LMFDB - Embedded newform 105.4.g.b.104.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(104,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("105.104");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			104.9
Character	$\chi$	$=$	105.104
Dual form			105.4.g.b.104.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.23327 q^{2} +(-3.88311 - 3.45274i) q^{3} +2.45405 q^{4} +(8.12252 + 7.68276i) q^{5} +(12.5552 + 11.1637i) q^{6} +(-17.9067 + 4.72745i) q^{7} +17.9316 q^{8} +(3.15713 + 26.8148i) q^{9} +O(q^{10})$	\(q-3.23327 q^{2} +(-3.88311 - 3.45274i) q^{3} +2.45405 q^{4} +(8.12252 + 7.68276i) q^{5} +(12.5552 + 11.1637i) q^{6} +(-17.9067 + 4.72745i) q^{7} +17.9316 q^{8} +(3.15713 + 26.8148i) q^{9} +(-26.2623 - 24.8404i) q^{10} -0.605380i q^{11} +(-9.52936 - 8.47321i) q^{12} +12.8386 q^{13} +(57.8974 - 15.2851i) q^{14} +(-5.01406 - 57.8780i) q^{15} -77.6100 q^{16} -117.765i q^{17} +(-10.2079 - 86.6995i) q^{18} -98.5363i q^{19} +(19.9331 + 18.8539i) q^{20} +(85.8565 + 43.4702i) q^{21} +1.95736i q^{22} +136.085 q^{23} +(-69.6303 - 61.9131i) q^{24} +(6.95051 + 124.807i) q^{25} -41.5106 q^{26} +(80.3251 - 115.026i) q^{27} +(-43.9440 + 11.6014i) q^{28} -77.5484i q^{29} +(16.2118 + 187.135i) q^{30} -131.050i q^{31} +107.482 q^{32} +(-2.09022 + 2.35076i) q^{33} +380.766i q^{34} +(-181.768 - 99.1743i) q^{35} +(7.74776 + 65.8048i) q^{36} +260.419i q^{37} +318.595i q^{38} +(-49.8536 - 44.3283i) q^{39} +(145.649 + 137.764i) q^{40} -58.0698 q^{41} +(-277.598 - 140.551i) q^{42} -519.487i q^{43} -1.48563i q^{44} +(-180.368 + 242.059i) q^{45} -440.001 q^{46} +104.603i q^{47} +(301.369 + 267.968i) q^{48} +(298.302 - 169.306i) q^{49} +(-22.4729 - 403.534i) q^{50} +(-406.612 + 457.294i) q^{51} +31.5065 q^{52} +550.436 q^{53} +(-259.713 + 371.909i) q^{54} +(4.65099 - 4.91721i) q^{55} +(-321.096 + 84.7705i) q^{56} +(-340.221 + 382.628i) q^{57} +250.735i q^{58} +498.426 q^{59} +(-12.3048 - 142.035i) q^{60} +172.038i q^{61} +423.720i q^{62} +(-183.299 - 465.240i) q^{63} +273.362 q^{64} +(104.282 + 98.6356i) q^{65} +(6.75826 - 7.60065i) q^{66} -622.829i q^{67} -289.001i q^{68} +(-528.435 - 469.868i) q^{69} +(587.704 + 320.658i) q^{70} -151.768i q^{71} +(56.6123 + 480.831i) q^{72} +242.271 q^{73} -842.005i q^{74} +(403.936 - 508.636i) q^{75} -241.813i q^{76} +(2.86190 + 10.8404i) q^{77} +(161.190 + 143.325i) q^{78} +94.6776 q^{79} +(-630.389 - 596.259i) q^{80} +(-709.065 + 169.316i) q^{81} +187.756 q^{82} -779.959i q^{83} +(210.696 + 106.678i) q^{84} +(904.759 - 956.547i) q^{85} +1679.64i q^{86} +(-267.755 + 301.129i) q^{87} -10.8554i q^{88} +1000.67 q^{89} +(583.178 - 782.643i) q^{90} +(-229.897 + 60.6937i) q^{91} +333.961 q^{92} +(-452.482 + 508.882i) q^{93} -338.211i q^{94} +(757.030 - 800.363i) q^{95} +(-417.364 - 371.107i) q^{96} -1127.53 q^{97} +(-964.493 + 547.413i) q^{98} +(16.2331 - 1.91126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 184 q^{4} + 4 q^{9}+O(q^{10}) $ 40 * q + 184 * q^4 + 4 * q^9	$ 40 q + 184 q^{4} + 4 q^{9} - 188 q^{15} + 184 q^{16} + 148 q^{21} + 712 q^{25} - 336 q^{30} - 1520 q^{36} + 644 q^{39} - 1488 q^{46} - 1496 q^{49} - 220 q^{51} + 1984 q^{60} + 40 q^{64} - 3000 q^{70} - 1192 q^{79} + 4636 q^{81} - 2192 q^{84} + 4808 q^{85} - 4408 q^{91} + 5276 q^{99}+O(q^{100}) $ 40 * q + 184 * q^4 + 4 * q^9 - 188 * q^15 + 184 * q^16 + 148 * q^21 + 712 * q^25 - 336 * q^30 - 1520 * q^36 + 644 * q^39 - 1488 * q^46 - 1496 * q^49 - 220 * q^51 + 1984 * q^60 + 40 * q^64 - 3000 * q^70 - 1192 * q^79 + 4636 * q^81 - 2192 * q^84 + 4808 * q^85 - 4408 * q^91 + 5276 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−3.23327			−1.14313			−0.571567	−	0.820555i	$-0.693664\pi$
$2$	−3.23327			−1.14313			−0.571567	+	0.820555i	$0.693664\pi$
$3$	−3.88311	−	3.45274i	−0.747305	−	0.664481i
$3$	−3.88311	−	3.45274i	−0.747305	−	0.664481i
$4$	2.45405			0.306756
$5$	8.12252	+	7.68276i	0.726500	+	0.687167i
$5$	8.12252	+	7.68276i	0.726500	+	0.687167i
$6$	12.5552	+	11.1637i	0.854271	+	0.759591i
$7$	−17.9067	+	4.72745i	−0.966873	+	0.255258i
$7$	−17.9067	+	4.72745i	−0.966873	+	0.255258i
$8$	17.9316			0.792471
$9$	3.15713	+	26.8148i	0.116931	+	0.993140i
$10$	−26.2623	−	24.8404i	−0.830487	−	0.785524i
$11$		−	0.605380i		−	0.0165935i	−0.999966	−	0.00829677i	$-0.997359\pi$
$11$		−	0.605380i		−	0.0165935i	0.999966	−	0.00829677i	$-0.00264098\pi$
$12$	−9.52936	−	8.47321i	−0.229241	−	0.203834i
$13$	12.8386			0.273906			0.136953	−	0.990578i	$-0.456269\pi$
$13$	12.8386			0.273906			0.136953	+	0.990578i	$0.456269\pi$
$14$	57.8974	−	15.2851i	1.10527	−	0.291794i
$15$	−5.01406	−	57.8780i	−0.0863083	−	0.996268i
$16$	−77.6100			−1.21266
$17$		−	117.765i		−	1.68013i	−0.542487	−	0.840064i	$-0.682517\pi$
$17$		−	117.765i		−	1.68013i	0.542487	−	0.840064i	$-0.317483\pi$
$18$	−10.2079	−	86.6995i	−0.133668	−	1.13529i
$19$		−	98.5363i		−	1.18978i	−0.803808	−	0.594889i	$-0.797196\pi$
$19$		−	98.5363i		−	1.18978i	0.803808	−	0.594889i	$-0.202804\pi$
$20$	19.9331	+	18.8539i	0.222858	+	0.210793i
$21$	85.8565	+	43.4702i	0.892163	+	0.451713i
$22$			1.95736i			0.0189687i
$23$	136.085			1.23373			0.616865	−	0.787069i	$-0.288403\pi$
$23$	136.085			1.23373			0.616865	+	0.787069i	$0.288403\pi$
$24$	−69.6303	−	61.9131i	−0.592218	−	0.526581i
$25$	6.95051	+	124.807i	0.0556040	+	0.998453i
$26$	−41.5106			−0.313112
$27$	80.3251	−	115.026i	0.572539	−	0.819877i
$28$	−43.9440	+	11.6014i	−0.296594	+	0.0783021i
$29$		−	77.5484i		−	0.496565i	−0.968688	−	0.248283i	$-0.920134\pi$
$29$		−	77.5484i		−	0.496565i	0.968688	−	0.248283i	$-0.0798661\pi$
$30$	16.2118	+	187.135i	0.0986620	+	1.13887i
$31$		−	131.050i		−	0.759267i	−0.925137	−	0.379633i	$-0.876050\pi$
$31$		−	131.050i		−	0.759267i	0.925137	−	0.379633i	$-0.123950\pi$
$32$	107.482			0.593759
$33$	−2.09022	+	2.35076i	−0.0110261	+	0.0124004i
$34$			380.766i			1.92061i
$35$	−181.768	−	99.1743i	−0.877838	−	0.478958i
$36$	7.74776	+	65.8048i	0.0358693	+	0.304652i
$37$			260.419i			1.15710i	0.815648	+	0.578548i	$0.196381\pi$
$37$			260.419i			1.15710i	−0.815648	+	0.578548i	$0.803619\pi$
$38$			318.595i			1.36008i
$39$	−49.8536	−	44.3283i	−0.204692	−	0.182005i
$40$	145.649	+	137.764i	0.575730	+	0.544559i
$41$	−58.0698			−0.221195			−0.110597	−	0.993865i	$-0.535276\pi$
$41$	−58.0698			−0.221195			−0.110597	+	0.993865i	$0.535276\pi$
$42$	−277.598	−	140.551i	−1.01986	−	0.516368i
$43$		−	519.487i		−	1.84235i	−0.389150	−	0.921174i	$-0.627231\pi$
$43$		−	519.487i		−	1.84235i	0.389150	−	0.921174i	$-0.372769\pi$
$44$		−	1.48563i		−	0.00509018i
$45$	−180.368	+	242.059i	−0.597503	+	0.801867i
$46$	−440.001			−1.41032
$47$			104.603i			0.324638i	0.986738	+	0.162319i	$0.0518973\pi$
$47$			104.603i			0.324638i	−0.986738	+	0.162319i	$0.948103\pi$
$48$	301.369	+	267.968i	0.906225	+	0.805787i
$49$	298.302	−	169.306i	0.869687	−	0.493604i
$50$	−22.4729	−	403.534i	−0.0635629	−	1.14137i
$51$	−406.612	+	457.294i	−1.11641	+	1.25557i
$52$	31.5065			0.0840225
$53$	550.436			1.42657			0.713285	−	0.700874i	$-0.247206\pi$
$53$	550.436			1.42657			0.713285	+	0.700874i	$0.247206\pi$
$54$	−259.713	+	371.909i	−0.654490	+	0.937230i
$55$	4.65099	−	4.91721i	0.0114025	−	0.0120552i
$56$	−321.096	+	84.7705i	−0.766218	+	0.202285i
$57$	−340.221	+	382.628i	−0.790584	+	0.889127i
$58$			250.735i			0.567641i
$59$	498.426			1.09982			0.549911	−	0.835223i	$-0.314662\pi$
$59$	498.426			1.09982			0.549911	+	0.835223i	$0.314662\pi$
$60$	−12.3048	−	142.035i	−0.0264756	−	0.305612i
$61$			172.038i			0.361101i	0.983566	+	0.180551i	$0.0577880\pi$
$61$			172.038i			0.361101i	−0.983566	+	0.180551i	$0.942212\pi$
$62$			423.720i			0.867944i
$63$	−183.299	−	465.240i	−0.366564	−	0.930393i
$64$	273.362			0.533910
$65$	104.282	+	98.6356i	0.198993	+	0.188219i
$66$	6.75826	−	7.60065i	0.0126043	−	0.0141754i
$67$		−	622.829i		−	1.13568i	−0.823139	−	0.567840i	$-0.807779\pi$
$67$		−	622.829i		−	1.13568i	0.823139	−	0.567840i	$-0.192221\pi$
$68$		−	289.001i		−	0.515390i
