LMFDB - Embedded newform 315.2.be.b.236.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (of order $6$, 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:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			236.15
Character	$\chi$	$=$	315.236
Dual form			315.2.be.b.311.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.36259 - 1.36404i) q^{2} +(-1.43297 + 0.972928i) q^{3} +(2.72121 - 4.71328i) q^{4} +1.00000 q^{5} +(-2.05841 + 4.25326i) q^{6} +(1.49231 + 2.18472i) q^{7} -9.39122i q^{8} +(1.10682 - 2.78836i) q^{9} +O(q^{10})$	\(q+(2.36259 - 1.36404i) q^{2} +(-1.43297 + 0.972928i) q^{3} +(2.72121 - 4.71328i) q^{4} +1.00000 q^{5} +(-2.05841 + 4.25326i) q^{6} +(1.49231 + 2.18472i) q^{7} -9.39122i q^{8} +(1.10682 - 2.78836i) q^{9} +(2.36259 - 1.36404i) q^{10} +0.284157i q^{11} +(0.686259 + 9.40155i) q^{12} +(-2.89807 + 1.67320i) q^{13} +(6.50577 + 3.12602i) q^{14} +(-1.43297 + 0.972928i) q^{15} +(-7.36758 - 12.7610i) q^{16} +(-2.65611 - 4.60051i) q^{17} +(-1.18847 - 8.09749i) q^{18} +(0.743281 + 0.429133i) q^{19} +(2.72121 - 4.71328i) q^{20} +(-4.26402 - 1.67873i) q^{21} +(0.387602 + 0.671346i) q^{22} +7.91127i q^{23} +(9.13698 + 13.4574i) q^{24} +1.00000 q^{25} +(-4.56463 + 7.90618i) q^{26} +(1.12683 + 5.07250i) q^{27} +(14.3581 - 1.08860i) q^{28} +(-1.98489 - 1.14598i) q^{29} +(-2.05841 + 4.25326i) q^{30} +(0.992032 + 0.572750i) q^{31} +(-18.5470 - 10.7081i) q^{32} +(-0.276464 - 0.407189i) q^{33} +(-12.5506 - 7.24607i) q^{34} +(1.49231 + 2.18472i) q^{35} +(-10.1304 - 12.8045i) q^{36} +(-4.53064 + 7.84730i) q^{37} +2.34142 q^{38} +(2.52495 - 5.21727i) q^{39} -9.39122i q^{40} +(3.15733 + 5.46865i) q^{41} +(-12.3640 + 1.85015i) q^{42} +(0.223973 - 0.387932i) q^{43} +(1.33931 + 0.773252i) q^{44} +(1.10682 - 2.78836i) q^{45} +(10.7913 + 18.6911i) q^{46} +(-3.00982 - 5.21316i) q^{47} +(22.9731 + 11.1181i) q^{48} +(-2.54600 + 6.52057i) q^{49} +(2.36259 - 1.36404i) q^{50} +(8.28210 + 4.00821i) q^{51} +18.2126i q^{52} +(0.483757 - 0.279297i) q^{53} +(9.58133 + 10.4472i) q^{54} +0.284157i q^{55} +(20.5172 - 14.0146i) q^{56} +(-1.48262 + 0.108223i) q^{57} -6.25264 q^{58} +(4.59808 - 7.96411i) q^{59} +(0.686259 + 9.40155i) q^{60} +(-6.96542 + 4.02149i) q^{61} +3.12502 q^{62} +(7.74351 - 1.74301i) q^{63} -28.9550 q^{64} +(-2.89807 + 1.67320i) q^{65} +(-1.20859 - 0.584912i) q^{66} +(-0.802881 + 1.39063i) q^{67} -28.9113 q^{68} +(-7.69710 - 11.3366i) q^{69} +(6.50577 + 3.12602i) q^{70} -8.30424i q^{71} +(-26.1861 - 10.3944i) q^{72} +(3.55813 - 2.05429i) q^{73} +24.7199i q^{74} +(-1.43297 + 0.972928i) q^{75} +(4.04525 - 2.33553i) q^{76} +(-0.620803 + 0.424051i) q^{77} +(-1.15115 - 15.7704i) q^{78} +(-2.29456 - 3.97429i) q^{79} +(-7.36758 - 12.7610i) q^{80} +(-6.54990 - 6.17243i) q^{81} +(14.9189 + 8.61345i) q^{82} +(2.29623 - 3.97719i) q^{83} +(-19.5156 + 15.5293i) q^{84} +(-2.65611 - 4.60051i) q^{85} -1.22203i q^{86} +(3.95925 - 0.289002i) q^{87} +2.66858 q^{88} +(5.97567 - 10.3502i) q^{89} +(-1.18847 - 8.09749i) q^{90} +(-7.98031 - 3.83453i) q^{91} +(37.2880 + 21.5282i) q^{92} +(-1.97880 + 0.144441i) q^{93} +(-14.2219 - 8.21103i) q^{94} +(0.743281 + 0.429133i) q^{95} +(36.9956 - 2.70047i) q^{96} +(-3.69117 - 2.13110i) q^{97} +(2.87918 + 18.8783i) q^{98} +(0.792332 + 0.314511i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.36259	−	1.36404i	1.67060	−	0.964522i	0.703300	−	0.710893i	$-0.251709\pi$
$2$	2.36259	−	1.36404i	1.67060	−	0.964522i	0.967301	−	0.253629i	$-0.0816244\pi$
$3$	−1.43297	+	0.972928i	−0.827327	+	0.561720i
$3$	−1.43297	+	0.972928i	−0.827327	+	0.561720i
$4$	2.72121	−	4.71328i	1.36061	−	2.35664i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−2.05841	+	4.25326i	−0.840342	+	1.73639i
$7$	1.49231	+	2.18472i	0.564042	+	0.825746i
$7$	1.49231	+	2.18472i	0.564042	+	0.825746i
$8$		−	9.39122i		−	3.32030i
$9$	1.10682	−	2.78836i	0.368940	−	0.929453i
$10$	2.36259	−	1.36404i	0.747116	−	0.431348i
$11$			0.284157i			0.0856766i	0.999082	+	0.0428383i	$0.0136400\pi$
$11$			0.284157i			0.0856766i	−0.999082	+	0.0428383i	$0.986360\pi$
$12$	0.686259	+	9.40155i	0.198106	+	2.71399i
$13$	−2.89807	+	1.67320i	−0.803781	+	0.464063i	−0.844792	−	0.535096i	$-0.820276\pi$
$13$	−2.89807	+	1.67320i	−0.803781	+	0.464063i	0.0410106	+	0.999159i	$0.486942\pi$
$14$	6.50577	+	3.12602i	1.73874	+	0.835463i
$15$	−1.43297	+	0.972928i	−0.369992	+	0.251209i
$16$	−7.36758	−	12.7610i	−1.84189	−	3.19025i
$17$	−2.65611	−	4.60051i	−0.644200	−	1.11579i	−0.984486	−	0.175466i	$-0.943857\pi$
$17$	−2.65611	−	4.60051i	−0.644200	−	1.11579i	0.340285	−	0.940322i	$-0.389476\pi$
$18$	−1.18847	−	8.09749i	−0.280126	−	1.90860i
$19$	0.743281	+	0.429133i	0.170520	+	0.0984499i	0.582831	−	0.812593i	$-0.301945\pi$
$19$	0.743281	+	0.429133i	0.170520	+	0.0984499i	−0.412311	+	0.911043i	$0.635278\pi$
$20$	2.72121	−	4.71328i	0.608482	−	1.05392i
$21$	−4.26402	−	1.67873i	−0.930485	−	0.366329i
$22$	0.387602	+	0.671346i	0.0826370	+	0.143131i
$23$			7.91127i			1.64961i	0.565415	+	0.824807i	$0.308716\pi$
$23$			7.91127i			1.64961i	−0.565415	+	0.824807i	$0.691284\pi$
$24$	9.13698	+	13.4574i	1.86508	+	2.74697i
$25$	1.00000			0.200000
$26$	−4.56463	+	7.90618i	−0.895198	+	1.55053i
$27$	1.12683	+	5.07250i	0.216858	+	0.976203i
$28$	14.3581	−	1.08860i	2.71343	−	0.205727i
$29$	−1.98489	−	1.14598i	−0.368585	−	0.212803i	0.304255	−	0.952591i	$-0.401592\pi$
$29$	−1.98489	−	1.14598i	−0.368585	−	0.212803i	−0.672840	+	0.739788i	$0.734926\pi$
$30$	−2.05841	+	4.25326i	−0.375812	+	0.776536i
$31$	0.992032	+	0.572750i	0.178174	+	0.102869i	0.586435	−	0.809997i	$-0.300531\pi$
$31$	0.992032	+	0.572750i	0.178174	+	0.102869i	−0.408260	+	0.912866i	$0.633864\pi$
$32$	−18.5470	−	10.7081i	−3.27868	−	1.89295i
$33$	−0.276464	−	0.407189i	−0.0481263	−	0.0708825i
$34$	−12.5506	−	7.24607i	−2.15240	−	1.24269i
$35$	1.49231	+	2.18472i	0.252247	+	0.369285i
$36$	−10.1304	−	12.8045i	−1.68840	−	2.13408i
$37$	−4.53064	+	7.84730i	−0.744832	+	1.29009i	0.205441	+	0.978670i	$0.434137\pi$
$37$	−4.53064	+	7.84730i	−0.744832	+	1.29009i	−0.950273	+	0.311418i	$0.899196\pi$
$38$	2.34142			0.379829
$39$	2.52495	−	5.21727i	0.404316	−	0.835432i
$40$		−	9.39122i		−	1.48488i
$41$	3.15733	+	5.46865i	0.493092	+	0.854060i	0.999968	−	0.00795875i	$-0.00253337\pi$
$41$	3.15733	+	5.46865i	0.493092	+	0.854060i	−0.506877	+	0.862019i	$0.669200\pi$
$42$	−12.3640	+	1.85015i	−1.90780	+	0.285485i
$43$	0.223973	−	0.387932i	0.0341555	−	0.0591591i	−0.848442	−	0.529288i	$-0.822459\pi$
$43$	0.223973	−	0.387932i	0.0341555	−	0.0591591i	0.882598	+	0.470129i	$0.155793\pi$
$44$	1.33931	+	0.773252i	0.201909	+	0.116572i
$45$	1.10682	−	2.78836i	0.164995	−	0.415664i
$46$	10.7913	+	18.6911i	1.59109	+	2.75585i
$47$	−3.00982	−	5.21316i	−0.439027	−	0.760418i	0.558587	−	0.829446i	$-0.311344\pi$
$47$	−3.00982	−	5.21316i	−0.439027	−	0.760418i	−0.997615	+	0.0690279i	$0.978010\pi$
$48$	22.9731	+	11.1181i	3.31588	+	1.60475i
$49$	−2.54600	+	6.52057i	−0.363714	+	0.931511i
$50$	2.36259	−	1.36404i	0.334120	−	0.192904i
$51$	8.28210	+	4.00821i	1.15973	+	0.561261i
$52$			18.2126i			2.52563i
$53$	0.483757	−	0.279297i	0.0664491	−	0.0383644i	−0.466407	−	0.884570i	$-0.654452\pi$
$53$	0.483757	−	0.279297i	0.0664491	−	0.0383644i	0.532856	+	0.846206i	$0.321119\pi$
$54$	9.58133	+	10.4472i	1.30385	+	1.42168i
$55$			0.284157i			0.0383157i
$56$	20.5172	−	14.0146i	2.74172	−	1.87279i
$57$	−1.48262	+	0.108223i	−0.196377	+	0.0143344i
$58$	−6.25264			−0.821011
$59$	4.59808	−	7.96411i	0.598619	−	1.03684i	−0.394406	−	0.918936i	$-0.629050\pi$
$59$	4.59808	−	7.96411i	0.598619	−	1.03684i	0.993025	−	0.117903i	$-0.0376171\pi$
$60$	0.686259	+	9.40155i	0.0885957	+	1.21373i
$61$	−6.96542	+	4.02149i	−0.891831	+	0.514899i	−0.874541	−	0.484952i	$-0.838837\pi$
$61$	−6.96542	+	4.02149i	−0.891831	+	0.514899i	−0.0172898	+	0.999851i	$0.505504\pi$
$62$	3.12502			0.396877
$63$	7.74351	−	1.74301i	0.975590	−	0.219599i
$64$	−28.9550			−3.61937
$65$	−2.89807	+	1.67320i	−0.359462	+	0.207535i
$66$	−1.20859	−	0.584912i	−0.148768	−	0.0719976i
$67$	−0.802881	+	1.39063i	−0.0980875	+	0.169893i	−0.910893	−	0.412643i	$-0.864606\pi$
$67$	−0.802881	+	1.39063i	−0.0980875	+	0.169893i	0.812805	+	0.582535i	$0.197939\pi$
$68$	−28.9113			−3.50601
$69$	−7.69710	−	11.3366i	−0.926622	−	1.36477i
$70$	6.50577	+	3.12602i	0.777588	+	0.373630i
$71$		−	8.30424i		−	0.985532i	−0.870162	−	0.492766i	$-0.835986\pi$
$71$		−	8.30424i		−	0.985532i	0.870162	−	0.492766i	$-0.164014\pi$
$72$	−26.1861	−	10.3944i	−3.08606	−	1.22499i
$73$	3.55813	−	2.05429i	0.416448	−	0.240436i	−0.277109	−	0.960839i	$-0.589376\pi$
$73$	3.55813	−	2.05429i	0.416448	−	0.240436i	0.693556	+	0.720402i	$0.256043\pi$
$74$			24.7199i			2.87363i
$75$	−1.43297	+	0.972928i	−0.165465	+	0.112344i
$76$	4.04525	−	2.33553i	0.464022	−	0.267903i
