LMFDB - Embedded newform 76.4.d.a.75.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,4,Mod(75,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	76.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.48414516044$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.14
Character	$\chi$	$=$	76.75
Dual form			76.4.d.a.75.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.603834 + 2.76322i) q^{2} +8.93329 q^{3} +(-7.27077 - 3.33705i) q^{4} +6.23571 q^{5} +(-5.39422 + 24.6847i) q^{6} +11.1035i q^{7} +(13.6113 - 18.0757i) q^{8} +52.8037 q^{9} +O(q^{10})$	\(q+(-0.603834 + 2.76322i) q^{2} +8.93329 q^{3} +(-7.27077 - 3.33705i) q^{4} +6.23571 q^{5} +(-5.39422 + 24.6847i) q^{6} +11.1035i q^{7} +(13.6113 - 18.0757i) q^{8} +52.8037 q^{9} +(-3.76533 + 17.2306i) q^{10} +15.9580i q^{11} +(-64.9519 - 29.8109i) q^{12} -34.4364i q^{13} +(-30.6813 - 6.70465i) q^{14} +55.7054 q^{15} +(41.7282 + 48.5259i) q^{16} -97.5522 q^{17} +(-31.8847 + 145.908i) q^{18} +(6.66130 + 82.5508i) q^{19} +(-45.3384 - 20.8089i) q^{20} +99.1906i q^{21} +(-44.0956 - 9.63601i) q^{22} -96.9200i q^{23} +(121.594 - 161.476i) q^{24} -86.1159 q^{25} +(95.1554 + 20.7939i) q^{26} +230.512 q^{27} +(37.0528 - 80.7308i) q^{28} -222.677i q^{29} +(-33.6368 + 153.926i) q^{30} +91.0575 q^{31} +(-159.285 + 86.0026i) q^{32} +142.558i q^{33} +(58.9053 - 269.558i) q^{34} +69.2380i q^{35} +(-383.924 - 176.209i) q^{36} -395.443i q^{37} +(-232.128 - 31.4403i) q^{38} -307.631i q^{39} +(84.8764 - 112.715i) q^{40} +266.667i q^{41} +(-274.085 - 59.8946i) q^{42} -384.400i q^{43} +(53.2528 - 116.027i) q^{44} +329.269 q^{45} +(267.811 + 58.5236i) q^{46} +400.978i q^{47} +(372.770 + 433.496i) q^{48} +219.713 q^{49} +(51.9997 - 237.957i) q^{50} -871.462 q^{51} +(-114.916 + 250.379i) q^{52} +201.804i q^{53} +(-139.191 + 636.956i) q^{54} +99.5097i q^{55} +(200.703 + 151.133i) q^{56} +(59.5074 + 737.450i) q^{57} +(615.304 + 134.460i) q^{58} +18.7442 q^{59} +(-405.021 - 185.892i) q^{60} -400.276 q^{61} +(-54.9836 + 251.612i) q^{62} +586.305i q^{63} +(-141.463 - 492.069i) q^{64} -214.736i q^{65} +(-393.919 - 86.0813i) q^{66} +839.849 q^{67} +(709.279 + 325.537i) q^{68} -865.815i q^{69} +(-191.320 - 41.8082i) q^{70} -855.502 q^{71} +(718.730 - 954.465i) q^{72} -754.693 q^{73} +(1092.70 + 238.782i) q^{74} -769.299 q^{75} +(227.043 - 622.437i) q^{76} -177.190 q^{77} +(850.051 + 185.758i) q^{78} -533.704 q^{79} +(260.205 + 302.593i) q^{80} +633.533 q^{81} +(-736.859 - 161.022i) q^{82} +1096.29i q^{83} +(331.004 - 721.192i) q^{84} -608.307 q^{85} +(1062.18 + 232.114i) q^{86} -1989.23i q^{87} +(288.453 + 217.210i) q^{88} +129.885i q^{89} +(-198.823 + 909.842i) q^{90} +382.364 q^{91} +(-323.427 + 704.683i) q^{92} +813.443 q^{93} +(-1107.99 - 242.124i) q^{94} +(41.5379 + 514.762i) q^{95} +(-1422.94 + 768.286i) q^{96} +681.176i q^{97} +(-132.670 + 607.115i) q^{98} +842.644i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9}+O(q^{10}) $ 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9	$ 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9} - 134 q^{16} - 80 q^{17} - 300 q^{20} - 26 q^{24} + 496 q^{25} - 90 q^{26} + 254 q^{28} - 16 q^{30} - 556 q^{36} - 626 q^{38} - 850 q^{42} + 976 q^{44} - 612 q^{45} + 188 q^{49} + 354 q^{54} - 580 q^{57} + 2534 q^{58} - 948 q^{61} - 1068 q^{62} - 1634 q^{64} + 1244 q^{66} + 1630 q^{68} - 184 q^{73} + 2276 q^{74} + 1688 q^{76} + 308 q^{77} + 3376 q^{80} - 2284 q^{81} - 740 q^{82} + 684 q^{85} + 1810 q^{92} + 824 q^{93} - 5222 q^{96}+O(q^{100}) $ 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9 - 134 * q^16 - 80 * q^17 - 300 * q^20 - 26 * q^24 + 496 * q^25 - 90 * q^26 + 254 * q^28 - 16 * q^30 - 556 * q^36 - 626 * q^38 - 850 * q^42 + 976 * q^44 - 612 * q^45 + 188 * q^49 + 354 * q^54 - 580 * q^57 + 2534 * q^58 - 948 * q^61 - 1068 * q^62 - 1634 * q^64 + 1244 * q^66 + 1630 * q^68 - 184 * q^73 + 2276 * q^74 + 1688 * q^76 + 308 * q^77 + 3376 * q^80 - 2284 * q^81 - 740 * q^82 + 684 * q^85 + 1810 * q^92 + 824 * q^93 - 5222 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−0.603834	+	2.76322i	−0.213487	+	0.976946i
$2$	−0.603834	+	2.76322i	−0.213487	+	0.976946i
$3$	8.93329			1.71921			0.859607	−	0.510957i	$-0.170709\pi$
$3$	8.93329			1.71921			0.859607	+	0.510957i	$0.170709\pi$
$4$	−7.27077	−	3.33705i	−0.908846	−	0.417131i
$5$	6.23571			0.557739			0.278869	−	0.960329i	$-0.410040\pi$
$5$	6.23571			0.557739			0.278869	+	0.960329i	$0.410040\pi$
$6$	−5.39422	+	24.6847i	−0.367030	+	1.67958i
$7$			11.1035i			0.599531i	0.954013	+	0.299766i	$0.0969084\pi$
$7$			11.1035i			0.599531i	−0.954013	+	0.299766i	$0.903092\pi$
$8$	13.6113	−	18.0757i	0.601542	−	0.798841i
$9$	52.8037			1.95569
$10$	−3.76533	+	17.2306i	−0.119070	+	0.544880i
$11$			15.9580i			0.437412i	0.975791	+	0.218706i	$0.0701835\pi$
$11$			15.9580i			0.437412i	−0.975791	+	0.218706i	$0.929816\pi$
$12$	−64.9519	−	29.8109i	−1.56250	−	0.717138i
$13$		−	34.4364i		−	0.734688i	−0.930085	−	0.367344i	$-0.880267\pi$
$13$		−	34.4364i		−	0.734688i	0.930085	−	0.367344i	$-0.119733\pi$
$14$	−30.6813	−	6.70465i	−0.585709	−	0.127992i
$15$	55.7054			0.958872
$16$	41.7282	+	48.5259i	0.652003	+	0.758217i
$17$	−97.5522			−1.39176			−0.695879	−	0.718159i	$-0.744985\pi$
$17$	−97.5522			−1.39176			−0.695879	+	0.718159i	$0.744985\pi$
$18$	−31.8847	+	145.908i	−0.417516	+	1.91061i
$19$	6.66130	+	82.5508i	0.0804320	+	0.996760i
$19$	6.66130	+	82.5508i	0.0804320	+	0.996760i
$20$	−45.3384	−	20.8089i	−0.506899	−	0.232650i
$21$			99.1906i			1.03072i
$22$	−44.0956	−	9.63601i	−0.427328	−	0.0933820i
$23$		−	96.9200i		−	0.878661i	−0.898325	−	0.439331i	$-0.855216\pi$
$23$		−	96.9200i		−	0.878661i	0.898325	−	0.439331i	$-0.144784\pi$
$24$	121.594	−	161.476i	1.03418	−	1.37338i
$25$	−86.1159			−0.688928
$26$	95.1554	+	20.7939i	0.717751	+	0.156847i
$27$	230.512			1.64304
$28$	37.0528	−	80.7308i	0.250083	−	0.544882i
$29$		−	222.677i		−	1.42586i	−0.701234	−	0.712931i	$-0.747367\pi$
$29$		−	222.677i		−	1.42586i	0.701234	−	0.712931i	$-0.252633\pi$
$30$	−33.6368	+	153.926i	−0.204707	+	0.936766i
$31$	91.0575			0.527561			0.263781	−	0.964583i	$-0.415030\pi$
$31$	91.0575			0.527561			0.263781	+	0.964583i	$0.415030\pi$
$32$	−159.285	+	86.0026i	−0.879931	+	0.475102i
$33$			142.558i			0.752004i
$34$	58.9053	−	269.558i	0.297123	−	1.35967i
$35$			69.2380i			0.334382i
$36$	−383.924	−	176.209i	−1.77742	−	0.815781i
$37$		−	395.443i		−	1.75704i	−0.477708	−	0.878519i	$-0.658532\pi$
$37$		−	395.443i		−	1.75704i	0.477708	−	0.878519i	$-0.341468\pi$
$38$	−232.128	−	31.4403i	−0.990952	−	0.134218i
$39$		−	307.631i		−	1.26309i
$40$	84.8764	−	112.715i	0.335503	−	0.445545i
$41$			266.667i			1.01576i	0.861426	+	0.507882i	$0.169572\pi$
$41$			266.667i			1.01576i	−0.861426	+	0.507882i	$0.830428\pi$
$42$	−274.085	−	59.8946i	−1.00696	−	0.220046i
$43$		−	384.400i		−	1.36327i	−0.731694	−	0.681633i	$-0.761270\pi$
$43$		−	384.400i		−	1.36327i	0.731694	−	0.681633i	$-0.238730\pi$
$44$	53.2528	−	116.027i	0.182458	−	0.397540i
$45$	329.269			1.09077
$46$	267.811	+	58.5236i	0.858405	+	0.187583i
$47$			400.978i			1.24444i	0.782842	+	0.622220i	$0.213769\pi$
$47$			400.978i			1.24444i	−0.782842	+	0.622220i	$0.786231\pi$
$48$	372.770	+	433.496i	1.12093	+	1.30354i
$49$	219.713			0.640563
$50$	51.9997	−	237.957i	0.147077	−	0.673045i
$51$	−871.462			−2.39273
$52$	−114.916	+	250.379i	−0.306462	+	0.667719i
$53$			201.804i			0.523017i	0.965201	+	0.261509i	$0.0842200\pi$
$53$			201.804i			0.523017i	−0.965201	+	0.261509i	$0.915780\pi$
$54$	−139.191	+	636.956i	−0.350769	+	1.60516i
$55$			99.5097i			0.243962i
$56$	200.703	+	151.133i	0.478930	+	0.360643i
$57$	59.5074	+	737.450i	0.138280	+	1.71364i
$58$	615.304	+	134.460i	1.39299	+	0.304404i
$59$	18.7442			0.0413607			0.0206804	−	0.999786i	$-0.493417\pi$
$59$	18.7442			0.0413607			0.0206804	+	0.999786i	$0.493417\pi$
$60$	−405.021	−	185.892i	−0.871467	−	0.399975i
$61$	−400.276			−0.840166			−0.420083	−	0.907486i	$-0.637999\pi$
