LMFDB - Embedded newform 361.2.c.h.68.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(68,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("361.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.c (of order $3$, degree $2$, not 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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			68.2
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	361.68
Dual form			361.2.c.h.292.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.673648 + 1.16679i) q^{2} +(-1.43969 + 2.49362i) q^{3} +(0.0923963 + 0.160035i) q^{4} +(-0.439693 + 0.761570i) q^{5} +(-1.93969 - 3.35965i) q^{6} +0.347296 q^{7} -2.94356 q^{8} +(-2.64543 - 4.58202i) q^{9} +O(q^{10})$	\(q+(-0.673648 + 1.16679i) q^{2} +(-1.43969 + 2.49362i) q^{3} +(0.0923963 + 0.160035i) q^{4} +(-0.439693 + 0.761570i) q^{5} +(-1.93969 - 3.35965i) q^{6} +0.347296 q^{7} -2.94356 q^{8} +(-2.64543 - 4.58202i) q^{9} +(-0.592396 - 1.02606i) q^{10} -2.22668 q^{11} -0.532089 q^{12} +(1.28699 + 2.22913i) q^{13} +(-0.233956 + 0.405223i) q^{14} +(-1.26604 - 2.19285i) q^{15} +(1.79813 - 3.11446i) q^{16} +(-0.233956 + 0.405223i) q^{17} +7.12836 q^{18} -0.162504 q^{20} +(-0.500000 + 0.866025i) q^{21} +(1.50000 - 2.59808i) q^{22} +(1.34730 + 2.33359i) q^{23} +(4.23783 - 7.34013i) q^{24} +(2.11334 + 3.66041i) q^{25} -3.46791 q^{26} +6.59627 q^{27} +(0.0320889 + 0.0555796i) q^{28} +(-3.43969 - 5.95772i) q^{29} +3.41147 q^{30} +7.10607 q^{31} +(-0.520945 - 0.902302i) q^{32} +(3.20574 - 5.55250i) q^{33} +(-0.315207 - 0.545955i) q^{34} +(-0.152704 + 0.264490i) q^{35} +(0.488856 - 0.846723i) q^{36} -4.94356 q^{37} -7.41147 q^{39} +(1.29426 - 2.24173i) q^{40} +(1.23783 - 2.14398i) q^{41} +(-0.673648 - 1.16679i) q^{42} +(-1.95084 + 3.37895i) q^{43} +(-0.205737 - 0.356347i) q^{44} +4.65270 q^{45} -3.63041 q^{46} +(3.64543 + 6.31407i) q^{47} +(5.17752 + 8.96773i) q^{48} -6.87939 q^{49} -5.69459 q^{50} +(-0.673648 - 1.16679i) q^{51} +(-0.237826 + 0.411927i) q^{52} +(-1.41875 - 2.45734i) q^{53} +(-4.44356 + 7.69648i) q^{54} +(0.979055 - 1.69577i) q^{55} -1.02229 q^{56} +9.26857 q^{58} +(-3.15270 + 5.46064i) q^{59} +(0.233956 - 0.405223i) q^{60} +(-4.56418 - 7.90539i) q^{61} +(-4.78699 + 8.29131i) q^{62} +(-0.918748 - 1.59132i) q^{63} +8.59627 q^{64} -2.26352 q^{65} +(4.31908 + 7.48086i) q^{66} +(3.83750 + 6.64674i) q^{67} -0.0864665 q^{68} -7.75877 q^{69} +(-0.205737 - 0.356347i) q^{70} +(-4.65270 + 8.05872i) q^{71} +(7.78699 + 13.4875i) q^{72} +(-0.694593 + 1.20307i) q^{73} +(3.33022 - 5.76811i) q^{74} -12.1702 q^{75} -0.773318 q^{77} +(4.99273 - 8.64766i) q^{78} +(-5.92262 + 10.2583i) q^{79} +(1.58125 + 2.73881i) q^{80} +(-1.56031 + 2.70253i) q^{81} +(1.66772 + 2.88857i) q^{82} -14.8307 q^{83} -0.184793 q^{84} +(-0.205737 - 0.356347i) q^{85} +(-2.62836 - 4.55245i) q^{86} +19.8084 q^{87} +6.55438 q^{88} +(-5.14543 - 8.91215i) q^{89} +(-3.13429 + 5.42874i) q^{90} +(0.446967 + 0.774169i) q^{91} +(-0.248970 + 0.431229i) q^{92} +(-10.2306 + 17.7198i) q^{93} -9.82295 q^{94} +3.00000 q^{96} +(4.72668 - 8.18685i) q^{97} +(4.63429 - 8.02682i) q^{98} +(5.89053 + 10.2027i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 12 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 12 * q^8	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 12 q^{8} + 6 q^{12} - 6 q^{14} - 3 q^{15} - 3 q^{16} - 6 q^{17} + 6 q^{18} - 6 q^{20} - 3 q^{21} + 9 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{25} - 30 q^{26} + 12 q^{27} - 9 q^{28} - 15 q^{29} + 18 q^{31} + 9 q^{33} - 9 q^{34} - 3 q^{35} + 9 q^{36} - 24 q^{39} + 18 q^{40} - 12 q^{41} - 3 q^{42} + 9 q^{44} + 30 q^{45} - 36 q^{46} + 6 q^{47} + 6 q^{48} - 30 q^{49} - 30 q^{50} - 3 q^{51} + 18 q^{52} - 6 q^{53} + 3 q^{54} + 9 q^{55} + 6 q^{56} + 36 q^{58} - 21 q^{59} + 6 q^{60} - 9 q^{61} - 21 q^{62} - 3 q^{63} + 24 q^{64} - 24 q^{65} + 9 q^{66} + 18 q^{67} + 30 q^{68} - 24 q^{69} + 9 q^{70} - 30 q^{71} + 39 q^{72} - 3 q^{74} - 30 q^{75} - 18 q^{77} + 12 q^{78} - 9 q^{79} + 12 q^{80} - 15 q^{81} - 18 q^{82} + 6 q^{84} + 9 q^{85} + 21 q^{86} + 42 q^{87} + 18 q^{88} - 15 q^{89} - 9 q^{90} + 15 q^{91} + 24 q^{92} - 24 q^{93} - 18 q^{94} + 18 q^{96} + 15 q^{97} + 18 q^{98} + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 12 * q^8 + 6 * q^12 - 6 * q^14 - 3 * q^15 - 3 * q^16 - 6 * q^17 + 6 * q^18 - 6 * q^20 - 3 * q^21 + 9 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^25 - 30 * q^26 + 12 * q^27 - 9 * q^28 - 15 * q^29 + 18 * q^31 + 9 * q^33 - 9 * q^34 - 3 * q^35 + 9 * q^36 - 24 * q^39 + 18 * q^40 - 12 * q^41 - 3 * q^42 + 9 * q^44 + 30 * q^45 - 36 * q^46 + 6 * q^47 + 6 * q^48 - 30 * q^49 - 30 * q^50 - 3 * q^51 + 18 * q^52 - 6 * q^53 + 3 * q^54 + 9 * q^55 + 6 * q^56 + 36 * q^58 - 21 * q^59 + 6 * q^60 - 9 * q^61 - 21 * q^62 - 3 * q^63 + 24 * q^64 - 24 * q^65 + 9 * q^66 + 18 * q^67 + 30 * q^68 - 24 * q^69 + 9 * q^70 - 30 * q^71 + 39 * q^72 - 3 * q^74 - 30 * q^75 - 18 * q^77 + 12 * q^78 - 9 * q^79 + 12 * q^80 - 15 * q^81 - 18 * q^82 + 6 * q^84 + 9 * q^85 + 21 * q^86 + 42 * q^87 + 18 * q^88 - 15 * q^89 - 9 * q^90 + 15 * q^91 + 24 * q^92 - 24 * q^93 - 18 * q^94 + 18 * q^96 + 15 * q^97 + 18 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.673648	+	1.16679i	−0.476341	+	0.825047i	−0.999633	−	0.0271067i	$-0.991371\pi$
$2$	−0.673648	+	1.16679i	−0.476341	+	0.825047i	0.523291	+	0.852154i	$0.324704\pi$
$3$	−1.43969	+	2.49362i	−0.831207	+	1.43969i	0.0658748	+	0.997828i	$0.479016\pi$
$3$	−1.43969	+	2.49362i	−0.831207	+	1.43969i	−0.897082	+	0.441865i	$0.854317\pi$
$4$	0.0923963	+	0.160035i	0.0461981	+	0.0800175i
$5$	−0.439693	+	0.761570i	−0.196637	+	0.340584i	−0.947436	−	0.319946i	$-0.896335\pi$
$5$	−0.439693	+	0.761570i	−0.196637	+	0.340584i	0.750799	+	0.660530i	$0.229669\pi$
$6$	−1.93969	−	3.35965i	−0.791876	−	1.37157i
$7$	0.347296			0.131266			0.0656328	−	0.997844i	$-0.479093\pi$
$7$	0.347296			0.131266			0.0656328	+	0.997844i	$0.479093\pi$
$8$	−2.94356			−1.04071
$9$	−2.64543	−	4.58202i	−0.881810	−	1.52734i
$10$	−0.592396	−	1.02606i	−0.187332	−	0.324469i
$11$	−2.22668			−0.671370			−0.335685	−	0.941974i	$-0.608968\pi$
$11$	−2.22668			−0.671370			−0.335685	+	0.941974i	$0.608968\pi$
$12$	−0.532089			−0.153601
$13$	1.28699	+	2.22913i	0.356947	+	0.618250i	0.987449	−	0.157938i	$-0.0504845\pi$
$13$	1.28699	+	2.22913i	0.356947	+	0.618250i	−0.630503	+	0.776187i	$0.717151\pi$
$14$	−0.233956	+	0.405223i	−0.0625273	+	0.108300i
$15$	−1.26604	−	2.19285i	−0.326891	−	0.566192i
$16$	1.79813	−	3.11446i	0.449533	−	0.778615i
$17$	−0.233956	+	0.405223i	−0.0567426	+	0.0982810i	−0.893001	−	0.450054i	$-0.851405\pi$
$17$	−0.233956	+	0.405223i	−0.0567426	+	0.0982810i	0.836259	+	0.548335i	$0.184738\pi$
$18$	7.12836			1.68017
$19$		0			0
$19$		0			0
$20$	−0.162504			−0.0363370
$21$	−0.500000	+	0.866025i	−0.109109	+	0.188982i
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	1.34730	+	2.33359i	0.280931	+	0.486586i	0.971614	−	0.236571i	$-0.0760236\pi$
$23$	1.34730	+	2.33359i	0.280931	+	0.486586i	−0.690684	+	0.723157i	$0.742690\pi$
$24$	4.23783	−	7.34013i	0.865043	−	1.49830i
$25$	2.11334	+	3.66041i	0.422668	+	0.732083i
$26$	−3.46791			−0.680113
$27$	6.59627			1.26945
$28$	0.0320889	+	0.0555796i	0.00606423	+	0.0105036i
$29$	−3.43969	−	5.95772i	−0.638735	−	1.10632i	−0.985711	−	0.168447i	$-0.946125\pi$
$29$	−3.43969	−	5.95772i	−0.638735	−	1.10632i	0.346976	−	0.937874i	$-0.387209\pi$
$30$	3.41147			0.622847
$31$	7.10607			1.27629			0.638144	−	0.769917i	$-0.279703\pi$
$31$	7.10607			1.27629			0.638144	+	0.769917i	$0.279703\pi$
$32$	−0.520945	−	0.902302i	−0.0920909	−	0.159506i
$33$	3.20574	−	5.55250i	0.558047	−	0.966566i
$34$	−0.315207	−	0.545955i	−0.0540576	−	0.0936306i
$35$	−0.152704	+	0.264490i	−0.0258116	+	0.0447070i
$36$	0.488856	−	0.846723i	0.0814759	−	0.141120i
$37$	−4.94356			−0.812717			−0.406358	−	0.913714i	$-0.633202\pi$
$37$	−4.94356			−0.812717			−0.406358	+	0.913714i	$0.633202\pi$
$38$		0			0
$39$	−7.41147			−1.18679
$40$	1.29426	−	2.24173i	0.204641	−	0.354449i
$41$	1.23783	−	2.14398i	0.193316	−	0.334833i	−0.753031	−	0.657985i	$-0.771409\pi$
$41$	1.23783	−	2.14398i	0.193316	−	0.334833i	0.946347	+	0.323152i	$0.104742\pi$
$42$	−0.673648	−	1.16679i	−0.103946	−	0.180040i
$43$	−1.95084	+	3.37895i	−0.297500	+	0.515285i	−0.975563	−	0.219719i	$-0.929486\pi$
$43$	−1.95084	+	3.37895i	−0.297500	+	0.515285i	0.678063	+	0.735003i	$0.262819\pi$
$44$	−0.205737	−	0.356347i	−0.0310160	−	0.0537213i
$45$	4.65270			0.693584
$46$	−3.63041			−0.535275
$47$	3.64543	+	6.31407i	0.531741	+	0.921002i	0.999314	+	0.0370472i	$0.0117952\pi$
$47$	3.64543	+	6.31407i	0.531741	+	0.921002i	−0.467573	+	0.883954i	$0.654871\pi$
$48$	5.17752	+	8.96773i	0.747310	+	1.29438i
$49$	−6.87939			−0.982769
$50$	−5.69459			−0.805337
$51$	−0.673648	−	1.16679i	−0.0943296	−	0.163384i
$52$	−0.237826	+	0.411927i	−0.0329805	+	0.0571239i
$53$	−1.41875	−	2.45734i	−0.194880	−	0.337542i	0.751981	−	0.659185i	$-0.229098\pi$
