LMFDB - Embedded newform 861.2.s.b.698.50

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			698.50
Character	$\chi$	$=$	861.698
Dual form			861.2.s.b.206.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.15448 + 1.24389i) q^{2} +(0.624490 + 1.61555i) q^{3} +(2.09453 + 3.62783i) q^{4} +(1.86942 - 3.23792i) q^{5} +(-0.664120 + 4.25748i) q^{6} +(1.06496 + 2.42195i) q^{7} +5.44590i q^{8} +(-2.22003 + 2.01779i) q^{9} +O(q^{10})$	\(q+(2.15448 + 1.24389i) q^{2} +(0.624490 + 1.61555i) 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} +(-2.22003 + 2.01779i) q^{9} +(8.05525 - 4.65070i) q^{10} +(1.36004 - 0.785219i) q^{11} +(-4.55294 + 5.64937i) 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} +(-7.29292 + 1.58583i) q^{18} +(1.08967 + 0.629120i) q^{19} +15.6622 q^{20} +(-3.24773 + 3.23299i) q^{21} +3.90691 q^{22} +(-5.97351 - 3.44881i) q^{23} +(-8.79815 + 3.40091i) 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} +(12.5439 + 10.1094i) q^{30} +(-6.09696 + 3.52008i) q^{31} +(-1.70631 + 0.985137i) q^{32} +(2.11789 + 1.70686i) 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} +(3.64272 - 1.40809i) q^{39} +(17.6334 + 10.1807i) q^{40} -1.00000 q^{41} +(-11.0187 + 2.92559i) q^{42} -4.61323 q^{43} +(5.69729 + 3.28933i) q^{44} +(2.38331 + 10.9604i) 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} +(7.49768 - 9.30325i) q^{51} +(8.17997 - 4.72271i) q^{52} +(-3.90268 + 2.25322i) q^{53} +(-7.11634 - 10.7918i) 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} +(9.78087 + 25.3031i) q^{60} +(4.77305 + 2.75572i) q^{61} -17.5144 q^{62} +(-7.25124 - 3.22792i) q^{63} +5.43859 q^{64} +(-7.30081 - 4.21513i) q^{65} +(2.43982 + 6.31182i) 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} +(-10.9887 - 12.0900i) q^{72} +(2.63855 - 1.52337i) q^{73} +(-14.8091 + 8.55001i) q^{74} +(9.75882 - 12.1089i) 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} +(0.857027 - 8.95910i) q^{81} +(-2.15448 - 1.24389i) q^{82} +10.4985 q^{83} +(-18.5312 - 5.01064i) q^{84} -25.7921 q^{85} +(-9.93912 - 5.73836i) q^{86} +(-11.5570 + 4.46735i) 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} +(-9.49436 - 7.65171i) q^{93} +(17.2935 - 9.98443i) q^{94} +(4.07409 - 2.35218i) q^{95} +(-2.65711 - 2.14142i) 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} - 8 q^{12} + 20 q^{14} - 4 q^{15} - 42 q^{16} - 5 q^{18} + 3 q^{19} + 36 q^{20} - 16 q^{21} - 12 q^{22} - 18 q^{23} - 57 q^{25} - 42 q^{26} - 18 q^{27} - 14 q^{28} + 103 q^{30} - 21 q^{31} + 26 q^{33} + 48 q^{35} - 16 q^{36} - q^{37} + 4 q^{39} - 18 q^{40} - 106 q^{41} - 43 q^{42} - 6 q^{43} - 210 q^{44} - 8 q^{46} - 16 q^{47} - 70 q^{48} - 3 q^{49} + 54 q^{51} + 6 q^{52} + 82 q^{54} + 60 q^{56} - 22 q^{57} + 10 q^{58} + 16 q^{59} - 4 q^{60} + 18 q^{61} + 104 q^{62} - 71 q^{63} - 84 q^{64} - 36 q^{65} - 32 q^{66} + 21 q^{67} - 36 q^{68} + 12 q^{69} + 38 q^{70} + 176 q^{72} + 21 q^{73} - 8 q^{75} + 100 q^{77} + 60 q^{78} - 11 q^{79} + 36 q^{80} - 2 q^{81} + 20 q^{83} - 186 q^{84} - 4 q^{85} - 90 q^{86} - 47 q^{87} - 14 q^{88} - 16 q^{89} - 44 q^{90} + 19 q^{91} + 87 q^{93} + 24 q^{94} + 54 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 - 8 * q^12 + 20 * q^14 - 4 * q^15 - 42 * q^16 - 5 * q^18 + 3 * q^19 + 36 * q^20 - 16 * q^21 - 12 * q^22 - 18 * q^23 - 57 * q^25 - 42 * q^26 - 18 * q^27 - 14 * q^28 + 103 * q^30 - 21 * q^31 + 26 * q^33 + 48 * q^35 - 16 * q^36 - q^37 + 4 * q^39 - 18 * q^40 - 106 * q^41 - 43 * q^42 - 6 * q^43 - 210 * q^44 - 8 * q^46 - 16 * q^47 - 70 * q^48 - 3 * q^49 + 54 * q^51 + 6 * q^52 + 82 * q^54 + 60 * q^56 - 22 * q^57 + 10 * q^58 + 16 * q^59 - 4 * q^60 + 18 * q^61 + 104 * q^62 - 71 * q^63 - 84 * q^64 - 36 * q^65 - 32 * q^66 + 21 * q^67 - 36 * q^68 + 12 * q^69 + 38 * q^70 + 176 * q^72 + 21 * q^73 - 8 * q^75 + 100 * q^77 + 60 * q^78 - 11 * q^79 + 36 * q^80 - 2 * q^81 + 20 * q^83 - 186 * q^84 - 4 * q^85 - 90 * q^86 - 47 * q^87 - 14 * q^88 - 16 * q^89 - 44 * q^90 + 19 * q^91 + 87 * q^93 + 24 * q^94 + 54 * q^96 + 268 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$493$	$575$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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	0.999615	+	0.0277434i	$0.00883213\pi$
$2$	2.15448	+	1.24389i	1.52345	+	0.879564i	0.523834	+	0.851820i	$0.324501\pi$
$3$	0.624490	+	1.61555i	0.360549	+	0.932740i
$3$	0.624490	+	1.61555i	0.360549	+	0.932740i
$4$	2.09453	+	3.62783i	1.04726	+	1.81392i
$5$	1.86942	−	3.23792i	0.836028	−	1.44804i	−0.0571623	−	0.998365i	$-0.518205\pi$
$5$	1.86942	−	3.23792i	0.836028	−	1.44804i	0.893191	−	0.449678i	$-0.148461\pi$
$6$	−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
$9$	−2.22003	+	2.01779i	−0.740009	+	0.672598i
$10$	8.05525	−	4.65070i	2.54729	−	1.47068i
$11$	1.36004	−	0.785219i	0.410067	−	0.236753i	−0.280751	−	0.959781i	$-0.590584\pi$
$11$	1.36004	−	0.785219i	0.410067	−	0.236753i	0.690819	+	0.723028i	$0.257250\pi$
$12$	−4.55294	+	5.64937i	−1.31432	+	1.63083i
$13$		−	2.25478i		−	0.625364i	−0.949858	−	0.312682i	$-0.898773\pi$
$13$		−	2.25478i		−	0.625364i	0.949858	−	0.312682i	$-0.101227\pi$
$14$	−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	−0.892754	−	0.450544i	$-0.851230\pi$
$17$	−3.44922	−	5.97423i	−0.836560	−	1.44896i	0.0561948	−	0.998420i	$-0.482103\pi$
$18$	−7.29292	+	1.58583i	−1.71896	+	0.373783i
$19$	1.08967	+	0.629120i	0.249987	+	0.144330i	0.619758	−	0.784793i	$-0.287231\pi$
$19$	1.08967	+	0.629120i	0.249987	+	0.144330i	−0.369771	+	0.929123i	$0.620564\pi$
$20$	15.6622			3.50217
$21$	−3.24773	+	3.23299i	−0.708714	+	0.705496i
$22$	3.90691			0.832956
$23$	−5.97351	−	3.44881i	−1.24556	−	0.719126i	−0.275341	−	0.961347i	$-0.588791\pi$
$23$	−5.97351	−	3.44881i	−1.24556	−	0.719126i	−0.970221	+	0.242221i	$0.922124\pi$
$24$	−8.79815	+	3.40091i	−1.79591	+	0.694208i
$25$	−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	$0.768775\pi$
$30$	12.5439	+	10.1094i	2.29019	+	1.84571i
$31$	−6.09696	+	3.52008i	−1.09505	+	0.632225i	−0.934915	−	0.354871i	$-0.884525\pi$
$31$	−6.09696	+	3.52008i	−1.09505	+	0.632225i	−0.160131	+	0.987096i	$0.551192\pi$
$32$	−1.70631	+	0.985137i	−0.301635	+	0.174149i
$33$	2.11789	+	1.70686i	0.368678	+	0.297125i
$34$		−	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	0.432042	+	0.901853i	$0.357793\pi$
$37$	−3.43680	+	5.95271i	−0.565007	+	0.978620i	−0.997049	+	0.0767670i	$0.975540\pi$
$38$	1.56511	+	2.71086i	0.253895	+	0.439759i
$39$	3.64272	−	1.40809i	0.583302	−	0.225475i
$40$	17.6334	+	10.1807i	2.78809	+	1.60970i
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$	−11.0187	+	2.92559i	−1.70022	+	0.451429i
$43$	−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
$45$	2.38331	+	10.9604i	0.355282	+	1.63387i
$46$	−8.57988	−	14.8608i	−1.26503	−	2.19110i
$47$	4.01339	−	6.95139i	0.585413	−	1.01396i	−0.409411	−	0.912350i	$-0.634266\pi$
$47$	4.01339	−	6.95139i	0.585413	−	1.01396i	0.994824	−	0.101614i	$-0.0324008\pi$
$48$	−8.84787	−	1.38017i	−1.27708	−	0.199211i
$49$	−4.73170	+	5.15858i	−0.675957	+	0.736941i
$50$		−	22.3375i		−	3.15899i
$51$	7.49768	−	9.30325i	1.04989	−	1.30272i
$52$	8.17997	−	4.72271i	1.13436	−	0.654922i
