LMFDB - Embedded newform 585.2.i.g.391.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.2
Character	$\chi$	$=$	585.391
Dual form			585.2.i.g.196.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20515 - 2.08737i) q^{2} +(1.64592 + 0.539392i) q^{3} +(-1.90475 + 3.29913i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.857662 - 4.08570i) q^{6} +(-0.497502 - 0.861700i) q^{7} +4.36143 q^{8} +(2.41811 + 1.77559i) q^{9} +O(q^{10})$	\(q+(-1.20515 - 2.08737i) q^{2} +(1.64592 + 0.539392i) q^{3} +(-1.90475 + 3.29913i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.857662 - 4.08570i) q^{6} +(-0.497502 - 0.861700i) q^{7} +4.36143 q^{8} +(2.41811 + 1.77559i) q^{9} +2.41029 q^{10} +(-2.77651 - 4.80905i) q^{11} +(-4.91459 + 4.40270i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-1.19913 + 2.07695i) q^{14} +(-1.29009 + 1.15571i) q^{15} +(-1.44666 - 2.50568i) q^{16} +5.33677 q^{17} +(0.792149 - 7.18735i) q^{18} +4.35370 q^{19} +(-1.90475 - 3.29913i) q^{20} +(-0.354056 - 1.68664i) q^{21} +(-6.69219 + 11.5912i) q^{22} +(2.82607 - 4.89489i) q^{23} +(7.17857 + 2.35252i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.41029 q^{26} +(3.02228 + 4.22680i) q^{27} +3.79048 q^{28} +(-3.44182 - 5.96140i) q^{29} +(3.96715 + 1.30009i) q^{30} +(1.67161 - 2.89531i) q^{31} +(0.874568 - 1.51480i) q^{32} +(-1.97595 - 9.41295i) q^{33} +(-6.43159 - 11.1398i) q^{34} +0.995005 q^{35} +(-10.4638 + 4.59560i) q^{36} -3.77345 q^{37} +(-5.24684 - 9.08779i) q^{38} +(1.29009 - 1.15571i) q^{39} +(-2.18072 + 3.77711i) q^{40} +(5.36985 - 9.30086i) q^{41} +(-3.09396 + 2.77169i) q^{42} +(5.80032 + 10.0464i) q^{43} +21.1542 q^{44} +(-2.74677 + 1.20635i) q^{45} -13.6233 q^{46} +(-0.320387 - 0.554927i) q^{47} +(-1.02954 - 4.90447i) q^{48} +(3.00498 - 5.20478i) q^{49} +(-1.20515 + 2.08737i) q^{50} +(8.78391 + 2.87861i) q^{51} +(1.90475 + 3.29913i) q^{52} -0.0369803 q^{53} +(5.18062 - 11.4025i) q^{54} +5.55302 q^{55} +(-2.16982 - 3.75824i) q^{56} +(7.16584 + 2.34835i) q^{57} +(-8.29578 + 14.3687i) q^{58} +(-6.89721 + 11.9463i) q^{59} +(-1.35555 - 6.45751i) q^{60} +(-1.48053 - 2.56435i) q^{61} -8.05813 q^{62} +(0.327011 - 2.96705i) q^{63} -10.0026 q^{64} +(0.500000 + 0.866025i) q^{65} +(-17.2670 + 15.4685i) q^{66} +(-4.83990 + 8.38295i) q^{67} +(-10.1652 + 17.6067i) q^{68} +(7.29175 - 6.53225i) q^{69} +(-1.19913 - 2.07695i) q^{70} +3.39534 q^{71} +(10.5464 + 7.74413i) q^{72} -6.18622 q^{73} +(4.54755 + 7.87660i) q^{74} +(-0.355833 - 1.69511i) q^{75} +(-8.29272 + 14.3634i) q^{76} +(-2.76264 + 4.78503i) q^{77} +(-3.96715 - 1.30009i) q^{78} +(-0.938227 - 1.62506i) q^{79} +2.89331 q^{80} +(2.69454 + 8.58717i) q^{81} -25.8858 q^{82} +(5.80594 + 10.0562i) q^{83} +(6.23882 + 2.04455i) q^{84} +(-2.66839 + 4.62178i) q^{85} +(13.9805 - 24.2149i) q^{86} +(-2.44943 - 11.6685i) q^{87} +(-12.1096 - 20.9744i) q^{88} -3.37263 q^{89} +(5.82836 + 4.27970i) q^{90} -0.995005 q^{91} +(10.7659 + 18.6471i) q^{92} +(4.31305 - 3.86380i) q^{93} +(-0.772227 + 1.33754i) q^{94} +(-2.17685 + 3.77041i) q^{95} +(2.25654 - 2.02150i) q^{96} +(-2.93628 - 5.08578i) q^{97} -14.4858 q^{98} +(1.82502 - 16.5588i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) $ 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	−1.20515	−	2.08737i	−0.852167	−	1.47600i	−0.879249	−	0.476363i	$-0.841955\pi$
$2$	−1.20515	−	2.08737i	−0.852167	−	1.47600i	0.0270822	−	0.999633i	$-0.491378\pi$
$3$	1.64592	+	0.539392i	0.950273	+	0.311418i
$3$	1.64592	+	0.539392i	0.950273	+	0.311418i
$4$	−1.90475	+	3.29913i	−0.952376	+	1.64956i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.857662	−	4.08570i	−0.350139	−	1.66798i
$7$	−0.497502	−	0.861700i	−0.188038	−	0.325692i	0.756558	−	0.653927i	$-0.226880\pi$
$7$	−0.497502	−	0.861700i	−0.188038	−	0.325692i	−0.944596	+	0.328235i	$0.893546\pi$
$8$	4.36143			1.54200
$9$	2.41811	+	1.77559i	0.806037	+	0.591865i
$10$	2.41029			0.762201
$11$	−2.77651	−	4.80905i	−0.837149	−	1.44998i	−0.892269	−	0.451505i	$-0.850887\pi$
$11$	−2.77651	−	4.80905i	−0.837149	−	1.44998i	0.0551200	−	0.998480i	$-0.482446\pi$
$12$	−4.91459	+	4.40270i	−1.41872	+	1.27095i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	−1.19913	+	2.07695i	−0.320480	+	0.555087i
$15$	−1.29009	+	1.15571i	−0.333099	+	0.298404i
$16$	−1.44666	−	2.50568i	−0.361664	−	0.626421i
$17$	5.33677			1.29436			0.647179	−	0.762338i	$-0.275949\pi$
$17$	5.33677			1.29436			0.647179	+	0.762338i	$0.275949\pi$
$18$	0.792149	−	7.18735i	0.186711	−	1.69408i
$19$	4.35370			0.998807			0.499403	−	0.866370i	$-0.333553\pi$
$19$	4.35370			0.998807			0.499403	+	0.866370i	$0.333553\pi$
$20$	−1.90475	−	3.29913i	−0.425916	−	0.737707i
$21$	−0.354056	−	1.68664i	−0.0772613	−	0.368055i
$22$	−6.69219	+	11.5912i	−1.42678	+	2.47126i
$23$	2.82607	−	4.89489i	0.589276	−	1.02066i	−0.405051	−	0.914294i	$-0.632746\pi$
$23$	2.82607	−	4.89489i	0.589276	−	1.02066i	0.994327	−	0.106362i	$-0.0339203\pi$
$24$	7.17857	+	2.35252i	1.46532	+	0.480206i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.41029			−0.472697
$27$	3.02228	+	4.22680i	0.581638	+	0.813448i
$28$	3.79048			0.716333
$29$	−3.44182	−	5.96140i	−0.639130	−	1.10700i	−0.985624	−	0.168953i	$-0.945961\pi$
$29$	−3.44182	−	5.96140i	−0.639130	−	1.10700i	0.346495	−	0.938052i	$-0.387372\pi$
$30$	3.96715	+	1.30009i	0.724299	+	0.237363i
$31$	1.67161	−	2.89531i	0.300230	−	0.520014i	−0.675958	−	0.736940i	$-0.736270\pi$
$31$	1.67161	−	2.89531i	0.300230	−	0.520014i	0.976188	+	0.216927i	$0.0696033\pi$
$32$	0.874568	−	1.51480i	0.154603	−	0.267781i
$33$	−1.97595	−	9.41295i	−0.343968	−	1.63858i
$34$	−6.43159	−	11.1398i	−1.10301	−	1.91047i
$35$	0.995005			0.168187
$36$	−10.4638	+	4.59560i	−1.74397	+	0.765933i
$37$	−3.77345			−0.620351			−0.310176	−	0.950679i	$-0.600388\pi$
$37$	−3.77345			−0.620351			−0.310176	+	0.950679i	$0.600388\pi$
$38$	−5.24684	−	9.08779i	−0.851150	−	1.47423i
$39$	1.29009	−	1.15571i	0.206579	−	0.185062i
$40$	−2.18072	+	3.77711i	−0.344801	+	0.597214i
$41$	5.36985	−	9.30086i	0.838630	−	1.45255i	−0.0524104	−	0.998626i	$-0.516690\pi$
$41$	5.36985	−	9.30086i	0.838630	−	1.45255i	0.891040	−	0.453924i	$-0.149976\pi$
$42$	−3.09396	+	2.77169i	−0.477408	+	0.427681i
$43$	5.80032	+	10.0464i	0.884540	+	1.53207i	0.846240	+	0.532802i	$0.178861\pi$
$43$	5.80032	+	10.0464i	0.884540	+	1.53207i	0.0382999	+	0.999266i	$0.487806\pi$
$44$	21.1542			3.18912
$45$	−2.74677	+	1.20635i	−0.409464	+	0.179832i
$46$	−13.6233			−2.00865
$47$	−0.320387	−	0.554927i	−0.0467333	−	0.0809444i	0.841713	−	0.539926i	$-0.181548\pi$
$47$	−0.320387	−	0.554927i	−0.0467333	−	0.0809444i	−0.888446	+	0.458981i	$0.848214\pi$
$48$	−1.02954	−	4.90447i	−0.148601	−	0.707899i
$49$	3.00498	−	5.20478i	0.429283	−	0.743540i
$50$	−1.20515	+	2.08737i	−0.170433	+	0.295199i
$51$	8.78391	+	2.87861i	1.22999	+	0.403086i
$52$	1.90475	+	3.29913i	0.264142	+	0.457507i
$53$	−0.0369803			−0.00507964			−0.00253982	−	0.999997i	$-0.500808\pi$
$53$	−0.0369803			−0.00507964			−0.00253982	+	0.999997i	$0.500808\pi$
$54$	5.18062	−	11.4025i	0.704993	−	1.55169i
$55$	5.55302			0.748769
$56$	−2.16982	−	3.75824i	−0.289955	−	0.502216i
$57$	7.16584	+	2.34835i	0.949139	+	0.311047i
$58$	−8.29578	+	14.3687i	−1.08929	+	1.88671i
$59$	−6.89721	+	11.9463i	−0.897941	+	1.55528i	−0.0678188	+	0.997698i	$0.521604\pi$
$59$	−6.89721	+	11.9463i	−0.897941	+	1.55528i	−0.830122	+	0.557582i	$0.811729\pi$
$60$	−1.35555	−	6.45751i	−0.175001	−	0.833661i
$61$	−1.48053	−	2.56435i	−0.189562	−	0.328331i	0.755542	−	0.655100i	$-0.227373\pi$
$61$	−1.48053	−	2.56435i	−0.189562	−	0.328331i	−0.945104	+	0.326769i	$0.894040\pi$
$62$	−8.05813			−1.02338
$63$	0.327011	−	2.96705i	0.0411995	−	0.373813i
$64$	−10.0026			−1.25032
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$	−17.2670	+	15.4685i	−2.12543	+	1.90404i
$67$	−4.83990	+	8.38295i	−0.591288	+	1.02414i	0.402771	+	0.915301i	$0.368047\pi$
$67$	−4.83990	+	8.38295i	−0.591288	+	1.02414i	−0.994059	+	0.108840i	$0.965286\pi$
$68$	−10.1652	+	17.6067i	−1.23272	+	2.13513i
$69$	7.29175	−	6.53225i	0.877824	−	0.786391i
$70$	−1.19913	−	2.07695i	−0.143323	−	0.248243i
$71$	3.39534			0.402953			0.201476	−	0.979493i	$-0.435426\pi$
$71$	3.39534			0.402953			0.201476	+	0.979493i	$0.435426\pi$
$72$	10.5464	+	7.74413i	1.24291	+	0.912655i
$73$	−6.18622			−0.724043			−0.362021	−	0.932170i	$-0.617913\pi$
$73$	−6.18622			−0.724043			−0.362021	+	0.932170i	$0.617913\pi$
$74$	4.54755	+	7.87660i	0.528642	+	0.915636i
$75$	−0.355833	−	1.69511i	−0.0410881	−	0.195734i
$76$	−8.29272	+	14.3634i	−0.951240	+	1.64760i
$77$	−2.76264	+	4.78503i	−0.314832	+	0.545305i
$78$	−3.96715	−	1.30009i	−0.449191	−	0.147206i
