LMFDB - Embedded newform 354.3.b.a.119.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,3,Mod(119,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.119");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	354.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.64580135835$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.18
Character	$\chi$	$=$	354.119
Dual form			354.3.b.a.119.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(2.68322 + 1.34177i) q^{3} -2.00000 q^{4} -2.14890i q^{5} +(1.89755 - 3.79464i) q^{6} +6.97234 q^{7} +2.82843i q^{8} +(5.39932 + 7.20051i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(2.68322 + 1.34177i) q^{3} -2.00000 q^{4} -2.14890i q^{5} +(1.89755 - 3.79464i) q^{6} +6.97234 q^{7} +2.82843i q^{8} +(5.39932 + 7.20051i) q^{9} -3.03900 q^{10} +7.24220i q^{11} +(-5.36644 - 2.68354i) q^{12} +14.9487 q^{13} -9.86037i q^{14} +(2.88332 - 5.76597i) q^{15} +4.00000 q^{16} +13.0567i q^{17} +(10.1831 - 7.63579i) q^{18} -24.8098 q^{19} +4.29780i q^{20} +(18.7083 + 9.35525i) q^{21} +10.2420 q^{22} -34.0644i q^{23} +(-3.79509 + 7.58929i) q^{24} +20.3822 q^{25} -21.1406i q^{26} +(4.82614 + 26.5652i) q^{27} -13.9447 q^{28} -44.6957i q^{29} +(-8.15431 - 4.07764i) q^{30} +46.3333 q^{31} -5.65685i q^{32} +(-9.71735 + 19.4324i) q^{33} +18.4650 q^{34} -14.9829i q^{35} +(-10.7986 - 14.4010i) q^{36} -35.4075 q^{37} +35.0864i q^{38} +(40.1105 + 20.0576i) q^{39} +6.07801 q^{40} +35.3328i q^{41} +(13.2303 - 26.4575i) q^{42} +81.6137 q^{43} -14.4844i q^{44} +(15.4732 - 11.6026i) q^{45} -48.1744 q^{46} +70.1295i q^{47} +(10.7329 + 5.36707i) q^{48} -0.386534 q^{49} -28.8248i q^{50} +(-17.5191 + 35.0340i) q^{51} -29.8973 q^{52} -35.4472i q^{53} +(37.5688 - 6.82519i) q^{54} +15.5628 q^{55} +19.7207i q^{56} +(-66.5701 - 33.2890i) q^{57} -63.2092 q^{58} -7.68115i q^{59} +(-5.76665 + 11.5319i) q^{60} -42.7396 q^{61} -65.5252i q^{62} +(37.6459 + 50.2044i) q^{63} -8.00000 q^{64} -32.1232i q^{65} +(27.4816 + 13.7424i) q^{66} -131.858 q^{67} -26.1134i q^{68} +(45.7066 - 91.4023i) q^{69} -21.1890 q^{70} -128.718i q^{71} +(-20.3661 + 15.2716i) q^{72} -67.8681 q^{73} +50.0738i q^{74} +(54.6900 + 27.3482i) q^{75} +49.6196 q^{76} +50.4950i q^{77} +(28.3658 - 56.7248i) q^{78} -31.1503 q^{79} -8.59560i q^{80} +(-22.6947 + 77.7557i) q^{81} +49.9681 q^{82} -30.8474i q^{83} +(-37.4166 - 18.7105i) q^{84} +28.0576 q^{85} -115.419i q^{86} +(59.9712 - 119.928i) q^{87} -20.4840 q^{88} +148.420i q^{89} +(-16.4085 - 21.8824i) q^{90} +104.227 q^{91} +68.1289i q^{92} +(124.322 + 62.1686i) q^{93} +99.1782 q^{94} +53.3138i q^{95} +(7.59018 - 15.1786i) q^{96} -118.098 q^{97} +0.546642i q^{98} +(-52.1475 + 39.1029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	2.68322	+	1.34177i	0.894406	+	0.447256i
$3$	2.68322	+	1.34177i	0.894406	+	0.447256i
$4$	−2.00000			−0.500000
$5$		−	2.14890i		−	0.429780i	−0.976638	−	0.214890i	$-0.931061\pi$
$5$		−	2.14890i		−	0.429780i	0.976638	−	0.214890i	$-0.0689393\pi$
$6$	1.89755	−	3.79464i	0.316258	−	0.632441i
$7$	6.97234			0.996048			0.498024	−	0.867163i	$-0.334059\pi$
$7$	6.97234			0.996048			0.498024	+	0.867163i	$0.334059\pi$
$8$			2.82843i			0.353553i
$9$	5.39932	+	7.20051i	0.599924	+	0.800057i
$10$	−3.03900			−0.303900
$11$			7.24220i			0.658382i	0.944263	+	0.329191i	$0.106776\pi$
$11$			7.24220i			0.658382i	−0.944263	+	0.329191i	$0.893224\pi$
$12$	−5.36644	−	2.68354i	−0.447203	−	0.223628i
$13$	14.9487			1.14990			0.574949	−	0.818190i	$-0.305022\pi$
$13$	14.9487			1.14990			0.574949	+	0.818190i	$0.305022\pi$
$14$		−	9.86037i		−	0.704312i
$15$	2.88332	−	5.76597i	0.192222	−	0.384398i
$16$	4.00000			0.250000
$17$			13.0567i			0.768042i	0.923324	+	0.384021i	$0.125461\pi$
$17$			13.0567i			0.768042i	−0.923324	+	0.384021i	$0.874539\pi$
$18$	10.1831	−	7.63579i	0.565726	−	0.424211i
$19$	−24.8098			−1.30578			−0.652890	−	0.757453i	$-0.726444\pi$
$19$	−24.8098			−1.30578			−0.652890	+	0.757453i	$0.726444\pi$
$20$			4.29780i			0.214890i
$21$	18.7083	+	9.35525i	0.890871	+	0.445488i
$22$	10.2420			0.465546
$23$		−	34.0644i		−	1.48106i	−0.672022	−	0.740531i	$-0.734574\pi$
$23$		−	34.0644i		−	1.48106i	0.672022	−	0.740531i	$-0.265426\pi$
$24$	−3.79509	+	7.58929i	−0.158129	+	0.316220i
$25$	20.3822			0.815289
$26$		−	21.1406i		−	0.813100i
$27$	4.82614	+	26.5652i	0.178746	+	0.983895i
$28$	−13.9447			−0.498024
$29$		−	44.6957i		−	1.54123i	−0.637301	−	0.770615i	$-0.719949\pi$
$29$		−	44.6957i		−	1.54123i	0.637301	−	0.770615i	$-0.280051\pi$
$30$	−8.15431	−	4.07764i	−0.271810	−	0.135921i
$31$	46.3333			1.49462			0.747312	−	0.664473i	$-0.231344\pi$
$31$	46.3333			1.49462			0.747312	+	0.664473i	$0.231344\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−9.71735	+	19.4324i	−0.294465	+	0.588861i
$34$	18.4650			0.543087
$35$		−	14.9829i		−	0.428081i
$36$	−10.7986	−	14.4010i	−0.299962	−	0.400028i
$37$	−35.4075			−0.956960			−0.478480	−	0.878099i	$-0.658812\pi$
$37$	−35.4075			−0.956960			−0.478480	+	0.878099i	$0.658812\pi$
$38$			35.0864i			0.923326i
$39$	40.1105	+	20.0576i	1.02848	+	0.514298i
$40$	6.07801			0.151950
$41$			35.3328i			0.861775i	0.902406	+	0.430888i	$0.141799\pi$
$41$			35.3328i			0.861775i	−0.902406	+	0.430888i	$0.858201\pi$
$42$	13.2303	−	26.4575i	0.315008	−	0.629941i
$43$	81.6137			1.89799			0.948996	−	0.315287i	$-0.102101\pi$
$43$	81.6137			1.89799			0.948996	+	0.315287i	$0.102101\pi$
$44$		−	14.4844i		−	0.329191i
$45$	15.4732	−	11.6026i	0.343848	−	0.257835i
$46$	−48.1744			−1.04727
$47$			70.1295i			1.49212i	0.665880	+	0.746059i	$0.268056\pi$
$47$			70.1295i			1.49212i	−0.665880	+	0.746059i	$0.731944\pi$
$48$	10.7329	+	5.36707i	0.223602	+	0.111814i
$49$	−0.386534			−0.00788845
$50$		−	28.8248i		−	0.576497i
$51$	−17.5191	+	35.0340i	−0.343511	+	0.686941i
$52$	−29.8973			−0.574949
$53$		−	35.4472i		−	0.668815i	−0.942429	−	0.334408i	$-0.891464\pi$
$53$		−	35.4472i		−	0.668815i	0.942429	−	0.334408i	$-0.108536\pi$
$54$	37.5688	−	6.82519i	0.695719	−	0.126392i
$55$	15.5628			0.282959
$56$			19.7207i			0.352156i
$57$	−66.5701	−	33.2890i	−1.16790	−	0.584018i
$58$	−63.2092			−1.08981
$59$		−	7.68115i		−	0.130189i
$59$		−	7.68115i		−	0.130189i
$60$	−5.76665	+	11.5319i	−0.0961108	+	0.192199i
$61$	−42.7396			−0.700649			−0.350325	−	0.936628i	$-0.613929\pi$
$61$	−42.7396			−0.700649			−0.350325	+	0.936628i	$0.613929\pi$
$62$		−	65.5252i		−	1.05686i
$63$	37.6459	+	50.2044i	0.597553	+	0.796895i
$64$	−8.00000			−0.125000
$65$		−	32.1232i		−	0.494203i
$66$	27.4816	+	13.7424i	0.416387	+	0.208218i
$67$	−131.858			−1.96803			−0.984014	−	0.178093i	$-0.943007\pi$
$67$	−131.858			−1.96803			−0.984014	+	0.178093i	$0.943007\pi$
$68$		−	26.1134i		−	0.384021i
$69$	45.7066	−	91.4023i	0.662414	−	1.32467i
$70$	−21.1890			−0.302699
$71$		−	128.718i		−	1.81293i	−0.422283	−	0.906464i	$-0.638771\pi$
$71$		−	128.718i		−	1.81293i	0.422283	−	0.906464i	$-0.361229\pi$
$72$	−20.3661	+	15.2716i	−0.282863	+	0.212105i
$73$	−67.8681			−0.929700			−0.464850	−	0.885389i	$-0.653892\pi$
$73$	−67.8681			−0.929700			−0.464850	+	0.885389i	$0.653892\pi$
$74$			50.0738i			0.676673i
$75$	54.6900	+	27.3482i	0.729200	+	0.364643i
