LMFDB - Embedded newform 861.2.s.a.206.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(206,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("861.206");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.s (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:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$106$
Relative dimension:	$53$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			206.4
Character	$\chi$	$=$	861.206
Dual form			861.2.s.a.698.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15448 + 1.24389i) q^{2} +(-1.08687 + 1.34860i) q^{3} +(2.09453 - 3.62783i) q^{4} +(-1.86942 - 3.23792i) q^{5} +(0.664120 - 4.25748i) q^{6} +(1.06496 - 2.42195i) q^{7} +5.44590i q^{8} +(-0.637447 - 2.93149i) q^{9} +O(q^{10})$	\(q+(-2.15448 + 1.24389i) q^{2} +(-1.08687 + 1.34860i) q^{3} +(2.09453 - 3.62783i) q^{4} +(-1.86942 - 3.23792i) q^{5} +(0.664120 - 4.25748i) q^{6} +(1.06496 - 2.42195i) q^{7} +5.44590i q^{8} +(-0.637447 - 2.93149i) q^{9} +(8.05525 + 4.65070i) q^{10} +(-1.36004 - 0.785219i) q^{11} +(2.61602 + 6.76765i) q^{12} +2.25478i q^{13} +(0.718197 + 6.54275i) q^{14} +(6.39847 + 0.998092i) q^{15} +(-2.58505 - 4.47744i) q^{16} +(3.44922 - 5.97423i) q^{17} +(5.01983 + 5.52294i) q^{18} +(1.08967 - 0.629120i) q^{19} -15.6622 q^{20} +(2.10877 + 4.06855i) q^{21} +3.90691 q^{22} +(5.97351 - 3.44881i) q^{23} +(-7.34435 - 5.91896i) q^{24} +(-4.48943 + 7.77592i) q^{25} +(-2.80470 - 4.85789i) q^{26} +(4.64623 + 2.32648i) q^{27} +(-6.55583 - 8.93636i) q^{28} +7.15360i q^{29} +(-15.0269 + 5.80863i) q^{30} +(-6.09696 - 3.52008i) q^{31} +(1.70631 + 0.985137i) q^{32} +(2.53713 - 0.980723i) q^{33} +17.1618i q^{34} +(-9.83296 + 1.07936i) q^{35} +(-11.9701 - 3.82755i) q^{36} +(-3.43680 - 5.95271i) q^{37} +(-1.56511 + 2.71086i) q^{38} +(-3.04080 - 2.45064i) q^{39} +(17.6334 - 10.1807i) q^{40} +1.00000 q^{41} +(-9.60414 - 6.14253i) q^{42} -4.61323 q^{43} +(-5.69729 + 3.28933i) q^{44} +(-8.30030 + 7.54419i) q^{45} +(-8.57988 + 14.8608i) q^{46} +(-4.01339 - 6.95139i) q^{47} +(8.84787 + 1.38017i) q^{48} +(-4.73170 - 5.15858i) q^{49} -22.3375i q^{50} +(4.30801 + 11.1448i) q^{51} +(8.17997 + 4.72271i) q^{52} +(3.90268 + 2.25322i) q^{53} +(-12.9041 + 0.767050i) q^{54} +5.87161i q^{55} +(13.1897 + 5.79969i) q^{56} +(-0.335891 + 2.15330i) q^{57} +(-8.89829 - 15.4123i) q^{58} +(-2.56318 + 4.43956i) q^{59} +(17.0227 - 21.1220i) q^{60} +(4.77305 - 2.75572i) q^{61} +17.5144 q^{62} +(-7.77880 - 1.57807i) q^{63} +5.43859 q^{64} +(7.30081 - 4.21513i) q^{65} +(-4.24628 + 5.26886i) q^{66} +(3.40888 - 5.90435i) q^{67} +(-14.4490 - 25.0264i) q^{68} +(-1.84134 + 11.8043i) q^{69} +(19.8423 - 14.5566i) q^{70} -7.12407i q^{71} +(15.9646 - 3.47147i) q^{72} +(2.63855 + 1.52337i) q^{73} +(14.8091 + 8.55001i) q^{74} +(-5.60721 - 14.5058i) q^{75} -5.27085i q^{76} +(-3.35016 + 2.45772i) q^{77} +(9.59968 + 1.49745i) q^{78} +(7.18503 + 12.4448i) q^{79} +(-9.66506 + 16.7404i) q^{80} +(-8.18732 + 3.73734i) q^{81} +(-2.15448 + 1.24389i) q^{82} -10.4985 q^{83} +(19.1769 + 0.871421i) q^{84} -25.7921 q^{85} +(9.93912 - 5.73836i) q^{86} +(-9.64734 - 7.77500i) q^{87} +(4.27623 - 7.40664i) q^{88} +(3.12888 + 5.41938i) q^{89} +(8.49871 - 26.5785i) q^{90} +(5.46097 + 2.40126i) q^{91} -28.8945i q^{92} +(11.3738 - 4.39651i) q^{93} +(17.2935 + 9.98443i) q^{94} +(-4.07409 - 2.35218i) q^{95} +(-3.18308 + 1.23042i) q^{96} -6.03979i q^{97} +(16.6111 + 5.22836i) q^{98} +(-1.43491 + 4.48749i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q + 52 q^{4} - 5 q^{7} - 2 q^{9}+O(q^{10}) $ 106 * q + 52 * q^4 - 5 * q^7 - 2 * q^9	$ 106 q + 52 q^{4} - 5 q^{7} - 2 q^{9} - 6 q^{10} - 22 q^{12} - 20 q^{14} - 4 q^{15} - 42 q^{16} - 5 q^{18} + 3 q^{19} - 36 q^{20} + 8 q^{21} - 12 q^{22} + 18 q^{23} - 57 q^{25} + 42 q^{26} + 18 q^{27} - 14 q^{28} - 107 q^{30} - 21 q^{31} - 2 q^{33} - 48 q^{35} - 16 q^{36} - q^{37} + 4 q^{39} - 18 q^{40} + 106 q^{41} + 77 q^{42} - 6 q^{43} + 210 q^{44} + 24 q^{45} - 8 q^{46} + 16 q^{47} + 70 q^{48} - 3 q^{49} - 42 q^{51} + 6 q^{52} - 16 q^{54} - 60 q^{56} - 22 q^{57} + 10 q^{58} - 16 q^{59} - 4 q^{60} + 18 q^{61} - 104 q^{62} + 33 q^{63} - 84 q^{64} + 36 q^{65} + 8 q^{66} + 21 q^{67} + 36 q^{68} - 12 q^{69} + 38 q^{70} - 148 q^{72} + 21 q^{73} - 40 q^{75} - 100 q^{77} + 60 q^{78} - 11 q^{79} - 36 q^{80} - 2 q^{81} - 20 q^{83} + 118 q^{84} - 4 q^{85} + 90 q^{86} + 17 q^{87} - 14 q^{88} + 16 q^{89} + 44 q^{90} + 19 q^{91} - 87 q^{93} + 24 q^{94} - 156 q^{96} - 268 q^{98} + 18 q^{99}+O(q^{100}) $ 106 * q + 52 * q^4 - 5 * q^7 - 2 * q^9 - 6 * q^10 - 22 * q^12 - 20 * q^14 - 4 * q^15 - 42 * q^16 - 5 * q^18 + 3 * q^19 - 36 * q^20 + 8 * q^21 - 12 * q^22 + 18 * q^23 - 57 * q^25 + 42 * q^26 + 18 * q^27 - 14 * q^28 - 107 * q^30 - 21 * q^31 - 2 * q^33 - 48 * q^35 - 16 * q^36 - q^37 + 4 * q^39 - 18 * q^40 + 106 * q^41 + 77 * q^42 - 6 * q^43 + 210 * q^44 + 24 * q^45 - 8 * q^46 + 16 * q^47 + 70 * q^48 - 3 * q^49 - 42 * q^51 + 6 * q^52 - 16 * q^54 - 60 * q^56 - 22 * q^57 + 10 * q^58 - 16 * q^59 - 4 * q^60 + 18 * q^61 - 104 * q^62 + 33 * q^63 - 84 * q^64 + 36 * q^65 + 8 * q^66 + 21 * q^67 + 36 * q^68 - 12 * q^69 + 38 * q^70 - 148 * q^72 + 21 * q^73 - 40 * q^75 - 100 * q^77 + 60 * q^78 - 11 * q^79 - 36 * q^80 - 2 * q^81 - 20 * q^83 + 118 * q^84 - 4 * q^85 + 90 * q^86 + 17 * q^87 - 14 * q^88 + 16 * q^89 + 44 * q^90 + 19 * q^91 - 87 * q^93 + 24 * q^94 - 156 * q^96 - 268 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−2.15448	+	1.24389i	−1.52345	+	0.879564i	−0.523834	+	0.851820i	$0.675499\pi$
$2$	−2.15448	+	1.24389i	−1.52345	+	0.879564i	−0.999615	+	0.0277434i	$0.991168\pi$
$3$	−1.08687	+	1.34860i	−0.627502	+	0.778615i
$3$	−1.08687	+	1.34860i	−0.627502	+	0.778615i
$4$	2.09453	−	3.62783i	1.04726	−	1.81392i
$5$	−1.86942	−	3.23792i	−0.836028	−	1.44804i	−0.893191	−	0.449678i	$-0.851539\pi$
$5$	−1.86942	−	3.23792i	−0.836028	−	1.44804i	0.0571623	−	0.998365i	$-0.481795\pi$
$6$	0.664120	−	4.25748i	0.271126	−	1.73811i
$7$	1.06496	−	2.42195i	0.402519	−	0.915412i
$7$	1.06496	−	2.42195i	0.402519	−	0.915412i
$8$			5.44590i			1.92542i
$9$	−0.637447	−	2.93149i	−0.212482	−	0.977165i
$10$	8.05525	+	4.65070i	2.54729	+	1.47068i
$11$	−1.36004	−	0.785219i	−0.410067	−	0.236753i	0.280751	−	0.959781i	$-0.409416\pi$
$11$	−1.36004	−	0.785219i	−0.410067	−	0.236753i	−0.690819	+	0.723028i	$0.742750\pi$
$12$	2.61602	+	6.76765i	0.755181	+	1.95365i
$13$			2.25478i			0.625364i	0.949858	+	0.312682i	$0.101227\pi$
$13$			2.25478i			0.625364i	−0.949858	+	0.312682i	$0.898773\pi$
$14$	0.718197	+	6.54275i	0.191946	+	1.74862i
$15$	6.39847	+	0.998092i	1.65208	+	0.257706i
$16$	−2.58505	−	4.47744i	−0.646262	−	1.11936i
$17$	3.44922	−	5.97423i	0.836560	−	1.44896i	−0.0561948	−	0.998420i	$-0.517897\pi$
$17$	3.44922	−	5.97423i	0.836560	−	1.44896i	0.892754	−	0.450544i	$-0.148770\pi$
$18$	5.01983	+	5.52294i	1.18318	+	1.30177i
$19$	1.08967	−	0.629120i	0.249987	−	0.144330i	−0.369771	−	0.929123i	$-0.620564\pi$
$19$	1.08967	−	0.629120i	0.249987	−	0.144330i	0.619758	+	0.784793i	$0.287231\pi$
$20$	−15.6622			−3.50217
$21$	2.10877	+	4.06855i	0.460172	+	0.887830i
$22$	3.90691			0.832956
$23$	5.97351	−	3.44881i	1.24556	−	0.719126i	0.275341	−	0.961347i	$-0.411209\pi$
$23$	5.97351	−	3.44881i	1.24556	−	0.719126i	0.970221	+	0.242221i	$0.0778759\pi$
$24$	−7.34435	−	5.91896i	−1.49916	−	1.20820i
$25$	−4.48943	+	7.77592i	−0.897886	+	1.55518i
$26$	−2.80470	−	4.85789i	−0.550047	−	0.952710i
$27$	4.64623	+	2.32648i	0.894168	+	0.447731i
$28$	−6.55583	−	8.93636i	−1.23894	−	1.68881i
$29$			7.15360i			1.32839i	0.747560	+	0.664195i	$0.231225\pi$
$29$			7.15360i			1.32839i	−0.747560	+	0.664195i	$0.768775\pi$
$30$	−15.0269	+	5.80863i	−2.74353	+	1.06051i
$31$	−6.09696	−	3.52008i	−1.09505	−	0.632225i	−0.160131	−	0.987096i	$-0.551192\pi$
$31$	−6.09696	−	3.52008i	−1.09505	−	0.632225i	−0.934915	+	0.354871i	$0.884525\pi$
$32$	1.70631	+	0.985137i	0.301635	+	0.174149i
$33$	2.53713	−	0.980723i	0.441657	−	0.170722i
$34$			17.1618i			2.94323i
$35$	−9.83296	+	1.07936i	−1.66207	+	0.182446i
$36$	−11.9701	−	3.82755i	−1.99502	−	0.637925i
$37$	−3.43680	−	5.95271i	−0.565007	−	0.978620i	−0.997049	−	0.0767670i	$-0.975540\pi$
$37$	−3.43680	−	5.95271i	−0.565007	−	0.978620i	0.432042	−	0.901853i	$-0.357793\pi$
$38$	−1.56511	+	2.71086i	−0.253895	+	0.439759i
$39$	−3.04080	−	2.45064i	−0.486918	−	0.392417i
$40$	17.6334	−	10.1807i	2.78809	−	1.60970i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−9.60414	−	6.14253i	−1.48195	−	0.947813i
$43$	−4.61323			−0.703511			−0.351756	−	0.936092i	$-0.614415\pi$
$43$	−4.61323			−0.703511			−0.351756	+	0.936092i	$0.614415\pi$
$44$	−5.69729	+	3.28933i	−0.858898	+	0.495885i
$45$	−8.30030	+	7.54419i	−1.23734	+	1.12462i
$46$	−8.57988	+	14.8608i	−1.26503	+	2.19110i
$47$	−4.01339	−	6.95139i	−0.585413	−	1.01396i	−0.994824	−	0.101614i	$-0.967599\pi$
$47$	−4.01339	−	6.95139i	−0.585413	−	1.01396i	0.409411	−	0.912350i	$-0.365734\pi$
$48$	8.84787	+	1.38017i	1.27708	+	0.199211i
$49$	−4.73170	−	5.15858i	−0.675957	−	0.736941i
$50$		−	22.3375i		−	3.15899i
$51$	4.30801	+	11.1448i	0.603242	+	1.56059i
$52$	8.17997	+	4.72271i	1.13436	+	0.654922i
$53$	3.90268	+	2.25322i	0.536075	+	0.309503i	0.743487	−	0.668751i	$-0.233171\pi$
