626i
$629$	1.93931	+	2.35477i	0.0773253	+	0.0938909i
$630$	47.7113	+	29.3280i	1.90086	+	1.16846i
$631$	−4.17742	+	2.56785i	−0.166300	+	0.102224i	−0.604323	−	0.796740i	$-0.706556\pi$
$631$	−4.17742	+	2.56785i	−0.166300	+	0.102224i	0.438022	+	0.898964i	$0.355679\pi$
$632$	1.52336	−	1.48195i	0.0605960	−	0.0589487i
$633$	4.32717	+	4.20954i	0.171990	+	0.167314i
$634$	−23.5416	+	8.08183i	−0.934955	+	0.320970i
$635$	−34.9281	−	18.9022i	−1.38608	−	0.750109i
$636$	−0.585320	+	21.2343i	−0.0232094	+	0.841995i
$637$	11.5264	+	11.2131i	0.456693	+	0.444278i
$638$	−22.9439	+	24.9237i	−0.908357	+	0.986739i
$639$	21.5190	−	11.6455i	0.851278	−	0.460689i
$640$	−1.53992	−	3.04297i	−0.0608707	−	0.120284i
$641$	−6.81854	−	8.27929i	−0.269316	−	0.327012i	0.619743	−	0.784805i	$-0.287237\pi$
$641$	−6.81854	−	8.27929i	−0.269316	−	0.327012i	−0.889059	+	0.457792i	$0.848640\pi$
$642$	32.2553	−	1.77957i	1.27301	−	0.0702342i
$643$	−5.86484	−	15.6643i	−0.231287	−	0.617739i	0.768468	−	0.639888i	$-0.221019\pi$
$643$	−5.86484	−	15.6643i	−0.231287	−	0.617739i	−0.999755	+	0.0221489i	$0.992949\pi$
$644$	5.20255	−	16.6335i	0.205009	−	0.655451i
$645$	13.7491	−	2.29432i	0.541370	−	0.0903387i
$646$	3.33319	+	3.30665i	0.131143	+	0.130099i
$647$	30.3970	+	5.07236i	1.19503	+	0.199415i	0.728472	−	0.685076i	$-0.240231\pi$
$647$	30.3970	+	5.07236i	1.19503	+	0.199415i	0.466558	+	0.884491i	$0.345494\pi$
$648$	2.12808	−	4.20520i	0.0835989	−	0.165196i
$649$	20.4506	−	19.8946i	0.802756	−	0.780933i
$650$	−0.313039	+	11.3565i	−0.0122784	+	0.445438i
$651$	−24.0177	+	32.6773i	−0.941329	+	1.28072i
$652$	−4.08623	−	0.452264i	−0.160029	−	0.0177120i
$653$	−37.9251			−1.48412			−0.742061	−	0.670332i	$-0.766152\pi$
$653$	−37.9251			−1.48412			−0.742061	+	0.670332i	$0.766152\pi$
$654$	42.2605			1.65252
$655$	−60.4522	−	6.69084i	−2.36206	−	0.261433i
$656$	3.57035	−	4.33524i	0.139399	−	0.169263i
$657$	34.5602	−	11.8645i	1.34832	−	0.462880i
$658$	−26.2260	+	28.4890i	−1.02240	+	1.11062i
$659$	−0.742150	+	3.79939i	−0.0289100	+	0.148003i	−0.993113	−	0.117163i	$-0.962620\pi$
$659$	−0.742150	+	3.79939i	−0.0289100	+	0.148003i	0.964203	+	0.265167i	$0.0854269\pi$
$660$	−17.4228	−	30.1772i	−0.678182	−	1.17465i
$661$	6.76725	+	9.20718i	0.263216	+	0.358118i	0.917226	−	0.398368i	$-0.130423\pi$
$661$	6.76725	+	9.20718i	0.263216	+	0.358118i	−0.654010	+	0.756486i	$0.726915\pi$
$662$	7.28993	−	5.05472i	0.283331	−	0.196457i
$663$	3.69687	+	3.21961i	0.143575	+	0.125039i
$664$	−7.93644	−	6.17718i	−0.307994	−	0.239721i
$665$	−37.7989	−	46.8226i	−1.46578	−	1.81570i
$666$	9.06655	−	7.05678i	0.351322	−	0.273445i
$667$	37.8630	+	2.08896i	1.46606	+	0.0808850i
$668$	−10.3753	−	17.9706i	−0.401434	−	0.695303i
$669$	−17.5538	−	12.1715i	−0.678668	−	0.470578i
$670$	9.46935	−	18.7119i	0.365833	−	0.722906i
$671$	−40.5658	+	24.9357i	−1.56603	+	0.962633i
$672$	10.1706	+	3.49156i	0.392338	+	0.134690i
$673$	14.2719	−	7.72356i	0.550141	−	0.297722i	−0.176998	−	0.984211i	$-0.556639\pi$
$673$	14.2719	−	7.72356i	0.550141	−	0.297722i	0.727140	+	0.686490i	$0.240849\pi$
$674$	3.44054	−	17.6136i	0.132525	−	0.678452i
$675$	−15.2971	−	10.6068i	−0.588787	−	0.408256i
$676$	9.92739	+	1.65659i	0.381823	+	0.0637149i
$677$	10.1910	−	23.2331i	0.391672	−	0.892921i	−0.603735	−	0.797185i	$-0.706322\pi$
$677$	10.1910	−	23.2331i	0.391672	−	0.892921i	0.995407	−	0.0957364i	$-0.0305206\pi$
$678$	−35.8269	+	31.2016i	−1.37592	+	1.19829i
$679$	10.9052	+	29.1264i	0.418502	+	1.11777i
$680$	1.28806	−	3.44026i	0.0493949	−	0.131928i
$681$	28.0164	+	24.3995i	1.07359	+	0.934992i
$682$	13.1183	−	6.19066i	0.502325	−	0.237053i
$683$	−0.665820	−	8.03525i	−0.0254769	−	0.307460i	−0.997395	−	0.0721392i	$-0.977017\pi$
$683$	−0.665820	−	8.03525i	−0.0254769	−	0.307460i	0.971918	−	0.235321i	$-0.0756142\pi$
