LMFDB - Embedded newform 418.2.m.b.189.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(151,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("418.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.m (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			189.10
Character	$\chi$	$=$	418.189
Dual form			418.2.m.b.303.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(1.52806 + 2.10319i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.852902 + 2.62496i) q^{5} +(-2.47245 + 0.803349i) q^{6} +(-1.95228 + 2.68709i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-1.16141 + 3.57445i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(1.52806 + 2.10319i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.852902 + 2.62496i) q^{5} +(-2.47245 + 0.803349i) q^{6} +(-1.95228 + 2.68709i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-1.16141 + 3.57445i) q^{9} -2.76005 q^{10} +(3.28192 - 0.478561i) q^{11} -2.59969i q^{12} +(2.20071 - 6.77309i) q^{13} +(-1.95228 - 2.68709i) q^{14} +(-4.21752 + 5.80492i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.75748 + 1.54580i) q^{17} +(-3.04061 - 2.20913i) q^{18} +(-0.551672 - 4.32385i) q^{19} +(0.852902 - 2.62496i) q^{20} -8.63468 q^{21} +(-0.559030 + 3.26917i) q^{22} +6.23407 q^{23} +(2.47245 + 0.803349i) q^{24} +(-2.11790 + 1.53875i) q^{25} +(5.76154 + 4.18600i) q^{26} +(-1.87510 + 0.609258i) q^{27} +(3.15886 - 1.02638i) q^{28} +(2.53429 + 1.84127i) q^{29} +(-4.21752 - 5.80492i) q^{30} +(-1.98885 - 0.646215i) q^{31} -1.00000 q^{32} +(6.02147 + 6.17124i) q^{33} -5.00231i q^{34} +(-8.71862 - 2.83285i) q^{35} +(3.04061 - 2.20913i) q^{36} +(-1.78383 + 2.45523i) q^{37} +(4.28270 + 0.811472i) q^{38} +(17.6080 - 5.72117i) q^{39} +(2.23293 + 1.62232i) q^{40} +(1.76226 - 1.28035i) q^{41} +(2.66826 - 8.21207i) q^{42} +3.76578i q^{43} +(-2.93642 - 1.54190i) q^{44} -10.3734 q^{45} +(-1.92643 + 5.92896i) q^{46} +(-5.86900 + 4.26408i) q^{47} +(-1.52806 + 2.10319i) q^{48} +(-1.24592 - 3.83453i) q^{49} +(-0.808967 - 2.48974i) q^{50} +(-10.5208 - 7.64383i) q^{51} +(-5.76154 + 4.18600i) q^{52} +(-9.05172 - 2.94108i) q^{53} -1.97160i q^{54} +(4.05536 + 8.20674i) q^{55} +3.32143i q^{56} +(8.25091 - 7.76737i) q^{57} +(-2.53429 + 1.84127i) q^{58} +(-0.181254 + 0.249475i) q^{59} +(6.82409 - 2.21728i) q^{60} +(-5.06934 + 1.64713i) q^{61} +(1.22917 - 1.69181i) q^{62} +(-7.33746 - 10.0992i) q^{63} +(0.309017 - 0.951057i) q^{64} +19.6561 q^{65} +(-7.72994 + 3.81974i) q^{66} -3.89518i q^{67} +(4.75748 + 1.54580i) q^{68} +(9.52604 + 13.1115i) q^{69} +(5.38840 - 7.41650i) q^{70} +(9.57288 - 3.11042i) q^{71} +(1.16141 + 3.57445i) q^{72} +(-2.63359 + 3.62482i) q^{73} +(-1.78383 - 2.45523i) q^{74} +(-6.47257 - 2.10306i) q^{75} +(-2.09518 + 3.82233i) q^{76} +(-5.12130 + 9.75309i) q^{77} +18.5141i q^{78} +(0.0577018 - 0.177588i) q^{79} +(-2.23293 + 1.62232i) q^{80} +(4.97516 + 3.61467i) q^{81} +(0.673122 + 2.07166i) q^{82} +(14.3889 - 4.67523i) q^{83} +(6.98560 + 5.07534i) q^{84} +(-8.11533 - 11.1698i) q^{85} +(-3.58147 - 1.16369i) q^{86} +8.14368i q^{87} +(2.37384 - 2.31623i) q^{88} -7.75741i q^{89} +(3.20554 - 9.86565i) q^{90} +(13.9035 + 19.1365i) q^{91} +(-5.04347 - 3.66430i) q^{92} +(-1.67996 - 5.17039i) q^{93} +(-2.24176 - 6.89943i) q^{94} +(10.8794 - 5.13594i) q^{95} +(-1.52806 - 2.10319i) q^{96} +(8.91786 + 2.89759i) q^{97} +4.03187 q^{98} +(-2.10106 + 12.2868i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	1.52806	+	2.10319i	0.882226	+	1.21428i	0.975799	+	0.218668i	$0.0701711\pi$
$3$	1.52806	+	2.10319i	0.882226	+	1.21428i	−0.0935732	+	0.995612i	$0.529829\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.852902	+	2.62496i	0.381429	+	1.17392i	0.939038	+	0.343815i	$0.111719\pi$
$5$	0.852902	+	2.62496i	0.381429	+	1.17392i	−0.557608	+	0.830104i	$0.688281\pi$
$6$	−2.47245	+	0.803349i	−1.00938	+	0.327966i
$7$	−1.95228	+	2.68709i	−0.737894	+	1.01562i	0.260843	+	0.965381i	$0.416000\pi$
$7$	−1.95228	+	2.68709i	−0.737894	+	1.01562i	−0.998737	+	0.0502431i	$0.984000\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−1.16141	+	3.57445i	−0.387136	+	1.19148i
$10$	−2.76005			−0.872804
$11$	3.28192	−	0.478561i	0.989535	−	0.144292i
$11$	3.28192	−	0.478561i	0.989535	−	0.144292i
$12$		−	2.59969i		−	0.750466i
$13$	2.20071	−	6.77309i	0.610367	−	1.87852i	0.155847	−	0.987781i	$-0.450189\pi$
$13$	2.20071	−	6.77309i	0.610367	−	1.87852i	0.454520	−	0.890737i	$-0.349811\pi$
$14$	−1.95228	−	2.68709i	−0.521770	−	0.718155i
$15$	−4.21752	+	5.80492i	−1.08896	+	1.49882i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−4.75748	+	1.54580i	−1.15386	+	0.374911i	−0.822595	−	0.568627i	$-0.807475\pi$
$17$	−4.75748	+	1.54580i	−1.15386	+	0.374911i	−0.331263	+	0.943538i	$0.607475\pi$
$18$	−3.04061	−	2.20913i	−0.716678	−	0.520697i
$19$	−0.551672	−	4.32385i	−0.126562	−	0.991959i
$19$	−0.551672	−	4.32385i	−0.126562	−	0.991959i
$20$	0.852902	−	2.62496i	0.190715	−	0.586960i
$21$	−8.63468			−1.88424
$22$	−0.559030	+	3.26917i	−0.119185	+	0.696990i
$23$	6.23407			1.29989			0.649947	−	0.759979i	$-0.274791\pi$
$23$	6.23407			1.29989			0.649947	+	0.759979i	$0.274791\pi$
$24$	2.47245	+	0.803349i	0.504688	+	0.163983i
$25$	−2.11790	+	1.53875i	−0.423580	+	0.307749i
$26$	5.76154	+	4.18600i	1.12993	+	0.820942i
$27$	−1.87510	+	0.609258i	−0.360864	+	0.117252i
$28$	3.15886	−	1.02638i	0.596969	−	0.193967i
$29$	2.53429	+	1.84127i	0.470606	+	0.341915i	0.797677	−	0.603084i	$-0.206062\pi$
$29$	2.53429	+	1.84127i	0.470606	+	0.341915i	−0.327071	+	0.945000i	$0.606062\pi$
$30$	−4.21752	−	5.80492i	−0.770011	−	1.05983i
$31$	−1.98885	−	0.646215i	−0.357207	−	0.116064i	0.124915	−	0.992167i	$-0.460134\pi$
$31$	−1.98885	−	0.646215i	−0.357207	−	0.116064i	−0.482123	+	0.876104i	$0.660134\pi$
$32$	−1.00000			−0.176777
$33$	6.02147	+	6.17124i	1.04820	+	1.07428i
$34$		−	5.00231i		−	0.857889i
$35$	−8.71862	−	2.83285i	−1.47372	−	0.478839i
$36$	3.04061	−	2.20913i	0.506768	−	0.368188i
$37$	−1.78383	+	2.45523i	−0.293260	+	0.403637i	−0.930070	−	0.367384i	$-0.880254\pi$
$37$	−1.78383	+	2.45523i	−0.293260	+	0.403637i	0.636810	+	0.771021i	$0.280254\pi$
$38$	4.28270	+	0.811472i	0.694746	+	0.131638i
$39$	17.6080	−	5.72117i	2.81953	−	0.916120i
$40$	2.23293	+	1.62232i	0.353057	+	0.256511i
$41$	1.76226	−	1.28035i	0.275218	−	0.199958i	−0.441611	−	0.897207i	$-0.645593\pi$
$41$	1.76226	−	1.28035i	0.275218	−	0.199958i	0.716829	+	0.697249i	$0.245593\pi$
$42$	2.66826	−	8.21207i	0.411722	−	1.26715i
$43$			3.76578i			0.574276i	0.957889	+	0.287138i	$0.0927038\pi$
$43$			3.76578i			0.574276i	−0.957889	+	0.287138i	$0.907296\pi$
$44$	−2.93642	−	1.54190i	−0.442682	−	0.232450i
$45$	−10.3734			−1.54637
$46$	−1.92643	+	5.92896i	−0.284037	+	0.874177i
$47$	−5.86900	+	4.26408i	−0.856082	+	0.621980i	−0.926816	−	0.375515i	$-0.877466\pi$
$47$	−5.86900	+	4.26408i	−0.856082	+	0.621980i	0.0707340	+	0.997495i	$0.477466\pi$
$48$	−1.52806	+	2.10319i	−0.220557	+	0.303570i
$49$	−1.24592	−	3.83453i	−0.177988	−	0.547790i
$50$	−0.808967	−	2.48974i	−0.114405	−	0.352103i
$51$	−10.5208	−	7.64383i	−1.47321	−	1.07035i
$52$	−5.76154	+	4.18600i	−0.798981	+	0.580494i
$53$	−9.05172	−	2.94108i	−1.24335	−	0.403989i	−0.387816	−	0.921737i	$-0.626771\pi$
$53$	−9.05172	−	2.94108i	−1.24335	−	0.403989i	−0.855533	+	0.517748i	$0.826771\pi$
$54$		−	1.97160i		−	0.268301i
$55$	4.05536	+	8.20674i	0.546824	+	1.10660i
$56$			3.32143i			0.443844i
$57$	8.25091	−	7.76737i	1.09286	−	1.02881i
$58$	−2.53429	+	1.84127i	−0.332769	+	0.241771i
$59$	−0.181254	+	0.249475i	−0.0235973	+	0.0324788i	−0.820653	−	0.571427i	$-0.806390\pi$
$59$	−0.181254	+	0.249475i	−0.0235973	+	0.0324788i	0.797055	+	0.603906i	$0.206390\pi$
$60$	6.82409	−	2.21728i	0.880987	−	0.286250i
$61$	−5.06934	+	1.64713i	−0.649063	+	0.210893i	−0.615001	−	0.788526i	$-0.710844\pi$
$61$	−5.06934	+	1.64713i	−0.649063	+	0.210893i	−0.0340620	+	0.999420i	$0.510844\pi$
$62$	1.22917	−	1.69181i	0.156105	−	0.214861i
$63$	−7.33746	−	10.0992i	−0.924433	−	1.27237i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	19.6561			2.43804
$66$	−7.72994	+	3.81974i	−0.951489	+	0.470178i
$67$		−	3.89518i		−	0.475872i	−0.971281	−	0.237936i	$-0.923529\pi$
$67$		−	3.89518i		−	0.475872i	0.971281	−	0.237936i	$-0.0764709\pi$
$68$	4.75748	+	1.54580i	0.576929	+	0.187456i
$69$	9.52604	+	13.1115i	1.14680	+	1.57844i
$70$	5.38840	−	7.41650i	0.644037	−	0.886441i
$71$	9.57288	−	3.11042i	1.13609	−	0.369138i	0.320204	−	0.947349i	$-0.396249\pi$
$71$	9.57288	−	3.11042i	1.13609	−	0.369138i	0.815888	+	0.578210i	$0.196249\pi$
$72$	1.16141	+	3.57445i	0.136873	+	0.421253i
$73$	−2.63359	+	3.62482i	−0.308238	+	0.424254i	−0.934831	−	0.355093i	$-0.884449\pi$
$73$	−2.63359	+	3.62482i	−0.308238	+	0.424254i	0.626593	+	0.779347i	$0.284449\pi$
$74$	−1.78383	−	2.45523i	−0.207366	−	0.285415i
$75$	−6.47257	−	2.10306i	−0.747388	−	0.242841i