$69$	−528.435	−	469.868i	−0.921973	−	0.819789i
$70$	587.704	+	320.658i	1.00349	+	0.547513i
$71$		−	151.768i		−	0.253684i	−0.991923	−	0.126842i	$-0.959516\pi$
$71$		−	151.768i		−	0.253684i	0.991923	−	0.126842i	$-0.0404842\pi$
$72$	56.6123	+	480.831i	0.0926642	+	0.787034i
$73$	242.271			0.388435			0.194217	−	0.980959i	$-0.437783\pi$
$73$	242.271			0.388435			0.194217	+	0.980959i	$0.437783\pi$
$74$		−	842.005i		−	1.32272i
$75$	403.936	−	508.636i	0.621899	−	0.783097i
$76$		−	241.813i		−	0.364972i
$77$	2.86190	+	10.8404i	0.00423564	+	0.0160439i
$78$	161.190	+	143.325i	0.233990	+	0.208057i
$79$	94.6776			0.134836			0.0674181	−	0.997725i	$-0.478524\pi$
$79$	94.6776			0.134836			0.0674181	+	0.997725i	$0.478524\pi$
$80$	−630.389	−	596.259i	−0.880995	−	0.833297i
$81$	−709.065	+	169.316i	−0.972654	+	0.232257i
$82$	187.756			0.252855
$83$		−	779.959i		−	1.03147i	−0.856750	−	0.515733i	$-0.827520\pi$
$83$		−	779.959i		−	1.03147i	0.856750	−	0.515733i	$-0.172480\pi$
$84$	210.696	+	106.678i	0.273677	+	0.138566i
$85$	904.759	−	956.547i	1.15453	−	1.22061i
$86$			1679.64i			2.10605i
$87$	−267.755	+	301.129i	−0.329958	+	0.371086i
$88$		−	10.8554i		−	0.0131499i
$89$	1000.67			1.19180			0.595902	−	0.803057i	$-0.296795\pi$
$89$	1000.67			1.19180			0.595902	+	0.803057i	$0.296795\pi$
$90$	583.178	−	782.643i	0.683026	−	0.916642i
$91$	−229.897	+	60.6937i	−0.264832	+	0.0699168i
$92$	333.961			0.378454
$93$	−452.482	+	508.882i	−0.504518	+	0.567404i
$94$		−	338.211i		−	0.371104i
$95$	757.030	−	800.363i	0.817576	−	0.864373i
$96$	−417.364	−	371.107i	−0.443720	−	0.394542i
$97$	−1127.53			−1.18024			−0.590120	−	0.807316i	$-0.700920\pi$
$97$	−1127.53			−1.18024			−0.590120	+	0.807316i	$0.700920\pi$
$98$	−964.493	+	547.413i	−0.994169	+	0.564256i
$99$	16.2331	−	1.91126i	0.0164797	−	0.00194030i
$100$	17.0569	+	306.282i	0.0170569	+	0.306282i
$101$	485.611			0.478416			0.239208	−	0.970968i	$-0.423112\pi$
$101$	485.611			0.478416			0.239208	+	0.970968i	$0.423112\pi$
$102$	1314.69	−	1478.56i	1.27621	−	1.43528i
$103$	−1560.10			−1.49244			−0.746218	−	0.665702i	$-0.768132\pi$
$103$	−1560.10			−1.49244			−0.746218	+	0.665702i	$0.768132\pi$
$104$	230.216			0.217063
$105$	363.400	+	1012.70i	0.337755	+	0.941234i
$106$	−1779.71			−1.63076
$107$	−756.538			−0.683526			−0.341763	−	0.939786i	$-0.611024\pi$
$107$	−756.538			−0.683526			−0.341763	+	0.939786i	$0.611024\pi$
$108$	197.122	−	282.279i	0.175630	−	0.251503i
$109$	−795.599			−0.699124			−0.349562	−	0.936913i	$-0.613670\pi$
$109$	−795.599			−0.699124			−0.349562	+	0.936913i	$0.613670\pi$
$110$	−15.0379	+	15.8987i	−0.0130346	+	0.0137807i
$111$	899.159	−	1011.24i	0.768868	−	0.864704i
$112$	1389.74	−	366.897i	1.17249	−	0.309541i
$113$	−391.491			−0.325915			−0.162957	−	0.986633i	$-0.552103\pi$
$113$	−391.491			−0.325915			−0.162957	+	0.986633i	$0.552103\pi$
$114$	1100.03	−	1237.14i	0.903744	−	1.01639i
$115$	1105.36	+	1045.51i	0.896304	+	0.847778i
$116$		−	190.308i		−	0.152324i
$117$	40.5331	+	344.264i	0.0320281	+	0.272027i
$118$	−1611.55			−1.25724
$119$	556.727	+	2108.78i	0.428866	+	1.62447i
$120$	−89.9099	−	1037.84i	−0.0683968	−	0.789514i
$121$	1330.63			0.999725
$122$		−	556.245i		−	0.412788i
$123$	225.492	+	200.500i	0.165300	+	0.146980i
$124$		−	321.603i		−	0.232910i
$125$	−902.403	+	1067.14i	−0.645707	+	0.763585i
$126$	592.657	+	1504.25i	0.419032	+	1.06356i
$127$			1360.11i			0.950314i	0.879901	+	0.475157i	$0.157609\pi$
$127$			1360.11i			0.950314i	−0.879901	+	0.475157i	$0.842391\pi$
$128$	−1743.71			−1.20409
$129$	−1793.65	+	2017.23i	−1.22421	+	1.37680i
$130$	−337.171	−	318.916i	−0.227475	−	0.215160i
$131$	−1235.28			−0.823871			−0.411935	−	0.911213i	$-0.635147\pi$
$131$	−1235.28			−0.823871			−0.411935	+	0.911213i	$0.635147\pi$
$132$	−5.12951	+	5.76888i	−0.00338232	+	0.00380392i
$133$	465.825	+	1764.46i	0.303700	+	1.15036i
$134$			2013.77i			1.29824i
$135$	1536.16	−	317.179i	0.979342	−	0.202211i
$136$		−	2111.71i		−	1.33145i
$137$	141.306			0.0881213			0.0440606	−	0.999029i	$-0.485971\pi$
$137$	141.306			0.0881213			0.0440606	+	0.999029i	$0.485971\pi$
$138$	1708.57	+	1519.21i	1.05394	+	0.937130i
$139$			894.717i			0.545963i	0.962019	+	0.272982i	$0.0880098\pi$
$139$			894.717i			0.545963i	−0.962019	+	0.272982i	$0.911990\pi$
$140$	−446.067	−	243.379i	−0.269282	−	0.146923i
$141$	361.168	−	406.187i	0.215715	−	0.242603i
$142$			490.709i			0.289995i
$143$		−	7.77222i		−	0.00454507i
$144$	−245.025	−	2081.10i	−0.141797	−	1.20434i
$145$	595.786	−	629.888i	0.341223	−	0.360754i
$146$	−783.330			−0.444033
$147$	−1742.91	−	372.526i	−0.977912	−	0.209017i
$148$			639.081i			0.354947i
$149$		−	2252.95i		−	1.23872i	−0.785108	−	0.619359i	$-0.787392\pi$
$149$		−	2252.95i		−	1.23872i	0.785108	−	0.619359i	$-0.212608\pi$
$150$	−1306.03	+	1644.56i	−0.710915	+	0.895185i
$151$	−835.424			−0.450237			−0.225119	−	0.974331i	$-0.572277\pi$
$151$	−835.424			−0.450237			−0.225119	+	0.974331i	$0.572277\pi$
$152$		−	1766.91i		−	0.942864i
$153$	3157.84	−	371.799i	1.66860	−	0.196459i
$154$	−9.25331	−	35.0499i	−0.00484190	−	0.0183403i
$155$	1006.82	−	1064.46i	0.521743	−	0.551607i
$156$	−122.343	−	108.784i	−0.0627904	−	0.0558313i
$157$	2999.64			1.52483			0.762413	−	0.647091i	$-0.224014\pi$
$157$	2999.64			1.52483			0.762413	+	0.647091i	$0.224014\pi$
$158$	−306.118			−0.154136
$159$	−2137.41	−	1900.52i	−1.06608	−	0.947929i
$160$	873.023	+	825.757i	0.431366	+	0.408012i
$161$	−2436.85	+	643.337i	−1.19286	+	0.314919i
$162$	2292.60	−	547.443i	1.11187	−	0.265501i
$163$		−	802.994i		−	0.385861i	−0.981212	−	0.192930i	$-0.938201\pi$
$163$		−	802.994i		−	0.385861i	0.981212	−	0.192930i	$-0.0617992\pi$
$164$	−142.506			−0.0678529
$165$	−35.0382	+	3.03541i	−0.0165316	+	0.00143216i
$166$			2521.82i			1.17910i
$167$			1489.38i			0.690129i	0.938579	+	0.345065i	$0.112143\pi$
$167$			1489.38i			0.690129i	−0.938579	+	0.345065i	$0.887857\pi$
$168$	1539.54	+	779.488i	0.707013	+	0.357969i
$169$	−2032.17			−0.924975
$170$	−2925.33	+	3092.78i	−1.31978	+	1.39532i
$171$	2642.23	−	311.092i	1.18162	−	0.139122i
$172$		−	1274.85i		−	0.565152i
$173$		−	263.075i		−	0.115614i	−0.998328	−	0.0578069i	$-0.981589\pi$
$173$		−	263.075i		−	0.115614i	0.998328	−	0.0578069i	$-0.0184108\pi$
$174$	865.724	−	973.633i	0.377186	−	0.424201i
$175$	−714.477	−	2202.02i	−0.308625	−	0.951184i
$176$			46.9836i			0.0201223i
$177$	−1935.44	−	1720.94i	−0.821903	−	0.730811i
$178$	−3235.43			−1.36239
$179$			347.625i			0.145155i	0.997363	+	0.0725774i	$0.0231224\pi$
$179$			347.625i			0.145155i	−0.997363	+	0.0725774i	$0.976878\pi$
$180$	−442.631	+	594.025i	−0.183288	+	0.245978i
$181$			2556.58i			1.04988i	0.851138	+	0.524942i	$0.175913\pi$
$181$			2556.58i			1.04988i	−0.851138	+	0.524942i	$0.824087\pi$
$182$	743.320	−	196.239i	0.302739	−	0.0799243i
$183$	594.002	−	668.042i	0.239945	−	0.269853i
$184$	2440.22			0.977694
$185$	−2000.73	+	2115.25i	−0.795118	+	0.840630i
$186$	1463.00	−	1645.35i	0.576732	−	0.648619i
$187$	−71.2925			−0.0278793
$188$			256.702i			0.0995846i
$189$	−894.582	+	2439.47i	−0.344293	+	0.938862i
$190$	−2447.69	+	2587.79i	−0.934599	+	0.988095i
$191$		−	2990.51i		−	1.13291i	−0.824093	−	0.566455i	$-0.808315\pi$
$191$		−	2990.51i		−	1.13291i	0.824093	−	0.566455i	$-0.191685\pi$
$192$	−1061.50	−	943.849i	−0.398994	−	0.354773i
$193$		−	3949.63i		−	1.47306i	−0.676406	−	0.736529i	$-0.736463\pi$
$193$		−	3949.63i		−	1.47306i	0.676406	−	0.736529i	$-0.263537\pi$
$194$	3645.61			1.34917
$195$	−64.3734	−	743.071i	−0.0236404	−	0.272884i
$196$	732.050	−	415.486i	0.266782	−	0.151416i
$197$	−1583.28			−0.572610			−0.286305	−	0.958139i	$-0.592427\pi$
$197$	−1583.28			−0.572610			−0.286305	+	0.958139i	$0.592427\pi$
$198$	−52.4862	+	6.17964i	−0.0188385	+	0.00221802i
$199$		−	101.664i		−	0.0362151i	−0.999836	−	0.0181075i	$-0.994236\pi$
$199$		−	101.664i		−	0.0362151i	0.999836	−	0.0181075i	$-0.00576413\pi$
$200$	124.633	+	2237.98i	0.0440646	+	0.791245i
$201$	−2150.47	+	2418.51i	−0.754638	+	0.848700i
