LMFDB - Embedded newform 115.2.g.b.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 12 x^{18} - 12 x^{17} + 56 x^{16} - 155 x^{15} + 551 x^{14} - 1189 x^{13} + \cdots + 1437601 $ x^20 - x^19 + 12x^18 - 12x^17 + 56x^16 - 155x^15 + 551x^14 - 1189x^13 + 3851x^12 - 10594x^11 + 18470x^10 - 22715x^9 + 56089x^8 + 1474x^7 - 31240x^6 + 12001x^5 + 243089x^4 + 225907x^3 + 23958x^2 + 857285x + 1437601
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			26.1
Root			$0.460349 + 3.20180i$ of defining polynomial
Character	$\chi$	$=$	115.26
Dual form			115.2.g.b.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.273100 + 1.89945i) q^{2} +(-1.34375 + 2.94241i) q^{3} +(-1.61435 + 0.474017i) q^{4} +(0.654861 - 0.755750i) q^{5} +(-5.95594 - 1.74882i) q^{6} +(3.10213 - 1.99362i) q^{7} +(0.253098 + 0.554206i) q^{8} +(-4.88751 - 5.64048i) q^{9} +O(q^{10})$	\(q+(0.273100 + 1.89945i) q^{2} +(-1.34375 + 2.94241i) q^{3} +(-1.61435 + 0.474017i) q^{4} +(0.654861 - 0.755750i) q^{5} +(-5.95594 - 1.74882i) q^{6} +(3.10213 - 1.99362i) q^{7} +(0.253098 + 0.554206i) q^{8} +(-4.88751 - 5.64048i) q^{9} +(1.61435 + 1.03748i) q^{10} +(-0.00937662 + 0.0652158i) q^{11} +(0.774540 - 5.38705i) q^{12} +(0.395203 + 0.253982i) q^{13} +(4.63397 + 5.34789i) q^{14} +(1.34375 + 2.94241i) q^{15} +(-3.81440 + 2.45137i) q^{16} +(-4.79414 - 1.40769i) q^{17} +(9.37906 - 10.8240i) q^{18} +(4.37646 - 1.28504i) q^{19} +(-0.698939 + 1.53046i) q^{20} +(1.69754 + 11.8066i) q^{21} -0.126435 q^{22} +(0.809276 + 4.72706i) q^{23} -1.97080 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-0.374496 + 0.820033i) q^{26} +(13.8531 - 4.06764i) q^{27} +(-4.06292 + 4.68886i) q^{28} +(0.472416 + 0.138714i) q^{29} +(-5.22199 + 3.35597i) q^{30} +(-3.09241 - 6.77144i) q^{31} +(-4.90000 - 5.65490i) q^{32} +(-0.179292 - 0.115224i) q^{33} +(1.36455 - 9.49068i) q^{34} +(0.524787 - 3.64997i) q^{35} +(10.5639 + 6.78897i) q^{36} +(2.29422 + 2.64767i) q^{37} +(3.63609 + 7.96193i) q^{38} +(-1.27837 + 0.821560i) q^{39} +(0.584585 + 0.171650i) q^{40} +(1.51293 - 1.74601i) q^{41} +(-21.9626 + 6.44879i) q^{42} +(1.64058 - 3.59236i) q^{43} +(-0.0157762 - 0.109726i) q^{44} -7.46343 q^{45} +(-8.75781 + 2.82814i) q^{46} +0.621575 q^{47} +(-2.08731 - 14.5175i) q^{48} +(2.74078 - 6.00147i) q^{49} +(1.84125 - 0.540641i) q^{50} +(10.5841 - 12.2147i) q^{51} +(-0.758389 - 0.222683i) q^{52} +(-3.03196 + 1.94852i) q^{53} +(11.5096 + 25.2025i) q^{54} +(0.0431465 + 0.0497937i) q^{55} +(1.89002 + 1.21464i) q^{56} +(-2.09975 + 14.6041i) q^{57} +(-0.134464 + 0.935215i) q^{58} +(4.46281 + 2.86808i) q^{59} +(-3.56404 - 4.11312i) q^{60} +(-4.24510 - 9.29548i) q^{61} +(12.0175 - 7.72318i) q^{62} +(-26.4066 - 7.75368i) q^{63} +(3.46451 - 3.99826i) q^{64} +(0.450750 - 0.132352i) q^{65} +(0.169898 - 0.372024i) q^{66} +(0.198409 + 1.37996i) q^{67} +8.40670 q^{68} +(-14.9964 - 3.97077i) q^{69} +7.07627 q^{70} +(1.52723 + 10.6221i) q^{71} +(1.88898 - 4.13628i) q^{72} +(-14.2562 + 4.18599i) q^{73} +(-4.40257 + 5.08083i) q^{74} +(3.10369 + 0.911327i) q^{75} +(-6.45602 + 4.14903i) q^{76} +(0.100928 + 0.221001i) q^{77} +(-1.90964 - 2.20384i) q^{78} +(-2.48575 - 1.59749i) q^{79} +(-0.645282 + 4.48803i) q^{80} +(-3.46003 + 24.0650i) q^{81} +(3.72965 + 2.39690i) q^{82} +(3.52485 + 4.06790i) q^{83} +(-8.33698 - 18.2554i) q^{84} +(-4.20335 + 2.70133i) q^{85} +(7.27157 + 2.13513i) q^{86} +(-1.04296 + 1.20364i) q^{87} +(-0.0385162 + 0.0113094i) q^{88} +(2.97699 - 6.51870i) q^{89} +(-2.03826 - 14.1764i) q^{90} +1.73231 q^{91} +(-3.54716 - 7.24753i) q^{92} +24.0798 q^{93} +(0.169752 + 1.18065i) q^{94} +(1.89480 - 4.14903i) q^{95} +(23.2234 - 6.81901i) q^{96} +(2.09845 - 2.42174i) q^{97} +(12.1480 + 3.56698i) q^{98} +(0.413677 - 0.265854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	0.273100	+	1.89945i	0.193111	+	1.34312i	0.823712	+	0.567009i	$0.191900\pi$
$2$	0.273100	+	1.89945i	0.193111	+	1.34312i	−0.630601	+	0.776107i	$0.717191\pi$
$3$	−1.34375	+	2.94241i	−0.775816	+	1.69880i	−0.0624077	+	0.998051i	$0.519878\pi$
$3$	−1.34375	+	2.94241i	−0.775816	+	1.69880i	−0.713408	+	0.700749i	$0.752849\pi$
$4$	−1.61435	+	0.474017i	−0.807177	+	0.237009i
$5$	0.654861	−	0.755750i	0.292863	−	0.337981i
$5$	0.654861	−	0.755750i	0.292863	−	0.337981i
$6$	−5.95594	−	1.74882i	−2.43150	−	0.713954i
$7$	3.10213	−	1.99362i	1.17249	−	0.753516i	0.198502	−	0.980100i	$-0.436392\pi$
$7$	3.10213	−	1.99362i	1.17249	−	0.753516i	0.973991	+	0.226585i	$0.0727560\pi$
$8$	0.253098	+	0.554206i	0.0894835	+	0.195942i
$9$	−4.88751	−	5.64048i	−1.62917	−	1.88016i
$10$	1.61435	+	1.03748i	0.510503	+	0.328081i
$11$	−0.00937662	+	0.0652158i	−0.00282716	+	0.0196633i	−0.991186	−	0.132476i	$-0.957707\pi$
$11$	−0.00937662	+	0.0652158i	−0.00282716	+	0.0196633i	0.988359	+	0.152139i	$0.0486163\pi$
$12$	0.774540	−	5.38705i	0.223591	−	1.55511i
$13$	0.395203	+	0.253982i	0.109610	+	0.0704418i	0.594297	−	0.804246i	$-0.297430\pi$
$13$	0.395203	+	0.253982i	0.109610	+	0.0704418i	−0.484688	+	0.874687i	$0.661067\pi$
$14$	4.63397	+	5.34789i	1.23848	+	1.42928i
$15$	1.34375	+	2.94241i	0.346955	+	0.759726i
$16$	−3.81440	+	2.45137i	−0.953600	+	0.612841i
$17$	−4.79414	−	1.40769i	−1.16275	−	0.341414i	−0.357249	−	0.934009i	$-0.616285\pi$
$17$	−4.79414	−	1.40769i	−1.16275	−	0.341414i	−0.805500	+	0.592595i	$0.798103\pi$
$18$	9.37906	−	10.8240i	2.21067	−	2.55124i
$19$	4.37646	−	1.28504i	1.00403	−	0.294809i	0.261920	−	0.965089i	$-0.415644\pi$
$19$	4.37646	−	1.28504i	1.00403	−	0.294809i	0.742108	+	0.670280i	$0.233826\pi$
$20$	−0.698939	+	1.53046i	−0.156287	+	0.342222i
$21$	1.69754	+	11.8066i	0.370433	+	2.57642i
$22$	−0.126435			−0.0269561
$23$	0.809276	+	4.72706i	0.168746	+	0.985660i
$23$	0.809276	+	4.72706i	0.168746	+	0.985660i
$24$	−1.97080			−0.402288
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	−0.374496	+	0.820033i	−0.0734448	+	0.160822i
$27$	13.8531	−	4.06764i	2.66603	−	0.782818i
$28$	−4.06292	+	4.68886i	−0.767820	+	0.886111i
$29$	0.472416	+	0.138714i	0.0877255	+	0.0257585i	0.325301	−	0.945611i	$-0.394534\pi$
$29$	0.472416	+	0.138714i	0.0877255	+	0.0257585i	−0.237575	+	0.971369i	$0.576353\pi$
$30$	−5.22199	+	3.35597i	−0.953400	+	0.612713i
$31$	−3.09241	−	6.77144i	−0.555414	−	1.21619i	−0.954207	−	0.299146i	$-0.903298\pi$
$31$	−3.09241	−	6.77144i	−0.555414	−	1.21619i	0.398793	−	0.917041i	$-0.369429\pi$
$32$	−4.90000	−	5.65490i	−0.866206	−	0.999655i
$33$	−0.179292	−	0.115224i	−0.0312107	−	0.0200579i
$34$	1.36455	−	9.49068i	0.234019	−	1.62764i
$35$	0.524787	−	3.64997i	0.0887051	−	0.616958i
$36$	10.5639	+	6.78897i	1.76064	+	1.13150i
$37$	2.29422	+	2.64767i	0.377167	+	0.435274i	0.912318	−	0.409483i	$-0.134291\pi$
$37$	2.29422	+	2.64767i	0.377167	+	0.435274i	−0.535151	+	0.844756i	$0.679745\pi$
$38$	3.63609	+	7.96193i	0.589852	+	1.29160i
$39$	−1.27837	+	0.821560i	−0.204703	+	0.131555i
$40$	0.584585	+	0.171650i	0.0924310	+	0.0271402i
$41$	1.51293	−	1.74601i	0.236280	−	0.272681i	−0.625210	−	0.780457i	$-0.714987\pi$
$41$	1.51293	−	1.74601i	0.236280	−	0.272681i	0.861489	+	0.507775i	$0.169532\pi$
$42$	−21.9626	+	6.44879i	−3.38890	+	0.995070i
$43$	1.64058	−	3.59236i	0.250186	−	0.547830i	−0.742318	−	0.670048i	$-0.766273\pi$
$43$	1.64058	−	3.59236i	0.250186	−	0.547830i	0.992503	+	0.122218i	$0.0390006\pi$
$44$	−0.0157762	−	0.109726i	−0.00237836	−	0.0165418i
$45$	−7.46343			−1.11258
$46$	−8.75781	+	2.82814i	−1.29127	+	0.416987i
$47$	0.621575			0.0906660			0.0453330	−	0.998972i	$-0.485565\pi$
$47$	0.621575			0.0906660			0.0453330	+	0.998972i	$0.485565\pi$
$48$	−2.08731	−	14.5175i	−0.301277	−	2.09543i
$49$	2.74078	−	6.00147i	0.391540	−	0.857353i
$50$	1.84125	−	0.540641i	0.260393	−	0.0764582i
$51$	10.5841	−	12.2147i	1.48207	−	1.71040i
$52$	−0.758389	−	0.222683i	−0.105170	−	0.0308806i
$53$	−3.03196	+	1.94852i	−0.416471	+	0.267650i	−0.732052	−	0.681249i	$-0.761437\pi$
$53$	−3.03196	+	1.94852i	−0.416471	+	0.267650i	0.315581	+	0.948899i	$0.397801\pi$
$54$	11.5096	+	25.2025i	1.56626	+	3.42962i
$55$	0.0431465	+	0.0497937i	0.00581787	+	0.00671418i
$56$	1.89002	+	1.21464i	0.252564	+	0.162313i
$57$	−2.09975	+	14.6041i	−0.278119	+	1.93436i
$58$	−0.134464	+	0.935215i	−0.0176559	+	0.122800i
$59$	4.46281	+	2.86808i	0.581009	+	0.373392i	0.797887	−	0.602807i	$-0.205951\pi$
$59$	4.46281	+	2.86808i	0.581009	+	0.373392i	−0.216878	+	0.976199i	$0.569587\pi$
$60$	−3.56404	−	4.11312i	−0.460116	−	0.531002i
$61$	−4.24510	−	9.29548i	−0.543530	−	1.19016i	−0.959739	−	0.280895i	$-0.909369\pi$
$61$	−4.24510	−	9.29548i	−0.543530	−	1.19016i	0.416209	−	0.909269i	$-0.363359\pi$
$62$	12.0175	−	7.72318i	1.52622	−	0.980845i
$63$	−26.4066	−	7.75368i	−3.32692	−	0.976872i
$64$	3.46451	−	3.99826i	0.433064	−	0.499783i
$65$	0.450750	−	0.132352i	0.0559086	−	0.0164162i
$66$	0.169898	−	0.372024i	0.0209129	−	0.0457930i
$67$	0.198409	+	1.37996i	0.0242395	+	0.168589i	0.998345	−	0.0575031i	$-0.0183139\pi$
$67$	0.198409	+	1.37996i	0.0242395	+	0.168589i	−0.974106	+	0.226093i	$0.927405\pi$
$68$	8.40670			1.01946
$69$	−14.9964	−	3.97077i	−1.80535	−	0.478025i
$70$	7.07627			0.845776
$71$	1.52723	+	10.6221i	0.181249	+	1.26061i	0.853815	+	0.520576i	$0.174283\pi$
$71$	1.52723	+	10.6221i	0.181249	+	1.26061i	−0.672567	+	0.740037i	$0.734808\pi$
$72$	1.88898	−	4.13628i	0.222618	−	0.487465i
