LMFDB - Embedded newform 100.4.e.f.43.7

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:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.7
Character	$\chi$	$=$	100.43
Dual form			100.4.e.f.7.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.933623 - 2.66990i) q^{2} +(-3.69377 + 3.69377i) q^{3} +(-6.25670 - 4.98535i) q^{4} +(6.41339 + 13.3106i) q^{6} +(19.3489 + 19.3489i) q^{7} +(-19.1518 + 12.0503i) q^{8} -0.287847i q^{9} +O(q^{10})$	\(q+(0.933623 - 2.66990i) q^{2} +(-3.69377 + 3.69377i) q^{3} +(-6.25670 - 4.98535i) q^{4} +(6.41339 + 13.3106i) q^{6} +(19.3489 + 19.3489i) q^{7} +(-19.1518 + 12.0503i) q^{8} -0.287847i q^{9} -23.4011i q^{11} +(41.5255 - 4.69604i) q^{12} +(62.9078 + 62.9078i) q^{13} +(69.7241 - 33.5950i) q^{14} +(14.2925 + 62.3837i) q^{16} +(-0.872206 + 0.872206i) q^{17} +(-0.768522 - 0.268741i) q^{18} +57.0354 q^{19} -142.941 q^{21} +(-62.4786 - 21.8479i) q^{22} +(-116.421 + 116.421i) q^{23} +(26.2312 - 115.253i) q^{24} +(226.690 - 109.225i) q^{26} +(-98.6685 - 98.6685i) q^{27} +(-24.5991 - 217.521i) q^{28} +121.516i q^{29} -66.8861i q^{31} +(179.902 + 20.0834i) q^{32} +(86.4384 + 86.4384i) q^{33} +(1.51439 + 3.14301i) q^{34} +(-1.43502 + 1.80097i) q^{36} +(-36.6685 + 36.6685i) q^{37} +(53.2496 - 152.279i) q^{38} -464.734 q^{39} -302.608 q^{41} +(-133.453 + 381.637i) q^{42} +(190.704 - 190.704i) q^{43} +(-116.663 + 146.414i) q^{44} +(202.139 + 419.526i) q^{46} +(54.1794 + 54.1794i) q^{47} +(-283.224 - 177.638i) q^{48} +405.760i q^{49} -6.44345i q^{51} +(-79.9774 - 707.213i) q^{52} +(-36.5947 - 36.5947i) q^{53} +(-355.554 + 171.316i) q^{54} +(-603.726 - 137.406i) q^{56} +(-210.676 + 210.676i) q^{57} +(324.436 + 113.451i) q^{58} +401.800 q^{59} +509.974 q^{61} +(-178.579 - 62.4464i) q^{62} +(5.56952 - 5.56952i) q^{63} +(221.581 - 461.569i) q^{64} +(311.483 - 150.081i) q^{66} +(187.627 + 187.627i) q^{67} +(9.80538 - 1.10887i) q^{68} -860.066i q^{69} -584.349i q^{71} +(3.46864 + 5.51278i) q^{72} +(-436.179 - 436.179i) q^{73} +(63.6666 + 132.136i) q^{74} +(-356.853 - 284.342i) q^{76} +(452.786 - 452.786i) q^{77} +(-433.886 + 1240.79i) q^{78} +608.649 q^{79} +736.689 q^{81} +(-282.522 + 807.933i) q^{82} +(124.596 - 124.596i) q^{83} +(894.337 + 712.610i) q^{84} +(-331.115 - 687.206i) q^{86} +(-448.853 - 448.853i) q^{87} +(281.991 + 448.174i) q^{88} -684.600i q^{89} +2434.39i q^{91} +(1308.81 - 148.011i) q^{92} +(247.062 + 247.062i) q^{93} +(195.237 - 94.0703i) q^{94} +(-738.699 + 590.332i) q^{96} +(384.093 - 384.093i) q^{97} +(1083.34 + 378.827i) q^{98} -6.73595 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 36 q^{6}+O(q^{10}) $ 24 * q + 36 * q^6	$ 24 q + 36 q^{6} - 676 q^{16} + 512 q^{21} + 2072 q^{26} - 4600 q^{36} - 392 q^{41} + 5016 q^{46} - 8224 q^{56} + 1088 q^{61} + 11140 q^{66} - 6700 q^{76} - 2424 q^{81} + 5216 q^{86} + 796 q^{96}+O(q^{100}) $ 24 * q + 36 * q^6 - 676 * q^16 + 512 * q^21 + 2072 * q^26 - 4600 * q^36 - 392 * q^41 + 5016 * q^46 - 8224 * q^56 + 1088 * q^61 + 11140 * q^66 - 6700 * q^76 - 2424 * q^81 + 5216 * q^86 + 796 * 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 $

$2$	0.933623	−	2.66990i	0.330086	−	0.943951i
$2$	0.933623	−	2.66990i	0.330086	−	0.943951i
$3$	−3.69377	+	3.69377i	−0.710866	+	0.710866i	−0.966716	−	0.255850i	$-0.917645\pi$
$3$	−3.69377	+	3.69377i	−0.710866	+	0.710866i	0.255850	+	0.966716i	$0.417645\pi$
$4$	−6.25670	−	4.98535i	−0.782087	−	0.623169i
$5$		0			0
$5$		0			0
$6$	6.41339	+	13.3106i	0.436376	+	0.905669i
$7$	19.3489	+	19.3489i	1.04474	+	1.04474i	0.998951	+	0.0457914i	$0.0145809\pi$
$7$	19.3489	+	19.3489i	1.04474	+	1.04474i	0.0457914	+	0.998951i	$0.485419\pi$
$8$	−19.1518	+	12.0503i	−0.846397	+	0.532553i
$9$		−	0.287847i		−	0.0106610i
$10$		0			0
$11$		−	23.4011i		−	0.641428i	−0.947176	−	0.320714i	$-0.896077\pi$
$11$		−	23.4011i		−	0.641428i	0.947176	−	0.320714i	$-0.103923\pi$
$12$	41.5255	−	4.69604i	0.998949	−	0.112969i
$13$	62.9078	+	62.9078i	1.34211	+	1.34211i	0.893952	+	0.448163i	$0.147922\pi$
$13$	62.9078	+	62.9078i	1.34211	+	1.34211i	0.448163	+	0.893952i	$0.352078\pi$
$14$	69.7241	−	33.5950i	1.33104	−	0.641331i
$15$		0			0
$16$	14.2925	+	62.3837i	0.223320	+	0.974745i
$17$	−0.872206	+	0.872206i	−0.0124436	+	0.0124436i	−0.713301	−	0.700858i	$-0.752801\pi$
$17$	−0.872206	+	0.872206i	−0.0124436	+	0.0124436i	0.700858	+	0.713301i	$0.252801\pi$
$18$	−0.768522	−	0.268741i	−0.0100635	−	0.00351904i
$19$	57.0354			0.688675			0.344337	−	0.938846i	$-0.388104\pi$
$19$	57.0354			0.688675			0.344337	+	0.938846i	$0.388104\pi$
$20$		0			0
$21$	−142.941			−1.48534
$22$	−62.4786	−	21.8479i	−0.605477	−	0.211726i
$23$	−116.421	+	116.421i	−1.05546	+	1.05546i	−0.0570869	+	0.998369i	$0.518181\pi$
$23$	−116.421	+	116.421i	−1.05546	+	1.05546i	−0.998369	+	0.0570869i	$0.981819\pi$
$24$	26.2312	−	115.253i	0.223101	−	0.980248i
$25$		0			0
$26$	226.690	−	109.225i	1.70990	−	0.823878i
$27$	−98.6685	−	98.6685i	−0.703287	−	0.703287i
$28$	−24.5991	−	217.521i	−0.166028	−	1.46813i
$29$			121.516i			0.778104i	0.921216	+	0.389052i	$0.127197\pi$
$29$			121.516i			0.778104i	−0.921216	+	0.389052i	$0.872803\pi$
$30$		0			0
$31$		−	66.8861i		−	0.387519i	−0.981049	−	0.193760i	$-0.937932\pi$
$31$		−	66.8861i		−	0.387519i	0.981049	−	0.193760i	$-0.0620682\pi$
$32$	179.902	+	20.0834i	0.993826	+	0.110946i
$33$	86.4384	+	86.4384i	0.455970	+	0.455970i
$34$	1.51439	+	3.14301i	0.00763869	+	0.0158536i
$35$		0			0
$36$	−1.43502	+	1.80097i	−0.00664361	+	0.00833783i
$37$	−36.6685	+	36.6685i	−0.162926	+	0.162926i	−0.783862	−	0.620935i	$-0.786753\pi$
$37$	−36.6685	+	36.6685i	−0.162926	+	0.162926i	0.620935	+	0.783862i	$0.286753\pi$
$38$	53.2496	−	152.279i	0.227322	−	0.650075i
$39$	−464.734			−1.90813
$40$		0			0
$41$	−302.608			−1.15267			−0.576335	−	0.817213i	$-0.695518\pi$
$41$	−302.608			−1.15267			−0.576335	+	0.817213i	$0.695518\pi$
$42$	−133.453	+	381.637i	−0.490291	+	1.40209i
$43$	190.704	−	190.704i	0.676328	−	0.676328i	−0.282839	−	0.959167i	$-0.591276\pi$
$43$	190.704	−	190.704i	0.676328	−	0.676328i	0.959167	+	0.282839i	$0.0912762\pi$
$44$	−116.663	+	146.414i	−0.399718	+	0.501653i
$45$		0			0
$46$	202.139	+	419.526i	0.647908	+	1.34469i
$47$	54.1794	+	54.1794i	0.168146	+	0.168146i	0.786164	−	0.618018i	$-0.212064\pi$
$47$	54.1794	+	54.1794i	0.168146	+	0.168146i	−0.618018	+	0.786164i	$0.712064\pi$
$48$	−283.224	−	177.638i	−0.851664	−	0.534162i
$49$			405.760i			1.18297i
$50$		0			0
$51$		−	6.44345i		−	0.0176914i
$52$	−79.9774	−	707.213i	−0.213286	−	1.88602i
$53$	−36.5947	−	36.5947i	−0.0948428	−	0.0948428i	0.658093	−	0.752936i	$-0.271363\pi$
$53$	−36.5947	−	36.5947i	−0.0948428	−	0.0948428i	−0.752936	+	0.658093i	$0.771363\pi$
$54$	−355.554	+	171.316i	−0.896014	+	0.431724i
$55$		0			0
$56$	−603.726	−	137.406i	−1.44065	−	0.327886i
$57$	−210.676	+	210.676i	−0.489556	+	0.489556i
$58$	324.436	+	113.451i	0.734492	+	0.256841i
$59$	401.800			0.886609			0.443305	−	0.896371i	$-0.353806\pi$
$59$	401.800			0.886609			0.443305	+	0.896371i	$0.353806\pi$
$60$		0			0
$61$	509.974			1.07042			0.535208	−	0.844720i	$-0.320233\pi$
