LMFDB - Embedded newform 315.2.be.b.236.1

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			236.1
Character	$\chi$	$=$	315.236
Dual form			315.2.be.b.311.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.43144 + 1.40379i) q^{2} +(-1.45528 - 0.939239i) q^{3} +(2.94126 - 5.09441i) q^{4} +1.00000 q^{5} +(4.85691 + 0.240797i) q^{6} +(0.979355 - 2.45782i) q^{7} +10.9005i q^{8} +(1.23566 + 2.73371i) q^{9} +O(q^{10})$	\(q+(-2.43144 + 1.40379i) q^{2} +(-1.45528 - 0.939239i) q^{3} +(2.94126 - 5.09441i) q^{4} +1.00000 q^{5} +(4.85691 + 0.240797i) q^{6} +(0.979355 - 2.45782i) q^{7} +10.9005i q^{8} +(1.23566 + 2.73371i) q^{9} +(-2.43144 + 1.40379i) q^{10} -2.94940i q^{11} +(-9.06521 + 4.65123i) q^{12} +(-1.90869 + 1.10198i) q^{13} +(1.06902 + 7.35084i) q^{14} +(-1.45528 - 0.939239i) q^{15} +(-9.41949 - 16.3150i) q^{16} +(-1.11622 - 1.93336i) q^{17} +(-6.84198 - 4.91223i) q^{18} +(2.10445 + 1.21501i) q^{19} +(2.94126 - 5.09441i) q^{20} +(-3.73371 + 2.65695i) q^{21} +(4.14034 + 7.17128i) q^{22} -0.164154i q^{23} +(10.2382 - 15.8632i) q^{24} +1.00000 q^{25} +(3.09390 - 5.35879i) q^{26} +(0.769378 - 5.13888i) q^{27} +(-9.64059 - 12.2183i) q^{28} +(-1.75552 - 1.01355i) q^{29} +(4.85691 + 0.240797i) q^{30} +(-1.43033 - 0.825801i) q^{31} +(26.9256 + 15.5455i) q^{32} +(-2.77019 + 4.29219i) q^{33} +(5.42806 + 3.13389i) q^{34} +(0.979355 - 2.45782i) q^{35} +(17.5610 + 1.74558i) q^{36} +(0.761906 - 1.31966i) q^{37} -6.82246 q^{38} +(3.81269 + 0.189027i) q^{39} +10.9005i q^{40} +(-3.32404 - 5.75741i) q^{41} +(5.34848 - 11.7016i) q^{42} +(4.57974 - 7.93235i) q^{43} +(-15.0254 - 8.67495i) q^{44} +(1.23566 + 2.73371i) q^{45} +(0.230437 + 0.399129i) q^{46} +(-5.97720 - 10.3528i) q^{47} +(-1.61576 + 32.5900i) q^{48} +(-5.08173 - 4.81415i) q^{49} +(-2.43144 + 1.40379i) q^{50} +(-0.191470 + 3.86197i) q^{51} +12.9648i q^{52} +(-2.54984 + 1.47215i) q^{53} +(5.34322 + 13.5749i) q^{54} -2.94940i q^{55} +(26.7914 + 10.6754i) q^{56} +(-1.92138 - 3.74475i) q^{57} +5.69125 q^{58} +(-1.12306 + 1.94520i) q^{59} +(-9.06521 + 4.65123i) q^{60} +(-6.17771 + 3.56670i) q^{61} +4.63701 q^{62} +(7.92910 - 0.359755i) q^{63} -49.6126 q^{64} +(-1.90869 + 1.10198i) q^{65} +(0.710208 - 14.3250i) q^{66} +(1.68442 - 2.91751i) q^{67} -13.1324 q^{68} +(-0.154180 + 0.238889i) q^{69} +(1.06902 + 7.35084i) q^{70} -6.49137i q^{71} +(-29.7987 + 13.4693i) q^{72} +(3.71139 - 2.14277i) q^{73} +4.27823i q^{74} +(-1.45528 - 0.939239i) q^{75} +(12.3795 - 7.14729i) q^{76} +(-7.24908 - 2.88851i) q^{77} +(-9.53566 + 4.89261i) q^{78} +(-0.143327 - 0.248249i) q^{79} +(-9.41949 - 16.3150i) q^{80} +(-5.94629 + 6.75586i) q^{81} +(16.1644 + 9.33253i) q^{82} +(-2.67210 + 4.62821i) q^{83} +(2.55380 + 26.8358i) q^{84} +(-1.11622 - 1.93336i) q^{85} +25.7160i q^{86} +(1.60280 + 3.12385i) q^{87} +32.1499 q^{88} +(-0.937011 + 1.62295i) q^{89} +(-6.84198 - 4.91223i) q^{90} +(0.839184 + 5.77043i) q^{91} +(-0.836266 - 0.482818i) q^{92} +(1.30590 + 2.54519i) q^{93} +(29.0664 + 16.7815i) q^{94} +(2.10445 + 1.21501i) q^{95} +(-24.5832 - 47.9126i) q^{96} +(-10.0550 - 5.80528i) q^{97} +(19.1140 + 4.57163i) q^{98} +(8.06279 - 3.64445i) 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 $

$2$	−2.43144	+	1.40379i	−1.71929	+	0.992630i	−0.799051	+	0.601263i	$0.794665\pi$
$2$	−2.43144	+	1.40379i	−1.71929	+	0.992630i	−0.920234	+	0.391367i	$0.872002\pi$
$3$	−1.45528	−	0.939239i	−0.840204	−	0.542270i
$3$	−1.45528	−	0.939239i	−0.840204	−	0.542270i
$4$	2.94126	−	5.09441i	1.47063	−	2.54720i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	4.85691	+	0.240797i	1.98282	+	0.0983051i
$7$	0.979355	−	2.45782i	0.370162	−	0.928967i
$7$	0.979355	−	2.45782i	0.370162	−	0.928967i
$8$			10.9005i			3.85390i
$9$	1.23566	+	2.73371i	0.411886	+	0.911235i
$10$	−2.43144	+	1.40379i	−0.768888	+	0.443918i
$11$		−	2.94940i		−	0.889277i	−0.895710	−	0.444639i	$-0.853332\pi$
$11$		−	2.94940i		−	0.889277i	0.895710	−	0.444639i	$-0.146668\pi$
$12$	−9.06521	+	4.65123i	−2.61690	+	1.34269i
$13$	−1.90869	+	1.10198i	−0.529374	+	0.305634i	−0.740761	−	0.671768i	$-0.765535\pi$
$13$	−1.90869	+	1.10198i	−0.529374	+	0.305634i	0.211388	+	0.977402i	$0.432202\pi$
$14$	1.06902	+	7.35084i	0.285708	+	1.96459i
$15$	−1.45528	−	0.939239i	−0.375751	−	0.242511i
$16$	−9.41949	−	16.3150i	−2.35487	−	4.07876i
$17$	−1.11622	−	1.93336i	−0.270724	−	0.468908i	0.698323	−	0.715782i	$-0.253930\pi$
$17$	−1.11622	−	1.93336i	−0.270724	−	0.468908i	−0.969047	+	0.246875i	$0.920596\pi$
$18$	−6.84198	−	4.91223i	−1.61267	−	1.15782i
$19$	2.10445	+	1.21501i	0.482794	+	0.278741i	0.721580	−	0.692331i	$-0.243416\pi$
$19$	2.10445	+	1.21501i	0.482794	+	0.278741i	−0.238786	+	0.971072i	$0.576749\pi$
$20$	2.94126	−	5.09441i	0.657685	−	1.13914i
$21$	−3.73371	+	2.65695i	−0.814762	+	0.579795i
$22$	4.14034	+	7.17128i	0.882723	+	1.52892i
$23$		−	0.164154i		−	0.0342284i	−0.999854	−	0.0171142i	$-0.994552\pi$
$23$		−	0.164154i		−	0.0342284i	0.999854	−	0.0171142i	$-0.00544788\pi$
$24$	10.2382	−	15.8632i	2.08986	−	3.23807i
$25$	1.00000			0.200000
$26$	3.09390	−	5.35879i	0.606763	−	1.05095i
$27$	0.769378	−	5.13888i	0.148067	−	0.988977i
$28$	−9.64059	−	12.2183i	−1.82190	−	2.30904i
$29$	−1.75552	−	1.01355i	−0.325992	−	0.188212i	0.328068	−	0.944654i	$-0.393602\pi$
$29$	−1.75552	−	1.01355i	−0.325992	−	0.188212i	−0.654060	+	0.756442i	$0.726936\pi$
$30$	4.85691	+	0.240797i	0.886746	+	0.0439634i
$31$	−1.43033	−	0.825801i	−0.256895	−	0.148318i	0.366022	−	0.930606i	$-0.380719\pi$
$31$	−1.43033	−	0.825801i	−0.256895	−	0.148318i	−0.622917	+	0.782288i	$0.714053\pi$
$32$	26.9256	+	15.5455i	4.75982	+	2.74808i
$33$	−2.77019	+	4.29219i	−0.482228	+	0.747175i
$34$	5.42806	+	3.13389i	0.930904	+	0.537458i
$35$	0.979355	−	2.45782i	0.165541	−	0.415447i
$36$	17.5610	+	1.74558i	2.92683	+	0.290930i
$37$	0.761906	−	1.31966i	0.125257	−	0.216951i	−0.796577	−	0.604538i	$-0.793358\pi$
$37$	0.761906	−	1.31966i	0.125257	−	0.216951i	0.921833	+	0.387587i	$0.126691\pi$
$38$	−6.82246			−1.10675
$39$	3.81269	+	0.189027i	0.610519	+	0.0302685i
$40$			10.9005i			1.72352i
$41$	−3.32404	−	5.75741i	−0.519129	−	0.899157i	−0.999753	−	0.0222304i	$-0.992923\pi$
$41$	−3.32404	−	5.75741i	−0.519129	−	0.899157i	0.480624	−	0.876927i	$-0.340410\pi$
$42$	5.34848	−	11.7016i	0.825288	−	1.80559i
$43$	4.57974	−	7.93235i	0.698405	−	1.20967i	−0.270615	−	0.962688i	$-0.587227\pi$
$43$	4.57974	−	7.93235i	0.698405	−	1.20967i	0.969019	−	0.246984i	$-0.0794397\pi$
$44$	−15.0254	−	8.67495i	−2.26517	−	1.30780i
$45$	1.23566	+	2.73371i	0.184201	+	0.407517i
$46$	0.230437	+	0.399129i	0.0339761	+	0.0588484i
$47$	−5.97720	−	10.3528i	−0.871864	−	1.51011i	−0.860067	−	0.510182i	$-0.829578\pi$
$47$	−5.97720	−	10.3528i	−0.871864	−	1.51011i	−0.0117969	−	0.999930i	$-0.503755\pi$
$48$	−1.61576	+	32.5900i	−0.233215	+	4.70397i
$49$	−5.08173	−	4.81415i	−0.725961	−	0.687736i
$50$	−2.43144	+	1.40379i	−0.343857	+	0.198526i
$51$	−0.191470	+	3.86197i	−0.0268112	+	0.540784i
$52$			12.9648i			1.79790i
$53$	−2.54984	+	1.47215i	−0.350247	+	0.202215i	−0.664794	−	0.747027i	$-0.731481\pi$
$53$	−2.54984	+	1.47215i	−0.350247	+	0.202215i	0.314547	+	0.949242i	$0.398147\pi$
$54$	5.34322	+	13.5749i	0.727119	+	1.84731i
$55$		−	2.94940i		−	0.397697i
$56$	26.7914	+	10.6754i	3.58015	+	1.42657i
$57$	−1.92138	−	3.74475i	−0.254493	−	0.496005i
$58$	5.69125			0.747298
$59$	−1.12306	+	1.94520i	−0.146210	+	0.253243i	−0.929824	−	0.368005i	$-0.880041\pi$
$59$	−1.12306	+	1.94520i	−0.146210	+	0.253243i	0.783614	+	0.621248i	$0.213374\pi$
$60$	−9.06521	+	4.65123i	−1.17031	+	0.600471i
$61$	−6.17771	+	3.56670i	−0.790975	+	0.456669i	−0.840306	−	0.542113i	$-0.817624\pi$
$61$	−6.17771	+	3.56670i	−0.790975	+	0.456669i	0.0493309	+	0.998782i	$0.484291\pi$
$62$	4.63701			0.588901
$63$	7.92910	−	0.359755i	0.998972	−	0.0453248i
$64$	−49.6126			−6.20157
$65$	−1.90869	+	1.10198i	−0.236743	+	0.136684i
$66$	0.710208	−	14.3250i	0.0874205	−	1.76328i
$67$	1.68442	−	2.91751i	0.205785	−	0.356430i	−0.744597	−	0.667514i	$-0.767359\pi$
$67$	1.68442	−	2.91751i	0.205785	−	0.356430i	0.950383	+	0.311083i	$0.100692\pi$
$68$	−13.1324			−1.59254
$69$	−0.154180	+	0.238889i	−0.0185610	+	0.0287588i
$70$	1.06902	+	7.35084i	0.127772	+	0.878593i
$71$		−	6.49137i		−	0.770384i	−0.922836	−	0.385192i	$-0.874135\pi$
$71$		−	6.49137i		−	0.770384i	0.922836	−	0.385192i	$-0.125865\pi$
$72$	−29.7987	+	13.4693i	−3.51181	+	1.58737i
$73$	3.71139	−	2.14277i	0.434386	−	0.250793i	−0.266828	−	0.963744i	$-0.585975\pi$
$73$	3.71139	−	2.14277i	0.434386	−	0.250793i	0.701213	+	0.712952i	$0.252642\pi$
$74$			4.27823i			0.497334i
$75$	−1.45528	−	0.939239i	−0.168041	−	0.108454i
$76$	12.3795	−	7.14729i	1.42002	−	0.819851i
$77$	−7.24908	−	2.88851i	−0.826110	−	0.329176i
$78$	−9.53566	+	4.89261i	−1.07970	+	0.553979i
