LMFDB - Embedded newform 315.2.l.b.121.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.12
Character	$\chi$	$=$	315.121
Dual form			315.2.l.b.151.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.34008 q^{2} +(0.308978 + 1.70427i) q^{3} +3.47596 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.723033 + 3.98812i) q^{6} +(-1.61838 - 2.09305i) q^{7} +3.45385 q^{8} +(-2.80906 + 1.05316i) q^{9} +O(q^{10})$	\(q+2.34008 q^{2} +(0.308978 + 1.70427i) q^{3} +3.47596 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.723033 + 3.98812i) q^{6} +(-1.61838 - 2.09305i) q^{7} +3.45385 q^{8} +(-2.80906 + 1.05316i) q^{9} +(1.17004 + 2.02657i) q^{10} +(1.62831 - 2.82031i) q^{11} +(1.07400 + 5.92396i) q^{12} +(0.549485 - 0.951736i) q^{13} +(-3.78714 - 4.89789i) q^{14} +(-1.32145 + 1.11972i) q^{15} +1.13035 q^{16} +(0.763940 + 1.32318i) q^{17} +(-6.57342 + 2.46448i) q^{18} +(-3.06883 + 5.31536i) q^{19} +(1.73798 + 3.01027i) q^{20} +(3.06707 - 3.40486i) q^{21} +(3.81036 - 6.59974i) q^{22} +(-2.15303 - 3.72915i) q^{23} +(1.06716 + 5.88628i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.28584 - 2.22714i) q^{26} +(-2.66282 - 4.46200i) q^{27} +(-5.62542 - 7.27533i) q^{28} +(-1.48384 - 2.57008i) q^{29} +(-3.09230 + 2.62022i) q^{30} +4.09900 q^{31} -4.26258 q^{32} +(5.30968 + 1.90366i) q^{33} +(1.78768 + 3.09635i) q^{34} +(1.00344 - 2.44808i) q^{35} +(-9.76418 + 3.66075i) q^{36} +(4.94725 - 8.56889i) q^{37} +(-7.18129 + 12.4384i) q^{38} +(1.79179 + 0.642405i) q^{39} +(1.72692 + 2.99112i) q^{40} +(-0.222291 + 0.385018i) q^{41} +(7.17717 - 7.96764i) q^{42} +(2.84617 + 4.92971i) q^{43} +(5.65993 - 9.80328i) q^{44} +(-2.31660 - 1.90614i) q^{45} +(-5.03824 - 8.72650i) q^{46} +6.23292 q^{47} +(0.349255 + 1.92643i) q^{48} +(-1.76168 + 6.77469i) q^{49} +(-1.17004 + 2.02657i) q^{50} +(-2.01902 + 1.71079i) q^{51} +(1.90999 - 3.30819i) q^{52} +(5.48563 + 9.50139i) q^{53} +(-6.23119 - 10.4414i) q^{54} +3.25662 q^{55} +(-5.58964 - 7.22906i) q^{56} +(-10.0070 - 3.58777i) q^{57} +(-3.47229 - 6.01419i) q^{58} -7.55293 q^{59} +(-4.59330 + 3.89209i) q^{60} -7.48572 q^{61} +9.59196 q^{62} +(6.75046 + 4.17508i) q^{63} -12.2355 q^{64} +1.09897 q^{65} +(12.4251 + 4.45471i) q^{66} +2.13929 q^{67} +(2.65542 + 4.59932i) q^{68} +(5.69024 - 4.82156i) q^{69} +(2.34813 - 5.72870i) q^{70} -15.7970 q^{71} +(-9.70208 + 3.63747i) q^{72} +(4.96804 + 8.60490i) q^{73} +(11.5769 - 20.0518i) q^{74} +(-1.63043 - 0.584551i) q^{75} +(-10.6671 + 18.4760i) q^{76} +(-8.53827 + 1.15622i) q^{77} +(4.19293 + 1.50328i) q^{78} +7.86225 q^{79} +(0.565177 + 0.978916i) q^{80} +(6.78169 - 5.91681i) q^{81} +(-0.520177 + 0.900972i) q^{82} +(-8.19187 - 14.1887i) q^{83} +(10.6610 - 11.8352i) q^{84} +(-0.763940 + 1.32318i) q^{85} +(6.66025 + 11.5359i) q^{86} +(3.92164 - 3.32296i) q^{87} +(5.62393 - 9.74093i) q^{88} +(0.440119 - 0.762308i) q^{89} +(-5.42102 - 4.46051i) q^{90} +(-2.88130 + 0.390175i) q^{91} +(-7.48382 - 12.9624i) q^{92} +(1.26650 + 6.98579i) q^{93} +14.5855 q^{94} -6.13765 q^{95} +(-1.31705 - 7.26458i) q^{96} +(7.41446 + 12.8422i) q^{97} +(-4.12247 + 15.8533i) q^{98} +(-1.60377 + 9.63731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.34008			1.65468			0.827342	−	0.561699i	$-0.189852\pi$
$2$	2.34008			1.65468			0.827342	+	0.561699i	$0.189852\pi$
$3$	0.308978	+	1.70427i	0.178389	+	0.983960i
$3$	0.308978	+	1.70427i	0.178389	+	0.983960i
$4$	3.47596			1.73798
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.723033	+	3.98812i	0.295177	+	1.62814i
$7$	−1.61838	−	2.09305i	−0.611691	−	0.791097i
$7$	−1.61838	−	2.09305i	−0.611691	−	0.791097i
$8$	3.45385			1.22112
$9$	−2.80906	+	1.05316i	−0.936355	+	0.351055i
$10$	1.17004	+	2.02657i	0.369998	+	0.640856i
$11$	1.62831	−	2.82031i	0.490953	−	0.850356i	−0.508992	−	0.860771i	$-0.669982\pi$
$11$	1.62831	−	2.82031i	0.490953	−	0.850356i	0.999946	+	0.0104149i	$0.00331523\pi$
$12$	1.07400	+	5.92396i	0.310036	+	1.71010i
$13$	0.549485	−	0.951736i	0.152400	−	0.263964i	−0.779709	−	0.626142i	$-0.784633\pi$
$13$	0.549485	−	0.951736i	0.152400	−	0.263964i	0.932109	+	0.362177i	$0.117967\pi$
$14$	−3.78714	−	4.89789i	−1.01215	−	1.30902i
$15$	−1.32145	+	1.11972i	−0.341197	+	0.289110i
$16$	1.13035			0.282589
$17$	0.763940	+	1.32318i	0.185283	+	0.320919i	0.943672	−	0.330883i	$-0.107347\pi$
$17$	0.763940	+	1.32318i	0.185283	+	0.320919i	−0.758389	+	0.651802i	$0.774013\pi$
$18$	−6.57342	+	2.46448i	−1.54937	+	0.580885i
$19$	−3.06883	+	5.31536i	−0.704037	+	1.21943i	0.263001	+	0.964796i	$0.415288\pi$
$19$	−3.06883	+	5.31536i	−0.704037	+	1.21943i	−0.967038	+	0.254632i	$0.918046\pi$
$20$	1.73798	+	3.01027i	0.388624	+	0.673116i
$21$	3.06707	−	3.40486i	0.669289	−	0.743002i
$22$	3.81036	−	6.59974i	0.812372	−	1.40707i
$23$	−2.15303	−	3.72915i	−0.448937	−	0.777582i	0.549380	−	0.835573i	$-0.314864\pi$
$23$	−2.15303	−	3.72915i	−0.448937	−	0.777582i	−0.998317	+	0.0579909i	$0.981531\pi$
$24$	1.06716	+	5.88628i	0.217834	+	1.20153i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.28584	−	2.22714i	0.252173	−	0.436777i
$27$	−2.66282	−	4.46200i	−0.512459	−	0.858712i
$28$	−5.62542	−	7.27533i	−1.06310	−	1.37491i
$29$	−1.48384	−	2.57008i	−0.275542	−	0.477253i	0.694730	−	0.719271i	$-0.255524\pi$
$29$	−1.48384	−	2.57008i	−0.275542	−	0.477253i	−0.970272	+	0.242018i	$0.922191\pi$
$30$	−3.09230	+	2.62022i	−0.564573	+	0.478385i
$31$	4.09900			0.736201			0.368101	−	0.929786i	$-0.380008\pi$
$31$	4.09900			0.736201			0.368101	+	0.929786i	$0.380008\pi$
$32$	−4.26258			−0.753525
$33$	5.30968	+	1.90366i	0.924297	+	0.331384i
$34$	1.78768	+	3.09635i	0.306584	+	0.531019i
$35$	1.00344	−	2.44808i	0.169612	−	0.413801i
$36$	−9.76418	+	3.66075i	−1.62736	+	0.610125i
$37$	4.94725	−	8.56889i	0.813323	−	1.40872i	−0.0972035	−	0.995265i	$-0.530990\pi$
$37$	4.94725	−	8.56889i	0.813323	−	1.40872i	0.910526	−	0.413452i	$-0.135677\pi$
$38$	−7.18129	+	12.4384i	−1.16496	+	2.01777i
$39$	1.79179	+	0.642405i	0.286917	+	0.102867i
$40$	1.72692	+	2.99112i	0.273051	+	0.472938i
$41$	−0.222291	+	0.385018i	−0.0347159	+	0.0601298i	−0.882861	−	0.469634i	$-0.844386\pi$
$41$	−0.222291	+	0.385018i	−0.0347159	+	0.0601298i	0.848145	+	0.529764i	$0.177719\pi$
$42$	7.17717	−	7.96764i	1.10746	−	1.22943i
$43$	2.84617	+	4.92971i	0.434037	+	0.751773i	0.997216	−	0.0745609i	$-0.0237555\pi$
$43$	2.84617	+	4.92971i	0.434037	+	0.751773i	−0.563180	+	0.826334i	$0.690422\pi$
$44$	5.65993	−	9.80328i	0.853266	−	1.47790i
$45$	−2.31660	−	1.90614i	−0.345338	−	0.284150i
$46$	−5.03824	−	8.72650i	−0.742849	−	1.28665i
$47$	6.23292			0.909164			0.454582	−	0.890705i	$-0.349789\pi$
$47$	6.23292			0.909164			0.454582	+	0.890705i	$0.349789\pi$
$48$	0.349255	+	1.92643i	0.0504106	+	0.278056i
$49$	−1.76168	+	6.77469i	−0.251669	+	0.967813i
$50$	−1.17004	+	2.02657i	−0.165468	+	0.286600i
$51$	−2.01902	+	1.71079i	−0.282719	+	0.239559i
$52$	1.90999	−	3.30819i	0.264867	−	0.458764i
$53$	5.48563	+	9.50139i	0.753509	+	1.30512i	0.946112	+	0.323839i	$0.104974\pi$
$53$	5.48563	+	9.50139i	0.753509	+	1.30512i	−0.192603	+	0.981277i	$0.561693\pi$
$54$	−6.23119	−	10.4414i	−0.847958	−	1.42090i
$55$	3.25662			0.439122
$56$	−5.58964	−	7.22906i	−0.746947	−	0.966024i
$57$	−10.0070	−	3.58777i	−1.32546	−	0.475212i
$58$	−3.47229	−	6.01419i	−0.455935	−	0.789702i
$59$	−7.55293			−0.983307			−0.491654	−	0.870791i	$-0.663607\pi$
$59$	−7.55293			−0.983307			−0.491654	+	0.870791i	$0.663607\pi$
$60$	−4.59330	+	3.89209i	−0.592993	+	0.502466i
$61$	−7.48572			−0.958448			−0.479224	−	0.877693i	$-0.659082\pi$
$61$	−7.48572			−0.958448			−0.479224	+	0.877693i	$0.659082\pi$
$62$	9.59196			1.21818
$63$	6.75046	+	4.17508i	0.850478	+	0.526011i
$64$	−12.2355			−1.52943
$65$	1.09897			0.136311
$66$	12.4251	+	4.45471i	1.52942	+	0.548336i
$67$	2.13929			0.261355			0.130678	−	0.991425i	$-0.458285\pi$
$67$	2.13929			0.261355			0.130678	+	0.991425i	$0.458285\pi$
$68$	2.65542	+	4.59932i	0.322017	+	0.557750i
$69$	5.69024	−	4.82156i	0.685024	−	0.580448i
$70$	2.34813	−	5.72870i	0.280655	−	0.684710i
$71$	−15.7970			−1.87476			−0.937380	−	0.348308i	$-0.886756\pi$
$71$	−15.7970			−1.87476			−0.937380	+	0.348308i	$0.886756\pi$
$72$	−9.70208	+	3.63747i	−1.14340	+	0.428680i
$73$	4.96804	+	8.60490i	0.581465	+	1.00713i	0.995306	+	0.0967780i	$0.0308537\pi$
$73$	4.96804	+	8.60490i	0.581465	+	1.00713i	−0.413841	+	0.910349i	$0.635813\pi$
$74$	11.5769	−	20.0518i	1.34579	−	2.33098i
$75$	−1.63043	−	0.584551i	−0.188266	−	0.0674982i
$76$	−10.6671	+	18.4760i	−1.22360	+	2.11934i
$77$	−8.53827	+	1.15622i	−0.973026	+	0.131763i
$78$	4.19293	+	1.50328i	0.474756	+	0.170212i
$79$	7.86225			0.884572			0.442286	−	0.896874i	$-0.354168\pi$
$79$	7.86225			0.884572			0.442286	+	0.896874i	$0.354168\pi$