$61$	509.974			1.07042			0.535208	+	0.844720i	$0.320233\pi$
$62$	−178.579	−	62.4464i	−0.365799	−	0.127915i
$63$	5.56952	−	5.56952i	0.0111380	−	0.0111380i
$64$	221.581	−	461.569i	0.432775	−	0.901502i
$65$		0			0
$66$	311.483	−	150.081i	0.580922	−	0.279904i
$67$	187.627	+	187.627i	0.342124	+	0.342124i	0.857165	−	0.515041i	$-0.172223\pi$
$67$	187.627	+	187.627i	0.342124	+	0.342124i	−0.515041	+	0.857165i	$0.672223\pi$
$68$	9.80538	−	1.10887i	0.0174864	−	0.00197751i
$69$		−	860.066i		−	1.50058i
$70$		0			0
$71$		−	584.349i		−	0.976753i	−0.872633	−	0.488376i	$-0.837589\pi$
$71$		−	584.349i		−	0.976753i	0.872633	−	0.488376i	$-0.162411\pi$
$72$	3.46864	+	5.51278i	0.00567754	+	0.00902344i
$73$	−436.179	−	436.179i	−0.699327	−	0.699327i	0.264939	−	0.964265i	$-0.414648\pi$
$73$	−436.179	−	436.179i	−0.699327	−	0.699327i	−0.964265	+	0.264939i	$0.914648\pi$
$74$	63.6666	+	132.136i	0.100015	+	0.207574i
$75$		0			0
$76$	−356.853	−	284.342i	−0.538604	−	0.429161i
$77$	452.786	−	452.786i	0.670127	−	0.670127i
$78$	−433.886	+	1240.79i	−0.629845	+	1.80118i
$79$	608.649			0.866815			0.433408	−	0.901198i	$-0.357311\pi$
$79$	608.649			0.866815			0.433408	+	0.901198i	$0.357311\pi$
$80$		0			0
$81$	736.689			1.01055
$82$	−282.522	+	807.933i	−0.380480	+	1.08806i
$83$	124.596	−	124.596i	0.164774	−	0.164774i	−0.619904	−	0.784678i	$-0.712828\pi$
$83$	124.596	−	124.596i	0.164774	−	0.164774i	0.784678	+	0.619904i	$0.212828\pi$
$84$	894.337	+	712.610i	1.16167	+	0.925621i
$85$		0			0
$86$	−331.115	−	687.206i	−0.415175	−	0.861667i
$87$	−448.853	−	448.853i	−0.553128	−	0.553128i
$88$	281.991	+	448.174i	0.341594	+	0.542903i
$89$		−	684.600i		−	0.815365i	−0.913124	−	0.407682i	$-0.866337\pi$
$89$		−	684.600i		−	0.815365i	0.913124	−	0.407682i	$-0.133663\pi$
$90$		0			0
$91$			2434.39i			2.80433i
$92$	1308.81	−	148.011i	1.48319	−	0.167731i
$93$	247.062	+	247.062i	0.275474	+	0.275474i
$94$	195.237	−	94.0703i	0.214225	−	0.103219i
$95$		0			0
$96$	−738.699	+	590.332i	−0.785345	+	0.627610i
$97$	384.093	−	384.093i	0.402049	−	0.402049i	−0.476906	−	0.878954i	$-0.658242\pi$
$97$	384.093	−	384.093i	0.402049	−	0.402049i	0.878954	+	0.476906i	$0.158242\pi$
$98$	1083.34	+	378.827i	1.11667	+	0.390482i
$99$	−6.73595			−0.00683827
$100$		0			0
$101$	144.608			0.142466			0.0712329	−	0.997460i	$-0.477307\pi$
$101$	144.608			0.142466			0.0712329	+	0.997460i	$0.477307\pi$
$102$	−17.2034	−	6.01576i	−0.0166999	−	0.00583969i
$103$	−856.311	+	856.311i	−0.819173	+	0.819173i	−0.985988	−	0.166815i	$-0.946652\pi$
$103$	−856.311	+	856.311i	−0.819173	+	0.819173i	0.166815	+	0.985988i	$0.446652\pi$
$104$	−1962.85	−	446.739i	−1.85071	−	0.421215i
$105$		0			0
$106$	−131.870	+	63.5384i	−0.120833	+	0.0582207i
$107$	987.035	+	987.035i	0.891778	+	0.891778i	0.994690	−	0.102912i	$-0.0328161\pi$
$107$	987.035	+	987.035i	0.891778	+	0.891778i	−0.102912	+	0.994690i	$0.532816\pi$
$108$	125.441	+	1109.24i	0.111765	+	0.988299i
$109$		−	291.754i		−	0.256375i	−0.991750	−	0.128188i	$-0.959084\pi$
$109$		−	291.754i		−	0.256375i	0.991750	−	0.128188i	$-0.0409160\pi$
$110$		0			0
$111$		−	270.890i		−	0.231637i
$112$	−930.512	+	1483.60i	−0.785046	+	1.25167i
$113$	−1418.89	−	1418.89i	−1.18122	−	1.18122i	−0.979428	−	0.201794i	$-0.935323\pi$
$113$	−1418.89	−	1418.89i	−1.18122	−	1.18122i	−0.201794	−	0.979428i	$-0.564677\pi$
$114$	365.790	+	759.174i	0.300521	+	0.623712i
$115$		0			0
$116$	605.802	−	760.291i	0.484891	−	0.608545i
$117$	18.1078	−	18.1078i	0.0143083	−	0.0143083i
$118$	375.130	−	1072.77i	0.292657	−	0.836916i
$119$	−33.7524			−0.0260007
$120$		0			0
$121$	783.386			0.588570
$122$	476.123	−	1361.58i	0.353329	−	1.01042i
$123$	1117.77	−	1117.77i	0.819395	−	0.819395i
$124$	−333.451	+	418.486i	−0.241490	+	0.303074i
$125$		0			0
$126$	−9.67021	−	20.0699i	−0.00683723	−	0.0141902i
$127$	−395.277	−	395.277i	−0.276183	−	0.276183i	0.555400	−	0.831583i	$-0.312565\pi$
$127$	−395.277	−	395.277i	−0.276183	−	0.276183i	−0.831583	+	0.555400i	$0.812565\pi$
$128$	−1025.47	−	1022.53i	−0.708121	−	0.706092i
$129$			1408.83i			0.961558i
$130$		0			0
$131$		−	2261.83i		−	1.50852i	−0.656573	−	0.754262i	$-0.727995\pi$
$131$		−	2261.83i		−	1.50852i	0.656573	−	0.754262i	$-0.272005\pi$
$132$	−109.893	−	971.745i	−0.0724617	−	0.640754i
$133$	1103.57	+	1103.57i	0.719488	+	0.719488i
$134$	676.119	−	325.773i	0.435879	−	0.210018i
$135$		0			0
$136$	6.19396	−	27.2146i	0.00390535	−	0.0171591i
$137$	−1509.78	+	1509.78i	−0.941529	+	0.941529i	−0.998383	−	0.0568534i	$-0.981893\pi$
$137$	−1509.78	+	1509.78i	−0.941529	+	0.941529i	0.0568534	+	0.998383i	$0.481893\pi$
$138$	−2296.29	−	802.977i	−1.41647	−	0.495318i
$139$	−1482.80			−0.904814			−0.452407	−	0.891812i	$-0.649435\pi$
$139$	−1482.80			−0.904814			−0.452407	+	0.891812i	$0.649435\pi$
$140$		0			0
$141$	−400.252			−0.239059
$142$	−1560.15	−	545.561i	−0.922007	−	0.322412i
$143$	1472.12	−	1472.12i	0.860871	−	0.860871i
$144$	17.9570	−	4.11405i	0.0103918	−	0.00238082i
$145$		0			0
$146$	−1571.78	+	757.326i	−0.890968	+	0.429293i
$147$	−1498.78	−	1498.78i	−0.840936	−	0.840936i
$148$	412.229	−	46.6182i	0.228953	−	0.0258919i
$149$		−	787.753i		−	0.433122i	−0.976269	−	0.216561i	$-0.930516\pi$
$149$		−	787.753i		−	0.433122i	0.976269	−	0.216561i	$-0.0694841\pi$
$150$		0			0
$151$		−	914.146i		−	0.492663i	−0.969186	−	0.246332i	$-0.920775\pi$
$151$		−	914.146i		−	0.492663i	0.969186	−	0.246332i	$-0.0792252\pi$
$152$	−1092.33	+	687.293i	−0.582892	+	0.366756i
$153$	0.251062	+	0.251062i	0.000132661	+	0.000132661i
$154$	−786.161	−	1631.63i	−0.411368	−	0.853767i
$155$		0			0
$156$	2907.70	+	2316.86i	1.49232	+	1.18909i
$157$	578.898	−	578.898i	0.294275	−	0.294275i	−0.544492	−	0.838766i	$-0.683277\pi$
$157$	578.898	−	578.898i	0.294275	−	0.294275i	0.838766	+	0.544492i	$0.183277\pi$
$158$	568.249	−	1625.03i	0.286123	−	0.818231i
$159$	270.345			0.134841
$160$		0			0
$161$	−4505.24			−2.20536
$162$	687.790	−	1966.88i	0.333567	−	0.953907i
$163$	−1400.01	+	1400.01i	−0.672745	+	0.672745i	−0.958348	−	0.285603i	$-0.907806\pi$
$163$	−1400.01	+	1400.01i	−0.672745	+	0.672745i	0.285603	+	0.958348i	$0.407806\pi$
$164$	1893.33	+	1508.61i	0.901489	+	0.718309i
$165$		0			0
$166$	−216.333	−	448.986i	−0.101149	−	0.209928i
$167$	1190.71	+	1190.71i	0.551735	+	0.551735i	0.926941	−	0.375206i	$-0.122428\pi$
$167$	1190.71	+	1190.71i	0.551735	+	0.551735i	−0.375206	+	0.926941i	$0.622428\pi$
$168$	2737.57	−	1722.48i	1.25719	−	0.791024i
$169$			5717.79i			2.60254i
$170$		0			0
$171$		−	16.4175i		−	0.00734196i
$172$	−2143.91	+	242.450i	−0.950415	+	0.107481i
$173$	1972.92	+	1972.92i	0.867042	+	0.867042i	0.992144	−	0.125102i	$-0.0399257\pi$
$173$	1972.92	+	1972.92i	0.867042	+	0.867042i	−0.125102	+	0.992144i	$0.539926\pi$
$174$	−1617.45	+	779.332i	−0.704705	+	0.339546i
$175$		0			0
$176$	1459.85	−	334.461i	0.625229	−	0.143244i
$177$	−1484.16	+	1484.16i	−0.630261	+	0.630261i
$178$	−1827.81	−	639.159i	−0.769665	−	0.269140i
$179$	974.707			0.407000			0.203500	−	0.979075i	$-0.434768\pi$
$179$	974.707			0.407000			0.203500	+	0.979075i	$0.434768\pi$
$180$		0			0