$79$	−0.143327	−	0.248249i	−0.0161255	−	0.0279302i	0.857850	−	0.513900i	$-0.171800\pi$
$79$	−0.143327	−	0.248249i	−0.0161255	−	0.0279302i	−0.873976	+	0.485970i	$0.838466\pi$
$80$	−9.41949	−	16.3150i	−1.05313	−	1.82408i
$81$	−5.94629	+	6.75586i	−0.660699	+	0.750651i
$82$	16.1644	+	9.33253i	1.78506	+	1.03061i
$83$	−2.67210	+	4.62821i	−0.293301	+	0.508012i	−0.974588	−	0.224004i	$-0.928087\pi$
$83$	−2.67210	+	4.62821i	−0.293301	+	0.508012i	0.681287	+	0.732016i	$0.261420\pi$
$84$	2.55380	+	26.8358i	0.278643	+	2.92803i
$85$	−1.11622	−	1.93336i	−0.121071	−	0.209702i
$86$			25.7160i			2.77303i
$87$	1.60280	+	3.12385i	0.171838	+	0.334912i
$88$	32.1499			3.42719
$89$	−0.937011	+	1.62295i	−0.0993230	+	0.172032i	−0.911405	−	0.411511i	$-0.865001\pi$
$89$	−0.937011	+	1.62295i	−0.0993230	+	0.172032i	0.812082	+	0.583544i	$0.198334\pi$
$90$	−6.84198	−	4.91223i	−0.721208	−	0.517794i
$91$	0.839184	+	5.77043i	0.0879704	+	0.604905i
$92$	−0.836266	−	0.482818i	−0.0871867	−	0.0503373i
$93$	1.30590	+	2.54519i	0.135416	+	0.263924i
$94$	29.0664	+	16.7815i	2.99797	+	1.73088i
$95$	2.10445	+	1.21501i	0.215912	+	0.124657i
$96$	−24.5832	−	47.9126i	−2.50902	−	4.89006i
$97$	−10.0550	−	5.80528i	−1.02094	−	0.589437i	−0.106561	−	0.994306i	$-0.533984\pi$
$97$	−10.0550	−	5.80528i	−1.02094	−	0.589437i	−0.914375	+	0.404869i	$0.867317\pi$
$98$	19.1140	+	4.57163i	1.93080	+	0.461804i
$99$	8.06279	−	3.64445i	0.810341	−	0.366281i
$100$	2.94126	−	5.09441i	0.294126	−	0.509441i
$101$	−4.05928			−0.403914			−0.201957	−	0.979394i	$-0.564730\pi$
$101$	−4.05928			−0.403914			−0.201957	+	0.979394i	$0.564730\pi$
$102$	−4.95585	−	9.65892i	−0.490702	−	0.956376i
$103$			7.44308i			0.733388i	0.930342	+	0.366694i	$0.119510\pi$
$103$			7.44308i			0.733388i	−0.930342	+	0.366694i	$0.880490\pi$
$104$	−12.0121	−	20.8056i	−1.17788	−	2.04016i
$105$	−3.73371	+	2.65695i	−0.364373	+	0.259292i
$106$	4.13318	−	7.15888i	0.401450	−	0.695332i
$107$	4.30346	+	2.48460i	0.416031	+	0.240196i	0.693378	−	0.720574i	$-0.256122\pi$
$107$	4.30346	+	2.48460i	0.416031	+	0.240196i	−0.277347	+	0.960770i	$0.589455\pi$
$108$	−23.9166	−	19.0343i	−2.30138	−	1.83158i
$109$	8.70832	+	15.0833i	0.834106	+	1.44471i	0.894756	+	0.446555i	$0.147349\pi$
$109$	8.70832	+	15.0833i	0.834106	+	1.44471i	−0.0606504	+	0.998159i	$0.519317\pi$
$110$	4.14034	+	7.17128i	0.394766	+	0.683755i
$111$	−2.34826	+	1.20486i	−0.222887	+	0.114360i
$112$	−49.3244	+	7.17316i	−4.66072	+	0.677800i
$113$	12.5129	−	7.22431i	1.17711	−	0.679606i	0.221767	−	0.975100i	$-0.428817\pi$
$113$	12.5129	−	7.22431i	1.17711	−	0.679606i	0.955345	+	0.295494i	$0.0954841\pi$
$114$	9.92856	+	6.40792i	0.929895	+	0.600157i
$115$		−	0.164154i		−	0.0153074i
$116$	−10.3269	+	5.96223i	−0.958827	+	0.553579i
$117$	−5.37097	−	3.85611i	−0.496547	−	0.356498i
$118$		−	6.30617i		−	0.580530i
$119$	−5.84502	+	0.850031i	−0.535812	+	0.0779222i
$120$	10.2382	−	15.8632i	0.934612	−	1.44811i
$121$	2.30105			0.209186
$122$	10.0138	−	17.3444i	0.906608	−	1.57029i
$123$	−0.570186	+	11.5007i	−0.0514119	+	1.03698i
$124$	−8.41394	+	4.85779i	−0.755594	+	0.436242i
$125$	1.00000			0.0894427
$126$	−18.7741	+	12.0055i	−1.67253	+	1.06954i
$127$	16.5547			1.46899			0.734497	−	0.678612i	$-0.237418\pi$
$127$	16.5547			1.46899			0.734497	+	0.678612i	$0.237418\pi$
$128$	66.7787	−	38.5547i	5.90246	−	3.40779i
$129$	−14.1152	+	7.24229i	−1.24277	+	0.637648i
$130$	3.09390	−	5.35879i	0.271353	−	0.469997i
$131$	15.1466			1.32336			0.661680	−	0.749786i	$-0.269844\pi$
$131$	15.1466			1.32336			0.661680	+	0.749786i	$0.269844\pi$
$132$	13.7183	+	26.7369i	1.19403	+	2.32715i
$133$	5.04727	−	3.98243i	0.437654	−	0.345321i
$134$			9.45832i			0.817074i
$135$	0.769378	−	5.13888i	0.0662175	−	0.442284i
$136$	21.0745	−	12.1674i	1.80713	−	1.04334i
$137$		−	10.5805i		−	0.903951i	−0.892030	−	0.451976i	$-0.850719\pi$
$137$		−	10.5805i		−	0.903951i	0.892030	−	0.451976i	$-0.149281\pi$
$138$	0.0395278	−	0.797279i	0.00336483	−	0.0678689i
$139$	−12.4906	+	7.21144i	−1.05944	+	0.611666i	−0.925277	−	0.379293i	$-0.876167\pi$
$139$	−12.4906	+	7.21144i	−1.05944	+	0.611666i	−0.134161	+	0.990960i	$0.542834\pi$
$140$	−9.64059	−	12.2183i	−0.814778	−	1.03264i
$141$	−1.02529	+	20.6802i	−0.0863450	+	1.74159i
$142$	9.11253	+	15.7834i	0.764706	+	1.32451i
$143$	3.25018	+	5.62947i	0.271794	+	0.470760i
$144$	32.9612	−	45.9099i	2.74677	−	3.82583i
$145$	−1.75552	−	1.01355i	−0.145788	−	0.0841708i
$146$	−6.01601	+	10.4200i	−0.497889	+	0.862369i
$147$	2.87368	+	11.7789i	0.237017	+	0.971506i
$148$	−4.48192	−	7.76292i	−0.368412	−	0.638108i
$149$		−	7.75202i		−	0.635070i	−0.948247	−	0.317535i	$-0.897145\pi$
$149$		−	7.75202i		−	0.635070i	0.948247	−	0.317535i	$-0.102855\pi$
$150$	4.85691	+	0.240797i	0.396565	+	0.0196610i
$151$	13.5361			1.10155			0.550776	−	0.834653i	$-0.314332\pi$
$151$	13.5361			1.10155			0.550776	+	0.834653i	$0.314332\pi$
$152$	−13.2442	+	22.9395i	−1.07424	+	1.86064i
$153$	3.90596	−	5.44040i	0.315778	−	0.439830i
$154$	21.6806	−	3.15297i	1.74707	−	0.254073i
$155$	−1.43033	−	0.825801i	−0.114887	−	0.0663299i
$156$	12.1771	−	18.8674i	0.974947	−	1.51060i
$157$	1.22778	+	0.708858i	0.0979873	+	0.0565730i	0.548193	−	0.836352i	$-0.315316\pi$
$157$	1.22778	+	0.708858i	0.0979873	+	0.0565730i	−0.450206	+	0.892925i	$0.648649\pi$
$158$	0.696979	+	0.402401i	0.0554487	+	0.0320133i
$159$	5.09342	+	0.252523i	0.403935	+	0.0200264i
$160$	26.9256	+	15.5455i	2.12866	+	1.22898i
$161$	−0.403460	−	0.160765i	−0.0317971	−	0.0126700i
$162$	4.97423	−	24.7738i	0.390812	−	1.94641i
$163$	−5.13568	+	8.89525i	−0.402257	+	0.696730i	−0.993998	−	0.109398i	$-0.965108\pi$
$163$	−5.13568	+	8.89525i	−0.402257	+	0.696730i	0.591741	+	0.806128i	$0.298441\pi$
$164$	−39.1075			−3.05378
$165$	−2.77019	+	4.29219i	−0.215659	+	0.334147i
$166$		−	15.0043i		−	1.16456i
$167$	−5.76531	−	9.98582i	−0.446133	−	0.772726i	0.551997	−	0.833846i	$-0.313866\pi$
$167$	−5.76531	−	9.98582i	−0.446133	−	0.772726i	−0.998130	+	0.0611204i	$0.980533\pi$
$168$	−28.9621	−	40.6993i	−2.23447	−	3.14002i
$169$	−4.07128	+	7.05167i	−0.313175	+	0.542436i
$170$	5.42806	+	3.13389i	0.416313	+	0.240358i
$171$	−0.721083	+	7.25429i	−0.0551426	+	0.554749i
$172$	−26.9404	−	46.6622i	−2.05419	−	3.55796i
$173$	4.57767	+	7.92875i	0.348034	+	0.602812i	0.985900	−	0.167335i	$-0.0535162\pi$
$173$	4.57767	+	7.92875i	0.348034	+	0.602812i	−0.637866	+	0.770147i	$0.720183\pi$
$174$	−8.28235	−	5.34545i	−0.627883	−	0.405237i
$175$	0.979355	−	2.45782i	0.0740323	−	0.185793i
$176$	−48.1195	+	27.7818i	−3.62715	+	2.09413i
$177$	3.46137	−	1.77598i	0.260173	−	0.133491i
$178$		−	5.26147i		−	0.394364i
$179$	−3.20254	+	1.84899i	−0.239369	+	0.138200i	−0.614887	−	0.788615i	$-0.710798\pi$
$179$	−3.20254	+	1.84899i	−0.239369	+	0.138200i	0.375518	+	0.926815i	$0.377465\pi$
$180$	17.5610	+	1.74558i	1.30892	+	0.130108i
$181$		−	22.0444i		−	1.63855i	−0.573404	−	0.819273i	$-0.694378\pi$
$181$		−	22.0444i		−	1.63855i	0.573404	−	0.819273i	$-0.305622\pi$
$182$	−10.1409	−	12.8524i	−0.751693	−	0.952683i
$183$	12.3403	+	0.611810i	0.912218	+	0.0452263i
$184$	1.78935			0.131913
$185$	0.761906	−	1.31966i	0.0560164	−	0.0970233i
$186$	−6.74813	−	4.35526i	−0.494797	−	0.319343i
$187$	−5.70224	+	3.29219i	−0.416989	+	0.240749i
$188$	−70.3219			−5.12875
$189$	−11.8769	−	6.92378i	−0.863919	−	0.503631i
$190$	−6.82246			−0.494953
$191$	−0.929487	+	0.536639i	−0.0672553	+	0.0388299i	−0.533251	−	0.845957i	$-0.679030\pi$
$191$	−0.929487	+	0.536639i	−0.0672553	+	0.0388299i	0.465995	+	0.884787i	$0.345696\pi$
$192$	72.2000	+	46.5981i	5.21059	+	3.36293i
$193$	−10.0777	+	17.4551i	−0.725407	+	1.25644i	0.233399	+	0.972381i	$0.425015\pi$
$193$	−10.0777	+	17.4551i	−0.725407	+	1.25644i	−0.958806	+	0.284061i	$0.908318\pi$
$194$	32.5976			2.34037
$195$	3.81269	+	0.189027i	0.273032	+	0.0135365i
$196$	−39.4719	+	11.7287i	−2.81942	+	0.837766i
$197$			23.7875i			1.69479i	0.530964	+	0.847394i	$0.321830\pi$
$197$			23.7875i			1.69479i	−0.530964	+	0.847394i	$0.678170\pi$
$198$	−14.4881	+	20.1797i	−1.02963	+	1.43411i
$199$	−2.68240	+	1.54868i	−0.190150	+	0.109783i	−0.592053	−	0.805899i	$-0.701682\pi$
$199$	−2.68240	+	1.54868i	−0.190150	+	0.109783i	0.401903	+	0.915682i	$0.368349\pi$
$200$			10.9005i			0.770781i
$201$	−5.19154	+	2.66370i	−0.366183	+	0.187883i
$202$	9.86989	−	5.69838i	0.694443	−	0.400937i
$203$	−4.21040	+	3.32212i	−0.295512	+	0.233167i
$204$	19.1113	+	12.3345i	1.33806	+	0.863586i
$205$	−3.32404	−	5.75741i	−0.232161	−	0.402115i
$206$	−10.4485	−	18.0974i	−0.727983	−	1.26090i
$207$	0.448748	−	0.202838i	0.0311901	−	0.0140982i
$208$	35.9577	+	20.7602i	2.49322	+	1.43946i
$209$	3.58354	−	6.20687i	0.247878	−	0.429338i
$210$	5.34848	−	11.7016i	0.369080	−	0.807485i
$211$	−2.81889	−	4.88246i	−0.194060	−	0.336123i	0.752532	−	0.658556i	$-0.228832\pi$