$73$	−14.2562	+	4.18599i	−1.66856	+	0.489933i	−0.973436	−	0.228958i	$-0.926468\pi$
$73$	−14.2562	+	4.18599i	−1.66856	+	0.489933i	−0.695122	+	0.718891i	$0.744650\pi$
$74$	−4.40257	+	5.08083i	−0.511788	+	0.590635i
$75$	3.10369	+	0.911327i	0.358384	+	0.105231i
$76$	−6.45602	+	4.14903i	−0.740556	+	0.475927i
$77$	0.100928	+	0.221001i	0.0115018	+	0.0251854i
$78$	−1.90964	−	2.20384i	−0.216224	−	0.249536i
$79$	−2.48575	−	1.59749i	−0.279668	−	0.179732i	0.393285	−	0.919416i	$-0.371338\pi$
$79$	−2.48575	−	1.59749i	−0.279668	−	0.179732i	−0.672954	+	0.739684i	$0.734975\pi$
$80$	−0.645282	+	4.48803i	−0.0721447	+	0.501777i
$81$	−3.46003	+	24.0650i	−0.384448	+	2.67389i
$82$	3.72965	+	2.39690i	0.411871	+	0.264693i
$83$	3.52485	+	4.06790i	0.386903	+	0.446510i	0.915473	−	0.402380i	$-0.131817\pi$
$83$	3.52485	+	4.06790i	0.386903	+	0.446510i	−0.528570	+	0.848890i	$0.677272\pi$
$84$	−8.33698	−	18.2554i	−0.909639	−	1.99183i
$85$	−4.20335	+	2.70133i	−0.455917	+	0.293000i
$86$	7.27157	+	2.13513i	0.784114	+	0.230237i
$87$	−1.04296	+	1.20364i	−0.111817	+	0.129044i
$88$	−0.0385162	+	0.0113094i	−0.00410584	+	0.00120558i
$89$	2.97699	−	6.51870i	0.315560	−	0.690981i	−0.683687	−	0.729776i	$-0.739625\pi$
$89$	2.97699	−	6.51870i	0.315560	−	0.690981i	0.999247	+	0.0387945i	$0.0123518\pi$
$90$	−2.03826	−	14.1764i	−0.214852	−	1.49433i
$91$	1.73231			0.181596
$92$	−3.54716	−	7.24753i	−0.369817	−	0.755607i
$93$	24.0798			2.49696
$94$	0.169752	+	1.18065i	0.0175086	+	0.121775i
$95$	1.89480	−	4.14903i	0.194402	−	0.425682i
$96$	23.2234	−	6.81901i	2.37023	−	0.695962i
$97$	2.09845	−	2.42174i	0.213066	−	0.245891i	−0.639149	−	0.769083i	$-0.720713\pi$
$97$	2.09845	−	2.42174i	0.213066	−	0.245891i	0.852215	+	0.523192i	$0.175259\pi$
$98$	12.1480	+	3.56698i	1.22714	+	0.360319i
$99$	0.413677	−	0.265854i	0.0415761	−	0.0267193i
$100$	0.698939	+	1.53046i	0.0698939	+	0.153046i
$101$	−11.7860	−	13.6018i	−1.17275	−	1.35343i	−0.922851	−	0.385157i	$-0.874147\pi$
$101$	−11.7860	−	13.6018i	−1.17275	−	1.35343i	−0.249902	−	0.968271i	$-0.580398\pi$
$102$	26.0918	+	16.7682i	2.58348	+	1.66030i
$103$	−0.0275793	+	0.191818i	−0.00271747	+	0.0189004i	−0.991135	−	0.132858i	$-0.957585\pi$
$103$	−0.0275793	+	0.191818i	−0.00271747	+	0.0189004i	0.988418	+	0.151759i	$0.0484936\pi$
$104$	−0.0407333	+	0.283306i	−0.00399423	+	0.0277805i
$105$	10.0345	+	6.44879i	0.979269	+	0.629338i
$106$	−4.52915	−	5.22692i	−0.439910	−	0.507683i
$107$	−3.31160	−	7.25138i	−0.320144	−	0.701018i	0.679317	−	0.733845i	$-0.262276\pi$
$107$	−3.31160	−	7.25138i	−0.320144	−	0.701018i	−0.999461	+	0.0328272i	$0.989549\pi$
$108$	−20.4357	+	13.1332i	−1.96643	+	1.26375i
$109$	16.3146	+	4.79040i	1.56266	+	0.458837i	0.944853	−	0.327495i	$-0.106204\pi$
$109$	16.3146	+	4.79040i	1.56266	+	0.458837i	0.617804	+	0.786332i	$0.288023\pi$
$110$	−0.0827974	+	0.0955533i	−0.00789443	+	0.00911065i
$111$	−10.8734	+	3.19271i	−1.03205	+	0.303038i
$112$	−6.94567	+	15.2089i	−0.656304	+	1.43710i
$113$	−1.16375	−	8.09404i	−0.109476	−	0.761423i	−0.968415	−	0.249345i	$-0.919785\pi$
$113$	−1.16375	−	8.09404i	−0.109476	−	0.761423i	0.858939	−	0.512078i	$-0.171124\pi$
$114$	−28.3133			−2.65178
$115$	4.10243	+	2.48395i	0.382554	+	0.231630i
$116$	−0.828400			−0.0769150
$117$	−0.498979	−	3.47047i	−0.0461306	−	0.320846i
$118$	−4.22898	+	9.26018i	−0.389309	+	0.852468i
$119$	−17.6784	+	5.19085i	−1.62058	+	0.475844i
$120$	−1.29060	+	1.48943i	−0.117815	+	0.135966i
$121$	10.5503	+	3.09784i	0.959114	+	0.281621i
$122$	16.4970	−	10.6020i	1.49357	−	0.959857i
$123$	3.10448	+	6.79786i	0.279921	+	0.612942i
$124$	8.20203	+	9.46565i	0.736564	+	0.850040i
$125$	−0.841254	−	0.540641i	−0.0752440	−	0.0483564i
$126$	7.51611	−	52.2757i	0.669588	−	4.65709i
$127$	−0.339556	+	2.36166i	−0.0301307	+	0.209564i	−0.999325	−	0.0367333i	$-0.988305\pi$
$127$	−0.339556	+	2.36166i	−0.0301307	+	0.209564i	0.969194	+	0.246297i	$0.0792139\pi$
$128$	−4.04870	−	2.60194i	−0.357858	−	0.229981i
$129$	8.36567	+	9.65450i	0.736556	+	0.850031i
$130$	0.374496	+	0.820033i	0.0328455	+	0.0719216i
$131$	8.43203	−	5.41894i	0.736710	−	0.473455i	−0.117703	−	0.993049i	$-0.537553\pi$
$131$	8.43203	−	5.41894i	0.736710	−	0.473455i	0.854413	+	0.519594i	$0.173917\pi$
$132$	0.344058	+	0.101025i	0.0299464	+	0.00879306i
$133$	11.0144	−	12.7113i	0.955073	−	1.10221i
$134$	−2.56699	+	0.753737i	−0.221754	+	0.0651129i
$135$	5.99774	−	13.1332i	0.516204	−	1.13033i
$136$	−0.433236	−	3.01322i	−0.0371497	−	0.258382i
$137$	−16.2556			−1.38881			−0.694403	−	0.719587i	$-0.744331\pi$
$137$	−16.2556			−1.38881			−0.694403	+	0.719587i	$0.744331\pi$
$138$	3.44678	−	29.5694i	0.293410	−	2.51711i
$139$	−13.0492			−1.10682			−0.553410	−	0.832909i	$-0.686674\pi$
$139$	−13.0492			−1.10682			−0.553410	+	0.832909i	$0.686674\pi$
$140$	0.882957	+	6.14110i	0.0746235	+	0.519018i
$141$	−0.835243	+	1.82893i	−0.0703401	+	0.154023i
$142$	−19.7591	+	5.80180i	−1.65815	+	0.486876i
$143$	−0.0202693	+	0.0233920i	−0.00169500	+	0.00195614i
$144$	32.4698	+	9.53399i	2.70582	+	0.794499i
$145$	0.414200	−	0.266190i	0.0343974	−	0.0221059i
$146$	−11.8445	−	25.9357i	−0.980254	−	2.14646i
$147$	13.9758	+	16.1290i	1.15271	+	1.33030i
$148$	−4.95871	−	3.18677i	−0.407604	−	0.261951i
$149$	−2.22207	+	15.4548i	−0.182039	+	1.26611i	0.669894	+	0.742457i	$0.266339\pi$
$149$	−2.22207	+	15.4548i	−0.182039	+	1.26611i	−0.851933	+	0.523651i	$0.824570\pi$
$150$	−0.883403	+	6.14420i	−0.0721296	+	0.501672i
$151$	−5.37481	−	3.45418i	−0.437396	−	0.281097i	0.303354	−	0.952878i	$-0.401893\pi$
$151$	−5.37481	−	3.45418i	−0.437396	−	0.281097i	−0.740750	+	0.671780i	$0.765530\pi$
$152$	1.81985	+	2.10022i	0.147609	+	0.170350i
$153$	15.4914	+	33.9213i	1.25240	+	2.74238i
$154$	−0.392218	+	0.252063i	−0.0316058	+	0.0203118i
$155$	−7.14262	−	2.09726i	−0.573709	−	0.168456i
$156$	1.67431	−	1.93226i	0.134052	−	0.154705i
$157$	−5.97486	+	1.75438i	−0.476845	+	0.140014i	−0.511319	−	0.859391i	$-0.670843\pi$
$157$	−5.97486	+	1.75438i	−0.476845	+	0.140014i	0.0344733	+	0.999406i	$0.489025\pi$
$158$	2.35550	−	5.15784i	0.187394	−	0.410335i
$159$	−1.65914	−	11.5396i	−0.131578	−	0.915148i
$160$	−7.48251			−0.591544
$161$	11.9344	+	13.0505i	0.940563	+	1.02853i
$162$	−46.6553			−3.66559
$163$	3.41468	+	23.7496i	0.267458	+	1.86021i	0.472326	+	0.881424i	$0.343415\pi$
$163$	3.41468	+	23.7496i	0.267458	+	1.86021i	−0.204867	+	0.978790i	$0.565676\pi$
$164$	−1.61476	+	3.53583i	−0.126092	+	0.276102i
$165$	−0.204491	+	0.0600441i	−0.0159196	+	0.00467443i
$166$	−6.76414	+	7.80624i	−0.524999	+	0.605882i
$167$	−11.7251	−	3.44279i	−0.907313	−	0.266411i	−0.205403	−	0.978677i	$-0.565851\pi$
$167$	−11.7251	−	3.44279i	−0.907313	−	0.266411i	−0.701909	+	0.712266i	$0.747669\pi$
$168$	−6.11368	+	3.92902i	−0.471680	+	0.303131i
$169$	−5.30872	−	11.6245i	−0.408363	−	0.894190i
$170$	−6.27898	−	7.24633i	−0.481576	−	0.555768i
$171$	−28.6382	−	18.4047i	−2.19002	−	1.40744i
$172$	−0.945631	+	6.57701i	−0.0721037	+	0.501492i
$173$	0.631221	−	4.39024i	0.0479909	−	0.333784i	−0.951655	−	0.307169i	$-0.900618\pi$
$173$	0.631221	−	4.39024i	0.0479909	−	0.333784i	0.999646	−	0.0266146i	$-0.00847268\pi$
$174$	−2.57110	−	1.65234i	−0.194914	−	0.125264i
$175$	−2.41480	−	2.78683i	−0.182542	−	0.210665i
$176$	−0.124102	−	0.271745i	−0.00935451	−	0.0204835i
$177$	−14.4360	+	9.27743i	−1.08507	+	0.697334i
$178$	13.1950	+	3.87440i	0.989006	+	0.290398i
$179$	−11.8183	+	13.6391i	−0.883344	+	1.01943i	0.116312	+	0.993213i	$0.462893\pi$
$179$	−11.8183	+	13.6391i	−0.883344	+	1.01943i	−0.999656	+	0.0262203i	$0.991653\pi$
$180$	12.0486	−	3.53779i	0.898051	−	0.263692i
$181$	−4.56372	+	9.99315i	−0.339219	+	0.742785i	−0.999969	−	0.00782009i	$-0.997511\pi$
$181$	−4.56372	+	9.99315i	−0.339219	+	0.742785i	0.660751	+	0.750605i	$0.270238\pi$
$182$	0.473095	+	3.29045i	0.0350681	+	0.243904i
$183$	33.0554			2.44353
$184$	−2.41494	+	1.64491i	−0.178032	+	0.121265i
$185$	3.50336			0.257572
$186$	6.57619	+	45.7384i	0.482190	+	3.35370i
$187$	0.136756	−	0.299454i	0.0100006	−	0.0218983i
$188$	−1.00344	+	0.294637i	−0.0731835	+	0.0214886i
$189$	34.8648	−	40.2361i	2.53604	−	2.92675i
$190$	8.39836	+	2.46598i	0.609281	+	0.178901i
$191$	−8.03294	+	5.16246i	−0.581243	+	0.373542i	−0.797977	−	0.602688i	$-0.794096\pi$
$191$	−8.03294	+	5.16246i	−0.581243	+	0.373542i	0.216733	+	0.976231i	$0.430460\pi$
$192$	7.10906	+	15.5667i	0.513052	+	1.12343i
$193$	−0.798917	−	0.922000i	−0.0575073	−	0.0663670i	0.726267	−	0.687413i	$-0.241254\pi$
$193$	−0.798917	−	0.922000i	−0.0575073	−	0.0663670i	−0.783774	+	0.621046i	$0.786708\pi$
$194$	5.17308	+	3.32454i	0.371405	+	0.238688i
$195$	−0.216262	+	1.50414i	−0.0154869	+	0.107714i
$196$	−1.57979	+	10.9877i	−0.112842	+	0.784834i
$197$	−4.82641	−	3.10174i	−0.343867	−	0.220990i	0.357295	−	0.933991i	$-0.383699\pi$
$197$	−4.82641	−	3.10174i	−0.343867	−	0.220990i	−0.701163	+	0.713001i	$0.747335\pi$
$198$	0.617953	+	0.713156i	0.0439160	+	0.0506818i
$199$	1.44748	+	3.16954i	0.102609	+	0.224683i	0.953973	−	0.299893i	$-0.0969510\pi$
$199$	1.44748	+	3.16954i	0.102609	+	0.224683i	−0.851363	+	0.524576i	$0.824224\pi$
$200$	0.512546	−	0.329393i	0.0362425	−	0.0232916i
$201$	−4.32703	−	1.27053i	−0.305205	−	0.0896163i
$202$	22.6172	−	26.1016i	1.59134	−	1.83651i
$203$	1.74204	−	0.511508i	0.122267	−	0.0359008i
$204$	−11.2965	+	24.7359i	−0.790915	+	1.73186i
