LMFDB - Embedded newform 403.2.bi.b.14.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(14,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 22]))

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

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

chi := DirichletCharacter("403.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bi (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$17$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			14.14
Character	$\chi$	$=$	403.14
Dual form			403.2.bi.b.144.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.563363 - 1.73385i) q^{2} +(-0.719072 + 0.798611i) q^{3} +(-1.07083 - 0.778005i) q^{4} +(1.03814 - 1.79811i) q^{5} +(0.979574 + 1.69667i) q^{6} +(0.0320232 - 0.304681i) q^{7} +(0.997593 - 0.724794i) q^{8} +(0.192871 + 1.83505i) q^{9} +O(q^{10})$	\(q+(0.563363 - 1.73385i) q^{2} +(-0.719072 + 0.798611i) q^{3} +(-1.07083 - 0.778005i) q^{4} +(1.03814 - 1.79811i) q^{5} +(0.979574 + 1.69667i) q^{6} +(0.0320232 - 0.304681i) q^{7} +(0.997593 - 0.724794i) q^{8} +(0.192871 + 1.83505i) q^{9} +(-2.53281 - 2.81297i) q^{10} +(4.08252 - 1.81766i) q^{11} +(1.39133 - 0.295736i) q^{12} +(-0.978148 - 0.207912i) q^{13} +(-0.510231 - 0.227169i) q^{14} +(0.689492 + 2.12204i) q^{15} +(-1.51272 - 4.65568i) q^{16} +(-2.00777 - 0.893918i) q^{17} +(3.29036 + 0.699387i) q^{18} +(-3.63540 + 0.772729i) q^{19} +(-2.51061 + 1.11780i) q^{20} +(0.220294 + 0.244662i) q^{21} +(-0.851606 - 8.10249i) q^{22} +(5.94509 - 4.31936i) q^{23} +(-0.138513 + 1.31787i) q^{24} +(0.344535 + 0.596753i) q^{25} +(-0.911540 + 1.57883i) q^{26} +(-4.21238 - 3.06047i) q^{27} +(-0.271335 + 0.301348i) q^{28} +(1.89612 - 5.83567i) q^{29} +4.06774 q^{30} +(-5.43226 + 1.22087i) q^{31} -6.45828 q^{32} +(-1.48403 + 4.56737i) q^{33} +(-2.68103 + 2.97758i) q^{34} +(-0.514605 - 0.373882i) q^{35} +(1.22114 - 2.11508i) q^{36} +(3.65728 + 6.33460i) q^{37} +(-0.708253 + 6.73858i) q^{38} +(0.869399 - 0.631656i) q^{39} +(-0.267618 - 2.54622i) q^{40} +(-6.27790 - 6.97231i) q^{41} +(0.548313 - 0.244124i) q^{42} +(0.278079 - 0.0591076i) q^{43} +(-5.78584 - 1.22982i) q^{44} +(3.49984 + 1.55823i) q^{45} +(-4.13989 - 12.7413i) q^{46} +(3.94505 + 12.1416i) q^{47} +(4.80583 + 2.13969i) q^{48} +(6.75523 + 1.43587i) q^{49} +(1.22878 - 0.261185i) q^{50} +(2.15763 - 0.960637i) q^{51} +(0.885675 + 0.983642i) q^{52} +(1.39506 + 13.2731i) q^{53} +(-7.67950 + 5.57948i) q^{54} +(0.969881 - 9.22780i) q^{55} +(-0.188885 - 0.327158i) q^{56} +(1.99701 - 3.45892i) q^{57} +(-9.04998 - 6.57519i) q^{58} +(-6.62093 + 7.35329i) q^{59} +(0.912626 - 2.80878i) q^{60} +8.33237 q^{61} +(-0.943518 + 10.1065i) q^{62} +0.565280 q^{63} +(-0.612912 + 1.88635i) q^{64} +(-1.38930 + 1.54298i) q^{65} +(7.08310 + 5.14617i) q^{66} +(-7.28351 + 12.6154i) q^{67} +(1.45451 + 2.51929i) q^{68} +(-0.825462 + 7.85375i) q^{69} +(-0.938166 + 0.681617i) q^{70} +(0.244089 + 2.32235i) q^{71} +(1.52244 + 1.69084i) q^{72} +(8.59934 - 3.82867i) q^{73} +(13.0436 - 2.77251i) q^{74} +(-0.724319 - 0.153959i) q^{75} +(4.49409 + 2.00090i) q^{76} +(-0.423069 - 1.30207i) q^{77} +(-0.605410 - 1.86326i) q^{78} +(-13.1867 - 5.87111i) q^{79} +(-9.94183 - 2.11320i) q^{80} +(0.0586196 - 0.0124600i) q^{81} +(-15.6257 + 6.95701i) q^{82} +(2.56479 + 2.84849i) q^{83} +(-0.0455502 - 0.433381i) q^{84} +(-3.69171 + 2.68218i) q^{85} +(0.0541757 - 0.515447i) q^{86} +(3.29698 + 5.71053i) q^{87} +(2.75527 - 4.77227i) q^{88} +(-1.42729 - 1.03699i) q^{89} +(4.67342 - 5.19036i) q^{90} +(-0.0946702 + 0.291365i) q^{91} -9.72668 q^{92} +(2.93119 - 5.21616i) q^{93} +23.2743 q^{94} +(-2.38460 + 7.33905i) q^{95} +(4.64397 - 5.15765i) q^{96} +(4.23382 + 3.07605i) q^{97} +(6.29523 - 10.9037i) q^{98} +(4.12289 + 7.14105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9	\( 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9} + 7 q^{10} + 5 q^{11} + 28 q^{12} + 17 q^{13} - 3 q^{14} + 17 q^{15} - 78 q^{16} - 12 q^{17} + 34 q^{18} - 23 q^{19} + 8 q^{20} - 38 q^{21} + 8 q^{22} + 9 q^{23} + 46 q^{24} - 69 q^{25} - 12 q^{26} - 58 q^{27} + 7 q^{28} + 18 q^{29} + 60 q^{30} + 14 q^{31} + 212 q^{32} - 41 q^{33} - 30 q^{35} - 106 q^{36} + 6 q^{37} - 62 q^{38} + 6 q^{39} + 39 q^{40} - 5 q^{41} + 37 q^{42} + q^{43} - 88 q^{44} - 168 q^{45} + 6 q^{46} - 81 q^{47} - 101 q^{48} + 117 q^{49} - 20 q^{50} + 35 q^{51} + 7 q^{52} + 25 q^{53} + 57 q^{54} + 19 q^{55} - 63 q^{56} - 20 q^{57} - 44 q^{58} + 9 q^{59} + 113 q^{60} + 8 q^{61} + 57 q^{62} + 112 q^{63} - 146 q^{64} - 5 q^{65} + 70 q^{66} - 99 q^{67} - 56 q^{68} - 65 q^{69} + 169 q^{70} - q^{71} - 43 q^{72} + 50 q^{73} - 26 q^{74} - 18 q^{75} - 94 q^{76} + 114 q^{77} - 17 q^{79} + 217 q^{80} + 54 q^{81} - 25 q^{82} - 53 q^{83} - 22 q^{84} + 2 q^{85} - 54 q^{86} - 28 q^{87} + 70 q^{88} - 101 q^{89} + 165 q^{90} - 4 q^{91} + 64 q^{92} + 61 q^{93} - 90 q^{94} - 33 q^{95} - 217 q^{96} + 73 q^{97} + 33 q^{98} - 15 q^{99}+O(q^{100}) \) 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9 + 7 * q^10 + 5 * q^11 + 28 * q^12 + 17 * q^13 - 3 * q^14 + 17 * q^15 - 78 * q^16 - 12 * q^17 + 34 * q^18 - 23 * q^19 + 8 * q^20 - 38 * q^21 + 8 * q^22 + 9 * q^23 + 46 * q^24 - 69 * q^25 - 12 * q^26 - 58 * q^27 + 7 * q^28 + 18 * q^29 + 60 * q^30 + 14 * q^31 + 212 * q^32 - 41 * q^33 - 30 * q^35 - 106 * q^36 + 6 * q^37 - 62 * q^38 + 6 * q^39 + 39 * q^40 - 5 * q^41 + 37 * q^42 + q^43 - 88 * q^44 - 168 * q^45 + 6 * q^46 - 81 * q^47 - 101 * q^48 + 117 * q^49 - 20 * q^50 + 35 * q^51 + 7 * q^52 + 25 * q^53 + 57 * q^54 + 19 * q^55 - 63 * q^56 - 20 * q^57 - 44 * q^58 + 9 * q^59 + 113 * q^60 + 8 * q^61 + 57 * q^62 + 112 * q^63 - 146 * q^64 - 5 * q^65 + 70 * q^66 - 99 * q^67 - 56 * q^68 - 65 * q^69 + 169 * q^70 - q^71 - 43 * q^72 + 50 * q^73 - 26 * q^74 - 18 * q^75 - 94 * q^76 + 114 * q^77 - 17 * q^79 + 217 * q^80 + 54 * q^81 - 25 * q^82 - 53 * q^83 - 22 * q^84 + 2 * q^85 - 54 * q^86 - 28 * q^87 + 70 * q^88 - 101 * q^89 + 165 * q^90 - 4 * q^91 + 64 * q^92 + 61 * q^93 - 90 * q^94 - 33 * q^95 - 217 * q^96 + 73 * q^97 + 33 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{11}{15}\right)$

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 $

$2$	0.563363	−	1.73385i	0.398358	−	1.22602i	−0.527958	−	0.849270i	$-0.677042\pi$
$2$	0.563363	−	1.73385i	0.398358	−	1.22602i	0.926316	−	0.376748i	$-0.122958\pi$
$3$	−0.719072	+	0.798611i	−0.415157	+	0.461078i	−0.914060	−	0.405580i	$-0.867070\pi$
$3$	−0.719072	+	0.798611i	−0.415157	+	0.461078i	0.498903	+	0.866658i	$0.333736\pi$
$4$	−1.07083	−	0.778005i	−0.535416	−	0.389002i
$5$	1.03814	−	1.79811i	0.464270	−	0.804139i	−0.534898	−	0.844916i	$-0.679650\pi$
$5$	1.03814	−	1.79811i	0.464270	−	0.804139i	0.999168	+	0.0407775i	$0.0129835\pi$
$6$	0.979574	+	1.69667i	0.399909	+	0.692664i
$7$	0.0320232	−	0.304681i	0.0121036	−	0.115159i	−0.986802	−	0.161932i	$-0.948227\pi$
$7$	0.0320232	−	0.304681i	0.0121036	−	0.115159i	0.998906	+	0.0467739i	$0.0148940\pi$
$8$	0.997593	−	0.724794i	0.352703	−	0.256253i
$9$	0.192871	+	1.83505i	0.0642905	+	0.611683i
$10$	−2.53281	−	2.81297i	−0.800944	−	0.889538i
$11$	4.08252	−	1.81766i	1.23093	−	0.548044i	0.314886	−	0.949129i	$-0.398034\pi$
$11$	4.08252	−	1.81766i	1.23093	−	0.548044i	0.916041	+	0.401085i	$0.131367\pi$
$12$	1.39133	−	0.295736i	0.401642	−	0.0853716i
$13$	−0.978148	−	0.207912i	−0.271289	−	0.0576643i
$13$	−0.978148	−	0.207912i	−0.271289	−	0.0576643i
$14$	−0.510231	−	0.227169i	−0.136365	−	0.0607136i
$15$	0.689492	+	2.12204i	0.178026	+	0.547908i
$16$	−1.51272	−	4.65568i	−0.378180	−	1.16392i
$17$	−2.00777	−	0.893918i	−0.486956	−	0.216807i	0.148546	−	0.988905i	$-0.452541\pi$
$17$	−2.00777	−	0.893918i	−0.486956	−	0.216807i	−0.635503	+	0.772098i	$0.719207\pi$
$18$	3.29036	+	0.699387i	0.775545	+	0.164847i
$19$	−3.63540	+	0.772729i	−0.834018	+	0.177276i	−0.605080	−	0.796165i	$-0.706859\pi$
$19$	−3.63540	+	0.772729i	−0.834018	+	0.177276i	−0.228939	+	0.973441i	$0.573526\pi$
$20$	−2.51061	+	1.11780i	−0.561389	+	0.249947i
$21$	0.220294	+	0.244662i	0.0480722	+	0.0533895i
$22$	−0.851606	−	8.10249i	−0.181563	−	1.72746i
$23$	5.94509	−	4.31936i	1.23964	−	0.900649i	0.242063	−	0.970260i	$-0.422176\pi$
$23$	5.94509	−	4.31936i	1.23964	−	0.900649i	0.997574	+	0.0696111i	$0.0221758\pi$
$24$	−0.138513	+	1.31787i	−0.0282739	+	0.269009i
$25$	0.344535	+	0.596753i	0.0689071	+	0.119351i
$26$	−0.911540	+	1.57883i	−0.178768	+	0.309635i
$27$	−4.21238	−	3.06047i	−0.810672	−	0.588988i
$28$	−0.271335	+	0.301348i	−0.0512774	+	0.0569493i
$29$	1.89612	−	5.83567i	0.352101	−	1.08366i	−0.605570	−	0.795792i	$-0.707055\pi$
$29$	1.89612	−	5.83567i	0.352101	−	1.08366i	0.957671	−	0.287864i	$-0.0929451\pi$
$30$	4.06774			0.742664
$31$	−5.43226	+	1.22087i	−0.975663	+	0.219275i
$31$	−5.43226	+	1.22087i	−0.975663	+	0.219275i
$32$	−6.45828			−1.14167
$33$	−1.48403	+	4.56737i	−0.258336	+	0.795077i
$34$	−2.68103	+	2.97758i	−0.459792	+	0.510651i
$35$	−0.514605	−	0.373882i	−0.0869841	−	0.0631976i
$36$	1.22114	−	2.11508i	0.203524	−	0.352514i
$37$	3.65728	+	6.33460i	0.601253	+	1.04140i	0.992632	+	0.121171i	$0.0386651\pi$
$37$	3.65728	+	6.33460i	0.601253	+	1.04140i	−0.391378	+	0.920230i	$0.628002\pi$
$38$	−0.708253	+	6.73858i	−0.114894	+	1.09314i
$39$	0.869399	−	0.631656i	0.139215	−	0.101146i
$40$	−0.267618	−	2.54622i	−0.0423142	−	0.402593i
$41$	−6.27790	−	6.97231i	−0.980443	−	1.08889i	−0.996030	−	0.0890135i	$-0.971629\pi$
$41$	−6.27790	−	6.97231i	−0.980443	−	1.08889i	0.0155876	−	0.999879i	$-0.495038\pi$
$42$	0.548313	−	0.244124i	0.0846065	−	0.0376692i
$43$	0.278079	−	0.0591076i	0.0424067	−	0.00901382i	−0.186659	−	0.982425i	$-0.559766\pi$
$43$	0.278079	−	0.0591076i	0.0424067	−	0.00901382i	0.229066	+	0.973411i	$0.426433\pi$
$44$	−5.78584	−	1.22982i	−0.872248	−	0.185402i
$45$	3.49984	+	1.55823i	0.521726	+	0.232287i
$46$	−4.13989	−	12.7413i	−0.610394	−	1.87860i
$47$	3.94505	+	12.1416i	0.575445	+	1.77104i	0.634658	+	0.772793i	$0.281141\pi$
