LMFDB - Embedded newform 100.4.e.d.43.1

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			43.1
Root			$0.500000 + 3.27635i$ of defining polynomial
Character	$\chi$	$=$	100.43
Dual form			100.4.e.d.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.77635 + 0.540278i) q^{2} +(-2.23607 + 2.23607i) q^{3} +(7.41620 - 3.00000i) q^{4} +(5.00000 - 7.41620i) q^{6} +(-11.1803 - 11.1803i) q^{7} +(-18.9691 + 12.3359i) q^{8} +17.0000i q^{9} +O(q^{10})$	\(q+(-2.77635 + 0.540278i) 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} +(-18.9691 + 12.3359i) q^{8} +17.0000i q^{9} -59.3296i q^{11} +(-9.87492 + 23.2913i) 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} +(-9.18473 - 47.1979i) q^{18} +59.3296 q^{19} +50.0000 q^{21} +(32.0545 + 164.719i) 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} +(-116.457 - 49.3746i) q^{28} -46.0000i q^{29} +118.659i q^{31} +(-103.671 + 148.392i) 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} +(-164.719 + 32.0545i) q^{38} -118.659 q^{39} -188.000 q^{41} +(-138.817 + 27.0139i) 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} +(-3.36038 + 202.358i) q^{48} -93.0000i q^{49} +355.978i q^{51} +(276.373 + 117.175i) 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} +(24.8528 + 127.712i) q^{58} -415.307 q^{59} +72.0000 q^{61} +(-64.1090 - 329.439i) 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} +(351.525 - 829.119i) q^{68} +470.000i q^{69} -711.955i q^{71} +(-209.709 - 322.475i) 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} +(329.439 - 64.1090i) q^{78} +830.614 q^{79} -19.0000 q^{81} +(521.953 - 101.572i) 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} +(731.881 + 1125.43i) q^{88} -726.000i q^{89} -593.296i q^{91} +(464.121 - 1094.69i) 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} +(50.2459 + 258.200i) 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 $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.77635	+	0.540278i	−0.981587	+	0.191017i
$2$	−2.77635	+	0.540278i	−0.981587	+	0.191017i
$3$	−2.23607	+	2.23607i	−0.430331	+	0.430331i	−0.888741	−	0.458410i	$-0.848419\pi$
$3$	−2.23607	+	2.23607i	−0.430331	+	0.430331i	0.458410	+	0.888741i	$0.348419\pi$
$4$	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	$-0.390383\pi$
$7$	−11.1803	−	11.1803i	−0.603682	−	0.603682i	−0.941288	+	0.337606i	$0.890383\pi$
$8$	−18.9691	+	12.3359i	−0.838324	+	0.545173i
$9$			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	$-0.302230\pi$
$12$	−9.87492	+	23.2913i	−0.237554	+	0.560302i
$13$	26.5330	+	26.5330i	0.566072	+	0.566072i	0.931026	−	0.364954i	$-0.118915\pi$
$13$	26.5330	+	26.5330i	0.566072	+	0.566072i	−0.364954	+	0.931026i	$0.618915\pi$
$14$	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	0.146397	−	0.989226i	$-0.453232\pi$
$17$	79.5990	−	79.5990i	1.13562	−	1.13562i	0.989226	−	0.146397i	$-0.0467677\pi$
$18$	−9.18473	−	47.1979i	−0.120270	−	0.618036i
$19$	59.3296			0.716376			0.358188	−	0.933650i	$-0.383395\pi$
$19$	59.3296			0.716376			0.358188	+	0.933650i	$0.383395\pi$
$20$		0			0
$21$	50.0000			0.519566
$22$	32.0545	+	164.719i	0.310638	+	1.59629i
$23$	105.095	−	105.095i	0.952777	−	0.952777i	−0.0461575	−	0.998934i	$-0.514698\pi$
$23$	105.095	−	105.095i	0.952777	−	0.952777i	0.998934	+	0.0461575i	$0.0146976\pi$
$24$	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
$28$	−116.457	−	49.3746i	−0.786008	−	0.333247i
$29$		−	46.0000i		−	0.294551i	−0.989095	−	0.147276i	$-0.952950\pi$
$29$		−	46.0000i		−	0.294551i	0.989095	−	0.147276i	$-0.0470504\pi$
$30$		0			0
$31$			118.659i			0.687478i	0.939065	+	0.343739i	$0.111694\pi$
$31$			118.659i			0.687478i	−0.939065	+	0.343739i	$0.888306\pi$
$32$	−103.671	+	148.392i	−0.572707	+	0.819760i
$33$	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	−0.0553332	−	0.998468i	$-0.517622\pi$
$37$	212.264	−	212.264i	0.943135	−	0.943135i	0.998468	+	0.0553332i	$0.0176221\pi$
$38$	−164.719	+	32.0545i	−0.703185	+	0.136840i
$39$	−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	$0.616561\pi$
$42$	−138.817	+	27.0139i	−0.509999	+	0.0992462i
$43$	−122.984	+	122.984i	−0.436159	+	0.436159i	−0.890717	−	0.454558i	$-0.849797\pi$
$43$	−122.984	+	122.984i	−0.436159	+	0.436159i	0.454558	+	0.890717i	$0.349797\pi$
$44$	−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	$-0.390400\pi$
$47$	−194.538	−	194.538i	−0.603750	−	0.603750i	−0.941306	+	0.337555i	$0.890400\pi$
$48$	−3.36038	+	202.358i	−0.0101048	+	0.608497i
$49$		−	93.0000i		−	0.271137i
$50$		0			0
$51$			355.978i			0.977389i
$52$	276.373	+	117.175i	0.737039	+	0.312486i
$53$	26.5330	+	26.5330i	0.0687658	+	0.0687658i	0.740653	−	0.671887i	$-0.234516\pi$
$53$	26.5330	+	26.5330i	0.0687658	+	0.0687658i	−0.671887	+	0.740653i	$0.734516\pi$
$54$	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
$58$	24.8528	+	127.712i	0.0562644	+	0.289128i
$59$	−415.307			−0.916413			−0.458207	−	0.888846i	$-0.651508\pi$
$59$	−415.307			−0.916413			−0.458207	+	0.888846i	$0.651508\pi$
$60$		0			0
$61$	72.0000			0.151125			0.0755627	−	0.997141i	$-0.475925\pi$
$61$	72.0000			0.151125			0.0755627	+	0.997141i	$0.475925\pi$
$62$	−64.1090	−	329.439i	−0.131320	−	0.674819i
$63$	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	0.995669	+	0.0929706i	$0.0296363\pi$
$67$	597.030	+	597.030i	1.08864	+	1.08864i	0.0929706	+	0.995669i	$0.470364\pi$
$68$	351.525	−	829.119i	0.626892	−	1.47861i
$69$			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	$-0.202858\pi$