$53$	−3.90268	+	2.25322i	−0.536075	+	0.309503i	−0.743487	−	0.668751i	$-0.766829\pi$
$53$	−3.90268	+	2.25322i	−0.536075	+	0.309503i	0.207412	+	0.978254i	$0.433496\pi$
$54$	−7.11634	−	10.7918i	−0.968412	−	1.46857i
$55$		−	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	$-0.0583701\pi$
$59$	2.56318	+	4.43956i	0.333698	+	0.577982i	−0.649536	+	0.760331i	$0.725037\pi$
$60$	9.78087	+	25.3031i	1.26271	+	3.26662i
$61$	4.77305	+	2.75572i	0.611127	+	0.352834i	0.773406	−	0.633910i	$-0.218551\pi$
$61$	4.77305	+	2.75572i	0.611127	+	0.352834i	−0.162279	+	0.986745i	$0.551885\pi$
$62$	−17.5144			−2.22433
$63$	−7.25124	−	3.22792i	−0.913571	−	0.406679i
$64$	5.43859			0.679823
$65$	−7.30081	−	4.21513i	−0.905554	−	0.522822i
$66$	2.43982	+	6.31182i	0.300322	+	0.776931i
$67$	3.40888	+	5.90435i	0.416461	+	0.721331i	0.995581	−	0.0939112i	$-0.0299370\pi$
$67$	3.40888	+	5.90435i	0.416461	+	0.721331i	−0.579120	+	0.815242i	$0.696604\pi$
$68$	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	$-0.138930\pi$
$72$	−10.9887	−	12.0900i	−1.29503	−	1.42483i
$73$	2.63855	−	1.52337i	0.308819	−	0.178297i	−0.337579	−	0.941297i	$-0.609608\pi$
$73$	2.63855	−	1.52337i	0.308819	−	0.178297i	0.646398	+	0.763000i	$0.276275\pi$
$74$	−14.8091	+	8.55001i	−1.72152	+	0.993919i
$75$	9.75882	−	12.1089i	1.12685	−	1.39822i
$76$			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	−0.105607	−	0.994408i	$-0.533679\pi$
$79$	7.18503	−	12.4448i	0.808379	−	1.40015i	0.913986	−	0.405746i	$-0.132988\pi$
$80$	9.66506	+	16.7404i	1.08059	+	1.87163i
$81$	0.857027	−	8.95910i	0.0952252	−	0.995456i
$82$	−2.15448	−	1.24389i	−0.237923	−	0.137365i
$83$	10.4985			1.15236			0.576180	−	0.817323i	$-0.304543\pi$
$83$	10.4985			1.15236			0.576180	+	0.817323i	$0.304543\pi$
$84$	−18.5312	−	5.01064i	−2.02192	−	0.546705i
$85$	−25.7921			−2.79755
$86$	−9.93912	−	5.73836i	−1.07176	−	0.618783i
$87$	−11.5570	+	4.46735i	−1.23904	+	0.478950i
$88$	4.27623	+	7.40664i	0.455847	+	0.789551i
$89$	−3.12888	+	5.41938i	−0.331661	+	0.574454i	−0.982838	−	0.184473i	$-0.940942\pi$
$89$	−3.12888	+	5.41938i	−0.331661	+	0.574454i	0.651177	+	0.758926i	$0.274276\pi$
$90$	−8.49871	+	26.5785i	−0.895843	+	2.80162i
$91$	5.46097	−	2.40126i	0.572466	−	0.251721i
$92$		−	28.8945i		−	3.01246i
$93$	−9.49436	−	7.65171i	−0.984520	−	0.793445i
$94$	17.2935	−	9.98443i	1.78369	−	1.02982i
$95$	4.07409	−	2.35218i	0.417993	−	0.241328i
$96$	−2.65711	−	2.14142i	−0.271190	−	0.218558i
$97$			6.03979i			0.613248i	0.951831	+	0.306624i	$0.0991994\pi$
$97$			6.03979i			0.613248i	−0.951831	+	0.306624i	$0.900801\pi$
$98$	−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	$-0.122819\pi$
$101$	1.38002	+	2.39027i	0.137318	+	0.237841i	−0.789163	+	0.614184i	$0.789485\pi$
$102$	27.7259	−	10.7174i	2.74527	−	1.06118i
$103$	8.20073	+	4.73469i	0.808042	+	0.466523i	0.846275	−	0.532746i	$-0.178840\pi$
$103$	8.20073	+	4.73469i	0.808042	+	0.466523i	−0.0382336	+	0.999269i	$0.512173\pi$
$104$	12.2793			1.20409
$105$	4.39681	+	16.5597i	0.429085	+	1.61606i
$106$	−11.2110			−1.08891
$107$	10.5130	+	6.06971i	1.01633	+	0.586781i	0.913040	−	0.407870i	$-0.133728\pi$
$107$	10.5130	+	6.06971i	1.01633	+	0.586781i	0.103294	+	0.994651i	$0.467062\pi$
$108$	−1.29160	−	21.7286i	−0.124284	−	2.09084i
$109$	−4.76283	−	8.24947i	−0.456197	−	0.790156i	0.542559	−	0.840017i	$-0.317455\pi$
$109$	−4.76283	−	8.24947i	−0.456197	−	0.790156i	−0.998756	+	0.0498614i	$0.984122\pi$
$110$	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	$0.913119\pi$
$114$	−3.40214	+	4.22143i	−0.318639	+	0.395373i
$115$	−22.3339	+	12.8945i	−2.08265	+	1.20242i
$116$	−25.9520	+	14.9834i	−2.40959	+	1.39118i
$117$	4.54968	+	5.00567i	0.420618	+	0.462775i
$118$			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
$123$	−0.624490	−	1.61555i	−0.0563083	−	0.145670i
$124$	−25.5405	−	14.7458i	−2.29361	−	1.32421i
$125$	−14.8763			−1.33058
$126$	−11.6075	−	15.9742i	−1.03408	−	1.42310i
$127$	−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
$129$	−2.88091	−	7.45292i	−0.253650	−	0.656193i
$130$	−10.4863	−	18.1628i	−0.919710	−	1.59299i
$131$	8.45939	−	14.6521i	0.739100	−	1.28016i	−0.213801	−	0.976877i	$-0.568584\pi$
$131$	8.45939	−	14.6521i	0.739100	−	1.28016i	0.952901	−	0.303281i	$-0.0980822\pi$
$132$	−1.75619	+	11.2584i	−0.152857	+	0.979920i
$133$	−0.363241	+	3.30912i	−0.0314970	+	0.286937i
$134$			16.9611i			1.46522i
$135$	−16.2187	+	10.6950i	−1.39588	+	0.920478i
$136$	32.5351	−	18.7841i	2.78986	−	1.61073i
$137$	−5.91289	+	3.41381i	−0.505172	+	0.291661i	−0.730847	−	0.682541i	$-0.760875\pi$
$137$	−5.91289	+	3.41381i	−0.505172	+	0.291661i	0.225675	+	0.974203i	$0.427541\pi$
$138$	18.6503	−	23.1417i	1.58762	−	1.96995i
$139$			5.84608i			0.495858i	0.968778	+	0.247929i	$0.0797500\pi$
$139$			5.84608i			0.495858i	−0.968778	+	0.247929i	$0.920250\pi$
$140$	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
$144$	−3.29566	−	15.1561i	−0.274639	−	1.26301i
$145$	23.1628	+	13.3730i	1.92357	+	1.11057i
$146$	7.57962			0.627294
$147$	−11.2889	−	4.42283i	−0.931090	−	0.364789i
$148$	−28.7939			−2.36685
$149$	10.9019	+	6.29419i	0.893115	+	0.515640i	0.874960	−	0.484195i	$-0.160887\pi$
$149$	10.9019	+	6.29419i	0.893115	+	0.515640i	0.0181549	+	0.999835i	$0.494221\pi$
$150$	36.0873	−	13.9495i	2.94652	−	1.13897i
$151$	−8.95031	−	15.5024i	−0.728366	−	1.26157i	−0.957574	−	0.288189i	$-0.906947\pi$
$151$	−8.95031	−	15.5024i	−0.728366	−	1.26157i	0.229208	−	0.973377i	$-0.426386\pi$
$152$	−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
$156$	12.7381	+	10.2659i	1.01986	+	0.821929i
$157$	10.1719	−	5.87274i	0.811804	−	0.468696i	−0.0357777	−	0.999360i	$-0.511391\pi$
$157$	10.1719	−	5.87274i	0.811804	−	0.468696i	0.847582	+	0.530664i	$0.178057\pi$
$158$	30.9600	−	17.8748i	2.46305	−	1.42204i
$159$	−6.07737	−	4.89788i	−0.481967	−	0.388427i
$160$			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	−0.908586	−	0.417697i	$-0.862837\pi$
$163$	−1.18169	+	2.04674i	−0.0925569	+	0.160313i	0.816029	+	0.578010i	$0.196171\pi$
$164$	−2.09453	−	3.62783i	−0.163555	−	0.283286i
$165$	9.48589	−	3.66676i	0.738476	−	0.285457i
$166$	22.6188	+	13.0590i	1.75556	+	1.01357i
$167$	14.4062			1.11478			0.557391	−	0.830250i	$-0.311802\pi$
$167$	14.4062			1.11478			0.557391	+	0.830250i	$0.311802\pi$
$168$	−17.6065	−	17.6868i	−1.35837	−	1.36457i
$169$	7.91596			0.608920
$170$	−55.5687	−	32.0826i	−4.26192	−	2.46062i
$171$	−3.68853	+	0.802062i	−0.282069	+	0.0613352i
$172$	−9.66255	−	16.7360i	−0.736762	−	1.27611i
$173$	−0.192354	+	0.333167i	−0.0146244	+	0.0253302i	−0.873245	−	0.487281i	$-0.837989\pi$
$173$	−0.192354	+	0.333167i	−0.0146244	+	0.0253302i	0.858621	+	0.512612i	$0.171322\pi$
$174$	−30.4563	−	4.75085i	−2.30888	−	0.360161i
$175$	14.0518	−	19.1543i	1.06222	−	1.44793i
$176$			8.11932i			0.612017i
$177$	−5.57167	+	6.91342i	−0.418792	+	0.519645i
$178$	−13.4822	+	7.78398i	−1.01054	+	0.583434i
$179$	6.86648	−	3.96436i	0.513225	−	0.296310i	−0.220934	−	0.975289i	$-0.570910\pi$
$179$	6.86648	−	3.96436i	0.513225	−	0.296310i	0.734158	+	0.678979i	$0.237577\pi$
$180$	−34.7705	+	31.6030i	−2.59164	+	2.35555i