$47$	3.94505	+	12.1416i	0.575445	+	1.77104i	−0.0592129	+	0.998245i	$0.518859\pi$
$48$	4.80583	+	2.13969i	0.693662	+	0.308838i
$49$	6.75523	+	1.43587i	0.965033	+	0.205124i
$50$	1.22878	−	0.261185i	0.173776	−	0.0369372i
$51$	2.15763	−	0.960637i	0.302128	−	0.134516i
$52$	0.885675	+	0.983642i	0.122821	+	0.136407i
$53$	1.39506	+	13.2731i	0.191626	+	1.82320i	0.493383	+	0.869812i	$0.335760\pi$
$53$	1.39506	+	13.2731i	0.191626	+	1.82320i	−0.301757	+	0.953385i	$0.597573\pi$
$54$	−7.67950	+	5.57948i	−1.04505	+	0.759271i
$55$	0.969881	−	9.22780i	0.130779	−	1.24428i
$56$	−0.188885	−	0.327158i	−0.0252408	−	0.0437183i
$57$	1.99701	−	3.45892i	0.264510	−	0.458145i
$58$	−9.04998	−	6.57519i	−1.18832	−	0.863365i
$59$	−6.62093	+	7.35329i	−0.861971	+	0.957316i	−0.999449	−	0.0331887i	$-0.989434\pi$
$59$	−6.62093	+	7.35329i	−0.861971	+	0.957316i	0.137478	+	0.990505i	$0.456100\pi$
$60$	0.912626	−	2.80878i	0.117820	−	0.362611i
$61$	8.33237			1.06685			0.533425	−	0.845847i	$-0.320905\pi$
$61$	8.33237			1.06685			0.533425	+	0.845847i	$0.320905\pi$
$62$	−0.943518	+	10.1065i	−0.119827	+	1.28353i
$63$	0.565280			0.0712186
$64$	−0.612912	+	1.88635i	−0.0766140	+	0.235794i
$65$	−1.38930	+	1.54298i	−0.172322	+	0.191382i
$66$	7.08310	+	5.14617i	0.871870	+	0.633450i
$67$	−7.28351	+	12.6154i	−0.889823	+	1.54122i	−0.0497389	+	0.998762i	$0.515839\pi$
$67$	−7.28351	+	12.6154i	−0.889823	+	1.54122i	−0.840084	+	0.542456i	$0.817494\pi$
$68$	1.45451	+	2.51929i	0.176386	+	0.305509i
$69$	−0.825462	+	7.85375i	−0.0993740	+	0.945480i
$70$	−0.938166	+	0.681617i	−0.112132	+	0.0814688i
$71$	0.244089	+	2.32235i	0.0289680	+	0.275613i	0.999412	+	0.0342861i	$0.0109158\pi$
$71$	0.244089	+	2.32235i	0.0289680	+	0.275613i	−0.970444	+	0.241326i	$0.922418\pi$
$72$	1.52244	+	1.69084i	0.179421	+	0.199267i
$73$	8.59934	−	3.82867i	1.00648	−	0.448112i	0.163778	−	0.986497i	$-0.447632\pi$
$73$	8.59934	−	3.82867i	1.00648	−	0.448112i	0.842699	+	0.538385i	$0.180965\pi$
$74$	13.0436	−	2.77251i	1.51629	−	0.322298i
$75$	−0.724319	−	0.153959i	−0.0836372	−	0.0177776i
$76$	4.49409	+	2.00090i	0.515508	+	0.229519i
$77$	−0.423069	−	1.30207i	−0.0482132	−	0.148385i
$78$	−0.605410	−	1.86326i	−0.0685492	−	0.210973i
$79$	−13.1867	−	5.87111i	−1.48362	−	0.660551i	−0.504424	−	0.863456i	$-0.668295\pi$
$79$	−13.1867	−	5.87111i	−1.48362	−	0.660551i	−0.979198	+	0.202905i	$0.934962\pi$
$80$	−9.94183	−	2.11320i	−1.11153	−	0.236263i
$81$	0.0586196	−	0.0124600i	0.00651329	−	0.00138444i
$82$	−15.6257	+	6.95701i	−1.72557	+	0.768273i
$83$	2.56479	+	2.84849i	0.281522	+	0.312662i	0.867277	−	0.497826i	$-0.165868\pi$
$83$	2.56479	+	2.84849i	0.281522	+	0.312662i	−0.585754	+	0.810489i	$0.699202\pi$
$84$	−0.0455502	−	0.433381i	−0.00496994	−	0.0472858i
$85$	−3.69171	+	2.68218i	−0.400422	+	0.290924i
$86$	0.0541757	−	0.515447i	0.00584192	−	0.0555821i
$87$	3.29698	+	5.71053i	0.353473	+	0.612233i
$88$	2.75527	−	4.77227i	0.293713	−	0.508726i
$89$	−1.42729	−	1.03699i	−0.151292	−	0.109920i	0.509564	−	0.860433i	$-0.329807\pi$
$89$	−1.42729	−	1.03699i	−0.151292	−	0.109920i	−0.660856	+	0.750512i	$0.729807\pi$
$90$	4.67342	−	5.19036i	0.492622	−	0.547112i
$91$	−0.0946702	+	0.291365i	−0.00992413	+	0.0305433i
$92$	−9.72668			−1.01408
$93$	2.93119	−	5.21616i	0.303950	−	0.540890i
$94$	23.2743			2.40056
$95$	−2.38460	+	7.33905i	−0.244655	+	0.752971i
$96$	4.64397	−	5.15765i	0.473973	−	0.526401i
$97$	4.23382	+	3.07605i	0.429880	+	0.312326i	0.781601	−	0.623779i	$-0.214403\pi$
$97$	4.23382	+	3.07605i	0.429880	+	0.312326i	−0.351721	+	0.936105i	$0.614403\pi$
$98$	6.29523	−	10.9037i	0.635914	−	1.10144i
$99$	4.12289	+	7.14105i	0.414366	+	0.717703i
$100$	0.0953371	−	0.907072i	0.00953371	−	0.0907072i
$101$	−7.89036	+	5.73268i	−0.785120	+	0.570423i	−0.906511	−	0.422182i	$-0.861264\pi$
$101$	−7.89036	+	5.73268i	−0.785120	+	0.570423i	0.121391	+	0.992605i	$0.461264\pi$
$102$	−0.450077	−	4.28219i	−0.0445642	−	0.424000i
$103$	−3.85387	−	4.28016i	−0.379733	−	0.421737i	0.522733	−	0.852496i	$-0.324912\pi$
$103$	−3.85387	−	4.28016i	−0.379733	−	0.421737i	−0.902467	+	0.430760i	$0.858246\pi$
$104$	−1.12649	+	0.501544i	−0.110461	+	0.0491805i
$105$	0.668624	−	0.142120i	0.0652510	−	0.0138695i
$106$	23.7995	+	5.05873i	2.31161	+	0.491348i
$107$	−11.0065	−	4.90042i	−1.06404	−	0.473741i	−0.201373	−	0.979515i	$-0.564540\pi$
$107$	−11.0065	−	4.90042i	−1.06404	−	0.473741i	−0.862666	+	0.505774i	$0.831207\pi$
$108$	2.12968	+	6.55450i	0.204929	+	0.630707i
$109$	0.817409	+	2.51573i	0.0782936	+	0.240963i	0.982541	−	0.186046i	$-0.0595673\pi$
$109$	0.817409	+	2.51573i	0.0782936	+	0.240963i	−0.904247	+	0.427009i	$0.859567\pi$
$110$	−15.4533	−	6.88023i	−1.47341	−	0.656004i
$111$	−7.68873	−	1.63429i	−0.729782	−	0.155120i
$112$	−1.46694	+	0.311807i	−0.138613	+	0.0294630i
$113$	19.2490	−	8.57021i	1.81079	−	0.806217i	0.851192	−	0.524855i	$-0.175880\pi$
$113$	19.2490	−	8.57021i	1.81079	−	0.806217i	0.959602	−	0.281362i	$-0.0907863\pi$
$114$	−4.87221	−	5.41114i	−0.456325	−	0.506800i
$115$	−1.59485	−	15.1740i	−0.148721	−	1.41499i
$116$	−6.57060	+	4.77382i	−0.610065	+	0.443238i
$117$	0.192871	−	1.83505i	0.0178310	−	0.169650i
$118$	9.01953	+	15.6223i	0.830315	+	1.43815i
$119$	−0.336655	+	0.583104i	−0.0308611	+	0.0534530i
$120$	2.22587	+	1.61719i	0.203194	+	0.147629i
$121$	6.00268	−	6.66666i	0.545699	−	0.606060i
$122$	4.69415	−	14.4471i	0.424988	−	1.30798i
$123$	10.0824			0.909101
$124$	6.76688	+	2.91897i	0.607684	+	0.262132i
$125$	11.8121			1.05651
$126$	0.318458	−	0.980113i	0.0283705	−	0.0873154i
$127$	−3.11697	+	3.46175i	−0.276587	+	0.307181i	−0.865393	−	0.501093i	$-0.832931\pi$
$127$	−3.11697	+	3.46175i	−0.276587	+	0.307181i	0.588807	+	0.808274i	$0.299598\pi$
$128$	−7.52436	−	5.46677i	−0.665066	−	0.483199i
$129$	−0.152755	+	0.264580i	−0.0134493	+	0.0232949i
$130$	1.89261	+	3.27810i	0.165993	+	0.287508i
$131$	−1.29225	+	12.2950i	−0.112905	+	1.07421i	0.780560	+	0.625081i	$0.214934\pi$
$131$	−1.29225	+	12.2950i	−0.112905	+	1.07421i	−0.893464	+	0.449134i	$0.851733\pi$
$132$	5.14258	−	3.73631i	0.447604	−	0.325204i
$133$	0.119018	+	1.13238i	0.0103202	+	0.0981900i
$134$	17.7700	+	19.7356i	1.53509	+	1.70490i
$135$	−9.87609	+	4.39712i	−0.849998	+	0.378444i
$136$	−2.65085	+	0.563455i	−0.227308	+	0.0483159i
$137$	3.46526	+	0.736565i	0.296057	+	0.0629290i	0.353546	−	0.935417i	$-0.384976\pi$
$137$	3.46526	+	0.736565i	0.296057	+	0.0629290i	−0.0574883	+	0.998346i	$0.518309\pi$
$138$	13.1522	+	5.85574i	1.11959	+	0.498474i
$139$	−4.19728	−	12.9179i	−0.356009	−	1.09568i	−0.955422	−	0.295243i	$-0.904599\pi$
$139$	−4.19728	−	12.9179i	−0.356009	−	1.09568i	0.599413	−	0.800440i	$-0.295401\pi$
$140$	0.260173	+	0.800730i	0.0219886	+	0.0676740i
$141$	−12.5332	−	5.58014i	−1.05549	−	0.469933i
$142$	4.16413	+	0.885112i	0.349446	+	0.0742770i
$143$	−4.37122	+	0.929132i	−0.365540	+	0.0776979i
$144$	8.25163	−	3.67386i	0.687636	−	0.306155i
$145$	−8.52473	−	9.46767i	−0.707940	−	0.786247i
$146$	−1.79380	−	17.0669i	−0.148456	−	1.41247i
$147$	−6.00420	+	4.36230i	−0.495218	+	0.359797i
$148$	1.01201	−	9.62867i	0.0831870	−	0.791472i
$149$	6.22724	+	10.7859i	0.510155	+	0.883615i	0.999931	+	0.0117664i	$0.00374544\pi$
$149$	6.22724	+	10.7859i	0.510155	+	0.883615i	−0.489775	+	0.871849i	$0.662921\pi$
$150$	−0.674996	+	1.16913i	−0.0551132	+	0.0954589i
$151$	−3.17128	−	2.30407i	−0.258075	−	0.187502i	0.451223	−	0.892411i	$-0.350988\pi$
$151$	−3.17128	−	2.30407i	−0.258075	−	0.187502i	−0.709298	+	0.704909i	$0.750988\pi$
$152$	−3.06658	+	3.40579i	−0.248733	+	0.276246i
$153$	1.25314	−	3.85677i	0.101310	−	0.311802i
$154$	−2.49594			−0.201129
$155$	−3.44418	+	11.0352i	−0.276643	+	0.886372i
$156$	−1.42241			−0.113884
$157$	2.49250	−	7.67111i	0.198923	−	0.612222i	−0.800986	−	0.598684i	$-0.795691\pi$
$157$	2.49250	−	7.67111i	0.198923	−	0.612222i	0.999908	−	0.0135378i	$-0.00430936\pi$
$158$	−17.6085	+	19.5563i	−1.40086	+	1.55581i
$159$	−11.6032	−	8.43019i	−0.920191	−	0.668558i
$160$	−6.70459	+	11.6127i	−0.530045	+	0.918064i
$161$	−1.12565	−	1.94968i	−0.0887133	−	0.153656i
$162$	0.0114203	−	0.108657i	0.000897266	−	0.00853692i
$163$	−3.25235	+	2.36297i	−0.254744	+	0.185082i	−0.707827	−	0.706386i	$-0.750324\pi$
$163$	−3.25235	+	2.36297i	−0.254744	+	0.185082i	0.453083	+	0.891468i	$0.350324\pi$
$164$	1.29808	+	12.3504i	0.101363	+	0.964405i
$165$	6.67201	+	7.41001i	0.519415	+	0.576869i
$166$	6.38376	−	2.84223i	0.495476	−	0.220600i
$167$	−0.937883	+	0.199353i	−0.0725756	+	0.0154264i	−0.244056	−	0.969761i	$-0.578478\pi$
$167$	−0.937883	+	0.199353i	−0.0725756	+	0.0154264i	0.171481	+	0.985187i	$0.445145\pi$
$168$	0.397093	+	0.0844048i	0.0306364	+	0.00651197i
$169$	0.913545	+	0.406737i	0.0702727	+	0.0312874i
$170$	2.57074	+	7.91192i	0.197167	+	0.606817i
$171$	−2.11916	−	6.52210i	−0.162056	−	0.498758i
$172$	−0.343762	−	0.153053i	−0.0262116	−	0.0116702i
$173$	−21.5295	−	4.57624i	−1.63686	−	0.347925i	−0.704569	−	0.709635i	$-0.748860\pi$
$173$	−21.5295	−	4.57624i	−1.63686	−	0.347925i	−0.932291	+	0.361710i	$0.882193\pi$
$174$	11.7586	−	2.49937i	0.891418	−	0.189477i
$175$	0.192852	−	0.0858634i	0.0145783	−	0.00649066i
$176$	−14.6381	−	16.2573i	−1.10339	−	1.22544i
$177$	−1.11149	−	10.5751i	−0.0835444	−	0.794872i
$178$	−2.60206	+	1.89051i	−0.195033	+	0.141700i
$179$	0.749202	−	7.12818i	0.0559980	−	0.532785i	−0.930181	−	0.367101i	$-0.880350\pi$
$179$	0.749202	−	7.12818i	0.0559980	−	0.532785i	0.986179	−	0.165684i	$-0.0529831\pi$
$180$	−2.53543	−	4.39150i	−0.188980	−	0.327323i
$181$	2.73422	−	4.73581i	0.203233	−	0.352010i	−0.746335	−	0.665570i	$-0.768188\pi$
$181$	2.73422	−	4.73581i	0.203233	−	0.352010i	0.949568	+	0.313560i	$0.101522\pi$
$182$	0.451850	+	0.328288i	0.0334933	+	0.0243343i
$183$	−5.99157	+	6.65432i	−0.442910	+	0.491901i
$184$	2.80014	−	8.61794i	0.206429	−	0.635323i
$185$	15.1871			1.11658
$186$	−7.39273	−	8.02083i	−0.542061	−	0.588116i