$53$	3.90268	+	2.25322i	0.536075	+	0.309503i	−0.207412	+	0.978254i	$0.566504\pi$
$54$	−12.9041	+	0.767050i	−1.75603	+	0.104382i
$55$			5.87161i			0.791727i
$56$	13.1897	+	5.79969i	1.76255	+	0.775016i
$57$	−0.335891	+	2.15330i	−0.0444898	+	0.285211i
$58$	−8.89829	−	15.4123i	−1.16840	−	2.02373i
$59$	−2.56318	+	4.43956i	−0.333698	+	0.577982i	−0.983234	−	0.182349i	$-0.941630\pi$
$59$	−2.56318	+	4.43956i	−0.333698	+	0.577982i	0.649536	+	0.760331i	$0.274963\pi$
$60$	17.0227	−	21.1220i	2.19762	−	2.72684i
$61$	4.77305	−	2.75572i	0.611127	−	0.352834i	−0.162279	−	0.986745i	$-0.551885\pi$
$61$	4.77305	−	2.75572i	0.611127	−	0.352834i	0.773406	+	0.633910i	$0.218551\pi$
$62$	17.5144			2.22433
$63$	−7.77880	−	1.57807i	−0.980036	−	0.198818i
$64$	5.43859			0.679823
$65$	7.30081	−	4.21513i	0.905554	−	0.522822i
$66$	−4.24628	+	5.26886i	−0.522682	+	0.648552i
$67$	3.40888	−	5.90435i	0.416461	−	0.721331i	−0.579120	−	0.815242i	$-0.696604\pi$
$67$	3.40888	−	5.90435i	0.416461	−	0.721331i	0.995581	+	0.0939112i	$0.0299370\pi$
$68$	−14.4490	−	25.0264i	−1.75220	−	3.03490i
$69$	−1.84134	+	11.8043i	−0.221671	+	1.42107i
$70$	19.8423	−	14.5566i	2.37161	−	1.73985i
$71$		−	7.12407i		−	0.845472i	−0.906253	−	0.422736i	$-0.861070\pi$
$71$		−	7.12407i		−	0.845472i	0.906253	−	0.422736i	$-0.138930\pi$
$72$	15.9646	−	3.47147i	1.88145	−	0.409117i
$73$	2.63855	+	1.52337i	0.308819	+	0.178297i	0.646398	−	0.763000i	$-0.276275\pi$
$73$	2.63855	+	1.52337i	0.308819	+	0.178297i	−0.337579	+	0.941297i	$0.609608\pi$
$74$	14.8091	+	8.55001i	1.72152	+	0.993919i
$75$	−5.60721	−	14.5058i	−0.647464	−	1.67499i
$76$		−	5.27085i		−	0.604607i
$77$	−3.35016	+	2.45772i	−0.381786	+	0.280083i
$78$	9.59968	+	1.49745i	1.08695	+	0.169552i
$79$	7.18503	+	12.4448i	0.808379	+	1.40015i	0.913986	+	0.405746i	$0.132988\pi$
$79$	7.18503	+	12.4448i	0.808379	+	1.40015i	−0.105607	+	0.994408i	$0.533679\pi$
$80$	−9.66506	+	16.7404i	−1.08059	+	1.87163i
$81$	−8.18732	+	3.73734i	−0.909703	+	0.415260i
$82$	−2.15448	+	1.24389i	−0.237923	+	0.137365i
$83$	−10.4985			−1.15236			−0.576180	−	0.817323i	$-0.695457\pi$
$83$	−10.4985			−1.15236			−0.576180	+	0.817323i	$0.695457\pi$
$84$	19.1769	+	0.871421i	2.09237	+	0.0950798i
$85$	−25.7921			−2.79755
$86$	9.93912	−	5.73836i	1.07176	−	0.618783i
$87$	−9.64734	−	7.77500i	−1.03430	−	0.833567i
$88$	4.27623	−	7.40664i	0.455847	−	0.789551i
$89$	3.12888	+	5.41938i	0.331661	+	0.574454i	0.982838	−	0.184473i	$-0.0590577\pi$
$89$	3.12888	+	5.41938i	0.331661	+	0.574454i	−0.651177	+	0.758926i	$0.725724\pi$
$90$	8.49871	−	26.5785i	0.895843	−	2.80162i
$91$	5.46097	+	2.40126i	0.572466	+	0.251721i
$92$		−	28.8945i		−	3.01246i
$93$	11.3738	−	4.39651i	1.17940	−	0.455897i
$94$	17.2935	+	9.98443i	1.78369	+	1.02982i
$95$	−4.07409	−	2.35218i	−0.417993	−	0.241328i
$96$	−3.18308	+	1.23042i	−0.324872	+	0.125579i
$97$		−	6.03979i		−	0.613248i	−0.951831	−	0.306624i	$-0.900801\pi$
$97$		−	6.03979i		−	0.613248i	0.951831	−	0.306624i	$-0.0991994\pi$
$98$	16.6111	+	5.22836i	1.67797	+	0.528144i
$99$	−1.43491	+	4.48749i	−0.144214	+	0.451009i
$100$	18.8065	+	32.5738i	1.88065	+	3.25738i
$101$	−1.38002	+	2.39027i	−0.137318	+	0.237841i	−0.926480	−	0.376343i	$-0.877181\pi$
$101$	−1.38002	+	2.39027i	−0.137318	+	0.237841i	0.789163	+	0.614184i	$0.210515\pi$
$102$	−23.1445	−	18.6526i	−2.29164	−	1.84688i
$103$	8.20073	−	4.73469i	0.808042	−	0.466523i	−0.0382336	−	0.999269i	$-0.512173\pi$
$103$	8.20073	−	4.73469i	0.808042	−	0.466523i	0.846275	+	0.532746i	$0.178840\pi$
$104$	−12.2793			−1.20409
$105$	9.23147	−	14.4339i	0.900899	−	1.40860i
$106$	−11.2110			−1.08891
$107$	−10.5130	+	6.06971i	−1.01633	+	0.586781i	−0.913040	−	0.407870i	$-0.866272\pi$
$107$	−10.5130	+	6.06971i	−1.01633	+	0.586781i	−0.103294	+	0.994651i	$0.532938\pi$
$108$	18.1718	−	11.9829i	1.74858	−	1.15305i
$109$	−4.76283	+	8.24947i	−0.456197	+	0.790156i	−0.998756	−	0.0498614i	$-0.984122\pi$
$109$	−4.76283	+	8.24947i	−0.456197	+	0.790156i	0.542559	+	0.840017i	$0.317455\pi$
$110$	−7.30364	−	12.6503i	−0.696375	−	1.20616i
$111$	11.7632	+	1.83493i	1.11651	+	0.174164i
$112$	−13.5971	+	1.49255i	−1.28481	+	0.141033i
$113$			5.73108i			0.539135i	0.962981	+	0.269568i	$0.0868807\pi$
$113$			5.73108i			0.539135i	−0.962981	+	0.269568i	$0.913119\pi$
$114$	−1.95480	−	5.05705i	−0.183083	−	0.473636i
$115$	−22.3339	−	12.8945i	−2.08265	−	1.20242i
$116$	25.9520	+	14.9834i	2.40959	+	1.39118i
$117$	6.60988	−	1.43730i	0.611084	−	0.132879i
$118$		−	12.7533i		−	1.17403i
$119$	−10.7960	−	14.7162i	−0.989668	−	1.34903i
$120$	−5.43551	+	34.8454i	−0.496192	+	3.18094i
$121$	−4.26686	−	7.39042i	−0.387896	−	0.671856i
$122$	−6.85564	+	11.8743i	−0.620681	+	1.07505i
$123$	−1.08687	+	1.34860i	−0.0979994	+	0.121599i
$124$	−25.5405	+	14.7458i	−2.29361	+	1.32421i
$125$	14.8763			1.33058
$126$	18.7222	−	6.27605i	1.66791	−	0.559115i
$127$	−15.5409			−1.37903			−0.689514	−	0.724272i	$-0.742176\pi$
$127$	−15.5409			−1.37903			−0.689514	+	0.724272i	$0.742176\pi$
$128$	−15.1300	+	8.73528i	−1.33731	+	0.772097i
$129$	5.01396	−	6.22141i	0.441455	−	0.547764i
$130$	−10.4863	+	18.1628i	−0.919710	+	1.59299i
$131$	−8.45939	−	14.6521i	−0.739100	−	1.28016i	−0.952901	−	0.303281i	$-0.901918\pi$
$131$	−8.45939	−	14.6521i	−0.739100	−	1.28016i	0.213801	−	0.976877i	$-0.431416\pi$
$132$	1.75619	−	11.2584i	0.152857	−	0.979920i
$133$	−0.363241	−	3.30912i	−0.0314970	−	0.286937i
$134$			16.9611i			1.46522i
$135$	−1.15278	−	19.3933i	−0.0992158	−	1.66911i
$136$	32.5351	+	18.7841i	2.78986	+	1.61073i
$137$	5.91289	+	3.41381i	0.505172	+	0.291661i	0.730847	−	0.682541i	$-0.239125\pi$
$137$	5.91289	+	3.41381i	0.505172	+	0.291661i	−0.225675	+	0.974203i	$0.572459\pi$
$138$	−10.7161	−	27.7225i	−0.912214	−	2.35990i
$139$		−	5.84608i		−	0.495858i	−0.968778	−	0.247929i	$-0.920250\pi$
$139$		−	5.84608i		−	0.495858i	0.968778	−	0.247929i	$-0.0797500\pi$
$140$	−16.6797	+	37.9331i	−1.40969	+	3.20593i
$141$	13.7367	+	2.14277i	1.15684	+	0.180454i
$142$	8.86157	+	15.3487i	0.743646	+	1.28803i
$143$	1.77050	−	3.06659i	0.148057	−	0.256441i
$144$	−11.4777	+	10.4322i	−0.956479	+	0.869349i
$145$	23.1628	−	13.3730i	1.92357	−	1.11057i
$146$	−7.57962			−0.627294
$147$	12.0996	−	0.774488i	0.997958	−	0.0638787i
$148$	−28.7939			−2.36685
$149$	−10.9019	+	6.29419i	−0.893115	+	0.515640i	−0.874960	−	0.484195i	$-0.839113\pi$
$149$	−10.9019	+	6.29419i	−0.893115	+	0.515640i	−0.0181549	+	0.999835i	$0.505779\pi$
$150$	30.1243	+	24.2778i	2.45964	+	1.98227i
$151$	−8.95031	+	15.5024i	−0.728366	+	1.26157i	0.229208	+	0.973377i	$0.426386\pi$
$151$	−8.95031	+	15.5024i	−0.728366	+	1.26157i	−0.957574	+	0.288189i	$0.906947\pi$
$152$	3.42613	+	5.93423i	0.277896	+	0.481329i
$153$	−19.7121	−	6.30313i	−1.59363	−	0.509578i
$154$	4.16072	−	9.46235i	0.335280	−	0.762498i
$155$			26.3220i			2.11423i
$156$	−15.2596	+	5.89856i	−1.22174	+	0.472263i
$157$	10.1719	+	5.87274i	0.811804	+	0.468696i	0.847582	−	0.530664i	$-0.178057\pi$
$157$	10.1719	+	5.87274i	0.811804	+	0.468696i	−0.0357777	+	0.999360i	$0.511391\pi$
$158$	−30.9600	−	17.8748i	−2.46305	−	1.42204i
$159$	−7.28038	+	2.81422i	−0.577372	+	0.223182i
$160$		−	7.36652i		−	0.582375i
$161$	−1.99127	−	18.1404i	−0.156934	−	1.42966i
$162$	12.9906	−	18.2362i	1.02064	−	1.43277i
$163$	−1.18169	−	2.04674i	−0.0925569	−	0.160313i	0.816029	−	0.578010i	$-0.196171\pi$
$163$	−1.18169	−	2.04674i	−0.0925569	−	0.160313i	−0.908586	+	0.417697i	$0.862837\pi$
$164$	2.09453	−	3.62783i	0.163555	−	0.283286i
$165$	−7.91845	−	6.38165i	−0.616451	−	0.496810i
$166$	22.6188	−	13.0590i	1.75556	−	1.01357i
$167$	−14.4062			−1.11478			−0.557391	−	0.830250i	$-0.688198\pi$
$167$	−14.4062			−1.11478			−0.557391	+	0.830250i	$0.688198\pi$
$168$	−22.1569	+	11.4842i	−1.70944	+	0.886023i
$169$	7.91596			0.608920
$170$	55.5687	−	32.0826i	4.26192	−	2.46062i
$171$	−2.53887	−	2.79333i	−0.194152	−	0.213611i
$172$	−9.66255	+	16.7360i	−0.736762	+	1.27611i
$173$	0.192354	+	0.333167i	0.0146244	+	0.0253302i	0.873245	−	0.487281i	$-0.162011\pi$
$173$	0.192354	+	0.333167i	0.0146244	+	0.0253302i	−0.858621	+	0.512612i	$0.828678\pi$
$174$	30.4563	+	4.75085i	2.30888	+	0.360161i
$175$	14.0518	+	19.1543i	1.06222	+	1.44793i
$176$			8.11932i			0.612017i
$177$	−3.20136	−	8.28192i	−0.240629	−	0.622507i
$178$	−13.4822	−	7.78398i	−1.01054	−	0.583434i
$179$	−6.86648	−	3.96436i	−0.513225	−	0.296310i	0.220934	−	0.975289i	$-0.429090\pi$
$179$	−6.86648	−	3.96436i	−0.513225	−	0.296310i	−0.734158	+	0.678979i	$0.762423\pi$
$180$	9.98381	+	45.9136i	0.744149	+	3.42220i
$181$		−	3.35125i		−	0.249096i	−0.992214	−	0.124548i	$-0.960252\pi$
$181$		−	3.35125i		−	0.249096i	0.992214	−	0.124548i	$-0.0397482\pi$
$182$	−14.7525	+	1.61938i	−1.09353	+	0.120036i
$183$	−1.47130	+	9.43205i	−0.108761	+	0.697237i
$184$	18.7819	+	32.5311i	1.38462	+	2.39823i
$185$	−12.8496	+	22.2562i	−0.944723	+	1.63631i
$186$	−19.0358	+	23.6199i	−1.39577	+	1.73190i
$187$	−9.38216	+	5.41679i	−0.686092	+	0.396115i
$188$	−33.6246			−2.45233
$189$	10.5827	−	8.77534i	0.769778	−	0.638312i
$190$	11.7034			0.849054
$191$	−23.0068	+	13.2830i	−1.66471	+	0.961122i	−0.694293	+	0.719692i	$0.744283\pi$
$191$	−23.0068	+	13.2830i	−1.66471	+	0.961122i	−0.970418	+	0.241430i	$0.922384\pi$
