LMFDB - Embedded newform 95.2.b.b.39.4

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			39.4
Root			$0.285442i$ of defining polynomial
Character	$\chi$	$=$	95.39
Dual form			95.2.b.b.39.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.906968i q^{2} +3.21789i q^{3} +1.17741 q^{4} +(-0.370556 - 2.20515i) q^{5} -2.91852 q^{6} -2.59637i q^{7} +2.88181i q^{8} -7.35482 q^{9} +O(q^{10})$	\(q+0.906968i q^{2} +3.21789i q^{3} +1.17741 q^{4} +(-0.370556 - 2.20515i) q^{5} -2.91852 q^{6} -2.59637i q^{7} +2.88181i q^{8} -7.35482 q^{9} +(2.00000 - 0.336083i) q^{10} +0.741113 q^{11} +3.78878i q^{12} -3.78878i q^{13} +2.35482 q^{14} +(7.09593 - 1.19241i) q^{15} -0.258887 q^{16} +3.16725i q^{17} -6.67058i q^{18} +1.00000 q^{19} +(-0.436297 - 2.59637i) q^{20} +8.35482 q^{21} +0.672165i q^{22} +0.570885i q^{23} -9.27334 q^{24} +(-4.72538 + 1.63427i) q^{25} +3.43630 q^{26} -14.0133i q^{27} -3.05699i q^{28} -6.00000 q^{29} +(1.08148 + 6.43578i) q^{30} +5.83705 q^{31} +5.52881i q^{32} +2.38482i q^{33} -2.87259 q^{34} +(-5.72538 + 0.962100i) q^{35} -8.65964 q^{36} +1.40396i q^{37} +0.906968i q^{38} +12.1919 q^{39} +(6.35482 - 1.06787i) q^{40} -3.83705 q^{41} +7.57755i q^{42} -2.59637i q^{43} +0.872594 q^{44} +(2.72538 + 16.2185i) q^{45} -0.517774 q^{46} -5.08247i q^{47} -0.833070i q^{48} +0.258887 q^{49} +(-1.48223 - 4.28576i) q^{50} -10.1919 q^{51} -4.46094i q^{52} -0.160905i q^{53} +12.7096 q^{54} +(-0.274624 - 1.63427i) q^{55} +7.48223 q^{56} +3.21789i q^{57} -5.44181i q^{58} -8.35482 q^{59} +(8.35482 - 1.40396i) q^{60} -8.57816 q^{61} +5.29401i q^{62} +19.0958i q^{63} -5.53223 q^{64} +(-8.35482 + 1.40396i) q^{65} -2.16295 q^{66} +14.8464i q^{67} +3.72915i q^{68} -1.83705 q^{69} +(-0.872594 - 5.19273i) q^{70} +3.64518 q^{71} -21.1952i q^{72} -10.8461i q^{73} -1.27334 q^{74} +(-5.25889 - 15.2057i) q^{75} +1.17741 q^{76} -1.92420i q^{77} +11.0576i q^{78} -1.83705 q^{79} +(0.0959323 + 0.570885i) q^{80} +23.0289 q^{81} -3.48008i q^{82} -4.19876i q^{83} +9.83705 q^{84} +(6.98426 - 1.17365i) q^{85} +2.35482 q^{86} -19.3073i q^{87} +2.13574i q^{88} +16.9015 q^{89} +(-14.7096 + 2.47183i) q^{90} -9.83705 q^{91} +0.672165i q^{92} +18.7830i q^{93} +4.60963 q^{94} +(-0.370556 - 2.20515i) q^{95} -17.7911 q^{96} +3.78878i q^{97} +0.234802i q^{98} -5.45075 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			0.906968i			0.641323i	0.947194	+	0.320661i	$0.103905\pi$
$2$			0.906968i			0.641323i	−0.947194	+	0.320661i	$0.896095\pi$
$3$			3.21789i			1.85785i	0.370268	+	0.928925i	$0.379266\pi$
$3$			3.21789i			1.85785i	−0.370268	+	0.928925i	$0.620734\pi$
$4$	1.17741			0.588705
$5$	−0.370556	−	2.20515i	−0.165718	−	0.986173i
$5$	−0.370556	−	2.20515i	−0.165718	−	0.986173i
$6$	−2.91852			−1.19148
$7$		−	2.59637i		−	0.981334i	−0.871347	−	0.490667i	$-0.836753\pi$
$7$		−	2.59637i		−	0.981334i	0.871347	−	0.490667i	$-0.163247\pi$
$8$			2.88181i			1.01887i
$9$	−7.35482			−2.45161
$10$	2.00000	−	0.336083i	0.632456	−	0.106279i
$11$	0.741113			0.223454			0.111727	−	0.993739i	$-0.464362\pi$
$11$	0.741113			0.223454			0.111727	+	0.993739i	$0.464362\pi$
$12$			3.78878i			1.09373i
$13$		−	3.78878i		−	1.05082i	−0.850850	−	0.525409i	$-0.823912\pi$
$13$		−	3.78878i		−	1.05082i	0.850850	−	0.525409i	$-0.176088\pi$
$14$	2.35482			0.629352
$15$	7.09593	−	1.19241i	1.83216	−	0.307879i
$16$	−0.258887			−0.0647218
$17$			3.16725i			0.768171i	0.923298	+	0.384086i	$0.125483\pi$
$17$			3.16725i			0.768171i	−0.923298	+	0.384086i	$0.874517\pi$
$18$		−	6.67058i		−	1.57227i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−0.436297	−	2.59637i	−0.0975589	−	0.580565i
$21$	8.35482			1.82317
$22$			0.672165i			0.143306i
$23$			0.570885i			0.119038i	0.998227	+	0.0595189i	$0.0189566\pi$
$23$			0.570885i			0.119038i	−0.998227	+	0.0595189i	$0.981043\pi$
$24$	−9.27334			−1.89291
$25$	−4.72538	+	1.63427i	−0.945075	+	0.326853i
$26$	3.43630			0.673913
$27$		−	14.0133i		−	2.69687i
$28$		−	3.05699i		−	0.577716i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	1.08148	+	6.43578i	0.197450	+	1.17501i
$31$	5.83705			1.04836			0.524182	−	0.851606i	$-0.324371\pi$
$31$	5.83705			1.04836			0.524182	+	0.851606i	$0.324371\pi$
$32$			5.52881i			0.977365i
$33$			2.38482i			0.415144i
$34$	−2.87259			−0.492646
$35$	−5.72538	+	0.962100i	−0.967765	+	0.162625i
$36$	−8.65964			−1.44327
$37$			1.40396i			0.230809i	0.993319	+	0.115404i	$0.0368164\pi$
$37$			1.40396i			0.230809i	−0.993319	+	0.115404i	$0.963184\pi$
$38$			0.906968i			0.147130i
$39$	12.1919			1.95226
$40$	6.35482	−	1.06787i	1.00479	−	0.168845i
$41$	−3.83705			−0.599246			−0.299623	−	0.954058i	$-0.596861\pi$
$41$	−3.83705			−0.599246			−0.299623	+	0.954058i	$0.596861\pi$
$42$			7.57755i			1.16924i
$43$		−	2.59637i		−	0.395942i	−0.980208	−	0.197971i	$-0.936565\pi$
$43$		−	2.59637i		−	0.395942i	0.980208	−	0.197971i	$-0.0634352\pi$
$44$	0.872594			0.131548
$45$	2.72538	+	16.2185i	0.406275	+	2.41771i
$46$	−0.517774			−0.0763416
$47$		−	5.08247i		−	0.741354i	−0.928762	−	0.370677i	$-0.879126\pi$
$47$		−	5.08247i		−	0.741354i	0.928762	−	0.370677i	$-0.120874\pi$
$48$		−	0.833070i		−	0.120243i
$49$	0.258887			0.0369839
$50$	−1.48223	−	4.28576i	−0.209618	−	0.606098i
$51$	−10.1919			−1.42715
$52$		−	4.46094i		−	0.618621i
$53$		−	0.160905i		−	0.0221020i	−0.999939	−	0.0110510i	$-0.996482\pi$
$53$		−	0.160905i		−	0.0221020i	0.999939	−	0.0110510i	$-0.00351771\pi$
$54$	12.7096			1.72956
$55$	−0.274624	−	1.63427i	−0.0370303	−	0.220364i
$56$	7.48223			0.999854
$57$			3.21789i			0.426220i
$58$		−	5.44181i		−	0.714544i
$59$	−8.35482			−1.08770			−0.543852	−	0.839181i	$-0.683035\pi$
$59$	−8.35482			−1.08770			−0.543852	+	0.839181i	$0.683035\pi$
$60$	8.35482	−	1.40396i	1.07860	−	0.181250i
$61$	−8.57816			−1.09832			−0.549160	−	0.835717i	$-0.685052\pi$
$61$	−8.57816			−1.09832			−0.549160	+	0.835717i	$0.685052\pi$
$62$			5.29401i			0.672340i
$63$			19.0958i			2.40584i
$64$	−5.53223			−0.691529
$65$	−8.35482	+	1.40396i	−1.03629	+	0.174139i
$66$	−2.16295			−0.266241
$67$			14.8464i			1.81378i	0.421371	+	0.906888i	$0.361549\pi$
$67$			14.8464i			1.81378i	−0.421371	+	0.906888i	$0.638451\pi$
$68$			3.72915i			0.452226i
$69$	−1.83705			−0.221154
$70$	−0.872594	−	5.19273i	−0.104295	−	0.620650i
$71$	3.64518			0.432603			0.216302	−	0.976327i	$-0.430601\pi$
$71$	3.64518			0.432603			0.216302	+	0.976327i	$0.430601\pi$
$72$		−	21.1952i		−	2.49788i
$73$		−	10.8461i		−	1.26944i	−0.772743	−	0.634719i	$-0.781116\pi$
$73$		−	10.8461i		−	1.26944i	0.772743	−	0.634719i	$-0.218884\pi$
$74$	−1.27334			−0.148023
$75$	−5.25889	−	15.2057i	−0.607244	−	1.75581i
$76$	1.17741			0.135058
$77$		−	1.92420i		−	0.219283i
$78$			11.0576i			1.25203i
$79$	−1.83705			−0.206684			−0.103342	−	0.994646i	$-0.532954\pi$
$79$	−1.83705			−0.206684			−0.103342	+	0.994646i	$0.532954\pi$
$80$	0.0959323	+	0.570885i	0.0107256	+	0.0638269i
$81$	23.0289			2.55877