$187$	−9.82162			−0.718228
$188$	5.22176	−	16.0709i	0.380836	−	1.17209i
$189$	−1.06736	+	1.18542i	−0.0776390	+	0.0862269i
$190$	11.3814	+	8.26909i	0.825696	+	0.599903i
$191$	−4.60067	+	7.96859i	−0.332893	+	0.576587i	−0.983078	−	0.183189i	$-0.941358\pi$
$191$	−4.60067	+	7.96859i	−0.332893	+	0.576587i	0.650185	+	0.759776i	$0.274691\pi$
$192$	−1.06573	−	1.84590i	−0.0769125	−	0.133216i
$193$	−1.78996	+	17.0304i	−0.128844	+	1.22587i	0.718765	+	0.695253i	$0.244708\pi$
$193$	−1.78996	+	17.0304i	−0.128844	+	1.22587i	−0.847610	+	0.530620i	$0.821959\pi$
$194$	7.71860	−	5.60789i	0.554163	−	0.402623i
$195$	−0.233228	−	2.21902i	−0.0167018	−	0.158907i
$196$	−6.11660	−	6.79317i	−0.436900	−	0.485227i
$197$	−21.9339	+	9.76562i	−1.56273	+	0.695772i	−0.992102	−	0.125437i	$-0.959967\pi$
$197$	−21.9339	+	9.76562i	−1.56273	+	0.695772i	−0.570627	+	0.821209i	$0.693300\pi$
$198$	14.7042	−	3.12548i	1.04498	−	0.222118i
$199$	−5.62830	−	1.19633i	−0.398980	−	0.0848058i	0.00405195	−	0.999992i	$-0.498710\pi$
$199$	−5.62830	−	1.19633i	−0.398980	−	0.0848058i	−0.403032	+	0.915186i	$0.632044\pi$
$200$	0.776229	+	0.345600i	0.0548877	+	0.0244376i
$201$	−4.83743	−	14.8881i	−0.341206	−	1.05012i
$202$	5.49449	+	16.9103i	0.386591	+	1.18980i
$203$	−1.71730	−	0.764589i	−0.120530	−	0.0536636i
$204$	−3.05784	−	0.649963i	−0.214091	−	0.0455065i
$205$	−19.0543	+	4.05012i	−1.33081	+	0.282872i
$206$	−9.59229	+	4.27076i	−0.668327	+	0.297558i
$207$	9.07288	+	10.0765i	0.630609	+	0.700362i
$208$	0.511695	+	4.86845i	0.0354797	+	0.337566i
$209$	−13.4371	+	9.76259i	−0.929461	+	0.675293i
$210$	0.130262	−	1.23936i	0.00898894	−	0.0855240i
$211$	−8.59338	−	14.8842i	−0.591593	−	1.02467i	−0.994018	−	0.109216i	$-0.965166\pi$
$211$	−8.59338	−	14.8842i	−0.591593	−	1.02467i	0.402425	−	0.915453i	$-0.368167\pi$
$212$	8.83265	−	15.2986i	0.606629	−	1.05071i
$213$	−2.03017	−	1.47501i	−0.139105	−	0.101066i
$214$	−14.6973	+	16.3230i	−1.00468	+	1.11581i
$215$	0.182403	−	0.561379i	0.0124398	−	0.0382857i
$216$	−6.42045			−0.436856
$217$	0.198018	+	1.69420i	0.0134424	+	0.115010i
$218$	4.82240			0.326614
$219$	−3.12593	+	9.62062i	−0.211231	+	0.650101i
$220$	−8.21785	+	9.12685i	−0.554048	+	0.615332i
$221$	1.77804	+	1.29182i	0.119604	+	0.0868974i
$222$	−7.16516	+	12.4104i	−0.480894	+	0.832933i
$223$	5.19339	+	8.99522i	0.347775	+	0.602365i	0.985854	−	0.167607i	$-0.0536039\pi$
$223$	5.19339	+	8.99522i	0.347775	+	0.602365i	−0.638079	+	0.769971i	$0.720271\pi$
$224$	−0.206815	+	1.96771i	−0.0138184	+	0.131473i
$225$	−1.02862	+	0.747336i	−0.0685746	+	0.0498224i
$226$	−4.01530	−	38.2031i	−0.267094	−	2.54123i
$227$	−11.6976	−	12.9914i	−0.776394	−	0.862273i	0.217101	−	0.976149i	$-0.430340\pi$
$227$	−11.6976	−	12.9914i	−0.776394	−	0.862273i	−0.993495	+	0.113876i	$0.963673\pi$
$228$	−4.82951	+	2.15024i	−0.319842	+	0.142403i
$229$	−4.94614	+	1.05133i	−0.326850	+	0.0694741i	−0.368414	−	0.929662i	$-0.620099\pi$
$229$	−4.94614	+	1.05133i	−0.326850	+	0.0694741i	0.0415642	+	0.999136i	$0.486766\pi$
$230$	−27.2080	−	5.78324i	−1.79404	−	0.381335i
$231$	1.34407	+	0.598417i	0.0884331	+	0.0393730i
$232$	−2.33810	−	7.19592i	−0.153504	−	0.472435i
$233$	7.11017	+	21.8829i	0.465803	+	1.43359i	0.857970	+	0.513700i	$0.171725\pi$
$233$	7.11017	+	21.8829i	0.465803	+	1.43359i	−0.392167	+	0.919894i	$0.628275\pi$
$234$	−3.07305	−	1.36821i	−0.200891	−	0.0894426i
$235$	25.9275	+	5.51106i	1.69132	+	0.359502i
$236$	12.8108	−	2.72302i	0.833911	−	0.177253i
$237$	14.1709	−	6.30931i	0.920501	−	0.409833i
$238$	0.821357	+	0.912209i	0.0532406	+	0.0591297i
$239$	−2.36458	−	22.4975i	−0.152952	−	1.45524i	−0.754445	−	0.656364i	$-0.772094\pi$
$239$	−2.36458	−	22.4975i	−0.152952	−	1.45524i	0.601492	−	0.798878i	$-0.294573\pi$
$240$	8.83652	−	6.42011i	0.570395	−	0.414416i
$241$	−1.29524	+	12.3233i	−0.0834335	+	0.793816i	0.870170	+	0.492751i	$0.164009\pi$
$241$	−1.29524	+	12.3233i	−0.0834335	+	0.793816i	−0.953604	+	0.301065i	$0.902658\pi$
$242$	−8.17731	−	14.1635i	−0.525657	−	0.910465i
$243$	7.77797	−	13.4718i	0.498957	−	0.864219i
$244$	−8.92256	−	6.48262i	−0.571209	−	0.415007i
$245$	9.59471	−	10.6560i	0.612984	−	0.680787i
$246$	5.68006	−	17.4814i	0.362147	−	1.11458i
$247$	3.71662			0.236483
$248$	−4.53431	+	5.15521i	−0.287929	+	0.327356i
$249$	−4.11910			−0.261037
$250$	6.65449	−	20.4804i	0.420867	−	1.29530i
$251$	9.59792	−	10.6596i	0.605815	−	0.672826i	−0.359732	−	0.933056i	$-0.617132\pi$
$251$	9.59792	−	10.6596i	0.605815	−	0.672826i	0.965547	+	0.260230i	$0.0837984\pi$
$252$	−0.605320	−	0.439791i	−0.0381316	−	0.0277042i
$253$	16.4199	−	28.4400i	1.03231	−	1.78801i
$254$	4.24618	+	7.35459i	0.266429	+	0.461468i
$255$	0.512585	−	4.87692i	0.0320993	−	0.305405i
$256$	−16.9268	+	12.2980i	−1.05792	+	0.768626i
$257$	−2.16914	−	20.6380i	−0.135307	−	1.28736i	−0.825776	−	0.563998i	$-0.809262\pi$
$257$	−2.16914	−	20.6380i	−0.135307	−	1.28736i	0.690469	−	0.723362i	$-0.257404\pi$
$258$	0.372685	+	0.413909i	0.0232024	+	0.0257689i
$259$	2.04715	−	0.911449i	0.127204	−	0.0566347i
$260$	2.68815	−	0.571384i	0.166712	−	0.0354357i
$261$	11.0744	+	2.35394i	0.685490	+	0.145705i
$262$	20.5896	+	9.16709i	1.27203	+	0.566345i
$263$	8.21769	+	25.2915i	0.506725	+	1.55954i	0.797852	+	0.602854i	$0.205970\pi$
$263$	8.21769	+	25.2915i	0.506725	+	1.55954i	−0.291127	+	0.956684i	$0.594030\pi$
$264$	1.82995	+	5.63200i	0.112625	+	0.346625i
$265$	25.3147	+	11.2708i	1.55507	+	0.692362i
$266$	2.03043	+	0.431582i	0.124494	+	0.0264620i
$267$	1.85447	−	0.394180i	0.113492	−	0.0241234i
$268$	17.6143	−	7.84238i	1.07596	−	0.479050i
$269$	1.24651	+	1.38438i	0.0760008	+	0.0844074i	0.779946	−	0.625847i	$-0.215247\pi$
$269$	1.24651	+	1.38438i	0.0760008	+	0.0844074i	−0.703945	+	0.710254i	$0.748580\pi$
$270$	2.06013	+	19.6009i	0.125376	+	1.19287i
$271$	2.31689	−	1.68332i	0.140741	−	0.102254i	−0.515187	−	0.857078i	$-0.672278\pi$
$271$	2.31689	−	1.68332i	0.140741	−	0.102254i	0.655928	+	0.754824i	$0.272278\pi$
$272$	−1.12459	+	10.6998i	−0.0681885	+	0.648770i
$273$	−0.164612	−	0.285117i	−0.00996279	−	0.0172561i
$274$	3.22929	−	5.59330i	0.195089	−	0.337904i
$275$	2.49127	+	1.81001i	0.150229	+	0.109148i
$276$	6.99418	−	7.76783i	0.421000	−	0.467568i
$277$	4.87507	−	15.0039i	0.292915	−	0.901498i	−0.690999	−	0.722855i	$-0.742829\pi$
$277$	4.87507	−	15.0039i	0.292915	−	0.901498i	0.983914	−	0.178643i	$-0.0571707\pi$
$278$	−24.7623			−1.48515
$279$	−3.28809	−	9.73299i	−0.196853	−	0.582699i
$280$	−0.784354			−0.0468741
$281$	4.54883	−	13.9998i	0.271360	−	0.835161i	−0.718799	−	0.695218i	$-0.755308\pi$
$281$	4.54883	−	13.9998i	0.271360	−	0.835161i	0.990160	−	0.139943i	$-0.0446920\pi$
$282$	−16.7359	+	18.5871i	−0.996608	+	1.10685i
$283$	17.5844	+	12.7758i	1.04528	+	0.759443i	0.971310	−	0.237817i	$-0.0764318\pi$
$283$	17.5844	+	12.7758i	1.04528	+	0.759443i	0.0739739	+	0.997260i	$0.476432\pi$
$284$	1.54542	−	2.67675i	0.0917040	−	0.158836i
$285$	−4.14634	−	7.18168i	−0.245608	−	0.425406i
$286$	−0.851606	+	8.10249i	−0.0503565	+	0.479110i
$287$	−2.32537	+	1.68948i	−0.137262	+	0.0997268i
$288$	−1.24562	−	11.8513i	−0.0733987	−	0.698342i
$289$	−8.14316	−	9.04389i	−0.479009	−	0.531994i
$290$	−21.2180	+	9.44688i	−1.24597	+	0.554740i
$291$	−5.50099	+	1.16927i	−0.322474	+	0.0685439i
$292$	−12.1872	−	2.59046i	−0.713200	−	0.151595i
$293$	24.7134	+	11.0031i	1.44377	+	0.642808i	0.971152	−	0.238460i	$-0.0766425\pi$
$293$	24.7134	+	11.0031i	1.44377	+	0.642808i	0.472618	+	0.881268i	$0.343309\pi$
$294$	4.18105	+	12.8679i	0.243844	+	0.750474i
$295$	6.34857	+	19.5389i	0.369628	+	1.13760i
$296$	8.23976	+	3.66858i	0.478926	+	0.213232i
$297$	−22.7600	−	4.83779i	−1.32067	−	0.280717i
$298$	22.2093	−	4.72074i	1.28655	−	0.273465i
$299$	−6.71322	+	2.98892i	−0.388236	+	0.172854i
$300$	0.655843	+	0.728388i	0.0378651	+	0.0420535i
$301$	−0.00910394	−	0.0866182i	−0.000524742	−	0.00499259i
$302$	−5.78149	+	4.20050i	−0.332687	+	0.241712i
$303$	1.09556	−	10.4235i	0.0629381	−	0.598816i
$304$	9.09693	+	15.7563i	0.521745	+	0.903688i
$305$	8.65016	−	14.9825i	0.495306	−	0.857896i
$306$	−5.98110	−	4.34552i	−0.341917	−	0.248417i
$307$	0.987125	−	1.09631i	0.0563382	−	0.0625699i	−0.714317	−	0.699822i	$-0.753262\pi$
$307$	0.987125	−	1.09631i	0.0563382	−	0.0625699i	0.770655	+	0.637252i	$0.219929\pi$
$308$	−0.559983	+	1.72345i	−0.0319080	+	0.0982028i
$309$	6.18939			0.352102
$310$	17.1931	+	12.1885i	0.976505	+	0.692262i
$311$	12.8853			0.730660			0.365330	−	0.930878i	$-0.380956\pi$
$311$	12.8853			0.730660			0.365330	+	0.930878i	$0.380956\pi$
$312$	0.409487	−	1.26027i	0.0231826	−	0.0713488i
$313$	11.1724	−	12.4082i	0.631500	−	0.701352i	−0.339452	−	0.940623i	$-0.610242\pi$
$313$	11.1724	−	12.4082i	0.631500	−	0.701352i	0.970953	+	0.239271i	$0.0769084\pi$
$314$	−11.8964	−	8.64324i	−0.671353	−	0.487766i
$315$	0.586839	−	1.01644i	0.0330647	−	0.0572697i
$316$	9.55301	+	16.5463i	0.537399	+	0.930802i
$317$	0.502776	−	4.78360i	0.0282387	−	0.268674i	−0.971288	−	0.237907i	$-0.923539\pi$
$317$	0.502776	−	4.78360i	0.0282387	−	0.268674i	0.999527	−	0.0307663i	$-0.00979478\pi$
$318$	−21.1535	+	15.3689i	−1.18623	+	0.861846i
$319$	−2.86627	−	27.2707i	−0.160480	−	1.52687i
$320$	2.75557	+	3.06038i	0.154041	+	0.171080i
$321$	11.8280	−	5.26617i	0.660175	−	0.293929i
$322$	−4.01460	+	0.853329i	−0.223725	+	0.0475541i
$323$	7.98982	+	1.69829i	0.444565	+	0.0944953i
$324$	−0.0724656	−	0.0322638i	−0.00402587	−	0.00179243i
$325$	−0.212935	−	0.655345i	−0.0118115	−	0.0363520i
$326$	2.26479	+	6.97031i	0.125435	+	0.386050i
$327$	−2.59686	−	1.15620i	−0.143607	−	0.0639379i
$328$	−11.3163	−	2.40535i	−0.624837	−	0.132813i
$329$	3.82565	−	0.813168i	0.210915	−	0.0448314i
$330$	16.6066	−	7.39375i	0.914165	−	0.407012i
$331$	20.9214	+	23.2356i	1.14994	+	1.27714i	0.955092	+	0.296309i	$0.0957558\pi$
$331$	20.9214	+	23.2356i	1.14994	+	1.27714i	0.194851	+	0.980833i	$0.437578\pi$
$332$	−0.530321	−	5.04567i	−0.0291052	−	0.276917i