$53$	−1.41875	−	2.45734i	−0.194880	−	0.337542i	−0.946861	+	0.321642i	$0.895765\pi$
$54$	−4.44356	+	7.69648i	−0.604692	+	1.04736i
$55$	0.979055	−	1.69577i	0.132016	−	0.228658i
$56$	−1.02229			−0.136609
$57$		0			0
$58$	9.26857			1.21702
$59$	−3.15270	+	5.46064i	−0.410447	+	0.710915i	−0.994939	−	0.100485i	$-0.967961\pi$
$59$	−3.15270	+	5.46064i	−0.410447	+	0.710915i	0.584492	+	0.811400i	$0.301294\pi$
$60$	0.233956	−	0.405223i	0.0302035	−	0.0523141i
$61$	−4.56418	−	7.90539i	−0.584383	−	1.01218i	−0.994952	−	0.100352i	$-0.968003\pi$
$61$	−4.56418	−	7.90539i	−0.584383	−	1.01218i	0.410569	−	0.911830i	$-0.365330\pi$
$62$	−4.78699	+	8.29131i	−0.607948	+	1.05300i
$63$	−0.918748	−	1.59132i	−0.115751	−	0.200487i
$64$	8.59627			1.07453
$65$	−2.26352			−0.280755
$66$	4.31908	+	7.48086i	0.531642	+	0.920830i
$67$	3.83750	+	6.64674i	0.468825	+	0.812028i	0.999365	−	0.0356314i	$-0.0113442\pi$
$67$	3.83750	+	6.64674i	0.468825	+	0.812028i	−0.530540	+	0.847660i	$0.678011\pi$
$68$	−0.0864665			−0.0104856
$69$	−7.75877			−0.934046
$70$	−0.205737	−	0.356347i	−0.0245903	−	0.0425916i
$71$	−4.65270	+	8.05872i	−0.552174	+	0.956394i	0.445943	+	0.895061i	$0.352868\pi$
$71$	−4.65270	+	8.05872i	−0.552174	+	0.956394i	−0.998117	+	0.0613327i	$0.980465\pi$
$72$	7.78699	+	13.4875i	0.917705	+	1.58951i
$73$	−0.694593	+	1.20307i	−0.0812959	+	0.140809i	−0.903807	−	0.427941i	$-0.859239\pi$
$73$	−0.694593	+	1.20307i	−0.0812959	+	0.140809i	0.822511	+	0.568749i	$0.192573\pi$
$74$	3.33022	−	5.76811i	0.387130	−	0.670530i
$75$	−12.1702			−1.40530
$76$		0			0
$77$	−0.773318			−0.0881278
$78$	4.99273	−	8.64766i	0.565315	−	0.979154i
$79$	−5.92262	+	10.2583i	−0.666347	+	1.15415i	0.312572	+	0.949894i	$0.398810\pi$
$79$	−5.92262	+	10.2583i	−0.666347	+	1.15415i	−0.978918	+	0.204252i	$0.934524\pi$
$80$	1.58125	+	2.73881i	0.176789	+	0.306208i
$81$	−1.56031	+	2.70253i	−0.173367	+	0.300281i
$82$	1.66772	+	2.88857i	0.184169	+	0.318990i
$83$	−14.8307			−1.62788			−0.813940	−	0.580949i	$-0.802681\pi$
$83$	−14.8307			−1.62788			−0.813940	+	0.580949i	$0.802681\pi$
$84$	−0.184793			−0.0201625
$85$	−0.205737	−	0.356347i	−0.0223153	−	0.0386513i
$86$	−2.62836	−	4.55245i	−0.283423	−	0.490903i
$87$	19.8084			2.12368
$88$	6.55438			0.698699
$89$	−5.14543	−	8.91215i	−0.545414	−	0.944686i	−0.998581	−	0.0532595i	$-0.983039\pi$
$89$	−5.14543	−	8.91215i	−0.545414	−	0.944686i	0.453166	−	0.891426i	$-0.350294\pi$
$90$	−3.13429	+	5.42874i	−0.330383	+	0.572240i
$91$	0.446967	+	0.774169i	0.0468548	+	0.0811549i
$92$	−0.248970	+	0.431229i	−0.0259569	+	0.0449588i
$93$	−10.2306	+	17.7198i	−1.06086	+	1.83746i
$94$	−9.82295			−1.01316
$95$		0			0
$96$	3.00000			0.306186
$97$	4.72668	−	8.18685i	0.479922	−	0.831249i	−0.519813	−	0.854280i	$-0.673998\pi$
$97$	4.72668	−	8.18685i	0.479922	−	0.831249i	0.999735	+	0.0230312i	$0.00733169\pi$
$98$	4.63429	−	8.02682i	0.468134	−	0.810831i
$99$	5.89053	+	10.2027i	0.592020	+	1.02541i
$100$	−0.390530	+	0.676417i	−0.0390530	+	0.0676417i
$101$	4.62449	+	8.00984i	0.460153	+	0.797009i	0.998968	−	0.0454151i	$-0.0144610\pi$
$101$	4.62449	+	8.00984i	0.460153	+	0.797009i	−0.538815	+	0.842424i	$0.681128\pi$
$102$	1.81521			0.179732
$103$	5.50980			0.542897			0.271448	−	0.962453i	$-0.412497\pi$
$103$	5.50980			0.542897			0.271448	+	0.962453i	$0.412497\pi$
$104$	−3.78833	−	6.56159i	−0.371477	−	0.643416i
$105$	−0.439693	−	0.761570i	−0.0429096	−	0.0743216i
$106$	3.82295			0.371318
$107$	−10.2344			−0.989399			−0.494699	−	0.869064i	$-0.664722\pi$
$107$	−10.2344			−0.989399			−0.494699	+	0.869064i	$0.664722\pi$
$108$	0.609470	+	1.05563i	0.0586463	+	0.101578i
$109$	−0.911474	+	1.57872i	−0.0873034	+	0.151214i	−0.906370	−	0.422484i	$-0.861158\pi$
$109$	−0.911474	+	1.57872i	−0.0873034	+	0.151214i	0.819067	+	0.573698i	$0.194492\pi$
$110$	1.31908	+	2.28471i	0.125769	+	0.217839i
$111$	7.11721	−	12.3274i	0.675536	−	1.17006i
$112$	0.624485	−	1.08164i	0.0590083	−	0.102205i
$113$	17.6878			1.66393			0.831963	−	0.554830i	$-0.187217\pi$
$113$	17.6878			1.66393			0.831963	+	0.554830i	$0.187217\pi$
$114$		0			0
$115$	−2.36959			−0.220965
$116$	0.635630	−	1.10094i	0.0590167	−	0.102220i
$117$	6.80928	−	11.7940i	0.629518	−	1.09036i
$118$	−4.24763	−	7.35710i	−0.391026	−	0.677276i
$119$	−0.0812519	+	0.140732i	−0.00744835	+	0.0129009i
$120$	3.72668	+	6.45480i	0.340198	+	0.589240i
$121$	−6.04189			−0.549263
$122$	12.2986			1.11346
$123$	3.56418	+	6.17334i	0.321371	+	0.556631i
$124$	0.656574	+	1.13722i	0.0589621	+	0.102125i
$125$	−8.11381			−0.725721
$126$	2.47565			0.220549
$127$	5.80200	+	10.0494i	0.514845	+	0.891737i	0.999852	+	0.0172267i	$0.00548370\pi$
$127$	5.80200	+	10.0494i	0.514845	+	0.891737i	−0.485007	+	0.874510i	$0.661183\pi$
$128$	−4.74897	+	8.22546i	−0.419754	+	0.727035i
$129$	−5.61721	−	9.72930i	−0.494568	−	0.856617i
$130$	1.52481	−	2.64106i	0.133735	−	0.231636i
$131$	−0.922618	+	1.59802i	−0.0806096	+	0.139620i	−0.903512	−	0.428563i	$-0.859020\pi$
$131$	−0.922618	+	1.59802i	−0.0806096	+	0.139620i	0.822902	+	0.568183i	$0.192353\pi$
$132$	1.18479			0.103123
$133$		0			0
$134$	−10.3405			−0.893282
$135$	−2.90033	+	5.02352i	−0.249621	+	0.432356i
$136$	0.688663	−	1.19280i	0.0590524	−	0.102282i
$137$	−0.127889	−	0.221510i	−0.0109263	−	0.0189249i	0.860511	−	0.509433i	$-0.170145\pi$
$137$	−0.127889	−	0.221510i	−0.0109263	−	0.0189249i	−0.871437	+	0.490508i	$0.836811\pi$
$138$	5.22668	−	9.05288i	0.444925	−	0.770632i
$139$	−2.13176	−	3.69232i	−0.180813	−	0.313178i	0.761344	−	0.648348i	$-0.224540\pi$
$139$	−2.13176	−	3.69232i	−0.180813	−	0.313178i	−0.942158	+	0.335170i	$0.891206\pi$
$140$	−0.0564370			−0.00476980
$141$	−20.9932			−1.76795
$142$	−6.26857	−	10.8575i	−0.526047	−	0.911140i
$143$	−2.86571	−	4.96356i	−0.239643	−	0.415074i
$144$	−19.0273			−1.58561
$145$	6.04963			0.502394
$146$	−0.935822	−	1.62089i	−0.0774492	−	0.134146i
$147$	9.90420	−	17.1546i	0.816885	−	1.41489i
$148$	−0.456767	−	0.791143i	−0.0375460	−	0.0650316i
$149$	−8.27972	+	14.3409i	−0.678301	+	1.17485i	0.297192	+	0.954818i	$0.403950\pi$
$149$	−8.27972	+	14.3409i	−0.678301	+	1.17485i	−0.975492	+	0.220033i	$0.929383\pi$
$150$	8.19846	−	14.2002i	0.669402	−	1.15944i
$151$	4.36184			0.354962			0.177481	−	0.984124i	$-0.443205\pi$
$151$	4.36184			0.354962			0.177481	+	0.984124i	$0.443205\pi$
$152$		0			0
$153$	2.47565			0.200145
$154$	0.520945	−	0.902302i	0.0419789	−	0.0727096i
$155$	−3.12449	+	5.41177i	−0.250965	+	0.434684i
$156$	−0.684793	−	1.18610i	−0.0548273	−	0.0949636i
$157$	4.80928	−	8.32991i	0.383822	−	0.664799i	−0.607783	−	0.794103i	$-0.707941\pi$
$157$	4.80928	−	8.32991i	0.383822	−	0.664799i	0.991605	+	0.129304i	$0.0412742\pi$
$158$	−7.97952	−	13.8209i	−0.634817	−	1.09953i
$159$	8.17024			0.647943
$160$	0.916222			0.0724337
$161$	0.467911	+	0.810446i	0.0368766	+	0.0638721i
$162$	−2.10220	−	3.64111i	−0.165164	−	0.286073i
$163$	8.35504			0.654417			0.327209	−	0.944952i	$-0.393892\pi$
$163$	8.35504			0.654417			0.327209	+	0.944952i	$0.393892\pi$
$164$	0.457482			0.0357233
$165$	2.81908	+	4.88279i	0.219465	+	0.380124i
$166$	9.99067	−	17.3043i	0.775426	−	1.34308i
$167$	2.01754	+	3.49448i	0.156122	+	0.270411i	0.933467	−	0.358663i	$-0.116767\pi$
$167$	2.01754	+	3.49448i	0.156122	+	0.270411i	−0.777345	+	0.629075i	$0.783434\pi$
$168$	1.47178	−	2.54920i	0.113550	−	0.196675i
$169$	3.18732	−	5.52060i	0.245178	−	0.424661i
$170$	0.554378			0.0425188
$171$		0			0
$172$	−0.721000			−0.0549758
$173$	−10.0719	+	17.4451i	−0.765754	+	1.32632i	0.174093	+	0.984729i	$0.444301\pi$
$173$	−10.0719	+	17.4451i	−0.765754	+	1.32632i	−0.939847	+	0.341595i	$0.889033\pi$
$174$	−13.3439	+	23.1123i	−1.01160	+	1.75214i
$175$	0.733956	+	1.27125i	0.0554818	+	0.0960973i
$176$	−4.00387	+	6.93491i	−0.301803	+	0.522738i
$177$	−9.07785	−	15.7233i	−0.682333	−	1.18184i
$178$	13.8648			1.03921
$179$	11.5125			0.860484			0.430242	−	0.902714i	$-0.358428\pi$
$179$	11.5125			0.860484			0.430242	+	0.902714i	$0.358428\pi$
$180$	0.429892	+	0.744596i	0.0320423	+	0.0554989i
$181$	4.26857	+	7.39338i	0.317280	+	0.549546i	0.979920	−	0.199393i	$-0.0638970\pi$
$181$	4.26857	+	7.39338i	0.317280	+	0.549546i	−0.662639	+	0.748939i	$0.730564\pi$
$182$	−1.20439			−0.0892755
$183$	26.2841			1.94297
$184$	−3.96585	−	6.86906i	−0.292366	−	0.506394i
$185$	2.17365	−	3.76487i	0.159810	−	0.276799i
$186$	−13.7836	−	23.8739i	−1.01066	−	1.75052i
$187$	0.520945	−	0.902302i	0.0380952	−	0.0659829i
$188$	−0.673648	+	1.16679i	−0.0491308	+	0.0850971i
$189$	2.29086			0.166635
$190$		0			0
$191$	18.3354			1.32671			0.663353	−	0.748307i	$-0.269133\pi$
$191$	18.3354			1.32671			0.663353	+	0.748307i	$0.269133\pi$
$192$	−12.3760	+	21.4358i	−0.893160	+	1.54700i
$193$	0.148833	−	0.257787i	0.0107133	−	0.0185559i	−0.860619	−	0.509249i	$-0.829923\pi$
$193$	0.148833	−	0.257787i	0.0107133	−	0.0185559i	0.871332	+	0.490693i	$0.163256\pi$
$194$	6.36824	+	11.0301i	0.457213	+	0.791916i
$195$	3.25877	−	5.64436i	0.233365	−	0.404201i
$196$	−0.635630	−	1.10094i	−0.0454021	−	0.0786388i