$76$	49.6196			0.652890
$77$			50.4950i			0.655780i
$78$	28.3658	−	56.7248i	0.363664	−	0.727242i
$79$	−31.1503			−0.394307			−0.197154	−	0.980373i	$-0.563170\pi$
$79$	−31.1503			−0.394307			−0.197154	+	0.980373i	$0.563170\pi$
$80$		−	8.59560i		−	0.107445i
$81$	−22.6947	+	77.7557i	−0.280182	+	0.959947i
$82$	49.9681			0.609367
$83$		−	30.8474i		−	0.371656i	−0.982582	−	0.185828i	$-0.940503\pi$
$83$		−	30.8474i		−	0.371656i	0.982582	−	0.185828i	$-0.0594967\pi$
$84$	−37.4166	−	18.7105i	−0.445436	−	0.222744i
$85$	28.0576			0.330089
$86$		−	115.419i		−	1.34208i
$87$	59.9712	−	119.928i	0.689324	−	1.37849i
$88$	−20.4840			−0.232773
$89$			148.420i			1.66764i	0.552038	+	0.833819i	$0.313850\pi$
$89$			148.420i			1.66764i	−0.552038	+	0.833819i	$0.686150\pi$
$90$	−16.4085	−	21.8824i	−0.182317	−	0.243137i
$91$	104.227			1.14535
$92$			68.1289i			0.740531i
$93$	124.322	+	62.1686i	1.33680	+	0.668479i
$94$	99.1782			1.05509
$95$			53.3138i			0.561198i
$96$	7.59018	−	15.1786i	0.0790644	−	0.158110i
$97$	−118.098			−1.21751			−0.608754	−	0.793359i	$-0.708331\pi$
$97$	−118.098			−1.21751			−0.608754	+	0.793359i	$0.708331\pi$
$98$			0.546642i			0.00557798i
$99$	−52.1475	+	39.1029i	−0.526743	+	0.394979i
$100$	−40.7645			−0.407645
$101$		−	13.3653i		−	0.132330i	−0.997809	−	0.0661650i	$-0.978924\pi$
$101$		−	13.3653i		−	0.132330i	0.997809	−	0.0661650i	$-0.0210764\pi$
$102$	49.5456	+	24.7757i	0.485741	+	0.242899i
$103$	−156.764			−1.52198			−0.760991	−	0.648763i	$-0.775287\pi$
$103$	−156.764			−1.52198			−0.760991	+	0.648763i	$0.775287\pi$
$104$			42.2812i			0.406550i
$105$	20.1035	−	40.2023i	0.191462	−	0.382879i
$106$	−50.1299			−0.472924
$107$			90.8546i			0.849108i	0.905403	+	0.424554i	$0.139569\pi$
$107$			90.8546i			0.849108i	−0.905403	+	0.424554i	$0.860431\pi$
$108$	−9.65228	−	53.1303i	−0.0893730	−	0.491948i
$109$	−88.9548			−0.816099			−0.408049	−	0.912960i	$-0.633791\pi$
$109$	−88.9548			−0.816099			−0.408049	+	0.912960i	$0.633791\pi$
$110$		−	22.0091i		−	0.200082i
$111$	−95.0061	−	47.5086i	−0.855911	−	0.428006i
$112$	27.8893			0.249012
$113$			32.5850i			0.288363i	0.989551	+	0.144182i	$0.0460549\pi$
$113$			32.5850i			0.288363i	−0.989551	+	0.144182i	$0.953945\pi$
$114$	−47.0778	+	94.1444i	−0.412963	+	0.825828i
$115$	−73.2011			−0.636531
$116$			89.3913i			0.770615i
$117$	80.7126	+	107.638i	0.689851	+	0.919983i
$118$	−10.8628			−0.0920575
$119$			91.0358i			0.765006i
$120$	16.3086	+	8.15527i	0.135905	+	0.0679606i
$121$	68.5506			0.566534
$122$			60.4429i			0.495434i
$123$	−47.4084	+	94.8056i	−0.385434	+	0.770777i
$124$	−92.6667			−0.747312
$125$		−	97.5219i		−	0.780175i
$126$	70.9997	−	53.2393i	0.563490	−	0.422534i
$127$	15.6903			0.123546			0.0617728	−	0.998090i	$-0.480325\pi$
$127$	15.6903			0.123546			0.0617728	+	0.998090i	$0.480325\pi$
$128$			11.3137i			0.0883883i
$129$	218.987	+	109.507i	1.69758	+	0.848888i
$130$	−45.4290			−0.349454
$131$		−	169.864i		−	1.29667i	−0.761354	−	0.648337i	$-0.775465\pi$
$131$		−	169.864i		−	1.29667i	0.761354	−	0.648337i	$-0.224535\pi$
$132$	19.4347	−	38.8648i	0.147233	−	0.294430i
$133$	−172.982			−1.30062
$134$			186.475i			1.39161i
$135$	57.0859	−	10.3709i	0.422858	−	0.0768214i
$136$	−36.9299			−0.271544
$137$		−	4.55507i		−	0.0332487i	−0.999862	−	0.0166243i	$-0.994708\pi$
$137$		−	4.55507i		−	0.0332487i	0.999862	−	0.0166243i	$-0.00529193\pi$
$138$	−129.262	−	64.6388i	−0.936684	−	0.468397i
$139$	−89.7771			−0.645879			−0.322939	−	0.946420i	$-0.604671\pi$
$139$	−89.7771			−0.645879			−0.322939	+	0.946420i	$0.604671\pi$
$140$			29.9657i			0.214041i
$141$	−94.0976	+	188.173i	−0.667359	+	1.33456i
$142$	−182.035			−1.28193
$143$			108.261i			0.757071i
$144$	21.5973	+	28.8020i	0.149981	+	0.200014i
$145$	−96.0465			−0.662390
$146$			95.9800i			0.657397i
$147$	−1.03716	−	0.518639i	−0.00705548	−	0.00352816i
$148$	70.8150			0.478480
$149$			32.1885i			0.216030i	0.994149	+	0.108015i	$0.0344495\pi$
$149$			32.1885i			0.216030i	−0.994149	+	0.108015i	$0.965550\pi$
$150$	38.6762	−	77.3433i	0.257841	−	0.515622i
$151$	29.3995			0.194699			0.0973493	−	0.995250i	$-0.468964\pi$
$151$	29.3995			0.194699			0.0973493	+	0.995250i	$0.468964\pi$
$152$		−	70.1727i		−	0.461663i
$153$	−94.0150	+	70.4973i	−0.614477	+	0.460767i
$154$	71.4108			0.463706
$155$		−	99.5657i		−	0.642359i
$156$	−80.2211	−	40.1153i	−0.514238	−	0.257149i
$157$	−19.0915			−0.121602			−0.0608009	−	0.998150i	$-0.519365\pi$
$157$	−19.0915			−0.121602			−0.0608009	+	0.998150i	$0.519365\pi$
$158$			44.0531i			0.278817i
$159$	47.5619	−	95.1126i	0.299132	−	0.598192i
$160$	−12.1560			−0.0759751
$161$		−	237.509i		−	1.47521i
$162$	109.963	+	32.0952i	0.678785	+	0.198118i
$163$	93.8678			0.575876			0.287938	−	0.957649i	$-0.407030\pi$
$163$	93.8678			0.575876			0.287938	+	0.957649i	$0.407030\pi$
$164$		−	70.6656i		−	0.430888i
$165$	41.7583	+	20.8816i	0.253080	+	0.126555i
$166$	−43.6248			−0.262800
$167$			213.266i			1.27704i	0.769604	+	0.638522i	$0.220454\pi$
$167$			213.266i			1.27704i	−0.769604	+	0.638522i	$0.779546\pi$
$168$	−26.4607	+	52.9151i	−0.157504	+	0.314971i
$169$	54.4625			0.322264
$170$		−	39.6794i		−	0.233408i
$171$	−133.956	−	178.643i	−0.783369	−	1.04470i
$172$	−163.227			−0.948996
$173$			173.582i			1.00336i	0.865052	+	0.501682i	$0.167285\pi$
$173$			173.582i			1.00336i	−0.865052	+	0.501682i	$0.832715\pi$
$174$	−169.604	−	84.8121i	−0.974736	−	0.487426i
$175$	142.112			0.812067
$176$			28.9688i			0.164595i
$177$	10.3063	−	20.6102i	0.0582278	−	0.116442i
$178$	209.897			1.17920
$179$			11.5657i			0.0646131i	0.999478	+	0.0323066i	$0.0102853\pi$
$179$			11.5657i			0.0646131i	−0.999478	+	0.0323066i	$0.989715\pi$
$180$	−30.9464	+	23.2052i	−0.171924	+	0.128918i
$181$	−25.8189			−0.142646			−0.0713228	−	0.997453i	$-0.522722\pi$
$181$	−25.8189			−0.142646			−0.0713228	+	0.997453i	$0.522722\pi$
$182$		−	147.399i		−	0.809887i
$183$	−114.680	−	57.3466i	−0.626665	−	0.313370i
$184$	96.3488			0.523635
$185$			76.0872i			0.411282i
$186$	87.9196	−	175.818i	0.472686	−	0.945261i
$187$	−94.5593			−0.505665
$188$		−	140.259i		−	0.746059i
$189$	33.6495	+	185.221i	0.178039	+	0.980007i
$190$	75.3971			0.396827
$191$		−	215.927i		−	1.13051i	−0.824916	−	0.565255i	$-0.808778\pi$
$191$		−	215.927i		−	1.13051i	0.824916	−	0.565255i	$-0.191222\pi$
$192$	−21.4657	−	10.7341i	−0.111801	−	0.0559070i
$193$	354.576			1.83718			0.918591	−	0.395208i	$-0.129328\pi$
$193$	354.576			1.83718			0.918591	+	0.395208i	$0.129328\pi$
$194$			167.016i			0.860909i
$195$	43.1018	−	86.1935i	0.221035	−	0.442018i
$196$	0.773068			0.00394423
$197$			146.752i			0.744932i	0.928046	+	0.372466i	$0.121488\pi$
$197$			146.752i			0.744932i	−0.928046	+	0.372466i	$0.878512\pi$
$198$	55.2999	+	73.7477i	0.279292	+	0.372463i
$199$	159.523			0.801622			0.400811	−	0.916161i	$-0.368728\pi$
$199$	159.523			0.801622			0.400811	+	0.916161i	$0.368728\pi$
$200$			57.6497i			0.288248i
$201$	−353.803	−	176.923i	−1.76022	−	0.880212i
$202$	−18.9014			−0.0935714
$203$		−	311.633i		−	1.53514i
$204$	35.0381	−	70.0680i	0.171756	−	0.343471i
$205$	75.9266			0.370374
$206$			221.698i			1.07620i
$207$	245.281	−	183.925i	1.18493	−	0.888525i
