LMFDB - Embedded newform 156.3.f.a.79.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,3,Mod(79,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("156.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.f (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:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			79.15
Character	$\chi$	$=$	156.79
Dual form			156.3.f.a.79.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.969763 - 1.74916i) q^{2} +1.73205i q^{3} +(-2.11912 - 3.39254i) q^{4} -4.25416 q^{5} +(3.02963 + 1.67968i) q^{6} -10.6496i q^{7} +(-7.98914 + 0.416717i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(0.969763 - 1.74916i) q^{2} +1.73205i q^{3} +(-2.11912 - 3.39254i) q^{4} -4.25416 q^{5} +(3.02963 + 1.67968i) q^{6} -10.6496i q^{7} +(-7.98914 + 0.416717i) q^{8} -3.00000 q^{9} +(-4.12553 + 7.44120i) q^{10} -9.55431i q^{11} +(5.87605 - 3.67042i) q^{12} -3.60555 q^{13} +(-18.6278 - 10.3275i) q^{14} -7.36842i q^{15} +(-7.01867 + 14.3784i) q^{16} +8.28441 q^{17} +(-2.90929 + 5.24748i) q^{18} -28.7987i q^{19} +(9.01507 + 14.4324i) q^{20} +18.4456 q^{21} +(-16.7120 - 9.26541i) q^{22} +36.7606i q^{23} +(-0.721775 - 13.8376i) q^{24} -6.90212 q^{25} +(-3.49653 + 6.30668i) q^{26} -5.19615i q^{27} +(-36.1291 + 22.5677i) q^{28} +47.9195 q^{29} +(-12.8885 - 7.14562i) q^{30} +15.3212i q^{31} +(18.3437 + 26.2204i) q^{32} +16.5485 q^{33} +(8.03392 - 14.4908i) q^{34} +45.3049i q^{35} +(6.35736 + 10.1776i) q^{36} +34.5699 q^{37} +(-50.3736 - 27.9279i) q^{38} -6.24500i q^{39} +(33.9871 - 1.77278i) q^{40} -43.7577 q^{41} +(17.8878 - 32.2643i) q^{42} -58.5254i q^{43} +(-32.4134 + 20.2467i) q^{44} +12.7625 q^{45} +(64.3002 + 35.6491i) q^{46} -25.6288i q^{47} +(-24.9041 - 12.1567i) q^{48} -64.4131 q^{49} +(-6.69342 + 12.0729i) q^{50} +14.3490i q^{51} +(7.64059 + 12.2320i) q^{52} +39.7067 q^{53} +(-9.08890 - 5.03904i) q^{54} +40.6456i q^{55} +(4.43785 + 85.0808i) q^{56} +49.8808 q^{57} +(46.4706 - 83.8189i) q^{58} -4.84928i q^{59} +(-24.9977 + 15.6146i) q^{60} +66.1400 q^{61} +(26.7993 + 14.8580i) q^{62} +31.9487i q^{63} +(63.6527 - 6.65842i) q^{64} +15.3386 q^{65} +(16.0482 - 28.9460i) q^{66} -121.628i q^{67} +(-17.5557 - 28.1052i) q^{68} -63.6713 q^{69} +(79.2455 + 43.9350i) q^{70} -17.5131i q^{71} +(23.9674 - 1.25015i) q^{72} +30.7084 q^{73} +(33.5246 - 60.4682i) q^{74} -11.9548i q^{75} +(-97.7008 + 61.0279i) q^{76} -101.749 q^{77} +(-10.9235 - 6.05617i) q^{78} -31.4497i q^{79} +(29.8585 - 61.1680i) q^{80} +9.00000 q^{81} +(-42.4346 + 76.5391i) q^{82} +116.303i q^{83} +(-39.0884 - 62.5774i) q^{84} -35.2432 q^{85} +(-102.370 - 56.7558i) q^{86} +82.9991i q^{87} +(3.98144 + 76.3307i) q^{88} -16.2630 q^{89} +(12.3766 - 22.3236i) q^{90} +38.3975i q^{91} +(124.712 - 77.9001i) q^{92} -26.5371 q^{93} +(-44.8289 - 24.8539i) q^{94} +122.514i q^{95} +(-45.4151 + 31.7722i) q^{96} -116.138 q^{97} +(-62.4654 + 112.669i) q^{98} +28.6629i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9	$ 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9 - 12 * q^10 + 12 * q^12 + 32 * q^14 + 4 * q^16 - 12 * q^18 + 84 * q^20 + 28 * q^22 - 36 * q^24 + 104 * q^25 - 96 * q^28 + 64 * q^29 - 12 * q^30 + 44 * q^32 + 48 * q^33 + 40 * q^34 - 24 * q^36 - 192 * q^37 - 104 * q^38 + 220 * q^40 - 220 * q^44 - 104 * q^46 - 144 * q^48 - 248 * q^49 + 100 * q^50 - 52 * q^52 + 336 * q^53 + 36 * q^54 + 168 * q^56 - 16 * q^58 + 60 * q^60 + 16 * q^61 + 152 * q^62 - 16 * q^64 - 132 * q^66 + 400 * q^68 - 192 * q^69 + 208 * q^70 + 96 * q^72 + 112 * q^73 - 104 * q^74 - 264 * q^76 - 272 * q^77 - 300 * q^80 + 216 * q^81 - 4 * q^82 + 96 * q^84 + 64 * q^85 + 288 * q^86 - 492 * q^88 + 36 * q^90 + 328 * q^92 - 96 * q^93 - 884 * q^94 + 72 * q^96 - 80 * q^97 - 572 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	0.969763	−	1.74916i	0.484882	−	0.874580i
$2$	0.969763	−	1.74916i	0.484882	−	0.874580i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−2.11912	−	3.39254i	−0.529780	−	0.848135i
$5$	−4.25416			−0.850832			−0.425416	−	0.904998i	$-0.639872\pi$
$5$	−4.25416			−0.850832			−0.425416	+	0.904998i	$0.639872\pi$
$6$	3.02963	+	1.67968i	0.504939	+	0.279946i
$7$		−	10.6496i		−	1.52137i	−0.649124	−	0.760683i	$-0.724864\pi$
$7$		−	10.6496i		−	1.52137i	0.649124	−	0.760683i	$-0.275136\pi$
$8$	−7.98914	+	0.416717i	−0.998642	+	0.0520897i
$9$	−3.00000			−0.333333
$10$	−4.12553	+	7.44120i	−0.412553	+	0.744120i
$11$		−	9.55431i		−	0.868573i	−0.900775	−	0.434287i	$-0.857000\pi$
$11$		−	9.55431i		−	0.868573i	0.900775	−	0.434287i	$-0.143000\pi$
$12$	5.87605	−	3.67042i	0.489671	−	0.305869i
$13$	−3.60555			−0.277350
$13$	−3.60555			−0.277350
$14$	−18.6278	−	10.3275i	−1.33056	−	0.737682i
$15$		−	7.36842i		−	0.491228i
$16$	−7.01867	+	14.3784i	−0.438667	+	0.898650i
$17$	8.28441			0.487319			0.243659	−	0.969861i	$-0.421652\pi$
$17$	8.28441			0.487319			0.243659	+	0.969861i	$0.421652\pi$
$18$	−2.90929	+	5.24748i	−0.161627	+	0.291527i
$19$		−	28.7987i		−	1.51572i	−0.652416	−	0.757861i	$-0.726245\pi$
$19$		−	28.7987i		−	1.51572i	0.652416	−	0.757861i	$-0.273755\pi$
$20$	9.01507	+	14.4324i	0.450754	+	0.721621i
$21$	18.4456			0.878361
$22$	−16.7120	−	9.26541i	−0.759637	−	0.421155i
$23$			36.7606i			1.59829i	0.601140	+	0.799144i	$0.294714\pi$
$23$			36.7606i			1.59829i	−0.601140	+	0.799144i	$0.705286\pi$
$24$	−0.721775	−	13.8376i	−0.0300740	−	0.576566i
$25$	−6.90212			−0.276085
$26$	−3.49653	+	6.30668i	−0.134482	+	0.242565i
$27$		−	5.19615i		−	0.192450i
$28$	−36.1291	+	22.5677i	−1.29032	+	0.805989i
$29$	47.9195			1.65240			0.826199	−	0.563378i	$-0.190499\pi$
$29$	47.9195			1.65240			0.826199	+	0.563378i	$0.190499\pi$
$30$	−12.8885	−	7.14562i	−0.429618	−	0.238187i
$31$			15.3212i			0.494233i	0.968986	+	0.247117i	$0.0794831\pi$
$31$			15.3212i			0.494233i	−0.968986	+	0.247117i	$0.920517\pi$
$32$	18.3437	+	26.2204i	0.573240	+	0.819388i
$33$	16.5485			0.501471
$34$	8.03392	−	14.4908i	0.236292	−	0.426199i
$35$			45.3049i			1.29443i
$36$	6.35736	+	10.1776i	0.176593	+	0.282712i
$37$	34.5699			0.934320			0.467160	−	0.884173i	$-0.345277\pi$
$37$	34.5699			0.934320			0.467160	+	0.884173i	$0.345277\pi$
$38$	−50.3736	−	27.9279i	−1.32562	−	0.734946i
$39$		−	6.24500i		−	0.160128i
$40$	33.9871	−	1.77278i	0.849677	−	0.0443195i
$41$	−43.7577			−1.06726			−0.533630	−	0.845718i	$-0.679173\pi$
$41$	−43.7577			−1.06726			−0.533630	+	0.845718i	$0.679173\pi$
$42$	17.8878	−	32.2643i	0.425901	−	0.768197i
$43$		−	58.5254i		−	1.36106i	−0.732722	−	0.680528i	$-0.761750\pi$
$43$		−	58.5254i		−	1.36106i	0.732722	−	0.680528i	$-0.238250\pi$
$44$	−32.4134	+	20.2467i	−0.736668	+	0.460153i
$45$	12.7625			0.283611
$46$	64.3002	+	35.6491i	1.39783	+	0.774980i
$47$		−	25.6288i		−	0.545294i	−0.962114	−	0.272647i	$-0.912101\pi$
$47$		−	25.6288i		−	0.545294i	0.962114	−	0.272647i	$-0.0878992\pi$
$48$	−24.9041	−	12.1567i	−0.518836	−	0.253264i
$49$	−64.4131			−1.31455
$50$	−6.69342	+	12.0729i	−0.133868	+	0.241458i
$51$			14.3490i			0.281353i
$52$	7.64059	+	12.2320i	0.146934	+	0.235230i
$53$	39.7067			0.749183			0.374592	−	0.927190i	$-0.377783\pi$
$53$	39.7067			0.749183			0.374592	+	0.927190i	$0.377783\pi$
$54$	−9.08890	−	5.03904i	−0.168313	−	0.0933155i
$55$			40.6456i			0.739010i
$56$	4.43785	+	85.0808i	0.0792474	+	1.51930i
$57$	49.8808			0.875102
$58$	46.4706	−	83.8189i	0.801217	−	1.44515i
$59$		−	4.84928i		−	0.0821912i	−0.999155	−	0.0410956i	$-0.986915\pi$
$59$		−	4.84928i		−	0.0821912i	0.999155	−	0.0410956i	$-0.0130848\pi$
$60$	−24.9977	+	15.6146i	−0.416628	+	0.260243i
$61$	66.1400			1.08426			0.542131	−	0.840294i	$-0.317618\pi$
$61$	66.1400			1.08426			0.542131	+	0.840294i	$0.317618\pi$
$62$	26.7993	+	14.8580i	0.432246	+	0.239645i
$63$			31.9487i			0.507122i
$64$	63.6527	−	6.65842i	0.994573	−	0.104038i
$65$	15.3386			0.235978
$66$	16.0482	−	28.9460i	0.243154	−	0.438576i
