LMFDB - Embedded newform 950.2.h.b.381.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			381.9
Character	$\chi$	$=$	950.381
Dual form			950.2.h.b.571.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(2.18620 - 1.58837i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.58887 + 1.57337i) q^{5} +(2.18620 + 1.58837i) q^{6} +2.75740 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.32952 - 4.09183i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(2.18620 - 1.58837i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.58887 + 1.57337i) q^{5} +(2.18620 + 1.58837i) q^{6} +2.75740 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.32952 - 4.09183i) q^{9} +(-1.00537 + 1.99731i) q^{10} +(-1.12517 - 3.46291i) q^{11} +(-0.835056 + 2.57004i) q^{12} +(1.45018 - 4.46319i) q^{13} +(0.852083 + 2.62244i) q^{14} +(5.97269 + 0.915978i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.60148 - 2.61663i) q^{17} +4.30241 q^{18} +(-0.809017 - 0.587785i) q^{19} +(-2.21023 - 0.338963i) q^{20} +(6.02824 - 4.37977i) q^{21} +(2.94572 - 2.14019i) q^{22} +(0.857130 + 2.63798i) q^{23} -2.70230 q^{24} +(0.0490418 + 4.99976i) q^{25} +4.69288 q^{26} +(-1.08758 - 3.34724i) q^{27} +(-2.23078 + 1.62076i) q^{28} +(-5.97487 + 4.34100i) q^{29} +(0.974516 + 5.96342i) q^{30} +(6.58225 + 4.78228i) q^{31} +1.00000 q^{32} +(-7.96022 - 5.78344i) q^{33} +(1.37564 - 4.23380i) q^{34} +(4.38116 + 4.33840i) q^{35} +(1.32952 + 4.09183i) q^{36} +(-0.355015 + 1.09262i) q^{37} +(0.309017 - 0.951057i) q^{38} +(-3.91882 - 12.0609i) q^{39} +(-0.360625 - 2.20680i) q^{40} +(-2.62913 + 8.09163i) q^{41} +(6.02824 + 4.37977i) q^{42} -8.29601 q^{43} +(2.94572 + 2.14019i) q^{44} +(8.55039 - 4.40959i) q^{45} +(-2.24400 + 1.63036i) q^{46} +(-0.209955 + 0.152541i) q^{47} +(-0.835056 - 2.57004i) q^{48} +0.603252 q^{49} +(-4.73990 + 1.59165i) q^{50} -12.0298 q^{51} +(1.45018 + 4.46319i) q^{52} +(4.12319 - 2.99567i) q^{53} +(2.84733 - 2.06871i) q^{54} +(3.66067 - 7.27242i) q^{55} +(-2.23078 - 1.62076i) q^{56} -2.70230 q^{57} +(-5.97487 - 4.34100i) q^{58} +(-3.26001 + 10.0333i) q^{59} +(-5.37041 + 2.76962i) q^{60} +(2.11719 + 6.51606i) q^{61} +(-2.51420 + 7.73790i) q^{62} +(3.66601 - 11.2828i) q^{63} +(0.309017 + 0.951057i) q^{64} +(9.32639 - 4.80979i) q^{65} +(3.04053 - 9.35780i) q^{66} +(8.79116 + 6.38715i) q^{67} +4.45168 q^{68} +(6.06394 + 4.40571i) q^{69} +(-2.77221 + 5.50737i) q^{70} +(5.62550 - 4.08716i) q^{71} +(-3.48072 + 2.52889i) q^{72} +(-0.202399 - 0.622920i) q^{73} -1.14885 q^{74} +(8.04868 + 10.8526i) q^{75} +1.00000 q^{76} +(-3.10253 - 9.54862i) q^{77} +(10.2596 - 7.45403i) q^{78} +(-6.82057 + 4.95544i) q^{79} +(1.98735 - 1.02491i) q^{80} +(2.74783 + 1.99642i) q^{81} -8.50804 q^{82} +(-8.01950 - 5.82651i) q^{83} +(-2.30258 + 7.08662i) q^{84} +(-1.60539 - 9.82395i) q^{85} +(-2.56361 - 7.88998i) q^{86} +(-6.16718 + 18.9806i) q^{87} +(-1.12517 + 3.46291i) q^{88} +(-5.36659 - 16.5167i) q^{89} +(6.83599 + 6.76926i) q^{90} +(3.99872 - 12.3068i) q^{91} +(-2.24400 - 1.63036i) q^{92} +21.9862 q^{93} +(-0.209955 - 0.152541i) q^{94} +(-0.360625 - 2.20680i) q^{95} +(2.18620 - 1.58837i) q^{96} +(11.8783 - 8.63010i) q^{97} +(0.186415 + 0.573727i) q^{98} -15.6656 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 5 q^{6} - 12 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) $ 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 5 * q^6 - 12 * q^7 - 10 * q^8 - 3 * q^9	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 5 q^{6} - 12 q^{7} - 10 q^{8} - 3 q^{9} - 6 q^{11} + 16 q^{13} - 2 q^{14} + 16 q^{15} - 10 q^{16} - 2 q^{17} + 22 q^{18} - 10 q^{19} - 5 q^{20} + 3 q^{21} + 14 q^{22} + 4 q^{23} - 10 q^{24} - 2 q^{25} - 34 q^{26} + 29 q^{27} + 8 q^{28} + 16 q^{30} + 19 q^{31} + 40 q^{32} - 16 q^{33} + 3 q^{34} - 24 q^{35} - 3 q^{36} + q^{37} - 10 q^{38} - 7 q^{39} + 5 q^{40} + 20 q^{41} + 3 q^{42} - 48 q^{43} + 14 q^{44} + 53 q^{45} + 4 q^{46} + 29 q^{47} + 28 q^{49} + 3 q^{50} - 122 q^{51} + 16 q^{52} - 5 q^{53} - 6 q^{54} + 56 q^{55} + 8 q^{56} - 10 q^{57} + 20 q^{59} - 19 q^{60} + 42 q^{61} - 21 q^{62} + 9 q^{63} - 10 q^{64} + 35 q^{65} + 24 q^{66} - 3 q^{67} - 2 q^{68} - 9 q^{69} - 19 q^{70} + 18 q^{71} - 8 q^{72} + 8 q^{73} - 64 q^{74} + 7 q^{75} + 40 q^{76} + 35 q^{77} - 2 q^{78} + q^{79} + 59 q^{81} - 30 q^{82} + 11 q^{83} - 7 q^{84} - 125 q^{85} + 32 q^{86} - 31 q^{87} - 6 q^{88} - 34 q^{89} - 7 q^{90} + 10 q^{91} + 4 q^{92} + 24 q^{93} + 29 q^{94} + 5 q^{95} + 5 q^{96} + 90 q^{97} - 12 q^{98} + 10 q^{99}+O(q^{100}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 5 * q^6 - 12 * q^7 - 10 * q^8 - 3 * q^9 - 6 * q^11 + 16 * q^13 - 2 * q^14 + 16 * q^15 - 10 * q^16 - 2 * q^17 + 22 * q^18 - 10 * q^19 - 5 * q^20 + 3 * q^21 + 14 * q^22 + 4 * q^23 - 10 * q^24 - 2 * q^25 - 34 * q^26 + 29 * q^27 + 8 * q^28 + 16 * q^30 + 19 * q^31 + 40 * q^32 - 16 * q^33 + 3 * q^34 - 24 * q^35 - 3 * q^36 + q^37 - 10 * q^38 - 7 * q^39 + 5 * q^40 + 20 * q^41 + 3 * q^42 - 48 * q^43 + 14 * q^44 + 53 * q^45 + 4 * q^46 + 29 * q^47 + 28 * q^49 + 3 * q^50 - 122 * q^51 + 16 * q^52 - 5 * q^53 - 6 * q^54 + 56 * q^55 + 8 * q^56 - 10 * q^57 + 20 * q^59 - 19 * q^60 + 42 * q^61 - 21 * q^62 + 9 * q^63 - 10 * q^64 + 35 * q^65 + 24 * q^66 - 3 * q^67 - 2 * q^68 - 9 * q^69 - 19 * q^70 + 18 * q^71 - 8 * q^72 + 8 * q^73 - 64 * q^74 + 7 * q^75 + 40 * q^76 + 35 * q^77 - 2 * q^78 + q^79 + 59 * q^81 - 30 * q^82 + 11 * q^83 - 7 * q^84 - 125 * q^85 + 32 * q^86 - 31 * q^87 - 6 * q^88 - 34 * q^89 - 7 * q^90 + 10 * q^91 + 4 * q^92 + 24 * q^93 + 29 * q^94 + 5 * q^95 + 5 * q^96 + 90 * q^97 - 12 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	2.18620	−	1.58837i	1.26221	−	0.917046i	0.263342	−	0.964703i	$-0.415175\pi$
$3$	2.18620	−	1.58837i	1.26221	−	0.917046i	0.998864	+	0.0476566i	$0.0151753\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	1.58887	+	1.57337i	0.710566	+	0.703630i
$5$	1.58887	+	1.57337i	0.710566	+	0.703630i
$6$	2.18620	+	1.58837i	0.892514	+	0.648449i
$7$	2.75740			1.04220			0.521100	−	0.853496i	$-0.325522\pi$
$7$	2.75740			1.04220			0.521100	+	0.853496i	$0.325522\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	1.32952	−	4.09183i	0.443172	−	1.36394i
$10$	−1.00537	+	1.99731i	−0.317926	+	0.631604i
$11$	−1.12517	−	3.46291i	−0.339250	−	1.04411i	−0.964590	−	0.263753i	$-0.915040\pi$
$11$	−1.12517	−	3.46291i	−0.339250	−	1.04411i	0.625340	−	0.780353i	$-0.284960\pi$
$12$	−0.835056	+	2.57004i	−0.241060	+	0.741906i
$13$	1.45018	−	4.46319i	0.402207	−	1.23787i	−0.520997	−	0.853558i	$-0.674440\pi$
$13$	1.45018	−	4.46319i	0.402207	−	1.23787i	0.923205	−	0.384309i	$-0.125560\pi$
$14$	0.852083	+	2.62244i	0.227729	+	0.700877i
$15$	5.97269	+	0.915978i	1.54214	+	0.236504i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−3.60148	−	2.61663i	−0.873488	−	0.634626i	0.0580324	−	0.998315i	$-0.481517\pi$
$17$	−3.60148	−	2.61663i	−0.873488	−	0.634626i	−0.931521	+	0.363688i	$0.881517\pi$
$18$	4.30241			1.01409
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i
$20$	−2.21023	−	0.338963i	−0.494222	−	0.0757944i
$21$	6.02824	−	4.37977i	1.31547	−	0.955744i
$22$	2.94572	−	2.14019i	0.628030	−	0.456291i
$23$	0.857130	+	2.63798i	0.178724	+	0.550056i	0.999784	−	0.0207861i	$-0.00661690\pi$
$23$	0.857130	+	2.63798i	0.178724	+	0.550056i	−0.821060	+	0.570842i	$0.806617\pi$
$24$	−2.70230			−0.551604
$25$	0.0490418	+	4.99976i	0.00980835	+	0.999952i
$26$	4.69288			0.920350
$27$	−1.08758	−	3.34724i	−0.209306	−	0.644176i
$28$	−2.23078	+	1.62076i	−0.421578	+	0.306295i
$29$	−5.97487	+	4.34100i	−1.10951	+	0.806103i	−0.982586	−	0.185810i	$-0.940509\pi$
$29$	−5.97487	+	4.34100i	−1.10951	+	0.806103i	−0.126920	+	0.991913i	$0.540509\pi$
$30$	0.974516	+	5.96342i	0.177921	+	1.08877i
$31$	6.58225	+	4.78228i	1.18221	+	0.858924i	0.992419	−	0.122901i	$-0.0392199\pi$
$31$	6.58225	+	4.78228i	1.18221	+	0.858924i	0.189788	+	0.981825i	$0.439220\pi$
$32$	1.00000			0.176777
$33$	−7.96022	−	5.78344i	−1.38570	−	1.00677i
$34$	1.37564	−	4.23380i	0.235921	−	0.726091i
$35$	4.38116	+	4.33840i	0.740551	+	0.733323i
$36$	1.32952	+	4.09183i	0.221586	+	0.681972i
$37$	−0.355015	+	1.09262i	−0.0583640	+	0.179626i	−0.975988	−	0.217823i	$-0.930104\pi$
$37$	−0.355015	+	1.09262i	−0.0583640	+	0.179626i	0.917624	+	0.397449i	$0.130104\pi$
$38$	0.309017	−	0.951057i	0.0501292	−	0.154282i
$39$	−3.91882	−	12.0609i	−0.627513	−	1.93129i
$40$	−0.360625	−	2.20680i	−0.0570198	−	0.348925i
$41$	−2.62913	+	8.09163i	−0.410601	+	1.26370i	0.505525	+	0.862812i	$0.331299\pi$
$41$	−2.62913	+	8.09163i	−0.410601	+	1.26370i	−0.916127	+	0.400889i	$0.868701\pi$
$42$	6.02824	+	4.37977i	0.930177	+	0.675813i
$43$	−8.29601			−1.26513			−0.632565	−	0.774507i	$-0.717998\pi$
$43$	−8.29601			−1.26513			−0.632565	+	0.774507i	$0.717998\pi$
$44$	2.94572	+	2.14019i	0.444085	+	0.322646i
$45$	8.55039	−	4.40959i	1.27462	−	0.657343i
$46$	−2.24400	+	1.63036i	−0.330859	+	0.240383i
$47$	−0.209955	+	0.152541i	−0.0306251	+	0.0222504i	−0.602992	−	0.797747i	$-0.706025\pi$
$47$	−0.209955	+	0.152541i	−0.0306251	+	0.0222504i	0.572367	+	0.819997i	$0.306025\pi$
$48$	−0.835056	−	2.57004i	−0.120530	−	0.370953i
$49$	0.603252			0.0861788
$50$	−4.73990	+	1.59165i	−0.670323	+	0.225094i
$51$	−12.0298			−1.68450
$52$	1.45018	+	4.46319i	0.201104	+	0.618934i
$53$	4.12319	−	2.99567i	0.566364	−	0.411487i	−0.267419	−	0.963580i	$-0.586171\pi$