$80$	0.565177	+	0.978916i	0.0631887	+	0.109446i
$81$	6.78169	−	5.91681i	0.753521	−	0.657424i
$82$	−0.520177	+	0.900972i	−0.0574439	+	0.0994958i
$83$	−8.19187	−	14.1887i	−0.899174	−	1.55742i	−0.828552	−	0.559912i	$-0.810835\pi$
$83$	−8.19187	−	14.1887i	−0.899174	−	1.55742i	−0.0706223	−	0.997503i	$-0.522499\pi$
$84$	10.6610	−	11.8352i	1.16321	−	1.29132i
$85$	−0.763940	+	1.32318i	−0.0828609	+	0.143519i
$86$	6.66025	+	11.5359i	0.718193	+	1.24395i
$87$	3.92164	−	3.32296i	0.420444	−	0.356259i
$88$	5.62393	−	9.74093i	0.599513	−	1.03839i
$89$	0.440119	−	0.762308i	0.0466525	−	0.0808045i	−0.841756	−	0.539858i	$-0.818478\pi$
$89$	0.440119	−	0.762308i	0.0466525	−	0.0808045i	0.888409	+	0.459053i	$0.151811\pi$
$90$	−5.42102	−	4.46051i	−0.571426	−	0.470179i
$91$	−2.88130	+	0.390175i	−0.302043	+	0.0409014i
$92$	−7.48382	−	12.9624i	−0.780242	−	1.35142i
$93$	1.26650	+	6.98579i	0.131330	+	0.724393i
$94$	14.5855			1.50438
$95$	−6.13765			−0.629710
$96$	−1.31705	−	7.26458i	−0.134420	−	0.741438i
$97$	7.41446	+	12.8422i	0.752824	+	1.30393i	0.946449	+	0.322854i	$0.104642\pi$
$97$	7.41446	+	12.8422i	0.752824	+	1.30393i	−0.193624	+	0.981076i	$0.562024\pi$
$98$	−4.12247	+	15.8533i	−0.416432	+	1.60142i
$99$	−1.60377	+	9.63731i	−0.161185	+	0.968587i
$100$	−1.73798	+	3.01027i	−0.173798	+	0.301027i
$101$	−7.53794	+	13.0561i	−0.750053	+	1.29913i	0.197743	+	0.980254i	$0.436639\pi$
$101$	−7.53794	+	13.0561i	−0.750053	+	1.29913i	−0.947796	+	0.318876i	$0.896695\pi$
$102$	−4.72466	+	4.00339i	−0.467811	+	0.396394i
$103$	−4.45670	−	7.71923i	−0.439132	−	0.760598i	0.558491	−	0.829510i	$-0.311380\pi$
$103$	−4.45670	−	7.71923i	−0.439132	−	0.760598i	−0.997623	+	0.0689124i	$0.978047\pi$
$104$	1.89784	−	3.28715i	0.186098	−	0.322332i
$105$	4.48223	+	0.953727i	0.437421	+	0.0930742i
$106$	12.8368	+	22.2340i	1.24682	+	2.15955i
$107$	−1.52574	+	2.64266i	−0.147499	+	0.255476i	−0.930302	−	0.366793i	$-0.880456\pi$
$107$	−1.52574	+	2.64266i	−0.147499	+	0.255476i	0.782803	+	0.622269i	$0.213789\pi$
$108$	−9.25583	−	15.5097i	−0.890643	−	1.49242i
$109$	9.98551	+	17.2954i	0.956438	+	1.65660i	0.731042	+	0.682332i	$0.239034\pi$
$109$	9.98551	+	17.2954i	0.956438	+	1.65660i	0.225396	+	0.974267i	$0.427632\pi$
$110$	7.62073			0.726608
$111$	16.1323	+	5.78384i	1.53121	+	0.548978i
$112$	−1.82934	−	2.36588i	−0.172857	−	0.223555i
$113$	−4.49399	+	7.78382i	−0.422759	+	0.732240i	−0.996208	−	0.0870011i	$-0.972272\pi$
$113$	−4.49399	+	7.78382i	−0.422759	+	0.732240i	0.573449	+	0.819241i	$0.305605\pi$
$114$	−23.4172	−	8.39566i	−2.19322	−	0.786326i
$115$	2.15303	−	3.72915i	0.200771	−	0.347745i
$116$	−5.15776	−	8.93350i	−0.478886	−	0.829454i
$117$	−0.541205	+	3.25219i	−0.0500344	+	0.300665i
$118$	−17.6744			−1.62706
$119$	1.53314	−	3.74038i	0.140542	−	0.342880i
$120$	−4.56409	+	3.86733i	−0.416642	+	0.353038i
$121$	0.197227	+	0.341607i	0.0179297	+	0.0310552i
$122$	−17.5171			−1.58593
$123$	−0.724858	−	0.259880i	−0.0653582	−	0.0234326i
$124$	14.2479			1.27950
$125$	−1.00000			−0.0894427
$126$	15.7966	+	9.77000i	1.40727	+	0.870381i
$127$	14.1353			1.25431			0.627154	−	0.778895i	$-0.284220\pi$
$127$	14.1353			1.25431			0.627154	+	0.778895i	$0.284220\pi$
$128$	−20.1068			−1.77720
$129$	−7.52214	+	6.37381i	−0.662288	+	0.561183i
$130$	2.57167			0.225551
$131$	−2.83714	−	4.91406i	−0.247882	−	0.429344i	0.715056	−	0.699067i	$-0.246401\pi$
$131$	−2.83714	−	4.91406i	−0.247882	−	0.429344i	−0.962938	+	0.269723i	$0.913068\pi$
$132$	18.4562	+	6.61703i	1.60641	+	0.575939i
$133$	16.0918	−	2.17909i	1.39534	−	0.188951i
$134$	5.00609			0.432460
$135$	2.53279	−	4.53706i	0.217988	−	0.390488i
$136$	2.63853	+	4.57007i	0.226252	+	0.391880i
$137$	10.8220	−	18.7442i	0.924585	−	1.60143i	0.132358	−	0.991202i	$-0.457745\pi$
$137$	10.8220	−	18.7442i	0.924585	−	1.60143i	0.792227	−	0.610226i	$-0.208921\pi$
$138$	13.3156	−	11.2828i	1.13350	−	0.960458i
$139$	1.27376	−	2.20622i	0.108039	−	0.187129i	−0.806937	−	0.590638i	$-0.798876\pi$
$139$	1.27376	−	2.20622i	0.108039	−	0.187129i	0.914976	+	0.403509i	$0.132210\pi$
$140$	3.48791	−	8.50943i	0.294782	−	0.719178i
$141$	1.92584	+	10.6226i	0.162185	+	0.894581i
$142$	−36.9662			−3.10214
$143$	−1.78946	−	3.09944i	−0.149642	−	0.259188i
$144$	−3.17524	+	1.19045i	−0.264603	+	0.0992041i
$145$	1.48384	−	2.57008i	0.123226	−	0.213434i
$146$	11.6256	+	20.1361i	0.962141	+	1.66648i
$147$	−12.0902	−	0.909147i	−0.997185	−	0.0749851i
$148$	17.1964	−	29.7851i	1.41354	−	2.44832i
$149$	−3.20515	−	5.55148i	−0.262576	−	0.454795i	0.704350	−	0.709853i	$-0.251239\pi$
$149$	−3.20515	−	5.55148i	−0.262576	−	0.454795i	−0.966926	+	0.255058i	$0.917905\pi$
$150$	−3.81533	−	1.36789i	−0.311520	−	0.111688i
$151$	−0.933306	+	1.61653i	−0.0759513	+	0.131552i	−0.901500	−	0.432780i	$-0.857533\pi$
$151$	−0.933306	+	1.61653i	−0.0759513	+	0.131552i	0.825548	+	0.564332i	$0.190866\pi$
$152$	−10.5993	+	18.3585i	−0.859713	+	1.48907i
$153$	−3.53949	−	2.91235i	−0.286150	−	0.235450i
$154$	−19.9802	+	2.70564i	−1.61005	+	0.218026i
$155$	2.04950	+	3.54983i	0.164620	+	0.285130i
$156$	6.22819	+	2.23297i	0.498655	+	0.178781i
$157$	−19.2871			−1.53928			−0.769639	−	0.638480i	$-0.779564\pi$
$157$	−19.2871			−1.53928			−0.769639	+	0.638480i	$0.779564\pi$
$158$	18.3983			1.46369
$159$	−14.4980	+	12.2847i	−1.14976	+	0.974241i
$160$	−2.13129	−	3.69150i	−0.168493	−	0.291839i
$161$	−4.32087	+	10.5416i	−0.340532	+	0.830792i
$162$	15.8697	−	13.8458i	1.24684	−	1.08783i
$163$	4.41723	−	7.65086i	0.345984	−	0.599262i	−0.639548	−	0.768751i	$-0.720879\pi$
$163$	4.41723	−	7.65086i	0.345984	−	0.599262i	0.985532	+	0.169489i	$0.0542119\pi$
$164$	−0.772672	+	1.33831i	−0.0603355	+	0.104504i
$165$	1.00622	+	5.55015i	0.0783344	+	0.432078i
$166$	−19.1696	−	33.2027i	−1.48785	−	2.57703i
$167$	10.1846	−	17.6402i	0.788105	−	1.36504i	−0.139022	−	0.990289i	$-0.544396\pi$
$167$	10.1846	−	17.6402i	0.788105	−	1.36504i	0.927127	−	0.374748i	$-0.122271\pi$
$168$	10.5932	−	11.7599i	0.817282	−	0.907294i
$169$	5.89613	+	10.2124i	0.453549	+	0.785569i
$170$	−1.78768	+	3.09635i	−0.137109	+	0.237479i
$171$	3.02258	−	18.1632i	0.231142	−	1.38897i
$172$	9.89315	+	17.1354i	0.754346	+	1.30657i
$173$	5.49084			0.417461			0.208730	−	0.977973i	$-0.433067\pi$
$173$	5.49084			0.417461			0.208730	+	0.977973i	$0.433067\pi$
$174$	9.17693	−	7.77598i	0.695702	−	0.589495i
$175$	2.62182	−	0.355037i	0.198191	−	0.0268382i
$176$	1.84057	−	3.18795i	0.138738	−	0.240301i
$177$	−2.33369	−	12.8722i	−0.175411	−	0.967535i
$178$	1.02991	−	1.78386i	0.0771951	−	0.133706i
$179$	−2.96012	−	5.12708i	−0.221250	−	0.383216i	0.733938	−	0.679216i	$-0.237680\pi$
$179$	−2.96012	−	5.12708i	−0.221250	−	0.383216i	−0.955188	+	0.296001i	$0.904347\pi$
$180$	−8.05240	−	6.62565i	−0.600190	−	0.493847i
$181$	−1.20377			−0.0894752			−0.0447376	−	0.998999i	$-0.514245\pi$
$181$	−1.20377			−0.0894752			−0.0447376	+	0.998999i	$0.514245\pi$
$182$	−6.74247	+	0.913038i	−0.499785	+	0.0676789i
$183$	−2.31293	−	12.7577i	−0.170976	−	0.943075i
$184$	−7.43622	−	12.8799i	−0.548206	−	0.949520i
$185$	9.89450			0.727458
$186$	2.96371	+	16.3473i	0.217310	+	1.19864i
$187$	4.97572			0.363860
$188$	21.6653			1.58011
$189$	−5.02971	+	12.7946i	−0.365858	+	0.930671i
$190$	−14.3626			−1.04197
$191$	2.96302			0.214397			0.107198	−	0.994238i	$-0.465812\pi$
$191$	2.96302			0.214397			0.107198	+	0.994238i	$0.465812\pi$
$192$	−3.78050	−	20.8525i	−0.272834	−	1.50490i
$193$	−5.51322			−0.396850			−0.198425	−	0.980116i	$-0.563583\pi$
$193$	−5.51322			−0.396850			−0.198425	+	0.980116i	$0.563583\pi$
$194$	17.3504	+	30.0518i	1.24569	+	2.15759i
$195$	0.339558	+	1.87294i	0.0243163	+	0.134124i
$196$	−6.12353	+	23.5485i	−0.437395	+	1.68204i
$197$	10.8939			0.776157			0.388078	−	0.921626i	$-0.373139\pi$
$197$	10.8939			0.776157			0.388078	+	0.921626i	$0.373139\pi$
$198$	−3.75294	+	22.5520i	−0.266710	+	1.60270i
$199$	7.03715	+	12.1887i	0.498850	+	0.864034i	0.999999	−	0.00132701i	$-0.000422399\pi$
$199$	7.03715	+	12.1887i	0.498850	+	0.864034i	−0.501149	+	0.865361i	$0.667089\pi$
$200$	−1.72692	+	2.99112i	−0.122112	+	0.211504i
$201$	0.660993	+	3.64592i	0.0466228	+	0.257163i
$202$	−17.6393	+	30.5522i	−1.24110	+	2.14965i
$203$	−2.97789	+	7.26512i	−0.209007	+	0.509911i
$204$	−7.01802	+	5.94664i	−0.491359	+	0.416348i
$205$	−0.444581			−0.0310509
$206$	−10.4290	−	18.0636i	−0.726624	−	1.25855i
$207$	9.97540	+	8.20793i	0.693338	+	0.570491i
$208$	0.621113	−	1.07580i	0.0430664	−	0.0745933i
$209$	9.99399	+	17.3101i	0.691299	+	1.19736i
$210$	10.4888	+	2.23179i	0.723793	+	0.154008i
$211$	5.77175	−	9.99696i	0.397343	−	0.688219i	−0.596054	−	0.802945i	$-0.703266\pi$
$211$	5.77175	−	9.99696i	0.397343	−	0.688219i	0.993397	+	0.114725i	$0.0365988\pi$