$333$	−10.9189	+	7.93305i	−0.598352	+	0.434729i
$334$	−0.182719	+	1.73846i	−0.00999796	+	0.0951242i
$335$	15.1226	+	26.1931i	0.826236	+	1.43108i
$336$	0.805822	−	1.39572i	0.0439612	−	0.0761430i
$337$	−8.28524	−	6.01958i	−0.451326	−	0.327908i	0.338793	−	0.940861i	$-0.389981\pi$
$337$	−8.28524	−	6.01958i	−0.451326	−	0.327908i	−0.790119	+	0.612953i	$0.789981\pi$
$338$	1.21988	−	1.35481i	0.0663527	−	0.0736921i
$339$	−6.99716	+	21.5351i	−0.380034	+	1.16962i
$340$	6.03995			0.327562
$341$	−19.9582	+	14.8582i	−1.08080	+	0.804618i
$342$	−12.5022			−0.676042
$343$	1.31650	−	4.05176i	0.0710841	−	0.218775i
$344$	0.234569	−	0.260516i	0.0126471	−	0.0140461i
$345$	13.2650	+	9.63755i	0.714161	+	0.518868i
$346$	−20.0635	+	34.7509i	−1.07862	+	1.86822i
$347$	−5.83305	−	10.1031i	−0.313134	−	0.542365i	0.665905	−	0.746037i	$-0.268046\pi$
$347$	−5.83305	−	10.1031i	−0.313134	−	0.542365i	−0.979039	+	0.203672i	$0.934712\pi$
$348$	0.912313	−	8.68008i	0.0489051	−	0.465301i
$349$	−1.51102	+	1.09782i	−0.0808828	+	0.0587648i	−0.627492	−	0.778623i	$-0.715918\pi$
$349$	−1.51102	+	1.09782i	−0.0808828	+	0.0587648i	0.546609	+	0.837388i	$0.315918\pi$
$350$	−0.0402286	−	0.382750i	−0.00215031	−	0.0204588i
$351$	3.48402	+	3.86939i	0.185963	+	0.206533i
$352$	−26.3661	+	11.7389i	−1.40532	+	0.625687i
$353$	2.02976	−	0.431439i	0.108033	−	0.0229632i	−0.153578	−	0.988137i	$-0.549080\pi$
$353$	2.02976	−	0.431439i	0.108033	−	0.0229632i	0.261611	+	0.965173i	$0.415746\pi$
$354$	−18.9618	−	4.03046i	−1.00781	−	0.214216i
$355$	4.42924	+	1.97203i	0.235080	+	0.104664i
$356$	0.721607	+	2.22088i	0.0382451	+	0.117706i
$357$	−0.223593	−	0.688150i	−0.0118338	−	0.0364208i
$358$	−11.9371	−	5.31475i	−0.630897	−	0.280893i
$359$	−6.07382	−	1.29103i	−0.320564	−	0.0681380i	0.0448193	−	0.998995i	$-0.485729\pi$
$359$	−6.07382	−	1.29103i	−0.320564	−	0.0681380i	−0.365383	+	0.930857i	$0.619062\pi$
$360$	4.62082	−	0.982185i	0.243539	−	0.0517657i
$361$	−4.73832	+	2.10964i	−0.249385	+	0.111034i
$362$	−6.67084	−	7.40872i	−0.350611	−	0.389393i
$363$	1.00770	+	9.58761i	0.0528905	+	0.503219i
$364$	0.328059	−	0.238349i	0.0171950	−	0.0124929i
$365$	2.04294	−	19.4372i	0.106932	−	1.01739i
$366$	8.16217	+	14.1373i	0.426644	+	0.738968i
$367$	12.2075	−	21.1439i	0.637224	−	1.10370i	−0.348815	−	0.937191i	$-0.613416\pi$
$367$	12.2075	−	21.1439i	0.637224	−	1.10370i	0.986039	−	0.166513i	$-0.0532507\pi$
$368$	−29.1028	−	21.1444i	−1.51709	−	1.10223i
$369$	11.5837	−	12.8650i	0.603023	−	0.669725i
$370$	8.55583	−	26.3321i	0.444796	−	1.36894i
$371$	4.08872			0.212276
$372$	−7.19700	+	3.30515i	−0.373147	+	0.171364i
$373$	−1.25492			−0.0649772			−0.0324886	−	0.999472i	$-0.510343\pi$
$373$	−1.25492			−0.0649772			−0.0324886	+	0.999472i	$0.510343\pi$
$374$	−5.53313	+	17.0292i	−0.286111	+	0.880561i
$375$	−8.49375	+	9.43326i	−0.438615	+	0.487131i
$376$	12.7357	+	9.25306i	0.656796	+	0.477190i
$377$	−3.06799	+	5.31392i	−0.158010	+	0.273681i
$378$	1.45404	+	2.51847i	0.0747877	+	0.129536i
$379$	1.70521	−	16.2239i	0.0875905	−	0.833368i	−0.859226	−	0.511595i	$-0.829055\pi$
$379$	1.70521	−	16.2239i	0.0875905	−	0.833368i	0.946817	−	0.321773i	$-0.104279\pi$
$380$	8.26332	−	6.00366i	0.423900	−	0.307981i
$381$	−0.523261	−	4.97850i	−0.0268075	−	0.255056i
$382$	11.2245	+	12.4661i	0.574296	+	0.637820i
$383$	10.8297	−	4.82169i	0.553371	−	0.246377i	−0.110947	−	0.993826i	$-0.535389\pi$
$383$	10.8297	−	4.82169i	0.553371	−	0.246377i	0.664319	+	0.747450i	$0.268722\pi$
$384$	9.77638	−	2.07803i	0.498899	−	0.106044i
$385$	−2.78048	−	0.591008i	−0.141706	−	0.0301206i
$386$	28.5197	+	12.6978i	1.45162	+	0.646302i
$387$	0.162099	+	0.498889i	0.00823994	+	0.0253599i
$388$	−2.14053	−	6.58787i	−0.108669	−	0.334448i
$389$	−14.6473	−	6.52142i	−0.742650	−	0.330649i	0.000296392	−	1.00000i	$-0.499906\pi$
$389$	−14.6473	−	6.52142i	−0.742650	−	0.330649i	−0.742946	+	0.669351i	$0.766572\pi$
$390$	−3.97885	−	0.845730i	−0.201477	−	0.0428252i
$391$	−15.7976	+	3.35787i	−0.798917	+	0.169815i
$392$	7.77968	−	3.46374i	0.392933	−	0.174945i
$393$	−8.88966	−	9.87296i	−0.448424	−	0.498025i
$394$	4.57538	+	43.5318i	0.230504	+	2.19310i
$395$	−24.2465	+	17.6161i	−1.21998	+	0.886364i
$396$	1.14085	−	10.8545i	0.0573300	−	0.545459i
$397$	−6.35588	−	11.0087i	−0.318993	−	0.552511i	0.661286	−	0.750134i	$-0.270011\pi$
$397$	−6.35588	−	11.0087i	−0.318993	−	0.552511i	−0.980278	+	0.197623i	$0.936678\pi$
$398$	−5.24504	+	9.08467i	−0.262910	+	0.455374i
$399$	−0.989915	−	0.719216i	−0.0495578	−	0.0360058i
$400$	2.25710	−	2.50677i	0.112855	−	0.125338i
$401$	7.21759	−	22.2135i	0.360429	−	1.10929i	−0.592365	−	0.805670i	$-0.701805\pi$
$401$	7.21759	−	22.2135i	0.360429	−	1.10929i	0.952794	−	0.303618i	$-0.0981945\pi$
$402$	−28.5390			−1.42339
$403$	5.56739	−	0.0647645i	0.277331	−	0.00322615i
$404$	12.9093			0.642262
$405$	0.0384509	−	0.118340i	0.00191064	−	0.00588034i
$406$	−2.29314	+	2.54679i	−0.113807	+	0.126395i
$407$	26.4451	+	19.2135i	1.31083	+	0.952376i
$408$	1.45617	−	2.52216i	0.0720911	−	0.124866i
$409$	4.64894	+	8.05220i	0.229875	+	0.398155i	0.957771	−	0.287532i	$-0.0928349\pi$
$409$	4.64894	+	8.05220i	0.229875	+	0.398155i	−0.727896	+	0.685688i	$0.759502\pi$
$410$	−3.71218	+	35.3190i	−0.183332	+	1.74428i
$411$	−3.08000	+	2.23775i	−0.151925	+	0.110380i
$412$	0.796865	+	7.58166i	0.0392587	+	0.373522i
$413$	2.02838	+	2.25275i	0.0998101	+	0.110850i
$414$	22.5824	−	10.0543i	1.10986	−	0.494143i
$415$	7.78450	−	1.65465i	0.382126	−	0.0812234i
$416$	6.31715	+	1.34275i	0.309724	+	0.0658338i
$417$	13.3345	+	5.93692i	0.652995	+	0.290732i
$418$	9.35696	+	28.7978i	0.457664	+	1.40854i
$419$	−2.10704	−	6.48480i	−0.102936	−	0.316803i	0.886305	−	0.463102i	$-0.153264\pi$
$419$	−2.10704	−	6.48480i	−0.102936	−	0.316803i	−0.989240	+	0.146299i	$0.953264\pi$
$420$	−0.826555	−	0.368006i	−0.0403317	−	0.0179568i
$421$	−14.7887	−	3.14343i	−0.720756	−	0.153202i	−0.167092	−	0.985941i	$-0.553438\pi$
$421$	−14.7887	−	3.14343i	−0.720756	−	0.153202i	−0.553665	+	0.832740i	$0.686771\pi$
$422$	−30.6482	+	6.51447i	−1.49193	+	0.317119i
$423$	−21.5196	+	9.58114i	−1.04632	+	0.465851i
$424$	11.0119	+	12.2300i	0.534787	+	0.593941i
$425$	−0.158301	−	1.50613i	−0.00767871	−	0.0730581i
$426$	−3.70117	+	2.68906i	−0.179322	+	0.130285i
$427$	0.266829	−	2.53871i	0.0129128	−	0.122857i
$428$	7.97358	+	13.8106i	0.385417	+	0.667563i
$429$	2.40121	−	4.15902i	0.115932	−	0.200799i
$430$	−0.870589	−	0.632520i	−0.0419835	−	0.0305028i
$431$	15.6352	−	17.3646i	0.753120	−	0.836424i	−0.237739	−	0.971329i	$-0.576406\pi$
$431$	15.6352	−	17.3646i	0.753120	−	0.836424i	0.990859	+	0.134905i	$0.0430729\pi$
$432$	−7.87641	+	24.2411i	−0.378954	+	1.16630i
$433$	−0.549764			−0.0264200			−0.0132100	−	0.999913i	$-0.504205\pi$
$433$	−0.549764			−0.0264200			−0.0132100	+	0.999913i	$0.504205\pi$
$434$	3.04905	+	0.611116i	0.146359	+	0.0293345i
$435$	13.6909			0.656427
$436$	1.08194	−	3.32987i	0.0518155	−	0.159472i
$437$	−18.2751	+	20.2966i	−0.874217	+	0.970916i
$438$	14.9197	+	10.8398i	0.712891	+	0.517945i
$439$	−10.5064	+	18.1977i	−0.501445	+	0.868527i	0.498554	+	0.866859i	$0.333865\pi$
$439$	−10.5064	+	18.1977i	−0.501445	+	0.868527i	−0.999999	+	0.00166883i	$0.999469\pi$
$440$	−5.72071	−	9.90856i	−0.272724	−	0.472372i
$441$	−1.33200	+	12.6731i	−0.0634284	+	0.603481i
$442$	3.24151	−	2.35510i	0.154183	−	0.112021i
$443$	−1.78286	−	16.9628i	−0.0847062	−	0.805926i	−0.951581	−	0.307399i	$-0.900541\pi$
$443$	−1.78286	−	16.9628i	−0.0847062	−	0.805926i	0.866874	−	0.498527i	$-0.166125\pi$
$444$	6.96185	+	7.73191i	0.330395	+	0.366940i
$445$	−3.34634	+	1.48989i	−0.158632	+	0.0706274i
$446$	18.5221	−	3.93700i	0.877049	−	0.186423i
$447$	−13.0916	−	2.78270i	−0.619210	−	0.131617i
$448$	0.555107	+	0.247150i	0.0262263	+	0.0116767i
$449$	−4.86440	−	14.9711i	−0.229565	−	0.706529i	−0.997796	−	0.0663560i	$-0.978863\pi$
$449$	−4.86440	−	14.9711i	−0.229565	−	0.706529i	0.768231	−	0.640173i	$-0.221137\pi$
$450$	0.716284	+	2.20450i	0.0337659	+	0.103921i
$451$	−38.3029	−	17.0536i	−1.80361	−	0.803021i
$452$	−27.2801	−	5.79856i	−1.28315	−	0.272742i
$453$	4.12043	−	0.875824i	0.193595	−	0.0411498i
$454$	−29.1152	+	12.9629i	−1.36644	+	0.608380i
$455$	0.425625	+	0.472704i	0.0199536	+	0.0221607i
$456$	−0.514802	−	4.89801i	−0.0241078	−	0.229370i
$457$	−6.58845	+	4.78679i	−0.308195	+	0.223917i	−0.731121	−	0.682247i	$-0.761003\pi$
$457$	−6.58845	+	4.78679i	−0.308195	+	0.223917i	0.422927	+	0.906164i	$0.361003\pi$
$458$	−0.963612	+	9.16816i	−0.0450266	+	0.428400i
$459$	5.72168	+	9.91025i	0.267065	+	0.462571i
$460$	−10.0976	+	17.4896i	−0.470805	+	0.815458i
$461$	26.2958	+	19.1050i	1.22472	+	0.889809i	0.996483	−	0.0837971i	$-0.0267048\pi$
$461$	26.2958	+	19.1050i	1.22472	+	0.889809i	0.228234	+	0.973606i	$0.426705\pi$
$462$	1.79476	−	1.99329i	0.0835000	−	0.0927361i
$463$	−5.49861	+	16.9230i	−0.255542	+	0.786477i	0.738181	+	0.674603i	$0.235685\pi$
$463$	−5.49861	+	16.9230i	−0.255542	+	0.786477i	−0.993722	+	0.111874i	$0.964315\pi$
$464$	−30.0373			−1.39445
$465$	−6.33625	−	10.6857i	−0.293836	−	0.495537i
$466$	41.9472			1.94317
$467$	−10.4947	+	32.2993i	−0.485635	+	1.49463i	0.345423	+	0.938447i	$0.387735\pi$
$467$	−10.4947	+	32.2993i	−0.485635	+	1.49463i	−0.831058	+	0.556185i	$0.812265\pi$
$468$	−1.63421	+	1.81497i	−0.0755414	+	0.0838972i
$469$	3.61043	+	2.62313i	0.166714	+	0.121125i
$470$	24.1619	−	41.8497i	1.11451	−	1.93038i
$471$	4.33395	+	7.50662i	0.199698	+	0.345887i
$472$	−1.27538	+	12.1344i	−0.0587040	+	0.558531i
$473$	1.02783	−	0.746761i	0.0472596	−	0.0343361i
$474$	−2.95603	−	28.1247i	−0.135775	−	1.29181i
$475$	−1.71365	−	1.90320i	−0.0786278	−	0.0873250i
$476$	0.814158	−	0.362487i	0.0373169	−	0.0166146i
$477$	−24.0877	+	5.11999i	−1.10290	+	0.234428i
$478$	−40.3395	−	8.57442i	−1.84508	−	0.392185i
$479$	−9.74212	−	4.33747i	−0.445129	−	0.198184i	0.171917	−	0.985111i	$-0.445004\pi$
$479$	−9.74212	−	4.33747i	−0.445129	−	0.198184i	−0.617046	+	0.786927i	$0.711671\pi$