$208$	59.7947			0.287474
$209$		−	179.678i		−	0.859701i
$210$	−56.8546	−	28.4306i	−0.270736	−	0.135384i
$211$	−157.695			−0.747369			−0.373685	−	0.927556i	$-0.621906\pi$
$211$	−157.695			−0.747369			−0.373685	+	0.927556i	$0.621906\pi$
$212$			70.8944i			0.334408i
$213$	172.709	−	345.378i	0.810843	−	1.62149i
$214$	128.488			0.600410
$215$		−	175.380i		−	0.815719i
$216$	−75.1377	+	13.6504i	−0.347860	+	0.0631962i
$217$	323.052			1.48872
$218$			125.801i			0.577069i
$219$	−182.105	−	91.0632i	−0.831529	−	0.415814i
$220$	−31.1255			−0.141480
$221$			195.180i			0.883169i
$222$	−67.1874	+	134.359i	−0.302646	+	0.605220i
$223$	−113.488			−0.508917			−0.254458	−	0.967084i	$-0.581897\pi$
$223$	−113.488			−0.508917			−0.254458	+	0.967084i	$0.581897\pi$
$224$		−	39.4415i		−	0.176078i
$225$	110.050	+	146.762i	0.489112	+	0.652278i
$226$	46.0822			0.203903
$227$		−	279.527i		−	1.23140i	−0.787981	−	0.615699i	$-0.788874\pi$
$227$		−	279.527i		−	1.23140i	0.787981	−	0.615699i	$-0.211126\pi$
$228$	133.140	+	66.5780i	0.583949	+	0.292009i
$229$	347.376			1.51693			0.758463	−	0.651716i	$-0.225950\pi$
$229$	347.376			1.51693			0.758463	+	0.651716i	$0.225950\pi$
$230$			103.522i			0.450095i
$231$	−67.7526	+	135.489i	−0.293301	+	0.586533i
$232$	126.418			0.544907
$233$		−	189.738i		−	0.814326i	−0.913356	−	0.407163i	$-0.866518\pi$
$233$		−	189.738i		−	0.814326i	0.913356	−	0.407163i	$-0.133482\pi$
$234$	152.223	−	114.145i	0.650526	−	0.487799i
$235$	150.701			0.641282
$236$			15.3623i			0.0650945i
$237$	−83.5830	−	41.7964i	−0.352671	−	0.176356i
$238$	128.744			0.540941
$239$		−	235.032i		−	0.983398i	−0.870765	−	0.491699i	$-0.836376\pi$
$239$		−	235.032i		−	0.983398i	0.870765	−	0.491699i	$-0.163624\pi$
$240$	11.5333	−	23.0639i	0.0480554	−	0.0960994i
$241$	−244.500			−1.01452			−0.507261	−	0.861792i	$-0.669342\pi$
$241$	−244.500			−1.01452			−0.507261	+	0.861792i	$0.669342\pi$
$242$		−	96.9451i		−	0.400600i
$243$	−165.225	+	178.185i	−0.679938	+	0.733270i
$244$	85.4792			0.350325
$245$			0.830623i			0.00339030i
$246$	134.075	+	67.0456i	0.545022	+	0.272543i
$247$	−370.874			−1.50151
$248$			131.050i			0.528429i
$249$	41.3901	−	82.7704i	0.166225	−	0.332411i
$250$	−137.917			−0.551667
$251$		−	380.927i		−	1.51764i	−0.651303	−	0.758818i	$-0.725777\pi$
$251$		−	380.927i		−	1.51764i	0.651303	−	0.758818i	$-0.274223\pi$
$252$	−75.2917	−	100.409i	−0.298777	−	0.398447i
$253$	246.701			0.975104
$254$		−	22.1894i		−	0.0873599i
$255$	75.2845	+	37.6467i	0.295234	+	0.147634i
$256$	16.0000			0.0625000
$257$		−	147.684i		−	0.574647i	−0.957834	−	0.287323i	$-0.907235\pi$
$257$		−	147.684i		−	0.574647i	0.957834	−	0.287323i	$-0.0927655\pi$
$258$	154.866	−	309.695i	0.600255	−	1.20037i
$259$	−246.873			−0.953178
$260$			64.2464i			0.247101i
$261$	321.832	−	241.326i	1.23307	−	0.924621i
$262$	−240.224			−0.916887
$263$		−	81.5016i		−	0.309892i	−0.987923	−	0.154946i	$-0.950480\pi$
$263$		−	81.5016i		−	0.309892i	0.987923	−	0.154946i	$-0.0495204\pi$
$264$	−54.9631	−	27.4848i	−0.208194	−	0.104109i
$265$	−76.1725			−0.287443
$266$			244.634i			0.919677i
$267$	−199.145	+	398.243i	−0.745861	+	1.49155i
$268$	263.716			0.984014
$269$		−	54.7584i		−	0.203563i	−0.994807	−	0.101781i	$-0.967546\pi$
$269$		−	54.7584i		−	0.203563i	0.994807	−	0.101781i	$-0.0324542\pi$
$270$	−14.6667	−	80.7316i	−0.0543209	−	0.299006i
$271$	−15.4584			−0.0570422			−0.0285211	−	0.999593i	$-0.509080\pi$
$271$	−15.4584			−0.0570422			−0.0285211	+	0.999593i	$0.509080\pi$
$272$			52.2268i			0.192010i
$273$	279.664	+	139.849i	1.02441	+	0.512266i
$274$	−6.44184			−0.0235104
$275$			147.612i			0.536771i
$276$	−91.4131	+	182.805i	−0.331207	+	0.662336i
$277$	−324.980			−1.17321			−0.586606	−	0.809873i	$-0.699536\pi$
$277$	−324.980			−1.17321			−0.586606	+	0.809873i	$0.699536\pi$
$278$			126.964i			0.456705i
$279$	250.168	+	333.624i	0.896661	+	1.19578i
$280$	42.3779			0.151350
$281$			268.830i			0.956689i	0.878172	+	0.478344i	$0.158763\pi$
$281$			268.830i			0.956689i	−0.878172	+	0.478344i	$0.841237\pi$
$282$	266.117	+	133.074i	0.943676	+	0.471894i
$283$	−194.724			−0.688072			−0.344036	−	0.938956i	$-0.611794\pi$
$283$	−194.724			−0.688072			−0.344036	+	0.938956i	$0.611794\pi$
$284$			257.436i			0.906464i
$285$	−71.5347	+	143.053i	−0.250999	+	0.501939i
$286$	153.104			0.535330
$287$			246.352i			0.858369i
$288$	40.7322	−	30.5432i	0.141431	−	0.106053i
$289$	118.522			0.410112
$290$			135.830i			0.468380i
$291$	−316.884	−	158.461i	−1.08895	−	0.544538i
$292$	135.736			0.464850
$293$		−	137.927i		−	0.470741i	−0.971906	−	0.235370i	$-0.924370\pi$
$293$		−	137.927i		−	0.470741i	0.971906	−	0.235370i	$-0.0756303\pi$
$294$	−0.733466	+	1.46676i	−0.00249478	+	0.00498898i
$295$	−16.5060			−0.0559526
$296$		−	100.148i		−	0.338336i
$297$	−192.390	+	34.9519i	−0.647779	+	0.117683i
$298$	45.5214			0.152756
$299$		−	509.218i		−	1.70307i
$300$	−109.380	−	54.6964i	−0.364600	−	0.182321i
$301$	569.038			1.89049
$302$		−	41.5771i		−	0.137673i
$303$	17.9332	−	35.8621i	0.0591854	−	0.118357i
$304$	−99.2392			−0.326445
$305$			91.8432i			0.301125i
$306$	99.6983	+	132.957i	0.325811	+	0.434501i
$307$	389.589			1.26902			0.634511	−	0.772914i	$-0.281202\pi$
$307$	389.589			1.26902			0.634511	+	0.772914i	$0.281202\pi$
$308$		−	100.990i		−	0.327890i
$309$	−420.632	−	210.341i	−1.36127	−	0.680715i
$310$	−140.807			−0.454217
$311$		−	34.9565i		−	0.112400i	−0.998420	−	0.0562002i	$-0.982101\pi$
$311$		−	34.9565i		−	0.112400i	0.998420	−	0.0562002i	$-0.0178985\pi$
$312$	−56.7316	+	113.450i	−0.181832	+	0.363621i
$313$	−84.6438			−0.270428			−0.135214	−	0.990816i	$-0.543172\pi$
$313$	−84.6438			−0.270428			−0.135214	+	0.990816i	$0.543172\pi$
$314$			26.9994i			0.0859855i
$315$	107.884	−	80.8972i	0.342489	−	0.256816i
$316$	62.3005			0.197154
$317$			293.145i			0.924748i	0.886685	+	0.462374i	$0.153002\pi$
$317$			293.145i			0.924748i	−0.886685	+	0.462374i	$0.846998\pi$
$318$	−134.510	−	67.2627i	−0.422986	−	0.211518i
$319$	323.695			1.01472
$320$			17.1912i			0.0537225i
$321$	−121.906	+	243.783i	−0.379769	+	0.759447i
$322$	−335.888			−1.04313
$323$		−	323.934i		−	1.00289i
$324$	45.3894	−	155.511i	0.140091	−	0.479974i
$325$	304.687			0.937499
$326$		−	132.749i		−	0.407206i
$327$	−238.685	−	119.357i	−0.729924	−	0.365005i
$328$	−99.9362			−0.304684
$329$			488.967i			1.48622i
$330$	29.5311	−	59.0551i	0.0894880	−	0.178955i
$331$	365.504			1.10424			0.552121	−	0.833764i	$-0.313818\pi$
$331$	365.504			1.10424			0.552121	+	0.833764i	$0.313818\pi$
$332$			61.6948i			0.185828i
$333$	−191.176	−	254.952i	−0.574103	−	0.765622i
$334$	301.604			0.903006
$335$			283.349i			0.845819i
$336$	74.8332	+	37.4210i	0.222718	+	0.111372i
$337$	−539.089			−1.59967			−0.799836	−	0.600219i	$-0.795080\pi$
$337$	−539.089			−1.59967			−0.799836	+	0.600219i	$0.795080\pi$
$338$		−	77.0217i		−	0.227875i
$339$	−43.7215	+	87.4327i	−0.128972	+	0.257914i
$340$	−56.1151			−0.165044
$341$			335.555i			0.984033i
$342$	−252.640	+	189.443i	−0.738713	+	0.553925i
$343$	−344.339			−1.00391
$344$			230.838i			0.671042i
$345$	−196.414	−	98.2188i	−0.569317	−	0.284692i
$346$	245.482			0.709486