$53$	4.12319	−	2.99567i	0.566364	−	0.411487i	0.833782	+	0.552093i	$0.186171\pi$
$54$	2.84733	−	2.06871i	0.387473	−	0.281515i
$55$	3.66067	−	7.27242i	0.493605	−	0.980613i
$56$	−2.23078	−	1.62076i	−0.298101	−	0.216583i
$57$	−2.70230			−0.357928
$58$	−5.97487	−	4.34100i	−0.784539	−	0.570001i
$59$	−3.26001	+	10.0333i	−0.424417	+	1.30622i	0.479135	+	0.877741i	$0.340950\pi$
$59$	−3.26001	+	10.0333i	−0.424417	+	1.30622i	−0.903552	+	0.428479i	$0.859050\pi$
$60$	−5.37041	+	2.76962i	−0.693316	+	0.357556i
$61$	2.11719	+	6.51606i	0.271079	+	0.834295i	0.990230	+	0.139442i	$0.0445308\pi$
$61$	2.11719	+	6.51606i	0.271079	+	0.834295i	−0.719151	+	0.694854i	$0.755469\pi$
$62$	−2.51420	+	7.73790i	−0.319303	+	0.982714i
$63$	3.66601	−	11.2828i	0.461874	−	1.42150i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	9.32639	−	4.80979i	1.15680	−	0.596581i
$66$	3.04053	−	9.35780i	0.374264	−	1.15187i
$67$	8.79116	+	6.38715i	1.07401	+	0.780315i	0.976629	−	0.214933i	$-0.0689532\pi$
$67$	8.79116	+	6.38715i	1.07401	+	0.780315i	0.0973820	+	0.995247i	$0.468953\pi$
$68$	4.45168			0.539845
$69$	6.06394	+	4.40571i	0.730013	+	0.530385i
$70$	−2.77221	+	5.50737i	−0.331342	+	0.658257i
$71$	5.62550	−	4.08716i	0.667624	−	0.485057i	−0.201605	−	0.979467i	$-0.564616\pi$
$71$	5.62550	−	4.08716i	0.667624	−	0.485057i	0.869229	+	0.494410i	$0.164616\pi$
$72$	−3.48072	+	2.52889i	−0.410207	+	0.298033i
$73$	−0.202399	−	0.622920i	−0.0236890	−	0.0729073i	0.938513	−	0.345244i	$-0.112204\pi$
$73$	−0.202399	−	0.622920i	−0.0236890	−	0.0729073i	−0.962202	+	0.272336i	$0.912204\pi$
$74$	−1.14885			−0.133551
$75$	8.04868	+	10.8526i	0.929382	+	1.25315i
$76$	1.00000			0.114708
$77$	−3.10253	−	9.54862i	−0.353566	−	1.08817i
$78$	10.2596	−	7.45403i	1.16167	−	0.844003i
$79$	−6.82057	+	4.95544i	−0.767375	+	0.557530i	−0.901163	−	0.433480i	$-0.857286\pi$
$79$	−6.82057	+	4.95544i	−0.767375	+	0.557530i	0.133789	+	0.991010i	$0.457286\pi$
$80$	1.98735	−	1.02491i	0.222192	−	0.114589i
$81$	2.74783	+	1.99642i	0.305315	+	0.221824i
$82$	−8.50804			−0.939556
$83$	−8.01950	−	5.82651i	−0.880255	−	0.639542i	0.0530641	−	0.998591i	$-0.483101\pi$
$83$	−8.01950	−	5.82651i	−0.880255	−	0.639542i	−0.933319	+	0.359049i	$0.883101\pi$
$84$	−2.30258	+	7.08662i	−0.251232	+	0.773214i
$85$	−1.60539	−	9.82395i	−0.174129	−	1.06556i
$86$	−2.56361	−	7.88998i	−0.276441	−	0.850798i
$87$	−6.16718	+	18.9806i	−0.661191	+	2.03494i
$88$	−1.12517	+	3.46291i	−0.119943	+	0.369147i
$89$	−5.36659	−	16.5167i	−0.568858	−	1.75076i	−0.656202	−	0.754585i	$-0.727838\pi$
$89$	−5.36659	−	16.5167i	−0.568858	−	1.75076i	0.0873444	−	0.996178i	$-0.472162\pi$
$90$	6.83599	+	6.76926i	0.720576	+	0.713543i
$91$	3.99872	−	12.3068i	0.419180	−	1.29010i
$92$	−2.24400	−	1.63036i	−0.233953	−	0.169977i
$93$	21.9862			2.27986
$94$	−0.209955	−	0.152541i	−0.0216552	−	0.0157334i
$95$	−0.360625	−	2.20680i	−0.0369994	−	0.226413i
$96$	2.18620	−	1.58837i	0.223129	−	0.162112i
$97$	11.8783	−	8.63010i	1.20606	−	0.876254i	0.211193	−	0.977444i	$-0.432265\pi$
$97$	11.8783	−	8.63010i	1.20606	−	0.876254i	0.994867	+	0.101190i	$0.0322651\pi$
$98$	0.186415	+	0.573727i	0.0188308	+	0.0579551i
$99$	−15.6656			−1.57445
$100$	−2.97846	−	4.01606i	−0.297846	−	0.401606i
$101$	−3.76472			−0.374604			−0.187302	−	0.982302i	$-0.559974\pi$
$101$	−3.76472			−0.374604			−0.187302	+	0.982302i	$0.559974\pi$
$102$	−3.71740	−	11.4410i	−0.368077	−	1.13283i
$103$	7.88390	−	5.72799i	0.776824	−	0.564396i	−0.127200	−	0.991877i	$-0.540599\pi$
$103$	7.88390	−	5.72799i	0.776824	−	0.564396i	0.904024	+	0.427481i	$0.140599\pi$
$104$	−3.79662	+	2.75841i	−0.372289	+	0.270484i
$105$	16.4691	+	2.52572i	1.60722	+	0.246485i
$106$	4.12319	+	2.99567i	0.400480	+	0.290965i
$107$	−13.0739			−1.26390			−0.631952	−	0.775008i	$-0.717746\pi$
$107$	−13.0739			−1.26390			−0.631952	+	0.775008i	$0.717746\pi$
$108$	2.84733	+	2.06871i	0.273985	+	0.199061i
$109$	−2.41799	+	7.44182i	−0.231602	+	0.712797i	0.765952	+	0.642897i	$0.222268\pi$
$109$	−2.41799	+	7.44182i	−0.231602	+	0.712797i	−0.997554	+	0.0698993i	$0.977732\pi$
$110$	8.04769	+	1.23420i	0.767317	+	0.117677i
$111$	0.959355	+	2.95259i	0.0910579	+	0.280248i
$112$	0.852083	−	2.62244i	0.0805143	−	0.247798i
$113$	0.0237756	−	0.0731737i	0.00223662	−	0.00688360i	−0.949932	−	0.312457i	$-0.898848\pi$
$113$	0.0237756	−	0.0731737i	0.00223662	−	0.00688360i	0.952169	+	0.305573i	$0.0988481\pi$
$114$	−0.835056	−	2.57004i	−0.0782101	−	0.240706i
$115$	−2.78863	+	5.53999i	−0.260041	+	0.516607i
$116$	2.28220	−	7.02388i	0.211897	−	0.652151i
$117$	−16.3346	−	11.8678i	−1.51014	−	1.09718i
$118$	−10.5496			−0.971169
$119$	−9.93073	−	7.21510i	−0.910349	−	0.661407i
$120$	−4.29361	−	4.25170i	−0.391951	−	0.388125i
$121$	−1.82653	+	1.32705i	−0.166048	+	0.120641i
$122$	−5.54289	+	4.02714i	−0.501830	+	0.364600i
$123$	7.10469	+	21.8660i	0.640608	+	1.97159i
$124$	−8.13611			−0.730644
$125$	−7.78853	+	8.02115i	−0.696627	+	0.717433i
$126$	11.8635			1.05688
$127$	−1.05635	−	3.25111i	−0.0937358	−	0.288489i	0.893186	−	0.449687i	$-0.148464\pi$
$127$	−1.05635	−	3.25111i	−0.0937358	−	0.288489i	−0.986922	+	0.161197i	$0.948464\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−18.1368	+	13.1771i	−1.59685	+	1.16018i
$130$	7.45640	+	7.38362i	0.653969	+	0.647586i
$131$	6.89014	+	5.00598i	0.601994	+	0.437374i	0.846586	−	0.532252i	$-0.178654\pi$
$131$	6.89014	+	5.00598i	0.601994	+	0.437374i	−0.244592	+	0.969626i	$0.578654\pi$
$132$	9.83937			0.856408
$133$	−2.23078	−	1.62076i	−0.193433	−	0.140538i
$134$	−3.35792	+	10.3346i	−0.290080	+	0.892776i
$135$	3.53840	−	7.02951i	0.304537	−	0.605004i
$136$	1.37564	+	4.23380i	0.117961	+	0.363045i
$137$	1.09467	−	3.36906i	0.0935243	−	0.287838i	−0.893342	−	0.449378i	$-0.851646\pi$
$137$	1.09467	−	3.36906i	0.0935243	−	0.287838i	0.986866	+	0.161539i	$0.0516458\pi$
$138$	−2.31622	+	7.12859i	−0.197170	+	0.606826i
$139$	2.80818	+	8.64270i	0.238187	+	0.733064i	0.996683	+	0.0813860i	$0.0259347\pi$
$139$	2.80818	+	8.64270i	0.238187	+	0.733064i	−0.758496	+	0.651678i	$0.774065\pi$
$140$	−6.09448	−	0.934656i	−0.515078	−	0.0789928i
$141$	−0.216712	+	0.666972i	−0.0182505	+	0.0561692i
$142$	5.62550	+	4.08716i	0.472081	+	0.342987i
$143$	−17.0873			−1.42891
$144$	−3.48072	−	2.52889i	−0.290060	−	0.210741i
$145$	−16.3233	−	2.50336i	−1.35558	−	0.207892i
$146$	0.529888	−	0.384986i	0.0438538	−	0.0318617i
$147$	1.31883	−	0.958187i	0.108775	−	0.0790299i
$148$	−0.355015	−	1.09262i	−0.0291820	−	0.0898130i
$149$	19.4014			1.58943			0.794714	−	0.606984i	$-0.207621\pi$
$149$	19.4014			1.58943			0.794714	+	0.606984i	$0.207621\pi$
$150$	−7.83425	+	11.0084i	−0.639664	+	0.898831i
$151$	−12.0276			−0.978791			−0.489396	−	0.872062i	$-0.662783\pi$
$151$	−12.0276			−0.978791			−0.489396	+	0.872062i	$0.662783\pi$
$152$	0.309017	+	0.951057i	0.0250646	+	0.0771409i
$153$	−15.4951	+	11.2578i	−1.25270	+	0.910141i
$154$	8.12254	−	5.90137i	0.654533	−	0.475546i
$155$	2.93408	+	17.9547i	0.235671	+	1.44216i
$156$	10.2596	+	7.45403i	0.821425	+	0.596800i
$157$	−1.75157			−0.139791			−0.0698954	−	0.997554i	$-0.522267\pi$
$157$	−1.75157			−0.139791			−0.0698954	+	0.997554i	$0.522267\pi$
$158$	−6.82057	−	4.95544i	−0.542616	−	0.394233i
$159$	4.25590	−	13.0983i	0.337515	−	1.03876i
$160$	1.58887	+	1.57337i	0.125612	+	0.124385i
$161$	2.36345	+	7.27395i	0.186266	+	0.573268i
$162$	−1.04958	+	3.23027i	−0.0824626	+	0.253794i
$163$	−5.63653	+	17.3475i	−0.441487	+	1.35876i	0.444803	+	0.895629i	$0.353274\pi$
$163$	−5.63653	+	17.3475i	−0.441487	+	1.35876i	−0.886290	+	0.463130i	$0.846726\pi$
$164$	−2.62913	−	8.09163i	−0.205301	−	0.631850i
$165$	−3.54833	−	21.7135i	−0.276237	−	1.69039i
$166$	3.06318	−	9.42749i	0.237749	−	0.731715i
$167$	−8.89830	−	6.46499i	−0.688571	−	0.500276i	0.187619	−	0.982242i	$-0.439923\pi$
$167$	−8.89830	−	6.46499i	−0.688571	−	0.500276i	−0.876190	+	0.481966i	$0.839923\pi$
$168$	−7.45131			−0.574881
$169$	−7.29986	−	5.30366i	−0.561528	−	0.407974i
$170$	8.84704	−	4.56258i	0.678537	−	0.349934i
$171$	−3.48072	+	2.52889i	−0.266177	+	0.193389i
$172$	6.71161	−	4.87627i	0.511756	−	0.371812i
$173$	−0.491247	−	1.51190i	−0.0373488	−	0.114948i	0.930644	−	0.365926i	$-0.119248\pi$
$173$	−0.491247	−	1.51190i	−0.0373488	−	0.114948i	−0.967993	+	0.250978i	$0.919248\pi$
$174$	−19.9574			−1.51297
$175$	0.135228	+	13.7863i	0.0102223	+	1.04215i
$176$	−3.64112			−0.274459
$177$	8.80950	+	27.1129i	0.662163	+	2.03793i
$178$	14.0499	−	10.2079i	1.05309	−	0.765112i
$179$	−7.60664	+	5.52655i	−0.568547	+	0.413074i	−0.834577	−	0.550891i	$-0.814288\pi$
$179$	−7.60664	+	5.52655i	−0.568547	+	0.413074i	0.266030	+	0.963965i	$0.414288\pi$
$180$	−4.32551	+	8.59323i	−0.322405	+	0.640501i
$181$	−14.3853	−	10.4515i	−1.06925	−	0.776855i	−0.0934717	−	0.995622i	$-0.529796\pi$
$181$	−14.3853	−	10.4515i	−1.06925	−	0.776855i	−0.975777	+	0.218767i	$0.929796\pi$
$182$	12.9401			0.959187
$183$	14.9785	+	10.8825i	1.10724	+	0.804460i
$184$	0.857130	−	2.63798i	0.0631885	−	0.194474i
$185$	−2.28317	+	1.17747i	−0.167862	+	0.0865695i
$186$	6.79410	+	20.9101i	0.498168	+	1.53320i
$187$	−5.00888	+	15.4157i	−0.366286	+	1.12731i
$188$	0.0801956	−	0.246817i	0.00584887	−	0.0180010i
$189$	−2.99890	−	9.22967i	−0.218138	−	0.671360i
$190$	1.98735	−	1.02491i	0.144177	−	0.0743550i
$191$	4.35231	−	13.3950i	0.314922	−	0.969230i	−0.660865	−	0.750505i	$-0.729810\pi$
$191$	4.35231	−	13.3950i	0.314922	−	0.969230i	0.975787	−	0.218725i	$-0.0701897\pi$