$72$	−209.709	−	322.475i	−0.343257	−	0.527833i
$73$	−504.127	−	504.127i	−0.808268	−	0.808268i	0.176103	−	0.984372i	$-0.443651\pi$
$73$	−504.127	−	504.127i	−0.808268	−	0.808268i	−0.984372	+	0.176103i	$0.943651\pi$
$74$	−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
$78$	329.439	−	64.1090i	0.478226	−	0.0930630i
$79$	830.614			1.18293			0.591465	−	0.806331i	$-0.298550\pi$
$79$	830.614			1.18293			0.591465	+	0.806331i	$0.298550\pi$
$80$		0			0
$81$	−19.0000			−0.0260631
$82$	521.953	−	101.572i	0.702928	−	0.136790i
$83$	−221.371	+	221.371i	−0.292754	+	0.292754i	−0.838167	−	0.545413i	$-0.816373\pi$
$83$	−221.371	+	221.371i	−0.292754	+	0.292754i	0.545413	+	0.838167i	$0.316373\pi$
$84$	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
$88$	731.881	+	1125.43i	0.886577	+	1.36331i
$89$		−	726.000i		−	0.864672i	−0.901712	−	0.432336i	$-0.857689\pi$
$89$		−	726.000i		−	0.864672i	0.901712	−	0.432336i	$-0.142311\pi$
$90$		0			0
$91$		−	593.296i		−	0.683454i
$92$	464.121	−	1094.69i	0.525956	−	1.24054i
$93$	−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	−0.902609	−	0.430461i	$-0.858351\pi$
$97$	−451.061	+	451.061i	−0.472147	+	0.472147i	0.430461	+	0.902609i	$0.358351\pi$
$98$	50.2459	+	258.200i	0.0517919	+	0.266144i
$99$	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	$0.261648\pi$
$102$	−192.327	−	988.317i	−0.186698	−	0.959392i
$103$	−1053.19	+	1053.19i	−1.00751	+	1.00751i	−0.00754007	+	0.999972i	$0.502400\pi$
$103$	−1053.19	+	1053.19i	−1.00751	+	1.00751i	−0.999972	+	0.00754007i	$0.997600\pi$
$104$	−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	$-0.136184\pi$
$107$	547.837	+	547.837i	0.494966	+	0.494966i	−0.414901	+	0.909867i	$0.636184\pi$
$108$	−1024.82	−	434.496i	−0.913085	−	0.387124i
$109$			784.000i			0.688932i	0.938799	+	0.344466i	$0.111940\pi$
$109$			784.000i			0.688932i	−0.938799	+	0.344466i	$0.888060\pi$
$110$		0			0
$111$			949.273i			0.811721i
$112$	−1011.79	−	16.8019i	−0.853617	−	0.0141753i
$113$	159.198	+	159.198i	0.132532	+	0.132532i	0.770261	−	0.637729i	$-0.220126\pi$
$113$	159.198	+	159.198i	0.132532	+	0.132532i	−0.637729	+	0.770261i	$0.720126\pi$
$114$	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
$118$	1153.04	−	224.381i	0.899539	−	0.175051i
$119$	−1779.89			−1.37111
$120$		0			0
$121$	−2189.00			−1.64463
$122$	−199.897	+	38.9000i	−0.148343	+	0.0288676i
$123$	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	$-0.372948\pi$
$127$	−762.499	−	762.499i	−0.532763	−	0.532763i	−0.921394	+	0.388631i	$0.872948\pi$
$128$	−323.668	+	1411.52i	−0.223504	+	0.974703i
$129$		−	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	$-0.0189043\pi$
$132$	1381.86	+	585.875i	0.911181	+	0.386317i
$133$	−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	−0.542329	−	0.840166i	$-0.682458\pi$
$137$	477.594	−	477.594i	0.297837	−	0.297837i	0.840166	+	0.542329i	$0.182458\pi$
$138$	−253.931	−	1304.88i	−0.156638	−	0.804920i
$139$	−771.285			−0.470644			−0.235322	−	0.971917i	$-0.575614\pi$
$139$	−771.285			−0.470644			−0.235322	+	0.971917i	$0.575614\pi$
$140$		0			0
$141$	870.000			0.519626
$142$	384.654	+	1976.63i	0.227320	+	1.16814i
$143$	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
$148$	937.400	−	2210.98i	0.520634	−	1.22798i
$149$			104.000i			0.0571813i	0.999591	+	0.0285906i	$0.00910193\pi$
$149$			104.000i			0.0571813i	−0.999591	+	0.0285906i	$0.990898\pi$
$150$		0			0
$151$			1779.89i			0.959240i	0.877476	+	0.479620i	$0.159225\pi$
$151$			1779.89i			0.959240i	−0.877476	+	0.479620i	$0.840775\pi$
$152$	−1125.43	+	731.881i	−0.600555	+	0.390549i
$153$	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	0.409466	−	0.912325i	$-0.365715\pi$
$157$	2600.23	−	2600.23i	1.32179	−	1.32179i	0.912325	−	0.409466i	$-0.134285\pi$
$158$	−2306.07	+	448.763i	−1.16115	+	0.225960i
$159$	−118.659			−0.0591842
$160$		0			0
$161$	−2350.00			−1.15035
$162$	52.7506	−	10.2653i	0.0255832	−	0.00497850i
$163$	−15.6525	+	15.6525i	−0.00752145	+	0.00752145i	−0.710858	−	0.703336i	$-0.751693\pi$
$163$	−15.6525	+	15.6525i	−0.00752145	+	0.00752145i	0.703336	+	0.710858i	$0.251693\pi$
$164$	−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	$-0.257697\pi$
$167$	−73.7902	−	73.7902i	−0.0341920	−	0.0341920i	−0.723996	+	0.689804i	$0.757697\pi$
$168$	−948.455	+	616.793i	−0.435565	+	0.283253i
$169$		−	789.000i		−	0.359126i
$170$		0			0
$171$			1008.60i			0.451051i
$172$	−543.121	+	1281.02i	−0.240771	+	0.567890i
$173$	2281.84	+	2281.84i	1.00280	+	1.00280i	0.999996	+	0.00280694i	$0.000893479\pi$
$173$	2281.84	+	2281.84i	1.00280	+	1.00280i	0.00280694	+	0.999996i	$0.499107\pi$
$174$	−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
$178$	392.242	+	2015.63i	0.165167	+	0.848751i
$179$	−652.625			−0.272511			−0.136256	−	0.990674i	$-0.543507\pi$
$179$	−652.625			−0.272511			−0.136256	+	0.990674i	$0.543507\pi$
$180$		0			0
$181$	4202.00			1.72559			0.862796	−	0.505552i	$-0.168711\pi$
$181$	4202.00			1.72559			0.862796	+	0.505552i	$0.168711\pi$
$182$	320.545	+	1647.19i	0.130551	+	0.670869i
$183$	−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
$188$	−2026.35	−	859.118i	−0.786098	−	0.333285i
$189$			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	$-0.255508\pi$
$192$	582.152	+	1510.81i	0.218819	+	0.567881i
$193$	−1830.78	−	1830.78i	−0.682809	−	0.682809i	0.277823	−	0.960632i	$-0.410387\pi$
$193$	−1830.78	−	1830.78i	−0.682809	−	0.682809i	−0.960632	+	0.277823i	$0.910387\pi$
