LMFDB - Embedded newform 65.2.c.a.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(51,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, 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("65.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.c (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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.5089536.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 16x^2 - 24*x + 18
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.1
Root			$1.66044 + 1.66044i$ of defining polynomial
Character	$\chi$	$=$	65.51
Dual form			65.2.c.a.51.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51414i q^{2} +1.51414 q^{3} -4.32088 q^{4} +1.00000i q^{5} -3.80675i q^{6} +3.32088i q^{7} +5.83502i q^{8} -0.707389 q^{9} +O(q^{10})$	\(q-2.51414i q^{2} +1.51414 q^{3} -4.32088 q^{4} +1.00000i q^{5} -3.80675i q^{6} +3.32088i q^{7} +5.83502i q^{8} -0.707389 q^{9} +2.51414 q^{10} -2.83502i q^{11} -6.54241 q^{12} +(-3.51414 - 0.806748i) q^{13} +8.34916 q^{14} +1.51414i q^{15} +6.02827 q^{16} +6.64177 q^{17} +1.77847i q^{18} -2.19325i q^{19} -4.32088i q^{20} +5.02827i q^{21} -7.12763 q^{22} +0.485863 q^{23} +8.83502i q^{24} -1.00000 q^{25} +(-2.02827 + 8.83502i) q^{26} -5.61350 q^{27} -14.3492i q^{28} -3.32088 q^{29} +3.80675 q^{30} -3.80675i q^{31} -3.48586i q^{32} -4.29261i q^{33} -16.6983i q^{34} -3.32088 q^{35} +3.05655 q^{36} +9.32088i q^{37} -5.51414 q^{38} +(-5.32088 - 1.22153i) q^{39} -5.83502 q^{40} +1.61350i q^{41} +12.6418 q^{42} +0.872368 q^{43} +12.2498i q^{44} -0.707389i q^{45} -1.22153i q^{46} -3.32088i q^{47} +9.12763 q^{48} -4.02827 q^{49} +2.51414i q^{50} +10.0565 q^{51} +(15.1842 + 3.48586i) q^{52} +11.6700 q^{53} +14.1131i q^{54} +2.83502 q^{55} -19.3774 q^{56} -3.32088i q^{57} +8.34916i q^{58} -8.83502i q^{59} -6.54241i q^{60} -3.70739 q^{61} -9.57068 q^{62} -2.34916i q^{63} +3.29261 q^{64} +(0.806748 - 3.51414i) q^{65} -10.7922 q^{66} -4.29261i q^{67} -28.6983 q^{68} +0.735663 q^{69} +8.34916i q^{70} -2.19325i q^{71} -4.12763i q^{72} +12.7357i q^{73} +23.4340 q^{74} -1.51414 q^{75} +9.47679i q^{76} +9.41478 q^{77} +(-3.07108 + 13.3774i) q^{78} +0.585221 q^{79} +6.02827i q^{80} -6.37743 q^{81} +4.05655 q^{82} -7.70739i q^{83} -21.7266i q^{84} +6.64177i q^{85} -2.19325i q^{86} -5.02827 q^{87} +16.5424 q^{88} +3.41478i q^{89} -1.77847 q^{90} +(2.67912 - 11.6700i) q^{91} -2.09936 q^{92} -5.76394i q^{93} -8.34916 q^{94} +2.19325 q^{95} -5.27807i q^{96} -0.641769i q^{97} +10.1276i q^{98} +2.00546i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{3} - 10 q^{4} + 6 q^{9}+O(q^{10}) $ 6 * q - 4 * q^3 - 10 * q^4 + 6 * q^9	$ 6 q - 4 q^{3} - 10 q^{4} + 6 q^{9} + 2 q^{10} - 8 q^{13} + 8 q^{14} + 10 q^{16} + 8 q^{17} - 24 q^{22} + 16 q^{23} - 6 q^{25} + 14 q^{26} - 28 q^{27} - 4 q^{29} + 20 q^{30} - 4 q^{35} - 34 q^{36} - 20 q^{38} - 16 q^{39} - 6 q^{40} + 44 q^{42} + 24 q^{43} + 36 q^{48} + 2 q^{49} + 8 q^{51} + 20 q^{52} + 12 q^{53} - 12 q^{55} - 48 q^{56} - 12 q^{61} + 8 q^{62} + 30 q^{64} + 2 q^{65} + 24 q^{66} - 88 q^{68} - 32 q^{69} + 20 q^{74} + 4 q^{75} + 36 q^{77} - 52 q^{78} + 24 q^{79} + 30 q^{81} - 28 q^{82} - 4 q^{87} + 60 q^{88} - 34 q^{90} + 32 q^{91} - 20 q^{92} - 8 q^{94} + 16 q^{95}+O(q^{100}) $ 6 * q - 4 * q^3 - 10 * q^4 + 6 * q^9 + 2 * q^10 - 8 * q^13 + 8 * q^14 + 10 * q^16 + 8 * q^17 - 24 * q^22 + 16 * q^23 - 6 * q^25 + 14 * q^26 - 28 * q^27 - 4 * q^29 + 20 * q^30 - 4 * q^35 - 34 * q^36 - 20 * q^38 - 16 * q^39 - 6 * q^40 + 44 * q^42 + 24 * q^43 + 36 * q^48 + 2 * q^49 + 8 * q^51 + 20 * q^52 + 12 * q^53 - 12 * q^55 - 48 * q^56 - 12 * q^61 + 8 * q^62 + 30 * q^64 + 2 * q^65 + 24 * q^66 - 88 * q^68 - 32 * q^69 + 20 * q^74 + 4 * q^75 + 36 * q^77 - 52 * q^78 + 24 * q^79 + 30 * q^81 - 28 * q^82 - 4 * q^87 + 60 * q^88 - 34 * q^90 + 32 * q^91 - 20 * q^92 - 8 * q^94 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	2.51414i		−	1.77776i	−0.458137	−	0.888882i	$-0.651483\pi$
$2$		−	2.51414i		−	1.77776i	0.458137	−	0.888882i	$-0.348517\pi$
$3$	1.51414			0.874187			0.437094	−	0.899416i	$-0.356008\pi$
$3$	1.51414			0.874187			0.437094	+	0.899416i	$0.356008\pi$
$4$	−4.32088			−2.16044
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		−	3.80675i		−	1.55410i
$7$			3.32088i			1.25518i	0.778545	+	0.627588i	$0.215958\pi$
$7$			3.32088i			1.25518i	−0.778545	+	0.627588i	$0.784042\pi$
$8$			5.83502i			2.06299i
$9$	−0.707389			−0.235796
$10$	2.51414			0.795040
$11$		−	2.83502i		−	0.854791i	−0.904065	−	0.427396i	$-0.859431\pi$
$11$		−	2.83502i		−	0.854791i	0.904065	−	0.427396i	$-0.140569\pi$
$12$	−6.54241			−1.88863
$13$	−3.51414	−	0.806748i	−0.974646	−	0.223752i
$13$	−3.51414	−	0.806748i	−0.974646	−	0.223752i
$14$	8.34916			2.23141
$15$			1.51414i			0.390948i
$16$	6.02827			1.50707
$17$	6.64177			1.61087			0.805433	−	0.592687i	$-0.201933\pi$
$17$	6.64177			1.61087			0.805433	+	0.592687i	$0.201933\pi$
$18$			1.77847i			0.419190i
$19$		−	2.19325i		−	0.503167i	−0.967836	−	0.251583i	$-0.919049\pi$
$19$		−	2.19325i		−	0.503167i	0.967836	−	0.251583i	$-0.0809512\pi$
$20$		−	4.32088i		−	0.966179i
$21$			5.02827i			1.09726i
$22$	−7.12763			−1.51962
$23$	0.485863			0.101309			0.0506547	−	0.998716i	$-0.483869\pi$
$23$	0.485863			0.101309			0.0506547	+	0.998716i	$0.483869\pi$
$24$			8.83502i			1.80344i
$25$	−1.00000			−0.200000
$26$	−2.02827	+	8.83502i	−0.397777	+	1.73269i
$27$	−5.61350			−1.08032
$28$		−	14.3492i		−	2.71174i
$29$	−3.32088			−0.616673			−0.308336	−	0.951277i	$-0.599772\pi$
$29$	−3.32088			−0.616673			−0.308336	+	0.951277i	$0.599772\pi$
$30$	3.80675			0.695014
$31$		−	3.80675i		−	0.683712i	−0.939752	−	0.341856i	$-0.888944\pi$
$31$		−	3.80675i		−	0.683712i	0.939752	−	0.341856i	$-0.111056\pi$
$32$		−	3.48586i		−	0.616219i
$33$		−	4.29261i		−	0.747248i
$34$		−	16.6983i		−	2.86374i
$35$	−3.32088			−0.561332
$36$	3.05655			0.509425
$37$			9.32088i			1.53234i	0.642636	+	0.766172i	$0.277841\pi$
$37$			9.32088i			1.53234i	−0.642636	+	0.766172i	$0.722159\pi$
$38$	−5.51414			−0.894511
$39$	−5.32088	−	1.22153i	−0.852023	−	0.195601i
$40$	−5.83502			−0.922598
$41$			1.61350i			0.251986i	0.992031	+	0.125993i	$0.0402116\pi$
$41$			1.61350i			0.251986i	−0.992031	+	0.125993i	$0.959788\pi$
$42$	12.6418			1.95067
$43$	0.872368			0.133035			0.0665174	−	0.997785i	$-0.478811\pi$
$43$	0.872368			0.133035			0.0665174	+	0.997785i	$0.478811\pi$
$44$			12.2498i			1.84673i
$45$		−	0.707389i		−	0.105451i
$46$		−	1.22153i		−	0.180104i
$47$		−	3.32088i		−	0.484401i	−0.970226	−	0.242200i	$-0.922131\pi$
$47$		−	3.32088i		−	0.484401i	0.970226	−	0.242200i	$-0.0778691\pi$
$48$	9.12763			1.31746
$49$	−4.02827			−0.575468
$50$			2.51414i			0.355553i
$51$	10.0565			1.40820
$52$	15.1842	+	3.48586i	2.10567	+	0.483402i
$53$	11.6700			1.60300			0.801502	−	0.597992i	$-0.204035\pi$
$53$	11.6700			1.60300			0.801502	+	0.597992i	$0.204035\pi$
$54$			14.1131i			1.92055i
$55$	2.83502			0.382274
$56$	−19.3774			−2.58942
