LMFDB - Embedded newform 95.2.b.b.39.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,2,Mod(39,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("95.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.b (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:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.16516096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 9x^{4} + 13x^{2} + 1 $ x^6 + 9x^4 + 13x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.1
Root			$1.30397i$ of defining polynomial
Character	$\chi$	$=$	95.39
Dual form			95.2.b.b.39.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41987i q^{2} -0.537080i q^{3} -3.85577 q^{4} +(-2.07772 + 0.826491i) q^{5} -1.29966 q^{6} -3.18676i q^{7} +4.49073i q^{8} +2.71155 q^{9} +O(q^{10})$	\(q-2.41987i q^{2} -0.537080i q^{3} -3.85577 q^{4} +(-2.07772 + 0.826491i) q^{5} -1.29966 q^{6} -3.18676i q^{7} +4.49073i q^{8} +2.71155 q^{9} +(2.00000 + 5.02781i) q^{10} +4.15544 q^{11} +2.07086i q^{12} -2.07086i q^{13} -7.71155 q^{14} +(0.443892 + 1.11590i) q^{15} +3.15544 q^{16} +5.79470i q^{17} -6.56159i q^{18} +1.00000 q^{19} +(8.01121 - 3.18676i) q^{20} -1.71155 q^{21} -10.0556i q^{22} +2.60794i q^{23} +2.41188 q^{24} +(3.63383 - 3.43443i) q^{25} -5.01121 q^{26} -3.06756i q^{27} +12.2874i q^{28} -6.00000 q^{29} +(2.70034 - 1.07416i) q^{30} +2.59933 q^{31} +1.34571i q^{32} -2.23180i q^{33} +14.0224 q^{34} +(2.63383 + 6.62119i) q^{35} -10.4551 q^{36} +4.30266i q^{37} -2.41987i q^{38} -1.11222 q^{39} +(-3.71155 - 9.33047i) q^{40} -0.599328 q^{41} +4.14172i q^{42} -3.18676i q^{43} -16.0224 q^{44} +(-5.63383 + 2.24107i) q^{45} +6.31087 q^{46} +11.7086i q^{47} -1.69472i q^{48} -3.15544 q^{49} +(-8.31087 - 8.79339i) q^{50} +3.11222 q^{51} +7.98476i q^{52} -11.7503i q^{53} -7.42309 q^{54} +(-8.63383 + 3.43443i) q^{55} +14.3109 q^{56} -0.537080i q^{57} +14.5192i q^{58} +1.71155 q^{59} +(-1.71155 - 4.30266i) q^{60} -8.75476 q^{61} -6.29004i q^{62} -8.64104i q^{63} +9.56732 q^{64} +(1.71155 + 4.30266i) q^{65} -5.40067 q^{66} +4.76228i q^{67} -22.3430i q^{68} +1.40067 q^{69} +(16.0224 - 6.37352i) q^{70} +13.7115 q^{71} +12.1768i q^{72} +2.72714i q^{73} +10.4119 q^{74} +(-1.84456 - 1.95166i) q^{75} -3.85577 q^{76} -13.2424i q^{77} +2.69142i q^{78} +1.40067 q^{79} +(-6.55611 + 2.60794i) q^{80} +6.48711 q^{81} +1.45030i q^{82} +7.07154i q^{83} +6.59933 q^{84} +(-4.78926 - 12.0398i) q^{85} -7.71155 q^{86} +3.22248i q^{87} +18.6609i q^{88} -16.5353 q^{89} +(5.42309 + 13.6331i) q^{90} -6.59933 q^{91} -10.0556i q^{92} -1.39605i q^{93} +28.3333 q^{94} +(-2.07772 + 0.826491i) q^{95} +0.722754 q^{96} +2.07086i q^{97} +7.63575i q^{98} +11.2677 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 8 q^{4} - q^{5} - 14 q^{9}+O(q^{10}) $ 6 * q - 8 * q^4 - q^5 - 14 * q^9	$ 6 q - 8 q^{4} - q^{5} - 14 q^{9} + 12 q^{10} + 2 q^{11} - 16 q^{14} + 10 q^{15} - 4 q^{16} + 6 q^{19} + 10 q^{20} + 20 q^{21} - 8 q^{24} + 3 q^{25} + 8 q^{26} - 36 q^{29} + 24 q^{30} + 8 q^{34} - 3 q^{35} - 32 q^{36} + 8 q^{39} + 8 q^{40} + 12 q^{41} - 20 q^{44} - 15 q^{45} - 8 q^{46} + 4 q^{49} - 4 q^{50} + 4 q^{51} + 16 q^{54} - 33 q^{55} + 40 q^{56} - 20 q^{59} + 20 q^{60} - 14 q^{61} + 12 q^{64} - 20 q^{65} - 48 q^{66} + 24 q^{69} + 20 q^{70} + 52 q^{71} + 40 q^{74} - 34 q^{75} - 8 q^{76} + 24 q^{79} - 32 q^{80} + 38 q^{81} + 24 q^{84} + 13 q^{85} - 16 q^{86} - 24 q^{89} - 28 q^{90} - 24 q^{91} + 48 q^{94} - q^{95} - 64 q^{96} + 30 q^{99}+O(q^{100}) $ 6 * q - 8 * q^4 - q^5 - 14 * q^9 + 12 * q^10 + 2 * q^11 - 16 * q^14 + 10 * q^15 - 4 * q^16 + 6 * q^19 + 10 * q^20 + 20 * q^21 - 8 * q^24 + 3 * q^25 + 8 * q^26 - 36 * q^29 + 24 * q^30 + 8 * q^34 - 3 * q^35 - 32 * q^36 + 8 * q^39 + 8 * q^40 + 12 * q^41 - 20 * q^44 - 15 * q^45 - 8 * q^46 + 4 * q^49 - 4 * q^50 + 4 * q^51 + 16 * q^54 - 33 * q^55 + 40 * q^56 - 20 * q^59 + 20 * q^60 - 14 * q^61 + 12 * q^64 - 20 * q^65 - 48 * q^66 + 24 * q^69 + 20 * q^70 + 52 * q^71 + 40 * q^74 - 34 * q^75 - 8 * q^76 + 24 * q^79 - 32 * q^80 + 38 * q^81 + 24 * q^84 + 13 * q^85 - 16 * q^86 - 24 * q^89 - 28 * q^90 - 24 * q^91 + 48 * q^94 - q^95 - 64 * q^96 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	2.41987i		−	1.71111i	−0.517715	−	0.855553i	$-0.673217\pi$
$2$		−	2.41987i		−	1.71111i	0.517715	−	0.855553i	$-0.326783\pi$
$3$		−	0.537080i		−	0.310083i	−0.987908	−	0.155042i	$-0.950449\pi$
$3$		−	0.537080i		−	0.310083i	0.987908	−	0.155042i	$-0.0495512\pi$
$4$	−3.85577			−1.92789
$5$	−2.07772	+	0.826491i	−0.929184	+	0.369618i
$5$	−2.07772	+	0.826491i	−0.929184	+	0.369618i
$6$	−1.29966			−0.530586
$7$		−	3.18676i		−	1.20448i	−0.798314	−	0.602241i	$-0.794275\pi$
$7$		−	3.18676i		−	1.20448i	0.798314	−	0.602241i	$-0.205725\pi$
$8$			4.49073i			1.58771i
$9$	2.71155			0.903848
$10$	2.00000	+	5.02781i	0.632456	+	1.58993i
$11$	4.15544			1.25291			0.626456	−	0.779457i	$-0.284505\pi$
$11$	4.15544			1.25291			0.626456	+	0.779457i	$0.284505\pi$
$12$			2.07086i			0.597805i
$13$		−	2.07086i		−	0.574353i	−0.957878	−	0.287176i	$-0.907283\pi$
$13$		−	2.07086i		−	0.574353i	0.957878	−	0.287176i	$-0.0927166\pi$
$14$	−7.71155			−2.06100
$15$	0.443892	+	1.11590i	0.114612	+	0.288124i
$16$	3.15544			0.788859
$17$			5.79470i			1.40542i	0.711476	+	0.702710i	$0.248027\pi$
$17$			5.79470i			1.40542i	−0.711476	+	0.702710i	$0.751973\pi$
$18$		−	6.56159i		−	1.54658i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	8.01121	−	3.18676i	1.79136	−	0.712581i
$21$	−1.71155			−0.373490
$22$		−	10.0556i		−	2.14386i
$23$			2.60794i			0.543793i	0.962327	+	0.271896i	$0.0876508\pi$
$23$			2.60794i			0.543793i	−0.962327	+	0.271896i	$0.912349\pi$
$24$	2.41188			0.492323
$25$	3.63383	−	3.43443i	0.726765	−	0.686886i
$26$	−5.01121			−0.982779
$27$		−	3.06756i		−	0.590352i
$28$			12.2874i			2.32210i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	2.70034	−	1.07416i	0.493012	−	0.196114i
$31$	2.59933			0.466853			0.233427	−	0.972374i	$-0.425006\pi$
$31$	2.59933			0.466853			0.233427	+	0.972374i	$0.425006\pi$
$32$			1.34571i			0.237890i
$33$		−	2.23180i		−	0.388507i
$34$	14.0224			2.40482
$35$	2.63383	+	6.62119i	0.445198	+	1.11919i
$36$	−10.4551			−1.74252
$37$			4.30266i			0.707353i	0.935368	+	0.353677i	$0.115069\pi$
$37$			4.30266i			0.707353i	−0.935368	+	0.353677i	$0.884931\pi$
$38$		−	2.41987i		−	0.392555i
$39$	−1.11222			−0.178097
$40$	−3.71155	−	9.33047i	−0.586847	−	1.47528i
$41$	−0.599328			−0.0935993			−0.0467997	−	0.998904i	$-0.514902\pi$
$41$	−0.599328			−0.0935993			−0.0467997	+	0.998904i	$0.514902\pi$
$42$			4.14172i			0.639081i
$43$		−	3.18676i		−	0.485976i	−0.970029	−	0.242988i	$-0.921872\pi$
$43$		−	3.18676i		−	0.485976i	0.970029	−	0.242988i	$-0.0781276\pi$
$44$	−16.0224			−2.41547
$45$	−5.63383	+	2.24107i	−0.839841	+	0.334078i
$46$	6.31087			0.930487
$47$			11.7086i			1.70787i	0.520376	+	0.853937i	$0.325792\pi$
$47$			11.7086i			1.70787i	−0.520376	+	0.853937i	$0.674208\pi$
$48$		−	1.69472i		−	0.244612i
$49$	−3.15544			−0.450777
$50$	−8.31087	−	8.79339i	−1.17533	−	1.24357i
$51$	3.11222			0.435798
$52$			7.98476i			1.10729i
$53$		−	11.7503i		−	1.61403i	−0.590529	−	0.807017i	$-0.701081\pi$
$53$		−	11.7503i		−	1.61403i	0.590529	−	0.807017i	$-0.298919\pi$
$54$	−7.42309			−1.01015
$55$	−8.63383	+	3.43443i	−1.16418	+	0.463098i