$197$	13.1411			0.936268			0.468134	−	0.883657i	$-0.344926\pi$
$197$	13.1411			0.936268			0.468134	+	0.883657i	$0.344926\pi$
$198$	−15.8726			−1.12802
$199$	0.128356	+	0.222318i	0.00909888	+	0.0157597i	0.870539	−	0.492099i	$-0.163770\pi$
$199$	0.128356	+	0.222318i	0.00909888	+	0.0157597i	−0.861440	+	0.507859i	$0.830437\pi$
$200$	−6.22075	−	10.7747i	−0.439874	−	0.761883i
$201$	−22.0993			−1.55876
$202$	−12.4611			−0.876760
$203$	−1.19459	−	2.06910i	−0.0838440	−	0.145222i
$204$	0.124485	−	0.215615i	0.00871570	−	0.0150960i
$205$	1.08853	+	1.88538i	0.0760259	+	0.131681i
$206$	−3.71167	+	6.42880i	−0.258604	+	0.447915i
$207$	7.12836	−	12.3467i	0.495455	−	0.858153i
$208$	9.25671			0.641837
$209$		0			0
$210$	1.18479			0.0817585
$211$	1.22416	−	2.12030i	0.0842743	−	0.145967i	−0.820807	−	0.571205i	$-0.806476\pi$
$211$	1.22416	−	2.12030i	0.0842743	−	0.145967i	0.905082	+	0.425238i	$0.139809\pi$
$212$	0.262174	−	0.454099i	0.0180062	−	0.0311876i
$213$	−13.3969	−	23.2042i	−0.917942	−	1.58992i
$214$	6.89440	−	11.9415i	0.471291	−	0.816301i
$215$	−1.71554	−	2.97140i	−0.116999	−	0.202648i
$216$	−19.4165			−1.32113
$217$	2.46791			0.167533
$218$	−1.22803	−	2.12700i	−0.0831724	−	0.144059i
$219$	−2.00000	−	3.46410i	−0.135147	−	0.234082i
$220$	0.361844			0.0243955
$221$	−1.20439			−0.0810162
$222$	9.58899	+	16.6086i	0.643571	+	1.11470i
$223$	−4.25490	+	7.36970i	−0.284929	+	0.493512i	−0.972592	−	0.232518i	$-0.925303\pi$
$223$	−4.25490	+	7.36970i	−0.284929	+	0.493512i	0.687663	+	0.726030i	$0.258637\pi$
$224$	−0.180922	−	0.313366i	−0.0120884	−	0.0209377i
$225$	11.1814	−	19.3667i	0.745426	−	1.29112i
$226$	−11.9153	+	20.6380i	−0.792597	+	1.37282i
$227$	14.1506			0.939211			0.469606	−	0.882876i	$-0.344396\pi$
$227$	14.1506			0.939211			0.469606	+	0.882876i	$0.344396\pi$
$228$		0			0
$229$	−20.5330			−1.35686			−0.678430	−	0.734665i	$-0.737339\pi$
$229$	−20.5330			−1.35686			−0.678430	+	0.734665i	$0.737339\pi$
$230$	1.59627	−	2.76481i	0.105255	−	0.182306i
$231$	1.11334	−	1.92836i	0.0732524	−	0.126877i
$232$	10.1250	+	17.5369i	0.664736	+	1.15136i
$233$	−8.82547	+	15.2862i	−0.578176	+	1.00143i	0.417513	+	0.908671i	$0.362902\pi$
$233$	−8.82547	+	15.2862i	−0.578176	+	1.00143i	−0.995689	+	0.0927591i	$0.970431\pi$
$234$	9.17412	+	15.8900i	0.599731	+	1.03876i
$235$	−6.41147			−0.418238
$236$	−1.16519			−0.0758475
$237$	−17.0535	−	29.5375i	−1.10774	−	1.91867i
$238$	−0.109470	−	0.189608i	−0.00709591	−	0.0122905i
$239$	2.35235			0.152161			0.0760804	−	0.997102i	$-0.475759\pi$
$239$	2.35235			0.152161			0.0760804	+	0.997102i	$0.475759\pi$
$240$	−9.10607			−0.587794
$241$	6.90033	+	11.9517i	0.444489	+	0.769878i	0.998016	−	0.0629530i	$-0.0200518\pi$
$241$	6.90033	+	11.9517i	0.444489	+	0.769878i	−0.553527	+	0.832831i	$0.686719\pi$
$242$	4.07011	−	7.04963i	0.261636	−	0.453168i
$243$	5.40167	+	9.35597i	0.346518	+	0.600186i
$244$	0.843426	−	1.46086i	0.0539948	−	0.0935218i
$245$	3.02481	−	5.23913i	0.193248	−	0.334716i
$246$	−9.60401			−0.612329
$247$		0			0
$248$	−20.9172			−1.32824
$249$	21.3516	−	36.9821i	1.35310	−	2.34365i
$250$	5.46585	−	9.46713i	0.345691	−	0.598754i
$251$	2.08260	+	3.60716i	0.131452	+	0.227682i	0.924237	−	0.381820i	$-0.124703\pi$
$251$	2.08260	+	3.60716i	0.131452	+	0.227682i	−0.792784	+	0.609502i	$0.791369\pi$
$252$	0.169778	−	0.294064i	0.0106950	−	0.0185243i
$253$	−3.00000	−	5.19615i	−0.188608	−	0.326679i
$254$	−15.6340			−0.980967
$255$	1.18479			0.0741946
$256$	2.19800	+	3.80704i	0.137375	+	0.237940i
$257$	0.333626	+	0.577857i	0.0208110	+	0.0360457i	0.876243	−	0.481869i	$-0.160042\pi$
$257$	0.333626	+	0.577857i	0.0208110	+	0.0360457i	−0.855432	+	0.517915i	$0.826709\pi$
$258$	15.1361			0.942332
$259$	−1.71688			−0.106682
$260$	−0.209141	−	0.362242i	−0.0129704	−	0.0224653i
$261$	−18.1989	+	31.5215i	−1.12649	+	1.95113i
$262$	−1.24304	−	2.15301i	−0.0767953	−	0.133013i
$263$	−5.69981	+	9.87236i	−0.351465	+	0.608756i	−0.986506	−	0.163723i	$-0.947650\pi$
$263$	−5.69981	+	9.87236i	−0.351465	+	0.608756i	0.635041	+	0.772478i	$0.280983\pi$
$264$	−9.43629	+	16.3441i	−0.580763	+	1.00591i
$265$	2.49525			0.153282
$266$		0			0
$267$	29.6313			1.81341
$268$	−0.709141	+	1.22827i	−0.0433177	+	0.0750284i
$269$	9.69506	−	16.7923i	0.591118	−	1.02385i	−0.402964	−	0.915216i	$-0.632020\pi$
$269$	9.69506	−	16.7923i	0.591118	−	1.02385i	0.994082	−	0.108631i	$-0.0346467\pi$
$270$	−3.90760	−	6.76817i	−0.237809	−	0.411898i
$271$	6.69712	−	11.5998i	0.406821	−	0.704635i	−0.587711	−	0.809071i	$-0.699971\pi$
$271$	6.69712	−	11.5998i	0.406821	−	0.704635i	0.994532	+	0.104437i	$0.0333039\pi$
$272$	0.841367	+	1.45729i	0.0510153	+	0.0883612i
$273$	−2.57398			−0.155784
$274$	0.344608			0.0208185
$275$	−4.70574	−	8.15058i	−0.283767	−	0.491498i
$276$	−0.716881	−	1.24168i	−0.0431512	−	0.0747401i
$277$	17.7469			1.06631			0.533154	−	0.846018i	$-0.321007\pi$
$277$	17.7469			1.06631			0.533154	+	0.846018i	$0.321007\pi$
$278$	5.74422			0.344516
$279$	−18.7986	−	32.5601i	−1.12544	−	1.94932i
$280$	0.449493	−	0.778544i	0.0268623	−	0.0465269i
$281$	9.13950	+	15.8301i	0.545217	+	0.944343i	0.998593	+	0.0530241i	$0.0168860\pi$
$281$	9.13950	+	15.8301i	0.545217	+	0.944343i	−0.453376	+	0.891319i	$0.649781\pi$
$282$	14.1420	−	24.4947i	0.842145	−	1.45864i
$283$	−3.84389	+	6.65782i	−0.228496	+	0.395766i	−0.957362	−	0.288889i	$-0.906714\pi$
$283$	−3.84389	+	6.65782i	−0.228496	+	0.395766i	0.728867	+	0.684656i	$0.240047\pi$
$284$	−1.71957			−0.102038
$285$		0			0
$286$	7.72193			0.456608
$287$	0.429892	−	0.744596i	0.0253757	−	0.0439521i
$288$	−2.75624	+	4.77396i	−0.162413	+	0.281308i
$289$	8.39053	+	14.5328i	0.493561	+	0.854872i
$290$	−4.07532	+	7.05866i	−0.239311	+	0.414499i
$291$	13.6099	+	23.5731i	0.797829	+	1.38188i
$292$	−0.256711			−0.0150229
$293$	10.5030			0.613591			0.306796	−	0.951775i	$-0.400743\pi$
$293$	10.5030			0.613591			0.306796	+	0.951775i	$0.400743\pi$
$294$	13.3439	+	23.1123i	0.778232	+	1.34794i
$295$	−2.77244	−	4.80201i	−0.161418	−	0.279584i
$296$	14.5517			0.845800
$297$	−14.6878			−0.852272
$298$	−11.1552	−	19.3214i	−0.646205	−	1.11926i
$299$	−3.46791	+	6.00660i	−0.200554	+	0.347371i
$300$	−1.12449	−	1.94767i	−0.0649222	−	0.112449i
$301$	−0.677519	+	1.17350i	−0.0390515	+	0.0676392i
$302$	−2.93835	+	5.08937i	−0.169083	+	0.292860i
$303$	−26.6313			−1.52993
$304$		0			0
$305$	8.02734			0.459644
$306$	−1.66772	+	2.88857i	−0.0953371	+	0.165129i
$307$	−5.84776	+	10.1286i	−0.333749	+	0.578071i	−0.983244	−	0.182295i	$-0.941647\pi$
$307$	−5.84776	+	10.1286i	−0.333749	+	0.578071i	0.649494	+	0.760366i	$0.274981\pi$
$308$	−0.0714517	−	0.123758i	−0.00407134	−	0.00705177i
$309$	−7.93242	+	13.7394i	−0.451260	+	0.781604i
$310$	−4.20961	−	7.29125i	−0.239090	−	0.414115i
$311$	15.9659			0.905340			0.452670	−	0.891678i	$-0.350471\pi$
$311$	15.9659			0.905340			0.452670	+	0.891678i	$0.350471\pi$
$312$	21.8161			1.23510
$313$	13.3143	+	23.0611i	0.752570	+	1.30349i	0.946573	+	0.322489i	$0.104520\pi$
$313$	13.3143	+	23.0611i	0.752570	+	1.30349i	−0.194003	+	0.981001i	$0.562147\pi$
$314$	6.47952	+	11.2229i	0.365661	+	0.633343i
$315$	1.61587			0.0910438
$316$	−2.18891			−0.123136
$317$	14.7660	+	25.5755i	0.829344	+	1.43647i	0.898554	+	0.438863i	$0.144619\pi$
$317$	14.7660	+	25.5755i	0.829344	+	1.43647i	−0.0692102	+	0.997602i	$0.522048\pi$
$318$	−5.50387	+	9.53298i	−0.308642	+	0.534583i
$319$	7.65910	+	13.2660i	0.428827	+	0.742751i
$320$	−3.77972	+	6.54666i	−0.211292	+	0.365969i
$321$	14.7344	−	25.5208i	0.822395	−	1.42443i
$322$	−1.26083			−0.0702633
$323$		0			0
$324$	−0.576666			−0.0320370
$325$	−5.43969	+	9.42182i	−0.301740	+	0.522629i
$326$	−5.62836	+	9.74860i	−0.311726	+	0.539925i
$327$	−2.62449	−	4.54574i	−0.145134	−	0.251380i
$328$	−3.64362	+	6.31093i	−0.201185	+	0.348463i
$329$	1.26604	+	2.19285i	0.0697993	+	0.120896i
$330$	−7.59627			−0.418161
$331$	−27.6655			−1.52063			−0.760317	−	0.649553i	$-0.774956\pi$
$331$	−27.6655			−1.52063			−0.760317	+	0.649553i	$0.774956\pi$
$332$	−1.37030	−	2.37343i	−0.0752050	−	0.130259i
$333$	13.0778	+	22.6515i	0.716662	+	1.24129i
$334$	−5.43645			−0.297469
$335$	−6.74928			−0.368752
$336$	1.79813	+	3.11446i	0.0980962	+	0.169908i
$337$	8.92989	−	15.4670i	0.486442	−	0.842543i	−0.513436	−	0.858128i	$-0.671628\pi$
$337$	8.92989	−	15.4670i	0.486442	−	0.842543i	0.999879	+	0.0155850i	$0.00496107\pi$
$338$	4.29426	+	7.43788i	0.233577	+	0.404567i
$339$	−25.4650	+	44.1066i	−1.38307	+	2.39554i
$340$	0.0380187	−	0.0658503i	0.00206185	−	0.00357123i
$341$	−15.8229			−0.856861
$342$		0			0
$343$	−4.82026			−0.260270
$344$	5.74241	−	9.94615i	0.309610	−	0.536260i
$345$	3.41147	−	5.90885i	0.183668	−	0.318122i
$346$	−13.5699	−	23.5037i	−0.729520	−	1.26357i
$347$	2.90033	−	5.02352i	0.155698	−	0.269677i	−0.777615	−	0.628741i	$-0.783571\pi$
$347$	2.90033	−	5.02352i	0.155698	−	0.269677i	0.933313	+	0.359064i	$0.116904\pi$
$348$	1.83022	+	3.17004i	0.0981102	+	0.169932i
$349$	5.37227			0.287571			0.143786	−	0.989609i	$-0.454072\pi$