$205$	−0.328791	−	2.28679i	−0.0229637	−	0.159716i
$206$	−0.371882			−0.0259102
$207$	22.7075	−	27.6682i	1.57828	−	1.92308i
$208$	−2.13006			−0.147693
$209$	0.0427688	+	0.297464i	0.00295838	+	0.0205760i
$210$	−9.50875	+	20.8213i	−0.656166	+	1.43680i
$211$	23.6243	−	6.93671i	1.62636	−	0.477543i	0.663643	−	0.748049i	$-0.269009\pi$
$211$	23.6243	−	6.93671i	1.62636	−	0.477543i	0.962718	+	0.270507i	$0.0871912\pi$
$212$	3.97102	−	4.58280i	0.272731	−	0.314748i
$213$	−33.3068	−	9.77976i	−2.28214	−	0.670098i
$214$	12.8693	−	8.27058i	0.879725	−	0.565365i
$215$	−1.64058	−	3.59236i	−0.111886	−	0.244997i
$216$	5.76051	+	6.64798i	0.391953	+	0.452338i
$217$	−23.0927	−	14.8408i	−1.56764	−	1.00746i
$218$	−4.64362	+	32.2971i	−0.314506	+	2.18744i
$219$	6.83988	−	47.5724i	0.462196	−	3.21464i
$220$	−0.0932567	−	0.0599324i	−0.00628736	−	0.00404064i
$221$	−1.53713	−	1.77394i	−0.103399	−	0.119328i
$222$	−9.03392	−	19.7815i	−0.606317	−	1.32765i
$223$	−1.78229	+	1.14541i	−0.119351	+	0.0767022i	−0.598954	−	0.800783i	$-0.704417\pi$
$223$	−1.78229	+	1.14541i	−0.119351	+	0.0767022i	0.479603	+	0.877485i	$0.340781\pi$
$224$	−26.4741	−	7.77350i	−1.76888	−	0.519389i
$225$	−4.88751	+	5.64048i	−0.325834	+	0.376032i
$226$	15.0564	−	4.42097i	1.00154	−	0.294078i
$227$	−2.02056	+	4.42442i	−0.134110	+	0.293659i	−0.964758	−	0.263138i	$-0.915243\pi$
$227$	−2.02056	+	4.42442i	−0.134110	+	0.293659i	0.830649	+	0.556797i	$0.187970\pi$
$228$	−3.53285	−	24.5715i	−0.233969	−	1.62729i
$229$	23.4801			1.55161			0.775804	−	0.630974i	$-0.217345\pi$
$229$	23.4801			1.55161			0.775804	+	0.630974i	$0.217345\pi$
$230$	−3.59778	+	8.47075i	−0.237231	+	0.558545i
$231$	−0.785897			−0.0517082
$232$	0.0426913	+	0.296924i	0.00280282	+	0.0194940i
$233$	4.99919	−	10.9467i	0.327508	−	0.717143i	−0.672223	−	0.740349i	$-0.734660\pi$
$233$	4.99919	−	10.9467i	0.327508	−	0.717143i	0.999731	+	0.0232063i	$0.00738747\pi$
$234$	6.45573	−	1.89557i	0.422025	−	0.123918i
$235$	0.407045	−	0.469755i	0.0265527	−	0.0306434i
$236$	−8.56407	−	2.51464i	−0.557474	−	0.163689i
$237$	8.04070	−	5.16745i	0.522300	−	0.335662i
$238$	−14.6877	−	32.1617i	−0.952065	−	2.08473i
$239$	9.76534	+	11.2698i	0.631667	+	0.728983i	0.977878	−	0.209174i	$-0.0670774\pi$
$239$	9.76534	+	11.2698i	0.631667	+	0.728983i	−0.346211	+	0.938157i	$0.612532\pi$
$240$	−12.3385	−	7.92949i	−0.796448	−	0.511846i
$241$	−2.48528	+	17.2855i	−0.160091	+	1.11346i	0.738368	+	0.674398i	$0.235597\pi$
$241$	−2.48528	+	17.2855i	−0.160091	+	1.11346i	−0.898459	+	0.439058i	$0.855312\pi$
$242$	−3.00292	+	20.8857i	−0.193035	+	1.34259i
$243$	−29.7217	−	19.1010i	−1.90665	−	1.22533i
$244$	11.2593	+	12.9939i	0.720804	+	0.831852i
$245$	−2.74078	−	6.00147i	−0.175102	−	0.383420i
$246$	−12.0644	+	7.75331i	−0.769197	+	0.494333i
$247$	2.05597	+	0.603687i	0.130818	+	0.0384117i
$248$	2.97009	−	3.42767i	0.188601	−	0.217657i
$249$	−16.7059	+	4.90531i	−1.05870	+	0.310861i
$250$	0.797176	−	1.74557i	0.0504178	−	0.110400i
$251$	0.0361096	+	0.251148i	0.00227922	+	0.0158523i	0.990929	−	0.134384i	$-0.0429056\pi$
$251$	0.0361096	+	0.251148i	0.00227922	+	0.0158523i	−0.988650	+	0.150236i	$0.951997\pi$
$252$	46.3050			2.91694
$253$	−0.315867	+	0.00845380i	−0.0198584	+	0.000531486i
$254$	−4.57860			−0.287287
$255$	−2.30015	−	15.9979i	−0.144041	−	1.00183i
$256$	8.23204	−	18.0256i	0.514502	−	1.12660i
$257$	−1.57888	+	0.463600i	−0.0984876	+	0.0289186i	−0.330605	−	0.943769i	$-0.607253\pi$
$257$	−1.57888	+	0.463600i	−0.0984876	+	0.0289186i	0.232117	+	0.972688i	$0.425435\pi$
$258$	−16.0536	+	18.5268i	−0.999454	+	1.15343i
$259$	12.3954	+	3.63961i	0.770211	+	0.226154i
$260$	−0.664932	+	0.427326i	−0.0412373	+	0.0265016i
$261$	−1.52652	−	3.34262i	−0.0944895	−	0.206903i
$262$	12.5958	+	14.5363i	0.778172	+	0.898058i
$263$	16.9995	+	10.9249i	1.04824	+	0.673660i	0.947010	−	0.321203i	$-0.104087\pi$
$263$	16.9995	+	10.9249i	1.04824	+	0.673660i	0.101226	+	0.994863i	$0.467724\pi$
$264$	0.0184795	−	0.128527i	0.00113733	−	0.00791032i
$265$	−0.512916	+	3.56741i	−0.0315082	+	0.219144i
$266$	27.1527	+	17.4500i	1.66484	+	1.06993i
$267$	15.1803	+	17.5190i	0.929022	+	1.07215i
$268$	−0.974428	−	2.13370i	−0.0595227	−	0.130337i
$269$	−3.50125	+	2.25012i	−0.213475	+	0.137192i	−0.643009	−	0.765859i	$-0.722314\pi$
$269$	−3.50125	+	2.25012i	−0.213475	+	0.137192i	0.429534	+	0.903051i	$0.358678\pi$
$270$	26.5839	+	7.80575i	1.61785	+	0.475043i
$271$	−7.97132	+	9.19939i	−0.484223	+	0.558823i	−0.944313	−	0.329049i	$-0.893272\pi$
$271$	−7.97132	+	9.19939i	−0.484223	+	0.558823i	0.460090	+	0.887873i	$0.347817\pi$
$272$	21.7375	−	6.38271i	1.31803	−	0.387008i
$273$	−2.32780	+	5.09717i	−0.140885	+	0.308495i
$274$	−4.43939	−	30.8767i	−0.268194	−	1.86533i
$275$	0.0658865			0.00397310
$276$	26.0917	−	0.698312i	1.57054	−	0.0420334i
$277$	−0.594549			−0.0357230			−0.0178615	−	0.999840i	$-0.505686\pi$
$277$	−0.594549			−0.0357230			−0.0178615	+	0.999840i	$0.505686\pi$
$278$	−3.56374	−	24.7864i	−0.213739	−	1.48659i
$279$	−23.0800	+	50.5382i	−1.38176	+	3.02564i
$280$	2.15566	−	0.632959i	0.128825	−	0.0378265i
$281$	14.1759	−	16.3598i	0.845661	−	0.975945i	−0.154266	−	0.988029i	$-0.549301\pi$
$281$	14.1759	−	16.3598i	0.845661	−	0.975945i	0.999927	+	0.0120847i	$0.00384679\pi$
$282$	−3.70207	−	1.08702i	−0.220455	−	0.0647314i
$283$	6.60763	−	4.24646i	0.392783	−	0.252426i	−0.329311	−	0.944222i	$-0.606816\pi$
$283$	6.60763	−	4.24646i	0.392783	−	0.252426i	0.722094	+	0.691795i	$0.243180\pi$
$284$	−7.50055	−	16.4239i	−0.445076	−	0.974580i
$285$	9.66200	+	11.1505i	0.572327	+	0.660501i
$286$	−0.0499676	−	0.0321122i	−0.00295465	−	0.00189884i
$287$	1.21242	−	8.43255i	0.0715667	−	0.497757i
$288$	−7.94760	+	55.2767i	−0.468317	+	3.25721i
$289$	6.70086	+	4.30638i	0.394168	+	0.253317i
$290$	0.618734	+	0.714057i	0.0363333	+	0.0419308i
$291$	4.30596	+	9.42873i	0.252420	+	0.552722i
$292$	21.0303	−	13.5153i	1.23070	−	0.790925i
$293$	−15.8155	−	4.64386i	−0.923953	−	0.271297i	−0.215050	−	0.976603i	$-0.568991\pi$
$293$	−15.8155	−	4.64386i	−0.923953	−	0.271297i	−0.708903	+	0.705306i	$0.750810\pi$
$294$	−26.8194	+	30.9513i	−1.56414	+	1.80512i
$295$	5.09007	−	1.49458i	0.296355	−	0.0870177i
$296$	−0.886693	+	1.94159i	−0.0515380	+	0.112852i
$297$	0.135379	+	0.941583i	0.00785550	+	0.0546362i
$298$	−29.9625			−1.73568
$299$	−0.880757	+	2.07369i	−0.0509355	+	0.119925i
$300$	−5.44244			−0.314220
$301$	−2.07251	−	14.4147i	−0.119458	−	0.830847i
$302$	5.09320	−	11.1525i	0.293081	−	0.641757i
$303$	55.8595	−	16.4018i	3.20904	−	0.942260i
$304$	−13.5434	+	15.6300i	−0.776770	+	0.896440i
$305$	−9.80500	−	2.87901i	−0.561433	−	0.164852i
$306$	−60.2013	+	38.6890i	−3.44148	+	2.21170i
$307$	7.55042	+	16.5331i	0.430925	+	0.943594i	0.993176	+	0.116627i	$0.0372083\pi$
$307$	7.55042	+	16.5331i	0.430925	+	0.943594i	−0.562251	+	0.826967i	$0.690064\pi$
$308$	−0.267691	−	0.308932i	−0.0152531	−	0.0176031i
$309$	−0.527348	−	0.338906i	−0.0299998	−	0.0192797i
$310$	2.03300	−	14.1398i	0.115467	−	0.803088i
$311$	−1.19779	+	8.33083i	−0.0679206	+	0.472398i	0.927266	+	0.374402i	$0.122152\pi$
$311$	−1.19779	+	8.33083i	−0.0679206	+	0.472398i	−0.995187	+	0.0979954i	$0.968757\pi$
$312$	−0.778867	−	0.500548i	−0.0440947	−	0.0283379i
$313$	0.393280	+	0.453870i	0.0222295	+	0.0256542i	0.766755	−	0.641939i	$-0.221870\pi$
$313$	0.393280	+	0.453870i	0.0222295	+	0.0256542i	−0.744526	+	0.667594i	$0.767324\pi$
$314$	−4.96409	−	10.8698i	−0.280140	−	0.613421i
$315$	−23.1525	+	14.8792i	−1.30450	+	0.838348i
$316$	4.77011	+	1.40063i	0.268340	+	0.0787917i
$317$	11.6723	−	13.4705i	0.655579	−	0.756579i	−0.326469	−	0.945208i	$-0.605859\pi$
$317$	11.6723	−	13.4705i	0.655579	−	0.756579i	0.982048	+	0.188629i	$0.0604044\pi$
$318$	21.4658	−	6.30292i	1.20374	−	0.353450i
$319$	−0.0134760	+	0.0295083i	−0.000754512	+	0.00165215i
$320$	−0.752911	−	5.23661i	−0.0420890	−	0.292735i
$321$	25.7865			1.43926
$322$	−21.5296	+	26.2330i	−1.19980	+	1.46191i
$323$	−22.7903			−1.26809
$324$	−5.82152	−	40.4896i	−0.323418	−	2.24942i
$325$	0.195153	−	0.427326i	0.0108252	−	0.0237038i
$326$	−44.1787	+	12.9721i	−2.44683	+	0.718455i
$327$	−36.0181	+	41.5671i	−1.99181	+	2.29867i
$328$	1.35057	+	0.396563i	0.0745727	+	0.0218965i
$329$	1.92820	−	1.23918i	0.106305	−	0.0683183i
$330$	−0.169898	−	0.372024i	−0.00935255	−	0.0204792i
$331$	9.88844	+	11.4119i	0.543518	+	0.627253i	0.959360	−	0.282183i	$-0.0910587\pi$
$331$	9.88844	+	11.4119i	0.543518	+	0.627253i	−0.415842	+	0.909437i	$0.636513\pi$
$332$	−7.61861	−	4.89618i	−0.418126	−	0.268713i
$333$	3.72112	−	25.8810i	0.203916	−	1.41827i
$334$	3.33730	−	23.2114i	0.182609	−	1.27007i
$335$	1.17284	+	0.753737i	0.0640789	+	0.0411810i
$336$	−35.4175	−	40.8740i	−1.93218	−	2.22986i
$337$	−3.99750	−	8.75331i	−0.217758	−	0.476823i	0.768954	−	0.639304i	$-0.220778\pi$
$337$	−3.99750	−	8.75331i	−0.217758	−	0.476823i	−0.986712	+	0.162481i	$0.948050\pi$
$338$	20.6303	−	13.2583i	1.12214	−	0.721157i
$339$	25.3797	+	7.45217i	1.37844	+	0.404746i
$340$	5.50522	−	6.35336i	0.298562	−	0.344559i
$341$	0.470602	−	0.138181i	0.0254845	−	0.00748293i
$342$	27.1377	−	59.4233i	1.46744	−	3.21325i
$343$	0.211127	+	1.46842i	0.0113998	+	0.0792872i
$344$	2.40614			0.129730
$345$	−12.8215	+	8.73321i	−0.690284	+	0.470180i
$346$	8.51144			0.457578
