LMFDB - Embedded newform 555.2.g.a.184.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(184,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("555.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.g (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:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			184.2
Character	$\chi$	$=$	555.184
Dual form			555.2.g.a.184.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71549 q^{2} +1.00000i q^{3} +5.37390 q^{4} +(0.734693 + 2.11192i) q^{5} -2.71549i q^{6} -1.35808i q^{7} -9.16180 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.71549 q^{2} +1.00000i q^{3} +5.37390 q^{4} +(0.734693 + 2.11192i) q^{5} -2.71549i q^{6} -1.35808i q^{7} -9.16180 q^{8} -1.00000 q^{9} +(-1.99505 - 5.73492i) q^{10} +2.97912 q^{11} +5.37390i q^{12} +5.29371 q^{13} +3.68784i q^{14} +(-2.11192 + 0.734693i) q^{15} +14.1310 q^{16} +5.19397 q^{17} +2.71549 q^{18} -8.16246i q^{19} +(3.94816 + 11.3493i) q^{20} +1.35808 q^{21} -8.08977 q^{22} -2.36681 q^{23} -9.16180i q^{24} +(-3.92045 + 3.10323i) q^{25} -14.3750 q^{26} -1.00000i q^{27} -7.29816i q^{28} -8.38167i q^{29} +(5.73492 - 1.99505i) q^{30} +6.98231i q^{31} -20.0490 q^{32} +2.97912i q^{33} -14.1042 q^{34} +(2.86815 - 0.997769i) q^{35} -5.37390 q^{36} +(5.71477 - 2.08360i) q^{37} +22.1651i q^{38} +5.29371i q^{39} +(-6.73111 - 19.3490i) q^{40} +0.765086 q^{41} -3.68784 q^{42} -2.65872 q^{43} +16.0095 q^{44} +(-0.734693 - 2.11192i) q^{45} +6.42707 q^{46} +2.48237i q^{47} +14.1310i q^{48} +5.15563 q^{49} +(10.6460 - 8.42680i) q^{50} +5.19397i q^{51} +28.4479 q^{52} -3.57466i q^{53} +2.71549i q^{54} +(2.18874 + 6.29167i) q^{55} +12.4424i q^{56} +8.16246 q^{57} +22.7604i q^{58} -0.162508i q^{59} +(-11.3493 + 3.94816i) q^{60} +11.2982i q^{61} -18.9604i q^{62} +1.35808i q^{63} +26.1809 q^{64} +(3.88925 + 11.1799i) q^{65} -8.08977i q^{66} -2.92828i q^{67} +27.9119 q^{68} -2.36681i q^{69} +(-7.78845 + 2.70943i) q^{70} -7.77585 q^{71} +9.16180 q^{72} +1.81844i q^{73} +(-15.5184 + 5.65800i) q^{74} +(-3.10323 - 3.92045i) q^{75} -43.8643i q^{76} -4.04587i q^{77} -14.3750i q^{78} +10.6681i q^{79} +(10.3819 + 29.8436i) q^{80} +1.00000 q^{81} -2.07758 q^{82} +6.27919i q^{83} +7.29816 q^{84} +(3.81597 + 10.9693i) q^{85} +7.21972 q^{86} +8.38167 q^{87} -27.2941 q^{88} +7.15474i q^{89} +(1.99505 + 5.73492i) q^{90} -7.18926i q^{91} -12.7190 q^{92} -6.98231 q^{93} -6.74086i q^{94} +(17.2385 - 5.99690i) q^{95} -20.0490i q^{96} -9.38896 q^{97} -14.0001 q^{98} -2.97912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) $ 40 * q + 44 * q^4 - 40 * q^9	$ 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) $ 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−2.71549			−1.92014			−0.960072	−	0.279755i	$-0.909747\pi$
$2$	−2.71549			−1.92014			−0.960072	+	0.279755i	$0.909747\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	5.37390			2.68695
$5$	0.734693	+	2.11192i	0.328565	+	0.944482i
$5$	0.734693	+	2.11192i	0.328565	+	0.944482i
$6$		−	2.71549i		−	1.10860i
$7$		−	1.35808i		−	0.513304i	−0.966504	−	0.256652i	$-0.917381\pi$
$7$		−	1.35808i		−	0.513304i	0.966504	−	0.256652i	$-0.0826195\pi$
$8$	−9.16180			−3.23918
$9$	−1.00000			−0.333333
$10$	−1.99505	−	5.73492i	−0.630891	−	1.81354i
$11$	2.97912			0.898238			0.449119	−	0.893472i	$-0.351738\pi$
$11$	2.97912			0.898238			0.449119	+	0.893472i	$0.351738\pi$
$12$			5.37390i			1.55131i
$13$	5.29371			1.46821			0.734106	−	0.679035i	$-0.237602\pi$
$13$	5.29371			1.46821			0.734106	+	0.679035i	$0.237602\pi$
$14$			3.68784i			0.985618i
$15$	−2.11192	+	0.734693i	−0.545297	+	0.189697i
$16$	14.1310			3.53275
$17$	5.19397			1.25972			0.629861	−	0.776708i	$-0.283112\pi$
$17$	5.19397			1.25972			0.629861	+	0.776708i	$0.283112\pi$
$18$	2.71549			0.640048
$19$		−	8.16246i		−	1.87260i	−0.351204	−	0.936299i	$-0.614228\pi$
$19$		−	8.16246i		−	1.87260i	0.351204	−	0.936299i	$-0.385772\pi$
$20$	3.94816	+	11.3493i	0.882836	+	2.53777i
$21$	1.35808			0.296356
$22$	−8.08977			−1.72475
$23$	−2.36681			−0.493515			−0.246757	−	0.969077i	$-0.579365\pi$
$23$	−2.36681			−0.493515			−0.246757	+	0.969077i	$0.579365\pi$
$24$		−	9.16180i		−	1.87014i
$25$	−3.92045	+	3.10323i	−0.784091	+	0.620646i
$26$	−14.3750			−2.81918
$27$		−	1.00000i		−	0.192450i
$28$		−	7.29816i		−	1.37922i
$29$		−	8.38167i		−	1.55644i	−0.627993	−	0.778219i	$-0.716123\pi$
$29$		−	8.38167i		−	1.55644i	0.627993	−	0.778219i	$-0.283877\pi$
$30$	5.73492	−	1.99505i	1.04705	−	0.364245i
$31$			6.98231i			1.25406i	0.778995	+	0.627030i	$0.215730\pi$
$31$			6.98231i			1.25406i	−0.778995	+	0.627030i	$0.784270\pi$
$32$	−20.0490			−3.54420
$33$			2.97912i			0.518598i
$34$	−14.1042			−2.41885
$35$	2.86815	−	0.997769i	0.484807	−	0.168654i
$36$	−5.37390			−0.895650
$37$	5.71477	−	2.08360i	0.939503	−	0.342542i
$37$	5.71477	−	2.08360i	0.939503	−	0.342542i
$38$			22.1651i			3.59566i
$39$			5.29371i			0.847672i
$40$	−6.73111	−	19.3490i	−1.06428	−	3.05935i
$41$	0.765086			0.119486			0.0597432	−	0.998214i	$-0.480972\pi$
$41$	0.765086			0.119486			0.0597432	+	0.998214i	$0.480972\pi$
$42$	−3.68784			−0.569047
$43$	−2.65872			−0.405450			−0.202725	−	0.979236i	$-0.564980\pi$
$43$	−2.65872			−0.405450			−0.202725	+	0.979236i	$0.564980\pi$
$44$	16.0095			2.41352
$45$	−0.734693	−	2.11192i	−0.109522	−	0.314827i
$46$	6.42707			0.947619
$47$			2.48237i			0.362091i	0.983475	+	0.181046i	$0.0579482\pi$
$47$			2.48237i			0.362091i	−0.983475	+	0.181046i	$0.942052\pi$
$48$			14.1310i			2.03963i
$49$	5.15563			0.736519
$50$	10.6460	−	8.42680i	1.50557	−	1.19173i
$51$			5.19397i			0.727301i
$52$	28.4479			3.94501
$53$		−	3.57466i		−	0.491017i	−0.969394	−	0.245509i	$-0.921045\pi$
$53$		−	3.57466i		−	0.491017i	0.969394	−	0.245509i	$-0.0789549\pi$
$54$			2.71549i			0.369532i
$55$	2.18874	+	6.29167i	0.295129	+	0.848369i
$56$			12.4424i			1.66269i
$57$	8.16246			1.08114
$58$			22.7604i			2.98858i
$59$		−	0.162508i		−	0.0211568i	−0.999944	−	0.0105784i	$-0.996633\pi$
$59$		−	0.162508i		−	0.0211568i	0.999944	−	0.0105784i	$-0.00336727\pi$
$60$	−11.3493	+	3.94816i	−1.46518	+	0.509706i
$61$			11.2982i			1.44659i	0.690540	+	0.723294i	$0.257373\pi$
$61$			11.2982i			1.44659i	−0.690540	+	0.723294i	$0.742627\pi$
$62$		−	18.9604i		−	2.40797i
$63$			1.35808i			0.171101i
$64$	26.1809			3.27262
$65$	3.88925	+	11.1799i	0.482402	+	1.38670i
$66$		−	8.08977i		−	0.995782i
$67$		−	2.92828i		−	0.357747i	−0.983872	−	0.178873i	$-0.942755\pi$
$67$		−	2.92828i		−	0.357747i	0.983872	−	0.178873i	$-0.0572453\pi$
$68$	27.9119			3.38481
$69$		−	2.36681i		−	0.284931i
$70$	−7.78845	+	2.70943i	−0.930898	+	0.323839i
$71$	−7.77585			−0.922824			−0.461412	−	0.887186i	$-0.652657\pi$
$71$	−7.77585			−0.922824			−0.461412	+	0.887186i	$0.652657\pi$
$72$	9.16180			1.07973
$73$			1.81844i			0.212832i	0.994322	+	0.106416i	$0.0339375\pi$
$73$			1.81844i			0.212832i	−0.994322	+	0.106416i	$0.966063\pi$