$67$		−	121.628i		−	1.81535i	−0.419678	−	0.907673i	$-0.637857\pi$
$67$		−	121.628i		−	1.81535i	0.419678	−	0.907673i	$-0.362143\pi$
$68$	−17.5557	−	28.1052i	−0.258172	−	0.413312i
$69$	−63.6713			−0.922772
$70$	79.2455	+	43.9350i	1.13208	+	0.627643i
$71$		−	17.5131i		−	0.246664i	−0.992365	−	0.123332i	$-0.960642\pi$
$71$		−	17.5131i		−	0.246664i	0.992365	−	0.123332i	$-0.0393579\pi$
$72$	23.9674	−	1.25015i	0.332881	−	0.0173632i
$73$	30.7084			0.420663			0.210331	−	0.977630i	$-0.432546\pi$
$73$	30.7084			0.420663			0.210331	+	0.977630i	$0.432546\pi$
$74$	33.5246	−	60.4682i	0.453035	−	0.817138i
$75$		−	11.9548i		−	0.159398i
$76$	−97.7008	+	61.0279i	−1.28554	+	0.802999i
$77$	−101.749			−1.32142
$78$	−10.9235	−	6.05617i	−0.140045	−	0.0776432i
$79$		−	31.4497i		−	0.398098i	−0.979990	−	0.199049i	$-0.936215\pi$
$79$		−	31.4497i		−	0.398098i	0.979990	−	0.199049i	$-0.0637853\pi$
$80$	29.8585	−	61.1680i	0.373232	−	0.764600i
$81$	9.00000			0.111111
$82$	−42.4346	+	76.5391i	−0.517495	+	0.933404i
$83$			116.303i			1.40125i	0.713531	+	0.700623i	$0.247095\pi$
$83$			116.303i			1.40125i	−0.713531	+	0.700623i	$0.752905\pi$
$84$	−39.0884	−	62.5774i	−0.465338	−	0.744969i
$85$	−35.2432			−0.414626
$86$	−102.370	−	56.7558i	−1.19035	−	0.659951i
$87$			82.9991i			0.954013i
$88$	3.98144	+	76.3307i	0.0452437	+	0.867394i
$89$	−16.2630			−0.182730			−0.0913649	−	0.995817i	$-0.529123\pi$
$89$	−16.2630			−0.182730			−0.0913649	+	0.995817i	$0.529123\pi$
$90$	12.3766	−	22.3236i	0.137518	−	0.248040i
$91$			38.3975i			0.421951i
$92$	124.712	−	77.9001i	1.35556	−	0.846741i
$93$	−26.5371			−0.285346
$94$	−44.8289	−	24.8539i	−0.476904	−	0.264403i
$95$			122.514i			1.28962i
$96$	−45.4151	+	31.7722i	−0.473074	+	0.330960i
$97$	−116.138			−1.19730			−0.598651	−	0.801010i	$-0.704296\pi$
$97$	−116.138			−1.19730			−0.598651	+	0.801010i	$0.704296\pi$
$98$	−62.4654	+	112.669i	−0.637402	+	1.14968i
$99$			28.6629i			0.289524i
$100$	14.6264	+	23.4157i	0.146264	+	0.234157i
$101$	−121.370			−1.20168			−0.600841	−	0.799369i	$-0.705167\pi$
$101$	−121.370			−1.20168			−0.600841	+	0.799369i	$0.705167\pi$
$102$	25.0987	+	13.9152i	0.246066	+	0.136423i
$103$			63.3218i			0.614775i	0.951584	+	0.307387i	$0.0994548\pi$
$103$			63.3218i			0.614775i	−0.951584	+	0.307387i	$0.900545\pi$
$104$	28.8053	−	1.50250i	0.276974	−	0.0144471i
$105$	−78.4704			−0.747337
$106$	38.5061	−	69.4534i	0.363265	−	0.655220i
$107$		−	110.600i		−	1.03364i	−0.856094	−	0.516821i	$-0.827115\pi$
$107$		−	110.600i		−	1.03364i	0.856094	−	0.516821i	$-0.172885\pi$
$108$	−17.6282	+	11.0113i	−0.163224	+	0.101956i
$109$	−39.7177			−0.364383			−0.182191	−	0.983263i	$-0.558319\pi$
$109$	−39.7177			−0.364383			−0.182191	+	0.983263i	$0.558319\pi$
$110$	71.0956	+	39.4166i	0.646323	+	0.358332i
$111$			59.8767i			0.539430i
$112$	153.124	+	74.7457i	1.36717	+	0.667372i
$113$	−109.371			−0.967888			−0.483944	−	0.875099i	$-0.660796\pi$
$113$	−109.371			−0.967888			−0.483944	+	0.875099i	$0.660796\pi$
$114$	48.3726	−	87.2496i	0.424321	−	0.765347i
$115$		−	156.386i		−	1.35987i
$116$	−101.547	−	162.569i	−0.875407	−	1.40146i
$117$	10.8167			0.0924500
$118$	−8.48216	−	4.70265i	−0.0718828	−	0.0398530i
$119$		−	88.2254i		−	0.741390i
$120$	3.07055	+	58.8673i	0.0255879	+	0.490561i
$121$	29.7152			0.245580
$122$	64.1401	−	115.689i	0.525739	−	0.948274i
$123$		−	75.7905i		−	0.616183i
$124$	51.9779	−	32.4675i	0.419177	−	0.261835i
$125$	135.717			1.08573
$126$	55.8833	+	30.9826i	0.443519	+	0.245894i
$127$			9.23082i			0.0726836i	0.999339	+	0.0363418i	$0.0115705\pi$
$127$			9.23082i			0.0726836i	−0.999339	+	0.0363418i	$0.988430\pi$
$128$	50.0814	−	117.796i	0.391261	−	0.920280i
$129$	101.369			0.785806
$130$	14.8748	−	26.8296i	0.114422	−	0.206382i
$131$			91.2491i			0.696558i	0.937391	+	0.348279i	$0.113234\pi$
$131$			91.2491i			0.696558i	−0.937391	+	0.348279i	$0.886766\pi$
$132$	−35.0683	−	56.1416i	−0.265669	−	0.425315i
$133$	−306.694			−2.30597
$134$	−212.747	−	117.951i	−1.58767	−	0.880228i
$135$			22.1053i			0.163743i
$136$	−66.1853	+	3.45226i	−0.486657	+	0.0253843i
$137$	107.488			0.784583			0.392292	−	0.919841i	$-0.371682\pi$
$137$	107.488			0.784583			0.392292	+	0.919841i	$0.371682\pi$
$138$	−61.7460	+	111.371i	−0.447435	+	0.807038i
$139$			21.7561i			0.156519i	0.996933	+	0.0782593i	$0.0249362\pi$
$139$			21.7561i			0.156519i	−0.996933	+	0.0782593i	$0.975064\pi$
$140$	153.699	−	96.0065i	1.09785	−	0.685761i
$141$	44.3905			0.314826
$142$	−30.6332	−	16.9836i	−0.215727	−	0.119603i
$143$			34.4485i			0.240899i
$144$	21.0560	−	43.1352i	0.146222	−	0.299550i
$145$	−203.857			−1.40591
$146$	29.7798	−	53.7138i	0.203971	−	0.367903i
$147$		−	111.567i		−	0.758957i
$148$	−73.2577	−	117.280i	−0.494984	−	0.792430i
$149$	125.533			0.842505			0.421253	−	0.906943i	$-0.361591\pi$
$149$	125.533			0.842505			0.421253	+	0.906943i	$0.361591\pi$
$150$	−20.9109	−	11.5934i	−0.139406	−	0.0772890i
$151$		−	12.8813i		−	0.0853067i	−0.999090	−	0.0426534i	$-0.986419\pi$
$151$		−	12.8813i		−	0.0853067i	0.999090	−	0.0426534i	$-0.0135811\pi$
$152$	12.0009	+	230.077i	0.0789534	+	1.51366i
$153$	−24.8532			−0.162440
$154$	−98.6726	+	177.976i	−0.640731	+	1.15569i
$155$		−	65.1790i		−	0.420509i
$156$	−21.1864	+	13.2339i	−0.135810	+	0.0848327i
$157$	287.204			1.82933			0.914664	−	0.404216i	$-0.132455\pi$
$157$	287.204			1.82933			0.914664	+	0.404216i	$0.132455\pi$
$158$	−55.0106	−	30.4988i	−0.348168	−	0.193030i
$159$			68.7740i			0.432541i
$160$	−78.0369	−	111.546i	−0.487731	−	0.697161i
$161$	391.484			2.43158
$162$	8.72787	−	15.7424i	0.0538757	−	0.0971755i
$163$			93.2925i			0.572347i	0.958178	+	0.286173i	$0.0923833\pi$
$163$			93.2925i			0.572347i	−0.958178	+	0.286173i	$0.907617\pi$
$164$	92.7277	+	148.450i	0.565413	+	0.905181i
$165$	−70.4002			−0.426668
$166$	203.433	+	112.787i	1.22550	+	0.679438i
$167$		−	72.5096i		−	0.434189i	−0.976151	−	0.217095i	$-0.930342\pi$
$167$		−	72.5096i		−	0.434189i	0.976151	−	0.217095i	$-0.0696580\pi$
$168$	−147.364	+	7.68659i	−0.877168	+	0.0457535i
$169$	13.0000			0.0769231
$170$	−34.1776	+	61.6460i	−0.201045	+	0.362624i
$171$			86.3962i			0.505241i
$172$	−198.550	+	124.022i	−1.15436	+	0.721060i
$173$	210.381			1.21608			0.608038	−	0.793908i	$-0.291957\pi$
$173$	210.381			1.21608			0.608038	+	0.793908i	$0.291957\pi$
$174$	145.179	+	80.4895i	0.834360	+	0.462583i
$175$			73.5046i			0.420026i
$176$	137.376	+	67.0585i	0.780543	+	0.381014i
$177$	8.39920			0.0474531
$178$	−15.7712	+	28.4465i	−0.0886023	+	0.159812i
$179$			146.543i			0.818675i	0.912383	+	0.409337i	$0.134240\pi$
$179$			146.543i			0.818675i	−0.912383	+	0.409337i	$0.865760\pi$
$180$	−27.0452	−	43.2972i	−0.150251	−	0.240540i
$181$	−334.916			−1.85037			−0.925183	−	0.379522i	$-0.876089\pi$
$181$	−334.916			−1.85037			−0.925183	+	0.379522i	$0.876089\pi$
$182$	67.1634	+	37.2365i	0.369030	+	0.204596i
$183$			114.558i			0.625999i
$184$	−15.3188	−	293.686i	−0.0832543	−	1.59612i
$185$	−147.066			−0.794950
$186$	−25.7347	+	46.4177i	−0.138359	+	0.249558i
$187$		−	79.1518i		−	0.423272i
$188$	−86.9469	+	54.3106i	−0.462483	+	0.288886i
$189$	−55.3367			−0.292787
$190$	214.297	+	118.810i	1.12788	+	0.625315i
$191$		−	236.870i		−	1.24016i	−0.784540	−	0.620079i	$-0.787101\pi$
$191$		−	236.870i		−	1.24016i	0.784540	−	0.620079i	$-0.212899\pi$
$192$	11.5327	+	110.250i	0.0600663	+	0.574217i
$193$	355.859			1.84383			0.921915	−	0.387393i	$-0.126624\pi$
$193$	355.859			1.84383			0.921915	+	0.387393i	$0.126624\pi$
$194$	−112.627	+	203.144i	−0.580550	+	1.04714i
$195$			26.5672i			0.136242i
$196$	136.499	+	218.524i	0.696423	+	1.11492i
$197$	−172.567			−0.875973			−0.437986	−	0.898982i	$-0.644308\pi$
$197$	−172.567			−0.875973			−0.437986	+	0.898982i	$0.644308\pi$
$198$	50.1360	+	27.7962i	0.253212	+	0.140385i
$199$		−	59.4356i		−	0.298671i	−0.988787	−	0.149336i	$-0.952287\pi$