$212$	19.0678	+	33.0264i	1.30958	+	2.26826i
$213$	−4.88094	−	26.9224i	−0.334436	−	1.84469i
$214$	−3.57035	+	6.18403i	−0.244064	+	0.422732i
$215$	−2.84617	+	4.92971i	−0.194107	+	0.336203i
$216$	−9.19696	−	15.4111i	−0.625774	−	1.04859i
$217$	−6.63374	−	8.57939i	−0.450328	−	0.582407i
$218$	23.3668	+	40.4726i	1.58260	+	2.74115i
$219$	−13.1300	+	11.1256i	−0.887246	+	0.751799i
$220$	11.3199			0.763184
$221$	1.67909			0.112948
$222$	37.7508	+	13.5346i	2.53366	+	0.908385i
$223$	−10.7665	−	18.6481i	−0.720976	−	1.24877i	−0.960609	−	0.277903i	$-0.910361\pi$
$223$	−10.7665	−	18.6481i	−0.720976	−	1.24877i	0.239634	−	0.970863i	$-0.422973\pi$
$224$	6.89848	+	8.92177i	0.460924	+	0.596111i
$225$	0.492465	−	2.95930i	0.0328310	−	0.197287i
$226$	−10.5163	+	18.2147i	−0.699532	+	1.21163i
$227$	−4.58885	+	7.94811i	−0.304572	+	0.527535i	−0.977166	−	0.212477i	$-0.931847\pi$
$227$	−4.58885	+	7.94811i	−0.304572	+	0.527535i	0.672594	+	0.740012i	$0.265180\pi$
$228$	−34.7839	−	12.4709i	−2.30362	−	0.825908i
$229$	−4.49324	−	7.78252i	−0.296922	−	0.514283i	0.678508	−	0.734593i	$-0.262627\pi$
$229$	−4.49324	−	7.78252i	−0.296922	−	0.514283i	−0.975430	+	0.220309i	$0.929293\pi$
$230$	5.03824	−	8.72650i	0.332212	−	0.575408i
$231$	−4.60865	−	14.1943i	−0.303227	−	0.933913i
$232$	−5.12495	−	8.87668i	−0.336470	−	0.582782i
$233$	4.70726	−	8.15321i	0.308383	−	0.534134i	−0.669626	−	0.742698i	$-0.733546\pi$
$233$	4.70726	−	8.15321i	0.308383	−	0.534134i	0.978009	+	0.208564i	$0.0668790\pi$
$234$	−1.26646	+	7.61037i	−0.0827911	+	0.497505i
$235$	3.11646	+	5.39786i	0.203295	+	0.352118i
$236$	−26.2536			−1.70897
$237$	2.42927	+	13.3994i	0.157798	+	0.870384i
$238$	3.58765	−	8.75276i	0.232553	−	0.567357i
$239$	7.36865	−	12.7629i	0.476638	−	0.825562i	−0.523003	−	0.852331i	$-0.675188\pi$
$239$	7.36865	−	12.7629i	0.476638	−	0.825562i	0.999642	+	0.0267687i	$0.00852177\pi$
$240$	−1.49371	+	1.26568i	−0.0964184	+	0.0816991i
$241$	3.56784	−	6.17968i	0.229825	−	0.398068i	−0.727931	−	0.685650i	$-0.759518\pi$
$241$	3.56784	−	6.17968i	0.229825	−	0.398068i	0.957756	+	0.287582i	$0.0928514\pi$
$242$	0.461526	+	0.799387i	0.0296680	+	0.0513865i
$243$	12.1792	+	9.72965i	0.781299	+	0.624158i
$244$	−26.0200			−1.66576
$245$	−6.74790	+	1.86169i	−0.431107	+	0.118939i
$246$	−1.69622	−	0.608140i	−0.108147	−	0.0387736i
$247$	3.37255	+	5.84143i	0.214590	+	0.371681i
$248$	14.1573			0.898990
$249$	21.6503	−	18.3452i	1.37203	−	1.16258i
$250$	−2.34008			−0.147999
$251$	−13.5593			−0.855853			−0.427927	−	0.903813i	$-0.640756\pi$
$251$	−13.5593			−0.855853			−0.427927	+	0.903813i	$0.640756\pi$
$252$	23.4643	+	14.5124i	1.47811	+	0.914195i
$253$	−14.0232			−0.881628
$254$	33.0777			2.07548
$255$	−2.49110	−	0.893124i	−0.155999	−	0.0559296i
$256$	−22.5804			−1.41128
$257$	−10.6074	−	18.3726i	−0.661672	−	1.14605i	−0.980176	−	0.198128i	$-0.936514\pi$
$257$	−10.6074	−	18.3726i	−0.661672	−	1.14605i	0.318504	−	0.947922i	$-0.396820\pi$
$258$	−17.6024	+	14.9152i	−1.09588	+	0.928580i
$259$	−25.9416	+	3.51291i	−1.61193	+	0.218281i
$260$	3.81997			0.236905
$261$	6.87492	+	5.65681i	0.425547	+	0.350147i
$262$	−6.63911	−	11.4993i	−0.410166	−	0.710428i
$263$	−3.75197	+	6.49861i	−0.231357	+	0.400721i	−0.958208	−	0.286074i	$-0.907650\pi$
$263$	−3.75197	+	6.49861i	−0.231357	+	0.400721i	0.726851	+	0.686795i	$0.240983\pi$
$264$	18.3388	+	6.57495i	1.12868	+	0.404660i
$265$	−5.48563	+	9.50139i	−0.336980	+	0.583666i
$266$	37.6561	−	5.09924i	2.30884	−	0.312654i
$267$	1.43516	+	0.514544i	0.0878307	+	0.0314896i
$268$	7.43606			0.454230
$269$	13.5820	+	23.5247i	0.828110	+	1.43433i	0.899519	+	0.436881i	$0.143917\pi$
$269$	13.5820	+	23.5247i	0.828110	+	1.43433i	−0.0714097	+	0.997447i	$0.522750\pi$
$270$	5.92693	−	10.6171i	0.360702	−	0.646135i
$271$	1.65552	−	2.86744i	0.100566	−	0.174185i	−0.811352	−	0.584558i	$-0.801268\pi$
$271$	1.65552	−	2.86744i	0.100566	−	0.174185i	0.911918	+	0.410373i	$0.134601\pi$
$272$	0.863523	+	1.49567i	0.0523588	+	0.0906880i
$273$	−1.55522	−	4.78996i	−0.0941264	−	0.289902i
$274$	25.3243	−	43.8629i	1.52990	−	2.64986i
$275$	1.62831	+	2.82031i	0.0981907	+	0.170071i
$276$	19.7790	−	16.7595i	1.19056	−	1.00881i
$277$	14.1422	−	24.4951i	0.849724	−	1.47177i	−0.0317308	−	0.999496i	$-0.510102\pi$
$277$	14.1422	−	24.4951i	0.849724	−	1.47177i	0.881455	−	0.472269i	$-0.156565\pi$
$278$	2.98069	−	5.16271i	0.178770	−	0.309639i
$279$	−11.5143	+	4.31692i	−0.689346	+	0.258447i
$280$	3.46573	−	8.45530i	0.207117	−	0.505301i
$281$	−3.32484	−	5.75879i	−0.198343	−	0.343540i	0.749648	−	0.661837i	$-0.230223\pi$
$281$	−3.32484	−	5.75879i	−0.198343	−	0.343540i	−0.947991	+	0.318296i	$0.896889\pi$
$282$	4.50660	+	24.8576i	0.268364	+	1.48025i
$283$	8.92347			0.530445			0.265223	−	0.964187i	$-0.414555\pi$
$283$	8.92347			0.530445			0.265223	+	0.964187i	$0.414555\pi$
$284$	−54.9097			−3.25829
$285$	−1.89640	−	10.4602i	−0.112333	−	0.619609i
$286$	−4.18748	−	7.25292i	−0.247611	−	0.428874i
$287$	1.16561	−	0.157843i	0.0688039	−	0.00931715i
$288$	11.9739	−	4.48920i	0.705567	−	0.264529i
$289$	7.33279	−	12.7008i	0.431341	−	0.747104i
$290$	3.47229	−	6.01419i	0.203900	−	0.353165i
$291$	−19.5957	+	16.6042i	−1.14872	+	0.973356i
$292$	17.2687	+	29.9102i	1.01057	+	1.75036i
$293$	5.91498	−	10.2450i	0.345557	−	0.598522i	−0.639898	−	0.768460i	$-0.721023\pi$
$293$	5.91498	−	10.2450i	0.345557	−	0.598522i	0.985455	+	0.169938i	$0.0543567\pi$
$294$	−28.2920	−	2.12747i	−1.65003	−	0.124077i
$295$	−3.77646	−	6.54103i	−0.219874	−	0.380833i
$296$	17.0870	−	29.5956i	0.993164	−	1.72021i
$297$	−16.9201	+	0.244468i	−0.981804	+	0.0141855i
$298$	−7.50029	−	12.9909i	−0.434480	−	0.752542i
$299$	−4.73222			−0.273672
$300$	−5.66730	−	2.03187i	−0.327202	−	0.117310i
$301$	5.71192	−	13.9353i	0.329230	−	0.803218i
$302$	−2.18401	+	3.78281i	−0.125675	+	0.217676i
$303$	−24.5802	−	8.81262i	−1.41209	−	0.506272i
$304$	−3.46886	+	6.00825i	−0.198953	+	0.344596i
$305$	−3.74286	−	6.48282i	−0.214315	−	0.371205i
$306$	−8.28266	−	6.81512i	−0.473488	−	0.389595i
$307$	−1.60111			−0.0913799			−0.0456900	−	0.998956i	$-0.514549\pi$
$307$	−1.60111			−0.0913799			−0.0456900	+	0.998956i	$0.514549\pi$
$308$	−29.6786	+	4.01896i	−1.69110	+	0.229002i
$309$	11.7786	−	9.98049i	0.670062	−	0.567770i
$310$	4.79598	+	8.30688i	0.272393	+	0.471799i
$311$	4.66270			0.264398			0.132199	−	0.991223i	$-0.457796\pi$
$311$	4.66270			0.264398			0.132199	+	0.991223i	$0.457796\pi$
$312$	6.18858	+	2.21877i	0.350359	+	0.125613i
$313$	−23.6047			−1.33422			−0.667108	−	0.744961i	$-0.732468\pi$
$313$	−23.6047			−1.33422			−0.667108	+	0.744961i	$0.732468\pi$
$314$	−45.1333			−2.54702
$315$	−0.240495	+	7.93361i	−0.0135503	+	0.447008i
$316$	27.3288			1.53737
$317$	−8.60108			−0.483085			−0.241542	−	0.970390i	$-0.577653\pi$
$317$	−8.60108			−0.483085			−0.241542	+	0.970390i	$0.577653\pi$
$318$	−33.9264	+	28.7472i	−1.90250	+	1.61206i
$319$	−9.66458			−0.541113
$320$	−6.11773	−	10.5962i	−0.341992	−	0.592347i
$321$	−4.97523	−	1.78375i	−0.277690	−	0.0995591i
$322$	−10.1112	+	24.6681i	−0.563473	+	1.37470i
$323$	−9.37760			−0.521783
$324$	23.5728	−	20.5666i	1.30960	−	1.14259i
$325$	0.549485	+	0.951736i	0.0304800	+	0.0527928i
$326$	10.3366	−	17.9036i	0.572494	−	0.991588i
$327$	−26.3907	+	22.3619i	−1.45941	+	1.23662i
$328$	−0.767758	+	1.32980i	−0.0423923	+	0.0734256i
$329$	−10.0872	−	13.0458i	−0.556127	−	0.719237i
$330$	2.35464	+	12.9878i	0.129619	+	0.714953i
$331$	−22.9657			−1.26231			−0.631154	−	0.775657i	$-0.717418\pi$
$331$	−22.9657			−1.26231			−0.631154	+	0.775657i	$0.717418\pi$
$332$	−28.4746	−	49.3194i	−1.56274	−	2.70675i
$333$	−4.87269	+	29.2808i	−0.267022	+	1.60458i
$334$	23.8326	−	41.2793i	1.30406	−	2.25871i
$335$	1.06964	+	1.85268i	0.0584408	+	0.101222i
$336$	3.46687	−	3.84870i	0.189133	−	0.209964i
$337$	−15.1857	+	26.3025i	−0.827220	+	1.43279i	0.0729904	+	0.997333i	$0.476746\pi$
$337$	−15.1857	+	26.3025i	−0.827220	+	1.43279i	−0.900211	+	0.435455i	$0.856588\pi$
$338$	13.7974	+	23.8978i	0.750479	+	1.29987i
$339$	−14.6543	−	5.25393i	−0.795910	−	0.285355i
$340$	−2.65542	+	4.59932i	−0.144010	+	0.249433i
$341$	6.67443	−	11.5604i	0.361441	−	0.626033i
$342$	7.07307	−	42.5032i	0.382468	−	2.29831i
$343$	17.0308	−	7.27676i	0.919578	−	0.392908i
$344$	9.83023	+	17.0265i	0.530010	+	0.918005i
$345$	7.02071	+	2.51711i	0.377983	+	0.135517i
$346$	12.8490			0.690765
$347$	7.79674			0.418551			0.209275	−	0.977857i	$-0.432889\pi$
$347$	7.79674			0.418551			0.209275	+	0.977857i	$0.432889\pi$
$348$	13.6314	−	11.5505i	0.730722	−	0.619170i
$349$	10.4057	+	18.0232i	0.557004	+	0.964760i	0.997745	+	0.0671252i	$0.0213827\pi$
$349$	10.4057	+	18.0232i	0.557004	+	0.964760i	−0.440740	+	0.897635i	$0.645284\pi$
$350$	6.13526	−	0.830812i	0.327944	−	0.0444088i