$61$	−400.276			−0.840166			−0.420083	+	0.907486i	$0.637999\pi$
$62$	−54.9836	+	251.612i	−0.112628	+	0.515399i
$63$			586.305i			1.17250i
$64$	−141.463	−	492.069i	−0.276294	−	0.961073i
$65$		−	214.736i		−	0.409764i
$66$	−393.919	−	86.0813i	−0.734667	−	0.160543i
$67$	839.849			1.53140			0.765701	−	0.643197i	$-0.222392\pi$
$67$	839.849			1.53140			0.765701	+	0.643197i	$0.222392\pi$
$68$	709.279	+	325.537i	1.26489	+	0.580546i
$69$		−	865.815i		−	1.51061i
$70$	−191.320	−	41.8082i	−0.326673	−	0.0713863i
$71$	−855.502			−1.42999			−0.714996	−	0.699129i	$-0.753571\pi$
$71$	−855.502			−1.42999			−0.714996	+	0.699129i	$0.753571\pi$
$72$	718.730	−	954.465i	1.17643	−	1.56229i
$73$	−754.693			−1.21000			−0.605001	−	0.796225i	$-0.706827\pi$
$73$	−754.693			−1.21000			−0.605001	+	0.796225i	$0.706827\pi$
$74$	1092.70	+	238.782i	1.71653	+	0.375105i
$75$	−769.299			−1.18441
$76$	227.043	−	622.437i	0.342680	−	0.939452i
$77$	−177.190			−0.262242
$78$	850.051	+	185.758i	1.23397	+	0.269653i
$79$	−533.704			−0.760080			−0.380040	−	0.924970i	$-0.624090\pi$
$79$	−533.704			−0.760080			−0.380040	+	0.924970i	$0.624090\pi$
$80$	260.205	+	302.593i	0.363647	+	0.422887i
$81$	633.533			0.869043
$82$	−736.859	−	161.022i	−0.992347	−	0.216853i
$83$			1096.29i			1.44979i	0.688857	+	0.724897i	$0.258113\pi$
$83$			1096.29i			1.44979i	−0.688857	+	0.724897i	$0.741887\pi$
$84$	331.004	−	721.192i	0.429946	−	0.936767i
$85$	−608.307			−0.776237
$86$	1062.18	+	232.114i	1.33184	+	0.291040i
$87$		−	1989.23i		−	2.45136i
$88$	288.453	+	217.210i	0.349423	+	0.263122i
$89$			129.885i			0.154694i	0.997004	+	0.0773471i	$0.0246450\pi$
$89$			129.885i			0.154694i	−0.997004	+	0.0773471i	$0.975355\pi$
$90$	−198.823	+	909.842i	−0.232865	+	1.06562i
$91$	382.364			0.440468
$92$	−323.427	+	704.683i	−0.366517	+	0.798568i
$93$	813.443			0.906990
$94$	−1107.99	−	242.124i	−1.21575	−	0.265672i
$95$	41.5379	+	514.762i	0.0448600	+	0.555932i
$96$	−1422.94	+	768.286i	−1.51279	+	0.816801i
$97$			681.176i			0.713020i	0.934292	+	0.356510i	$0.116033\pi$
$97$			681.176i			0.713020i	−0.934292	+	0.356510i	$0.883967\pi$
$98$	−132.670	+	607.115i	−0.136752	+	0.625795i
$99$			842.644i			0.855444i
$100$	626.129	+	287.373i	0.626129	+	0.287373i
$101$	696.054			0.685742			0.342871	−	0.939382i	$-0.388601\pi$
$101$	696.054			0.685742			0.342871	+	0.939382i	$0.388601\pi$
$102$	526.218	−	2408.04i	0.510817	−	2.33757i
$103$	1593.92			1.52480			0.762398	−	0.647108i	$-0.224022\pi$
$103$	1593.92			1.52480			0.762398	+	0.647108i	$0.224022\pi$
$104$	−622.463	−	468.726i	−0.586899	−	0.441946i
$105$			618.523i			0.574873i
$106$	−557.629	−	121.856i	−0.510960	−	0.111658i
$107$	−260.878			−0.235701			−0.117850	−	0.993031i	$-0.537600\pi$
$107$	−260.878			−0.235701			−0.117850	+	0.993031i	$0.537600\pi$
$108$	−1676.00	−	769.231i	−1.49327	−	0.685364i
$109$			419.138i			0.368313i	0.982897	+	0.184157i	$0.0589554\pi$
$109$			419.138i			0.368313i	−0.982897	+	0.184157i	$0.941045\pi$
$110$	−274.967	−	60.0873i	−0.238337	−	0.0520827i
$111$		−	3532.61i		−	3.02072i
$112$	−538.805	+	463.328i	−0.454574	+	0.390896i
$113$			628.881i			0.523541i	0.965130	+	0.261771i	$0.0843064\pi$
$113$			628.881i			0.523541i	−0.965130	+	0.261771i	$0.915694\pi$
$114$	−2073.67	−	280.865i	−1.70366	−	0.230750i
$115$		−	604.365i		−	0.490063i
$116$	−743.083	+	1619.03i	−0.594772	+	1.29589i
$117$		−	1818.37i		−	1.43683i
$118$	−11.3184	+	51.7942i	−0.00882999	+	0.0404072i
$119$		−	1083.17i		−	0.834402i
$120$	758.225	−	1006.91i	0.576802	−	0.765986i
$121$	1076.34			0.808671
$122$	241.700	−	1106.05i	0.179365	−	0.820797i
$123$			2382.21i			1.74632i
$124$	−662.058	−	303.863i	−0.479472	−	0.220062i
$125$	−1316.46			−0.941980
$126$	−1620.09	−	354.030i	−1.14547	−	0.250314i
$127$	236.092			0.164959			0.0824795	−	0.996593i	$-0.473716\pi$
$127$	236.092			0.164959			0.0824795	+	0.996593i	$0.473716\pi$
$128$	1445.12	−	93.7645i	0.997902	−	0.0647475i
$129$		−	3433.96i		−	2.34374i
$130$	593.362	+	129.665i	0.400317	+	0.0874795i
$131$			1409.02i			0.939744i	0.882735	+	0.469872i	$0.155700\pi$
$131$			1409.02i			0.939744i	−0.882735	+	0.469872i	$0.844300\pi$
$132$	475.723	−	1036.51i	0.313685	−	0.683456i
$133$	−916.600	+	73.9636i	−0.597589	+	0.0482215i
$134$	−507.129	+	2320.69i	−0.326935	+	1.49610i
$135$	1437.41			0.916387
$136$	−1327.82	+	1763.33i	−0.837201	+	1.11179i
$137$	105.810			0.0659851			0.0329926	−	0.999456i	$-0.489496\pi$
$137$	105.810			0.0659851			0.0329926	+	0.999456i	$0.489496\pi$
$138$	2392.44	+	522.808i	1.47578	+	0.322496i
$139$			1633.00i			0.996470i	0.867042	+	0.498235i	$0.166018\pi$
$139$			1633.00i			0.996470i	−0.867042	+	0.498235i	$0.833982\pi$
$140$	231.051	−	503.414i	0.139481	−	0.303902i
$141$			3582.06i			2.13946i
$142$	516.581	−	2363.94i	0.305285	−	1.39702i
$143$	549.538			0.321361
$144$	2203.40	+	2562.35i	1.27512	+	1.48284i
$145$		−	1388.55i		−	0.795258i
$146$	455.709	−	2085.38i	0.258320	−	1.18211i
$147$	1962.76			1.10126
$148$	−1319.61	+	2875.17i	−0.732915	+	1.59688i
$149$	831.304			0.457068			0.228534	−	0.973536i	$-0.426607\pi$
$149$	831.304			0.457068			0.228534	+	0.973536i	$0.426607\pi$
$150$	464.529	−	2125.74i	0.252857	−	1.15711i
$151$	1807.29			0.974008			0.487004	−	0.873400i	$-0.338090\pi$
$151$	1807.29			0.974008			0.487004	+	0.873400i	$0.338090\pi$
$152$	1582.83	+	1003.22i	0.844636	+	0.535341i
$153$	−5151.12			−2.72185
$154$	106.993	−	489.614i	0.0559854	−	0.256196i
$155$	567.808			0.294241
$156$	−1026.58	+	2236.71i	−0.526873	+	1.14795i
$157$	1937.16			0.984726			0.492363	−	0.870390i	$-0.336133\pi$
$157$	1937.16			0.984726			0.492363	+	0.870390i	$0.336133\pi$
$158$	322.268	−	1474.74i	0.162268	−	0.742557i
$159$			1802.78i			0.899178i
$160$	−993.252	+	536.287i	−0.490772	+	0.264983i
$161$	1076.15			0.526785
$162$	−382.548	+	1750.59i	−0.185530	+	0.849008i
$163$		−	2608.39i		−	1.25340i	−0.779259	−	0.626702i	$-0.784404\pi$
$163$		−	2608.39i		−	1.25340i	0.779259	−	0.626702i	$-0.215596\pi$
$164$	889.881	−	1938.87i	0.423707	−	0.923174i
$165$			888.949i			0.419422i
$166$	−3029.28	−	661.974i	−1.41637	−	0.309513i
$167$	−2540.59			−1.17723			−0.588613	−	0.808415i	$-0.700326\pi$
$167$	−2540.59			−1.17723			−0.588613	+	0.808415i	$0.700326\pi$
$168$	1792.94	+	1350.12i	0.823383	+	0.620022i
$169$	1011.13			0.460233
$170$	367.316	−	1680.89i	0.165717	−	0.758342i
$171$	351.742	+	4358.99i	0.157300	+	1.94936i
$172$	−1282.76	+	2794.88i	−0.568661	+	1.23900i
$173$			463.936i			0.203887i	0.994790	+	0.101943i	$0.0325061\pi$
$173$			463.936i			0.203887i	−0.994790	+	0.101943i	$0.967494\pi$
$174$	5496.69	+	1201.17i	2.39485	+	0.523335i
$175$		−	956.186i		−	0.413033i
$176$	−774.378	+	665.900i	−0.331653	+	0.285194i
$177$	167.447			0.0711079
$178$	−358.901	−	78.4289i	−0.151128	−	0.0330253i
$179$	−3143.83			−1.31274			−0.656370	−	0.754439i	$-0.727909\pi$
$179$	−3143.83			−1.31274			−0.656370	+	0.754439i	$0.727909\pi$
$180$	−2394.04	−	1098.79i	−0.991338	−	0.454993i
$181$		−	157.448i		−	0.0646578i	−0.999477	−	0.0323289i	$-0.989708\pi$
$181$		−	157.448i		−	0.0646578i	0.999477	−	0.0323289i	$-0.0102924\pi$
$182$	−230.884	+	1056.56i	−0.0940345	+	0.430314i
$183$	−3575.79			−1.44442
$184$	−1751.90	−	1319.21i	−0.701911	−	0.528552i
$185$		−	2465.87i		−	0.979968i
$186$	−491.184	+	2247.72i	−0.193631	+	0.886080i
$187$		−	1556.74i		−	0.608771i
$188$	1338.09	−	2915.42i	0.519095	−	1.13101i
$189$			2559.49i			0.985054i
$190$	−1447.48	−	196.052i	−0.552692	−	0.0748586i
$191$		−	843.063i		−	0.319382i	−0.987167	−	0.159691i	$-0.948950\pi$
$191$		−	843.063i		−	0.319382i	0.987167	−	0.159691i	$-0.0510497\pi$
$192$	−1263.73	−	4395.80i	−0.475009	−	1.65229i
$193$		−	2319.63i		−	0.865131i	−0.901603	−	0.432565i	$-0.857608\pi$
$193$		−	2319.63i		−	0.865131i	0.901603	−	0.432565i	$-0.142392\pi$
$194$	−1882.24	−	411.317i	−0.696582	−	0.152221i
$195$		−	1918.30i		−	0.704472i
$196$	−1597.48	−	733.193i	−0.582173	−	0.267199i
$197$	4304.71			1.55684			0.778421	−	0.627742i	$-0.216021\pi$
