LMFDB - Embedded newform 117.2.t.c.103.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(25,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("117.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.t (of order $6$, degree $2$, 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
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} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 $ x^20 - 6x^16 + 9x^14 + 54x^12 + 81x^10 + 486x^8 + 729x^6 - 4374*x^4 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.2
Root			$-1.23798 - 1.21137i$ of defining polynomial
Character	$\chi$	$=$	117.103
Dual form			117.2.t.c.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.97712 + 1.14149i) q^{2} +(0.833228 + 1.51846i) q^{3} +(1.60600 - 2.78168i) q^{4} +(2.78501 + 1.60793i) q^{5} +(-3.38070 - 2.05106i) q^{6} +(2.09815 - 1.21137i) q^{7} +2.76698i q^{8} +(-1.61146 + 2.53045i) q^{9} -7.34174 q^{10} +(-1.27730 + 0.737448i) q^{11} +(5.56204 + 0.120883i) q^{12} +(-2.24652 - 2.82013i) q^{13} +(-2.76553 + 4.79003i) q^{14} +(-0.121028 + 5.56871i) q^{15} +(0.0535232 + 0.0927049i) q^{16} -5.12974 q^{17} +(0.297563 - 6.84248i) q^{18} +1.13065i q^{19} +(8.94547 - 5.16467i) q^{20} +(3.58765 + 2.17662i) q^{21} +(1.68358 - 2.91604i) q^{22} +(4.61735 - 7.99748i) q^{23} +(-4.20155 + 2.30552i) q^{24} +(2.67087 + 4.62608i) q^{25} +(7.66079 + 3.01136i) q^{26} +(-5.18512 - 0.338499i) q^{27} -7.78182i q^{28} +(-0.487293 - 0.844016i) q^{29} +(-6.11735 - 11.1482i) q^{30} +(3.16380 + 1.82662i) q^{31} +(-5.00419 - 2.88917i) q^{32} +(-2.18407 - 1.32507i) q^{33} +(10.1421 - 5.85555i) q^{34} +7.79116 q^{35} +(4.45089 + 8.54647i) q^{36} -4.22691i q^{37} +(-1.29063 - 2.23543i) q^{38} +(2.41041 - 5.76107i) q^{39} +(-4.44910 + 7.70607i) q^{40} +(-3.47188 - 2.00449i) q^{41} +(-9.57780 - 0.208159i) q^{42} +(4.33040 + 7.50047i) q^{43} +4.73737i q^{44} +(-8.55673 + 4.45623i) q^{45} +21.0826i q^{46} +(-1.33337 + 0.769820i) q^{47} +(-0.0961719 + 0.158517i) q^{48} +(-0.565185 + 0.978929i) q^{49} +(-10.5613 - 6.09755i) q^{50} +(-4.27425 - 7.78932i) q^{51} +(-11.4526 + 1.71995i) q^{52} +0.739889 q^{53} +(10.6380 - 5.24951i) q^{54} -4.74305 q^{55} +(3.35182 + 5.80553i) q^{56} +(-1.71685 + 0.942089i) q^{57} +(1.92687 + 1.11248i) q^{58} +(6.72630 + 3.88343i) q^{59} +(15.2960 + 9.28002i) q^{60} +(-4.06781 - 7.04566i) q^{61} -8.34028 q^{62} +(-0.315778 + 7.26133i) q^{63} +12.9777 q^{64} +(-1.72201 - 11.4664i) q^{65} +(5.83071 + 0.126722i) q^{66} +(0.669411 + 0.386485i) q^{67} +(-8.23837 + 14.2693i) q^{68} +(15.9912 + 0.347545i) q^{69} +(-15.4041 + 8.89354i) q^{70} +3.01136i q^{71} +(-7.00171 - 4.45888i) q^{72} -9.21010i q^{73} +(4.82498 + 8.35711i) q^{74} +(-4.79909 + 7.91020i) q^{75} +(3.14510 + 1.81582i) q^{76} +(-1.78664 + 3.09455i) q^{77} +(1.81054 + 14.1418i) q^{78} +(-1.86858 - 3.23648i) q^{79} +0.344246i q^{80} +(-3.80639 - 8.15545i) q^{81} +9.15243 q^{82} +(12.3640 - 7.13838i) q^{83} +(11.8164 - 6.48403i) q^{84} +(-14.2864 - 8.24826i) q^{85} +(-17.1234 - 9.88621i) q^{86} +(0.875581 - 1.44319i) q^{87} +(-2.04050 - 3.53425i) q^{88} -8.21257i q^{89} +(11.8309 - 18.5779i) q^{90} +(-8.12974 - 3.19570i) q^{91} +(-14.8309 - 25.6879i) q^{92} +(-0.137489 + 6.32611i) q^{93} +(1.75748 - 3.04405i) q^{94} +(-1.81800 + 3.14887i) q^{95} +(0.217466 - 10.0060i) q^{96} +(-13.1880 + 7.61407i) q^{97} -2.58061i q^{98} +(0.192237 - 4.42051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 12 q^{4} - 2 q^{9} - 16 q^{10} - 2 q^{12} - 4 q^{13} - 18 q^{14} + 4 q^{16} - 12 q^{17} - 10 q^{22} + 24 q^{23} - 12 q^{25} - 12 q^{26} - 22 q^{27} + 12 q^{29} - 54 q^{30} - 12 q^{35} + 50 q^{36}+ \cdots + 24 q^{95}+O(q^{100}) $ 20 * q + 2 * q^3 + 12 * q^4 - 2 * q^9 - 16 * q^10 - 2 * q^12 - 4 * q^13 - 18 * q^14 + 4 * q^16 - 12 * q^17 - 10 * q^22 + 24 * q^23 - 12 * q^25 - 12 * q^26 - 22 * q^27 + 12 * q^29 - 54 * q^30 - 12 * q^35 + 50 * q^36 + 12 * q^38 - 8 * q^39 - 8 * q^40 + 6 * q^42 + 4 * q^43 + 38 * q^48 - 10 * q^49 - 78 * q^51 + 108 * q^53 + 20 * q^55 + 36 * q^56 - 2 * q^61 - 72 * q^62 + 8 * q^64 - 24 * q^65 + 78 * q^66 + 24 * q^68 + 72 * q^69 - 42 * q^74 - 8 * q^75 - 6 * q^77 + 66 * q^78 - 14 * q^79 + 46 * q^81 - 4 * q^82 - 54 * q^87 + 22 * q^88 + 24 * q^90 - 72 * q^91 - 84 * q^92 + 20 * q^94 + 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.97712	+	1.14149i	−1.39803	+	0.807156i	−0.994187	−	0.107670i	$-0.965661\pi$
$2$	−1.97712	+	1.14149i	−1.39803	+	0.807156i	−0.403848	+	0.914826i	$0.632328\pi$
$3$	0.833228	+	1.51846i	0.481065	+	0.876685i
$3$	0.833228	+	1.51846i	0.481065	+	0.876685i
$4$	1.60600	−	2.78168i	0.803001	−	1.39084i
$5$	2.78501	+	1.60793i	1.24550	+	0.719088i	0.970208	−	0.242274i	$-0.0778933\pi$
$5$	2.78501	+	1.60793i	1.24550	+	0.719088i	0.275289	+	0.961362i	$0.411227\pi$
$6$	−3.38070	−	2.05106i	−1.38017	−	0.837342i
$7$	2.09815	−	1.21137i	0.793025	−	0.457853i	−0.0480013	−	0.998847i	$-0.515285\pi$
$7$	2.09815	−	1.21137i	0.793025	−	0.457853i	0.841026	+	0.540994i	$0.181952\pi$
$8$			2.76698i			0.978274i
$9$	−1.61146	+	2.53045i	−0.537154	+	0.843484i
$10$	−7.34174			−2.32166
$11$	−1.27730	+	0.737448i	−0.385119	+	0.222349i	−0.680043	−	0.733172i	$-0.738039\pi$
$11$	−1.27730	+	0.737448i	−0.385119	+	0.222349i	0.294924	+	0.955521i	$0.404706\pi$
$12$	5.56204	+	0.120883i	1.60562	+	0.0348958i
$13$	−2.24652	−	2.82013i	−0.623072	−	0.782164i
$13$	−2.24652	−	2.82013i	−0.623072	−	0.782164i
$14$	−2.76553	+	4.79003i	−0.739118	+	1.28019i
$15$	−0.121028	+	5.56871i	−0.0312492	+	1.43784i
$16$	0.0535232	+	0.0927049i	0.0133808	+	0.0231762i
$17$	−5.12974			−1.24414			−0.622072	−	0.782960i	$-0.713709\pi$
$17$	−5.12974			−1.24414			−0.622072	+	0.782960i	$0.713709\pi$
$18$	0.297563	−	6.84248i	0.0701362	−	1.61279i
$19$			1.13065i			0.259389i	0.991554	+	0.129694i	$0.0413996\pi$
$19$			1.13065i			0.259389i	−0.991554	+	0.129694i	$0.958600\pi$
$20$	8.94547	−	5.16467i	2.00027	−	1.15486i
$21$	3.58765	+	2.17662i	0.782890	+	0.474976i
$22$	1.68358	−	2.91604i	0.358940	−	0.621703i
$23$	4.61735	−	7.99748i	0.962784	−	1.66759i	0.247328	−	0.968932i	$-0.420447\pi$
$23$	4.61735	−	7.99748i	0.962784	−	1.66759i	0.715455	−	0.698658i	$-0.246219\pi$
$24$	−4.20155	+	2.30552i	−0.857639	+	0.470613i
$25$	2.67087	+	4.62608i	0.534174	+	0.925217i
$26$	7.66079	+	3.01136i	1.50240	+	0.590577i
$27$	−5.18512	−	0.338499i	−0.997876	−	0.0651442i
$28$		−	7.78182i		−	1.47063i
$29$	−0.487293	−	0.844016i	−0.0904880	−	0.156730i	0.817229	−	0.576314i	$-0.195509\pi$
$29$	−0.487293	−	0.844016i	−0.0904880	−	0.156730i	−0.907717	+	0.419584i	$0.862176\pi$
$30$	−6.11735	−	11.1482i	−1.11687	−	2.03537i
$31$	3.16380	+	1.82662i	0.568235	+	0.328071i	0.756444	−	0.654058i	$-0.226935\pi$
$31$	3.16380	+	1.82662i	0.568235	+	0.328071i	−0.188209	+	0.982129i	$0.560268\pi$
$32$	−5.00419	−	2.88917i	−0.884624	−	0.510738i
$33$	−2.18407	−	1.32507i	−0.380197	−	0.230664i
$34$	10.1421	−	5.85555i	1.73936	−	1.00422i
$35$	7.79116			1.31695
$36$	4.45089	+	8.54647i	0.741815	+	1.42441i
$37$		−	4.22691i		−	0.694900i	−0.937698	−	0.347450i	$-0.887048\pi$
$37$		−	4.22691i		−	0.694900i	0.937698	−	0.347450i	$-0.112952\pi$
$38$	−1.29063	−	2.23543i	−0.209367	−	0.362634i
$39$	2.41041	−	5.76107i	0.385974	−	0.922510i
$40$	−4.44910	+	7.70607i	−0.703465	+	1.21844i
$41$	−3.47188	−	2.00449i	−0.542217	−	0.313049i	0.203760	−	0.979021i	$-0.434684\pi$
$41$	−3.47188	−	2.00449i	−0.542217	−	0.313049i	−0.745977	+	0.665972i	$0.768017\pi$
$42$	−9.57780	−	0.208159i	−1.47789	−	0.0321197i
$43$	4.33040	+	7.50047i	0.660379	+	1.14381i	0.980516	+	0.196439i	$0.0629377\pi$
$43$	4.33040	+	7.50047i	0.660379	+	1.14381i	−0.320137	+	0.947371i	$0.603729\pi$
$44$			4.73737i			0.714185i
$45$	−8.55673	+	4.45623i	−1.27556	+	0.664296i
$46$			21.0826i			3.10847i
$47$	−1.33337	+	0.769820i	−0.194492	+	0.112290i	−0.594084	−	0.804403i	$-0.702485\pi$
$47$	−1.33337	+	0.769820i	−0.194492	+	0.112290i	0.399592	+	0.916693i	$0.369152\pi$
$48$	−0.0961719	+	0.158517i	−0.0138812	+	0.0228800i
$49$	−0.565185	+	0.978929i	−0.0807407	+	0.139847i
$50$	−10.5613	−	6.09755i	−1.49359	−	0.862324i
$51$	−4.27425	−	7.78932i	−0.598514	−	1.09072i
$52$	−11.4526	+	1.71995i	−1.58819	+	0.238514i
$53$	0.739889			0.101632			0.0508158	−	0.998708i	$-0.483818\pi$
$53$	0.739889			0.101632			0.0508158	+	0.998708i	$0.483818\pi$
$54$	10.6380	−	5.24951i	1.44765	−	0.714367i
$55$	−4.74305			−0.639553
$56$	3.35182	+	5.80553i	0.447906	+	0.775796i
$57$	−1.71685	+	0.942089i	−0.227402	+	0.124783i
$58$	1.92687	+	1.11248i	0.253011	+	0.146076i
$59$	6.72630	+	3.88343i	0.875689	+	0.505580i	0.869235	−	0.494400i	$-0.164612\pi$
$59$	6.72630	+	3.88343i	0.875689	+	0.505580i	0.00645471	+	0.999979i	$0.497945\pi$
$60$	15.2960	+	9.28002i	1.97470	+	1.19805i
$61$	−4.06781	−	7.04566i	−0.520830	−	0.902104i	−0.999707	−	0.0242218i	$-0.992289\pi$
$61$	−4.06781	−	7.04566i	−0.520830	−	0.902104i	0.478877	−	0.877882i	$-0.341044\pi$
$62$	−8.34028			−1.05922
$63$	−0.315778	+	7.26133i	−0.0397843	+	0.914842i
$64$	12.9777			1.62222
$65$	−1.72201	−	11.4664i	−0.213589	−	1.42223i