$181$			3.35125i			0.249096i	0.992214	+	0.124548i	$0.0397482\pi$
$181$			3.35125i			0.249096i	−0.992214	+	0.124548i	$0.960252\pi$
$182$	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
$186$	−10.9376	−	28.2954i	−0.801980	−	2.07472i
$187$	−9.38216	−	5.41679i	−0.686092	−	0.396115i
$188$	33.6246			2.45233
$189$	0.686547	−	13.7306i	0.0499389	−	0.998752i
$190$	11.7034			0.849054
$191$	23.0068	+	13.2830i	1.66471	+	0.961122i	0.970418	+	0.241430i	$0.0776163\pi$
$191$	23.0068	+	13.2830i	1.66471	+	0.961122i	0.694293	+	0.719692i	$0.255717\pi$
$192$	3.39634	+	8.78633i	0.245110	+	0.634098i
$193$	−2.20151	−	3.81313i	−0.158468	−	0.274475i	0.775848	−	0.630920i	$-0.217322\pi$
$193$	−2.20151	−	3.81313i	−0.158468	−	0.274475i	−0.934317	+	0.356444i	$0.883989\pi$
$194$	−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	$0.938143\pi$
$198$	−8.67344	+	7.88333i	−0.616394	+	0.560244i
$199$	10.2785	−	5.93430i	0.728624	−	0.420671i	−0.0892948	−	0.996005i	$-0.528461\pi$
$199$	10.2785	−	5.93430i	0.728624	−	0.420671i	0.817918	+	0.575334i	$0.195128\pi$
$200$	42.3469	−	24.4490i	2.99438	−	1.72881i
$201$	−7.40999	+	9.19443i	−0.522660	+	0.648525i
$202$			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
$207$	20.2203	−	4.39686i	1.40541	−	0.305603i
$208$	10.0956	+	5.82872i	0.700007	+	0.404149i
$209$	1.97599			0.136682
$210$	−11.1256	+	41.1468i	−0.767741	+	2.83940i
$211$	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
$213$	11.5093	−	4.44891i	0.788605	−	0.304834i
$214$	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
$219$	4.10883	+	3.31139i	0.277649	+	0.223763i
$220$	21.3012	−	12.2983i	1.43613	−	0.829148i
$221$	−13.4706	+	7.77725i	−0.906130	+	0.523154i
$222$	−23.0611	−	18.5854i	−1.54776	−	1.24737i
$223$			20.4103i			1.36677i	0.730057	+	0.683387i	$0.239494\pi$
$223$			20.4103i			1.36677i	−0.730057	+	0.683387i	$0.760506\pi$
$224$	−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	$-0.306771\pi$
$227$	−6.41950	−	11.1189i	−0.426077	−	0.737987i	−0.996520	+	0.0833497i	$0.973438\pi$
$228$	−8.51533	+	3.29159i	−0.563942	+	0.217991i
$229$	−7.89284	−	4.55693i	−0.521574	−	0.301131i	0.216005	−	0.976392i	$-0.430697\pi$
$229$	−7.89284	−	4.55693i	−0.521574	−	0.301131i	−0.737578	+	0.675262i	$0.764031\pi$
$230$	−64.1574			−4.23042
$231$	−1.87844	+	6.94718i	−0.123592	+	0.457091i
$232$	−38.9578			−2.55770
$233$	−24.7111	−	14.2669i	−1.61887	−	0.934658i	−0.987212	−	0.159415i	$-0.949039\pi$
$233$	−24.7111	−	14.2669i	−1.61887	−	0.934658i	−0.631663	−	0.775243i	$-0.717627\pi$
$234$	3.57570	+	16.4439i	0.233751	+	1.07497i
$235$	−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	$0.918513\pi$
$240$	−21.0092	+	26.0686i	−1.35614	+	1.68272i
$241$	−16.3837	+	9.45912i	−1.05537	+	0.609316i	−0.924147	−	0.382038i	$-0.875222\pi$
$241$	−16.3837	+	9.45912i	−1.05537	+	0.609316i	−0.131219	+	0.991353i	$0.541889\pi$
$242$	−18.3858	+	10.6150i	−1.18188	+	0.682359i
$243$	15.0091	−	4.21029i	0.962835	−	0.270090i
$244$			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
$249$	6.55620	+	16.9609i	0.415482	+	1.07485i
$250$	−32.0507	−	18.5045i	−2.02707	−	1.17033i
$251$	−13.4609			−0.849643			−0.424822	−	0.905277i	$-0.639663\pi$
$251$	−13.4609			−0.849643			−0.424822	+	0.905277i	$0.639663\pi$
$252$	−3.47760	−	33.0673i	−0.219068	−	2.08304i
$253$	−10.8323			−0.681019
$254$	−33.4825	−	19.3311i	−2.10088	−	1.21294i
$255$	−16.1069	−	41.6686i	−1.00865	−	2.60939i
$256$	16.2929	+	28.2201i	1.01831	+	1.76376i
$257$	10.4593	−	18.1160i	0.652432	−	1.13005i	−0.330099	−	0.943946i	$-0.607082\pi$
$257$	10.4593	−	18.1160i	0.652432	−	1.13005i	0.982531	−	0.186099i	$-0.0595846\pi$
$258$	3.06374	−	19.6407i	0.190740	−	1.22278i
$259$	−18.0773	−	1.98434i	−1.12327	−	0.123301i
$260$		−	35.3148i		−	2.19013i
$261$	−14.4345	−	15.8812i	−0.893472	−	0.983020i
$262$	36.4512	−	21.0451i	2.25196	−	1.30017i
$263$	−15.3023	+	8.83480i	−0.943581	+	0.544777i	−0.891081	−	0.453844i	$-0.850052\pi$
$263$	−15.3023	+	8.83480i	−0.943581	+	0.544777i	−0.0525002	+	0.998621i	$0.516719\pi$
$264$	−9.29537	+	11.5338i	−0.572090	+	0.709859i
$265$			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	$-0.0906025\pi$
$269$	3.88209	+	6.72397i	0.236695	+	0.409968i	−0.723069	+	0.690776i	$0.757269\pi$
$270$	−48.2463	+	2.86787i	−2.93618	+	0.174533i
$271$	−8.70167	−	5.02391i	−0.528589	−	0.305181i	0.211853	−	0.977302i	$-0.432050\pi$
$271$	−8.70167	−	5.02391i	−0.528589	−	0.305181i	−0.740442	+	0.672121i	$0.765384\pi$
$272$	35.6656			2.16255
$273$	7.28969	+	7.32293i	0.441192	+	0.443204i
$274$	−16.9856			−1.02614
$275$	−12.2116	−	7.05038i	−0.736388	−	0.425154i
$276$	46.6806	−	18.0443i	2.80984	−	1.08614i
$277$	13.7226	+	23.7682i	0.824509	+	1.42809i	0.902294	+	0.431121i	$0.141882\pi$
$277$	13.7226	+	23.7682i	0.824509	+	1.42809i	−0.0777852	+	0.996970i	$0.524785\pi$
$278$	−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	$0.943503\pi$
$282$	26.9300	+	21.7035i	1.60366	+	1.29242i
$283$	−15.9349	+	9.20000i	−0.947229	+	0.546883i	−0.892219	−	0.451603i	$-0.850852\pi$
$283$	−15.9349	+	9.20000i	−0.947229	+	0.546883i	−0.0550101	+	0.998486i	$0.517519\pi$
$284$	25.8449	−	14.9216i	1.53361	−	0.885433i
$285$	6.34429	+	5.11300i	0.375803	+	0.302868i
$286$		−	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
$291$	−9.75761	+	3.77179i	−0.572001	+	0.221106i
$292$	11.0531	+	6.38148i	0.646831	+	0.373448i
$293$	−30.1443			−1.76105			−0.880525	−	0.474000i	$-0.842810\pi$
$293$	−30.1443			−1.76105			−0.880525	+	0.474000i	$0.842810\pi$
$294$	−18.8201	−	23.5710i	−1.09761	−	1.37469i
$295$	19.1666			1.11592
$296$	−32.4179	−	18.7165i	−1.88425	−	1.08787i
$297$	−8.14586	+	0.484209i	−0.472671	+	0.0280966i
$298$	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
$303$	−2.99980	+	3.72220i	−0.172334	+	0.213835i
$304$	−5.63369	+	3.25261i	−0.323114	+	0.186550i
$305$	17.8456	−	10.3032i	1.02184	−	0.589959i
$306$	34.6290	+	38.0997i	1.97961	+	2.17802i
$307$		−	32.6159i		−	1.86149i	−0.365670	−	0.930744i	$-0.619160\pi$
$307$		−	32.6159i		−	1.86149i	0.365670	−	0.930744i	$-0.380840\pi$
$308$	−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	$-0.190211\pi$
$311$	−1.30324	−	2.25728i	−0.0739001	−	0.127999i	−0.900607	+	0.434633i	$0.856878\pi$
$312$	7.66831	+	19.8379i	0.434132	+	1.12310i
$313$	−1.70807	−	0.986156i	−0.0965460	−	0.0557408i	0.450950	−	0.892549i	$-0.351085\pi$
$313$	−1.70807	−	0.986156i	−0.0965460	−	0.0557408i	−0.547496	+	0.836809i	$0.684419\pi$
$314$	29.2202			1.64899
$315$	−24.0073	+	17.4447i	−1.35266	+	0.982895i
$316$	60.1970			3.38635
$317$	11.8831	+	6.86071i	0.667421	+	0.385336i	0.795099	−	0.606480i	$-0.207419\pi$
$317$	11.8831	+	6.86071i	0.667421	+	0.385336i	−0.127678	+	0.991816i	$0.540752\pi$
$318$	−7.00116	−	18.1120i	−0.392606	−	1.01567i
$319$	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
$324$	34.2972	−	15.6560i	1.90540	−	0.869775i
$325$	−17.5330	+	10.1227i	−0.972556	+	0.561506i
$326$	−5.09185	+	2.93978i	−0.282012	+	0.162819i
$327$	10.3531	−	12.8463i	0.572529	−	0.710403i
$328$		−	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	−0.782859	−	0.622199i	$-0.786240\pi$