$74$	−15.5184	+	5.65800i	−1.80398	+	0.657729i
$75$	−3.10323	−	3.92045i	−0.358330	−	0.452695i
$76$		−	43.8643i		−	5.03158i
$77$		−	4.04587i		−	0.461070i
$78$		−	14.3750i		−	1.62765i
$79$			10.6681i			1.20026i	0.799904	+	0.600128i	$0.204884\pi$
$79$			10.6681i			1.20026i	−0.799904	+	0.600128i	$0.795116\pi$
$80$	10.3819	+	29.8436i	1.16074	+	3.33661i
$81$	1.00000			0.111111
$82$	−2.07758			−0.229431
$83$			6.27919i			0.689231i	0.938744	+	0.344615i	$0.111991\pi$
$83$			6.27919i			0.689231i	−0.938744	+	0.344615i	$0.888009\pi$
$84$	7.29816			0.796295
$85$	3.81597	+	10.9693i	0.413900	+	1.18978i
$86$	7.21972			0.778523
$87$	8.38167			0.898610
$88$	−27.2941			−2.90956
$89$			7.15474i			0.758401i	0.925314	+	0.379201i	$0.123801\pi$
$89$			7.15474i			0.758401i	−0.925314	+	0.379201i	$0.876199\pi$
$90$	1.99505	+	5.73492i	0.210297	+	0.604513i
$91$		−	7.18926i		−	0.753640i
$92$	−12.7190			−1.32605
$93$	−6.98231			−0.724032
$94$		−	6.74086i		−	0.695267i
$95$	17.2385	−	5.99690i	1.76863	−	0.615269i
$96$		−	20.0490i		−	2.04624i
$97$	−9.38896			−0.953304			−0.476652	−	0.879092i	$-0.658150\pi$
$97$	−9.38896			−0.953304			−0.476652	+	0.879092i	$0.658150\pi$
$98$	−14.0001			−1.41422
$99$	−2.97912			−0.299413
$100$	−21.0681	+	16.6765i	−2.10681	+	1.66765i
$101$	14.5422			1.44701			0.723503	−	0.690321i	$-0.242531\pi$
$101$	14.5422			1.44701			0.723503	+	0.690321i	$0.242531\pi$
$102$		−	14.1042i		−	1.39652i
$103$	4.71423			0.464507			0.232253	−	0.972655i	$-0.425390\pi$
$103$	4.71423			0.464507			0.232253	+	0.972655i	$0.425390\pi$
$104$	−48.4999			−4.75581
$105$	0.997769	+	2.86815i	0.0973722	+	0.279903i
$106$			9.70696i			0.942823i
$107$			3.63552i			0.351459i	0.984439	+	0.175729i	$0.0562284\pi$
$107$			3.63552i			0.351459i	−0.984439	+	0.175729i	$0.943772\pi$
$108$		−	5.37390i		−	0.517104i
$109$			8.22404i			0.787720i	0.919170	+	0.393860i	$0.128860\pi$
$109$			8.22404i			0.787720i	−0.919170	+	0.393860i	$0.871140\pi$
$110$	−5.94350	−	17.0850i	−0.566690	−	1.62899i
$111$	2.08360	+	5.71477i	0.197766	+	0.542422i
$112$		−	19.1910i		−	1.81337i
$113$	3.27536			0.308120			0.154060	−	0.988061i	$-0.450765\pi$
$113$	3.27536			0.308120			0.154060	+	0.988061i	$0.450765\pi$
$114$	−22.1651			−2.07595
$115$	−1.73888	−	4.99853i	−0.162152	−	0.466116i
$116$		−	45.0423i		−	4.18207i
$117$	−5.29371			−0.489404
$118$			0.441290i			0.0406240i
$119$		−	7.05381i		−	0.646621i
$120$	19.3490	−	6.73111i	1.76632	−	0.614463i
$121$	−2.12486			−0.193169
$122$		−	30.6802i		−	2.77766i
$123$			0.765086i			0.0689855i
$124$			37.5222i			3.36959i
$125$	−9.43412	−	5.99978i	−0.843813	−	0.536637i
$126$		−	3.68784i		−	0.328539i
$127$		−	7.69097i		−	0.682463i	−0.939979	−	0.341232i	$-0.889156\pi$
$127$		−	7.69097i		−	0.682463i	0.939979	−	0.341232i	$-0.110844\pi$
$128$	−30.9961			−2.73970
$129$		−	2.65872i		−	0.234087i
$130$	−10.5612	−	30.3590i	−0.926282	−	2.66266i
$131$		−	5.84994i		−	0.511111i	−0.966794	−	0.255556i	$-0.917742\pi$
$131$		−	5.84994i		−	0.511111i	0.966794	−	0.255556i	$-0.0822584\pi$
$132$			16.0095i			1.39345i
$133$	−11.0852			−0.961213
$134$			7.95173i			0.686925i
$135$	2.11192	−	0.734693i	0.181766	−	0.0632323i
$136$	−47.5861			−4.08047
$137$		−	11.5569i		−	0.987370i	−0.869641	−	0.493685i	$-0.835650\pi$
$137$		−	11.5569i		−	0.987370i	0.869641	−	0.493685i	$-0.164350\pi$
$138$			6.42707i			0.547108i
$139$	9.45387			0.801867			0.400933	−	0.916107i	$-0.368686\pi$
$139$	9.45387			0.801867			0.400933	+	0.916107i	$0.368686\pi$
$140$	15.4132	−	5.36191i	1.30265	−	0.453164i
$141$	−2.48237			−0.209053
$142$	21.1153			1.77195
$143$	15.7706			1.31880
$144$	−14.1310			−1.17758
$145$	17.7015	−	6.15796i	1.47003	−	0.511390i
$146$		−	4.93795i		−	0.408668i
$147$			5.15563i			0.425229i
$148$	30.7106	−	11.1970i	2.52440	−	0.920392i
$149$	−6.02914			−0.493927			−0.246963	−	0.969025i	$-0.579433\pi$
$149$	−6.02914			−0.493927			−0.246963	+	0.969025i	$0.579433\pi$
$150$	8.42680	+	10.6460i	0.688046	+	0.869239i
$151$	−16.6226			−1.35273			−0.676363	−	0.736568i	$-0.736445\pi$
$151$	−16.6226			−1.35273			−0.676363	+	0.736568i	$0.736445\pi$
$152$			74.7828i			6.06569i
$153$	−5.19397			−0.419908
$154$			10.9865i			0.885319i
$155$	−14.7461	+	5.12985i	−1.18444	+	0.412040i
$156$			28.4479i			2.27765i
$157$			11.5569i			0.922343i	0.887311	+	0.461171i	$0.152571\pi$
$157$			11.5569i			0.922343i	−0.887311	+	0.461171i	$0.847429\pi$
$158$		−	28.9692i		−	2.30466i
$159$	3.57466			0.283489
$160$	−14.7299	−	42.3420i	−1.16450	−	3.34743i
$161$			3.21431i			0.253323i
$162$	−2.71549			−0.213349
$163$	−2.82071			−0.220935			−0.110468	−	0.993880i	$-0.535235\pi$
$163$	−2.82071			−0.220935			−0.110468	+	0.993880i	$0.535235\pi$
$164$	4.11149			0.321054
$165$	−6.29167	+	2.18874i	−0.489806	+	0.170393i
$166$		−	17.0511i		−	1.32342i
$167$	−14.1477			−1.09478			−0.547390	−	0.836878i	$-0.684379\pi$
$167$	−14.1477			−1.09478			−0.547390	+	0.836878i	$0.684379\pi$
$168$	−12.4424			−0.959953
$169$	15.0234			1.15565
$170$	−10.3622	−	29.7870i	−0.794748	−	2.28456i
$171$			8.16246i			0.624199i
$172$	−14.2877			−1.08942
$173$			12.9160i			0.981989i	0.871163	+	0.490994i	$0.163366\pi$
$173$			12.9160i			0.981989i	−0.871163	+	0.490994i	$0.836634\pi$
$174$	−22.7604			−1.72546
$175$	4.21442	+	5.32427i	0.318581	+	0.402477i
$176$	42.0979			3.17325
$177$	0.162508			0.0122149
$178$		−	19.4286i		−	1.45624i
$179$		−	15.2614i		−	1.14069i	−0.821404	−	0.570346i	$-0.806809\pi$
$179$		−	15.2614i		−	1.14069i	0.821404	−	0.570346i	$-0.193191\pi$
$180$	−3.94816	−	11.3493i	−0.294279	−	0.845925i
$181$	−2.21198			−0.164415			−0.0822077	−	0.996615i	$-0.526197\pi$
$181$	−2.21198			−0.164415			−0.0822077	+	0.996615i	$0.526197\pi$
$182$			19.5224i			1.44710i
$183$	−11.2982			−0.835188
$184$	21.6843			1.59859
$185$	8.59901	+	10.5384i	0.632211	+	0.774796i
$186$	18.9604			1.39024
$187$	15.4735			1.13153
$188$			13.3400i			0.972921i
$189$	−1.35808			−0.0987855
$190$	−46.8110	+	16.2845i	−3.39603	+	1.18141i
$191$		−	22.7972i		−	1.64955i	−0.565461	−	0.824775i	$-0.691302\pi$
$191$		−	22.7972i		−	1.64955i	0.565461	−	0.824775i	$-0.308698\pi$
$192$			26.1809i			1.88945i
$193$	−20.1256			−1.44867			−0.724336	−	0.689448i	$-0.757853\pi$
$193$	−20.1256			−1.44867			−0.724336	+	0.689448i	$0.757853\pi$
$194$	25.4956			1.83048
$195$	−11.1799	+	3.88925i	−0.800611	+	0.278515i
$196$	27.7058			1.97899
$197$		−	8.87079i		−	0.632018i	−0.948756	−	0.316009i	$-0.897657\pi$
$197$		−	8.87079i		−	0.632018i	0.948756	−	0.316009i	$-0.102343\pi$
$198$	8.08977			0.574915
$199$			9.34694i			0.662587i	0.943528	+	0.331293i	$0.107485\pi$
$199$			9.34694i			0.662587i	−0.943528	+	0.331293i	$0.892515\pi$
$200$	35.9184	−	28.4312i	2.53981	−	2.01039i
$201$	2.92828			0.206545
$202$	−39.4893			−2.77846
$203$	−11.3829			−0.798926
$204$			27.9119i			1.95422i
$205$	0.562103	+	1.61580i	0.0392590	+	0.112853i
$206$	−12.8015			−0.891920
$207$	2.36681			0.164505