$194$	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	−0.739894	−	0.672723i	$-0.765125\pi$
$197$	−185.731	+	185.731i	−0.0671715	+	0.0671715i	0.672723	+	0.739894i	$0.265125\pi$
$198$	−2800.23	+	544.926i	−1.00507	+	0.195587i
$199$	4746.37			1.69076			0.845379	−	0.534166i	$-0.179374\pi$
$199$	4746.37			1.69076			0.845379	+	0.534166i	$0.179374\pi$
$200$		0			0
$201$	−2670.00			−0.936952
$202$	−3836.91	+	746.665i	−1.33646	+	0.260075i
$203$	−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
$208$	2401.16	+	39.8740i	0.800436	+	0.0132921i
$209$		−	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	$-0.0339535\pi$
$212$	276.373	+	117.175i	0.0895348	+	0.0379604i
$213$	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
$218$	−423.578	−	2176.66i	−0.131598	−	0.676246i
$219$	2254.52			0.695647
$220$		0			0
$221$	4224.00			1.28569
$222$	−512.872	−	2635.51i	−0.155053	−	0.796775i
$223$	149.817	−	149.817i	0.0449886	−	0.0449886i	−0.684255	−	0.729243i	$-0.739872\pi$
$223$	149.817	−	149.817i	0.0449886	−	0.0449886i	0.729243	+	0.684255i	$0.239872\pi$
$224$	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	$-0.153001\pi$
$227$	1451.21	+	1451.21i	0.424317	+	0.424317i	−0.462370	+	0.886687i	$0.653001\pi$
$228$	−585.875	+	1381.86i	−0.170178	+	0.401387i
$229$			3334.00i			0.962083i	0.876698	+	0.481041i	$0.159741\pi$
$229$			3334.00i			0.962083i	−0.876698	+	0.481041i	$0.840259\pi$
$230$		0			0
$231$		−	2966.48i		−	0.844935i
$232$	567.449	+	872.579i	0.160581	+	0.246929i
$233$	1087.85	+	1087.85i	0.305870	+	0.305870i	0.843305	−	0.537435i	$-0.180607\pi$
$233$	1087.85	+	1087.85i	0.305870	+	0.305870i	−0.537435	+	0.843305i	$0.680607\pi$
$234$	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
$238$	4941.58	−	961.635i	1.34586	−	0.261906i
$239$	−3441.12			−0.931328			−0.465664	−	0.884962i	$-0.654184\pi$
$239$	−3441.12			−0.931328			−0.465664	+	0.884962i	$0.654184\pi$
$240$		0			0
$241$	−3028.00			−0.809339			−0.404669	−	0.914463i	$-0.632613\pi$
$241$	−3028.00			−0.809339			−0.404669	+	0.914463i	$0.632613\pi$
$242$	6077.42	−	1182.67i	1.61435	−	0.314152i
$243$	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
$248$	−1463.76	−	2250.86i	−0.374794	−	0.576329i
$249$		−	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	$0.915916\pi$
$252$	839.368	−	1979.76i	0.209822	−	0.494894i
$253$	−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	−0.938301	−	0.345820i	$-0.887601\pi$
$257$	−2441.04	+	2441.04i	−0.592481	+	0.592481i	0.345820	+	0.938301i	$0.387601\pi$
$258$	297.153	+	1526.99i	0.0717052	+	0.368474i
$259$	−4746.37			−1.13871
$260$		0			0
$261$	782.000			0.185458
$262$	96.1635	+	494.158i	0.0226756	+	0.116524i
$263$	−1402.01	+	1402.01i	−0.328715	+	0.328715i	−0.852098	−	0.523383i	$-0.824670\pi$
$263$	−1402.01	+	1402.01i	−0.328715	+	0.328715i	0.523383	+	0.852098i	$0.324670\pi$
$264$	−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
$268$	6218.78	+	2636.60i	1.41744	+	0.600956i
$269$			5544.00i			1.25659i	0.777974	+	0.628297i	$0.216248\pi$
$269$			5544.00i			1.25659i	−0.777974	+	0.628297i	$0.783752\pi$
$270$		0			0
$271$			4627.71i			1.03732i	0.854981	+	0.518659i	$0.173569\pi$
$271$			4627.71i			1.03732i	−0.854981	+	0.518659i	$0.826431\pi$
$272$	119.622	−	7203.49i	0.0266660	−	1.60579i
$273$	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	−0.840730	−	0.541455i	$-0.817874\pi$
$277$	−1379.72	+	1379.72i	−0.299275	+	0.299275i	0.541455	+	0.840730i	$0.317874\pi$
$278$	2141.35	−	416.708i	0.461978	−	0.0899011i
$279$	−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	$0.690519\pi$
$282$	−2415.42	+	470.042i	−0.510058	+	0.0992575i
$283$	−4894.75	+	4894.75i	−1.02814	+	1.02814i	−0.0285448	+	0.999593i	$0.509087\pi$
$283$	−4894.75	+	4894.75i	−1.02814	+	1.02814i	−0.999593	+	0.0285448i	$0.990913\pi$
$284$	−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
$288$	−2522.67	−	1762.41i	−0.516145	−	0.360593i
$289$		−	7759.00i		−	1.57928i
$290$		0			0
$291$		−	2017.21i		−	0.406360i
$292$	−5251.09	−	2226.32i	−1.05239	−	0.446184i
$293$	−371.462	−	371.462i	−0.0740650	−	0.0740650i	0.669104	−	0.743169i	$-0.266678\pi$
$293$	−371.462	−	371.462i	−0.0740650	−	0.0740650i	−0.743169	+	0.669104i	$0.766678\pi$
$294$	−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
$298$	−56.1890	−	288.740i	−0.0109226	−	0.0561284i
$299$	5576.98			1.07868
$300$		0			0
$301$	2750.00			0.526603
$302$	−961.635	−	4941.58i	−0.183231	−	0.941577i
$303$	−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	$-0.287984\pi$
$307$	−905.608	−	905.608i	−0.168357	−	0.168357i	−0.786257	+	0.617900i	$0.787984\pi$
$308$	−2929.37	+	6909.32i	−0.541937	+	1.27823i
$309$		−	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	$0.609765\pi$
$312$	2250.86	−	1463.76i	0.408429	−	0.265606i
$313$	−4882.07	−	4882.07i	−0.881633	−	0.881633i	0.112068	−	0.993701i	$-0.464253\pi$
$313$	−4882.07	−	4882.07i	−0.881633	−	0.881633i	−0.993701	+	0.112068i	$0.964253\pi$
$314$	−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	−0.926448	−	0.376422i	$-0.877154\pi$
$317$	−3104.36	+	3104.36i	−0.550026	+	0.550026i	0.376422	+	0.926448i	$0.377154\pi$
$318$	329.439	−	64.1090i	0.0580944	−	0.0113052i
$319$	−2729.16			−0.479008
$320$		0			0
$321$	−2450.00			−0.425999
$322$	6524.41	−	1269.65i	1.12917	−	0.219736i
$323$	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
$328$	3566.19	−	2319.14i	0.600335	−	0.390406i
$329$			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	$-0.0840790\pi$