$181$	456.001			0.187261			0.0936306	−	0.995607i	$-0.470153\pi$
$181$	456.001			0.187261			0.0936306	+	0.995607i	$0.470153\pi$
$182$	6499.58	+	2272.81i	2.64715	+	0.925668i
$183$	−1883.72	+	1883.72i	−0.760923	+	0.760923i
$184$	826.763	−	3632.58i	0.331249	−	1.45542i
$185$		0			0
$186$	890.292	−	428.967i	0.350964	−	0.169104i
$187$	20.4106	+	20.4106i	0.00798167	+	0.00798167i
$188$	−68.8806	−	609.088i	−0.0267214	−	0.236289i
$189$		−	3818.25i		−	1.46951i
$190$		0			0
$191$			2746.08i			1.04031i	0.854072	+	0.520155i	$0.174126\pi$
$191$			2746.08i			1.04031i	−0.854072	+	0.520155i	$0.825874\pi$
$192$	886.460	+	2523.40i	0.333202	+	0.948492i
$193$	529.426	+	529.426i	0.197455	+	0.197455i	0.798908	−	0.601453i	$-0.205411\pi$
$193$	529.426	+	529.426i	0.197455	+	0.197455i	−0.601453	+	0.798908i	$0.705411\pi$
$194$	−666.890	−	1384.09i	−0.246804	−	0.512225i
$195$		0			0
$196$	2022.86	−	2538.72i	0.737193	−	0.925188i
$197$	2632.17	−	2632.17i	0.951950	−	0.951950i	−0.0469471	−	0.998897i	$-0.514949\pi$
$197$	2632.17	−	2632.17i	0.951950	−	0.951950i	0.998897	+	0.0469471i	$0.0149492\pi$
$198$	−6.28884	+	17.9843i	−0.00225721	+	0.00645499i
$199$	−4801.28			−1.71032			−0.855161	−	0.518363i	$-0.826542\pi$
$199$	−4801.28			−1.71032			−0.855161	+	0.518363i	$0.826542\pi$
$200$		0			0
$201$	−1386.10			−0.486409
$202$	135.009	−	386.089i	0.0470259	−	0.134481i
$203$	−2351.21	+	2351.21i	−0.812919	+	0.812919i
$204$	−32.1229	+	40.3147i	−0.0110248	+	0.0138363i
$205$		0			0
$206$	1486.79	+	3085.73i	0.502862	+	1.04366i
$207$	33.5115	+	33.5115i	0.0112522	+	0.0112522i
$208$	−3025.31	+	4823.53i	−1.00850	+	1.60794i
$209$		−	1334.69i		−	0.441736i
$210$		0			0
$211$		−	2785.38i		−	0.908784i	−0.890802	−	0.454392i	$-0.849857\pi$
$211$		−	2785.38i		−	0.908784i	0.890802	−	0.454392i	$-0.150143\pi$
$212$	46.5244	+	411.399i	0.0150722	+	0.133278i
$213$	2158.45	+	2158.45i	0.694340	+	0.694340i
$214$	3556.80	−	1713.76i	1.13616	−	0.547432i
$215$		0			0
$216$	3078.66	+	700.693i	0.969798	+	0.220723i
$217$	1294.17	−	1294.17i	0.404858	−	0.404858i
$218$	−778.952	−	272.388i	−0.242006	−	0.0846258i
$219$	3222.29			0.994255
$220$		0			0
$221$	−109.737			−0.0334014
$222$	−723.248	−	252.909i	−0.218654	−	0.0764602i
$223$	1114.21	−	1114.21i	0.334589	−	0.334589i	−0.519737	−	0.854326i	$-0.673970\pi$
$223$	1114.21	−	1114.21i	0.334589	−	0.334589i	0.854326	+	0.519737i	$0.173970\pi$
$224$	3092.31	+	3869.49i	0.922383	+	1.15420i
$225$		0			0
$226$	−5113.00	+	2463.58i	−1.50492	+	0.725111i
$227$	−1943.85	−	1943.85i	−0.568361	−	0.568361i	0.363308	−	0.931669i	$-0.381647\pi$
$227$	−1943.85	−	1943.85i	−0.568361	−	0.568361i	−0.931669	+	0.363308i	$0.881647\pi$
$228$	2368.43	−	267.841i	0.687951	−	0.0777991i
$229$			274.452i			0.0791979i	0.999216	+	0.0395990i	$0.0126080\pi$
$229$			274.452i			0.0791979i	−0.999216	+	0.0395990i	$0.987392\pi$
$230$		0			0
$231$			3344.98i			0.952742i
$232$	−1464.31	−	2327.25i	−0.414382	−	0.658585i
$233$	−2762.59	−	2762.59i	−0.776753	−	0.776753i	0.202525	−	0.979277i	$-0.435085\pi$
$233$	−2762.59	−	2762.59i	−0.776753	−	0.776753i	−0.979277	+	0.202525i	$0.935085\pi$
$234$	−31.4401	−	65.2519i	−0.00878336	−	0.0182293i
$235$		0			0
$236$	−2513.94	−	2003.12i	−0.693406	−	0.552508i
$237$	−2248.21	+	2248.21i	−0.616189	+	0.616189i
$238$	−31.5121	+	90.1155i	−0.00858245	+	0.0245434i
$239$	6911.68			1.87062			0.935312	−	0.353823i	$-0.115118\pi$
$239$	6911.68			1.87062			0.935312	+	0.353823i	$0.115118\pi$
$240$		0			0
$241$	4046.37			1.08153			0.540766	−	0.841173i	$-0.318134\pi$
$241$	4046.37			1.08153			0.540766	+	0.841173i	$0.318134\pi$
$242$	731.387	−	2091.56i	0.194278	−	0.555581i
$243$	−57.1089	+	57.1089i	−0.0150763	+	0.0150763i
$244$	−3190.75	−	2542.40i	−0.837159	−	0.667051i
$245$		0			0
$246$	−1940.75	−	4027.89i	−0.502998	−	1.04394i
$247$	3587.97	+	3587.97i	0.924281	+	0.924281i
$248$	805.997	+	1280.99i	0.206374	+	0.327995i
$249$			920.461i			0.234264i
$250$		0			0
$251$		−	4340.63i		−	1.09155i	−0.837933	−	0.545773i	$-0.816236\pi$
$251$		−	4340.63i		−	1.09155i	0.837933	−	0.545773i	$-0.183764\pi$
$252$	−62.6128	+	7.08077i	−0.0156517	+	0.00177003i
$253$	2724.39	+	2724.39i	0.676999	+	0.676999i
$254$	−1424.39	+	686.310i	−0.351867	+	0.169539i
$255$		0			0
$256$	−3687.45	+	1783.24i	−0.900256	+	0.435361i
$257$	−3380.28	+	3380.28i	−0.820452	+	0.820452i	−0.986173	−	0.165721i	$-0.947005\pi$
$257$	−3380.28	+	3380.28i	−0.820452	+	0.820452i	0.165721	+	0.986173i	$0.447005\pi$
$258$	3761.44	+	1315.32i	0.907664	+	0.317396i
$259$	−1418.99			−0.340432
$260$		0			0
$261$	34.9781			0.00829537
$262$	−6038.84	−	2111.69i	−1.42397	−	0.497942i
$263$	5667.18	−	5667.18i	1.32872	−	1.32872i	0.422230	−	0.906489i	$-0.361247\pi$
$263$	5667.18	−	5667.18i	1.32872	−	1.32872i	0.906489	−	0.422230i	$-0.138753\pi$
$264$	−2697.06	−	613.841i	−0.628759	−	0.143103i
$265$		0			0
$266$	3976.75	−	1916.10i	0.916654	−	0.441669i
$267$	2528.75	+	2528.75i	0.579615	+	0.579615i
$268$	−238.539	−	2109.32i	−0.0543696	−	0.480772i
$269$		−	4863.03i		−	1.10225i	−0.834424	−	0.551123i	$-0.814200\pi$
$269$		−	4863.03i		−	1.10225i	0.834424	−	0.551123i	$-0.185800\pi$
$270$		0			0
$271$			6.44235i			0.00144408i	1.00000		0.000722039i	$0.000229832\pi$
$271$			6.44235i			0.00144408i	−1.00000		0.000722039i	$0.999770\pi$
$272$	−66.8774	−	41.9454i	−0.0149082	−	0.00935042i
$273$	−8992.09	−	8992.09i	−1.99350	−	1.99350i
$274$	2621.40	+	5440.53i	0.577972	+	1.19954i
$275$		0			0
$276$	−4287.73	+	5381.17i	−0.935113	+	1.17358i
$277$	5660.47	−	5660.47i	1.22781	−	1.22781i	0.263025	−	0.964789i	$-0.415280\pi$
$277$	5660.47	−	5660.47i	1.22781	−	1.22781i	0.964789	−	0.263025i	$-0.0847203\pi$
$278$	−1384.37	+	3958.91i	−0.298666	+	0.854100i
$279$	−19.2530			−0.00413134
$280$		0			0
$281$	5779.01			1.22686			0.613428	−	0.789751i	$-0.289790\pi$
$281$	5779.01			1.22686			0.613428	+	0.789751i	$0.289790\pi$
$282$	−373.685	+	1068.63i	−0.0789099	+	0.225660i
$283$	1743.48	−	1743.48i	0.366215	−	0.366215i	−0.499880	−	0.866095i	$-0.666622\pi$
$283$	1743.48	−	1743.48i	0.366215	−	0.366215i	0.866095	+	0.499880i	$0.166622\pi$
$284$	−2913.18	+	3656.09i	−0.608682	+	0.763905i
$285$		0			0
$286$	−2556.00	−	5304.80i	−0.528459	−	1.09678i
$287$	−5855.14	−	5855.14i	−1.20424	−	1.20424i
$288$	5.78094	−	51.7842i	0.00118280	−	0.0105952i
$289$			4911.48i			0.999690i
$290$		0			0
$291$			2837.50i			0.571605i
$292$	554.532	+	4903.54i	0.111135	+	0.982733i
$293$	−1296.73	−	1296.73i	−0.258552	−	0.258552i	0.565913	−	0.824465i	$-0.308524\pi$
$293$	−1296.73	−	1296.73i	−0.258552	−	0.258552i	−0.824465	+	0.565913i	$0.808524\pi$
$294$	−5400.89	+	2602.30i	−1.07138	+	0.516221i
$295$		0			0
$296$	260.401	−	1144.13i	0.0511334	−	0.224667i
$297$	−2308.96	+	2308.96i	−0.451109	+	0.451109i
$298$	−2103.22	−	735.464i	−0.408846	−	0.142967i
$299$	−14647.6			−2.83309
$300$		0			0
$301$	7379.83			1.41318
$302$	−2440.68	−	853.468i	−0.465050	−	0.162621i
$303$	−534.149	+	534.149i	−0.101274	+	0.101274i
$304$	815.178	+	3558.08i	0.153795	+	0.671282i
$305$		0			0
$306$	0.904706	−	0.435912i	0.000169015	−	8.14360e-5i
$307$	−521.805	−	521.805i	−0.0970064	−	0.0970064i	0.656938	−	0.753945i	$-0.271851\pi$