$349$	5.37227			0.287571			0.143786	+	0.989609i	$0.454072\pi$
$350$	−1.97771			−0.105713
$351$	8.48932	+	14.7039i	0.453127	+	0.784838i
$352$	1.15998	+	2.00914i	0.0618270	+	0.107088i
$353$	−25.2344			−1.34309			−0.671546	−	0.740963i	$-0.734370\pi$
$353$	−25.2344			−1.34309			−0.671546	+	0.740963i	$0.734370\pi$
$354$	24.4611			1.30009
$355$	−4.09152	−	7.08672i	−0.217155	−	0.376124i
$356$	0.950837	−	1.64690i	0.0503943	−	0.0872854i
$357$	−0.233956	−	0.405223i	−0.0123822	−	0.0214467i
$358$	−7.75537	+	13.4327i	−0.409884	+	0.709940i
$359$	−3.34343	+	5.79098i	−0.176459	+	0.305636i	−0.940665	−	0.339336i	$-0.889798\pi$
$359$	−3.34343	+	5.79098i	−0.176459	+	0.305636i	0.764206	+	0.644972i	$0.223131\pi$
$360$	−13.6955			−0.721818
$361$		0			0
$362$	−11.5021			−0.604535
$363$	8.69846	−	15.0662i	0.456551	−	0.790769i
$364$	−0.0825961	+	0.143061i	−0.00432921	+	0.00749841i
$365$	−0.610815	−	1.05796i	−0.0319715	−	0.0553763i
$366$	−17.7062	+	30.6680i	−0.925518	+	1.60304i
$367$	−4.05943	−	7.03114i	−0.211901	−	0.367022i	0.740409	−	0.672157i	$-0.234632\pi$
$367$	−4.05943	−	7.03114i	−0.211901	−	0.367022i	−0.952309	+	0.305134i	$0.901299\pi$
$368$	9.69047			0.505151
$369$	−13.0983			−0.681872
$370$	2.92855	+	5.07239i	0.152248	+	0.263701i
$371$	−0.492726	−	0.853427i	−0.0255811	−	0.0443077i
$372$	−3.78106			−0.196039
$373$	−34.8976			−1.80693			−0.903463	−	0.428665i	$-0.858984\pi$
$373$	−34.8976			−1.80693			−0.903463	+	0.428665i	$0.858984\pi$
$374$	0.701867	+	1.21567i	0.0362927	+	0.0628607i
$375$	11.6814	−	20.2328i	0.603224	−	1.04482i
$376$	−10.7306	−	18.5859i	−0.553386	−	0.958493i
$377$	8.85369	−	15.3350i	0.455988	−	0.789795i
$378$	−1.54323	+	2.67296i	−0.0793754	+	0.137482i
$379$	−1.70140			−0.0873950			−0.0436975	−	0.999045i	$-0.513914\pi$
$379$	−1.70140			−0.0873950			−0.0436975	+	0.999045i	$0.513914\pi$
$380$		0			0
$381$	−33.4124			−1.71177
$382$	−12.3516	+	21.3937i	−0.631965	+	1.09459i
$383$	1.46838	−	2.54331i	0.0750306	−	0.129957i	−0.826069	−	0.563569i	$-0.809428\pi$
$383$	1.46838	−	2.54331i	0.0750306	−	0.129957i	0.901100	+	0.433612i	$0.142761\pi$
$384$	−13.6741	−	23.6843i	−0.697804	−	1.20863i
$385$	0.340022	−	0.588936i	0.0173291	−	0.0300150i
$386$	0.200522	+	0.347315i	0.0102063	+	0.0176779i
$387$	20.6432			1.04935
$388$	1.74691			0.0886860
$389$	12.2836	+	21.2758i	0.622803	+	1.07873i	0.988961	+	0.148173i	$0.0473393\pi$
$389$	12.2836	+	21.2758i	0.622803	+	1.07873i	−0.366159	+	0.930552i	$0.619327\pi$
$390$	4.39053	+	7.60462i	0.222323	+	0.385075i
$391$	−1.26083			−0.0637629
$392$	20.2499			1.02277
$393$	−2.65657	−	4.60132i	−0.134006	−	0.232106i
$394$	−8.85251	+	15.3330i	−0.445983	+	0.772465i
$395$	−5.20826	−	9.02098i	−0.262056	−	0.453895i
$396$	−1.08853	+	1.88538i	−0.0547005	+	0.0947440i
$397$	15.9179	−	27.5706i	0.798895	−	1.38373i	−0.121441	−	0.992599i	$-0.538752\pi$
$397$	15.9179	−	27.5706i	0.798895	−	1.38373i	0.920336	−	0.391128i	$-0.127915\pi$
$398$	−0.345866			−0.0173367
$399$		0			0
$400$	15.2003			0.760014
$401$	−0.0432332	+	0.0748822i	−0.00215896	+	0.00373944i	−0.867103	−	0.498129i	$-0.834021\pi$
$401$	−0.0432332	+	0.0748822i	−0.00215896	+	0.00373944i	0.864944	+	0.501869i	$0.167354\pi$
$402$	14.8871	−	25.7853i	0.742502	−	1.28605i
$403$	9.14543	+	15.8403i	0.455566	+	0.789064i
$404$	−0.854570	+	1.48016i	−0.0425165	+	0.0736407i
$405$	−1.37211	−	2.37657i	−0.0681808	−	0.118093i
$406$	3.21894			0.159753
$407$	11.0077			0.545633
$408$	1.98293	+	3.43453i	0.0981695	+	0.170034i
$409$	10.0030	+	17.3257i	0.494616	+	0.856700i	0.999981	−	0.00620559i	$-0.00197531\pi$
$409$	10.0030	+	17.3257i	0.494616	+	0.856700i	−0.505365	+	0.862906i	$0.668642\pi$
$410$	−2.93313			−0.144857
$411$	0.736482			0.0363280
$412$	0.509085	+	0.881761i	0.0250808	+	0.0434412i
$413$	−1.09492	+	1.89646i	−0.0538776	+	0.0933188i
$414$	9.60401	+	16.6346i	0.472011	+	0.817547i
$415$	6.52094	−	11.2946i	0.320101	−	0.554430i
$416$	1.34090	−	2.32251i	0.0657430	−	0.113870i
$417$	12.2763			0.601174
$418$		0			0
$419$	25.4097			1.24135			0.620673	−	0.784070i	$-0.286859\pi$
$419$	25.4097			1.24135			0.620673	+	0.784070i	$0.286859\pi$
$420$	0.0812519	−	0.140732i	0.00396469	−	0.00686704i
$421$	2.18479	−	3.78417i	0.106480	−	0.184429i	−0.807862	−	0.589372i	$-0.799375\pi$
$421$	2.18479	−	3.78417i	0.106480	−	0.184429i	0.914342	+	0.404943i	$0.132709\pi$
$422$	1.64930	+	2.85667i	0.0802867	+	0.139061i
$423$	19.2875	−	33.4069i	0.937788	−	1.62430i
$424$	4.17617	+	7.23335i	0.202813	+	0.351282i
$425$	−1.97771			−0.0959331
$426$	36.0993			1.74901
$427$	−1.58512	−	2.74551i	−0.0767094	−	0.132865i
$428$	−0.945622	−	1.63787i	−0.0457084	−	0.0791692i
$429$	16.5030			0.796772
$430$	4.62267			0.222925
$431$	−19.1532	−	33.1743i	−0.922576	−	1.59795i	−0.795414	−	0.606066i	$-0.792747\pi$
$431$	−19.1532	−	33.1743i	−0.922576	−	1.59795i	−0.127161	−	0.991882i	$-0.540587\pi$
$432$	11.8610	−	20.5438i	0.570661	−	0.988414i
$433$	−9.06552	−	15.7019i	−0.435661	−	0.754587i	0.561688	−	0.827349i	$-0.310152\pi$
$433$	−9.06552	−	15.7019i	−0.435661	−	0.754587i	−0.997349	+	0.0727617i	$0.976819\pi$
$434$	−1.66250	+	2.87954i	−0.0798027	+	0.138222i
$435$	−8.70961	+	15.0855i	−0.417594	+	0.723294i
$436$	−0.336867			−0.0161330
$437$		0			0
$438$	5.38919			0.257505
$439$	−3.04529	+	5.27460i	−0.145344	+	0.251743i	−0.929501	−	0.368819i	$-0.879762\pi$
$439$	−3.04529	+	5.27460i	−0.145344	+	0.251743i	0.784157	+	0.620562i	$0.213096\pi$
$440$	−2.88191	+	4.99162i	−0.137390	+	0.237966i
$441$	18.1989	+	31.5215i	0.866616	+	1.50102i
$442$	0.811337	−	1.40528i	0.0385914	−	0.0668422i
$443$	14.9466	+	25.8882i	0.710132	+	1.22999i	0.964807	+	0.262958i	$0.0846982\pi$
$443$	14.9466	+	25.8882i	0.710132	+	1.22999i	−0.254675	+	0.967027i	$0.581968\pi$
$444$	2.63041			0.124834
$445$	9.04963			0.428994
$446$	−5.73261	−	9.92917i	−0.271447	−	0.470160i
$447$	−23.8405	−	41.2929i	−1.12762	−	1.95309i
$448$	2.98545			0.141049
$449$	11.2499			0.530916			0.265458	−	0.964122i	$-0.414477\pi$
$449$	11.2499			0.530916			0.265458	+	0.964122i	$0.414477\pi$
$450$	15.0646	+	26.0927i	0.710154	+	1.23002i
$451$	−2.75624	+	4.77396i	−0.129786	+	0.224797i
$452$	1.63429	+	2.83067i	0.0768703	+	0.133143i
$453$	−6.27972	+	10.8768i	−0.295047	+	0.511036i
$454$	−9.53256	+	16.5109i	−0.447385	+	0.774894i
$455$	−0.786112			−0.0368535
$456$		0			0
$457$	−23.3901			−1.09414			−0.547072	−	0.837086i	$-0.684258\pi$
$457$	−23.3901			−1.09414			−0.547072	+	0.837086i	$0.684258\pi$
$458$	13.8320	−	23.9578i	0.646328	−	1.11947i
$459$	−1.54323	+	2.67296i	−0.0720320	+	0.124763i
$460$	−0.218941	−	0.379217i	−0.0102082	−	0.0176811i
$461$	18.3118	−	31.7170i	0.852866	−	1.47721i	−0.0257452	−	0.999669i	$-0.508196\pi$
$461$	18.3118	−	31.7170i	0.852866	−	1.47721i	0.878611	−	0.477538i	$-0.158471\pi$
$462$	1.50000	+	2.59808i	0.0697863	+	0.120873i
$463$	−42.9864			−1.99775			−0.998873	−	0.0474549i	$-0.984889\pi$
$463$	−42.9864			−1.99775			−0.998873	+	0.0474549i	$0.984889\pi$
$464$	−24.7401			−1.14853
$465$	−8.99660	−	15.5826i	−0.417207	−	0.722624i
$466$	−11.8905	−	20.5950i	−0.550818	−	0.954045i
$467$	25.5963			1.18445			0.592227	−	0.805771i	$-0.298249\pi$
$467$	25.5963			1.18445			0.592227	+	0.805771i	$0.298249\pi$
$468$	2.51661			0.116330
$469$	1.33275	+	2.30839i	0.0615406	+	0.106591i
$470$	4.31908	−	7.48086i	0.199224	−	0.345066i
$471$	13.8478	+	23.9850i	0.638071	+	1.10517i
$472$	9.28018	−	16.0737i	0.427155	−	0.739854i
$473$	4.34389	−	7.52384i	0.199732	−	0.345947i
$474$	45.9522			2.11066
$475$		0			0
$476$	−0.0300295			−0.00137640
$477$	−7.50640	+	13.0015i	−0.343694	+	0.595296i
$478$	−1.58466	+	2.74470i	−0.0724805	+	0.125540i
$479$	−19.0881	−	33.0616i	−0.872158	−	1.51062i	−0.859759	−	0.510699i	$-0.829387\pi$
$479$	−19.0881	−	33.0616i	−0.872158	−	1.51062i	−0.0123988	−	0.999923i	$-0.503947\pi$
$480$	−1.31908	+	2.28471i	−0.0602074	+	0.104282i
$481$	−6.36231	−	11.0198i	−0.290096	−	0.502462i
$482$	−18.5936			−0.846914
$483$	−2.69459			−0.122608
$484$	−0.558248	−	0.966914i	−0.0253749	−	0.0439506i
$485$	4.15657	+	7.19940i	0.188740	+	0.326908i
$486$	−14.5553			−0.660242
$487$	−7.76382			−0.351812			−0.175906	−	0.984407i	$-0.556286\pi$
$487$	−7.76382			−0.351812			−0.175906	+	0.984407i	$0.556286\pi$
$488$	13.4349	+	23.2700i	0.608171	+	1.05338i
$489$	−12.0287	+	20.8343i	−0.543956	+	0.942159i
$490$	4.07532	+	7.05866i	0.184104	+	0.318878i
$491$	18.3614	−	31.8029i	0.828640	−	1.43525i	−0.0704655	−	0.997514i	$-0.522448\pi$
$491$	18.3614	−	31.8029i	0.828640	−	1.43525i	0.899105	−	0.437732i	$-0.144218\pi$
$492$	−0.658633	+	1.14079i	−0.0296935	+	0.0514306i
$493$	3.21894			0.144974
$494$		0			0
$495$	−10.3601			−0.465651
$496$	12.7777	−	22.1315i	0.573734	−	0.993736i
$497$	−1.61587	+	2.79876i	−0.0724815	+	0.125542i
$498$	28.7670	+	49.8259i	1.28908	+	2.23275i
$499$	−2.46316	+	4.26632i	−0.110266	+	0.190987i	−0.915878	−	0.401458i	$-0.868504\pi$
$499$	−2.46316	+	4.26632i	−0.110266	+	0.190987i	0.805611	+	0.592444i	$0.201837\pi$
$500$	−0.749686	−	1.29849i	−0.0335270	−	0.0580704i
$501$	−11.6186			−0.519079
$502$	−5.61175			−0.250465
