LMFDB - Embedded newform 100.4.e.d.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,4,Mod(7,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("100.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	100.e (of order $4$, degree $2$, 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:	$5.90019100057$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.2342560000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 24x^{6} - 58x^{5} + 141x^{4} - 190x^{3} + 186x^{2} - 100x + 20 $ x^8 - 4x^7 + 24x^6 - 58x^5 + 141x^4 - 190x^3 + 186x^2 - 100*x + 20
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.2
Root			$0.500000 - 1.04028i$ of defining polynomial
Character	$\chi$	$=$	100.7
Dual form			100.4.e.d.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540278 - 2.77635i) q^{2} +(2.23607 + 2.23607i) q^{3} +(-7.41620 + 3.00000i) q^{4} +(5.00000 - 7.41620i) q^{6} +(11.1803 - 11.1803i) q^{7} +(12.3359 + 18.9691i) q^{8} -17.0000i q^{9} +O(q^{10})$	\(q+(-0.540278 - 2.77635i) q^{2} +(2.23607 + 2.23607i) q^{3} +(-7.41620 + 3.00000i) q^{4} +(5.00000 - 7.41620i) q^{6} +(11.1803 - 11.1803i) q^{7} +(12.3359 + 18.9691i) q^{8} -17.0000i q^{9} -59.3296i q^{11} +(-23.2913 - 9.87492i) q^{12} +(26.5330 - 26.5330i) q^{13} +(-37.0810 - 25.0000i) q^{14} +(46.0000 - 44.4972i) q^{16} +(79.5990 + 79.5990i) q^{17} +(-47.1979 + 9.18473i) q^{18} -59.3296 q^{19} +50.0000 q^{21} +(-164.719 + 32.0545i) q^{22} +(-105.095 - 105.095i) q^{23} +(-14.8324 + 70.0000i) q^{24} +(-88.0000 - 59.3296i) q^{26} +(98.3870 - 98.3870i) q^{27} +(-49.3746 + 116.457i) q^{28} +46.0000i q^{29} +118.659i q^{31} +(-148.392 - 103.671i) q^{32} +(132.665 - 132.665i) q^{33} +(177.989 - 264.000i) q^{34} +(51.0000 + 126.075i) q^{36} +(212.264 + 212.264i) q^{37} +(32.0545 + 164.719i) q^{38} +118.659 q^{39} -188.000 q^{41} +(-27.0139 - 138.817i) q^{42} +(122.984 + 122.984i) q^{43} +(177.989 + 440.000i) q^{44} +(-235.000 + 348.561i) q^{46} +(194.538 - 194.538i) q^{47} +(202.358 + 3.36038i) q^{48} +93.0000i q^{49} +355.978i q^{51} +(-117.175 + 276.373i) q^{52} +(26.5330 - 26.5330i) q^{53} +(-326.313 - 220.000i) q^{54} +(350.000 + 74.1620i) q^{56} +(-132.665 - 132.665i) q^{57} +(127.712 - 24.8528i) q^{58} +415.307 q^{59} +72.0000 q^{61} +(329.439 - 64.1090i) q^{62} +(-190.066 - 190.066i) q^{63} +(-207.654 + 468.000i) q^{64} +(-440.000 - 296.648i) q^{66} +(-597.030 + 597.030i) q^{67} +(-829.119 - 351.525i) q^{68} -470.000i q^{69} -711.955i q^{71} +(322.475 - 209.709i) q^{72} +(-504.127 + 504.127i) q^{73} +(474.637 - 704.000i) q^{74} +(440.000 - 177.989i) q^{76} +(-663.325 - 663.325i) q^{77} +(-64.1090 - 329.439i) q^{78} -830.614 q^{79} -19.0000 q^{81} +(101.572 + 521.953i) q^{82} +(221.371 + 221.371i) q^{83} +(-370.810 + 150.000i) q^{84} +(275.000 - 407.891i) q^{86} +(-102.859 + 102.859i) q^{87} +(1125.43 - 731.881i) q^{88} +726.000i q^{89} -593.296i q^{91} +(1094.69 + 464.121i) q^{92} +(-265.330 + 265.330i) q^{93} +(-645.209 - 435.000i) q^{94} +(-100.000 - 563.631i) q^{96} +(-451.061 - 451.061i) q^{97} +(258.200 - 50.2459i) q^{98} -1008.60 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 40 q^{6}+O(q^{10}) $ 8 * q + 40 * q^6	$ 8 q + 40 q^{6} + 368 q^{16} + 400 q^{21} - 704 q^{26} + 408 q^{36} - 1504 q^{41} - 1880 q^{46} + 2800 q^{56} + 576 q^{61} - 3520 q^{66} + 3520 q^{76} - 152 q^{81} + 2200 q^{86} - 800 q^{96}+O(q^{100}) $ 8 * q + 40 * q^6 + 368 * q^16 + 400 * q^21 - 704 * q^26 + 408 * q^36 - 1504 * q^41 - 1880 * q^46 + 2800 * q^56 + 576 * q^61 - 3520 * q^66 + 3520 * q^76 - 152 * q^81 + 2200 * q^86 - 800 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.540278	−	2.77635i	−0.191017	−	0.981587i
$2$	−0.540278	−	2.77635i	−0.191017	−	0.981587i
$3$	2.23607	+	2.23607i	0.430331	+	0.430331i	0.888741	−	0.458410i	$-0.151581\pi$
$3$	2.23607	+	2.23607i	0.430331	+	0.430331i	−0.458410	+	0.888741i	$0.651581\pi$
$4$	−7.41620	+	3.00000i	−0.927025	+	0.375000i
$5$		0			0
$5$		0			0
$6$	5.00000	−	7.41620i	0.340207	−	0.504608i
$7$	11.1803	−	11.1803i	0.603682	−	0.603682i	−0.337606	−	0.941288i	$-0.609617\pi$
$7$	11.1803	−	11.1803i	0.603682	−	0.603682i	0.941288	+	0.337606i	$0.109617\pi$
$8$	12.3359	+	18.9691i	0.545173	+	0.838324i
$9$		−	17.0000i		−	0.629630i
$10$		0			0
$11$		−	59.3296i		−	1.62623i	−0.582102	−	0.813116i	$-0.697770\pi$
$11$		−	59.3296i		−	1.62623i	0.582102	−	0.813116i	$-0.302230\pi$
$12$	−23.2913	−	9.87492i	−0.560302	−	0.237554i
$13$	26.5330	−	26.5330i	0.566072	−	0.566072i	−0.364954	−	0.931026i	$-0.618915\pi$
$13$	26.5330	−	26.5330i	0.566072	−	0.566072i	0.931026	+	0.364954i	$0.118915\pi$
$14$	−37.0810	−	25.0000i	−0.707879	−	0.477252i
$15$		0			0
$16$	46.0000	−	44.4972i	0.718750	−	0.695269i
$17$	79.5990	+	79.5990i	1.13562	+	1.13562i	0.989226	+	0.146397i	$0.0467677\pi$
$17$	79.5990	+	79.5990i	1.13562	+	1.13562i	0.146397	+	0.989226i	$0.453232\pi$
$18$	−47.1979	+	9.18473i	−0.618036	+	0.120270i
$19$	−59.3296			−0.716376			−0.358188	−	0.933650i	$-0.616605\pi$
$19$	−59.3296			−0.716376			−0.358188	+	0.933650i	$0.616605\pi$
$20$		0			0
$21$	50.0000			0.519566
$22$	−164.719	+	32.0545i	−1.59629	+	0.310638i
$23$	−105.095	−	105.095i	−0.952777	−	0.952777i	0.0461575	−	0.998934i	$-0.485302\pi$
$23$	−105.095	−	105.095i	−0.952777	−	0.952777i	−0.998934	+	0.0461575i	$0.985302\pi$
$24$	−14.8324	+	70.0000i	−0.126152	+	0.595362i
$25$		0			0
$26$	−88.0000	−	59.3296i	−0.663778	−	0.447519i
$27$	98.3870	−	98.3870i	0.701281	−	0.701281i
$28$	−49.3746	+	116.457i	−0.333247	+	0.786008i
$29$			46.0000i			0.294551i	0.989095	+	0.147276i	$0.0470504\pi$
$29$			46.0000i			0.294551i	−0.989095	+	0.147276i	$0.952950\pi$
$30$		0			0
$31$			118.659i			0.687478i	0.939065	+	0.343739i	$0.111694\pi$
$31$			118.659i			0.687478i	−0.939065	+	0.343739i	$0.888306\pi$
$32$	−148.392	−	103.671i	−0.819760	−	0.572707i
$33$	132.665	−	132.665i	0.699819	−	0.699819i
$34$	177.989	−	264.000i	0.897789	−	1.33164i
$35$		0			0
$36$	51.0000	+	126.075i	0.236111	+	0.583682i
$37$	212.264	+	212.264i	0.943135	+	0.943135i	0.998468	−	0.0553332i	$-0.0176221\pi$
$37$	212.264	+	212.264i	0.943135	+	0.943135i	−0.0553332	+	0.998468i	$0.517622\pi$
$38$	32.0545	+	164.719i	0.136840	+	0.703185i
$39$	118.659			0.487197
$40$		0			0
$41$	−188.000			−0.716114			−0.358057	−	0.933700i	$-0.616561\pi$
$41$	−188.000			−0.716114			−0.358057	+	0.933700i	$0.616561\pi$
$42$	−27.0139	−	138.817i	−0.0992462	−	0.509999i
$43$	122.984	+	122.984i	0.436159	+	0.436159i	0.890717	−	0.454558i	$-0.150203\pi$
$43$	122.984	+	122.984i	0.436159	+	0.436159i	−0.454558	+	0.890717i	$0.650203\pi$
$44$	177.989	+	440.000i	0.609837	+	1.50756i
$45$		0			0
$46$	−235.000	+	348.561i	−0.753236	+	1.11723i
$47$	194.538	−	194.538i	0.603750	−	0.603750i	−0.337555	−	0.941306i	$-0.609600\pi$
$47$	194.538	−	194.538i	0.603750	−	0.603750i	0.941306	+	0.337555i	$0.109600\pi$
$48$	202.358	+	3.36038i	0.608497	+	0.0101048i
$49$			93.0000i			0.271137i
$50$		0			0
$51$			355.978i			0.977389i
$52$	−117.175	+	276.373i	−0.312486	+	0.737039i
$53$	26.5330	−	26.5330i	0.0687658	−	0.0687658i	−0.671887	−	0.740653i	$-0.734516\pi$
$53$	26.5330	−	26.5330i	0.0687658	−	0.0687658i	0.740653	+	0.671887i	$0.234516\pi$
$54$	−326.313	−	220.000i	−0.822325	−	0.554411i
$55$		0			0
$56$	350.000	+	74.1620i	0.835191	+	0.176970i
$57$	−132.665	−	132.665i	−0.308279	−	0.308279i
$58$	127.712	−	24.8528i	0.289128	−	0.0562644i
$59$	415.307			0.916413			0.458207	−	0.888846i	$-0.348492\pi$
$59$	415.307			0.916413			0.458207	+	0.888846i	$0.348492\pi$
$60$		0			0
$61$	72.0000			0.151125			0.0755627	−	0.997141i	$-0.475925\pi$
$61$	72.0000			0.151125			0.0755627	+	0.997141i	$0.475925\pi$
$62$	329.439	−	64.1090i	0.674819	−	0.131320i
$63$	−190.066	−	190.066i	−0.380096	−	0.380096i
$64$	−207.654	+	468.000i	−0.405573	+	0.914062i
$65$		0			0
$66$	−440.000	−	296.648i	−0.820610	−	0.553255i
$67$	−597.030	+	597.030i	−1.08864	+	1.08864i	−0.0929706	+	0.995669i	$0.529636\pi$