$199$		−	59.4356i		−	0.298671i	0.988787	−	0.149336i	$-0.0477135\pi$
$200$	55.1420	−	2.87623i	0.275710	−	0.0143812i
$201$	210.666			1.04809
$202$	−117.700	+	212.295i	−0.582673	+	1.05097i
$203$		−	510.322i		−	2.51390i
$204$	48.6797	−	30.4073i	0.238626	−	0.149055i
$205$	186.152			0.908059
$206$	110.760	+	61.4072i	0.537670	+	0.298093i
$207$		−	110.282i		−	0.532763i
$208$	25.3062	−	51.8420i	0.121664	−	0.249241i
$209$	−275.152			−1.31652
$210$	−76.0977	+	137.257i	−0.362370	+	0.653606i
$211$			96.0016i			0.454984i	0.973780	+	0.227492i	$0.0730525\pi$
$211$			96.0016i			0.454984i	−0.973780	+	0.227492i	$0.926947\pi$
$212$	−84.1432	−	134.707i	−0.396902	−	0.635409i
$213$	30.3336			0.142411
$214$	−193.456	−	107.255i	−0.904002	−	0.501193i
$215$			248.976i			1.15803i
$216$	2.16533	+	41.5128i	0.0100247	+	0.192189i
$217$	163.164			0.751909
$218$	−38.5168	+	69.4726i	−0.176682	+	0.318682i
$219$			53.1885i			0.242870i
$220$	137.892	−	86.1328i	0.626780	−	0.391513i
$221$	−29.8699			−0.135158
$222$	104.734	+	58.0663i	0.471775	+	0.261560i
$223$			270.099i			1.21121i	0.795766	+	0.605604i	$0.207068\pi$
$223$			270.099i			1.21121i	−0.795766	+	0.605604i	$0.792932\pi$
$224$	279.236	−	195.352i	1.24659	−	0.872107i
$225$	20.7064			0.0920283
$226$	−106.064	+	191.308i	−0.469311	+	0.846495i
$227$			56.8805i			0.250575i	0.992120	+	0.125287i	$0.0399853\pi$
$227$			56.8805i			0.250575i	−0.992120	+	0.125287i	$0.960015\pi$
$228$	−105.703	−	169.223i	−0.463612	−	0.742205i
$229$	230.447			1.00632			0.503160	−	0.864193i	$-0.332171\pi$
$229$	230.447			1.00632			0.503160	+	0.864193i	$0.332171\pi$
$230$	−273.543	−	151.657i	−1.18932	−	0.659378i
$231$		−	176.235i		−	0.762921i
$232$	−382.836	+	19.9689i	−1.65015	+	0.0860729i
$233$	116.655			0.500665			0.250332	−	0.968160i	$-0.419460\pi$
$233$	116.655			0.500665			0.250332	+	0.968160i	$0.419460\pi$
$234$	10.4896	−	18.9201i	0.0448273	−	0.0808549i
$235$			109.029i			0.463954i
$236$	−16.4514	+	10.2762i	−0.0697092	+	0.0435432i
$237$	54.4725			0.229842
$238$	−154.320	−	85.5577i	−0.648404	−	0.359486i
$239$			102.119i			0.427274i	0.976913	+	0.213637i	$0.0685310\pi$
$239$			102.119i			0.427274i	−0.976913	+	0.213637i	$0.931469\pi$
$240$	105.946	+	51.7165i	0.441442	+	0.215485i
$241$	76.0561			0.315585			0.157793	−	0.987472i	$-0.449562\pi$
$241$	76.0561			0.315585			0.157793	+	0.987472i	$0.449562\pi$
$242$	28.8167	−	51.9767i	0.119077	−	0.214780i
$243$			15.5885i			0.0641500i
$244$	−140.159	−	224.383i	−0.574420	−	0.919601i
$245$	274.024			1.11846
$246$	−132.570	−	73.4988i	−0.538901	−	0.298776i
$247$			103.835i			0.420386i
$248$	−6.38462	−	122.403i	−0.0257444	−	0.493562i
$249$	−201.443			−0.809010
$250$	131.613	−	237.390i	0.526452	−	0.949561i
$251$		−	481.631i		−	1.91885i	−0.281964	−	0.959425i	$-0.590986\pi$
$251$		−	481.631i		−	1.91885i	0.281964	−	0.959425i	$-0.409014\pi$
$252$	108.387	−	67.7030i	0.430108	−	0.268663i
$253$	351.222			1.38823
$254$	16.1462	+	8.95170i	0.0635676	+	0.0352429i
$255$		−	61.0431i		−	0.239385i
$256$	−157.477	−	201.834i	−0.615143	−	0.788416i
$257$	−225.517			−0.877499			−0.438749	−	0.898609i	$-0.644578\pi$
$257$	−225.517			−0.877499			−0.438749	+	0.898609i	$0.644578\pi$
$258$	98.3039	−	177.311i	0.381023	−	0.687250i
$259$		−	368.154i		−	1.42144i
$260$	−32.5043	−	52.0368i	−0.125017	−	0.200142i
$261$	−143.759			−0.550799
$262$	159.609	+	88.4900i	0.609196	+	0.337748i
$263$		−	90.0622i		−	0.342442i	−0.985233	−	0.171221i	$-0.945229\pi$
$263$		−	90.0622i		−	0.342442i	0.985233	−	0.171221i	$-0.0547712\pi$
$264$	−132.209	+	6.89606i	−0.500790	+	0.0261215i
$265$	−168.919			−0.637429
$266$	−297.420	+	536.456i	−1.11812	+	2.01675i
$267$		−	28.1683i		−	0.105499i
$268$	−412.629	+	257.745i	−1.53966	+	0.961734i
$269$	−268.438			−0.997912			−0.498956	−	0.866627i	$-0.666283\pi$
$269$	−268.438			−0.997912			−0.498956	+	0.866627i	$0.666283\pi$
$270$	38.6656	+	21.4369i	0.143206	+	0.0793958i
$271$			203.164i			0.749684i	0.927089	+	0.374842i	$0.122303\pi$
$271$			203.164i			0.749684i	−0.927089	+	0.374842i	$0.877697\pi$
$272$	−58.1455	+	119.117i	−0.213770	+	0.437929i
$273$	−66.5065			−0.243613
$274$	104.238	−	188.014i	0.380430	−	0.686181i
$275$			65.9450i			0.239800i
$276$	134.927	+	216.007i	0.488866	+	0.782635i
$277$	464.550			1.67708			0.838538	−	0.544843i	$-0.183411\pi$
$277$	464.550			1.67708			0.838538	+	0.544843i	$0.183411\pi$
$278$	38.0549	+	21.0983i	0.136888	+	0.0758930i
$279$		−	45.9637i		−	0.164744i
$280$	−18.8793	−	361.947i	−0.0674262	−	1.29267i
$281$	−107.129			−0.381241			−0.190621	−	0.981664i	$-0.561050\pi$
$281$	−107.129			−0.381241			−0.190621	+	0.981664i	$0.561050\pi$
$282$	43.0482	−	77.6460i	0.152653	−	0.275340i
$283$		−	345.157i		−	1.21963i	−0.792542	−	0.609817i	$-0.791243\pi$
$283$		−	345.157i		−	1.21963i	0.792542	−	0.609817i	$-0.208757\pi$
$284$	−59.4139	+	37.1124i	−0.209204	+	0.130677i
$285$	−212.201			−0.744565
$286$	60.2560	+	33.4069i	0.210685	+	0.116807i
$287$			466.000i			1.62369i
$288$	−55.0310	−	78.6612i	−0.191080	−	0.273129i
$289$	−220.368			−0.762521
$290$	−197.693	+	356.579i	−0.681701	+	1.22958i
$291$		−	201.157i		−	0.691263i
$292$	−65.0747	−	104.179i	−0.222859	−	0.356779i
$293$	22.1790			0.0756964			0.0378482	−	0.999284i	$-0.487950\pi$
$293$	22.1790			0.0756964			0.0378482	+	0.999284i	$0.487950\pi$
$294$	−195.148	−	108.193i	−0.663769	−	0.368004i
$295$			20.6296i			0.0699309i
$296$	−276.183	+	14.4059i	−0.933052	+	0.0486684i
$297$	−49.6456			−0.167157
$298$	121.738	−	219.578i	0.408515	−	0.736838i
$299$		−	132.542i		−	0.443285i
$300$	−40.5572	+	25.3337i	−0.135191	+	0.0844457i
$301$	−623.270			−2.07066
$302$	−22.5315	−	12.4918i	−0.0746075	−	0.0413637i
$303$		−	210.219i		−	0.693791i
$304$	414.079	+	202.129i	1.36210	+	0.664897i
$305$	−281.370			−0.922525
$306$	−24.1018	+	43.4723i	−0.0787639	+	0.142066i
$307$			504.748i			1.64413i	0.569393	+	0.822065i	$0.307178\pi$
$307$			504.748i			1.64413i	−0.569393	+	0.822065i	$0.692822\pi$
$308$	215.619	+	345.188i	0.700060	+	1.12074i
$309$	−109.677			−0.354940
$310$	−114.008	−	63.2081i	−0.367769	−	0.203897i
$311$			333.338i			1.07183i	0.844273	+	0.535914i	$0.180033\pi$
$311$			333.338i			1.07183i	−0.844273	+	0.535914i	$0.819967\pi$
$312$	2.60240	+	49.8922i	0.00834102	+	0.159911i
$313$	300.630			0.960481			0.480240	−	0.877137i	$-0.340549\pi$
$313$	300.630			0.960481			0.480240	+	0.877137i	$0.340549\pi$
$314$	278.520	−	502.366i	0.887007	−	1.59989i
$315$		−	135.915i		−	0.431475i
$316$	−106.694	+	66.6457i	−0.337641	+	0.210904i
$317$	203.308			0.641351			0.320676	−	0.947189i	$-0.396090\pi$
$317$	203.308			0.641351			0.320676	+	0.947189i	$0.396090\pi$
$318$	120.297	+	66.6945i	0.378292	+	0.209731i
$319$		−	457.838i		−	1.43523i
$320$	−270.789	+	28.3260i	−0.846215	+	0.0885188i
$321$	191.564			0.596773
$322$	379.647	−	684.769i	1.17903	−	2.12661i
$323$		−	238.581i		−	0.738639i
$324$	−19.0721	−	30.5329i	−0.0588644	−	0.0942372i
$325$	24.8860			0.0765722
$326$	163.184	+	90.4716i	0.500563	+	0.277520i
$327$		−	68.7931i		−	0.210377i
$328$	349.586	−	18.2346i	1.06581	−	0.0555932i
$329$	−272.936			−0.829592
$330$	−68.2715	+	123.141i	−0.206883	+	0.373155i
$331$			244.392i			0.738345i	0.929361	+	0.369173i	$0.120359\pi$
$331$			244.392i			0.738345i	−0.929361	+	0.369173i	$0.879641\pi$
$332$	394.564	−	246.461i	1.18845	−	0.742352i
$333$	−103.710			−0.311440
$334$	−126.831	−	70.3171i	−0.379733	−	0.210530i
$335$			517.426i			1.54455i
$336$	−129.463	+	265.218i	−0.385308	+	0.789339i
$337$	322.903			0.958171			0.479085	−	0.877768i	$-0.340968\pi$
$337$	322.903			0.958171			0.479085	+	0.877768i	$0.340968\pi$
$338$	12.6069	−	22.7391i	0.0372986	−	0.0672754i
$339$		−	189.437i		−	0.558810i
$340$	74.6846	+	119.564i	0.219661	+	0.351659i
$341$	146.384			0.429278
$342$	151.121	+	83.7838i	0.441873	+	0.244982i
$343$			164.143i			0.478550i
$344$	24.3886	+	467.568i	0.0708970	+	1.35921i