$82$		−	3.48008i		−	0.384310i
$83$		−	4.19876i		−	0.460873i	−0.973087	−	0.230437i	$-0.925985\pi$
$83$		−	4.19876i		−	0.460873i	0.973087	−	0.230437i	$-0.0740154\pi$
$84$	9.83705			1.07331
$85$	6.98426	−	1.17365i	0.757550	−	0.127300i
$86$	2.35482			0.253927
$87$		−	19.3073i		−	2.06996i
$88$			2.13574i			0.227671i
$89$	16.9015			1.79156			0.895778	−	0.444502i	$-0.146619\pi$
$89$	16.9015			1.79156			0.895778	+	0.444502i	$0.146619\pi$
$90$	−14.7096	+	2.47183i	−1.55053	+	0.260554i
$91$	−9.83705			−1.03120
$92$			0.672165i			0.0700781i
$93$			18.7830i			1.94770i
$94$	4.60963			0.475447
$95$	−0.370556	−	2.20515i	−0.0380183	−	0.226244i
$96$	−17.7911			−1.81580
$97$			3.78878i			0.384692i	0.981327	+	0.192346i	$0.0616096\pi$
$97$			3.78878i			0.384692i	−0.981327	+	0.192346i	$0.938390\pi$
$98$			0.234802i			0.0237186i
$99$	−5.45075			−0.547821
$100$	−5.56370	+	1.92420i	−0.556370	+	0.192420i
$101$	8.35482			0.831336			0.415668	−	0.909517i	$-0.363548\pi$
$101$	8.35482			0.831336			0.415668	+	0.909517i	$0.363548\pi$
$102$		−	9.24369i		−	0.915262i
$103$			2.07612i			0.204566i	0.994755	+	0.102283i	$0.0326148\pi$
$103$			2.07612i			0.204566i	−0.994755	+	0.102283i	$0.967385\pi$
$104$	10.9185			1.07065
$105$	−3.09593	−	18.4236i	−0.302132	−	1.79796i
$106$	0.145935			0.0141745
$107$			5.70399i			0.551426i	0.961240	+	0.275713i	$0.0889139\pi$
$107$			5.70399i			0.551426i	−0.961240	+	0.275713i	$0.911086\pi$
$108$		−	16.4994i		−	1.58766i
$109$	−1.64518			−0.157580			−0.0787899	−	0.996891i	$-0.525106\pi$
$109$	−1.64518			−0.157580			−0.0787899	+	0.996891i	$0.525106\pi$
$110$	1.48223	−	0.249075i	0.141325	−	0.0237484i
$111$	−4.51777			−0.428808
$112$			0.672165i			0.0635137i
$113$		−	3.89006i		−	0.365946i	−0.983118	−	0.182973i	$-0.941428\pi$
$113$		−	3.89006i		−	0.365946i	0.983118	−	0.182973i	$-0.0585720\pi$
$114$	−2.91852			−0.273345
$115$	1.25889	−	0.211545i	0.117392	−	0.0197267i
$116$	−7.06446			−0.655918
$117$			27.8658i			2.57619i
$118$		−	7.57755i		−	0.697570i
$119$	8.22334			0.753832
$120$	3.43630	+	20.4491i	0.313690	+	1.86674i
$121$	−10.4508			−0.950068
$122$		−	7.78011i		−	0.704378i
$123$		−	12.3472i		−	1.11331i
$124$	6.87259			0.617177
$125$	5.35482	+	9.81458i	0.478950	+	0.877842i
$126$	−17.3193			−1.54292
$127$			14.4233i			1.27986i	0.768432	+	0.639931i	$0.221037\pi$
$127$			14.4233i			1.27986i	−0.768432	+	0.639931i	$0.778963\pi$
$128$			6.04007i			0.533872i
$129$	8.35482			0.735601
$130$	−1.27334	−	7.57755i	−0.111679	−	0.664595i
$131$	9.96853			0.870954			0.435477	−	0.900200i	$-0.356580\pi$
$131$	9.96853			0.870954			0.435477	+	0.900200i	$0.356580\pi$
$132$			2.80791i			0.244397i
$133$		−	2.59637i		−	0.225133i
$134$	−13.4652			−1.16322
$135$	−30.9015	+	5.19273i	−2.65958	+	0.446919i
$136$	−9.12741			−0.782669
$137$			9.70431i			0.829095i	0.910028	+	0.414548i	$0.136060\pi$
$137$			9.70431i			0.829095i	−0.910028	+	0.414548i	$0.863940\pi$
$138$		−	1.66614i		−	0.141831i
$139$	13.4508			1.14088			0.570439	−	0.821340i	$-0.306773\pi$
$139$	13.4508			1.14088			0.570439	+	0.821340i	$0.306773\pi$
$140$	−6.74111	+	1.13279i	−0.569728	+	0.0957379i
$141$	16.3548			1.37732
$142$			3.30606i			0.277438i
$143$		−	2.80791i		−	0.234809i
$144$	1.90407			0.158672
$145$	2.22334	+	13.2309i	0.184638	+	1.09877i
$146$	9.83705			0.814120
$147$			0.833070i			0.0687105i
$148$			1.65303i			0.135878i
$149$	−15.0959			−1.23671			−0.618353	−	0.785900i	$-0.712200\pi$
$149$	−15.0959			−1.23671			−0.618353	+	0.785900i	$0.712200\pi$
$150$	13.7911	−	4.76964i	1.12604	−	0.389440i
$151$	14.1919			1.15492			0.577459	−	0.816420i	$-0.304044\pi$
$151$	14.1919			1.15492			0.577459	+	0.816420i	$0.304044\pi$
$152$			2.88181i			0.233745i
$153$		−	23.2946i		−	1.88325i
$154$	1.74519			0.140631
$155$	−2.16295	−	12.8716i	−0.173733	−	1.03387i
$156$	14.3548			1.14931
$157$			7.57755i			0.604754i	0.953188	+	0.302377i	$0.0977802\pi$
$157$			7.57755i			0.604754i	−0.953188	+	0.302377i	$0.902220\pi$
$158$		−	1.66614i		−	0.132551i
$159$	0.517774			0.0410622
$160$	12.1919	−	2.04874i	0.963852	−	0.161967i
$161$	1.48223			0.116816
$162$			20.8865i			1.64100i
$163$			19.6757i			1.54112i	0.637369	+	0.770559i	$0.280023\pi$
$163$			19.6757i			1.54112i	−0.637369	+	0.770559i	$0.719977\pi$
$164$	−4.51777			−0.352779
$165$	5.25889	−	0.883711i	0.409404	−	0.0687968i
$166$	3.80814			0.295569
$167$		−	10.7954i		−	0.835376i	−0.908590	−	0.417688i	$-0.862840\pi$
$167$		−	10.7954i		−	0.835376i	0.908590	−	0.417688i	$-0.137160\pi$
$168$			24.0770i			1.85758i
$169$	−1.35482			−0.104217
$170$	1.06446	+	6.33450i	0.0816402	+	0.485834i
$171$	−7.35482			−0.562437
$172$		−	3.05699i		−	0.233093i
$173$		−	20.3895i		−	1.55018i	−0.631848	−	0.775092i	$-0.717703\pi$
$173$		−	20.3895i		−	1.55018i	0.631848	−	0.775092i	$-0.282297\pi$
$174$	17.5111			1.32752
$175$	4.24315	+	12.2688i	0.320752	+	0.927434i
$176$	−0.191865			−0.0144623
$177$		−	26.8849i		−	2.02079i
$178$			15.3291i			1.14897i
$179$	−25.0645			−1.87341			−0.936703	−	0.350126i	$-0.886139\pi$
$179$	−25.0645			−1.87341			−0.936703	+	0.350126i	$0.886139\pi$
$180$	3.20888	+	19.0958i	0.239176	+	1.42332i
$181$	−19.4193			−1.44342			−0.721712	−	0.692194i	$-0.756644\pi$
$181$	−19.4193			−1.44342			−0.721712	+	0.692194i	$0.756644\pi$
$182$		−	8.92188i		−	0.661334i
$183$		−	27.6036i		−	2.04051i
$184$	−1.64518			−0.121284
$185$	3.09593	−	0.520245i	0.227617	−	0.0382491i
$186$	−17.0355			−1.24911
$187$			2.34729i			0.171651i
$188$		−	5.98414i		−	0.436439i
$189$	−36.3837			−2.64653
$190$	2.00000	−	0.336083i	0.145095	−	0.0243820i
$191$	11.4508			0.828547			0.414274	−	0.910152i	$-0.364036\pi$
$191$	11.4508			0.828547			0.414274	+	0.910152i	$0.364036\pi$
$192$		−	17.8021i		−	1.28476i
$193$		−	3.78878i		−	0.272722i	−0.990659	−	0.136361i	$-0.956459\pi$
$193$		−	3.78878i		−	0.272722i	0.990659	−	0.136361i	$-0.0435407\pi$
$194$	−3.43630			−0.246712
$195$	−4.51777	−	26.8849i	−0.323525	−	1.92527i
$196$	0.304816			0.0217726
$197$			2.28354i			0.162695i	0.996686	+	0.0813477i	$0.0259224\pi$
$197$			2.28354i			0.162695i	−0.996686	+	0.0813477i	$0.974078\pi$
$198$		−	4.94366i		−	0.351330i
$199$	19.4508			1.37883			0.689414	−	0.724368i	$-0.257868\pi$
$199$	19.4508			1.37883			0.689414	+	0.724368i	$0.257868\pi$
$200$	−4.70964	−	13.6176i	−0.333022	−	0.962911i
$201$	−47.7741			−3.36972
$202$			7.57755i			0.533155i
$203$			15.5782i			1.09337i
$204$	−12.0000			−0.840168
$205$	1.42184	+	8.46126i	0.0993057	+	0.590960i
$206$	−1.88297			−0.131193
$207$		−	4.19876i		−	0.291834i
$208$			0.980865i			0.0680108i
$209$	0.741113			0.0512639
$210$	16.7096	−	2.80791i	1.15307	−	0.193764i
$211$	11.2274			0.772927			0.386463	−	0.922305i	$-0.373697\pi$
$211$	11.2274			0.772927			0.386463	+	0.922305i	$0.373697\pi$
$212$		−	0.189451i		−	0.0130115i
$213$			11.7298i			0.803712i
$214$	−5.17334			−0.353642
$215$	−5.72538	+	0.962100i	−0.390467	+	0.0656147i
$216$	40.3837			2.74776