$57$		−	3.32088i		−	0.439862i
$58$			8.34916i			1.09630i
$59$		−	8.83502i		−	1.15022i	−0.818075	−	0.575111i	$-0.804959\pi$
$59$		−	8.83502i		−	1.15022i	0.818075	−	0.575111i	$-0.195041\pi$
$60$		−	6.54241i		−	0.844622i
$61$	−3.70739			−0.474683			−0.237341	−	0.971426i	$-0.576276\pi$
$61$	−3.70739			−0.474683			−0.237341	+	0.971426i	$0.576276\pi$
$62$	−9.57068			−1.21548
$63$		−	2.34916i		−	0.295966i
$64$	3.29261			0.411576
$65$	0.806748	−	3.51414i	0.100065	−	0.435875i
$66$	−10.7922			−1.32843
$67$		−	4.29261i		−	0.524426i	−0.965010	−	0.262213i	$-0.915548\pi$
$67$		−	4.29261i		−	0.524426i	0.965010	−	0.262213i	$-0.0844523\pi$
$68$	−28.6983			−3.48018
$69$	0.735663			0.0885634
$70$			8.34916i			0.997915i
$71$		−	2.19325i		−	0.260291i	−0.991495	−	0.130146i	$-0.958456\pi$
$71$		−	2.19325i		−	0.260291i	0.991495	−	0.130146i	$-0.0415445\pi$
$72$		−	4.12763i		−	0.486446i
$73$			12.7357i			1.49060i	0.666731	+	0.745298i	$0.267693\pi$
$73$			12.7357i			1.49060i	−0.666731	+	0.745298i	$0.732307\pi$
$74$	23.4340			2.72414
$75$	−1.51414			−0.174837
$76$			9.47679i			1.08706i
$77$	9.41478			1.07291
$78$	−3.07108	+	13.3774i	−0.347732	+	1.51470i
$79$	0.585221			0.0658425			0.0329213	−	0.999458i	$-0.489519\pi$
$79$	0.585221			0.0658425			0.0329213	+	0.999458i	$0.489519\pi$
$80$			6.02827i			0.673982i
$81$	−6.37743			−0.708604
$82$	4.05655			0.447971
$83$		−	7.70739i		−	0.845996i	−0.906131	−	0.422998i	$-0.860978\pi$
$83$		−	7.70739i		−	0.845996i	0.906131	−	0.422998i	$-0.139022\pi$
$84$		−	21.7266i		−	2.37057i
$85$			6.64177i			0.720401i
$86$		−	2.19325i		−	0.236504i
$87$	−5.02827			−0.539088
$88$	16.5424			1.76343
$89$			3.41478i			0.361966i	0.983486	+	0.180983i	$0.0579279\pi$
$89$			3.41478i			0.361966i	−0.983486	+	0.180983i	$0.942072\pi$
$90$	−1.77847			−0.187468
$91$	2.67912	−	11.6700i	0.280848	−	1.22335i
$92$	−2.09936			−0.218873
$93$		−	5.76394i		−	0.597692i
$94$	−8.34916			−0.861150
$95$	2.19325			0.225023
$96$		−	5.27807i		−	0.538691i
$97$		−	0.641769i		−	0.0651618i	−0.999469	−	0.0325809i	$-0.989627\pi$
$97$		−	0.641769i		−	0.0651618i	0.999469	−	0.0325809i	$-0.0103727\pi$
$98$			10.1276i			1.02305i
$99$			2.00546i			0.201557i
$100$	4.32088			0.432088
$101$	−6.97173			−0.693713			−0.346856	−	0.937918i	$-0.612751\pi$
$101$	−6.97173			−0.693713			−0.346856	+	0.937918i	$0.612751\pi$
$102$		−	25.2835i		−	2.50344i
$103$	7.18418			0.707878			0.353939	−	0.935268i	$-0.384842\pi$
$103$	7.18418			0.707878			0.353939	+	0.935268i	$0.384842\pi$
$104$	4.70739	−	20.5051i	0.461598	−	2.01069i
$105$	−5.02827			−0.490709
$106$		−	29.3401i		−	2.84976i
$107$	−9.57068			−0.925233			−0.462617	−	0.886558i	$-0.653089\pi$
$107$	−9.57068			−0.925233			−0.462617	+	0.886558i	$0.653089\pi$
$108$	24.2553			2.33396
$109$			10.6983i			1.02471i	0.858773	+	0.512356i	$0.171227\pi$
$109$			10.6983i			1.02471i	−0.858773	+	0.512356i	$0.828773\pi$
$110$		−	7.12763i		−	0.679593i
$111$			14.1131i			1.33956i
$112$			20.0192i			1.89164i
$113$	−3.22699			−0.303570			−0.151785	−	0.988414i	$-0.548502\pi$
$113$	−3.22699			−0.303570			−0.151785	+	0.988414i	$0.548502\pi$
$114$	−8.34916			−0.781970
$115$			0.485863i			0.0453070i
$116$	14.3492			1.33229
$117$	2.48586	+	0.570685i	0.229818	+	0.0527598i
$118$	−22.2125			−2.04482
$119$			22.0565i			2.02192i
$120$	−8.83502			−0.806523
$121$	2.96265			0.269332
$122$			9.32088i			0.843873i
$123$			2.44305i			0.220283i
$124$			16.4485i			1.47712i
$125$		−	1.00000i		−	0.0894427i
$126$	−5.90611			−0.526158
$127$	−5.90064			−0.523597			−0.261799	−	0.965123i	$-0.584316\pi$
$127$	−5.90064			−0.523597			−0.261799	+	0.965123i	$0.584316\pi$
$128$		−	15.2498i		−	1.34790i
$129$	1.32088			0.116297
$130$	−8.83502	−	2.02827i	−0.774883	−	0.177891i
$131$	3.41478			0.298351			0.149175	−	0.988811i	$-0.452338\pi$
$131$	3.41478			0.298351			0.149175	+	0.988811i	$0.452338\pi$
$132$			18.5479i			1.61439i
$133$	7.28354			0.631563
$134$	−10.7922			−0.932305
$135$		−	5.61350i		−	0.483133i
$136$			38.7549i			3.32320i
$137$		−	15.0848i		−	1.28878i	−0.764696	−	0.644392i	$-0.777111\pi$
$137$		−	15.0848i		−	1.28878i	0.764696	−	0.644392i	$-0.222889\pi$
$138$		−	1.84956i		−	0.157445i
$139$	−20.6983			−1.75561			−0.877804	−	0.479020i	$-0.840992\pi$
$139$	−20.6983			−1.75561			−0.877804	+	0.479020i	$0.840992\pi$
$140$	14.3492			1.21273
$141$		−	5.02827i		−	0.423457i
$142$	−5.51414			−0.462736
$143$	−2.28715	+	9.96265i	−0.191261	+	0.833119i
$144$	−4.26434			−0.355361
$145$		−	3.32088i		−	0.275784i
$146$	32.0192			2.64993
$147$	−6.09936			−0.503067
$148$		−	40.2745i		−	3.31054i
$149$		−	0.641769i		−	0.0525758i	−0.999654	−	0.0262879i	$-0.991631\pi$
$149$		−	0.641769i		−	0.0525758i	0.999654	−	0.0262879i	$-0.00836866\pi$
$150$			3.80675i			0.310820i
$151$			16.6363i			1.35384i	0.736055	+	0.676922i	$0.236686\pi$
$151$			16.6363i			1.35384i	−0.736055	+	0.676922i	$0.763314\pi$
$152$	12.7977			1.03803
$153$	−4.69832			−0.379836
$154$		−	23.6700i		−	1.90739i
$155$	3.80675			0.305765
$156$	22.9909	+	5.27807i	1.84075	+	0.422584i
$157$	10.2553			0.818459			0.409230	−	0.912431i	$-0.365798\pi$
$157$	10.2553			0.818459			0.409230	+	0.912431i	$0.365798\pi$
$158$		−	1.47133i		−	0.117052i
$159$	17.6700			1.40133
$160$	3.48586			0.275582
$161$			1.61350i			0.127161i
$162$			16.0337i			1.25973i
$163$		−	1.37743i		−	0.107889i	−0.998544	−	0.0539444i	$-0.982821\pi$
$163$		−	1.37743i		−	0.107889i	0.998544	−	0.0539444i	$-0.0171794\pi$
$164$		−	6.97173i		−	0.544400i
$165$	4.29261			0.334179
$166$	−19.3774			−1.50398
$167$			17.5761i			1.36008i	0.733174	+	0.680042i	$0.238038\pi$
$167$			17.5761i			1.36008i	−0.733174	+	0.680042i	$0.761962\pi$
$168$	−29.3401			−2.26364
$169$	11.6983	+	5.67004i	0.899871	+	0.436157i
$170$	16.6983			1.28070
$171$			1.55148i			0.118645i
$172$	−3.76940			−0.287414
$173$	−6.31181			−0.479878			−0.239939	−	0.970788i	$-0.577127\pi$
$173$	−6.31181			−0.479878			−0.239939	+	0.970788i	$0.577127\pi$
$174$			12.6418i			0.958370i
$175$		−	3.32088i		−	0.251035i
$176$		−	17.0903i		−	1.28823i
$177$		−	13.3774i		−	1.00551i
$178$	8.58522			0.643490
$179$	9.08482			0.679031			0.339516	−	0.940600i	$-0.389737\pi$
$179$	9.08482			0.679031			0.339516	+	0.940600i	$0.389737\pi$
$180$			3.05655i			0.227822i
$181$	−12.0192			−0.893380			−0.446690	−	0.894689i	$-0.647397\pi$
$181$	−12.0192			−0.893380			−0.446690	+	0.894689i	$0.647397\pi$
$182$	−29.3401	−	6.73566i	−2.17483	−	0.499281i
$183$	−5.61350			−0.414962
$184$			2.83502i			0.209001i
$185$	−9.32088			−0.685285
$186$	−14.4913			−1.06256
$187$		−	18.8296i		−	1.37695i
$188$			14.3492i			1.04652i
$189$		−	18.6418i		−	1.35599i
$190$		−	5.51414i		−	0.400038i
$191$	13.2835			0.961163			0.480582	−	0.876950i	$-0.340426\pi$
$191$	13.2835			0.961163			0.480582	+	0.876950i	$0.340426\pi$
$192$	4.98546			0.359795
$193$			16.3684i			1.17822i	0.808053	+	0.589110i	$0.200522\pi$
$193$			16.3684i			1.17822i	−0.808053	+	0.589110i	$0.799478\pi$
$194$	−1.61350			−0.115842