$67$	−597.030	+	597.030i	−1.08864	+	1.08864i	−0.995669	+	0.0929706i	$0.970364\pi$
$68$	−829.119	−	351.525i	−1.47861	−	0.626892i
$69$		−	470.000i		−	0.820020i
$70$		0			0
$71$		−	711.955i		−	1.19005i	−0.803707	−	0.595025i	$-0.797142\pi$
$71$		−	711.955i		−	1.19005i	0.803707	−	0.595025i	$-0.202858\pi$
$72$	322.475	−	209.709i	0.527833	−	0.343257i
$73$	−504.127	+	504.127i	−0.808268	+	0.808268i	−0.984372	−	0.176103i	$-0.943651\pi$
$73$	−504.127	+	504.127i	−0.808268	+	0.808268i	0.176103	+	0.984372i	$0.443651\pi$
$74$	474.637	−	704.000i	0.745613	−	1.10592i
$75$		0			0
$76$	440.000	−	177.989i	0.664098	−	0.268641i
$77$	−663.325	−	663.325i	−0.981726	−	0.981726i
$78$	−64.1090	−	329.439i	−0.0930630	−	0.478226i
$79$	−830.614			−1.18293			−0.591465	−	0.806331i	$-0.701450\pi$
$79$	−830.614			−1.18293			−0.591465	+	0.806331i	$0.701450\pi$
$80$		0			0
$81$	−19.0000			−0.0260631
$82$	101.572	+	521.953i	0.136790	+	0.702928i
$83$	221.371	+	221.371i	0.292754	+	0.292754i	0.838167	−	0.545413i	$-0.183627\pi$
$83$	221.371	+	221.371i	0.292754	+	0.292754i	−0.545413	+	0.838167i	$0.683627\pi$
$84$	−370.810	+	150.000i	−0.481651	+	0.194837i
$85$		0			0
$86$	275.000	−	407.891i	0.344814	−	0.511442i
$87$	−102.859	+	102.859i	−0.126755	+	0.126755i
$88$	1125.43	−	731.881i	1.36331	−	0.886577i
$89$			726.000i			0.864672i	0.901712	+	0.432336i	$0.142311\pi$
$89$			726.000i			0.864672i	−0.901712	+	0.432336i	$0.857689\pi$
$90$		0			0
$91$		−	593.296i		−	0.683454i
$92$	1094.69	+	464.121i	1.24054	+	0.525956i
$93$	−265.330	+	265.330i	−0.295843	+	0.295843i
$94$	−645.209	−	435.000i	−0.707960	−	0.477307i
$95$		0			0
$96$	−100.000	−	563.631i	−0.106315	−	0.599222i
$97$	−451.061	−	451.061i	−0.472147	−	0.472147i	0.430461	−	0.902609i	$-0.358351\pi$
$97$	−451.061	−	451.061i	−0.472147	−	0.472147i	−0.902609	+	0.430461i	$0.858351\pi$
$98$	258.200	−	50.2459i	0.266144	−	0.0517919i
$99$	−1008.60			−1.02392
$100$		0			0
$101$	1382.00			1.36153			0.680763	−	0.732504i	$-0.261648\pi$
$101$	1382.00			1.36153			0.680763	+	0.732504i	$0.261648\pi$
$102$	988.317	−	192.327i	0.959392	−	0.186698i
$103$	1053.19	+	1053.19i	1.00751	+	1.00751i	0.999972	+	0.00754007i	$0.00240010\pi$
$103$	1053.19	+	1053.19i	1.00751	+	1.00751i	0.00754007	+	0.999972i	$0.497600\pi$
$104$	830.614	+	176.000i	0.783158	+	0.165944i
$105$		0			0
$106$	−88.0000	−	59.3296i	−0.0806351	−	0.0543641i
$107$	−547.837	+	547.837i	−0.494966	+	0.494966i	−0.909867	−	0.414901i	$-0.863816\pi$
$107$	−547.837	+	547.837i	−0.494966	+	0.494966i	0.414901	+	0.909867i	$0.363816\pi$
$108$	−434.496	+	1024.82i	−0.387124	+	0.913085i
$109$		−	784.000i		−	0.688932i	−0.938799	−	0.344466i	$-0.888060\pi$
$109$		−	784.000i		−	0.688932i	0.938799	−	0.344466i	$-0.111940\pi$
$110$		0			0
$111$			949.273i			0.811721i
$112$	16.8019	−	1011.79i	0.0141753	−	0.853617i
$113$	159.198	−	159.198i	0.132532	−	0.132532i	−0.637729	−	0.770261i	$-0.720126\pi$
$113$	159.198	−	159.198i	0.132532	−	0.132532i	0.770261	+	0.637729i	$0.220126\pi$
$114$	−296.648	+	440.000i	−0.243716	+	0.361489i
$115$		0			0
$116$	−138.000	−	341.145i	−0.110457	−	0.273056i
$117$	−451.061	−	451.061i	−0.356415	−	0.356415i
$118$	−224.381	−	1153.04i	−0.175051	−	0.899539i
$119$	1779.89			1.37111
$120$		0			0
$121$	−2189.00			−1.64463
$122$	−38.9000	−	199.897i	−0.0288676	−	0.148343i
$123$	−420.381	−	420.381i	−0.308166	−	0.308166i
$124$	−355.978	−	880.000i	−0.257804	−	0.637309i
$125$		0			0
$126$	−425.000	+	630.377i	−0.300492	+	0.445702i
$127$	762.499	−	762.499i	0.532763	−	0.532763i	−0.388631	−	0.921394i	$-0.627052\pi$
$127$	762.499	−	762.499i	0.532763	−	0.532763i	0.921394	+	0.388631i	$0.127052\pi$
$128$	1411.52	+	323.668i	0.974703	+	0.223504i
$129$			550.000i			0.375386i
$130$		0			0
$131$		−	177.989i		−	0.118710i	−0.998237	−	0.0593548i	$-0.981096\pi$
$131$		−	177.989i		−	0.118710i	0.998237	−	0.0593548i	$-0.0189043\pi$
$132$	−585.875	+	1381.86i	−0.386317	+	0.911181i
$133$	−663.325	+	663.325i	−0.432463	+	0.432463i
$134$	1980.12	+	1335.00i	1.27654	+	0.860645i
$135$		0			0
$136$	−528.000	+	2491.84i	−0.332909	+	1.57113i
$137$	477.594	+	477.594i	0.297837	+	0.297837i	0.840166	−	0.542329i	$-0.182458\pi$
$137$	477.594	+	477.594i	0.297837	+	0.297837i	−0.542329	+	0.840166i	$0.682458\pi$
$138$	−1304.88	+	253.931i	−0.804920	+	0.156638i
$139$	771.285			0.470644			0.235322	−	0.971917i	$-0.424386\pi$
$139$	771.285			0.470644			0.235322	+	0.971917i	$0.424386\pi$
$140$		0			0
$141$	870.000			0.519626
$142$	−1976.63	+	384.654i	−1.16814	+	0.227320i
$143$	−1574.19	−	1574.19i	−0.920563	−	0.920563i
$144$	−756.452	−	782.000i	−0.437762	−	0.452546i
$145$		0			0
$146$	1672.00	+	1127.26i	0.947779	+	0.638992i
$147$	−207.954	+	207.954i	−0.116679	+	0.116679i
$148$	−2210.98	−	937.400i	−1.22798	−	0.520634i
$149$		−	104.000i		−	0.0571813i	−0.999591	−	0.0285906i	$-0.990898\pi$
$149$		−	104.000i		−	0.0571813i	0.999591	−	0.0285906i	$-0.00910193\pi$
$150$		0			0
$151$			1779.89i			0.959240i	0.877476	+	0.479620i	$0.159225\pi$
$151$			1779.89i			0.959240i	−0.877476	+	0.479620i	$0.840775\pi$
$152$	−731.881	−	1125.43i	−0.390549	−	0.600555i
$153$	1353.18	−	1353.18i	0.715022	−	0.715022i
$154$	−1483.24	+	2200.00i	−0.776122	+	1.15118i
$155$		0			0
$156$	−880.000	+	355.978i	−0.451644	+	0.182699i
$157$	2600.23	+	2600.23i	1.32179	+	1.32179i	0.912325	+	0.409466i	$0.134285\pi$
$157$	2600.23	+	2600.23i	1.32179	+	1.32179i	0.409466	+	0.912325i	$0.365715\pi$
$158$	448.763	+	2306.07i	0.225960	+	1.16115i
$159$	118.659			0.0591842
$160$		0			0
$161$	−2350.00			−1.15035
$162$	10.2653	+	52.7506i	0.00497850	+	0.0255832i
$163$	15.6525	+	15.6525i	0.00752145	+	0.00752145i	0.710858	−	0.703336i	$-0.248307\pi$
$163$	15.6525	+	15.6525i	0.00752145	+	0.00752145i	−0.703336	+	0.710858i	$0.748307\pi$
$164$	1394.25	−	564.000i	0.663855	−	0.268543i
$165$		0			0
$166$	495.000	−	734.204i	0.231442	−	0.343285i
$167$	73.7902	−	73.7902i	0.0341920	−	0.0341920i	−0.689804	−	0.723996i	$-0.742303\pi$
$167$	73.7902	−	73.7902i	0.0341920	−	0.0341920i	0.723996	+	0.689804i	$0.242303\pi$
$168$	616.793	+	948.455i	0.283253	+	0.435565i
$169$			789.000i			0.359126i
$170$		0			0
$171$			1008.60i			0.451051i
$172$	−1281.02	−	543.121i	−0.567890	−	0.240771i
$173$	2281.84	−	2281.84i	1.00280	−	1.00280i	0.00280694	−	0.999996i	$-0.499107\pi$
$173$	2281.84	−	2281.84i	1.00280	−	1.00280i	0.999996	−	0.00280694i	$-0.000893479\pi$
$174$	341.145	+	230.000i	0.148633	+	0.100208i
$175$		0			0
$176$	−2640.00	−	2729.16i	−1.13067	−	1.16885i
$177$	928.655	+	928.655i	0.394361	+	0.394361i
$178$	2015.63	−	392.242i	0.848751	−	0.165167i
$179$	652.625			0.272511			0.136256	−	0.990674i	$-0.456493\pi$
$179$	652.625			0.272511			0.136256	+	0.990674i	$0.456493\pi$
$180$		0			0
$181$	4202.00			1.72559			0.862796	−	0.505552i	$-0.168711\pi$
$181$	4202.00			1.72559			0.862796	+	0.505552i	$0.168711\pi$
$182$	−1647.19	+	320.545i	−0.670869	+	0.130551i
$183$	160.997	+	160.997i	0.0650341	+	0.0650341i
$184$	697.123	−	3290.00i	0.279307	−	1.31816i
$185$		0			0
$186$	880.000	+	593.296i	0.346907	+	0.233885i
$187$	4722.58	−	4722.58i	1.84679	−	1.84679i
$188$	−859.118	+	2026.35i	−0.333285	+	0.786098i
$189$		−	2200.00i		−	0.846701i
$190$		0			0
$191$		−	3797.09i		−	1.43847i	−0.694766	−	0.719236i	$-0.744492\pi$
$191$		−	3797.09i		−	1.43847i	0.694766	−	0.719236i	$-0.255508\pi$
$192$	−1510.81	+	582.152i	−0.567881	+	0.218819i
$193$	−1830.78	+	1830.78i	−0.682809	+	0.682809i	−0.960632	−	0.277823i	$-0.910387\pi$
$193$	−1830.78	+	1830.78i	−0.682809	+	0.682809i	0.277823	+	0.960632i	$0.410387\pi$
$194$	−1008.60	+	1496.00i	−0.373265	+	0.553642i
$195$		0			0
$196$	−279.000	−	689.706i	−0.101676	−	0.251351i
$197$	−185.731	−	185.731i	−0.0671715	−	0.0671715i	0.672723	−	0.739894i	$-0.265125\pi$
$197$	−185.731	−	185.731i	−0.0671715	−	0.0671715i	−0.739894	+	0.672723i	$0.765125\pi$