$79$	−0.938227	−	1.62506i	−0.105559	−	0.182833i	0.808408	−	0.588623i	$-0.200330\pi$
$79$	−0.938227	−	1.62506i	−0.105559	−	0.182833i	−0.913966	+	0.405790i	$0.866996\pi$
$80$	2.89331			0.323482
$81$	2.69454	+	8.58717i	0.299393	+	0.954130i
$82$	−25.8858			−2.85861
$83$	5.80594	+	10.0562i	0.637284	+	1.10381i	0.986026	+	0.166590i	$0.0532756\pi$
$83$	5.80594	+	10.0562i	0.637284	+	1.10381i	−0.348742	+	0.937219i	$0.613391\pi$
$84$	6.23882	+	2.04455i	0.680711	+	0.223079i
$85$	−2.66839	+	4.62178i	−0.289427	+	0.501303i
$86$	13.9805	−	24.2149i	1.50755	−	2.61115i
$87$	−2.44943	−	11.6685i	−0.262606	−	1.25099i
$88$	−12.1096	−	20.9744i	−1.29088	−	2.23587i
$89$	−3.37263			−0.357498			−0.178749	−	0.983895i	$-0.557205\pi$
$89$	−3.37263			−0.357498			−0.178749	+	0.983895i	$0.557205\pi$
$90$	5.82836	+	4.27970i	0.614363	+	0.451120i
$91$	−0.995005			−0.104305
$92$	10.7659	+	18.6471i	1.12242	+	1.94410i
$93$	4.31305	−	3.86380i	0.447242	−	0.400658i
$94$	−0.772227	+	1.33754i	−0.0796491	+	0.137956i
$95$	−2.17685	+	3.77041i	−0.223340	+	0.386836i
$96$	2.25654	−	2.02150i	0.230307	−	0.206319i
$97$	−2.93628	−	5.08578i	−0.298134	−	0.516383i	0.677575	−	0.735453i	$-0.263031\pi$
$97$	−2.93628	−	5.08578i	−0.298134	−	0.516383i	−0.975709	+	0.219071i	$0.929697\pi$
$98$	−14.4858			−1.46328
$99$	1.82502	−	16.5588i	0.183421	−	1.66422i
$100$	3.80950			0.380950
$101$	−2.32354	−	4.02449i	−0.231201	−	0.400452i	0.726961	−	0.686679i	$-0.240932\pi$
$101$	−2.32354	−	4.02449i	−0.231201	−	0.400452i	−0.958162	+	0.286227i	$0.907599\pi$
$102$	−4.57715	−	21.8044i	−0.453205	−	2.15896i
$103$	−3.47600	+	6.02061i	−0.342500	+	0.593228i	−0.984896	−	0.173145i	$-0.944607\pi$
$103$	−3.47600	+	6.02061i	−0.342500	+	0.593228i	0.642396	+	0.766373i	$0.277940\pi$
$104$	2.18072	−	3.77711i	0.213837	−	0.370376i
$105$	1.63770	+	0.536698i	0.159823	+	0.0523763i
$106$	0.0445667	+	0.0771918i	0.00432870	+	0.00749753i
$107$	−11.3106			−1.09344			−0.546719	−	0.837316i	$-0.684123\pi$
$107$	−11.3106			−1.09344			−0.546719	+	0.837316i	$0.684123\pi$
$108$	−19.7014	+	1.91989i	−1.89577	+	0.184741i
$109$	13.5121			1.29423			0.647114	−	0.762393i	$-0.275976\pi$
$109$	13.5121			1.29423			0.647114	+	0.762393i	$0.275976\pi$
$110$	−6.69219	−	11.5912i	−0.638076	−	1.10518i
$111$	−6.21080	−	2.03537i	−0.589503	−	0.193189i
$112$	−1.43943	+	2.49317i	−0.136013	+	0.235582i
$113$	−3.34840	+	5.79961i	−0.314991	+	0.545581i	−0.979436	−	0.201757i	$-0.935335\pi$
$113$	−3.34840	+	5.79961i	−0.314991	+	0.545581i	0.664444	+	0.747338i	$0.268668\pi$
$114$	−3.73400	−	17.7879i	−0.349721	−	1.66599i
$115$	2.82607	+	4.89489i	0.263532	+	0.456451i
$116$	26.2232			2.43477
$117$	2.74677	−	1.20635i	0.253939	−	0.111527i
$118$	33.2486			3.06078
$119$	−2.65506	−	4.59870i	−0.243389	−	0.421562i
$120$	−5.62663	+	5.04057i	−0.513639	+	0.460139i
$121$	−9.91800	+	17.1785i	−0.901636	+	1.56168i
$122$	−3.56850	+	6.18082i	−0.323077	+	0.559585i
$123$	13.8552	−	12.4120i	1.24928	−	1.11915i
$124$	6.36800	+	11.0297i	0.571864	+	0.990497i
$125$	1.00000			0.0894427
$126$	−6.58743	+	2.89313i	−0.586855	+	0.257741i
$127$	4.36604			0.387424			0.193712	−	0.981058i	$-0.437947\pi$
$127$	4.36604			0.387424			0.193712	+	0.981058i	$0.437947\pi$
$128$	10.3054	+	17.8495i	0.910877	+	1.57769i
$129$	4.12789	+	19.6643i	0.363441	+	1.73134i
$130$	1.20515	−	2.08737i	0.105698	−	0.183075i
$131$	−8.54552	+	14.8013i	−0.746625	+	1.29319i	0.202806	+	0.979219i	$0.434994\pi$
$131$	−8.54552	+	14.8013i	−0.746625	+	1.29319i	−0.949432	+	0.313974i	$0.898340\pi$
$132$	34.8182	+	11.4104i	3.03054	+	0.993150i
$133$	−2.16598	−	3.75158i	−0.187814	−	0.325303i
$134$	23.3311			2.01550
$135$	−5.17165	+	0.503973i	−0.445105	+	0.0433751i
$136$	23.2760			1.99590
$137$	−0.652550	−	1.13025i	−0.0557511	−	0.0965638i	0.836803	−	0.547504i	$-0.184422\pi$
$137$	−0.652550	−	1.13025i	−0.0557511	−	0.0965638i	−0.892554	+	0.450940i	$0.851089\pi$
$138$	−22.4229	−	7.34830i	−1.90876	−	0.625529i
$139$	10.9230	−	18.9192i	0.926478	−	1.60471i	0.137310	−	0.990528i	$-0.456154\pi$
$139$	10.9230	−	18.9192i	0.926478	−	1.60471i	0.789167	−	0.614178i	$-0.210512\pi$
$140$	−1.89524	+	3.28265i	−0.160177	+	0.277434i
$141$	−0.228009	−	1.08618i	−0.0192018	−	0.0914729i
$142$	−4.09188	−	7.08735i	−0.343383	−	0.594757i
$143$	−5.55302			−0.464367
$144$	0.950896	−	8.62770i	0.0792413	−	0.718975i
$145$	6.88364			0.571655
$146$	7.45530	+	12.9130i	0.617005	+	1.06868i
$147$	7.75338	−	6.94580i	0.639488	−	0.572880i
$148$	7.18748	−	12.4491i	0.590807	−	1.02331i
$149$	0.597375	−	1.03468i	0.0489389	−	0.0847646i	−0.840518	−	0.541783i	$-0.817749\pi$
$149$	0.597375	−	1.03468i	0.0489389	−	0.0847646i	0.889457	+	0.457019i	$0.151083\pi$
$150$	−3.10949	+	2.78561i	−0.253889	+	0.227444i
$151$	3.50248	+	6.06647i	0.285028	+	0.493682i	0.972616	−	0.232418i	$-0.0746639\pi$
$151$	3.50248	+	6.06647i	0.285028	+	0.493682i	−0.687588	+	0.726101i	$0.741331\pi$
$152$	18.9884			1.54016
$153$	12.9049	+	9.47594i	1.04330	+	0.766084i
$154$	13.3175			1.07316
$155$	1.67161	+	2.89531i	0.134267	+	0.232557i
$156$	1.35555	+	6.45751i	0.108531	+	0.517015i
$157$	−0.0276524	+	0.0478954i	−0.00220690	+	0.00382247i	−0.867127	−	0.498088i	$-0.834036\pi$
$157$	−0.0276524	+	0.0478954i	−0.00220690	+	0.00382247i	0.864920	+	0.501910i	$0.167369\pi$
$158$	−2.26140	+	3.91686i	−0.179907	+	0.311609i
$159$	−0.0608667	−	0.0199469i	−0.00482704	−	0.00158189i
$160$	0.874568	+	1.51480i	0.0691407	+	0.119755i
$161$	−5.62390			−0.443226
$162$	14.6773	−	15.9733i	1.15316	−	1.25498i
$163$	14.6944			1.15095			0.575477	−	0.817818i	$-0.304816\pi$
$163$	14.6944			1.15095			0.575477	+	0.817818i	$0.304816\pi$
$164$	20.4565	+	35.4316i	1.59738	+	2.76675i
$165$	9.13983	+	2.99525i	0.711535	+	0.233180i
$166$	13.9940	−	24.2383i	1.08614	−	1.88126i
$167$	3.09149	−	5.35461i	0.239226	−	0.414352i	−0.721266	−	0.692658i	$-0.756440\pi$
$167$	3.09149	−	5.35461i	0.239226	−	0.414352i	0.960493	+	0.278306i	$0.0897729\pi$
$168$	−1.54419	−	7.35616i	−0.119137	−	0.567540i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	12.8632			0.986561
$171$	10.5277	+	7.73040i	0.805076	+	0.591158i
$172$	−44.1927			−3.36966
$173$	2.32274	+	4.02311i	0.176595	+	0.305871i	0.940712	−	0.339206i	$-0.110158\pi$
$173$	2.32274	+	4.02311i	0.176595	+	0.305871i	−0.764117	+	0.645078i	$0.776825\pi$
$174$	−21.4046	+	19.1751i	−1.62268	+	1.45366i
$175$	−0.497502	+	0.861700i	−0.0376077	+	0.0651384i
$176$	−8.03331	+	13.9141i	−0.605533	+	1.04881i
$177$	−17.7960	+	15.9424i	−1.33763	+	1.19830i
$178$	4.06451	+	7.03994i	0.304648	+	0.527666i
$179$	5.64704			0.422080			0.211040	−	0.977477i	$-0.432315\pi$
$179$	5.64704			0.422080			0.211040	+	0.977477i	$0.432315\pi$
$180$	1.25200	−	11.3597i	0.0933189	−	0.846704i
$181$	20.1352			1.49664			0.748320	−	0.663338i	$-0.230861\pi$
$181$	20.1352			1.49664			0.748320	+	0.663338i	$0.230861\pi$
$182$	1.19913	+	2.07695i	0.0888851	+	0.153954i
$183$	−1.05364	−	5.01929i	−0.0778874	−	0.371037i
$184$	12.3257	−	21.3487i	0.908663	−	1.57385i
$185$	1.88672	−	3.26790i	0.138715	−	0.240261i
$186$	−13.2630	−	4.34649i	−0.972494	−	0.318700i
$187$	−14.8176	−	25.6648i	−1.08357	−	1.87680i
$188$	2.44103			0.178031
$189$	2.13864	−	4.70714i	0.155563	−	0.342394i
$190$	10.4937			0.761292
$191$	−7.85347	−	13.6026i	−0.568257	−	0.984251i	−0.996738	−	0.0807000i	$-0.974284\pi$
$191$	−7.85347	−	13.6026i	−0.568257	−	0.984251i	0.428481	−	0.903551i	$-0.359049\pi$
$192$	−16.4634	−	5.39530i	−1.18814	−	0.389372i
$193$	1.41849	−	2.45690i	0.102105	−	0.176851i	−0.810447	−	0.585812i	$-0.800776\pi$
$193$	1.41849	−	2.45690i	0.102105	−	0.176851i	0.912552	+	0.408961i	$0.134109\pi$
$194$	−7.07728	+	12.2582i	−0.508119	+	0.880088i
$195$	0.355833	+	1.69511i	0.0254818	+	0.121389i
$196$	11.4475	+	19.8276i	0.817678	+	1.41626i
$197$	−14.8597			−1.05871			−0.529356	−	0.848400i	$-0.677566\pi$
$197$	−14.8597			−1.05871			−0.529356	+	0.848400i	$0.677566\pi$
$198$	−36.7638	+	16.1463i	−2.61269	+	1.14746i
$199$	−24.1994			−1.71545			−0.857725	−	0.514108i	$-0.828123\pi$
$199$	−24.1994			−1.71545			−0.857725	+	0.514108i	$0.828123\pi$
$200$	−2.18072	−	3.77711i	−0.154200	−	0.267082i
$201$	−12.4878	+	11.1871i	−0.880821	+	0.789075i
$202$	−5.60041	+	9.70019i	−0.394043	+	0.682503i
$203$	−3.42463	+	5.93163i	−0.240362	+	0.416319i
$204$	−26.2281	+	23.4962i	−1.83633	+	1.64506i
$205$	5.36985	+	9.30086i	0.375047	+	0.649600i
$206$	16.7563			1.16747
$207$	15.5251	−	6.81846i	1.07907	−	0.473915i
$208$	−2.89331			−0.200615
$209$	−12.0881	−	20.9372i	−0.836150	−	1.44825i
$210$	−0.853378	−	4.06529i	−0.0588887	−	0.280532i
$211$	1.49494	−	2.58932i	0.102916	−	0.178256i	−0.809969	−	0.586473i	$-0.800516\pi$
