LMFDB - Embedded newform 465.2.c.a.94.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(94,465)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("465.94"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.1016580161536.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 12x^{8} + 48x^{6} + 72x^{4} + 36x^{2} + 4 $ x^10 + 12x^8 + 48x^6 + 72x^4 + 36x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			94.1
Root			$2.10518i$ of defining polynomial
Character	$\chi$	$=$	465.94
Dual form			465.2.c.a.94.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.58691i q^{2} -1.00000i q^{3} -4.69208 q^{4} +(-2.10518 - 0.753811i) q^{5} -2.58691 q^{6} -3.58691i q^{7} +6.96416i q^{8} -1.00000 q^{9} +(-1.95004 + 5.44589i) q^{10} +0.908949 q^{11} +4.69208i q^{12} +2.27208i q^{13} -9.27899 q^{14} +(-0.753811 + 2.10518i) q^{15} +8.63147 q^{16} -0.477180i q^{17} +2.58691i q^{18} +2.95004 q^{19} +(9.87766 + 3.53695i) q^{20} -3.58691 q^{21} -2.35137i q^{22} -6.10865i q^{23} +6.96416 q^{24} +(3.86354 + 3.17381i) q^{25} +5.87766 q^{26} +1.00000i q^{27} +16.8301i q^{28} -6.96871 q^{29} +(5.44589 + 1.95004i) q^{30} -1.00000 q^{31} -8.40048i q^{32} -0.908949i q^{33} -1.23442 q^{34} +(-2.70385 + 7.55107i) q^{35} +4.69208 q^{36} +8.99461i q^{37} -7.63147i q^{38} +2.27208 q^{39} +(5.24967 - 14.6608i) q^{40} +1.06752 q^{41} +9.27899i q^{42} +2.99545i q^{43} -4.26486 q^{44} +(2.10518 + 0.753811i) q^{45} -15.8025 q^{46} -12.7484i q^{47} -8.63147i q^{48} -5.86589 q^{49} +(8.21035 - 9.99461i) q^{50} -0.477180 q^{51} -10.6608i q^{52} -11.2038i q^{53} +2.58691 q^{54} +(-1.91350 - 0.685176i) q^{55} +24.9798 q^{56} -2.95004i q^{57} +18.0274i q^{58} -7.93217 q^{59} +(3.53695 - 9.87766i) q^{60} -10.9783 q^{61} +2.58691i q^{62} +3.58691i q^{63} -4.46831 q^{64} +(1.71272 - 4.78313i) q^{65} -2.35137 q^{66} -10.8018i q^{67} +2.23897i q^{68} -6.10865 q^{69} +(19.5339 + 6.99461i) q^{70} -13.9150 q^{71} -6.96416i q^{72} +3.35526i q^{73} +23.2682 q^{74} +(3.17381 - 3.86354i) q^{75} -13.8418 q^{76} -3.26031i q^{77} -5.87766i q^{78} +15.3540 q^{79} +(-18.1708 - 6.50650i) q^{80} +1.00000 q^{81} -2.76156i q^{82} +14.6010i q^{83} +16.8301 q^{84} +(-0.359704 + 1.00455i) q^{85} +7.74895 q^{86} +6.96871i q^{87} +6.33007i q^{88} -4.85556 q^{89} +(1.95004 - 5.44589i) q^{90} +8.14974 q^{91} +28.6623i q^{92} +1.00000i q^{93} -32.9790 q^{94} +(-6.21035 - 2.22377i) q^{95} -8.40048 q^{96} -11.1914i q^{97} +15.1745i q^{98} -0.908949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 6 q^{4} - 6 q^{6} - 10 q^{9} + 2 q^{10} - 32 q^{14} + 2 q^{15} + 6 q^{16} + 8 q^{19} + 28 q^{20} - 16 q^{21} + 18 q^{24} - 2 q^{25} - 12 q^{26} - 8 q^{29} + 4 q^{30} - 10 q^{31} - 12 q^{34} + 4 q^{35}+ \cdots - 2 q^{96}+O(q^{100}) $ 10 * q - 6 * q^4 - 6 * q^6 - 10 * q^9 + 2 * q^10 - 32 * q^14 + 2 * q^15 + 6 * q^16 + 8 * q^19 + 28 * q^20 - 16 * q^21 + 18 * q^24 - 2 * q^25 - 12 * q^26 - 8 * q^29 + 4 * q^30 - 10 * q^31 - 12 * q^34 + 4 * q^35 + 6 * q^36 + 12 * q^39 + 14 * q^40 - 12 * q^44 - 32 * q^46 + 22 * q^49 + 40 * q^50 - 16 * q^51 + 6 * q^54 + 36 * q^56 - 20 * q^59 - 6 * q^60 - 28 * q^61 - 22 * q^64 + 20 * q^65 - 12 * q^66 + 8 * q^69 + 32 * q^70 + 12 * q^71 + 8 * q^74 - 8 * q^75 - 16 * q^76 + 48 * q^79 - 20 * q^80 + 10 * q^81 + 36 * q^84 - 4 * q^85 + 8 * q^86 - 20 * q^89 - 2 * q^90 - 24 * q^94 - 20 * q^95 - 2 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	2.58691i		−	1.82922i	−0.404339	−	0.914609i	$-0.632498\pi$
$2$		−	2.58691i		−	1.82922i	0.404339	−	0.914609i	$-0.367502\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−4.69208			−2.34604
$5$	−2.10518	−	0.753811i	−0.941464	−	0.337115i
$5$	−2.10518	−	0.753811i	−0.941464	−	0.337115i
$6$	−2.58691			−1.05610
$7$		−	3.58691i		−	1.35572i	−0.735190	−	0.677862i	$-0.762907\pi$
$7$		−	3.58691i		−	1.35572i	0.735190	−	0.677862i	$-0.237093\pi$
$8$			6.96416i			2.46220i
$9$	−1.00000			−0.333333
$10$	−1.95004	+	5.44589i	−0.616656	+	1.72214i
$11$	0.908949			0.274058			0.137029	−	0.990567i	$-0.456245\pi$
$11$	0.908949			0.274058			0.137029	+	0.990567i	$0.456245\pi$
$12$			4.69208i			1.35449i
$13$			2.27208i			0.630162i	0.949065	+	0.315081i	$0.102032\pi$
$13$			2.27208i			0.630162i	−0.949065	+	0.315081i	$0.897968\pi$
$14$	−9.27899			−2.47991
$15$	−0.753811	+	2.10518i	−0.194633	+	0.543554i
$16$	8.63147			2.15787
$17$		−	0.477180i		−	0.115733i	−0.998324	−	0.0578666i	$-0.981570\pi$
$17$		−	0.477180i		−	0.115733i	0.998324	−	0.0578666i	$-0.0184298\pi$
$18$			2.58691i			0.609740i
$19$	2.95004			0.676785			0.338393	−	0.941005i	$-0.390117\pi$
$19$	2.95004			0.676785			0.338393	+	0.941005i	$0.390117\pi$
$20$	9.87766	+	3.53695i	2.20871	+	0.790885i
$21$	−3.58691			−0.782727
$22$		−	2.35137i		−	0.501313i
$23$		−	6.10865i		−	1.27374i	−0.770970	−	0.636871i	$-0.780228\pi$
$23$		−	6.10865i		−	1.27374i	0.770970	−	0.636871i	$-0.219772\pi$
$24$	6.96416			1.42155
$25$	3.86354	+	3.17381i	0.772707	+	0.634762i
$26$	5.87766			1.15270
$27$			1.00000i			0.192450i
$28$			16.8301i			3.18058i
$29$	−6.96871			−1.29406			−0.647029	−	0.762466i	$-0.723989\pi$
$29$	−6.96871			−1.29406			−0.647029	+	0.762466i	$0.723989\pi$
$30$	5.44589	+	1.95004i	0.994280	+	0.356027i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$		−	8.40048i		−	1.48501i
$33$		−	0.908949i		−	0.158228i
$34$	−1.23442			−0.211701
$35$	−2.70385	+	7.55107i	−0.457034	+	1.27636i
$36$	4.69208			0.782014
$37$			8.99461i			1.47870i	0.673319	+	0.739352i	$0.264868\pi$
$37$			8.99461i			1.47870i	−0.673319	+	0.739352i	$0.735132\pi$
$38$		−	7.63147i		−	1.23799i
$39$	2.27208			0.363824
$40$	5.24967	−	14.6608i	0.830045	−	2.31808i
$41$	1.06752			0.166718			0.0833590	−	0.996520i	$-0.473435\pi$
$41$	1.06752			0.166718			0.0833590	+	0.996520i	$0.473435\pi$
$42$			9.27899i			1.43178i
$43$			2.99545i			0.456802i	0.973567	+	0.228401i	$0.0733497\pi$
$43$			2.99545i			0.456802i	−0.973567	+	0.228401i	$0.926650\pi$
$44$	−4.26486			−0.642952
$45$	2.10518	+	0.753811i	0.313821	+	0.112372i
$46$	−15.8025			−2.32995
$47$		−	12.7484i		−	1.85955i	−0.368131	−	0.929774i	$-0.620002\pi$
$47$		−	12.7484i		−	1.85955i	0.368131	−	0.929774i	$-0.379998\pi$
$48$		−	8.63147i		−	1.24585i
$49$	−5.86589			−0.837985
$50$	8.21035	−	9.99461i	1.16112	−	1.41345i
$51$	−0.477180			−0.0668186
$52$		−	10.6608i		−	1.47839i
$53$		−	11.2038i		−	1.53897i	−0.638667	−	0.769483i	$-0.720514\pi$
$53$		−	11.2038i		−	1.53897i	0.638667	−	0.769483i	$-0.279486\pi$
$54$	2.58691			0.352033
$55$	−1.91350	−	0.685176i	−0.258016	−	0.0923891i
$56$	24.9798			3.33807
$57$		−	2.95004i		−	0.390742i
$58$			18.0274i			2.36711i
$59$	−7.93217			−1.03268			−0.516340	−	0.856383i	$-0.672706\pi$
$59$	−7.93217			−1.03268			−0.516340	+	0.856383i	$0.672706\pi$
$60$	3.53695	−	9.87766i	0.456618	−	1.27520i
$61$	−10.9783			−1.40563			−0.702813	−	0.711375i	$-0.748073\pi$
$61$	−10.9783			−1.40563			−0.702813	+	0.711375i	$0.748073\pi$
$62$			2.58691i			0.328537i
$63$			3.58691i			0.451908i
$64$	−4.46831			−0.558539
$65$	1.71272	−	4.78313i	0.212437	−	0.593275i