$684$	12.7949	−	12.2057i	0.489224	−	0.466697i
$685$	5.85779	−	70.6930i	0.223815	−	2.70104i
$686$	3.38649	+	9.04492i	0.129297	+	0.345337i
$687$	57.4647	−	16.2495i	2.19242	−	0.619956i
$688$	1.42551	−	0.578991i	0.0543470	−	0.0220738i
$689$	4.08974	−	13.0756i	0.155807	−	0.498142i
$690$	−13.6768	+	36.5291i	−0.520667	+	1.39064i
$691$	−33.3233	−	25.9366i	−1.26768	−	0.986674i	−0.999730	−	0.0232403i	$-0.992602\pi$
$691$	−33.3233	−	25.9366i	−1.26768	−	0.986674i	−0.267948	−	0.963433i	$-0.586346\pi$
$692$	4.55336	−	6.96944i	0.173093	−	0.264938i
$693$	60.7781	+	17.1864i	2.30877	+	0.652858i
$694$	−9.42680	+	16.3277i	−0.357837	+	0.619791i
$695$	55.2711	+	43.0192i	2.09655	+	1.63181i
$696$	−1.93212	+	23.3172i	−0.0732369	+	0.883838i
$697$	6.04021	−	0.333248i	0.228789	−	0.0126227i
$698$	3.74730	+	19.1841i	0.141837	+	0.726128i
$699$	−59.2292	+	13.2736i	−2.24025	+	0.502052i
$700$	−12.1200	+	23.9499i	−0.458095	+	0.905220i
$701$	−1.13695	−	41.2464i	−0.0429420	−	1.55785i	−0.647979	−	0.761658i	$-0.724386\pi$
$701$	−1.13695	−	41.2464i	−0.0429420	−	1.55785i	0.605037	−	0.796197i	$-0.293158\pi$
$702$	3.25743	−	3.53851i	0.122944	−	0.133553i
$703$	−11.7146	+	3.89396i	−0.441825	+	0.146863i
$704$	−2.60499	−	2.82978i	−0.0981793	−	0.106651i
$705$	62.1192	−	60.4305i	2.33954	−	2.27594i
$706$	0.317952	+	11.5347i	0.0119663	+	0.434114i
$707$	−5.76586	+	29.5180i	−0.216847	+	1.11014i
$708$	2.70660	−	19.5186i	0.101720	−	0.733553i
$709$	3.20026	+	10.2318i	0.120188	+	0.384264i	0.994960	−	0.100272i	$-0.0319712\pi$
$709$	3.20026	+	10.2318i	0.120188	+	0.384264i	−0.874772	+	0.484535i	$0.838989\pi$
$710$	11.2506	+	17.2203i	0.422227	+	0.646266i
$711$	0.711976	−	8.59228i	0.0267012	−	0.322236i
$712$	−4.38643	+	11.7156i	−0.164389	+	0.439062i
$713$	−14.6843	−	6.92971i	−0.549933	−	0.259520i
$714$	4.65269	+	10.6071i	0.174123	+	0.396960i
$715$	5.51697	+	21.7860i	0.206323	+	0.814752i
$716$	−13.5124	−	9.36929i	−0.504982	−	0.350147i
$717$	1.29650	+	47.0346i	0.0484187	+	1.75654i
$718$	10.3960	+	10.1133i	0.387974	+	0.377427i
$719$	1.75212	+	0.392660i	0.0653432	+	0.0146438i	0.251230	−	0.967927i	$-0.419165\pi$
$719$	1.75212	+	0.392660i	0.0653432	+	0.0146438i	−0.185887	+	0.982571i	$0.559516\pi$
$720$	−12.8183	−	5.20634i	−0.477709	−	0.194029i
$721$	−11.9823			−0.446245
$722$	−17.3381	+	7.77105i	−0.645258	+	0.289209i
$723$	−7.47393			−0.277958
$724$	20.9859	+	8.52372i	0.779933	+	0.316782i
$725$	−56.9900	−	12.7718i	−2.11656	−	0.474331i
$726$	−7.22341	−	7.02704i	−0.268086	−	0.260798i
$727$	−0.435742	−	15.8079i	−0.0161608	−	0.586283i	−0.963752	−	0.266799i	$-0.914034\pi$
$727$	−0.435742	−	15.8079i	−0.0161608	−	0.586283i	0.947591	−	0.319485i	$-0.103510\pi$
$728$	−5.69927	−	3.95179i	−0.211229	−	0.146463i
$729$	−10.1855	−	40.2217i	−0.377241	−	1.48969i
$730$	12.3395	+	28.1311i	0.456704	+	1.04118i
$731$	1.49878	+	0.707289i	0.0554342	+	0.0261600i
$732$	−11.5315	+	30.7993i	−0.426217	+	1.13837i
$733$	2.26129	−	27.2897i	0.0835225	−	1.00797i	−0.817995	−	0.575225i	$-0.804914\pi$
$733$	2.26129	−	27.2897i	0.0835225	−	1.00797i	0.901518	−	0.432742i	$-0.142454\pi$
$734$	19.3129	+	29.5606i	0.712853	+	1.09110i
$735$	−25.3836	−	81.1560i	−0.936290	−	2.99348i
$736$	−0.591364	+	4.26461i	−0.0217980	+	0.157196i
$737$	4.53425	−	23.2128i	0.167021	−	0.855055i
$738$	−0.627785	−	22.7749i	−0.0231091	−	0.838355i
$739$	34.9351	−	33.9854i	1.28511	−	1.25017i	0.333539	−	0.942736i	$-0.391757\pi$
$739$	34.9351	−	33.9854i	1.28511	−	1.25017i	0.951569	−	0.307436i	$-0.0994708\pi$
$740$	6.54164	+	7.10612i	0.240475	+	0.261226i
$741$	−17.5390	+	9.27096i	−0.644310	+	0.340577i
$742$	21.9233	−	23.8150i	0.804828	−	0.874277i
$743$	−1.20690	−	43.7840i	−0.0442768	−	1.60628i	−0.617291	−	0.786735i	$-0.711770\pi$