$208$	74.8054			5.18682
$209$		−	24.3169i		−	1.68204i
$210$	−2.70943	−	7.78845i	−0.186969	−	0.537454i
$211$	−8.75665			−0.602832			−0.301416	−	0.953493i	$-0.597459\pi$
$211$	−8.75665			−0.602832			−0.301416	+	0.953493i	$0.597459\pi$
$212$		−	19.2099i		−	1.31934i
$213$		−	7.77585i		−	0.532792i
$214$		−	9.87222i		−	0.674851i
$215$	−1.95334	−	5.61501i	−0.133217	−	0.382940i
$216$			9.16180i			0.623381i
$217$	9.48250			0.643714
$218$		−	22.3323i		−	1.51253i
$219$	−1.81844			−0.122879
$220$	11.7620	+	33.8108i	0.792997	+	2.27952i
$221$	27.4954			1.84954
$222$	−5.65800	−	15.5184i	−0.379740	−	1.04153i
$223$		−	13.8965i		−	0.930582i	−0.885158	−	0.465291i	$-0.845950\pi$
$223$		−	13.8965i		−	0.930582i	0.885158	−	0.465291i	$-0.154050\pi$
$224$			27.2281i			1.81925i
$225$	3.92045	−	3.10323i	0.261364	−	0.206882i
$226$	−8.89423			−0.591635
$227$	−19.3784			−1.28619			−0.643095	−	0.765787i	$-0.722350\pi$
$227$	−19.3784			−1.28619			−0.643095	+	0.765787i	$0.722350\pi$
$228$	43.8643			2.90498
$229$	−7.60630			−0.502639			−0.251319	−	0.967904i	$-0.580864\pi$
$229$	−7.60630			−0.502639			−0.251319	+	0.967904i	$0.580864\pi$
$230$	4.72192	+	13.5735i	0.311354	+	0.895009i
$231$	4.04587			0.266199
$232$			76.7912i			5.04159i
$233$			26.7665i			1.75353i	0.480920	+	0.876764i	$0.340303\pi$
$233$			26.7665i			1.75353i	−0.480920	+	0.876764i	$0.659697\pi$
$234$	14.3750			0.939726
$235$	−5.24258	+	1.82378i	−0.341988	+	0.118970i
$236$		−	0.873303i		−	0.0568472i
$237$	−10.6681			−0.692968
$238$			19.1546i			1.24161i
$239$		−	10.2977i		−	0.666104i	−0.942908	−	0.333052i	$-0.891921\pi$
$239$		−	10.2977i		−	0.666104i	0.942908	−	0.333052i	$-0.108079\pi$
$240$	−29.8436	+	10.3819i	−1.92640	+	0.670151i
$241$		−	19.3983i		−	1.24956i	−0.780802	−	0.624778i	$-0.785189\pi$
$241$		−	19.3983i		−	1.24956i	0.780802	−	0.624778i	$-0.214811\pi$
$242$	5.77003			0.370911
$243$			1.00000i			0.0641500i
$244$			60.7154i			3.88691i
$245$	3.78780	+	10.8883i	0.241994	+	0.695628i
$246$		−	2.07758i		−	0.132462i
$247$		−	43.2097i		−	2.74937i
$248$		−	63.9705i		−	4.06213i
$249$	−6.27919			−0.397928
$250$	25.6183	+	16.2924i	1.62024	+	1.03042i
$251$			23.1675i			1.46232i	0.682206	+	0.731160i	$0.261021\pi$
$251$			23.1675i			1.46232i	−0.682206	+	0.731160i	$0.738979\pi$
$252$			7.29816i			0.459741i
$253$	−7.05102			−0.443294
$254$			20.8848i			1.31043i
$255$	−10.9693	+	3.81597i	−0.686923	+	0.238965i
$256$	31.8079			1.98799
$257$	26.8211			1.67305			0.836527	−	0.547925i	$-0.184582\pi$
$257$	26.8211			1.67305			0.836527	+	0.547925i	$0.184582\pi$
$258$			7.21972i			0.449480i
$259$	−2.82969	−	7.76109i	−0.175828	−	0.482251i
$260$	20.9004	+	60.0798i	1.29619	+	3.72599i
$261$			8.38167i			0.518813i
$262$			15.8855i			0.981407i
$263$			6.86941i			0.423586i	0.977315	+	0.211793i	$0.0679303\pi$
$263$			6.86941i			0.423586i	−0.977315	+	0.211793i	$0.932070\pi$
$264$		−	27.2941i		−	1.67983i
$265$	7.54941	−	2.62628i	0.463757	−	0.161331i
$266$	30.1019			1.84567
$267$	−7.15474			−0.437863
$268$		−	15.7363i		−	0.961248i
$269$	6.29440			0.383777			0.191888	−	0.981417i	$-0.438539\pi$
$269$	6.29440			0.383777			0.191888	+	0.981417i	$0.438539\pi$
$270$	−5.73492	+	1.99505i	−0.349016	+	0.121415i
$271$	2.40375			0.146017			0.0730086	−	0.997331i	$-0.476740\pi$
$271$	2.40375			0.146017			0.0730086	+	0.997331i	$0.476740\pi$
$272$	73.3959			4.45028
$273$	7.18926			0.435114
$274$			31.3826i			1.89589i
$275$	−11.6795	+	9.24489i	−0.704300	+	0.557488i
$276$		−	12.7190i		−	0.765595i
$277$	1.97632			0.118746			0.0593728	−	0.998236i	$-0.481090\pi$
$277$	1.97632			0.118746			0.0593728	+	0.998236i	$0.481090\pi$
$278$	−25.6719			−1.53970
$279$		−	6.98231i		−	0.418020i
$280$	−26.2774	+	9.14135i	−1.57038	+	0.546300i
$281$		−	6.49523i		−	0.387473i	−0.981054	−	0.193736i	$-0.937939\pi$
$281$		−	6.49523i		−	0.387473i	0.981054	−	0.193736i	$-0.0620606\pi$
$282$	6.74086			0.401413
$283$	17.7124			1.05289			0.526446	−	0.850209i	$-0.323524\pi$
$283$	17.7124			1.05289			0.526446	+	0.850209i	$0.323524\pi$
$284$	−41.7866			−2.47958
$285$	5.99690	+	17.2385i	0.355226	+	1.02112i
$286$	−42.8249			−2.53229
$287$		−	1.03904i		−	0.0613329i
$288$	20.0490			1.18140
$289$	9.97733			0.586902
$290$	−48.0682	+	16.7219i	−2.82266	+	0.981943i
$291$		−	9.38896i		−	0.550391i
$292$			9.77209i			0.571868i
$293$			10.8660i			0.634796i	0.948292	+	0.317398i	$0.102809\pi$
$293$			10.8660i			0.634796i	−0.948292	+	0.317398i	$0.897191\pi$
$294$		−	14.0001i		−	0.816501i
$295$	0.343205	−	0.119394i	0.0199822	−	0.00695137i
$296$	−52.3576	+	19.0895i	−3.04322	+	1.10955i
$297$		−	2.97912i		−	0.172866i
$298$	16.3721			0.948410
$299$	−12.5292			−0.724584
$300$	−16.6765	−	21.0681i	−0.962815	−	1.21637i
$301$			3.61074i			0.208120i
$302$	45.1385			2.59743
$303$			14.5422i			0.835429i
$304$		−	115.344i		−	6.61541i
$305$	−23.8610	+	8.30071i	−1.36628	+	0.475297i
$306$	14.1042			0.806283
$307$		−	27.1188i		−	1.54775i	−0.633336	−	0.773877i	$-0.718315\pi$
$307$		−	27.1188i		−	1.54775i	0.633336	−	0.773877i	$-0.281685\pi$
$308$		−	21.7421i		−	1.23887i
$309$			4.71423i			0.268183i
$310$	40.0430	−	13.9301i	2.27429	−	0.791175i
$311$			7.37607i			0.418259i	0.977888	+	0.209129i	$0.0670630\pi$
$311$			7.37607i			0.418259i	−0.977888	+	0.209129i	$0.932937\pi$
$312$		−	48.4999i		−	2.74577i
$313$	−20.2055			−1.14208			−0.571041	−	0.820921i	$-0.693460\pi$
$313$	−20.2055			−1.14208			−0.571041	+	0.820921i	$0.693460\pi$
$314$		−	31.3827i		−	1.77103i
$315$	−2.86815	+	0.997769i	−0.161602	+	0.0562179i
$316$			57.3293i			3.22503i
$317$		−	8.25242i		−	0.463502i	−0.972775	−	0.231751i	$-0.925555\pi$
$317$		−	8.25242i		−	0.463502i	0.972775	−	0.231751i	$-0.0744455\pi$
$318$	−9.70696			−0.544339
$319$		−	24.9700i		−	1.39805i
$320$	19.2349	+	55.2922i	1.07527	+	3.09093i
$321$	−3.63552			−0.202915
$322$		−	8.72844i		−	0.486417i
$323$		−	42.3956i		−	2.35895i
$324$	5.37390			0.298550
$325$	−20.7538	+	16.4276i	−1.15121	+	0.911240i
$326$	7.65962			0.424227
$327$	−8.22404			−0.454790
$328$	−7.00956			−0.387038
$329$	3.37125			0.185863
$330$	17.0850	−	5.94350i	0.940498	−	0.327179i
$331$			15.0653i			0.828065i	0.910262	+	0.414033i	$0.135880\pi$
$331$			15.0653i			0.828065i	−0.910262	+	0.414033i	$0.864120\pi$
$332$			33.7437i			1.85193i
$333$	−5.71477	+	2.08360i	−0.313168	+	0.114181i
$334$	38.4179			2.10213
$335$	6.18432	−	2.15139i	0.337885	−	0.117543i
$336$	19.1910			1.04695
$337$		−	19.3435i		−	1.05371i	−0.849956	−	0.526854i	$-0.823372\pi$
$337$		−	19.3435i		−	1.05371i	0.849956	−	0.526854i	$-0.176628\pi$
$338$	−40.7959			−2.21901
$339$			3.27536i			0.177893i
$340$	20.5066	+	58.9478i	1.11213	+	3.19689i
$341$			20.8011i			1.12644i
$342$		−	22.1651i		−	1.19855i
$343$		−	16.5083i		−	0.891363i
$344$	24.3586			1.31333
$345$	4.99853	−	1.73888i	0.269112	−	0.0936182i
$346$		−	35.0734i		−	1.88556i
$347$	−13.7394			−0.737571			−0.368785	−	0.929515i	$-0.620226\pi$