$307$	−521.805	−	521.805i	−0.0970064	−	0.0970064i	−0.753945	+	0.656938i	$0.771851\pi$
$308$	−5090.25	+	575.647i	−0.941701	+	0.106495i
$309$		−	6326.03i		−	1.16464i
$310$		0			0
$311$			5362.10i			0.977674i	0.872375	+	0.488837i	$0.162579\pi$
$311$			5362.10i			0.977674i	−0.872375	+	0.488837i	$0.837421\pi$
$312$	8900.48	−	5600.18i	1.61503	−	1.01618i
$313$	−2856.75	−	2856.75i	−0.515888	−	0.515888i	0.400436	−	0.916325i	$-0.368859\pi$
$313$	−2856.75	−	2856.75i	−0.515888	−	0.515888i	−0.916325	+	0.400436i	$0.868859\pi$
$314$	−1005.13	−	2086.07i	−0.180645	−	0.374917i
$315$		0			0
$316$	−3808.13	−	3034.33i	−0.677925	−	0.540173i
$317$	−782.618	+	782.618i	−0.138663	+	0.138663i	−0.773031	−	0.634368i	$-0.781260\pi$
$317$	−782.618	+	782.618i	−0.138663	+	0.138663i	0.634368	+	0.773031i	$0.281260\pi$
$318$	252.400	−	721.792i	0.0445091	−	0.127283i
$319$	2843.62			0.499098
$320$		0			0
$321$	−7291.76			−1.26787
$322$	−4206.20	+	12028.5i	−0.727957	+	2.08175i
$323$	−49.7466	+	49.7466i	−0.00856959	+	0.00856959i
$324$	−4609.24	−	3672.66i	−0.790336	−	0.629742i
$325$		0			0
$326$	2430.80	+	5044.97i	0.412975	+	0.857102i
$327$	1077.67	+	1077.67i	0.182249	+	0.182249i
$328$	5795.49	−	3646.52i	0.975617	−	0.613858i
$329$			2096.62i			0.351339i
$330$		0			0
$331$			9093.24i			1.51000i	0.655725	+	0.755000i	$0.272363\pi$
$331$			9093.24i			1.51000i	−0.655725	+	0.755000i	$0.727637\pi$
$332$	−1400.72	+	158.405i	−0.231550	+	0.0261855i
$333$	10.5549	+	10.5549i	0.00173696	+	0.00173696i
$334$	4290.74	−	2067.40i	0.702931	−	0.338691i
$335$		0			0
$336$	−2042.98	−	8917.17i	−0.331707	−	1.44783i
$337$	4556.11	−	4556.11i	0.736461	−	0.736461i	−0.235430	−	0.971891i	$-0.575650\pi$
$337$	4556.11	−	4556.11i	0.736461	−	0.736461i	0.971891	+	0.235430i	$0.0756500\pi$
$338$	15265.9	+	5338.26i	2.45667	+	0.859063i
$339$	10482.1			1.67938
$340$		0			0
$341$	−1565.21			−0.248566
$342$	−43.8329	−	15.3277i	−0.00693045	−	0.00242348i
$343$	−1214.33	+	1214.33i	−0.191160	+	0.191160i
$344$	−1354.28	+	5950.37i	−0.212262	+	0.932623i
$345$		0			0
$346$	7109.46	−	3425.53i	1.10464	−	0.532247i
$347$	1223.84	+	1223.84i	0.189334	+	0.189334i	0.795408	−	0.606074i	$-0.207256\pi$
$347$	1223.84	+	1223.84i	0.189334	+	0.189334i	−0.606074	+	0.795408i	$0.707256\pi$
$348$	570.646	+	5046.03i	0.0879019	+	0.777287i
$349$			2200.43i			0.337496i	0.985659	+	0.168748i	$0.0539724\pi$
$349$			2200.43i			0.337496i	−0.985659	+	0.168748i	$0.946028\pi$
$350$		0			0
$351$		−	12414.0i		−	1.88779i
$352$	469.974	−	4209.91i	0.0711639	−	0.637468i
$353$	5473.59	+	5473.59i	0.825297	+	0.825297i	0.986862	−	0.161565i	$-0.0516541\pi$
$353$	5473.59	+	5473.59i	0.825297	+	0.825297i	−0.161565	+	0.986862i	$0.551654\pi$
$354$	2576.90	+	5348.19i	0.386895	+	0.802975i
$355$		0			0
$356$	−3412.97	+	4283.34i	−0.508110	+	0.637686i
$357$	124.674	−	124.674i	0.0184830	−	0.0184830i
$358$	910.009	−	2602.37i	0.134345	−	0.384188i
$359$	6232.16			0.916214			0.458107	−	0.888897i	$-0.348528\pi$
$359$	6232.16			0.916214			0.458107	+	0.888897i	$0.348528\pi$
$360$		0			0
$361$	−3605.96			−0.525727
$362$	425.733	−	1217.48i	0.0618122	−	0.176765i
$363$	−2893.65	+	2893.65i	−0.418394	+	0.418394i
$364$	12136.3	−	15231.3i	1.74757	−	2.19323i
$365$		0			0
$366$	3270.66	+	6788.04i	0.467104	+	0.969444i
$367$	−1668.07	−	1668.07i	−0.237255	−	0.237255i	0.578457	−	0.815713i	$-0.303655\pi$
$367$	−1668.07	−	1668.07i	−0.237255	−	0.237255i	−0.815713	+	0.578457i	$0.803655\pi$
$368$	−8926.73	−	5598.83i	−1.26451	−	0.793096i
$369$			87.1049i			0.0122886i
$370$		0			0
$371$		−	1416.13i		−	0.198173i
$372$	−314.100	−	2777.48i	−0.0437778	−	0.387112i
$373$	931.073	+	931.073i	0.129247	+	0.129247i	0.768771	−	0.639524i	$-0.220869\pi$
$373$	931.073	+	931.073i	0.129247	+	0.129247i	−0.639524	+	0.768771i	$0.720869\pi$
$374$	73.5501	−	35.4384i	0.0101689	−	0.00489967i
$375$		0			0
$376$	−1690.51	−	384.754i	−0.231865	−	0.0527718i
$377$	−7644.33	+	7644.33i	−1.04431	+	1.04431i
$378$	−10194.3	−	3564.81i	−1.38714	−	0.485064i
$379$	−1254.98			−0.170090			−0.0850448	−	0.996377i	$-0.527103\pi$
$379$	−1254.98			−0.170090			−0.0850448	+	0.996377i	$0.527103\pi$
$380$		0			0
$381$	2920.13			0.392658
$382$	7331.74	+	2563.80i	0.982001	+	0.343391i
$383$	−5993.78	+	5993.78i	−0.799654	+	0.799654i	−0.983041	−	0.183387i	$-0.941294\pi$
$383$	−5993.78	+	5993.78i	−0.799654	+	0.799654i	0.183387	+	0.983041i	$0.441294\pi$
$384$	7564.83	−	10.8540i	1.00532	−	0.00144242i
$385$		0			0
$386$	1907.80	−	919.228i	0.251565	−	0.121211i
$387$	−54.8936	−	54.8936i	−0.00721034	−	0.00721034i
$388$	−4317.99	+	488.313i	−0.564981	+	0.0638927i
$389$		−	7291.03i		−	0.950309i	−0.879903	−	0.475154i	$-0.842392\pi$
$389$		−	7291.03i		−	0.950309i	0.879903	−	0.475154i	$-0.157608\pi$
$390$		0			0
$391$		−	203.086i		−	0.0262673i
$392$	−4889.52	−	7771.02i	−0.629996	−	1.00127i
$393$	8354.66	+	8354.66i	1.07236	+	1.07236i
$394$	−4570.16	−	9485.07i	−0.584369	−	1.21282i
$395$		0			0
$396$	42.1448	+	33.5811i	0.00534812	+	0.00426140i
$397$	3961.85	−	3961.85i	0.500855	−	0.500855i	−0.410848	−	0.911704i	$-0.634767\pi$
$397$	3961.85	−	3961.85i	0.500855	−	0.500855i	0.911704	+	0.410848i	$0.134767\pi$
$398$	−4482.59	+	12818.9i	−0.564553	+	1.61446i
$399$	−8152.68			−1.02292
$400$		0			0
$401$	−2328.57			−0.289984			−0.144992	−	0.989433i	$-0.546316\pi$
$401$	−2328.57			−0.289984			−0.144992	+	0.989433i	$0.546316\pi$
$402$	−1294.10	+	3700.76i	−0.160557	+	0.459146i
$403$	4207.66	−	4207.66i	0.520096	−	0.520096i
$404$	−904.769	−	720.922i	−0.111421	−	0.0887803i
$405$		0			0
$406$	4082.34	+	8472.63i	0.499023	+	1.03569i
$407$	858.086	+	858.086i	0.104505	+	0.104505i
$408$	77.6455	+	123.404i	0.00942163	+	0.0149740i
$409$			1759.60i			0.212730i	0.994327	+	0.106365i	$0.0339212\pi$
$409$			1759.60i			0.212730i	−0.994327	+	0.106365i	$0.966079\pi$
$410$		0			0
$411$		−	11153.6i		−	1.33860i
$412$	9626.69	−	1088.66i	1.15115	−	0.130181i
$413$	7774.40	+	7774.40i	0.926278	+	0.926278i
$414$	120.759	−	58.1851i	0.0143357	−	0.00690735i
$415$		0			0
$416$	10053.8	+	12580.6i	1.18493	+	1.48273i
$417$	5477.11	−	5477.11i	0.643202	−	0.643202i
$418$	−3563.50	−	1246.10i	−0.416977	−	0.145811i
$419$	6088.54			0.709892			0.354946	−	0.934887i	$-0.384499\pi$
$419$	6088.54			0.709892			0.354946	+	0.934887i	$0.384499\pi$
$420$		0			0
$421$	−10250.4			−1.18664			−0.593319	−	0.804967i	$-0.702183\pi$
$421$	−10250.4			−1.18664			−0.593319	+	0.804967i	$0.702183\pi$
$422$	−7436.67	−	2600.49i	−0.857847	−	0.299976i
$423$	15.5954	−	15.5954i	0.00179261	−	0.00179261i
$424$	1141.83	+	259.877i	0.130783	+	0.0297659i
$425$		0			0
$426$	7778.01	−	3747.66i	0.884615	−	0.426231i
$427$	9867.43	+	9867.43i	1.11831	+	1.11831i
$428$	−1254.86	−	11096.3i	−0.141719	−	1.25318i
$429$			10875.3i			1.22393i
$430$		0			0
$431$		−	3401.38i		−	0.380136i	−0.981771	−	0.190068i	$-0.939129\pi$
$431$		−	3401.38i		−	0.380136i	0.981771	−	0.190068i	$-0.0608709\pi$
$432$	4745.09	−	7565.52i	0.528468	−	0.842584i
$433$	−4131.06	−	4131.06i	−0.458490	−	0.458490i	0.439670	−	0.898160i	$-0.355095\pi$