$66$	5.83071	+	0.126722i	0.717711	+	0.0155984i
$67$	0.669411	+	0.386485i	0.0817816	+	0.0472166i	0.540333	−	0.841451i	$-0.318298\pi$
$67$	0.669411	+	0.386485i	0.0817816	+	0.0472166i	−0.458552	+	0.888668i	$0.651632\pi$
$68$	−8.23837	+	14.2693i	−0.999049	+	1.73040i
$69$	15.9912	+	0.347545i	1.92511	+	0.0418395i
$70$	−15.4041	+	8.89354i	−1.84114	+	1.06298i
$71$			3.01136i			0.357383i	0.983905	+	0.178692i	$0.0571864\pi$
$71$			3.01136i			0.357383i	−0.983905	+	0.178692i	$0.942814\pi$
$72$	−7.00171	−	4.45888i	−0.825159	−	0.525484i
$73$		−	9.21010i		−	1.07796i	−0.842318	−	0.538980i	$-0.818810\pi$
$73$		−	9.21010i		−	1.07796i	0.842318	−	0.538980i	$-0.181190\pi$
$74$	4.82498	+	8.35711i	0.560893	+	0.971495i
$75$	−4.79909	+	7.91020i	−0.554152	+	0.913392i
$76$	3.14510	+	1.81582i	0.360768	+	0.208289i
$77$	−1.78664	+	3.09455i	−0.203606	+	0.352656i
$78$	1.81054	+	14.1418i	0.205004	+	1.60124i
$79$	−1.86858	−	3.23648i	−0.210232	−	0.364133i	0.741555	−	0.670892i	$-0.234089\pi$
$79$	−1.86858	−	3.23648i	−0.210232	−	0.364133i	−0.951787	+	0.306759i	$0.900755\pi$
$80$			0.344246i			0.0384879i
$81$	−3.80639	−	8.15545i	−0.422932	−	0.906161i
$82$	9.15243			1.01072
$83$	12.3640	−	7.13838i	1.35713	−	0.783539i	0.367893	−	0.929868i	$-0.380079\pi$
$83$	12.3640	−	7.13838i	1.35713	−	0.783539i	0.989236	+	0.146329i	$0.0467460\pi$
$84$	11.8164	−	6.48403i	1.28928	−	0.707466i
$85$	−14.2864	−	8.24826i	−1.54958	−	0.894649i
$86$	−17.1234	−	9.88621i	−1.84647	−	1.06606i
$87$	0.875581	−	1.44319i	0.0938721	−	0.154727i
$88$	−2.04050	−	3.53425i	−0.217518	−	0.376752i
$89$		−	8.21257i		−	0.870531i	−0.900302	−	0.435265i	$-0.856655\pi$
$89$		−	8.21257i		−	0.870531i	0.900302	−	0.435265i	$-0.143345\pi$
$90$	11.8309	−	18.5779i	1.24709	−	1.95829i
$91$	−8.12974	−	3.19570i	−0.852228	−	0.335000i
$92$	−14.8309	−	25.6879i	−1.54623	−	2.67815i
$93$	−0.137489	+	6.32611i	−0.0142569	+	0.655987i
$94$	1.75748	−	3.04405i	0.181271	−	0.313970i
$95$	−1.81800	+	3.14887i	−0.186523	+	0.323068i
$96$	0.217466	−	10.0060i	0.0221950	−	1.02123i
$97$	−13.1880	+	7.61407i	−1.33903	+	0.773092i	−0.986664	−	0.162769i	$-0.947957\pi$
$97$	−13.1880	+	7.61407i	−1.33903	+	0.773092i	−0.352370	+	0.935861i	$0.614624\pi$
$98$		−	2.58061i		−	0.260681i
$99$	0.192237	−	4.42051i	0.0193206	−	0.444278i
$100$	17.1577			1.71577
$101$	7.45316	+	12.9092i	0.741617	+	1.28452i	0.951759	+	0.306847i	$0.0992741\pi$
$101$	7.45316	+	12.9092i	0.741617	+	1.28452i	−0.210142	+	0.977671i	$0.567393\pi$
$102$	17.3421	+	10.5214i	1.71713	+	1.04177i
$103$	3.26553	−	5.65606i	0.321762	−	0.557308i	−0.659090	−	0.752064i	$-0.729058\pi$
$103$	3.26553	−	5.65606i	0.321762	−	0.557308i	0.980852	+	0.194756i	$0.0623916\pi$
$104$	7.80325	−	6.21607i	0.765171	−	0.609535i
$105$	6.49182	+	11.8306i	0.633536	+	1.15455i
$106$	−1.46285	+	0.844576i	−0.142084	+	0.0820325i
$107$	−9.37527			−0.906341			−0.453171	−	0.891424i	$-0.649707\pi$
$107$	−9.37527			−0.906341			−0.453171	+	0.891424i	$0.649707\pi$
$108$	−9.26889	+	13.8797i	−0.891900	+	1.33557i
$109$			14.5859i			1.39707i	0.715574	+	0.698537i	$0.246165\pi$
$109$			14.5859i			1.39707i	−0.715574	+	0.698537i	$0.753835\pi$
$110$	9.37758	−	5.41415i	0.894117	−	0.516219i
$111$	6.41841	−	3.52198i	0.609209	−	0.334292i
$112$	0.224599	+	0.129672i	0.0212226	+	0.0122529i
$113$	−1.53382	+	2.65665i	−0.144290	+	0.249917i	−0.929108	−	0.369809i	$-0.879423\pi$
$113$	−1.53382	+	2.65665i	−0.144290	+	0.249917i	0.784818	+	0.619726i	$0.212756\pi$
$114$	2.31903	−	3.82239i	0.217197	−	0.358000i
$115$	25.7188	−	14.8487i	2.39829	−	1.38465i
$116$	−3.13037			−0.290648
$117$	10.7564	−	1.14017i	0.994429	−	0.105409i
$118$	−17.7316			−1.63233
$119$	−10.7630	+	6.21399i	−0.986638	+	0.569636i
$120$	−15.4085	−	0.334881i	−1.40660	−	0.0305703i
$121$	−4.41234	+	7.64240i	−0.401122	+	0.694764i
$122$	16.0851	+	9.28674i	1.45628	+	0.840782i
$123$	0.150877	−	6.94212i	0.0136041	−	0.625950i
$124$	10.1621	−	5.86711i	0.912587	−	0.526882i
$125$			1.09900i			0.0982972i
$126$	−7.66441	−	14.7170i	−0.682800	−	1.31109i
$127$	0.163893			0.0145432			0.00727160	−	0.999974i	$-0.497685\pi$
$127$	0.163893			0.0145432			0.00727160	+	0.999974i	$0.497685\pi$
$128$	−15.6502	+	9.03564i	−1.38329	+	0.798645i
$129$	−7.78097	+	12.8251i	−0.685076	+	1.12919i
$130$	16.4934	+	20.7047i	1.44656	+	1.81592i
$131$	−3.26584	+	5.65660i	−0.285338	+	0.494220i	−0.972691	−	0.232104i	$-0.925439\pi$
$131$	−3.26584	+	5.65660i	−0.285338	+	0.494220i	0.687353	+	0.726323i	$0.258772\pi$
$132$	−7.19352	+	3.94731i	−0.626115	+	0.343569i
$133$	1.36963	+	2.37227i	0.118762	+	0.205702i
$134$	−1.76467			−0.152445
$135$	−13.8963	−	9.28002i	−1.19601	−	0.798697i
$136$		−	14.1939i		−	1.21712i
$137$	−12.0632	+	6.96467i	−1.03063	+	0.595032i	−0.917164	−	0.398511i	$-0.869527\pi$
$137$	−12.0632	+	6.96467i	−1.03063	+	0.595032i	−0.113462	+	0.993542i	$0.536194\pi$
$138$	−32.0132	+	17.5666i	−2.72515	+	1.49537i
$139$	7.09082	−	12.2817i	0.601436	−	1.04172i	−0.391168	−	0.920319i	$-0.627929\pi$
$139$	7.09082	−	12.2817i	0.601436	−	1.04172i	0.992604	−	0.121398i	$-0.0387377\pi$
$140$	12.5126	−	21.6725i	1.05751	−	1.83166i
$141$	−2.27994	−	1.38323i	−0.192006	−	0.116489i
$142$	−3.43744	−	5.95382i	−0.288464	−	0.499634i
$143$	4.94917	+	1.94546i	0.413870	+	0.162687i
$144$	−0.320836	−	0.0139524i	−0.0267363	−	0.00116270i
$145$		−	3.13413i		−	0.260275i
$146$	10.5132	+	18.2095i	0.870082	+	1.50703i
$147$	−1.95740	−	0.0425411i	−0.161443	−	0.00350873i
$148$	−11.7579	−	6.78843i	−0.966493	−	0.558005i
$149$	16.0882	+	9.28851i	1.31799	+	0.760945i	0.983406	−	0.181419i	$-0.0580691\pi$
$149$	16.0882	+	9.28851i	1.31799	+	0.760945i	0.334589	+	0.942364i	$0.391402\pi$
$150$	0.458959	−	21.1175i	0.0374738	−	1.72424i
$151$	−10.2989	+	5.94609i	−0.838115	+	0.483886i	−0.856623	−	0.515943i	$-0.827442\pi$
$151$	−10.2989	+	5.94609i	−0.838115	+	0.483886i	0.0185081	+	0.999829i	$0.494108\pi$
$152$	−3.12848			−0.253753
$153$	8.26638	−	12.9806i	0.668297	−	1.04942i
$154$		−	8.15772i		−	0.657368i
$155$	5.87415	+	10.1743i	0.471823	+	0.817222i
$156$	−12.1543	−	15.9573i	−0.973124	−	1.27760i
$157$	−1.99459	+	3.45472i	−0.159185	+	0.275717i	−0.934575	−	0.355766i	$-0.884220\pi$
$157$	−1.99459	+	3.45472i	−0.159185	+	0.275717i	0.775390	+	0.631483i	$0.217553\pi$
$158$	7.38883	+	4.26594i	0.587824	+	0.339380i
$159$	0.616497	+	1.12349i	0.0488914	+	0.0890989i
$160$	−9.29116	−	16.0928i	−0.734531	−	1.27224i
$161$		−	22.3732i		−	1.76325i
$162$	16.8351	+	11.7794i	1.32269	+	0.925473i
$163$			5.18096i			0.405804i	0.979199	+	0.202902i	$0.0650373\pi$
$163$			5.18096i			0.405804i	−0.979199	+	0.202902i	$0.934963\pi$
$164$	−11.1517	+	6.43843i	−0.870801	+	0.502757i
$165$	−3.95205	−	7.20215i	−0.307666	−	0.560687i
$166$	−16.2968	+	28.2268i	−1.26488	+	2.19083i
$167$	−0.706703	−	0.408015i	−0.0546863	−	0.0315732i	0.472408	−	0.881380i	$-0.343385\pi$
$167$	−0.706703	−	0.408015i	−0.0546863	−	0.0315732i	−0.527094	+	0.849807i	$0.676718\pi$
$168$	−6.02265	+	9.92695i	−0.464657	+	0.765881i
$169$	−2.90631	+	12.6710i	−0.223562	+	0.974690i
$170$	37.6612			2.88848
$171$	−2.86105	−	1.82200i	−0.218790	−	0.139332i
$172$	27.8185			2.12114
$173$	−0.261538	−	0.452997i	−0.0198844	−	0.0344407i	0.855912	−	0.517122i	$-0.172996\pi$
$173$	−0.261538	−	0.452997i	−0.0198844	−	0.0344407i	−0.875796	+	0.482681i	$0.839663\pi$
$174$	−0.0837357	+	3.85283i	−0.00634798	+	0.292083i
$175$	11.2078	+	6.47081i	0.847227	+	0.489147i
$176$	−0.136730	−	0.0789411i	−0.0103064	−	0.00595041i
$177$	−0.292303	+	13.4494i	−0.0219709	+	1.01092i
$178$	9.37457	+	16.2372i	0.702654	+	1.21703i
$179$	−14.1750			−1.05949			−0.529746	−	0.848156i	$-0.677713\pi$
$179$	−14.1750			−1.05949			−0.529746	+	0.848156i	$0.677713\pi$
$180$	−1.34632	+	30.9588i	−0.100349	+	2.30753i
$181$	−17.9757			−1.33612			−0.668060	−	0.744107i	$-0.732875\pi$
$181$	−17.9757			−1.33612			−0.668060	+	0.744107i	$0.732875\pi$
$182$	19.7213	−	2.96174i	1.46184	−	0.219539i
$183$	7.30916	−	12.0475i	0.540308	−	0.890574i
$184$	22.1289	+	12.7761i	1.63136	+	0.941867i
$185$	6.79658	−	11.7720i	0.499694	−	0.865496i
$186$	−6.94936	−	12.6644i	−0.509552	−	0.928600i
$187$	6.55220	−	3.78291i	0.479144	−	0.276634i
$188$			4.94532i			0.360675i
$189$	−11.2892	+	5.57085i	−0.821167	+	0.405220i
$190$		−	8.30093i		−	0.602213i
$191$	−4.64755	−	8.04979i	−0.336285	−	0.582462i	0.647446	−	0.762111i	$-0.275837\pi$
$191$	−4.64755	−	8.04979i	−0.336285	−	0.582462i	−0.983731	+	0.179649i	$0.942504\pi$
$192$	10.8134	+	19.7062i	0.780392	+	1.42217i
$193$	−9.93585	−	5.73646i	−0.715198	−	0.412920i	0.0977848	−	0.995208i	$-0.468824\pi$
$193$	−9.93585	−	5.73646i	−0.715198	−	0.412920i	−0.812983	+	0.582288i	$0.802158\pi$
$194$	17.3828	−	30.1079i	1.24801	−	2.16162i
$195$	15.9764	−	12.1689i	1.14409	−	0.871433i
$196$	1.81538	+	3.14432i	0.129670	+	0.224595i
$197$		−	11.0296i		−	0.785828i	−0.919575	−	0.392914i	$-0.871467\pi$
$197$		−	11.0296i		−	0.785828i	0.919575	−	0.392914i	$-0.128533\pi$
$198$	4.66589	+	8.95931i	0.331590	+	0.636710i
$199$	−1.38397			−0.0981068			−0.0490534	−	0.998796i	$-0.515620\pi$