$77$	−0.620803	+	0.424051i	−0.0707471	+	0.0483251i
$78$	−1.15115	−	15.7704i	−0.130342	−	1.78565i
$79$	−2.29456	−	3.97429i	−0.258158	−	0.447142i	0.707591	−	0.706623i	$-0.249782\pi$
$79$	−2.29456	−	3.97429i	−0.258158	−	0.447142i	−0.965748	+	0.259480i	$0.916449\pi$
$80$	−7.36758	−	12.7610i	−0.823720	−	1.42673i
$81$	−6.54990	−	6.17243i	−0.727766	−	0.685825i
$82$	14.9189	+	8.61345i	1.64752	+	0.951196i
$83$	2.29623	−	3.97719i	0.252044	−	0.436553i	−0.712044	−	0.702134i	$-0.752231\pi$
$83$	2.29623	−	3.97719i	0.252044	−	0.436553i	0.964088	+	0.265581i	$0.0855639\pi$
$84$	−19.5156	+	15.5293i	−2.12933	+	1.69439i
$85$	−2.65611	−	4.60051i	−0.288095	−	0.498996i
$86$		−	1.22203i		−	0.131775i
$87$	3.95925	−	0.289002i	0.424476	−	0.0309843i
$88$	2.66858			0.284472
$89$	5.97567	−	10.3502i	0.633419	−	1.09711i	−0.353428	−	0.935462i	$-0.614984\pi$
$89$	5.97567	−	10.3502i	0.633419	−	1.09711i	0.986848	−	0.161653i	$-0.0516825\pi$
$90$	−1.18847	−	8.09749i	−0.125276	−	0.853551i
$91$	−7.98031	−	3.83453i	−0.836564	−	0.401968i
$92$	37.2880	+	21.5282i	3.88754	+	2.24448i
$93$	−1.97880	+	0.144441i	−0.205192	+	0.0149778i
$94$	−14.2219	−	8.21103i	−1.46688	−	0.846903i
$95$	0.743281	+	0.429133i	0.0762590	+	0.0440281i
$96$	36.9956	−	2.70047i	3.77585	−	0.275616i
$97$	−3.69117	−	2.13110i	−0.374781	−	0.216380i	0.300764	−	0.953699i	$-0.402758\pi$
$97$	−3.69117	−	2.13110i	−0.374781	−	0.216380i	−0.675545	+	0.737319i	$0.736092\pi$
$98$	2.87918	+	18.8783i	0.290841	+	1.90699i
$99$	0.792332	+	0.314511i	0.0796324	+	0.0316095i
$100$	2.72121	−	4.71328i	0.272121	−	0.471328i
$101$	−17.4540			−1.73674			−0.868369	−	0.495919i	$-0.834831\pi$
$101$	−17.4540			−1.73674			−0.868369	+	0.495919i	$0.834831\pi$
$102$	25.0345	−	1.82738i	2.47879	−	0.180937i
$103$			6.04027i			0.595166i	0.954696	+	0.297583i	$0.0961805\pi$
$103$			6.04027i			0.595166i	−0.954696	+	0.297583i	$0.903820\pi$
$104$	15.7134	+	27.2164i	1.54083	+	2.66879i
$105$	−4.26402	−	1.67873i	−0.416126	−	0.163827i
$106$	0.761945	−	1.31973i	0.0740066	−	0.128183i
$107$	16.6602	+	9.61880i	1.61061	+	0.929884i	0.989230	+	0.146372i	$0.0467597\pi$
$107$	16.6602	+	9.61880i	1.61061	+	0.929884i	0.621377	+	0.783512i	$0.286574\pi$
$108$	26.9745	+	8.49229i	2.59562	+	0.817171i
$109$	−9.81002	−	16.9915i	−0.939630	−	1.62749i	−0.766163	−	0.642647i	$-0.777836\pi$
$109$	−9.81002	−	16.9915i	−0.939630	−	1.62749i	−0.173467	−	0.984840i	$-0.555497\pi$
$110$	0.387602	+	0.671346i	0.0369564	+	0.0640103i
$111$	−1.14258	−	15.6529i	−0.108449	−	1.48571i
$112$	16.8845	−	35.1395i	1.59544	−	3.32037i
$113$	15.1511	−	8.74750i	1.42530	−	0.822895i	0.428552	−	0.903517i	$-0.359024\pi$
$113$	15.1511	−	8.74750i	1.42530	−	0.822895i	0.996745	+	0.0806222i	$0.0256907\pi$
$114$	−3.35519	+	2.27803i	−0.314243	+	0.213357i
$115$			7.91127i			0.737730i
$116$	−10.8026	+	6.23689i	−1.00300	+	0.579081i
$117$	1.45784	+	9.93281i	0.134778	+	0.918288i
$118$		−	25.0879i		−	2.30953i
$119$	6.08708	−	12.6683i	0.558002	−	1.16130i
$120$	9.13698	+	13.4574i	0.834089	+	1.22848i
$121$	10.9193			0.992660
$122$	−10.9709	+	19.0022i	−0.993263	+	1.72038i
$123$	−9.84497	−	4.76457i	−0.887691	−	0.429607i
$124$	5.39906	−	3.11715i	0.484850	−	0.279928i
$125$	1.00000			0.0894427
$126$	15.9172	−	14.6805i	1.41801	−	1.30784i
$127$	−2.11951			−0.188076			−0.0940381	−	0.995569i	$-0.529978\pi$
$127$	−2.11951			−0.188076			−0.0940381	+	0.995569i	$0.529978\pi$
$128$	−31.3146	+	18.0795i	−2.76785	+	1.59802i
$129$	0.0564834	+	0.773806i	0.00497309	+	0.0681298i
$130$	−4.56463	+	7.90618i	−0.400345	+	0.693418i
$131$	14.0986			1.23180			0.615900	−	0.787825i	$-0.288793\pi$
$131$	14.0986			1.23180			0.615900	+	0.787825i	$0.288793\pi$
$132$	−2.67152	+	0.195005i	−0.232526	+	0.0169730i
$133$	0.171672	+	2.26426i	0.0148858	+	0.196336i
$134$			4.38065i			0.378430i
$135$	1.12683	+	5.07250i	0.0969821	+	0.436571i
$136$	−43.2044	+	24.9441i	−3.70475	+	2.13894i
$137$		−	5.70613i		−	0.487507i	−0.969837	−	0.243754i	$-0.921621\pi$
$137$		−	5.70613i		−	0.487507i	0.969837	−	0.243754i	$-0.0783788\pi$
$138$	−33.6487	−	16.2846i	−2.86437	−	1.38624i
$139$	−5.63256	+	3.25196i	−0.477747	+	0.275828i	−0.719477	−	0.694516i	$-0.755619\pi$
$139$	−5.63256	+	3.25196i	−0.477747	+	0.275828i	0.241730	+	0.970344i	$0.422285\pi$
$140$	14.3581	−	1.08860i	1.21348	−	0.0920038i
$141$	9.38502	+	4.54198i	0.790361	+	0.382504i
$142$	−11.3273	−	19.6195i	−0.950567	−	1.64643i
$143$	−0.475453	−	0.823508i	−0.0397593	−	0.0688652i
$144$	−43.7369	+	6.41929i	−3.64474	+	0.534941i
$145$	−1.98489	−	1.14598i	−0.164836	−	0.0951682i
$146$	5.60427	−	9.70687i	0.463812	−	0.803347i
$147$	−2.69570	−	11.8209i	−0.222338	−	0.974970i
$148$	24.6577	+	42.7083i	2.02685	+	3.51060i
$149$		−	9.81189i		−	0.803821i	−0.915679	−	0.401911i	$-0.868346\pi$
$149$		−	9.81189i		−	0.803821i	0.915679	−	0.401911i	$-0.131654\pi$
$150$	−2.05841	+	4.25326i	−0.168068	+	0.347277i
$151$	9.72438			0.791359			0.395680	−	0.918389i	$-0.370509\pi$
$151$	9.72438			0.791359			0.395680	+	0.918389i	$0.370509\pi$
$152$	4.03008	−	6.98031i	0.326883	−	0.566178i
$153$	−15.7677	+	2.31424i	−1.27474	+	0.187095i
$154$	−0.888279	+	1.84866i	−0.0715796	+	0.148969i
$155$	0.992032	+	0.572750i	0.0796819	+	0.0460044i
$156$	−17.7195	−	26.0981i	−1.41870	−	2.08952i
$157$	5.43947	+	3.14048i	0.434117	+	0.250637i	0.701099	−	0.713064i	$-0.252693\pi$
$157$	5.43947	+	3.14048i	0.434117	+	0.250637i	−0.266982	+	0.963701i	$0.586026\pi$
$158$	−10.8422	−	6.25974i	−0.862558	−	0.497998i
$159$	−0.421474	+	0.870886i	−0.0334251	+	0.0690657i
$160$	−18.5470	−	10.7081i	−1.46627	−	0.846552i
$161$	−17.2839	+	11.8061i	−1.36216	+	0.930450i
$162$	−23.8941	−	5.64858i	−1.87730	−	0.443794i
$163$	−9.14675	+	15.8426i	−0.716429	+	1.24089i	0.245977	+	0.969276i	$0.420891\pi$
$163$	−9.14675	+	15.8426i	−0.716429	+	1.24089i	−0.962406	+	0.271615i	$0.912442\pi$
$164$	34.3670			2.68362
$165$	−0.276464	−	0.407189i	−0.0215227	−	0.0316996i
$166$		−	12.5286i		−	0.972409i
$167$	−3.77161	−	6.53262i	−0.291856	−	0.505510i	0.682393	−	0.730986i	$-0.260939\pi$
$167$	−3.77161	−	6.53262i	−0.291856	−	0.505510i	−0.974249	+	0.225476i	$0.927606\pi$
$168$	−15.7653	+	40.0443i	−1.21632	+	3.08949i
$169$	−0.900781	+	1.56020i	−0.0692908	+	0.120015i
$170$	−12.5506	−	7.24607i	−0.962585	−	0.555749i
$171$	2.01926	−	1.59756i	0.154416	−	0.122168i
$172$	−1.21896	−	2.11129i	−0.0929445	−	0.160985i
$173$	−1.23435	−	2.13795i	−0.0938458	−	0.162546i	0.815281	−	0.579066i	$-0.196583\pi$
$173$	−1.23435	−	2.13795i	−0.0938458	−	0.162546i	−0.909126	+	0.416521i	$0.863249\pi$
$174$	8.95986	−	6.08337i	0.679245	−	0.461179i
$175$	1.49231	+	2.18472i	0.112808	+	0.165149i
$176$	3.62613	−	2.09355i	0.273330	−	0.157807i
$177$	1.15958	+	15.8860i	0.0871597	+	1.19406i
$178$		−	32.6042i		−	2.44379i
$179$	−0.894686	+	0.516547i	−0.0668720	+	0.0386085i	−0.533063	−	0.846075i	$-0.678959\pi$
$179$	−0.894686	+	0.516547i	−0.0668720	+	0.0386085i	0.466191	+	0.884684i	$0.345626\pi$
$180$	−10.1304	−	12.8045i	−0.755077	−	0.954389i
$181$			4.90430i			0.364534i	0.983249	+	0.182267i	$0.0583435\pi$
$181$			4.90430i			0.364534i	−0.983249	+	0.182267i	$0.941656\pi$
$182$	−24.0847	+	1.82605i	−1.78527	+	0.135356i
$183$	6.06864	−	12.5395i	0.448607	−	0.926949i
$184$	74.2965			5.47721
$185$	−4.53064	+	7.84730i	−0.333099	+	0.576945i
$186$	−4.47806	+	3.04042i	−0.328348	+	0.222934i
$187$	1.30727	−	0.754751i	0.0955969	−	0.0551929i
$188$	−32.7615			−2.38937
$189$	−9.40041	+	10.0316i	−0.683779	+	0.729689i
$190$	2.34142			0.169865
$191$	1.63620	−	0.944661i	0.118391	−	0.0683533i	−0.439635	−	0.898177i	$-0.644892\pi$
$191$	1.63620	−	0.944661i	0.118391	−	0.0683533i	0.558026	+	0.829823i	$0.311559\pi$
$192$	41.4917	−	28.1711i	2.99441	−	2.03308i
$193$	−6.19129	+	10.7236i	−0.445659	+	0.771904i	−0.998098	−	0.0616495i	$-0.980364\pi$
$193$	−6.19129	+	10.7236i	−0.445659	+	0.771904i	0.552439	+	0.833553i	$0.313697\pi$
$194$	−11.6276			−0.834813
$195$	2.52495	−	5.21727i	0.180816	−	0.373617i
$196$	23.8051	+	29.7439i	1.70036	+	2.12456i
$197$		−	2.13992i		−	0.152463i	−0.997090	−	0.0762316i	$-0.975711\pi$
$197$		−	2.13992i		−	0.152463i	0.997090	−	0.0762316i	$-0.0242888\pi$
$198$	2.30096	−	0.337713i	0.163522	−	0.0240002i
$199$	2.61298	−	1.50861i	0.185230	−	0.106942i	−0.404518	−	0.914530i	$-0.632561\pi$
$199$	2.61298	−	1.50861i	0.185230	−	0.106942i	0.589747	+	0.807588i	$0.299227\pi$
$200$		−	9.39122i		−	0.664059i
$201$	−0.202478	−	2.77388i	−0.0142817	−	0.195655i
$202$	−41.2366	+	23.8080i	−2.90140	+	1.67512i
$203$	−0.458440	−	6.04659i	−0.0321762	−	0.424387i
$204$	41.4291	−	28.1287i	2.90062	−	1.96940i
$205$	3.15733	+	5.46865i	0.220517	+	0.381947i
$206$	8.23918	+	14.2707i	0.574051	+	0.994285i
$207$	22.0595	+	8.75636i	1.53324	+	0.608609i
$208$	42.7036	+	24.6549i	2.96096	+	1.70951i
$209$	−0.121941	+	0.211208i	−0.00843485	+	0.0146096i