$202$	−1570.11			−0.546894
$203$	366.606	+	1388.64i	0.126752	+	0.480115i
$204$	−997.846	+	1122.22i	−0.342467	+	0.385154i
$205$	−471.673	−	446.136i	−0.160698	−	0.151998i
$206$	5044.22			1.70605
$207$	429.640	+	3649.10i	0.144261	+	1.22527i
$208$	−996.402			−0.332154
$209$	−59.6519			−0.0197426
$210$	−1174.97	−	3274.34i	−0.386099	−	1.07596i
$211$	5047.18			1.64674			0.823370	−	0.567506i	$-0.192091\pi$
$211$	5047.18			1.64674			0.823370	+	0.567506i	$0.192091\pi$
$212$	1350.80			0.437610
$213$	−524.017	+	589.334i	−0.168568	+	0.189580i
$214$	2446.09			0.781362
$215$	3991.09	−	4219.54i	1.26600	−	1.33847i
$216$	1440.35	−	2062.59i	0.453721	−	0.649729i
$217$	619.532	+	2346.68i	0.193809	+	0.734114i
$218$	2572.39			0.799193
$219$	−940.768	−	836.501i	−0.290279	−	0.258107i
$220$	11.4138	−	12.0671i	0.00349780	−	0.00369801i
$221$		−	1511.93i		−	0.460197i
$222$	−2907.23	+	3269.60i	−0.878920	+	0.988473i
$223$	−1866.03			−0.560353			−0.280177	−	0.959948i	$-0.590393\pi$
$223$	−1866.03			−0.560353			−0.280177	+	0.959948i	$0.590393\pi$
$224$	−1924.65	+	508.115i	−0.574090	+	0.151562i
$225$	−3324.72	+	580.407i	−0.985102	+	0.171972i
$226$	1265.80			0.372565
$227$		−	2270.46i		−	0.663857i	−0.943305	−	0.331929i	$-0.892301\pi$
$227$		−	2270.46i		−	0.663857i	0.943305	−	0.331929i	$-0.107699\pi$
$228$	−834.919	+	938.988i	−0.242517	+	0.272745i
$229$			998.351i			0.288091i	0.989571	+	0.144046i	$0.0460112\pi$
$229$			998.351i			0.288091i	−0.989571	+	0.144046i	$0.953989\pi$
$230$	−3573.92	−	3380.42i	−1.02460	−	0.969124i
$231$	26.3160	−	51.9759i	0.00749551	−	0.0148042i
$232$		−	1390.56i		−	0.393513i
$233$	4098.89			1.15248			0.576238	−	0.817282i	$-0.304520\pi$
$233$	4098.89			1.15248			0.576238	+	0.817282i	$0.304520\pi$
$234$	−131.054	−	1113.10i	−0.0366124	−	0.310964i
$235$	−803.642	+	849.642i	−0.223080	+	0.235849i
$236$	1223.16			0.337377
$237$	−367.644	−	326.897i	−0.100764	−	0.0895961i
$238$	−1800.05	−	6818.28i	−0.490252	−	1.85699i
$239$			4118.06i			1.11454i	0.830332	+	0.557270i	$0.188151\pi$
$239$			4118.06i			1.11454i	−0.830332	+	0.557270i	$0.811849\pi$
$240$	389.141	+	4491.91i	0.104662	+	1.20813i
$241$		−	6644.14i		−	1.77588i	−0.459961	−	0.887939i	$-0.652137\pi$
$241$		−	6644.14i		−	1.77588i	0.459961	−	0.887939i	$-0.347863\pi$
$242$	−4302.30			−1.14282
$243$	3337.98	+	1790.75i	0.881200	+	0.472743i
$244$			422.190i			0.110770i
$245$	3723.71	+	916.593i	0.971016	+	0.239016i
$246$	−729.076	−	648.272i	−0.188960	−	0.168017i
$247$		−	1265.07i		−	0.325887i
$248$		−	2349.93i		−	0.601697i
$249$	−2693.00	+	3028.67i	−0.685389	+	0.770820i
$250$	2917.72	−	3450.36i	0.738130	−	0.872880i
$251$	160.793			0.0404349			0.0202174	−	0.999796i	$-0.493564\pi$
$251$	160.793			0.0404349			0.0202174	+	0.999796i	$0.493564\pi$
$252$	−449.826	−	1141.72i	−0.112446	−	0.285404i
$253$		−	82.3834i		−	0.0204719i
$254$		−	4397.59i		−	1.08634i
$255$	−6815.99	+	590.480i	−1.67386	+	0.145009i
$256$	3450.99			0.842527
$257$			587.416i			0.142576i	0.997456	+	0.0712879i	$0.0227109\pi$
$257$			587.416i			0.142576i	−0.997456	+	0.0712879i	$0.977289\pi$
$258$	5799.37	−	6522.24i	1.39943	−	1.57386i
$259$	−1231.12	−	4663.25i	−0.295358	−	1.11877i
$260$	255.912	+	242.057i	0.0610423	+	0.0577374i
$261$	2079.44	−	244.831i	0.493159	−	0.0580637i
$262$	3994.00			0.941795
$263$	4760.99			1.11626			0.558128	−	0.829755i	$-0.311520\pi$
$263$	4760.99			1.11626			0.558128	+	0.829755i	$0.311520\pi$
$264$	−37.4810	+	42.1528i	−0.00873785	+	0.00982699i
$265$	4470.93	+	4228.87i	1.03640	+	0.980292i
$266$	−1506.14	−	5704.99i	−0.347170	−	1.31502i
$267$	−3885.70	−	3455.05i	−0.890641	−	0.791930i
$268$		−	1528.45i		−	0.348377i
$269$	−5639.75			−1.27830			−0.639148	−	0.769084i	$-0.720713\pi$
$269$	−5639.75			−1.27830			−0.639148	+	0.769084i	$0.720713\pi$
$270$	−4966.81	+	1025.53i	−1.11952	+	0.231154i
$271$			2250.90i			0.504547i	0.967656	+	0.252274i	$0.0811783\pi$
$271$			2250.90i			0.504547i	−0.967656	+	0.252274i	$0.918822\pi$
$272$			9139.74i			2.03742i
$273$	1102.28	+	558.095i	0.244369	+	0.123727i
$274$	−456.882			−0.100734
$275$	75.5555	−	4.20770i	0.0165679	−	0.000922668i
$276$	−1296.81	−	1153.08i	−0.282821	−	0.251476i
$277$			6323.83i			1.37170i	0.727741	+	0.685852i	$0.240570\pi$
$277$			6323.83i			1.37170i	−0.727741	+	0.685852i	$0.759430\pi$
$278$		−	2892.86i		−	0.624109i
$279$	3514.08	−	413.742i	0.754058	−	0.0887816i
$280$	−3259.38	−	1778.35i	−0.695661	−	0.379560i
$281$		−	7909.21i		−	1.67909i	−0.543291	−	0.839544i	$-0.682822\pi$
$281$		−	7909.21i		−	1.67909i	0.543291	−	0.839544i	$-0.317178\pi$
$282$	−1167.76	+	1313.31i	−0.246592	+	0.277328i
$283$	−1364.88			−0.286692			−0.143346	−	0.989673i	$-0.545786\pi$
$283$	−1364.88			−0.286692			−0.143346	+	0.989673i	$0.545786\pi$
$284$		−	372.447i		−	0.0778193i
$285$	−5703.08	+	494.067i	−1.18534	+	0.102688i
$286$			25.1297i			0.00519563i
$287$	1039.84	−	274.522i	0.213867	−	0.0564617i
$288$	339.334	+	2882.10i	0.0694287	+	0.589686i
$289$	−8955.57			−1.82283
$290$	−1926.34	+	2036.60i	−0.390064	+	0.412391i
$291$	4378.32	+	3893.07i	0.882000	+	0.784246i
$292$	594.547			0.119155
$293$			6158.77i			1.22798i	0.789312	+	0.613992i	$0.210437\pi$
$293$			6158.77i			1.22798i	−0.789312	+	0.613992i	$0.789563\pi$
$294$	5635.31	+	1204.48i	1.11788	+	0.238934i
$295$	4048.47	+	3829.28i	0.799021	+	0.755761i
$296$			4669.71i			0.916965i
$297$	−69.6342	−	48.6272i	−0.0136047	−	0.00950046i
$298$			7284.41i			1.41602i
$299$	1747.14			0.337926
$300$	991.279	−	1248.22i	0.190772	−	0.240220i
$301$	2455.85	+	9302.31i	0.470274	+	1.78132i
$302$	2701.15			0.514682
$303$	−1885.68	−	1676.69i	−0.357523	−	0.317898i
$304$			7647.41i			1.44279i
$305$	−1321.72	+	1397.38i	−0.248137	+	0.262340i
$306$	−10210.2	+	1202.13i	−1.90744	+	0.224579i
$307$	−7256.37			−1.34900			−0.674500	−	0.738275i	$-0.735641\pi$
$307$	−7256.37			−1.34900			−0.674500	+	0.738275i	$0.735641\pi$
$308$	7.02326	+	26.6029i	0.00129931	+	0.00492155i
$309$	6058.03	+	5386.61i	1.11530	+	0.991694i
$310$	−3255.34	+	3441.67i	−0.596422	+	0.630561i
$311$	8404.97			1.53248			0.766241	−	0.642553i	$-0.222125\pi$
$311$	8404.97			1.53248			0.766241	+	0.642553i	$0.222125\pi$
$312$	−893.954	−	794.876i	−0.162212	−	0.144234i
$313$	−3012.62			−0.544035			−0.272018	−	0.962292i	$-0.587691\pi$
$313$	−3012.62			−0.544035			−0.272018	+	0.962292i	$0.587691\pi$
$314$	−9698.67			−1.74308
$315$	2085.47	−	5187.16i	0.373026	−	0.927821i
$316$	232.344			0.0413619
$317$	8375.12			1.48389			0.741946	−	0.670459i	$-0.233903\pi$
$317$	8375.12			1.48389			0.741946	+	0.670459i	$0.233903\pi$
$318$	6910.82	+	6144.88i	1.21868	+	1.08361i
$319$	−46.9463			−0.00823977
$320$	2220.39	+	2100.17i	0.387886	+	0.366885i
$321$	2937.72	+	2612.13i	0.510803	+	0.454190i
$322$	7878.99	−	2080.08i	1.36360	−	0.359995i
$323$	−11604.1			−1.99898
$324$	−1740.08	+	415.509i	−0.298368	+	0.0712464i
$325$	89.2346	+	1602.34i	0.0152303	+	0.273482i
$326$			2596.30i			0.441091i
$327$	3089.40	+	2747.00i	0.522459	+	0.464555i
$328$	−1041.28			−0.175290
$329$	−494.507	−	1873.10i	−0.0828664	−	0.313883i
$330$	113.288	−	9.81432i	0.0188979	−	0.00163715i
$331$	−7389.43			−1.22707			−0.613535	−	0.789668i	$-0.710253\pi$
$331$	−7389.43			−1.22707			−0.613535	+	0.789668i	$0.710253\pi$
$332$		−	1914.06i		−	0.316409i
$333$	−6983.07	+	822.176i	−1.14916	+	0.135300i
$334$		−	4815.57i		−	0.788911i
$335$	4785.04	−	5058.93i	0.780402	−	0.825072i
$336$	−6663.33	−	3373.72i	−1.08189	−	0.547772i
$337$		−	7612.87i		−	1.23056i	−0.788308	−	0.615281i	$-0.789043\pi$
$337$		−	7612.87i		−	1.23056i	0.788308	−	0.615281i	$-0.210957\pi$
$338$	6570.56			1.05737
$339$	1520.20	+	1351.72i	0.243558	+	0.216564i
$340$	2220.32	−	2347.42i	0.354159	−	0.374431i
$341$	−79.3350			−0.0125989
$342$	−8543.05	+	1005.85i	−1.35075	+	0.159035i
$343$	−4541.24	+	4441.93i	−0.714880	+	0.699247i
$344$		−	9315.21i		−	1.46001i
$345$	−682.340	−	7876.35i	−0.106481	−	1.22913i
$346$			850.592i			0.132162i
$347$	−2248.77			−0.347898			−0.173949	−	0.984755i	$-0.555653\pi$
