LMFDB - Embedded newform 605.2.r.a.32.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(32,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 2]))

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

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

chi := DirichletCharacter("605.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.r (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$64$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			32.1
Character	$\chi$	$=$	605.32
Dual form			605.2.r.a.208.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65403 - 2.20953i) q^{2} +(-1.20427 + 1.20427i) q^{3} +(-1.58273 + 5.39029i) q^{4} +(0.661016 + 2.13613i) q^{5} +(4.65276 + 0.668966i) q^{6} +(-0.992826 + 4.56395i) q^{7} +(9.35584 - 3.48955i) q^{8} +0.0994872i q^{9} +O(q^{10})$	\(q+(-1.65403 - 2.20953i) q^{2} +(-1.20427 + 1.20427i) q^{3} +(-1.58273 + 5.39029i) q^{4} +(0.661016 + 2.13613i) q^{5} +(4.65276 + 0.668966i) q^{6} +(-0.992826 + 4.56395i) q^{7} +(9.35584 - 3.48955i) q^{8} +0.0994872i q^{9} +(3.62650 - 4.99377i) q^{10} +(2.63561 + 2.01334i) q^{11} +(-4.58531 - 8.39737i) q^{12} +(-1.03312 - 1.89202i) q^{13} +(11.7263 - 5.35524i) q^{14} +(-3.36851 - 1.77643i) q^{15} +(-13.7331 - 8.82571i) q^{16} +(0.291007 + 4.06881i) q^{17} +(0.219820 - 0.164555i) q^{18} +(3.47012 + 4.00473i) q^{19} +(-12.5606 + 0.182146i) q^{20} +(-4.30058 - 6.69183i) q^{21} +(0.0891419 - 9.15360i) q^{22} +(0.646509 - 0.140639i) q^{23} +(-7.06458 + 15.4693i) q^{24} +(-4.12611 + 2.82404i) q^{25} +(-2.47166 + 5.41219i) q^{26} +(-3.73261 - 3.73261i) q^{27} +(-23.0296 - 12.5751i) q^{28} +(3.57993 + 4.13146i) q^{29} +(1.64655 + 10.3811i) q^{30} +(6.55556 - 1.92489i) q^{31} +(1.78959 + 25.0217i) q^{32} +(-5.59858 + 0.749383i) q^{33} +(8.50882 - 7.37294i) q^{34} +(-10.4055 + 0.896037i) q^{35} +(-0.536264 - 0.157461i) q^{36} +(-3.18454 - 1.73889i) q^{37} +(3.10888 - 14.2913i) q^{38} +(3.52265 + 1.03434i) q^{39} +(13.6385 + 17.6787i) q^{40} +(0.583675 + 0.0839197i) q^{41} +(-7.67250 + 20.5708i) q^{42} +(3.01439 - 1.12431i) q^{43} +(-15.0239 + 11.0201i) q^{44} +(-0.212518 + 0.0657626i) q^{45} +(-1.38009 - 1.19586i) q^{46} +(0.440833 - 0.588885i) q^{47} +(27.1668 - 5.90977i) q^{48} +(-13.4765 - 6.15451i) q^{49} +(13.0645 + 4.44573i) q^{50} +(-5.25038 - 4.54948i) q^{51} +(11.8337 - 2.57427i) q^{52} +(0.0969851 - 0.445833i) q^{53} +(-2.07345 + 14.4212i) q^{54} +(-2.55858 + 6.96087i) q^{55} +(6.63740 + 46.1641i) q^{56} +(-9.00171 - 0.643815i) q^{57} +(3.20726 - 14.7435i) q^{58} +(3.61054 - 0.519117i) q^{59} +(14.9069 - 15.3456i) q^{60} +(1.94109 - 0.279087i) q^{61} +(-15.0962 - 11.3009i) q^{62} +(-0.454054 - 0.0987735i) q^{63} +(27.6516 - 23.9602i) q^{64} +(3.35870 - 3.45755i) q^{65} +(10.9160 + 11.1307i) q^{66} +(10.8967 - 8.15717i) q^{67} +(-22.3926 - 4.87122i) q^{68} +(-0.609202 + 0.947936i) q^{69} +(19.1908 + 21.5091i) q^{70} +(-1.38789 - 1.60171i) q^{71} +(0.347165 + 0.930786i) q^{72} +(-0.628427 - 2.88883i) q^{73} +(1.42520 + 9.91251i) q^{74} +(1.56805 - 8.36983i) q^{75} +(-27.0789 + 12.3665i) q^{76} +(-11.8055 + 10.0299i) q^{77} +(-3.54117 - 9.49425i) q^{78} +(2.17252 + 4.75715i) q^{79} +(9.77509 - 35.1696i) q^{80} +8.69164 q^{81} +(-0.779994 - 1.42845i) q^{82} +(6.50397 + 1.41485i) q^{83} +(42.8776 - 12.5900i) q^{84} +(-8.49915 + 3.31118i) q^{85} +(-7.47010 - 4.80074i) q^{86} +(-9.28657 - 0.664189i) q^{87} +(31.6840 + 9.63939i) q^{88} +(-5.37435 - 4.65690i) q^{89} +(0.496816 + 0.360791i) q^{90} +(9.66081 - 2.83667i) q^{91} +(-0.265163 + 3.70746i) q^{92} +(-5.57657 + 10.2127i) q^{93} -2.03031 q^{94} +(-6.26083 + 10.0598i) q^{95} +(-32.2879 - 27.9776i) q^{96} +(-8.05600 + 3.00473i) q^{97} +(8.69200 + 39.9565i) q^{98} +(-0.200302 + 0.262210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 22 q^{2} - 40 q^{3} - 14 q^{5} - 44 q^{6} - 22 q^{7} - 22 q^{8}+O(q^{10}) $ 1280 * q - 22 * q^2 - 40 * q^3 - 14 * q^5 - 44 * q^6 - 22 * q^7 - 22 * q^8	$ 1280 q - 22 q^{2} - 40 q^{3} - 14 q^{5} - 44 q^{6} - 22 q^{7} - 22 q^{8} - 66 q^{10} - 48 q^{11} + 44 q^{12} - 66 q^{13} - 26 q^{15} + 80 q^{16} - 22 q^{17} - 44 q^{18} - 54 q^{20} - 44 q^{21} - 90 q^{22} - 34 q^{23} - 30 q^{25} - 12 q^{26} + 80 q^{27} - 22 q^{28} - 22 q^{30} - 52 q^{31} - 22 q^{32} - 62 q^{33} - 22 q^{35} + 216 q^{36} + 52 q^{37} + 70 q^{38} - 44 q^{41} + 44 q^{42} - 22 q^{43} + 104 q^{45} - 44 q^{46} - 18 q^{47} - 72 q^{48} + 88 q^{50} - 484 q^{51} - 22 q^{52} + 14 q^{53} + 140 q^{55} - 316 q^{56} + 44 q^{57} - 6 q^{58} + 34 q^{60} - 44 q^{61} - 22 q^{62} - 44 q^{63} - 22 q^{65} - 84 q^{66} - 138 q^{67} - 22 q^{68} - 126 q^{70} - 4 q^{71} + 220 q^{72} - 22 q^{73} - 66 q^{75} + 88 q^{76} - 22 q^{77} - 104 q^{78} - 324 q^{80} - 1056 q^{81} - 58 q^{82} - 22 q^{83} - 110 q^{85} - 52 q^{86} + 44 q^{87} - 2 q^{88} + 176 q^{90} + 104 q^{91} - 278 q^{92} - 128 q^{93} - 22 q^{95} - 44 q^{96} + 46 q^{97} - 22 q^{98}+O(q^{100}) $ 1280 * q - 22 * q^2 - 40 * q^3 - 14 * q^5 - 44 * q^6 - 22 * q^7 - 22 * q^8 - 66 * q^10 - 48 * q^11 + 44 * q^12 - 66 * q^13 - 26 * q^15 + 80 * q^16 - 22 * q^17 - 44 * q^18 - 54 * q^20 - 44 * q^21 - 90 * q^22 - 34 * q^23 - 30 * q^25 - 12 * q^26 + 80 * q^27 - 22 * q^28 - 22 * q^30 - 52 * q^31 - 22 * q^32 - 62 * q^33 - 22 * q^35 + 216 * q^36 + 52 * q^37 + 70 * q^38 - 44 * q^41 + 44 * q^42 - 22 * q^43 + 104 * q^45 - 44 * q^46 - 18 * q^47 - 72 * q^48 + 88 * q^50 - 484 * q^51 - 22 * q^52 + 14 * q^53 + 140 * q^55 - 316 * q^56 + 44 * q^57 - 6 * q^58 + 34 * q^60 - 44 * q^61 - 22 * q^62 - 44 * q^63 - 22 * q^65 - 84 * q^66 - 138 * q^67 - 22 * q^68 - 126 * q^70 - 4 * q^71 + 220 * q^72 - 22 * q^73 - 66 * q^75 + 88 * q^76 - 22 * q^77 - 104 * q^78 - 324 * q^80 - 1056 * q^81 - 58 * q^82 - 22 * q^83 - 110 * q^85 - 52 * q^86 + 44 * q^87 - 2 * q^88 + 176 * q^90 + 104 * q^91 - 278 * q^92 - 128 * q^93 - 22 * q^95 - 44 * q^96 + 46 * q^97 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{22}\right)$

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 $

$2$	−1.65403	−	2.20953i	−1.16958	−	1.56237i	−0.759756	−	0.650208i	$-0.774682\pi$
$2$	−1.65403	−	2.20953i	−1.16958	−	1.56237i	−0.409822	−	0.912165i	$-0.634409\pi$
$3$	−1.20427	+	1.20427i	−0.695283	+	0.695283i	−0.963389	−	0.268106i	$-0.913602\pi$
$3$	−1.20427	+	1.20427i	−0.695283	+	0.695283i	0.268106	+	0.963389i	$0.413602\pi$
$4$	−1.58273	+	5.39029i	−0.791365	+	2.69514i
$5$	0.661016	+	2.13613i	0.295615	+	0.955307i
$5$	0.661016	+	2.13613i	0.295615	+	0.955307i
$6$	4.65276	+	0.668966i	1.89948	+	0.273104i
$7$	−0.992826	+	4.56395i	−0.375253	+	1.72501i	0.271613	+	0.962407i	$0.412443\pi$
$7$	−0.992826	+	4.56395i	−0.375253	+	1.72501i	−0.646866	+	0.762604i	$0.723921\pi$
$8$	9.35584	−	3.48955i	3.30779	−	1.23374i
$9$			0.0994872i			0.0331624i
$10$	3.62650	−	4.99377i	1.14680	−	1.57917i
$11$	2.63561	+	2.01334i	0.794668	+	0.607045i
$11$	2.63561	+	2.01334i	0.794668	+	0.607045i
$12$	−4.58531	−	8.39737i	−1.32366	−	2.42411i
$13$	−1.03312	−	1.89202i	−0.286537	−	0.524753i	0.694275	−	0.719710i	$-0.255725\pi$
$13$	−1.03312	−	1.89202i	−0.286537	−	0.524753i	−0.980812	+	0.194957i	$0.937543\pi$
$14$	11.7263	−	5.35524i	3.13400	−	1.43125i
$15$	−3.36851	−	1.77643i	−0.869745	−	0.458672i
$16$	−13.7331	−	8.82571i	−3.43327	−	2.20643i
$17$	0.291007	+	4.06881i	0.0705796	+	0.986832i	0.902153	+	0.431417i	$0.141986\pi$
$17$	0.291007	+	4.06881i	0.0705796	+	0.986832i	−0.831573	+	0.555415i	$0.812559\pi$
$18$	0.219820	−	0.164555i	0.0518120	−	0.0387860i
$19$	3.47012	+	4.00473i	0.796100	+	0.918749i	0.998161	−	0.0606243i	$-0.0193092\pi$
$19$	3.47012	+	4.00473i	0.796100	+	0.918749i	−0.202060	+	0.979373i	$0.564764\pi$
$20$	−12.5606	+	0.182146i	−2.80863	+	0.0407291i
$21$	−4.30058	−	6.69183i	−0.938464	−	1.46028i
$22$	0.0891419	−	9.15360i	0.0190051	−	1.95155i
$23$	0.646509	−	0.140639i	0.134806	−	0.0293253i	−0.144656	−	0.989482i	$-0.546207\pi$
$23$	0.646509	−	0.140639i	0.134806	−	0.0293253i	0.279462	+	0.960157i	$0.409844\pi$
$24$	−7.06458	+	15.4693i	−1.44205	+	3.15765i
$25$	−4.12611	+	2.82404i	−0.825223	+	0.564807i
$26$	−2.47166	+	5.41219i	−0.484733	+	1.06142i
$27$	−3.73261	−	3.73261i	−0.718341	−	0.718341i
$28$	−23.0296	−	12.5751i	−4.35219	−	2.37647i
$29$	3.57993	+	4.13146i	0.664777	+	0.767193i	0.983550	−	0.180638i	$-0.0578162\pi$
$29$	3.57993	+	4.13146i	0.664777	+	0.767193i	−0.318773	+	0.947831i	$0.603271\pi$
$30$	1.64655	+	10.3811i	0.300618	+	1.89532i
$31$	6.55556	−	1.92489i	1.17741	−	0.345720i	0.366238	−	0.930521i	$-0.380646\pi$
$31$	6.55556	−	1.92489i	1.17741	−	0.345720i	0.811177	+	0.584801i	$0.198828\pi$
$32$	1.78959	+	25.0217i	0.316357	+	4.42325i
$33$	−5.59858	+	0.749383i	−0.974587	+	0.130451i
$34$	8.50882	−	7.37294i	1.45925	−	1.26445i
$35$	−10.4055	+	0.896037i	−1.75885	+	0.151458i
$36$	−0.536264	−	0.157461i	−0.0893774	−	0.0262436i
$37$	−3.18454	−	1.73889i	−0.523534	−	0.285871i	0.195670	−	0.980670i	$-0.437312\pi$
$37$	−3.18454	−	1.73889i	−0.523534	−	0.285871i	−0.719205	+	0.694798i	$0.755494\pi$
$38$	3.10888	−	14.2913i	0.504327	−	2.31835i
$39$	3.52265	+	1.03434i	0.564076	+	0.165628i
$40$	13.6385	+	17.6787i	2.15644	+	2.79524i
$41$	0.583675	+	0.0839197i	0.0911547	+	0.0131061i	0.187741	−	0.982219i	$-0.439883\pi$
$41$	0.583675	+	0.0839197i	0.0911547	+	0.0131061i	−0.0965866	+	0.995325i	$0.530792\pi$
$42$	−7.67250	+	20.5708i	−1.18389	+	3.17414i
$43$	3.01439	−	1.12431i	0.459690	−	0.171456i	−0.108941	−	0.994048i	$-0.534746\pi$
$43$	3.01439	−	1.12431i	0.459690	−	0.171456i	0.568631	+	0.822593i	$0.307473\pi$
$44$	−15.0239	+	11.0201i	−2.26495	+	1.66135i
$45$	−0.212518	+	0.0657626i	−0.0316803	+	0.00980332i
$46$	−1.38009	−	1.19586i	−0.203484	−	0.176320i
$47$	0.440833	−	0.588885i	0.0643022	−	0.0858976i	−0.767237	−	0.641363i	$-0.778369\pi$
$47$	0.440833	−	0.588885i	0.0643022	−	0.0858976i	0.831539	+	0.555466i	$0.187460\pi$
$48$	27.1668	−	5.90977i	3.92118	−	0.853001i
$49$	−13.4765	−	6.15451i	−1.92521	−	0.879216i