$192$	−5.91101	+	7.33448i	−0.426590	+	0.529320i
$193$	−2.20151	+	3.81313i	−0.158468	+	0.274475i	−0.934317	−	0.356444i	$-0.883989\pi$
$193$	−2.20151	+	3.81313i	−0.158468	+	0.274475i	0.775848	+	0.630920i	$0.217322\pi$
$194$	7.51284	+	13.0126i	0.539391	+	0.934252i
$195$	−2.25048	+	14.4272i	−0.161160	+	1.03315i
$196$	−28.6252	+	6.36101i	−2.04465	+	0.454358i
$197$			5.42084i			0.386219i	0.981177	+	0.193110i	$0.0618573\pi$
$197$			5.42084i			0.386219i	−0.981177	+	0.193110i	$0.938143\pi$
$198$	−2.49045	−	11.4531i	−0.176988	−	0.813935i
$199$	10.2785	+	5.93430i	0.728624	+	0.420671i	0.817918	−	0.575334i	$-0.195128\pi$
$199$	10.2785	+	5.93430i	0.728624	+	0.420671i	−0.0892948	+	0.996005i	$0.528461\pi$
$200$	−42.3469	−	24.4490i	−2.99438	−	1.72881i
$201$	4.25762	+	11.0145i	0.300309	+	0.776900i
$202$		−	6.86640i		−	0.483118i
$203$	17.3257	+	7.61833i	1.21602	+	0.534702i
$204$	49.4547	+	7.71440i	3.46252	+	0.540116i
$205$	−1.86942	−	3.23792i	−0.130566	−	0.226146i
$206$	−11.7789	+	20.4016i	−0.820674	+	1.42145i
$207$	−13.9179	−	15.3129i	−0.967364	−	1.06432i
$208$	10.0956	−	5.82872i	0.700007	−	0.404149i
$209$	−1.97599			−0.136682
$210$	−1.93491	+	42.5804i	−0.133521	+	2.93833i
$211$	2.99103			0.205911			0.102956	−	0.994686i	$-0.467170\pi$
$211$	2.99103			0.205911			0.102956	+	0.994686i	$0.467170\pi$
$212$	16.3486	−	9.43885i	1.12282	−	0.648263i
$213$	9.60753	+	7.74291i	0.658297	+	0.530535i
$214$	15.1001	−	26.1542i	1.03222	−	1.78786i
$215$	8.62405	+	14.9373i	0.588155	+	1.01871i
$216$	−12.6698	+	25.3029i	−0.862069	+	1.72165i
$217$	−15.0185	+	11.0178i	−1.01952	+	0.747936i
$218$		−	23.6978i		−	1.60502i
$219$	−4.92217	+	1.90266i	−0.332609	+	0.128570i
$220$	21.3012	+	12.2983i	1.43613	+	0.829148i
$221$	13.4706	+	7.77725i	0.906130	+	0.523154i
$222$	−27.6260	+	10.6788i	−1.85414	+	0.716713i
$223$		−	20.4103i		−	1.36677i	−0.730057	−	0.683387i	$-0.760506\pi$
$223$		−	20.4103i		−	1.36677i	0.730057	−	0.683387i	$-0.239494\pi$
$224$	4.20311	−	3.08346i	0.280832	−	0.206022i
$225$	25.6569	+	8.20401i	1.71046	+	0.546934i
$226$	−7.12884	−	12.3475i	−0.474204	−	0.821345i
$227$	6.41950	−	11.1189i	0.426077	−	0.737987i	−0.570443	−	0.821337i	$-0.693229\pi$
$227$	6.41950	−	11.1189i	0.426077	−	0.737987i	0.996520	+	0.0833497i	$0.0265619\pi$
$228$	7.10826	+	5.72870i	0.470756	+	0.379392i
$229$	−7.89284	+	4.55693i	−0.521574	+	0.301131i	−0.737578	−	0.675262i	$-0.764031\pi$
$229$	−7.89284	+	4.55693i	−0.521574	+	0.301131i	0.216005	+	0.976392i	$0.430697\pi$
$230$	64.1574			4.23042
$231$	0.326688	−	7.18924i	0.0214945	−	0.473017i
$232$	−38.9578			−2.55770
$233$	24.7111	−	14.2669i	1.61887	−	0.934658i	0.631663	−	0.775243i	$-0.282373\pi$
$233$	24.7111	−	14.2669i	1.61887	−	0.934658i	0.987212	−	0.159415i	$-0.0509607\pi$
$234$	−12.4530	+	11.3186i	−0.814080	+	0.739921i
$235$	−15.0054	+	25.9901i	−0.978843	+	1.69541i
$236$	10.7373	+	18.5976i	0.698941	+	1.21060i
$237$	−24.5923	−	3.83613i	−1.59744	−	0.249183i
$238$	41.5651	+	18.2767i	2.69427	+	1.18471i
$239$			7.82909i			0.506422i	0.967411	+	0.253211i	$0.0814866\pi$
$239$			7.82909i			0.506422i	−0.967411	+	0.253211i	$0.918513\pi$
$240$	−12.0715	−	31.2289i	−0.779210	−	2.01581i
$241$	−16.3837	−	9.45912i	−1.05537	−	0.609316i	−0.131219	−	0.991353i	$-0.541889\pi$
$241$	−16.3837	−	9.45912i	−1.05537	−	0.609316i	−0.924147	+	0.382038i	$0.875222\pi$
$242$	18.3858	+	10.6150i	1.18188	+	0.682359i
$243$	3.85833	−	15.1034i	0.247512	−	0.968885i
$244$		−	23.0878i		−	1.47804i
$245$	−7.85758	+	24.9644i	−0.502003	+	1.59492i
$246$	0.664120	−	4.25748i	0.0423428	−	0.271447i
$247$	1.41853	+	2.45696i	0.0902589	+	0.156333i
$248$	19.1700	−	33.2034i	1.21730	−	2.10842i
$249$	11.4105	−	14.1583i	0.723108	−	0.897244i
$250$	−32.0507	+	18.5045i	−2.02707	+	1.17033i
$251$	13.4609			0.849643			0.424822	−	0.905277i	$-0.360337\pi$
$251$	13.4609			0.849643			0.424822	+	0.905277i	$0.360337\pi$
$252$	−22.0179	+	24.9148i	−1.38700	+	1.56949i
$253$	−10.8323			−0.681019
$254$	33.4825	−	19.3311i	2.10088	−	1.21294i
$255$	28.0326	−	34.7833i	1.75547	−	2.17821i
$256$	16.2929	−	28.2201i	1.01831	−	1.76376i
$257$	−10.4593	−	18.1160i	−0.652432	−	1.13005i	−0.982531	−	0.186099i	$-0.940415\pi$
$257$	−10.4593	−	18.1160i	−0.652432	−	1.13005i	0.330099	−	0.943946i	$-0.392918\pi$
$258$	−3.06374	+	19.6407i	−0.190740	+	1.22278i
$259$	−18.0773	+	1.98434i	−1.12327	+	0.123301i
$260$		−	35.3148i		−	2.19013i
$261$	20.9707	−	4.56004i	1.29806	−	0.282259i
$262$	36.4512	+	21.0451i	2.25196	+	1.30017i
$263$	15.3023	+	8.83480i	0.943581	+	0.544777i	0.891081	−	0.453844i	$-0.149948\pi$
$263$	15.3023	+	8.83480i	0.943581	+	0.544777i	0.0525002	+	0.998621i	$0.483281\pi$
$264$	5.34092	+	13.8169i	0.328711	+	0.850374i
$265$		−	16.8488i		−	1.03501i
$266$	4.89878	+	6.67760i	0.300363	+	0.409430i
$267$	−10.7093	−	1.67053i	−0.655396	−	0.102235i
$268$	−14.2800	−	24.7337i	−0.872290	−	1.51085i
$269$	−3.88209	+	6.72397i	−0.236695	+	0.409968i	−0.959764	−	0.280808i	$-0.909398\pi$
$269$	−3.88209	+	6.72397i	−0.236695	+	0.409968i	0.723069	+	0.690776i	$0.242731\pi$
$270$	26.6068	+	40.3486i	1.61924	+	2.45554i
$271$	−8.70167	+	5.02391i	−0.528589	+	0.305181i	−0.740442	−	0.672121i	$-0.765384\pi$
$271$	−8.70167	+	5.02391i	−0.528589	+	0.305181i	0.211853	+	0.977302i	$0.432050\pi$
$272$	−35.6656			−2.16255
$273$	−9.17369	+	4.75482i	−0.555217	+	0.287775i
$274$	−16.9856			−1.02614
$275$	12.2116	−	7.05038i	0.736388	−	0.425154i
$276$	38.9671	+	31.4044i	2.34555	+	1.89032i
$277$	13.7226	−	23.7682i	0.824509	−	1.42809i	−0.0777852	−	0.996970i	$-0.524785\pi$
$277$	13.7226	−	23.7682i	0.824509	−	1.42809i	0.902294	−	0.431121i	$-0.141882\pi$
$278$	7.27189	+	12.5953i	0.436139	+	0.755415i
$279$	−6.43261	+	20.1171i	−0.385110	+	1.20438i
$280$	−5.87810	−	53.5493i	−0.351284	−	3.20018i
$281$			5.91936i			0.353120i	0.984290	+	0.176560i	$0.0564969\pi$
$281$			5.91936i			0.353120i	−0.984290	+	0.176560i	$0.943503\pi$
$282$	−32.2608	+	12.4703i	−1.92110	+	0.742598i
$283$	−15.9349	−	9.20000i	−0.947229	−	0.546883i	−0.0550101	−	0.998486i	$-0.517519\pi$
$283$	−15.9349	−	9.20000i	−0.947229	−	0.546883i	−0.892219	+	0.451603i	$0.850852\pi$
$284$	−25.8449	−	14.9216i	−1.53361	−	0.885433i
$285$	7.60013	−	2.93782i	0.450193	−	0.174021i
$286$			8.80923i			0.520901i
$287$	1.06496	−	2.42195i	0.0628629	−	0.142963i
$288$	1.80024	−	5.63000i	0.106080	−	0.331751i
$289$	−15.2943	−	26.4905i	−0.899664	−	1.55826i
$290$	−33.2692	+	57.6240i	−1.95364	+	3.38380i
$291$	8.14527	+	6.56444i	0.477484	+	0.384814i
$292$	11.0531	−	6.38148i	0.646831	−	0.373448i
$293$	30.1443			1.76105			0.880525	−	0.474000i	$-0.157190\pi$
$293$	30.1443			1.76105			0.880525	+	0.474000i	$0.157190\pi$
$294$	−25.1050	+	16.7192i	−1.46415	+	0.975083i
$295$	19.1666			1.11592
$296$	32.4179	−	18.7165i	1.88425	−	1.08787i
$297$	−4.49227	−	6.81242i	−0.260668	−	0.395297i
$298$	15.6586	−	27.1214i	0.907077	−	1.57110i
$299$	7.77630	+	13.4690i	0.449715	+	0.778930i
$300$	−64.3692	−	10.0409i	−3.71636	−	0.579711i
$301$	−4.91293	+	11.1730i	−0.283176	+	0.644002i
$302$		−	44.5328i		−	2.56258i
$303$	−1.72362	−	4.45901i	−0.0990195	−	0.256163i
$304$	−5.63369	−	3.25261i	−0.323114	−	0.186550i
$305$	−17.8456	−	10.3032i	−1.02184	−	0.589959i
$306$	50.3098	−	10.9398i	2.87602	−	0.625384i
$307$			32.6159i			1.86149i	0.365670	+	0.930744i	$0.380840\pi$
$307$			32.6159i			1.86149i	−0.365670	+	0.930744i	$0.619160\pi$
$308$	1.89919	+	17.3016i	0.108216	+	0.985849i
$309$	−2.52788	+	16.2055i	−0.143806	+	0.921898i
$310$	−32.7417	−	56.7102i	−1.85960	−	3.22092i
$311$	1.30324	−	2.25728i	0.0739001	−	0.127999i	−0.826707	−	0.562632i	$-0.809789\pi$
$311$	1.30324	−	2.25728i	0.0739001	−	0.127999i	0.900607	+	0.434633i	$0.143122\pi$
$312$	13.3460	−	16.5599i	0.755567	−	0.937520i
$313$	−1.70807	+	0.986156i	−0.0965460	+	0.0557408i	−0.547496	−	0.836809i	$-0.684419\pi$
$313$	−1.70807	+	0.986156i	−0.0965460	+	0.0557408i	0.450950	+	0.892549i	$0.351085\pi$
$314$	−29.2202			−1.64899
$315$	9.43213	+	28.1372i	0.531440	+	1.58535i
$316$	60.1970			3.38635
$317$	−11.8831	+	6.86071i	−0.667421	+	0.385336i	−0.795099	−	0.606480i	$-0.792581\pi$
$317$	−11.8831	+	6.86071i	−0.667421	+	0.385336i	0.127678	+	0.991816i	$0.459248\pi$
$318$	12.1849	−	15.1192i	0.683293	−	0.847842i
$319$	5.61714	−	9.72918i	0.314500	−	0.544729i
$320$	−10.1670	−	17.6097i	−0.568351	−	0.984413i
$321$	3.24065	−	20.7749i	0.180876	−	1.15954i
$322$	26.8548	+	36.6063i	1.49656	+	2.03999i
$323$		−	8.67991i		−	0.482963i
$324$	−3.59013	+	37.5302i	−0.199452	+	2.08501i
$325$	−17.5330	−	10.1227i	−0.972556	−	0.561506i
$326$	5.09185	+	2.93978i	0.282012	+	0.162819i
$327$	−5.94868	−	15.3892i	−0.328963	−	0.851026i
$328$			5.44590i			0.300700i
$329$	−21.1100	+	2.31725i	−1.16383	+	0.127754i
$330$	24.9982	+	3.89945i	1.37611	+	0.214658i
$331$	2.68189	+	4.64517i	0.147410	+	0.255322i	0.930270	−	0.366877i	$-0.119573\pi$
$331$	2.68189	+	4.64517i	0.147410	+	0.255322i	−0.782859	+	0.622199i	$0.786240\pi$
$332$	−21.9894	+	38.0868i	−1.20683	+	2.09028i
$333$	−15.2596	+	13.8695i	−0.836220	+	0.760044i
$334$	31.0378	−	17.9197i	1.69831	−	0.980522i
$335$	−25.4904			−1.39269
$336$	12.7654	−	19.9593i	0.696409	−	1.08887i
$337$	−23.5159			−1.28099			−0.640496	−	0.767962i	$-0.721271\pi$