$347$	−2248.77			−0.347898			−0.173949	+	0.984755i	$0.555653\pi$
$348$	−657.084	+	738.987i	−0.101217	+	0.113833i
$349$		−	4137.50i		−	0.634600i	−0.948325	−	0.317300i	$-0.897224\pi$
$349$		−	4137.50i		−	0.634600i	0.948325	−	0.317300i	$-0.102776\pi$
$350$	2310.10	+	7119.73i	0.352800	+	1.08733i
$351$	1031.26	−	1476.76i	0.156822	−	0.224569i
$352$		−	65.0674i		−	0.00985257i
$353$			4970.30i			0.749412i	0.927144	+	0.374706i	$0.122256\pi$
$353$			4970.30i			0.749412i	−0.927144	+	0.374706i	$0.877744\pi$
$354$	6257.82	+	5564.26i	0.939546	+	0.835415i
$355$	1166.00	−	1232.74i	0.174323	−	0.184302i
$356$	2455.69			0.365593
$357$	5119.26	−	10110.9i	0.758935	−	1.49895i
$358$		−	1123.97i		−	0.165932i
$359$			2942.19i			0.432543i	0.976333	+	0.216271i	$0.0693896\pi$
$359$			2942.19i			0.432543i	−0.976333	+	0.216271i	$0.930610\pi$
$360$	−3234.27	+	4340.50i	−0.473503	+	0.635456i
$361$	−2850.40			−0.415571
$362$		−	8266.11i		−	1.20016i
$363$	−5167.00	−	4594.34i	−0.747100	−	0.664298i
$364$	−564.179	+	148.945i	−0.0812390	+	0.0214474i
$365$	1967.85	+	1861.31i	0.282198	+	0.266919i
$366$	−1920.57	+	2159.96i	−0.274289	+	0.308478i
$367$	2416.72			0.343738			0.171869	−	0.985120i	$-0.445019\pi$
$367$	2416.72			0.343738			0.171869	+	0.985120i	$0.445019\pi$
$368$	−10561.6			−1.49609
$369$	−183.334	−	1557.13i	−0.0258645	−	0.219677i
$370$	6468.92	−	6839.19i	0.908927	−	0.960954i
$371$	−9856.52	+	2602.16i	−1.37931	+	0.364144i
$372$	−1110.41	+	1248.82i	−0.154764	+	0.174055i
$373$			4691.02i			0.651185i	0.945510	+	0.325592i	$0.105564\pi$
$373$			4691.02i			0.651185i	−0.945510	+	0.325592i	$0.894436\pi$
$374$	230.508			0.0318698
$375$	7188.70	−	1028.07i	0.989928	−	0.141571i
$376$			1875.70i			0.257266i
$377$		−	995.612i		−	0.136012i
$378$	2892.43	−	7887.46i	0.393573	−	1.07325i
$379$	736.245			0.0997846			0.0498923	−	0.998755i	$-0.484112\pi$
$379$	736.245			0.0997846			0.0498923	+	0.998755i	$0.484112\pi$
$380$	1857.79	−	1964.13i	0.250797	−	0.265152i
$381$	4696.10	−	5281.45i	0.631465	−	0.710175i
$382$			9669.14i			1.29507i
$383$		−	11813.2i		−	1.57605i	−0.615641	−	0.788027i	$-0.711103\pi$
$383$		−	11813.2i		−	1.57605i	0.615641	−	0.788027i	$-0.288897\pi$
$384$	6771.02	+	6020.58i	0.899823	+	0.800095i
$385$	−60.0382	+	110.038i	−0.00794761	+	0.0145664i
$386$			12770.2i			1.68390i
$387$	13929.9	−	1640.09i	1.82971	−	0.215427i
$388$	−2767.01			−0.362046
$389$			3748.94i			0.488635i	0.969695	+	0.244318i	$0.0785639\pi$
$389$			3748.94i			0.488635i	−0.969695	+	0.244318i	$0.921436\pi$
$390$	208.137	+	2402.55i	0.0270241	+	0.311943i
$391$		−	16026.1i		−	2.07282i
$392$	5349.03	−	3035.93i	0.689201	−	0.391167i
$393$	4796.74	+	4265.11i	0.615683	+	0.547446i
$394$	5119.18			0.654570
$395$	769.020	+	727.385i	0.0979585	+	0.0926549i
$396$	39.8370	−	4.69034i	0.00505526	−	0.000595198i
$397$	−5770.01			−0.729443			−0.364721	−	0.931117i	$-0.618836\pi$
$397$	−5770.01			−0.729443			−0.364721	+	0.931117i	$0.618836\pi$
$398$			328.709i			0.0413987i
$399$	4283.39	−	8459.99i	0.537438	−	1.06148i
$400$	−539.429	−	9686.25i	−0.0674286	−	1.21078i
$401$		−	6380.54i		−	0.794586i	−0.917692	−	0.397293i	$-0.869950\pi$
$401$		−	6380.54i		−	0.794586i	0.917692	−	0.397293i	$-0.130050\pi$
$402$	6953.05	−	7819.71i	0.862653	−	0.970179i
$403$		−	1682.49i		−	0.207968i
$404$	1191.71			0.146757
$405$	−7060.20	−	4072.31i	−0.866233	−	0.499641i
$406$	−1185.34	−	4489.85i	−0.144895	−	0.548836i
$407$	157.652			0.0192003
$408$	−7291.19	+	8200.00i	−0.884724	+	0.995002i
$409$		−	5529.03i		−	0.668443i	−0.942495	−	0.334221i	$-0.891527\pi$
$409$		−	5529.03i		−	0.668443i	0.942495	−	0.334221i	$-0.108473\pi$
$410$	1525.05	+	1442.48i	0.183699	+	0.173754i
$411$	−548.708	−	487.894i	−0.0658535	−	0.0585549i
$412$	−3828.56			−0.457814
$413$	−8925.18	+	2356.28i	−1.06339	+	0.280739i
$414$	−1389.14	−	11798.5i	−0.164910	−	1.40064i
$415$	5992.24	−	6335.23i	0.708789	−	0.749359i
$416$	1379.91			0.162634
$417$	3089.23	−	3474.29i	0.362782	−	0.408001i
$418$	192.871			0.0225685
$419$	−4493.27			−0.523892			−0.261946	−	0.965083i	$-0.584364\pi$
$419$	−4493.27			−0.523892			−0.261946	+	0.965083i	$0.584364\pi$
$420$	891.803	+	2485.22i	0.103608	+	0.288730i
$421$	−99.8897			−0.0115637			−0.00578186	−	0.999983i	$-0.501840\pi$
$421$	−99.8897			−0.0115637			−0.00578186	+	0.999983i	$0.501840\pi$
$422$	−16318.9			−1.88244
$423$	−2804.92	+	330.246i	−0.322411	+	0.0379601i
$424$	9870.18			1.13052
$425$	14697.8	−	818.525i	1.67753	−	0.0934219i
$426$	1694.29	−	1905.48i	0.192696	−	0.216715i
$427$	−813.300	−	3080.64i	−0.0921741	−	0.349139i
$428$	−1856.58			−0.209676
$429$	−26.8355	+	30.1804i	−0.00302011	+	0.00339656i
$430$	−12904.3	+	13642.9i	−1.44721	+	1.53005i
$431$			13563.7i			1.51588i	0.652327	+	0.757938i	$0.273793\pi$
$431$			13563.7i			1.51588i	−0.652327	+	0.757938i	$0.726207\pi$
$432$	−6234.03	+	8927.14i	−0.694294	+	0.994230i
$433$	10400.5			1.15431			0.577155	−	0.816634i	$-0.304163\pi$
$433$	10400.5			1.15431			0.577155	+	0.816634i	$0.304163\pi$
$434$	−2003.11	−	7587.45i	−0.221550	−	0.839191i
$435$	−4488.35	+	388.833i	−0.494712	+	0.0428577i
$436$	−1952.44			−0.214461
$437$		−	13409.4i		−	1.46786i
$438$	3041.76	+	2704.64i	0.331828	+	0.295051i
$439$			6478.07i			0.704286i	0.935946	+	0.352143i	$0.114547\pi$
$439$			6478.07i			0.704286i	−0.935946	+	0.352143i	$0.885453\pi$
$440$	83.3995	−	88.1733i	0.00903617	−	0.00955340i
$441$	5481.69	+	7464.39i	0.591911	+	0.806003i
$442$			4888.49i			0.526068i
$443$	8331.80			0.893579			0.446790	−	0.894639i	$-0.352567\pi$
$443$	8331.80			0.893579			0.446790	+	0.894639i	$0.352567\pi$
$444$	2206.58	−	2481.62i	0.235855	−	0.265254i
$445$	8127.93	+	7687.88i	0.865845	+	0.818968i
$446$	6033.39			0.640559
$447$	−7778.87	+	8748.47i	−0.823105	+	0.925701i
$448$	−4895.02	+	1292.30i	−0.516223	+	0.136285i
$449$			5571.92i			0.585646i	0.956167	+	0.292823i	$0.0945947\pi$
$449$			5571.92i			0.585646i	−0.956167	+	0.292823i	$0.905405\pi$
$450$	10749.7	−	1876.61i	1.12610	−	0.196588i
$451$			35.1543i			0.00367040i
$452$	−960.739			−0.0999765
$453$	3244.05	+	2884.50i	0.336465	+	0.299174i
$454$			7341.01i			0.758878i
$455$	−2333.64	−	1273.26i	−0.240445	−	0.131189i
$456$	−6100.69	+	6861.11i	−0.626515	+	0.704607i
$457$		−	9668.94i		−	0.989702i	−0.868978	−	0.494851i	$-0.835223\pi$
$457$		−	9668.94i		−	0.989702i	0.868978	−	0.494851i	$-0.164777\pi$
$458$		−	3227.94i		−	0.329327i
$459$	−13546.0	−	9459.47i	−1.37750	−	0.961940i
$460$	2712.60	+	2565.74i	0.274947	+	0.260061i
$461$	−9540.16			−0.963838			−0.481919	−	0.876216i	$-0.660060\pi$
$461$	−9540.16			−0.963838			−0.481919	+	0.876216i	$0.660060\pi$
$462$	−85.0867	+	168.052i	−0.00856838	+	0.0169231i
$463$		−	291.188i		−	0.0292282i	−0.999893	−	0.0146141i	$-0.995348\pi$
$463$		−	291.188i		−	0.0292282i	0.999893	−	0.0146141i	$-0.00465198\pi$
$464$			6018.54i			0.602163i
$465$	−7584.90	+	657.092i	−0.756433	+	0.0655310i
$466$	−13252.8			−1.31744
$467$			12431.2i			1.23180i	0.787825	+	0.615899i	$0.211207\pi$
$467$			12431.2i			1.23180i	−0.787825	+	0.615899i	$0.788793\pi$
$468$	99.4702	+	844.840i	0.00982481	+	0.0834461i
$469$	2944.39	+	11152.8i	0.289892	+	1.09806i
$470$	2598.39	−	2747.12i	0.255011	−	0.269607i
$471$	−11648.0	−	10357.0i	−1.13951	−	1.01322i
$472$	8937.55			0.871577
$473$	−314.487			−0.0305711
$474$	1188.69	+	1056.95i	0.115187	+	0.102420i
$475$	12298.0	−	684.877i	1.18794	−	0.0661565i
$476$	1366.24	+	5175.07i	0.131558	+	0.498317i
$477$	1737.80	+	14759.8i	0.166810	+	1.41678i
$478$		−	13314.8i		−	1.27407i
$479$	2250.43			0.214665			0.107333	−	0.994223i	$-0.465769\pi$
$479$	2250.43			0.214665			0.107333	+	0.994223i	$0.465769\pi$
$480$	−538.921	−	6220.83i	−0.0512464	−	0.591544i
$481$			3343.40i			0.316936i
$482$			21482.3i			2.03007i
$483$	11683.8	+	5915.66i	1.10069	+	0.557291i
$484$	3265.44			0.306672
$485$	−9158.37	−	8662.53i	−0.857444	−	0.811021i
$486$	−10792.6	−	5789.98i	−1.00733	−	0.540409i
$487$		−	18863.6i		−	1.75522i	−0.479380	−	0.877608i	$-0.659138\pi$