$66$	−2.35137			−0.289433
$67$		−	10.8018i		−	1.31965i	−0.751419	−	0.659825i	$-0.770630\pi$
$67$		−	10.8018i		−	1.31965i	0.751419	−	0.659825i	$-0.229370\pi$
$68$			2.23897i			0.271515i
$69$	−6.10865			−0.735396
$70$	19.5339	+	6.99461i	2.33475	+	0.836015i
$71$	−13.9150			−1.65141			−0.825704	−	0.564104i	$-0.809222\pi$
$71$	−13.9150			−1.65141			−0.825704	+	0.564104i	$0.809222\pi$
$72$		−	6.96416i		−	0.820735i
$73$			3.35526i			0.392703i	0.980534	+	0.196352i	$0.0629094\pi$
$73$			3.35526i			0.392703i	−0.980534	+	0.196352i	$0.937091\pi$
$74$	23.2682			2.70487
$75$	3.17381	−	3.86354i	0.366480	−	0.446123i
$76$	−13.8418			−1.58777
$77$		−	3.26031i		−	0.371547i
$78$		−	5.87766i		−	0.665514i
$79$	15.3540			1.72745			0.863727	−	0.503960i	$-0.168124\pi$
$79$	15.3540			1.72745			0.863727	+	0.503960i	$0.168124\pi$
$80$	−18.1708	−	6.50650i	−2.03155	−	0.727449i
$81$	1.00000			0.111111
$82$		−	2.76156i		−	0.304964i
$83$			14.6010i			1.60267i	0.598215	+	0.801336i	$0.295877\pi$
$83$			14.6010i			1.60267i	−0.598215	+	0.801336i	$0.704123\pi$
$84$	16.8301			1.83631
$85$	−0.359704	+	1.00455i	−0.0390154	+	0.108959i
$86$	7.74895			0.835591
$87$			6.96871i			0.747125i
$88$			6.33007i			0.674788i
$89$	−4.85556			−0.514688			−0.257344	−	0.966320i	$-0.582847\pi$
$89$	−4.85556			−0.514688			−0.257344	+	0.966320i	$0.582847\pi$
$90$	1.95004	−	5.44589i	0.205552	−	0.574048i
$91$	8.14974			0.854325
$92$			28.6623i			2.98825i
$93$			1.00000i			0.103695i
$94$	−32.9790			−3.40152
$95$	−6.21035	−	2.22377i	−0.637169	−	0.228154i
$96$	−8.40048			−0.857371
$97$		−	11.1914i		−	1.13631i	−0.822921	−	0.568156i	$-0.807657\pi$
$97$		−	11.1914i		−	1.13631i	0.822921	−	0.568156i	$-0.192343\pi$
$98$			15.1745i			1.53286i
$99$	−0.908949			−0.0913528
$100$	−18.1280	−	14.8918i	−1.81280	−	1.48918i
$101$	0.0849038			0.00844824			0.00422412	−	0.999991i	$-0.498655\pi$
$101$	0.0849038			0.00844824			0.00422412	+	0.999991i	$0.498655\pi$
$102$			1.23442i			0.122226i
$103$		−	12.1556i		−	1.19772i	−0.800852	−	0.598862i	$-0.795620\pi$
$103$		−	12.1556i		−	1.19772i	0.800852	−	0.598862i	$-0.204380\pi$
$104$	−15.8232			−1.55159
$105$	7.55107	+	2.70385i	0.736909	+	0.263869i
$106$	−28.9833			−2.81511
$107$		−	2.01952i		−	0.195234i	−0.995224	−	0.0976171i	$-0.968878\pi$
$107$		−	2.01952i		−	0.195234i	0.995224	−	0.0976171i	$-0.0311221\pi$
$108$		−	4.69208i		−	0.451496i
$109$	6.73295			0.644899			0.322450	−	0.946587i	$-0.395494\pi$
$109$	6.73295			0.644899			0.322450	+	0.946587i	$0.395494\pi$
$110$	−1.77249	+	4.95004i	−0.169000	+	0.471968i
$111$	8.99461			0.853730
$112$		−	30.9603i		−	2.92547i
$113$			15.6406i			1.47134i	0.677339	+	0.735671i	$0.263133\pi$
$113$			15.6406i			1.47134i	−0.677339	+	0.735671i	$0.736867\pi$
$114$	−7.63147			−0.714753
$115$	−4.60477	+	12.8598i	−0.429397	+	1.19918i
$116$	32.6978			3.03591
$117$		−	2.27208i		−	0.210054i
$118$			20.5198i			1.88900i
$119$	−1.71160			−0.156902
$120$	−14.6608	−	5.24967i	−1.33834	−	0.479227i
$121$	−10.1738			−0.924892
$122$			28.3998i			2.57120i
$123$		−	1.06752i		−	0.0962546i
$124$	4.69208			0.421361
$125$	−5.74097	−	9.59381i	−0.513488	−	0.858097i
$126$	9.27899			0.826638
$127$			1.96737i			0.174576i	0.996183	+	0.0872878i	$0.0278200\pi$
$127$			1.96737i			0.174576i	−0.996183	+	0.0872878i	$0.972180\pi$
$128$		−	5.24187i		−	0.463320i
$129$	2.99545			0.263735
$130$	−12.3735	−	4.43065i	−1.08523	−	0.388594i
$131$	18.2065			1.59071			0.795355	−	0.606144i	$-0.207284\pi$
$131$	18.2065			1.59071			0.795355	+	0.606144i	$0.207284\pi$
$132$			4.26486i			0.371209i
$133$		−	10.5815i		−	0.917534i
$134$	−27.9433			−2.41393
$135$	0.753811	−	2.10518i	0.0648778	−	0.181185i
$136$	3.32316			0.284959
$137$		−	9.22738i		−	0.788348i	−0.919036	−	0.394174i	$-0.871031\pi$
$137$		−	9.22738i		−	0.788348i	0.919036	−	0.394174i	$-0.128969\pi$
$138$			15.8025i			1.34520i
$139$	−1.67631			−0.142182			−0.0710912	−	0.997470i	$-0.522648\pi$
$139$	−1.67631			−0.142182			−0.0710912	+	0.997470i	$0.522648\pi$
$140$	12.6867	−	35.4302i	1.07222	−	2.99440i
$141$	−12.7484			−1.07361
$142$			35.9968i			3.02079i
$143$			2.06521i			0.172701i
$144$	−8.63147			−0.719289
$145$	14.6704	+	5.25310i	1.21831	+	0.436246i
$146$	8.67973			0.718340
$147$			5.86589i			0.483811i
$148$		−	42.2034i		−	3.46910i
$149$	15.2671			1.25073			0.625364	−	0.780333i	$-0.284950\pi$
$149$	15.2671			1.25073			0.625364	+	0.780333i	$0.284950\pi$
$150$	−9.99461	−	8.21035i	−0.816056	−	0.670373i
$151$	−7.33698			−0.597075			−0.298537	−	0.954398i	$-0.596499\pi$
$151$	−7.33698			−0.597075			−0.298537	+	0.954398i	$0.596499\pi$
$152$			20.5446i			1.66638i
$153$			0.477180i			0.0385777i
$154$	−8.43413			−0.679641
$155$	2.10518	+	0.753811i	0.169092	+	0.0605476i
$156$	−10.6608			−0.853547
$157$			1.78946i			0.142814i	0.997447	+	0.0714072i	$0.0227490\pi$
$157$			1.78946i			0.142814i	−0.997447	+	0.0714072i	$0.977251\pi$
$158$		−	39.7192i		−	3.15989i
$159$	−11.2038			−0.888522
$160$	−6.33238	+	17.6845i	−0.500618	+	1.39808i
$161$	−21.9112			−1.72684
$162$		−	2.58691i		−	0.203247i
$163$		−	15.0336i		−	1.17752i	−0.808308	−	0.588759i	$-0.799617\pi$
$163$		−	15.0336i		−	1.17752i	0.808308	−	0.588759i	$-0.200383\pi$
$164$	−5.00887			−0.391127
$165$	−0.685176	+	1.91350i	−0.0533409	+	0.148966i
$166$	37.7715			2.93164
$167$			7.26503i			0.562185i	0.959681	+	0.281092i	$0.0906967\pi$
$167$			7.26503i			0.562185i	−0.959681	+	0.281092i	$0.909303\pi$
$168$		−	24.9798i		−	1.92723i
$169$	7.83764			0.602896
$170$	2.59867	+	0.930520i	0.199309	+	0.0713677i
$171$	−2.95004			−0.225595
$172$		−	14.0549i		−	1.07168i
$173$		−	10.3984i		−	0.790575i	−0.918557	−	0.395288i	$-0.870645\pi$
$173$		−	10.3984i		−	0.790575i	0.918557	−	0.395288i	$-0.129355\pi$
$174$	18.0274			1.36665
$175$	11.3842	−	13.8581i	0.860562	−	1.04758i
$176$	7.84557			0.591382
$177$			7.93217i			0.596219i
$178$			12.5609i			0.941477i
$179$	12.6366			0.944504			0.472252	−	0.881464i	$-0.343441\pi$
$179$	12.6366			0.944504			0.472252	+	0.881464i	$0.343441\pi$
$180$	−9.87766	−	3.53695i	−0.736237	−	0.263628i
$181$	11.6810			0.868243			0.434122	−	0.900854i	$-0.357059\pi$
$181$	11.6810			0.868243			0.434122	+	0.900854i	$0.357059\pi$
$182$		−	21.0826i		−	1.56275i
$183$			10.9783i			0.811539i
$184$	42.5417			3.13621
$185$	6.78024	−	18.9352i	0.498493	−	1.39215i
$186$	2.58691			0.189681
$187$		−	0.433733i		−	0.0317177i
$188$			59.8166i			4.36258i
$189$	3.58691			0.260909
$190$	−5.75269	+	16.0656i	−0.417344	+	1.16552i
$191$	−2.43675			−0.176317			−0.0881584	−	0.996106i	$-0.528098\pi$
$191$	−2.43675			−0.176317			−0.0881584	+	0.996106i	$0.528098\pi$
$192$			4.46831i			0.322472i
$193$		−	11.5074i		−	0.828323i	−0.910203	−	0.414162i	$-0.864075\pi$
$193$		−	11.5074i		−	0.828323i	0.910203	−	0.414162i	$-0.135925\pi$
$194$	−28.9510			−2.07856
$195$	−4.78313	−	1.71272i	−0.342527	−	0.122651i
$196$	27.5233			1.96595
$197$		−	13.5963i		−	0.968696i	−0.874875	−	0.484348i	$-0.839057\pi$
$197$		−	13.5963i		−	0.968696i	0.874875	−	0.484348i	$-0.160943\pi$