$743$	−1.20690	−	43.7840i	−0.0442768	−	1.60628i	0.573014	−	0.819546i	$-0.305774\pi$
$744$	4.52368	−	8.93904i	0.165846	−	0.327721i
$745$	−58.4460	+	13.0981i	−2.14130	+	0.479876i
$746$	−1.84992	−	9.47055i	−0.0677303	−	0.346742i
$747$	−40.7371	+	2.24753i	−1.49049	+	0.0822328i
$748$	0.342120	−	4.12877i	0.0125091	−	0.150963i
$749$	−38.8462	−	30.2352i	−1.41941	−	1.10477i
$750$	7.38814	−	12.7966i	0.269777	−	0.467267i
$751$	−8.64472	−	2.44449i	−0.315450	−	0.0892008i	0.110698	−	0.993854i	$-0.464691\pi$
$751$	−8.64472	−	2.44449i	−0.315450	−	0.0892008i	−0.426149	+	0.904653i	$0.640130\pi$
$752$	5.23207	−	8.00828i	0.190794	−	0.292032i
$753$	−48.8047	−	37.9862i	−1.77854	−	1.38430i
$754$	5.29113	−	14.1320i	0.192692	−	0.514656i
$755$	−6.83312	+	21.8467i	−0.248683	+	0.795082i
$756$	10.5282	−	4.27619i	0.382907	−	0.155524i
$757$	−52.8033	+	14.9314i	−1.91917	+	0.542690i	−0.939280	+	0.343151i	$0.888506\pi$
$757$	−52.8033	+	14.9314i	−1.91917	+	0.542690i	−0.979890	+	0.199539i	$0.936056\pi$
$758$	−3.52144	−	9.40536i	−0.127905	−	0.341618i
$759$	−3.63267	+	43.8398i	−0.131858	+	1.59128i
$760$	11.1143	+	9.87227i	0.403157	+	0.358105i
$761$	−2.27383	−	27.4410i	−0.0824261	−	0.994735i	−0.904814	−	0.425808i	$-0.859990\pi$
$761$	−2.27383	−	27.4410i	−0.0824261	−	0.994735i	0.822388	−	0.568928i	$-0.192642\pi$
$762$	−27.9761	+	13.2022i	−1.01347	+	0.478266i
$763$	−48.5624	−	42.2930i	−1.75808	−	1.53111i
$764$	−0.328687	+	0.877884i	−0.0118915	+	0.0317607i
$765$	−5.22535	−	13.9563i	−0.188923	−	0.504591i
$766$	16.0963	−	14.0183i	0.581583	−	0.506501i
$767$	−5.10514	+	11.6386i	−0.184336	+	0.420244i
$768$	−2.62022	−	0.437238i	−0.0945492	−	0.0157775i
$769$	23.7630	+	16.4769i	0.856915	+	0.594172i	0.914689	−	0.404158i	$-0.132435\pi$
$769$	23.7630	+	16.4769i	0.856915	+	0.594172i	−0.0577739	+	0.998330i	$0.518400\pi$
$770$	−10.1795	+	52.1135i	−0.366844	+	1.87804i
$771$	−46.2204	+	25.0132i	−1.66459	+	0.900829i
$772$	2.16044	+	0.741680i	0.0777559	+	0.0266936i
$773$	−23.7051	+	14.5715i	−0.852613	+	0.524099i	−0.879697	−	0.475534i	$-0.842255\pi$
$773$	−23.7051	+	14.5715i	−0.852613	+	0.524099i	0.0270844	+	0.999633i	$0.491378\pi$
$774$	2.81835	−	5.56922i	0.101304	−	0.200181i
$775$	20.5510	+	14.2498i	0.738214	+	0.511866i
$776$	−3.84156	−	6.65379i	−0.137904	−	0.238857i
$777$	−30.4079	−	1.67765i	−1.09088	−	0.0601854i
$778$	−14.0673	+	10.9490i	−0.504336	+	0.392541i
$779$	−7.53597	+	23.2916i	−0.270004	+	0.834510i
$780$	12.2488	+	9.53365i	0.438579	+	0.341360i
$781$	17.4940	+	15.2356i	0.625986	+	0.545172i
$782$	−3.81100	+	2.64249i	−0.136281	+	0.0944952i
$783$	14.6430	+	19.9226i	0.523300	+	0.711975i
$784$	−4.69296	−	8.12845i	−0.167606	−	0.290302i
$785$	12.6358	−	64.6884i	0.450992	−	2.30883i
$786$	−32.0862	+	34.8550i	−1.14448	+	1.24324i
$787$	−2.09384	+	0.718817i	−0.0746374	+	0.0256230i	−0.361765	−	0.932269i	$-0.617826\pi$
$787$	−2.09384	+	0.718817i	−0.0746374	+	0.0256230i	0.287128	+	0.957892i	$0.407300\pi$
$788$	−0.496374	+	0.602713i	−0.0176826	+	0.0214708i
$789$	12.2882	+	1.36006i	0.437471	+	0.0484193i
$790$	7.24810			0.257876
$791$	72.3951			2.57407
$792$	−15.5086	−	1.71649i	−0.551073	−	0.0609928i
$793$	12.5617	−	17.0908i	0.446079	−	0.606913i
$794$	−0.244974	+	8.88720i	−0.00869380	+	0.315395i
$795$	−51.9277	+	50.5160i	−1.84169	+	1.79162i
$796$	−3.80045	+	7.50990i	−0.134703	+	0.266181i
$797$	−10.1946	−	1.70118i	−0.361112	−	0.0602590i	−0.0187426	−	0.999824i	$-0.505966\pi$
$797$	−10.1946	−	1.70118i	−0.361112	−	0.0602590i	−0.342370	+	0.939565i	$0.611229\pi$
$798$	−46.8240	+	2.12415i	−1.65755	+	0.0751940i
$799$	10.1633	−	1.69595i	0.359550	−	0.0599983i
$800$	1.97945	−	6.32866i	0.0699842	−	0.223752i
$801$	17.7947	+	47.5275i	0.628744	+	1.67930i
$802$	38.5611	−	2.12747i	1.36164	−	0.0751237i