$199$	−1.38397			−0.0981068			−0.0490534	+	0.998796i	$0.515620\pi$
$200$	−12.8003	+	7.39024i	−0.905116	+	0.522569i
$201$	−0.0290905	+	1.33851i	−0.00205188	+	0.0944109i
$202$	−29.4716	−	17.0154i	−2.07361	−	1.19720i
$203$	−2.04482	−	1.18058i	−0.143518	−	0.0828604i
$204$	−28.5318	−	0.620097i	−1.99763	−	0.0434155i
$205$	−6.44616	−	11.1651i	−0.450219	−	0.779803i
$206$			14.9103i			1.03885i
$207$	12.7966	+	24.5716i	0.889424	+	1.70785i
$208$	0.141199	−	0.359206i	0.00979042	−	0.0249064i
$209$	−0.833794	−	1.44417i	−0.0576748	−	0.0998956i
$210$	−26.3396	−	15.9801i	−1.81761	−	1.10273i
$211$	4.59187	−	7.95335i	0.316117	−	0.547531i	−0.663557	−	0.748126i	$-0.730954\pi$
$211$	4.59187	−	7.95335i	0.316117	−	0.547531i	0.979674	+	0.200595i	$0.0642874\pi$
$212$	1.18826	−	2.05813i	0.0816102	−	0.141353i
$213$	−4.57264	+	2.50915i	−0.313312	+	0.171924i
$214$	18.5360	−	10.7018i	1.26710	−	0.731558i
$215$			27.8519i			1.89948i
$216$	0.936619	−	14.3471i	0.0637289	−	0.976196i
$217$	8.85083			0.600833
$218$	−16.6496	−	28.8380i	−1.12766	−	1.95316i
$219$	13.9852	−	7.67412i	0.945032	−	0.518569i
$220$	−7.61735	+	13.1936i	−0.513562	+	0.889515i
$221$	11.5241	+	14.4666i	0.775192	+	0.973126i
$222$	−8.66966	+	14.2899i	−0.581869	+	0.959078i
$223$	−5.51495	+	3.18406i	−0.369308	+	0.213220i	−0.673156	−	0.739500i	$-0.735062\pi$
$223$	−5.51495	+	3.18406i	−0.369308	+	0.213220i	0.303848	+	0.952721i	$0.401729\pi$
$224$	−13.9994			−0.935372
$225$	−16.0101	−	0.696241i	−1.06734	−	0.0464160i
$226$		−	7.00336i		−	0.465857i
$227$	−8.83052	+	5.09830i	−0.586102	+	0.338386i	−0.763555	−	0.645743i	$-0.776548\pi$
$227$	−8.83052	+	5.09830i	−0.586102	+	0.338386i	0.177453	+	0.984129i	$0.443214\pi$
$228$	−0.136676	+	6.28871i	−0.00905158	+	0.416480i
$229$	7.02980	+	4.05866i	0.464542	+	0.268204i	0.713952	−	0.700194i	$-0.246903\pi$
$229$	7.02980	+	4.05866i	0.464542	+	0.268204i	−0.249410	+	0.968398i	$0.580237\pi$
$230$	−33.8994	+	58.7155i	−2.23526	+	3.87158i
$231$	−6.18763	−	0.134479i	−0.407116	−	0.00884807i
$232$	2.33537	−	1.34833i	0.153325	−	0.0885221i
$233$	8.37795			0.548858			0.274429	−	0.961607i	$-0.411511\pi$
$233$	8.37795			0.548858			0.274429	+	0.961607i	$0.411511\pi$
$234$	−19.9652	+	14.5326i	−1.30516	+	0.950024i
$235$	−4.95126			−0.322985
$236$	21.6049	−	12.4736i	1.40636	−	0.811961i
$237$	3.35752	−	5.53411i	0.218095	−	0.359479i
$238$	14.1864	−	24.5716i	0.919570	−	1.59274i
$239$	−3.99453	−	2.30624i	−0.258385	−	0.149178i	0.365213	−	0.930924i	$-0.380996\pi$
$239$	−3.99453	−	2.30624i	−0.258385	−	0.149178i	−0.623598	+	0.781746i	$0.714330\pi$
$240$	−0.522725	+	0.286836i	−0.0337418	+	0.0185152i
$241$	6.95910	−	4.01784i	0.448275	−	0.258812i	−0.258826	−	0.965924i	$-0.583336\pi$
$241$	6.95910	−	4.01784i	0.448275	−	0.258812i	0.707101	+	0.707112i	$0.250002\pi$
$242$		−	20.1466i		−	1.29507i
$243$	9.21217	−	12.5752i	0.590961	−	0.806700i
$244$	−26.1316			−1.67291
$245$	−3.14810	+	1.81756i	−0.201125	+	0.116119i
$246$	7.62607	+	13.8976i	0.486220	+	0.886081i
$247$	3.18858	−	2.54002i	0.202885	−	0.161618i
$248$	−5.05422	+	8.75417i	−0.320943	+	0.555890i
$249$	21.1414	+	12.8264i	1.33978	+	0.812842i
$250$	−1.25449	−	2.17285i	−0.0793411	−	0.137423i
$251$	17.1127			1.08015			0.540073	−	0.841618i	$-0.318396\pi$
$251$	17.1127			1.08015			0.540073	+	0.841618i	$0.318396\pi$
$252$	19.6915	+	12.5401i	1.24045	+	0.789952i
$253$			13.6202i			0.856295i
$254$	−0.324037	+	0.187083i	−0.0203319	+	0.0117386i
$255$	0.620841	−	28.5661i	0.0388786	−	1.78888i
$256$	7.65044	−	13.2509i	0.478152	−	0.828184i
$257$	4.75712	−	8.23957i	0.296741	−	0.513971i	−0.678647	−	0.734464i	$-0.737434\pi$
$257$	4.75712	−	8.23957i	0.296741	−	0.513971i	0.975388	+	0.220494i	$0.0707669\pi$
$258$	0.744129	−	34.2388i	0.0463274	−	2.13161i
$259$	−5.12034	−	8.86869i	−0.318162	−	0.551073i
$260$	−34.6612	−	13.6249i	−2.14960	−	0.844981i
$261$	2.92100	+	0.127027i	0.180805	+	0.00786278i
$262$		−	14.9117i		−	0.921248i
$263$	13.9945	+	24.2392i	0.862937	+	1.49465i	0.869081	+	0.494670i	$0.164711\pi$
$263$	13.9945	+	24.2392i	0.862937	+	1.49465i	−0.00614342	+	0.999981i	$0.501956\pi$
$264$	3.66643	−	6.04326i	0.225653	−	0.371937i
$265$	2.06060	+	1.18969i	0.126582	+	0.0730820i
$266$	−5.41584	−	3.12684i	−0.332067	−	0.191719i
$267$	12.4705	−	6.84295i	0.763181	−	0.418781i
$268$	2.15015	−	1.24139i	0.131341	−	0.0758299i
$269$	−11.4199			−0.696285			−0.348143	−	0.937442i	$-0.613188\pi$
$269$	−11.4199			−0.696285			−0.348143	+	0.937442i	$0.613188\pi$
$270$	38.0678	+	2.48517i	2.31673	+	0.151243i
$271$			13.2786i			0.806620i	0.915064	+	0.403310i	$0.132140\pi$
$271$			13.2786i			0.806620i	−0.915064	+	0.403310i	$0.867860\pi$
$272$	−0.274560	−	0.475552i	−0.0166477	−	0.0288346i
$273$	−1.92138	−	15.0075i	−0.116287	−	0.908293i
$274$	15.9002	−	27.5400i	0.960567	−	1.66375i
$275$	−6.82299	−	3.93925i	−0.411442	−	0.237546i
$276$	26.6486	−	43.9241i	1.60406	−	2.64392i
$277$	−0.900995	−	1.56057i	−0.0541356	−	0.0937655i	0.837688	−	0.546150i	$-0.183907\pi$
$277$	−0.900995	−	1.56057i	−0.0541356	−	0.0937655i	−0.891823	+	0.452384i	$0.850574\pi$
$278$			32.3764i			1.94181i
$279$	−9.72052	+	5.06232i	−0.581952	+	0.303073i
$280$			21.5580i			1.28834i
$281$	9.94035	−	5.73906i	0.592991	−	0.342364i	−0.173288	−	0.984871i	$-0.555439\pi$
$281$	9.94035	−	5.73906i	0.592991	−	0.342364i	0.766279	+	0.642507i	$0.222106\pi$
$282$	6.08666	+	0.132285i	0.362456	+	0.00787744i
$283$	11.3277	−	19.6201i	0.673360	−	1.16629i	−0.303585	−	0.952804i	$-0.598184\pi$
$283$	11.3277	−	19.6201i	0.673360	−	1.16629i	0.976945	−	0.213490i	$-0.0684831\pi$
$284$	8.37663	+	4.83625i	0.497062	+	0.286979i
$285$	−6.29626	−	0.136840i	−0.372958	−	0.00810570i
$286$	−12.0058	+	1.80303i	−0.709919	+	0.106615i
$287$	−9.71269			−0.573322
$288$	15.3750	−	8.00708i	0.905979	−	0.471822i
$289$	9.31424			0.547896
$290$	3.57758	+	6.19655i	0.210083	+	0.363874i
$291$	−22.5503	−	13.6812i	−1.32192	−	0.802004i
$292$	−25.6195	−	14.7914i	−1.49927	−	0.865603i
$293$	−14.1753	−	8.18413i	−0.828132	−	0.478122i	0.0250809	−	0.999685i	$-0.492016\pi$
$293$	−14.1753	−	8.18413i	−0.828132	−	0.478122i	−0.853213	+	0.521563i	$0.825349\pi$
$294$	3.91857	−	2.15024i	0.228535	−	0.125405i
$295$	12.4886	+	21.6308i	0.727112	+	1.25940i
$296$	11.6958			0.679803
$297$	6.87255	−	3.39139i	0.398786	−	0.196788i
$298$	−42.4110			−2.45680
$299$	−32.9269	+	4.94495i	−1.90421	+	0.285974i
$300$	14.2963	+	26.0533i	0.825396	+	1.50419i
$301$	18.1716	+	10.4914i	1.04739	+	0.604714i
$302$	13.5748	−	23.5123i	0.781142	−	1.35298i
$303$	−13.3920	+	22.0737i	−0.769352	+	1.26810i
$304$	−0.104817	+	0.0605160i	−0.00601165	+	0.00347083i
$305$		−	26.1630i		−	1.49809i
$306$	−1.52642	+	35.1001i	−0.0872596	+	2.00654i
$307$			16.6786i			0.951898i	0.879473	+	0.475949i	$0.157895\pi$
$307$			16.6786i			0.951898i	−0.879473	+	0.475949i	$0.842105\pi$
$308$	5.73868	+	9.93969i	0.326992	+	0.566367i
$309$	11.3094	+	0.245794i	0.643372	+	0.0139827i
$310$	−23.2278	−	13.4106i	−1.31925	−	0.761670i
$311$	−4.05615	+	7.02546i	−0.230003	+	0.398377i	−0.957809	−	0.287406i	$-0.907207\pi$
$311$	−4.05615	+	7.02546i	−0.230003	+	0.398377i	0.727806	+	0.685784i	$0.240540\pi$
$312$	15.9408	+	6.66954i	0.902468	+	0.377589i
$313$	11.0021	+	19.0562i	0.621877	+	1.07712i	0.989136	+	0.147003i	$0.0469628\pi$
$313$	11.0021	+	19.0562i	0.621877	+	1.07712i	−0.367260	+	0.930119i	$0.619704\pi$
$314$		−	9.10720i		−	0.513949i
$315$	−12.5552	+	19.7152i	−0.707403	+	1.11082i
$316$	−12.0038			−0.675266
$317$	5.82742	−	3.36446i	0.327301	−	0.188967i	−0.327341	−	0.944906i	$-0.606153\pi$
$317$	5.82742	−	3.36446i	0.327301	−	0.188967i	0.654642	+	0.755939i	$0.272819\pi$
$318$	−2.50135	−	1.51756i	−0.140269	−	0.0851004i
$319$	1.24483	+	0.718706i	0.0696974	+	0.0402398i
$320$	36.1432	+	20.8673i	2.02047	+	1.16652i
$321$	−7.81174	−	14.2360i	−0.436009	−	0.794576i
$322$	25.5388	+	44.2345i	1.42322	+	2.46509i
$323$		−	5.79994i		−	0.322717i
$324$	−28.7989	−	2.50953i	−1.59994	−	0.139419i
$325$	7.04602	−	17.9248i	0.390843	−	0.994289i
$326$	−5.91402	−	10.2434i	−0.327547	−	0.567328i
$327$	−22.1481	+	12.1534i	−1.22479	+	0.672083i
$328$	5.54639	−	9.60662i	0.306248	−	0.530437i
$329$	−1.86507	+	3.23039i	−0.102824	+	0.178097i
$330$	16.0349	+	9.72829i	0.882690	+	0.535525i
$331$	0.226288	−	0.130648i	0.0124379	−	0.00718104i	−0.493768	−	0.869594i	$-0.664381\pi$
$331$	0.226288	−	0.130648i	0.0124379	−	0.00718104i	0.506206	+	0.862413i	$0.331048\pi$
$332$		−	45.8570i		−	2.51673i
$333$	10.6960	+	6.81151i	0.586138	+	0.373268i
$334$	1.86298			0.101938
$335$	1.24288	+	2.15273i	0.0679058	+	0.117616i
$336$	−0.00976036	+	0.449092i	−0.000532471	+	0.0245000i
$337$	−2.94402	+	5.09920i	−0.160371	+	0.277771i	−0.935002	−	0.354643i	$-0.884602\pi$
$337$	−2.94402	+	5.09920i	−0.160371	+	0.277771i	0.774631	+	0.632414i	$0.217936\pi$
$338$	−8.71766	−	28.3695i	−0.474178	−	1.54310i
$339$	−5.31205	−	0.115450i	−0.288511	−	0.00627036i
$340$	−45.8880	+	26.4934i	−2.48862	+	1.43681i
$341$	−5.38815			−0.291785
$342$	7.73644	+	0.336439i	0.418339	+	0.0181925i