$217$		−	15.1551i		−	1.02880i
$218$		−	1.49213i		−	0.101059i
$219$	34.9015			2.35843
$220$	−0.323345	−	1.92420i	−0.0217999	−	0.129730i
$221$	12.0000			0.807207
$222$		−	4.09748i		−	0.275005i
$223$			4.03785i			0.270394i	0.990819	+	0.135197i	$0.0431668\pi$
$223$			4.03785i			0.270394i	−0.990819	+	0.135197i	$0.956833\pi$
$224$	14.3548			0.959122
$225$	34.7543	−	12.0197i	2.31695	−	0.801315i
$226$	3.52815			0.234689
$227$		−	11.2185i		−	0.744600i	−0.928112	−	0.372300i	$-0.878569\pi$
$227$		−	11.2185i		−	0.744600i	0.928112	−	0.372300i	$-0.121431\pi$
$228$			3.78878i			0.250918i
$229$	−16.1315			−1.06600			−0.532999	−	0.846116i	$-0.678935\pi$
$229$	−16.1315			−1.06600			−0.532999	+	0.846116i	$0.678935\pi$
$230$	0.191865	+	1.14177i	0.0126512	+	0.0752861i
$231$	6.19186			0.407395
$232$		−	17.2908i		−	1.13520i
$233$			2.12676i			0.139329i	0.997570	+	0.0696644i	$0.0221928\pi$
$233$			2.12676i			0.139329i	−0.997570	+	0.0696644i	$0.977807\pi$
$234$	−25.2733			−1.65217
$235$	−11.2076	+	1.88334i	−0.731103	+	0.122856i
$236$	−9.83705			−0.640337
$237$		−	5.91141i		−	0.383987i
$238$			7.45830i			0.483450i
$239$	14.4152			0.932442			0.466221	−	0.884668i	$-0.345615\pi$
$239$	14.4152			0.932442			0.466221	+	0.884668i	$0.345615\pi$
$240$	−1.83705	+	0.308700i	−0.118581	+	0.0199265i
$241$	−0.162955			−0.0104968			−0.00524842	−	0.999986i	$-0.501671\pi$
$241$	−0.162955			−0.0104968			−0.00524842	+	0.999986i	$0.501671\pi$
$242$		−	9.47849i		−	0.609301i
$243$			32.0645i			2.05694i
$244$	−10.1000			−0.646587
$245$	−0.0959323	−	0.570885i	−0.00612889	−	0.0364725i
$246$	11.1985			0.713990
$247$		−	3.78878i		−	0.241074i
$248$			16.8212i			1.06815i
$249$	13.5111			0.856233
$250$	−8.90150	+	4.85665i	−0.562980	+	0.307161i
$251$	12.9330			0.816322			0.408161	−	0.912910i	$-0.366170\pi$
$251$	12.9330			0.816322			0.408161	+	0.912910i	$0.366170\pi$
$252$			22.4836i			1.41633i
$253$			0.423090i			0.0265995i
$254$	−13.0815			−0.820805
$255$	3.77666	+	22.4746i	0.236504	+	1.40741i
$256$	−16.5426			−1.03391
$257$		−	11.0445i		−	0.688938i	−0.938798	−	0.344469i	$-0.888059\pi$
$257$		−	11.0445i		−	0.688938i	0.938798	−	0.344469i	$-0.111941\pi$
$258$			7.57755i			0.471758i
$259$	3.64518			0.226501
$260$	−9.83705	+	1.65303i	−0.610068	+	0.102517i
$261$	44.1289			2.73151
$262$			9.04113i			0.558563i
$263$		−	17.8527i		−	1.10085i	−0.834885	−	0.550424i	$-0.814466\pi$
$263$		−	17.8527i		−	1.10085i	0.834885	−	0.550424i	$-0.185534\pi$
$264$	−6.87259			−0.422979
$265$	−0.354819	+	0.0596243i	−0.0217964	+	0.00366269i
$266$	2.35482			0.144383
$267$			54.3872i			3.32844i
$268$			17.4803i			1.06778i
$269$	−24.9934			−1.52387			−0.761936	−	0.647652i	$-0.775751\pi$
$269$	−24.9934			−1.52387			−0.761936	+	0.647652i	$0.775751\pi$
$270$	−4.70964	−	28.0267i	−0.286619	−	1.70565i
$271$	−23.8660			−1.44975			−0.724877	−	0.688879i	$-0.758103\pi$
$271$	−23.8660			−1.44975			−0.724877	+	0.688879i	$0.758103\pi$
$272$		−	0.819960i		−	0.0497174i
$273$		−	31.6545i		−	1.91582i
$274$	−8.80150			−0.531718
$275$	−3.50204	+	1.21118i	−0.211181	+	0.0730366i
$276$	−2.16295			−0.130195
$277$		−	21.2315i		−	1.27568i	−0.770169	−	0.637840i	$-0.779828\pi$
$277$		−	21.2315i		−	1.27568i	0.770169	−	0.637840i	$-0.220172\pi$
$278$			12.1994i			0.731671i
$279$	−42.9304			−2.57018
$280$	−2.77259	−	16.4994i	−0.165694	−	0.986030i
$281$	3.83705			0.228899			0.114449	−	0.993429i	$-0.463490\pi$
$281$	3.83705			0.228899			0.114449	+	0.993429i	$0.463490\pi$
$282$			14.8333i			0.883310i
$283$		−	0.211545i		−	0.0125751i	−0.999980	−	0.00628753i	$-0.997999\pi$
$283$		−	0.211545i		−	0.0125751i	0.999980	−	0.00628753i	$-0.00200139\pi$
$284$	4.29187			0.254676
$285$	7.09593	−	1.19241i	0.420327	−	0.0706323i
$286$	2.54668			0.150589
$287$			9.96237i			0.588060i
$288$		−	40.6634i		−	2.39612i
$289$	6.96853			0.409913
$290$	−12.0000	+	2.01650i	−0.704664	+	0.118413i
$291$	−12.1919			−0.714700
$292$		−	12.7703i		−	0.747324i
$293$			14.9942i			0.875970i	0.898982	+	0.437985i	$0.144308\pi$
$293$			14.9942i			0.875970i	−0.898982	+	0.437985i	$0.855692\pi$
$294$	−0.755568			−0.0440656
$295$	3.09593	+	18.4236i	0.180252	+	1.07267i
$296$	−4.04593			−0.235165
$297$		−	10.3855i		−	0.602626i
$298$		−	13.6915i		−	0.793129i
$299$	2.16295			0.125087
$300$	−6.19186	−	17.9034i	−0.357487	−	1.03365i
$301$	−6.74111			−0.388551
$302$			12.8716i			0.740675i
$303$			26.8849i			1.54450i
$304$	−0.258887			−0.0148482
$305$	3.17869	+	18.9161i	0.182011	+	1.08313i
$306$	21.1274			1.20777
$307$			1.65303i			0.0943434i	0.998887	+	0.0471717i	$0.0150208\pi$
$307$			1.65303i			0.0943434i	−0.998887	+	0.0471717i	$0.984979\pi$
$308$		−	2.26557i		−	0.129093i
$309$	−6.68073			−0.380053
$310$	11.6741	−	1.96173i	0.663044	−	0.111419i
$311$	−0.741113			−0.0420247			−0.0210123	−	0.999779i	$-0.506689\pi$
$311$	−0.741113			−0.0420247			−0.0210123	+	0.999779i	$0.506689\pi$
$312$			35.1346i			1.98911i
$313$			26.8849i			1.51962i	0.650143	+	0.759812i	$0.274709\pi$
$313$			26.8849i			1.51962i	−0.650143	+	0.759812i	$0.725291\pi$
$314$	−6.87259			−0.387843
$315$	42.1091	−	7.07607i	2.37258	−	0.398691i
$316$	−2.16295			−0.121676
$317$		−	8.16155i		−	0.458398i	−0.973380	−	0.229199i	$-0.926389\pi$
$317$		−	8.16155i		−	0.458398i	0.973380	−	0.229199i	$-0.0736107\pi$
$318$			0.469604i			0.0263341i
$319$	−4.44668			−0.248966
$320$	2.05000	+	12.1994i	0.114599	+	0.681967i
$321$	−18.3548			−1.02447
$322$			1.34433i			0.0749166i
$323$			3.16725i			0.176231i
$324$	27.1145			1.50636
$325$	6.19186	+	17.9034i	0.343463	+	0.993101i
$326$	−17.8452			−0.988354
$327$		−	5.29401i		−	0.292759i
$328$		−	11.0576i		−	0.610555i
$329$	−13.1959			−0.727516
$330$	0.801497	+	4.76964i	0.0441210	+	0.262560i
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$		−	4.94366i		−	0.271318i
$333$		−	10.3258i		−	0.565852i
$334$	9.79112			0.535746
$335$	32.7385	−	5.50143i	1.78870	−	0.300575i
$336$	−2.16295			−0.117999
$337$		−	9.90275i		−	0.539437i	−0.962939	−	0.269718i	$-0.913069\pi$
$337$		−	9.90275i		−	0.539437i	0.962939	−	0.269718i	$-0.0869306\pi$
$338$		−	1.22878i		−	0.0668367i
$339$	12.5178			0.679872
$340$	8.22334	−	1.38186i	0.445973	−	0.0749419i
$341$	4.32591			0.234261
$342$		−	6.67058i		−	0.360704i
$343$		−	18.8467i		−	1.01763i
$344$	7.48223			0.403415
$345$	0.680729	+	4.05096i	0.0366492	+	0.218096i
$346$	18.4926			0.994169
$347$		−	21.2781i		−	1.14227i	−0.820858	−	0.571133i	$-0.806504\pi$
$347$		−	21.2781i		−	1.14227i	0.820858	−	0.571133i	$-0.193496\pi$
$348$		−	22.7327i		−	1.21860i
$349$	16.4152			0.878686			0.439343	−	0.898319i	$-0.355211\pi$
$349$	16.4152			0.878686			0.439343	+	0.898319i	$0.355211\pi$
$350$	−11.1274	+	3.84840i	−0.594785	+	0.205706i
$351$	−53.0934			−2.83391
$352$			4.09748i			0.218396i
$353$		−	23.8744i		−	1.27071i	−0.772221	−	0.635354i	$-0.780854\pi$
$353$		−	23.8744i		−	1.27071i	0.772221	−	0.635354i	$-0.219146\pi$
$354$	24.3837			1.29598