$192$	2.18620	+	1.58837i	0.157776	+	0.114631i
$193$	14.3563			1.03339			0.516694	−	0.856170i	$-0.327162\pi$
$193$	14.3563			1.03339			0.516694	+	0.856170i	$0.327162\pi$
$194$	11.8783	+	8.63010i	0.852813	+	0.619605i
$195$	12.7497	−	25.3289i	0.913022	−	1.81384i
$196$	−0.488041	+	0.354582i	−0.0348601	+	0.0253273i
$197$	−4.89741	+	3.55818i	−0.348926	+	0.253510i	−0.748418	−	0.663227i	$-0.769186\pi$
$197$	−4.89741	+	3.55818i	−0.348926	+	0.253510i	0.399492	+	0.916737i	$0.369186\pi$
$198$	−4.84093	−	14.8988i	−0.344030	−	1.05881i
$199$	−4.02546			−0.285357			−0.142678	−	0.989769i	$-0.545571\pi$
$199$	−4.02546			−0.285357			−0.142678	+	0.989769i	$0.545571\pi$
$200$	2.89911	−	4.07372i	0.204998	−	0.288055i
$201$	29.3644			2.07121
$202$	−1.16336	−	3.58047i	−0.0818540	−	0.251921i
$203$	−16.4751	+	11.9699i	−1.15633	+	0.840120i
$204$	9.73228	−	7.07092i	0.681396	−	0.495063i
$205$	−16.9085	+	8.72000i	−1.18094	+	0.609031i
$206$	7.88390	+	5.72799i	0.549298	+	0.399088i
$207$	11.9337			0.829451
$208$	−3.79662	−	2.75841i	−0.263248	−	0.191261i
$209$	−1.12517	+	3.46291i	−0.0778294	+	0.239534i
$210$	2.68713	+	16.4435i	0.185430	+	1.13471i
$211$	−6.98208	−	21.4886i	−0.480666	−	1.47934i	−0.838161	−	0.545423i	$-0.816369\pi$
$211$	−6.98208	−	21.4886i	−0.480666	−	1.47934i	0.357494	−	0.933915i	$-0.383631\pi$
$212$	−1.57492	+	4.84710i	−0.108166	+	0.332900i
$213$	5.80656	−	17.8707i	0.397859	−	1.22448i
$214$	−4.04006	−	12.4340i	−0.276173	−	0.849973i
$215$	−13.1813	−	13.0527i	−0.898958	−	0.890184i
$216$	−1.08758	+	3.34724i	−0.0740007	+	0.227751i
$217$	18.1499	+	13.1867i	1.23210	+	0.895169i
$218$	−7.82479			−0.529961
$219$	−1.43191	−	1.04035i	−0.0967598	−	0.0703001i
$220$	1.31308	+	8.03520i	0.0885277	+	0.541733i
$221$	−16.9013	+	12.2795i	−1.13691	+	0.826011i
$222$	−2.51162	+	1.82480i	−0.168569	+	0.122473i
$223$	3.92636	+	12.0841i	0.262928	+	0.809210i	0.992163	+	0.124947i	$0.0398761\pi$
$223$	3.92636	+	12.0841i	0.262928	+	0.809210i	−0.729235	+	0.684263i	$0.760124\pi$
$224$	2.75740			0.184237
$225$	20.5234	+	6.44660i	1.36823	+	0.429773i
$226$	0.0769394			0.00511793
$227$	−8.13850	−	25.0477i	−0.540171	−	1.66248i	−0.732202	−	0.681087i	$-0.761507\pi$
$227$	−8.13850	−	25.0477i	−0.540171	−	1.66248i	0.192031	−	0.981389i	$-0.438493\pi$
$228$	2.18620	−	1.58837i	0.144785	−	0.105192i
$229$	17.2248	−	12.5145i	1.13825	−	0.826984i	0.151373	−	0.988477i	$-0.451631\pi$
$229$	17.2248	−	12.5145i	1.13825	−	0.826984i	0.986874	+	0.161492i	$0.0516307\pi$
$230$	−6.13058	−	0.940191i	−0.404238	−	0.0619944i
$231$	−21.9495	−	15.9473i	−1.44417	−	1.04925i
$232$	7.38535			0.484872
$233$	18.8454	+	13.6920i	1.23460	+	0.896993i	0.997227	−	0.0744249i	$-0.0237121\pi$
$233$	18.8454	+	13.6920i	1.23460	+	0.896993i	0.237378	+	0.971417i	$0.423712\pi$
$234$	6.23927	−	19.2025i	0.407874	−	1.25531i
$235$	−0.573595	−	0.0879671i	−0.0374172	−	0.00573834i
$236$	−3.26001	−	10.0333i	−0.212208	−	0.653110i
$237$	−7.04010	+	21.6672i	−0.457304	+	1.40744i
$238$	3.79320	−	11.6743i	0.245877	−	0.756731i
$239$	−6.94171	−	21.3644i	−0.449022	−	1.38195i	−0.878012	−	0.478639i	$-0.841130\pi$
$239$	−6.94171	−	21.3644i	−0.449022	−	1.38195i	0.428990	−	0.903309i	$-0.358870\pi$
$240$	2.71681	−	5.39731i	0.175369	−	0.348395i
$241$	5.53867	−	17.0463i	0.356777	−	1.09805i	−0.598195	−	0.801351i	$-0.704115\pi$
$241$	5.53867	−	17.0463i	0.356777	−	1.09805i	0.954972	−	0.296697i	$-0.0958850\pi$
$242$	−1.82653	−	1.32705i	−0.117414	−	0.0853062i
$243$	19.7369			1.26612
$244$	−5.54289	−	4.02714i	−0.354847	−	0.257811i
$245$	0.958491	+	0.949136i	0.0612358	+	0.0606380i
$246$	−18.6003	+	13.5139i	−1.18591	+	0.861616i
$247$	−3.79662	+	2.75841i	−0.241573	+	0.175513i
$248$	−2.51420	−	7.73790i	−0.159652	−	0.491357i
$249$	−26.7869			−1.69755
$250$	−10.0354	−	4.92866i	−0.634691	−	0.311716i
$251$	−2.75135			−0.173664			−0.0868319	−	0.996223i	$-0.527674\pi$
$251$	−2.75135			−0.173664			−0.0868319	+	0.996223i	$0.527674\pi$
$252$	3.66601	+	11.2828i	0.230937	+	0.710751i
$253$	8.17065	−	5.93632i	0.513684	−	0.373213i
$254$	2.76556	−	2.00930i	0.173527	−	0.126074i
$255$	−19.1138	−	18.9272i	−1.19695	−	1.18527i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−15.7881			−0.984832			−0.492416	−	0.870360i	$-0.663886\pi$
$257$	−15.7881			−0.984832			−0.492416	+	0.870360i	$0.663886\pi$
$258$	−18.1368	−	13.1771i	−1.12915	−	0.820373i
$259$	−0.978917	+	3.01280i	−0.0608270	+	0.187206i
$260$	−4.71808	+	9.37312i	−0.292603	+	0.581296i
$261$	9.81895	+	30.2196i	0.607778	+	1.87055i
$262$	−2.63180	+	8.09984i	−0.162593	+	0.500410i
$263$	−8.84467	+	27.2211i	−0.545386	+	1.67853i	0.174685	+	0.984624i	$0.444109\pi$
$263$	−8.84467	+	27.2211i	−0.545386	+	1.67853i	−0.720071	+	0.693901i	$0.755891\pi$
$264$	3.04053	+	9.35780i	0.187132	+	0.575933i
$265$	11.2645	+	1.72754i	0.691974	+	0.106122i
$266$	0.852083	−	2.62244i	0.0522446	−	0.160792i
$267$	−37.9671	−	27.5847i	−2.32355	−	1.68815i
$268$	−10.8665			−0.663775
$269$	6.44719	+	4.68416i	0.393092	+	0.285598i	0.766721	−	0.641980i	$-0.221887\pi$
$269$	6.44719	+	4.68416i	0.393092	+	0.285598i	−0.373629	+	0.927578i	$0.621887\pi$
$270$	7.77888	+	1.19298i	0.473408	+	0.0726023i
$271$	16.8112	−	12.2140i	1.02121	−	0.741950i	0.0546772	−	0.998504i	$-0.482587\pi$
$271$	16.8112	−	12.2140i	1.02121	−	0.741950i	0.966530	+	0.256554i	$0.0825870\pi$
$272$	−3.60148	+	2.61663i	−0.218372	+	0.158657i
$273$	−10.8057	−	33.2567i	−0.653993	−	2.01278i
$274$	3.54244			0.214007
$275$	17.2585	−	5.79539i	1.04073	−	0.349475i
$276$	−7.49545			−0.451173
$277$	−1.33976	−	4.12336i	−0.0804984	−	0.247749i	0.902706	−	0.430259i	$-0.141578\pi$
$277$	−1.33976	−	4.12336i	−0.0804984	−	0.247749i	−0.983204	+	0.182510i	$0.941578\pi$
$278$	−7.35192	+	5.34148i	−0.440939	+	0.320361i
$279$	28.3195	−	20.5753i	1.69545	−	1.23181i
$280$	−0.994387	−	6.08502i	−0.0594260	−	0.363649i
$281$	−20.2620	−	14.7212i	−1.20873	−	0.878193i	−0.213614	−	0.976918i	$-0.568524\pi$
$281$	−20.2620	−	14.7212i	−1.20873	−	0.878193i	−0.995115	+	0.0987252i	$0.968524\pi$
$282$	−0.701296			−0.0417616
$283$	21.7011	+	15.7668i	1.29000	+	0.937238i	0.999805	−	0.0197299i	$-0.00628064\pi$
$283$	21.7011	+	15.7668i	1.29000	+	0.937238i	0.290193	+	0.956968i	$0.406281\pi$
$284$	−2.14875	+	6.61317i	−0.127505	+	0.392419i
$285$	−4.29361	−	4.25170i	−0.254331	−	0.251849i
$286$	−5.28027	−	16.2510i	−0.312229	−	0.960942i
$287$	−7.24956	+	22.3119i	−0.427928	+	1.31703i
$288$	1.32952	−	4.09183i	0.0783426	−	0.241114i
$289$	0.870640	+	2.67955i	0.0512141	+	0.157621i
$290$	−2.66334	−	16.2980i	−0.156397	−	0.957049i
$291$	12.2606	−	37.7343i	0.718731	−	2.21203i
$292$	0.529888	+	0.384986i	0.0310093	+	0.0225296i
$293$	11.1395			0.650779			0.325390	−	0.945580i	$-0.394505\pi$
$293$	11.1395			0.650779			0.325390	+	0.945580i	$0.394505\pi$
$294$	1.31883	+	0.958187i	0.0769158	+	0.0558826i
$295$	−20.9657	+	10.8124i	−1.22067	+	0.629523i
$296$	0.929440	−	0.675278i	0.0540226	−	0.0392497i
$297$	−10.3675	+	7.53240i	−0.601581	+	0.437074i
$298$	5.99537	+	18.4519i	0.347303	+	1.06889i
$299$	13.0168			0.752780
$300$	−12.8905	−	4.04904i	−0.744235	−	0.233771i
$301$	−22.8754			−1.31852
$302$	−3.71673	−	11.4389i	−0.213874	−	0.658236i
$303$	−8.23046	+	5.97978i	−0.472827	+	0.343529i
$304$	−0.809017	+	0.587785i	−0.0464003	+	0.0337118i
$305$	−6.88818	+	13.6843i	−0.394416	+	0.783562i
$306$	−15.4951	−	11.2578i	−0.885793	−	0.643567i
$307$	17.2808			0.986268			0.493134	−	0.869953i	$-0.335851\pi$
$307$	17.2808			0.986268			0.493134	+	0.869953i	$0.335851\pi$
$308$	8.12254	+	5.90137i	0.462825	+	0.336262i
$309$	8.13765	−	25.0451i	0.462935	−	1.42477i
$310$	−16.1693	+	8.33880i	−0.918354	+	0.473612i
$311$	0.826872	+	2.54485i	0.0468876	+	0.144305i	0.971759	−	0.235974i	$-0.0758280\pi$
$311$	0.826872	+	2.54485i	0.0468876	+	0.144305i	−0.924872	+	0.380279i	$0.875828\pi$
$312$	−3.91882	+	12.0609i	−0.221859	+	0.682813i
$313$	5.34242	−	16.4423i	0.301971	−	0.929372i	−0.678819	−	0.734306i	$-0.737508\pi$
$313$	5.34242	−	16.4423i	0.301971	−	0.929372i	0.980790	−	0.195066i	$-0.0624921\pi$
$314$	−0.541266	−	1.66584i	−0.0305454	−	0.0940090i
$315$	23.5768	−	12.1590i	1.32840	−	0.685082i
$316$	2.60523	−	8.01807i	0.146555	−	0.451051i
$317$	−3.47272	−	2.52308i	−0.195047	−	0.141710i	0.485975	−	0.873973i	$-0.338464\pi$
$317$	−3.47272	−	2.52308i	−0.195047	−	0.141710i	−0.681023	+	0.732262i	$0.738464\pi$
$318$	13.7724			0.772316
$319$	21.7552	+	15.8061i	1.21806	+	0.884970i
$320$	−1.00537	+	1.99731i	−0.0562019	+	0.111653i
$321$	−28.5823	+	20.7662i	−1.59531	+	1.15906i
$322$	−6.18759	+	4.49555i	−0.344821	+	0.250527i
$323$	1.37564	+	4.23380i	0.0765429	+	0.235575i
$324$	−3.39651			−0.188695
$325$	22.3860	+	7.03167i	1.24175	+	0.390047i
$326$	−18.2402			−1.01023
$327$	6.53413	+	20.1100i	0.361338	+	1.11209i
$328$	6.88315	−	5.00090i	0.380059	−	0.276129i
$329$	−0.578929	+	0.420617i	−0.0319174	+	0.0231894i
$330$	19.5543	−	10.0845i	1.07643	−	0.555133i
$331$	−25.5491	−	18.5625i	−1.40430	−	1.02029i	−0.994120	−	0.108285i	$-0.965464\pi$
$331$	−25.5491	−	18.5625i	−1.40430	−	1.02029i	−0.410185	−	0.912002i	$-0.634536\pi$
$332$	9.91265			0.544027
$333$	3.99883	+	2.90532i	0.219135	+	0.159211i
$334$	3.39885	−	10.4606i	0.185977	−	0.572377i
$335$	3.91872	+	23.9801i	0.214103	+	1.31017i
$336$	−2.30258	−	7.08662i	−0.125616	−	0.386607i
$337$	−4.96981	+	15.2955i	−0.270723	+	0.833200i	0.719596	+	0.694392i	$0.244327\pi$
$337$	−4.96981	+	15.2955i	−0.270723	+	0.833200i	−0.990319	+	0.138807i	$0.955673\pi$