$211$	−2.81889	−	4.88246i	−0.194060	−	0.336123i	−0.946592	+	0.322434i	$0.895499\pi$
$212$			17.3199i			1.18954i
$213$	−6.09695	+	9.44674i	−0.417756	+	0.647280i
$214$	−13.9515			−0.953702
$215$	4.57974	−	7.93235i	0.312336	−	0.540982i
$216$	56.0163	+	8.38659i	3.81142	+	0.570635i
$217$	−3.43047	+	2.70674i	−0.232875	+	0.183745i
$218$	−42.3475	−	24.4493i	−2.86813	−	1.65592i
$219$	−7.41368	−	0.367558i	−0.500970	−	0.0248373i
$220$	−15.0254	−	8.67495i	−1.01302	−	0.584865i
$221$	4.26104	+	2.46011i	0.286629	+	0.165485i
$222$	4.01828	−	6.22600i	0.269689	−	0.417862i
$223$	−7.91481	−	4.56962i	−0.530015	−	0.306004i	0.211008	−	0.977484i	$-0.432326\pi$
$223$	−7.91481	−	4.56962i	−0.530015	−	0.306004i	−0.741023	+	0.671480i	$0.765659\pi$
$224$	64.5777	−	50.9536i	4.31478	−	3.40448i
$225$	1.23566	+	2.73371i	0.0823773	+	0.182247i
$226$	−20.2828	+	35.1309i	−1.34919	+	2.33687i
$227$	1.26089			0.0836885			0.0418442	−	0.999124i	$-0.486677\pi$
$227$	1.26089			0.0836885			0.0418442	+	0.999124i	$0.486677\pi$
$228$	−24.7286	−	1.22600i	−1.63769	−	0.0811939i
$229$		−	15.7353i		−	1.03982i	−0.854221	−	0.519910i	$-0.825965\pi$
$229$		−	15.7353i		−	1.03982i	0.854221	−	0.519910i	$-0.174035\pi$
$230$	0.230437	+	0.399129i	0.0151946	+	0.0263178i
$231$	7.83642	+	11.0122i	0.515598	+	0.724550i
$232$	11.0482	−	19.1360i	0.725350	−	1.25634i
$233$	17.0711	+	9.85603i	1.11837	+	0.645690i	0.940984	−	0.338452i	$-0.109903\pi$
$233$	17.0711	+	9.85603i	1.11837	+	0.645690i	0.177384	+	0.984142i	$0.443237\pi$
$234$	18.4724	+	1.83617i	1.20758	+	0.120034i
$235$	−5.97720	−	10.3528i	−0.389909	−	0.675343i
$236$	6.60643	+	11.4427i	0.430042	+	0.744854i
$237$	−0.0245853	+	0.495889i	−0.00159699	+	0.0322114i
$238$	13.0185	−	10.2720i	0.843866	−	0.665833i
$239$	20.2559	−	11.6948i	1.31025	−	0.756471i	0.328109	−	0.944640i	$-0.393589\pi$
$239$	20.2559	−	11.6948i	1.31025	−	0.756471i	0.982137	+	0.188169i	$0.0602554\pi$
$240$	−1.61576	+	32.5900i	−0.104297	+	2.10368i
$241$			4.49113i			0.289299i	0.989483	+	0.144650i	$0.0462055\pi$
$241$			4.49113i			0.289299i	−0.989483	+	0.144650i	$0.953795\pi$
$242$	−5.59485	+	3.23019i	−0.359650	+	0.207644i
$243$	14.9989	−	4.24665i	0.962178	−	0.272423i
$244$			41.9624i			2.68637i
$245$	−5.08173	−	4.81415i	−0.324660	−	0.307565i
$246$	−14.7582	−	28.7637i	−0.940949	−	1.83390i
$247$	−5.35565			−0.340772
$248$	9.00163	−	15.5913i	0.571604	−	0.990048i
$249$	8.23564	−	4.22558i	0.521912	−	0.267786i
$250$	−2.43144	+	1.40379i	−0.153778	+	0.0887835i
$251$	27.2837			1.72213			0.861065	−	0.508495i	$-0.169798\pi$
$251$	27.2837			1.72213			0.861065	+	0.508495i	$0.169798\pi$
$252$	21.4888	−	41.4522i	1.35367	−	2.61124i
$253$	−0.484155			−0.0304385
$254$	−40.2518	+	23.2394i	−2.52562	+	1.45817i
$255$	−0.191470	+	3.86197i	−0.0119903	+	0.241846i
$256$	−58.6329	+	101.555i	−3.66456	+	6.34720i
$257$	−7.80863			−0.487089			−0.243544	−	0.969890i	$-0.578310\pi$
$257$	−7.80863			−0.487089			−0.243544	+	0.969890i	$0.578310\pi$
$258$	24.1535	−	37.4239i	1.50373	−	2.32991i
$259$	−2.49730	−	3.16504i	−0.155175	−	0.196666i
$260$			12.9648i			0.804045i
$261$	0.601523	−	6.05148i	0.0372334	−	0.374577i
$262$	−36.8279	+	21.2626i	−2.27524	+	1.31361i
$263$		−	5.43158i		−	0.334925i	−0.985878	−	0.167463i	$-0.946443\pi$
$263$		−	5.43158i		−	0.334925i	0.985878	−	0.167463i	$-0.0535574\pi$
$264$	−46.7870	−	30.1964i	−2.87954	−	1.85846i
$265$	−2.54984	+	1.47215i	−0.156635	+	0.0904334i
$266$	−6.68161	+	16.7684i	−0.409676	+	1.02813i
$267$	2.88795	−	1.48176i	0.176740	−	0.0906825i
$268$	−9.90865	−	17.1623i	−0.605267	−	1.04835i
$269$	10.8168	+	18.7353i	0.659512	+	1.14231i	0.980742	+	0.195307i	$0.0625705\pi$
$269$	10.8168	+	18.7353i	0.659512	+	1.14231i	−0.321230	+	0.947001i	$0.604096\pi$
$270$	5.34322	+	13.5749i	0.325178	+	0.826142i
$271$	−15.8993	−	9.17946i	−0.965813	−	0.557612i	−0.0678557	−	0.997695i	$-0.521616\pi$
$271$	−15.8993	−	9.17946i	−0.965813	−	0.557612i	−0.897957	+	0.440083i	$0.854949\pi$
$272$	−21.0285	+	36.4225i	−1.27504	+	2.20844i
$273$	4.19857	−	9.18576i	0.254109	−	0.555948i
$274$	14.8528	+	25.7258i	0.897289	+	1.55415i
$275$		−	2.94940i		−	0.177855i
$276$	0.763516	+	1.48809i	0.0459583	+	0.0895724i
$277$	28.1485			1.69128			0.845641	−	0.533753i	$-0.179219\pi$
$277$	28.1485			1.69128			0.845641	+	0.533753i	$0.179219\pi$
$278$	20.2467	−	35.0683i	1.21432	−	2.10326i
$279$	0.490097	−	4.93051i	0.0293414	−	0.295182i
$280$	26.7914	+	10.6754i	1.60109	+	0.637980i
$281$	22.0307	+	12.7194i	1.31424	+	0.758777i	0.982796	−	0.184697i	$-0.0591304\pi$
$281$	22.0307	+	12.7194i	1.31424	+	0.758777i	0.331445	+	0.943474i	$0.392464\pi$
$282$	−26.5378	−	51.7219i	−1.58030	−	3.08000i
$283$	19.5162	+	11.2677i	1.16012	+	0.669794i	0.951332	−	0.308167i	$-0.0997157\pi$
$283$	19.5162	+	11.2677i	1.16012	+	0.669794i	0.208785	+	0.977962i	$0.433049\pi$
$284$	−33.0697	−	19.0928i	−1.96233	−	1.13295i
$285$	−1.92138	−	3.74475i	−0.113813	−	0.221820i
$286$	−15.8052	−	9.12514i	−0.934582	−	0.539581i
$287$	−17.4061	+	2.53134i	−1.02745	+	0.149420i
$288$	−9.22596	+	92.8156i	−0.543645	+	5.46921i
$289$	6.00809	−	10.4063i	0.353417	−	0.612136i
$290$	5.69125			0.334202
$291$	9.18032	+	17.8924i	0.538160	+	1.04887i
$292$		−	25.2098i		−	1.47529i
$293$	9.49676	+	16.4489i	0.554806	+	0.960953i	0.997919	+	0.0644868i	$0.0205410\pi$
$293$	9.49676	+	16.4489i	0.554806	+	0.960953i	−0.443112	+	0.896466i	$0.646126\pi$
$294$	−23.5222	−	24.6056i	−1.37185	−	1.43503i
$295$	−1.12306	+	1.94520i	−0.0653872	+	0.113254i
$296$	14.3849	+	8.30514i	0.836107	+	0.482727i
$297$	−15.1566	−	2.26920i	−0.879475	−	0.131672i
$298$	10.8822	+	18.8485i	0.630390	+	1.09187i
$299$	0.180894	+	0.313318i	0.0104614	+	0.0181196i
$300$	−9.06521	+	4.65123i	−0.523380	+	0.268539i
$301$	−15.0111	−	19.0248i	−0.865224	−	1.09657i
$302$	−32.9122	+	19.0019i	−1.89388	+	1.09343i
$303$	5.90738	+	3.81264i	0.339370	+	0.219030i
$304$		−	45.7789i		−	2.62560i
$305$	−6.17771	+	3.56670i	−0.353735	+	0.204229i
$306$	−1.85990	+	18.7111i	−0.106324	+	1.06964i
$307$		−	22.4589i		−	1.28180i	−0.767626	−	0.640898i	$-0.778562\pi$
$307$		−	22.4589i		−	1.28180i	0.767626	−	0.640898i	$-0.221438\pi$
$308$	−36.0367	+	28.4339i	−2.05338	+	1.62017i
$309$	6.99083	−	10.8317i	0.397695	−	0.616196i
$310$	4.63701			0.263364
$311$	15.4543	−	26.7677i	0.876335	−	1.51786i	0.0210003	−	0.999779i	$-0.493315\pi$
$311$	15.4543	−	26.7677i	0.876335	−	1.51786i	0.855334	−	0.518077i	$-0.173352\pi$
$312$	−2.06048	+	41.5601i	−0.116652	+	2.35288i
$313$	−10.5736	+	6.10465i	−0.597653	+	0.345055i	−0.768118	−	0.640309i	$-0.778806\pi$
$313$	−10.5736	+	6.10465i	−0.597653	+	0.345055i	0.170465	+	0.985364i	$0.445473\pi$
$314$	−3.98035			−0.224624
$315$	7.92910	−	0.359755i	0.446754	−	0.0202699i
$316$	−1.68624			−0.0948585
$317$	−16.1747	+	9.33844i	−0.908459	+	0.524499i	−0.879935	−	0.475094i	$-0.842414\pi$
$317$	−16.1747	+	9.33844i	−0.908459	+	0.524499i	−0.0285240	+	0.999593i	$0.509081\pi$
$318$	−12.7388	+	6.53610i	−0.714358	+	0.366526i
$319$	−2.98937	+	5.17773i	−0.167372	+	0.289897i
$320$	−49.6126			−2.77343
$321$	−3.92909	−	7.65776i	−0.219300	−	0.427415i
$322$	1.20667	−	0.175484i	0.0672449	−	0.00977931i
$323$		−	5.42487i		−	0.301848i
$324$	16.9275	+	50.1636i	0.940418	+	2.78687i
$325$	−1.90869	+	1.10198i	−0.105875	+	0.0611268i
$326$		−	28.8377i		−	1.59717i
$327$	1.49377	−	30.1295i	0.0826057	−	1.66617i
$328$	62.7586	−	36.2337i	3.46526	−	2.00067i
$329$	−31.2991	+	4.55178i	−1.72558	+	0.250948i
$330$	0.710208	−	14.3250i	0.0390957	−	0.788563i
$331$	5.59694	+	9.69419i	0.307636	+	0.532841i	0.977845	−	0.209332i	$-0.0671288\pi$
$331$	5.59694	+	9.69419i	0.307636	+	0.532841i	−0.670209	+	0.742173i	$0.733795\pi$
$332$	15.7187	+	27.2255i	0.862674	+	1.49419i
$333$	4.54902	+	0.452177i	0.249285	+	0.0247791i
$334$	28.0360	+	16.1866i	1.53406	+	0.885691i
$335$	1.68442	−	2.91751i	0.0920299	−	0.159401i
$336$	78.5179	+	35.8885i	4.28350	+	1.95788i
$337$	−1.64474	−	2.84877i	−0.0895947	−	0.155183i	0.817745	−	0.575580i	$-0.195224\pi$
$337$	−1.64474	−	2.84877i	−0.0895947	−	0.155183i	−0.907340	+	0.420398i	$0.861891\pi$
$338$		−	22.8609i		−	1.24347i
$339$	−24.9950	−	1.23921i	−1.35754	−	0.0673048i
$340$	−13.1324			−0.712205
$341$	−2.43562	+	4.21861i	−0.131896	+	0.228451i
$342$	−8.43023	−	18.6506i	−0.455855	−	1.00851i
$343$	−16.8091	+	7.77519i	−0.907607	+	0.419821i
$344$	86.4665	+	49.9214i	4.66196	+	2.69158i
$345$	−0.154180	+	0.238889i	−0.00830075	+	0.0128613i
$346$	−22.2606	−	12.8522i	−1.19674	−	0.690937i
$347$	−4.34767	−	2.51013i	−0.233395	−	0.134751i	0.378742	−	0.925502i	$-0.376357\pi$
$347$	−4.34767	−	2.51013i	−0.233395	−	0.134751i	−0.612137	+	0.790751i	$0.709690\pi$
$348$	20.6284	+	1.02272i	1.10580	+	0.0548237i
$349$	13.4611	+	7.77179i	0.720558	+	0.416014i	0.814958	−	0.579520i	$-0.196760\pi$