$211$	1.49494	−	2.58932i	0.102916	−	0.178256i	0.912885	+	0.408217i	$0.133849\pi$
$212$	0.0704384	−	0.122003i	0.00483773	−	0.00837919i
$213$	5.58847	+	1.83142i	0.382915	+	0.125487i
$214$	13.6309	+	23.6095i	0.931791	+	1.61391i
$215$	−11.6006			−0.791157
$216$	13.1815	+	18.4349i	0.896886	+	1.25434i
$217$	−3.32652			−0.225819
$218$	−16.2841	−	28.2049i	−1.10290	−	1.91028i
$219$	−10.1820	−	3.33680i	−0.688038	−	0.225480i
$220$	−10.5771	+	18.3201i	−0.713109	+	1.23514i
$221$	2.66839	−	4.62178i	0.179495	−	0.310895i
$222$	3.23634	+	15.4172i	0.217209	+	1.03473i
$223$	2.68848	+	4.65658i	0.180034	+	0.311828i	0.941892	−	0.335916i	$-0.109046\pi$
$223$	2.68848	+	4.65658i	0.180034	+	0.311828i	−0.761858	+	0.647744i	$0.775713\pi$
$224$	−1.74040			−0.116285
$225$	0.328653	−	2.98194i	0.0219102	−	0.198796i
$226$	16.1413			1.07370
$227$	2.63485	+	4.56369i	0.174881	+	0.302903i	0.940120	−	0.340843i	$-0.110713\pi$
$227$	2.63485	+	4.56369i	0.174881	+	0.302903i	−0.765239	+	0.643746i	$0.777379\pi$
$228$	−21.3967	+	19.1680i	−1.41703	+	1.26943i
$229$	−0.0817388	+	0.141576i	−0.00540145	+	0.00935559i	−0.868713	−	0.495315i	$-0.835053\pi$
$229$	−0.0817388	+	0.141576i	−0.00540145	+	0.00935559i	0.863312	+	0.504671i	$0.168386\pi$
$230$	6.81165	−	11.7981i	0.449147	−	0.777945i
$231$	−7.12810	+	6.38564i	−0.468994	+	0.420144i
$232$	−15.0113	−	26.0003i	−0.985537	−	1.70700i
$233$	−9.66393			−0.633105			−0.316553	−	0.948575i	$-0.602525\pi$
$233$	−9.66393			−0.633105			−0.316553	+	0.948575i	$0.602525\pi$
$234$	−5.82836	−	4.27970i	−0.381012	−	0.279773i
$235$	0.640775			0.0417995
$236$	−26.2750	−	45.5096i	−1.71035	−	2.96242i
$237$	−0.667705	−	3.18079i	−0.0433721	−	0.206614i
$238$	−6.39946	+	11.0842i	−0.414816	+	0.718482i
$239$	−3.39989	+	5.88877i	−0.219920	+	0.380913i	−0.954783	−	0.297302i	$-0.903913\pi$
$239$	−3.39989	+	5.88877i	−0.219920	+	0.380913i	0.734863	+	0.678215i	$0.237246\pi$
$240$	4.76217	+	1.56063i	0.307396	+	0.100738i
$241$	−0.400687	−	0.694011i	−0.0258105	−	0.0447052i	0.852832	−	0.522186i	$-0.174883\pi$
$241$	−0.400687	−	0.694011i	−0.0258105	−	0.0447052i	−0.878642	+	0.477481i	$0.841550\pi$
$242$	47.8105			3.07338
$243$	−0.196859	+	15.5872i	−0.0126285	+	0.999920i
$244$	11.2801			0.722137
$245$	3.00498	+	5.20478i	0.191981	+	0.332521i
$246$	−42.6060	−	13.9626i	−2.71646	−	0.890223i
$247$	2.17685	−	3.77041i	0.138510	−	0.239906i
$248$	7.29061	−	12.6277i	0.462954	−	0.801860i
$249$	4.13189	+	19.6833i	0.261848	+	1.24738i
$250$	−1.20515	−	2.08737i	−0.0762201	−	0.132017i
$251$	−25.8804			−1.63356			−0.816779	−	0.576951i	$-0.804243\pi$
$251$	−25.8804			−1.63356			−0.816779	+	0.576951i	$0.804243\pi$
$252$	9.16580	+	6.73034i	0.577391	+	0.423972i
$253$	−31.3864			−1.97325
$254$	−5.26172	−	9.11357i	−0.330150	−	0.571836i
$255$	−6.88491	+	6.16778i	−0.431150	+	0.386241i
$256$	14.8365	−	25.6975i	0.927279	−	1.60609i
$257$	10.7123	−	18.5543i	0.668216	−	1.15738i	−0.310187	−	0.950676i	$-0.600392\pi$
$257$	10.7123	−	18.5543i	0.668216	−	1.15738i	0.978403	−	0.206708i	$-0.0662749\pi$
$258$	36.0720	−	32.3148i	2.24575	−	2.01183i
$259$	1.87730	+	3.25158i	0.116650	+	0.202043i
$260$	−3.80950			−0.236255
$261$	2.26233	−	20.5266i	0.140035	−	1.27057i
$262$	41.1944			2.54500
$263$	15.4484	+	26.7574i	0.952590	+	1.64993i	0.739789	+	0.672839i	$0.234925\pi$
$263$	15.4484	+	26.7574i	0.952590	+	1.64993i	0.212801	+	0.977095i	$0.431741\pi$
$264$	−8.61796	−	41.0539i	−0.530399	−	2.52670i
$265$	0.0184902	−	0.0320259i	0.00113584	−	0.00196734i
$266$	−5.22063	+	9.04240i	−0.320098	+	0.554425i
$267$	−5.55108	−	1.81917i	−0.339721	−	0.111331i
$268$	−18.4376	−	31.9349i	−1.12626	−	1.95073i
$269$	6.38014			0.389004			0.194502	−	0.980902i	$-0.437691\pi$
$269$	6.38014			0.389004			0.194502	+	0.980902i	$0.437691\pi$
$270$	7.28458	+	10.1878i	0.443325	+	0.620011i
$271$	−18.3304			−1.11349			−0.556747	−	0.830682i	$-0.687951\pi$
$271$	−18.3304			−1.11349			−0.556747	+	0.830682i	$0.687951\pi$
$272$	−7.72048	−	13.3723i	−0.468123	−	0.810812i
$273$	−1.63770	−	0.536698i	−0.0991181	−	0.0324824i
$274$	−1.57284	+	2.72423i	−0.0950185	+	0.164577i
$275$	−2.77651	+	4.80905i	−0.167430	+	0.289997i
$276$	7.66175	+	36.4987i	0.461183	+	2.19697i
$277$	15.7008	+	27.1945i	0.943367	+	1.63396i	0.758988	+	0.651104i	$0.225694\pi$
$277$	15.7008	+	27.1945i	0.943367	+	1.63396i	0.184379	+	0.982855i	$0.440973\pi$
$278$	−52.6553			−3.15805
$279$	9.18304	−	4.03309i	0.549774	−	0.241455i
$280$	4.33965			0.259343
$281$	15.2031	+	26.3326i	0.906944	+	1.57087i	0.818287	+	0.574810i	$0.194924\pi$
$281$	15.2031	+	26.3326i	0.906944	+	1.57087i	0.0886567	+	0.996062i	$0.471743\pi$
$282$	−1.99248	+	1.78495i	−0.118650	+	0.106292i
$283$	−8.34932	+	14.4614i	−0.496315	+	0.859644i	−0.999991	−	0.00424928i	$-0.998647\pi$
$283$	−8.34932	+	14.4614i	−0.496315	+	0.859644i	0.503675	+	0.863893i	$0.331981\pi$
$284$	−6.46728	+	11.2017i	−0.383763	+	0.664697i
$285$	−5.61665	+	5.03163i	−0.332702	+	0.298048i
$286$	6.69219	+	11.5912i	0.395718	+	0.685403i
$287$	−10.6861			−0.630778
$288$	4.80447	−	2.11007i	0.283106	−	0.124337i
$289$	11.4811			0.675362
$290$	−8.29578	−	14.3687i	−0.487145	−	0.843760i
$291$	−2.08965	−	9.95460i	−0.122497	−	0.583549i
$292$	11.7832	−	20.4091i	0.689561	−	1.19435i
$293$	−3.64625	+	6.31549i	−0.213016	+	0.368955i	−0.952657	−	0.304047i	$-0.901662\pi$
$293$	−3.64625	+	6.31549i	−0.213016	+	0.368955i	0.739641	+	0.673002i	$0.234995\pi$
$294$	−23.8424	−	7.81351i	−1.39052	−	0.455693i
$295$	−6.89721	−	11.9463i	−0.401571	−	0.695542i
$296$	−16.4576			−0.956581
$297$	11.9355	−	26.2701i	0.692568	−	1.52434i
$298$	−2.87970			−0.166816
$299$	−2.82607	−	4.89489i	−0.163436	−	0.283079i
$300$	6.27014	+	2.05482i	0.362007	+	0.118635i
$301$	5.77134	−	9.99626i	0.332655	−	0.576175i
$302$	8.44199	−	14.6220i	0.485782	−	0.841399i
$303$	−1.65359	−	7.87729i	−0.0949960	−	0.452538i
$304$	−6.29831	−	10.9090i	−0.361233	−	0.625673i
$305$	2.96105			0.169549
$306$	4.22752	−	38.3573i	0.241671	−	2.19274i
$307$	0.618605			0.0353056			0.0176528	−	0.999844i	$-0.494381\pi$
$307$	0.618605			0.0353056			0.0176528	+	0.999844i	$0.494381\pi$
$308$	−10.5243	−	18.2286i	−0.599677	−	1.03867i
$309$	−8.96869	+	8.03452i	−0.510211	+	0.457068i
$310$	4.02907	−	6.97855i	0.228836	−	0.396355i
$311$	5.30852	−	9.19463i	0.301019	−	0.521379i	−0.675348	−	0.737499i	$-0.736007\pi$
$311$	5.30852	−	9.19463i	0.301019	−	0.521379i	0.976367	+	0.216119i	$0.0693401\pi$
$312$	5.62663	−	5.04057i	0.318545	−	0.285366i
$313$	−4.55547	−	7.89030i	−0.257490	−	0.445986i	0.708079	−	0.706134i	$-0.249562\pi$
$313$	−4.55547	−	7.89030i	−0.257490	−	0.445986i	−0.965569	+	0.260147i	$0.916229\pi$
$314$	0.133301			0.00752260
$315$	2.40603	+	1.76672i	0.135565	+	0.0995436i
$316$	7.14836			0.402127
$317$	2.68853	+	4.65667i	0.151003	+	0.261544i	0.931596	−	0.363494i	$-0.118416\pi$
$317$	2.68853	+	4.65667i	0.151003	+	0.261544i	−0.780594	+	0.625039i	$0.785083\pi$
$318$	0.0317166	+	0.151090i	0.00177858	+	0.00847273i
$319$	−19.1125	+	33.1038i	−1.07009	+	1.85346i
$320$	5.00128	−	8.66247i	0.279580	−	0.484247i
$321$	−18.6164	−	6.10085i	−1.03906	−	0.340516i
$322$	6.77762	+	11.7392i	0.377702	+	0.654199i
$323$	23.2347			1.29281
$324$	−33.4626	−	7.46681i	−1.85903	−	0.414823i
$325$	−1.00000			−0.0554700
$326$	−17.7089	−	30.6727i	−0.980805	−	1.69880i
$327$	22.2399	+	7.28834i	1.22987	+	0.403046i
$328$	23.4202	−	40.5651i	1.29317	−	2.23983i
$329$	−0.318787	+	0.552155i	−0.0175753	+	0.0304413i
$330$	−4.76261	−	22.6880i	−0.262173	−	1.24893i
$331$	2.07973	+	3.60219i	0.114312	+	0.197994i	0.917505	−	0.397725i	$-0.130200\pi$
$331$	2.07973	+	3.60219i	0.114312	+	0.197994i	−0.803192	+	0.595720i	$0.796867\pi$
$332$	−44.2355			−2.42774
$333$	−9.12462	−	6.70011i	−0.500026	−	0.367164i
$334$	−14.9028			−0.815443
$335$	−4.83990	−	8.38295i	−0.264432	−	0.458010i
$336$	−3.71398	+	3.32714i	−0.202614	+	0.181510i
$337$	7.74991	−	13.4232i	0.422164	−	0.731210i	−0.573987	−	0.818865i	$-0.694604\pi$
$337$	7.74991	−	13.4232i	0.422164	−	0.731210i	0.996151	+	0.0876546i	$0.0279372\pi$
$338$	−1.20515	+	2.08737i	−0.0655513	+	0.113538i
$339$	−8.63947	+	7.73959i	−0.469232	+	0.420357i
$340$	−10.1652	−	17.6067i	−0.551287	−	0.954857i
$341$	−18.5650			−1.00535
$342$	3.44878	−	31.2916i	0.186489	−	1.69205i
$343$	−12.9450			−0.698963
$344$	25.2977	+	43.8169i	1.36396	+	2.36245i
$345$	2.01122	+	9.58097i	0.108280	+	0.515822i
$346$	5.59849	−	9.69687i	0.300977	−	0.521307i
$347$	−15.7836	+	27.3381i	−0.847310	+	1.46758i	0.0362899	+	0.999341i	$0.488446\pi$
$347$	−15.7836	+	27.3381i	−0.847310	+	1.46758i	−0.883600	+	0.468243i	$0.844887\pi$
$348$	43.1614	+	14.1446i	2.31369	+	0.758231i