$480$	−4.45294	−	13.7047i	−0.203248	−	0.625532i
$481$	−2.26032	−	6.95656i	−0.103062	−	0.317192i
$482$	20.6372	+	9.18826i	0.939997	+	0.418514i
$483$	2.36645	+	0.503005i	0.107677	+	0.0228875i
$484$	−11.6146	+	2.46875i	−0.527934	+	0.112216i
$485$	9.92637	−	4.41951i	0.450733	−	0.200679i
$486$	−18.9764	−	21.0754i	−0.860785	−	0.955999i
$487$	2.07533	+	19.7454i	0.0940422	+	0.894752i	0.935238	+	0.354020i	$0.115186\pi$
$487$	2.07533	+	19.7454i	0.0940422	+	0.894752i	−0.841196	+	0.540731i	$0.818148\pi$
$488$	8.31232	−	6.03925i	0.376281	−	0.273384i
$489$	0.451581	−	4.29651i	0.0204212	−	0.194295i
$490$	−13.0706	−	22.6390i	−0.590471	−	1.02273i
$491$	11.7062	−	20.2757i	0.528293	−	0.915030i	−0.471163	−	0.882046i	$-0.656166\pi$
$491$	11.7062	−	20.2757i	0.528293	−	0.915030i	0.999456	−	0.0329838i	$-0.0105010\pi$
$492$	−10.7966	−	7.84417i	−0.486747	−	0.353643i
$493$	−9.02359	+	10.0217i	−0.406402	+	0.451355i
$494$	2.09380	−	6.44407i	0.0942047	−	0.289932i
$495$	17.1205			0.769510
$496$	13.9015	+	23.4440i	0.624196	+	1.05267i
$497$	0.715393			0.0320897
$498$	−2.32055	+	7.14191i	−0.103986	+	0.320037i
$499$	11.4122	−	12.6745i	0.510881	−	0.567391i	−0.431423	−	0.902150i	$-0.641988\pi$
$499$	11.4122	−	12.6745i	0.510881	−	0.567391i	0.942304	+	0.334759i	$0.108655\pi$
$500$	−12.6488	−	9.18986i	−0.565670	−	0.410983i
$501$	0.515200	−	0.892353i	0.0230174	−	0.0398674i
$502$	−13.0750	−	22.6466i	−0.583566	−	1.01077i
$503$	−1.28095	+	12.1874i	−0.0571147	+	0.543410i	0.928130	+	0.372257i	$0.121416\pi$
$503$	−1.28095	+	12.1874i	−0.0571147	+	0.543410i	−0.985244	+	0.171153i	$0.945251\pi$
$504$	0.563920	−	0.409712i	0.0251190	−	0.0182500i
$505$	2.11670	+	20.1390i	0.0941919	+	0.896176i
$506$	−40.0605	−	44.4917i	−1.78091	−	1.97790i
$507$	−0.981729	+	0.437094i	−0.0436001	+	0.0194120i
$508$	6.03101	−	1.28193i	0.267583	−	0.0568765i
$509$	−8.16745	−	1.73605i	−0.362016	−	0.0769488i	0.0233129	−	0.999728i	$-0.492579\pi$
$509$	−8.16745	−	1.73605i	−0.362016	−	0.0769488i	−0.385329	+	0.922779i	$0.625912\pi$
$510$	−8.16709	−	3.63622i	−0.361645	−	0.161015i
$511$	−0.891144	−	2.74266i	−0.0394219	−	0.121328i
$512$	6.03893	+	18.5859i	0.266885	+	0.821389i
$513$	17.6786	+	7.87102i	0.780529	+	0.347514i
$514$	−37.0052	−	7.86569i	−1.63223	−	0.346941i
$515$	−11.6970	+	2.48628i	−0.515433	+	0.109559i
$516$	0.369419	−	0.164476i	0.0162628	−	0.00724066i
$517$	38.1751	+	42.3977i	1.67894	+	1.86465i
$518$	−0.427031	−	4.06293i	−0.0187627	−	0.178515i
$519$	19.1359	−	13.9031i	0.839974	−	0.610277i
$520$	−0.267618	+	2.54622i	−0.0117358	+	0.111659i
$521$	−1.21211	−	2.09943i	−0.0531033	−	0.0919776i	0.838252	−	0.545283i	$-0.183578\pi$
$521$	−1.21211	−	2.09943i	−0.0531033	−	0.0919776i	−0.891355	+	0.453306i	$0.850245\pi$
$522$	10.3203	−	17.8753i	0.451708	−	0.782381i
$523$	−36.2364	−	26.3273i	−1.58451	−	1.15121i	−0.911290	−	0.411765i	$-0.864913\pi$
$523$	−36.2364	−	26.3273i	−1.58451	−	1.15121i	−0.673216	−	0.739446i	$-0.735087\pi$
$524$	10.9493	−	12.1604i	0.478323	−	0.531232i
$525$	−0.0701033	+	0.215756i	−0.00305956	+	0.00941636i
$526$	48.4812			2.11388
$527$	11.9981	+	2.40476i	0.522646	+	0.104753i
$528$	23.5091			1.02310
$529$	9.57984	−	29.4837i	0.416515	−	1.28190i
$530$	33.8033	−	37.5424i	1.46832	−	1.63074i
$531$	−14.7706	−	10.7315i	−0.640990	−	0.465707i
$532$	0.753551	−	1.30519i	0.0326706	−	0.0565871i
$533$	4.69108	+	8.12520i	0.203193	+	0.351941i
$534$	0.361290	−	3.43745i	0.0156346	−	0.148753i
$535$	−20.2378	+	14.7036i	−0.874955	+	0.635692i
$536$	1.87759	+	17.8641i	0.0810997	+	0.771612i
$537$	5.15391	+	5.72399i	0.222408	+	0.247009i
$538$	3.10255	−	1.38135i	0.133761	−	0.0595540i
$539$	30.1883	−	6.41672i	1.30030	−	0.276388i
$540$	13.9966	+	2.97507i	0.602318	+	0.128027i
$541$	−22.6188	−	10.0706i	−0.972460	−	0.432967i	−0.141891	−	0.989882i	$-0.545318\pi$
$541$	−22.6188	−	10.0706i	−0.972460	−	0.432967i	−0.830569	+	0.556915i	$0.811985\pi$
$542$	−1.61337	−	4.96546i	−0.0693004	−	0.213285i
$543$	1.81597	+	5.58897i	0.0779306	+	0.239846i
$544$	12.9668	+	5.77318i	0.555945	+	0.247523i
$545$	5.37214	+	1.14188i	0.230117	+	0.0489129i
$546$	−0.587087	+	0.124789i	−0.0251250	+	0.00534048i
$547$	6.89463	−	3.06969i	0.294793	−	0.131250i	−0.254011	−	0.967201i	$-0.581750\pi$
$547$	6.89463	−	3.06969i	0.294793	−	0.131250i	0.548804	+	0.835951i	$0.315083\pi$
$548$	−3.13766	−	3.48473i	−0.134034	−	0.148860i
$549$	1.60708	+	15.2903i	0.0685883	+	0.652574i
$550$	4.54178	−	3.29979i	0.193662	−	0.140704i
$551$	−2.38378	+	22.6802i	−0.101553	+	0.966208i
$552$	4.86887	+	8.43314i	0.207233	+	0.358938i
$553$	−2.21109	+	3.82973i	−0.0940253	+	0.162857i
$554$	−23.2681	−	16.9053i	−0.988569	−	0.718237i
$555$	−10.9206	+	12.1286i	−0.463553	+	0.514828i
$556$	−5.55561	+	17.0984i	−0.235610	+	0.725134i
$557$	15.6213			0.661894			0.330947	−	0.943649i	$-0.392632\pi$
$557$	15.6213			0.661894			0.330947	+	0.943649i	$0.392632\pi$
$558$	−18.7280	+	0.217859i	−0.792818	+	0.00922271i
$559$	−0.284292			−0.0120243
$560$	−0.962222	+	2.96141i	−0.0406613	+	0.125143i
$561$	7.06245	−	7.84365i	0.298177	−	0.331159i
$562$	−21.7110	−	15.7740i	−0.915824	−	0.665385i
$563$	15.1272	−	26.2010i	0.637533	−	1.10424i	−0.348439	−	0.937332i	$-0.613288\pi$
$563$	15.1272	−	26.2010i	0.637533	−	1.10424i	0.985972	−	0.166909i	$-0.0533786\pi$
$564$	9.07958	+	15.7263i	0.382319	+	0.662196i
$565$	4.57297	−	43.5089i	0.192386	−	1.83043i
$566$	32.0578	−	23.2913i	1.34749	−	0.979008i
$567$	−0.00191913	−	0.0182593i	−8.05957e−5	−	0.000766817i
$568$	1.92673	+	2.13985i	0.0808437	+	0.0897861i
$569$	28.7157	−	12.7850i	1.20382	−	0.535977i	0.295943	−	0.955205i	$-0.404366\pi$
$569$	28.7157	−	12.7850i	1.20382	−	0.535977i	0.907881	+	0.419228i	$0.137699\pi$
$570$	−14.7879	+	3.14326i	−0.619395	+	0.131657i
$571$	−13.6656	−	2.90472i	−0.571888	−	0.121559i	−0.0871147	−	0.996198i	$-0.527765\pi$
$571$	−13.6656	−	2.90472i	−0.571888	−	0.121559i	−0.484774	+	0.874640i	$0.661098\pi$
$572$	5.40371	+	2.40589i	0.225941	+	0.100595i
$573$	−3.05559	−	9.40413i	−0.127649	−	0.392863i
$574$	1.61928	+	4.98363i	0.0675875	+	0.208013i
$575$	4.62589	+	2.05958i	0.192913	+	0.0858903i
$576$	−3.57976	−	0.760901i	−0.149157	−	0.0317042i
$577$	−1.83782	+	0.390640i	−0.0765094	+	0.0162626i	−0.246007	−	0.969268i	$-0.579119\pi$
$577$	−1.83782	+	0.390640i	−0.0765094	+	0.0162626i	0.169498	+	0.985531i	$0.445785\pi$
$578$	−20.2683	+	9.02404i	−0.843051	+	0.375351i
$579$	−12.3135	−	13.6756i	−0.511733	−	0.568337i
$580$	1.76266	+	16.7706i	0.0731903	+	0.696359i
$581$	0.950012	−	0.690224i	0.0394132	−	0.0286353i
$582$	−1.07171	+	10.1966i	−0.0444238	+	0.422664i
$583$	29.8212	+	51.6519i	1.23507	+	2.13920i
$584$	5.80365	−	10.0522i	0.240157	−	0.415963i
$585$	−3.09939	−	2.25184i	−0.128144	−	0.0931021i
$586$	33.0003	−	36.6506i	1.36323	−	1.51402i
$587$	−4.51201	+	13.8865i	−0.186230	+	0.573159i	−0.999967	−	0.00807486i	$-0.997430\pi$
$587$	−4.51201	+	13.8865i	−0.186230	+	0.573159i	0.813737	+	0.581233i	$0.197430\pi$
$588$	9.82338			0.405109
$589$	18.8051	−	8.63603i	0.774849	−	0.355842i
$590$	37.4541			1.54196
$591$	7.97316	−	24.5389i	0.327972	−	1.00939i
$592$	23.9594	−	26.6096i	0.984725	−	1.09365i
$593$	7.49794	+	5.44757i	0.307903	+	0.223705i	0.730996	−	0.682381i	$-0.239056\pi$
$593$	7.49794	+	5.44757i	0.307903	+	0.223705i	−0.423093	+	0.906086i	$0.639056\pi$
$594$	−21.2101	+	36.7370i	−0.870263	+	1.50734i
$595$	0.698989	+	1.21069i	0.0286558	+	0.0496333i
$596$	1.72315	−	16.3947i	0.0705831	−	0.671553i
$597$	5.00256	−	3.63457i	0.204741	−	0.148753i
$598$	1.40037	+	13.3236i	0.0572652	+	0.544842i
$599$	−14.5191	−	16.1251i	−0.593236	−	0.658855i	0.369522	−	0.929222i	$-0.379522\pi$
$599$	−14.5191	−	16.1251i	−0.593236	−	0.658855i	−0.962757	+	0.270367i	$0.912855\pi$
$600$	−0.834164	+	0.371394i	−0.0340546	+	0.0151621i
$601$	9.27708	−	1.97190i	0.378420	−	0.0804356i	−0.0147749	−	0.999891i	$-0.504703\pi$
$601$	9.27708	−	1.97190i	0.378420	−	0.0804356i	0.393195	+	0.919455i	$0.371370\pi$
$602$	−0.155312	−	0.0330126i	−0.00633004	−	0.00134549i
$603$	−24.5547	−	10.9324i	−0.999944	−	0.445204i
$604$	1.60333	+	4.93454i	0.0652385	+	0.200784i
$605$	−5.75576	−	17.7144i	−0.234005	−	0.720193i
$606$	−17.4557	−	7.77177i	−0.709088	−	0.315706i
$607$	22.8773	+	4.86271i	0.928560	+	0.197371i	0.647278	−	0.762254i	$-0.275907\pi$
$607$	22.8773	+	4.86271i	0.928560	+	0.197371i	0.281282	+	0.959625i	$0.409241\pi$
$608$	23.4785	−	4.99050i	0.952177	−	0.202391i
$609$	1.84547	−	0.821655i	0.0747821	−	0.0332952i
$610$	−21.1043	−	23.4387i	−0.854487	−	0.949004i
$611$	−1.33446	−	12.6965i	−0.0539864	−	0.513646i
$612$	−4.34249	+	3.15500i	−0.175535	+	0.127533i
$613$	2.20580	−	20.9868i	0.0890916	−	0.847650i	−0.855146	−	0.518387i	$-0.826533\pi$
$613$	2.20580	−	20.9868i	0.0890916	−	0.847650i	0.944238	−	0.329264i	$-0.106800\pi$
$614$	−1.34474	−	2.32915i	−0.0542691	−	0.0939968i
$615$	10.4670	−	18.1293i	0.422068	−	0.731044i
$616$	−1.36579	−	0.992302i	−0.0550291	−	0.0399810i
$617$	−0.000398321	0	0.000442380i	−1.60358e−5	0	1.78095e-5i	−0.743153	−	0.669122i	$-0.766670\pi$
$617$	−0.000398321	0	0.000442380i	−1.60358e−5	0	1.78095e-5i	0.743137	+	0.669140i	$0.233337\pi$
$618$	3.48687	−	10.7315i	0.140263	−	0.431684i
$619$	−43.0843			−1.73171			−0.865853	−	0.500299i	$-0.833224\pi$
$619$	−43.0843			−1.73171			−0.865853	+	0.500299i	$0.833224\pi$
$620$	12.2736	−	9.13730i	0.492920	−	0.366963i
$621$	−38.2622			−1.53541
$622$	7.25911	−	22.3413i	0.291064	−	0.895803i
$623$	−0.361656	+	0.401660i	−0.0144895	+	0.0160922i
$624$	−4.25594	−	3.09212i	−0.170374	−	0.123784i
$625$	10.5399	−	18.2557i	0.421597	−	0.730227i
$626$	−15.2199	−	26.3616i	−0.608308	−	1.05362i
$627$	1.86570	−	17.7510i	0.0745090	−	0.708906i
$628$	−8.63721	+	6.27530i	−0.344662	+	0.250412i
$629$	−1.68038	−	15.9877i	−0.0670011	−	0.637473i
$630$	−1.43175	−	1.59011i	−0.0570421	−	0.0633517i
$631$	−15.2377	+	6.78427i	−0.606604	+	0.270077i	−0.686967	−	0.726688i	$-0.741058\pi$