$56$	14.3109			1.91237
$57$		−	0.537080i		−	0.0711380i
$58$			14.5192i			1.90647i
$59$	1.71155			0.222824			0.111412	−	0.993774i	$-0.464463\pi$
$59$	1.71155			0.222824			0.111412	+	0.993774i	$0.464463\pi$
$60$	−1.71155	−	4.30266i	−0.220960	−	0.555471i
$61$	−8.75476			−1.12093			−0.560466	−	0.828177i	$-0.689378\pi$
$61$	−8.75476			−1.12093			−0.560466	+	0.828177i	$0.689378\pi$
$62$		−	6.29004i		−	0.798836i
$63$		−	8.64104i		−	1.08867i
$64$	9.56732			1.19591
$65$	1.71155	+	4.30266i	0.212291	+	0.533679i
$66$	−5.40067			−0.664777
$67$			4.76228i			0.581805i	0.956753	+	0.290902i	$0.0939555\pi$
$67$			4.76228i			0.581805i	−0.956753	+	0.290902i	$0.906044\pi$
$68$		−	22.3430i		−	2.70949i
$69$	1.40067			0.168621
$70$	16.0224	−	6.37352i	1.91505	−	0.761781i
$71$	13.7115			1.62726			0.813631	−	0.581382i	$-0.197488\pi$
$71$	13.7115			1.62726			0.813631	+	0.581382i	$0.197488\pi$
$72$			12.1768i			1.43505i
$73$			2.72714i			0.319188i	0.987183	+	0.159594i	$0.0510185\pi$
$73$			2.72714i			0.319188i	−0.987183	+	0.159594i	$0.948982\pi$
$74$	10.4119			1.21036
$75$	−1.84456	−	1.95166i	−0.212992	−	0.225358i
$76$	−3.85577			−0.442287
$77$		−	13.2424i		−	1.50911i
$78$			2.69142i			0.304743i
$79$	1.40067			0.157588			0.0787939	−	0.996891i	$-0.474893\pi$
$79$	1.40067			0.157588			0.0787939	+	0.996891i	$0.474893\pi$
$80$	−6.55611	+	2.60794i	−0.732995	+	0.291576i
$81$	6.48711			0.720790
$82$			1.45030i			0.160158i
$83$			7.07154i			0.776203i	0.921617	+	0.388101i	$0.126869\pi$
$83$			7.07154i			0.776203i	−0.921617	+	0.388101i	$0.873131\pi$
$84$	6.59933			0.720046
$85$	−4.78926	−	12.0398i	−0.519469	−	1.30589i
$86$	−7.71155			−0.831557
$87$			3.22248i			0.345486i
$88$			18.6609i			1.98926i
$89$	−16.5353			−1.75274			−0.876370	−	0.481639i	$-0.840042\pi$
$89$	−16.5353			−1.75274			−0.876370	+	0.481639i	$0.840042\pi$
$90$	5.42309	+	13.6331i	0.571644	+	1.43706i
$91$	−6.59933			−0.691798
$92$		−	10.0556i		−	1.04837i
$93$		−	1.39605i		−	0.144763i
$94$	28.3333			2.92236
$95$	−2.07772	+	0.826491i	−0.213169	+	0.0847961i
$96$	0.722754			0.0737658
$97$			2.07086i			0.210264i	0.994458	+	0.105132i	$0.0335265\pi$
$97$			2.07086i			0.210264i	−0.994458	+	0.105132i	$0.966474\pi$
$98$			7.63575i			0.771327i
$99$	11.2677			1.13244
$100$	−14.0112	+	13.2424i	−1.40112	+	1.32424i
$101$	−1.71155			−0.170305			−0.0851525	−	0.996368i	$-0.527138\pi$
$101$	−1.71155			−0.170305			−0.0851525	+	0.996368i	$0.527138\pi$
$102$		−	7.53116i		−	0.745696i
$103$		−	5.75296i		−	0.566856i	−0.958994	−	0.283428i	$-0.908528\pi$
$103$		−	5.75296i		−	0.566856i	0.958994	−	0.283428i	$-0.0914716\pi$
$104$	9.29966			0.911907
$105$	3.55611	−	1.41458i	0.347041	−	0.138048i
$106$	−28.4343			−2.76178
$107$		−	15.4324i		−	1.49191i	−0.665996	−	0.745955i	$-0.731993\pi$
$107$		−	15.4324i		−	1.49191i	0.665996	−	0.745955i	$-0.268007\pi$
$108$			11.8278i			1.13813i
$109$	−11.7115			−1.12176			−0.560881	−	0.827896i	$-0.689538\pi$
$109$	−11.7115			−1.12176			−0.560881	+	0.827896i	$0.689538\pi$
$110$	8.31087	+	20.8927i	0.792411	+	1.99204i
$111$	2.31087			0.219338
$112$		−	10.0556i		−	0.950167i
$113$			10.5927i			0.996477i	0.867040	+	0.498239i	$0.166020\pi$
$113$			10.5927i			0.996477i	−0.867040	+	0.498239i	$0.833980\pi$
$114$	−1.29966			−0.121725
$115$	−2.15544	−	5.41856i	−0.200996	−	0.505283i
$116$	23.1346			2.14800
$117$		−	5.61523i		−	0.519128i
$118$		−	4.14172i		−	0.381276i
$119$	18.4663			1.69280
$120$	−5.01121	+	1.99340i	−0.457459	+	0.181971i
$121$	6.26765			0.569787
$122$			21.1854i			1.91804i
$123$			0.321887i			0.0290236i
$124$	−10.0224			−0.900040
$125$	−4.71155	+	10.1391i	−0.421413	+	0.906869i
$126$	−20.9102			−1.86283
$127$		−	6.07484i		−	0.539055i	−0.962993	−	0.269528i	$-0.913132\pi$
$127$		−	6.07484i		−	0.539055i	0.962993	−	0.269528i	$-0.0868676\pi$
$128$		−	20.4602i		−	1.80845i
$129$	−1.71155			−0.150693
$130$	10.4119	−	4.14172i	0.913182	−	0.363253i
$131$	−13.5785			−1.18636			−0.593181	−	0.805069i	$-0.702128\pi$
$131$	−13.5785			−1.18636			−0.593181	+	0.805069i	$0.702128\pi$
$132$			8.60532i			0.748997i
$133$		−	3.18676i		−	0.276327i
$134$	11.5241			0.995530
$135$	2.53531	+	6.37352i	0.218204	+	0.548545i
$136$	−26.0224			−2.23140
$137$		−	7.94302i		−	0.678618i	−0.940675	−	0.339309i	$-0.889807\pi$
$137$		−	7.94302i		−	0.678618i	0.940675	−	0.339309i	$-0.110193\pi$
$138$		−	3.38944i		−	0.288529i
$139$	−3.26765			−0.277159			−0.138579	−	0.990351i	$-0.544254\pi$
$139$	−3.26765			−0.277159			−0.138579	+	0.990351i	$0.544254\pi$
$140$	−10.1554	−	25.5298i	−0.858291	−	2.15766i
$141$	6.28845			0.529583
$142$		−	33.1802i		−	2.78442i
$143$		−	8.60532i		−	0.719613i
$144$	8.55611			0.713009
$145$	12.4663	−	4.95894i	1.03527	−	0.411818i
$146$	6.59933			0.546164
$147$			1.69472i			0.139778i
$148$		−	16.5901i		−	1.36370i
$149$	−8.44389			−0.691751			−0.345875	−	0.938280i	$-0.612418\pi$
$149$	−8.44389			−0.691751			−0.345875	+	0.938280i	$0.612418\pi$
$150$	−4.72275	+	4.46360i	−0.385611	+	0.364452i
$151$	0.887783			0.0722468			0.0361234	−	0.999347i	$-0.488499\pi$
$151$	0.887783			0.0722468			0.0361234	+	0.999347i	$0.488499\pi$
$152$			4.49073i			0.364246i
$153$			15.7126i			1.27029i
$154$	−32.0448			−2.58225
$155$	−5.40067	+	2.14832i	−0.433792	+	0.172557i
$156$	4.28845			0.343351
$157$			4.14172i			0.330545i	0.986248	+	0.165273i	$0.0528504\pi$
$157$			4.14172i			0.330545i	−0.986248	+	0.165273i	$0.947150\pi$
$158$		−	3.38944i		−	0.269650i
$159$	−6.31087			−0.500485
$160$	−1.11222	−	2.79601i	−0.0879285	−	0.221044i
$161$	8.31087			0.654989
$162$		−	15.6980i		−	1.23335i
$163$			24.7126i			1.93564i	0.251647	+	0.967819i	$0.419028\pi$
$163$			24.7126i			1.93564i	−0.251647	+	0.967819i	$0.580972\pi$
$164$	2.31087			0.180449
$165$	1.84456	+	4.63706i	0.143599	+	0.360994i
$166$	17.1122			1.32817
$167$		−	3.60464i		−	0.278935i	−0.990227	−	0.139468i	$-0.955461\pi$
$167$		−	3.60464i		−	0.278935i	0.990227	−	0.139468i	$-0.0445391\pi$
$168$		−	7.68608i		−	0.592994i
$169$	8.71155			0.670119
$170$	−29.1346	+	11.5894i	−2.23452	+	0.888866i
$171$	2.71155			0.207357
$172$			12.2874i			0.936907i
$173$			22.4205i			1.70460i	0.523054	+	0.852300i	$0.324793\pi$
$173$			22.4205i			1.70460i	−0.523054	+	0.852300i	$0.675207\pi$
$174$	7.79798			0.591164
$175$	−10.9447	−	11.5801i	−0.827342	−	0.875376i
$176$	13.1122			0.988371
$177$		−	0.919237i		−	0.0690941i
$178$			40.0133i			2.99912i
$179$	5.13464			0.383781			0.191890	−	0.981416i	$-0.438538\pi$
$179$	5.13464			0.383781			0.191890	+	0.981416i	$0.438538\pi$
$180$	21.7228	−	8.64104i	1.61912	−	0.644065i
$181$	20.8462			1.54948			0.774742	−	0.632277i	$-0.217880\pi$
$181$	20.8462			1.54948			0.774742	+	0.632277i	$0.217880\pi$
$182$			15.9695i			1.18374i
$183$			4.70201i			0.347583i
$184$	−11.7115			−0.863387
$185$	−3.55611	−	8.93972i	−0.261450	−	0.657261i
$186$	−3.37825			−0.247706
$187$			24.0795i			1.76087i
$188$		−	45.1457i		−	3.29259i
$189$	−9.77557			−0.711068
$190$	2.00000	+	5.02781i	0.145095	+	0.364756i
$191$	−5.26765			−0.381154			−0.190577	−	0.981672i	$-0.561036\pi$
$191$	−5.26765			−0.381154			−0.190577	+	0.981672i	$0.561036\pi$
$192$		−	5.13842i		−	0.370833i
$193$		−	2.07086i		−	0.149064i	−0.997219	−	0.0745318i	$-0.976254\pi$
$193$		−	2.07086i		−	0.149064i	0.997219	−	0.0745318i	$-0.0237462\pi$