$210$	−12.3640	+	1.85015i	−0.853195	+	0.127673i
$211$	2.43826	+	4.22319i	0.167857	+	0.290736i	0.937666	−	0.347538i	$-0.112982\pi$
$211$	2.43826	+	4.22319i	0.167857	+	0.290736i	−0.769809	+	0.638274i	$0.779649\pi$
$212$		−	3.04011i		−	0.208795i
$213$	8.07943	+	11.8997i	0.553593	+	0.815357i
$214$	52.4817			3.58758
$215$	0.223973	−	0.387932i	0.0152748	−	0.0264568i
$216$	47.6370	−	10.5823i	3.24128	−	0.720035i
$217$	0.229125	+	3.02203i	0.0155540	+	0.205149i
$218$	−46.3541	−	26.7625i	−3.13949	−	1.81259i
$219$	−3.10003	+	6.40555i	−0.209481	+	0.432847i
$220$	1.33931	+	0.773252i	0.0902964	+	0.0521326i
$221$	15.3952	+	8.88841i	1.03559	+	0.597899i
$222$	−24.0507	−	35.4229i	−1.61418	−	2.37743i
$223$	−3.25079	−	1.87684i	−0.217689	−	0.125683i	0.387191	−	0.922000i	$-0.373445\pi$
$223$	−3.25079	−	1.87684i	−0.217689	−	0.125683i	−0.604880	+	0.796317i	$0.706779\pi$
$224$	−4.28372	−	56.4999i	−0.286218	−	3.77506i
$225$	1.10682	−	2.78836i	0.0737881	−	0.185891i
$226$	23.8639	−	41.3334i	1.58740	−	2.74946i
$227$	−8.57244			−0.568973			−0.284487	−	0.958680i	$-0.591823\pi$
$227$	−8.57244			−0.568973			−0.284487	+	0.958680i	$0.591823\pi$
$228$	−3.52443	+	7.28248i	−0.233411	+	0.482294i
$229$		−	1.43175i		−	0.0946126i	−0.998880	−	0.0473063i	$-0.984936\pi$
$229$		−	1.43175i		−	0.0946126i	0.998880	−	0.0473063i	$-0.0150637\pi$
$230$	10.7913	+	18.6911i	0.711557	+	1.23245i
$231$	0.477023	−	1.21165i	0.0313858	−	0.0797208i
$232$	−10.7621	+	18.6405i	−0.706568	+	1.22381i
$233$	−2.40835	−	1.39046i	−0.157777	−	0.0910923i	0.419033	−	0.907971i	$-0.362369\pi$
$233$	−2.40835	−	1.39046i	−0.157777	−	0.0910923i	−0.576809	+	0.816879i	$0.695702\pi$
$234$	16.9930	+	21.4786i	1.11087	+	1.40410i
$235$	−3.00982	−	5.21316i	−0.196339	−	0.340069i
$236$	−25.0247	−	43.3441i	−1.62897	−	2.82146i
$237$	7.15474	+	3.46261i	0.464750	+	0.224921i
$238$	−2.89874	−	38.2329i	−0.187898	−	2.47827i
$239$	−6.19653	+	3.57757i	−0.400820	+	0.231414i	−0.686838	−	0.726811i	$-0.741002\pi$
$239$	−6.19653	+	3.57757i	−0.400820	+	0.231414i	0.286018	+	0.958224i	$0.407668\pi$
$240$	22.9731	+	11.1181i	1.48291	+	0.717668i
$241$		−	26.7513i		−	1.72320i	−0.507585	−	0.861602i	$-0.669462\pi$
$241$		−	26.7513i		−	1.72320i	0.507585	−	0.861602i	$-0.330538\pi$
$242$	25.7977	−	14.8943i	1.65834	−	0.957442i
$243$	15.3912	+	2.47234i	0.987343	+	0.158601i
$244$			43.7733i			2.80230i
$245$	−2.54600	+	6.52057i	−0.162658	+	0.416584i
$246$	−29.7587	+	2.17221i	−1.89734	+	0.138495i
$247$	−2.87211			−0.182748
$248$	5.37882	−	9.31639i	0.341555	−	0.591591i
$249$	0.579084	+	7.93327i	0.0366979	+	0.502751i
$250$	2.36259	−	1.36404i	0.149423	−	0.0862695i
$251$	−9.60803			−0.606453			−0.303227	−	0.952918i	$-0.598064\pi$
$251$	−9.60803			−0.606453			−0.303227	+	0.952918i	$0.598064\pi$
$252$	12.8564	−	41.2404i	0.809879	−	2.59790i
$253$	−2.24804			−0.141333
$254$	−5.00753	+	2.89110i	−0.314201	+	0.181404i
$255$	8.28210	+	4.00821i	0.518645	+	0.251004i
$256$	−20.3674	+	35.2774i	−1.27296	+	2.20484i
$257$	9.96259			0.621449			0.310725	−	0.950500i	$-0.399428\pi$
$257$	9.96259			0.621449			0.310725	+	0.950500i	$0.399428\pi$
$258$	1.18895	+	1.75114i	0.0740207	+	0.109021i
$259$	−23.9053	+	1.81245i	−1.48540	+	0.112620i
$260$			18.2126i			1.12950i
$261$	−5.39231	+	4.26620i	−0.333776	+	0.264071i
$262$	33.3091	−	19.2310i	2.05785	−	1.18810i
$263$			13.7261i			0.846387i	0.906039	+	0.423194i	$0.139091\pi$
$263$			13.7261i			0.846387i	−0.906039	+	0.423194i	$0.860909\pi$
$264$	−3.82400	+	2.59634i	−0.235351	+	0.159794i
$265$	0.483757	−	0.279297i	0.0297169	−	0.0171571i
$266$	3.49413	+	5.11535i	0.214239	+	0.313642i
$267$	1.50700	+	20.6454i	0.0922266	+	1.26348i
$268$	4.36962	+	7.56841i	0.266917	+	0.462314i
$269$	4.29238	+	7.43463i	0.261711	+	0.453297i	0.966697	−	0.255925i	$-0.0823799\pi$
$269$	4.29238	+	7.43463i	0.261711	+	0.453297i	−0.704986	+	0.709222i	$0.749047\pi$
$270$	9.58133	+	10.4472i	0.583101	+	0.635795i
$271$	25.7871	+	14.8882i	1.56645	+	0.904393i	0.996578	+	0.0826626i	$0.0263424\pi$
$271$	25.7871	+	14.8882i	1.56645	+	0.904393i	0.569877	+	0.821730i	$0.306991\pi$
$272$	−39.1381	+	67.7893i	−2.37310	+	4.11033i
$273$	15.1663	−	2.26949i	0.917906	−	0.137356i
$274$	−7.78339	−	13.4812i	−0.470212	−	0.814431i
$275$			0.284157i			0.0171353i
$276$	−74.3782	+	5.42918i	−4.47704	+	0.326798i
$277$	−19.8539			−1.19291			−0.596453	−	0.802648i	$-0.703424\pi$
$277$	−19.8539			−1.19291			−0.596453	+	0.802648i	$0.703424\pi$
$278$	−8.87161	+	15.3661i	−0.532084	+	0.921596i
$279$	2.69503	−	2.13221i	0.161347	−	0.127652i
$280$	20.5172	−	14.0146i	1.22614	−	0.837535i
$281$	8.54068	+	4.93096i	0.509494	+	0.294157i	0.732626	−	0.680632i	$-0.238295\pi$
$281$	8.54068	+	4.93096i	0.509494	+	0.294157i	−0.223132	+	0.974788i	$0.571628\pi$
$282$	28.3684	−	2.07073i	1.68931	−	0.123310i
$283$	9.14106	+	5.27759i	0.543380	+	0.313720i	0.746448	−	0.665444i	$-0.231758\pi$
$283$	9.14106	+	5.27759i	0.543380	+	0.313720i	−0.203068	+	0.979165i	$0.565091\pi$
$284$	−39.1402	−	22.5976i	−2.32254	−	1.34092i
$285$	−1.48262	+	0.108223i	−0.0878226	+	0.00641055i
$286$	−2.24660	−	1.29707i	−0.132844	−	0.0766975i
$287$	−7.23575	+	15.0588i	−0.427113	+	0.888894i
$288$	−50.3863	+	39.8638i	−2.96904	+	2.34900i
$289$	−5.60981	+	9.71647i	−0.329989	+	0.571557i
$290$	−6.25264			−0.367167
$291$	7.36274	−	0.537438i	0.431612	−	0.0315052i
$292$		−	22.3606i		−	1.30856i
$293$	−4.31392	−	7.47192i	−0.252022	−	0.436514i	0.712061	−	0.702118i	$-0.247762\pi$
$293$	−4.31392	−	7.47192i	−0.252022	−	0.436514i	−0.964082	+	0.265604i	$0.914429\pi$
$294$	−22.4930	−	24.2508i	−1.31182	−	1.41434i
$295$	4.59808	−	7.96411i	0.267711	−	0.463689i
$296$	73.6957	+	42.5482i	4.28347	+	2.47307i
$297$	−1.44139	+	0.320197i	−0.0836377	+	0.0185797i
$298$	−13.3838	−	23.1814i	−0.775303	−	1.34286i
$299$	−13.2372	−	22.9274i	−0.765525	−	1.32593i
$300$	0.686259	+	9.40155i	0.0396212	+	0.542799i
$301$	1.18176	−	0.0895988i	0.0681155	−	0.00516439i
$302$	22.9747	−	13.2645i	1.32205	−	0.763284i
$303$	25.0111	−	16.9815i	1.43685	−	0.975561i
$304$		−	12.6467i		−	0.725337i
$305$	−6.96542	+	4.02149i	−0.398839	+	0.230270i
$306$	−34.0959	+	26.9754i	−1.94913	+	1.54208i
$307$			11.5914i			0.661558i	0.943708	+	0.330779i	$0.107311\pi$
$307$			11.5914i			0.661558i	−0.943708	+	0.330779i	$0.892689\pi$
$308$	0.309334	+	4.07995i	0.0176260	+	0.232477i
$309$	−5.87675	−	8.65555i	−0.334317	−	0.492397i
$310$	3.12502			0.177489
$311$	−2.48593	+	4.30576i	−0.140964	+	0.244157i	−0.927860	−	0.372929i	$-0.878354\pi$
$311$	−2.48593	+	4.30576i	−0.140964	+	0.244157i	0.786896	+	0.617086i	$0.211687\pi$
$312$	−48.9965	−	23.7124i	−2.77388	−	1.34245i
$313$	16.9588	−	9.79118i	0.958569	−	0.553430i	0.0628367	−	0.998024i	$-0.479985\pi$
$313$	16.9588	−	9.79118i	0.958569	−	0.553430i	0.895732	+	0.444594i	$0.146652\pi$
$314$	17.1350			0.966982
$315$	7.74351	−	1.74301i	0.436297	−	0.0982077i
$316$	−24.9759			−1.40500
$317$	1.01867	−	0.588131i	0.0572144	−	0.0330327i	−0.471120	−	0.882069i	$-0.656150\pi$
$317$	1.01867	−	0.588131i	0.0572144	−	0.0330327i	0.528334	+	0.849036i	$0.322817\pi$
$318$	0.192154	+	2.63245i	0.0107755	+	0.147621i
$319$	0.325637	−	0.564020i	0.0182322	−	0.0315791i
$320$	−28.9550			−1.61863
$321$	−33.2321	+	2.42575i	−1.85483	+	0.135392i
$322$	−24.7307	+	51.4689i	−1.37819	+	2.86825i
$323$		−	4.55930i		−	0.253686i
$324$	−46.9160	+	14.0750i	−2.60645	+	0.781944i
$325$	−2.89807	+	1.67320i	−0.160756	+	0.0928126i
$326$			49.9062i			2.76405i
$327$	30.5890	+	14.8038i	1.69157	+	0.818654i
$328$	51.3573	−	29.6512i	2.83573	−	1.63721i
$329$	6.89770	−	14.3553i	0.380283	−	0.791433i
$330$	−1.20859	−	0.584912i	−0.0665309	−	0.0321983i
$331$	15.6571	+	27.1188i	0.860590	+	1.49059i	0.871360	+	0.490644i	$0.163239\pi$
$331$	15.6571	+	27.1188i	0.860590	+	1.49059i	−0.0107695	+	0.999942i	$0.503428\pi$
$332$	−12.4971	−	21.6456i	−0.685866	−	1.18795i
$333$	16.8665	+	21.3186i	0.924277	+	1.16825i
$334$	−17.8215	−	10.2893i	−0.975150	−	0.563003i
$335$	−0.802881	+	1.39063i	−0.0438661	+	0.0759783i
$336$	9.99320	+	66.7814i	0.545174	+	3.64322i
$337$	−12.2086	−	21.1459i	−0.665043	−	1.15189i	−0.979274	−	0.202542i	$-0.935080\pi$
$337$	−12.2086	−	21.1459i	−0.665043	−	1.15189i	0.314230	−	0.949347i	$-0.398254\pi$
$338$			4.91481i			0.267330i
$339$	−13.2004	+	27.2759i	−0.716949	+	1.48142i
$340$	−28.9113			−1.56794
$341$	−0.162751	+	0.281893i	−0.00881346	+	0.0152654i
$342$	2.59153	−	6.52872i	0.140134	−	0.353033i
$343$	−18.0451	+	4.16844i	−0.974341	+	0.225075i
$344$	−3.64316	−	2.10338i	−0.196426	−	0.113406i
$345$	−7.69710	−	11.3366i	−0.414398	−	0.610344i
$346$	−5.83251	−	3.36740i	−0.313558	−	0.181033i
$347$	−15.6017	−	9.00762i	−0.837540	−	0.483554i	0.0188870	−	0.999822i	$-0.493988\pi$
$347$	−15.6017	−	9.00762i	−0.837540	−	0.483554i	−0.856427	+	0.516267i	$0.827321\pi$