$338$	2.78830	−	8.58150i	0.151663	−	0.466772i
$339$	−0.0642487	−	0.197737i	−0.00348951	−	0.0107396i
$340$	7.07316	+	7.00412i	0.383596	+	0.379852i
$341$	9.15448	−	28.1746i	0.495743	−	1.52574i
$342$	−3.48072	−	2.52889i	−0.188216	−	0.136747i
$343$	−17.6384			−0.952384
$344$	6.71161	+	4.87627i	0.361866	+	0.262911i
$345$	2.70305	+	16.5409i	0.145527	+	0.890533i
$346$	1.28610	−	0.934407i	0.0691412	−	0.0502340i
$347$	−1.38451	+	1.00590i	−0.0743242	+	0.0539997i	−0.624327	−	0.781163i	$-0.714627\pi$
$347$	−1.38451	+	1.00590i	−0.0743242	+	0.0539997i	0.550003	+	0.835163i	$0.314627\pi$
$348$	−6.16718	−	18.9806i	−0.330595	−	1.01747i
$349$	−0.698736			−0.0374025			−0.0187013	−	0.999825i	$-0.505953\pi$
$349$	−0.698736			−0.0374025			−0.0187013	+	0.999825i	$0.505953\pi$
$350$	−13.0698	+	4.38882i	−0.698610	+	0.234592i
$351$	−16.5166			−0.881589
$352$	−1.12517	−	3.46291i	−0.0599716	−	0.184574i
$353$	−0.324538	+	0.235791i	−0.0172734	+	0.0125499i	−0.596388	−	0.802696i	$-0.703398\pi$
$353$	−0.324538	+	0.235791i	−0.0172734	+	0.0125499i	0.579115	+	0.815246i	$0.303398\pi$
$354$	−23.0636	+	16.7567i	−1.22582	+	0.890607i
$355$	15.3688	+	2.35698i	0.815692	+	0.125095i
$356$	14.0499	+	10.2079i	0.744644	+	0.541016i
$357$	−33.1709			−1.75559
$358$	−7.60664	−	5.52655i	−0.402024	−	0.292087i
$359$	6.67106	−	20.5314i	0.352085	−	1.08361i	−0.605595	−	0.795773i	$-0.707065\pi$
$359$	6.67106	−	20.5314i	0.352085	−	1.08361i	0.957680	−	0.287834i	$-0.0929350\pi$
$360$	−9.50930	−	1.45836i	−0.501184	−	0.0768621i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	5.49468	−	16.9109i	0.288794	−	0.888817i
$363$	−1.88532	+	5.80242i	−0.0989537	+	0.304548i
$364$	3.99872	+	12.3068i	0.209590	+	0.645052i
$365$	0.658495	−	1.30819i	0.0344672	−	0.0684738i
$366$	−5.72129	+	17.6083i	−0.299057	+	0.920402i
$367$	−27.8243	−	20.2155i	−1.45242	−	1.05524i	−0.985260	−	0.171066i	$-0.945279\pi$
$367$	−27.8243	−	20.2155i	−1.45242	−	1.05524i	−0.467156	−	0.884175i	$-0.654721\pi$
$368$	2.77373			0.144591
$369$	29.6141	+	21.5159i	1.54165	+	1.12007i
$370$	−1.82538	−	1.80756i	−0.0948970	−	0.0939707i
$371$	11.3693	−	8.26027i	0.590264	−	0.428852i
$372$	−17.7872	+	12.9232i	−0.922223	+	0.670034i
$373$	−4.29482	−	13.2181i	−0.222377	−	0.684407i	−0.998547	−	0.0538830i	$-0.982840\pi$
$373$	−4.29482	−	13.2181i	−0.222377	−	0.684407i	0.776170	−	0.630524i	$-0.217160\pi$
$374$	−16.2091			−0.838151
$375$	−4.28676	+	29.9069i	−0.221367	+	1.54439i
$376$	0.259518			0.0133836
$377$	10.7101	+	32.9622i	0.551597	+	1.69764i
$378$	7.85123	−	5.70425i	0.403824	−	0.293395i
$379$	10.3940	−	7.55171i	0.533906	−	0.387905i	−0.287911	−	0.957657i	$-0.592961\pi$
$379$	10.3940	−	7.55171i	0.533906	−	0.387905i	0.821817	+	0.569752i	$0.192961\pi$
$380$	1.58887	+	1.57337i	0.0815075	+	0.0807119i
$381$	−7.47336	−	5.42971i	−0.382872	−	0.278173i
$382$	14.0844			0.720619
$383$	2.61778	+	1.90192i	0.133762	+	0.0971838i	0.652654	−	0.757656i	$-0.273655\pi$
$383$	2.61778	+	1.90192i	0.133762	+	0.0971838i	−0.518892	+	0.854840i	$0.673655\pi$
$384$	−0.835056	+	2.57004i	−0.0426138	+	0.131152i
$385$	10.0939	−	20.0530i	0.514434	−	1.02199i
$386$	4.43634	+	13.6536i	0.225804	+	0.694952i
$387$	−11.0297	+	33.9459i	−0.560671	+	1.72557i
$388$	−4.53711	+	13.9638i	−0.230337	+	0.708904i
$389$	7.43370	+	22.8786i	0.376904	+	1.15999i	0.942185	+	0.335092i	$0.108767\pi$
$389$	7.43370	+	22.8786i	0.376904	+	1.15999i	−0.565282	+	0.824898i	$0.691233\pi$
$390$	28.0291	+	4.29857i	1.41931	+	0.217667i
$391$	3.81567	−	11.7434i	0.192967	−	0.593890i
$392$	−0.488041	−	0.354582i	−0.0246498	−	0.0179091i
$393$	23.0146			1.16093
$394$	−4.89741	−	3.55818i	−0.246728	−	0.179258i
$395$	−18.6337	−	2.85769i	−0.937566	−	0.143786i
$396$	12.6737	−	9.20799i	0.636878	−	0.462719i
$397$	19.5192	−	14.1815i	0.979642	−	0.711751i	0.0220133	−	0.999758i	$-0.492992\pi$
$397$	19.5192	−	14.1815i	0.979642	−	0.711751i	0.957629	+	0.288006i	$0.0929924\pi$
$398$	−1.24393	−	3.82844i	−0.0623528	−	0.191902i
$399$	−7.45131			−0.373032
$400$	4.77021	+	1.49837i	0.238510	+	0.0749185i
$401$	−21.1428			−1.05582			−0.527911	−	0.849300i	$-0.677024\pi$
$401$	−21.1428			−1.05582			−0.527911	+	0.849300i	$0.677024\pi$
$402$	9.07411	+	27.9272i	0.452575	+	1.39288i
$403$	30.8897	−	22.4427i	1.53873	−	1.11795i
$404$	3.04573	−	2.21285i	0.151531	−	0.110093i
$405$	1.22487	+	7.49540i	0.0608640	+	0.372449i
$406$	−16.4751	−	11.9699i	−0.817646	−	0.594054i
$407$	4.18310			0.207349
$408$	9.73228	+	7.07092i	0.481820	+	0.350062i
$409$	2.03044	−	6.24905i	0.100399	−	0.308995i	−0.888224	−	0.459410i	$-0.848061\pi$
$409$	2.03044	−	6.24905i	0.100399	−	0.308995i	0.988623	+	0.150415i	$0.0480608\pi$
$410$	−13.5182	−	13.3863i	−0.667617	−	0.661100i
$411$	−2.95814	−	9.10420i	−0.145914	−	0.449077i
$412$	−3.01138	+	9.26809i	−0.148360	+	0.456606i
$413$	−8.98914	+	27.6657i	−0.442327	+	1.36134i
$414$	3.68772	+	11.3496i	0.181242	+	0.557805i
$415$	−3.57475	−	21.8752i	−0.175478	−	1.07381i
$416$	1.45018	−	4.46319i	0.0711009	−	0.218826i
$417$	19.8671	+	14.4343i	0.972894	+	0.706849i
$418$	−3.64112			−0.178093
$419$	−19.0352	−	13.8299i	−0.929932	−	0.675635i	0.0160441	−	0.999871i	$-0.494893\pi$
$419$	−19.0352	−	13.8299i	−0.929932	−	0.675635i	−0.945976	+	0.324236i	$0.894893\pi$
$420$	−14.8084	+	7.63694i	−0.722574	+	0.372645i
$421$	−23.5110	+	17.0817i	−1.14585	+	0.832512i	−0.987924	−	0.154938i	$-0.950482\pi$
$421$	−23.5110	+	17.0817i	−1.14585	+	0.832512i	−0.157930	+	0.987450i	$0.550482\pi$
$422$	18.2793	−	13.2807i	0.889824	−	0.646495i
$423$	0.345034	+	1.06191i	0.0167761	+	0.0516317i
$424$	−5.09654			−0.247510
$425$	12.9059	−	18.1349i	0.626028	−	0.879671i
$426$	18.7904			0.910398
$427$	5.83795	+	17.9674i	0.282518	+	0.869502i
$428$	10.5770	−	7.68466i	0.511260	−	0.371452i
$429$	−37.3564	+	27.1410i	−1.80358	+	1.31038i
$430$	8.34057	−	16.5697i	0.402218	−	0.799061i
$431$	−20.6614	−	15.0114i	−0.995224	−	0.723073i	−0.0341652	−	0.999416i	$-0.510877\pi$
$431$	−20.6614	−	15.0114i	−0.995224	−	0.723073i	−0.961059	+	0.276344i	$0.910877\pi$
$432$	−3.51949			−0.169332
$433$	10.6792	+	7.75888i	0.513209	+	0.372868i	0.814039	−	0.580810i	$-0.197264\pi$
$433$	10.6792	+	7.75888i	0.513209	+	0.372868i	−0.300831	+	0.953678i	$0.597264\pi$
$434$	−6.93264	+	21.3365i	−0.332777	+	1.02418i
$435$	−39.6623	+	20.4546i	−1.90166	+	0.980722i
$436$	−2.41799	−	7.44182i	−0.115801	−	0.356398i
$437$	0.857130	−	2.63798i	0.0410021	−	0.126191i
$438$	0.546942	−	1.68332i	0.0261339	−	0.0804319i
$439$	−2.73157	−	8.40692i	−0.130371	−	0.401241i	0.864470	−	0.502684i	$-0.167654\pi$
$439$	−2.73157	−	8.40692i	−0.130371	−	0.401241i	−0.994841	+	0.101443i	$0.967654\pi$
$440$	−7.23616	+	3.73182i	−0.344971	+	0.177908i
$441$	0.802034	−	2.46841i	0.0381921	−	0.117543i
$442$	−16.9013	−	12.2795i	−0.803914	−	0.584078i
$443$	30.7117			1.45916			0.729578	−	0.683898i	$-0.239717\pi$
$443$	30.7117			1.45916			0.729578	+	0.683898i	$0.239717\pi$
$444$	−2.51162	−	1.82480i	−0.119196	−	0.0866012i
$445$	17.4599	−	34.6865i	0.827680	−	1.64430i
$446$	−10.2793	+	7.46838i	−0.486741	+	0.353638i
$447$	42.4155	−	30.8167i	2.00618	−	1.45758i
$448$	0.852083	+	2.62244i	0.0402572	+	0.123899i
$449$	16.7809			0.791938			0.395969	−	0.918264i	$-0.370409\pi$
$449$	16.7809			0.791938			0.395969	+	0.918264i	$0.370409\pi$
$450$	0.210998	+	21.5110i	0.00994653	+	1.01404i
$451$	30.9788			1.45873
$452$	0.0237756	+	0.0731737i	0.00111831	+	0.00344180i
$453$	−26.2948	+	19.1043i	−1.23544	+	0.897597i
$454$	21.3069	−	15.4803i	0.999981	−	0.726529i
$455$	25.7166	−	13.2625i	1.20561	−	0.621756i
$456$	2.18620	+	1.58837i	0.102378	+	0.0743823i
$457$	22.8179			1.06738			0.533688	−	0.845681i	$-0.320806\pi$
$457$	22.8179			1.06738			0.533688	+	0.845681i	$0.320806\pi$
$458$	17.2248	+	12.5145i	0.804862	+	0.584766i
$459$	−4.84157	+	14.9008i	−0.225985	+	0.695511i
$460$	−1.00028	−	6.12106i	−0.0466382	−	0.285396i
$461$	10.9495	+	33.6992i	0.509971	+	1.56953i	0.792249	+	0.610197i	$0.208910\pi$
$461$	10.9495	+	33.6992i	0.509971	+	1.56953i	−0.282278	+	0.959333i	$0.591090\pi$
$462$	8.38397	−	25.8032i	0.390057	−	1.20047i
$463$	2.88691	−	8.88500i	0.134166	−	0.412921i	−0.861293	−	0.508108i	$-0.830345\pi$
$463$	2.88691	−	8.88500i	0.134166	−	0.412921i	0.995459	+	0.0951872i	$0.0303450\pi$
$464$	2.28220	+	7.02388i	0.105948	+	0.326076i
$465$	34.9333	+	34.5923i	1.61999	+	1.60418i
$466$	−7.19831	+	22.1541i	−0.333455	+	1.02627i
$467$	3.66597	+	2.66348i	0.169641	+	0.123251i	0.669366	−	0.742933i	$-0.266566\pi$
$467$	3.66597	+	2.66348i	0.169641	+	0.123251i	−0.499725	+	0.866184i	$0.666566\pi$
$468$	20.1907			0.933315
$469$	24.2407	+	17.6119i	1.11933	+	0.813243i
$470$	−0.0935889	−	0.572704i	−0.00431693	−	0.0264169i
$471$	−3.82930	+	2.78215i	−0.176445	+	0.128195i
$472$	8.53481	−	6.20090i	0.392846	−	0.285420i
$473$	9.33439	+	28.7283i	0.429196	+	1.32093i
$474$	−22.7822			−1.04642
$475$	2.89911	−	4.07372i	0.133020	−	0.186915i
$476$	12.2751			0.562626
$477$	−6.77594	−	20.8542i	−0.310249	−	0.954848i
$478$	18.1736	−	13.2039i	0.831243	−	0.603933i
$479$	−11.5202	+	8.36991i	−0.526371	+	0.382431i	−0.818999	−	0.573795i	$-0.805470\pi$
$479$	−11.5202	+	8.36991i	−0.526371	+	0.382431i	0.292627	+	0.956227i	$0.405470\pi$
$480$	5.97269	+	0.915978i	0.272615	+	0.0418085i
$481$	4.36175	+	3.16900i	0.198879	+	0.144494i
$482$	17.9235			0.816394
$483$	16.7207	+	12.1483i	0.760819	+	0.552767i
$484$	0.697673	−	2.14722i	0.0317124	−	0.0976008i
$485$	32.4515	+	4.97679i	1.47354	+	0.225984i