$194$	5.01121			0.359784
$195$	2.31087	−	0.919237i	0.165485	−	0.0658279i
$196$	12.1666			0.869046
$197$			10.4318i			0.743232i	0.928387	+	0.371616i	$0.121196\pi$
$197$			10.4318i			0.743232i	−0.928387	+	0.371616i	$0.878804\pi$
$198$		−	27.2663i		−	1.93773i
$199$	2.73235			0.193691			0.0968455	−	0.995299i	$-0.469125\pi$
$199$	2.73235			0.193691			0.0968455	+	0.995299i	$0.469125\pi$
$200$	15.4231	+	16.3185i	1.09058	+	1.15389i
$201$	2.55773			0.180408
$202$			4.14172i			0.291410i
$203$			19.1206i			1.34200i
$204$	−12.0000			−0.840168
$205$	1.24524	−	0.495339i	0.0869710	−	0.0345960i
$206$	−13.9214			−0.969951
$207$			7.07154i			0.491506i
$208$		−	6.53446i		−	0.453083i
$209$	4.15544			0.287438
$210$	−3.42309	−	8.60532i	−0.236216	−	0.593824i
$211$	−15.7340			−1.08317			−0.541585	−	0.840646i	$-0.682176\pi$
$211$	−15.7340			−1.08317			−0.541585	+	0.840646i	$0.682176\pi$
$212$			45.3066i			3.11167i
$213$		−	7.36420i		−	0.504586i
$214$	−37.3445			−2.55282
$215$	2.63383	+	6.62119i	0.179625	+	0.451561i
$216$	13.7756			0.937309
$217$		−	8.28343i		−	0.562316i
$218$			28.3404i			1.91946i
$219$	1.46469			0.0989748
$220$	33.2901	−	13.2424i	2.24442	−	0.892801i
$221$	12.0000			0.807207
$222$		−	5.59201i		−	0.375311i
$223$		−	18.8219i		−	1.26041i	−0.776430	−	0.630203i	$-0.782972\pi$
$223$		−	18.8219i		−	1.26041i	0.776430	−	0.630203i	$-0.217028\pi$
$224$	4.28845			0.286534
$225$	9.85328	−	9.31261i	0.656886	−	0.620841i
$226$	25.6330			1.70508
$227$		−	14.4418i		−	0.958533i	−0.877669	−	0.479267i	$-0.840903\pi$
$227$		−	14.4418i		−	0.958533i	0.877669	−	0.479267i	$-0.159097\pi$
$228$			2.07086i			0.137146i
$229$	4.17785			0.276080			0.138040	−	0.990427i	$-0.455920\pi$
$229$	4.17785			0.276080			0.138040	+	0.990427i	$0.455920\pi$
$230$	−13.1122	+	5.21588i	−0.864594	+	0.343925i
$231$	−7.11222			−0.467950
$232$		−	26.9444i		−	1.76898i
$233$		−	12.0847i		−	0.791697i	−0.918316	−	0.395849i	$-0.870450\pi$
$233$		−	12.0847i		−	0.791697i	0.918316	−	0.395849i	$-0.129550\pi$
$234$	−13.5881			−0.888283
$235$	−9.67705	−	24.3272i	−0.631261	−	1.58693i
$236$	−6.59933			−0.429580
$237$		−	0.752273i		−	0.0488654i
$238$		−	44.6861i		−	2.89657i
$239$	11.3541			0.734435			0.367218	−	0.930135i	$-0.380310\pi$
$239$	11.3541			0.734435			0.367218	+	0.930135i	$0.380310\pi$
$240$	1.40067	+	3.52116i	0.0904130	+	0.227290i
$241$	−3.40067			−0.219057			−0.109528	−	0.993984i	$-0.534934\pi$
$241$	−3.40067			−0.219057			−0.109528	+	0.993984i	$0.534934\pi$
$242$		−	15.1669i		−	0.974966i
$243$		−	12.6868i		−	0.813857i
$244$	33.7564			2.16103
$245$	6.55611	−	2.60794i	0.418854	−	0.166615i
$246$	0.778925			0.0496625
$247$		−	2.07086i		−	0.131766i
$248$			11.6729i			0.741229i
$249$	3.79798			0.240687
$250$	24.5353	+	11.4013i	1.55175	+	0.721083i
$251$	3.04322			0.192086			0.0960432	−	0.995377i	$-0.469381\pi$
$251$	3.04322			0.192086			0.0960432	+	0.995377i	$0.469381\pi$
$252$			33.3179i			2.09883i
$253$			10.8371i			0.681324i
$254$	−14.7003			−0.922381
$255$	−6.46631	+	2.57222i	−0.404936	+	0.161079i
$256$	−30.3765			−1.89853
$257$			17.2881i			1.07840i	0.842177	+	0.539201i	$0.181274\pi$
$257$			17.2881i			1.07840i	−0.842177	+	0.539201i	$0.818726\pi$
$258$			4.14172i			0.257852i
$259$	13.7115			0.851994
$260$	−6.59933	−	16.5901i	−0.409273	−	1.02887i
$261$	−16.2693			−1.00704
$262$			32.8583i			2.02999i
$263$			1.19336i			0.0735859i	0.999323	+	0.0367930i	$0.0117142\pi$
$263$			1.19336i			0.0735859i	−0.999323	+	0.0367930i	$0.988286\pi$
$264$	10.0224			0.616837
$265$	9.71155	+	24.4139i	0.596575	+	1.49973i
$266$	−7.71155			−0.472825
$267$			8.88078i			0.543495i
$268$		−	18.3623i		−	1.12165i
$269$	−22.1089			−1.34800			−0.674000	−	0.738731i	$-0.735425\pi$
$269$	−22.1089			−1.34800			−0.674000	+	0.738731i	$0.735425\pi$
$270$	15.4231	−	6.13511i	0.938619	−	0.373371i
$271$	−4.08644			−0.248234			−0.124117	−	0.992268i	$-0.539610\pi$
$271$	−4.08644			−0.248234			−0.124117	+	0.992268i	$0.539610\pi$
$272$			18.2848i			1.10868i
$273$			3.54437i			0.214515i
$274$	−19.2211			−1.16119
$275$	15.1001	−	14.2716i	0.910572	−	0.860607i
$276$	−5.40067			−0.325082
$277$		−	10.0199i		−	0.602037i	−0.953618	−	0.301019i	$-0.902673\pi$
$277$		−	10.0199i		−	0.602037i	0.953618	−	0.301019i	$-0.0973266\pi$
$278$			7.90730i			0.474248i
$279$	7.04820			0.421964
$280$	−29.7340	+	11.8278i	−1.77694	+	0.706846i
$281$	0.599328			0.0357529			0.0178765	−	0.999840i	$-0.494309\pi$
$281$	0.599328			0.0357529			0.0178765	+	0.999840i	$0.494309\pi$
$282$		−	15.2172i		−	0.906174i
$283$		−	5.41856i		−	0.322100i	−0.986946	−	0.161050i	$-0.948512\pi$
$283$		−	5.41856i		−	0.322100i	0.986946	−	0.161050i	$-0.0514880\pi$
$284$	−52.8686			−3.13717
$285$	0.443892	+	1.11590i	0.0262939	+	0.0661003i
$286$	−20.8238			−1.23133
$287$			1.90991i			0.112739i
$288$			3.64895i			0.215017i
$289$	−16.5785			−0.975207
$290$	−12.0000	−	30.1669i	−0.704664	−	1.77146i
$291$	1.11222			0.0651993
$292$		−	10.5152i		−	0.615358i
$293$		−	3.46691i		−	0.202539i	−0.994859	−	0.101269i	$-0.967710\pi$
$293$		−	3.46691i		−	0.202539i	0.994859	−	0.101269i	$-0.0322904\pi$
$294$	4.10101			0.239176
$295$	−3.55611	+	1.41458i	−0.207045	+	0.0823598i
$296$	−19.3221			−1.12307
$297$		−	12.7470i		−	0.739658i
$298$			20.4331i			1.18366i
$299$	5.40067			0.312329
$300$	7.11222	+	7.52514i	0.410624	+	0.434464i
$301$	−10.1554			−0.585350
$302$		−	2.14832i		−	0.123622i
$303$			0.919237i			0.0528088i
$304$	3.15544			0.180977
$305$	18.1899	−	7.23573i	1.04155	−	0.414317i
$306$	38.0224			2.17360
$307$		−	16.5901i		−	0.946846i	−0.880835	−	0.473423i	$-0.843018\pi$
$307$		−	16.5901i		−	0.946846i	0.880835	−	0.473423i	$-0.156982\pi$
$308$			51.0596i			2.90939i
$309$	−3.08980			−0.175772
$310$	5.19866	+	13.0689i	0.295264	+	0.742265i
$311$	−4.15544			−0.235633			−0.117817	−	0.993035i	$-0.537589\pi$
$311$	−4.15544			−0.235633			−0.117817	+	0.993035i	$0.537589\pi$
$312$		−	4.99466i		−	0.282767i
$313$			0.919237i			0.0519583i	0.999662	+	0.0259792i	$0.00827036\pi$
$313$			0.919237i			0.0519583i	−0.999662	+	0.0259792i	$0.991730\pi$
$314$	10.0224			0.565598
$315$	7.14174	+	17.9537i	0.402391	+	1.01157i
$316$	−5.40067			−0.303812
$317$		−	26.7292i		−	1.50126i	−0.660723	−	0.750630i	$-0.729750\pi$
$317$		−	26.7292i		−	1.50126i	0.660723	−	0.750630i	$-0.270250\pi$
$318$			15.2715i			0.856383i
$319$	−24.9326			−1.39596
$320$	−19.8782	+	7.90730i	−1.11122	+	0.442031i
$321$	−8.28845			−0.462616
$322$		−	20.1112i		−	1.12076i
$323$			5.79470i			0.322426i
$324$	−25.0128			−1.38960
$325$	−7.11222	−	7.52514i	−0.394515	−	0.417420i
$326$	59.8012			3.31208
$327$			6.29004i			0.347840i
$328$		−	2.69142i		−	0.148609i
$329$	37.3125			2.05710
$330$	11.2211	−	4.46360i	0.617700	−	0.245713i
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$		−	27.2663i		−	1.49643i
$333$			11.6669i			0.639340i
$334$	−8.72275			−0.477288
$335$	−3.93598	−	9.89467i	−0.215045	−	0.540604i
$336$	−5.40067			−0.294631
$337$			22.5040i			1.22587i	0.790133	+	0.612935i	$0.210011\pi$
$337$			22.5040i			1.22587i	−0.790133	+	0.612935i	$0.789989\pi$
$338$		−	21.0808i		−	1.14664i
$339$	5.68913			0.308991
$340$	18.4663	+	46.4225i	1.00148	+	2.51762i
$341$	10.8013			0.584926
$342$		−	6.56159i		−	0.354810i
$343$		−	12.2517i		−	0.661530i