$503$	−16.4748	−	28.5351i	−0.734574	−	1.27232i	−0.954910	−	0.296895i	$-0.904049\pi$
$503$	−16.4748	−	28.5351i	−0.734574	−	1.27232i	0.220336	−	0.975424i	$-0.429285\pi$
$504$	2.70439	+	4.68415i	0.120463	+	0.208648i
$505$	−8.13341			−0.361932
$506$	8.08378			0.359368
$507$	9.17752	+	15.8959i	0.407588	+	0.705963i
$508$	−1.07217	+	1.85705i	−0.0475697	+	0.0823932i
$509$	−18.4675	−	31.9866i	−0.818558	−	1.41778i	−0.906745	−	0.421679i	$-0.861441\pi$
$509$	−18.4675	−	31.9866i	−0.818558	−	1.41778i	0.0881874	−	0.996104i	$-0.471893\pi$
$510$	−0.798133	+	1.38241i	−0.0353419	+	0.0612140i
$511$	−0.241230	+	0.417822i	−0.0106714	+	0.0184833i
$512$	−24.9186			−1.10126
$513$		0			0
$514$	−0.898986			−0.0396526
$515$	−2.42262	+	4.19610i	−0.106753	+	0.184902i
$516$	1.03802	−	1.79790i	0.0456962	−	0.0791482i
$517$	−8.11721	−	14.0594i	−0.356995	−	0.618333i
$518$	1.15657	−	2.00324i	0.0508169	−	0.0880175i
$519$	−29.0009	−	50.2311i	−1.27300	−	2.20490i
$520$	6.66281			0.292183
$521$	−9.29179			−0.407081			−0.203540	−	0.979067i	$-0.565245\pi$
$521$	−9.29179			−0.407081			−0.203540	+	0.979067i	$0.565245\pi$
$522$	−24.5194	−	42.4688i	−1.07318	−	1.85881i
$523$	−14.2075	−	24.6082i	−0.621253	−	1.07604i	−0.989253	−	0.146215i	$-0.953291\pi$
$523$	−14.2075	−	24.6082i	−0.621253	−	1.07604i	0.368000	−	0.929826i	$-0.380043\pi$
$524$	−0.340986			−0.0148960
$525$	−4.22668			−0.184468
$526$	−7.67933	−	13.3010i	−0.334835	−	0.579951i
$527$	−1.66250	+	2.87954i	−0.0724198	+	0.125435i
$528$	−11.5287	−	19.9683i	−0.501722	−	0.869007i
$529$	7.86959	−	13.6305i	0.342156	−	0.592631i
$530$	−1.68092	+	2.91144i	−0.0730146	+	0.126465i
$531$	33.3610			1.44775
$532$		0			0
$533$	6.37227			0.276014
$534$	−19.9611	+	34.5736i	−0.863801	+	1.49615i
$535$	4.50000	−	7.79423i	0.194552	−	0.336974i
$536$	−11.2959	−	19.5651i	−0.487909	−	0.845083i
$537$	−16.5744	+	28.7078i	−0.715240	+	1.23883i
$538$	13.0621	+	22.6243i	0.563148	+	0.975401i
$539$	15.3182			0.659802
$540$	−1.07192			−0.0461280
$541$	−7.49273	−	12.9778i	−0.322137	−	0.557958i	0.658791	−	0.752326i	$-0.271068\pi$
$541$	−7.49273	−	12.9778i	−0.322137	−	0.557958i	−0.980929	+	0.194367i	$0.937735\pi$
$542$	9.02300	+	15.6283i	0.387571	+	0.671293i
$543$	−24.5817			−1.05490
$544$	0.487511			0.0209019
$545$	−0.801537	−	1.38830i	−0.0343341	−	0.0594684i
$546$	1.73396	−	3.00330i	0.0742064	−	0.128529i
$547$	−1.94356	−	3.36635i	−0.0831008	−	0.143935i	0.821480	−	0.570238i	$-0.193149\pi$
$547$	−1.94356	−	3.36635i	−0.0831008	−	0.143935i	−0.904580	+	0.426303i	$0.859816\pi$
$548$	0.0236329	−	0.0409333i	0.00100955	−	0.00174859i
$549$	−24.1484	+	41.8263i	−1.03063	+	1.78510i
$550$	12.6800			0.540679
$551$		0			0
$552$	22.8384			0.972068
$553$	−2.05690	+	3.56266i	−0.0874684	+	0.151500i
$554$	−11.9552	+	20.7070i	−0.507927	+	0.879755i
$555$	6.25877	+	10.8405i	0.265670	+	0.460154i
$556$	0.393933	−	0.682312i	0.0167065	−	0.0289365i
$557$	−6.60220	−	11.4353i	−0.279744	−	0.484531i	0.691577	−	0.722303i	$-0.256916\pi$
$557$	−6.60220	−	11.4353i	−0.279744	−	0.484531i	−0.971321	+	0.237772i	$0.923583\pi$
$558$	50.6546			2.14438
$559$	−10.0428			−0.424766
$560$	0.549163	+	0.951178i	0.0232064	+	0.0401946i
$561$	1.50000	+	2.59808i	0.0633300	+	0.109691i
$562$	−24.6272			−1.03884
$563$	−10.7128			−0.451489			−0.225745	−	0.974187i	$-0.572481\pi$
$563$	−10.7128			−0.451489			−0.225745	+	0.974187i	$0.572481\pi$
$564$	−1.93969	−	3.35965i	−0.0816758	−	0.141467i
$565$	−7.77719	+	13.4705i	−0.327189	+	0.566708i
$566$	−5.17886	−	8.97005i	−0.217684	−	0.377039i
$567$	−0.541889	+	0.938579i	−0.0227572	+	0.0394166i
$568$	13.6955	−	23.7213i	0.574652	−	0.995326i
$569$	13.4706			0.564717			0.282358	−	0.959309i	$-0.408883\pi$
$569$	13.4706			0.564717			0.282358	+	0.959309i	$0.408883\pi$
$570$		0			0
$571$	12.6655			0.530035			0.265017	−	0.964244i	$-0.414622\pi$
$571$	12.6655			0.530035			0.265017	+	0.964244i	$0.414622\pi$
$572$	0.529563	−	0.917229i	0.0221421	−	0.0383513i
$573$	−26.3974	+	45.7216i	−1.10277	+	1.91005i
$574$	0.579193	+	1.00319i	0.0241750	+	0.0418724i
$575$	−5.69459	+	9.86332i	−0.237481	+	0.411329i
$576$	−22.7408	−	39.3883i	−0.947534	−	1.64118i
$577$	−10.5544			−0.439384			−0.219692	−	0.975569i	$-0.570505\pi$
$577$	−10.5544			−0.439384			−0.219692	+	0.975569i	$0.570505\pi$
$578$	−22.6091			−0.940413
$579$	0.428548	+	0.742267i	0.0178099	+	0.0308476i
$580$	0.558963	+	0.968153i	0.0232097	+	0.0402004i
$581$	−5.15064			−0.213685
$582$	−36.6732			−1.52015
$583$	3.15910	+	5.47172i	0.130837	+	0.226616i
$584$	2.04458	−	3.54131i	0.0846052	−	0.146541i
$585$	5.98798	+	10.3715i	0.247572	+	0.428808i
$586$	−7.07532	+	12.2548i	−0.292279	+	0.506242i
$587$	9.57738	−	16.5885i	0.395301	−	0.684681i	−0.597839	−	0.801616i	$-0.703974\pi$
$587$	9.57738	−	16.5885i	0.395301	−	0.684681i	0.993140	+	0.116935i	$0.0373070\pi$
$588$	3.66044			0.150954
$589$		0			0
$590$	7.47060			0.307560
$591$	−18.9192	+	32.7690i	−0.778233	+	1.34794i
$592$	−8.88919	+	15.3965i	−0.365343	+	0.632793i
$593$	4.34730	+	7.52974i	0.178522	+	0.309209i	0.941375	−	0.337363i	$-0.109535\pi$
$593$	4.34730	+	7.52974i	0.178522	+	0.309209i	−0.762852	+	0.646573i	$0.776202\pi$
$594$	9.89440	−	17.1376i	0.405972	−	0.703164i
$595$	−0.0714517	−	0.123758i	−0.00292924	−	0.00507358i
$596$	−3.06006			−0.125345
$597$	−0.739170			−0.0302522
$598$	−4.67230	−	8.09267i	−0.191065	−	0.330934i
$599$	9.91581	+	17.1747i	0.405149	+	0.701739i	0.994339	−	0.106256i	$-0.0338863\pi$
$599$	9.91581	+	17.1747i	0.405149	+	0.701739i	−0.589190	+	0.807995i	$0.700553\pi$
$600$	35.8239			1.46250
$601$	33.7615			1.37716			0.688579	−	0.725161i	$-0.258235\pi$
$601$	33.7615			1.37716			0.688579	+	0.725161i	$0.258235\pi$
$602$	−0.912818	−	1.58105i	−0.0372037	−	0.0644387i
$603$	20.3037	−	35.1670i	0.826829	−	1.43211i
$604$	0.403018	+	0.698048i	0.0163986	+	0.0284032i
$605$	2.65657	−	4.60132i	0.108005	−	0.187070i
$606$	17.9402	−	31.0733i	0.728769	−	1.26227i
$607$	−35.2850			−1.43217			−0.716087	−	0.698011i	$-0.754068\pi$
$607$	−35.2850			−1.43217			−0.716087	+	0.698011i	$0.754068\pi$
$608$		0			0
$609$	6.87939			0.278767
$610$	−5.40760	+	9.36624i	−0.218947	+	0.379228i
$611$	−9.38326	+	16.2523i	−0.379606	+	0.657497i
$612$	0.228741	+	0.396191i	0.00924631	+	0.0160151i
$613$	−9.22668	+	15.9811i	−0.372662	+	0.645470i	−0.989974	−	0.141249i	$-0.954888\pi$
$613$	−9.22668	+	15.9811i	−0.372662	+	0.645470i	0.617312	+	0.786718i	$0.288222\pi$
$614$	−7.87867	−	13.6463i	−0.317957	−	0.550718i
$615$	−6.26857			−0.252773
$616$	2.27631			0.0917152
$617$	17.8427	+	30.9045i	0.718320	+	1.24417i	0.961665	+	0.274228i	$0.0884222\pi$
$617$	17.8427	+	30.9045i	0.718320	+	1.24417i	−0.243344	+	0.969940i	$0.578244\pi$
$618$	−10.6873	−	18.5110i	−0.429907	−	0.744621i
$619$	3.65951			0.147088			0.0735441	−	0.997292i	$-0.476569\pi$
$619$	3.65951			0.147088			0.0735441	+	0.997292i	$0.476569\pi$
$620$	−1.15476			−0.0463764
$621$	8.88713	+	15.3930i	0.356628	+	0.617698i
$622$	−10.7554	+	18.6288i	−0.431251	+	0.746949i
$623$	−1.78699	−	3.09516i	−0.0715942	−	0.124005i
$624$	−13.3268	+	23.0827i	−0.533500	+	0.924049i
$625$	−6.99912	+	12.1228i	−0.279965	+	0.484913i
$626$	−35.8767			−1.43392
$627$		0			0
$628$	1.77744			0.0709275
$629$	1.15657	−	2.00324i	0.0461156	−	0.0798746i
$630$	−1.08853	+	1.88538i	−0.0433679	+	0.0751154i
$631$	0.396926	+	0.687496i	0.0158014	+	0.0273688i	0.873818	−	0.486253i	$-0.161637\pi$
$631$	0.396926	+	0.687496i	0.0158014	+	0.0273688i	−0.858017	+	0.513622i	$0.828303\pi$
$632$	17.4336	−	30.1959i	0.693471	−	1.20113i
$633$	3.52481	+	6.10516i	0.140099	+	0.242658i
$634$	−39.7885			−1.58020
$635$	−10.2044			−0.404949
$636$	0.754900	+	1.30753i	0.0299337	+	0.0518468i
$637$	−8.85369	−	15.3350i	−0.350796	−	0.607597i
$638$	−20.6382			−0.817072
$639$	49.2336			1.94765
$640$	−4.17617	−	7.23335i	−0.165078	−	0.285923i
$641$	14.6912	−	25.4459i	0.580267	−	1.00505i	−0.415180	−	0.909739i	$-0.636281\pi$
$641$	14.6912	−	25.4459i	0.580267	−	1.00505i	0.995447	−	0.0953129i	$-0.0303852\pi$
$642$	19.8516	+	34.3840i	0.783481	+	1.35703i
$643$	−11.1069	+	19.2378i	−0.438015	+	0.758664i	−0.997536	−	0.0701516i	$-0.977652\pi$
$643$	−11.1069	+	19.2378i	−0.438015	+	0.758664i	0.559521	+	0.828816i	$0.310985\pi$
$644$	−0.0864665	+	0.149764i	−0.00340726	+	0.00590154i
$645$	9.87939			0.389000
$646$		0			0
$647$	11.2591			0.442640			0.221320	−	0.975201i	$-0.428963\pi$
$647$	11.2591			0.442640			0.221320	+	0.975201i	$0.428963\pi$
$648$	4.59286	−	7.95507i	0.180425	−	0.312505i
$649$	7.02007	−	12.1591i	0.275562	−	0.477287i
$650$	−7.32888	−	12.6940i	−0.287462	−	0.497899i
$651$	−3.55303	+	6.15403i	−0.139254	+	0.241196i
$652$	0.771974	+	1.33710i	0.0302328	+	0.0523648i
$653$	27.0000			1.05659			0.528296	−	0.849060i	$-0.322831\pi$
$653$	27.0000			1.05659			0.528296	+	0.849060i	$0.322831\pi$
$654$	7.07192			0.276534
$655$	−0.811337	−	1.40528i	−0.0317016	−	0.0549087i
$656$	−4.45155	−	7.71031i	−0.173804	−	0.301037i
$657$	7.34998			0.286750
$658$	−3.41147			−0.132993