$331$	2.68189	−	4.64517i	0.147410	−	0.255322i	0.930270	+	0.366877i	$0.119573\pi$
$332$	21.9894	+	38.0868i	1.20683	+	2.09028i
$333$	−4.38156	−	20.1499i	−0.240108	−	1.10421i
$334$	31.0378	+	17.9197i	1.69831	+	0.980522i
$335$	25.4904			1.39269
$336$	−6.07996	−	22.8990i	−0.331689	−	1.24924i
$337$	−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
$339$	−9.25887	+	3.57900i	−0.502873	+	0.194385i
$340$	−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
$345$	−34.7791	−	28.0292i	−1.87244	−	1.50904i
$346$	−0.828846	+	0.478534i	−0.0445590	+	0.0257262i
$347$	−17.5365	+	10.1247i	−0.941409	+	0.543523i	−0.890402	−	0.455176i	$-0.849576\pi$
$347$	−17.5365	+	10.1247i	−0.941409	+	0.543523i	−0.0510070	+	0.998698i	$0.516243\pi$
$348$	−40.4133	−	32.5699i	−2.16638	−	1.74593i
$349$			5.71391i			0.305859i	0.988237	+	0.152929i	$0.0488707\pi$
$349$			5.71391i			0.305859i	−0.988237	+	0.152929i	$0.951129\pi$
$350$	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	−0.999232	−	0.0391913i	$-0.987522\pi$
$353$	−10.0246	−	17.3631i	−0.533557	−	0.924147i	0.465675	−	0.884956i	$-0.345812\pi$
$354$	−20.6036	+	7.96429i	−1.09507	+	0.423297i
$355$	−23.0672	−	13.3179i	−1.22428	−	0.706838i
$356$	−26.2142			−1.38935
$357$	30.5168	+	8.25140i	1.61512	+	0.436710i
$358$	19.7249			1.04250
$359$	24.5405	+	14.1685i	1.29520	+	0.747783i	0.979571	−	0.201100i	$-0.0644515\pi$
$359$	24.5405	+	14.1685i	1.29520	+	0.747783i	0.315628	+	0.948883i	$0.397785\pi$
$360$	−59.6891	+	12.9793i	−3.14589	+	0.684067i
$361$	−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
$366$	−14.9023	+	18.4910i	−0.778957	+	0.966542i
$367$	−0.845514	+	0.488158i	−0.0441355	+	0.0254816i	−0.521905	−	0.853003i	$-0.674779\pi$
$367$	−0.845514	+	0.488158i	−0.0441355	+	0.0254816i	0.477770	+	0.878485i	$0.341445\pi$
$368$	30.8836	−	17.8307i	1.60992	−	0.929488i
$369$	2.22003	−	2.01779i	0.115570	−	0.105042i
$370$			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	−0.724685	−	0.689080i	$-0.758015\pi$
$373$	4.52737	−	7.84164i	0.234419	−	0.406025i	0.959104	+	0.283055i	$0.0913481\pi$
$374$	−13.4758	−	23.3408i	−0.696817	−	1.20692i
$375$	−9.29009	−	24.0335i	−0.479738	−	1.24108i
$376$	37.8566	+	21.8565i	1.95230	+	1.12716i
$377$	16.1298			0.830727
$378$	18.5585	−	28.7283i	0.954546	−	1.47762i
$379$	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
$381$	−9.70510	−	25.1071i	−0.497207	−	1.28627i
$382$	33.0451	+	57.2358i	1.69074	+	2.92844i
$383$	15.0152	−	26.0071i	0.767242	−	1.32890i	−0.171811	−	0.985130i	$-0.554962\pi$
$383$	15.0152	−	26.0071i	0.767242	−	1.32890i	0.939053	−	0.343772i	$-0.111705\pi$
$384$	−4.66382	+	29.8983i	−0.237999	+	1.52574i
$385$	14.2207	−	6.25305i	0.724756	−	0.318685i
$386$		−	10.9538i		−	0.557532i
$387$	10.2415	−	9.30854i	0.520604	−	0.473180i
$388$	−21.9113	+	12.6505i	−1.11238	+	0.642233i
$389$	−0.346881	+	0.200272i	−0.0175876	+	0.0101542i	−0.508768	−	0.860904i	$-0.669899\pi$
$389$	−0.346881	+	0.200272i	−0.0175876	+	0.0101542i	0.491180	+	0.871058i	$0.336566\pi$
$390$	22.7944	−	28.2837i	1.15424	−	1.43220i
$391$			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
$396$	−19.2853	+	4.19355i	−0.969123	+	0.210734i
$397$	−14.2812	−	8.24528i	−0.716755	−	0.413818i	0.0968024	−	0.995304i	$-0.469139\pi$
$397$	−14.2812	−	8.24528i	−0.716755	−	0.413818i	−0.813557	+	0.581485i	$0.802472\pi$
$398$	29.5265			1.48003
$399$	−5.57289	+	1.47967i	−0.278994	+	0.0740763i
$400$	46.4216			2.32108
$401$	−2.79132	−	1.61157i	−0.139392	−	0.0804779i	0.428682	−	0.903455i	$-0.358978\pi$
$401$	−2.79132	−	1.61157i	−0.139392	−	0.0804779i	−0.568074	+	0.822977i	$0.692311\pi$
$402$	−27.4016	+	10.5920i	−1.36667	+	0.528282i
$403$	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
$408$	50.6646	+	40.8317i	2.50827	+	2.02147i
$409$	24.4255	−	14.1021i	1.20776	−	0.697302i	0.245493	−	0.969398i	$-0.421050\pi$
$409$	24.4255	−	14.1021i	1.20776	−	0.697302i	0.962270	+	0.272096i	$0.0877169\pi$
$410$	−8.05525	+	4.65070i	−0.397820	+	0.229682i
$411$	−9.20772	−	7.42070i	−0.454184	−	0.366036i
$412$			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
$417$	−9.44466	+	3.65082i	−0.462507	+	0.178781i
$418$	4.25724	+	2.45792i	0.208228	+	0.120221i
$419$	−12.0366			−0.588026			−0.294013	−	0.955801i	$-0.594991\pi$
$419$	−12.0366			−0.588026			−0.294013	+	0.955801i	$0.594991\pi$
$420$	−50.8666	+	50.6357i	−2.48204	+	2.47077i
$421$	−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
$423$	5.11664	+	23.5304i	0.248780	+	1.14409i
$424$	−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
$429$	3.84859	−	4.77539i	0.185812	−	0.230558i
$430$	−37.1607	+	21.4547i	−1.79205	+	1.03464i
$431$	6.25266	−	3.60998i	0.301180	−	0.173886i	−0.341793	−	0.939775i	$-0.611034\pi$
$431$	6.25266	−	3.60998i	0.301180	−	0.173886i	0.642973	+	0.765889i	$0.277701\pi$
$432$	22.4274	−	14.7892i	1.07904	−	0.711544i
$433$		−	17.6079i		−	0.846184i	−0.906087	−	0.423092i	$-0.860945\pi$
$433$		−	17.6079i		−	0.846184i	0.906087	−	0.423092i	$-0.139055\pi$
$434$	−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
$438$	4.73339	+	12.2453i	0.226170	+	0.585102i
$439$	−21.1988	−	12.2391i	−1.01176	−	0.584142i	−0.100056	−	0.994982i	$-0.531902\pi$
$439$	−21.1988	−	12.2391i	−1.01176	−	0.584142i	−0.911707	+	0.410840i	$0.865235\pi$
$440$	31.9762			1.52441
$441$	0.0955442	−	20.9998i	0.00454972	−	0.999990i
$442$	−38.6962			−1.84059
$443$	−9.19705	−	5.30992i	−0.436965	−	0.252282i	0.265344	−	0.964154i	$-0.414514\pi$
$443$	−9.19705	−	5.30992i	−0.436965	−	0.252282i	−0.702309	+	0.711872i	$0.747848\pi$
$444$	−17.9815	−	46.5181i	−0.853365	−	2.20765i
$445$	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	$0.992378\pi$
$450$	45.0723	+	49.5897i	2.12473	+	2.33768i
$451$	−1.36004	+	0.785219i	−0.0640418	+	0.0369745i
$452$	−20.7914	+	12.0039i	−0.977946	+	0.564617i
$453$	19.4556	−	24.1408i	0.914102	−	1.13423i
$454$		−	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	−0.668340	−	0.743856i	$-0.732995\pi$
$457$	6.62763	−	11.4794i	0.310028	−	0.536983i	0.978368	+	0.206872i	$0.0663284\pi$
$458$	−11.3367	−	19.6357i	−0.529727	−	0.917514i
$459$	2.12698	+	35.7822i	0.0992788	+	1.67017i
$460$	−93.5582	−	54.0158i	−4.36217	−	2.51850i
$461$	−31.9499			−1.48806			−0.744028	−	0.668148i	$-0.767087\pi$
$461$	−31.9499			−1.48806			−0.744028	+	0.668148i	$0.767087\pi$
$462$	−12.6886	+	12.6310i	−0.590327	+	0.587647i
$463$	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
$465$	−42.5246	+	16.4378i	−1.97203	+	0.762285i
$466$	−35.4930	−	61.4757i	−1.64418	−	2.84781i
$467$	−3.65816	+	6.33611i	−0.169279	+	0.293200i	−0.938167	−	0.346184i	$-0.887477\pi$
$467$	−3.65816	+	6.33611i	−0.169279	+	0.293200i	0.768887	+	0.639384i	$0.220811\pi$
$468$	−8.63030	+	26.9900i	−0.398936	+	1.24761i
$469$	−10.6697	+	14.5441i	−0.492682	+	0.671582i
$470$		−	74.6602i		−	3.44382i
$471$	15.8400	+	12.7658i	0.729867	+	0.588215i
$472$	−24.1774	+	13.9588i	−1.11286	+	0.642508i
$473$	−6.27418	+	3.62240i	−0.288487	+	0.166558i
$474$	48.2119	+	38.8550i	2.21445	+	1.78467i
$475$		−	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	$-0.252990\pi$
$479$	−5.86289	−	10.1548i	−0.267882	−	0.463985i	−0.968315	+	0.249733i	$0.919657\pi$