$433$	−4131.06	−	4131.06i	−0.458490	−	0.458490i	−0.898160	+	0.439670i	$0.855095\pi$
$434$	−2247.04	−	4663.58i	−0.248528	−	0.515804i
$435$		0			0
$436$	−1454.49	+	1825.41i	−0.159765	+	0.200508i
$437$	−6640.13	+	6640.13i	−0.726866	+	0.726866i
$438$	3008.40	−	8603.17i	0.328189	−	0.938528i
$439$	−9421.34			−1.02427			−0.512137	−	0.858904i	$-0.671146\pi$
$439$	−9421.34			−1.02427			−0.512137	+	0.858904i	$0.671146\pi$
$440$		0			0
$441$	116.797			0.0126117
$442$	−102.453	+	292.987i	−0.0110253	+	0.0315293i
$443$	−8174.05	+	8174.05i	−0.876662	+	0.876662i	−0.993188	−	0.116526i	$-0.962824\pi$
$443$	−8174.05	+	8174.05i	−0.876662	+	0.876662i	0.116526	+	0.993188i	$0.462824\pi$
$444$	−1350.48	+	1694.88i	−0.144349	+	0.181161i
$445$		0			0
$446$	−1934.58	−	4015.10i	−0.205393	−	0.426279i
$447$	2909.78	+	2909.78i	0.307892	+	0.307892i
$448$	13218.2	−	4643.50i	1.39398	−	0.489698i
$449$			9388.28i			0.986772i	0.869811	+	0.493386i	$0.164241\pi$
$449$			9388.28i			0.986772i	−0.869811	+	0.493386i	$0.835759\pi$
$450$		0			0
$451$			7081.39i			0.739356i
$452$	1803.90	+	15951.2i	0.187717	+	1.65992i
$453$	3376.64	+	3376.64i	0.350218	+	0.350218i
$454$	−7004.70	+	3375.06i	−0.724112	+	0.348897i
$455$		0			0
$456$	1496.11	−	6573.51i	0.153644	−	0.675072i
$457$	−7370.52	+	7370.52i	−0.754438	+	0.754438i	−0.975304	−	0.220866i	$-0.929112\pi$
$457$	−7370.52	+	7370.52i	−0.754438	+	0.754438i	0.220866	+	0.975304i	$0.429112\pi$
$458$	732.760	+	256.235i	0.0747590	+	0.0261421i
$459$	172.118			0.0175028
$460$		0			0
$461$	−6970.65			−0.704242			−0.352121	−	0.935955i	$-0.614539\pi$
$461$	−6970.65			−0.704242			−0.352121	+	0.935955i	$0.614539\pi$
$462$	8930.74	+	3122.95i	0.899341	+	0.314486i
$463$	−2379.65	+	2379.65i	−0.238859	+	0.238859i	−0.816377	−	0.577519i	$-0.804021\pi$
$463$	−2379.65	+	2379.65i	−0.238859	+	0.238859i	0.577519	+	0.816377i	$0.304021\pi$
$464$	−7580.64	+	1736.77i	−0.758454	+	0.173766i
$465$		0			0
$466$	−9955.05	+	4796.61i	−0.989611	+	0.476822i
$467$	−10534.1	−	10534.1i	−1.04382	−	1.04382i	−0.998995	−	0.0448214i	$-0.985728\pi$
$467$	−10534.1	−	10534.1i	−1.04382	−	1.04382i	−0.0448214	−	0.998995i	$-0.514272\pi$
$468$	−203.569	+	23.0212i	−0.0201068	+	0.00227384i
$469$			7260.77i			0.714864i
$470$		0			0
$471$			4276.63i			0.418380i
$472$	−7695.19	+	4841.81i	−0.750423	+	0.472166i
$473$	−4462.70	−	4462.70i	−0.433816	−	0.433816i
$474$	3903.51	+	8101.47i	0.378257	+	0.785048i
$475$		0			0
$476$	211.179	+	168.268i	0.0203348	+	0.0162028i
$477$	−10.5337	+	10.5337i	−0.00101112	+	0.00101112i
$478$	6452.90	−	18453.5i	0.617466	−	1.76578i
$479$	−11778.8			−1.12356			−0.561782	−	0.827285i	$-0.689884\pi$
$479$	−11778.8			−1.12356			−0.561782	+	0.827285i	$0.689884\pi$
$480$		0			0
$481$	−4613.47			−0.437331
$482$	3777.78	−	10803.4i	0.356998	−	1.02091i
$483$	16641.3	−	16641.3i	1.56772	−	1.56772i
$484$	−4901.41	−	3905.46i	−0.460313	−	0.366779i
$485$		0			0
$486$	99.1567	+	205.793i	0.00925481	+	0.0192077i
$487$	−3158.43	−	3158.43i	−0.293885	−	0.293885i	0.544728	−	0.838613i	$-0.316633\pi$
$487$	−3158.43	−	3158.43i	−0.293885	−	0.293885i	−0.838613	+	0.544728i	$0.816633\pi$
$488$	−9766.90	+	6145.33i	−0.905997	+	0.570053i
$489$		−	10342.6i		−	0.956463i
$490$		0			0
$491$			11830.6i			1.08739i	0.839284	+	0.543693i	$0.182974\pi$
$491$			11830.6i			1.08739i	−0.839284	+	0.543693i	$0.817026\pi$
$492$	−12566.0	+	1421.06i	−1.15146	+	0.130216i
$493$	−105.987	−	105.987i	−0.00968241	−	0.00968241i
$494$	12929.3	−	6229.71i	1.17757	−	0.567384i
$495$		0			0
$496$	4172.60	−	955.969i	0.377733	−	0.0865409i
$497$	11306.5	−	11306.5i	1.02045	−	1.02045i
$498$	2457.53	+	859.363i	0.221134	+	0.0773273i
$499$	8839.70			0.793025			0.396512	−	0.918029i	$-0.370220\pi$
$499$	8839.70			0.793025			0.396512	+	0.918029i	$0.370220\pi$
$500$		0			0
$501$	−8796.40			−0.784420
$502$	−11589.0	−	4052.51i	−1.03037	−	0.360304i
$503$	−4620.97	+	4620.97i	−0.409620	+	0.409620i	−0.881606	−	0.471986i	$-0.843537\pi$
$503$	−4620.97	+	4620.97i	−0.409620	+	0.409620i	0.471986	+	0.881606i	$0.343537\pi$
$504$	−39.5519	+	173.781i	−0.00349560	+	0.0153587i
$505$		0			0
$506$	9817.39	−	4730.28i	0.862522	−	0.415587i
$507$	−21120.2	−	21120.2i	−1.85006	−	1.85006i
$508$	502.533	+	4443.73i	0.0438903	+	0.388107i
$509$			2853.35i			0.248473i	0.992253	+	0.124236i	$0.0396481\pi$
$509$			2853.35i			0.248473i	−0.992253	+	0.124236i	$0.960352\pi$
$510$		0			0
$511$		−	16879.2i		−	1.46123i
$512$	1318.37	+	11510.0i	0.113797	+	0.993504i
$513$	−5627.60	−	5627.60i	−0.484336	−	0.484336i
$514$	5869.09	+	12180.9i	0.503647	+	1.04529i
$515$		0			0
$516$	7023.54	−	8814.65i	0.599213	−	0.752022i
$517$	1267.86	−	1267.86i	0.107854	−	0.107854i
$518$	−1324.80	+	3788.56i	−0.112372	+	0.321351i
$519$	−14575.0			−1.23270
$520$		0			0
$521$	18911.3			1.59025			0.795124	−	0.606446i	$-0.207406\pi$
$521$	18911.3			1.59025			0.795124	+	0.606446i	$0.207406\pi$
$522$	32.6564	−	93.3880i	0.00273818	−	0.00783042i
$523$	5377.26	−	5377.26i	0.449582	−	0.449582i	−0.445634	−	0.895215i	$-0.647022\pi$
$523$	5377.26	−	5377.26i	0.449582	−	0.449582i	0.895215	+	0.445634i	$0.147022\pi$
$524$	−11276.0	+	14151.6i	−0.940066	+	1.17980i
$525$		0			0
$526$	−9839.77	−	20421.8i	−0.815655	−	1.69284i
$527$	58.3385	+	58.3385i	0.00482213	+	0.00482213i
$528$	−4156.93	+	6627.77i	−0.342627	+	0.546281i
$529$		−	14940.8i		−	1.22798i
$530$		0			0
$531$		−	115.657i		−	0.00945214i
$532$	−1403.02	−	12406.4i	−0.114339	−	1.01106i
$533$	−19036.4	−	19036.4i	−1.54702	−	1.54702i
$534$	9112.42	−	4390.61i	0.738451	−	0.355806i
$535$		0			0
$536$	−5854.36	−	1332.43i	−0.471772	−	0.107374i
$537$	−3600.34	+	3600.34i	−0.289323	+	0.289323i
$538$	−12983.8	−	4540.23i	−1.04047	−	0.363835i
$539$	9495.25			0.758793
$540$		0			0
$541$	20897.4			1.66072			0.830360	−	0.557227i	$-0.188135\pi$
$541$	20897.4			1.66072			0.830360	+	0.557227i	$0.188135\pi$
$542$	17.2004	+	6.01473i	0.00136314	+	0.000476669i
$543$	−1684.36	+	1684.36i	−0.133118	+	0.133118i
$544$	−174.428	+	139.395i	−0.0137473	+	0.0109862i
$545$		0			0
$546$	−32403.2	+	15612.7i	−2.53979	+	1.22374i
$547$	13521.1	+	13521.1i	1.05689	+	1.05689i	0.998281	+	0.0586130i	$0.0186678\pi$
$547$	13521.1	+	13521.1i	1.05689	+	1.05689i	0.0586130	+	0.998281i	$0.481332\pi$
$548$	16973.1	−	1919.45i	1.32309	−	0.149626i
$549$		−	146.794i		−	0.0114117i
$550$		0			0
$551$			6930.74i			0.535861i
$552$	10364.0	+	16471.8i	0.799136	+	1.27008i
$553$	11776.7	+	11776.7i	0.905599	+	0.905599i
$554$	−9828.12	−	20397.6i	−0.753713	−	1.56428i
$555$		0			0
$556$	9277.41	+	7392.26i	0.707643	+	0.563852i
$557$	−12578.8	+	12578.8i	−0.956879	+	0.956879i	−0.999108	−	0.0422290i	$-0.986554\pi$
$557$	−12578.8	+	12578.8i	−0.956879	+	0.956879i	0.0422290	+	0.999108i	$0.486554\pi$
$558$	−17.9750	+	51.4034i	−0.00136370	+	0.00389979i
$559$	23993.6			1.81542
$560$		0			0
$561$	−150.784			−0.0113478
$562$	5395.41	−	15429.3i	0.404968	−	1.15809i
$563$	795.795	−	795.795i	0.0595715	−	0.0595715i	−0.676693	−	0.736265i	$-0.736588\pi$
$563$	795.795	−	795.795i	0.0595715	−	0.0595715i	0.736265	+	0.676693i	$0.236588\pi$
$564$	2504.26	+	1995.40i	0.186965	+	0.148974i
$565$		0			0