$349$	−3.54172	−	6.13445i	−0.189584	−	0.328369i	0.755528	−	0.655117i	$-0.227381\pi$
$349$	−3.54172	−	6.13445i	−0.189584	−	0.328369i	−0.945112	+	0.326748i	$0.894047\pi$
$350$	2.39825			0.128192
$351$	5.17165	−	0.503973i	0.276042	−	0.0269001i
$352$	−9.71298			−0.517704
$353$	9.06065	+	15.6935i	0.482250	+	0.835281i	0.999792	−	0.0203766i	$-0.00648653\pi$
$353$	9.06065	+	15.6935i	0.482250	+	0.835281i	−0.517543	+	0.855657i	$0.673153\pi$
$354$	54.7246	+	17.9340i	2.90858	+	0.953183i
$355$	−1.69767	+	2.94045i	−0.0901030	+	0.156063i
$356$	6.42403	−	11.1267i	0.340473	−	0.589716i
$357$	−1.88952	−	9.00121i	−0.100004	−	0.476394i
$358$	−6.80551	−	11.7875i	−0.359682	−	0.622988i
$359$	−4.30657			−0.227292			−0.113646	−	0.993521i	$-0.536253\pi$
$359$	−4.30657			−0.227292			−0.113646	+	0.993521i	$0.536253\pi$
$360$	−11.9798	+	5.26141i	−0.631392	+	0.277301i
$361$	−0.0453102			−0.00238475
$362$	−24.2659	−	42.0297i	−1.27539	−	2.20903i
$363$	−25.5902	+	22.9247i	−1.34314	+	1.20324i
$364$	1.89524	−	3.28265i	0.0993374	−	0.172058i
$365$	3.09311	−	5.35743i	0.161901	−	0.280420i
$366$	−9.20735	+	8.24832i	−0.481276	+	0.431147i
$367$	−6.37372	−	11.0396i	−0.332706	−	0.576263i	0.650336	−	0.759647i	$-0.274628\pi$
$367$	−6.37372	−	11.0396i	−0.332706	−	0.576263i	−0.983041	+	0.183384i	$0.941295\pi$
$368$	−16.3534			−0.852480
$369$	29.4994	−	12.9558i	1.53568	−	0.674454i
$370$	−9.09511			−0.472832
$371$	0.0183978	+	0.0318659i	0.000955167	+	0.00165440i
$372$	4.53190	+	21.5889i	0.234968	+	1.11933i
$373$	8.91873	−	15.4477i	0.461794	−	0.799852i	−0.537256	−	0.843419i	$-0.680539\pi$
$373$	8.91873	−	15.4477i	0.461794	−	0.799852i	0.999050	+	0.0435677i	$0.0138724\pi$
$374$	−35.7147	+	61.8597i	−1.84676	+	3.19869i
$375$	1.64592	+	0.539392i	0.0849950	+	0.0278541i
$376$	−1.39735	−	2.42028i	−0.0720627	−	0.124816i
$377$	−6.88364			−0.354525
$378$	−12.4029	+	1.20866i	−0.637938	+	0.0621665i
$379$	16.1970			0.831983			0.415991	−	0.909369i	$-0.363435\pi$
$379$	16.1970			0.831983			0.415991	+	0.909369i	$0.363435\pi$
$380$	−8.29272	−	14.3634i	−0.425407	−	0.736827i
$381$	7.18617	+	2.35501i	0.368158	+	0.120651i
$382$	−18.9292	+	32.7863i	−0.968500	+	1.67749i
$383$	1.19373	−	2.06760i	0.0609968	−	0.105649i	−0.833914	−	0.551894i	$-0.813905\pi$
$383$	1.19373	−	2.06760i	0.0609968	−	0.105649i	0.894911	+	0.446244i	$0.147239\pi$
$384$	7.33401	+	34.9375i	0.374262	+	1.78290i
$385$	−2.76264	−	4.78503i	−0.140797	−	0.243868i
$386$	−6.83794			−0.348042
$387$	−3.81258	+	34.5924i	−0.193804	+	1.75843i
$388$	22.3715			1.13574
$389$	−15.3850	−	26.6476i	−0.780050	−	1.35109i	−0.931912	−	0.362684i	$-0.881860\pi$
$389$	−15.3850	−	26.6476i	−0.780050	−	1.35109i	0.151862	−	0.988402i	$-0.451473\pi$
$390$	3.10949	−	2.78561i	0.157455	−	0.141055i
$391$	15.0821	−	26.1229i	0.762734	−	1.32109i
$392$	13.1060	−	22.7003i	0.661954	−	1.14654i
$393$	−22.0489	+	19.7523i	−1.11222	+	0.996373i
$394$	17.9081	+	31.0178i	0.902198	+	1.56265i
$395$	1.87645			0.0944146
$396$	51.1533	+	37.5613i	2.57055	+	1.88753i
$397$	30.0408			1.50770			0.753851	−	0.657045i	$-0.228194\pi$
$397$	30.0408			1.50770			0.753851	+	0.657045i	$0.228194\pi$
$398$	29.1638	+	50.5132i	1.46185	+	2.53200i
$399$	−1.54145	−	7.34311i	−0.0771692	−	0.367616i
$400$	−1.44666	+	2.50568i	−0.0723328	+	0.125284i
$401$	−2.70948	+	4.69296i	−0.135305	+	0.234355i	−0.925714	−	0.378224i	$-0.876535\pi$
$401$	−2.70948	+	4.69296i	−0.135305	+	0.234355i	0.790409	+	0.612580i	$0.209868\pi$
$402$	38.4012	+	12.5846i	1.91528	+	0.627664i
$403$	−1.67161	−	2.89531i	−0.0832688	−	0.144226i
$404$	17.7031			0.880760
$405$	−8.78397	−	1.96005i	−0.436479	−	0.0973956i
$406$	16.5087			0.819313
$407$	10.4770	+	18.1467i	0.519326	+	0.899499i
$408$	38.3104	+	12.5549i	1.89665	+	0.621559i
$409$	−1.43522	+	2.48588i	−0.0709672	+	0.122919i	−0.899325	−	0.437280i	$-0.855942\pi$
$409$	−1.43522	+	2.48588i	−0.0709672	+	0.122919i	0.828358	+	0.560199i	$0.189275\pi$
$410$	12.9429	−	22.4178i	0.639205	−	1.10713i
$411$	−0.464398	−	2.21228i	−0.0229071	−	0.109124i
$412$	−13.2418	−	22.9355i	−0.652378	−	1.12995i
$413$	13.7255			0.675389
$414$	−32.9427	−	24.1894i	−1.61904	−	1.18885i
$415$	−11.6119			−0.570004
$416$	−0.874568	−	1.51480i	−0.0428792	−	0.0742690i
$417$	28.1833	−	25.2477i	1.38014	−	1.23639i
$418$	−29.1358	+	50.4647i	−1.42508	+	2.46831i
$419$	−0.429130	+	0.743275i	−0.0209644	+	0.0363114i	−0.876317	−	0.481734i	$-0.840007\pi$
$419$	−0.429130	+	0.743275i	−0.0209644	+	0.0363114i	0.855353	+	0.518046i	$0.173340\pi$
$420$	−4.89005	+	4.38070i	−0.238610	+	0.213756i
$421$	2.70772	+	4.68990i	0.131966	+	0.228572i	0.924434	−	0.381341i	$-0.124538\pi$
$421$	2.70772	+	4.68990i	0.131966	+	0.228572i	−0.792468	+	0.609913i	$0.791204\pi$
$422$	−7.20649			−0.350806
$423$	0.210592	−	1.91075i	0.0102394	−	0.0929040i
$424$	−0.161287			−0.00783280
$425$	−2.66839	−	4.62178i	−0.129436	−	0.224189i
$426$	−2.91206	−	13.8723i	−0.141090	−	0.672117i
$427$	−1.47313	+	2.55154i	−0.0712898	+	0.123478i
$428$	21.5439	−	37.3151i	1.04136	−	1.80370i
$429$	−9.13983	−	2.99525i	−0.441275	−	0.144612i
$430$	13.9805	+	24.2149i	0.674197	+	1.16774i
$431$	−17.5867			−0.847121			−0.423561	−	0.905868i	$-0.639220\pi$
$431$	−17.5867			−0.847121			−0.423561	+	0.905868i	$0.639220\pi$
$432$	6.21881	−	13.6876i	0.299203	−	0.658545i
$433$	16.6547			0.800374			0.400187	−	0.916434i	$-0.368945\pi$
$433$	16.6547			0.800374			0.400187	+	0.916434i	$0.368945\pi$
$434$	4.00894	+	6.94369i	0.192435	+	0.333308i
$435$	11.3299	+	3.71298i	0.543228	+	0.178024i
$436$	−25.7373	+	44.5783i	−1.23259	+	2.13491i
$437$	12.3039	−	21.3109i	0.588573	−	1.01944i
$438$	5.30569	+	25.2750i	0.253516	+	1.20769i
$439$	−19.7895	−	34.2765i	−0.944503	−	1.63593i	−0.756744	−	0.653711i	$-0.773211\pi$
$439$	−19.7895	−	34.2765i	−0.944503	−	1.63593i	−0.187759	−	0.982215i	$-0.560122\pi$
$440$	24.2191			1.15460
$441$	16.5080	−	7.25012i	0.786094	−	0.345244i
$442$	−12.8632			−0.611839
$443$	14.6061	+	25.2984i	0.693955	+	1.20197i	0.970532	+	0.240973i	$0.0774666\pi$
$443$	14.6061	+	25.2984i	0.693955	+	1.20197i	−0.276577	+	0.960992i	$0.589200\pi$
$444$	18.5450	−	16.6133i	0.880105	−	0.788434i
$445$	1.68632	−	2.92078i	0.0799390	−	0.138458i
$446$	6.48001	−	11.2237i	0.306838	−	0.531458i
$447$	1.54133	−	1.38079i	0.0729026	−	0.0653091i
$448$	4.97630	+	8.61920i	0.235108	+	0.407219i
$449$	−19.3679			−0.914027			−0.457013	−	0.889460i	$-0.651081\pi$
$449$	−19.3679			−0.914027			−0.457013	+	0.889460i	$0.651081\pi$
$450$	−6.62050	+	2.90765i	−0.312094	+	0.137068i
$451$	−59.6378			−2.80823
$452$	−12.7558	−	22.0936i	−0.599980	−	1.03920i
$453$	2.49260	+	11.8741i	0.117112	+	0.557896i
$454$	6.35076	−	10.9998i	0.298056	−	0.516248i
$455$	0.497502	−	0.861700i	0.0233233	−	0.0403971i
$456$	31.2533	+	10.2422i	1.46357	+	0.479634i
$457$	6.97566	+	12.0822i	0.326308	+	0.565181i	0.981776	−	0.190041i	$-0.0608621\pi$
$457$	6.97566	+	12.0822i	0.326308	+	0.565181i	−0.655469	+	0.755223i	$0.727529\pi$
$458$	0.394029			0.0184118
$459$	16.1292	+	22.5575i	0.752848	+	1.05289i
$460$	−21.5318			−1.00393
$461$	−10.6825	−	18.5026i	−0.497533	−	0.861752i	0.502463	−	0.864599i	$-0.332427\pi$
$461$	−10.6825	−	18.5026i	−0.497533	−	0.861752i	−0.999996	+	0.00284633i	$0.999094\pi$
$462$	21.9196	+	7.18337i	1.01979	+	0.334201i
$463$	−16.7903	+	29.0816i	−0.780309	+	1.35154i	0.151452	+	0.988465i	$0.451605\pi$
$463$	−16.7903	+	29.0816i	−0.780309	+	1.35154i	−0.931762	+	0.363071i	$0.881728\pi$
$464$	−9.95826	+	17.2482i	−0.462300	+	0.800728i
$465$	1.18963	+	5.66711i	0.0551677	+	0.262806i
$466$	11.6464	+	20.1722i	0.539511	+	0.934461i
$467$	23.1486			1.07119			0.535595	−	0.844475i	$-0.320087\pi$
$467$	23.1486			1.07119			0.535595	+	0.844475i	$0.320087\pi$
$468$	−1.25200	+	11.3597i	−0.0578739	+	0.525104i
$469$	9.63145			0.444739
$470$	−0.772227	−	1.33754i	−0.0356202	−	0.0616959i
$471$	−0.0713481	+	0.0639165i	−0.00328755	+	0.00294512i
$472$	−30.0817	+	52.1031i	−1.38462	+	2.39824i
$473$	32.2093	−	55.7881i	1.48098	−	2.56514i
$474$	−5.83481	+	5.22706i	−0.268002	+	0.240087i
$475$	−2.17685	−	3.77041i	−0.0998807	−	0.172998i
$476$	20.2289			0.927190
$477$	−0.0894226	−	0.0656620i	−0.00409438	−	0.00300646i
$478$	16.3894			0.749635
$479$	18.3588	+	31.7984i	0.838835	+	1.45290i	0.890870	+	0.454259i	$0.150096\pi$
$479$	18.3588	+	31.7984i	0.838835	+	1.45290i	−0.0520353	+	0.998645i	$0.516571\pi$
$480$	0.622401	+	2.96497i	0.0284086	+	0.135332i
$481$	−1.88672	+	3.26790i	−0.0860272	+	0.149003i
$482$	−0.965773	+	1.67277i	−0.0439898	+	0.0761925i
$483$	−9.25650	−	3.03349i	−0.421185	−	0.138029i
$484$	−37.7827	−	65.4415i	−1.71739	−	2.97461i
$485$	5.87255			0.266659
$486$	32.7736	−	18.3739i	1.48664	−	0.833459i
