LMFDB - Embedded newform 370.2.d.c.221.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(221,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("370.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.d (of order $2$, degree $1$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			221.3
Root			$0.264658 - 1.38923i$ of defining polynomial
Character	$\chi$	$=$	370.221
Dual form			370.2.d.c.221.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +2.24914 q^{3} -1.00000 q^{4} +1.00000i q^{5} -2.24914i q^{6} +1.52932 q^{7} +1.00000i q^{8} +2.05863 q^{9} +1.00000 q^{10} +2.71982 q^{11} -2.24914 q^{12} +0.941367i q^{13} -1.52932i q^{14} +2.24914i q^{15} +1.00000 q^{16} -4.83709i q^{17} -2.05863i q^{18} -0.249141i q^{19} -1.00000i q^{20} +3.43965 q^{21} -2.71982i q^{22} +0.941367i q^{23} +2.24914i q^{24} -1.00000 q^{25} +0.941367 q^{26} -2.11727 q^{27} -1.52932 q^{28} +0.719824i q^{29} +2.24914 q^{30} +4.02760i q^{31} -1.00000i q^{32} +6.11727 q^{33} -4.83709 q^{34} +1.52932i q^{35} -2.05863 q^{36} +(-4.71982 - 3.83709i) q^{37} -0.249141 q^{38} +2.11727i q^{39} -1.00000 q^{40} -8.27674 q^{41} -3.43965i q^{42} +2.71982i q^{43} -2.71982 q^{44} +2.05863i q^{45} +0.941367 q^{46} -3.30777 q^{47} +2.24914 q^{48} -4.66119 q^{49} +1.00000i q^{50} -10.8793i q^{51} -0.941367i q^{52} +8.39400 q^{53} +2.11727i q^{54} +2.71982i q^{55} +1.52932i q^{56} -0.560352i q^{57} +0.719824 q^{58} -7.30777i q^{59} -2.24914i q^{60} +6.83709i q^{61} +4.02760 q^{62} +3.14830 q^{63} -1.00000 q^{64} -0.941367 q^{65} -6.11727i q^{66} -7.68879 q^{67} +4.83709i q^{68} +2.11727i q^{69} +1.52932 q^{70} -3.05863 q^{71} +2.05863i q^{72} +9.11383 q^{73} +(-3.83709 + 4.71982i) q^{74} -2.24914 q^{75} +0.249141i q^{76} +4.15947 q^{77} +2.11727 q^{78} -1.75086i q^{79} +1.00000i q^{80} -10.9379 q^{81} +8.27674i q^{82} +0.131874 q^{83} -3.43965 q^{84} +4.83709 q^{85} +2.71982 q^{86} +1.61899i q^{87} +2.71982i q^{88} -8.99656i q^{89} +2.05863 q^{90} +1.43965i q^{91} -0.941367i q^{92} +9.05863i q^{93} +3.30777i q^{94} +0.249141 q^{95} -2.24914i q^{96} +16.2767i q^{97} +4.66119i q^{98} +5.59912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{3} - 6 q^{4} + 10 q^{7} + 14 q^{9} + 6 q^{10} - 2 q^{11} + 4 q^{12} + 6 q^{16} - 16 q^{21} - 6 q^{25} + 4 q^{26} - 16 q^{27} - 10 q^{28} - 4 q^{30} + 40 q^{33} - 14 q^{34} - 14 q^{36} - 10 q^{37}+ \cdots - 58 q^{99}+O(q^{100}) $ 6 * q - 4 * q^3 - 6 * q^4 + 10 * q^7 + 14 * q^9 + 6 * q^10 - 2 * q^11 + 4 * q^12 + 6 * q^16 - 16 * q^21 - 6 * q^25 + 4 * q^26 - 16 * q^27 - 10 * q^28 - 4 * q^30 + 40 * q^33 - 14 * q^34 - 14 * q^36 - 10 * q^37 + 16 * q^38 - 6 * q^40 + 2 * q^41 + 2 * q^44 + 4 * q^46 - 4 * q^47 - 4 * q^48 - 8 * q^49 + 2 * q^53 - 14 * q^58 - 10 * q^62 + 58 * q^63 - 6 * q^64 - 4 * q^65 + 8 * q^67 + 10 * q^70 - 20 * q^71 - 12 * q^73 - 8 * q^74 + 4 * q^75 - 30 * q^77 + 16 * q^78 + 6 * q^81 - 20 * q^83 + 16 * q^84 + 14 * q^85 - 2 * q^86 + 14 * q^90 - 16 * q^95 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	2.24914			1.29854			0.649271	−	0.760557i	$-0.275074\pi$
$3$	2.24914			1.29854			0.649271	+	0.760557i	$0.275074\pi$
$4$	−1.00000			−0.500000
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		−	2.24914i		−	0.918208i
$7$	1.52932			0.578027			0.289014	−	0.957325i	$-0.406673\pi$
$7$	1.52932			0.578027			0.289014	+	0.957325i	$0.406673\pi$
$8$			1.00000i			0.353553i
$9$	2.05863			0.686211
$10$	1.00000			0.316228
$11$	2.71982			0.820058			0.410029	−	0.912073i	$-0.365519\pi$
$11$	2.71982			0.820058			0.410029	+	0.912073i	$0.365519\pi$
$12$	−2.24914			−0.649271
$13$			0.941367i			0.261088i	0.991443	+	0.130544i	$0.0416724\pi$
$13$			0.941367i			0.261088i	−0.991443	+	0.130544i	$0.958328\pi$
$14$		−	1.52932i		−	0.408727i
$15$			2.24914i			0.580726i
$16$	1.00000			0.250000
$17$		−	4.83709i		−	1.17317i	−0.809889	−	0.586583i	$-0.800473\pi$
$17$		−	4.83709i		−	1.17317i	0.809889	−	0.586583i	$-0.199527\pi$
$18$		−	2.05863i		−	0.485224i
$19$		−	0.249141i		−	0.0571568i	−0.999592	−	0.0285784i	$-0.990902\pi$
$19$		−	0.249141i		−	0.0571568i	0.999592	−	0.0285784i	$-0.00909802\pi$
$20$		−	1.00000i		−	0.223607i
$21$	3.43965			0.750593
$22$		−	2.71982i		−	0.579868i
$23$			0.941367i			0.196289i	0.995172	+	0.0981443i	$0.0312907\pi$
$23$			0.941367i			0.196289i	−0.995172	+	0.0981443i	$0.968709\pi$
$24$			2.24914i			0.459104i
$25$	−1.00000			−0.200000
$26$	0.941367			0.184617
$27$	−2.11727			−0.407468
$28$	−1.52932			−0.289014
$29$			0.719824i			0.133668i	0.997764	+	0.0668340i	$0.0212898\pi$
$29$			0.719824i			0.133668i	−0.997764	+	0.0668340i	$0.978710\pi$
$30$	2.24914			0.410635
$31$			4.02760i			0.723378i	0.932299	+	0.361689i	$0.117800\pi$
$31$			4.02760i			0.723378i	−0.932299	+	0.361689i	$0.882200\pi$
$32$		−	1.00000i		−	0.176777i
$33$	6.11727			1.06488
$34$	−4.83709			−0.829554
$35$			1.52932i			0.258502i
$36$	−2.05863			−0.343106
$37$	−4.71982	−	3.83709i	−0.775934	−	0.630814i
$37$	−4.71982	−	3.83709i	−0.775934	−	0.630814i
$38$	−0.249141			−0.0404159
$39$			2.11727i			0.339034i
$40$	−1.00000			−0.158114
$41$	−8.27674			−1.29261			−0.646305	−	0.763079i	$-0.723686\pi$
$41$	−8.27674			−1.29261			−0.646305	+	0.763079i	$0.723686\pi$
$42$		−	3.43965i		−	0.530749i
$43$			2.71982i			0.414769i	0.978259	+	0.207385i	$0.0664952\pi$
$43$			2.71982i			0.414769i	−0.978259	+	0.207385i	$0.933505\pi$
$44$	−2.71982			−0.410029
$45$			2.05863i			0.306883i
$46$	0.941367			0.138797
$47$	−3.30777			−0.482488			−0.241244	−	0.970464i	$-0.577555\pi$
$47$	−3.30777			−0.482488			−0.241244	+	0.970464i	$0.577555\pi$
$48$	2.24914			0.324635
$49$	−4.66119			−0.665884
$50$			1.00000i			0.141421i
$51$		−	10.8793i		−	1.52341i
$52$		−	0.941367i		−	0.130544i
$53$	8.39400			1.15301			0.576503	−	0.817095i	$-0.304417\pi$
$53$	8.39400			1.15301			0.576503	+	0.817095i	$0.304417\pi$
$54$			2.11727i			0.288123i
$55$			2.71982i			0.366741i
$56$			1.52932i			0.204364i
$57$		−	0.560352i		−	0.0742204i
$58$	0.719824			0.0945175
$59$		−	7.30777i		−	0.951391i	−0.879610	−	0.475696i	$-0.842196\pi$
$59$		−	7.30777i		−	0.951391i	0.879610	−	0.475696i	$-0.157804\pi$
$60$		−	2.24914i		−	0.290363i
$61$			6.83709i			0.875400i	0.899121	+	0.437700i	$0.144207\pi$
$61$			6.83709i			0.875400i	−0.899121	+	0.437700i	$0.855793\pi$
$62$	4.02760			0.511505
$63$	3.14830			0.396649
$64$	−1.00000			−0.125000
$65$	−0.941367			−0.116762
$66$		−	6.11727i		−	0.752983i
$67$	−7.68879			−0.939335			−0.469668	−	0.882843i	$-0.655626\pi$
$67$	−7.68879			−0.939335			−0.469668	+	0.882843i	$0.655626\pi$
$68$			4.83709i			0.586583i
$69$			2.11727i			0.254889i