$198$	544.926	+	2800.23i	0.195587	+	1.00507i
$199$	−4746.37			−1.69076			−0.845379	−	0.534166i	$-0.820626\pi$
$199$	−4746.37			−1.69076			−0.845379	+	0.534166i	$0.820626\pi$
$200$		0			0
$201$	−2670.00			−0.936952
$202$	−746.665	−	3836.91i	−0.260075	−	1.33646i
$203$	514.296	+	514.296i	0.177815	+	0.177815i
$204$	−1067.93	−	2640.00i	−0.366521	−	0.906064i
$205$		0			0
$206$	2355.00	−	3493.03i	0.796508	−	1.18141i
$207$	−1786.62	+	1786.62i	−0.599896	+	0.599896i
$208$	39.8740	−	2401.16i	0.0132921	−	0.800436i
$209$			3520.00i			1.16499i
$210$		0			0
$211$		−	652.625i		−	0.212932i	−0.994316	−	0.106466i	$-0.966047\pi$
$211$		−	652.625i		−	0.212932i	0.994316	−	0.106466i	$-0.0339535\pi$
$212$	−117.175	+	276.373i	−0.0379604	+	0.0895348i
$213$	1591.98	−	1591.98i	0.512116	−	0.512116i
$214$	1816.97	+	1225.00i	0.580399	+	0.391305i
$215$		0			0
$216$	3080.00	+	652.625i	0.970220	+	0.205581i
$217$	1326.65	+	1326.65i	0.415018	+	0.415018i
$218$	−2176.66	+	423.578i	−0.676246	+	0.131598i
$219$	−2254.52			−0.695647
$220$		0			0
$221$	4224.00			1.28569
$222$	2635.51	−	512.872i	0.796775	−	0.155053i
$223$	−149.817	−	149.817i	−0.0449886	−	0.0449886i	0.684255	−	0.729243i	$-0.260128\pi$
$223$	−149.817	−	149.817i	−0.0449886	−	0.0449886i	−0.729243	+	0.684255i	$0.760128\pi$
$224$	−2818.16	+	500.000i	−0.840607	+	0.149141i
$225$		0			0
$226$	−528.000	−	355.978i	−0.155407	−	0.104776i
$227$	−1451.21	+	1451.21i	−0.424317	+	0.424317i	−0.886687	−	0.462370i	$-0.846999\pi$
$227$	−1451.21	+	1451.21i	−0.424317	+	0.424317i	0.462370	+	0.886687i	$0.346999\pi$
$228$	1381.86	+	585.875i	0.401387	+	0.170178i
$229$		−	3334.00i		−	0.962083i	−0.876698	−	0.481041i	$-0.840259\pi$
$229$		−	3334.00i		−	0.962083i	0.876698	−	0.481041i	$-0.159741\pi$
$230$		0			0
$231$		−	2966.48i		−	0.844935i
$232$	−872.579	+	567.449i	−0.246929	+	0.160581i
$233$	1087.85	−	1087.85i	0.305870	−	0.305870i	−0.537435	−	0.843305i	$-0.680607\pi$
$233$	1087.85	−	1087.85i	0.305870	−	0.305870i	0.843305	+	0.537435i	$0.180607\pi$
$234$	−1008.60	+	1496.00i	−0.281771	+	0.417934i
$235$		0			0
$236$	−3080.00	+	1245.92i	−0.849538	+	0.343655i
$237$	−1857.31	−	1857.31i	−0.509052	−	0.509052i
$238$	−961.635	−	4941.58i	−0.261906	−	1.34586i
$239$	3441.12			0.931328			0.465664	−	0.884962i	$-0.345816\pi$
$239$	3441.12			0.931328			0.465664	+	0.884962i	$0.345816\pi$
$240$		0			0
$241$	−3028.00			−0.809339			−0.404669	−	0.914463i	$-0.632613\pi$
$241$	−3028.00			−0.809339			−0.404669	+	0.914463i	$0.632613\pi$
$242$	1182.67	+	6077.42i	0.314152	+	1.61435i
$243$	−2698.93	−	2698.93i	−0.712497	−	0.712497i
$244$	−533.966	+	216.000i	−0.140097	+	0.0566721i
$245$		0			0
$246$	−940.000	+	1394.25i	−0.243627	+	0.361357i
$247$	−1574.19	+	1574.19i	−0.405520	+	0.405520i
$248$	−2250.86	+	1463.76i	−0.576329	+	0.374794i
$249$			990.000i			0.251963i
$250$		0			0
$251$			2076.54i			0.522190i	0.965313	+	0.261095i	$0.0840836\pi$
$251$			2076.54i			0.522190i	−0.965313	+	0.261095i	$0.915916\pi$
$252$	1979.76	+	839.368i	0.494894	+	0.209822i
$253$	−6235.25	+	6235.25i	−1.54944	+	1.54944i
$254$	−2528.92	−	1705.00i	−0.624720	−	0.421186i
$255$		0			0
$256$	136.000	−	4093.74i	0.0332031	−	0.999449i
$257$	−2441.04	−	2441.04i	−0.592481	−	0.592481i	0.345820	−	0.938301i	$-0.387601\pi$
$257$	−2441.04	−	2441.04i	−0.592481	−	0.592481i	−0.938301	+	0.345820i	$0.887601\pi$
$258$	1526.99	−	297.153i	0.368474	−	0.0717052i
$259$	4746.37			1.13871
$260$		0			0
$261$	782.000			0.185458
$262$	−494.158	+	96.1635i	−0.116524	+	0.0226756i
$263$	1402.01	+	1402.01i	0.328715	+	0.328715i	0.852098	−	0.523383i	$-0.175330\pi$
$263$	1402.01	+	1402.01i	0.328715	+	0.328715i	−0.523383	+	0.852098i	$0.675330\pi$
$264$	4153.07	+	880.000i	0.968196	+	0.205152i
$265$		0			0
$266$	2200.00	+	1483.24i	0.507108	+	0.341892i
$267$	−1623.39	+	1623.39i	−0.372096	+	0.372096i
$268$	2636.60	−	6218.78i	0.600956	−	1.41744i
$269$		−	5544.00i		−	1.25659i	−0.777974	−	0.628297i	$-0.783752\pi$
$269$		−	5544.00i		−	1.25659i	0.777974	−	0.628297i	$-0.216248\pi$
$270$		0			0
$271$			4627.71i			1.03732i	0.854981	+	0.518659i	$0.173569\pi$
$271$			4627.71i			1.03732i	−0.854981	+	0.518659i	$0.826431\pi$
$272$	7203.49	+	119.622i	1.60579	+	0.0266660i
$273$	1326.65	−	1326.65i	0.294112	−	0.294112i
$274$	1067.93	−	1584.00i	0.235460	−	0.349244i
$275$		0			0
$276$	1410.00	+	3485.61i	0.307507	+	0.760178i
$277$	−1379.72	−	1379.72i	−0.299275	−	0.299275i	0.541455	−	0.840730i	$-0.317874\pi$
$277$	−1379.72	−	1379.72i	−0.299275	−	0.299275i	−0.840730	+	0.541455i	$0.817874\pi$
$278$	−416.708	−	2141.35i	−0.0899011	−	0.461978i
$279$	2017.21			0.432857
$280$		0			0
$281$	−5308.00			−1.12686			−0.563432	−	0.826163i	$-0.690519\pi$
$281$	−5308.00			−1.12686			−0.563432	+	0.826163i	$0.690519\pi$
$282$	−470.042	−	2415.42i	−0.0992575	−	0.510058i
$283$	4894.75	+	4894.75i	1.02814	+	1.02814i	0.999593	+	0.0285448i	$0.00908732\pi$
$283$	4894.75	+	4894.75i	1.02814	+	1.02814i	0.0285448	+	0.999593i	$0.490913\pi$
$284$	2135.87	+	5280.00i	0.446269	+	1.10321i
$285$		0			0
$286$	−3520.00	+	5221.00i	−0.727769	+	1.07946i
$287$	−2101.90	+	2101.90i	−0.432305	+	0.432305i
$288$	−1762.41	+	2522.67i	−0.360593	+	0.516145i
$289$			7759.00i			1.57928i
$290$		0			0
$291$		−	2017.21i		−	0.406360i
$292$	2226.32	−	5251.09i	0.446184	−	1.05239i
$293$	−371.462	+	371.462i	−0.0740650	+	0.0740650i	−0.743169	−	0.669104i	$-0.766678\pi$
$293$	−371.462	+	371.462i	−0.0740650	+	0.0740650i	0.669104	+	0.743169i	$0.266678\pi$
$294$	689.706	+	465.000i	0.136818	+	0.0922427i
$295$		0			0
$296$	−1408.00	+	6644.91i	−0.276481	+	1.30482i
$297$	−5837.26	−	5837.26i	−1.14044	−	1.14044i
$298$	−288.740	+	56.1890i	−0.0561284	+	0.0109226i
$299$	−5576.98			−1.07868
$300$		0			0
$301$	2750.00			0.526603
$302$	4941.58	−	961.635i	0.941577	−	0.183231i
$303$	3090.25	+	3090.25i	0.585908	+	0.585908i
$304$	−2729.16	+	2640.00i	−0.514895	+	0.498074i
$305$		0			0
$306$	−4488.00	−	3025.81i	−0.838438	−	0.565274i
$307$	905.608	−	905.608i	0.168357	−	0.168357i	−0.617900	−	0.786257i	$-0.712016\pi$
$307$	905.608	−	905.608i	0.168357	−	0.168357i	0.786257	+	0.617900i	$0.212016\pi$
$308$	6909.32	+	2929.37i	1.27823	+	0.541937i
$309$			4710.00i			0.867128i
$310$		0			0
$311$			10323.3i			1.88226i	0.338043	+	0.941131i	$0.390235\pi$
$311$			10323.3i			1.88226i	−0.338043	+	0.941131i	$0.609765\pi$
$312$	1463.76	+	2250.86i	0.265606	+	0.408429i
$313$	−4882.07	+	4882.07i	−0.881633	+	0.881633i	−0.993701	−	0.112068i	$-0.964253\pi$
$313$	−4882.07	+	4882.07i	−0.881633	+	0.881633i	0.112068	+	0.993701i	$0.464253\pi$
$314$	5814.30	−	8624.00i	1.04497	−	1.54994i
$315$		0			0
$316$	6160.00	−	2491.84i	1.09660	−	0.443598i
$317$	−3104.36	−	3104.36i	−0.550026	−	0.550026i	0.376422	−	0.926448i	$-0.377154\pi$
$317$	−3104.36	−	3104.36i	−0.550026	−	0.550026i	−0.926448	+	0.376422i	$0.877154\pi$
$318$	−64.1090	−	329.439i	−0.0113052	−	0.0580944i
$319$	2729.16			0.479008
$320$		0			0
$321$	−2450.00			−0.425999
$322$	1269.65	+	6524.41i	0.219736	+	1.12917i
$323$	−4722.58	−	4722.58i	−0.813533	−	0.813533i
$324$	140.908	−	57.0000i	0.0241611	−	0.00977366i
$325$		0			0
$326$	35.0000	−	51.9134i	0.00594623	−	0.00881968i
$327$	1753.08	−	1753.08i	0.296469	−	0.296469i
$328$	−2319.14	−	3566.19i	−0.390406	−	0.600335i
$329$		−	4350.00i		−	0.728946i
$330$		0			0
$331$		−	3144.47i		−	0.522162i	−0.965317	−	0.261081i	$-0.915921\pi$
$331$		−	3144.47i		−	0.522162i	0.965317	−	0.261081i	$-0.0840790\pi$
$332$	−2305.84	−	977.617i	−0.381173	−	0.161608i
$333$	3608.49	−	3608.49i	0.593826	−	0.593826i
$334$	−244.735	−	165.000i	−0.0400936	−	0.0270311i
$335$		0			0
$336$	2300.00	−	2224.86i	0.373438	−	0.361238i
$337$	4988.20	+	4988.20i	0.806305	+	0.806305i	0.984073	−	0.177768i	$-0.0568875\pi$
$337$	4988.20	+	4988.20i	0.806305	+	0.806305i	−0.177768	+	0.984073i	$0.556888\pi$
$338$	2190.54	−	426.280i	0.352513	−	0.0685993i
$339$	711.955			0.114065
$340$		0			0
$341$	7040.00			1.11800