$198$			2.35137i			0.167104i
$199$	11.5595			0.819433			0.409717	−	0.912213i	$-0.365628\pi$
$199$	11.5595			0.819433			0.409717	+	0.912213i	$0.365628\pi$
$200$	−22.1029	+	26.9063i	−1.56291	+	1.90256i
$201$	−10.8018			−0.761901
$202$		−	0.219638i		−	0.0154537i
$203$			24.9961i			1.75438i
$204$	2.23897			0.156759
$205$	−2.24731	−	0.804705i	−0.156959	−	0.0562031i
$206$	−31.4453			−2.19090
$207$			6.10865i			0.424581i
$208$			19.6114i			1.35981i
$209$	2.68143			0.185479
$210$	6.99461	−	19.5339i	0.482674	−	1.34797i
$211$	4.88493			0.336292			0.168146	−	0.985762i	$-0.446222\pi$
$211$	4.88493			0.336292			0.168146	+	0.985762i	$0.446222\pi$
$212$			52.5693i			3.61048i
$213$			13.9150i			0.953441i
$214$	−5.22430			−0.357126
$215$	2.25800	−	6.30595i	0.153995	−	0.430062i
$216$	−6.96416			−0.473851
$217$			3.58691i			0.243495i
$218$		−	17.4175i		−	1.17966i
$219$	3.35526			0.226727
$220$	8.97829	+	3.21490i	0.605316	+	0.216749i
$221$	1.08419			0.0729307
$222$		−	23.2682i		−	1.56166i
$223$		−	2.71673i		−	0.181926i	−0.995854	−	0.0909629i	$-0.971006\pi$
$223$		−	2.71673i		−	0.181926i	0.995854	−	0.0909629i	$-0.0289945\pi$
$224$	−30.1317			−2.01326
$225$	−3.86354	−	3.17381i	−0.257569	−	0.211587i
$226$	40.4607			2.69140
$227$		−	15.8826i		−	1.05417i	−0.849813	−	0.527084i	$-0.823285\pi$
$227$		−	15.8826i		−	1.05417i	0.849813	−	0.527084i	$-0.176715\pi$
$228$			13.8418i			0.916697i
$229$	4.20248			0.277708			0.138854	−	0.990313i	$-0.455658\pi$
$229$	4.20248			0.277708			0.138854	+	0.990313i	$0.455658\pi$
$230$	33.2671	+	11.9121i	2.19357	+	0.785462i
$231$	−3.26031			−0.214513
$232$		−	48.5313i		−	3.18623i
$233$		−	15.7806i		−	1.03382i	−0.856039	−	0.516912i	$-0.827081\pi$
$233$		−	15.7806i		−	1.03382i	0.856039	−	0.516912i	$-0.172919\pi$
$234$	−5.87766			−0.384235
$235$	−9.60990	+	26.8377i	−0.626881	+	1.75070i
$236$	37.2184			2.42271
$237$		−	15.3540i		−	0.997346i
$238$			4.42775i			0.287008i
$239$	8.89923			0.575643			0.287822	−	0.957684i	$-0.407069\pi$
$239$	8.89923			0.575643			0.287822	+	0.957684i	$0.407069\pi$
$240$	−6.50650	+	18.1708i	−0.419993	+	1.17292i
$241$	−24.9570			−1.60762			−0.803811	−	0.594885i	$-0.797197\pi$
$241$	−24.9570			−1.60762			−0.803811	+	0.594885i	$0.797197\pi$
$242$			26.3187i			1.69183i
$243$		−	1.00000i		−	0.0641500i
$244$	51.5110			3.29766
$245$	12.3487	+	4.42178i	0.788932	+	0.282497i
$246$	−2.76156			−0.176071
$247$			6.70273i			0.426485i
$248$		−	6.96416i		−	0.442225i
$249$	14.6010			0.925303
$250$	−24.8183	+	14.8514i	−1.56965	+	0.939282i
$251$	−19.3924			−1.22404			−0.612020	−	0.790842i	$-0.709643\pi$
$251$	−19.3924			−1.22404			−0.612020	+	0.790842i	$0.709643\pi$
$252$		−	16.8301i		−	1.06019i
$253$		−	5.55245i		−	0.349080i
$254$	5.08939			0.319337
$255$	1.00455	+	0.359704i	0.0629073	+	0.0225255i
$256$	−22.4968			−1.40605
$257$			3.00568i			0.187489i	0.995596	+	0.0937447i	$0.0298838\pi$
$257$			3.00568i			0.187489i	−0.995596	+	0.0937447i	$0.970116\pi$
$258$		−	7.74895i		−	0.482429i
$259$	32.2628			2.00471
$260$	−8.03623	+	22.4429i	−0.498386	+	1.39185i
$261$	6.96871			0.431353
$262$		−	47.0985i		−	2.90976i
$263$			19.8092i			1.22149i	0.791828	+	0.610744i	$0.209129\pi$
$263$			19.8092i			1.22149i	−0.791828	+	0.610744i	$0.790871\pi$
$264$	6.33007			0.389589
$265$	−8.44558	+	23.5861i	−0.518808	+	1.44888i
$266$	−27.3734			−1.67837
$267$			4.85556i			0.297155i
$268$			50.6830i			3.09596i
$269$	18.1586			1.10715			0.553574	−	0.832800i	$-0.313264\pi$
$269$	18.1586			1.10715			0.553574	+	0.832800i	$0.313264\pi$
$270$	−5.44589	−	1.95004i	−0.331427	−	0.118676i
$271$	−8.15979			−0.495672			−0.247836	−	0.968802i	$-0.579719\pi$
$271$	−8.15979			−0.495672			−0.247836	+	0.968802i	$0.579719\pi$
$272$		−	4.11877i		−	0.249737i
$273$		−	8.14974i		−	0.493245i
$274$	−23.8704			−1.44206
$275$	3.51176	+	2.88483i	0.211767	+	0.173962i
$276$	28.6623			1.72527
$277$		−	7.51962i		−	0.451810i	−0.974149	−	0.225905i	$-0.927466\pi$
$277$		−	7.51962i		−	0.451810i	0.974149	−	0.225905i	$-0.0725339\pi$
$278$			4.33644i			0.260083i
$279$	1.00000			0.0598684
$280$	−52.5869	−	18.8301i	−3.14267	−	1.12531i
$281$	17.2223			1.02740			0.513698	−	0.857971i	$-0.328275\pi$
$281$	17.2223			1.02740			0.513698	+	0.857971i	$0.328275\pi$
$282$			32.9790i			1.96387i
$283$			19.1614i			1.13903i	0.821981	+	0.569515i	$0.192869\pi$
$283$			19.1614i			1.13903i	−0.821981	+	0.569515i	$0.807131\pi$
$284$	65.2904			3.87427
$285$	−2.22377	+	6.21035i	−0.131725	+	0.367870i
$286$	5.34249			0.315908
$287$		−	3.82908i		−	0.226023i
$288$			8.40048i			0.495003i
$289$	16.7723			0.986606
$290$	13.5893	−	37.9509i	0.797989	−	2.22855i
$291$	−11.1914			−0.656050
$292$		−	15.7431i		−	0.921298i
$293$		−	14.5797i		−	0.851757i	−0.904780	−	0.425879i	$-0.859965\pi$
$293$		−	14.5797i		−	0.851757i	0.904780	−	0.425879i	$-0.140035\pi$
$294$	15.1745			0.884996
$295$	16.6986	+	5.97936i	0.972231	+	0.348132i
$296$	−62.6399			−3.64087
$297$			0.908949i			0.0527426i
$298$		−	39.4945i		−	2.28786i
$299$	13.8794			0.802664
$300$	−14.8918	+	18.1280i	−0.859778	+	1.04662i
$301$	10.7444			0.619297
$302$			18.9801i			1.09218i
$303$		−	0.0849038i		−	0.00487759i
$304$	25.4632			1.46041
$305$	23.1112	+	8.27556i	1.32335	+	0.473857i
$306$	1.23442			0.0705671
$307$			8.86561i			0.505987i	0.967468	+	0.252993i	$0.0814151\pi$
$307$			8.86561i			0.505987i	−0.967468	+	0.252993i	$0.918585\pi$
$308$			15.2977i			0.871665i
$309$	−12.1556			−0.691507
$310$	1.95004	−	5.44589i	0.110755	−	0.309306i
$311$	−16.5334			−0.937524			−0.468762	−	0.883324i	$-0.655300\pi$
$311$	−16.5334			−0.937524			−0.468762	+	0.883324i	$0.655300\pi$
$312$			15.8232i			0.895810i
$313$		−	12.5419i		−	0.708911i	−0.935073	−	0.354455i	$-0.884666\pi$
$313$		−	12.5419i		−	0.708911i	0.935073	−	0.354455i	$-0.115334\pi$
$314$	4.62916			0.261239
$315$	2.70385	−	7.55107i	0.152345	−	0.425455i
$316$	−72.0420			−4.05268
$317$			6.14459i			0.345115i	0.984999	+	0.172557i	$0.0552030\pi$
$317$			6.14459i			0.345115i	−0.984999	+	0.172557i	$0.944797\pi$
$318$			28.9833i			1.62530i
$319$	−6.33420			−0.354647
$320$	9.40658	+	3.36826i	0.525844	+	0.188292i
$321$	−2.01952			−0.112719
$322$			56.6821i			3.15877i
$323$		−	1.40770i		−	0.0783266i
$324$	−4.69208			−0.260671
$325$	−7.21116	+	8.77827i	−0.400003	+	0.486931i
$326$	−38.8904			−2.15394
$327$		−	6.73295i		−	0.372333i
$328$			7.43435i			0.410493i
$329$	−45.7274			−2.52103
$330$	4.95004	+	1.77249i	0.272491	+	0.0975721i
$331$	23.1429			1.27205			0.636023	−	0.771670i	$-0.280578\pi$
$331$	23.1429			1.27205			0.636023	+	0.771670i	$0.280578\pi$
$332$		−	68.5092i		−	3.75993i
$333$		−	8.99461i		−	0.492901i
$334$	18.7939			1.02836
$335$	−8.14253	+	22.7397i	−0.444874	+	1.24240i
$336$	−30.9603			−1.68902
$337$		−	32.5847i		−	1.77500i	−0.460804	−	0.887502i	$-0.652439\pi$
$337$		−	32.5847i		−	1.77500i	0.460804	−	0.887502i	$-0.347561\pi$
$338$		−	20.2752i		−	1.10283i
$339$	15.6406			0.849479
$340$	1.68776	−	4.71343i	0.0915317	−	0.255621i
$341$	−0.908949			−0.0492223