$480$	−11.9010	+	4.60032i	−0.543204	+	0.209975i
$481$	13.4221	+	7.74924i	0.611994	+	0.353335i
$482$	−47.0645			−2.14373
$483$	30.5503	−	8.11149i	1.39009	−	0.369086i
$484$	−35.7483			−1.62492
$485$	19.5564	+	11.2909i	0.888010	+	0.512693i
$486$	37.5740	+	9.59869i	1.70439	+	0.435406i
$487$	4.33247	+	7.50406i	0.196323	+	0.340041i	0.947333	−	0.320249i	$-0.103767\pi$
$487$	4.33247	+	7.50406i	0.196323	+	0.340041i	−0.751010	+	0.660290i	$0.770433\pi$
$488$	−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	$0.655679\pi$
$492$	4.55294	−	5.64937i	0.205263	−	0.254693i
$493$	42.7372	−	24.6744i	1.92479	−	1.11128i
$494$	6.11239	−	3.52899i	0.275010	−	0.158777i
$495$	11.8477	+	13.0351i	0.532514	+	0.585885i
$496$		−	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	−0.915758	−	0.401730i	$-0.868409\pi$
$499$	−2.45656	+	4.25488i	−0.109971	+	0.190475i	0.805787	+	0.592205i	$0.201742\pi$
$500$	−31.1588	−	53.9687i	−1.39347	−	2.41355i
$501$	8.99650	+	23.2739i	0.401934	+	1.03980i
$502$	−29.0012	−	16.7439i	−1.29439	−	0.747315i
$503$	−13.4706			−0.600624			−0.300312	−	0.953841i	$-0.597091\pi$
$503$	−13.4706			−0.600624			−0.300312	+	0.953841i	$0.597091\pi$
$504$	17.5789	−	39.4896i	0.783027	−	1.75901i
$505$	10.3194			0.459205
$506$	−23.3379	−	13.4742i	−1.03750	−	0.599000i
$507$	4.94343	+	12.7887i	0.219546	+	0.567964i
$508$	−32.5508	−	56.3796i	−1.44421	−	2.50144i
$509$	19.8371	−	34.3589i	0.879264	−	1.52293i	0.0271143	−	0.999632i	$-0.491368\pi$
$509$	19.8371	−	34.3589i	0.879264	−	1.52293i	0.852150	−	0.523298i	$-0.175298\pi$
$510$	17.1291	−	109.809i	0.758489	−	4.86244i
$511$	6.49949	+	4.76811i	0.287521	+	0.210929i
$512$			46.1252i			2.03846i
$513$	−3.59922	−	5.45813i	−0.158909	−	0.240982i
$514$	45.0687	−	26.0204i	1.98789	−	1.14771i
$515$	30.6611	−	17.7022i	1.35109	−	0.780053i
$516$	21.0038	−	26.0618i	0.924640	−	1.14731i
$517$		−	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	$-0.259833\pi$
$521$	−6.58581	−	11.4070i	−0.288530	−	0.499748i	−0.973459	+	0.228861i	$0.926500\pi$
$522$	−11.3444	−	52.1706i	−0.496530	−	2.28345i
$523$	−21.0395	−	12.1471i	−0.919992	−	0.531157i	−0.0363593	−	0.999339i	$-0.511576\pi$
$523$	−21.0395	−	12.1471i	−0.919992	−	0.531157i	−0.883632	+	0.468181i	$0.844909\pi$
$524$	70.8737			3.09613
$525$	39.7200	+	10.7398i	1.73352	+	0.468725i
$526$	−43.9581			−1.91666
$527$	42.0595	+	24.2831i	1.83214	+	1.05779i
$528$	−13.1172	+	5.07043i	−0.570853	+	0.220662i
$529$	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
$534$	−20.9950	−	16.9203i	−0.908541	−	0.732212i
$535$	39.3065	−	22.6936i	1.69937	−	0.981131i
$536$	−32.1545	+	18.5644i	−1.38886	+	0.801861i
$537$	10.6927	+	8.61746i	0.461423	+	0.371871i
$538$			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	−0.755477	−	0.655175i	$-0.772595\pi$
$541$	4.41139	−	7.64074i	0.189660	−	0.328501i	0.945137	+	0.326674i	$0.105928\pi$
$542$	−12.4984	−	21.6479i	−0.536852	−	0.929855i
$543$	−5.41412	+	2.09282i	−0.232342	+	0.0898115i
$544$	11.7709	+	6.79591i	0.504672	+	0.291372i
$545$	−35.6149			−1.52557
$546$	6.59658	+	24.8447i	0.282307	+	1.06326i
$547$	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
$549$	−16.1568	+	3.51326i	−0.689555	+	0.149942i
$550$	−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
$555$	−27.9316	+	34.6580i	−1.18563	+	1.47115i
$556$	−21.2086	+	12.2448i	−0.899445	+	0.519295i
$557$	12.1156	−	6.99494i	0.513354	−	0.296385i	−0.220857	−	0.975306i	$-0.570885\pi$
$557$	12.1156	−	6.99494i	0.513354	−	0.296385i	0.734211	+	0.678921i	$0.237552\pi$
$558$	38.8824	−	35.3404i	1.64602	−	1.49608i
$559$			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	0.857200	+	0.514983i	$0.172202\pi$
$563$	20.7519	+	35.9434i	0.874589	+	1.51483i	0.0173885	+	0.999849i	$0.494465\pi$
$564$	20.9982	+	54.3224i	0.884185	+	2.28738i
$565$	18.5568	+	10.7138i	0.780691	+	0.450732i
$566$	−45.7752			−1.92407
$567$	22.6112	−	7.46545i	0.949582	−	0.313519i
$568$	38.7970			1.62789
$569$	−27.3488	−	15.7898i	−1.14652	−	0.661944i	−0.198484	−	0.980104i	$-0.563602\pi$
$569$	−27.3488	−	15.7898i	−1.14652	−	0.661944i	−0.948037	+	0.318160i	$0.896935\pi$
$570$	7.30865	+	18.9075i	0.306126	+	0.791947i
$571$	13.2149	+	22.8889i	0.553028	+	0.957873i	0.998054	+	0.0623550i	$0.0198611\pi$
$571$	13.2149	+	22.8889i	0.553028	+	0.957873i	−0.445026	+	0.895518i	$0.646806\pi$
$572$	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
$576$	−12.0738	+	10.9739i	−0.503075	+	0.457247i
$577$	−3.37317	+	1.94750i	−0.140427	+	0.0810755i	−0.568567	−	0.822637i	$-0.692502\pi$
$577$	−3.37317	+	1.94750i	−0.140427	+	0.0810755i	0.428141	+	0.903712i	$0.359169\pi$
$578$	−65.9025	+	38.0488i	−2.74118	+	1.58262i
$579$	4.78550	−	5.93792i	0.198878	−	0.246772i
$580$			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
$585$	24.7132	−	5.37384i	1.02177	−	0.222181i
$586$	−64.9454	−	37.4962i	−2.68287	−	1.54896i
$587$	−23.4871			−0.969416			−0.484708	−	0.874676i	$-0.661074\pi$
$587$	−23.4871			−0.969416			−0.484708	+	0.874676i	$0.661074\pi$
$588$	−7.59957	−	50.2179i	−0.313401	−	2.07095i
$589$	−8.85822			−0.364996
$590$	41.2942	+	23.8412i	1.70005	+	0.981526i
$591$	−8.75766	+	3.38526i	−0.360242	+	0.139251i
$592$	−17.7686	−	30.7761i	−0.730285	−	1.26489i
$593$	3.60607	−	6.24590i	0.148084	−	0.256488i	−0.782436	−	0.622732i	$-0.786023\pi$
$593$	3.60607	−	6.24590i	0.148084	−	0.256488i	0.930519	+	0.366243i	$0.119356\pi$
$594$	−18.1524	−	9.08934i	−0.744803	−	0.372940i
$595$	−27.4677	−	62.4673i	−1.12607	−	2.56091i
$596$			52.7335i			2.16005i
$597$	16.0060	+	12.8996i	0.655082	+	0.527944i
$598$	−33.5078	+	19.3458i	−1.37024	+	0.791107i
$599$	35.9713	−	20.7680i	1.46975	−	0.848559i	0.470323	−	0.882495i	$-0.344138\pi$
$599$	35.9713	−	20.7680i	1.46975	−	0.848559i	0.999424	+	0.0339361i	$0.0108043\pi$
$600$	65.9439	+	53.1456i	2.69215	+	2.16966i
$601$			24.0964i			0.982912i	0.870902	+	0.491456i	$0.163535\pi$
$601$			24.0964i			0.982912i	−0.870902	+	0.491456i	$0.836465\pi$
$602$	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
$606$	−11.0930	+	4.28800i	−0.450624	+	0.174188i
$607$	19.6303	+	11.3335i	0.796768	+	0.460014i	0.842340	−	0.538947i	$-0.181178\pi$
$607$	19.6303	+	11.3335i	0.796768	+	0.460014i	−0.0455717	+	0.998961i	$0.514511\pi$
$608$	−2.47908			−0.100540
$609$	−23.1275	−	23.2330i	−0.937174	−	0.941448i
$610$	51.2642			2.07563
$611$	−15.6739	−	9.04931i	−0.634097	−	0.366096i
$612$	18.4209	+	84.7143i	0.744622	+	3.42437i
$613$	−5.49453	−	9.51681i	−0.221922	−	0.384380i	0.733469	−	0.679722i	$-0.237900\pi$
$613$	−5.49453	−	9.51681i	−0.221922	−	0.384380i	−0.955392	+	0.295342i	$0.904566\pi$
$614$	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	$-0.180696\pi$
$618$	−25.6041	+	31.7700i	−1.02995	+	1.27798i
$619$	7.32331	−	4.22811i	0.294349	−	0.169942i	−0.345553	−	0.938399i	$-0.612309\pi$
$619$	7.32331	−	4.22811i	0.294349	−	0.169942i	0.639901	+	0.768457i	$0.278975\pi$
$620$	−95.4917	+	55.1322i	−3.83504	+	2.21416i
$621$	19.7307	+	29.9212i	0.791767	+	1.20070i
$622$		−	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
$627$	1.23399	+	3.19232i	0.0492806	+	0.127489i
$628$	42.6106	+	24.6012i	1.70035	+	0.981697i
$629$	47.4172			1.89065