$347$	1.89016	+	13.1463i	0.101469	+	0.705732i	0.975522	+	0.219901i	$0.0705736\pi$
$347$	1.89016	+	13.1463i	0.101469	+	0.705732i	−0.874053	+	0.485830i	$0.838517\pi$
$348$	1.11316	−	2.43749i	0.0596718	−	0.130663i
$349$	9.25415	−	2.71726i	0.495363	−	0.145452i	−0.0245025	−	0.999700i	$-0.507800\pi$
$349$	9.25415	−	2.71726i	0.495363	−	0.145452i	0.519866	+	0.854248i	$0.325982\pi$
$350$	4.63397	−	5.34789i	0.247696	−	0.285857i
$351$	6.50790	+	1.91089i	0.347366	+	0.101996i
$352$	0.414734	−	0.266534i	0.0221054	−	0.0142063i
$353$	−7.52913	−	16.4865i	−0.400735	−	0.877487i	−0.997195	−	0.0748445i	$-0.976154\pi$
$353$	−7.52913	−	16.4865i	−0.400735	−	0.877487i	0.596460	−	0.802643i	$-0.296573\pi$
$354$	−21.5645	−	24.8868i	−1.14614	−	1.32272i
$355$	9.02778	+	5.80180i	0.479145	+	0.307928i
$356$	−1.71594	+	11.9346i	−0.0909447	+	0.632534i
$357$	8.48181	−	58.9923i	0.448905	−	3.12220i
$358$	−29.1344	−	18.7235i	−1.53980	−	0.989570i
$359$	−11.3242	−	13.0689i	−0.597671	−	0.689749i	0.373637	−	0.927575i	$-0.378111\pi$
$359$	−11.3242	−	13.0689i	−0.597671	−	0.689749i	−0.971308	+	0.237826i	$0.923565\pi$
$360$	−1.88898	−	4.13628i	−0.0995578	−	0.218001i
$361$	1.51824	−	0.975711i	0.0799072	−	0.0513532i
$362$	−20.2279	−	5.93944i	−1.06315	−	0.312170i
$363$	−23.2920	+	26.8804i	−1.22251	+	1.41086i
$364$	−2.79656	+	0.821145i	−0.146580	+	0.0430397i
$365$	−6.17225	+	13.5153i	−0.323070	+	0.707425i
$366$	9.02745	+	62.7873i	0.471872	+	3.28194i
$367$	18.9302			0.988148			0.494074	−	0.869420i	$-0.335507\pi$
$367$	18.9302			0.988148			0.494074	+	0.869420i	$0.335507\pi$
$368$	−14.6746	−	16.0470i	−0.764969	−	0.836510i
$369$	−17.2428			−0.897624
$370$	0.956769	+	6.65448i	0.0497401	+	0.345950i
$371$	−5.52091	+	12.0891i	−0.286631	+	0.627635i
$372$	−38.8733	+	11.4142i	−2.01549	+	0.591800i
$373$	−20.9182	+	24.1409i	−1.08310	+	1.24997i	−0.116635	+	0.993175i	$0.537211\pi$
$373$	−20.9182	+	24.1409i	−1.08310	+	1.24997i	−0.966467	+	0.256791i	$0.917335\pi$
$374$	0.606148	+	0.177981i	0.0313431	+	0.00920318i
$375$	2.72122	−	1.74882i	0.140523	−	0.0903088i
$376$	0.157319	+	0.344481i	0.00811311	+	0.0177652i
$377$	0.151470	+	0.174805i	0.00780108	+	0.00900293i
$378$	85.9482	+	55.2356i	4.42070	+	2.84101i
$379$	−2.00720	+	13.9604i	−0.103103	+	0.717098i	0.871048	+	0.491198i	$0.163441\pi$
$379$	−2.00720	+	13.9604i	−0.103103	+	0.717098i	−0.974151	+	0.225899i	$0.927468\pi$
$380$	−1.09216	+	7.59617i	−0.0560269	+	0.389675i
$381$	−6.49270	−	4.17260i	−0.332631	−	0.213769i
$382$	−11.9996	−	13.8483i	−0.613955	−	0.708542i
$383$	−16.0712	−	35.1910i	−0.821199	−	1.79818i	−0.548699	−	0.836020i	$-0.684877\pi$
$383$	−16.0712	−	35.1910i	−0.821199	−	1.79818i	−0.272500	−	0.962156i	$-0.587850\pi$
$384$	13.0964	−	8.41656i	0.668324	−	0.429506i
$385$	0.233115	+	0.0684488i	0.0118806	+	0.00348847i
$386$	1.53311	−	1.76930i	0.0780333	−	0.0900552i
$387$	−28.2810	+	8.30405i	−1.43760	+	0.422119i
$388$	−2.23970	+	4.90426i	−0.113703	+	0.248976i
$389$	1.77865	+	12.3708i	0.0901813	+	0.627225i	0.983916	+	0.178630i	$0.0571663\pi$
$389$	1.77865	+	12.3708i	0.0901813	+	0.627225i	−0.893735	+	0.448595i	$0.851925\pi$
$390$	−2.91610			−0.147662
$391$	2.77443	−	23.8014i	0.140309	−	1.20369i
$392$	4.01974			0.203027
$393$	4.61416	+	32.0922i	0.232753	+	1.61884i
$394$	4.57353	−	10.0146i	0.230411	−	0.504530i
$395$	−2.83512	+	0.832467i	−0.142650	+	0.0418860i
$396$	−0.541802	+	0.625273i	−0.0272266	+	0.0314211i
$397$	15.9291	+	4.67720i	0.799458	+	0.234742i	0.655849	−	0.754892i	$-0.272311\pi$
$397$	15.9291	+	4.67720i	0.799458	+	0.234742i	0.143610	+	0.989634i	$0.454129\pi$
$398$	−5.62509	+	3.61503i	−0.281961	+	0.181205i
$399$	22.6013	+	49.4899i	1.13148	+	2.47759i
$400$	2.96926	+	3.42671i	0.148463	+	0.171335i
$401$	17.9361	+	11.5269i	0.895688	+	0.575623i	0.905508	−	0.424328i	$-0.139490\pi$
$401$	17.9361	+	11.5269i	0.895688	+	0.575623i	−0.00982083	+	0.999952i	$0.503126\pi$
$402$	1.23160	−	8.56597i	0.0614267	−	0.427232i
$403$	0.497690	−	3.46151i	0.0247917	−	0.172430i
$404$	25.4743	+	16.3713i	1.26739	+	0.814504i
$405$	15.9213	+	18.3742i	0.791136	+	0.913019i
$406$	1.44734	+	3.16922i	0.0718301	+	0.157286i
$407$	−0.194182	+	0.124793i	−0.00962523	+	0.00618576i
$408$	9.44829	+	2.77427i	0.467760	+	0.137347i
$409$	1.58673	−	1.83119i	0.0784588	−	0.0905463i	−0.715163	−	0.698958i	$-0.753648\pi$
$409$	1.58673	−	1.83119i	0.0784588	−	0.0905463i	0.793622	+	0.608411i	$0.208193\pi$
$410$	4.25386	−	1.24905i	0.210083	−	0.0616859i
$411$	21.8434	−	47.8304i	1.07746	−	2.35930i
$412$	−0.0464024	−	0.322736i	−0.00228608	−	0.0159000i
$413$	19.5620			0.962585
$414$	58.7560	+	35.5757i	2.88770	+	1.74845i
$415$	5.38260			0.264221
$416$	−0.500254	−	3.47935i	−0.0245270	−	0.170589i
$417$	17.5349	−	38.3961i	0.858688	−	1.88026i
$418$	−0.553338	+	0.162475i	−0.0270647	+	0.00794690i
$419$	17.9022	−	20.6602i	0.874578	−	1.00932i	−0.125274	−	0.992122i	$-0.539981\pi$
$419$	17.9022	−	20.6602i	0.874578	−	1.00932i	0.999852	−	0.0171945i	$-0.00547345\pi$
$420$	−19.2561	−	5.65410i	−0.939601	−	0.275892i
$421$	−26.5485	+	17.0617i	−1.29389	+	0.831536i	−0.992533	−	0.121974i	$-0.961077\pi$
$421$	−26.5485	+	17.0617i	−1.29389	+	0.831536i	−0.301361	+	0.953510i	$0.597441\pi$
$422$	19.6277	+	42.9788i	0.955464	+	2.09217i
$423$	−3.03795	−	3.50598i	−0.147710	−	0.170467i
$424$	−1.84726	−	1.18716i	−0.0897110	−	0.0576538i
$425$	−0.711081	+	4.94567i	−0.0344925	+	0.239900i
$426$	9.48010	−	65.9356i	0.459312	−	3.19459i
$427$	−31.7005	−	20.3726i	−1.53409	−	0.985901i
$428$	8.78337	+	10.1365i	0.424560	+	0.489968i
$429$	−0.0415919	−	0.0910736i	−0.00200808	−	0.00439707i
$430$	6.37549	−	4.09728i	0.307453	−	0.197588i
$431$	−7.77955	−	2.28428i	−0.374728	−	0.110030i	0.0889450	−	0.996037i	$-0.471650\pi$
$431$	−7.77955	−	2.28428i	−0.374728	−	0.110030i	−0.463673	+	0.886007i	$0.653469\pi$
$432$	−42.8700	+	49.4747i	−2.06259	+	2.38035i
$433$	−11.7435	+	3.44822i	−0.564359	+	0.165711i	−0.551453	−	0.834206i	$-0.685926\pi$
$433$	−11.7435	+	3.44822i	−0.564359	+	0.165711i	−0.0129059	+	0.999917i	$0.504108\pi$
$434$	21.8828	−	47.9165i	1.05041	−	2.30007i
$435$	0.226658	+	1.57644i	0.0108674	+	0.0755844i
$436$	−28.6083			−1.37009
$437$	9.61624	+	19.6478i	0.460007	+	0.939883i
$438$	92.2295			4.40690
$439$	1.31991	+	9.18019i	0.0629959	+	0.438146i	0.996772	+	0.0802878i	$0.0255839\pi$
$439$	1.31991	+	9.18019i	0.0629959	+	0.438146i	−0.933776	+	0.357859i	$0.883507\pi$
$440$	−0.0166757	+	0.0365147i	−0.000794983	+	0.00174077i
$441$	−47.2468	+	13.8729i	−2.24985	+	0.660615i
$442$	2.94973	−	3.40418i	0.140305	−	0.161920i
$443$	−7.61107	−	2.23481i	−0.361613	−	0.106179i	0.0958789	−	0.995393i	$-0.469434\pi$
$443$	−7.61107	−	2.23481i	−0.361613	−	0.106179i	−0.457492	+	0.889214i	$0.651252\pi$
$444$	16.0401	−	10.3083i	0.761228	−	0.489211i
$445$	−2.97699	−	6.51870i	−0.141123	−	0.309016i
$446$	−2.66239	−	3.07256i	−0.126068	−	0.145490i
$447$	−42.4884	−	27.3057i	−2.00963	−	1.29151i
$448$	2.77636	−	19.3100i	0.131171	−	0.912312i
$449$	0.253758	−	1.76493i	0.0119756	−	0.0832921i	−0.982957	−	0.183835i	$-0.941149\pi$
$449$	0.253758	−	1.76493i	0.0119756	−	0.0832921i	0.994933	+	0.100543i	$0.0320579\pi$
$450$	−12.0486	−	7.74318i	−0.567977	−	0.365017i
$451$	0.0996815	+	0.115039i	0.00469382	+	0.00541695i
$452$	5.71541	+	12.5150i	0.268830	+	0.588656i
$453$	17.3860	−	11.1733i	0.816867	−	0.524969i
$454$	−8.95579	−	2.62966i	−0.420316	−	0.123416i
$455$	1.13442	−	1.30919i	0.0531826	−	0.0613760i
$456$	−8.62513	+	2.53257i	−0.403909	+	0.118598i
$457$	−11.1048	+	24.3162i	−0.519463	+	1.13746i	0.450180	+	0.892938i	$0.351360\pi$
$457$	−11.1048	+	24.3162i	−0.519463	+	1.13746i	−0.969643	+	0.244527i	$0.921367\pi$
$458$	6.41242	+	44.5993i	0.299633	+	2.08399i
$459$	−72.1397			−3.36719
$460$	−7.80022	−	2.06536i	−0.363687	−	0.0962977i
$461$	27.4447			1.27823			0.639113	−	0.769113i	$-0.279302\pi$
$461$	27.4447			1.27823			0.639113	+	0.769113i	$0.279302\pi$
$462$	−0.214629	−	1.49278i	−0.00998543	−	0.0694502i
$463$	−8.55132	+	18.7248i	−0.397414	+	0.870215i	0.600112	+	0.799916i	$0.295123\pi$
$463$	−8.55132	+	18.7248i	−0.397414	+	0.870215i	−0.997526	+	0.0702989i	$0.977605\pi$
$464$	−2.14202	+	0.628954i	−0.0994409	+	0.0291985i
$465$	15.7689	−	18.1983i	0.731265	−	0.843925i
$466$	22.1580	+	6.50619i	1.02645	+	0.301393i
$467$	−29.7282	+	19.1052i	−1.37566	+	0.884081i	−0.999104	−	0.0423138i	$-0.986527\pi$
$467$	−29.7282	+	19.1052i	−1.37566	+	0.884081i	−0.376553	+	0.926395i	$0.622891\pi$
$468$	2.45059	+	5.36605i	0.113279	+	0.248046i
$469$	3.36661	+	3.88527i	0.155455	+	0.179405i
$470$	1.00344	+	0.644873i	0.0462853	+	0.0297458i
$471$	2.86664	−	19.9379i	0.132088	−	0.918690i
$472$	−0.459979	+	3.19922i	−0.0211722	+	0.147256i
$473$	0.218896	+	0.140676i	0.0100648	+	0.00646828i
$474$	12.0112	+	13.8617i	0.551694	+	0.636689i
$475$	−1.89480	−	4.14903i	−0.0869394	−	0.190371i
$476$	26.0786	−	16.7597i	1.19531	−	0.768181i
$477$	25.8093	+	7.57829i	1.18173	+	0.346986i
$478$	−18.7395	+	21.6266i	−0.857127	+	0.989177i
$479$	37.3836	−	10.9768i	1.70810	−	0.501544i	0.725650	−	0.688064i	$-0.241539\pi$
$479$	37.3836	−	10.9768i	1.70810	−	0.501544i	0.982451	+	0.186520i	$0.0597208\pi$
$480$	10.0546	−	22.0166i	0.458929	−	1.00491i
$481$	0.234223	+	1.62905i	0.0106796	+	0.0742785i
$482$	−33.5117			−1.52642
$483$	−54.4369	+	17.5792i	−2.47696	+	0.799881i
$484$	−18.5003			−0.840922