$343$			19.6977i			1.06358i
$344$	−20.7536	+	11.9821i	−1.11896	+	0.646032i
$345$	43.9769	+	26.6806i	2.36763	+	1.43644i
$346$	1.03418	+	0.597086i	0.0555980	+	0.0320995i
$347$	−1.59900	+	2.76956i	−0.0858391	+	0.148678i	−0.905748	−	0.423816i	$-0.860690\pi$
$347$	−1.59900	+	2.76956i	−0.0858391	+	0.148678i	0.819909	+	0.572493i	$0.194024\pi$
$348$	−2.60831	−	4.75335i	−0.139820	−	0.254806i
$349$	−12.0677	+	6.96727i	−0.645967	+	0.372949i	−0.786909	−	0.617069i	$-0.788320\pi$
$349$	−12.0677	+	6.96727i	−0.645967	+	0.372949i	0.140942	+	0.990018i	$0.454987\pi$
$350$	−29.5454			−1.57927
$351$	10.6938	+	15.3832i	0.570795	+	0.821093i
$352$	8.52245			0.454248
$353$	−13.5867	+	7.84426i	−0.723145	+	0.417508i	−0.815909	−	0.578180i	$-0.803763\pi$
$353$	−13.5867	+	7.84426i	−0.723145	+	0.417508i	0.0927643	+	0.995688i	$0.470430\pi$
$354$	−14.7745	−	26.9248i	−0.785254	−	1.43104i
$355$	−4.84206	+	8.38669i	−0.256990	+	0.445119i
$356$	−22.8447	−	13.1894i	−1.21077	−	0.699036i
$357$	−18.4037	−	11.1655i	−0.974028	−	0.590939i
$358$	28.0257	−	16.1807i	1.48121	−	0.855175i
$359$			5.86486i			0.309535i	0.987951	+	0.154768i	$0.0494629\pi$
$359$			5.86486i			0.309535i	−0.987951	+	0.154768i	$0.950537\pi$
$360$	−12.3303	−	23.6763i	−0.649864	−	1.24785i
$361$	17.7216			0.932718
$362$	35.5400	−	20.5190i	1.86794	−	1.07846i
$363$	−15.2812	−	0.332114i	−0.802055	−	0.0174315i
$364$	−21.9458	+	17.4820i	−1.15027	+	0.916306i
$365$	14.8092	−	25.6503i	0.775148	−	1.34260i
$366$	−0.699007	+	32.1626i	−0.0365377	+	1.68117i
$367$	−1.66786	−	2.88882i	−0.0870617	−	0.150795i	0.819206	−	0.573499i	$-0.194414\pi$
$367$	−1.66786	−	2.88882i	−0.0870617	−	0.150795i	−0.906268	+	0.422704i	$0.861081\pi$
$368$	0.988541			0.0515313
$369$	10.6671	−	5.55527i	0.555306	−	0.289196i
$370$			31.0329i			1.61332i
$371$	1.55240	−	0.896277i	0.0805964	−	0.0465324i
$372$	17.3764	+	10.5422i	0.900923	+	0.546587i
$373$	−13.3206	+	23.0720i	−0.689716	+	1.19462i	0.282214	+	0.959352i	$0.408931\pi$
$373$	−13.3206	+	23.0720i	−0.689716	+	1.19462i	−0.971930	+	0.235272i	$0.924402\pi$
$374$	−8.63632	+	14.9585i	−0.446574	+	0.773488i
$375$	−1.66878	+	0.915714i	−0.0861757	+	0.0472873i
$376$	−2.13007	−	3.68940i	−0.109850	−	0.190266i
$377$	−1.28553	+	3.27033i	−0.0662079	+	0.168430i
$378$	15.9610	−	23.9007i	0.820945	−	1.22932i
$379$		−	30.4926i		−	1.56630i	−0.621832	−	0.783150i	$-0.713611\pi$
$379$		−	30.4926i		−	1.56630i	0.621832	−	0.783150i	$-0.286389\pi$
$380$	5.83943	+	10.1142i	0.299556	+	0.518847i
$381$	0.136561	+	0.248866i	0.00699622	+	0.0127498i
$382$	18.3775	+	10.6103i	0.940275	+	0.542868i
$383$	−21.6814	−	12.5178i	−1.10787	−	0.639628i	−0.169592	−	0.985514i	$-0.554245\pi$
$383$	−21.6814	−	12.5178i	−1.10787	−	0.639628i	−0.938276	+	0.345886i	$0.887578\pi$
$384$	−26.7605	−	16.2355i	−1.36561	−	0.828513i
$385$	−9.95162	+	5.74557i	−0.507182	+	0.292821i
$386$	26.1925			1.33316
$387$	−25.9578	−	1.12884i	−1.31951	−	0.0573824i
$388$			48.9128i			2.48317i
$389$	1.05615	+	1.82931i	0.0535490	+	0.0927495i	0.891557	−	0.452908i	$-0.149613\pi$
$389$	1.05615	+	1.82931i	0.0535490	+	0.0927495i	−0.838008	+	0.545657i	$0.816280\pi$
$390$	−17.6966	+	42.2963i	−0.896102	+	2.14176i
$391$	−23.6858	+	41.0250i	−1.19784	+	2.07472i
$392$	−2.70868	−	1.56385i	−0.136809	−	0.0789866i
$393$	−11.3105	−	0.245818i	−0.570541	−	0.0123999i
$394$	12.5902	+	21.8069i	0.634286	+	1.09861i
$395$		−	12.0182i		−	0.604701i
$396$	−11.9877	−	7.63408i	−0.602404	−	0.383627i
$397$		−	28.7853i		−	1.44469i	−0.691533	−	0.722345i	$-0.743064\pi$
$397$		−	28.7853i		−	1.44469i	0.691533	−	0.722345i	$-0.256936\pi$
$398$	2.73627	−	1.57979i	0.137157	−	0.0791875i
$399$	−2.46099	+	4.05637i	−0.123203	+	0.203073i
$400$	−0.285907	+	0.495206i	−0.0142954	+	0.0247603i
$401$	9.86207	+	5.69387i	0.492488	+	0.284338i	0.725606	−	0.688110i	$-0.241560\pi$
$401$	9.86207	+	5.69387i	0.492488	+	0.284338i	−0.233118	+	0.972448i	$0.574893\pi$
$402$	−1.47038	−	2.67959i	−0.0733357	−	0.133646i
$403$	−1.95622	−	13.0259i	−0.0974462	−	0.648865i
$404$	47.8791			2.38208
$405$	2.51255	−	28.8335i	0.124849	−	1.43275i
$406$	5.39048			0.267525
$407$	3.11713	+	5.39902i	0.154510	+	0.267620i
$408$	21.5529	−	11.8267i	1.06703	−	0.585511i
$409$	2.90604	+	1.67780i	0.143695	+	0.0829621i	0.570124	−	0.821559i	$-0.306895\pi$
$409$	2.90604	+	1.67780i	0.143695	+	0.0829621i	−0.426429	+	0.904521i	$0.640229\pi$
$410$	25.4897	+	14.7165i	1.25884	+	0.726794i
$411$	−20.6270	−	12.5143i	−1.01745	−	0.617285i
$412$	−10.4889	−	18.1673i	−0.516750	−	0.895037i
$413$	18.8170			0.925925
$414$	−53.3486	−	33.9738i	−2.62194	−	1.66972i
$415$	45.9120			2.25373
$416$	3.09416	+	20.6031i	0.151703	+	1.01015i
$417$	24.5575	+	0.533722i	1.20259	+	0.0261365i
$418$	3.29702	+	1.90354i	0.161263	+	0.0931050i
$419$	−1.03279	+	1.78885i	−0.0504552	+	0.0873910i	−0.890150	−	0.455668i	$-0.849401\pi$
$419$	−1.03279	+	1.78885i	−0.0504552	+	0.0873910i	0.839695	+	0.543059i	$0.182734\pi$
$420$	43.3347	+	0.941817i	2.11452	+	0.0459559i
$421$	29.3605	−	16.9513i	1.43094	−	0.826156i	0.433752	−	0.901032i	$-0.357189\pi$
$421$	29.3605	−	16.9513i	1.43094	−	0.826156i	0.997193	+	0.0748758i	$0.0238560\pi$
$422$			20.9663i			1.02062i
$423$	0.200676	−	4.61456i	0.00975720	−	0.224367i
$424$			2.04726i			0.0994236i
$425$	−13.7009	−	23.7306i	−0.664590	−	1.15110i
$426$	6.17649	−	10.1805i	0.299252	−	0.493248i
$427$	−17.0697	−	9.85522i	−0.826063	−	0.476927i
$428$	−15.0567	+	26.0789i	−0.727792	+	1.26057i
$429$	1.16968	+	9.13614i	0.0564728	+	0.441097i
$430$	−31.7927	−	55.0665i	−1.53318	−	2.65554i
$431$			30.6212i			1.47497i	0.675364	+	0.737485i	$0.263987\pi$
$431$			30.6212i			1.47497i	−0.675364	+	0.737485i	$0.736013\pi$
$432$	−0.246143	−	0.498803i	−0.0118426	−	0.0239987i
$433$	8.63597			0.415018			0.207509	−	0.978233i	$-0.433464\pi$
$433$	8.63597			0.415018			0.207509	+	0.978233i	$0.433464\pi$
$434$	−17.4991	+	10.1031i	−0.839986	+	0.484966i
$435$	4.75906	−	2.61144i	0.228179	−	0.125209i
$436$	40.5732	+	23.4249i	1.94310	+	1.12185i
$437$	9.04234	+	5.22060i	0.432554	+	0.249735i
$438$	−18.8905	+	31.1366i	−0.902622	+	1.48777i
$439$	−14.7827	−	25.6043i	−0.705538	−	1.22203i	−0.966497	−	0.256678i	$-0.917372\pi$
$439$	−14.7827	−	25.6043i	−0.705538	−	1.22203i	0.260959	−	0.965350i	$-0.415961\pi$
$440$		−	13.1239i		−	0.625658i
$441$	−1.56636	−	3.00768i	−0.0745886	−	0.143223i
$442$	−39.2979	−	15.4475i	−1.86921	−	0.734763i
$443$	−15.6331	−	27.0773i	−0.742751	−	1.28648i	−0.951238	−	0.308457i	$-0.900187\pi$
$443$	−15.6331	−	27.0773i	−0.742751	−	1.28648i	0.208487	−	0.978025i	$-0.433146\pi$
$444$	0.510961	−	23.5102i	0.0242491	−	1.11575i
$445$	13.2052	−	22.8721i	0.625988	−	1.08424i
$446$	7.26915	−	12.5905i	0.344204	−	0.596179i
$447$	−0.699141	+	32.1688i	−0.0330682	+	1.52153i
$448$	27.2292	−	15.7208i	1.28646	−	0.742738i
$449$		−	10.8346i		−	0.511316i	−0.966767	−	0.255658i	$-0.917708\pi$
$449$		−	10.8346i		−	0.511316i	0.966767	−	0.255658i	$-0.0822922\pi$
$450$	32.4486	−	16.8988i	1.52964	−	0.796618i
$451$	5.91283			0.278424
$452$	4.92663	+	8.53318i	0.231729	+	0.401367i
$453$	−17.6103	−	10.6841i	−0.827403	−	0.501983i
$454$	11.6393	−	20.1599i	0.546261	−	0.946152i
$455$	−17.5030	−	21.9721i	−0.820553	−	1.03007i
$456$	−2.60674	−	4.75048i	−0.122072	−	0.222462i
$457$	−13.8936	+	8.02147i	−0.649915	+	0.375229i	−0.788424	−	0.615133i	$-0.789102\pi$
$457$	−13.8936	+	8.02147i	−0.649915	+	0.375229i	0.138509	+	0.990361i	$0.455769\pi$
$458$	−18.5317			−0.865929
$459$	26.5983	+	1.73641i	1.24150	+	0.0810488i
$460$		−	95.3883i		−	4.44750i
$461$	22.1953	−	12.8145i	1.03374	−	0.596830i	0.115686	−	0.993286i	$-0.463093\pi$
$461$	22.1953	−	12.8145i	1.03374	−	0.596830i	0.918054	+	0.396456i	$0.129760\pi$
$462$	12.3872	−	6.79724i	0.576305	−	0.316236i
$463$	28.1926	+	16.2770i	1.31022	+	0.756457i	0.982133	−	0.188189i	$-0.0602619\pi$
$463$	28.1926	+	16.2770i	1.31022	+	0.756457i	0.328090	+	0.944647i	$0.393595\pi$
$464$	0.0521629	−	0.0903488i	0.00242160	−	0.00419434i
$465$	−10.5548	+	17.3972i	−0.489469	+	0.806777i
$466$	−16.5642	+	9.56335i	−0.767322	+	0.443014i
$467$	16.2179			0.750474			0.375237	−	0.926929i	$-0.377561\pi$
$467$	16.2179			0.750474			0.375237	+	0.926929i	$0.377561\pi$
$468$	14.1032	−	31.7519i	0.651920	−	1.46773i
$469$	1.87270			0.0864731
$470$	9.78924	−	5.65182i	0.451544	−	0.260699i
$471$	−6.90782	−	0.150131i	−0.318295	−	0.00691768i
$472$	−10.7454	+	18.6115i	−0.494596	+	0.856665i
$473$	−11.0624	−	6.38688i	−0.508650	−	0.293669i
$474$	−0.321095	+	14.7742i	−0.0147484	+	0.678600i
$475$	−5.23048	+	3.01982i	−0.239991	+	0.138559i
$476$			39.9187i			1.82967i
$477$	−1.19230	+	1.87225i	−0.0545918	+	0.0857247i
$478$	10.5302			0.481641
$479$	−8.86463	+	5.11800i	−0.405035	+	0.233847i	−0.688654	−	0.725090i	$-0.741798\pi$
$479$	−8.86463	+	5.11800i	−0.405035	+	0.233847i	0.283619	+	0.958937i	$0.408465\pi$
$480$	16.6946	−	27.5172i	0.762001	−	1.25598i
$481$	−11.9205	+	9.49584i	−0.543526	+	0.432973i
$482$	−9.17265	+	15.8875i	−0.417803	+	0.723655i
$483$	33.9729	−	18.6420i	1.54582	−	0.848239i
$484$	14.1725	+	24.5474i	0.644202	+	1.11579i