$487$		−	18863.6i		−	1.75522i	0.479380	−	0.877608i	$-0.340862\pi$
$488$			3084.91i			0.286162i
$489$	−2772.53	+	3118.12i	−0.256397	+	0.288356i
$490$	−12039.8	−	2963.59i	−1.11000	−	0.273228i
$491$			10861.4i			0.998309i	0.866513	+	0.499155i	$0.166356\pi$
$491$			10861.4i			0.998309i	−0.866513	+	0.499155i	$0.833644\pi$
$492$	553.368	+	492.038i	0.0507068	+	0.0450869i
$493$	−9132.48			−0.834293
$494$			4090.30i			0.372533i
$495$	146.538	+	109.191i	0.0133058	+	0.00991469i
$496$			10170.8i			0.920730i
$497$	717.477	+	2717.68i	0.0647550	+	0.245281i
$498$	8707.20	−	9792.51i	0.783492	−	0.881151i
$499$	1749.79			0.156977			0.0784883	−	0.996915i	$-0.474991\pi$
$499$	1749.79			0.156977			0.0784883	+	0.996915i	$0.474991\pi$
$500$	−2214.54	+	2618.82i	−0.198075	+	0.234235i
$501$	5142.44	−	5783.43i	0.458578	−	0.515737i
$502$	−519.887			−0.0462225
$503$		−	12989.4i		−	1.15143i	−0.817651	−	0.575715i	$-0.804724\pi$
$503$		−	12989.4i		−	1.15143i	0.817651	−	0.575715i	$-0.195276\pi$
$504$	−3286.84	−	8342.48i	−0.290491	−	0.737309i
$505$	3944.38	+	3730.83i	0.347569	+	0.328752i
$506$			266.368i			0.0234022i
$507$	7891.15	+	7016.56i	0.691239	+	0.614628i
$508$			3337.77i			0.291515i
$509$	−4913.86			−0.427904			−0.213952	−	0.976844i	$-0.568634\pi$
$509$	−4913.86			−0.427904			−0.213952	+	0.976844i	$0.568634\pi$
$510$	22038.0	−	1909.18i	1.91345	−	0.165765i
$511$	−4338.29	+	1145.33i	−0.375567	+	0.0991511i
$512$	2791.68			0.240969
$513$	−11334.2	−	7914.93i	−0.975472	−	0.681195i
$514$		−	1899.27i		−	0.162983i
$515$	−12671.9	−	11985.8i	−1.08425	−	1.02555i
$516$	−4401.72	+	4950.38i	−0.375533	+	0.422341i
$517$	63.3248			0.00538689
$518$	3980.53	+	15077.6i	0.337634	+	1.27890i
$519$	−908.329	+	1021.55i	−0.0768231	+	0.0863988i
$520$	1869.93	+	1768.69i	0.157696	+	0.149158i
$521$	−6450.02			−0.542381			−0.271190	−	0.962526i	$-0.587417\pi$
$521$	−6450.02			−0.542381			−0.271190	+	0.962526i	$0.587417\pi$
$522$	−6723.41	+	791.604i	−0.563747	+	0.0663747i
$523$	21041.2			1.75921			0.879606	−	0.475702i	$-0.157806\pi$
$523$	21041.2			1.75921			0.879606	+	0.475702i	$0.157806\pi$
$524$	−3031.44			−0.252728
$525$	−4828.62	+	11017.6i	−0.401406	+	0.915900i
$526$	−15393.6			−1.27603
$527$	−15433.1			−1.27567
$528$	162.222	−	182.443i	0.0133709	−	0.0150375i
$529$	6352.25			0.522088
$530$	−14455.7	−	13673.1i	−1.18475	−	1.12061i
$531$	1573.60	+	13365.2i	0.128603	+	1.09228i
$532$	1143.16	+	4330.08i	0.0931620	+	0.352881i
$533$	−745.534			−0.0605866
$534$	12563.5	+	11171.1i	1.01812	+	0.905283i
$535$	−6144.99	−	5812.30i	−0.496582	−	0.469696i
$536$		−	11168.3i		−	0.899994i
$537$	1200.26	−	1349.87i	0.0964526	−	0.108475i
$538$	18234.9			1.46126
$539$	−102.495	−	180.586i	−0.00819065	−	0.0144312i
$540$	3769.80	−	778.374i	0.300419	−	0.0620294i
$541$	16947.6			1.34683			0.673415	−	0.739264i	$-0.264827\pi$
$541$	16947.6			1.34683			0.673415	+	0.739264i	$0.264827\pi$
$542$		−	7277.77i		−	0.576765i
$543$	8827.20	−	9927.47i	0.697627	−	0.784583i
$544$		−	12657.6i		−	0.997592i
$545$	−6462.27	−	6112.39i	−0.507914	−	0.480415i
$546$	−3563.96	−	1804.47i	−0.279347	−	0.141436i
$547$			23736.9i			1.85542i	0.373298	+	0.927712i	$0.378227\pi$
$547$			23736.9i			1.85542i	−0.373298	+	0.927712i	$0.621773\pi$
$548$	346.773			0.0270318
$549$	−4613.16	+	543.146i	−0.358624	+	0.0422239i
$550$	−244.291	+	13.6046i	−0.0189393	+	0.00105473i
$551$	−7641.34			−0.590802
$552$	−9475.67	−	8425.47i	−0.730636	−	0.649659i
$553$	−1695.37	+	447.583i	−0.130369	+	0.0344180i
$554$		−	20446.7i		−	1.56804i
$555$	15072.5	−	1305.75i	1.15278	−	0.0998670i
$556$			2195.68i			0.167478i
$557$	8025.91			0.610537			0.305268	−	0.952266i	$-0.401254\pi$
$557$	8025.91			0.610537			0.305268	+	0.952266i	$0.401254\pi$
$558$	−11362.0	+	1337.74i	−0.861990	+	0.101489i
$559$		−	6669.47i		−	0.504631i
$560$	14107.0	+	7696.93i	1.06452	+	0.580812i
$561$	276.837	+	246.155i	0.0208343	+	0.0185252i
$562$			25572.6i			1.91942i
$563$			8553.71i			0.640313i	0.947365	+	0.320156i	$0.103735\pi$
$563$			8553.71i			0.640313i	−0.947365	+	0.320156i	$0.896265\pi$
$564$	886.326	−	996.803i	0.0661721	−	0.0744201i
$565$	−3179.89	−	3007.73i	−0.236777	−	0.223958i
$566$	4413.04			0.327728
$567$	11896.6	−	6383.96i	0.881148	−	0.472841i
$568$		−	2721.44i		−	0.201037i
$569$			8983.39i			0.661868i	0.943654	+	0.330934i	$0.107364\pi$
$569$			8983.39i			0.661868i	−0.943654	+	0.330934i	$0.892636\pi$
$570$	18439.6	−	1597.45i	1.35500	−	0.117386i
$571$	−8976.45			−0.657886			−0.328943	−	0.944350i	$-0.606692\pi$
$571$	−8976.45			−0.657886			−0.328943	+	0.944350i	$0.606692\pi$
$572$		−	19.0734i		−	0.00139423i
$573$	−10325.5	+	11612.5i	−0.752797	+	0.846630i
$574$	−3362.09	+	887.604i	−0.244479	+	0.0645434i
$575$	945.863	+	16984.4i	0.0686003	+	1.23182i
$576$	863.040	+	7330.14i	0.0624305	+	0.530248i
$577$	1444.10			0.104192			0.0520958	−	0.998642i	$-0.483410\pi$
$577$	1444.10			0.104192			0.0520958	+	0.998642i	$0.483410\pi$
$578$	28955.8			2.08374
$579$	−13637.0	+	15336.8i	−0.978819	+	1.10082i
$580$	1462.09	−	1545.78i	0.104672	−	0.110664i
$581$	3687.21	+	13966.5i	0.263290	+	0.997296i
$582$	−14156.3	−	12587.4i	−1.00824	−	0.896499i
$583$		−	333.223i		−	0.0236719i
$584$	4344.31			0.307823
$585$	−2315.66	+	3107.69i	−0.163660	+	0.219636i
$586$		−	19913.0i		−	1.40375i
$587$			21411.0i			1.50549i	0.658310	+	0.752747i	$0.271272\pi$
$587$			21411.0i			1.50549i	−0.658310	+	0.752747i	$0.728728\pi$
$588$	−4277.20	−	914.199i	−0.299981	−	0.0641172i
$589$	−12913.2			−0.903358
$590$	−13089.8	−	12381.1i	−0.913388	−	0.863937i
$591$	6148.06	+	5466.67i	0.427915	+	0.380488i
$592$		−	20211.1i		−	1.40316i
$593$		−	2596.21i		−	0.179787i	−0.995951	−	0.0898935i	$-0.971347\pi$
$593$		−	2596.21i		−	0.179787i	0.995951	−	0.0898935i	$-0.0286527\pi$
$594$	225.146	+	157.225i	0.0155520	+	0.0108603i
$595$	−11679.3	+	21405.8i	−0.804711	+	1.47488i
$596$		−	5528.86i		−	0.379985i
$597$	−351.021	+	394.775i	−0.0240642	+	0.0270637i
$598$	−5648.99			−0.386295
$599$		−	13043.3i		−	0.889709i	−0.895603	−	0.444854i	$-0.853255\pi$
$599$		−	13043.3i		−	0.889709i	0.895603	−	0.444854i	$-0.146745\pi$
$600$	7243.20	−	9120.65i	0.492837	−	0.620581i
$601$		−	320.380i		−	0.0217447i	−0.999941	−	0.0108724i	$-0.996539\pi$
$601$		−	320.380i		−	0.0217447i	0.999941	−	0.0108724i	$-0.00346085\pi$
$602$	−7940.42	−	30076.9i	−0.537587	−	2.03628i
$603$	16701.0	−	1966.35i	1.12789	−	0.132796i
$604$	−2050.17			−0.138113
$605$	10808.1	+	10222.9i	0.726300	+	0.686977i
$606$	6096.92	+	5421.19i	0.408697	+	0.363401i
$607$	−9539.65			−0.637895			−0.318948	−	0.947772i	$-0.603329\pi$
$607$	−9539.65			−0.637895			−0.318948	+	0.947772i	$0.603329\pi$
$608$		−	10590.9i		−	0.706442i
$609$	3371.04	−	6658.04i	0.224305	−	0.443017i
$610$	4273.50	−	4518.11i	0.283654	−	0.299890i
$611$			1342.96i			0.0889202i
$612$	7749.50	−	912.414i	0.511855	−	0.0602650i
$613$		−	10566.9i		−	0.696235i	−0.937451	−	0.348118i	$-0.886821\pi$
$613$		−	10566.9i		−	0.696235i	0.937451	−	0.348118i	$-0.113179\pi$
$614$	23461.8			1.54209
$615$	291.165	+	3360.96i	0.0190909	+	0.220369i
$616$	51.3184	+	194.385i	0.00335662	+	0.0127143i
$617$	10459.5			0.682467			0.341233	−	0.939979i	$-0.389155\pi$
$617$	10459.5			0.682467			0.341233	+	0.939979i	$0.389155\pi$
$618$	−19587.3	−	17416.4i	−1.27494	−	1.13364i
$619$			12347.7i			0.801768i	0.916129	+	0.400884i	$0.131297\pi$
$619$			12347.7i			0.801768i	−0.916129	+	0.400884i	$0.868703\pi$
$620$	2470.80	−	2612.23i	0.160048	−	0.169209i
$621$	10931.1	−	15653.3i	0.706359	−	1.01151i
$622$	−27175.6			−1.75183
$623$	−17918.7	+	4730.60i	−1.15232	+	0.304217i
$624$	3869.14	+	3440.32i	0.248221	+	0.220710i
$625$	−15528.4	+	1734.94i	−0.993816	+	0.111036i
$626$	9740.61			0.621906
$627$	231.635	+	205.963i	0.0147538	+	0.0131186i
$628$	7361.28			0.467750
$629$	30668.2			1.94407
$630$	−6742.91	+	16771.5i	−0.426419	+	1.06062i
$631$	−7403.86			−0.467105			−0.233552	−	0.972344i	$-0.575035\pi$
$631$	−7403.86			−0.467105			−0.233552	+	0.972344i	$0.575035\pi$
$632$	1697.72			0.106854