$195$	1.22153	−	5.32088i	0.0874753	−	0.381036i
$196$	17.4057			1.24326
$197$		−	14.8970i		−	1.06137i	−0.847569	−	0.530685i	$-0.821935\pi$
$197$		−	14.8970i		−	1.06137i	0.847569	−	0.530685i	$-0.178065\pi$
$198$	5.04201			0.358320
$199$	16.3118			1.15631			0.578157	−	0.815926i	$-0.303772\pi$
$199$	16.3118			1.15631			0.578157	+	0.815926i	$0.303772\pi$
$200$		−	5.83502i		−	0.412598i
$201$		−	6.49960i		−	0.458446i
$202$			17.5279i			1.23326i
$203$		−	11.0283i		−	0.774033i
$204$	−43.4532			−3.04233
$205$	−1.61350			−0.112691
$206$		−	18.0620i		−	1.25844i
$207$	−0.343694			−0.0238884
$208$	−21.1842	−	4.86330i	−1.46886	−	0.337209i
$209$	−6.21792			−0.430102
$210$			12.6418i			0.872365i
$211$	11.8013			0.812434			0.406217	−	0.913777i	$-0.366848\pi$
$211$	11.8013			0.812434			0.406217	+	0.913777i	$0.366848\pi$
$212$	−50.4249			−3.46320
$213$		−	3.32088i		−	0.227543i
$214$			24.0620i			1.64485i
$215$			0.872368i			0.0594950i
$216$		−	32.7549i		−	2.22869i
$217$	12.6418			0.858179
$218$	26.8970			1.82170
$219$			19.2835i			1.30306i
$220$	−12.2498			−0.825881
$221$	−23.3401	−	5.35823i	−1.57002	−	0.360434i
$222$	35.4823			2.38141
$223$			20.0192i			1.34058i	0.742097	+	0.670292i	$0.233831\pi$
$223$			20.0192i			1.34058i	−0.742097	+	0.670292i	$0.766169\pi$
$224$	11.5761			0.773464
$225$	0.707389			0.0471593
$226$			8.11310i			0.539675i
$227$			22.4623i			1.49087i	0.666577	+	0.745436i	$0.267759\pi$
$227$			22.4623i			1.49087i	−0.666577	+	0.745436i	$0.732241\pi$
$228$			14.3492i			0.950296i
$229$		−	10.3684i		−	0.685160i	−0.939489	−	0.342580i	$-0.888699\pi$
$229$		−	10.3684i		−	0.685160i	0.939489	−	0.342580i	$-0.111301\pi$
$230$	1.22153			0.0805451
$231$	14.2553			0.937928
$232$		−	19.3774i		−	1.27219i
$233$	−11.3582			−0.744102			−0.372051	−	0.928212i	$-0.621345\pi$
$233$	−11.3582			−0.744102			−0.372051	+	0.928212i	$0.621345\pi$
$234$	1.43478	−	6.24980i	0.0937945	−	0.408562i
$235$	3.32088			0.216631
$236$			38.1751i			2.48499i
$237$	0.886105			0.0575587
$238$	55.4532			3.59450
$239$		−	28.1186i		−	1.81884i	−0.415881	−	0.909419i	$-0.636527\pi$
$239$		−	28.1186i		−	1.81884i	0.415881	−	0.909419i	$-0.363473\pi$
$240$			9.12763i			0.589186i
$241$		−	15.0848i		−	0.971699i	−0.874043	−	0.485849i	$-0.838510\pi$
$241$		−	15.0848i		−	0.971699i	0.874043	−	0.485849i	$-0.161490\pi$
$242$		−	7.44852i		−	0.478809i
$243$	7.18418			0.460865
$244$	16.0192			1.02552
$245$		−	4.02827i		−	0.257357i
$246$	6.14217			0.391610
$247$	−1.76940	+	7.70739i	−0.112584	+	0.490409i
$248$	22.2125			1.41049
$249$		−	11.6700i		−	0.739559i
$250$	−2.51414			−0.159008
$251$	−1.15951			−0.0731879			−0.0365940	−	0.999330i	$-0.511651\pi$
$251$	−1.15951			−0.0731879			−0.0365940	+	0.999330i	$0.511651\pi$
$252$			10.1504i			0.639418i
$253$		−	1.37743i		−	0.0865984i
$254$			14.8350i			0.930832i
$255$			10.0565i			0.629765i
$256$	−31.7549			−1.98468
$257$	0.829557			0.0517464			0.0258732	−	0.999665i	$-0.491763\pi$
$257$	0.829557			0.0517464			0.0258732	+	0.999665i	$0.491763\pi$
$258$		−	3.32088i		−	0.206749i
$259$	−30.9536			−1.92336
$260$	−3.48586	+	15.1842i	−0.216184	+	0.941683i
$261$	2.34916			0.145409
$262$		−	8.58522i		−	0.530397i
$263$	−25.6272			−1.58024			−0.790121	−	0.612950i	$-0.789983\pi$
$263$	−25.6272			−1.58024			−0.790121	+	0.612950i	$0.789983\pi$
$264$	25.0475			1.54157
$265$			11.6700i			0.716885i
$266$		−	18.3118i		−	1.12277i
$267$			5.17044i			0.316426i
$268$			18.5479i			1.13299i
$269$	5.02827			0.306579			0.153290	−	0.988181i	$-0.451013\pi$
$269$	5.02827			0.306579			0.153290	+	0.988181i	$0.451013\pi$
$270$	−14.1131			−0.858896
$271$		−	18.8916i		−	1.14758i	−0.819002	−	0.573791i	$-0.805472\pi$
$271$		−	18.8916i		−	1.14758i	0.819002	−	0.573791i	$-0.194528\pi$
$272$	40.0384			2.42768
$273$	4.05655	−	17.6700i	0.245513	−	1.06944i
$274$	−37.9253			−2.29115
$275$			2.83502i			0.170958i
$276$	−3.17872			−0.191336
$277$	−23.7831			−1.42899			−0.714495	−	0.699640i	$-0.753344\pi$
$277$	−23.7831			−1.42899			−0.714495	+	0.699640i	$0.753344\pi$
$278$			52.0384i			3.12106i
$279$			2.69285i			0.161217i
$280$		−	19.3774i		−	1.15802i
$281$			31.5953i			1.88482i	0.334459	+	0.942410i	$0.391446\pi$
$281$			31.5953i			1.88482i	−0.334459	+	0.942410i	$0.608554\pi$
$282$	−12.6418			−0.752806
$283$	−6.35462			−0.377743			−0.188872	−	0.982002i	$-0.560483\pi$
$283$	−6.35462			−0.377743			−0.188872	+	0.982002i	$0.560483\pi$
$284$			9.47679i			0.562344i
$285$	3.32088			0.196712
$286$	25.0475	+	5.75020i	1.48109	+	0.340016i
$287$	−5.35823			−0.316286
$288$			2.46586i			0.145302i
$289$	27.1131			1.59489
$290$	−8.34916			−0.490279
$291$		−	0.971726i		−	0.0569636i
$292$		−	55.0293i		−	3.22035i
$293$		−	8.03735i		−	0.469547i	−0.972050	−	0.234773i	$-0.924565\pi$
$293$		−	8.03735i		−	0.469547i	0.972050	−	0.234773i	$-0.0754348\pi$
$294$			15.3346i			0.894333i
$295$	8.83502			0.514395
$296$	−54.3876			−3.16121
$297$			15.9144i			0.923446i
$298$	−1.61350			−0.0934673
$299$	−1.70739	−	0.391969i	−0.0987409	−	0.0226681i
$300$	6.54241			0.377726
$301$			2.89703i			0.166982i
$302$	41.8259			2.40681
$303$	−10.5561			−0.606435
$304$		−	13.2215i		−	0.758307i
$305$		−	3.70739i		−	0.212284i
$306$			11.8122i			0.675259i
$307$		−	15.8205i		−	0.902923i	−0.892291	−	0.451461i	$-0.850903\pi$
$307$		−	15.8205i		−	0.902923i	0.892291	−	0.451461i	$-0.149097\pi$
$308$	−40.6802			−2.31797
$309$	10.8778			0.618818
$310$		−	9.57068i		−	0.543578i
$311$	−24.3118			−1.37860			−0.689298	−	0.724478i	$-0.742081\pi$
$311$	−24.3118			−1.37860			−0.689298	+	0.724478i	$0.742081\pi$
$312$	7.12763	−	31.0475i	0.403523	−	1.75772i
$313$	−11.2270			−0.634587			−0.317294	−	0.948327i	$-0.602774\pi$
$313$	−11.2270			−0.634587			−0.317294	+	0.948327i	$0.602774\pi$
$314$		−	25.7831i		−	1.45503i
$315$	2.34916			0.132360
$316$	−2.52867			−0.142249
$317$			16.1504i			0.907099i	0.891231	+	0.453550i	$0.149843\pi$
$317$			16.1504i			0.907099i	−0.891231	+	0.453550i	$0.850157\pi$
$318$		−	44.4249i		−	2.49123i
$319$			9.41478i			0.527126i
$320$			3.29261i			0.184063i
$321$	−14.4913			−0.808827
$322$	4.05655			0.226063
$323$		−	14.5671i		−	0.810534i
$324$	27.5561			1.53090
$325$	3.51414	+	0.806748i	0.194929	+	0.0447503i
$326$	−3.46305			−0.191801
$327$			16.1987i			0.895791i
$328$	−9.41478			−0.519844
$329$	11.0283			0.608008
$330$		−	10.7922i		−	0.594092i
$331$		−	30.0620i		−	1.65236i	−0.563408	−	0.826179i	$-0.690510\pi$
$331$		−	30.0620i		−	1.65236i	0.563408	−	0.826179i	$-0.309490\pi$
$332$			33.3027i			1.82773i
$333$		−	6.59349i		−	0.361321i
$334$	44.1888			2.41791
$335$	4.29261			0.234530
$336$			30.3118i			1.65364i
$337$	17.4713			0.951724			0.475862	−	0.879520i	$-0.342136\pi$
$337$	17.4713			0.951724			0.475862	+	0.879520i	$0.342136\pi$
$338$	14.2553	−	29.4112i	0.775384	−	1.59976i
$339$	−4.88611			−0.265377
$340$		−	28.6983i		−	1.55638i
$341$	−10.7922			−0.584431
$342$	3.90064			0.210923
$343$			9.86876i			0.532863i
$344$			5.09029i			0.274450i
$345$			0.735663i			0.0396068i