$347$	−13.7394			−0.737571			−0.368785	+	0.929515i	$0.620226\pi$
$348$	45.0423			2.41452
$349$	30.3935			1.62693			0.813464	−	0.581615i	$-0.197579\pi$
$349$	30.3935			1.62693			0.813464	+	0.581615i	$0.197579\pi$
$350$	−11.4442	−	14.4580i	−0.611720	−	0.772814i
$351$		−	5.29371i		−	0.282557i
$352$	−59.7283			−3.18353
$353$	13.6907			0.728684			0.364342	−	0.931265i	$-0.381294\pi$
$353$	13.6907			0.728684			0.364342	+	0.931265i	$0.381294\pi$
$354$	−0.441290			−0.0234543
$355$	−5.71286	−	16.4220i	−0.303207	−	0.871590i
$356$			38.4489i			2.03779i
$357$	7.05381			0.373327
$358$			41.4423i			2.19029i
$359$	20.6617			1.09048			0.545240	−	0.838280i	$-0.316438\pi$
$359$	20.6617			1.09048			0.545240	+	0.838280i	$0.316438\pi$
$360$	6.73111	+	19.3490i	0.354760	+	1.01978i
$361$	−47.6258			−2.50662
$362$	6.00662			0.315701
$363$		−	2.12486i		−	0.111526i
$364$		−	38.6344i		−	2.02499i
$365$	−3.84040	+	1.33599i	−0.201016	+	0.0699290i
$366$	30.6802			1.60368
$367$		−	3.21064i		−	0.167594i	−0.996483	−	0.0837971i	$-0.973295\pi$
$367$		−	3.21064i		−	0.167594i	0.996483	−	0.0837971i	$-0.0267048\pi$
$368$	−33.4454			−1.74346
$369$	−0.765086			−0.0398288
$370$	−23.3505	−	28.6168i	−1.21394	−	1.48772i
$371$	−4.85466			−0.252041
$372$	−37.5222			−1.94544
$373$		−	30.9683i		−	1.60348i	−0.597676	−	0.801738i	$-0.703909\pi$
$373$		−	30.9683i		−	1.60348i	0.597676	−	0.801738i	$-0.296091\pi$
$374$	−42.0180			−2.17270
$375$	5.99978	−	9.43412i	0.309827	−	0.487176i
$376$		−	22.7430i		−	1.17288i
$377$		−	44.3702i		−	2.28518i
$378$	3.68784			0.189682
$379$	−11.0626			−0.568246			−0.284123	−	0.958788i	$-0.591702\pi$
$379$	−11.0626			−0.568246			−0.284123	+	0.958788i	$0.591702\pi$
$380$	92.6380	−	32.2268i	4.75223	−	1.65320i
$381$	7.69097			0.394020
$382$			61.9057i			3.16737i
$383$	−19.1650			−0.979286			−0.489643	−	0.871923i	$-0.662873\pi$
$383$	−19.1650			−0.979286			−0.489643	+	0.871923i	$0.662873\pi$
$384$		−	30.9961i		−	1.58176i
$385$	8.54457	−	2.97247i	0.435472	−	0.151491i
$386$	54.6509			2.78166
$387$	2.65872			0.135150
$388$	−50.4553			−2.56148
$389$			30.7456i			1.55886i	0.626487	+	0.779432i	$0.284492\pi$
$389$			30.7456i			1.55886i	−0.626487	+	0.779432i	$0.715508\pi$
$390$	30.3590	−	10.5612i	1.53729	−	0.534789i
$391$	−12.2932			−0.621692
$392$	−47.2348			−2.38572
$393$	5.84994			0.295090
$394$			24.0886i			1.21356i
$395$	−22.5302	+	7.83778i	−1.13362	+	0.394362i
$396$	−16.0095			−0.804507
$397$			30.1572i			1.51354i	0.653678	+	0.756772i	$0.273225\pi$
$397$			30.1572i			1.51354i	−0.653678	+	0.756772i	$0.726775\pi$
$398$		−	25.3815i		−	1.27226i
$399$		−	11.0852i		−	0.554956i
$400$	−55.3999	+	43.8517i	−2.76999	+	2.19259i
$401$			10.1698i			0.507855i	0.967223	+	0.253927i	$0.0817224\pi$
$401$			10.1698i			0.507855i	−0.967223	+	0.253927i	$0.918278\pi$
$402$	−7.95173			−0.396596
$403$			36.9623i			1.84123i
$404$	78.1485			3.88803
$405$	0.734693	+	2.11192i	0.0365072	+	0.104942i
$406$	30.9103			1.53405
$407$	17.0250	−	6.20729i	0.843897	−	0.307684i
$408$		−	47.5861i		−	2.35586i
$409$		−	5.79195i		−	0.286393i	−0.989694	−	0.143197i	$-0.954262\pi$
$409$		−	5.79195i		−	0.286393i	0.989694	−	0.143197i	$-0.0457381\pi$
$410$	−1.52639	−	4.38770i	−0.0753828	−	0.216693i
$411$	11.5569			0.570058
$412$	25.3338			1.24811
$413$	−0.220699			−0.0108599
$414$	−6.42707			−0.315873
$415$	−13.2612	+	4.61328i	−0.650966	+	0.226457i
$416$	−106.134			−5.20363
$417$			9.45387i			0.462958i
$418$			66.0325i			3.22975i
$419$	−15.6425			−0.764187			−0.382094	−	0.924124i	$-0.624797\pi$
$419$	−15.6425			−0.764187			−0.382094	+	0.924124i	$0.624797\pi$
$420$	5.36191	+	15.4132i	0.261634	+	0.752086i
$421$			0.256794i			0.0125154i	0.999980	+	0.00625768i	$0.00199189\pi$
$421$			0.256794i			0.0125154i	−0.999980	+	0.00625768i	$0.998008\pi$
$422$	23.7786			1.15752
$423$		−	2.48237i		−	0.120697i
$424$			32.7503i			1.59049i
$425$	−20.3627	+	16.1181i	−0.987737	+	0.781842i
$426$			21.1153i			1.02304i
$427$	15.3438			0.742540
$428$			19.5369i			0.944352i
$429$			15.7706i			0.761412i
$430$	5.30428	+	15.2475i	0.255795	+	0.735301i
$431$		−	29.8357i		−	1.43713i	−0.695458	−	0.718567i	$-0.744798\pi$
$431$		−	29.8357i		−	1.43713i	0.695458	−	0.718567i	$-0.255202\pi$
$432$		−	14.1310i		−	0.679878i
$433$			19.2262i			0.923953i	0.886892	+	0.461977i	$0.152860\pi$
$433$			19.2262i			0.923953i	−0.886892	+	0.461977i	$0.847140\pi$
$434$	−25.7497			−1.23602
$435$	6.15796	+	17.7015i	0.295251	+	0.848720i
$436$			44.1951i			2.11656i
$437$			19.3190i			0.924155i
$438$	4.93795			0.235944
$439$		−	6.51507i		−	0.310947i	−0.987840	−	0.155474i	$-0.950310\pi$
$439$		−	6.51507i		−	0.310947i	0.987840	−	0.155474i	$-0.0496904\pi$
$440$	−20.0528	−	57.6430i	−0.955978	−	2.74802i
$441$	−5.15563			−0.245506
$442$	−74.6635			−3.55138
$443$			21.7286i			1.03236i	0.856480	+	0.516180i	$0.172646\pi$
$443$			21.7286i			1.03236i	−0.856480	+	0.516180i	$0.827354\pi$
$444$	11.1970	+	30.7106i	0.531388	+	1.45746i
$445$	−15.1103	+	5.25654i	−0.716296	+	0.249184i
$446$			37.7360i			1.78685i
$447$		−	6.02914i		−	0.285169i
$448$		−	35.5557i		−	1.67985i
$449$		−	10.8252i		−	0.510873i	−0.966826	−	0.255437i	$-0.917781\pi$
$449$		−	10.8252i		−	0.510873i	0.966826	−	0.255437i	$-0.0822192\pi$
$450$	−10.6460	+	8.42680i	−0.501855	+	0.397243i
$451$	2.27928			0.107327
$452$	17.6015			0.827904
$453$		−	16.6226i		−	0.780997i
$454$	52.6219			2.46967
$455$	15.1832	−	5.28190i	0.711799	−	0.247619i
$456$	−74.7828			−3.50203
$457$	−9.33380			−0.436617			−0.218308	−	0.975880i	$-0.570054\pi$
$457$	−9.33380			−0.436617			−0.218308	+	0.975880i	$0.570054\pi$
$458$	20.6549			0.965138
$459$		−	5.19397i		−	0.242434i
$460$	−9.34457	−	26.8616i	−0.435693	−	1.25243i
$461$		−	5.96486i		−	0.277811i	−0.990306	−	0.138906i	$-0.955642\pi$
$461$		−	5.96486i		−	0.277811i	0.990306	−	0.138906i	$-0.0443585\pi$
$462$	−10.9865			−0.511139
$463$	35.7571			1.66177			0.830887	−	0.556441i	$-0.187834\pi$
$463$	35.7571			1.66177			0.830887	+	0.556441i	$0.187834\pi$
$464$		−	118.441i		−	5.49850i
$465$	−5.12985	−	14.7461i	−0.237891	−	0.683835i
$466$		−	72.6841i		−	3.36703i
$467$	0.575842			0.0266468			0.0133234	−	0.999911i	$-0.495759\pi$
$467$	0.575842			0.0266468			0.0133234	+	0.999911i	$0.495759\pi$
$468$	−28.4479			−1.31500
$469$	−3.97683			−0.183633
$470$	14.2362	−	4.95246i	0.656667	−	0.228440i
$471$	−11.5569			−0.532515
$472$			1.48887i			0.0685307i
$473$	−7.92063			−0.364191
$474$	28.9692			1.33060
$475$	25.3300	+	32.0006i	1.16222	+	1.46829i
$476$		−	37.9064i		−	1.73744i
$477$			3.57466i			0.163672i
$478$			27.9634i			1.27902i
$479$			10.6374i			0.486034i	0.970022	+	0.243017i	$0.0781371\pi$
$479$			10.6374i			0.486034i	−0.970022	+	0.243017i	$0.921863\pi$
$480$	42.3420	−	14.7299i	1.93264	−	0.672323i
$481$	30.2524	−	11.0300i	1.37939	−	0.502923i
$482$			52.6760i			2.39933i
$483$	−3.21431			−0.146256
$484$	−11.4188			−0.519034
$485$	−6.89800	−	19.8288i	−0.313222	−	0.900378i