$70$	1.52932			0.182788
$71$	−3.05863			−0.362993			−0.181496	−	0.983392i	$-0.558094\pi$
$71$	−3.05863			−0.362993			−0.181496	+	0.983392i	$0.558094\pi$
$72$			2.05863i			0.242612i
$73$	9.11383			1.06669			0.533346	−	0.845897i	$-0.320934\pi$
$73$	9.11383			1.06669			0.533346	+	0.845897i	$0.320934\pi$
$74$	−3.83709	+	4.71982i	−0.446053	+	0.548668i
$75$	−2.24914			−0.259708
$76$			0.249141i			0.0285784i
$77$	4.15947			0.474016
$78$	2.11727			0.239733
$79$		−	1.75086i		−	0.196987i	−0.995138	−	0.0984935i	$-0.968598\pi$
$79$		−	1.75086i		−	0.196987i	0.995138	−	0.0984935i	$-0.0314024\pi$
$80$			1.00000i			0.111803i
$81$	−10.9379			−1.21533
$82$			8.27674i			0.914013i
$83$	0.131874			0.0144751			0.00723754	−	0.999974i	$-0.497696\pi$
$83$	0.131874			0.0144751			0.00723754	+	0.999974i	$0.497696\pi$
$84$	−3.43965			−0.375296
$85$	4.83709			0.524656
$86$	2.71982			0.293286
$87$			1.61899i			0.173573i
$88$			2.71982i			0.289934i
$89$		−	8.99656i		−	0.953634i	−0.879003	−	0.476817i	$-0.841790\pi$
$89$		−	8.99656i		−	0.953634i	0.879003	−	0.476817i	$-0.158210\pi$
$90$	2.05863			0.216999
$91$			1.43965i			0.150916i
$92$		−	0.941367i		−	0.0981443i
$93$			9.05863i			0.939337i
$94$			3.30777i			0.341171i
$95$	0.249141			0.0255613
$96$		−	2.24914i		−	0.229552i
$97$			16.2767i			1.65265i	0.563192	+	0.826326i	$0.309573\pi$
$97$			16.2767i			1.65265i	−0.563192	+	0.826326i	$0.690427\pi$
$98$			4.66119i			0.470851i
$99$	5.59912			0.562733
$100$	1.00000			0.100000
$101$	−11.1138			−1.10587			−0.552934	−	0.833225i	$-0.686492\pi$
$101$	−11.1138			−1.10587			−0.552934	+	0.833225i	$0.686492\pi$
$102$	−10.8793			−1.07721
$103$			14.1725i			1.39645i	0.715876	+	0.698227i	$0.246027\pi$
$103$			14.1725i			1.39645i	−0.715876	+	0.698227i	$0.753973\pi$
$104$	−0.941367			−0.0923086
$105$			3.43965i			0.335675i
$106$		−	8.39400i		−	0.815298i
$107$	10.6922			1.03366			0.516828	−	0.856089i	$-0.327113\pi$
$107$	10.6922			1.03366			0.516828	+	0.856089i	$0.327113\pi$
$108$	2.11727			0.203734
$109$			12.2767i			1.17590i	0.808898	+	0.587949i	$0.200064\pi$
$109$			12.2767i			1.17590i	−0.808898	+	0.587949i	$0.799936\pi$
$110$	2.71982			0.259325
$111$	−10.6155	−	8.63016i	−1.00758	−	0.819138i
$112$	1.52932			0.144507
$113$		−	2.95436i		−	0.277922i	−0.990298	−	0.138961i	$-0.955624\pi$
$113$		−	2.95436i		−	0.277922i	0.990298	−	0.138961i	$-0.0443763\pi$
$114$	−0.560352			−0.0524818
$115$	−0.941367			−0.0877829
$116$		−	0.719824i		−	0.0668340i
$117$			1.93793i			0.179162i
$118$	−7.30777			−0.672735
$119$		−	7.39744i		−	0.678122i
$120$	−2.24914			−0.205318
$121$	−3.60256			−0.327505
$122$	6.83709			0.619001
$123$	−18.6155			−1.67851
$124$		−	4.02760i		−	0.361689i
$125$		−	1.00000i		−	0.0894427i
$126$		−	3.14830i		−	0.280473i
$127$	8.30434			0.736891			0.368445	−	0.929649i	$-0.379890\pi$
$127$	8.30434			0.736891			0.368445	+	0.929649i	$0.379890\pi$
$128$			1.00000i			0.0883883i
$129$			6.11727i			0.538595i
$130$			0.941367i			0.0825633i
$131$		−	11.0732i		−	0.967474i	−0.875214	−	0.483737i	$-0.839279\pi$
$131$		−	11.0732i		−	0.967474i	0.875214	−	0.483737i	$-0.160721\pi$
$132$	−6.11727			−0.532440
$133$		−	0.381015i		−	0.0330382i
$134$			7.68879i			0.664210i
$135$		−	2.11727i		−	0.182225i
$136$	4.83709			0.414777
$137$	0.325819			0.0278366			0.0139183	−	0.999903i	$-0.495570\pi$
$137$	0.325819			0.0278366			0.0139183	+	0.999903i	$0.495570\pi$
$138$	2.11727			0.180234
$139$	−13.3906			−1.13577			−0.567887	−	0.823107i	$-0.692239\pi$
$139$	−13.3906			−1.13577			−0.567887	+	0.823107i	$0.692239\pi$
$140$		−	1.52932i		−	0.129251i
$141$	−7.43965			−0.626531
$142$			3.05863i			0.256675i
$143$			2.56035i			0.214107i
$144$	2.05863			0.171553
$145$	−0.719824			−0.0597781
$146$		−	9.11383i		−	0.754266i
$147$	−10.4837			−0.864679
$148$	4.71982	+	3.83709i	0.387967	+	0.315407i
$149$	8.44309			0.691685			0.345842	−	0.938293i	$-0.387593\pi$
$149$	8.44309			0.691685			0.345842	+	0.938293i	$0.387593\pi$
$150$			2.24914i			0.183642i
$151$	−4.94137			−0.402123			−0.201061	−	0.979579i	$-0.564439\pi$
$151$	−4.94137			−0.402123			−0.201061	+	0.979579i	$0.564439\pi$
$152$	0.249141			0.0202080
$153$		−	9.95779i		−	0.805040i
$154$		−	4.15947i		−	0.335180i
$155$	−4.02760			−0.323504
$156$		−	2.11727i		−	0.169517i
$157$	19.2733			1.53818			0.769088	−	0.639142i	$-0.220711\pi$
$157$	19.2733			1.53818			0.769088	+	0.639142i	$0.220711\pi$
$158$	−1.75086			−0.139291
$159$	18.8793			1.49723
$160$	1.00000			0.0790569
$161$			1.43965i			0.113460i
$162$			10.9379i			0.859365i
$163$		−	17.3354i		−	1.35781i	−0.734226	−	0.678906i	$-0.762455\pi$
$163$		−	17.3354i		−	1.35781i	0.734226	−	0.678906i	$-0.237545\pi$
$164$	8.27674			0.646305
$165$			6.11727i			0.476229i
$166$		−	0.131874i		−	0.0102354i
$167$		−	17.0518i		−	1.31950i	−0.751483	−	0.659752i	$-0.770661\pi$
$167$		−	17.0518i		−	1.31950i	0.751483	−	0.659752i	$-0.229339\pi$
$168$			3.43965i			0.265375i
$169$	12.1138			0.931833
$170$		−	4.83709i		−	0.370988i
$171$		−	0.512889i		−	0.0392216i
$172$		−	2.71982i		−	0.207385i
$173$	10.7198			0.815013			0.407507	−	0.913202i	$-0.366398\pi$
$173$	10.7198			0.815013			0.407507	+	0.913202i	$0.366398\pi$
$174$	1.61899			0.122735
$175$	−1.52932			−0.115605
$176$	2.71982			0.205014
$177$		−	16.4362i		−	1.23542i
$178$	−8.99656			−0.674321
$179$		−	9.48024i		−	0.708586i	−0.935134	−	0.354293i	$-0.884722\pi$
$179$		−	9.48024i		−	0.708586i	0.935134	−	0.354293i	$-0.115278\pi$
$180$		−	2.05863i		−	0.153441i
$181$	20.9966			1.56066			0.780331	−	0.625367i	$-0.215051\pi$
$181$	20.9966			1.56066			0.780331	+	0.625367i	$0.215051\pi$
$182$	1.43965			0.106714
$183$			15.3776i			1.13674i
$184$	−0.941367			−0.0693985
$185$	3.83709	−	4.71982i	0.282108	−	0.347008i
$186$	9.05863			0.664211
$187$		−	13.1560i		−	0.962064i
$188$	3.30777			0.241244
$189$	−3.23797			−0.235528
$190$		−	0.249141i		−	0.0180746i
$191$		−	11.0862i		−	0.802172i	−0.916041	−	0.401086i	$-0.868633\pi$
$191$		−	11.0862i		−	0.802172i	0.916041	−	0.401086i	$-0.131367\pi$
$192$	−2.24914			−0.162318
$193$			2.23453i			0.160845i	0.996761	+	0.0804226i	$0.0256270\pi$
$193$			2.23453i			0.160845i	−0.996761	+	0.0804226i	$0.974373\pi$
$194$	16.2767			1.16860
$195$	−2.11727			−0.151621
$196$	4.66119			0.332942
$197$	13.4396			0.957535			0.478768	−	0.877942i	$-0.341084\pi$
$197$	13.4396			0.957535			0.478768	+	0.877942i	$0.341084\pi$
$198$		−	5.59912i		−	0.397912i
$199$		−	23.4802i		−	1.66447i	−0.554423	−	0.832235i	$-0.687061\pi$
$199$		−	23.4802i		−	1.66447i	0.554423	−	0.832235i	$-0.312939\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−17.2932			−1.21977