$485$	−0.456038	−	3.17181i	−0.0207076	−	0.144025i
$486$	28.1645	−	61.6716i	1.27757	−	2.79748i
$487$	14.0317	−	4.12008i	0.635837	−	0.186699i	0.0521005	−	0.998642i	$-0.483408\pi$
$487$	14.0317	−	4.12008i	0.635837	−	0.186699i	0.583736	+	0.811943i	$0.301590\pi$
$488$	4.07719	−	4.70533i	0.184566	−	0.213000i
$489$	−74.4695	−	21.8662i	−3.36763	−	0.988825i
$490$	10.6510	−	6.84499i	0.481163	−	0.309225i
$491$	−11.9689	−	26.2081i	−0.540147	−	1.18276i	−0.961233	−	0.275736i	$-0.911078\pi$
$491$	−11.9689	−	26.2081i	−0.540147	−	1.18276i	0.421087	−	0.907020i	$-0.361649\pi$
$492$	−8.23403	−	9.50257i	−0.371219	−	0.428409i
$493$	−2.06956	−	1.33003i	−0.0932084	−	0.0599014i
$494$	−0.585190	+	4.07008i	−0.0263289	+	0.183122i
$495$	0.0699817	−	0.486734i	0.00314545	−	0.0218771i
$496$	28.3950	+	18.2483i	1.27497	+	0.819375i
$497$	25.9141	+	29.9064i	1.16240	+	1.34149i
$498$	−13.8798	−	30.3925i	−0.621969	−	1.36192i
$499$	6.88700	−	4.42601i	0.308304	−	0.198135i	−0.377334	−	0.926077i	$-0.623159\pi$
$499$	6.88700	−	4.42601i	0.308304	−	0.198135i	0.685639	+	0.727942i	$0.259523\pi$
$500$	1.61435	+	0.474017i	0.0721961	+	0.0211987i
$501$	25.8857	−	29.8737i	1.15649	−	1.33466i
$502$	−0.467183	+	0.137177i	−0.0208514	+	0.00612252i
$503$	6.56240	−	14.3697i	0.292603	−	0.640711i	−0.705052	−	0.709156i	$-0.749076\pi$
$503$	6.56240	−	14.3697i	0.292603	−	0.640711i	0.997655	+	0.0684445i	$0.0218036\pi$
$504$	−2.38631	−	16.5972i	−0.106295	−	0.739296i
$505$	−17.9977			−0.800889
$506$	−0.102321	−	0.597666i	−0.00454872	−	0.0265695i
$507$	41.3375			1.83586
$508$	−0.571305	−	3.97352i	−0.0253476	−	0.176296i
$509$	6.83629	−	14.9694i	0.303013	−	0.663507i	−0.695470	−	0.718555i	$-0.744804\pi$
$509$	6.83629	−	14.9694i	0.303013	−	0.663507i	0.998484	+	0.0550481i	$0.0175312\pi$
$510$	29.7591	−	8.73805i	1.31775	−	0.386927i
$511$	−35.8792	+	41.4068i	−1.58720	+	1.83173i
$512$	27.2515	+	8.00178i	1.20436	+	0.353632i
$513$	55.4005	−	35.6037i	2.44599	−	1.57194i
$514$	−1.31178	−	2.87239i	−0.0578600	−	0.126696i
$515$	0.126906	+	0.146457i	0.00559215	+	0.00645368i
$516$	−18.0815	−	11.6203i	−0.795996	−	0.511555i
$517$	−0.00582827	+	0.0405365i	−0.000256327	+	0.00178279i
$518$	−3.52809	+	24.5384i	−0.155015	+	1.07816i
$519$	12.0697	+	7.75671i	0.529800	+	0.340482i
$520$	0.187434	+	0.216310i	0.00821952	+	0.00948584i
$521$	11.9803	+	26.2331i	0.524864	+	1.14929i	0.967565	+	0.252623i	$0.0812933\pi$
$521$	11.9803	+	26.2331i	0.524864	+	1.14929i	−0.442700	+	0.896670i	$0.645979\pi$
$522$	5.93226	−	3.81243i	0.259648	−	0.166866i
$523$	31.7016	+	9.30842i	1.38621	+	0.407029i	0.887927	−	0.459984i	$-0.152145\pi$
$523$	31.7016	+	9.30842i	1.38621	+	0.407029i	0.498286	+	0.867013i	$0.333963\pi$
$524$	−11.0436	+	12.7450i	−0.482442	+	0.556768i
$525$	11.4449	−	3.36052i	0.499496	−	0.146665i
$526$	−16.1088	+	35.2734i	−0.702378	+	1.53799i
$527$	5.29339	+	36.8164i	0.230584	+	1.60375i
$528$	0.966345			0.0420548
$529$	−21.6901	+	7.65099i	−0.943050	+	0.332652i
$530$	−6.91620			−0.300421
$531$	−5.63469	−	39.1902i	−0.244525	−	1.70071i
$532$	−11.7558	+	25.7416i	−0.509679	+	1.11604i
$533$	1.04137	−	0.305774i	0.0451067	−	0.0132445i
$534$	−29.1309	+	33.6188i	−1.26062	+	1.45483i
$535$	−7.64886	−	2.24591i	−0.330689	−	0.0970991i
$536$	−0.714568	+	0.459225i	−0.0308646	+	0.0198355i
$537$	−24.2508	−	53.1019i	−1.04650	−	2.29152i
$538$	−5.23018	−	6.03595i	−0.225489	−	0.260228i
$539$	0.365692	+	0.235016i	0.0157515	+	0.0101228i
$540$	−3.45711	+	24.0447i	−0.148770	+	1.03472i
$541$	2.66305	−	18.5219i	0.114494	−	0.796320i	−0.848962	−	0.528453i	$-0.822772\pi$
$541$	2.66305	−	18.5219i	0.114494	−	0.796320i	0.963456	−	0.267867i	$-0.0863188\pi$
$542$	−19.6508	−	12.6288i	−0.844074	−	0.542453i
$543$	−23.2714	−	26.8566i	−0.998672	−	1.15253i
$544$	15.5309	+	34.0080i	0.665884	+	1.45808i
$545$	14.3041	−	9.19271i	0.612722	−	0.393773i
$546$	−10.3176	−	3.02951i	−0.441551	−	0.129651i
$547$	23.5948	−	27.2298i	1.00884	−	1.16426i	0.0224661	−	0.999748i	$-0.492848\pi$
$547$	23.5948	−	27.2298i	1.00884	−	1.16426i	0.986374	−	0.164516i	$-0.0526063\pi$
$548$	26.2422	−	7.70541i	1.12101	−	0.329159i
$549$	−31.6830	+	69.3762i	−1.35220	+	2.96090i
$550$	0.0179936	+	0.125148i	0.000767250	+	0.00533634i
$551$	2.24576			0.0956727
$552$	−1.59492	−	9.31609i	−0.0678844	−	0.396519i
$553$	−10.8959			−0.463340
$554$	−0.162371	−	1.12932i	−0.00689850	−	0.0479801i
$555$	−4.70765	+	10.3083i	−0.199829	+	0.437564i
$556$	21.0660	−	6.18555i	0.893399	−	0.262326i
$557$	−0.425707	+	0.491292i	−0.0180378	+	0.0208167i	−0.764697	−	0.644390i	$-0.777111\pi$
$557$	−0.425707	+	0.491292i	−0.0180378	+	0.0208167i	0.746659	+	0.665207i	$0.231657\pi$
$558$	−102.298	−	30.0374i	−4.33062	−	1.27159i
$559$	1.56076	−	1.00304i	0.0660130	−	0.0424240i
$560$	6.94567	+	15.2089i	0.293508	+	0.642693i
$561$	0.697350	+	0.804785i	0.0294421	+	0.0339780i
$562$	34.9461	+	22.4585i	1.47411	+	0.947355i
$563$	−4.07134	+	28.3168i	−0.171586	+	1.19341i	0.703947	+	0.710252i	$0.251419\pi$
$563$	−4.07134	+	28.3168i	−0.171586	+	1.19341i	−0.875534	+	0.483157i	$0.839490\pi$
$564$	0.481435	−	3.34845i	0.0202721	−	0.140995i
$565$	−6.87916	−	4.42097i	−0.289408	−	0.185991i
$566$	9.87051	+	11.3912i	0.414888	+	0.478807i
$567$	37.2430	+	81.5507i	1.56406	+	3.42481i
$568$	−5.50030	+	3.53483i	−0.230788	+	0.148318i
$569$	12.7714	+	3.75002i	0.535405	+	0.157209i	0.538247	−	0.842787i	$-0.319087\pi$
$569$	12.7714	+	3.75002i	0.535405	+	0.157209i	−0.00284249	+	0.999996i	$0.500905\pi$
$570$	−18.5412	+	21.3977i	−0.776607	+	0.896252i
$571$	−30.1292	+	8.84674i	−1.26087	+	0.370225i	−0.842818	−	0.538199i	$-0.819105\pi$
$571$	−30.1292	+	8.84674i	−1.26087	+	0.370225i	−0.418051	+	0.908423i	$0.637287\pi$
$572$	0.0216336	−	0.0473710i	0.000904546	−	0.00198068i
$573$	−4.39577	−	30.5733i	−0.183636	−	1.27722i
$574$	16.3483			0.682367
$575$	4.56377	−	1.47377i	0.190322	−	0.0614604i
$576$	−39.4850			−1.64521
$577$	−6.09943	−	42.4225i	−0.253923	−	1.76607i	−0.574169	−	0.818737i	$-0.694675\pi$
$577$	−6.09943	−	42.4225i	−0.253923	−	1.76607i	0.320246	−	0.947334i	$-0.396234\pi$
$578$	−6.34976	+	13.9040i	−0.264115	+	0.578332i
$579$	3.78645	−	1.11180i	0.157359	−	0.0462049i
$580$	−0.542486	+	0.626063i	−0.0225255	+	0.0259958i
$581$	19.0444	+	5.59193i	0.790093	+	0.231992i
$582$	−16.7335	+	10.7540i	−0.693625	+	0.445766i
$583$	−0.0986448	−	0.216002i	−0.00408545	−	0.00894589i
$584$	−5.92811	−	6.84140i	−0.245307	−	0.283099i
$585$	−2.94957	−	1.89557i	−0.121950	−	0.0783724i
$586$	4.50157	−	31.3091i	0.185958	−	1.29337i
$587$	0.261308	−	1.81744i	0.0107854	−	0.0750138i	−0.983718	−	0.179720i	$-0.942481\pi$
$587$	0.261308	−	1.81744i	0.0107854	−	0.0750138i	0.994503	+	0.104706i	$0.0333901\pi$
$588$	−30.2074	−	19.4131i	−1.24573	−	0.800582i
$589$	−22.2354	−	25.6610i	−0.916195	−	1.05735i
$590$	4.22898	+	9.26018i	0.174104	+	0.381235i
$591$	15.6121	−	10.0333i	0.642196	−	0.412714i
$592$	−15.2414	−	4.47529i	−0.626420	−	0.183933i
$593$	−7.30816	+	8.43407i	−0.300110	+	0.346346i	−0.885697	−	0.464264i	$-0.846319\pi$
$593$	−7.30816	+	8.43407i	−0.300110	+	0.346346i	0.585586	+	0.810610i	$0.300864\pi$
$594$	−1.75152	+	0.514293i	−0.0718658	+	0.0211017i
$595$	−7.65391	+	16.7597i	−0.313780	+	0.687082i
$596$	−3.73864	−	26.0028i	−0.153141	−	1.06512i
$597$	−11.2711			−0.461297
$598$	−4.17941	−	1.10663i	−0.170909	−	0.0452536i
$599$	−32.2275			−1.31678			−0.658391	−	0.752676i	$-0.728763\pi$
$599$	−32.2275			−1.31678			−0.658391	+	0.752676i	$0.728763\pi$
$600$	0.280474	+	1.95074i	0.0114503	+	0.0796387i
$601$	−7.88596	+	17.2679i	−0.321675	+	0.704370i	−0.999525	−	0.0308303i	$-0.990185\pi$
$601$	−7.88596	+	17.2679i	−0.321675	+	0.704370i	0.677849	+	0.735201i	$0.262912\pi$
$602$	26.8140	−	7.87329i	1.09286	−	0.320891i
$603$	6.81394	−	7.86371i	0.277485	−	0.320235i
$604$	10.3142	+	3.02852i	0.419679	+	0.123229i
$605$	9.25014	−	5.94470i	0.376072	−	0.241687i
$606$	46.4097	+	101.623i	1.88527	+	4.12816i
$607$	1.39792	+	1.61329i	0.0567399	+	0.0654814i	0.783410	−	0.621505i	$-0.213479\pi$
$607$	1.39792	+	1.61329i	0.0567399	+	0.0654814i	−0.726670	+	0.686987i	$0.758933\pi$
$608$	−28.7114	−	18.4517i	−1.16440	−	0.748316i
$609$	−0.835801	+	5.81312i	−0.0338684	+	0.235560i
$610$	2.79080	−	19.4104i	0.112996	−	0.785904i
$611$	0.245648	+	0.157869i	0.00993787	+	0.00638668i
$612$	−41.0878	−	47.4179i	−1.66088	−	1.91675i
$613$	4.54607	+	9.95451i	0.183614	+	0.402059i	0.978947	−	0.204114i	$-0.0654313\pi$
$613$	4.54607	+	9.95451i	0.183614	+	0.402059i	−0.795333	+	0.606173i	$0.792704\pi$
$614$	−29.3418	+	18.8569i	−1.18414	+	0.761001i
$615$	7.17048	+	2.10544i	0.289142	+	0.0848996i
$616$	−0.0969357	+	0.111870i	−0.00390565	+	0.00450736i
$617$	44.7470	−	13.1389i	1.80145	−	0.528952i	0.803638	−	0.595119i	$-0.202895\pi$
$617$	44.7470	−	13.1389i	1.80145	−	0.528952i	0.997809	+	0.0661666i	$0.0210769\pi$
$618$	0.499717	−	1.09423i	0.0201016	−	0.0440163i
$619$	3.33220	+	23.1760i	0.133932	+	0.931521i	0.940358	+	0.340185i	$0.110490\pi$
$619$	3.33220	+	23.1760i	0.133932	+	0.931521i	−0.806426	+	0.591335i	$0.798601\pi$
$620$	12.5248			0.503010
$621$	30.4390	+	62.1926i	1.22147	+	2.49570i
$622$	−16.1511			−0.647601
$623$	−3.76078	−	26.1568i	−0.150673	−	1.04795i
$624$	2.86228	−	6.26752i	0.114583	−	0.250901i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	−0.754699	+	0.870969i	−0.0301638	+	0.0348109i
