LMFDB - Embedded newform 312.4.m.a.181.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (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:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.30
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33907 + 2.49136i) q^{2} -3.00000i q^{3} +(-4.41379 - 6.67222i) q^{4} +12.3731 q^{5} +(7.47409 + 4.01721i) q^{6} +26.6265i q^{7} +(22.5333 - 2.06180i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+(-1.33907 + 2.49136i) q^{2} -3.00000i q^{3} +(-4.41379 - 6.67222i) q^{4} +12.3731 q^{5} +(7.47409 + 4.01721i) q^{6} +26.6265i q^{7} +(22.5333 - 2.06180i) q^{8} -9.00000 q^{9} +(-16.5684 + 30.8259i) q^{10} -33.2518 q^{11} +(-20.0166 + 13.2414i) q^{12} +(46.5141 - 5.78242i) q^{13} +(-66.3362 - 35.6547i) q^{14} -37.1193i q^{15} +(-25.0369 + 58.8995i) q^{16} +16.3112 q^{17} +(12.0516 - 22.4223i) q^{18} -43.9139 q^{19} +(-54.6122 - 82.5560i) q^{20} +79.8794 q^{21} +(44.5265 - 82.8424i) q^{22} +60.7638 q^{23} +(-6.18539 - 67.5999i) q^{24} +28.0936 q^{25} +(-47.8795 + 123.627i) q^{26} +27.0000i q^{27} +(177.657 - 117.524i) q^{28} +218.423i q^{29} +(92.4777 + 49.7053i) q^{30} +12.9421i q^{31} +(-113.214 - 141.247i) q^{32} +99.7554i q^{33} +(-21.8418 + 40.6372i) q^{34} +329.452i q^{35} +(39.7241 + 60.0499i) q^{36} +295.814 q^{37} +(58.8037 - 109.405i) q^{38} +(-17.3473 - 139.542i) q^{39} +(278.807 - 25.5108i) q^{40} +241.804i q^{41} +(-106.964 + 199.009i) q^{42} +290.617i q^{43} +(146.766 + 221.863i) q^{44} -111.358 q^{45} +(-81.3669 + 151.385i) q^{46} +385.921i q^{47} +(176.699 + 75.1108i) q^{48} -365.968 q^{49} +(-37.6192 + 69.9913i) q^{50} -48.9337i q^{51} +(-243.885 - 284.830i) q^{52} -220.063i q^{53} +(-67.2668 - 36.1549i) q^{54} -411.428 q^{55} +(54.8983 + 599.981i) q^{56} +131.742i q^{57} +(-544.171 - 292.484i) q^{58} +310.241 q^{59} +(-247.668 + 163.837i) q^{60} +156.672i q^{61} +(-32.2434 - 17.3303i) q^{62} -239.638i q^{63} +(503.498 - 92.9181i) q^{64} +(575.524 - 71.5465i) q^{65} +(-248.527 - 133.579i) q^{66} -586.837 q^{67} +(-71.9943 - 108.832i) q^{68} -182.291i q^{69} +(-820.784 - 441.159i) q^{70} +1144.05i q^{71} +(-202.800 + 18.5562i) q^{72} -792.744i q^{73} +(-396.115 + 736.981i) q^{74} -84.2808i q^{75} +(193.827 + 293.003i) q^{76} -885.378i q^{77} +(370.880 + 143.639i) q^{78} -1067.92 q^{79} +(-309.785 + 728.769i) q^{80} +81.0000 q^{81} +(-602.423 - 323.793i) q^{82} +1488.87 q^{83} +(-352.571 - 532.972i) q^{84} +201.820 q^{85} +(-724.033 - 389.156i) q^{86} +655.269 q^{87} +(-749.273 + 68.5585i) q^{88} +216.421i q^{89} +(149.116 - 277.433i) q^{90} +(153.965 + 1238.51i) q^{91} +(-268.199 - 405.429i) q^{92} +38.8262 q^{93} +(-961.469 - 516.774i) q^{94} -543.351 q^{95} +(-423.740 + 339.642i) q^{96} +789.333i q^{97} +(490.056 - 911.759i) q^{98} +299.266 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9}+O(q^{10}) $ 84 * q - 756 * q^9	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52} - 1616 q^{55} + 608 q^{56} - 2120 q^{62} - 2856 q^{64} + 696 q^{65} - 396 q^{66} - 2536 q^{68} - 3936 q^{74} - 156 q^{78} + 3160 q^{79} + 6804 q^{81} + 4276 q^{82} - 2088 q^{87} + 1780 q^{88} + 324 q^{90} + 4792 q^{92} - 860 q^{94} + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−1.33907	+	2.49136i	−0.473432	+	0.880830i
$2$	−1.33907	+	2.49136i	−0.473432	+	0.880830i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−4.41379	−	6.67222i	−0.551724	−	0.834027i
$5$	12.3731			1.10668			0.553342	−	0.832954i	$-0.313352\pi$
$5$	12.3731			1.10668			0.553342	+	0.832954i	$0.313352\pi$
$6$	7.47409	+	4.01721i	0.508548	+	0.273336i
$7$			26.6265i			1.43769i	0.695169	+	0.718847i	$0.255330\pi$
$7$			26.6265i			1.43769i	−0.695169	+	0.718847i	$0.744670\pi$
$8$	22.5333	−	2.06180i	0.995840	−	0.0911194i
$9$	−9.00000			−0.333333
$10$	−16.5684	+	30.8259i	−0.523940	+	0.974800i
$11$	−33.2518			−0.911436			−0.455718	−	0.890124i	$-0.650617\pi$
$11$	−33.2518			−0.911436			−0.455718	+	0.890124i	$0.650617\pi$
$12$	−20.0166	+	13.2414i	−0.481526	+	0.318538i
$13$	46.5141	−	5.78242i	0.992361	−	0.123366i
$13$	46.5141	−	5.78242i	0.992361	−	0.123366i
$14$	−66.3362	−	35.6547i	−1.26636	−	0.680651i
$15$		−	37.1193i		−	0.638944i
$16$	−25.0369	+	58.8995i	−0.391202	+	0.920305i
$17$	16.3112			0.232709			0.116354	−	0.993208i	$-0.462879\pi$
$17$	16.3112			0.232709			0.116354	+	0.993208i	$0.462879\pi$
$18$	12.0516	−	22.4223i	0.157811	−	0.293610i
$19$	−43.9139			−0.530239			−0.265119	−	0.964216i	$-0.585411\pi$
$19$	−43.9139			−0.530239			−0.265119	+	0.964216i	$0.585411\pi$
$20$	−54.6122	−	82.5560i	−0.610583	−	0.923004i
$21$	79.8794			0.830053
$22$	44.5265	−	82.8424i	0.431503	−	0.802821i
$23$	60.7638			0.550875			0.275438	−	0.961319i	$-0.411177\pi$
$23$	60.7638			0.550875			0.275438	+	0.961319i	$0.411177\pi$
$24$	−6.18539	−	67.5999i	−0.0526078	−	0.574948i
$25$	28.0936			0.224749
$26$	−47.8795	+	123.627i	−0.361152	+	0.932507i
$27$			27.0000i			0.192450i
$28$	177.657	−	117.524i	1.19908	−	0.793209i
$29$			218.423i			1.39863i	0.714816	+	0.699313i	$0.246511\pi$
$29$			218.423i			1.39863i	−0.714816	+	0.699313i	$0.753489\pi$
$30$	92.4777	+	49.7053i	0.562801	+	0.302497i
$31$			12.9421i			0.0749827i	0.999297	+	0.0374914i	$0.0119367\pi$
$31$			12.9421i			0.0749827i	−0.999297	+	0.0374914i	$0.988063\pi$
$32$	−113.214	−	141.247i	−0.625424	−	0.780285i
$33$			99.7554i			0.526218i
$34$	−21.8418	+	40.6372i	−0.110172	+	0.204977i
$35$			329.452i			1.59107i
$36$	39.7241	+	60.0499i	0.183908	+	0.278009i
$37$	295.814			1.31437			0.657183	−	0.753731i	$-0.271748\pi$
$37$	295.814			1.31437			0.657183	+	0.753731i	$0.271748\pi$
$38$	58.8037	−	109.405i	0.251032	−	0.467050i
$39$	−17.3473	−	139.542i	−0.0712252	−	0.572940i
$40$	278.807	−	25.5108i	1.10208	−	0.100840i
$41$			241.804i			0.921061i	0.887644	+	0.460530i	$0.152341\pi$
$41$			241.804i			0.921061i	−0.887644	+	0.460530i	$0.847659\pi$
$42$	−106.964	+	199.009i	−0.392974	+	0.731135i
$43$			290.617i			1.03067i	0.856990	+	0.515333i	$0.172332\pi$
$43$			290.617i			1.03067i	−0.856990	+	0.515333i	$0.827668\pi$
$44$	146.766	+	221.863i	0.502861	+	0.760162i
$45$	−111.358			−0.368895
$46$	−81.3669	+	151.385i	−0.260802	+	0.485227i
$47$			385.921i			1.19771i	0.800858	+	0.598854i	$0.204377\pi$
