LMFDB - Embedded newform 76.4.d.a.75.16

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			75.16
Character	$\chi$	$=$	76.75
Dual form			76.4.d.a.75.15

$q$-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} +(224.084 - 68.2536i) 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} +(323.909 + 577.978i) 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	$-0.829291\pi$
$3$	−8.93329			−1.71921			−0.859607	+	0.510957i	$0.829291\pi$
$4$	−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	$-0.903092\pi$
$7$		−	11.1035i		−	0.599531i	0.954013	−	0.299766i	$-0.0969084\pi$
$8$	−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	$-0.929816\pi$
$11$		−	15.9580i		−	0.437412i	0.975791	−	0.218706i	$-0.0701835\pi$
$12$	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	$0.144784\pi$
$23$			96.9200i			0.878661i	−0.898325	+	0.439331i	$0.855216\pi$
$24$	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	$-0.584970\pi$
$31$	−91.0575			−0.527561			−0.263781	+	0.964583i	$0.584970\pi$
$32$	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	$-0.341468\pi$
$38$	224.084	−	68.2536i	0.956609	−	0.291373i
$39$			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	$0.238730\pi$
$43$			384.400i			1.36327i	−0.731694	+	0.681633i	$0.761270\pi$
$44$	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	$-0.786231\pi$
$47$		−	400.978i		−	1.24444i	0.782842	−	0.622220i	$-0.213769\pi$
$48$	−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	$-0.506583\pi$
$59$	−18.7442			−0.0413607			−0.0206804	+	0.999786i	$0.506583\pi$
$60$	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	$-0.777608\pi$
$67$	−839.849			−1.53140			−0.765701	+	0.643197i	$0.777608\pi$
$68$	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	$-0.246429\pi$
$71$	855.502			1.42999			0.714996	+	0.699129i	$0.246429\pi$
$72$	−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
$76$	323.909	+	577.978i	0.488880	+	0.872351i
$77$	−177.190			−0.262242
$78$	−850.051	+	185.758i	−1.23397	+	0.269653i
$79$	533.704			0.760080			0.380040	−	0.924970i	$-0.375910\pi$
$79$	533.704			0.760080			0.380040	+	0.924970i	$0.375910\pi$
$80$	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	$-0.741887\pi$
$83$		−	1096.29i		−	1.44979i	0.688857	−	0.724897i	$-0.258113\pi$
$84$	−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	$-0.775978\pi$
$103$	−1593.92			−1.52480			−0.762398	+	0.647108i	$0.775978\pi$
$104$	−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	$-0.462400\pi$
$107$	260.878			0.235701			0.117850	+	0.993031i	$0.462400\pi$
$108$	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	$0.915694\pi$
$114$	−2001.80	+	609.729i	−1.64462	+	0.500933i
$115$			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	$-0.526284\pi$
$127$	−236.092			−0.164959			−0.0824795	+	0.996593i	$0.526284\pi$
$128$	−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	$-0.844300\pi$
$131$		−	1409.02i		−	0.939744i	0.882735	−	0.469872i	$-0.155700\pi$
$132$	−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	$-0.833982\pi$
$139$		−	1633.00i		−	0.996470i	0.867042	−	0.498235i	$-0.166018\pi$
$140$	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	$-0.661910\pi$
$151$	−1807.29			−0.974008			−0.487004	+	0.873400i	$0.661910\pi$
$152$	−1401.49	+	1244.03i	−0.747870	+	0.663845i
$153$	−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	$0.215596\pi$
$163$			2608.39i			1.25340i	−0.779259	+	0.626702i	$0.784404\pi$
$164$	−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	$-0.299674\pi$
$167$	2540.59			1.17723			0.588613	+	0.808415i	$0.299674\pi$
$168$	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	$-0.272091\pi$
$179$	3143.83			1.31274			0.656370	+	0.754439i	$0.272091\pi$
$180$	−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
$190$	1397.32	−	425.609i	0.533538	−	0.162510i
$191$			843.063i			0.319382i	0.987167	+	0.159691i	$0.0510497\pi$
$191$			843.063i			0.319382i	−0.987167	+	0.159691i	$0.948950\pi$