$344$	14.3109			0.771591
$345$	−2.91020	+	1.15764i	−0.156680	+	0.0623254i
$346$	54.2547			2.91675
$347$		−	14.4543i		−	0.775946i	−0.921671	−	0.387973i	$-0.873175\pi$
$347$		−	14.4543i		−	0.775946i	0.921671	−	0.387973i	$-0.126825\pi$
$348$		−	12.4252i		−	0.666058i
$349$	13.3541			0.714828			0.357414	−	0.933946i	$-0.383658\pi$
$349$	13.3541			0.714828			0.357414	+	0.933946i	$0.383658\pi$
$350$	−28.0224	+	26.4848i	−1.49786	+	1.41567i
$351$	−6.35248			−0.339070
$352$			5.59201i			0.298055i
$353$		−	17.6410i		−	0.938937i	−0.882949	−	0.469469i	$-0.844446\pi$
$353$		−	17.6410i		−	0.938937i	0.882949	−	0.469469i	$-0.155554\pi$
$354$	−2.22443			−0.118227
$355$	−28.4887	+	11.3325i	−1.51202	+	0.601465i
$356$	63.7564			3.37908
$357$		−	9.91789i		−	0.524910i
$358$		−	12.4252i		−	0.656690i
$359$	−12.4663			−0.657947			−0.328973	−	0.944339i	$-0.606703\pi$
$359$	−12.4663			−0.657947			−0.328973	+	0.944339i	$0.606703\pi$
$360$	−10.0640	−	25.3000i	−0.530420	−	1.33343i
$361$	1.00000			0.0526316
$362$		−	50.4451i		−	2.65133i
$363$		−	3.36623i		−	0.176681i
$364$	25.4455			1.33371
$365$	−2.25396	−	5.66623i	−0.117977	−	0.296584i
$366$	11.3783			0.594751
$367$		−	16.4291i		−	0.857594i	−0.903401	−	0.428797i	$-0.858938\pi$
$367$		−	16.4291i		−	0.857594i	0.903401	−	0.428797i	$-0.141062\pi$
$368$			8.22918i			0.428976i
$369$	−1.62511			−0.0845996
$370$	−21.6330	+	8.60532i	−1.12464	+	0.447369i
$371$	−37.4455			−1.94407
$372$			5.38284i			0.279087i
$373$			5.29334i			0.274079i	0.990566	+	0.137039i	$0.0437587\pi$
$373$			5.29334i			0.274079i	−0.990566	+	0.137039i	$0.956241\pi$
$374$	58.2693			3.01303
$375$	5.44551	+	2.53048i	0.281205	+	0.130673i
$376$	−52.5801			−2.71161
$377$			12.4252i			0.639928i
$378$			23.6556i			1.21671i
$379$	−14.5353			−0.746629			−0.373314	−	0.927705i	$-0.621779\pi$
$379$	−14.5353			−0.746629			−0.373314	+	0.927705i	$0.621779\pi$
$380$	8.01121	−	3.18676i	0.410966	−	0.163477i
$381$	−3.26268			−0.167152
$382$			12.7470i			0.652195i
$383$		−	0.453598i		−	0.0231778i	−0.999933	−	0.0115889i	$-0.996311\pi$
$383$		−	0.453598i		−	0.0231778i	0.999933	−	0.0115889i	$-0.00368894\pi$
$384$	−10.9888			−0.560769
$385$	10.9447	+	27.5139i	0.557794	+	1.40224i
$386$	−5.01121			−0.255064
$387$		−	8.64104i		−	0.439249i
$388$		−	7.98476i		−	0.405365i
$389$	−16.1554			−0.819113			−0.409557	−	0.912285i	$-0.634317\pi$
$389$	−16.1554			−0.819113			−0.409557	+	0.912285i	$0.634317\pi$
$390$	−2.22443	−	5.59201i	−0.112639	−	0.283163i
$391$	−15.1122			−0.764258
$392$		−	14.1702i		−	0.715704i
$393$			7.29276i			0.367871i
$394$	25.2435			1.27175
$395$	−2.91020	+	1.15764i	−0.146428	+	0.0582473i
$396$	−43.4455			−2.18322
$397$			32.7563i			1.64399i	0.569495	+	0.821995i	$0.307139\pi$
$397$			32.7563i			1.64399i	−0.569495	+	0.821995i	$0.692861\pi$
$398$		−	6.61192i		−	0.331426i
$399$	−1.71155			−0.0856844
$400$	11.4663	−	10.8371i	0.573315	−	0.541856i
$401$	12.0864			0.603568			0.301784	−	0.953376i	$-0.402418\pi$
$401$	12.0864			0.603568			0.301784	+	0.953376i	$0.402418\pi$
$402$		−	6.18936i		−	0.308697i
$403$		−	5.38284i		−	0.268138i
$404$	6.59933			0.328329
$405$	−13.4784	+	5.36154i	−0.669747	+	0.266417i
$406$	46.2693			2.29631
$407$			17.8794i			0.886251i
$408$			13.9761i			0.691921i
$409$	19.1346			0.946147			0.473073	−	0.881023i	$-0.343145\pi$
$409$	19.1346			0.946147			0.473073	+	0.881023i	$0.343145\pi$
$410$	−1.19866	−	3.01331i	−0.0591974	−	0.148817i
$411$	−4.26604			−0.210428
$412$			22.1821i			1.09283i
$413$		−	5.45428i		−	0.268388i
$414$	17.1122			0.841020
$415$	−5.84456	−	14.6927i	−0.286898	−	0.721235i
$416$	2.78678			0.136633
$417$			1.75499i			0.0859423i
$418$		−	10.0556i		−	0.491836i
$419$	−8.04484			−0.393016			−0.196508	−	0.980502i	$-0.562960\pi$
$419$	−8.04484			−0.393016			−0.196508	+	0.980502i	$0.562960\pi$
$420$	−13.7115	+	5.45428i	−0.669055	+	0.266142i
$421$	−29.3591			−1.43087			−0.715437	−	0.698678i	$-0.753772\pi$
$421$	−29.3591			−1.43087			−0.715437	+	0.698678i	$0.753772\pi$
$422$			38.0742i			1.85342i
$423$			31.7484i			1.54366i
$424$	52.7676			2.56262
$425$	19.9015	+	21.0569i	0.965364	+	1.02141i
$426$	−17.8204			−0.863401
$427$			27.8993i			1.35014i
$428$			59.5040i			2.87623i
$429$	−4.62175			−0.223140
$430$	16.0224	−	6.37352i	0.772670	−	0.307358i
$431$	−32.0448			−1.54355			−0.771773	−	0.635898i	$-0.780630\pi$
$431$	−32.0448			−1.54355			−0.771773	+	0.635898i	$0.780630\pi$
$432$		−	9.67948i		−	0.465704i
$433$		−	0.482831i		−	0.0232034i	−0.999933	−	0.0116017i	$-0.996307\pi$
$433$		−	0.482831i		−	0.0232034i	0.999933	−	0.0116017i	$-0.00369301\pi$
$434$	−20.0448			−0.962183
$435$	−2.66335	−	6.69541i	−0.127698	−	0.321020i
$436$	45.1571			2.16263
$437$			2.60794i			0.124755i
$438$		−	3.54437i		−	0.169356i
$439$	27.3591			1.30578			0.652889	−	0.757454i	$-0.273557\pi$
$439$	27.3591			1.30578			0.652889	+	0.757454i	$0.273557\pi$
$440$	−15.4231	−	38.7722i	−0.735267	−	1.84839i
$441$	−8.55611			−0.407434
$442$		−	29.0384i		−	1.38122i
$443$		−	23.3815i		−	1.11089i	−0.831554	−	0.555444i	$-0.812548\pi$
$443$		−	23.3815i		−	1.11089i	0.831554	−	0.555444i	$-0.187452\pi$
$444$	−8.91020			−0.422859
$445$	34.3557	−	13.6663i	1.62862	−	0.647844i
$446$	−45.5465			−2.15669
$447$			4.53505i			0.214500i
$448$		−	30.4887i		−	1.44046i
$449$	−23.1346			−1.09179			−0.545895	−	0.837853i	$-0.683810\pi$
$449$	−23.1346			−1.09179			−0.545895	+	0.837853i	$0.683810\pi$
$450$	−22.5353	−	23.8437i	−1.06232	−	1.12400i
$451$	−2.49047			−0.117272
$452$		−	40.8430i		−	1.92109i
$453$		−	0.476811i		−	0.0224025i
$454$	−34.9472			−1.64015
$455$	13.7115	−	5.45428i	0.642807	−	0.255701i
$456$	2.41188			0.112947
$457$			21.2503i			0.994049i	0.867736	+	0.497025i	$0.165574\pi$
$457$			21.2503i			0.994049i	−0.867736	+	0.497025i	$0.834426\pi$
$458$		−	10.1099i		−	0.472403i
$459$	17.7756			0.829692
$460$	8.31087	+	20.8927i	0.387496	+	0.974129i
$461$	31.5785			1.47076			0.735379	−	0.677656i	$-0.237004\pi$
$461$	31.5785			1.47076			0.735379	+	0.677656i	$0.237004\pi$
$462$			17.2106i			0.800712i
$463$			15.6119i			0.725547i	0.931877	+	0.362774i	$0.118170\pi$
$463$			15.6119i			0.725547i	−0.931877	+	0.362774i	$0.881830\pi$
$464$	−18.9326			−0.878925
$465$	1.15382	+	2.90059i	0.0535071	+	0.134512i
$466$	−29.2435			−1.35468
$467$		−	29.8264i		−	1.38020i	−0.723713	−	0.690101i	$-0.757566\pi$
$467$		−	29.8264i		−	1.38020i	0.723713	−	0.690101i	$-0.242434\pi$
$468$			21.6510i			1.00082i
$469$	15.1762			0.700774
$470$	−58.8686	+	23.4172i	−2.71541	+	1.08015i
$471$	2.22443			0.102496
$472$			7.68608i			0.353781i
$473$		−	13.2424i		−	0.608885i
$474$	−1.82040			−0.0836139
$475$	3.63383	−	3.43443i	0.166731	−	0.157582i
$476$	−71.2019			−3.26353
$477$		−	31.8616i		−	1.45884i
$478$		−	27.4754i		−	1.25670i
$479$	−4.53531			−0.207223			−0.103612	−	0.994618i	$-0.533040\pi$
$479$	−4.53531			−0.207223			−0.103612	+	0.994618i	$0.533040\pi$
$480$	−1.50168	+	0.597349i	−0.0685420	+	0.0272651i
$481$	8.91020			0.406270
$482$			8.22918i			0.374829i
$483$		−	4.46360i		−	0.203101i
$484$	−24.1666			−1.09848
$485$	−1.71155	−	4.30266i	−0.0777173	−	0.195374i
$486$	−30.7003			−1.39260
$487$			39.2550i			1.77881i	0.457116	+	0.889407i	$0.348882\pi$
$487$			39.2550i			1.77881i	−0.457116	+	0.889407i	$0.651118\pi$
$488$		−	39.3153i		−	1.77972i