$631$	−15.2377	+	6.78427i	−0.606604	+	0.270077i	0.0803637	+	0.996766i	$0.474392\pi$
$632$	−17.4103	+	3.70068i	−0.692546	+	0.147205i
$633$	18.0659	+	3.84003i	0.718056	+	0.152628i
$634$	−8.01081	−	3.56664i	−0.318150	−	0.141649i
$635$	2.98875	+	9.19844i	0.118605	+	0.365029i
$636$	5.86631	+	18.0546i	0.232614	+	0.715913i
$637$	−6.30908	−	2.80898i	−0.249975	−	0.111296i
$638$	−48.8982	−	10.3936i	−1.93590	−	0.411488i
$639$	−4.21455	+	0.895830i	−0.166725	+	0.0354385i
$640$	−17.6412	+	7.85436i	−0.697329	+	0.310471i
$641$	25.2772	+	28.0732i	0.998389	+	1.10882i	0.994060	+	0.108833i	$0.0347114\pi$
$641$	25.2772	+	28.0732i	0.998389	+	1.10882i	0.00432943	+	0.999991i	$0.498622\pi$
$642$	−2.46730	−	23.4748i	−0.0973765	−	0.926475i
$643$	−28.1970	+	20.4864i	−1.11198	+	0.807903i	−0.982975	−	0.183741i	$-0.941179\pi$
$643$	−28.1970	+	20.4864i	−1.11198	+	0.807903i	−0.129008	+	0.991644i	$0.541179\pi$
$644$	−0.311480	+	2.96353i	−0.0122740	+	0.116780i
$645$	0.317162	+	0.549341i	0.0124882	+	0.0216303i
$646$	7.44575	−	12.8964i	0.292949	−	0.507403i
$647$	−28.4774	−	20.6901i	−1.11956	−	0.813410i	−0.135420	−	0.990788i	$-0.543238\pi$
$647$	−28.4774	−	20.6901i	−1.11956	−	0.813410i	−0.984143	+	0.177378i	$0.943238\pi$
$648$	0.0494476	−	0.0549171i	0.00194249	−	0.00215735i
$649$	−13.6643	+	42.0545i	−0.536372	+	1.65078i
$650$	−1.25623			−0.0492735
$651$	−1.49540	−	1.06011i	−0.0586092	−	0.0415491i
$652$	5.32112			0.208391
$653$	3.01926	−	9.29231i	0.118153	−	0.363636i	−0.874439	−	0.485136i	$-0.838770\pi$
$653$	3.01926	−	9.29231i	0.118153	−	0.363636i	0.992592	+	0.121499i	$0.0387702\pi$
$654$	−3.46765	+	3.85122i	−0.135596	+	0.150594i
$655$	20.7661	+	15.0875i	0.811400	+	0.589517i
$656$	−22.9641	+	39.7750i	−0.896598	+	1.55295i
$657$	8.68437	+	15.0418i	0.338809	+	0.586835i
$658$	0.745318	−	7.09123i	0.0290555	−	0.276445i
$659$	−10.8553	+	7.88685i	−0.422863	+	0.307228i	−0.778789	−	0.627286i	$-0.784166\pi$
$659$	−10.8553	+	7.88685i	−0.422863	+	0.307228i	0.355926	+	0.934514i	$0.384166\pi$
$660$	−1.37957	−	13.1257i	−0.0536997	−	0.510918i
$661$	−7.67754	−	8.52677i	−0.298622	−	0.331653i	0.575096	−	0.818086i	$-0.304965\pi$
$661$	−7.67754	−	8.52677i	−0.298622	−	0.331653i	−0.873718	+	0.486433i	$0.838298\pi$
$662$	52.0733	−	23.1845i	2.02389	−	0.901093i
$663$	−2.31020	+	0.491049i	−0.0897209	+	0.0190708i
$664$	4.62318	+	0.982688i	0.179414	+	0.0381357i
$665$	2.15970	+	0.961563i	0.0837498	+	0.0372878i
$666$	7.60343	+	23.4010i	0.294627	+	0.906769i
$667$	−13.9337	−	42.8836i	−0.539516	−	1.66046i
$668$	1.15941	+	0.516204i	0.0448590	+	0.0199725i
$669$	−10.9181	−	2.32071i	−0.422118	−	0.0897240i
$670$	53.9345	−	11.4641i	2.08367	−	0.442898i
$671$	34.0171	−	15.1454i	1.31322	−	0.584681i
$672$	−1.42272	−	1.58009i	−0.0548827	−	0.0609534i
$673$	−2.31617	−	22.0368i	−0.0892816	−	0.849458i	−0.943907	−	0.330212i	$-0.892880\pi$
$673$	−2.31617	−	22.0368i	−0.0892816	−	0.849458i	0.854625	−	0.519246i	$-0.173787\pi$
$674$	−15.1047	+	10.9742i	−0.581810	+	0.422710i
$675$	0.375032	−	3.56819i	0.0144350	−	0.137340i
$676$	−0.661810	−	1.14629i	−0.0254542	−	0.0440881i
$677$	−17.4656	+	30.2514i	−0.671259	+	1.16265i	0.306289	+	0.951939i	$0.400913\pi$
$677$	−17.4656	+	30.2514i	−0.671259	+	1.16265i	−0.977547	+	0.210716i	$0.932421\pi$
$678$	33.3967	+	24.2641i	1.28259	+	0.931857i
$679$	1.07279	−	1.19146i	0.0411701	−	0.0457240i
$680$	−1.73879	+	5.35146i	−0.0666797	+	0.205219i
$681$	18.7865			0.719900
$682$	14.5183	+	42.9751i	0.555933	+	1.64560i
$683$	2.99526			0.114610			0.0573052	−	0.998357i	$-0.481749\pi$
$683$	2.99526			0.114610			0.0573052	+	0.998357i	$0.481749\pi$
$684$	−2.80496	+	8.63279i	−0.107250	+	0.330083i
$685$	4.92185	−	5.46627i	0.188054	−	0.208855i
$686$	−6.28349	−	4.56522i	−0.239905	−	0.174301i
$687$	2.71703	−	4.70603i	0.103661	−	0.179546i
$688$	−0.695842	−	1.20523i	−0.0265287	−	0.0459491i
$689$	1.39506	−	13.2731i	0.0531474	−	0.505664i
$690$	24.1831	−	17.5700i	0.920634	−	0.668880i
$691$	−1.42138	−	13.5236i	−0.0540720	−	0.514461i	−0.987716	−	0.156259i	$-0.950057\pi$
$691$	−1.42138	−	13.5236i	−0.0540720	−	0.514461i	0.933644	−	0.358202i	$-0.116610\pi$
$692$	19.4942	+	21.6505i	0.741057	+	0.823027i
$693$	2.30777	−	1.02749i	0.0876649	−	0.0390309i
$694$	−20.8035	+	4.42191i	−0.789689	+	0.167854i
$695$	−27.5852	−	5.86341i	−1.04637	−	0.222412i
$696$	7.42800	+	3.30716i	0.281558	+	0.125357i
$697$	6.37192	+	19.6107i	0.241354	+	0.742810i
$698$	1.05220	+	3.23835i	0.0398265	+	0.122573i
$699$	−22.5886	−	10.0571i	−0.854380	−	0.380394i
$700$	−0.273314	−	0.0580948i	−0.0103303	−	0.00219578i
$701$	−35.5685	+	7.56032i	−1.34340	+	0.285549i	−0.822840	−	0.568273i	$-0.807612\pi$
$701$	−35.5685	+	7.56032i	−1.34340	+	0.285549i	−0.520564	+	0.853822i	$0.674278\pi$
$702$	8.67172	−	3.86090i	0.327293	−	0.145720i
$703$	−18.1906	−	20.2027i	−0.686072	−	0.761960i
$704$	0.926507	+	8.81513i	0.0349191	+	0.332233i
$705$	−23.0449	+	16.7431i	−0.867922	+	0.630582i
$706$	0.395440	−	3.76236i	0.0148826	−	0.141598i
$707$	1.49396	+	2.58762i	0.0561863	+	0.0973175i
$708$	−7.03725	+	12.1889i	−0.264476	+	0.458086i
$709$	11.8388	+	8.60142i	0.444617	+	0.323033i	0.787467	−	0.616357i	$-0.211392\pi$
$709$	11.8388	+	8.60142i	0.444617	+	0.323033i	−0.342850	+	0.939390i	$0.611392\pi$
$710$	5.91447	−	6.56868i	0.221966	−	0.246518i
$711$	8.23042	−	25.3306i	0.308665	−	0.949973i
$712$	−2.17546			−0.0815287
$713$	−27.0219	+	30.7221i	−1.01198	+	1.15055i
$714$	−1.31911			−0.0493666
$715$	−2.86725	+	8.82450i	−0.107229	+	0.330018i
$716$	−6.34802	+	7.05020i	−0.237237	+	0.263478i
$717$	19.6670	+	14.2889i	0.734479	+	0.533630i
$718$	−5.66022	+	9.80379i	−0.211238	+	0.365874i
$719$	−4.75708	−	8.23950i	−0.177409	−	0.307281i	0.763583	−	0.645709i	$-0.223438\pi$
$719$	−4.75708	−	8.23950i	−0.177409	−	0.307281i	−0.940992	+	0.338428i	$0.890105\pi$
$720$	1.96033	−	18.6513i	0.0730573	−	0.695094i
$721$	−1.42750	+	1.03714i	−0.0531627	+	0.0386250i
$722$	0.988405	+	9.40404i	0.0367846	+	0.349982i
$723$	−8.91019	−	9.89576i	−0.331373	−	0.368027i
$724$	−6.61238	+	2.94402i	−0.245747	+	0.109414i
$725$	4.13573	−	0.879077i	0.153597	−	0.0326481i
$726$	17.1912	+	3.65410i	0.638025	+	0.135617i
$727$	14.0918	+	6.27408i	0.522636	+	0.232693i	0.651059	−	0.759027i	$-0.274325\pi$
$727$	14.0918	+	6.27408i	0.522636	+	0.232693i	−0.128423	+	0.991719i	$0.540992\pi$
$728$	0.116737	+	0.359280i	0.00432657	+	0.0133158i
$729$	5.22139	+	16.0698i	0.193385	+	0.595177i
$730$	−32.5504	−	14.4924i	−1.20474	−	0.536387i
$731$	−0.611157	−	0.129906i	−0.0226045	−	0.00480473i
$732$	11.5931	−	2.46418i	0.428492	−	0.0910787i
$733$	−22.3602	+	9.95542i	−0.825894	+	0.367712i	−0.775758	−	0.631031i	$-0.782632\pi$
$733$	−22.3602	+	9.95542i	−0.825894	+	0.367712i	−0.0501361	+	0.998742i	$0.515965\pi$
$734$	−29.7832	−	33.0776i	−1.09932	−	1.22092i
$735$	1.61071	+	15.3249i	0.0594119	+	0.565267i
$736$	−38.3951	+	27.8957i	−1.41526	+	1.02825i
$737$	−6.80462	+	64.7417i	−0.250652	+	2.38479i
$738$	−15.7802	−	27.3321i	−0.580877	−	1.00611i
$739$	−9.83618	+	17.0368i	−0.361830	+	0.626707i	−0.988262	−	0.152768i	$-0.951181\pi$
$739$	−9.83618	+	17.0368i	−0.361830	+	0.626707i	0.626432	+	0.779476i	$0.284514\pi$
$740$	−16.2628	−	11.8156i	−0.597832	−	0.434350i
$741$	−2.67252	+	2.96813i	−0.0981774	+	0.109037i
$742$	2.30344	−	7.08924i	0.0845618	−	0.260254i
$743$	0.229636			0.00842453			0.00421227	−	0.999991i	$-0.498659\pi$
$743$	0.229636			0.00842453			0.00421227	+	0.999991i	$0.498659\pi$
$744$	−0.856509	−	7.32811i	−0.0314012	−	0.268662i
$745$	25.8590			0.947399
$746$	−0.706974	+	2.17584i	−0.0258842	+	0.0796633i
$747$	−4.73244	+	5.25591i	−0.173151	+	0.192304i
$748$	10.5173	+	7.64126i	0.384551	+	0.279392i
$749$	−1.84553	+	3.19655i	−0.0674341	+	0.116799i
$750$	11.5708	+	20.0412i	0.422507	+	0.731803i
$751$	−1.65629	+	15.7585i	−0.0604388	+	0.575037i	0.921835	+	0.387583i	$0.126690\pi$
$751$	−1.65629	+	15.7585i	−0.0604388	+	0.575037i	−0.982274	+	0.187453i	$0.939977\pi$
$752$	50.5597	−	36.7338i	1.84372	−	1.33954i
$753$	1.61125	+	15.3300i	0.0587171	+	0.558656i
$754$	7.48515	+	8.31310i	0.272593	+	0.302745i
$755$	−7.43519	+	3.31036i	−0.270594	+	0.120476i
$756$	2.06523	−	0.438978i	0.0751116	−	0.0159655i
$757$	−39.6667	−	8.43141i	−1.44171	−	0.306445i	−0.580319	−	0.814389i	$-0.697072\pi$
$757$	−39.6667	−	8.43141i	−1.44171	−	0.306445i	−0.861390	+	0.507944i	$0.830406\pi$
$758$	−27.1693	−	12.0965i	−0.986832	−	0.439366i
$759$	10.9054	+	33.5635i	0.395843	+	1.21828i
$760$	2.94044	+	9.04973i	0.106661	+	0.328268i
$761$	47.6965	+	21.2358i	1.72900	+	0.769798i	0.995979	+	0.0895877i	$0.0285549\pi$
$761$	47.6965	+	21.2358i	1.72900	+	0.769798i	0.733017	+	0.680211i	$0.238112\pi$
$762$	−8.92676	−	1.89744i	−0.323383	−	0.0687371i
$763$	0.792670	−	0.168487i	0.0286966	−	0.00609964i
$764$	11.1261	−	4.95368i	0.402530	−	0.179218i
$765$	−5.63396	−	6.25715i	−0.203696	−	0.226228i
$766$	−2.25905	−	21.4934i	−0.0816228	−	0.776589i
$767$	8.00508	−	5.81603i	0.289047	−	0.210005i
$768$	2.35024	−	22.3610i	0.0848070	−	0.806885i
$769$	−14.5523	−	25.2054i	−0.524770	−	0.908929i	−0.999584	−	0.0288427i	$-0.990818\pi$
$769$	−14.5523	−	25.2054i	−0.524770	−	0.908929i	0.474813	−	0.880086i	$-0.342516\pi$
$770$	−2.59114	+	4.48798i	−0.0933781	+	0.161736i
$771$	18.0415	+	13.1079i	0.649747	+	0.472069i
$772$	15.1665	−	16.8441i	0.545853	−	0.606231i
$773$	−8.71957	+	26.8361i	−0.313621	+	0.965226i	0.662697	+	0.748887i	$0.269412\pi$
$773$	−8.71957	+	26.8361i	−0.313621	+	0.965226i	−0.976318	+	0.216339i	$0.930588\pi$
$774$	0.956320			0.0343742
$775$	−2.60017	−	2.82108i	−0.0934008	−	0.101336i
$776$	6.45314			0.231654
$777$	−0.744154	+	2.29027i	−0.0266964	+	0.0821630i
$778$	−19.5589	+	21.7224i	−0.701222	+	0.778786i
$779$	28.2104	+	20.4960i	1.01074	+	0.734347i
$780$	−1.47666	+	2.55765i	−0.0528729	+	0.0915786i
$781$	5.21774	+	9.03739i	0.186705	+	0.323383i
$782$	−3.07770	+	29.2823i	−0.110058	+	1.04713i
$783$	−25.8471	+	18.7790i	−0.923698	+	0.671106i