$486$	6.09902	+	18.7709i	0.276657	+	0.851464i
$487$	−5.92301	+	18.2291i	−0.268397	+	0.826042i	0.722494	+	0.691377i	$0.242996\pi$
$487$	−5.92301	+	18.2291i	−0.268397	+	0.826042i	−0.990891	+	0.134664i	$0.957004\pi$
$488$	2.11719	−	6.51606i	0.0958409	−	0.294968i
$489$	15.2316	+	46.8780i	0.688796	+	2.11990i
$490$	−0.606492	+	1.20488i	−0.0273985	+	0.0544309i
$491$	−12.7783	+	39.3277i	−0.576678	+	1.77483i	0.0537156	+	0.998556i	$0.482894\pi$
$491$	−12.7783	+	39.3277i	−0.576678	+	1.77483i	−0.630393	+	0.776276i	$0.717106\pi$
$492$	−18.6003	−	13.5139i	−0.838567	−	0.609255i
$493$	32.8772			1.48071
$494$	−3.79662	−	2.75841i	−0.170818	−	0.124107i
$495$	−24.8906	−	24.6477i	−1.11875	−	1.10783i
$496$	6.58225	−	4.78228i	0.295552	−	0.214731i
$497$	15.5117	−	11.2699i	0.695797	−	0.505526i
$498$	−8.27761	−	25.4759i	−0.370929	−	1.14160i
$499$	−3.56412			−0.159552			−0.0797759	−	0.996813i	$-0.525420\pi$
$499$	−3.56412			−0.159552			−0.0797759	+	0.996813i	$0.525420\pi$
$500$	1.58634	−	11.0672i	0.0709432	−	0.494941i
$501$	−29.7223			−1.32789
$502$	−0.850214	−	2.61669i	−0.0379469	−	0.116789i
$503$	27.6951	−	20.1217i	1.23487	−	0.897182i	0.237620	−	0.971358i	$-0.423633\pi$
$503$	27.6951	−	20.1217i	1.23487	−	0.897182i	0.997245	+	0.0741759i	$0.0236326\pi$
$504$	−9.59774	+	6.97317i	−0.427517	+	0.310610i
$505$	−5.98167	−	5.92329i	−0.266181	−	0.263583i
$506$	8.17065	+	5.93632i	0.363230	+	0.263902i
$507$	−24.3832			−1.08289
$508$	2.76556	+	2.00930i	0.122702	+	0.0891481i
$509$	−12.1016	+	37.2449i	−0.536394	+	1.65085i	0.204225	+	0.978924i	$0.434533\pi$
$509$	−12.1016	+	37.2449i	−0.536394	+	1.65085i	−0.740618	+	0.671926i	$0.765467\pi$
$510$	12.0944	−	24.0271i	0.535547	−	1.06394i
$511$	−0.558095	−	1.71764i	−0.0246887	−	0.0759839i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−1.08758	+	3.34724i	−0.0480180	+	0.147784i
$514$	−4.87878	−	15.0153i	−0.215194	−	0.662298i
$515$	21.5388	+	3.30321i	0.949111	+	0.145557i
$516$	6.92763	−	21.3211i	0.304972	−	0.938607i
$517$	0.764470	+	0.555420i	0.0336213	+	0.0244273i
$518$	−3.16784			−0.139187
$519$	−3.47543	−	2.52504i	−0.152554	−	0.110837i
$520$	−10.3723	−	1.59071i	−0.454857	−	0.0697573i
$521$	28.7937	−	20.9198i	1.26147	−	0.916514i	0.262644	−	0.964893i	$-0.415406\pi$
$521$	28.7937	−	20.9198i	1.26147	−	0.916514i	0.998829	+	0.0483793i	$0.0154056\pi$
$522$	−25.7063	+	18.6767i	−1.12514	+	0.817459i
$523$	−1.61659	−	4.97534i	−0.0706884	−	0.217556i	0.909471	−	0.415767i	$-0.136487\pi$
$523$	−1.61659	−	4.97534i	−0.0706884	−	0.217556i	−0.980159	+	0.198211i	$0.936487\pi$
$524$	−8.51668			−0.372053
$525$	22.1934	+	29.9249i	0.968601	+	1.30603i
$526$	−28.6220			−1.24798
$527$	−11.1924	−	34.4466i	−0.487548	−	1.50052i
$528$	−7.96022	+	5.78344i	−0.346424	+	0.251692i
$529$	12.3832	−	8.99689i	0.538398	−	0.391169i
$530$	1.83794	+	11.2470i	0.0798351	+	0.488540i
$531$	36.7202	+	26.6788i	1.59352	+	1.15776i
$532$	2.75740			0.119548
$533$	32.3018	+	23.4686i	1.39915	+	1.01654i
$534$	14.5021	−	44.6329i	0.627568	−	1.93146i
$535$	−20.7728	−	20.5701i	−0.898087	−	0.889321i
$536$	−3.35792	−	10.3346i	−0.145040	−	0.446388i
$537$	−7.85147	+	24.1643i	−0.338816	+	1.04277i
$538$	−2.46261	+	7.57913i	−0.106171	+	0.326760i
$539$	−0.678759	−	2.08900i	−0.0292362	−	0.0899798i
$540$	1.26922	+	7.76681i	0.0546185	+	0.334230i
$541$	3.63302	−	11.1813i	0.156196	−	0.480721i	−0.842084	−	0.539346i	$-0.818672\pi$
$541$	3.63302	−	11.1813i	0.156196	−	0.480721i	0.998280	+	0.0586251i	$0.0186716\pi$
$542$	16.8112	+	12.2140i	0.722103	+	0.524638i
$543$	−48.0500			−2.06202
$544$	−3.60148	−	2.61663i	−0.154412	−	0.112187i
$545$	−15.5506	+	8.01972i	−0.666114	+	0.343527i
$546$	28.2898	−	20.5537i	1.21069	−	0.879619i
$547$	−27.7377	+	20.1526i	−1.18598	+	0.861664i	−0.992833	−	0.119507i	$-0.961869\pi$
$547$	−27.7377	+	20.1526i	−1.18598	+	0.861664i	−0.193145	+	0.981170i	$0.561869\pi$
$548$	1.09467	+	3.36906i	0.0467622	+	0.143919i
$549$	29.4775			1.25807
$550$	10.8449	+	14.6230i	0.462429	+	0.623525i
$551$	7.38535			0.314626
$552$	−2.31622	−	7.12859i	−0.0985849	−	0.303413i
$553$	−18.8070	+	13.6641i	−0.799757	+	0.581057i
$554$	3.50754	−	2.54838i	0.149021	−	0.108270i
$555$	−3.12121	+	6.20071i	−0.132488	+	0.263206i
$556$	−7.35192	−	5.34148i	−0.311791	−	0.226529i
$557$	20.3092			0.860528			0.430264	−	0.902703i	$-0.358420\pi$
$557$	20.3092			0.860528			0.430264	+	0.902703i	$0.358420\pi$
$558$	28.3195	+	20.5753i	1.19886	+	0.871024i
$559$	−12.0307	+	37.0267i	−0.508845	+	1.56606i
$560$	5.47991	−	2.82609i	0.231569	−	0.119424i
$561$	13.5355	+	41.6579i	0.571468	+	1.75880i
$562$	7.73939	−	23.8194i	0.326466	−	1.00476i
$563$	−11.6446	+	35.8384i	−0.490762	+	1.51041i	0.332697	+	0.943034i	$0.392041\pi$
$563$	−11.6446	+	35.8384i	−0.490762	+	1.51041i	−0.823459	+	0.567376i	$0.807959\pi$
$564$	−0.216712	−	0.666972i	−0.00912524	−	0.0280846i
$565$	0.152905	−	0.0788561i	0.00643278	−	0.00331750i
$566$	−8.28909	+	25.5112i	−0.348417	+	1.07232i
$567$	7.57687	+	5.50492i	0.318199	+	0.231185i
$568$	−6.95350			−0.291762
$569$	−21.8574	−	15.8803i	−0.916310	−	0.665738i	0.0262931	−	0.999654i	$-0.491630\pi$
$569$	−21.8574	−	15.8803i	−0.916310	−	0.665738i	−0.942603	+	0.333916i	$0.891630\pi$
$570$	2.71681	−	5.39731i	0.113795	−	0.226069i
$571$	16.1202	−	11.7120i	0.674611	−	0.490133i	−0.196955	−	0.980413i	$-0.563105\pi$
$571$	16.1202	−	11.7120i	0.674611	−	0.490133i	0.871565	+	0.490279i	$0.163105\pi$
$572$	13.8239	−	10.0437i	0.578008	−	0.419947i
$573$	−11.7612	−	36.1973i	−0.491332	−	1.51217i
$574$	−23.4601			−0.979205
$575$	−13.1472	+	4.41482i	−0.548276	+	0.184111i
$576$	4.30241			0.179267
$577$	2.16982	+	6.67803i	0.0903309	+	0.278010i	0.986009	−	0.166694i	$-0.0533091\pi$
$577$	2.16982	+	6.67803i	0.0903309	+	0.278010i	−0.895678	+	0.444703i	$0.853309\pi$
$578$	−2.27937	+	1.65606i	−0.0948091	+	0.0688828i
$579$	31.3858	−	22.8031i	1.30435	−	0.947665i
$580$	14.6773	−	7.56933i	0.609440	−	0.314299i
$581$	−22.1130	−	16.0660i	−0.917401	−	0.666531i
$582$	39.6762			1.64463
$583$	−15.0130	−	10.9076i	−0.621775	−	0.451746i
$584$	−0.202399	+	0.622920i	−0.00837533	+	0.0257766i
$585$	−7.28127	−	44.5567i	−0.301043	−	1.84219i
$586$	3.44231	+	10.5943i	0.142200	+	0.437648i
$587$	2.60890	−	8.02936i	0.107681	−	0.331407i	−0.882670	−	0.469994i	$-0.844256\pi$
$587$	2.60890	−	8.02936i	0.107681	−	0.331407i	0.990350	+	0.138587i	$0.0442561\pi$
$588$	−0.503749	+	1.55038i	−0.0207743	+	0.0639366i
$589$	−2.51420	−	7.73790i	−0.103596	−	0.318835i
$590$	−16.7620	−	16.5984i	−0.690080	−	0.683344i
$591$	−5.05504	+	15.5578i	−0.207936	+	0.639963i
$592$	0.929440	+	0.675278i	0.0381998	+	0.0277538i
$593$	−19.5813			−0.804109			−0.402055	−	0.915616i	$-0.631704\pi$
$593$	−19.5813			−0.804109			−0.402055	+	0.915616i	$0.631704\pi$
$594$	−10.3675	−	7.53240i	−0.425382	−	0.309058i
$595$	−4.42669	−	27.0886i	−0.181477	−	1.11052i
$596$	−15.6961	+	11.4039i	−0.642937	+	0.467121i
$597$	−8.80047	+	6.39391i	−0.360179	+	0.261685i
$598$	4.02241	+	12.3797i	0.164489	+	0.506244i
$599$	−5.12598			−0.209442			−0.104721	−	0.994502i	$-0.533395\pi$
$599$	−5.12598			−0.209442			−0.104721	+	0.994502i	$0.533395\pi$
$600$	−0.132525	−	13.5108i	−0.00541033	−	0.551578i
$601$	35.8085			1.46066			0.730329	−	0.683096i	$-0.239367\pi$
$601$	35.8085			1.46066			0.730329	+	0.683096i	$0.239367\pi$
$602$	−7.06889	−	21.7558i	−0.288107	−	0.886701i
$603$	37.8232	−	27.4801i	1.54028	−	1.11908i
$604$	9.73052	−	7.06964i	0.395929	−	0.287660i
$605$	−4.99007	−	0.765282i	−0.202875	−	0.0311132i
$606$	−8.23046	−	5.97978i	−0.334339	−	0.242912i
$607$	−33.5688			−1.36251			−0.681257	−	0.732045i	$-0.738566\pi$
$607$	−33.5688			−1.36251			−0.681257	+	0.732045i	$0.738566\pi$
$608$	−0.809017	−	0.587785i	−0.0328100	−	0.0238378i
$609$	−17.0054	+	52.3371i	−0.689092	+	2.12081i
$610$	−15.1431	−	2.32236i	−0.613127	−	0.0940298i
$611$	0.376348	+	1.15828i	0.0152254	+	0.0468590i
$612$	5.91859	−	18.2155i	0.239245	−	0.736319i
$613$	−5.21308	+	16.0442i	−0.210554	+	0.648019i	0.788885	+	0.614541i	$0.210659\pi$
$613$	−5.21308	+	16.0442i	−0.210554	+	0.648019i	−0.999439	+	0.0334787i	$0.989341\pi$
$614$	5.34006	+	16.4350i	0.215507	+	0.663264i
$615$	−23.1147	+	45.9206i	−0.932076	+	1.85170i
$616$	−3.10253	+	9.54862i	−0.125005	+	0.384725i
$617$	4.06378	+	2.95251i	0.163602	+	0.118863i	0.666574	−	0.745439i	$-0.267760\pi$
$617$	4.06378	+	2.95251i	0.163602	+	0.118863i	−0.502972	+	0.864303i	$0.667760\pi$
$618$	26.3340			1.05931
$619$	−8.29406	−	6.02599i	−0.333367	−	0.242205i	0.408491	−	0.912762i	$-0.366055\pi$
$619$	−8.29406	−	6.02599i	−0.333367	−	0.242205i	−0.741858	+	0.670557i	$0.766055\pi$
$620$	−12.9273	−	12.8011i	−0.519171	−	0.514103i
$621$	7.89773	−	5.73804i	0.316925	−	0.230260i
$622$	−2.16478	+	1.57280i	−0.0867997	+	0.0630637i
$623$	−14.7978	−	45.5431i	−0.592863	−	1.82464i
$624$	−12.6816			−0.507669
$625$	−24.9952	+	0.490394i	−0.999808	+	0.0196158i
$626$	17.2884			0.690984
$627$	3.04053	+	9.35780i	0.121427	+	0.373715i
$628$	1.41705	−	1.02955i	0.0565465	−	0.0410835i
$629$	4.13757	−	3.00612i	0.164976	−	0.119862i
$630$	18.8495	+	18.6656i	0.750984	+	0.743654i
$631$	−8.03119	−	5.83500i	−0.319717	−	0.232288i	0.416338	−	0.909210i	$-0.363313\pi$
$631$	−8.03119	−	5.83500i	−0.319717	−	0.232288i	−0.736055	+	0.676922i	$0.763313\pi$
$632$	8.43069			0.335355
$633$	−49.3962	−	35.8884i	−1.96332	−	1.42644i
$634$	1.32646	−	4.08243i	0.0526805	−	0.162134i
$635$	3.43678	−	6.82763i	0.136384	−	0.270946i
$636$	4.25590	+	13.0983i	0.168757	+	0.519381i