$345$	270.868			0.785124
$346$	204.020	−	367.990i	0.589653	−	1.06356i
$347$			20.1924i			0.0581914i	0.999577	+	0.0290957i	$0.00926275\pi$
$347$			20.1924i			0.0581914i	−0.999577	+	0.0290957i	$0.990737\pi$
$348$	281.578	−	175.885i	0.809132	−	0.505417i
$349$	−681.071			−1.95149			−0.975746	−	0.218907i	$-0.929751\pi$
$349$	−681.071			−1.95149			−0.975746	+	0.218907i	$0.929751\pi$
$350$	128.571	+	71.2820i	0.367346	+	0.203663i
$351$			18.7350i			0.0533761i
$352$	250.518	−	175.261i	0.711698	−	0.497901i
$353$	−279.309			−0.791244			−0.395622	−	0.918413i	$-0.629471\pi$
$353$	−279.309			−0.791244			−0.395622	+	0.918413i	$0.629471\pi$
$354$	8.14523	−	14.6915i	0.0230091	−	0.0415015i
$355$			74.5036i			0.209869i
$356$	34.4631	+	55.1727i	0.0968066	+	0.154980i
$357$	152.811			0.428041
$358$	256.327	+	142.112i	0.715996	+	0.396960i
$359$			598.088i			1.66598i	0.553285	+	0.832992i	$0.313374\pi$
$359$			598.088i			1.66598i	−0.553285	+	0.832992i	$0.686626\pi$
$360$	−101.961	+	5.31835i	−0.283226	+	0.0147732i
$361$	−468.366			−1.29741
$362$	−324.789	+	585.822i	−0.897208	+	1.61829i
$363$			51.4683i			0.141786i
$364$	130.265	−	81.3689i	0.357871	−	0.223541i
$365$	−130.638			−0.357913
$366$	200.380	+	111.094i	0.547486	+	0.303535i
$367$			483.740i			1.31809i	0.752103	+	0.659046i	$0.229040\pi$
$367$			483.740i			1.31809i	−0.752103	+	0.659046i	$0.770960\pi$
$368$	−528.559	−	258.011i	−1.43630	−	0.701116i
$369$	131.273			0.355753
$370$	−142.619	+	257.241i	−0.385456	+	0.695247i
$371$		−	422.859i		−	1.13978i
$372$	56.2354	+	90.0284i	0.151170	+	0.242012i
$373$	250.677			0.672057			0.336029	−	0.941852i	$-0.390916\pi$
$373$	250.677			0.672057			0.336029	+	0.941852i	$0.390916\pi$
$374$	−138.449	−	76.7585i	−0.370185	−	0.205237i
$375$			235.068i			0.626849i
$376$	10.6800	+	204.752i	0.0284042	+	0.544554i
$377$	−172.776			−0.458293
$378$	−53.6635	+	96.7928i	−0.141967	+	0.256066i
$379$			398.517i			1.05150i	0.850640	+	0.525749i	$0.176215\pi$
$379$			398.517i			1.05150i	−0.850640	+	0.525749i	$0.823785\pi$
$380$	415.635	−	259.623i	1.09378	−	0.683217i
$381$	−15.9882			−0.0419639
$382$	−414.323	−	229.708i	−1.08462	−	0.601329i
$383$		−	76.2686i		−	0.199135i	−0.995031	−	0.0995673i	$-0.968254\pi$
$383$		−	76.2686i		−	0.199135i	0.995031	−	0.0995673i	$-0.0317459\pi$
$384$	204.028	+	86.7435i	0.531324	+	0.225895i
$385$	432.857			1.12430
$386$	345.099	−	622.454i	0.894039	−	1.61258i
$387$			175.576i			0.453685i
$388$	246.111	+	394.004i	0.634306	+	1.01547i
$389$	−630.856			−1.62174			−0.810869	−	0.585228i	$-0.801005\pi$
$389$	−630.856			−1.62174			−0.810869	+	0.585228i	$0.801005\pi$
$390$	46.4703	+	25.7639i	0.119155	+	0.0660613i
$391$			304.540i			0.778875i
$392$	514.605	−	26.8420i	1.31277	−	0.0684746i
$393$	−158.048			−0.402158
$394$	−167.349	+	301.847i	−0.424743	+	0.766108i
$395$			133.792i			0.338714i
$396$	97.2401	−	60.7401i	0.245556	−	0.153384i
$397$	−250.068			−0.629894			−0.314947	−	0.949109i	$-0.601987\pi$
$397$	−250.068			−0.629894			−0.314947	+	0.949109i	$0.601987\pi$
$398$	−103.962	−	57.6384i	−0.261212	−	0.144820i
$399$		−	531.209i		−	1.33135i
$400$	48.4437	−	99.2415i	0.121109	−	0.248104i
$401$	703.830			1.75519			0.877593	−	0.479406i	$-0.159148\pi$
$401$	703.830			1.75519			0.877593	+	0.479406i	$0.159148\pi$
$402$	204.296	−	368.489i	0.508200	−	0.916639i
$403$		−	55.2415i		−	0.137076i
$404$	257.197	+	411.752i	0.636626	+	1.01919i
$405$	−38.2874			−0.0945369
$406$	−892.635	−	494.891i	−2.19861	−	1.21894i
$407$		−	330.291i		−	0.811526i
$408$	−5.97949	−	114.636i	−0.0146556	−	0.280972i
$409$	104.737			0.256082			0.128041	−	0.991769i	$-0.459131\pi$
$409$	104.737			0.256082			0.128041	+	0.991769i	$0.459131\pi$
$410$	180.523	−	325.610i	0.440301	−	0.794170i
$411$			186.175i			0.452979i
$412$	214.822	−	134.186i	0.521412	−	0.325695i
$413$	−51.6427			−0.125043
$414$	−192.901	−	106.947i	−0.465943	−	0.258327i
$415$		−	494.773i		−	1.19223i
$416$	−66.1390	−	94.5390i	−0.158988	−	0.227257i
$417$	−37.6827			−0.0903661
$418$	−266.832	+	481.284i	−0.638354	+	1.15140i
$419$		−	0.181142i		−	0.000432319i	−1.00000		0.000216159i	$-0.999931\pi$
$419$		−	0.181142i		−	0.000432319i	1.00000		0.000216159i	$-6.88057e-5\pi$
$420$	166.288	+	266.214i	0.395924	+	0.633843i
$421$	−469.098			−1.11425			−0.557124	−	0.830430i	$-0.688095\pi$
$421$	−469.098			−1.11425			−0.557124	+	0.830430i	$0.688095\pi$
$422$	167.922	+	93.0988i	0.397920	+	0.220613i
$423$			76.8865i			0.181765i
$424$	−317.222	+	16.5465i	−0.748166	+	0.0390247i
$425$	−57.1801			−0.134541
$426$	29.4164	−	53.0583i	0.0690526	−	0.124550i
$427$		−	704.362i		−	1.64956i
$428$	−375.214	+	234.374i	−0.876667	+	0.547602i
$429$	−59.6666			−0.139083
$430$	435.500	+	241.448i	1.01279	+	0.561507i
$431$		−	292.516i		−	0.678691i	−0.940662	−	0.339345i	$-0.889794\pi$
$431$		−	292.516i		−	0.678691i	0.940662	−	0.339345i	$-0.110206\pi$
$432$	74.7123	+	36.4701i	0.172945	+	0.0844214i
$433$	723.820			1.67164			0.835820	−	0.549004i	$-0.184993\pi$
$433$	723.820			1.67164			0.835820	+	0.549004i	$0.184993\pi$
$434$	158.231	−	285.400i	0.364587	−	0.657605i
$435$		−	353.091i		−	0.811704i
$436$	84.1666	+	134.744i	0.193043	+	0.309046i
$437$	1058.66			2.42256
$438$	93.0351	+	51.5802i	0.212409	+	0.117763i
$439$			736.376i			1.67739i	0.544599	+	0.838697i	$0.316682\pi$
$439$			736.376i			1.67739i	−0.544599	+	0.838697i	$0.683318\pi$
$440$	−16.9377	−	324.723i	−0.0384948	−	0.738007i
$441$	193.239			0.438184
$442$	−28.9667	+	52.2472i	−0.0655355	+	0.118206i
$443$		−	316.908i		−	0.715367i	−0.933843	−	0.357683i	$-0.883567\pi$
$443$		−	316.908i		−	0.715367i	0.933843	−	0.357683i	$-0.116433\pi$
$444$	203.134	−	126.886i	0.457510	−	0.285779i
$445$	69.1852			0.155472
$446$	472.447	+	261.932i	1.05930	+	0.587292i
$447$			217.430i			0.486421i
$448$	−70.9093	−	677.873i	−0.158280	−	1.51311i
$449$	−162.328			−0.361532			−0.180766	−	0.983526i	$-0.557858\pi$
$449$	−162.328			−0.361532			−0.180766	+	0.983526i	$0.557858\pi$
$450$	20.0803	−	36.2188i	0.0446228	−	0.0804861i
$451$			418.074i			0.926994i
$452$	231.771	+	371.047i	0.512768	+	0.820900i
$453$	22.3111			0.0492519
$454$	99.4931	+	55.1606i	0.219148	+	0.121499i
$455$		−	163.349i		−	0.359009i
$456$	−398.505	+	20.7862i	−0.873914	+	0.0455838i
$457$	573.169			1.25420			0.627100	−	0.778939i	$-0.284242\pi$
$457$	573.169			1.25420			0.627100	+	0.778939i	$0.284242\pi$
$458$	223.479	−	403.089i	0.487946	−	0.880107i
$459$		−	43.0471i		−	0.0937845i
$460$	−530.544	+	331.400i	−1.15336	+	0.720434i
$461$	−128.452			−0.278639			−0.139319	−	0.990248i	$-0.544491\pi$
$461$	−128.452			−0.278639			−0.139319	+	0.990248i	$0.544491\pi$
$462$	−308.263	−	170.906i	−0.667235	−	0.369926i
$463$		−	480.854i		−	1.03856i	−0.854604	−	0.519281i	$-0.826200\pi$
$463$		−	480.854i		−	1.03856i	0.854604	−	0.519281i	$-0.173800\pi$
$464$	−336.331	+	689.006i	−0.724852	+	1.48493i
$465$	112.893			0.242781
$466$	113.128	−	204.048i	0.242763	−	0.437872i
$467$			834.277i			1.78646i	0.449601	+	0.893230i	$0.351566\pi$
$467$			834.277i			1.78646i	−0.449601	+	0.893230i	$0.648434\pi$
$468$	−22.9218	−	36.6959i	−0.0489782	−	0.0784101i
$469$	−1295.29			−2.76181
$470$	190.709	+	105.732i	0.405765	+	0.224963i
$471$			497.453i			1.05616i
$472$	2.02078	+	38.7416i	0.00428131	+	0.0820796i
$473$	−559.170			−1.18218
$474$	52.8254	−	95.2811i	0.111446	−	0.201015i
$475$			198.772i			0.418468i
$476$	−299.308	+	186.960i	−0.628799	+	0.392773i
$477$	−119.120			−0.249728
$478$	178.622	+	99.0308i	0.373685	+	0.207177i
$479$		−	480.357i		−	1.00283i	−0.865206	−	0.501416i	$-0.832812\pi$
$479$		−	480.357i		−	1.00283i	0.865206	−	0.501416i	$-0.167188\pi$
$480$	193.203	−	135.164i	0.402506	−	0.281591i
$481$	−124.643			−0.259134
$482$	73.7564	−	133.034i	0.153022	−	0.276005i
$483$			678.071i			1.40387i
$484$	−62.9701	−	100.810i	−0.130103	−	0.208285i
$485$	494.071			1.01870
$486$	27.2667	+	15.1171i	0.0561043	+	0.0311052i