$355$	−1.35075	−	8.03817i	−0.0716901	−	0.426622i
$356$	19.9000			1.05470
$357$			26.4618i			1.40051i
$358$		−	22.7327i		−	1.20146i
$359$	−2.22334			−0.117343			−0.0586717	−	0.998277i	$-0.518687\pi$
$359$	−2.22334			−0.117343			−0.0586717	+	0.998277i	$0.518687\pi$
$360$	−46.7385	+	7.85401i	−2.46334	+	0.413943i
$361$	1.00000			0.0526316
$362$		−	17.6127i		−	0.925701i
$363$		−	33.6294i		−	1.76508i
$364$	−11.5822			−0.607074
$365$	−23.9172	+	4.01909i	−1.25189	+	0.210369i
$366$	25.0355			1.30863
$367$		−	4.52057i		−	0.235972i	−0.993015	−	0.117986i	$-0.962356\pi$
$367$		−	4.52057i		−	0.235972i	0.993015	−	0.117986i	$-0.0376437\pi$
$368$		−	0.147795i		−	0.00770433i
$369$	28.2208			1.46911
$370$	0.471845	+	2.80791i	0.0245301	+	0.145976i
$371$	−0.417768			−0.0216894
$372$			22.1153i			1.14662i
$373$		−	15.5186i		−	0.803521i	−0.915745	−	0.401760i	$-0.868398\pi$
$373$		−	15.5186i		−	0.803521i	0.915745	−	0.401760i	$-0.131602\pi$
$374$	−2.12892			−0.110084
$375$	−31.5822	+	17.2312i	−1.63090	+	0.889817i
$376$	14.6467			0.755345
$377$			22.7327i			1.17079i
$378$		−	32.9989i		−	1.69728i
$379$	18.9015			0.970905			0.485453	−	0.874263i	$-0.338655\pi$
$379$	18.9015			0.970905			0.485453	+	0.874263i	$0.338655\pi$
$380$	−0.436297	−	2.59637i	−0.0223816	−	0.133191i
$381$	−46.4126			−2.37779
$382$			10.3855i			0.531366i
$383$			13.7046i			0.700274i	0.936699	+	0.350137i	$0.113865\pi$
$383$			13.7046i			0.700274i	−0.936699	+	0.350137i	$0.886135\pi$
$384$	−19.4363			−0.991854
$385$	−4.24315	+	0.713025i	−0.216251	+	0.0363391i
$386$	3.43630			0.174903
$387$			19.0958i			0.970694i
$388$			4.46094i			0.226470i
$389$	−12.7411			−0.646000			−0.323000	−	0.946399i	$-0.604691\pi$
$389$	−12.7411			−0.646000			−0.323000	+	0.946399i	$0.604691\pi$
$390$	24.3837	−	4.09748i	1.23472	−	0.207484i
$391$	−1.80814			−0.0914413
$392$			0.746063i			0.0376819i
$393$			32.0776i			1.61810i
$394$	−2.07110			−0.104340
$395$	0.680729	+	4.05096i	0.0342512	+	0.203826i
$396$	−6.41777			−0.322505
$397$		−	38.6522i		−	1.93990i	−0.243306	−	0.969950i	$-0.578232\pi$
$397$		−	38.6522i		−	1.93990i	0.243306	−	0.969950i	$-0.421768\pi$
$398$			17.6412i			0.884274i
$399$	8.35482			0.418264
$400$	1.22334	−	0.423090i	0.0611669	−	0.0211545i
$401$	31.8660			1.59131			0.795655	−	0.605750i	$-0.207127\pi$
$401$	31.8660			1.59131			0.795655	+	0.605750i	$0.207127\pi$
$402$		−	43.3296i		−	2.16108i
$403$		−	22.1153i		−	1.10164i
$404$	9.83705			0.489411
$405$	−8.53351	−	50.7822i	−0.424034	−	2.52339i
$406$	−14.1289			−0.701206
$407$			1.04049i			0.0515751i
$408$		−	29.3710i		−	1.45408i
$409$	−11.0645			−0.547102			−0.273551	−	0.961857i	$-0.588198\pi$
$409$	−11.0645			−0.547102			−0.273551	+	0.961857i	$0.588198\pi$
$410$	−7.67409	+	1.28956i	−0.378996	+	0.0636871i
$411$	−31.2274			−1.54033
$412$			2.44444i			0.120429i
$413$			21.6922i			1.06740i
$414$	3.80814			0.187160
$415$	−9.25889	+	1.55588i	−0.454501	+	0.0763749i
$416$	20.9474			1.02703
$417$			43.2830i			2.11958i
$418$			0.672165i			0.0328767i
$419$	25.7452			1.25773			0.628867	−	0.777513i	$-0.283519\pi$
$419$	25.7452			1.25773			0.628867	+	0.777513i	$0.283519\pi$
$420$	−3.64518	−	21.6922i	−0.177867	−	1.05847i
$421$	27.4482			1.33774			0.668871	−	0.743378i	$-0.266778\pi$
$421$	27.4482			1.33774			0.668871	+	0.743378i	$0.266778\pi$
$422$			10.1829i			0.495696i
$423$			37.3806i			1.81751i
$424$	0.463697			0.0225191
$425$	−5.17613	−	14.9664i	−0.251079	−	0.725979i
$426$	−10.6385			−0.515439
$427$			22.2720i			1.07782i
$428$			6.71593i			0.324627i
$429$	9.03555			0.436240
$430$	−0.872594	−	5.19273i	−0.0420802	−	0.250416i
$431$	1.74519			0.0840627			0.0420314	−	0.999116i	$-0.486617\pi$
$431$	1.74519			0.0840627			0.0420314	+	0.999116i	$0.486617\pi$
$432$			3.62787i			0.174546i
$433$			18.5208i			0.890052i	0.895518	+	0.445026i	$0.146806\pi$
$433$			18.5208i			0.890052i	−0.895518	+	0.445026i	$0.853194\pi$
$434$	13.7452			0.659790
$435$	−42.5756	+	7.15446i	−2.04134	+	0.343030i
$436$	−1.93705			−0.0927679
$437$			0.570885i			0.0273091i
$438$			31.6545i			1.51251i
$439$	−29.4482			−1.40549			−0.702743	−	0.711444i	$-0.748041\pi$
$439$	−29.4482			−1.40549			−0.702743	+	0.711444i	$0.748041\pi$
$440$	4.70964	−	0.791414i	0.224523	−	0.0377292i
$441$	−1.90407			−0.0906699
$442$			10.8836i			0.517681i
$443$		−	11.7388i		−	0.557726i	−0.960331	−	0.278863i	$-0.910042\pi$
$443$		−	11.7388i		−	0.557726i	0.960331	−	0.278863i	$-0.0899576\pi$
$444$	−5.31927			−0.252441
$445$	−6.26296	−	37.2704i	−0.296893	−	1.76678i
$446$	−3.66220			−0.173410
$447$		−	48.5771i		−	2.29762i
$448$			14.3637i			0.678620i
$449$	7.06446			0.333392			0.166696	−	0.986008i	$-0.446690\pi$
$449$	7.06446			0.333392			0.166696	+	0.986008i	$0.446690\pi$
$450$	10.9015	+	31.5210i	0.513902	+	1.48591i
$451$	−2.84368			−0.133904
$452$		−	4.58019i		−	0.215434i
$453$			45.6679i			2.14566i
$454$	10.1748			0.477529
$455$	3.64518	+	21.6922i	0.170889	+	1.01694i
$456$	−9.27334			−0.434264
$457$		−	34.5000i		−	1.61384i	−0.590660	−	0.806920i	$-0.701133\pi$
$457$		−	34.5000i		−	1.61384i	0.590660	−	0.806920i	$-0.298867\pi$
$458$		−	14.6307i		−	0.683649i
$459$	44.3837			2.07166
$460$	1.48223	−	0.249075i	0.0691091	−	0.0116132i
$461$	8.03147			0.374063			0.187032	−	0.982354i	$-0.440113\pi$
$461$	8.03147			0.374063			0.187032	+	0.982354i	$0.440113\pi$
$462$			5.61582i			0.261272i
$463$			25.3290i			1.17714i	0.808447	+	0.588570i	$0.200309\pi$
$463$			25.3290i			1.17714i	−0.808447	+	0.588570i	$0.799691\pi$
$464$	1.55332			0.0721112
$465$	41.4193	−	6.96015i	1.92077	−	0.322769i
$466$	−1.92890			−0.0893547
$467$			26.8759i			1.24367i	0.783149	+	0.621834i	$0.213612\pi$
$467$			26.8759i			1.24367i	−0.783149	+	0.621834i	$0.786388\pi$
$468$			32.8094i			1.51662i
$469$	38.5467			1.77992
$470$	−1.70813	−	10.1649i	−0.0787901	−	0.468873i
$471$	−24.3837			−1.12354
$472$		−	24.0770i		−	1.10823i
$473$		−	1.92420i		−	0.0884748i
$474$	5.36146			0.246260
$475$	−4.72538	+	1.63427i	−0.216815	+	0.0749852i
$476$	9.68224			0.443785
$477$			1.18343i			0.0541854i
$478$			13.0741i			0.597996i
$479$	28.9015			1.32054			0.660272	−	0.751027i	$-0.270441\pi$
$479$	28.9015			1.32054			0.660272	+	0.751027i	$0.270441\pi$
$480$	6.59261	+	39.2321i	0.300910	+	1.79069i
$481$	5.31927			0.242538
$482$		−	0.147795i		−	0.00673187i
$483$			4.76964i			0.217026i
$484$	−12.3048			−0.559310
$485$	8.35482	−	1.40396i	0.379373	−	0.0637503i
$486$	−29.0815			−1.31916
$487$		−	17.7294i		−	0.803395i	−0.915773	−	0.401697i	$-0.868420\pi$
$487$		−	17.7294i		−	0.803395i	0.915773	−	0.401697i	$-0.131580\pi$
$488$		−	24.7206i		−	1.11905i
$489$	−63.3141			−2.86316
$490$	0.517774	−	0.0870075i	0.0233907	−	0.00393060i
$491$	−35.1645			−1.58695			−0.793475	−	0.608603i	$-0.791730\pi$
$491$	−35.1645			−1.58695			−0.793475	+	0.608603i	$0.791730\pi$
$492$		−	14.5377i		−	0.655410i
$493$		−	19.0035i		−	0.855875i
$494$	3.43630			0.154606
$495$	2.01981	+	12.0197i	0.0907838	+	0.540247i