$349$	13.4611	+	7.77179i	0.720558	+	0.416014i	−0.0943999	+	0.995534i	$0.530093\pi$
$350$	1.06902	+	7.35084i	0.0571415	+	0.392919i
$351$	4.19444	+	10.6563i	0.223883	+	0.568793i
$352$	45.8499	−	79.4143i	2.44381	−	4.23280i
$353$	28.1091			1.49610			0.748048	−	0.663644i	$-0.230991\pi$
$353$	28.1091			1.49610			0.748048	+	0.663644i	$0.230991\pi$
$354$	−5.92301	+	9.17723i	−0.314804	+	0.487764i
$355$		−	6.49137i		−	0.344526i
$356$	5.51198	+	9.54704i	0.292135	+	0.505992i
$357$	9.30450	+	4.25284i	0.492446	+	0.225084i
$358$	5.19119	−	8.99140i	0.274363	−	0.475210i
$359$	−4.32665	−	2.49799i	−0.228352	−	0.131839i	0.381460	−	0.924386i	$-0.375422\pi$
$359$	−4.32665	−	2.49799i	−0.228352	−	0.131839i	−0.609812	+	0.792546i	$0.708755\pi$
$360$	−29.7987	+	13.4693i	−1.57053	+	0.709894i
$361$	−6.54752	−	11.3406i	−0.344606	−	0.596876i
$362$	30.9457	+	53.5995i	1.62647	+	2.81713i
$363$	−3.34866	−	2.16123i	−0.175759	−	0.113435i
$364$	31.8652	+	12.6972i	1.67019	+	0.665513i
$365$	3.71139	−	2.14277i	0.194263	−	0.112158i
$366$	−30.8634	+	15.8356i	−1.61326	+	0.827739i
$367$			7.71817i			0.402885i	0.979500	+	0.201443i	$0.0645630\pi$
$367$			7.71817i			0.402885i	−0.979500	+	0.201443i	$0.935437\pi$
$368$	−2.67817	+	1.54624i	−0.139609	+	0.0806035i
$369$	11.6317	−	16.2012i	0.605522	−	0.843399i
$370$			4.27823i			0.222414i
$371$	1.12108	+	7.70879i	0.0582034	+	0.400221i
$372$	16.8072	+	0.833275i	0.871414	+	0.0432033i
$373$	−7.38671			−0.382469			−0.191235	−	0.981544i	$-0.561249\pi$
$373$	−7.38671			−0.382469			−0.191235	+	0.981544i	$0.561249\pi$
$374$	9.24309	−	16.0095i	0.477949	−	0.827832i
$375$	−1.45528	−	0.939239i	−0.0751502	−	0.0485021i
$376$	112.851	−	65.1543i	5.81983	−	3.36008i
$377$	4.46765			0.230096
$378$	38.5975	+	0.162010i	1.98524	+	0.00833290i
$379$	−30.6026			−1.57195			−0.785976	−	0.618258i	$-0.787839\pi$
$379$	−30.6026			−1.57195			−0.785976	+	0.618258i	$0.787839\pi$
$380$	12.3795	−	7.14729i	0.635054	−	0.366648i
$381$	−24.0917	−	15.5488i	−1.23426	−	0.796592i
$382$	1.50666	−	2.60961i	0.0770874	−	0.133519i
$383$	−25.4486			−1.30036			−0.650181	−	0.759779i	$-0.725307\pi$
$383$	−25.4486			−1.30036			−0.650181	+	0.759779i	$0.725307\pi$
$384$	−133.394	−	6.61343i	−6.80721	−	0.337490i
$385$	−7.24908	−	2.88851i	−0.369447	−	0.147212i
$386$		−	56.5878i		−	2.88024i
$387$	27.3437	+	2.71799i	1.38996	+	0.138163i
$388$	−59.1490	+	34.1497i	−3.00283	+	1.73369i
$389$		−	12.3034i		−	0.623805i	−0.950114	−	0.311903i	$-0.899034\pi$
$389$		−	12.3034i		−	0.623805i	0.950114	−	0.311903i	$-0.100966\pi$
$390$	−9.53566	+	4.89261i	−0.482857	+	0.247747i
$391$	−0.317367	+	0.183232i	−0.0160500	+	0.00926645i
$392$	52.4766	−	55.3933i	2.65047	−	2.79778i
$393$	−22.0424	−	14.2262i	−1.11189	−	0.717619i
$394$	−33.3927	−	57.8378i	−1.68230	−	2.91383i
$395$	−0.143327	−	0.248249i	−0.00721154	−	0.0124908i
$396$	5.14842	−	51.7944i	0.258718	−	2.60277i
$397$	29.0621	+	16.7790i	1.45858	+	0.842114i	0.998942	−	0.0459896i	$-0.0146441\pi$
$397$	29.0621	+	16.7790i	1.45858	+	0.842114i	0.459643	+	0.888104i	$0.347977\pi$
$398$	4.34806	−	7.53105i	0.217948	−	0.377498i
$399$	−11.0856	+	1.05495i	−0.554976	+	0.0528136i
$400$	−9.41949	−	16.3150i	−0.470974	−	0.815752i
$401$		−	19.2338i		−	0.960493i	−0.877134	−	0.480246i	$-0.840547\pi$
$401$		−	19.2338i		−	0.960493i	0.877134	−	0.480246i	$-0.159453\pi$
$402$	8.88362	−	13.7645i	0.443075	−	0.686509i
$403$	3.64006			0.181325
$404$	−11.9394	+	20.6796i	−0.594007	+	1.02885i
$405$	−5.94629	+	6.75586i	−0.295474	+	0.335701i
$406$	5.57376	−	13.9881i	0.276621	−	0.694216i
$407$	−3.89220	−	2.24716i	−0.192929	−	0.111388i
$408$	−42.0973	−	2.08712i	−2.08413	−	0.103328i
$409$	−0.00853353	−	0.00492683i	−0.000421956	−	0.000243616i	0.499789	−	0.866147i	$-0.333411\pi$
$409$	−0.00853353	−	0.00492683i	−0.000421956	−	0.000243616i	−0.500211	+	0.865904i	$0.666744\pi$
$410$	16.1644	+	9.33253i	0.798303	+	0.460901i
$411$	−9.93760	+	15.3975i	−0.490186	+	0.759504i
$412$	37.9181	+	21.8920i	1.86809	+	1.07854i
$413$	3.68107	+	4.66532i	0.181133	+	0.229565i
$414$	−0.806360	+	1.12314i	−0.0396304	+	0.0551991i
$415$	−2.67210	+	4.62821i	−0.131168	+	0.227190i
$416$	−68.5233			−3.35963
$417$	24.9505	+	1.23701i	1.22183	+	0.0605764i
$418$			20.1221i			0.984207i
$419$	12.8389	+	22.2377i	0.627223	+	1.08638i	0.988106	+	0.153771i	$0.0491418\pi$
$419$	12.8389	+	22.2377i	0.627223	+	1.08638i	−0.360884	+	0.932611i	$0.617525\pi$
$420$	2.55380	+	26.8358i	0.124613	+	1.30945i
$421$	−12.1429	+	21.0321i	−0.591807	+	1.02504i	0.402182	+	0.915560i	$0.368252\pi$
$421$	−12.1429	+	21.0321i	−0.591807	+	1.02504i	−0.993989	+	0.109481i	$0.965081\pi$
$422$	13.7079	+	7.91427i	0.667291	+	0.385260i
$423$	20.9157	−	29.1324i	1.01696	−	1.41647i
$424$	−16.0471	−	27.7945i	−0.779318	−	1.34982i
$425$	−1.11622	−	1.93336i	−0.0541448	−	0.0937816i
$426$	1.56311	−	31.5280i	0.0757327	−	1.52754i
$427$	2.71613	+	18.6767i	0.131443	+	0.903831i
$428$	25.3152	−	14.6157i	1.22366	−	0.706478i
$429$	0.557515	−	11.2451i	0.0269171	−	0.542920i
$430$			25.7160i			1.24014i
$431$	8.37286	−	4.83408i	0.403307	−	0.232849i	−0.284603	−	0.958645i	$-0.591862\pi$
$431$	8.37286	−	4.83408i	0.403307	−	0.232849i	0.687910	+	0.725796i	$0.258528\pi$
$432$	−91.0881	+	35.8532i	−4.38248	+	1.72499i
$433$		−	16.9020i		−	0.812260i	−0.913815	−	0.406130i	$-0.866878\pi$
$433$		−	16.9020i		−	0.812260i	0.913815	−	0.406130i	$-0.133122\pi$
$434$	4.54128	−	11.3969i	0.217988	−	0.547070i
$435$	1.60280	+	3.12385i	0.0768485	+	0.149777i
$436$	102.454			4.90664
$437$	0.199448	−	0.345453i	0.00954087	−	0.0165253i
$438$	18.5419	−	9.51357i	0.885965	−	0.454576i
$439$	−6.85359	+	3.95692i	−0.327104	+	0.188854i	−0.654555	−	0.756015i	$-0.727144\pi$
$439$	−6.85359	+	3.95692i	−0.327104	+	0.188854i	0.327451	+	0.944868i	$0.393810\pi$
$440$	32.1499			1.53269
$441$	6.88119	−	19.8406i	0.327676	−	0.944790i
$442$	−13.8139			−0.657062
$443$	−13.6603	+	7.88678i	−0.649021	+	0.374712i	−0.788081	−	0.615572i	$-0.788925\pi$
$443$	−13.6603	+	7.88678i	−0.649021	+	0.374712i	0.139060	+	0.990284i	$0.455592\pi$
$444$	−0.768801	+	15.5068i	−0.0364857	+	0.735920i
$445$	−0.937011	+	1.62295i	−0.0444186	+	0.0769353i
$446$	25.6592			1.21500
$447$	−7.28100	+	11.2813i	−0.344379	+	0.533588i
$448$	−48.5883	+	121.939i	−2.29558	+	5.76106i
$449$			8.11819i			0.383121i	0.981481	+	0.191560i	$0.0613548\pi$
$449$			8.11819i			0.383121i	−0.981481	+	0.191560i	$0.938645\pi$
$450$	−6.84198	−	4.91223i	−0.322534	−	0.231565i
$451$	−16.9809	+	9.80393i	−0.799600	+	0.461649i
$452$		−	84.9943i		−	3.99779i
$453$	−19.6988	−	12.7136i	−0.925529	−	0.597339i
$454$	−3.06578	+	1.77003i	−0.143884	+	0.0830717i
$455$	0.839184	+	5.77043i	0.0393415	+	0.270522i
$456$	40.8196	−	20.9440i	1.91155	−	0.980791i
$457$	3.25476	+	5.63740i	0.152251	+	0.263707i	0.932055	−	0.362318i	$-0.118014\pi$
$457$	3.25476	+	5.63740i	0.152251	+	0.263707i	−0.779804	+	0.626024i	$0.784681\pi$
$458$	22.0891	+	38.2595i	1.03216	+	1.78775i
$459$	−10.7941	+	4.24866i	−0.503824	+	0.198310i
$460$	−0.836266	−	0.482818i	−0.0389911	−	0.0225115i
$461$	−16.8907	+	29.2556i	−0.786680	+	1.36257i	0.141310	+	0.989965i	$0.454869\pi$
$461$	−16.8907	+	29.2556i	−0.786680	+	1.36257i	−0.927990	+	0.372604i	$0.878465\pi$
$462$	−34.5126	−	15.7748i	−1.60567	−	0.733910i
$463$	1.89382	+	3.28019i	0.0880133	+	0.152443i	0.906671	−	0.421838i	$-0.138615\pi$
$463$	1.89382	+	3.28019i	0.0880133	+	0.152443i	−0.818658	+	0.574281i	$0.805282\pi$
$464$			38.1885i			1.77286i
$465$	1.30590	+	2.54519i	0.0605597	+	0.118030i
$466$	−55.3432			−2.56372
$467$	5.45274	−	9.44443i	0.252323	−	0.437036i	−0.711842	−	0.702340i	$-0.752139\pi$
$467$	5.45274	−	9.44443i	0.252323	−	0.437036i	0.964165	+	0.265303i	$0.0854722\pi$
$468$	−35.4420	+	16.0201i	−1.63831	+	0.740530i
$469$	−5.52105	−	6.99728i	−0.254938	−	0.323105i
$470$	29.0664	+	16.7815i	1.34073	+	0.774071i
$471$	−1.12097	−	2.18476i	−0.0516515	−	0.100668i
$472$	−21.2036	−	12.2419i	−0.975976	−	0.563480i
$473$	−23.3957	−	13.5075i	−1.07573	−	0.621075i
$474$	−0.636347	−	1.24024i	−0.0292284	−	0.0569659i
$475$	2.10445	+	1.21501i	0.0965589	+	0.0557483i
$476$	−12.8613	+	32.2771i	−0.589497	+	1.47942i
$477$	−7.17516	−	5.15143i	−0.328528	−	0.235868i
$478$	−32.8340	+	56.8701i	−1.50179	+	2.60118i
$479$	12.0307			0.549695			0.274848	−	0.961488i	$-0.411373\pi$
$479$	12.0307			0.549695			0.274848	+	0.961488i	$0.411373\pi$
$480$	−24.5832	−	47.9126i	−1.12207	−	2.18690i
$481$			3.35842i			0.153131i
$482$	−6.30461	−	10.9199i	−0.287167	−	0.497388i
$483$	0.436149	+	0.612902i	0.0198454	+	0.0278880i
$484$	6.76797	−	11.7225i	0.307635	−	0.532839i
$485$	−10.0550	−	5.80528i	−0.456576	−	0.263604i
$486$	−30.5074	+	31.3807i	−1.38384	+	1.42346i
$487$	14.7479	+	25.5442i	0.668292	+	1.15752i	0.978381	+	0.206809i	$0.0663078\pi$