$487$	−17.9211			−0.812082			−0.406041	−	0.913855i	$-0.633091\pi$
$487$	−17.9211			−0.812082			−0.406041	+	0.913855i	$0.633091\pi$
$488$	−6.45721	−	11.1842i	−0.292304	−	0.506286i
$489$	24.1858	+	7.92604i	1.09372	+	0.358428i
$490$	7.24288	−	12.5450i	0.327200	−	0.566727i
$491$	−0.769258	+	1.33239i	−0.0347161	+	0.0601301i	−0.882861	−	0.469634i	$-0.844386\pi$
$491$	−0.769258	+	1.33239i	−0.0347161	+	0.0601301i	0.848145	+	0.529764i	$0.177719\pi$
$492$	14.5582	+	69.3518i	0.656334	+	3.12662i
$493$	−18.3682	−	31.8147i	−0.827262	−	1.43286i
$494$	−10.4937			−0.472133
$495$	13.4278	+	9.85990i	0.603536	+	0.443170i
$496$	−9.67298			−0.434330
$497$	−1.68919	−	2.92576i	−0.0757706	−	0.131238i
$498$	36.1070	−	32.3461i	1.61799	−	1.44946i
$499$	10.7120	−	18.5538i	0.479536	−	0.830581i	−0.520188	−	0.854052i	$-0.674138\pi$
$499$	10.7120	−	18.5538i	0.479536	−	0.830581i	0.999725	+	0.0234706i	$0.00747161\pi$
$500$	−1.90475	+	3.29913i	−0.0851831	+	0.147541i
$501$	7.97658	−	7.14575i	0.356367	−	0.319248i
$502$	31.1897	+	54.0221i	1.39206	+	2.41113i
$503$	42.5500			1.89721			0.948606	−	0.316459i	$-0.102494\pi$
$503$	42.5500			1.89721			0.948606	+	0.316459i	$0.102494\pi$
$504$	1.42624	−	12.9406i	0.0635297	−	0.576419i
$505$	4.64708			0.206792
$506$	37.8252	+	65.5152i	1.68154	+	2.91250i
$507$	−0.355833	−	1.69511i	−0.0158031	−	0.0752823i
$508$	−8.31623	+	14.4041i	−0.368973	+	0.639080i
$509$	−19.5558	+	33.8717i	−0.866797	+	1.50134i	−0.00154441	+	0.999999i	$0.500492\pi$
$509$	−19.5558	+	33.8717i	−0.866797	+	1.50134i	−0.865252	+	0.501337i	$0.832842\pi$
$510$	21.1718	+	6.93830i	0.937502	+	0.307233i
$511$	3.07766	+	5.33066i	0.136148	+	0.235815i
$512$	−30.2988			−1.33903
$513$	13.1581	+	18.4022i	0.580944	+	0.812477i
$514$	−51.6396			−2.27772
$515$	−3.47600	−	6.02061i	−0.153171	−	0.265300i
$516$	−72.7376	−	23.8372i	−3.20210	−	1.04937i
$517$	−1.77912	+	3.08152i	−0.0782454	+	0.135525i
$518$	4.52484	−	7.83725i	0.198810	−	0.344349i
$519$	1.65302	+	7.87459i	0.0725595	+	0.345656i
$520$	2.18072	+	3.77711i	0.0956307	+	0.165637i
$521$	−26.6579			−1.16791			−0.583953	−	0.811788i	$-0.698495\pi$
$521$	−26.6579			−1.16791			−0.583953	+	0.811788i	$0.698495\pi$
$522$	−45.5731	+	20.0152i	−1.99468	+	0.876043i
$523$	34.2818			1.49904			0.749519	−	0.661983i	$-0.230285\pi$
$523$	34.2818			1.49904			0.749519	+	0.661983i	$0.230285\pi$
$524$	−32.5542	−	56.3855i	−1.42214	−	2.46321i
$525$	−1.28364	+	1.14994i	−0.0560228	+	0.0501875i
$526$	37.2352	−	64.4932i	1.62353	−	2.81204i
$527$	8.92100	−	15.4516i	0.388605	−	0.673083i
$528$	−20.7273	+	18.5684i	−0.902042	+	0.808086i
$529$	−4.47333	−	7.74803i	−0.194492	−	0.336871i
$530$	−0.0891334			−0.00387171
$531$	−37.8901	+	16.6409i	−1.64429	+	0.722154i
$532$	16.5026			0.715478
$533$	−5.36985	−	9.30086i	−0.232594	−	0.402865i
$534$	2.89258	+	13.7796i	0.125174	+	0.596300i
$535$	5.65530	−	9.79527i	0.244500	−	0.423487i
$536$	−21.1089	+	36.5617i	−0.911765	+	1.57922i
$537$	9.29459	+	3.04597i	0.401091	+	0.131443i
$538$	−7.68900	−	13.3177i	−0.331496	−	0.574168i
$539$	−33.3734			−1.43750
$540$	8.18805	−	18.0219i	0.352357	−	0.775539i
$541$	−6.13387			−0.263716			−0.131858	−	0.991269i	$-0.542094\pi$
$541$	−6.13387			−0.263716			−0.131858	+	0.991269i	$0.542094\pi$
$542$	22.0908	+	38.2625i	0.948883	+	1.64351i
$543$	33.1410	+	10.8608i	1.42222	+	0.466081i
$544$	4.66737	−	8.08413i	0.200112	−	0.346604i
$545$	−6.75607	+	11.7019i	−0.289398	+	0.501253i
$546$	0.853378	+	4.06529i	0.0365212	+	0.173978i
$547$	5.59571	+	9.69206i	0.239255	+	0.414402i	0.960501	−	0.278277i	$-0.0897634\pi$
$547$	5.59571	+	9.69206i	0.239255	+	0.414402i	−0.721245	+	0.692680i	$0.756430\pi$
$548$	4.97179			0.212384
$549$	0.973158	−	8.82969i	0.0415334	−	0.376842i
$550$	13.3844			0.570712
$551$	−14.9846	−	25.9542i	−0.638367	−	1.10568i
$552$	31.8025	−	28.4900i	1.35360	−	1.21261i
$553$	−0.933540	+	1.61694i	−0.0396982	+	0.0687593i
$554$	37.8434	−	65.5467i	1.60781	−	2.78481i
$555$	4.86808	−	4.36102i	0.206638	−	0.185115i
$556$	41.6112	+	72.0728i	1.76471	+	3.05657i
$557$	−35.8708			−1.51989			−0.759947	−	0.649985i	$-0.774775\pi$
$557$	−35.8708			−1.51989			−0.759947	+	0.649985i	$0.774775\pi$
$558$	−19.4855	−	14.3080i	−0.824886	−	0.605705i
$559$	11.6006			0.490654
$560$	−1.43943	−	2.49317i	−0.0608270	−	0.105356i
$561$	−10.5452	−	50.2348i	−0.445218	−	2.12091i
$562$	36.6440	−	63.4693i	1.54573	−	2.67729i
$563$	−3.37866	+	5.85202i	−0.142394	+	0.246633i	−0.928398	−	0.371588i	$-0.878813\pi$
$563$	−3.37866	+	5.85202i	−0.142394	+	0.246633i	0.786004	+	0.618222i	$0.212147\pi$
$564$	4.01775	+	1.31667i	0.169178	+	0.0554420i
$565$	−3.34840	−	5.79961i	−0.140868	−	0.243991i
$566$	40.2486			1.69177
$567$	6.05902	−	6.59402i	0.254455	−	0.276923i
$568$	14.8086			0.621353
$569$	4.66583	+	8.08146i	0.195602	+	0.338792i	0.947098	−	0.320945i	$-0.104001\pi$
$569$	4.66583	+	8.08146i	0.195602	+	0.338792i	−0.751496	+	0.659738i	$0.770667\pi$
$570$	17.2718	+	5.66021i	0.723435	+	0.237080i
$571$	−11.7739	+	20.3930i	−0.492723	+	0.853422i	−0.999965	−	0.00838230i	$-0.997332\pi$
$571$	−11.7739	+	20.3930i	−0.492723	+	0.853422i	0.507242	+	0.861804i	$0.330665\pi$
$572$	10.5771	−	18.3201i	0.442252	−	0.766002i
$573$	−5.58906	−	26.6249i	−0.233486	−	1.11227i
$574$	12.8783	+	22.3058i	0.537528	+	0.931026i
$575$	−5.65214			−0.235710
$576$	−24.1873	−	17.7605i	−1.00780	−	0.740020i
$577$	−21.5682			−0.897894			−0.448947	−	0.893558i	$-0.648201\pi$
$577$	−21.5682			−0.897894			−0.448947	+	0.893558i	$0.648201\pi$
$578$	−13.8365	−	23.9654i	−0.575521	−	0.996831i
$579$	3.65995	−	3.27873i	0.152102	−	0.136260i
$580$	−13.1116	+	22.7100i	−0.544430	+	0.942981i
$581$	5.77693	−	10.0059i	0.239668	−	0.415116i
$582$	−18.2606	+	16.3586i	−0.756927	+	0.678087i
$583$	0.102676	+	0.177840i	0.00425241	+	0.00736540i
$584$	−26.9808			−1.11647
$585$	−0.328653	+	2.98194i	−0.0135881	+	0.123288i
$586$	17.5771			0.726101
$587$	9.06951	+	15.7089i	0.374339	+	0.648374i	0.990228	−	0.139459i	$-0.0445363\pi$
$587$	9.06951	+	15.7089i	0.374339	+	0.648374i	−0.615889	+	0.787833i	$0.711203\pi$
$588$	8.14680	+	38.8094i	0.335968	+	1.60047i
$589$	7.27768	−	12.6053i	0.299872	−	0.519393i
$590$	−16.6243	+	28.7941i	−0.684411	+	1.18544i
$591$	−24.4579	−	8.01522i	−1.00606	−	0.329702i
$592$	5.45888	+	9.45506i	0.224359	+	0.388601i
$593$	−24.7861			−1.01784			−0.508922	−	0.860813i	$-0.669956\pi$
$593$	−24.7861			−1.01784			−0.508922	+	0.860813i	$0.669956\pi$
$594$	−69.2194	+	6.74538i	−2.84011	+	0.276766i
$595$	5.31012			0.217694
$596$	2.27570	+	3.94163i	0.0932165	+	0.161456i
$597$	−39.8303	−	13.0530i	−1.63015	−	0.534222i
$598$	−6.81165	+	11.7981i	−0.278549	+	0.482461i
$599$	23.2828	−	40.3270i	0.951310	−	1.64772i	0.208715	−	0.977976i	$-0.433072\pi$
$599$	23.2828	−	40.3270i	0.951310	−	1.64772i	0.742595	−	0.669741i	$-0.233595\pi$
$600$	−1.55194	−	7.39309i	−0.0633578	−	0.301822i
$601$	5.45183	+	9.44284i	0.222385	+	0.385182i	0.955532	−	0.294889i	$-0.0952826\pi$
$601$	5.45183	+	9.44284i	0.222385	+	0.385182i	−0.733147	+	0.680070i	$0.761949\pi$
$602$	−27.8212			−1.13391
$603$	−26.5881	+	11.6772i	−1.08275	+	0.475533i
$604$	−26.6854			−1.08581
$605$	−9.91800	−	17.1785i	−0.403224	−	0.698405i
$606$	−14.4500	+	12.9449i	−0.586992	+	0.525852i
$607$	−8.81107	+	15.2612i	−0.357630	+	0.619434i	−0.987564	−	0.157215i	$-0.949749\pi$
$607$	−8.81107	+	15.2612i	−0.357630	+	0.619434i	0.629934	+	0.776649i	$0.283082\pi$
$608$	3.80761	−	6.59497i	0.154419	−	0.267461i
$609$	−8.83614	+	7.91577i	−0.358058	+	0.320763i
$610$	−3.56850	−	6.18082i	−0.144484	−	0.250254i
$611$	−0.640775			−0.0259230
$612$	−55.8430	+	24.5256i	−2.25732	+	0.991391i
$613$	14.3063			0.577824			0.288912	−	0.957356i	$-0.406706\pi$
$613$	14.3063			0.577824			0.288912	+	0.957356i	$0.406706\pi$
$614$	−0.745509	−	1.29126i	−0.0300863	−	0.0521110i
$615$	3.82154	+	18.2049i	0.154100	+	0.734094i
$616$	−12.0491	+	20.8696i	−0.485471	+	0.840860i
$617$	14.5216	−	25.1521i	0.584616	−	1.01259i	−0.410307	−	0.911948i	$-0.634578\pi$
$617$	14.5216	−	25.1521i	0.584616	−	1.01259i	0.994923	−	0.100638i	$-0.0320883\pi$
$618$	27.5796	+	9.03824i	1.10941	+	0.363571i
$619$	−13.6571	−	23.6547i	−0.548924	−	0.950764i	−0.998349	−	0.0574458i	$-0.981704\pi$
$619$	−13.6571	−	23.6547i	−0.548924	−	0.950764i	0.449425	−	0.893318i	$-0.351629\pi$
$620$	−12.7360			−0.511490
$621$	29.2309	−	2.84853i	1.17300	−	0.114307i
$622$	−25.5902			−1.02607
$623$	1.67789	+	2.90619i	0.0672233	+	0.116434i
$624$	−4.76217	−	1.56063i	−0.190639	−	0.0624752i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−10.9800	+	19.0179i	−0.438849	+	0.760109i
$627$	−8.60268	−	40.9811i	−0.343558	−	1.63663i