$342$	2800.23	−	544.926i	0.442746	−	0.0861586i
$343$	4874.63	+	4874.63i	0.767362	+	0.767362i
$344$	−815.782	+	3850.00i	−0.127860	+	0.603425i
$345$		0			0
$346$	−7568.00	−	5102.34i	−1.17589	−	0.792785i
$347$	−3360.81	+	3360.81i	−0.519936	+	0.519936i	−0.917552	−	0.397616i	$-0.869838\pi$
$347$	−3360.81	+	3360.81i	−0.519936	+	0.519936i	0.397616	+	0.917552i	$0.369838\pi$
$348$	454.246	−	1071.40i	0.0699717	−	0.165038i
$349$		−	5774.00i		−	0.885602i	−0.896620	−	0.442801i	$-0.853985\pi$
$349$		−	5774.00i		−	0.885602i	0.896620	−	0.442801i	$-0.146015\pi$
$350$		0			0
$351$		−	5221.00i		−	0.793950i
$352$	−6150.76	+	8804.06i	−0.931354	+	1.33312i
$353$	424.528	−	424.528i	0.0640095	−	0.0640095i	−0.674377	−	0.738387i	$-0.735588\pi$
$353$	424.528	−	424.528i	0.0640095	−	0.0640095i	0.738387	+	0.674377i	$0.235588\pi$
$354$	2076.54	−	3080.00i	0.311770	−	0.462430i
$355$		0			0
$356$	−2178.00	−	5384.16i	−0.324252	−	0.801573i
$357$	3979.95	+	3979.95i	0.590032	+	0.590032i
$358$	−352.599	−	1811.91i	−0.0520544	−	0.267493i
$359$	−7000.89			−1.02923			−0.514614	−	0.857422i	$-0.672065\pi$
$359$	−7000.89			−1.02923			−0.514614	+	0.857422i	$0.672065\pi$
$360$		0			0
$361$	−3339.00			−0.486806
$362$	−2270.25	−	11666.2i	−0.329618	−	1.69382i
$363$	−4894.75	−	4894.75i	−0.707735	−	0.707735i
$364$	1779.89	+	4400.00i	0.256295	+	0.633579i
$365$		0			0
$366$	360.000	−	533.966i	0.0514139	−	0.0762592i
$367$	−1603.26	+	1603.26i	−0.228037	+	0.228037i	−0.811872	−	0.583835i	$-0.801551\pi$
$367$	−1603.26	+	1603.26i	−0.228037	+	0.228037i	0.583835	+	0.811872i	$0.301551\pi$
$368$	−9510.82	−	157.938i	−1.34724	−	0.0223725i
$369$			3196.00i			0.450886i
$370$		0			0
$371$		−	593.296i		−	0.0830253i
$372$	1171.75	−	2763.73i	0.163313	−	0.385195i
$373$	1220.52	−	1220.52i	0.169426	−	0.169426i	−0.617301	−	0.786727i	$-0.711774\pi$
$373$	1220.52	−	1220.52i	0.169426	−	0.169426i	0.786727	+	0.617301i	$0.211774\pi$
$374$	−15663.0	−	10560.0i	−2.16555	−	1.46001i
$375$		0			0
$376$	6090.00	+	1290.42i	0.835287	+	0.176990i
$377$	1220.52	+	1220.52i	0.166737	+	0.166737i
$378$	−6107.96	+	1188.61i	−0.831110	+	0.161734i
$379$	1839.22			0.249272			0.124636	−	0.992203i	$-0.460224\pi$
$379$	1839.22			0.249272			0.124636	+	0.992203i	$0.460224\pi$
$380$		0			0
$381$	3410.00			0.458529
$382$	−10542.0	+	2051.49i	−1.41198	+	0.274773i
$383$	−8789.98	−	8789.98i	−1.17271	−	1.17271i	−0.981562	−	0.191146i	$-0.938779\pi$
$383$	−8789.98	−	8789.98i	−1.17271	−	1.17271i	−0.191146	−	0.981562i	$-0.561221\pi$
$384$	2432.51	+	3880.00i	0.323265	+	0.515626i
$385$		0			0
$386$	6072.00	+	4093.74i	0.800665	+	0.539808i
$387$	2090.72	−	2090.72i	0.274619	−	0.274619i
$388$	4698.34	+	1991.97i	0.614748	+	0.260637i
$389$			3096.00i			0.403531i	0.979434	+	0.201765i	$0.0646678\pi$
$389$			3096.00i			0.403531i	−0.979434	+	0.201765i	$0.935332\pi$
$390$		0			0
$391$		−	16730.9i		−	2.16399i
$392$	−1764.13	+	1147.23i	−0.227301	+	0.147817i
$393$	397.995	−	397.995i	0.0510845	−	0.0510845i
$394$	−415.307	+	616.000i	−0.0531037	+	0.0787656i
$395$		0			0
$396$	7480.00	−	3025.81i	0.949202	−	0.383971i
$397$	2998.23	+	2998.23i	0.379035	+	0.379035i	0.870754	−	0.491719i	$-0.163631\pi$
$397$	2998.23	+	2998.23i	0.379035	+	0.379035i	−0.491719	+	0.870754i	$0.663631\pi$
$398$	2564.36	+	13177.6i	0.322964	+	1.65963i
$399$	−2966.48			−0.372205
$400$		0			0
$401$	−1778.00			−0.221419			−0.110710	−	0.993853i	$-0.535312\pi$
$401$	−1778.00			−0.221419			−0.110710	+	0.993853i	$0.535312\pi$
$402$	1442.54	+	7412.84i	0.178974	+	0.919699i
$403$	3148.38	+	3148.38i	0.389162	+	0.389162i
$404$	−10249.2	+	4146.00i	−1.26217	+	0.510572i
$405$		0			0
$406$	1150.00	−	1705.73i	0.140575	−	0.208507i
$407$	12593.5	−	12593.5i	1.53376	−	1.53376i
$408$	−6752.57	+	4391.29i	−0.819368	+	0.532846i
$409$		−	5804.00i		−	0.701685i	−0.936434	−	0.350843i	$-0.885895\pi$
$409$		−	5804.00i		−	0.701685i	0.936434	−	0.350843i	$-0.114105\pi$
$410$		0			0
$411$			2135.87i			0.256337i
$412$	−10970.2	−	4651.09i	−1.31181	−	0.556171i
$413$	4643.27	−	4643.27i	0.553222	−	0.553222i
$414$	5925.54	+	3995.00i	0.703441	+	0.474260i
$415$		0			0
$416$	−6688.00	+	1186.59i	−0.788236	+	0.139850i
$417$	1724.64	+	1724.64i	0.202533	+	0.202533i
$418$	9772.74	−	1901.78i	1.14354	−	0.222534i
$419$	−4805.70			−0.560319			−0.280159	−	0.959953i	$-0.590387\pi$
$419$	−4805.70			−0.560319			−0.280159	+	0.959953i	$0.590387\pi$
$420$		0			0
$421$	1672.00			0.193559			0.0967794	−	0.995306i	$-0.469146\pi$
$421$	1672.00			0.193559			0.0967794	+	0.995306i	$0.469146\pi$
$422$	−1811.91	+	352.599i	−0.209011	+	0.0406736i
$423$	−3307.14	−	3307.14i	−0.380139	−	0.380139i
$424$	830.614	+	176.000i	0.0951372	+	0.0201588i
$425$		0			0
$426$	−5280.00	−	3559.78i	−0.600509	−	0.404863i
$427$	804.984	−	804.984i	0.0912317	−	0.0912317i
$428$	2419.36	−	5706.38i	0.273234	−	0.644458i
$429$		−	7040.00i		−	0.792295i
$430$		0			0
$431$			118.659i			0.0132613i	0.999978	+	0.00663064i	$0.00211061\pi$
$431$			118.659i			0.0132613i	−0.999978	+	0.00663064i	$0.997889\pi$
$432$	147.857	−	8903.75i	0.0164671	−	0.991624i
$433$	6394.45	−	6394.45i	0.709695	−	0.709695i	−0.256776	−	0.966471i	$-0.582660\pi$
$433$	6394.45	−	6394.45i	0.709695	−	0.709695i	0.966471	+	0.256776i	$0.0826603\pi$
$434$	2966.48	−	4400.00i	0.328100	−	0.486652i
$435$		0			0
$436$	2352.00	+	5814.30i	0.258349	+	0.638657i
$437$	6235.25	+	6235.25i	0.682546	+	0.682546i
$438$	1218.07	+	6259.34i	0.132881	+	0.682838i
$439$	10560.7			1.14814			0.574070	−	0.818806i	$-0.305364\pi$
$439$	10560.7			1.14814			0.574070	+	0.818806i	$0.305364\pi$
$440$		0			0
$441$	1581.00			0.170716
$442$	−2282.14	−	11727.3i	−0.245589	−	1.26201i
$443$	12153.0	+	12153.0i	1.30340	+	1.30340i	0.926082	+	0.377321i	$0.123155\pi$
$443$	12153.0	+	12153.0i	1.30340	+	1.30340i	0.377321	+	0.926082i	$0.376845\pi$
$444$	−2847.82	−	7040.00i	−0.304395	−	0.752486i
$445$		0			0
$446$	−335.000	+	496.885i	−0.0355666	+	0.0527538i
$447$	232.551	−	232.551i	0.0246069	−	0.0246069i
$448$	2910.76	+	7554.04i	0.306966	+	0.796640i
$449$			2476.00i			0.260244i	0.991498	+	0.130122i	$0.0415369\pi$
$449$			2476.00i			0.260244i	−0.991498	+	0.130122i	$0.958463\pi$
$450$		0			0
$451$			11154.0i			1.16457i
$452$	−703.050	+	1658.24i	−0.0731608	+	0.172560i
$453$	−3979.95	+	3979.95i	−0.412791	+	0.412791i
$454$	4813.11	+	3245.00i	0.497556	+	0.335452i
$455$		0			0
$456$	880.000	−	4153.07i	0.0903723	−	0.426503i
$457$	8702.82	+	8702.82i	0.890812	+	0.890812i	0.994599	−	0.103788i	$-0.0330963\pi$
$457$	8702.82	+	8702.82i	0.890812	+	0.890812i	−0.103788	+	0.994599i	$0.533096\pi$
$458$	−9256.34	+	1801.29i	−0.944367	+	0.183774i
$459$	15663.0			1.59278
$460$		0			0
$461$	−13918.0			−1.40613			−0.703065	−	0.711126i	$-0.748186\pi$
$461$	−13918.0			−1.40613			−0.703065	+	0.711126i	$0.748186\pi$
$462$	−8235.97	+	1602.72i	−0.829377	+	0.161397i
$463$	−3204.29	−	3204.29i	−0.321632	−	0.321632i	0.527761	−	0.849393i	$-0.323032\pi$
$463$	−3204.29	−	3204.29i	−0.321632	−	0.321632i	−0.849393	+	0.527761i	$0.823032\pi$
$464$	2046.87	+	2116.00i	0.204792	+	0.211709i
$465$		0			0
$466$	−3608.00	−	2432.51i	−0.358664	−	0.241811i
$467$	1415.43	−	1415.43i	0.140253	−	0.140253i	−0.633494	−	0.773748i	$-0.718380\pi$
$467$	1415.43	−	1415.43i	0.140253	−	0.140253i	0.773748	+	0.633494i	$0.218380\pi$
$468$	4698.34	+	1991.97i	0.464062	+	0.196750i
$469$			13350.0i			1.31438i
$470$		0			0
$471$			11628.6i			1.13762i
$472$	5123.17	+	7878.00i	0.499604	+	0.768251i
$473$	7296.57	−	7296.57i	0.709296	−	0.709296i
$474$	−4153.07	+	6160.00i	−0.402441	+	0.596916i
$475$		0			0
$476$	−13200.0	+	5339.66i	−1.27105	+	0.514166i
$477$	−451.061	−	451.061i	−0.0432970	−	0.0432970i
$478$	−1859.16	−	9553.73i	−0.177900	−	0.914179i
$479$	−14476.4			−1.38089			−0.690443	−	0.723387i	$-0.742584\pi$
$479$	−14476.4			−1.38089			−0.690443	+	0.723387i	$0.742584\pi$
$480$		0			0
$481$	11264.0			1.06776