$803$	22.0240	+	26.7423i	0.777210	+	0.943714i
$804$	−7.37589	−	14.5751i	−0.260127	−	0.514026i
$805$	52.2735	−	28.2890i	1.84240	−	0.997057i
$806$	−4.37621	+	4.75384i	−0.154146	+	0.167447i
$807$	−26.0519	−	25.3436i	−0.917069	−	0.892139i
$808$	0.204726	−	7.42707i	0.00720223	−	0.261283i
$809$	−36.7239	−	19.8740i	−1.29114	−	0.698732i	−0.322355	−	0.946619i	$-0.604474\pi$
$809$	−36.7239	−	19.8740i	−1.29114	−	0.698732i	−0.968789	+	0.247887i	$0.920264\pi$
$810$	15.2025	−	5.21901i	0.534160	−	0.183377i
$811$	36.7293	+	35.7309i	1.28974	+	1.25468i	0.949284	+	0.314420i	$0.101810\pi$
$811$	36.7293	+	35.7309i	1.28974	+	1.25468i	0.340458	+	0.940260i	$0.389418\pi$
$812$	25.5554	−	24.8607i	0.896820	−	0.872440i
$813$	−17.5702	+	10.8004i	−0.616215	+	0.378786i
$814$	9.27992	+	5.70435i	0.325261	+	0.199937i
$815$	−8.91341	−	10.8230i	−0.312223	−	0.379111i
$816$	−1.56501	−	2.39543i	−0.0547865	−	0.0838569i
$817$	−4.85270	+	4.62926i	−0.169775	+	0.161957i
$818$	−5.21252	+	7.97836i	−0.182252	+	0.278957i
$819$	−27.9640	+	3.09506i	−0.977142	+	0.108150i
$820$	19.0374	−	2.10706i	0.664814	−	0.0735816i
$821$	14.8665	−	25.7496i	0.518845	−	0.898666i	−0.480915	−	0.876767i	$-0.659695\pi$
$821$	14.8665	−	25.7496i	0.518845	−	0.898666i	0.999760	−	0.0218990i	$-0.00697121\pi$
$822$	−41.6667	−	36.2875i	−1.45329	−	1.26567i
$823$	−27.7761	−	13.1079i	−0.968214	−	0.456911i	−0.123627	−	0.992329i	$-0.539453\pi$
$823$	−27.7761	−	13.1079i	−0.968214	−	0.456911i	−0.844588	+	0.535417i	$0.820154\pi$
$824$	2.91972	−	0.487216i	0.101713	−	0.0169730i
$825$	16.6320	−	65.6783i	0.579052	−	2.28662i
$826$	−22.6438	+	19.7205i	−0.787879	+	0.686165i
$827$	48.6593	−	2.68461i	1.69205	−	0.0933530i	0.816768	−	0.576966i	$-0.195764\pi$
$827$	48.6593	−	2.68461i	1.69205	−	0.0933530i	0.875282	+	0.483613i	$0.160676\pi$
$828$	9.55300	+	14.6220i	0.331990	+	0.508148i
$829$	7.53072	−	5.86140i	0.261553	−	0.203575i	−0.474943	−	0.880016i	$-0.657531\pi$
$829$	7.53072	−	5.86140i	0.261553	−	0.203575i	0.736496	+	0.676442i	$0.236479\pi$
$830$	−4.71107	−	33.9738i	−0.163524	−	1.17925i
$831$	−46.5316	+	32.2643i	−1.61416	+	1.11924i
$832$	1.54942	+	0.731190i	0.0537165	+	0.0253494i
$833$	3.01795	−	9.64893i	0.104566	−	0.334316i
$834$	52.4969	−	14.8447i	1.81782	−	0.514030i
$835$	17.3727	−	68.6031i	0.601206	−	2.37411i
$836$	15.0912	+	7.30305i	0.521940	+	0.252581i
$837$	−2.59897	−	10.2631i	−0.0898337	−	0.354745i
$838$	9.55544	+	16.5505i	0.330087	+	0.571728i
$839$	−2.81148	+	20.2749i	−0.0970632	+	0.699969i	0.878099	+	0.478478i	$0.158812\pi$
$839$	−2.81148	+	20.2749i	−0.0970632	+	0.699969i	−0.975163	+	0.221491i	$0.928908\pi$
$840$	16.5591	+	32.7216i	0.571343	+	1.12900i
$841$	41.3819	+	25.4373i	1.42696	+	0.877150i
$842$	−22.0687	+	4.94570i	−0.760536	+	0.170440i
$843$	−13.4357	−	2.24202i	−0.462749	−	0.0772192i
$844$	0.557879	+	2.20302i	0.0192030	+	0.0758309i
$845$	20.3283	+	27.6577i	0.699316	+	0.951453i
$846$	−5.33023	−	38.4388i	−0.183257	−	1.32155i
$847$	1.26812	+	15.3039i	0.0435730	+	0.525848i
$848$	−4.37368	+	6.69441i	−0.150193	+	0.229887i
$849$	−12.4667	+	21.5929i	−0.427855	+	0.741066i
$850$	6.45935	−	3.04824i	0.221554	−	0.104554i
$851$	−1.67480	−	12.0778i	−0.0574115	−	0.414022i
$852$	15.9979	+	0.882629i	0.548079	+	0.0302384i
$853$	−3.39833	+	24.5070i	−0.116356	+	0.839102i	0.839101	+	0.543975i	$0.183081\pi$
$853$	−3.39833	+	24.5070i	−0.116356	+	0.839102i	−0.955458	+	0.295127i	$0.904638\pi$
$854$	44.0741	−	23.8517i	1.50818	−	0.816188i
$855$	60.3036	+	0.589923i	2.06234	+	0.0201750i
$856$	10.6950	+	5.78785i	0.365548	+	0.197825i
$857$	6.19761	−	8.43215i	0.211706	−	0.288037i	−0.686937	−	0.726717i	$-0.741045\pi$
$857$	6.19761	−	8.43215i	0.211706	−	0.288037i	0.898643	+	0.438680i	$0.144554\pi$
$858$	16.2185	+	6.58740i	0.553692	+	0.224890i