$637$	0.874823	−	2.69243i	0.0346618	−	0.106678i
$638$	−8.30974	+	25.5748i	−0.328986	+	1.01251i
$639$	−9.24479	−	28.4526i	−0.365718	−	1.12557i
$640$	−2.21023	−	0.338963i	−0.0873669	−	0.0133987i
$641$	−0.253142	+	0.779090i	−0.00999849	+	0.0307722i	−0.955931	−	0.293590i	$-0.905150\pi$
$641$	−0.253142	+	0.779090i	−0.00999849	+	0.0307722i	0.945933	+	0.324363i	$0.105150\pi$
$642$	−28.5823	−	20.7662i	−1.12805	−	0.819577i
$643$	36.7688			1.45002			0.725010	−	0.688739i	$-0.241835\pi$
$643$	36.7688			1.45002			0.725010	+	0.688739i	$0.241835\pi$
$644$	−6.18759	−	4.49555i	−0.243825	−	0.177149i
$645$	−49.5495	−	7.59896i	−1.95101	−	0.299209i
$646$	−3.60148	+	2.61663i	−0.141699	+	0.102950i
$647$	8.89031	−	6.45919i	0.349514	−	0.253937i	−0.399151	−	0.916885i	$-0.630695\pi$
$647$	8.89031	−	6.45919i	0.349514	−	0.253937i	0.748665	+	0.662948i	$0.230695\pi$
$648$	−1.04958	−	3.23027i	−0.0412313	−	0.126897i
$649$	38.4123			1.50781
$650$	0.230147	+	23.4633i	0.00902711	+	0.920305i
$651$	60.6247			2.37607
$652$	−5.63653	−	17.3475i	−0.220744	−	0.679379i
$653$	−21.3399	+	15.5044i	−0.835096	+	0.606732i	−0.920996	−	0.389571i	$-0.872623\pi$
$653$	−21.3399	+	15.5044i	−0.835096	+	0.606732i	0.0859007	+	0.996304i	$0.472623\pi$
$654$	−17.1066	+	12.4287i	−0.668920	+	0.485999i
$655$	3.07133	+	18.7946i	0.120007	+	0.734365i
$656$	6.88315	+	5.00090i	0.268742	+	0.195252i
$657$	−2.81798			−0.109940
$658$	−0.578929	−	0.420617i	−0.0225690	−	0.0163973i
$659$	−10.6721	+	32.8453i	−0.415726	+	1.27947i	0.495875	+	0.868394i	$0.334848\pi$
$659$	−10.6721	+	32.8453i	−0.415726	+	1.27947i	−0.911600	+	0.411078i	$0.865152\pi$
$660$	15.6335	+	15.4809i	0.608534	+	0.602594i
$661$	−8.61525	−	26.5150i	−0.335094	−	1.03131i	−0.966676	−	0.256005i	$-0.917594\pi$
$661$	−8.61525	−	26.5150i	−0.335094	−	1.03131i	0.631581	−	0.775310i	$-0.282406\pi$
$662$	9.75888	−	30.0348i	0.379290	−	1.16733i
$663$	−17.4453	+	53.6912i	−0.677520	+	2.08519i
$664$	3.06318	+	9.42749i	0.118874	+	0.365858i
$665$	−0.994387	−	6.08502i	−0.0385607	−	0.235967i
$666$	−1.52742	+	4.70091i	−0.0591862	+	0.182157i
$667$	−16.5727	−	12.0408i	−0.641697	−	0.466220i
$668$	10.9989			0.425560
$669$	27.7778	+	20.1818i	1.07395	+	0.780272i
$670$	−21.5955	+	11.1372i	−0.834305	+	0.430267i
$671$	20.1823	−	14.6633i	0.779129	−	0.566070i
$672$	6.02824	−	4.37977i	0.232544	−	0.168953i
$673$	−9.16640	−	28.2113i	−0.353339	−	1.08746i	−0.956966	−	0.290198i	$-0.906279\pi$
$673$	−9.16640	−	28.2113i	−0.353339	−	1.08746i	0.603628	−	0.797266i	$-0.293721\pi$
$674$	−16.0827			−0.619481
$675$	16.6821	−	5.60181i	0.642092	−	0.215614i
$676$	9.02312			0.347043
$677$	13.0677	+	40.2182i	0.502232	+	1.54571i	0.805375	+	0.592765i	$0.201964\pi$
$677$	13.0677	+	40.2182i	0.502232	+	1.54571i	−0.303144	+	0.952945i	$0.598036\pi$
$678$	0.168205	−	0.122208i	0.00645988	−	0.00469338i
$679$	32.7533	−	23.7966i	1.25695	−	0.913231i
$680$	−4.47559	+	8.89137i	−0.171631	+	0.340968i
$681$	−57.5775	−	41.8325i	−2.20637	−	1.60302i
$682$	29.6245			1.13438
$683$	−21.5782	−	15.6775i	−0.825667	−	0.599882i	0.0926634	−	0.995697i	$-0.470462\pi$
$683$	−21.5782	−	15.6775i	−0.825667	−	0.599882i	−0.918330	+	0.395816i	$0.870462\pi$
$684$	1.32952	−	4.09183i	0.0508354	−	0.156455i
$685$	7.04006	−	3.63069i	0.268987	−	0.138722i
$686$	−5.45056	−	16.7751i	−0.208103	−	0.640477i
$687$	17.7792	−	54.7187i	0.678318	−	2.08765i
$688$	−2.56361	+	7.88998i	−0.0977367	+	0.300803i
$689$	−7.39090	−	22.7469i	−0.281571	−	0.866586i
$690$	−14.8961	+	7.68217i	−0.567083	+	0.292455i
$691$	12.0412	−	37.0590i	0.458069	−	1.40979i	−0.409425	−	0.912344i	$-0.634271\pi$
$691$	12.0412	−	37.0590i	0.458069	−	1.40979i	0.867494	−	0.497448i	$-0.165729\pi$
$692$	1.28610	+	0.934407i	0.0488902	+	0.0355208i
$693$	−43.1962			−1.64089
$694$	−1.38451	−	1.00590i	−0.0525551	−	0.0381835i
$695$	−9.13627	+	18.1505i	−0.346559	+	0.688486i
$696$	16.1459	−	11.7307i	0.612008	−	0.444650i
$697$	30.6416	−	22.2624i	1.16063	−	0.843249i
$698$	−0.215921	−	0.664538i	−0.00817275	−	0.0251531i
$699$	62.9479			2.38091
$700$	−8.21281	−	11.0739i	−0.310415	−	0.418554i
$701$	−12.2671			−0.463321			−0.231660	−	0.972797i	$-0.574416\pi$
$701$	−12.2671			−0.463321			−0.231660	+	0.972797i	$0.574416\pi$
$702$	−5.10390	−	15.7082i	−0.192634	−	0.592867i
$703$	0.929440	−	0.675278i	0.0350545	−	0.0254686i
$704$	2.94572	−	2.14019i	0.111021	−	0.0806616i
$705$	−1.39372	+	0.718767i	−0.0524905	+	0.0270703i
$706$	−0.324538	−	0.235791i	−0.0122142	−	0.00887411i
$707$	−10.3809			−0.390412
$708$	−23.0636	−	16.7567i	−0.866782	−	0.629754i
$709$	0.155916	−	0.479861i	0.00585556	−	0.0180216i	−0.948086	−	0.318014i	$-0.896984\pi$
$709$	0.155916	−	0.479861i	0.00585556	−	0.0180216i	0.953942	+	0.299992i	$0.0969841\pi$
$710$	2.50761	+	15.3450i	0.0941088	+	0.575886i
$711$	11.2088	+	34.4970i	0.420361	+	1.29374i
$712$	−5.36659	+	16.5167i	−0.201122	+	0.618988i
$713$	−6.97370	+	21.4629i	−0.261167	+	0.803790i
$714$	−10.2504	−	31.5474i	−0.383610	−	1.18063i
$715$	−27.1496	−	26.8846i	−1.01534	−	1.00543i
$716$	2.90548	−	8.94215i	0.108583	−	0.334184i
$717$	−49.1106	−	35.6809i	−1.83407	−	1.33253i
$718$	21.5880			0.805657
$719$	−42.6138	−	30.9607i	−1.58923	−	1.15464i	−0.905033	−	0.425340i	$-0.860154\pi$
$719$	−42.6138	−	30.9607i	−1.58923	−	1.15464i	−0.684193	−	0.729301i	$-0.739846\pi$
$720$	−1.55156	−	9.49454i	−0.0578231	−	0.353841i
$721$	21.7391	−	15.7944i	0.809605	−	0.588213i
$722$	−0.809017	+	0.587785i	−0.0301085	+	0.0218751i
$723$	−14.9671	−	46.0641i	−0.556634	−	1.71314i
$724$	17.7812			0.660832
$725$	−21.9970	−	29.6600i	−0.816947	−	1.10155i
$726$	−6.10103			−0.226430
$727$	−6.71168	−	20.6564i	−0.248922	−	0.766104i	−0.994967	−	0.100208i	$-0.968049\pi$
$727$	−6.71168	−	20.6564i	−0.248922	−	0.766104i	0.746044	−	0.665896i	$-0.231951\pi$
$728$	−10.4688	+	7.60603i	−0.387999	+	0.281898i
$729$	34.9053	−	25.3602i	1.29279	−	0.939266i
$730$	1.44765	+	0.222013i	0.0535799	+	0.00821706i
$731$	29.8780	+	21.7076i	1.10508	+	0.802885i
$732$	−18.5145			−0.684315
$733$	−22.4052	−	16.2783i	−0.827554	−	0.601253i	0.0913121	−	0.995822i	$-0.470894\pi$
$733$	−22.4052	−	16.2783i	−0.827554	−	0.601253i	−0.918866	+	0.394569i	$0.870894\pi$
$734$	10.6279	−	32.7094i	0.392284	−	1.20733i
$735$	3.60304	+	0.552565i	0.132900	+	0.0203817i
$736$	0.857130	+	2.63798i	0.0315942	+	0.0972371i
$737$	12.2266	−	37.6296i	0.450372	−	1.38610i
$738$	−11.3116	+	34.8135i	−0.416386	+	1.28150i
$739$	4.58345	+	14.1064i	0.168605	+	0.518912i	0.999284	−	0.0378394i	$-0.0120475\pi$
$739$	4.58345	+	14.1064i	0.168605	+	0.518912i	−0.830679	+	0.556752i	$0.812048\pi$
$740$	1.15502	−	2.29461i	0.0424594	−	0.0843515i
$741$	−3.91882	+	12.0609i	−0.143961	+	0.443067i
$742$	11.3693	+	8.26027i	0.417379	+	0.303244i
$743$	−33.4538			−1.22730			−0.613651	−	0.789578i	$-0.710300\pi$
$743$	−33.4538			−1.22730			−0.613651	+	0.789578i	$0.710300\pi$
$744$	−17.7872	−	12.9232i	−0.652110	−	0.473786i
$745$	30.8264	+	30.5256i	1.12939	+	1.11837i
$746$	11.2440	−	8.16923i	0.411671	−	0.299097i
$747$	−34.5032	+	25.0680i	−1.26241	+	0.917191i
$748$	−5.00888	−	15.4157i	−0.183143	−	0.563656i
$749$	−36.0500			−1.31724
$750$	−29.7679	+	5.16480i	−1.08697	+	0.188592i
$751$	32.4546			1.18429			0.592143	−	0.805833i	$-0.298282\pi$
$751$	32.4546			1.18429			0.592143	+	0.805833i	$0.298282\pi$
$752$	0.0801956	+	0.246817i	0.00292443	+	0.00900048i
$753$	−6.01502	+	4.37017i	−0.219199	+	0.159258i
$754$	−28.0394	+	20.3718i	−1.02113	+	0.741897i
$755$	−19.1103	−	18.9238i	−0.695496	−	0.688707i
$756$	7.85123	+	5.70425i	0.285546	+	0.207462i
$757$	13.3728			0.486044			0.243022	−	0.970021i	$-0.421861\pi$
$757$	13.3728			0.486044			0.243022	+	0.970021i	$0.421861\pi$
$758$	10.3940	+	7.55171i	0.377528	+	0.274290i
$759$	8.43362	−	25.9560i	0.306121	−	0.942144i
$760$	−1.00537	+	1.99731i	−0.0364686	+	0.0724499i
$761$	9.44930	+	29.0820i	0.342537	+	1.05422i	0.962889	+	0.269897i	$0.0869896\pi$
$761$	9.44930	+	29.0820i	0.342537	+	1.05422i	−0.620352	+	0.784323i	$0.713010\pi$
$762$	2.85457	−	8.78546i	0.103410	−	0.318264i
$763$	−6.66737	+	20.5201i	−0.241375	+	0.742876i
$764$	4.35231	+	13.3950i	0.157461	+	0.484615i
$765$	−42.3324	−	6.49213i	−1.53053	−	0.234724i
$766$	−0.999901	+	3.07738i	−0.0361279	+	0.111190i
$767$	40.0528	+	29.1001i	1.44622	+	1.05074i
$768$	−2.70230			−0.0975107
$769$	5.58956	+	4.06105i	0.201565	+	0.146445i	0.683989	−	0.729492i	$-0.260244\pi$
$769$	5.58956	+	4.06105i	0.201565	+	0.146445i	−0.482424	+	0.875938i	$0.660244\pi$
$770$	22.1907	+	3.40319i	0.799697	+	0.122642i
$771$	−34.5159	+	25.0773i	−1.24306	+	0.903136i
$772$	−11.6145	+	8.43842i	−0.418014	+	0.303705i
$773$	10.5731	+	32.5406i	0.380287	+	1.17040i	0.939842	+	0.341610i	$0.110972\pi$
$773$	10.5731	+	32.5406i	0.380287	+	1.17040i	−0.559554	+	0.828794i	$0.689028\pi$
$774$	−35.6928			−1.28295
$775$	−23.5875	+	33.1442i	−0.847287	+	1.19057i
$776$	−14.6824			−0.527068
$777$	2.64532	+	8.14147i	0.0949005	+	0.292074i
$778$	−19.4617	+	14.1397i	−0.697735	+	0.506934i
$779$	6.88315	−	5.00090i	0.246615	−	0.179176i
$780$	4.57329	+	27.9856i	0.163750	+	1.00205i
$781$	−20.4831	−	14.8818i	−0.732942	−	0.532514i
$782$	12.3478			0.441555
$783$	21.0285	+	15.2781i	0.751498	+	0.545995i
$784$	0.186415	−	0.573727i	0.00665768	−	0.0204902i
$785$	−2.78303	−	2.75586i	−0.0993305	−	0.0983610i
$786$	7.11190	+	21.8882i	0.253673	+	0.780726i
$787$	−13.2318	+	40.7232i	−0.471662	+	1.45163i	0.378746	+	0.925501i	$0.376355\pi$