$348$	9.41180	−	19.4475i	0.504526	−	1.04249i
$349$	11.6741	+	6.74005i	0.624901	+	0.360787i	0.778775	−	0.627304i	$-0.215842\pi$
$349$	11.6741	+	6.74005i	0.624901	+	0.360787i	−0.153874	+	0.988091i	$0.549175\pi$
$350$	6.50577	+	3.12602i	0.347748	+	0.167093i
$351$	−11.7530	−	12.8151i	−0.627327	−	0.684017i
$352$	3.04279	−	5.27027i	0.162181	−	0.280906i
$353$	3.23874			0.172381			0.0861903	−	0.996279i	$-0.472531\pi$
$353$	3.23874			0.172381			0.0861903	+	0.996279i	$0.472531\pi$
$354$	24.4087	+	35.9502i	1.29731	+	1.91073i
$355$		−	8.30424i		−	0.440743i
$356$	−32.5221	−	56.3300i	−1.72367	−	2.98548i
$357$	3.60268	+	24.0756i	0.190674	+	1.27421i
$358$	−1.40918	+	2.44078i	−0.0744776	+	0.128999i
$359$	−25.9750	−	14.9967i	−1.37091	−	0.791494i	−0.379865	−	0.925042i	$-0.624030\pi$
$359$	−25.9750	−	14.9967i	−1.37091	−	0.791494i	−0.991042	+	0.133548i	$0.957363\pi$
$360$	−26.1861	−	10.3944i	−1.38013	−	0.547833i
$361$	−9.13169	−	15.8165i	−0.480615	−	0.832450i
$362$	6.68967	+	11.5868i	0.351601	+	0.608991i
$363$	−15.6470	+	10.6237i	−0.821254	+	0.557597i
$364$	−39.7894	+	27.1789i	−2.08553	+	1.42456i
$365$	3.55813	−	2.05429i	0.186241	−	0.107526i
$366$	−2.76675	−	37.9036i	−0.144620	−	1.98125i
$367$			1.24882i			0.0651877i	0.999469	+	0.0325938i	$0.0103768\pi$
$367$			1.24882i			0.0651877i	−0.999469	+	0.0325938i	$0.989623\pi$
$368$	100.956	−	58.2869i	5.26269	−	3.03841i
$369$	18.7432	−	2.75095i	0.975730	−	0.143208i
$370$			24.7199i			1.28513i
$371$	1.33210	+	0.640074i	0.0691593	+	0.0332310i
$372$	−4.70394	+	9.71969i	−0.243888	+	0.503942i
$373$	10.1096			0.523457			0.261728	−	0.965142i	$-0.415708\pi$
$373$	10.1096			0.523457			0.261728	+	0.965142i	$0.415708\pi$
$374$	2.05902	−	3.56633i	0.106470	−	0.184411i
$375$	−1.43297	+	0.972928i	−0.0739984	+	0.0502418i
$376$	−48.9579	+	28.2659i	−2.52481	+	1.45770i
$377$	7.66981			0.395015
$378$	−8.52582	+	36.5230i	−0.438521	+	1.87854i
$379$	15.8027			0.811729			0.405865	−	0.913933i	$-0.366970\pi$
$379$	15.8027			0.811729			0.405865	+	0.913933i	$0.366970\pi$
$380$	4.04525	−	2.33553i	0.207517	−	0.119810i
$381$	3.03720	−	2.06213i	0.155601	−	0.105646i
$382$	2.57711	−	4.46369i	0.131857	−	0.228382i
$383$	5.90462			0.301712			0.150856	−	0.988556i	$-0.451797\pi$
$383$	5.90462			0.301712			0.150856	+	0.988556i	$0.451797\pi$
$384$	27.2829	−	56.3743i	1.39228	−	2.87684i
$385$	−0.620803	+	0.424051i	−0.0316391	+	0.0216117i
$386$			33.7807i			1.71939i
$387$	−0.833797	−	1.05389i	−0.0423843	−	0.0535721i
$388$	−20.0889	+	11.5983i	−1.01986	+	0.588816i
$389$		−	5.61909i		−	0.284899i	−0.989802	−	0.142450i	$-0.954502\pi$
$389$		−	5.61909i		−	0.284899i	0.989802	−	0.142450i	$-0.0454979\pi$
$390$	−1.15115	−	15.7704i	−0.0582907	−	0.798565i
$391$	36.3959	−	21.0132i	1.84062	−	1.06268i
$392$	61.2361	+	23.9100i	3.09289	+	1.20764i
$393$	−20.2029	+	13.7169i	−1.01910	+	0.691927i
$394$	−2.91894	−	5.05576i	−0.147054	−	0.254705i
$395$	−2.29456	−	3.97429i	−0.115452	−	0.199968i
$396$	3.63848	−	2.87863i	0.182841	−	0.144657i
$397$	−16.4935	−	9.52254i	−0.827786	−	0.477923i	0.0253078	−	0.999680i	$-0.491943\pi$
$397$	−16.4935	−	9.52254i	−0.827786	−	0.477923i	−0.853094	+	0.521757i	$0.825277\pi$
$398$	4.11560	−	7.12843i	0.206297	−	0.357316i
$399$	−2.44897	−	3.07760i	−0.122602	−	0.154073i
$400$	−7.36758	−	12.7610i	−0.368379	−	0.638051i
$401$			21.8989i			1.09358i	0.837270	+	0.546789i	$0.184150\pi$
$401$			21.8989i			1.09358i	−0.837270	+	0.546789i	$0.815850\pi$
$402$	−4.26206	−	6.27735i	−0.212572	−	0.313086i
$403$	−3.83331			−0.190951
$404$	−47.4961	+	82.2656i	−2.36302	+	4.09287i
$405$	−6.54990	−	6.17243i	−0.325467	−	0.306710i
$406$	−9.33089	−	13.6603i	−0.463084	−	0.677947i
$407$	−2.22986	−	1.28741i	−0.110530	−	0.0638147i
$408$	37.6419	−	77.7790i	1.86355	−	3.85063i
$409$	31.7418	+	18.3261i	1.56953	+	0.906168i	0.996223	+	0.0868262i	$0.0276725\pi$
$409$	31.7418	+	18.3261i	1.56953	+	0.906168i	0.573305	+	0.819342i	$0.305661\pi$
$410$	14.9189	+	8.61345i	0.736793	+	0.425388i
$411$	5.55165	+	8.17672i	0.273843	+	0.403328i
$412$	28.4695	+	16.4369i	1.40259	+	0.809787i
$413$	24.2611	−	1.83943i	1.19381	−	0.0905125i
$414$	64.0614	−	9.40234i	3.14845	−	0.462100i
$415$	2.29623	−	3.97719i	0.112718	−	0.195232i
$416$	71.6675			3.51379
$417$	4.90738	−	10.1400i	0.240315	−	0.496560i
$418$			0.665331i			0.0325424i
$419$	6.55229	+	11.3489i	0.320100	+	0.554430i	0.980508	−	0.196477i	$-0.0629500\pi$
$419$	6.55229	+	11.3489i	0.320100	+	0.554430i	−0.660408	+	0.750907i	$0.729617\pi$
$420$	−19.5156	+	15.5293i	−0.952265	+	0.757754i
$421$	1.47281	−	2.55098i	0.0717803	−	0.124327i	−0.827901	−	0.560874i	$-0.810465\pi$
$421$	1.47281	−	2.55098i	0.0717803	−	0.124327i	0.899682	+	0.436547i	$0.143799\pi$
$422$	11.5212	+	6.65176i	0.560843	+	0.323803i
$423$	−17.8675	+	2.62242i	−0.868748	+	0.127507i
$424$	−2.62294	−	4.54307i	−0.127381	−	0.220631i
$425$	−2.65611	−	4.60051i	−0.128840	−	0.223158i
$426$	35.3201	+	17.0935i	1.71126	+	0.828184i
$427$	−19.1804	−	9.21617i	−0.928205	−	0.446002i
$428$	90.6721	−	52.3496i	4.38280	−	2.53041i
$429$	1.48252	+	0.717483i	0.0715770	+	0.0346404i
$430$		−	1.22203i		−	0.0589316i
$431$	−15.9680	+	9.21911i	−0.769150	+	0.444069i	−0.832571	−	0.553918i	$-0.813132\pi$
$431$	−15.9680	+	9.21911i	−0.769150	+	0.444069i	0.0634211	+	0.997987i	$0.479799\pi$
$432$	56.4283	−	51.7515i	2.71491	−	2.48990i
$433$		−	5.22327i		−	0.251014i	−0.992093	−	0.125507i	$-0.959944\pi$
$433$		−	5.22327i		−	0.251014i	0.992093	−	0.125507i	$-0.0400558\pi$
$434$	4.66350	+	6.82729i	0.223855	+	0.327720i
$435$	3.95925	−	0.289002i	0.189831	−	0.0138566i
$436$	−106.781			−5.11387
$437$	−3.39499	+	5.88029i	−0.162404	+	0.281293i
$438$	1.41333	+	19.3622i	0.0675316	+	0.925163i
$439$	13.5381	−	7.81621i	0.646137	−	0.373048i	−0.140837	−	0.990033i	$-0.544979\pi$
$439$	13.5381	−	7.81621i	0.646137	−	0.373048i	0.786975	+	0.616985i	$0.211646\pi$
$440$	2.66858			0.127220
$441$	15.3637	+	14.3163i	0.731606	+	0.681727i
$442$	48.4966			2.30675
$443$	5.30992	−	3.06568i	0.252282	−	0.145655i	−0.368527	−	0.929617i	$-0.620138\pi$
$443$	5.30992	−	3.06568i	0.252282	−	0.145655i	0.620809	+	0.783962i	$0.286804\pi$
$444$	−76.8859	−	37.2097i	−3.64884	−	1.76590i
$445$	5.97567	−	10.3502i	0.283274	−	0.490645i
$446$	−10.2404			−0.484895
$447$	9.54626	+	14.0602i	0.451523	+	0.665023i
$448$	−43.2099	−	63.2585i	−2.04148	−	2.98868i
$449$			40.6165i			1.91681i	0.285407	+	0.958407i	$0.407871\pi$
$449$			40.6165i			1.91681i	−0.285407	+	0.958407i	$0.592129\pi$
$450$	−1.18847	−	8.09749i	−0.0560252	−	0.381719i
$451$	−1.55396	+	0.897177i	−0.0731729	+	0.0422464i
$452$		−	95.2152i		−	4.47855i
$453$	−13.9348	+	9.46113i	−0.654713	+	0.444523i
$454$	−20.2532	+	11.6932i	−0.950528	+	0.548787i
$455$	−7.98031	−	3.83453i	−0.374123	−	0.179766i
$456$	1.01634	+	13.9236i	0.0475946	+	0.652031i
$457$	−10.9639	−	18.9901i	−0.512872	−	0.888320i	−0.999889	−	0.0149271i	$-0.995248\pi$
$457$	−10.9639	−	18.9901i	−0.512872	−	0.888320i	0.487017	−	0.873392i	$-0.338085\pi$
$458$	−1.95296	−	3.38263i	−0.0912560	−	0.158060i
$459$	20.3431	−	18.6571i	0.949535	−	0.870839i
$460$	37.2880	+	21.5282i	1.73856	+	1.00376i
$461$	−14.8897	+	25.7897i	−0.693483	+	1.20115i	0.277206	+	0.960810i	$0.410591\pi$
$461$	−14.8897	+	25.7897i	−0.693483	+	1.20115i	−0.970689	+	0.240338i	$0.922742\pi$
$462$	−0.525734	−	3.51331i	−0.0244593	−	0.163454i
$463$	1.64857	+	2.85540i	0.0766153	+	0.132702i	0.901788	−	0.432180i	$-0.142255\pi$
$463$	1.64857	+	2.85540i	0.0766153	+	0.132702i	−0.825172	+	0.564881i	$0.808922\pi$
$464$			33.7723i			1.56784i
$465$	−1.97880	+	0.144441i	−0.0917646	+	0.00669829i
$466$	−7.58660			−0.351442
$467$	−16.5766	+	28.7116i	−0.767075	+	1.32861i	0.172067	+	0.985085i	$0.444955\pi$
$467$	−16.5766	+	28.7116i	−0.767075	+	1.32861i	−0.939142	+	0.343528i	$0.888378\pi$
$468$	50.7832	+	20.1581i	2.34745	+	0.931807i
$469$	−4.23629	+	0.321187i	−0.195614	+	0.0148310i
$470$	−14.2219	−	8.21103i	−0.656009	−	0.378747i
$471$	−10.8501	+	0.791993i	−0.499945	+	0.0364931i
$472$	−74.7927	−	43.1816i	−3.44261	−	1.98759i
$473$	0.110234	+	0.0636434i	0.00506855	+	0.00292633i
$474$	21.6268	−	1.57864i	0.993353	−	0.0725091i
$475$	0.743281	+	0.429133i	0.0341041	+	0.0196900i
$476$	−43.1448	−	63.1632i	−1.97754	−	2.89508i
$477$	−0.243349	−	1.65802i	−0.0111422	−	0.0759155i
$478$	−9.75990	+	16.9046i	−0.446407	+	0.773200i
$479$	−22.2625			−1.01720			−0.508599	−	0.861004i	$-0.669836\pi$
$479$	−22.2625			−1.01720			−0.508599	+	0.861004i	$0.669836\pi$
$480$	36.9956	−	2.70047i	1.68861	−	0.123259i
$481$		−	30.3227i		−	1.38260i
$482$	−36.4899	−	63.2023i	−1.66207	−	2.87879i
$483$	13.2809	−	33.7338i	0.604301	−	1.53494i
$484$	29.7136	−	51.4655i	1.35062	−	2.33934i
$485$	−3.69117	−	2.13110i	−0.167607	−	0.0967681i
$486$	39.7353	−	15.1530i	1.80243	−	0.687355i
$487$	−3.44182	−	5.96141i	−0.155964	−	0.270137i	0.777446	−	0.628950i	$-0.216515\pi$