$202$			11.1138i			0.781966i
$203$			1.10084i			0.0772637i
$204$			10.8793i			0.761703i
$205$		−	8.27674i		−	0.578072i
$206$	14.1725			0.987442
$207$			1.93793i			0.134695i
$208$			0.941367i			0.0652720i
$209$		−	0.677618i		−	0.0468718i
$210$	3.43965			0.237358
$211$	−19.7716			−1.36113			−0.680566	−	0.732687i	$-0.738266\pi$
$211$	−19.7716			−1.36113			−0.680566	+	0.732687i	$0.738266\pi$
$212$	−8.39400			−0.576503
$213$	−6.87930			−0.471362
$214$		−	10.6922i		−	0.730906i
$215$	−2.71982			−0.185490
$216$		−	2.11727i		−	0.144062i
$217$			6.15947i			0.418132i
$218$	12.2767			0.831486
$219$	20.4983			1.38515
$220$		−	2.71982i		−	0.183370i
$221$	4.55348			0.306300
$222$	−8.63016	+	10.6155i	−0.579218	+	0.712469i
$223$	−9.14143			−0.612155			−0.306078	−	0.952007i	$-0.599017\pi$
$223$	−9.14143			−0.612155			−0.306078	+	0.952007i	$0.599017\pi$
$224$		−	1.52932i		−	0.102182i
$225$	−2.05863			−0.137242
$226$	−2.95436			−0.196521
$227$		−	18.7198i		−	1.24248i	−0.783621	−	0.621239i	$-0.786630\pi$
$227$		−	18.7198i		−	1.24248i	0.783621	−	0.621239i	$-0.213370\pi$
$228$			0.560352i			0.0371102i
$229$	−25.1138			−1.65957			−0.829784	−	0.558084i	$-0.811537\pi$
$229$	−25.1138			−1.65957			−0.829784	+	0.558084i	$0.811537\pi$
$230$			0.941367i			0.0620719i
$231$	9.35524			0.615529
$232$	−0.719824			−0.0472588
$233$	20.4362			1.33882			0.669410	−	0.742893i	$-0.266547\pi$
$233$	20.4362			1.33882			0.669410	+	0.742893i	$0.266547\pi$
$234$	1.93793			0.126686
$235$		−	3.30777i		−	0.215775i
$236$			7.30777i			0.475696i
$237$		−	3.93793i		−	0.255796i
$238$	−7.39744			−0.479505
$239$			8.91377i			0.576584i	0.957543	+	0.288292i	$0.0930873\pi$
$239$			8.91377i			0.576584i	−0.957543	+	0.288292i	$0.906913\pi$
$240$			2.24914i			0.145181i
$241$			13.8827i			0.894265i	0.894468	+	0.447133i	$0.147555\pi$
$241$			13.8827i			0.894265i	−0.894468	+	0.447133i	$0.852445\pi$
$242$			3.60256i			0.231581i
$243$	−18.2491			−1.17068
$244$		−	6.83709i		−	0.437700i
$245$		−	4.66119i		−	0.297793i
$246$			18.6155i			1.18688i
$247$	0.234533			0.0149230
$248$	−4.02760			−0.255753
$249$	0.296604			0.0187965
$250$	−1.00000			−0.0632456
$251$			3.80605i			0.240236i	0.992760	+	0.120118i	$0.0383273\pi$
$251$			3.80605i			0.240236i	−0.992760	+	0.120118i	$0.961673\pi$
$252$	−3.14830			−0.198324
$253$			2.56035i			0.160968i
$254$		−	8.30434i		−	0.521060i
$255$	10.8793			0.681288
$256$	1.00000			0.0625000
$257$		−	8.78801i		−	0.548181i	−0.961704	−	0.274090i	$-0.911623\pi$
$257$		−	8.78801i		−	0.548181i	0.961704	−	0.274090i	$-0.0883768\pi$
$258$	6.11727			0.380844
$259$	−7.21811	−	5.86813i	−0.448511	−	0.364628i
$260$	0.941367			0.0583811
$261$			1.48185i			0.0917244i
$262$	−11.0732			−0.684107
$263$	−10.4707			−0.645650			−0.322825	−	0.946459i	$-0.604633\pi$
$263$	−10.4707			−0.645650			−0.322825	+	0.946459i	$0.604633\pi$
$264$			6.11727i			0.376492i
$265$			8.39400i			0.515640i
$266$	−0.381015			−0.0233615
$267$		−	20.2345i		−	1.23833i
$268$	7.68879			0.469668
$269$	−5.88273			−0.358677			−0.179338	−	0.983787i	$-0.557396\pi$
$269$	−5.88273			−0.358677			−0.179338	+	0.983787i	$0.557396\pi$
$270$	−2.11727			−0.128853
$271$	7.61211			0.462403			0.231201	−	0.972906i	$-0.425734\pi$
$271$	7.61211			0.462403			0.231201	+	0.972906i	$0.425734\pi$
$272$		−	4.83709i		−	0.293292i
$273$			3.23797i			0.195971i
$274$		−	0.325819i		−	0.0196835i
$275$	−2.71982			−0.164012
$276$		−	2.11727i		−	0.127444i
$277$			26.4914i			1.59171i	0.605484	+	0.795857i	$0.292979\pi$
$277$			26.4914i			1.59171i	−0.605484	+	0.795857i	$0.707021\pi$
$278$			13.3906i			0.803113i
$279$			8.29135i			0.496390i
$280$	−1.52932			−0.0913941
$281$			26.6707i			1.59104i	0.605925	+	0.795522i	$0.292803\pi$
$281$			26.6707i			1.59104i	−0.605925	+	0.795522i	$0.707197\pi$
$282$			7.43965i			0.443025i
$283$			8.73281i			0.519112i	0.965728	+	0.259556i	$0.0835762\pi$
$283$			8.73281i			0.519112i	−0.965728	+	0.259556i	$0.916424\pi$
$284$	3.05863			0.181496
$285$	0.560352			0.0331924
$286$	2.56035			0.151397
$287$	−12.6578			−0.747164
$288$		−	2.05863i		−	0.121306i
$289$	−6.39744			−0.376320
$290$			0.719824i			0.0422695i
$291$			36.6087i			2.14604i
$292$	−9.11383			−0.533346
$293$	23.4819			1.37182			0.685912	−	0.727684i	$-0.259403\pi$
$293$	23.4819			1.37182			0.685912	+	0.727684i	$0.259403\pi$
$294$			10.4837i			0.611420i
$295$	7.30777			0.425475
$296$	3.83709	−	4.71982i	0.223026	−	0.274334i
$297$	−5.75859			−0.334147
$298$		−	8.44309i		−	0.489095i
$299$	−0.886172			−0.0512486
$300$	2.24914			0.129854
$301$			4.15947i			0.239748i
$302$			4.94137i			0.284344i
$303$	−24.9966			−1.43601
$304$		−	0.249141i		−	0.0142892i
$305$	−6.83709			−0.391491
$306$	−9.95779			−0.569249
$307$	27.2457			1.55499			0.777497	−	0.628886i	$-0.216489\pi$
$307$	27.2457			1.55499			0.777497	+	0.628886i	$0.216489\pi$
$308$	−4.15947			−0.237008
$309$			31.8759i			1.81335i
$310$			4.02760i			0.228752i
$311$			17.7018i			1.00378i	0.864933	+	0.501888i	$0.167361\pi$
$311$			17.7018i			1.00378i	−0.864933	+	0.501888i	$0.832639\pi$
$312$	−2.11727			−0.119867
$313$		−	23.9931i		−	1.35617i	−0.734983	−	0.678086i	$-0.762810\pi$
$313$		−	23.9931i		−	1.35617i	0.734983	−	0.678086i	$-0.237190\pi$
$314$		−	19.2733i		−	1.08766i
$315$			3.14830i			0.177387i
$316$			1.75086i			0.0984935i
$317$	−3.16291			−0.177647			−0.0888234	−	0.996047i	$-0.528311\pi$
$317$	−3.16291			−0.177647			−0.0888234	+	0.996047i	$0.528311\pi$
$318$		−	18.8793i		−	1.05870i
$319$			1.95779i			0.109615i
$320$		−	1.00000i		−	0.0559017i
$321$	24.0483			1.34225
$322$	1.43965			0.0802284
$323$	−1.20512			−0.0670544
$324$	10.9379			0.607663
$325$		−	0.941367i		−	0.0522176i
$326$	−17.3354			−0.960117
$327$			27.6121i			1.52695i
$328$		−	8.27674i		−	0.457006i
$329$	−5.05863			−0.278891
$330$	6.11727			0.336744
$331$			4.48367i			0.246445i	0.992379	+	0.123222i	$0.0393229\pi$
$331$			4.48367i			0.246445i	−0.992379	+	0.123222i	$0.960677\pi$
$332$	−0.131874			−0.00723754
$333$	−9.71639	−	7.89916i	−0.532455	−	0.432871i
$334$	−17.0518			−0.933031
$335$		−	7.68879i		−	0.420083i
$336$	3.43965			0.187648
$337$	−11.2051			−0.610382			−0.305191	−	0.952291i	$-0.598720\pi$
$337$	−11.2051			−0.610382			−0.305191	+	0.952291i	$0.598720\pi$
$338$		−	12.1138i		−	0.658905i
$339$		−	6.64476i		−	0.360894i
$340$	−4.83709			−0.262328
$341$			10.9544i			0.593212i
$342$	−0.512889			−0.0277339
$343$	−17.8337			−0.962927
$344$	−2.71982			−0.146643
$345$	−2.11727			−0.113990
$346$		−	10.7198i		−	0.576301i
$347$			13.9931i			0.751190i	0.926784	+	0.375595i	$0.122562\pi$