$337$	−23.5159			−1.28099			−0.640496	+	0.767962i	$0.721271\pi$
$338$	−17.0548	+	9.84659i	−0.927658	+	0.535584i
$339$	−7.72894	−	6.22892i	−0.419779	−	0.338308i
$340$	−54.0224	+	93.5695i	−2.92978	+	5.07452i
$341$	5.52807	+	9.57490i	0.299362	+	0.518510i
$342$	8.94454	+	2.86010i	0.483665	+	0.154656i
$343$	−17.5329	+	5.96624i	−0.946690	+	0.322147i
$344$		−	25.1232i		−	1.35455i
$345$	41.6635	−	16.1050i	2.24309	−	0.867062i
$346$	−0.828846	−	0.478534i	−0.0445590	−	0.0257262i
$347$	17.5365	+	10.1247i	0.941409	+	0.543523i	0.890402	−	0.455176i	$-0.150424\pi$
$347$	17.5365	+	10.1247i	0.941409	+	0.543523i	0.0510070	+	0.998698i	$0.483757\pi$
$348$	−48.4130	+	18.7140i	−2.59521	+	1.00317i
$349$		−	5.71391i		−	0.305859i	−0.988237	−	0.152929i	$-0.951129\pi$
$349$		−	5.71391i		−	0.305859i	0.988237	−	0.152929i	$-0.0488707\pi$
$350$	−54.1002	−	23.7886i	−2.89178	−	1.27155i
$351$	−5.24570	+	10.4762i	−0.279995	+	0.559181i
$352$	−1.54710	−	2.67965i	−0.0824605	−	0.142826i
$353$	10.0246	−	17.3631i	0.533557	−	0.924147i	−0.465675	−	0.884956i	$-0.654188\pi$
$353$	10.0246	−	17.3631i	0.533557	−	0.924147i	0.999232	−	0.0391913i	$-0.0124782\pi$
$354$	17.1991	+	13.8611i	0.914121	+	0.736709i
$355$	−23.0672	+	13.3179i	−1.22428	+	0.706838i
$356$	26.2142			1.38935
$357$	31.5801	+	1.43504i	1.67139	+	0.0759502i
$358$	19.7249			1.04250
$359$	−24.5405	+	14.1685i	−1.29520	+	0.747783i	−0.979571	−	0.201100i	$-0.935548\pi$
$359$	−24.5405	+	14.1685i	−1.29520	+	0.747783i	−0.315628	+	0.948883i	$0.602215\pi$
$360$	−41.0849	−	45.2026i	−2.16536	−	2.38239i
$361$	−8.70842	+	15.0834i	−0.458338	+	0.793864i
$362$	4.16859	+	7.22021i	0.219096	+	0.379486i
$363$	14.6042	+	2.27810i	0.766523	+	0.119569i
$364$	20.1495	−	14.7820i	1.05612	−	0.774786i
$365$		−	11.3912i		−	0.596245i
$366$	−8.56255	−	22.1513i	−0.447572	−	1.15787i
$367$	−0.845514	−	0.488158i	−0.0441355	−	0.0254816i	0.477770	−	0.878485i	$-0.341445\pi$
$367$	−0.845514	−	0.488158i	−0.0441355	−	0.0254816i	−0.521905	+	0.853003i	$0.674779\pi$
$368$	−30.8836	−	17.8307i	−1.60992	−	0.929488i
$369$	−0.637447	−	2.93149i	−0.0331842	−	0.152608i
$370$		−	63.9341i		−	3.32378i
$371$	9.61340	−	7.05252i	0.499103	−	0.366148i
$372$	7.87288	−	50.4707i	0.408190	−	2.61678i
$373$	4.52737	+	7.84164i	0.234419	+	0.406025i	0.959104	−	0.283055i	$-0.0913481\pi$
$373$	4.52737	+	7.84164i	0.234419	+	0.406025i	−0.724685	+	0.689080i	$0.758015\pi$
$374$	13.4758	−	23.3408i	0.696817	−	1.20692i
$375$	−16.1685	+	20.0622i	−0.834940	+	1.03601i
$376$	37.8566	−	21.8565i	1.95230	−	1.12716i
$377$	−16.1298			−0.830727
$378$	−11.8847	+	32.0700i	−0.611281	+	1.64950i
$379$	6.74593			0.346515			0.173258	−	0.984877i	$-0.444571\pi$
$379$	6.74593			0.346515			0.173258	+	0.984877i	$0.444571\pi$
$380$	−17.0666	+	9.85340i	−0.875498	+	0.505469i
$381$	16.8908	−	20.9584i	0.865343	−	1.07373i
$382$	33.0451	−	57.2358i	1.69074	−	2.92844i
$383$	−15.0152	−	26.0071i	−0.767242	−	1.32890i	−0.939053	−	0.343772i	$-0.888295\pi$
$383$	−15.0152	−	26.0071i	−0.767242	−	1.32890i	0.171811	−	0.985130i	$-0.445038\pi$
$384$	4.66382	−	29.8983i	0.237999	−	1.52574i
$385$	14.2207	+	6.25305i	0.724756	+	0.318685i
$386$		−	10.9538i		−	0.557532i
$387$	2.94069	+	13.5237i	0.149484	+	0.687446i
$388$	−21.9113	−	12.6505i	−1.11238	−	0.642233i
$389$	0.346881	+	0.200272i	0.0175876	+	0.0101542i	0.508768	−	0.860904i	$-0.330101\pi$
$389$	0.346881	+	0.200272i	0.0175876	+	0.0101542i	−0.491180	+	0.871058i	$0.663434\pi$
$390$	−13.0972	−	33.8824i	−0.663202	−	1.71570i
$391$		−	47.5828i		−	2.40637i
$392$	28.0931	−	25.7684i	1.41892	−	1.30150i
$393$	28.9540	+	4.51651i	1.46054	+	0.227828i
$394$	−6.74294	−	11.6791i	−0.339704	−	0.588385i
$395$	26.8636	−	46.5291i	1.35166	−	2.34114i
$396$	13.2744	+	14.6048i	0.667062	+	0.733919i
$397$	−14.2812	+	8.24528i	−0.716755	+	0.413818i	−0.813557	−	0.581485i	$-0.802472\pi$
$397$	−14.2812	+	8.24528i	−0.716755	+	0.413818i	0.0968024	+	0.995304i	$0.469139\pi$
$398$	−29.5265			−1.48003
$399$	4.85747	+	3.10670i	0.243178	+	0.155529i
$400$	46.4216			2.32108
$401$	2.79132	−	1.61157i	0.139392	−	0.0804779i	−0.428682	−	0.903455i	$-0.641022\pi$
$401$	2.79132	−	1.61157i	0.139392	−	0.0804779i	0.568074	+	0.822977i	$0.307689\pi$
$402$	−22.8737	−	18.4344i	−1.14084	−	0.919426i
$403$	7.93701	−	13.7473i	0.395371	−	0.684802i
$404$	5.78100	+	10.0130i	0.287616	+	0.498165i
$405$	27.4067	+	19.5233i	1.36185	+	0.970119i
$406$	−46.8042	+	5.13769i	−2.32285	+	0.254979i
$407$			10.7946i			0.535067i
$408$	−60.6935	+	23.4610i	−3.00478	+	1.16149i
$409$	24.4255	+	14.1021i	1.20776	+	0.697302i	0.962270	−	0.272096i	$-0.0877169\pi$
$409$	24.4255	+	14.1021i	1.20776	+	0.697302i	0.245493	+	0.969398i	$0.421050\pi$
$410$	8.05525	+	4.65070i	0.397820	+	0.229682i
$411$	−11.0304	+	4.26377i	−0.544088	+	0.210316i
$412$		−	39.6678i		−	1.95429i
$413$	8.02271	+	10.9359i	0.394772	+	0.538120i
$414$	49.0335	+	15.6789i	2.40987	+	0.770576i
$415$	19.6261	+	33.9933i	0.963405	+	1.66867i
$416$	−2.22127	+	3.84735i	−0.108907	+	0.188632i
$417$	7.88403	+	6.35390i	0.386082	+	0.311152i
$418$	4.25724	−	2.45792i	0.208228	−	0.120221i
$419$	12.0366			0.588026			0.294013	−	0.955801i	$-0.405009\pi$
$419$	12.0366			0.588026			0.294013	+	0.955801i	$0.405009\pi$
$420$	−33.0280	−	63.7224i	−1.61160	−	3.10933i
$421$	−9.93068			−0.483992			−0.241996	−	0.970277i	$-0.577802\pi$
$421$	−9.93068			−0.483992			−0.241996	+	0.970277i	$0.577802\pi$
$422$	−6.44413	+	3.72052i	−0.313695	+	0.181112i
$423$	−17.8196	+	16.1964i	−0.866420	+	0.787494i
$424$	−12.2708	+	21.2536i	−0.595922	+	1.03217i
$425$	30.9701	+	53.6418i	1.50227	+	2.60201i
$426$	−30.3306	−	4.73124i	−1.46952	−	0.229229i
$427$	−1.59110	−	14.4949i	−0.0769987	−	0.701455i
$428$			50.8527i			2.45806i
$429$	2.21132	+	5.72067i	0.106763	+	0.276197i
$430$	−37.1607	−	21.4547i	−1.79205	−	1.03464i
$431$	−6.25266	−	3.60998i	−0.301180	−	0.173886i	0.341793	−	0.939775i	$-0.388966\pi$
$431$	−6.25266	−	3.60998i	−0.301180	−	0.173886i	−0.642973	+	0.765889i	$0.722299\pi$
$432$	−1.59408	−	26.8173i	−0.0766953	−	1.29025i
$433$			17.6079i			0.846184i	0.906087	+	0.423092i	$0.139055\pi$
$433$			17.6079i			0.846184i	−0.906087	+	0.423092i	$0.860945\pi$
$434$	18.6522	−	42.4190i	0.895334	−	2.03618i
$435$	−7.13995	+	45.7721i	−0.342334	+	2.19460i
$436$	19.9518	+	34.5575i	0.955518	+	1.65501i
$437$	4.33943	−	7.51611i	0.207583	−	0.359544i
$438$	8.23803	−	10.2219i	0.393628	−	0.488420i
$439$	−21.1988	+	12.2391i	−1.01176	+	0.584142i	−0.911707	−	0.410840i	$-0.865235\pi$
$439$	−21.1988	+	12.2391i	−1.01176	+	0.584142i	−0.100056	+	0.994982i	$0.531902\pi$
$440$	−31.9762			−1.52441
$441$	−12.1062	+	17.1593i	−0.576484	+	0.817109i
$442$	−38.6962			−1.84059
$443$	9.19705	−	5.30992i	0.436965	−	0.252282i	−0.265344	−	0.964154i	$-0.585486\pi$
$443$	9.19705	−	5.30992i	0.436965	−	0.252282i	0.702309	+	0.711872i	$0.252152\pi$
$444$	31.2951	−	38.8315i	1.48520	−	1.84286i
$445$	11.6984	−	20.2622i	0.554556	−	0.960519i
$446$	25.3882	+	43.9736i	1.20216	+	2.08221i
$447$	3.36050	−	21.5432i	0.158946	−	1.01896i
$448$	5.79190	−	13.1720i	0.273642	−	0.622318i
$449$			1.01474i			0.0478887i	0.999713	+	0.0239444i	$0.00762246\pi$
$449$			1.01474i			0.0478887i	−0.999713	+	0.0239444i	$0.992378\pi$
$450$	−65.4821	+	14.2389i	−3.08686	+	0.671230i
$451$	−1.36004	−	0.785219i	−0.0640418	−	0.0369745i
$452$	20.7914	+	12.0039i	0.977946	+	0.564617i
$453$	−11.1787	−	28.9194i	−0.525223	−	1.35875i
$454$			31.9406i			1.49905i
$455$	−2.43373	−	22.1712i	−0.114095	−	1.03940i
$456$	−11.7266	−	1.82923i	−0.549150	−	0.0856615i
$457$	6.62763	+	11.4794i	0.310028	+	0.536983i	0.978368	−	0.206872i	$-0.0663284\pi$
$457$	6.62763	+	11.4794i	0.310028	+	0.536983i	−0.668340	+	0.743856i	$0.732995\pi$
$458$	11.3367	−	19.6357i	0.529727	−	0.917514i
$459$	29.9248	−	19.7331i	1.39677	−	0.921063i
$460$	−93.5582	+	54.0158i	−4.36217	+	2.51850i
$461$	31.9499			1.48806			0.744028	−	0.668148i	$-0.232913\pi$
$461$	31.9499			1.48806			0.744028	+	0.668148i	$0.232913\pi$
$462$	8.23878	+	15.8954i	0.383303	+	0.739523i
$463$	19.1493			0.889944			0.444972	−	0.895545i	$-0.353214\pi$
$463$	19.1493			0.889944			0.444972	+	0.895545i	$0.353214\pi$
$464$	32.0298	−	18.4924i	1.48694	−	0.858488i
$465$	−35.4978	−	28.6084i	−1.64617	−	1.32668i
$466$	−35.4930	+	61.4757i	−1.64418	+	2.84781i
$467$	3.65816	+	6.33611i	0.169279	+	0.293200i	0.938167	−	0.346184i	$-0.112523\pi$
$467$	3.65816	+	6.33611i	0.169279	+	0.293200i	−0.768887	+	0.639384i	$0.779189\pi$
$468$	8.63030	−	26.9900i	0.398936	−	1.24761i
$469$	−10.6697	−	14.5441i	−0.492682	−	0.671582i
$470$		−	74.6602i		−	3.44382i
$471$	−18.9754	+	7.33493i	−0.874342	+	0.337976i
$472$	−24.1774	−	13.9588i	−1.11286	−	0.642508i
$473$	6.27418	+	3.62240i	0.288487	+	0.166558i
$474$	57.7553	−	22.3252i	2.65279	−	1.02543i
$475$			11.2976i			0.518368i
$476$	−76.0004	+	8.34256i	−3.48347	+	0.382380i
$477$	4.11754	−	12.8770i	0.188529	−	0.589597i
$478$	−9.73853	−	16.8676i	−0.445430	−	0.771508i
$479$	5.86289	−	10.1548i	0.267882	−	0.463985i	−0.700433	−	0.713719i	$-0.747010\pi$
$479$	5.86289	−	10.1548i	0.267882	−	0.463985i	0.968315	+	0.249733i	$0.0803429\pi$
$480$	9.93449	+	8.00642i	0.453446	+	0.365441i
$481$	13.4221	−	7.74924i	0.611994	−	0.353335i
$482$	47.0645			2.14373