$485$	−48.9715			−2.22368
$486$	−3.85907	+	35.3783i	−0.175051	+	1.60479i
$487$		−	16.0863i		−	0.728940i	−0.931215	−	0.364470i	$-0.881250\pi$
$487$		−	16.0863i		−	0.728940i	0.931215	−	0.364470i	$-0.118750\pi$
$488$	19.4952	−	11.2555i	0.882505	−	0.509515i
$489$	−7.86710	+	4.31692i	−0.355762	+	0.195218i
$490$	4.14944	−	7.18705i	0.187453	−	0.324678i
$491$	−2.20943	+	3.82684i	−0.0997101	+	0.172703i	−0.911565	−	0.411157i	$-0.865125\pi$
$491$	−2.20943	+	3.82684i	−0.0997101	+	0.172703i	0.811855	+	0.583860i	$0.198458\pi$
$492$	−19.0684	−	11.5688i	−0.859671	−	0.521560i
$493$	2.49969	+	4.32958i	0.112580	+	0.194995i
$494$	−3.40479	+	8.66167i	−0.153189	+	0.389707i
$495$	7.64324	−	12.0021i	0.343538	−	0.539453i
$496$			0.391066i			0.0175594i
$497$	3.64786	+	6.31828i	0.163629	+	0.283414i
$498$	−56.4404	−	1.22665i	−2.52915	−	0.0549674i
$499$	6.39369	+	3.69140i	0.286221	+	0.165250i	0.636236	−	0.771494i	$-0.280490\pi$
$499$	6.39369	+	3.69140i	0.286221	+	0.165250i	−0.350015	+	0.936744i	$0.613824\pi$
$500$	3.05705	+	1.76499i	0.136715	+	0.0789327i
$501$	0.0307110	−	1.41307i	0.00137207	−	0.0631314i
$502$	−33.8339	+	19.5340i	−1.51008	+	0.871847i
$503$	5.65418			0.252107			0.126054	−	0.992023i	$-0.459769\pi$
$503$	5.65418			0.252107			0.126054	+	0.992023i	$0.459769\pi$
$504$	−20.0919	−	0.873750i	−0.894966	−	0.0389199i
$505$			47.9366i			2.13315i
$506$	−15.5473	−	26.9288i	−0.691163	−	1.19713i
$507$	−21.6620	+	6.14468i	−0.962044	+	0.272895i
$508$	0.263213	−	0.455898i	0.0116782	−	0.0202272i
$509$	23.2192	+	13.4056i	1.02917	+	0.594193i	0.916747	−	0.399467i	$-0.130805\pi$
$509$	23.2192	+	13.4056i	1.02917	+	0.594193i	0.112425	+	0.993660i	$0.464138\pi$
$510$	31.3804	+	57.1872i	1.38955	+	2.53229i
$511$	−11.1568	−	19.3242i	−0.493548	−	0.854850i
$512$		−	1.21094i		−	0.0535165i
$513$	0.382723	−	5.86254i	0.0168977	−	0.258838i
$514$			21.7208i			0.958065i
$515$	18.1891	−	10.5015i	0.801506	−	0.462750i
$516$	23.1791	+	42.2413i	1.02041	+	1.85957i
$517$	1.13540	−	1.96658i	0.0499350	−	0.0864899i
$518$	20.2470	+	11.6896i	0.889604	+	0.513613i
$519$	0.469938	−	0.774586i	0.0206280	−	0.0340005i
$520$	31.7272	−	4.76477i	1.39133	−	0.208949i
$521$	−20.3407			−0.891143			−0.445572	−	0.895246i	$-0.647000\pi$
$521$	−20.3407			−0.891143			−0.445572	+	0.895246i	$0.647000\pi$
$522$	−5.92016	+	3.08314i	−0.259118	+	0.134945i
$523$	5.74660			0.251281			0.125641	−	0.992076i	$-0.459901\pi$
$523$	5.74660			0.251281			0.125641	+	0.992076i	$0.459901\pi$
$524$	10.4899	+	18.1690i	0.458253	+	0.793717i
$525$	−0.487053	+	22.4102i	−0.0212568	+	0.978063i
$526$	−55.3376	−	31.9492i	−2.41283	−	1.39305i
$527$	−16.2295	−	9.37009i	−0.706967	−	0.408168i
$528$	0.00594185	−	0.273395i	0.000258586	−	0.0118980i
$529$	−31.1398	−	53.9357i	−1.35390	−	2.34503i
$530$	−5.43208			−0.235954
$531$	−20.6660	+	10.7626i	−0.896828	+	0.467056i
$532$	8.79851			0.381464
$533$	2.14671	+	14.2943i	0.0929843	+	0.619155i
$534$	−16.8445	+	27.7643i	−0.728932	+	1.20148i
$535$	−26.1103	−	15.0748i	−1.12884	−	0.651739i
$536$	−1.06939	+	1.85225i	−0.0461908	+	0.0800048i
$537$	−11.8110	−	21.5243i	−0.509684	−	0.928841i
$538$	22.5786	−	13.0357i	0.973431	−	0.562011i
$539$		−	1.66718i		−	0.0718104i
$540$	−48.1315	+	23.7514i	−2.07125	+	1.02210i
$541$		−	43.0286i		−	1.84994i	−0.380036	−	0.924972i	$-0.624088\pi$
$541$		−	43.0286i		−	1.84994i	0.380036	−	0.924972i	$-0.375912\pi$
$542$	−15.1574	−	26.2534i	−0.651068	−	1.12768i
$543$	−14.9778	−	27.2954i	−0.642760	−	1.17136i
$544$	25.6702	+	14.8207i	1.10060	+	0.635432i
$545$	−23.4531	+	40.6219i	−1.00462	+	1.74005i
$546$	20.9297	+	27.4783i	0.895707	+	1.17596i
$547$	11.1581	+	19.3265i	0.477088	+	0.826340i	0.999655	−	0.0262576i	$-0.00835902\pi$
$547$	11.1581	+	19.3265i	0.477088	+	0.826340i	−0.522567	+	0.852598i	$0.675026\pi$
$548$			44.7411i			1.91124i
$549$	24.3838	+	1.06039i	1.04068	+	0.0452565i
$550$	17.9865			0.766946
$551$	0.954285	−	0.550957i	0.0406539	−	0.0234716i
$552$	−0.961649	+	44.2473i	−0.0409305	+	1.88329i
$553$	−7.84113	−	4.52708i	−0.333439	−	0.192511i
$554$	3.56275	+	2.05696i	0.151367	+	0.0873917i
$555$	23.5385	+	0.511574i	0.999152	+	0.0217151i
$556$	−22.7757	−	39.4487i	−0.965906	−	1.67300i
$557$			28.7460i			1.21801i	0.793168	+	0.609003i	$0.208430\pi$
$557$			28.7460i			1.21801i	−0.793168	+	0.609003i	$0.791570\pi$
$558$	13.4400	−	21.1047i	0.568962	−	0.893433i
$559$	11.4240	−	29.0622i	0.483184	−	1.22920i
$560$	0.417008	+	0.722279i	0.0176218	+	0.0305219i
$561$	11.2037	+	6.79724i	0.473020	+	0.286980i
$562$	−13.1022	+	22.6936i	−0.552682	+	0.957273i
$563$	5.91647	−	10.2476i	0.249350	−	0.431886i	−0.713996	−	0.700150i	$-0.753117\pi$
$563$	5.91647	−	10.2476i	0.249350	−	0.431886i	0.963346	+	0.268264i	$0.0864499\pi$
$564$	−7.50929	+	4.12058i	−0.316198	+	0.173508i
$565$	−8.54342	+	4.93255i	−0.359424	+	0.207514i
$566$			51.7217i			2.17403i
$567$	−17.8656	−	12.5004i	−0.750285	−	0.524968i
$568$	−8.33237			−0.349619
$569$	4.39661	+	7.61515i	0.184315	+	0.319244i	0.943346	−	0.331812i	$-0.107660\pi$
$569$	4.39661	+	7.61515i	0.184315	+	0.319244i	−0.759030	+	0.651055i	$0.774327\pi$
$570$	12.6047	−	6.91657i	0.527951	−	0.289703i
$571$	−15.6380	+	27.0858i	−0.654430	+	1.13351i	0.327606	+	0.944814i	$0.393758\pi$
$571$	−15.6380	+	27.0858i	−0.654430	+	1.13351i	−0.982036	+	0.188692i	$0.939575\pi$
$572$	13.3600	−	10.6426i	0.558610	−	0.444989i
$573$	8.35084	−	13.7644i	0.348861	−	0.575018i
$574$	19.2032	−	11.0869i	0.801524	−	0.462760i
$575$	49.3294			2.05718
$576$	−20.9131	+	32.8396i	−0.871381	+	1.36832i
$577$			45.2450i			1.88357i	0.336210	+	0.941787i	$0.390855\pi$
$577$			45.2450i			1.88357i	−0.336210	+	0.941787i	$0.609145\pi$
$578$	−18.4154	+	10.6321i	−0.765978	+	0.442238i
$579$	0.431780	−	19.8670i	0.0179442	−	0.825644i
$580$	−8.71813	−	5.03341i	−0.362001	−	0.209001i
$581$	17.2944	−	29.9547i	0.717492	−	1.24273i
$582$	60.2015	+	1.30839i	2.49543	+	0.0542345i
$583$	−0.945058	+	0.545629i	−0.0391403	+	0.0225977i
$584$	25.4841			1.05454
$585$	31.7900	+	14.1201i	1.31436	+	0.583795i
$586$	37.3684			1.54368
$587$	25.1277	−	14.5075i	1.03713	−	0.598788i	0.118112	−	0.993000i	$-0.462316\pi$
$587$	25.1277	−	14.5075i	1.03713	−	0.598788i	0.919020	+	0.394212i	$0.128982\pi$
$588$	−3.26192	+	5.37652i	−0.134519	+	0.221724i
$589$	−2.06527	+	3.57715i	−0.0850978	+	0.147394i
$590$	−49.3828	−	28.5111i	−2.03306	−	1.17379i
$591$	16.7481	−	9.19019i	0.688924	−	0.378034i
$592$	0.391856	−	0.226238i	0.0161052	−	0.00929832i
$593$		−	25.7497i		−	1.05741i	−0.848805	−	0.528707i	$-0.822677\pi$
$593$		−	25.7497i		−	1.05741i	0.848805	−	0.528707i	$-0.177323\pi$
$594$	−9.71663	+	14.5501i	−0.398678	+	0.596999i
$595$	−39.9666			−1.63847
$596$	51.6753	−	29.8347i	2.11670	−	1.22208i
$597$	−1.15316	−	2.10150i	−0.0471957	−	0.0860088i
$598$	59.4559	−	47.3625i	2.43133	−	1.93680i
$599$	−18.8670	+	32.6786i	−0.770885	+	1.33521i	0.166194	+	0.986093i	$0.446852\pi$
$599$	−18.8670	+	32.6786i	−0.770885	+	1.33521i	−0.937079	+	0.349118i	$0.886481\pi$
$600$	−21.8874	−	13.2790i	−0.893548	−	0.542112i
$601$	−8.46451	−	14.6610i	−0.345274	−	0.598033i	0.640129	−	0.768267i	$-0.278881\pi$
$601$	−8.46451	−	14.6610i	−0.345274	−	0.598033i	−0.985404	+	0.170235i	$0.945547\pi$
$602$	−47.9033			−1.95239
$603$	−2.05671	+	1.07111i	−0.0837557	+	0.0436189i
$604$			38.1977i			1.55424i
$605$	−24.5769	+	14.1895i	−0.999192	+	0.576884i
$606$	1.28074	−	58.9292i	0.0520265	−	2.39384i
$607$	6.13946	−	10.6339i	0.249193	−	0.431615i	−0.714109	−	0.700034i	$-0.753168\pi$
$607$	6.13946	−	10.6339i	0.249193	−	0.431615i	0.963302	+	0.268420i	$0.0865014\pi$
$608$	3.26664	−	5.65798i	0.132480	−	0.229461i
$609$	0.0888615	−	4.08868i	0.00360085	−	0.165682i
$610$	29.8648	+	51.7274i	1.20919	+	2.09438i
$611$	5.16643	+	2.03086i	0.209011	+	0.0821598i
$612$	−22.8319	−	43.8412i	−0.922926	−	1.77217i
$613$		−	3.84764i		−	0.155405i	−0.996977	−	0.0777023i	$-0.975242\pi$
$613$		−	3.84764i		−	0.155405i	0.996977	−	0.0777023i	$-0.0247584\pi$
$614$	−19.0385	−	32.9756i	−0.768330	−	1.33079i
$615$	11.5826	−	19.0913i	0.467057	−	0.769836i
$616$	−8.56254	−	4.94359i	−0.344995	−	0.199183i
$617$	29.7198	+	17.1587i	1.19647	+	0.690785i	0.959767	−	0.280796i	$-0.0905986\pi$
$617$	29.7198	+	17.1587i	1.19647	+	0.690785i	0.236707	+	0.971581i	$0.423932\pi$
$618$	−22.6407	+	12.4237i	−0.910742	+	0.499753i
$619$	−36.7880	+	21.2396i	−1.47864	+	0.853691i	−0.999708	−	0.0241630i	$-0.992308\pi$
$619$	−36.7880	+	21.2396i	−1.47864	+	0.853691i	−0.478928	+	0.877854i	$0.658975\pi$
$620$	37.7356			1.51550
$621$	−26.6486	+	39.9049i	−1.06937	+	1.60133i
$622$		−	18.5202i		−	0.742594i
$623$	−9.94843	−	17.2312i	−0.398575	−	0.690353i
$624$	0.663092	−	0.0848944i	0.0265449	−	0.00339850i
$625$	11.5872	−	20.0697i	0.463490	−	0.802788i
$626$	−43.5050	−	25.1176i	−1.73881	−	1.00390i
$627$	1.49818	−	2.46941i	0.0598317	−	0.0986188i
$628$	6.40661	+	11.0966i	0.255652	+	0.442802i
$629$			21.6830i			0.864557i
$630$	2.31836	−	53.3108i	0.0923657	−	2.12395i
$631$		−	17.9430i		−	0.714300i	−0.934047	−	0.357150i	$-0.883748\pi$