$630$	−73.4226	+	7.72168i	−2.92523	+	0.307639i
$631$	−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
$633$	1.86787	+	4.83217i	0.0742411	+	0.192062i
$634$	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
$639$	14.3749	+	15.8156i	0.568662	+	0.625656i
$640$	56.5683	−	32.6597i	2.23606	−	1.29099i
$641$	−40.6603	+	23.4753i	−1.60599	+	0.927217i	−0.615731	+	0.787956i	$0.711139\pi$
$641$	−40.6603	+	23.4753i	−1.60599	+	0.927217i	−0.990256	+	0.139261i	$0.955527\pi$
$642$	−32.8236	+	40.7280i	−1.29544	+	1.60741i
$643$			17.9110i			0.706339i	0.935559	+	0.353170i	$0.114896\pi$
$643$			17.9110i			0.706339i	−0.935559	+	0.353170i	$0.885104\pi$
$644$	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	$-0.282686\pi$
$647$	−9.06721	−	15.7049i	−0.356469	−	0.617422i	−0.987368	+	0.158443i	$0.949353\pi$
$648$	48.7904	+	4.66728i	1.91667	+	0.183348i
$649$	6.97206	+	4.02532i	0.273677	+	0.158008i
$650$	−50.3661			−1.97552
$651$	8.42091	−	31.1437i	0.330041	−	1.22062i
$652$	−9.90032			−0.387726
$653$	−20.0233	−	11.5605i	−0.783572	−	0.452395i	0.0541228	−	0.998534i	$-0.482764\pi$
$653$	−20.0233	−	11.5605i	−0.783572	−	0.452395i	−0.837695	+	0.546139i	$0.816097\pi$
$654$	38.2850	−	14.7990i	1.49706	−	0.578688i
$655$	−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	$-0.275478\pi$
$660$	33.1709	+	26.7331i	1.29117	+	1.04058i
$661$	22.9350	−	13.2416i	0.892070	−	0.515037i	0.0174507	−	0.999848i	$-0.494445\pi$
$661$	22.9350	−	13.2416i	0.892070	−	0.515037i	0.874619	+	0.484811i	$0.161112\pi$
$662$	11.5562	−	6.67196i	0.449144	−	0.259313i
$663$	−20.9768	−	16.9056i	−0.814671	−	0.656561i
$664$			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
$669$	−32.9739	+	12.7460i	−1.27484	+	0.492789i
$670$	54.9187	+	31.7073i	2.12170	+	1.22496i
$671$	8.65539			0.334138
$672$	2.35669	−	8.71594i	0.0909114	−	0.336225i
$673$	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
$675$	2.76843	+	46.5733i	0.106557	+	1.79261i
$676$	16.5802	+	28.7178i	0.637700	+	1.10453i
$677$	11.3809	−	19.7123i	0.437404	−	0.757606i	−0.560085	−	0.828435i	$-0.689231\pi$
$677$	11.3809	−	19.7123i	0.437404	−	0.757606i	0.997488	+	0.0708298i	$0.0225647\pi$
$678$	−24.4000	−	3.80613i	−0.937075	−	0.146174i
$679$	−14.6281	+	6.43216i	−0.561374	+	0.246844i
$680$		−	140.461i		−	5.38645i
$681$	13.9543	−	17.3147i	0.534729	−	0.663500i
$682$	−23.8203	+	13.7526i	−0.912125	+	0.526616i
$683$	11.1897	−	6.46038i	0.428162	−	0.247199i	−0.270401	−	0.962748i	$-0.587156\pi$
$683$	11.1897	−	6.46038i	0.428162	−	0.247199i	0.698563	+	0.715548i	$0.253823\pi$
$684$	−10.6355	−	11.7014i	−0.406657	−	0.447415i
$685$			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
$690$	−40.0656	−	103.650i	−1.52527	−	3.94588i
$691$	6.07678	+	3.50843i	0.231172	+	0.133467i	0.611112	−	0.791544i	$-0.290722\pi$
$691$	6.07678	+	3.50843i	0.231172	+	0.133467i	−0.379941	+	0.925011i	$0.624056\pi$
$692$	−1.61156			−0.0612624
$693$	−12.3966	+	1.30372i	−0.470908	+	0.0495243i
$694$	−50.3761			−1.91225
$695$	18.9292	+	10.9288i	0.718024	+	0.414551i
$696$	−24.3287	−	62.9384i	−0.922178	−	2.38567i
$697$	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	$0.988997\pi$
$702$	−24.3331	+	16.0458i	−0.918393	+	0.605610i
$703$	−7.48995	+	4.32432i	−0.282489	+	0.163095i
$704$	7.39669	−	4.27048i	0.278773	−	0.160950i
$705$	32.6176	−	40.4725i	1.22845	−	1.52428i
$706$		−	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	−0.808003	−	0.589178i	$-0.799452\pi$
$709$	2.82891	−	4.89981i	0.106242	−	0.184016i	0.914245	+	0.405162i	$0.132785\pi$
$710$	−33.1319	−	57.3862i	−1.24342	−	2.15366i
$711$	9.16015	+	42.1258i	0.343532	+	1.57984i
$712$	−29.5134	−	17.0396i	−1.10606	−	0.638586i
$713$	48.5603			1.81860
$714$	55.4840	+	55.7371i	2.07644	+	2.08591i
$715$	−13.2392			−0.495118
$716$	28.7641	+	16.6069i	1.07496	+	0.620631i
$717$	−12.6483	+	4.88918i	−0.472360	+	0.182590i
$718$	35.2481	+	61.0514i	1.31545	+	2.27842i
$719$	4.18481	−	7.24831i	0.156067	−	0.270316i	−0.777380	−	0.629031i	$-0.783452\pi$
$719$	4.18481	−	7.24831i	0.156067	−	0.270316i	0.933447	+	0.358715i	$0.116785\pi$
$720$	−55.2353	−	17.6620i	−2.05850	−	0.658223i
$721$	−2.73371	+	24.9040i	−0.101809	+	0.927475i
$722$		−	43.3293i		−	1.61255i
$723$	−25.5132	−	20.5616i	−0.948845	−	0.764694i
$724$	−12.1578	+	7.01929i	−0.451840	+	0.260870i
$725$	55.6258	−	32.1156i	2.06589	−	1.19274i
$726$	−28.6308	−	23.0742i	−1.06259	−	0.856364i
$727$		−	1.94352i		−	0.0720810i	−0.999350	−	0.0360405i	$-0.988525\pi$
$727$		−	1.94352i		−	0.0720810i	0.999350	−	0.0360405i	$-0.0114745\pi$
$728$	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
$732$	−37.2995	+	14.4181i	−1.37863	+	0.532908i
$733$	0.745890	+	0.430640i	0.0275501	+	0.0159060i	0.513712	−	0.857963i	$-0.328270\pi$
$733$	0.745890	+	0.430640i	0.0275501	+	0.0159060i	−0.486162	+	0.873869i	$0.661603\pi$
$734$	−2.42886			−0.0896509
$735$	−35.4244	+	28.2844i	−1.30665	+	1.04328i
$736$	13.5902			0.500941
$737$	9.27242	+	5.35344i	0.341554	+	0.197196i
$738$	7.29292	−	1.58583i	0.268456	−	0.0583752i
$739$	10.8935	+	18.8680i	0.400722	+	0.694071i	0.993813	−	0.111064i	$-0.0354259\pi$
$739$	10.8935	+	18.8680i	0.400722	+	0.694071i	−0.593091	+	0.805135i	$0.702093\pi$
$740$	−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	$0.774941\pi$
$744$	41.6704	−	51.7054i	1.52771	−	1.89561i
$745$	40.7602	−	23.5329i	1.49334	−	0.862180i
$746$	19.5083	−	11.2631i	0.714249	−	0.412372i
$747$	−23.3069	+	21.1838i	−0.852756	+	0.775074i
$748$		−	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	−0.964181	−	0.265245i	$-0.914547\pi$
$751$	−6.91635	+	11.9795i	−0.252381	+	0.437137i	0.711800	+	0.702383i	$0.247880\pi$
$752$	20.7496	+	35.9394i	0.756660	+	1.31057i
$753$	−8.40618	−	21.7468i	−0.306338	−	0.792496i
$754$	34.7514	+	20.0637i	1.26557	+	0.730677i
$755$	−66.9274			−2.43574
$756$	51.2502	−	26.2684i	1.86395	−	0.955373i
$757$	−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
$759$	−6.76464	−	17.5001i	−0.245541	−	0.635214i
$760$	12.8097	+	22.1871i	0.464657	+	0.804810i
$761$	−11.4562	+	19.8428i	−0.415288	+	0.719300i	−0.995459	−	0.0951952i	$-0.969652\pi$
$761$	−11.4562	+	19.8428i	−0.415288	+	0.719300i	0.580171	+	0.814495i	$0.302986\pi$
$762$	10.3210	−	66.1649i	0.373890	−	2.39690i
$763$	14.9076	−	20.3207i	0.539690	−	0.735660i
$764$			111.286i			4.02620i
$765$	57.2592	−	52.0432i	2.07021	−	1.88162i
$766$	64.7001	−	37.3546i	2.33771	−	1.34968i
$767$	10.0102	−	5.77942i	0.361449	−	0.208683i
$768$	−35.4164	+	43.9452i	−1.27798	+	1.58574i
$769$			41.6937i			1.50351i	0.659440	+	0.751757i	$0.270794\pi$
$769$			41.6937i			1.50351i	−0.659440	+	0.751757i	$0.729206\pi$
$770$	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	$-0.287338\pi$
$773$	−10.2894	−	17.8218i	−0.370085	−	0.641006i	−0.989578	+	0.143996i	$0.954005\pi$
$774$	33.6439	−	7.31579i	1.20931	−	0.262961i
$775$	54.7437	+	31.6063i	1.96645	+	1.13533i
$776$	−32.8921			−1.18076
$777$	−8.08326	−	30.4440i	−0.289985	−	1.09217i
$778$	−0.996466			−0.0357250
$779$	−1.08967	−	0.629120i	−0.0390414	−	0.0225406i
$780$	57.0530	−	22.0537i	2.04282	−	0.789650i
$781$	−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