$197$	4304.71			1.55684			0.778421	+	0.627742i	$0.216021\pi$
$198$	−2328.41	−	508.817i	−0.835722	−	0.182626i
$199$			3324.44i			1.18424i	0.805851	+	0.592118i	$0.201708\pi$
$199$			3324.44i			1.18424i	−0.805851	+	0.592118i	$0.798292\pi$
$200$	−1172.15	+	1556.61i	−0.414419	+	0.550344i
$201$	7502.62			2.63280
$202$	−420.301	+	1923.35i	−0.146397	+	0.669933i
$203$	2472.48			0.854849
$204$	6336.20	+	2908.11i	2.17462	+	0.998082i
$205$			1662.86i			0.566531i
$206$	−962.465	+	4404.36i	−0.325525	+	1.48964i
$207$		−	5117.74i		−	1.71839i
$208$	1671.06	−	1436.97i	0.557053	−	0.479019i
$209$	−1317.35	+	106.301i	−0.435995	+	0.0351819i
$210$	−1709.12	−	373.485i	−0.561620	−	0.122728i
$211$	194.995			0.0636208			0.0318104	−	0.999494i	$-0.489873\pi$
$211$	194.995			0.0636208			0.0318104	+	0.999494i	$0.489873\pi$
$212$	673.431	−	1467.27i	0.218167	−	0.475342i
$213$	−7642.45			−2.45846
$214$	157.527	−	720.863i	0.0503192	−	0.230267i
$215$		−	2397.01i		−	0.760346i
$216$	3137.58	−	4166.67i	0.988358	−	1.31253i
$217$			1011.05i			0.316289i
$218$	−1158.17	−	253.090i	−0.359822	−	0.0786302i
$219$	−6741.90			−2.08025
$220$	332.069	−	723.512i	0.101764	−	0.221724i
$221$			3359.35i			1.02251i
$222$	9761.37	+	2133.11i	2.95108	+	0.644886i
$223$	1470.65			0.441623			0.220812	−	0.975316i	$-0.429129\pi$
$223$	1470.65			0.441623			0.220812	+	0.975316i	$0.429129\pi$
$224$	−954.927	−	1768.61i	−0.284838	−	0.527546i
$225$	−4547.24			−1.34733
$226$	−1737.74	−	379.739i	−0.511471	−	0.111769i
$227$	−1161.12			−0.339499			−0.169749	−	0.985487i	$-0.554296\pi$
$227$	−1161.12			−0.339499			−0.169749	+	0.985487i	$0.554296\pi$
$228$	2028.24	−	5560.41i	0.589139	−	1.61512i
$229$	854.643			0.246622			0.123311	−	0.992368i	$-0.460649\pi$
$229$	854.643			0.246622			0.123311	+	0.992368i	$0.460649\pi$
$230$	1669.99	+	364.936i	0.478765	+	0.104622i
$231$	−1582.89			−0.450850
$232$	−4025.04	−	3030.93i	−1.13904	−	0.857716i
$233$	−1660.27			−0.466816			−0.233408	−	0.972379i	$-0.574988\pi$
$233$	−1660.27			−0.466816			−0.233408	+	0.972379i	$0.574988\pi$
$234$	5024.56	+	1097.99i	1.40370	+	0.306744i
$235$			2500.38i			0.694073i
$236$	−136.284	−	62.5502i	−0.0375905	−	0.0172529i
$237$	−4767.73			−1.30674
$238$	2993.03	+	654.053i	0.815165	+	0.178134i
$239$		−	2630.84i		−	0.712030i	−0.934480	−	0.356015i	$-0.884135\pi$
$239$		−	2630.84i		−	0.712030i	0.934480	−	0.356015i	$-0.115865\pi$
$240$	2324.49	+	2703.15i	0.625187	+	0.727032i
$241$		−	4724.19i		−	1.26270i	−0.775497	−	0.631352i	$-0.782500\pi$
$241$		−	4724.19i		−	1.26270i	0.775497	−	0.631352i	$-0.217500\pi$
$242$	−649.931	+	2974.17i	−0.172641	+	0.790028i
$243$	−564.298			−0.148970
$244$	2910.32	+	1335.74i	0.763582	+	0.350460i
$245$	1370.07			0.357266
$246$	−6582.58	−	1438.46i	−1.70606	−	0.372817i
$247$	2842.75	−	229.392i	0.732308	−	0.0590924i
$248$	1239.41	−	1645.93i	0.317350	−	0.421438i
$249$			9793.44i			2.49251i
$250$	794.921	−	3637.66i	0.201101	−	0.920264i
$251$			2113.07i			0.531378i	0.964059	+	0.265689i	$0.0855995\pi$
$251$			2113.07i			0.531378i	−0.964059	+	0.265689i	$0.914401\pi$
$252$	1956.53	−	4262.89i	0.489086	−	1.06562i
$253$	1546.65			0.384337
$254$	−142.560	+	652.375i	−0.0352167	+	0.161156i
$255$	−5434.18			−1.33452
$256$	−613.518	+	4049.79i	−0.149785	+	0.988719i
$257$		−	7689.80i		−	1.86645i	−0.359297	−	0.933223i	$-0.616983\pi$
$257$		−	7689.80i		−	1.86645i	0.359297	−	0.933223i	$-0.383017\pi$
$258$	9488.78	+	2073.54i	2.28971	+	0.500360i
$259$	4390.79			1.05340
$260$	−716.584	+	1561.29i	−0.170925	+	0.372413i
$261$		−	11758.2i		−	2.78855i
$262$	−3893.42	−	850.812i	−0.918079	−	0.200623i
$263$			3366.97i			0.789416i	0.918807	+	0.394708i	$0.129154\pi$
$263$			3366.97i			0.789416i	−0.918807	+	0.394708i	$0.870846\pi$
$264$	2576.83	+	1940.40i	0.600732	+	0.452362i
$265$			1258.39i			0.291707i
$266$	349.096	−	2577.43i	0.0804679	−	0.594106i
$267$			1160.30i			0.265952i
$268$	−6106.35	−	2802.62i	−1.39181	−	0.638796i
$269$			1733.86i			0.392994i	0.980504	+	0.196497i	$0.0629566\pi$
$269$			1733.86i			0.392994i	−0.980504	+	0.196497i	$0.937043\pi$
$270$	−867.955	+	3971.87i	−0.195637	+	0.895261i
$271$		−	3311.74i		−	0.742339i	−0.928565	−	0.371170i	$-0.878957\pi$
$271$		−	3311.74i		−	0.742339i	0.928565	−	0.371170i	$-0.121043\pi$
$272$	−4070.68	−	4733.80i	−0.907430	−	1.05525i
$273$	3415.77			0.757259
$274$	−63.8917	+	292.376i	−0.0140870	+	0.0644639i
$275$		−	1374.24i		−	0.301345i
$276$	−2889.27	+	6295.14i	−0.630121	+	1.37291i
$277$	−5259.34			−1.14081			−0.570403	−	0.821365i	$-0.693213\pi$
$277$	−5259.34			−1.14081			−0.570403	+	0.821365i	$0.693213\pi$
$278$	−4512.34	−	986.062i	−0.973498	−	0.212734i
$279$	4808.17			1.03175
$280$	1251.53	+	942.422i	0.267118	+	0.201145i
$281$			5593.66i			1.18751i	0.804647	+	0.593754i	$0.202355\pi$
$281$			5593.66i			1.18751i	−0.804647	+	0.593754i	$0.797645\pi$
$282$	−9898.01	−	2162.97i	−2.09013	−	0.456748i
$283$			5749.12i			1.20760i	0.797137	+	0.603799i	$0.206347\pi$
$283$			5749.12i			1.20760i	−0.797137	+	0.603799i	$0.793653\pi$
$284$	6220.16	+	2854.85i	1.29964	+	0.596494i
$285$	371.071	+	4598.52i	0.0771239	+	0.955765i
$286$	−331.830	+	1518.49i	−0.0686066	+	0.313953i
$287$	−2960.93			−0.608982
$288$	−8410.81	+	4541.26i	−1.72088	+	0.929153i
$289$	4603.43			0.936989
$290$	3836.86	+	838.451i	0.776924	+	0.169778i
$291$			6085.14i			1.22583i
$292$	5487.20	+	2518.45i	1.09971	+	0.504730i
$293$		−	1915.86i		−	0.381999i	−0.981590	−	0.191000i	$-0.938827\pi$
$293$		−	1915.86i		−	0.381999i	0.981590	−	0.191000i	$-0.0611729\pi$
$294$	−1185.18	+	5423.54i	−0.235106	+	1.07587i
$295$	116.883			0.0230685
$296$	−7147.91	−	5382.51i	−1.40359	−	1.05693i
$297$			3678.52i			0.718685i
$298$	−501.970	+	2297.08i	−0.0975782	+	0.446530i
$299$	−3337.58			−0.645542
$300$	5593.40	+	2567.19i	1.07645	+	0.494056i
$301$	4268.17			0.817320
$302$	−1091.30	+	4993.94i	−0.207938	+	0.951553i
$303$	6218.06			1.17894
$304$	−3727.88	+	3767.94i	−0.703318	+	0.710875i
$305$	−2496.01			−0.468593
$306$	3110.42	−	14233.7i	0.581081	−	2.65910i
$307$	3108.52			0.577891			0.288945	−	0.957346i	$-0.406695\pi$
$307$	3108.52			0.577891			0.288945	+	0.957346i	$0.406695\pi$
$308$	1288.31	+	591.291i	0.238338	+	0.109389i
$309$	14239.0			2.62145
$310$	−342.861	+	1568.98i	−0.0628168	+	0.287458i
$311$		−	8226.97i		−	1.50003i	−0.661422	−	0.750014i	$-0.730047\pi$
$311$		−	8226.97i		−	1.50003i	0.661422	−	0.750014i	$-0.269953\pi$
$312$	−5560.64	−	4187.27i	−1.00900	−	0.759799i
$313$	3032.13			0.547560			0.273780	−	0.961792i	$-0.411726\pi$
$313$	3032.13			0.547560			0.273780	+	0.961792i	$0.411726\pi$
$314$	−1169.72	+	5352.79i	−0.210227	+	0.962024i
$315$			3656.02i			0.653948i
$316$	3880.44	+	1781.00i	0.690796	+	0.317053i
$317$			5445.37i			0.964803i	0.875950	+	0.482401i	$0.160235\pi$
$317$			5445.37i			0.964803i	−0.875950	+	0.482401i	$0.839765\pi$
$318$	−4981.46	−	1088.58i	−0.878449	−	0.191963i
$319$	3553.48			0.623689
$320$	−882.120	−	3068.40i	−0.154100	−	0.536028i
$321$	−2330.50			−0.405220
$322$	−649.815	+	2973.63i	−0.112462	+	0.514640i
$323$	−649.825	−	8053.01i	−0.111942	−	1.38725i
$324$	−4606.27	−	2114.13i	−0.789827	−	0.362505i
$325$			2965.53i			0.506147i
$326$	7207.55	+	1575.03i	1.22451	+	0.267586i
$327$			3744.28i			0.633209i
$328$	4820.19	+	3629.69i	0.811435	+	0.611025i
$329$	−4452.25			−0.746081
$330$	−2456.36	−	536.778i	−0.409752	−	0.0895413i
$331$	11566.9			1.92077			0.960386	−	0.278672i	$-0.0898941\pi$
$331$	11566.9			1.92077			0.960386	+	0.278672i	$0.0898941\pi$
$332$	3658.36	−	7970.84i	0.604755	−	1.31764i
$333$		−	20880.8i		−	3.43623i
$334$	1534.09	−	7020.21i	0.251323	−	1.15009i
$335$	5237.05			0.854122
$336$	−4813.31	+	4139.04i	−0.781510	+	0.672033i
$337$		−	1271.77i		−	0.205572i	−0.994704	−	0.102786i	$-0.967224\pi$
$337$		−	1271.77i		−	0.205572i	0.994704	−	0.102786i	$-0.0327756\pi$
$338$	−610.556	+	2793.98i	−0.0982540	+	0.449623i
$339$			5617.98i			0.900079i
$340$	4422.86	+	2029.95i	0.705480	+	0.323793i
$341$			1453.10i			0.230762i
