LMFDB - Embedded newform 315.2.l.b.121.5

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			121.5
Character	$\chi$	$=$	315.121
Dual form			315.2.l.b.151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.609814 q^{2} +(1.67160 - 0.453588i) q^{3} -1.62813 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.01937 + 0.276604i) q^{6} +(0.731085 + 2.54274i) q^{7} +2.21248 q^{8} +(2.58852 - 1.51644i) q^{9} +O(q^{10})$	\(q-0.609814 q^{2} +(1.67160 - 0.453588i) q^{3} -1.62813 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.01937 + 0.276604i) q^{6} +(0.731085 + 2.54274i) q^{7} +2.21248 q^{8} +(2.58852 - 1.51644i) q^{9} +(-0.304907 - 0.528114i) q^{10} +(-1.29580 + 2.24439i) q^{11} +(-2.72158 + 0.738499i) q^{12} +(0.424083 - 0.734533i) q^{13} +(-0.445826 - 1.55060i) q^{14} +(1.22862 + 1.22086i) q^{15} +1.90705 q^{16} +(2.86094 + 4.95529i) q^{17} +(-1.57851 + 0.924745i) q^{18} +(1.85316 - 3.20976i) q^{19} +(-0.814064 - 1.41000i) q^{20} +(2.37544 + 3.91884i) q^{21} +(0.790197 - 1.36866i) q^{22} +(0.410661 + 0.711286i) q^{23} +(3.69839 - 1.00356i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.258611 + 0.447928i) q^{26} +(3.63913 - 3.70900i) q^{27} +(-1.19030 - 4.13990i) q^{28} +(-0.710523 - 1.23066i) q^{29} +(-0.749230 - 0.744495i) q^{30} +2.57528 q^{31} -5.58791 q^{32} +(-1.14803 + 4.33949i) q^{33} +(-1.74464 - 3.02180i) q^{34} +(-1.83653 + 1.90451i) q^{35} +(-4.21443 + 2.46896i) q^{36} +(3.88789 - 6.73402i) q^{37} +(-1.13008 + 1.95736i) q^{38} +(0.375723 - 1.42021i) q^{39} +(1.10624 + 1.91607i) q^{40} +(-5.02127 + 8.69709i) q^{41} +(-1.44858 - 2.38976i) q^{42} +(-4.78564 - 8.28897i) q^{43} +(2.10973 - 3.65416i) q^{44} +(2.60753 + 1.48350i) q^{45} +(-0.250427 - 0.433752i) q^{46} -3.09301 q^{47} +(3.18784 - 0.865017i) q^{48} +(-5.93103 + 3.71792i) q^{49} +(0.304907 - 0.528114i) q^{50} +(7.03001 + 6.98559i) q^{51} +(-0.690460 + 1.19591i) q^{52} +(1.63632 + 2.83418i) q^{53} +(-2.21919 + 2.26180i) q^{54} -2.59160 q^{55} +(1.61751 + 5.62576i) q^{56} +(1.64183 - 6.20602i) q^{57} +(0.433286 + 0.750474i) q^{58} +5.69381 q^{59} +(-2.00035 - 1.98771i) q^{60} +1.00764 q^{61} -1.57044 q^{62} +(5.74833 + 5.47327i) q^{63} -0.406523 q^{64} +0.848165 q^{65} +(0.700087 - 2.64628i) q^{66} -0.870806 q^{67} +(-4.65797 - 8.06784i) q^{68} +(1.00909 + 1.00272i) q^{69} +(1.11994 - 1.16139i) q^{70} -10.3908 q^{71} +(5.72704 - 3.35509i) q^{72} +(-7.98812 - 13.8358i) q^{73} +(-2.37089 + 4.10650i) q^{74} +(-0.442983 + 1.67445i) q^{75} +(-3.01718 + 5.22590i) q^{76} +(-6.65424 - 1.65404i) q^{77} +(-0.229121 + 0.866061i) q^{78} -9.77140 q^{79} +(0.953527 + 1.65156i) q^{80} +(4.40083 - 7.85065i) q^{81} +(3.06204 - 5.30361i) q^{82} +(-7.18628 - 12.4470i) q^{83} +(-3.86752 - 6.38037i) q^{84} +(-2.86094 + 4.95529i) q^{85} +(2.91835 + 5.05473i) q^{86} +(-1.74593 - 1.73489i) q^{87} +(-2.86693 + 4.96568i) q^{88} +(1.48923 - 2.57942i) q^{89} +(-1.59011 - 0.904659i) q^{90} +(2.17776 + 0.541325i) q^{91} +(-0.668609 - 1.15806i) q^{92} +(4.30485 - 1.16812i) q^{93} +1.88616 q^{94} +3.70632 q^{95} +(-9.34077 + 2.53461i) q^{96} +(-6.02424 - 10.4343i) q^{97} +(3.61682 - 2.26724i) q^{98} +(0.0492835 + 7.77465i) 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 $

$2$	−0.609814			−0.431203			−0.215602	−	0.976481i	$-0.569171\pi$
$2$	−0.609814			−0.431203			−0.215602	+	0.976481i	$0.569171\pi$
$3$	1.67160	−	0.453588i	0.965101	−	0.261879i
$3$	1.67160	−	0.453588i	0.965101	−	0.261879i
$4$	−1.62813			−0.814064
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.01937	+	0.276604i	−0.416155	+	0.112923i
$7$	0.731085	+	2.54274i	0.276324	+	0.961064i
$7$	0.731085	+	2.54274i	0.276324	+	0.961064i
$8$	2.21248			0.782230
$9$	2.58852	−	1.51644i	0.862839	−	0.505480i
$10$	−0.304907	−	0.528114i	−0.0964200	−	0.167004i
$11$	−1.29580	+	2.24439i	−0.390699	+	0.676710i	−0.992542	−	0.121904i	$-0.961100\pi$
$11$	−1.29580	+	2.24439i	−0.390699	+	0.676710i	0.601843	+	0.798614i	$0.294433\pi$
$12$	−2.72158	+	0.738499i	−0.785653	+	0.213186i
$13$	0.424083	−	0.734533i	0.117619	−	0.203723i	−0.801204	−	0.598391i	$-0.795807\pi$
$13$	0.424083	−	0.734533i	0.117619	−	0.203723i	0.918824	+	0.394668i	$0.129140\pi$
$14$	−0.445826	−	1.55060i	−0.119152	−	0.414414i
$15$	1.22862	+	1.22086i	0.317228	+	0.315224i
$16$	1.90705			0.476763
$17$	2.86094	+	4.95529i	0.693879	+	1.20183i	0.970557	+	0.240872i	$0.0774333\pi$
$17$	2.86094	+	4.95529i	0.693879	+	1.20183i	−0.276678	+	0.960963i	$0.589233\pi$
$18$	−1.57851	+	0.924745i	−0.372059	+	0.217964i
$19$	1.85316	−	3.20976i	0.425144	−	0.736370i	−0.571290	−	0.820748i	$-0.693557\pi$
$19$	1.85316	−	3.20976i	0.425144	−	0.736370i	0.996434	+	0.0843777i	$0.0268902\pi$
$20$	−0.814064	−	1.41000i	−0.182030	−	0.315285i
$21$	2.37544	+	3.91884i	0.518363	+	0.855160i
$22$	0.790197	−	1.36866i	0.168471	−	0.291800i
$23$	0.410661	+	0.711286i	0.0856288	+	0.148313i	0.905659	−	0.424007i	$-0.139377\pi$
$23$	0.410661	+	0.711286i	0.0856288	+	0.148313i	−0.820030	+	0.572320i	$0.806043\pi$
$24$	3.69839	−	1.00356i	0.754931	−	0.204850i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.258611	+	0.447928i	−0.0507179	+	0.0878459i
$27$	3.63913	−	3.70900i	0.700351	−	0.713798i
$28$	−1.19030	−	4.13990i	−0.224945	−	0.782368i
$29$	−0.710523	−	1.23066i	−0.131941	−	0.228528i	0.792484	−	0.609893i	$-0.208788\pi$
$29$	−0.710523	−	1.23066i	−0.131941	−	0.228528i	−0.924425	+	0.381365i	$0.875454\pi$
$30$	−0.749230	−	0.744495i	−0.136790	−	0.135926i
$31$	2.57528			0.462534			0.231267	−	0.972890i	$-0.425713\pi$
$31$	2.57528			0.462534			0.231267	+	0.972890i	$0.425713\pi$
$32$	−5.58791			−0.987812
$33$	−1.14803	+	4.33949i	−0.199847	+	0.755409i
$34$	−1.74464	−	3.02180i	−0.299203	−	0.518235i
$35$	−1.83653	+	1.90451i	−0.310431	+	0.321920i
$36$	−4.21443	+	2.46896i	−0.702406	+	0.411493i
$37$	3.88789	−	6.73402i	0.639165	−	1.10707i	−0.346451	−	0.938068i	$-0.612613\pi$
$37$	3.88789	−	6.73402i	0.639165	−	1.10707i	0.985616	−	0.168998i	$-0.0540533\pi$
$38$	−1.13008	+	1.95736i	−0.183323	+	0.317525i
$39$	0.375723	−	1.42021i	0.0601638	−	0.227415i
$40$	1.10624	+	1.91607i	0.174912	+	0.302957i
$41$	−5.02127	+	8.69709i	−0.784191	+	1.35826i	0.145291	+	0.989389i	$0.453588\pi$
$41$	−5.02127	+	8.69709i	−0.784191	+	1.35826i	−0.929481	+	0.368869i	$0.879745\pi$
$42$	−1.44858	−	2.38976i	−0.223520	−	0.368748i
$43$	−4.78564	−	8.28897i	−0.729803	−	1.26406i	−0.956966	−	0.290199i	$-0.906278\pi$
$43$	−4.78564	−	8.28897i	−0.729803	−	1.26406i	0.227163	−	0.973857i	$-0.427055\pi$
$44$	2.10973	−	3.65416i	0.318053	−	0.550885i
$45$	2.60753	+	1.48350i	0.388708	+	0.221147i
$46$	−0.250427	−	0.433752i	−0.0369234	−	0.0639532i
$47$	−3.09301			−0.451162			−0.225581	−	0.974224i	$-0.572428\pi$
$47$	−3.09301			−0.451162			−0.225581	+	0.974224i	$0.572428\pi$
$48$	3.18784	−	0.865017i	0.460125	−	0.124854i
$49$	−5.93103	+	3.71792i	−0.847290	+	0.531131i
$50$	0.304907	−	0.528114i	0.0431203	−	0.0746866i
$51$	7.03001	+	6.98559i	0.984399	+	0.978179i
$52$	−0.690460	+	1.19591i	−0.0957496	+	0.165843i
$53$	1.63632	+	2.83418i	0.224765	+	0.389305i	0.956249	−	0.292554i	$-0.0945051\pi$
$53$	1.63632	+	2.83418i	0.224765	+	0.389305i	−0.731484	+	0.681859i	$0.761172\pi$
$54$	−2.21919	+	2.26180i	−0.301994	+	0.307792i
$55$	−2.59160			−0.349451
$56$	1.61751	+	5.62576i	0.216149	+	0.751774i
$57$	1.64183	−	6.20602i	0.217466	−	0.822008i
$58$	0.433286	+	0.750474i	0.0568933	+	0.0985421i
$59$	5.69381			0.741270			0.370635	−	0.928779i	$-0.379140\pi$
$59$	5.69381			0.741270			0.370635	+	0.928779i	$0.379140\pi$
$60$	−2.00035	−	1.98771i	−0.258244	−	0.256612i
$61$	1.00764			0.129016			0.0645078	−	0.997917i	$-0.479452\pi$
$61$	1.00764			0.129016			0.0645078	+	0.997917i	$0.479452\pi$
$62$	−1.57044			−0.199446
$63$	5.74833	+	5.47327i	0.724222	+	0.689567i
$64$	−0.406523			−0.0508153
$65$	0.848165			0.105202
$66$	0.700087	−	2.64628i	0.0861748	−	0.325735i
$67$	−0.870806			−0.106386			−0.0531929	−	0.998584i	$-0.516940\pi$
$67$	−0.870806			−0.106386			−0.0531929	+	0.998584i	$0.516940\pi$
$68$	−4.65797	−	8.06784i	−0.564862	−	0.978370i
$69$	1.00909	+	1.00272i	0.121481	+	0.120713i
$70$	1.11994	−	1.16139i	0.133859	−	0.138813i
$71$	−10.3908			−1.23316			−0.616581	−	0.787292i	$-0.711483\pi$
$71$	−10.3908			−1.23316			−0.616581	+	0.787292i	$0.711483\pi$
$72$	5.72704	−	3.35509i	0.674939	−	0.395401i
$73$	−7.98812	−	13.8358i	−0.934939	−	1.61936i	−0.774743	−	0.632276i	$-0.782121\pi$
$73$	−7.98812	−	13.8358i	−0.934939	−	1.61936i	−0.160195	−	0.987085i	$-0.551212\pi$
$74$	−2.37089	+	4.10650i	−0.275610	+	0.477371i
$75$	−0.442983	+	1.67445i	−0.0511513	+	0.193348i
$76$	−3.01718	+	5.22590i	−0.346094	+	0.599452i
$77$	−6.65424	−	1.65404i	−0.758321	−	0.188495i
$78$	−0.229121	+	0.866061i	−0.0259428	+	0.0980621i
$79$	−9.77140			−1.09937			−0.549684	−	0.835373i	$-0.685252\pi$