$50$	13.0645	+	4.44573i	1.84760	+	0.628721i
$51$	−5.25038	−	4.54948i	−0.735200	−	0.637055i
$52$	11.8337	−	2.57427i	1.64104	−	0.356986i
$53$	0.0969851	−	0.445833i	0.0133219	−	0.0612399i	−0.970006	−	0.243081i	$-0.921842\pi$
$53$	0.0969851	−	0.445833i	0.0133219	−	0.0612399i	0.983328	+	0.181841i	$0.0582056\pi$
$54$	−2.07345	+	14.4212i	−0.282161	+	1.96247i
$55$	−2.55858	+	6.96087i	−0.344998	+	0.938603i
$56$	6.63740	+	46.1641i	0.886959	+	6.16894i
$57$	−9.00171	−	0.643815i	−1.19231	−	0.0852754i
$58$	3.20726	−	14.7435i	0.421134	−	1.93592i
$59$	3.61054	−	0.519117i	0.470052	−	0.0675833i	0.0967814	−	0.995306i	$-0.469145\pi$
$59$	3.61054	−	0.519117i	0.470052	−	0.0675833i	0.373271	+	0.927722i	$0.378236\pi$
$60$	14.9069	−	15.3456i	1.92447	−	1.98111i
$61$	1.94109	−	0.279087i	0.248531	−	0.0357334i	−0.0169231	−	0.999857i	$-0.505387\pi$
$61$	1.94109	−	0.279087i	0.248531	−	0.0357334i	0.265455	+	0.964123i	$0.414478\pi$
$62$	−15.0962	−	11.3009i	−1.91722	−	1.43521i
$63$	−0.454054	−	0.0987735i	−0.0572055	−	0.0124443i
$64$	27.6516	−	23.9602i	3.45645	−	2.99503i
$65$	3.35870	−	3.45755i	0.416595	−	0.428856i
$66$	10.9160	+	11.1307i	1.34367	+	1.37010i
$67$	10.8967	−	8.15717i	1.33124	−	0.996557i	0.332677	−	0.943041i	$-0.392048\pi$
$67$	10.8967	−	8.15717i	1.33124	−	0.996557i	0.998567	−	0.0535156i	$-0.0170427\pi$
$68$	−22.3926	−	4.87122i	−2.71551	−	0.590722i
$69$	−0.609202	+	0.947936i	−0.0733392	+	0.114118i
$70$	19.1908	+	21.5091i	2.29374	+	2.57083i
$71$	−1.38789	−	1.60171i	−0.164713	−	0.190088i	0.667393	−	0.744706i	$-0.267410\pi$
$71$	−1.38789	−	1.60171i	−0.164713	−	0.190088i	−0.832106	+	0.554617i	$0.812865\pi$
$72$	0.347165	+	0.930786i	0.0409138	+	0.109694i
$73$	−0.628427	−	2.88883i	−0.0735519	−	0.338112i	0.925636	−	0.378416i	$-0.123531\pi$
$73$	−0.628427	−	2.88883i	−0.0735519	−	0.338112i	−0.999187	+	0.0403036i	$0.987167\pi$
$74$	1.42520	+	9.91251i	0.165676	+	1.15231i
$75$	1.56805	−	8.36983i	0.181063	−	0.966465i
$76$	−27.0789	+	12.3665i	−3.10617	+	1.41854i
$77$	−11.8055	+	10.0299i	−1.34536	+	1.14301i
$78$	−3.54117	−	9.49425i	−0.400959	−	1.07501i
$79$	2.17252	+	4.75715i	0.244428	+	0.535222i	0.991590	−	0.129420i	$-0.0413115\pi$
$79$	2.17252	+	4.75715i	0.244428	+	0.535222i	−0.747162	+	0.664642i	$0.768584\pi$
$80$	9.77509	−	35.1696i	1.09289	−	3.93208i
$81$	8.69164			0.965738
$82$	−0.779994	−	1.42845i	−0.0861359	−	0.157746i
$83$	6.50397	+	1.41485i	0.713904	+	0.155300i	0.554827	−	0.831966i	$-0.312785\pi$
$83$	6.50397	+	1.41485i	0.713904	+	0.155300i	0.159077	+	0.987266i	$0.449148\pi$
$84$	42.8776	−	12.5900i	4.67833	−	1.37368i
$85$	−8.49915	+	3.31118i	−0.921863	+	0.359148i
$86$	−7.47010	−	4.80074i	−0.805522	−	0.517677i
$87$	−9.28657	−	0.664189i	−0.995625	−	0.0712085i
$88$	31.6840	+	9.63939i	3.37753	+	1.02756i
$89$	−5.37435	−	4.65690i	−0.569680	−	0.493630i	0.321728	−	0.946832i	$-0.395736\pi$
$89$	−5.37435	−	4.65690i	−0.569680	−	0.493630i	−0.891408	+	0.453202i	$0.850282\pi$
$90$	0.496816	+	0.360791i	0.0523690	+	0.0380307i
$91$	9.66081	−	2.83667i	1.01273	−	0.297364i
$92$	−0.265163	+	3.70746i	−0.0276452	+	0.386530i
$93$	−5.57657	+	10.2127i	−0.578263	+	1.05901i
$94$	−2.03031			−0.209411
$95$	−6.26083	+	10.0598i	−0.642348	+	1.03212i
$96$	−32.2879	−	27.9776i	−3.29537	−	2.85545i
$97$	−8.05600	+	3.00473i	−0.817963	+	0.305085i	−0.723396	−	0.690434i	$-0.757420\pi$
$97$	−8.05600	+	3.00473i	−0.817963	+	0.305085i	−0.0945678	+	0.995518i	$0.530147\pi$
$98$	8.69200	+	39.9565i	0.878025	+	4.03621i
$99$	−0.200302	+	0.262210i	−0.0201311	+	0.0263531i
$100$	−8.69183	−	26.7106i	−0.869183	−	2.67106i
$101$	12.3367	−	1.77375i	1.22755	−	0.176495i	0.502122	−	0.864797i	$-0.332553\pi$
$101$	12.3367	−	1.77375i	1.22755	−	0.176495i	0.725424	+	0.688302i	$0.241644\pi$
$102$	−1.36791	+	19.1259i	−0.135443	+	1.89374i
$103$	−1.91511	−	2.55828i	−0.188701	−	0.252075i	0.696207	−	0.717841i	$-0.254870\pi$
$103$	−1.91511	−	2.55828i	−0.188701	−	0.252075i	−0.884908	+	0.465766i	$0.845779\pi$
$104$	−16.2680	−	14.0963i	−1.59521	−	1.38226i
$105$	11.4519	−	13.6100i	1.11759	−	1.32820i
$106$	−1.14550	+	0.523131i	−0.111261	+	0.0508110i
$107$	−4.61583	−	1.72162i	−0.446230	−	0.166435i	0.116297	−	0.993215i	$-0.462898\pi$
$107$	−4.61583	−	1.72162i	−0.446230	−	0.166435i	−0.562526	+	0.826780i	$0.690170\pi$
$108$	26.0275	−	14.2121i	2.50450	−	1.36756i
$109$	−11.2128	−	3.29237i	−1.07399	−	0.315352i	−0.303518	−	0.952826i	$-0.598161\pi$
$109$	−11.2128	−	3.29237i	−1.07399	−	0.315352i	−0.770472	+	0.637474i	$0.779980\pi$
$110$	19.6122	−	5.86026i	1.86995	−	0.558754i
$111$	5.92911	−	1.74094i	0.562766	−	0.165243i
$112$	53.9146	−	53.9146i	5.09445	−	5.09445i
$113$	1.33009	+	3.56611i	0.125124	+	0.335471i	0.984375	−	0.176083i	$-0.0563427\pi$
$113$	1.33009	+	3.56611i	0.125124	+	0.335471i	−0.859251	+	0.511554i	$0.829070\pi$
$114$	13.4666	+	20.9544i	1.26126	+	1.96256i
$115$	0.727777	+	1.28806i	0.0678656	+	0.120113i
$116$	−27.9358	+	12.7579i	−2.59378	+	1.18454i
$117$	0.188232	−	0.102782i	0.0174021	−	0.00950225i
$118$	−7.11896	−	7.11896i	−0.655354	−	0.655354i
$119$	−18.8588	−	2.71148i	−1.72878	−	0.248561i
$120$	−37.7142	−	4.86543i	−3.44282	−	0.444151i
$121$	2.89292	+	10.6128i	0.262993	+	0.964798i
$122$	−3.82728	−	3.82728i	−0.346506	−	0.346506i
$123$	−0.803961	+	0.601838i	−0.0724907	+	0.0542659i
$124$			38.3830i			3.44689i
$125$	−8.75994	−	6.94719i	−0.783513	−	0.621376i
$126$	0.532778	+	1.16662i	0.0474636	+	0.103931i
$127$	9.82003	+	13.1180i	0.871387	+	1.16404i	0.985349	+	0.170551i	$0.0545548\pi$
$127$	9.82003	+	13.1180i	0.871387	+	1.16404i	−0.113962	+	0.993485i	$0.536354\pi$
$128$	−49.6529	−	10.8013i	−4.38874	−	0.954711i
$129$	−2.27616	+	4.98410i	−0.200405	+	0.438825i
$130$	−13.1950	−	1.70225i	−1.15727	−	0.149297i
$131$	0.217956	+	0.742289i	0.0190429	+	0.0648541i	0.968466	−	0.249145i	$-0.0801494\pi$
$131$	0.217956	+	0.742289i	0.0190429	+	0.0648541i	−0.949423	+	0.313999i	$0.898331\pi$
$132$	4.82165	−	31.3640i	0.419671	−	2.72989i
$133$	−21.7226	+	11.8614i	−1.88359	+	1.02852i
$134$	−36.0470	−	10.5844i	−3.11399	−	0.914349i
$135$	5.50602	−	10.4407i	0.473883	−	0.898588i
$136$	16.9209	+	37.0517i	1.45096	+	3.17715i
$137$	0.679617	+	3.12415i	0.0580636	+	0.266914i	0.997022	−	0.0771163i	$-0.0245713\pi$
$137$	0.679617	+	3.12415i	0.0580636	+	0.266914i	−0.938958	+	0.344030i	$0.888208\pi$
$138$	3.10213	−	0.221869i	0.264071	−	0.0188867i
$139$	1.17950	−	8.20357i	0.100044	−	0.695818i	−0.876642	−	0.481143i	$-0.840222\pi$
$139$	1.17950	−	8.20357i	0.100044	−	0.695818i	0.976686	−	0.214675i	$-0.0688692\pi$
$140$	11.6392	−	57.5066i	0.983689	−	4.86020i
$141$	0.178293	+	1.24005i	0.0150150	+	0.104431i
$142$	−1.24341	+	5.71588i	−0.104345	+	0.479666i
$143$	1.08637	−	7.06667i	0.0908471	−	0.590945i
$144$	0.878045	−	1.36626i	0.0731704	−	0.113855i
$145$	−6.45895	+	10.3782i	−0.536387	+	0.861860i
$146$	−5.34353	+	6.16676i	−0.442233	+	0.510364i
$147$	23.6410	−	8.81762i	1.94987	−	0.727265i
$148$	14.4134	−	14.4134i	1.18477	−	1.18477i
$149$	−7.97296	+	2.34107i	−0.653170	+	0.191788i	−0.591496	−	0.806308i	$-0.701462\pi$
$149$	−7.97296	+	2.34107i	−0.653170	+	0.191788i	−0.0616745	+	0.998096i	$0.519644\pi$
$150$	−21.0870	+	10.3793i	−1.72175	+	0.847468i
$151$	−6.54544	−	22.2917i	−0.532660	−	1.81407i	−0.579238	−	0.815159i	$-0.696650\pi$
$151$	−6.54544	−	22.2917i	−0.532660	−	1.81407i	0.0465777	−	0.998915i	$-0.485168\pi$
$152$	46.4406	+	25.3585i	3.76683	+	2.05685i
$153$	−0.404794	+	0.0289515i	−0.0327257	+	0.00234059i
$154$	41.6881	+	9.49477i	3.35932	+	0.765111i
$155$	8.44515	+	12.7312i	0.678331	+	1.02259i
$156$	−11.1508	+	17.3510i	−0.892781	+	1.38919i
$157$	−6.69713	−	12.2649i	−0.534489	−	0.978844i	−0.995796	−	0.0916030i	$-0.970801\pi$
$157$	−6.69713	−	12.2649i	−0.534489	−	0.978844i	0.461306	−	0.887241i	$-0.347381\pi$
$158$	6.91765	−	12.6687i	0.550339	−	1.00787i
$159$	0.420106	+	0.653697i	0.0333166	+	0.0518416i
$160$	−52.2666	+	20.3625i	−4.13204	+	1.60980i
$161$			3.09026i			0.243547i
$162$	−14.3763	−	19.2044i	−1.12951	−	1.50884i
$163$	−5.63933	−	2.10336i	−0.441707	−	0.164748i	0.118764	−	0.992923i	$-0.462107\pi$
$163$	−5.63933	−	2.10336i	−0.441707	−	0.164748i	−0.560470	+	0.828175i	$0.689380\pi$
$164$	−1.37615	+	3.01335i	−0.107459	+	0.235303i
$165$	−5.30153	−	11.4639i	−0.412724	−	0.892467i
$166$	−7.63163	−	16.7109i	−0.592329	−	1.29702i
$167$	−1.49412	−	20.8905i	−0.115619	−	1.61656i	−0.642270	−	0.766478i	$-0.722007\pi$
$167$	−1.49412	−	20.8905i	−0.115619	−	1.61656i	0.526652	−	0.850081i	$-0.323447\pi$
$168$	−63.5870	−	47.6007i	−4.90585	−	3.67247i
$169$	4.51592	−	7.02691i	0.347378	−	0.540531i
$170$	21.3740	+	13.3023i	1.63931	+	1.02024i
$171$	−0.398420	+	0.345233i	−0.0304679	+	0.0264006i
$172$	1.28938	+	18.0279i	0.0983144	+	1.37462i
$173$	4.81898	+	22.1525i	0.366380	+	1.68422i	0.678835	+	0.734291i	$0.262485\pi$
$173$	4.81898	+	22.1525i	0.366380	+	1.68422i	−0.312454	+	0.949933i	$0.601151\pi$
$174$	13.8928	+	21.6175i	1.05321	+	1.63882i
$175$	−8.79224	−	21.6352i	−0.664631	−	1.63546i
$176$	−18.4259	−	50.9105i	−1.38891	−	3.83752i
$177$	−3.72290	+	4.97321i	−0.279830	+	0.373809i
$178$	−1.40021	+	19.5774i	−0.104950	+	1.46739i
$179$	0.515515	+	0.802156i	0.0385314	+	0.0599560i	0.859985	−	0.510319i	$-0.170473\pi$
$179$	0.515515	+	0.802156i	0.0385314	+	0.0599560i	−0.821454	+	0.570275i	$0.806836\pi$
$180$	−0.0181212	−	1.24962i	−0.00135067	−	0.0931409i
$181$	−0.853862	−	5.93874i	−0.0634671	−	0.441423i	−0.996634	−	0.0819799i	$-0.973876\pi$
$181$	−0.853862	−	5.93874i	−0.0634671	−	0.441423i	0.933167	−	0.359443i	$-0.117033\pi$
$182$	−22.2470	−	16.6539i	−1.64906	−	1.23447i
$183$	−2.00150	+	2.67369i	−0.147955	+	0.197645i
$184$	5.55787	−	3.57183i	0.409732	−	0.263318i
$185$	1.60946	−	7.95202i	0.118330	−	0.584644i
$186$	31.7891	−	4.57059i	2.33089	−	0.335132i
$187$	−7.42492	+	11.3097i	−0.542964	+	0.827048i
$188$	2.47654	+	3.30826i	0.180620	+	0.241280i
$189$	20.7413	−	13.3296i	1.50870	−	0.969585i
$190$	32.5831	−	2.80580i	2.36383	−	0.203554i