$342$	−12257.2	−	1660.16i	−1.93800	−	0.262489i
$343$			6248.07i			0.983568i
$344$	−6948.30	−	5232.20i	−1.08903	−	0.820062i
$345$		−	5398.97i		−	0.842524i
$346$	−1281.96	−	280.141i	−0.199186	−	0.0435273i
$347$		−	524.255i		−	0.0811052i	−0.999177	−	0.0405526i	$-0.987088\pi$
$347$		−	524.255i		−	0.0811052i	0.999177	−	0.0405526i	$-0.0129118\pi$
$348$	−6638.18	+	14463.3i	−1.02254	+	2.22791i
$349$	−7598.90			−1.16550			−0.582750	−	0.812651i	$-0.698023\pi$
$349$	−7598.90			−1.16550			−0.582750	+	0.812651i	$0.698023\pi$
$350$	2642.15	+	577.377i	0.403511	+	0.0881775i
$351$		−	7938.02i		−	1.20712i
$352$	−1372.43	−	2541.87i	−0.207815	−	0.384892i
$353$	2357.87			0.355515			0.177757	−	0.984074i	$-0.443116\pi$
$353$	2357.87			0.355515			0.177757	+	0.984074i	$0.443116\pi$
$354$	−101.110	+	462.693i	−0.0151806	+	0.0694685i
$355$	−5334.66			−0.797562
$356$	433.433	−	944.364i	0.0645278	−	0.140593i
$357$		−	9676.26i		−	1.43451i
$358$	1898.35	−	8687.08i	0.280254	−	1.28248i
$359$			2181.10i			0.320651i	0.987064	+	0.160326i	$0.0512545\pi$
$359$			2181.10i			0.320651i	−0.987064	+	0.160326i	$0.948746\pi$
$360$	4481.79	−	5951.76i	0.656142	−	0.871349i
$361$	−6770.25	+	1099.79i	−0.987061	+	0.160343i
$362$	435.065	+	95.0727i	0.0631671	+	0.0138036i
$363$	9615.27			1.39028
$364$	−2780.08	−	1275.97i	−0.400318	−	0.183733i
$365$	−4706.05			−0.674865
$366$	2159.18	−	9880.68i	0.308367	−	1.41112i
$367$		−	7592.72i		−	1.07994i	−0.841685	−	0.539969i	$-0.818436\pi$
$367$		−	7592.72i		−	1.07994i	0.841685	−	0.539969i	$-0.181564\pi$
$368$	4703.13	−	4044.29i	0.666216	−	0.572890i
$369$			14081.0i			1.98652i
$370$	6813.73	+	1488.97i	0.957375	+	0.209211i
$371$	−2240.73			−0.313565
$372$	−5914.36	−	2714.50i	−0.824315	−	0.378334i
$373$			2653.44i			0.368338i	0.982895	+	0.184169i	$0.0589593\pi$
$373$			2653.44i			0.368338i	−0.982895	+	0.184169i	$0.941041\pi$
$374$	4301.62	+	940.013i	0.594737	+	0.129965i
$375$	−11760.3			−1.61946
$376$	7247.97	+	5457.85i	0.994110	+	0.748583i
$377$	−7668.19			−1.04756
$378$	−7072.42	−	1545.50i	−0.962344	−	0.210297i
$379$	−6203.24			−0.840736			−0.420368	−	0.907354i	$-0.638099\pi$
$379$	−6203.24			−0.840736			−0.420368	+	0.907354i	$0.638099\pi$
$380$	1415.78	−	3881.33i	0.191126	−	0.523969i
$381$	2109.08			0.283600
$382$	2329.57	+	509.070i	0.312019	+	0.0681840i
$383$	3182.99			0.424656			0.212328	−	0.977198i	$-0.431895\pi$
$383$	3182.99			0.424656			0.212328	+	0.977198i	$0.431895\pi$
$384$	12909.6	−	837.625i	1.71561	−	0.111315i
$385$	−1104.90			−0.146263
$386$	6409.63	+	1400.67i	0.845186	+	0.184695i
$387$		−	20297.7i		−	2.66613i
$388$	2273.12	−	4952.67i	0.297423	−	0.648025i
$389$	−10223.4			−1.33251			−0.666255	−	0.745724i	$-0.732104\pi$
$389$	−10223.4			−1.33251			−0.666255	+	0.745724i	$0.732104\pi$
$390$	5300.67	+	1158.33i	0.688231	+	0.150396i
$391$			9454.76i			1.22288i
$392$	2990.59	−	3971.47i	0.385325	−	0.511708i
$393$			12587.2i			1.61562i
$394$	−2599.33	+	11894.9i	−0.332366	+	1.52095i
$395$	−3328.02			−0.423926
$396$	2811.95	−	6126.67i	0.356832	−	0.777467i
$397$	1749.03			0.221112			0.110556	−	0.993870i	$-0.464737\pi$
$397$	1749.03			0.221112			0.110556	+	0.993870i	$0.464737\pi$
$398$	−9186.15	−	2007.41i	−1.15693	−	0.252820i
$399$	−8188.26	+	660.738i	−1.02738	+	0.0829030i
$400$	−3593.46	−	4178.85i	−0.449183	−	0.522356i
$401$			1420.63i			0.176915i	0.996080	+	0.0884576i	$0.0281938\pi$
$401$			1420.63i			0.176915i	−0.996080	+	0.0884576i	$0.971806\pi$
$402$	−4530.33	+	20731.4i	−0.562071	+	2.57211i
$403$		−	3135.69i		−	0.387593i
$404$	−5060.85	−	2322.77i	−0.623234	−	0.286045i
$405$	3950.52			0.484699
$406$	−1492.97	+	6832.01i	−0.182499	+	0.835141i
$407$	6310.49			0.768549
$408$	−11861.8	+	15752.3i	−1.43933	+	1.91141i
$409$		−	888.631i		−	0.107433i	−0.998556	−	0.0537163i	$-0.982893\pi$
$409$		−	888.631i		−	0.107433i	0.998556	−	0.0537163i	$-0.0171067\pi$
$410$	−4594.84	−	1004.09i	−0.553470	−	0.120947i
$411$	945.232			0.113442
$412$	−11589.1	−	5319.01i	−1.38581	−	0.636040i
$413$			208.125i			0.0247970i
$414$	14141.4	+	3090.26i	1.67878	+	0.366855i
$415$			6836.12i			0.808607i
$416$	2961.62	+	5485.19i	0.349052	+	0.646475i
$417$			14588.1i			1.71314i
$418$	501.725	−	3704.31i	0.0587086	−	0.433454i
$419$			6285.87i			0.732900i	0.930438	+	0.366450i	$0.119427\pi$
$419$			6285.87i			0.732900i	−0.930438	+	0.366450i	$0.880573\pi$
$420$	2064.04	−	4497.14i	0.239798	−	0.522471i
$421$		−	12590.2i		−	1.45750i	−0.684779	−	0.728751i	$-0.740101\pi$
$421$		−	12590.2i		−	1.45750i	0.684779	−	0.728751i	$-0.259899\pi$
$422$	−117.744	+	538.813i	−0.0135822	+	0.0621541i
$423$			21173.1i			2.43374i
$424$	3647.75	+	2746.82i	0.417808	+	0.314617i
$425$	8400.80			0.958820
$426$	4614.77	−	21117.8i	0.524851	−	2.40178i
$427$		−	4444.46i		−	0.503706i
$428$	1896.78	+	870.562i	0.214216	+	0.0983183i
$429$	4909.18			0.552489
$430$	6623.45	+	1447.39i	0.742817	+	0.162324i
$431$	−9497.02			−1.06138			−0.530691	−	0.847566i	$-0.678067\pi$
$431$	−9497.02			−1.06138			−0.530691	+	0.847566i	$0.678067\pi$
$432$	9618.85	+	11185.8i	1.07127	+	1.24578i
$433$		−	9104.67i		−	1.01049i	−0.862976	−	0.505246i	$-0.831402\pi$
$433$		−	9104.67i		−	1.01049i	0.862976	−	0.505246i	$-0.168598\pi$
$434$	−2793.76	−	610.508i	−0.308998	−	0.0675238i
$435$		−	12404.3i		−	1.36722i
$436$	1398.68	−	3047.46i	0.153635	−	0.334740i
$437$	8000.82	−	645.613i	0.875815	−	0.0706725i
$438$	4070.98	−	18629.3i	0.444108	−	2.03229i
$439$	−17986.2			−1.95543			−0.977716	−	0.209932i	$-0.932676\pi$
$439$	−17986.2			−1.95543			−0.977716	+	0.209932i	$0.932676\pi$
$440$	1798.71	+	1354.46i	0.194887	+	0.146753i
$441$	11601.7			1.25274
$442$	−9282.62	−	2028.49i	−0.998935	−	0.218293i
$443$		−	14001.7i		−	1.50167i	−0.660490	−	0.750835i	$-0.729651\pi$
$443$		−	14001.7i		−	1.50167i	0.660490	−	0.750835i	$-0.270349\pi$
$444$	−11788.5	+	25684.8i	−1.26004	+	2.74537i
$445$			809.925i			0.0862789i
$446$	−888.028	+	4063.73i	−0.0942810	+	0.431442i
$447$	7426.28			0.785797
$448$	5463.68	−	1570.73i	0.576193	−	0.165647i
$449$		−	12938.1i		−	1.35988i	−0.733270	−	0.679938i	$-0.762007\pi$
$449$		−	12938.1i		−	1.35988i	0.733270	−	0.679938i	$-0.237993\pi$
$450$	2745.78	−	12565.0i	0.287638	−	1.31627i
$451$	−4255.48			−0.444308
$452$	2098.61	−	4572.45i	0.218385	−	0.475818i
$453$	16145.1			1.67453
$454$	701.123	−	3208.43i	0.0724787	−	0.331672i
$455$	2384.31			0.245666
$456$	14139.9	+	8962.05i	1.45211	+	0.920365i
$457$	−51.4967			−0.00527115			−0.00263557	−	0.999997i	$-0.500839\pi$
$457$	−51.4967			−0.00527115			−0.00263557	+	0.999997i	$0.500839\pi$
$458$	−516.063	+	2361.57i	−0.0526507	+	0.240936i
$459$	−22487.0			−2.28671
$460$	−2016.80	+	4394.20i	−0.204421	+	0.445392i
$461$	−13062.4			−1.31969			−0.659843	−	0.751403i	$-0.729377\pi$
$461$	−13062.4			−1.31969			−0.659843	+	0.751403i	$0.729377\pi$
$462$	955.801	−	4373.87i	0.0962508	−	0.440456i
$463$			5544.55i			0.556538i	0.960503	+	0.278269i	$0.0897606\pi$
$463$			5544.55i			0.556538i	−0.960503	+	0.278269i	$0.910239\pi$
$464$	10805.6	−	9291.89i	1.08111	−	0.929666i
$465$	5072.39			0.505864
$466$	1002.53	−	4587.70i	0.0996594	−	0.456054i
$467$			18232.0i			1.80659i	0.429021	+	0.903294i	$0.358859\pi$
$467$			18232.0i			1.80659i	−0.429021	+	0.903294i	$0.641141\pi$
$468$	−6068.00	+	13221.0i	−0.599345	+	1.30585i
$469$			9325.24i			0.918123i
$470$	−6909.11	−	1509.82i	−0.678071	−	0.148176i
$471$	17305.2			1.69295
$472$	255.133	−	338.814i	0.0248802	−	0.0330406i
$473$	6134.27			0.596309
$474$	2878.92	−	13174.3i	0.278973	−	1.27661i
$475$	−573.644	−	7108.94i	−0.0554118	−	0.686695i
$476$	−3614.59	+	7875.46i	−0.348055	+	0.758343i
$477$			10656.0i			1.02286i
$478$	7269.60	+	1588.59i	0.695615	+	0.152009i
$479$			2517.07i			0.240100i	0.992768	+	0.120050i	$0.0383055\pi$
$479$			2517.07i			0.240100i	−0.992768	+	0.120050i	$0.961694\pi$
$480$	−8873.01	+	4790.81i	−0.843741	+	0.455562i
$481$	−13617.6			−1.29087
$482$	13054.0	+	2852.62i	1.23359	+	0.269571i
$483$	9613.55			0.905655