$631$		−	17.9430i		−	0.714300i	0.934047	−	0.357150i	$-0.116252\pi$
$632$	8.95528	−	5.17033i	0.356222	−	0.205665i
$633$	15.9029	+	0.345627i	0.632085	+	0.0137374i
$634$	−7.68100	+	13.3039i	−0.305052	+	0.528365i
$635$	0.456446	+	0.263529i	0.0181135	+	0.0104578i
$636$	4.11529	+	0.0894398i	0.163182	+	0.00354652i
$637$	4.03041	−	0.605285i	0.159691	−	0.0239823i
$638$	−3.28158			−0.129919
$639$	−7.62011	−	4.85269i	−0.301447	−	0.191970i
$640$	−58.1146			−2.29718
$641$	8.43114	+	14.6032i	0.333010	+	0.576790i	0.983101	−	0.183066i	$-0.0586023\pi$
$641$	8.43114	+	14.6032i	0.333010	+	0.576790i	−0.650090	+	0.759857i	$0.725269\pi$
$642$	31.6950	+	19.2292i	1.25090	+	0.758918i
$643$	43.2179	+	24.9519i	1.70435	+	0.984006i	0.941242	+	0.337732i	$0.109660\pi$
$643$	43.2179	+	24.9519i	1.70435	+	0.984006i	0.763105	+	0.646274i	$0.223674\pi$
$644$	−62.2350	−	35.9314i	−2.45240	−	1.41589i
$645$	−42.2920	+	23.2070i	−1.66525	+	0.913774i
$646$	6.62057	+	11.4672i	0.260483	+	0.451170i
$647$	28.5920			1.12407			0.562034	−	0.827114i	$-0.310019\pi$
$647$	28.5920			1.12407			0.562034	+	0.827114i	$0.310019\pi$
$648$	22.5660	−	10.5322i	0.886475	−	0.413743i
$649$	−11.4553			−0.449660
$650$	6.53017	+	43.4824i	0.256134	+	1.70552i
$651$	7.37476	+	13.4397i	0.289040	+	0.526742i
$652$	14.4118	+	8.32063i	0.564408	+	0.325861i
$653$	−13.2734	+	22.9902i	−0.519429	+	0.899677i	0.480316	+	0.877095i	$0.340522\pi$
$653$	−13.2734	+	22.9902i	−0.519429	+	0.899677i	−0.999745	+	0.0225814i	$0.992812\pi$
$654$	29.9165	−	49.3105i	1.16983	−	1.92819i
$655$	−18.1908	+	10.5025i	−0.710774	+	0.410366i
$656$		−	0.429147i		−	0.0167554i
$657$	23.3057	+	14.8417i	0.909243	+	0.579031i
$658$		−	8.51582i		−	0.331981i
$659$	21.7318	+	37.6406i	0.846552	+	1.46627i	0.884266	+	0.466983i	$0.154659\pi$
$659$	21.7318	+	37.6406i	0.846552	+	1.46627i	−0.0377144	+	0.999289i	$0.512008\pi$
$660$	−26.3810	−	0.573353i	−1.02688	−	0.0223177i
$661$	−13.6716	−	7.89332i	−0.531765	−	0.307015i	0.209970	−	0.977708i	$-0.432663\pi$
$661$	−13.6716	−	7.89332i	−0.531765	−	0.307015i	−0.741735	+	0.670693i	$0.765997\pi$
$662$	−0.298266	+	0.516612i	−0.0115924	+	0.0200787i
$663$	−12.3648	+	29.5528i	−0.480208	+	1.14774i
$664$	19.7517	+	34.2110i	0.766516	+	1.32764i
$665$			8.80907i			0.341601i
$666$	−28.9226	−	1.25777i	−1.12073	−	0.0487377i
$667$	−9.00000			−0.348481
$668$	−2.26993	+	1.31055i	−0.0878263	+	0.0507065i
$669$	−9.43009	−	5.72120i	−0.364588	−	0.221194i
$670$	−4.91464	−	2.83747i	−0.189869	−	0.109621i
$671$	10.3916	+	5.99960i	0.401163	+	0.231612i
$672$	−11.6647	−	21.2575i	−0.449974	−	0.820027i
$673$	8.76355	+	15.1789i	0.337810	+	0.585104i	0.984021	−	0.178055i	$-0.0569805\pi$
$673$	8.76355	+	15.1789i	0.337810	+	0.585104i	−0.646210	+	0.763159i	$0.723647\pi$
$674$		−	13.4423i		−	0.517778i
$675$	−12.2829	−	24.8909i	−0.472767	−	0.958050i
$676$	30.5790	+	28.4340i	1.17611	+	1.09362i
$677$	9.25036	+	16.0221i	0.355520	+	0.615779i	0.987207	−	0.159445i	$-0.0509703\pi$
$677$	9.25036	+	16.0221i	0.355520	+	0.615779i	−0.631687	+	0.775224i	$0.717637\pi$
$678$	10.6343	−	5.83540i	0.408410	−	0.224107i
$679$	−18.4469	+	31.9509i	−0.707925	+	1.22616i
$680$	22.8227	−	39.5302i	0.875212	−	1.51591i
$681$	−15.0994	−	9.16077i	−0.578611	−	0.351041i
$682$	10.6530	−	6.15052i	0.407925	−	0.235516i
$683$		−	4.68607i		−	0.179307i	−0.995973	−	0.0896537i	$-0.971424\pi$
$683$		−	4.68607i		−	0.179307i	0.995973	−	0.0896537i	$-0.0285760\pi$
$684$	−9.66306	+	5.03240i	−0.369476	+	0.192418i
$685$	−44.7948			−1.71152
$686$	−22.4847	−	38.9447i	−0.858472	−	1.48692i
$687$	−0.305493	+	14.0563i	−0.0116553	+	0.536281i
$688$	−0.463553	+	0.802898i	−0.0176728	+	0.0306102i
$689$	−1.66217	−	2.08659i	−0.0633238	−	0.0794926i
$690$	−117.403	−	2.55159i	−4.46946	−	0.0971372i
$691$	37.3398	−	21.5581i	1.42047	−	0.820110i	0.424133	−	0.905600i	$-0.360579\pi$
$691$	37.3398	−	21.5581i	1.42047	−	0.820110i	0.996339	+	0.0854897i	$0.0272455\pi$
$692$	−1.68012			−0.0638686
$693$	−4.95151	−	9.50774i	−0.188092	−	0.361169i
$694$		−	7.30099i		−	0.277142i
$695$	39.4961	−	22.8031i	1.49817	−	0.864970i
$696$	3.99329	+	2.42271i	0.151365	+	0.0918327i
$697$	17.8099	+	10.2825i	0.674596	+	0.389478i
$698$	15.9061	−	27.5502i	0.602056	−	1.04279i
$699$	6.98074	+	12.7216i	0.264036	+	0.481175i
$700$	35.9994	−	20.7842i	1.36065	−	0.785570i
$701$	35.9226			1.35678			0.678389	−	0.734703i	$-0.262678\pi$
$701$	35.9226			1.35678			0.678389	+	0.734703i	$0.262678\pi$
$702$	−38.7027	−	18.2074i	−1.46074	−	0.687195i
$703$	4.77915			0.180249
$704$	−16.5764	+	9.57041i	−0.624748	+	0.360698i
$705$	−4.12553	−	7.51831i	−0.155377	−	0.283156i
$706$	17.9083	−	31.0181i	0.673988	−	1.16738i
$707$	31.2756	+	18.0570i	1.17624	+	0.679104i
$708$	36.9425	+	22.4129i	1.38838	+	0.842327i
$709$	20.9125	−	12.0738i	0.785384	−	0.453442i	−0.0529511	−	0.998597i	$-0.516863\pi$
$709$	20.9125	−	12.0738i	0.785384	−	0.453442i	0.838335	+	0.545156i	$0.183529\pi$
$710$		−	22.1087i		−	0.829723i
$711$	11.2009	+	0.487101i	0.420067	+	0.0182677i
$712$	22.7240			0.851618
$713$	29.2167	−	16.8683i	1.09418	−	0.631722i
$714$	49.1316	+	1.06780i	1.83870	+	0.0399615i
$715$	10.6554	+	13.3760i	0.398488	+	0.500236i
$716$	−22.7651	+	39.4303i	−0.850772	+	1.47358i
$717$	0.173589	−	7.98718i	0.00648282	−	0.298287i
$718$	−6.69468	−	11.5955i	−0.249843	−	0.432741i
$719$	−32.3717			−1.20726			−0.603630	−	0.797265i	$-0.706280\pi$
$719$	−32.3717			−1.20726			−0.603630	+	0.797265i	$0.706280\pi$
$720$	−0.871099	−	0.554739i	−0.0324639	−	0.0206739i
$721$		−	15.8230i		−	0.589279i
$722$	−35.0378	+	20.2291i	−1.30397	+	0.752848i
$723$	11.8995	+	7.21936i	0.442546	+	0.268491i
$724$	−28.8689	+	50.0024i	−1.07291	+	1.85833i
$725$	2.60299	−	4.50851i	0.0966727	−	0.167442i
$726$	30.5919	−	16.7867i	1.13537	−	0.623013i
$727$	−9.76910	−	16.9206i	−0.362316	−	0.627549i	0.626026	−	0.779802i	$-0.284680\pi$
$727$	−9.76910	−	16.9206i	−0.362316	−	0.627549i	−0.988342	+	0.152253i	$0.951347\pi$
$728$	8.84243	−	22.4948i	0.327722	−	0.833713i
$729$	26.7708	+	3.51031i	0.991512	+	0.130012i
$730$			67.6182i			2.50266i
$731$	−22.2138	−	38.4754i	−0.821607	−	1.42307i
$732$	−21.7736	−	39.6799i	−0.804776	−	1.46661i
$733$	−35.7224	−	20.6243i	−1.31944	−	0.761777i	−0.335799	−	0.941934i	$-0.609006\pi$
$733$	−35.7224	−	20.6243i	−1.31944	−	0.761777i	−0.983638	+	0.180157i	$0.942340\pi$
$734$	6.59513	+	3.80770i	0.243431	+	0.140545i
$735$	−5.38298	−	3.26583i	−0.198554	−	0.120462i
$736$	−46.2122	+	26.6806i	−1.70340	+	0.983460i
$737$	−1.14005			−0.0419942
$738$	−14.7488	+	23.1598i	−0.542911	+	0.852524i
$739$			12.6677i			0.465988i	0.972478	+	0.232994i	$0.0748523\pi$
$739$			12.6677i			0.465988i	−0.972478	+	0.232994i	$0.925148\pi$
$740$	−21.8306	−	37.8117i	−0.802509	−	1.38999i
$741$	6.51375	+	2.72532i	0.239289	+	0.100117i
$742$	−2.04618	+	3.54409i	−0.0751177	+	0.130108i
$743$	10.3523	+	5.97690i	0.379789	+	0.219271i	0.677726	−	0.735314i	$-0.262965\pi$
$743$	10.3523	+	5.97690i	0.379789	+	0.219271i	−0.297938	+	0.954585i	$0.596299\pi$
$744$	−17.5042	−	0.380428i	−0.641735	−	0.0139472i
$745$	29.8705	+	51.7373i	1.09437	+	1.89551i
$746$		−	60.8215i		−	2.22683i
$747$	−1.86083	+	42.7898i	−0.0680841	+	1.56560i
$748$		−	24.3015i		−	0.888549i
$749$	−19.6707	+	11.3569i	−0.718751	+	0.414971i
$750$	2.25411	−	3.71538i	0.0823084	−	0.135666i
$751$	6.59296	−	11.4193i	0.240581	−	0.416698i	−0.720299	−	0.693663i	$-0.755996\pi$
$751$	6.59296	−	11.4193i	0.240581	−	0.416698i	0.960880	+	0.276966i	$0.0893289\pi$
$752$	−0.142732	−	0.0824064i	−0.00520490	−	0.00300505i
$753$	14.2588	+	25.9851i	0.519620	+	0.946949i
$754$	−1.19141	−	7.93324i	−0.0433886	−	0.288912i
$755$	−38.2436			−1.39183
$756$	−2.63414	+	40.3496i	−0.0958027	+	1.46750i
$757$	−26.1835			−0.951657			−0.475829	−	0.879538i	$-0.657852\pi$
$757$	−26.1835			−0.951657			−0.475829	+	0.879538i	$0.657852\pi$
$758$	34.8070	+	60.2876i	1.26425	+	2.18974i
$759$	−20.6818	+	11.3487i	−0.750701	+	0.411933i
$760$	−8.71286	−	5.03037i	−0.316049	−	0.182471i
$761$	6.00320	+	3.46595i	0.217616	+	0.125640i	0.604846	−	0.796343i	$-0.293235\pi$
$761$	6.00320	+	3.46595i	0.217616	+	0.125640i	−0.387230	+	0.921983i	$0.626568\pi$
$762$	−0.554075	−	0.336156i	−0.0200720	−	0.0121776i
$763$	17.6688	+	30.6033i	0.639655	+	1.10792i
$764$	−29.8559			−1.08015
$765$	43.8938	−	22.8593i	1.58698	−	0.826481i
$766$	57.1557			2.06512
$767$	−4.15896	−	27.6933i	−0.150171	−	0.999946i
$768$	26.4956	+	0.575844i	0.956079	+	0.0207790i
$769$	−33.4083	−	19.2883i	−1.20473	−	0.695553i	−0.243129	−	0.969994i	$-0.578174\pi$
$769$	−33.4083	−	19.2883i	−1.20473	−	0.695553i	−0.961604	+	0.274441i	$0.911507\pi$
$770$	13.1170	−	22.7194i	0.472705	−	0.818749i
$771$	16.4753	+	0.358065i	0.593342	+	0.0128954i
$772$	−31.9140	+	18.4255i	−1.14861	+	0.663149i
$773$		−	34.7210i		−	1.24883i	−0.781093	−	0.624415i	$-0.785338\pi$
$773$		−	34.7210i		−	1.24883i	0.781093	−	0.624415i	$-0.214662\pi$
$774$	52.6103	−	27.3988i	1.89104	−	0.984828i
$775$			19.5147i			0.700988i
$776$	−21.0680	−	36.4908i	−0.756296	−	1.30994i
$777$	9.20036	−	15.1647i	0.330061	−	0.544030i