$784$	−3.53384	−	33.6222i	−0.126209	−	1.20079i
$785$	−11.2059	−	12.4455i	−0.399957	−	0.444198i
$786$	−22.1264	+	9.85129i	−0.789221	+	0.351384i
$787$	−9.78166	+	2.07916i	−0.348679	+	0.0741139i	−0.378922	−	0.925429i	$-0.623705\pi$
$787$	−9.78166	+	2.07916i	−0.348679	+	0.0741139i	0.0302433	+	0.999543i	$0.490372\pi$
$788$	31.0853	+	6.60738i	1.10737	+	0.235378i
$789$	−26.1071	−	11.6237i	−0.929439	−	0.413813i
$790$	16.8842	+	51.9642i	0.600712	+	1.84880i
$791$	−1.99476	−	6.13925i	−0.0709256	−	0.218286i
$792$	9.28876	+	4.13562i	0.330062	+	0.146953i
$793$	−8.15029	−	1.73240i	−0.289425	−	0.0615192i
$794$	−22.6681	+	4.81826i	−0.804462	+	0.170994i
$795$	−27.2041	+	12.1120i	−0.964830	+	0.429570i
$796$	5.09621	+	5.65992i	0.180630	+	0.200610i
$797$	4.55418	+	43.3301i	0.161317	+	1.53483i	0.713231	+	0.700929i	$0.247231\pi$
$797$	4.55418	+	43.3301i	0.161317	+	1.53483i	−0.551914	+	0.833901i	$0.686102\pi$
$798$	−1.80469	+	1.31119i	−0.0638855	+	0.0464155i
$799$	2.93285	−	27.9042i	0.103757	−	0.987179i
$800$	−2.22511	−	3.85400i	−0.0786694	−	0.136259i
$801$	1.62764	−	2.81915i	0.0575097	−	0.0996098i
$802$	−34.4487	−	25.0285i	−1.21643	−	0.883786i
$803$	28.1478	−	31.2613i	0.993314	−	1.10319i
$804$	−6.40293	+	19.7062i	−0.225814	+	0.694984i
$805$	−4.67431			−0.164748
$806$	3.02417	−	9.68951i	0.106522	−	0.341299i
$807$	−2.00191			−0.0704706
$808$	−3.71636	+	11.4378i	−0.130741	+	0.402379i
$809$	−9.72748	+	10.8035i	−0.342000	+	0.379829i	−0.889468	−	0.456997i	$-0.848925\pi$
$809$	−9.72748	+	10.8035i	−0.342000	+	0.379829i	0.547468	+	0.836826i	$0.315592\pi$
$810$	−0.183522	−	0.133336i	−0.00644829	−	0.00468496i
$811$	1.04369	−	1.80773i	0.0366490	−	0.0634780i	−0.847119	−	0.531403i	$-0.821665\pi$
$811$	1.04369	−	1.80773i	0.0366490	−	0.0634780i	0.883768	+	0.467925i	$0.154998\pi$
$812$	1.24408	+	2.15481i	0.0436587	+	0.0756190i
$813$	−0.321694	+	3.06072i	−0.0112823	+	0.107344i
$814$	48.2115	−	35.0277i	1.68981	−	1.22772i
$815$	0.872489	+	8.30118i	0.0305619	+	0.290778i
$816$	−7.73630	−	8.59204i	−0.270825	−	0.300781i
$817$	−0.965256	+	0.429760i	−0.0337700	+	0.0150354i
$818$	16.5804	−	3.52426i	0.579719	−	0.123223i
$819$	−0.552928	−	0.117528i	−0.0193209	−	0.00410677i
$820$	23.5550	+	10.4873i	0.822575	+	0.366234i
$821$	−15.1564	−	46.6466i	−0.528962	−	1.62798i	−0.756345	−	0.654173i	$-0.773017\pi$
$821$	−15.1564	−	46.6466i	−0.528962	−	1.62798i	0.227382	−	0.973806i	$-0.426983\pi$
$822$	2.14477	+	6.60094i	0.0748076	+	0.230234i
$823$	28.2332	+	12.5702i	0.984149	+	0.438171i	0.834764	−	0.550608i	$-0.185604\pi$
$823$	28.2332	+	12.5702i	0.984149	+	0.438171i	0.149385	+	0.988779i	$0.452271\pi$
$824$	−6.94683	−	1.47659i	−0.242004	−	0.0514396i
$825$	−3.23689	+	0.688023i	−0.112694	+	0.0239539i
$826$	5.04864	−	2.24780i	0.175665	−	0.0782110i
$827$	3.46852	+	3.85218i	0.120612	+	0.133953i	0.800427	−	0.599431i	$-0.204606\pi$
$827$	3.46852	+	3.85218i	0.120612	+	0.133953i	−0.679814	+	0.733384i	$0.737940\pi$
$828$	−1.87600	−	17.8489i	−0.0651954	−	0.620293i
$829$	29.4093	−	21.3671i	1.02143	−	0.742111i	0.0548526	−	0.998494i	$-0.482531\pi$
$829$	29.4093	−	21.3671i	1.02143	−	0.742111i	0.966575	+	0.256384i	$0.0825311\pi$
$830$	1.51658	−	14.4293i	0.0526414	−	0.500850i
$831$	8.47676	+	14.6822i	0.294056	+	0.509319i
$832$	0.991713	−	1.71770i	0.0343815	−	0.0595504i
$833$	−12.2794	−	8.92152i	−0.425457	−	0.309112i
$834$	17.8059	−	19.7755i	0.616568	−	0.684768i
$835$	−0.615194	+	1.89337i	−0.0212897	+	0.0655228i
$836$	21.9842			0.760339
$837$	26.6192	+	11.4825i	0.920093	+	0.396893i
$838$	−12.4307			−0.429412
$839$	−1.76834	+	5.44241i	−0.0610500	+	0.187893i	−0.976930	−	0.213559i	$-0.931494\pi$
$839$	−1.76834	+	5.44241i	−0.0610500	+	0.187893i	0.915880	+	0.401452i	$0.131494\pi$
$840$	0.564007	−	0.626393i	0.0194601	−	0.0216126i
$841$	−6.99822	−	5.08450i	−0.241318	−	0.175328i
$842$	−13.7816	+	23.8705i	−0.474947	+	0.822632i
$843$	7.90949	+	13.6996i	0.272417	+	0.471841i
$844$	−2.37789	+	22.6241i	−0.0818505	+	0.778755i
$845$	1.67974	−	1.22041i	0.0577849	−	0.0419832i
$846$	4.48894	+	42.7094i	0.154333	+	1.46838i
$847$	−1.83898	−	2.04239i	−0.0631880	−	0.0701774i
$848$	59.6848	−	26.5734i	2.04959	−	0.912534i
$849$	−22.8473	+	4.85635i	−0.784119	+	0.166670i
$850$	−2.70059	−	0.574028i	−0.0926294	−	0.0196890i
$851$	49.1043	+	21.8626i	1.68327	+	0.749442i
$852$	1.02641	+	3.15897i	0.0351643	+	0.108224i
$853$	−11.5484	−	35.5423i	−0.395410	−	1.21695i	−0.928642	−	0.370977i	$-0.879023\pi$
$853$	−11.5484	−	35.5423i	−0.395410	−	1.21695i	0.533232	−	0.845969i	$-0.320977\pi$
$854$	−4.25143	−	1.89286i	−0.145481	−	0.0647723i
$855$	−13.9274	−	2.96037i	−0.476308	−	0.101242i
$856$	−14.5318	+	3.08883i	−0.496687	+	0.105574i
$857$	−16.7243	+	7.44613i	−0.571291	+	0.254355i	−0.671988	−	0.740562i	$-0.734559\pi$
$857$	−16.7243	+	7.44613i	−0.571291	+	0.254355i	0.100697	+	0.994917i	$0.467893\pi$
$858$	−5.85837	−	6.50638i	−0.200001	−	0.222124i
$859$	3.74267	+	35.6091i	0.127698	+	1.21497i	0.851273	+	0.524723i	$0.175831\pi$
$859$	3.74267	+	35.6091i	0.127698	+	1.21497i	−0.723575	+	0.690246i	$0.757502\pi$
$860$	−0.632078	+	0.459232i	−0.0215537	+	0.0156597i
$861$	0.322872	−	3.07192i	0.0110034	−	0.104691i
$862$	−21.2994	−	36.8917i	−0.725461	−	1.25653i
$863$	10.0261	−	17.3658i	0.341294	−	0.591138i	−0.643379	−	0.765548i	$-0.722468\pi$
$863$	10.0261	−	17.3658i	0.341294	−	0.591138i	0.984673	+	0.174409i	$0.0558015\pi$
$864$	27.2047	+	19.7654i	0.925523	+	0.672432i
$865$	−30.5792	+	33.9617i	−1.03972	+	1.15473i
$866$	−0.309717	+	0.953210i	−0.0105246	+	0.0323914i
$867$	13.0781			0.444154
$868$	1.10605	−	1.96826i	0.0375419	−	0.0668073i
$869$	−64.5067			−2.18824
$870$	7.71293	−	23.7379i	0.261493	−	0.804792i
$871$	9.74725	−	10.8254i	0.330273	−	0.366805i
$872$	2.63883	+	1.91722i	0.0893619	+	0.0649252i
$873$	−4.82812	+	8.36255i	−0.163407	+	0.283030i
$874$	24.8957	+	43.1207i	0.842111	+	1.45858i
$875$	0.378261	−	3.59892i	0.0127876	−	0.121666i
$876$	10.8322	−	7.87007i	0.365987	−	0.265905i
$877$	−0.357736	−	3.40363i	−0.0120799	−	0.114933i	0.986820	−	0.161820i	$-0.0517364\pi$
$877$	−0.357736	−	3.40363i	−0.0120799	−	0.114933i	−0.998900	+	0.0468876i	$0.985070\pi$
$878$	25.6331	+	28.4685i	0.865077	+	0.960765i
$879$	−26.5579	+	11.8243i	−0.895775	+	0.398825i
$880$	−44.4288	+	9.44364i	−1.49770	+	0.318345i
$881$	14.9640	+	3.18069i	0.504149	+	0.107160i	0.452964	−	0.891529i	$-0.350367\pi$
$881$	14.9640	+	3.18069i	0.504149	+	0.107160i	0.0511853	+	0.998689i	$0.483700\pi$
$882$	21.2229	+	9.44904i	0.714612	+	0.318166i
$883$	−3.86540	−	11.8965i	−0.130081	−	0.400348i	0.864712	−	0.502269i	$-0.167501\pi$
$883$	−3.86540	−	11.8965i	−0.130081	−	0.400348i	−0.994793	+	0.101921i	$0.967501\pi$
$884$	−0.898939	−	2.76665i	−0.0302346	−	0.0930525i
$885$	−20.1690	−	8.97983i	−0.677975	−	0.301854i
$886$	−30.4153	−	6.46498i	−1.02182	−	0.217195i
$887$	33.2026	−	7.05744i	1.11484	−	0.236966i	0.386570	−	0.922260i	$-0.373660\pi$
$887$	33.2026	−	7.05744i	1.11484	−	0.236966i	0.728266	+	0.685295i	$0.240327\pi$
$888$	−8.85475	+	3.94239i	−0.297146	+	0.132298i
$889$	0.954913	+	1.06054i	0.0320268	+	0.0355693i
$890$	0.698040	+	6.64141i	0.0233984	+	0.222620i
$891$	0.216668	−	0.157418i	0.00725865	−	0.00527372i
$892$	1.43707	−	13.6729i	0.0481168	−	0.457801i
$893$	−23.7240	−	41.0912i	−0.793895	−	1.37507i
$894$	−12.2001	+	21.1312i	−0.408032	+	0.706732i
$895$	−12.0395	−	8.74718i	−0.402435	−	0.292386i
$896$	−1.90657	+	2.11746i	−0.0636941	+	0.0707395i
$897$	2.44031	−	7.51050i	0.0814796	−	0.250768i
$898$	−28.6981			−0.957667
$899$	−3.17562	+	34.0158i	−0.105913	+	1.13449i
$900$	1.68291			0.0560970
$901$	9.06409	−	27.8964i	0.301968	−	0.929363i
$902$	−51.1468	+	56.8043i	−1.70300	+	1.89138i
$903$	0.0757206	+	0.0550142i	0.00251982	+	0.00183076i
$904$	12.9910	−	22.5011i	0.432076	−	0.748377i
$905$	−5.67700	−	9.83286i	−0.188710	−	0.326855i
$906$	0.802747	−	7.63762i	0.0266695	−	0.253743i
$907$	16.7249	−	12.1513i	0.555340	−	0.403478i	−0.274410	−	0.961613i	$-0.588483\pi$
$907$	16.7249	−	12.1513i	0.555340	−	0.403478i	0.829751	+	0.558134i	$0.188483\pi$
$908$	2.41870	+	23.0124i	0.0802674	+	0.763694i
$909$	−12.0416	−	13.3735i	−0.399394	−	0.443572i
$910$	1.05938	−	0.471667i	0.0351181	−	0.0156356i
$911$	25.6795	−	5.45834i	0.850799	−	0.180843i	0.238180	−	0.971221i	$-0.423449\pi$
$911$	25.6795	−	5.45834i	0.850799	−	0.180843i	0.612619	+	0.790378i	$0.290116\pi$
$912$	−19.1245	−	4.06504i	−0.633276	−	0.134607i
$913$	15.6484	+	6.96711i	0.517886	+	0.230578i
$914$	4.58790	+	14.1201i	0.151754	+	0.467051i
$915$	5.74510	+	17.6816i	0.189927	+	0.584536i
$916$	6.11443	+	2.72232i	0.202026	+	0.0899479i
$917$	3.70465	+	0.787448i	0.122338	+	0.0260038i
$918$	20.4063	−	4.33749i	0.673508	−	0.143159i
$919$	19.7036	−	8.77259i	0.649960	−	0.289381i	−0.0551505	−	0.998478i	$-0.517564\pi$
$919$	19.7036	−	8.77259i	0.649960	−	0.289381i	0.705111	+	0.709097i	$0.250897\pi$
$920$	−12.5891	−	13.9816i	−0.415049	−	0.460959i
$921$	0.165713	+	1.57666i	0.00546044	+	0.0519526i
$922$	47.9393	−	34.8300i	1.57880	−	1.14706i
$923$	0.244089	−	2.32235i	0.00803429	−	0.0764412i
$924$	−0.973698	−	1.68649i	−0.0320323	−	0.0554816i
$925$	−2.52013	+	4.36499i	−0.0828612	+	0.143520i
$926$	26.2442	+	19.0675i	0.862438	+	0.626598i
$927$	7.11100	−	7.89756i	0.233556	−	0.259390i
$928$	−12.2457	+	37.6884i	−0.401985	+	1.23718i
$929$	27.1108			0.889475			0.444738	−	0.895661i	$-0.353297\pi$
$929$	27.1108			0.889475			0.444738	+	0.895661i	$0.353297\pi$
$930$	−22.0970	+	4.96619i	−0.724589	+	0.162848i
$931$	−25.6675			−0.841219
$932$	9.41117	−	28.9646i	0.308273	−	0.948767i
$933$	−9.26548	+	10.2904i	−0.303338	+	0.336891i
$934$	50.0899	+	36.3924i	1.63899	+	1.19080i
$935$	−10.1962	+	17.6603i	−0.333451	+	0.577555i
$936$	−1.13762	−	1.97042i	−0.0371844	−	0.0644053i
$937$	3.26518	−	31.0661i	0.106669	−	1.01488i	−0.801988	−	0.597340i	$-0.796224\pi$
$937$	3.26518	−	31.0661i	0.106669	−	1.01488i	0.908657	−	0.417544i	$-0.137109\pi$