$191$	−8.02137	+	9.25716i	−0.580406	+	0.669825i	−0.967692	−	0.252135i	$-0.918867\pi$
$191$	−8.02137	+	9.25716i	−0.580406	+	0.669825i	0.387286	+	0.921960i	$0.373413\pi$
$192$	−4.44537	+	62.1543i	−0.320817	+	4.48560i
$193$	21.0926	−	7.86714i	1.51828	−	0.566289i	0.554312	−	0.832309i	$-0.312981\pi$
$193$	21.0926	−	7.86714i	1.51828	−	0.566289i	0.963968	+	0.266020i	$0.0857086\pi$
$194$	19.9640	+	12.8301i	1.43333	+	0.921144i
$195$	0.119036	+	8.20857i	0.00852433	+	0.587828i
$196$	54.5042	−	62.9012i	3.89316	−	4.49295i
$197$	12.7166	+	4.74303i	0.906018	+	0.337927i	0.758912	−	0.651194i	$-0.225731\pi$
$197$	12.7166	+	4.74303i	0.906018	+	0.337927i	0.147106	+	0.989121i	$0.453004\pi$
$198$	0.910666	+	0.00886847i	0.0647182	+	0.000630255i
$199$	−1.08403	−	0.495062i	−0.0768452	−	0.0350940i	0.376622	−	0.926367i	$-0.377086\pi$
$199$	−1.08403	−	0.495062i	−0.0768452	−	0.0350940i	−0.453467	+	0.891273i	$0.649813\pi$
$200$	−28.7487	+	40.8195i	−2.03284	+	2.88638i
$201$	−3.29913	+	22.9459i	−0.232702	+	1.61848i
$202$	−24.3245	−	24.3245i	−1.71146	−	1.71146i
$203$	−22.4100	+	12.2368i	−1.57288	+	0.858855i
$204$	32.8329	−	21.1005i	2.29877	−	1.47733i
$205$	0.206555	+	1.30228i	0.0144264	+	0.0909550i
$206$	−2.48495	+	8.46297i	−0.173135	+	0.589643i
$207$	0.0139918	+	0.0643194i	0.000972499	+	0.00447050i
$208$	−2.51050	+	35.1013i	−0.174072	+	2.43384i
$209$	1.08301	+	17.5415i	0.0749133	+	1.21337i
$210$	−49.0135	−	2.79186i	−3.38226	−	0.192656i
$211$	−4.58462	−	15.6138i	−0.315618	−	1.07490i	−0.952652	−	0.304061i	$-0.901657\pi$
$211$	−4.58462	−	15.6138i	−0.315618	−	1.07490i	0.637034	−	0.770836i	$-0.280161\pi$
$212$	2.24967	+	1.22841i	0.154508	+	0.0843676i
$213$	3.60028	+	0.257497i	0.246687	+	0.0176434i
$214$	3.83078	+	13.0464i	0.261867	+	0.891836i
$215$	4.39424	+	5.69595i	0.299684	+	0.388461i
$216$	−47.9468	−	21.8966i	−3.26237	−	1.48987i
$217$	2.27655	+	31.8303i	0.154542	+	2.16078i
$218$	11.2717	+	30.2207i	0.763418	+	2.04680i
$219$	4.23572	+	2.72213i	0.286223	+	0.183945i
$220$	−33.4715	−	24.8086i	−2.25665	−	1.67260i
$221$	7.39764	−	4.75417i	0.497619	−	0.319800i
$222$	−13.6536	−	10.2210i	−0.916371	−	0.685987i
$223$	18.9302	+	1.35391i	1.26766	+	0.0906648i	0.688914	−	0.724843i	$-0.258088\pi$
$223$	18.9302	+	1.35391i	1.26766	+	0.0906648i	0.578746	+	0.815508i	$0.303542\pi$
$224$	−115.974	−	16.6746i	−7.74886	−	1.11412i
$225$	−0.280955	−	0.410495i	−0.0187304	−	0.0273664i
$226$	5.67941	−	8.83734i	0.377789	−	0.587851i
$227$	26.1963	+	9.77072i	1.73871	+	0.648505i	0.999683	−	0.0251703i	$-0.00801280\pi$
$227$	26.1963	+	9.77072i	1.73871	+	0.648505i	0.739027	+	0.673676i	$0.235286\pi$
$228$	17.7176	−	47.5028i	1.17338	−	3.14595i
$229$	2.77068	−	9.43606i	0.183092	−	0.623553i	−0.815880	−	0.578221i	$-0.803747\pi$
$229$	2.77068	−	9.43606i	0.183092	−	0.623553i	0.998972	−	0.0453319i	$-0.0144345\pi$
$230$	1.64225	−	3.73855i	0.108287	−	0.246512i
$231$	2.13827	−	26.2956i	0.140688	−	1.73013i
$232$	47.9102	+	26.1610i	3.14546	+	1.71755i
$233$	1.47911	+	1.47911i	0.0969000	+	0.0969000i	0.753895	−	0.656995i	$-0.228173\pi$
$233$	1.47911	+	1.47911i	0.0969000	+	0.0969000i	−0.656995	+	0.753895i	$0.728173\pi$
$234$	−0.538443	−	0.245899i	−0.0351991	−	0.0160749i
$235$	1.54933	+	0.552416i	0.101067	+	0.0360356i
$236$	−2.91632	+	20.2835i	−0.189836	+	1.32034i
$237$	−8.34517	−	3.11259i	−0.542077	−	0.202184i
$238$	25.2019	+	46.1539i	1.63360	+	2.99171i
$239$	17.6232			1.13995			0.569976	−	0.821662i	$-0.306953\pi$
$239$	17.6232			1.13995			0.569976	+	0.821662i	$0.306953\pi$
$240$	30.5817	+	54.1253i	1.97404	+	3.49377i
$241$		−	2.02406i		−	0.130381i	−0.997873	−	0.0651906i	$-0.979234\pi$
$241$		−	2.02406i		−	0.130381i	0.997873	−	0.0651906i	$-0.0207655\pi$
$242$	18.6643	−	23.9459i	1.19978	−	1.53930i
$243$	0.730773	−	0.730773i	0.0468791	−	0.0468791i
$244$	−1.56787	+	10.9048i	−0.100373	+	0.698106i
$245$	4.23866	−	32.8558i	0.270798	−	2.09908i
$246$	2.65956	+	0.780916i	0.169567	+	0.0497894i
$247$	3.99199	−	10.7029i	0.254004	−	0.681011i
$248$	54.6158	−	40.8849i	3.46811	−	2.59619i
$249$	−9.53637	+	6.12866i	−0.604343	+	0.388388i
$250$	−0.860792	+	30.8462i	−0.0544413	+	1.95089i
$251$	14.2527			0.899621			0.449810	−	0.893124i	$-0.351492\pi$
$251$	14.2527			0.899621			0.449810	+	0.893124i	$0.351492\pi$
$252$	1.25106	−	2.29115i	0.0788096	−	0.144329i
$253$	1.98710	+	0.930971i	0.124928	+	0.0585297i
$254$	12.7420	−	43.3953i	0.799505	−	2.72286i
$255$	6.24770	−	14.2228i	0.391246	−	0.890665i
$256$	27.8630	+	61.0115i	1.74144	+	3.81322i
$257$	1.88480	−	5.05334i	0.117570	−	0.315219i	−0.864813	−	0.502094i	$-0.832563\pi$
$257$	1.88480	−	5.05334i	0.117570	−	0.315219i	0.982384	+	0.186875i	$0.0598360\pi$
$258$	14.7774	−	3.21462i	0.919998	−	0.200133i
$259$	11.0979	−	12.8076i	0.689589	−	0.795828i
$260$	13.3212	+	23.5767i	0.826148	+	1.46217i
$261$	−0.411027	+	0.356157i	−0.0254420	+	0.0220456i
$262$	1.27960	−	1.70935i	0.0790542	−	0.105604i
$263$	19.8205	+	4.31169i	1.22219	+	0.265870i	0.776961	−	0.629549i	$-0.216760\pi$
$263$	19.8205	+	4.31169i	1.22219	+	0.265870i	0.445224	+	0.895419i	$0.353124\pi$
$264$	−49.7644	+	26.5476i	−3.06279	+	1.63389i
$265$	1.01647	−	0.0875301i	0.0624411	−	0.00537693i
$266$	62.1382	+	28.3776i	3.80994	+	1.73994i
$267$	12.0803	−	0.863999i	0.739301	−	0.0528759i
$268$	26.7229	+	71.6469i	1.63236	+	4.37653i
$269$		−	1.12797i		−	0.0687735i	−0.999409	−	0.0343867i	$-0.989052\pi$
$269$		−	1.12797i		−	0.0687735i	0.999409	−	0.0343867i	$-0.0109478\pi$
$270$	−32.1761	+	5.10346i	−1.95817	+	0.310587i
$271$	13.4161	−	11.6251i	0.814969	−	0.706175i	−0.144033	−	0.989573i	$-0.546007\pi$
$271$	13.4161	−	11.6251i	0.814969	−	0.706175i	0.959002	+	0.283398i	$0.0914618\pi$
$272$	31.9137	−	58.4456i	1.93505	−	3.54378i
$273$	−8.21808	+	15.0503i	−0.497381	+	0.910885i
$274$	5.77879	−	6.66908i	0.349110	−	0.402894i
$275$	−16.5606	−	0.864206i	−0.998641	−	0.0521136i
$276$	−4.14545	−	4.78410i	−0.249526	−	0.287969i
$277$	−23.0642	+	5.01731i	−1.38579	+	0.301461i	−0.842778	−	0.538262i	$-0.819081\pi$
$277$	−23.0642	+	5.01731i	−1.38579	+	0.301461i	−0.543016	+	0.839723i	$0.682718\pi$
$278$	−20.0770	+	10.9629i	−1.20414	+	0.657508i
$279$	0.191502	+	0.652195i	0.0114649	+	0.0390459i
$280$	−94.2252	+	44.6936i	−5.63103	+	2.67095i
$281$	5.44975	−	18.5601i	0.325105	−	1.10720i	−0.621126	−	0.783711i	$-0.713324\pi$
$281$	5.44975	−	18.5601i	0.325105	−	1.10720i	0.946230	−	0.323494i	$-0.104857\pi$
$282$	2.44503	−	2.44503i	0.145600	−	0.145600i
$283$	−23.6995	+	17.7413i	−1.40879	+	1.05461i	−0.419643	+	0.907689i	$0.637845\pi$
$283$	−23.6995	+	17.7413i	−1.40879	+	1.05461i	−0.989149	+	0.146919i	$0.953064\pi$
$284$	10.8304	−	4.94606i	0.642664	−	0.293495i
$285$	−4.57500	−	19.6544i	−0.271000	−	1.16423i
$286$	−17.4109	+	9.28814i	−1.02953	+	0.549219i
$287$	−0.962493	+	2.58054i	−0.0568141	+	0.152325i
$288$	−2.48934	+	0.178041i	−0.146685	+	0.0104912i
$289$	0.356429	−	0.0512467i	0.0209664	−	0.00301451i
$290$	33.6142	−	2.89459i	1.97389	−	0.169976i
$291$	6.08307	−	13.3201i	0.356596	−	0.780836i
$292$	16.5663	+	1.18484i	0.969468	+	0.0693377i
$293$	20.0398	−	1.43328i	1.17074	−	0.0837328i	0.527607	−	0.849489i	$-0.323089\pi$
$293$	20.0398	−	1.43328i	1.17074	−	0.0837328i	0.643131	+	0.765756i	$0.277635\pi$
$294$	−58.5857	−	37.6508i	−3.41679	−	2.19584i
$295$	3.49553	+	7.36945i	0.203518	+	0.429066i
$296$	−35.8619	−	5.15617i	−2.08443	−	0.299696i
$297$	−2.32270	−	17.3527i	−0.134777	−	1.00691i
$298$	18.3602	+	13.7443i	1.06358	+	0.796185i
$299$	−0.934017	−	1.07791i	−0.0540156	−	0.0623373i
$300$	42.6340	+	21.6994i	2.46147	+	1.25282i
$301$	2.13853	+	14.8738i	0.123263	+	0.857310i
$302$	−38.4278	+	51.3336i	−2.21127	+	2.95391i
$303$	−12.7206	+	16.9927i	−0.730779	+	0.976206i
$304$	−12.3108	−	85.6235i	−0.706073	−	4.91085i
$305$	1.87926	+	3.96195i	0.107606	+	0.226860i
$306$	0.733513	+	0.846519i	0.0419321	+	0.0483923i
$307$	1.13738	+	0.851432i	0.0649137	+	0.0485938i	0.631242	−	0.775586i	$-0.282546\pi$
$307$	1.13738	+	0.851432i	0.0649137	+	0.0485938i	−0.566328	+	0.824180i	$0.691636\pi$
$308$	−35.3792	−	79.5096i	−2.01592	−	4.53048i
$309$	5.38715	+	0.774555i	0.306464	+	0.0440629i
$310$	14.1613	−	39.7176i	0.804310	−	2.25581i
$311$	−19.7226	−	12.6749i	−1.11837	−	0.718730i	−0.155266	−	0.987873i	$-0.549623\pi$
$311$	−19.7226	−	12.6749i	−1.11837	−	0.718730i	−0.963100	+	0.269143i	$0.913260\pi$
$312$	36.5668	−	2.61531i	2.07019	−	0.148063i
$313$	−4.90398	−	0.350740i	−0.277190	−	0.0198250i	−0.0679476	−	0.997689i	$-0.521645\pi$
$313$	−4.90398	−	0.350740i	−0.277190	−	0.0198250i	−0.209242	+	0.977864i	$0.567100\pi$
$314$	−16.0223	+	35.0840i	−0.904193	+	1.97991i
$315$	−0.0891442	−	1.03521i	−0.00502271	−	0.0583275i
$316$	−29.0809	+	4.18121i	−1.63593	+	0.235211i
$317$	−30.1437	+	2.15592i	−1.69304	+	0.121089i	−0.884251	−	0.467011i	$-0.845331\pi$
$317$	−30.1437	+	2.15592i	−1.69304	+	0.121089i	−0.808788	+	0.588100i	$0.799876\pi$
$318$	0.749495	−	2.00947i	0.0420296	−	0.112686i
$319$	1.11728	+	18.0966i	0.0625557	+	1.01321i
$320$	69.4603	+	43.2293i	3.88295	+	2.41659i
$321$	7.63198	−	3.48541i	0.425975	−	0.194536i
$322$	6.82803	−	5.11140i	0.380511	−	0.284847i
$323$	−15.2847	+	15.2847i	−0.850462	+	0.850462i
$324$	−13.7565	+	46.8504i	−0.764252	+	2.60280i
$325$	9.60593	+	4.88913i	0.532841	+	0.271200i
$326$	4.68020	+	15.9393i	0.259212	+	0.882796i
$327$	17.4681	−	9.53829i	0.965987	−	0.527469i
$328$	5.75361	−	1.25162i	0.317690	−	0.0691092i
$329$	2.24997	+	2.59660i	0.124045	+	0.143155i
$330$	−16.5610	+	30.6756i	−0.911654	+	1.68864i
$331$	−11.3478	+	13.0961i	−0.623732	+	0.719825i	−0.976411	−	0.215919i	$-0.930725\pi$
$331$	−11.3478	+	13.0961i	−0.623732	+	0.719825i	0.352679	+	0.935744i	$0.385271\pi$
$332$	−17.9205	+	32.8190i	−0.983516	+	1.80117i
$333$	0.172997	−	0.316820i	0.00948018	−	0.0173617i
$334$	−43.6870	+	37.8550i	−2.39044	+	2.07133i
$335$	24.6277	+	17.8848i	1.34555	+	0.977149i
$336$			129.855i			7.08418i