$778$	−4.17627	−	2.41117i	−0.149727	−	0.0864447i
$779$	2.26638	−	3.92548i	0.0812014	−	0.140645i
$780$	−8.19181	−	63.9845i	−0.293314	−	2.29101i
$781$	−2.22072	−	3.84640i	−0.0794637	−	0.137635i
$782$		−	108.148i		−	3.86738i
$783$	2.24097	+	4.54127i	0.0800857	+	0.162292i
$784$	−0.121002			−0.00432150
$785$	−11.1099	+	6.41430i	−0.396529	+	0.228936i
$786$	22.6429	−	12.4249i	0.807644	−	0.443180i
$787$	−31.0375	−	17.9195i	−1.10637	−	0.638761i	−0.168480	−	0.985705i	$-0.553886\pi$
$787$	−31.0375	−	17.9195i	−1.10637	−	0.638761i	−0.937886	+	0.346944i	$0.887219\pi$
$788$	−30.6808	−	17.7136i	−1.09296	−	0.631020i
$789$	−25.1457	+	41.4469i	−0.895210	+	1.47555i
$790$	13.7187	+	23.7614i	0.488088	+	0.845394i
$791$			7.43207i			0.264254i
$792$	12.2314	+	0.531916i	0.434625	+	0.0189008i
$793$	−10.7313	+	27.3000i	−0.381079	+	0.969451i
$794$	32.8581	+	56.9119i	1.16609	+	2.01973i
$795$	−0.0895472	+	4.12023i	−0.00317591	+	0.146130i
$796$	−2.22265	+	3.84975i	−0.0787798	+	0.136451i
$797$	19.4271	−	33.6487i	0.688144	−	1.19190i	−0.284294	−	0.958737i	$-0.591759\pi$
$797$	19.4271	−	33.6487i	0.688144	−	1.19190i	0.972438	−	0.233163i	$-0.0749075\pi$
$798$	0.235355	−	10.8291i	0.00833148	−	0.383347i
$799$	6.83983	−	3.94898i	0.241976	−	0.139705i
$800$		−	30.8664i		−	1.09129i
$801$	20.7815	+	13.2342i	0.734279	+	0.467609i
$802$	−25.9980			−0.918020
$803$	6.79197	+	11.7640i	0.239683	+	0.415144i
$804$	3.67657	+	2.23056i	0.129663	+	0.0786659i
$805$	35.9745	−	62.3097i	1.26793	−	2.19613i
$806$	18.7366	+	23.5207i	0.659968	+	0.828482i
$807$	−9.51541	−	17.3407i	−0.334958	−	0.610423i
$808$	−35.7196	+	20.6227i	−1.25661	+	0.725505i
$809$	−12.2765			−0.431619			−0.215809	−	0.976435i	$-0.569239\pi$
$809$	−12.2765			−0.431619			−0.215809	+	0.976435i	$0.569239\pi$
$810$	27.9455	+	59.8752i	0.981905	+	2.10380i
$811$		−	13.8855i		−	0.487585i	−0.969827	−	0.243792i	$-0.921608\pi$
$811$		−	13.8855i		−	0.487585i	0.969827	−	0.243792i	$-0.0783915\pi$
$812$	−6.56798	+	3.79202i	−0.230491	+	0.133074i
$813$	−20.1631	+	11.0641i	−0.707151	+	0.388036i
$814$	−12.3259	−	7.11634i	−0.432021	−	0.249428i
$815$	−8.33062	+	14.4291i	−0.291809	+	0.505428i
$816$	0.493337	−	0.813153i	0.0172703	−	0.0284660i
$817$	−8.48039	+	4.89616i	−0.296691	+	0.171295i
$818$	−7.66079			−0.267853
$819$	21.1873	−	15.4222i	0.740345	−	0.538895i
$820$	−41.4102			−1.44611
$821$	−7.91360	+	4.56892i	−0.276187	+	0.159456i	−0.631696	−	0.775216i	$-0.717641\pi$
$821$	−7.91360	+	4.56892i	−0.276187	+	0.159456i	0.355509	+	0.934673i	$0.384307\pi$
$822$	55.0669	+	1.19680i	1.92068	+	0.0417431i
$823$	−1.95741	+	3.39033i	−0.0682310	+	0.118180i	−0.898123	−	0.439745i	$-0.855069\pi$
$823$	−1.95741	+	3.39033i	−0.0682310	+	0.118180i	0.829892	+	0.557925i	$0.188402\pi$
$824$	15.6502	+	9.03564i	0.545200	+	0.314771i
$825$	0.296505	−	13.6428i	0.0103230	−	0.474980i
$826$	−37.2035	+	21.4794i	−1.29448	+	0.747366i
$827$			18.1786i			0.632131i	0.948737	+	0.316065i	$0.102362\pi$
$827$			18.1786i			0.632131i	−0.948737	+	0.316065i	$0.897638\pi$
$828$	88.9016	+	3.86612i	3.08954	+	0.134357i
$829$	38.0468			1.32142			0.660711	−	0.750641i	$-0.270255\pi$
$829$	38.0468			1.32142			0.660711	+	0.750641i	$0.270255\pi$
$830$	−90.7735	+	52.4081i	−3.15080	+	1.81911i
$831$	1.61893	−	2.66844i	0.0561602	−	0.0925671i
$832$	−29.1548	−	36.5990i	−1.01076	−	1.26884i
$833$	2.89925	−	5.02165i	0.100453	−	0.173990i
$834$	−49.1624	+	26.9770i	−1.70235	+	0.934135i
$835$	−1.31212	−	2.27266i	−0.0454077	−	0.0786485i
$836$	−5.35630			−0.185251
$837$	−15.7864	−	10.5422i	−0.545656	−	0.364391i
$838$		−	4.71569i		−	0.162901i
$839$	24.7704	−	14.3012i	0.855171	−	0.493733i	−0.00722153	−	0.999974i	$-0.502299\pi$
$839$	24.7704	−	14.3012i	0.855171	−	0.493733i	0.862392	+	0.506241i	$0.168965\pi$
$840$	−32.7350	+	17.9627i	−1.12946	+	0.619772i
$841$	14.0251	−	24.2922i	0.483624	−	0.837661i
$842$	−38.6995	+	67.0295i	−1.33367	+	2.30999i
$843$	16.9971	+	10.3121i	0.585412	+	0.355168i
$844$	−14.7491	−	25.5462i	−0.507684	−	0.879335i
$845$	−28.4681	+	30.6157i	−0.979334	+	1.05321i
$846$	4.87071	+	9.35260i	0.167459	+	0.321549i
$847$			21.3798i			0.734620i
$848$	0.0396012	+	0.0685914i	0.00135991	+	0.00235544i
$849$	39.2310	+	0.852627i	1.34640	+	0.0292621i
$850$	54.1765	+	31.2788i	1.85824	+	1.07286i
$851$	−33.8047	−	19.5171i	−1.15881	−	0.669039i
$852$	−0.364022	+	16.7493i	−0.0124712	+	0.573822i
$853$	26.0272	−	15.0268i	0.891154	−	0.514508i	0.0168345	−	0.999858i	$-0.494641\pi$
$853$	26.0272	−	15.0268i	0.891154	−	0.514508i	0.874320	+	0.485350i	$0.161308\pi$
$854$	44.9986			1.53982
$855$	−5.03844	−	9.67466i	−0.172311	−	0.330866i
$856$		−	25.9412i		−	0.886650i
$857$	0.668881	+	1.15854i	0.0228485	+	0.0395748i	0.877224	−	0.480082i	$-0.159393\pi$
$857$	0.668881	+	1.15854i	0.0228485	+	0.0395748i	−0.854375	+	0.519657i	$0.826060\pi$
$858$	−12.7414	−	16.7281i	−0.434985	−	0.571087i
$859$	20.6362	−	35.7429i	0.704097	−	1.21953i	−0.262920	−	0.964818i	$-0.584685\pi$
$859$	20.6362	−	35.7429i	0.704097	−	1.21953i	0.967017	−	0.254714i	$-0.0819812\pi$
$860$	77.4749	+	44.7301i	2.64187	+	1.52529i
$861$	−8.09289	−	14.7484i	−0.275805	−	0.502623i
$862$	−34.9538	−	60.5417i	−1.19053	−	2.06206i
$863$			37.3326i			1.27082i	0.772176	+	0.635408i	$0.219168\pi$
$863$			37.3326i			1.27082i	−0.772176	+	0.635408i	$0.780832\pi$
$864$	24.9693	+	16.6746i	0.849473	+	0.567281i
$865$		−	1.68214i		−	0.0571944i
$866$	−17.0743	+	9.85788i	−0.580210	+	0.334984i
$867$	7.76089	+	14.1433i	0.263574	+	0.480333i
$868$	14.2144	−	24.6201i	0.482469	−	0.835661i
$869$	4.77347	+	2.75597i	0.161929	+	0.0934897i
$870$	−6.42829	+	10.5956i	−0.217939	+	0.359223i
$871$	−0.413906	−	2.75607i	−0.0140247	−	0.0933860i
$872$	−40.3588			−1.36672
$873$	1.98483	−	45.6413i	0.0671763	−	1.54472i
$874$	−23.8371			−0.806301
$875$	1.33129	+	2.30586i	0.0450057	+	0.0779521i
$876$	1.11334	−	51.2269i	0.0376163	−	1.73080i
$877$	34.8042	+	20.0942i	1.17526	+	0.678534i	0.954912	−	0.296889i	$-0.0959490\pi$
$877$	34.8042	+	20.0942i	1.17526	+	0.678534i	0.220343	+	0.975422i	$0.429282\pi$
$878$	58.4542	+	33.7485i	1.97273	+	1.13896i
$879$	0.616014	−	28.3440i	0.0207776	−	0.956018i
$880$	−0.253863	−	0.439704i	−0.00855773	−	0.0148224i
$881$	13.8402			0.466289			0.233144	−	0.972442i	$-0.425099\pi$
$881$	13.8402			0.466289			0.233144	+	0.972442i	$0.425099\pi$
$882$	6.53012	+	4.15856i	0.219881	+	0.140026i
$883$	−29.1280			−0.980235			−0.490118	−	0.871656i	$-0.663046\pi$
$883$	−29.1280			−0.980235			−0.490118	+	0.871656i	$0.663046\pi$
$884$	58.7489	−	8.82288i	1.97594	−	0.296746i
$885$	−22.4398	+	36.9868i	−0.754305	+	1.24330i
$886$	61.8170	+	35.6901i	2.07678	+	1.19903i
$887$	−9.07561	+	15.7194i	−0.304729	+	0.527806i	−0.977201	−	0.212316i	$-0.931899\pi$
$887$	−9.07561	+	15.7194i	−0.304729	+	0.527806i	0.672472	+	0.740123i	$0.265233\pi$
$888$	9.74525	+	17.7596i	0.327029	+	0.595973i
$889$	0.343873	−	0.198535i	0.0115331	−	0.00665865i
$890$			60.2946i			2.02108i
$891$	10.8761	+	7.60992i	0.364363	+	0.254942i
$892$			20.4544i			0.684864i
$893$	−0.870396	−	1.50757i	−0.0291267	−	0.0504489i
$894$	−35.3380	−	64.3995i	−1.18188	−	2.15384i
$895$	−39.4777	−	22.7924i	−1.31959	−	0.761867i
$896$	−21.8909	+	37.9162i	−0.731324	+	1.26669i
$897$	−34.9444	−	45.8781i	−1.16676	−	1.53182i
$898$	12.3676	+	21.4213i	0.412712	+	0.714838i
$899$		−	3.56040i		−	0.118746i
$900$	−27.6489	+	43.4167i	−0.921632	+	1.44722i
$901$	−3.79544			−0.126444
$902$	−11.6904	+	6.74944i	−0.389247	+	0.224732i
$903$	−0.789680	+	36.3347i	−0.0262789	+	1.20914i
$904$	−7.35090	−	4.24404i	−0.244487	−	0.141155i
$905$	−50.0625	−	28.9036i	−1.66413	−	0.960788i
$906$	47.0134	+	1.02177i	1.56192	+	0.0339459i
$907$	−2.55936	−	4.43293i	−0.0849820	−	0.147193i	0.820402	−	0.571788i	$-0.193750\pi$
$907$	−2.55936	−	4.43293i	−0.0849820	−	0.147193i	−0.905384	+	0.424595i	$0.860417\pi$
$908$			32.7515i			1.08690i
$909$	−44.6767	−	1.94288i	−1.48183	−	0.0644414i
$910$	59.6865	+	23.4620i	1.97859	+	0.777758i
$911$	−21.1217	−	36.5839i	−0.699794	−	1.21208i	−0.968538	−	0.248867i	$-0.919942\pi$
$911$	−21.1217	−	36.5839i	−0.699794	−	1.21208i	0.268744	−	0.963212i	$-0.413392\pi$
$912$	−0.179228	−	0.108737i	−0.00593482	−	0.00360063i
$913$	−10.5284	+	18.2356i	−0.348438	+	0.603512i
$914$	18.3129	−	31.7188i	0.605736	−	1.04916i
$915$	39.7276	−	21.7998i	1.31335	−	0.720678i
$916$	22.5797	−	13.0364i	0.746056	−	0.430735i
$917$			15.8245i			0.522571i
$918$	−54.5701	+	26.9286i	−1.80108	+	0.888776i
$919$	37.2207			1.22780			0.613899	−	0.789384i	$-0.289600\pi$
$919$	37.2207			1.22780			0.613899	+	0.789384i	$0.289600\pi$
$920$	41.0861	+	71.1633i	1.35457	+	2.34618i
$921$	−25.3259	+	13.8971i	−0.834515	+	0.457925i
$922$	−29.2552	+	50.6715i	−0.963469	+	1.66878i
$923$	8.49245	−	6.76508i	0.279532	−	0.222675i
$924$	−10.3114	+	16.9960i	−0.339221	+	0.559128i
$925$	19.5541	−	11.2895i	0.642933	−	0.371198i
$926$	−74.3202			−2.44231
$927$	9.05012	+	17.3778i	0.297245	+	0.570761i
$928$			5.63149i			0.184863i
$929$	−18.3982	+	10.6222i	−0.603624	+	0.348502i	−0.770466	−	0.637481i	$-0.779976\pi$