$482$	1635.96	+	8406.78i	0.154598	+	0.794436i
$483$	−5254.76	−	5254.76i	−0.495031	−	0.495031i
$484$	16234.1	−	6567.00i	1.52461	−	0.616736i
$485$		0			0
$486$	−6035.00	+	8951.35i	−0.563278	+	0.835476i
$487$	−494.171	+	494.171i	−0.0459816	+	0.0459816i	−0.729724	−	0.683742i	$-0.760351\pi$
$487$	−494.171	+	494.171i	−0.0459816	+	0.0459816i	0.683742	+	0.729724i	$0.260351\pi$
$488$	888.181	+	1365.78i	0.0823895	+	0.126692i
$489$			70.0000i			0.00647343i
$490$		0			0
$491$			1245.92i			0.114517i	0.998359	+	0.0572583i	$0.0182359\pi$
$491$			1245.92i			0.114517i	−0.998359	+	0.0572583i	$0.981764\pi$
$492$	4378.77	+	1856.48i	0.401240	+	0.170115i
$493$	−3661.55	+	3661.55i	−0.334499	+	0.334499i
$494$	5221.00	+	3520.00i	0.475514	+	0.320592i
$495$		0			0
$496$	5280.00	+	5458.32i	0.477982	+	0.494125i
$497$	−7959.90	−	7959.90i	−0.718411	−	0.718411i
$498$	2748.58	−	534.876i	0.247323	−	0.0481292i
$499$	−11569.3			−1.03790			−0.518950	−	0.854805i	$-0.673677\pi$
$499$	−11569.3			−1.03790			−0.518950	+	0.854805i	$0.673677\pi$
$500$		0			0
$501$	330.000			0.0294278
$502$	5765.18	−	1121.91i	0.512575	−	0.0997474i
$503$	−6549.44	−	6549.44i	−0.580567	−	0.580567i	0.354492	−	0.935059i	$-0.384654\pi$
$503$	−6549.44	−	6549.44i	−0.580567	−	0.580567i	−0.935059	+	0.354492i	$0.884654\pi$
$504$	1260.75	−	5950.00i	0.111425	−	0.525861i
$505$		0			0
$506$	20680.0	+	13942.5i	1.81687	+	1.22494i
$507$	−1764.26	+	1764.26i	−0.154543	+	0.154543i
$508$	−3367.35	+	7942.34i	−0.294098	+	0.693670i
$509$		−	1554.00i		−	0.135324i	−0.997708	−	0.0676619i	$-0.978446\pi$
$509$		−	1554.00i		−	0.135324i	0.997708	−	0.0676619i	$-0.0215539\pi$
$510$		0			0
$511$			11272.6i			0.975874i
$512$	−11439.1	+	1834.18i	−0.987388	+	0.158320i
$513$	−5837.26	+	5837.26i	−0.502381	+	0.502381i
$514$	−5458.32	+	8096.00i	−0.468397	+	0.694746i
$515$		0			0
$516$	−1650.00	−	4078.91i	−0.140770	−	0.347992i
$517$	−11541.9	−	11541.9i	−0.981838	−	0.981838i
$518$	−2564.36	−	13177.6i	−0.217513	−	1.11774i
$519$	10204.7			0.863075
$520$		0			0
$521$	−5638.00			−0.474098			−0.237049	−	0.971498i	$-0.576180\pi$
$521$	−5638.00			−0.474098			−0.237049	+	0.971498i	$0.576180\pi$
$522$	−422.498	−	2171.10i	−0.0354257	−	0.182043i
$523$	−2475.33	−	2475.33i	−0.206957	−	0.206957i	0.596016	−	0.802973i	$-0.296750\pi$
$523$	−2475.33	−	2475.33i	−0.206957	−	0.206957i	−0.802973	+	0.596016i	$0.796750\pi$
$524$	533.966	+	1320.00i	0.0445161	+	0.110047i
$525$		0			0
$526$	3135.00	−	4649.96i	0.259872	−	0.385452i
$527$	−9445.15	+	9445.15i	−0.780716	+	0.780716i
$528$	199.370	−	12005.8i	0.0164327	−	0.989556i
$529$			9923.00i			0.815567i
$530$		0			0
$531$		−	7060.22i		−	0.577001i
$532$	2929.37	−	6909.32i	0.238730	−	0.563077i
$533$	−4988.20	+	4988.20i	−0.405372	+	0.405372i
$534$	5384.16	+	3630.00i	0.436321	+	0.294168i
$535$		0			0
$536$	−18690.0	−	3960.25i	−1.50613	−	0.319136i
$537$	1459.31	+	1459.31i	0.117270	+	0.117270i
$538$	−15392.1	+	2995.30i	−1.23346	+	0.240031i
$539$	5517.65			0.440932
$540$		0			0
$541$	−16078.0			−1.27772			−0.638861	−	0.769322i	$-0.720594\pi$
$541$	−16078.0			−1.27772			−0.638861	+	0.769322i	$0.720594\pi$
$542$	12848.1	−	2500.25i	1.01822	−	0.198146i
$543$	9395.96	+	9395.96i	0.742577	+	0.742577i
$544$	−3559.78	−	20064.0i	−0.280559	−	1.58132i
$545$		0			0
$546$	−4400.00	−	2966.48i	−0.344877	−	0.232516i
$547$	−7944.75	+	7944.75i	−0.621011	+	0.621011i	−0.945790	−	0.324779i	$-0.894710\pi$
$547$	−7944.75	+	7944.75i	−0.621011	+	0.621011i	0.324779	+	0.945790i	$0.394710\pi$
$548$	−4974.71	−	2109.15i	−0.387791	−	0.164413i
$549$		−	1224.00i		−	0.0951531i
$550$		0			0
$551$		−	2729.16i		−	0.211009i
$552$	8915.48	−	5797.85i	0.687442	−	0.447052i
$553$	−9286.55	+	9286.55i	−0.714113	+	0.714113i
$554$	−3085.14	+	4576.00i	−0.236597	+	0.350931i
$555$		0			0
$556$	−5720.00	+	2313.85i	−0.436299	+	0.176491i
$557$	1273.58	+	1273.58i	0.0968824	+	0.0968824i	0.753887	−	0.657004i	$-0.228177\pi$
$557$	1273.58	+	1273.58i	0.0968824	+	0.0968824i	−0.657004	+	0.753887i	$0.728177\pi$
$558$	−1089.85	−	5600.46i	−0.0826831	−	0.424886i
$559$	6526.25			0.493795
$560$		0			0
$561$	21120.0			1.58946
$562$	2867.80	+	14736.8i	0.215250	+	1.10611i
$563$	8803.40	+	8803.40i	0.659004	+	0.659004i	0.955144	−	0.296141i	$-0.0956997\pi$
$563$	8803.40	+	8803.40i	0.659004	+	0.659004i	−0.296141	+	0.955144i	$0.595700\pi$
$564$	−6452.09	+	2610.00i	−0.481706	+	0.194860i
$565$		0			0
$566$	10945.0	−	16234.1i	0.812814	−	1.20560i
$567$	−212.426	+	212.426i	−0.0157338	+	0.0157338i
$568$	13505.1	−	8782.57i	0.997647	−	0.648783i
$569$		−	24564.0i		−	1.80980i	−0.425624	−	0.904900i	$-0.639945\pi$
$569$		−	24564.0i		−	1.80980i	0.425624	−	0.904900i	$-0.360055\pi$
$570$		0			0
$571$		−	17027.6i		−	1.24796i	−0.781442	−	0.623978i	$-0.785516\pi$
$571$		−	17027.6i		−	1.24796i	0.781442	−	0.623978i	$-0.214484\pi$
$572$	16397.1	+	6951.94i	1.19860	+	0.508174i
$573$	8490.56	−	8490.56i	0.619020	−	0.619020i
$574$	6971.23	+	4700.00i	0.506922	+	0.341767i
$575$		0			0
$576$	7956.00	+	3530.11i	0.575521	+	0.255361i
$577$	−13850.2	−	13850.2i	−0.999294	−	0.999294i	0.000706135	−	1.00000i	$-0.499775\pi$
$577$	−13850.2	−	13850.2i	−0.999294	−	0.999294i	−1.00000		0.000706135i	$0.999775\pi$
$578$	21541.7	−	4192.02i	1.55020	−	0.301670i
$579$	−8187.48			−0.587669
$580$		0			0
$581$	4950.00			0.353461
$582$	−5600.46	+	1089.85i	−0.398877	+	0.0776217i
$583$	−1574.19	−	1574.19i	−0.111829	−	0.111829i
$584$	−15781.7	−	3344.00i	−1.11824	−	0.236945i
$585$		0			0
$586$	1232.00	+	830.614i	0.0868489	+	0.0585535i
$587$	−2774.96	+	2774.96i	−0.195119	+	0.195119i	−0.797904	−	0.602785i	$-0.794058\pi$
$587$	−2774.96	+	2774.96i	−0.195119	+	0.195119i	0.602785	+	0.797904i	$0.294058\pi$
$588$	918.368	−	2166.09i	0.0644096	−	0.151919i
$589$		−	7040.00i		−	0.492493i
$590$		0			0
$591$		−	830.614i		−	0.0578120i
$592$	19209.3	+	318.992i	1.33361	+	0.0221461i
$593$	−13638.0	+	13638.0i	−0.944425	+	0.944425i	−0.998535	−	0.0541101i	$-0.982768\pi$
$593$	−13638.0	+	13638.0i	−0.944425	+	0.944425i	0.0541101	+	0.998535i	$0.482768\pi$
$594$	−13052.5	+	19360.0i	−0.901601	+	1.33729i
$595$		0			0
$596$	312.000	+	771.285i	0.0214430	+	0.0530085i
$597$	−10613.2	−	10613.2i	−0.727587	−	0.727587i
$598$	3013.12	+	15483.6i	0.206046	+	1.05882i
$599$	3559.78			0.242819			0.121409	−	0.992603i	$-0.461259\pi$
$599$	3559.78			0.242819			0.121409	+	0.992603i	$0.461259\pi$
$600$		0			0
$601$	2572.00			0.174566			0.0872829	−	0.996184i	$-0.472182\pi$
$601$	2572.00			0.174566			0.0872829	+	0.996184i	$0.472182\pi$
$602$	−1485.77	−	7634.95i	−0.100590	−	0.516906i
$603$	10149.5	+	10149.5i	0.685440	+	0.685440i
$604$	−5339.66	−	13200.0i	−0.359715	−	0.889239i
$605$		0			0
$606$	6910.00	−	10249.2i	0.463201	−	0.687038i
$607$	10945.6	−	10945.6i	0.731905	−	0.731905i	−0.239092	−	0.970997i	$-0.576850\pi$
$607$	10945.6	−	10945.6i	0.731905	−	0.731905i	0.970997	+	0.239092i	$0.0768498\pi$
$608$	8804.06	+	6150.76i	0.587256	+	0.410274i
$609$			2300.00i			0.153039i
$610$		0			0
$611$		−	10323.3i		−	0.683532i
$612$	−5975.92	+	14095.0i	−0.394710	+	0.930976i
$613$	10109.1	−	10109.1i	0.666071	−	0.666071i	−0.290733	−	0.956804i	$-0.593899\pi$
$613$	10109.1	−	10109.1i	0.666071	−	0.666071i	0.956804	+	0.290733i	$0.0938992\pi$
$614$	−3003.56	−	2025.00i	−0.197417	−	0.133098i
$615$		0			0
$616$	4400.00	−	20765.4i	0.287794	−	1.35821i
$617$	−4961.67	−	4961.67i	−0.323743	−	0.323743i	0.526458	−	0.850201i	$-0.323520\pi$
$617$	−4961.67	−	4961.67i	−0.323743	−	0.323743i	−0.850201	+	0.526458i	$0.823520\pi$
$618$	13076.6	−	2544.71i	0.851161	−	0.165636i
$619$	−19638.1			−1.27516			−0.637578	−	0.770386i	$-0.720064\pi$
$619$	−19638.1			−1.27516			−0.637578	+	0.770386i	$0.720064\pi$
$620$		0			0
$621$	−20680.0			−1.33633
$622$	28661.2	−	5577.48i	1.84760	−	0.359544i
$623$	8116.93	+	8116.93i	0.521987	+	0.521987i
$624$	5458.32	−	5280.00i	0.350173	−	0.338733i
$625$		0			0
$626$	16192.0	+	10916.6i	1.03381	+	0.696992i