$484$	−7825.83	−	3591.80i	−0.734957	−	0.337322i
$485$			4247.61i			0.397679i
$486$	340.742	−	1559.28i	0.0318032	−	0.145536i
$487$	−7261.05			−0.675625			−0.337813	−	0.941213i	$-0.609687\pi$
$487$	−7261.05			−0.675625			−0.337813	+	0.941213i	$0.609687\pi$
$488$	−5448.30	+	7235.28i	−0.505395	+	0.671159i
$489$		−	23301.5i		−	2.15487i
$490$	−827.292	+	3785.79i	−0.0762719	+	0.349030i
$491$			15353.3i			1.41117i	0.708627	+	0.705584i	$0.249315\pi$
$491$			15353.3i			1.41117i	−0.708627	+	0.705584i	$0.750685\pi$
$492$	7949.56	−	17320.5i	0.728443	−	1.58713i
$493$			21722.6i			1.98445i
$494$	−1082.69	+	7993.67i	−0.0986085	+	0.728041i
$495$			5254.48i			0.477114i
$496$	3799.66	+	4418.64i	0.343971	+	0.400006i
$497$		−	9499.04i		−	0.857324i
$498$	−27061.4	−	5913.61i	−2.43504	−	0.532119i
$499$		−	8608.89i		−	0.772319i	−0.922432	−	0.386159i	$-0.873801\pi$
$499$		−	8608.89i		−	0.772319i	0.922432	−	0.386159i	$-0.126199\pi$
$500$	9571.66	+	4393.09i	0.856115	+	0.392930i
$501$	−22695.8			−2.02390
$502$	−5838.89	−	1275.94i	−0.519128	−	0.113443i
$503$		−	7527.61i		−	0.667276i	−0.942701	−	0.333638i	$-0.891724\pi$
$503$		−	7527.61i		−	0.667276i	0.942701	−	0.333638i	$-0.108276\pi$
$504$	10597.9	+	7980.39i	0.936640	+	0.705307i
$505$	4340.39			0.382465
$506$	−933.921	+	4273.74i	−0.0820511	+	0.375476i
$507$	9032.74			0.791239
$508$	−1716.57	−	787.852i	−0.149922	−	0.0688096i
$509$		−	6596.91i		−	0.574465i	−0.957861	−	0.287233i	$-0.907265\pi$
$509$		−	6596.91i		−	0.574465i	0.957861	−	0.287233i	$-0.0927353\pi$
$510$	3281.34	−	15015.8i	0.284903	−	1.30375i
$511$		−	8379.72i		−	0.725434i
$512$	−10820.0	−	4140.69i	−0.933947	−	0.357411i
$513$	1535.51	+	19029.0i	0.132153	+	1.63772i
$514$	21248.6	+	4643.36i	1.82342	+	0.398463i
$515$	9939.25			0.850438
$516$	−11459.3	+	24967.5i	−0.977649	+	2.13010i
$517$	−6398.83			−0.544333
$518$	−2651.31	+	12132.7i	−0.224887	+	1.02911i
$519$			4144.48i			0.350525i
$520$	−3881.50	−	2922.84i	−0.327336	−	0.246490i
$521$			10659.7i			0.896369i	0.893941	+	0.448184i	$0.147929\pi$
$521$			10659.7i			0.896369i	−0.893941	+	0.448184i	$0.852071\pi$
$522$	32490.4	+	7099.97i	2.72426	+	0.595320i
$523$	−2200.87			−0.184010			−0.0920049	−	0.995759i	$-0.529328\pi$
$523$	−2200.87			−0.184010			−0.0920049	+	0.995759i	$0.529328\pi$
$524$	4701.96	−	10244.6i	0.391997	−	0.854082i
$525$		−	8541.89i		−	0.710093i
$526$	−9303.69	−	2033.09i	−0.771217	−	0.168530i
$527$	−8882.85			−0.734238
$528$	−6917.74	+	5948.68i	−0.570182	+	0.490309i
$529$	2773.52			0.227954
$530$	−3477.21	−	759.859i	−0.284982	−	0.0622758i
$531$	989.762			0.0808889
$532$	6911.21	+	2520.97i	0.563231	+	0.205447i
$533$	9183.05			0.746270
$534$	−3206.17	−	700.629i	−0.259821	−	0.0567775i
$535$	−1626.76			−0.131460
$536$	11431.5	−	15180.9i	0.921202	−	1.22335i
$537$	−28084.7			−2.25688
$538$	−4791.04	−	1046.96i	−0.383934	−	0.0838993i
$539$			3506.19i			0.280190i
$540$	−10451.1	−	4796.70i	−0.832855	−	0.382254i
$541$	7167.76			0.569623			0.284811	−	0.958584i	$-0.408069\pi$
$541$	7167.76			0.569623			0.284811	+	0.958584i	$0.408069\pi$
$542$	9151.07	+	1999.74i	0.725225	+	0.158480i
$543$		−	1406.53i		−	0.111160i
$544$	15538.6	−	8389.74i	1.22465	−	0.661226i
$545$			2613.62i			0.205423i
$546$	−2062.56	+	9438.52i	−0.161665	+	0.739801i
$547$	−17756.8			−1.38798			−0.693991	−	0.719983i	$-0.744149\pi$
$547$	−17756.8			−1.38798			−0.693991	+	0.719983i	$0.744149\pi$
$548$	−769.320	−	353.094i	−0.0599703	−	0.0275245i
$549$	−21136.1			−1.64311
$550$	3797.33	+	829.814i	0.294398	+	0.0643334i
$551$	18382.1	−	1483.32i	1.42124	−	0.114685i
$552$	−15650.2	−	11784.9i	−1.20673	−	0.908693i
$553$		−	5925.96i		−	0.455692i
$554$	3175.77	−	14532.7i	0.243548	−	1.11451i
$555$		−	22028.3i		−	1.68477i
$556$	5449.41	−	11873.2i	0.415659	−	0.905638i
$557$	16634.1			1.26537			0.632685	−	0.774409i	$-0.281953\pi$
$557$	16634.1			1.26537			0.632685	+	0.774409i	$0.281953\pi$
$558$	−2903.34	+	13286.0i	−0.220265	+	1.00796i
$559$	−13237.4			−1.00158
$560$	−3359.83	+	2889.18i	−0.253534	+	0.218018i
$561$		−	13906.8i		−	1.04661i
$562$	−15456.5	−	3377.64i	−1.16013	−	0.253518i
$563$	15132.6			1.13279			0.566396	−	0.824133i	$-0.308337\pi$
$563$	15132.6			1.13279			0.566396	+	0.824133i	$0.308337\pi$
$564$	11953.5	−	26044.3i	0.892435	−	1.94444i
$565$			3921.52i			0.291999i
$566$	−15886.1	−	3471.52i	−1.17976	−	0.257807i
$567$			7034.41i			0.521018i
$568$	−11644.5	+	15463.8i	−0.860200	+	1.14234i
$569$		−	27043.1i		−	1.99245i	−0.0867948	−	0.996226i	$-0.527662\pi$
$569$		−	27043.1i		−	1.99245i	0.0867948	−	0.996226i	$-0.472338\pi$
$570$	−12930.8	−	1751.39i	−0.950196	−	0.128698i
$571$		−	3088.89i		−	0.226386i	−0.993573	−	0.113193i	$-0.963892\pi$
$571$		−	3088.89i		−	0.226386i	0.993573	−	0.113193i	$-0.0361078\pi$
$572$	−3995.56	−	1833.84i	−0.292068	−	0.134050i
$573$		−	7531.33i		−	0.549085i
$574$	1787.91	−	8181.69i	0.130010	−	0.594943i
$575$			8346.36i			0.605334i
$576$	−7469.76	−	25983.1i	−0.540347	−	1.87956i
$577$	−843.253			−0.0608407			−0.0304203	−	0.999537i	$-0.509685\pi$
$577$	−843.253			−0.0608407			−0.0304203	+	0.999537i	$0.509685\pi$
$578$	−2779.71	+	12720.3i	−0.200035	+	0.915388i
$579$		−	20721.9i		−	1.48734i
$580$	−4633.65	+	10095.8i	−0.331727	+	0.722768i
$581$	−12172.6			−0.869197
$582$	−16814.6	−	3674.41i	−1.19757	−	0.261700i
$583$	−3220.40			−0.228774
$584$	−10272.4	+	13641.6i	−0.727867	+	0.966600i
$585$		−	11338.8i		−	0.801373i
$586$	5293.95	+	1156.86i	0.373193	+	0.0815521i
$587$			1985.60i			0.139616i	0.997560	+	0.0698078i	$0.0222386\pi$
$587$			1985.60i			0.139616i	−0.997560	+	0.0698078i	$0.977761\pi$
$588$	−14270.8	−	6549.83i	−1.00088	−	0.459372i
$589$	606.561	+	7516.86i	0.0424328	+	0.525852i
$590$	−70.5780	+	322.974i	−0.00492483	+	0.0225366i
$591$	38455.2			2.67654
$592$	19189.2	−	16501.1i	1.33221	−	1.14559i
$593$	8751.21			0.606019			0.303009	−	0.952988i	$-0.402009\pi$
$593$	8751.21			0.606019			0.303009	+	0.952988i	$0.402009\pi$
$594$	−10164.6	−	2221.22i	−0.702117	−	0.153430i
$595$		−	6754.32i		−	0.465378i
$596$	−6044.22	−	2774.10i	−0.415404	−	0.190657i
$597$			29698.2i			2.03595i
$598$	2015.34	−	9222.46i	0.137815	−	0.630660i
$599$	4099.98			0.279667			0.139834	−	0.990175i	$-0.455343\pi$
$599$	4099.98			0.279667			0.139834	+	0.990175i	$0.455343\pi$
$600$	−10471.2	+	13905.6i	−0.712474	+	0.946158i
$601$			2118.77i			0.143804i	0.997412	+	0.0719020i	$0.0229069\pi$
$601$			2118.77i			0.143804i	−0.997412	+	0.0719020i	$0.977093\pi$
$602$	−2577.27	+	11793.9i	−0.174488	+	0.798478i
$603$	44347.2			2.99495
$604$	−13140.4	−	6031.02i	−0.885223	−	0.406289i
$605$	6711.75			0.451027
$606$	−3754.67	+	17181.9i	−0.251688	+	1.15176i
$607$	9760.99			0.652696			0.326348	−	0.945250i	$-0.394182\pi$
$607$	9760.99			0.652696			0.326348	+	0.945250i	$0.394182\pi$
$608$	−8160.62	−	12576.2i	−0.544337	−	0.838867i
$609$	22087.4			1.46967
$610$	1507.17	−	6897.01i	0.100039	−	0.457790i
$611$	13808.3			0.914276
$612$	37452.6	+	17189.5i	2.47374	+	1.13537i
$613$	19045.4			1.25487			0.627435	−	0.778669i	$-0.284105\pi$
$613$	19045.4			1.25487			0.627435	+	0.778669i	$0.284105\pi$
$614$	−1877.03	+	8589.52i	−0.123372	+	0.564568i
$615$			14854.8i			0.973988i
$616$	−2411.79	+	3202.83i	−0.157750	+	0.209490i
$617$	20577.5			1.34266			0.671329	−	0.741160i	$-0.265724\pi$
$617$	20577.5			1.34266			0.671329	+	0.741160i	$0.265724\pi$
$618$	−8597.99	+	39345.5i	−0.559647	+	2.56101i
$619$		−	2878.89i		−	0.186934i	−0.995622	−	0.0934671i	$-0.970205\pi$
$619$		−	2878.89i		−	0.186934i	0.995622	−	0.0934671i	$-0.0297950\pi$
$620$	−4128.40	−	1894.80i	−0.267420	−	0.122737i
$621$		−	22341.2i		−	1.44368i
$622$	22732.9	+	4967.72i	1.46545	+	0.320237i
$623$	−1442.17			−0.0927439
$624$	14928.0	−	12836.9i	0.957693	−	0.823535i
$625$	2555.45			0.163549
$626$	−1830.90	+	8378.45i	−0.116897	+	0.534936i
$627$	−11768.3	+	949.621i	−0.749568	+	0.0604852i
$628$	−14084.6	−	6464.39i	−0.894964	−	0.410760i
$629$			38576.3i			2.44537i
$630$	−10102.4	−	2207.63i	−0.638872	−	0.139610i