$79$	−9.77140			−1.09937			−0.549684	+	0.835373i	$0.685252\pi$
$80$	0.953527	+	1.65156i	0.106608	+	0.184650i
$81$	4.40083	−	7.85065i	0.488981	−	0.872295i
$82$	3.06204	−	5.30361i	0.338146	−	0.585685i
$83$	−7.18628	−	12.4470i	−0.788797	−	1.36624i	−0.926704	−	0.375791i	$-0.877371\pi$
$83$	−7.18628	−	12.4470i	−0.788797	−	1.36624i	0.137907	−	0.990445i	$-0.455962\pi$
$84$	−3.86752	−	6.38037i	−0.421981	−	0.696155i
$85$	−2.86094	+	4.95529i	−0.310312	+	0.537477i
$86$	2.91835	+	5.05473i	0.314694	+	0.545065i
$87$	−1.74593	−	1.73489i	−0.187183	−	0.186000i
$88$	−2.86693	+	4.96568i	−0.305616	+	0.529343i
$89$	1.48923	−	2.57942i	0.157858	−	0.273418i	−0.776238	−	0.630440i	$-0.782875\pi$
$89$	1.48923	−	2.57942i	0.157858	−	0.273418i	0.934096	+	0.357022i	$0.116208\pi$
$90$	−1.59011	−	0.904659i	−0.167612	−	0.0953594i
$91$	2.17776	+	0.541325i	0.228292	+	0.0567463i
$92$	−0.668609	−	1.15806i	−0.0697073	−	0.120737i
$93$	4.30485	−	1.16812i	0.446392	−	0.121128i
$94$	1.88616			0.194543
$95$	3.70632			0.380260
$96$	−9.34077	+	2.53461i	−0.953338	+	0.258687i
$97$	−6.02424	−	10.4343i	−0.611668	−	1.05944i	−0.990959	−	0.134163i	$-0.957165\pi$
$97$	−6.02424	−	10.4343i	−0.611668	−	1.05944i	0.379291	−	0.925278i	$-0.376168\pi$
$98$	3.61682	−	2.26724i	0.365354	−	0.229025i
$99$	0.0492835	+	7.77465i	0.00495317	+	0.781381i
$100$	0.814064	−	1.41000i	0.0814064	−	0.141000i
$101$	0.0916944	−	0.158819i	0.00912394	−	0.0158031i	−0.861427	−	0.507881i	$-0.830429\pi$
$101$	0.0916944	−	0.158819i	0.00912394	−	0.0158031i	0.870551	+	0.492078i	$0.163762\pi$
$102$	−4.28700	−	4.25991i	−0.424476	−	0.421794i
$103$	5.01296	+	8.68271i	0.493942	+	0.855532i	0.999976	−	0.00698127i	$-0.00222223\pi$
$103$	5.01296	+	8.68271i	0.493942	+	0.855532i	−0.506034	+	0.862514i	$0.668889\pi$
$104$	0.938275	−	1.62514i	0.0920054	−	0.159358i
$105$	−2.20609	+	4.01661i	−0.215293	+	0.391981i
$106$	−0.997848	−	1.72832i	−0.0969195	−	0.167870i
$107$	−0.753244	+	1.30466i	−0.0728189	+	0.126126i	−0.900136	−	0.435610i	$-0.856533\pi$
$107$	−0.753244	+	1.30466i	−0.0728189	+	0.126126i	0.827317	+	0.561736i	$0.189866\pi$
$108$	−5.92497	+	6.03873i	−0.570131	+	0.581077i
$109$	7.48045	+	12.9565i	0.716497	+	1.24101i	0.962379	+	0.271709i	$0.0875889\pi$
$109$	7.48045	+	12.9565i	0.716497	+	1.24101i	−0.245883	+	0.969300i	$0.579078\pi$
$110$	1.58039			0.150685
$111$	3.44454	−	13.0201i	0.326941	−	1.23581i
$112$	1.39422	+	4.84914i	0.131741	+	0.458200i
$113$	6.34240	−	10.9854i	0.596643	−	1.03342i	−0.396670	−	0.917961i	$-0.629834\pi$
$113$	6.34240	−	10.9854i	0.596643	−	1.03342i	0.993313	−	0.115455i	$-0.0368325\pi$
$114$	−1.00121	+	3.78452i	−0.0937722	+	0.354453i
$115$	−0.410661	+	0.711286i	−0.0382944	+	0.0663278i
$116$	1.15682	+	2.00367i	0.107408	+	0.186036i
$117$	−0.0161292	−	2.54444i	−0.00149115	−	0.235234i
$118$	−3.47216			−0.319638
$119$	−10.5084	+	10.8974i	−0.963305	+	0.998959i
$120$	2.71830	+	2.70112i	0.248146	+	0.246578i
$121$	2.14180	+	3.70971i	0.194709	+	0.337246i
$122$	−0.614475			−0.0556320
$123$	−4.44867	+	16.8157i	−0.401123	+	1.51622i
$124$	−4.19288			−0.376532
$125$	−1.00000			−0.0894427
$126$	−3.50541	−	3.33768i	−0.312287	−	0.297344i
$127$	12.2153			1.08393			0.541964	−	0.840401i	$-0.317681\pi$
$127$	12.2153			1.08393			0.541964	+	0.840401i	$0.317681\pi$
$128$	11.4237			1.00972
$129$	−11.7595	−	11.6852i	−1.03536	−	1.02882i
$130$	−0.517223			−0.0453634
$131$	−7.28076	−	12.6106i	−0.636123	−	1.10180i	−0.986276	−	0.165105i	$-0.947204\pi$
$131$	−7.28076	−	12.6106i	−0.636123	−	1.10180i	0.350153	−	0.936692i	$-0.386129\pi$
$132$	1.86915	−	7.06525i	0.162688	−	0.614951i
$133$	9.51640	+	2.36548i	0.825177	+	0.205114i
$134$	0.531029			0.0458739
$135$	5.03166	+	1.29708i	0.433056	+	0.111635i
$136$	6.32977	+	10.9635i	0.542774	+	0.940111i
$137$	10.4393	−	18.0814i	0.891890	−	1.54480i	0.0542822	−	0.998526i	$-0.482713\pi$
$137$	10.4393	−	18.0814i	0.891890	−	1.54480i	0.837607	−	0.546273i	$-0.183954\pi$
$138$	−0.615359	−	0.611471i	−0.0523828	−	0.0520518i
$139$	9.91507	−	17.1734i	0.840986	−	1.45663i	−0.0480768	−	0.998844i	$-0.515309\pi$
$139$	9.91507	−	17.1734i	0.840986	−	1.45663i	0.889062	−	0.457786i	$-0.151357\pi$
$140$	2.99011	−	3.10078i	0.252710	−	0.262064i
$141$	−5.17029	+	1.40295i	−0.435417	+	0.118150i
$142$	6.33645			0.531743
$143$	1.09905	+	1.90362i	0.0919074	+	0.159188i
$144$	4.93644	−	2.89193i	0.411370	−	0.240994i
$145$	0.710523	−	1.23066i	0.0590057	−	0.102201i
$146$	4.87126	+	8.43728i	0.403149	+	0.698274i
$147$	−8.22793	+	8.90512i	−0.678628	+	0.734482i
$148$	−6.32998	+	10.9638i	−0.520321	+	0.901223i
$149$	7.15959	+	12.4008i	0.586536	+	1.01591i	0.994682	+	0.102994i	$0.0328421\pi$
$149$	7.15959	+	12.4008i	0.586536	+	1.01591i	−0.408146	+	0.912917i	$0.633825\pi$
$150$	0.270137	−	1.02110i	0.0220566	−	0.0833724i
$151$	−5.58506	+	9.67360i	−0.454505	+	0.787226i	−0.998660	−	0.0517588i	$-0.983517\pi$
$151$	−5.58506	+	9.67360i	−0.454505	+	0.787226i	0.544154	+	0.838985i	$0.316851\pi$
$152$	4.10008	−	7.10154i	0.332560	−	0.576011i
$153$	14.9200	+	8.48841i	1.20621	+	0.686247i
$154$	4.05785	+	1.00866i	0.326991	+	0.0812798i
$155$	1.28764	+	2.23026i	0.103426	+	0.179139i
$156$	−0.611724	+	2.31228i	−0.0489771	+	0.185130i
$157$	2.75863			0.220163			0.110081	−	0.993923i	$-0.464889\pi$
$157$	2.75863			0.220163			0.110081	+	0.993923i	$0.464889\pi$
$158$	5.95873			0.474051
$159$	4.02082	+	3.99541i	0.318872	+	0.316857i
$160$	−2.79396	−	4.83927i	−0.220882	−	0.382578i
$161$	−1.50839	+	1.56421i	−0.118877	+	0.123277i
$162$	−2.68368	+	4.78743i	−0.210850	+	0.376136i
$163$	−7.91058	+	13.7015i	−0.619604	+	1.07319i	0.369954	+	0.929050i	$0.379373\pi$
$163$	−7.91058	+	13.7015i	−0.619604	+	1.07319i	−0.989558	+	0.144136i	$0.953960\pi$
$164$	8.17527	−	14.1600i	0.638381	−	1.10571i
$165$	−4.33213	+	1.17552i	−0.337256	+	0.0915141i
$166$	4.38229	+	7.59035i	0.340132	+	0.589126i
$167$	−8.28485	+	14.3498i	−0.641101	+	1.11042i	0.344086	+	0.938938i	$0.388189\pi$
$167$	−8.28485	+	14.3498i	−0.641101	+	1.11042i	−0.985187	+	0.171482i	$0.945145\pi$
$168$	5.25562	+	8.67036i	0.405480	+	0.668932i
$169$	6.14031	+	10.6353i	0.472331	+	0.818102i
$170$	1.74464	−	3.02180i	0.133808	−	0.231762i
$171$	−0.0704816	−	11.1187i	−0.00538986	−	0.850270i
$172$	7.79163	+	13.4955i	0.594106	+	1.02902i
$173$	−1.04793			−0.0796726			−0.0398363	−	0.999206i	$-0.512684\pi$
$173$	−1.04793			−0.0796726			−0.0398363	+	0.999206i	$0.512684\pi$
$174$	1.06469	+	1.05796i	0.0807139	+	0.0802038i
$175$	−2.56762	−	0.638231i	−0.194094	−	0.0482457i
$176$	−2.47116	+	4.28018i	−0.186271	+	0.322630i
$177$	9.51779	−	2.58264i	0.715401	−	0.194123i
$178$	−0.908152	+	1.57297i	−0.0680689	+	0.117899i
$179$	0.924721	+	1.60166i	0.0691169	+	0.119714i	0.898513	−	0.438947i	$-0.144649\pi$
$179$	0.924721	+	1.60166i	0.0691169	+	0.119714i	−0.829396	+	0.558661i	$0.811315\pi$
$180$	−4.24539	−	2.41533i	−0.316433	−	0.180028i
$181$	17.5376			1.30356			0.651780	−	0.758408i	$-0.274022\pi$
$181$	17.5376			1.30356			0.651780	+	0.758408i	$0.274022\pi$
$182$	−1.32803	−	0.330107i	−0.0984401	−	0.0244692i
$183$	1.68438	−	0.457056i	0.124513	−	0.0337865i
$184$	0.908580	+	1.57371i	0.0669814	+	0.116015i
$185$	7.77578			0.571687
$186$	−2.62515	+	0.712333i	−0.192486	+	0.0522308i
$187$	−14.8288			−1.08439
$188$	5.03582			0.367275
$189$	12.0915	+	6.54176i	0.879530	+	0.475843i
$190$	−2.26016			−0.163969
$191$	14.6563			1.06049			0.530247	−	0.847843i	$-0.322099\pi$
$191$	14.6563			1.06049			0.530247	+	0.847843i	$0.322099\pi$
$192$	−0.679544	+	0.184394i	−0.0490419	+	0.0133075i
$193$	−19.3771			−1.39480			−0.697398	−	0.716684i	$-0.745659\pi$
$193$	−19.3771			−1.39480			−0.697398	+	0.716684i	$0.745659\pi$
$194$	3.67366	+	6.36297i	0.263753	+	0.456834i
$195$	1.41780	−	0.384718i	0.101530	−	0.0275502i
$196$	9.65647	−	6.05324i	0.689748	−	0.432374i
$197$	14.1208			1.00607			0.503034	−	0.864267i	$-0.332217\pi$
$197$	14.1208			1.00607			0.503034	+	0.864267i	$0.332217\pi$
$198$	−0.0300537	−	4.74109i	−0.00213583	−	0.336934i
$199$	−7.44208	−	12.8901i	−0.527555	−	0.913752i	−0.999484	−	0.0321156i	$-0.989776\pi$
$199$	−7.44208	−	12.8901i	−0.527555	−	0.913752i	0.471929	−	0.881636i	$-0.343558\pi$
$200$	−1.10624	+	1.91607i	−0.0782230	+	0.135486i
$201$	−1.45564	+	0.394987i	−0.102673	+	0.0278602i
$202$	−0.0559165	+	0.0968503i	−0.00393427	+	0.00681436i
$203$	2.60980	−	2.70639i	0.183172	−	0.189951i
$204$	−11.4458	−	11.3734i	−0.801363	−	0.796300i
$205$	−10.0425			−0.701401
$206$	−3.05697	−	5.29483i	−0.212989	−	0.368908i
$207$	2.14162	+	1.21843i	0.148853	+	0.0846869i
$208$	0.808748	−	1.40079i	0.0560766	−	0.0971275i
$209$	4.80265	+	8.31843i	0.332206	+	0.575398i
$210$	1.34531	−	2.44938i	0.0928349	−	0.169024i
$211$	9.98630	−	17.2968i	0.687485	−	1.19076i	−0.285164	−	0.958479i	$-0.592048\pi$
$211$	9.98630	−	17.2968i	0.687485	−	1.19076i	0.972649	−	0.232280i	$-0.0746187\pi$