$627$	−7870.96	+	7870.96i	−0.501333	+	0.501333i
$628$	−27084.6	−	11483.1i	−1.72101	−	0.729662i
$629$			33792.0i			2.14209i
$630$		0			0
$631$		−	16493.6i		−	1.04057i	−0.853992	−	0.520286i	$-0.825825\pi$
$631$		−	16493.6i		−	1.04057i	0.853992	−	0.520286i	$-0.174175\pi$
$632$	−10246.3	−	15756.0i	−0.644901	−	0.991678i
$633$	1459.31	−	1459.31i	0.0916312	−	0.0916312i
$634$	−6941.56	+	10296.0i	−0.434834	+	0.644963i
$635$		0			0
$636$	−880.000	+	355.978i	−0.0548652	+	0.0221941i
$637$	2467.57	+	2467.57i	0.153483	+	0.153483i
$638$	−1474.51	−	7577.10i	−0.0914989	−	0.470188i
$639$	−12103.2			−0.749290
$640$		0			0
$641$	27492.0			1.69402			0.847011	−	0.531575i	$-0.178399\pi$
$641$	27492.0			1.69402			0.847011	+	0.531575i	$0.178399\pi$
$642$	1323.68	+	6802.05i	0.0813732	+	0.418155i
$643$	−10095.8	−	10095.8i	−0.619193	−	0.619193i	0.326131	−	0.945325i	$-0.394255\pi$
$643$	−10095.8	−	10095.8i	−0.619193	−	0.619193i	−0.945325	+	0.326131i	$0.894255\pi$
$644$	17428.1	−	7050.00i	1.06640	−	0.431380i
$645$		0			0
$646$	−10560.0	+	15663.0i	−0.643154	+	0.953952i
$647$	−14429.3	+	14429.3i	−0.876779	+	0.876779i	−0.993200	−	0.116421i	$-0.962858\pi$
$647$	−14429.3	+	14429.3i	−0.876779	+	0.876779i	0.116421	+	0.993200i	$0.462858\pi$
$648$	−234.381	−	360.413i	−0.0142089	−	0.0218493i
$649$		−	24640.0i		−	1.49030i
$650$		0			0
$651$			5932.96i			0.357190i
$652$	−163.039	−	69.1244i	−0.00979312	−	0.00415203i
$653$	−21730.5	+	21730.5i	−1.30227	+	1.30227i	−0.375409	+	0.926859i	$0.622498\pi$
$653$	−21730.5	+	21730.5i	−1.30227	+	1.30227i	−0.926859	+	0.375409i	$0.877502\pi$
$654$	−5814.30	−	3920.00i	−0.347641	−	0.234379i
$655$		0			0
$656$	−8648.00	+	8365.47i	−0.514707	+	0.497891i
$657$	8570.16	+	8570.16i	0.508910	+	0.508910i
$658$	−12077.1	+	2350.21i	−0.715524	+	0.139241i
$659$	19400.8			1.14681			0.573404	−	0.819273i	$-0.305622\pi$
$659$	19400.8			1.14681			0.573404	+	0.819273i	$0.305622\pi$
$660$		0			0
$661$	−6048.00			−0.355885			−0.177942	−	0.984041i	$-0.556944\pi$
$661$	−6048.00			−0.355885			−0.177942	+	0.984041i	$0.556944\pi$
$662$	−8730.13	+	1698.89i	−0.512547	+	0.0997419i
$663$	9445.15	+	9445.15i	0.553272	+	0.553272i
$664$	−1468.41	+	6930.00i	−0.0858212	+	0.405024i
$665$		0			0
$666$	−11968.0	−	8068.82i	−0.696322	−	0.469460i
$667$	4834.38	−	4834.38i	0.280642	−	0.280642i
$668$	−325.872	+	768.614i	−0.0188748	+	0.0445188i
$669$		−	670.000i		−	0.0387200i
$670$		0			0
$671$		−	4271.73i		−	0.245765i
$672$	−7419.62	−	5183.55i	−0.425920	−	0.297559i
$673$	17538.3	−	17538.3i	1.00454	−	1.00454i	0.00454561	−	0.999990i	$-0.498553\pi$
$673$	17538.3	−	17538.3i	1.00454	−	1.00454i	0.999990	−	0.00454561i	$-0.00144692\pi$
$674$	11154.0	−	16544.0i	0.637440	−	0.945476i
$675$		0			0
$676$	−2367.00	−	5851.38i	−0.134672	−	0.332919i
$677$	6712.85	+	6712.85i	0.381087	+	0.381087i	0.871494	−	0.490407i	$-0.163152\pi$
$677$	6712.85	+	6712.85i	0.381087	+	0.381087i	−0.490407	+	0.871494i	$0.663152\pi$
$678$	−384.654	−	1976.63i	−0.0217884	−	0.111965i
$679$	−10086.0			−0.570053
$680$		0			0
$681$	−6490.00			−0.365194
$682$	−3803.56	−	19545.5i	−0.213557	−	1.09741i
$683$	−22720.7	−	22720.7i	−1.27289	−	1.27289i	−0.944565	−	0.328323i	$-0.893517\pi$
$683$	−22720.7	−	22720.7i	−1.27289	−	1.27289i	−0.328323	−	0.944565i	$-0.606483\pi$
$684$	−3025.81	−	7480.00i	−0.169144	−	0.418136i
$685$		0			0
$686$	10900.0	−	16167.3i	0.606653	−	0.899812i
$687$	7455.05	−	7455.05i	0.414014	−	0.414014i
$688$	11129.7	+	184.821i	0.616737	+	0.0102416i
$689$		−	1408.00i		−	0.0778527i
$690$		0			0
$691$			33877.2i			1.86505i	0.361106	+	0.932525i	$0.382399\pi$
$691$			33877.2i			1.86505i	−0.361106	+	0.932525i	$0.617601\pi$
$692$	−10077.0	+	23768.1i	−0.553572	+	1.30567i
$693$	−11276.5	+	11276.5i	−0.618124	+	0.618124i
$694$	11146.5	+	7515.00i	0.609679	+	0.411045i
$695$		0			0
$696$	−3220.00	−	682.290i	−0.175365	−	0.0371583i
$697$	−14964.6	−	14964.6i	−0.813235	−	0.813235i
$698$	−16030.6	+	3119.57i	−0.869295	+	0.169165i
$699$	4865.03			0.263251
$700$		0			0
$701$	−14928.0			−0.804312			−0.402156	−	0.915571i	$-0.631739\pi$
$701$	−14928.0			−0.804312			−0.402156	+	0.915571i	$0.631739\pi$
$702$	−14495.3	+	2820.80i	−0.779331	+	0.151658i
$703$	−12593.5	−	12593.5i	−0.675639	−	0.675639i
$704$	27766.2	+	12320.0i	1.48648	+	0.659556i
$705$		0			0
$706$	−1408.00	−	949.273i	−0.0750578	−	0.0506039i
$707$	15451.2	−	15451.2i	0.821928	−	0.821928i
$708$	−9673.05	−	4101.12i	−0.513468	−	0.217697i
$709$			20966.0i			1.11057i	0.831660	+	0.555285i	$0.187391\pi$
$709$			20966.0i			1.11057i	−0.831660	+	0.555285i	$0.812609\pi$
$710$		0			0
$711$			14120.4i			0.744807i
$712$	−13771.6	+	8955.83i	−0.724875	+	0.471396i
$713$	12470.5	−	12470.5i	0.655013	−	0.655013i
$714$	8899.44	−	13200.0i	0.466461	−	0.691873i
$715$		0			0
$716$	−4840.00	+	1957.88i	−0.252625	+	0.102192i
$717$	7694.57	+	7694.57i	0.400780	+	0.400780i
$718$	3782.43	+	19436.9i	0.196600	+	1.01028i
$719$	13883.1			0.720102			0.360051	−	0.932933i	$-0.382759\pi$
$719$	13883.1			0.720102			0.360051	+	0.932933i	$0.382759\pi$
$720$		0			0
$721$	23550.0			1.21643
$722$	1803.99	+	9270.22i	0.0929883	+	0.477842i
$723$	−6770.81	−	6770.81i	−0.348284	−	0.348284i
$724$	−31162.9	+	12606.0i	−1.59967	+	0.647097i
$725$		0			0
$726$	−10945.0	+	16234.1i	−0.559514	+	0.829893i
$727$	−11222.8	+	11222.8i	−0.572533	+	0.572533i	−0.932836	−	0.360302i	$-0.882673\pi$
$727$	−11222.8	+	11222.8i	−0.572533	+	0.572533i	0.360302	+	0.932836i	$0.382673\pi$
$728$	11254.3	−	7318.81i	0.572956	−	0.372600i
$729$		−	11557.0i		−	0.587156i
$730$		0			0
$731$			19578.8i			0.990625i
$732$	−1676.98	−	710.994i	−0.0846760	−	0.0359004i
$733$	18732.3	−	18732.3i	0.943920	−	0.943920i	−0.0545892	−	0.998509i	$-0.517385\pi$
$733$	18732.3	−	18732.3i	0.943920	−	0.943920i	0.998509	+	0.0545892i	$0.0173849\pi$
$734$	5317.41	+	3585.00i	0.267397	+	0.180279i
$735$		0			0
$736$	4700.00	+	26490.7i	0.235386	+	1.32671i
$737$	35421.6	+	35421.6i	1.77038	+	1.77038i
$738$	8873.20	−	1726.73i	0.442584	−	0.0861271i
$739$	16790.3			0.835778			0.417889	−	0.908498i	$-0.362770\pi$
$739$	16790.3			0.835778			0.417889	+	0.908498i	$0.362770\pi$
$740$		0			0
$741$	−7040.00			−0.349016
$742$	−1647.19	+	320.545i	−0.0814965	+	0.0158593i
$743$	18078.6	+	18078.6i	0.892651	+	0.892651i	0.994772	−	0.102121i	$-0.0325628\pi$
$743$	18078.6	+	18078.6i	0.892651	+	0.892651i	−0.102121	+	0.994772i	$0.532563\pi$
$744$	−8306.14	−	1760.00i	−0.409298	−	0.0867268i
$745$		0			0
$746$	−4048.00	−	2729.16i	−0.198670	−	0.133943i
$747$	3763.30	−	3763.30i	0.184327	−	0.184327i
$748$	−20855.8	+	49191.3i	−1.01947	+	2.40456i
$749$			12250.0i			0.597604i
$750$		0			0
$751$		−	1186.59i		−	0.0576556i	−0.999584	−	0.0288278i	$-0.990823\pi$
$751$		−	1186.59i		−	0.0576556i	0.999584	−	0.0288278i	$-0.00917744\pi$
$752$	292.353	−	17605.1i	0.0141769	−	0.853714i
$753$	−4643.27	+	4643.27i	−0.224715	+	0.224715i
$754$	2729.16	−	4048.00i	0.131817	−	0.195517i
$755$		0			0
$756$	6600.00	+	16315.6i	0.317513	+	0.784913i
$757$	14805.4	+	14805.4i	0.710848	+	0.710848i	0.966713	−	0.255865i	$-0.0823601\pi$
$757$	14805.4	+	14805.4i	0.710848	+	0.710848i	−0.255865	+	0.966713i	$0.582360\pi$
$758$	−993.689	−	5106.30i	−0.0476153	−	0.244682i
$759$	−27884.9			−1.33354
$760$		0			0
$761$	−678.000			−0.0322963			−0.0161481	−	0.999870i	$-0.505140\pi$
$761$	−678.000			−0.0322963			−0.0161481	+	0.999870i	$0.505140\pi$
$762$	−1842.35	−	9467.34i	−0.0875870	−	0.450086i
$763$	−8765.39	−	8765.39i	−0.415896	−	0.415896i
$764$	11391.3	+	28160.0i	0.539427	+	1.33350i
$765$		0			0
$766$	−19655.0	+	29153.1i	−0.927107	+	1.37512i
$767$	11019.3	−	11019.3i	0.518755	−	0.518755i
$768$	9457.99	−	8849.78i	0.444383	−	0.415806i
$769$			10546.0i			0.494536i	0.968947	+	0.247268i	$0.0795329\pi$
$769$			10546.0i			0.494536i	−0.968947	+	0.247268i	$0.920467\pi$
$770$		0			0
$771$		−	10916.6i		−	0.509927i