$659$	14.0130	+	24.2712i	0.545867	+	0.945470i	0.998552	+	0.0537991i	$0.0171330\pi$
$659$	14.0130	+	24.2712i	0.545867	+	0.945470i	−0.452685	+	0.891671i	$0.649534\pi$
$660$	−0.520945	+	0.902302i	−0.0202777	+	0.0351221i
$661$	5.68392	+	9.84483i	0.221079	+	0.382920i	0.955136	−	0.296168i	$-0.0957089\pi$
$661$	5.68392	+	9.84483i	0.221079	+	0.382920i	−0.734057	+	0.679088i	$0.762376\pi$
$662$	18.6368	−	32.2799i	0.724340	−	1.25459i
$663$	1.73396	−	3.00330i	0.0673413	−	0.116638i
$664$	43.6551			1.69415
$665$		0			0
$666$	−35.2395			−1.36550
$667$	9.26857	−	16.0536i	0.358880	−	0.621599i
$668$	−0.372827	+	0.645754i	−0.0144251	+	0.0249850i
$669$	−12.2515	−	21.2202i	−0.473670	−	0.820421i
$670$	4.54664	−	7.87501i	0.175652	−	0.304238i
$671$	10.1630	+	17.6028i	0.392337	+	0.679548i
$672$	1.04189			0.0401917
$673$	16.5672			0.638618			0.319309	−	0.947651i	$-0.396549\pi$
$673$	16.5672			0.638618			0.319309	+	0.947651i	$0.396549\pi$
$674$	12.0312	+	20.8387i	0.463425	+	0.802676i
$675$	13.9402	+	24.1451i	0.536557	+	0.929344i
$676$	1.17799			0.0453071
$677$	9.04963			0.347806			0.173903	−	0.984763i	$-0.444362\pi$
$677$	9.04963			0.347806			0.173903	+	0.984763i	$0.444362\pi$
$678$	−34.3089	−	59.4247i	−1.31762	−	2.28219i
$679$	1.64156	−	2.84326i	0.0629973	−	0.109114i
$680$	0.605600	+	1.04893i	0.0232237	+	0.0402246i
$681$	−20.3726	+	35.2863i	−0.780679	+	1.35218i
$682$	10.6591	−	18.4621i	0.408158	−	0.706950i
$683$	−8.73143			−0.334099			−0.167049	−	0.985949i	$-0.553424\pi$
$683$	−8.73143			−0.334099			−0.167049	+	0.985949i	$0.553424\pi$
$684$		0			0
$685$	0.224927			0.00859402
$686$	3.24716	−	5.62424i	0.123977	−	0.214735i
$687$	29.5612	−	51.2016i	1.12783	−	1.95346i
$688$	7.01573	+	12.1516i	0.267472	+	0.463275i
$689$	3.65183	−	6.32515i	0.139124	−	0.240969i
$690$	4.59627	+	7.96097i	0.174977	+	0.303069i
$691$	34.7202			1.32082			0.660409	−	0.750906i	$-0.270383\pi$
$691$	34.7202			1.32082			0.660409	+	0.750906i	$0.270383\pi$
$692$	−3.72243			−0.141506
$693$	2.04576	+	3.54336i	0.0777120	+	0.134601i
$694$	3.90760	+	6.76817i	0.148331	+	0.256916i
$695$	3.74928			0.142218
$696$	−58.3073			−2.21013
$697$	0.579193	+	1.00319i	0.0219385	+	0.0379986i
$698$	−3.61902	+	6.26833i	−0.136982	+	0.237260i
$699$	−25.4119	−	44.0148i	−0.961168	−	1.66479i
$700$	−0.135630	+	0.234917i	−0.00512631	+	0.00887904i
$701$	−19.7075	+	34.1345i	−0.744344	+	1.28924i	0.206157	+	0.978519i	$0.433904\pi$
$701$	−19.7075	+	34.1345i	−0.744344	+	1.28924i	−0.950501	+	0.310722i	$0.899429\pi$
$702$	−22.8753			−0.863371
$703$		0			0
$704$	−19.1411			−0.721409
$705$	9.23055	−	15.9878i	0.347643	−	0.602135i
$706$	16.9991	−	29.4433i	0.639770	−	1.10811i
$707$	1.60607	+	2.78179i	0.0604024	+	0.104620i
$708$	1.67752	−	2.90555i	0.0630450	−	0.109197i
$709$	20.5608	+	35.6123i	0.772176	+	1.33745i	0.936368	+	0.351020i	$0.114165\pi$
$709$	20.5608	+	35.6123i	0.772176	+	1.33745i	−0.164192	+	0.986428i	$0.552502\pi$
$710$	11.0250			0.413760
$711$	62.6715			2.35036
$712$	15.1459	+	26.2335i	0.567616	+	0.983141i
$713$	9.57398	+	16.5826i	0.358548	+	0.621024i
$714$	0.630415			0.0235927
$715$	5.04013			0.188490
$716$	1.06371	+	1.84240i	0.0397527	+	0.0688538i
$717$	−3.38666	+	5.86587i	−0.126477	+	0.219065i
$718$	−4.50459	−	7.80217i	−0.168110	−	0.291174i
$719$	21.1977	−	36.7156i	0.790543	−	1.36926i	−0.135089	−	0.990834i	$-0.543132\pi$
$719$	21.1977	−	36.7156i	0.790543	−	1.36926i	0.925631	−	0.378426i	$-0.123535\pi$
$720$	8.36618	−	14.4907i	0.311789	−	0.540035i
$721$	1.91353			0.0712637
$722$		0			0
$723$	−39.7374			−1.47785
$724$	−0.788800	+	1.36624i	−0.0293155	+	0.0507760i
$725$	14.5385	−	25.1814i	0.539946	−	0.935214i
$726$	11.7194	+	20.2986i	0.434948	+	0.753352i
$727$	−25.8282	+	44.7357i	−0.957914	+	1.65915i	−0.230358	+	0.973106i	$0.573990\pi$
$727$	−25.8282	+	44.7357i	−0.957914	+	1.65915i	−0.727555	+	0.686049i	$0.759344\pi$
$728$	−1.31567	−	2.27881i	−0.0487621	−	0.0844585i
$729$	−40.4688			−1.49885
$730$	1.64590			0.0609174
$731$	−0.912818	−	1.58105i	−0.0337618	−	0.0584772i
$732$	2.42855	+	4.20637i	0.0897617	+	0.155472i
$733$	−22.9162			−0.846430			−0.423215	−	0.906029i	$-0.639098\pi$
$733$	−22.9162			−0.846430			−0.423215	+	0.906029i	$0.639098\pi$
$734$	10.9385			0.403748
$735$	8.70961	+	15.0855i	0.321259	+	0.556436i
$736$	1.40373	−	2.43134i	0.0517423	−	0.0896203i
$737$	−8.54488	−	14.8002i	−0.314755	−	0.545171i
$738$	8.82366	−	15.2830i	0.324804	−	0.562576i
$739$	−14.0633	+	24.3584i	−0.517327	+	0.896036i	0.482471	+	0.875912i	$0.339740\pi$
$739$	−14.0633	+	24.3584i	−0.517327	+	0.896036i	−0.999797	+	0.0201243i	$0.993594\pi$
$740$	0.803348			0.0295317
$741$		0			0
$742$	1.32770			0.0487413
$743$	3.06624	−	5.31088i	0.112489	−	0.194837i	−0.804284	−	0.594245i	$-0.797451\pi$
$743$	3.06624	−	5.31088i	0.112489	−	0.194837i	0.916773	+	0.399408i	$0.130784\pi$
$744$	30.1143	−	52.1595i	1.10404	−	1.91226i
$745$	−7.28106	−	12.6112i	−0.266757	−	0.462037i
$746$	23.5087	−	40.7182i	0.860714	−	1.49080i
$747$	39.2335	+	67.9545i	1.43548	+	2.48632i
$748$	0.192533			0.00703972
$749$	−3.55438			−0.129874
$750$	15.7383	+	27.2595i	0.574681	+	0.995377i
$751$	2.82042	+	4.88511i	0.102919	+	0.178260i	0.912886	−	0.408215i	$-0.133849\pi$
$751$	2.82042	+	4.88511i	0.102919	+	0.178260i	−0.809967	+	0.586475i	$0.800515\pi$
$752$	26.2199			0.956140
$753$	−11.9932			−0.437056
$754$	11.9285	+	20.6609i	0.434412	+	0.752424i
$755$	−1.91787	+	3.32185i	−0.0697985	+	0.120894i
$756$	0.211667	+	0.366618i	0.00769825	+	0.0133338i
$757$	−7.84595	+	13.5896i	−0.285166	+	0.493922i	−0.972649	−	0.232278i	$-0.925382\pi$
$757$	−7.84595	+	13.5896i	−0.285166	+	0.493922i	0.687483	+	0.726200i	$0.258715\pi$
$758$	1.14614	−	1.98518i	0.0416299	−	0.0721050i
$759$	17.2763			0.627090
$760$		0			0
$761$	4.86484			0.176350			0.0881751	−	0.996105i	$-0.471896\pi$
$761$	4.86484			0.176350			0.0881751	+	0.996105i	$0.471896\pi$
$762$	22.5082	−	38.9854i	0.815386	−	1.41229i
$763$	−0.316552	+	0.548284i	−0.0114599	+	0.0198492i
$764$	1.69413	+	2.93431i	0.0612913	+	0.106160i
$765$	−1.08853	+	1.88538i	−0.0393557	+	0.0681661i
$766$	1.97834	+	3.42659i	0.0714803	+	0.123808i
$767$	−16.2300			−0.586031
$768$	−12.6578			−0.456747
$769$	−11.2660	−	19.5134i	−0.406264	−	0.703670i	0.588204	−	0.808713i	$-0.299835\pi$
$769$	−11.2660	−	19.5134i	−0.406264	−	0.703670i	−0.994468	+	0.105043i	$0.966502\pi$
$770$	0.458111	+	0.793471i	0.0165092	+	0.0285947i
$771$	−1.92127			−0.0691930
$772$	0.0550065			0.00197973
$773$	−13.2160	−	22.8908i	−0.475347	−	0.823325i	0.524255	−	0.851562i	$-0.324344\pi$
$773$	−13.2160	−	22.8908i	−0.475347	−	0.823325i	−0.999601	+	0.0282370i	$0.991011\pi$
$774$	−13.9063	+	24.0863i	−0.499850	+	0.865766i
$775$	15.0175	+	26.0111i	0.539446	+	0.934348i
$776$	−13.9133	+	24.0985i	−0.499458	+	0.865086i
$777$	2.47178	−	4.28125i	0.0886747	−	0.153589i
$778$	−33.0993			−1.18667
$779$		0			0
$780$	1.20439			0.0431242
$781$	10.3601	−	17.9442i	0.370713	−	0.642094i
$782$	0.849356	−	1.47113i	0.0303729	−	0.0526074i
$783$	−22.6891	−	39.2987i	−0.810843	−	1.40442i
$784$	−12.3701	+	21.4256i	−0.441788	+	0.765199i
$785$	4.22921	+	7.32520i	0.150947	+	0.261448i
$786$	7.15839			0.255331
$787$	15.5577			0.554571			0.277286	−	0.960788i	$-0.410565\pi$
$787$	15.5577			0.554571			0.277286	+	0.960788i	$0.410565\pi$
$788$	1.21419	+	2.10304i	0.0432538	+	0.0749178i
$789$	−16.4119	−	28.4263i	−0.584281	−	1.01200i
$790$	14.0341			0.499313
$791$	6.14290			0.218417
$792$	−17.3391	−	30.0323i	−0.616120	−	1.06715i
$793$	11.7481	−	20.3483i	0.417187	−	0.722589i
$794$	21.4461	+	37.1457i	0.761093	+	1.31825i
$795$	−3.59240	+	6.22221i	−0.127409	+	0.220679i
$796$	−0.0237191	+	0.0410828i	−0.000840703	+	0.00145614i
$797$	−33.4935			−1.18640			−0.593200	−	0.805055i	$-0.702136\pi$
$797$	−33.4935			−1.18640			−0.593200	+	0.805055i	$0.702136\pi$
$798$		0			0
$799$	−3.41147			−0.120689
$800$	2.20187	−	3.81374i	0.0778477	−	0.134836i
$801$	−27.2237	+	47.1529i	−0.961904	+	1.66607i
$802$	−0.0582480	−	0.100888i	−0.00205681	−	0.00356250i
$803$	1.54664	−	2.67885i	0.0545796	−	0.0945347i
$804$	−2.04189	−	3.53666i	−0.0720119	−	0.124728i
$805$	−0.822948			−0.0290051
$806$	−24.6432			−0.868020
$807$	27.9158	+	48.3516i	0.982683	+	1.70206i
$808$	−13.6125	−	23.5775i	−0.478885	−	0.829453i
$809$	41.1162			1.44557			0.722784	−	0.691074i	$-0.242862\pi$
$809$	41.1162			1.44557			0.722784	+	0.691074i	$0.242862\pi$
$810$	3.69728			0.129909
$811$	8.34389	+	14.4520i	0.292994	+	0.507480i	0.974516	−	0.224317i	$-0.0720152\pi$
$811$	8.34389	+	14.4520i	0.292994	+	0.507480i	−0.681522	+	0.731797i	$0.738682\pi$
$812$	0.220752	−	0.382353i	0.00774687	−	0.0134180i
$813$	19.2836	+	33.4001i	0.676305	+	1.17139i
$814$	−7.41534	+	12.8438i	−0.259908	+	0.450173i
$815$	−3.67365	+	6.36295i	−0.128682	+	0.222884i
$816$	−4.84524			−0.169617
$817$		0			0
$818$	−26.9540			−0.942424
$819$	2.36484	−	4.09602i	0.0826341	−	0.143126i
$820$	−0.201151	+	0.348405i	−0.00702451	+	0.0121668i
$821$	15.6951	+	27.1846i	0.547761	+	0.948750i	0.998428	+	0.0560579i	$0.0178532\pi$