$489$	13.2726			0.600209
$490$	−6.31087	−	15.8649i	−0.285096	−	0.716705i
$491$	38.8910			1.75513			0.877564	−	0.479460i	$-0.159168\pi$
$491$	38.8910			1.75513			0.877564	+	0.479460i	$0.159168\pi$
$492$		−	1.24112i		−	0.0559542i
$493$		−	34.7682i		−	1.56588i
$494$	−5.01121			−0.225465
$495$	−23.4110	+	9.31261i	−1.05225	+	0.418571i
$496$	8.20202			0.368281
$497$		−	43.6954i		−	1.96001i
$498$		−	9.19063i		−	0.411842i
$499$	−4.73235			−0.211849			−0.105924	−	0.994374i	$-0.533780\pi$
$499$	−4.73235			−0.211849			−0.105924	+	0.994374i	$0.533780\pi$
$500$	18.1666	−	39.0941i	0.812437	−	1.74834i
$501$	−1.93598			−0.0864931
$502$		−	7.36420i		−	0.328680i
$503$		−	1.85567i		−	0.0827400i	−0.999144	−	0.0413700i	$-0.986828\pi$
$503$		−	1.85567i		−	0.0827400i	0.999144	−	0.0413700i	$-0.0131722\pi$
$504$	38.8046			1.72849
$505$	3.55611	−	1.41458i	0.158245	−	0.0629478i
$506$	26.2244			1.16582
$507$		−	4.67880i		−	0.207793i
$508$			23.4232i			1.03924i
$509$	−22.8878			−1.01448			−0.507242	−	0.861804i	$-0.669335\pi$
$509$	−22.8878			−1.01448			−0.507242	+	0.861804i	$0.669335\pi$
$510$	6.22443	+	15.6476i	0.275623	+	0.692889i
$511$	8.69074			0.384456
$512$			32.5867i			1.44014i
$513$		−	3.06756i		−	0.135436i
$514$	41.8350			1.84526
$515$	4.75476	+	11.9530i	0.209520	+	0.526713i
$516$	6.59933			0.290519
$517$			48.6543i			2.13982i
$518$		−	33.1802i		−	1.45785i
$519$	12.0416			0.528568
$520$	−19.3221	+	7.68608i	−0.847329	+	0.337057i
$521$	−29.7340			−1.30267			−0.651334	−	0.758791i	$-0.725790\pi$
$521$	−29.7340			−1.30267			−0.651334	+	0.758791i	$0.725790\pi$
$522$			39.3695i			1.72316i
$523$		−	30.6497i		−	1.34022i	−0.742263	−	0.670109i	$-0.766248\pi$
$523$		−	30.6497i		−	1.34022i	0.742263	−	0.670109i	$-0.233752\pi$
$524$	52.3557			2.28717
$525$	−6.21946	+	5.87818i	−0.271439	+	0.256545i
$526$	2.88778			0.125913
$527$			15.0623i			0.656125i
$528$		−	7.04231i		−	0.306477i
$529$	16.1987			0.704289
$530$	59.0785	−	23.5007i	2.56620	−	1.02080i
$531$	4.64093			0.201399
$532$			12.2874i			0.532727i
$533$			1.24112i			0.0537590i
$534$	21.4903			0.929978
$535$	12.7548	+	32.0643i	0.551437	+	1.38626i
$536$	−21.3861			−0.923739
$537$		−	2.75771i		−	0.119004i
$538$			53.5006i			2.30657i
$539$	−13.1122			−0.564783
$540$	−9.77557	−	24.5748i	−0.420673	−	1.05753i
$541$	2.21946			0.0954220			0.0477110	−	0.998861i	$-0.484807\pi$
$541$	2.21946			0.0954220			0.0477110	+	0.998861i	$0.484807\pi$
$542$			9.88865i			0.424754i
$543$		−	11.1961i		−	0.480469i
$544$	−7.79798			−0.334336
$545$	24.3333	−	9.67948i	1.04232	−	0.414623i
$546$	8.57691			0.367058
$547$		−	14.4297i		−	0.616970i	−0.951229	−	0.308485i	$-0.900178\pi$
$547$		−	14.4297i		−	0.616970i	0.951229	−	0.308485i	$-0.0998220\pi$
$548$			30.6265i			1.30830i
$549$	−23.7389			−1.01315
$550$	−34.5353	−	36.5404i	−1.47259	−	1.55809i
$551$	−6.00000			−0.255609
$552$			6.29004i			0.267722i
$553$		−	4.46360i		−	0.189812i
$554$	−24.2469			−1.03015
$555$	−4.80134	+	1.90991i	−0.203806	+	0.0810714i
$556$	12.5993			0.534331
$557$			19.4610i			0.824588i	0.911051	+	0.412294i	$0.135272\pi$
$557$			19.4610i			0.824588i	−0.911051	+	0.412294i	$0.864728\pi$
$558$		−	17.0557i		−	0.722026i
$559$	−6.59933			−0.279122
$560$	8.31087	+	20.8927i	0.351198	+	0.882879i
$561$	12.9326			0.546016
$562$		−	1.45030i		−	0.0611771i
$563$			12.3649i			0.521118i	0.965458	+	0.260559i	$0.0839068\pi$
$563$			12.3649i			0.521118i	−0.965458	+	0.260559i	$0.916093\pi$
$564$	−24.2469			−1.02098
$565$	−8.75476	−	22.0086i	−0.368316	−	0.925911i
$566$	−13.1122			−0.551148
$567$		−	20.6729i		−	0.868179i
$568$			61.5748i			2.58362i
$569$	−15.0898			−0.632597			−0.316299	−	0.948660i	$-0.602440\pi$
$569$	−15.0898			−0.632597			−0.316299	+	0.948660i	$0.602440\pi$
$570$	2.70034	−	1.07416i	0.113105	−	0.0449916i
$571$	17.1571			0.718000			0.359000	−	0.933337i	$-0.383118\pi$
$571$	17.1571			0.718000			0.359000	+	0.933337i	$0.383118\pi$
$572$			33.1802i			1.38733i
$573$			2.82915i			0.118190i
$574$	4.62175			0.192908
$575$	8.95678	+	9.47680i	0.373524	+	0.395210i
$576$	25.9422			1.08093
$577$		−	22.5165i		−	0.937374i	−0.883364	−	0.468687i	$-0.844727\pi$
$577$		−	22.5165i		−	0.937374i	0.883364	−	0.468687i	$-0.155273\pi$
$578$			40.1179i			1.66868i
$579$	−1.11222			−0.0462222
$580$	−48.0673	+	19.1206i	−1.99588	+	0.793938i
$581$	22.5353			0.934922
$582$		−	2.69142i		−	0.111563i
$583$		−	48.8278i		−	2.02224i
$584$	−12.2469			−0.506778
$585$	4.64093	+	11.6669i	0.191879	+	0.482365i
$586$	−8.38946			−0.346566
$587$			7.49544i			0.309370i	0.987964	+	0.154685i	$0.0494363\pi$
$587$			7.49544i			0.309370i	−0.987964	+	0.154685i	$0.950564\pi$
$588$		−	6.53446i		−	0.269477i
$589$	2.59933			0.107103
$590$	3.42309	+	8.60532i	0.140926	+	0.354275i
$591$	5.60269			0.230464
$592$			13.5768i			0.558002i
$593$		−	27.8094i		−	1.14199i	−0.820952	−	0.570997i	$-0.806557\pi$
$593$		−	27.8094i		−	1.14199i	0.820952	−	0.570997i	$-0.193443\pi$
$594$	−30.8462			−1.26563
$595$	−38.3678	+	15.2622i	−1.57293	+	0.625690i
$596$	32.5577			1.33362
$597$		−	1.46749i		−	0.0600603i
$598$		−	13.0689i		−	0.534428i
$599$	45.4903			1.85869			0.929343	−	0.369219i	$-0.120375\pi$
$599$	45.4903			1.85869			0.929343	+	0.369219i	$0.120375\pi$
$600$	8.76436	−	8.28343i	0.357803	−	0.338170i
$601$	−16.5993			−0.677101			−0.338550	−	0.940948i	$-0.609937\pi$
$601$	−16.5993			−0.677101			−0.338550	+	0.940948i	$0.609937\pi$
$602$			24.5748i			1.00160i
$603$			12.9131i			0.525863i
$604$	−3.42309			−0.139284
$605$	−13.0224	+	5.18016i	−0.529437	+	0.210603i
$606$	2.22443			0.0903614
$607$		−	5.08417i		−	0.206360i	−0.994663	−	0.103180i	$-0.967098\pi$
$607$		−	5.08417i		−	0.206360i	0.994663	−	0.103180i	$-0.0329018\pi$
$608$			1.34571i			0.0545758i
$609$	10.2693			0.416132
$610$	−17.5095	−	44.0173i	−0.708940	−	1.78221i
$611$	24.2469			0.980923
$612$		−	60.5842i		−	2.44897i
$613$		−	4.63706i		−	0.187289i	−0.995606	−	0.0936445i	$-0.970148\pi$
$613$		−	4.63706i		−	0.187289i	0.995606	−	0.0936445i	$-0.0298517\pi$
$614$	−40.1458			−1.62015
$615$	−0.266037	−	0.668791i	−0.0107276	−	0.0269683i
$616$	59.4679			2.39603
$617$			40.2874i			1.62191i	0.585108	+	0.810955i	$0.301052\pi$
$617$			40.2874i			1.62191i	−0.585108	+	0.810955i	$0.698948\pi$
$618$			7.47691i			0.300766i
$619$	43.3815			1.74365			0.871825	−	0.489818i	$-0.162937\pi$
$619$	43.3815			1.74365			0.871825	+	0.489818i	$0.162937\pi$
$620$	20.8238	−	8.28343i	0.836302	−	0.332671i
$621$	8.00000			0.321029
$622$			10.0556i			0.403194i
$623$			52.6940i			2.11114i
$624$	−3.50953			−0.140494
$625$	1.40939	−	24.9602i	0.0563757	−	0.998410i
$626$	2.22443			0.0889062
$627$		−	2.23180i		−	0.0891296i
$628$		−	15.9695i		−	0.637253i
$629$	−24.9326			−0.994129
$630$	43.4455	−	17.2821i	1.73091	−	0.688535i
$631$	7.53369			0.299911			0.149956	−	0.988693i	$-0.452087\pi$
$631$	7.53369			0.299911			0.149956	+	0.988693i	$0.452087\pi$
$632$			6.29004i			0.250204i
$633$			8.45040i			0.335873i
$634$	−64.6812			−2.56882
$635$	5.02080	+	12.6218i	0.199244	+	0.500881i
$636$	24.3333			0.964878
$637$			6.53446i			0.258905i
$638$			60.3337i			2.38863i
$639$	37.1795			1.47080
$640$	16.9102	+	42.5106i	0.668434	+	1.68038i
$641$	−23.3075			−0.920591			−0.460296	−	0.887766i	$-0.652257\pi$