$633$	−19598.8	−	17426.6i	−1.23062	−	1.09423i
$634$	−27079.1			−1.69629
$635$	−10449.4	+	11047.5i	−0.653024	+	0.690403i
$636$	−5245.30	−	4663.96i	−0.327028	−	0.290783i
$637$	3829.78	−	2173.65i	0.238212	−	0.135201i
$638$	151.790			0.00941917
$639$	4069.64	−	479.153i	0.251944	−	0.0296635i
$640$	−14163.3	−	13396.5i	−0.874772	−	0.827411i
$641$		−	24209.2i		−	1.49174i	−0.666089	−	0.745872i	$-0.732033\pi$
$641$		−	24209.2i		−	1.49174i	0.666089	−	0.745872i	$-0.267967\pi$
$642$	−9498.46	−	8445.74i	−0.583916	−	0.519200i
$643$	11848.9			0.726712			0.363356	−	0.931650i	$-0.381631\pi$
$643$	11848.9			0.726712			0.363356	+	0.931650i	$0.381631\pi$
$644$	−5980.15	+	1578.78i	−0.365917	+	0.0966036i
$645$	−30066.8	+	2604.74i	−1.83547	+	0.159010i
$646$	37519.3			2.28510
$647$		−	6193.88i		−	0.376362i	−0.982134	−	0.188181i	$-0.939741\pi$
$647$		−	6193.88i		−	0.376362i	0.982134	−	0.188181i	$-0.0602592\pi$
$648$	−12714.6	+	3036.09i	−0.770800	+	0.184057i
$649$		−	301.737i		−	0.0182500i
$650$	−288.520	−	5180.80i	−0.0174103	−	0.312627i
$651$	5696.76	−	11251.5i	0.342970	−	0.677390i
$652$		−	1970.59i		−	0.118365i
$653$	27763.0			1.66378			0.831892	−	0.554938i	$-0.187258\pi$
$653$	27763.0			1.66378			0.831892	+	0.554938i	$0.187258\pi$
$654$	−9988.87	−	8881.80i	−0.597241	−	0.531048i
$655$	−10033.6	−	9490.37i	−0.598542	−	0.566136i
$656$	4506.80			0.268233
$657$	764.883	+	6496.46i	0.0454200	+	0.385770i
$658$	1598.87	+	6056.26i	0.0947274	+	0.358811i
$659$			6793.61i			0.401581i	0.979634	+	0.200790i	$0.0643510\pi$
$659$			6793.61i			0.401581i	−0.979634	+	0.200790i	$0.935649\pi$
$660$	−85.9855	+	7.44906i	−0.00507118	+	0.000439324i
$661$			11194.7i			0.658732i	0.944202	+	0.329366i	$0.106835\pi$
$661$			11194.7i			0.658732i	−0.944202	+	0.329366i	$0.893165\pi$
$662$	23892.1			1.40271
$663$	−5220.32	+	5871.01i	−0.305792	+	0.343908i
$664$		−	13985.9i		−	0.817406i
$665$	−9772.27	+	17910.7i	−0.569853	+	1.04443i
$666$	22578.2	−	2658.32i	1.31364	−	0.154666i
$667$		−	10553.2i		−	0.612627i
$668$			3655.01i			0.211702i
$669$	7246.01	+	6442.93i	0.418755	+	0.372344i
$670$	−15471.3	+	16356.9i	−0.892104	+	0.943168i
$671$	104.148			0.00599195
$672$	9228.02	+	4672.25i	0.529730	+	0.268209i
$673$			9778.19i			0.560062i	0.959991	+	0.280031i	$0.0903447\pi$
$673$			9778.19i			0.560062i	−0.959991	+	0.280031i	$0.909655\pi$
$674$			24614.5i			1.40670i
$675$	14914.3	+	9225.61i	0.850444	+	0.526065i
$676$	−4987.05			−0.283742
$677$		−	18617.5i		−	1.05691i	−0.848961	−	0.528455i	$-0.822772\pi$
$677$		−	18617.5i		−	1.05691i	0.848961	−	0.528455i	$-0.177228\pi$
$678$	−4915.23	−	4370.47i	−0.278419	−	0.247562i
$679$	20190.4	−	5330.33i	1.14114	−	0.301266i
$680$	16223.7	−	17152.4i	0.914930	−	0.967300i
$681$	−7839.31	+	8816.44i	−0.441120	+	0.496104i
$682$	256.512			0.0144023
$683$	−7222.59			−0.404634			−0.202317	−	0.979320i	$-0.564847\pi$
$683$	−7222.59			−0.404634			−0.202317	+	0.979320i	$0.564847\pi$
$684$	6484.17	−	763.436i	0.362468	−	0.0426765i
$685$	1147.76	+	1085.62i	0.0640201	+	0.0605540i
$686$	14683.1	−	14362.0i	0.817204	−	0.799334i
$687$	3447.05	−	3876.71i	0.191431	−	0.215292i
$688$			40317.4i			2.23414i
$689$	7066.82			0.390746
$690$	2206.19	+	25466.4i	0.121722	+	1.40506i
$691$			10418.8i			0.573589i	0.957992	+	0.286795i	$0.0925898\pi$
$691$			10418.8i			0.573589i	−0.957992	+	0.286795i	$0.907410\pi$
$692$		−	645.598i		−	0.0354653i
$693$	−281.647	+	110.966i	−0.0154385	+	0.00608260i
$694$	7270.90			0.397694
$695$	−6873.89	+	7267.35i	−0.375168	+	0.396642i
$696$	−4801.26	+	5399.72i	−0.261482	+	0.294075i
$697$			6838.58i			0.371635i
$698$			13377.7i			0.725433i
$699$	−15916.4	−	14152.4i	−0.861252	−	0.765799i
$700$	−1753.36	−	5403.87i	−0.0946728	−	0.291782i
$701$		−	30401.8i		−	1.63803i	−0.573772	−	0.819015i	$-0.694520\pi$
$701$		−	30401.8i		−	1.63803i	0.573772	−	0.819015i	$-0.305480\pi$
$702$	−3334.34	+	4774.78i	−0.179269	+	0.256713i
$703$	25660.7			1.37669
$704$		−	165.488i		−	0.00885946i
$705$	6054.23	−	524.487i	0.323426	−	0.0280189i
$706$		−	16070.3i		−	0.856678i
$707$	−8695.70	+	2295.70i	−0.462568	+	0.122120i
$708$	−4749.68	−	4223.27i	−0.252124	−	0.224181i
$709$	−20621.4			−1.09232			−0.546159	−	0.837682i	$-0.683911\pi$
$709$	−20621.4			−1.09232			−0.546159	+	0.837682i	$0.683911\pi$
$710$	−3769.99	+	3985.79i	−0.199275	+	0.210682i
$711$	298.910	+	2538.76i	0.0157665	+	0.133911i
$712$	17943.5			0.944469
$713$		−	17834.0i		−	0.936730i
$714$	−16552.0	+	32691.2i	−0.867565	+	1.71350i
$715$	59.7121	−	63.1300i	0.00312322	−	0.00330200i
$716$			853.090i			0.0445272i
$717$	14218.6	−	15990.9i	0.740590	−	0.832901i
$718$		−	9512.91i		−	0.494455i
$719$	−12233.8			−0.634555			−0.317278	−	0.948333i	$-0.602769\pi$
$719$	−12233.8			−0.634555			−0.317278	+	0.948333i	$0.602769\pi$
$720$	13998.3	−	18786.2i	0.724566	−	0.972390i
$721$	27936.2	−	7375.27i	1.44300	−	0.380956i
$722$	9216.13			0.475054
$723$	−22940.5	+	25799.9i	−1.18004	+	1.32712i
$724$			6273.97i			0.322058i
$725$	9678.56	−	539.001i	0.495797	−	0.0276110i
$726$	16706.3	+	14854.7i	0.854035	+	0.759382i
$727$	−27169.3			−1.38604			−0.693021	−	0.720918i	$-0.743721\pi$
$727$	−27169.3			−1.38604			−0.693021	+	0.720918i	$0.743721\pi$
$728$	−4122.41	+	1088.33i	−0.209872	+	0.0554070i
$729$	−6778.77	−	18478.9i	−0.344397	−	0.938824i
$730$	−6362.61	−	6018.13i	−0.322590	−	0.305125i
$731$	−61177.3			−3.09538
$732$	1457.71	−	1639.41i	0.0736046	−	0.0827792i
$733$	−13215.7			−0.665937			−0.332968	−	0.942938i	$-0.608050\pi$
$733$	−13215.7			−0.665937			−0.332968	+	0.942938i	$0.608050\pi$
$734$	−7813.92			−0.392939
$735$	−11294.8	−	16416.2i	−0.566824	−	0.823839i
$736$	14626.7			0.732538
$737$	−377.048			−0.0188450
$738$	592.769	+	5034.62i	0.0295666	+	0.251121i
$739$	12158.0			0.605194			0.302597	−	0.953119i	$-0.402146\pi$
$739$	12158.0			0.605194			0.302597	+	0.953119i	$0.402146\pi$
$740$	−4909.90	+	5190.94i	−0.243908	+	0.257869i
$741$	−4367.95	+	4912.39i	−0.216546	+	0.243537i
$742$	31868.8	−	8413.49i	1.57674	−	0.416265i
$743$	−28694.3			−1.41681			−0.708406	−	0.705805i	$-0.750586\pi$
$743$	−28694.3			−1.41681			−0.708406	+	0.705805i	$0.750586\pi$
$744$	−8113.71	+	9125.05i	−0.399816	+	0.449651i
$745$	17308.9	−	18299.6i	0.851206	−	0.899929i
$746$		−	15167.4i		−	0.744392i
$747$	20914.4	−	2462.43i	1.02439	−	0.120610i
$748$	−174.956			−0.00855215
$749$	13547.1	−	3576.49i	0.660883	−	0.174476i
$750$	−23243.0	+	3324.03i	−1.13162	+	0.161835i
$751$	−5141.82			−0.249837			−0.124919	−	0.992167i	$-0.539867\pi$
$751$	−5141.82			−0.249837			−0.124919	+	0.992167i	$0.539867\pi$
$752$		−	8118.27i		−	0.393674i
$753$	−624.376	−	555.176i	−0.0302172	−	0.0268682i
$754$			3219.08i			0.155480i
$755$	−6785.75	−	6418.36i	−0.327097	−	0.309388i
$756$	−2195.35	+	5986.57i	−0.105614	+	0.288002i
$757$		−	23836.1i		−	1.14444i	−0.820102	−	0.572218i	$-0.806083\pi$
$757$		−	23836.1i		−	1.14444i	0.820102	−	0.572218i	$-0.193917\pi$
$758$	−2380.48			−0.114067
$759$	−284.449	+	319.904i	−0.0136032	+	0.0152988i
$760$	13574.7	−	14351.8i	0.647905	−	0.684990i
$761$	29237.9			1.39274			0.696369	−	0.717684i	$-0.254798\pi$
$761$	29237.9			1.39274			0.696369	+	0.717684i	$0.254798\pi$
$762$	−15183.8	+	17076.4i	−0.721850	+	0.811825i
$763$	14246.6	−	3761.15i	0.675965	−	0.178457i
$764$		−	7338.87i		−	0.347527i
$765$	28506.0	+	21241.0i	1.34724	+	1.00388i
$766$			38195.4i			1.80164i
$767$	6399.08			0.301248
$768$	−13400.6	−	11915.4i	−0.629625	−	0.559843i
$769$		−	11924.6i		−	0.559185i	−0.960119	−	0.279592i	$-0.909801\pi$
$769$		−	11924.6i		−	0.559185i	0.960119	−	0.279592i	$-0.0901993\pi$
$770$	194.120	−	355.784i	0.00908519	−	0.0166514i
$771$	2028.20	−	2281.00i	0.0947389	−	0.106548i
$772$		−	9692.58i		−	0.451870i
$773$			16127.3i			0.750400i	0.926944	+	0.375200i	$0.122426\pi$
$773$			16127.3i			0.750400i	−0.926944	+	0.375200i	$0.877574\pi$
$774$	−45039.2	+	5302.85i	−2.09160	+	0.246262i
$775$	16355.9	−	910.863i	0.758092	−	0.0422183i
$776$	−20218.4			−0.935305
$777$	−11320.4	+	22358.6i	−0.522675	+	1.03232i