$821$	15.6951	+	27.1846i	0.547761	+	0.948750i	−0.450666	+	0.892693i	$0.648814\pi$
$822$	−0.496130	+	0.859322i	−0.0173045	+	0.0299723i
$823$	−23.1630	−	40.1194i	−0.807410	−	1.39848i	−0.914652	−	0.404243i	$-0.867535\pi$
$823$	−23.1630	−	40.1194i	−0.807410	−	1.39848i	0.107241	−	0.994233i	$-0.465798\pi$
$824$	−16.2184			−0.564996
$825$	27.0993			0.943475
$826$	−1.47519	−	2.55510i	−0.0513283	−	0.0889031i
$827$	20.3794	+	35.2981i	0.708661	+	1.22744i	0.965354	+	0.260943i	$0.0840336\pi$
$827$	20.3794	+	35.2981i	0.708661	+	1.22744i	−0.256693	+	0.966493i	$0.582633\pi$
$828$	2.63453			0.0915564
$829$	35.4834			1.23239			0.616195	−	0.787594i	$-0.288673\pi$
$829$	35.4834			1.23239			0.616195	+	0.787594i	$0.288673\pi$
$830$	8.78564	+	15.2172i	0.304954	+	0.528196i
$831$	−25.5501	+	44.2541i	−0.886323	+	1.53516i
$832$	11.0633	+	19.1622i	0.383551	+	0.664330i
$833$	1.60947	−	2.78768i	0.0557648	−	0.0965875i
$834$	−8.26991	+	14.3239i	−0.286364	+	0.495997i
$835$	−3.54839			−0.122797
$836$		0			0
$837$	46.8735			1.62019
$838$	−17.1172	+	29.6479i	−0.591304	+	1.02417i
$839$	−19.1013	+	33.0845i	−0.659451	+	1.14220i	0.321307	+	0.946975i	$0.395878\pi$
$839$	−19.1013	+	33.0845i	−0.659451	+	1.14220i	−0.980758	+	0.195227i	$0.937456\pi$
$840$	1.29426	+	2.24173i	0.0446563	+	0.0773470i
$841$	−9.16297	+	15.8707i	−0.315965	+	0.547267i
$842$	2.94356	+	5.09840i	0.101442	+	0.175702i
$843$	−52.6323			−1.81275
$844$	0.452430			0.0155733
$845$	2.80288	+	4.85473i	0.0964220	+	0.167008i
$846$	25.9859	+	45.0089i	0.893414	+	1.54744i
$847$	−2.09833			−0.0720993
$848$	−10.2044			−0.350420
$849$	−11.0680	−	19.1704i	−0.379854	−	0.657927i
$850$	1.33228	−	2.30758i	0.0456969	−	0.0791493i
$851$	−6.66044	−	11.5362i	−0.228317	−	0.395457i
$852$	2.47565	−	4.28795i	0.0848144	−	0.146903i
$853$	12.8008	−	22.1717i	0.438292	−	0.759144i	−0.559266	−	0.828988i	$-0.688917\pi$
$853$	12.8008	−	22.1717i	0.438292	−	0.759144i	0.997558	+	0.0698446i	$0.0222503\pi$
$854$	4.27126			0.146159
$855$		0			0
$856$	30.1257			1.02967
$857$	−10.5432	+	18.2614i	−0.360150	+	0.623798i	−0.987985	−	0.154548i	$-0.950608\pi$
$857$	−10.5432	+	18.2614i	−0.360150	+	0.623798i	0.627835	+	0.778346i	$0.283941\pi$
$858$	−11.1172	+	19.2556i	−0.379535	+	0.657374i
$859$	9.78359	+	16.9457i	0.333812	+	0.578179i	0.983256	−	0.182231i	$-0.0583317\pi$
$859$	9.78359	+	16.9457i	0.333812	+	0.578179i	−0.649444	+	0.760409i	$0.724998\pi$
$860$	0.317018	−	0.549092i	0.0108102	−	0.0187239i
$861$	1.23783	+	2.14398i	0.0421850	+	0.0730666i
$862$	51.6100			1.75784
$863$	−4.94894			−0.168464			−0.0842319	−	0.996446i	$-0.526844\pi$
$863$	−4.94894			−0.168464			−0.0842319	+	0.996446i	$0.526844\pi$
$864$	−3.43629	−	5.95183i	−0.116905	−	0.202485i
$865$	−8.85710	−	15.3409i	−0.301150	−	0.521608i
$866$	24.4279			0.830093
$867$	−48.3191			−1.64100
$868$	0.228026	+	0.394952i	0.00773970	+	0.0134056i
$869$	13.1878	−	22.8419i	0.447365	−	0.774859i
$870$	−11.7344	−	20.3246i	−0.397834	−	0.689069i
$871$	−9.87763	+	17.1086i	−0.334691	+	0.579701i
$872$	2.68298	−	4.64706i	0.0908572	−	0.157369i
$873$	−50.0164			−1.69280
$874$		0			0
$875$	−2.81790			−0.0952623
$876$	0.369585	−	0.640140i	0.0124871	−	0.0216283i
$877$	0.609937	−	1.05644i	0.0205961	−	0.0356735i	−0.855544	−	0.517731i	$-0.826777\pi$
$877$	0.609937	−	1.05644i	0.0205961	−	0.0356735i	0.876140	+	0.482057i	$0.160110\pi$
$878$	−4.10291	−	7.10645i	−0.138467	−	0.239831i
$879$	−15.1211	+	26.1905i	−0.510021	+	0.883383i
$880$	−3.52094	−	6.09845i	−0.118691	−	0.205579i
$881$	46.5030			1.56673			0.783363	−	0.621565i	$-0.213503\pi$
$881$	46.5030			1.56673			0.783363	+	0.621565i	$0.213503\pi$
$882$	−49.0387			−1.65122
$883$	−6.46245	−	11.1933i	−0.217479	−	0.376684i	0.736558	−	0.676375i	$-0.236450\pi$
$883$	−6.46245	−	11.1933i	−0.217479	−	0.376684i	−0.954036	+	0.299690i	$0.903117\pi$
$884$	−0.111281	−	0.192745i	−0.00374280	−	0.00648272i
$885$	15.9659			0.536686
$886$	−40.2749			−1.35306
$887$	−11.6122	−	20.1128i	−0.389898	−	0.675323i	0.602537	−	0.798091i	$-0.294156\pi$
$887$	−11.6122	−	20.1128i	−0.389898	−	0.675323i	−0.992435	+	0.122767i	$0.960823\pi$
$888$	−20.9500	+	36.2864i	−0.703035	+	1.21769i
$889$	2.01501	+	3.49011i	0.0675814	+	0.117054i
$890$	−6.09627	+	10.5590i	−0.204347	+	0.353940i
$891$	3.47431	−	6.01768i	0.116394	−	0.201600i
$892$	−1.57255			−0.0526528
$893$		0			0
$894$	64.2404			2.14852
$895$	−5.06196	+	8.76757i	−0.169203	+	0.293067i
$896$	−1.64930	+	2.85667i	−0.0550992	+	0.0954347i
$897$	−9.98545	−	17.2953i	−0.333405	−	0.577474i
$898$	−7.57848	+	13.1263i	−0.252897	+	0.438031i
$899$	−24.4427	−	42.3360i	−0.815209	−	1.41198i
$900$	4.13247			0.137749
$901$	1.32770			0.0442320
$902$	−3.71348	−	6.43193i	−0.123645	−	0.214160i
$903$	−1.95084	−	3.37895i	−0.0649198	−	0.112444i
$904$	−52.0651			−1.73166
$905$	−7.50744			−0.249556
$906$	−8.46064	−	14.6543i	−0.281086	−	0.486855i
$907$	−19.9984	+	34.6383i	−0.664036	+	1.15014i	0.315509	+	0.948922i	$0.397825\pi$
$907$	−19.9984	+	34.6383i	−0.664036	+	1.15014i	−0.979546	+	0.201222i	$0.935509\pi$
$908$	1.30747	+	2.26460i	0.0433898	+	0.0751533i
$909$	24.4675	−	42.3790i	0.811536	−	1.40562i
$910$	0.529563	−	0.917229i	0.0175548	−	0.0304059i
$911$	18.7997			0.622863			0.311431	−	0.950269i	$-0.399192\pi$
$911$	18.7997			0.622863			0.311431	+	0.950269i	$0.399192\pi$
$912$		0			0
$913$	33.0232			1.09291
$914$	15.7567	−	27.2914i	0.521186	−	0.902720i
$915$	−11.5569	+	20.0171i	−0.382059	+	0.661746i
$916$	−1.89717	−	3.28600i	−0.0626844	−	0.108573i
$917$	−0.320422	+	0.554987i	−0.0105813	+	0.0183273i
$918$	−2.07919	−	3.60127i	−0.0686236	−	0.118860i
$919$	39.8316			1.31392			0.656962	−	0.753924i	$-0.271841\pi$
$919$	39.8316			1.31392			0.656962	+	0.753924i	$0.271841\pi$
$920$	6.97502			0.229960
$921$	−16.8380	−	29.1642i	−0.554830	−	0.960993i
$922$	24.6714	+	42.7322i	0.812510	+	1.40731i
$923$	−23.9519			−0.788387
$924$	0.411474			0.0135365
$925$	−10.4474	−	18.0955i	−0.343509	−	0.594976i
$926$	28.9577	−	50.1562i	0.951609	−	1.64824i
$927$	−14.5758	−	25.2460i	−0.478732	−	0.829188i
$928$	−3.58378	+	6.20729i	−0.117643	+	0.203764i
$929$	−13.4770	+	23.3428i	−0.442166	+	0.765854i	−0.997850	−	0.0655397i	$-0.979123\pi$
$929$	−13.4770	+	23.3428i	−0.442166	+	0.765854i	0.555684	+	0.831394i	$0.312456\pi$
$930$	24.2422			0.794932
$931$		0			0
$932$	−3.26176			−0.106843
$933$	−22.9859	+	39.8128i	−0.752525	+	1.30341i
$934$	−17.2429	+	29.8655i	−0.564204	+	0.977230i
$935$	0.458111	+	0.793471i	0.0149818	+	0.0259493i
$936$	−20.0435	+	34.7164i	−0.655144	+	1.13474i
$937$	−1.31180	−	2.27211i	−0.0428548	−	0.0742266i	0.843802	−	0.536654i	$-0.180312\pi$
$937$	−1.31180	−	2.27211i	−0.0428548	−	0.0742266i	−0.886657	+	0.462427i	$0.846979\pi$
$938$	−3.59121			−0.117257
$939$	−76.6742			−2.50217
$940$	−0.592396	−	1.02606i	−0.0193218	−	0.0334664i
$941$	−9.33481	−	16.1684i	−0.304306	−	0.527074i	0.672801	−	0.739824i	$-0.265091\pi$
$941$	−9.33481	−	16.1684i	−0.304306	−	0.527074i	−0.977107	+	0.212750i	$0.931758\pi$
$942$	−37.3141			−1.21576
$943$	6.67087			0.217234
$944$	11.3380	+	19.6379i	0.369019	+	0.639160i
$945$	−1.00727	+	1.74465i	−0.0327666	+	0.0567535i
$946$	5.85251	+	10.1368i	0.190282	+	0.329577i
$947$	−4.19981	+	7.27428i	−0.136475	+	0.236382i	−0.926160	−	0.377131i	$-0.876911\pi$
$947$	−4.19981	+	7.27428i	−0.136475	+	0.236382i	0.789685	+	0.613513i	$0.210244\pi$
$948$	3.15136	−	5.45831i	0.102351	−	0.177278i
$949$	−3.57573			−0.116073
$950$		0			0
$951$	−85.0343			−2.75742
$952$	0.239170	−	0.414255i	0.00775155	−	0.0134261i
$953$	16.8464	−	29.1789i	0.545709	−	0.945196i	−0.452853	−	0.891585i	$-0.649594\pi$
$953$	16.8464	−	29.1789i	0.545709	−	0.945196i	0.998562	−	0.0536105i	$-0.0170729\pi$
$954$	−10.1133	−	17.5168i	−0.327431	−	0.567128i
$955$	−8.06196	+	13.9637i	−0.260879	+	0.451855i
$956$	0.217348	+	0.376458i	0.00702954	+	0.0121755i
$957$	−44.1070			−1.42578
$958$	51.4347			1.66178
$959$	−0.0444153	−	0.0769295i	−0.00143424	−	0.00248418i
$960$	−10.8833	−	18.8504i	−0.351256	−	0.608392i
$961$	19.4962			0.628909
$962$	17.1438			0.552739
$963$	27.0744	+	46.8943i	0.872462	+	1.51115i
$964$	−1.27513	+	2.20859i	−0.0410692	+	0.0711339i
$965$	0.130882	+	0.226694i	0.00421323	+	0.00729753i
$966$	1.81521	−	3.14403i	0.0584033	−	0.101158i
$967$	−5.87164	+	10.1700i	−0.188819	+	0.327045i	−0.944857	−	0.327484i	$-0.893799\pi$
$967$	−5.87164	+	10.1700i	−0.188819	+	0.327045i	0.756038	+	0.654528i	$0.227133\pi$
$968$	17.7847			0.571621
$969$		0			0
$970$	−11.2003			−0.359619
$971$	6.40467	−	11.0932i	0.205536	−	0.355998i	−0.744768	−	0.667324i	$-0.767440\pi$
$971$	6.40467	−	11.0932i	0.205536	−	0.355998i	0.950303	+	0.311326i	$0.100773\pi$
$972$	−0.998189	+	1.72891i	−0.0320169	+	0.0554549i
$973$	−0.740352	−	1.28233i	−0.0237346	−	0.0411095i
$974$	5.23009	−	9.05877i	0.167583	−	0.290262i
$975$	−15.6630	−	27.1291i	−0.501617	−	0.868825i
$976$	−32.8280			−1.05080
$977$	−14.5276			−0.464781			−0.232390	−	0.972623i	$-0.574655\pi$
$977$	−14.5276			−0.464781			−0.232390	+	0.972623i	$0.574655\pi$
$978$	−16.2062	−	28.0700i	−0.518217	−	0.897579i