$76$	−2.09518	+	3.82233i	−0.240334	+	0.438451i
$77$	−5.12130	+	9.75309i	−0.583626	+	1.11147i
$78$			18.5141i			2.09631i
$79$	0.0577018	−	0.177588i	0.00649196	−	0.0199802i	−0.947758	−	0.318990i	$-0.896656\pi$
$79$	0.0577018	−	0.177588i	0.00649196	−	0.0199802i	0.954250	+	0.299010i	$0.0966563\pi$
$80$	−2.23293	+	1.62232i	−0.249649	+	0.181380i
$81$	4.97516	+	3.61467i	0.552796	+	0.401630i
$82$	0.673122	+	2.07166i	0.0743339	+	0.228776i
$83$	14.3889	−	4.67523i	1.57938	−	0.513173i	0.617486	−	0.786582i	$-0.288151\pi$
$83$	14.3889	−	4.67523i	1.57938	−	0.513173i	0.961898	+	0.273409i	$0.0881513\pi$
$84$	6.98560	+	5.07534i	0.762192	+	0.553765i
$85$	−8.11533	−	11.1698i	−0.880231	−	1.21153i
$86$	−3.58147	−	1.16369i	−0.386199	−	0.125484i
$87$			8.14368i			0.873094i
$88$	2.37384	−	2.31623i	0.253052	−	0.246911i
$89$		−	7.75741i		−	0.822284i	−0.911571	−	0.411142i	$-0.865130\pi$
$89$		−	7.75741i		−	0.822284i	0.911571	−	0.411142i	$-0.134870\pi$
$90$	3.20554	−	9.86565i	0.337894	−	1.03993i
$91$	13.9035	+	19.1365i	1.45748	+	2.00605i
$92$	−5.04347	−	3.66430i	−0.525818	−	0.382029i
$93$	−1.67996	−	5.17039i	−0.174204	−	0.536144i
$94$	−2.24176	−	6.89943i	−0.231220	−	0.711622i
$95$	10.8794	−	5.13594i	1.11620	−	0.526936i
$96$	−1.52806	−	2.10319i	−0.155957	−	0.214656i
$97$	8.91786	+	2.89759i	0.905471	+	0.294206i	0.724494	−	0.689282i	$-0.242074\pi$
$97$	8.91786	+	2.89759i	0.905471	+	0.294206i	0.180978	+	0.983487i	$0.442074\pi$
$98$	4.03187			0.407280
$99$	−2.10106	+	12.2868i	−0.211164	+	1.23487i
$100$	2.61787			0.261787
$101$	−10.5946	−	3.44238i	−1.05420	−	0.342530i	−0.269883	−	0.962893i	$-0.586985\pi$
$101$	−10.5946	−	3.44238i	−1.05420	−	0.342530i	−0.784314	+	0.620364i	$0.786985\pi$
$102$	10.5208	−	7.64383i	1.04172	−	0.756852i
$103$	−6.12592	+	8.43161i	−0.603605	+	0.830791i	−0.996032	−	0.0889919i	$-0.971635\pi$
$103$	−6.12592	+	8.43161i	−0.603605	+	0.830791i	0.392427	+	0.919783i	$0.371635\pi$
$104$	−2.20071	−	6.77309i	−0.215797	−	0.664156i
$105$	−7.36454	−	22.6657i	−0.718705	−	2.21195i
$106$	5.59427	−	7.69985i	0.543364	−	0.747876i
$107$	8.32201	−	6.04629i	0.804519	−	0.584517i	−0.107718	−	0.994182i	$-0.534354\pi$
$107$	8.32201	−	6.04629i	0.804519	−	0.584517i	0.912236	+	0.409664i	$0.134354\pi$
$108$	1.87510	+	0.609258i	0.180432	+	0.0586259i
$109$	−18.0139			−1.72542			−0.862708	−	0.505702i	$-0.831234\pi$
$109$	−18.0139			−1.72542			−0.862708	+	0.505702i	$0.831234\pi$
$110$	−9.05825	+	1.32085i	−0.863670	+	0.125938i
$111$	−7.88963			−0.748850
$112$	−3.15886	−	1.02638i	−0.298485	−	0.0969835i
$113$	−3.56006	−	4.90001i	−0.334903	−	0.460954i	0.608041	−	0.793905i	$-0.291955\pi$
$113$	−3.56006	−	4.90001i	−0.334903	−	0.460954i	−0.942944	+	0.332952i	$0.891955\pi$
$114$	4.83754	+	10.2473i	0.453077	+	0.959750i
$115$	5.31705	+	16.3642i	0.495818	+	1.52597i
$116$	−0.968013	−	2.97924i	−0.0898778	−	0.276615i
$117$	21.6541	+	15.7327i	2.00193	+	1.45448i
$118$	−0.181254	−	0.249475i	−0.0166858	−	0.0229660i
$119$	5.13426	−	15.8016i	0.470657	−	1.44853i
$120$			7.17528i			0.655010i
$121$	10.5420	−	3.14120i	0.958360	−	0.285563i
$122$		−	5.33022i		−	0.482576i
$123$	5.38567	+	1.74991i	0.485609	+	0.157784i
$124$	1.22917	+	1.69181i	0.110383	+	0.151929i
$125$	5.31912	+	3.86457i	0.475756	+	0.345657i
$126$	11.8723	−	3.85753i	1.05767	−	0.343656i
$127$	5.54238	+	17.0577i	0.491807	+	1.51363i	0.821874	+	0.569669i	$0.192929\pi$
$127$	5.54238	+	17.0577i	0.491807	+	1.51363i	−0.330067	+	0.943957i	$0.607071\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−7.92016	+	5.75433i	−0.697331	+	0.506641i
$130$	−6.07407	+	18.6941i	−0.532731	+	1.63958i
$131$		−	17.7052i		−	1.54691i	−0.633851	−	0.773455i	$-0.718527\pi$
$131$		−	17.7052i		−	1.54691i	0.633851	−	0.773455i	$-0.281473\pi$
$132$	−1.24411	−	8.53197i	−0.108286	−	0.742613i
$133$	12.6956	+	6.95899i	1.10085	+	0.603421i
$134$	3.70454	+	1.20368i	0.320024	+	0.103982i
$135$	−3.19856	−	4.40244i	−0.275288	−	0.378901i
$136$	−2.94028	+	4.04695i	−0.252127	+	0.347024i
$137$	5.03916	+	15.5090i	0.430525	+	1.32502i	0.897604	+	0.440804i	$0.145306\pi$
$137$	5.03916	+	15.5090i	0.430525	+	1.32502i	−0.467079	+	0.884216i	$0.654694\pi$
$138$	−15.4135	+	5.00814i	−1.31208	+	0.426321i
$139$	9.32394	−	12.8333i	0.790846	−	1.08851i	−0.203156	−	0.979146i	$-0.565120\pi$
$139$	9.32394	−	12.8333i	0.790846	−	1.08851i	0.994002	−	0.109360i	$-0.0348802\pi$
$140$	5.38840	+	7.41650i	0.455403	+	0.626809i
$141$	−17.9364	−	5.82789i	−1.51052	−	0.490796i
$142$			10.0655i			0.844680i
$143$	3.98121	−	23.2819i	0.332926	−	1.94693i
$144$	−3.75840			−0.313200
$145$	−2.67176	+	8.22284i	−0.221878	+	0.682870i
$146$	−2.63359	−	3.62482i	−0.217957	−	0.299993i
$147$	6.16094	−	8.47980i	0.508145	−	0.699402i
$148$	2.88630	−	0.937814i	0.237252	−	0.0770879i
$149$	2.23724	−	0.726922i	0.183282	−	0.0595518i	−0.215938	−	0.976407i	$-0.569281\pi$
$149$	2.23724	−	0.726922i	0.183282	−	0.0595518i	0.399220	+	0.916855i	$0.369281\pi$
$150$	4.00027	−	5.50589i	0.326620	−	0.449554i
$151$	−4.33624	+	3.15046i	−0.352878	+	0.256381i	−0.750076	−	0.661352i	$-0.769983\pi$
$151$	−4.33624	+	3.15046i	−0.352878	+	0.256381i	0.397197	+	0.917733i	$0.369983\pi$
$152$	−2.98781	−	3.17380i	−0.242343	−	0.257429i
$153$		−	18.8007i		−	1.51994i
$154$	−7.69317	−	7.88452i	−0.619934	−	0.635353i
$155$		−	5.77180i		−	0.463603i
$156$	−17.6080	−	5.72117i	−1.40976	−	0.458060i
$157$	11.1143	−	8.07504i	0.887021	−	0.644458i	−0.0480788	−	0.998844i	$-0.515310\pi$
$157$	11.1143	−	8.07504i	0.887021	−	0.644458i	0.935099	+	0.354385i	$0.115310\pi$
$158$	0.151065	+	0.109755i	0.0120181	+	0.00873167i
$159$	−7.64591	−	23.5317i	−0.606360	−	1.86618i
$160$	−0.852902	−	2.62496i	−0.0674278	−	0.207522i
$161$	−12.1707	+	16.7515i	−0.959185	+	1.32020i
$162$	−4.97516	+	3.61467i	−0.390886	+	0.283995i
$163$	0.185946	−	0.572282i	0.0145644	−	0.0448246i	−0.943510	−	0.331343i	$-0.892498\pi$
$163$	0.185946	−	0.572282i	0.0145644	−	0.0448246i	0.958075	+	0.286519i	$0.0924981\pi$
$164$	−2.17827			−0.170094
$165$	−11.0635	+	21.0696i	−0.861296	+	1.64027i
$166$			15.1294i			1.17427i
$167$	1.41124	−	4.34336i	0.109205	−	0.336099i	−0.881489	−	0.472204i	$-0.843458\pi$
$167$	1.41124	−	4.34336i	0.109205	−	0.336099i	0.990694	+	0.136105i	$0.0434585\pi$
$168$	−6.98560	+	5.07534i	−0.538951	+	0.391571i
$169$	−30.5144	−	22.1700i	−2.34726	−	1.70539i
$170$	13.1309	−	4.26648i	1.00709	−	0.327224i
$171$	16.0961	+	3.04983i	1.23090	+	0.233227i
$172$	2.21347	−	3.04658i	0.168775	−	0.232299i
$173$	8.27266	−	6.01044i	0.628959	−	0.456965i	−0.227081	−	0.973876i	$-0.572918\pi$
$173$	8.27266	−	6.01044i	0.628959	−	0.456965i	0.856039	+	0.516911i	$0.172918\pi$
$174$	−7.74510	−	2.51654i	−0.587154	−	0.190778i
$175$		−	8.69506i		−	0.657285i
$176$	1.46931	+	2.97341i	0.110753	+	0.224129i
$177$	−0.801661			−0.0602565
$178$	7.37774	+	2.39717i	0.552985	+	0.179676i
$179$	−5.01491	−	6.90244i	−0.374832	−	0.515912i	0.579374	−	0.815062i	$-0.303297\pi$
$179$	−5.01491	−	6.90244i	−0.374832	−	0.515912i	−0.954206	+	0.299149i	$0.903297\pi$
$180$	8.39223	+	6.09731i	0.625520	+	0.454467i
$181$	−10.3775	+	3.37185i	−0.771352	+	0.250628i	−0.668144	−	0.744032i	$-0.732911\pi$
$181$	−10.3775	+	3.37185i	−0.771352	+	0.250628i	−0.103209	+	0.994660i	$0.532911\pi$
$182$	−22.4963	+	7.30950i	−1.66754	+	0.541816i
$183$	−11.2105	−	8.14490i	−0.828704	−	0.602089i
$184$	5.04347	−	3.66430i	0.371810	−	0.270136i
$185$	−7.96632	−	2.58841i	−0.585695	−	0.190304i
$186$	5.43647			0.398621
$187$	−14.8739	+	7.34993i	−1.08769	+	0.537480i
$188$	7.25449			0.529088
$189$	2.02360	−	6.22801i	0.147196	−	0.453021i
$190$	1.52264	+	11.9340i	0.110464	+	0.865786i
$191$	−10.1285	−	7.35879i	−0.732873	−	0.532463i	0.157598	−	0.987503i	$-0.449625\pi$
$191$	−10.1285	−	7.35879i	−0.732873	−	0.532463i	−0.890471	+	0.455040i	$0.849625\pi$
$192$	2.47245	−	0.803349i	0.178434	−	0.0579767i
$193$	2.46950	+	7.60033i	0.177758	+	0.547083i	0.999749	−	0.0224178i	$-0.00713640\pi$
$193$	2.46950	+	7.60033i	0.177758	+	0.547083i	−0.821991	+	0.569501i	$0.807136\pi$
$194$	−5.51154	+	7.58598i	−0.395706	+	0.544642i
$195$	30.0357	+	41.3406i	2.15090	+	2.96046i
$196$	−1.24592	+	3.83453i	−0.0889940	+	0.273895i
$197$			20.8884i			1.48823i	0.668050	+	0.744117i	$0.267129\pi$
$197$			20.8884i			1.48823i	−0.668050	+	0.744117i	$0.732871\pi$
$198$	−11.0362	−	5.79507i	−0.784310	−	0.411837i
$199$	−10.4699			−0.742190			−0.371095	−	0.928595i	$-0.621018\pi$
$199$	−10.4699			−0.742190			−0.371095	+	0.928595i	$0.621018\pi$
$200$	−0.808967	+	2.48974i	−0.0572026	+	0.176051i
$201$	8.19233	−	5.95208i	0.577842	−	0.419827i
$202$	6.54779	−	9.01227i	0.460701	−	0.634101i
$203$	−9.89532	+	3.21518i	−0.694515	+	0.225662i
$204$	4.01860	+	12.3680i	0.281358	+	0.865932i
$205$	4.86391	+	3.53384i	0.339710	+	0.246814i
$206$	−6.12592	−	8.43161i	−0.426813	−	0.587458i
$207$	−7.24031	+	22.2834i	−0.503236	+	1.54880i
$208$	7.12165			0.493798
$209$	−3.87977	−	13.9265i	−0.268369	−	0.963316i