$483$	26.6284	+	17.0307i	1.21163	+	0.774926i
$484$	−35.7483			−1.62492
$485$	−19.5564	+	11.2909i	−0.888010	+	0.512693i
$486$	10.4743	+	37.3394i	0.475124	+	1.69375i
$487$	4.33247	−	7.50406i	0.196323	−	0.340041i	−0.751010	−	0.660290i	$-0.770433\pi$
$487$	4.33247	−	7.50406i	0.196323	−	0.340041i	0.947333	+	0.320249i	$0.103767\pi$
$488$	15.0074	+	25.9936i	0.679353	+	1.17667i
$489$	4.04457	+	0.630910i	0.182902	+	0.0285307i
$490$	−14.1240	−	63.5594i	−0.638057	−	2.87132i
$491$			39.1216i			1.76553i	0.469813	+	0.882766i	$0.344321\pi$
$491$			39.1216i			1.76553i	−0.469813	+	0.882766i	$0.655679\pi$
$492$	2.61602	+	6.76765i	0.117939	+	0.305109i
$493$	42.7372	+	24.6744i	1.92479	+	1.11128i
$494$	−6.11239	−	3.52899i	−0.275010	−	0.158777i
$495$	17.2126	−	3.74284i	0.773648	−	0.168228i
$496$			36.3983i			1.63433i
$497$	−17.2542	−	7.58688i	−0.773955	−	0.340318i
$498$	−6.97226	+	44.6971i	−0.312435	+	2.00293i
$499$	−2.45656	−	4.25488i	−0.109971	−	0.190475i	0.805787	−	0.592205i	$-0.201742\pi$
$499$	−2.45656	−	4.25488i	−0.109971	−	0.190475i	−0.915758	+	0.401730i	$0.868409\pi$
$500$	31.1588	−	53.9687i	1.39347	−	2.41355i
$501$	15.6576	−	19.4282i	0.699528	−	0.867986i
$502$	−29.0012	+	16.7439i	−1.29439	+	0.747315i
$503$	13.4706			0.600624			0.300312	−	0.953841i	$-0.402909\pi$
$503$	13.4706			0.600624			0.300312	+	0.953841i	$0.402909\pi$
$504$	8.59402	−	42.3626i	0.382808	−	1.88698i
$505$	10.3194			0.459205
$506$	23.3379	−	13.4742i	1.03750	−	0.599000i
$507$	−8.60358	+	10.6755i	−0.382098	+	0.474114i
$508$	−32.5508	+	56.3796i	−1.44421	+	2.50144i
$509$	−19.8371	−	34.3589i	−0.879264	−	1.52293i	−0.852150	−	0.523298i	$-0.824702\pi$
$509$	−19.8371	−	34.3589i	−0.879264	−	1.52293i	−0.0271143	−	0.999632i	$-0.508632\pi$
$510$	−17.1291	+	109.809i	−0.758489	+	4.86244i
$511$	6.49949	−	4.76811i	0.287521	−	0.210929i
$512$			46.1252i			2.03846i
$513$	6.52649	−	0.387950i	0.288152	−	0.0171284i
$514$	45.0687	+	26.0204i	1.98789	+	1.14771i
$515$	−30.6611	−	17.7022i	−1.35109	−	0.780053i
$516$	−12.0683	−	31.2207i	−0.531278	−	1.37442i
$517$			12.6056i			0.554392i
$518$	36.4788	−	26.7614i	1.60279	−	1.17583i
$519$	−0.658371	−	0.102699i	−0.0288993	−	0.00450798i
$520$	22.9552	+	39.7595i	1.00665	+	1.74357i
$521$	6.58581	−	11.4070i	0.288530	−	0.499748i	−0.684929	−	0.728610i	$-0.740167\pi$
$521$	6.58581	−	11.4070i	0.288530	−	0.499748i	0.973459	+	0.228861i	$0.0735002\pi$
$522$	−39.5089	+	35.9098i	−1.72926	+	1.57173i
$523$	−21.0395	+	12.1471i	−0.919992	+	0.531157i	−0.883632	−	0.468181i	$-0.844909\pi$
$523$	−21.0395	+	12.1471i	−0.919992	+	0.531157i	−0.0363593	+	0.999339i	$0.511576\pi$
$524$	−70.8737			−3.09613
$525$	−41.1039	−	1.86781i	−1.79392	−	0.0815179i
$526$	−43.9581			−1.91666
$527$	−42.0595	+	24.2831i	−1.83214	+	1.05779i
$528$	−10.9497	−	8.82461i	−0.476526	−	0.384042i
$529$	12.2885	−	21.2843i	0.534284	−	0.925406i
$530$	20.9581	+	36.3004i	0.910360	+	1.57679i
$531$	14.6485	+	4.68397i	0.635689	+	0.203267i
$532$	−12.7657	−	5.61326i	−0.553465	−	0.243366i
$533$			2.25478i			0.0976654i
$534$	25.1509	−	9.72203i	1.08838	−	0.420713i
$535$	39.3065	+	22.6936i	1.69937	+	0.981131i
$536$	32.1545	+	18.5644i	1.38886	+	0.801861i
$537$	12.8093	−	4.95141i	0.552761	−	0.213669i
$538$		−	19.3156i		−	0.832753i
$539$	2.38468	+	10.7313i	0.102716	+	0.462230i
$540$	−72.7702	−	36.4378i	−3.13153	−	1.56803i
$541$	4.41139	+	7.64074i	0.189660	+	0.328501i	0.945137	−	0.326674i	$-0.105928\pi$
$541$	4.41139	+	7.64074i	0.189660	+	0.328501i	−0.755477	+	0.655175i	$0.772595\pi$
$542$	12.4984	−	21.6479i	0.536852	−	0.929855i
$543$	4.51950	+	3.64236i	0.193950	+	0.156309i
$544$	11.7709	−	6.79591i	0.504672	−	0.291372i
$545$	35.6149			1.52557
$546$	13.8501	−	21.6552i	0.592728	−	0.926759i
$547$	37.8440			1.61809			0.809045	−	0.587746i	$-0.199985\pi$
$547$	37.8440			1.61809			0.809045	+	0.587746i	$0.199985\pi$
$548$	24.7694	−	14.3006i	1.05810	−	0.610893i
$549$	−11.1210	−	12.2356i	−0.474631	−	0.522201i
$550$	−17.5398	+	30.3798i	−0.747900	+	1.29540i
$551$	4.50047	+	7.79505i	0.191727	+	0.332080i
$552$	−64.2849	−	10.0277i	−2.73615	−	0.426809i
$553$	37.7926	−	4.14849i	1.60710	−	0.176412i
$554$			68.2775i			2.90083i
$555$	−16.0489	−	41.5185i	−0.681238	−	1.76236i
$556$	−21.2086	−	12.2448i	−0.899445	−	0.519295i
$557$	−12.1156	−	6.99494i	−0.513354	−	0.296385i	0.220857	−	0.975306i	$-0.429115\pi$
$557$	−12.1156	−	6.99494i	−0.513354	−	0.296385i	−0.734211	+	0.678921i	$0.762448\pi$
$558$	−11.1645	−	51.3433i	−0.472630	−	2.17354i
$559$		−	10.4018i		−	0.439951i
$560$	30.2514	+	41.2362i	1.27836	+	1.74255i
$561$	2.89206	−	18.5401i	0.122103	−	0.782764i
$562$	−7.36304	−	12.7532i	−0.310591	−	0.537960i
$563$	−20.7519	+	35.9434i	−0.874589	+	1.51483i	−0.0173885	+	0.999849i	$0.505535\pi$
$563$	−20.7519	+	35.9434i	−0.874589	+	1.51483i	−0.857200	+	0.514983i	$0.827798\pi$
$564$	36.5454	−	45.3462i	1.53884	−	1.90942i
$565$	18.5568	−	10.7138i	0.780691	−	0.450732i
$566$	45.7752			1.92407
$567$	0.332460	+	23.8094i	0.0139620	+	0.999903i
$568$	38.7970			1.62789
$569$	27.3488	−	15.7898i	1.14652	−	0.661944i	0.198484	−	0.980104i	$-0.436398\pi$
$569$	27.3488	−	15.7898i	1.14652	−	0.661944i	0.948037	+	0.318160i	$0.103065\pi$
$570$	−12.7200	+	15.7832i	−0.532783	+	0.661086i
$571$	13.2149	−	22.8889i	0.553028	−	0.957873i	−0.445026	−	0.895518i	$-0.646806\pi$
$571$	13.2149	−	22.8889i	0.553028	−	0.957873i	0.998054	−	0.0623550i	$-0.0198611\pi$
$572$	−7.41672	−	12.8461i	−0.310109	−	0.537124i
$573$	7.09185	−	45.4637i	0.296266	−	1.89928i
$574$	0.718197	+	6.54275i	0.0299770	+	0.273089i
$575$			61.9327i			2.58277i
$576$	−3.46681	−	15.9432i	−0.144450	−	0.664299i
$577$	−3.37317	−	1.94750i	−0.140427	−	0.0810755i	0.428141	−	0.903712i	$-0.359169\pi$
$577$	−3.37317	−	1.94750i	−0.140427	−	0.0810755i	−0.568567	+	0.822637i	$0.692502\pi$
$578$	65.9025	+	38.0488i	2.74118	+	1.58262i
$579$	−2.74964	−	7.11332i	−0.114271	−	0.295620i
$580$		−	112.041i		−	4.65225i
$581$	−11.1805	+	25.4268i	−0.463846	+	1.05488i
$582$	−25.7143	−	4.01115i	−1.06589	−	0.166267i
$583$	−3.53854	−	6.12893i	−0.146551	−	0.253834i
$584$	−8.29612	+	14.3693i	−0.343296	+	0.594606i
$585$	−17.0105	−	18.7154i	−0.703297	−	0.773785i
$586$	−64.9454	+	37.4962i	−2.68287	+	1.54896i
$587$	23.4871			0.969416			0.484708	−	0.874676i	$-0.338926\pi$
$587$	23.4871			0.969416			0.484708	+	0.874676i	$0.338926\pi$
$588$	22.5332	−	45.5175i	0.929255	−	1.87711i
$589$	−8.85822			−0.364996
$590$	−41.2942	+	23.8412i	−1.70005	+	0.981526i
$591$	−7.31055	−	5.89173i	−0.300716	−	0.242353i
$592$	−17.7686	+	30.7761i	−0.730285	+	1.26489i
$593$	−3.60607	−	6.24590i	−0.148084	−	0.256488i	0.782436	−	0.622732i	$-0.213977\pi$
$593$	−3.60607	−	6.24590i	−0.148084	−	0.256488i	−0.930519	+	0.366243i	$0.880644\pi$
$594$	18.1524	+	9.08934i	0.744803	+	0.372940i
$595$	−27.4677	+	62.4673i	−1.12607	+	2.56091i
$596$			52.7335i			2.16005i
$597$	−19.1743	+	7.41181i	−0.784754	+	0.303345i
$598$	−33.5078	−	19.3458i	−1.37024	−	0.791107i
$599$	−35.9713	−	20.7680i	−1.46975	−	0.848559i	−0.470323	−	0.882495i	$-0.655862\pi$
$599$	−35.9713	−	20.7680i	−1.46975	−	0.848559i	−0.999424	+	0.0339361i	$0.989196\pi$
$600$	78.9973	−	30.5363i	3.22505	−	1.24664i
$601$		−	24.0964i		−	0.982912i	−0.870902	−	0.491456i	$-0.836465\pi$
$601$		−	24.0964i		−	0.982912i	0.870902	−	0.491456i	$-0.163535\pi$
$602$	−3.31321	−	30.1832i	−0.135036	−	1.23018i
$603$	−19.4816	−	6.22940i	−0.793350	−	0.253681i
$604$	37.4934	+	64.9404i	1.52558	+	2.64239i
$605$	−15.9531	+	27.6315i	−0.648585	+	1.12338i
$606$	9.26003	+	7.46285i	0.376163	+	0.303158i
$607$	19.6303	−	11.3335i	0.796768	−	0.460014i	−0.0455717	−	0.998961i	$-0.514511\pi$
$607$	19.6303	−	11.3335i	0.796768	−	0.460014i	0.842340	+	0.538947i	$0.181178\pi$
$608$	2.47908			0.100540
$609$	−29.1047	+	15.0853i	−1.17938	+	0.611288i
$610$	51.2642			2.07563
$611$	15.6739	−	9.04931i	0.634097	−	0.366096i
$612$	−64.1543	+	58.3102i	−2.59328	+	2.35705i
$613$	−5.49453	+	9.51681i	−0.221922	+	0.384380i	−0.955392	−	0.295342i	$-0.904566\pi$
$613$	−5.49453	+	9.51681i	−0.221922	+	0.384380i	0.733469	+	0.679722i	$0.237900\pi$
$614$	−40.5706	−	70.2704i	−1.63730	−	2.83588i
$615$	6.39847	+	0.998092i	0.258011	+	0.0402469i
$616$	−13.3845	−	18.2446i	−0.539277	−	0.735097i
$617$		−	26.7110i		−	1.07535i	−0.843154	−	0.537673i	$-0.819304\pi$
$617$		−	26.7110i		−	1.07535i	0.843154	−	0.537673i	$-0.180696\pi$
$618$	−14.7116	−	38.0588i	−0.591787	−	1.53095i
$619$	7.32331	+	4.22811i	0.294349	+	0.169942i	0.639901	−	0.768457i	$-0.278975\pi$
$619$	7.32331	+	4.22811i	0.294349	+	0.169942i	−0.345553	+	0.938399i	$0.612309\pi$
$620$	95.4917	+	55.1322i	3.83504	+	2.21416i
$621$	35.7779	−	2.12672i	1.43572	−	0.0853423i
$622$			6.48437i			0.260000i
$623$	16.4576	−	1.80655i	0.659361	−	0.0723780i
$624$	−3.11199	+	19.9500i	−0.124579	+	0.798640i
$625$	−5.36283	−	9.28870i	−0.214513	−	0.371548i
$626$	2.45334	−	4.24931i	0.0980552	−	0.169837i
$627$	2.14764	−	2.66482i	0.0857683	−	0.106423i
$628$	42.6106	−	24.6012i	1.70035	−	0.981697i
$629$	−47.4172			−1.89065
$630$	−55.3210	−	48.8886i	−2.20404	−	1.94777i
$631$	−23.6012			−0.939549			−0.469774	−	0.882786i	$-0.655665\pi$
$631$	−23.6012			−0.939549			−0.469774	+	0.882786i	$0.655665\pi$
$632$	−67.7734	+	39.1290i	−2.69588	+	1.55647i