$212$	−2.66413	−	4.61441i	−0.182973	−	0.316919i
$213$	−17.3693	+	4.71314i	−1.19012	+	0.322939i
$214$	0.459339	−	0.795598i	0.0313997	−	0.0543860i
$215$	4.78564	−	8.28897i	0.326378	−	0.565303i
$216$	8.05151	−	8.20610i	0.547836	−	0.558355i
$217$	1.88275	+	6.54826i	0.127809	+	0.444525i
$218$	−4.56168	−	7.90106i	−0.308956	−	0.535127i
$219$	−19.6287	−	19.5047i	−1.32639	−	1.31801i
$220$	4.21946			0.284476
$221$	4.85310			0.326455
$222$	−2.10053	+	7.93984i	−0.140978	+	0.532887i
$223$	−12.7041	−	22.0042i	−0.850731	−	1.47351i	−0.880550	−	0.473954i	$-0.842826\pi$
$223$	−12.7041	−	22.0042i	−0.850731	−	1.47351i	0.0298185	−	0.999555i	$-0.490507\pi$
$224$	−4.08524	−	14.2086i	−0.272956	−	0.949351i
$225$	0.0190166	+	2.99994i	0.00126777	+	0.199996i
$226$	−3.86768	+	6.69902i	−0.257274	+	0.445612i
$227$	−6.30271	+	10.9166i	−0.418326	+	0.724562i	−0.995771	−	0.0918677i	$-0.970716\pi$
$227$	−6.30271	+	10.9166i	−0.418326	+	0.724562i	0.577445	+	0.816429i	$0.304050\pi$
$228$	−2.67312	+	10.1042i	−0.177031	+	0.669167i
$229$	4.14196	+	7.17409i	0.273708	+	0.474077i	0.969808	−	0.243868i	$-0.0784163\pi$
$229$	4.14196	+	7.17409i	0.273708	+	0.474077i	−0.696100	+	0.717945i	$0.745083\pi$
$230$	0.250427	−	0.433752i	0.0165127	−	0.0286008i
$231$	−11.8735	+	0.253387i	−0.781219	+	0.0166717i
$232$	−1.57202	−	2.72282i	−0.103208	−	0.178762i
$233$	−7.23136	+	12.5251i	−0.473742	+	0.820546i	−0.999548	−	0.0300589i	$-0.990430\pi$
$233$	−7.23136	+	12.5251i	−0.473742	+	0.820546i	0.525806	+	0.850605i	$0.323764\pi$
$234$	0.00983582	+	1.55164i	0.000642988	+	0.101434i
$235$	−1.54651	−	2.67863i	−0.100883	−	0.174734i
$236$	−9.27024			−0.603441
$237$	−16.3339	+	4.43219i	−1.06100	+	0.287902i
$238$	6.40817	−	6.64536i	0.415380	−	0.430754i
$239$	−4.79788	+	8.31018i	−0.310349	+	0.537541i	−0.978438	−	0.206541i	$-0.933779\pi$
$239$	−4.79788	+	8.31018i	−0.310349	+	0.537541i	0.668089	+	0.744082i	$0.267113\pi$
$240$	2.34304	+	2.32824i	0.151243	+	0.150287i
$241$	−3.16167	+	5.47617i	−0.203661	+	0.352751i	−0.949705	−	0.313145i	$-0.898617\pi$
$241$	−3.16167	+	5.47617i	−0.203661	+	0.352751i	0.746044	+	0.665896i	$0.231951\pi$
$242$	−1.30610	−	2.26223i	−0.0839593	−	0.145422i
$243$	3.79548	−	15.1193i	0.243480	−	0.969906i
$244$	−1.64057			−0.105027
$245$	−6.18532	−	3.27746i	−0.395166	−	0.209390i
$246$	2.71286	−	10.2544i	0.172966	−	0.653799i
$247$	−1.57178	−	2.72241i	−0.100010	−	0.173223i
$248$	5.69776			0.361808
$249$	−17.6584	−	17.5468i	−1.11906	−	1.11199i
$250$	0.609814			0.0385680
$251$	−23.2432			−1.46710			−0.733548	−	0.679638i	$-0.762137\pi$
$251$	−23.2432			−1.46710			−0.733548	+	0.679638i	$0.762137\pi$
$252$	−9.35901	−	8.91118i	−0.589563	−	0.561352i
$253$	−2.12854			−0.133820
$254$	−7.44903			−0.467394
$255$	−2.53469	+	9.58097i	−0.158729	+	0.599983i
$256$	−6.15330			−0.384581
$257$	5.03943	+	8.72855i	0.314351	+	0.544472i	0.979299	−	0.202417i	$-0.0648798\pi$
$257$	5.03943	+	8.72855i	0.314351	+	0.544472i	−0.664948	+	0.746889i	$0.731546\pi$
$258$	7.17108	+	7.12577i	0.446452	+	0.443631i
$259$	19.9652	+	4.96274i	1.24058	+	0.308370i
$260$	−1.38092			−0.0856411
$261$	−3.70542	−	2.10812i	−0.229360	−	0.130489i
$262$	4.43991	+	7.69014i	0.274298	+	0.475099i
$263$	10.8133	−	18.7291i	0.666774	−	1.15489i	−0.312027	−	0.950073i	$-0.601008\pi$
$263$	10.8133	−	18.7291i	0.666774	−	1.15489i	0.978801	−	0.204813i	$-0.0656586\pi$
$264$	−2.54001	+	9.60105i	−0.156327	+	0.590904i
$265$	−1.63632	+	2.83418i	−0.100518	+	0.174102i
$266$	−5.80323	−	1.44250i	−0.355819	−	0.0884456i
$267$	1.31941	−	4.98726i	0.0807463	−	0.305216i
$268$	1.41778			0.0866048
$269$	−9.66852	−	16.7464i	−0.589500	−	1.02104i	−0.994298	−	0.106638i	$-0.965991\pi$
$269$	−9.66852	−	16.7464i	−0.589500	−	1.02104i	0.404798	−	0.914406i	$-0.367342\pi$
$270$	−3.06837	−	0.790977i	−0.186735	−	0.0481373i
$271$	11.3865	−	19.7220i	0.691681	−	1.19803i	−0.279606	−	0.960115i	$-0.590204\pi$
$271$	11.3865	−	19.7220i	0.691681	−	1.19803i	0.971287	−	0.237912i	$-0.0764629\pi$
$272$	5.45596	+	9.45000i	0.330816	+	0.572991i
$273$	3.88590	−	0.0829273i	0.235185	−	0.00501899i
$274$	−6.36603	+	11.0263i	−0.384586	+	0.666122i
$275$	−1.29580	−	2.24439i	−0.0781397	−	0.135342i
$276$	−1.64293	−	1.63255i	−0.0988929	−	0.0982680i
$277$	−6.50287	+	11.2633i	−0.390720	+	0.676747i	−0.992545	−	0.121882i	$-0.961107\pi$
$277$	−6.50287	+	11.2633i	−0.390720	+	0.676747i	0.601825	+	0.798628i	$0.294441\pi$
$278$	−6.04635	+	10.4726i	−0.362636	+	0.628104i
$279$	6.66615	−	3.90525i	0.399092	−	0.233801i
$280$	−4.06329	+	4.21369i	−0.242828	+	0.251816i
$281$	2.44922	+	4.24218i	0.146108	+	0.253067i	0.929786	−	0.368101i	$-0.119992\pi$
$281$	2.44922	+	4.24218i	0.146108	+	0.253067i	−0.783677	+	0.621168i	$0.786658\pi$
$282$	3.15291	−	0.855540i	0.187753	−	0.0509467i
$283$	10.6730			0.634445			0.317222	−	0.948351i	$-0.397250\pi$
$283$	10.6730			0.634445			0.317222	+	0.948351i	$0.397250\pi$
$284$	16.9175			1.00387
$285$	6.19549	−	1.68114i	0.366989	−	0.0995822i
$286$	−0.670217	−	1.16085i	−0.0396308	−	0.0686425i
$287$	−25.7854	−	6.40946i	−1.52206	−	0.378338i
$288$	−14.4644	+	8.47372i	−0.852323	+	0.499319i
$289$	−7.86993	+	13.6311i	−0.462937	+	0.801831i
$290$	−0.433286	+	0.750474i	−0.0254435	+	0.0440694i
$291$	−14.8030	−	14.7095i	−0.867767	−	0.862284i
$292$	13.0057	+	22.5265i	0.761100	+	1.31826i
$293$	−4.44394	+	7.69713i	−0.259618	+	0.449671i	−0.966140	−	0.258020i	$-0.916930\pi$
$293$	−4.44394	+	7.69713i	−0.259618	+	0.449671i	0.706522	+	0.707691i	$0.250263\pi$
$294$	5.01750	−	5.43047i	0.292627	−	0.316711i
$295$	2.84690	+	4.93098i	0.165753	+	0.287093i
$296$	8.60188	−	14.8989i	0.499974	−	0.865981i
$297$	3.60887	+	12.9738i	0.209408	+	0.752815i
$298$	−4.36601	−	7.56216i	−0.252916	−	0.438064i
$299$	0.696617			0.0402864
$300$	0.721233	−	2.72621i	0.0416404	−	0.157398i
$301$	17.5780	−	18.2286i	1.01318	−	1.05068i
$302$	3.40584	−	5.89909i	0.195984	−	0.339455i
$303$	0.0812381	−	0.307075i	0.00466701	−	0.0176410i
$304$	3.53407	−	6.12119i	0.202693	−	0.351074i
$305$	0.503822	+	0.872646i	0.0288488	+	0.0499676i
$306$	−9.09841	−	5.17635i	−0.520121	−	0.295912i
$307$	−29.1276			−1.66240			−0.831199	−	0.555975i	$-0.812345\pi$
$307$	−29.1276			−1.66240			−0.831199	+	0.555975i	$0.812345\pi$
$308$	10.8340	+	2.69299i	0.617322	+	0.153447i
$309$	12.3181	+	12.2402i	0.700750	+	0.696322i
$310$	−0.785220	−	1.36004i	−0.0445975	−	0.0772452i
$311$	−14.8989			−0.844838			−0.422419	−	0.906401i	$-0.638819\pi$
$311$	−14.8989			−0.844838			−0.422419	+	0.906401i	$0.638819\pi$
$312$	0.831279	−	3.14218i	0.0470619	−	0.177891i
$313$	13.6999			0.774366			0.387183	−	0.922003i	$-0.373448\pi$
$313$	13.6999			0.774366			0.387183	+	0.922003i	$0.373448\pi$
$314$	−1.68225			−0.0949348
$315$	−1.86583	+	7.71484i	−0.105127	+	0.434682i
$316$	15.9091			0.894956
$317$	18.6157			1.04556			0.522780	−	0.852468i	$-0.324895\pi$
$317$	18.6157			1.04556			0.522780	+	0.852468i	$0.324895\pi$
$318$	−2.45195	−	2.43646i	−0.137499	−	0.136630i
$319$	3.68278			0.206196
$320$	−0.203261	−	0.352059i	−0.0113627	−	0.0196807i
$321$	−0.667349	+	2.52253i	−0.0372478	+	0.140794i
$322$	0.919834	−	0.953879i	0.0512603	−	0.0531576i
$323$	21.2071			1.17999
$324$	−7.16511	+	12.7819i	−0.398061	+	0.710103i
$325$	0.424083	+	0.734533i	0.0235239	+	0.0407445i
$326$	4.82398	−	8.35537i	0.267175	−	0.462761i
$327$	18.3813	+	18.2651i	1.01649	+	1.01006i
$328$	−11.1095	+	19.2422i	−0.613418	+	1.06247i
$329$	−2.26125	−	7.86472i	−0.124667	−	0.433596i
$330$	2.64179	−	0.716848i	0.145426	−	0.0394612i
$331$	−25.3329			−1.39242			−0.696211	−	0.717837i	$-0.745132\pi$
$331$	−25.3329			−1.39242			−0.696211	+	0.717837i	$0.745132\pi$
$332$	11.7002	+	20.2653i	0.642131	+	1.11220i
$333$	−0.147869	−	23.3269i	−0.00810317	−	1.27830i
$334$	5.05222	−	8.75069i	0.276445	−	0.478817i
$335$	−0.435403	−	0.754140i	−0.0237886	−	0.0412031i
$336$	4.53009	+	7.47343i	0.247137	+	0.407709i
$337$	0.447094	−	0.774389i	0.0243548	−	0.0421837i	−0.853591	−	0.520944i	$-0.825580\pi$
$337$	0.447094	−	0.774389i	0.0243548	−	0.0421837i	0.877946	+	0.478760i	$0.158914\pi$
$338$	−3.74444	−	6.48557i	−0.203671	−	0.352768i
$339$	5.61915	−	21.2400i	0.305190	−	1.15360i
$340$	4.65797	−	8.06784i	0.252614	−	0.437540i
$341$	−3.33705	+	5.77994i	−0.180711	+	0.313001i
$342$	0.0429806	+	6.78035i	0.00232413	+	0.366639i
$343$	−13.7898	−	12.3629i	−0.744578	−	0.667536i
$344$	−10.5881	−	18.3392i	−0.570874	−	0.988783i
$345$	−0.363832	+	1.37526i	−0.0195880	+	0.0740415i
$346$	0.639041			0.0343551
$347$	10.2366			0.549530			0.274765	−	0.961511i	$-0.411400\pi$
$347$	10.2366			0.549530			0.274765	+	0.961511i	$0.411400\pi$
$348$	2.84259	+	2.82463i	0.152379	+	0.151416i
$349$	8.59290	+	14.8833i	0.459967	+	0.796687i	0.998959	−	0.0456246i	$-0.0145278\pi$
$349$	8.59290	+	14.8833i	0.459967	+	0.796687i	−0.538991	+	0.842311i	$0.681194\pi$