$859$	24.3538	+	2.69548i	0.830941	+	0.0919685i	0.515407	−	0.856946i	$-0.327641\pi$
$859$	24.3538	+	2.69548i	0.830941	+	0.0919685i	0.315534	+	0.948914i	$0.397816\pi$
$860$	4.86159	+	1.97461i	0.165779	+	0.0673335i
$861$	−38.3927	+	46.6177i	−1.30842	+	1.58873i
$862$	29.4117	+	15.9168i	1.00177	+	0.542129i
$863$	−23.0761	−	25.0673i	−0.785519	−	0.853301i	0.206623	−	0.978421i	$-0.433753\pi$
$863$	−23.0761	−	25.0673i	−0.785519	−	0.853301i	−0.992142	+	0.125120i	$0.960068\pi$
$864$	−2.39153	+	1.47007i	−0.0813614	+	0.0500126i
$865$	27.7047	−	6.20877i	0.941988	−	0.211105i
$866$	−12.4845	+	28.4618i	−0.424241	+	0.967172i
$867$	−10.3295	+	40.7901i	−0.350807	+	1.38530i
$868$	−14.1442	+	5.74487i	−0.480085	+	0.194994i
$869$	7.86590	−	2.22426i	0.266832	−	0.0754530i
$870$	−60.1734	+	52.4050i	−2.04007	+	1.77670i
$871$	2.01975	+	10.3400i	0.0684366	+	0.350357i
$872$	13.5528	+	8.33091i	0.458957	+	0.282120i
$873$	−29.4798	−	10.1204i	−0.997739	−	0.342524i
$874$	−4.42881	−	18.2368i	−0.149807	−	0.616869i
$875$	−21.2964	+	7.31105i	−0.719948	+	0.247159i
$876$	23.3481	+	5.23244i	0.788861	+	0.176788i
$877$	−4.63255	+	6.30281i	−0.156430	+	0.212831i	−0.876922	−	0.480632i	$-0.840407\pi$
$877$	−4.63255	+	6.30281i	−0.156430	+	0.212831i	0.720492	+	0.693463i	$0.243916\pi$
$878$	−7.66228	+	9.30379i	−0.258589	+	0.313988i
$879$	30.8594	+	6.91575i	1.04086	+	0.233262i
$880$	0.361440	−	13.1124i	0.0121841	−	0.442017i
$881$	−12.8560	−	13.9653i	−0.433128	−	0.470503i	0.480534	−	0.876976i	$-0.340443\pi$
$881$	−12.8560	−	13.9653i	−0.433128	−	0.470503i	−0.913663	+	0.406473i	$0.866759\pi$
$882$	−36.0133	−	12.3634i	−1.21263	−	0.416297i
$883$	−1.12584	−	2.22472i	−0.0378875	−	0.0748676i	0.872525	−	0.488570i	$-0.162481\pi$
$883$	−1.12584	−	2.22472i	−0.0378875	−	0.0748676i	−0.910412	+	0.413702i	$0.864236\pi$
$884$	0.550890	+	1.76129i	0.0185284	+	0.0592387i
$885$	53.0331	−	41.2773i	1.78269	−	1.38752i
$886$	0.212186	+	2.56070i	0.00712852	+	0.0860284i
$887$	−36.5149	−	10.3254i	−1.22605	−	0.346694i	−0.403284	−	0.915075i	$-0.632131\pi$
$887$	−36.5149	−	10.3254i	−1.22605	−	0.346694i	−0.822765	+	0.568381i	$0.807570\pi$
$888$	7.47769	−	0.827630i	0.250935	−	0.0277735i
$889$	45.3603	+	12.8267i	1.52133	+	0.430192i
$890$	−38.5835	+	18.2080i	−1.29332	+	0.610333i
$891$	14.8967	−	10.3291i	0.499058	−	0.346039i
$892$	−3.23006	−	7.36379i	−0.108150	−	0.246558i
$893$	−8.39368	+	40.8434i	−0.280884	+	1.36677i
$894$	−18.7407	+	42.7246i	−0.626784	+	1.42892i
$895$	−10.7506	−	55.0371i	−0.359353	−	1.83969i
$896$	2.57338	+	3.12468i	0.0859706	+	0.104388i
$897$	−5.84942	−	18.7016i	−0.195307	−	0.624430i
$898$	11.6035	+	0.640181i	0.387212	+	0.0213631i
$899$	−19.6723	−	26.7651i	−0.656107	−	0.892666i
$900$	−10.8057	−	24.6346i	−0.360191	−	0.821154i
$901$	−8.49584	+	1.41770i	−0.283037	+	0.0472306i
$902$	20.0134	−	8.12876i	0.666375	−	0.270658i
$903$	−15.3288	+	6.22601i	−0.510110	+	0.207189i
$904$	−17.6404	+	2.94367i	−0.586712	+	0.0979050i
$905$	31.0306	+	70.7425i	1.03149	+	2.35156i
$906$	10.5594	+	14.3666i	0.350814	+	0.477300i
$907$	−3.31445	−	0.182863i	−0.110055	−	0.00607188i	−2.32625e−5	−	1.00000i	$-0.500007\pi$
$907$	−3.31445	−	0.182863i	−0.110055	−	0.00607188i	−0.110031	+	0.993928i	$0.535095\pi$
$908$	4.17487	+	13.3478i	0.138548	+	0.442963i
$909$	−19.1615	−	23.2665i	−0.635547	−	0.771702i
$910$	−4.53440	−	23.2136i	−0.150314	−	0.769523i
$911$	16.8676	−	38.4543i	0.558849	−	1.27405i	−0.378483	−	0.925608i	$-0.623554\pi$
$911$	16.8676	−	38.4543i	0.558849	−	1.27405i	0.937332	−	0.348439i	$-0.113288\pi$
$912$	11.3232	−	2.42151i	0.374948	−	0.0801841i
$913$	−15.5384	−	35.4239i	−0.514245	−	1.17236i
$914$	5.53962	−	3.84109i	0.183234	−	0.127052i
$915$	−101.432	+	47.8670i	−3.35325	+	1.58244i