$210$	23.8321			1.64457
$211$	6.87827	−	21.1691i	0.473520	−	1.45734i	−0.374424	−	0.927257i	$-0.622160\pi$
$211$	6.87827	−	21.1691i	0.473520	−	1.45734i	0.847944	−	0.530086i	$-0.177840\pi$
$212$	5.59427	+	7.69985i	0.384216	+	0.528828i
$213$	21.1697	+	15.3807i	1.45053	+	1.05387i
$214$	3.17872	+	9.78310i	0.217293	+	0.668759i
$215$	−9.88502	+	3.21184i	−0.674153	+	0.219046i
$216$	−1.15888	+	1.59506i	−0.0788516	+	0.108530i
$217$	5.61923	−	4.08261i	0.381458	−	0.277146i
$218$	5.56660	−	17.1322i	0.377017	−	1.16034i
$219$	−11.6480			−0.787098
$220$	1.54295	−	9.02308i	0.104026	−	0.608336i
$221$			35.6247i			2.39638i
$222$	2.43803	−	7.50348i	0.163630	−	0.503601i
$223$	−4.50304	−	6.19790i	−0.301546	−	0.415042i	0.631176	−	0.775640i	$-0.282573\pi$
$223$	−4.50304	−	6.19790i	−0.301546	−	0.415042i	−0.932721	+	0.360598i	$0.882573\pi$
$224$	1.95228	−	2.68709i	0.130443	−	0.179539i
$225$	−3.04042	−	9.35745i	−0.202695	−	0.623830i
$226$	5.76030	−	1.87164i	0.383170	−	0.124499i
$227$	−14.6204	−	10.6224i	−0.970393	−	0.705032i	−0.0148520	−	0.999890i	$-0.504728\pi$
$227$	−14.6204	−	10.6224i	−0.970393	−	0.705032i	−0.955541	+	0.294858i	$0.904728\pi$
$228$	−11.2407	+	1.43418i	−0.744432	+	0.0949806i
$229$	0.591608	−	1.82078i	0.0390946	−	0.120321i	−0.929605	−	0.368558i	$-0.879851\pi$
$229$	0.591608	−	1.82078i	0.0390946	−	0.120321i	0.968699	+	0.248238i	$0.0798514\pi$
$230$	−17.2064			−1.13455
$231$	−28.3383	+	4.13222i	−1.86452	+	0.271880i
$232$	3.13256			0.205662
$233$	−24.3861	−	7.92353i	−1.59759	−	0.519088i	−0.631078	−	0.775719i	$-0.717387\pi$
$233$	−24.3861	−	7.92353i	−1.59759	−	0.519088i	−0.966509	+	0.256632i	$0.917387\pi$
$234$	−21.6541	+	15.7327i	−1.41558	+	1.02848i
$235$	−16.1987	−	11.7691i	−1.05669	−	0.767730i
$236$	0.293275	−	0.0952908i	0.0190906	−	0.00620291i
$237$	0.461674	−	0.150007i	0.0299889	−	0.00974399i
$238$	13.4417	+	9.76594i	0.871293	+	0.633032i
$239$	8.96744	+	12.3426i	0.580055	+	0.798378i	0.993701	−	0.112060i	$-0.0357449\pi$
$239$	8.96744	+	12.3426i	0.580055	+	0.798378i	−0.413646	+	0.910438i	$0.635745\pi$
$240$	−6.82409	−	2.21728i	−0.440493	−	0.143125i
$241$	−24.2859			−1.56440			−0.782198	−	0.623030i	$-0.785901\pi$
$241$	−24.2859			−1.56440			−0.782198	+	0.623030i	$0.785901\pi$
$242$	−0.270190	+	10.9967i	−0.0173685	+	0.706893i
$243$			21.9020i			1.40501i
$244$	5.06934	+	1.64713i	0.324531	+	0.105447i
$245$	9.00286	−	6.54096i	0.575172	−	0.417887i
$246$	−3.32853	+	4.58132i	−0.212219	+	0.292095i
$247$	−30.4999	−	5.77902i	−1.94066	−	0.367710i
$248$	−1.98885	+	0.646215i	−0.126292	+	0.0410347i
$249$	31.8200	+	23.1186i	2.01651	+	1.46508i
$250$	−5.31912	+	3.86457i	−0.336411	+	0.244417i
$251$	2.65266	−	8.16406i	0.167435	−	0.515311i	−0.831773	−	0.555116i	$-0.812674\pi$
$251$	2.65266	−	8.16406i	0.167435	−	0.515311i	0.999207	+	0.0398055i	$0.0126738\pi$
$252$			12.4832i			0.786370i
$253$	20.4597	−	2.98339i	1.28629	−	0.187564i
$254$	−17.9355			−1.12538
$255$	11.0915	−	34.1362i	0.694579	−	2.13769i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	6.89425	−	9.48912i	0.430051	−	0.591915i	−0.537914	−	0.843000i	$-0.680787\pi$
$257$	6.89425	−	9.48912i	0.430051	−	0.591915i	0.967965	+	0.251085i	$0.0807874\pi$
$258$	−3.02523	−	9.31071i	−0.188343	−	0.579659i
$259$	−3.11488	−	9.58662i	−0.193549	−	0.595683i
$260$	−15.9021	−	11.5536i	−0.986208	−	0.716522i
$261$	−9.52487	+	6.92022i	−0.589575	+	0.428351i
$262$	16.8386	+	5.47120i	1.04029	+	0.338012i
$263$			15.7717i			0.972525i	0.873813	+	0.486262i	$0.161640\pi$
$263$			15.7717i			0.972525i	−0.873813	+	0.486262i	$0.838360\pi$
$264$	8.49884	+	1.45330i	0.523067	+	0.0894447i
$265$		−	26.2689i		−	1.61368i
$266$	−10.5415	+	9.92377i	−0.646344	+	0.608466i
$267$	16.3154	−	11.8538i	0.998483	−	0.725441i
$268$	−2.28953	+	3.15127i	−0.139855	+	0.192494i
$269$	−7.42525	+	2.41261i	−0.452725	+	0.147099i	−0.526499	−	0.850176i	$-0.676496\pi$
$269$	−7.42525	+	2.41261i	−0.452725	+	0.147099i	0.0737739	+	0.997275i	$0.476496\pi$
$270$	5.17538	−	1.68158i	0.314963	−	0.102338i
$271$	6.87879	−	9.46785i	0.417857	−	0.575131i	−0.547256	−	0.836965i	$-0.684327\pi$
$271$	6.87879	−	9.46785i	0.417857	−	0.575131i	0.965113	+	0.261835i	$0.0843275\pi$
$272$	−2.94028	−	4.04695i	−0.178281	−	0.245383i
$273$	−19.0024	+	58.4835i	−1.15008	+	3.53958i
$274$	−16.3071			−0.985147
$275$	−6.21440	+	6.06358i	−0.374742	+	0.365648i
$276$		−	16.2067i		−	0.975527i
$277$	7.16990	+	2.32964i	0.430797	+	0.139975i	0.516386	−	0.856356i	$-0.327277\pi$
$277$	7.16990	+	2.32964i	0.430797	+	0.139975i	−0.0855884	+	0.996331i	$0.527277\pi$
$278$	9.32394	+	12.8333i	0.559213	+	0.769690i
$279$	4.61973	−	6.35851i	0.276576	−	0.380674i
$280$	−8.71862	+	2.83285i	−0.521037	+	0.169295i
$281$	2.21044	+	6.80303i	0.131864	+	0.405835i	0.995089	−	0.0989841i	$-0.0315593\pi$
$281$	2.21044	+	6.80303i	0.131864	+	0.405835i	−0.863225	+	0.504819i	$0.831559\pi$
$282$	11.0853	−	15.2576i	0.660120	−	0.908577i
$283$	−0.0690119	−	0.0949868i	−0.00410233	−	0.00564638i	0.806961	−	0.590605i	$-0.201111\pi$
$283$	−0.0690119	−	0.0949868i	−0.00410233	−	0.00564638i	−0.811063	+	0.584958i	$0.801111\pi$
$284$	−9.57288	−	3.11042i	−0.568046	−	0.184569i
$285$	27.4263	+	15.0335i	1.62459	+	0.890508i
$286$	20.9121	+	10.9809i	1.23656	+	0.649312i
$287$			7.23496i			0.427066i
$288$	1.16141	−	3.57445i	0.0684367	−	0.210626i
$289$	6.49084	−	4.71587i	0.381814	−	0.277404i
$290$	−6.99477	−	5.08200i	−0.410747	−	0.298425i
$291$	7.53284	+	23.1837i	0.441583	+	1.35905i
$292$	4.26124	−	1.38456i	0.249370	−	0.0810252i
$293$	−16.0838	−	11.6856i	−0.939625	−	0.682678i	0.00870518	−	0.999962i	$-0.497229\pi$
$293$	−16.0838	−	11.6856i	−0.939625	−	0.682678i	−0.948330	+	0.317284i	$0.897229\pi$
$294$	6.16094	+	8.47980i	0.359313	+	0.494552i
$295$	−0.809454	−	0.263007i	−0.0471282	−	0.0153129i
$296$			3.03483i			0.176396i
$297$	−5.86236	+	2.89688i	−0.340169	+	0.168094i
$298$			2.35237i			0.136269i
$299$	13.7194	−	42.2240i	0.793413	−	2.44187i
$300$	4.00027	+	5.50589i	0.230955	+	0.317883i
$301$	−10.1190	−	7.35187i	−0.583248	−	0.423755i
$302$	−1.65630	−	5.09756i	−0.0953092	−	0.293332i
$303$	−8.94913	−	27.5426i	−0.514114	−	1.58228i
$304$	3.94175	−	1.86081i	0.226075	−	0.106725i
$305$	−8.64731	−	11.9020i	−0.495143	−	0.681506i
$306$	17.8805	+	5.80973i	1.02216	+	0.332120i
$307$	22.9869			1.31193			0.655965	−	0.754791i	$-0.272262\pi$
$307$	22.9869			1.31193			0.655965	+	0.754791i	$0.272262\pi$
$308$	9.87594	−	4.88019i	0.562734	−	0.278075i
$309$	−27.0941			−1.54133
$310$	5.48931	+	1.78359i	0.311772	+	0.101301i
$311$	18.7135	−	13.5961i	1.06114	−	0.770965i	0.0868431	−	0.996222i	$-0.472322\pi$
$311$	18.7135	−	13.5961i	1.06114	−	0.770965i	0.974299	+	0.225257i	$0.0723221\pi$
$312$	10.8823	−	14.9782i	0.616090	−	0.847975i
$313$	−1.30550	−	4.01793i	−0.0737914	−	0.227107i	0.907357	−	0.420360i	$-0.138096\pi$
$313$	−1.30550	−	4.01793i	−0.0737914	−	0.227107i	−0.981149	+	0.193253i	$0.938096\pi$
$314$	4.24530	+	13.0657i	0.239576	+	0.737339i
$315$	20.2518	−	27.8742i	1.14106	−	1.57053i
$316$	−0.151065	+	0.109755i	−0.00849808	+	0.00617422i
$317$	−2.32386	−	0.755069i	−0.130521	−	0.0424089i	0.243028	−	0.970019i	$-0.421859\pi$
$317$	−2.32386	−	0.755069i	−0.130521	−	0.0424089i	−0.373549	+	0.927610i	$0.621859\pi$
$318$	24.7427			1.38750
$319$	9.19849	+	4.83008i	0.515017	+	0.270433i
$320$	2.76005			0.154291
$321$	25.4331	+	8.26370i	1.41953	+	0.461235i
$322$	−12.1707	−	16.7515i	−0.678246	−	0.933525i
$323$	9.30837	+	19.7178i	0.517931	+	1.09713i
$324$	−1.90034	−	5.84866i	−0.105575	−	0.324925i
$325$	5.76118	+	17.7311i	0.319573	+	0.983544i
$326$	0.486812	+	0.353690i	0.0269620	+	0.0195891i
$327$	−27.5263	−	37.8867i	−1.52221	−	2.09514i
$328$	0.673122	−	2.07166i	0.0371669	−	0.114388i
$329$		−	24.0952i		−	1.32841i
$330$	−16.6196	−	17.0329i	−0.914877	−	0.937632i
$331$			3.51894i			0.193419i	0.995313	+	0.0967093i	$0.0308317\pi$
$331$			3.51894i			0.193419i	−0.995313	+	0.0967093i	$0.969168\pi$
$332$	−14.3889	−	4.67523i	−0.789692	−	0.256586i
$333$	−6.70434	−	9.22773i	−0.367396	−	0.505677i
$334$	3.69468	+	2.68434i	0.202164	+	0.146881i
$335$	10.2247	−	3.32221i	0.558636	−	0.181512i
$336$	−2.66826	−	8.21207i	−0.145566	−	0.448005i
$337$	10.2810	+	7.46960i	0.560043	+	0.406895i	0.831475	−	0.555562i	$-0.187497\pi$
$337$	10.2810	+	7.46960i	0.560043	+	0.406895i	−0.271431	+	0.962458i	$0.587497\pi$
$338$	30.5144	−	22.1700i	1.65977	−	1.20589i
$339$	4.86568	−	14.9750i	0.264267	−	0.813331i
$340$			13.8066i			0.748769i
$341$	−6.83648	−	1.16904i	−0.370216	−	0.0633071i
$342$	−7.87453	+	14.3658i	−0.425806	+	0.776816i
$343$	−9.37593	−	3.04642i	−0.506252	−	0.164491i
$344$	2.21347	+	3.04658i	0.119342	+	0.164260i
$345$	−26.2923	+	36.1883i	−1.41553	+	1.94831i
$346$	3.15988	+	9.72510i	0.169876	+	0.522825i
$347$	1.75359	−	0.569775i	0.0941376	−	0.0305871i	−0.261570	−	0.965185i	$-0.584240\pi$
$347$	1.75359	−	0.569775i	0.0941376	−	0.0305871i	0.355707	+	0.934597i	$0.384240\pi$