$342$			7.63147i			0.412663i
$343$		−	4.06793i		−	0.219648i
$344$	−20.8608			−1.12474
$345$	12.8598	+	4.60477i	0.692348	+	0.247913i
$346$	−26.8997			−1.44613
$347$			18.8088i			1.00971i	0.863204	+	0.504856i	$0.168454\pi$
$347$			18.8088i			1.00971i	−0.863204	+	0.504856i	$0.831546\pi$
$348$		−	32.6978i		−	1.75278i
$349$	−33.0149			−1.76725			−0.883623	−	0.468198i	$-0.844903\pi$
$349$	−33.0149			−1.76725			−0.883623	+	0.468198i	$0.844903\pi$
$350$	−35.8497	−	29.4498i	−1.91625	−	1.57416i
$351$	−2.27208			−0.121275
$352$		−	7.63561i		−	0.406979i
$353$		−	22.3180i		−	1.18787i	−0.804514	−	0.593933i	$-0.797574\pi$
$353$		−	22.3180i		−	1.18787i	0.804514	−	0.593933i	$-0.202426\pi$
$354$	20.5198			1.09061
$355$	29.2936	+	10.4893i	1.55474	+	0.556714i
$356$	22.7827			1.20748
$357$			1.71160i			0.0905875i
$358$		−	32.6897i		−	1.72770i
$359$	−3.91977			−0.206878			−0.103439	−	0.994636i	$-0.532985\pi$
$359$	−3.91977			−0.206878			−0.103439	+	0.994636i	$0.532985\pi$
$360$	−5.24967	+	14.6608i	−0.276682	+	0.772692i
$361$	−10.2973			−0.541962
$362$		−	30.2177i		−	1.58821i
$363$			10.1738i			0.533987i
$364$	−38.2393			−2.00428
$365$	2.52923	−	7.06341i	0.132386	−	0.369716i
$366$	28.3998			1.48448
$367$		−	1.21874i		−	0.0636177i	−0.999494	−	0.0318089i	$-0.989873\pi$
$367$		−	1.21874i		−	0.0636177i	0.999494	−	0.0318089i	$-0.0101268\pi$
$368$		−	52.7267i		−	2.74857i
$369$	−1.06752			−0.0555726
$370$	−48.9837	−	17.5398i	−2.54654	−	0.911853i
$371$	−40.1871			−2.08641
$372$		−	4.69208i		−	0.243273i
$373$			25.0440i			1.29673i	0.761331	+	0.648363i	$0.224546\pi$
$373$			25.0440i			1.29673i	−0.761331	+	0.648363i	$0.775454\pi$
$374$	−1.12203			−0.0580186
$375$	−9.59381	+	5.74097i	−0.495422	+	0.296463i
$376$	88.7821			4.57859
$377$		−	15.8335i		−	0.815466i
$378$		−	9.27899i		−	0.477260i
$379$	−21.3191			−1.09509			−0.547543	−	0.836777i	$-0.684437\pi$
$379$	−21.3191			−1.09509			−0.547543	+	0.836777i	$0.684437\pi$
$380$	29.1395	+	10.4341i	1.49482	+	0.535259i
$381$	1.96737			0.100791
$382$			6.30364i			0.322522i
$383$			20.2362i			1.03402i	0.855979	+	0.517011i	$0.172955\pi$
$383$			20.2362i			1.03402i	−0.855979	+	0.517011i	$0.827045\pi$
$384$	−5.24187			−0.267498
$385$	−2.45766	+	6.86354i	−0.125254	+	0.349798i
$386$	−29.7687			−1.51518
$387$		−	2.99545i		−	0.152267i
$388$			52.5108i			2.66583i
$389$	−28.4523			−1.44259			−0.721295	−	0.692628i	$-0.756453\pi$
$389$	−28.4523			−1.44259			−0.721295	+	0.692628i	$0.756453\pi$
$390$	−4.43065	+	12.3735i	−0.224355	+	0.626557i
$391$	−2.91493			−0.147414
$392$		−	40.8511i		−	2.06329i
$393$		−	18.2065i		−	0.918397i
$394$	−35.1723			−1.77196
$395$	−32.3228	−	11.5740i	−1.62634	−	0.582350i
$396$	4.26486			0.214317
$397$		−	0.525011i		−	0.0263495i	−0.999913	−	0.0131748i	$-0.995806\pi$
$397$		−	0.525011i		−	0.0263495i	0.999913	−	0.0131748i	$-0.00419378\pi$
$398$		−	29.9034i		−	1.49892i
$399$	−10.5815			−0.529738
$400$	33.3480	+	27.3947i	1.66740	+	1.36973i
$401$	18.3870			0.918205			0.459103	−	0.888383i	$-0.348171\pi$
$401$	18.3870			0.918205			0.459103	+	0.888383i	$0.348171\pi$
$402$			27.9433i			1.39368i
$403$		−	2.27208i		−	0.113180i
$404$	−0.398376			−0.0198199
$405$	−2.10518	−	0.753811i	−0.104607	−	0.0374572i
$406$	64.6626			3.20915
$407$			8.17564i			0.405251i
$408$		−	3.32316i		−	0.164521i
$409$	1.38591			0.0685291			0.0342645	−	0.999413i	$-0.489091\pi$
$409$	1.38591			0.0685291			0.0342645	+	0.999413i	$0.489091\pi$
$410$	−2.08170	+	5.81358i	−0.102808	+	0.287112i
$411$	−9.22738			−0.455153
$412$			57.0350i			2.80991i
$413$			28.4520i			1.40003i
$414$	15.8025			0.776651
$415$	11.0064	−	30.7377i	0.540284	−	1.50886i
$416$	19.0866			0.935797
$417$			1.67631i			0.0820890i
$418$		−	6.93662i		−	0.339281i
$419$	22.6214			1.10513			0.552564	−	0.833471i	$-0.313650\pi$
$419$	22.6214			1.10513			0.552564	+	0.833471i	$0.313650\pi$
$420$	−35.4302	−	12.6867i	−1.72882	−	0.619047i
$421$	14.5501			0.709127			0.354564	−	0.935032i	$-0.384629\pi$
$421$	14.5501			0.709127			0.354564	+	0.935032i	$0.384629\pi$
$422$		−	12.6369i		−	0.615152i
$423$			12.7484i			0.619849i
$424$	78.0254			3.78925
$425$	1.51448	−	1.84360i	0.0734631	−	0.0894279i
$426$	35.9968			1.74405
$427$			39.3781i			1.90564i
$428$			9.47575i			0.458028i
$429$	2.06521			0.0997091
$430$	−16.3129	−	5.84125i	−0.786678	−	0.281690i
$431$	39.6668			1.91068			0.955341	−	0.295506i	$-0.0954883\pi$
$431$	39.6668			1.91068			0.955341	+	0.295506i	$0.0954883\pi$
$432$			8.63147i			0.415282i
$433$			12.1560i			0.584181i	0.956391	+	0.292090i	$0.0943508\pi$
$433$			12.1560i			0.584181i	−0.956391	+	0.292090i	$0.905649\pi$
$434$	9.27899			0.445406
$435$	5.25310	−	14.6704i	0.251867	−	0.703391i
$436$	−31.5915			−1.51296
$437$		−	18.0208i		−	0.862050i
$438$		−	8.67973i		−	0.414734i
$439$	−10.7469			−0.512923			−0.256462	−	0.966554i	$-0.582557\pi$
$439$	−10.7469			−0.512923			−0.256462	+	0.966554i	$0.582557\pi$
$440$	4.77168	−	13.3259i	0.227481	−	0.635288i
$441$	5.86589			0.279328
$442$		−	2.80471i		−	0.133406i
$443$			11.1782i			0.531093i	0.964098	+	0.265547i	$0.0855524\pi$
$443$			11.1782i			0.531093i	−0.964098	+	0.265547i	$0.914448\pi$
$444$	−42.2034			−2.00289
$445$	10.2218	+	3.66018i	0.484560	+	0.173509i
$446$	−7.02793			−0.332782
$447$		−	15.2671i		−	0.722108i
$448$			16.0274i			0.757224i
$449$	22.4414			1.05908			0.529538	−	0.848286i	$-0.322365\pi$
$449$	22.4414			1.05908			0.529538	+	0.848286i	$0.322365\pi$
$450$	−8.21035	+	9.99461i	−0.387040	+	0.471150i
$451$	0.970317			0.0456904
$452$		−	73.3869i		−	3.45183i
$453$			7.33698i			0.344721i
$454$	−41.0869			−1.92830
$455$	−17.1567	−	6.14337i	−0.804316	−	0.288006i
$456$	20.5446			0.962087
$457$		−	2.19944i		−	0.102885i	−0.998676	−	0.0514427i	$-0.983618\pi$
$457$		−	2.19944i		−	0.102885i	0.998676	−	0.0514427i	$-0.0163819\pi$
$458$		−	10.8714i		−	0.507988i
$459$	0.477180			0.0222729
$460$	21.6060	−	60.3392i	1.00738	−	2.81333i
$461$	−24.0260			−1.11900			−0.559502	−	0.828829i	$-0.689007\pi$
$461$	−24.0260			−1.11900			−0.559502	+	0.828829i	$0.689007\pi$
$462$			8.43413i			0.392391i
$463$		−	18.5061i		−	0.860051i	−0.902817	−	0.430026i	$-0.858504\pi$
$463$		−	18.5061i		−	0.860051i	0.902817	−	0.430026i	$-0.141496\pi$
$464$	−60.1503			−2.79241
$465$	0.753811	−	2.10518i	0.0349572	−	0.0976252i
$466$	−40.8230			−1.89109
$467$			0.448198i			0.0207401i	0.999946	+	0.0103701i	$0.00330095\pi$
$467$			0.448198i			0.0207401i	−0.999946	+	0.0103701i	$0.996699\pi$
$468$			10.6608i			0.492795i
$469$	−38.7451			−1.78908
$470$	69.4265	+	24.8599i	3.20241	+	1.14670i
$471$	1.78946			0.0824540
$472$		−	55.2410i		−	2.54267i
$473$			2.72271i			0.125190i
$474$	−39.7192			−1.82436
$475$	11.3976	+	9.36287i	0.522957	+	0.429598i
$476$	8.03097			0.368099
$477$			11.2038i			0.512989i
$478$		−	23.0215i		−	1.05298i
$479$	17.1315			0.782759			0.391379	−	0.920229i	$-0.371998\pi$
$479$	17.1315			0.782759			0.391379	+	0.920229i	$0.371998\pi$
$480$	17.6845	+	6.33238i	0.807183	+	0.289032i
$481$	−20.4365			−0.931823
$482$			64.5614i			2.94069i