$929$	−18.3982	+	10.6222i	−0.603624	+	0.348502i	0.166842	+	0.985984i	$0.446643\pi$
$930$	1.00941	−	46.4446i	0.0330997	−	1.52298i
$931$	−1.10683	−	0.639026i	−0.0362747	−	0.0209432i
$932$	13.4550	−	23.3047i	0.440733	−	0.763372i
$933$	−14.0476	−	0.305304i	−0.459898	−	0.00999520i
$934$	−32.0647	+	18.5126i	−1.04919	+	0.605750i
$935$	24.3306			0.795697
$936$	3.15483	+	29.7627i	0.103119	+	0.972824i
$937$	−55.6976			−1.81956			−0.909781	−	0.415089i	$-0.863750\pi$
$937$	−55.6976			−1.81956			−0.909781	+	0.415089i	$0.863750\pi$
$938$	−3.70255	+	2.13767i	−0.120892	+	0.0697973i
$939$	−19.7689	+	32.5845i	−0.645134	+	1.06336i
$940$	−7.95173	+	13.7728i	−0.259357	+	0.449219i
$941$	−17.2655	−	9.96821i	−0.562838	−	0.324954i	0.191446	−	0.981503i	$-0.438682\pi$
$941$	−17.2655	−	9.96821i	−0.562838	−	0.324954i	−0.754284	+	0.656549i	$0.772016\pi$
$942$	13.8290	−	7.58838i	0.450572	−	0.247243i
$943$	−32.0618	+	18.5109i	−1.04408	+	0.602797i
$944$			0.831414i			0.0270602i
$945$	−40.3981	−	2.63730i	−1.31415	−	0.0857914i
$946$	29.1622			0.948146
$947$	−28.2364	+	16.3023i	−0.917560	+	0.529754i	−0.882856	−	0.469644i	$-0.844382\pi$
$947$	−28.2364	+	16.3023i	−0.917560	+	0.529754i	−0.0347045	+	0.999398i	$0.511049\pi$
$948$	−10.0019	−	18.2273i	−0.324847	−	0.591996i
$949$	−25.9737	+	20.6907i	−0.843143	+	0.671647i
$950$	6.89419	−	11.9411i	0.223677	−	0.387420i
$951$	9.96438	+	6.04536i	0.323117	+	0.196034i
$952$	−17.1940	−	29.7808i	−0.557260	−	0.965203i
$953$	−15.6146			−0.505808			−0.252904	−	0.967491i	$-0.581386\pi$
$953$	−15.6146			−0.505808			−0.252904	+	0.967491i	$0.581386\pi$
$954$	0.220163	−	5.06267i	0.00712806	−	0.163910i
$955$		−	29.8917i		−	0.967273i
$956$	−12.8304	+	7.40766i	−0.414966	+	0.239581i
$957$	−0.0540965	+	2.48908i	−0.00174869	+	0.0804606i
$958$	11.6843	−	20.2378i	0.377502	−	0.653853i
$959$	−16.8735	+	29.2258i	−0.544875	+	0.943750i
$960$	−1.57067	+	72.2694i	−0.0506931	+	2.33248i
$961$	−8.82691	−	15.2887i	−0.284739	−	0.493183i
$962$	12.7288	−	32.3815i	0.410392	−	1.04402i
$963$	15.1079	−	23.7237i	0.486844	−	0.764485i
$964$		−	25.8106i		−	0.831304i
$965$	−18.4477	−	31.9523i	−0.593851	−	1.02858i
$966$	−45.8888	+	75.6371i	−1.47645	+	2.43358i
$967$	−3.47716	−	2.00754i	−0.111818	−	0.0645581i	0.443048	−	0.896498i	$-0.353897\pi$
$967$	−3.47716	−	2.00754i	−0.111818	−	0.0645581i	−0.554866	+	0.831940i	$0.687230\pi$
$968$	−21.1464	−	12.2089i	−0.679670	−	0.392407i
$969$	8.80699	−	4.83267i	0.282921	−	0.155248i
$970$	96.8226	−	55.9006i	3.10879	−	1.79486i
$971$	−27.3969			−0.879209			−0.439604	−	0.898192i	$-0.644881\pi$
$971$	−27.3969			−0.879209			−0.439604	+	0.898192i	$0.644881\pi$
$972$	−20.1854	−	45.8211i	−0.647447	−	1.46971i
$973$		−	34.3583i		−	1.10148i
$974$	18.3624	+	31.8045i	0.588368	+	1.01908i
$975$	33.0891	−	4.23633i	1.05970	−	0.135671i
$976$	0.435445	−	0.754212i	0.0139382	−	0.0241417i
$977$	−33.3866	−	19.2758i	−1.06813	−	0.616687i	−0.140462	−	0.990086i	$-0.544859\pi$
$977$	−33.3866	−	19.2758i	−1.06813	−	0.616687i	−0.927671	+	0.373399i	$0.878192\pi$
$978$	10.6265	−	17.5153i	0.339797	−	0.560077i
$979$	6.05634	+	10.4899i	0.193561	+	0.335258i
$980$			11.6760i			0.372976i
$981$	−36.9089	−	23.5046i	−1.17841	−	0.750444i
$982$		−	10.0882i		−	0.321926i
$983$	40.2933	−	23.2633i	1.28516	−	0.741986i	0.307370	−	0.951590i	$-0.400551\pi$
$983$	40.2933	−	23.2633i	1.28516	−	0.741986i	0.977786	+	0.209604i	$0.0672176\pi$
$984$	19.2087	+	0.417473i	0.612351	+	0.0133086i
$985$	17.7349	−	30.7177i	0.565079	−	0.978746i
$986$	−9.88435	−	5.70673i	−0.314782	−	0.181739i
$987$	−6.45925	−	0.140382i	−0.205600	−	0.00446842i
$988$	−1.94466	−	12.9489i	−0.0618677	−	0.411959i
$989$	79.9798			2.54321
$990$	−1.41136	+	32.4542i	−0.0448558	+	1.03146i
$991$	41.1031			1.30568			0.652841	−	0.757495i	$-0.273577\pi$
$991$	41.1031			1.30568			0.652841	+	0.757495i	$0.273577\pi$
$992$	−10.5548	−	18.2815i	−0.335116	−	0.580439i
$993$	0.386933	+	0.234751i	0.0122790	+	0.00744960i
$994$	−14.4245	−	8.32800i	−0.457518	−	0.264148i
$995$	−3.85437	−	2.22532i	−0.122192	−	0.0705474i
$996$	69.6321	−	38.2093i	2.20638	−	1.21071i
$997$	27.8886	+	48.3045i	0.883241	+	1.52982i	0.847716	+	0.530450i	$0.177977\pi$
$997$	27.8886	+	48.3045i	0.883241	+	1.52982i	0.0355252	+	0.999369i	$0.488690\pi$
$998$	−16.8548			−0.533529
$999$	−1.43081	+	21.9170i	−0.0452687	+	0.693424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.t.c.103.2	yes	20
3.2	odd	2		351.2.t.c.64.9		20
9.2	odd	6		351.2.t.c.181.2		20
9.4	even	3		1053.2.b.j.649.2		10
9.5	odd	6		1053.2.b.i.649.9		10
9.7	even	3	inner	117.2.t.c.25.9	yes	20
13.12	even	2	inner	117.2.t.c.103.9	yes	20
39.38	odd	2		351.2.t.c.64.2		20
117.25	even	6	inner	117.2.t.c.25.2	✓	20
117.38	odd	6		351.2.t.c.181.9		20
117.77	odd	6		1053.2.b.i.649.2		10
117.103	even	6		1053.2.b.j.649.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.t.c.25.2	✓	20	117.25	even	6	inner
117.2.t.c.25.9	yes	20	9.7	even	3	inner
117.2.t.c.103.2	yes	20	1.1	even	1	trivial
117.2.t.c.103.9	yes	20	13.12	even	2	inner
351.2.t.c.64.2		20	39.38	odd	2
351.2.t.c.64.9		20	3.2	odd	2
351.2.t.c.181.2		20	9.2	odd	6
351.2.t.c.181.9		20	117.38	odd	6
1053.2.b.i.649.2		10	117.77	odd	6
1053.2.b.i.649.9		10	9.5	odd	6
1053.2.b.j.649.2		10	9.4	even	3
1053.2.b.j.649.9		10	117.103	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.97712 + 1.14149i) q^{2} +(0.833228 + 1.51846i) q^{3} +(1.60600 - 2.78168i) q^{4} +(2.78501 + 1.60793i) q^{5} +(-3.38070 - 2.05106i) q^{6} +(2.09815 - 1.21137i) q^{7} +2.76698i q^{8} +(-1.61146 + 2.53045i) q^{9} -7.34174 q^{10} +(-1.27730 + 0.737448i) q^{11} +(5.56204 + 0.120883i) q^{12} +(-2.24652 - 2.82013i) q^{13} +(-2.76553 + 4.79003i) q^{14} +(-0.121028 + 5.56871i) q^{15} +(0.0535232 + 0.0927049i) q^{16} -5.12974 q^{17} +(0.297563 - 6.84248i) q^{18} +1.13065i q^{19} +(8.94547 - 5.16467i) q^{20} +(3.58765 + 2.17662i) q^{21} +(1.68358 - 2.91604i) q^{22} +(4.61735 - 7.99748i) q^{23} +(-4.20155 + 2.30552i) q^{24} +(2.67087 + 4.62608i) q^{25} +(7.66079 + 3.01136i) q^{26} +(-5.18512 - 0.338499i) q^{27} -7.78182i q^{28} +(-0.487293 - 0.844016i) q^{29} +(-6.11735 - 11.1482i) q^{30} +(3.16380 + 1.82662i) q^{31} +(-5.00419 - 2.88917i) q^{32} +(-2.18407 - 1.32507i) q^{33} +(10.1421 - 5.85555i) q^{34} +7.79116 q^{35} +(4.45089 + 8.54647i) q^{36} -4.22691i q^{37} +(-1.29063 - 2.23543i) q^{38} +(2.41041 - 5.76107i) q^{39} +(-4.44910 + 7.70607i) q^{40} +(-3.47188 - 2.00449i) q^{41} +(-9.57780 - 0.208159i) q^{42} +(4.33040 + 7.50047i) q^{43} +4.73737i q^{44} +(-8.55673 + 4.45623i) q^{45} +21.0826i q^{46} +(-1.33337 + 0.769820i) q^{47} +(-0.0961719 + 0.158517i) q^{48} +(-0.565185 + 0.978929i) q^{49} +(-10.5613 - 6.09755i) q^{50} +(-4.27425 - 7.78932i) q^{51} +(-11.4526 + 1.71995i) q^{52} +0.739889 q^{53} +(10.6380 - 5.24951i) q^{54} -4.74305 q^{55} +(3.35182 + 5.80553i) q^{56} +(-1.71685 + 0.942089i) q^{57} +(1.92687 + 1.11248i) q^{58} +(6.72630 + 3.88343i) q^{59} +(15.2960 + 9.28002i) q^{60} +(-4.06781 - 7.04566i) q^{61} -8.34028 q^{62} +(-0.315778 + 7.26133i) q^{63} +12.9777 q^{64} +(-1.72201 - 11.4664i) q^{65} +(5.83071 + 0.126722i) q^{66} +(0.669411 + 0.386485i) q^{67} +(-8.23837 + 14.2693i) q^{68} +(15.9912 + 0.347545i) q^{69} +(-15.4041 + 8.89354i) q^{70} +3.01136i q^{71} +(-7.00171 - 4.45888i) q^{72} -9.21010i q^{73} +(4.82498 + 8.35711i) q^{74} +(-4.79909 + 7.91020i) q^{75} +(3.14510 + 1.81582i) q^{76} +(-1.78664 + 3.09455i) q^{77} +(1.81054 + 14.1418i) q^{78} +(-1.86858 - 3.23648i) q^{79} +0.344246i q^{80} +(-3.80639 - 8.15545i) q^{81} +9.15243 q^{82} +(12.3640 - 7.13838i) q^{83} +(11.8164 - 6.48403i) q^{84} +(-14.2864 - 8.24826i) q^{85} +(-17.1234 - 9.88621i) q^{86} +(0.875581 - 1.44319i) q^{87} +(-2.04050 - 3.53425i) q^{88} -8.21257i q^{89} +(11.8309 - 18.5779i) q^{90} +(-8.12974 - 3.19570i) q^{91} +(-14.8309 - 25.6879i) q^{92} +(-0.137489 + 6.32611i) q^{93} +(1.75748 - 3.04405i) q^{94} +(-1.81800 + 3.14887i) q^{95} +(0.217466 - 10.0060i) q^{96} +(-13.1880 + 7.61407i) q^{97} -2.58061i q^{98} +(0.192237 - 4.42051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 12 q^{4} - 2 q^{9} - 16 q^{10} - 2 q^{12} - 4 q^{13} - 18 q^{14} + 4 q^{16} - 12 q^{17} - 10 q^{22} + 24 q^{23} - 12 q^{25} - 12 q^{26} - 22 q^{27} + 12 q^{29} - 54 q^{30} - 12 q^{35} + 50 q^{36}+ \cdots + 24 q^{95}+O(q^{100}) \) 20 * q + 2 * q^3 + 12 * q^4 - 2 * q^9 - 16 * q^10 - 2 * q^12 - 4 * q^13 - 18 * q^14 + 4 * q^16 - 12 * q^17 - 10 * q^22 + 24 * q^23 - 12 * q^25 - 12 * q^26 - 22 * q^27 + 12 * q^29 - 54 * q^30 - 12 * q^35 + 50 * q^36 + 12 * q^38 - 8 * q^39 - 8 * q^40 + 6 * q^42 + 4 * q^43 + 38 * q^48 - 10 * q^49 - 78 * q^51 + 108 * q^53 + 20 * q^55 + 36 * q^56 - 2 * q^61 - 72 * q^62 + 8 * q^64 - 24 * q^65 + 78 * q^66 + 24 * q^68 + 72 * q^69 - 42 * q^74 - 8 * q^75 - 6 * q^77 + 66 * q^78 - 14 * q^79 + 46 * q^81 - 4 * q^82 - 54 * q^87 + 22 * q^88 + 24 * q^90 - 72 * q^91 - 84 * q^92 + 20 * q^94 + 24 * q^95

Introduction

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