$496$	−1.51114			−0.0678520
$497$		−	9.46422i		−	0.424528i
$498$			12.2542i			0.549122i
$499$	−21.4508			−0.960268			−0.480134	−	0.877195i	$-0.659412\pi$
$499$	−21.4508			−0.960268			−0.480134	+	0.877195i	$0.659412\pi$
$500$	6.30482	+	11.5558i	0.281960	+	0.516790i
$501$	34.7385			1.55200
$502$			11.7298i			0.523526i
$503$			5.34053i			0.238122i	0.992887	+	0.119061i	$0.0379884\pi$
$503$			5.34053i			0.238122i	−0.992887	+	0.119061i	$0.962012\pi$
$504$	−55.0304			−2.45125
$505$	−3.09593	−	18.4236i	−0.137767	−	0.819841i
$506$	−0.383729			−0.0170588
$507$		−	4.35966i		−	0.193619i
$508$			16.9821i			0.753461i
$509$	−36.1919			−1.60418			−0.802088	−	0.597206i	$-0.796278\pi$
$509$	−36.1919			−1.60418			−0.802088	+	0.597206i	$0.796278\pi$
$510$	−20.3837	+	3.42531i	−0.902607	+	0.151675i
$511$	−28.1604			−1.24574
$512$		−	2.92346i		−	0.129200i
$513$		−	14.0133i		−	0.618704i
$514$	10.0170			0.441832
$515$	4.57816	−	0.769320i	0.201738	−	0.0339003i
$516$	9.83705			0.433052
$517$		−	3.76668i		−	0.165658i
$518$			3.30606i			0.145260i
$519$	65.6111			2.88001
$520$	−4.04593	−	24.0770i	−0.177426	−	1.05585i
$521$	−2.77259			−0.121469			−0.0607346	−	0.998154i	$-0.519344\pi$
$521$	−2.77259			−0.121469			−0.0607346	+	0.998154i	$0.519344\pi$
$522$			40.0235i			1.75178i
$523$			20.5373i			0.898033i	0.893524	+	0.449016i	$0.148226\pi$
$523$			20.5373i			0.898033i	−0.893524	+	0.449016i	$0.851774\pi$
$524$	11.7370			0.512735
$525$	−39.4797	+	13.6540i	−1.72303	+	0.595909i
$526$	16.1919			0.705999
$527$			18.4874i			0.805323i
$528$		−	0.617399i		−	0.0268688i
$529$	22.6741			0.985830
$530$	−0.0540773	−	0.321810i	−0.00234897	−	0.0139785i
$531$	61.4482			2.66662
$532$		−	3.05699i		−	0.132537i
$533$			14.5377i			0.629698i
$534$	−49.3274			−2.13461
$535$	12.5782	−	2.11365i	0.543801	−	0.0913811i
$536$	−42.7845			−1.84801
$537$		−	80.6547i		−	3.48051i
$538$		−	22.6682i		−	0.977294i
$539$	0.191865			0.00826419
$540$	−36.3837	+	6.11397i	−1.56571	+	0.263103i
$541$	35.4797			1.52539			0.762695	−	0.646758i	$-0.223876\pi$
$541$	35.4797			1.52539			0.762695	+	0.646758i	$0.223876\pi$
$542$		−	21.6456i		−	0.929760i
$543$		−	62.4891i		−	2.68166i
$544$	−17.5111			−0.750784
$545$	0.609632	+	3.62787i	0.0261138	+	0.155401i
$546$	28.7096			1.22866
$547$			43.0756i			1.84178i	0.389822	+	0.920890i	$0.372537\pi$
$547$			43.0756i			1.84178i	−0.389822	+	0.920890i	$0.627463\pi$
$548$			11.4260i			0.488092i
$549$	63.0908			2.69265
$550$	−1.09850	−	3.17623i	−0.0468401	−	0.135435i
$551$	−6.00000			−0.255609
$552$		−	5.29401i		−	0.225328i
$553$			4.76964i			0.202826i
$554$	19.2563			0.818123
$555$	1.67409	+	9.96237i	0.0710612	+	0.422879i
$556$	15.8370			0.671640
$557$			40.4376i			1.71340i	0.515818	+	0.856698i	$0.327488\pi$
$557$			40.4376i			1.71340i	−0.515818	+	0.856698i	$0.672512\pi$
$558$		−	38.9365i		−	1.64831i
$559$	−9.83705			−0.416063
$560$	1.48223	−	0.249075i	0.0626355	−	0.0105254i
$561$	−7.55332			−0.318902
$562$			3.48008i			0.146798i
$563$		−	19.7173i		−	0.830986i	−0.909596	−	0.415493i	$-0.863609\pi$
$563$		−	19.7173i		−	0.830986i	0.909596	−	0.415493i	$-0.136391\pi$
$564$	19.2563			0.810837
$565$	−8.57816	+	1.44149i	−0.360886	+	0.0606437i
$566$	0.191865			0.00806467
$567$		−	59.7915i		−	2.51101i
$568$			10.5047i			0.440768i
$569$	−18.6807			−0.783137			−0.391568	−	0.920149i	$-0.628067\pi$
$569$	−18.6807			−0.783137			−0.391568	+	0.920149i	$0.628067\pi$
$570$	1.08148	+	6.43578i	0.0452981	+	0.269565i
$571$	−29.9371			−1.25283			−0.626413	−	0.779491i	$-0.715478\pi$
$571$	−29.9371			−1.25283			−0.626413	+	0.779491i	$0.715478\pi$
$572$		−	3.30606i		−	0.138233i
$573$			36.8473i			1.53932i
$574$	−9.03555			−0.377137
$575$	−0.932977	−	2.69765i	−0.0389079	−	0.112500i
$576$	40.6885			1.69536
$577$		−	0.156779i		−	0.00652679i	−0.999995	−	0.00326339i	$-0.998961\pi$
$577$		−	0.156779i		−	0.00652679i	0.999995	−	0.00326339i	$-0.00103877\pi$
$578$			6.32023i			0.262887i
$579$	12.1919			0.506677
$580$	2.61778	+	15.5782i	0.108697	+	0.646849i
$581$	−10.9015			−0.452271
$582$		−	11.0576i		−	0.458353i
$583$		−	0.119249i		−	0.00493877i
$584$	31.2563			1.29340
$585$	61.4482	−	10.3258i	2.54057	−	0.426921i
$586$	−13.5993			−0.561780
$587$			31.1474i			1.28559i	0.766038	+	0.642795i	$0.222225\pi$
$587$			31.1474i			1.28559i	−0.766038	+	0.642795i	$0.777775\pi$
$588$			0.980865i			0.0404502i
$589$	5.83705			0.240511
$590$	−16.7096	+	2.80791i	−0.687925	+	0.115600i
$591$	−7.34818			−0.302264
$592$		−	0.363466i		−	0.0149384i
$593$		−	28.8728i		−	1.18567i	−0.805326	−	0.592833i	$-0.798009\pi$
$593$		−	28.8728i		−	1.18567i	0.805326	−	0.592833i	$-0.201991\pi$
$594$	9.41928			0.386478
$595$	−3.04721	−	18.1337i	−0.124923	−	0.743409i
$596$	−17.7741			−0.728055
$597$			62.5904i			2.56165i
$598$			1.96173i			0.0802211i
$599$	−25.3274			−1.03485			−0.517425	−	0.855728i	$-0.673109\pi$
$599$	−25.3274			−1.03485			−0.517425	+	0.855728i	$0.673109\pi$
$600$	43.8200	−	15.1551i	1.78895	−	0.618704i
$601$	−19.8370			−0.809170			−0.404585	−	0.914500i	$-0.632584\pi$
$601$	−19.8370			−0.809170			−0.404585	+	0.914500i	$0.632584\pi$
$602$		−	6.11397i		−	0.249187i
$603$		−	109.193i		−	4.44667i
$604$	16.7096			0.679906
$605$	3.87259	+	23.0455i	0.157443	+	0.936932i
$606$	−24.3837			−0.990521
$607$		−	2.49921i		−	0.101440i	−0.998713	−	0.0507199i	$-0.983848\pi$
$607$		−	2.49921i		−	0.101440i	0.998713	−	0.0507199i	$-0.0161516\pi$
$608$			5.52881i			0.224223i
$609$	−50.1289			−2.03133
$610$	−17.1563	+	2.88297i	−0.694639	+	0.116728i
$611$	−19.2563			−0.779027
$612$		−	27.4272i		−	1.10868i
$613$			0.883711i			0.0356927i	0.999841	+	0.0178464i	$0.00568098\pi$
$613$			0.883711i			0.0356927i	−0.999841	+	0.0178464i	$0.994319\pi$
$614$	−1.49925			−0.0605046
$615$	−27.2274	+	4.57533i	−1.09792	+	0.184495i
$616$	5.54517			0.223421
$617$		−	29.4085i		−	1.18394i	−0.805959	−	0.591971i	$-0.798350\pi$
$617$		−	29.4085i		−	1.18394i	0.805959	−	0.591971i	$-0.201650\pi$
$618$		−	6.05921i		−	0.243737i
$619$	−30.3208			−1.21870			−0.609348	−	0.792903i	$-0.708569\pi$
$619$	−30.3208			−1.21870			−0.609348	+	0.792903i	$0.708569\pi$
$620$	−2.54668	−	15.1551i	−0.102277	−	0.608644i
$621$	8.00000			0.321029
$622$		−	0.672165i		−	0.0269514i
$623$		−	43.8825i		−	1.75811i
$624$	−3.15632			−0.126354
$625$	19.6584	−	15.4450i	0.786334	−	0.617801i
$626$	−24.3837			−0.974570
$627$			2.38482i			0.0952405i
$628$			8.92188i			0.356022i
$629$	−4.44668			−0.177301
$630$	6.41777	+	38.1916i	0.255690	+	1.52159i
$631$	17.7767			0.707678			0.353839	−	0.935306i	$-0.384876\pi$
$631$	17.7767			0.707678			0.353839	+	0.935306i	$0.384876\pi$
$632$		−	5.29401i		−	0.210584i
$633$			36.1286i			1.43598i
$634$	7.40226			0.293981
$635$	31.8056	−	5.34465i	1.26217	−	0.212096i
$636$	0.609632			0.0241735
$637$		−	0.980865i		−	0.0388633i
$638$		−	4.03299i		−	0.159668i
$639$	−26.8096			−1.06057
$640$	13.3193	−	2.23819i	0.526490	−	0.0884722i