$633$	−3.25085	+	4.03371i	−0.129210	+	0.160325i
$634$	17.0679	−	29.5625i	0.677854	−	1.17408i
$635$	29.0523	+	50.3201i	1.15291	+	1.99689i
$636$	−5.03946	+	32.3065i	−0.199827	+	1.28103i
$637$	11.6315	−	10.6690i	0.460856	−	0.422719i
$638$			27.9485i			1.10649i
$639$	−20.8842	+	4.54122i	−0.826165	+	0.179648i
$640$	56.5683	+	32.6597i	2.23606	+	1.29099i
$641$	40.6603	+	23.4753i	1.60599	+	0.927217i	0.990256	+	0.139261i	$0.0444726\pi$
$641$	40.6603	+	23.4753i	1.60599	+	0.927217i	0.615731	+	0.787956i	$0.288861\pi$
$642$	18.8597	+	48.7901i	0.744334	+	1.92559i
$643$		−	17.9110i		−	0.706339i	−0.935559	−	0.353170i	$-0.885104\pi$
$643$		−	17.9110i		−	0.706339i	0.935559	−	0.353170i	$-0.114896\pi$
$644$	−69.9811	−	30.7716i	−2.75764	−	1.21257i
$645$	−29.5176	−	4.60443i	−1.16225	−	0.181299i
$646$	10.7969	+	18.7007i	0.424797	+	0.735769i
$647$	9.06721	−	15.7049i	0.356469	−	0.617422i	−0.630899	−	0.775865i	$-0.717314\pi$
$647$	9.06721	−	15.7049i	0.356469	−	0.617422i	0.987368	+	0.158443i	$0.0506473\pi$
$648$	−20.3532	−	44.5874i	−0.799550	−	1.75156i
$649$	6.97206	−	4.02532i	0.273677	−	0.158008i
$650$	50.3661			1.97552
$651$	1.46452	−	32.2288i	0.0573989	−	1.26315i
$652$	−9.90032			−0.387726
$653$	20.0233	−	11.5605i	0.783572	−	0.452395i	−0.0541228	−	0.998534i	$-0.517236\pi$
$653$	20.0233	−	11.5605i	0.783572	−	0.452395i	0.837695	+	0.546139i	$0.183903\pi$
$654$	31.9588	+	25.7563i	1.24969	+	1.00715i
$655$	−31.6282	+	54.7817i	−1.23582	+	2.14050i
$656$	−2.58505	−	4.47744i	−0.100929	−	0.174815i
$657$	2.78381	−	8.70597i	0.108607	−	0.339652i
$658$	42.5988	−	31.2511i	1.66067	−	1.21829i
$659$		−	39.0907i		−	1.52276i	−0.648306	−	0.761380i	$-0.724522\pi$
$659$		−	39.0907i		−	1.52276i	0.648306	−	0.761380i	$-0.275478\pi$
$660$	−39.7370	+	15.3603i	−1.54676	+	0.597897i
$661$	22.9350	+	13.2416i	0.892070	+	0.515037i	0.874619	−	0.484811i	$-0.161112\pi$
$661$	22.9350	+	13.2416i	0.892070	+	0.515037i	0.0174507	+	0.999848i	$0.494445\pi$
$662$	−11.5562	−	6.67196i	−0.449144	−	0.259313i
$663$	−25.1291	+	9.71362i	−0.975934	+	0.377246i
$664$		−	57.1738i		−	2.21877i
$665$	−10.0356	+	7.36226i	−0.389164	+	0.285496i
$666$	15.6243	−	48.8629i	0.605431	−	1.89340i
$667$	24.6714	+	42.7321i	0.955279	+	1.65459i
$668$	−30.1741	+	52.2631i	−1.16747	+	2.02212i
$669$	27.5253	+	22.1832i	1.06419	+	0.857653i
$670$	54.9187	−	31.7073i	2.12170	−	1.22496i
$671$	−8.65539			−0.334138
$672$	−0.409862	+	9.01962i	−0.0158108	+	0.347939i
$673$	42.0467			1.62078			0.810390	−	0.585891i	$-0.199255\pi$
$673$	42.0467			1.62078			0.810390	+	0.585891i	$0.199255\pi$
$674$	50.6645	−	29.2512i	1.95152	−	1.12671i
$675$	−38.9495	+	25.6842i	−1.49917	+	0.988585i
$676$	16.5802	−	28.7178i	0.637700	−	1.10453i
$677$	−11.3809	−	19.7123i	−0.437404	−	0.757606i	0.560085	−	0.828435i	$-0.310769\pi$
$677$	−11.3809	−	19.7123i	−0.437404	−	0.757606i	−0.997488	+	0.0708298i	$0.977435\pi$
$678$	24.4000	+	3.80613i	0.937075	+	0.146174i
$679$	−14.6281	−	6.43216i	−0.561374	−	0.246844i
$680$		−	140.461i		−	5.38645i
$681$	8.01782	+	20.7421i	0.307244	+	0.794839i
$682$	−23.8203	−	13.7526i	−0.912125	−	0.526616i
$683$	−11.1897	−	6.46038i	−0.428162	−	0.247199i	0.270401	−	0.962748i	$-0.412844\pi$
$683$	−11.1897	−	6.46038i	−0.428162	−	0.247199i	−0.698563	+	0.715548i	$0.746177\pi$
$684$	−15.4515	+	3.35988i	−0.590801	+	0.128468i
$685$		−	25.5273i		−	0.975348i
$686$	30.3530	−	34.6632i	1.15888	−	1.32345i
$687$	2.43297	−	15.5971i	0.0928237	−	0.595065i
$688$	11.9254	+	20.6554i	0.454653	+	0.787482i
$689$	−5.08051	+	8.79970i	−0.193552	+	0.335242i
$690$	−69.7305	+	86.5227i	−2.65459	+	3.29386i
$691$	6.07678	−	3.50843i	0.231172	−	0.133467i	−0.379941	−	0.925011i	$-0.624056\pi$
$691$	6.07678	−	3.50843i	0.231172	−	0.133467i	0.611112	+	0.791544i	$0.290722\pi$
$692$	1.61156			0.0612624
$693$	9.34034	+	8.25430i	0.354810	+	0.313555i
$694$	−50.3761			−1.91225
$695$	−18.9292	+	10.9288i	−0.718024	+	0.414551i
$696$	42.3419	−	52.5385i	1.60496	−	1.99147i
$697$	3.44922	−	5.97423i	0.130649	−	0.226290i
$698$	7.10749	+	12.3105i	0.269022	+	0.465960i
$699$	−7.61720	+	48.8316i	−0.288109	+	1.84698i
$700$	98.9204	−	10.8585i	3.73884	−	0.410412i
$701$			1.83002i			0.0691190i	0.999403	+	0.0345595i	$0.0110028\pi$
$701$			1.83002i			0.0691190i	−0.999403	+	0.0345595i	$0.988997\pi$
$702$	−1.72953	−	29.0960i	−0.0652770	−	1.09816i
$703$	−7.48995	−	4.32432i	−0.282489	−	0.163095i
$704$	−7.39669	−	4.27048i	−0.278773	−	0.160950i
$705$	−18.7414	−	48.4840i	−0.705842	−	1.82601i
$706$			49.8781i			1.87719i
$707$	4.31945	+	5.88791i	0.162450	+	0.221438i
$708$	−36.7508	−	5.73272i	−1.38118	−	0.215449i
$709$	2.82891	+	4.89981i	0.106242	+	0.184016i	0.914245	−	0.405162i	$-0.132785\pi$
$709$	2.82891	+	4.89981i	0.106242	+	0.184016i	−0.808003	+	0.589178i	$0.799452\pi$
$710$	33.1319	−	57.3862i	1.24342	−	2.15366i
$711$	31.9019	−	28.9958i	1.19641	−	1.08743i
$712$	−29.5134	+	17.0396i	−1.10606	+	0.638586i
$713$	−48.5603			−1.81860
$714$	−69.8237	+	36.1904i	−2.61309	+	1.35439i
$715$	−13.2392			−0.495118
$716$	−28.7641	+	16.6069i	−1.07496	+	0.620631i
$717$	−10.5583	−	8.50917i	−0.394307	−	0.317781i
$718$	35.2481	−	61.0514i	1.31545	−	2.27842i
$719$	−4.18481	−	7.24831i	−0.156067	−	0.270316i	0.777380	−	0.629031i	$-0.216548\pi$
$719$	−4.18481	−	7.24831i	−0.156067	−	0.270316i	−0.933447	+	0.358715i	$0.883215\pi$
$720$	55.2353	+	17.6620i	2.05850	+	0.658223i
$721$	−2.73371	−	24.9040i	−0.101809	−	0.927475i
$722$		−	43.3293i		−	1.61255i
$723$	30.5634	−	11.8142i	1.13667	−	0.439377i
$724$	−12.1578	−	7.01929i	−0.451840	−	0.260870i
$725$	−55.6258	−	32.1156i	−2.06589	−	1.19274i
$726$	−34.2983	+	13.2579i	−1.27293	+	0.492048i
$727$			1.94352i			0.0720810i	0.999350	+	0.0360405i	$0.0114745\pi$
$727$			1.94352i			0.0720810i	−0.999350	+	0.0360405i	$0.988525\pi$
$728$	−13.0770	+	29.7399i	−0.484667	+	1.10223i
$729$	16.1750	+	21.6187i	0.599074	+	0.800694i
$730$	14.1695	+	24.5422i	0.524435	+	0.908349i
$731$	−15.9121	+	27.5605i	−0.588529	+	1.01936i
$732$	31.1362	+	25.0933i	1.15083	+	0.927476i
$733$	0.745890	−	0.430640i	0.0275501	−	0.0159060i	−0.486162	−	0.873869i	$-0.661603\pi$
$733$	0.745890	−	0.430640i	0.0275501	−	0.0159060i	0.513712	+	0.857963i	$0.328270\pi$
$734$	2.42886			0.0896509
$735$	−25.1269	−	37.7297i	−0.926820	−	1.39168i
$736$	13.5902			0.500941
$737$	−9.27242	+	5.35344i	−0.341554	+	0.197196i
$738$	5.01983	+	5.52294i	0.184782	+	0.203302i
$739$	10.8935	−	18.8680i	0.400722	−	0.694071i	−0.593091	−	0.805135i	$-0.702093\pi$
$739$	10.8935	−	18.8680i	0.400722	−	0.694071i	0.993813	+	0.111064i	$0.0354259\pi$
$740$	53.8278	+	93.2325i	1.97875	+	3.42730i
$741$	−4.85521	−	0.757361i	−0.178361	−	0.0278223i
$742$	−11.9393	+	27.1525i	−0.438307	+	0.996801i
$743$			35.4130i			1.29918i	0.760285	+	0.649589i	$0.225059\pi$
$743$			35.4130i			1.29918i	−0.760285	+	0.649589i	$0.774941\pi$
$744$	23.9429	+	61.9404i	0.877791	+	2.27084i
$745$	40.7602	+	23.5329i	1.49334	+	0.862180i
$746$	−19.5083	−	11.2631i	−0.714249	−	0.412372i
$747$	6.69223	+	30.7763i	0.244856	+	1.12605i
$748$			45.3825i			1.65935i
$749$	3.50452	+	31.9261i	0.128053	+	1.16655i
$750$	9.87966	−	63.3355i	0.360754	−	2.31269i
$751$	−6.91635	−	11.9795i	−0.252381	−	0.437137i	0.711800	−	0.702383i	$-0.247880\pi$
$751$	−6.91635	−	11.9795i	−0.252381	−	0.437137i	−0.964181	+	0.265245i	$0.914547\pi$
$752$	−20.7496	+	35.9394i	−0.756660	+	1.31057i
$753$	−14.6302	+	18.1533i	−0.533153	+	0.661545i
$754$	34.7514	−	20.0637i	1.26557	−	0.730677i
$755$	66.9274			2.43574
$756$	−9.66968	−	56.7724i	−0.351683	−	2.06479i
$757$	−42.7555			−1.55397			−0.776987	−	0.629517i	$-0.783253\pi$
$757$	−42.7555			−1.55397			−0.776987	+	0.629517i	$0.783253\pi$
$758$	−14.5340	+	8.39121i	−0.527899	+	0.304782i
$759$	11.7732	−	14.6084i	0.427341	−	0.530252i
$760$	12.8097	−	22.1871i	0.464657	−	0.804810i
$761$	11.4562	+	19.8428i	0.415288	+	0.719300i	0.995459	−	0.0951952i	$-0.0303475\pi$
$761$	11.4562	+	19.8428i	0.415288	+	0.719300i	−0.580171	+	0.814495i	$0.697014\pi$
$762$	−10.3210	+	66.1649i	−0.373890	+	2.39690i
$763$	14.9076	+	20.3207i	0.539690	+	0.735660i
$764$			111.286i			4.02620i
$765$	16.4411	+	75.6095i	0.594430	+	2.73367i
$766$	64.7001	+	37.3546i	2.33771	+	1.34968i
$767$	−10.0102	−	5.77942i	−0.361449	−	0.208683i
$768$	20.3495	+	52.6441i	0.734299	+	1.89963i
$769$		−	41.6937i		−	1.50351i	−0.659440	−	0.751757i	$-0.729206\pi$
$769$		−	41.6937i		−	1.50351i	0.659440	−	0.751757i	$-0.270794\pi$
$770$	−38.4165	+	4.21697i	−1.38443	+	0.151969i
$771$	35.7991	+	5.58427i	1.28927	+	0.201113i
$772$	9.22227	+	15.9734i	0.331917	+	0.574897i
$773$	10.2894	−	17.8218i	0.370085	−	0.641006i	−0.619493	−	0.785002i	$-0.712662\pi$
$773$	10.2894	−	17.8218i	0.370085	−	0.641006i	0.989578	+	0.143996i	$0.0459953\pi$
$774$	−23.1576	−	25.4786i	−0.832384	−	0.915809i
$775$	54.7437	−	31.6063i	1.96645	−	1.13533i
$776$	32.8921			1.18076
$777$	16.9715	−	26.5357i	0.608848	−	0.951963i
$778$	−0.996466			−0.0357250
$779$	1.08967	−	0.629120i	0.0390414	−	0.0225406i
$780$	47.6256	+	38.3825i	1.70527	+	1.37431i
$781$	−5.59396	+	9.68902i	−0.200168	+	0.346700i
$782$	59.1878	+	102.516i	2.11655	+	3.66598i
$783$	−16.6427	+	33.2373i	−0.594761	+	1.18780i
$784$	−10.8656	+	34.5211i	−0.388056	+	1.23290i
$785$		−	43.9144i		−	1.56737i