$192$	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	$-0.798292\pi$
$199$		−	3324.44i		−	1.18424i	0.805851	−	0.592118i	$-0.201708\pi$
$200$	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	$-0.510127\pi$
$211$	−194.995			−0.0636208			−0.0318104	+	0.999494i	$0.510127\pi$
$212$	−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	$-0.570871\pi$
$223$	−1470.65			−0.441623			−0.220812	+	0.975316i	$0.570871\pi$
$224$	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	$-0.445704\pi$
$227$	1161.12			0.339499			0.169749	+	0.985487i	$0.445704\pi$
$228$	−2893.57	−	5163.25i	−0.840489	−	1.49976i
$229$	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	$0.115865\pi$
$239$			2630.84i			0.712030i	−0.934480	+	0.356015i	$0.884135\pi$
$240$	−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	$-0.914401\pi$
$251$		−	2113.07i		−	0.531378i	0.964059	−	0.265689i	$-0.0855995\pi$
$252$	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	$-0.870846\pi$
$263$		−	3366.97i		−	0.789416i	0.918807	−	0.394708i	$-0.129154\pi$
$264$	2576.83	−	1940.40i	0.600732	−	0.452362i
$265$			1258.39i			0.291707i
$266$	−757.852	−	2488.11i	−0.174687	−	0.573517i
$267$		−	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	$0.121043\pi$
$271$			3311.74i			0.742339i	−0.928565	+	0.371170i	$0.878957\pi$
$272$	−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	$-0.793653\pi$
$283$		−	5749.12i		−	1.20760i	0.797137	−	0.603799i	$-0.206347\pi$
$284$	−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
$304$	−4283.81	−	3121.45i	−0.808202	−	0.588906i
$305$	−2496.01			−0.468593
$306$	−3110.42	−	14233.7i	−0.581081	−	2.65910i
$307$	−3108.52			−0.577891			−0.288945	−	0.957346i	$-0.593305\pi$
$307$	−3108.52			−0.577891			−0.288945	+	0.957346i	$0.593305\pi$
$308$	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	$0.269953\pi$
$311$			8226.97i			1.50003i	−0.661422	+	0.750014i	$0.730047\pi$
$312$	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	$-0.910106\pi$
$331$	−11566.9			−1.92077			−0.960386	+	0.278672i	$0.910106\pi$
$332$	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
$342$	11832.4	−	3604.04i	1.87083	−	0.569837i
$343$		−	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	$0.0129118\pi$
$347$			524.255i			0.0811052i	−0.999177	+	0.0405526i	$0.987088\pi$
$348$	−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	$-0.948746\pi$
$359$		−	2181.10i		−	0.320651i	0.987064	−	0.160326i	$-0.0512545\pi$
$360$	−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	$0.181564\pi$
$367$			7592.72i			1.07994i	−0.841685	+	0.539969i	$0.818436\pi$
$368$	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	$-0.361901\pi$
$379$	6203.24			0.840736			0.420368	+	0.907354i	$0.361901\pi$
$380$	2019.80	+	3604.10i	0.272667	+	0.486544i
$381$	2109.08			0.283600
$382$	−2329.57	+	509.070i	−0.312019	+	0.0681840i
$383$	−3182.99			−0.424656			−0.212328	−	0.977198i	$-0.568105\pi$
$383$	−3182.99			−0.424656			−0.212328	+	0.977198i	$0.568105\pi$
$384$	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
$418$	−1089.19	−	3575.94i	−0.127450	−	0.418432i
$419$		−	6285.87i		−	0.732900i	−0.930438	−	0.366450i	$-0.880573\pi$
$419$		−	6285.87i		−	0.732900i	0.930438	−	0.366450i	$-0.119427\pi$
$420$	−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	$-0.321933\pi$
$431$	9497.02			1.06138			0.530691	+	0.847566i	$0.321933\pi$
$432$	−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	$-0.0673243\pi$
$439$	17986.2			1.95543			0.977716	+	0.209932i	$0.0673243\pi$
$440$	−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	$0.270349\pi$
$443$			14001.7i			1.50167i	−0.660490	+	0.750835i	$0.729651\pi$
$444$	−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
$456$	12520.0	−	11113.3i	1.28575	−	1.14129i
$457$	−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	$-0.910239\pi$
$463$		−	5544.55i		−	0.556538i	0.960503	−	0.278269i	$-0.0897606\pi$
$464$	−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	$-0.641141\pi$