$627$	−0.932730	−	0.273874i	−0.0372497	−	0.0109375i
$628$	8.81393	−	5.66437i	0.351714	−	0.226033i
$629$	−7.27170	−	15.9228i	−0.289942	−	0.634884i
$630$	−34.5853	−	39.9136i	−1.37791	−	1.59020i
$631$	−14.7263	−	9.46403i	−0.586245	−	0.376757i	0.213638	−	0.976913i	$-0.431469\pi$
$631$	−14.7263	−	9.46403i	−0.586245	−	0.376757i	−0.799883	+	0.600156i	$0.795105\pi$
$632$	0.256204	−	1.78194i	0.0101913	−	0.0708817i
$633$	−11.3345	+	78.8334i	−0.450507	+	3.13335i
$634$	28.7743	+	18.4921i	1.14277	+	0.734416i
$635$	1.56246	+	1.80318i	0.0620045	+	0.0715570i
$636$	8.14839	+	17.8425i	0.323105	+	0.707501i
$637$	2.60743	−	1.67569i	0.103310	−	0.0663934i
$638$	−0.0597300	−	0.0175383i	−0.00236473	−	0.000694349i
$639$	52.4495	−	60.5300i	2.07487	−	2.39453i
$640$	−4.61775	+	1.35589i	−0.182533	+	0.0535964i
$641$	9.85390	−	21.5770i	0.389206	−	0.852241i	−0.609046	−	0.793135i	$-0.708448\pi$
$641$	9.85390	−	21.5770i	0.389206	−	0.852241i	0.998252	−	0.0591065i	$-0.0188252\pi$
$642$	7.04229	+	48.9802i	0.277937	+	1.93310i
$643$	7.53294			0.297070			0.148535	−	0.988907i	$-0.452544\pi$
$643$	7.53294			0.297070			0.148535	+	0.988907i	$0.452544\pi$
$644$	−25.4525	−	15.4111i	−1.00297	−	0.607282i
$645$	12.7747			0.503004
$646$	−6.22403	−	43.2891i	−0.244881	−	1.70319i
$647$	−2.49950	+	5.47315i	−0.0982657	+	0.215172i	−0.952380	−	0.304913i	$-0.901373\pi$
$647$	−2.49950	+	5.47315i	−0.0982657	+	0.215172i	0.854114	+	0.520085i	$0.174100\pi$
$648$	−14.2127	+	4.17323i	−0.558328	+	0.163940i
$649$	−0.228890	+	0.264153i	−0.00898472	+	0.0103689i
$650$	0.864982	+	0.253982i	0.0339274	+	0.00996198i
$651$	74.6985	−	48.0058i	2.92767	−	1.88150i
$652$	−16.7702	−	36.7217i	−0.656773	−	1.43813i
$653$	−26.0197	−	30.0284i	−1.01823	−	1.17510i	−0.984449	−	0.175672i	$-0.943790\pi$
$653$	−26.0197	−	30.0284i	−1.01823	−	1.17510i	−0.0337819	−	0.999429i	$-0.510755\pi$
$654$	−88.7914	−	57.0627i	−3.47202	−	2.23133i
$655$	1.42645	−	9.92115i	0.0557359	−	0.387651i
$656$	−1.49080	+	10.3687i	−0.0582059	+	0.404831i
$657$	93.2881	+	59.9527i	3.63952	+	2.33898i
$658$	2.88036	+	3.32411i	0.112288	+	0.129587i
$659$	8.88735	+	19.4606i	0.346202	+	0.758077i	0.999999	+	0.00140659i	$0.000447732\pi$
$659$	8.88735	+	19.4606i	0.346202	+	0.758077i	−0.653797	+	0.756670i	$0.726825\pi$
$660$	0.301659	−	0.193865i	0.0117421	−	0.00754618i
$661$	−30.7146	−	9.01863i	−1.19466	−	0.350784i	−0.376852	−	0.926274i	$-0.622993\pi$
$661$	−30.7146	−	9.01863i	−1.19466	−	0.350784i	−0.817809	+	0.575489i	$0.804812\pi$
$662$	−18.9758	+	21.8992i	−0.737515	+	0.851137i
$663$	7.28519	−	2.13913i	0.282933	−	0.0830768i
$664$	−1.36232	+	2.98307i	−0.0528684	+	0.115766i
$665$	−2.39367	−	16.6483i	−0.0928224	−	0.645594i
$666$	50.1759			1.94428
$667$	−0.273393	+	2.34540i	−0.0105858	+	0.0908141i
$668$	20.5603			0.795503
$669$	−0.975301	−	6.78337i	−0.0377073	−	0.262260i
$670$	−1.11139	+	2.43360i	−0.0429366	+	0.0940180i
$671$	0.646017	−	0.189688i	0.0249392	−	0.00732281i
$672$	58.4475	−	67.4520i	2.25466	−	2.60202i
$673$	17.6305	+	5.17678i	0.679606	+	0.199550i	0.603276	−	0.797532i	$-0.293862\pi$
$673$	17.6305	+	5.17678i	0.679606	+	0.199550i	0.0763296	+	0.997083i	$0.475680\pi$
$674$	15.5348	−	9.98360i	0.598378	−	0.384554i
$675$	−5.99774	−	13.1332i	−0.230853	−	0.505498i
$676$	14.0803	+	16.2496i	0.541552	+	0.624984i
$677$	8.38103	+	5.38616i	0.322109	+	0.207007i	0.691695	−	0.722189i	$-0.256864\pi$
$677$	8.38103	+	5.38616i	0.322109	+	0.207007i	−0.369586	+	0.929197i	$0.620500\pi$
$678$	−7.22383	+	50.2428i	−0.277429	+	1.92956i
$679$	1.68164	−	11.6961i	0.0645354	−	0.448854i
$680$	−2.56095	−	1.64582i	−0.0982080	−	0.0631145i
$681$	−10.3033	−	11.8906i	−0.394823	−	0.455651i
$682$	0.390990	+	0.856149i	0.0149718	+	0.0327836i
$683$	−15.0040	+	9.64246i	−0.574111	+	0.368959i	−0.795248	−	0.606284i	$-0.792659\pi$
$683$	−15.0040	+	9.64246i	−0.574111	+	0.368959i	0.221137	+	0.975243i	$0.429023\pi$
$684$	54.9564	+	16.1367i	2.10131	+	0.617000i
$685$	−10.6451	+	12.2851i	−0.406729	+	0.469391i
$686$	−2.73153	+	0.802051i	−0.104290	+	0.0306224i
$687$	−31.5514	+	69.0880i	−1.20376	+	2.63587i
$688$	2.54838	+	17.7244i	0.0971560	+	0.675735i
$689$	−1.69313			−0.0645030
$690$	−20.0899	−	21.9687i	−0.764809	−	0.836335i
$691$	−44.0919			−1.67734			−0.838668	−	0.544642i	$-0.816665\pi$
$691$	−44.0919			−1.67734			−0.838668	+	0.544642i	$0.816665\pi$
$692$	1.06203	+	7.38661i	0.0403725	+	0.280797i
$693$	0.753268	−	1.64943i	0.0286143	−	0.0626565i
$694$	−24.4546	+	7.18053i	−0.928285	+	0.272569i
$695$	−8.54541	+	9.86193i	−0.324146	+	0.374084i
$696$	−0.931039	−	0.273378i	−0.0352909	−	0.0103624i
$697$	−9.71102	+	6.24089i	−0.367831	+	0.236391i
$698$	7.68862	+	16.8357i	0.291019	+	0.637242i
$699$	25.4920	+	29.4193i	0.964196	+	1.11274i
$700$	5.21935	+	3.35427i	0.197273	+	0.126780i
$701$	−2.71568	+	18.8880i	−0.102570	+	0.713389i	0.872033	+	0.489447i	$0.162801\pi$
$701$	−2.71568	+	18.8880i	−0.102570	+	0.713389i	−0.974603	+	0.223941i	$0.928108\pi$
$702$	−1.85234	+	12.8833i	−0.0699122	+	0.486250i
$703$	13.4429	+	8.63923i	0.507009	+	0.325835i
$704$	0.228264	+	0.263431i	0.00860304	+	0.00992844i
$705$	0.835243	+	1.82893i	0.0314571	+	0.0688813i
$706$	29.2591	−	18.8037i	1.10118	−	0.707686i
$707$	−63.6785	−	18.6977i	−2.39487	−	0.703199i
$708$	18.9071	−	21.8199i	0.710572	−	0.820044i
$709$	35.5903	−	10.4503i	1.33662	−	0.392468i	0.466160	−	0.884701i	$-0.345637\pi$
$709$	35.5903	−	10.4503i	1.33662	−	0.392468i	0.870464	+	0.492233i	$0.163819\pi$
$710$	−8.55476	+	18.7323i	−0.321055	+	0.703011i
$711$	3.13848	+	21.8286i	0.117702	+	0.818635i
$712$	4.36618			0.163629
$713$	29.5064	−	20.0980i	1.10502	−	0.752675i
$714$	114.369			4.28017
$715$	0.00440494	+	0.0306370i	0.000164735	+	0.00114576i
$716$	12.6138	−	27.6204i	0.471400	−	1.03222i
$717$	−46.2825	+	13.5898i	−1.72845	+	0.507520i
$718$	21.7311	−	25.0790i	0.810996	−	0.935939i
$719$	−7.06446	−	2.07431i	−0.263460	−	0.0773588i	0.147335	−	0.989087i	$-0.452930\pi$
$719$	−7.06446	−	2.07431i	−0.263460	−	0.0773588i	−0.410795	+	0.911728i	$0.634749\pi$
$720$	28.4685	−	18.2956i	1.06096	−	0.681836i
$721$	0.296857	+	0.650027i	0.0110555	+	0.0242083i
$722$	2.26795	+	2.61735i	0.0844043	+	0.0974078i
$723$	−47.5214	−	30.5401i	−1.76734	−	1.13580i
$724$	2.63053	−	18.2958i	0.0977630	−	0.679957i
$725$	0.0700702	−	0.487349i	0.00260234	−	0.0180997i
$726$	−57.4192	−	36.9011i	−2.13103	−	1.36953i
$727$	−19.0728	−	22.0111i	−0.707370	−	0.816348i	0.282359	−	0.959309i	$-0.408883\pi$
$727$	−19.0728	−	22.0111i	−0.707370	−	0.816348i	−0.989728	+	0.142961i	$0.954338\pi$
$728$	0.438444	+	0.960059i	0.0162498	+	0.0355821i
$729$	34.7827	−	22.3535i	1.28825	−	0.827906i
$730$	−27.3574	−	8.03286i	−1.01254	−	0.297309i
$731$	−12.9221	+	14.9129i	−0.477940	+	0.551572i
$732$	−53.3632	+	15.6688i	−1.97236	+	0.579137i
$733$	15.2614	−	33.4179i	0.563693	−	1.23432i	−0.386394	−	0.922334i	$-0.626280\pi$
$733$	15.2614	−	33.4179i	0.563693	−	1.23432i	0.950088	−	0.311983i	$-0.100993\pi$
$734$	5.16984	+	35.9570i	0.190822	+	1.32720i
$735$	21.3417			0.787200
$736$	22.7656	−	27.7390i	0.839151	−	1.02247i
$737$	−0.0918559			−0.00338356
$738$	−4.70901	−	32.7519i	−0.173341	−	1.20561i
$739$	−8.68215	+	19.0113i	−0.319378	+	0.699340i	−0.999428	−	0.0338257i	$-0.989231\pi$
$739$	−8.68215	+	19.0113i	−0.319378	+	0.699340i	0.680050	+	0.733166i	$0.261958\pi$
$740$	−5.65567	+	1.66065i	−0.207906	+	0.0610468i
$741$	−4.53900	+	5.23829i	−0.166744	+	0.192433i
$742$	−24.4705	−	7.18517i	−0.898339	−	0.263776i
$743$	39.8130	−	25.5863i	1.46060	−	0.938669i	0.461938	−	0.886912i	$-0.347154\pi$
$743$	39.8130	−	25.5863i	1.46060	−	0.938669i	0.998660	−	0.0517567i	$-0.0164820\pi$
$744$	6.09453	+	13.3452i	0.223436	+	0.489258i
$745$	10.2248	+	11.8001i	0.374609	+	0.432321i
$746$	−51.5672	−	33.1402i	−1.88801	−	1.21335i
$747$	5.71716	−	39.7638i	0.209180	−	1.45488i
$748$	−0.0788264	+	0.548250i	−0.00288218	+	0.0200460i
$749$	−24.7295	−	15.8927i	−0.903595	−	0.580705i
$750$	4.06497	+	4.69123i	0.148432	+	0.171300i
$751$	−1.54832	−	3.39034i	−0.0564989	−	0.123715i	0.879277	−	0.476311i	$-0.158026\pi$
$751$	−1.54832	−	3.39034i	−0.0564989	−	0.123715i	−0.935776	+	0.352596i	$0.885299\pi$
$752$	−2.37093	+	1.52371i	−0.0864591	+	0.0555639i
$753$	−0.787502	−	0.231232i	−0.0286982	−	0.00842655i
$754$	−0.290668	+	0.335449i	−0.0105855	+	0.0122163i
$755$	−6.13025	+	1.80000i	−0.223103	+	0.0655089i
$756$	−37.2115	+	81.4819i	−1.35337	+	2.96347i
$757$	−7.03396	−	48.9223i	−0.255654	−	1.77811i	−0.562944	−	0.826495i	$-0.690331\pi$
$757$	−7.03396	−	48.9223i	−0.255654	−	1.77811i	0.307290	−	0.951616i	$-0.400578\pi$
$758$	−27.0653			−0.983056
$759$	0.399573	−	0.940770i	0.0145036	−	0.0341478i
$760$	2.77899			0.100805
$761$	6.58379	+	45.7913i	0.238662	+	1.65993i	0.658685	+	0.752419i	$0.271113\pi$
$761$	6.58379	+	45.7913i	0.238662	+	1.65993i	−0.420023	+	0.907514i	$0.637978\pi$
$762$	6.15251	−	13.4721i	0.222882	−	0.488043i
$763$	60.1602	−	17.6646i	2.17795	−	0.639503i
$764$	10.5209	−	12.1418i	0.380633	−	0.439274i
$765$	35.7807	+	10.5062i	1.29365	+	0.379851i
$766$	62.4546	−	40.1371i	2.25658	−	1.45021i
$767$	1.03528	+	2.26695i	0.0373818	+	0.0818546i
$768$	41.9770	+	48.4440i	1.51471	+	1.74807i
$769$	20.0315	+	12.8735i	0.722354	+	0.464229i	0.849455	−	0.527661i	$-0.176931\pi$
$769$	20.0315	+	12.8735i	0.722354	+	0.464229i	−0.127101	+	0.991890i	$0.540567\pi$