$938$	6.58211	−	4.78218i	0.214913	−	0.156144i
$939$	1.87556	+	17.8448i	0.0612066	+	0.582342i
$940$	−23.4763	−	26.0731i	−0.765714	−	0.850412i
$941$	5.05971	−	2.25273i	0.164942	−	0.0734368i	−0.322605	−	0.946534i	$-0.604559\pi$
$941$	5.05971	−	2.25273i	0.164942	−	0.0734368i	0.487547	+	0.873097i	$0.337892\pi$
$942$	15.4570	−	3.28548i	0.503615	−	0.107047i
$943$	−67.4386	−	14.3345i	−2.19610	−	0.466796i
$944$	44.2501	+	19.7014i	1.44022	+	0.641227i
$945$	1.02345	+	3.14986i	0.0332929	+	0.102465i
$946$	−0.715733	−	2.20280i	−0.0232705	−	0.0716192i
$947$	18.3089	+	8.15166i	0.594960	+	0.264893i	0.682048	−	0.731307i	$-0.261090\pi$
$947$	18.3089	+	8.15166i	0.594960	+	0.264893i	−0.0870881	+	0.996201i	$0.527756\pi$
$948$	−20.0834	−	4.26885i	−0.652277	−	0.138646i
$949$	−9.20745	+	1.95710i	−0.298886	+	0.0635303i
$950$	−4.26528	+	1.89903i	−0.138384	+	0.0616126i
$951$	3.45870	+	3.84127i	0.112156	+	0.124562i
$952$	0.0867852	+	0.825706i	0.00281272	+	0.0267613i
$953$	11.5067	−	8.36010i	0.372738	−	0.270810i	−0.385607	−	0.922663i	$-0.626008\pi$
$953$	11.5067	−	8.36010i	0.372738	−	0.270810i	0.758345	+	0.651853i	$0.226008\pi$
$954$	−4.69278	+	44.6489i	−0.151935	+	1.44556i
$955$	9.55226	+	16.5450i	0.309104	+	0.535384i
$956$	−14.9711	+	25.9307i	−0.484200	+	0.838659i
$957$	23.8398	+	17.3206i	0.770630	+	0.559895i
$958$	−13.0089	+	14.4478i	−0.420298	+	0.466788i
$959$	0.335386	−	1.03221i	0.0108302	−	0.0333319i
$960$	−4.42551			−0.142833
$961$	28.0189	−	13.2642i	0.903837	−	0.427878i
$962$	−13.3350			−0.429939
$963$	6.86966	−	21.1426i	0.221372	−	0.681312i
$964$	10.9746	−	12.1885i	0.353468	−	0.392566i
$965$	28.7642	+	20.8984i	0.925954	+	0.672745i
$966$	2.20531	−	3.81970i	0.0709546	−	0.122897i
$967$	−7.47239	−	12.9426i	−0.240296	−	0.416205i	0.720503	−	0.693452i	$-0.243911\pi$
$967$	−7.47239	−	12.9426i	−0.240296	−	0.416205i	−0.960799	+	0.277248i	$0.910578\pi$
$968$	1.15629	−	11.0013i	0.0371644	−	0.353596i
$969$	−7.10153	+	5.15956i	−0.228134	+	0.165749i
$970$	−2.07062	−	19.7007i	−0.0664837	−	0.632550i
$971$	9.53113	+	10.5854i	0.305869	+	0.339702i	0.876409	−	0.481568i	$-0.159933\pi$
$971$	9.53113	+	10.5854i	0.305869	+	0.339702i	−0.570540	+	0.821270i	$0.693266\pi$
$972$	−18.8101	+	8.37478i	−0.603333	+	0.268621i
$973$	−4.07025	+	0.865158i	−0.130486	+	0.0277357i
$974$	35.4048	+	7.52553i	1.13444	+	0.241134i
$975$	0.676481	+	0.301189i	0.0216647	+	0.00964576i
$976$	−12.6046	−	38.7928i	−0.403462	−	1.24173i
$977$	10.9610	+	33.7344i	0.350673	+	1.07926i	0.958476	+	0.285173i	$0.0920509\pi$
$977$	10.9610	+	33.7344i	0.350673	+	1.07926i	−0.607803	+	0.794088i	$0.707949\pi$
$978$	−7.19511	−	3.20347i	−0.230074	−	0.102436i
$979$	−7.71183	−	1.63920i	−0.246471	−	0.0523891i
$980$	−18.5647	+	3.94606i	−0.593029	+	0.126052i
$981$	−4.45883	+	1.98520i	−0.142359	+	0.0633825i
$982$	−28.5603	−	31.7194i	−0.911394	−	1.01221i
$983$	1.33886	+	12.7384i	0.0427029	+	0.406291i	0.994905	+	0.100821i	$0.0321469\pi$
$983$	1.33886	+	12.7384i	0.0427029	+	0.406291i	−0.952202	+	0.305470i	$0.901186\pi$
$984$	10.0582	−	7.30768i	0.320642	−	0.232960i
$985$	−5.21083	+	49.5777i	−0.166031	+	1.57968i
$986$	12.2926	+	21.2914i	0.391477	+	0.678057i
$987$	−2.10152	+	3.63993i	−0.0668920	+	0.115860i
$988$	−3.97987	−	2.89155i	−0.126617	−	0.0919924i
$989$	1.39790	−	1.55253i	0.0444506	−	0.0493674i
$990$	9.64507	−	29.6845i	0.306540	−	0.943434i
$991$	−21.1870			−0.673027			−0.336514	−	0.941679i	$-0.609248\pi$
$991$	−21.1870			−0.673027			−0.336514	+	0.941679i	$0.609248\pi$
$992$	35.0831	−	7.88475i	1.11389	−	0.250341i
$993$	−33.6001			−1.06627
$994$	0.403026	−	1.24039i	0.0127832	−	0.0393426i
$995$	−7.99409	+	8.87834i	−0.253430	+	0.281462i
$996$	4.41087	+	3.20468i	0.139764	+	0.101544i
$997$	−3.67927	+	6.37269i	−0.116524	+	0.201825i	−0.918388	−	0.395681i	$-0.870508\pi$
$997$	−3.67927	+	6.37269i	−0.116524	+	0.201825i	0.801864	+	0.597506i	$0.203842\pi$
$998$	−15.5466	−	26.9275i	−0.492118	−	0.852374i
$999$	3.98100	−	37.8767i	0.125953	−	1.19837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bi.b.14.14	✓	136
31.20	even	15	inner	403.2.bi.b.144.14	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bi.b.14.14	✓	136	1.1	even	1	trivial
403.2.bi.b.144.14	yes	136	31.20	even	15	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bi (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.563363 - 1.73385i) q^{2} +(-0.719072 + 0.798611i) q^{3} +(-1.07083 - 0.778005i) q^{4} +(1.03814 - 1.79811i) q^{5} +(0.979574 + 1.69667i) q^{6} +(0.0320232 - 0.304681i) q^{7} +(0.997593 - 0.724794i) q^{8} +(0.192871 + 1.83505i) q^{9} +O(q^{10})\)	\(q+(0.563363 - 1.73385i) q^{2} +(-0.719072 + 0.798611i) q^{3} +(-1.07083 - 0.778005i) q^{4} +(1.03814 - 1.79811i) q^{5} +(0.979574 + 1.69667i) q^{6} +(0.0320232 - 0.304681i) q^{7} +(0.997593 - 0.724794i) q^{8} +(0.192871 + 1.83505i) q^{9} +(-2.53281 - 2.81297i) q^{10} +(4.08252 - 1.81766i) q^{11} +(1.39133 - 0.295736i) q^{12} +(-0.978148 - 0.207912i) q^{13} +(-0.510231 - 0.227169i) q^{14} +(0.689492 + 2.12204i) q^{15} +(-1.51272 - 4.65568i) q^{16} +(-2.00777 - 0.893918i) q^{17} +(3.29036 + 0.699387i) q^{18} +(-3.63540 + 0.772729i) q^{19} +(-2.51061 + 1.11780i) q^{20} +(0.220294 + 0.244662i) q^{21} +(-0.851606 - 8.10249i) q^{22} +(5.94509 - 4.31936i) q^{23} +(-0.138513 + 1.31787i) q^{24} +(0.344535 + 0.596753i) q^{25} +(-0.911540 + 1.57883i) q^{26} +(-4.21238 - 3.06047i) q^{27} +(-0.271335 + 0.301348i) q^{28} +(1.89612 - 5.83567i) q^{29} +4.06774 q^{30} +(-5.43226 + 1.22087i) q^{31} -6.45828 q^{32} +(-1.48403 + 4.56737i) q^{33} +(-2.68103 + 2.97758i) q^{34} +(-0.514605 - 0.373882i) q^{35} +(1.22114 - 2.11508i) q^{36} +(3.65728 + 6.33460i) q^{37} +(-0.708253 + 6.73858i) q^{38} +(0.869399 - 0.631656i) q^{39} +(-0.267618 - 2.54622i) q^{40} +(-6.27790 - 6.97231i) q^{41} +(0.548313 - 0.244124i) q^{42} +(0.278079 - 0.0591076i) q^{43} +(-5.78584 - 1.22982i) q^{44} +(3.49984 + 1.55823i) q^{45} +(-4.13989 - 12.7413i) q^{46} +(3.94505 + 12.1416i) q^{47} +(4.80583 + 2.13969i) q^{48} +(6.75523 + 1.43587i) q^{49} +(1.22878 - 0.261185i) q^{50} +(2.15763 - 0.960637i) q^{51} +(0.885675 + 0.983642i) q^{52} +(1.39506 + 13.2731i) q^{53} +(-7.67950 + 5.57948i) q^{54} +(0.969881 - 9.22780i) q^{55} +(-0.188885 - 0.327158i) q^{56} +(1.99701 - 3.45892i) q^{57} +(-9.04998 - 6.57519i) q^{58} +(-6.62093 + 7.35329i) q^{59} +(0.912626 - 2.80878i) q^{60} +8.33237 q^{61} +(-0.943518 + 10.1065i) q^{62} +0.565280 q^{63} +(-0.612912 + 1.88635i) q^{64} +(-1.38930 + 1.54298i) q^{65} +(7.08310 + 5.14617i) q^{66} +(-7.28351 + 12.6154i) q^{67} +(1.45451 + 2.51929i) q^{68} +(-0.825462 + 7.85375i) q^{69} +(-0.938166 + 0.681617i) q^{70} +(0.244089 + 2.32235i) q^{71} +(1.52244 + 1.69084i) q^{72} +(8.59934 - 3.82867i) q^{73} +(13.0436 - 2.77251i) q^{74} +(-0.724319 - 0.153959i) q^{75} +(4.49409 + 2.00090i) q^{76} +(-0.423069 - 1.30207i) q^{77} +(-0.605410 - 1.86326i) q^{78} +(-13.1867 - 5.87111i) q^{79} +(-9.94183 - 2.11320i) q^{80} +(0.0586196 - 0.0124600i) q^{81} +(-15.6257 + 6.95701i) q^{82} +(2.56479 + 2.84849i) q^{83} +(-0.0455502 - 0.433381i) q^{84} +(-3.69171 + 2.68218i) q^{85} +(0.0541757 - 0.515447i) q^{86} +(3.29698 + 5.71053i) q^{87} +(2.75527 - 4.77227i) q^{88} +(-1.42729 - 1.03699i) q^{89} +(4.67342 - 5.19036i) q^{90} +(-0.0946702 + 0.291365i) q^{91} -9.72668 q^{92} +(2.93119 - 5.21616i) q^{93} +23.2743 q^{94} +(-2.38460 + 7.33905i) q^{95} +(4.64397 - 5.15765i) q^{96} +(4.23382 + 3.07605i) q^{97} +(6.29523 - 10.9037i) q^{98} +(4.12289 + 7.14105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9	\( 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9} + 7 q^{10} + 5 q^{11} + 28 q^{12} + 17 q^{13} - 3 q^{14} + 17 q^{15} - 78 q^{16} - 12 q^{17} + 34 q^{18} - 23 q^{19} + 8 q^{20} - 38 q^{21} + 8 q^{22} + 9 q^{23} + 46 q^{24} - 69 q^{25} - 12 q^{26} - 58 q^{27} + 7 q^{28} + 18 q^{29} + 60 q^{30} + 14 q^{31} + 212 q^{32} - 41 q^{33} - 30 q^{35} - 106 q^{36} + 6 q^{37} - 62 q^{38} + 6 q^{39} + 39 q^{40} - 5 q^{41} + 37 q^{42} + q^{43} - 88 q^{44} - 168 q^{45} + 6 q^{46} - 81 q^{47} - 101 q^{48} + 117 q^{49} - 20 q^{50} + 35 q^{51} + 7 q^{52} + 25 q^{53} + 57 q^{54} + 19 q^{55} - 63 q^{56} - 20 q^{57} - 44 q^{58} + 9 q^{59} + 113 q^{60} + 8 q^{61} + 57 q^{62} + 112 q^{63} - 146 q^{64} - 5 q^{65} + 70 q^{66} - 99 q^{67} - 56 q^{68} - 65 q^{69} + 169 q^{70} - q^{71} - 43 q^{72} + 50 q^{73} - 26 q^{74} - 18 q^{75} - 94 q^{76} + 114 q^{77} - 17 q^{79} + 217 q^{80} + 54 q^{81} - 25 q^{82} - 53 q^{83} - 22 q^{84} + 2 q^{85} - 54 q^{86} - 28 q^{87} + 70 q^{88} - 101 q^{89} + 165 q^{90} - 4 q^{91} + 64 q^{92} + 61 q^{93} - 90 q^{94} - 33 q^{95} - 217 q^{96} + 73 q^{97} + 33 q^{98} - 15 q^{99}+O(q^{100}) \) 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9 + 7 * q^10 + 5 * q^11 + 28 * q^12 + 17 * q^13 - 3 * q^14 + 17 * q^15 - 78 * q^16 - 12 * q^17 + 34 * q^18 - 23 * q^19 + 8 * q^20 - 38 * q^21 + 8 * q^22 + 9 * q^23 + 46 * q^24 - 69 * q^25 - 12 * q^26 - 58 * q^27 + 7 * q^28 + 18 * q^29 + 60 * q^30 + 14 * q^31 + 212 * q^32 - 41 * q^33 - 30 * q^35 - 106 * q^36 + 6 * q^37 - 62 * q^38 + 6 * q^39 + 39 * q^40 - 5 * q^41 + 37 * q^42 + q^43 - 88 * q^44 - 168 * q^45 + 6 * q^46 - 81 * q^47 - 101 * q^48 + 117 * q^49 - 20 * q^50 + 35 * q^51 + 7 * q^52 + 25 * q^53 + 57 * q^54 + 19 * q^55 - 63 * q^56 - 20 * q^57 - 44 * q^58 + 9 * q^59 + 113 * q^60 + 8 * q^61 + 57 * q^62 + 112 * q^63 - 146 * q^64 - 5 * q^65 + 70 * q^66 - 99 * q^67 - 56 * q^68 - 65 * q^69 + 169 * q^70 - q^71 - 43 * q^72 + 50 * q^73 - 26 * q^74 - 18 * q^75 - 94 * q^76 + 114 * q^77 - 17 * q^79 + 217 * q^80 + 54 * q^81 - 25 * q^82 - 53 * q^83 - 22 * q^84 + 2 * q^85 - 54 * q^86 - 28 * q^87 + 70 * q^88 - 101 * q^89 + 165 * q^90 - 4 * q^91 + 64 * q^92 + 61 * q^93 - 90 * q^94 - 33 * q^95 - 217 * q^96 + 73 * q^97 + 33 * q^98 - 15 * q^99

Introduction

L-functions

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