$346$			15.8688i			0.853110i
$347$	33.2407			1.78446			0.892228	−	0.451585i	$-0.149141\pi$
$347$	33.2407			1.78446			0.892228	+	0.451585i	$0.149141\pi$
$348$	21.7266			1.16467
$349$		−	20.8970i		−	1.11859i	−0.828968	−	0.559296i	$-0.811071\pi$
$349$		−	20.8970i		−	1.11859i	0.828968	−	0.559296i	$-0.188929\pi$
$350$	−8.34916			−0.446281
$351$	19.7266	+	4.52867i	1.05293	+	0.241723i
$352$	−9.88250			−0.526739
$353$		−	12.5479i		−	0.667856i	−0.942599	−	0.333928i	$-0.891626\pi$
$353$		−	12.5479i		−	0.667856i	0.942599	−	0.333928i	$-0.108374\pi$
$354$	−33.6327			−1.78756
$355$	2.19325			0.116406
$356$		−	14.7549i		−	0.782006i
$357$			33.3966i			1.76754i
$358$		−	22.8405i		−	1.20716i
$359$		−	2.97719i		−	0.157130i	−0.996909	−	0.0785650i	$-0.974966\pi$
$359$		−	2.97719i		−	0.157130i	0.996909	−	0.0785650i	$-0.0250338\pi$
$360$	4.12763			0.217545
$361$	14.1896			0.746823
$362$			30.2179i			1.58822i
$363$	4.48586			0.235447
$364$	−11.5761	+	50.4249i	−0.606755	+	2.64298i
$365$	−12.7357			−0.666615
$366$			14.1131i			0.737703i
$367$	−30.5990			−1.59725			−0.798626	−	0.601827i	$-0.794440\pi$
$367$	−30.5990			−1.59725			−0.798626	+	0.601827i	$0.794440\pi$
$368$	2.92892			0.152680
$369$		−	1.14137i		−	0.0594173i
$370$			23.4340i			1.21827i
$371$			38.7549i			2.01205i
$372$			24.9053i			1.29128i
$373$	18.2553			0.945222			0.472611	−	0.881271i	$-0.343312\pi$
$373$	18.2553			0.945222			0.472611	+	0.881271i	$0.343312\pi$
$374$	−47.3401			−2.44790
$375$		−	1.51414i		−	0.0781897i
$376$	19.3774			0.999315
$377$	11.6700	+	2.67912i	0.601038	+	0.137981i
$378$	−46.8680			−2.41063
$379$		−	15.9945i		−	0.821584i	−0.911729	−	0.410792i	$-0.865252\pi$
$379$		−	15.9945i		−	0.821584i	0.911729	−	0.410792i	$-0.134748\pi$
$380$	−9.47679			−0.486149
$381$	−8.93438			−0.457722
$382$		−	33.3966i		−	1.70872i
$383$			2.16137i			0.110441i	0.998474	+	0.0552204i	$0.0175862\pi$
$383$			2.16137i			0.110441i	−0.998474	+	0.0552204i	$0.982414\pi$
$384$		−	23.0903i		−	1.17832i
$385$			9.41478i			0.479822i
$386$	41.1523			2.09460
$387$	−0.617104			−0.0313691
$388$			2.77301i			0.140778i
$389$	0.453981			0.0230177			0.0115089	−	0.999934i	$-0.496337\pi$
$389$	0.453981			0.0230177			0.0115089	+	0.999934i	$0.496337\pi$
$390$	−13.3774	−	3.07108i	−0.677393	−	0.155510i
$391$	3.22699			0.163196
$392$		−	23.5051i		−	1.18719i
$393$	5.17044			0.260814
$394$	−37.4532			−1.88686
$395$			0.585221i			0.0294457i
$396$		−	8.66538i		−	0.435452i
$397$		−	29.2462i		−	1.46782i	−0.679244	−	0.733912i	$-0.737692\pi$
$397$		−	29.2462i		−	1.46782i	0.679244	−	0.733912i	$-0.262308\pi$
$398$		−	41.0101i		−	2.05565i
$399$	11.0283			0.552104
$400$	−6.02827			−0.301414
$401$			15.2270i			0.760400i	0.924904	+	0.380200i	$0.124145\pi$
$401$			15.2270i			0.760400i	−0.924904	+	0.380200i	$0.875855\pi$
$402$	−16.3409			−0.815009
$403$	−3.07108	+	13.3774i	−0.152982	+	0.666377i
$404$	30.1240			1.49873
$405$		−	6.37743i		−	0.316897i
$406$	−27.7266			−1.37605
$407$	26.4249			1.30983
$408$			58.6802i			2.90510i
$409$			23.6700i			1.17041i	0.810886	+	0.585204i	$0.198986\pi$
$409$			23.6700i			1.17041i	−0.810886	+	0.585204i	$0.801014\pi$
$410$			4.05655i			0.200339i
$411$		−	22.8405i		−	1.12664i
$412$	−31.0420			−1.52933
$413$	29.3401			1.44373
$414$			0.864095i			0.0424679i
$415$	7.70739			0.378341
$416$	−2.81221	+	12.2498i	−0.137880	+	0.600596i
$417$	−31.3401			−1.53473
$418$			15.6327i			0.764620i
$419$	−5.67004			−0.277000			−0.138500	−	0.990362i	$-0.544228\pi$
$419$	−5.67004			−0.277000			−0.138500	+	0.990362i	$0.544228\pi$
$420$	21.7266			1.06015
$421$			26.3009i			1.28183i	0.767613	+	0.640913i	$0.221444\pi$
$421$			26.3009i			1.28183i	−0.767613	+	0.640913i	$0.778556\pi$
$422$		−	29.6700i		−	1.44432i
$423$			2.34916i			0.114220i
$424$			68.0950i			3.30698i
$425$	−6.64177			−0.322173
$426$	−8.34916			−0.404518
$427$		−	12.3118i		−	0.595810i
$428$	41.3538			1.99891
$429$	−3.46305	+	15.0848i	−0.167198	+	0.728302i
$430$	2.19325			0.105768
$431$		−	5.09029i		−	0.245190i	−0.992457	−	0.122595i	$-0.960878\pi$
$431$		−	5.09029i		−	0.245190i	0.992457	−	0.122595i	$-0.0391217\pi$
$432$	−33.8397			−1.62811
$433$	−24.0565			−1.15608			−0.578042	−	0.816007i	$-0.696183\pi$
$433$	−24.0565			−1.15608			−0.578042	+	0.816007i	$0.696183\pi$
$434$		−	31.7831i		−	1.52564i
$435$		−	5.02827i		−	0.241087i
$436$		−	46.2262i		−	2.21383i
$437$		−	1.06562i		−	0.0509755i
$438$	48.4815			2.31653
$439$	7.21606			0.344404			0.172202	−	0.985062i	$-0.444912\pi$
$439$	7.21606			0.344404			0.172202	+	0.985062i	$0.444912\pi$
$440$			16.5424i			0.788628i
$441$	2.84956			0.135693
$442$	−13.4713	+	58.6802i	−0.640766	+	2.79113i
$443$	27.3829			1.30100			0.650500	−	0.759506i	$-0.274559\pi$
$443$	27.3829			1.30100			0.650500	+	0.759506i	$0.274559\pi$
$444$		−	60.9811i		−	2.89403i
$445$	−3.41478			−0.161876
$446$	50.3310			2.38324
$447$		−	0.971726i		−	0.0459611i
$448$			10.9344i			0.516601i
$449$			1.42571i			0.0672833i	0.999434	+	0.0336416i	$0.0107105\pi$
$449$			1.42571i			0.0672833i	−0.999434	+	0.0336416i	$0.989290\pi$
$450$		−	1.77847i		−	0.0838381i
$451$	4.57429			0.215395
$452$	13.9435			0.655845
$453$			25.1896i			1.18351i
$454$	56.4732			2.65042
$455$	11.6700	+	2.67912i	0.547100	+	0.125599i
$456$	19.3774			0.907431
$457$			35.3219i			1.65229i	0.563457	+	0.826145i	$0.309471\pi$
$457$			35.3219i			1.65229i	−0.563457	+	0.826145i	$0.690529\pi$
$458$	−26.0675			−1.21805
$459$	−37.2835			−1.74025
$460$		−	2.09936i		−	0.0978831i
$461$		−	29.1979i		−	1.35988i	−0.733267	−	0.679941i	$-0.762005\pi$
$461$		−	29.1979i		−	1.35988i	0.733267	−	0.679941i	$-0.237995\pi$
$462$		−	35.8397i		−	1.66741i
$463$		−	3.32088i		−	0.154335i	−0.997018	−	0.0771673i	$-0.975412\pi$
$463$		−	3.32088i		−	0.154335i	0.997018	−	0.0771673i	$-0.0245876\pi$
$464$	−20.0192			−0.929368
$465$	5.76394			0.267296
$466$			28.5561i			1.32284i
$467$	−21.5525			−0.997333			−0.498666	−	0.866794i	$-0.666177\pi$
$467$	−21.5525			−0.997333			−0.498666	+	0.866794i	$0.666177\pi$
$468$	−10.7411	−	2.46586i	−0.496509	−	0.113985i
$469$	14.2553			0.658247
$470$		−	8.34916i		−	0.385118i
$471$	15.5279			0.715487
$472$	51.5525			2.37290
$473$		−	2.47318i		−	0.113717i
$474$		−	2.22779i		−	0.102326i
$475$			2.19325i			0.100633i
$476$		−	95.3038i		−	4.36824i
$477$	−8.25526			−0.377983
$478$	−70.6939			−3.23346
$479$			5.42024i			0.247657i	0.992304	+	0.123829i	$0.0395173\pi$
$479$			5.42024i			0.247657i	−0.992304	+	0.123829i	$0.960483\pi$
$480$	5.27807			0.240910
$481$	7.51960	−	32.7549i	0.342864	−	1.49349i
$482$	−37.9253			−1.72745
$483$			2.44305i			0.111163i
$484$	−12.8013			−0.581877
$485$	0.641769			0.0291412
$486$		−	18.0620i		−	0.819309i
$487$		−	17.4521i		−	0.790831i	−0.918502	−	0.395416i	$-0.870601\pi$
$487$		−	17.4521i		−	0.790831i	0.918502	−	0.395416i	$-0.129399\pi$
$488$		−	21.6327i		−	0.979266i
$489$		−	2.08562i		−	0.0943150i
$490$	−10.1276			−0.457520
$491$	−24.6236			−1.11125			−0.555624	−	0.831433i	$-0.687521\pi$