$628$	−0.105342	−	0.182458i	−0.00420360	−	0.00728085i
$629$	−20.1380			−0.802956
$630$	0.788192	−	7.15145i	0.0314023	−	0.284921i
$631$	23.5760			0.938547			0.469274	−	0.883053i	$-0.344516\pi$
$631$	23.5760			0.938547			0.469274	+	0.883053i	$0.344516\pi$
$632$	−4.09201	−	7.08757i	−0.162772	−	0.281929i
$633$	3.85721	−	3.45545i	0.153310	−	0.137342i
$634$	6.48013	−	11.2239i	0.257359	−	0.445759i
$635$	−2.18302	+	3.78111i	−0.0866306	+	0.150049i
$636$	0.181743	−	0.162813i	0.00720659	−	0.00645596i
$637$	−3.00498	−	5.20478i	−0.119062	−	0.206221i
$638$	92.1333			3.64759
$639$	8.21032	+	6.02875i	0.324795	+	0.238494i
$640$	−20.6108			−0.814713
$641$	16.6478	+	28.8349i	0.657550	+	1.13891i	0.981248	+	0.192750i	$0.0617406\pi$
$641$	16.6478	+	28.8349i	0.657550	+	1.13891i	−0.323698	+	0.946161i	$0.604926\pi$
$642$	9.70068	+	46.2117i	0.382855	+	1.82383i
$643$	9.39883	−	16.2792i	0.370654	−	0.641991i	−0.619013	−	0.785381i	$-0.712467\pi$
$643$	9.39883	−	16.2792i	0.370654	−	0.641991i	0.989666	+	0.143390i	$0.0458004\pi$
$644$	10.7121	−	18.5540i	0.422118	−	0.731129i
$645$	−19.0937	−	6.25729i	−0.751815	−	0.246381i
$646$	−28.0012	−	48.4995i	−1.10169	−	1.90819i
$647$	−26.7277			−1.05078			−0.525388	−	0.850863i	$-0.676080\pi$
$647$	−26.7277			−1.05078			−0.525388	+	0.850863i	$0.676080\pi$
$648$	11.7520	+	37.4524i	0.461663	+	1.47127i
$649$	76.6007			3.00684
$650$	1.20515	+	2.08737i	0.0472697	+	0.0818735i
$651$	−5.47519	−	1.79430i	−0.214590	−	0.0703241i
$652$	−27.9892	+	48.4787i	−1.09614	+	1.89857i
$653$	5.52042	−	9.56164i	0.216031	−	0.374176i	−0.737560	−	0.675281i	$-0.764022\pi$
$653$	5.52042	−	9.56164i	0.216031	−	0.374176i	0.953591	+	0.301105i	$0.0973556\pi$
$654$	−11.5889	−	55.2065i	−0.453160	−	2.15875i
$655$	−8.54552	−	14.8013i	−0.333901	−	0.578333i
$656$	−31.0733			−1.21321
$657$	−14.9590	−	10.9842i	−0.583605	−	0.428535i
$658$	1.53674			0.0599083
$659$	16.2685	+	28.1779i	0.633730	+	1.09765i	0.986783	+	0.162050i	$0.0518105\pi$
$659$	16.2685	+	28.1779i	0.633730	+	1.09765i	−0.353052	+	0.935604i	$0.614856\pi$
$660$	−27.2908	+	24.4482i	−1.06229	+	0.951646i
$661$	−14.7590	+	25.5633i	−0.574058	+	0.994297i	0.422085	+	0.906556i	$0.361298\pi$
$661$	−14.7590	+	25.5633i	−0.574058	+	0.994297i	−0.996143	+	0.0877414i	$0.972035\pi$
$662$	5.01275	−	8.68233i	0.194826	−	0.337449i
$663$	6.88491	−	6.16778i	0.267388	−	0.239537i
$664$	25.3222	+	43.8593i	0.982692	+	1.70207i
$665$	4.33195			0.167986
$666$	−2.98913	+	27.1211i	−0.115827	+	1.05092i
$667$	−38.9073			−1.50649
$668$	11.7770	+	20.3984i	0.455667	+	0.789238i
$669$	1.91330	+	9.11451i	0.0739724	+	0.352387i
$670$	−11.6656	+	20.2054i	−0.450680	+	0.780601i
$671$	−8.22138	+	14.2399i	−0.317383	+	0.549724i
$672$	−2.86456	−	0.938758i	−0.110503	−	0.0362134i
$673$	−16.1731	−	28.0127i	−0.623428	−	1.07981i	−0.988843	−	0.148964i	$-0.952406\pi$
$673$	−16.1731	−	28.0127i	−0.623428	−	1.07981i	0.365415	−	0.930845i	$-0.380927\pi$
$674$	−37.3591			−1.43902
$675$	2.14937	−	4.73077i	0.0827294	−	0.182087i
$676$	3.80950			0.146519
$677$	−24.2480	−	41.9988i	−0.931927	−	1.61415i	−0.780023	−	0.625750i	$-0.784793\pi$
$677$	−24.2480	−	41.9988i	−0.931927	−	1.61415i	−0.151904	−	0.988395i	$-0.548540\pi$
$678$	26.5672	+	8.70647i	1.02031	+	0.334370i
$679$	−2.92161	+	5.06038i	−0.112121	+	0.194199i
$680$	−11.6380	+	20.1576i	−0.446296	+	0.773008i
$681$	1.87513	+	8.93270i	0.0718553	+	0.342302i
$682$	22.3735	+	38.7520i	0.856725	+	1.48389i
$683$	−29.5722			−1.13155			−0.565774	−	0.824560i	$-0.691423\pi$
$683$	−29.5722			−1.13155			−0.565774	+	0.824560i	$0.691423\pi$
$684$	−45.5563	+	20.0078i	−1.74189	+	0.765019i
$685$	1.30510			0.0498653
$686$	15.6006	+	27.0210i	0.595633	+	1.03167i
$687$	−0.210900	+	0.188933i	−0.00804636	+	0.00720825i
$688$	16.7821	−	29.0675i	0.639813	−	1.10819i
$689$	−0.0184902	+	0.0320259i	−0.000704419	+	0.00122009i
$690$	17.5752	−	15.7446i	0.669078	−	0.599388i
$691$	11.7138	+	20.2888i	0.445613	+	0.771824i	0.998095	−	0.0617009i	$-0.0196525\pi$
$691$	11.7138	+	20.2888i	0.445613	+	0.771824i	−0.552482	+	0.833525i	$0.686319\pi$
$692$	−17.6970			−0.672739
$693$	−15.1766	+	6.66542i	−0.576513	+	0.253198i
$694$	76.0863			2.88820
$695$	10.9230	+	18.9192i	0.414333	+	0.717646i
$696$	−10.6830	−	50.8913i	−0.404938	−	1.92903i
$697$	28.6577	−	49.6366i	1.08549	−	1.88012i
$698$	−8.53659	+	14.7858i	−0.323115	+	0.559651i
$699$	−15.9061	−	5.21265i	−0.601623	−	0.197160i
$700$	−1.89524	−	3.28265i	−0.0716333	−	0.124072i
$701$	40.7864			1.54048			0.770241	−	0.637753i	$-0.220136\pi$
$701$	40.7864			1.54048			0.770241	+	0.637753i	$0.220136\pi$
$702$	−7.28458	−	10.1878i	−0.274939	−	0.384514i
$703$	−16.4285			−0.619611
$704$	27.7722	+	48.1028i	1.04670	+	1.81294i
$705$	1.05466	+	0.345629i	0.0397210	+	0.0130171i
$706$	21.8388	−	37.8259i	0.821914	−	1.42360i
$707$	−2.31193	+	4.00439i	−0.0869492	+	0.150600i
$708$	−18.6990	−	89.0777i	−0.702752	−	3.34774i
$709$	−17.7413	−	30.7289i	−0.666289	−	1.15405i	−0.978934	−	0.204177i	$-0.934548\pi$
$709$	−17.7413	−	30.7289i	−0.666289	−	1.15405i	0.312645	−	0.949870i	$-0.398785\pi$
$710$	8.18376			0.307131
$711$	0.616702	−	5.59548i	0.0231281	−	0.209847i
$712$	−14.7095			−0.551262
$713$	−9.44817	−	16.3647i	−0.353837	−	0.612863i
$714$	−16.5117	+	14.7919i	−0.617936	+	0.553573i
$715$	2.77651	−	4.80905i	0.103836	−	0.179848i
$716$	−10.7562	+	18.6303i	−0.401979	+	0.696247i
$717$	−8.77230	+	7.85859i	−0.327608	+	0.293484i
$718$	5.19005	+	8.98943i	0.193691	+	0.335482i
$719$	−34.7146			−1.29464			−0.647318	−	0.762220i	$-0.724109\pi$
$719$	−34.7146			−1.29464			−0.647318	+	0.762220i	$0.724109\pi$
$720$	6.99636	+	5.13735i	0.260739	+	0.191458i
$721$	6.91727			0.257613
$722$	0.0546053	+	0.0945792i	0.00203220	+	0.00351987i
$723$	−0.285156	−	1.35841i	−0.0106051	−	0.0505200i
$724$	−38.3526	+	66.4287i	−1.42536	+	2.46880i
$725$	−3.44182	+	5.96140i	−0.127826	+	0.221401i
$726$	78.6924	+	25.7886i	2.92055	+	0.957106i
$727$	−12.4562	−	21.5748i	−0.461975	−	0.800165i	0.537084	−	0.843529i	$-0.319526\pi$
$727$	−12.4562	−	21.5748i	−0.461975	−	0.800165i	−0.999059	+	0.0433641i	$0.986192\pi$
$728$	−4.33965			−0.160838
$729$	−8.73163	+	25.5491i	−0.323394	+	0.946264i
$730$	−14.9106			−0.551866
$731$	30.9550	+	53.6156i	1.14491	+	1.98304i
$732$	18.5662	+	6.08442i	0.686227	+	0.224887i
$733$	−21.4879	+	37.2182i	−0.793675	+	1.37469i	0.130003	+	0.991514i	$0.458501\pi$
$733$	−21.4879	+	37.2182i	−0.793675	+	1.37469i	−0.923677	+	0.383171i	$0.874832\pi$
$734$	−15.3625	+	26.6087i	−0.567041	+	0.982144i
$735$	2.13855	+	10.1875i	0.0788815	+	0.375773i
$736$	−4.94318	−	8.56184i	−0.182208	−	0.315594i
$737$	53.7521			1.97998
$738$	−62.5948	−	45.9627i	−2.30415	−	1.69191i
$739$	32.2456			1.18617			0.593087	−	0.805139i	$-0.297909\pi$
$739$	32.2456			1.18617			0.593087	+	0.805139i	$0.297909\pi$
$740$	7.18748	+	12.4491i	0.264217	+	0.457637i
$741$	5.61665	−	5.03163i	0.206333	−	0.184841i
$742$	0.0443441	−	0.0768062i	0.00162792	−	0.00281964i
$743$	3.03621	−	5.25886i	0.111388	−	0.192929i	−0.804942	−	0.593353i	$-0.797804\pi$
$743$	3.03621	−	5.25886i	0.111388	−	0.192929i	0.916330	+	0.400424i	$0.131137\pi$
$744$	18.8111	−	16.8517i	0.689647	−	0.617814i
$745$	0.597375	+	1.03468i	0.0218861	+	0.0379079i
$746$	−42.9935			−1.57410
$747$	−3.81627	+	34.6259i	−0.139630	+	1.26690i
$748$	112.895			4.12786
$749$	5.62706	+	9.74635i	0.205608	+	0.356124i
$750$	−0.857662	−	4.08570i	−0.0313174	−	0.149189i
$751$	−17.3274	+	30.0120i	−0.632286	+	1.09515i	0.354797	+	0.934943i	$0.384550\pi$
$751$	−17.3274	+	30.0120i	−0.632286	+	1.09515i	−0.987083	+	0.160209i	$0.948783\pi$
$752$	−0.926981	+	1.60558i	−0.0338035	+	0.0585494i
$753$	−42.5971	−	13.9597i	−1.55233	−	0.508720i
$754$	8.29578	+	14.3687i	0.302115	+	0.523278i
$755$	−7.00496			−0.254936
$756$	11.4559	+	16.0216i	0.416646	+	0.582699i
$757$	3.21746			0.116940			0.0584702	−	0.998289i	$-0.481378\pi$
$757$	3.21746			0.116940			0.0584702	+	0.998289i	$0.481378\pi$
$758$	−19.5197	−	33.8091i	−0.708988	−	1.22800i
$759$	−51.6596	−	16.9296i	−1.87512	−	0.614505i
$760$	−9.49418	+	16.4444i	−0.344390	+	0.596501i
$761$	−3.34188	+	5.78830i	−0.121143	+	0.209826i	−0.920219	−	0.391405i	$-0.871989\pi$
$761$	−3.34188	+	5.78830i	−0.121143	+	0.209826i	0.799076	+	0.601230i	$0.205323\pi$
$762$	−3.74459	−	17.8383i	−0.135652	−	0.646215i
$763$	−6.72232	−	11.6434i	−0.243364	−	0.421520i
$764$	59.8357			2.16478
$765$	−14.6589	+	6.43802i	−0.529992	+	0.232767i
$766$	−5.75447			−0.207918
$767$	6.89721	+	11.9463i	0.249044	+	0.431357i
$768$	38.2807	−	34.2934i	1.38133	−	1.23746i
$769$	9.80475	−	16.9823i	0.353568	−	0.612398i	−0.633304	−	0.773904i	$-0.718302\pi$
$769$	9.80475	−	16.9823i	0.353568	−	0.612398i	0.986872	+	0.161505i	$0.0516349\pi$