$487$	14.7479	+	25.5442i	0.668292	+	1.15752i	−0.310089	+	0.950707i	$0.600359\pi$
$488$	−38.8788	−	67.3400i	−1.75996	−	3.04834i
$489$	15.8286	−	8.12142i	0.715794	−	0.367263i
$490$	19.1140	+	4.57163i	0.863481	+	0.206525i
$491$	22.5435	−	13.0155i	1.01738	−	0.587382i	0.104033	−	0.994574i	$-0.466825\pi$
$491$	22.5435	−	13.0155i	1.01738	−	0.587382i	0.913343	+	0.407192i	$0.133492\pi$
$492$	56.9122	+	36.7313i	2.56580	+	1.65597i
$493$			4.52540i			0.203814i
$494$	13.0219	−	7.51821i	0.585884	−	0.338260i
$495$	8.06279	−	3.64445i	0.362395	−	0.163806i
$496$			31.1145i			1.39708i
$497$	−15.9546	−	6.35736i	−0.715661	−	0.285166i
$498$	−14.0926	+	21.8354i	−0.631504	+	0.978466i
$499$	1.39270			0.0623458			0.0311729	−	0.999514i	$-0.490076\pi$
$499$	1.39270			0.0623458			0.0311729	+	0.999514i	$0.490076\pi$
$500$	2.94126	−	5.09441i	0.131537	−	0.227829i
$501$	−0.988946	+	19.9471i	−0.0441828	+	0.891172i
$502$	−66.3385	+	38.3006i	−2.96083	+	1.70944i
$503$	−21.0669			−0.939329			−0.469664	−	0.882845i	$-0.655625\pi$
$503$	−21.0669			−0.939329			−0.469664	+	0.882845i	$0.655625\pi$
$504$	3.92150	+	86.4310i	0.174678	+	3.84994i
$505$	−4.05928			−0.180636
$506$	1.17719	−	0.679652i	0.0523325	−	0.0302142i
$507$	12.5480	−	6.43822i	0.557278	−	0.285931i
$508$	48.6917	−	84.3365i	2.16035	−	3.74183i
$509$	−4.44575			−0.197054			−0.0985271	−	0.995134i	$-0.531413\pi$
$509$	−4.44575			−0.197054			−0.0985271	+	0.995134i	$0.531413\pi$
$510$	−4.95585	−	9.65892i	−0.219449	−	0.427704i
$511$	−1.63177	−	11.2205i	−0.0721854	−	0.496364i
$512$		−	175.015i		−	7.73462i
$513$	7.86289	−	9.87972i	0.347155	−	0.436200i
$514$	18.9862	−	10.9617i	0.837445	−	0.483499i
$515$			7.44308i			0.327981i
$516$	−4.62119	+	93.2099i	−0.203437	+	4.10334i
$517$	−30.5346	+	17.6291i	−1.34291	+	0.775328i
$518$	10.5151	+	4.18990i	0.462007	+	0.184094i
$519$	0.785224	−	15.8381i	0.0344675	−	0.695213i
$520$	−12.0121	−	20.8056i	−0.526766	−	0.912386i
$521$	10.4781	+	18.1485i	0.459052	+	0.795101i	0.998911	−	0.0466540i	$-0.0148558\pi$
$521$	10.4781	+	18.1485i	0.459052	+	0.795101i	−0.539859	+	0.841755i	$0.681522\pi$
$522$	7.03245	+	15.5582i	0.307802	+	0.680964i
$523$	−28.8880	−	16.6785i	−1.26318	−	0.729300i	−0.289495	−	0.957180i	$-0.593487\pi$
$523$	−28.8880	−	16.6785i	−1.26318	−	0.729300i	−0.973689	+	0.227880i	$0.926821\pi$
$524$	44.5499	−	77.1627i	1.94617	−	3.37087i
$525$	−3.73371	+	2.65695i	−0.162952	+	0.115959i
$526$	7.62480	+	13.2065i	0.332457	+	0.575833i
$527$			3.68712i			0.160613i
$528$	96.1210	+	4.76552i	4.18313	+	0.207393i
$529$	22.9731			0.998828
$530$	4.13318	−	7.15888i	0.179534	−	0.310962i
$531$	−6.70532	−	0.666516i	−0.290986	−	0.0289243i
$532$	−5.44283	−	37.4262i	−0.235977	−	1.62263i
$533$	12.6891	+	7.32606i	0.549626	+	0.317327i
$534$	−4.94178	+	7.65690i	−0.213852	+	0.331346i
$535$	4.30346	+	2.48460i	0.186055	+	0.107419i
$536$	31.8023	+	18.3610i	1.37365	+	0.793076i
$537$	6.39723	+	0.317164i	0.276061	+	0.0136866i
$538$	−52.6008	−	30.3691i	−2.26778	−	1.30930i
$539$	−14.1989	+	14.9880i	−0.611588	+	0.645581i
$540$	−23.9166	−	19.0343i	−1.02921	−	0.819106i
$541$	4.69718	−	8.13575i	0.201947	−	0.349783i	−0.747208	−	0.664590i	$-0.768606\pi$
$541$	4.69718	−	8.13575i	0.201947	−	0.349783i	0.949156	+	0.314807i	$0.101940\pi$
$542$	51.5442			2.21401
$543$	−20.7049	+	32.0807i	−0.888534	+	1.37671i
$544$		−	69.4090i		−	2.97589i
$545$	8.70832	+	15.0833i	0.373024	+	0.646096i
$546$	2.68633	+	28.2285i	0.114965	+	1.20807i
$547$	2.58139	−	4.47110i	0.110372	−	0.191170i	−0.805548	−	0.592530i	$-0.798129\pi$
$547$	2.58139	−	4.47110i	0.110372	−	0.191170i	0.915920	+	0.401360i	$0.131462\pi$
$548$	−53.9013	−	31.1199i	−2.30255	−	1.32938i
$549$	−17.3839	−	12.4808i	−0.741925	−	0.532668i
$550$	4.14034	+	7.17128i	0.176545	+	0.305784i
$551$	−2.46294	−	4.26594i	−0.104925	−	0.181735i
$552$	−2.60401	−	1.68063i	−0.110834	−	0.0715324i
$553$	−0.750518	+	0.109147i	−0.0319153	+	0.00464139i
$554$	−68.4414	+	39.5147i	−2.90780	+	1.67882i
$555$	−2.34826	+	1.20486i	−0.0996781	+	0.0511434i
$556$			84.8428i			3.59814i
$557$	−26.6079	+	15.3621i	−1.12741	+	0.650911i	−0.943283	−	0.331991i	$-0.892280\pi$
$557$	−26.6079	+	15.3621i	−1.12741	+	0.650911i	−0.184128	+	0.982902i	$0.558946\pi$
$558$	5.72976	+	12.6762i	0.242560	+	0.536627i
$559$			20.1871i			0.853825i
$560$	−49.3244	+	7.17316i	−2.08434	+	0.303121i
$561$	11.3905	+	0.564721i	0.480907	+	0.0238426i
$562$	−71.4217			−3.01274
$563$	16.5085	−	28.5935i	0.695748	−	1.20507i	−0.274179	−	0.961679i	$-0.588406\pi$
$563$	16.5085	−	28.5935i	0.695748	−	1.20507i	0.969928	−	0.243393i	$-0.0782605\pi$
$564$	102.338	+	66.0491i	4.30920	+	2.78117i
$565$	12.5129	−	7.22431i	0.526421	−	0.303929i
$566$	−63.2699			−2.65943
$567$	10.7811	+	21.2313i	0.452765	+	0.891630i
$568$	70.7591			2.96899
$569$	17.6042	−	10.1638i	0.738008	−	0.426089i	−0.0833364	−	0.996521i	$-0.526558\pi$
$569$	17.6042	−	10.1638i	0.738008	−	0.426089i	0.821345	+	0.570432i	$0.193224\pi$
$570$	9.92856	+	6.40792i	0.415862	+	0.268398i
$571$	14.4198	−	24.9759i	0.603451	−	1.04521i	−0.388843	−	0.921304i	$-0.627125\pi$
$571$	14.4198	−	24.9759i	0.603451	−	1.04521i	0.992294	−	0.123904i	$-0.0395416\pi$
$572$	38.2385			1.59883
$573$	1.85669	+	0.0920517i	0.0775644	+	0.00384552i
$574$	38.7683	−	30.5893i	1.61816	−	1.27677i
$575$		−	0.164154i		−	0.00684568i
$576$	−61.3042	−	135.626i	−2.55434	−	5.65109i
$577$	32.5802	−	18.8102i	1.35633	−	0.783079i	0.367205	−	0.930140i	$-0.380315\pi$
$577$	32.5802	−	18.8102i	1.35633	−	0.783079i	0.989127	+	0.147061i	$0.0469814\pi$
$578$			33.7364i			1.40325i
$579$	31.0603	−	15.9366i	1.29082	−	0.662301i
$580$	−10.3269	+	5.96223i	−0.428801	+	0.247568i
$581$	8.75836	+	11.1002i	0.363358	+	0.460513i
$582$	−47.4386	−	30.6170i	−1.96639	−	1.26911i
$583$	4.34196	+	7.52049i	0.179825	+	0.311467i
$584$	23.3573	+	40.4560i	0.966531	+	1.67408i
$585$	−5.37097	−	3.85611i	−0.222062	−	0.159431i
$586$	−46.1815	−	26.6629i	−1.90774	−	1.10144i
$587$	−4.93482	+	8.54736i	−0.203682	+	0.352787i	−0.949712	−	0.313125i	$-0.898624\pi$
$587$	−4.93482	+	8.54736i	−0.203682	+	0.352787i	0.746030	+	0.665912i	$0.231957\pi$
$588$	68.4587	+	20.0050i	2.82319	+	0.824994i
$589$	−2.00671	−	3.47572i	−0.0826849	−	0.143214i
$590$		−	6.30617i		−	0.259621i
$591$	22.3421	−	34.6174i	0.919033	−	1.42397i
$592$	−28.7070			−1.17985
$593$	−5.20292	+	9.01172i	−0.213658	+	0.370067i	−0.952857	−	0.303421i	$-0.901871\pi$
$593$	−5.20292	+	9.01172i	−0.213658	+	0.370067i	0.739198	+	0.673488i	$0.235205\pi$
$594$	40.0378	−	15.7593i	1.64277	−	0.646611i
$595$	−5.84502	+	0.850031i	−0.239622	+	0.0348479i
$596$	−39.4919	−	22.8007i	−1.61765	−	0.933952i
$597$	5.35822	+	0.265651i	0.219297	+	0.0108724i
$598$	−0.879665	−	0.507875i	−0.0359722	−	0.0207685i
$599$	−3.17154	−	1.83109i	−0.129586	−	0.0748163i	0.433806	−	0.901006i	$-0.357170\pi$
$599$	−3.17154	−	1.83109i	−0.129586	−	0.0748163i	−0.563391	+	0.826190i	$0.690504\pi$
$600$	10.2382	−	15.8632i	0.417971	−	0.647613i
$601$	11.6789	+	6.74281i	0.476392	+	0.275045i	0.718912	−	0.695102i	$-0.244641\pi$
$601$	11.6789	+	6.74281i	0.476392	+	0.275045i	−0.242520	+	0.970146i	$0.577974\pi$
$602$	63.2053	+	25.1851i	2.57605	+	1.02647i
$603$	10.0570	+	0.999674i	0.409552	+	0.0407099i
$604$	39.8132	−	68.9584i	1.61997	−	2.80588i
$605$	2.30105			0.0935508
$606$	−19.7156	−	0.977465i	−0.800890	−	0.0397068i
$607$			22.3352i			0.906557i	0.891369	+	0.453278i	$0.149746\pi$
$607$			22.3352i			0.906557i	−0.891369	+	0.453278i	$0.850254\pi$
$608$	37.7757	+	65.4295i	1.53201	+	2.65352i
$609$	9.24757	−	0.880034i	0.374730	−	0.0356608i
$610$	10.0138	−	17.3444i	0.405447	−	0.702255i
$611$	22.8172	+	13.1735i	0.923084	+	0.532943i
$612$	−16.2272	−	35.9002i	−0.655945	−	1.45118i
$613$	−2.40282	−	4.16180i	−0.0970489	−	0.168094i	0.813413	−	0.581687i	$-0.197607\pi$
$613$	−2.40282	−	4.16180i	−0.0970489	−	0.168094i	−0.910462	+	0.413593i	$0.864274\pi$
$614$	31.5276	+	54.6074i	1.27235	+	2.20377i
$615$	−0.570186	+	11.5007i	−0.0229921	+	0.463753i
$616$	31.4862	−	79.0185i	1.26861	−	3.18375i
$617$	−3.02489	+	1.74642i	−0.121777	+	0.0703082i	−0.559651	−	0.828728i	$-0.689065\pi$
$617$	−3.02489	+	1.74642i	−0.121777	+	0.0703082i	0.437874	+	0.899036i	$0.355732\pi$
$618$	−1.79227	+	36.1504i	−0.0720959	+	1.45418i
$619$			35.8707i			1.44176i	0.693058	+	0.720882i	$0.256263\pi$
$619$			35.8707i			1.44176i	−0.693058	+	0.720882i	$0.743737\pi$
$620$	−8.41394	+	4.85779i	−0.337912	+	0.195094i
$621$	−0.843565	−	0.126296i	−0.0338511	−	0.00506809i
$622$			86.7786i			3.47950i
$623$	3.07125	+	3.89245i	0.123047	+	0.155948i
$624$	−32.8296	−	63.9846i	−1.31424	−	2.56144i
$625$	1.00000			0.0400000
$626$	17.1393	−	29.6861i	0.685024	−	1.18650i
$627$	−11.0448	+	5.66691i	−0.441086	+	0.226315i
$628$	7.22242	−	4.16987i	0.288206	−	0.166396i
$629$	−3.40183			−0.135640