$641$	−23.3075			−0.920591			−0.460296	+	0.887766i	$0.652257\pi$
$642$			20.0570i			0.791586i
$643$		−	1.87419i		−	0.0739110i	−0.999317	−	0.0369555i	$-0.988234\pi$
$643$		−	1.87419i		−	0.0739110i	0.999317	−	0.0369555i	$-0.0117660\pi$
$644$	−32.0448			−1.26274
$645$	3.55611	−	1.41458i	0.140022	−	0.0556989i
$646$	14.0224			0.551705
$647$		−	47.0371i		−	1.84922i	−0.380917	−	0.924609i	$-0.624392\pi$
$647$		−	47.0371i		−	1.84922i	0.380917	−	0.924609i	$-0.375608\pi$
$648$			29.1319i			1.14441i
$649$	7.11222			0.279179
$650$	−18.2099	+	17.2106i	−0.714250	+	0.675057i
$651$	−4.44887			−0.174365
$652$		−	95.2861i		−	3.73169i
$653$		−	24.1630i		−	0.945571i	−0.881178	−	0.472785i	$-0.843249\pi$
$653$		−	24.1630i		−	0.945571i	0.881178	−	0.472785i	$-0.156751\pi$
$654$	15.2211			0.595191
$655$	28.2124	−	11.2225i	1.10235	−	0.438500i
$656$	−1.89114			−0.0738367
$657$			7.39477i			0.288497i
$658$		−	90.2914i		−	3.51992i
$659$	−10.2885			−0.400781			−0.200391	−	0.979716i	$-0.564221\pi$
$659$	−10.2885			−0.400781			−0.200391	+	0.979716i	$0.564221\pi$
$660$	−7.11222	−	17.8794i	−0.276843	−	0.695956i
$661$	5.93598			0.230883			0.115441	−	0.993314i	$-0.463172\pi$
$661$	5.93598			0.230883			0.115441	+	0.993314i	$0.463172\pi$
$662$		−	19.3590i		−	0.752407i
$663$		−	6.44496i		−	0.250302i
$664$	−31.7564			−1.23239
$665$	2.63383	+	6.62119i	0.102135	+	0.256759i
$666$	28.2323			1.09398
$667$		−	15.6476i		−	0.605879i
$668$			13.8987i			0.537755i
$669$	−10.1089			−0.390831
$670$	−23.9438	+	9.52456i	−0.925031	+	0.367966i
$671$	−36.3799			−1.40443
$672$		−	2.30324i		−	0.0888496i
$673$			40.7053i			1.56907i	0.620082	+	0.784537i	$0.287099\pi$
$673$			40.7053i			1.56907i	−0.620082	+	0.784537i	$0.712901\pi$
$674$	54.4567			2.09759
$675$	−10.5353	−	11.1470i	−0.405504	−	0.429047i
$676$	−33.5897			−1.29191
$677$			18.8761i			0.725469i	0.931893	+	0.362734i	$0.118157\pi$
$677$			18.8761i			0.725469i	−0.931893	+	0.362734i	$0.881843\pi$
$678$		−	13.7669i		−	0.528716i
$679$	6.59933			0.253259
$680$	54.0673	−	21.5073i	2.07338	−	0.824767i
$681$	−7.75638			−0.297225
$682$		−	26.1379i		−	1.00087i
$683$			19.6576i			0.752179i	0.926583	+	0.376089i	$0.122731\pi$
$683$			19.6576i			0.752179i	−0.926583	+	0.376089i	$0.877269\pi$
$684$	−10.4551			−0.399761
$685$	6.56483	+	16.5034i	0.250829	+	0.630561i
$686$	−29.6475			−1.13195
$687$		−	2.24384i		−	0.0856079i
$688$		−	10.0556i		−	0.383367i
$689$	−24.3333			−0.927025
$690$	2.80134	+	7.04231i	0.106645	+	0.268096i
$691$	−48.2451			−1.83533			−0.917665	−	0.397354i	$-0.869928\pi$
$691$	−48.2451			−1.83533			−0.917665	+	0.397354i	$0.869928\pi$
$692$		−	86.4483i		−	3.28627i
$693$		−	35.9073i		−	1.36401i
$694$	−34.9775			−1.32773
$695$	6.78926	−	2.70068i	0.257531	−	0.102443i
$696$	−14.4713			−0.548533
$697$		−	3.47293i		−	0.131546i
$698$		−	32.3152i		−	1.22315i
$699$	−6.49047			−0.245492
$700$	42.2003	+	44.6504i	1.59502	+	1.68762i
$701$	0.512889			0.0193715			0.00968577	−	0.999953i	$-0.496917\pi$
$701$	0.512889			0.0193715			0.00968577	+	0.999953i	$0.496917\pi$
$702$			15.3722i			0.580185i
$703$			4.30266i			0.162278i
$704$	39.7564			1.49838
$705$	−13.0656	+	5.19735i	−0.492080	+	0.195743i
$706$	−42.6890			−1.60662
$707$			5.45428i			0.205129i
$708$			3.54437i			0.133205i
$709$	8.84618			0.332225			0.166113	−	0.986107i	$-0.446878\pi$
$709$	8.84618			0.332225			0.166113	+	0.986107i	$0.446878\pi$
$710$	27.4231	+	68.9390i	1.02917	+	2.58724i
$711$	3.79798			0.142436
$712$		−	74.2556i		−	2.78285i
$713$			6.77889i			0.253871i
$714$	−24.0000			−0.898177
$715$	7.11222	+	17.8794i	0.265982	+	0.668653i
$716$	−19.7980			−0.739885
$717$		−	6.09806i		−	0.227736i
$718$			30.1669i			1.12582i
$719$	−7.84456			−0.292553			−0.146276	−	0.989244i	$-0.546729\pi$
$719$	−7.84456			−0.292553			−0.146276	+	0.989244i	$0.546729\pi$
$720$	−17.7772	+	7.07154i	−0.662516	+	0.263541i
$721$	−18.3333			−0.682767
$722$		−	2.41987i		−	0.0900582i
$723$			1.82643i			0.0679258i
$724$	−80.3781			−2.98723
$725$	−21.8030	+	20.6066i	−0.809742	+	0.765309i
$726$	−8.14584			−0.302321
$727$		−	2.91130i		−	0.107974i	−0.998542	−	0.0539870i	$-0.982807\pi$
$727$		−	2.91130i		−	0.107974i	0.998542	−	0.0539870i	$-0.0171930\pi$
$728$		−	29.6358i		−	1.09838i
$729$	12.6475			0.468427
$730$	−13.7115	+	5.45428i	−0.507487	+	0.201872i
$731$	18.4663			0.683001
$732$		−	18.1299i		−	0.670100i
$733$			33.7775i			1.24760i	0.781584	+	0.623800i	$0.214412\pi$
$733$			33.7775i			1.24760i	−0.781584	+	0.623800i	$0.785588\pi$
$734$	−39.7564			−1.46743
$735$	−1.40067	−	3.52116i	−0.0516646	−	0.129880i
$736$	−3.50953			−0.129363
$737$			19.7893i			0.728950i
$738$			3.93254i			0.144759i
$739$	35.8030			1.31703			0.658517	−	0.752566i	$-0.271184\pi$
$739$	35.8030			1.31703			0.658517	+	0.752566i	$0.271184\pi$
$740$	13.7115	+	34.4695i	0.504046	+	1.26712i
$741$	−1.11222			−0.0408583
$742$			90.6133i			3.32652i
$743$			5.66948i			0.207993i	0.994578	+	0.103996i	$0.0331631\pi$
$743$			5.66948i			0.207993i	−0.994578	+	0.103996i	$0.966837\pi$
$744$	6.26927			0.229843
$745$	17.5440	−	6.97880i	0.642763	−	0.255683i
$746$	12.8092			0.468978
$747$			19.1748i			0.701569i
$748$		−	92.8451i		−	3.39475i
$749$	−49.1795			−1.79698
$750$	6.12343	−	13.1774i	0.223596	−	0.481171i
$751$	−27.4679			−1.00232			−0.501159	−	0.865355i	$-0.667093\pi$
$751$	−27.4679			−1.00232			−0.501159	+	0.865355i	$0.667093\pi$
$752$			36.9457i			1.34727i
$753$		−	1.63445i		−	0.0595628i
$754$	30.0673			1.09498
$755$	−1.84456	+	0.733744i	−0.0671305	+	0.0267037i
$756$	37.6924			1.37086
$757$		−	41.6370i		−	1.51332i	−0.653806	−	0.756662i	$-0.726829\pi$
$757$		−	41.6370i		−	1.51332i	0.653806	−	0.756662i	$-0.273171\pi$
$758$			35.1736i			1.27756i
$759$	5.82040			0.211267
$760$	−3.71155	−	9.33047i	−0.134632	−	0.338452i
$761$	−9.46967			−0.343275			−0.171638	−	0.985160i	$-0.554906\pi$
$761$	−9.46967			−0.343275			−0.171638	+	0.985160i	$0.554906\pi$
$762$			7.89526i			0.286015i
$763$			37.3219i			1.35114i
$764$	20.3109			0.734822
$765$	−12.9863	−	32.6463i	−0.469521	−	1.18033i
$766$	−1.09765			−0.0396597
$767$		−	3.54437i		−	0.127980i
$768$			16.3146i			0.588703i
$769$	−1.90858			−0.0688253			−0.0344127	−	0.999408i	$-0.510956\pi$
$769$	−1.90858			−0.0688253			−0.0344127	+	0.999408i	$0.510956\pi$
$770$	66.5801	−	26.4848i	2.39938	−	0.954444i
$771$	9.28510			0.334395
$772$			7.98476i			0.287378i
$773$			28.4007i			1.02150i	0.859729	+	0.510751i	$0.170633\pi$
$773$			28.4007i			1.02150i	−0.859729	+	0.510751i	$0.829367\pi$
$774$	−20.9102			−0.751602
$775$	9.44551	−	8.92721i	0.339293	−	0.320675i
$776$	−9.29966			−0.333838
$777$		−	7.36420i		−	0.264189i
$778$			39.0941i			1.40159i
$779$	−0.599328			−0.0214732
$780$	−8.91020	+	3.54437i	−0.319036	+	0.126909i
$781$	56.9775			2.03881
$782$			36.5696i			1.30773i
$783$			18.4053i			0.657753i
$784$	−9.95678			−0.355599
$785$	−3.42309	−	8.60532i	−0.122175	−	0.307137i
$786$	17.6475			0.629466
$787$			15.6708i			0.558605i	0.960203	+	0.279303i	$0.0901033\pi$
$787$			15.6708i			0.558605i	−0.960203	+	0.279303i	$0.909897\pi$
$788$		−	40.2225i		−	1.43287i
$789$	0.640931			0.0228178
$790$	2.80134	+	7.04231i	0.0996673	+	0.250554i
$791$	33.7564			1.20024
$792$			50.6000i			1.79799i
$793$			18.1299i			0.643811i
$794$	79.2659			2.81304
$795$	13.1122	−	5.21588i	0.465042	−	0.184988i