$347$			13.9931i			0.751190i	−0.926784	+	0.375595i	$0.877438\pi$
$348$		−	1.61899i		−	0.0867867i
$349$	−6.56035			−0.351168			−0.175584	−	0.984464i	$-0.556181\pi$
$349$	−6.56035			−0.351168			−0.175584	+	0.984464i	$0.556181\pi$
$350$			1.52932i			0.0817454i
$351$		−	1.99312i		−	0.106385i
$352$		−	2.71982i		−	0.144967i
$353$		−	36.5957i		−	1.94779i	−0.226995	−	0.973896i	$-0.572890\pi$
$353$		−	36.5957i		−	1.94779i	0.226995	−	0.973896i	$-0.427110\pi$
$354$	−16.4362			−0.873575
$355$		−	3.05863i		−	0.162335i
$356$			8.99656i			0.476817i
$357$		−	16.6379i		−	0.880570i
$358$	−9.48024			−0.501046
$359$	21.2311			1.12053			0.560267	−	0.828312i	$-0.310698\pi$
$359$	21.2311			1.12053			0.560267	+	0.828312i	$0.310698\pi$
$360$	−2.05863			−0.108499
$361$	18.9379			0.996733
$362$		−	20.9966i		−	1.10355i
$363$	−8.10266			−0.425279
$364$		−	1.43965i		−	0.0754581i
$365$			9.11383i			0.477040i
$366$	15.3776			0.803799
$367$	23.4932			1.22634			0.613168	−	0.789952i	$-0.289895\pi$
$367$	23.4932			1.22634			0.613168	+	0.789952i	$0.289895\pi$
$368$			0.941367i			0.0490721i
$369$	−17.0388			−0.887003
$370$	−4.71982	−	3.83709i	−0.245372	−	0.199481i
$371$	12.8371			0.666469
$372$		−	9.05863i		−	0.469668i
$373$	−7.55691			−0.391282			−0.195641	−	0.980676i	$-0.562679\pi$
$373$	−7.55691			−0.391282			−0.195641	+	0.980676i	$0.562679\pi$
$374$	−13.1560			−0.680282
$375$		−	2.24914i		−	0.116145i
$376$		−	3.30777i		−	0.170585i
$377$	−0.677618			−0.0348991
$378$			3.23797i			0.166543i
$379$	12.2637			0.629946			0.314973	−	0.949101i	$-0.398004\pi$
$379$	12.2637			0.629946			0.314973	+	0.949101i	$0.398004\pi$
$380$	−0.249141			−0.0127806
$381$	18.6776			0.956883
$382$	−11.0862			−0.567221
$383$			33.5208i			1.71283i	0.516285	+	0.856417i	$0.327315\pi$
$383$			33.5208i			1.71283i	−0.516285	+	0.856417i	$0.672685\pi$
$384$			2.24914i			0.114776i
$385$			4.15947i			0.211986i
$386$	2.23453			0.113735
$387$			5.59912i			0.284619i
$388$		−	16.2767i		−	0.826326i
$389$			9.95092i			0.504532i	0.967658	+	0.252266i	$0.0811757\pi$
$389$			9.95092i			0.504532i	−0.967658	+	0.252266i	$0.918824\pi$
$390$			2.11727i			0.107212i
$391$	4.55348			0.230279
$392$		−	4.66119i		−	0.235426i
$393$		−	24.9053i		−	1.25630i
$394$		−	13.4396i		−	0.677080i
$395$	1.75086			0.0880953
$396$	−5.59912			−0.281366
$397$	8.67762			0.435517			0.217759	−	0.976003i	$-0.430125\pi$
$397$	8.67762			0.435517			0.217759	+	0.976003i	$0.430125\pi$
$398$	−23.4802			−1.17696
$399$		−	0.856956i		−	0.0429014i
$400$	−1.00000			−0.0500000
$401$		−	11.5569i		−	0.577125i	−0.957461	−	0.288562i	$-0.906823\pi$
$401$		−	11.5569i		−	0.577125i	0.957461	−	0.288562i	$-0.0931773\pi$
$402$			17.2932i			0.862505i
$403$	−3.79145			−0.188865
$404$	11.1138			0.552934
$405$		−	10.9379i		−	0.543510i
$406$	1.10084			0.0546337
$407$	−12.8371	−	10.4362i	−0.636311	−	0.517304i
$408$	10.8793			0.538605
$409$			3.34836i			0.165566i	0.996568	+	0.0827829i	$0.0263808\pi$
$409$			3.34836i			0.165566i	−0.996568	+	0.0827829i	$0.973619\pi$
$410$	−8.27674			−0.408759
$411$	0.732814			0.0361470
$412$		−	14.1725i		−	0.698227i
$413$		−	11.1759i		−	0.549930i
$414$	1.93793			0.0952440
$415$			0.131874i			0.00647345i
$416$	0.941367			0.0461543
$417$	−30.1173			−1.47485
$418$	−0.677618			−0.0331434
$419$	−11.3776			−0.555831			−0.277916	−	0.960606i	$-0.589644\pi$
$419$	−11.3776			−0.555831			−0.277916	+	0.960606i	$0.589644\pi$
$420$		−	3.43965i		−	0.167838i
$421$		−	3.23109i		−	0.157474i	−0.996895	−	0.0787370i	$-0.974911\pi$
$421$		−	3.23109i		−	0.157474i	0.996895	−	0.0787370i	$-0.0250887\pi$
$422$			19.7716i			0.962466i
$423$	−6.80949			−0.331089
$424$			8.39400i			0.407649i
$425$			4.83709i			0.234633i
$426$			6.87930i			0.333303i
$427$			10.4561i			0.506005i
$428$	−10.6922			−0.516828
$429$			5.75859i			0.278027i
$430$			2.71982i			0.131162i
$431$			29.2327i			1.40809i	0.710155	+	0.704045i	$0.248625\pi$
$431$			29.2327i			1.40809i	−0.710155	+	0.704045i	$0.751375\pi$
$432$	−2.11727			−0.101867
$433$	17.7655			0.853754			0.426877	−	0.904310i	$-0.359614\pi$
$433$	17.7655			0.853754			0.426877	+	0.904310i	$0.359614\pi$
$434$	6.15947			0.295664
$435$	−1.61899			−0.0776244
$436$		−	12.2767i		−	0.587949i
$437$	0.234533			0.0112192
$438$		−	20.4983i		−	0.979446i
$439$		−	32.7604i		−	1.56357i	−0.623549	−	0.781785i	$-0.714310\pi$
$439$		−	32.7604i		−	1.56357i	0.623549	−	0.781785i	$-0.285690\pi$
$440$	−2.71982			−0.129663
$441$	−9.59568			−0.456937
$442$		−	4.55348i		−	0.216587i
$443$	−0.600939			−0.0285515			−0.0142757	−	0.999898i	$-0.504544\pi$
$443$	−0.600939			−0.0285515			−0.0142757	+	0.999898i	$0.504544\pi$
$444$	10.6155	+	8.63016i	0.503792	+	0.409569i
$445$	8.99656			0.426478
$446$			9.14143i			0.432859i
$447$	18.9897			0.898181
$448$	−1.52932			−0.0722534
$449$			34.0191i			1.60546i	0.596342	+	0.802730i	$0.296620\pi$
$449$			34.0191i			1.60546i	−0.596342	+	0.802730i	$0.703380\pi$
$450$			2.05863i			0.0970449i
$451$	−22.5113			−1.06001
$452$			2.95436i			0.138961i
$453$	−11.1138			−0.522173
$454$	−18.7198			−0.878565
$455$	−1.43965			−0.0674917
$456$	0.560352			0.0262409
$457$			30.9215i			1.44645i	0.690614	+	0.723223i	$0.257340\pi$
$457$			30.9215i			1.44645i	−0.690614	+	0.723223i	$0.742660\pi$
$458$			25.1138i			1.17349i
$459$			10.2414i			0.478028i
$460$	0.941367			0.0438915
$461$		−	1.27330i		−	0.0593035i	−0.999560	−	0.0296518i	$-0.990560\pi$
$461$		−	1.27330i		−	0.0593035i	0.999560	−	0.0296518i	$-0.00943983\pi$
$462$		−	9.35524i		−	0.435245i
$463$		−	2.61555i		−	0.121555i	−0.998151	−	0.0607774i	$-0.980642\pi$
$463$		−	2.61555i		−	0.121555i	0.998151	−	0.0607774i	$-0.0193580\pi$
$464$			0.719824i			0.0334170i
$465$	−9.05863			−0.420084
$466$		−	20.4362i		−	0.946689i
$467$		−	19.0096i		−	0.879657i	−0.898082	−	0.439829i	$-0.855039\pi$
$467$		−	19.0096i		−	0.879657i	0.898082	−	0.439829i	$-0.144961\pi$
$468$		−	1.93793i		−	0.0895808i
$469$	−11.7586			−0.542961
$470$	−3.30777			−0.152576
$471$	43.3484			1.99739
$472$	7.30777			0.336368
$473$			7.39744i			0.340135i
$474$	−3.93793			−0.180875
$475$			0.249141i			0.0114314i
$476$			7.39744i			0.339061i
$477$	17.2802			0.791205
$478$	8.91377			0.407706
$479$			38.8578i			1.77546i	0.460366	+	0.887729i	$0.347718\pi$
$479$			38.8578i			1.77546i	−0.460366	+	0.887729i	$0.652282\pi$
$480$	2.24914			0.102659
$481$	3.61211	−	4.44309i	0.164698	−	0.202587i
$482$	13.8827			0.632341
$483$			3.23797i			0.147333i
$484$	3.60256			0.163753
$485$	−16.2767			−0.739089
$486$			18.2491i			0.827798i
$487$			38.4914i			1.74421i	0.489317	+	0.872106i	$0.337246\pi$