$47$			385.921i			1.19771i	−0.800858	+	0.598854i	$0.795623\pi$
$48$	176.699	+	75.1108i	0.531338	+	0.225861i
$49$	−365.968			−1.06696
$50$	−37.6192	+	69.9913i	−0.106403	+	0.197965i
$51$		−	48.9337i		−	0.134355i
$52$	−243.885	−	284.830i	−0.650399	−	0.759592i
$53$		−	220.063i		−	0.570338i	−0.958477	−	0.285169i	$-0.907950\pi$
$53$		−	220.063i		−	0.570338i	0.958477	−	0.285169i	$-0.0920498\pi$
$54$	−67.2668	−	36.1549i	−0.169516	−	0.0911121i
$55$	−411.428			−1.00867
$56$	54.8983	+	599.981i	0.131002	+	1.43171i
$57$			131.742i			0.306133i
$58$	−544.171	−	292.484i	−1.23195	−	0.662155i
$59$	310.241			0.684575			0.342288	−	0.939595i	$-0.388798\pi$
$59$	310.241			0.684575			0.342288	+	0.939595i	$0.388798\pi$
$60$	−247.668	+	163.837i	−0.532897	+	0.352521i
$61$			156.672i			0.328848i	0.986390	+	0.164424i	$0.0525766\pi$
$61$			156.672i			0.328848i	−0.986390	+	0.164424i	$0.947423\pi$
$62$	−32.2434	−	17.3303i	−0.0660470	−	0.0354992i
$63$		−	239.638i		−	0.479231i
$64$	503.498	−	92.9181i	0.983395	−	0.181481i
$65$	575.524	−	71.5465i	1.09823	−	0.136527i
$66$	−248.527	−	133.579i	−0.463509	−	0.249129i
$67$	−586.837			−1.07005			−0.535027	−	0.844835i	$-0.679699\pi$
$67$	−586.837			−1.07005			−0.535027	+	0.844835i	$0.679699\pi$
$68$	−71.9943	−	108.832i	−0.128391	−	0.194086i
$69$		−	182.291i		−	0.318048i
$70$	−820.784	−	441.159i	−1.40146	−	0.753265i
$71$			1144.05i			1.91231i	0.292857	+	0.956156i	$0.405394\pi$
$71$			1144.05i			1.91231i	−0.292857	+	0.956156i	$0.594606\pi$
$72$	−202.800	+	18.5562i	−0.331947	+	0.0303731i
$73$		−	792.744i		−	1.27101i	−0.772097	−	0.635505i	$-0.780792\pi$
$73$		−	792.744i		−	1.27101i	0.772097	−	0.635505i	$-0.219208\pi$
$74$	−396.115	+	736.981i	−0.622263	+	1.15773i
$75$		−	84.2808i		−	0.129759i
$76$	193.827	+	293.003i	0.292545	+	0.442233i
$77$		−	885.378i		−	1.31037i
$78$	370.880	+	143.639i	0.538383	+	0.208511i
$79$	−1067.92			−1.52090			−0.760449	−	0.649398i	$-0.775021\pi$
$79$	−1067.92			−1.52090			−0.760449	+	0.649398i	$0.775021\pi$
$80$	−309.785	+	728.769i	−0.432937	+	1.01849i
$81$	81.0000			0.111111
$82$	−602.423	−	323.793i	−0.811298	−	0.436060i
$83$	1488.87			1.96897			0.984484	−	0.175474i	$-0.0561457\pi$
$83$	1488.87			1.96897			0.984484	+	0.175474i	$0.0561457\pi$
$84$	−352.571	−	532.972i	−0.457960	−	0.692286i
$85$	201.820			0.257535
$86$	−724.033	−	389.156i	−0.907842	−	0.487951i
$87$	655.269			0.807497
$88$	−749.273	+	68.5585i	−0.907645	+	0.0830495i
$89$			216.421i			0.257759i	0.991660	+	0.128879i	$0.0411380\pi$
$89$			216.421i			0.257759i	−0.991660	+	0.128879i	$0.958862\pi$
$90$	149.116	−	277.433i	0.174647	−	0.324933i
$91$	153.965	+	1238.51i	0.177362	+	1.42671i
$92$	−268.199	−	405.429i	−0.303931	−	0.459445i
$93$	38.8262			0.0432913
$94$	−961.469	−	516.774i	−1.05498	−	0.567034i
$95$	−543.351			−0.586806
$96$	−423.740	+	339.642i	−0.450498	+	0.361089i
$97$			789.333i			0.826233i	0.910678	+	0.413116i	$0.135560\pi$
$97$			789.333i			0.826233i	−0.910678	+	0.413116i	$0.864440\pi$
$98$	490.056	−	911.759i	0.505134	−	0.939812i
$99$	299.266			0.303812
$100$	−123.999	−	187.446i	−0.123999	−	0.187446i
$101$			330.153i			0.325262i	0.986687	+	0.162631i	$0.0519980\pi$
$101$			330.153i			0.325262i	−0.986687	+	0.162631i	$0.948002\pi$
$102$	121.912	+	65.5255i	0.118344	+	0.0636078i
$103$	1253.95			1.19957			0.599786	−	0.800161i	$-0.295253\pi$
$103$	1253.95			1.19957			0.599786	+	0.800161i	$0.295253\pi$
$104$	1036.19	−	226.200i	0.976992	−	0.213276i
$105$	988.355			0.918606
$106$	548.256	+	294.679i	0.502371	+	0.270017i
$107$			338.058i			0.305433i	0.988270	+	0.152716i	$0.0488021\pi$
$107$			338.058i			0.305433i	−0.988270	+	0.152716i	$0.951198\pi$
$108$	180.150	−	119.172i	0.160509	−	0.106179i
$109$	2042.84			1.79512			0.897560	−	0.440892i	$-0.145338\pi$
$109$	2042.84			1.79512			0.897560	+	0.440892i	$0.145338\pi$
$110$	550.930	−	1025.02i	0.477538	−	0.888468i
$111$		−	887.442i		−	0.758849i
$112$	−1568.28	−	666.645i	−1.32312	−	0.562429i
$113$	698.175			0.581228			0.290614	−	0.956840i	$-0.406140\pi$
$113$	698.175			0.581228			0.290614	+	0.956840i	$0.406140\pi$
$114$	−328.216	−	176.411i	−0.269652	−	0.144933i
$115$	751.836			0.609644
$116$	1457.37	−	964.073i	1.16649	−	0.771655i
$117$	−418.627	+	52.0418i	−0.330787	+	0.0411219i
$118$	−415.434	+	772.923i	−0.324100	+	0.602994i
$119$			434.310i			0.334564i
$120$	−76.5324	−	836.420i	−0.0582202	−	0.636286i
$121$	−225.317			−0.169284
$122$	−390.326	−	209.794i	−0.289660	−	0.155687i
$123$	725.413			0.531775
$124$	86.3523	−	57.1236i	0.0625376	−	0.0413697i
$125$	−1199.03			−0.857958
$126$	597.026	+	320.892i	0.422121	+	0.226884i
$127$	−2143.64			−1.49777			−0.748887	−	0.662698i	$-0.769411\pi$
$127$	−2143.64			−1.49777			−0.748887	+	0.662698i	$0.769411\pi$
$128$	−442.726	+	1378.82i	−0.305717	+	0.952122i
$129$	871.851			0.595056
$130$	−592.418	+	1529.65i	−0.399681	+	1.03199i
$131$		−	737.484i		−	0.491865i	−0.969287	−	0.245932i	$-0.920906\pi$
$131$		−	737.484i		−	0.491865i	0.969287	−	0.245932i	$-0.0790941\pi$
$132$	665.590	−	440.299i	0.438880	−	0.290327i
$133$		−	1169.27i		−	0.762321i
$134$	785.816	−	1462.03i	0.506598	−	0.942536i
$135$			334.074i			0.212981i
$136$	367.545	−	33.6304i	0.231741	−	0.0212043i
$137$			675.377i			0.421178i	0.977575	+	0.210589i	$0.0675381\pi$
$137$			675.377i			0.421178i	−0.977575	+	0.210589i	$0.932462\pi$
$138$	454.154	+	244.101i	0.280146	+	0.150574i
$139$		−	1169.92i		−	0.713894i	−0.934125	−	0.356947i	$-0.883818\pi$
$139$		−	1169.92i		−	0.713894i	0.934125	−	0.356947i	$-0.116182\pi$
$140$	2198.17	−	1454.13i	1.32700	−	0.877832i
$141$	1157.76			0.691497
$142$	−2850.25	−	1531.97i	−1.68442	−	0.905351i
$143$	−1546.68	+	192.276i	−0.904474	+	0.112440i
$144$	225.332	−	530.096i	0.130401	−	0.306768i
$145$			2702.57i			1.54784i
$146$	1975.01	+	1061.54i	1.11954	+	0.601737i
$147$			1097.90i			0.616011i
$148$	−1305.66	−	1973.74i	−0.725167	−	1.09622i
$149$	345.352			0.189881			0.0949407	−	0.995483i	$-0.469734\pi$
$149$	345.352			0.189881			0.0949407	+	0.995483i	$0.469734\pi$
$150$	209.974	+	112.858i	0.114295	+	0.0614320i
$151$		−	3320.28i		−	1.78941i	−0.446659	−	0.894704i	$-0.647386\pi$
$151$		−	3320.28i		−	1.78941i	0.446659	−	0.894704i	$-0.352614\pi$
$152$	−989.524	+	90.5415i	−0.528033	+	0.0483150i
$153$	−146.801			−0.0775696