$487$	−3.44182	−	5.96141i	−0.155964	−	0.270137i	−0.933410	+	0.358813i	$0.883182\pi$
$488$	37.7667	+	65.4138i	1.70962	+	2.96114i
$489$	−2.30671	−	31.6012i	−0.104313	−	1.42906i
$490$	2.87918	+	18.8783i	0.130068	+	0.852833i
$491$	−10.3634	+	5.98332i	−0.467694	+	0.270023i	−0.715274	−	0.698844i	$-0.753698\pi$
$491$	−10.3634	+	5.98332i	−0.467694	+	0.270023i	0.247580	+	0.968868i	$0.420365\pi$
$492$	−49.2470	+	33.4367i	−2.22023	+	1.50744i
$493$			12.1753i			0.548350i
$494$	−6.78561	+	3.91767i	−0.305299	+	0.176264i
$495$	0.792332	+	0.314511i	0.0356127	+	0.0141362i
$496$		−	16.8791i		−	0.757895i
$497$	18.1424	−	12.3925i	0.813799	−	0.555881i
$498$	12.1894	+	17.9532i	0.546222	+	0.804500i
$499$	−21.2056			−0.949291			−0.474645	−	0.880177i	$-0.657424\pi$
$499$	−21.2056			−0.949291			−0.474645	+	0.880177i	$0.657424\pi$
$500$	2.72121	−	4.71328i	0.121696	−	0.210784i
$501$	11.7604	+	5.69156i	0.525415	+	0.254280i
$502$	−22.6998	+	13.1057i	−1.01314	+	0.584938i
$503$	−10.5680			−0.471203			−0.235601	−	0.971850i	$-0.575706\pi$
$503$	−10.5680			−0.471203			−0.235601	+	0.971850i	$0.575706\pi$
$504$	−16.3690	−	72.7210i	−0.729134	−	3.23925i
$505$	−17.4540			−0.776693
$506$	−5.31120	+	3.06642i	−0.236112	+	0.136319i
$507$	−0.227167	−	3.11212i	−0.0100888	−	0.138214i
$508$	−5.76764	+	9.98985i	−0.255898	+	0.443228i
$509$	21.5549			0.955403			0.477702	−	0.878522i	$-0.341470\pi$
$509$	21.5549			0.955403			0.477702	+	0.878522i	$0.341470\pi$
$510$	25.0345	−	1.82738i	1.10855	−	0.0809177i
$511$	9.79789	+	4.70788i	0.433433	+	0.208264i
$512$			38.8098i			1.71517i
$513$	−1.33923	+	4.25385i	−0.0591283	+	0.187812i
$514$	23.5375	−	13.5894i	1.03819	−	0.599401i
$515$			6.04027i			0.266166i
$516$	3.80087	+	1.83947i	0.167324	+	0.0809781i
$517$	1.48136	−	0.855262i	0.0651500	−	0.0376144i
$518$	−54.0061	+	36.8898i	−2.37289	+	1.62085i
$519$	3.84886	+	1.86270i	0.168946	+	0.0817633i
$520$	15.7134	+	27.2164i	0.689079	+	1.19352i
$521$	−17.9132	−	31.0265i	−0.784791	−	1.35930i	−0.929124	−	0.369768i	$-0.879437\pi$
$521$	−17.9132	−	31.0265i	−0.784791	−	1.35930i	0.144333	−	0.989529i	$-0.453896\pi$
$522$	−6.92055	+	17.4346i	−0.302904	+	0.763091i
$523$	5.63357	+	3.25254i	0.246339	+	0.142224i	0.618087	−	0.786110i	$-0.287908\pi$
$523$	5.63357	+	3.25254i	0.246339	+	0.142224i	−0.371748	+	0.928334i	$0.621241\pi$
$524$	38.3653	−	66.4506i	1.67599	−	2.90291i
$525$	−4.26402	−	1.67873i	−0.186097	−	0.0732658i
$526$	18.7230	+	32.4291i	0.816359	+	1.41398i
$527$		−	6.08514i		−	0.265073i
$528$	−3.15928	+	6.52797i	−0.137490	+	0.284093i
$529$	−39.5882			−1.72122
$530$	0.761945	−	1.31973i	0.0330968	−	0.0573253i
$531$	−17.1176	−	21.6360i	−0.742838	−	0.938920i
$532$	11.1393	+	5.35240i	0.482948	+	0.232056i
$533$	−18.3003	−	10.5657i	−0.792675	−	0.457651i
$534$	31.7216	+	46.7209i	1.37273	+	2.02181i
$535$	16.6602	+	9.61880i	0.720285	+	0.415857i
$536$	13.0597	+	7.54003i	0.564094	+	0.325680i
$537$	0.779497	−	1.61066i	0.0336378	−	0.0695052i
$538$	20.2823	+	11.7100i	0.874430	+	0.504853i
$539$	−1.85287	−	0.723464i	−0.0798086	−	0.0311618i
$540$	26.9745	+	8.49229i	1.16080	+	0.365450i
$541$	−17.8864	+	30.9801i	−0.768994	+	1.33194i	0.169114	+	0.985596i	$0.445909\pi$
$541$	−17.8864	+	30.9801i	−0.768994	+	1.33194i	−0.938109	+	0.346341i	$0.887424\pi$
$542$	81.2324			3.48923
$543$	−4.77154	−	7.02773i	−0.204766	−	0.301589i
$544$			113.768i			4.87775i
$545$	−9.81002	−	16.9915i	−0.420215	−	0.727834i
$546$	32.7360	−	26.0493i	1.40097	−	1.11481i
$547$	5.55863	−	9.62783i	0.237670	−	0.411656i	−0.722375	−	0.691501i	$-0.756950\pi$
$547$	5.55863	−	9.62783i	0.237670	−	0.411656i	0.960045	+	0.279845i	$0.0902831\pi$
$548$	−26.8946	−	15.5276i	−1.14888	−	0.663306i
$549$	3.50388	+	23.8732i	0.149542	+	1.01888i
$550$	0.387602	+	0.671346i	0.0165274	+	0.0286263i
$551$	−0.983554	−	1.70356i	−0.0419008	−	0.0725743i
$552$	−106.465	+	72.2851i	−4.53144	+	3.07666i
$553$	5.25851	−	10.9438i	0.223615	−	0.465380i
$554$	−46.9066	+	27.0816i	−1.99287	+	1.15058i
$555$	−1.14258	−	15.6529i	−0.0484996	−	0.664431i
$556$			35.3971i			1.50117i
$557$	−26.1440	+	15.0942i	−1.10776	+	0.639564i	−0.938247	−	0.345965i	$-0.887552\pi$
$557$	−26.1440	+	15.0942i	−1.10776	+	0.639564i	−0.169509	+	0.985529i	$0.554218\pi$
$558$	3.45883	−	8.71367i	0.146424	−	0.368879i
$559$			1.49901i			0.0634013i
$560$	16.8845	−	35.1395i	0.713501	−	1.48492i
$561$	−1.13896	+	2.35342i	−0.0480869	+	0.0993613i
$562$	26.9041			1.13488
$563$	−10.8494	+	18.7917i	−0.457248	+	0.791978i	−0.998814	−	0.0486807i	$-0.984498\pi$
$563$	−10.8494	+	18.7917i	−0.457248	+	0.791978i	0.541566	+	0.840658i	$0.317832\pi$
$564$	46.9463	−	31.8745i	1.97679	−	1.34216i
$565$	15.1511	−	8.74750i	0.637412	−	0.368010i
$566$	28.7954			1.21036
$567$	3.71053	−	23.5209i	0.155828	−	0.987784i
$568$	−77.9869			−3.27226
$569$	18.7418	−	10.8206i	0.785699	−	0.453624i	−0.0527472	−	0.998608i	$-0.516798\pi$
$569$	18.7418	−	10.8206i	0.785699	−	0.453624i	0.838446	+	0.544984i	$0.183464\pi$
$570$	−3.35519	+	2.27803i	−0.140534	+	0.0954164i
$571$	8.70565	−	15.0786i	0.364320	−	0.631021i	−0.624347	−	0.781147i	$-0.714635\pi$
$571$	8.70565	−	15.0786i	0.364320	−	0.631021i	0.988667	+	0.150126i	$0.0479681\pi$
$572$	−5.17523			−0.216387
$573$	−1.42554	+	2.94558i	−0.0595529	+	0.123053i
$574$	3.44575	+	45.4476i	0.143823	+	1.89695i
$575$			7.91127i			0.329923i
$576$	−32.0480	+	80.7369i	−1.33533	+	3.36404i
$577$	31.1294	−	17.9726i	1.29593	−	0.748207i	0.316234	−	0.948681i	$-0.397582\pi$
$577$	31.1294	−	17.9726i	1.29593	−	0.748207i	0.979699	+	0.200474i	$0.0642482\pi$
$578$			30.6080i			1.27313i
$579$	−1.56137	−	21.3904i	−0.0648885	−	0.888953i
$580$	−10.8026	+	6.23689i	−0.448554	+	0.258973i
$581$	12.1157	−	0.918592i	0.502646	−	0.0381096i
$582$	16.6620	−	11.3128i	0.690664	−	0.468932i
$583$	0.0793642	+	0.137463i	0.00328693	+	0.00569313i
$584$	−19.2923	−	33.4152i	−0.798320	−	1.38273i
$585$	1.45784	+	9.93281i	0.0602744	+	0.410671i
$586$	−20.3840	−	11.7687i	−0.842055	−	0.486161i
$587$	21.2857	−	36.8680i	0.878556	−	1.52170i	0.0256305	−	0.999671i	$-0.491841\pi$
$587$	21.2857	−	36.8680i	0.878556	−	1.52170i	0.852926	−	0.522032i	$-0.174826\pi$
$588$	−63.0507	−	19.4615i	−2.60017	−	0.802580i
$589$	0.491572	+	0.851428i	0.0202549	+	0.0350825i
$590$		−	25.0879i		−	1.03285i
$591$	2.08199	+	3.06645i	0.0856417	+	0.126137i
$592$	133.519			5.48761
$593$	−12.0906	+	20.9416i	−0.496503	+	0.859968i	−0.999992	−	0.00403339i	$-0.998716\pi$
$593$	−12.0906	+	20.9416i	−0.496503	+	0.859968i	0.503489	+	0.864002i	$0.332049\pi$
$594$	−2.96864	+	2.72260i	−0.121805	+	0.111710i
$595$	6.08708	−	12.6683i	0.249546	−	0.519348i
$596$	−46.2462	−	26.7002i	−1.89432	−	1.09368i
$597$	−2.27657	+	4.70404i	−0.0931737	+	0.192524i
$598$	−62.5479	−	36.1120i	−2.55777	−	1.47673i
$599$	−17.4661	−	10.0840i	−0.713644	−	0.412023i	0.0987646	−	0.995111i	$-0.468511\pi$
$599$	−17.4661	−	10.0840i	−0.713644	−	0.412023i	−0.812409	+	0.583088i	$0.801844\pi$
$600$	9.13698	+	13.4574i	0.373016	+	0.549394i
$601$	5.59991	+	3.23311i	0.228425	+	0.131881i	0.609845	−	0.792520i	$-0.291232\pi$
$601$	5.59991	+	3.23311i	0.228425	+	0.131881i	−0.381420	+	0.924402i	$0.624565\pi$
$602$	2.66980	−	1.82365i	0.108813	−	0.0743266i
$603$	2.98893	+	3.77790i	0.121719	+	0.153848i
$604$	26.4621	−	45.8337i	1.07673	−	1.86495i
$605$	10.9193			0.443931
$606$	35.9275	−	74.2364i	1.45945	−	3.01565i
$607$			30.8419i			1.25184i	0.779889	+	0.625918i	$0.215276\pi$
$607$			30.8419i			1.25184i	−0.779889	+	0.625918i	$0.784724\pi$
$608$	−9.19043	−	15.9183i	−0.372721	−	0.645572i
$609$	6.53983	+	8.21856i	0.265007	+	0.333033i
$610$	−10.9709	+	19.0022i	−0.444201	+	0.769378i
$611$	17.4454	+	10.0721i	0.705764	+	0.407473i
$612$	−31.9997	+	80.6152i	−1.29351	+	3.25868i
$613$	−19.4865	−	33.7516i	−0.787052	−	1.36321i	−0.927765	−	0.373164i	$-0.878273\pi$
$613$	−19.4865	−	33.7516i	−0.787052	−	1.36321i	0.140713	−	0.990050i	$-0.455061\pi$
$614$	15.8112	+	27.3858i	0.638087	+	1.10520i
$615$	−9.84497	−	4.76457i	−0.396987	−	0.192126i
$616$	3.98236	+	5.83010i	0.160454	+	0.234901i
$617$	−6.83491	+	3.94614i	−0.275163	+	0.158866i	−0.631232	−	0.775594i	$-0.717450\pi$
$617$	−6.83491	+	3.94614i	−0.275163	+	0.158866i	0.356068	+	0.934460i	$0.384117\pi$
$618$	−25.6909	−	12.4334i	−1.03344	−	0.500143i
$619$		−	30.7413i		−	1.23560i	−0.786336	−	0.617799i	$-0.788024\pi$
$619$		−	30.7413i		−	1.23560i	0.786336	−	0.617799i	$-0.211976\pi$
$620$	5.39906	−	3.11715i	0.216832	−	0.125188i
$621$	−40.1299	+	8.91465i	−1.61036	+	0.357733i
$622$			13.5637i			0.543853i
$623$	31.5298	−	2.39053i	1.26321	−	0.0957744i
$624$	−85.1805	+	6.21769i	−3.40995	+	0.248907i
$625$	1.00000			0.0400000
$626$	26.7111	−	46.2650i	1.06759	−	1.84912i
$627$	−0.0307522	−	0.421296i	−0.00122812	−	0.0168249i
$628$	29.6039	−	17.0918i	1.18132	−	0.682038i