$487$			38.4914i			1.74421i	−0.489317	+	0.872106i	$0.662754\pi$
$488$	−6.83709			−0.309501
$489$		−	38.9897i		−	1.76317i
$490$	−4.66119			−0.210571
$491$	−11.2672			−0.508481			−0.254240	−	0.967141i	$-0.581825\pi$
$491$	−11.2672			−0.508481			−0.254240	+	0.967141i	$0.581825\pi$
$492$	18.6155			0.839254
$493$	3.48185			0.156815
$494$		−	0.234533i		−	0.0105521i
$495$			5.59912i			0.251662i
$496$			4.02760i			0.180844i
$497$	−4.67762			−0.209820
$498$		−	0.296604i		−	0.0132911i
$499$		−	20.8578i		−	0.933724i	−0.884330	−	0.466862i	$-0.845384\pi$
$499$		−	20.8578i		−	0.933724i	0.884330	−	0.466862i	$-0.154616\pi$
$500$			1.00000i			0.0447214i
$501$		−	38.3518i		−	1.71343i
$502$	3.80605			0.169873
$503$			6.64476i			0.296275i	0.988967	+	0.148138i	$0.0473279\pi$
$503$			6.64476i			0.296275i	−0.988967	+	0.148138i	$0.952672\pi$
$504$			3.14830i			0.140237i
$505$		−	11.1138i		−	0.494559i
$506$	2.56035			0.113822
$507$	27.2457			1.21002
$508$	−8.30434			−0.368445
$509$	−18.5535			−0.822368			−0.411184	−	0.911552i	$-0.634885\pi$
$509$	−18.5535			−0.822368			−0.411184	+	0.911552i	$0.634885\pi$
$510$		−	10.8793i		−	0.481743i
$511$	13.9379			0.616578
$512$		−	1.00000i		−	0.0441942i
$513$			0.527497i			0.0232896i
$514$	−8.78801			−0.387622
$515$	−14.1725			−0.624513
$516$		−	6.11727i		−	0.269298i
$517$	−8.99656			−0.395668
$518$	−5.86813	+	7.21811i	−0.257831	+	0.317145i
$519$	24.1104			1.05833
$520$		−	0.941367i		−	0.0412817i
$521$	−42.6509			−1.86857			−0.934284	−	0.356529i	$-0.883960\pi$
$521$	−42.6509			−1.86857			−0.934284	+	0.356529i	$0.883960\pi$
$522$	1.48185			0.0648590
$523$		−	12.3879i		−	0.541685i	−0.962624	−	0.270842i	$-0.912698\pi$
$523$		−	12.3879i		−	0.541685i	0.962624	−	0.270842i	$-0.0873022\pi$
$524$			11.0732i			0.483737i
$525$	−3.43965			−0.150119
$526$			10.4707i			0.456543i
$527$	19.4819			0.848643
$528$	6.11727			0.266220
$529$	22.1138			0.961471
$530$	8.39400			0.364612
$531$		−	15.0440i		−	0.652855i
$532$			0.381015i			0.0165191i
$533$		−	7.79145i		−	0.337485i
$534$	−20.2345			−0.875634
$535$			10.6922i			0.462265i
$536$		−	7.68879i		−	0.332105i
$537$		−	21.3224i		−	0.920129i
$538$			5.88273i			0.253623i
$539$	−12.6776			−0.546064
$540$			2.11727i			0.0911126i
$541$			7.64820i			0.328822i	0.986392	+	0.164411i	$0.0525723\pi$
$541$			7.64820i			0.328822i	−0.986392	+	0.164411i	$0.947428\pi$
$542$		−	7.61211i		−	0.326968i
$543$	47.2242			2.02659
$544$	−4.83709			−0.207389
$545$	−12.2767			−0.525878
$546$	3.23797			0.138572
$547$		−	12.6837i		−	0.542317i	−0.962535	−	0.271159i	$-0.912593\pi$
$547$		−	12.6837i		−	0.542317i	0.962535	−	0.271159i	$-0.0874068\pi$
$548$	−0.325819			−0.0139183
$549$			14.0751i			0.600709i
$550$			2.71982i			0.115974i
$551$	0.179337			0.00764003
$552$	−2.11727			−0.0901168
$553$		−	2.67762i		−	0.113864i
$554$	26.4914			1.12551
$555$	8.63016	−	10.6155i	0.366330	−	0.450605i
$556$	13.3906			0.567887
$557$		−	2.61555i		−	0.110824i	−0.998464	−	0.0554121i	$-0.982353\pi$
$557$		−	2.61555i		−	0.110824i	0.998464	−	0.0554121i	$-0.0176473\pi$
$558$	8.29135			0.351001
$559$	−2.56035			−0.108291
$560$			1.52932i			0.0646254i
$561$		−	29.5898i		−	1.24928i
$562$	26.6707			1.12504
$563$		−	35.3285i		−	1.48892i	−0.667668	−	0.744459i	$-0.732707\pi$
$563$		−	35.3285i		−	1.48892i	0.667668	−	0.744459i	$-0.267293\pi$
$564$	7.43965			0.313266
$565$	2.95436			0.124291
$566$	8.73281			0.367068
$567$	−16.7276			−0.702491
$568$		−	3.05863i		−	0.128337i
$569$		−	28.8724i		−	1.21039i	−0.796075	−	0.605197i	$-0.793094\pi$
$569$		−	28.8724i		−	1.21039i	0.796075	−	0.605197i	$-0.206906\pi$
$570$		−	0.560352i		−	0.0234706i
$571$	−8.15947			−0.341463			−0.170732	−	0.985318i	$-0.554613\pi$
$571$	−8.15947			−0.341463			−0.170732	+	0.985318i	$0.554613\pi$
$572$		−	2.56035i		−	0.107054i
$573$		−	24.9345i		−	1.04165i
$574$			12.6578i			0.528324i
$575$		−	0.941367i		−	0.0392577i
$576$	−2.05863			−0.0857764
$577$			37.5500i			1.56323i	0.623762	+	0.781614i	$0.285603\pi$
$577$			37.5500i			1.56323i	−0.623762	+	0.781614i	$0.714397\pi$
$578$			6.39744i			0.266099i
$579$			5.02578i			0.208864i
$580$	0.719824			0.0298891
$581$	0.201677			0.00836699
$582$	36.6087			1.51748
$583$	22.8302			0.945531
$584$			9.11383i			0.377133i
$585$	−1.93793			−0.0801235
$586$		−	23.4819i		−	0.970026i
$587$			19.5078i			0.805174i	0.915382	+	0.402587i	$0.131889\pi$
$587$			19.5078i			0.805174i	−0.915382	+	0.402587i	$0.868111\pi$
$588$	10.4837			0.432339
$589$	1.00344			0.0413459
$590$		−	7.30777i		−	0.300856i
$591$	30.2277			1.24340
$592$	−4.71982	−	3.83709i	−0.193984	−	0.157703i
$593$	41.5569			1.70654			0.853269	−	0.521471i	$-0.174617\pi$
$593$	41.5569			1.70654			0.853269	+	0.521471i	$0.174617\pi$
$594$			5.75859i			0.236278i
$595$	7.39744			0.303266
$596$	−8.44309			−0.345842
$597$		−	52.8103i		−	2.16138i
$598$			0.886172i			0.0362382i
$599$	27.6381			1.12926			0.564631	−	0.825344i	$-0.309019\pi$
$599$	27.6381			1.12926			0.564631	+	0.825344i	$0.309019\pi$
$600$		−	2.24914i		−	0.0918208i
$601$	14.4301			0.588616			0.294308	−	0.955711i	$-0.404911\pi$
$601$	14.4301			0.588616			0.294308	+	0.955711i	$0.404911\pi$
$602$	4.15947			0.169527
$603$	−15.8284			−0.644582
$604$	4.94137			0.201061
$605$		−	3.60256i		−	0.146465i
$606$			24.9966i			1.01542i
$607$			47.4880i			1.92748i	0.266848	+	0.963739i	$0.414018\pi$
$607$			47.4880i			1.92748i	−0.266848	+	0.963739i	$0.585982\pi$
$608$	−0.249141			−0.0101040
$609$			2.47594i			0.100330i
$610$			6.83709i			0.276826i
$611$		−	3.11383i		−	0.125972i
$612$			9.95779i			0.402520i
$613$	−18.7198			−0.756087			−0.378043	−	0.925788i	$-0.623403\pi$
$613$	−18.7198			−0.756087			−0.378043	+	0.925788i	$0.623403\pi$
$614$		−	27.2457i		−	1.09955i
$615$		−	18.6155i		−	0.750651i
$616$			4.15947i			0.167590i
$617$	−15.0225			−0.604785			−0.302392	−	0.953184i	$-0.597785\pi$
$617$	−15.0225			−0.604785			−0.302392	+	0.953184i	$0.597785\pi$
$618$	31.8759			1.28224
$619$	16.6318			0.668487			0.334244	−	0.942487i	$-0.391519\pi$
$619$	16.6318			0.668487			0.334244	+	0.942487i	$0.391519\pi$
$620$	4.02760			0.161752
$621$		−	1.99312i		−	0.0799813i
$622$	17.7018			0.709777
$623$		−	13.7586i		−	0.551226i
$624$			2.11727i			0.0847585i
$625$	1.00000			0.0400000
$626$	−23.9931			−0.958958
$627$		−	1.52406i		−	0.0608651i
$628$	−19.2733			−0.769088
$629$	−18.5604	+	22.8302i	−0.740050	+	0.910300i
$630$	3.14830			0.125431
$631$		−	35.9294i		−	1.43033i	−0.698957	−	0.715164i	$-0.746352\pi$
$631$		−	35.9294i		−	1.43033i	0.698957	−	0.715164i	$-0.253648\pi$
$632$	1.75086			0.0696454
$633$	−44.4691			−1.76749