$979$	11.4572	+	19.8445i	0.366175	+	0.634233i
$980$	1.11793			0.0357108
$981$	9.64496			0.307940
$982$	24.7383	+	42.8480i	0.789431	+	1.36733i
$983$	−18.5251	+	32.0864i	−0.590860	+	1.02340i	0.403257	+	0.915087i	$0.367878\pi$
$983$	−18.5251	+	32.0864i	−0.590860	+	1.02340i	−0.994117	+	0.108312i	$0.965455\pi$
$984$	−10.4914	−	18.1716i	−0.334453	−	0.579290i
$985$	−5.77807	+	10.0079i	−0.184104	+	0.318878i
$986$	−2.16843	+	3.75584i	−0.0690570	+	0.119610i
$987$	−7.29086			−0.232071
$988$		0			0
$989$	−10.5134			−0.334307
$990$	6.97906	−	12.0881i	0.221809	−	0.384184i
$991$	1.71570	−	2.97168i	0.0545010	−	0.0943985i	−0.837488	−	0.546456i	$-0.815977\pi$
$991$	1.71570	−	2.97168i	0.0545010	−	0.0943985i	0.891989	+	0.452058i	$0.149310\pi$
$992$	−3.70187	−	6.41182i	−0.117534	−	0.203576i
$993$	39.8298	−	68.9873i	1.26396	−	2.18924i
$994$	−2.17705	−	3.77076i	−0.0690519	−	0.119601i
$995$	−0.225748			−0.00715669
$996$	7.89124			0.250044
$997$	−6.38800	−	11.0643i	−0.202310	−	0.350411i	0.746962	−	0.664866i	$-0.231512\pi$
$997$	−6.38800	−	11.0643i	−0.202310	−	0.350411i	−0.949272	+	0.314455i	$0.898178\pi$
$998$	−3.31861	−	5.74800i	−0.105049	−	0.181950i
$999$	−32.6091			−1.03170

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.c.h.68.2		6
19.2	odd	18		361.2.e.g.234.1		6
19.3	odd	18		361.2.e.f.99.1		6
19.4	even	9		361.2.e.b.62.1		6
19.5	even	9		361.2.e.h.28.1		6
19.6	even	9		361.2.e.a.54.1		6
19.7	even	3	inner	361.2.c.h.292.2		6
19.8	odd	6		361.2.a.g.1.2		3
19.9	even	9		361.2.e.h.245.1		6
19.10	odd	18		19.2.e.a.17.1	yes	6
19.11	even	3		361.2.a.h.1.2		3
19.12	odd	6		361.2.c.i.292.2		6
19.13	odd	18		361.2.e.g.54.1		6
19.14	odd	18		19.2.e.a.9.1	✓	6
19.15	odd	18		361.2.e.f.62.1		6
19.16	even	9		361.2.e.b.99.1		6
19.17	even	9		361.2.e.a.234.1		6
19.18	odd	2		361.2.c.i.68.2		6
57.8	even	6		3249.2.a.z.1.2		3
57.11	odd	6		3249.2.a.s.1.2		3
57.14	even	18		171.2.u.c.28.1		6
57.29	even	18		171.2.u.c.55.1		6
76.11	odd	6		5776.2.a.bi.1.1		3
76.27	even	6		5776.2.a.br.1.3		3
76.67	even	18		304.2.u.b.17.1		6
76.71	even	18		304.2.u.b.161.1		6
95.14	odd	18		475.2.l.a.351.1		6
95.29	odd	18		475.2.l.a.226.1		6
95.33	even	36		475.2.u.a.199.1		12
95.48	even	36		475.2.u.a.74.2		12
95.49	even	6		9025.2.a.x.1.2		3
95.52	even	36		475.2.u.a.199.2		12
95.67	even	36		475.2.u.a.74.1		12
95.84	odd	6		9025.2.a.bd.1.2		3
133.10	even	18		931.2.x.b.226.1		6
133.33	even	18		931.2.x.b.655.1		6
133.48	even	18		931.2.w.a.834.1		6
133.52	even	18		931.2.v.a.275.1		6
133.67	odd	18		931.2.x.a.226.1		6
133.86	odd	18		931.2.v.b.606.1		6
133.90	even	18		931.2.w.a.883.1		6
133.109	odd	18		931.2.v.b.275.1		6
133.124	even	18		931.2.v.a.606.1		6
133.128	odd	18		931.2.x.a.655.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	19.14	odd	18
19.2.e.a.17.1	yes	6	19.10	odd	18
171.2.u.c.28.1		6	57.14	even	18
171.2.u.c.55.1		6	57.29	even	18
304.2.u.b.17.1		6	76.67	even	18
304.2.u.b.161.1		6	76.71	even	18
361.2.a.g.1.2		3	19.8	odd	6
361.2.a.h.1.2		3	19.11	even	3
361.2.c.h.68.2		6	1.1	even	1	trivial
361.2.c.h.292.2		6	19.7	even	3	inner
361.2.c.i.68.2		6	19.18	odd	2
361.2.c.i.292.2		6	19.12	odd	6
361.2.e.a.54.1		6	19.6	even	9
361.2.e.a.234.1		6	19.17	even	9
361.2.e.b.62.1		6	19.4	even	9
361.2.e.b.99.1		6	19.16	even	9
361.2.e.f.62.1		6	19.15	odd	18
361.2.e.f.99.1		6	19.3	odd	18
361.2.e.g.54.1		6	19.13	odd	18
361.2.e.g.234.1		6	19.2	odd	18
361.2.e.h.28.1		6	19.5	even	9
361.2.e.h.245.1		6	19.9	even	9
475.2.l.a.226.1		6	95.29	odd	18
475.2.l.a.351.1		6	95.14	odd	18
475.2.u.a.74.1		12	95.67	even	36
475.2.u.a.74.2		12	95.48	even	36
475.2.u.a.199.1		12	95.33	even	36
475.2.u.a.199.2		12	95.52	even	36
931.2.v.a.275.1		6	133.52	even	18
931.2.v.a.606.1		6	133.124	even	18
931.2.v.b.275.1		6	133.109	odd	18
931.2.v.b.606.1		6	133.86	odd	18
931.2.w.a.834.1		6	133.48	even	18
931.2.w.a.883.1		6	133.90	even	18
931.2.x.a.226.1		6	133.67	odd	18
931.2.x.a.655.1		6	133.128	odd	18
931.2.x.b.226.1		6	133.10	even	18
931.2.x.b.655.1		6	133.33	even	18
3249.2.a.s.1.2		3	57.11	odd	6
3249.2.a.z.1.2		3	57.8	even	6
5776.2.a.bi.1.1		3	76.11	odd	6
5776.2.a.br.1.3		3	76.27	even	6
9025.2.a.x.1.2		3	95.49	even	6
9025.2.a.bd.1.2		3	95.84	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.673648 + 1.16679i) q^{2} +(-1.43969 + 2.49362i) q^{3} +(0.0923963 + 0.160035i) q^{4} +(-0.439693 + 0.761570i) q^{5} +(-1.93969 - 3.35965i) q^{6} +0.347296 q^{7} -2.94356 q^{8} +(-2.64543 - 4.58202i) q^{9} +O(q^{10})\)	\(q+(-0.673648 + 1.16679i) q^{2} +(-1.43969 + 2.49362i) q^{3} +(0.0923963 + 0.160035i) q^{4} +(-0.439693 + 0.761570i) q^{5} +(-1.93969 - 3.35965i) q^{6} +0.347296 q^{7} -2.94356 q^{8} +(-2.64543 - 4.58202i) q^{9} +(-0.592396 - 1.02606i) q^{10} -2.22668 q^{11} -0.532089 q^{12} +(1.28699 + 2.22913i) q^{13} +(-0.233956 + 0.405223i) q^{14} +(-1.26604 - 2.19285i) q^{15} +(1.79813 - 3.11446i) q^{16} +(-0.233956 + 0.405223i) q^{17} +7.12836 q^{18} -0.162504 q^{20} +(-0.500000 + 0.866025i) q^{21} +(1.50000 - 2.59808i) q^{22} +(1.34730 + 2.33359i) q^{23} +(4.23783 - 7.34013i) q^{24} +(2.11334 + 3.66041i) q^{25} -3.46791 q^{26} +6.59627 q^{27} +(0.0320889 + 0.0555796i) q^{28} +(-3.43969 - 5.95772i) q^{29} +3.41147 q^{30} +7.10607 q^{31} +(-0.520945 - 0.902302i) q^{32} +(3.20574 - 5.55250i) q^{33} +(-0.315207 - 0.545955i) q^{34} +(-0.152704 + 0.264490i) q^{35} +(0.488856 - 0.846723i) q^{36} -4.94356 q^{37} -7.41147 q^{39} +(1.29426 - 2.24173i) q^{40} +(1.23783 - 2.14398i) q^{41} +(-0.673648 - 1.16679i) q^{42} +(-1.95084 + 3.37895i) q^{43} +(-0.205737 - 0.356347i) q^{44} +4.65270 q^{45} -3.63041 q^{46} +(3.64543 + 6.31407i) q^{47} +(5.17752 + 8.96773i) q^{48} -6.87939 q^{49} -5.69459 q^{50} +(-0.673648 - 1.16679i) q^{51} +(-0.237826 + 0.411927i) q^{52} +(-1.41875 - 2.45734i) q^{53} +(-4.44356 + 7.69648i) q^{54} +(0.979055 - 1.69577i) q^{55} -1.02229 q^{56} +9.26857 q^{58} +(-3.15270 + 5.46064i) q^{59} +(0.233956 - 0.405223i) q^{60} +(-4.56418 - 7.90539i) q^{61} +(-4.78699 + 8.29131i) q^{62} +(-0.918748 - 1.59132i) q^{63} +8.59627 q^{64} -2.26352 q^{65} +(4.31908 + 7.48086i) q^{66} +(3.83750 + 6.64674i) q^{67} -0.0864665 q^{68} -7.75877 q^{69} +(-0.205737 - 0.356347i) q^{70} +(-4.65270 + 8.05872i) q^{71} +(7.78699 + 13.4875i) q^{72} +(-0.694593 + 1.20307i) q^{73} +(3.33022 - 5.76811i) q^{74} -12.1702 q^{75} -0.773318 q^{77} +(4.99273 - 8.64766i) q^{78} +(-5.92262 + 10.2583i) q^{79} +(1.58125 + 2.73881i) q^{80} +(-1.56031 + 2.70253i) q^{81} +(1.66772 + 2.88857i) q^{82} -14.8307 q^{83} -0.184793 q^{84} +(-0.205737 - 0.356347i) q^{85} +(-2.62836 - 4.55245i) q^{86} +19.8084 q^{87} +6.55438 q^{88} +(-5.14543 - 8.91215i) q^{89} +(-3.13429 + 5.42874i) q^{90} +(0.446967 + 0.774169i) q^{91} +(-0.248970 + 0.431229i) q^{92} +(-10.2306 + 17.7198i) q^{93} -9.82295 q^{94} +3.00000 q^{96} +(4.72668 - 8.18685i) q^{97} +(4.63429 - 8.02682i) q^{98} +(5.89053 + 10.2027i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 12 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 12 * q^8	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 12 q^{8} + 6 q^{12} - 6 q^{14} - 3 q^{15} - 3 q^{16} - 6 q^{17} + 6 q^{18} - 6 q^{20} - 3 q^{21} + 9 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{25} - 30 q^{26} + 12 q^{27} - 9 q^{28} - 15 q^{29} + 18 q^{31} + 9 q^{33} - 9 q^{34} - 3 q^{35} + 9 q^{36} - 24 q^{39} + 18 q^{40} - 12 q^{41} - 3 q^{42} + 9 q^{44} + 30 q^{45} - 36 q^{46} + 6 q^{47} + 6 q^{48} - 30 q^{49} - 30 q^{50} - 3 q^{51} + 18 q^{52} - 6 q^{53} + 3 q^{54} + 9 q^{55} + 6 q^{56} + 36 q^{58} - 21 q^{59} + 6 q^{60} - 9 q^{61} - 21 q^{62} - 3 q^{63} + 24 q^{64} - 24 q^{65} + 9 q^{66} + 18 q^{67} + 30 q^{68} - 24 q^{69} + 9 q^{70} - 30 q^{71} + 39 q^{72} - 3 q^{74} - 30 q^{75} - 18 q^{77} + 12 q^{78} - 9 q^{79} + 12 q^{80} - 15 q^{81} - 18 q^{82} + 6 q^{84} + 9 q^{85} + 21 q^{86} + 42 q^{87} + 18 q^{88} - 15 q^{89} - 9 q^{90} + 15 q^{91} + 24 q^{92} - 24 q^{93} - 18 q^{94} + 18 q^{96} + 15 q^{97} + 18 q^{98} + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 12 * q^8 + 6 * q^12 - 6 * q^14 - 3 * q^15 - 3 * q^16 - 6 * q^17 + 6 * q^18 - 6 * q^20 - 3 * q^21 + 9 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^25 - 30 * q^26 + 12 * q^27 - 9 * q^28 - 15 * q^29 + 18 * q^31 + 9 * q^33 - 9 * q^34 - 3 * q^35 + 9 * q^36 - 24 * q^39 + 18 * q^40 - 12 * q^41 - 3 * q^42 + 9 * q^44 + 30 * q^45 - 36 * q^46 + 6 * q^47 + 6 * q^48 - 30 * q^49 - 30 * q^50 - 3 * q^51 + 18 * q^52 - 6 * q^53 + 3 * q^54 + 9 * q^55 + 6 * q^56 + 36 * q^58 - 21 * q^59 + 6 * q^60 - 9 * q^61 - 21 * q^62 - 3 * q^63 + 24 * q^64 - 24 * q^65 + 9 * q^66 + 18 * q^67 + 30 * q^68 - 24 * q^69 + 9 * q^70 - 30 * q^71 + 39 * q^72 - 3 * q^74 - 30 * q^75 - 18 * q^77 + 12 * q^78 - 9 * q^79 + 12 * q^80 - 15 * q^81 - 18 * q^82 + 6 * q^84 + 9 * q^85 + 21 * q^86 + 42 * q^87 + 18 * q^88 - 15 * q^89 - 9 * q^90 + 15 * q^91 + 24 * q^92 - 24 * q^93 - 18 * q^94 + 18 * q^96 + 15 * q^97 + 18 * q^98 + 18 * q^99

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