$796$	−10.5353			−0.373414
$797$		−	36.9225i		−	1.30786i	−0.756554	−	0.653932i	$-0.773118\pi$
$797$		−	36.9225i		−	1.30786i	0.756554	−	0.653932i	$-0.226882\pi$
$798$			4.14172i			0.146615i
$799$	−67.8478			−2.40028
$800$	4.62175	+	4.89008i	0.163403	+	0.172890i
$801$	−44.8362			−1.58421
$802$		−	29.2476i		−	1.03277i
$803$			11.3325i			0.399914i
$804$	−9.86201			−0.347806
$805$	−17.2677	+	6.86886i	−0.608605	+	0.242095i
$806$	−13.0258			−0.458813
$807$			11.8742i			0.417993i
$808$		−	7.68608i		−	0.270396i
$809$	−43.0465			−1.51343			−0.756716	−	0.653743i	$-0.773198\pi$
$809$	−43.0465			−1.51343			−0.756716	+	0.653743i	$0.773198\pi$
$810$	12.9742	+	32.6160i	0.455868	+	1.14601i
$811$	32.2469			1.13234			0.566170	−	0.824288i	$-0.308425\pi$
$811$	32.2469			1.13234			0.566170	+	0.824288i	$0.308425\pi$
$812$		−	73.7245i		−	2.58722i
$813$			2.19475i			0.0769731i
$814$	43.2659			1.51647
$815$	−20.4247	−	51.3458i	−0.715446	−	1.79856i
$816$	9.82040			0.343783
$817$		−	3.18676i		−	0.111491i
$818$		−	46.3033i		−	1.61896i
$819$	−17.8944			−0.625280
$820$	−4.80134	+	1.90991i	−0.167670	+	0.0666971i
$821$	5.18121			0.180826			0.0904128	−	0.995904i	$-0.471181\pi$
$821$	5.18121			0.180826			0.0904128	+	0.995904i	$0.471181\pi$
$822$			10.3233i			0.360065i
$823$			25.8517i			0.901133i	0.892743	+	0.450567i	$0.148778\pi$
$823$			25.8517i			0.901133i	−0.892743	+	0.450567i	$0.851222\pi$
$824$	25.8350			0.900004
$825$	−7.66497	−	8.10998i	−0.266860	−	0.282353i
$826$	−13.1987			−0.459240
$827$		−	9.97816i		−	0.346974i	−0.984836	−	0.173487i	$-0.944496\pi$
$827$		−	9.97816i		−	0.346974i	0.984836	−	0.173487i	$-0.0555035\pi$
$828$		−	27.2663i		−	0.947568i
$829$	−21.9808			−0.763425			−0.381713	−	0.924281i	$-0.624666\pi$
$829$	−21.9808			−0.763425			−0.381713	+	0.924281i	$0.624666\pi$
$830$	−35.5544	+	14.1431i	−1.23411	+	0.490914i
$831$	−5.38149			−0.186682
$832$		−	19.8126i		−	0.686877i
$833$		−	18.2848i		−	0.633531i
$834$	4.24685			0.147056
$835$	2.97920	+	7.48942i	0.103099	+	0.259182i
$836$	−16.0224			−0.554147
$837$		−	7.97359i		−	0.275607i
$838$			19.4675i			0.672492i
$839$	16.1089			0.556140			0.278070	−	0.960561i	$-0.410305\pi$
$839$	16.1089			0.556140			0.278070	+	0.960561i	$0.410305\pi$
$840$	6.35248	+	15.9695i	0.219181	+	0.551001i
$841$	7.00000			0.241379
$842$			71.0451i			2.44838i
$843$		−	0.321887i		−	0.0110864i
$844$	60.6666			2.08823
$845$	−18.1001	+	7.20001i	−0.622664	+	0.247688i
$846$	76.8270			2.64137
$847$		−	19.9735i		−	0.686298i
$848$		−	37.0775i		−	1.27324i
$849$	−2.91020			−0.0998779
$850$	50.9550	−	48.1590i	1.74774	−	1.65184i
$851$	−11.2211			−0.384653
$852$			28.3947i			0.972785i
$853$		−	44.9615i		−	1.53945i	−0.638373	−	0.769727i	$-0.720392\pi$
$853$		−	44.9615i		−	1.53945i	0.638373	−	0.769727i	$-0.279608\pi$
$854$	67.5128			2.31024
$855$	−5.63383	+	2.24107i	−0.192673	+	0.0766429i
$856$	69.3029			2.36872
$857$		−	46.2431i		−	1.57963i	−0.613343	−	0.789817i	$-0.710176\pi$
$857$		−	46.2431i		−	1.57963i	0.613343	−	0.789817i	$-0.289824\pi$
$858$			11.1840i			0.381816i
$859$	10.7772			0.367713			0.183856	−	0.982953i	$-0.441142\pi$
$859$	10.7772			0.367713			0.183856	+	0.982953i	$0.441142\pi$
$860$	−10.1554	−	25.5298i	−0.346298	−	0.870559i
$861$	1.02578			0.0349584
$862$			77.5443i			2.64117i
$863$		−	22.7966i		−	0.776007i	−0.921658	−	0.388003i	$-0.873165\pi$
$863$		−	22.7966i		−	0.776007i	0.921658	−	0.388003i	$-0.126835\pi$
$864$	4.12804			0.140439
$865$	−18.5303	−	46.5835i	−0.630050	−	1.58389i
$866$	−1.16839			−0.0397034
$867$			8.90400i			0.302396i
$868$			31.9390i			1.08408i
$869$	5.82040			0.197444
$870$	−16.2020	+	6.44496i	−0.549300	+	0.218505i
$871$	9.86201			0.334161
$872$		−	52.5934i		−	1.78104i
$873$			5.61523i			0.190047i
$874$	6.31087			0.213468
$875$	32.3109	+	15.0146i	1.09231	+	0.507585i
$876$	−5.64752			−0.190812
$877$		−	4.94644i		−	0.167029i	−0.996507	−	0.0835146i	$-0.973385\pi$
$877$		−	4.94644i		−	0.167029i	0.996507	−	0.0835146i	$-0.0266145\pi$
$878$		−	66.2054i		−	2.23432i
$879$	−1.86201			−0.0628039
$880$	−27.2435	+	10.8371i	−0.918378	+	0.365319i
$881$	2.53033			0.0852490			0.0426245	−	0.999091i	$-0.486428\pi$
$881$	2.53033			0.0852490			0.0426245	+	0.999091i	$0.486428\pi$
$882$			20.7047i			0.697163i
$883$		−	29.7430i		−	1.00093i	−0.865757	−	0.500465i	$-0.833162\pi$
$883$		−	29.7430i		−	1.00093i	0.865757	−	0.500465i	$-0.166838\pi$
$884$	−46.2693			−1.55620
$885$	0.759740	+	1.90991i	0.0255384	+	0.0642011i
$886$	−56.5801			−1.90085
$887$			45.5450i			1.52925i	0.644474	+	0.764626i	$0.277076\pi$
$887$			45.5450i			1.52925i	−0.644474	+	0.764626i	$0.722924\pi$
$888$			10.3775i			0.348246i
$889$	−19.3591			−0.649282
$890$	−33.0706	−	83.1364i	−1.10853	−	2.78674i
$891$	26.9568			0.903086
$892$			72.5729i			2.42992i
$893$			11.7086i			0.391813i
$894$	10.9742			0.367033
$895$	−10.6683	+	4.24373i	−0.356603	+	0.141852i
$896$	−65.2019			−2.17824
$897$		−	2.90059i		−	0.0968480i
$898$			55.9828i			1.86817i
$899$	−15.5960			−0.520155
$900$	−37.9920	+	35.9073i	−1.26640	+	1.19691i
$901$	68.0897			2.26840
$902$			6.02662i			0.200664i
$903$			5.45428i			0.181507i
$904$	−47.5689			−1.58212
$905$	−43.3125	+	17.2292i	−1.43976	+	0.572717i
$906$	−1.15382			−0.0383331
$907$			33.2034i			1.10250i	0.834340	+	0.551250i	$0.185849\pi$
$907$			33.2034i			1.10250i	−0.834340	+	0.551250i	$0.814151\pi$
$908$			55.6841i			1.84794i
$909$	−4.64093			−0.153930
$910$	−13.1987	−	33.1802i	−0.437531	−	1.09991i
$911$	55.7788			1.84803			0.924017	−	0.382351i	$-0.124886\pi$
$911$	55.7788			1.84803			0.924017	+	0.382351i	$0.124886\pi$
$912$		−	1.69472i		−	0.0561179i
$913$			29.3853i			0.972513i
$914$	51.4231			1.70092
$915$	−3.88617	−	9.76945i	−0.128473	−	0.322968i
$916$	−16.1089			−0.532252
$917$			43.2715i			1.42895i
$918$		−	43.0146i		−	1.41969i
$919$	28.5769			0.942665			0.471333	−	0.881956i	$-0.343773\pi$
$919$	28.5769			0.942665			0.471333	+	0.881956i	$0.343773\pi$
$920$	24.3333	−	9.67948i	0.802245	−	0.319123i
$921$	−8.91020			−0.293601
$922$		−	76.4159i		−	2.51662i
$923$		−	28.3947i		−	0.934622i
$924$	27.4231			0.902153
$925$	14.7772	+	15.6351i	0.485871	+	0.514080i
$926$	37.7788			1.24149
$927$		−	15.5994i		−	0.512352i
$928$		−	8.07426i		−	0.265051i
$929$	54.4937			1.78788			0.893940	−	0.448186i	$-0.147930\pi$
$929$	54.4937			1.78788			0.893940	+	0.448186i	$0.147930\pi$
$930$	7.01906	−	2.79209i	0.230164	−	0.0915564i
$931$	−3.15544			−0.103415
$932$			46.5960i			1.52630i
$933$			2.23180i			0.0730659i
$934$	−72.1761			−2.36167
$935$	−19.9015	−	50.0304i	−0.650848	−	1.63617i
$936$	25.2165			0.824226
$937$		−	37.1484i		−	1.21359i	−0.794860	−	0.606793i	$-0.792456\pi$
$937$		−	37.1484i		−	1.21359i	0.794860	−	0.606793i	$-0.207544\pi$
$938$		−	36.7245i		−	1.19910i
$939$	0.493704			0.0161114
$940$	37.3125	+	93.8000i	1.21700	+	3.05942i
$941$	32.3973			1.05612			0.528061	−	0.849206i	$-0.322919\pi$
$941$	32.3973			1.05612			0.528061	+	0.849206i	$0.322919\pi$
$942$		−	5.38284i		−	0.175382i
$943$		−	1.56301i		−	0.0508986i
$944$	5.40067			0.175777
$945$	20.3109	−	8.07941i	0.660713	−	0.262823i
$946$	−32.0448			−1.04187
$947$			35.4662i			1.15250i	0.817275	+	0.576249i	$0.195484\pi$
$947$			35.4662i			1.15250i	−0.817275	+	0.576249i	$0.804516\pi$