$634$			3.16291i			0.125615i
$635$			8.30434i			0.329548i
$636$	−18.8793			−0.748613
$637$		−	4.38789i		−	0.173855i
$638$	1.95779			0.0775098
$639$	−6.29660			−0.249090
$640$	−1.00000			−0.0395285
$641$	29.3354			1.15868			0.579339	−	0.815087i	$-0.303311\pi$
$641$	29.3354			1.15868			0.579339	+	0.815087i	$0.303311\pi$
$642$		−	24.0483i		−	0.949111i
$643$		−	0.368025i		−	0.0145135i	−0.999974	−	0.00725674i	$-0.997690\pi$
$643$		−	0.368025i		−	0.0145135i	0.999974	−	0.00725674i	$-0.00230991\pi$
$644$		−	1.43965i		−	0.0567301i
$645$	−6.11727			−0.240867
$646$			1.20512i			0.0474146i
$647$			26.7811i			1.05287i	0.850214	+	0.526437i	$0.176473\pi$
$647$			26.7811i			1.05287i	−0.850214	+	0.526437i	$0.823527\pi$
$648$		−	10.9379i		−	0.429682i
$649$		−	19.8759i		−	0.780196i
$650$	−0.941367			−0.0369234
$651$			13.8535i			0.542962i
$652$			17.3354i			0.678906i
$653$			2.00000i			0.0782660i	0.999234	+	0.0391330i	$0.0124596\pi$
$653$			2.00000i			0.0782660i	−0.999234	+	0.0391330i	$0.987540\pi$
$654$	27.6121			1.07972
$655$	11.0732			0.432667
$656$	−8.27674			−0.323152
$657$	18.7620			0.731976
$658$			5.05863i			0.197206i
$659$	−12.9966			−0.506274			−0.253137	−	0.967430i	$-0.581462\pi$
$659$	−12.9966			−0.506274			−0.253137	+	0.967430i	$0.581462\pi$
$660$		−	6.11727i		−	0.238114i
$661$		−	18.6026i		−	0.723556i	−0.932264	−	0.361778i	$-0.882170\pi$
$661$		−	18.6026i		−	0.723556i	0.932264	−	0.361778i	$-0.117830\pi$
$662$	4.48367			0.174263
$663$	10.2414			0.397743
$664$			0.131874i			0.00511771i
$665$	0.381015			0.0147751
$666$	−7.89916	+	9.71639i	−0.306086	+	0.376502i
$667$	−0.677618			−0.0262375
$668$			17.0518i			0.659752i
$669$	−20.5604			−0.794909
$670$	−7.68879			−0.297044
$671$			18.5957i			0.717878i
$672$		−	3.43965i		−	0.132687i
$673$	20.4622			0.788759			0.394380	−	0.918948i	$-0.370959\pi$
$673$	20.4622			0.788759			0.394380	+	0.918948i	$0.370959\pi$
$674$			11.2051i			0.431605i
$675$	2.11727			0.0814936
$676$	−12.1138			−0.465916
$677$	−39.9018			−1.53355			−0.766776	−	0.641915i	$-0.778140\pi$
$677$	−39.9018			−1.53355			−0.766776	+	0.641915i	$0.778140\pi$
$678$	−6.64476			−0.255191
$679$			24.8923i			0.955278i
$680$			4.83709i			0.185494i
$681$		−	42.1035i		−	1.61341i
$682$	10.9544			0.419464
$683$			12.3940i			0.474243i	0.971480	+	0.237122i	$0.0762040\pi$
$683$			12.3940i			0.474243i	−0.971480	+	0.237122i	$0.923796\pi$
$684$			0.512889i			0.0196108i
$685$			0.325819i			0.0124489i
$686$			17.8337i			0.680892i
$687$	−56.4845			−2.15502
$688$			2.71982i			0.103692i
$689$			7.90184i			0.301036i
$690$			2.11727i			0.0806030i
$691$	−51.5630			−1.96155			−0.980775	−	0.195142i	$-0.937483\pi$
$691$	−51.5630			−1.96155			−0.980775	+	0.195142i	$0.937483\pi$
$692$	−10.7198			−0.407507
$693$	8.56283			0.325275
$694$	13.9931			0.531172
$695$		−	13.3906i		−	0.507933i
$696$	−1.61899			−0.0613675
$697$			40.0353i			1.51645i
$698$			6.56035i			0.248313i
$699$	45.9639			1.73851
$700$	1.52932			0.0578027
$701$		−	9.76547i		−	0.368837i	−0.982848	−	0.184418i	$-0.940960\pi$
$701$		−	9.76547i		−	0.368837i	0.982848	−	0.184418i	$-0.0590401\pi$
$702$	−1.99312			−0.0752256
$703$	−0.955975	+	1.17590i	−0.0360553	+	0.0443499i
$704$	−2.71982			−0.102507
$705$		−	7.43965i		−	0.280193i
$706$	−36.5957			−1.37730
$707$	−16.9966			−0.639222
$708$			16.4362i			0.617711i
$709$		−	49.8268i		−	1.87128i	−0.352951	−	0.935642i	$-0.614822\pi$
$709$		−	49.8268i		−	1.87128i	0.352951	−	0.935642i	$-0.385178\pi$
$710$	−3.05863			−0.114788
$711$		−	3.60438i		−	0.135175i
$712$	8.99656			0.337160
$713$	−3.79145			−0.141991
$714$	−16.6379			−0.622657
$715$	−2.56035			−0.0957517
$716$			9.48024i			0.354293i
$717$			20.0483i			0.748718i
$718$		−	21.2311i		−	0.792337i
$719$	−4.26375			−0.159011			−0.0795055	−	0.996834i	$-0.525334\pi$
$719$	−4.26375			−0.159011			−0.0795055	+	0.996834i	$0.525334\pi$
$720$			2.05863i			0.0767207i
$721$			21.6742i			0.807189i
$722$		−	18.9379i		−	0.704797i
$723$			31.2242i			1.16124i
$724$	−20.9966			−0.780331
$725$		−	0.719824i		−	0.0267336i
$726$			8.10266i			0.300718i
$727$		−	13.1759i		−	0.488667i	−0.969691	−	0.244334i	$-0.921431\pi$
$727$		−	13.1759i		−	0.488667i	0.969691	−	0.244334i	$-0.0785692\pi$
$728$	−1.43965			−0.0533569
$729$	−8.23109			−0.304855
$730$	9.11383			0.337318
$731$	13.1560			0.486593
$732$		−	15.3776i		−	0.568372i
$733$	9.39057			0.346848			0.173424	−	0.984847i	$-0.444517\pi$
$733$	9.39057			0.346848			0.173424	+	0.984847i	$0.444517\pi$
$734$		−	23.4932i		−	0.867151i
$735$		−	10.4837i		−	0.386696i
$736$	0.941367			0.0346992
$737$	−20.9122			−0.770309
$738$			17.0388i			0.627206i
$739$	−9.62510			−0.354065			−0.177033	−	0.984205i	$-0.556650\pi$
$739$	−9.62510			−0.354065			−0.177033	+	0.984205i	$0.556650\pi$
$740$	−3.83709	+	4.71982i	−0.141054	+	0.173504i
$741$	0.527497			0.0193781
$742$		−	12.8371i		−	0.471264i
$743$	−25.6137			−0.939677			−0.469838	−	0.882753i	$-0.655688\pi$
$743$	−25.6137			−0.939677			−0.469838	+	0.882753i	$0.655688\pi$
$744$	−9.05863			−0.332106
$745$			8.44309i			0.309331i
$746$			7.55691i			0.276678i
$747$	0.271481			0.00993296
$748$			13.1560i			0.481032i
$749$	16.3518			0.597482
$750$	−2.24914			−0.0821270
$751$	11.9740			0.436938			0.218469	−	0.975844i	$-0.429894\pi$
$751$	11.9740			0.436938			0.218469	+	0.975844i	$0.429894\pi$
$752$	−3.30777			−0.120622
$753$			8.56035i			0.311957i
$754$			0.677618i			0.0246774i
$755$		−	4.94137i		−	0.179835i
$756$	3.23797			0.117764
$757$		−	19.2051i		−	0.698022i	−0.937119	−	0.349011i	$-0.886518\pi$
$757$		−	19.2051i		−	0.698022i	0.937119	−	0.349011i	$-0.113482\pi$
$758$		−	12.2637i		−	0.445439i
$759$			5.75859i			0.209024i
$760$			0.249141i			0.00903728i
$761$	−31.8596			−1.15491			−0.577455	−	0.816422i	$-0.695954\pi$
$761$	−31.8596			−1.15491			−0.577455	+	0.816422i	$0.695954\pi$
$762$		−	18.6776i		−	0.676619i
$763$			18.7750i			0.679701i
$764$			11.0862i			0.401086i
$765$	9.95779			0.360025
$766$	33.5208			1.21116
$767$	6.87930			0.248397
$768$	2.24914			0.0811589
$769$			35.2242i			1.27022i	0.772423	+	0.635109i	$0.219045\pi$
$769$			35.2242i			1.27022i	−0.772423	+	0.635109i	$0.780955\pi$
$770$	4.15947			0.149897
$771$		−	19.7655i		−	0.711836i
$772$		−	2.23453i		−	0.0804226i
$773$	−50.2630			−1.80783			−0.903917	−	0.427708i	$-0.859321\pi$
$773$	−50.2630			−1.80783			−0.903917	+	0.427708i	$0.859321\pi$
$774$	5.59912			0.201256
$775$		−	4.02760i		−	0.144676i
$776$	−16.2767			−0.584301
$777$	−16.2345	−	13.1982i	−0.582411	−	0.473484i
$778$	9.95092			0.356758
$779$			2.06207i			0.0738814i
$780$	2.11727			0.0758103