$332$	−977.617	+	2305.84i	−0.161608	+	0.381173i
$333$	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	−0.177768	−	0.984073i	$-0.556888\pi$
$337$	4988.20	−	4988.20i	0.806305	−	0.806305i	0.984073	+	0.177768i	$0.0568875\pi$
$338$	426.280	+	2190.54i	0.0685993	+	0.352513i
$339$	−711.955			−0.114065
$340$		0			0
$341$	7040.00			1.11800
$342$	−544.926	−	2800.23i	−0.0861586	−	0.442746i
$343$	−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	$-0.130162\pi$
$347$	3360.81	+	3360.81i	0.519936	+	0.519936i	−0.397616	+	0.917552i	$0.630162\pi$
$348$	1071.40	+	454.246i	0.165038	+	0.0699717i
$349$			5774.00i			0.885602i	0.896620	+	0.442801i	$0.146015\pi$
$349$			5774.00i			0.885602i	−0.896620	+	0.442801i	$0.853985\pi$
$350$		0			0
$351$		−	5221.00i		−	0.793950i
$352$	8804.06	+	6150.76i	1.33312	+	0.931354i
$353$	424.528	+	424.528i	0.0640095	+	0.0640095i	0.738387	−	0.674377i	$-0.235588\pi$
$353$	424.528	+	424.528i	0.0640095	+	0.0640095i	−0.674377	+	0.738387i	$0.735588\pi$
$354$	−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
$358$	1811.91	−	352.599i	0.267493	−	0.0520544i
$359$	7000.89			1.02923			0.514614	−	0.857422i	$-0.327935\pi$
$359$	7000.89			1.02923			0.514614	+	0.857422i	$0.327935\pi$
$360$		0			0
$361$	−3339.00			−0.486806
$362$	−11666.2	+	2270.25i	−1.69382	+	0.329618i
$363$	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	$-0.198449\pi$
$367$	1603.26	+	1603.26i	0.228037	+	0.228037i	−0.583835	+	0.811872i	$0.698449\pi$
$368$	157.938	−	9510.82i	0.0223725	−	1.34724i
$369$		−	3196.00i		−	0.450886i
$370$		0			0
$371$		−	593.296i		−	0.0830253i
$372$	−2763.73	−	1171.75i	−0.385195	−	0.163313i
$373$	1220.52	+	1220.52i	0.169426	+	0.169426i	0.786727	−	0.617301i	$-0.211774\pi$
$373$	1220.52	+	1220.52i	0.169426	+	0.169426i	−0.617301	+	0.786727i	$0.711774\pi$
$374$	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
$378$	−1188.61	−	6107.96i	−0.161734	−	0.831110i
$379$	−1839.22			−0.249272			−0.124636	−	0.992203i	$-0.539776\pi$
$379$	−1839.22			−0.249272			−0.124636	+	0.992203i	$0.539776\pi$
$380$		0			0
$381$	3410.00			0.458529
$382$	2051.49	+	10542.0i	0.274773	+	1.41198i
$383$	8789.98	−	8789.98i	1.17271	−	1.17271i	0.191146	−	0.981562i	$-0.438779\pi$
$383$	8789.98	−	8789.98i	1.17271	−	1.17271i	0.981562	−	0.191146i	$-0.0612205\pi$
$384$	−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
$388$	−1991.97	+	4698.34i	−0.260637	+	0.614748i
$389$		−	3096.00i		−	0.403531i	−0.979434	−	0.201765i	$-0.935332\pi$
$389$		−	3096.00i		−	0.403531i	0.979434	−	0.201765i	$-0.0646678\pi$
$390$		0			0
$391$		−	16730.9i		−	2.16399i
$392$	1147.23	+	1764.13i	0.147817	+	0.227301i
$393$	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	−0.491719	−	0.870754i	$-0.663631\pi$
$397$	2998.23	−	2998.23i	0.379035	−	0.379035i	0.870754	+	0.491719i	$0.163631\pi$
$398$	−13177.6	+	2564.36i	−1.65963	+	0.322964i
$399$	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	$0.535312\pi$
$402$	7412.84	−	1442.54i	0.919699	−	0.178974i
$403$	−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
$408$	−4391.29	−	6752.57i	−0.532846	−	0.819368i
$409$			5804.00i			0.701685i	0.936434	+	0.350843i	$0.114105\pi$
$409$			5804.00i			0.701685i	−0.936434	+	0.350843i	$0.885895\pi$
$410$		0			0
$411$			2135.87i			0.256337i
$412$	−4651.09	+	10970.2i	−0.556171	+	1.31181i
$413$	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
$418$	1901.78	+	9772.74i	0.222534	+	1.14354i
$419$	4805.70			0.560319			0.280159	−	0.959953i	$-0.409613\pi$
$419$	4805.70			0.560319			0.280159	+	0.959953i	$0.409613\pi$
$420$		0			0
$421$	1672.00			0.193559			0.0967794	−	0.995306i	$-0.469146\pi$
$421$	1672.00			0.193559			0.0967794	+	0.995306i	$0.469146\pi$
$422$	352.599	+	1811.91i	0.0406736	+	0.209011i
$423$	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
$428$	5706.38	+	2419.36i	0.644458	+	0.273234i
$429$			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	$0.997889\pi$
$432$	−8903.75	−	147.857i	−0.991624	−	0.0164671i
$433$	6394.45	+	6394.45i	0.709695	+	0.709695i	0.966471	−	0.256776i	$-0.0826603\pi$
$433$	6394.45	+	6394.45i	0.709695	+	0.709695i	−0.256776	+	0.966471i	$0.582660\pi$
$434$	−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
$438$	−6259.34	+	1218.07i	−0.682838	+	0.132881i
$439$	−10560.7			−1.14814			−0.574070	−	0.818806i	$-0.694636\pi$
$439$	−10560.7			−1.14814			−0.574070	+	0.818806i	$0.694636\pi$
$440$		0			0
$441$	1581.00			0.170716
$442$	−11727.3	+	2282.14i	−1.26201	+	0.245589i
$443$	−12153.0	+	12153.0i	−1.30340	+	1.30340i	−0.377321	+	0.926082i	$0.623155\pi$
$443$	−12153.0	+	12153.0i	−1.30340	+	1.30340i	−0.926082	+	0.377321i	$0.876845\pi$
$444$	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
$448$	−7554.04	+	2910.76i	−0.796640	+	0.306966i
$449$		−	2476.00i		−	0.260244i	−0.991498	−	0.130122i	$-0.958463\pi$
$449$		−	2476.00i		−	0.260244i	0.991498	−	0.130122i	$-0.0415369\pi$
$450$		0			0
$451$			11154.0i			1.16457i
$452$	1658.24	+	703.050i	0.172560	+	0.0731608i
$453$	−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	−0.103788	−	0.994599i	$-0.533096\pi$
$457$	8702.82	−	8702.82i	0.890812	−	0.890812i	0.994599	+	0.103788i	$0.0330963\pi$
$458$	−1801.29	−	9256.34i	−0.183774	−	0.944367i
$459$	−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	$0.748186\pi$
$462$	1602.72	+	8235.97i	0.161397	+	0.829377i
$463$	3204.29	−	3204.29i	0.321632	−	0.321632i	−0.527761	−	0.849393i	$-0.676968\pi$
$463$	3204.29	−	3204.29i	0.321632	−	0.321632i	0.849393	+	0.527761i	$0.176968\pi$