$483$			21.9112i			0.996993i
$484$	47.7364			2.16983
$485$	−8.43618	+	23.5598i	−0.383067	+	1.06980i
$486$	−2.58691			−0.117344
$487$		−	1.81921i		−	0.0824364i	−0.999150	−	0.0412182i	$-0.986876\pi$
$487$		−	1.81921i		−	0.0824364i	0.999150	−	0.0412182i	$-0.0131239\pi$
$488$		−	76.4546i		−	3.46094i
$489$	−15.0336			−0.679841
$490$	11.4387	−	31.9450i	0.516749	−	1.44313i
$491$	14.1569			0.638891			0.319445	−	0.947605i	$-0.396503\pi$
$491$	14.1569			0.638891			0.319445	+	0.947605i	$0.396503\pi$
$492$			5.00887i			0.225817i
$493$			3.32533i			0.149765i
$494$	17.3393			0.780134
$495$	1.91350	+	0.685176i	0.0860053	+	0.0307964i
$496$	−8.63147			−0.387565
$497$			49.9118i			2.23885i
$498$		−	37.7715i		−	1.69258i
$499$	39.9176			1.78696			0.893479	−	0.449104i	$-0.148257\pi$
$499$	39.9176			1.78696			0.893479	+	0.449104i	$0.148257\pi$
$500$	26.9371	+	45.0150i	1.20466	+	2.01313i
$501$	7.26503			0.324578
$502$			50.1664i			2.23904i
$503$			1.87127i			0.0834359i	0.999129	+	0.0417179i	$0.0132831\pi$
$503$			1.87127i			0.0834359i	−0.999129	+	0.0417179i	$0.986717\pi$
$504$	−24.9798			−1.11269
$505$	−0.178737	−	0.0640014i	−0.00795371	−	0.00284803i
$506$	−14.3637			−0.638543
$507$		−	7.83764i		−	0.348082i
$508$		−	9.23105i		−	0.409561i
$509$	10.8226			0.479701			0.239851	−	0.970810i	$-0.422902\pi$
$509$	10.8226			0.479701			0.239851	+	0.970810i	$0.422902\pi$
$510$	0.930520	−	2.59867i	0.0412041	−	0.115071i
$511$	12.0350			0.532397
$512$			47.7135i			2.10866i
$513$			2.95004i			0.130247i
$514$	7.77542			0.342959
$515$	−9.16301	+	25.5896i	−0.403771	+	1.12761i
$516$	−14.0549			−0.618733
$517$		−	11.5877i		−	0.509625i
$518$		−	83.4609i		−	3.66706i
$519$	−10.3984			−0.456439
$520$	33.3105	+	11.9277i	1.46076	+	0.523063i
$521$	−33.0540			−1.44812			−0.724060	−	0.689737i	$-0.757726\pi$
$521$	−33.0540			−1.44812			−0.724060	+	0.689737i	$0.757726\pi$
$522$		−	18.0274i		−	0.789038i
$523$			22.3790i			0.978564i	0.872126	+	0.489282i	$0.162741\pi$
$523$			22.3790i			0.978564i	−0.872126	+	0.489282i	$0.837259\pi$
$524$	−85.4264			−3.73187
$525$	−13.8581	−	11.3842i	−0.604819	−	0.496846i
$526$	51.2445			2.23437
$527$			0.477180i			0.0207863i
$528$		−	7.84557i		−	0.341435i
$529$	−14.3157			−0.622420
$530$	61.0149	+	21.8479i	2.65032	+	0.949013i
$531$	7.93217			0.344227
$532$			49.6493i			2.15257i
$533$			2.42548i			0.105059i
$534$	12.5609			0.543562
$535$	−1.52234	+	4.25144i	−0.0658163	+	0.183806i
$536$	75.2256			3.24925
$537$		−	12.6366i		−	0.545310i
$538$		−	46.9745i		−	2.02522i
$539$	−5.33180			−0.229657
$540$	−3.53695	+	9.87766i	−0.152206	+	0.425067i
$541$	−16.9863			−0.730297			−0.365149	−	0.930949i	$-0.618982\pi$
$541$	−16.9863			−0.730297			−0.365149	+	0.930949i	$0.618982\pi$
$542$			21.1086i			0.906692i
$543$		−	11.6810i		−	0.501281i
$544$	−4.00855			−0.171865
$545$	−14.1740	−	5.07537i	−0.607149	−	0.217405i
$546$	−21.0826			−0.902253
$547$		−	2.98239i		−	0.127518i	−0.997965	−	0.0637589i	$-0.979691\pi$
$547$		−	2.98239i		−	0.127518i	0.997965	−	0.0637589i	$-0.0203089\pi$
$548$			43.2956i			1.84950i
$549$	10.9783			0.468542
$550$	7.46279	−	9.08459i	0.318214	−	0.387368i
$551$	−20.5580			−0.875799
$552$		−	42.5417i		−	1.81069i
$553$		−	55.0732i		−	2.34195i
$554$	−19.4525			−0.826459
$555$	−18.9352	−	6.78024i	−0.803756	−	0.287805i
$556$	7.86536			0.333566
$557$			14.9261i			0.632441i	0.948686	+	0.316220i	$0.102414\pi$
$557$			14.9261i			0.632441i	−0.948686	+	0.316220i	$0.897586\pi$
$558$		−	2.58691i		−	0.109512i
$559$	−6.80591			−0.287859
$560$	−23.3382	+	65.1769i	−0.986220	+	2.75423i
$561$	−0.433733			−0.0183122
$562$		−	44.5525i		−	1.87933i
$563$			30.9852i			1.30587i	0.757414	+	0.652935i	$0.226462\pi$
$563$			30.9852i			1.30587i	−0.757414	+	0.652935i	$0.773538\pi$
$564$	59.8166			2.51873
$565$	11.7900	−	32.9262i	0.496011	−	1.38521i
$566$	49.5689			2.08353
$567$		−	3.58691i		−	0.150636i
$568$		−	96.9064i		−	4.06610i
$569$	−16.4732			−0.690594			−0.345297	−	0.938493i	$-0.612222\pi$
$569$	−16.4732			−0.690594			−0.345297	+	0.938493i	$0.612222\pi$
$570$	16.0656	+	5.75269i	0.672914	+	0.240954i
$571$	21.0082			0.879164			0.439582	−	0.898202i	$-0.355127\pi$
$571$	21.0082			0.879164			0.439582	+	0.898202i	$0.355127\pi$
$572$		−	9.69012i		−	0.405164i
$573$			2.43675i			0.101797i
$574$	−9.90546			−0.413446
$575$	19.3877	−	23.6010i	0.808524	−	0.984230i
$576$	4.46831			0.186180
$577$			21.7202i			0.904225i	0.891961	+	0.452113i	$0.149329\pi$
$577$			21.7202i			0.904225i	−0.891961	+	0.452113i	$0.850671\pi$
$578$		−	43.3884i		−	1.80472i
$579$	−11.5074			−0.478233
$580$	−68.8346	−	24.6480i	−2.85820	−	1.02345i
$581$	52.3725			2.17278
$582$			28.9510i			1.20006i
$583$		−	10.1837i		−	0.421766i
$584$	−23.3666			−0.966915
$585$	−1.71272	+	4.78313i	−0.0708123	+	0.197758i
$586$	−37.7164			−1.55805
$587$		−	13.6467i		−	0.563261i	−0.959523	−	0.281631i	$-0.909125\pi$
$587$		−	13.6467i		−	0.563261i	0.959523	−	0.281631i	$-0.0908753\pi$
$588$		−	27.5233i		−	1.13504i
$589$	−2.95004			−0.121554
$590$	15.4680	−	43.1978i	0.636809	−	1.77842i
$591$	−13.5963			−0.559277
$592$			77.6367i			3.19085i
$593$			43.5050i			1.78654i	0.449525	+	0.893268i	$0.351593\pi$
$593$			43.5050i			1.78654i	−0.449525	+	0.893268i	$0.648407\pi$
$594$	2.35137			0.0964777
$595$	3.60322	+	1.29022i	0.147718	+	0.0528940i
$596$	−71.6344			−2.93426
$597$		−	11.5595i		−	0.473100i
$598$		−	35.9046i		−	1.46825i
$599$	−33.1813			−1.35575			−0.677875	−	0.735177i	$-0.737099\pi$
$599$	−33.1813			−1.35575			−0.677875	+	0.735177i	$0.737099\pi$
$600$	26.9063	+	22.1029i	1.09845	+	0.902349i
$601$	−5.25186			−0.214228			−0.107114	−	0.994247i	$-0.534161\pi$
$601$	−5.25186			−0.214228			−0.107114	+	0.994247i	$0.534161\pi$
$602$		−	27.7948i		−	1.13283i
$603$			10.8018i			0.439884i
$604$	34.4257			1.40076
$605$	21.4177	+	7.66913i	0.870752	+	0.311795i
$606$	−0.219638			−0.00892219
$607$		−	41.0991i		−	1.66816i	−0.551644	−	0.834080i	$-0.685999\pi$
$607$		−	41.0991i		−	1.66816i	0.551644	−	0.834080i	$-0.314001\pi$
$608$		−	24.7818i		−	1.00503i
$609$	24.9961			1.01289
$610$	21.4081	−	59.7866i	0.866788	−	2.42069i
$611$	28.9655			1.17182
$612$		−	2.23897i		−	0.0905050i
$613$		−	23.3829i		−	0.944425i	−0.881485	−	0.472213i	$-0.843455\pi$
$613$		−	23.3829i		−	0.944425i	0.881485	−	0.472213i	$-0.156545\pi$
$614$	22.9345			0.925561
$615$	−0.804705	+	2.24731i	−0.0324488	+	0.0906202i
$616$	22.7054			0.914825
$617$			9.23931i			0.371961i	0.982553	+	0.185980i	$0.0595461\pi$
$617$			9.23931i			0.371961i	−0.982553	+	0.185980i	$0.940454\pi$
$618$			31.4453i			1.26492i
$619$	−33.1051			−1.33061			−0.665303	−	0.746573i	$-0.731698\pi$
$619$	−33.1051			−1.33061			−0.665303	+	0.746573i	$0.731698\pi$
$620$	−9.87766	−	3.53695i	−0.396696	−	0.142047i
$621$	6.10865			0.245132
$622$			42.7704i			1.71494i
$623$			17.4164i			0.697775i
$624$	19.6114			0.785085
$625$	4.85384	+	24.5243i	0.194153	+	0.980971i
$626$	−32.4447			−1.29675
$627$		−	2.68143i		−	0.107086i
$628$		−	8.39629i		−	0.335049i
$629$	4.29205			0.171135