$337$	8.88116	+	23.8113i	0.483788	+	1.29708i	0.918109	+	0.396327i	$0.129715\pi$
$337$	8.88116	+	23.8113i	0.483788	+	1.29708i	−0.434322	+	0.900758i	$0.643012\pi$
$338$	−22.9956	+	1.64468i	−1.25080	+	0.0894589i
$339$	−5.89633	−	2.69276i	−0.320244	−	0.146251i
$340$	−4.39633	−	51.0536i	−0.238425	−	2.76877i
$341$	21.1534	+	8.12532i	1.14552	+	0.440011i
$342$	1.42180	+	0.309294i	0.0768822	+	0.0167247i
$343$	21.8754	−	29.2221i	1.18116	−	1.57785i
$344$	24.2788	−	21.0377i	1.30903	−	1.13428i
$345$	−2.42761	−	0.674733i	−0.130698	−	0.0363264i
$346$	40.9759	−	47.2887i	2.20288	−	2.54225i
$347$	4.09609	−	0.891050i	0.219890	−	0.0478341i	−0.101271	−	0.994859i	$-0.532291\pi$
$347$	4.09609	−	0.891050i	0.219890	−	0.0478341i	0.321160	+	0.947025i	$0.395927\pi$
$348$	18.2783	−	49.0060i	0.979820	−	2.62700i
$349$	5.74385	+	12.5773i	0.307461	+	0.673246i	0.998784	−	0.0492999i	$-0.0156990\pi$
$349$	5.74385	+	12.5773i	0.307461	+	0.673246i	−0.691323	+	0.722546i	$0.742972\pi$
$350$	−33.2609	+	55.2120i	−1.77787	+	2.95120i
$351$	−3.20594	+	10.9184i	−0.171120	+	0.582782i
$352$	−45.6605	+	69.5505i	−2.43371	+	3.70705i
$353$	−4.70451	+	8.61566i	−0.250396	+	0.458565i	−0.972399	−	0.233324i	$-0.925040\pi$
$353$	−4.70451	+	8.61566i	−0.250396	+	0.458565i	0.722003	+	0.691890i	$0.243221\pi$
$354$	17.1462			0.911313
$355$	2.50405	−	4.02348i	0.132901	−	0.213544i
$356$	33.6082	−	21.5987i	1.78123	−	1.14473i
$357$	25.9763	−	19.4456i	1.37481	−	1.02917i
$358$	0.919710	−	2.46584i	0.0486082	−	0.130324i
$359$	−12.9092	−	3.79049i	−0.681322	−	0.200054i	−0.0772833	−	0.997009i	$-0.524625\pi$
$359$	−12.9092	−	3.79049i	−0.681322	−	0.200054i	−0.604039	+	0.796955i	$0.706443\pi$
$360$	−1.75880	+	1.35686i	−0.0926969	+	0.0715126i
$361$	−1.29217	+	8.98721i	−0.0680087	+	0.473011i
$362$	−11.7095	+	11.7095i	−0.615438	+	0.615438i
$363$	−16.2645	−	9.29676i	−0.853662	−	0.487953i
$364$			56.5642i			2.96477i
$365$	5.75553	−	3.25197i	0.301258	−	0.170216i
$366$	9.21813			0.481840
$367$	−7.78800	−	14.2627i	−0.406530	−	0.744505i	0.591561	−	0.806260i	$-0.298512\pi$
$367$	−7.78800	−	14.2627i	−0.406530	−	0.744505i	−0.998091	+	0.0617554i	$0.980330\pi$
$368$	−10.1198	−	3.77449i	−0.527531	−	0.196759i
$369$	−0.00834894	+	0.0580681i	−0.000434628	+	0.00302291i
$370$	−20.2323	+	9.59675i	−1.05183	+	0.498911i
$371$	1.93847	+	0.885270i	0.100640	+	0.0459609i
$372$	−46.2233	−	46.2233i	−2.39657	−	2.39657i
$373$	−26.1652	−	14.2873i	−1.35478	−	0.739766i	−0.372651	−	0.927972i	$-0.621551\pi$
$373$	−26.1652	−	14.2873i	−1.35478	−	0.739766i	−0.982130	+	0.188206i	$0.939733\pi$
$374$	37.2702	−	2.30106i	1.92720	−	0.118985i
$375$	18.9156	−	2.18303i	0.976795	−	0.112731i
$376$	2.06943	−	7.04782i	0.106723	−	0.363464i
$377$	4.11831	−	11.0416i	0.212104	−	0.568673i
$378$	−63.7589	−	23.7808i	−3.27940	−	1.22315i
$379$	−0.317867	+	0.494611i	−0.0163277	+	0.0254065i	−0.849321	−	0.527876i	$-0.822989\pi$
$379$	−0.317867	+	0.494611i	−0.0163277	+	0.0254065i	0.832994	+	0.553282i	$0.186625\pi$
$380$	−44.3161	−	49.6697i	−2.27337	−	2.54800i
$381$	−27.6235	−	3.97166i	−1.41520	−	0.203474i
$382$	33.7216	+	2.41182i	1.72535	+	0.123399i
$383$	−2.04304	−	1.52940i	−0.104394	−	0.0781487i	0.545805	−	0.837912i	$-0.316224\pi$
$383$	−2.04304	−	1.52940i	−0.104394	−	0.0781487i	−0.650200	+	0.759763i	$0.725315\pi$
$384$	72.8029	−	46.7876i	3.71521	−	2.38762i
$385$	−29.2288	−	18.5881i	−1.48964	−	0.947339i
$386$	−52.2706	−	33.5923i	−2.66050	−	1.70980i
$387$	0.111854	+	0.299893i	0.00568588	+	0.0152444i
$388$	−3.44589	−	48.1799i	−0.174939	−	2.44596i
$389$	9.57365	+	4.37214i	0.485404	+	0.221676i	0.643057	−	0.765818i	$-0.277666\pi$
$389$	9.57365	+	4.37214i	0.485404	+	0.221676i	−0.157654	+	0.987494i	$0.550393\pi$
$390$	17.9402	−	13.8403i	0.908437	−	0.700829i
$391$	0.760374	+	2.58960i	0.0384538	+	0.130961i
$392$	−147.560	−	10.5537i	−7.45293	−	0.533044i
$393$	−1.15639	−	0.631437i	−0.0583322	−	0.0318518i
$394$	−10.5537	−	35.9428i	−0.531690	−	1.81077i
$395$	−8.72584	+	7.78534i	−0.439044	+	0.391723i
$396$	−1.09636	−	1.49469i	−0.0550943	−	0.0751110i
$397$	0.467935	−	6.54259i	0.0234850	−	0.328363i	−0.972105	−	0.234548i	$-0.924639\pi$
$397$	0.467935	−	6.54259i	0.0234850	−	0.328363i	0.995590	−	0.0938155i	$-0.0299064\pi$
$398$	0.699175	+	3.21406i	0.0350465	+	0.161106i
$399$	11.8755	−	40.4442i	0.594517	−	2.02474i
$400$	81.5883	−	2.36679i	4.07942	−	0.118339i
$401$	−23.8506	+	15.3279i	−1.19104	+	0.765437i	−0.977384	−	0.211471i	$-0.932175\pi$
$401$	−23.8506	+	15.3279i	−1.19104	+	0.765437i	−0.213659	+	0.976908i	$0.568538\pi$
$402$	56.1566	−	30.6638i	2.80083	−	1.52937i
$403$	−10.4146	−	10.4146i	−0.518790	−	0.518790i
$404$	−9.96465	+	69.3057i	−0.495760	+	3.44809i
$405$	5.74532	+	18.5665i	0.285487	+	0.922576i
$406$	64.1045	+	29.2756i	3.18145	+	1.45292i
$407$	−4.89223	−	10.9946i	−0.242499	−	0.544982i
$408$	−64.9974	−	24.2428i	−3.21785	−	1.20020i
$409$	−2.20884	+	2.54913i	−0.109220	+	0.126047i	−0.807727	−	0.589556i	$-0.799303\pi$
$409$	−2.20884	+	2.54913i	−0.109220	+	0.126047i	0.698507	+	0.715603i	$0.253848\pi$
$410$	2.53577	−	2.61040i	0.125233	−	0.128918i
$411$	−4.58075	−	2.94387i	−0.225952	−	0.145210i
$412$	16.8210	−	6.27390i	0.828710	−	0.309093i
$413$	−1.21541	+	16.9937i	−0.0598066	+	0.836206i
$414$	0.118973	−	0.137302i	0.00584718	−	0.00674801i
$415$	1.27692	+	14.8286i	0.0626816	+	0.727907i
$416$	45.4927	−	29.2364i	2.23046	−	1.43343i
$417$	8.45886	+	11.2997i	0.414232	+	0.553349i
$418$	36.9671	−	31.4071i	1.80812	−	1.53617i
$419$	−11.8863	+	1.70899i	−0.580684	+	0.0834898i	−0.426397	−	0.904536i	$-0.640217\pi$
$419$	−11.8863	+	1.70899i	−0.580684	+	0.0834898i	−0.154288	+	0.988026i	$0.549308\pi$
$420$	55.2366	+	83.2699i	2.69527	+	4.06316i
$421$	−16.8784	+	10.8471i	−0.822602	+	0.528654i	−0.882919	−	0.469525i	$-0.844425\pi$
$421$	−16.8784	+	10.8471i	−0.822602	+	0.528654i	0.0603169	+	0.998179i	$0.480789\pi$
$422$	−26.9160	+	35.9556i	−1.31025	+	1.75029i
$423$	0.0585865	+	0.0438573i	0.00284857	+	0.00213241i
$424$	−0.648380	−	4.50958i	−0.0314881	−	0.219004i
$425$	−12.6912	−	15.9666i	−0.615613	−	0.774492i
$426$	−5.38604	−	8.38084i	−0.260954	−	0.406053i
$427$	−0.653429	+	9.13613i	−0.0316216	+	0.442128i
$428$	16.5856	−	22.1558i	0.801697	−	1.07094i
$429$	7.20187	+	9.81844i	0.347710	+	0.474039i
$430$	5.31716	−	19.1305i	0.256416	−	0.922554i
$431$	7.67418	+	11.9413i	0.369652	+	0.575190i	0.975393	−	0.220472i	$-0.0707597\pi$
$431$	7.67418	+	11.9413i	0.369652	+	0.575190i	−0.605741	+	0.795662i	$0.707123\pi$
$432$	18.3172	+	84.2030i	0.881289	+	4.05122i
$433$	−2.20641	−	30.8496i	−0.106033	−	1.48254i	−0.720422	−	0.693536i	$-0.756052\pi$
$433$	−2.20641	−	30.8496i	−0.106033	−	1.48254i	0.614389	−	0.789003i	$-0.289403\pi$
$434$	66.5646	−	57.6785i	3.19520	−	2.76866i
$435$	−4.71978	−	20.2764i	−0.226296	−	0.972178i
$436$	35.4937	−	55.2292i	1.69984	−	2.64500i
$437$	2.80669	+	2.10106i	0.134262	+	0.100507i
$438$	−0.991390	−	13.8614i	−0.0473704	−	0.662325i
$439$	−10.4826	−	22.9538i	−0.500309	−	1.09552i	−0.976369	−	0.216111i	$-0.930663\pi$
$439$	−10.4826	−	22.9538i	−0.500309	−	1.09552i	0.476060	−	0.879413i	$-0.342064\pi$
$440$	0.352662	+	74.0531i	0.0168125	+	3.53034i
$441$	0.612295	−	1.34074i	0.0291569	−	0.0638447i
$442$	−22.7404	−	8.48174i	−1.08165	−	0.403435i
$443$	14.1508	+	18.9032i	0.672324	+	0.898120i	0.998892	−	0.0470539i	$-0.0149833\pi$
$443$	14.1508	+	18.9032i	0.672324	+	0.898120i	−0.326568	+	0.945174i	$0.605892\pi$
$444$			34.7151i			1.64750i
$445$	6.39521	−	14.5586i	0.303162	−	0.690144i
$446$	−28.3197	−	44.0663i	−1.34097	−	2.08660i
$447$	6.78229	−	12.4208i	0.320791	−	0.587485i
$448$	81.9000	+	149.989i	3.86941	+	7.08630i
$449$	−0.439529	+	0.683920i	−0.0207426	+	0.0322762i	−0.851470	−	0.524403i	$-0.824288\pi$
$449$	−0.439529	+	0.683920i	−0.0207426	+	0.0322762i	0.830727	+	0.556679i	$0.187925\pi$
$450$	−0.442293	+	1.29975i	−0.0208499	+	0.0612709i
$451$	1.36938	+	1.39632i	0.0644817	+	0.0657499i
$452$	−21.3275	+	1.52537i	−1.00316	+	0.0717476i
$453$	34.7276	+	18.9627i	1.63164	+	0.890945i
$454$	−21.7409	−	74.0426i	−1.02035	−	3.47499i
$455$	12.4455	+	18.7617i	0.583452	+	0.879561i
$456$	−86.4652	+	25.3885i	−4.04911	+	1.18892i
$457$	13.6542	−	13.6542i	0.638717	−	0.638717i	−0.311522	−	0.950239i	$-0.600839\pi$
$457$	13.6542	−	13.6542i	0.638717	−	0.638717i	0.950239	+	0.311522i	$0.100839\pi$
$458$	−25.4321	+	9.48567i	−1.18836	+	0.443236i
$459$	14.1011	−	16.2735i	0.658181	−	0.759581i
$460$	−8.09491	+	1.88427i	−0.377427	+	0.0878546i
$461$	−3.78270	+	5.88600i	−0.176178	+	0.274138i	−0.918101	−	0.396347i	$-0.870278\pi$
$461$	−3.78270	+	5.88600i	−0.176178	+	0.274138i	0.741923	+	0.670485i	$0.233914\pi$
$462$	−61.6377	+	38.7693i	−2.86765	+	1.80371i
$463$	−4.66189	+	21.4304i	−0.216656	+	0.995953i	0.732407	+	0.680867i	$0.238397\pi$
$463$	−4.66189	+	21.4304i	−0.216656	+	0.995953i	−0.949063	+	0.315086i	$0.897967\pi$
$464$	−12.7004	−	88.3331i	−0.589600	−	4.10076i
$465$	−25.5019	−	5.16151i	−1.18262	−	0.239359i
$466$	0.821643	−	5.71465i	0.0380619	−	0.264726i
$467$	41.8509	−	2.99324i	1.93663	−	0.138511i	0.951199	−	0.308579i	$-0.0998535\pi$
$467$	41.8509	−	2.99324i	1.93663	−	0.138511i	0.985432	+	0.170069i	$0.0543989\pi$
$468$	0.256106	+	1.17730i	0.0118385	+	0.0544208i
$469$	26.4104	+	57.8306i	1.21952	+	2.67037i
$470$	−1.34207	−	4.33701i	−0.0619050	−	0.200051i
$471$	22.8353	+	6.70505i	1.05220	+	0.308952i
$472$	31.9682	−	17.4559i	1.47145	−	0.803475i
$473$	10.2084	+	3.10575i	0.469382	+	0.142802i
$474$	6.92583	+	23.5872i	0.318114	+	1.08340i
$475$	−25.6276	−	6.72424i	−1.17588	−	0.308530i
$476$	44.4640	−	97.3626i	2.03800	−	4.46261i
$477$	0.0443547	+	0.00964877i	0.00203086	+	0.000441787i
$478$	−29.1494	−	38.9390i	−1.33326	−	1.78103i
$479$	2.67449	+	5.85633i	0.122201	+	0.267582i	0.960839	−	0.277106i	$-0.0893753\pi$
$479$	2.67449	+	5.85633i	0.122201	+	0.267582i	−0.838639	+	0.544688i	$0.816648\pi$
$480$	38.4210	−	87.4648i	1.75367	−	3.99220i
$481$			7.82170i			0.356639i