$464$	−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	$-0.281620\pi$
$467$	−1415.43	−	1415.43i	−0.140253	−	0.140253i	−0.773748	+	0.633494i	$0.781620\pi$
$468$	−1991.97	+	4698.34i	−0.196750	+	0.464062i
$469$		−	13350.0i		−	1.31438i
$470$		0			0
$471$			11628.6i			1.13762i
$472$	7878.00	−	5123.17i	0.768251	−	0.499604i
$473$	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
$478$	9553.73	−	1859.16i	0.914179	−	0.177900i
$479$	14476.4			1.38089			0.690443	−	0.723387i	$-0.257416\pi$
$479$	14476.4			1.38089			0.690443	+	0.723387i	$0.257416\pi$
$480$		0			0
$481$	11264.0			1.06776
$482$	8406.78	−	1635.96i	0.794436	−	0.154598i
$483$	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	$-0.239649\pi$
$487$	494.171	+	494.171i	0.0459816	+	0.0459816i	−0.683742	+	0.729724i	$0.739649\pi$
$488$	−1365.78	+	888.181i	−0.126692	+	0.0823895i
$489$		−	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	$0.981764\pi$
$492$	1856.48	−	4378.77i	0.170115	−	0.401240i
$493$	−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
$498$	534.876	+	2748.58i	0.0481292	+	0.247323i
$499$	11569.3			1.03790			0.518950	−	0.854805i	$-0.326323\pi$
$499$	11569.3			1.03790			0.518950	+	0.854805i	$0.326323\pi$
$500$		0			0
$501$	330.000			0.0294278
$502$	−1121.91	−	5765.18i	−0.0997474	−	0.512575i
$503$	6549.44	−	6549.44i	0.580567	−	0.580567i	−0.354492	−	0.935059i	$-0.615346\pi$
$503$	6549.44	−	6549.44i	0.580567	−	0.580567i	0.935059	+	0.354492i	$0.115346\pi$
$504$	−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
$508$	−7942.34	−	3367.35i	−0.693670	−	0.294098i
$509$			1554.00i			0.135324i	0.997708	+	0.0676619i	$0.0215539\pi$
$509$			1554.00i			0.135324i	−0.997708	+	0.0676619i	$0.978446\pi$
$510$		0			0
$511$			11272.6i			0.975874i
$512$	1834.18	+	11439.1i	0.158320	+	0.987388i
$513$	−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
$518$	13177.6	−	2564.36i	1.11774	−	0.217513i
$519$	−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	$0.576180\pi$
$522$	−2171.10	+	422.498i	−0.182043	+	0.0354257i
$523$	2475.33	−	2475.33i	0.206957	−	0.206957i	−0.596016	−	0.802973i	$-0.703250\pi$
$523$	2475.33	−	2475.33i	0.206957	−	0.206957i	0.802973	+	0.596016i	$0.203250\pi$
$524$	−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
$528$	12005.8	+	199.370i	0.989556	+	0.0164327i
$529$		−	9923.00i		−	0.815567i
$530$		0			0
$531$		−	7060.22i		−	0.577001i
$532$	−6909.32	−	2929.37i	−0.563077	−	0.238730i
$533$	−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
$538$	−2995.30	−	15392.1i	−0.240031	−	1.23346i
$539$	−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	$0.720594\pi$
$542$	−2500.25	−	12848.1i	−0.198146	−	1.01822i
$543$	−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	$-0.105290\pi$
$547$	7944.75	+	7944.75i	0.621011	+	0.621011i	−0.324779	+	0.945790i	$0.605290\pi$
$548$	2109.15	−	4974.71i	0.164413	−	0.387791i
$549$			1224.00i			0.0951531i
$550$		0			0
$551$		−	2729.16i		−	0.211009i
$552$	−5797.85	−	8915.48i	−0.447052	−	0.687442i
$553$	−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	−0.657004	−	0.753887i	$-0.728177\pi$
$557$	1273.58	−	1273.58i	0.0968824	−	0.0968824i	0.753887	+	0.657004i	$0.228177\pi$
$558$	5600.46	−	1089.85i	0.424886	−	0.0826831i
$559$	−6526.25			−0.493795
$560$		0			0
$561$	21120.0			1.58946
$562$	14736.8	−	2867.80i	1.10611	−	0.215250i
$563$	−8803.40	+	8803.40i	−0.659004	+	0.659004i	−0.955144	−	0.296141i	$-0.904300\pi$
$563$	−8803.40	+	8803.40i	−0.659004	+	0.659004i	0.296141	+	0.955144i	$0.404300\pi$
$564$	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
$568$	8782.57	+	13505.1i	0.648783	+	0.997647i
$569$			24564.0i			1.80980i	0.425624	+	0.904900i	$0.360055\pi$
$569$			24564.0i			1.80980i	−0.425624	+	0.904900i	$0.639945\pi$
$570$		0			0
$571$		−	17027.6i		−	1.24796i	−0.781442	−	0.623978i	$-0.785516\pi$
$571$		−	17027.6i		−	1.24796i	0.781442	−	0.623978i	$-0.214484\pi$
$572$	6951.94	−	16397.1i	0.508174	−	1.19860i
$573$	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	−1.00000		0.000706135i	$-0.999775\pi$
$577$	−13850.2	+	13850.2i	−0.999294	+	0.999294i	0.000706135		1.00000i	$0.499775\pi$
$578$	4192.02	+	21541.7i	0.301670	+	1.55020i
$579$	8187.48			0.587669
$580$		0			0
$581$	4950.00			0.353461
$582$	1089.85	+	5600.46i	0.0776217	+	0.398877i
$583$	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	$-0.205942\pi$
$587$	2774.96	+	2774.96i	0.195119	+	0.195119i	−0.602785	+	0.797904i	$0.705942\pi$
$588$	2166.09	+	918.368i	0.151919	+	0.0644096i
$589$			7040.00i			0.492493i
$590$		0			0
$591$		−	830.614i		−	0.0578120i
$592$	318.992	−	19209.3i	0.0221461	−	1.33361i
$593$	−13638.0	−	13638.0i	−0.944425	−	0.944425i	0.0541101	−	0.998535i	$-0.482768\pi$
$593$	−13638.0	−	13638.0i	−0.944425	−	0.944425i	−0.998535	+	0.0541101i	$0.982768\pi$
$594$	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
$598$	−15483.6	+	3013.12i	−1.05882	+	0.206046i
$599$	−3559.78			−0.242819			−0.121409	−	0.992603i	$-0.538741\pi$
$599$	−3559.78			−0.242819			−0.121409	+	0.992603i	$0.538741\pi$
$600$		0			0
$601$	2572.00			0.174566			0.0872829	−	0.996184i	$-0.472182\pi$
$601$	2572.00			0.174566			0.0872829	+	0.996184i	$0.472182\pi$
$602$	−7634.95	+	1485.77i	−0.516906	+	0.100590i
$603$	−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	$-0.423150\pi$
$607$	−10945.6	−	10945.6i	−0.731905	−	0.731905i	−0.970997	+	0.239092i	$0.923150\pi$
$608$	−6150.76	+	8804.06i	−0.410274	+	0.587256i