$630$	−19.5339	−	6.99461i	−0.778250	−	0.278672i
$631$	−21.8256			−0.868865			−0.434433	−	0.900704i	$-0.643051\pi$
$631$	−21.8256			−0.868865			−0.434433	+	0.900704i	$0.643051\pi$
$632$			106.927i			4.25334i
$633$		−	4.88493i		−	0.194159i
$634$	15.8955			0.631290
$635$	1.48302	−	4.14165i	0.0588520	−	0.164357i
$636$	52.5693			2.08451
$637$		−	13.3278i		−	0.528066i
$638$			16.3860i			0.648728i
$639$	13.9150			0.550469
$640$	−3.95138	+	11.0351i	−0.156192	+	0.436199i
$641$	4.15493			0.164110			0.0820549	−	0.996628i	$-0.473852\pi$
$641$	4.15493			0.164110			0.0820549	+	0.996628i	$0.473852\pi$
$642$			5.22430i			0.206187i
$643$			37.8064i			1.49094i	0.666540	+	0.745469i	$0.267774\pi$
$643$			37.8064i			1.49094i	−0.666540	+	0.745469i	$0.732226\pi$
$644$	102.809			4.05124
$645$	−6.30595	−	2.25800i	−0.248297	−	0.0889089i
$646$	−3.64159			−0.143276
$647$		−	18.2144i		−	0.716084i	−0.933706	−	0.358042i	$-0.883445\pi$
$647$		−	18.2144i		−	0.716084i	0.933706	−	0.358042i	$-0.116555\pi$
$648$			6.96416i			0.273578i
$649$	−7.20994			−0.283015
$650$	22.7086	+	18.6546i	0.890703	+	0.731693i
$651$	3.58691			0.140582
$652$			70.5387i			2.76251i
$653$		−	13.8263i		−	0.541065i	−0.962711	−	0.270532i	$-0.912800\pi$
$653$		−	13.8263i		−	0.541065i	0.962711	−	0.270532i	$-0.0871997\pi$
$654$	−17.4175			−0.681078
$655$	−38.3279	−	13.7243i	−1.49760	−	0.536252i
$656$	9.21423			0.359755
$657$		−	3.35526i		−	0.130901i
$658$			118.292i			4.61152i
$659$	−18.5085			−0.720988			−0.360494	−	0.932762i	$-0.617392\pi$
$659$	−18.5085			−0.720988			−0.360494	+	0.932762i	$0.617392\pi$
$660$	3.21490	−	8.97829i	0.125140	−	0.349479i
$661$	18.0568			0.702328			0.351164	−	0.936314i	$-0.385786\pi$
$661$	18.0568			0.702328			0.351164	+	0.936314i	$0.385786\pi$
$662$		−	59.8684i		−	2.32685i
$663$		−	1.08419i		−	0.0421066i
$664$	−101.684			−3.94610
$665$	−7.97646	+	22.2760i	−0.309314	+	0.863824i
$666$	−23.2682			−0.901625
$667$			42.5695i			1.64830i
$668$		−	34.0881i		−	1.31891i
$669$	−2.71673			−0.105035
$670$	58.8255	+	21.0639i	2.27263	+	0.813771i
$671$	−9.97870			−0.385224
$672$			30.1317i			1.16236i
$673$		−	17.8925i		−	0.689706i	−0.938657	−	0.344853i	$-0.887929\pi$
$673$		−	17.8925i		−	0.689706i	0.938657	−	0.344853i	$-0.112071\pi$
$674$	−84.2937			−3.24687
$675$	−3.17381	+	3.86354i	−0.122160	+	0.148708i
$676$	−36.7749			−1.41442
$677$			28.7140i			1.10357i	0.833986	+	0.551785i	$0.186053\pi$
$677$			28.7140i			1.10357i	−0.833986	+	0.551785i	$0.813947\pi$
$678$		−	40.4607i		−	1.55388i
$679$	−40.1424			−1.54052
$680$	−6.99584	−	2.50504i	−0.268278	−	0.0960638i
$681$	−15.8826			−0.608624
$682$			2.35137i			0.0900384i
$683$			26.1456i			1.00043i	0.865900	+	0.500217i	$0.166746\pi$
$683$			26.1456i			1.00043i	−0.865900	+	0.500217i	$0.833254\pi$
$684$	13.8418			0.529255
$685$	−6.95570	+	19.4253i	−0.265764	+	0.742201i
$686$	−10.5234			−0.401783
$687$		−	4.20248i		−	0.160335i
$688$			25.8552i			0.985719i
$689$	25.4560			0.969798
$690$	11.9121	−	33.2671i	0.453486	−	1.26646i
$691$	17.8853			0.680391			0.340195	−	0.940355i	$-0.389507\pi$
$691$	17.8853			0.680391			0.340195	+	0.940355i	$0.389507\pi$
$692$			48.7901i			1.85472i
$693$			3.26031i			0.123849i
$694$	48.6567			1.84698
$695$	3.52892	+	1.26362i	0.133860	+	0.0479318i
$696$	−48.5313			−1.83957
$697$		−	0.509397i		−	0.0192948i
$698$			85.4064i			3.23268i
$699$	−15.7806			−0.596879
$700$	−53.4154	+	65.0236i	−2.01891	+	2.45766i
$701$	31.5651			1.19220			0.596098	−	0.802912i	$-0.296717\pi$
$701$	31.5651			1.19220			0.596098	+	0.802912i	$0.296717\pi$
$702$			5.87766i			0.221838i
$703$			26.5344i			1.00077i
$704$	−4.06146			−0.153072
$705$	26.8377	+	9.60990i	1.01077	+	0.361930i
$706$	−57.7345			−2.17287
$707$		−	0.304542i		−	0.0114535i
$708$		−	37.2184i		−	1.39875i
$709$	26.3434			0.989349			0.494674	−	0.869078i	$-0.335287\pi$
$709$	26.3434			0.989349			0.494674	+	0.869078i	$0.335287\pi$
$710$	27.1348	−	75.7797i	1.01835	−	2.84396i
$711$	−15.3540			−0.575818
$712$		−	33.8149i		−	1.26727i
$713$			6.10865i			0.228771i
$714$	4.42775			0.165704
$715$	1.55678	−	4.34762i	0.0582201	−	0.162592i
$716$	−59.2920			−2.21585
$717$		−	8.89923i		−	0.332348i
$718$			10.1401i			0.378424i
$719$	−39.6072			−1.47710			−0.738550	−	0.674199i	$-0.764489\pi$
$719$	−39.6072			−1.47710			−0.738550	+	0.674199i	$0.764489\pi$
$720$	18.1708	+	6.50650i	0.677185	+	0.242483i
$721$	−43.6009			−1.62378
$722$			26.6381i			0.991366i
$723$			24.9570i			0.928161i
$724$	−54.8083			−2.03693
$725$	−26.9239	−	22.1174i	−0.999928	−	0.821419i
$726$	26.3187			0.976778
$727$		−	2.37556i		−	0.0881046i	−0.999029	−	0.0440523i	$-0.985973\pi$
$727$		−	2.37556i		−	0.0881046i	0.999029	−	0.0440523i	$-0.0140268\pi$
$728$			56.7562i			2.10352i
$729$	−1.00000			−0.0370370
$730$	−18.2724	−	6.54288i	−0.676291	−	0.242163i
$731$	1.42937			0.0528672
$732$		−	51.5110i		−	1.90390i
$733$		−	48.3399i		−	1.78547i	−0.450578	−	0.892737i	$-0.648782\pi$
$733$		−	48.3399i		−	1.78547i	0.450578	−	0.892737i	$-0.351218\pi$
$734$	−3.15277			−0.116371
$735$	4.42178	−	12.3487i	0.163100	−	0.455490i
$736$	−51.3156			−1.89152
$737$		−	9.81829i		−	0.361661i
$738$			2.76156i			0.101655i
$739$	46.1708			1.69842			0.849210	−	0.528055i	$-0.177079\pi$
$739$	46.1708			1.69842			0.849210	+	0.528055i	$0.177079\pi$
$740$	−31.8134	+	88.8457i	−1.16948	+	3.26603i
$741$	6.70273			0.246231
$742$			103.960i			3.81650i
$743$		−	42.9194i		−	1.57456i	−0.616596	−	0.787279i	$-0.711489\pi$
$743$		−	42.9194i		−	1.57456i	0.616596	−	0.787279i	$-0.288511\pi$
$744$	−6.96416			−0.255319
$745$	−32.1399	−	11.5085i	−1.17751	−	0.421639i
$746$	64.7863			2.37200
$747$		−	14.6010i		−	0.534224i
$748$			2.03511i			0.0744110i
$749$	−7.24382			−0.264684
$750$	14.8514	+	24.8183i	0.542295	+	0.906236i
$751$	21.5735			0.787229			0.393614	−	0.919276i	$-0.371225\pi$
$751$	21.5735			0.787229			0.393614	+	0.919276i	$0.371225\pi$
$752$		−	110.038i		−	4.01266i
$753$			19.3924i			0.706700i
$754$	−40.9597			−1.49167
$755$	15.4456	+	5.53070i	0.562124	+	0.201283i
$756$	−16.8301			−0.612103
$757$			10.9537i			0.398120i	0.979987	+	0.199060i	$0.0637888\pi$
$757$			10.9537i			0.398120i	−0.979987	+	0.199060i	$0.936211\pi$
$758$			55.1504i			2.00315i
$759$	−5.55245			−0.201541
$760$	15.4867	−	43.2499i	0.561762	−	1.56884i
$761$	36.0005			1.30502			0.652509	−	0.757781i	$-0.273717\pi$
$761$	36.0005			1.30502			0.652509	+	0.757781i	$0.273717\pi$
$762$		−	5.08939i		−	0.184369i
$763$		−	24.1504i		−	0.874305i
$764$	11.4334			0.413647
$765$	0.359704	−	1.00455i	0.0130051	−	0.0363195i
$766$	52.3492			1.89145
$767$		−	18.0225i		−	0.650756i
$768$			22.4968i			0.811785i
$769$	−25.6291			−0.924208			−0.462104	−	0.886826i	$-0.652905\pi$
$769$	−25.6291			−0.924208			−0.462104	+	0.886826i	$0.652905\pi$
$770$	17.7553	+	6.35774i	0.639857	+	0.229117i
$771$	3.00568			0.108247
$772$			53.9938i			1.94328i
$773$			25.4171i			0.914190i	0.889418	+	0.457095i	$0.151110\pi$
$773$			25.4171i			0.914190i	−0.889418	+	0.457095i	$0.848890\pi$