$348$	4.78673	−	6.58838i	0.256596	−	0.353174i
$349$	14.2487	+	19.6117i	0.762716	+	1.04979i	0.996983	+	0.0776160i	$0.0247308\pi$
$349$	14.2487	+	19.6117i	0.762716	+	1.04979i	−0.234268	+	0.972172i	$0.575269\pi$
$350$	8.26950	+	2.68692i	0.442023	+	0.143622i
$351$			14.0410i			0.749455i
$352$	−3.28192	+	0.478561i	−0.174927	+	0.0255074i
$353$	2.31587			0.123262			0.0616308	−	0.998099i	$-0.480370\pi$
$353$	2.31587			0.123262			0.0616308	+	0.998099i	$0.480370\pi$
$354$	0.247727	−	0.762425i	0.0131665	−	0.0405224i
$355$	16.3295	+	22.4756i	0.866677	+	1.19288i
$356$	−4.55969	+	6.27588i	−0.241663	+	0.332621i
$357$	41.0793	−	13.3475i	2.17415	−	0.706424i
$358$	8.11430	−	2.63650i	0.428854	−	0.139343i
$359$	−3.39764	+	4.67646i	−0.179321	+	0.246814i	−0.889210	−	0.457500i	$-0.848745\pi$
$359$	−3.39764	+	4.67646i	−0.179321	+	0.246814i	0.709889	+	0.704314i	$0.248745\pi$
$360$	−8.39223	+	6.09731i	−0.442309	+	0.321356i
$361$	−18.3913	+	4.77069i	−0.967964	+	0.251089i
$362$		−	10.9115i		−	0.573497i
$363$	22.7153	+	17.3719i	1.19224	+	0.911786i
$364$		−	23.6540i		−	1.23981i
$365$	−11.7612	−	3.82145i	−0.615610	−	0.200024i
$366$	11.2105	−	8.14490i	0.585982	−	0.425741i
$367$	−0.355488	−	0.258277i	−0.0185563	−	0.0134819i	0.578468	−	0.815705i	$-0.303651\pi$
$367$	−0.355488	−	0.258277i	−0.0185563	−	0.0134819i	−0.597025	+	0.802223i	$0.703651\pi$
$368$	1.92643	+	5.92896i	0.100422	+	0.309068i
$369$	2.52986	+	7.78611i	0.131699	+	0.405329i
$370$	4.92346	−	6.77656i	0.255958	−	0.352296i
$371$	25.5745	−	18.5810i	1.32776	−	0.964675i
$372$	−1.67996	+	5.17039i	−0.0871019	+	0.268072i
$373$	−33.2951			−1.72395			−0.861977	−	0.506947i	$-0.830774\pi$
$373$	−33.2951			−1.72395			−0.861977	+	0.506947i	$0.830774\pi$
$374$	−2.39391	−	16.4172i	−0.123786	−	0.848912i
$375$			17.0924i			0.882649i
$376$	−2.24176	+	6.89943i	−0.115610	+	0.355811i
$377$	18.0483	−	13.1129i	0.929536	−	0.675348i
$378$	5.29786	+	3.84912i	0.272493	+	0.197978i
$379$	8.62180	−	2.80139i	0.442872	−	0.143898i	−0.0790882	−	0.996868i	$-0.525201\pi$
$379$	8.62180	−	2.80139i	0.442872	−	0.143898i	0.521960	+	0.852970i	$0.325201\pi$
$380$	−11.8205	−	2.23970i	−0.606377	−	0.114894i
$381$	−27.4066	+	37.7219i	−1.40408	+	1.93255i
$382$	10.1285	−	7.35879i	0.518219	−	0.376508i
$383$	30.4735	+	9.90143i	1.55712	+	0.505940i	0.956037	−	0.293245i	$-0.0947353\pi$
$383$	30.4735	+	9.90143i	1.55712	+	0.505940i	0.601085	+	0.799185i	$0.294735\pi$
$384$			2.59969i			0.132665i
$385$	−29.9695	−	5.12479i	−1.52739	−	0.261183i
$386$	−7.99145			−0.406754
$387$	−13.4606	−	4.37361i	−0.684239	−	0.222323i
$388$	−5.51154	−	7.58598i	−0.279806	−	0.385120i
$389$	1.11575	+	0.810638i	0.0565707	+	0.0411010i	0.615711	−	0.787972i	$-0.288869\pi$
$389$	1.11575	+	0.810638i	0.0565707	+	0.0411010i	−0.559141	+	0.829073i	$0.688869\pi$
$390$	−48.5988	+	15.7907i	−2.46090	+	0.799594i
$391$	−29.6585	+	9.63663i	−1.49989	+	0.487345i
$392$	−3.26185	−	2.36987i	−0.164748	−	0.119697i
$393$	37.2375	−	27.0546i	1.87838	−	1.36472i
$394$	−19.8660	−	6.45486i	−1.00083	−	0.325191i
$395$	0.515375			0.0259314
$396$	8.92182	−	8.70530i	0.448338	−	0.437458i
$397$	22.2477			1.11658			0.558289	−	0.829646i	$-0.311458\pi$
$397$	22.2477			1.11658			0.558289	+	0.829646i	$0.311458\pi$
$398$	3.23537	−	9.95745i	0.162175	−	0.499122i
$399$	4.76351	+	37.3351i	0.238474	+	1.86909i
$400$	−2.11790	−	1.53875i	−0.105895	−	0.0769373i
$401$	−17.6066	+	5.72073i	−0.879232	+	0.285680i	−0.713638	−	0.700514i	$-0.752954\pi$
$401$	−17.6066	+	5.72073i	−0.879232	+	0.285680i	−0.165593	+	0.986194i	$0.552954\pi$
$402$	3.12919	+	9.63066i	0.156070	+	0.480334i
$403$	−8.75375	+	12.0485i	−0.436055	+	0.600179i
$404$	6.54779	+	9.01227i	0.325765	+	0.448377i
$405$	−5.24504	+	16.1426i	−0.260628	+	0.802131i
$406$		−	10.4046i		−	0.516369i
$407$	−4.67940	+	8.91153i	−0.231949	+	0.441728i
$408$	−13.0045			−0.643817
$409$	0.946280	−	2.91235i	0.0467905	−	0.144006i	−0.924932	−	0.380133i	$-0.875878\pi$
$409$	0.946280	−	2.91235i	0.0467905	−	0.144006i	0.971722	+	0.236127i	$0.0758781\pi$
$410$	−4.86391	+	3.53384i	−0.240212	+	0.174524i
$411$	−24.9182	+	34.2970i	−1.22912	+	1.69174i
$412$	9.91195	−	3.22059i	0.488327	−	0.158667i
$413$	−0.316501	−	0.974091i	−0.0155740	−	0.0479319i
$414$	−18.9554	−	13.7719i	−0.931606	−	0.676851i
$415$	24.5446	+	33.7827i	1.20485	+	1.65833i
$416$	−2.20071	+	6.77309i	−0.107899	+	0.332078i
$417$	41.2385			2.01946
$418$	14.4438	+	0.613649i	0.706469	+	0.0300146i
$419$	0.804610			0.0393078			0.0196539	−	0.999807i	$-0.493744\pi$
$419$	0.804610			0.0393078			0.0196539	+	0.999807i	$0.493744\pi$
$420$	−7.36454	+	22.6657i	−0.359353	+	1.10597i
$421$	−22.3111	−	30.7086i	−1.08738	−	1.49665i	−0.851130	−	0.524954i	$-0.824082\pi$
$421$	−22.3111	−	30.7086i	−1.08738	−	1.49665i	−0.236248	−	0.971693i	$-0.575918\pi$
$422$	18.0075	+	13.0832i	0.876593	+	0.636882i
$423$	−8.42543	−	25.9308i	−0.409658	−	1.26080i
$424$	−9.05172	+	2.94108i	−0.439590	+	0.142832i
$425$	7.69729	−	10.5944i	0.373373	−	0.513904i
$426$	−21.1697	+	15.3807i	−1.02568	+	0.745198i
$427$	5.47082	−	16.8374i	0.264751	−	0.814821i
$428$	−10.2866			−0.497220
$429$	55.0499	−	27.2029i	2.65783	−	1.31337i
$430$		−	10.3937i		−	0.501230i
$431$	−10.8889	+	33.5126i	−0.524500	+	1.61424i	0.240804	+	0.970574i	$0.422589\pi$
$431$	−10.8889	+	33.5126i	−0.524500	+	1.61424i	−0.765303	+	0.643670i	$0.777411\pi$
$432$	−1.15888	−	1.59506i	−0.0557565	−	0.0767422i
$433$	−1.47245	+	2.02665i	−0.0707615	+	0.0973948i	−0.842931	−	0.538022i	$-0.819172\pi$
$433$	−1.47245	+	2.02665i	−0.0707615	+	0.0973948i	0.772169	+	0.635417i	$0.219172\pi$
$434$	2.14636	+	6.60580i	0.103028	+	0.317089i
$435$	−21.3769	+	6.94576i	−1.02494	+	0.333024i
$436$	14.5735	+	10.5883i	0.697946	+	0.507087i
$437$	−3.43916	−	26.9552i	−0.164517	−	1.28944i
$438$	3.59943	−	11.0779i	0.171987	−	0.529323i
$439$	−9.64942			−0.460542			−0.230271	−	0.973127i	$-0.573961\pi$
$439$	−9.64942			−0.460542			−0.230271	+	0.973127i	$0.573961\pi$
$440$	8.10466	+	4.25572i	0.386374	+	0.202883i
$441$	15.1534			0.721588
$442$	−33.8811	−	11.0086i	−1.61156	−	0.523628i
$443$	22.7101	−	16.4999i	1.07899	−	0.783932i	0.101484	−	0.994837i	$-0.467641\pi$
$443$	22.7101	−	16.4999i	1.07899	−	0.783932i	0.977507	+	0.210905i	$0.0676410\pi$
$444$	6.38284	+	4.63741i	0.302916	+	0.220082i
$445$	20.3629	−	6.61631i	0.965295	−	0.313643i
$446$	7.28607	−	2.36739i	0.345005	−	0.112099i
$447$	4.94749	+	3.59456i	0.234008	+	0.170017i
$448$	1.95228	+	2.68709i	0.0922368	+	0.126953i
$449$	22.1669	+	7.20247i	1.04612	+	0.339905i	0.781145	−	0.624349i	$-0.214636\pi$
$449$	22.1669	+	7.20247i	1.04612	+	0.339905i	0.264976	+	0.964255i	$0.414636\pi$
$450$	9.83900			0.463815
$451$	5.17085	−	5.04536i	0.243486	−	0.237577i
$452$			6.05674i			0.284885i
$453$	−13.2521	−	4.30586i	−0.622637	−	0.202307i
$454$	14.6204	−	10.6224i	0.686172	−	0.498533i
$455$	−38.3743	+	52.8177i	−1.79902	+	2.47613i
$456$	2.10958	−	11.1337i	0.0987899	−	0.521383i
$457$	−20.2302	+	6.57320i	−0.946330	+	0.307481i	−0.741223	−	0.671259i	$-0.765754\pi$
$457$	−20.2302	+	6.57320i	−0.946330	+	0.307481i	−0.205106	+	0.978740i	$0.565754\pi$
$458$	1.54885	+	1.12531i	0.0723730	+	0.0525821i
$459$	7.97897	−	5.79706i	0.372427	−	0.270584i
$460$	5.31705	−	16.3642i	0.247909	−	0.762985i
$461$			7.27928i			0.339030i	0.985528	+	0.169515i	$0.0542201\pi$
$461$			7.27928i			0.339030i	−0.985528	+	0.169515i	$0.945780\pi$
$462$	4.82704	−	28.2283i	0.224574	−	1.31330i
$463$	−30.4607			−1.41563			−0.707814	−	0.706398i	$-0.750319\pi$
$463$	−30.4607			−1.41563			−0.707814	+	0.706398i	$0.750319\pi$
$464$	−0.968013	+	2.97924i	−0.0449389	+	0.138308i
$465$	12.1392	−	8.81967i	0.562943	−	0.409002i
$466$	15.0714	−	20.7441i	0.698171	−	0.960950i
$467$	1.84529	+	5.67923i	0.0853900	+	0.262803i	0.984630	−	0.174652i	$-0.0558799\pi$
$467$	1.84529	+	5.67923i	0.0853900	+	0.262803i	−0.899240	+	0.437455i	$0.855880\pi$
$468$	−8.27115	−	25.4560i	−0.382334	−	1.17670i
$469$	10.4667	+	7.60451i	0.483308	+	0.351144i
$470$	16.1987	−	11.7691i	0.747192	−	0.542867i
$471$	33.9668	+	11.0365i	1.56511	+	0.508534i
$472$			0.308368i			0.0141938i
$473$	1.80215	+	12.3590i	0.0828631	+	0.568266i
$474$			0.485432i			0.0222967i
$475$	7.82169	+	8.30860i	0.358884	+	0.381225i
$476$	−13.4417	+	9.76594i	−0.616097	+	0.447621i
$477$	21.0255	−	28.9391i	0.962691	−	1.32503i
$478$	−14.5096	+	4.71446i	−0.663655	+	0.215634i
$479$	5.92253	−	1.92435i	0.270607	−	0.0879256i	−0.170570	−	0.985346i	$-0.554561\pi$
$479$	5.92253	−	1.92435i	0.270607	−	0.0879256i	0.441177	+	0.897420i	$0.354561\pi$
$480$	4.21752	−	5.80492i	0.192503	−	0.264957i
$481$	12.7038	+	17.4853i	0.579244	+	0.797261i
$482$	7.50477	−	23.0973i	0.341833	−	1.05205i
$483$	−53.8292			−2.44932
$484$	−10.3750	−	3.65513i	−0.471590	−	0.166142i
$485$			25.8804i			1.17517i
$486$	−20.8300	−	6.76808i	−0.944869	−	0.307006i