$491$	−24.6236			−1.11125			−0.555624	+	0.831433i	$0.687521\pi$
$492$		−	10.5561i		−	0.475908i
$493$	−22.0565			−0.993377
$494$	19.3774	+	4.44852i	0.871832	+	0.200148i
$495$	−2.00546			−0.0901389
$496$		−	22.9481i		−	1.03040i
$497$	7.28354			0.326711
$498$	−29.3401			−1.31476
$499$		−	32.3629i		−	1.44876i	−0.689400	−	0.724381i	$-0.742126\pi$
$499$		−	32.3629i		−	1.44876i	0.689400	−	0.724381i	$-0.257874\pi$
$500$			4.32088i			0.193236i
$501$			26.6127i			1.18897i
$502$			2.91518i			0.130111i
$503$	−26.7411			−1.19233			−0.596164	−	0.802863i	$-0.703309\pi$
$503$	−26.7411			−1.19233			−0.596164	+	0.802863i	$0.703309\pi$
$504$	13.7074			0.610576
$505$		−	6.97173i		−	0.310238i
$506$	−3.46305			−0.153951
$507$	17.7129	+	8.58522i	0.786655	+	0.381283i
$508$	25.4960			1.13120
$509$		−	9.74474i		−	0.431928i	−0.976401	−	0.215964i	$-0.930711\pi$
$509$		−	9.74474i		−	0.431928i	0.976401	−	0.215964i	$-0.0692894\pi$
$510$	25.2835			1.11957
$511$	−42.2937			−1.87096
$512$			49.3365i			2.18038i
$513$			12.3118i			0.543580i
$514$		−	2.08562i		−	0.0919928i
$515$			7.18418i			0.316573i
$516$	−5.70739			−0.251254
$517$	−9.41478			−0.414061
$518$			77.8215i			3.41928i
$519$	−9.55695			−0.419503
$520$	20.5051	+	4.70739i	0.899207	+	0.206433i
$521$	−11.4340			−0.500932			−0.250466	−	0.968125i	$-0.580584\pi$
$521$	−11.4340			−0.500932			−0.250466	+	0.968125i	$0.580584\pi$
$522$		−	5.90611i		−	0.258503i
$523$	33.6272			1.47042			0.735208	−	0.677841i	$-0.237084\pi$
$523$	33.6272			1.47042			0.735208	+	0.677841i	$0.237084\pi$
$524$	−14.7549			−0.644569
$525$		−	5.02827i		−	0.219452i
$526$			64.4304i			2.80930i
$527$		−	25.2835i		−	1.10137i
$528$		−	25.8770i		−	1.12615i
$529$	−22.7639			−0.989736
$530$	29.3401			1.27445
$531$			6.24980i			0.271218i
$532$	−31.4713			−1.36446
$533$	1.30168	−	5.67004i	0.0563822	−	0.245597i
$534$	12.9992			0.562530
$535$		−	9.57068i		−	0.413777i
$536$	25.0475			1.08189
$537$	13.7557			0.593601
$538$		−	12.6418i		−	0.545025i
$539$			11.4202i			0.491905i
$540$			24.2553i			1.04378i
$541$			26.4431i			1.13688i	0.822726	+	0.568438i	$0.192452\pi$
$541$			26.4431i			1.13688i	−0.822726	+	0.568438i	$0.807548\pi$
$542$	−47.4960			−2.04013
$543$	−18.1987			−0.780982
$544$		−	23.1523i		−	0.992647i
$545$	−10.6983			−0.458266
$546$	−44.4249	−	10.1987i	−1.90121	−	0.436465i
$547$	−21.9681			−0.939289			−0.469644	−	0.882856i	$-0.655618\pi$
$547$	−21.9681			−0.939289			−0.469644	+	0.882856i	$0.655618\pi$
$548$			65.1798i			2.78434i
$549$	2.62257			0.111928
$550$	7.12763			0.303923
$551$			7.28354i			0.310289i
$552$			4.29261i			0.182706i
$553$			1.94345i			0.0826440i
$554$			59.7941i			2.54041i
$555$	−14.1131			−0.599068
$556$	89.4350			3.79289
$557$		−	39.3027i		−	1.66531i	−0.553792	−	0.832655i	$-0.686820\pi$
$557$		−	39.3027i		−	1.66531i	0.553792	−	0.832655i	$-0.313180\pi$
$558$	6.77020			0.286605
$559$	−3.06562	−	0.703781i	−0.129662	−	0.0297668i
$560$	−20.0192			−0.845966
$561$		−	28.5105i		−	1.20372i
$562$	79.4350			3.35076
$563$	23.0420			0.971105			0.485552	−	0.874208i	$-0.338618\pi$
$563$	23.0420			0.971105			0.485552	+	0.874208i	$0.338618\pi$
$564$			21.7266i			0.914854i
$565$		−	3.22699i		−	0.135761i
$566$			15.9764i			0.671538i
$567$		−	21.1787i		−	0.889422i
$568$	12.7977			0.536979
$569$	3.63270			0.152291			0.0761453	−	0.997097i	$-0.475739\pi$
$569$	3.63270			0.152291			0.0761453	+	0.997097i	$0.475739\pi$
$570$		−	8.34916i		−	0.349708i
$571$	43.3785			1.81533			0.907667	−	0.419692i	$-0.137862\pi$
$571$	43.3785			1.81533			0.907667	+	0.419692i	$0.137862\pi$
$572$	9.88250	−	43.0475i	0.413208	−	1.79991i
$573$	20.1131			0.840237
$574$			13.4713i			0.562282i
$575$	−0.485863			−0.0202619
$576$	−2.32916			−0.0970482
$577$		−	8.84876i		−	0.368379i	−0.982891	−	0.184189i	$-0.941034\pi$
$577$		−	8.84876i		−	0.368379i	0.982891	−	0.184189i	$-0.0589660\pi$
$578$		−	68.1660i		−	2.83533i
$579$			24.7839i			1.02999i
$580$			14.3492i			0.595816i
$581$	25.5953			1.06187
$582$	−2.44305			−0.101268
$583$		−	33.0848i		−	1.37023i
$584$	−74.3129			−3.07509
$585$	−0.570685	+	2.48586i	−0.0235949	+	0.102778i
$586$	−20.2070			−0.834743
$587$			15.3209i			0.632361i	0.948699	+	0.316180i	$0.102400\pi$
$587$			15.3209i			0.632361i	−0.948699	+	0.316180i	$0.897600\pi$
$588$	26.3546			1.08685
$589$	−8.34916			−0.344021
$590$		−	22.2125i		−	0.914472i
$591$		−	22.5561i		−	0.927836i
$592$			56.1888i			2.30935i
$593$		−	4.52867i		−	0.185970i	−0.995667	−	0.0929852i	$-0.970359\pi$
$593$		−	4.52867i		−	0.185970i	0.995667	−	0.0929852i	$-0.0296409\pi$
$594$	40.0109			1.64167
$595$	−22.0565			−0.904230
$596$			2.77301i			0.113587i
$597$	24.6983			1.01083
$598$	−0.985463	+	4.29261i	−0.0402986	+	0.175538i
$599$	23.0283			0.940910			0.470455	−	0.882424i	$-0.344090\pi$
$599$	23.0283			0.940910			0.470455	+	0.882424i	$0.344090\pi$
$600$		−	8.83502i		−	0.360688i
$601$	−12.0565			−0.491797			−0.245898	−	0.969296i	$-0.579083\pi$
$601$	−12.0565			−0.491797			−0.245898	+	0.969296i	$0.579083\pi$
$602$	7.28354			0.296855
$603$			3.03655i			0.123658i
$604$		−	71.8836i		−	2.92490i
$605$			2.96265i			0.120449i
$606$			26.5396i			1.07810i
$607$	−8.99639			−0.365152			−0.182576	−	0.983192i	$-0.558444\pi$
$607$	−8.99639			−0.365152			−0.182576	+	0.983192i	$0.558444\pi$
$608$	−7.64538			−0.310061
$609$		−	16.6983i		−	0.676650i
$610$	−9.32088			−0.377392
$611$	−2.67912	+	11.6700i	−0.108385	+	0.472119i
$612$	20.3009			0.820615
$613$			14.1131i			0.570023i	0.958524	+	0.285011i	$0.0919973\pi$
$613$			14.1131i			0.570023i	−0.958524	+	0.285011i	$0.908003\pi$
$614$	−39.7749			−1.60518
$615$	−2.44305			−0.0985134
$616$			54.9354i			2.21341i
$617$			2.46120i			0.0990841i	0.998772	+	0.0495420i	$0.0157762\pi$
$617$			2.46120i			0.0990841i	−0.998772	+	0.0495420i	$0.984224\pi$
$618$		−	27.3484i		−	1.10011i
$619$			5.73205i			0.230391i	0.993343	+	0.115195i	$0.0367494\pi$
$619$			5.73205i			0.230391i	−0.993343	+	0.115195i	$0.963251\pi$
$620$	−16.4485			−0.660588
$621$	−2.72739			−0.109446
$622$			61.1232i			2.45082i
$623$	−11.3401			−0.454331
$624$	−32.0757	−	7.36369i	−1.28406	−	0.294784i
$625$	1.00000			0.0400000
$626$			28.2262i			1.12815i
$627$	−9.41478			−0.375990
$628$	−44.3118			−1.76823
$629$			61.9072i			2.46840i
$630$		−	5.90611i		−	0.235305i
$631$		−	5.27807i		−	0.210117i	−0.994466	−	0.105058i	$-0.966497\pi$
$631$		−	5.27807i		−	0.210117i	0.994466	−	0.105058i	$-0.0335030\pi$
$632$			3.41478i			0.135833i
$633$	17.8688			0.710219
$634$	40.6044			1.61261
$635$		−	5.90064i		−	0.234160i
$636$	−76.3502			−3.02748
$637$	14.1559	+	3.24980i	0.560877	+	0.128762i
$638$	23.6700			0.937106
$639$			1.55148i			0.0613757i
$640$	15.2498			0.602801
$641$	42.9992			1.69837			0.849183	−	0.528098i	$-0.177095\pi$
$641$	42.9992			1.69837			0.849183	+	0.528098i	$0.177095\pi$
$642$			36.4332i			1.43790i
$643$		−	43.3593i		−	1.70992i	−0.518691	−	0.854962i	$-0.673581\pi$
$643$		−	43.3593i		−	1.70992i	0.518691	−	0.854962i	$-0.326419\pi$