$351$	−5.70982	+	0.0824975i	−0.304768	+	0.00440339i
$352$	−6.94079	+	12.0218i	−0.369945	+	0.640764i
$353$	6.05228	−	10.4829i	0.322130	−	0.557946i	−0.658797	−	0.752321i	$-0.728934\pi$
$353$	6.05228	−	10.4829i	0.322130	−	0.557946i	0.980927	+	0.194375i	$0.0622678\pi$
$354$	−5.46102	−	30.1220i	−0.290250	−	1.60096i
$355$	−7.89851	−	13.6806i	−0.419209	−	0.726092i
$356$	1.52983	−	2.64975i	0.0810810	−	0.140436i
$357$	6.84831	+	1.45718i	0.362451	+	0.0771222i
$358$	−6.92690	−	11.9977i	−0.366098	−	0.634101i
$359$	5.74290	−	9.94699i	0.303099	−	0.524982i	−0.673738	−	0.738971i	$-0.735312\pi$
$359$	5.74290	−	9.94699i	0.303099	−	0.524982i	0.976836	+	0.213988i	$0.0686455\pi$
$360$	−8.00118	−	6.58351i	−0.421699	−	0.346982i
$361$	−9.33540	−	16.1694i	−0.491337	−	0.851020i
$362$	−2.81690			−0.148053
$363$	−0.521252	+	0.441677i	−0.0273586	+	0.0231820i
$364$	−10.0153	+	1.35623i	−0.524944	+	0.0710858i
$365$	−4.96804	+	8.60490i	−0.260039	+	0.450401i
$366$	−5.41242	−	29.8539i	−0.282912	−	1.56049i
$367$	1.94772	−	3.37356i	0.101670	−	0.176098i	−0.810703	−	0.585458i	$-0.800915\pi$
$367$	1.94772	−	3.37356i	0.101670	−	0.176098i	0.912373	+	0.409360i	$0.134248\pi$
$368$	−2.43368	−	4.21526i	−0.126864	−	0.219736i
$369$	0.218941	−	1.31565i	0.0113976	−	0.0684900i
$370$	23.1539			1.20371
$371$	11.0090	−	26.8585i	0.571559	−	1.39443i
$372$	4.40230	+	24.2823i	0.228249	+	1.25898i
$373$	11.4157	+	19.7726i	0.591084	+	1.02379i	0.994087	+	0.108588i	$0.0346331\pi$
$373$	11.4157	+	19.7726i	0.591084	+	1.02379i	−0.403003	+	0.915199i	$0.632034\pi$
$374$	11.6436			0.602074
$375$	−0.308978	−	1.70427i	−0.0159556	−	0.0880081i
$376$	21.5275			1.11020
$377$	−3.26139			−0.167970
$378$	−11.7699	+	29.9404i	−0.605379	+	1.53997i
$379$	−30.0012			−1.54106			−0.770530	−	0.637403i	$-0.780008\pi$
$379$	−30.0012			−1.54106			−0.770530	+	0.637403i	$0.780008\pi$
$380$	−21.3342			−1.09442
$381$	4.36751	+	24.0904i	0.223754	+	1.23419i
$382$	6.93370			0.354759
$383$	−11.1387	−	19.2928i	−0.569162	−	0.985817i	−0.996649	−	0.0817960i	$-0.973934\pi$
$383$	−11.1387	−	19.2928i	−0.569162	−	0.985817i	0.427487	−	0.904021i	$-0.359399\pi$
$384$	−6.21256	−	34.2673i	−0.317033	−	1.74870i
$385$	−5.27045	−	6.81625i	−0.268607	−	0.347388i
$386$	−12.9014			−0.656662
$387$	−13.1869	−	10.8504i	−0.670326	−	0.551556i
$388$	25.7723	+	44.6390i	1.30839	+	2.26620i
$389$	−3.04686	+	5.27732i	−0.154482	+	0.267571i	−0.932870	−	0.360212i	$-0.882704\pi$
$389$	−3.04686	+	5.27732i	−0.154482	+	0.267571i	0.778388	+	0.627783i	$0.216038\pi$
$390$	0.794592	+	4.38282i	0.0402357	+	0.221933i
$391$	3.28956	−	5.69769i	0.166360	−	0.288145i
$392$	−6.08458	+	23.3988i	−0.307318	+	1.18182i
$393$	7.49827	−	6.35358i	0.378238	−	0.320496i
$394$	25.4925			1.28429
$395$	3.93113	+	6.80891i	0.197796	+	0.342593i
$396$	−5.57463	+	33.4989i	−0.280136	+	1.68338i
$397$	12.8751	−	22.3002i	0.646180	−	1.11922i	−0.337847	−	0.941201i	$-0.609699\pi$
$397$	12.8751	−	22.3002i	0.646180	−	1.11922i	0.984028	−	0.178016i	$-0.0569679\pi$
$398$	16.4675	+	28.5225i	0.825439	+	1.42970i
$399$	8.68579	+	26.7515i	0.434833	+	1.33925i
$400$	−0.565177	+	0.978916i	−0.0282589	+	0.0489458i
$401$	5.61140	+	9.71923i	0.280220	+	0.485355i	0.971439	−	0.237290i	$-0.0762593\pi$
$401$	5.61140	+	9.71923i	0.280220	+	0.485355i	−0.691219	+	0.722645i	$0.742926\pi$
$402$	1.54677	+	8.53172i	0.0771461	+	0.425524i
$403$	2.25234	−	3.90116i	0.112197	−	0.194331i
$404$	−26.2015	+	45.3824i	−1.30358	+	2.25786i
$405$	8.51496	+	2.91471i	0.423112	+	0.144833i
$406$	−6.96848	+	17.0009i	−0.345840	+	0.843742i
$407$	−16.1113	−	27.9056i	−0.798607	−	1.38323i
$408$	−6.97338	+	5.90882i	−0.345234	+	0.292530i
$409$	−4.57051			−0.225997			−0.112999	−	0.993595i	$-0.536046\pi$
$409$	−4.57051			−0.225997			−0.112999	+	0.993595i	$0.536046\pi$
$410$	−1.04035			−0.0513794
$411$	35.2890	+	12.6520i	1.74068	+	0.624078i
$412$	−15.4913	−	26.8317i	−0.763201	−	1.32190i
$413$	12.2235	+	15.8086i	0.601480	+	0.777892i
$414$	23.3432	+	19.2072i	1.14726	+	0.943982i
$415$	8.19187	−	14.1887i	0.402123	−	0.696497i
$416$	−2.34222	+	4.05685i	−0.114837	+	0.198904i
$417$	4.15355	+	1.48916i	0.203400	+	0.0729242i
$418$	23.3867	+	40.5069i	1.14388	+	1.98126i
$419$	1.10806	−	1.91922i	0.0541324	−	0.0937601i	−0.837689	−	0.546147i	$-0.816094\pi$
$419$	1.10806	−	1.91922i	0.0541324	−	0.0937601i	0.891822	+	0.452387i	$0.149427\pi$
$420$	15.5800	+	3.31511i	0.760228	+	0.161761i
$421$	6.75580	+	11.7014i	0.329257	+	0.570290i	0.982365	−	0.186975i	$-0.0598683\pi$
$421$	6.75580	+	11.7014i	0.329257	+	0.570290i	−0.653107	+	0.757265i	$0.726535\pi$
$422$	13.5063	−	23.3936i	0.657478	−	1.13878i
$423$	−17.5087	+	6.56429i	−0.851300	+	0.319167i
$424$	18.9465	+	32.8163i	0.920125	+	1.59370i
$425$	−1.52788			−0.0741131
$426$	−11.4218	−	63.0004i	−0.553386	−	3.05238i
$427$	12.1147	+	15.6680i	0.586274	+	0.758225i
$428$	−5.30341	+	9.18577i	−0.256350	+	0.444011i
$429$	4.72937	−	4.00738i	0.228336	−	0.193478i
$430$	−6.66025	+	11.5359i	−0.321186	+	0.556310i
$431$	−3.41681	−	5.91809i	−0.164582	−	0.285064i	0.771925	−	0.635714i	$-0.219294\pi$
$431$	−3.41681	−	5.91809i	−0.164582	−	0.285064i	−0.936507	+	0.350650i	$0.885961\pi$
$432$	−3.00993	−	5.04364i	−0.144815	−	0.242662i
$433$	−9.28532			−0.446224			−0.223112	−	0.974793i	$-0.571622\pi$
$433$	−9.28532			−0.446224			−0.223112	+	0.974793i	$0.571622\pi$
$434$	−15.5235	−	20.0764i	−0.745150	−	0.963699i
$435$	4.83859	+	1.73476i	0.231993	+	0.0831753i
$436$	34.7092	+	60.1181i	1.66227	+	2.87913i
$437$	26.4291			1.26427
$438$	−30.7253	+	26.0348i	−1.46811	+	1.24399i
$439$	18.6396			0.889619			0.444809	−	0.895625i	$-0.353271\pi$
$439$	18.6396			0.889619			0.444809	+	0.895625i	$0.353271\pi$
$440$	11.2479			0.536220
$441$	−2.18619	−	20.8859i	−0.104104	−	0.994566i
$442$	3.92921			0.186893
$443$	3.26578			0.155162			0.0775809	−	0.996986i	$-0.475280\pi$
$443$	3.26578			0.155162			0.0775809	+	0.996986i	$0.475280\pi$
$444$	56.0751	+	20.1044i	2.66121	+	0.954111i
$445$	0.880237			0.0417273
$446$	−25.1943	−	43.6379i	−1.19299	−	2.06631i
$447$	8.47089	−	7.17772i	0.400659	−	0.339495i
$448$	19.8017	+	25.6094i	0.935540	+	1.20993i
$449$	−18.4183			−0.869215			−0.434607	−	0.900620i	$-0.643113\pi$
$449$	−18.4183			−0.869215			−0.434607	+	0.900620i	$0.643113\pi$
$450$	1.15241	−	6.92500i	0.0543249	−	0.326447i
$451$	0.723915	+	1.25386i	0.0340878	+	0.0590418i
$452$	−15.6209	+	27.0562i	−0.734746	+	1.27262i
$453$	−3.04338	−	1.09113i	−0.142990	−	0.0512658i
$454$	−10.7382	+	18.5992i	−0.503971	+	0.872903i
$455$	−1.77855	−	2.30020i	−0.0833799	−	0.107835i
$456$	−34.5627	−	12.3916i	−1.61855	−	0.580291i
$457$	16.7628			0.784130			0.392065	−	0.919938i	$-0.371761\pi$
$457$	16.7628			0.784130			0.392065	+	0.919938i	$0.371761\pi$
$458$	−10.5145	−	18.2117i	−0.491311	−	0.850976i
$459$	3.86980	−	6.93209i	0.180627	−	0.323562i
$460$	7.48382	−	12.9624i	0.348935	−	0.604373i
$461$	5.98073	+	10.3589i	0.278550	+	0.482463i	0.971025	−	0.238979i	$-0.0768128\pi$
$461$	5.98073	+	10.3589i	0.278550	+	0.482463i	−0.692474	+	0.721442i	$0.743479\pi$
$462$	−10.7846	−	33.2156i	−0.501744	−	1.54533i
$463$	−11.7397	+	20.3338i	−0.545592	+	0.944993i	0.452977	+	0.891522i	$0.350362\pi$
$463$	−11.7397	+	20.3338i	−0.545592	+	0.944993i	−0.998569	+	0.0534711i	$0.982971\pi$
$464$	−1.67726	−	2.90511i	−0.0778650	−	0.134866i
$465$	−5.41662	+	4.58972i	−0.251190	+	0.212843i
$466$	11.0153	−	19.0791i	0.510276	−	0.883823i
$467$	−15.1457	+	26.2331i	−0.700858	+	1.21392i	0.267307	+	0.963611i	$0.413866\pi$
$467$	−15.1457	+	26.2331i	−0.700858	+	1.21392i	−0.968166	+	0.250311i	$0.919467\pi$
$468$	−1.88120	+	11.3045i	−0.0869586	+	0.522549i
$469$	−3.46218	−	4.47762i	−0.159869	−	0.206757i
$470$	7.29275	+	12.6314i	0.336389	+	0.582644i
$471$	−5.95929	−	32.8704i	−0.274590	−	1.51459i
$472$	−26.0867			−1.20074
$473$	18.5378			0.852367
$474$	5.68467	+	31.3556i	0.261105	+	1.44021i
$475$	−3.06883	−	5.31536i	−0.140807	−	0.243886i
$476$	5.32911	−	13.0014i	0.244259	−	0.595917i
$477$	−25.4160	−	20.9127i	−1.16372	−	0.957529i
$478$	17.2432	−	29.8661i	0.788686	−	1.36604i
$479$	0.144950	−	0.251061i	0.00662293	−	0.0114713i	−0.862695	−	0.505725i	$-0.831225\pi$
$479$	0.144950	−	0.251061i	0.00662293	−	0.0114713i	0.869318	+	0.494253i	$0.164559\pi$
$480$	5.63279	−	4.77289i	0.257100	−	0.217851i
$481$	−5.43688	−	9.41695i	−0.247900	−	0.429376i
$482$	8.34901	−	14.4609i	0.380287	−	0.658676i
$483$	−19.3007	−	4.10680i	−0.878213	−	0.186866i
$484$	0.685552	+	1.18741i	0.0311615	+	0.0539732i
$485$	−7.41446	+	12.8422i	−0.336673	+	0.583135i
$486$	28.5003	+	22.7681i	1.29280	+	1.03278i
$487$	13.3737	+	23.1640i	0.606021	+	1.04966i	0.991889	+	0.127106i	$0.0405687\pi$
$487$	13.3737	+	23.1640i	0.606021	+	1.04966i	−0.385868	+	0.922554i	$0.626098\pi$