$778$		−	12121.4i		−	0.558576i
$779$			5721.98i			0.263172i
$780$	−157.976	−	1823.53i	−0.00725184	−	0.0837089i
$781$	−91.8776			−0.00420952
$782$			51816.7i			2.36952i
$783$	−8920.06	−	6229.08i	−0.407122	−	0.284303i
$784$	−23151.3	+	13139.9i	−1.05463	+	0.598573i
$785$	24364.7	+	23045.5i	1.10779	+	1.04781i
$786$	−15509.2	−	13790.3i	−0.703808	−	0.625805i
$787$	17480.8			0.791770			0.395885	−	0.918300i	$-0.370438\pi$
$787$	17480.8			0.791770			0.395885	+	0.918300i	$0.370438\pi$
$788$	−3885.46			−0.175652
$789$	−18487.5	−	16438.5i	−0.834184	−	0.741730i
$790$	−2486.45	−	2351.83i	−0.111980	−	0.105917i
$791$	7010.33	−	1850.75i	0.315118	−	0.0831924i
$792$	291.086	−	34.2720i	0.0130597	−	0.00153763i
$793$			2208.72i			0.0989079i
$794$	18656.0			0.833851
$795$	−2759.92	−	31858.1i	−0.123125	−	1.42125i
$796$		−	249.490i		−	0.0111092i
$797$		−	317.152i		−	0.0140955i	−0.999975	−	0.00704775i	$-0.997757\pi$
$797$		−	317.152i		−	0.0140955i	0.999975	−	0.00704775i	$-0.00224339\pi$
$798$	−13849.4	+	27353.4i	−0.614363	+	1.21341i
$799$	12318.6			0.545433
$800$	747.054	+	13414.5i	0.0330154	+	0.592841i
$801$	3159.24	+	26832.7i	0.139359	+	1.18363i
$802$			20630.0i			0.908318i
$803$		−	146.666i		−	0.00644551i
$804$	−5277.36	+	5935.16i	−0.231490	+	0.260344i
$805$	−24735.9	−	13496.2i	−1.08301	−	0.590904i
$806$			5439.96i			0.237735i
$807$	21899.8	+	19472.6i	0.955278	+	0.849403i
$808$	8707.76			0.379131
$809$			6248.49i			0.271552i	0.990740	+	0.135776i	$0.0433527\pi$
$809$			6248.49i			0.271552i	−0.990740	+	0.135776i	$0.956647\pi$
$810$	22827.6	+	13166.9i	0.990220	+	0.571157i
$811$			36680.9i			1.58821i	0.607778	+	0.794107i	$0.292061\pi$
$811$			36680.9i			1.58821i	−0.607778	+	0.794107i	$0.707939\pi$
$812$	899.670	+	3407.79i	0.0388821	+	0.147278i
$813$	7771.77	−	8740.49i	0.335262	−	0.377051i
$814$	−509.733			−0.0219486
$815$	6169.21	−	6522.33i	0.265151	−	0.280328i
$816$	31557.2	−	35490.6i	1.35383	−	1.52257i
$817$	−51188.3			−2.19199
$818$			17876.9i			0.764120i
$819$	−2353.30	−	5973.02i	−0.100404	−	0.254840i
$820$	−1157.51	−	1094.84i	−0.0492951	−	0.0466262i
$821$		−	18852.3i		−	0.801402i	−0.916209	−	0.400701i	$-0.868767\pi$
$821$		−	18852.3i		−	0.801402i	0.916209	−	0.400701i	$-0.131233\pi$
$822$	1774.12	+	1577.50i	0.0752794	+	0.0669361i
$823$			21450.8i			0.908539i	0.890864	+	0.454270i	$0.150100\pi$
$823$			21450.8i			0.908539i	−0.890864	+	0.454270i	$0.849900\pi$
$824$	−27975.0			−1.18271
$825$	−307.918	−	244.535i	−0.0129944	−	0.0103195i
$826$	28857.5	−	7618.50i	1.21560	−	0.320922i
$827$	−16908.5			−0.710964			−0.355482	−	0.934683i	$-0.615683\pi$
$827$	−16908.5			−0.710964			−0.355482	+	0.934683i	$0.615683\pi$
$828$	1054.36	+	8955.08i	0.0442530	+	0.375858i
$829$		−	31015.2i		−	1.29940i	−0.760191	−	0.649699i	$-0.774895\pi$
$829$		−	31015.2i		−	1.29940i	0.760191	−	0.649699i	$-0.225105\pi$
$830$	−19374.5	+	20483.5i	−0.810241	+	0.856619i
$831$	21834.6	−	24556.2i	0.911471	−	1.02508i
$832$	3509.58			0.146241
$833$	−19938.3	−	35129.6i	−0.829319	−	1.46119i
$834$	−9988.31	+	11233.3i	−0.414709	+	0.466400i
$835$	−11442.5	+	12097.5i	−0.474234	+	0.501379i
$836$	−146.389			−0.00605618
$837$	−15074.1	−	10526.6i	−0.622505	−	0.434710i
$838$	14528.0			0.598878
$839$	38712.1			1.59296			0.796478	−	0.604668i	$-0.206694\pi$
$839$	38712.1			1.59296			0.796478	+	0.604668i	$0.206694\pi$
$840$	6516.34	+	18159.3i	0.267661	+	0.745900i
$841$	18375.2			0.753423
$842$	322.971			0.0132189
$843$	−27308.5	+	30712.4i	−1.11572	+	1.25479i
$844$	12386.0			0.505148
$845$	−16506.3	−	15612.7i	−0.671995	−	0.635612i
$846$	9069.06	−	1067.78i	0.368559	−	0.0433935i
$847$	−23827.3	+	6290.50i	−0.966607	+	0.255188i
$848$	−42719.4			−1.72994
$849$	5300.00	+	4712.59i	0.214247	+	0.190501i
$850$	−47522.1	+	2646.52i	−1.91764	+	0.106794i
$851$			35439.2i			1.42754i
$852$	−1285.96	+	1446.26i	−0.0517094	+	0.0581548i
$853$	26344.4			1.05746			0.528731	−	0.848790i	$-0.322668\pi$
$853$	26344.4			1.05746			0.528731	+	0.848790i	$0.322668\pi$
$854$	2629.62	+	9960.54i	0.105367	+	0.399113i
$855$	23851.6	+	17772.8i	0.954044	+	0.710895i
$856$	−13565.9			−0.541675
$857$			15218.9i			0.606615i	0.952893	+	0.303308i	$0.0980909\pi$
$857$			15218.9i			0.606615i	−0.952893	+	0.303308i	$0.901909\pi$
$858$	86.7664	−	97.5815i	0.00345240	−	0.00388272i
$859$			48018.8i			1.90731i	0.300899	+	0.953656i	$0.402713\pi$
$859$			48018.8i			1.90731i	−0.300899	+	0.953656i	$0.597287\pi$
$860$	9794.34	−	10355.0i	0.388354	−	0.410583i
$861$	−4985.67	−	2524.30i	−0.197342	−	0.0999164i
$862$		−	43855.3i		−	1.73285i
$863$	35618.5			1.40495			0.702473	−	0.711710i	$-0.252079\pi$
$863$	35618.5			1.40495			0.702473	+	0.711710i	$0.252079\pi$
$864$	8633.49	−	12363.2i	0.339951	−	0.486810i
$865$	2021.14	−	2136.83i	0.0794459	−	0.0839934i
$866$	−33627.7			−1.31953
$867$	34775.5	+	30921.3i	1.36221	+	1.21124i
$868$	1520.36	+	5758.87i	0.0594521	+	0.225194i
$869$		−	57.3159i		−	0.00223741i
$870$	14512.0	−	1257.20i	0.565522	−	0.0489921i
$871$		−	7996.23i		−	0.311070i
$872$	−14266.3			−0.554036
$873$	−3559.76	−	30234.5i	−0.138006	−	1.17214i
$874$			43356.1i			1.67797i
$875$	11114.2	−	23375.1i	0.429406	−	0.903112i
$876$	−2308.69	−	2052.82i	−0.0890450	−	0.0791761i
$877$			21298.0i			0.820049i	0.912074	+	0.410025i	$0.134480\pi$
$877$			21298.0i			0.820049i	−0.912074	+	0.410025i	$0.865520\pi$
$878$		−	20945.4i		−	0.805094i
$879$	21264.7	−	23915.2i	0.815972	−	0.917679i
$880$	−360.963	+	381.625i	−0.0138274	+	0.0146188i
$881$	19493.5			0.745464			0.372732	−	0.927939i	$-0.378421\pi$
$881$	19493.5			0.745464			0.372732	+	0.927939i	$0.378421\pi$
$882$	−17723.8	−	24134.4i	−0.676634	−	0.921370i
$883$			31577.5i			1.20347i	0.798694	+	0.601737i	$0.205524\pi$
$883$			31577.5i			1.20347i	−0.798694	+	0.601737i	$0.794476\pi$
$884$		−	3710.36i		−	0.141169i
$885$	−2499.14	−	28847.9i	−0.0949238	−	1.09572i
$886$	−26939.0			−1.02148
$887$		−	6376.75i		−	0.241387i	−0.992690	−	0.120693i	$-0.961488\pi$
$887$		−	6376.75i		−	0.241387i	0.992690	−	0.120693i	$-0.0385118\pi$
$888$	16123.3	−	18133.0i	0.609306	−	0.685253i
$889$	−6429.83	−	24355.1i	−0.242575	−	0.918833i
$890$	−26279.8	−	24857.0i	−0.989777	−	0.936190i
$891$	102.500	+	429.254i	0.00385397	+	0.0161398i
$892$	−4579.34			−0.171892
$893$	10307.2			0.386247
$894$	25151.2	−	28286.2i	0.940920	−	1.05820i
$895$	−2670.72	+	2823.59i	−0.0997456	+	0.105455i
$896$	31224.1	−	8243.29i	1.16420	−	0.307354i
$897$	−6784.35	−	6032.44i	−0.252534	−	0.224545i
$898$		−	18015.5i		−	0.669472i
$899$	−10162.7			−0.377025
$900$	−8159.03	+	1424.35i	−0.302186	+	0.0527537i
$901$		−	64822.1i		−	2.39682i
$902$		−	113.663i		−	0.00419576i
$903$	22582.2	−	44601.3i	0.832212	−	1.64368i
$904$	−7020.05			−0.258278
$905$	−19641.6	+	20765.8i	−0.721445	+	0.762740i
$906$	−10488.9	−	9326.39i	−0.384625	−	0.341996i
$907$			19030.9i			0.696704i	0.937364	+	0.348352i	$0.113259\pi$
$907$			19030.9i			0.696704i	−0.937364	+	0.348352i	$0.886741\pi$
$908$		−	5571.82i		−	0.203642i
$909$	1533.14	+	13021.5i	0.0559416	+	0.475135i
$910$	7545.28	+	4116.79i	0.274861	+	0.149967i
$911$			17120.3i			0.622635i	0.950306	+	0.311317i	$0.100770\pi$
$911$			17120.3i			0.622635i	−0.950306	+	0.311317i	$0.899230\pi$
$912$	26404.5	−	29695.7i	0.958708	−	1.07821i
$913$	−472.172			−0.0171157
$914$			31262.3i			1.13136i
$915$	9957.20	−	862.608i	0.359754	−	0.0311661i
$916$			2450.00i			0.0883738i
$917$	22119.9	−	5839.73i	0.796578	−	0.210300i
$918$	43797.8	+	30585.0i	1.57467	+	1.09963i
$919$	19873.5			0.713348			0.356674	−	0.934229i	$-0.383911\pi$
$919$	19873.5			0.713348			0.356674	+	0.934229i	$0.383911\pi$
$920$	19820.8	+	18747.7i	0.710295	+	0.671839i
$921$	28177.3	+	25054.4i	1.00812	+	0.896385i
$922$	30845.9			1.10180
$923$		−	1948.49i		−	0.0694857i
$924$	64.5807	−	127.551i	0.00229930	−	0.00454127i
$925$	−32502.0	+	1810.04i	−1.15531	+	0.0643392i
$926$			941.490i			0.0334117i
$927$	−4925.43	−	41833.6i	−0.174512	−	1.48220i
$928$		−	8335.05i		−	0.294840i
$929$	−19136.9			−0.675848			−0.337924	−	0.941173i	$-0.609725\pi$