$630$	−18.7741	+	12.0055i	−0.747977	+	0.478311i
$631$	1.00411			0.0399728			0.0199864	−	0.999800i	$-0.493638\pi$
$631$	1.00411			0.0399728			0.0199864	+	0.999800i	$0.493638\pi$
$632$	2.70603	−	1.56233i	0.107640	−	0.0621461i
$633$	−0.483535	+	9.75294i	−0.0192188	+	0.387645i
$634$	26.2184	−	45.4117i	1.04127	−	1.80353i
$635$	16.5547			0.656954
$636$	16.2675	−	25.2052i	0.645049	−	0.999452i
$637$	15.0045	+	3.58874i	0.594500	+	0.142191i
$638$		−	16.7858i		−	0.664555i
$639$	17.7455	−	8.02112i	0.702001	−	0.317311i
$640$	66.7787	−	38.5547i	2.63966	−	1.52401i
$641$		−	8.04971i		−	0.317945i	−0.987283	−	0.158972i	$-0.949182\pi$
$641$		−	8.04971i		−	0.317945i	0.987283	−	0.158972i	$-0.0508181\pi$
$642$	20.3032	+	13.1038i	0.801305	+	0.517164i
$643$	−6.37812	+	3.68241i	−0.251529	+	0.145220i	−0.620464	−	0.784235i	$-0.713056\pi$
$643$	−6.37812	+	3.68241i	−0.251529	+	0.145220i	0.368935	+	0.929455i	$0.379722\pi$
$644$	−2.00568	+	1.58254i	−0.0790349	+	0.0623607i
$645$	−14.1152	+	7.24229i	−0.555784	+	0.285165i
$646$	7.61539	+	13.1902i	0.299624	+	0.518963i
$647$	−19.1587	−	33.1838i	−0.753205	−	1.30459i	−0.946262	−	0.323402i	$-0.895173\pi$
$647$	−19.1587	−	33.1838i	−0.753205	−	1.30459i	0.193057	−	0.981188i	$-0.438160\pi$
$648$	−73.6421	−	64.8175i	−2.89294	−	2.54627i
$649$	5.73717	+	3.31236i	0.225204	+	0.130021i
$650$	3.09390	−	5.35879i	0.121353	−	0.210189i
$651$	7.53455	−	0.717017i	0.295302	−	0.0281021i
$652$	30.2107	+	52.3265i	1.18314	+	2.04926i
$653$			19.3159i			0.755889i	0.925828	+	0.377944i	$0.123369\pi$
$653$			19.3159i			0.755889i	−0.925828	+	0.377944i	$0.876631\pi$
$654$	38.6635	+	75.3549i	1.51186	+	2.94661i
$655$	15.1466			0.591825
$656$	−62.6216	+	108.464i	−2.44496	+	4.23480i
$657$	10.4437	+	7.49812i	0.407449	+	0.292529i
$658$	69.7121	−	55.0048i	2.71766	−	2.14431i
$659$	−20.7017	−	11.9521i	−0.806422	−	0.465588i	0.0392895	−	0.999228i	$-0.487491\pi$
$659$	−20.7017	−	11.9521i	−0.806422	−	0.465588i	−0.845712	+	0.533640i	$0.820824\pi$
$660$	13.7183	+	26.7369i	0.533985	+	1.04073i
$661$	−30.9675	−	17.8791i	−1.20450	−	0.695416i	−0.242944	−	0.970040i	$-0.578113\pi$
$661$	−30.9675	−	17.8791i	−1.20450	−	0.695416i	−0.961552	+	0.274625i	$0.911446\pi$
$662$	−27.2172	−	15.7139i	−1.05783	−	0.610737i
$663$	−3.89036	−	7.58228i	−0.151089	−	0.294471i
$664$	−50.4497	−	29.1272i	−1.95783	−	1.13035i
$665$	5.04727	−	3.98243i	0.195725	−	0.154432i
$666$	−11.6954	+	5.28643i	−0.453188	+	0.204845i
$667$	−0.166378	+	0.288175i	−0.00644218	+	0.0111582i
$668$	−67.8291			−2.62439
$669$	7.22627	+	14.0840i	0.279384	+	0.544517i
$670$			9.45832i			0.365407i
$671$	10.5196	+	18.2205i	0.406106	+	0.703396i
$672$	−141.836	+	13.4977i	−5.47144	+	0.520684i
$673$	9.60719	−	16.6401i	0.370330	−	0.641431i	−0.619286	−	0.785165i	$-0.712578\pi$
$673$	9.60719	−	16.6401i	0.370330	−	0.641431i	0.989616	+	0.143735i	$0.0459112\pi$
$674$	7.99817	+	4.61774i	0.308078	+	0.177869i
$675$	0.769378	−	5.13888i	0.0296134	−	0.197795i
$676$	23.9494	+	41.4815i	0.921130	+	1.59544i
$677$	15.1753	+	26.2843i	0.583233	+	1.01019i	0.995093	+	0.0989416i	$0.0315457\pi$
$677$	15.1753	+	26.2843i	0.583233	+	1.01019i	−0.411861	+	0.911247i	$0.635121\pi$
$678$	62.5135	−	32.0748i	2.40082	−	1.23182i
$679$	−24.1158	+	19.0280i	−0.925479	+	0.730229i
$680$	21.0745	−	12.1674i	0.808171	−	0.466598i
$681$	−1.83495	−	1.18428i	−0.0703154	−	0.0453818i
$682$		−	13.6764i		−	0.523696i
$683$	−3.34744	+	1.93265i	−0.128086	+	0.0739506i	−0.562674	−	0.826679i	$-0.690227\pi$
$683$	−3.34744	+	1.93265i	−0.128086	+	0.0739506i	0.434588	+	0.900629i	$0.356894\pi$
$684$	34.8354	+	25.0102i	1.33197	+	0.956290i
$685$		−	10.5805i		−	0.404259i
$686$	29.9556	−	42.5014i	1.14371	−	1.62271i
$687$	−14.7792	+	22.8993i	−0.563863	+	0.873661i
$688$	−172.555			−6.57861
$689$	3.24456	−	5.61974i	0.123608	−	0.214095i
$690$	0.0395278	−	0.797279i	0.00150480	−	0.0303519i
$691$	−22.5356	+	13.0109i	−0.857294	+	0.494959i	−0.863105	−	0.505024i	$-0.831484\pi$
$691$	−22.5356	+	13.0109i	−0.857294	+	0.494959i	0.00581104	+	0.999983i	$0.498150\pi$
$692$	53.8564			2.04731
$693$	−1.06106	−	23.3861i	−0.0403063	−	0.888363i
$694$	14.0948			0.535031
$695$	−12.4906	+	7.21144i	−0.473795	+	0.273546i
$696$	−34.0515	+	17.4713i	−1.29072	+	0.662249i
$697$	−7.42076	+	12.8531i	−0.281081	+	0.486847i
$698$	−43.6399			−1.65179
$699$	−15.5861	−	30.3771i	−0.589519	−	1.14897i
$700$	−9.64059	−	12.2183i	−0.364380	−	0.461809i
$701$			7.20712i			0.272209i	0.990694	+	0.136105i	$0.0434583\pi$
$701$			7.20712i			0.272209i	−0.990694	+	0.136105i	$0.956542\pi$
$702$	−25.1578	−	20.0221i	−0.949519	−	0.755685i
$703$	3.20679	−	1.85144i	0.120946	−	0.0698284i
$704$			146.327i			5.51492i
$705$	−1.02529	+	20.6802i	−0.0386147	+	0.778862i
$706$	−68.3455	+	39.4593i	−2.57222	+	1.48507i
$707$	−3.97548	+	9.97697i	−0.149513	+	0.375223i
$708$	1.13322	−	22.8573i	0.0425892	−	0.859028i
$709$	−7.87267	−	13.6359i	−0.295664	−	0.512105i	0.679475	−	0.733699i	$-0.262208\pi$
$709$	−7.87267	−	13.6359i	−0.295664	−	0.512105i	−0.975139	+	0.221593i	$0.928874\pi$
$710$	9.11253	+	15.7834i	0.341987	+	0.592339i
$711$	0.501537	−	0.698564i	0.0188091	−	0.0261982i
$712$	−17.6910	−	10.2139i	−0.662997	−	0.382781i
$713$	−0.135558	+	0.234794i	−0.00507670	+	0.00879310i
$714$	−28.5934	+	2.72106i	−1.07008	+	0.101833i
$715$	3.25018	+	5.62947i	0.121550	+	0.210530i
$716$			21.7534i			0.812963i
$717$	−40.4621	−	2.00604i	−1.51109	−	0.0749171i
$718$	14.0266			0.523470
$719$	7.36885	−	12.7632i	0.274812	−	0.475988i	−0.695276	−	0.718743i	$-0.744718\pi$
$719$	7.36885	−	12.7632i	0.274812	−	0.475988i	0.970088	+	0.242755i	$0.0780511\pi$
$720$	32.9612	−	45.9099i	1.22839	−	1.71096i
$721$	18.2937	+	7.28942i	0.681294	+	0.271472i
$722$	31.8398	+	18.3827i	1.18495	+	0.684133i
$723$	4.21825	−	6.53584i	0.156878	−	0.243070i
$724$	−112.303	−	64.8382i	−4.17371	−	2.40969i
$725$	−1.75552	−	1.01355i	−0.0651984	−	0.0376423i
$726$	11.1760	+	0.554086i	0.414779	+	0.0205641i
$727$	−39.3361	−	22.7107i	−1.45890	−	0.842294i	−0.459938	−	0.887951i	$-0.652129\pi$
$727$	−39.3361	−	22.7107i	−1.45890	−	0.842294i	−0.998957	+	0.0456571i	$0.985462\pi$
$728$	−62.9005	+	9.14751i	−2.33125	+	0.339029i
$729$	−25.8161	−	7.90748i	−0.956152	−	0.292870i
$730$	−6.01601	+	10.4200i	−0.222663	+	0.385663i
$731$	−20.4481			−0.756300
$732$	39.4127	−	61.0669i	1.45674	−	2.25710i
$733$			19.5834i			0.723329i	0.932308	+	0.361665i	$0.117791\pi$
$733$			19.5834i			0.723329i	−0.932308	+	0.361665i	$0.882209\pi$
$734$	−10.8347	−	18.7663i	−0.399916	−	0.692675i
$735$	2.87368	+	11.7789i	0.105997	+	0.434470i
$736$	2.55185	−	4.41993i	0.0940624	−	0.162921i
$737$	−8.60490	−	4.96804i	−0.316965	−	0.183000i
$738$	−5.53868	+	55.7206i	−0.203882	+	2.05110i
$739$	−18.8037	−	32.5690i	−0.691706	−	1.19807i	−0.971279	−	0.237945i	$-0.923526\pi$
$739$	−18.8037	−	32.5690i	−0.691706	−	1.19807i	0.279572	−	0.960125i	$-0.409807\pi$
$740$	−4.48192	−	7.76292i	−0.164759	−	0.285371i
$741$	7.79395	+	5.03023i	0.286318	+	0.184790i
$742$	−13.5474	−	17.1697i	−0.497339	−	0.630319i
$743$	−8.38009	+	4.83825i	−0.307436	+	0.177498i	−0.645778	−	0.763525i	$-0.723467\pi$
$743$	−8.38009	+	4.83825i	−0.307436	+	0.177498i	0.338343	+	0.941023i	$0.390134\pi$
$744$	−27.7438	+	14.2349i	−1.01714	+	0.521878i
$745$		−	7.75202i		−	0.284012i
$746$	17.9603	−	10.3694i	0.657574	−	0.379651i
$747$	−15.9540	−	1.58584i	−0.583725	−	0.0580228i
$748$			38.7327i			1.41621i
$749$	10.3213	−	8.14381i	0.377133	−	0.297568i
$750$	4.85691	+	0.240797i	0.177349	+	0.00879268i
$751$	5.37674			0.196200			0.0980999	−	0.995177i	$-0.468724\pi$
$751$	5.37674			0.196200			0.0980999	+	0.995177i	$0.468724\pi$
$752$	−112.604	+	195.036i	−4.10625	+	7.11224i
$753$	−39.7053	−	25.6259i	−1.44694	−	0.933860i
$754$	−10.8628	+	6.27165i	−0.395600	+	0.228400i
$755$	13.5361			0.492629
$756$	−70.2057	+	40.1413i	−2.55336	+	1.45992i
$757$	32.9029			1.19588			0.597938	−	0.801543i	$-0.295987\pi$
$757$	32.9029			1.19588			0.597938	+	0.801543i	$0.295987\pi$
$758$	74.4084	−	42.9597i	2.70263	−	1.56037i
$759$	0.704579	+	0.454737i	0.0255746	+	0.0165059i
$760$	−13.2442	+	22.9395i	−0.480416	+	0.832105i
$761$	−30.6469			−1.11095			−0.555475	−	0.831533i	$-0.687464\pi$
$761$	−30.6469			−1.11095			−0.555475	+	0.831533i	$0.687464\pi$
$762$	80.4048	+	3.98634i	2.91276	+	0.144410i
$763$	45.6004	−	6.63159i	1.65085	−	0.240080i
$764$			6.31358i			0.228417i
$765$	3.90596	−	5.44040i	0.141220	−	0.196698i
$766$	61.8766	−	35.7245i	2.23569	−	1.29078i
$767$		−	4.95036i		−	0.178747i
$768$	180.712	−	92.7205i	6.52087	−	3.34576i
$769$	33.6315	−	19.4171i	1.21278	−	0.700200i	0.249418	−	0.968396i	$-0.419761\pi$
$769$	33.6315	−	19.4171i	1.21278	−	0.700200i	0.963364	+	0.268196i	$0.0864275\pi$
$770$	21.6806	−	3.15297i	0.781313	−	0.113625i
$771$	11.3637	+	7.33417i	0.409254	+	0.264134i