$488$	−25.8545			−1.17038
$489$	14.4040	+	5.16419i	0.651369	+	0.233533i
$490$	−15.7906	+	4.35648i	−0.713346	+	0.196806i
$491$	−1.84307	+	3.19229i	−0.0831767	+	0.144066i	−0.904613	−	0.426234i	$-0.859840\pi$
$491$	−1.84307	+	3.19229i	−0.0831767	+	0.144066i	0.821436	+	0.570301i	$0.193173\pi$
$492$	−2.51957	−	0.903333i	−0.113591	−	0.0407254i
$493$	2.26713	−	3.92678i	0.102106	−	0.176853i
$494$	7.89202	+	13.6694i	0.355079	+	0.615015i
$495$	−9.14804	+	3.42975i	−0.411174	+	0.154156i
$496$	4.63332			0.208042
$497$	25.5656	+	33.0639i	1.14677	+	1.48312i
$498$	50.6633	−	42.9291i	2.27028	−	1.92370i
$499$	−1.68055	−	2.91079i	−0.0752315	−	0.130305i	0.825955	−	0.563735i	$-0.190636\pi$
$499$	−1.68055	−	2.91079i	−0.0752315	−	0.130305i	−0.901187	+	0.433431i	$0.857303\pi$
$500$	−3.47596			−0.155449
$501$	33.2104	+	11.9068i	1.48373	+	0.531956i
$502$	−31.7297			−1.41617
$503$	−7.93752			−0.353916			−0.176958	−	0.984218i	$-0.556626\pi$
$503$	−7.93752			−0.353916			−0.176958	+	0.984218i	$0.556626\pi$
$504$	23.3151	+	14.4201i	1.03854	+	0.642322i
$505$	−15.0759			−0.670868
$506$	−32.8153			−1.45882
$507$	−15.5829	+	13.2040i	−0.692061	+	0.586410i
$508$	49.1338			2.17996
$509$	−6.72366	−	11.6457i	−0.298021	−	0.516187i	0.677662	−	0.735373i	$-0.262993\pi$
$509$	−6.72366	−	11.6457i	−0.298021	−	0.516187i	−0.975683	+	0.219186i	$0.929660\pi$
$510$	−5.82936	−	2.08998i	−0.258129	−	0.0925458i
$511$	9.97026	−	24.3243i	0.441059	−	1.07605i
$512$	−12.6264			−0.558012
$513$	31.8889	−	0.460741i	1.40793	−	0.0203422i
$514$	−24.8221	−	42.9932i	−1.09486	−	1.89635i
$515$	4.45670	−	7.71923i	0.196386	−	0.340150i
$516$	−26.1466	+	22.1551i	−1.15104	+	0.975323i
$517$	10.1491	−	17.5788i	0.446357	−	0.773113i
$518$	−60.7053	+	8.22047i	−2.66724	+	0.361187i
$519$	1.69655	+	9.35786i	0.0744703	+	0.410764i
$520$	3.79568			0.166451
$521$	9.26516	+	16.0477i	0.405914	+	0.703064i	0.994427	−	0.105424i	$-0.0336199\pi$
$521$	9.26516	+	16.0477i	0.405914	+	0.703064i	−0.588513	+	0.808487i	$0.700287\pi$
$522$	16.0878	+	13.2374i	0.704145	+	0.579383i
$523$	−18.3171	+	31.7262i	−0.800952	+	1.38729i	0.118038	+	0.993009i	$0.462339\pi$
$523$	−18.3171	+	31.7262i	−0.800952	+	1.38729i	−0.918990	+	0.394280i	$0.870994\pi$
$524$	−9.86176	−	17.0811i	−0.430813	−	0.746190i
$525$	1.41516	+	4.35859i	0.0617628	+	0.190224i
$526$	−8.77990	+	15.2072i	−0.382822	+	0.663067i
$527$	3.13139	+	5.42372i	0.136405	+	0.236261i
$528$	6.00182	+	2.15181i	0.261196	+	0.0936455i
$529$	2.22896	−	3.86067i	0.0969112	−	0.167855i
$530$	−12.8368	+	22.2340i	−0.557595	+	0.965782i
$531$	21.2167	−	7.95448i	0.920725	−	0.345195i
$532$	55.9345	−	7.57442i	2.42507	−	0.328393i
$533$	0.244291	+	0.423124i	0.0105814	+	0.0183275i
$534$	3.35839	+	1.20407i	0.145332	+	0.0521053i
$535$	−3.05148			−0.131927
$536$	7.38876			0.319146
$537$	7.82330	−	6.62899i	0.337600	−	0.286062i
$538$	31.7829	+	55.0497i	1.37026	+	2.37336i
$539$	16.2382	+	15.9998i	0.699428	+	0.689159i
$540$	8.80388	−	15.7706i	0.378859	−	0.678660i
$541$	−4.11892	+	7.13418i	−0.177086	+	0.306722i	−0.940881	−	0.338737i	$-0.890000\pi$
$541$	−4.11892	+	7.13418i	−0.177086	+	0.306722i	0.763795	+	0.645459i	$0.223334\pi$
$542$	3.87404	−	6.71004i	0.166404	−	0.288221i
$543$	−0.371938	−	2.05154i	−0.0159614	−	0.0880400i
$544$	−3.25635	−	5.64017i	−0.139615	−	0.241820i
$545$	−9.98551	+	17.2954i	−0.427732	+	0.740854i
$546$	−3.63934	−	11.2089i	−0.155749	−	0.479696i
$547$	9.35515	+	16.2036i	0.399997	+	0.692816i	0.993725	−	0.111850i	$-0.0356777\pi$
$547$	9.35515	+	16.2036i	0.399997	+	0.692816i	−0.593728	+	0.804666i	$0.702344\pi$
$548$	37.6168	−	65.1541i	1.60691	−	2.78325i
$549$	21.0279	−	7.88369i	0.897448	−	0.336468i
$550$	3.81036	+	6.59974i	0.162474	+	0.281414i
$551$	18.2146			0.775967
$552$	19.6532	−	16.6529i	0.836496	−	0.708796i
$553$	−12.7241	−	16.4561i	−0.541085	−	0.699783i
$554$	33.0939	−	57.3203i	1.40602	−	2.43531i
$555$	3.05719	+	16.8629i	0.129770	+	0.715790i
$556$	4.42753	−	7.66871i	0.187769	−	0.325226i
$557$	8.91417	+	15.4398i	0.377706	+	0.654205i	0.990728	−	0.135860i	$-0.0433798\pi$
$557$	8.91417	+	15.4398i	0.377706	+	0.654205i	−0.613022	+	0.790066i	$0.710046\pi$
$558$	−26.9444	+	10.1019i	−1.14065	+	0.427648i
$559$	6.25571			0.264588
$560$	1.13424	−	2.76720i	0.0479305	−	0.116936i
$561$	1.53739	+	8.47996i	0.0649086	+	0.358024i
$562$	−7.78037	−	13.4760i	−0.328195	−	0.568451i
$563$	32.7633			1.38081			0.690404	−	0.723424i	$-0.257433\pi$
$563$	32.7633			1.38081			0.690404	+	0.723424i	$0.257433\pi$
$564$	6.69412	+	36.9236i	0.281873	+	1.55476i
$565$	−8.98798			−0.378127
$566$	20.8816			0.877719
$567$	−23.3595	−	4.61872i	−0.981008	−	0.193968i
$568$	−54.5605			−2.28931
$569$	−8.03721			−0.336937			−0.168469	−	0.985707i	$-0.553882\pi$
$569$	−8.03721			−0.336937			−0.168469	+	0.985707i	$0.553882\pi$
$570$	−4.43773	−	24.4777i	−0.185876	−	1.02526i
$571$	−8.22845			−0.344350			−0.172175	−	0.985066i	$-0.555079\pi$
$571$	−8.22845			−0.344350			−0.172175	+	0.985066i	$0.555079\pi$
$572$	−6.22009	−	10.7735i	−0.260075	−	0.450463i
$573$	0.915510	+	5.04979i	0.0382460	+	0.210958i
$574$	2.72762	−	0.369363i	0.113849	−	0.0154169i
$575$	4.30605			0.179575
$576$	34.3702	−	12.8860i	1.43209	−	0.536915i
$577$	−10.2344	−	17.7266i	−0.426065	−	0.737966i	0.570454	−	0.821329i	$-0.306767\pi$
$577$	−10.2344	−	17.7266i	−0.426065	−	0.737966i	−0.996519	+	0.0833630i	$0.973434\pi$
$578$	17.1593	−	29.7208i	0.713732	−	1.23622i
$579$	−1.70347	−	9.39601i	−0.0707936	−	0.390485i
$580$	5.15776	−	8.93350i	0.214164	−	0.370943i
$581$	−16.4401	+	40.1087i	−0.682050	+	1.66399i
$582$	−45.8554	+	38.8551i	−1.90077	+	1.61060i
$583$	35.7292			1.47975
$584$	17.1589	+	29.7200i	0.710038	+	1.22982i
$585$	−3.08708	+	1.15740i	−0.127635	+	0.0478525i
$586$	13.8415	−	23.9742i	0.571787	−	0.990365i
$587$	12.9160	+	22.3712i	0.533101	+	0.923359i	0.999253	+	0.0386538i	$0.0123069\pi$
$587$	12.9160	+	22.3712i	0.533101	+	0.923359i	−0.466151	+	0.884705i	$0.654360\pi$
$588$	−42.0251	−	3.16015i	−1.73308	−	0.130323i
$589$	−12.5791	+	21.7877i	−0.518313	+	0.897745i
$590$	−8.83721	−	15.3065i	−0.363822	−	0.630159i
$591$	3.36597	+	18.5661i	0.138458	+	0.763707i
$592$	5.59214	−	9.68588i	0.229836	−	0.398087i
$593$	22.2664	−	38.5665i	0.914370	−	1.58373i	0.106548	−	0.994308i	$-0.466020\pi$
$593$	22.2664	−	38.5665i	0.914370	−	1.58373i	0.807822	−	0.589427i	$-0.200646\pi$
$594$	−39.5943	+	0.572073i	−1.62458	+	0.0234724i
$595$	4.00583	−	0.542453i	0.164223	−	0.0222384i
$596$	−11.1409	−	19.2967i	−0.456351	−	0.790423i
$597$	−18.5985	+	15.7592i	−0.761186	+	0.644983i
$598$	−11.0738			−0.452840
$599$	−26.0872			−1.06589			−0.532946	−	0.846149i	$-0.678915\pi$
$599$	−26.0872			−1.06589			−0.532946	+	0.846149i	$0.678915\pi$
$600$	−5.63125	−	2.01895i	−0.229895	−	0.0824233i
$601$	−21.7328	−	37.6424i	−0.886500	−	1.53546i	−0.843984	−	0.536368i	$-0.819796\pi$
$601$	−21.7328	−	37.6424i	−0.886500	−	1.53546i	−0.0425160	−	0.999096i	$-0.513537\pi$
$602$	13.3663	−	32.6097i	0.544771	−	1.32907i
$603$	−6.00939	+	2.25302i	−0.244721	+	0.0917500i
$604$	−3.24413	+	5.61900i	−0.132002	+	0.228634i
$605$	−0.197227	+	0.341607i	−0.00801842	+	0.0138883i
$606$	−57.5194	−	20.6222i	−2.33657	−	0.837720i
$607$	3.86039	+	6.68639i	0.156688	+	0.271392i	0.933672	−	0.358128i	$-0.116585\pi$
$607$	3.86039	+	6.68639i	0.156688	+	0.271392i	−0.776984	+	0.629520i	$0.783252\pi$
$608$	13.0811	−	22.6572i	0.530509	−	0.918869i
$609$	−13.3018	−	2.83035i	−0.539017	−	0.114692i
$610$	−8.75857	−	15.1703i	−0.354624	−	0.614227i
$611$	3.42490	−	5.93209i	0.138556	−	0.239987i
$612$	−12.3031	−	10.1232i	−0.497323	−	0.409206i
$613$	3.51912	+	6.09529i	0.142136	+	0.246186i	0.928301	−	0.371830i	$-0.121270\pi$
$613$	3.51912	+	6.09529i	0.142136	+	0.246186i	−0.786165	+	0.618017i	$0.787936\pi$
$614$	−3.74671			−0.151205
$615$	−0.137366	−	0.757686i	−0.00553913	−	0.0305528i
$616$	−29.4899	+	3.99340i	−1.18818	+	0.160899i
$617$	−9.98197	+	17.2893i	−0.401859	+	0.696040i	−0.993950	−	0.109831i	$-0.964969\pi$
$617$	−9.98197	+	17.2893i	−0.401859	+	0.696040i	0.592091	+	0.805871i	$0.298302\pi$
$618$	27.5629	−	23.3551i	1.10874	−	0.939480i
$619$	−5.56346	+	9.63619i	−0.223614	+	0.387311i	−0.955903	−	0.293683i	$-0.905119\pi$
$619$	−5.56346	+	9.63619i	−0.223614	+	0.387311i	0.732289	+	0.680995i	$0.238452\pi$
$620$	7.12396	+	12.3391i	0.286105	+	0.495549i
$621$	−10.9063	+	19.5368i	−0.437657	+	0.783986i
$622$	10.9111			0.437495
$623$	−2.30783	+	0.312516i	−0.0924611	+	0.0125207i
$624$	2.02536	+	0.726145i	0.0810794	+	0.0290691i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−55.2368			−2.20771
$627$	−26.4131	+	22.3809i	−1.05484	+	0.893807i
$628$	−67.0411			−2.67523
$629$	15.1176			0.602778
$630$	−0.562776	+	18.5652i	−0.0224215	+	0.739657i