$566$	−3027.15	−	6282.66i	−0.224807	−	0.466572i
$567$	14254.1	+	14254.1i	1.05576	+	1.05576i
$568$	7041.57	+	11191.3i	0.520172	+	0.826720i
$569$		−	574.064i		−	0.0422953i	−0.999776	−	0.0211476i	$-0.993268\pi$
$569$		−	574.064i		−	0.0422953i	0.999776	−	0.0211476i	$-0.00673200\pi$
$570$		0			0
$571$		−	6029.11i		−	0.441875i	−0.975288	−	0.220937i	$-0.929088\pi$
$571$		−	6029.11i		−	0.441875i	0.975288	−	0.220937i	$-0.0709116\pi$
$572$	−16549.6	+	1871.56i	−1.20974	+	0.136808i
$573$	−10143.4	−	10143.4i	−0.739521	−	0.739521i
$574$	−21099.1	+	10166.1i	−1.53425	+	0.739244i
$575$		0			0
$576$	−132.861	−	63.7814i	−0.00961091	−	0.00461382i
$577$	5369.95	−	5369.95i	0.387442	−	0.387442i	−0.486332	−	0.873774i	$-0.661666\pi$
$577$	5369.95	−	5369.95i	0.387442	−	0.387442i	0.873774	+	0.486332i	$0.161666\pi$
$578$	13113.1	+	4585.47i	0.943659	+	0.329983i
$579$	−3911.15			−0.280729
$580$		0			0
$581$	4821.61			0.344293
$582$	7575.83	+	2649.15i	0.539567	+	0.188679i
$583$	−856.358	+	856.358i	−0.0608349	+	0.0608349i
$584$	13609.7	+	3097.52i	0.964336	+	0.219480i
$585$		0			0
$586$	−4672.78	+	2251.47i	−0.329404	+	0.158716i
$587$	18386.6	+	18386.6i	1.29284	+	1.29284i	0.933023	+	0.359818i	$0.117161\pi$
$587$	18386.6	+	18386.6i	1.29284	+	1.29284i	0.359818	+	0.933023i	$0.382839\pi$
$588$	1905.47	+	16849.4i	0.133640	+	1.18173i
$589$		−	3814.88i		−	0.266875i
$590$		0			0
$591$			19445.2i			1.35342i
$592$	−2811.60	−	1763.43i	−0.195196	−	0.122427i
$593$	14464.2	+	14464.2i	1.00164	+	1.00164i	0.999999	+	0.00164100i	$0.000522346\pi$
$593$	14464.2	+	14464.2i	1.00164	+	1.00164i	0.00164100	+	0.999999i	$0.499478\pi$
$594$	4008.98	+	8320.37i	0.276920	+	0.574729i
$595$		0			0
$596$	−3927.23	+	4928.73i	−0.269908	+	0.338739i
$597$	17734.8	−	17734.8i	1.21581	−	1.21581i
$598$	−13675.3	+	39107.6i	−0.935161	+	2.67430i
$599$	17213.1			1.17414			0.587068	−	0.809537i	$-0.300282\pi$
$599$	17213.1			1.17414			0.587068	+	0.809537i	$0.300282\pi$
$600$		0			0
$601$	3341.24			0.226776			0.113388	−	0.993551i	$-0.463830\pi$
$601$	3341.24			0.226776			0.113388	+	0.993551i	$0.463830\pi$
$602$	6889.98	−	19703.4i	0.466470	−	1.33397i
$603$	54.0080	−	54.0080i	0.00364739	−	0.00364739i
$604$	−4557.34	+	5719.53i	−0.307013	+	0.385306i
$605$		0			0
$606$	927.428	+	1924.82i	0.0621686	+	0.129027i
$607$	−7932.89	−	7932.89i	−0.530455	−	0.530455i	0.390253	−	0.920708i	$-0.372388\pi$
$607$	−7932.89	−	7932.89i	−0.530455	−	0.530455i	−0.920708	+	0.390253i	$0.872388\pi$
$608$	10260.8	+	1145.46i	0.684423	+	0.0764057i
$609$		−	17369.6i		−	1.15575i
$610$		0			0
$611$			6816.62i			0.451343i
$612$	−0.319185	−	2.82245i	−2.10822e−5	−	0.000186423i
$613$	−12467.2	−	12467.2i	−0.821447	−	0.821447i	0.164869	−	0.986316i	$-0.447280\pi$
$613$	−12467.2	−	12467.2i	−0.821447	−	0.821447i	−0.986316	+	0.164869i	$0.947280\pi$
$614$	−1880.33	+	905.996i	−0.123590	+	0.0595489i
$615$		0			0
$616$	−3215.46	+	14127.9i	−0.210316	+	0.924072i
$617$	10741.4	−	10741.4i	0.700864	−	0.700864i	−0.263732	−	0.964596i	$-0.584954\pi$
$617$	10741.4	−	10741.4i	0.700864	−	0.700864i	0.964596	+	0.263732i	$0.0849536\pi$
$618$	−16889.8	−	5906.13i	−1.09937	−	0.384432i
$619$	−14442.0			−0.937756			−0.468878	−	0.883263i	$-0.655342\pi$
$619$	−14442.0			−0.937756			−0.468878	+	0.883263i	$0.655342\pi$
$620$		0			0
$621$	22974.2			1.48458
$622$	14316.2	+	5006.18i	0.922876	+	0.322716i
$623$	13246.3	−	13246.3i	0.851846	−	0.851846i
$624$	−6642.21	−	28991.8i	−0.426123	−	1.85994i
$625$		0			0
$626$	−10294.3	+	4960.10i	−0.657260	+	0.316686i
$627$	4930.05	+	4930.05i	0.314015	+	0.314015i
$628$	−6508.00	+	735.978i	−0.413531	+	0.0467655i
$629$		−	63.9650i		−	0.00405477i
$630$		0			0
$631$		−	5626.38i		−	0.354964i	−0.984124	−	0.177482i	$-0.943205\pi$
$631$		−	5626.38i		−	0.354964i	0.984124	−	0.177482i	$-0.0567952\pi$
$632$	−11656.7	+	7334.40i	−0.733670	+	0.461625i
$633$	10288.5	+	10288.5i	0.646024	+	0.646024i
$634$	1358.84	+	2820.18i	0.0851204	+	0.176662i
$635$		0			0
$636$	−1691.46	−	1347.76i	−0.105457	−	0.0840288i
$637$	−25525.5	+	25525.5i	−1.58769	+	1.58769i
$638$	2654.87	−	7592.18i	0.164745	−	0.471124i
$639$	−168.203			−0.0104132
$640$		0			0
$641$	−3249.09			−0.200205			−0.100102	−	0.994977i	$-0.531917\pi$
$641$	−3249.09			−0.200205			−0.100102	+	0.994977i	$0.531917\pi$
$642$	−6807.75	+	19468.2i	−0.418506	+	1.19681i
$643$	−22377.0	+	22377.0i	−1.37241	+	1.37241i	−0.515556	+	0.856856i	$0.672415\pi$
$643$	−22377.0	+	22377.0i	−1.37241	+	1.37241i	−0.856856	+	0.515556i	$0.827585\pi$
$644$	28187.9	+	22460.2i	1.72478	+	1.37431i
$645$		0			0
$646$	86.3737	+	179.263i	0.00526057	+	0.0109180i
$647$	−9336.87	−	9336.87i	−0.567342	−	0.567342i	0.364041	−	0.931383i	$-0.381397\pi$
$647$	−9336.87	−	9336.87i	−0.567342	−	0.567342i	−0.931383	+	0.364041i	$0.881397\pi$
$648$	−14108.9	+	8877.32i	−0.855324	+	0.538170i
$649$		−	9402.59i		−	0.568696i
$650$		0			0
$651$			9560.75i			0.575600i
$652$	15739.0	−	1779.89i	0.945379	−	0.106911i
$653$	−502.340	−	502.340i	−0.0301042	−	0.0301042i	0.691894	−	0.721999i	$-0.256776\pi$
$653$	−502.340	−	502.340i	−0.0301042	−	0.0301042i	−0.721999	+	0.691894i	$0.756776\pi$
$654$	3883.41	−	1871.13i	0.232191	−	0.111876i
$655$		0			0
$656$	−4325.03	−	18877.8i	−0.257415	−	1.12356i
$657$	−125.553	+	125.553i	−0.00745552	+	0.00745552i
$658$	5597.77	+	1957.46i	0.331647	+	0.115972i
$659$	−15059.8			−0.890206			−0.445103	−	0.895480i	$-0.646833\pi$
$659$	−15059.8			−0.890206			−0.445103	+	0.895480i	$0.646833\pi$
$660$		0			0
$661$	−15858.4			−0.933163			−0.466581	−	0.884478i	$-0.654515\pi$
$661$	−15858.4			−0.933163			−0.466581	+	0.884478i	$0.654515\pi$
$662$	24278.0	+	8489.66i	1.42537	+	0.498429i
$663$	405.344	−	405.344i	0.0237440	−	0.0237440i
$664$	−884.819	+	3887.67i	−0.0517133	+	0.227215i
$665$		0			0
$666$	38.0349	−	18.3262i	0.00221294	−	0.00106626i
$667$	−14147.1	−	14147.1i	−0.821255	−	0.821255i
$668$	−1513.80	−	13386.0i	−0.0876806	−	0.775330i
$669$			8231.30i			0.475696i
$670$		0			0
$671$		−	11934.0i		−	0.686596i
$672$	−25715.3	−	2870.73i	−1.47617	−	0.164793i
$673$	−15571.5	−	15571.5i	−0.891883	−	0.891883i	0.102817	−	0.994700i	$-0.467214\pi$
$673$	−15571.5	−	15571.5i	−0.891883	−	0.891883i	−0.994700	+	0.102817i	$0.967214\pi$
$674$	−7910.66	−	16418.0i	−0.452088	−	0.938278i
$675$		0			0
$676$	28505.2	−	35774.5i	1.62183	−	2.03542i
$677$	22618.4	−	22618.4i	1.28404	−	1.28404i	0.345694	−	0.938347i	$-0.387643\pi$
$677$	22618.4	−	22618.4i	1.28404	−	1.28404i	0.938347	−	0.345694i	$-0.112357\pi$
$678$	9786.34	−	27986.1i	0.554339	−	1.58525i
$679$	14863.5			0.840074
$680$		0			0
$681$	14360.3			0.808057
$682$	−1461.32	+	4178.95i	−0.0820480	+	0.234634i
$683$	9213.79	−	9213.79i	0.516187	−	0.516187i	−0.400228	−	0.916415i	$-0.631069\pi$
$683$	9213.79	−	9213.79i	0.516187	−	0.516187i	0.916415	+	0.400228i	$0.131069\pi$
$684$	−81.8469	+	102.719i	−0.00457528	+	0.00574205i
$685$		0			0
$686$	2108.42	+	4375.88i	0.117347	+	0.243545i
$687$	−1013.76	−	1013.76i	−0.0562991	−	0.0562991i
$688$	14622.5	+	9171.20i	0.810286	+	0.508210i
$689$		−	4604.19i		−	0.254580i
$690$		0			0
$691$		−	14440.8i		−	0.795015i	−0.917599	−	0.397508i	$-0.869875\pi$