$482$	−4.47222	+	3.34786i	−0.203704	+	0.152491i
$483$	−3.72150	−	3.72150i	−0.169334	−	0.169334i
$484$	−61.7846	−	1.20349i	−2.80839	−	0.0547040i
$485$	−11.7437	−	15.2225i	−0.533252	−	0.691218i
$486$	−2.82339	−	0.405942i	−0.128072	−	0.0184139i
$487$	17.3643	+	17.3643i	0.786851	+	0.786851i	0.980977	−	0.194125i	$-0.0621869\pi$
$487$	17.3643	+	17.3643i	0.786851	+	0.786851i	−0.194125	+	0.980977i	$0.562187\pi$
$488$	17.1867	−	9.38463i	0.778004	−	0.424822i
$489$	9.32426	−	4.25825i	0.421658	−	0.192565i
$490$	−79.6068	+	44.9791i	−3.59627	+	2.03195i
$491$	19.1476	+	29.7942i	0.864119	+	1.34459i	0.937751	+	0.347309i	$0.112905\pi$
$491$	19.1476	+	29.7942i	0.864119	+	1.34459i	−0.0736319	+	0.997285i	$0.523459\pi$
$492$	−1.97162	−	5.28613i	−0.0888877	−	0.238317i
$493$	−15.7684	+	15.7684i	−0.710171	+	0.710171i
$494$	−30.2513	+	8.88259i	−1.36107	+	0.399647i
$495$	−0.692517	−	0.254545i	−0.0311263	−	0.0114410i
$496$	−107.017	−	31.4229i	−4.80518	−	1.41093i
$497$	8.68808	−	4.74405i	0.389714	−	0.212800i
$498$	29.3149	+	10.9339i	1.31363	+	0.489960i
$499$	−4.46460	+	2.03891i	−0.199863	+	0.0912743i	−0.512832	−	0.858489i	$-0.671404\pi$
$499$	−4.46460	+	2.03891i	−0.199863	+	0.0912743i	0.312969	+	0.949763i	$0.398676\pi$
$500$	51.3120	−	36.2231i	2.29474	−	1.61994i
$501$	26.9571	+	23.3585i	1.20435	+	1.04358i
$502$	−23.5744	−	31.4917i	−1.05218	−	1.40554i
$503$	0.426587	−	5.96446i	0.0190206	−	0.265942i	−0.979039	−	0.203674i	$-0.934712\pi$
$503$	0.426587	−	5.96446i	0.0190206	−	0.265942i	0.998059	−	0.0622687i	$-0.0198336\pi$
$504$	−4.59274	+	0.660336i	−0.204577	+	0.0294137i
$505$	11.9437	+	25.1803i	0.531488	+	1.12051i
$506$	−1.22973	−	5.93042i	−0.0546680	−	0.263639i
$507$	3.02390	+	13.9006i	0.134296	+	0.617349i
$508$	−86.2524	+	32.1705i	−3.82683	+	1.42733i
$509$	18.0202	+	15.6146i	0.798732	+	0.692105i	0.955325	−	0.295558i	$-0.0955056\pi$
$509$	18.0202	+	15.6146i	0.798732	+	0.692105i	−0.156593	+	0.987663i	$0.550051\pi$
$510$	−41.7596	+	9.72047i	−1.84914	+	0.430430i
$511$	13.8084			0.610848
$512$	40.0152	−	73.2823i	1.76844	−	3.23865i
$513$	1.99550	−	27.9007i	0.0881033	−	1.23185i
$514$	−14.2830	+	4.19387i	−0.629997	+	0.184984i
$515$	4.19891	−	5.78199i	0.185026	−	0.254785i
$516$	−23.2632	−	20.1576i	−1.02410	−	0.887391i
$517$	2.34749	−	0.664525i	0.103243	−	0.0292258i
$518$	−46.6551	−	3.33684i	−2.04991	−	0.146612i
$519$	−32.4808	−	20.8742i	−1.42575	−	0.916274i
$520$	19.3582	−	44.0686i	0.848913	−	1.93254i
$521$	−18.2370	+	5.35486i	−0.798976	+	0.234600i	−0.655640	−	0.755074i	$-0.727601\pi$
$521$	−18.2370	+	5.35486i	−0.798976	+	0.234600i	−0.143336	+	0.989674i	$0.545783\pi$
$522$	1.46679	+	0.319081i	0.0641998	+	0.0139658i
$523$	11.1966	+	20.5051i	0.489594	+	0.896624i	0.999341	+	0.0362995i	$0.0115570\pi$
$523$	11.1966	+	20.5051i	0.489594	+	0.896624i	−0.509747	+	0.860324i	$0.670261\pi$
$524$	−4.34612			−0.189861
$525$	36.6427	+	15.4663i	1.59922	+	0.675004i
$526$	−23.2570	−	50.9257i	−1.01405	−	2.22047i
$527$	9.73972	+	26.1132i	0.424269	+	1.13751i
$528$	83.4995	+	39.1201i	3.63385	+	1.70248i
$529$	−20.5233	+	9.37270i	−0.892319	+	0.407509i
$530$	−1.87467	−	2.10114i	−0.0814305	−	0.0912675i
$531$	0.0516455	+	0.359203i	0.00224122	+	0.0155881i
$532$	−29.5555	−	135.865i	−1.28140	−	5.89048i
$533$	−0.444230	−	1.19103i	−0.0192417	−	0.0515890i
$534$	−21.8902	−	25.2627i	−0.947283	−	1.09322i
$535$	0.626459	−	10.9980i	0.0270842	−	0.475487i
$536$	73.4830	−	114.342i	3.17398	−	4.93881i
$537$	−1.58683	−	0.345193i	−0.0684766	−	0.0148962i
$538$	−2.49228	+	1.86570i	−0.107450	+	0.0804359i
$539$	−23.1277	−	43.3537i	−0.996181	−	1.86738i
$540$	47.5636	+	46.2038i	2.04681	+	1.98829i
$541$	0.483481	−	0.418939i	0.0207865	−	0.0180116i	−0.644406	−	0.764684i	$-0.722895\pi$
$541$	0.483481	−	0.418939i	0.0207865	−	0.0180116i	0.665192	+	0.746672i	$0.268350\pi$
$542$	−47.8767	−	10.4149i	−2.05648	−	0.447360i
$543$	8.18010	+	6.12355i	0.351042	+	0.262787i
$544$	−101.288	+	14.5630i	−4.34267	+	0.624382i
$545$	−0.378897	−	26.1283i	−0.0162302	−	1.11921i
$546$	46.8470	−	6.73559i	2.00487	−	0.288257i
$547$	−3.83296	+	17.6198i	−0.163885	+	0.753369i	0.819681	+	0.572821i	$0.194151\pi$
$547$	−3.83296	+	17.6198i	−0.163885	+	0.753369i	−0.983566	+	0.180548i	$0.942213\pi$
$548$	−17.9157	−	1.28136i	−0.765322	−	0.0547369i
$549$	0.0277656	+	0.193114i	0.00118501	+	0.00824190i
$550$	25.4823	+	38.0205i	1.08657	+	1.62120i
$551$	−4.12260	+	28.6733i	−0.175629	+	1.22153i
$552$	−2.39172	+	10.9946i	−0.101799	+	0.467960i
$553$	−23.8683	+	5.19224i	−1.01498	+	0.220796i
$554$	49.2349	+	42.6622i	2.09179	+	1.81255i
$555$	7.63812	+	11.5146i	0.324220	+	0.488766i
$556$	42.3528	+	19.3419i	1.79616	+	0.820278i
$557$	−1.10751	+	0.240925i	−0.0469269	+	0.0102083i	−0.235967	−	0.971761i	$-0.575826\pi$
$557$	−1.10751	+	0.240925i	−0.0469269	+	0.0102083i	0.189041	+	0.981969i	$0.439462\pi$
$558$	1.12429	−	1.50188i	0.0475951	−	0.0635797i
$559$	−5.24146	−	4.54175i	−0.221690	−	0.192096i
$560$	150.807	+	79.5303i	6.37277	+	3.36077i
$561$	−4.67832	−	22.5615i	−0.197519	−	0.952546i
$562$	−50.0232	+	18.6577i	−2.11010	+	0.787028i
$563$	−10.0468	+	26.9366i	−0.423423	+	1.13524i	0.533729	+	0.845656i	$0.320790\pi$
$563$	−10.0468	+	26.9366i	−0.423423	+	1.13524i	−0.957152	+	0.289586i	$0.906482\pi$
$564$	−6.96644	−	1.00162i	−0.293340	−	0.0421759i
$565$	−6.73847	+	5.19850i	−0.283489	+	0.218703i
$566$	78.3997	+	23.0202i	3.29538	+	0.967612i
$567$	−8.62929	+	39.6682i	−0.362396	+	1.66591i
$568$	−18.5742	−	10.1423i	−0.779355	−	0.425560i
$569$	−16.0684	−	4.71810i	−0.673621	−	0.197793i	−0.0730064	−	0.997331i	$-0.523259\pi$
$569$	−16.0684	−	4.71810i	−0.673621	−	0.197793i	−0.600615	+	0.799538i	$0.705078\pi$
$570$	−35.8598	+	42.6177i	−1.50200	+	1.78506i
$571$	−3.02674	+	2.62269i	−0.126665	+	0.109756i	−0.715890	−	0.698213i	$-0.753979\pi$
$571$	−3.02674	+	2.62269i	−0.126665	+	0.109756i	0.589225	+	0.807969i	$0.299433\pi$
$572$	36.3720	+	17.0405i	1.52079	+	0.712499i
$573$	−1.48821	−	20.8079i	−0.0621710	−	0.869265i
$574$	7.29378	−	2.14165i	0.304437	−	0.0893906i
$575$	−2.27040	+	2.40606i	−0.0946822	+	0.100340i
$576$	2.38374	+	2.75098i	0.0993223	+	0.114624i
$577$	−10.8967	−	5.95006i	−0.453636	−	0.247704i	0.236151	−	0.971716i	$-0.424114\pi$
$577$	−10.8967	−	5.95006i	−0.453636	−	0.247704i	−0.689787	+	0.724012i	$0.742296\pi$
$578$	−0.702776	−	0.702776i	−0.0292316	−	0.0292316i
$579$	−15.9270	+	34.8752i	−0.661903	+	1.44937i
$580$	−45.7185	−	51.2415i	−1.89836	−	2.12769i
$581$	−12.9146	+	28.2791i	−0.535789	+	1.17321i
$582$	−39.4927	+	8.59111i	−1.63703	+	0.356113i
$583$	1.15323	−	0.979780i	0.0477619	−	0.0405783i
$584$	−15.9602	−	24.8345i	−0.660438	−	1.02766i
$585$	0.343981	+	0.334148i	0.0142219	+	0.0138153i
$586$	−36.3134	−	41.9079i	−1.50009	−	1.73120i
$587$	19.9803	−	14.9570i	0.824674	−	0.617343i	−0.101332	−	0.994853i	$-0.532310\pi$
$587$	19.9803	−	14.9570i	0.824674	−	0.617343i	0.926006	+	0.377510i	$0.123219\pi$
$588$	10.1122	+	141.387i	0.417021	+	5.83072i
$589$	30.4573	+	19.5737i	1.25497	+	0.806520i
$590$	10.5013	−	19.9128i	0.432331	−	0.819796i
$591$	−21.0260	+	9.60225i	−0.864894	+	0.394984i
$592$	28.3865	+	51.9860i	1.16668	+	2.13661i
$593$	−10.8293	−	19.8324i	−0.444707	−	0.814420i	0.555143	−	0.831755i	$-0.312664\pi$
$593$	−10.8293	−	19.8324i	−0.444707	−	0.814420i	−0.999850	+	0.0173350i	$0.994482\pi$
$594$	−34.4995	+	33.8341i	−1.41553	+	1.38823i
$595$	−6.67387	−	42.0771i	−0.273602	−	1.72499i
$596$		−	46.6818i		−	1.91216i
$597$	1.90165	−	0.709280i	0.0778294	−	0.0290289i
$598$	−0.836786	+	3.84664i	−0.0342187	+	0.157301i
$599$	20.2763	+	2.91530i	0.828468	+	0.119116i	0.543487	−	0.839417i	$-0.317104\pi$
$599$	20.2763	+	2.91530i	0.828468	+	0.119116i	0.284981	+	0.958533i	$0.408013\pi$
$600$	−14.5365	−	83.7786i	−0.593450	−	3.42025i
$601$	−5.16984	+	17.6068i	−0.210882	+	0.718198i	0.784320	+	0.620356i	$0.213012\pi$
$601$	−5.16984	+	17.6068i	−0.210882	+	0.718198i	−0.995202	+	0.0978417i	$0.968806\pi$
$602$	29.3269	−	29.3269i	1.19527	−	1.19527i
$603$	0.811533	+	1.08408i	0.0330482	+	0.0441472i
$604$	130.518			5.31072
$605$	−20.7580	+	13.1949i	−0.843933	+	0.536448i
$606$	58.5862			2.37990
$607$	−14.0191	−	18.7273i	−0.569018	−	0.760119i	0.420063	−	0.907495i	$-0.362008\pi$
$607$	−14.0191	−	18.7273i	−0.569018	−	0.760119i	−0.989080	+	0.147376i	$0.952917\pi$
$608$	−93.9950	+	93.9950i	−3.81200	+	3.81200i
$609$	12.2513	−	41.7240i	0.496447	−	1.69074i
$610$	5.64568	−	10.7055i	0.228587	−	0.433452i
$611$	−1.56962	−	0.225677i	−0.0635000	−	0.00912992i
$612$	0.484624	−	2.22778i	0.0195898	−	0.0900527i
$613$	−40.1762	+	14.9850i	−1.62270	+	0.605237i	−0.986129	−	0.165980i	$-0.946921\pi$
$613$	−40.1762	+	14.9850i	−1.62270	+	0.605237i	−0.636573	+	0.771217i	$0.719649\pi$
$614$		−	3.92137i		−	0.158254i
$615$	−1.81704	−	1.31954i	−0.0732700	−	0.0532091i
$616$	−75.4504	+	135.034i	−3.03998	+	5.44068i
$617$	0.478356	+	0.876043i	0.0192579	+	0.0352682i	0.887131	−	0.461518i	$-0.152695\pi$
$617$	0.478356	+	0.876043i	0.0192579	+	0.0352682i	−0.867873	+	0.496786i	$0.834513\pi$
$618$	−7.19912	−	13.1842i	−0.289591	−	0.530347i
$619$	−15.0275	+	6.86281i	−0.604004	+	0.275840i	−0.693854	−	0.720116i	$-0.744089\pi$
$619$	−15.0275	+	6.86281i	−0.604004	+	0.275840i	0.0898495	+	0.995955i	$0.471361\pi$
$620$	−81.9910	+	25.3718i	−3.29284	+	1.01895i
$621$	−2.93812	−	1.88821i	−0.117903	−	0.0757714i
$622$	4.61617	+	64.5425i	0.185091	+	2.58792i
$623$	26.5896	−	19.9047i	1.06529	−	0.797467i
$624$	−39.2480	−	45.2946i	−1.57118	−	1.81324i
$625$	9.04965	−	23.3046i	0.361986	−	0.932184i
$626$	7.33638	+	11.4156i	0.293221	+	0.456261i
$627$	−22.4288	−	19.8204i	−0.895721	−	0.791549i
$628$	76.7110	−	16.6874i	3.06110	−	0.665902i
$629$	6.14848	−	13.4633i	0.245156	−	0.536817i
$630$	−2.13988	+	1.90924i	−0.0852549	+	0.0760659i
$631$	15.3748	−	33.6660i	0.612060	−	1.34022i	−0.309097	−	0.951031i	$-0.600027\pi$
$631$	15.3748	−	33.6660i	0.612060	−	1.34022i	0.921156	−	0.389193i	$-0.127246\pi$
$632$	36.9261	+	36.9261i	1.46884	+	1.46884i