$631$	3.94010			0.156853			0.0784265	−	0.996920i	$-0.475010\pi$
$631$	3.94010			0.156853			0.0784265	+	0.996920i	$0.475010\pi$
$632$	27.1550			1.08017
$633$	18.8209	+	6.74776i	0.748062	+	0.268200i
$634$	−20.1272			−0.799353
$635$	7.06767	+	12.2416i	0.280472	+	0.485791i
$636$	−50.3943	+	42.7011i	−1.99827	+	1.69321i
$637$	5.47970	+	5.39925i	0.217114	+	0.213926i
$638$	−22.6159			−0.895370
$639$	44.3748	−	16.6369i	1.75544	−	0.658144i
$640$	−10.0534	−	17.4130i	−0.397395	−	0.688308i
$641$	−4.72655	+	8.18662i	−0.186687	+	0.323352i	−0.944144	−	0.329534i	$-0.893109\pi$
$641$	−4.72655	+	8.18662i	−0.186687	+	0.323352i	0.757456	+	0.652886i	$0.226442\pi$
$642$	−11.6424	−	4.17411i	−0.459489	−	0.164739i
$643$	2.84191	−	4.92233i	0.112074	−	0.194118i	−0.804532	−	0.593909i	$-0.797584\pi$
$643$	2.84191	−	4.92233i	0.112074	−	0.194118i	0.916606	+	0.399791i	$0.130917\pi$
$644$	−15.0191	+	36.6420i	−0.591837	+	1.44390i
$645$	−9.28095	−	3.32746i	−0.365437	−	0.131019i
$646$	−21.9443			−0.863386
$647$	−1.00965	−	1.74877i	−0.0396935	−	0.0687512i	0.845496	−	0.533982i	$-0.179305\pi$
$647$	−1.00965	−	1.74877i	−0.0396935	−	0.0687512i	−0.885190	+	0.465230i	$0.845972\pi$
$648$	23.4229	−	20.4358i	0.920139	−	0.802793i
$649$	−12.2985	+	21.3016i	−0.482758	+	0.836161i
$650$	1.28584	+	2.22714i	0.0504347	+	0.0873554i
$651$	12.5719	−	13.9565i	0.492732	−	0.546999i
$652$	15.3541	−	26.5940i	0.601312	−	1.04150i
$653$	−23.2510	−	40.2719i	−0.909882	−	1.57596i	−0.814227	−	0.580547i	$-0.802839\pi$
$653$	−23.2510	−	40.2719i	−0.909882	−	1.57596i	−0.0956554	−	0.995415i	$-0.530495\pi$
$654$	−61.7563	+	52.3285i	−2.41486	+	2.04621i
$655$	2.83714	−	4.91406i	0.110856	−	0.192008i
$656$	−0.251267	+	0.435207i	−0.00981033	+	0.0169920i
$657$	−23.0179	−	18.9396i	−0.898015	−	0.738902i
$658$	−23.6049	−	30.5281i	−0.920215	−	1.19011i
$659$	−14.4190	−	24.9744i	−0.561685	−	0.972866i	−0.997350	−	0.0727574i	$-0.976820\pi$
$659$	−14.4190	−	24.9744i	−0.561685	−	0.972866i	0.435665	−	0.900109i	$-0.356513\pi$
$660$	3.49759	+	19.2921i	0.136143	+	0.750943i
$661$	7.26117			0.282427			0.141213	−	0.989979i	$-0.454900\pi$
$661$	7.26117			0.282427			0.141213	+	0.989979i	$0.454900\pi$
$662$	−53.7414			−2.08872
$663$	0.518804	+	2.86163i	0.0201487	+	0.111136i
$664$	−28.2935	−	49.0057i	−1.09800	−	1.90179i
$665$	9.93306	+	12.8464i	0.385188	+	0.498162i
$666$	−11.4025	+	68.5193i	−0.441837	+	2.65507i
$667$	−6.38949	+	11.0669i	−0.247402	+	0.428513i
$668$	35.4011	−	61.3164i	1.36971	−	2.37240i
$669$	28.4547	−	24.1108i	1.10012	−	0.932177i
$670$	2.50304	+	4.33540i	0.0967011	+	0.167491i
$671$	−12.1891	+	21.1121i	−0.470553	+	0.815022i
$672$	−13.0736	+	14.5135i	−0.504326	+	0.559870i
$673$	−14.3678	−	24.8857i	−0.553837	−	0.959274i	−0.997993	−	0.0633242i	$-0.979830\pi$
$673$	−14.3678	−	24.8857i	−0.553837	−	0.959274i	0.444156	−	0.895949i	$-0.353504\pi$
$674$	−35.5358	+	61.5498i	−1.36879	+	2.37081i
$675$	5.19561	−	0.0750680i	0.199979	−	0.00288937i
$676$	20.4947	+	35.4978i	0.788257	+	1.36530i
$677$	21.7025			0.834097			0.417048	−	0.908884i	$-0.363065\pi$
$677$	21.7025			0.834097			0.417048	+	0.908884i	$0.363065\pi$
$678$	−34.2921	−	12.2946i	−1.31698	−	0.472171i
$679$	14.8799	−	36.3024i	0.571039	−	1.39316i
$680$	−2.63853	+	4.57007i	−0.101183	+	0.175254i
$681$	−14.9636	−	5.36483i	−0.573406	−	0.205581i
$682$	15.6187	−	27.0523i	0.598070	−	1.03589i
$683$	−21.1996	−	36.7188i	−0.811180	−	1.40501i	−0.912038	−	0.410105i	$-0.865492\pi$
$683$	−21.1996	−	36.7188i	−0.811180	−	1.40501i	0.100858	−	0.994901i	$-0.467841\pi$
$684$	10.5064	−	63.1344i	0.401720	−	2.41400i
$685$	21.6440			0.826974
$686$	39.8534	−	17.0282i	1.52161	−	0.650138i
$687$	11.8752	−	10.0623i	0.453067	−	0.383901i
$688$	3.21718	+	5.57232i	0.122654	+	0.212443i
$689$	12.0571			0.459339
$690$	16.4290	+	5.89022i	0.625441	+	0.224237i
$691$	6.88019			0.261735			0.130867	−	0.991400i	$-0.458224\pi$
$691$	6.88019			0.261735			0.130867	+	0.991400i	$0.458224\pi$
$692$	19.0859			0.725537
$693$	22.7669	−	12.2401i	0.864841	−	0.464963i
$694$	18.2450			0.692569
$695$	2.54752			0.0966329
$696$	13.5447	−	11.4770i	0.513412	−	0.435034i
$697$	−0.679266			−0.0257290
$698$	24.3501	+	42.1757i	0.921666	+	1.59637i
$699$	15.3497	+	5.50327i	0.580579	+	0.208153i
$700$	9.11333	−	1.23409i	0.344452	−	0.0466443i
$701$	10.0762			0.380572			0.190286	−	0.981729i	$-0.439059\pi$
$701$	10.0762			0.380572			0.190286	+	0.981729i	$0.439059\pi$
$702$	−13.3614	+	0.193050i	−0.504294	+	0.00728622i
$703$	30.3645	+	52.5928i	1.14522	+	1.98358i
$704$	−19.9231	+	34.5078i	−0.750880	+	1.30056i
$705$	−8.23649	+	6.97911i	−0.310204	+	0.262848i
$706$	14.1628	−	24.5307i	0.533024	−	0.923224i
$707$	39.5263	−	5.35249i	1.48654	−	0.201301i
$708$	−8.11181	−	44.7433i	−0.304860	−	1.68155i
$709$	−5.20697			−0.195552			−0.0977758	−	0.995208i	$-0.531173\pi$
$709$	−5.20697			−0.195552			−0.0977758	+	0.995208i	$0.531173\pi$
$710$	−18.4831	−	32.0137i	−0.693659	−	1.20145i
$711$	−22.0856	+	8.28024i	−0.828274	+	0.310533i
$712$	1.52010	−	2.63290i	0.0569683	−	0.0986719i
$713$	−8.82525	−	15.2858i	−0.330508	−	0.572457i
$714$	16.0256	+	3.40991i	0.599742	+	0.127613i
$715$	1.78946	−	3.09944i	0.0669221	−	0.115912i
$716$	−10.2892	−	17.8215i	−0.384527	−	0.666020i
$717$	24.0281	+	8.61471i	0.897347	+	0.321722i
$718$	13.4388	−	23.2767i	0.501532	−	0.868679i
$719$	10.9108	−	18.8980i	0.406902	−	0.704776i	−0.587638	−	0.809124i	$-0.699942\pi$
$719$	10.9108	−	18.8980i	0.406902	−	0.704776i	0.994541	+	0.104348i	$0.0332756\pi$
$720$	−2.61858	−	2.15461i	−0.0975887	−	0.0802977i
$721$	−8.94406	+	21.8207i	−0.333094	+	0.812646i
$722$	−21.8455	−	37.8376i	−0.813007	−	1.40817i
$723$	11.6342	+	4.17117i	0.432681	+	0.155127i
$724$	−4.18424			−0.155506
$725$	2.96768			0.110217
$726$	−1.21977	+	1.03356i	−0.0452699	+	0.0383589i
$727$	−9.27100	−	16.0578i	−0.343842	−	0.595553i	0.641300	−	0.767290i	$-0.278395\pi$
$727$	−9.27100	−	16.0578i	−0.343842	−	0.595553i	−0.985143	+	0.171737i	$0.945062\pi$
$728$	−9.95159	+	1.34760i	−0.368830	+	0.0499455i
$729$	−12.8188	+	23.7629i	−0.474771	+	0.880109i
$730$	−11.6256	+	20.1361i	−0.430283	+	0.745271i
$731$	−4.34860	+	7.53200i	−0.160839	+	0.278581i
$732$	−8.03962	−	44.3451i	−0.297153	−	1.63904i
$733$	5.67411	+	9.82784i	0.209578	+	0.363000i	0.951582	−	0.307396i	$-0.0994577\pi$
$733$	5.67411	+	9.82784i	0.209578	+	0.363000i	−0.742004	+	0.670396i	$0.766124\pi$
$734$	4.55782	−	7.89438i	0.168232	−	0.291387i
$735$	−5.25777	−	10.9250i	−0.193936	−	0.402975i
$736$	9.17744	+	15.8958i	0.338285	+	0.585927i
$737$	3.48341	−	6.03345i	0.128313	−	0.222245i
$738$	0.512338	−	3.07872i	0.0188594	−	0.113329i
$739$	1.73717	+	3.00887i	0.0639029	+	0.110683i	0.896207	−	0.443637i	$-0.146312\pi$
$739$	1.73717	+	3.00887i	0.0639029	+	0.110683i	−0.832304	+	0.554320i	$0.812979\pi$
$740$	34.3928			1.26431
$741$	−8.91332	+	7.55261i	−0.327439	+	0.277452i
$742$	25.7619	−	62.8510i	0.945749	−	2.30733i
$743$	−20.7664	+	35.9685i	−0.761846	+	1.31956i	0.180051	+	0.983657i	$0.442374\pi$
$743$	−20.7664	+	35.9685i	−0.761846	+	1.31956i	−0.941898	+	0.335899i	$0.890960\pi$
$744$	4.37430	+	24.1279i	0.160370	+	0.884570i
$745$	3.20515	−	5.55148i	0.117428	−	0.203390i
$746$	26.7137	+	46.2694i	0.978057	+	1.69404i
$747$	37.9546	+	31.2297i	1.38868	+	1.14263i
$748$	17.2954			0.632381
$749$	8.00044	−	1.08339i	0.292330	−	0.0395861i
$750$	−0.723033	−	3.98812i	−0.0264014	−	0.145625i
$751$	16.6207	+	28.7878i	0.606497	+	1.05048i	0.991813	+	0.127699i	$0.0407591\pi$
$751$	16.6207	+	28.7878i	0.606497	+	1.05048i	−0.385316	+	0.922785i	$0.625908\pi$
$752$	7.04540			0.256919
$753$	−4.18952	−	23.1086i	−0.152675	−	0.842126i
$754$	−7.63190			−0.277937
$755$	−1.86661			−0.0679329
$756$	−17.4831	+	44.4735i	−0.635852	+	1.61749i
$757$	13.7487			0.499705			0.249853	−	0.968284i	$-0.419618\pi$
$757$	13.7487			0.499705			0.249853	+	0.968284i	$0.419618\pi$
$758$	−70.2052			−2.54997
$759$	−4.33285	−	23.8992i	−0.157273	−	0.867487i
$760$	−21.1985			−0.768951
$761$	26.2399	+	45.4489i	0.951197	+	1.64752i	0.742841	+	0.669467i	$0.233478\pi$
$761$	26.2399	+	45.4489i	0.951197	+	1.64752i	0.208355	+	0.978053i	$0.433189\pi$
$762$	10.2203	+	56.3734i	0.370243	+	2.04219i
$763$	20.0397	−	48.8907i	0.725487	−	1.76996i
$764$	10.2993			0.372617
$765$	0.752427	−	4.52146i	0.0272041	−	0.163474i
$766$	−26.0654	−	45.1467i	−0.941783	−	1.63122i
$767$	−4.15022	+	7.18840i	−0.149856	+	0.259558i
$768$	−6.97686	−	38.4831i	−0.251756	−	1.38864i
$769$	−17.0666	+	29.5602i	−0.615436	+	1.06597i	0.374872	+	0.927077i	$0.377687\pi$
$769$	−17.0666	+	29.5602i	−0.615436	+	1.06597i	−0.990308	+	0.138890i	$0.955647\pi$
$770$	−12.3332	−	15.9505i	−0.444459	−	0.574817i
$771$	28.0343	−	23.7546i	1.00963	−	0.855501i
$772$	−19.1637			−0.689717