$154$	2205.80	+	1185.58i	1.15421	+	0.620370i
$155$			160.134i			0.0829821i
$156$	−854.490	+	731.655i	−0.438551	+	0.375508i
$157$		−	1992.84i		−	1.01303i	−0.862231	−	0.506515i	$-0.830934\pi$
$157$		−	1992.84i		−	1.01303i	0.862231	−	0.506515i	$-0.169066\pi$
$158$	1430.03	−	2660.59i	0.720042	−	1.33965i
$159$	−660.188			−0.329285
$160$	−1400.81	−	1747.66i	−0.692147	−	0.863528i
$161$			1617.92i			0.791989i
$162$	−108.465	+	201.800i	−0.0526036	+	0.0978700i
$163$	1280.70			0.615411			0.307706	−	0.951482i	$-0.400439\pi$
$163$	1280.70			0.615411			0.307706	+	0.951482i	$0.400439\pi$
$164$	1613.37	−	1067.27i	0.768190	−	0.508171i
$165$			1234.28i			0.582357i
$166$	−1993.70	+	3709.31i	−0.932173	+	1.73433i
$167$		−	607.816i		−	0.281642i	−0.990035	−	0.140821i	$-0.955026\pi$
$167$		−	607.816i		−	0.281642i	0.990035	−	0.140821i	$-0.0449742\pi$
$168$	1799.94	−	164.695i	0.826600	−	0.0756339i
$169$	2130.13	−	537.928i	0.969562	−	0.244847i
$170$	−270.251	+	502.808i	−0.121925	+	0.226845i
$171$	395.225			0.176746
$172$	1939.06	−	1282.72i	0.859604	−	0.568643i
$173$		−	880.682i		−	0.387035i	−0.981097	−	0.193517i	$-0.938010\pi$
$173$		−	880.682i		−	0.387035i	0.981097	−	0.193517i	$-0.0619896\pi$
$174$	−877.451	+	1632.51i	−0.382295	+	0.711268i
$175$			748.032i			0.323120i
$176$	832.524	−	1958.52i	0.356556	−	0.838799i
$177$		−	930.723i		−	0.395240i
$178$	−539.182	−	289.802i	−0.227042	−	0.122031i
$179$		−	592.328i		−	0.247333i	−0.992324	−	0.123667i	$-0.960535\pi$
$179$		−	592.328i		−	0.247333i	0.992324	−	0.123667i	$-0.0394654\pi$
$180$	491.510	+	743.004i	0.203528	+	0.307668i
$181$		−	4237.05i		−	1.73999i	−0.493062	−	0.869994i	$-0.664123\pi$
$181$		−	4237.05i		−	1.73999i	0.493062	−	0.869994i	$-0.335877\pi$
$182$	−3291.74	−	1274.86i	−1.34066	−	0.519225i
$183$	470.015			0.189861
$184$	1369.21	−	125.283i	0.548583	−	0.0501954i
$185$	3660.14			1.45459
$186$	−51.9910	+	96.7302i	−0.0204955	+	0.0381323i
$187$	−542.378			−0.212099
$188$	2574.95	−	1703.37i	0.998921	−	0.660804i
$189$	−718.914			−0.276684
$190$	727.584	−	1353.68i	0.277813	−	0.516877i
$191$	−3247.76			−1.23037			−0.615183	−	0.788385i	$-0.710918\pi$
$191$	−3247.76			−1.23037			−0.615183	+	0.788385i	$0.710918\pi$
$192$	−278.754	−	1510.49i	−0.104778	−	0.567763i
$193$		−	3309.31i		−	1.23424i	−0.786868	−	0.617122i	$-0.788299\pi$
$193$		−	3309.31i		−	1.23424i	0.786868	−	0.617122i	$-0.211701\pi$
$194$	−1966.52	−	1056.97i	−0.727771	−	0.391165i
$195$	−214.639	−	1726.57i	−0.0788238	−	0.634063i
$196$	1615.31	+	2441.82i	0.588668	+	0.889875i
$197$	−927.123			−0.335304			−0.167652	−	0.985846i	$-0.553618\pi$
$197$	−927.123			−0.335304			−0.167652	+	0.985846i	$0.553618\pi$
$198$	−400.738	+	745.581i	−0.143834	+	0.267607i
$199$	−2866.60			−1.02114			−0.510572	−	0.859835i	$-0.670566\pi$
$199$	−2866.60			−1.02114			−0.510572	+	0.859835i	$0.670566\pi$
$200$	633.041	−	57.9233i	0.223814	−	0.0204790i
$201$			1760.51i			0.617796i
$202$	−822.532	−	442.098i	−0.286501	−	0.153990i
$203$	−5815.83			−2.01079
$204$	−326.496	+	215.983i	−0.112055	+	0.0741266i
$205$			2991.87i			1.01932i
$206$	−1679.13	+	3124.06i	−0.567916	+	1.05662i
$207$	−546.874			−0.183625
$208$	−823.990	+	2884.43i	−0.274680	+	0.961536i
$209$	1460.22			0.483279
$210$	−1323.48	+	2462.35i	−0.434898	+	0.809136i
$211$		−	2889.60i		−	0.942788i	−0.881923	−	0.471394i	$-0.843751\pi$
$211$		−	2889.60i		−	0.942788i	0.881923	−	0.471394i	$-0.156249\pi$
$212$	−1468.31	+	971.310i	−0.475678	+	0.314669i
$213$	3432.16			1.10407
$214$	−842.226	−	452.683i	−0.269035	−	0.144602i
$215$			3595.83i			1.14062i
$216$	55.6685	+	608.399i	0.0175359	+	0.191649i
$217$	−344.601			−0.107802
$218$	−2735.50	+	5089.45i	−0.849868	+	1.58120i
$219$	−2378.23			−0.733818
$220$	1815.96	+	2745.14i	0.556508	+	0.841259i
$221$	758.702	−	94.3183i	0.230931	−	0.0287083i
$222$	2210.94	+	1188.35i	0.668417	+	0.359264i
$223$			2734.42i			0.821122i	0.911833	+	0.410561i	$0.134667\pi$
$223$			2734.42i			0.821122i	−0.911833	+	0.410561i	$0.865333\pi$
$224$	3760.90	−	3014.48i	1.12181	−	0.899168i
$225$	−252.842			−0.0749162
$226$	−934.904	+	1739.41i	−0.275172	+	0.511963i
$227$	−5723.82			−1.67358			−0.836792	−	0.547522i	$-0.815571\pi$
$227$	−5723.82			−1.67358			−0.836792	+	0.547522i	$0.815571\pi$
$228$	879.009	−	581.480i	0.255324	−	0.168901i
$229$	−1732.49			−0.499940			−0.249970	−	0.968254i	$-0.580421\pi$
$229$	−1732.49			−0.499940			−0.249970	+	0.968254i	$0.580421\pi$
$230$	−1006.76	+	1873.10i	−0.288625	+	0.536993i
$231$	−2656.13			−0.756540
$232$	450.344	+	4921.79i	0.127442	+	1.39281i
$233$	−215.288			−0.0605321			−0.0302661	−	0.999542i	$-0.509635\pi$
$233$	−215.288			−0.0605321			−0.0302661	+	0.999542i	$0.509635\pi$
$234$	430.916	−	1112.64i	0.120384	−	0.310836i
$235$			4775.03i			1.32548i
$236$	−1369.34	−	2069.99i	−0.377696	−	0.570954i
$237$			3203.77i			0.878091i
$238$	−1082.02	−	581.571i	−0.294694	−	0.158393i
$239$		−	1089.11i		−	0.294765i	−0.989080	−	0.147382i	$-0.952915\pi$
$239$		−	1089.11i		−	0.294765i	0.989080	−	0.147382i	$-0.0470848\pi$
$240$	2186.31	+	929.354i	0.588023	+	0.249956i
$241$		−	662.017i		−	0.176947i	−0.996079	−	0.0884736i	$-0.971801\pi$
$241$		−	662.017i		−	0.176947i	0.996079	−	0.0884736i	$-0.0281989\pi$
$242$	301.715	−	561.347i	0.0801445	−	0.149110i
$243$		−	243.000i		−	0.0641500i
$244$	1045.35	−	691.516i	0.274268	−	0.181433i
$245$	−4528.16			−1.18079
$246$	−971.378	+	1807.27i	−0.251759	+	0.468403i
$247$	−2042.62	+	253.928i	−0.526188	+	0.0654133i
$248$	26.6839	+	291.627i	0.00683238	+	0.0746708i
$249$		−	4466.60i		−	1.13678i
$250$	1605.59	−	2987.23i	0.406185	−	0.755715i
$251$			3890.75i			0.978414i	0.872168	+	0.489207i	$0.162714\pi$
$251$			3890.75i			0.978414i	−0.872168	+	0.489207i	$0.837286\pi$
$252$	−1598.92	+	1057.71i	−0.399692	+	0.264403i
$253$	−2020.51			−0.502088
$254$	2870.48	−	5340.59i	0.709095	−	1.31928i
$255$		−	605.461i		−	0.148688i
$256$	−2842.30	−	2949.33i	−0.693922	−	0.720050i
$257$	5412.97			1.31382			0.656910	−	0.753969i	$-0.271863\pi$
$257$	5412.97			1.31382			0.656910	+	0.753969i	$0.271863\pi$
$258$	−1167.47	+	2172.10i	−0.281719	+	0.524143i
$259$			7876.48i			1.88965i
$260$	−3017.61	−	3524.23i	−0.719786	−	0.840628i
$261$		−	1965.81i		−	0.466209i
$262$	1837.34	+	987.542i	0.433249	+	0.232865i