$781$	−8.31894			−0.297675
$782$		−	4.55348i		−	0.162832i
$783$		−	1.52406i		−	0.0544654i
$784$	−4.66119			−0.166471
$785$			19.2733i			0.687894i
$786$	−24.9053			−0.888342
$787$	−51.9525			−1.85191			−0.925954	−	0.377636i	$-0.876737\pi$
$787$	−51.9525			−1.85191			−0.925954	+	0.377636i	$0.876737\pi$
$788$	−13.4396			−0.478768
$789$	−23.5500			−0.838404
$790$		−	1.75086i		−	0.0622928i
$791$		−	4.51815i		−	0.160647i
$792$			5.59912i			0.198956i
$793$	−6.43621			−0.228557
$794$		−	8.67762i		−	0.307957i
$795$			18.8793i			0.669580i
$796$			23.4802i			0.832235i
$797$		−	35.4880i		−	1.25705i	−0.777790	−	0.628524i	$-0.783659\pi$
$797$		−	35.4880i		−	1.25705i	0.777790	−	0.628524i	$-0.216341\pi$
$798$	−0.856956			−0.0303359
$799$			16.0000i			0.566039i
$800$			1.00000i			0.0353553i
$801$		−	18.5206i		−	0.654394i
$802$	−11.5569			−0.408089
$803$	24.7880			0.874750
$804$	17.2932			0.609883
$805$	−1.43965			−0.0507409
$806$			3.79145i			0.133548i
$807$	−13.2311			−0.465757
$808$		−	11.1138i		−	0.390983i
$809$		−	13.2051i		−	0.464267i	−0.972684	−	0.232134i	$-0.925429\pi$
$809$		−	13.2051i		−	0.464267i	0.972684	−	0.232134i	$-0.0745706\pi$
$810$	−10.9379			−0.384320
$811$	−10.1173			−0.355265			−0.177633	−	0.984097i	$-0.556844\pi$
$811$	−10.1173			−0.355265			−0.177633	+	0.984097i	$0.556844\pi$
$812$		−	1.10084i		−	0.0386319i
$813$	17.1207			0.600449
$814$	−10.4362	+	12.8371i	−0.365789	+	0.449940i
$815$	17.3354			0.607232
$816$		−	10.8793i		−	0.380852i
$817$	0.677618			0.0237069
$818$	3.34836			0.117073
$819$			2.96371i			0.103560i
$820$			8.27674i			0.289036i
$821$	5.68106			0.198270			0.0991351	−	0.995074i	$-0.468392\pi$
$821$	5.68106			0.198270			0.0991351	+	0.995074i	$0.468392\pi$
$822$		−	0.732814i		−	0.0255598i
$823$	−22.3404			−0.778738			−0.389369	−	0.921082i	$-0.627307\pi$
$823$	−22.3404			−0.778738			−0.389369	+	0.921082i	$0.627307\pi$
$824$	−14.1725			−0.493721
$825$	−6.11727			−0.212976
$826$	−11.1759			−0.388859
$827$		−	3.71639i		−	0.129231i	−0.997910	−	0.0646157i	$-0.979418\pi$
$827$		−	3.71639i		−	0.129231i	0.997910	−	0.0646157i	$-0.0205822\pi$
$828$		−	1.93793i		−	0.0673477i
$829$		−	15.8596i		−	0.550828i	−0.961326	−	0.275414i	$-0.911185\pi$
$829$		−	15.8596i		−	0.550828i	0.961326	−	0.275414i	$-0.0888149\pi$
$830$	0.131874			0.00457742
$831$			59.5829i			2.06691i
$832$		−	0.941367i		−	0.0326360i
$833$			22.5466i			0.781193i
$834$			30.1173i			1.04288i
$835$	17.0518			0.590100
$836$			0.677618i			0.0234359i
$837$		−	8.52750i		−	0.294753i
$838$			11.3776i			0.393032i
$839$	−33.8950			−1.17018			−0.585092	−	0.810967i	$-0.698942\pi$
$839$	−33.8950			−1.17018			−0.585092	+	0.810967i	$0.698942\pi$
$840$	−3.43965			−0.118679
$841$	28.4819			0.982133
$842$	−3.23109			−0.111351
$843$			59.9862i			2.06604i
$844$	19.7716			0.680566
$845$			12.1138i			0.416728i
$846$			6.80949i			0.234115i
$847$	−5.50945			−0.189307
$848$	8.39400			0.288251
$849$			19.6413i			0.674089i
$850$	4.83709			0.165911
$851$	3.61211	−	4.44309i	0.123822	−	0.152307i
$852$	6.87930			0.235681
$853$			35.7586i			1.22435i	0.790722	+	0.612175i	$0.209705\pi$
$853$			35.7586i			1.22435i	−0.790722	+	0.612175i	$0.790295\pi$
$854$	10.4561			0.357800
$855$	0.512889			0.0175404
$856$			10.6922i			0.365453i
$857$			17.3837i			0.593816i	0.954906	+	0.296908i	$0.0959554\pi$
$857$			17.3837i			0.593816i	−0.954906	+	0.296908i	$0.904045\pi$
$858$	5.75859			0.196595
$859$		−	43.3922i		−	1.48052i	−0.672319	−	0.740261i	$-0.734702\pi$
$859$		−	43.3922i		−	1.48052i	0.672319	−	0.740261i	$-0.265298\pi$
$860$	2.71982			0.0927452
$861$	−28.4691			−0.970223
$862$	29.2327			0.995670
$863$	34.8708			1.18702			0.593508	−	0.804828i	$-0.297743\pi$
$863$	34.8708			1.18702			0.593508	+	0.804828i	$0.297743\pi$
$864$			2.11727i			0.0720309i
$865$			10.7198i			0.364485i
$866$		−	17.7655i		−	0.603695i
$867$	−14.3887			−0.488667
$868$		−	6.15947i		−	0.209066i
$869$		−	4.76203i		−	0.161541i
$870$			1.61899i			0.0548887i
$871$		−	7.23797i		−	0.245249i
$872$	−12.2767			−0.415743
$873$			33.5078i			1.13407i
$874$		−	0.234533i		−	0.00793318i
$875$		−	1.52932i		−	0.0517003i
$876$	−20.4983			−0.692573
$877$	47.0907			1.59014			0.795070	−	0.606517i	$-0.207434\pi$
$877$	47.0907			1.59014			0.795070	+	0.606517i	$0.207434\pi$
$878$	−32.7604			−1.10561
$879$	52.8140			1.78137
$880$			2.71982i			0.0916852i
$881$	29.0027			0.977125			0.488562	−	0.872529i	$-0.337521\pi$
$881$	29.0027			0.977125			0.488562	+	0.872529i	$0.337521\pi$
$882$			9.59568i			0.323103i
$883$		−	11.0388i		−	0.371484i	−0.982599	−	0.185742i	$-0.940531\pi$
$883$		−	11.0388i		−	0.371484i	0.982599	−	0.185742i	$-0.0594689\pi$
$884$	−4.55348			−0.153150
$885$	16.4362			0.552497
$886$			0.600939i			0.0201890i
$887$	−5.76709			−0.193640			−0.0968199	−	0.995302i	$-0.530867\pi$
$887$	−5.76709			−0.193640			−0.0968199	+	0.995302i	$0.530867\pi$
$888$	8.63016	−	10.6155i	0.289609	−	0.356234i
$889$	12.7000			0.425943
$890$		−	8.99656i		−	0.301565i
$891$	−29.7492			−0.996637
$892$	9.14143			0.306078
$893$			0.824101i			0.0275775i
$894$		−	18.9897i		−	0.635110i
$895$	9.48024			0.316889
$896$			1.52932i			0.0510909i
$897$	−1.99312			−0.0665485
$898$	34.0191			1.13523
$899$	−2.89916			−0.0966924
$900$	2.05863			0.0686211
$901$		−	40.6026i		−	1.35267i
$902$			22.5113i			0.749543i
$903$			9.35524i			0.311323i
$904$	2.95436			0.0982604
$905$			20.9966i			0.697949i
$906$			11.1138i			0.369232i
$907$		−	54.2139i		−	1.80014i	−0.435742	−	0.900072i	$-0.643514\pi$
$907$		−	54.2139i		−	1.80014i	0.435742	−	0.900072i	$-0.356486\pi$
$908$			18.7198i			0.621239i
$909$	−22.8793			−0.758858
$910$			1.43965i			0.0477239i
$911$		−	37.1284i		−	1.23012i	−0.788480	−	0.615060i	$-0.789132\pi$
$911$		−	37.1284i		−	1.23012i	0.788480	−	0.615060i	$-0.210868\pi$
$912$		−	0.560352i		−	0.0185551i
$913$	0.358675			0.0118704
$914$	30.9215			1.02279
$915$	−15.3776			−0.508367
$916$	25.1138			0.829784
$917$		−	16.9345i		−	0.559226i
$918$	10.2414			0.338017
$919$		−	20.0889i		−	0.662672i	−0.943513	−	0.331336i	$-0.892501\pi$
$919$		−	20.0889i		−	0.662672i	0.943513	−	0.331336i	$-0.107499\pi$
$920$		−	0.941367i		−	0.0310359i
$921$	61.2794			2.01923
$922$	−1.27330			−0.0419339
$923$		−	2.87930i		−	0.0947732i
$924$	−9.35524			−0.307765
$925$	4.71982	+	3.83709i	0.155187	+	0.126163i
$926$	−2.61555			−0.0859522
$927$			29.1759i			0.958262i
$928$	0.719824			0.0236294
$929$	12.9803			0.425871			0.212936	−	0.977066i	$-0.431698\pi$
$929$	12.9803			0.425871			0.212936	+	0.977066i	$0.431698\pi$
$930$			9.05863i			0.297044i
$931$			1.16129i			0.0380598i