$486$		−	2.71549i		−	0.123177i
$487$	0.182304			0.00826099			0.00413050	−	0.999991i	$-0.498685\pi$
$487$	0.182304			0.00826099			0.00413050	+	0.999991i	$0.498685\pi$
$488$		−	103.512i		−	4.68576i
$489$		−	2.82071i		−	0.127557i
$490$	−10.2858	−	29.5671i	−0.464663	−	1.33571i
$491$	8.92187			0.402638			0.201319	−	0.979526i	$-0.435477\pi$
$491$	8.92187			0.402638			0.201319	+	0.979526i	$0.435477\pi$
$492$			4.11149i			0.185360i
$493$		−	43.5342i		−	1.96068i
$494$			117.336i			5.27918i
$495$	−2.18874	−	6.29167i	−0.0983764	−	0.282790i
$496$			98.6669i			4.43028i
$497$			10.5602i			0.473689i
$498$	17.0511			0.764078
$499$		−	28.1796i		−	1.26149i	−0.775990	−	0.630746i	$-0.782749\pi$
$499$		−	28.1796i		−	1.26149i	0.775990	−	0.630746i	$-0.217251\pi$
$500$	−50.6980	−	32.2422i	−2.26728	−	1.44192i
$501$		−	14.1477i		−	0.632071i
$502$		−	62.9112i		−	2.80786i
$503$	24.4775			1.09140			0.545698	−	0.837982i	$-0.316264\pi$
$503$	24.4775			1.09140			0.545698	+	0.837982i	$0.316264\pi$
$504$		−	12.4424i		−	0.554229i
$505$	10.6841	+	30.7121i	0.475435	+	1.36667i
$506$	19.1470			0.851188
$507$			15.0234i			0.667212i
$508$		−	41.3305i		−	1.83374i
$509$	−8.39148			−0.371946			−0.185973	−	0.982555i	$-0.559544\pi$
$509$	−8.39148			−0.371946			−0.185973	+	0.982555i	$0.559544\pi$
$510$	29.7870	−	10.3622i	1.31899	−	0.458848i
$511$	2.46957			0.109248
$512$	−24.3817			−1.07753
$513$	−8.16246			−0.360382
$514$	−72.8325			−3.21250
$515$	3.46351	+	9.95610i	0.152621	+	0.438718i
$516$		−	14.2877i		−	0.628980i
$517$			7.39528i			0.325244i
$518$	7.68399	+	21.0752i	0.337615	+	0.925991i
$519$	−12.9160			−0.566952
$520$	−35.6325	−	102.428i	−1.56259	−	4.49177i
$521$	−18.9435			−0.829929			−0.414964	−	0.909838i	$-0.636206\pi$
$521$	−18.9435			−0.829929			−0.414964	+	0.909838i	$0.636206\pi$
$522$		−	22.7604i		−	0.996194i
$523$	34.6966			1.51718			0.758589	−	0.651570i	$-0.225889\pi$
$523$	34.6966			1.51718			0.758589	+	0.651570i	$0.225889\pi$
$524$		−	31.4370i		−	1.37333i
$525$	−5.32427	+	4.21442i	−0.232370	+	0.183933i
$526$		−	18.6538i		−	0.813346i
$527$			36.2659i			1.57977i
$528$			42.0979i			1.83208i
$529$	−17.3982			−0.756443
$530$	−20.5004	+	7.13163i	−0.890479	+	0.309778i
$531$			0.162508i			0.00705226i
$532$	−59.5710			−2.58273
$533$	4.05014			0.175431
$534$	19.4286			0.840760
$535$	−7.67794	+	2.67099i	−0.331946	+	0.115477i
$536$			26.8283i			1.15881i
$537$	15.2614			0.658579
$538$	−17.0924			−0.736906
$539$	15.3592			0.661569
$540$	11.3493	−	3.94816i	0.488395	−	0.169902i
$541$		−	3.84115i		−	0.165144i	−0.996585	−	0.0825720i	$-0.973687\pi$
$541$		−	3.84115i		−	0.165144i	0.996585	−	0.0825720i	$-0.0263134\pi$
$542$	−6.52736			−0.280374
$543$		−	2.21198i		−	0.0949253i
$544$	−104.134			−4.46471
$545$	−17.3685	+	6.04214i	−0.743987	+	0.258817i
$546$	−19.5224			−0.835481
$547$	−17.3358			−0.741227			−0.370614	−	0.928787i	$-0.620853\pi$
$547$	−17.3358			−0.741227			−0.370614	+	0.928787i	$0.620853\pi$
$548$		−	62.1054i		−	2.65301i
$549$		−	11.2982i		−	0.482196i
$550$	31.7156	−	25.1044i	1.35236	−	1.07046i
$551$	−68.4151			−2.91458
$552$			21.6843i			0.922944i
$553$	14.4881			0.616097
$554$	−5.36668			−0.228009
$555$	−10.5384	+	8.59901i	−0.447329	+	0.365007i
$556$	50.8041			2.15458
$557$	−36.9913			−1.56737			−0.783687	−	0.621156i	$-0.786663\pi$
$557$	−36.9913			−1.56737			−0.783687	+	0.621156i	$0.786663\pi$
$558$			18.9604i			0.802658i
$559$	−14.0745			−0.595287
$560$	40.5299	−	14.0995i	1.71270	−	0.595811i
$561$			15.4735i			0.653290i
$562$			17.6377i			0.744003i
$563$	2.67097			0.112568			0.0562840	−	0.998415i	$-0.482075\pi$
$563$	2.67097			0.112568			0.0562840	+	0.998415i	$0.482075\pi$
$564$	−13.3400			−0.561716
$565$	2.40639	+	6.91732i	0.101237	+	0.291014i
$566$	−48.0978			−2.02170
$567$		−	1.35808i		−	0.0570338i
$568$	71.2407			2.98920
$569$			17.5044i			0.733824i	0.930256	+	0.366912i	$0.119585\pi$
$569$			17.5044i			0.733824i	−0.930256	+	0.366912i	$0.880415\pi$
$570$	−16.2845	−	46.8110i	−0.682085	−	1.96070i
$571$	3.43218			0.143632			0.0718161	−	0.997418i	$-0.477121\pi$
$571$	3.43218			0.143632			0.0718161	+	0.997418i	$0.477121\pi$
$572$	84.7496			3.54356
$573$	22.7972			0.952368
$574$			2.82152i			0.117768i
$575$	9.27899	−	7.34477i	0.386960	−	0.306298i
$576$	−26.1809			−1.09087
$577$	26.5724			1.10622			0.553111	−	0.833107i	$-0.313440\pi$
$577$	26.5724			1.10622			0.553111	+	0.833107i	$0.313440\pi$
$578$	−27.0934			−1.12694
$579$		−	20.1256i		−	0.836391i
$580$	95.1259	−	33.0922i	3.94989	−	1.37408i
$581$	8.52762			0.353785
$582$			25.4956i			1.05683i
$583$		−	10.6493i		−	0.441050i
$584$		−	16.6601i		−	0.689401i
$585$	−3.88925	−	11.1799i	−0.160801	−	0.462233i
$586$		−	29.5064i		−	1.21890i
$587$	−1.40819			−0.0581221			−0.0290610	−	0.999578i	$-0.509252\pi$
$587$	−1.40819			−0.0581221			−0.0290610	+	0.999578i	$0.509252\pi$
$588$			27.7058i			1.14257i
$589$	56.9928			2.34835
$590$	−0.931971	+	0.324212i	−0.0383686	+	0.0133476i
$591$	8.87079			0.364896
$592$	80.7554	−	29.4433i	3.31903	−	1.21011i
$593$			13.8523i			0.568847i	0.958699	+	0.284424i	$0.0918022\pi$
$593$			13.8523i			0.568847i	−0.958699	+	0.284424i	$0.908198\pi$
$594$			8.08977i			0.331927i
$595$	14.8971	−	5.18238i	0.610722	−	0.212457i
$596$	−32.4000			−1.32716
$597$	−9.34694			−0.382545
$598$	34.0230			1.39131
$599$	−22.6069			−0.923692			−0.461846	−	0.886960i	$-0.652813\pi$
$599$	−22.6069			−0.923692			−0.461846	+	0.886960i	$0.652813\pi$
$600$	28.4312	+	35.9184i	1.16070	+	1.46636i
$601$	14.6690			0.598362			0.299181	−	0.954196i	$-0.403287\pi$
$601$	14.6690			0.598362			0.299181	+	0.954196i	$0.403287\pi$
$602$		−	9.80493i		−	0.399619i
$603$			2.92828i			0.119249i
$604$	−89.3281			−3.63471
$605$	−1.56112	−	4.48753i	−0.0634684	−	0.182444i
$606$		−	39.4893i		−	1.60414i
$607$	22.9716			0.932390			0.466195	−	0.884682i	$-0.345625\pi$
$607$	22.9716			0.932390			0.466195	+	0.884682i	$0.345625\pi$
$608$			163.649i			6.63685i
$609$		−	11.3829i		−	0.461260i
$610$	64.7943	−	22.5405i	2.62344	−	0.912639i
$611$			13.1410i			0.531627i
$612$	−27.9119			−1.12827
$613$			37.2360i			1.50395i	0.659193	+	0.751974i	$0.270898\pi$
$613$			37.2360i			1.50395i	−0.659193	+	0.751974i	$0.729102\pi$
$614$			73.6410i			2.97191i
$615$	−1.61580	+	0.562103i	−0.0651555	+	0.0226662i
$616$			37.0674i			1.49349i
$617$			23.2097i			0.934388i	0.884155	+	0.467194i	$0.154735\pi$
$617$			23.2097i			0.934388i	−0.884155	+	0.467194i	$0.845265\pi$
$618$		−	12.8015i		−	0.514950i
$619$	−12.2705			−0.493191			−0.246596	−	0.969118i	$-0.579312\pi$
$619$	−12.2705			−0.493191			−0.246596	+	0.969118i	$0.579312\pi$
$620$	−79.2441	+	27.5673i	−3.18252	+	1.10713i
$621$			2.36681i			0.0949770i
$622$		−	20.0297i		−	0.803116i
$623$	9.71668			0.389291
$624$			74.8054i			2.99461i
$625$	5.73990	−	24.3321i	0.229596	−	0.973286i
$626$	54.8679			2.19296
$627$	24.3169			0.971125
$628$			62.1057i			2.47829i