$487$		−	352.253i		−	0.723313i	−0.932311	−	0.361656i	$-0.882211\pi$
$487$		−	352.253i		−	0.723313i	0.932311	−	0.361656i	$-0.117789\pi$
$488$	−528.402	+	27.5617i	−1.08279	+	0.0564788i
$489$	−161.587			−0.330445
$490$	265.738	−	479.311i	0.542322	−	0.978186i
$491$			144.354i			0.294000i	0.989136	+	0.147000i	$0.0469617\pi$
$491$			144.354i			0.294000i	−0.989136	+	0.147000i	$0.953038\pi$
$492$	−257.122	+	160.609i	−0.522606	+	0.326441i
$493$	396.985			0.805244
$494$	181.624	+	100.696i	0.367661	+	0.203837i
$495$		−	121.937i		−	0.246337i
$496$	−220.295	−	107.535i	−0.444143	−	0.216804i
$497$	−186.507			−0.375265
$498$	−195.352	+	352.357i	−0.392274	+	0.707544i
$499$		−	525.436i		−	1.05298i	−0.850182	−	0.526489i	$-0.823508\pi$
$499$		−	525.436i		−	1.05298i	0.850182	−	0.526489i	$-0.176492\pi$
$500$	−287.600	−	460.425i	−0.575200	−	0.920849i
$501$	125.590			0.250679
$502$	−842.450	−	467.068i	−1.67819	−	0.930415i
$503$			49.9631i			0.0993302i	0.998766	+	0.0496651i	$0.0158154\pi$
$503$			49.9631i			0.0993302i	−0.998766	+	0.0496651i	$0.984185\pi$
$504$	−13.3136	−	255.242i	−0.0264158	−	0.506433i
$505$	516.327			1.02243
$506$	340.602	−	614.344i	0.673127	−	1.21412i
$507$			22.5167i			0.0444116i
$508$	31.3159	−	19.5612i	0.0616455	−	0.0385063i
$509$	387.200			0.760708			0.380354	−	0.924841i	$-0.375802\pi$
$509$	387.200			0.760708			0.380354	+	0.924841i	$0.375802\pi$
$510$	−106.774	−	59.1973i	−0.209361	−	0.116073i
$511$		−	327.031i		−	0.639981i
$512$	−505.756	+	79.7203i	−0.987804	+	0.155704i
$513$	−149.643			−0.291701
$514$	−218.698	+	394.466i	−0.425483	+	0.767443i
$515$		−	269.381i		−	0.523070i
$516$	−214.813	−	343.898i	−0.416304	−	0.666470i
$517$	−244.866			−0.473628
$518$	−643.960	−	357.022i	−1.24317	−	0.689231i
$519$			364.391i			0.702102i
$520$	−122.542	+	6.39186i	−0.235658	+	0.0122920i
$521$	−218.565			−0.419510			−0.209755	−	0.977754i	$-0.567267\pi$
$521$	−218.565			−0.419510			−0.209755	+	0.977754i	$0.567267\pi$
$522$	−139.412	+	251.457i	−0.267072	+	0.481718i
$523$		−	326.655i		−	0.624579i	−0.949987	−	0.312289i	$-0.898904\pi$
$523$		−	326.655i		−	0.624579i	0.949987	−	0.312289i	$-0.101096\pi$
$524$	309.566	−	193.368i	0.590776	−	0.369023i
$525$	−127.314			−0.242502
$526$	−157.533	−	87.3390i	−0.299493	−	0.166044i
$527$			126.927i			0.240849i
$528$	−116.149	+	237.942i	−0.219979	+	0.450647i
$529$	−822.343			−1.55452
$530$	−163.811	+	295.466i	−0.309077	+	0.557482i
$531$			14.5478i			0.0273971i
$532$	649.920	+	1040.47i	1.22165	+	1.95577i
$533$	157.770			0.296005
$534$	−49.2708	−	27.3165i	−0.0922674	−	0.0511546i
$535$			470.508i			0.879455i
$536$	50.6846	+	971.705i	0.0945608	+	1.81288i
$537$	−253.819			−0.472662
$538$	−260.322	+	469.542i	−0.483869	+	0.872754i
$539$			615.422i			1.14179i
$540$	74.9930	−	46.8437i	0.138876	−	0.0867476i
$541$	374.948			0.693064			0.346532	−	0.938038i	$-0.387359\pi$
$541$	374.948			0.693064			0.346532	+	0.938038i	$0.387359\pi$
$542$	355.367	+	197.021i	0.655659	+	0.363508i
$543$		−	580.092i		−	1.06831i
$544$	151.967	+	217.221i	0.279350	+	0.399303i
$545$	168.966			0.310029
$546$	−64.4955	+	116.330i	−0.118124	+	0.213059i
$547$			207.501i			0.379343i	0.981848	+	0.189671i	$0.0607423\pi$
$547$			207.501i			0.379343i	−0.981848	+	0.189671i	$0.939258\pi$
$548$	−227.780	−	364.657i	−0.415656	−	0.665433i
$549$	−198.420			−0.361421
$550$	115.348	+	63.9510i	0.209724	+	0.116275i
$551$		−	1380.02i		−	2.50458i
$552$	508.679	−	26.5329i	0.921519	−	0.0480669i
$553$	−334.926			−0.605652
$554$	450.504	−	812.573i	0.813184	−	1.46674i
$555$		−	254.725i		−	0.458964i
$556$	73.8085	−	46.1038i	0.132749	−	0.0829204i
$557$	654.954			1.17586			0.587930	−	0.808912i	$-0.299943\pi$
$557$	654.954			1.17586			0.587930	+	0.808912i	$0.299943\pi$
$558$	−80.3978	−	44.5739i	−0.144082	−	0.0798815i
$559$			211.016i			0.377489i
$560$	−651.412	−	317.980i	−1.16324	−	0.567822i
$561$	137.095			0.244376
$562$	−103.889	+	187.385i	−0.184857	+	0.333426i
$563$			46.1792i			0.0820235i	0.999159	+	0.0410118i	$0.0130581\pi$
$563$			46.1792i			0.0820235i	−0.999159	+	0.0410118i	$0.986942\pi$
$564$	−94.0687	−	150.596i	−0.166788	−	0.267015i
$565$	465.283			0.823510
$566$	−603.734	−	334.720i	−1.06667	−	0.591378i
$567$		−	95.8460i		−	0.169041i
$568$	7.29801	+	139.915i	0.0128486	+	0.246329i
$569$	−798.899			−1.40404			−0.702021	−	0.712157i	$-0.747719\pi$
$569$	−798.899			−1.40404			−0.702021	+	0.712157i	$0.747719\pi$
$570$	−205.785	+	371.174i	−0.361026	+	0.651182i
$571$		−	597.945i		−	1.04719i	−0.851967	−	0.523595i	$-0.824591\pi$
$571$		−	597.945i		−	1.04719i	0.851967	−	0.523595i	$-0.175409\pi$
$572$	116.868	−	73.0006i	0.204315	−	0.127623i
$573$	410.271			0.716005
$574$	815.108	+	451.909i	1.42005	+	0.787299i
$575$		−	253.726i		−	0.441263i
$576$	−190.958	+	19.9753i	−0.331524	+	0.0346793i
$577$	118.733			0.205776			0.102888	−	0.994693i	$-0.467192\pi$
$577$	118.733			0.205776			0.102888	+	0.994693i	$0.467192\pi$
$578$	−213.705	+	385.460i	−0.369732	+	0.666885i
$579$			616.366i			1.06454i
$580$	431.998	+	691.595i	0.744824	+	1.19240i
$581$	1238.58			2.13181
$582$	−351.856	−	195.075i	−0.604564	−	0.335180i
$583$		−	379.370i		−	0.650720i
$584$	−245.333	+	12.7967i	−0.420091	+	0.0219122i
$585$	−46.0158			−0.0786594
$586$	21.5084	−	38.7947i	0.0367038	−	0.0662025i
$587$		−	489.163i		−	0.833327i	−0.909061	−	0.416664i	$-0.863199\pi$
$587$		−	489.163i		−	0.833327i	0.909061	−	0.416664i	$-0.136801\pi$
$588$	−378.495	+	236.423i	−0.643698	+	0.402080i
$589$	441.232			0.749120
$590$	36.0845	+	20.0058i	0.0611601	+	0.0339082i
$591$		−	298.894i		−	0.505743i
$592$	−242.634	+	497.059i	−0.409855	+	0.839627i
$593$	−389.243			−0.656396			−0.328198	−	0.944609i	$-0.606441\pi$
$593$	−389.243			−0.656396			−0.328198	+	0.944609i	$0.606441\pi$
$594$	−48.1445	+	86.8381i	−0.0810514	+	0.146192i
$595$			375.325i			0.630798i
$596$	−266.020	−	425.877i	−0.446342	−	0.714559i
$597$	102.945			0.172438
$598$	−231.838	−	128.535i	−0.387688	−	0.214941i
$599$		−	499.614i		−	0.834080i	−0.908888	−	0.417040i	$-0.863068\pi$
$599$		−	499.614i		−	0.834080i	0.908888	−	0.417040i	$-0.136932\pi$
$600$	4.98178	+	95.5088i	0.00830297	+	0.159181i
$601$	−134.397			−0.223622			−0.111811	−	0.993729i	$-0.535665\pi$
$601$	−134.397			−0.223622			−0.111811	+	0.993729i	$0.535665\pi$
$602$	−604.424	+	1090.20i	−1.00403	+	1.81096i
$603$			364.885i			0.605115i
$604$	−43.7004	+	27.2970i	−0.0723516	+	0.0451938i
$605$	−126.413			−0.208948
$606$	−367.706	−	203.862i	−0.606776	−	0.336406i
$607$		−	287.966i		−	0.474409i	−0.971460	−	0.237205i	$-0.923769\pi$
$607$		−	287.966i		−	0.474409i	0.971460	−	0.237205i	$-0.0762312\pi$
$608$	755.114	−	528.274i	1.24196	−	0.868872i
$609$	883.904			1.45140
$610$	−272.862	+	492.161i	−0.447315	+	0.806822i
$611$			92.4061i			0.151237i
$612$	52.6670	+	84.3156i	0.0860572	+	0.137771i
$613$	−382.457			−0.623910			−0.311955	−	0.950097i	$-0.600984\pi$
$613$	−382.457			−0.623910			−0.311955	+	0.950097i	$0.600984\pi$
$614$	882.885	+	489.486i	1.43792	+	0.797209i
$615$			322.425i			0.524268i
$616$	812.888	−	42.4006i	1.31962	−	0.0688322i
$617$	−781.910			−1.26728			−0.633639	−	0.773629i	$-0.718439\pi$
$617$	−781.910			−1.26728			−0.633639	+	0.773629i	$0.718439\pi$
$618$	−106.360	+	191.842i	−0.172104	+	0.310424i
$619$		−	966.724i		−	1.56175i	−0.624686	−	0.780876i	$-0.714773\pi$
$619$		−	966.724i		−	1.56175i	0.624686	−	0.780876i	$-0.285227\pi$
$620$	−221.122	+	138.122i	−0.356649	+	0.222777i
$621$	191.014			0.307591
$622$	583.062	+	323.259i	0.937398	+	0.519709i
$623$			173.193i			0.277999i
$624$	89.7931	+	43.8316i	0.143899	+	0.0702429i
$625$	−404.808			−0.647692
$626$	291.540	−	525.851i	0.465719	−	0.840017i
$627$		−	476.577i		−	0.760091i
$628$	−608.620	−	974.353i	−0.969141	−	1.55152i
$629$	286.391			0.455312
$630$	−237.737	−	131.805i	−0.377360	−	0.209214i