$786$	−67.9990	+	26.2849i	−2.42544	+	0.937551i
$787$	−13.0432	−	7.53050i	−0.464940	−	0.268433i	0.249179	−	0.968457i	$-0.419839\pi$
$787$	−13.0432	−	7.53050i	−0.464940	−	0.268433i	−0.714119	+	0.700024i	$0.753173\pi$
$788$	19.6659	+	11.3541i	0.700569	+	0.404474i
$789$	−28.5462	+	11.0345i	−1.01627	+	0.392838i
$790$			133.662i			4.75547i
$791$	13.8804	+	6.10340i	0.493531	+	0.217012i
$792$	−24.4384	−	7.81440i	−0.868381	−	0.277673i
$793$	6.21356	+	10.7622i	0.220650	+	0.382177i
$794$	20.5124	−	35.5286i	0.727959	−	1.26086i
$795$	22.7223	+	18.3124i	0.805876	+	0.649473i
$796$	43.0573	−	24.8591i	1.52612	−	0.881108i
$797$	−17.1311			−0.606814			−0.303407	−	0.952861i	$-0.598124\pi$
$797$	−17.1311			−0.606814			−0.303407	+	0.952861i	$0.598124\pi$
$798$	−14.3297	−	0.651160i	−0.507267	−	0.0230508i
$799$	−55.3723			−1.95893
$800$	−15.3207	+	8.84541i	−0.541668	+	0.312732i
$801$	13.8924	−	12.6269i	0.490864	−	0.446149i
$802$	−4.00923	+	6.94420i	−0.141571	+	0.245208i
$803$	−2.39236	−	4.14369i	−0.0844245	−	0.146227i
$804$	48.8763	+	7.62417i	1.72373	+	0.268884i
$805$	−55.0147	+	40.3595i	−1.93901	+	1.42249i
$806$			39.4911i			1.39102i
$807$	−4.84864	−	12.5434i	−0.170680	−	0.441550i
$808$	−13.0172	−	7.51548i	−0.457943	−	0.264394i
$809$	−15.5787	−	8.99434i	−0.547717	−	0.316224i	0.200484	−	0.979697i	$-0.435749\pi$
$809$	−15.5787	−	8.99434i	−0.547717	−	0.316224i	−0.748201	+	0.663473i	$0.769082\pi$
$810$	−83.3322	−	7.97154i	−2.92799	−	0.280092i
$811$		−	7.05128i		−	0.247604i	−0.992307	−	0.123802i	$-0.960491\pi$
$811$		−	7.05128i		−	0.247604i	0.992307	−	0.123802i	$-0.0395088\pi$
$812$	63.9271	−	46.8978i	2.24340	−	1.64579i
$813$	2.68230	−	17.1954i	0.0940722	−	0.603069i
$814$	−13.4273	−	23.2567i	−0.470626	−	0.815147i
$815$	−4.41813	+	7.65243i	−0.154760	+	0.268053i
$816$	38.7638	−	48.0987i	1.35700	−	1.68379i
$817$	−5.02689	+	2.90228i	−0.175869	+	0.101538i
$818$	−70.1657			−2.45329
$819$	3.55821	−	17.5395i	0.124334	−	0.612879i
$820$	−15.6622			−0.546947
$821$	−26.7485	+	15.4432i	−0.933528	+	0.538973i	−0.887926	−	0.459987i	$-0.847854\pi$
$821$	−26.7485	+	15.4432i	−0.933528	+	0.538973i	−0.0456023	+	0.998960i	$0.514521\pi$
$822$	18.4611	−	22.9068i	0.643904	−	0.798967i
$823$	−0.181508	+	0.314381i	−0.00632696	+	0.0109586i	−0.869172	−	0.494511i	$-0.835347\pi$
$823$	−0.181508	+	0.314381i	−0.00632696	+	0.0109586i	0.862845	+	0.505469i	$0.168681\pi$
$824$	25.7847	+	44.6604i	0.898252	+	1.55582i
$825$	−3.76424	+	24.1314i	−0.131054	+	0.840147i
$826$	−30.8878	−	13.5818i	−1.07473	−	0.472571i
$827$		−	33.9896i		−	1.18193i	−0.806696	−	0.590967i	$-0.798747\pi$
$827$		−	33.9896i		−	1.18193i	0.806696	−	0.590967i	$-0.201253\pi$
$828$	−84.7041	+	18.4187i	−2.94367	+	0.640094i
$829$	−21.1969	−	12.2380i	−0.736198	−	0.425044i	0.0844875	−	0.996425i	$-0.473075\pi$
$829$	−21.1969	−	12.2380i	−0.736198	−	0.425044i	−0.820685	+	0.571381i	$0.806408\pi$
$830$	−84.5680	−	48.8253i	−2.93540	−	1.69475i
$831$	17.1392	+	44.3391i	0.594552	+	1.53811i
$832$			12.2628i			0.425137i
$833$	−47.1393	+	10.4752i	−1.63328	+	0.362943i
$834$	−24.8896	−	3.88250i	−0.861855	−	0.134440i
$835$	26.9311	+	46.6460i	0.931989	+	1.61425i
$836$	−4.13877	+	7.16856i	−0.143142	+	0.247930i
$837$	−20.1385	−	30.5396i	−0.696088	−	1.05560i
$838$	−25.9326	+	14.9722i	−0.895827	+	0.517206i
$839$	−29.0807			−1.00398			−0.501989	−	0.864874i	$-0.667398\pi$
$839$	−29.0807			−1.00398			−0.501989	+	0.864874i	$0.667398\pi$
$840$	78.6053	+	50.2737i	2.71214	+	1.73461i
$841$	−22.1739			−0.764619
$842$	21.3955	−	12.3527i	0.737337	−	0.425702i
$843$	−7.98286	−	6.43355i	−0.274944	−	0.221583i
$844$	6.26481	−	10.8510i	0.215643	−	0.373505i
$845$	−14.7982	−	25.6313i	−0.509074	−	0.881742i
$846$	18.2456	−	57.0605i	0.627296	−	1.96178i
$847$	−22.4433	+	2.46360i	−0.771161	+	0.0846502i
$848$		−	23.2987i		−	0.800080i
$849$	29.7262	−	11.4906i	1.02020	−	0.394357i
$850$	−133.449	−	77.0469i	−4.57727	−	2.64269i
$851$	−41.0595	−	23.7057i	−1.40750	−	0.812622i
$852$	48.2132	−	18.6367i	1.65176	−	0.638484i
$853$			42.8489i			1.46712i	0.679626	+	0.733559i	$0.262142\pi$
$853$			42.8489i			1.46712i	−0.679626	+	0.733559i	$0.737858\pi$
$854$	21.4580	+	29.2498i	0.734278	+	1.00091i
$855$	−4.29838	+	13.4426i	−0.147001	+	0.459726i
$856$	−33.0550	−	57.2530i	−1.12980	−	1.95687i
$857$	−6.11562	+	10.5926i	−0.208906	+	0.361835i	−0.951370	−	0.308050i	$-0.900324\pi$
$857$	−6.11562	+	10.5926i	−0.208906	+	0.361835i	0.742464	+	0.669886i	$0.233657\pi$
$858$	−11.8801	−	9.57445i	−0.405581	−	0.326866i
$859$	18.8044	−	10.8567i	0.641598	−	0.370427i	−0.143632	−	0.989631i	$-0.545878\pi$
$859$	18.8044	−	10.8567i	0.641598	−	0.370427i	0.785230	+	0.619204i	$0.212545\pi$
$860$	72.2533			2.46382
$861$	2.10877	+	4.06855i	0.0718668	+	0.138656i
$862$	17.9617			0.611777
$863$	13.3295	−	7.69580i	0.453742	−	0.261968i	−0.255667	−	0.966765i	$-0.582295\pi$
$863$	13.3295	−	7.69580i	0.453742	−	0.261968i	0.709409	+	0.704797i	$0.248962\pi$
$864$	5.63600	+	8.54686i	0.191741	+	0.290770i
$865$	0.719179	−	1.24565i	0.0244528	−	0.0423535i
$866$	−21.9024	−	37.9360i	−0.744273	−	1.28912i
$867$	52.3479	+	8.16571i	1.77783	+	0.277322i
$868$	8.51394	+	77.5617i	0.288982	+	2.63261i
$869$		−	22.5673i		−	0.765543i
$870$	−41.5526	−	107.496i	−1.40876	−	3.64447i
$871$	13.3130	+	7.68628i	0.451095	+	0.260440i
$872$	−44.9258	−	25.9379i	−1.52138	−	0.878369i
$873$	−17.7056	+	3.85005i	−0.599244	+	0.130304i
$874$			21.5911i			0.730330i
$875$	15.8427	−	36.0297i	0.535582	−	1.21803i
$876$	−3.40711	+	21.8420i	−0.115116	+	0.737972i
$877$	−18.6353	−	32.2772i	−0.629268	−	1.08992i	−0.987699	−	0.156368i	$-0.950021\pi$
$877$	−18.6353	−	32.2772i	−0.629268	−	1.08992i	0.358431	−	0.933556i	$-0.383312\pi$
$878$	30.4483	−	52.7380i	1.02758	−	1.77982i
$879$	−32.7628	+	40.6526i	−1.10506	+	1.37118i
$880$	26.2897	−	15.1784i	0.886227	−	0.511663i
$881$	40.7343			1.37237			0.686187	−	0.727425i	$-0.259283\pi$
$881$	40.7343			1.37237			0.686187	+	0.727425i	$0.259283\pi$
$882$	4.73822	−	52.0281i	0.159544	−	1.75188i
$883$	−32.3370			−1.08823			−0.544113	−	0.839012i	$-0.683134\pi$
$883$	−32.3370			−1.08823			−0.544113	+	0.839012i	$0.683134\pi$
$884$	56.4291	−	32.5793i	1.89792	−	1.09576i
$885$	−20.8315	+	25.8481i	−0.700245	+	0.868875i
$886$	−13.2099	+	22.8802i	−0.443796	+	0.768677i
$887$	−6.62678	−	11.4779i	−0.222505	−	0.385391i	0.733063	−	0.680161i	$-0.238090\pi$
$887$	−6.62678	−	11.4779i	−0.222505	−	0.385391i	−0.955568	+	0.294770i	$0.904757\pi$
$888$	−9.99284	+	64.0611i	−0.335338	+	2.14975i
$889$	−16.5505	+	37.6392i	−0.555085	+	1.26238i
$890$			58.2060i			1.95107i
$891$	14.0697	+	1.34591i	0.471353	+	0.0450896i
$892$	−74.0451	−	42.7499i	−2.47921	−	1.43137i
$893$	−8.74652	−	5.04981i	−0.292691	−	0.168985i
$894$	19.5572	+	50.5945i	0.654092	+	1.69213i
$895$			29.6442i			0.990895i
$896$	5.04357	+	45.9468i	0.168494	+	1.53497i
$897$	−26.6160	−	4.15181i	−0.888684	−	0.138625i
$898$	−1.26223	−	2.18625i	−0.0421212	−	0.0729561i
$899$	25.1812	−	43.6152i	0.839841	−	1.45465i
$900$	83.5018	−	75.8952i	2.78339	−	2.52984i
$901$	26.9225	−	15.5437i	0.896917	−	0.517835i
$902$	3.90691			0.130086
$903$	−9.72826	−	18.7691i	−0.323736	−	0.624598i
$904$	−31.2109			−1.03806
$905$	−10.8511	+	6.26488i	−0.360702	+	0.208252i
$906$	60.0570	+	48.4012i	1.99526	+	1.60802i
$907$	−8.48521	+	14.6968i	−0.281747	+	0.488000i	−0.971815	−	0.235744i	$-0.924247\pi$
$907$	−8.48521	+	14.6968i	−0.281747	+	0.488000i	0.690068	+	0.723744i	$0.257581\pi$
$908$	−26.8917	−	46.5777i	−0.892431	−	1.54574i
$909$	7.88676	+	2.52186i	0.261587	+	0.0836449i
$910$	32.8219	+	44.7401i	1.08804	+	1.48312i
$911$			52.5499i			1.74106i	0.492118	+	0.870528i	$0.336223\pi$
$911$			52.5499i			1.74106i	−0.492118	+	0.870528i	$0.663777\pi$
$912$	10.5095	−	4.06245i	0.348006	−	0.134521i
$913$	14.2784	+	8.24362i	0.472545	+	0.272824i
$914$	−28.5582	−	16.4881i	−0.944622	−	0.545378i
$915$	33.2907	−	12.8685i	1.10056	−	0.425418i
$916$			38.1785i			1.26145i
$917$	−44.4956	+	4.88428i	−1.46937	+	0.161293i
$918$	−39.9266	+	79.7379i	−1.31778	+	2.63174i
$919$	−9.83558	−	17.0357i	−0.324446	−	0.561957i	0.656954	−	0.753930i	$-0.271844\pi$
$919$	−9.83558	−	17.0357i	−0.324446	−	0.561957i	−0.981400	+	0.191974i	$0.938511\pi$
$920$	70.2222	−	121.628i	2.31516	−	4.00997i
$921$	−43.9858	−	35.4491i	−1.44938	−	1.16809i
$922$	−68.8356	+	39.7422i	−2.26698	+	1.30884i
$923$	16.0632			0.528728
$924$	−25.3971	−	16.2432i	−0.835503	−	0.534363i
$925$	61.7171			2.02925
$926$	−41.2569	+	23.8197i	−1.35578	+	0.782762i
$927$	−19.1073	−	21.0223i	−0.627565	−	0.690462i
$928$	−7.04727	+	12.2062i	−0.231338	+	0.400689i
$929$	7.02635	+	12.1700i	0.230527	+	0.399284i	0.957963	−	0.286891i	$-0.0926217\pi$
$929$	7.02635	+	12.1700i	0.230527	+	0.399284i	−0.727436	+	0.686175i	$0.759288\pi$
$930$	112.065	+	17.4810i	3.67476	+	0.573223i
$931$	−8.40136	−	2.64434i	−0.275343	−	0.0866647i
$932$		−	119.530i		−	3.91534i
$933$	1.62772	+	4.21092i	0.0532893	+	0.137859i
$934$	−15.7629	−	9.10069i	−0.515777	−	0.297784i
$935$	35.0783	+	20.2525i	1.14718	+	0.662327i
$936$	7.82741	+	35.9968i	0.255847	+	1.17659i
$937$		−	32.2220i		−	1.05265i	−0.850285	−	0.526323i	$-0.823570\pi$
$937$		−	32.2220i		−	1.05265i	0.850285	−	0.526323i	$-0.176430\pi$
$938$	41.0790	+	18.0630i	1.34128	+	0.589777i