$631$			22023.5i			1.38945i	0.719277	+	0.694724i	$0.244473\pi$
$631$			22023.5i			1.38945i	−0.719277	+	0.694724i	$0.755527\pi$
$632$	−7264.42	+	9647.07i	−0.457220	+	0.607183i
$633$	1741.94			0.109378
$634$	−15046.8	−	3288.10i	−0.942560	−	0.205973i
$635$	1472.20			0.0920040
$636$	6015.95	−	13107.6i	0.375076	−	0.817215i
$637$		−	7566.13i		−	0.470614i
$638$	−2145.71	+	9819.05i	−0.133150	+	0.609310i
$639$	−45173.7			−2.79663
$640$	9011.32	−	584.688i	0.556568	−	0.0361122i
$641$			4558.06i			0.280862i	0.990090	+	0.140431i	$0.0448489\pi$
$641$			4558.06i			0.280862i	−0.990090	+	0.140431i	$0.955151\pi$
$642$	1407.23	−	6439.68i	0.0865094	−	0.395878i
$643$		−	27860.1i		−	1.70870i	−0.519699	−	0.854350i	$-0.673956\pi$
$643$		−	27860.1i		−	1.70870i	0.519699	−	0.854350i	$-0.326044\pi$
$644$	−7824.43	−	3591.16i	−0.478766	−	0.219738i
$645$		−	21413.2i		−	1.30720i
$646$	22644.6	+	3067.07i	1.37916	+	0.186799i
$647$			4053.33i			0.246295i	0.992388	+	0.123148i	$0.0392989\pi$
$647$			4053.33i			0.246295i	−0.992388	+	0.123148i	$0.960701\pi$
$648$	8623.23	−	11451.6i	0.522766	−	0.694227i
$649$			299.120i			0.0180917i
$650$	−8194.40	−	1790.68i	−0.494478	−	0.108056i
$651$			9032.04i			0.543769i
$652$	−8704.33	+	18965.0i	−0.522834	+	1.13915i
$653$	−5609.02			−0.336137			−0.168069	−	0.985775i	$-0.553753\pi$
$653$	−5609.02			−0.336137			−0.168069	+	0.985775i	$0.553753\pi$
$654$	−10346.3	−	2260.92i	−0.618611	−	0.135182i
$655$			8786.22i			0.524131i
$656$	−12940.2	+	11127.5i	−0.770170	+	0.662281i
$657$	−39850.6			−2.36639
$658$	2688.42	−	12302.6i	0.159279	−	0.728880i
$659$	4442.28			0.262590			0.131295	−	0.991343i	$-0.458087\pi$
$659$	4442.28			0.262590			0.131295	+	0.991343i	$0.458087\pi$
$660$	2966.47	−	6463.35i	0.174954	−	0.381190i
$661$			24200.7i			1.42405i	0.702154	+	0.712026i	$0.252222\pi$
$661$			24200.7i			1.42405i	−0.702154	+	0.712026i	$0.747778\pi$
$662$	−6984.50	+	31962.0i	−0.410061	+	1.87649i
$663$			30010.1i			1.75791i
$664$	19816.1	+	14921.9i	1.15816	+	0.872112i
$665$	−5715.65	+	461.215i	−0.333298	+	0.0268950i
$666$	57698.4	+	12608.6i	3.35701	+	0.733591i
$667$	−21581.8			−1.25285
$668$	18472.0	+	8478.07i	1.06992	+	0.491058i
$669$	13137.7			0.759244
$670$	−3162.31	+	14471.1i	−0.182344	+	0.834431i
$671$		−	6387.63i		−	0.367499i
$672$	−8530.64	−	15799.5i	−0.489698	−	0.906964i
$673$		−	9009.06i		−	0.516008i	−0.966144	−	0.258004i	$-0.916935\pi$
$673$		−	9009.06i		−	0.516008i	0.966144	−	0.258004i	$-0.0830648\pi$
$674$	3514.18	+	767.937i	0.200832	+	0.0438870i
$675$	−19850.8			−1.13194
$676$	−7351.71	−	3374.20i	−0.418281	−	0.191978i
$677$		−	3820.36i		−	0.216881i	−0.994103	−	0.108440i	$-0.965414\pi$
$677$		−	3820.36i		−	0.216881i	0.994103	−	0.108440i	$-0.0345857\pi$
$678$	−15523.7	−	3392.32i	−0.879328	−	0.192155i
$679$	−7563.41			−0.427477
$680$	−8279.87	+	10995.6i	−0.466939	+	0.620090i
$681$	−10372.6			−0.583671
$682$	−4015.23	−	877.430i	−0.225442	−	0.0492647i
$683$	−19834.3			−1.11118			−0.555592	−	0.831455i	$-0.687508\pi$
$683$	−19834.3			−1.11118			−0.555592	+	0.831455i	$0.687508\pi$
$684$	11988.7	−	32867.0i	0.670176	−	1.83728i
$685$	659.801			0.0368025
$686$	−17264.8	−	3772.79i	−0.960893	−	0.209979i
$687$	7634.78			0.423996
$688$	18653.3	−	16040.3i	1.03365	−	0.888853i
$689$	6949.41			0.384255
$690$	14918.5	+	3260.08i	0.823100	+	0.179868i
$691$		−	1544.63i		−	0.0850369i	−0.999096	−	0.0425184i	$-0.986462\pi$
$691$		−	1544.63i		−	0.0850369i	0.999096	−	0.0425184i	$-0.0135381\pi$
$692$	1548.18	−	3373.18i	0.0850476	−	0.185302i
$693$	−9356.27			−0.512865
$694$	1448.63	+	316.563i	0.0792354	+	0.0173149i
$695$			10182.9i			0.555770i
$696$	−35956.8	−	27076.2i	−1.95825	−	1.47460i
$697$		−	26013.9i		−	1.41370i
$698$	4588.47	−	20997.4i	0.248820	−	1.13863i
$699$	−14831.7			−0.802556
$700$	−3190.84	+	6952.21i	−0.172289	+	0.375384i
$701$	−12826.6			−0.691093			−0.345546	−	0.938402i	$-0.612306\pi$
$701$	−12826.6			−0.691093			−0.345546	+	0.938402i	$0.612306\pi$
$702$	21934.5	+	4793.24i	1.17929	+	0.257706i
$703$	32644.1	−	2634.16i	1.75134	−	0.141322i
$704$	7852.46	−	2257.47i	0.420385	−	0.120854i
$705$			22336.7i			1.19326i
$706$	−1423.76	+	6515.31i	−0.0758979	+	0.347319i
$707$			7728.62i			0.411124i
$708$	−1217.47	−	558.780i	−0.0646261	−	0.0296613i
$709$	−14360.0			−0.760652			−0.380326	−	0.924852i	$-0.624188\pi$
$709$	−14360.0			−0.760652			−0.380326	+	0.924852i	$0.624188\pi$
$710$	3221.25	−	14740.8i	0.170269	−	0.779175i
$711$	−28181.5			−1.48648
$712$	2347.76	+	1767.91i	0.123576	+	0.0930550i
$713$		−	8825.29i		−	0.463548i
$714$	26737.6	+	5842.85i	1.40144	+	0.306251i
$715$	3426.76			0.179236
$716$	22858.0	+	10491.1i	1.19308	+	0.547585i
$717$		−	23502.1i		−	1.22413i
$718$	−6026.85	−	1317.02i	−0.313259	−	0.0684551i
$719$		−	30280.4i		−	1.57061i	−0.619108	−	0.785306i	$-0.712506\pi$
$719$		−	30280.4i		−	1.57061i	0.619108	−	0.785306i	$-0.287494\pi$
$720$	13739.8	+	15978.0i	0.711182	+	0.827037i
$721$			17698.1i			0.914163i
$722$	1049.14	−	19371.8i	0.0540790	−	0.998537i
$723$		−	42202.5i		−	2.17086i
$724$	−525.414	+	1144.77i	−0.0269708	+	0.0587640i
$725$			19176.0i			0.982316i
$726$	−5806.02	+	26569.1i	−0.296807	+	1.35823i
$727$		−	7401.01i		−	0.377563i	−0.982019	−	0.188781i	$-0.939546\pi$
$727$		−	7401.01i		−	0.377563i	0.982019	−	0.188781i	$-0.0604538\pi$
$728$	5204.49	−	6911.50i	0.264960	−	0.351864i
$729$	−22146.4			−1.12515
$730$	2841.67	−	13003.8i	0.144075	−	0.659307i
$731$			37499.0i			1.89734i
$732$	25998.7	+	11932.6i	1.31276	+	0.602515i
$733$	23979.5			1.20832			0.604162	−	0.796861i	$-0.293508\pi$
$733$	23979.5			1.20832			0.604162	+	0.796861i	$0.293508\pi$
$734$	20980.4	+	4584.74i	1.05504	+	0.230553i
$735$	12239.2			0.614217
$736$	8335.37	+	15437.9i	0.417454	+	0.773161i
$737$			13402.3i			0.669853i
$738$	−38908.9	−	8502.58i	−1.94073	−	0.424098i
$739$			14138.1i			0.703762i	0.936045	+	0.351881i	$0.114458\pi$
$739$			14138.1i			0.703762i	−0.936045	+	0.351881i	$0.885542\pi$
$740$	−8228.72	+	17928.7i	−0.408775	+	0.890640i
$741$	25395.2	−	2049.22i	1.25899	−	0.101592i
$742$	1353.03	−	6191.62i	0.0669422	−	0.306336i
$743$	−12528.1			−0.618590			−0.309295	−	0.950966i	$-0.600093\pi$
$743$	−12528.1			−0.618590			−0.309295	+	0.950966i	$0.600093\pi$
$744$	11072.1	−	14703.6i	0.545593	−	0.724541i
$745$	5183.77			0.254924
$746$	−7332.04	−	1602.24i	−0.359846	−	0.0786355i
$747$			57888.0i			2.83535i
$748$	−5194.93	+	11318.7i	−0.253938	+	0.553280i
$749$		−	2896.65i		−	0.141310i
$750$	7101.27	−	32496.3i	0.345735	−	1.58213i
$751$	−20617.5			−1.00179			−0.500894	−	0.865509i	$-0.666995\pi$
$751$	−20617.5			−1.00179			−0.500894	+	0.865509i	$0.666995\pi$
$752$	−19457.8	+	16732.1i	−0.943555	+	0.811379i
$753$			18876.7i			0.913553i
$754$	4630.31	−	21188.9i	0.223642	−	1.02341i
$755$	11269.7			0.543242
$756$	8541.13	−	18609.4i	0.410897	−	0.895262i
$757$	−16938.0			−0.813239			−0.406619	−	0.913598i	$-0.633292\pi$
$757$	−16938.0			−0.813239			−0.406619	+	0.913598i	$0.633292\pi$
$758$	3745.72	−	17140.9i	0.179487	−	0.821353i
$759$	13816.7			0.660757
$760$	9870.08	+	6255.78i	0.471086	+	0.298580i
$761$	1093.15			0.0520720			0.0260360	−	0.999661i	$-0.491712\pi$
$761$	1093.15			0.0520720			0.0260360	+	0.999661i	$0.491712\pi$
$762$	−1273.53	+	5827.85i	−0.0605450	+	0.277062i
$763$	−4653.89			−0.220815
$764$	−2813.34	+	6129.72i	−0.133224	+	0.290269i
$765$	−32120.9			−1.51808
$766$	−1922.00	+	8795.31i	−0.0906588	+	0.414866i
$767$		−	645.482i		−	0.0303872i
$768$	−5480.74	+	36178.0i	−0.257512	+	1.69982i
$769$	−4884.82			−0.229065			−0.114533	−	0.993419i	$-0.536537\pi$
$769$	−4884.82			−0.229065			−0.114533	+	0.993419i	$0.536537\pi$
$770$	667.178	−	3053.09i	0.0312252	−	0.142891i
$771$		−	68695.3i		−	3.20882i
$772$	−7740.71	+	16865.5i	−0.360873	+	0.786271i
$773$		−	29157.6i		−	1.35669i	−0.734742	−	0.678347i	$-0.762697\pi$
$773$		−	29157.6i		−	1.35669i	0.734742	−	0.678347i	$-0.237303\pi$
$774$	56087.1	+	12256.5i	2.60466	+	0.569185i
$775$	−7841.50			−0.363452
$776$	12312.7	+	9271.72i	0.569589	+	0.428911i