$350$	1.56577	+	0.389202i	0.0836938	+	0.0208037i
$351$	−1.18109	−	4.24599i	−0.0630420	−	0.226634i
$352$	7.24082	−	12.5415i	0.385937	−	0.668462i
$353$	9.86432	−	17.0855i	0.525025	−	0.909370i	−0.474551	−	0.880228i	$-0.657389\pi$
$353$	9.86432	−	17.0855i	0.525025	−	0.909370i	0.999575	−	0.0291413i	$-0.00927728\pi$
$354$	−5.80408	+	1.57493i	−0.308483	+	0.0837066i
$355$	−5.19540	−	8.99870i	−0.275743	−	0.477601i
$356$	−2.42465	+	4.19962i	−0.128506	+	0.222580i
$357$	−12.6230	+	22.9825i	−0.668079	+	1.21637i
$358$	−0.563908	−	0.976717i	−0.0298035	−	0.0516211i
$359$	−11.2039	+	19.4056i	−0.591317	+	1.02419i	0.402739	+	0.915315i	$0.368058\pi$
$359$	−11.2039	+	19.4056i	−0.591317	+	1.02419i	−0.994055	+	0.108876i	$0.965275\pi$
$360$	5.76912	+	3.28222i	0.304059	+	0.172988i
$361$	2.63161	+	4.55808i	0.138506	+	0.239899i
$362$	−10.6947			−0.562100
$363$	5.26292	+	5.22967i	0.276232	+	0.274486i
$364$	−3.54568	−	0.881346i	−0.185844	−	0.0461951i
$365$	7.98812	−	13.8358i	0.418117	−	0.724200i
$366$	−1.02716	+	0.278719i	−0.0536905	+	0.0145689i
$367$	−9.26126	+	16.0410i	−0.483434	+	0.837332i	−0.999819	−	0.0190246i	$-0.993944\pi$
$367$	−9.26126	+	16.0410i	−0.483434	+	0.837332i	0.516385	+	0.856356i	$0.327277\pi$
$368$	0.783153	+	1.35646i	0.0408247	+	0.0707104i
$369$	0.190975	+	30.1270i	0.00994176	+	1.56835i
$370$	−4.74178			−0.246513
$371$	−6.01029	+	6.23275i	−0.312039	+	0.323588i
$372$	−7.00884	+	1.90184i	−0.363391	+	0.0986059i
$373$	−5.50973	−	9.54313i	−0.285283	−	0.494124i	0.687395	−	0.726284i	$-0.258754\pi$
$373$	−5.50973	−	9.54313i	−0.285283	−	0.494124i	−0.972678	+	0.232159i	$0.925421\pi$
$374$	9.04282			0.467593
$375$	−1.67160	+	0.453588i	−0.0863212	+	0.0234232i
$376$	−6.84323			−0.352913
$377$	−1.20528			−0.0620751
$378$	−7.37359	−	3.98926i	−0.379256	−	0.205185i
$379$	−13.3492			−0.685702			−0.342851	−	0.939390i	$-0.611393\pi$
$379$	−13.3492			−0.685702			−0.342851	+	0.939390i	$0.611393\pi$
$380$	−6.03435			−0.309556
$381$	20.4191	−	5.54069i	1.04610	−	0.283858i
$382$	−8.93762			−0.457288
$383$	−13.4212	−	23.2462i	−0.685792	−	1.18783i	−0.973187	−	0.230014i	$-0.926123\pi$
$383$	−13.4212	−	23.2462i	−0.685792	−	1.18783i	0.287396	−	0.957812i	$-0.407211\pi$
$384$	19.0959	−	5.18166i	0.974485	−	0.264426i
$385$	−1.89468	−	6.58976i	−0.0965619	−	0.335845i
$386$	11.8164			0.601441
$387$	−24.9574	−	14.1990i	−1.26866	−	0.721776i
$388$	9.80822	+	16.9883i	0.497937	+	0.862452i
$389$	−13.8475	+	23.9846i	−0.702097	+	1.21607i	0.265631	+	0.964075i	$0.414420\pi$
$389$	−13.8475	+	23.9846i	−0.702097	+	1.21607i	−0.967729	+	0.251994i	$0.918914\pi$
$390$	−0.864591	+	0.234606i	−0.0437803	+	0.0118797i
$391$	−2.34975	+	4.06989i	−0.118832	+	0.205823i
$392$	−13.1223	+	8.22582i	−0.662776	+	0.415467i
$393$	−17.8906	−	17.7775i	−0.902460	−	0.896758i
$394$	−8.61107			−0.433820
$395$	−4.88570	−	8.46228i	−0.245826	−	0.425784i
$396$	−0.0802397	−	12.6581i	−0.00403220	−	0.636094i
$397$	8.58155	−	14.8637i	0.430696	−	0.745987i	−0.566238	−	0.824242i	$-0.691602\pi$
$397$	8.58155	−	14.8637i	0.430696	−	0.745987i	0.996933	+	0.0782551i	$0.0249349\pi$
$398$	4.53828	+	7.86053i	0.227484	+	0.394013i
$399$	16.9806	−	0.362376i	0.850094	−	0.0181415i
$400$	−0.953527	+	1.65156i	−0.0476763	+	0.0825778i
$401$	−16.2050	−	28.0679i	−0.809239	−	1.40164i	−0.913392	−	0.407082i	$-0.866546\pi$
$401$	−16.2050	−	28.0679i	−0.809239	−	1.40164i	0.104152	−	0.994561i	$-0.466787\pi$
$402$	0.887670	−	0.240868i	0.0442730	−	0.0120134i
$403$	1.09213	−	1.89163i	0.0544029	−	0.0942287i
$404$	−0.149290	+	0.258578i	−0.00742747	+	0.0128647i
$405$	8.99928	−	0.114097i	0.447178	−	0.00566954i
$406$	−1.59149	+	1.65039i	−0.0789843	+	0.0819077i
$407$	10.0759	+	17.4519i	0.499442	+	0.865059i
$408$	15.5538	+	15.4555i	0.770027	+	0.765161i
$409$	−4.00952			−0.198258			−0.0991289	−	0.995075i	$-0.531606\pi$
$409$	−4.00952			−0.198258			−0.0991289	+	0.995075i	$0.531606\pi$
$410$	6.12408			0.302447
$411$	9.24886	−	34.9601i	0.456213	−	1.72445i
$412$	−8.16174	−	14.1365i	−0.402100	−	0.696458i
$413$	4.16266	+	14.4779i	0.204831	+	0.712409i
$414$	−1.30599	−	0.743017i	−0.0641860	−	0.0365173i
$415$	7.18628	−	12.4470i	0.352761	−	0.610999i
$416$	−2.36974	+	4.10450i	−0.116186	+	0.201240i
$417$	8.78442	−	33.2045i	0.430175	−	1.62603i
$418$	−2.92872	−	5.07269i	−0.143248	−	0.248113i
$419$	−8.65843	+	14.9968i	−0.422992	+	0.732644i	−0.996231	−	0.0867448i	$-0.972354\pi$
$419$	−8.65843	+	14.9968i	−0.422992	+	0.732644i	0.573238	+	0.819389i	$0.305687\pi$
$420$	3.59180	−	6.53955i	0.175262	−	0.319097i
$421$	14.6623	+	25.3959i	0.714598	+	1.23772i	0.963114	+	0.269092i	$0.0867236\pi$
$421$	14.6623	+	25.3959i	0.714598	+	1.23772i	−0.248517	+	0.968628i	$0.579943\pi$
$422$	−6.08978	+	10.5478i	−0.296446	+	0.513459i
$423$	−8.00631	+	4.69036i	−0.389280	+	0.228053i
$424$	3.62032	+	6.27057i	0.175818	+	0.304526i
$425$	−5.72188			−0.277552
$426$	10.5920	−	2.87414i	0.513186	−	0.139252i
$427$	0.736674	+	2.56218i	0.0356502	+	0.123992i
$428$	1.22638	−	2.12415i	0.0592792	−	0.102675i
$429$	2.70064	+	2.68357i	0.130388	+	0.129564i
$430$	−2.91835	+	5.05473i	−0.140735	+	0.243761i
$431$	11.6728	+	20.2178i	0.562258	+	0.973859i	0.997299	+	0.0734485i	$0.0234005\pi$
$431$	11.6728	+	20.2178i	0.562258	+	0.973859i	−0.435041	+	0.900411i	$0.643266\pi$
$432$	6.94002	−	7.07327i	0.333902	−	0.340313i
$433$	−4.00111			−0.192281			−0.0961406	−	0.995368i	$-0.530650\pi$
$433$	−4.00111			−0.192281			−0.0961406	+	0.995368i	$0.530650\pi$
$434$	−1.14813	−	3.99322i	−0.0551118	−	0.191681i
$435$	0.629499	−	2.37946i	0.0301822	−	0.114086i
$436$	−12.1791	−	21.0949i	−0.583274	−	1.01026i
$437$	3.04408			0.145618
$438$	11.9699	+	11.8942i	0.571942	+	0.568328i
$439$	−4.14749			−0.197949			−0.0989745	−	0.995090i	$-0.531556\pi$
$439$	−4.14749			−0.197949			−0.0989745	+	0.995090i	$0.531556\pi$
$440$	−5.73387			−0.273351
$441$	−9.71457	+	18.6179i	−0.462599	+	0.886568i
$442$	−2.95948			−0.140768
$443$	−21.8505			−1.03815			−0.519075	−	0.854729i	$-0.673723\pi$
$443$	−21.8505			−1.03815			−0.519075	+	0.854729i	$0.673723\pi$
$444$	−5.60814	+	21.1984i	−0.266151	+	1.00603i
$445$	2.97846			0.141192
$446$	7.74715	+	13.4185i	0.366838	+	0.635382i
$447$	17.5928	+	17.4817i	0.832112	+	0.826854i
$448$	−0.297203	−	1.03368i	−0.0140415	−	0.0488368i
$449$	6.28701			0.296702			0.148351	−	0.988935i	$-0.452603\pi$
$449$	6.28701			0.296702			0.148351	+	0.988935i	$0.452603\pi$
$450$	−0.0115966	−	1.82940i	−0.000546668	−	0.0862389i
$451$	−13.0131	−	22.5394i	−0.612764	−	1.06134i
$452$	−10.3262	+	17.8856i	−0.485705	+	0.841266i
$453$	−4.94817	+	18.7037i	−0.232485	+	0.878778i
$454$	3.84348	−	6.65710i	0.180384	−	0.312433i
$455$	0.620081	+	2.15666i	0.0290698	+	0.101106i
$456$	3.63253	−	13.7307i	0.170109	−	0.642999i
$457$	22.8032			1.06669			0.533343	−	0.845899i	$-0.320935\pi$
$457$	22.8032			1.06669			0.533343	+	0.845899i	$0.320935\pi$
$458$	−2.52582	−	4.37486i	−0.118024	−	0.204424i
$459$	28.7905	+	7.42173i	1.34383	+	0.346417i
$460$	0.668609	−	1.15806i	0.0311740	−	0.0539950i
$461$	−0.276239	−	0.478459i	−0.0128657	−	0.0222841i	0.859521	−	0.511101i	$-0.170762\pi$
$461$	−0.276239	−	0.478459i	−0.0128657	−	0.0222841i	−0.872387	+	0.488817i	$0.837429\pi$
$462$	7.24062	−	0.154519i	0.336864	−	0.00718888i
$463$	4.80357	−	8.32002i	0.223241	−	0.386664i	−0.732550	−	0.680714i	$-0.761670\pi$
$463$	4.80357	−	8.32002i	0.223241	−	0.386664i	0.955790	+	0.294050i	$0.0950031\pi$
$464$	−1.35500	−	2.34694i	−0.0629045	−	0.108954i
$465$	3.16404	+	3.14405i	0.146729	+	0.145802i
$466$	4.40978	−	7.63797i	0.204279	−	0.353822i
$467$	9.57895	−	16.5912i	0.443261	−	0.767750i	−0.554668	−	0.832072i	$-0.687155\pi$
$467$	9.57895	−	16.5912i	0.443261	−	0.767750i	0.997929	+	0.0643211i	$0.0204882\pi$
$468$	0.0262604	+	4.14268i	0.00121389	+	0.191495i
$469$	−0.636633	−	2.21423i	−0.0293970	−	0.102244i
$470$	0.943080	+	1.63346i	0.0435010	+	0.0753460i
$471$	4.61133	−	1.25128i	0.212479	−	0.0576560i
$472$	12.5974			0.579844
$473$	24.8049			1.14053
$474$	9.96064	−	2.70281i	0.457507	−	0.124144i
$475$	1.85316	+	3.20976i	0.0850287	+	0.147274i
$476$	17.1090	−	17.7423i	0.784191	−	0.813216i
$477$	8.53349	+	4.85495i	0.390722	+	0.222293i
$478$	2.92582	−	5.06766i	0.133824	−	0.231789i
$479$	−18.8490	+	32.6474i	−0.861231	+	1.49170i	0.00951011	+	0.999955i	$0.496973\pi$
$479$	−18.8490	+	32.6474i	−0.861231	+	1.49170i	−0.870741	+	0.491741i	$0.836361\pi$
$480$	−6.86542	−	6.82204i	−0.313362	−	0.311382i
$481$	−3.29757	−	5.71156i	−0.150356	−	0.260425i
$482$	1.92803	−	3.33944i	0.0878193	−	0.152108i
$483$	−1.81191	+	3.29893i	−0.0824449	+	0.150107i
$484$	−3.48713	−	6.03988i	−0.158506	−	0.274540i
$485$	6.02424	−	10.4343i	0.273546	−	0.473796i
$486$	−2.31453	+	9.21998i	−0.104989	+	0.418227i
$487$	0.455759	+	0.789397i	0.0206524	+	0.0357710i	0.876167	−	0.482008i	$-0.160092\pi$