$916$	21.6321	+	6.11698i	0.714745	+	0.202111i
$917$	71.7528	−	7.94160i	2.36949	−	0.262255i
$918$	−2.90966	−	0.822773i	−0.0960331	−	0.0271556i
$919$	−2.24206	−	27.0576i	−0.0739587	−	0.892549i	−0.928057	−	0.372438i	$-0.878522\pi$
$919$	−2.24206	−	27.0576i	−0.0739587	−	0.892549i	0.854098	−	0.520111i	$-0.174110\pi$
$920$	−11.5872	+	9.01867i	−0.382018	+	0.297337i
$921$	−5.77228	−	18.4550i	−0.190203	−	0.608113i
$922$	−14.6492	−	28.9476i	−0.482445	−	0.953338i
$923$	−9.77366	−	3.35530i	−0.321704	−	0.110441i
$924$	28.0120	+	30.4292i	0.921527	+	1.00105i
$925$	−0.517461	+	18.7725i	−0.0170140	+	0.617237i
$926$	17.3571	+	3.88981i	0.570389	+	0.127827i
$927$	7.63401	−	9.26947i	0.250734	−	0.304449i
$928$	−5.21621	+	7.09691i	−0.171230	+	0.232967i
$929$	−47.1135	−	10.5584i	−1.54574	−	0.346409i	−0.639374	−	0.768896i	$-0.720806\pi$
$929$	−47.1135	−	10.5584i	−1.54574	−	0.346409i	−0.906369	+	0.422487i	$0.861157\pi$
$930$	32.3160	−	11.0941i	1.05968	−	0.363790i
$931$	32.0382	+	25.4435i	1.05001	+	0.833876i
$932$	−21.6113	−	7.41917i	−0.707902	−	0.243023i
$933$	7.66242	+	4.71007i	0.250856	+	0.154201i
$934$	−0.827132	−	4.23445i	−0.0270646	−	0.138556i
$935$	10.6549	−	9.27933i	0.348451	−	0.303467i
$936$	6.68812	−	1.89122i	0.218608	−	0.0618165i
$937$	13.6510	−	5.54456i	0.445959	−	0.181133i	−0.142269	−	0.989828i	$-0.545440\pi$
$937$	13.6510	−	5.54456i	0.445959	−	0.181133i	0.588228	+	0.808695i	$0.299826\pi$
$938$	−6.11059	+	24.1302i	−0.199518	+	0.787878i
$939$	22.9230	−	52.2592i	0.748064	−	1.70541i
$940$	31.8343	−	7.13423i	1.03832	−	0.232693i
$941$	16.2262	−	9.97418i	0.528957	−	0.325149i	−0.233319	−	0.972400i	$-0.574959\pi$
$941$	16.2262	−	9.97418i	0.528957	−	0.325149i	0.762277	+	0.647251i	$0.224082\pi$
$942$	−34.7713	−	37.7717i	−1.13291	−	1.23067i
$943$	−21.2657	−	11.5084i	−0.692507	−	0.374766i
$944$	4.71574	−	5.72601i	0.153484	−	0.186366i
$945$	35.9057	+	14.5836i	1.16801	+	0.474405i
$946$	5.88193	+	0.651012i	0.191238	+	0.0211662i
$947$	−12.1292	−	4.92645i	−0.394146	−	0.160088i	0.170625	−	0.985336i	$-0.445421\pi$
$947$	−12.1292	−	4.92645i	−0.394146	−	0.160088i	−0.564771	+	0.825248i	$0.691035\pi$
$948$	3.34358	−	4.54911i	0.108595	−	0.147748i
$949$	−13.5720	−	7.34479i	−0.440565	−	0.238422i
$950$	2.10497	+	28.8271i	0.0682944	+	0.935275i
$951$	−58.1505	+	31.4695i	−1.88566	+	1.02047i
$952$	−0.598887	+	4.31886i	−0.0194100	+	0.139975i
$953$	3.62176	+	0.199818i	0.117320	+	0.00647274i	0.113653	−	0.993521i	$-0.463745\pi$
$953$	3.62176	+	0.199818i	0.117320	+	0.00647274i	0.00366749	+	0.999993i	$0.498833\pi$
$954$	4.45573	+	32.1324i	0.144260	+	1.04033i
$955$	−2.89116	+	1.36437i	−0.0935559	+	0.0441501i
$956$	−8.85625	+	15.3395i	−0.286432	+	0.496114i
$957$	−49.2205	+	75.3376i	−1.59107	+	2.43532i
$958$	−1.68646	−	20.3526i	−0.0544871	−	0.657562i
$959$	11.5646	+	83.3975i	0.373439	+	2.69305i
$960$	−5.36544	−	7.29994i	−0.173169	−	0.235605i
$961$	−4.11844	−	16.2634i	−0.132853	−	0.524625i
$962$	−4.78602	−	0.798645i	−0.154307	−	0.0257494i
$963$	48.1389	−	10.7882i	1.55126	−	0.347644i
$964$	−2.39687	−	1.47335i	−0.0771981	−	0.0474535i
$965$	3.51749	+	6.95076i	0.113232	+	0.223753i
$966$	6.35906	−	45.8582i	0.204599	−	1.47546i
$967$	−0.803335	−	1.39142i	−0.0258335	−	0.0447450i	0.852820	−	0.522206i	$-0.174891\pi$
$967$	−0.803335	−	1.39142i	−0.0258335	−	0.0447450i	−0.878653	+	0.477461i	$0.841557\pi$
$968$	−0.931275	−	3.67752i	−0.0299323	−	0.118200i
$969$	10.1795	+	7.20678i	0.327013	+	0.231515i
$970$	6.43239	−	25.4009i	0.206532	−	0.815575i
$971$	7.53985	−	2.13207i	0.241965	−	0.0684213i	−0.148962	−	0.988843i	$-0.547593\pi$
$971$	7.53985	−	2.13207i	0.241965	−	0.0684213i	0.390927	+	0.920422i	$0.372155\pi$
$972$	6.25136	−	19.9867i	0.200513	−	0.641074i
$973$	−75.1815	−	35.4790i	−2.41021	−	1.13740i