$347$		−	123.675i		−	0.356412i	−0.983993	−	0.178206i	$-0.942971\pi$
$347$		−	123.675i		−	0.356412i	0.983993	−	0.178206i	$-0.0570293\pi$
$348$	−119.942	+	239.856i	−0.344662	+	0.689243i
$349$	138.120			0.395760			0.197880	−	0.980226i	$-0.436594\pi$
$349$	138.120			0.395760			0.197880	+	0.980226i	$0.436594\pi$
$350$		−	200.976i		−	0.574218i
$351$	72.1443	+	397.114i	0.205539	+	1.13138i
$352$	40.9681			0.116387
$353$			345.047i			0.977471i	0.872432	+	0.488735i	$0.162542\pi$
$353$			345.047i			0.977471i	−0.872432	+	0.488735i	$0.837458\pi$
$354$	−29.1472	−	14.5753i	−0.0823368	−	0.0411732i
$355$	−276.602			−0.779160
$356$		−	296.840i		−	0.833819i
$357$	−122.149	+	244.269i	−0.342154	+	0.684226i
$358$	16.3564			0.0456884
$359$			15.3667i			0.0428041i	0.999771	+	0.0214020i	$0.00681300\pi$
$359$			15.3667i			0.0428041i	−0.999771	+	0.0214020i	$0.993187\pi$
$360$	32.8171	+	43.7647i	0.0911586	+	0.121569i
$361$	254.527			0.705060
$362$			36.5134i			0.100866i
$363$	183.936	+	91.9789i	0.506711	+	0.253385i
$364$	−208.454			−0.572676
$365$			145.842i			0.399567i
$366$	−81.1004	+	162.182i	−0.221586	+	0.443119i
$367$	−426.161			−1.16120			−0.580600	−	0.814189i	$-0.697182\pi$
$367$	−426.161			−1.16120			−0.580600	+	0.814189i	$0.697182\pi$
$368$		−	136.258i		−	0.370266i
$369$	−254.414	+	190.773i	−0.689469	+	0.517000i
$370$	107.604			0.290820
$371$		−	247.150i		−	0.666172i
$372$	−248.645	−	124.337i	−0.668400	−	0.334240i
$373$	114.130			0.305979			0.152990	−	0.988228i	$-0.451110\pi$
$373$	114.130			0.305979			0.152990	+	0.988228i	$0.451110\pi$
$374$			133.727i			0.357559i
$375$	130.852	−	261.672i	0.348938	−	0.697793i
$376$	−198.356			−0.527543
$377$		−	668.140i		−	1.77226i
$378$	261.942	−	47.5875i	0.692970	−	0.125893i
$379$	−173.621			−0.458103			−0.229052	−	0.973414i	$-0.573562\pi$
$379$	−173.621			−0.458103			−0.229052	+	0.973414i	$0.573562\pi$
$380$		−	106.628i		−	0.280599i
$381$	42.1005	+	21.0527i	0.110500	+	0.0552565i
$382$	−305.368			−0.799391
$383$		−	277.239i		−	0.723863i	−0.932205	−	0.361931i	$-0.882117\pi$
$383$		−	277.239i		−	0.723863i	0.932205	−	0.361931i	$-0.117883\pi$
$384$	−15.1804	+	30.3571i	−0.0395322	+	0.0790551i
$385$	108.509			0.281841
$386$		−	501.447i		−	1.29908i
$387$	440.658	+	587.660i	1.13865	+	1.51850i
$388$	236.197			0.608754
$389$			601.688i			1.54676i	0.633945	+	0.773378i	$0.281434\pi$
$389$			601.688i			1.54676i	−0.633945	+	0.773378i	$0.718566\pi$
$390$	−121.896	−	60.9552i	−0.312554	−	0.156295i
$391$	444.769			1.13752
$392$		−	1.09328i		−	0.00278899i
$393$	227.918	−	455.783i	0.579945	−	1.15975i
$394$	207.538			0.526746
$395$			66.9388i			0.169465i
$396$	104.295	−	78.2059i	0.263371	−	0.197490i
$397$	364.132			0.917209			0.458604	−	0.888641i	$-0.348350\pi$
$397$	364.132			0.917209			0.458604	+	0.888641i	$0.348350\pi$
$398$		−	225.599i		−	0.566832i
$399$	−464.149	−	232.102i	−1.16328	−	0.581709i
$400$	81.5289			0.203822
$401$		−	486.925i		−	1.21428i	−0.794596	−	0.607138i	$-0.792317\pi$
$401$		−	486.925i		−	1.21428i	0.794596	−	0.607138i	$-0.207683\pi$
$402$	−250.206	+	500.353i	−0.622404	+	1.24466i
$403$	692.621			1.71866
$404$			26.7307i			0.0661650i
$405$	167.089	+	48.7686i	0.412566	+	0.120416i
$406$	−440.716			−1.08551
$407$		−	256.428i		−	0.630045i
$408$	−99.0911	−	49.5514i	−0.242870	−	0.121450i
$409$	−45.2904			−0.110734			−0.0553672	−	0.998466i	$-0.517633\pi$
$409$	−45.2904			−0.110734			−0.0553672	+	0.998466i	$0.517633\pi$
$410$		−	107.376i		−	0.261894i
$411$	6.11184	−	12.2222i	0.0148707	−	0.0297378i
$412$	313.528			0.760991
$413$		−	53.5555i		−	0.129674i
$414$	−260.109	−	346.880i	−0.628282	−	0.837875i
$415$	−66.2880			−0.159730
$416$		−	84.5624i		−	0.203275i
$417$	−240.892	−	120.460i	−0.577678	−	0.288873i
$418$	−254.102			−0.607901
$419$		−	195.770i		−	0.467231i	−0.972329	−	0.233615i	$-0.924944\pi$
$419$		−	195.770i		−	0.467231i	0.972329	−	0.233615i	$-0.0750556\pi$
$420$	−40.2070	+	80.4045i	−0.0957310	+	0.191439i
$421$	−47.1973			−0.112108			−0.0560538	−	0.998428i	$-0.517852\pi$
$421$	−47.1973			−0.112108			−0.0560538	+	0.998428i	$0.517852\pi$
$422$			223.014i			0.528470i
$423$	−504.969	+	378.652i	−1.19378	+	0.895158i
$424$	100.260			0.236462
$425$			266.125i			0.626176i
$426$	−488.438	−	244.248i	−1.14657	−	0.573352i
$427$	−297.995			−0.697880
$428$		−	181.709i		−	0.424554i
$429$	−145.261	+	290.488i	−0.338605	+	0.677129i
$430$	−248.024			−0.576801
$431$		−	40.9082i		−	0.0949147i	−0.998873	−	0.0474573i	$-0.984888\pi$
$431$		−	40.9082i		−	0.0949147i	0.998873	−	0.0474573i	$-0.0151118\pi$
$432$	19.3046	+	106.261i	0.0446865	+	0.245974i
$433$	89.8351			0.207471			0.103736	−	0.994605i	$-0.466920\pi$
$433$	89.8351			0.207471			0.103736	+	0.994605i	$0.466920\pi$
$434$		−	456.864i		−	1.05268i
$435$	−257.714	−	128.872i	−0.592445	−	0.296258i
$436$	177.910			0.408049
$437$			845.132i			1.93394i
$438$	−128.783	+	257.535i	−0.294025	+	0.587980i
$439$	33.6510			0.0766537			0.0383268	−	0.999265i	$-0.487797\pi$
$439$	33.6510			0.0766537			0.0383268	+	0.999265i	$0.487797\pi$
$440$			44.0181i			0.100041i
$441$	−2.08702	−	2.78324i	−0.00473247	−	0.00631121i
$442$	276.027			0.624495
$443$		−	760.498i		−	1.71670i	−0.513066	−	0.858349i	$-0.671490\pi$
$443$		−	760.498i		−	1.71670i	0.513066	−	0.858349i	$-0.328510\pi$
$444$	190.012	+	95.0173i	0.427955	+	0.214003i
$445$	318.939			0.716717
$446$			160.497i			0.359858i
$447$	−43.1895	+	86.3688i	−0.0966208	+	0.193219i
$448$	−55.7787			−0.124506
$449$			786.432i			1.75152i	0.482748	+	0.875759i	$0.339639\pi$
$449$			786.432i			1.75152i	−0.482748	+	0.875759i	$0.660361\pi$
$450$	207.553	−	155.634i	0.461230	−	0.345854i
$451$	−255.887			−0.567377
$452$		−	65.1701i		−	0.144182i
$453$	78.8852	+	39.4473i	0.174140	+	0.0870801i
$454$	−395.312			−0.870730
$455$		−	223.974i		−	0.492250i
$456$	94.1555	−	188.289i	0.206481	−	0.412914i
$457$	92.3442			0.202066			0.101033	−	0.994883i	$-0.467785\pi$
$457$	92.3442			0.202066			0.101033	+	0.994883i	$0.467785\pi$
$458$		−	491.264i		−	1.07263i
$459$	−346.854	+	63.0135i	−0.755673	+	0.137284i
$460$	146.402			0.318265
$461$		−	160.546i		−	0.348255i	−0.984723	−	0.174128i	$-0.944290\pi$
$461$		−	160.546i		−	0.348255i	0.984723	−	0.174128i	$-0.0557105\pi$
$462$	191.611	+	95.8167i	0.414742	+	0.207395i
$463$	−143.414			−0.309749			−0.154874	−	0.987934i	$-0.549497\pi$
$463$	−143.414			−0.309749			−0.154874	+	0.987934i	$0.549497\pi$
$464$		−	178.783i		−	0.385307i
$465$	133.594	−	267.156i	0.287299	−	0.574530i
$466$	−268.330			−0.575815
$467$			701.939i			1.50308i	0.659687	+	0.751540i	$0.270689\pi$
$467$			701.939i			1.50308i	−0.659687	+	0.751540i	$0.729311\pi$
$468$	−161.425	−	215.276i	−0.344926	−	0.459992i
$469$	−919.357			−1.96025
$470$		−	213.124i		−	0.453455i
$471$	−51.2266	−	25.6163i	−0.108761	−	0.0543871i
$472$	21.7256			0.0460287
$473$			591.063i			1.24960i
$474$	−59.1091	+	118.204i	−0.124703	+	0.249376i
$475$	−505.679			−1.06459
$476$		−	182.072i		−	0.382503i
$477$	255.238	−	191.391i	0.535090	−	0.401239i
$478$	−332.386			−0.695368
$479$			567.295i			1.18433i	0.805816	+	0.592166i	$0.201727\pi$
$479$			567.295i			1.18433i	−0.805816	+	0.592166i	$0.798273\pi$