$641$	−32.6675			−1.29029			−0.645143	−	0.764062i	$-0.723202\pi$
$641$	−32.6675			−1.29029			−0.645143	+	0.764062i	$0.723202\pi$
$642$		−	16.6472i		−	0.657014i
$643$		−	31.8661i		−	1.25668i	−0.777941	−	0.628338i	$-0.783736\pi$
$643$		−	31.8661i		−	1.25668i	0.777941	−	0.628338i	$-0.216264\pi$
$644$	1.74519			0.0687700
$645$	−3.09593	−	18.4236i	−0.121902	−	0.725430i
$646$	−2.87259			−0.113021
$647$			21.2601i			0.835820i	0.908488	+	0.417910i	$0.137237\pi$
$647$			21.2601i			0.835820i	−0.908488	+	0.417910i	$0.862763\pi$
$648$			66.3649i			2.60706i
$649$	−6.19186			−0.243052
$650$	−16.2378	+	5.61582i	−0.636899	+	0.220271i
$651$	48.7675			1.91135
$652$			23.1663i			0.907263i
$653$		−	12.8340i		−	0.502234i	−0.967957	−	0.251117i	$-0.919202\pi$
$653$		−	12.8340i		−	0.502234i	0.967957	−	0.251117i	$-0.0807980\pi$
$654$	4.80150			0.187753
$655$	−3.69390	−	21.9821i	−0.144333	−	0.858912i
$656$	0.993361			0.0387842
$657$			79.7710i			3.11216i
$658$		−	11.9683i		−	0.466573i
$659$	−20.3548			−0.792911			−0.396456	−	0.918054i	$-0.629760\pi$
$659$	−20.3548			−0.792911			−0.396456	+	0.918054i	$0.629760\pi$
$660$	6.19186	−	1.04049i	0.241018	−	0.0405010i
$661$	−30.7385			−1.19559			−0.597795	−	0.801649i	$-0.703957\pi$
$661$	−30.7385			−1.19559			−0.597795	+	0.801649i	$0.703957\pi$
$662$			7.25574i			0.282002i
$663$			38.6147i			1.49967i
$664$	12.1000			0.469571
$665$	−5.72538	+	0.962100i	−0.222021	+	0.0373086i
$666$	9.36520			0.362894
$667$		−	3.42531i		−	0.132629i
$668$		−	12.7107i		−	0.491790i
$669$	−12.9934			−0.502352
$670$	4.98962	+	29.6928i	0.192766	+	1.14713i
$671$	−6.35738			−0.245424
$672$			46.1922i			1.78190i
$673$		−	21.2094i		−	0.817564i	−0.912632	−	0.408782i	$-0.865954\pi$
$673$		−	21.2094i		−	0.817564i	0.912632	−	0.408782i	$-0.134046\pi$
$674$	8.98147			0.345953
$675$	22.9015	+	66.2183i	0.881479	+	2.54874i
$676$	−1.59518			−0.0613530
$677$			11.2650i			0.432951i	0.976288	+	0.216475i	$0.0694561\pi$
$677$			11.2650i			0.432951i	−0.976288	+	0.216475i	$0.930544\pi$
$678$			11.3532i			0.436018i
$679$	9.83705			0.377511
$680$	3.38222	+	20.1273i	0.129702	+	0.771847i
$681$	36.1000			1.38336
$682$			3.92346i			0.150237i
$683$			12.3603i			0.472954i	0.971637	+	0.236477i	$0.0759928\pi$
$683$			12.3603i			0.472954i	−0.971637	+	0.236477i	$0.924007\pi$
$684$	−8.65964			−0.331109
$685$	21.3995	−	3.59600i	0.817632	−	0.137396i
$686$	17.0934			0.652628
$687$		−	51.9093i		−	1.98046i
$688$			0.672165i			0.0256261i
$689$	−0.609632			−0.0232251
$690$	−3.67409	+	0.617399i	−0.139870	+	0.0235040i
$691$	22.7493			0.865423			0.432711	−	0.901533i	$-0.357557\pi$
$691$	22.7493			0.865423			0.432711	+	0.901533i	$0.357557\pi$
$692$		−	24.0068i		−	0.912601i
$693$			14.1521i			0.537595i
$694$	19.2985			0.732561
$695$	−4.98426	−	29.6609i	−0.189064	−	1.12510i
$696$	55.6401			2.10903
$697$		−	12.1529i		−	0.460323i
$698$			14.8881i			0.563521i
$699$	−6.84368			−0.258852
$700$	4.99593	+	14.4454i	0.188828	+	0.545985i
$701$	−16.0289			−0.605404			−0.302702	−	0.953085i	$-0.597889\pi$
$701$	−16.0289			−0.605404			−0.302702	+	0.953085i	$0.597889\pi$
$702$		−	48.1540i		−	1.81745i
$703$			1.40396i			0.0529512i
$704$	−4.10001			−0.154525
$705$	−6.06038	−	36.0648i	−0.228247	−	1.35828i
$706$	21.6533			0.814934
$707$		−	21.6922i		−	0.815818i
$708$		−	31.6545i		−	1.18965i
$709$	−31.4193			−1.17998			−0.589988	−	0.807412i	$-0.700867\pi$
$709$	−31.4193			−1.17998			−0.589988	+	0.807412i	$0.700867\pi$
$710$	7.29036	−	1.22508i	0.273602	−	0.0459765i
$711$	13.5111			0.506707
$712$			48.7069i			1.82537i
$713$			3.33228i			0.124795i
$714$	−24.0000			−0.898177
$715$	−6.19186	+	1.04049i	−0.231563	+	0.0389121i
$716$	−29.5111			−1.10288
$717$			46.3865i			1.73234i
$718$		−	2.01650i		−	0.0752550i
$719$	−11.2589			−0.419886			−0.209943	−	0.977714i	$-0.567328\pi$
$719$	−11.2589			−0.419886			−0.209943	+	0.977714i	$0.567328\pi$
$720$	−0.705565	−	4.19876i	−0.0262948	−	0.156478i
$721$	5.39037			0.200748
$722$			0.906968i			0.0337538i
$723$		−	0.524371i		−	0.0195016i
$724$	−22.8644			−0.849750
$725$	28.3523	−	9.80559i	1.05298	−	0.364171i
$726$	30.5008			1.13199
$727$			48.9829i			1.81668i	0.418237	+	0.908338i	$0.362648\pi$
$727$			48.9829i			1.81668i	−0.418237	+	0.908338i	$0.637352\pi$
$728$		−	28.3485i		−	1.05066i
$729$	−34.0934			−1.26272
$730$	−3.64518	−	21.6922i	−0.134914	−	0.802863i
$731$	8.22334			0.304151
$732$		−	32.5007i		−	1.20126i
$733$			35.9260i			1.32696i	0.748195	+	0.663479i	$0.230921\pi$
$733$			35.9260i			1.32696i	−0.748195	+	0.663479i	$0.769079\pi$
$734$	4.10001			0.151334
$735$	1.83705	−	0.308700i	0.0677604	−	0.0113866i
$736$	−3.15632			−0.116343
$737$			11.0029i			0.405296i
$738$			25.5953i			0.942177i
$739$	−14.3523			−0.527956			−0.263978	−	0.964529i	$-0.585035\pi$
$739$	−14.3523			−0.527956			−0.263978	+	0.964529i	$0.585035\pi$
$740$	3.64518	−	0.612541i	0.134000	−	0.0225175i
$741$	12.1919			0.447879
$742$		−	0.378902i		−	0.0139099i
$743$		−	12.5629i		−	0.460887i	−0.973086	−	0.230443i	$-0.925982\pi$
$743$		−	12.5629i		−	0.460887i	0.973086	−	0.230443i	$-0.0740176\pi$
$744$	−54.1289			−1.98446
$745$	5.59390	+	33.2888i	0.204944	+	1.21961i
$746$	14.0748			0.515316
$747$			30.8811i			1.12988i
$748$			2.76372i			0.101052i
$749$	14.8096			0.541133
$750$	−15.6282	−	28.6441i	−0.570660	−	1.04593i
$751$	26.4548			0.965350			0.482675	−	0.875799i	$-0.339665\pi$
$751$	26.4548			0.965350			0.482675	+	0.875799i	$0.339665\pi$
$752$			1.31578i			0.0479817i
$753$			41.6169i			1.51660i
$754$	−20.6178			−0.750855
$755$	−5.25889	−	31.2952i	−0.191390	−	1.13895i
$756$	−42.8386			−1.55802
$757$		−	15.7350i		−	0.571897i	−0.958245	−	0.285949i	$-0.907691\pi$
$757$		−	15.7350i		−	0.571897i	0.958245	−	0.285949i	$-0.0923087\pi$
$758$			17.1431i			0.622664i
$759$	−1.36146			−0.0494178
$760$	6.35482	−	1.06787i	0.230514	−	0.0387358i
$761$	16.9619			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$761$	16.9619			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$762$		−	42.0948i		−	1.52493i
$763$			4.27149i			0.154638i
$764$	13.4822			0.487770
$765$	−51.3680	+	8.63195i	−1.85721	+	0.312089i
$766$	−12.4297			−0.449102
$767$			31.6545i			1.14298i
$768$		−	53.2323i		−	1.92086i
$769$	−41.9974			−1.51447			−0.757233	−	0.653145i	$-0.773449\pi$
$769$	−41.9974			−1.51447			−0.757233	+	0.653145i	$0.773449\pi$
$770$	−0.646690	−	3.84840i	−0.0233051	−	0.138687i
$771$	35.5400			1.27994
$772$		−	4.46094i		−	0.160553i
$773$			40.9579i			1.47315i	0.676355	+	0.736576i	$0.263559\pi$
$773$			40.9579i			1.47315i	−0.676355	+	0.736576i	$0.736441\pi$
$774$	−17.3193			−0.622528
$775$	−27.5822	+	9.53928i	−0.990783	+	0.342661i
$776$	−10.9185			−0.391952
$777$			11.7298i			0.420804i
$778$		−	11.5558i		−	0.414295i
$779$	−3.83705			−0.137476
$780$	−5.31927	−	31.6545i	−0.190460	−	1.13341i
$781$	2.70149			0.0966669
$782$		−	1.63992i		−	0.0586434i
$783$			84.0800i			3.00477i