$929$	−19136.9			−0.675848			−0.337924	+	0.941173i	$0.609725\pi$
$930$	24524.1	−	2124.56i	0.864705	−	0.0749108i
$931$	−16682.8	−	29393.6i	−0.587279	−	1.03473i
$932$	10058.9			0.353530
$933$	−32637.5	−	29020.2i	−1.14523	−	1.01831i
$934$		−	40193.6i		−	1.40811i
$935$	−579.075	−	547.723i	−0.0202543	−	0.0191577i
$936$	726.821	+	6173.18i	0.0253813	+	0.215574i
$937$	−41598.2			−1.45032			−0.725162	−	0.688579i	$-0.758235\pi$
$937$	−41598.2			−1.45032			−0.725162	+	0.688579i	$0.758235\pi$
$938$	−9520.01	−	36060.1i	−0.331385	−	1.25523i
$939$	11698.3	+	10401.8i	0.406561	+	0.361501i
$940$	−1972.18	+	2085.07i	−0.0684312	+	0.0723482i
$941$	7521.59			0.260570			0.130285	−	0.991477i	$-0.458411\pi$
$941$	7521.59			0.260570			0.130285	+	0.991477i	$0.458411\pi$
$942$	37661.0	+	33487.0i	1.30261	+	1.15824i
$943$	−7902.46			−0.272894
$944$	−38682.8			−1.33371
$945$	−26008.1	+	12941.7i	−0.895283	+	0.445497i
$946$	1016.82			0.0349469
$947$	−40980.9			−1.40623			−0.703115	−	0.711076i	$-0.748208\pi$
$947$	−40980.9			−1.40623			−0.703115	+	0.711076i	$0.748208\pi$
$948$	−902.217	−	802.223i	−0.0309099	−	0.0274842i
$949$	3110.42			0.106395
$950$	−39762.7	+	2214.39i	−1.35797	+	0.0756257i
$951$	−32521.6	−	28917.2i	−1.10892	−	0.986018i
$952$	9982.99	+	37813.8i	0.339864	+	1.28735i
$953$	35640.8			1.21146			0.605729	−	0.795671i	$-0.292882\pi$
$953$	35640.8			1.21146			0.605729	+	0.795671i	$0.292882\pi$
$954$	−5618.78	−	47722.5i	−0.190686	−	1.61958i
$955$	22975.4	−	24290.5i	0.778498	−	0.823059i
$956$			10105.9i			0.341892i
$957$	182.298	+	162.093i	0.00615763	+	0.00547517i
$958$	−7276.25			−0.245391
$959$	−2530.34	+	668.018i	−0.0852021	+	0.0224937i
$960$	−1370.65	−	15821.6i	−0.0460809	−	0.531918i
$961$	12616.9			0.423514
$962$		−	10810.1i		−	0.362300i
$963$	−2388.49	−	20286.4i	−0.0799253	−	0.678837i
$964$		−	16305.1i		−	0.544762i
$965$	30344.0	−	32080.9i	1.01224	−	1.07018i
$966$	−37777.0	−	19126.9i	−1.25823	−	0.637059i
$967$			4062.19i			0.135089i	0.997716	+	0.0675446i	$0.0215165\pi$
$967$			4062.19i			0.135089i	−0.997716	+	0.0675446i	$0.978484\pi$
$968$	23860.3			0.792252
$969$	45060.1	+	40066.0i	1.49385	+	1.32828i
$970$	29611.5	+	28008.3i	0.980174	+	0.927106i
$971$	26187.3			0.865489			0.432745	−	0.901517i	$-0.357545\pi$
$971$	26187.3			0.865489			0.432745	+	0.901517i	$0.357545\pi$
$972$	8191.58	+	4394.59i	0.270314	+	0.145017i
$973$	−4229.73	−	16021.5i	−0.139362	−	0.527877i
$974$			60991.0i			2.00645i
$975$	5185.96	−	6530.17i	0.170342	−	0.214495i
$976$		−	13351.9i		−	0.437892i
$977$	−52450.5			−1.71754			−0.858771	−	0.512359i	$-0.828772\pi$
$977$	−52450.5			−1.71754			−0.858771	+	0.512359i	$0.828772\pi$
$978$	8964.35	−	10081.7i	0.293096	−	0.329630i
$979$		−	605.784i		−	0.0197762i
$980$	9138.16	+	2249.37i	0.297865	+	0.0733197i
$981$	−2511.81	−	21333.8i	−0.0817492	−	0.694329i
$982$		−	35118.0i		−	1.14120i
$983$			29302.0i			0.950750i	0.879783	+	0.475375i	$0.157688\pi$
$983$			29302.0i			0.950750i	−0.879783	+	0.475375i	$0.842312\pi$
$984$	4043.42	+	3595.28i	0.130995	+	0.116477i
$985$	−12860.2	−	12164.0i	−0.416001	−	0.393479i
$986$	29527.8			0.953709
$987$	−4547.12	+	8980.88i	−0.146643	+	0.289630i
$988$		−	3104.54i		−	0.0999681i
$989$		−	70694.6i		−	2.27296i
$990$	−473.796	−	353.044i	−0.0152103	−	0.0113338i
$991$	−47052.6			−1.50825			−0.754124	−	0.656732i	$-0.771938\pi$
$991$	−47052.6			−1.50825			−0.754124	+	0.656732i	$0.771938\pi$
$992$		−	14085.5i		−	0.450822i
$993$	28694.0	+	25513.8i	0.916996	+	0.815364i
$994$	−2319.80	−	8786.99i	−0.0740237	−	0.280389i
$995$	781.063	−	825.771i	0.0248858	−	0.0263103i
$996$	−6608.76	+	7432.51i	−0.210247	+	0.236454i
$997$	1936.22			0.0615051			0.0307526	−	0.999527i	$-0.490210\pi$
$997$	1936.22			0.0615051			0.0307526	+	0.999527i	$0.490210\pi$
$998$	−5657.54			−0.179445
$999$	29954.8	+	20918.1i	0.948677	+	0.662483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.g.b.104.9	✓	40
3.2	odd	2	inner	105.4.g.b.104.30	yes	40
5.4	even	2	inner	105.4.g.b.104.32	yes	40
7.6	odd	2	inner	105.4.g.b.104.12	yes	40
15.14	odd	2	inner	105.4.g.b.104.11	yes	40
21.20	even	2	inner	105.4.g.b.104.31	yes	40
35.34	odd	2	inner	105.4.g.b.104.29	yes	40
105.104	even	2	inner	105.4.g.b.104.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.g.b.104.9	✓	40	1.1	even	1	trivial
105.4.g.b.104.10	yes	40	105.104	even	2	inner
105.4.g.b.104.11	yes	40	15.14	odd	2	inner
105.4.g.b.104.12	yes	40	7.6	odd	2	inner
105.4.g.b.104.29	yes	40	35.34	odd	2	inner
105.4.g.b.104.30	yes	40	3.2	odd	2	inner
105.4.g.b.104.31	yes	40	21.20	even	2	inner
105.4.g.b.104.32	yes	40	5.4	even	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.23327 q^{2} +(-3.88311 - 3.45274i) q^{3} +2.45405 q^{4} +(8.12252 + 7.68276i) q^{5} +(12.5552 + 11.1637i) q^{6} +(-17.9067 + 4.72745i) q^{7} +17.9316 q^{8} +(3.15713 + 26.8148i) q^{9} +O(q^{10})\)	\(q-3.23327 q^{2} +(-3.88311 - 3.45274i) q^{3} +2.45405 q^{4} +(8.12252 + 7.68276i) q^{5} +(12.5552 + 11.1637i) q^{6} +(-17.9067 + 4.72745i) q^{7} +17.9316 q^{8} +(3.15713 + 26.8148i) q^{9} +(-26.2623 - 24.8404i) q^{10} -0.605380i q^{11} +(-9.52936 - 8.47321i) q^{12} +12.8386 q^{13} +(57.8974 - 15.2851i) q^{14} +(-5.01406 - 57.8780i) q^{15} -77.6100 q^{16} -117.765i q^{17} +(-10.2079 - 86.6995i) q^{18} -98.5363i q^{19} +(19.9331 + 18.8539i) q^{20} +(85.8565 + 43.4702i) q^{21} +1.95736i q^{22} +136.085 q^{23} +(-69.6303 - 61.9131i) q^{24} +(6.95051 + 124.807i) q^{25} -41.5106 q^{26} +(80.3251 - 115.026i) q^{27} +(-43.9440 + 11.6014i) q^{28} -77.5484i q^{29} +(16.2118 + 187.135i) q^{30} -131.050i q^{31} +107.482 q^{32} +(-2.09022 + 2.35076i) q^{33} +380.766i q^{34} +(-181.768 - 99.1743i) q^{35} +(7.74776 + 65.8048i) q^{36} +260.419i q^{37} +318.595i q^{38} +(-49.8536 - 44.3283i) q^{39} +(145.649 + 137.764i) q^{40} -58.0698 q^{41} +(-277.598 - 140.551i) q^{42} -519.487i q^{43} -1.48563i q^{44} +(-180.368 + 242.059i) q^{45} -440.001 q^{46} +104.603i q^{47} +(301.369 + 267.968i) q^{48} +(298.302 - 169.306i) q^{49} +(-22.4729 - 403.534i) q^{50} +(-406.612 + 457.294i) q^{51} +31.5065 q^{52} +550.436 q^{53} +(-259.713 + 371.909i) q^{54} +(4.65099 - 4.91721i) q^{55} +(-321.096 + 84.7705i) q^{56} +(-340.221 + 382.628i) q^{57} +250.735i q^{58} +498.426 q^{59} +(-12.3048 - 142.035i) q^{60} +172.038i q^{61} +423.720i q^{62} +(-183.299 - 465.240i) q^{63} +273.362 q^{64} +(104.282 + 98.6356i) q^{65} +(6.75826 - 7.60065i) q^{66} -622.829i q^{67} -289.001i q^{68} +(-528.435 - 469.868i) q^{69} +(587.704 + 320.658i) q^{70} -151.768i q^{71} +(56.6123 + 480.831i) q^{72} +242.271 q^{73} -842.005i q^{74} +(403.936 - 508.636i) q^{75} -241.813i q^{76} +(2.86190 + 10.8404i) q^{77} +(161.190 + 143.325i) q^{78} +94.6776 q^{79} +(-630.389 - 596.259i) q^{80} +(-709.065 + 169.316i) q^{81} +187.756 q^{82} -779.959i q^{83} +(210.696 + 106.678i) q^{84} +(904.759 - 956.547i) q^{85} +1679.64i q^{86} +(-267.755 + 301.129i) q^{87} -10.8554i q^{88} +1000.67 q^{89} +(583.178 - 782.643i) q^{90} +(-229.897 + 60.6937i) q^{91} +333.961 q^{92} +(-452.482 + 508.882i) q^{93} -338.211i q^{94} +(757.030 - 800.363i) q^{95} +(-417.364 - 371.107i) q^{96} -1127.53 q^{97} +(-964.493 + 547.413i) q^{98} +(16.2331 - 1.91126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 184 q^{4} + 4 q^{9}+O(q^{10}) \) 40 * q + 184 * q^4 + 4 * q^9	\( 40 q + 184 q^{4} + 4 q^{9} - 188 q^{15} + 184 q^{16} + 148 q^{21} + 712 q^{25} - 336 q^{30} - 1520 q^{36} + 644 q^{39} - 1488 q^{46} - 1496 q^{49} - 220 q^{51} + 1984 q^{60} + 40 q^{64} - 3000 q^{70} - 1192 q^{79} + 4636 q^{81} - 2192 q^{84} + 4808 q^{85} - 4408 q^{91} + 5276 q^{99}+O(q^{100}) \) 40 * q + 184 * q^4 + 4 * q^9 - 188 * q^15 + 184 * q^16 + 148 * q^21 + 712 * q^25 - 336 * q^30 - 1520 * q^36 + 644 * q^39 - 1488 * q^46 - 1496 * q^49 - 220 * q^51 + 1984 * q^60 + 40 * q^64 - 3000 * q^70 - 1192 * q^79 + 4636 * q^81 - 2192 * q^84 + 4808 * q^85 - 4408 * q^91 + 5276 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more