$609$		−	2300.00i		−	0.153039i
$610$		0			0
$611$		−	10323.3i		−	0.683532i
$612$	14095.0	+	5975.92i	0.930976	+	0.394710i
$613$	10109.1	+	10109.1i	0.666071	+	0.666071i	0.956804	−	0.290733i	$-0.0938992\pi$
$613$	10109.1	+	10109.1i	0.666071	+	0.666071i	−0.290733	+	0.956804i	$0.593899\pi$
$614$	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	−0.850201	−	0.526458i	$-0.823520\pi$
$617$	−4961.67	+	4961.67i	−0.323743	+	0.323743i	0.526458	+	0.850201i	$0.323520\pi$
$618$	2544.71	+	13076.6i	0.165636	+	0.851161i
$619$	19638.1			1.27516			0.637578	−	0.770386i	$-0.279936\pi$
$619$	19638.1			1.27516			0.637578	+	0.770386i	$0.279936\pi$
$620$		0			0
$621$	−20680.0			−1.33633
$622$	−5577.48	−	28661.2i	−0.359544	−	1.84760i
$623$	−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
$628$	11483.1	−	27084.6i	0.729662	−	1.72101i
$629$		−	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	$-0.174175\pi$
$632$	−15756.0	+	10246.3i	−0.991678	+	0.644901i
$633$	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
$638$	7577.10	−	1474.51i	0.470188	−	0.0914989i
$639$	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	$0.178399\pi$
$642$	6802.05	−	1323.68i	0.418155	−	0.0813732i
$643$	10095.8	−	10095.8i	0.619193	−	0.619193i	−0.326131	−	0.945325i	$-0.605745\pi$
$643$	10095.8	−	10095.8i	0.619193	−	0.619193i	0.945325	+	0.326131i	$0.105745\pi$
$644$	−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	$-0.0371421\pi$
$647$	14429.3	+	14429.3i	0.876779	+	0.876779i	−0.116421	+	0.993200i	$0.537142\pi$
$648$	360.413	−	234.381i	0.0218493	−	0.0142089i
$649$			24640.0i			1.49030i
$650$		0			0
$651$			5932.96i			0.357190i
$652$	−69.1244	+	163.039i	−0.00415203	+	0.00979312i
$653$	−21730.5	−	21730.5i	−1.30227	−	1.30227i	−0.926859	−	0.375409i	$-0.877502\pi$
$653$	−21730.5	−	21730.5i	−1.30227	−	1.30227i	−0.375409	−	0.926859i	$-0.622498\pi$
$654$	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
$658$	−2350.21	−	12077.1i	−0.139241	−	0.715524i
$659$	−19400.8			−1.14681			−0.573404	−	0.819273i	$-0.694378\pi$
$659$	−19400.8			−1.14681			−0.573404	+	0.819273i	$0.694378\pi$
$660$		0			0
$661$	−6048.00			−0.355885			−0.177942	−	0.984041i	$-0.556944\pi$
$661$	−6048.00			−0.355885			−0.177942	+	0.984041i	$0.556944\pi$
$662$	1698.89	+	8730.13i	0.0997419	+	0.512547i
$663$	−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
$668$	−768.614	−	325.872i	−0.0445188	−	0.0188748i
$669$			670.000i			0.0387200i
$670$		0			0
$671$		−	4271.73i		−	0.245765i
$672$	−5183.55	+	7419.62i	−0.297559	+	0.425920i
$673$	17538.3	+	17538.3i	1.00454	+	1.00454i	0.999990	+	0.00454561i	$0.00144692\pi$
$673$	17538.3	+	17538.3i	1.00454	+	1.00454i	0.00454561	+	0.999990i	$0.498553\pi$
$674$	−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	−0.490407	−	0.871494i	$-0.663152\pi$
$677$	6712.85	−	6712.85i	0.381087	−	0.381087i	0.871494	+	0.490407i	$0.163152\pi$
$678$	1976.63	−	384.654i	0.111965	−	0.0217884i
$679$	10086.0			0.570053
$680$		0			0
$681$	−6490.00			−0.365194
$682$	−19545.5	+	3803.56i	−1.09741	+	0.213557i
$683$	22720.7	−	22720.7i	1.27289	−	1.27289i	0.328323	−	0.944565i	$-0.393517\pi$
$683$	22720.7	−	22720.7i	1.27289	−	1.27289i	0.944565	−	0.328323i	$-0.106483\pi$
$684$	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
$688$	−184.821	+	11129.7i	−0.0102416	+	0.616737i
$689$			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	$0.617601\pi$
$692$	23768.1	+	10077.0i	1.30567	+	0.553572i
$693$	−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
$698$	−3119.57	−	16030.6i	−0.169165	−	0.869295i
$699$	−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	$0.631739\pi$
$702$	2820.80	+	14495.3i	0.151658	+	0.779331i
$703$	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
$708$	4101.12	−	9673.05i	0.217697	−	0.513468i
$709$		−	20966.0i		−	1.11057i	−0.831660	−	0.555285i	$-0.812609\pi$
$709$		−	20966.0i		−	1.11057i	0.831660	−	0.555285i	$-0.187391\pi$
$710$		0			0
$711$			14120.4i			0.744807i
$712$	8955.83	+	13771.6i	0.471396	+	0.724875i
$713$	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
$718$	−19436.9	+	3782.43i	−1.01028	+	0.196600i
$719$	−13883.1			−0.720102			−0.360051	−	0.932933i	$-0.617241\pi$
$719$	−13883.1			−0.720102			−0.360051	+	0.932933i	$0.617241\pi$
$720$		0			0
$721$	23550.0			1.21643
$722$	9270.22	−	1803.99i	0.477842	−	0.0929883i
$723$	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	$-0.117327\pi$
$727$	11222.8	+	11222.8i	0.572533	+	0.572533i	−0.360302	+	0.932836i	$0.617327\pi$
$728$	7318.81	+	11254.3i	0.372600	+	0.572956i
$729$			11557.0i			0.587156i
$730$		0			0
$731$			19578.8i			0.990625i
$732$	−710.994	+	1676.98i	−0.0359004	+	0.0846760i
$733$	18732.3	+	18732.3i	0.943920	+	0.943920i	0.998509	−	0.0545892i	$-0.0173849\pi$
$733$	18732.3	+	18732.3i	0.943920	+	0.943920i	−0.0545892	+	0.998509i	$0.517385\pi$
$734$	−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
$738$	1726.73	+	8873.20i	0.0861271	+	0.442584i
$739$	−16790.3			−0.835778			−0.417889	−	0.908498i	$-0.637230\pi$
$739$	−16790.3			−0.835778			−0.417889	+	0.908498i	$0.637230\pi$
$740$		0			0
$741$	−7040.00			−0.349016
$742$	320.545	+	1647.19i	0.0158593	+	0.0814965i
$743$	−18078.6	+	18078.6i	−0.892651	+	0.892651i	−0.994772	−	0.102121i	$-0.967437\pi$
$743$	−18078.6	+	18078.6i	−0.892651	+	0.892651i	0.102121	+	0.994772i	$0.467437\pi$
$744$	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
$748$	−49191.3	−	20855.8i	−2.40456	−	1.01947i