$263$	4583.78			1.07471			0.537354	−	0.843357i	$-0.319424\pi$
$263$	4583.78			1.07471			0.537354	+	0.843357i	$0.319424\pi$
$264$	205.675	+	2247.82i	0.0479487	+	0.524029i
$265$		−	2722.86i		−	0.631184i
$266$	2913.08	+	1565.73i	0.671475	+	0.360907i
$267$	649.262			0.148817
$268$	2590.18	+	3915.51i	0.590374	+	0.892454i
$269$			7190.74i			1.62984i	0.579574	+	0.814920i	$0.303219\pi$
$269$			7190.74i			1.62984i	−0.579574	+	0.814920i	$0.696781\pi$
$270$	−832.299	−	447.348i	−0.187600	−	0.100832i
$271$		−	4023.60i		−	0.901906i	−0.892548	−	0.450953i	$-0.851084\pi$
$271$		−	4023.60i		−	0.901906i	0.892548	−	0.450953i	$-0.148916\pi$
$272$	−408.383	+	960.723i	−0.0910362	+	0.214163i
$273$	3715.52	−	461.896i	0.823712	−	0.102400i
$274$	−1682.61	−	904.376i	−0.370986	−	0.199399i
$275$	−934.163			−0.204844
$276$	−1216.29	+	804.596i	−0.265261	+	0.175475i
$277$		−	4021.05i		−	0.872208i	−0.899896	−	0.436104i	$-0.856358\pi$
$277$		−	4021.05i		−	0.872208i	0.899896	−	0.436104i	$-0.143642\pi$
$278$	2914.69	+	1566.60i	0.628819	+	0.337980i
$279$		−	116.479i		−	0.0249942i
$280$	679.262	+	7423.63i	0.144977	+	1.58445i
$281$		−	3305.74i		−	0.701794i	−0.936414	−	0.350897i	$-0.885877\pi$
$281$		−	3305.74i		−	0.701794i	0.936414	−	0.350897i	$-0.114123\pi$
$282$	−1550.32	+	2884.41i	−0.327377	+	0.609092i
$283$			1829.42i			0.384268i	0.981369	+	0.192134i	$0.0615409\pi$
$283$			1829.42i			0.384268i	−0.981369	+	0.192134i	$0.938459\pi$
$284$	7633.37	−	5049.61i	1.59492	−	1.05507i
$285$			1630.05i			0.338793i
$286$	1592.08	−	4110.81i	0.329167	−	0.849921i
$287$	−6438.39			−1.32420
$288$	1018.93	+	1271.22i	0.208475	+	0.260095i
$289$	−4646.94			−0.945847
$290$	−6733.09	−	3618.93i	−1.36338	−	0.732796i
$291$	2368.00			0.477026
$292$	−5289.36	+	3499.00i	−1.06006	+	0.701246i
$293$	2987.24			0.595620			0.297810	−	0.954625i	$-0.403744\pi$
$293$	2987.24			0.595620			0.297810	+	0.954625i	$0.403744\pi$
$294$	−2735.28	−	1470.17i	−0.542601	−	0.291639i
$295$	3838.64			0.757608
$296$	6665.66	−	609.908i	1.30890	−	0.119764i
$297$		−	897.799i		−	0.175406i
$298$	−462.450	+	860.398i	−0.0898960	+	0.167253i
$299$	2826.37	−	351.362i	0.546667	−	0.0679591i
$300$	−562.339	+	371.997i	−0.108222	+	0.0715909i
$301$	−7738.10			−1.48178
$302$	8272.03	+	4446.09i	1.57617	+	0.847164i
$303$	990.460			0.187790
$304$	1099.47	−	2586.51i	0.207431	−	0.487981i
$305$			1938.51i			0.363931i
$306$	196.577	−	365.735i	0.0367240	−	0.0683257i
$307$	2216.84			0.412123			0.206061	−	0.978539i	$-0.433935\pi$
$307$	2216.84			0.412123			0.206061	+	0.978539i	$0.433935\pi$
$308$	−5907.43	+	3907.87i	−1.09288	+	0.722960i
$309$		−	3761.86i		−	0.692573i
$310$	−398.951	−	214.430i	−0.0730932	−	0.0392864i
$311$	5640.21			1.02838			0.514191	−	0.857676i	$-0.328092\pi$
$311$	5640.21			1.02838			0.514191	+	0.857676i	$0.328092\pi$
$312$	−678.599	−	3108.58i	−0.123135	−	0.564067i
$313$	9322.22			1.68346			0.841730	−	0.539899i	$-0.181537\pi$
$313$	9322.22			1.68346			0.841730	+	0.539899i	$0.181537\pi$
$314$	4964.88	+	2668.54i	0.892307	+	0.479601i
$315$		−	2965.07i		−	0.530357i
$316$	4713.59	+	7125.43i	0.839115	+	1.26847i
$317$	−5397.79			−0.956372			−0.478186	−	0.878259i	$-0.658705\pi$
$317$	−5397.79			−0.956372			−0.478186	+	0.878259i	$0.658705\pi$
$318$	884.037	−	1644.77i	0.155894	−	0.290044i
$319$		−	7262.96i		−	1.27476i
$320$	6229.83	−	1149.68i	1.08831	−	0.200842i
$321$	1014.17			0.176342
$322$	−4030.84	−	2166.51i	−0.697608	−	0.374953i
$323$	−716.289			−0.123391
$324$	−357.517	−	540.450i	−0.0613026	−	0.0926697i
$325$	1306.75	−	162.449i	0.223032	−	0.0277263i
$326$	−1714.94	+	3190.69i	−0.291356	+	0.542073i
$327$		−	6128.51i		−	1.03641i
$328$	498.551	+	5448.65i	0.0839265	+	0.917229i
$329$	−10275.7			−1.72194
$330$	−3075.05	−	1652.79i	−0.512957	−	0.275707i
$331$	3179.90			0.528046			0.264023	−	0.964516i	$-0.414951\pi$
$331$	3179.90			0.528046			0.264023	+	0.964516i	$0.414951\pi$
$332$	−6571.54	−	9934.04i	−1.08633	−	1.64217i
$333$	−2662.33			−0.438122
$334$	1514.29	+	813.908i	0.248079	+	0.133339i
$335$	−7261.00			−1.18421
$336$	−1999.93	+	4704.85i	−0.324718	+	0.763901i
$337$	−3425.43			−0.553694			−0.276847	−	0.960914i	$-0.589290\pi$
$337$	−3425.43			−0.553694			−0.276847	+	0.960914i	$0.589290\pi$
$338$	−1512.21	+	6027.25i	−0.243353	+	0.969938i
$339$		−	2094.52i		−	0.335572i
$340$	−890.792	−	1346.59i	−0.142088	−	0.214791i
$341$		−	430.347i		−	0.0683420i
$342$	−529.233	+	984.649i	−0.0836774	+	0.155683i
$343$		−	611.554i		−	0.0962706i
$344$	599.193	+	6548.55i	0.0939137	+	1.02638i
$345$		−	2255.51i		−	0.351978i
$346$	2194.10	+	1179.29i	0.340912	+	0.183235i
$347$		−	12219.0i		−	1.89035i	−0.326558	−	0.945177i	$-0.605889\pi$
$347$		−	12219.0i		−	1.89035i	0.326558	−	0.945177i	$-0.394111\pi$
$348$	−2892.22	−	4372.10i	−0.445515	−	0.673474i
$349$	5703.61			0.874805			0.437403	−	0.899266i	$-0.355898\pi$
$349$	5703.61			0.874805			0.437403	+	0.899266i	$0.355898\pi$
$350$	−1863.62	−	1001.67i	−0.284614	−	0.152975i
$351$	156.125	+	1255.88i	0.0237417	+	0.190980i
$352$	3764.57	+	4696.71i	0.570035	+	0.711180i
$353$			6902.30i			1.04071i	0.853949	+	0.520357i	$0.174201\pi$
$353$			6902.30i			1.04071i	−0.853949	+	0.520357i	$0.825799\pi$
$354$	2318.77	+	1246.30i	0.348139	+	0.187119i
$355$			14155.5i			2.11632i
$356$	1444.01	−	955.235i	0.214978	−	0.142212i
$357$	1302.93			0.193161
$358$	1475.70	+	793.168i	0.217859	+	0.117096i
$359$		−	5910.58i		−	0.868937i	−0.900687	−	0.434468i	$-0.856936\pi$
$359$		−	5910.58i		−	0.868937i	0.900687	−	0.434468i	$-0.143064\pi$
$360$	−2509.26	+	229.597i	−0.367360	+	0.0336134i
$361$	−4930.57			−0.718847
$362$	10556.0	+	5673.71i	1.53263	+	0.823767i
$363$			675.951i			0.0977362i
$364$	7584.01	−	6493.79i	1.09206	−	0.935075i
$365$		−	9808.70i		−	1.40661i
$366$	−629.383	+	1170.98i	−0.0898862	+	0.167235i
$367$	8817.17			1.25409			0.627047	−	0.778982i	$-0.284263\pi$
$367$	8817.17			1.25409			0.627047	+	0.778982i	$0.284263\pi$
$368$	−1521.34	+	3578.96i	−0.215504	+	0.506973i
$369$		−	2176.24i		−	0.307020i
$370$	−4901.18	+	9118.73i	−0.688649	+	1.28124i
$371$	5859.49			0.819972
$372$	−171.371	−	259.057i	−0.0238848	−	0.0361061i
$373$		−	7090.83i		−	0.984314i	−0.870506	−	0.492157i	$-0.836209\pi$
$373$		−	7090.83i		−	0.984314i	0.870506	−	0.492157i	$-0.163791\pi$