$772$	8085.07	−	19069.7i	0.376928	−	0.889035i
$773$	19395.6	−	19395.6i	0.902474	−	0.902474i	−0.0931761	−	0.995650i	$-0.529702\pi$
$773$	19395.6	−	19395.6i	0.902474	−	0.902474i	0.995650	+	0.0931761i	$0.0297020\pi$
$774$	−6934.15	−	4675.00i	−0.322019	−	0.217105i
$775$		0			0
$776$	2992.00	−	14120.4i	0.138410	−	0.653214i
$777$	10613.2	+	10613.2i	0.490021	+	0.490021i
$778$	8595.57	−	1672.70i	0.396100	−	0.0770813i
$779$	11154.0			0.513007
$780$		0			0
$781$	−42240.0			−1.93530
$782$	−46450.9	+	9039.37i	−2.12414	+	0.413359i
$783$	4525.80	+	4525.80i	0.206563	+	0.206563i
$784$	4138.24	+	4278.00i	0.188513	+	0.194880i
$785$		0			0
$786$	−1320.00	−	889.944i	−0.0599018	−	0.0403858i
$787$	15068.9	−	15068.9i	0.682525	−	0.682525i	−0.278044	−	0.960568i	$-0.589686\pi$
$787$	15068.9	−	15068.9i	0.682525	−	0.682525i	0.960568	+	0.278044i	$0.0896860\pi$
$788$	1934.61	+	820.225i	0.0874590	+	0.0370803i
$789$			6270.00i			0.282912i
$790$		0			0
$791$		−	3559.78i		−	0.160014i
$792$	−12442.0	−	19132.3i	−0.558215	−	0.858379i
$793$	1910.38	−	1910.38i	0.0855478	−	0.0855478i
$794$	6704.24	−	9944.00i	0.299653	−	0.444458i
$795$		0			0
$796$	35200.0	−	14239.1i	1.56738	−	0.634035i
$797$	−17432.2	−	17432.2i	−0.774755	−	0.774755i	0.204179	−	0.978934i	$-0.434548\pi$
$797$	−17432.2	−	17432.2i	−0.774755	−	0.774755i	−0.978934	+	0.204179i	$0.934548\pi$
$798$	1602.72	+	8235.97i	0.0710975	+	0.365351i
$799$	30970.0			1.37127
$800$		0			0
$801$	12342.0			0.544423
$802$	960.615	+	4936.34i	0.0422949	+	0.217342i
$803$	29909.6	+	29909.6i	1.31443	+	1.31443i
$804$	19801.2	−	8010.00i	0.868577	−	0.351357i
$805$		0			0
$806$	7040.00	−	10442.0i	0.307659	−	0.456333i
$807$	12396.8	−	12396.8i	0.540752	−	0.540752i
$808$	17048.1	+	26215.3i	0.742267	+	1.14140i
$809$		−	34854.0i		−	1.51471i	−0.653003	−	0.757356i	$-0.726491\pi$
$809$		−	34854.0i		−	1.51471i	0.653003	−	0.757356i	$-0.273509\pi$
$810$		0			0
$811$		−	10738.7i		−	0.464963i	−0.972601	−	0.232482i	$-0.925315\pi$
$811$		−	10738.7i		−	0.464963i	0.972601	−	0.232482i	$-0.0746846\pi$
$812$	−5357.01	−	2271.23i	−0.231520	−	0.0981584i
$813$	−10347.9	+	10347.9i	−0.446391	+	0.446391i
$814$	−41768.0	−	28160.0i	−1.79849	−	1.21254i
$815$		0			0
$816$	15840.0	+	16375.0i	0.679548	+	0.702498i
$817$	−7296.57	−	7296.57i	−0.312454	−	0.312454i
$818$	−16113.9	+	3135.78i	−0.688765	+	0.134034i
$819$	−10086.0			−0.430323
$820$		0			0
$821$	9392.00			0.399249			0.199624	−	0.979873i	$-0.436028\pi$
$821$	9392.00			0.399249			0.199624	+	0.979873i	$0.436028\pi$
$822$	5929.90	−	1153.96i	0.251617	−	0.0489648i
$823$	−31499.5	−	31499.5i	−1.33415	−	1.33415i	−0.901622	−	0.432526i	$-0.857623\pi$
$823$	−31499.5	−	31499.5i	−1.33415	−	1.33415i	−0.432526	−	0.901622i	$-0.642377\pi$
$824$	−6986.06	+	32970.0i	−0.295353	+	1.39389i
$825$		0			0
$826$	−15400.0	−	10382.7i	−0.648710	−	0.437360i
$827$	22631.2	−	22631.2i	0.951591	−	0.951591i	−0.0472905	−	0.998881i	$-0.515059\pi$
$827$	22631.2	−	22631.2i	0.951591	−	0.951591i	0.998881	+	0.0472905i	$0.0150587\pi$
$828$	7890.06	−	18609.8i	0.331158	−	0.781080i
$829$		−	43384.0i		−	1.81760i	−0.417234	−	0.908799i	$-0.637001\pi$
$829$		−	43384.0i		−	1.81760i	0.417234	−	0.908799i	$-0.362999\pi$
$830$		0			0
$831$		−	6170.28i		−	0.257575i
$832$	6907.77	+	17927.1i	0.287841	+	0.747008i
$833$	−7402.71	+	7402.71i	−0.307909	+	0.307909i
$834$	3856.42	−	5720.00i	0.160116	−	0.237491i
$835$		0			0
$836$	−10560.0	−	26105.0i	−0.436872	−	1.07998i
$837$	11674.5	+	11674.5i	0.482115	+	0.482115i
$838$	2596.41	+	13342.3i	0.107031	+	0.550002i
$839$	11747.3			0.483385			0.241693	−	0.970353i	$-0.422297\pi$
$839$	11747.3			0.483385			0.241693	+	0.970353i	$0.422297\pi$
$840$		0			0
$841$	22273.0			0.913240
$842$	−903.345	−	4642.05i	−0.0369731	−	0.189995i
$843$	−11869.0	−	11869.0i	−0.484925	−	0.484925i
$844$	1957.88	+	4840.00i	0.0798494	+	0.197393i
$845$		0			0
$846$	−7395.00	+	10968.6i	−0.300526	+	0.445753i
$847$	−24473.8	+	24473.8i	−0.992832	+	0.992832i
$848$	39.8740	−	2401.16i	0.00161472	−	0.0972361i
$849$			21890.0i			0.884880i
$850$		0			0
$851$		−	44615.9i		−	1.79719i
$852$	−7030.50	+	16582.4i	−0.282701	+	0.666787i
$853$	17273.0	−	17273.0i	0.693336	−	0.693336i	−0.269628	−	0.962964i	$-0.586901\pi$
$853$	17273.0	−	17273.0i	0.693336	−	0.693336i	0.962964	+	0.269628i	$0.0869009\pi$
$854$	−2669.83	−	1800.00i	−0.106979	−	0.0721250i
$855$		0			0
$856$	−17150.0	−	3633.94i	−0.684784	−	0.145100i
$857$	7376.17	+	7376.17i	0.294009	+	0.294009i	0.838662	−	0.544653i	$-0.183339\pi$
$857$	7376.17	+	7376.17i	0.294009	+	0.294009i	−0.544653	+	0.838662i	$0.683339\pi$
$858$	−19545.5	+	3803.56i	−0.777706	+	0.151342i
$859$	−43488.6			−1.72737			−0.863685	−	0.504031i	$-0.831850\pi$
$859$	−43488.6			−1.72737			−0.863685	+	0.504031i	$0.831850\pi$
$860$		0			0
$861$	−9400.00			−0.372069
$862$	329.439	−	64.1090i	0.0130171	−	0.00253313i
$863$	−8816.82	−	8816.82i	−0.347773	−	0.347773i	0.511507	−	0.859279i	$-0.329088\pi$
$863$	−8816.82	−	8816.82i	−0.347773	−	0.347773i	−0.859279	+	0.511507i	$0.829088\pi$
$864$	−24799.8	+	4400.00i	−0.976511	+	0.173254i
$865$		0			0
$866$	−21208.0	−	14298.4i	−0.832191	−	0.561063i
$867$	−17349.7	+	17349.7i	−0.679614	+	0.679614i
$868$	−13818.6	−	5858.75i	−0.540363	−	0.229100i
$869$			49280.0i			1.92372i
$870$		0			0
$871$			31682.0i			1.23250i
$872$	14871.8	−	9671.31i	0.577548	−	0.375587i
$873$	−7668.04	+	7668.04i	−0.297278	+	0.297278i
$874$	13942.5	−	20680.0i	0.539600	−	0.800356i
$875$		0			0
$876$	16720.0	−	6763.57i	0.644882	−	0.260868i
$877$	−6420.99	−	6420.99i	−0.247231	−	0.247231i	0.572602	−	0.819833i	$-0.305934\pi$
$877$	−6420.99	−	6420.99i	−0.247231	−	0.247231i	−0.819833	+	0.572602i	$0.805934\pi$
$878$	−5705.70	−	29320.1i	−0.219314	−	1.12700i
$879$	−1661.23			−0.0637450
$880$		0			0
$881$	22372.0			0.855541			0.427771	−	0.903887i	$-0.359299\pi$
$881$	22372.0			0.855541			0.427771	+	0.903887i	$0.359299\pi$
$882$	−854.180	−	4389.40i	−0.0326097	−	0.167572i
$883$	16477.6	+	16477.6i	0.627990	+	0.627990i	0.947562	−	0.319572i	$-0.103539\pi$
$883$	16477.6	+	16477.6i	0.627990	+	0.627990i	−0.319572	+	0.947562i	$0.603539\pi$
$884$	−31326.0	+	12672.0i	−1.19186	+	0.482133i
$885$		0			0
$886$	27175.0	−	40307.0i	1.03043	−	1.52838i
$887$	−16750.4	+	16750.4i	−0.634073	+	0.634073i	−0.949087	−	0.315014i	$-0.897991\pi$
$887$	−16750.4	+	16750.4i	−0.634073	+	0.634073i	0.315014	+	0.949087i	$0.397991\pi$
$888$	−18006.9	+	11710.1i	−0.680485	+	0.442528i
$889$		−	17050.0i		−	0.643238i
$890$		0			0
$891$			1127.26i			0.0423846i
$892$	1560.52	+	661.620i	0.0585763	+	0.0248348i
$893$	−11541.9	+	11541.9i	−0.432512	+	0.432512i
$894$	−771.285	−	520.000i	−0.0288542	−	0.0194535i
$895$		0			0
$896$	19400.0	−	12162.6i	0.723335	−	0.453485i
$897$	−12470.5	−	12470.5i	−0.464190	−	0.464190i
$898$	6874.23	−	1337.73i	0.255452	−	0.0497111i
$899$	−5458.32			−0.202497
$900$		0			0
$901$	4224.00			0.156184
$902$	30967.3	−	6026.25i	1.14312	−	0.222452i
$903$	6149.19	+	6149.19i	0.226614	+	0.226614i
$904$	4983.69	+	1056.00i	0.183357	+	0.0388518i
$905$		0			0
$906$	13200.0	+	8899.44i	0.484040	+	0.326340i
$907$	−22886.2	+	22886.2i	−0.837842	+	0.837842i	−0.988575	−	0.150733i	$-0.951837\pi$
$907$	−22886.2	+	22886.2i	−0.837842	+	0.837842i	0.150733	+	0.988575i	$0.451837\pi$
$908$	6408.82	−	15116.1i	0.234234	−	0.552472i
$909$		−	23494.0i		−	0.857257i
$910$		0			0
$911$		−	24087.8i		−	0.876032i	−0.898967	−	0.438016i	$-0.855681\pi$
$911$		−	24087.8i		−	0.876032i	0.898967	−	0.438016i	$-0.144319\pi$
$912$	−12005.8	−	199.370i	−0.435912	−	0.00723882i
$913$	13133.8	−	13133.8i	0.476086	−	0.476086i
$914$	19460.1	−	28864.0i	0.704248	−	1.04457i
$915$		0			0
$916$	10002.0	+	24725.6i	0.360781	+	0.891874i
$917$	−1989.97	−	1989.97i	−0.0716628	−	0.0716628i
$918$	−8462.39	−	43485.9i	−0.304249	−	1.56345i
$919$	−34173.8			−1.22665			−0.613325	−	0.789831i	$-0.710168\pi$
$919$	−34173.8			−1.22665			−0.613325	+	0.789831i	$0.710168\pi$