$633$	24.3242	+	13.2820i	0.966802	+	0.527914i
$634$	54.6223	+	63.0375i	2.16933	+	2.50354i
$635$	−21.5306	+	29.6481i	−0.854417	+	1.17655i
$636$	−4.18853	+	1.22986i	−0.166086	+	0.0487673i
$637$	2.27840	+	31.8562i	0.0902736	+	1.26219i
$638$	38.1369	−	32.4010i	1.50985	−	1.28277i
$639$	0.159350	−	0.138078i	0.00630379	−	0.00546226i
$640$	−9.74832	−	113.205i	−0.385336	−	4.47482i
$641$	−24.9582	−	7.32839i	−0.985790	−	0.289454i	−0.251178	−	0.967941i	$-0.580818\pi$
$641$	−24.9582	−	7.32839i	−0.985790	−	0.289454i	−0.734612	+	0.678487i	$0.762636\pi$
$642$	−20.3247	−	11.0981i	−0.802150	−	0.438007i
$643$	−9.79946	+	45.0474i	−0.386453	+	1.77650i	0.213997	+	0.976834i	$0.431352\pi$
$643$	−9.79946	+	45.0474i	−0.386453	+	1.77650i	−0.600450	+	0.799662i	$0.705012\pi$
$644$	−16.6574	−	4.89106i	−0.656394	−	0.192735i
$645$	−12.1513	−	1.56761i	−0.478456	−	0.0617246i
$646$	59.0533	+	8.49058i	2.32342	+	0.334057i
$647$	10.9420	−	29.3367i	0.430175	−	1.15334i	−0.523374	−	0.852103i	$-0.675327\pi$
$647$	10.9420	−	29.3367i	0.430175	−	1.15334i	0.953548	−	0.301240i	$-0.0974004\pi$
$648$	81.3176	−	30.3299i	3.19446	−	1.19147i
$649$	10.5612	+	5.90105i	0.414562	+	0.231637i
$650$	−5.08584	−	29.3114i	−0.199483	−	1.14969i
$651$	−41.0738	−	35.5906i	−1.60981	−	1.39491i
$652$	20.2633	−	27.0686i	0.793571	−	1.06009i
$653$	47.5315	−	10.3399i	1.86005	−	0.404630i	0.864814	−	0.502093i	$-0.167436\pi$
$653$	47.5315	−	10.3399i	1.86005	−	0.404630i	0.995239	+	0.0974631i	$0.0310728\pi$
$654$	−49.9679	−	22.8196i	−1.95390	−	0.892316i
$655$	−1.44156	+	0.956248i	−0.0563262	+	0.0373637i
$656$	−7.27499	−	6.30382i	−0.284041	−	0.246123i
$657$	0.287402	−	0.0625205i	0.0112126	−	0.00243916i
$658$	2.01575	−	9.26624i	0.0785820	−	0.361235i
$659$	−6.15312	+	42.7959i	−0.239691	+	1.66709i	0.413961	+	0.910295i	$0.364145\pi$
$659$	−6.15312	+	42.7959i	−0.239691	+	1.66709i	−0.653652	+	0.756795i	$0.726764\pi$
$660$	70.1848	−	10.4324i	2.73194	−	0.406082i
$661$	−4.01247	−	27.9074i	−0.156067	−	1.08547i	−0.905793	−	0.423721i	$-0.860724\pi$
$661$	−4.01247	−	27.9074i	−0.156067	−	1.08547i	0.749725	−	0.661749i	$-0.230186\pi$
$662$	47.7058	+	3.41199i	1.85414	+	0.132611i
$663$	−3.18344	+	14.6340i	−0.123634	+	0.568338i
$664$	65.7874	−	9.45880i	2.55304	−	0.367072i
$665$	−39.6966	−	38.5618i	−1.53937	−	1.49536i
$666$	−0.986167	+	0.141789i	−0.0382132	+	0.00549423i
$667$	2.89550	+	2.16755i	0.112114	+	0.0839278i
$668$	114.971	+	25.0104i	4.44836	+	0.967680i
$669$	−24.4275	+	21.1665i	−0.944420	+	0.818345i
$670$	−1.21808	−	83.9976i	−0.0470587	−	3.24511i
$671$	5.67787	+	3.17251i	0.219192	+	0.122474i
$672$	159.745	−	119.583i	6.16228	−	4.61303i
$673$	15.5087	+	3.37370i	0.597815	+	0.130047i	0.501283	−	0.865283i	$-0.332861\pi$
$673$	15.5087	+	3.37370i	0.597815	+	0.130047i	0.0965317	+	0.995330i	$0.469225\pi$
$674$	37.9221	−	59.0079i	1.46070	−	2.27290i
$675$	25.9422	+	4.86015i	0.998515	+	0.187067i
$676$	30.7296	+	35.4638i	1.18191	+	1.36399i
$677$	−10.8092	−	28.9805i	−0.415430	−	1.11381i	−0.961195	−	0.275871i	$-0.911034\pi$
$677$	−10.8092	−	28.9805i	−0.415430	−	1.11381i	0.545765	−	0.837938i	$-0.316239\pi$
$678$	3.80298	+	17.4820i	0.146053	+	0.671393i
$679$	−5.71524	−	39.7504i	−0.219331	−	1.52548i
$680$	−67.9622	+	60.6371i	−2.60623	+	2.32533i
$681$	−43.3139	+	19.7808i	−1.65979	+	0.758001i
$682$	−17.0353	−	60.1786i	−0.652314	−	2.30436i
$683$	13.1535	+	35.2658i	0.503303	+	1.34941i	0.901767	+	0.432223i	$0.142271\pi$
$683$	13.1535	+	35.2658i	0.503303	+	1.34941i	−0.398464	+	0.917184i	$0.630456\pi$
$684$	−1.23031	−	2.69401i	−0.0470421	−	0.103008i
$685$	−6.22436	+	3.51687i	−0.237820	+	0.134373i
$686$	−100.750			−3.84665
$687$	8.02690	+	14.7002i	0.306245	+	0.560846i
$688$	−51.3197	−	11.1639i	−1.95654	−	0.425620i
$689$	−0.943724	+	0.277102i	−0.0359530	+	0.0105568i
$690$	2.52450	+	6.47990i	0.0961061	+	0.246686i
$691$	−18.4462	−	11.8546i	−0.701725	−	0.450971i	0.140512	−	0.990079i	$-0.455125\pi$
$691$	−18.4462	−	11.8546i	−0.701725	−	0.450971i	−0.842237	+	0.539108i	$0.818762\pi$
$692$	−127.036	−	9.08576i	−4.82917	−	0.345389i
$693$	−0.997847	−	1.17449i	−0.0379051	−	0.0446154i
$694$	−8.74387	−	7.57661i	−0.331913	−	0.287604i
$695$	18.3036	−	2.90314i	0.694294	−	0.110122i
$696$	−89.2014	+	26.1919i	−3.38117	+	0.992801i
$697$	−0.171600	+	2.39928i	−0.00649982	+	0.0908793i
$698$	18.2894	−	33.4944i	0.692262	−	1.26778i
$699$	−3.56250			−0.134746
$700$	130.535	−	13.1501i	4.93377	−	0.497025i
$701$	10.5578	+	9.14835i	0.398761	+	0.345528i	0.831041	−	0.556211i	$-0.187745\pi$
$701$	10.5578	+	9.14835i	0.398761	+	0.345528i	−0.432280	+	0.901739i	$0.642291\pi$
$702$	29.4273	−	10.9758i	1.11066	−	0.414256i
$703$	−4.08694	−	18.7874i	−0.154142	−	0.708579i
$704$	121.119	−	7.47788i	4.56484	−	0.281833i
$705$	−2.53106	+	1.20055i	−0.0953254	+	0.0452154i
$706$	26.8180	−	3.85584i	1.00931	−	0.145117i
$707$	−4.15289	+	58.0651i	−0.156186	+	2.18376i
$708$	−20.9147	−	27.9387i	−0.786021	−	1.05000i
$709$	24.8549	+	21.5369i	0.933447	+	0.808837i	0.981785	−	0.189994i	$-0.0608470\pi$
$709$	24.8549	+	21.5369i	0.933447	+	0.808837i	−0.0483379	+	0.998831i	$0.515392\pi$
$710$	−13.0318	+	1.12220i	−0.489074	+	0.0421152i
$711$	−0.473276	+	0.216138i	−0.0177492	+	0.00810580i
$712$	−66.5320	−	24.8152i	−2.49339	−	0.929987i
$713$	3.96752	−	2.16643i	0.148585	−	0.0811334i
$714$	−85.9314	−	25.2317i	−3.21590	−	0.944274i
$715$	15.8135	−	2.35055i	0.591390	−	0.0879055i
$716$	−5.13977	+	1.50917i	−0.192082	+	0.0564005i
$717$	−21.2230	+	21.2230i	−0.792589	+	0.792589i
$718$	12.9771	+	34.7929i	0.484300	+	1.29846i
$719$	−11.2527	−	17.5096i	−0.419656	−	0.652997i	0.565482	−	0.824760i	$-0.308690\pi$
$719$	−11.2527	−	17.5096i	−0.419656	−	0.652997i	−0.985138	+	0.171763i	$0.945054\pi$
$720$	3.49892	+	0.972496i	0.130397	+	0.0362428i
$721$	13.5772	−	6.20052i	0.505643	−	0.230919i
$722$	21.9948	−	12.0101i	0.818561	−	0.446968i
$723$	2.43751	+	2.43751i	0.0906519	+	0.0906519i
$724$	33.3630	+	4.79687i	1.23992	+	0.178274i
$725$	−26.4386	−	6.93703i	−0.981905	−	0.257635i
$726$	6.36049	+	51.3139i	0.236060	+	1.90444i
$727$	2.76273	+	2.76273i	0.102464	+	0.102464i	0.756480	−	0.654016i	$-0.226917\pi$
$727$	2.76273	+	2.76273i	0.102464	+	0.102464i	−0.654016	+	0.756480i	$0.726917\pi$
$728$	80.4863	−	60.2513i	2.98302	−	2.23306i
$729$			27.8350i			1.03093i
$730$	−16.7052	−	7.33815i	−0.618286	−	0.271597i
$731$	5.45181	+	11.9378i	0.201643	+	0.441536i
$732$	−11.2441	−	15.0204i	−0.415594	−	0.555169i
$733$	−49.2019	−	10.7032i	−1.81732	−	0.395333i	−0.830478	−	0.557051i	$-0.811933\pi$
$733$	−49.2019	−	10.7032i	−1.81732	−	0.395333i	−0.986837	+	0.161718i	$0.948296\pi$
$734$	−18.6322	+	40.7987i	−0.687726	+	1.50591i
$735$	34.4626	+	44.6716i	1.27117	+	1.64774i
$736$	4.67602	+	15.9250i	0.172360	+	0.587005i
$737$	45.1426	+	0.439619i	1.66285	+	0.0161936i
$738$	0.142113	−	0.0775994i	0.00523124	−	0.00285647i
$739$	26.5892	+	7.80728i	0.978098	+	0.287196i	0.731439	−	0.681907i	$-0.238849\pi$
$739$	26.5892	+	7.80728i	0.978098	+	0.287196i	0.246659	+	0.969102i	$0.420667\pi$
$740$	40.3163	+	21.2614i	1.48206	+	0.781584i
$741$	8.08176	+	17.6966i	0.296891	+	0.650101i
$742$	−1.25026	−	5.74737i	−0.0458987	−	0.210993i
$743$	−41.2213	+	2.94821i	−1.51226	+	0.108159i	−0.802658	−	0.596439i	$-0.796582\pi$
$743$	−41.2213	+	2.94821i	−1.51226	+	0.108159i	−0.709606	+	0.704599i	$0.751127\pi$
$744$	−16.5357	+	115.008i	−0.606228	+	4.21641i
$745$	−10.2711	−	15.4838i	−0.376304	−	0.567282i
$746$	11.7099	+	81.4443i	0.428731	+	2.98189i
$747$	−0.140760	+	0.647062i	−0.00515013	+	0.0236748i
$748$	−49.2109	−	57.9227i	−1.79933	−	2.11786i
$749$	12.4401	−	19.3572i	0.454551	−	0.707295i
$750$	−36.1104	−	38.1837i	−1.31857	−	1.39427i
$751$	−15.5222	+	17.9136i	−0.566414	+	0.653677i	−0.964628	−	0.263616i	$-0.915085\pi$
$751$	−15.5222	+	17.9136i	−0.566414	+	0.653677i	0.398213	+	0.917293i	$0.369630\pi$
$752$	−11.2513	+	4.19652i	−0.410293	+	0.153032i
$753$	−17.1640	+	17.1640i	−0.625491	+	0.625491i
$754$	−31.2086	+	9.16368i	−1.13655	+	0.333722i
$755$	43.2914	−	28.7171i	1.57553	−	1.04512i
$756$	39.0225	+	132.898i	1.41924	+	4.83347i
$757$	9.23373	+	5.04200i	0.335606	+	0.183255i	0.638211	−	0.769861i	$-0.279675\pi$
$757$	9.23373	+	5.04200i	0.335606	+	0.183255i	−0.302606	+	0.953116i	$0.597856\pi$
$758$	1.61862	−	0.115766i	0.0587910	−	0.00420481i
$759$	−3.51414	+	1.27186i	−0.127555	+	0.0461657i
$760$	−23.4711	+	115.966i	−0.851385	+	4.20652i
$761$	9.85491	−	15.3345i	0.357240	−	0.555876i	−0.615394	−	0.788220i	$-0.711003\pi$
$761$	9.85491	−	15.3345i	0.357240	−	0.555876i	0.972634	+	0.232343i	$0.0746393\pi$
$762$	36.9147	+	67.6042i	1.33728	+	2.44904i
$763$	26.1586	−	47.9058i	0.947004	−	1.73431i
$764$	−37.2031	−	57.8891i	−1.34596	−	2.09435i
$765$	−0.329420	−	0.845557i	−0.0119102	−	0.0305712i
$766$			7.04384i			0.254504i
$767$	−4.71232	−	6.29492i	−0.170152	−	0.227296i
$768$	−107.029	−	39.9196i	−3.86206	−	1.44047i
$769$	11.2123	−	24.5514i	0.404324	−	0.885346i	−0.592489	−	0.805578i	$-0.701855\pi$
$769$	11.2123	−	24.5514i	0.404324	−	0.885346i	0.996813	−	0.0797681i	$-0.0254180\pi$
$770$	7.27440	+	95.3274i	0.262151	+	3.43536i
$771$	3.81577	+	8.35536i	0.137421	+	0.300911i
$772$	9.02220	+	126.147i	0.324716	+	4.54012i
$773$	11.0406	+	8.26492i	0.397104	+	0.297269i	0.779105	−	0.626893i	$-0.215674\pi$
$773$	11.0406	+	8.26492i	0.397104	+	0.297269i	−0.382001	+	0.924162i	$0.624765\pi$
$774$	0.477612	−	0.743179i	0.0171674	−	0.0267130i
$775$	−21.6131	+	26.4555i	−0.776364	+	0.950308i
$776$	−64.8855	+	56.2236i	−2.32926	+	2.01831i
$777$	2.05900	+	28.7886i	0.0738663	+	1.03279i
$778$	−6.17477	−	28.3849i	−0.221376	−	1.01765i
$779$	1.68935	+	2.62867i	0.0605271	+	0.0941820i
$780$	−44.4350	−	12.3503i	−1.59103	−	0.442213i
$781$	−0.433155	−	7.01580i	−0.0154995	−	0.251045i
$782$	4.46411	−	5.96335i	0.159636	−	0.213249i
$783$	2.05864	−	28.7836i	0.0735699	−	1.02864i
$784$	130.756	+	203.460i	4.66985	+	7.26643i
$785$	21.7725	−	22.4132i	0.777093	−	0.799963i