$374$	726.281	−	1351.26i	0.100415	−	0.186823i
$375$			3597.10i			0.495342i
$376$	795.690	+	8696.06i	0.109134	+	1.19273i
$377$	1263.01	+	10159.8i	0.172543	+	1.38794i
$378$	962.676	−	1791.08i	0.130991	−	0.243712i
$379$	−7150.31			−0.969094			−0.484547	−	0.874765i	$-0.661016\pi$
$379$	−7150.31			−0.969094			−0.484547	+	0.874765i	$0.661016\pi$
$380$	2398.24	+	3625.35i	0.323755	+	0.489412i
$381$			6430.92i			0.864740i
$382$	4348.98	−	8091.36i	0.582495	−	1.08374i
$383$			6280.67i			0.837930i	0.908002	+	0.418965i	$0.137607\pi$
$383$			6280.67i			0.837930i	−0.908002	+	0.418965i	$0.862393\pi$
$384$	4136.46	+	1328.18i	0.549708	+	0.176506i
$385$		−	10954.9i		−	1.45016i
$386$	8244.69	+	4431.39i	1.08716	+	0.584331i
$387$		−	2615.55i		−	0.343556i
$388$	5266.60	−	3483.95i	0.689101	−	0.455852i
$389$		−	5719.43i		−	0.745467i	−0.927938	−	0.372734i	$-0.878421\pi$
$389$		−	5719.43i		−	0.745467i	0.927938	−	0.372734i	$-0.121579\pi$
$390$	4588.94	+	1777.25i	0.595820	+	0.230756i
$391$	991.132			0.128194
$392$	−8246.46	+	754.551i	−1.06252	+	0.0972209i
$393$	−2212.45			−0.283978
$394$	1241.48	−	2309.80i	0.158744	−	0.295345i
$395$	−13213.5			−1.68315
$396$	−1320.90	−	1996.77i	−0.167620	−	0.253387i
$397$	2754.07			0.348168			0.174084	−	0.984731i	$-0.444304\pi$
$397$	2754.07			0.348168			0.174084	+	0.984731i	$0.444304\pi$
$398$	3838.57	−	7141.73i	0.483442	−	0.899454i
$399$	−3507.81			−0.440126
$400$	−703.377	+	1654.70i	−0.0879222	+	0.206837i
$401$			12405.6i			1.54490i	0.635073	+	0.772452i	$0.280970\pi$
$401$			12405.6i			1.54490i	−0.635073	+	0.772452i	$0.719030\pi$
$402$	−4386.08	−	2357.45i	−0.544173	−	0.292485i
$403$	74.8365	+	601.989i	0.00925030	+	0.0744099i
$404$	2202.85	−	1457.23i	0.271277	−	0.179455i
$405$	1002.22			0.122965
$406$	7787.80	−	14489.4i	0.951975	−	1.77117i
$407$	−9836.35			−1.19796
$408$	−100.891	−	1102.64i	−0.0122423	−	0.133796i
$409$			2163.40i			0.261549i	0.991412	+	0.130774i	$0.0417463\pi$
$409$			2163.40i			0.261549i	−0.991412	+	0.130774i	$0.958254\pi$
$410$	−7453.84	−	4006.32i	−0.897851	−	0.482581i
$411$	2026.13			0.243167
$412$	−5534.69	−	8366.66i	−0.661832	−	1.00047i
$413$			8260.61i			0.984209i
$414$	732.302	−	1362.46i	0.0869340	−	0.161742i
$415$	18421.9			2.17902
$416$	−6082.79	−	5915.31i	−0.716907	−	0.697168i
$417$	−3509.76			−0.412167
$418$	−1955.33	+	3637.93i	−0.228800	+	0.425687i
$419$		−	1787.02i		−	0.208357i	−0.994559	−	0.104178i	$-0.966779\pi$
$419$		−	1787.02i		−	0.208357i	0.994559	−	0.104178i	$-0.0332213\pi$
$420$	−4362.39	−	6594.52i	−0.506816	−	0.766142i
$421$	6432.75			0.744686			0.372343	−	0.928095i	$-0.378554\pi$
$421$	6432.75			0.744686			0.372343	+	0.928095i	$0.378554\pi$
$422$	7199.05	+	3869.37i	0.830436	+	0.446346i
$423$		−	3473.29i		−	0.399236i
$424$	−453.724	−	4958.73i	−0.0519689	−	0.567966i
$425$	458.241			0.0523010
$426$	−4595.90	+	8550.76i	−0.522704	+	0.972502i
$427$	−4171.61			−0.472783
$428$	2255.60	−	1492.12i	0.254739	−	0.168515i
$429$	576.828	+	4640.04i	0.0649173	+	0.522198i
$430$	−8958.53	−	4815.07i	−1.00469	−	0.540007i
$431$		−	13495.7i		−	1.50828i	−0.656716	−	0.754138i	$-0.728055\pi$
$431$		−	13495.7i		−	1.50828i	0.656716	−	0.754138i	$-0.271945\pi$
$432$	−1590.29	−	675.997i	−0.177113	−	0.0752869i
$433$	−8248.31			−0.915447			−0.457724	−	0.889095i	$-0.651335\pi$
$433$	−8248.31			−0.915447			−0.457724	+	0.889095i	$0.651335\pi$
$434$	461.445	−	858.527i	0.0510370	−	0.0949554i
$435$	8107.71			0.893644
$436$	−9016.64	−	13630.2i	−0.990410	−	1.49718i
$437$	−2668.37			−0.292095
$438$	3184.62	−	5925.04i	0.347413	−	0.646369i
$439$	−1721.73			−0.187184			−0.0935918	−	0.995611i	$-0.529835\pi$
$439$	−1721.73			−0.187184			−0.0935918	+	0.995611i	$0.529835\pi$
$440$	−9270.82	+	848.281i	−1.00448	+	0.0919095i
$441$	3293.71			0.355654
$442$	−780.973	+	2016.50i	−0.0840432	+	0.217003i
$443$		−	6001.77i		−	0.643686i	−0.946793	−	0.321843i	$-0.895698\pi$
$443$		−	6001.77i		−	0.643686i	0.946793	−	0.321843i	$-0.104302\pi$
$444$	−5921.21	+	3916.98i	−0.632901	+	0.418675i
$445$			2677.79i			0.285258i
$446$	−6812.44	−	3661.58i	−0.723269	−	0.388746i
$447$		−	1036.06i		−	0.109628i
$448$	2474.08	+	13406.4i	0.260914	+	1.41382i
$449$			2201.06i			0.231346i	0.993287	+	0.115673i	$0.0369025\pi$
$449$			2201.06i			0.231346i	−0.993287	+	0.115673i	$0.963098\pi$
$450$	338.573	−	629.922i	0.0354678	−	0.0659885i
$451$		−	8040.43i		−	0.839488i
$452$	−3081.60	−	4658.37i	−0.320677	−	0.484760i
$453$	−9960.85			−1.03312
$454$	7664.59	−	14260.1i	0.792328	−	1.47414i
$455$	1905.03	+	15324.2i	0.196284	+	1.57892i
$456$	271.624	+	2968.57i	0.0278947	+	0.304860i
$457$			3684.35i			0.377126i	0.982061	+	0.188563i	$0.0603830\pi$
$457$			3684.35i			0.377126i	−0.982061	+	0.188563i	$0.939617\pi$
$458$	2319.93	−	4316.27i	0.236688	−	0.440363i
$459$			440.403i			0.0447848i
$460$	−3318.45	−	5016.42i	−0.336355	−	0.508460i
$461$	−9222.51			−0.931746			−0.465873	−	0.884851i	$-0.654260\pi$
$461$	−9222.51			−0.931746			−0.465873	+	0.884851i	$0.654260\pi$
$462$	3556.75	−	6617.39i	0.358171	−	0.666383i
$463$			8406.97i			0.843856i	0.906629	+	0.421928i	$0.138646\pi$
$463$			8406.97i			0.843856i	−0.906629	+	0.421928i	$0.861354\pi$
$464$	−12865.0	−	5468.64i	−1.28716	−	0.547145i
$465$	480.401			0.0479098
$466$	288.285	−	536.361i	0.0286579	−	0.0533185i
$467$			2355.31i			0.233385i	0.993168	+	0.116692i	$0.0372291\pi$
$467$			2355.31i			0.233385i	−0.993168	+	0.116692i	$0.962771\pi$
$468$	2194.97	+	2563.47i	0.216800	+	0.253197i
$469$		−	15625.4i		−	1.53841i
$470$	−11896.3	−	6394.10i	−1.16753	−	0.627527i
$471$	−5978.51			−0.584873
$472$	6990.75	−	639.654i	0.681727	−	0.0623781i
$473$		−	9663.54i		−	0.939387i
$474$	−7981.77	−	4290.08i	−0.773449	−	0.415717i
$475$	−1233.70			−0.119170
$476$	2897.81	−	1916.95i	0.279035	−	0.184587i
$477$			1980.56i			0.190113i
$478$	2713.37	+	1458.40i	0.259638	+	0.139551i
$479$			15585.6i			1.48669i	0.668909	+	0.743345i	$0.266762\pi$
$479$			15585.6i			1.48669i	−0.668909	+	0.743345i	$0.733238\pi$
$480$	−5242.98	+	4202.42i	−0.498558	+	0.399611i
$481$	13759.5	−	1710.52i	1.30433	−	0.162148i
$482$	1649.33	+	886.487i	0.155860	+	0.0837726i
$483$	4853.77			0.457255
$484$	994.502	+	1503.36i	0.0933980	+	0.141187i
$485$			9766.49i			0.914379i