$487$	−8.23249	−	11.3310i	−0.373050	−	0.513459i	0.580677	−	0.814134i	$-0.302788\pi$
$487$	−8.23249	−	11.3310i	−0.373050	−	0.513459i	−0.953727	+	0.300675i	$0.902788\pi$
$488$	−3.13303	+	4.31224i	−0.141825	+	0.195206i
$489$	1.48776	−	0.483402i	0.0672787	−	0.0218602i
$490$	3.43879	+	10.5835i	0.155349	+	0.478114i
$491$	−16.7135	+	23.0041i	−0.754268	+	1.03816i	0.243401	+	0.969926i	$0.421737\pi$
$491$	−16.7135	+	23.0041i	−0.754268	+	1.03816i	−0.997669	+	0.0682353i	$0.978263\pi$
$492$	−3.32853	−	4.58132i	−0.150062	−	0.206542i
$493$	−14.9031	−	4.84230i	−0.671201	−	0.218086i
$494$	14.9212	−	27.2213i	0.671334	−	1.22474i
$495$	−34.0445	+	4.96429i	−1.53019	+	0.223128i
$496$		−	2.09120i		−	0.0938975i
$497$	−10.3310	+	31.7956i	−0.463409	+	1.42623i
$498$	−31.8200	+	23.1186i	−1.42589	+	1.03597i
$499$	14.3335	+	10.4139i	0.641654	+	0.466189i	0.860418	−	0.509589i	$-0.170203\pi$
$499$	14.3335	+	10.4139i	0.641654	+	0.466189i	−0.218764	+	0.975778i	$0.570203\pi$
$500$	−2.03172	−	6.25300i	−0.0908614	−	0.279643i
$501$	11.2914	−	3.66880i	0.504462	−	0.163910i
$502$	6.94476	+	5.04566i	0.309960	+	0.225199i
$503$	19.1530	+	26.3619i	0.853992	+	1.17542i	0.982969	+	0.183771i	$0.0588305\pi$
$503$	19.1530	+	26.3619i	0.853992	+	1.17542i	−0.128977	+	0.991648i	$0.541169\pi$
$504$	−11.8723	−	3.85753i	−0.528833	−	0.171828i
$505$		−	30.7463i		−	1.36819i
$506$	−3.48503	+	20.3803i	−0.154929	+	0.906013i
$507$		−	98.0549i		−	4.35477i
$508$	5.54238	−	17.0577i	0.245903	−	0.756813i
$509$	−0.702006	−	0.966229i	−0.0311159	−	0.0428273i	0.793176	−	0.608993i	$-0.208426\pi$
$509$	−0.702006	−	0.966229i	−0.0311159	−	0.0428273i	−0.824291	+	0.566166i	$0.808426\pi$
$510$	29.0380	+	21.0974i	1.28583	+	0.934207i
$511$	−4.59871	−	14.1534i	−0.203435	−	0.626109i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	3.66878	+	7.77155i	0.161981	+	0.343122i
$514$	6.89425	+	9.48912i	0.304092	+	0.418547i
$515$	−27.3575	−	8.88898i	−1.20551	−	0.391695i
$516$	9.78986			0.430975
$517$	−17.2210	+	16.8030i	−0.757377	+	0.738997i
$518$	10.0800			0.442888
$519$	25.2823	+	8.21470i	1.10977	+	0.360585i
$520$	15.9021	−	11.5536i	0.697354	−	0.506657i
$521$	20.1136	−	27.6840i	0.881194	−	1.21286i	−0.0948949	−	0.995487i	$-0.530252\pi$
$521$	20.1136	−	27.6840i	0.881194	−	1.21286i	0.976089	−	0.217372i	$-0.0697485\pi$
$522$	−3.63818	−	11.1972i	−0.159239	−	0.490086i
$523$	−3.25941	−	10.0314i	−0.142524	−	0.438644i	0.854160	−	0.520010i	$-0.174072\pi$
$523$	−3.25941	−	10.0314i	−0.142524	−	0.438644i	−0.996684	+	0.0813659i	$0.974072\pi$
$524$	−10.4068	+	14.3238i	−0.454625	+	0.625738i
$525$	18.2874	−	13.2866i	0.798128	−	0.579874i
$526$	−14.9998	−	4.87372i	−0.654022	−	0.212504i
$527$	10.4608			0.455680
$528$	−4.00846	+	7.63378i	−0.174446	+	0.332218i
$529$	15.8637			0.689725
$530$	24.9832	+	8.11753i	1.08520	+	0.352603i
$531$	−0.681224	−	0.937625i	−0.0295626	−	0.0406895i
$532$	−6.18055	−	13.0922i	−0.267961	−	0.567620i
$533$	−4.79374	−	14.7536i	−0.207640	−	0.639050i
$534$	6.23191	+	19.1798i	0.269681	+	0.829993i
$535$	22.9691	+	16.6881i	0.993043	+	0.721488i
$536$	−2.28953	−	3.15127i	−0.0988927	−	0.136114i
$537$	6.85408	−	21.0947i	0.295775	−	0.910303i
$538$		−	7.80737i		−	0.336599i
$539$	−5.92405	−	11.9884i	−0.255167	−	0.516376i
$540$			5.44171i			0.234174i
$541$	22.3691	+	7.26817i	0.961724	+	0.312483i	0.747471	−	0.664295i	$-0.231268\pi$
$541$	22.3691	+	7.26817i	0.961724	+	0.312483i	0.214254	+	0.976778i	$0.431268\pi$
$542$	6.87879	+	9.46785i	0.295470	+	0.406679i
$543$	−22.9491	−	16.6735i	−0.984839	−	0.715528i
$544$	4.75748	−	1.54580i	0.203975	−	0.0662756i
$545$	−15.3641	−	47.2858i	−0.658125	−	2.02550i
$546$	−49.7490	−	36.1448i	−2.12906	−	1.54685i
$547$	−23.3085	+	16.9346i	−0.996599	+	0.724071i	−0.961356	−	0.275308i	$-0.911220\pi$
$547$	−23.3085	+	16.9346i	−0.996599	+	0.724071i	−0.0352424	+	0.999379i	$0.511220\pi$
$548$	5.03916	−	15.5090i	0.215262	−	0.662510i
$549$		−	20.0331i		−	0.854992i
$550$	−3.84646	−	7.78399i	−0.164013	−	0.331911i
$551$	6.56328	−	11.9737i	0.279605	−	0.510095i
$552$	15.4135	+	5.00814i	0.656040	+	0.213160i
$553$	0.364544	+	0.501752i	0.0155020	+	0.0213367i
$554$	−4.43124	+	6.09908i	−0.188265	+	0.259125i
$555$	−6.72908	−	20.7100i	−0.285633	−	0.879089i
$556$	−15.0865	+	4.90189i	−0.639808	+	0.207886i
$557$	1.30948	−	1.80234i	0.0554842	−	0.0763675i	−0.780373	−	0.625314i	$-0.784971\pi$
$557$	1.30948	−	1.80234i	0.0554842	−	0.0763675i	0.835858	+	0.548946i	$0.184971\pi$
$558$	4.61973	+	6.35851i	0.195569	+	0.269177i
$559$	25.5060	+	8.28739i	1.07879	+	0.350519i
$560$		−	9.16730i		−	0.387389i
$561$	−38.1866	−	20.0516i	−1.61224	−	0.846578i
$562$	−7.15313			−0.301737
$563$	−4.28818	+	13.1977i	−0.180725	+	0.556216i	−0.999849	−	0.0174021i	$-0.994460\pi$
$563$	−4.28818	+	13.1977i	−0.180725	+	0.556216i	0.819123	+	0.573618i	$0.194460\pi$
$564$	11.0853	+	15.2576i	0.466775	+	0.642461i
$565$	9.82595	−	13.5243i	0.413381	−	0.568970i
$566$	0.111664	−	0.0362817i	0.00469357	−	0.00152503i
$567$	−19.4259	+	6.31185i	−0.815810	+	0.265073i
$568$	5.91636	−	8.14318i	0.248245	−	0.341680i
$569$	7.50028	−	5.44927i	0.314428	−	0.228445i	−0.419366	−	0.907817i	$-0.637748\pi$
$569$	7.50028	−	5.44927i	0.314428	−	0.228445i	0.733794	+	0.679372i	$0.237748\pi$
$570$	−22.7729	+	21.4383i	−0.953852	+	0.897953i
$571$			14.2238i			0.595246i	0.954683	+	0.297623i	$0.0961938\pi$
$571$			14.2238i			0.595246i	−0.954683	+	0.297623i	$0.903806\pi$
$572$	−16.9056	+	16.4954i	−0.706860	+	0.689705i
$573$		−	32.5469i		−	1.35967i
$574$	−6.88085	−	2.23572i	−0.287201	−	0.0933173i
$575$	−13.2032	+	9.59266i	−0.550610	+	0.400041i
$576$	3.04061	+	2.20913i	0.126692	+	0.0920471i
$577$	−6.46819	−	19.9070i	−0.269274	−	0.828741i	−0.990678	−	0.136226i	$-0.956503\pi$
$577$	−6.46819	−	19.9070i	−0.269274	−	0.828741i	0.721404	−	0.692515i	$-0.243497\pi$
$578$	2.47928	+	7.63044i	0.103124	+	0.317384i
$579$	−12.2114	+	16.8076i	−0.507490	+	0.698499i
$580$	6.99477	−	5.08200i	0.290442	−	0.211018i
$581$	−15.5284	+	47.7916i	−0.644227	+	1.98273i
$582$	−24.3768			−1.01045
$583$	−31.1145	−	5.32059i	−1.28863	−	0.220356i
$584$			4.48053i			0.185406i
$585$	−22.8288	+	70.2597i	−0.943853	+	2.90488i
$586$	16.0838	−	11.6856i	0.664415	−	0.482726i
$587$	−8.67436	−	6.30229i	−0.358029	−	0.260124i	0.394200	−	0.919025i	$-0.371022\pi$
$587$	−8.67436	−	6.30229i	−0.358029	−	0.260124i	−0.752230	+	0.658901i	$0.771022\pi$
$588$	−9.96860	+	3.23900i	−0.411098	+	0.133574i
$589$	−1.69695	+	8.95597i	−0.0699215	+	0.369024i
$590$	0.500270	−	0.688562i	0.0205958	−	0.0283477i
$591$	−43.9323	+	31.9187i	−1.80713	+	1.31296i
$592$	−2.88630	−	0.937814i	−0.118626	−	0.0385439i
$593$			1.60542i			0.0659267i	0.999457	+	0.0329633i	$0.0104945\pi$
$593$			1.60542i			0.0659267i	−0.999457	+	0.0329633i	$0.989506\pi$
$594$	−0.943531	−	6.47063i	−0.0387135	−	0.265493i
$595$	45.8577			1.87998
$596$	−2.23724	−	0.726922i	−0.0916408	−	0.0297759i
$597$	−15.9986	−	22.0202i	−0.654780	−	0.901227i
$598$	35.9178	+	26.0958i	1.46879	+	1.06714i
$599$	37.0961	−	12.0533i	1.51571	−	0.492483i	0.571154	−	0.820843i	$-0.306496\pi$
$599$	37.0961	−	12.0533i	1.51571	−	0.492483i	0.944553	+	0.328360i	$0.106496\pi$
$600$	−6.47257	+	2.10306i	−0.264241	+	0.0858572i
$601$	−37.3098	−	27.1072i	−1.52190	−	1.10573i	−0.960536	−	0.278156i	$-0.910277\pi$
$601$	−37.3098	−	27.1072i	−1.52190	−	1.10573i	−0.561364	−	0.827569i	$-0.689723\pi$
$602$	10.1190	−	7.35187i	0.412419	−	0.299640i
$603$	13.9231	+	4.52390i	0.566994	+	0.184227i
$604$	5.35989			0.218091
$605$	17.2368	+	24.9931i	0.700775	+	1.01611i
$606$	28.9600			1.17642
$607$	6.54315	−	20.1378i	0.265578	−	0.817366i	−0.725981	−	0.687715i	$-0.758614\pi$
$607$	6.54315	−	20.1378i	0.265578	−	0.817366i	0.991560	−	0.129652i	$-0.0413859\pi$
$608$	0.551672	+	4.32385i	0.0223732	+	0.175355i
$609$	−21.8828	−	15.8988i	−0.886736	−	0.644251i
$610$	13.9916	−	4.54616i	0.566505	−	0.184069i
$611$	15.9650	+	49.1353i	0.645876	+	1.98780i
$612$	−11.0508	+	15.2101i	−0.446700	+	0.614830i
$613$	−9.45418	−	13.0126i	−0.381851	−	0.525572i	0.574223	−	0.818699i	$-0.305304\pi$
$613$	−9.45418	−	13.0126i	−0.381851	−	0.525572i	−0.956074	+	0.293127i	$0.905304\pi$
$614$	−7.10334	+	21.8618i	−0.286667	+	0.882272i
$615$			15.6297i			0.630250i
$616$	1.58950	+	10.9006i	0.0640430	+	0.439199i
$617$	37.9711			1.52866			0.764330	−	0.644825i	$-0.223070\pi$
$617$	37.9711			1.52866			0.764330	+	0.644825i	$0.223070\pi$
$618$	8.37254	−	25.7680i	0.336793	−	1.03654i
$619$	−27.3309	+	19.8571i	−1.09852	+	0.798123i	−0.980818	−	0.194926i	$-0.937553\pi$
$619$	−27.3309	+	19.8571i	−1.09852	+	0.798123i	−0.117704	+	0.993049i	$0.537553\pi$
$620$	−3.39258	+	4.66949i	−0.136249	+	0.187531i
$621$	−11.6895	+	3.79816i	−0.469085	+	0.152415i
$622$	7.14790	+	21.9990i	0.286605	+	0.882079i
$623$	20.8449	+	15.1447i	0.835132	+	0.606759i
$624$	10.8823	+	14.9782i	0.435641	+	0.599609i
$625$	−9.65249	+	29.7073i	−0.386100	+	1.18829i
$626$	4.22470			0.168853