$948$			2.90059i			0.0942069i
$949$	5.64752			0.183326
$950$	−8.31087	−	8.79339i	−0.269640	−	0.285295i
$951$	−14.3557			−0.465516
$952$			82.9272i			2.68769i
$953$			14.3411i			0.464553i	0.972650	+	0.232277i	$0.0746175\pi$
$953$			14.3411i			0.464553i	−0.972650	+	0.232277i	$0.925383\pi$
$954$	−77.1009			−2.49623
$955$	10.9447	−	4.35367i	0.354162	−	0.140881i
$956$	−43.7788			−1.41591
$957$			13.3908i			0.432864i
$958$			10.9749i			0.354581i
$959$	−25.3125			−0.817383
$960$	4.24685	+	10.6762i	0.137067	+	0.344572i
$961$	−24.2435			−0.782048
$962$		−	21.5615i		−	0.695172i
$963$		−	41.8458i		−	1.34846i
$964$	13.1122			0.422316
$965$	1.71155	+	4.30266i	0.0550966	+	0.138508i
$966$	−10.8013			−0.347528
$967$		−	27.9351i		−	0.898331i	−0.893449	−	0.449165i	$-0.851721\pi$
$967$		−	27.9351i		−	0.898331i	0.893449	−	0.449165i	$-0.148279\pi$
$968$			28.1463i			0.904657i
$969$	3.11222			0.0999788
$970$	−10.4119	+	4.14172i	−0.334305	+	0.132983i
$971$	−42.5993			−1.36708			−0.683539	−	0.729914i	$-0.739560\pi$
$971$	−42.5993			−1.36708			−0.683539	+	0.729914i	$0.739560\pi$
$972$			48.9173i			1.56902i
$973$			10.4132i			0.333833i
$974$	94.9920			3.04374
$975$	−4.04160	+	3.81983i	−0.129435	+	0.122332i
$976$	−27.6251			−0.884258
$977$			39.5597i			1.26563i	0.774304	+	0.632813i	$0.218100\pi$
$977$			39.5597i			1.26563i	−0.774304	+	0.632813i	$0.781900\pi$
$978$		−	32.1180i		−	1.02702i
$979$	−68.7114			−2.19603
$980$	−25.2789	+	10.0556i	−0.807504	+	0.321215i
$981$	−31.7564			−1.01390
$982$		−	94.1112i		−	3.00321i
$983$			39.7689i			1.26843i	0.773157	+	0.634215i	$0.218677\pi$
$983$			39.7689i			1.26843i	−0.773157	+	0.634215i	$0.781323\pi$
$984$	−1.44551			−0.0460811
$985$	−8.62175	−	21.6742i	−0.274712	−	0.690599i
$986$	−84.1345			−2.67939
$987$		−	20.0398i		−	0.637874i
$988$			7.98476i			0.254029i
$989$	8.31087			0.264270
$990$	22.5353	+	56.6516i	0.716219	+	1.80051i
$991$	55.2019			1.75355			0.876773	−	0.480905i	$-0.159692\pi$
$991$	55.2019			1.75355			0.876773	+	0.480905i	$0.159692\pi$
$992$			3.49794i			0.111060i
$993$		−	4.29664i		−	0.136350i
$994$	−105.737			−3.35378
$995$	−5.67705	+	2.25826i	−0.179974	+	0.0715916i
$996$	−14.6442			−0.464018
$997$		−	11.6543i		−	0.369097i	−0.982823	−	0.184548i	$-0.940918\pi$
$997$		−	11.6543i		−	0.369097i	0.982823	−	0.184548i	$-0.0590823\pi$
$998$			11.4517i			0.362496i
$999$	13.1987			0.417587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.b.b.39.1	✓	6
3.2	odd	2		855.2.c.d.514.6		6
4.3	odd	2		1520.2.d.h.609.4		6
5.2	odd	4		475.2.a.j.1.6		6
5.3	odd	4		475.2.a.j.1.1		6
5.4	even	2	inner	95.2.b.b.39.6	yes	6
15.2	even	4		4275.2.a.br.1.1		6
15.8	even	4		4275.2.a.br.1.6		6
15.14	odd	2		855.2.c.d.514.1		6
19.18	odd	2		1805.2.b.e.1084.6		6
20.3	even	4		7600.2.a.ck.1.3		6
20.7	even	4		7600.2.a.ck.1.4		6
20.19	odd	2		1520.2.d.h.609.3		6
95.18	even	4		9025.2.a.bx.1.6		6
95.37	even	4		9025.2.a.bx.1.1		6
95.94	odd	2		1805.2.b.e.1084.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.b.b.39.1	✓	6	1.1	even	1	trivial
95.2.b.b.39.6	yes	6	5.4	even	2	inner
475.2.a.j.1.1		6	5.3	odd	4
475.2.a.j.1.6		6	5.2	odd	4
855.2.c.d.514.1		6	15.14	odd	2
855.2.c.d.514.6		6	3.2	odd	2
1520.2.d.h.609.3		6	20.19	odd	2
1520.2.d.h.609.4		6	4.3	odd	2
1805.2.b.e.1084.1		6	95.94	odd	2
1805.2.b.e.1084.6		6	19.18	odd	2
4275.2.a.br.1.1		6	15.2	even	4
4275.2.a.br.1.6		6	15.8	even	4
7600.2.a.ck.1.3		6	20.3	even	4
7600.2.a.ck.1.4		6	20.7	even	4
9025.2.a.bx.1.1		6	95.37	even	4
9025.2.a.bx.1.6		6	95.18	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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.41987i q^{2} -0.537080i q^{3} -3.85577 q^{4} +(-2.07772 + 0.826491i) q^{5} -1.29966 q^{6} -3.18676i q^{7} +4.49073i q^{8} +2.71155 q^{9} +O(q^{10})\)	\(q-2.41987i q^{2} -0.537080i q^{3} -3.85577 q^{4} +(-2.07772 + 0.826491i) q^{5} -1.29966 q^{6} -3.18676i q^{7} +4.49073i q^{8} +2.71155 q^{9} +(2.00000 + 5.02781i) q^{10} +4.15544 q^{11} +2.07086i q^{12} -2.07086i q^{13} -7.71155 q^{14} +(0.443892 + 1.11590i) q^{15} +3.15544 q^{16} +5.79470i q^{17} -6.56159i q^{18} +1.00000 q^{19} +(8.01121 - 3.18676i) q^{20} -1.71155 q^{21} -10.0556i q^{22} +2.60794i q^{23} +2.41188 q^{24} +(3.63383 - 3.43443i) q^{25} -5.01121 q^{26} -3.06756i q^{27} +12.2874i q^{28} -6.00000 q^{29} +(2.70034 - 1.07416i) q^{30} +2.59933 q^{31} +1.34571i q^{32} -2.23180i q^{33} +14.0224 q^{34} +(2.63383 + 6.62119i) q^{35} -10.4551 q^{36} +4.30266i q^{37} -2.41987i q^{38} -1.11222 q^{39} +(-3.71155 - 9.33047i) q^{40} -0.599328 q^{41} +4.14172i q^{42} -3.18676i q^{43} -16.0224 q^{44} +(-5.63383 + 2.24107i) q^{45} +6.31087 q^{46} +11.7086i q^{47} -1.69472i q^{48} -3.15544 q^{49} +(-8.31087 - 8.79339i) q^{50} +3.11222 q^{51} +7.98476i q^{52} -11.7503i q^{53} -7.42309 q^{54} +(-8.63383 + 3.43443i) q^{55} +14.3109 q^{56} -0.537080i q^{57} +14.5192i q^{58} +1.71155 q^{59} +(-1.71155 - 4.30266i) q^{60} -8.75476 q^{61} -6.29004i q^{62} -8.64104i q^{63} +9.56732 q^{64} +(1.71155 + 4.30266i) q^{65} -5.40067 q^{66} +4.76228i q^{67} -22.3430i q^{68} +1.40067 q^{69} +(16.0224 - 6.37352i) q^{70} +13.7115 q^{71} +12.1768i q^{72} +2.72714i q^{73} +10.4119 q^{74} +(-1.84456 - 1.95166i) q^{75} -3.85577 q^{76} -13.2424i q^{77} +2.69142i q^{78} +1.40067 q^{79} +(-6.55611 + 2.60794i) q^{80} +6.48711 q^{81} +1.45030i q^{82} +7.07154i q^{83} +6.59933 q^{84} +(-4.78926 - 12.0398i) q^{85} -7.71155 q^{86} +3.22248i q^{87} +18.6609i q^{88} -16.5353 q^{89} +(5.42309 + 13.6331i) q^{90} -6.59933 q^{91} -10.0556i q^{92} -1.39605i q^{93} +28.3333 q^{94} +(-2.07772 + 0.826491i) q^{95} +0.722754 q^{96} +2.07086i q^{97} +7.63575i q^{98} +11.2677 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 8 q^{4} - q^{5} - 14 q^{9}+O(q^{10}) \) 6 * q - 8 * q^4 - q^5 - 14 * q^9	\( 6 q - 8 q^{4} - q^{5} - 14 q^{9} + 12 q^{10} + 2 q^{11} - 16 q^{14} + 10 q^{15} - 4 q^{16} + 6 q^{19} + 10 q^{20} + 20 q^{21} - 8 q^{24} + 3 q^{25} + 8 q^{26} - 36 q^{29} + 24 q^{30} + 8 q^{34} - 3 q^{35} - 32 q^{36} + 8 q^{39} + 8 q^{40} + 12 q^{41} - 20 q^{44} - 15 q^{45} - 8 q^{46} + 4 q^{49} - 4 q^{50} + 4 q^{51} + 16 q^{54} - 33 q^{55} + 40 q^{56} - 20 q^{59} + 20 q^{60} - 14 q^{61} + 12 q^{64} - 20 q^{65} - 48 q^{66} + 24 q^{69} + 20 q^{70} + 52 q^{71} + 40 q^{74} - 34 q^{75} - 8 q^{76} + 24 q^{79} - 32 q^{80} + 38 q^{81} + 24 q^{84} + 13 q^{85} - 16 q^{86} - 24 q^{89} - 28 q^{90} - 24 q^{91} + 48 q^{94} - q^{95} - 64 q^{96} + 30 q^{99}+O(q^{100}) \) 6 * q - 8 * q^4 - q^5 - 14 * q^9 + 12 * q^10 + 2 * q^11 - 16 * q^14 + 10 * q^15 - 4 * q^16 + 6 * q^19 + 10 * q^20 + 20 * q^21 - 8 * q^24 + 3 * q^25 + 8 * q^26 - 36 * q^29 + 24 * q^30 + 8 * q^34 - 3 * q^35 - 32 * q^36 + 8 * q^39 + 8 * q^40 + 12 * q^41 - 20 * q^44 - 15 * q^45 - 8 * q^46 + 4 * q^49 - 4 * q^50 + 4 * q^51 + 16 * q^54 - 33 * q^55 + 40 * q^56 - 20 * q^59 + 20 * q^60 - 14 * q^61 + 12 * q^64 - 20 * q^65 - 48 * q^66 + 24 * q^69 + 20 * q^70 + 52 * q^71 + 40 * q^74 - 34 * q^75 - 8 * q^76 + 24 * q^79 - 32 * q^80 + 38 * q^81 + 24 * q^84 + 13 * q^85 - 16 * q^86 - 24 * q^89 - 28 * q^90 - 24 * q^91 + 48 * q^94 - q^95 - 64 * q^96 + 30 * q^99

Introduction

L-functions

Modular forms

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Database

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