$480$	−32.6172	−	16.3105i	−0.0679526	−	0.0339803i
$481$	−529.295			−1.10041
$482$			345.775i			0.717376i
$483$	318.681	−	637.288i	0.659796	−	1.31944i
$484$	−137.101			−0.283267
$485$			253.782i			0.523261i
$486$	251.991	+	233.663i	0.518500	+	0.480789i
$487$	850.347			1.74609			0.873047	−	0.487637i	$-0.162141\pi$
$487$	850.347			1.74609			0.873047	+	0.487637i	$0.162141\pi$
$488$		−	120.886i		−	0.247717i
$489$	251.868	+	125.949i	0.515067	+	0.257564i
$490$	1.17468			0.00239730
$491$		−	73.6870i		−	0.150075i	−0.997181	−	0.0750377i	$-0.976092\pi$
$491$		−	73.6870i		−	0.150075i	0.997181	−	0.0750377i	$-0.0239077\pi$
$492$	94.8168	−	189.611i	0.192717	−	0.385388i
$493$	583.578			1.18373
$494$			524.494i			1.06173i
$495$	84.0283	+	112.060i	0.169754	+	0.226383i
$496$	185.333			0.373656
$497$		−	897.464i		−	1.80576i
$498$	−117.055	−	58.5344i	−0.235050	−	0.117539i
$499$	−555.750			−1.11373			−0.556863	−	0.830604i	$-0.687995\pi$
$499$	−555.750			−1.11373			−0.556863	+	0.830604i	$0.687995\pi$
$500$			195.044i			0.390087i
$501$	−286.154	+	572.240i	−0.571165	+	1.14220i
$502$	−538.712			−1.07313
$503$		−	931.407i		−	1.85170i	−0.377887	−	0.925852i	$-0.623349\pi$
$503$		−	931.407i		−	1.85170i	0.377887	−	0.925852i	$-0.376651\pi$
$504$	−141.999	+	106.479i	−0.281745	+	0.211267i
$505$	−28.7208			−0.0568728
$506$		−	348.888i		−	0.689503i
$507$	146.135	+	73.0761i	0.288235	+	0.144134i
$508$	−31.3806			−0.0617728
$509$			529.689i			1.04065i	0.853970	+	0.520323i	$0.174188\pi$
$509$			529.689i			1.04065i	−0.853970	+	0.520323i	$0.825812\pi$
$510$	53.2405	−	106.468i	0.104393	−	0.208762i
$511$	−473.199			−0.926026
$512$		−	22.6274i		−	0.0441942i
$513$	−119.736	−	659.077i	−0.233403	−	1.28475i
$514$	−208.857			−0.406337
$515$			336.870i			0.654117i
$516$	−437.975	−	219.013i	−0.848788	−	0.424444i
$517$	−507.892			−0.982383
$518$			349.131i			0.673998i
$519$	−232.907	+	465.758i	−0.448761	+	0.897415i
$520$	90.8581			0.174727
$521$			462.603i			0.887915i	0.896048	+	0.443957i	$0.146426\pi$
$521$			462.603i			0.887915i	−0.896048	+	0.443957i	$0.853574\pi$
$522$	−341.287	−	455.139i	−0.653806	−	0.871913i
$523$	770.904			1.47400			0.737002	−	0.675891i	$-0.236241\pi$
$523$	770.904			1.47400			0.737002	+	0.675891i	$0.236241\pi$
$524$			339.728i			0.648337i
$525$	381.317	+	190.681i	0.726318	+	0.363202i
$526$	−115.261			−0.219127
$527$			604.961i			1.14793i
$528$	−38.8694	+	77.7296i	−0.0736163	+	0.147215i
$529$	−631.386			−1.19355
$530$			107.724i			0.203253i
$531$	55.3082	−	41.4730i	0.104159	−	0.0781035i
$532$	345.965			0.650309
$533$			528.178i			0.990953i
$534$	563.200	+	281.633i	1.05468	+	0.527403i
$535$	195.237			0.364930
$536$		−	372.950i		−	0.695803i
$537$	−15.5185	+	31.0334i	−0.0288986	+	0.0577904i
$538$	−77.4401			−0.143941
$539$		−	2.79936i		−	0.00519361i
$540$	−114.172	+	20.7418i	−0.211429	+	0.0384107i
$541$	−81.5864			−0.150807			−0.0754034	−	0.997153i	$-0.524024\pi$
$541$	−81.5864			−0.150807			−0.0754034	+	0.997153i	$0.524024\pi$
$542$			21.8615i			0.0403349i
$543$	−69.2776	−	34.6429i	−0.127583	−	0.0637991i
$544$	73.8599			0.135772
$545$			191.155i			0.350743i
$546$	197.776	−	395.505i	0.362227	−	0.724368i
$547$	635.191			1.16123			0.580613	−	0.814179i	$-0.302813\pi$
$547$	635.191			1.16123			0.580613	+	0.814179i	$0.302813\pi$
$548$			9.11013i			0.0166243i
$549$	−230.765	−	307.747i	−0.420337	−	0.560559i
$550$	208.755			0.379555
$551$			1108.89i			2.01251i
$552$	258.525	+	129.278i	0.468342	+	0.234199i
$553$	−217.190			−0.392749
$554$			459.591i			0.829586i
$555$	−102.091	+	204.159i	−0.183948	+	0.367853i
$556$	179.554			0.322939
$557$		−	921.540i		−	1.65447i	−0.561856	−	0.827235i	$-0.689912\pi$
$557$		−	921.540i		−	1.65447i	0.561856	−	0.827235i	$-0.310088\pi$
$558$	471.815	−	353.792i	0.845547	−	0.634035i
$559$	1220.02			2.18250
$560$		−	59.9314i		−	0.107020i
$561$	−253.723	−	126.877i	−0.452269	−	0.226161i
$562$	380.182			0.676481
$563$			189.524i			0.336632i	0.985733	+	0.168316i	$0.0538328\pi$
$563$			189.524i			0.336632i	−0.985733	+	0.168316i	$0.946167\pi$
$564$	188.195	−	376.346i	0.333679	−	0.667280i
$565$	70.0220			0.123933
$566$			275.382i			0.486540i
$567$	−158.235	+	542.139i	−0.279074	+	0.956153i
$568$	364.069			0.640967
$569$		−	546.709i		−	0.960825i	−0.877043	−	0.480413i	$-0.840487\pi$
$569$		−	546.709i		−	0.960825i	0.877043	−	0.480413i	$-0.159513\pi$
$570$	202.307	+	101.165i	0.354924	+	0.177483i
$571$	−830.410			−1.45431			−0.727154	−	0.686474i	$-0.759157\pi$
$571$	−830.410			−1.45431			−0.727154	+	0.686474i	$0.759157\pi$
$572$		−	216.522i		−	0.378536i
$573$	289.724	−	579.380i	0.505627	−	1.01114i
$574$	348.394			0.606959
$575$		−	694.309i		−	1.20749i
$576$	−43.1946	−	57.6041i	−0.0749905	−	0.100007i
$577$	657.424			1.13938			0.569692	−	0.821859i	$-0.307063\pi$
$577$	657.424			1.13938			0.569692	+	0.821859i	$0.307063\pi$
$578$		−	167.616i		−	0.289993i
$579$	951.406	+	475.759i	1.64319	+	0.821691i
$580$	192.093			0.331195
$581$		−	215.079i		−	0.370187i
$582$	−224.097	+	448.141i	−0.385046	+	0.770002i
$583$	256.716			0.440336
$584$		−	191.960i		−	0.328699i
$585$	231.303	−	173.443i	0.395390	−	0.296484i
$586$	−195.058			−0.332864
$587$		−	451.124i		−	0.768525i	−0.923224	−	0.384262i	$-0.874456\pi$
$587$		−	451.124i		−	0.768525i	0.923224	−	0.384262i	$-0.125544\pi$
$588$	2.07431	+	1.03728i	0.00352774	+	0.00176408i
$589$	−1149.52			−1.95165
$590$			23.3430i			0.0395645i
$591$	−196.907	+	393.767i	−0.333175	+	0.666272i
$592$	−141.630			−0.239240
$593$			427.836i			0.721476i	0.932667	+	0.360738i	$0.117475\pi$
$593$			427.836i			0.721476i	−0.932667	+	0.360738i	$0.882525\pi$
$594$	49.4294	+	272.081i	0.0832145	+	0.458049i
$595$	195.627			0.328784
$596$		−	64.3770i		−	0.108015i
$597$	428.035	+	214.043i	0.716976	+	0.358530i
$598$	−720.143			−1.20425
$599$		−	870.382i		−	1.45306i	−0.687136	−	0.726529i	$-0.741132\pi$
$599$		−	870.382i		−	1.45306i	0.687136	−	0.726529i	$-0.258868\pi$
$600$	−77.3524	+	154.687i	−0.128921	+	0.257811i
$601$	979.728			1.63016			0.815081	−	0.579346i	$-0.196692\pi$
$601$	979.728			1.63016			0.815081	+	0.579346i	$0.196692\pi$
$602$		−	804.741i		−	1.33678i
$603$	−711.943	−	949.444i	−1.18067	−	1.57453i
$604$	−58.7990			−0.0973493
$605$		−	147.308i		−	0.243485i
$606$	−50.7167	−	25.3613i	−0.0836909	−	0.0418504i
$607$	−456.479			−0.752024			−0.376012	−	0.926615i	$-0.622705\pi$
$607$	−456.479			−0.752024			−0.376012	+	0.926615i	$0.622705\pi$
$608$			140.345i			0.230831i
$609$	418.139	−	836.180i	0.686600	−	1.37304i
$610$	129.886			0.212928
$611$			1048.34i			1.71578i
$612$	188.030	−	140.995i	0.307238	−	0.230383i
$613$	630.097			1.02789			0.513946	−	0.857823i	$-0.328183\pi$
$613$	630.097			1.02789			0.513946	+	0.857823i	$0.328183\pi$
$614$		−	550.963i		−	0.897333i
$615$	203.728	+	101.876i	0.331265	+	0.165652i
$616$	−142.822			−0.231853
$617$			148.545i			0.240754i	0.992728	+	0.120377i	$0.0384104\pi$
$617$			148.545i			0.240754i	−0.992728	+	0.120377i	$0.961590\pi$
$618$	−297.467	+	594.864i	−0.481338	+	0.962563i
$619$	3.26113			0.00526838			0.00263419	−	0.999997i	$-0.499162\pi$
$619$	3.26113			0.00526838			0.00263419	+	0.999997i	$0.499162\pi$
$620$			199.131i			0.321180i