$487$	0.455759	+	0.789397i	0.0206524	+	0.0357710i	−0.855514	+	0.517779i	$0.826759\pi$
$488$	2.22940			0.100920
$489$	−7.00850	+	26.4916i	−0.316935	+	1.19799i
$490$	3.77189	+	1.99864i	0.170397	+	0.0902895i
$491$	−13.5035	+	23.3887i	−0.609403	+	1.05552i	0.381935	+	0.924189i	$0.375258\pi$
$491$	−13.5035	+	23.3887i	−0.609403	+	1.05552i	−0.991339	+	0.131329i	$0.958076\pi$
$492$	7.24301	−	27.3781i	0.326540	−	1.23430i
$493$	4.06552	−	7.04169i	0.183102	−	0.317142i
$494$	0.958495	+	1.66016i	0.0431247	+	0.0746943i
$495$	−6.70840	+	3.93000i	−0.301520	+	0.176641i
$496$	4.91120			0.220519
$497$	−7.59656	−	26.4211i	−0.340752	−	1.18515i
$498$	10.7683	+	10.7003i	0.482541	+	0.479492i
$499$	7.82633	+	13.5556i	0.350355	+	0.606832i	0.986312	−	0.164893i	$-0.0527277\pi$
$499$	7.82633	+	13.5556i	0.350355	+	0.606832i	−0.635957	+	0.771725i	$0.719394\pi$
$500$	1.62813			0.0728121
$501$	−7.34009	+	27.7451i	−0.327931	+	1.23956i
$502$	14.1740			0.632617
$503$	21.7298			0.968882			0.484441	−	0.874824i	$-0.339023\pi$
$503$	21.7298			0.968882			0.484441	+	0.874824i	$0.339023\pi$
$504$	12.7181	+	12.1095i	0.566508	+	0.539400i
$505$	0.183389			0.00816070
$506$	1.29801			0.0577037
$507$	15.0882	+	14.9929i	0.670091	+	0.665857i
$508$	−19.8880			−0.882387
$509$	−8.86209	−	15.3496i	−0.392805	−	0.680359i	0.600013	−	0.799990i	$-0.295162\pi$
$509$	−8.86209	−	15.3496i	−0.392805	−	0.680359i	−0.992818	+	0.119631i	$0.961829\pi$
$510$	1.54569	−	5.84260i	0.0684443	−	0.258715i
$511$	29.3409	−	30.4269i	1.29796	−	1.34600i
$512$	−19.0951			−0.843891
$513$	−5.16114	−	18.5541i	−0.227870	−	0.819185i
$514$	−3.07311	−	5.32279i	−0.135549	−	0.234778i
$515$	−5.01296	+	8.68271i	−0.220898	+	0.382606i
$516$	19.1459	+	19.0249i	0.842852	+	0.837526i
$517$	4.00793	−	6.94193i	0.176268	−	0.305306i
$518$	−12.1751	−	3.02635i	−0.534942	−	0.132970i
$519$	−1.75172	+	0.475328i	−0.0768920	+	0.0208646i
$520$	1.87655			0.0822921
$521$	17.8247	+	30.8733i	0.780915	+	1.35259i	0.931409	+	0.363974i	$0.118580\pi$
$521$	17.8247	+	30.8733i	0.780915	+	1.35259i	−0.150494	+	0.988611i	$0.548086\pi$
$522$	2.25962	+	1.28556i	0.0989007	+	0.0562675i
$523$	−7.63530	+	13.2247i	−0.333868	+	0.578277i	−0.983267	−	0.182171i	$-0.941687\pi$
$523$	−7.63530	+	13.2247i	−0.333868	+	0.578277i	0.649399	+	0.760448i	$0.275021\pi$
$524$	11.8540	+	20.5317i	0.517844	+	0.896933i
$525$	−4.58153	+	0.0977725i	−0.199954	+	0.00426714i
$526$	−6.59407	+	11.4213i	−0.287515	+	0.497991i
$527$	7.36772	+	12.7613i	0.320943	+	0.555889i
$528$	−2.18936	+	8.27564i	−0.0952798	+	0.360151i
$529$	11.1627	−	19.3344i	0.485335	−	0.840626i
$530$	0.997848	−	1.72832i	0.0433437	−	0.0750735i
$531$	14.7385	−	8.63431i	0.639597	−	0.374697i
$532$	−15.4939	−	3.85131i	−0.671747	−	0.166975i
$533$	4.25887	+	7.37657i	0.184472	+	0.319515i
$534$	−0.804592	+	3.04130i	−0.0348181	+	0.131610i
$535$	−1.50649			−0.0651312
$536$	−1.92664			−0.0832182
$537$	2.27226	+	2.25791i	0.0980554	+	0.0974358i
$538$	5.89600	+	10.2122i	0.254194	+	0.440278i
$539$	−0.659029	−	18.1292i	−0.0283864	−	0.780881i
$540$	−8.19218	−	2.11181i	−0.352535	−	0.0908779i
$541$	−18.3417	+	31.7688i	−0.788573	+	1.36585i	0.138269	+	0.990395i	$0.455846\pi$
$541$	−18.3417	+	31.7688i	−0.788573	+	1.36585i	−0.926841	+	0.375453i	$0.877487\pi$
$542$	−6.94365	+	12.0267i	−0.298255	+	0.516593i
$543$	29.3159	−	7.95485i	1.25807	−	0.341375i
$544$	−15.9867	−	27.6897i	−0.685423	−	1.18719i
$545$	−7.48045	+	12.9565i	−0.320427	+	0.554996i
$546$	−2.36967	+	0.0505702i	−0.101413	+	0.00216420i
$547$	10.7334	+	18.5908i	0.458928	+	0.794887i	0.998905	−	0.0467935i	$-0.0149003\pi$
$547$	10.7334	+	18.5908i	0.458928	+	0.794887i	−0.539977	+	0.841680i	$0.681567\pi$
$548$	−16.9965	+	29.4388i	−0.726055	+	1.25756i
$549$	2.60830	−	1.52803i	0.111320	−	0.0652148i
$550$	0.790197	+	1.36866i	0.0336941	+	0.0583599i
$551$	−5.26684			−0.224375
$552$	2.23260	+	2.21849i	0.0950258	+	0.0944253i
$553$	−7.14372	−	24.8461i	−0.303782	−	1.05656i
$554$	3.96554	−	6.86852i	0.168480	−	0.291815i
$555$	12.9980	−	3.52700i	0.551735	−	0.149713i
$556$	−16.1430	+	27.9605i	−0.684616	+	1.18579i
$557$	−20.8397	−	36.0954i	−0.883006	−	1.52941i	−0.847983	−	0.530024i	$-0.822183\pi$
$557$	−20.8397	−	36.0954i	−0.883006	−	1.52941i	−0.0350230	−	0.999387i	$-0.511150\pi$
$558$	−4.06511	+	2.38148i	−0.172090	+	0.100816i
$559$	−8.11802			−0.343356
$560$	−3.50237	+	3.63200i	−0.148002	+	0.153480i
$561$	−24.7879	+	6.72618i	−1.04655	+	0.283979i
$562$	−1.49357	−	2.58694i	−0.0630025	−	0.109123i
$563$	−31.6328			−1.33316			−0.666582	−	0.745432i	$-0.732243\pi$
$563$	−31.6328			−1.33316			−0.666582	+	0.745432i	$0.732243\pi$
$564$	8.41789	−	2.28419i	0.354457	−	0.0961816i
$565$	12.6848			0.533654
$566$	−6.50855			−0.273575
$567$	23.1795	+	5.45065i	0.973449	+	0.228906i
$568$	−22.9895			−0.964616
$569$	−17.0906			−0.716475			−0.358237	−	0.933630i	$-0.616622\pi$
$569$	−17.0906			−0.716475			−0.358237	+	0.933630i	$0.616622\pi$
$570$	−3.77809	+	1.02518i	−0.158247	+	0.0429402i
$571$	9.58708			0.401207			0.200603	−	0.979673i	$-0.435710\pi$
$571$	9.58708			0.401207			0.200603	+	0.979673i	$0.435710\pi$
$572$	−1.78940	−	3.09933i	−0.0748185	−	0.129589i
$573$	24.4995	−	6.64793i	1.02348	−	0.277721i
$574$	15.7243	+	3.90857i	0.656319	+	0.163141i
$575$	−0.821322			−0.0342515
$576$	−1.05229	+	0.616467i	−0.0438454	+	0.0256861i
$577$	−1.38408	−	2.39729i	−0.0576199	−	0.0998007i	0.835777	−	0.549070i	$-0.185018\pi$
$577$	−1.38408	−	2.39729i	−0.0576199	−	0.0998007i	−0.893397	+	0.449269i	$0.851684\pi$
$578$	4.79919	−	8.31245i	0.199620	−	0.345752i
$579$	−32.3909	+	8.78924i	−1.34612	+	0.365268i
$580$	−1.15682	+	2.00367i	−0.0480344	+	0.0831980i
$581$	26.3957	−	27.3727i	1.09508	−	1.13561i
$582$	9.02707	+	8.97003i	0.374184	+	0.371820i
$583$	−8.48135			−0.351262
$584$	−17.6736	−	30.6115i	−0.731337	−	1.26671i
$585$	2.19549	−	1.28619i	0.0907723	−	0.0531774i
$586$	2.70998	−	4.69382i	0.111948	−	0.193900i
$587$	−3.93124	−	6.80910i	−0.162260	−	0.281042i	0.773419	−	0.633895i	$-0.218545\pi$
$587$	−3.93124	−	6.80910i	−0.162260	−	0.281042i	−0.935679	+	0.352853i	$0.885212\pi$
$588$	13.3961	−	14.4987i	0.552446	−	0.597915i
$589$	4.77240	−	8.26604i	0.196643	−	0.340596i
$590$	−1.73608	−	3.00698i	−0.0714733	−	0.123795i
$591$	23.6044	−	6.40504i	0.970956	−	0.263468i
$592$	7.41441	−	12.8421i	0.304730	−	0.527809i
$593$	−13.2930	+	23.0242i	−0.545878	+	0.945489i	0.452673	+	0.891677i	$0.350471\pi$
$593$	−13.2930	+	23.0242i	−0.545878	+	0.945489i	−0.998551	+	0.0538121i	$0.982863\pi$
$594$	−2.20074	−	7.91158i	−0.0902974	−	0.324616i
$595$	−14.6916	−	3.65188i	−0.602297	−	0.149712i
$596$	−11.6567	−	20.1900i	−0.477478	−	0.827016i
$597$	−18.2870	−	18.1714i	−0.748436	−	0.743707i
$598$	−0.424807			−0.0173716
$599$	3.05485			0.124818			0.0624090	−	0.998051i	$-0.480122\pi$
$599$	3.05485			0.124818			0.0624090	+	0.998051i	$0.480122\pi$
$600$	−0.980091	+	3.70468i	−0.0400121	+	0.151243i
$601$	6.02622	+	10.4377i	0.245815	+	0.425764i	0.962360	−	0.271777i	$-0.0876112\pi$
$601$	6.02622	+	10.4377i	0.245815	+	0.425764i	−0.716546	+	0.697540i	$0.754278\pi$
$602$	−10.7193	+	11.1160i	−0.436885	+	0.453055i
$603$	−2.25409	+	1.32052i	−0.0917938	+	0.0537759i
$604$	9.09318	−	15.7499i	0.369996	−	0.640852i
$605$	−2.14180	+	3.70971i	−0.0870766	+	0.150821i
$606$	−0.0495401	+	0.187258i	−0.00201243	+	0.00760685i
$607$	−1.29212	−	2.23801i	−0.0524454	−	0.0908380i	0.838611	−	0.544731i	$-0.183368\pi$
$607$	−1.29212	−	2.23801i	−0.0524454	−	0.0908380i	−0.891056	+	0.453893i	$0.850035\pi$
$608$	−10.3553	+	17.9359i	−0.419962	+	0.727396i
$609$	3.13496	−	5.70778i	0.127035	−	0.231291i
$610$	−0.307238	−	0.532151i	−0.0124397	−	0.0215462i
$611$	−1.31169	+	2.27192i	−0.0530654	+	0.0919119i
$612$	−24.2916	−	13.8202i	−0.981931	−	0.558649i
$613$	22.7845	+	39.4640i	0.920259	+	1.59393i	0.799014	+	0.601312i	$0.205355\pi$
$613$	22.7845	+	39.4640i	0.920259	+	1.59393i	0.121244	+	0.992623i	$0.461312\pi$
$614$	17.7624			0.716832
$615$	−16.7871	+	4.55518i	−0.676923	+	0.183682i
$616$	−14.7224	−	3.65953i	−0.593182	−	0.147447i
$617$	3.71170	−	6.42886i	0.149428	−	0.258816i	−0.781588	−	0.623794i	$-0.785590\pi$
$617$	3.71170	−	6.42886i	0.149428	−	0.258816i	0.931016	+	0.364978i	$0.118924\pi$
$618$	−7.51172	−	7.46425i	−0.302166	−	0.300256i
$619$	3.68391	−	6.38072i	0.148069	−	0.256463i	−0.782445	−	0.622720i	$-0.786028\pi$
$619$	3.68391	−	6.38072i	0.148069	−	0.256463i	0.930514	+	0.366257i	$0.119361\pi$
$620$	−2.09644	−	3.63114i	−0.0841951	−	0.145830i
$621$	4.13261	+	1.06532i	0.165836	+	0.0427498i
$622$	9.08554			0.364297
$623$	7.64754	+	1.90094i	0.306392	+	0.0761597i
$624$	0.716523	−	2.70841i	0.0286839	−	0.108423i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−8.35441			−0.333909
$627$	11.8013	+	11.7267i	0.471297	+	0.468319i
$628$	−4.49140			−0.179226
$629$	44.4920			1.77401
$630$	1.13781	−	4.70461i	0.0453313	−	0.187436i