$786$	56.7629	+	45.7464i	2.02467	+	1.63172i
$787$	−13.0432	+	7.53050i	−0.464940	+	0.268433i	−0.714119	−	0.700024i	$-0.753173\pi$
$787$	−13.0432	+	7.53050i	−0.464940	+	0.268433i	0.249179	+	0.968457i	$0.419839\pi$
$788$	−19.6659	+	11.3541i	−0.700569	+	0.404474i
$789$	−23.8292	−	19.2045i	−0.848343	−	0.683697i
$790$		−	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
$795$	−27.2201	+	10.5219i	−0.965398	+	0.373173i
$796$	43.0573	+	24.8591i	1.52612	+	0.881108i
$797$	17.1311			0.606814			0.303407	−	0.952861i	$-0.401876\pi$
$797$	17.1311			0.606814			0.303407	+	0.952861i	$0.401876\pi$
$798$	−13.8473	−	3.74414i	−0.490187	−	0.132541i
$799$	−55.3723			−1.95893
$800$	15.3207	+	8.84541i	0.541668	+	0.312732i
$801$	−3.98899	−	18.3446i	−0.140944	−	0.648175i
$802$	−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
$807$	−8.43861	+	10.4708i	−0.297053	+	0.368588i
$808$	−13.0172	+	7.51548i	−0.457943	+	0.264394i
$809$	15.5787	−	8.99434i	0.547717	−	0.316224i	−0.200484	−	0.979697i	$-0.564251\pi$
$809$	15.5787	−	8.99434i	0.547717	−	0.316224i	0.748201	+	0.663473i	$0.230918\pi$
$810$	−34.7625	−	76.1536i	−1.22143	−	2.67576i
$811$			7.05128i			0.247604i	0.992307	+	0.123802i	$0.0395088\pi$
$811$			7.05128i			0.247604i	−0.992307	+	0.123802i	$0.960491\pi$
$812$	−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
$816$	22.2728	+	57.6198i	0.779705	+	2.01710i
$817$	−5.02689	−	2.90228i	−0.175869	−	0.101538i
$818$	70.1657			2.45329
$819$	−7.27825	+	16.3500i	−0.254323	+	0.571314i
$820$	−15.6622			−0.546947
$821$	26.7485	+	15.4432i	0.933528	+	0.538973i	0.887926	−	0.459987i	$-0.152146\pi$
$821$	26.7485	+	15.4432i	0.933528	+	0.538973i	0.0456023	+	0.998960i	$0.485479\pi$
$822$	−10.6073	−	27.4412i	−0.369973	−	0.957121i
$823$	−0.181508	−	0.314381i	−0.00632696	−	0.0109586i	0.862845	−	0.505469i	$-0.168681\pi$
$823$	−0.181508	−	0.314381i	−0.00632696	−	0.0109586i	−0.869172	+	0.494511i	$0.835347\pi$
$824$	−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	$-0.201253\pi$
$828$	58.3031	+	64.1465i	2.02617	+	2.22925i
$829$	−21.1969	+	12.2380i	−0.736198	+	0.425044i	−0.820685	−	0.571381i	$-0.806408\pi$
$829$	−21.1969	+	12.2380i	−0.736198	+	0.425044i	0.0844875	+	0.996425i	$0.473075\pi$
$830$	84.5680	−	48.8253i	2.93540	−	1.69475i
$831$	−29.8292	+	37.0125i	−1.03476	+	1.28395i
$832$		−	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
$837$	36.5173	−	2.17067i	1.26222	−	0.0750294i
$838$	−25.9326	−	14.9722i	−0.895827	−	0.517206i
$839$	29.0807			1.00398			0.501989	−	0.864874i	$-0.332602\pi$
$839$	29.0807			1.00398			0.501989	+	0.864874i	$0.332602\pi$
$840$	−90.1826	+	23.9446i	−3.11159	+	0.826167i
$841$	−22.1739			−0.764619
$842$	−21.3955	−	12.3527i	−0.737337	−	0.425702i
$843$	−9.56305	+	3.69658i	−0.329369	+	0.127317i
$844$	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
$849$	−24.8142	−	19.9983i	−0.851623	−	0.686340i
$850$	−133.449	+	77.0469i	−4.57727	+	2.64269i
$851$	41.0595	−	23.7057i	1.40750	−	0.812622i
$852$	40.2465	+	32.4355i	1.37882	+	1.11122i
$853$		−	42.8489i		−	1.46712i	−0.679626	−	0.733559i	$-0.737858\pi$
$853$		−	42.8489i		−	1.46712i	0.679626	−	0.733559i	$-0.262142\pi$
$854$	−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	$-0.0996765\pi$
$857$	6.11562	+	10.5926i	0.208906	+	0.361835i	−0.742464	+	0.669886i	$0.766343\pi$
$858$	14.2318	−	5.50127i	0.485865	−	0.187810i
$859$	18.8044	+	10.8567i	0.641598	+	0.370427i	0.785230	−	0.619204i	$-0.212545\pi$
$859$	18.8044	+	10.8567i	0.641598	+	0.370427i	−0.143632	+	0.989631i	$0.545878\pi$
$860$	−72.2533			−2.46382
$861$	3.24773	−	3.23299i	0.110682	−	0.110180i
$862$	17.9617			0.611777
$863$	−13.3295	−	7.69580i	−0.453742	−	0.261968i	0.255667	−	0.966765i	$-0.417705\pi$
$863$	−13.3295	−	7.69580i	−0.453742	−	0.261968i	−0.709409	+	0.704797i	$0.751038\pi$
$864$	10.2198	−	0.607489i	0.347685	−	0.0206672i
$865$	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
$870$	−72.3183	+	89.7338i	−2.45182	+	3.04226i
$871$	13.3130	−	7.68628i	0.451095	−	0.260440i
$872$	44.9258	−	25.9379i	1.52138	−	0.878369i
$873$	−12.1870	−	13.4085i	−0.412469	−	0.453809i
$874$		−	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	0.358431	+	0.933556i	$0.383312\pi$
$877$	−18.6353	+	32.2772i	−0.629268	+	1.08992i	−0.987699	+	0.156368i	$0.950021\pi$
$878$	−30.4483	−	52.7380i	−1.02758	−	1.77982i
$879$	−18.8248	−	48.6998i	−0.634945	−	1.64260i
$880$	26.2897	+	15.1784i	0.886227	+	0.511663i
$881$	−40.7343			−1.37237			−0.686187	−	0.727425i	$-0.740717\pi$
$881$	−40.7343			−1.37237			−0.686187	+	0.727425i	$0.740717\pi$
$882$	26.3273	−	45.1248i	0.886486	−	1.51943i
$883$	−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
$885$	11.9694	+	30.9647i	0.402346	+	1.04087i
$886$	−13.2099	−	22.8802i	−0.443796	−	0.768677i
$887$	6.62678	−	11.4779i	0.222505	−	0.385391i	−0.733063	−	0.680161i	$-0.761910\pi$
$887$	6.62678	−	11.4779i	0.222505	−	0.385391i	0.955568	+	0.294770i	$0.0952431\pi$
$888$	9.99284	−	64.0611i	0.335338	−	2.14975i
$889$	−16.5505	−	37.6392i	−0.555085	−	1.26238i
$890$			58.2060i			1.95107i
$891$	−5.86927	−	12.8577i	−0.196628	−	0.430749i
$892$	−74.0451	+	42.7499i	−2.47921	+	1.43137i
$893$	8.74652	−	5.04981i	0.292691	−	0.168985i
$894$	−34.0375	+	42.2343i	−1.13839	+	1.41253i
$895$		−	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
$900$	23.9763	+	110.262i	0.799209	+	3.67541i
$901$	26.9225	+	15.5437i	0.896917	+	0.517835i
$902$	−3.90691			−0.130086
$903$	14.9825	−	14.9145i	0.498588	−	0.496325i
$904$	−31.2109			−1.03806
$905$	10.8511	+	6.26488i	0.360702	+	0.208252i
$906$	71.9451	−	27.8103i	2.39022	−	0.923935i
$907$	−8.48521	−	14.6968i	−0.281747	−	0.488000i	0.690068	−	0.723744i	$-0.257581\pi$
$907$	−8.48521	−	14.6968i	−0.281747	−	0.488000i	−0.971815	+	0.235744i	$0.924247\pi$
$908$	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	$0.663777\pi$
$912$	−8.77295	−	7.07031i	−0.290502	−	0.234121i
$913$	14.2784	−	8.24362i	0.472545	−	0.272824i
$914$	28.5582	−	16.4881i	0.944622	−	0.545378i
$915$	27.7898	+	22.3964i	0.918702	+	0.740401i
$916$		−	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	−0.981400	−	0.191974i	$-0.938511\pi$
$919$	−9.83558	+	17.0357i	−0.324446	+	0.561957i	0.656954	+	0.753930i	$0.271844\pi$
$920$	−70.2222	−	121.628i	−2.31516	−	4.00997i
$921$	52.6928	−	20.3683i	1.73629	−	0.671158i
$922$	−68.8356	−	39.7422i	−2.26698	−	1.30884i
$923$	−16.0632			−0.528728
$924$	−29.1376	+	7.73641i	−0.958558	+	0.254509i
$925$	61.7171			2.02925
$926$	41.2569	+	23.8197i	1.35578	+	0.782762i
$927$	−27.7595	+	6.03623i	−0.911740	+	0.198256i
$928$	−7.04727	−	12.2062i	−0.231338	−	0.400689i
$929$	−7.02635	+	12.1700i	−0.230527	+	0.399284i	−0.957963	−	0.286891i	$-0.907378\pi$
$929$	−7.02635	+	12.1700i	−0.230527	+	0.399284i	0.727436	+	0.686175i	$0.240712\pi$
$930$	−112.065	−	17.4810i	−3.67476	−	0.573223i
$931$	−8.40136	+	2.64434i	−0.275343	+	0.0866647i
$932$		−	119.530i		−	3.91534i
$933$	2.83290	−	3.51511i	0.0927450	−	0.115080i
$934$	−15.7629	+	9.10069i	−0.515777	+	0.297784i
$935$	−35.0783	+	20.2525i	−1.14718	+	0.662327i
$936$	−27.2604	+	24.7771i	−0.891034	+	0.809866i
$937$			32.2220i			1.05265i	0.850285	+	0.526323i	$0.176430\pi$