$627$	23.3616	−	29.4404i	0.932974	−	1.17574i
$628$	−13.7381			−0.548209
$629$	4.69124	−	14.4382i	0.187052	−	0.575687i
$630$	20.2518	+	27.8742i	0.806849	+	1.11053i
$631$	6.30582	+	4.58145i	0.251031	+	0.182384i	0.706183	−	0.708029i	$-0.250415\pi$
$631$	6.30582	+	4.58145i	0.251031	+	0.182384i	−0.455153	+	0.890413i	$0.650415\pi$
$632$	−0.0577018	−	0.177588i	−0.00229525	−	0.00706407i
$633$	55.0332	−	17.8814i	2.18737	−	0.710721i
$634$	1.43623	−	1.97680i	0.0570399	−	0.0785086i
$635$	−40.0487	+	29.0971i	−1.58928	+	1.15468i
$636$	−7.64591	+	23.5317i	−0.303180	+	0.933092i
$637$	−28.7135			−1.13767
$638$	−7.43617	+	7.25571i	−0.294401	+	0.287256i
$639$			37.8302i			1.49654i
$640$	−0.852902	+	2.62496i	−0.0337139	+	0.103761i
$641$	−15.1617	−	20.8683i	−0.598853	−	0.824250i	0.396750	−	0.917927i	$-0.370138\pi$
$641$	−15.1617	−	20.8683i	−0.598853	−	0.824250i	−0.995603	+	0.0936768i	$0.970138\pi$
$642$	−15.7185	+	21.6347i	−0.620359	+	0.853852i
$643$	6.30631	+	19.4088i	0.248697	+	0.765410i	0.995006	+	0.0998109i	$0.0318238\pi$
$643$	6.30631	+	19.4088i	0.248697	+	0.765410i	−0.746310	+	0.665599i	$0.768176\pi$
$644$	19.6926	−	6.39851i	0.775997	−	0.252137i
$645$	−21.8600	−	15.8822i	−0.860738	−	0.625363i
$646$	−21.6292	+	2.75963i	−0.850991	+	0.108576i
$647$	−10.6745	+	32.8526i	−0.419656	+	1.29157i	0.488363	+	0.872641i	$0.337594\pi$
$647$	−10.6745	+	32.8526i	−0.419656	+	1.29157i	−0.908019	+	0.418929i	$0.862406\pi$
$648$	6.14964			0.241581
$649$	−0.475472	+	0.905496i	−0.0186639	+	0.0355438i
$650$	−18.6436			−0.731261
$651$	17.1731	+	5.57986i	0.673065	+	0.218692i
$652$	−0.486812	+	0.353690i	−0.0190650	+	0.0138516i
$653$	−3.43929	−	2.49879i	−0.134590	−	0.0977853i	0.518453	−	0.855106i	$-0.326508\pi$
$653$	−3.43929	−	2.49879i	−0.134590	−	0.0977853i	−0.653043	+	0.757321i	$0.726508\pi$
$654$	44.5385	−	14.4714i	1.74159	−	0.565878i
$655$	46.4755	−	15.1008i	1.81595	−	0.590037i
$656$	1.76226	+	1.28035i	0.0688046	+	0.0499894i
$657$	−9.89807	−	13.6235i	−0.386161	−	0.531504i
$658$	22.9159	+	7.44584i	0.893356	+	0.290269i
$659$	−22.4903			−0.876098			−0.438049	−	0.898951i	$-0.644330\pi$
$659$	−22.4903			−0.876098			−0.438049	+	0.898951i	$0.644330\pi$
$660$	21.3350	−	10.5427i	0.830464	−	0.410373i
$661$			34.2539i			1.33232i	0.745807	+	0.666162i	$0.232064\pi$
$661$			34.2539i			1.33232i	−0.745807	+	0.666162i	$0.767936\pi$
$662$	−3.34671	−	1.08741i	−0.130074	−	0.0422635i
$663$	−74.9257	+	54.4367i	−2.90987	+	2.11415i
$664$	8.89281	−	12.2399i	0.345108	−	0.475000i
$665$	−7.43900	+	39.2608i	−0.288472	+	1.52247i
$666$	10.8478	−	3.52468i	0.420346	−	0.136579i
$667$	15.7990	+	11.4786i	0.611738	+	0.444454i
$668$	−3.69468	+	2.68434i	−0.142952	+	0.103860i
$669$	6.15447	−	18.9415i	0.237946	−	0.732322i
$670$			10.7509i			0.415343i
$671$	−15.8489	+	7.83173i	−0.611841	+	0.302341i
$672$	8.63468			0.333090
$673$	−5.81870	+	17.9081i	−0.224295	+	0.690308i	0.774068	+	0.633103i	$0.218219\pi$
$673$	−5.81870	+	17.9081i	−0.224295	+	0.690308i	−0.998362	+	0.0572050i	$0.981781\pi$
$674$	−10.2810	+	7.46960i	−0.396010	+	0.287718i
$675$	3.03379	−	4.17566i	0.116771	−	0.160721i
$676$	11.6555	+	35.8719i	0.448287	+	1.37969i
$677$	−2.04245	−	6.28602i	−0.0784977	−	0.241591i	0.904105	−	0.427310i	$-0.140539\pi$
$677$	−2.04245	−	6.28602i	−0.0784977	−	0.241591i	−0.982603	+	0.185719i	$0.940539\pi$
$678$	12.7385	+	9.25507i	0.489219	+	0.355439i
$679$	−25.1963	+	18.3062i	−0.966945	+	0.702526i
$680$	−13.1309	−	4.26648i	−0.503546	−	0.163612i
$681$		−	46.9813i		−	1.80033i
$682$	3.22441	−	6.14063i	0.123469	−	0.235137i
$683$		−	0.735979i		−	0.0281615i	−0.999901	−	0.0140807i	$-0.995518\pi$
$683$		−	0.735979i		−	0.0281615i	0.999901	−	0.0140807i	$-0.00448219\pi$
$684$	−11.2294	−	11.9284i	−0.429365	−	0.456094i
$685$	−36.4125	+	26.4552i	−1.39125	+	1.01080i
$686$	5.79464	−	7.97564i	0.221240	−	0.304511i
$687$	4.73347	−	1.53800i	0.180593	−	0.0586783i
$688$	−3.58147	+	1.16369i	−0.136542	+	0.0443652i
$689$	−39.8404	+	54.8357i	−1.51780	+	2.08907i
$690$	−26.2923	−	36.1883i	−1.00093	−	1.37767i
$691$	10.6986	−	32.9269i	0.406993	−	1.25260i	−0.512226	−	0.858851i	$-0.671179\pi$
$691$	10.6986	−	32.9269i	0.406993	−	1.25260i	0.919219	−	0.393746i	$-0.128821\pi$
$692$	−10.2256			−0.388718
$693$	−28.9140	−	29.6332i	−1.09835	−	1.12567i
$694$			1.84383i			0.0699909i
$695$	41.6394	+	13.5294i	1.57947	+	0.513201i
$696$	4.78673	+	6.58838i	0.181441	+	0.249732i
$697$	−6.40473	+	8.81536i	−0.242596	+	0.333905i
$698$	−23.0549	+	7.49099i	−0.872640	+	0.283538i
$699$	−20.5987	−	63.3964i	−0.779116	−	2.39787i
$700$	−5.11083	+	7.03445i	−0.193171	+	0.265877i
$701$	−18.0850	−	24.8918i	−0.683060	−	0.940152i	0.316905	−	0.948457i	$-0.397356\pi$
$701$	−18.0850	−	24.8918i	−0.683060	−	0.940152i	−0.999966	+	0.00830560i	$0.997356\pi$
$702$	−13.3538	−	4.33892i	−0.504008	−	0.163762i
$703$	11.6001	+	6.35852i	0.437507	+	0.239816i
$704$	0.559030	−	3.26917i	0.0210692	−	0.123212i
$705$		−	52.0530i		−	1.96043i
$706$	−0.715644	+	2.20253i	−0.0269336	+	0.0828932i
$707$	29.9336	−	21.7480i	1.12577	−	0.817918i
$708$	0.648557	+	0.471204i	0.0243743	+	0.0177089i
$709$	−1.61116	−	4.95863i	−0.0605083	−	0.186225i	0.916233	−	0.400645i	$-0.131214\pi$
$709$	−1.61116	−	4.95863i	−0.0605083	−	0.186225i	−0.976742	+	0.214420i	$0.931214\pi$
$710$	−26.4216	+	8.58490i	−0.991585	+	0.322186i
$711$	0.567763	+	0.412504i	0.0212928	+	0.0154701i
$712$	−4.55969	−	6.27588i	−0.170882	−	0.235198i
$713$	−12.3986	−	4.02855i	−0.464332	−	0.150871i
$714$			43.1934i			1.61647i
$715$	64.5097	−	9.40665i	2.41253	−	0.351789i
$716$			8.53188i			0.318851i
$717$	−12.2561	+	37.7205i	−0.457714	+	1.40870i
$718$	−3.39764	−	4.67646i	−0.126799	−	0.174524i
$719$	−2.22029	−	1.61313i	−0.0828027	−	0.0601597i	0.545614	−	0.838037i	$-0.316297\pi$
$719$	−2.22029	−	1.61313i	−0.0828027	−	0.0601597i	−0.628416	+	0.777877i	$0.716297\pi$
$720$	−3.20554	−	9.86565i	−0.119464	−	0.367671i
$721$	−10.6969	−	32.9218i	−0.398375	−	1.22607i
$722$	1.14604	−	18.9654i	0.0426510	−	0.705819i
$723$	−37.1104	−	51.0781i	−1.38015	−	1.89961i
$724$	10.3775	+	3.37185i	0.385676	+	0.125314i
$725$	−8.20063			−0.304564
$726$	−23.5410	+	16.2353i	−0.873690	+	0.602550i
$727$	−39.1648			−1.45254			−0.726271	−	0.687408i	$-0.758748\pi$
$727$	−39.1648			−1.45254			−0.726271	+	0.687408i	$0.758748\pi$
$728$	22.4963	+	7.30950i	0.833769	+	0.270908i
$729$	−31.1386	+	22.6235i	−1.15328	+	0.837909i
$730$	7.26883	−	10.0047i	0.269032	−	0.370290i
$731$	−5.82113	−	17.9156i	−0.215302	−	0.662633i
$732$	4.28203	+	13.1787i	0.158268	+	0.487100i
$733$	9.74199	−	13.4087i	0.359829	−	0.495262i	−0.590272	−	0.807204i	$-0.700980\pi$
$733$	9.74199	−	13.4087i	0.359829	−	0.495262i	0.950101	+	0.311942i	$0.100980\pi$
$734$	0.355488	−	0.258277i	0.0131213	−	0.00953318i
$735$	27.5138	+	8.93979i	1.01486	+	0.329749i
$736$	−6.23407			−0.229791
$737$	−1.86408	−	12.7837i	−0.0686644	−	0.470893i
$738$	−8.18680			−0.301360
$739$	29.0403	+	9.43576i	1.06826	+	0.347100i	0.789811	−	0.613350i	$-0.210178\pi$
$739$	29.0403	+	9.43576i	1.06826	+	0.347100i	0.278453	+	0.960450i	$0.410178\pi$
$740$	4.92346	+	6.77656i	0.180990	+	0.249111i
$741$	−34.4513	−	72.9779i	−1.26560	−	2.68091i
$742$	9.76859	+	30.0646i	0.358616	+	1.10371i
$743$	0.544423	+	1.67556i	0.0199730	+	0.0614704i	0.960546	−	0.278120i	$-0.0897114\pi$
$743$	0.544423	+	1.67556i	0.0199730	+	0.0614704i	−0.940573	+	0.339591i	$0.889711\pi$
$744$	−4.39819	−	3.19547i	−0.161246	−	0.117152i
$745$	3.81629	+	5.25267i	0.139818	+	0.192443i
$746$	10.2887	−	31.6655i	0.376698	−	1.15936i
$747$			56.8621i			2.08048i
$748$	16.3534	+	2.79644i	0.597940	+	0.102248i
$749$			34.1661i			1.24840i
$750$	−16.2559	−	5.28185i	−0.593580	−	0.192866i
$751$	−12.2723	−	16.8914i	−0.447824	−	0.616377i	0.524104	−	0.851654i	$-0.324400\pi$
$751$	−12.2723	−	16.8914i	−0.447824	−	0.616377i	−0.971928	+	0.235277i	$0.924400\pi$
$752$	−5.86900	−	4.26408i	−0.214021	−	0.155495i
$753$	21.2240	−	6.89610i	0.773447	−	0.251308i
$754$	6.89385	+	21.2171i	0.251059	+	0.772681i
$755$	−11.9682	−	8.69544i	−0.435569	−	0.316459i
$756$	−5.29786	+	3.84912i	−0.192681	+	0.139991i
$757$	12.0368	−	37.0453i	0.437483	−	1.34644i	−0.453037	−	0.891492i	$-0.649659\pi$
$757$	12.0368	−	37.0453i	0.437483	−	1.34644i	0.890520	−	0.454943i	$-0.150341\pi$
$758$			9.06550i			0.329274i
$759$	37.5383	+	38.4720i	1.36255	+	1.39644i
$760$	5.78281	−	10.5498i	0.209764	−	0.382682i
$761$	23.1142	+	7.51025i	0.837889	+	0.272246i	0.696364	−	0.717688i	$-0.254800\pi$
$761$	23.1142	+	7.51025i	0.837889	+	0.272246i	0.141524	+	0.989935i	$0.454800\pi$
$762$	−27.4066	−	37.7219i	−0.992835	−	1.36652i
$763$	35.1682	−	48.4049i	1.27318	−	1.75238i
$764$	3.86874	+	11.9068i	0.139966	+	0.430772i
$765$	49.3511	−	16.0351i	1.78429	−	0.579752i
$766$	−18.8336	+	25.9223i	−0.680487	+	0.936610i
$767$	1.29083	+	1.77667i	0.0466091	+	0.0641519i
$768$	−2.47245	−	0.803349i	−0.0892170	−	0.0289884i