$621$	904.928	−	164.400i	1.45721	−	0.264734i
$622$	−49.4360			−0.0794791
$623$			1034.83i			1.66105i
$624$	160.442	+	80.2305i	0.257119	+	0.128575i
$625$	299.991			0.479986
$626$			119.704i			0.191221i
$627$	241.086	−	482.114i	0.384506	−	0.768922i
$628$	38.1830			0.0608009
$629$		−	462.306i		−	0.734985i
$630$	−114.406	−	152.571i	−0.181597	−	0.242177i
$631$	465.210			0.737258			0.368629	−	0.929577i	$-0.379827\pi$
$631$	465.210			0.737258			0.368629	+	0.929577i	$0.379827\pi$
$632$		−	88.1063i		−	0.139409i
$633$	−423.130	−	211.590i	−0.668451	−	0.334265i
$634$	414.570			0.653896
$635$		−	33.7169i		−	0.0530974i
$636$	−95.1238	+	190.225i	−0.149566	+	0.299096i
$637$	−5.77817			−0.00907091
$638$		−	457.774i		−	0.717513i
$639$	926.834	−	694.989i	1.45044	−	1.08762i
$640$	24.3120			0.0379875
$641$			771.370i			1.20339i	0.798728	+	0.601693i	$0.205507\pi$
$641$			771.370i			1.20339i	−0.798728	+	0.601693i	$0.794493\pi$
$642$	344.761	+	172.401i	0.537010	+	0.268537i
$643$	1211.65			1.88437			0.942184	−	0.335096i	$-0.108769\pi$
$643$	1211.65			1.88437			0.942184	+	0.335096i	$0.108769\pi$
$644$			475.017i			0.737605i
$645$	235.319	−	470.582i	0.364835	−	0.729584i
$646$	−458.112			−0.709152
$647$			238.116i			0.368031i	0.982923	+	0.184015i	$0.0589096\pi$
$647$			238.116i			0.368031i	−0.982923	+	0.184015i	$0.941090\pi$
$648$	−219.926	−	64.1903i	−0.339393	−	0.0990591i
$649$	55.6284			0.0857140
$650$		−	430.893i		−	0.662912i
$651$	866.818	+	433.460i	1.33152	+	0.665837i
$652$	−187.736			−0.287938
$653$			336.371i			0.515117i	0.966263	+	0.257559i	$0.0829180\pi$
$653$			336.371i			0.515117i	−0.966263	+	0.257559i	$0.917082\pi$
$654$	−168.796	+	337.552i	−0.258098	+	0.516134i
$655$	−365.021			−0.557284
$656$			141.331i			0.215444i
$657$	−366.442	−	488.685i	−0.557750	−	0.743813i
$658$	691.503			1.05092
$659$		−	452.311i		−	0.686359i	−0.939270	−	0.343180i	$-0.888496\pi$
$659$		−	452.311i		−	0.686359i	0.939270	−	0.343180i	$-0.111504\pi$
$660$	−83.5166	−	41.7632i	−0.126540	−	0.0632776i
$661$	266.489			0.403160			0.201580	−	0.979472i	$-0.435392\pi$
$661$	266.489			0.403160			0.201580	+	0.979472i	$0.435392\pi$
$662$		−	516.901i		−	0.780818i
$663$	−261.887	+	523.711i	−0.395003	+	0.789912i
$664$	87.2497			0.131400
$665$			371.722i			0.558980i
$666$	−360.557	+	270.364i	−0.541377	+	0.405952i
$667$	−1522.53			−2.28266
$668$		−	426.533i		−	0.638522i
$669$	−304.514	−	152.275i	−0.455178	−	0.227616i
$670$	400.716			0.598084
$671$		−	309.529i		−	0.461295i
$672$	52.9213	−	105.830i	0.0787520	−	0.157485i
$673$	−292.179			−0.434144			−0.217072	−	0.976156i	$-0.569651\pi$
$673$	−292.179			−0.434144			−0.217072	+	0.976156i	$0.569651\pi$
$674$			762.388i			1.13114i
$675$	98.3675	+	541.457i	0.145730	+	0.802159i
$676$	−108.925			−0.161132
$677$		−	519.039i		−	0.766674i	−0.923608	−	0.383337i	$-0.874775\pi$
$677$		−	519.039i		−	0.766674i	0.923608	−	0.383337i	$-0.125225\pi$
$678$	123.649	+	61.8316i	0.182373	+	0.0911970i
$679$	−823.421			−1.21270
$680$			79.3588i			0.116704i
$681$	375.061	−	750.033i	0.550750	−	1.10137i
$682$	474.547			0.695816
$683$		−	260.465i		−	0.381354i	−0.981653	−	0.190677i	$-0.938932\pi$
$683$		−	260.465i		−	0.381354i	0.981653	−	0.190677i	$-0.0610684\pi$
$684$	267.912	+	357.287i	0.391684	+	0.522349i
$685$	−9.78838			−0.0142896
$686$			486.970i			0.709868i
$687$	932.086	+	466.098i	1.35675	+	0.678454i
$688$	326.455			0.474498
$689$		−	529.888i		−	0.769069i
$690$	−138.902	+	277.772i	−0.201308	+	0.402568i
$691$	−1298.23			−1.87877			−0.939387	−	0.342859i	$-0.888605\pi$
$691$	−1298.23			−1.87877			−0.939387	+	0.342859i	$0.888605\pi$
$692$		−	347.164i		−	0.501682i
$693$	−363.590	+	272.639i	−0.524661	+	0.393418i
$694$	−174.903			−0.252021
$695$			192.922i			0.277586i
$696$	339.208	+	169.624i	0.487368	+	0.243713i
$697$	−461.330			−0.661879
$698$		−	195.332i		−	0.279845i
$699$	254.584	−	509.108i	0.364212	−	0.728338i
$700$	−284.223			−0.406034
$701$		−	522.223i		−	0.744969i	−0.928038	−	0.372484i	$-0.878506\pi$
$701$		−	522.223i		−	0.744969i	0.928038	−	0.372484i	$-0.121494\pi$
$702$	561.604	−	102.027i	0.800005	−	0.145338i
$703$	878.454			1.24958
$704$		−	57.9376i		−	0.0822977i
$705$	404.365	+	202.206i	0.573567	+	0.286817i
$706$	487.970			0.691176
$707$		−	93.1876i		−	0.131807i
$708$	−20.6126	+	41.2204i	−0.0291139	+	0.0582209i
$709$	346.029			0.488052			0.244026	−	0.969769i	$-0.421532\pi$
$709$	346.029			0.488052			0.244026	+	0.969769i	$0.421532\pi$
$710$			391.174i			0.550949i
$711$	−168.190	−	224.298i	−0.236554	−	0.315468i
$712$	−419.795			−0.589599
$713$		−	1578.32i		−	2.21363i
$714$	345.448	+	172.745i	0.483821	+	0.241939i
$715$	232.642			0.325374
$716$		−	23.1315i		−	0.0323066i
$717$	315.359	−	630.643i	0.439831	−	0.879557i
$718$	21.7317			0.0302670
$719$			1206.12i			1.67749i	0.544524	+	0.838745i	$0.316710\pi$
$719$			1206.12i			1.67749i	−0.544524	+	0.838745i	$0.683290\pi$
$720$	61.8927	−	46.4104i	0.0859621	−	0.0644589i
$721$	−1093.01			−1.51597
$722$		−	359.955i		−	0.498553i
$723$	−656.047	−	328.062i	−0.907395	−	0.453751i
$724$	51.6377			0.0713228
$725$		−	910.997i		−	1.25655i
$726$	130.078	−	260.125i	0.179171	−	0.358299i
$727$	100.417			0.138125			0.0690624	−	0.997612i	$-0.477999\pi$
$727$	100.417			0.138125			0.0690624	+	0.997612i	$0.477999\pi$
$728$			294.799i			0.404943i
$729$	−682.417	+	256.414i	−0.936100	+	0.351734i
$730$	206.251			0.282536
$731$			1065.61i			1.45774i
$732$	229.359	+	114.693i	0.313333	+	0.156685i
$733$	−685.792			−0.935596			−0.467798	−	0.883836i	$-0.654952\pi$
$733$	−685.792			−0.935596			−0.467798	+	0.883836i	$0.654952\pi$
$734$			602.682i			0.821093i
$735$	−1.11450	+	2.22874i	−0.00151633	+	0.00303230i
$736$	−192.698			−0.261817
$737$		−	954.941i		−	1.29571i
$738$	269.794	+	359.796i	0.365574	+	0.487528i
$739$	−322.478			−0.436371			−0.218185	−	0.975907i	$-0.570014\pi$
$739$	−322.478			−0.436371			−0.218185	+	0.975907i	$0.570014\pi$
$740$		−	152.174i		−	0.205641i
$741$	−995.135	−	497.626i	−1.34296	−	0.671560i
$742$	−349.523			−0.471055
$743$			679.451i			0.914470i	0.889346	+	0.457235i	$0.151160\pi$
$743$			679.451i			0.914470i	−0.889346	+	0.457235i	$0.848840\pi$
$744$	−175.839	+	351.637i	−0.236343	+	0.472630i
$745$	69.1699			0.0928455
$746$		−	161.405i		−	0.216360i
$747$	222.117	−	166.555i	0.297346	−	0.222965i
$748$	189.119			0.252832
$749$			633.469i			0.845752i
$750$	−370.061	−	185.052i	−0.493414	−	0.246736i
$751$	−713.811			−0.950481			−0.475240	−	0.879856i	$-0.657639\pi$
$751$	−713.811			−0.950481			−0.475240	+	0.879856i	$0.657639\pi$
$752$			280.518i			0.373029i
$753$	511.115	−	1022.11i	0.678772	−	1.35738i
$754$	−944.893			−1.25317
$755$		−	63.1765i		−	0.0836775i
$756$	−67.2989	−	370.443i	−0.0890197	−	0.490003i
$757$	−152.728			−0.201755			−0.100877	−	0.994899i	$-0.532165\pi$
$757$	−152.728			−0.201755			−0.100877	+	0.994899i	$0.532165\pi$
$758$			245.537i			0.323928i
$759$	661.954	+	331.016i	0.872139	+	0.436121i
$760$	−150.794			−0.198413
$761$			1079.01i			1.41789i	0.705264	+	0.708945i	$0.250829\pi$
$761$			1079.01i			1.41789i	−0.705264	+	0.708945i	$0.749171\pi$
$762$	29.7730	−	59.5390i	0.0390722	−	0.0781352i