$644$		−	6.97173i		−	0.274724i
$645$			1.32088i			0.0520098i
$646$	−36.6236			−1.44094
$647$	19.6454			0.772339			0.386170	−	0.922428i	$-0.373798\pi$
$647$	19.6454			0.772339			0.386170	+	0.922428i	$0.373798\pi$
$648$		−	37.2125i		−	1.46184i
$649$	−25.0475			−0.983199
$650$	2.02827	−	8.83502i	0.0795554	−	0.346538i
$651$	19.1414			0.750209
$652$			5.95173i			0.233088i
$653$	9.93252			0.388690			0.194345	−	0.980933i	$-0.437742\pi$
$653$	9.93252			0.388690			0.194345	+	0.980933i	$0.437742\pi$
$654$	40.7258			1.59250
$655$			3.41478i			0.133426i
$656$			9.72659i			0.379760i
$657$		−	9.00907i		−	0.351477i
$658$		−	27.7266i		−	1.08090i
$659$	10.1806			0.396579			0.198289	−	0.980144i	$-0.436461\pi$
$659$	10.1806			0.396579			0.198289	+	0.980144i	$0.436461\pi$
$660$	−18.5479			−0.721975
$661$		−	32.9427i		−	1.28132i	−0.767824	−	0.640660i	$-0.778661\pi$
$661$		−	32.9427i		−	1.28132i	0.767824	−	0.640660i	$-0.221339\pi$
$662$	−75.5800			−2.93750
$663$	−35.3401	−	8.11310i	−1.37250	−	0.315087i
$664$	44.9728			1.74528
$665$			7.28354i			0.282443i
$666$	−16.5769			−0.642344
$667$	−1.61350			−0.0624748
$668$		−	75.9445i		−	2.93838i
$669$			30.3118i			1.17192i
$670$		−	10.7922i		−	0.416939i
$671$			10.5105i			0.405754i
$672$	17.5279			0.676152
$673$	11.2270			0.432769			0.216384	−	0.976308i	$-0.430574\pi$
$673$	11.2270			0.432769			0.216384	+	0.976308i	$0.430574\pi$
$674$		−	43.9253i		−	1.69194i
$675$	5.61350			0.216064
$676$	−50.5471	−	24.4996i	−1.94412	−	0.942292i
$677$	−15.7447			−0.605119			−0.302560	−	0.953130i	$-0.597841\pi$
$677$	−15.7447			−0.605119			−0.302560	+	0.953130i	$0.597841\pi$
$678$			12.2843i			0.471777i
$679$	2.13124			0.0817895
$680$	−38.7549			−1.48618
$681$			34.0109i			1.30330i
$682$			27.1331i			1.03898i
$683$			50.3492i			1.92656i	0.268504	+	0.963279i	$0.413471\pi$
$683$			50.3492i			1.92656i	−0.268504	+	0.963279i	$0.586529\pi$
$684$		−	6.70378i		−	0.256325i
$685$	15.0848			0.576361
$686$	24.8114			0.947304
$687$		−	15.6991i		−	0.598959i
$688$	5.25887			0.200493
$689$	−41.0101	−	9.41478i	−1.56236	−	0.358675i
$690$	1.84956			0.0704115
$691$		−	8.19325i		−	0.311686i	−0.987782	−	0.155843i	$-0.950191\pi$
$691$		−	8.19325i		−	0.311686i	0.987782	−	0.155843i	$-0.0498094\pi$
$692$	27.2726			1.03675
$693$	−6.65991			−0.252989
$694$		−	83.5717i		−	3.17234i
$695$		−	20.6983i		−	0.785132i
$696$		−	29.3401i		−	1.11213i
$697$			10.7165i			0.405915i
$698$	−52.5380			−1.98859
$699$	−17.1979			−0.650485
$700$			14.3492i			0.542347i
$701$	8.25526			0.311797			0.155899	−	0.987773i	$-0.450173\pi$
$701$	8.25526			0.311797			0.155899	+	0.987773i	$0.450173\pi$
$702$	11.3857	−	49.5953i	0.429726	−	1.87186i
$703$	20.4431			0.771024
$704$		−	9.33462i		−	0.351812i
$705$	5.02827			0.189376
$706$	−31.5471			−1.18729
$707$		−	23.1523i		−	0.870732i
$708$			57.8023i			2.17234i
$709$			37.7831i			1.41898i	0.704718	+	0.709488i	$0.251074\pi$
$709$			37.7831i			1.41898i	−0.704718	+	0.709488i	$0.748926\pi$
$710$		−	5.51414i		−	0.206942i
$711$	−0.413979			−0.0155254
$712$	−19.9253			−0.746732
$713$		−	1.84956i		−	0.0692665i
$714$	83.9637			3.14226
$715$	−9.96265	−	2.28715i	−0.372582	−	0.0855344i
$716$	−39.2545			−1.46701
$717$		−	42.5753i		−	1.59001i
$718$	−7.48506			−0.279340
$719$	22.2443			0.829574			0.414787	−	0.909919i	$-0.363856\pi$
$719$	22.2443			0.829574			0.414787	+	0.909919i	$0.363856\pi$
$720$		−	4.26434i		−	0.158922i
$721$			23.8578i			0.888512i
$722$		−	35.6747i		−	1.32768i
$723$		−	22.8405i		−	0.849447i
$724$	51.9336			1.93010
$725$	3.32088			0.123335
$726$		−	11.2781i		−	0.418569i
$727$	30.0812			1.11565			0.557825	−	0.829958i	$-0.311636\pi$
$727$	30.0812			1.11565			0.557825	+	0.829958i	$0.311636\pi$
$728$	68.0950	+	15.6327i	2.52377	+	0.579386i
$729$	30.0101			1.11149
$730$			32.0192i			1.18508i
$731$	5.79407			0.214301
$732$	24.2553			0.896500
$733$			35.0101i			1.29313i	0.762859	+	0.646564i	$0.223795\pi$
$733$			35.0101i			1.29313i	−0.762859	+	0.646564i	$0.776205\pi$
$734$			76.9300i			2.83954i
$735$		−	6.09936i		−	0.224978i
$736$		−	1.69365i		−	0.0624288i
$737$	−12.1696			−0.448275
$738$	−2.86956			−0.105630
$739$			42.6856i			1.57022i	0.619359	+	0.785108i	$0.287393\pi$
$739$			42.6856i			1.57022i	−0.619359	+	0.785108i	$0.712607\pi$
$740$	40.2745			1.48052
$741$	−2.67912	+	11.6700i	−0.0984198	+	0.428710i
$742$	97.4350			3.57695
$743$		−	13.6892i		−	0.502210i	−0.967960	−	0.251105i	$-0.919206\pi$
$743$		−	13.6892i		−	0.502210i	0.967960	−	0.251105i	$-0.0807939\pi$
$744$	33.6327			1.23303
$745$	0.641769			0.0235126
$746$		−	45.8962i		−	1.68038i
$747$			5.45213i			0.199483i
$748$			81.3603i			2.97483i
$749$		−	31.7831i		−	1.16133i
$750$	−3.80675			−0.139003
$751$	−17.7831			−0.648916			−0.324458	−	0.945900i	$-0.605182\pi$
$751$	−17.7831			−0.648916			−0.324458	+	0.945900i	$0.605182\pi$
$752$		−	20.0192i		−	0.730025i
$753$	−1.75566			−0.0639799
$754$	6.73566	−	29.3401i	0.245298	−	1.06850i
$755$	−16.6363			−0.605457
$756$			80.5489i			2.92954i
$757$	−26.9717			−0.980304			−0.490152	−	0.871637i	$-0.663059\pi$
$757$	−26.9717			−0.980304			−0.490152	+	0.871637i	$0.663059\pi$
$758$	−40.2125			−1.46058
$759$		−	2.08562i		−	0.0757032i
$760$			12.7977i			0.464220i
$761$		−	35.1523i		−	1.27427i	−0.770752	−	0.637135i	$-0.780119\pi$
$761$		−	35.1523i		−	1.27427i	0.770752	−	0.637135i	$-0.219881\pi$
$762$			22.4623i			0.813722i
$763$	−35.5279			−1.28620
$764$	−57.3966			−2.07654
$765$		−	4.69832i		−	0.169868i
$766$	5.43398			0.196338
$767$	−7.12763	+	31.0475i	−0.257364	+	1.12106i
$768$	−48.0812			−1.73498
$769$		−	23.1523i		−	0.834893i	−0.908701	−	0.417447i	$-0.862925\pi$
$769$		−	23.1523i		−	0.834893i	0.908701	−	0.417447i	$-0.137075\pi$
$770$	23.6700			0.853009
$771$	1.25606			0.0452360
$772$		−	70.7258i		−	2.54548i
$773$			41.6218i			1.49703i	0.663117	+	0.748515i	$0.269233\pi$
$773$			41.6218i			1.49703i	−0.663117	+	0.748515i	$0.730767\pi$
$774$			1.55148i			0.0557669i
$775$			3.80675i			0.136742i
$776$	3.74474			0.134428
$777$	−46.8680			−1.68138
$778$		−	1.14137i		−	0.0409201i
$779$	3.53880			0.126791
$780$	−5.27807	+	22.9909i	−0.188985	+	0.823207i
$781$	−6.21792			−0.222495
$782$		−	8.11310i		−	0.290124i
$783$	18.6418			0.666202
$784$	−24.2835			−0.867269
$785$			10.2553i			0.366026i
$786$		−	12.9992i		−	0.463666i
$787$			43.2353i			1.54117i	0.637337	+	0.770585i	$0.280036\pi$
$787$			43.2353i			1.54117i	−0.637337	+	0.770585i	$0.719964\pi$
$788$			64.3684i			2.29303i
$789$	−38.8031			−1.38143
$790$	1.47133			0.0523474
$791$		−	10.7165i		−	0.381034i
$792$	−11.7019			−0.415810
$793$	13.0283	+	2.99093i	0.462648	+	0.106211i
$794$	−73.5289			−2.60944
$795$			17.6700i			0.626692i
$796$	−70.4815			−2.49815
$797$	14.4431			0.511599			0.255800	−	0.966730i	$-0.417661\pi$
$797$	14.4431			0.511599			0.255800	+	0.966730i	$0.417661\pi$
$798$		−	27.7266i		−	0.981511i
$799$		−	22.0565i		−	0.780305i
$800$			3.48586i			0.123244i
$801$		−	2.41558i		−	0.0853503i
$802$	38.2827			1.35181