$631$	−37.8581			−1.50711			−0.753554	−	0.657386i	$-0.771662\pi$
$631$	−37.8581			−1.50711			−0.753554	+	0.657386i	$0.771662\pi$
$632$	−21.6190			−0.859959
$633$	8.84752	−	33.4430i	0.351657	−	1.32924i
$634$	−11.3521			−0.450849
$635$	6.10763	+	10.5787i	0.242374	+	0.419804i
$636$	−6.54641	−	6.50504i	−0.259582	−	0.257942i
$637$	0.215684	+	5.93324i	0.00854569	+	0.235083i
$638$	−2.24581			−0.0889125
$639$	−26.8967	+	15.7570i	−1.06402	+	0.623338i
$640$	5.71186	+	9.89323i	0.225781	+	0.391064i
$641$	3.80737	−	6.59457i	0.150382	−	0.260470i	−0.780986	−	0.624549i	$-0.785283\pi$
$641$	3.80737	−	6.59457i	0.150382	−	0.260470i	0.931368	+	0.364079i	$0.118616\pi$
$642$	0.406958	−	1.53827i	0.0160614	−	0.0607109i
$643$	8.97170	−	15.5394i	0.353809	−	0.612815i	−0.633104	−	0.774067i	$-0.718220\pi$
$643$	8.97170	−	15.5394i	0.353809	−	0.612815i	0.986913	+	0.161251i	$0.0515529\pi$
$644$	2.45584	−	2.54674i	0.0967738	−	0.100356i
$645$	4.23991	−	16.0266i	0.166946	−	0.631046i
$646$	−12.9324			−0.508817
$647$	17.2402	+	29.8610i	0.677784	+	1.17396i	0.975647	+	0.219347i	$0.0703928\pi$
$647$	17.2402	+	29.8610i	0.677784	+	1.17396i	−0.297863	+	0.954609i	$0.596274\pi$
$648$	9.73675	−	17.3694i	0.382496	−	0.682335i
$649$	−7.37804	+	12.7791i	−0.289613	+	0.501625i
$650$	−0.258611	−	0.447928i	−0.0101436	−	0.0175692i
$651$	6.11742	+	10.0921i	0.239761	+	0.395541i
$652$	12.8794	−	22.3078i	0.504397	−	0.873642i
$653$	6.05053	+	10.4798i	0.236775	+	0.410107i	0.959787	−	0.280729i	$-0.0905761\pi$
$653$	6.05053	+	10.4798i	0.236775	+	0.410107i	−0.723012	+	0.690836i	$0.757243\pi$
$654$	−11.2091	−	11.1383i	−0.438312	−	0.435543i
$655$	7.28076	−	12.6106i	0.284483	−	0.492739i
$656$	−9.57583	+	16.5858i	−0.373873	+	0.647568i
$657$	−41.6586	−	23.7008i	−1.62526	−	0.924655i
$658$	1.37894	+	4.79601i	0.0537568	+	0.186968i
$659$	−4.89965	−	8.48645i	−0.190863	−	0.330585i	0.754673	−	0.656101i	$-0.227795\pi$
$659$	−4.89965	−	8.48645i	−0.190863	−	0.330585i	−0.945537	+	0.325516i	$0.894462\pi$
$660$	7.05326	−	1.91390i	0.274548	−	0.0744983i
$661$	−23.2408			−0.903961			−0.451981	−	0.892028i	$-0.649282\pi$
$661$	−23.2408			−0.903961			−0.451981	+	0.892028i	$0.649282\pi$
$662$	15.4483			0.600417
$663$	8.11245	−	2.20131i	0.315062	−	0.0854917i
$664$	−15.8995	−	27.5388i	−0.617021	−	1.06871i
$665$	2.70963	+	9.42419i	0.105075	+	0.365454i
$666$	0.0901725	+	14.2250i	0.00349411	+	0.551209i
$667$	0.583568	−	1.01077i	0.0225958	−	0.0391372i
$668$	13.4888	−	23.3633i	0.521897	−	0.903952i
$669$	−31.2171	−	31.0198i	−1.20692	−	1.19930i
$670$	0.265515	+	0.459885i	0.0102577	+	0.0177669i
$671$	−1.30571	+	2.26155i	−0.0504062	+	0.0873062i
$672$	−13.2737	−	21.8981i	−0.512046	−	0.844738i
$673$	25.6329	+	44.3975i	0.988076	+	1.71140i	0.627376	+	0.778716i	$0.284129\pi$
$673$	25.6329	+	44.3975i	0.988076	+	1.71140i	0.360700	+	0.932682i	$0.382538\pi$
$674$	−0.272644	+	0.472233i	−0.0105019	+	0.0181897i
$675$	1.39253	+	5.00608i	0.0535983	+	0.192684i
$676$	−9.99720	−	17.3157i	−0.384508	−	0.665987i
$677$	7.31177			0.281014			0.140507	−	0.990080i	$-0.455127\pi$
$677$	7.31177			0.281014			0.140507	+	0.990080i	$0.455127\pi$
$678$	−3.42664	+	12.9524i	−0.131599	+	0.497436i
$679$	22.1274	−	22.9464i	0.849172	−	0.880602i
$680$	−6.32977	+	10.9635i	−0.242736	+	0.420431i
$681$	−5.58399	+	21.1071i	−0.213979	+	0.808826i
$682$	2.03498	−	3.52469i	0.0779233	−	0.134967i
$683$	−4.08644	−	7.07792i	−0.156363	−	0.270829i	0.777191	−	0.629264i	$-0.216644\pi$
$683$	−4.08644	−	7.07792i	−0.156363	−	0.270829i	−0.933555	+	0.358435i	$0.883310\pi$
$684$	0.114753	+	18.1027i	0.00438769	+	0.692174i
$685$	20.8786			0.797730
$686$	8.40919	+	7.53909i	0.321064	+	0.287844i
$687$	10.1778	+	10.1135i	0.388307	+	0.385853i
$688$	−9.12647	−	15.8075i	−0.347943	−	0.602655i
$689$	2.77573			0.105747
$690$	0.221870	−	0.838652i	0.00844643	−	0.0319269i
$691$	33.9086			1.28995			0.644973	−	0.764206i	$-0.276869\pi$
$691$	33.9086			1.28995			0.644973	+	0.764206i	$0.276869\pi$
$692$	1.70616			0.0648585
$693$	−19.7329	+	5.80924i	−0.749589	+	0.220675i
$694$	−6.24242			−0.236959
$695$	19.8301			0.752200
$696$	−3.86283	−	3.83842i	−0.146420	−	0.145495i
$697$	−57.4622			−2.17653
$698$	−5.24007	−	9.07606i	−0.198339	−	0.343534i
$699$	−6.40674	+	24.2170i	−0.242325	+	0.915972i
$700$	4.18041	+	1.03912i	0.158005	+	0.0392751i
$701$	−17.5312			−0.662144			−0.331072	−	0.943606i	$-0.607410\pi$
$701$	−17.5312			−0.662144			−0.331072	+	0.943606i	$0.607410\pi$
$702$	0.720246	+	2.58926i	0.0271839	+	0.0977253i
$703$	−14.4097	−	24.9584i	−0.543474	−	0.941325i
$704$	0.526772	−	0.912396i	0.0198535	−	0.0343872i
$705$	−3.80014	−	3.77612i	−0.143121	−	0.142217i
$706$	−6.01540	+	10.4190i	−0.226392	+	0.392123i
$707$	0.470873	+	0.117044i	0.0177090	+	0.00440191i
$708$	−15.4962	+	4.20487i	−0.582382	+	0.158029i
$709$	19.0692			0.716160			0.358080	−	0.933691i	$-0.383432\pi$
$709$	19.0692			0.716160			0.358080	+	0.933691i	$0.383432\pi$
$710$	3.16823	+	5.48753i	0.118901	+	0.205943i
$711$	−25.2934	+	14.8177i	−0.948577	+	0.555708i
$712$	3.29489	−	5.70692i	0.123481	−	0.213876i
$713$	1.05757	+	1.83176i	0.0396062	+	0.0686000i
$714$	7.69767	−	14.0151i	0.288078	−	0.524501i
$715$	−1.09905	+	1.90362i	−0.0411022	+	0.0711912i
$716$	−1.50556	−	2.60771i	−0.0562656	−	0.0974548i
$717$	−4.25076	+	16.0676i	−0.158748	+	0.600055i
$718$	6.83226	−	11.8338i	0.254978	−	0.441634i
$719$	15.5912	−	27.0047i	0.581452	−	1.00710i	−0.413856	−	0.910343i	$-0.635818\pi$
$719$	15.5912	−	27.0047i	0.581452	−	1.00710i	0.995308	−	0.0967619i	$-0.0308485\pi$
$720$	4.97270	+	2.82912i	0.185322	+	0.105435i
$721$	−18.4129	+	19.0944i	−0.685734	+	0.711114i
$722$	−1.60479	−	2.77958i	−0.0597242	−	0.103445i
$723$	−2.80113	+	10.5881i	−0.104175	+	0.393775i
$724$	−28.5535			−1.06118
$725$	1.42105			0.0527763
$726$	−3.20940	−	3.18912i	−0.119112	−	0.118359i
$727$	−7.47472	−	12.9466i	−0.277222	−	0.480162i	0.693471	−	0.720484i	$-0.256080\pi$
$727$	−7.47472	−	12.9466i	−0.277222	−	0.480162i	−0.970693	+	0.240322i	$0.922747\pi$
$728$	4.81826	+	1.19767i	0.178577	+	0.0443887i
$729$	−0.513421	−	26.9951i	−0.0190156	−	0.999819i
$730$	−4.87126	+	8.43728i	−0.180294	+	0.312278i
$731$	27.3828	−	47.4285i	1.01279	−	1.75420i
$732$	−2.74239	+	0.744145i	−0.101362	+	0.0275044i
$733$	21.3405	+	36.9629i	0.788231	+	1.36526i	0.927050	+	0.374938i	$0.122336\pi$
$733$	21.3405	+	36.9629i	0.788231	+	1.36526i	−0.138819	+	0.990318i	$0.544331\pi$
$734$	5.64764	−	9.78200i	0.208458	−	0.361060i
$735$	−11.8260	−	2.67303i	−0.436210	−	0.0985963i
$736$	−2.29474	−	3.97460i	−0.0845852	−	0.146506i
$737$	1.12839	−	1.95443i	0.0415648	−	0.0719923i
$738$	−0.116459	−	18.3719i	−0.00428692	−	0.676278i
$739$	20.0227	+	34.6804i	0.736548	+	1.27574i	0.954041	+	0.299676i	$0.0968786\pi$
$739$	20.0227	+	34.6804i	0.736548	+	1.27574i	−0.217493	+	0.976062i	$0.569788\pi$
$740$	−12.6600			−0.465389
$741$	−3.86225	−	3.83785i	−0.141883	−	0.140987i
$742$	3.66516	−	3.80082i	0.134552	−	0.139532i
$743$	−13.8153	+	23.9289i	−0.506836	+	0.877865i	0.493133	+	0.869954i	$0.335852\pi$
$743$	−13.8153	+	23.9289i	−0.506836	+	0.877865i	−0.999969	+	0.00791113i	$0.997482\pi$
$744$	9.52439	−	2.58444i	0.349181	−	0.0947500i
$745$	−7.15959	+	12.4008i	−0.262307	+	0.454329i
$746$	3.35991	+	5.81953i	0.123015	+	0.213068i
$747$	−37.4769	−	21.3217i	−1.37121	−	0.780121i
$748$	24.1432			0.882763
$749$	−3.86809	−	0.961487i	−0.141337	−	0.0351320i
$750$	1.01937	−	0.276604i	0.0372220	−	0.0101002i
$751$	7.59477	+	13.1545i	0.277137	+	0.480016i	0.970672	−	0.240407i	$-0.0772810\pi$
$751$	7.59477	+	13.1545i	0.277137	+	0.480016i	−0.693535	+	0.720423i	$0.743948\pi$
$752$	−5.89854			−0.215098
$753$	−38.8534	+	10.5428i	−1.41590	+	0.384202i
$754$	0.734997			0.0267670
$755$	−11.1701			−0.406522
$756$	−19.6866	−	10.6508i	−0.715993	−	0.387367i
$757$	−3.51810			−0.127867			−0.0639337	−	0.997954i	$-0.520365\pi$
$757$	−3.51810			−0.127867			−0.0639337	+	0.997954i	$0.520365\pi$
$758$	8.14052			0.295677
$759$	−3.55807	+	0.965480i	−0.129150	+	0.0350447i
$760$	8.20016			0.297451
$761$	7.24407	+	12.5471i	0.262597	+	0.454832i	0.966931	−	0.255037i	$-0.0820876\pi$
$761$	7.24407	+	12.5471i	0.262597	+	0.454832i	−0.704334	+	0.709869i	$0.748754\pi$
$762$	−12.4518	+	3.37879i	−0.451082	+	0.122401i
$763$	−27.4762	+	28.4931i	−0.994704	+	1.03152i
$764$	−23.8623			−0.863309
$765$	0.108811	+	17.1653i	0.00393406	+	0.620612i
$766$	8.18444	+	14.1759i	0.295716	+	0.512195i
$767$	2.41464	−	4.18229i	0.0871877	−	0.151014i
$768$	−10.2859	+	2.79106i	−0.371159	+	0.100714i
$769$	3.48120	−	6.02962i	0.125535	−	0.217434i	−0.796407	−	0.604761i	$-0.793268\pi$
$769$	3.48120	−	6.02962i	0.125535	−	0.217434i	0.921942	+	0.387328i	$0.126602\pi$
$770$	1.15540	+	4.01853i	0.0416378	+	0.144818i
$771$	12.3831	+	12.3048i	0.445966	+	0.443148i
$772$	31.5484			1.13545