$777$	39224.2			1.81102
$778$	6173.22	−	28249.5i	0.284474	−	1.30179i
$779$	−22013.5	+	1776.35i	−1.01247	+	0.0817000i
$780$	−6401.45	+	13947.5i	−0.293857	+	0.640257i
$781$		−	13652.1i		−	0.625495i
$782$	−26125.6	−	5709.10i	−1.19469	−	0.261070i
$783$		−	51329.7i		−	2.34275i
$784$	9168.22	+	10661.8i	0.417649	+	0.485685i
$785$	12079.5			0.549220
$786$	−34781.1	−	7600.55i	−1.57837	−	0.344915i
$787$	8266.76			0.374432			0.187216	−	0.982319i	$-0.440054\pi$
$787$	8266.76			0.374432			0.187216	+	0.982319i	$0.440054\pi$
$788$	−31298.6	−	14365.0i	−1.41493	−	0.649408i
$789$			30078.2i			1.35717i
$790$	2009.57	−	9196.05i	0.0905029	−	0.414153i
$791$	−6982.76			−0.313879
$792$	15231.4	+	11469.5i	0.683364	+	0.514585i
$793$			13784.1i			0.617260i
$794$	−1056.13	+	4832.96i	−0.0472046	+	0.216014i
$795$			11241.6i			0.501507i
$796$	11093.8	−	24171.2i	0.493982	−	1.07629i
$797$		−	3785.61i		−	0.168248i	−0.996455	−	0.0841238i	$-0.973191\pi$
$797$		−	3785.61i		−	0.168248i	0.996455	−	0.0841238i	$-0.0268091\pi$
$798$	3118.58	−	23024.9i	0.138342	−	1.02140i
$799$		−	39116.3i		−	1.73196i
$800$	13716.9	−	7406.19i	0.606209	−	0.327311i
$801$			6858.41i			0.302534i
$802$	−3925.52	−	857.826i	−0.172837	−	0.0377692i
$803$		−	12043.4i		−	0.529269i
$804$	−54549.8	−	25036.6i	−2.39281	−	1.09823i
$805$	6710.55			0.293808
$806$	8664.61	+	1893.44i	0.378658	+	0.0827463i
$807$			15489.1i			0.675640i
$808$	9474.23	−	12581.7i	0.412503	−	0.547799i
$809$	−11769.5			−0.511486			−0.255743	−	0.966745i	$-0.582320\pi$
$809$	−11769.5			−0.511486			−0.255743	+	0.966745i	$0.582320\pi$
$810$	−2385.46	+	10916.2i	−0.103477	+	0.473525i
$811$	3030.58			0.131219			0.0656093	−	0.997845i	$-0.479101\pi$
$811$	3030.58			0.131219			0.0656093	+	0.997845i	$0.479101\pi$
$812$	−17976.9	−	8250.80i	−0.776926	−	0.356584i
$813$		−	29584.7i		−	1.27624i
$814$	−3810.49	+	17437.3i	−0.164076	+	0.750831i
$815$		−	16265.2i		−	0.699072i
$816$	−36364.5	−	42288.5i	−1.56007	−	1.81421i
$817$	31732.5	−	2560.60i	1.35885	−	0.109650i
$818$	2455.48	+	536.585i	0.104956	+	0.0229355i
$819$	20190.2			0.861421
$820$	5549.04	−	12090.2i	0.236318	−	0.514890i
$821$	33662.2			1.43096			0.715480	−	0.698633i	$-0.246208\pi$
$821$	33662.2			1.43096			0.715480	+	0.698633i	$0.246208\pi$
$822$	−570.763	+	2611.88i	−0.0242186	+	0.110827i
$823$			11779.5i			0.498915i	0.968386	+	0.249457i	$0.0802523\pi$
$823$			11779.5i			0.498915i	−0.968386	+	0.249457i	$0.919748\pi$
$824$	21695.5	−	28811.3i	0.917229	−	1.21807i
$825$		−	12276.5i		−	0.518076i
$826$	−575.096	−	125.673i	−0.0242254	−	0.00529386i
$827$	23656.4			0.994695			0.497347	−	0.867552i	$-0.334307\pi$
$827$	23656.4			0.994695			0.497347	+	0.867552i	$0.334307\pi$
$828$	−17078.1	+	37209.9i	−0.716795	+	1.56175i
$829$		−	15450.8i		−	0.647322i	−0.946173	−	0.323661i	$-0.895086\pi$
$829$		−	15450.8i		−	0.647322i	0.946173	−	0.323661i	$-0.104914\pi$
$830$	−18889.7	−	4127.88i	−0.789965	−	0.172627i
$831$	−46983.2			−1.96129
$832$	−16945.1	+	4871.47i	−0.706089	+	0.202990i
$833$	−21433.5			−0.891508
$834$	−40310.1	−	8808.78i	−1.67365	−	0.365735i
$835$	−15842.4			−0.656584
$836$	9932.87	+	3623.17i	0.410928	+	0.149892i
$837$	20989.9			0.866805
$838$	−17369.2	−	3795.62i	−0.716003	−	0.156465i
$839$	29352.8			1.20783			0.603916	−	0.797048i	$-0.293606\pi$
$839$	29352.8			1.20783			0.603916	+	0.797048i	$0.293606\pi$
$840$	11180.2	+	8418.93i	0.459232	+	0.345810i
$841$	−25195.9			−1.03308
$842$	34789.5	+	7602.38i	1.42390	+	0.311158i
$843$			49969.8i			2.04158i
$844$	−1417.76	−	650.707i	−0.0578215	−	0.0265382i
$845$	6305.12			0.256690
$846$	−58506.1	−	12785.1i	−2.37764	−	0.519574i
$847$			11951.1i			0.484823i
$848$	−9792.72	+	8420.92i	−0.396560	+	0.341009i
$849$			51358.6i			2.07612i
$850$	−5072.69	+	23213.3i	−0.204696	+	0.936715i
$851$	−38326.3			−1.54384
$852$	55566.5	+	25503.2i	2.23436	+	1.02550i
$853$	−25393.5			−1.01929			−0.509646	−	0.860384i	$-0.670224\pi$
$853$	−25393.5			−1.01929			−0.509646	+	0.860384i	$0.670224\pi$
$854$	12281.0	+	2683.71i	0.492093	+	0.107535i
$855$	2193.36	+	27181.4i	0.0877325	+	1.08723i
$856$	−3550.90	+	4715.55i	−0.141784	+	0.188288i
$857$		−	14.0596i		−	0.000560406i	−1.00000		0.000280203i	$-0.999911\pi$
$857$		−	14.0596i		−	0.000560406i	1.00000		0.000280203i	$-8.91914e-5\pi$
$858$	−2964.33	+	13565.2i	−0.117949	+	0.539752i
$859$			24429.1i			0.970327i	0.874424	+	0.485163i	$0.161240\pi$
$859$			24429.1i			0.970327i	−0.874424	+	0.485163i	$0.838760\pi$
$860$	−7998.93	+	17428.1i	−0.317164	+	0.691038i
$861$	−26450.8			−1.04697
$862$	5734.62	−	26242.4i	0.226592	−	1.03691i
$863$	−648.335			−0.0255731			−0.0127865	−	0.999918i	$-0.504070\pi$
$863$	−648.335			−0.0255731			−0.0127865	+	0.999918i	$0.504070\pi$
$864$	−36717.0	+	19824.6i	−1.44576	+	0.780611i
$865$			2892.97i			0.113716i
$866$	25158.2	+	5497.71i	0.987195	+	0.215727i
$867$	41123.8			1.61088
$868$	3373.94	−	7351.14i	0.131934	−	0.287458i
$869$		−	8516.86i		−	0.332468i
$870$	34275.8	+	7490.13i	1.33570	+	0.291884i
$871$		−	28921.4i		−	1.12510i
$872$	7576.22	+	5705.03i	0.294224	+	0.221556i
$873$			35968.6i			1.39445i
$874$	−3047.19	+	22497.9i	−0.117932	+	0.870711i
$875$		−	14617.2i		−	0.564746i
$876$	49018.8	+	22498.1i	1.89063	+	0.867738i
$877$		−	40887.6i		−	1.57432i	−0.616750	−	0.787159i	$-0.711551\pi$
$877$		−	40887.6i		−	1.57432i	0.616750	−	0.787159i	$-0.288449\pi$
$878$	10860.7	−	49699.8i	0.417460	−	1.91035i
$879$		−	17114.9i		−	0.656738i
$880$	−4828.79	+	4152.36i	−0.184976	+	0.159064i
$881$	26042.4			0.995903			0.497952	−	0.867205i	$-0.334086\pi$
$881$	26042.4			0.995903			0.497952	+	0.867205i	$0.334086\pi$
$882$	−7005.47	+	32057.9i	−0.267445	+	1.22386i
$883$			20575.7i			0.784175i	0.919928	+	0.392087i	$0.128247\pi$
$883$			20575.7i			0.784175i	−0.919928	+	0.392087i	$0.871753\pi$
$884$	11210.3	−	24425.1i	0.426520	−	0.929303i
$885$	1044.15			0.0396596
$886$	38689.7	+	8454.69i	1.46705	+	0.320588i
$887$	−11142.0			−0.421773			−0.210887	−	0.977511i	$-0.567635\pi$
$887$	−11142.0			−0.421773			−0.210887	+	0.977511i	$0.567635\pi$
$888$	−63854.4	−	48083.5i	−2.41308	−	1.81709i
$889$			2621.44i			0.0988981i
$890$	−2238.00	−	489.060i	−0.0842898	−	0.0184195i
$891$			10109.9i			0.380130i
$892$	−10692.8	−	4907.63i	−0.401368	−	0.184215i
$893$	−33101.1	+	2671.04i	−1.24041	+	0.100093i
$894$	−4484.24	+	20520.5i	−0.167758	+	0.767681i
$895$	−19604.0			−0.732166
$896$	1041.11	+	16045.8i	0.0388182	+	0.598273i
$897$	−29815.6			−1.10982
$898$	35750.7	+	7812.43i	1.32853	+	0.290317i
$899$		−	20276.4i		−	0.752230i
$900$	33062.0	+	15174.4i	1.22452	+	0.562014i
$901$		−	19686.4i		−	0.727913i
$902$	2569.60	−	11758.8i	0.0948541	−	0.434064i
$903$	38128.8			1.40515
$904$	11367.5	+	8559.91i	0.418226	+	0.314932i
$905$		−	981.803i		−	0.0360621i
$906$	−9748.93	+	44612.3i	−0.357491	+	1.63592i
$907$	34286.9			1.25521			0.627607	−	0.778530i	$-0.284035\pi$
$907$	34286.9			1.25521			0.627607	+	0.778530i	$0.284035\pi$
$908$	8442.23	+	3874.72i	0.308552	+	0.141616i
$909$	36754.3			1.34110
$910$	−1439.73	+	6588.37i	−0.0524467	+	0.240003i
$911$	38861.2			1.41332			0.706658	−	0.707555i	$-0.250202\pi$
$911$	38861.2			1.41332			0.706658	+	0.707555i	$0.250202\pi$
$912$	−33302.3	+	33660.1i	−1.20915	+	1.22215i
$913$	−17494.6			−0.634157
$914$	31.0954	−	142.297i	0.00112532	−	0.00514962i
$915$	−22297.6			−0.805611
$916$	−6213.92	−	2851.99i	−0.224141	−	0.102874i
$917$	−15645.0			−0.563405
$918$	13578.4	−	62136.4i	0.488185	−	2.23400i
$919$			50244.7i			1.80350i	0.432253	+	0.901752i	$0.357719\pi$
$919$			50244.7i			1.80350i	−0.432253	+	0.901752i	$0.642281\pi$
$920$	−10924.3	−	8226.22i	−0.391483	−	0.294794i
$921$	27769.3			0.993518
$922$	7887.50	−	36094.2i	0.281736	−	1.28926i
$923$			29460.4i			1.05060i
$924$	11508.8	+	5282.18i	0.409753	+	0.188064i
$925$			34053.9i			1.21047i
$926$	−15320.8	−	3347.98i	−0.543707	−	0.118814i
$927$	84165.1			2.98203
$928$	19150.8	+	35468.9i	0.677429	+	1.25466i
$929$	−49235.0			−1.73880			−0.869402	−	0.494106i	$-0.835496\pi$