$932$	−20.4362			−0.669410
$933$			39.8138i			1.30344i
$934$	−19.0096			−0.622012
$935$	13.1560			0.430248
$936$	−1.93793			−0.0633432
$937$	−9.32238			−0.304549			−0.152274	−	0.988338i	$-0.548660\pi$
$937$	−9.32238			−0.304549			−0.152274	+	0.988338i	$0.548660\pi$
$938$			11.7586i			0.383932i
$939$		−	53.9639i		−	1.76105i
$940$			3.30777i			0.107888i
$941$	−17.7586			−0.578914			−0.289457	−	0.957191i	$-0.593475\pi$
$941$	−17.7586			−0.578914			−0.289457	+	0.957191i	$0.593475\pi$
$942$		−	43.3484i		−	1.41237i
$943$		−	7.79145i		−	0.253724i
$944$		−	7.30777i		−	0.237848i
$945$		−	3.23797i		−	0.105331i
$946$	7.39744			0.240512
$947$		−	17.3354i		−	0.563324i	−0.959514	−	0.281662i	$-0.909114\pi$
$947$		−	17.3354i		−	0.563324i	0.959514	−	0.281662i	$-0.0908857\pi$
$948$			3.93793i			0.127898i
$949$			8.57946i			0.278501i
$950$	0.249141			0.00808319
$951$	−7.11383			−0.230682
$952$	7.39744			0.239752
$953$	−5.88961			−0.190783			−0.0953916	−	0.995440i	$-0.530410\pi$
$953$	−5.88961			−0.190783			−0.0953916	+	0.995440i	$0.530410\pi$
$954$		−	17.2802i		−	0.559466i
$955$	11.0862			0.358742
$956$		−	8.91377i		−	0.288292i
$957$			4.40335i			0.142340i
$958$	38.8578			1.25544
$959$	0.498281			0.0160903
$960$		−	2.24914i		−	0.0725907i
$961$	14.7785			0.476724
$962$	−4.44309	−	3.61211i	−0.143251	−	0.116459i
$963$	22.0114			0.709307
$964$		−	13.8827i		−	0.447133i
$965$	−2.23453			−0.0719322
$966$	3.23797			0.104180
$967$		−	32.3189i		−	1.03931i	−0.854377	−	0.519654i	$-0.826061\pi$
$967$		−	32.3189i		−	1.03931i	0.854377	−	0.519654i	$-0.173939\pi$
$968$		−	3.60256i		−	0.115791i
$969$	−2.71047			−0.0870730
$970$			16.2767i			0.522615i
$971$	6.11115			0.196116			0.0980581	−	0.995181i	$-0.468737\pi$
$971$	6.11115			0.196116			0.0980581	+	0.995181i	$0.468737\pi$
$972$	18.2491			0.585341
$973$	−20.4784			−0.656508
$974$	38.4914			1.23334
$975$		−	2.11727i		−	0.0678068i
$976$			6.83709i			0.218850i
$977$			47.3906i			1.51616i	0.652162	+	0.758079i	$0.273862\pi$
$977$			47.3906i			1.51616i	−0.652162	+	0.758079i	$0.726138\pi$
$978$	−38.9897			−1.24675
$979$		−	24.4691i		−	0.782035i
$980$			4.66119i			0.148896i
$981$			25.2733i			0.806914i
$982$			11.2672i			0.359550i
$983$	−55.7862			−1.77930			−0.889652	−	0.456640i	$-0.849053\pi$
$983$	−55.7862			−1.77930			−0.889652	+	0.456640i	$0.849053\pi$
$984$		−	18.6155i		−	0.593442i
$985$			13.4396i			0.428223i
$986$		−	3.48185i		−	0.110885i
$987$	−11.3776			−0.362152
$988$	−0.234533			−0.00746148
$989$	−2.56035			−0.0814145
$990$	5.59912			0.177952
$991$			29.9655i			0.951886i	0.879476	+	0.475943i	$0.157893\pi$
$991$			29.9655i			0.951886i	−0.879476	+	0.475943i	$0.842107\pi$
$992$	4.02760			0.127876
$993$			10.0844i			0.320019i
$994$			4.67762i			0.148365i
$995$	23.4802			0.744374
$996$	−0.296604			−0.00939825
$997$		−	20.7811i		−	0.658145i	−0.944305	−	0.329073i	$-0.893264\pi$
$997$		−	20.7811i		−	0.658145i	0.944305	−	0.329073i	$-0.106736\pi$
$998$	−20.8578			−0.660243
$999$	9.99312	+	8.12414i	0.316168	+	0.257036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.d.c.221.3	✓	6
3.2	odd	2		3330.2.h.n.2071.5		6
4.3	odd	2		2960.2.p.g.961.2		6
5.2	odd	4		1850.2.c.j.1849.2		6
5.3	odd	4		1850.2.c.i.1849.5		6
5.4	even	2		1850.2.d.f.1701.4		6
37.36	even	2	inner	370.2.d.c.221.6	yes	6
111.110	odd	2		3330.2.h.n.2071.2		6
148.147	odd	2		2960.2.p.g.961.1		6
185.73	odd	4		1850.2.c.j.1849.5		6
185.147	odd	4		1850.2.c.i.1849.2		6
185.184	even	2		1850.2.d.f.1701.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.d.c.221.3	✓	6	1.1	even	1	trivial
370.2.d.c.221.6	yes	6	37.36	even	2	inner
1850.2.c.i.1849.2		6	185.147	odd	4
1850.2.c.i.1849.5		6	5.3	odd	4
1850.2.c.j.1849.2		6	5.2	odd	4
1850.2.c.j.1849.5		6	185.73	odd	4
1850.2.d.f.1701.1		6	185.184	even	2
1850.2.d.f.1701.4		6	5.4	even	2
2960.2.p.g.961.1		6	148.147	odd	2
2960.2.p.g.961.2		6	4.3	odd	2
3330.2.h.n.2071.2		6	111.110	odd	2
3330.2.h.n.2071.5		6	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +2.24914 q^{3} -1.00000 q^{4} +1.00000i q^{5} -2.24914i q^{6} +1.52932 q^{7} +1.00000i q^{8} +2.05863 q^{9} +1.00000 q^{10} +2.71982 q^{11} -2.24914 q^{12} +0.941367i q^{13} -1.52932i q^{14} +2.24914i q^{15} +1.00000 q^{16} -4.83709i q^{17} -2.05863i q^{18} -0.249141i q^{19} -1.00000i q^{20} +3.43965 q^{21} -2.71982i q^{22} +0.941367i q^{23} +2.24914i q^{24} -1.00000 q^{25} +0.941367 q^{26} -2.11727 q^{27} -1.52932 q^{28} +0.719824i q^{29} +2.24914 q^{30} +4.02760i q^{31} -1.00000i q^{32} +6.11727 q^{33} -4.83709 q^{34} +1.52932i q^{35} -2.05863 q^{36} +(-4.71982 - 3.83709i) q^{37} -0.249141 q^{38} +2.11727i q^{39} -1.00000 q^{40} -8.27674 q^{41} -3.43965i q^{42} +2.71982i q^{43} -2.71982 q^{44} +2.05863i q^{45} +0.941367 q^{46} -3.30777 q^{47} +2.24914 q^{48} -4.66119 q^{49} +1.00000i q^{50} -10.8793i q^{51} -0.941367i q^{52} +8.39400 q^{53} +2.11727i q^{54} +2.71982i q^{55} +1.52932i q^{56} -0.560352i q^{57} +0.719824 q^{58} -7.30777i q^{59} -2.24914i q^{60} +6.83709i q^{61} +4.02760 q^{62} +3.14830 q^{63} -1.00000 q^{64} -0.941367 q^{65} -6.11727i q^{66} -7.68879 q^{67} +4.83709i q^{68} +2.11727i q^{69} +1.52932 q^{70} -3.05863 q^{71} +2.05863i q^{72} +9.11383 q^{73} +(-3.83709 + 4.71982i) q^{74} -2.24914 q^{75} +0.249141i q^{76} +4.15947 q^{77} +2.11727 q^{78} -1.75086i q^{79} +1.00000i q^{80} -10.9379 q^{81} +8.27674i q^{82} +0.131874 q^{83} -3.43965 q^{84} +4.83709 q^{85} +2.71982 q^{86} +1.61899i q^{87} +2.71982i q^{88} -8.99656i q^{89} +2.05863 q^{90} +1.43965i q^{91} -0.941367i q^{92} +9.05863i q^{93} +3.30777i q^{94} +0.249141 q^{95} -2.24914i q^{96} +16.2767i q^{97} +4.66119i q^{98} +5.59912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{3} - 6 q^{4} + 10 q^{7} + 14 q^{9} + 6 q^{10} - 2 q^{11} + 4 q^{12} + 6 q^{16} - 16 q^{21} - 6 q^{25} + 4 q^{26} - 16 q^{27} - 10 q^{28} - 4 q^{30} + 40 q^{33} - 14 q^{34} - 14 q^{36} - 10 q^{37}+ \cdots - 58 q^{99}+O(q^{100}) \) 6 * q - 4 * q^3 - 6 * q^4 + 10 * q^7 + 14 * q^9 + 6 * q^10 - 2 * q^11 + 4 * q^12 + 6 * q^16 - 16 * q^21 - 6 * q^25 + 4 * q^26 - 16 * q^27 - 10 * q^28 - 4 * q^30 + 40 * q^33 - 14 * q^34 - 14 * q^36 - 10 * q^37 + 16 * q^38 - 6 * q^40 + 2 * q^41 + 2 * q^44 + 4 * q^46 - 4 * q^47 - 4 * q^48 - 8 * q^49 + 2 * q^53 - 14 * q^58 - 10 * q^62 + 58 * q^63 - 6 * q^64 - 4 * q^65 + 8 * q^67 + 10 * q^70 - 20 * q^71 - 12 * q^73 - 8 * q^74 + 4 * q^75 - 30 * q^77 + 16 * q^78 + 6 * q^81 - 20 * q^83 + 16 * q^84 + 14 * q^85 - 2 * q^86 + 14 * q^90 - 16 * q^95 - 58 * q^99

Introduction

L-functions

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