$631$		−	764.225i		−	1.21113i	−0.795795	−	0.605566i	$-0.792947\pi$
$631$		−	764.225i		−	1.21113i	0.795795	−	0.605566i	$-0.207053\pi$
$632$	13.1056	+	251.256i	0.0207368	+	0.397557i
$633$	−166.280			−0.262685
$634$	197.161	−	355.619i	0.310979	−	0.560913i
$635$		−	39.2694i		−	0.0618415i
$636$	233.319	−	145.740i	0.366853	−	0.229152i
$637$	232.245			0.364591
$638$	−800.832	−	443.994i	−1.25522	−	0.695916i
$639$			52.5393i			0.0822212i
$640$	−213.054	+	501.122i	−0.332897	+	0.783004i
$641$	878.937			1.37120			0.685598	−	0.727980i	$-0.259541\pi$
$641$	878.937			1.37120			0.685598	+	0.727980i	$0.259541\pi$
$642$	185.772	−	335.076i	0.289364	−	0.521926i
$643$		−	117.370i		−	0.182536i	−0.995826	−	0.0912678i	$-0.970908\pi$
$643$		−	117.370i		−	0.182536i	0.995826	−	0.0912678i	$-0.0290919\pi$
$644$	−829.602	−	1328.13i	−1.28820	−	2.06231i
$645$	−431.240			−0.668589
$646$	−417.315	−	231.367i	−0.645999	−	0.358153i
$647$			792.444i			1.22480i	0.790549	+	0.612399i	$0.209795\pi$
$647$			792.444i			1.22480i	−0.790549	+	0.612399i	$0.790205\pi$
$648$	−71.9023	+	3.75046i	−0.110960	+	0.00578774i
$649$	−46.3315			−0.0713891
$650$	24.1335	−	43.5295i	0.0371284	−	0.0669685i
$651$			282.609i			0.434115i
$652$	316.499	−	197.698i	0.485427	−	0.303218i
$653$	835.261			1.27911			0.639556	−	0.768744i	$-0.279118\pi$
$653$	835.261			1.27911			0.639556	+	0.768744i	$0.279118\pi$
$654$	−120.330	−	66.7130i	−0.183991	−	0.102008i
$655$		−	388.188i		−	0.592654i
$656$	307.120	−	629.165i	0.468171	−	0.959093i
$657$	−92.1251			−0.140221
$658$	−264.683	+	477.408i	−0.402254	+	0.725545i
$659$			969.370i			1.47097i	0.677540	+	0.735486i	$0.263046\pi$
$659$			969.370i			1.47097i	−0.677540	+	0.735486i	$0.736954\pi$
$660$	149.186	+	238.835i	0.226040	+	0.361872i
$661$	−282.283			−0.427054			−0.213527	−	0.976937i	$-0.568495\pi$
$661$	−282.283			−0.427054			−0.213527	+	0.976937i	$0.568495\pi$
$662$	427.481	+	237.003i	0.645742	+	0.358010i
$663$		−	51.7362i		−	0.0780334i
$664$	−48.4657	−	929.164i	−0.0729904	−	1.39934i
$665$	1304.72			1.96199
$666$	−100.574	+	181.405i	−0.151012	+	0.272379i
$667$			1761.55i			2.64101i
$668$	−245.992	+	153.657i	−0.368251	+	0.230025i
$669$	−467.826			−0.699291
$670$	905.060	+	501.780i	1.35084	+	0.748926i
$671$		−	631.922i		−	0.941761i
$672$	338.360	+	483.651i	0.503511	+	0.719718i
$673$	464.656			0.690425			0.345213	−	0.938524i	$-0.387807\pi$
$673$	464.656			0.690425			0.345213	+	0.938524i	$0.387807\pi$
$674$	313.140	−	564.810i	0.464599	−	0.837997i
$675$			35.8645i			0.0531326i
$676$	−27.5486	−	44.1030i	−0.0407523	−	0.0652412i
$677$	3.70553			0.00547345			0.00273673	−	0.999996i	$-0.499129\pi$
$677$	3.70553			0.00547345			0.00273673	+	0.999996i	$0.499129\pi$
$678$	−331.355	−	183.709i	−0.488724	−	0.270957i
$679$			1236.82i			1.82153i
$680$	281.563	−	14.6865i	0.414063	−	0.0215977i
$681$	−98.5199			−0.144670
$682$	141.958	−	256.049i	0.208149	−	0.375438i
$683$			763.896i			1.11844i	0.829019	+	0.559221i	$0.188900\pi$
$683$			763.896i			1.11844i	−0.829019	+	0.559221i	$0.811100\pi$
$684$	293.102	−	183.084i	0.428512	−	0.267666i
$685$	−457.271			−0.667549
$686$	287.111	+	159.179i	0.418530	+	0.232040i
$687$			399.146i			0.580999i
$688$	841.502	+	410.770i	1.22311	+	0.597050i
$689$	−143.165			−0.207786
$690$	262.678	−	473.791i	0.380692	−	0.686654i
$691$		−	317.013i		−	0.458774i	−0.973335	−	0.229387i	$-0.926328\pi$
$691$		−	317.013i		−	0.458774i	0.973335	−	0.229387i	$-0.0736722\pi$
$692$	−445.823	−	713.727i	−0.644253	−	1.03140i
$693$	305.247			0.440473
$694$	35.3197	+	19.5818i	0.0508930	+	0.0282159i
$695$		−	92.5539i		−	0.133171i
$696$	−34.5872	−	663.091i	−0.0496942	−	0.952717i
$697$	−362.507			−0.520096
$698$	−660.477	+	1191.30i	−0.946242	+	1.70674i
$699$			202.052i			0.289059i
$700$	249.367	−	155.765i	0.356239	−	0.222521i
$701$	93.2472			0.133020			0.0665102	−	0.997786i	$-0.478814\pi$
$701$	93.2472			0.133020			0.0665102	+	0.997786i	$0.478814\pi$
$702$	32.7705	+	18.1685i	0.0466816	+	0.0258811i
$703$		−	995.568i		−	1.41617i
$704$	−63.6166	−	608.157i	−0.0903645	−	0.863860i
$705$	−188.844			−0.267864
$706$	−270.864	+	488.556i	−0.383660	+	0.692006i
$707$			1292.53i			1.82820i
$708$	−17.7989	−	28.4946i	−0.0251397	−	0.0402466i
$709$	−122.566			−0.172872			−0.0864358	−	0.996257i	$-0.527548\pi$
$709$	−122.566			−0.172872			−0.0864358	+	0.996257i	$0.527548\pi$
$710$	130.319	+	72.2508i	0.183547	+	0.101762i
$711$			94.3492i			0.132699i
$712$	129.927	−	6.77705i	0.182482	−	0.00951834i
$713$	−563.218			−0.789927
$714$	148.190	−	267.290i	0.207549	−	0.374356i
$715$		−	146.550i		−	0.204964i
$716$	497.152	−	310.542i	0.694347	−	0.433717i
$717$	−176.875			−0.246687
$718$	1046.15	+	580.004i	1.45704	+	0.807805i
$719$			48.0241i			0.0667929i	0.999442	+	0.0333965i	$0.0106324\pi$
$719$			48.0241i			0.0667929i	−0.999442	+	0.0333965i	$0.989368\pi$
$720$	−89.5756	+	183.504i	−0.124411	+	0.254867i
$721$	674.349			0.935297
$722$	−454.204	+	819.247i	−0.629092	+	1.13469i
$723$			131.733i			0.182203i
$724$	709.727	+	1136.22i	0.980286	+	1.56936i
$725$	−330.747			−0.456202
$726$	90.0262	+	49.9120i	0.124003	+	0.0687493i
$727$		−	787.414i		−	1.08310i	−0.840668	−	0.541550i	$-0.817838\pi$
$727$		−	787.414i		−	1.08310i	0.840668	−	0.541550i	$-0.182162\pi$
$728$	−16.0009	−	306.763i	−0.0219793	−	0.421378i
$729$	−27.0000			−0.0370370
$730$	−126.688	+	228.507i	−0.173545	+	0.313024i
$731$		−	484.849i		−	0.663268i
$732$	388.642	−	242.762i	0.530932	−	0.331642i
$733$	548.216			0.747908			0.373954	−	0.927447i	$-0.378002\pi$
$733$	548.216			0.747908			0.373954	+	0.927447i	$0.378002\pi$
$734$	846.138	+	469.113i	1.15278	+	0.639118i
$735$			474.623i			0.645745i
$736$	−963.879	+	674.325i	−1.30962	+	0.916202i
$737$	−1162.07			−1.57676
$738$	127.304	−	229.617i	0.172498	−	0.311135i
$739$			698.895i			0.945731i	0.881135	+	0.472865i	$0.156780\pi$
$739$			698.895i			0.945731i	−0.881135	+	0.472865i	$0.843220\pi$
$740$	311.650	+	498.926i	0.421148	+	0.674225i
$741$	−179.848			−0.242710
$742$	−739.648	−	410.073i	−0.996830	−	0.552659i
$743$			406.805i			0.547516i	0.961799	+	0.273758i	$0.0882668\pi$
$743$			406.805i			0.547516i	−0.961799	+	0.273758i	$0.911733\pi$
$744$	212.009	−	11.0585i	0.284958	−	0.0148636i
$745$	−534.039			−0.716831
$746$	243.098	−	438.475i	0.325868	−	0.587768i
$747$		−	348.910i		−	0.467082i
$748$	−268.526	+	167.732i	−0.358992	+	0.224241i
$749$	−1177.84			−1.57255
$750$	411.172	+	227.961i	0.548229	+	0.303947i
$751$		−	1267.39i		−	1.68760i	−0.536658	−	0.843800i	$-0.680314\pi$
$751$		−	1267.39i		−	1.68760i	0.536658	−	0.843800i	$-0.319686\pi$
$752$	368.502	+	179.880i	0.490029	+	0.239203i
$753$	834.210			1.10785
$754$	−167.552	+	302.214i	−0.222218	+	0.400814i
$755$			54.7992i			0.0725817i
$756$	117.265	+	187.732i	0.155113	+	0.248323i
$757$	296.692			0.391932			0.195966	−	0.980611i	$-0.437216\pi$
$757$	296.692			0.391932			0.195966	+	0.980611i	$0.437216\pi$
$758$	697.071	+	386.468i	0.919618	+	0.509852i
$759$			608.335i			0.801495i
$760$	−51.0538	−	978.784i	−0.0671761	−	1.28787i
$761$	−78.7675			−0.103505			−0.0517527	−	0.998660i	$-0.516481\pi$
$761$	−78.7675			−0.103505			−0.0517527	+	0.998660i	$0.516481\pi$
$762$	−15.5048	+	27.9660i	−0.0203475	+	0.0367008i
$763$			422.976i			0.554359i
$764$	−803.591	+	501.956i	−1.05182	+	0.657010i
$765$	105.730			0.138209
$766$	−133.406	−	73.9624i	−0.174159	−	0.0965567i
$767$			17.4843i			0.0227957i
$768$	349.587	−	272.758i	0.455192	−	0.355153i
$769$	469.425			0.610435			0.305218	−	0.952283i	$-0.401271\pi$
$769$	469.425			0.610435			0.305218	+	0.952283i	$0.401271\pi$
$770$	419.769	−	757.136i	0.545154	−	0.983294i
$771$		−	390.607i		−	0.506624i
$772$	−754.108	−	1207.27i	−0.976824	−	1.56382i
$773$	649.941			0.840803			0.420402	−	0.907338i	$-0.361889\pi$
$773$	649.941			0.840803			0.420402	+	0.907338i	$0.361889\pi$
$774$	307.111	+	170.267i	0.396784	+	0.219984i
$775$		−	105.749i		−	0.136450i