$629$	48.1354			1.91929
$630$	15.9172	−	14.6805i	0.634155	−	0.584884i
$631$	23.5241			0.936478			0.468239	−	0.883602i	$-0.344889\pi$
$631$	23.5241			0.936478			0.468239	+	0.883602i	$0.344889\pi$
$632$	−37.3234	+	21.5487i	−1.48465	+	0.857161i
$633$	−7.60281	−	3.67946i	−0.302185	−	0.146245i
$634$	1.60447	−	2.77902i	0.0637216	−	0.110369i
$635$	−2.11951			−0.0841103
$636$	2.95781	+	4.35639i	0.117285	+	0.172742i
$637$	−3.53175	−	23.1571i	−0.139933	−	0.917517i
$638$		−	1.77673i		−	0.0703414i
$639$	−23.1552	−	9.19130i	−0.916005	−	0.363602i
$640$	−31.3146	+	18.0795i	−1.23782	+	0.714656i
$641$			30.7331i			1.21389i	0.794745	+	0.606943i	$0.207604\pi$
$641$			30.7331i			1.21389i	−0.794745	+	0.606943i	$0.792396\pi$
$642$	−75.2048	+	51.0609i	−2.96810	+	2.01521i
$643$	−17.2128	+	9.93780i	−0.678806	+	0.391909i	−0.799405	−	0.600793i	$-0.794852\pi$
$643$	−17.2128	+	9.93780i	−0.678806	+	0.391909i	0.120599	+	0.992701i	$0.461518\pi$
$644$	8.61223	+	113.591i	0.339369	+	4.47610i
$645$	0.0564834	+	0.773806i	0.00222403	+	0.0304686i
$646$	−6.21906	−	10.7717i	−0.244686	−	0.423808i
$647$	−11.7226	−	20.3041i	−0.460861	−	0.798235i	0.538143	−	0.842854i	$-0.319126\pi$
$647$	−11.7226	−	20.3041i	−0.460861	−	0.798235i	−0.999004	+	0.0446187i	$0.985793\pi$
$648$	−57.9666	+	61.5115i	−2.27714	+	2.41640i
$649$	2.26306	+	1.30658i	0.0888328	+	0.0512876i
$650$	−4.56463	+	7.90618i	−0.179040	+	0.310106i
$651$	−3.26855	−	4.10757i	−0.128105	−	0.160988i
$652$	49.7805	+	86.2224i	1.94956	+	3.37673i
$653$			16.1529i			0.632113i	0.948740	+	0.316057i	$0.102359\pi$
$653$			16.1529i			0.632113i	−0.948740	+	0.316057i	$0.897641\pi$
$654$	92.4621	−	6.74921i	3.61556	−	0.263915i
$655$	14.0986			0.550877
$656$	46.5237	−	80.5814i	1.81645	−	3.14618i
$657$	−1.78988	−	12.1951i	−0.0698299	−	0.475775i
$658$	−3.28477	−	43.3244i	−0.128054	−	1.68896i
$659$	−4.06154	−	2.34493i	−0.158215	−	0.0913455i	0.418802	−	0.908078i	$-0.362450\pi$
$659$	−4.06154	−	2.34493i	−0.158215	−	0.0913455i	−0.577017	+	0.816732i	$0.695783\pi$
$660$	−2.67152	+	0.195005i	−0.103989	+	0.00759058i
$661$	16.3751	+	9.45416i	0.636917	+	0.367724i	0.783426	−	0.621485i	$-0.213470\pi$
$661$	16.3751	+	9.45416i	0.636917	+	0.367724i	−0.146509	+	0.989209i	$0.546804\pi$
$662$	73.9824	+	42.7138i	2.87541	+	1.66012i
$663$	−30.7087	+	2.24156i	−1.19263	+	0.0870549i
$664$	−37.3506	−	21.5644i	−1.44949	−	0.836861i
$665$	0.171672	+	2.26426i	0.00665715	+	0.0878043i
$666$	68.9280	+	27.3605i	2.67090	+	1.06020i
$667$	9.06613	−	15.7030i	0.351042	−	0.608022i
$668$	−41.0534			−1.58841
$669$	6.48433	−	0.473319i	0.250699	−	0.0182996i
$670$			4.38065i			0.169239i
$671$	−1.14273	−	1.97927i	−0.0441148	−	0.0764090i
$672$	61.1088	+	76.7951i	2.35732	+	2.96244i
$673$	13.1728	−	22.8160i	0.507775	−	0.879492i	−0.492185	−	0.870491i	$-0.663802\pi$
$673$	13.1728	−	22.8160i	0.507775	−	0.879492i	0.999959	−	0.00900082i	$-0.00286509\pi$
$674$	−57.6876	−	33.3060i	−2.22204	−	1.28290i
$675$	1.12683	+	5.07250i	0.0433717	+	0.195241i
$676$	4.90243	+	8.49126i	0.188555	+	0.326587i
$677$	−22.0887	−	38.2587i	−0.848936	−	1.47040i	−0.882159	−	0.470952i	$-0.843910\pi$
$677$	−22.0887	−	38.2587i	−0.848936	−	1.47040i	0.0332229	−	0.999448i	$-0.489423\pi$
$678$	6.01820	+	82.4475i	0.231128	+	3.16638i
$679$	−0.852530	−	11.2444i	−0.0327171	−	0.431521i
$680$	−43.2044	+	24.9441i	−1.65681	+	0.956562i
$681$	12.2841	−	8.34037i	0.470727	−	0.319604i
$682$			0.887995i			0.0340031i
$683$	10.2520	−	5.91898i	0.392281	−	0.226484i	−0.290867	−	0.956764i	$-0.593944\pi$
$683$	10.2520	−	5.91898i	0.392281	−	0.226484i	0.683148	+	0.730280i	$0.260610\pi$
$684$	−2.03492	−	13.8646i	−0.0778071	−	0.530127i
$685$		−	5.70613i		−	0.218020i
$686$	−36.9471	+	34.4625i	−1.41065	+	1.31578i
$687$	1.39299	+	2.05166i	0.0531458	+	0.0782756i
$688$	−6.60055			−0.251643
$689$	−0.934642	+	1.61885i	−0.0356070	+	0.0616732i
$690$	−33.6487	−	16.2846i	−1.28098	−	0.619945i
$691$	−34.9953	+	20.2045i	−1.33128	+	0.768616i	−0.985496	−	0.169697i	$-0.945721\pi$
$691$	−34.9953	+	20.2045i	−1.33128	+	0.768616i	−0.345786	+	0.938313i	$0.612388\pi$
$692$	−13.4357			−0.510749
$693$	0.495289	+	2.20037i	0.0188145	+	0.0835852i
$694$	−49.1470			−1.86560
$695$	−5.63256	+	3.25196i	−0.213655	+	0.123354i
$696$	−2.71409	−	37.1822i	−0.102877	−	1.40939i
$697$	16.7724	−	29.0506i	0.635300	−	1.10037i
$698$	36.7748			1.39195
$699$	4.80393	−	0.350659i	0.181701	−	0.0132632i
$700$	14.3581	−	1.08860i	0.542685	−	0.0411453i
$701$		−	30.0434i		−	1.13472i	−0.823468	−	0.567362i	$-0.807964\pi$
$701$		−	30.0434i		−	1.13472i	0.823468	−	0.567362i	$-0.192036\pi$
$702$	−45.2477	−	14.2452i	−1.70776	−	0.537650i
$703$	−6.73507	+	3.88850i	−0.254018	+	0.146657i
$704$		−	8.22776i		−	0.310095i
$705$	9.38502	+	4.54198i	0.353460	+	0.171061i
$706$	7.65180	−	4.41777i	0.287979	−	0.166265i
$707$	−26.0468	−	38.1321i	−0.979592	−	1.43411i
$708$	78.0304	+	37.7636i	2.93256	+	1.41924i
$709$	−0.901305	−	1.56111i	−0.0338492	−	0.0586286i	0.848605	−	0.529028i	$-0.177443\pi$
$709$	−0.901305	−	1.56111i	−0.0338492	−	0.0586286i	−0.882454	+	0.470399i	$0.844110\pi$
$710$	−11.3273	−	19.6195i	−0.425107	−	0.736306i
$711$	−13.6214	+	1.99922i	−0.510843	+	0.0749767i
$712$	−97.2006	−	56.1188i	−3.64275	−	2.10314i
$713$	−4.53118	+	7.84823i	−0.169694	+	0.293919i
$714$	41.3517	+	51.9664i	1.54755	+	1.94479i
$715$	−0.475453	−	0.823508i	−0.0177809	−	0.0307974i
$716$			5.62254i			0.210124i
$717$	5.39874	−	11.1553i	0.201620	−	0.416604i
$718$	−81.8242			−3.05365
$719$	13.5692	−	23.5026i	0.506047	−	0.876499i	−0.493929	−	0.869502i	$-0.664440\pi$
$719$	13.5692	−	23.5026i	0.506047	−	0.876499i	0.999976	−	0.00699644i	$-0.00222705\pi$
$720$	−43.7369	+	6.41929i	−1.62998	+	0.239233i
$721$	−13.1963	+	9.01398i	−0.491456	+	0.335698i
$722$	−43.1488	−	24.9120i	−1.60583	−	0.927128i
$723$	26.0271	+	38.3339i	0.967959	+	1.42565i
$724$	23.1154	+	13.3457i	0.859075	+	0.495987i
$725$	−1.98489	−	1.14598i	−0.0737170	−	0.0425605i
$726$	−22.4763	+	46.4424i	−0.834174	+	1.72364i
$727$	9.18421	+	5.30251i	0.340624	+	0.196659i	0.660548	−	0.750784i	$-0.270324\pi$
$727$	9.18421	+	5.30251i	0.340624	+	0.196659i	−0.319924	+	0.947443i	$0.603657\pi$
$728$	−36.0109	+	74.9449i	−1.33465	+	2.77764i
$729$	−24.4605	+	11.4317i	−0.905945	+	0.423396i
$730$	5.60427	−	9.70687i	0.207423	−	0.359268i
$731$	−2.37958			−0.0880120
$732$	−42.5883	−	62.7259i	−1.57411	−	2.31842i
$733$			44.3831i			1.63933i	0.572845	+	0.819663i	$0.305839\pi$
$733$			44.3831i			1.63933i	−0.572845	+	0.819663i	$0.694161\pi$
$734$	1.70344	+	2.95044i	0.0628750	+	0.108903i
$735$	−2.69570	−	11.8209i	−0.0994325	−	0.436020i
$736$	84.7149	−	146.730i	3.12263	−	5.40856i
$737$	−0.395158	−	0.228144i	−0.0145558	−	0.00840380i
$738$	40.5300	−	32.0658i	1.49193	−	1.18036i
$739$	21.2312	+	36.7736i	0.781004	+	1.35274i	0.931358	+	0.364106i	$0.118625\pi$
$739$	21.2312	+	36.7736i	0.781004	+	1.35274i	−0.150354	+	0.988632i	$0.548041\pi$
$740$	24.6577	+	42.7083i	0.906434	+	1.56999i
$741$	4.11565	−	2.79436i	0.151192	−	0.102653i
$742$	4.02030	−	0.304811i	0.147590	−	0.0111900i
$743$	−8.84967	+	5.10936i	−0.324663	+	0.187444i	−0.653469	−	0.756953i	$-0.726687\pi$
$743$	−8.84967	+	5.10936i	−0.324663	+	0.187444i	0.328806	+	0.944397i	$0.393354\pi$
$744$	1.35648	+	18.5833i	0.0497309	+	0.681298i
$745$		−	9.81189i		−	0.359480i
$746$	23.8849	−	13.7899i	0.874488	−	0.504886i
$747$	−8.54831	−	10.8048i	−0.312766	−	0.395325i
$748$		−	8.21536i		−	0.300383i
$749$	3.84793	+	50.7522i	0.140600	+	1.85445i
$750$	−2.05841	+	4.25326i	−0.0751625	+	0.155307i
$751$	29.9846			1.09415			0.547076	−	0.837083i	$-0.315741\pi$
$751$	29.9846			1.09415			0.547076	+	0.837083i	$0.315741\pi$
$752$	−44.3502	+	76.8167i	−1.61728	+	2.80122i
$753$	13.7680	−	9.34792i	0.501735	−	0.340657i
$754$	18.1206	−	10.4619i	0.659913	−	0.381001i
$755$	9.72438			0.353907
$756$	21.7011	+	71.6048i	0.789260	+	2.60424i
$757$	−39.0362			−1.41879			−0.709397	−	0.704809i	$-0.751033\pi$
$757$	−39.0362			−1.41879			−0.709397	+	0.704809i	$0.751033\pi$
$758$	37.3352	−	21.5555i	1.35608	−	0.782931i
$759$	3.22138	−	2.18718i	0.116929	−	0.0793898i
$760$	4.03008	−	6.98031i	0.146187	−	0.253203i
$761$	9.67729			0.350801			0.175401	−	0.984497i	$-0.443878\pi$
$761$	9.67729			0.350801			0.175401	+	0.984497i	$0.443878\pi$
$762$	4.36282	−	9.01484i	0.158048	−	0.326573i
$763$	22.4819	−	46.7887i	0.813901	−	1.69387i
$764$		−	10.2825i		−	0.372008i
$765$	−15.7677	+	2.31424i	−0.570083	+	0.0836714i
$766$	13.9502	−	8.05414i	0.504040	−	0.291008i
$767$			30.7741i			1.11119i
$768$	−5.13643	−	70.3675i	−0.185345	−	2.53917i
$769$	4.16188	−	2.40286i	0.150081	−	0.0866494i	−0.423079	−	0.906093i	$-0.639051\pi$
$769$	4.16188	−	2.40286i	0.150081	−	0.0866494i	0.573160	+	0.819443i	$0.305717\pi$
$770$	−0.888279	+	1.84866i	−0.0320114	+	0.0666211i