$786$	0.517530	+	3.59950i	0.0184597	+	0.128390i
$787$	−21.6107	−	16.1776i	−0.770338	−	0.576668i	0.140185	−	0.990125i	$-0.455230\pi$
$787$	−21.6107	−	16.1776i	−0.770338	−	0.576668i	−0.910524	+	0.413457i	$0.864321\pi$
$788$	−45.6932	+	61.0390i	−1.62775	+	2.17442i
$789$	−29.0616	+	18.6767i	−1.03462	+	0.664910i
$790$	31.6348	+	6.40278i	1.12551	+	0.227801i
$791$	−17.5961	+	2.52993i	−0.625645	+	0.0899541i
$792$	−0.958996	+	3.15216i	−0.0340764	+	0.112007i
$793$	−2.53343	−	3.38426i	−0.0899646	−	0.120179i
$794$	−15.2300	+	9.78775i	−0.540494	+	0.347354i
$795$	−1.11869	+	1.32951i	−0.0396757	+	0.0471527i
$796$	4.38426	−	5.05971i	0.155396	−	0.179337i
$797$	2.50587	−	35.0367i	0.0887625	−	1.24106i	−0.736549	−	0.676384i	$-0.763546\pi$
$797$	2.50587	−	35.0367i	0.0887625	−	1.24106i	0.825311	−	0.564678i	$-0.191000\pi$
$798$	−109.005	+	40.6568i	−3.85873	+	1.43923i
$799$	2.52435	+	1.62230i	0.0893049	+	0.0573928i
$800$	−78.0461	−	98.1884i	−2.75935	−	3.47149i
$801$	0.463302	−	0.534678i	0.0163700	−	0.0188919i
$802$	73.3171	+	27.3459i	2.58892	+	0.965616i
$803$	4.15991	−	8.87909i	0.146800	−	0.313336i
$804$	−118.463	−	54.1005i	−4.17788	−	1.90798i
$805$	−6.60121	+	2.04272i	−0.232662	+	0.0719962i
$806$	−5.78530	+	40.2376i	−0.203778	+	1.41731i
$807$	1.35837	+	1.35837i	0.0478170	+	0.0478170i
$808$	109.231	−	59.6444i	3.84272	−	2.09828i
$809$	−7.08329	+	4.55215i	−0.249035	+	0.160045i	−0.659203	−	0.751965i	$-0.729106\pi$
$809$	−7.08329	+	4.55215i	−0.249035	+	0.160045i	0.410168	+	0.912010i	$0.365470\pi$
$810$	31.5203	−	43.4040i	1.10751	−	1.52506i
$811$	−9.23038	+	31.4358i	−0.324122	+	1.10386i	0.622796	+	0.782385i	$0.285997\pi$
$811$	−9.23038	+	31.4358i	−0.324122	+	1.10386i	−0.946918	+	0.321475i	$0.895821\pi$
$812$	−30.4908	−	140.164i	−1.07002	−	4.91879i
$813$	−2.15682	+	30.1562i	−0.0756429	+	1.05763i
$814$	−16.2010	+	28.9950i	−0.567843	+	1.01627i
$815$	0.765367	−	13.4367i	0.0268097	−	0.470667i
$816$	31.9514	+	108.817i	1.11852	+	3.80934i
$817$	14.9629	+	8.17034i	0.523484	+	0.285844i
$818$	9.28588	+	0.664139i	0.324673	+	0.0232211i
$819$	0.282212	+	0.961127i	0.00986129	+	0.0335845i
$820$	−7.34657	−	0.947766i	−0.256553	−	0.0330974i
$821$	12.7332	+	5.81508i	0.444393	+	0.202948i	0.625027	−	0.780603i	$-0.285088\pi$
$821$	12.7332	+	5.81508i	0.444393	+	0.202948i	−0.180634	+	0.983550i	$0.557815\pi$
$822$	1.07215	+	14.9906i	0.0373954	+	0.522856i
$823$	−19.6991	−	52.8153i	−0.686668	−	1.84103i	−0.518062	−	0.855343i	$-0.673346\pi$
$823$	−19.6991	−	52.8153i	−0.686668	−	1.84103i	−0.168606	−	0.985684i	$-0.553927\pi$
$824$	−26.8447	−	17.2520i	−0.935179	−	0.601003i
$825$	20.9841	−	18.9026i	0.730572	−	0.658105i
$826$	39.5585	−	25.4227i	1.37641	−	0.884568i
$827$	−15.3629	−	11.5005i	−0.534222	−	0.399913i	0.297824	−	0.954621i	$-0.403739\pi$
$827$	−15.3629	−	11.5005i	−0.534222	−	0.399913i	−0.832045	+	0.554708i	$0.812830\pi$
$828$	−0.368845	−	0.0263803i	−0.0128183	−	0.000916779i
$829$	6.41462	+	0.922283i	0.222789	+	0.0320322i	0.252805	−	0.967517i	$-0.418647\pi$
$829$	6.41462	+	0.922283i	0.222789	+	0.0320322i	−0.0300162	+	0.999549i	$0.509556\pi$
$830$	30.6521	−	27.3484i	1.06395	−	0.949276i
$831$	21.7333	−	33.8176i	0.753918	−	1.17312i
$832$	−73.9008	−	27.5636i	−2.56205	−	0.955595i
$833$	21.1198	−	56.6243i	0.731757	−	1.96192i
$834$	10.9758	−	37.3802i	0.380061	−	1.29437i
$835$	43.6373	−	17.0006i	1.51013	−	0.588331i
$836$	−96.2676	−	21.9257i	−3.32949	−	0.758316i
$837$	−31.6542	−	17.2845i	−1.09413	−	0.597440i
$838$	23.4364	+	23.4364i	0.809598	+	0.809598i
$839$	−4.13220	−	1.88711i	−0.142659	−	0.0651504i	0.342806	−	0.939406i	$-0.388623\pi$
$839$	−4.13220	−	1.88711i	−0.142659	−	0.0651504i	−0.485466	+	0.874256i	$0.661350\pi$
$840$	59.6492	−	167.295i	2.05809	−	5.77223i
$841$	−0.125933	+	0.875883i	−0.00434252	+	0.0302029i
$842$	51.8844	+	19.3519i	1.78805	+	0.666909i
$843$	15.7884	+	28.9143i	0.543781	+	0.995861i
$844$	91.4190			3.14677
$845$	17.9955	+	5.00170i	0.619064	+	0.172064i
$846$		−	0.201990i		−	0.00694456i
$847$	−51.3083	+	2.66651i	−1.76297	+	0.0916223i
$848$	−5.26669	+	5.26669i	−0.180859	+	0.180859i
$849$	7.17536	−	49.9057i	0.246258	−	1.71276i
$850$	−14.2869	+	54.4508i	−0.490038	+	1.86765i
$851$	−2.30339	−	0.676336i	−0.0789591	−	0.0231845i
$852$	−7.08626	+	18.9990i	−0.242771	+	0.650895i
$853$	1.15072	−	0.861422i	0.0394001	−	0.0294945i	−0.579396	−	0.815046i	$-0.696712\pi$
$853$	1.15072	−	0.861422i	0.0394001	−	0.0294945i	0.618796	+	0.785552i	$0.287621\pi$
$854$	21.2674	−	13.6677i	0.727754	−	0.467699i
$855$	−1.00082	−	0.622872i	−0.0342275	−	0.0213018i
$856$	−49.1927			−1.68137
$857$	−19.2259	+	35.2096i	−0.656745	+	1.20274i	0.310905	+	0.950441i	$0.399368\pi$
$857$	−19.2259	+	35.2096i	−0.656745	+	1.20274i	−0.967650	+	0.252298i	$0.918814\pi$
$858$	9.78199	−	32.1528i	0.333952	−	1.09768i
$859$	9.05011	−	30.8218i	0.308786	−	1.05163i	−0.648194	−	0.761475i	$-0.724476\pi$
$859$	9.05011	−	30.8218i	0.308786	−	1.05163i	0.956980	−	0.290153i	$-0.0937062\pi$
$860$	−37.6577	+	14.6710i	−1.28412	+	0.500278i
$861$	−1.94856	−	4.26676i	−0.0664068	−	0.145411i
$862$	13.6912	−	36.7075i	0.466324	−	1.25026i
$863$	28.3515	−	6.16749i	0.965097	−	0.209944i	0.297711	−	0.954656i	$-0.403777\pi$
$863$	28.3515	−	6.16749i	0.965097	−	0.209944i	0.667386	+	0.744712i	$0.267413\pi$
$864$	86.7162	−	100.076i	2.95015	−	3.40465i
$865$	−44.1352	+	24.9371i	−1.50064	+	0.847888i
$866$	−64.5137	+	55.9015i	−2.19227	+	1.89961i
$867$	−0.367520	+	0.490949i	−0.0124816	+	0.0166735i
$868$	−175.178	−	38.1076i	−5.94592	−	1.29346i
$869$	−3.85185	+	16.9120i	−0.130665	+	0.573702i
$870$	−36.9946	+	43.9663i	−1.25423	+	1.49060i
$871$	−26.6912	−	12.1895i	−0.904396	−	0.413024i
$872$	−116.394	+	8.32466i	−3.94160	+	0.281909i
$873$	−0.298933	−	0.801469i	−0.0101173	−	0.0271256i
$874$		−	9.67669i		−	0.327319i
$875$	40.4037	−	33.0826i	1.36589	−	1.11839i
$876$	−21.3771	+	18.5233i	−0.722264	+	0.625845i
$877$	−6.25430	+	11.4539i	−0.211193	+	0.386770i	−0.961705	−	0.274086i	$-0.911625\pi$
$877$	−6.25430	+	11.4539i	−0.211193	+	0.386770i	0.750513	+	0.660856i	$0.229807\pi$
$878$	−33.3784	+	61.1280i	−1.12647	+	2.06297i
$879$	−22.4072	+	25.8593i	−0.755777	+	0.872213i
$880$	96.5717	−	73.0128i	3.25543	−	2.46126i
$881$	−10.1254	−	11.6853i	−0.341133	−	0.393689i	0.559097	−	0.829102i	$-0.311148\pi$
$881$	−10.1254	−	11.6853i	−0.341133	−	0.393689i	−0.900231	+	0.435413i	$0.856602\pi$
$882$	−3.97516	+	0.864743i	−0.133851	+	0.0291174i
$883$	−2.15185	+	1.17500i	−0.0724154	+	0.0395418i	−0.515049	−	0.857161i	$-0.672226\pi$
$883$	−2.15185	+	1.17500i	−0.0724154	+	0.0395418i	0.442633	+	0.896703i	$0.354044\pi$
$884$	13.9179	+	47.4000i	0.468109	+	1.59423i
$885$	−13.0843	−	4.66522i	−0.439825	−	0.156820i
$886$	18.3614	−	62.5332i	0.616863	−	2.10084i
$887$	29.1334	−	29.1334i	0.978205	−	0.978205i	−0.0215626	−	0.999768i	$-0.506864\pi$
$887$	29.1334	−	29.1334i	0.978205	−	0.978205i	0.999768	+	0.0215626i	$0.00686411\pi$
$888$	49.3967	−	36.9779i	1.65765	−	1.24090i
$889$	−69.6196	+	31.7942i	−2.33496	+	1.06634i
$890$	−42.7455	+	9.94998i	−1.43283	+	0.333524i
$891$	22.9078	+	17.4992i	0.767441	+	0.586246i
$892$	−37.2594	+	99.8963i	−1.24754	+	3.34478i
$893$	3.88807	−	0.278080i	0.130109	−	0.00930560i
$894$	−38.6623	+	5.55880i	−1.29306	+	0.185914i
$895$	−1.37275	+	1.63145i	−0.0458859	+	0.0545332i
$896$	98.5934	−	215.889i	3.29377	−	7.21236i
$897$	2.42290	+	0.173289i	0.0808982	+	0.00578595i
$898$	2.23814	−	0.160075i	0.0746876	−	0.00534176i
$899$	31.4211	+	20.1931i	1.04795	+	0.673478i
$900$	2.65736	−	0.864726i	0.0885788	−	0.0288242i
$901$	1.84223	+	0.264873i	0.0613737	+	0.00882421i
$902$	0.820198	−	5.33524i	0.0273096	−	0.177644i
$903$	−20.4873	−	15.3366i	−0.681776	−	0.510371i
$904$	24.8882	+	28.7225i	0.827770	+	0.955297i
$905$	12.1215	−	5.74957i	0.402933	−	0.191122i
$906$	−15.5419	−	108.097i	−0.516346	−	3.59127i
$907$	−9.45527	+	12.6308i	−0.313957	+	0.419397i	−0.929567	−	0.368654i	$-0.879819\pi$
$907$	−9.45527	+	12.6308i	−0.313957	+	0.419397i	0.615610	+	0.788051i	$0.288910\pi$
$908$	−94.1287	+	125.741i	−3.12377	+	4.17287i
$909$	0.176465	+	1.22734i	0.00585298	+	0.0407084i
$910$	20.8693	−	58.5310i	0.691810	−	1.94029i
$911$	−11.0721	−	12.7779i	−0.366835	−	0.423351i	0.542083	−	0.840325i	$-0.317636\pi$
$911$	−11.0721	−	12.7779i	−0.366835	−	0.423351i	−0.908918	+	0.416974i	$0.863090\pi$
$912$	117.939	+	88.2880i	3.90535	+	2.92351i
$913$	14.2934	+	16.8237i	0.473042	+	0.556784i
$914$	−52.7539	−	7.58487i	−1.74494	−	0.250885i
$915$	−7.03437	−	2.50811i	−0.232549	−	0.0829156i
$916$	46.4778	+	29.8695i	1.53567	+	0.986916i
$917$	−3.60416	+	0.257775i	−0.119020	+	0.00851247i
$918$	−59.2804	−	4.23982i	−1.95654	−	0.139935i
$919$	−8.29938	+	18.1731i	−0.273771	+	0.599475i	−0.995715	−	0.0924765i	$-0.970522\pi$
$919$	−8.29938	+	18.1731i	−0.273771	+	0.599475i	0.721944	+	0.691952i	$0.243249\pi$
$920$	11.3037	+	9.51130i	0.372673	+	0.313578i
$921$	−2.39506	+	0.344358i	−0.0789199	+	0.0113470i
$922$	19.2620	−	1.37765i	0.634360	−	0.0453704i
$923$	−1.59662	+	4.28069i	−0.0525533	+	0.140901i
$924$	138.357	+	53.1448i	4.55160	+	1.74833i
$925$	18.0504	−	1.81839i	0.593495	−	0.0597883i
$926$	55.0619	−	25.1459i	1.80945	−	0.826347i
$927$	0.254516	−	0.190529i	0.00835941	−	0.00625778i
$928$	−96.9695	+	96.9695i	−3.18318	+	3.18318i
$929$	−13.5266	+	46.0673i	−0.443792	+	1.51142i	0.369315	+	0.929304i	$0.379592\pi$
$929$	−13.5266	+	46.0673i	−0.443792	+	1.51142i	−0.813107	+	0.582114i	$0.802226\pi$
$930$	30.7765	+	64.8845i	1.00920	+	2.12765i
$931$	−22.1179	−	75.3267i	−0.724885	−	2.46873i
$932$	−10.3139	+	5.63181i	−0.337843	+	0.184476i
$933$	39.0153	−	8.48725i	1.27730	−	0.277860i
$934$	−75.8365	−	87.5200i	−2.48145	−	2.86374i
$935$	−29.0670	−	8.38470i	−0.950593	−	0.274209i
$936$	1.40241	−	1.61846i	0.0458390	−	0.0529011i
$937$	3.35481	−	6.14388i	0.109597	−	0.200712i	−0.817124	−	0.576462i	$-0.804433\pi$
$937$	3.35481	−	6.14388i	0.109597	−	0.200712i	0.926721	+	0.375750i	$0.122615\pi$