$629$	29.6824	−	10.8221i	1.18351	−	0.431507i
$630$	7.78845	−	2.70943i	0.310299	−	0.107946i
$631$			35.6225i			1.41811i	0.705154	+	0.709055i	$0.250878\pi$
$631$			35.6225i			1.41811i	−0.705154	+	0.709055i	$0.749122\pi$
$632$		−	97.7390i		−	3.88785i
$633$		−	8.75665i		−	0.348045i
$634$			22.4094i			0.889990i
$635$	16.2428	−	5.65050i	0.644574	−	0.224233i
$636$	19.2099			0.761720
$637$	27.2924			1.08137
$638$			67.8058i			2.68446i
$639$	7.77585			0.307608
$640$	−22.7726	−	65.4615i	−0.900167	−	2.58759i
$641$	38.0197			1.50169			0.750844	−	0.660480i	$-0.229647\pi$
$641$	38.0197			1.50169			0.750844	+	0.660480i	$0.229647\pi$
$642$	9.87222			0.389626
$643$	−47.3400			−1.86691			−0.933453	−	0.358698i	$-0.883221\pi$
$643$	−47.3400			−1.86691			−0.933453	+	0.358698i	$0.883221\pi$
$644$			17.2734i			0.680667i
$645$	5.61501	−	1.95334i	0.221091	−	0.0769127i
$646$			115.125i			4.52953i
$647$	15.4200			0.606223			0.303111	−	0.952955i	$-0.401975\pi$
$647$	15.4200			0.606223			0.303111	+	0.952955i	$0.401975\pi$
$648$	−9.16180			−0.359909
$649$		−	0.484131i		−	0.0190038i
$650$	56.3567	−	44.6091i	2.21049	−	1.74971i
$651$			9.48250i			0.371649i
$652$	−15.1582			−0.593641
$653$	5.09201			0.199266			0.0996328	−	0.995024i	$-0.468233\pi$
$653$	5.09201			0.199266			0.0996328	+	0.995024i	$0.468233\pi$
$654$	22.3323			0.873262
$655$	12.3546	−	4.29791i	0.482735	−	0.167933i
$656$	10.8114			0.422115
$657$		−	1.81844i		−	0.0709439i
$658$	−9.15460			−0.356884
$659$	14.6572			0.570964			0.285482	−	0.958384i	$-0.407846\pi$
$659$	14.6572			0.570964			0.285482	+	0.958384i	$0.407846\pi$
$660$	−33.8108	+	11.7620i	−1.31608	+	0.457837i
$661$		−	50.7078i		−	1.97231i	−0.165841	−	0.986153i	$-0.553034\pi$
$661$		−	50.7078i		−	1.97231i	0.165841	−	0.986153i	$-0.446966\pi$
$662$		−	40.9098i		−	1.59000i
$663$			27.4954i			1.06783i
$664$		−	57.5287i		−	2.23255i
$665$	−8.14425	−	23.4112i	−0.315820	−	0.907848i
$666$	15.5184	−	5.65800i	0.601327	−	0.219243i
$667$			19.8379i			0.768125i
$668$	−76.0282			−2.94162
$669$	13.8965			0.537272
$670$	−16.7935	+	5.84208i	−0.648788	+	0.225699i
$671$			33.6587i			1.29938i
$672$	−27.2281			−1.05035
$673$		−	6.95057i		−	0.267925i	−0.990986	−	0.133962i	$-0.957230\pi$
$673$		−	6.95057i		−	0.267925i	0.990986	−	0.133962i	$-0.0427701\pi$
$674$			52.5271i			2.02327i
$675$	3.10323	+	3.92045i	0.119443	+	0.150898i
$676$	80.7342			3.10516
$677$		−	15.0561i		−	0.578654i	−0.957230	−	0.289327i	$-0.906568\pi$
$677$		−	15.0561i		−	0.578654i	0.957230	−	0.289327i	$-0.0934316\pi$
$678$		−	8.89423i		−	0.341581i
$679$			12.7509i			0.489335i
$680$	−34.9612	−	100.498i	−1.34070	−	3.85393i
$681$		−	19.3784i		−	0.742582i
$682$		−	56.4853i		−	2.16293i
$683$	−11.1313			−0.425926			−0.212963	−	0.977060i	$-0.568311\pi$
$683$	−11.1313			−0.425926			−0.212963	+	0.977060i	$0.568311\pi$
$684$			43.8643i			1.67719i
$685$	24.4072	−	8.49075i	0.932553	−	0.324415i
$686$			44.8281i			1.71154i
$687$		−	7.60630i		−	0.290199i
$688$	−37.5703			−1.43235
$689$		−	18.9232i		−	0.720917i
$690$	−13.5735	+	4.72192i	−0.516734	+	0.179760i
$691$	−38.4529			−1.46282			−0.731409	−	0.681939i	$-0.761137\pi$
$691$	−38.4529			−1.46282			−0.731409	+	0.681939i	$0.761137\pi$
$692$			69.4095i			2.63855i
$693$			4.04587i			0.153690i
$694$	37.3093			1.41624
$695$	6.94569	+	19.9659i	0.263465	+	0.757348i
$696$	−76.7912			−2.91076
$697$	3.97383			0.150520
$698$	−82.5334			−3.12394
$699$	−26.7665			−1.01240
$700$	22.6479	+	28.6121i	0.856010	+	1.08144i
$701$			5.43667i			0.205340i	0.994715	+	0.102670i	$0.0327386\pi$
$701$			5.43667i			0.205340i	−0.994715	+	0.102670i	$0.967261\pi$
$702$			14.3750i			0.542551i
$703$	−17.0073	−	46.6466i	−0.641442	−	1.75931i
$704$	77.9961			2.93959
$705$	−1.82378	−	5.24258i	−0.0686876	−	0.197447i
$706$	−37.1771			−1.39918
$707$		−	19.7495i		−	0.742755i
$708$	0.873303			0.0328207
$709$		−	6.18233i		−	0.232182i	−0.993239	−	0.116091i	$-0.962964\pi$
$709$		−	6.18233i		−	0.232182i	0.993239	−	0.116091i	$-0.0370365\pi$
$710$	15.5132	+	44.5938i	0.582201	+	1.67358i
$711$		−	10.6681i		−	0.400085i
$712$		−	65.5503i		−	2.45660i
$713$		−	16.5258i		−	0.618897i
$714$	−19.1546			−0.716841
$715$	11.5865	+	33.3063i	0.433312	+	1.24559i
$716$		−	82.0133i		−	3.06498i
$717$	10.2977			0.384575
$718$	−56.1066			−2.09388
$719$	−36.0943			−1.34609			−0.673044	−	0.739602i	$-0.735014\pi$
$719$	−36.0943			−1.34609			−0.673044	+	0.739602i	$0.735014\pi$
$720$	−10.3819	−	29.8436i	−0.386912	−	1.11220i
$721$		−	6.40228i		−	0.238433i
$722$	129.328			4.81307
$723$	19.3983			0.721432
$724$	−11.8870			−0.441776
$725$	26.0103	+	32.8600i	0.965998	+	1.22039i
$726$			5.77003i			0.214146i
$727$	−36.1116			−1.33931			−0.669653	−	0.742674i	$-0.733557\pi$
$727$	−36.1116			−1.33931			−0.669653	+	0.742674i	$0.733557\pi$
$728$			65.8666i			2.44118i
$729$	−1.00000			−0.0370370
$730$	10.4286	−	3.62788i	0.385979	−	0.134274i
$731$	−13.8093			−0.510755
$732$	−60.7154			−2.24411
$733$			36.5087i			1.34848i	0.738512	+	0.674240i	$0.235529\pi$
$733$			36.5087i			1.34848i	−0.738512	+	0.674240i	$0.764471\pi$
$734$			8.71847i			0.321805i
$735$	−10.8883	+	3.78780i	−0.401621	+	0.139715i
$736$	47.4523			1.74911
$737$		−	8.72370i		−	0.321342i
$738$	2.07758			0.0764769
$739$	4.00770			0.147425			0.0737127	−	0.997280i	$-0.476515\pi$
$739$	4.00770			0.147425			0.0737127	+	0.997280i	$0.476515\pi$
$740$	46.2102	+	56.6321i	1.69872	+	2.08184i
$741$	43.2097			1.58735
$742$	13.1828			0.483955
$743$			0.829522i			0.0304322i	0.999884	+	0.0152161i	$0.00484362\pi$
$743$			0.829522i			0.0304322i	−0.999884	+	0.0152161i	$0.995156\pi$
$744$	63.9705			2.34527
$745$	−4.42957	−	12.7331i	−0.162287	−	0.466505i
$746$			84.0941i			3.07890i
$747$		−	6.27919i		−	0.229744i
$748$	83.1528			3.04037
$749$	4.93731			0.180405
$750$	−16.2924	+	25.6183i	−0.594913	+	0.935447i
$751$	9.47652			0.345803			0.172902	−	0.984939i	$-0.444686\pi$
$751$	9.47652			0.345803			0.172902	+	0.984939i	$0.444686\pi$
$752$			35.0784i			1.27918i
$753$	−23.1675			−0.844271
$754$			120.487i			4.38787i
$755$	−12.2125	−	35.1056i	−0.444458	−	1.27763i
$756$	−7.29816			−0.265432
$757$	17.4897			0.635675			0.317838	−	0.948145i	$-0.397043\pi$
$757$	17.4897			0.635675			0.317838	+	0.948145i	$0.397043\pi$
$758$	30.0403			1.09111
$759$		−	7.05102i		−	0.255936i
$760$	−157.936	+	54.9424i	−5.72893	+	1.99297i
$761$	−29.7483			−1.07837			−0.539187	−	0.842186i	$-0.681268\pi$
$761$	−29.7483			−1.07837			−0.539187	+	0.842186i	$0.681268\pi$
$762$	−20.8848			−0.756576
$763$	11.1689			0.404340
$764$		−	122.510i		−	4.43226i
$765$	−3.81597	−	10.9693i	−0.137967	−	0.396595i
$766$	52.0424			1.88037
$767$		−	0.860272i		−	0.0310626i
$768$			31.8079i			1.14777i
$769$		−	19.7672i		−	0.712823i	−0.934329	−	0.356412i	$-0.884000\pi$
$769$		−	19.7672i		−	0.712823i	0.934329	−	0.356412i	$-0.116000\pi$
$770$	−23.2027	+	8.07172i	−0.836168	+	0.290885i
$771$			26.8211i			0.965938i