$691$		−	14440.8i		−	0.795015i	0.917599	−	0.397508i	$-0.130125\pi$
$692$	−2508.26	−	22179.7i	−0.137788	−	1.21842i
$693$	−130.333	−	130.333i	−0.00714423	−	0.00714423i
$694$	4410.12	−	2124.92i	0.241219	−	0.116226i
$695$		0			0
$696$	14005.2	+	3187.53i	0.762736	+	0.173596i
$697$	263.937	−	263.937i	0.0143434	−	0.0143434i
$698$	5874.91	+	2054.37i	0.318580	+	0.111403i
$699$	20408.7			1.10433
$700$		0			0
$701$	−23288.4			−1.25476			−0.627382	−	0.778712i	$-0.715874\pi$
$701$	−23288.4			−1.25476			−0.627382	+	0.778712i	$0.715874\pi$
$702$	−33144.2	−	11590.0i	−1.78198	−	0.623131i
$703$	−2091.40	+	2091.40i	−0.112203	+	0.112203i
$704$	−10801.2	−	5185.25i	−0.578249	−	0.277594i
$705$		0			0
$706$	19724.2	−	9503.65i	1.05146	−	0.506621i
$707$	2798.01	+	2798.01i	0.148840	+	0.148840i
$708$	16685.0	−	1886.87i	0.885678	−	0.100160i
$709$			22128.3i			1.17214i	0.810261	+	0.586070i	$0.199326\pi$
$709$			22128.3i			1.17214i	−0.810261	+	0.586070i	$0.800674\pi$
$710$		0			0
$711$		−	175.198i		−	0.00924111i
$712$	8249.63	+	13111.3i	0.434225	+	0.690122i
$713$	7786.96	+	7786.96i	0.409010	+	0.409010i
$714$	−216.468	−	449.264i	−0.0113461	−	0.0235480i
$715$		0			0
$716$	−6098.45	−	4859.26i	−0.318310	−	0.253630i
$717$	−25530.1	+	25530.1i	−1.32976	+	1.32976i
$718$	5818.49	−	16639.2i	0.302429	−	0.864861i
$719$	−8643.64			−0.448336			−0.224168	−	0.974551i	$-0.571966\pi$
$719$	−8643.64			−0.448336			−0.224168	+	0.974551i	$0.571966\pi$
$720$		0			0
$721$	−33137.4			−1.71165
$722$	−3366.61	+	9627.54i	−0.173535	+	0.496261i
$723$	−14946.3	+	14946.3i	−0.768825	+	0.768825i
$724$	−2853.06	−	2273.33i	−0.146455	−	0.116695i
$725$		0			0
$726$	5024.16	+	10427.3i	0.256838	+	0.533049i
$727$	−26688.5	−	26688.5i	−1.36152	−	1.36152i	−0.871985	−	0.489533i	$-0.837167\pi$
$727$	−26688.5	−	26688.5i	−1.36152	−	1.36152i	−0.489533	−	0.871985i	$-0.662833\pi$
$728$	−29335.2	−	46623.0i	−1.49345	−	2.37358i
$729$			19468.7i			0.989113i
$730$		0			0
$731$			332.667i			0.0168319i
$732$	21176.9	−	2394.86i	1.06929	−	0.120924i
$733$	6627.41	+	6627.41i	0.333955	+	0.333955i	0.854086	−	0.520131i	$-0.174117\pi$
$733$	6627.41	+	6627.41i	0.333955	+	0.333955i	−0.520131	+	0.854086i	$0.674117\pi$
$734$	−6010.93	+	2896.23i	−0.302272	+	0.145643i
$735$		0			0
$736$	−23282.5	+	18606.2i	−1.16604	+	0.931842i
$737$	4390.70	−	4390.70i	0.219448	−	0.219448i
$738$	232.561	+	81.3232i	0.0115999	+	0.00405630i
$739$	−33036.1			−1.64445			−0.822227	−	0.569160i	$-0.807269\pi$
$739$	−33036.1			−1.64445			−0.822227	+	0.569160i	$0.807269\pi$
$740$		0			0
$741$	−26506.3			−1.31408
$742$	−3780.93	−	1322.14i	−0.187065	−	0.0654139i
$743$	12481.6	−	12481.6i	0.616292	−	0.616292i	−0.328287	−	0.944578i	$-0.606471\pi$
$743$	12481.6	−	12481.6i	0.616292	−	0.616292i	0.944578	+	0.328287i	$0.106471\pi$
$744$	−7708.84	−	1754.51i	−0.379865	−	0.0864560i
$745$		0			0
$746$	3355.14	−	1616.60i	0.164665	−	0.0793402i
$747$	−35.8647	−	35.8647i	−0.00175665	−	0.00175665i
$748$	−25.9489	−	229.457i	−0.00126843	−	0.0112163i
$749$			38196.1i			1.86336i
$750$		0			0
$751$			36869.1i			1.79144i	0.444617	+	0.895721i	$0.353340\pi$
$751$			36869.1i			1.79144i	−0.444617	+	0.895721i	$0.646660\pi$
$752$	−2605.55	+	4154.27i	−0.126349	+	0.201450i
$753$	16033.3	+	16033.3i	0.775943	+	0.775943i
$754$	13272.7	+	27546.5i	0.641063	+	1.33048i
$755$		0			0
$756$	−19035.3	+	23889.7i	−0.915753	+	1.14928i
$757$	−20029.2	+	20029.2i	−0.961655	+	0.961655i	−0.999291	−	0.0376366i	$-0.988017\pi$
$757$	−20029.2	+	20029.2i	−0.961655	+	0.961655i	0.0376366	+	0.999291i	$0.488017\pi$
$758$	−1171.68	+	3350.67i	−0.0561442	+	0.160556i
$759$	−20126.5			−0.962512
$760$		0			0
$761$	25147.6			1.19790			0.598948	−	0.800788i	$-0.295586\pi$
$761$	25147.6			1.19790			0.598948	+	0.800788i	$0.295586\pi$
$762$	2726.30	−	7796.44i	0.129611	−	0.370650i
$763$	5645.11	−	5645.11i	0.267846	−	0.267846i
$764$	13690.2	−	17181.4i	0.648289	−	0.813613i
$765$		0			0
$766$	10406.8	+	21598.7i	0.490880	+	1.01879i
$767$	25276.4	+	25276.4i	1.18993	+	1.18993i
$768$	7033.72	−	20207.4i	0.330479	−	0.949445i
$769$		−	42286.8i		−	1.98296i	−0.130243	−	0.991482i	$-0.541576\pi$
$769$		−	42286.8i		−	1.98296i	0.130243	−	0.991482i	$-0.458424\pi$
$770$		0			0
$771$		−	24971.9i		−	1.16646i
$772$	−673.081	−	5951.83i	−0.0313792	−	0.277476i
$773$	−13564.2	−	13564.2i	−0.631140	−	0.631140i	0.317214	−	0.948354i	$-0.397253\pi$
$773$	−13564.2	−	13564.2i	−0.631140	−	0.631140i	−0.948354	+	0.317214i	$0.897253\pi$
$774$	−197.810	+	95.3104i	−0.00918623	+	0.00442618i
$775$		0			0
$776$	−2727.63	+	11984.5i	−0.126181	+	0.554405i
$777$	5241.42	−	5241.42i	0.242001	−	0.242001i
$778$	−19466.3	−	6807.08i	−0.897045	−	0.313683i
$779$	−17259.4			−0.793815
$780$		0			0
$781$	−13674.4			−0.626517
$782$	−542.220	−	189.606i	−0.0247951	−	0.00867046i
$783$	11989.8	−	11989.8i	0.547231	−	0.547231i
$784$	−25312.8	+	5799.32i	−1.15310	+	0.264182i
$785$		0			0
$786$	30106.2	−	14506.0i	1.36622	−	0.658284i
$787$	−10981.7	−	10981.7i	−0.497403	−	0.497403i	0.413226	−	0.910629i	$-0.364402\pi$
$787$	−10981.7	−	10981.7i	−0.497403	−	0.497403i	−0.910629	+	0.413226i	$0.864402\pi$
$788$	−29591.0	+	3346.39i	−1.33773	+	0.151282i
$789$			41866.5i			1.88908i
$790$		0			0
$791$		−	54908.0i		−	2.46814i
$792$	129.005	−	81.1701i	0.00578789	−	0.00364174i
$793$	32081.3	+	32081.3i	1.43662	+	1.43662i
$794$	−6878.86	−	14276.6i	−0.307458	−	0.638108i
$795$		0			0
$796$	30040.2	+	23936.1i	1.33762	+	1.06582i
$797$	10468.6	−	10468.6i	0.465266	−	0.465266i	−0.435111	−	0.900377i	$-0.643291\pi$
$797$	10468.6	−	10468.6i	0.465266	−	0.465266i	0.900377	+	0.435111i	$0.143291\pi$
$798$	−7611.53	+	21766.8i	−0.337651	+	0.965585i
$799$	−94.5112			−0.00418469
$800$		0			0
$801$	−197.060			−0.00869260
$802$	−2174.01	+	6217.05i	−0.0957194	+	0.273730i
$803$	−10207.1	+	10207.1i	−0.448568	+	0.448568i
$804$	8672.43	+	6910.22i	0.380414	+	0.303115i
$805$		0			0
$806$	−7305.65	−	15162.4i	−0.319269	−	0.662621i
$807$	17962.9	+	17962.9i	0.783549	+	0.783549i
$808$	−2769.50	+	1742.57i	−0.120583	+	0.0758705i
$809$		−	4008.43i		−	0.174201i	−0.996200	−	0.0871007i	$-0.972240\pi$
$809$		−	4008.43i		−	0.174201i	0.996200	−	0.0871007i	$-0.0277602\pi$
$810$		0			0
$811$		−	22758.2i		−	0.985387i	−0.870203	−	0.492694i	$-0.836012\pi$
$811$		−	22758.2i		−	0.985387i	0.870203	−	0.492694i	$-0.163988\pi$
$812$	26432.4	−	2989.19i	1.14236	−	0.129187i
$813$	−23.7966	−	23.7966i	−0.00102655	−	0.00102655i
$814$	3092.13	−	1489.87i	0.133144	−	0.0641523i
$815$		0			0
$816$	401.966	−	92.0930i	0.0172447	−	0.00395086i
$817$	10876.9	−	10876.9i	0.465770	−	0.465770i
$818$	4697.94	+	1642.80i	0.200807	+	0.0702190i
$819$	700.733			0.0298969
$820$		0			0
$821$	−9500.27			−0.403851			−0.201925	−	0.979401i	$-0.564720\pi$
$821$	−9500.27			−0.403851			−0.201925	+	0.979401i	$0.564720\pi$
$822$	−29778.9	−	10413.2i	−1.26357	−	0.441853i
$823$	4113.92	−	4113.92i	0.174243	−	0.174243i	−0.614598	−	0.788841i	$-0.710682\pi$
$823$	4113.92	−	4113.92i	0.174243	−	0.174243i	0.788841	+	0.614598i	$0.210682\pi$
$824$	6081.08	−	26718.7i	0.257093	−	1.12960i
$825$		0			0