$787$	−13.2318	+	40.7232i	−0.471662	+	1.45163i	−0.850407	+	0.526125i	$0.823645\pi$
$788$	1.87064	−	5.75725i	0.0666390	−	0.205094i
$789$	23.9009	+	73.5595i	0.850896	+	2.61879i
$790$	−3.04032	−	18.6048i	−0.108170	−	0.661930i
$791$	0.0655588	−	0.201769i	0.00233100	−	0.00717408i
$792$	12.6737	+	9.20799i	0.450341	+	0.327192i
$793$	32.1527			1.14178
$794$	19.5192	+	14.1815i	0.692711	+	0.503284i
$795$	27.3705	−	14.1155i	0.970732	−	0.500624i
$796$	3.25666	−	2.36610i	0.115429	−	0.0838643i
$797$	28.8836	−	20.9851i	1.02311	−	0.743332i	0.0561904	−	0.998420i	$-0.482105\pi$
$797$	28.8836	−	20.9851i	1.02311	−	0.743332i	0.966918	+	0.255089i	$0.0821046\pi$
$798$	−2.30258	−	7.08662i	−0.0815105	−	0.250864i
$799$	1.15529			0.0408713
$800$	0.0490418	+	4.99976i	0.00173389	+	0.176768i
$801$	−74.7184			−2.64005
$802$	−6.53349	−	20.1080i	−0.230705	−	0.710038i
$803$	−1.92938	+	1.40178i	−0.0680864	+	0.0494677i
$804$	−23.7563	+	17.2600i	−0.837821	+	0.608712i
$805$	−7.68936	+	15.2760i	−0.271014	+	0.538407i
$806$	30.8897	+	22.4427i	1.08804	+	0.790510i
$807$	21.5351			0.758070
$808$	3.04573	+	2.21285i	0.107148	+	0.0778478i
$809$	−13.3125	+	40.9716i	−0.468041	+	1.44048i	0.387075	+	0.922048i	$0.373485\pi$
$809$	−13.3125	+	40.9716i	−0.468041	+	1.44048i	−0.855117	+	0.518435i	$0.826515\pi$
$810$	−6.75004	+	3.48112i	−0.237172	+	0.122314i
$811$	1.56814	+	4.82625i	0.0550649	+	0.169472i	0.974807	−	0.223052i	$-0.0716019\pi$
$811$	1.56814	+	4.82625i	0.0550649	+	0.169472i	−0.919742	+	0.392524i	$0.871602\pi$
$812$	6.29293	−	19.3676i	0.220839	−	0.679671i
$813$	17.3523	−	53.4048i	0.608571	−	1.87299i
$814$	1.29265	+	3.97836i	0.0453073	+	0.139442i
$815$	−36.2497	+	18.6946i	−1.26977	+	0.654844i
$816$	−3.71740	+	11.4410i	−0.130135	+	0.400514i
$817$	6.71161	+	4.87627i	0.234810	+	0.170599i
$818$	6.57064			0.229737
$819$	−45.0410	−	32.7242i	−1.57386	−	1.14348i
$820$	8.55374	−	16.9932i	0.298709	−	0.593427i
$821$	15.4883	−	11.2529i	0.540544	−	0.392728i	−0.283743	−	0.958900i	$-0.591576\pi$
$821$	15.4883	−	11.2529i	0.540544	−	0.392728i	0.824287	+	0.566172i	$0.191576\pi$
$822$	7.74450	−	5.62671i	0.270120	−	0.196254i
$823$	13.1721	+	40.5396i	0.459151	+	1.41312i	0.866191	+	0.499712i	$0.166561\pi$
$823$	13.1721	+	40.5396i	0.459151	+	1.41312i	−0.407040	+	0.913410i	$0.633439\pi$
$824$	−9.74504			−0.339485
$825$	28.5254	−	40.0828i	0.993128	−	1.39550i
$826$	−29.0895			−1.01215
$827$	0.877253	+	2.69991i	0.0305051	+	0.0938850i	0.965150	−	0.261698i	$-0.0842824\pi$
$827$	0.877253	+	2.69991i	0.0305051	+	0.0938850i	−0.934645	+	0.355583i	$0.884282\pi$
$828$	−9.65459	+	7.01447i	−0.335520	+	0.243770i
$829$	−11.7518	+	8.53822i	−0.408158	+	0.296545i	−0.772856	−	0.634582i	$-0.781172\pi$
$829$	−11.7518	+	8.53822i	−0.408158	+	0.296545i	0.364697	+	0.931126i	$0.381172\pi$
$830$	19.6999	−	10.1596i	0.683793	−	0.352645i
$831$	−9.47842	−	6.88647i	−0.328803	−	0.238889i
$832$	4.69288			0.162696
$833$	−2.17260	−	1.57849i	−0.0752762	−	0.0546914i
$834$	−7.58854	+	23.3551i	−0.262770	+	0.808722i
$835$	−3.96648	−	24.2723i	−0.137266	−	0.839979i
$836$	−1.12517	−	3.46291i	−0.0389147	−	0.119767i
$837$	8.84870	−	27.2335i	0.305856	−	0.941327i
$838$	7.27081	−	22.3773i	0.251166	−	0.773010i
$839$	9.16330	+	28.2017i	0.316352	+	0.973632i	0.975194	+	0.221351i	$0.0710465\pi$
$839$	9.16330	+	28.2017i	0.316352	+	0.973632i	−0.658842	+	0.752281i	$0.728953\pi$
$840$	−11.8392	−	11.7236i	−0.408491	−	0.404504i
$841$	7.89333	−	24.2932i	0.272184	−	0.837695i
$842$	−23.5110	−	17.0817i	−0.810241	−	0.588675i
$843$	−67.6796			−2.33101
$844$	18.2793	+	13.2807i	0.629200	+	0.457141i
$845$	−3.25396	−	19.9122i	−0.111940	−	0.685000i
$846$	−0.903311	+	0.656294i	−0.0310565	+	0.0225639i
$847$	−5.03648	+	3.65922i	−0.173056	+	0.125732i
$848$	−1.57492	−	4.84710i	−0.0540829	−	0.166450i
$849$	72.4866			2.48773
$850$	21.2354	+	6.67026i	0.728370	+	0.228788i
$851$	−3.18661			−0.109235
$852$	5.80656	+	17.8707i	0.198929	+	0.612242i
$853$	24.0777	−	17.4935i	0.824405	−	0.598965i	−0.0935658	−	0.995613i	$-0.529827\pi$
$853$	24.0777	−	17.4935i	0.824405	−	0.598965i	0.917971	+	0.396648i	$0.129827\pi$
$854$	−15.2840	+	11.1044i	−0.523006	+	0.379986i
$855$	−9.50930	−	1.45836i	−0.325211	−	0.0498747i
$856$	10.5770	+	7.68466i	0.361515	+	0.262656i
$857$	−28.1916			−0.963008			−0.481504	−	0.876444i	$-0.659909\pi$
$857$	−28.1916			−0.963008			−0.481504	+	0.876444i	$0.659909\pi$
$858$	−37.3564	−	27.1410i	−1.27533	−	0.926578i
$859$	0.486219	−	1.49643i	0.0165896	−	0.0510575i	−0.942419	−	0.334434i	$-0.891455\pi$
$859$	0.486219	−	1.49643i	0.0165896	−	0.0510575i	0.959009	+	0.283377i	$0.0914547\pi$
$860$	18.3361	+	2.81204i	0.625255	+	0.0958897i
$861$	19.5905	+	60.2933i	0.667641	+	2.05479i
$862$	7.89195	−	24.2889i	0.268801	−	0.827284i
$863$	2.39447	−	7.36941i	0.0815086	−	0.250858i	−0.901995	−	0.431747i	$-0.857897\pi$
$863$	2.39447	−	7.36941i	0.0815086	−	0.250858i	0.983504	+	0.180889i	$0.0578975\pi$
$864$	−1.08758	−	3.34724i	−0.0370004	−	0.113875i
$865$	1.59825	−	3.17513i	0.0543420	−	0.107958i
$866$	−4.07908	+	12.5541i	−0.138613	+	0.426607i
$867$	6.15952	+	4.47515i	0.209188	+	0.151984i
$868$	−22.4345			−0.761477
$869$	24.8345	+	18.0433i	0.842453	+	0.612078i
$870$	−31.7098	−	31.4003i	−1.07506	−	1.06457i
$871$	41.2558	−	29.9741i	1.39790	−	1.01563i
$872$	6.33039	−	4.59929i	0.214374	−	0.155752i
$873$	−19.5205	−	60.0780i	−0.660669	−	2.03333i
$874$	2.77373			0.0938229
$875$	−21.4761	+	22.1175i	−0.726024	+	0.747708i
$876$	1.76994			0.0598008
$877$	−16.0375	−	49.3584i	−0.541548	−	1.66671i	−0.729058	−	0.684452i	$-0.760042\pi$
$877$	−16.0375	−	49.3584i	−0.541548	−	1.66671i	0.187510	−	0.982263i	$-0.439958\pi$
$878$	7.15136	−	5.19576i	0.241347	−	0.175349i
$879$	24.3533	−	17.6937i	0.821417	−	0.596794i
$880$	−5.78527	−	5.72880i	−0.195022	−	0.193118i
$881$	−25.8652	−	18.7922i	−0.871421	−	0.633124i	0.0595468	−	0.998226i	$-0.481034\pi$
$881$	−25.8652	−	18.7922i	−0.871421	−	0.633124i	−0.930968	+	0.365101i	$0.881034\pi$
$882$	2.59544			0.0873929
$883$	−9.59093	−	6.96822i	−0.322761	−	0.234499i	0.414592	−	0.910007i	$-0.363924\pi$
$883$	−9.59093	−	6.96822i	−0.322761	−	0.234499i	−0.737353	+	0.675508i	$0.763924\pi$
$884$	6.45574	−	19.8687i	0.217130	−	0.668257i
$885$	−28.6613	+	56.9395i	−0.963438	+	1.91400i
$886$	9.49043	+	29.2085i	0.318837	+	0.981280i
$887$	8.95088	−	27.5480i	0.300541	−	0.924971i	−0.680762	−	0.732504i	$-0.738351\pi$
$887$	8.95088	−	27.5480i	0.300541	−	0.924971i	0.981304	−	0.192466i	$-0.0616486\pi$
$888$	0.959355	−	2.95259i	0.0321938	−	0.0990825i
$889$	−2.91278	−	8.96461i	−0.0976914	−	0.300663i
$890$	38.3843	+	5.88665i	1.28664	+	0.197321i
$891$	3.82163	−	11.7618i	0.128030	−	0.394034i
$892$	−10.2793	−	7.46838i	−0.344178	−	0.250060i
$893$	0.259518			0.00868445
$894$	42.4155	+	30.8167i	1.41859	+	1.03066i
$895$	−20.7813	−	3.18704i	−0.694642	−	0.106531i
$896$	−2.23078	+	1.62076i	−0.0745252	+	0.0541457i
$897$	28.4574	−	20.6755i	0.950163	−	0.690334i
$898$	5.18557	+	15.9595i	0.173045	+	0.532577i
$899$	−60.0880			−2.00405
$900$	−20.3930	+	6.84794i	−0.679766	+	0.228265i
$901$	−22.6882			−0.755853
$902$	9.57297	+	29.4626i	0.318745	+	0.980996i
$903$	−50.0103	+	36.3346i	−1.66424	+	1.20914i
$904$	−0.0622453	+	0.0452238i	−0.00207025	+	0.00150412i
$905$	−6.41234	−	39.2394i	−0.213153	−	1.30436i
$906$	−26.2948	−	19.1043i	−0.873585	−	0.634697i
$907$	28.6505			0.951326			0.475663	−	0.879628i	$-0.342208\pi$
$907$	28.6505			0.951326			0.475663	+	0.879628i	$0.342208\pi$
$908$	21.3069	+	15.4803i	0.707093	+	0.513733i
$909$	−5.00527	+	15.4046i	−0.166014	+	0.510939i
$910$	20.5603	+	20.3596i	0.681566	+	0.674913i
$911$	−10.4794	−	32.2523i	−0.347198	−	1.06857i	−0.960397	−	0.278637i	$-0.910117\pi$
$911$	−10.4794	−	32.2523i	−0.347198	−	1.06857i	0.613199	−	0.789929i	$-0.289883\pi$
$912$	−0.835056	+	2.57004i	−0.0276515	+	0.0851024i
$913$	−11.1534	+	34.3266i	−0.369123	+	1.13604i
$914$	7.05112	+	21.7011i	0.233230	+	0.717809i
$915$	6.67679	+	40.8577i	0.220728	+	1.35071i
$916$	−6.57929	+	20.2490i	−0.217386	+	0.669044i
$917$	18.9989	+	13.8035i	0.627398	+	0.455831i
$918$	−15.6677			−0.517110
$919$	13.0651	+	9.49238i	0.430979	+	0.313125i	0.782040	−	0.623228i	$-0.214179\pi$
$919$	13.0651	+	9.49238i	0.430979	+	0.313125i	−0.351061	+	0.936353i	$0.614179\pi$
$920$	5.51237	−	2.84283i	0.181737	−	0.0937254i
$921$	37.7794	−	27.4483i	1.24487	−	0.904453i
$922$	−28.6663	+	20.8273i	−0.944074	+	0.685910i
$923$	−10.0838	−	31.0348i	−0.331913	−	1.02152i
$924$	27.1311			0.892547
$925$	−5.48026	−	1.72140i	−0.180190	−	0.0565994i
$926$	9.34225			0.307005
$927$	−12.9562	−	39.8751i	−0.425538	−	1.30967i
$928$	−5.97487	+	4.34100i	−0.196135	+	0.142500i
$929$	35.0849	−	25.4907i	1.15110	−	0.836322i	0.162472	−	0.986713i	$-0.448053\pi$
$929$	35.0849	−	25.4907i	1.15110	−	0.836322i	0.988627	+	0.150391i	$0.0480532\pi$
$930$	−22.1043	+	43.9131i	−0.724827	+	1.43997i
$931$	−0.488041	−	0.354582i	−0.0159949	−	0.0116210i
$932$	−23.2942			−0.763027
$933$	5.84987	+	4.25018i	0.191516	+	0.139145i
$934$	−1.40027	+	4.30960i	−0.0458184	+	0.141014i
$935$	−32.2131	+	16.6129i	−1.05348	+	0.543299i
$936$	6.23927	+	19.2025i	0.203937	+	0.627653i
$937$	−11.5310	+	35.4887i	−0.376700	+	1.15936i	0.565624	+	0.824663i	$0.308635\pi$
$937$	−11.5310	+	35.4887i	−0.376700	+	1.15936i	−0.942324	+	0.334701i	$0.891365\pi$
$938$	−9.25914	+	28.4967i	−0.302322	+	0.930450i
$939$	−14.4368	−	44.4319i	−0.471127	−	1.44998i
$940$	0.515754	−	0.265984i	0.0168220	−	0.00867543i