$774$	−7.74895			−0.278530
$775$	−3.86354	−	3.17381i	−0.138782	−	0.114007i
$776$	77.9385			2.79783
$777$		−	32.2628i		−	1.15742i
$778$			73.6035i			2.63881i
$779$	3.14921			0.112832
$780$	22.4429	+	8.03623i	0.803583	+	0.287743i
$781$	−12.6480			−0.452582
$782$			7.54065i			0.269653i
$783$		−	6.96871i		−	0.249042i
$784$	−50.6313			−1.80826
$785$	1.34892	−	3.76713i	0.0481448	−	0.134455i
$786$	−47.0985			−1.67995
$787$		−	35.2155i		−	1.25530i	−0.778498	−	0.627648i	$-0.784018\pi$
$787$		−	35.2155i		−	1.25530i	0.778498	−	0.627648i	$-0.215982\pi$
$788$			63.7949i			2.27260i
$789$	19.8092			0.705226
$790$	−29.9408	+	83.6160i	−1.06525	+	2.97492i
$791$	56.1013			1.99473
$792$		−	6.33007i		−	0.224929i
$793$		−	24.9436i		−	0.885772i
$794$	−1.35815			−0.0481991
$795$	23.5861	+	8.44558i	0.836511	+	0.299534i
$796$	−54.2383			−1.92242
$797$		−	7.28674i		−	0.258110i	−0.991637	−	0.129055i	$-0.958806\pi$
$797$		−	7.28674i		−	0.258110i	0.991637	−	0.129055i	$-0.0411943\pi$
$798$			27.3734i			0.969007i
$799$	−6.08330			−0.215212
$800$	26.6616	−	32.4556i	0.942628	−	1.14748i
$801$	4.85556			0.171563
$802$		−	47.5656i		−	1.67960i
$803$			3.04976i			0.107624i
$804$	50.6830			1.78745
$805$	46.1269	+	16.5169i	1.62576	+	0.582144i
$806$	−5.87766			−0.207032
$807$		−	18.1586i		−	0.639212i
$808$			0.591284i			0.0208013i
$809$	−18.0220			−0.633621			−0.316811	−	0.948489i	$-0.602612\pi$
$809$	−18.0220			−0.633621			−0.316811	+	0.948489i	$0.602612\pi$
$810$	−1.95004	+	5.44589i	−0.0685174	+	0.191349i
$811$	6.05154			0.212498			0.106249	−	0.994340i	$-0.466116\pi$
$811$	6.05154			0.212498			0.106249	+	0.994340i	$0.466116\pi$
$812$		−	117.284i		−	4.11586i
$813$			8.15979i			0.286176i
$814$	21.1496			0.741293
$815$	−11.3325	+	31.6483i	−0.396959	+	1.10859i
$816$	−4.11877			−0.144186
$817$			8.83670i			0.309157i
$818$		−	3.58523i		−	0.125355i
$819$	−8.14974			−0.284775
$820$	10.5446	+	3.77574i	0.368232	+	0.131855i
$821$	−0.839710			−0.0293061			−0.0146530	−	0.999893i	$-0.504664\pi$
$821$	−0.839710			−0.0293061			−0.0146530	+	0.999893i	$0.504664\pi$
$822$			23.8704i			0.832574i
$823$		−	45.4617i		−	1.58469i	−0.610071	−	0.792347i	$-0.708859\pi$
$823$		−	45.4617i		−	1.58469i	0.610071	−	0.792347i	$-0.291141\pi$
$824$	84.6535			2.94904
$825$	2.88483	−	3.51176i	0.100437	−	0.122264i
$826$	73.6025			2.56096
$827$		−	23.2824i		−	0.809607i	−0.914404	−	0.404804i	$-0.867340\pi$
$827$		−	23.2824i		−	0.809607i	0.914404	−	0.404804i	$-0.132660\pi$
$828$		−	28.6623i		−	0.996084i
$829$	48.4844			1.68393			0.841967	−	0.539530i	$-0.181398\pi$
$829$	48.4844			1.68393			0.841967	+	0.539530i	$0.181398\pi$
$830$	−79.5157	−	28.4726i	−2.76003	−	0.988298i
$831$	−7.51962			−0.260853
$832$		−	10.1524i		−	0.351970i
$833$			2.79909i			0.0969827i
$834$	4.33644			0.150159
$835$	5.47646	−	15.2942i	0.189521	−	0.529277i
$836$	−12.5815			−0.435141
$837$		−	1.00000i		−	0.0345651i
$838$		−	58.5194i		−	2.02152i
$839$	11.3096			0.390450			0.195225	−	0.980758i	$-0.437456\pi$
$839$	11.3096			0.390450			0.195225	+	0.980758i	$0.437456\pi$
$840$	−18.8301	+	52.5869i	−0.649699	+	1.81442i
$841$	19.5630			0.674585
$842$		−	37.6397i		−	1.29715i
$843$		−	17.2223i		−	0.593167i
$844$	−22.9205			−0.788956
$845$	−16.4996	−	5.90810i	−0.567604	−	0.203245i
$846$	32.9790			1.13384
$847$			36.4925i			1.25390i
$848$		−	96.7057i		−	3.32089i
$849$	19.1614			0.657619
$850$	−4.76923	−	3.91782i	−0.163583	−	0.134380i
$851$	54.9449			1.88349
$852$		−	65.2904i		−	2.23681i
$853$		−	37.0550i		−	1.26874i	−0.773030	−	0.634369i	$-0.781260\pi$
$853$		−	37.0550i		−	1.26874i	0.773030	−	0.634369i	$-0.218740\pi$
$854$	101.867			3.48583
$855$	6.21035	+	2.22377i	0.212390	+	0.0760514i
$856$	14.0643			0.480707
$857$		−	20.5514i		−	0.702023i	−0.936371	−	0.351011i	$-0.885838\pi$
$857$		−	20.5514i		−	0.702023i	0.936371	−	0.351011i	$-0.114162\pi$
$858$		−	5.34249i		−	0.182390i
$859$	−25.4920			−0.869776			−0.434888	−	0.900485i	$-0.643212\pi$
$859$	−25.4920			−0.869776			−0.434888	+	0.900485i	$0.643212\pi$
$860$	−10.5947	+	29.5881i	−0.361278	+	1.00894i
$861$	−3.82908			−0.130495
$862$		−	102.614i		−	3.49505i
$863$			4.87914i			0.166088i	0.996546	+	0.0830439i	$0.0264642\pi$
$863$			4.87914i			0.166088i	−0.996546	+	0.0830439i	$0.973536\pi$
$864$	8.40048			0.285790
$865$	−7.83843	+	21.8905i	−0.266514	+	0.744298i
$866$	31.4465			1.06859
$867$		−	16.7723i		−	0.569617i
$868$		−	16.8301i		−	0.571249i
$869$	13.9560			0.473423
$870$	−37.9509	−	13.5893i	−1.28666	−	0.460719i
$871$	24.5426			0.831594
$872$			46.8893i			1.58787i
$873$			11.1914i			0.378770i
$874$	−46.6180			−1.57688
$875$	−34.4121	+	20.5923i	−1.16334	+	0.696148i
$876$	−15.7431			−0.531911
$877$		−	6.98895i		−	0.236000i	−0.993014	−	0.118000i	$-0.962352\pi$
$877$		−	6.98895i		−	0.236000i	0.993014	−	0.118000i	$-0.0376483\pi$
$878$			27.8013i			0.938249i
$879$	−14.5797			−0.491762
$880$	−16.5163	−	5.91408i	−0.556765	−	0.199364i
$881$	26.1553			0.881195			0.440597	−	0.897705i	$-0.354767\pi$
$881$	26.1553			0.881195			0.440597	+	0.897705i	$0.354767\pi$
$882$		−	15.1745i		−	0.510953i
$883$			29.3315i			0.987084i	0.869722	+	0.493542i	$0.164298\pi$
$883$			29.3315i			0.987084i	−0.869722	+	0.493542i	$0.835702\pi$
$884$	−5.08712			−0.171098
$885$	5.97936	−	16.6986i	0.200994	−	0.561318i
$886$	28.9170			0.971486
$887$		−	12.2360i		−	0.410845i	−0.978673	−	0.205422i	$-0.934143\pi$
$887$		−	12.2360i		−	0.410845i	0.978673	−	0.205422i	$-0.0658568\pi$
$888$			62.6399i			2.10206i
$889$	7.05676			0.236676
$890$	9.46853	−	26.4429i	0.317386	−	0.886367i
$891$	0.908949			0.0304509
$892$			12.7471i			0.426805i
$893$		−	37.6083i		−	1.25851i
$894$	−39.4945			−1.32089
$895$	−26.6023	−	9.52561i	−0.889216	−	0.318406i
$896$	−18.8021			−0.628134
$897$		−	13.8794i		−	0.463418i
$898$		−	58.0539i		−	1.93728i
$899$	6.96871			0.232420
$900$	18.1280	+	14.8918i	0.604268	+	0.496393i
$901$	−5.34625			−0.178110
$902$		−	2.51012i		−	0.0835778i
$903$		−	10.7444i		−	0.357551i
$904$	−108.924			−3.62274
$905$	−24.5906	−	8.80529i	−0.817420	−	0.292698i
$906$	18.9801			0.630570
$907$		−	54.0458i		−	1.79456i	−0.441459	−	0.897281i	$-0.645539\pi$
$907$		−	54.0458i		−	1.79456i	0.441459	−	0.897281i	$-0.354461\pi$
$908$			74.5227i			2.47312i
$909$	−0.0849038			−0.00281608
$910$	−15.8923	+	44.3826i	−0.526825	+	1.47127i
$911$	44.1506			1.46278			0.731388	−	0.681962i	$-0.238873\pi$
$911$	44.1506			1.46278			0.731388	+	0.681962i	$0.238873\pi$
$912$		−	25.4632i		−	0.843170i
$913$			13.2716i			0.439226i
$914$	−5.68974			−0.188200
$915$	8.27556	−	23.1112i	0.273582	−	0.764034i
$916$	−19.7184			−0.651513
$917$		−	65.3050i		−	2.15656i
$918$		−	1.23442i		−	0.0407420i
$919$	40.5340			1.33709			0.668547	−	0.743670i	$-0.266917\pi$
$919$	40.5340			1.33709			0.668547	+	0.743670i	$0.266917\pi$
$920$	−89.5577	−	32.0684i	−2.95263	−	1.05726i
$921$	8.86561			0.292132
$922$			62.1531i			2.04690i
$923$		−	31.6160i		−	1.04065i
$924$	15.2977			0.503256
$925$	−28.5472	+	34.7510i	−0.938626	+	1.14261i
$926$	−47.8735			−1.57322