$773$	2.36364	+	4.09395i	0.0850143	+	0.147249i	0.905397	−	0.424565i	$-0.139573\pi$
$773$	2.36364	+	4.09395i	0.0850143	+	0.147249i	−0.820383	+	0.571814i	$0.806240\pi$
$774$	−30.8583	−	25.3907i	−1.10918	−	0.912651i
$775$	−2.04950	+	3.54983i	−0.0736201	+	0.127514i
$776$	25.6084	+	44.3551i	0.919288	+	1.59225i
$777$	−14.0023	−	43.1261i	−0.502331	−	1.54714i
$778$	−7.12989	+	12.3493i	−0.255619	+	0.442745i
$779$	−1.36434	−	2.36311i	−0.0488826	−	0.0846672i
$780$	1.18029	+	6.51026i	0.0422611	+	0.233105i
$781$	−25.7224	+	44.5525i	−0.920420	+	1.59421i
$782$	7.69783	−	13.3330i	0.275274	−	0.476788i
$783$	−7.51652	+	13.4645i	−0.268618	+	0.481183i
$784$	−1.99133	+	7.65781i	−0.0711188	+	0.273493i
$785$	−9.64355	−	16.7031i	−0.344193	−	0.596160i
$786$	17.5465	−	14.8679i	0.625864	−	0.530319i
$787$	3.37811			0.120416			0.0602082	−	0.998186i	$-0.480824\pi$
$787$	3.37811			0.120416			0.0602082	+	0.998186i	$0.480824\pi$
$788$	37.8666			1.34894
$789$	−12.2347	−	4.38644i	−0.435565	−	0.156161i
$790$	9.19913	+	15.9334i	0.327290	+	0.566884i
$791$	23.5649	−	3.19106i	0.837871	−	0.113461i
$792$	−5.53918	+	33.2858i	−0.196826	+	1.18276i
$793$	−4.11329	+	7.12443i	−0.146067	+	0.252996i
$794$	30.1286	−	52.1843i	1.06922	−	1.85195i
$795$	−17.8879	−	6.41326i	−0.634417	−	0.227455i
$796$	24.4608	+	42.3674i	0.866991	+	1.50167i
$797$	1.93096	−	3.34453i	0.0683982	−	0.118469i	−0.829798	−	0.558064i	$-0.811544\pi$
$797$	1.93096	−	3.34453i	0.0683982	−	0.118469i	0.898196	+	0.439594i	$0.144878\pi$
$798$	20.3254	+	62.6006i	0.719511	+	2.21604i
$799$	4.76157	+	8.24729i	0.168452	+	0.291768i
$800$	2.13129	−	3.69150i	0.0753525	−	0.130514i
$801$	−0.433486	+	2.60489i	−0.0153165	+	0.0920393i
$802$	13.1311	+	22.7437i	0.463675	+	0.803109i
$803$	32.3580			1.14189
$804$	2.29758	+	12.6730i	0.0810295	+	0.446944i
$805$	−11.2897	+	1.52881i	−0.397910	+	0.0538833i
$806$	5.27064	−	9.12902i	0.185650	−	0.321556i
$807$	−35.8959	+	30.4160i	−1.26360	+	1.07069i
$808$	−26.0349	+	45.0938i	−0.915904	+	1.58639i
$809$	−24.9768	−	43.2610i	−0.878137	−	1.52098i	−0.853383	−	0.521284i	$-0.825453\pi$
$809$	−24.9768	−	43.2610i	−0.878137	−	1.52098i	−0.0247531	−	0.999694i	$-0.507880\pi$
$810$	19.9256	+	6.82064i	0.700116	+	0.239653i
$811$	−1.93538			−0.0679603			−0.0339801	−	0.999423i	$-0.510818\pi$
$811$	−1.93538			−0.0679603			−0.0339801	+	0.999423i	$0.510818\pi$
$812$	−10.3510	+	25.2532i	−0.363249	+	0.886214i
$813$	5.39842	+	1.93547i	0.189331	+	0.0678800i
$814$	−37.7016	−	65.3011i	−1.32144	−	2.28880i
$815$	8.83445			0.309457
$816$	−2.28221	+	1.93380i	−0.0798932	+	0.0676967i
$817$	−34.9376			−1.22231
$818$	−10.6953			−0.373954
$819$	7.68285	−	4.13051i	0.268461	−	0.144332i
$820$	−1.54534			−0.0539657
$821$	2.99473			0.104517			0.0522584	−	0.998634i	$-0.483358\pi$
$821$	2.99473			0.104517			0.0522584	+	0.998634i	$0.483358\pi$
$822$	82.5789	+	29.6067i	2.88027	+	1.03265i
$823$	−44.2285			−1.54171			−0.770855	−	0.637011i	$-0.780171\pi$
$823$	−44.2285			−1.54171			−0.770855	+	0.637011i	$0.780171\pi$
$824$	−15.3928	−	26.6610i	−0.536232	−	0.928781i
$825$	−4.30346	+	3.64649i	−0.149827	+	0.126954i
$826$	28.6040	+	36.9934i	0.995259	+	1.28716i
$827$	23.1676			0.805618			0.402809	−	0.915284i	$-0.368034\pi$
$827$	23.1676			0.805618			0.402809	+	0.915284i	$0.368034\pi$
$828$	34.6740	+	28.5304i	1.20501	+	0.991500i
$829$	−26.9945	−	46.7558i	−0.937556	−	1.62389i	−0.770011	−	0.638030i	$-0.779749\pi$
$829$	−26.9945	−	46.7558i	−0.937556	−	1.62389i	−0.167545	−	0.985864i	$-0.553584\pi$
$830$	19.1696	−	33.2027i	0.665386	−	1.15248i
$831$	46.1158	+	16.5337i	1.59974	+	0.573548i
$832$	−6.72321	+	11.6449i	−0.233085	+	0.403716i
$833$	−10.3100	+	2.84443i	−0.357220	+	0.0985537i
$834$	9.71962	+	3.48474i	0.336563	+	0.120667i
$835$	20.3691			0.704902
$836$	34.7387	+	60.1691i	1.20146	+	2.08099i
$837$	−10.9149	−	18.2897i	−0.377273	−	0.632185i
$838$	2.59295	−	4.49112i	0.0895720	−	0.155143i
$839$	19.6127	+	33.9702i	0.677106	+	1.17278i	0.975849	+	0.218448i	$0.0700994\pi$
$839$	19.6127	+	33.9702i	0.677106	+	1.17278i	−0.298743	+	0.954334i	$0.596567\pi$
$840$	15.4809	+	3.29403i	0.534143	+	0.113655i
$841$	10.0964	−	17.4876i	0.348153	−	0.603019i
$842$	15.8091	+	27.3821i	0.544817	+	0.943650i
$843$	8.78722	−	7.44576i	0.302648	−	0.256446i
$844$	20.0623	−	34.7490i	0.690574	−	1.19611i
$845$	−5.89613	+	10.2124i	−0.202833	+	0.351317i
$846$	−40.9716	+	15.3609i	−1.40863	+	0.528120i
$847$	0.395811	−	0.965656i	0.0136002	−	0.0331803i
$848$	6.20071	+	10.7399i	0.212933	+	0.368811i
$849$	2.75716	+	15.2080i	0.0946255	+	0.521937i
$850$	−3.57535			−0.122634
$851$	−42.6062			−1.46052
$852$	−16.9659	−	93.5809i	−0.581243	−	3.20603i
$853$	2.50400	+	4.33705i	0.0857353	+	0.148498i	0.905704	−	0.423910i	$-0.139343\pi$
$853$	2.50400	+	4.33705i	0.0857353	+	0.148498i	−0.819969	+	0.572408i	$0.806009\pi$
$854$	28.3494	+	36.6642i	0.970098	+	1.25462i
$855$	17.2411	−	6.46396i	0.589632	−	0.221063i
$856$	−5.26968	+	9.12735i	−0.180114	+	0.311966i
$857$	−24.6096	+	42.6250i	−0.840647	+	1.45604i	0.0487010	+	0.998813i	$0.484492\pi$
$857$	−24.6096	+	42.6250i	−0.840647	+	1.45604i	−0.889348	+	0.457230i	$0.848841\pi$
$858$	11.0671	−	9.37758i	0.377824	−	0.320145i
$859$	1.55662	+	2.69614i	0.0531111	+	0.0919912i	0.891359	−	0.453299i	$-0.149753\pi$
$859$	1.55662	+	2.69614i	0.0531111	+	0.0919912i	−0.838248	+	0.545290i	$0.816420\pi$
$860$	−9.89315	+	17.1354i	−0.337354	+	0.584314i
$861$	0.629155	+	1.93775i	0.0214415	+	0.0660382i
$862$	−7.99559	−	13.8488i	−0.272331	−	0.471691i
$863$	−10.0338	+	17.3790i	−0.341554	+	0.591589i	−0.984722	−	0.174136i	$-0.944287\pi$
$863$	−10.0338	+	17.3790i	−0.341554	+	0.591589i	0.643167	+	0.765726i	$0.277620\pi$
$864$	11.3505	+	19.0196i	0.386151	+	0.647060i
$865$	2.74542	+	4.75520i	0.0933470	+	0.161682i
$866$	−21.7284			−0.738360
$867$	23.9112	+	8.57279i	0.812067	+	0.291147i
$868$	−23.0586	−	29.8216i	−0.782659	−	1.01221i
$869$	12.8022	−	22.1740i	0.434284	−	0.752202i
$870$	11.3227	+	4.05947i	0.383874	+	0.137629i
$871$	1.17551	−	2.03604i	0.0398305	−	0.0689884i
$872$	34.4884	+	59.7357i	1.16793	+	2.02291i
$873$	−34.3527	−	28.2660i	−1.16266	−	0.956659i
$874$	61.8460			2.09197
$875$	1.61838	+	2.09305i	0.0547113	+	0.0707579i
$876$	−45.6394	+	38.6721i	−1.54201	+	1.30661i
$877$	10.7273	+	18.5803i	0.362236	+	0.627411i	0.988329	−	0.152338i	$-0.0486801\pi$
$877$	10.7273	+	18.5803i	0.362236	+	0.627411i	−0.626093	+	0.779749i	$0.715347\pi$
$878$	43.6180			1.47204
$879$	19.2879	+	6.91522i	0.650565	+	0.233245i
$880$	3.68113			0.124091
$881$	−10.5582			−0.355715			−0.177857	−	0.984056i	$-0.556917\pi$
$881$	−10.5582			−0.355715			−0.177857	+	0.984056i	$0.556917\pi$
$882$	−5.11584	−	48.8746i	−0.172259	−	1.64569i
$883$	38.3077			1.28916			0.644578	−	0.764539i	$-0.277033\pi$
$883$	38.3077			1.28916			0.644578	+	0.764539i	$0.277033\pi$
$884$	5.83646			0.196301
$885$	9.98082	−	8.45715i	0.335502	−	0.284284i
$886$	7.64217			0.256744
$887$	6.95285	+	12.0427i	0.233454	+	0.404354i	0.958822	−	0.284007i	$-0.0916639\pi$
$887$	6.95285	+	12.0427i	0.233454	+	0.404354i	−0.725368	+	0.688361i	$0.758331\pi$
$888$	55.7184	+	19.9765i	1.86979	+	0.670368i
$889$	−22.8764	−	29.5859i	−0.767248	−	0.992279i
$890$	2.05982			0.0690454
$891$	−5.64459	−	28.7609i	−0.189101	−	0.963526i
$892$	−37.4237	−	64.8198i	−1.25304	−	2.17033i
$893$	−19.1277	+	33.1302i	−0.640085	+	1.10866i
$894$	19.8225	−	16.7964i	0.662964	−	0.561756i
$895$	2.96012	−	5.12708i	0.0989458	−	0.171379i
$896$	32.5404	+	42.0844i	1.08710	+	1.40594i
$897$	−1.46216	−	8.06498i	−0.0488199	−	0.269282i
$898$	−43.1003			−1.43828
$899$	−6.08225	−	10.5348i	−0.202854	−	0.351354i
$900$	1.71179	−	10.2864i	0.0570596	−	0.342880i
$901$	−8.38138	+	14.5170i	−0.279224	+	0.483631i
$902$	1.69402	+	2.93412i	0.0564045	+	0.0976955i
$903$	25.5144	+	5.42894i	0.849065	+	0.180664i
$904$	−15.5216	+	26.8841i	−0.516239	+	0.894153i
$905$	−0.601883	−	1.04249i	−0.0200073	−	0.0346536i
$906$	−7.12173	−	2.55333i	−0.236604	−	0.0848286i
$907$	−7.42995	+	12.8691i	−0.246708	+	0.427310i	−0.962610	−	0.270890i	$-0.912682\pi$
$907$	−7.42995	+	12.8691i	−0.246708	+	0.427310i	0.715903	+	0.698200i	$0.246015\pi$
$908$	−15.9506	+	27.6273i	−0.529340	+	0.916844i
$909$	7.42434	−	44.6141i	0.246250	−	1.47976i
$910$	−4.16195	−	5.38263i	−0.137967	−	0.178433i
$911$	−23.6254	−	40.9204i	−0.782744	−	1.35575i	−0.930338	−	0.366704i	$-0.880486\pi$
$911$	−23.6254	−	40.9204i	−0.782744	−	1.35575i	0.147594	−	0.989048i	$-0.452847\pi$
$912$	−11.3115	−	4.05546i	−0.374560	−	0.134290i
$913$	−53.3555			−1.76581
$914$	39.2262			1.29749
$915$	9.89201	−	8.38189i	0.327020	−	0.277097i
$916$	−15.6183	−	27.0517i	−0.516043	−	0.893813i
$917$	−5.69379	+	13.8911i	−0.188026	+	0.458724i
$918$	9.05564	−	16.2216i	0.298881	−	0.535393i