$773$	−4.97387	−	8.61499i	−0.178898	−	0.309860i	0.762606	−	0.646864i	$-0.223920\pi$
$773$	−4.97387	−	8.61499i	−0.178898	−	0.309860i	−0.941503	+	0.337004i	$0.890586\pi$
$774$	15.2194	+	8.65874i	0.547049	+	0.311232i
$775$	−1.28764	+	2.23026i	−0.0462534	+	0.0801132i
$776$	−13.3285	−	23.0857i	−0.478466	−	0.828727i
$777$	35.6250	−	0.760258i	1.27804	−	0.0272741i
$778$	8.44441	−	14.6261i	0.302747	−	0.524373i
$779$	18.6104	+	32.2342i	0.666787	+	1.15491i
$780$	−2.30835	+	0.626369i	−0.0826523	+	0.0224276i
$781$	13.4644	−	23.3210i	0.481794	−	0.834492i
$782$	1.43291	−	2.48187i	0.0512408	−	0.0887517i
$783$	−7.15021	−	1.84321i	−0.255528	−	0.0658709i
$784$	−11.3108	+	7.09026i	−0.403957	+	0.253224i
$785$	1.37931	+	2.38904i	0.0492298	+	0.0852686i
$786$	10.9099	+	10.8410i	0.389144	+	0.386685i
$787$	−5.30529			−0.189113			−0.0945565	−	0.995519i	$-0.530143\pi$
$787$	−5.30529			−0.189113			−0.0945565	+	0.995519i	$0.530143\pi$
$788$	−22.9905			−0.819003
$789$	9.58017	−	36.2124i	0.341063	−	1.28920i
$790$	2.97937	+	5.16041i	0.106001	+	0.183599i
$791$	32.5697	+	8.09583i	1.15805	+	0.287855i
$792$	0.109039	+	17.2013i	0.00387452	+	0.611220i
$793$	0.427324	−	0.740148i	0.0151747	−	0.0262834i
$794$	−5.23315	+	9.06408i	−0.185717	+	0.321672i
$795$	−1.44972	+	5.47984i	−0.0514163	+	0.194350i
$796$	12.1167	+	20.9867i	0.429463	+	0.743852i
$797$	22.7137	−	39.3413i	0.804561	−	1.39354i	−0.112025	−	0.993705i	$-0.535734\pi$
$797$	22.7137	−	39.3413i	0.804561	−	1.39354i	0.916587	−	0.399836i	$-0.130933\pi$
$798$	−10.3550	+	0.220982i	−0.366563	+	0.00782267i
$799$	−8.84891	−	15.3268i	−0.313052	−	0.542222i
$800$	2.79396	−	4.83927i	0.0987812	−	0.171094i
$801$	−0.0566402	−	8.93519i	−0.00200128	−	0.315710i
$802$	9.88203	+	17.1162i	0.348947	+	0.604393i
$803$	41.4040			1.46112
$804$	2.36997	−	0.643089i	0.0835824	−	0.0226800i
$805$	−2.10884	−	0.524193i	−0.0743269	−	0.0184754i
$806$	−0.665997	+	1.15354i	−0.0234587	+	0.0406317i
$807$	−23.7579	−	23.6078i	−0.836317	−	0.831032i
$808$	0.202872	−	0.351385i	0.00713702	−	0.0123617i
$809$	−15.7751	−	27.3232i	−0.554622	−	0.960633i	−0.997933	−	0.0642652i	$-0.979530\pi$
$809$	−15.7751	−	27.3232i	−0.554622	−	0.960633i	0.443311	−	0.896368i	$-0.353804\pi$
$810$	−5.48788	+	0.0695781i	−0.192825	+	0.00244473i
$811$	0.692971			0.0243335			0.0121668	−	0.999926i	$-0.496127\pi$
$811$	0.692971			0.0243335			0.0121668	+	0.999926i	$0.496127\pi$
$812$	−4.24908	+	4.40635i	−0.149114	+	0.154633i
$813$	10.0881	−	38.1322i	0.353804	−	1.33735i
$814$	−6.14440	−	10.6424i	−0.215361	−	0.373016i
$815$	−15.8212			−0.554191
$816$	13.4066	+	13.3219i	0.469325	+	0.466360i
$817$	−35.4742			−1.24108
$818$	2.44506			0.0854895
$819$	6.45806	−	1.90122i	0.225663	−	0.0664339i
$820$	16.3505			0.570985
$821$	32.6165			1.13833			0.569163	−	0.822225i	$-0.307268\pi$
$821$	32.6165			1.13833			0.569163	+	0.822225i	$0.307268\pi$
$822$	−5.64008	+	21.3191i	−0.196720	+	0.743590i
$823$	22.4748			0.783423			0.391711	−	0.920088i	$-0.371883\pi$
$823$	22.4748			0.783423			0.391711	+	0.920088i	$0.371883\pi$
$824$	11.0911	+	19.2103i	0.386376	+	0.669223i
$825$	−3.18409	−	3.16397i	−0.110856	−	0.110155i
$826$	−2.53845	−	8.82879i	−0.0883238	−	0.307193i
$827$	2.64312			0.0919105			0.0459552	−	0.998944i	$-0.485367\pi$
$827$	2.64312			0.0919105			0.0459552	+	0.998944i	$0.485367\pi$
$828$	−3.48684	−	1.98376i	−0.121176	−	0.0689405i
$829$	−4.44867	−	7.70532i	−0.154509	−	0.267617i	0.778371	−	0.627804i	$-0.216046\pi$
$829$	−4.44867	−	7.70532i	−0.154509	−	0.267617i	−0.932880	+	0.360187i	$0.882713\pi$
$830$	−4.38229	+	7.59035i	−0.152112	+	0.263465i
$831$	−5.76132	+	21.7774i	−0.199858	+	0.755450i
$832$	−0.172399	+	0.298604i	−0.00597686	+	0.0103522i
$833$	−35.3917	−	18.7532i	−1.22625	−	0.649761i
$834$	−5.35686	+	20.2486i	−0.185493	+	0.701150i
$835$	−16.5697			−0.573418
$836$	−7.81932	−	13.5435i	−0.270437	−	0.468410i
$837$	9.37179	−	9.55172i	0.323936	−	0.330156i
$838$	5.28003	−	9.14528i	0.182396	−	0.315918i
$839$	−1.64205	−	2.84412i	−0.0566900	−	0.0981900i	0.836288	−	0.548291i	$-0.184721\pi$
$839$	−1.64205	−	2.84412i	−0.0566900	−	0.0981900i	−0.892978	+	0.450101i	$0.851388\pi$
$840$	−4.88094	+	8.88668i	−0.168408	+	0.306619i
$841$	13.4903	−	23.3659i	0.465183	−	0.805721i
$842$	−8.94128	−	15.4868i	−0.308137	−	0.533709i
$843$	6.01833	+	5.98030i	0.207282	+	0.205973i
$844$	−16.2590	+	28.1614i	−0.559657	+	0.969354i
$845$	−6.14031	+	10.6353i	−0.211233	+	0.365866i
$846$	4.88236	−	2.86025i	0.167859	−	0.0983373i
$847$	−7.86698	+	8.15815i	−0.270313	+	0.280318i
$848$	3.12054	+	5.40494i	0.107160	+	0.185606i
$849$	17.8410	−	4.84115i	0.612303	−	0.166148i
$850$	3.48928			0.119681
$851$	6.38642			0.218924
$852$	28.2794	−	7.67360i	0.968837	−	0.262893i
$853$	9.58073	+	16.5943i	0.328038	+	0.568178i	0.982122	−	0.188243i	$-0.0602793\pi$
$853$	9.58073	+	16.5943i	0.328038	+	0.568178i	−0.654084	+	0.756421i	$0.726946\pi$
$854$	−0.449234	−	1.56245i	−0.0153725	−	0.0534659i
$855$	9.59386	−	5.62040i	0.328103	−	0.192214i
$856$	−1.66654	+	2.88653i	−0.0569611	+	0.0986596i
$857$	21.3322	−	36.9485i	0.728695	−	1.26214i	−0.228739	−	0.973488i	$-0.573460\pi$
$857$	21.3322	−	36.9485i	0.728695	−	1.26214i	0.957435	−	0.288650i	$-0.0932063\pi$
$858$	−1.64689	−	1.63648i	−0.0562237	−	0.0558685i
$859$	19.7581	+	34.2220i	0.674138	+	1.16764i	0.976720	+	0.214518i	$0.0688180\pi$
$859$	19.7581	+	34.2220i	0.674138	+	1.16764i	−0.302582	+	0.953123i	$0.597849\pi$
$860$	−7.79163	+	13.4955i	−0.265692	+	0.460193i
$861$	−46.0102	+	0.981885i	−1.56802	+	0.0334625i
$862$	−7.11822	−	12.3291i	−0.242447	−	0.419931i
$863$	7.46972	−	12.9379i	0.254272	−	0.440412i	−0.710425	−	0.703773i	$-0.751497\pi$
$863$	7.46972	−	12.9379i	0.254272	−	0.440412i	0.964698	+	0.263360i	$0.0848307\pi$
$864$	−20.3351	+	20.7256i	−0.691816	+	0.705099i
$865$	−0.523964	−	0.907533i	−0.0178153	−	0.0308570i
$866$	2.43993			0.0829123
$867$	−6.97249	+	26.3555i	−0.236798	+	0.895081i
$868$	−3.06535	−	10.6614i	−0.104045	−	0.361872i
$869$	12.6618	−	21.9309i	0.429522	−	0.743953i
$870$	−0.383877	+	1.45103i	−0.0130146	+	0.0491945i
$871$	−0.369293	+	0.639635i	−0.0125130	+	0.0216732i
$872$	16.5504	+	28.6660i	0.560466	+	0.970755i
$873$	−31.4168	−	17.8739i	−1.06330	−	0.604941i
$874$	−1.85632			−0.0627910
$875$	−0.731085	−	2.54274i	−0.0247152	−	0.0859602i
$876$	31.9581	+	31.7561i	1.07976	+	1.07294i
$877$	8.17999	+	14.1682i	0.276219	+	0.478425i	0.970442	−	0.241335i	$-0.0775852\pi$
$877$	8.17999	+	14.1682i	0.276219	+	0.478425i	−0.694223	+	0.719760i	$0.744252\pi$
$878$	2.52920			0.0853563
$879$	−3.93718	+	14.8823i	−0.132798	+	0.501967i
$880$	−4.94232			−0.166606
$881$	−16.4786			−0.555177			−0.277588	−	0.960700i	$-0.589535\pi$
$881$	−16.4786			−0.555177			−0.277588	+	0.960700i	$0.589535\pi$
$882$	5.92408	−	11.3535i	0.199474	−	0.382291i
$883$	5.23072			0.176028			0.0880139	−	0.996119i	$-0.471948\pi$
$883$	5.23072			0.176028			0.0880139	+	0.996119i	$0.471948\pi$
$884$	−7.90146			−0.265755
$885$	6.99553	+	6.95132i	0.235152	+	0.233666i
$886$	13.3247			0.447653
$887$	−3.78286	−	6.55210i	−0.127016	−	0.219998i	0.795503	−	0.605949i	$-0.207207\pi$
$887$	−3.78286	−	6.55210i	−0.127016	−	0.219998i	−0.922519	+	0.385951i	$0.873873\pi$
$888$	7.62097	−	28.8068i	0.255743	−	0.966692i
$889$	8.93039	+	31.0602i	0.299516	+	1.04173i
$890$	−1.81630			−0.0608827
$891$	11.9173	+	20.0501i	0.399246	+	0.671702i
$892$	20.6839	+	35.8256i	0.692549	+	1.19953i
$893$	−5.73184	+	9.92784i	−0.191809	+	0.332222i
$894$	−10.7283	−	10.6606i	−0.358810	−	0.356542i
$895$	−0.924721	+	1.60166i	−0.0309100	+	0.0535377i
$896$	8.35171	+	29.0475i	0.279011	+	0.970410i
$897$	1.16447	−	0.315977i	0.0388804	−	0.0105502i
$898$	−3.83390			−0.127939
$899$	−1.82979	−	3.16930i	−0.0610271	−	0.105702i
$900$	−0.0309615	−	4.88428i	−0.00103205	−	0.162809i
$901$	−9.36280	+	16.2168i	−0.311920	+	0.540261i
$902$	7.93558	+	13.7448i	0.264226	+	0.457653i
$903$	21.1151	−	38.4441i	0.702667	−	1.27934i
$904$	14.0324	−	24.3049i	0.466712	−	0.808369i
$905$	8.76881	+	15.1880i	0.291485	+	0.504867i
$906$	3.01746	−	11.4058i	0.100248	−	0.378932i
$907$	4.65614	−	8.06467i	0.154605	−	0.267783i	−0.778310	−	0.627880i	$-0.783923\pi$
$907$	4.65614	−	8.06467i	0.154605	−	0.267783i	0.932915	+	0.360097i	$0.117256\pi$
$908$	10.2616	−	17.7736i	0.340544	−	0.589839i
$909$	−0.00348743	−	0.550156i	−0.000115671	−	0.0182475i
$910$	−0.378134	−	1.31516i	−0.0125350	−	0.0435972i
$911$	−1.89020	−	3.27392i	−0.0626251	−	0.108470i	0.833013	−	0.553253i	$-0.186614\pi$
$911$	−1.89020	−	3.27392i	−0.0626251	−	0.108470i	−0.895638	+	0.444784i	$0.853281\pi$
$912$	3.13107	−	11.8352i	0.103680	−	0.391903i
$913$	37.2480			1.23273
$914$	−13.9057			−0.459959
$915$	1.23801	+	1.23019i	0.0409274	+	0.0406688i
$916$	−6.74364	−	11.6803i	−0.222816	−	0.385929i
$917$	26.7427	−	27.7325i	0.883122	−	0.915808i