$763$	−620.223			−0.812874
$764$			431.855i			0.565255i
$765$	151.492	+	202.029i	0.198028	+	0.264090i
$766$	−392.076			−0.511848
$767$		−	114.823i		−	0.149704i
$768$	42.9315	+	21.4683i	0.0559004	+	0.0279535i
$769$	765.680			0.995682			0.497841	−	0.867268i	$-0.334126\pi$
$769$	765.680			0.995682			0.497841	+	0.867268i	$0.334126\pi$
$770$		−	153.455i		−	0.199292i
$771$	198.158	−	396.269i	0.257014	−	0.513968i
$772$	−709.153			−0.918591
$773$			173.335i			0.224237i	0.993695	+	0.112119i	$0.0357636\pi$
$773$			173.335i			0.224237i	−0.993695	+	0.112119i	$0.964236\pi$
$774$	831.077	−	623.185i	1.07374	−	0.805149i
$775$	944.377			1.21855
$776$		−	334.033i		−	0.430454i
$777$	−662.414	−	331.246i	−0.852528	−	0.426314i
$778$	850.915			1.09372
$779$		−	876.600i		−	1.12529i
$780$	−86.2037	+	172.387i	−0.110518	+	0.221009i
$781$	932.200			1.19360
$782$		−	628.999i		−	0.804346i
$783$	1187.35	−	215.707i	1.51641	−	0.275488i
$784$	−1.54614			−0.00197211
$785$			41.0257i			0.0522620i
$786$	−644.574	−	322.325i	−0.820069	−	0.410083i
$787$	1339.15			1.70159			0.850795	−	0.525498i	$-0.176121\pi$
$787$	1339.15			1.70159			0.850795	+	0.525498i	$0.176121\pi$
$788$		−	293.503i		−	0.372466i
$789$	109.356	−	218.687i	0.138601	−	0.277169i
$790$	94.6658			0.119830
$791$			227.194i			0.287223i
$792$	−110.600	−	147.495i	−0.139646	−	0.186232i
$793$	−638.900			−0.805675
$794$		−	514.960i		−	0.648564i
$795$	−204.387	−	102.206i	−0.257091	−	0.128561i
$796$	−319.046			−0.400811
$797$			569.633i			0.714722i	0.933966	+	0.357361i	$0.116323\pi$
$797$			569.633i			0.714722i	−0.933966	+	0.357361i	$0.883677\pi$
$798$	−328.242	+	656.406i	−0.411331	+	0.822564i
$799$	−915.661			−1.14601
$800$		−	115.299i		−	0.144124i
$801$	−1068.70	+	801.366i	−1.33420	+	1.00046i
$802$	−688.616			−0.858623
$803$		−	491.514i		−	0.612098i
$804$	707.607	+	353.845i	0.880108	+	0.440106i
$805$	−510.382			−0.634015
$806$		−	979.515i		−	1.21528i
$807$	73.4730	−	146.929i	0.0910447	−	0.182068i
$808$	37.8029			0.0467857
$809$			1392.64i			1.72143i	0.509085	+	0.860716i	$0.329984\pi$
$809$			1392.64i			1.72143i	−0.509085	+	0.860716i	$0.670016\pi$
$810$	68.9693	−	236.300i	0.0851473	−	0.291728i
$811$	−546.791			−0.674218			−0.337109	−	0.941466i	$-0.609449\pi$
$811$	−546.791			−0.674218			−0.337109	+	0.941466i	$0.609449\pi$
$812$			623.266i			0.767569i
$813$	−41.4783	−	20.7416i	−0.0510189	−	0.0255124i
$814$	−362.644			−0.445509
$815$		−	201.713i		−	0.247500i
$816$	−70.0763	+	140.136i	−0.0858778	+	0.171735i
$817$	−2024.82			−2.47836
$818$			64.0503i			0.0783011i
$819$	562.755	+	750.488i	0.687125	+	0.916347i
$820$	−151.853			−0.185187
$821$			356.394i			0.434097i	0.976161	+	0.217049i	$0.0696430\pi$
$821$			356.394i			0.434097i	−0.976161	+	0.217049i	$0.930357\pi$
$822$	−17.2849	−	8.64345i	−0.0210278	−	0.0105151i
$823$	1189.65			1.44551			0.722753	−	0.691106i	$-0.242876\pi$
$823$	1189.65			1.44551			0.722753	+	0.691106i	$0.242876\pi$
$824$		−	443.396i		−	0.538102i
$825$	−198.061	+	396.076i	−0.240074	+	0.480092i
$826$	−75.7390			−0.0916936
$827$		−	1114.06i		−	1.34711i	−0.739136	−	0.673556i	$-0.764766\pi$
$827$		−	1114.06i		−	1.34711i	0.739136	−	0.673556i	$-0.235234\pi$
$828$	−490.563	+	367.850i	−0.592467	+	0.444263i
$829$	269.743			0.325384			0.162692	−	0.986677i	$-0.447982\pi$
$829$	269.743			0.325384			0.162692	+	0.986677i	$0.447982\pi$
$830$			93.7454i			0.112946i
$831$	−871.991	−	436.047i	−1.04933	−	0.524726i
$832$	−119.589			−0.143737
$833$		−	5.04686i		−	0.00605866i
$834$	−170.356	+	340.672i	−0.204264	+	0.408480i
$835$	458.288			0.548848
$836$			359.355i			0.429851i
$837$	223.611	+	1230.85i	0.267158	+	1.47055i
$838$	−276.860			−0.330382
$839$			1169.33i			1.39371i	0.717210	+	0.696857i	$0.245419\pi$
$839$			1169.33i			1.39371i	−0.717210	+	0.696857i	$0.754581\pi$
$840$	113.709	+	56.8613i	0.135368	+	0.0676920i
$841$	−1156.70			−1.37539
$842$			66.7471i			0.0792721i
$843$	−360.707	+	721.328i	−0.427885	+	0.855668i
$844$	315.390			0.373685
$845$		−	117.035i		−	0.138502i
$846$	535.494	+	714.133i	0.632972	+	0.844129i
$847$	477.958			0.564295
$848$		−	141.789i		−	0.167204i
$849$	−522.488	−	261.275i	−0.615416	−	0.307744i
$850$	376.357			0.442773
$851$			1206.14i			1.41732i
$852$	−345.419	+	690.756i	−0.405421	+	0.810747i
$853$	−1506.76			−1.76642			−0.883211	−	0.468975i	$-0.844623\pi$
$853$	−1506.76			−1.76642			−0.883211	+	0.468975i	$0.844623\pi$
$854$			421.429i			0.493476i
$855$	−383.887	+	287.858i	−0.448990	+	0.336676i
$856$	−256.976			−0.300205
$857$			374.837i			0.437382i	0.975794	+	0.218691i	$0.0701787\pi$
$857$			374.837i			0.437382i	−0.975794	+	0.218691i	$0.929821\pi$
$858$	410.813	+	205.431i	0.478803	+	0.239430i
$859$	−270.736			−0.315176			−0.157588	−	0.987505i	$-0.550372\pi$
$859$	−270.736			−0.315176			−0.157588	+	0.987505i	$0.550372\pi$
$860$			350.759i			0.407860i
$861$	−330.547	+	661.016i	−0.383911	+	0.767731i
$862$	−57.8530			−0.0671148
$863$			976.456i			1.13147i	0.824588	+	0.565733i	$0.191407\pi$
$863$			976.456i			1.13147i	−0.824588	+	0.565733i	$0.808593\pi$
$864$	150.275	−	27.3008i	0.173930	−	0.0315981i
$865$	373.010			0.431226
$866$		−	127.046i		−	0.146704i
$867$	318.021	+	159.029i	0.366807	+	0.183425i
$868$	−646.103			−0.744358
$869$		−	225.596i		−	0.259605i
$870$	−182.253	+	364.462i	−0.209486	+	0.418922i
$871$	−1971.10			−2.26303
$872$		−	251.602i		−	0.288535i
$873$	−637.651	−	850.368i	−0.730413	−	0.974076i
$874$	1195.20			1.36750
$875$		−	679.955i		−	0.777092i
$876$	364.210	+	182.126i	0.415765	+	0.207907i
$877$	465.123			0.530357			0.265178	−	0.964199i	$-0.414569\pi$
$877$	465.123			0.530357			0.265178	+	0.964199i	$0.414569\pi$
$878$		−	47.5896i		−	0.0542023i
$879$	185.066	−	370.088i	0.210542	−	0.421033i
$880$	62.2510			0.0707398
$881$		−	487.309i		−	0.553132i	−0.960995	−	0.276566i	$-0.910804\pi$
$881$		−	487.309i		−	0.553132i	0.960995	−	0.276566i	$-0.0891964\pi$
$882$	−3.93610	+	2.95149i	−0.00446270	+	0.00334636i
$883$	679.640			0.769695			0.384847	−	0.922980i	$-0.374254\pi$
$883$	679.640			0.769695			0.384847	+	0.922980i	$0.374254\pi$
$884$		−	390.361i		−	0.441584i
$885$	−44.2892	−	22.1472i	−0.0500443	−	0.0250251i
$886$	−1075.51			−1.21389
$887$			159.068i			0.179332i	0.995972	+	0.0896662i	$0.0285800\pi$
$887$			159.068i			0.179332i	−0.995972	+	0.0896662i	$0.971420\pi$
$888$	134.375	−	268.718i	0.151323	−	0.302610i
$889$	109.398			0.123057
$890$		−	451.048i		−	0.506796i
$891$	−563.122	−	164.360i	−0.632012	−	0.184466i
$892$	226.977			0.254458
$893$		−	1739.90i		−	1.94838i
$894$	122.144	+	61.0792i	0.136626	+	0.0683212i
$895$	24.8536			0.0277694
$896$			78.8830i			0.0880390i
$897$	683.252	−	1366.34i	0.761708	−	1.52324i
$898$	1112.18			1.23851
$899$		−	2070.90i		−	2.30356i
$900$	−220.100	−	293.525i	−0.244556	−	0.326139i
$901$	462.824			0.513678
$902$			361.879i			0.401196i
$903$	1526.85	+	763.517i	1.69087	+	0.845534i
$904$	−92.1644			−0.101952
$905$			55.4821i			0.0613062i
$906$	55.7869	−	111.561i	0.0615749	−	0.123135i
$907$	144.077			0.158850			0.0794250	−	0.996841i	$-0.474692\pi$
$907$	144.077			0.158850			0.0794250	+	0.996841i	$0.474692\pi$
$908$			559.055i			0.615699i