$941$	5.99425	−	18.4484i	0.195407	−	0.601401i	−0.804564	−	0.593865i	$-0.797601\pi$
$941$	5.99425	−	18.4484i	0.195407	−	0.601401i	0.999972	−	0.00753597i	$-0.00239880\pi$
$942$	−3.82930	−	2.78215i	−0.124765	−	0.0906472i
$943$	−23.5990			−0.768490
$944$	8.53481	+	6.20090i	0.277784	+	0.201822i
$945$	9.75677	−	19.3832i	0.317388	−	0.630534i
$946$	−24.4378	+	17.7551i	−0.794540	+	0.577267i
$947$	−7.06540	+	5.13331i	−0.229595	+	0.166810i	−0.696635	−	0.717426i	$-0.745320\pi$
$947$	−7.06540	+	5.13331i	−0.229595	+	0.166810i	0.467040	+	0.884236i	$0.345320\pi$
$948$	−7.04010	−	21.6672i	−0.228652	−	0.703718i
$949$	−3.07373			−0.0997775
$950$	4.77021	+	1.49837i	0.154766	+	0.0486135i
$951$	−11.5997			−0.376145
$952$	3.79320	+	11.6743i	0.122938	+	0.378365i
$953$	36.2503	−	26.3374i	1.17426	−	0.853152i	0.182750	−	0.983159i	$-0.441500\pi$
$953$	36.2503	−	26.3374i	1.17426	−	0.853152i	0.991513	+	0.130007i	$0.0415001\pi$
$954$	17.7396	−	12.8886i	0.574342	−	0.417284i
$955$	27.9905	−	14.4352i	0.905752	−	0.467113i
$956$	18.1736	+	13.2039i	0.587778	+	0.427045i
$957$	72.6672			2.34900
$958$	−11.5202	−	8.36991i	−0.372201	−	0.270420i
$959$	3.01845	−	9.28985i	0.0974710	−	0.299985i
$960$	0.974516	+	5.96342i	0.0314524	+	0.192469i
$961$	10.8762	+	33.4736i	0.350847	+	1.07979i
$962$	−1.66604	+	5.12755i	−0.0537153	+	0.165319i
$963$	−17.3820	+	53.4963i	−0.560127	+	1.72389i
$964$	5.53867	+	17.0463i	0.178389	+	0.549024i
$965$	22.8103	+	22.5877i	0.734291	+	0.727124i
$966$	−6.38674	+	19.6564i	−0.205490	+	0.632434i
$967$	32.8559	+	23.8712i	1.05657	+	0.767645i	0.973451	−	0.228894i	$-0.0735110\pi$
$967$	32.8559	+	23.8712i	1.05657	+	0.767645i	0.0831217	+	0.996539i	$0.473511\pi$
$968$	2.25772			0.0725658
$969$	9.73228	+	7.07092i	0.312646	+	0.227151i
$970$	5.29484	+	32.4011i	0.170007	+	1.04034i
$971$	−15.5959	+	11.3311i	−0.500498	+	0.363633i	−0.809207	−	0.587524i	$-0.800103\pi$
$971$	−15.5959	+	11.3311i	−0.500498	+	0.363633i	0.308709	+	0.951156i	$0.400103\pi$
$972$	−15.9674	+	11.6010i	−0.512156	+	0.372103i
$973$	7.74328	+	23.8314i	0.248238	+	0.763999i
$974$	−19.1673			−0.614159
$975$	60.1093	−	20.1846i	1.92504	−	0.646425i
$976$	6.85139			0.219308
$977$	−4.99067	−	15.3597i	−0.159666	−	0.491400i	0.838938	−	0.544227i	$-0.183177\pi$
$977$	−4.99067	−	15.3597i	−0.159666	−	0.491400i	−0.998604	+	0.0528268i	$0.983177\pi$
$978$	−39.8768	+	28.9722i	−1.27512	+	0.926429i
$979$	−51.1574	+	37.1680i	−1.63500	+	1.18789i
$980$	−1.33332	−	0.204480i	−0.0425915	−	0.00653187i
$981$	27.2359	+	19.7880i	0.869576	+	0.631784i
$982$	−41.3515			−1.31958
$983$	2.12750	+	1.54572i	0.0678568	+	0.0493008i	0.621197	−	0.783655i	$-0.286647\pi$
$983$	2.12750	+	1.54572i	0.0678568	+	0.0493008i	−0.553340	+	0.832956i	$0.686647\pi$
$984$	7.10469	−	21.8660i	0.226489	−	0.697062i
$985$	−13.3797	−	2.05192i	−0.426312	−	0.0653797i
$986$	10.1596	+	31.2681i	0.323548	+	0.995778i
$987$	−0.597562	+	1.83911i	−0.0190206	+	0.0585395i
$988$	1.45018	−	4.46319i	0.0461364	−	0.141993i
$989$	−7.11076	−	21.8847i	−0.226109	−	0.695892i
$990$	15.7497	−	31.2889i	0.500558	−	0.994427i
$991$	−6.88408	+	21.1870i	−0.218680	+	0.673028i	0.780192	+	0.625540i	$0.215121\pi$
$991$	−6.88408	+	21.1870i	−0.218680	+	0.673028i	−0.998872	+	0.0474875i	$0.984879\pi$
$992$	6.58225	+	4.78228i	0.208987	+	0.151838i
$993$	−85.3396			−2.70817
$994$	15.5117	+	11.2699i	0.492003	+	0.357461i
$995$	−6.39594	−	6.33351i	−0.202765	−	0.200786i
$996$	21.6711	−	15.7450i	0.686674	−	0.498898i
$997$	27.2239	−	19.7793i	0.862189	−	0.626417i	−0.0662904	−	0.997800i	$-0.521116\pi$
$997$	27.2239	−	19.7793i	0.862189	−	0.626417i	0.928480	+	0.371383i	$0.121116\pi$
$998$	−1.10137	−	3.38968i	−0.0348634	−	0.107298i
$999$	4.04338			0.127927

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.b.381.9	✓	40
25.21	even	5	inner	950.2.h.b.571.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.b.381.9	✓	40	1.1	even	1	trivial
950.2.h.b.571.9	yes	40	25.21	even	5	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(2.18620 - 1.58837i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.58887 + 1.57337i) q^{5} +(2.18620 + 1.58837i) q^{6} +2.75740 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.32952 - 4.09183i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(2.18620 - 1.58837i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.58887 + 1.57337i) q^{5} +(2.18620 + 1.58837i) q^{6} +2.75740 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.32952 - 4.09183i) q^{9} +(-1.00537 + 1.99731i) q^{10} +(-1.12517 - 3.46291i) q^{11} +(-0.835056 + 2.57004i) q^{12} +(1.45018 - 4.46319i) q^{13} +(0.852083 + 2.62244i) q^{14} +(5.97269 + 0.915978i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.60148 - 2.61663i) q^{17} +4.30241 q^{18} +(-0.809017 - 0.587785i) q^{19} +(-2.21023 - 0.338963i) q^{20} +(6.02824 - 4.37977i) q^{21} +(2.94572 - 2.14019i) q^{22} +(0.857130 + 2.63798i) q^{23} -2.70230 q^{24} +(0.0490418 + 4.99976i) q^{25} +4.69288 q^{26} +(-1.08758 - 3.34724i) q^{27} +(-2.23078 + 1.62076i) q^{28} +(-5.97487 + 4.34100i) q^{29} +(0.974516 + 5.96342i) q^{30} +(6.58225 + 4.78228i) q^{31} +1.00000 q^{32} +(-7.96022 - 5.78344i) q^{33} +(1.37564 - 4.23380i) q^{34} +(4.38116 + 4.33840i) q^{35} +(1.32952 + 4.09183i) q^{36} +(-0.355015 + 1.09262i) q^{37} +(0.309017 - 0.951057i) q^{38} +(-3.91882 - 12.0609i) q^{39} +(-0.360625 - 2.20680i) q^{40} +(-2.62913 + 8.09163i) q^{41} +(6.02824 + 4.37977i) q^{42} -8.29601 q^{43} +(2.94572 + 2.14019i) q^{44} +(8.55039 - 4.40959i) q^{45} +(-2.24400 + 1.63036i) q^{46} +(-0.209955 + 0.152541i) q^{47} +(-0.835056 - 2.57004i) q^{48} +0.603252 q^{49} +(-4.73990 + 1.59165i) q^{50} -12.0298 q^{51} +(1.45018 + 4.46319i) q^{52} +(4.12319 - 2.99567i) q^{53} +(2.84733 - 2.06871i) q^{54} +(3.66067 - 7.27242i) q^{55} +(-2.23078 - 1.62076i) q^{56} -2.70230 q^{57} +(-5.97487 - 4.34100i) q^{58} +(-3.26001 + 10.0333i) q^{59} +(-5.37041 + 2.76962i) q^{60} +(2.11719 + 6.51606i) q^{61} +(-2.51420 + 7.73790i) q^{62} +(3.66601 - 11.2828i) q^{63} +(0.309017 + 0.951057i) q^{64} +(9.32639 - 4.80979i) q^{65} +(3.04053 - 9.35780i) q^{66} +(8.79116 + 6.38715i) q^{67} +4.45168 q^{68} +(6.06394 + 4.40571i) q^{69} +(-2.77221 + 5.50737i) q^{70} +(5.62550 - 4.08716i) q^{71} +(-3.48072 + 2.52889i) q^{72} +(-0.202399 - 0.622920i) q^{73} -1.14885 q^{74} +(8.04868 + 10.8526i) q^{75} +1.00000 q^{76} +(-3.10253 - 9.54862i) q^{77} +(10.2596 - 7.45403i) q^{78} +(-6.82057 + 4.95544i) q^{79} +(1.98735 - 1.02491i) q^{80} +(2.74783 + 1.99642i) q^{81} -8.50804 q^{82} +(-8.01950 - 5.82651i) q^{83} +(-2.30258 + 7.08662i) q^{84} +(-1.60539 - 9.82395i) q^{85} +(-2.56361 - 7.88998i) q^{86} +(-6.16718 + 18.9806i) q^{87} +(-1.12517 + 3.46291i) q^{88} +(-5.36659 - 16.5167i) q^{89} +(6.83599 + 6.76926i) q^{90} +(3.99872 - 12.3068i) q^{91} +(-2.24400 - 1.63036i) q^{92} +21.9862 q^{93} +(-0.209955 - 0.152541i) q^{94} +(-0.360625 - 2.20680i) q^{95} +(2.18620 - 1.58837i) q^{96} +(11.8783 - 8.63010i) q^{97} +(0.186415 + 0.573727i) q^{98} -15.6656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 5 q^{6} - 12 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 5 * q^6 - 12 * q^7 - 10 * q^8 - 3 * q^9	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 5 q^{6} - 12 q^{7} - 10 q^{8} - 3 q^{9} - 6 q^{11} + 16 q^{13} - 2 q^{14} + 16 q^{15} - 10 q^{16} - 2 q^{17} + 22 q^{18} - 10 q^{19} - 5 q^{20} + 3 q^{21} + 14 q^{22} + 4 q^{23} - 10 q^{24} - 2 q^{25} - 34 q^{26} + 29 q^{27} + 8 q^{28} + 16 q^{30} + 19 q^{31} + 40 q^{32} - 16 q^{33} + 3 q^{34} - 24 q^{35} - 3 q^{36} + q^{37} - 10 q^{38} - 7 q^{39} + 5 q^{40} + 20 q^{41} + 3 q^{42} - 48 q^{43} + 14 q^{44} + 53 q^{45} + 4 q^{46} + 29 q^{47} + 28 q^{49} + 3 q^{50} - 122 q^{51} + 16 q^{52} - 5 q^{53} - 6 q^{54} + 56 q^{55} + 8 q^{56} - 10 q^{57} + 20 q^{59} - 19 q^{60} + 42 q^{61} - 21 q^{62} + 9 q^{63} - 10 q^{64} + 35 q^{65} + 24 q^{66} - 3 q^{67} - 2 q^{68} - 9 q^{69} - 19 q^{70} + 18 q^{71} - 8 q^{72} + 8 q^{73} - 64 q^{74} + 7 q^{75} + 40 q^{76} + 35 q^{77} - 2 q^{78} + q^{79} + 59 q^{81} - 30 q^{82} + 11 q^{83} - 7 q^{84} - 125 q^{85} + 32 q^{86} - 31 q^{87} - 6 q^{88} - 34 q^{89} - 7 q^{90} + 10 q^{91} + 4 q^{92} + 24 q^{93} + 29 q^{94} + 5 q^{95} + 5 q^{96} + 90 q^{97} - 12 q^{98} + 10 q^{99}+O(q^{100}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 5 * q^6 - 12 * q^7 - 10 * q^8 - 3 * q^9 - 6 * q^11 + 16 * q^13 - 2 * q^14 + 16 * q^15 - 10 * q^16 - 2 * q^17 + 22 * q^18 - 10 * q^19 - 5 * q^20 + 3 * q^21 + 14 * q^22 + 4 * q^23 - 10 * q^24 - 2 * q^25 - 34 * q^26 + 29 * q^27 + 8 * q^28 + 16 * q^30 + 19 * q^31 + 40 * q^32 - 16 * q^33 + 3 * q^34 - 24 * q^35 - 3 * q^36 + q^37 - 10 * q^38 - 7 * q^39 + 5 * q^40 + 20 * q^41 + 3 * q^42 - 48 * q^43 + 14 * q^44 + 53 * q^45 + 4 * q^46 + 29 * q^47 + 28 * q^49 + 3 * q^50 - 122 * q^51 + 16 * q^52 - 5 * q^53 - 6 * q^54 + 56 * q^55 + 8 * q^56 - 10 * q^57 + 20 * q^59 - 19 * q^60 + 42 * q^61 - 21 * q^62 + 9 * q^63 - 10 * q^64 + 35 * q^65 + 24 * q^66 - 3 * q^67 - 2 * q^68 - 9 * q^69 - 19 * q^70 + 18 * q^71 - 8 * q^72 + 8 * q^73 - 64 * q^74 + 7 * q^75 + 40 * q^76 + 35 * q^77 - 2 * q^78 + q^79 + 59 * q^81 - 30 * q^82 + 11 * q^83 - 7 * q^84 - 125 * q^85 + 32 * q^86 - 31 * q^87 - 6 * q^88 - 34 * q^89 - 7 * q^90 + 10 * q^91 + 4 * q^92 + 24 * q^93 + 29 * q^94 + 5 * q^95 + 5 * q^96 + 90 * q^97 - 12 * q^98 + 10 * q^99

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