$939$	0.526514	−	3.37533i	0.0171821	−	0.110150i
$940$	62.8584	+	108.874i	2.05022	+	3.55108i
$941$	9.53589	−	16.5166i	0.310861	−	0.538427i	−0.667688	−	0.744441i	$-0.732716\pi$
$941$	9.53589	−	16.5166i	0.310861	−	0.538427i	0.978549	+	0.206014i	$0.0660493\pi$
$942$	31.7584	−	39.4064i	1.03474	−	1.28393i
$943$	5.97351	−	3.44881i	0.194524	−	0.112309i
$944$	26.5038			0.862626
$945$	−48.1973	−	17.8612i	−1.56786	−	0.581025i
$946$	−18.0235			−0.585994
$947$	17.5659	−	10.1417i	0.570816	−	0.329561i	−0.186659	−	0.982425i	$-0.559766\pi$
$947$	17.5659	−	10.1417i	0.570816	−	0.329561i	0.757475	+	0.652864i	$0.226433\pi$
$948$	−65.4261	+	81.1817i	−2.12494	+	2.63666i
$949$	−3.43487	+	5.94936i	−0.111500	+	0.193124i
$950$	−14.0529	−	24.3404i	−0.455938	−	0.789707i
$951$	3.66297	−	23.4822i	0.118780	−	0.761463i
$952$	80.1430	−	58.7939i	2.59745	−	1.90552i
$953$		−	8.62059i		−	0.279248i	−0.990205	−	0.139624i	$-0.955411\pi$
$953$		−	8.62059i		−	0.279248i	0.990205	−	0.139624i	$-0.0445894\pi$
$954$	7.14643	+	32.8650i	0.231374	+	1.06404i
$955$	86.0185	+	49.6628i	2.78349	+	1.60705i
$956$	28.4026	+	16.3983i	0.918606	+	0.530358i
$957$	7.01569	+	18.1496i	0.226785	+	0.586693i
$958$			29.1712i			0.942478i
$959$	14.5651	−	10.6851i	0.470331	−	0.345041i
$960$	34.7986	+	5.42821i	1.12312	+	0.175195i
$961$	9.28193	+	16.0768i	0.299417	+	0.518606i
$962$	−19.2784	+	33.3912i	−0.621561	+	1.07658i
$963$	24.4948	+	26.9498i	0.789335	+	0.868446i
$964$	−68.6322	+	39.6248i	−2.21049	+	1.27623i
$965$	16.4622			0.529936
$966$	−78.5548	−	3.56962i	−2.52746	−	0.114851i
$967$	17.9282			0.576533			0.288266	−	0.957550i	$-0.406921\pi$
$967$	17.9282			0.576533			0.288266	+	0.957550i	$0.406921\pi$
$968$	40.2475	−	23.2369i	1.29360	−	0.746862i
$969$	11.7057	+	9.43389i	0.376042	+	0.303060i
$970$	28.0893	−	48.6520i	0.901892	−	1.56212i
$971$	−8.41949	−	14.5830i	−0.270194	−	0.467990i	0.698717	−	0.715398i	$-0.253755\pi$
$971$	−8.41949	−	14.5830i	−0.270194	−	0.467990i	−0.968911	+	0.247408i	$0.920421\pi$
$972$	−46.7113	−	45.6319i	−1.49826	−	1.46365i
$973$	−14.1589	−	6.22587i	−0.453914	−	0.199592i
$974$			21.5565i			0.690715i
$975$	32.7075	−	12.6430i	1.04748	−	0.404901i
$976$	−24.6772	−	14.2474i	−0.789897	−	0.456047i
$977$	19.9678	+	11.5284i	0.638826	+	0.368826i	0.784162	−	0.620556i	$-0.213093\pi$
$977$	19.9678	+	11.5284i	0.638826	+	0.368826i	−0.145336	+	0.989382i	$0.546426\pi$
$978$	−9.49875	+	3.67173i	−0.303736	+	0.117409i
$979$		−	9.82744i		−	0.314086i
$980$	74.1088	+	80.7947i	2.36732	+	2.58089i
$981$	27.2193	+	8.70362i	0.869046	+	0.277885i
$982$	−48.6630	−	84.2867i	−1.55290	−	2.68970i
$983$	21.7207	−	37.6214i	0.692783	−	1.19994i	−0.278139	−	0.960541i	$-0.589718\pi$
$983$	21.7207	−	37.6214i	0.692783	−	1.19994i	0.970922	−	0.239395i	$-0.0769489\pi$
$984$	−7.34435	−	5.91896i	−0.234129	−	0.188690i
$985$	17.5523	−	10.1338i	0.559262	−	0.322890i
$986$	−122.769			−3.90976
$987$	19.8187	−	30.9875i	0.630837	−	0.986345i
$988$	11.8846			0.378100
$989$	−27.5572	+	15.9101i	−0.876267	+	0.505913i
$990$	−32.4285	+	29.4745i	−1.03065	+	0.936760i
$991$	15.5842	−	26.9927i	0.495049	−	0.857450i	−0.504935	−	0.863157i	$-0.668483\pi$
$991$	15.5842	−	26.9927i	0.495049	−	0.857450i	0.999984	+	0.00570766i	$0.00181681\pi$
$992$	−6.93552	−	12.0127i	−0.220203	−	0.381403i
$993$	−9.17934	−	1.43188i	−0.291297	−	0.0454393i
$994$	46.6110	−	5.11649i	1.47841	−	0.162285i
$995$		−	44.3747i		−	1.40677i
$996$	−27.4643	−	71.0501i	−0.870240	−	2.25131i
$997$	22.8831	+	13.2115i	0.724714	+	0.418414i	0.816485	−	0.577366i	$-0.195920\pi$
$997$	22.8831	+	13.2115i	0.724714	+	0.418414i	−0.0917712	+	0.995780i	$0.529253\pi$
$998$	10.5852	+	6.11138i	0.335069	+	0.193452i
$999$	−2.11932	−	35.6534i	−0.0670522	−	1.12802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.s.a.206.4	✓	106
3.2	odd	2		861.2.s.b.206.50	yes	106
7.5	odd	6		861.2.s.b.698.50	yes	106
21.5	even	6	inner	861.2.s.a.698.4	yes	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.s.a.206.4	✓	106	1.1	even	1	trivial
861.2.s.a.698.4	yes	106	21.5	even	6	inner
861.2.s.b.206.50	yes	106	3.2	odd	2
861.2.s.b.698.50	yes	106	7.5	odd	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:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.15448 + 1.24389i) q^{2} +(-1.08687 + 1.34860i) q^{3} +(2.09453 - 3.62783i) q^{4} +(-1.86942 - 3.23792i) q^{5} +(0.664120 - 4.25748i) q^{6} +(1.06496 - 2.42195i) q^{7} +5.44590i q^{8} +(-0.637447 - 2.93149i) q^{9} +O(q^{10})\)	\(q+(-2.15448 + 1.24389i) q^{2} +(-1.08687 + 1.34860i) q^{3} +(2.09453 - 3.62783i) q^{4} +(-1.86942 - 3.23792i) q^{5} +(0.664120 - 4.25748i) q^{6} +(1.06496 - 2.42195i) q^{7} +5.44590i q^{8} +(-0.637447 - 2.93149i) q^{9} +(8.05525 + 4.65070i) q^{10} +(-1.36004 - 0.785219i) q^{11} +(2.61602 + 6.76765i) q^{12} +2.25478i q^{13} +(0.718197 + 6.54275i) q^{14} +(6.39847 + 0.998092i) q^{15} +(-2.58505 - 4.47744i) q^{16} +(3.44922 - 5.97423i) q^{17} +(5.01983 + 5.52294i) q^{18} +(1.08967 - 0.629120i) q^{19} -15.6622 q^{20} +(2.10877 + 4.06855i) q^{21} +3.90691 q^{22} +(5.97351 - 3.44881i) q^{23} +(-7.34435 - 5.91896i) q^{24} +(-4.48943 + 7.77592i) q^{25} +(-2.80470 - 4.85789i) q^{26} +(4.64623 + 2.32648i) q^{27} +(-6.55583 - 8.93636i) q^{28} +7.15360i q^{29} +(-15.0269 + 5.80863i) q^{30} +(-6.09696 - 3.52008i) q^{31} +(1.70631 + 0.985137i) q^{32} +(2.53713 - 0.980723i) q^{33} +17.1618i q^{34} +(-9.83296 + 1.07936i) q^{35} +(-11.9701 - 3.82755i) q^{36} +(-3.43680 - 5.95271i) q^{37} +(-1.56511 + 2.71086i) q^{38} +(-3.04080 - 2.45064i) q^{39} +(17.6334 - 10.1807i) q^{40} +1.00000 q^{41} +(-9.60414 - 6.14253i) q^{42} -4.61323 q^{43} +(-5.69729 + 3.28933i) q^{44} +(-8.30030 + 7.54419i) q^{45} +(-8.57988 + 14.8608i) q^{46} +(-4.01339 - 6.95139i) q^{47} +(8.84787 + 1.38017i) q^{48} +(-4.73170 - 5.15858i) q^{49} -22.3375i q^{50} +(4.30801 + 11.1448i) q^{51} +(8.17997 + 4.72271i) q^{52} +(3.90268 + 2.25322i) q^{53} +(-12.9041 + 0.767050i) q^{54} +5.87161i q^{55} +(13.1897 + 5.79969i) q^{56} +(-0.335891 + 2.15330i) q^{57} +(-8.89829 - 15.4123i) q^{58} +(-2.56318 + 4.43956i) q^{59} +(17.0227 - 21.1220i) q^{60} +(4.77305 - 2.75572i) q^{61} +17.5144 q^{62} +(-7.77880 - 1.57807i) q^{63} +5.43859 q^{64} +(7.30081 - 4.21513i) q^{65} +(-4.24628 + 5.26886i) q^{66} +(3.40888 - 5.90435i) q^{67} +(-14.4490 - 25.0264i) q^{68} +(-1.84134 + 11.8043i) q^{69} +(19.8423 - 14.5566i) q^{70} -7.12407i q^{71} +(15.9646 - 3.47147i) q^{72} +(2.63855 + 1.52337i) q^{73} +(14.8091 + 8.55001i) q^{74} +(-5.60721 - 14.5058i) q^{75} -5.27085i q^{76} +(-3.35016 + 2.45772i) q^{77} +(9.59968 + 1.49745i) q^{78} +(7.18503 + 12.4448i) q^{79} +(-9.66506 + 16.7404i) q^{80} +(-8.18732 + 3.73734i) q^{81} +(-2.15448 + 1.24389i) q^{82} -10.4985 q^{83} +(19.1769 + 0.871421i) q^{84} -25.7921 q^{85} +(9.93912 - 5.73836i) q^{86} +(-9.64734 - 7.77500i) q^{87} +(4.27623 - 7.40664i) q^{88} +(3.12888 + 5.41938i) q^{89} +(8.49871 - 26.5785i) q^{90} +(5.46097 + 2.40126i) q^{91} -28.8945i q^{92} +(11.3738 - 4.39651i) q^{93} +(17.2935 + 9.98443i) q^{94} +(-4.07409 - 2.35218i) q^{95} +(-3.18308 + 1.23042i) q^{96} -6.03979i q^{97} +(16.6111 + 5.22836i) q^{98} +(-1.43491 + 4.48749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q + 52 q^{4} - 5 q^{7} - 2 q^{9}+O(q^{10}) \) 106 * q + 52 * q^4 - 5 * q^7 - 2 * q^9	\( 106 q + 52 q^{4} - 5 q^{7} - 2 q^{9} - 6 q^{10} - 22 q^{12} - 20 q^{14} - 4 q^{15} - 42 q^{16} - 5 q^{18} + 3 q^{19} - 36 q^{20} + 8 q^{21} - 12 q^{22} + 18 q^{23} - 57 q^{25} + 42 q^{26} + 18 q^{27} - 14 q^{28} - 107 q^{30} - 21 q^{31} - 2 q^{33} - 48 q^{35} - 16 q^{36} - q^{37} + 4 q^{39} - 18 q^{40} + 106 q^{41} + 77 q^{42} - 6 q^{43} + 210 q^{44} + 24 q^{45} - 8 q^{46} + 16 q^{47} + 70 q^{48} - 3 q^{49} - 42 q^{51} + 6 q^{52} - 16 q^{54} - 60 q^{56} - 22 q^{57} + 10 q^{58} - 16 q^{59} - 4 q^{60} + 18 q^{61} - 104 q^{62} + 33 q^{63} - 84 q^{64} + 36 q^{65} + 8 q^{66} + 21 q^{67} + 36 q^{68} - 12 q^{69} + 38 q^{70} - 148 q^{72} + 21 q^{73} - 40 q^{75} - 100 q^{77} + 60 q^{78} - 11 q^{79} - 36 q^{80} - 2 q^{81} - 20 q^{83} + 118 q^{84} - 4 q^{85} + 90 q^{86} + 17 q^{87} - 14 q^{88} + 16 q^{89} + 44 q^{90} + 19 q^{91} - 87 q^{93} + 24 q^{94} - 156 q^{96} - 268 q^{98} + 18 q^{99}+O(q^{100}) \) 106 * q + 52 * q^4 - 5 * q^7 - 2 * q^9 - 6 * q^10 - 22 * q^12 - 20 * q^14 - 4 * q^15 - 42 * q^16 - 5 * q^18 + 3 * q^19 - 36 * q^20 + 8 * q^21 - 12 * q^22 + 18 * q^23 - 57 * q^25 + 42 * q^26 + 18 * q^27 - 14 * q^28 - 107 * q^30 - 21 * q^31 - 2 * q^33 - 48 * q^35 - 16 * q^36 - q^37 + 4 * q^39 - 18 * q^40 + 106 * q^41 + 77 * q^42 - 6 * q^43 + 210 * q^44 + 24 * q^45 - 8 * q^46 + 16 * q^47 + 70 * q^48 - 3 * q^49 - 42 * q^51 + 6 * q^52 - 16 * q^54 - 60 * q^56 - 22 * q^57 + 10 * q^58 - 16 * q^59 - 4 * q^60 + 18 * q^61 - 104 * q^62 + 33 * q^63 - 84 * q^64 + 36 * q^65 + 8 * q^66 + 21 * q^67 + 36 * q^68 - 12 * q^69 + 38 * q^70 - 148 * q^72 + 21 * q^73 - 40 * q^75 - 100 * q^77 + 60 * q^78 - 11 * q^79 - 36 * q^80 - 2 * q^81 - 20 * q^83 + 118 * q^84 - 4 * q^85 + 90 * q^86 + 17 * q^87 - 14 * q^88 + 16 * q^89 + 44 * q^90 + 19 * q^91 - 87 * q^93 + 24 * q^94 - 156 * q^96 - 268 * q^98 + 18 * q^99

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