$486$	605.401	+	325.394i	0.0565053	+	0.0303707i
$487$			12945.1i			1.20452i	0.798302	+	0.602258i	$0.205732\pi$
$487$			12945.1i			1.20452i	−0.798302	+	0.602258i	$0.794268\pi$
$488$	323.025	+	3530.33i	0.0299645	+	0.327480i
$489$		−	3842.09i		−	0.355308i
$490$	6063.52	−	11281.3i	0.559024	−	1.04007i
$491$		−	2831.65i		−	0.260266i	−0.991497	−	0.130133i	$-0.958460\pi$
$491$		−	2831.65i		−	0.260266i	0.991497	−	0.130133i	$-0.0415404\pi$
$492$	−3201.82	−	4840.11i	−0.293393	−	0.443515i
$493$			3562.75i			0.325473i
$494$	2102.57	−	5428.93i	0.191497	−	0.494451i
$495$	3702.85			0.336224
$496$	−762.281	−	324.030i	−0.0690070	−	0.0293334i
$497$	−30462.1			−2.74932
$498$	11127.9	+	5981.09i	1.00131	+	0.538190i
$499$	−617.209			−0.0553708			−0.0276854	−	0.999617i	$-0.508814\pi$
$499$	−617.209			−0.0553708			−0.0276854	+	0.999617i	$0.508814\pi$
$500$	5292.28	+	8000.21i	0.473356	+	0.715560i
$501$	−1823.45			−0.162606
$502$	−9693.27	−	5209.98i	−0.861817	−	0.463213i
$503$	21442.2			1.90071			0.950356	−	0.311164i	$-0.100719\pi$
$503$	21442.2			1.90071			0.950356	+	0.311164i	$0.100719\pi$
$504$	−494.085	−	5399.83i	−0.0436672	−	0.477237i
$505$			4085.02i			0.359962i
$506$	2705.60	−	5033.82i	0.237704	−	0.442254i
$507$	−1613.79	−	6390.38i	−0.141362	−	0.559777i
$508$	9461.57	+	14302.8i	0.826357	+	1.24918i
$509$	21026.3			1.83099			0.915497	−	0.402324i	$-0.131797\pi$
$509$	21026.3			1.83099			0.915497	+	0.402324i	$0.131797\pi$
$510$	1508.42	+	810.754i	0.130969	+	0.0703937i
$511$	21108.0			1.82732
$512$	11153.9	−	3131.86i	0.962767	−	0.270332i
$513$		−	1185.67i		−	0.102044i
$514$	−7248.33	+	13485.7i	−0.622004	+	1.15725i
$515$	15515.3			1.32755
$516$	−3848.16	−	5817.18i	−0.328306	−	0.496292i
$517$		−	12832.6i		−	1.09163i
$518$	−19623.2	−	10547.1i	−1.66446	−	0.894624i
$519$	−2642.05			−0.223455
$520$	12820.9	−	2798.79i	1.08122	−	0.236029i
$521$	−13521.4			−1.13702			−0.568508	−	0.822678i	$-0.692479\pi$
$521$	−13521.4			−1.13702			−0.568508	+	0.822678i	$0.692479\pi$
$522$	4897.54	+	2632.35i	0.410651	+	0.220718i
$523$		−	7317.92i		−	0.611836i	−0.952058	−	0.305918i	$-0.901037\pi$
$523$		−	7317.92i		−	0.611836i	0.952058	−	0.305918i	$-0.0989634\pi$
$524$	−4920.65	+	3255.10i	−0.410229	+	0.271373i
$525$	2244.10			0.186553
$526$	−6138.00	+	11419.9i	−0.508801	+	0.946635i
$527$			211.101i			0.0174491i
$528$	−5875.55	−	2497.57i	−0.484281	−	0.205858i
$529$	−8474.76			−0.696537
$530$	6783.63	+	3646.09i	0.555966	+	0.298823i
$531$	−2792.17			−0.228192
$532$	−7801.63	+	5160.91i	−0.635796	+	0.420590i
$533$	1398.21	+	11247.3i	0.113627	+	0.914025i
$534$	−869.406	+	1617.55i	−0.0704549	+	0.131083i
$535$			4182.83i			0.338018i
$536$	−13223.4	+	1209.94i	−1.06560	+	0.0975026i
$537$	−1776.98			−0.142798
$538$	−17914.7	−	9628.89i	−1.43561	−	0.771619i
$539$	12169.1			0.972468
$540$	2229.01	−	1474.53i	0.177632	−	0.117507i
$541$	19861.4			1.57839			0.789196	−	0.614141i	$-0.210498\pi$
$541$	19861.4			1.57839			0.789196	+	0.614141i	$0.210498\pi$
$542$	10024.3	+	5387.88i	0.794426	+	0.426991i
$543$	−12711.2			−1.00458
$544$	−1846.66	−	2303.90i	−0.145542	−	0.181579i
$545$	25276.2			1.98663
$546$	−3824.58	+	9875.22i	−0.299775	+	0.774030i
$547$			5823.75i			0.455221i	0.973752	+	0.227610i	$0.0730912\pi$
$547$			5823.75i			0.455221i	−0.973752	+	0.227610i	$0.926909\pi$
$548$	4506.26	−	2980.97i	0.351273	−	0.232374i
$549$		−	1410.05i		−	0.109616i
$550$	1250.91	−	2327.34i	0.0969798	−	0.180433i
$551$		−	9591.80i		−	0.741605i
$552$	−375.848	−	4107.62i	−0.0289803	−	0.316725i
$553$		−	28435.1i		−	2.18658i
$554$	10017.9	+	5384.47i	0.768267	+	0.412932i
$555$		−	10980.4i		−	0.839806i
$556$	−7805.95	+	5163.77i	−0.595407	+	0.393872i
$557$	900.989			0.0685388			0.0342694	−	0.999413i	$-0.489090\pi$
$557$	900.989			0.0685388			0.0342694	+	0.999413i	$0.489090\pi$
$558$	290.191	+	155.973i	0.0220157	+	0.0118331i
$559$	1680.47	+	13517.8i	0.127149	+	1.02279i
$560$	−19404.5	−	8248.46i	−1.46427	−	0.622431i
$561$			1627.13i			0.122456i
$562$	8235.81	+	4426.62i	0.618161	+	0.332252i
$563$		−	21415.2i		−	1.60310i	−0.597930	−	0.801548i	$-0.704010\pi$
$563$		−	21415.2i		−	1.60310i	0.597930	−	0.801548i	$-0.295990\pi$
$564$	−5110.12	−	7724.84i	−0.381515	−	0.576727i
$565$	8638.58			0.643235
$566$	−4557.76	−	2449.72i	−0.338475	−	0.181925i
$567$			2156.74i			0.159744i
$568$	2358.81	+	25779.3i	0.174249	+	1.90436i
$569$	18554.5			1.36704			0.683519	−	0.729933i	$-0.260449\pi$
$569$	18554.5			1.36704			0.683519	+	0.729933i	$0.260449\pi$
$570$	−4061.05	−	2182.75i	−0.298419	−	0.160396i
$571$			3256.22i			0.238649i	0.992855	+	0.119325i	$0.0380729\pi$
$571$			3256.22i			0.238649i	−0.992855	+	0.119325i	$0.961927\pi$
$572$	8109.62	+	9471.11i	0.592798	+	0.692320i
$573$			9743.29i			0.710352i
$574$	8621.45	−	16040.4i	0.626921	−	1.16640i
$575$	1707.07			0.123808
$576$	−4531.48	+	836.263i	−0.327798	+	0.0604936i
$577$			25127.4i			1.81294i	0.422271	+	0.906469i	$0.361233\pi$
$577$			25127.4i			1.81294i	−0.422271	+	0.906469i	$0.638767\pi$
$578$	6222.58	−	11577.2i	0.447794	−	0.833130i
$579$	−9927.92			−0.712591
$580$	18032.1	−	11928.6i	1.29094	−	0.853978i
$581$			39643.2i			2.83077i
$582$	−3170.91	+	5899.55i	−0.225839	+	0.420179i
$583$			7317.48i			0.519827i
$584$	−1634.48	−	17863.1i	−0.115814	−	1.26572i
$585$	−5179.71	+	643.918i	−0.366077	+	0.0455090i
$586$	−4000.13	+	7442.31i	−0.281986	+	0.524640i
$587$	20095.7			1.41301			0.706506	−	0.707707i	$-0.250271\pi$
$587$	20095.7			1.41301			0.706506	+	0.707707i	$0.250271\pi$
$588$	7325.45	−	4845.92i	0.513770	−	0.339868i
$589$		−	568.336i		−	0.0397587i
$590$	−5140.21	+	9563.45i	−0.358676	+	0.667324i
$591$			2781.37i			0.193588i
$592$	−7406.28	+	17423.3i	−0.514183	+	1.20962i
$593$		−	13639.0i		−	0.944498i	−0.881465	−	0.472249i	$-0.843442\pi$
$593$		−	13639.0i		−	0.944498i	0.881465	−	0.472249i	$-0.156558\pi$
$594$	2236.74	+	1202.21i	0.154503	+	0.0830429i
$595$			5373.76i			0.370257i
$596$	−1524.31	−	2304.26i	−0.104762	−	0.158366i
$597$			8599.79i			0.589557i
$598$	−2909.34	+	7512.03i	−0.198949	+	0.513695i
$599$	185.240			0.0126356			0.00631779	−	0.999980i	$-0.497989\pi$
$599$	185.240			0.0126356			0.00631779	+	0.999980i	$0.497989\pi$
$600$	−173.770	−	1899.12i	−0.0118235	−	0.129219i
$601$	−14787.9			−1.00368			−0.501841	−	0.864960i	$-0.667344\pi$