$769$		−	8.24596i		−	0.297357i	−0.988886	−	0.148678i	$-0.952498\pi$
$769$		−	8.24596i		−	0.297357i	0.988886	−	0.148678i	$-0.0475019\pi$
$770$	14.1350	−	26.9190i	0.509392	−	0.970094i
$771$	30.4923			1.09815
$772$	2.46950	−	7.60033i	0.0888791	−	0.273542i
$773$	7.18206	+	9.88525i	0.258321	+	0.355548i	0.918404	−	0.395645i	$-0.129479\pi$
$773$	7.18206	+	9.88525i	0.258321	+	0.355548i	−0.660083	+	0.751193i	$0.729479\pi$
$774$	8.31909	−	11.4502i	0.299024	−	0.411571i
$775$	5.20654	−	1.69171i	0.187025	−	0.0607680i
$776$	8.91786	−	2.89759i	0.320133	−	0.104017i
$777$	15.4028	−	21.2001i	0.552572	−	0.760551i
$778$	−1.11575	+	0.810638i	−0.0400015	+	0.0290628i
$779$	−6.50824	−	6.91339i	−0.233182	−	0.247698i
$780$		−	51.0998i		−	1.82967i
$781$	29.9289	−	14.7893i	1.07094	−	0.529204i
$782$		−	31.1848i		−	1.11517i
$783$	−5.87386	−	1.90853i	−0.209915	−	0.0682054i
$784$	3.26185	−	2.36987i	0.116495	−	0.0846383i
$785$	30.6761	+	22.2875i	1.09488	+	0.795475i
$786$	14.2234	+	43.7753i	0.507333	+	1.56141i
$787$	11.2008	+	34.4724i	0.399264	+	1.22881i	0.925591	+	0.378525i	$0.123569\pi$
$787$	11.2008	+	34.4724i	0.399264	+	1.22881i	−0.526327	+	0.850282i	$0.676431\pi$
$788$	12.2779	−	16.8990i	0.437381	−	0.602003i
$789$	−33.1710	+	24.1001i	−1.18092	+	0.857987i
$790$	−0.159260	+	0.490151i	−0.00566621	+	0.0174388i
$791$	20.1170			0.715279
$792$	5.52224	+	11.1752i	0.196224	+	0.397095i
$793$			37.9600i			1.34800i
$794$	−6.87491	+	21.1588i	−0.243981	+	0.750898i
$795$	55.2486	−	40.1404i	1.95947	−	1.42363i
$796$	8.47031	+	6.15404i	0.300222	+	0.218124i
$797$	7.01135	−	2.27813i	0.248355	−	0.0806954i	−0.182194	−	0.983263i	$-0.558320\pi$
$797$	7.01135	−	2.27813i	0.248355	−	0.0806954i	0.430549	+	0.902567i	$0.358320\pi$
$798$	−36.9797	−	7.00680i	−1.30907	−	0.248038i
$799$	21.3303	−	29.3586i	0.754610	−	1.03863i
$800$	2.11790	−	1.53875i	0.0748792	−	0.0544029i
$801$	27.7285	+	9.00953i	0.979737	+	0.318336i
$802$		−	18.5127i		−	0.653705i
$803$	−6.90852	+	13.1567i	−0.243796	+	0.464290i
$804$	−10.1263			−0.357126
$805$	−54.3525	−	17.6602i	−1.91567	−	0.622440i
$806$	−8.75375	−	12.0485i	−0.308338	−	0.424390i
$807$	−16.4204	−	11.9301i	−0.578026	−	0.419960i
$808$	−10.5946	+	3.44238i	−0.372715	+	0.121102i
$809$	−13.0275	+	4.23289i	−0.458022	+	0.148820i	−0.528935	−	0.848662i	$-0.677409\pi$
$809$	−13.0275	+	4.23289i	−0.458022	+	0.148820i	0.0709132	+	0.997482i	$0.477409\pi$
$810$	−13.7317	−	9.97666i	−0.482483	−	0.350544i
$811$	−2.15370	+	1.56476i	−0.0756268	+	0.0549461i	−0.624956	−	0.780660i	$-0.714883\pi$
$811$	−2.15370	+	1.56476i	−0.0756268	+	0.0549461i	0.549329	+	0.835606i	$0.314883\pi$
$812$	9.89532	+	3.21518i	0.347258	+	0.112831i
$813$	30.4239			1.06701
$814$	−7.02936	−	7.20419i	−0.246379	−	0.252507i
$815$	1.66081			0.0581757
$816$	4.01860	−	12.3680i	0.140679	−	0.432966i
$817$	16.2826	−	2.07747i	0.569658	−	0.0726816i
$818$	2.47739	+	1.79993i	0.0866200	+	0.0629331i
$819$	−84.5501	+	27.4720i	−2.95442	+	0.959949i
$820$	−1.85785	−	5.71787i	−0.0648789	−	0.199677i
$821$	7.63502	−	10.5087i	0.266464	−	0.366756i	−0.654728	−	0.755865i	$-0.727217\pi$
$821$	7.63502	−	10.5087i	0.266464	−	0.366756i	0.921192	+	0.389108i	$0.127217\pi$
$822$	−24.9182	−	34.2970i	−0.869122	−	1.19624i
$823$	8.07469	−	24.8513i	0.281466	−	0.866263i	−0.705970	−	0.708242i	$-0.749489\pi$
$823$	8.07469	−	24.8513i	0.281466	−	0.866263i	0.987436	−	0.158021i	$-0.0505115\pi$
$824$			10.4220i			0.363069i
$825$	−22.2489	−	3.80456i	−0.774606	−	0.132458i
$826$	1.02422			0.0356372
$827$	−15.9397	+	49.0573i	−0.554277	+	1.70589i	0.143567	+	0.989641i	$0.454143\pi$
$827$	−15.9397	+	49.0573i	−0.554277	+	1.70589i	−0.697845	+	0.716249i	$0.745857\pi$
$828$	18.9554	−	13.7719i	0.658745	−	0.478606i
$829$	21.8532	−	30.0784i	0.758994	−	1.04467i	−0.238303	−	0.971191i	$-0.576591\pi$
$829$	21.8532	−	30.0784i	0.758994	−	1.04467i	0.997297	−	0.0734752i	$-0.0234090\pi$
$830$	−39.7140	+	12.9039i	−1.37849	+	0.447899i
$831$	6.05635	+	18.6395i	0.210092	+	0.646598i
$832$	−5.76154	−	4.18600i	−0.199745	−	0.145123i
$833$	11.8548	+	16.3168i	0.410746	+	0.565343i
$834$	−12.7434	+	39.2201i	−0.441268	+	1.35808i
$835$	12.6048			0.436207
$836$	−5.04700	+	13.5472i	−0.174554	+	0.468541i
$837$	4.12300			0.142512
$838$	−0.248638	+	0.765230i	−0.00858907	+	0.0264344i
$839$	−11.5423	−	15.8867i	−0.398486	−	0.548468i	0.561878	−	0.827220i	$-0.310079\pi$
$839$	−11.5423	−	15.8867i	−0.398486	−	0.548468i	−0.960363	+	0.278752i	$0.910079\pi$
$840$	−19.2806	−	14.0082i	−0.665244	−	0.483328i
$841$	−5.92914	−	18.2480i	−0.204453	−	0.629242i
$842$	36.1002	−	11.7297i	1.24409	−	0.404231i
$843$	−10.9304	+	15.0444i	−0.376463	+	0.518157i
$844$	−18.0075	+	13.0832i	−0.619845	+	0.450344i
$845$	32.1697	−	99.0081i	1.10667	−	3.40598i
$846$	27.2652			0.937399
$847$	−12.1402	+	34.4597i	−0.417143	+	1.18405i
$848$		−	9.51754i		−	0.326834i
$849$	0.0943213	−	0.290291i	0.00323710	−	0.00996276i
$850$	7.69729	+	10.5944i	0.264015	+	0.363385i
$851$	−11.1205	+	15.3061i	−0.381207	+	0.524686i
$852$	−8.08612	−	24.8865i	−0.277026	−	0.852598i
$853$	3.14550	−	1.02203i	0.107700	−	0.0349938i	−0.254671	−	0.967028i	$-0.581967\pi$
$853$	3.14550	−	1.02203i	0.107700	−	0.0349938i	0.362371	+	0.932034i	$0.381967\pi$
$854$	14.3228	+	10.4061i	0.490116	+	0.356090i
$855$	5.72269	+	44.8528i	0.195712	+	1.53393i
$856$	3.17872	−	9.78310i	0.108647	−	0.334380i
$857$	−34.5269			−1.17942			−0.589708	−	0.807616i	$-0.700757\pi$
$857$	−34.5269			−1.17942			−0.589708	+	0.807616i	$0.700757\pi$
$858$	8.86013	+	60.7617i	0.302480	+	2.07437i
$859$	31.6203			1.07887			0.539435	−	0.842027i	$-0.318638\pi$
$859$	31.6203			1.07887			0.539435	+	0.842027i	$0.318638\pi$
$860$	9.88502	+	3.21184i	0.337077	+	0.109523i
$861$	−15.2165	+	11.0555i	−0.518578	+	0.376769i
$862$	−28.5075	−	20.7119i	−0.970969	−	0.705450i
$863$	34.5101	−	11.2130i	1.17474	−	0.381696i	0.344329	−	0.938849i	$-0.388106\pi$
$863$	34.5101	−	11.2130i	1.17474	−	0.381696i	0.830410	+	0.557153i	$0.188106\pi$
$864$	1.87510	−	0.609258i	0.0637923	−	0.0207274i
$865$	22.8330	+	16.5891i	0.776344	+	0.564047i
$866$	−1.47245	−	2.02665i	−0.0500359	−	0.0688685i
$867$	19.8368	+	6.44537i	0.673693	+	0.218896i
$868$	−6.94575			−0.235754
$869$	0.104386	−	0.610442i	0.00354105	−	0.0207078i
$870$		−	22.4770i		−	0.762040i
$871$	−26.3824	−	8.57217i	−0.893935	−	0.290457i
$872$	−14.5735	+	10.5883i	−0.493522	+	0.358565i
$873$	−20.7146	+	28.5111i	−0.701082	+	0.964956i
$874$	26.6987	+	5.05877i	0.903096	+	0.171116i
$875$	−20.7689	+	6.74822i	−0.702116	+	0.228131i
$876$	9.42342	+	6.84652i	0.318388	+	0.231322i
$877$	−1.14429	+	0.831374i	−0.0386398	+	0.0280735i	−0.606938	−	0.794750i	$-0.707602\pi$
$877$	−1.14429	+	0.831374i	−0.0386398	+	0.0280735i	0.568298	+	0.822823i	$0.307602\pi$
$878$	2.98183	−	9.17714i	0.100632	−	0.309714i
$879$		−	51.6836i		−	1.74324i
$880$	−6.55190	+	6.39290i	−0.220865	+	0.215505i
$881$	4.80803			0.161987			0.0809933	−	0.996715i	$-0.474191\pi$
$881$	4.80803			0.161987			0.0809933	+	0.996715i	$0.474191\pi$
$882$	−4.68264	+	14.4117i	−0.157673	+	0.485267i
$883$	−7.06490	+	5.13295i	−0.237753	+	0.172737i	−0.700281	−	0.713867i	$-0.746942\pi$
$883$	−7.06490	+	5.13295i	−0.237753	+	0.172737i	0.462529	+	0.886604i	$0.346942\pi$
$884$	20.9397	−	28.8210i	0.704278	−	0.969355i
$885$	−0.683738	−	2.10433i	−0.0229836	−	0.0707363i
$886$	8.67449	+	26.6974i	0.291425	+	0.896915i
$887$	−42.5507	−	30.9149i	−1.42871	−	1.03802i	−0.990255	−	0.139268i	$-0.955525\pi$
$887$	−42.5507	−	30.9149i	−1.42871	−	1.03802i	−0.438457	−	0.898752i	$-0.644475\pi$
$888$	−6.38284	+	4.63741i	−0.214194	+	0.155621i
$889$	−56.6559	−	18.4086i	−1.90018	−	0.617405i
$890$			21.4108i			0.717693i
$891$	18.0579	+	9.48212i	0.604963	+	0.317663i
$892$			7.66102i			0.256510i
$893$	21.6750	+	23.0243i	0.725326	+	0.770479i
$894$	−4.94749	+	3.59456i	−0.165469	+	0.120220i
$895$	13.8414	−	19.0511i	0.462667	−	0.636807i
$896$	−3.15886	+	1.02638i	−0.105530	+	0.0342888i
$897$	109.769	−	35.6662i	3.66509	−	1.19086i
$898$	−13.6999	+	18.8563i	−0.457172	+	0.629243i
$899$	−3.85046	−	5.29970i	−0.128420	−	0.176755i
$900$	−3.04042	+	9.35745i	−0.101347	+	0.311915i
$901$	47.6097			1.58611
$902$	3.20054	+	6.47687i	0.106566	+	0.215656i
$903$		−	32.5163i		−	1.08207i
$904$	−5.76030	−	1.87164i	−0.191585	−	0.0622497i
$905$	−17.7020	−	24.3647i	−0.588433	−	0.809908i
$906$	8.19024	−	11.2729i	0.272102	−	0.374517i
$907$	12.1795	−	3.95737i	0.404414	−	0.131402i	−0.0997446	−	0.995013i	$-0.531803\pi$
$907$	12.1795	−	3.95737i	0.404414	−	0.131402i	0.504159	+	0.863611i	$0.331803\pi$
$908$	5.58451	+	17.1874i	0.185329	+	0.570383i
$909$	24.6092	−	33.8717i	0.816236	−	1.12345i
$910$	−38.3743	−	52.8177i	−1.27210	−	1.75089i
$911$	−42.5013	−	13.8095i	−1.40813	−	0.457530i	−0.496320	−	0.868140i	$-0.665316\pi$
$911$	−42.5013	−	13.8095i	−1.40813	−	0.457530i	−0.911811	+	0.410610i	$0.865316\pi$
$912$	9.93688	+	5.44683i	0.329043	+	0.180362i