$918$	−17.5569	−	4.52587i	−0.579463	−	0.149376i
$919$	7.78230	−	13.4793i	0.256714	−	0.444642i	−0.708645	−	0.705565i	$-0.750693\pi$
$919$	7.78230	−	13.4793i	0.256714	−	0.444642i	0.965360	+	0.260923i	$0.0840267\pi$
$920$	−0.908580	+	1.57371i	−0.0299550	+	0.0518836i
$921$	−48.6897	+	13.2119i	−1.60438	+	0.435347i
$922$	0.168454	+	0.291771i	0.00554774	+	0.00960896i
$923$	−4.40656	+	7.63238i	−0.145044	+	0.251223i
$924$	19.3316	−	0.412547i	0.635962	−	0.0135718i
$925$	3.88789	+	6.73402i	0.127833	+	0.221413i
$926$	−2.92928	+	5.07366i	−0.0962621	+	0.166731i
$927$	26.1429	+	14.8735i	0.858646	+	0.488509i
$928$	3.97034	+	6.87682i	0.130333	+	0.225743i
$929$	−42.4750			−1.39356			−0.696780	−	0.717285i	$-0.745385\pi$
$929$	−42.4750			−1.39356			−0.696780	+	0.717285i	$0.745385\pi$
$930$	−1.92948	−	1.91728i	−0.0632700	−	0.0628702i
$931$	0.942495	+	25.9271i	0.0308890	+	0.849726i
$932$	11.7736	−	20.3924i	0.385656	−	0.667976i
$933$	−24.9050	+	6.75795i	−0.815354	+	0.221245i
$934$	−5.84137	+	10.1176i	−0.191136	+	0.331057i
$935$	−7.41441	−	12.8421i	−0.242477	−	0.419983i
$936$	−0.0356856	−	5.62954i	−0.00116642	−	0.184007i
$937$	−35.8902			−1.17248			−0.586241	−	0.810137i	$-0.699393\pi$
$937$	−35.8902			−1.17248			−0.586241	+	0.810137i	$0.699393\pi$
$938$	0.388227	+	1.35027i	0.0126761	+	0.0440878i
$939$	22.9009	−	6.21413i	0.747341	−	0.202790i
$940$	2.51791	+	4.36114i	0.0821251	+	0.142245i
$941$	0.270822			0.00882855			0.00441428	−	0.999990i	$-0.498595\pi$
$941$	0.270822			0.00882855			0.00441428	+	0.999990i	$0.498595\pi$
$942$	−2.81205	+	0.763048i	−0.0916217	+	0.0248615i
$943$	−8.24816			−0.268597
$944$	10.8584			0.353411
$945$	0.380437	+	13.7425i	0.0123756	+	0.447042i
$946$	−15.1264			−0.491801
$947$	37.1417			1.20694			0.603472	−	0.797384i	$-0.293783\pi$
$947$	37.1417			1.20694			0.603472	+	0.797384i	$0.293783\pi$
$948$	26.5937	−	7.21617i	0.863722	−	0.234370i
$949$	−13.5505			−0.439867
$950$	−1.13008	−	1.95736i	−0.0366647	−	0.0635051i
$951$	31.1180	−	8.44384i	1.00907	−	0.273810i
$952$	−23.2497	+	24.1102i	−0.753526	+	0.781416i
$953$	−2.96964			−0.0961960			−0.0480980	−	0.998843i	$-0.515316\pi$
$953$	−2.96964			−0.0961960			−0.0480980	+	0.998843i	$0.515316\pi$
$954$	−5.20384	−	2.96062i	−0.168481	−	0.0958535i
$955$	7.32816	+	12.6927i	0.237134	+	0.410727i
$956$	7.81157	−	13.5300i	0.252644	−	0.437592i
$957$	6.15615	−	1.67047i	0.199000	−	0.0539985i
$958$	11.4944	−	19.9088i	0.371366	−	0.643224i
$959$	53.6083	+	13.3254i	1.73110	+	0.430298i
$960$	−0.499462	−	0.496306i	−0.0161201	−	0.0160182i
$961$	−24.3679			−0.786062
$962$	2.01090	+	3.48299i	0.0648342	+	0.112296i
$963$	0.0286483	+	4.51938i	0.000923179	+	0.145635i
$964$	5.14760	−	8.91591i	0.165793	−	0.287162i
$965$	−9.68857	−	16.7811i	−0.311886	−	0.540202i
$966$	1.10493	−	2.01173i	0.0355505	−	0.0647265i
$967$	8.85857	−	15.3435i	0.284872	−	0.493413i	−0.687706	−	0.725989i	$-0.741382\pi$
$967$	8.85857	−	15.3435i	0.284872	−	0.493413i	0.972578	+	0.232576i	$0.0747154\pi$
$968$	4.73870	+	8.20767i	0.152308	+	0.263804i
$969$	35.4498	−	9.61928i	1.13881	−	0.309016i
$970$	−3.67366	+	6.36297i	−0.117954	+	0.204303i
$971$	2.00281	−	3.46897i	0.0642733	−	0.111325i	−0.832098	−	0.554629i	$-0.812860\pi$
$971$	2.00281	−	3.46897i	0.0642733	−	0.111325i	0.896371	+	0.443304i	$0.146194\pi$
$972$	−6.17952	+	24.6162i	−0.198208	+	0.789565i
$973$	50.9162	+	12.6562i	1.63230	+	0.405739i
$974$	−0.277928	−	0.481385i	−0.00890538	−	0.0154246i
$975$	1.04207	+	1.03549i	0.0333730	+	0.0331622i
$976$	1.92163			0.0615099
$977$	−39.9497			−1.27810			−0.639052	−	0.769163i	$-0.720673\pi$
$977$	−39.9497			−1.27810			−0.639052	+	0.769163i	$0.720673\pi$
$978$	4.27388	−	16.1550i	0.136664	−	0.516579i
$979$	3.85949	+	6.68483i	0.123350	+	0.213648i
$980$	10.0705	+	5.33613i	0.321690	+	0.170456i
$981$	39.0110	+	22.1945i	1.24553	+	0.708616i
$982$	8.23461	−	14.2628i	0.262777	−	0.455143i
$983$	−20.9695	+	36.3202i	−0.668823	+	1.15844i	0.309410	+	0.950929i	$0.399868\pi$
$983$	−20.9695	+	36.3202i	−0.668823	+	1.15844i	−0.978234	+	0.207507i	$0.933465\pi$
$984$	−9.84261	+	37.2044i	−0.313771	+	1.18603i
$985$	7.06041	+	12.2290i	0.224963	+	0.389648i
$986$	−2.47921	+	4.29412i	−0.0789542	+	0.136753i
$987$	−7.34726	−	12.1210i	−0.233866	−	0.385816i
$988$	2.55906	+	4.43243i	0.0814147	+	0.141014i
$989$	3.93055	−	6.80792i	0.124984	−	0.216479i
$990$	4.09087	−	2.39657i	0.130017	−	0.0761680i
$991$	−1.22348	−	2.11912i	−0.0388650	−	0.0673162i	0.845939	−	0.533280i	$-0.179041\pi$
$991$	−1.22348	−	2.11912i	−0.0388650	−	0.0673162i	−0.884804	+	0.465964i	$0.845708\pi$
$992$	−14.3904			−0.456897
$993$	−42.3465	+	11.4907i	−1.34383	+	0.364646i
$994$	4.63249	+	16.1119i	0.146934	+	0.511039i
$995$	7.44208	−	12.8901i	0.235930	−	0.408642i
$996$	28.7502	+	28.5685i	0.910984	+	0.905227i
$997$	1.98710	−	3.44176i	0.0629321	−	0.109002i	−0.832843	−	0.553510i	$-0.813288\pi$
$997$	1.98710	−	3.44176i	0.0629321	−	0.109002i	0.895775	+	0.444508i	$0.146622\pi$
$998$	−4.77260	−	8.26639i	−0.151074	−	0.261668i
$999$	−10.8280	−	38.9262i	−0.342582	−	1.23157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.b.121.5	yes	24
3.2	odd	2		945.2.l.b.226.8		24
7.4	even	3		315.2.k.b.256.8	yes	24
9.2	odd	6		945.2.k.b.856.5		24
9.7	even	3		315.2.k.b.16.8	✓	24
21.11	odd	6		945.2.k.b.361.5		24
63.11	odd	6		945.2.l.b.46.8		24
63.25	even	3	inner	315.2.l.b.151.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.8	✓	24	9.7	even	3
315.2.k.b.256.8	yes	24	7.4	even	3
315.2.l.b.121.5	yes	24	1.1	even	1	trivial
315.2.l.b.151.5	yes	24	63.25	even	3	inner
945.2.k.b.361.5		24	21.11	odd	6
945.2.k.b.856.5		24	9.2	odd	6
945.2.l.b.46.8		24	63.11	odd	6
945.2.l.b.226.8		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)

\(f(q)\)	\(=\)	\(q-0.609814 q^{2} +(1.67160 - 0.453588i) q^{3} -1.62813 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.01937 + 0.276604i) q^{6} +(0.731085 + 2.54274i) q^{7} +2.21248 q^{8} +(2.58852 - 1.51644i) q^{9} +O(q^{10})\)	\(q-0.609814 q^{2} +(1.67160 - 0.453588i) q^{3} -1.62813 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.01937 + 0.276604i) q^{6} +(0.731085 + 2.54274i) q^{7} +2.21248 q^{8} +(2.58852 - 1.51644i) q^{9} +(-0.304907 - 0.528114i) q^{10} +(-1.29580 + 2.24439i) q^{11} +(-2.72158 + 0.738499i) q^{12} +(0.424083 - 0.734533i) q^{13} +(-0.445826 - 1.55060i) q^{14} +(1.22862 + 1.22086i) q^{15} +1.90705 q^{16} +(2.86094 + 4.95529i) q^{17} +(-1.57851 + 0.924745i) q^{18} +(1.85316 - 3.20976i) q^{19} +(-0.814064 - 1.41000i) q^{20} +(2.37544 + 3.91884i) q^{21} +(0.790197 - 1.36866i) q^{22} +(0.410661 + 0.711286i) q^{23} +(3.69839 - 1.00356i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.258611 + 0.447928i) q^{26} +(3.63913 - 3.70900i) q^{27} +(-1.19030 - 4.13990i) q^{28} +(-0.710523 - 1.23066i) q^{29} +(-0.749230 - 0.744495i) q^{30} +2.57528 q^{31} -5.58791 q^{32} +(-1.14803 + 4.33949i) q^{33} +(-1.74464 - 3.02180i) q^{34} +(-1.83653 + 1.90451i) q^{35} +(-4.21443 + 2.46896i) q^{36} +(3.88789 - 6.73402i) q^{37} +(-1.13008 + 1.95736i) q^{38} +(0.375723 - 1.42021i) q^{39} +(1.10624 + 1.91607i) q^{40} +(-5.02127 + 8.69709i) q^{41} +(-1.44858 - 2.38976i) q^{42} +(-4.78564 - 8.28897i) q^{43} +(2.10973 - 3.65416i) q^{44} +(2.60753 + 1.48350i) q^{45} +(-0.250427 - 0.433752i) q^{46} -3.09301 q^{47} +(3.18784 - 0.865017i) q^{48} +(-5.93103 + 3.71792i) q^{49} +(0.304907 - 0.528114i) q^{50} +(7.03001 + 6.98559i) q^{51} +(-0.690460 + 1.19591i) q^{52} +(1.63632 + 2.83418i) q^{53} +(-2.21919 + 2.26180i) q^{54} -2.59160 q^{55} +(1.61751 + 5.62576i) q^{56} +(1.64183 - 6.20602i) q^{57} +(0.433286 + 0.750474i) q^{58} +5.69381 q^{59} +(-2.00035 - 1.98771i) q^{60} +1.00764 q^{61} -1.57044 q^{62} +(5.74833 + 5.47327i) q^{63} -0.406523 q^{64} +0.848165 q^{65} +(0.700087 - 2.64628i) q^{66} -0.870806 q^{67} +(-4.65797 - 8.06784i) q^{68} +(1.00909 + 1.00272i) q^{69} +(1.11994 - 1.16139i) q^{70} -10.3908 q^{71} +(5.72704 - 3.35509i) q^{72} +(-7.98812 - 13.8358i) q^{73} +(-2.37089 + 4.10650i) q^{74} +(-0.442983 + 1.67445i) q^{75} +(-3.01718 + 5.22590i) q^{76} +(-6.65424 - 1.65404i) q^{77} +(-0.229121 + 0.866061i) q^{78} -9.77140 q^{79} +(0.953527 + 1.65156i) q^{80} +(4.40083 - 7.85065i) q^{81} +(3.06204 - 5.30361i) q^{82} +(-7.18628 - 12.4470i) q^{83} +(-3.86752 - 6.38037i) q^{84} +(-2.86094 + 4.95529i) q^{85} +(2.91835 + 5.05473i) q^{86} +(-1.74593 - 1.73489i) q^{87} +(-2.86693 + 4.96568i) q^{88} +(1.48923 - 2.57942i) q^{89} +(-1.59011 - 0.904659i) q^{90} +(2.17776 + 0.541325i) q^{91} +(-0.668609 - 1.15806i) q^{92} +(4.30485 - 1.16812i) q^{93} +1.88616 q^{94} +3.70632 q^{95} +(-9.34077 + 2.53461i) q^{96} +(-6.02424 - 10.4343i) q^{97} +(3.61682 - 2.26724i) q^{98} +(0.0492835 + 7.77465i) 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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