$601$	−14787.9			−1.00368			−0.501841	+	0.864960i	$0.667344\pi$
$602$	10361.8	−	19278.4i	0.701524	−	1.30520i
$603$	5281.54			0.356685
$604$	−22153.6	+	14655.0i	−1.49242	+	0.987259i
$605$	−2787.87			−0.187344
$606$	−1326.29	+	2467.60i	−0.0889060	+	0.165411i
$607$	17628.9			1.17880			0.589402	−	0.807840i	$-0.299363\pi$
$607$	17628.9			1.17880			0.589402	+	0.807840i	$0.299363\pi$
$608$	4971.66	+	6202.69i	0.331624	+	0.413737i
$609$			17447.5i			1.16093i
$610$	−4829.54	−	2595.80i	−0.320562	−	0.172297i
$611$	2231.55	+	17950.8i	0.147756	+	1.18856i
$612$	647.948	+	979.488i	0.0427970	+	0.0646952i
$613$	−952.713			−0.0627728			−0.0313864	−	0.999507i	$-0.509992\pi$
$613$	−952.713			−0.0627728			−0.0313864	+	0.999507i	$0.509992\pi$
$614$	−2968.50	+	5522.96i	−0.195112	+	0.363010i
$615$	8975.61			0.588506
$616$	−1825.47	−	19950.5i	−0.119400	−	1.30491i
$617$		−	5438.09i		−	0.354828i	−0.984136	−	0.177414i	$-0.943227\pi$
$617$		−	5438.09i		−	0.354828i	0.984136	−	0.177414i	$-0.0567732\pi$
$618$	9372.17	+	5037.40i	0.610039	+	0.327886i
$619$	6308.80			0.409648			0.204824	−	0.978799i	$-0.434338\pi$
$619$	6308.80			0.409648			0.204824	+	0.978799i	$0.434338\pi$
$620$	1068.45	−	706.795i	0.0692094	−	0.0457832i
$621$			1640.62i			0.106016i
$622$	−7552.62	+	14051.8i	−0.486869	+	0.905830i
$623$	−5762.51			−0.370578
$624$	8653.30	+	2471.97i	0.555143	+	0.158586i
$625$	−18347.4			−1.17424
$626$	−12483.1	+	23225.0i	−0.797004	+	1.48284i
$627$		−	4380.65i		−	0.279021i
$628$	−13296.6	+	8795.95i	−0.844894	+	0.558912i
$629$	4825.09			0.305865
$630$	7387.06	+	3970.43i	0.467155	+	0.251088i
$631$		−	27401.6i		−	1.72875i	−0.502847	−	0.864376i	$-0.667714\pi$
$631$		−	27401.6i		−	1.72875i	0.502847	−	0.864376i	$-0.332286\pi$
$632$	−24063.9	+	2201.84i	−1.51457	+	0.138583i
$633$	−8668.80			−0.544319
$634$	7228.01	−	13447.9i	0.452777	−	0.842401i
$635$	−26523.5			−1.65756
$636$	2913.93	+	4404.92i	0.181674	+	0.274633i
$637$	−17022.7	+	2116.18i	−1.05881	+	0.131627i
$638$	18094.7	+	9725.61i	1.12285	+	0.603512i
$639$		−	10296.5i		−	0.637437i
$640$	−5477.89	+	17060.3i	−0.338332	+	1.05370i
$641$	−12116.7			−0.746613			−0.373306	−	0.927708i	$-0.621776\pi$
$641$	−12116.7			−0.746613			−0.373306	+	0.927708i	$0.621776\pi$
$642$	−1358.05	+	2526.68i	−0.0834859	+	0.155327i
$643$	13041.8			0.799875			0.399938	−	0.916542i	$-0.369032\pi$
$643$	13041.8			0.799875			0.399938	+	0.916542i	$0.369032\pi$
$644$	10795.1	−	7141.18i	0.660541	−	0.436959i
$645$	10787.5			0.658538
$646$	959.160	−	1784.54i	0.0584174	−	0.108687i
$647$	−22126.1			−1.34446			−0.672232	−	0.740341i	$-0.734664\pi$
$647$	−22126.1			−1.34446			−0.672232	+	0.740341i	$0.734664\pi$
$648$	1825.20	−	167.006i	0.110649	−	0.0101244i
$649$	−10316.1			−0.623946
$650$	−1345.11	+	3473.12i	−0.0811684	+	0.209580i
$651$			1033.80i			0.0622396i
$652$	−5652.73	−	8545.10i	−0.339537	−	0.513270i
$653$		−	20990.8i		−	1.25794i	−0.777431	−	0.628969i	$-0.783477\pi$
$653$		−	20990.8i		−	1.25794i	0.777431	−	0.628969i	$-0.216523\pi$
$654$	15268.3	+	8206.49i	0.912904	+	0.490672i
$655$		−	9124.96i		−	0.544339i
$656$	−14242.2	−	6054.04i	−0.847657	−	0.360321i
$657$			7134.70i			0.423670i
$658$	13759.9	−	25600.5i	0.815221	−	1.51673i
$659$		−	8421.74i		−	0.497822i	−0.968526	−	0.248911i	$-0.919927\pi$
$659$		−	8421.74i		−	0.497822i	0.968526	−	0.248911i	$-0.0800726\pi$
$660$	8235.41	−	5447.87i	0.485701	−	0.321300i
$661$	23890.2			1.40578			0.702891	−	0.711298i	$-0.251892\pi$
$661$	23890.2			1.40578			0.702891	+	0.711298i	$0.251892\pi$
$662$	−4258.11	+	7922.29i	−0.249994	+	0.465119i
$663$	−282.955	−	2276.11i	−0.0165747	−	0.133328i
$664$	33549.1	−	3069.74i	1.96078	−	0.179411i
$665$		−	14467.5i		−	0.843648i
$666$	3565.04	−	6632.82i	0.207421	−	0.385911i
$667$			13272.2i			0.770468i
$668$	−4055.48	+	2682.77i	−0.234897	+	0.155389i
$669$	8203.26			0.474075
$670$	9722.98	−	18089.8i	0.560644	−	1.04309i
$671$		−	5209.62i		−	0.299724i
$672$	−9043.45	−	11282.7i	−0.519135	−	0.647677i
$673$	−22344.0			−1.27979			−0.639894	−	0.768463i	$-0.721022\pi$
$673$	−22344.0			−1.27979			−0.639894	+	0.768463i	$0.721022\pi$
$674$	4586.89	−	8533.99i	0.262137	−	0.487711i
$675$			758.527i			0.0432529i
$676$	−12991.1	−	11838.4i	−0.739139	−	0.673553i
$677$			28460.2i			1.61568i	0.589404	+	0.807838i	$0.299363\pi$
$677$			28460.2i			1.61568i	−0.589404	+	0.807838i	$0.700637\pi$
$678$	5218.22	+	2804.71i	0.295582	+	0.158871i
$679$	−21017.1			−1.18787
$680$	4547.67	−	416.112i	0.256464	−	0.0234664i
$681$			17171.5i			0.966244i
$682$	1072.15	+	576.265i	0.0601977	+	0.0323553i
$683$	18506.1			1.03677			0.518387	−	0.855146i	$-0.326533\pi$
$683$	18506.1			1.03677			0.518387	+	0.855146i	$0.326533\pi$
$684$	−1744.44	−	2637.03i	−0.0975151	−	0.147411i
$685$			8356.50i			0.466110i
$686$	1523.60	+	818.913i	0.0847981	+	0.0455776i
$687$			5197.48i			0.288641i
$688$	−17117.2	−	7276.16i	−0.948527	−	0.403199i
$689$	−1272.49	−	10236.0i	−0.0703602	−	0.565982i
$690$	5619.30	+	3020.28i	0.310033	+	0.166638i
$691$	827.958			0.0455818			0.0227909	−	0.999740i	$-0.492745\pi$
$691$	827.958			0.0455818			0.0227909	+	0.999740i	$0.492745\pi$
$692$	−5876.10	+	3887.14i	−0.322797	+	0.213536i
$693$			7968.40i			0.436789i
$694$	30442.1	+	16362.1i	1.66508	+	0.894955i
$695$		−	14475.5i		−	0.790054i
$696$	14765.4	−	1351.03i	0.804138	−	0.0735786i
$697$			3944.12i			0.214339i
$698$	−7637.52	+	14209.8i	−0.414161	+	0.770555i
$699$			645.864i			0.0349482i
$700$	4991.03	−	3301.66i	0.269491	−	0.178273i
$701$		−	14181.4i		−	0.764085i	−0.924145	−	0.382043i	$-0.875221\pi$
$701$		−	14181.4i		−	0.764085i	0.924145	−	0.382043i	$-0.124779\pi$
$702$	−3337.92	−	1292.75i	−0.179461	−	0.0695037i
$703$	−12990.3			−0.696928
$704$	−16742.2	+	3089.70i	−0.896301	+	0.165408i
$705$	14325.1			0.765269
$706$	−17196.1	−	9242.66i	−0.916693	−	0.492708i
$707$	−8790.81			−0.467627
$708$	−6209.98	+	4108.01i	−0.329640	+	0.218063i
$709$	−31124.9			−1.64869			−0.824343	−	0.566090i	$-0.808455\pi$
$709$	−31124.9			−1.64869			−0.824343	+	0.566090i	$0.808455\pi$
$710$	−35266.5	−	18955.2i	−1.86412	−	1.00194i
$711$	9611.32			0.506966
$712$	446.215	+	4876.67i	0.0234868	+	0.256687i
$713$			786.409i			0.0413061i
$714$	−1744.71	+	3246.07i	−0.0914485	+	0.170142i