$770$	−0.0663515	+	0.461485i	−0.00239114	+	0.0166308i
$771$	0.757519	−	5.26866i	0.0272814	−	0.189746i
$772$	1.72678	+	1.10973i	0.0621481	+	0.0399402i
$773$	16.0574	+	18.5313i	0.577546	+	0.666523i	0.967075	−	0.254491i	$-0.0819079\pi$
$773$	16.0574	+	18.5313i	0.577546	+	0.666523i	−0.389530	+	0.921014i	$0.627362\pi$
$774$	−23.4967	−	51.4506i	−0.844572	−	1.84935i
$775$	−6.26242	+	4.02461i	−0.224953	+	0.144568i
$776$	1.87326	+	0.550039i	0.0672461	+	0.0197452i
$777$	−27.3655	+	31.5815i	−0.981733	+	1.13298i
$778$	−23.0120	+	6.75694i	−0.825021	+	0.242248i
$779$	4.37756	−	9.58553i	0.156843	−	0.343437i
$780$	−0.363863	−	2.53072i	−0.0130284	−	0.0906144i
$781$	−0.707050			−0.0253002
$782$	45.9673	−	1.23026i	1.64379	−	0.0439939i
$783$	7.10868			0.254043
$784$	4.25737	+	29.6106i	0.152049	+	1.05752i
$785$	−2.58683	+	5.66437i	−0.0923279	+	0.202170i
$786$	−59.6975	+	17.5288i	−2.12934	+	0.625230i
$787$	18.0140	−	20.7893i	0.642130	−	0.741057i	−0.337620	−	0.941282i	$-0.609622\pi$
$787$	18.0140	−	20.7893i	0.642130	−	0.741057i	0.979750	+	0.200225i	$0.0641673\pi$
$788$	9.26181	+	2.71951i	0.329938	+	0.0968786i
$789$	−54.9888	+	35.3391i	−1.95765	+	1.25811i
$790$	−2.35550	−	5.15784i	−0.0838051	−	0.183508i
$791$	−19.7465	−	22.7887i	−0.702104	−	0.810272i
$792$	0.252039	+	0.161975i	0.00895581	+	0.00575555i
$793$	0.683203	−	4.75178i	0.0242613	−	0.168741i
$794$	−4.53389	+	31.5339i	−0.160902	+	1.11910i
$795$	−9.80753	−	6.30292i	−0.347837	−	0.223542i
$796$	−3.83917	−	4.43063i	−0.136076	−	0.157040i
$797$	−5.59408	−	12.2493i	−0.198152	−	0.433893i	0.784306	−	0.620374i	$-0.213019\pi$
$797$	−5.59408	−	12.2493i	−0.198152	−	0.433893i	−0.982459	+	0.186481i	$0.940292\pi$
$798$	−87.8313	+	56.4458i	−3.10919	+	1.99816i
$799$	−2.97991	−	0.874982i	−0.105422	−	0.0309546i
$800$	−4.90000	+	5.65490i	−0.173241	+	0.199931i
$801$	−51.3187	+	15.0685i	−1.81326	+	0.532420i
$802$	−16.9964	+	37.2168i	−0.600162	+	1.31417i
$803$	−0.139318	−	0.968978i	−0.00491643	−	0.0341945i
$804$	7.58761			0.267594
$805$	17.6783	−	0.473138i	0.623079	−	0.0166759i
$806$	6.71090			0.236381
$807$	−1.91595	−	13.3257i	−0.0674445	−	0.469087i
$808$	4.55519	−	9.97447i	0.160251	−	0.350901i
$809$	−3.90844	+	1.14762i	−0.137413	+	0.0403482i	−0.349716	−	0.936856i	$-0.613722\pi$
$809$	−3.90844	+	1.14762i	−0.137413	+	0.0403482i	0.212303	+	0.977204i	$0.431904\pi$
$810$	−30.5528	+	35.2598i	−1.07351	+	1.23890i
$811$	32.3390	+	9.49559i	1.13558	+	0.333435i	0.794897	−	0.606744i	$-0.207525\pi$
$811$	32.3390	+	9.49559i	1.13558	+	0.333435i	0.340679	+	0.940180i	$0.389343\pi$
$812$	−2.56980	+	1.65151i	−0.0901823	+	0.0579566i
$813$	−16.3569	−	35.8166i	−0.573661	−	1.25614i
$814$	−0.290070	−	0.334758i	−0.0101669	−	0.0117333i
$815$	20.1849	+	12.9721i	0.707046	+	0.454391i
$816$	−10.4293	+	72.5373i	−0.365098	+	2.53932i
$817$	2.56357	−	17.8301i	0.0896881	−	0.623795i
$818$	3.91159	+	2.51383i	0.136766	+	0.0878939i
$819$	−8.46669	−	9.77108i	−0.295850	−	0.341429i
$820$	1.61476	+	3.53583i	0.0563899	+	0.123477i
$821$	6.31723	−	4.05983i	0.220473	−	0.141689i	−0.425743	−	0.904844i	$-0.639987\pi$
$821$	6.31723	−	4.05983i	0.220473	−	0.141689i	0.646215	+	0.763155i	$0.276351\pi$
$822$	96.8172	+	28.4281i	3.37689	+	0.991543i
$823$	27.9980	−	32.3114i	0.975947	−	1.12630i	−0.0160281	−	0.999872i	$-0.505102\pi$
$823$	27.9980	−	32.3114i	0.975947	−	1.12630i	0.991975	−	0.126432i	$-0.0403524\pi$
$824$	−0.113287	+	0.0332641i	−0.00394655	+	0.00115881i
$825$	−0.0885351	+	0.193865i	−0.00308240	+	0.00674951i
$826$	5.34240	+	37.1572i	0.185886	+	1.29286i
$827$	−24.7662			−0.861205			−0.430603	−	0.902542i	$-0.641699\pi$
$827$	−24.7662			−0.861205			−0.430603	+	0.902542i	$0.641699\pi$
$828$	−23.5428	+	55.4301i	−0.818169	+	1.92633i
$829$	−29.4928			−1.02433			−0.512164	−	0.858888i	$-0.671156\pi$
$829$	−29.4928			−1.02433			−0.512164	+	0.858888i	$0.671156\pi$
$830$	1.46999	+	10.2240i	0.0510241	+	0.354880i
$831$	0.798926	−	1.74940i	0.0277144	−	0.0606862i
$832$	2.38467	−	0.700203i	0.0826736	−	0.0242752i
$833$	−21.5879	+	24.9137i	−0.747975	+	0.863209i
$834$	77.7204	+	22.8208i	2.69124	+	0.790218i
$835$	−10.2802	+	6.60666i	−0.355760	+	0.228633i
$836$	−0.210047	−	0.459939i	−0.00726462	−	0.0159073i
$837$	−70.3834	−	81.2268i	−2.43281	−	2.80761i
$838$	44.1322	+	28.3620i	1.52452	+	0.979750i
$839$	6.11419	−	42.5251i	0.211085	−	1.46813i	−0.558457	−	0.829533i	$-0.688606\pi$
$839$	6.11419	−	42.5251i	0.211085	−	1.46813i	0.769542	−	0.638596i	$-0.220484\pi$
$840$	−1.03425	+	7.19337i	−0.0356850	+	0.248195i
$841$	−24.1924	−	15.5475i	−0.834221	−	0.536121i
$842$	−39.6583	−	45.7681i	−1.36671	−	1.57727i
$843$	29.0884	+	63.6947i	1.00186	+	2.19376i
$844$	−34.8498	+	22.3966i	−1.19958	+	0.770923i
$845$	−12.2617	−	3.60035i	−0.421814	−	0.123856i
$846$	5.82979	−	6.72793i	0.200432	−	0.231311i
$847$	38.9041	−	11.4233i	1.33676	−	0.392509i
$848$	6.78855	−	14.8649i	0.233120	−	0.510461i
$849$	3.61581	+	25.1485i	0.124094	+	0.863095i
$850$	−9.58827			−0.328875
$851$	−10.6590	+	12.9876i	−0.365386	+	0.445208i
$852$	58.4047			2.00091
$853$	−1.09693	−	7.62929i	−0.0375581	−	0.261222i	0.962387	−	0.271681i	$-0.0875797\pi$
$853$	−1.09693	−	7.62929i	−0.0375581	−	0.261222i	−0.999945	+	0.0104594i	$0.996671\pi$
$854$	30.0395	−	65.7773i	1.02793	−	2.25085i
$855$	−32.6634	+	9.59084i	−1.11706	+	0.328000i
$856$	3.18061	−	3.67062i	0.108711	−	0.125459i
$857$	43.1165	+	12.6602i	1.47283	+	0.432463i	0.917019	−	0.398844i	$-0.130589\pi$
$857$	43.1165	+	12.6602i	1.47283	+	0.432463i	0.555814	+	0.831307i	$0.312407\pi$
$858$	0.161631	−	0.103874i	0.00551800	−	0.00354620i
$859$	−7.34953	−	16.0932i	−0.250763	−	0.549094i	0.741829	−	0.670589i	$-0.233958\pi$
$859$	−7.34953	−	16.0932i	−0.250763	−	0.549094i	−0.992592	+	0.121495i	$0.961231\pi$
$860$	4.35132	+	5.02169i	0.148379	+	0.171238i
$861$	23.1828	+	14.8987i	0.790068	+	0.507746i
$862$	2.21429	−	15.4007i	0.0754190	−	0.524551i
$863$	−0.796091	+	5.53693i	−0.0270992	+	0.188479i	−0.998875	−	0.0474287i	$-0.984897\pi$
$863$	−0.796091	+	5.53693i	−0.0270992	+	0.188479i	0.971775	+	0.235908i	$0.0758064\pi$
$864$	−90.8824	−	58.4066i	−3.09188	−	1.98703i
$865$	−2.90456	−	3.35204i	−0.0987580	−	0.113973i
$866$	−9.75689	−	21.3646i	−0.331553	−	0.725999i
$867$	−21.6754	+	13.9299i	−0.736136	+	0.473086i
$868$	44.3146	+	13.0119i	1.50414	+	0.441654i
$869$	0.127490	−	0.147131i	0.00432479	−	0.00499108i
$870$	−2.93247	+	0.861051i	−0.0994200	+	0.0291924i
$871$	−0.272074	+	0.595758i	−0.00921887	+	0.0201865i
$872$	1.47432	+	10.2541i	0.0499267	+	0.347248i
$873$	−23.9160			−0.809435
$874$	−34.6939	+	23.6314i	−1.17354	+	0.799345i
$875$	−3.68750			−0.124660
$876$	11.5081	+	80.0409i	0.388824	+	2.70433i
$877$	−12.4845	+	27.3372i	−0.421571	+	0.923111i	0.573049	+	0.819521i	$0.305760\pi$
$877$	−12.4845	+	27.3372i	−0.421571	+	0.923111i	−0.994620	+	0.103590i	$0.966967\pi$
$878$	−17.0769	+	5.01422i	−0.576316	+	0.169222i
$879$	34.9163	−	40.2955i	1.17770	−	1.35913i
$880$	−0.286640	−	0.0841652i	−0.00966264	−	0.00283721i
$881$	−11.7284	+	7.53738i	−0.395139	+	0.253941i	−0.723090	−	0.690754i	$-0.757279\pi$
$881$	−11.7284	+	7.53738i	−0.395139	+	0.253941i	0.327950	+	0.944695i	$0.393642\pi$
$882$	−39.2540	−	85.9544i	−1.32175	−	2.89423i
$883$	−6.77774	−	7.82193i	−0.228089	−	0.263229i	0.630156	−	0.776468i	$-0.282991\pi$
$883$	−6.77774	−	7.82193i	−0.228089	−	0.263229i	−0.858246	+	0.513239i	$0.828445\pi$
$884$	3.32235	+	2.13515i	0.111743	+	0.0718128i
$885$	−2.44213	+	16.9854i	−0.0820913	+	0.570958i
$886$	2.16634	−	15.0672i	0.0727795	−	0.506192i
$887$	−29.4128	−	18.9025i	−0.987587	−	0.634683i	−0.0560870	−	0.998426i	$-0.517862\pi$
$887$	−29.4128	−	18.9025i	−0.987587	−	0.634683i	−0.931500	+	0.363743i	$0.881499\pi$
$888$	−4.52144	−	5.21802i	−0.151730	−	0.175105i
$889$	3.65490	+	8.00312i	0.122582	+	0.268416i
$890$	11.5690	−	7.43492i	0.387792	−	0.249219i
$891$	−1.53698	−	0.451297i	−0.0514907	−	0.0151190i
$892$	2.33430	−	2.69393i	0.0781582	−	0.0901994i
$893$	2.72030	−	0.798751i	0.0910313	−	0.0267292i
$894$	40.2622	−	88.1620i	1.34657	−	2.94858i
$895$	2.56837	+	17.8634i	0.0858511	+	0.597108i
$896$	−17.7469			−0.592881
$897$	−4.91812	−	5.37807i	−0.164211	−	0.179569i
$898$	3.42170			0.114184
$899$	−0.521613	−	3.62790i	−0.0173968	−	0.120997i
$900$	5.21648	−	11.4225i	0.173883	−	0.380750i
$901$	17.2785	−	5.07343i	0.575631	−	0.169020i
$902$	−0.191287	+	0.220757i	−0.00636917	+	0.00735042i
$903$	45.1987	+	13.2715i	1.50412	+	0.441649i
$904$	4.19123	−	2.69354i	0.139398	−	0.0895858i
$905$	4.56372	+	9.99315i	0.151703	+	0.332184i
$906$	25.9713	+	29.9725i	0.862840	+	0.995770i
$907$	44.1855	+	28.3963i	1.46716	+	0.942885i	0.998219	+	0.0596534i	$0.0189995\pi$
$907$	44.1855	+	28.3963i	1.46716	+	0.942885i	0.468938	+	0.883231i	$0.344637\pi$
$908$	1.16466	−	8.10036i	0.0386505	−	0.268820i
$909$	−19.1164	+	132.958i	−0.634052	+	4.40993i
$910$	2.79656	+	1.79724i	0.0927052	+	0.0595780i
$911$	−1.67941	−	1.93814i	−0.0556412	−	0.0642134i	0.727247	−	0.686376i	$-0.240800\pi$
$911$	−1.67941	−	1.93814i	−0.0556412	−	0.0642134i	−0.782888	+	0.622163i	$0.786254\pi$
$912$	−27.7907	−	60.8531i	−0.920242	−	2.01505i
$913$	−0.298342	+	0.191733i	−0.00987369	+	0.00634544i
$914$	−49.2203	−	14.4524i	−1.62806	−	0.478042i
$915$	21.6467	−	24.9816i	0.715618	−	0.825868i
$916$	−37.9052	+	11.1300i	−1.25242	+	0.367744i
$917$	15.3539	−	33.6205i	0.507032	−	1.11025i