$770$	−6.65877	+	11.5333i	−0.239965	+	0.415632i
$771$	27.6396	−	24.7607i	0.995417	−	0.891736i
$772$	5.40374	+	9.35955i	0.194485	+	0.336858i
$773$	34.1022			1.22657			0.613285	−	0.789862i	$-0.289848\pi$
$773$	34.1022			1.22657			0.613285	+	0.789862i	$0.289848\pi$
$774$	76.8020	−	33.7306i	2.76059	−	1.21242i
$775$	−3.34322			−0.120092
$776$	−12.8064	−	22.1813i	−0.459722	−	0.796262i
$777$	1.33601	+	6.36444i	0.0479291	+	0.228323i
$778$	−37.0823	+	64.2284i	−1.32947	+	2.30270i
$779$	23.3787	−	40.4931i	0.837629	−	1.45082i
$780$	−6.27014	−	2.05482i	−0.224507	−	0.0735742i
$781$	−9.42720	−	16.3284i	−0.337332	−	0.584275i
$782$	−72.7044			−2.59991
$783$	14.7955	−	32.5649i	0.528748	−	1.16377i
$784$	−17.3887			−0.621025
$785$	−0.0276524	−	0.0478954i	−0.000986957	−	0.00170946i
$786$	67.8027	+	22.2199i	2.41844	+	0.792558i
$787$	11.7447	−	20.3424i	0.418653	−	0.725129i	−0.577151	−	0.816637i	$-0.695836\pi$
$787$	11.7447	−	20.3424i	0.418653	−	0.725129i	0.995804	+	0.0915087i	$0.0291689\pi$
$788$	28.3041	−	49.0241i	1.00829	−	1.74641i
$789$	10.9941	+	52.3734i	0.391401	+	1.86454i
$790$	−2.26140	−	3.91686i	−0.0804570	−	0.139356i
$791$	6.66336			0.236922
$792$	7.95968	−	72.2200i	0.282835	−	2.56623i
$793$	−2.96105			−0.105150
$794$	−36.2035	−	62.7063i	−1.28481	−	2.22536i
$795$	0.0477079	−	0.0427387i	0.00169202	−	0.00151578i
$796$	46.0939	−	79.8369i	1.63375	−	2.82975i
$797$	−1.84196	+	3.19037i	−0.0652457	+	0.113009i	−0.896803	−	0.442430i	$-0.854116\pi$
$797$	−1.84196	+	3.19037i	−0.0652457	+	0.113009i	0.831557	+	0.555439i	$0.187450\pi$
$798$	−13.4701	+	12.0671i	−0.476838	+	0.427171i
$799$	−1.70983	−	2.96152i	−0.0604896	−	0.104771i
$800$	−1.74914			−0.0618413
$801$	−8.15540	−	5.98842i	−0.288157	−	0.211590i
$802$	13.0613			0.461210
$803$	17.1761	+	29.7499i	0.606131	+	1.04985i
$804$	−13.1214	−	62.5074i	−0.462757	−	2.20447i
$805$	2.81195	−	4.87044i	0.0991083	−	0.171661i
$806$	−4.02907	+	6.97855i	−0.141918	+	0.245809i
$807$	10.5012	+	3.44140i	0.369660	+	0.121143i
$808$	−10.1340	−	17.5525i	−0.356511	−	0.617496i
$809$	11.7708			0.413838			0.206919	−	0.978358i	$-0.433656\pi$
$809$	11.7708			0.413838			0.206919	+	0.978358i	$0.433656\pi$
$810$	6.49461	+	20.6976i	0.228197	+	0.727239i
$811$	−31.5622			−1.10830			−0.554150	−	0.832417i	$-0.686957\pi$
$811$	−31.5622			−1.10830			−0.554150	+	0.832417i	$0.686957\pi$
$812$	−13.0461	−	22.5966i	−0.457829	−	0.792984i
$813$	−30.1705	−	9.88729i	−1.05812	−	0.346763i
$814$	25.2526	−	43.7389i	0.885105	−	1.53305i
$815$	−7.34720	+	12.7257i	−0.257361	+	0.445763i
$816$	−5.49441	−	26.1740i	−0.192343	−	0.916275i
$817$	25.2528	+	43.7392i	0.883485	+	1.53024i
$818$	6.91861			0.241904
$819$	−2.40603	−	1.76672i	−0.0840736	−	0.0617343i
$820$	−40.9129			−1.42874
$821$	12.2747	+	21.2604i	0.428391	+	0.741994i	0.996730	−	0.0807998i	$-0.0257474\pi$
$821$	12.2747	+	21.2604i	0.428391	+	0.741994i	−0.568340	+	0.822794i	$0.692414\pi$
$822$	−4.05819	+	3.63550i	−0.141546	+	0.126803i
$823$	6.38744	−	11.0634i	0.222652	−	0.385645i	−0.732960	−	0.680272i	$-0.761862\pi$
$823$	6.38744	−	11.0634i	0.222652	−	0.385645i	0.955613	+	0.294626i	$0.0951952\pi$
$824$	−15.1603	+	26.2585i	−0.528135	+	0.914757i
$825$	−7.16388	+	6.41770i	−0.249414	+	0.223436i
$826$	−16.5413	−	28.6503i	−0.575544	−	0.996871i
$827$	23.9345			0.832283			0.416141	−	0.909300i	$-0.363382\pi$
$827$	23.9345			0.832283			0.416141	+	0.909300i	$0.363382\pi$
$828$	−7.07650	+	64.2067i	−0.245925	+	2.23134i
$829$	−14.8456			−0.515609			−0.257805	−	0.966197i	$-0.582999\pi$
$829$	−14.8456			−0.515609			−0.257805	+	0.966197i	$0.582999\pi$
$830$	13.9940	+	24.2383i	0.485739	+	0.841324i
$831$	11.1737	+	53.2289i	0.387611	+	1.84649i
$832$	−5.00128	+	8.66247i	−0.173388	+	0.300317i
$833$	16.0369	−	27.7767i	0.555646	−	0.962407i
$834$	−86.6664	−	28.4018i	−3.00101	−	0.983475i
$835$	3.09149	+	5.35461i	0.106985	+	0.185304i
$836$	92.0992			3.18532
$837$	17.2900	−	1.68489i	0.597629	−	0.0582385i
$838$	2.06866			0.0714606
$839$	−23.3906	−	40.5137i	−0.807534	−	1.39869i	−0.914567	−	0.404434i	$-0.867469\pi$
$839$	−23.3906	−	40.5137i	−0.807534	−	1.39869i	0.107033	−	0.994255i	$-0.465865\pi$
$840$	7.14272	+	2.34077i	0.246447	+	0.0807643i
$841$	−9.19222	+	15.9214i	−0.316973	+	0.549014i
$842$	6.52639	−	11.3040i	0.224914	−	0.389563i
$843$	10.8196	+	51.5419i	0.372646	+	1.77520i
$844$	5.69499	+	9.86401i	0.196030	+	0.339533i
$845$	1.00000			0.0344010
$846$	−4.24225	+	1.86315i	−0.145852	+	0.0640565i
$847$	19.7369			0.678169
$848$	0.0534978	+	0.0926610i	0.00183712	+	0.00318199i
$849$	−21.5427	+	19.2988i	−0.739344	+	0.662334i
$850$	−6.43159	+	11.1398i	−0.220602	+	0.382093i
$851$	−10.6640	+	18.4706i	−0.365558	+	0.633165i
$852$	−16.6867	+	14.9487i	−0.571678	+	0.512133i
$853$	−6.36803	−	11.0298i	−0.218037	−	0.377652i	0.736171	−	0.676796i	$-0.236632\pi$
$853$	−6.36803	−	11.0298i	−0.218037	−	0.377652i	−0.954208	+	0.299144i	$0.903299\pi$
$854$	7.10135			0.243003
$855$	−11.9586	+	5.25208i	−0.408975	+	0.179617i
$856$	−49.3304			−1.68608
$857$	15.3889	+	26.6543i	0.525675	+	0.910495i	0.999553	+	0.0299048i	$0.00952040\pi$
$857$	15.3889	+	26.6543i	0.525675	+	0.910495i	−0.473878	+	0.880590i	$0.657146\pi$
$858$	4.76261	+	22.6880i	0.162593	+	0.774554i
$859$	−11.6416	+	20.1638i	−0.397205	+	0.687979i	−0.993380	−	0.114876i	$-0.963353\pi$
$859$	−11.6416	+	20.1638i	−0.397205	+	0.687979i	0.596175	+	0.802854i	$0.296686\pi$
$860$	22.0963	−	38.2720i	0.753479	−	1.30506i
$861$	−17.5884	−	5.76398i	−0.599411	−	0.196436i
$862$	21.1945	+	36.7100i	0.721888	+	1.25035i
$863$	−45.1287			−1.53620			−0.768099	−	0.640331i	$-0.778797\pi$
$863$	−45.1287			−1.53620			−0.768099	+	0.640331i	$0.778797\pi$
$864$	9.04593	−	0.881518i	0.307749	−	0.0299899i
$865$	−4.64549			−0.157951
$866$	−20.0713	−	34.7646i	−0.682052	−	1.18135i
$867$	18.8971	+	6.19284i	0.641778	+	0.210320i
$868$	6.33620	−	10.9746i	0.215064	−	0.372503i
$869$	−5.20999	+	9.02397i	−0.176737	+	0.306117i
$870$	−5.90383	−	28.1245i	−0.200159	−	0.953508i
$871$	4.83990	+	8.38295i	0.163994	+	0.284046i
$872$	58.9323			1.99570
$873$	1.93003	−	17.5116i	0.0653217	−	0.592679i
$874$	−59.3117			−2.00625
$875$	−0.497502	−	0.861700i	−0.0168187	−	0.0291308i
$876$	30.4028	−	27.2360i	1.02721	−	0.920221i
$877$	1.32013	−	2.28653i	0.0445775	−	0.0772105i	−0.842876	−	0.538108i	$-0.819139\pi$
$877$	1.32013	−	2.28653i	0.0445775	−	0.0772105i	0.887453	+	0.460898i	$0.152473\pi$
$878$	−47.6985	+	82.6163i	−1.60975	+	2.78816i
$879$	−9.40797	+	8.42804i	−0.317323	+	0.284271i
$880$	−8.03331	−	13.9141i	−0.270803	−	0.469044i
$881$	39.1892			1.32032			0.660159	−	0.751126i	$-0.270489\pi$
$881$	39.1892			1.32032			0.660159	+	0.751126i	$0.270489\pi$
$882$	−35.0282	−	25.7208i	−1.17946	−	0.866066i
$883$	2.73584			0.0920684			0.0460342	−	0.998940i	$-0.485342\pi$
$883$	2.73584			0.0920684			0.0460342	+	0.998940i	$0.485342\pi$
$884$	10.1652	+	17.6067i	0.341894	+	0.592177i
$885$	−4.90852	−	23.3830i	−0.164998	−	0.786011i
$886$	35.2049	−	60.9766i	1.18273	−	2.04855i
$887$	−13.5967	+	23.5502i	−0.456534	+	0.790740i	−0.998775	−	0.0494832i	$-0.984243\pi$
$887$	−13.5967	+	23.5502i	−0.456534	+	0.790740i	0.542241	+	0.840223i	$0.317576\pi$
$888$	−27.0880	−	8.87712i	−0.909013	−	0.297897i
$889$	−2.17212	−	3.76222i	−0.0728505	−	0.126181i
$890$	−8.12902			−0.272485
$891$	33.8148	−	36.8005i	1.13284	−	1.23286i
$892$	−20.4835			−0.685839
$893$	−1.39487	−	2.41599i	−0.0466775	−	0.0808479i
$894$	−4.73975	−	1.55329i	−0.158521	−	0.0519496i
$895$	−2.82352	+	4.89048i	−0.0943799	+	0.163471i
$896$	10.2539	−	17.7603i	0.342560	−	0.593330i
$897$	−2.01122	−	9.58097i	−0.0671526	−	0.319899i
$898$	23.3411	+	40.4280i	0.778903	+	1.34910i
$899$	−23.0135			−0.767543
$900$	9.21181	+	6.76413i	0.307060	+	0.225471i
$901$	−0.197356			−0.00657487
$902$	71.8722	+	124.486i	2.39308	+	4.14494i
$903$	14.8911	−	13.3400i	0.495544	−	0.443929i
$904$	−14.6038	+	25.2946i	−0.485716	+	0.841285i
$905$	−10.0676	+	17.4376i	−0.334659	+	0.579646i
$906$	21.7818	−	19.5130i	0.723653	−	0.648278i
$907$	−20.4996	−	35.5063i	−0.680677	−	1.17897i	−0.974775	−	0.223191i	$-0.928353\pi$
$907$	−20.4996	−	35.5063i	−0.680677	−	1.17897i	0.294098	−	0.955775i	$-0.404981\pi$
$908$	−20.0749			−0.666210
$909$	1.52728	−	13.8573i	0.0506565	−	0.459618i
$910$	−2.39825			−0.0795013
$911$	9.60507	+	16.6365i	0.318230	+	0.551191i	0.980119	−	0.198411i	$-0.0635782\pi$
$911$	9.60507	+	16.6365i	0.318230	+	0.551191i	−0.661889	+	0.749602i	$0.730245\pi$
$912$	−4.48229	−	21.3526i	−0.148424	−	0.707055i
$913$	32.2405	−	55.8421i	1.06700	−	1.84810i
$914$	16.8134	−	29.1216i	0.556137	−	0.963257i