$776$	927.845	−	48.3968i	1.19568	−	0.0623670i
$777$	637.661			0.820670
$778$	−611.781	+	1103.47i	−0.786350	+	1.41834i
$779$			1260.16i			1.61767i
$780$	90.1304	−	56.2991i	0.115552	−	0.0721783i
$781$	−167.326			−0.214245
$782$	532.690	+	295.332i	0.681189	+	0.377662i
$783$		−	248.997i		−	0.318004i
$784$	452.094	−	926.157i	0.576650	−	1.18132i
$785$	−1221.81			−1.55645
$786$	−153.269	+	276.451i	−0.194999	+	0.351719i
$787$		−	132.207i		−	0.167989i	−0.996466	−	0.0839943i	$-0.973232\pi$
$787$		−	132.207i		−	0.167989i	0.996466	−	0.0839943i	$-0.0267678\pi$
$788$	365.689	+	585.439i	0.464073	+	0.742943i
$789$	155.992			0.197709
$790$	234.024	+	129.747i	0.296233	+	0.164236i
$791$			1164.76i			1.47251i
$792$	−11.9443	−	228.992i	−0.0150812	−	0.289131i
$793$	−238.471			−0.300720
$794$	−242.507	+	437.409i	−0.305424	+	0.550893i
$795$		−	292.576i		−	0.368020i
$796$	−201.638	+	125.951i	−0.253314	+	0.158230i
$797$	−820.551			−1.02955			−0.514775	−	0.857325i	$-0.672125\pi$
$797$	−820.551			−1.02955			−0.514775	+	0.857325i	$0.672125\pi$
$798$	−929.169	−	515.147i	−1.16437	−	0.645547i
$799$		−	212.320i		−	0.265732i
$800$	−126.610	−	180.977i	−0.158263	−	0.226221i
$801$	48.7889			0.0609100
$802$	682.548	−	1231.11i	0.851058	−	1.53505i
$803$		−	293.397i		−	0.365376i
$804$	−446.427	−	714.694i	−0.555257	−	0.888923i
$805$	−1665.44			−2.06887
$806$	−96.6262	−	53.5711i	−0.119884	−	0.0664654i
$807$		−	464.949i		−	0.576145i
$808$	969.640	−	50.5769i	1.20005	−	0.0625952i
$809$	345.596			0.427189			0.213594	−	0.976922i	$-0.431483\pi$
$809$	345.596			0.427189			0.213594	+	0.976922i	$0.431483\pi$
$810$	−37.1297	+	66.9708i	−0.0458392	+	0.0826801i
$811$		−	470.701i		−	0.580396i	−0.956967	−	0.290198i	$-0.906279\pi$
$811$		−	470.701i		−	0.580396i	0.956967	−	0.290198i	$-0.0937211\pi$
$812$	−1731.29	+	1081.43i	−2.13213	+	1.33181i
$813$	−351.891			−0.432830
$814$	−577.732	−	320.304i	−0.709744	−	0.393494i
$815$		−	396.881i		−	0.486971i
$816$	−206.316	−	100.711i	−0.252838	−	0.123420i
$817$	−1685.46			−2.06298
$818$	101.570	−	183.202i	0.124169	−	0.223964i
$819$		−	115.193i		−	0.140650i
$820$	−394.478	−	631.529i	−0.481071	−	0.770157i
$821$	208.482			0.253936			0.126968	−	0.991907i	$-0.459475\pi$
$821$	208.482			0.253936			0.126968	+	0.991907i	$0.459475\pi$
$822$	325.649	+	180.545i	0.396167	+	0.219641i
$823$			1167.06i			1.41806i	0.705178	+	0.709030i	$0.250867\pi$
$823$			1167.06i			1.41806i	−0.705178	+	0.709030i	$0.749133\pi$
$824$	−26.3873	−	505.887i	−0.0320234	−	0.613940i
$825$	−114.220			−0.138449
$826$	−50.0812	+	90.3313i	−0.0606310	+	0.109360i
$827$		−	1113.26i		−	1.34614i	−0.739580	−	0.673069i	$-0.764976\pi$
$827$		−	1113.26i		−	1.34614i	0.739580	−	0.673069i	$-0.235024\pi$
$828$	−374.136	+	233.700i	−0.451855	+	0.282247i
$829$	−20.5813			−0.0248267			−0.0124133	−	0.999923i	$-0.503951\pi$
$829$	−20.5813			−0.0248267			−0.0124133	+	0.999923i	$0.503951\pi$
$830$	−865.438	−	479.813i	−1.04270	−	0.578088i
$831$			804.625i			0.968261i
$832$	−229.503	+	24.0073i	−0.275845	+	0.0288549i
$833$	−533.625			−0.640606
$834$	−36.5433	+	65.9130i	−0.0438169	+	0.0790324i
$835$			308.467i			0.369422i
$836$	583.079	+	933.464i	0.697463	+	1.11658i
$837$	79.6114			0.0951152
$838$	−0.316846	−	0.175664i	−0.000378097	−	0.000209623i
$839$			583.041i			0.694924i	0.937694	+	0.347462i	$0.112956\pi$
$839$			583.041i			0.694924i	−0.937694	+	0.347462i	$0.887044\pi$
$840$	626.911	−	32.7000i	0.746323	−	0.0389285i
$841$	1455.28			1.73042
$842$	−454.914	+	820.527i	−0.540278	+	0.974498i
$843$		−	185.552i		−	0.220110i
$844$	325.689	−	203.439i	0.385888	−	0.241041i
$845$	−55.3041			−0.0654486
$846$	134.487	+	74.5617i	0.158968	+	0.0881344i
$847$		−	316.454i		−	0.373617i
$848$	−278.688	+	570.919i	−0.328642	+	0.673253i
$849$	597.829			0.704157
$850$	−55.4511	+	100.017i	−0.0652366	+	0.117667i
$851$			1270.81i			1.49331i
$852$	−64.2805	−	102.908i	−0.0754466	−	0.120784i
$853$	−1576.65			−1.84836			−0.924178	−	0.381962i	$-0.875248\pi$
$853$	−1576.65			−1.84836			−0.924178	+	0.381962i	$0.875248\pi$
$854$	−1232.04	−	683.064i	−1.44267	−	0.799841i
$855$		−	367.543i		−	0.429875i
$856$	46.0888	+	883.596i	0.0538420	+	1.03224i
$857$	855.816			0.998619			0.499309	−	0.866424i	$-0.333587\pi$
$857$	855.816			0.998619			0.499309	+	0.866424i	$0.333587\pi$
$858$	−57.8625	+	104.366i	−0.0674388	+	0.121639i
$859$		−	685.158i		−	0.797623i	−0.917033	−	0.398811i	$-0.869423\pi$
$859$		−	685.158i		−	0.797623i	0.917033	−	0.398811i	$-0.130577\pi$
$860$	844.663	−	527.611i	0.982166	−	0.613501i
$861$	−807.135			−0.937439
$862$	−511.657	−	283.671i	−0.593569	−	0.329085i
$863$		−	885.288i		−	1.02583i	−0.858441	−	0.512913i	$-0.828566\pi$
$863$		−	885.288i		−	1.02583i	0.858441	−	0.512913i	$-0.171434\pi$
$864$	136.245	−	95.3165i	0.157691	−	0.110320i
$865$	−894.996			−1.03468
$866$	701.934	−	1266.08i	0.810547	−	1.46198i
$867$		−	381.689i		−	0.440242i
$868$	−345.765	−	553.542i	−0.398346	−	0.637721i
$869$	−300.480			−0.345777
$870$	−617.613	−	342.415i	−0.709900	−	0.393580i
$871$			438.537i			0.503486i
$872$	317.310	−	16.5511i	0.363888	−	0.0189806i
$873$	348.415			0.399101
$874$	1026.65	−	1851.76i	1.17465	−	2.11872i
$875$		−	1445.32i		−	1.65180i
$876$	180.444	−	112.713i	0.205986	−	0.128667i
$877$	−63.1374			−0.0719925			−0.0359962	−	0.999352i	$-0.511460\pi$
$877$	−63.1374			−0.0719925			−0.0359962	+	0.999352i	$0.511460\pi$
$878$	1288.04	+	714.110i	1.46701	+	0.813337i
$879$			38.4152i			0.0437033i
$880$	−584.418	−	285.278i	−0.664111	−	0.324179i
$881$	−116.778			−0.132551			−0.0662757	−	0.997801i	$-0.521112\pi$
$881$	−116.778			−0.132551			−0.0662757	+	0.997801i	$0.521112\pi$
$882$	187.396	−	338.006i	0.212467	−	0.383227i
$883$		−	443.524i		−	0.502292i	−0.967949	−	0.251146i	$-0.919193\pi$
$883$		−	443.524i		−	0.502292i	0.967949	−	0.251146i	$-0.0808074\pi$
$884$	63.2978	+	101.335i	0.0716039	+	0.114632i
$885$	−35.7315			−0.0403746
$886$	−554.322	−	307.325i	−0.625645	−	0.346868i
$887$		−	663.133i		−	0.747614i	−0.927507	−	0.373807i	$-0.878052\pi$
$887$		−	663.133i		−	0.747614i	0.927507	−	0.373807i	$-0.121948\pi$
$888$	−24.9517	−	478.364i	−0.0280987	−	0.538698i
$889$	98.3041			0.110578
$890$	67.0933	−	121.016i	0.0753857	−	0.135973i
$891$		−	85.9888i		−	0.0965082i
$892$	916.323	−	572.373i	1.02727	−	0.641674i
$893$	−738.078			−0.826515
$894$	380.320	+	210.856i	0.425414	+	0.235856i
$895$		−	623.416i		−	0.696554i
$896$	−1254.47	−	533.345i	−1.40008	−	0.595251i
$897$	229.570			0.255931
$898$	−157.419	+	283.937i	−0.175300	+	0.316188i
$899$			734.186i			0.816670i
$900$	−43.8793	−	70.2472i	−0.0487547	−	0.0780525i
$901$	328.947			0.365091
$902$	731.278	+	405.433i	0.810730	+	0.449482i
$903$		−	1079.54i		−	1.19550i
$904$	873.783	−	45.5769i	0.966574	−	0.0504170i
$905$	1424.79			1.57435
$906$	21.6365	−	39.0257i	0.0238813	−	0.0430747i
$907$			453.429i			0.499921i	0.968256	+	0.249961i	$0.0804177\pi$
$907$			453.429i			0.499921i	−0.968256	+	0.249961i	$0.919582\pi$
$908$	192.969	−	120.537i	0.212521	−	0.132750i
$909$	364.109			0.400560
$910$	−285.724	−	158.410i	−0.313982	−	0.174077i
$911$		−	1122.62i		−	1.23230i	−0.787630	−	0.616148i	$-0.788692\pi$
$911$		−	1122.62i		−	1.23230i	0.787630	−	0.616148i	$-0.211308\pi$
$912$	−350.097	+	717.207i	−0.383878	+	0.786411i
$913$	1111.20			1.21709
$914$	555.838	−	1002.56i	0.608138	−	1.09690i
$915$		−	487.347i		−	0.532620i
$916$	−488.345	−	781.802i	−0.533128	−	0.853495i
$917$	971.763			1.05972
$918$	−75.2962	−	41.7455i	−0.0820220	−	0.0454744i
$919$			145.892i			0.158750i	0.996845	+	0.0793752i	$0.0252925\pi$
$919$			145.892i			0.158750i	−0.996845	+	0.0793752i	$0.974707\pi$
$920$	65.1686	+	1249.39i	0.0708354	+	1.35803i
$921$	−874.249			−0.949239
$922$	−124.568	+	224.684i	−0.135107	+	0.243692i
$923$			63.1444i			0.0684121i
$924$	−597.883	+	373.462i	−0.647060	+	0.404180i
$925$	−238.605			−0.257952