$929$	−49235.0			−1.73880			−0.869402	+	0.494106i	$0.835496\pi$
$930$	−3062.88	+	14016.1i	−0.107996	+	0.494201i
$931$	1463.57	+	18137.5i	0.0515217	+	0.638487i
$932$	12071.5	+	5540.42i	0.424264	+	0.194724i
$933$		−	73494.0i		−	2.57887i
$934$	−50379.1	−	11009.1i	−1.76494	−	0.385684i
$935$		−	9707.39i		−	0.339535i
$936$	−32868.4	−	24750.5i	−1.14780	−	0.864311i
$937$	21386.2			0.745632			0.372816	−	0.927905i	$-0.378392\pi$
$937$	21386.2			0.745632			0.372816	+	0.927905i	$0.378392\pi$
$938$	−25767.7	−	5630.89i	−0.896956	−	0.196008i
$939$	27086.9			0.941372
$940$	8343.91	−	18179.7i	0.289519	−	0.630805i
$941$			6763.30i			0.234301i	0.993114	+	0.117150i	$0.0373760\pi$
$941$			6763.30i			0.234301i	−0.993114	+	0.117150i	$0.962624\pi$
$942$	−10449.5	+	47818.0i	−0.361424	+	1.65392i
$943$	25845.3			0.892513
$944$	782.160	+	909.577i	0.0269673	+	0.0313604i
$945$			15960.2i			0.549403i
$946$	−3704.08	+	16950.3i	−0.127304	+	0.582561i
$947$		−	35691.6i		−	1.22473i	−0.790574	−	0.612366i	$-0.790218\pi$
$947$		−	35691.6i		−	1.22473i	0.790574	−	0.612366i	$-0.209782\pi$
$948$	34665.1	+	15910.2i	1.18763	+	0.545082i
$949$			25988.9i			0.888975i
$950$	19989.9	+	2707.51i	0.682694	+	0.0924666i
$951$			48645.1i			1.65870i
$952$	−19579.0	−	14743.4i	−0.666555	−	0.501928i
$953$			3333.74i			0.113316i	0.998394	+	0.0566582i	$0.0180445\pi$
$953$			3333.74i			0.113316i	−0.998394	+	0.0566582i	$0.981955\pi$
$954$	−29444.9	−	6434.46i	−0.999280	−	0.218368i
$955$		−	5257.09i		−	0.178132i
$956$	−8779.26	+	19128.3i	−0.297010	+	0.647126i
$957$	31744.3			1.07225
$958$	−6955.23	−	1519.89i	−0.234565	−	0.0512584i
$959$			1174.86i			0.0395601i
$960$	−7880.24	−	27410.9i	−0.264931	−	0.921546i
$961$	−21499.5			−0.721679
$962$	8222.79	−	37628.5i	0.275586	−	1.26111i
$963$	−13775.3			−0.460959
$964$	−15764.9	+	34348.5i	−0.526713	+	1.14760i
$965$		−	14464.5i		−	0.482517i
$966$	−5804.98	+	26564.3i	−0.193346	+	0.884776i
$967$		−	31242.1i		−	1.03896i	−0.854482	−	0.519481i	$-0.826125\pi$
$967$		−	31242.1i		−	1.03896i	0.854482	−	0.519481i	$-0.173875\pi$
$968$	14650.4	−	19455.6i	0.486449	−	0.646000i
$969$	−5805.07	−	71939.9i	−0.192452	−	2.38498i
$970$	−11737.1	−	2564.85i	−0.388511	−	0.0848994i
$971$	11741.0			0.388039			0.194019	−	0.980998i	$-0.437848\pi$
$971$	11741.0			0.388039			0.194019	+	0.980998i	$0.437848\pi$
$972$	4102.88	+	1883.09i	0.135391	+	0.0621401i
$973$	−18132.0			−0.597415
$974$	4384.47	−	20063.9i	0.144238	−	0.660049i
$975$			26491.9i			0.870175i
$976$	−16702.8	−	19423.8i	−0.547791	−	0.637028i
$977$		−	18411.6i		−	0.602907i	−0.953481	−	0.301454i	$-0.902528\pi$
$977$		−	18411.6i		−	0.602907i	0.953481	−	0.301454i	$-0.0974718\pi$
$978$	64387.2	+	14070.2i	2.10519	+	0.460037i
$979$	−2072.71			−0.0676651
$980$	−9961.43	−	4571.98i	−0.324700	−	0.149027i
$981$			22132.0i			0.720308i
$982$	−42424.4	−	9270.82i	−1.37863	−	0.301267i
$983$	−53872.4			−1.74798			−0.873990	−	0.485945i	$-0.838476\pi$
$983$	−53872.4			−1.74798			−0.873990	+	0.485945i	$0.838476\pi$
$984$	43060.2	+	32425.1i	1.39503	+	1.05048i
$985$	26842.9			0.868311
$986$	−60024.3	−	13116.8i	−1.93870	−	0.423656i
$987$	−39773.3			−1.28267
$988$	−21434.5	−	7818.56i	−0.690205	−	0.251763i
$989$	−37256.0			−1.19785
$990$	−14519.3	−	3172.83i	−0.466114	−	0.101858i
$991$	−26155.9			−0.838415			−0.419207	−	0.907890i	$-0.637692\pi$
$991$	−26155.9			−0.838415			−0.419207	+	0.907890i	$0.637692\pi$
$992$	−14504.0	+	7831.18i	−0.464218	+	0.250645i
$993$	103331.			3.30222
$994$	26247.9	+	5735.84i	0.837560	+	0.183028i
$995$			20730.2i			0.660494i
$996$	32681.2	−	71205.8i	1.03970	−	2.26530i
$997$	23745.6			0.754295			0.377147	−	0.926153i	$-0.376905\pi$
$997$	23745.6			0.754295			0.377147	+	0.926153i	$0.376905\pi$
$998$	23788.3	+	5198.34i	0.754513	+	0.164880i
$999$		−	91154.4i		−	2.88688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.d.a.75.14	yes	28
4.3	odd	2	inner	76.4.d.a.75.16	yes	28
19.18	odd	2	inner	76.4.d.a.75.15	yes	28
76.75	even	2	inner	76.4.d.a.75.13	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.d.a.75.13	✓	28	76.75	even	2	inner
76.4.d.a.75.14	yes	28	1.1	even	1	trivial
76.4.d.a.75.15	yes	28	19.18	odd	2	inner
76.4.d.a.75.16	yes	28	4.3	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.603834 + 2.76322i) q^{2} +8.93329 q^{3} +(-7.27077 - 3.33705i) q^{4} +6.23571 q^{5} +(-5.39422 + 24.6847i) q^{6} +11.1035i q^{7} +(13.6113 - 18.0757i) q^{8} +52.8037 q^{9} +O(q^{10})\)	\(q+(-0.603834 + 2.76322i) q^{2} +8.93329 q^{3} +(-7.27077 - 3.33705i) q^{4} +6.23571 q^{5} +(-5.39422 + 24.6847i) q^{6} +11.1035i q^{7} +(13.6113 - 18.0757i) q^{8} +52.8037 q^{9} +(-3.76533 + 17.2306i) q^{10} +15.9580i q^{11} +(-64.9519 - 29.8109i) q^{12} -34.4364i q^{13} +(-30.6813 - 6.70465i) q^{14} +55.7054 q^{15} +(41.7282 + 48.5259i) q^{16} -97.5522 q^{17} +(-31.8847 + 145.908i) q^{18} +(6.66130 + 82.5508i) q^{19} +(-45.3384 - 20.8089i) q^{20} +99.1906i q^{21} +(-44.0956 - 9.63601i) q^{22} -96.9200i q^{23} +(121.594 - 161.476i) q^{24} -86.1159 q^{25} +(95.1554 + 20.7939i) q^{26} +230.512 q^{27} +(37.0528 - 80.7308i) q^{28} -222.677i q^{29} +(-33.6368 + 153.926i) q^{30} +91.0575 q^{31} +(-159.285 + 86.0026i) q^{32} +142.558i q^{33} +(58.9053 - 269.558i) q^{34} +69.2380i q^{35} +(-383.924 - 176.209i) q^{36} -395.443i q^{37} +(-232.128 - 31.4403i) q^{38} -307.631i q^{39} +(84.8764 - 112.715i) q^{40} +266.667i q^{41} +(-274.085 - 59.8946i) q^{42} -384.400i q^{43} +(53.2528 - 116.027i) q^{44} +329.269 q^{45} +(267.811 + 58.5236i) q^{46} +400.978i q^{47} +(372.770 + 433.496i) q^{48} +219.713 q^{49} +(51.9997 - 237.957i) q^{50} -871.462 q^{51} +(-114.916 + 250.379i) q^{52} +201.804i q^{53} +(-139.191 + 636.956i) q^{54} +99.5097i q^{55} +(200.703 + 151.133i) q^{56} +(59.5074 + 737.450i) q^{57} +(615.304 + 134.460i) q^{58} +18.7442 q^{59} +(-405.021 - 185.892i) q^{60} -400.276 q^{61} +(-54.9836 + 251.612i) q^{62} +586.305i q^{63} +(-141.463 - 492.069i) q^{64} -214.736i q^{65} +(-393.919 - 86.0813i) q^{66} +839.849 q^{67} +(709.279 + 325.537i) q^{68} -865.815i q^{69} +(-191.320 - 41.8082i) q^{70} -855.502 q^{71} +(718.730 - 954.465i) q^{72} -754.693 q^{73} +(1092.70 + 238.782i) q^{74} -769.299 q^{75} +(227.043 - 622.437i) q^{76} -177.190 q^{77} +(850.051 + 185.758i) q^{78} -533.704 q^{79} +(260.205 + 302.593i) q^{80} +633.533 q^{81} +(-736.859 - 161.022i) q^{82} +1096.29i q^{83} +(331.004 - 721.192i) q^{84} -608.307 q^{85} +(1062.18 + 232.114i) q^{86} -1989.23i q^{87} +(288.453 + 217.210i) q^{88} +129.885i q^{89} +(-198.823 + 909.842i) q^{90} +382.364 q^{91} +(-323.427 + 704.683i) q^{92} +813.443 q^{93} +(-1107.99 - 242.124i) q^{94} +(41.5379 + 514.762i) q^{95} +(-1422.94 + 768.286i) q^{96} +681.176i q^{97} +(-132.670 + 607.115i) q^{98} +842.644i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9}+O(q^{10}) \) 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9	\( 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9} - 134 q^{16} - 80 q^{17} - 300 q^{20} - 26 q^{24} + 496 q^{25} - 90 q^{26} + 254 q^{28} - 16 q^{30} - 556 q^{36} - 626 q^{38} - 850 q^{42} + 976 q^{44} - 612 q^{45} + 188 q^{49} + 354 q^{54} - 580 q^{57} + 2534 q^{58} - 948 q^{61} - 1068 q^{62} - 1634 q^{64} + 1244 q^{66} + 1630 q^{68} - 184 q^{73} + 2276 q^{74} + 1688 q^{76} + 308 q^{77} + 3376 q^{80} - 2284 q^{81} - 740 q^{82} + 684 q^{85} + 1810 q^{92} + 824 q^{93} - 5222 q^{96}+O(q^{100}) \) 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9 - 134 * q^16 - 80 * q^17 - 300 * q^20 - 26 * q^24 + 496 * q^25 - 90 * q^26 + 254 * q^28 - 16 * q^30 - 556 * q^36 - 626 * q^38 - 850 * q^42 + 976 * q^44 - 612 * q^45 + 188 * q^49 + 354 * q^54 - 580 * q^57 + 2534 * q^58 - 948 * q^61 - 1068 * q^62 - 1634 * q^64 + 1244 * q^66 + 1630 * q^68 - 184 * q^73 + 2276 * q^74 + 1688 * q^76 + 308 * q^77 + 3376 * q^80 - 2284 * q^81 - 740 * q^82 + 684 * q^85 + 1810 * q^92 + 824 * q^93 - 5222 * q^96

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