$772$	59.2821	+	102.680i	2.13361	+	3.69552i
$773$	−18.9882	−	32.8886i	−0.682960	−	1.18292i	−0.974073	−	0.226233i	$-0.927359\pi$
$773$	−18.9882	−	32.8886i	−0.682960	−	1.18292i	0.291114	−	0.956689i	$-0.405974\pi$
$774$	−70.3000	+	31.7762i	−2.52688	+	1.14217i
$775$	−1.43033	−	0.825801i	−0.0513790	−	0.0296637i
$776$	63.2804	−	109.605i	2.27163	−	3.93459i
$777$	0.661539	+	6.95157i	0.0237326	+	0.249386i
$778$	17.2714	+	29.9149i	0.619208	+	1.07250i
$779$		−	16.1549i		−	0.578811i
$780$	12.1771	−	18.8674i	0.436009	−	0.675562i
$781$	−19.1456			−0.685085
$782$	0.514439	−	0.891035i	0.0183963	−	0.0318634i
$783$	−6.55917	+	8.24160i	−0.234406	+	0.294531i
$784$	−30.6758	+	128.255i	−1.09556	+	4.58055i
$785$	1.22778	+	0.708858i	0.0438213	+	0.0253002i
$786$	73.5654	+	3.64725i	2.62399	+	0.130093i
$787$	44.7921	+	25.8607i	1.59666	+	0.921835i	0.992124	+	0.125261i	$0.0399768\pi$
$787$	44.7921	+	25.8607i	1.59666	+	0.921835i	0.604541	+	0.796574i	$0.293357\pi$
$788$	121.183	+	69.9651i	4.31697	+	2.49241i
$789$	−5.10155	+	7.90445i	−0.181620	+	0.281406i
$790$	0.696979	+	0.402401i	0.0247974	+	0.0143168i
$791$	−5.50148	−	37.8295i	−0.195610	−	1.34506i
$792$	39.7263	+	87.8883i	1.41161	+	3.12298i
$793$	7.86087	−	13.6154i	0.279148	−	0.483498i
$794$	−94.2169			−3.34363
$795$	5.09342	+	0.252523i	0.180645	+	0.00895608i
$796$			18.2203i			0.645802i
$797$	26.3231	+	45.5929i	0.932411	+	1.61498i	0.779187	+	0.626792i	$0.215632\pi$
$797$	26.3231	+	45.5929i	0.932411	+	1.61498i	0.153224	+	0.988191i	$0.451034\pi$
$798$	25.4731	−	18.1270i	0.901737	−	0.641687i
$799$	−13.3438	+	23.1121i	−0.472069	+	0.817647i
$800$	26.9256	+	15.5455i	0.951963	+	0.549616i
$801$	−5.59450	−	0.556098i	−0.197672	−	0.0196488i
$802$	27.0003	+	46.7659i	0.953414	+	1.65136i
$803$	−6.31990	−	10.9464i	−0.223024	−	0.386289i
$804$	−1.69967	+	34.2825i	−0.0599427	+	1.20905i
$805$	−0.403460	−	0.160765i	−0.0142201	−	0.00566621i
$806$	−8.85059	+	5.10989i	−0.311749	+	0.179988i
$807$	1.85545	−	37.4245i	0.0653148	−	1.31741i
$808$		−	44.2481i		−	1.55664i
$809$	−2.32844	+	1.34433i	−0.0818637	+	0.0472640i	−0.540373	−	0.841426i	$-0.681717\pi$
$809$	−2.32844	+	1.34433i	−0.0818637	+	0.0472640i	0.458509	+	0.888690i	$0.348384\pi$
$810$	4.97423	−	24.7738i	0.174777	−	0.870462i
$811$		−	14.0277i		−	0.492580i	−0.969196	−	0.246290i	$-0.920788\pi$
$811$		−	14.0277i		−	0.492580i	0.969196	−	0.246290i	$-0.0792116\pi$
$812$	4.54038	+	31.2207i	0.159336	+	1.09563i
$813$	14.5161	+	28.2919i	0.509104	+	0.992240i
$814$	12.6182			0.442267
$815$	−5.13568	+	8.89525i	−0.179895	+	0.311587i
$816$	64.8117	−	33.2539i	2.26886	−	1.16412i
$817$	19.2757	−	11.1288i	0.674372	−	0.389349i
$818$	0.0276650			0.000967283
$819$	−14.7377	+	9.42436i	−0.514977	+	0.329314i
$820$	−39.1075			−1.36569
$821$	−26.1455	+	15.0951i	−0.912484	+	0.526823i	−0.881230	−	0.472688i	$-0.843284\pi$
$821$	−26.1455	+	15.0951i	−0.912484	+	0.526823i	−0.0312546	+	0.999511i	$0.509950\pi$
$822$	2.54775	−	51.3884i	0.0888630	−	1.79238i
$823$	20.6164	−	35.7087i	0.718644	−	1.24473i	−0.242893	−	0.970053i	$-0.578097\pi$
$823$	20.6164	−	35.7087i	0.718644	−	1.24473i	0.961537	−	0.274675i	$-0.0885701\pi$
$824$	−81.1332			−2.82641
$825$	−2.77019	+	4.29219i	−0.0964457	+	0.149435i
$826$	−15.4994	−	6.17598i	−0.539294	−	0.214890i
$827$		−	24.5854i		−	0.854917i	−0.904035	−	0.427459i	$-0.859409\pi$
$827$		−	24.5854i		−	0.854917i	0.904035	−	0.427459i	$-0.140591\pi$
$828$	0.286544	−	2.88270i	0.00995808	−	0.100181i
$829$	2.25853	−	1.30396i	0.0784418	−	0.0452884i	−0.460266	−	0.887781i	$-0.652246\pi$
$829$	2.25853	−	1.30396i	0.0784418	−	0.0452884i	0.538708	+	0.842493i	$0.318913\pi$
$830$		−	15.0043i		−	0.520806i
$831$	−40.9639	−	26.4382i	−1.42102	−	0.917131i
$832$	94.6948	−	54.6721i	3.28295	−	1.89541i
$833$	−3.63513	+	15.1985i	−0.125950	+	0.526595i
$834$	−62.4021	+	32.0176i	−2.16081	+	1.10868i
$835$	−5.76531	−	9.98582i	−0.199517	−	0.345573i
$836$	−21.0802	−	36.5120i	−0.729075	−	1.26279i
$837$	−5.34415	+	6.71493i	−0.184721	+	0.232102i
$838$	−62.4341	−	36.0464i	−2.15675	−	1.24520i
$839$	−4.60759	+	7.98059i	−0.159072	+	0.275521i	−0.934534	−	0.355873i	$-0.884183\pi$
$839$	−4.60759	+	7.98059i	−0.159072	+	0.275521i	0.775462	+	0.631394i	$0.217517\pi$
$840$	−28.9621	−	40.6993i	−0.999287	−	1.40426i
$841$	−12.4454	−	21.5561i	−0.429153	−	0.743314i
$842$		−	68.1842i		−	2.34978i
$843$	−20.1142	−	39.2024i	−0.692769	−	1.35020i
$844$	−33.1643			−1.14156
$845$	−4.07128	+	7.05167i	−0.140056	+	0.242585i
$846$	−9.95948	+	100.195i	−0.342414	+	3.44478i
$847$	2.25354	−	5.65555i	0.0774326	−	0.194327i
$848$	48.0363	+	27.7338i	1.64957	+	0.952382i
$849$	−17.8184	−	34.7280i	−0.611526	−	1.19186i
$850$	5.42806	+	3.13389i	0.186181	+	0.107492i
$851$	−0.216627	−	0.125070i	−0.00742587	−	0.00428733i
$852$	30.1928	+	58.8457i	1.03439	+	2.01602i
$853$	34.2534	+	19.7762i	1.17282	+	0.677125i	0.954342	−	0.298718i	$-0.0965589\pi$
$853$	34.2534	+	19.7762i	1.17282	+	0.677125i	0.218474	+	0.975843i	$0.429892\pi$
$854$	−32.8223	−	41.5985i	−1.12316	−	1.42347i
$855$	−0.721083	+	7.25429i	−0.0246605	+	0.248091i
$856$	−27.0834	+	46.9098i	−0.925691	+	1.60334i
$857$	−30.4242			−1.03927			−0.519636	−	0.854388i	$-0.673932\pi$
$857$	−30.4242			−1.03927			−0.519636	+	0.854388i	$0.673932\pi$
$858$	14.4303	+	28.1245i	0.492641	+	0.960154i
$859$			15.3036i			0.522154i	0.965318	+	0.261077i	$0.0840776\pi$
$859$			15.3036i			0.522154i	−0.965318	+	0.261077i	$0.915922\pi$
$860$	−26.9404	−	46.6622i	−0.918661	−	1.59117i
$861$	27.7082	+	12.6647i	0.944293	+	0.431611i
$862$	−13.5721	+	23.5075i	−0.462266	+	0.800669i
$863$	43.4952	+	25.1119i	1.48059	+	0.854821i	0.999758	−	0.0219909i	$-0.00700049\pi$
$863$	43.4952	+	25.1119i	1.48059	+	0.854821i	0.480834	+	0.876811i	$0.340334\pi$
$864$	100.602	−	126.407i	3.42256	−	4.30045i
$865$	4.57767	+	7.92875i	0.155645	+	0.269586i
$866$	23.7269	+	41.0963i	0.806274	+	1.39651i
$867$	−18.5174	+	9.50103i	−0.628886	+	0.322672i
$868$	3.69932	+	25.4374i	0.125563	+	0.863402i
$869$	−0.732185	+	0.422727i	−0.0248377	+	0.0143400i
$870$	−8.28235	−	5.34545i	−0.280798	−	0.181228i
$871$			7.42481i			0.251580i
$872$	−164.415	+	94.9249i	−5.56779	+	3.21456i
$873$	3.44533	−	34.6609i	0.116607	−	1.17309i
$874$			1.11993i			0.0378822i
$875$	0.979355	−	2.45782i	0.0331083	−	0.0830894i
$876$	−23.6780	+	36.6872i	−0.800007	+	1.23955i
$877$	27.0950			0.914934			0.457467	−	0.889227i	$-0.348757\pi$
$877$	27.0950			0.914934			0.457467	+	0.889227i	$0.348757\pi$
$878$	11.1094	−	19.2420i	0.374924	−	0.649387i
$879$	1.62901	−	32.8574i	0.0549453	−	1.10825i
$880$	−48.1195	+	27.7818i	−1.62211	+	0.936525i
$881$	14.2216			0.479138			0.239569	−	0.970879i	$-0.422994\pi$
$881$	14.2216			0.479138			0.239569	+	0.970879i	$0.422994\pi$
$882$	11.1209	+	57.9009i	0.374459	+	1.94963i
$883$	−40.8611			−1.37508			−0.687542	−	0.726145i	$-0.741310\pi$
$883$	−40.8611			−1.37508			−0.687542	+	0.726145i	$0.741310\pi$
$884$	25.0656	−	14.4717i	0.843049	−	0.486734i
$885$	3.46137	−	1.77598i	0.116353	−	0.0596989i
$886$	22.1428	−	38.3524i	0.743902	−	1.28848i
$887$	−56.7843			−1.90663			−0.953315	−	0.301979i	$-0.902353\pi$
$887$	−56.7843			−1.90663			−0.953315	+	0.301979i	$0.902353\pi$
$888$	−13.1335	−	25.5972i	−0.440733	−	0.858985i
$889$	16.2130	−	40.6885i	0.543765	−	1.36465i
$890$		−	5.26147i		−	0.176365i
$891$	19.9257	+	17.5380i	0.667537	+	0.587545i
$892$	−46.5590	+	26.8809i	−1.55891	+	0.900038i
$893$		−	29.0493i		−	0.972098i
$894$	1.86667	−	37.6508i	0.0624306	−	1.25923i
$895$	−3.20254	+	1.84899i	−0.107049	+	0.0618049i
$896$	−29.3603	−	201.889i	−0.980859	−	6.74462i
$897$	0.0310294	−	0.625866i	0.00103604	−	0.0208971i
$898$	−11.3962	−	19.7389i	−0.380297	−	0.658694i
$899$	1.67398	+	2.89942i	0.0558304	+	0.0967012i
$900$	17.5610	+	1.74558i	0.585367	+	0.0581861i
$901$	5.69238	+	3.28650i	0.189641	+	0.109489i
$902$	27.5253	−	47.6753i	0.916494	−	1.58741i
$903$	3.97645	+	41.7853i	0.132328	+	1.39053i
$904$	78.7485	+	136.396i	2.61914	+	4.53648i
$905$		−	22.0444i		−	0.732780i
$906$	65.7436	+	3.25946i	2.18419	+	0.108288i
$907$	7.77577			0.258190			0.129095	−	0.991632i	$-0.458793\pi$
$907$	7.77577			0.258190			0.129095	+	0.991632i	$0.458793\pi$
$908$	3.70862	−	6.42351i	0.123075	−	0.213172i
$909$	−5.01589	−	11.0969i	−0.166367	−	0.368060i
$910$	−10.1409	−	12.8524i	−0.336167	−	0.426053i
$911$	−42.5224	−	24.5503i	−1.40883	−	0.813388i	−0.413554	−	0.910479i	$-0.635713\pi$
$911$	−42.5224	−	24.5503i	−1.40883	−	0.813388i	−0.995275	+	0.0970912i	$0.969046\pi$
$912$	−42.9974	+	66.6210i	−1.42379	+	2.20604i
$913$	13.6504	+	7.88108i	0.451763	+	0.260826i
$914$	−15.8275	−	9.13799i	−0.523526	−	0.302258i
$915$	12.3403	+	0.611810i	0.407956	+	0.0202258i
$916$	−80.1622	−	46.2817i	−2.64863	−	1.52919i
$917$	14.8339	−	37.2275i	0.489857	−	1.22936i
$918$	20.2809	−	25.4830i	0.669370	−	0.841063i