$749$		−	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	$-0.00917744\pi$
$752$	−17605.1	−	292.353i	−0.853714	−	0.0141769i
$753$	−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	−0.255865	−	0.966713i	$-0.582360\pi$
$757$	14805.4	−	14805.4i	0.710848	−	0.710848i	0.966713	+	0.255865i	$0.0823601\pi$
$758$	5106.30	−	993.689i	0.244682	−	0.0476153i
$759$	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	$0.505140\pi$
$762$	−9467.34	+	1842.35i	−0.450086	+	0.0875870i
$763$	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
$768$	8849.78	+	9457.99i	0.415806	+	0.444383i
$769$		−	10546.0i		−	0.494536i	−0.968947	−	0.247268i	$-0.920467\pi$
$769$		−	10546.0i		−	0.494536i	0.968947	−	0.247268i	$-0.0795329\pi$
$770$		0			0
$771$		−	10916.6i		−	0.509927i
$772$	−19069.7	−	8085.07i	−0.889035	−	0.376928i
$773$	19395.6	+	19395.6i	0.902474	+	0.902474i	0.995650	−	0.0931761i	$-0.0297020\pi$
$773$	19395.6	+	19395.6i	0.902474	+	0.902474i	−0.0931761	+	0.995650i	$0.529702\pi$
$774$	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
$778$	1672.70	+	8595.57i	0.0770813	+	0.396100i
$779$	−11154.0			−0.513007
$780$		0			0
$781$	−42240.0			−1.93530
$782$	9039.37	+	46450.9i	0.413359	+	2.12414i
$783$	−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	$-0.410314\pi$
$787$	−15068.9	−	15068.9i	−0.682525	−	0.682525i	−0.960568	+	0.278044i	$0.910314\pi$
$788$	−820.225	+	1934.61i	−0.0370803	+	0.0874590i
$789$		−	6270.00i		−	0.282912i
$790$		0			0
$791$		−	3559.78i		−	0.160014i
$792$	−19132.3	+	12442.0i	−0.858379	+	0.558215i
$793$	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	−0.978934	−	0.204179i	$-0.934548\pi$
$797$	−17432.2	+	17432.2i	−0.774755	+	0.774755i	0.204179	+	0.978934i	$0.434548\pi$
$798$	−8235.97	+	1602.72i	−0.365351	+	0.0710975i
$799$	−30970.0			−1.37127
$800$		0			0
$801$	12342.0			0.544423
$802$	4936.34	−	960.615i	0.217342	−	0.0422949i
$803$	−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
$808$	−26215.3	+	17048.1i	−1.14140	+	0.742267i
$809$			34854.0i			1.51471i	0.653003	+	0.757356i	$0.273509\pi$
$809$			34854.0i			1.51471i	−0.653003	+	0.757356i	$0.726491\pi$
$810$		0			0
$811$		−	10738.7i		−	0.464963i	−0.972601	−	0.232482i	$-0.925315\pi$
$811$		−	10738.7i		−	0.464963i	0.972601	−	0.232482i	$-0.0746846\pi$
$812$	−2271.23	+	5357.01i	−0.0981584	+	0.231520i
$813$	−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
$818$	−3135.78	−	16113.9i	−0.134034	−	0.688765i
$819$	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	$0.436028\pi$
$822$	−1153.96	−	5929.90i	−0.0489648	−	0.251617i
$823$	31499.5	−	31499.5i	1.33415	−	1.33415i	0.432526	−	0.901622i	$-0.357623\pi$
$823$	31499.5	−	31499.5i	1.33415	−	1.33415i	0.901622	−	0.432526i	$-0.142377\pi$
$824$	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	$-0.484941\pi$
$827$	−22631.2	−	22631.2i	−0.951591	−	0.951591i	−0.998881	+	0.0472905i	$0.984941\pi$
$828$	18609.8	+	7890.06i	0.781080	+	0.331158i
$829$			43384.0i			1.81760i	0.417234	+	0.908799i	$0.362999\pi$
$829$			43384.0i			1.81760i	−0.417234	+	0.908799i	$0.637001\pi$
$830$		0			0
$831$		−	6170.28i		−	0.257575i
$832$	17927.1	−	6907.77i	0.747008	−	0.287841i
$833$	−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
$838$	−13342.3	+	2596.41i	−0.550002	+	0.107031i
$839$	−11747.3			−0.483385			−0.241693	−	0.970353i	$-0.577703\pi$
$839$	−11747.3			−0.483385			−0.241693	+	0.970353i	$0.577703\pi$
$840$		0			0
$841$	22273.0			0.913240
$842$	−4642.05	+	903.345i	−0.189995	+	0.0369731i
$843$	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
$848$	2401.16	+	39.8740i	0.0972361	+	0.00161472i
$849$		−	21890.0i		−	0.884880i
$850$		0			0
$851$		−	44615.9i		−	1.79719i
$852$	16582.4	+	7030.50i	0.666787	+	0.282701i
$853$	17273.0	+	17273.0i	0.693336	+	0.693336i	0.962964	−	0.269628i	$-0.0869009\pi$
$853$	17273.0	+	17273.0i	0.693336	+	0.693336i	−0.269628	+	0.962964i	$0.586901\pi$
$854$	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	−0.544653	−	0.838662i	$-0.683339\pi$
$857$	7376.17	−	7376.17i	0.294009	−	0.294009i	0.838662	+	0.544653i	$0.183339\pi$
$858$	−3803.56	−	19545.5i	−0.151342	−	0.777706i
$859$	43488.6			1.72737			0.863685	−	0.504031i	$-0.168150\pi$
$859$	43488.6			1.72737			0.863685	+	0.504031i	$0.168150\pi$
$860$		0			0
$861$	−9400.00			−0.372069
$862$	−64.1090	−	329.439i	−0.00253313	−	0.0130171i
$863$	8816.82	−	8816.82i	0.347773	−	0.347773i	−0.511507	−	0.859279i	$-0.670912\pi$
$863$	8816.82	−	8816.82i	0.347773	−	0.347773i	0.859279	+	0.511507i	$0.170912\pi$
$864$	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
$868$	5858.75	−	13818.6i	0.229100	−	0.540363i
$869$		−	49280.0i		−	1.92372i
$870$		0			0
$871$			31682.0i			1.23250i
$872$	−9671.31	−	14871.8i	−0.375587	−	0.577548i
$873$	−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	−0.819833	−	0.572602i	$-0.805934\pi$
$877$	−6420.99	+	6420.99i	−0.247231	+	0.247231i	0.572602	+	0.819833i	$0.305934\pi$
$878$	29320.1	−	5705.70i	1.12700	−	0.219314i
$879$	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	$0.359299\pi$
$882$	−4389.40	+	854.180i	−0.167572	+	0.0326097i
$883$	−16477.6	+	16477.6i	−0.627990	+	0.627990i	−0.947562	−	0.319572i	$-0.896461\pi$
$883$	−16477.6	+	16477.6i	−0.627990	+	0.627990i	0.319572	+	0.947562i	$0.396461\pi$
$884$	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	$-0.102009\pi$
$887$	16750.4	+	16750.4i	0.634073	+	0.634073i	−0.315014	+	0.949087i	$0.602009\pi$
$888$	−11710.1	−	18006.9i	−0.442528	−	0.680485i
$889$			17050.0i			0.643238i