$938$	84.0949	−	154.008i	2.74579	−	5.02855i
$939$	6.32809	−	5.48332i	0.206509	−	0.178941i
$940$	−5.42986	+	7.47702i	−0.177102	+	0.243874i
$941$		−	31.6058i		−	1.03032i	−0.857094	−	0.515160i	$-0.827732\pi$
$941$		−	31.6058i		−	1.03032i	0.857094	−	0.515160i	$-0.172268\pi$
$942$	−22.9553	−	61.5457i	−0.747925	−	2.00527i
$943$	0.389153	−	0.0278328i	0.0126726	−	0.000906360i
$944$	−54.1654	−	24.7365i	−1.76293	−	0.805105i
$945$	42.1841	+	35.4950i	1.37225	+	1.15465i
$946$	−10.0228	−	27.6928i	−0.325869	−	0.900369i
$947$	−8.94635	−	1.94616i	−0.290717	−	0.0632417i	0.0648415	−	0.997896i	$-0.479346\pi$
$947$	−8.94635	−	1.94616i	−0.290717	−	0.0632417i	−0.355559	+	0.934654i	$0.615709\pi$
$948$	29.9859	−	40.0565i	0.973897	−	1.30097i
$949$	−4.81650	+	4.17352i	−0.156350	+	0.135478i
$950$	27.5315	+	67.7471i	0.893241	+	2.19801i
$951$	33.7047	−	38.8974i	1.09295	−	1.26133i
$952$	−185.901	+	40.4404i	−6.02510	+	1.31068i
$953$	2.30497	−	6.17985i	0.0746652	−	0.200185i	−0.894255	−	0.447557i	$-0.852294\pi$
$953$	2.30497	−	6.17985i	0.0746652	−	0.200185i	0.968921	+	0.247372i	$0.0795669\pi$
$954$	−0.0520449	−	0.113962i	−0.00168501	−	0.00368967i
$955$	−25.0768	−	11.0156i	−0.811465	−	0.356456i
$956$	−27.8928	+	94.9942i	−0.902118	+	3.07233i
$957$	−23.1386	−	20.4476i	−0.747964	−	0.660976i
$958$	8.51602	−	15.5959i	0.275140	−	0.503882i
$959$	−14.9332			−0.482218
$960$	−135.708	+	31.5891i	−4.37997	+	1.01954i
$961$	13.1914	−	8.47759i	0.425528	−	0.273470i
$962$	17.2823	−	12.9374i	0.557203	−	0.417117i
$963$	0.171279	−	0.459216i	0.00551938	−	0.0147980i
$964$	10.9103	+	3.20354i	0.351396	+	0.103179i
$965$	30.7478	+	39.8563i	0.989807	+	1.28302i
$966$	−2.06728	+	14.3783i	−0.0665137	+	0.462613i
$967$	−3.21211	+	3.21211i	−0.103294	+	0.103294i	−0.756865	−	0.653571i	$-0.773270\pi$
$967$	−3.21211	+	3.21211i	−0.103294	+	0.103294i	0.653571	+	0.756865i	$0.273270\pi$
$968$	64.0995	+	89.1965i	2.06024	+	2.86688i
$969$		−	36.8136i		−	1.18262i
$970$	−14.2102	+	51.1265i	−0.456261	+	1.64157i
$971$	−3.60179			−0.115587			−0.0577935	−	0.998329i	$-0.518407\pi$
$971$	−3.60179			−0.115587			−0.0577935	+	0.998329i	$0.518407\pi$
$972$	2.78246	+	5.09570i	0.0892475	+	0.163445i
$973$	36.2697	+	13.5279i	1.16275	+	0.433684i
$974$	9.64581	−	67.0881i	0.309072	−	2.14964i
$975$	−17.4559	+	5.68028i	−0.559036	+	0.181914i
$976$	−29.1203	−	13.2988i	−0.932118	−	0.425684i
$977$	28.3755	+	28.3755i	0.907812	+	0.907812i	0.996095	−	0.0882837i	$-0.0281382\pi$
$977$	28.3755	+	28.3755i	0.907812	+	0.907812i	−0.0882837	+	0.996095i	$0.528138\pi$
$978$	−24.8314	−	13.5590i	−0.794020	−	0.433567i
$979$	−4.78878	−	23.0942i	−0.153050	−	0.738093i
$980$	170.394	+	74.8495i	5.44302	+	2.39098i
$981$	0.327549	−	1.11553i	0.0104578	−	0.0356161i
$982$	34.1605	−	91.5878i	1.09011	−	2.92269i
$983$	−7.80406	−	2.91076i	−0.248911	−	0.0928389i	0.221912	−	0.975067i	$-0.428770\pi$
$983$	−7.80406	−	2.91076i	−0.248911	−	0.0928389i	−0.470823	+	0.882228i	$0.656043\pi$
$984$	−5.42159	+	8.43616i	−0.172834	+	0.268935i
$985$	−1.72589	+	30.2995i	−0.0549913	+	0.965422i
$986$	60.9220	+	8.75926i	1.94015	+	0.278952i
$987$	−5.83656	−	0.417439i	−0.185780	−	0.0132872i
$988$	51.3736	+	38.4578i	1.63441	+	1.22351i
$989$	1.79071	−	1.15082i	0.0569412	−	0.0365939i
$990$	0.583021	+	1.95116i	0.0185296	+	0.0620121i
$991$	−15.3034	−	9.83488i	−0.486128	−	0.312415i	0.274519	−	0.961582i	$-0.411482\pi$
$991$	−15.3034	−	9.83488i	−0.486128	−	0.312415i	−0.760646	+	0.649166i	$0.775118\pi$
$992$	59.8956	+	160.586i	1.90169	+	5.09862i
$993$	−2.10537	−	29.4369i	−0.0668120	−	0.934153i
$994$	−24.8525	−	11.3498i	−0.788273	−	0.359992i
$995$	0.340953	−	2.64288i	0.0108089	−	0.0837851i
$996$	−17.9417	−	61.1038i	−0.568504	−	1.93615i
$997$	−41.4252	−	2.96279i	−1.31195	−	0.0938324i	−0.602233	−	0.798320i	$-0.705722\pi$
$997$	−41.4252	−	2.96279i	−1.31195	−	0.0938324i	−0.709716	+	0.704488i	$0.751177\pi$
$998$	11.8896	+	6.49223i	0.376360	+	0.205508i
$999$	5.39603	+	18.3772i	0.170723	+	0.581429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.r.a.32.1	✓	1280
5.3	odd	4	inner	605.2.r.a.153.1	yes	1280
121.87	odd	22	inner	605.2.r.a.87.1	yes	1280
605.208	even	44	inner	605.2.r.a.208.1	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.r.a.32.1	✓	1280	1.1	even	1	trivial
605.2.r.a.87.1	yes	1280	121.87	odd	22	inner
605.2.r.a.153.1	yes	1280	5.3	odd	4	inner
605.2.r.a.208.1	yes	1280	605.208	even	44	inner

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.r (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65403 - 2.20953i) q^{2} +(-1.20427 + 1.20427i) q^{3} +(-1.58273 + 5.39029i) q^{4} +(0.661016 + 2.13613i) q^{5} +(4.65276 + 0.668966i) q^{6} +(-0.992826 + 4.56395i) q^{7} +(9.35584 - 3.48955i) q^{8} +0.0994872i q^{9} +O(q^{10})\)	\(q+(-1.65403 - 2.20953i) q^{2} +(-1.20427 + 1.20427i) q^{3} +(-1.58273 + 5.39029i) q^{4} +(0.661016 + 2.13613i) q^{5} +(4.65276 + 0.668966i) q^{6} +(-0.992826 + 4.56395i) q^{7} +(9.35584 - 3.48955i) q^{8} +0.0994872i q^{9} +(3.62650 - 4.99377i) q^{10} +(2.63561 + 2.01334i) q^{11} +(-4.58531 - 8.39737i) q^{12} +(-1.03312 - 1.89202i) q^{13} +(11.7263 - 5.35524i) q^{14} +(-3.36851 - 1.77643i) q^{15} +(-13.7331 - 8.82571i) q^{16} +(0.291007 + 4.06881i) q^{17} +(0.219820 - 0.164555i) q^{18} +(3.47012 + 4.00473i) q^{19} +(-12.5606 + 0.182146i) q^{20} +(-4.30058 - 6.69183i) q^{21} +(0.0891419 - 9.15360i) q^{22} +(0.646509 - 0.140639i) q^{23} +(-7.06458 + 15.4693i) q^{24} +(-4.12611 + 2.82404i) q^{25} +(-2.47166 + 5.41219i) q^{26} +(-3.73261 - 3.73261i) q^{27} +(-23.0296 - 12.5751i) q^{28} +(3.57993 + 4.13146i) q^{29} +(1.64655 + 10.3811i) q^{30} +(6.55556 - 1.92489i) q^{31} +(1.78959 + 25.0217i) q^{32} +(-5.59858 + 0.749383i) q^{33} +(8.50882 - 7.37294i) q^{34} +(-10.4055 + 0.896037i) q^{35} +(-0.536264 - 0.157461i) q^{36} +(-3.18454 - 1.73889i) q^{37} +(3.10888 - 14.2913i) q^{38} +(3.52265 + 1.03434i) q^{39} +(13.6385 + 17.6787i) q^{40} +(0.583675 + 0.0839197i) q^{41} +(-7.67250 + 20.5708i) q^{42} +(3.01439 - 1.12431i) q^{43} +(-15.0239 + 11.0201i) q^{44} +(-0.212518 + 0.0657626i) q^{45} +(-1.38009 - 1.19586i) q^{46} +(0.440833 - 0.588885i) q^{47} +(27.1668 - 5.90977i) q^{48} +(-13.4765 - 6.15451i) q^{49} +(13.0645 + 4.44573i) q^{50} +(-5.25038 - 4.54948i) q^{51} +(11.8337 - 2.57427i) q^{52} +(0.0969851 - 0.445833i) q^{53} +(-2.07345 + 14.4212i) q^{54} +(-2.55858 + 6.96087i) q^{55} +(6.63740 + 46.1641i) q^{56} +(-9.00171 - 0.643815i) q^{57} +(3.20726 - 14.7435i) q^{58} +(3.61054 - 0.519117i) q^{59} +(14.9069 - 15.3456i) q^{60} +(1.94109 - 0.279087i) q^{61} +(-15.0962 - 11.3009i) q^{62} +(-0.454054 - 0.0987735i) q^{63} +(27.6516 - 23.9602i) q^{64} +(3.35870 - 3.45755i) q^{65} +(10.9160 + 11.1307i) q^{66} +(10.8967 - 8.15717i) q^{67} +(-22.3926 - 4.87122i) q^{68} +(-0.609202 + 0.947936i) q^{69} +(19.1908 + 21.5091i) q^{70} +(-1.38789 - 1.60171i) q^{71} +(0.347165 + 0.930786i) q^{72} +(-0.628427 - 2.88883i) q^{73} +(1.42520 + 9.91251i) q^{74} +(1.56805 - 8.36983i) q^{75} +(-27.0789 + 12.3665i) q^{76} +(-11.8055 + 10.0299i) q^{77} +(-3.54117 - 9.49425i) q^{78} +(2.17252 + 4.75715i) q^{79} +(9.77509 - 35.1696i) q^{80} +8.69164 q^{81} +(-0.779994 - 1.42845i) q^{82} +(6.50397 + 1.41485i) q^{83} +(42.8776 - 12.5900i) q^{84} +(-8.49915 + 3.31118i) q^{85} +(-7.47010 - 4.80074i) q^{86} +(-9.28657 - 0.664189i) q^{87} +(31.6840 + 9.63939i) q^{88} +(-5.37435 - 4.65690i) q^{89} +(0.496816 + 0.360791i) q^{90} +(9.66081 - 2.83667i) q^{91} +(-0.265163 + 3.70746i) q^{92} +(-5.57657 + 10.2127i) q^{93} -2.03031 q^{94} +(-6.26083 + 10.0598i) q^{95} +(-32.2879 - 27.9776i) q^{96} +(-8.05600 + 3.00473i) q^{97} +(8.69200 + 39.9565i) q^{98} +(-0.200302 + 0.262210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 22 q^{2} - 40 q^{3} - 14 q^{5} - 44 q^{6} - 22 q^{7} - 22 q^{8}+O(q^{10}) \) 1280 * q - 22 * q^2 - 40 * q^3 - 14 * q^5 - 44 * q^6 - 22 * q^7 - 22 * q^8	\( 1280 q - 22 q^{2} - 40 q^{3} - 14 q^{5} - 44 q^{6} - 22 q^{7} - 22 q^{8} - 66 q^{10} - 48 q^{11} + 44 q^{12} - 66 q^{13} - 26 q^{15} + 80 q^{16} - 22 q^{17} - 44 q^{18} - 54 q^{20} - 44 q^{21} - 90 q^{22} - 34 q^{23} - 30 q^{25} - 12 q^{26} + 80 q^{27} - 22 q^{28} - 22 q^{30} - 52 q^{31} - 22 q^{32} - 62 q^{33} - 22 q^{35} + 216 q^{36} + 52 q^{37} + 70 q^{38} - 44 q^{41} + 44 q^{42} - 22 q^{43} + 104 q^{45} - 44 q^{46} - 18 q^{47} - 72 q^{48} + 88 q^{50} - 484 q^{51} - 22 q^{52} + 14 q^{53} + 140 q^{55} - 316 q^{56} + 44 q^{57} - 6 q^{58} + 34 q^{60} - 44 q^{61} - 22 q^{62} - 44 q^{63} - 22 q^{65} - 84 q^{66} - 138 q^{67} - 22 q^{68} - 126 q^{70} - 4 q^{71} + 220 q^{72} - 22 q^{73} - 66 q^{75} + 88 q^{76} - 22 q^{77} - 104 q^{78} - 324 q^{80} - 1056 q^{81} - 58 q^{82} - 22 q^{83} - 110 q^{85} - 52 q^{86} + 44 q^{87} - 2 q^{88} + 176 q^{90} + 104 q^{91} - 278 q^{92} - 128 q^{93} - 22 q^{95} - 44 q^{96} + 46 q^{97} - 22 q^{98}+O(q^{100}) \) 1280 * q - 22 * q^2 - 40 * q^3 - 14 * q^5 - 44 * q^6 - 22 * q^7 - 22 * q^8 - 66 * q^10 - 48 * q^11 + 44 * q^12 - 66 * q^13 - 26 * q^15 + 80 * q^16 - 22 * q^17 - 44 * q^18 - 54 * q^20 - 44 * q^21 - 90 * q^22 - 34 * q^23 - 30 * q^25 - 12 * q^26 + 80 * q^27 - 22 * q^28 - 22 * q^30 - 52 * q^31 - 22 * q^32 - 62 * q^33 - 22 * q^35 + 216 * q^36 + 52 * q^37 + 70 * q^38 - 44 * q^41 + 44 * q^42 - 22 * q^43 + 104 * q^45 - 44 * q^46 - 18 * q^47 - 72 * q^48 + 88 * q^50 - 484 * q^51 - 22 * q^52 + 14 * q^53 + 140 * q^55 - 316 * q^56 + 44 * q^57 - 6 * q^58 + 34 * q^60 - 44 * q^61 - 22 * q^62 - 44 * q^63 - 22 * q^65 - 84 * q^66 - 138 * q^67 - 22 * q^68 - 126 * q^70 - 4 * q^71 + 220 * q^72 - 22 * q^73 - 66 * q^75 + 88 * q^76 - 22 * q^77 - 104 * q^78 - 324 * q^80 - 1056 * q^81 - 58 * q^82 - 22 * q^83 - 110 * q^85 - 52 * q^86 + 44 * q^87 - 2 * q^88 + 176 * q^90 + 104 * q^91 - 278 * q^92 - 128 * q^93 - 22 * q^95 - 44 * q^96 + 46 * q^97 - 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more