$772$	−108.153			−3.89251
$773$		−	32.2770i		−	1.16092i	−0.814288	−	0.580461i	$-0.802872\pi$
$773$		−	32.2770i		−	1.16092i	0.814288	−	0.580461i	$-0.197128\pi$
$774$	−7.21972			−0.259508
$775$	−21.6677	−	27.3738i	−0.778328	−	0.983296i
$776$	86.0197			3.08793
$777$	7.76109	−	2.82969i	0.278428	−	0.101514i
$778$		−	83.4895i		−	2.99324i
$779$		−	6.24499i		−	0.223750i
$780$	−60.0798	+	20.9004i	−2.15120	+	0.748356i
$781$	−23.1652			−0.828915
$782$	33.3820			1.19374
$783$	−8.38167			−0.299537
$784$	72.8542			2.60193
$785$	−24.4073	+	8.49078i	−0.871135	+	0.303049i
$786$	−15.8855			−0.566616
$787$		−	29.3025i		−	1.04452i	−0.852786	−	0.522260i	$-0.825089\pi$
$787$		−	29.3025i		−	1.04452i	0.852786	−	0.522260i	$-0.174911\pi$
$788$		−	47.6707i		−	1.69820i
$789$	−6.86941			−0.244557
$790$	61.1807	−	21.2834i	2.17671	−	0.757231i
$791$		−	4.44819i		−	0.158160i
$792$	27.2941			0.969853
$793$			59.8095i			2.12390i
$794$		−	81.8916i		−	2.90622i
$795$	2.62628	+	7.54941i	0.0931444	+	0.267750i
$796$			50.2295i			1.78034i
$797$	−3.21200			−0.113775			−0.0568874	−	0.998381i	$-0.518118\pi$
$797$	−3.21200			−0.113775			−0.0568874	+	0.998381i	$0.518118\pi$
$798$			30.1019i			1.06560i
$799$			12.8934i			0.456135i
$800$	78.6012	−	62.2167i	2.77897	−	2.19969i
$801$		−	7.15474i		−	0.252800i
$802$		−	27.6160i		−	0.975153i
$803$			5.41734i			0.191174i
$804$	15.7363			0.554977
$805$	−6.78839	+	2.36153i	−0.239259	+	0.0832331i
$806$		−	100.371i		−	3.53542i
$807$			6.29440i			0.221574i
$808$	−133.233			−4.68712
$809$			5.99060i			0.210618i	0.994440	+	0.105309i	$0.0335832\pi$
$809$			5.99060i			0.210618i	−0.994440	+	0.105309i	$0.966417\pi$
$810$	−1.99505	−	5.73492i	−0.0700990	−	0.201504i
$811$	−34.8651			−1.22428			−0.612139	−	0.790750i	$-0.709691\pi$
$811$	−34.8651			−1.22428			−0.612139	+	0.790750i	$0.709691\pi$
$812$	−61.1708			−2.14667
$813$			2.40375i			0.0843031i
$814$	−46.2312	+	16.8558i	−1.62040	+	0.590797i
$815$	−2.07235	−	5.95713i	−0.0725914	−	0.208669i
$816$			73.3959i			2.56937i
$817$			21.7017i			0.759246i
$818$			15.7280i			0.549916i
$819$			7.18926i			0.251213i
$820$	3.02068	+	8.68316i	0.105487	+	0.303229i
$821$	20.6185			0.719589			0.359795	−	0.933032i	$-0.382847\pi$
$821$	20.6185			0.719589			0.359795	+	0.933032i	$0.382847\pi$
$822$	−31.3826			−1.09459
$823$			25.4237i			0.886216i	0.896468	+	0.443108i	$0.146124\pi$
$823$			25.4237i			0.886216i	−0.896468	+	0.443108i	$0.853876\pi$
$824$	−43.1908			−1.50462
$825$	−9.24489	−	11.6795i	−0.321866	−	0.406628i
$826$	0.599305			0.0208525
$827$	−23.0406			−0.801199			−0.400600	−	0.916253i	$-0.631198\pi$
$827$	−23.0406			−0.801199			−0.400600	+	0.916253i	$0.631198\pi$
$828$	12.7190			0.442017
$829$			56.0107i			1.94533i	0.232210	+	0.972666i	$0.425404\pi$
$829$			56.0107i			1.94533i	−0.232210	+	0.972666i	$0.574596\pi$
$830$	36.0106	−	12.5273i	1.24995	−	0.434829i
$831$			1.97632i			0.0685578i
$832$	138.594			4.80489
$833$	26.7782			0.927809
$834$		−	25.6719i		−	0.888946i
$835$	−10.3942	−	29.8788i	−0.359706	−	1.03400i
$836$		−	130.677i		−	4.51955i
$837$	6.98231			0.241344
$838$	42.4771			1.46735
$839$	−27.4024			−0.946037			−0.473019	−	0.881052i	$-0.656836\pi$
$839$	−27.4024			−0.946037			−0.473019	+	0.881052i	$0.656836\pi$
$840$	−9.14135	−	26.2774i	−0.315407	−	0.906658i
$841$	−41.2525			−1.42250
$842$		−	0.697321i		−	0.0240313i
$843$	6.49523			0.223707
$844$	−47.0573			−1.61978
$845$	11.0376	+	31.7283i	0.379704	+	1.09149i
$846$			6.74086i			0.231756i
$847$			2.88571i			0.0991543i
$848$		−	50.5135i		−	1.73464i
$849$			17.7124i			0.607887i
$850$	55.2948	−	43.7686i	1.89660	−	1.50125i
$851$	−13.5258	+	4.93149i	−0.463659	+	0.169049i
$852$		−	41.7866i		−	1.43159i
$853$	−17.1168			−0.586068			−0.293034	−	0.956102i	$-0.594665\pi$
$853$	−17.1168			−0.586068			−0.293034	+	0.956102i	$0.594665\pi$
$854$	−41.6660			−1.42578
$855$	−17.2385	+	5.99690i	−0.589545	+	0.205090i
$856$		−	33.3079i		−	1.13844i
$857$	−53.2478			−1.81891			−0.909455	−	0.415802i	$-0.863501\pi$
$857$	−53.2478			−1.81891			−0.909455	+	0.415802i	$0.863501\pi$
$858$		−	42.8249i		−	1.46202i
$859$		−	29.2811i		−	0.999058i	−0.866297	−	0.499529i	$-0.833506\pi$
$859$		−	29.2811i		−	0.999058i	0.866297	−	0.499529i	$-0.166494\pi$
$860$	−10.4971	−	30.1745i	−0.357946	−	1.02894i
$861$	1.03904			0.0354105
$862$			81.0185i			2.75950i
$863$			35.9842i			1.22492i	0.790503	+	0.612458i	$0.209819\pi$
$863$			35.9842i			1.22492i	−0.790503	+	0.612458i	$0.790181\pi$
$864$			20.0490i			0.682081i
$865$	−27.2777	+	9.48933i	−0.927470	+	0.322647i
$866$		−	52.2087i		−	1.77412i
$867$			9.97733i			0.338848i
$868$	50.9580			1.72963
$869$			31.7816i			1.07812i
$870$	−16.7219	−	48.0682i	−0.566925	−	1.62966i
$871$		−	15.5015i		−	0.525248i
$872$		−	75.3469i		−	2.55157i
$873$	9.38896			0.317768
$874$		−	52.4607i		−	1.77451i
$875$	−8.14816	+	12.8123i	−0.275458	+	0.433133i
$876$	−9.77209			−0.330168
$877$			49.6342i			1.67603i	0.545649	+	0.838014i	$0.316283\pi$
$877$			49.6342i			1.67603i	−0.545649	+	0.838014i	$0.683717\pi$
$878$			17.6916i			0.597063i
$879$	−10.8660			−0.366500
$880$	30.9290	+	88.9076i	1.04262	+	2.99707i
$881$	32.4663			1.09382			0.546909	−	0.837192i	$-0.315804\pi$
$881$	32.4663			1.09382			0.546909	+	0.837192i	$0.315804\pi$
$882$	14.0001			0.471407
$883$	27.5070			0.925684			0.462842	−	0.886441i	$-0.346830\pi$
$883$	27.5070			0.925684			0.462842	+	0.886441i	$0.346830\pi$
$884$	147.757			4.96962
$885$	0.119394	+	0.343205i	0.00401337	+	0.0115367i
$886$		−	59.0040i		−	1.98228i
$887$		−	43.1579i		−	1.44910i	−0.689222	−	0.724550i	$-0.742048\pi$
$887$		−	43.1579i		−	1.44910i	0.689222	−	0.724550i	$-0.257952\pi$
$888$	−19.0895	−	52.3576i	−0.640602	−	1.75701i
$889$	−10.4449			−0.350312
$890$	41.0318	−	14.2741i	1.37539	−	0.478469i
$891$	2.97912			0.0998042
$892$		−	74.6786i		−	2.50043i
$893$	20.2623			0.678051
$894$			16.3721i			0.547565i
$895$	32.2310	−	11.2125i	1.07736	−	0.374791i
$896$			42.0951i			1.40630i
$897$		−	12.5292i		−	0.418339i
$898$			29.3958i			0.980949i
$899$	58.5234			1.95187
$900$	21.0681	−	16.6765i	0.702271	−	0.555882i
$901$		−	18.5667i		−	0.618545i
$902$	−6.18937			−0.206083
$903$	−3.61074			−0.120158
$904$	−30.0082			−0.998058
$905$	−1.62513	−	4.67154i	−0.0540211	−	0.155287i
$906$			45.1385i			1.49963i
$907$	−49.2354			−1.63484			−0.817418	−	0.576046i	$-0.804595\pi$
$907$	−49.2354			−1.63484			−0.817418	+	0.576046i	$0.804595\pi$
$908$	−104.138			−3.45593
$909$	−14.5422			−0.482335
$910$	−41.2298	+	14.3430i	−1.36676	+	0.475464i
$911$			52.8697i			1.75165i	0.482627	+	0.875826i	$0.339683\pi$
$911$			52.8697i			1.75165i	−0.482627	+	0.875826i	$0.660317\pi$
$912$	115.344			3.81941
$913$			18.7065i			0.619093i
$914$	25.3459			0.838366
$915$	−8.30071	−	23.8610i	−0.274413	−	0.788819i
$916$	−40.8755			−1.35056
$917$	−7.94466			−0.262356
$918$			14.1042i			0.465508i
$919$		−	43.6488i		−	1.43984i	−0.694056	−	0.719921i	$-0.744178\pi$