$890$		0			0
$891$			1127.26i			0.0423846i
$892$	661.620	−	1560.52i	0.0248348	−	0.0585763i
$893$	−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
$898$	1337.73	+	6874.23i	0.0497111	+	0.255452i
$899$	5458.32			0.202497
$900$		0			0
$901$	4224.00			0.156184
$902$	−6026.25	−	30967.3i	−0.222452	−	1.14312i
$903$	−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	$-0.0481633\pi$
$907$	22886.2	+	22886.2i	0.837842	+	0.837842i	−0.150733	+	0.988575i	$0.548163\pi$
$908$	15116.1	+	6408.82i	0.552472	+	0.234234i
$909$			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	$-0.144319\pi$
$912$	−199.370	+	12005.8i	−0.00723882	+	0.435912i
$913$	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
$918$	43485.9	−	8462.39i	1.56345	−	0.304249i
$919$	34173.8			1.22665			0.613325	−	0.789831i	$-0.289832\pi$
$919$	34173.8			1.22665			0.613325	+	0.789831i	$0.289832\pi$
$920$		0			0
$921$	4050.00			0.144899
$922$	38641.2	−	7519.59i	1.38024	−	0.268595i
$923$	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
$928$	6826.05	+	4768.87i	0.241461	+	0.168692i
$929$		−	13996.0i		−	0.494288i	−0.968979	−	0.247144i	$-0.920508\pi$
$929$		−	13996.0i		−	0.494288i	0.968979	−	0.247144i	$-0.0794921\pi$
$930$		0			0
$931$		−	5517.65i		−	0.194236i
$932$	11331.3	+	4804.17i	0.398250	+	0.168848i
$933$	−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	−0.975553	−	0.219766i	$-0.929471\pi$
$937$	−21677.5	+	21677.5i	−0.755786	+	0.755786i	0.219766	+	0.975553i	$0.429471\pi$
$938$	7212.72	+	37064.2i	0.251070	+	1.29018i
$939$	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	$0.601380\pi$
$942$	−6282.68	−	32285.0i	−0.217304	−	1.11667i
$943$	−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	$-0.311114\pi$
$947$	−7864.25	−	7864.25i	−0.269856	−	0.269856i	−0.829042	+	0.559186i	$0.811114\pi$
$948$	−8202.25	+	19346.1i	−0.281009	+	0.662798i
$949$		−	26752.0i		−	0.915076i
$950$		0			0
$951$		−	13883.1i		−	0.473387i
$952$	33762.9	−	21956.4i	1.14943	−	0.747492i
$953$	−31680.4	−	31680.4i	−1.07684	−	1.07684i	−0.996791	−	0.0800494i	$-0.974492\pi$
$953$	−31680.4	−	31680.4i	−1.07684	−	1.07684i	−0.0800494	−	0.996791i	$-0.525508\pi$
$954$	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
$958$	−40191.6	+	7821.30i	−1.35546	+	0.263773i
$959$	−10679.3			−0.359597
$960$		0			0
$961$	15711.0			0.527374
$962$	−31272.8	+	6085.70i	−1.04810	+	0.203961i
$963$	−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	$-0.0288179\pi$
$967$	27228.6	+	27228.6i	0.905494	+	0.905494i	−0.0904105	+	0.995905i	$0.528818\pi$
$968$	41523.4	−	27003.2i	1.37873	−	0.896606i
$969$			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	$0.903991\pi$
$972$	11919.0	−	28112.6i	0.393316	−	0.927688i
$973$	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	−0.210020	+	0.977697i	$0.567353\pi$
$977$	−36270.6	+	36270.6i	−1.18772	+	1.18772i	−0.977697	+	0.210020i	$0.932647\pi$
$978$	37.8195	+	194.344i	0.00123654	+	0.00635424i
$979$	−43073.3			−1.40616
$980$		0			0
$981$	−13328.0			−0.433772
$982$	−673.144	−	3459.11i	−0.0218746	−	0.112408i
$983$	−3709.64	+	3709.64i	−0.120365	+	0.120365i	−0.764724	−	0.644358i	$-0.777125\pi$
$983$	−3709.64	+	3709.64i	−0.120365	+	0.120365i	0.644358	+	0.764724i	$0.277125\pi$
$984$	−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
$988$	16397.1	+	6951.94i	0.527997	+	0.223857i
$989$			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	$0.836756\pi$
$992$	−17608.1	−	12301.5i	−0.563567	−	0.393724i
$993$	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	−0.0886702	+	0.996061i	$0.528262\pi$
$997$	−34148.0	+	34148.0i	−1.08473	+	1.08473i	−0.996061	+	0.0886702i	$0.971738\pi$
$998$	−32120.3	+	6250.63i	−1.01879	+	0.198257i
$999$	−41768.0			−1.32280

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-2.77635 + 0.540278i) q^{2} +(-2.23607 + 2.23607i) q^{3} +(7.41620 - 3.00000i) q^{4} +(5.00000 - 7.41620i) q^{6} +(-11.1803 - 11.1803i) q^{7} +(-18.9691 + 12.3359i) q^{8} +17.0000i q^{9} +O(q^{10})\)	\(q+(-2.77635 + 0.540278i) 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} +(-18.9691 + 12.3359i) q^{8} +17.0000i q^{9} -59.3296i q^{11} +(-9.87492 + 23.2913i) 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} +(-9.18473 - 47.1979i) q^{18} +59.3296 q^{19} +50.0000 q^{21} +(32.0545 + 164.719i) 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} +(-116.457 - 49.3746i) q^{28} -46.0000i q^{29} +118.659i q^{31} +(-103.671 + 148.392i) 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} +(-164.719 + 32.0545i) q^{38} -118.659 q^{39} -188.000 q^{41} +(-138.817 + 27.0139i) 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} +(-3.36038 + 202.358i) q^{48} -93.0000i q^{49} +355.978i q^{51} +(276.373 + 117.175i) 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} +(24.8528 + 127.712i) q^{58} -415.307 q^{59} +72.0000 q^{61} +(-64.1090 - 329.439i) 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} +(351.525 - 829.119i) q^{68} +470.000i q^{69} -711.955i q^{71} +(-209.709 - 322.475i) 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} +(329.439 - 64.1090i) q^{78} +830.614 q^{79} -19.0000 q^{81} +(521.953 - 101.572i) 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} +(731.881 + 1125.43i) q^{88} -726.000i q^{89} -593.296i q^{91} +(464.121 - 1094.69i) 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} +(50.2459 + 258.200i) 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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