$784$	−0.0670225			−0.00239366
$785$	16.7096	−	2.80791i	0.596393	−	0.100219i
$786$	−29.0934			−1.03773
$787$		−	28.5379i		−	1.01727i	−0.860983	−	0.508634i	$-0.830151\pi$
$787$		−	28.5379i		−	1.01727i	0.860983	−	0.508634i	$-0.169849\pi$
$788$			2.68866i			0.0957796i
$789$	57.4482			2.04521
$790$	−3.67409	+	0.617399i	−0.130718	+	0.0219661i
$791$	−10.1000			−0.359115
$792$		−	15.7080i		−	0.558160i
$793$			32.5007i			1.15413i
$794$	35.0563			1.24410
$795$	−0.191865	−	1.14177i	−0.00680473	−	0.0404944i
$796$	22.9015			0.811722
$797$		−	33.2790i		−	1.17880i	−0.807840	−	0.589402i	$-0.799364\pi$
$797$		−	33.2790i		−	1.17880i	0.807840	−	0.589402i	$-0.200636\pi$
$798$			7.57755i			0.268242i
$799$	16.0974			0.569487
$800$	−9.03555	−	26.1257i	−0.319455	−	0.923684i
$801$	−124.308			−4.39219
$802$			28.9014i			1.02054i
$803$		−	8.03817i		−	0.283661i
$804$	−56.2497			−1.98377
$805$	−0.549248	−	3.26853i	−0.0193585	−	0.115201i
$806$	20.0578			0.706507
$807$		−	80.4259i		−	2.83113i
$808$			24.0770i			0.847025i
$809$	34.4234			1.21026			0.605130	−	0.796126i	$-0.293121\pi$
$809$	34.4234			1.21026			0.605130	+	0.796126i	$0.293121\pi$
$810$	46.0578	−	7.73962i	1.61831	−	0.271942i
$811$	−11.2563			−0.395263			−0.197631	−	0.980276i	$-0.563325\pi$
$811$	−11.2563			−0.395263			−0.197631	+	0.980276i	$0.563325\pi$
$812$			18.3419i			0.643675i
$813$		−	76.7980i		−	2.69342i
$814$	−0.943690			−0.0330763
$815$	43.3878	−	7.29095i	1.51981	−	0.255391i
$816$	2.63854			0.0923674
$817$		−	2.59637i		−	0.0908353i
$818$		−	10.0351i		−	0.350869i
$819$	72.3497			2.52810
$820$	1.67409	+	9.96237i	0.0584618	+	0.347901i
$821$	−31.3167			−1.09296			−0.546480	−	0.837472i	$-0.684033\pi$
$821$	−31.3167			−1.09296			−0.546480	+	0.837472i	$0.684033\pi$
$822$		−	28.3223i		−	0.987852i
$823$		−	13.4800i		−	0.469882i	−0.972010	−	0.234941i	$-0.924510\pi$
$823$		−	13.4800i		−	0.469882i	0.972010	−	0.234941i	$-0.0754898\pi$
$824$	−5.98298			−0.208427
$825$	−3.89743	−	11.2692i	−0.135691	−	0.392342i
$826$	−19.6741			−0.684549
$827$		−	15.9882i		−	0.555963i	−0.960586	−	0.277982i	$-0.910335\pi$
$827$		−	15.9882i		−	0.555963i	0.960586	−	0.277982i	$-0.0896654\pi$
$828$		−	4.94366i		−	0.171804i
$829$	48.4837			1.68391			0.841955	−	0.539548i	$-0.181405\pi$
$829$	48.4837			1.68391			0.841955	+	0.539548i	$0.181405\pi$
$830$	−1.41113	−	8.39751i	−0.0489810	−	0.291482i
$831$	68.3208			2.37002
$832$			20.9604i			0.726670i
$833$			0.819960i			0.0284099i
$834$	−39.2563			−1.35934
$835$	−23.8056	+	4.00032i	−0.823826	+	0.138437i
$836$	0.872594			0.0301793
$837$		−	81.7965i		−	2.82730i
$838$			23.3501i			0.806614i
$839$	18.9934			0.655724			0.327862	−	0.944726i	$-0.393672\pi$
$839$	18.9934			0.655724			0.327862	+	0.944726i	$0.393672\pi$
$840$	53.0934	−	8.92188i	1.83190	−	0.307834i
$841$	7.00000			0.241379
$842$			24.8946i			0.857925i
$843$			12.3472i			0.425260i
$844$	13.2193			0.455026
$845$	0.502037	+	2.98758i	0.0172706	+	0.102776i
$846$	−33.9030			−1.16561
$847$			27.1340i			0.932334i
$848$			0.0416562i			0.00143048i
$849$	0.680729			0.0233626
$850$	13.5741	−	4.69458i	0.465587	−	0.161023i
$851$	−0.801497			−0.0274750
$852$			13.8108i			0.473149i
$853$		−	44.1210i		−	1.51067i	−0.655337	−	0.755337i	$-0.727473\pi$
$853$		−	44.1210i		−	1.51067i	0.655337	−	0.755337i	$-0.272527\pi$
$854$	−20.2000			−0.691230
$855$	2.72538	+	16.2185i	0.0932059	+	0.554660i
$856$	−16.4378			−0.561833
$857$			32.4149i			1.10727i	0.832759	+	0.553635i	$0.186760\pi$
$857$			32.4149i			1.10727i	−0.832759	+	0.553635i	$0.813240\pi$
$858$			8.19495i			0.279771i
$859$	−6.29444			−0.214763			−0.107382	−	0.994218i	$-0.534247\pi$
$859$	−6.29444			−0.214763			−0.107382	+	0.994218i	$0.534247\pi$
$860$	−6.74111	+	1.13279i	−0.229870	+	0.0386277i
$861$	−32.0578			−1.09253
$862$			1.58283i			0.0539113i
$863$			17.4338i			0.593453i	0.954963	+	0.296726i	$0.0958950\pi$
$863$			17.4338i			0.593453i	−0.954963	+	0.296726i	$0.904105\pi$
$864$	77.4771			2.63582
$865$	−44.9619	+	7.55546i	−1.52875	+	0.256893i
$866$	−16.7978			−0.570811
$867$			22.4240i			0.761557i
$868$		−	17.8438i		−	0.605657i
$869$	−1.36146			−0.0461843
$870$	−6.48886	−	38.6147i	−0.219993	−	1.30916i
$871$	56.2497			1.90595
$872$		−	4.74109i		−	0.160554i
$873$		−	27.8658i		−	0.943113i
$874$	−0.517774			−0.0175140
$875$	25.4822	−	13.9031i	0.861456	−	0.470009i
$876$	41.0934			1.38842
$877$			23.2904i			0.786462i	0.919440	+	0.393231i	$0.128643\pi$
$877$			23.2904i			0.786462i	−0.919440	+	0.393231i	$0.871357\pi$
$878$		−	26.7086i		−	0.901370i
$879$	−48.2497			−1.62742
$880$	0.0710967	+	0.423090i	0.00239667	+	0.0142624i
$881$	28.9619			0.975751			0.487875	−	0.872913i	$-0.337772\pi$
$881$	28.9619			0.975751			0.487875	+	0.872913i	$0.337772\pi$
$882$		−	1.72693i		−	0.0581487i
$883$			37.3627i			1.25735i	0.777667	+	0.628677i	$0.216403\pi$
$883$			37.3627i			1.25735i	−0.777667	+	0.628677i	$0.783597\pi$
$884$	14.1289			0.475207
$885$	−59.2852	+	9.96237i	−1.99285	+	0.334881i
$886$	10.6467			0.357683
$887$		−	23.0234i		−	0.773050i	−0.922279	−	0.386525i	$-0.873675\pi$
$887$		−	23.0234i		−	0.773050i	0.922279	−	0.386525i	$-0.126325\pi$
$888$		−	13.0194i		−	0.436901i
$889$	37.4482			1.25597
$890$	33.8030	−	5.68030i	1.13308	−	0.190404i
$891$	17.0670			0.571767
$892$			4.75420i			0.159183i
$893$		−	5.08247i		−	0.170078i
$894$	44.0578			1.47351
$895$	9.28780	+	55.2709i	0.310457	+	1.84750i
$896$	15.6822			0.523907
$897$			6.96015i			0.232393i
$898$			6.40723i			0.213812i
$899$	−35.0223			−1.16806
$900$	40.9200	−	14.1521i	1.36400	−	0.471738i
$901$	0.509626			0.0169781
$902$		−	2.57913i		−	0.0858756i
$903$		−	21.6922i		−	0.721870i
$904$	11.2104			0.372852
$905$	7.19594	+	42.8224i	0.239201	+	1.42347i
$906$	−41.4193			−1.37606
$907$		−	35.2693i		−	1.17110i	−0.810637	−	0.585549i	$-0.800879\pi$
$907$		−	35.2693i		−	1.17110i	0.810637	−	0.585549i	$-0.199121\pi$
$908$		−	13.2088i		−	0.438350i
$909$	−61.4482			−2.03811
$910$	−19.6741	+	3.30606i	−0.652190	+	0.109595i
$911$	−4.97260			−0.164750			−0.0823748	−	0.996601i	$-0.526250\pi$
$911$	−4.97260			−0.164750			−0.0823748	+	0.996601i	$0.526250\pi$
$912$		−	0.833070i		−	0.0275857i
$913$		−	3.11175i		−	0.102984i
$914$	31.2904			1.03499
$915$	−60.8700	+	10.2287i	−2.01230	+	0.338150i
$916$	−18.9934			−0.627558
$917$		−	25.8819i		−	0.854697i
$918$			40.2546i			1.32860i
$919$	48.7096			1.60678			0.803391	−	0.595451i	$-0.203027\pi$
$919$	48.7096			1.60678			0.803391	+	0.595451i	$0.203027\pi$
$920$	0.609632	+	3.62787i	0.0200990	+	0.119607i
$921$	−5.31927			−0.175276
$922$			7.28429i			0.239895i
$923$		−	13.8108i		−	0.454587i
$924$	7.29036			0.239835
$925$	−2.29444	−	6.63422i	−0.0754406	−	0.218132i
$926$	−22.9726			−0.754926
$927$		−	15.2695i		−	0.501516i
$928$		−	33.1729i		−	1.08895i
$929$	−32.5126			−1.06671			−0.533353	−	0.845893i	$-0.679068\pi$
$929$	−32.5126			−1.06671			−0.533353	+	0.845893i	$0.679068\pi$