$919$		−	43.6488i		−	1.43984i	0.694056	−	0.719921i	$-0.255822\pi$
$920$	15.9313	+	45.7956i	0.525239	+	1.50983i
$921$	27.1188			0.893596
$922$			16.1975i			0.533437i
$923$	−41.1631			−1.35490
$924$	21.7421			0.715262
$925$	−15.9386	+	25.9029i	−0.524058	+	0.851683i
$926$	−97.0982			−3.19084
$927$	−4.71423			−0.154836
$928$			168.044i			5.51632i
$929$	−32.2873			−1.05931			−0.529656	−	0.848213i	$-0.677679\pi$
$929$	−32.2873			−1.05931			−0.529656	+	0.848213i	$0.677679\pi$
$930$	13.9301	+	40.0430i	0.456785	+	1.31306i
$931$		−	42.0826i		−	1.37920i
$932$			143.840i			4.71164i
$933$	−7.37607			−0.241482
$934$	−1.56370			−0.0511657
$935$	11.3682	+	32.6788i	0.371781	+	1.06871i
$936$	48.4999			1.58527
$937$		−	20.2761i		−	0.662391i	−0.943562	−	0.331196i	$-0.892548\pi$
$937$		−	20.2761i		−	0.662391i	0.943562	−	0.331196i	$-0.107452\pi$
$938$	10.7991			0.352602
$939$		−	20.2055i		−	0.659382i
$940$	−28.1731	+	9.80081i	−0.918906	+	0.319667i
$941$	55.6176			1.81308			0.906541	−	0.422117i	$-0.138713\pi$
$941$	55.6176			1.81308			0.906541	+	0.422117i	$0.138713\pi$
$942$	31.3827			1.02250
$943$	−1.81082			−0.0589683
$944$		−	2.29640i		−	0.0747415i
$945$	−0.997769	−	2.86815i	−0.0324574	−	0.0933011i
$946$	21.5084			0.699299
$947$	−22.9741			−0.746558			−0.373279	−	0.927719i	$-0.621767\pi$
$947$	−22.9741			−0.746558			−0.373279	+	0.927719i	$0.621767\pi$
$948$	−57.3293			−1.86197
$949$			9.62628i			0.312482i
$950$	−68.7835	−	86.8973i	−2.23163	−	2.81932i
$951$	8.25242			0.267603
$952$			64.6255i			2.09453i
$953$		−	39.0708i		−	1.26563i	−0.774304	−	0.632813i	$-0.781900\pi$
$953$		−	39.0708i		−	1.26563i	0.774304	−	0.632813i	$-0.218100\pi$
$954$		−	9.70696i		−	0.314274i
$955$	48.1461	−	16.7490i	1.55797	−	0.541984i
$956$		−	55.3389i		−	1.78979i
$957$	24.9700			0.807165
$958$		−	28.8857i		−	0.933255i
$959$	−15.6951			−0.506821
$960$	−55.2922	+	19.2349i	−1.78455	+	0.620805i
$961$	−17.7526			−0.572666
$962$	−82.1501	+	29.9518i	−2.64862	+	0.965685i
$963$		−	3.63552i		−	0.117153i
$964$		−	104.245i		−	3.35749i
$965$	−14.7861	−	42.5037i	−0.475982	−	1.36824i
$966$	8.72844			0.280833
$967$	44.8354			1.44181			0.720904	−	0.693035i	$-0.243727\pi$
$967$	44.8354			1.44181			0.720904	+	0.693035i	$0.243727\pi$
$968$	19.4675			0.625709
$969$	42.3956			1.36194
$970$	18.7315	+	53.8449i	0.601431	+	1.72886i
$971$	42.5845			1.36660			0.683301	−	0.730137i	$-0.260544\pi$
$971$	42.5845			1.36660			0.683301	+	0.730137i	$0.260544\pi$
$972$			5.37390i			0.172368i
$973$		−	12.8391i		−	0.411602i
$974$	−0.495046			−0.0158623
$975$	−16.4276	−	20.7538i	−0.526105	−	0.664652i
$976$			159.655i			5.11043i
$977$	−40.3923			−1.29226			−0.646132	−	0.763226i	$-0.723615\pi$
$977$	−40.3923			−1.29226			−0.646132	+	0.763226i	$0.723615\pi$
$978$			7.65962i			0.244927i
$979$			21.3148i			0.681225i
$980$	20.3553	+	58.5126i	0.650225	+	1.86912i
$981$		−	8.22404i		−	0.262573i
$982$	−24.2273			−0.773123
$983$			21.7910i			0.695024i	0.937676	+	0.347512i	$0.112973\pi$
$983$			21.7910i			0.695024i	−0.937676	+	0.347512i	$0.887027\pi$
$984$		−	7.00956i		−	0.223457i
$985$	18.7344	−	6.51731i	0.596929	−	0.207659i
$986$			118.217i			3.76479i
$987$			3.37125i			0.107308i
$988$		−	232.205i		−	7.38742i
$989$	6.29269			0.200096
$990$	5.94350	+	17.0850i	0.188897	+	0.542997i
$991$		−	10.7251i		−	0.340694i	−0.985384	−	0.170347i	$-0.945511\pi$
$991$		−	10.7251i		−	0.340694i	0.985384	−	0.170347i	$-0.0544889\pi$
$992$		−	139.988i		−	4.44463i
$993$	−15.0653			−0.478084
$994$		−	28.6761i		−	0.909551i
$995$	−19.7400	+	6.86713i	−0.625801	+	0.217703i
$996$	−33.7437			−1.06921
$997$	−22.1046			−0.700059			−0.350029	−	0.936739i	$-0.613828\pi$
$997$	−22.1046			−0.700059			−0.350029	+	0.936739i	$0.613828\pi$
$998$			76.5214i			2.42224i
$999$	−2.08360	−	5.71477i	−0.0659221	−	0.180807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.g.a.184.2	yes	40
3.2	odd	2		1665.2.g.e.739.40		40
5.4	even	2	inner	555.2.g.a.184.39	yes	40
15.14	odd	2		1665.2.g.e.739.1		40
37.36	even	2	inner	555.2.g.a.184.40	yes	40
111.110	odd	2		1665.2.g.e.739.2		40
185.184	even	2	inner	555.2.g.a.184.1	✓	40
555.554	odd	2		1665.2.g.e.739.39		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.g.a.184.1	✓	40	185.184	even	2	inner
555.2.g.a.184.2	yes	40	1.1	even	1	trivial
555.2.g.a.184.39	yes	40	5.4	even	2	inner
555.2.g.a.184.40	yes	40	37.36	even	2	inner
1665.2.g.e.739.1		40	15.14	odd	2
1665.2.g.e.739.2		40	111.110	odd	2
1665.2.g.e.739.39		40	555.554	odd	2
1665.2.g.e.739.40		40	3.2	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:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.71549 q^{2} +1.00000i q^{3} +5.37390 q^{4} +(0.734693 + 2.11192i) q^{5} -2.71549i q^{6} -1.35808i q^{7} -9.16180 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.71549 q^{2} +1.00000i q^{3} +5.37390 q^{4} +(0.734693 + 2.11192i) q^{5} -2.71549i q^{6} -1.35808i q^{7} -9.16180 q^{8} -1.00000 q^{9} +(-1.99505 - 5.73492i) q^{10} +2.97912 q^{11} +5.37390i q^{12} +5.29371 q^{13} +3.68784i q^{14} +(-2.11192 + 0.734693i) q^{15} +14.1310 q^{16} +5.19397 q^{17} +2.71549 q^{18} -8.16246i q^{19} +(3.94816 + 11.3493i) q^{20} +1.35808 q^{21} -8.08977 q^{22} -2.36681 q^{23} -9.16180i q^{24} +(-3.92045 + 3.10323i) q^{25} -14.3750 q^{26} -1.00000i q^{27} -7.29816i q^{28} -8.38167i q^{29} +(5.73492 - 1.99505i) q^{30} +6.98231i q^{31} -20.0490 q^{32} +2.97912i q^{33} -14.1042 q^{34} +(2.86815 - 0.997769i) q^{35} -5.37390 q^{36} +(5.71477 - 2.08360i) q^{37} +22.1651i q^{38} +5.29371i q^{39} +(-6.73111 - 19.3490i) q^{40} +0.765086 q^{41} -3.68784 q^{42} -2.65872 q^{43} +16.0095 q^{44} +(-0.734693 - 2.11192i) q^{45} +6.42707 q^{46} +2.48237i q^{47} +14.1310i q^{48} +5.15563 q^{49} +(10.6460 - 8.42680i) q^{50} +5.19397i q^{51} +28.4479 q^{52} -3.57466i q^{53} +2.71549i q^{54} +(2.18874 + 6.29167i) q^{55} +12.4424i q^{56} +8.16246 q^{57} +22.7604i q^{58} -0.162508i q^{59} +(-11.3493 + 3.94816i) q^{60} +11.2982i q^{61} -18.9604i q^{62} +1.35808i q^{63} +26.1809 q^{64} +(3.88925 + 11.1799i) q^{65} -8.08977i q^{66} -2.92828i q^{67} +27.9119 q^{68} -2.36681i q^{69} +(-7.78845 + 2.70943i) q^{70} -7.77585 q^{71} +9.16180 q^{72} +1.81844i q^{73} +(-15.5184 + 5.65800i) q^{74} +(-3.10323 - 3.92045i) q^{75} -43.8643i q^{76} -4.04587i q^{77} -14.3750i q^{78} +10.6681i q^{79} +(10.3819 + 29.8436i) q^{80} +1.00000 q^{81} -2.07758 q^{82} +6.27919i q^{83} +7.29816 q^{84} +(3.81597 + 10.9693i) q^{85} +7.21972 q^{86} +8.38167 q^{87} -27.2941 q^{88} +7.15474i q^{89} +(1.99505 + 5.73492i) q^{90} -7.18926i q^{91} -12.7190 q^{92} -6.98231 q^{93} -6.74086i q^{94} +(17.2385 - 5.99690i) q^{95} -20.0490i q^{96} -9.38896 q^{97} -14.0001 q^{98} -2.97912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) \) 40 * q + 44 * q^4 - 40 * q^9	\( 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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