$919$	−17.4778	+	30.2724i	−0.576539	+	0.998595i	0.419334	+	0.907832i	$0.362264\pi$
$919$	−17.4778	+	30.2724i	−0.576539	+	0.998595i	−0.995873	+	0.0907626i	$0.971070\pi$
$920$	7.43622	−	12.8799i	0.245165	−	0.424638i
$921$	−0.494707	−	2.72871i	−0.0163011	−	0.0899142i
$922$	13.9954	+	24.2407i	0.460913	+	0.798324i
$923$	−8.68023	+	15.0346i	−0.285713	+	0.494870i
$924$	−16.0194	−	49.3386i	−0.527001	−	1.62312i
$925$	4.94725	+	8.56889i	0.162665	+	0.281743i
$926$	−27.4719	+	47.5827i	−0.902782	+	1.56366i
$927$	20.6488	+	16.9902i	0.678195	+	0.558030i
$928$	6.32498	+	10.9552i	0.207628	+	0.359622i
$929$	−4.35550			−0.142899			−0.0714497	−	0.997444i	$-0.522763\pi$
$929$	−4.35550			−0.142899			−0.0714497	+	0.997444i	$0.522763\pi$
$930$	−12.6753	+	10.7403i	−0.415640	+	0.352188i
$931$	−30.6037	−	30.1543i	−1.00299	−	0.988269i
$932$	16.3622	−	28.3402i	0.535962	−	0.928314i
$933$	1.44068	+	7.94650i	0.0471656	+	0.260157i
$934$	−35.4420	+	61.3874i	−1.15970	+	2.00866i
$935$	2.48786	+	4.30910i	0.0813617	+	0.140923i
$936$	−1.86924	+	11.2326i	−0.0610980	+	0.367148i
$937$	−24.6433			−0.805063			−0.402531	−	0.915406i	$-0.631870\pi$
$937$	−24.6433			−0.805063			−0.402531	+	0.915406i	$0.631870\pi$
$938$	−8.10176	−	10.4780i	−0.264532	−	0.342118i
$939$	−7.29334	−	40.2287i	−0.238009	−	1.31282i
$940$	10.8327	+	18.7627i	0.353323	+	0.611973i
$941$	−7.13663			−0.232648			−0.116324	−	0.993211i	$-0.537111\pi$
$941$	−7.13663			−0.232648			−0.116324	+	0.993211i	$0.537111\pi$
$942$	−13.9452	−	76.9192i	−0.454359	−	2.50616i
$943$	1.91439			0.0623411
$944$	−8.53749			−0.277871
$945$	−13.5953	+	2.04145i	−0.442256	+	0.0664083i
$946$	43.3797			1.41040
$947$	−30.2791			−0.983940			−0.491970	−	0.870612i	$-0.663723\pi$
$947$	−30.2791			−0.983940			−0.491970	+	0.870612i	$0.663723\pi$
$948$	8.44402	+	46.5757i	0.274249	+	1.51271i
$949$	10.9195			0.354461
$950$	−7.18129	−	12.4384i	−0.232992	−	0.403554i
$951$	−2.65755	−	14.6586i	−0.0861769	−	0.475336i
$952$	5.29522	−	12.9187i	0.171619	−	0.418697i
$953$	8.57407			0.277741			0.138871	−	0.990311i	$-0.455653\pi$
$953$	8.57407			0.277741			0.138871	+	0.990311i	$0.455653\pi$
$954$	−59.4754	−	48.9374i	−1.92559	−	1.58441i
$955$	1.48151	+	2.56605i	0.0479406	+	0.0830355i
$956$	25.6131	−	44.3632i	0.828387	−	1.43481i
$957$	−2.98615	−	16.4710i	−0.0965284	−	0.532433i
$958$	0.339194	−	0.587501i	0.0109589	−	0.0189813i
$959$	−56.7467	+	7.68440i	−1.83245	+	0.248142i
$960$	16.1686	−	13.7003i	0.521838	−	0.442174i
$961$	−14.1982			−0.458007
$962$	−12.7227	−	22.0364i	−0.410197	−	0.710482i
$963$	1.50275	−	9.03026i	0.0484254	−	0.290996i
$964$	12.4016	−	21.4803i	0.399430	−	0.691833i
$965$	−2.75661	−	4.77459i	−0.0887384	−	0.153699i
$966$	−45.1652	−	9.61022i	−1.45317	−	0.309204i
$967$	−20.7447	+	35.9309i	−0.667105	+	1.15546i	0.311605	+	0.950212i	$0.399133\pi$
$967$	−20.7447	+	35.9309i	−0.667105	+	1.15546i	−0.978710	+	0.205248i	$0.934200\pi$
$968$	0.681192	+	1.17986i	0.0218943	+	0.0379221i
$969$	−2.89747	−	15.9819i	−0.0930803	−	0.513414i
$970$	−17.3504	+	30.0518i	−0.557088	+	0.964904i
$971$	1.84056	−	3.18794i	0.0590664	−	0.102306i	−0.834980	−	0.550280i	$-0.814521\pi$
$971$	1.84056	−	3.18794i	0.0590664	−	0.102306i	0.894047	+	0.447974i	$0.147854\pi$
$972$	42.3345	+	33.8198i	1.35788	+	1.08477i
$973$	−6.67914	+	0.904462i	−0.214123	+	0.0289957i
$974$	31.2955	+	54.2055i	1.00277	+	1.73685i
$975$	−1.45224	+	1.23054i	−0.0465088	+	0.0394087i
$976$	−8.46152			−0.270846
$977$	−6.44157			−0.206084			−0.103042	−	0.994677i	$-0.532858\pi$
$977$	−6.44157			−0.206084			−0.103042	+	0.994677i	$0.532858\pi$
$978$	33.7063	+	12.0846i	1.07781	+	0.386423i
$979$	−1.43330	−	2.48254i	−0.0458084	−	0.0793425i
$980$	−23.4554	+	6.47113i	−0.749255	+	0.206713i
$981$	−46.2648	−	38.0675i	−1.47712	−	1.21540i
$982$	−4.31293	+	7.47021i	−0.137631	+	0.238384i
$983$	3.76385	−	6.51917i	0.120048	−	0.207929i	−0.799738	−	0.600349i	$-0.795028\pi$
$983$	3.76385	−	6.51917i	0.120048	−	0.207929i	0.919786	+	0.392419i	$0.128362\pi$
$984$	−2.50355	−	0.897587i	−0.0798102	−	0.0286140i
$985$	5.44694	+	9.43438i	0.173554	+	0.300604i
$986$	5.30525	−	9.18896i	0.168954	−	0.292636i
$987$	19.1168	−	21.2222i	0.608494	−	0.675511i
$988$	11.7228	+	20.3045i	0.372953	+	0.645974i
$989$	12.2557	−	21.2276i	0.389710	−	0.674998i
$990$	−21.4071	+	8.02588i	−0.680363	+	0.255079i
$991$	−21.8853	−	37.9064i	−0.695209	−	1.20414i	−0.970110	−	0.242664i	$-0.921979\pi$
$991$	−21.8853	−	37.9064i	−0.695209	−	1.20414i	0.274902	−	0.961472i	$-0.411355\pi$
$992$	−17.4723			−0.554746
$993$	−7.09590	−	39.1397i	−0.225182	−	1.24206i
$994$	59.8254	+	77.3720i	1.89755	+	2.45409i
$995$	−7.03715	+	12.1887i	−0.223093	+	0.386408i
$996$	75.2555	−	63.7669i	2.38456	−	2.02053i
$997$	−5.32903	+	9.23015i	−0.168772	+	0.292322i	−0.937988	−	0.346667i	$-0.887314\pi$
$997$	−5.32903	+	9.23015i	−0.168772	+	0.292322i	0.769216	+	0.638988i	$0.220647\pi$
$998$	−3.93260	−	6.81147i	−0.124484	−	0.215613i
$999$	−51.4079	+	0.742760i	−1.62648	+	0.0234999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.b.121.12	yes	24
3.2	odd	2		945.2.l.b.226.1		24
7.4	even	3		315.2.k.b.256.1	yes	24
9.2	odd	6		945.2.k.b.856.12		24
9.7	even	3		315.2.k.b.16.1	✓	24
21.11	odd	6		945.2.k.b.361.12		24
63.11	odd	6		945.2.l.b.46.1		24
63.25	even	3	inner	315.2.l.b.151.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.1	✓	24	9.7	even	3
315.2.k.b.256.1	yes	24	7.4	even	3
315.2.l.b.121.12	yes	24	1.1	even	1	trivial
315.2.l.b.151.12	yes	24	63.25	even	3	inner
945.2.k.b.361.12		24	21.11	odd	6
945.2.k.b.856.12		24	9.2	odd	6
945.2.l.b.46.1		24	63.11	odd	6
945.2.l.b.226.1		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.34008 q^{2} +(0.308978 + 1.70427i) q^{3} +3.47596 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.723033 + 3.98812i) q^{6} +(-1.61838 - 2.09305i) q^{7} +3.45385 q^{8} +(-2.80906 + 1.05316i) q^{9} +O(q^{10})\)	\(q+2.34008 q^{2} +(0.308978 + 1.70427i) q^{3} +3.47596 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.723033 + 3.98812i) q^{6} +(-1.61838 - 2.09305i) q^{7} +3.45385 q^{8} +(-2.80906 + 1.05316i) q^{9} +(1.17004 + 2.02657i) q^{10} +(1.62831 - 2.82031i) q^{11} +(1.07400 + 5.92396i) q^{12} +(0.549485 - 0.951736i) q^{13} +(-3.78714 - 4.89789i) q^{14} +(-1.32145 + 1.11972i) q^{15} +1.13035 q^{16} +(0.763940 + 1.32318i) q^{17} +(-6.57342 + 2.46448i) q^{18} +(-3.06883 + 5.31536i) q^{19} +(1.73798 + 3.01027i) q^{20} +(3.06707 - 3.40486i) q^{21} +(3.81036 - 6.59974i) q^{22} +(-2.15303 - 3.72915i) q^{23} +(1.06716 + 5.88628i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.28584 - 2.22714i) q^{26} +(-2.66282 - 4.46200i) q^{27} +(-5.62542 - 7.27533i) q^{28} +(-1.48384 - 2.57008i) q^{29} +(-3.09230 + 2.62022i) q^{30} +4.09900 q^{31} -4.26258 q^{32} +(5.30968 + 1.90366i) q^{33} +(1.78768 + 3.09635i) q^{34} +(1.00344 - 2.44808i) q^{35} +(-9.76418 + 3.66075i) q^{36} +(4.94725 - 8.56889i) q^{37} +(-7.18129 + 12.4384i) q^{38} +(1.79179 + 0.642405i) q^{39} +(1.72692 + 2.99112i) q^{40} +(-0.222291 + 0.385018i) q^{41} +(7.17717 - 7.96764i) q^{42} +(2.84617 + 4.92971i) q^{43} +(5.65993 - 9.80328i) q^{44} +(-2.31660 - 1.90614i) q^{45} +(-5.03824 - 8.72650i) q^{46} +6.23292 q^{47} +(0.349255 + 1.92643i) q^{48} +(-1.76168 + 6.77469i) q^{49} +(-1.17004 + 2.02657i) q^{50} +(-2.01902 + 1.71079i) q^{51} +(1.90999 - 3.30819i) q^{52} +(5.48563 + 9.50139i) q^{53} +(-6.23119 - 10.4414i) q^{54} +3.25662 q^{55} +(-5.58964 - 7.22906i) q^{56} +(-10.0070 - 3.58777i) q^{57} +(-3.47229 - 6.01419i) q^{58} -7.55293 q^{59} +(-4.59330 + 3.89209i) q^{60} -7.48572 q^{61} +9.59196 q^{62} +(6.75046 + 4.17508i) q^{63} -12.2355 q^{64} +1.09897 q^{65} +(12.4251 + 4.45471i) q^{66} +2.13929 q^{67} +(2.65542 + 4.59932i) q^{68} +(5.69024 - 4.82156i) q^{69} +(2.34813 - 5.72870i) q^{70} -15.7970 q^{71} +(-9.70208 + 3.63747i) q^{72} +(4.96804 + 8.60490i) q^{73} +(11.5769 - 20.0518i) q^{74} +(-1.63043 - 0.584551i) q^{75} +(-10.6671 + 18.4760i) q^{76} +(-8.53827 + 1.15622i) q^{77} +(4.19293 + 1.50328i) q^{78} +7.86225 q^{79} +(0.565177 + 0.978916i) q^{80} +(6.78169 - 5.91681i) q^{81} +(-0.520177 + 0.900972i) q^{82} +(-8.19187 - 14.1887i) q^{83} +(10.6610 - 11.8352i) q^{84} +(-0.763940 + 1.32318i) q^{85} +(6.66025 + 11.5359i) q^{86} +(3.92164 - 3.32296i) q^{87} +(5.62393 - 9.74093i) q^{88} +(0.440119 - 0.762308i) q^{89} +(-5.42102 - 4.46051i) q^{90} +(-2.88130 + 0.390175i) q^{91} +(-7.48382 - 12.9624i) q^{92} +(1.26650 + 6.98579i) q^{93} +14.5855 q^{94} -6.13765 q^{95} +(-1.31705 - 7.26458i) q^{96} +(7.41446 + 12.8422i) q^{97} +(-4.12247 + 15.8533i) q^{98} +(-1.60377 + 9.63731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

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