$913$	44.9857	−	22.2297i	1.48881	−	0.735694i
$914$		−	21.2713i		−	0.703592i
$915$	11.8186	−	36.3739i	0.390711	−	1.20249i
$916$	−1.54885	+	1.12531i	−0.0511755	+	0.0371811i
$917$	47.5754	+	34.5656i	1.57108	+	1.14146i
$918$	3.04770	+	9.37985i	0.100589	+	0.309581i
$919$	−47.6536	+	15.4836i	−1.57195	+	0.510757i	−0.959966	−	0.280116i	$-0.909627\pi$
$919$	−47.6536	+	15.4836i	−1.57195	+	0.510757i	−0.611981	+	0.790873i	$0.709627\pi$
$920$	13.9202	+	10.1136i	0.458936	+	0.333437i
$921$	35.1254	+	48.3459i	1.15742	+	1.59305i
$922$	−6.92301	−	2.24942i	−0.227997	−	0.0740807i
$923$		−	71.6831i		−	2.35948i
$924$	25.3550	+	13.3138i	0.834119	+	0.437992i
$925$		−	7.94480i		−	0.261223i
$926$	9.41287	−	28.9698i	0.309326	−	0.952008i
$927$	−23.0237	−	31.6893i	−0.756196	−	1.04081i
$928$	−2.53429	−	1.84127i	−0.0831922	−	0.0604427i
$929$	15.4602	+	47.5815i	0.507232	+	1.56110i	0.796986	+	0.603998i	$0.206427\pi$
$929$	15.4602	+	47.5815i	0.507232	+	1.56110i	−0.289754	+	0.957101i	$0.593573\pi$
$930$	4.63677	+	14.2705i	0.152046	+	0.467949i
$931$	−15.8926	+	7.50255i	−0.520859	+	0.245886i
$932$	15.0714	+	20.7441i	0.493682	+	0.679494i
$933$	57.1906	+	18.5823i	1.87234	+	0.608359i
$934$	−5.97150			−0.195393
$935$	−31.9793	−	32.7747i	−1.04583	−	1.07185i
$936$	26.7660			0.874874
$937$	−43.5878	−	14.1625i	−1.42395	−	0.462670i	−0.507095	−	0.861890i	$-0.669281\pi$
$937$	−43.5878	−	14.1625i	−1.42395	−	0.462670i	−0.916855	+	0.399220i	$0.869281\pi$
$938$	−10.4667	+	7.60451i	−0.341750	+	0.248296i
$939$	6.45560	−	8.88537i	0.210670	−	0.289963i
$940$	6.18737	+	19.0428i	0.201810	+	0.621106i
$941$	−6.37668	−	19.6254i	−0.207874	−	0.639770i	−0.999583	−	0.0288720i	$-0.990808\pi$
$941$	−6.37668	−	19.6254i	−0.207874	−	0.639770i	0.791709	−	0.610898i	$-0.209192\pi$
$942$	−20.9926	+	28.8939i	−0.683976	+	0.941413i
$943$	10.9860	−	7.98182i	0.357755	−	0.259924i
$944$	−0.293275	−	0.0952908i	−0.00954529	−	0.00310145i
$945$	18.0742			0.587955
$946$	−12.3110	−	2.10518i	−0.400264	−	0.0684453i
$947$	−15.8936			−0.516471			−0.258236	−	0.966082i	$-0.583141\pi$
$947$	−15.8936			−0.516471			−0.258236	+	0.966082i	$0.583141\pi$
$948$	−0.461674	−	0.150007i	−0.0149945	−	0.00487200i
$949$	18.7555	+	25.8147i	0.608829	+	0.837982i
$950$	−10.3190	+	4.87137i	−0.334792	+	0.158048i
$951$	−1.96295	−	6.04133i	−0.0636529	−	0.195904i
$952$	−5.13426	−	15.8016i	−0.166402	−	0.512133i
$953$	24.0277	+	17.4571i	0.778333	+	0.565492i	0.904478	−	0.426520i	$-0.140261\pi$
$953$	24.0277	+	17.4571i	0.778333	+	0.565492i	−0.126145	+	0.992012i	$0.540261\pi$
$954$	21.0255	+	28.9391i	0.680726	+	0.936938i
$955$	10.6779	−	32.8633i	0.345530	−	1.06343i
$956$		−	15.2563i		−	0.493425i
$957$	3.89725	+	26.7269i	0.125980	+	0.863957i
$958$			6.22732i			0.201195i
$959$	−51.5118	−	16.7372i	−1.66340	−	0.540473i
$960$	4.21752	+	5.80492i	0.136120	+	0.187353i
$961$	−21.5416	−	15.6509i	−0.694891	−	0.504868i
$962$	−20.5552	+	6.67879i	−0.662726	+	0.215333i
$963$	11.9469	+	36.7688i	0.384984	+	1.18486i
$964$	19.6477	+	14.2749i	0.632811	+	0.459764i
$965$	−17.8443	+	12.9647i	−0.574429	+	0.417347i
$966$	16.6342	−	51.1947i	0.535195	−	1.64716i
$967$		−	1.86996i		−	0.0601339i	−0.999548	−	0.0300669i	$-0.990428\pi$
$967$		−	1.86996i		−	0.0601339i	0.999548	−	0.0300669i	$-0.00957205\pi$
$968$	6.68228	−	8.73769i	0.214776	−	0.280840i
$969$	−27.2467	+	49.7074i	−0.875291	+	1.59683i
$970$	−24.6137	−	7.99749i	−0.790299	−	0.256784i
$971$	33.5952	+	46.2398i	1.07812	+	1.48391i	0.861573	+	0.507633i	$0.169480\pi$
$971$	33.5952	+	46.2398i	1.07812	+	1.48391i	0.216547	+	0.976272i	$0.430520\pi$
$972$	12.8737	−	17.7191i	0.412923	−	0.568339i
$973$	16.2812	+	50.1085i	0.521953	+	1.60641i
$974$	13.3204	−	4.32807i	0.426815	−	0.138680i
$975$	−28.4885	+	39.2110i	−0.912362	+	1.25576i
$976$	−3.13303	−	4.31224i	−0.100286	−	0.138031i
$977$	18.5889	+	6.03991i	0.594713	+	0.193234i	0.590881	−	0.806759i	$-0.298780\pi$
$977$	18.5889	+	6.03991i	0.594713	+	0.193234i	0.00383198	+	0.999993i	$0.498780\pi$
$978$			1.56432i			0.0500214i
$979$	−3.71240	−	25.4592i	−0.118649	−	0.813679i
$980$	−11.1282			−0.355476
$981$	20.9215	−	64.3897i	0.667971	−	2.05580i
$982$	−16.7135	−	23.0041i	−0.533348	−	0.734091i
$983$	−0.339436	+	0.467193i	−0.0108263	+	0.0149011i	−0.814396	−	0.580310i	$-0.802931\pi$
$983$	−0.339436	+	0.467193i	−0.0108263	+	0.0149011i	0.803570	+	0.595211i	$0.202931\pi$
$984$	5.38567	−	1.74991i	0.171689	−	0.0557851i
$985$	−54.8311	+	17.8157i	−1.74707	+	0.567656i
$986$	9.21061	−	12.6773i	0.293325	−	0.403728i
$987$	50.6770	−	36.8190i	1.61307	−	1.17196i
$988$	21.2781	+	22.6027i	0.676947	+	0.719088i
$989$			23.4761i			0.746498i
$990$	5.79902	−	33.9123i	0.184305	−	1.07780i
$991$			27.0737i			0.860024i	0.902823	+	0.430012i	$0.141491\pi$
$991$			27.0737i			0.860024i	−0.902823	+	0.430012i	$0.858509\pi$
$992$	1.98885	+	0.646215i	0.0631459	+	0.0205174i
$993$	−7.40102	+	5.37716i	−0.234864	+	0.170639i
$994$	−27.0470	−	19.6508i	−0.857877	−	0.623284i
$995$	−8.92979	−	27.4831i	−0.283093	−	0.871272i
$996$	−12.1541	−	37.4066i	−0.385119	−	1.18527i
$997$	0.296835	−	0.408559i	0.00940086	−	0.0129392i	−0.804291	−	0.594236i	$-0.797454\pi$
$997$	0.296835	−	0.408559i	0.00940086	−	0.0129392i	0.813692	+	0.581297i	$0.197454\pi$
$998$	−14.3335	+	10.4139i	−0.453718	+	0.329645i
$999$	1.84899	−	5.69062i	0.0584996	−	0.180043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.m.b.189.10	yes	40
11.6	odd	10		418.2.m.a.303.1	yes	40
19.18	odd	2		418.2.m.a.189.1	✓	40
209.94	even	10	inner	418.2.m.b.303.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.m.a.189.1	✓	40	19.18	odd	2
418.2.m.a.303.1	yes	40	11.6	odd	10
418.2.m.b.189.10	yes	40	1.1	even	1	trivial
418.2.m.b.303.10	yes	40	209.94	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(1.52806 + 2.10319i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.852902 + 2.62496i) q^{5} +(-2.47245 + 0.803349i) q^{6} +(-1.95228 + 2.68709i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-1.16141 + 3.57445i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(1.52806 + 2.10319i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.852902 + 2.62496i) q^{5} +(-2.47245 + 0.803349i) q^{6} +(-1.95228 + 2.68709i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-1.16141 + 3.57445i) q^{9} -2.76005 q^{10} +(3.28192 - 0.478561i) q^{11} -2.59969i q^{12} +(2.20071 - 6.77309i) q^{13} +(-1.95228 - 2.68709i) q^{14} +(-4.21752 + 5.80492i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.75748 + 1.54580i) q^{17} +(-3.04061 - 2.20913i) q^{18} +(-0.551672 - 4.32385i) q^{19} +(0.852902 - 2.62496i) q^{20} -8.63468 q^{21} +(-0.559030 + 3.26917i) q^{22} +6.23407 q^{23} +(2.47245 + 0.803349i) q^{24} +(-2.11790 + 1.53875i) q^{25} +(5.76154 + 4.18600i) q^{26} +(-1.87510 + 0.609258i) q^{27} +(3.15886 - 1.02638i) q^{28} +(2.53429 + 1.84127i) q^{29} +(-4.21752 - 5.80492i) q^{30} +(-1.98885 - 0.646215i) q^{31} -1.00000 q^{32} +(6.02147 + 6.17124i) q^{33} -5.00231i q^{34} +(-8.71862 - 2.83285i) q^{35} +(3.04061 - 2.20913i) q^{36} +(-1.78383 + 2.45523i) q^{37} +(4.28270 + 0.811472i) q^{38} +(17.6080 - 5.72117i) q^{39} +(2.23293 + 1.62232i) q^{40} +(1.76226 - 1.28035i) q^{41} +(2.66826 - 8.21207i) q^{42} +3.76578i q^{43} +(-2.93642 - 1.54190i) q^{44} -10.3734 q^{45} +(-1.92643 + 5.92896i) q^{46} +(-5.86900 + 4.26408i) q^{47} +(-1.52806 + 2.10319i) q^{48} +(-1.24592 - 3.83453i) q^{49} +(-0.808967 - 2.48974i) q^{50} +(-10.5208 - 7.64383i) q^{51} +(-5.76154 + 4.18600i) q^{52} +(-9.05172 - 2.94108i) q^{53} -1.97160i q^{54} +(4.05536 + 8.20674i) q^{55} +3.32143i q^{56} +(8.25091 - 7.76737i) q^{57} +(-2.53429 + 1.84127i) q^{58} +(-0.181254 + 0.249475i) q^{59} +(6.82409 - 2.21728i) q^{60} +(-5.06934 + 1.64713i) q^{61} +(1.22917 - 1.69181i) q^{62} +(-7.33746 - 10.0992i) q^{63} +(0.309017 - 0.951057i) q^{64} +19.6561 q^{65} +(-7.72994 + 3.81974i) q^{66} -3.89518i q^{67} +(4.75748 + 1.54580i) q^{68} +(9.52604 + 13.1115i) q^{69} +(5.38840 - 7.41650i) q^{70} +(9.57288 - 3.11042i) q^{71} +(1.16141 + 3.57445i) q^{72} +(-2.63359 + 3.62482i) q^{73} +(-1.78383 - 2.45523i) q^{74} +(-6.47257 - 2.10306i) q^{75} +(-2.09518 + 3.82233i) q^{76} +(-5.12130 + 9.75309i) q^{77} +18.5141i q^{78} +(0.0577018 - 0.177588i) q^{79} +(-2.23293 + 1.62232i) q^{80} +(4.97516 + 3.61467i) q^{81} +(0.673122 + 2.07166i) q^{82} +(14.3889 - 4.67523i) q^{83} +(6.98560 + 5.07534i) q^{84} +(-8.11533 - 11.1698i) q^{85} +(-3.58147 - 1.16369i) q^{86} +8.14368i q^{87} +(2.37384 - 2.31623i) q^{88} -7.75741i q^{89} +(3.20554 - 9.86565i) q^{90} +(13.9035 + 19.1365i) q^{91} +(-5.04347 - 3.66430i) q^{92} +(-1.67996 - 5.17039i) q^{93} +(-2.24176 - 6.89943i) q^{94} +(10.8794 - 5.13594i) q^{95} +(-1.52806 - 2.10319i) q^{96} +(8.91786 + 2.89759i) q^{97} +4.03187 q^{98} +(-2.10106 + 12.2868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

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