$715$	−19137.2	+	2379.05i	−1.00097	+	0.124436i
$716$	−3952.14	+	2614.41i	−0.206283	+	0.136460i
$717$	−3267.33			−0.170182
$718$	14725.4	+	7914.67i	0.765386	+	0.411383i
$719$	32557.2			1.68871			0.844353	−	0.535787i	$-0.179985\pi$
$719$	32557.2			1.68871			0.844353	+	0.535787i	$0.179985\pi$
$720$	2788.06	−	6558.92i	0.144312	−	0.339495i
$721$			33388.4i			1.72462i
$722$	6602.37	−	12283.8i	0.340325	−	0.633182i
$723$	−1986.05			−0.102161
$724$	−28270.5	+	18701.5i	−1.45120	+	0.959992i
$725$			6136.29i			0.314339i
$726$	−1684.04	−	905.145i	−0.0860890	−	0.0462715i
$727$	7446.98			0.379908			0.189954	−	0.981793i	$-0.439166\pi$
$727$	7446.98			0.379908			0.189954	+	0.981793i	$0.439166\pi$
$728$	6022.89	+	27590.2i	0.306625	+	1.40461i
$729$	−729.000			−0.0370370
$730$	24437.0	+	13134.5i	1.23898	+	0.665932i
$731$			4740.32i			0.239845i
$732$	−2074.55	−	3136.04i	−0.104751	−	0.158349i
$733$	−20527.0			−1.03435			−0.517177	−	0.855878i	$-0.673017\pi$
$733$	−20527.0			−1.03435			−0.517177	+	0.855878i	$0.673017\pi$
$734$	−11806.8	+	21966.8i	−0.593728	+	1.10464i
$735$			13584.5i			0.681729i
$736$	−6879.31	−	8582.68i	−0.344531	−	0.429839i
$737$	19513.4			0.975286
$738$	5421.80	+	2914.13i	0.270433	+	0.145353i
$739$	29880.4			1.48737			0.743686	−	0.668529i	$-0.233076\pi$
$739$	29880.4			1.48737			0.743686	+	0.668529i	$0.233076\pi$
$740$	−16155.1	−	24421.2i	−0.802530	−	1.21316i
$741$	761.785	+	6127.85i	0.0377664	+	0.303795i
$742$	−7846.26	+	14598.1i	−0.388201	+	0.722256i
$743$			7500.75i			0.370358i	0.982705	+	0.185179i	$0.0592865\pi$
$743$			7500.75i			0.370358i	−0.982705	+	0.185179i	$0.940714\pi$
$744$	874.882	−	80.0517i	0.0431112	−	0.00394468i
$745$	4273.08			0.210139
$746$	17665.8	+	9495.11i	0.867014	+	0.466006i
$747$	−13399.8			−0.656323
$748$	2393.94	+	3618.86i	0.117020	+	0.176897i
$749$	−9001.29			−0.439119
$750$	−8961.68	−	4816.76i	−0.436312	−	0.234511i
$751$	27102.8			1.31691			0.658453	−	0.752622i	$-0.271211\pi$
$751$	27102.8			1.31691			0.658453	+	0.752622i	$0.271211\pi$
$752$	−22730.5	−	9662.27i	−1.10226	−	0.468546i
$753$	11672.3			0.564888
$754$	−27002.9	−	10458.0i	−1.30423	−	0.505116i
$755$		−	41082.2i		−	1.98031i
$756$	3173.14	+	4796.75i	0.152653	+	0.230762i
$757$			18795.2i			0.902409i	0.892421	+	0.451205i	$0.149006\pi$
$757$			18795.2i			0.902409i	−0.892421	+	0.451205i	$0.850994\pi$
$758$	9574.76	−	17814.0i	0.458801	−	0.853608i
$759$			6061.52i			0.289880i
$760$	−12243.5	+	1120.28i	−0.584365	+	0.0534694i
$761$		−	19585.4i		−	0.932942i	−0.884537	−	0.466471i	$-0.845525\pi$
$761$		−	19585.4i		−	0.932942i	0.884537	−	0.466471i	$-0.154475\pi$
$762$	−16021.8	−	8611.45i	−0.761689	−	0.409396i
$763$			54393.5i			2.58083i
$764$	14334.9	+	21669.8i	0.678822	+	1.02616i
$765$	−1816.38			−0.0858450
$766$	−15647.4	−	8410.25i	−0.738074	−	0.396703i
$767$	14430.6	−	1793.94i	0.679346	−	0.0844531i
$768$	−8847.98	+	8526.91i	−0.415721	+	0.400636i
$769$			39015.6i			1.82957i	0.403940	+	0.914785i	$0.367640\pi$
$769$			39015.6i			1.82957i	−0.403940	+	0.914785i	$0.632360\pi$
$770$	27292.6	+	14669.3i	1.27734	+	0.686553i
$771$		−	16238.9i		−	0.758534i
$772$	−22080.4	+	14606.6i	−1.02939	+	0.680961i
$773$	−38584.9			−1.79535			−0.897673	−	0.440663i

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33907 + 2.49136i) q^{2} -3.00000i q^{3} +(-4.41379 - 6.67222i) q^{4} +12.3731 q^{5} +(7.47409 + 4.01721i) q^{6} +26.6265i q^{7} +(22.5333 - 2.06180i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+(-1.33907 + 2.49136i) q^{2} -3.00000i q^{3} +(-4.41379 - 6.67222i) q^{4} +12.3731 q^{5} +(7.47409 + 4.01721i) q^{6} +26.6265i q^{7} +(22.5333 - 2.06180i) q^{8} -9.00000 q^{9} +(-16.5684 + 30.8259i) q^{10} -33.2518 q^{11} +(-20.0166 + 13.2414i) q^{12} +(46.5141 - 5.78242i) q^{13} +(-66.3362 - 35.6547i) q^{14} -37.1193i q^{15} +(-25.0369 + 58.8995i) q^{16} +16.3112 q^{17} +(12.0516 - 22.4223i) q^{18} -43.9139 q^{19} +(-54.6122 - 82.5560i) q^{20} +79.8794 q^{21} +(44.5265 - 82.8424i) q^{22} +60.7638 q^{23} +(-6.18539 - 67.5999i) q^{24} +28.0936 q^{25} +(-47.8795 + 123.627i) q^{26} +27.0000i q^{27} +(177.657 - 117.524i) q^{28} +218.423i q^{29} +(92.4777 + 49.7053i) q^{30} +12.9421i q^{31} +(-113.214 - 141.247i) q^{32} +99.7554i q^{33} +(-21.8418 + 40.6372i) q^{34} +329.452i q^{35} +(39.7241 + 60.0499i) q^{36} +295.814 q^{37} +(58.8037 - 109.405i) q^{38} +(-17.3473 - 139.542i) q^{39} +(278.807 - 25.5108i) q^{40} +241.804i q^{41} +(-106.964 + 199.009i) q^{42} +290.617i q^{43} +(146.766 + 221.863i) q^{44} -111.358 q^{45} +(-81.3669 + 151.385i) q^{46} +385.921i q^{47} +(176.699 + 75.1108i) q^{48} -365.968 q^{49} +(-37.6192 + 69.9913i) q^{50} -48.9337i q^{51} +(-243.885 - 284.830i) q^{52} -220.063i q^{53} +(-67.2668 - 36.1549i) q^{54} -411.428 q^{55} +(54.8983 + 599.981i) q^{56} +131.742i q^{57} +(-544.171 - 292.484i) q^{58} +310.241 q^{59} +(-247.668 + 163.837i) q^{60} +156.672i q^{61} +(-32.2434 - 17.3303i) q^{62} -239.638i q^{63} +(503.498 - 92.9181i) q^{64} +(575.524 - 71.5465i) q^{65} +(-248.527 - 133.579i) q^{66} -586.837 q^{67} +(-71.9943 - 108.832i) q^{68} -182.291i q^{69} +(-820.784 - 441.159i) q^{70} +1144.05i q^{71} +(-202.800 + 18.5562i) q^{72} -792.744i q^{73} +(-396.115 + 736.981i) q^{74} -84.2808i q^{75} +(193.827 + 293.003i) q^{76} -885.378i q^{77} +(370.880 + 143.639i) q^{78} -1067.92 q^{79} +(-309.785 + 728.769i) q^{80} +81.0000 q^{81} +(-602.423 - 323.793i) q^{82} +1488.87 q^{83} +(-352.571 - 532.972i) q^{84} +201.820 q^{85} +(-724.033 - 389.156i) q^{86} +655.269 q^{87} +(-749.273 + 68.5585i) q^{88} +216.421i q^{89} +(149.116 - 277.433i) q^{90} +(153.965 + 1238.51i) q^{91} +(-268.199 - 405.429i) q^{92} +38.8262 q^{93} +(-961.469 - 516.774i) q^{94} -543.351 q^{95} +(-423.740 + 339.642i) q^{96} +789.333i q^{97} +(490.056 - 911.759i) q^{98} +299.266 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9}+O(q^{10}) \) 84 * q - 756 * q^9	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52} - 1616 q^{55} + 608 q^{56} - 2120 q^{62} - 2856 q^{64} + 696 q^{65} - 396 q^{66} - 2536 q^{68} - 3936 q^{74} - 156 q^{78} + 3160 q^{79} + 6804 q^{81} + 4276 q^{82} - 2088 q^{87} + 1780 q^{88} + 324 q^{90} + 4792 q^{92} - 860 q^{94} + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more