$930$	6.31263	+	37.5659i	0.206999	+	1.23184i
$931$	0.258887			0.00848468
$932$			2.50407i			0.0820235i
$933$		−	2.38482i		−	0.0780755i
$934$	−24.3756			−0.797593
$935$	5.17613	−	0.869804i	0.169277	−	0.0284456i
$936$	−80.3038			−2.62481
$937$		−	0.385560i		−	0.0125957i	−0.999980	−	0.00629785i	$-0.997995\pi$
$937$		−	0.385560i		−	0.0125957i	0.999980	−	0.00629785i	$-0.00200468\pi$
$938$			34.9606i			1.14150i
$939$	−86.5126			−2.82323
$940$	−13.1959	+	2.21746i	−0.430404	+	0.0723257i
$941$	45.3482			1.47831			0.739154	−	0.673536i	$-0.235225\pi$
$941$	45.3482			1.47831			0.739154	+	0.673536i	$0.235225\pi$
$942$		−	22.1153i		−	0.720554i
$943$		−	2.19051i		−	0.0713329i
$944$	2.16295			0.0703982
$945$	13.4822	+	80.2316i	0.438577	+	2.60993i
$946$	1.74519			0.0567409
$947$			9.61202i			0.312349i	0.987730	+	0.156174i	$0.0499161\pi$
$947$			9.61202i			0.312349i	−0.987730	+	0.156174i	$0.950084\pi$
$948$		−	6.96015i		−	0.226055i
$949$	−41.0934			−1.33395
$950$	−1.48223	−	4.28576i	−0.0480898	−	0.139049i
$951$	26.2630			0.851635
$952$			23.6981i			0.768059i
$953$			59.8421i			1.93848i	0.246126	+	0.969238i	$0.420842\pi$
$953$			59.8421i			1.93848i	−0.246126	+	0.969238i	$0.579158\pi$
$954$	−1.07333			−0.0347503
$955$	−4.24315	−	25.2506i	−0.137305	−	0.817091i
$956$	16.9726			0.548933
$957$		−	14.3089i		−	0.462542i
$958$			26.2127i			0.846895i
$959$	25.1959			0.813619
$960$	−39.2563	+	6.59669i	−1.26699	+	0.212907i
$961$	3.07110			0.0990676
$962$			4.82441i			0.155545i
$963$		−	41.9518i		−	1.35188i
$964$	−0.191865			−0.00617954
$965$	−8.35482	+	1.40396i	−0.268951	+	0.0451949i
$966$	−4.32591			−0.139184
$967$		−	0.368324i		−	0.0118445i	−0.999982	−	0.00592225i	$-0.998115\pi$
$967$		−	0.368324i		−	0.0118445i	0.999982	−	0.00592225i	$-0.00188512\pi$
$968$		−	30.1171i		−	0.967999i
$969$	−10.1919			−0.327410
$970$	1.27334	+	7.57755i	0.0408845	+	0.243300i
$971$	−45.8370			−1.47098			−0.735490	−	0.677535i	$-0.763048\pi$
$971$	−45.8370			−1.47098			−0.735490	+	0.677535i	$0.763048\pi$
$972$			37.7531i			1.21093i
$973$		−	34.9231i		−	1.11958i
$974$	16.0800			0.515235
$975$	−57.6111	+	19.9247i	−1.84503	+	0.638102i
$976$	2.22077			0.0710853
$977$			29.0337i			0.928872i	0.885607	+	0.464436i	$0.153743\pi$
$977$			29.0337i			0.928872i	−0.885607	+	0.464436i	$0.846257\pi$
$978$		−	57.4239i		−	1.83621i
$979$	12.5259			0.400330
$980$	−0.112952	−	0.672165i	−0.00360811	−	0.0214715i
$981$	12.1000			0.386323
$982$		−	31.8930i		−	1.01775i
$983$			11.0160i			0.351355i	0.984448	+	0.175677i	$0.0562116\pi$
$983$			11.0160i			0.351355i	−0.984448	+	0.175677i	$0.943788\pi$
$984$	35.5822			1.13432
$985$	5.03555	−	0.846180i	0.160446	−	0.0269615i
$986$	17.2356			0.548892
$987$		−	42.4631i		−	1.35161i
$988$		−	4.46094i		−	0.141921i
$989$	1.48223			0.0471320
$990$	−10.9015	+	1.83190i	−0.346473	+	0.0582217i
$991$	−25.6822			−0.815823			−0.407912	−	0.913021i	$-0.633743\pi$
$991$	−25.6822			−0.815823			−0.407912	+	0.913021i	$0.633743\pi$
$992$			32.2719i			1.02463i
$993$			25.7431i			0.816933i
$994$	8.58374			0.272260
$995$	−7.20760	−	42.8918i	−0.228496	−	1.35976i
$996$	15.9081			0.504069
$997$			20.3854i			0.645611i	0.946465	+	0.322805i	$0.104626\pi$
$997$			20.3854i			0.645611i	−0.946465	+	0.322805i	$0.895374\pi$
$998$		−	19.4551i		−	0.615842i
$999$	19.6741			0.622461

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.b.b.39.4	yes	6
3.2	odd	2		855.2.c.d.514.3		6
4.3	odd	2		1520.2.d.h.609.1		6
5.2	odd	4		475.2.a.j.1.3		6
5.3	odd	4		475.2.a.j.1.4		6
5.4	even	2	inner	95.2.b.b.39.3	✓	6
15.2	even	4		4275.2.a.br.1.4		6
15.8	even	4		4275.2.a.br.1.3		6
15.14	odd	2		855.2.c.d.514.4		6
19.18	odd	2		1805.2.b.e.1084.3		6
20.3	even	4		7600.2.a.ck.1.6		6
20.7	even	4		7600.2.a.ck.1.1		6
20.19	odd	2		1520.2.d.h.609.6		6
95.18	even	4		9025.2.a.bx.1.3		6
95.37	even	4		9025.2.a.bx.1.4		6
95.94	odd	2		1805.2.b.e.1084.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.b.b.39.3	✓	6	5.4	even	2	inner
95.2.b.b.39.4	yes	6	1.1	even	1	trivial
475.2.a.j.1.3		6	5.2	odd	4
475.2.a.j.1.4		6	5.3	odd	4
855.2.c.d.514.3		6	3.2	odd	2
855.2.c.d.514.4		6	15.14	odd	2
1520.2.d.h.609.1		6	4.3	odd	2
1520.2.d.h.609.6		6	20.19	odd	2
1805.2.b.e.1084.3		6	19.18	odd	2
1805.2.b.e.1084.4		6	95.94	odd	2
4275.2.a.br.1.3		6	15.8	even	4
4275.2.a.br.1.4		6	15.2	even	4
7600.2.a.ck.1.1		6	20.7	even	4
7600.2.a.ck.1.6		6	20.3	even	4
9025.2.a.bx.1.3		6	95.18	even	4
9025.2.a.bx.1.4		6	95.37	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)

\(f(q)\)	\(=\)	\(q+0.906968i q^{2} +3.21789i q^{3} +1.17741 q^{4} +(-0.370556 - 2.20515i) q^{5} -2.91852 q^{6} -2.59637i q^{7} +2.88181i q^{8} -7.35482 q^{9} +O(q^{10})\)	\(q+0.906968i q^{2} +3.21789i q^{3} +1.17741 q^{4} +(-0.370556 - 2.20515i) q^{5} -2.91852 q^{6} -2.59637i q^{7} +2.88181i q^{8} -7.35482 q^{9} +(2.00000 - 0.336083i) q^{10} +0.741113 q^{11} +3.78878i q^{12} -3.78878i q^{13} +2.35482 q^{14} +(7.09593 - 1.19241i) q^{15} -0.258887 q^{16} +3.16725i q^{17} -6.67058i q^{18} +1.00000 q^{19} +(-0.436297 - 2.59637i) q^{20} +8.35482 q^{21} +0.672165i q^{22} +0.570885i q^{23} -9.27334 q^{24} +(-4.72538 + 1.63427i) q^{25} +3.43630 q^{26} -14.0133i q^{27} -3.05699i q^{28} -6.00000 q^{29} +(1.08148 + 6.43578i) q^{30} +5.83705 q^{31} +5.52881i q^{32} +2.38482i q^{33} -2.87259 q^{34} +(-5.72538 + 0.962100i) q^{35} -8.65964 q^{36} +1.40396i q^{37} +0.906968i q^{38} +12.1919 q^{39} +(6.35482 - 1.06787i) q^{40} -3.83705 q^{41} +7.57755i q^{42} -2.59637i q^{43} +0.872594 q^{44} +(2.72538 + 16.2185i) q^{45} -0.517774 q^{46} -5.08247i q^{47} -0.833070i q^{48} +0.258887 q^{49} +(-1.48223 - 4.28576i) q^{50} -10.1919 q^{51} -4.46094i q^{52} -0.160905i q^{53} +12.7096 q^{54} +(-0.274624 - 1.63427i) q^{55} +7.48223 q^{56} +3.21789i q^{57} -5.44181i q^{58} -8.35482 q^{59} +(8.35482 - 1.40396i) q^{60} -8.57816 q^{61} +5.29401i q^{62} +19.0958i q^{63} -5.53223 q^{64} +(-8.35482 + 1.40396i) q^{65} -2.16295 q^{66} +14.8464i q^{67} +3.72915i q^{68} -1.83705 q^{69} +(-0.872594 - 5.19273i) q^{70} +3.64518 q^{71} -21.1952i q^{72} -10.8461i q^{73} -1.27334 q^{74} +(-5.25889 - 15.2057i) q^{75} +1.17741 q^{76} -1.92420i q^{77} +11.0576i q^{78} -1.83705 q^{79} +(0.0959323 + 0.570885i) q^{80} +23.0289 q^{81} -3.48008i q^{82} -4.19876i q^{83} +9.83705 q^{84} +(6.98426 - 1.17365i) q^{85} +2.35482 q^{86} -19.3073i q^{87} +2.13574i q^{88} +16.9015 q^{89} +(-14.7096 + 2.47183i) q^{90} -9.83705 q^{91} +0.672165i q^{92} +18.7830i q^{93} +4.60963 q^{94} +(-0.370556 - 2.20515i) q^{95} -17.7911 q^{96} +3.78878i q^{97} +0.234802i q^{98} -5.45075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 8 q^{4} - q^{5} - 14 q^{9}+O(q^{10}) \) 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

Varieties

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Representations

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Database

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