$974$	−19.2177	+	13.3253i	−0.615775	+	0.426969i
$975$	4.14525	+	29.8934i	0.132754	+	0.957355i
$976$	−9.76966	+	7.60403i	−0.312719	+	0.243399i
$977$	29.2030	+	44.6985i	0.934286	+	1.43003i	0.902575	+	0.430534i	$0.141675\pi$
$977$	29.2030	+	44.6985i	0.934286	+	1.43003i	0.0317110	+	0.999497i	$0.489904\pi$
$978$	−10.9046	+	0.601623i	−0.348690	+	0.0192378i
$979$	−36.2846	+	31.6003i	−1.15966	+	1.00995i
$980$	7.85799	−	31.0305i	0.251014	−	0.991233i
$981$	63.6571	−	10.6225i	2.03241	−	0.339150i
$982$	13.7090	+	6.46943i	0.437472	+	0.206448i
$983$	10.5792	+	9.21346i	0.337425	+	0.293864i	0.808817	−	0.588060i	$-0.200108\pi$
$983$	10.5792	+	9.21346i	0.337425	+	0.293864i	−0.471392	+	0.881924i	$0.656248\pi$
$984$	7.45959	−	12.9204i	0.237803	−	0.411887i
$985$	−2.64670	+	0.292937i	−0.0843309	+	0.00933374i
$986$	−9.42945	+	1.04365i	−0.300295	+	0.0332366i
$987$	−56.2615	+	86.1146i	−1.79082	+	2.74106i
$988$	−7.45231	−	0.484320i	−0.237090	−	0.0154083i
$989$	−3.62316	−	5.54567i	−0.115210	−	0.176342i
$990$	−33.8293	−	41.0766i	−1.07517	−	1.30550i
$991$	−19.5151	−	11.9959i	−0.619918	−	0.381062i	0.177823	−	0.984062i	$-0.443094\pi$
$991$	−19.5151	−	11.9959i	−0.619918	−	0.381062i	−0.797741	+	0.603000i	$0.793972\pi$
$992$	3.21291	−	1.97497i	0.102010	−	0.0627053i
$993$	16.8911	−	16.4319i	0.536024	−	0.521452i
$994$	−17.5002	−	17.0245i	−0.555073	−	0.539983i
$995$	−27.1495	+	9.32042i	−0.860696	+	0.295477i
$996$	−23.4962	−	12.7155i	−0.744504	−	0.402905i
$997$	−0.564456	+	20.4774i	−0.0178765	+	0.648526i	0.936627	+	0.350327i	$0.113930\pi$
$997$	−0.564456	+	20.4774i	−0.0178765	+	0.648526i	−0.954504	+	0.298199i	$0.903614\pi$
$998$	−6.22101	−	6.05189i	−0.196923	−	0.191569i
$999$	5.38461	−	5.84925i	0.170362	−	0.185062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.i.a.501.15	yes	576
361.49	even	57	inner	722.2.i.a.49.15	✓	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.i.a.49.15	✓	576	361.49	even	57	inner
722.2.i.a.501.15	yes	576	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(0.926494 + 0.376309i) q^{2} +(2.59216 + 0.580917i) q^{3} +(0.716783 + 0.697297i) q^{4} +(0.0939720 + 3.40913i) q^{5} +(2.18302 + 1.51367i) q^{6} +(-0.993714 - 3.92409i) q^{7} +(0.401695 + 0.915773i) q^{8} +(3.66875 + 1.73133i) q^{9} +O(q^{10})\)	\(q+(0.926494 + 0.376309i) q^{2} +(2.59216 + 0.580917i) q^{3} +(0.716783 + 0.697297i) q^{4} +(0.0939720 + 3.40913i) q^{5} +(2.18302 + 1.51367i) q^{6} +(-0.993714 - 3.92409i) q^{7} +(0.401695 + 0.915773i) q^{8} +(3.66875 + 1.73133i) q^{9} +(-1.19582 + 3.19390i) q^{10} +(-0.317620 + 3.83311i) q^{11} +(1.45294 + 2.22390i) q^{12} +(-0.511441 - 1.63517i) q^{13} +(0.556001 - 4.00959i) q^{14} +(-1.73683 + 8.89160i) q^{15} +(0.0275543 + 0.999620i) q^{16} +(-0.772071 + 0.751082i) q^{17} +(2.74756 + 2.98465i) q^{18} +(-1.71182 - 4.00870i) q^{19} +(-2.30982 + 2.50913i) q^{20} +(-0.296298 - 10.7491i) q^{21} +(-1.73671 + 3.43183i) q^{22} +(4.20121 - 0.941513i) q^{23} +(0.509271 + 2.60718i) q^{24} +(-6.62093 + 0.365287i) q^{25} +(0.141482 - 1.70743i) q^{26} +(2.21529 + 1.72423i) q^{27} +(2.02398 - 3.50563i) q^{28} +(8.47533 + 2.39659i) q^{29} +(-4.95515 + 7.58443i) q^{30} +(-2.97614 - 2.31643i) q^{31} +(-0.350638 + 0.936511i) q^{32} +(-3.05004 + 9.75152i) q^{33} +(-0.997958 + 0.405336i) q^{34} +(13.2843 - 3.75645i) q^{35} +(1.42245 + 3.79920i) q^{36} +(0.233873 - 2.82243i) q^{37} +(-0.0774779 - 4.35821i) q^{38} +(-0.375840 - 4.53572i) q^{39} +(-3.08424 + 1.45549i) q^{40} +(-4.23521 - 3.68845i) q^{41} +(3.77048 - 10.0705i) q^{42} +(-0.539492 - 1.44092i) q^{43} +(-2.90048 + 2.52603i) q^{44} +(-5.55756 + 12.6700i) q^{45} +(4.24669 + 0.708648i) q^{46} +(-7.86107 - 5.45074i) q^{47} +(-0.509271 + 2.60718i) q^{48} +(-8.25467 + 4.46721i) q^{49} +(-6.27171 - 