$909$	96.2372	−	72.1637i	0.105872	−	0.0793880i
$910$	−316.746			−0.348073
$911$			1529.36i			1.67877i	0.543539	+	0.839384i	$0.317084\pi$
$911$			1529.36i			1.67877i	−0.543539	+	0.839384i	$0.682916\pi$
$912$	−266.281	−	133.156i	−0.291974	−	0.146004i
$913$	223.403			0.244691
$914$		−	130.594i		−	0.142882i
$915$	−123.232	+	246.435i	−0.134680	+	0.269328i
$916$	−694.753			−0.758463
$917$		−	1184.35i		−	1.29155i
$918$	89.1145	+	490.525i	0.0970747	+	0.534341i
$919$	−8.69903			−0.00946576			−0.00473288	−	0.999989i	$-0.501507\pi$
$919$	−8.69903			−0.00946576			−0.00473288	+	0.999989i	$0.501507\pi$
$920$		−	207.044i		−	0.225048i
$921$	1045.35	+	522.739i	1.13502	+	0.567577i
$922$	−227.046			−0.246253
$923$		−	1924.16i		−	2.08468i
$924$	135.505	−	270.978i	0.146651	−	0.293267i
$925$	−721.684			−0.780199
$926$			202.818i			0.219025i
$927$	−846.419	−	1128.78i	−0.913074	−	1.21767i
$928$	−252.837			−0.272453
$929$			144.134i			0.155150i	0.996987	+	0.0775750i	$0.0247177\pi$
$929$			144.134i			0.155150i	−0.996987	+	0.0775750i	$0.975282\pi$
$930$	−377.816	−	188.930i	−0.406254	−	0.203151i
$931$	9.58984			0.0103006
$932$			379.476i			0.407163i
$933$	46.9035	−	93.7960i	0.0502717	−	0.100532i
$934$	992.691			1.06284
$935$			203.198i			0.217324i
$936$	−304.446	+	228.290i	−0.325263	+	0.243899i
$937$	178.341			0.190332			0.0951659	−	0.995461i	$-0.469662\pi$
$937$	178.341			0.190332			0.0951659	+	0.995461i	$0.469662\pi$
$938$			1300.17i			1.38611i
$939$	−227.118	−	113.572i	−0.241872	−	0.120950i
$940$	−301.403			−0.320641
$941$			576.707i			0.612866i	0.951892	+	0.306433i	$0.0991356\pi$
$941$			576.707i			0.612866i	−0.951892	+	0.306433i	$0.900864\pi$
$942$	−36.2270	+	72.4454i	−0.0384575	+	0.0769059i
$943$	1203.59			1.27634
$944$		−	30.7246i		−	0.0325472i
$945$	398.022	−	72.3093i	0.421187	−	0.0765178i
$946$	835.889			0.883603
$947$			126.489i			0.133568i	0.997767	+	0.0667839i	$0.0212738\pi$
$947$			126.489i			0.133568i	−0.997767	+	0.0667839i	$0.978726\pi$
$948$	167.166	+	83.5928i	0.176335	+	0.0881781i
$949$	−1014.54			−1.06906
$950$			715.138i			0.752777i
$951$	−393.333	+	786.572i	−0.413599	+	0.827100i
$952$	−257.488			−0.270471
$953$		−	674.046i		−	0.707289i	−0.935380	−	0.353644i	$-0.884942\pi$
$953$		−	674.046i		−	0.707289i	0.935380	−	0.353644i	$-0.115058\pi$
$954$	−270.667	−	360.961i	−0.283718	−	0.378366i
$955$	−464.006			−0.485871
$956$			470.064i			0.491699i
$957$	868.544	+	434.323i	0.907569	+	0.453838i
$958$	802.276			0.837449
$959$		−	31.7595i		−	0.0331173i
$960$	−23.0666	+	46.1277i	−0.0240277	+	0.0480497i
$961$	1185.78			1.23390
$962$			748.536i			0.778104i
$963$	−654.199	+	490.553i	−0.679335	+	0.509401i
$964$	489.000			0.507261
$965$		−	761.949i		−	0.789584i
$966$	−901.261	−	450.684i	−0.932982	−	0.466546i
$967$	1048.30			1.08408			0.542039	−	0.840353i	$-0.317652\pi$
$967$	1048.30			1.08408			0.542039	+	0.840353i	$0.317652\pi$
$968$			193.890i			0.200300i
$969$	434.645	−	869.187i	0.448550	−	0.896994i
$970$	358.901			0.370001
$971$			432.561i			0.445480i	0.974878	+	0.222740i	$0.0715000\pi$
$971$			432.561i			0.445480i	−0.974878	+	0.222740i	$0.928500\pi$
$972$	330.450	−	356.369i	0.339969	−	0.366635i
$973$	−625.956			−0.643326
$974$		−	1202.57i		−	1.23467i
$975$	817.542	+	408.819i	0.838505	+	0.419302i
$976$	−170.958			−0.175162
$977$			1465.73i			1.50023i	0.661307	+	0.750116i	$0.270002\pi$
$977$			1465.73i			1.50023i	−0.661307	+	0.750116i	$0.729998\pi$
$978$	178.119	−	356.195i	0.182125	−	0.364208i
$979$	−1074.89			−1.09794
$980$		−	1.66125i		−	0.00169515i
$981$	−480.295	−	640.520i	−0.489598	−	0.652925i
$982$	−104.209			−0.106119
$983$			1196.78i			1.21747i	0.793372	+	0.608737i	$0.208323\pi$
$983$			1196.78i			1.21747i	−0.793372	+	0.608737i	$0.791677\pi$
$984$	−268.151	−	134.091i	−0.272511	−	0.136272i
$985$	315.354			0.320157
$986$		−	825.304i		−	0.837022i
$987$	−656.080	+	1312.00i	−0.664721	+	1.32929i
$988$	741.747			0.750756
$989$		−	2780.12i		−	2.81105i
$990$	158.477	−	118.834i	0.160077	−	0.120034i
$991$	−1897.38			−1.91462			−0.957308	−	0.289069i	$-0.906654\pi$
$991$	−1897.38			−1.91462			−0.957308	+	0.289069i	$0.906654\pi$
$992$		−	262.101i		−	0.264215i
$993$	980.728	+	490.422i	0.987642	+	0.493879i
$994$	−1269.21			−1.27687
$995$		−	342.799i		−	0.344521i
$996$	−82.7801	+	165.541i	−0.0831126	+	0.166206i
$997$	22.2368			0.0223037			0.0111519	−	0.999938i	$-0.496450\pi$
$997$	22.2368			0.0223037			0.0111519	+	0.999938i	$0.496450\pi$
$998$			785.949i			0.787524i
$999$	−170.882	−	940.607i	−0.171053	−	0.941548i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.b.a.119.18	✓	40
3.2	odd	2	inner	354.3.b.a.119.38	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.b.a.119.18	✓	40	1.1	even	1	trivial
354.3.b.a.119.38	yes	40	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	354.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(2.68322 + 1.34177i) q^{3} -2.00000 q^{4} -2.14890i q^{5} +(1.89755 - 3.79464i) q^{6} +6.97234 q^{7} +2.82843i q^{8} +(5.39932 + 7.20051i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(2.68322 + 1.34177i) q^{3} -2.00000 q^{4} -2.14890i q^{5} +(1.89755 - 3.79464i) q^{6} +6.97234 q^{7} +2.82843i q^{8} +(5.39932 + 7.20051i) q^{9} -3.03900 q^{10} +7.24220i q^{11} +(-5.36644 - 2.68354i) q^{12} +14.9487 q^{13} -9.86037i q^{14} +(2.88332 - 5.76597i) q^{15} +4.00000 q^{16} +13.0567i q^{17} +(10.1831 - 7.63579i) q^{18} -24.8098 q^{19} +4.29780i q^{20} +(18.7083 + 9.35525i) q^{21} +10.2420 q^{22} -34.0644i q^{23} +(-3.79509 + 7.58929i) q^{24} +20.3822 q^{25} -21.1406i q^{26} +(4.82614 + 26.5652i) q^{27} -13.9447 q^{28} -44.6957i q^{29} +(-8.15431 - 4.07764i) q^{30} +46.3333 q^{31} -5.65685i q^{32} +(-9.71735 + 19.4324i) q^{33} +18.4650 q^{34} -14.9829i q^{35} +(-10.7986 - 14.4010i) q^{36} -35.4075 q^{37} +35.0864i q^{38} +(40.1105 + 20.0576i) q^{39} +6.07801 q^{40} +35.3328i q^{41} +(13.2303 - 26.4575i) q^{42} +81.6137 q^{43} -14.4844i q^{44} +(15.4732 - 11.6026i) q^{45} -48.1744 q^{46} +70.1295i q^{47} +(10.7329 + 5.36707i) q^{48} -0.386534 q^{49} -28.8248i q^{50} +(-17.5191 + 35.0340i) q^{51} -29.8973 q^{52} -35.4472i q^{53} +(37.5688 - 6.82519i) q^{54} +15.5628 q^{55} +19.7207i q^{56} +(-66.5701 - 33.2890i) q^{57} -63.2092 q^{58} -7.68115i q^{59} +(-5.76665 + 11.5319i) q^{60} -42.7396 q^{61} -65.5252i q^{62} +(37.6459 + 50.2044i) q^{63} -8.00000 q^{64} -32.1232i q^{65} +(27.4816 + 13.7424i) q^{66} -131.858 q^{67} -26.1134i q^{68} +(45.7066 - 91.4023i) q^{69} -21.1890 q^{70} -128.718i q^{71} +(-20.3661 + 15.2716i) q^{72} -67.8681 q^{73} +50.0738i q^{74} +(54.6900 + 27.3482i) q^{75} +49.6196 q^{76} +50.4950i q^{77} +(28.3658 - 56.7248i) q^{78} -31.1503 q^{79} -8.59560i q^{80} +(-22.6947 + 77.7557i) q^{81} +49.9681 q^{82} -30.8474i q^{83} +(-37.4166 - 18.7105i) q^{84} +28.0576 q^{85} -115.419i q^{86} +(59.9712 - 119.928i) q^{87} -20.4840 q^{88} +148.420i q^{89} +(-16.4085 - 21.8824i) q^{90} +104.227 q^{91} +68.1289i q^{92} +(124.322 + 62.1686i) q^{93} +99.1782 q^{94} +53.3138i q^{95} +(7.59018 - 15.1786i) q^{96} -118.098 q^{97} +0.546642i q^{98} +(-52.1475 + 39.1029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more