$467$		−	18232.0i		−	1.80659i	0.429021	−	0.903294i	$-0.358859\pi$
$468$	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	$-0.961694\pi$
$479$		−	2517.07i		−	0.240100i	0.992768	−	0.120050i	$-0.0383055\pi$
$480$	−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	$-0.390313\pi$
$487$	7261.05			0.675625			0.337813	+	0.941213i	$0.390313\pi$
$488$	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	$-0.750685\pi$
$491$		−	15353.3i		−	1.41117i	0.708627	−	0.705584i	$-0.249315\pi$
$492$	7949.56	+	17320.5i	0.728443	+	1.58713i
$493$			21722.6i			1.98445i
$494$	−2350.41	−	7716.64i	−0.214069	−	0.702810i
$495$		−	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	$0.126199\pi$
$499$			8608.89i			0.772319i	−0.922432	+	0.386159i	$0.873801\pi$
$500$	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	$0.108276\pi$
$503$			7527.61i			0.667276i	−0.942701	+	0.333638i	$0.891724\pi$
$504$	−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	$-0.470672\pi$
$523$	2200.87			0.184010			0.0920049	+	0.995759i	$0.470672\pi$
$524$	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
$532$	6417.57	−	3596.51i	0.523001	−	0.293099i
$533$	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	$-0.255851\pi$
$547$	17756.8			1.38798			0.693991	+	0.719983i	$0.255851\pi$
$548$	−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	$-0.691663\pi$
$563$	−15132.6			−1.13279			−0.566396	+	0.824133i	$0.691663\pi$
$564$	−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	$-0.472338\pi$
$570$	−12482.7	+	3802.09i	−0.917266	+	0.279390i
$571$			3088.89i			0.226386i	0.993573	+	0.113193i	$0.0361078\pi$
$571$			3088.89i			0.226386i	−0.993573	+	0.113193i	$0.963892\pi$
$572$	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	$-0.977761\pi$
$587$		−	1985.60i		−	0.139616i	0.997560	−	0.0698078i	$-0.0222386\pi$
$588$	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	$-0.544657\pi$
$599$	−4099.98			−0.279667			−0.139834	+	0.990175i	$0.544657\pi$
$600$	−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	$-0.605818\pi$
$607$	−9760.99			−0.652696			−0.326348	+	0.945250i	$0.605818\pi$
$608$	6038.54	−	13721.9i	0.402788	−	0.915293i
$609$	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	$0.0297950\pi$
$619$			2878.89i			0.186934i	−0.995622	+	0.0934671i	$0.970205\pi$
$620$	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	$-0.755527\pi$
$631$		−	22023.5i		−	1.38945i	0.719277	−	0.694724i	$-0.244473\pi$
$632$	−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	$0.326044\pi$
$643$			27860.1i			1.70870i	−0.519699	+	0.854350i	$0.673956\pi$
$644$	−7824.43	+	3591.16i	−0.478766	+	0.219738i
$645$		−	21413.2i		−	1.30720i
$646$	−21859.8	+	6658.29i	−1.33137	+	0.405521i
$647$		−	4053.33i		−	0.246295i	−0.992388	−	0.123148i	$-0.960701\pi$
$647$		−	4053.33i		−	0.246295i	0.992388	−	0.123148i	$-0.0392989\pi$
$648$	−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	$-0.541913\pi$
$659$	−4442.28			−0.262590			−0.131295	+	0.991343i	$0.541913\pi$
$660$	−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	$-0.312492\pi$
$683$	19834.3			1.11118			0.555592	+	0.831455i	$0.312492\pi$
$684$	17103.6	+	30519.4i	0.956100	+	1.70605i
$685$	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	$0.0135381\pi$
$691$			1544.63i			0.0850369i	−0.999096	+	0.0425184i	$0.986462\pi$
$692$	−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	$0.287494\pi$
$719$			30280.4i			1.57061i	−0.619108	+	0.785306i	$0.712506\pi$
$720$	13739.8	−	15978.0i	0.711182	−	0.827037i
$721$			17698.1i			0.914163i
$722$	−7127.07	−	18043.6i	−0.367371	−	0.930074i
$723$			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	$0.0604538\pi$
$727$			7401.01i			0.377563i	−0.982019	+	0.188781i	$0.939546\pi$
$728$	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	$-0.885542\pi$
$739$		−	14138.1i		−	0.703762i	0.936045	−	0.351881i	$-0.114458\pi$
$740$	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	$-0.399907\pi$