$937$			32.2220i			1.05265i	−0.850285	+	0.526323i	$0.823570\pi$
$938$	−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	$-0.267284\pi$
$941$	−9.53589	−	16.5166i	−0.310861	−	0.538427i	−0.978549	+	0.206014i	$0.933951\pi$
$942$	18.2477	+	47.2068i	0.594542	+	1.53808i
$943$	5.97351	+	3.44881i	0.194524	+	0.112309i
$944$	−26.5038			−0.862626
$945$	−43.1751	−	27.8911i	−1.40449	−	0.907299i
$946$	−18.0235			−0.585994
$947$	−17.5659	−	10.1417i	−0.570816	−	0.329561i	0.186659	−	0.982425i	$-0.440234\pi$
$947$	−17.5659	−	10.1417i	−0.570816	−	0.329561i	−0.757475	+	0.652864i	$0.773567\pi$
$948$	37.5924	+	97.2515i	1.22094	+	3.15858i
$949$	−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	$-0.0445894\pi$
$954$	24.8887	−	22.6215i	0.805803	−	0.732398i
$955$	86.0185	−	49.6628i	2.78349	−	1.60705i
$956$	−28.4026	+	16.3983i	−0.918606	+	0.530358i
$957$	−12.2102	+	15.1506i	−0.394698	+	0.489748i
$958$		−	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
$963$	−35.5866	+	7.73823i	−1.14676	+	0.249361i
$964$	−68.6322	−	39.6248i	−2.21049	−	1.27623i
$965$	−16.4622			−0.529936
$966$	75.9099	+	20.5252i	2.44236	+	0.660387i
$967$	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
$969$	14.0229	−	5.42051i	0.450479	−	0.174132i
$970$	28.0893	+	48.6520i	0.901892	+	1.56212i
$971$	8.41949	−	14.5830i	0.270194	−	0.467990i	−0.698717	−	0.715398i	$-0.746245\pi$
$971$	8.41949	−	14.5830i	0.270194	−	0.467990i	0.968911	+	0.247408i	$0.0795787\pi$
$972$	46.7113	+	45.6319i	1.49826	+	1.46365i
$973$	−14.1589	+	6.22587i	−0.453914	+	0.199592i
$974$			21.5565i			0.690715i
$975$	−27.3029	−	22.0040i	−0.874393	−	0.704692i
$976$	−24.6772	+	14.2474i	−0.789897	+	0.456047i
$977$	−19.9678	+	11.5284i	−0.638826	+	0.368826i	−0.784162	−	0.620556i	$-0.786907\pi$
$977$	−19.9678	+	11.5284i	−0.638826	+	0.368826i	0.145336	+	0.989382i	$0.453574\pi$
$978$	−7.92918	−	6.39029i	−0.253547	−	0.204339i
$979$			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	−0.970922	−	0.239395i	$-0.923051\pi$
$983$	−21.7207	−	37.6214i	−0.692783	−	1.19994i	0.278139	−	0.960541i	$-0.410282\pi$
$984$	8.79815	−	3.40091i	0.280475	−	0.108417i
$985$	17.5523	+	10.1338i	0.559262	+	0.322890i
$986$	122.769			3.90976
$987$	9.43937	+	35.5515i	0.300458	+	1.13162i
$988$	11.8846			0.378100
$989$	27.5572	+	15.9101i	0.876267	+	0.505913i
$990$	9.31136	+	42.8212i	0.295935	+	1.36095i
$991$	15.5842	+	26.9927i	0.495049	+	0.857450i	0.999984	−	0.00570766i	$-0.00181681\pi$
$991$	15.5842	+	26.9927i	0.495049	+	0.857450i	−0.504935	+	0.863157i	$0.668483\pi$
$992$	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
$996$	−47.7991	+	59.3098i	−1.51457	+	1.87930i
$997$	22.8831	−	13.2115i	0.724714	−	0.418414i	−0.0917712	−	0.995780i	$-0.529253\pi$
$997$	22.8831	−	13.2115i	0.724714	−	0.418414i	0.816485	+	0.577366i	$0.195920\pi$
$998$	−10.5852	+	6.11138i	−0.335069	+	0.193452i
$999$	29.8171	−	19.6621i	0.943370	−	0.622080i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.s.a.206.4	✓	106	7.3	odd	6
861.2.s.a.698.4	yes	106	3.2	odd	2
861.2.s.b.206.50	yes	106	21.17	even	6	inner
861.2.s.b.698.50	yes	106	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(2.15448 + 1.24389i) q^{2} +(0.624490 + 1.61555i) q^{3} +(2.09453 + 3.62783i) q^{4} +(1.86942 - 3.23792i) q^{5} +(-0.664120 + 4.25748i) q^{6} +(1.06496 + 2.42195i) q^{7} +5.44590i q^{8} +(-2.22003 + 2.01779i) q^{9} +O(q^{10})\)	\(q+(2.15448 + 1.24389i) q^{2} +(0.624490 + 1.61555i) 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} +(-2.22003 + 2.01779i) q^{9} +(8.05525 - 4.65070i) q^{10} +(1.36004 - 0.785219i) q^{11} +(-4.55294 + 5.64937i) 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} +(-7.29292 + 1.58583i) q^{18} +(1.08967 + 0.629120i) q^{19} +15.6622 q^{20} +(-3.24773 + 3.23299i) q^{21} +3.90691 q^{22} +(-5.97351 - 3.44881i) q^{23} +(-8.79815 + 3.40091i) 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} +(12.5439 + 10.1094i) q^{30} +(-6.09696 + 3.52008i) q^{31} +(-1.70631 + 0.985137i) q^{32} +(2.11789 + 1.70686i) 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} +(3.64272 - 1.40809i) q^{39} +(17.6334 + 10.1807i) q^{40} -1.00000 q^{41} +(-11.0187 + 2.92559i) q^{42} -4.61323 q^{43} +(5.69729 + 3.28933i) q^{44} +(2.38331 + 10.9604i) 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} +(7.49768 - 9.30325i) q^{51} +(8.17997 - 4.72271i) q^{52} +(-3.90268 + 2.25322i) q^{53} +(-7.11634 - 10.7918i) 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} +(9.78087 + 25.3031i) q^{60} +(4.77305 + 2.75572i) q^{61} -17.5144 q^{62} +(-7.25124 - 3.22792i) q^{63} +5.43859 q^{64} +(-7.30081 - 4.21513i) q^{65} +(2.43982 + 6.31182i) 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} +(-10.9887 - 12.0900i) q^{72} +(2.63855 - 1.52337i) q^{73} +(-14.8091 + 8.55001i) q^{74} +(9.75882 - 12.1089i) 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} +(0.857027 - 8.95910i) q^{81} +(-2.15448 - 1.24389i) q^{82} +10.4985 q^{83} +(-18.5312 - 5.01064i) q^{84} -25.7921 q^{85} +(-9.93912 - 5.73836i) q^{86} +(-11.5570 + 4.46735i) 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} +(-9.49436 - 7.65171i) q^{93} +(17.2935 - 9.98443i) q^{94} +(4.07409 - 2.35218i) q^{95} +(-2.65711 - 2.14142i) 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	\( 106 q + 52 q^{4} - 5 q^{7} - 2 q^{9} - 6 q^{10} - 8 q^{12} + 20 q^{14} - 4 q^{15} - 42 q^{16} - 5 q^{18} + 3 q^{19} + 36 q^{20} - 16 q^{21} - 12 q^{22} - 18 q^{23} - 57 q^{25} - 42 q^{26} - 18 q^{27} - 14 q^{28} + 103 q^{30} - 21 q^{31} + 26 q^{33} + 48 q^{35} - 16 q^{36} - q^{37} + 4 q^{39} - 18 q^{40} - 106 q^{41} - 43 q^{42} - 6 q^{43} - 210 q^{44} - 8 q^{46} - 16 q^{47} - 70 q^{48} - 3 q^{49} + 54 q^{51} + 6 q^{52} + 82 q^{54} + 60 q^{56} - 22 q^{57} + 10 q^{58} + 16 q^{59} - 4 q^{60} + 18 q^{61} + 104 q^{62} - 71 q^{63} - 84 q^{64} - 36 q^{65} - 32 q^{66} + 21 q^{67} - 36 q^{68} + 12 q^{69} + 38 q^{70} + 176 q^{72} + 21 q^{73} - 8 q^{75} + 100 q^{77} + 60 q^{78} - 11 q^{79} + 36 q^{80} - 2 q^{81} + 20 q^{83} - 186 q^{84} - 4 q^{85} - 90 q^{86} - 47 q^{87} - 14 q^{88} - 16 q^{89} - 44 q^{90} + 19 q^{91} + 87 q^{93} + 24 q^{94} + 54 q^{96} + 268 q^{98} + 18 q^{99}+O(q^{100}) \) 106 * q + 52 * q^4 - 5 * q^7 - 2 * q^9 - 6 * q^10 - 8 * q^12 + 20 * q^14 - 4 * q^15 - 42 * q^16 - 5 * q^18 + 3 * q^19 + 36 * q^20 - 16 * q^21 - 12 * q^22 - 18 * q^23 - 57 * q^25 - 42 * q^26 - 18 * q^27 - 14 * q^28 + 103 * q^30 - 21 * q^31 + 26 * q^33 + 48 * q^35 - 16 * q^36 - q^37 + 4 * q^39 - 18 * q^40 - 106 * q^41 - 43 * q^42 - 6 * q^43 - 210 * q^44 - 8 * q^46 - 16 * q^47 - 70 * q^48 - 3 * q^49 + 54 * q^51 + 6 * q^52 + 82 * q^54 + 60 * q^56 - 22 * q^57 + 10 * q^58 + 16 * q^59 - 4 * q^60 + 18 * q^61 + 104 * q^62 - 71 * q^63 - 84 * q^64 - 36 * q^65 - 32 * q^66 + 21 * q^67 - 36 * q^68 + 12 * q^69 + 38 * q^70 + 176 * q^72 + 21 * q^73 - 8 * q^75 + 100 * q^77 + 60 * q^78 - 11 * q^79 + 36 * q^80 - 2 * q^81 + 20 * q^83 - 186 * q^84 - 4 * q^85 - 90 * q^86 - 47 * q^87 - 14 * q^88 - 16 * q^89 - 44 * q^90 + 19 * q^91 + 87 * q^93 + 24 * q^94 + 54 * q^96 + 268 * q^98 + 18 * q^99

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