$919$	8.94471	−	15.4927i	0.295059	−	0.511057i	−0.679940	−	0.733268i	$-0.737994\pi$
$919$	8.94471	−	15.4927i	0.295059	−	0.511057i	0.974999	+	0.222211i	$0.0713274\pi$
$920$	1.78935			0.0589933
$921$	−21.0943	+	32.6839i	−0.695080	+	1.07697i
$922$		−	94.8443i		−	3.12353i
$923$	7.15336	+	12.3900i	0.235456	+	0.407821i
$924$	79.1496	−	7.53218i	2.60383	−	0.247791i
$925$	0.761906	−	1.31966i	0.0250513	−	0.0433901i
$926$	−9.20941	−	5.31705i	−0.302640	−	0.174729i
$927$	−20.3472	+	9.19711i	−0.668289	+	0.302073i
$928$	−31.5123	−	54.5809i	−1.03444	−	1.79171i
$929$	1.09273	+	1.89267i	0.0358515	+	0.0620966i	0.883394	−	0.468630i	$-0.155252\pi$
$929$	1.09273	+	1.89267i	0.0358515	+	0.0620966i	−0.847543	+	0.530727i	$0.821919\pi$
$930$	−6.74813	−	4.35526i	−0.221280	−	0.142815i
$931$	−4.84503	−	16.3055i	−0.158789	−	0.534390i
$932$	100.421	−	57.9783i	3.28941	−	1.89914i
$933$	−47.6316	+	24.4391i	−1.55939	+	0.800099i
$934$			30.6181i			1.00185i
$935$	−5.70224	+	3.29219i	−0.186483	+	0.107666i
$936$	42.0335	−	58.5462i	1.37391	−	1.91364i
$937$		−	29.1897i		−	0.953587i	−0.879015	−	0.476794i	$-0.841799\pi$
$937$		−	29.1897i		−	0.953587i	0.879015	−	0.476794i	$-0.158201\pi$
$938$	23.2468	+	9.26305i	0.759035	+	0.302449i
$939$	21.1212	+	1.04715i	0.689263	+	0.0341725i
$940$	−70.3219			−2.29365
$941$	−3.36048	+	5.82052i	−0.109548	+	0.189743i	−0.915587	−	0.402119i	$-0.868274\pi$
$941$	−3.36048	+	5.82052i	−0.109548	+	0.189743i	0.806039	+	0.591862i	$0.201607\pi$
$942$	5.79251	+	3.73850i	0.188730	+	0.121807i
$943$	−0.945100	+	0.545654i	−0.0307767	+	0.0177689i
$944$	42.3146			1.37722
$945$	−11.8769	−	6.92378i	−0.386356	−	0.225230i
$946$	75.8468			2.46599
$947$	−11.8514	+	6.84240i	−0.385118	+	0.222348i	−0.680043	−	0.733172i	$-0.738039\pi$
$947$	−11.8514	+	6.84240i	−0.385118	+	0.222348i	0.294924	+	0.955521i	$0.404706\pi$
$948$	2.45395	+	1.58379i	0.0797006	+	0.0514389i
$949$	−4.72259	+	8.17976i	−0.153302	+	0.265526i
$950$	−6.82246			−0.221350
$951$	32.3096	+	1.60186i	1.04771	+	0.0519438i
$952$	−9.26575	−	63.7135i	−0.300305	−	2.06497i
$953$		−	50.3854i		−	1.63214i	−0.577951	−	0.816071i	$-0.696148\pi$
$953$		−	50.3854i		−	1.63214i	0.577951	−	0.816071i	$-0.303852\pi$
$954$	24.6775	+	2.45297i	0.798963	+	0.0794177i
$955$	−0.929487	+	0.536639i	−0.0300775	+	0.0173652i
$956$		−	137.589i		−	4.44995i
$957$	9.21348	−	4.72730i	0.297830	−	0.152812i
$958$	−29.2518	+	16.8885i	−0.945083	+	0.545644i
$959$	−26.0049	−	10.3620i	−0.839741	−	0.334608i
$960$	72.2000	+	46.5981i	2.33025	+	1.50395i
$961$	−14.1361	−	24.4845i	−0.456003	−	0.789821i
$962$	−4.71452	−	8.16579i	−0.152002	−	0.263275i
$963$	−1.47457	+	14.8345i	−0.0475172	+	0.478036i
$964$	22.8797	+	13.2096i	0.736904	+	0.425452i
$965$	−10.0777	+	17.4551i	−0.324412	+	0.561898i
$966$	−1.92085	−	0.877972i	−0.0618025	−	0.0282483i
$967$	−19.7514	−	34.2105i	−0.635163	−	1.10013i	−0.986481	−	0.163879i	$-0.947599\pi$
$967$	−19.7514	−	34.2105i	−0.635163	−	1.10013i	0.351317	−	0.936256i	$-0.385734\pi$
$968$			25.0825i			0.806183i
$969$	−5.09526	+	7.89469i	−0.163683	+	0.253614i
$970$	32.5976			1.04665
$971$	19.6127	−	33.9701i	0.629400	−	1.09015i	−0.358272	−	0.933617i	$-0.616634\pi$
$971$	19.6127	−	33.9701i	0.629400	−	1.09015i	0.987672	−	0.156536i	$-0.0500327\pi$
$972$	22.4814	−	88.9009i	0.721091	−	2.85150i
$973$	5.49168	+	37.7621i	0.176055	+	1.21060i
$974$	−71.7173	−	41.4060i	−2.29797	−	1.32673i
$975$	3.81269	+	0.189027i	0.122104	+	0.00605370i
$976$	116.382	+	67.1930i	3.72529	+	2.15080i
$977$	16.7595	+	9.67610i	0.536184	+	0.309566i	0.743531	−	0.668702i	$-0.233150\pi$
$977$	16.7595	+	9.67610i	0.536184	+	0.309566i	−0.207347	+	0.978267i	$0.566483\pi$
$978$	−27.0855	+	41.9668i	−0.866098	+	1.34195i
$979$	4.78673	+	2.76362i	0.152985	+	0.0883257i
$980$	−39.4719	+	11.7287i	−1.26088	+	0.374661i
$981$	−30.4727	+	42.4438i	−0.972917	+	1.35512i
$982$	−36.5421	+	63.2928i	−1.16611	+	2.01976i
$983$	13.2248			0.421805			0.210903	−	0.977507i	$-0.432360\pi$
$983$	13.2248			0.421805			0.210903	+	0.977507i	$0.432360\pi$
$984$	−125.363	−	6.21530i	−3.99643	−	0.198137i
$985$			23.7875i			0.757932i
$986$	−6.35271	−	11.0032i	−0.202312	−	0.350414i
$987$	49.8240	+	22.7733i	1.58592	+	0.724881i
$988$	−15.7523	+	27.2839i	−0.501149	+	0.868015i
$989$	−1.30212	−	0.751782i	−0.0414051	−	0.0239053i
$990$	−14.4881	+	20.1797i	−0.460463	+	0.641354i
$991$	16.7449	+	29.0030i	0.531919	+	0.921311i	0.999306	+	0.0372581i	$0.0118624\pi$
$991$	16.7449	+	29.0030i	0.531919	+	0.921311i	−0.467386	+	0.884053i	$0.654804\pi$
$992$	−25.6750	−	44.4704i	−0.815182	−	1.41194i
$993$	0.960064	−	19.3646i	0.0304667	−	0.614517i
$994$	47.7170	−	6.93940i	1.51349	−	0.220105i
$995$	−2.68240	+	1.54868i	−0.0850378	+	0.0490966i
$996$	2.69628	−	54.3842i	0.0854349	−	1.72323i
$997$		−	2.14952i		−	0.0680761i	−0.999421	−	0.0340380i	$-0.989163\pi$
$997$		−	2.14952i		−	0.0680761i	0.999421	−	0.0340380i	$-0.0108367\pi$
$998$	−3.38626	+	1.95506i	−0.107190	+	0.0618863i
$999$	−6.19537	−	4.93066i	−0.196013	−	0.155999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.b.236.1	yes	30
3.2	odd	2		945.2.be.b.656.15		30
7.3	odd	6		315.2.t.b.101.1	✓	30
9.4	even	3		945.2.t.b.341.1		30
9.5	odd	6		315.2.t.b.131.15	yes	30
21.17	even	6		945.2.t.b.521.15		30
63.31	odd	6		945.2.be.b.206.15		30
63.59	even	6	inner	315.2.be.b.311.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.1	✓	30	7.3	odd	6
315.2.t.b.131.15	yes	30	9.5	odd	6
315.2.be.b.236.1	yes	30	1.1	even	1	trivial
315.2.be.b.311.1	yes	30	63.59	even	6	inner
945.2.t.b.341.1		30	9.4	even	3
945.2.t.b.521.15		30	21.17	even	6
945.2.be.b.206.15		30	63.31	odd	6
945.2.be.b.656.15		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)

\(f(q)\)	\(=\)	\(q+(-2.43144 + 1.40379i) q^{2} +(-1.45528 - 0.939239i) q^{3} +(2.94126 - 5.09441i) q^{4} +1.00000 q^{5} +(4.85691 + 0.240797i) q^{6} +(0.979355 - 2.45782i) q^{7} +10.9005i q^{8} +(1.23566 + 2.73371i) q^{9} +O(q^{10})\)	\(q+(-2.43144 + 1.40379i) q^{2} +(-1.45528 - 0.939239i) q^{3} +(2.94126 - 5.09441i) q^{4} +1.00000 q^{5} +(4.85691 + 0.240797i) q^{6} +(0.979355 - 2.45782i) q^{7} +10.9005i q^{8} +(1.23566 + 2.73371i) q^{9} +(-2.43144 + 1.40379i) q^{10} -2.94940i q^{11} +(-9.06521 + 4.65123i) q^{12} +(-1.90869 + 1.10198i) q^{13} +(1.06902 + 7.35084i) q^{14} +(-1.45528 - 0.939239i) q^{15} +(-9.41949 - 16.3150i) q^{16} +(-1.11622 - 1.93336i) q^{17} +(-6.84198 - 4.91223i) q^{18} +(2.10445 + 1.21501i) q^{19} +(2.94126 - 5.09441i) q^{20} +(-3.73371 + 2.65695i) q^{21} +(4.14034 + 7.17128i) q^{22} -0.164154i q^{23} +(10.2382 - 15.8632i) q^{24} +1.00000 q^{25} +(3.09390 - 5.35879i) q^{26} +(0.769378 - 5.13888i) q^{27} +(-9.64059 - 12.2183i) q^{28} +(-1.75552 - 1.01355i) q^{29} +(4.85691 + 0.240797i) q^{30} +(-1.43033 - 0.825801i) q^{31} +(26.9256 + 15.5455i) q^{32} +(-2.77019 + 4.29219i) q^{33} +(5.42806 + 3.13389i) q^{34} +(0.979355 - 2.45782i) q^{35} +(17.5610 + 1.74558i) q^{36} +(0.761906 - 1.31966i) q^{37} -6.82246 q^{38} +(3.81269 + 0.189027i) q^{39} +10.9005i q^{40} +(-3.32404 - 5.75741i) q^{41} +(5.34848 - 11.7016i) q^{42} +(4.57974 - 7.93235i) q^{43} +(-15.0254 - 8.67495i) q^{44} +(1.23566 + 2.73371i) q^{45} +(0.230437 + 0.399129i) q^{46} +(-5.97720 - 10.3528i) q^{47} +(-1.61576 + 32.5900i) q^{48} +(-5.08173 - 4.81415i) q^{49} +(-2.43144 + 1.40379i) q^{50} +(-0.191470 + 3.86197i) q^{51} +12.9648i q^{52} +(-2.54984 + 1.47215i) q^{53} +(5.34322 + 13.5749i) q^{54} -2.94940i q^{55} +(26.7914 + 10.6754i) q^{56} +(-1.92138 - 3.74475i) q^{57} +5.69125 q^{58} +(-1.12306 + 1.94520i) q^{59} +(-9.06521 + 4.65123i) q^{60} +(-6.17771 + 3.56670i) q^{61} +4.63701 q^{62} +(7.92910 - 0.359755i) q^{63} -49.6126 q^{64} +(-1.90869 + 1.10198i) q^{65} +(0.710208 - 14.3250i) q^{66} +(1.68442 - 2.91751i) q^{67} -13.1324 q^{68} +(-0.154180 + 0.238889i) q^{69} +(1.06902 + 7.35084i) q^{70} -6.49137i q^{71} +(-29.7987 + 13.4693i) q^{72} +(3.71139 - 2.14277i) q^{73} +4.27823i q^{74} +(-1.45528 - 0.939239i) q^{75} +(12.3795 - 7.14729i) q^{76} +(-7.24908 - 2.88851i) q^{77} +(-9.53566 + 4.89261i) q^{78} +(-0.143327 - 0.248249i) q^{79} +(-9.41949 - 16.3150i) q^{80} +(-5.94629 + 6.75586i) q^{81} +(16.1644 + 9.33253i) q^{82} +(-2.67210 + 4.62821i) q^{83} +(2.55380 + 26.8358i) q^{84} +(-1.11622 - 1.93336i) q^{85} +25.7160i q^{86} +(1.60280 + 3.12385i) q^{87} +32.1499 q^{88} +(-0.937011 + 1.62295i) q^{89} +(-6.84198 - 4.91223i) q^{90} +(0.839184 + 5.77043i) q^{91} +(-0.836266 - 0.482818i) q^{92} +(1.30590 + 2.54519i) q^{93} +(29.0664 + 16.7815i) q^{94} +(2.10445 + 1.21501i) q^{95} +(-24.5832 - 47.9126i) q^{96} +(-10.0550 - 5.80528i) q^{97} +(19.1140 + 4.57163i) q^{98} +(8.06279 - 3.64445i) 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

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