$803$	36.1059			1.27415
$804$			28.0840i			0.990447i
$805$	−1.61350			−0.0568682
$806$	33.6327	+	7.72113i	1.18466	+	0.271965i
$807$	7.61350			0.268008
$808$		−	40.6802i		−	1.43112i
$809$	17.8880			0.628907			0.314454	−	0.949273i	$-0.398179\pi$
$809$	17.8880			0.628907			0.314454	+	0.949273i	$0.398179\pi$
$810$	−16.0337			−0.563368
$811$			8.69285i			0.305247i	0.988284	+	0.152624i	$0.0487722\pi$
$811$			8.69285i			0.305247i	−0.988284	+	0.152624i	$0.951228\pi$
$812$			47.6519i			1.67225i
$813$		−	28.6044i		−	1.00320i
$814$		−	66.4358i		−	2.32857i
$815$	1.37743			0.0482493
$816$	60.6236			2.12225
$817$		−	1.91332i		−	0.0669387i
$818$	59.5097			2.08071
$819$	−1.89518	+	8.25526i	−0.0662229	+	0.288462i
$820$	6.97173			0.243463
$821$			9.41478i			0.328578i	0.986412	+	0.164289i	$0.0525330\pi$
$821$			9.41478i			0.328578i	−0.986412	+	0.164289i	$0.947467\pi$
$822$	−57.4241			−2.00290
$823$	30.3365			1.05746			0.528732	−	0.848789i	$-0.322668\pi$
$823$	30.3365			1.05746			0.528732	+	0.848789i	$0.322668\pi$
$824$			41.9198i			1.46035i
$825$			4.29261i			0.149450i
$826$		−	73.7650i		−	2.56661i
$827$		−	18.2361i		−	0.634130i	−0.948404	−	0.317065i	$-0.897303\pi$
$827$		−	18.2361i		−	0.634130i	0.948404	−	0.317065i	$-0.102697\pi$
$828$	1.48506			0.0516095
$829$	−29.8023			−1.03508			−0.517539	−	0.855660i	$-0.673152\pi$
$829$	−29.8023			−1.03508			−0.517539	+	0.855660i	$0.673152\pi$
$830$		−	19.3774i		−	0.672600i
$831$	−36.0109			−1.24921
$832$	−11.5707	−	2.65631i	−0.401141	−	0.0920908i
$833$	−26.7549			−0.927001
$834$			78.7933i			2.72839i
$835$	−17.5761			−0.608248
$836$	26.8669			0.929211
$837$			21.3692i			0.738626i
$838$			14.2553i			0.492440i
$839$		−	46.1004i		−	1.59156i	−0.605584	−	0.795782i	$-0.707060\pi$
$839$		−	46.1004i		−	1.59156i	0.605584	−	0.795782i	$-0.292940\pi$
$840$		−	29.3401i		−	1.01233i
$841$	−17.9717			−0.619715
$842$	66.1240			2.27878
$843$			47.8397i			1.64769i
$844$	−50.9920			−1.75522
$845$	−5.67004	+	11.6983i	−0.195055	+	0.402434i
$846$	5.90611			0.203056
$847$			9.83863i			0.338059i
$848$	70.3502			2.41584
$849$	−9.62177			−0.330218
$850$			16.6983i			0.572748i
$851$			4.52867i			0.155241i
$852$			14.3492i			0.491594i
$853$		−	19.3774i		−	0.663471i	−0.943373	−	0.331735i	$-0.892366\pi$
$853$		−	19.3774i		−	0.663471i	0.943373	−	0.331735i	$-0.107634\pi$
$854$	−30.9536			−1.05921
$855$	−1.55148			−0.0530596
$856$		−	55.8452i		−	1.90875i
$857$	43.4713			1.48495			0.742476	−	0.669873i	$-0.233651\pi$
$857$	43.4713			1.48495			0.742476	+	0.669873i	$0.233651\pi$
$858$	37.9253	+	8.70659i	1.29475	+	0.297238i
$859$	−27.7375			−0.946392			−0.473196	−	0.880957i	$-0.656900\pi$
$859$	−27.7375			−0.946392			−0.473196	+	0.880957i	$0.656900\pi$
$860$		−	3.76940i		−	0.128536i
$861$	−8.11310			−0.276494
$862$	−12.7977			−0.435891
$863$		−	3.69646i		−	0.125829i	−0.998019	−	0.0629145i	$-0.979960\pi$
$863$		−	3.69646i		−	0.125829i	0.998019	−	0.0629145i	$-0.0200395\pi$
$864$			19.5679i			0.665713i
$865$		−	6.31181i		−	0.214608i
$866$			60.4815i			2.05524i
$867$	41.0529			1.39423
$868$	−54.6236			−1.85405
$869$		−	1.65911i		−	0.0562816i
$870$	−12.6418			−0.428596
$871$	−3.46305	+	15.0848i	−0.117341	+	0.511130i
$872$	−62.4249			−2.11397
$873$			0.453981i			0.0153649i
$874$	−2.67912			−0.0906224
$875$	3.32088			0.112266
$876$		−	83.3219i		−	2.81519i
$877$			20.5671i			0.694501i	0.937772	+	0.347250i	$0.112885\pi$
$877$			20.5671i			0.694501i	−0.937772	+	0.347250i	$0.887115\pi$
$878$		−	18.1422i		−	0.612269i
$879$		−	12.1696i		−	0.410472i
$880$	17.0903			0.576113
$881$	14.5369			0.489762			0.244881	−	0.969553i	$-0.421251\pi$
$881$	14.5369			0.489762			0.244881	+	0.969553i	$0.421251\pi$
$882$		−	7.16418i		−	0.241230i
$883$	36.2871			1.22116			0.610580	−	0.791955i	$-0.290936\pi$
$883$	36.2871			1.22116			0.610580	+	0.791955i	$0.290936\pi$
$884$	100.850	+	23.1523i	3.39195	+	0.778696i
$885$	13.3774			0.449677
$886$		−	68.8444i		−	2.31287i
$887$	−45.2407			−1.51903			−0.759517	−	0.650487i	$-0.774565\pi$
$887$	−45.2407			−1.51903			−0.759517	+	0.650487i	$0.774565\pi$
$888$	−82.3502			−2.76349
$889$		−	19.5953i		−	0.657207i
$890$			8.58522i			0.287777i
$891$			18.0802i			0.605708i
$892$		−	86.5007i		−	2.89626i
$893$	−7.28354			−0.243734
$894$	−2.44305			−0.0817079
$895$			9.08482i			0.303672i
$896$	50.6428			1.69186
$897$	−2.58522	−	0.593495i	−0.0863180	−	0.0198162i
$898$	3.58442			0.119614
$899$			12.6418i			0.421627i
$900$	−3.05655			−0.101885
$901$	77.5097			2.58222
$902$		−	11.5004i		−	0.382921i
$903$			4.38650i			0.145974i
$904$		−	18.8296i		−	0.626262i
$905$		−	12.0192i		−	0.399532i
$906$	63.3302			2.10401
$907$	11.2973			0.375120			0.187560	−	0.982253i	$-0.439942\pi$
$907$	11.2973			0.375120			0.187560	+	0.982253i	$0.439942\pi$
$908$		−	97.0568i		−	3.22094i
$909$	4.93172			0.163575
$910$	6.73566	−	29.3401i	0.223285	−	0.972614i
$911$	−41.1979			−1.36495			−0.682474	−	0.730910i	$-0.739096\pi$
$911$	−41.1979			−1.36495			−0.682474	+	0.730910i	$0.739096\pi$
$912$		−	20.0192i		−	0.662902i
$913$	−21.8506			−0.723150
$914$	88.8042			2.93738
$915$		−	5.61350i		−	0.185576i
$916$			44.8005i			1.48025i
$917$			11.3401i			0.374483i
$918$			93.7359i			3.09375i
$919$	1.74474			0.0575535			0.0287768	−	0.999586i	$-0.490839\pi$
$919$	1.74474			0.0575535			0.0287768	+	0.999586i	$0.490839\pi$
$920$	−2.83502			−0.0934679
$921$		−	23.9544i		−	0.789324i
$922$	−73.4076			−2.41755
$923$	−1.76940	+	7.70739i	−0.0582405	+	0.253692i
$924$	−61.5953			−2.02634
$925$		−	9.32088i		−	0.306469i
$926$	−8.34916			−0.274370
$927$	−5.08201			−0.166915
$928$			11.5761i			0.380006i
$929$		−	15.5569i		−	0.510407i	−0.966887	−	0.255203i	$-0.917858\pi$
$929$		−	15.5569i		−	0.510407i	0.966887	−	0.255203i	$-0.0821424\pi$
$930$		−	14.4913i		−	0.475189i
$931$			8.83502i			0.289556i
$932$	49.0776			1.60759
$933$	−36.8114			−1.20515
$934$			54.1860i			1.77302i
$935$	18.8296			0.615792
$936$	−3.32996	+	14.5051i	−0.108843	+	0.474113i
$937$	26.0384			0.850638			0.425319	−	0.905044i	$-0.360162\pi$
$937$	26.0384			0.850638			0.425319	+	0.905044i	$0.360162\pi$
$938$		−	35.8397i		−	1.17021i
$939$	−16.9992			−0.554748
$940$	−14.3492			−0.468018
$941$		−	50.8789i		−	1.65860i	−0.558800	−	0.829302i	$-0.688738\pi$
$941$		−	50.8789i		−	1.65860i	0.558800	−	0.829302i	$-0.311262\pi$
$942$		−	39.0392i		−	1.27197i
$943$			0.783938i			0.0255285i
$944$		−	53.2599i		−	1.73346i
$945$	18.6418			0.606417
$946$	−6.21792			−0.202162
$947$			37.8770i			1.23084i	0.788200	+	0.615419i	$0.211013\pi$
$947$			37.8770i			1.23084i	−0.788200	+	0.615419i	$0.788987\pi$
$948$	−3.82876			−0.124352
$949$	10.2745	−	44.7549i	0.333523	−	1.45280i
$950$	5.51414			0.178902
$951$			24.4540i			0.792975i
$952$	−128.700			−4.17120
$953$	32.0950			1.03966			0.519829	−	0.854271i	$-0.325996\pi$
$953$	32.0950			1.03966			0.519829	+	0.854271i	$0.325996\pi$
$954$			20.7549i			0.671964i
$955$			13.2835i			0.429845i
$956$			121.497i			3.92950i
$957$			14.2553i			0.460807i