$918$	−19.7014	−	137.026i	−0.650242	−	4.52253i
$919$	−32.2260			−1.06304			−0.531519	−	0.847046i	$-0.678379\pi$
$919$	−32.2260			−1.06304			−0.531519	+	0.847046i	$0.678379\pi$
$920$	−0.338307	+	2.90228i	−0.0111537	+	0.0956853i
$921$	−58.7930			−1.93730
$922$	7.49514	+	52.1299i	0.246839	+	1.71681i
$923$	−2.09426	+	4.58578i	−0.0689333	+	0.150943i
$924$	1.26872	−	0.372529i	0.0417377	−	0.0122553i
$925$	2.29422	−	2.64767i	0.0754333	−	0.0870547i
$926$	−37.9022	−	11.1291i	−1.24554	−	0.365725i
$927$	1.21674	−	0.781953i	0.0399631	−	0.0256827i
$928$	−1.53043	−	3.35116i	−0.0502387	−	0.110007i
$929$	18.4300	+	21.2694i	0.604670	+	0.697826i	0.972721	−	0.231980i	$-0.0745202\pi$
$929$	18.4300	+	21.2694i	0.604670	+	0.697826i	−0.368051	+	0.929806i	$0.619975\pi$
$930$	38.8733	+	24.9823i	1.27471	+	0.819203i
$931$	4.28275	−	29.7872i	0.140362	−	0.976236i
$932$	−2.88154	+	20.0416i	−0.0943880	+	0.656483i
$933$	−22.9031	−	14.7190i	−0.749815	−	0.481877i
$934$	−44.4081	−	51.2497i	−1.45308	−	1.67694i
$935$	−0.136756	−	0.299454i	−0.00447241	−	0.00979320i
$936$	1.79707	−	1.15491i	0.0587390	−	0.0377493i
$937$	42.4492	+	12.4642i	1.38676	+	0.407188i	0.888115	−	0.459621i	$-0.152015\pi$
$937$	42.4492	+	12.4642i	1.38676	+	0.407188i	0.498640	+	0.866809i	$0.333833\pi$
$938$	−6.46047	+	7.45578i	−0.210942	+	0.243440i
$939$	−1.86394	+	0.547302i	−0.0608274	+	0.0178605i
$940$	−0.434443	+	0.951297i	−0.0141700	+	0.0310279i
$941$	1.64965	+	11.4736i	0.0537771	+	0.374028i	0.998883	+	0.0472625i	$0.0150497\pi$
$941$	1.64965	+	11.4736i	0.0537771	+	0.374028i	−0.945105	+	0.326766i	$0.894041\pi$
$942$	38.6540			1.25942
$943$	9.47788	+	5.73869i	0.308642	+	0.186878i
$944$	−24.0536			−0.782879
$945$	−7.57685	−	52.6981i	−0.246475	−	1.71427i
$946$	−0.207427	+	0.454201i	−0.00674403	+	0.0147674i
$947$	35.2658	−	10.3550i	1.14598	−	0.336491i	0.347013	−	0.937860i	$-0.387196\pi$
$947$	35.2658	−	10.3550i	1.14598	−	0.336491i	0.798971	+	0.601369i	$0.205378\pi$
$948$	−10.5311	+	12.1535i	−0.342034	+	0.394728i
$949$	−6.69725	−	1.96649i	−0.217402	−	0.0638350i
$950$	7.36342	−	4.73218i	0.238901	−	0.153532i
$951$	23.9511	+	52.4456i	0.776667	+	1.70066i
$952$	−7.35116	−	8.48369i	−0.238253	−	0.274958i
$953$	2.05931	+	1.32344i	0.0667076	+	0.0428704i	0.573570	−	0.819157i	$-0.305558\pi$
$953$	2.05931	+	1.32344i	0.0667076	+	0.0428704i	−0.506862	+	0.862027i	$0.669195\pi$
$954$	−7.34609	+	51.0932i	−0.237839	+	1.65420i
$955$	−1.35893	+	9.45158i	−0.0439740	+	0.305846i
$956$	−21.1068	−	13.5645i	−0.682642	−	0.438708i
$957$	−0.0687171	−	0.0793038i	−0.00222131	−	0.00256353i
$958$	31.0594	+	68.0107i	1.00348	+	2.19733i
$959$	−50.4268	+	32.4073i	−1.62837	+	1.04649i
$960$	16.4200	+	4.82133i	0.529952	+	0.155608i
$961$	−15.9887	+	18.4520i	−0.515765	+	0.595225i
$962$	−3.03035	+	0.889790i	−0.0977023	+	0.0286880i
$963$	−24.7159	+	54.1202i	−0.796458	+	1.74400i
$964$	−4.18150	−	29.0830i	−0.134677	−	0.936699i
$965$	−1.21998			−0.0392726
$966$	−48.2576	−	98.5995i	−1.55266	−	3.17239i
$967$	1.16638			0.0375083			0.0187541	−	0.999824i	$-0.494030\pi$
$967$	1.16638			0.0375083			0.0187541	+	0.999824i	$0.494030\pi$
$968$	0.953405	+	6.63108i	0.0306436	+	0.213131i
$969$	30.6245	−	67.0583i	0.983800	−	2.15422i
$970$	5.90016	−	1.73244i	0.189443	−	0.0556254i
$971$	30.5983	−	35.3123i	0.981945	−	1.13322i	−0.00913566	−	0.999958i	$-0.502908\pi$
$971$	30.5983	−	35.3123i	0.981945	−	1.13322i	0.991080	−	0.133266i	$-0.0425465\pi$
$972$	57.0356	+	16.7472i	1.82942	+	0.537166i
$973$	−40.4803	+	26.0151i	−1.29774	+	0.834006i
$974$	11.6580	+	25.5274i	0.373545	+	0.817949i
$975$	0.995129	+	1.14844i	0.0318696	+	0.0367795i
$976$	38.9791	+	25.0504i	1.24769	+	0.801843i
$977$	3.65669	−	25.4328i	0.116988	−	0.813669i	−0.843854	−	0.536572i	$-0.819719\pi$
$977$	3.65669	−	25.4328i	0.116988	−	0.813669i	0.960842	−	0.277096i	$-0.0893721\pi$
$978$	21.1962	−	147.423i	0.677781	−	4.71407i
$979$	0.397208	+	0.255270i	0.0126948	+	0.00815848i
$980$	7.26939	+	8.38932i	0.232212	+	0.267987i
$981$	−52.7176	−	115.435i	−1.68314	−	3.68557i
$982$	46.5124	−	29.8917i	1.48427	−	0.953883i
$983$	21.6881	+	6.36821i	0.691744	+	0.203114i	0.608664	−	0.793428i	$-0.291706\pi$
$983$	21.6881	+	6.36821i	0.691744	+	0.203114i	0.0830806	+	0.996543i	$0.473524\pi$
$984$	−2.98168	+	3.44104i	−0.0950525	+	0.109696i
$985$	−5.50477	+	1.61635i	−0.175396	+	0.0515010i
$986$	1.96113	−	4.29427i	0.0624550	−	0.136757i
$987$	1.05515	+	7.33871i	0.0335857	+	0.233594i
$988$	−3.60522			−0.114697
$989$	18.3090	+	4.84789i	0.582192	+	0.154154i
$990$	0.943640			0.0299909
$991$	−8.41506	−	58.5280i	−0.267313	−	1.85920i	−0.473636	−	0.880721i	$-0.657059\pi$
$991$	−8.41506	−	58.5280i	−0.267313	−	1.85920i	0.206323	−	0.978484i	$-0.433850\pi$
$992$	−23.1390	+	50.6674i	−0.734664	+	1.60869i
$993$	−46.8660	+	13.7611i	−1.48725	+	0.436695i
$994$	−49.7287	+	57.3900i	−1.57730	+	1.82030i
$995$	3.34328	+	0.981676i	0.105989	+	0.0311212i
$996$	24.6441	−	15.8378i	0.780878	−	0.501840i
$997$	23.5652	+	51.6005i	0.746316	+	1.63421i	0.772875	+	0.634558i	$0.218818\pi$
$997$	23.5652	+	51.6005i	0.746316	+	1.63421i	−0.0265590	+	0.999647i	$0.508455\pi$
$998$	10.2878	+	11.8728i	0.325656	+	0.375827i
$999$	42.5518	+	27.3464i	1.34628	+	0.865201i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.b.26.1	✓	20
5.2	odd	4		575.2.p.c.49.2		40
5.3	odd	4		575.2.p.c.49.3		40
5.4	even	2		575.2.k.c.26.2		20
23.8	even	11	inner	115.2.g.b.31.1	yes	20
23.10	odd	22		2645.2.a.u.1.1		10
23.13	even	11		2645.2.a.t.1.1		10
115.8	odd	44		575.2.p.c.399.2		40
115.54	even	22		575.2.k.c.376.2		20
115.77	odd	44		575.2.p.c.399.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.b.26.1	✓	20	1.1	even	1	trivial
115.2.g.b.31.1	yes	20	23.8	even	11	inner
575.2.k.c.26.2		20	5.4	even	2
575.2.k.c.376.2		20	115.54	even	22
575.2.p.c.49.2		40	5.2	odd	4
575.2.p.c.49.3		40	5.3	odd	4
575.2.p.c.399.2		40	115.8	odd	44
575.2.p.c.399.3		40	115.77	odd	44
2645.2.a.t.1.1		10	23.13	even	11
2645.2.a.u.1.1		10	23.10	odd	22

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.273100 + 1.89945i) q^{2} +(-1.34375 + 2.94241i) q^{3} +(-1.61435 + 0.474017i) q^{4} +(0.654861 - 0.755750i) q^{5} +(-5.95594 - 1.74882i) q^{6} +(3.10213 - 1.99362i) q^{7} +(0.253098 + 0.554206i) q^{8} +(-4.88751 - 5.64048i) q^{9} +O(q^{10})\)	\(q+(0.273100 + 1.89945i) q^{2} +(-1.34375 + 2.94241i) q^{3} +(-1.61435 + 0.474017i) q^{4} +(0.654861 - 0.755750i) q^{5} +(-5.95594 - 1.74882i) q^{6} +(3.10213 - 1.99362i) q^{7} +(0.253098 + 0.554206i) q^{8} +(-4.88751 - 5.64048i) q^{9} +(1.61435 + 1.03748i) q^{10} +(-0.00937662 + 0.0652158i) q^{11} +(0.774540 - 5.38705i) q^{12} +(0.395203 + 0.253982i) q^{13} +(4.63397 + 5.34789i) q^{14} +(1.34375 + 2.94241i) q^{15} +(-3.81440 + 2.45137i) q^{16} +(-4.79414 - 1.40769i) q^{17} +(9.37906 - 10.8240i) q^{18} +(4.37646 - 1.28504i) q^{19} +(-0.698939 + 1.53046i) q^{20} +(1.69754 + 11.8066i) q^{21} -0.126435 q^{22} +(0.809276 + 4.72706i) q^{23} -1.97080 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-0.374496 + 0.820033i) q^{26} +(13.8531 - 4.06764i) q^{27} +(-4.06292 + 4.68886i) q^{28} +(0.472416 + 0.138714i) q^{29} +(-5.22199 + 3.35597i) q^{30} +(-3.09241 - 6.77144i) q^{31} +(-4.90000 - 5.65490i) q^{32} +(-0.179292 - 0.115224i) q^{33} +(1.36455 - 9.49068i) q^{34} +(0.524787 - 3.64997i) q^{35} +(10.5639 + 6.78897i) q^{36} +(2.29422 + 2.64767i) q^{37} +(3.63609 + 7.96193i) q^{38} +(-1.27837 + 0.821560i) q^{39} +(0.584585 + 0.171650i) q^{40} +(1.51293 - 1.74601i) q^{41} +(-21.9626 + 6.44879i) q^{42} +(1.64058 - 3.59236i) q^{43} +(-0.0157762 - 0.109726i) q^{44} -7.46343 q^{45} +(-8.75781 + 2.82814i) q^{46} +0.621575 q^{47} +(-2.08731 - 14.5175i) q^{48} +(2.74078 - 6.00147i) q^{49} +(1.84125 - 0.540641i) q^{50} +(10.5841 - 12.2147i) q^{51} +(-0.758389 - 0.222683i) q^{52} +(-3.03196 + 1.94852i) q^{53} +(11.5096 + 25.2025i) q^{54} +(0.0431465 + 0.0497937i) q^{55} +(1.89002 + 1.21464i) q^{56} +(-2.09975 + 14.6041i) q^{57} +(-0.134464 + 0.935215i) q^{58} +(4.46281 + 2.86808i) q^{59} +(-3.56404 - 4.11312i) q^{60} +(-4.24510 - 9.29548i) q^{61} +(12.0175 - 7.72318i) q^{62} +(-26.4066 - 7.75368i) q^{63} +(3.46451 - 3.99826i) q^{64} +(0.450750 - 0.132352i) q^{65} +(0.169898 - 0.372024i) q^{66} +(0.198409 + 1.37996i) q^{67} +8.40670 q^{68} +(-14.9964 - 3.97077i) q^{69} +7.07627 q^{70} +(1.52723 + 10.6221i) q^{71} +(1.88898 - 4.13628i) q^{72} +(-14.2562 + 4.18599i) q^{73} +(-4.40257 + 5.08083i) q^{74} +(3.10369 + 0.911327i) q^{75} +(-6.45602 + 4.14903i) q^{76} +(0.100928 + 0.221001i) q^{77} +(-1.90964 - 2.20384i) q^{78} +(-2.48575 - 1.59749i) q^{79} +(-0.645282 + 4.48803i) q^{80} +(-3.46003 + 24.0650i) q^{81} +(3.72965 + 2.39690i) q^{82} +(3.52485 + 4.06790i) q^{83} +(-8.33698 - 18.2554i) q^{84} +(-4.20335 + 2.70133i) q^{85} +(7.27157 + 2.13513i) q^{86} +(-1.04296 + 1.20364i) q^{87} +(-0.0385162 + 0.0113094i) q^{88} +(2.97699 - 6.51870i) q^{89} +(-2.03826 - 14.1764i) q^{90} +1.73231 q^{91} +(-3.54716 - 7.24753i) q^{92} +24.0798 q^{93} +(0.169752 + 1.18065i) q^{94} +(1.89480 - 4.14903i) q^{95} +(23.2234 - 6.81901i) q^{96} +(2.09845 - 2.42174i) q^{97} +(12.1480 + 3.56698i) q^{98} +(0.413677 - 0.265854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * q^99

Introduction

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