$771$	−14.2761	+	9.69288i	−0.514142	+	0.349081i
$772$	33.6957	+	58.3626i	1.21273	+	2.10052i
$773$	−7.44040	−	12.8872i	−0.267613	−	0.463519i	0.700632	−	0.713523i	$-0.252901\pi$
$773$	−7.44040	−	12.8872i	−0.267613	−	0.463519i	−0.968245	+	0.250004i	$0.919568\pi$
$774$	−3.40746	−	1.35257i	−0.122479	−	0.0486171i
$775$	0.992032	+	0.572750i	0.0356348	+	0.0205738i
$776$	−20.0136	+	34.6645i	−0.718446	+	1.24438i
$777$	32.4922	−	25.8553i	1.16565	−	0.927554i
$778$	−7.66467	−	13.2756i	−0.274792	−	0.475953i
$779$			5.41966i			0.194179i
$780$	−17.7195	−	26.0981i	−0.634461	−	0.934463i
$781$	2.35971			0.0844370
$782$	57.3256	−	99.2909i	2.04996	−	3.55064i
$783$	3.57633	−	11.3597i	0.127808	−	0.405962i
$784$	101.967	−	15.5513i	3.64168	−	0.555403i
$785$	5.43947	+	3.14048i	0.194143	+	0.112088i
$786$	−29.0207	+	59.9650i	−1.03513	+	2.13888i
$787$	−40.9130	−	23.6211i	−1.45839	−	0.842002i	−0.459458	−	0.888199i	$-0.651956\pi$
$787$	−40.9130	−	23.6211i	−1.45839	−	0.842002i	−0.998932	+	0.0461971i	$0.985290\pi$
$788$	−10.0861	−	5.82319i	−0.359301	−	0.207442i
$789$	−13.3545	−	19.6691i	−0.475433	−	0.700239i
$790$	−10.8422	−	6.25974i	−0.385748	−	0.222711i
$791$	41.7210	+	20.0469i	1.48343	+	0.712786i
$792$	2.95364	−	7.44096i	0.104953	−	0.264403i
$793$	13.4575	−	23.3091i	0.477891	−	0.827731i
$794$	−51.9565			−1.84387
$795$	−0.421474	+	0.870886i	−0.0149481	+	0.0308871i
$796$		−	16.4210i		−	0.582026i
$797$	−1.11087	−	1.92408i	−0.0393489	−	0.0681543i	0.845680	−	0.533690i	$-0.179195\pi$
$797$	−1.11087	−	1.92408i	−0.0393489	−	0.0681543i	−0.885029	+	0.465536i	$0.845862\pi$
$798$	−9.98387	−	3.93061i	−0.353425	−	0.139142i
$799$	−15.9888	+	27.6934i	−0.565643	+	0.979723i
$800$	−18.5470	−	10.7081i	−0.655736	−	0.378590i
$801$	−22.2460	−	28.1181i	−0.786023	−	0.993503i
$802$	29.8710	+	51.7380i	1.05478	+	1.82693i
$803$	0.583741	+	1.01107i	0.0205998	+	0.0356798i
$804$	−13.6251	−	6.59399i	−0.480519	−	0.232552i
$805$	−17.2839	+	11.8061i	−0.609178	+	0.416110i
$806$	−9.05653	+	5.22879i	−0.319003	+	0.184176i
$807$	−13.3842	−	6.47743i	−0.471147	−	0.228016i
$808$			163.914i			5.76649i
$809$	33.7187	−	19.4675i	1.18549	−	0.684442i	0.228210	−	0.973612i	$-0.426713\pi$
$809$	33.7187	−	19.4675i	1.18549	−	0.684442i	0.957278	+	0.289170i	$0.0933793\pi$
$810$	−23.8941	−	5.64858i	−0.839555	−	0.198471i
$811$			36.6692i			1.28763i	0.765181	+	0.643815i	$0.222649\pi$
$811$			36.6692i			1.28763i	−0.765181	+	0.643815i	$0.777351\pi$
$812$	−29.7468	−	14.2933i	−1.04391	−	0.501596i
$813$	−51.4373	+	3.75463i	−1.80399	+	0.131681i
$814$	−7.02433			−0.246203
$815$	−9.14675	+	15.8426i	−0.320397	+	0.554943i
$816$	−9.87020	−	135.219i	−0.345526	−	4.73360i
$817$	0.332949	−	0.192228i	0.0116484	−	0.00672522i
$818$	99.9902			3.49608
$819$	−19.5248	+	18.0078i	−0.682253	+	0.629245i
$820$	34.3670			1.20015
$821$	4.31256	−	2.48986i	0.150509	−	0.0868966i	−0.422854	−	0.906198i	$-0.638972\pi$
$821$	4.31256	−	2.48986i	0.150509	−	0.0868966i	0.573363	+	0.819301i	$0.305638\pi$
$822$	24.2696	+	11.7455i	0.846501	+	0.409673i
$823$	−23.6293	+	40.9272i	−0.823666	+	1.42663i	0.0792685	+	0.996853i	$0.474742\pi$
$823$	−23.6293	+	40.9272i	−0.823666	+	1.42663i	−0.902935	+	0.429778i	$0.858592\pi$
$824$	56.7255			1.97613
$825$	−0.276464	−	0.407189i	−0.00962526	−	0.0141765i
$826$	54.8100	−	37.4390i	1.90708	−	1.30267i
$827$			11.6675i			0.405720i	0.979208	+	0.202860i	$0.0650236\pi$
$827$			11.6675i			0.405720i	−0.979208	+	0.202860i	$0.934976\pi$
$828$	101.300	−	80.1445i	3.52041	−	2.78521i
$829$	−32.9245	+	19.0090i	−1.14352	+	0.660209i	−0.947299	−	0.320351i	$-0.896199\pi$
$829$	−32.9245	+	19.0090i	−1.14352	+	0.660209i	−0.196217	+	0.980560i	$0.562866\pi$
$830$		−	12.5286i		−	0.434874i
$831$	28.4501	−	19.3164i	0.986924	−	0.670080i
$832$	83.9137	−	48.4476i	2.90918	−	1.67962i
$833$	36.7604	−	5.60644i	1.27367	−	0.194251i
$834$	−2.23732	−	30.6506i	−0.0774720	−	1.06134i
$835$	−3.77161	−	6.53262i	−0.130522	−	0.226071i
$836$	0.663656	+	1.14949i	0.0229530	+	0.0397558i
$837$	−1.78742	+	5.67747i	−0.0617824	+	0.196242i
$838$	30.9607	+	17.8752i	1.06952	+	0.617488i
$839$	0.674120	−	1.16761i	0.0232732	−	0.0403104i	−0.854154	−	0.520020i	$-0.825925\pi$
$839$	0.674120	−	1.16761i	0.0232732	−	0.0403104i	0.877427	+	0.479709i	$0.159258\pi$
$840$	−15.7653	+	40.0443i	−0.543955	+	1.38166i
$841$	−11.8735	−	20.5655i	−0.409430	−	0.709154i
$842$		−	8.03588i		−	0.276935i
$843$	−17.0360	+	1.24353i	−0.586752	+	0.0428296i
$844$	26.5401			0.913547
$845$	−0.900781	+	1.56020i	−0.0309878	+	0.0536725i
$846$	−38.6364	+	30.5677i	−1.32835	+	1.05094i
$847$	16.2950	+	23.8555i	0.559901	+	0.819685i
$848$	−7.12823	−	4.11549i	−0.244784	−	0.141326i
$849$	−18.2336	+	1.33095i	−0.625776	+	0.0456781i
$850$	−12.5506	−	7.24607i	−0.430481	−	0.248538i
$851$	−62.0821	−	35.8431i	−2.12815	−	1.22869i
$852$	78.0727	−	5.69886i	2.67473	−	0.195240i
$853$	40.1559	+	23.1840i	1.37491	+	0.793805i	0.991541	−	0.129790i	$-0.0414304\pi$
$853$	40.1559	+	23.1840i	1.37491	+	0.793805i	0.383369	+	0.923595i	$0.374764\pi$
$854$	−57.8866	+	4.38885i	−1.98084	+	0.150183i
$855$	2.01926	−	1.59756i	0.0690571	−	0.0546354i
$856$	90.3322	−	156.460i	3.08749	−	5.34769i
$857$	28.7173			0.980966			0.490483	−	0.871451i	$-0.336820\pi$
$857$	28.7173			0.980966			0.490483	+	0.871451i	$0.336820\pi$
$858$	4.48127	−	0.327107i	0.152988	−	0.0111673i
$859$			45.4624i			1.55116i	0.631250	+	0.775579i	$0.282542\pi$
$859$			45.4624i			1.55116i	−0.631250	+	0.775579i	$0.717458\pi$
$860$	−1.21896	−	2.11129i	−0.0415660	−	0.0719945i
$861$	−4.28252	−	28.6187i	−0.145948	−	0.975324i
$862$	−25.1505	+	43.5619i	−0.856629	+	1.48373i
$863$	−9.01372	−	5.20407i	−0.306831	−	0.177149i	0.338677	−	0.940903i	$-0.390021\pi$
$863$	−9.01372	−	5.20407i	−0.306831	−	0.177149i	−0.645507	+	0.763754i	$0.723354\pi$
$864$	33.4176	−	106.146i	1.13689	−	3.61116i
$865$	−1.23435	−	2.13795i	−0.0419691	−	0.0726926i
$866$	−7.12475	−	12.3404i	−0.242109	−	0.419345i
$867$	−1.41473	−	19.3814i	−0.0480467	−	0.658226i
$868$	14.8672	+	7.14367i	0.504625	+	0.242472i
$869$	1.12932	−	0.652014i	0.0383096	−	0.0221181i
$870$	8.95986	−	6.08337i	0.303768	−	0.206245i
$871$		−	5.37353i		−	0.182075i
$872$	−159.571	+	92.1281i	−5.40374	+	3.11985i
$873$	−10.0277	+	7.93356i	−0.339387	+	0.268510i
$874$			18.5236i			0.626570i
$875$	1.49231	+	2.18472i	0.0504494	+	0.0738570i
$876$	21.7553	+	32.0422i	0.735043	+	1.08260i
$877$	42.6874			1.44145			0.720726	−	0.693220i	$-0.243809\pi$
$877$	42.6874			1.44145			0.720726	+	0.693220i	$0.243809\pi$
$878$	21.3233	−	36.9330i	0.719625	−	1.24643i
$879$	13.4514	+	6.50993i	0.453703	+	0.219574i
$880$	3.62613	−	2.09355i	0.122237	−	0.0705735i
$881$	−5.57362			−0.187780			−0.0938900	−	0.995583i	$-0.529930\pi$
$881$	−5.57362			−0.187780			−0.0938900	+	0.995583i	$0.529930\pi$
$882$	55.8261	+	12.8667i	1.87976	+	0.433244i
$883$	41.3715			1.39226			0.696131	−	0.717915i	$-0.254903\pi$
$883$	41.3715			1.39226			0.696131	+	0.717915i	$0.254903\pi$
$884$	83.7872	−	48.3745i	2.81807	−	1.62701i
$885$	1.15958	+	15.8860i	0.0389790	+	0.534001i
$886$	8.36344	−	14.4859i	0.280975	−	0.486663i
$887$	11.9236			0.400354			0.200177	−	0.979760i	$-0.435848\pi$
$887$	11.9236			0.400354			0.200177	+	0.979760i	$0.435848\pi$
$888$	−147.000	+	10.7302i	−4.93301	+	0.360081i
$889$	−3.16298	−	4.63054i	−0.106083	−	0.155303i
$890$		−	32.6042i		−	1.09290i
$891$	1.75394	−	1.86120i	0.0587592	−	0.0623525i
$892$	−17.6922	+	10.2146i	−0.592378	+	0.342010i
$893$		−	5.16646i		−	0.172889i
$894$	41.7325	+	20.1969i	1.39574	+	0.675485i
$895$	−0.894686	+	0.516547i	−0.0299060	+	0.0172663i
$896$	−86.2299	−	41.4334i	−2.88074	−	1.38419i
$897$	41.2752	+	19.9756i	1.37814	+	0.666965i
$898$	55.4026	+	95.9601i	1.84881	+	3.20223i
$899$	−1.31272	−	2.27369i	−0.0437815	−	0.0758319i
$900$	−10.1304	−	12.8045i	−0.337681	−	0.426816i
$901$	−2.56982	−	1.48369i	−0.0856131	−	0.0494287i
$902$	−2.44757	+	4.23932i	−0.0814952	+	0.141154i
$903$	−1.60626	+	1.27816i	−0.0534529	+	0.0425345i
$904$	−82.1497	−	142.287i	−2.73226	−	4.73241i
$905$			4.90430i			0.163025i
$906$	−20.0168	+	41.3603i	−0.665012	+	1.37411i
$907$	−43.4138			−1.44153			−0.720766	−	0.693179i	$-0.756210\pi$
$907$	−43.4138			−1.44153			−0.720766	+	0.693179i	$0.756210\pi$
$908$	−23.3275	+	40.4043i	−0.774149	+	1.34086i
$909$	−19.3185	+	48.6680i	−0.640753	+	1.61422i
$910$	−24.0847	+	1.82605i	−0.798398	+	0.0605330i
$911$	44.9154	+	25.9319i	1.48811	+	0.859163i	0.999908	−	0.0135658i	$-0.00431825\pi$
$911$	44.9154	+	25.9319i	1.48811	+	0.859163i	0.488206	+	0.872729i	$0.337652\pi$
$912$	12.3043	+	18.1224i	0.407437	+	0.600091i
$913$	1.13015	+	0.652490i	0.0374024	+	0.0215943i
$914$	−51.8065	−	29.9105i	−1.71361	−	0.989352i
$915$	6.06864	−	12.5395i	0.200623	−	0.414544i
$916$	−6.74823	−	3.89609i	−0.222968	−	0.128731i
$917$	21.0395	+	30.8015i	0.694786	+	1.01715i