$915$	4.87366	+	1.59717i	0.161118	+	0.0528007i
$916$	−0.311384	−	0.539334i	−0.0102884	−	0.0178201i
$917$	17.0057			0.561576
$918$	27.6478	−	60.8527i	0.912512	−	2.00844i
$919$	55.3492			1.82580			0.912901	−	0.408180i	$-0.133837\pi$
$919$	55.3492			1.82580			0.912901	+	0.408180i	$0.133837\pi$
$920$	12.3257	+	21.3487i	0.406366	+	0.703847i
$921$	1.01817	+	0.333671i	0.0335500	+	0.0109948i
$922$	−25.7479	+	44.5967i	−0.847962	+	1.46871i
$923$	1.69767	−	2.94045i	0.0558795	−	0.0967862i
$924$	−7.48978	−	35.6796i	−0.246396	−	1.17377i
$925$	1.88672	+	3.26790i	0.0620351	+	0.107448i
$926$	80.9388			2.65981
$927$	−19.0955	+	8.38654i	−0.627179	+	0.275450i
$928$	−12.0404			−0.395246
$929$	11.2236	+	19.4398i	0.368234	+	0.637800i	0.989290	−	0.145967i	$-0.0466292\pi$
$929$	11.2236	+	19.4398i	0.368234	+	0.637800i	−0.621056	+	0.783767i	$0.713296\pi$
$930$	10.3957	−	9.31289i	0.340888	−	0.305382i
$931$	13.0828	−	22.6601i	0.428771	−	0.742653i
$932$	18.4074	−	31.8825i	0.602954	−	1.04435i
$933$	13.6969	−	12.2703i	0.448417	−	0.401710i
$934$	−27.8975	−	48.3198i	−0.912833	−	1.58107i
$935$	29.6352			0.969174
$936$	11.9798	−	5.26141i	0.391573	−	0.171975i
$937$	13.3539			0.436254			0.218127	−	0.975920i	$-0.430005\pi$
$937$	13.3539			0.436254			0.218127	+	0.975920i	$0.430005\pi$
$938$	−11.6073	−	20.1044i	−0.378992	−	0.656433i
$939$	−3.24197	−	15.4440i	−0.105798	−	0.503996i
$940$	−1.22052	+	2.11400i	−0.0398089	+	0.0689510i
$941$	3.34940	−	5.80134i	0.109187	−	0.189118i	−0.806254	−	0.591570i	$-0.798508\pi$
$941$	3.34940	−	5.80134i	0.109187	−	0.189118i	0.915441	+	0.402451i	$0.131842\pi$
$942$	0.219403	+	0.0719014i	0.00714852	+	0.00234267i
$943$	−30.3511	−	52.5697i	−0.988369	−	1.71191i
$944$	39.9116			1.29901
$945$	3.00718	+	4.20568i	0.0978237	+	0.136811i
$946$	−155.267			−5.04818
$947$	−15.7048	−	27.2016i	−0.510339	−	0.883933i	−0.999928	−	0.0119799i	$-0.996187\pi$
$947$	−15.7048	−	27.2016i	−0.510339	−	0.883933i	0.489589	−	0.871953i	$-0.337147\pi$
$948$	11.7656	+	3.85577i	0.382130	+	0.125230i
$949$	−3.09311	+	5.35743i	−0.100407	+	0.173909i
$950$	−5.24684	+	9.08779i	−0.170230	+	0.294847i
$951$	1.91333	+	9.11467i	0.0620441	+	0.295564i
$952$	−11.5799	−	20.0569i	−0.375305	−	0.650048i
$953$	5.32025			0.172340			0.0861699	−	0.996280i	$-0.472537\pi$
$953$	5.32025			0.172340			0.0861699	+	0.996280i	$0.472537\pi$
$954$	−0.0292939	+	0.265791i	−0.000948426	+	0.00860529i
$955$	15.7069			0.508265
$956$	−12.9519	−	22.4333i	−0.418894	−	0.725545i
$957$	−49.3135	+	44.1771i	−1.59408	+	1.42804i
$958$	44.2500	−	76.6433i	1.42965	−	2.47623i
$959$	−0.649291	+	1.12460i	−0.0209667	+	0.0363154i
$960$	12.9042	−	11.5601i	0.416480	−	0.373100i
$961$	9.91144	+	17.1671i	0.319724	+	0.553778i
$962$	9.09511			0.293238
$963$	−27.3503	−	20.0830i	−0.881352	−	0.647167i
$964$	3.05284			0.0983254
$965$	1.41849	+	2.45690i	0.0456628	+	0.0790903i
$966$	4.82341	+	22.9776i	0.155191	+	0.739291i
$967$	14.0226	−	24.2879i	0.450937	−	0.781046i	−0.547507	−	0.836801i	$-0.684423\pi$
$967$	14.0226	−	24.2879i	0.450937	−	0.781046i	0.998444	+	0.0557549i	$0.0177566\pi$
$968$	−43.2567	+	74.9228i	−1.39032	+	2.40811i
$969$	38.2425	+	12.5326i	1.22853	+	0.402606i
$970$	−7.07728	−	12.2582i	−0.227238	−	0.393587i
$971$	42.9317			1.37774			0.688871	−	0.724884i	$-0.258107\pi$
$971$	42.9317			1.37774			0.688871	+	0.724884i	$0.258107\pi$
$972$	−51.0492	−	30.3392i	−1.63741	−	0.973132i
$973$	−21.7369			−0.696853
$974$	21.5975	+	37.4080i	0.692029	+	1.19863i
$975$	−1.64592	−	0.539392i	−0.0527117	−	0.0172744i
$976$	−4.28362	+	7.41946i	−0.137115	+	0.237491i
$977$	2.47785	−	4.29176i	0.0792733	−	0.137305i	−0.823663	−	0.567079i	$-0.808073\pi$
$977$	2.47785	−	4.29176i	0.0792733	−	0.137305i	0.902937	+	0.429774i	$0.141407\pi$
$978$	−12.6028	−	60.0369i	−0.402994	−	1.91977i
$979$	9.36414	+	16.2192i	0.299279	+	0.518367i
$980$	−22.8950			−0.731354
$981$	32.6739	+	23.9921i	1.04320	+	0.766008i
$982$	3.70827			0.118336
$983$	10.4998	+	18.1862i	0.334893	+	0.580051i	0.983464	−	0.181103i	$-0.0579667\pi$
$983$	10.4998	+	18.1862i	0.334893	+	0.580051i	−0.648572	+	0.761154i	$0.724633\pi$
$984$	60.4283	−	54.1342i	1.92639	−	1.72573i
$985$	7.42986	−	12.8689i	0.236735	−	0.410037i
$986$	−44.2727	+	76.6826i	−1.40993	+	2.44207i
$987$	−0.822526	+	0.736853i	−0.0261813	+	0.0234543i
$988$	8.29272	+	14.3634i	0.263826	+	0.456961i
$989$	65.5684			2.08495
$990$	4.39882	−	39.9115i	0.139804	−	1.26847i
$991$	−40.7367			−1.29404			−0.647022	−	0.762472i	$-0.723986\pi$
$991$	−40.7367			−1.29404			−0.647022	+	0.762472i	$0.723986\pi$
$992$	−2.92387	−	5.06430i	−0.0928331	−	0.160792i
$993$	1.48007	+	7.05071i	0.0469687	+	0.223748i
$994$	−4.07144	+	7.05195i	−0.129138	+	0.223674i
$995$	12.0997	−	20.9573i	0.383586	−	0.664391i
$996$	−72.8081	−	23.8603i	−2.30701	−	0.756041i
$997$	12.8223	+	22.2089i	0.406087	+	0.703363i	0.994447	−	0.105236i	$-0.0335598\pi$
$997$	12.8223	+	22.2089i	0.406087	+	0.703363i	−0.588361	+	0.808599i	$0.700226\pi$
$998$	−51.6382			−1.63458
$999$	−11.4044	−	15.9496i	−0.360820	−	0.504623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.g.391.2	yes	26
3.2	odd	2		1755.2.i.g.1171.12		26
9.2	odd	6		1755.2.i.g.586.12		26
9.4	even	3		5265.2.a.bg.1.12		13
9.5	odd	6		5265.2.a.bh.1.2		13
9.7	even	3	inner	585.2.i.g.196.2	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.g.196.2	✓	26	9.7	even	3	inner
585.2.i.g.391.2	yes	26	1.1	even	1	trivial
1755.2.i.g.586.12		26	9.2	odd	6
1755.2.i.g.1171.12		26	3.2	odd	2
5265.2.a.bg.1.12		13	9.4	even	3
5265.2.a.bh.1.2		13	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20515 - 2.08737i) q^{2} +(1.64592 + 0.539392i) q^{3} +(-1.90475 + 3.29913i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.857662 - 4.08570i) q^{6} +(-0.497502 - 0.861700i) q^{7} +4.36143 q^{8} +(2.41811 + 1.77559i) q^{9} +O(q^{10})\)	\(q+(-1.20515 - 2.08737i) q^{2} +(1.64592 + 0.539392i) q^{3} +(-1.90475 + 3.29913i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.857662 - 4.08570i) q^{6} +(-0.497502 - 0.861700i) q^{7} +4.36143 q^{8} +(2.41811 + 1.77559i) q^{9} +2.41029 q^{10} +(-2.77651 - 4.80905i) q^{11} +(-4.91459 + 4.40270i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-1.19913 + 2.07695i) q^{14} +(-1.29009 + 1.15571i) q^{15} +(-1.44666 - 2.50568i) q^{16} +5.33677 q^{17} +(0.792149 - 7.18735i) q^{18} +4.35370 q^{19} +(-1.90475 - 3.29913i) q^{20} +(-0.354056 - 1.68664i) q^{21} +(-6.69219 + 11.5912i) q^{22} +(2.82607 - 4.89489i) q^{23} +(7.17857 + 2.35252i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.41029 q^{26} +(3.02228 + 4.22680i) q^{27} +3.79048 q^{28} +(-3.44182 - 5.96140i) q^{29} +(3.96715 + 1.30009i) q^{30} +(1.67161 - 2.89531i) q^{31} +(0.874568 - 1.51480i) q^{32} +(-1.97595 - 9.41295i) q^{33} +(-6.43159 - 11.1398i) q^{34} +0.995005 q^{35} +(-10.4638 + 4.59560i) q^{36} -3.77345 q^{37} +(-5.24684 - 9.08779i) q^{38} +(1.29009 - 1.15571i) q^{39} +(-2.18072 + 3.77711i) q^{40} +(5.36985 - 9.30086i) q^{41} +(-3.09396 + 2.77169i) q^{42} +(5.80032 + 10.0464i) q^{43} +21.1542 q^{44} +(-2.74677 + 1.20635i) q^{45} -13.6233 q^{46} +(-0.320387 - 0.554927i) q^{47} +(-1.02954 - 4.90447i) q^{48} +(3.00498 - 5.20478i) q^{49} +(-1.20515 + 2.08737i) q^{50} +(8.78391 + 2.87861i) q^{51} +(1.90475 + 3.29913i) q^{52} -0.0369803 q^{53} +(5.18062 - 11.4025i) q^{54} +5.55302 q^{55} +(-2.16982 - 3.75824i) q^{56} +(7.16584 + 2.34835i) q^{57} +(-8.29578 + 14.3687i) q^{58} +(-6.89721 + 11.9463i) q^{59} +(-1.35555 - 6.45751i) q^{60} +(-1.48053 - 2.56435i) q^{61} -8.05813 q^{62} +(0.327011 - 2.96705i) q^{63} -10.0026 q^{64} +(0.500000 + 0.866025i) q^{65} +(-17.2670 + 15.4685i) q^{66} +(-4.83990 + 8.38295i) q^{67} +(-10.1652 + 17.6067i) q^{68} +(7.29175 - 6.53225i) q^{69} +(-1.19913 - 2.07695i) q^{70} +3.39534 q^{71} +(10.5464 + 7.74413i) q^{72} -6.18622 q^{73} +(4.54755 + 7.87660i) q^{74} +(-0.355833 - 1.69511i) q^{75} +(-8.29272 + 14.3634i) q^{76} +(-2.76264 + 4.78503i) q^{77} +(-3.96715 - 1.30009i) q^{78} +(-0.938227 - 1.62506i) q^{79} +2.89331 q^{80} +(2.69454 + 8.58717i) q^{81} -25.8858 q^{82} +(5.80594 + 10.0562i) q^{83} +(6.23882 + 2.04455i) q^{84} +(-2.66839 + 4.62178i) q^{85} +(13.9805 - 24.2149i) q^{86} +(-2.44943 - 11.6685i) q^{87} +(-12.1096 - 20.9744i) q^{88} -3.37263 q^{89} +(5.82836 + 4.27970i) q^{90} -0.995005 q^{91} +(10.7659 + 18.6471i) q^{92} +(4.31305 - 3.86380i) q^{93} +(-0.772227 + 1.33754i) q^{94} +(-2.17685 + 3.77041i) q^{95} +(2.25654 - 2.02150i) q^{96} +(-2.93628 - 5.08578i) q^{97} -14.4858 q^{98} +(1.82502 - 16.5588i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * q^99

Introduction

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