$927$			12.1556i			0.399242i
$928$			58.5406i			1.92169i
$929$	−6.35147			−0.208385			−0.104192	−	0.994557i	$-0.533226\pi$
$929$	−6.35147			−0.208385			−0.104192	+	0.994557i	$0.533226\pi$
$930$	−5.44589	−	1.95004i	−0.178578	−	0.0639443i
$931$	−17.3046			−0.567136
$932$			74.0441i			2.42539i
$933$			16.5334i			0.541280i
$934$	1.15945			0.0379382
$935$	−0.326953	+	0.913084i	−0.0106925	+	0.0298610i
$936$	15.8232			0.517196
$937$		−	16.3665i		−	0.534670i	−0.963604	−	0.267335i	$-0.913857\pi$
$937$		−	16.3665i		−	0.534670i	0.963604	−	0.267335i	$-0.0861430\pi$
$938$			100.230i			3.27262i
$939$	−12.5419			−0.409290
$940$	45.0905	−	125.925i	1.47069	−	4.10721i
$941$	3.42680			0.111710			0.0558552	−	0.998439i	$-0.482211\pi$
$941$	3.42680			0.111710			0.0558552	+	0.998439i	$0.482211\pi$
$942$		−	4.62916i		−	0.150826i
$943$		−	6.52108i		−	0.212356i
$944$	−68.4663			−2.22839
$945$	−7.55107	−	2.70385i	−0.245636	−	0.0879563i
$946$	7.04340			0.229001
$947$		−	29.6868i		−	0.964693i	−0.875981	−	0.482346i	$-0.839785\pi$
$947$		−	29.6868i		−	0.964693i	0.875981	−	0.482346i	$-0.160215\pi$
$948$			72.0420i			2.33982i
$949$	−7.62342			−0.247467
$950$	24.2209	−	29.4845i	0.785829	−	0.956603i
$951$	6.14459			0.199252
$952$		−	11.9199i		−	0.386325i
$953$			5.17355i			0.167588i	0.996483	+	0.0837939i	$0.0267037\pi$
$953$			5.17355i			0.167588i	−0.996483	+	0.0837939i	$0.973296\pi$
$954$	28.9833			0.938368
$955$	5.12978	+	1.83685i	0.165996	+	0.0594390i
$956$	−41.7559			−1.35048
$957$			6.33420i			0.204756i
$958$		−	44.3176i		−	1.43184i
$959$	−33.0977			−1.06878
$960$	3.36826	−	9.40658i	0.108710	−	0.303596i
$961$	1.00000			0.0322581
$962$			52.8673i			1.70451i
$963$			2.01952i			0.0650781i
$964$	117.100			3.77155
$965$	−8.67444	+	24.2252i	−0.279240	+	0.779836i
$966$	56.6821			1.82372
$967$			8.04994i			0.258869i	0.991588	+	0.129434i	$0.0413161\pi$
$967$			8.04994i			0.258869i	−0.991588	+	0.129434i	$0.958684\pi$
$968$		−	70.8521i		−	2.27727i
$969$	−1.40770			−0.0452219
$970$	60.9470	+	21.8236i	1.95689	+	0.700714i
$971$	−48.0753			−1.54281			−0.771405	−	0.636344i	$-0.780446\pi$
$971$	−48.0753			−1.54281			−0.771405	+	0.636344i	$0.780446\pi$
$972$			4.69208i			0.150499i
$973$			6.01275i			0.192760i
$974$	−4.70613			−0.150794
$975$	8.77827	+	7.21116i	0.281130	+	0.230942i
$976$	−94.7588			−3.03316
$977$			32.6999i			1.04616i	0.852283	+	0.523081i	$0.175217\pi$
$977$			32.6999i			1.04616i	−0.852283	+	0.523081i	$0.824783\pi$
$978$			38.8904i			1.24358i
$979$	−4.41345			−0.141055
$980$	−57.9413	−	20.7473i	−1.85087	−	0.662750i
$981$	−6.73295			−0.214966
$982$		−	36.6225i		−	1.16867i
$983$			33.0834i			1.05520i	0.849494	+	0.527599i	$0.176908\pi$
$983$			33.0834i			1.05520i	−0.849494	+	0.527599i	$0.823092\pi$
$984$	7.43435			0.236999
$985$	−10.2490	+	28.6226i	−0.326562	+	0.911992i
$986$	8.60233			0.273954
$987$			45.7274i			1.45552i
$988$		−	31.4498i		−	1.00055i
$989$	18.2982			0.581848
$990$	1.77249	−	4.95004i	0.0563333	−	0.157323i
$991$	46.9987			1.49296			0.746481	−	0.665406i	$-0.231742\pi$
$991$	46.9987			1.49296			0.746481	+	0.665406i	$0.231742\pi$
$992$			8.40048i			0.266716i
$993$		−	23.1429i		−	0.734417i
$994$	129.117			4.09535
$995$	−24.3348	−	8.71370i	−0.771466	−	0.276243i
$996$	−68.5092			−2.17080
$997$			10.0371i			0.317879i	0.987288	+	0.158939i	$0.0508074\pi$
$997$			10.0371i			0.317879i	−0.987288	+	0.158939i	$0.949193\pi$
$998$		−	103.263i		−	3.26874i
$999$	−8.99461			−0.284577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.c.a.94.1	✓	10
3.2	odd	2		1395.2.c.f.559.10		10
5.2	odd	4		2325.2.a.x.1.5		5
5.3	odd	4		2325.2.a.w.1.1		5
5.4	even	2	inner	465.2.c.a.94.10	yes	10
15.2	even	4		6975.2.a.bs.1.1		5
15.8	even	4		6975.2.a.bv.1.5		5
15.14	odd	2		1395.2.c.f.559.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.c.a.94.1	✓	10	1.1	even	1	trivial
465.2.c.a.94.10	yes	10	5.4	even	2	inner
1395.2.c.f.559.1		10	15.14	odd	2
1395.2.c.f.559.10		10	3.2	odd	2
2325.2.a.w.1.1		5	5.3	odd	4
2325.2.a.x.1.5		5	5.2	odd	4
6975.2.a.bs.1.1		5	15.2	even	4
6975.2.a.bv.1.5		5	15.8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.58691i q^{2} -1.00000i q^{3} -4.69208 q^{4} +(-2.10518 - 0.753811i) q^{5} -2.58691 q^{6} -3.58691i q^{7} +6.96416i q^{8} -1.00000 q^{9} +(-1.95004 + 5.44589i) q^{10} +0.908949 q^{11} +4.69208i q^{12} +2.27208i q^{13} -9.27899 q^{14} +(-0.753811 + 2.10518i) q^{15} +8.63147 q^{16} -0.477180i q^{17} +2.58691i q^{18} +2.95004 q^{19} +(9.87766 + 3.53695i) q^{20} -3.58691 q^{21} -2.35137i q^{22} -6.10865i q^{23} +6.96416 q^{24} +(3.86354 + 3.17381i) q^{25} +5.87766 q^{26} +1.00000i q^{27} +16.8301i q^{28} -6.96871 q^{29} +(5.44589 + 1.95004i) q^{30} -1.00000 q^{31} -8.40048i q^{32} -0.908949i q^{33} -1.23442 q^{34} +(-2.70385 + 7.55107i) q^{35} +4.69208 q^{36} +8.99461i q^{37} -7.63147i q^{38} +2.27208 q^{39} +(5.24967 - 14.6608i) q^{40} +1.06752 q^{41} +9.27899i q^{42} +2.99545i q^{43} -4.26486 q^{44} +(2.10518 + 0.753811i) q^{45} -15.8025 q^{46} -12.7484i q^{47} -8.63147i q^{48} -5.86589 q^{49} +(8.21035 - 9.99461i) q^{50} -0.477180 q^{51} -10.6608i q^{52} -11.2038i q^{53} +2.58691 q^{54} +(-1.91350 - 0.685176i) q^{55} +24.9798 q^{56} -2.95004i q^{57} +18.0274i q^{58} -7.93217 q^{59} +(3.53695 - 9.87766i) q^{60} -10.9783 q^{61} +2.58691i q^{62} +3.58691i q^{63} -4.46831 q^{64} +(1.71272 - 4.78313i) q^{65} -2.35137 q^{66} -10.8018i q^{67} +2.23897i q^{68} -6.10865 q^{69} +(19.5339 + 6.99461i) q^{70} -13.9150 q^{71} -6.96416i q^{72} +3.35526i q^{73} +23.2682 q^{74} +(3.17381 - 3.86354i) q^{75} -13.8418 q^{76} -3.26031i q^{77} -5.87766i q^{78} +15.3540 q^{79} +(-18.1708 - 6.50650i) q^{80} +1.00000 q^{81} -2.76156i q^{82} +14.6010i q^{83} +16.8301 q^{84} +(-0.359704 + 1.00455i) q^{85} +7.74895 q^{86} +6.96871i q^{87} +6.33007i q^{88} -4.85556 q^{89} +(1.95004 - 5.44589i) q^{90} +8.14974 q^{91} +28.6623i q^{92} +1.00000i q^{93} -32.9790 q^{94} +(-6.21035 - 2.22377i) q^{95} -8.40048 q^{96} -11.1914i q^{97} +15.1745i q^{98} -0.908949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 6 q^{4} - 6 q^{6} - 10 q^{9} + 2 q^{10} - 32 q^{14} + 2 q^{15} + 6 q^{16} + 8 q^{19} + 28 q^{20} - 16 q^{21} + 18 q^{24} - 2 q^{25} - 12 q^{26} - 8 q^{29} + 4 q^{30} - 10 q^{31} - 12 q^{34} + 4 q^{35}+ \cdots - 2 q^{96}+O(q^{100}) \) 10 * q - 6 * q^4 - 6 * q^6 - 10 * q^9 + 2 * q^10 - 32 * q^14 + 2 * q^15 + 6 * q^16 + 8 * q^19 + 28 * q^20 - 16 * q^21 + 18 * q^24 - 2 * q^25 - 12 * q^26 - 8 * q^29 + 4 * q^30 - 10 * q^31 - 12 * q^34 + 4 * q^35 + 6 * q^36 + 12 * q^39 + 14 * q^40 - 12 * q^44 - 32 * q^46 + 22 * q^49 + 40 * q^50 - 16 * q^51 + 6 * q^54 + 36 * q^56 - 20 * q^59 - 6 * q^60 - 28 * q^61 - 22 * q^64 + 20 * q^65 - 12 * q^66 + 8 * q^69 + 32 * q^70 + 12 * q^71 + 8 * q^74 - 8 * q^75 - 16 * q^76 + 48 * q^79 - 20 * q^80 + 10 * q^81 + 36 * q^84 - 4 * q^85 + 8 * q^86 - 20 * q^89 - 2 * q^90 - 24 * q^94 - 20 * q^95 - 2 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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