2.15308i) q^{50} +(-2.43765 + 1.49842i) q^{51} +(0.773605 - 1.52869i) q^{52} +(6.57136 + 4.55648i) q^{53} +(1.40361 + 2.43112i) q^{54} +(-13.0974 - 0.722605i) q^{55} +(3.19440 - 2.48630i) q^{56} +(-2.10859 - 11.3856i) q^{57} +(6.95048 + 5.40978i) q^{58} +(-5.59389 - 4.87173i) q^{59} +(-7.44501 + 5.16226i) q^{60} +(7.33195 + 9.97547i) q^{61} +(-1.88569 - 3.26611i) q^{62} +(3.14819 - 16.1170i) q^{63} +(-0.677282 + 0.735724i) q^{64} +(5.52644 - 1.89723i) q^{65} +(-6.49543 + 7.88697i) q^{66} +(-6.11192 - 0.676468i) q^{67} -1.07713 q^{68} +11.4371 q^{69} +(13.7215 + 1.51869i) q^{70} +(3.57203 - 4.85992i) q^{71} +(-0.111781 + 4.05521i) q^{72} +(6.45622 - 6.28071i) q^{73} +(1.27879 - 2.52695i) q^{74} +(-17.3747 - 2.89933i) q^{75} +(1.56825 - 4.06701i) q^{76} +(15.3571 - 2.56264i) q^{77} +(1.35862 - 4.34375i) q^{78} +(-0.745202 - 1.99035i) q^{79} +(-3.40525 + 0.187873i) q^{80} +(-2.99617 - 3.63805i) q^{81} +(-2.53590 - 5.01107i) q^{82} +(-8.84493 + 4.78663i) q^{83} +(7.28295 - 7.91139i) q^{84} +(-2.63309 - 2.56151i) q^{85} +(0.0423952 - 1.53802i) q^{86} +(20.5772 + 11.1358i) q^{87} +(-3.63785 + 1.24887i) q^{88} +(8.96686 + 8.72310i) q^{89} +(-9.91687 + 9.64728i) q^{90} +(-5.90831 + 3.63183i) q^{91} +(3.66787 + 2.25463i) q^{92} +(-6.36899 - 7.73344i) q^{93} +(-5.23207 - 8.00828i) q^{94} +(13.5053 - 6.21252i) q^{95} +(-1.45294 + 2.22390i) q^{96} +(-7.63650 + 0.845207i) q^{97} +(-9.32896 + 1.03253i) q^{98} +(-7.80164 + 13.5128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9}+O(q^{10}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9} + q^{10} + 34 q^{11} - 2 q^{12} + 2 q^{13} - 14 q^{14} + 38 q^{15} + 16 q^{16} + 12 q^{17} + 26 q^{18} + 7 q^{19} + 2 q^{20} + 75 q^{21} + 36 q^{22} - 45 q^{23} - q^{24} + 9 q^{25} + 4 q^{26} - 110 q^{27} + 33 q^{28} - 36 q^{29} - 57 q^{30} - 4 q^{31} - 16 q^{32} + 81 q^{33} + 7 q^{34} - 2 q^{35} + 13 q^{36} + 14 q^{37} - 30 q^{38} + 40 q^{39} + q^{40} + 11 q^{41} + q^{42} - 9 q^{43} + 2 q^{44} - 85 q^{45} - 33 q^{46} - 213 q^{47} + q^{48} - 76 q^{49} - 20 q^{50} - 3 q^{51} + 2 q^{52} - 144 q^{53} + 78 q^{54} - 6 q^{55} - 29 q^{56} - 8 q^{57} + 4 q^{58} - 5 q^{59} + 69 q^{61} - 2 q^{62} - 95 q^{63} - 32 q^{64} - 84 q^{65} - 5 q^{66} - 5 q^{67} - 62 q^{68} + 2 q^{69} + 211 q^{70} + 129 q^{71} - 13 q^{72} - 8 q^{73} - 31 q^{74} - 36 q^{75} - 18 q^{76} - 10 q^{77} + q^{78} - 2 q^{79} - q^{80} - 64 q^{81} - 49 q^{82} - 72 q^{83} + 2 q^{84} - 6 q^{85} - 10 q^{86} - 81 q^{87} + 4 q^{88} - 7 q^{89} + 81 q^{90} + 35 q^{91} - 7 q^{92} - 80 q^{93} - 27 q^{94} + 285 q^{95} + 2 q^{96} + 38 q^{97} - 171 q^{98} + 84 q^{99}+O(q^{100}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9 + q^10 + 34 * q^11 - 2 * q^12 + 2 * q^13 - 14 * q^14 + 38 * q^15 + 16 * q^16 + 12 * q^17 + 26 * q^18 + 7 * q^19 + 2 * q^20 + 75 * q^21 + 36 * q^22 - 45 * q^23 - q^24 + 9 * q^25 + 4 * q^26 - 110 * q^27 + 33 * q^28 - 36 * q^29 - 57 * q^30 - 4 * q^31 - 16 * q^32 + 81 * q^33 + 7 * q^34 - 2 * q^35 + 13 * q^36 + 14 * q^37 - 30 * q^38 + 40 * q^39 + q^40 + 11 * q^41 + q^42 - 9 * q^43 + 2 * q^44 - 85 * q^45 - 33 * q^46 - 213 * q^47 + q^48 - 76 * q^49 - 20 * q^50 - 3 * q^51 + 2 * q^52 - 144 * q^53 + 78 * q^54 - 6 * q^55 - 29 * q^56 - 8 * q^57 + 4 * q^58 - 5 * q^59 + 69 * q^61 - 2 * q^62 - 95 * q^63 - 32 * q^64 - 84 * q^65 - 5 * q^66 - 5 * q^67 - 62 * q^68 + 2 * q^69 + 211 * q^70 + 129 * q^71 - 13 * q^72 - 8 * q^73 - 31 * q^74 - 36 * q^75 - 18 * q^76 - 10 * q^77 + q^78 - 2 * q^79 - q^80 - 64 * q^81 - 49 * q^82 - 72 * q^83 + 2 * q^84 - 6 * q^85 - 10 * q^86 - 81 * q^87 + 4 * q^88 - 7 * q^89 + 81 * q^90 + 35 * q^91 - 7 * q^92 - 80 * q^93 - 27 * q^94 + 285 * q^95 + 2 * q^96 + 38 * q^97 - 171 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more