$920$		0			0
$921$	4050.00			0.144899
$922$	7519.59	+	38641.2i	0.268595	+	1.38024i
$923$	−18890.3	−	18890.3i	−0.673653	−	0.673653i
$924$	8899.44	+	22000.0i	0.316851	+	0.783276i
$925$		0			0
$926$	−7165.00	+	10627.4i	−0.254273	+	0.377147i
$927$	17904.2	−	17904.2i	0.634359	−	0.634359i
$928$	4768.87	−	6826.05i	0.168692	−	0.241461i
$929$			13996.0i			0.494288i	0.968979	+	0.247144i	$0.0794921\pi$
$929$			13996.0i			0.494288i	−0.968979	+	0.247144i	$0.920508\pi$
$930$		0			0
$931$		−	5517.65i		−	0.194236i
$932$	−4804.17	+	11331.3i	−0.168848	+	0.398250i
$933$	−23083.7	+	23083.7i	−0.809996	+	0.809996i
$934$	−4694.45	−	3165.00i	−0.164462	−	0.110880i
$935$		0			0
$936$	2992.00	−	14120.4i	0.104484	−	0.493099i
$937$	−21677.5	−	21677.5i	−0.755786	−	0.755786i	0.219766	−	0.975553i	$-0.429471\pi$
$937$	−21677.5	−	21677.5i	−0.755786	−	0.755786i	−0.975553	+	0.219766i	$0.929471\pi$
$938$	37064.2	−	7212.72i	1.29018	−	0.251070i
$939$	−21833.3			−0.758789
$940$		0			0
$941$	−18078.0			−0.626276			−0.313138	−	0.949708i	$-0.601380\pi$
$941$	−18078.0			−0.626276			−0.313138	+	0.949708i	$0.601380\pi$
$942$	32285.0	−	6282.68i	1.11667	−	0.217304i
$943$	19757.9	+	19757.9i	0.682297	+	0.682297i
$944$	19104.1	−	18480.0i	0.658672	−	0.637153i
$945$		0			0
$946$	−24200.0	−	16315.6i	−0.831723	−	0.560747i
$947$	7864.25	−	7864.25i	0.269856	−	0.269856i	−0.559186	−	0.829042i	$-0.688886\pi$
$947$	7864.25	−	7864.25i	0.269856	−	0.269856i	0.829042	+	0.559186i	$0.188886\pi$
$948$	19346.1	+	8202.25i	0.662798	+	0.281009i
$949$			26752.0i			0.915076i
$950$		0			0
$951$		−	13883.1i		−	0.473387i
$952$	21956.4	+	33762.9i	0.747492	+	1.14943i
$953$	−31680.4	+	31680.4i	−1.07684	+	1.07684i	−0.0800494	+	0.996791i	$0.525508\pi$
$953$	−31680.4	+	31680.4i	−1.07684	+	1.07684i	−0.996791	+	0.0800494i	$0.974492\pi$
$954$	−1008.60	+	1496.00i	−0.0342293	+	0.0507702i
$955$		0			0
$956$	−25520.0	+	10323.3i	−0.863364	+	0.349248i
$957$	6102.59	+	6102.59i	0.206132	+	0.206132i
$958$	7821.30	+	40191.6i	0.263773	+	1.35546i
$959$	10679.3			0.359597
$960$		0			0
$961$	15711.0			0.527374
$962$	−6085.70	−	31272.8i	−0.203961	−	1.04810i
$963$	9313.22	+	9313.22i	0.311645	+	0.311645i
$964$	22456.2	−	9084.00i	0.750277	−	0.303502i
$965$		0			0
$966$	−11750.0	+	17428.1i	−0.391356	+	0.580475i
$967$	−27228.6	+	27228.6i	−0.905494	+	0.905494i	−0.995905	−	0.0904105i	$-0.971182\pi$
$967$	−27228.6	+	27228.6i	−0.905494	+	0.905494i	0.0904105	+	0.995905i	$0.471182\pi$
$968$	−27003.2	−	41523.4i	−0.896606	−	1.37873i
$969$		−	21120.0i		−	0.700178i
$970$		0			0
$971$			17976.9i			0.594135i	0.954856	+	0.297067i	$0.0960086\pi$
$971$			17976.9i			0.594135i	−0.954856	+	0.297067i	$0.903991\pi$
$972$	28112.6	+	11919.0i	0.927688	+	0.393316i
$973$	8623.22	−	8623.22i	0.284119	−	0.284119i
$974$	1638.98	+	1105.00i	0.0539182	+	0.0363516i
$975$		0			0
$976$	3312.00	−	3203.80i	0.108621	−	0.105073i
$977$	−36270.6	−	36270.6i	−1.18772	−	1.18772i	−0.977697	−	0.210020i	$-0.932647\pi$
$977$	−36270.6	−	36270.6i	−1.18772	−	1.18772i	−0.210020	−	0.977697i	$-0.567353\pi$
$978$	194.344	−	37.8195i	0.00635424	−	0.00123654i
$979$	43073.3			1.40616
$980$		0			0
$981$	−13328.0			−0.433772
$982$	3459.11	−	673.144i	0.112408	−	0.0218746i
$983$	3709.64	+	3709.64i	0.120365	+	0.120365i	0.764724	−	0.644358i	$-0.222875\pi$
$983$	3709.64	+	3709.64i	0.120365	+	0.120365i	−0.644358	+	0.764724i	$0.722875\pi$
$984$	2788.49	−	13160.0i	0.0903393	−	0.426347i
$985$		0			0
$986$	12144.0	+	8187.48i	0.392235	+	0.264445i
$987$	9726.90	−	9726.90i	0.313688	−	0.313688i
$988$	6951.94	−	16397.1i	0.223857	−	0.527997i
$989$		−	25850.0i		−	0.831125i
$990$		0			0
$991$			30614.1i			0.981320i	0.871351	+	0.490660i	$0.163244\pi$
$991$			30614.1i			0.981320i	−0.871351	+	0.490660i	$0.836756\pi$
$992$	12301.5	−	17608.1i	0.393724	−	0.563567i
$993$	7031.24	−	7031.24i	0.224703	−	0.224703i
$994$	−17798.9	+	26400.0i	−0.567954	+	0.842412i
$995$		0			0
$996$	−2970.00	−	7342.04i	−0.0944860	−	0.233576i
$997$	−34148.0	−	34148.0i	−1.08473	−	1.08473i	−0.996061	−	0.0886702i	$-0.971738\pi$
$997$	−34148.0	−	34148.0i	−1.08473	−	1.08473i	−0.0886702	−	0.996061i	$-0.528262\pi$
$998$	6250.63	+	32120.3i	0.198257	+	1.01879i
$999$	41768.0			1.32280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.e.d.7.2	yes	8
4.3	odd	2	inner	100.4.e.d.7.1	✓	8
5.2	odd	4	inner	100.4.e.d.43.4	yes	8
5.3	odd	4	inner	100.4.e.d.43.1	yes	8
5.4	even	2	inner	100.4.e.d.7.3	yes	8
20.3	even	4	inner	100.4.e.d.43.2	yes	8
20.7	even	4	inner	100.4.e.d.43.3	yes	8
20.19	odd	2	inner	100.4.e.d.7.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.e.d.7.1	✓	8	4.3	odd	2	inner
100.4.e.d.7.2	yes	8	1.1	even	1	trivial
100.4.e.d.7.3	yes	8	5.4	even	2	inner
100.4.e.d.7.4	yes	8	20.19	odd	2	inner
100.4.e.d.43.1	yes	8	5.3	odd	4	inner
100.4.e.d.43.2	yes	8	20.3	even	4	inner
100.4.e.d.43.3	yes	8	20.7	even	4	inner
100.4.e.d.43.4	yes	8	5.2	odd	4	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540278 - 2.77635i) q^{2} +(2.23607 + 2.23607i) q^{3} +(-7.41620 + 3.00000i) q^{4} +(5.00000 - 7.41620i) q^{6} +(11.1803 - 11.1803i) q^{7} +(12.3359 + 18.9691i) q^{8} -17.0000i q^{9} +O(q^{10})\)	\(q+(-0.540278 - 2.77635i) q^{2} +(2.23607 + 2.23607i) q^{3} +(-7.41620 + 3.00000i) q^{4} +(5.00000 - 7.41620i) q^{6} +(11.1803 - 11.1803i) q^{7} +(12.3359 + 18.9691i) q^{8} -17.0000i q^{9} -59.3296i q^{11} +(-23.2913 - 9.87492i) q^{12} +(26.5330 - 26.5330i) q^{13} +(-37.0810 - 25.0000i) q^{14} +(46.0000 - 44.4972i) q^{16} +(79.5990 + 79.5990i) q^{17} +(-47.1979 + 9.18473i) q^{18} -59.3296 q^{19} +50.0000 q^{21} +(-164.719 + 32.0545i) q^{22} +(-105.095 - 105.095i) q^{23} +(-14.8324 + 70.0000i) q^{24} +(-88.0000 - 59.3296i) q^{26} +(98.3870 - 98.3870i) q^{27} +(-49.3746 + 116.457i) q^{28} +46.0000i q^{29} +118.659i q^{31} +(-148.392 - 103.671i) q^{32} +(132.665 - 132.665i) q^{33} +(177.989 - 264.000i) q^{34} +(51.0000 + 126.075i) q^{36} +(212.264 + 212.264i) q^{37} +(32.0545 + 164.719i) q^{38} +118.659 q^{39} -188.000 q^{41} +(-27.0139 - 138.817i) q^{42} +(122.984 + 122.984i) q^{43} +(177.989 + 440.000i) q^{44} +(-235.000 + 348.561i) q^{46} +(194.538 - 194.538i) q^{47} +(202.358 + 3.36038i) q^{48} +93.0000i q^{49} +355.978i q^{51} +(-117.175 + 276.373i) q^{52} +(26.5330 - 26.5330i) q^{53} +(-326.313 - 220.000i) q^{54} +(350.000 + 74.1620i) q^{56} +(-132.665 - 132.665i) q^{57} +(127.712 - 24.8528i) q^{58} +415.307 q^{59} +72.0000 q^{61} +(329.439 - 64.1090i) q^{62} +(-190.066 - 190.066i) q^{63} +(-207.654 + 468.000i) q^{64} +(-440.000 - 296.648i) q^{66} +(-597.030 + 597.030i) q^{67} +(-829.119 - 351.525i) q^{68} -470.000i q^{69} -711.955i q^{71} +(322.475 - 209.709i) q^{72} +(-504.127 + 504.127i) q^{73} +(474.637 - 704.000i) q^{74} +(440.000 - 177.989i) q^{76} +(-663.325 - 663.325i) q^{77} +(-64.1090 - 329.439i) q^{78} -830.614 q^{79} -19.0000 q^{81} +(101.572 + 521.953i) q^{82} +(221.371 + 221.371i) q^{83} +(-370.810 + 150.000i) q^{84} +(275.000 - 407.891i) q^{86} +(-102.859 + 102.859i) q^{87} +(1125.43 - 731.881i) q^{88} +726.000i q^{89} -593.296i q^{91} +(1094.69 + 464.121i) q^{92} +(-265.330 + 265.330i) q^{93} +(-645.209 - 435.000i) q^{94} +(-100.000 - 563.631i) q^{96} +(-451.061 - 451.061i) q^{97} +(258.200 - 50.2459i) q^{98} -1008.60 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 40 q^{6}+O(q^{10}) \) 8 * q + 40 * q^6	\( 8 q + 40 q^{6} + 368 q^{16} + 400 q^{21} - 704 q^{26} + 408 q^{36} - 1504 q^{41} - 1880 q^{46} + 2800 q^{56} + 576 q^{61} - 3520 q^{66} + 3520 q^{76} - 152 q^{81} + 2200 q^{86} - 800 q^{96}+O(q^{100}) \) 8 * q + 40 * q^6 + 368 * q^16 + 400 * q^21 - 704 * q^26 + 408 * q^36 - 1504 * q^41 - 1880 * q^46 + 2800 * q^56 + 576 * q^61 - 3520 * q^66 + 3520 * q^76 - 152 * q^81 + 2200 * q^86 - 800 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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