$918$	22.6134	−	71.8279i	0.746352	−	2.37067i
$919$	−20.6435	+	35.7555i	−0.680965	+	1.17947i	0.293721	+	0.955891i	$0.405106\pi$
$919$	−20.6435	+	35.7555i	−0.680965	+	1.17947i	−0.974687	+	0.223575i	$0.928227\pi$
$920$	74.2965			2.44948
$921$	−11.2776	−	16.6102i	−0.371610	−	0.547325i
$922$			81.2407i			2.67552i
$923$	13.8947	+	24.0663i	0.457349	+	0.792152i
$924$	−4.41277	−	5.54550i	−0.145170	−	0.182434i
$925$	−4.53064	+	7.84730i	−0.148966	+	0.258018i
$926$	7.78976	+	4.49742i	0.255987	+	0.147794i
$927$	16.8425	+	6.68550i	0.553179	+	0.219581i
$928$	24.5425	+	42.5089i	0.805648	+	1.39542i
$929$	−18.7874	−	32.5407i	−0.616395	−	1.06763i	−0.990138	−	0.140095i	$-0.955259\pi$
$929$	−18.7874	−	32.5407i	−0.616395	−	1.06763i	0.373743	−	0.927532i	$-0.378074\pi$
$930$	−4.47806	+	3.04042i	−0.146841	+	0.0996992i
$931$	−4.69059	+	3.75404i	−0.153728	+	0.123034i
$932$	−13.1073	+	7.56750i	−0.429344	+	0.247882i
$933$	−0.626924	−	8.58868i	−0.0205246	−	0.281181i
$934$			90.4448i			2.95944i
$935$	1.30727	−	0.754751i	0.0427522	−	0.0246830i
$936$	93.2812	−	13.6909i	3.04899	−	0.447502i
$937$			27.8462i			0.909695i	0.890569	+	0.454848i	$0.150306\pi$
$937$			27.8462i			0.909695i	−0.890569	+	0.454848i	$0.849694\pi$
$938$	−9.57049	+	6.53730i	−0.312488	+	0.213451i
$939$	−14.7754	+	30.5302i	−0.482177	+	0.996316i
$940$	−32.7615			−1.06856
$941$	−18.9891	+	32.8900i	−0.619026	+	1.07218i	0.370638	+	0.928778i	$0.379139\pi$
$941$	−18.9891	+	32.8900i	−0.619026	+	1.07218i	−0.989664	+	0.143407i	$0.954194\pi$
$942$	−24.5539	+	16.6711i	−0.800010	+	0.543173i
$943$	−43.2640	+	24.9785i	−1.40887	+	0.813411i
$944$	−135.507			−4.41037
$945$	−9.40041	+	10.0316i	−0.305795	+	0.326327i
$946$	0.347249			0.0112900
$947$	−2.62274	+	1.51424i	−0.0852278	+	0.0492063i	−0.542008	−	0.840373i	$-0.682336\pi$
$947$	−2.62274	+	1.51424i	−0.0852278	+	0.0492063i	0.456780	+	0.889579i	$0.349003\pi$
$948$	35.7898	−	24.2998i	1.16240	−	0.789220i
$949$	−6.87449	+	11.9070i	−0.223155	+	0.386516i
$950$	2.34142			0.0759657
$951$	−0.887521	+	1.83387i	−0.0287799	+	0.0594674i
$952$	−118.970	−	57.1651i	−3.85585	−	1.85273i
$953$		−	7.98502i		−	0.258660i	−0.991602	−	0.129330i	$-0.958717\pi$
$953$		−	7.98502i		−	0.258660i	0.991602	−	0.129330i	$-0.0412827\pi$
$954$	−2.83654	−	3.58528i	−0.0918363	−	0.116078i
$955$	1.63620	−	0.944661i	0.0529462	−	0.0305685i
$956$			38.9413i			1.25945i
$957$	0.0821221	+	1.12505i	0.00265463	+	0.0363676i
$958$	−52.5970	+	30.3669i	−1.69933	+	0.981110i
$959$	12.4663	−	8.51533i	0.402557	−	0.274974i
$960$	41.4917	−	28.1711i	1.33914	−	0.909219i
$961$	−14.8439	−	25.7104i	−0.478836	−	0.829368i
$962$	−41.3614	−	71.6401i	−1.33355	−	2.30977i
$963$	45.2606	−	35.8085i	1.45850	−	1.15391i
$964$	−126.086	−	72.7960i	−4.06097	−	2.34460i
$965$	−6.19129	+	10.7236i	−0.199305	+	0.345206i
$966$	−14.6370	−	97.8147i	−0.470939	−	3.14714i
$967$	−12.9808	−	22.4834i	−0.417435	−	0.723018i	0.578246	−	0.815863i	$-0.303737\pi$
$967$	−12.9808	−	22.4834i	−0.417435	−	0.723018i	−0.995681	+	0.0928442i	$0.970404\pi$
$968$		−	102.545i		−	3.29592i
$969$	4.43587	+	6.53334i	0.142501	+	0.209881i
$970$	−11.6276			−0.373340
$971$	−2.20423	+	3.81784i	−0.0707372	+	0.122520i	−0.899225	−	0.437487i	$-0.855868\pi$
$971$	−2.20423	+	3.81784i	−0.0707372	+	0.122520i	0.828487	+	0.560008i	$0.189202\pi$
$972$	53.5354	−	65.8150i	1.71715	−	2.11102i
$973$	−15.5102	−	7.45262i	−0.497233	−	0.238920i
$974$	−16.2632	−	9.38957i	−0.521107	−	0.300861i
$975$	2.52495	−	5.21727i	0.0808632	−	0.167086i
$976$	102.637	+	59.2572i	3.28532	+	1.89678i
$977$	26.6864	+	15.4074i	0.853772	+	0.492925i	0.861922	−	0.507041i	$-0.169261\pi$
$977$	26.6864	+	15.4074i	0.853772	+	0.492925i	−0.00814977	+	0.999967i	$0.502594\pi$
$978$	−48.5551	−	71.5142i	−1.55262	−	2.28677i
$979$	2.94107	+	1.69803i	0.0939970	+	0.0542692i
$980$	23.8051	+	29.7439i	0.760425	+	0.950134i
$981$	−58.2362	+	8.54737i	−1.85934	+	0.272896i
$982$	−16.3230	+	28.2722i	−0.520887	+	0.902203i
$983$	−49.8598			−1.59028			−0.795140	−	0.606425i	$-0.792603\pi$
$983$	−49.8598			−1.59028			−0.795140	+	0.606425i	$0.792603\pi$
$984$	−44.7452	+	92.4563i	−1.42642	+	2.94740i
$985$		−	2.13992i		−	0.0681836i
$986$	16.6077	+	28.7653i	0.528896	+	0.916075i
$987$	4.08245	+	27.2817i	0.129946	+	0.868386i
$988$	−7.81562	+	13.5371i	−0.248648	+	0.430671i
$989$	3.06904	+	1.77191i	0.0975896	+	0.0563434i
$990$	2.30096	−	0.337713i	0.0731293	−	0.0107332i
$991$	14.3732	+	24.8951i	0.456579	+	0.790818i	0.998777	−	0.0494322i	$-0.0157412\pi$
$991$	14.3732	+	24.8951i	0.456579	+	0.790818i	−0.542198	+	0.840251i	$0.682408\pi$
$992$	−12.2662	−	21.2456i	−0.389451	−	0.674549i
$993$	−48.8208	−	23.6273i	−1.54928	−	0.749791i
$994$	25.9592	−	54.0254i	0.823375	−	1.71358i
$995$	2.61298	−	1.50861i	0.0828372	−	0.0478261i
$996$	38.9675	+	18.8587i	1.23473	+	0.597562i
$997$		−	42.4777i		−	1.34528i	−0.739968	−	0.672642i	$-0.765160\pi$
$997$		−	42.4777i		−	1.34528i	0.739968	−	0.672642i	$-0.234840\pi$
$998$	−50.1000	+	28.9252i	−1.58589	+	0.915612i
$999$	−44.9107	−	14.1391i	−1.42091	−	0.447341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.b.236.15	yes	30
3.2	odd	2		945.2.be.b.656.1		30
7.3	odd	6		315.2.t.b.101.15	✓	30
9.4	even	3		945.2.t.b.341.15		30
9.5	odd	6		315.2.t.b.131.1	yes	30
21.17	even	6		945.2.t.b.521.1		30
63.31	odd	6		945.2.be.b.206.1		30
63.59	even	6	inner	315.2.be.b.311.15	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.15	✓	30	7.3	odd	6
315.2.t.b.131.1	yes	30	9.5	odd	6
315.2.be.b.236.15	yes	30	1.1	even	1	trivial
315.2.be.b.311.15	yes	30	63.59	even	6	inner
945.2.t.b.341.15		30	9.4	even	3
945.2.t.b.521.1		30	21.17	even	6
945.2.be.b.206.1		30	63.31	odd	6
945.2.be.b.656.1		30	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.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.36259 - 1.36404i) q^{2} +(-1.43297 + 0.972928i) q^{3} +(2.72121 - 4.71328i) q^{4} +1.00000 q^{5} +(-2.05841 + 4.25326i) q^{6} +(1.49231 + 2.18472i) q^{7} -9.39122i q^{8} +(1.10682 - 2.78836i) q^{9} +O(q^{10})\)	\(q+(2.36259 - 1.36404i) q^{2} +(-1.43297 + 0.972928i) q^{3} +(2.72121 - 4.71328i) q^{4} +1.00000 q^{5} +(-2.05841 + 4.25326i) q^{6} +(1.49231 + 2.18472i) q^{7} -9.39122i q^{8} +(1.10682 - 2.78836i) q^{9} +(2.36259 - 1.36404i) q^{10} +0.284157i q^{11} +(0.686259 + 9.40155i) q^{12} +(-2.89807 + 1.67320i) q^{13} +(6.50577 + 3.12602i) q^{14} +(-1.43297 + 0.972928i) q^{15} +(-7.36758 - 12.7610i) q^{16} +(-2.65611 - 4.60051i) q^{17} +(-1.18847 - 8.09749i) q^{18} +(0.743281 + 0.429133i) q^{19} +(2.72121 - 4.71328i) q^{20} +(-4.26402 - 1.67873i) q^{21} +(0.387602 + 0.671346i) q^{22} +7.91127i q^{23} +(9.13698 + 13.4574i) q^{24} +1.00000 q^{25} +(-4.56463 + 7.90618i) q^{26} +(1.12683 + 5.07250i) q^{27} +(14.3581 - 1.08860i) q^{28} +(-1.98489 - 1.14598i) q^{29} +(-2.05841 + 4.25326i) q^{30} +(0.992032 + 0.572750i) q^{31} +(-18.5470 - 10.7081i) q^{32} +(-0.276464 - 0.407189i) q^{33} +(-12.5506 - 7.24607i) q^{34} +(1.49231 + 2.18472i) q^{35} +(-10.1304 - 12.8045i) q^{36} +(-4.53064 + 7.84730i) q^{37} +2.34142 q^{38} +(2.52495 - 5.21727i) q^{39} -9.39122i q^{40} +(3.15733 + 5.46865i) q^{41} +(-12.3640 + 1.85015i) q^{42} +(0.223973 - 0.387932i) q^{43} +(1.33931 + 0.773252i) q^{44} +(1.10682 - 2.78836i) q^{45} +(10.7913 + 18.6911i) q^{46} +(-3.00982 - 5.21316i) q^{47} +(22.9731 + 11.1181i) q^{48} +(-2.54600 + 6.52057i) q^{49} +(2.36259 - 1.36404i) q^{50} +(8.28210 + 4.00821i) q^{51} +18.2126i q^{52} +(0.483757 - 0.279297i) q^{53} +(9.58133 + 10.4472i) q^{54} +0.284157i q^{55} +(20.5172 - 14.0146i) q^{56} +(-1.48262 + 0.108223i) q^{57} -6.25264 q^{58} +(4.59808 - 7.96411i) q^{59} +(0.686259 + 9.40155i) q^{60} +(-6.96542 + 4.02149i) q^{61} +3.12502 q^{62} +(7.74351 - 1.74301i) q^{63} -28.9550 q^{64} +(-2.89807 + 1.67320i) q^{65} +(-1.20859 - 0.584912i) q^{66} +(-0.802881 + 1.39063i) q^{67} -28.9113 q^{68} +(-7.69710 - 11.3366i) q^{69} +(6.50577 + 3.12602i) q^{70} -8.30424i q^{71} +(-26.1861 - 10.3944i) q^{72} +(3.55813 - 2.05429i) q^{73} +24.7199i q^{74} +(-1.43297 + 0.972928i) q^{75} +(4.04525 - 2.33553i) q^{76} +(-0.620803 + 0.424051i) q^{77} +(-1.15115 - 15.7704i) q^{78} +(-2.29456 - 3.97429i) q^{79} +(-7.36758 - 12.7610i) q^{80} +(-6.54990 - 6.17243i) q^{81} +(14.9189 + 8.61345i) q^{82} +(2.29623 - 3.97719i) q^{83} +(-19.5156 + 15.5293i) q^{84} +(-2.65611 - 4.60051i) q^{85} -1.22203i q^{86} +(3.95925 - 0.289002i) q^{87} +2.66858 q^{88} +(5.97567 - 10.3502i) q^{89} +(-1.18847 - 8.09749i) q^{90} +(-7.98031 - 3.83453i) q^{91} +(37.2880 + 21.5282i) q^{92} +(-1.97880 + 0.144441i) q^{93} +(-14.2219 - 8.21103i) q^{94} +(0.743281 + 0.429133i) q^{95} +(36.9956 - 2.70047i) q^{96} +(-3.69117 - 2.13110i) q^{97} +(2.87918 + 18.8783i) q^{98} +(0.792332 + 0.314511i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more