$926$	−841.090	−	466.314i	−0.908305	−	0.503579i
$927$		−	189.965i		−	0.204925i
$928$	879.020	+	1256.47i	0.947220	+	1.35395i
$929$	−1104.28			−1.18867			−0.594336	−	0.804217i	$-0.702585\pi$
$929$	−1104.28			−1.18867			−0.594336	+	0.804217i	$0.702585\pi$
$930$	109.480	−	197.468i	0.117720	−	0.212332i
$931$			1855.01i			1.99250i
$932$	−247.206	−	395.757i	−0.265242	−	0.424632i
$933$	−577.359			−0.618820
$934$	1459.28	+	809.051i	1.56240	+	0.866221i
$935$			336.725i			0.360133i
$936$	−86.4158	+	4.50749i	−0.0923245	+	0.00481569i
$937$	327.741			0.349777			0.174888	−	0.984588i	$-0.444044\pi$
$937$	327.741			0.349777			0.174888	+	0.984588i	$0.444044\pi$
$938$	−1256.12	+	2265.66i	−1.33915	+	2.41542i
$939$			520.707i			0.554534i
$940$	369.886	−	231.046i	0.393496	−	0.245793i
$941$	−719.373			−0.764477			−0.382239	−	0.924064i	$-0.624847\pi$
$941$	−719.373			−0.764477			−0.382239	+	0.924064i	$0.624847\pi$
$942$	870.124	+	482.411i	0.923699	+	0.512114i
$943$		−	1608.56i		−	1.70579i
$944$	69.7249	+	34.0355i	0.0738611	+	0.0360545i
$945$	235.411			0.249112
$946$	−542.262	+	978.077i	−0.573216	+	1.03391i
$947$		−	446.453i		−	0.471439i	−0.971821	−	0.235719i	$-0.924255\pi$
$947$		−	446.453i		−	0.471439i	0.971821	−	0.235719i	$-0.0757446\pi$
$948$	−115.434	−	184.800i	−0.121766	−	0.194937i
$949$	−110.721			−0.116671
$950$	347.685	+	192.762i	0.365984	+	0.202907i
$951$			352.140i			0.370284i
$952$	36.7650	+	704.845i	0.0386187	+	0.740383i
$953$	−448.767			−0.470899			−0.235449	−	0.971887i	$-0.575656\pi$
$953$	−448.767			−0.470899			−0.235449	+	0.971887i	$0.575656\pi$
$954$	−115.518	+	208.360i	−0.121088	+	0.218407i
$955$			1007.68i			1.05517i
$956$	346.441	−	216.401i	0.362386	−	0.226361i
$957$	792.999			0.828630
$958$	−840.221	−	465.832i	−0.877057	−	0.486255i
$959$		−	1144.70i		−	1.19364i
$960$	−49.0621	−	469.020i	−0.0511063	−	0.488562i
$961$	726.260			0.755734
$962$	−120.875	+	218.021i	−0.125649	+	0.226633i
$963$			331.799i			0.344547i
$964$	−161.172	−	258.023i	−0.167191	−	0.267659i
$965$	−1513.88			−1.56879
$966$	1186.05	+	657.568i	1.22780	+	0.680712i
$967$			28.9481i			0.0299360i	0.999888	+	0.0149680i	$0.00476464\pi$
$967$			28.9481i			0.0299360i	−0.999888	+	0.0149680i	$0.995235\pi$
$968$	−237.399	+	12.3828i	−0.245247	+	0.0127922i
$969$	413.234			0.426454
$970$	479.132	−	864.209i	0.493950	−	0.890937i
$971$			1340.19i			1.38022i	0.723707	+	0.690108i	$0.242437\pi$
$971$			1340.19i			1.38022i	−0.723707	+	0.690108i	$0.757563\pi$
$972$	52.8845	−	33.0338i	0.0544079	−	0.0339854i
$973$	231.693			0.238122
$974$	−616.147	−	341.602i	−0.632595	−	0.350721i
$975$			43.1038i			0.0442090i
$976$	−464.215	+	950.987i	−0.475630	+	0.974372i
$977$	−1707.49			−1.74769			−0.873845	−	0.486205i	$-0.838381\pi$
$977$	−1707.49			−1.74769			−0.873845	+	0.486205i	$0.838381\pi$
$978$	−156.701	+	282.642i	−0.160226	+	0.289000i
$979$			155.381i			0.158714i
$980$	−580.689	−	929.636i	−0.592539	−	0.948608i
$981$	119.153			0.121461
$982$	252.498	+	139.989i	0.257127	+	0.142555i
$983$			1299.24i			1.32171i	0.750513	+	0.660856i	$0.229806\pi$
$983$			1299.24i			1.32171i	−0.750513	+	0.660856i	$0.770194\pi$
$984$	31.5832	+	605.501i	0.0320968	+	0.615346i
$985$	734.126			0.745306
$986$	384.982	−	694.391i	0.390448	−	0.704250i
$987$		−	472.739i		−	0.478965i
$988$	352.265	−	220.039i	0.356544	−	0.222712i
$989$	2151.43			2.17536
$990$	−213.287	−	118.250i	−0.215441	−	0.119444i
$991$			1126.00i			1.13623i	0.822950	+	0.568114i	$0.192327\pi$
$991$			1126.00i			1.13623i	−0.822950	+	0.568114i	$0.807673\pi$
$992$	−401.729	+	281.048i	−0.404969	+	0.283314i
$993$	−423.300			−0.426284
$994$	−180.867	+	326.230i	−0.181959	+	0.328200i
$995$			252.848i			0.254119i
$996$	426.883	+	683.405i	0.428597	+	0.686150i
$997$	1425.50			1.42978			0.714892	−	0.699234i	$-0.246476\pi$
$997$	1425.50			1.42978			0.714892	+	0.699234i	$0.246476\pi$
$998$	−919.071	−	509.548i	−0.920913	−	0.510569i
$999$		−	179.630i		−	0.179810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.f.a.79.15	✓	24
3.2	odd	2		468.3.f.b.235.10		24
4.3	odd	2	inner	156.3.f.a.79.16	yes	24
8.3	odd	2		2496.3.k.e.703.4		24
8.5	even	2		2496.3.k.e.703.3		24
12.11	even	2		468.3.f.b.235.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.f.a.79.15	✓	24	1.1	even	1	trivial
156.3.f.a.79.16	yes	24	4.3	odd	2	inner
468.3.f.b.235.9		24	12.11	even	2
468.3.f.b.235.10		24	3.2	odd	2
2496.3.k.e.703.3		24	8.5	even	2
2496.3.k.e.703.4		24	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.969763 - 1.74916i) q^{2} +1.73205i q^{3} +(-2.11912 - 3.39254i) q^{4} -4.25416 q^{5} +(3.02963 + 1.67968i) q^{6} -10.6496i q^{7} +(-7.98914 + 0.416717i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(0.969763 - 1.74916i) q^{2} +1.73205i q^{3} +(-2.11912 - 3.39254i) q^{4} -4.25416 q^{5} +(3.02963 + 1.67968i) q^{6} -10.6496i q^{7} +(-7.98914 + 0.416717i) q^{8} -3.00000 q^{9} +(-4.12553 + 7.44120i) q^{10} -9.55431i q^{11} +(5.87605 - 3.67042i) q^{12} -3.60555 q^{13} +(-18.6278 - 10.3275i) q^{14} -7.36842i q^{15} +(-7.01867 + 14.3784i) q^{16} +8.28441 q^{17} +(-2.90929 + 5.24748i) q^{18} -28.7987i q^{19} +(9.01507 + 14.4324i) q^{20} +18.4456 q^{21} +(-16.7120 - 9.26541i) q^{22} +36.7606i q^{23} +(-0.721775 - 13.8376i) q^{24} -6.90212 q^{25} +(-3.49653 + 6.30668i) q^{26} -5.19615i q^{27} +(-36.1291 + 22.5677i) q^{28} +47.9195 q^{29} +(-12.8885 - 7.14562i) q^{30} +15.3212i q^{31} +(18.3437 + 26.2204i) q^{32} +16.5485 q^{33} +(8.03392 - 14.4908i) q^{34} +45.3049i q^{35} +(6.35736 + 10.1776i) q^{36} +34.5699 q^{37} +(-50.3736 - 27.9279i) q^{38} -6.24500i q^{39} +(33.9871 - 1.77278i) q^{40} -43.7577 q^{41} +(17.8878 - 32.2643i) q^{42} -58.5254i q^{43} +(-32.4134 + 20.2467i) q^{44} +12.7625 q^{45} +(64.3002 + 35.6491i) q^{46} -25.6288i q^{47} +(-24.9041 - 12.1567i) q^{48} -64.4131 q^{49} +(-6.69342 + 12.0729i) q^{50} +14.3490i q^{51} +(7.64059 + 12.2320i) q^{52} +39.7067 q^{53} +(-9.08890 - 5.03904i) q^{54} +40.6456i q^{55} +(4.43785 + 85.0808i) q^{56} +49.8808 q^{57} +(46.4706 - 83.8189i) q^{58} -4.84928i q^{59} +(-24.9977 + 15.6146i) q^{60} +66.1400 q^{61} +(26.7993 + 14.8580i) q^{62} +31.9487i q^{63} +(63.6527 - 6.65842i) q^{64} +15.3386 q^{65} +(16.0482 - 28.9460i) q^{66} -121.628i q^{67} +(-17.5557 - 28.1052i) q^{68} -63.6713 q^{69} +(79.2455 + 43.9350i) q^{70} -17.5131i q^{71} +(23.9674 - 1.25015i) q^{72} +30.7084 q^{73} +(33.5246 - 60.4682i) q^{74} -11.9548i q^{75} +(-97.7008 + 61.0279i) q^{76} -101.749 q^{77} +(-10.9235 - 6.05617i) q^{78} -31.4497i q^{79} +(29.8585 - 61.1680i) q^{80} +9.00000 q^{81} +(-42.4346 + 76.5391i) q^{82} +116.303i q^{83} +(-39.0884 - 62.5774i) q^{84} -35.2432 q^{85} +(-102.370 - 56.7558i) q^{86} +82.9991i q^{87} +(3.98144 + 76.3307i) q^{88} -16.2630 q^{89} +(12.3766 - 22.3236i) q^{90} +38.3975i q^{91} +(124.712 - 77.9001i) q^{92} -26.5371 q^{93} +(-44.8289 - 24.8539i) q^{94} +122.514i q^{95} +(-45.4151 + 31.7722i) q^{96} -116.138 q^{97} +(-62.4654 + 112.669i) q^{98} +28.6629i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9	\( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9 - 12 * q^10 + 12 * q^12 + 32 * q^14 + 4 * q^16 - 12 * q^18 + 84 * q^20 + 28 * q^22 - 36 * q^24 + 104 * q^25 - 96 * q^28 + 64 * q^29 - 12 * q^30 + 44 * q^32 + 48 * q^33 + 40 * q^34 - 24 * q^36 - 192 * q^37 - 104 * q^38 + 220 * q^40 - 220 * q^44 - 104 * q^46 - 144 * q^48 - 248 * q^49 + 100 * q^50 - 52 * q^52 + 336 * q^53 + 36 * q^54 + 168 * q^56 - 16 * q^58 + 60 * q^60 + 16 * q^61 + 152 * q^62 - 16 * q^64 - 132 * q^66 + 400 * q^68 - 192 * q^69 + 208 * q^70 + 96 * q^72 + 112 * q^73 - 104 * q^74 - 264 * q^76 - 272 * q^77 - 300 * q^80 + 216 * q^81 - 4 * q^82 + 96 * q^84 + 64 * q^85 + 288 * q^86 - 492 * q^88 + 36 * q^90 + 328 * q^92 - 96 * q^93 - 884 * q^94 + 72 * q^96 - 80 * q^97 - 572 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more