$743$	12528.1			0.618590			0.309295	+	0.950966i	$0.399907\pi$
$744$	−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	$-0.333005\pi$
$751$	20617.5			1.00179			0.500894	+	0.865509i	$0.333005\pi$
$752$	−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
$760$	−8739.31	+	7757.44i	−0.417116	+	0.370252i
$761$	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	$-0.559946\pi$
$787$	−8266.76			−0.374432			−0.187216	+	0.982319i	$0.559946\pi$
$788$	−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	$-0.0268091\pi$
$798$	6770.11	+	22227.0i	0.300325	+	0.985998i
$799$			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	$-0.520899\pi$
$811$	−3030.58			−0.131219			−0.0656093	+	0.997845i	$0.520899\pi$
$812$	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	$-0.919748\pi$
$823$		−	11779.5i		−	0.498915i	0.968386	−	0.249457i	$-0.0802523\pi$
$824$	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	$-0.665693\pi$
$827$	−23656.4			−0.994695			−0.497347	+	0.867552i	$0.665693\pi$
$828$	−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
$836$	9223.40	−	5168.95i	0.381577	−	0.213842i
$837$	20989.9			0.866805
$838$	17369.2	−	3795.62i	0.716003	−	0.156465i
$839$	−29352.8			−1.20783			−0.603916	−	0.797048i	$-0.706394\pi$
$839$	−29352.8			−1.20783			−0.603916	+	0.797048i	$0.706394\pi$
$840$	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	$-0.838760\pi$
$859$		−	24429.1i		−	0.970327i	0.874424	−	0.485163i	$-0.161240\pi$
$860$	−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	$-0.495930\pi$
$863$	648.335			0.0255731			0.0127865	+	0.999918i	$0.495930\pi$
$864$	−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
$874$	6615.14	+	21718.2i	0.256019	+	0.840536i
$875$			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	$-0.871753\pi$
$883$		−	20575.7i		−	0.784175i	0.919928	−	0.392087i	$-0.128247\pi$
$884$	−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	$-0.432365\pi$
$887$	11142.0			0.421773			0.210887	+	0.977511i	$0.432365\pi$
$888$	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	$-0.715965\pi$
$907$	−34286.9			−1.25521			−0.627607	+	0.778530i	$0.715965\pi$
$908$	−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	$-0.749798\pi$
$911$	−38861.2			−1.41332			−0.706658	+	0.707555i	$0.749798\pi$
$912$	38268.5	+	27884.8i	1.38947	+	1.01245i
$913$	−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	$-0.642281\pi$
$919$		−	50244.7i		−	1.80350i	0.432253	−	0.901752i	$-0.357719\pi$
$920$	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	$0.209782\pi$
$947$			35691.6i			1.22473i	−0.790574	+	0.612366i	$0.790218\pi$
$948$	34665.1	−	15910.2i	1.18763	−	0.545082i
$949$			25988.9i			0.888975i
$950$	−19297.2	+	5877.72i	−0.659035	+	0.200735i
$951$		−	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	$0.173875\pi$
$967$			31242.1i			1.03896i	−0.854482	+	0.519481i	$0.826125\pi$
$968$	−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	$-0.562152\pi$
$971$	−11741.0			−0.388039			−0.194019	+	0.980998i	$0.562152\pi$
$972$	−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	$-0.161524\pi$
$983$	53872.4			1.74798			0.873990	+	0.485945i	$0.161524\pi$
$984$	−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
$988$	19903.5	−	11154.3i	0.640906	−	0.359175i
$989$	−37256.0			−1.19785
$990$	14519.3	−	3172.83i	0.466114	−	0.101858i
$991$	26155.9			0.838415			0.419207	−	0.907890i	$-0.362308\pi$
$991$	26155.9			0.838415			0.419207	+	0.907890i	$0.362308\pi$
$992$	−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.75.16	yes	28
4.3	odd	2	inner	76.4.d.a.75.14	yes	28
19.18	odd	2	inner	76.4.d.a.75.13	✓	28
76.75	even	2	inner	76.4.d.a.75.15	yes	28

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

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} +(224.084 - 68.2536i) 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} +(323.909 + 577.978i) 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

Introduction

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