$958$	13.6272			0.440276
$959$	50.0950			1.61765
$960$			4.98546i			0.160905i
$961$	16.5087			0.532538
$962$	−82.3502	−	18.9053i	−2.65508	−	0.609532i
$963$	6.77020			0.218167
$964$			65.1798i			2.09930i
$965$	−16.3684			−0.526916
$966$	6.14217			0.197621
$967$			24.4057i			0.784835i	0.919787	+	0.392417i	$0.128361\pi$
$967$			24.4057i			0.784835i	−0.919787	+	0.392417i	$0.871639\pi$
$968$			17.2871i			0.555630i
$969$		−	22.0565i		−	0.708558i
$970$		−	1.61350i		−	0.0518062i
$971$	−36.9354			−1.18531			−0.592657	−	0.805455i	$-0.701921\pi$
$971$	−36.9354			−1.18531			−0.592657	+	0.805455i	$0.701921\pi$
$972$	−31.0420			−0.995673
$973$		−	68.7367i		−	2.20360i
$974$	−43.8770			−1.40591
$975$	5.32088	+	1.22153i	0.170405	+	0.0391201i
$976$	−22.3492			−0.715379
$977$			25.1715i			0.805308i	0.915352	+	0.402654i	$0.131912\pi$
$977$			25.1715i			0.805308i	−0.915352	+	0.402654i	$0.868088\pi$
$978$	−5.24354			−0.167670
$979$	9.68097			0.309405
$980$			17.4057i			0.556005i
$981$		−	7.56788i		−	0.241624i
$982$			61.9072i			1.97554i
$983$			13.1896i			0.420684i	0.977628	+	0.210342i	$0.0674578\pi$
$983$			13.1896i			0.420684i	−0.977628	+	0.210342i	$0.932542\pi$
$984$	−14.2553			−0.454441
$985$	14.8970			0.474659
$986$			55.4532i			1.76599i
$987$	16.6983			0.531513
$988$	7.64538	−	33.3027i	0.243232	−	1.05950i
$989$	0.423851			0.0134777
$990$			5.04201i			0.160246i
$991$	23.0667			0.732737			0.366369	−	0.930470i	$-0.380601\pi$
$991$	23.0667			0.732737			0.366369	+	0.930470i	$0.380601\pi$
$992$	−13.2698			−0.421317
$993$		−	45.5180i		−	1.44447i
$994$		−	18.3118i		−	0.580815i
$995$			16.3118i			0.517119i
$996$			50.4249i			1.59777i
$997$	−0.630841			−0.0199789			−0.00998947	−	0.999950i	$-0.503180\pi$
$997$	−0.630841			−0.0199789			−0.00998947	+	0.999950i	$0.503180\pi$
$998$	−81.3648			−2.57556
$999$		−	52.3227i		−	1.65542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.c.a.51.1	✓	6
3.2	odd	2		585.2.b.g.181.6		6
4.3	odd	2		1040.2.k.d.961.2		6
5.2	odd	4		325.2.d.f.324.5		6
5.3	odd	4		325.2.d.e.324.2		6
5.4	even	2		325.2.c.g.51.6		6
13.2	odd	12		845.2.e.k.191.3		6
13.3	even	3		845.2.m.h.316.6		12
13.4	even	6		845.2.m.h.361.6		12
13.5	odd	4		845.2.a.i.1.1		3
13.6	odd	12		845.2.e.k.146.3		6
13.7	odd	12		845.2.e.i.146.1		6
13.8	odd	4		845.2.a.k.1.3		3
13.9	even	3		845.2.m.h.361.1		12
13.10	even	6		845.2.m.h.316.1		12
13.11	odd	12		845.2.e.i.191.1		6
13.12	even	2	inner	65.2.c.a.51.6	yes	6
39.5	even	4		7605.2.a.cc.1.3		3
39.8	even	4		7605.2.a.bs.1.1		3
39.38	odd	2		585.2.b.g.181.1		6
52.51	odd	2		1040.2.k.d.961.1		6
65.12	odd	4		325.2.d.e.324.1		6
65.34	odd	4		4225.2.a.bc.1.1		3
65.38	odd	4		325.2.d.f.324.6		6
65.44	odd	4		4225.2.a.be.1.3		3
65.64	even	2		325.2.c.g.51.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.c.a.51.1	✓	6	1.1	even	1	trivial
65.2.c.a.51.6	yes	6	13.12	even	2	inner
325.2.c.g.51.1		6	65.64	even	2
325.2.c.g.51.6		6	5.4	even	2
325.2.d.e.324.1		6	65.12	odd	4
325.2.d.e.324.2		6	5.3	odd	4
325.2.d.f.324.5		6	5.2	odd	4
325.2.d.f.324.6		6	65.38	odd	4
585.2.b.g.181.1		6	39.38	odd	2
585.2.b.g.181.6		6	3.2	odd	2
845.2.a.i.1.1		3	13.5	odd	4
845.2.a.k.1.3		3	13.8	odd	4
845.2.e.i.146.1		6	13.7	odd	12
845.2.e.i.191.1		6	13.11	odd	12
845.2.e.k.146.3		6	13.6	odd	12
845.2.e.k.191.3		6	13.2	odd	12
845.2.m.h.316.1		12	13.10	even	6
845.2.m.h.316.6		12	13.3	even	3
845.2.m.h.361.1		12	13.9	even	3
845.2.m.h.361.6		12	13.4	even	6
1040.2.k.d.961.1		6	52.51	odd	2
1040.2.k.d.961.2		6	4.3	odd	2
4225.2.a.bc.1.1		3	65.34	odd	4
4225.2.a.be.1.3		3	65.44	odd	4
7605.2.a.bs.1.1		3	39.8	even	4
7605.2.a.cc.1.3		3	39.5	even	4

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.51414i q^{2} +1.51414 q^{3} -4.32088 q^{4} +1.00000i q^{5} -3.80675i q^{6} +3.32088i q^{7} +5.83502i q^{8} -0.707389 q^{9} +O(q^{10})\)	\(q-2.51414i q^{2} +1.51414 q^{3} -4.32088 q^{4} +1.00000i q^{5} -3.80675i q^{6} +3.32088i q^{7} +5.83502i q^{8} -0.707389 q^{9} +2.51414 q^{10} -2.83502i q^{11} -6.54241 q^{12} +(-3.51414 - 0.806748i) q^{13} +8.34916 q^{14} +1.51414i q^{15} +6.02827 q^{16} +6.64177 q^{17} +1.77847i q^{18} -2.19325i q^{19} -4.32088i q^{20} +5.02827i q^{21} -7.12763 q^{22} +0.485863 q^{23} +8.83502i q^{24} -1.00000 q^{25} +(-2.02827 + 8.83502i) q^{26} -5.61350 q^{27} -14.3492i q^{28} -3.32088 q^{29} +3.80675 q^{30} -3.80675i q^{31} -3.48586i q^{32} -4.29261i q^{33} -16.6983i q^{34} -3.32088 q^{35} +3.05655 q^{36} +9.32088i q^{37} -5.51414 q^{38} +(-5.32088 - 1.22153i) q^{39} -5.83502 q^{40} +1.61350i q^{41} +12.6418 q^{42} +0.872368 q^{43} +12.2498i q^{44} -0.707389i q^{45} -1.22153i q^{46} -3.32088i q^{47} +9.12763 q^{48} -4.02827 q^{49} +2.51414i q^{50} +10.0565 q^{51} +(15.1842 + 3.48586i) q^{52} +11.6700 q^{53} +14.1131i q^{54} +2.83502 q^{55} -19.3774 q^{56} -3.32088i q^{57} +8.34916i q^{58} -8.83502i q^{59} -6.54241i q^{60} -3.70739 q^{61} -9.57068 q^{62} -2.34916i q^{63} +3.29261 q^{64} +(0.806748 - 3.51414i) q^{65} -10.7922 q^{66} -4.29261i q^{67} -28.6983 q^{68} +0.735663 q^{69} +8.34916i q^{70} -2.19325i q^{71} -4.12763i q^{72} +12.7357i q^{73} +23.4340 q^{74} -1.51414 q^{75} +9.47679i q^{76} +9.41478 q^{77} +(-3.07108 + 13.3774i) q^{78} +0.585221 q^{79} +6.02827i q^{80} -6.37743 q^{81} +4.05655 q^{82} -7.70739i q^{83} -21.7266i q^{84} +6.64177i q^{85} -2.19325i q^{86} -5.02827 q^{87} +16.5424 q^{88} +3.41478i q^{89} -1.77847 q^{90} +(2.67912 - 11.6700i) q^{91} -2.09936 q^{92} -5.76394i q^{93} -8.34916 q^{94} +2.19325 q^{95} -5.27807i q^{96} -0.641769i q^{97} +10.1276i q^{98} +2.00546i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{3} - 10 q^{4} + 6 q^{9}+O(q^{10}) \) 6 * q - 4 * q^3 - 10 * q^4 + 6 * q^9	\( 6 q - 4 q^{3} - 10 q^{4} + 6 q^{9} + 2 q^{10} - 8 q^{13} + 8 q^{14} + 10 q^{16} + 8 q^{17} - 24 q^{22} + 16 q^{23} - 6 q^{25} + 14 q^{26} - 28 q^{27} - 4 q^{29} + 20 q^{30} - 4 q^{35} - 34 q^{36} - 20 q^{38} - 16 q^{39} - 6 q^{40} + 44 q^{42} + 24 q^{43} + 36 q^{48} + 2 q^{49} + 8 q^{51} + 20 q^{52} + 12 q^{53} - 12 q^{55} - 48 q^{56} - 12 q^{61} + 8 q^{62} + 30 q^{64} + 2 q^{65} + 24 q^{66} - 88 q^{68} - 32 q^{69} + 20 q^{74} + 4 q^{75} + 36 q^{77} - 52 q^{78} + 24 q^{79} + 30 q^{81} - 28 q^{82} - 4 q^{87} + 60 q^{88} - 34 q^{90} + 32 q^{91} - 20 q^{92} - 8 q^{94} + 16 q^{95}+O(q^{100}) \) 6 * q - 4 * q^3 - 10 * q^4 + 6 * q^9 + 2 * q^10 - 8 * q^13 + 8 * q^14 + 10 * q^16 + 8 * q^17 - 24 * q^22 + 16 * q^23 - 6 * q^25 + 14 * q^26 - 28 * q^27 - 4 * q^29 + 20 * q^30 - 4 * q^35 - 34 * q^36 - 20 * q^38 - 16 * q^39 - 6 * q^40 + 44 * q^42 + 24 * q^43 + 36 * q^48 + 2 * q^49 + 8 * q^51 + 20 * q^52 + 12 * q^53 - 12 * q^55 - 48 * q^56 - 12 * q^61 + 8 * q^62 + 30 * q^64 + 2 * q^65 + 24 * q^66 - 88 * q^68 - 32 * q^69 + 20 * q^74 + 4 * q^75 + 36 * q^77 - 52 * q^78 + 24 * q^79 + 30 * q^81 - 28 * q^82 - 4 * q^87 + 60 * q^88 - 34 * q^90 + 32 * q^91 - 20 * q^92 - 8 * q^94 + 16 * q^95

Introduction

L-functions

Modular forms

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