$826$	28015.2	−	13498.5i	1.18011	−	0.568610i
$827$	16515.2	+	16515.2i	0.694426	+	0.694426i	0.963203	−	0.268777i	$-0.0866194\pi$
$827$	16515.2	+	16515.2i	0.694426	+	0.694426i	−0.268777	+	0.963203i	$0.586619\pi$
$828$	−42.6046	−	376.738i	−0.00178818	−	0.0158122i
$829$		−	28320.1i		−	1.18649i	−0.805023	−	0.593243i	$-0.797847\pi$
$829$		−	28320.1i		−	1.18649i	0.805023	−	0.593243i	$-0.202153\pi$
$830$		0			0
$831$			41816.9i			1.74562i
$832$	42975.5	−	15097.1i	1.79075	−	0.629085i
$833$	−353.906	−	353.906i	−0.0147204	−	0.0147204i
$834$	−9509.75	−	19736.9i	−0.394839	−	0.819462i
$835$		0			0
$836$	−6653.92	+	8350.78i	−0.275276	+	0.345476i
$837$	−6599.55	+	6599.55i	−0.272538	+	0.272538i
$838$	5684.40	−	16255.8i	0.234325	−	0.670103i
$839$	20551.4			0.845665			0.422833	−	0.906208i	$-0.361036\pi$
$839$	20551.4			0.845665			0.422833	+	0.906208i	$0.361036\pi$
$840$		0			0
$841$	9622.76			0.394553
$842$	−9570.02	+	27367.6i	−0.391692	+	1.12013i
$843$	−21346.3	+	21346.3i	−0.872130	+	0.872130i
$844$	−13886.1	+	17427.3i	−0.566326	+	0.710748i
$845$		0			0
$846$	−27.0778	−	56.1982i	−0.00110042	−	0.00228385i
$847$	15157.7	+	15157.7i	0.614904	+	0.614904i
$848$	1759.88	−	2805.94i	0.0712673	−	0.113628i
$849$			12880.0i			0.520660i
$850$		0			0
$851$		−	8537.98i		−	0.343923i
$852$	−2744.13	−	24265.4i	−0.110343	−	0.975726i
$853$	−5591.50	−	5591.50i	−0.224442	−	0.224442i	0.585924	−	0.810366i	$-0.300732\pi$
$853$	−5591.50	−	5591.50i	−0.224442	−	0.224442i	−0.810366	+	0.585924i	$0.800732\pi$
$854$	35557.5	−	17132.6i	1.42477	−	0.686492i
$855$		0			0
$856$	−30797.5	−	7009.41i	−1.22972	−	0.279879i
$857$	−25385.3	+	25385.3i	−1.01184	+	1.01184i	−0.0119074	+	0.999929i	$0.503790\pi$
$857$	−25385.3	+	25385.3i	−1.01184	+	1.01184i	−0.999929	+	0.0119074i	$0.996210\pi$
$858$	29035.9	+	10153.4i	1.15533	+	0.404001i
$859$	43234.8			1.71729			0.858645	−	0.512570i	$-0.171307\pi$
$859$	43234.8			1.71729			0.858645	+	0.512570i	$0.171307\pi$
$860$		0			0
$861$	43255.1			1.71211
$862$	−9081.33	−	3175.61i	−0.358830	−	0.125478i
$863$	−21703.0	+	21703.0i	−0.856057	+	0.856057i	−0.990871	−	0.134814i	$-0.956956\pi$
$863$	−21703.0	+	21703.0i	−0.856057	+	0.856057i	0.134814	+	0.990871i	$0.456956\pi$
$864$	−15769.0	−	19732.2i	−0.620919	−	0.776973i
$865$		0			0
$866$	−14886.4	+	7172.65i	−0.584133	+	0.281451i
$867$	−18141.9	−	18141.9i	−0.710646	−	0.710646i
$868$	−14549.2	+	1645.34i	−0.568929	+	0.0643391i
$869$		−	14243.1i		−	0.556000i
$870$		0			0
$871$			23606.5i			0.918341i
$872$	3515.72	+	5587.60i	0.136533	+	0.216995i
$873$	−110.560	−	110.560i	−0.00428624	−	0.00428624i
$874$	11529.1	+	23927.8i	0.446198	+	0.926054i
$875$		0			0
$876$	−20160.9	−	16064.2i	−0.777594	−	0.619589i
$877$	−15547.0	+	15547.0i	−0.598614	+	0.598614i	−0.939944	−	0.341330i	$-0.889123\pi$
$877$	−15547.0	+	15547.0i	−0.598614	+	0.598614i	0.341330	+	0.939944i	$0.389123\pi$
$878$	−8795.98	+	25154.0i	−0.338098	+	0.966864i
$879$	9579.62			0.367591
$880$		0			0
$881$	−43967.4			−1.68138			−0.840691	−	0.541515i	$-0.817851\pi$
$881$	−43967.4			−1.68138			−0.840691	+	0.541515i	$0.817851\pi$
$882$	109.044	−	311.835i	0.00416293	−	0.0119048i
$883$	4407.27	−	4407.27i	0.167969	−	0.167969i	−0.618117	−	0.786086i	$-0.712104\pi$
$883$	4407.27	−	4407.27i	0.167969	−	0.167969i	0.786086	+	0.618117i	$0.212104\pi$
$884$	686.592	+	547.079i	0.0261228	+	0.0208148i
$885$		0			0
$886$	14192.4	+	29455.4i	0.538152	+	1.11690i
$887$	−18062.4	−	18062.4i	−0.683739	−	0.683739i	0.277102	−	0.960841i	$-0.410626\pi$
$887$	−18062.4	−	18062.4i	−0.683739	−	0.683739i	−0.960841	+	0.277102i	$0.910626\pi$
$888$	3264.30	+	5188.03i	0.123359	+	0.196057i
$889$		−	15296.4i		−	0.577080i
$890$		0			0
$891$		−	17239.4i		−	0.648194i
$892$	−12526.1	+	1416.55i	−0.470183	+	0.0531721i
$893$	3090.14	+	3090.14i	0.115798	+	0.115798i
$894$	10485.4	−	5052.17i	0.392266	−	0.189004i
$895$		0			0
$896$	−56.8558	−	39626.5i	−0.00211989	−	1.47749i
$897$	54104.9	−	54104.9i	2.01395	−	2.01395i
$898$	25065.7	+	8765.12i	0.931464	+	0.325719i
$899$	8127.76			0.301531
$900$		0			0
$901$	63.8362			0.00236037
$902$	18906.6	+	6611.35i	0.697916	+	0.244051i
$903$	−27259.4	+	27259.4i	−1.00458	+	1.00458i
$904$	44272.3	+	10076.2i	1.62885	+	0.370720i
$905$		0			0
$906$	12167.8	−	5862.78i	0.446190	−	0.214986i
$907$	−27551.2	−	27551.2i	−1.00862	−	1.00862i	−0.999962	−	0.00866129i	$-0.997243\pi$
$907$	−27551.2	−	27551.2i	−1.00862	−	1.00862i	−0.00866129	−	0.999962i	$-0.502757\pi$
$908$	2471.30	+	21852.9i	0.0903226	+	0.798692i
$909$		−	41.6250i		−	0.00151883i
$910$		0			0
$911$			38612.5i			1.40427i	0.712045	+	0.702134i	$0.247769\pi$
$911$			38612.5i			1.40427i	−0.712045	+	0.702134i	$0.752231\pi$
$912$	−16153.8	−	10131.6i	−0.586520	−	0.367864i
$913$	−2915.70	−	2915.70i	−0.105691	−	0.105691i
$914$	12797.2	+	26559.8i	0.463124	+	0.961182i
$915$		0			0
$916$	1368.24	−	1717.17i	0.0493537	−	0.0619397i
$917$	43763.9	−	43763.9i	1.57602	−	1.57602i
$918$	160.694	−	459.539i	0.00577743	−	0.0165218i
$919$	4629.65			0.166179			0.0830893	−	0.996542i	$-0.473521\pi$
$919$	4629.65			0.166179			0.0830893	+	0.996542i	$0.473521\pi$
$920$		0			0
$921$	3854.85			0.137917
$922$	−6507.96	+	18610.9i	−0.232460	+	0.664770i
$923$	36760.1	−	36760.1i	1.31091	−	1.31091i
$924$	16675.9	−	20928.5i	0.593719	−	0.745127i
$925$		0			0
$926$	4131.72	+	8575.10i	0.146627	+	0.304315i
$927$	246.487	+	246.487i	0.00873320	+	0.00873320i
$928$	−2440.46	+	21861.0i	−0.0863276	+	0.773301i
$929$		−	12620.3i		−	0.445705i	−0.974852	−	0.222853i	$-0.928463\pi$
$929$		−	12620.3i		−	0.445705i	0.974852	−	0.222853i	$-0.0715369\pi$
$930$		0			0
$931$			23142.7i			0.814684i
$932$	3512.20	+	31057.2i	0.123440	+	1.09154i
$933$	−19806.3	−	19806.3i	−0.694995	−	0.694995i
$934$	−37960.0	+	18290.2i	−1.32986	+	0.640763i
$935$		0			0
$936$	−128.592	+	565.002i	−0.00449057	+	0.0197304i
$937$	−37000.8	+	37000.8i	−1.29003	+	1.29003i	−0.355272	+	0.934763i	$0.615612\pi$
$937$	−37000.8	+	37000.8i	−1.29003	+	1.29003i	−0.934763	+	0.355272i	$0.884388\pi$
$938$	19385.5	+	6778.82i	0.674796	+	0.235966i
$939$	21104.3			0.733455
$940$		0			0
$941$	28402.7			0.983955			0.491978	−	0.870608i	$-0.336274\pi$
$941$	28402.7			0.983955			0.491978	+	0.870608i	$0.336274\pi$
$942$	11418.2	+	3992.76i	0.394930	+	0.138101i
$943$	35230.0	−	35230.0i	1.21659	−	1.21659i
$944$	5742.73	+	25065.8i	0.197998	+	0.864218i
$945$		0			0
$946$	−16081.4	+	7748.47i	−0.552698	+	0.266305i
$947$	15370.6	+	15370.6i	0.527432	+	0.527432i	0.919806	−	0.392374i	$-0.128346\pi$
$947$	15370.6	+	15370.6i	0.527432	+	0.527432i	−0.392374	+	0.919806i	$0.628346\pi$
$948$	25274.5	−	2858.24i	0.865904	−	0.0979235i
$949$		−	54878.1i		−	1.87715i
$950$		0			0
$951$		−	5781.62i		−	0.197142i
$952$	646.419	−	406.727i	0.0220069	−	0.0138467i
$953$	18338.9	+	18338.9i	0.623352	+	0.623352i	0.946387	−	0.323035i	$-0.104703\pi$
$953$	18338.9	+	18338.9i	0.623352	+	0.623352i	−0.323035	+	0.946387i	$0.604703\pi$
$954$	18.2893	+	37.9583i	0.000620691	+	0.00128820i
$955$		0			0
$956$	−43244.3	−	34457.2i	−1.46299	−	1.16572i
$957$	−10503.7	+	10503.7i	−0.354792	+	0.354792i
$958$	−10997.0	+	31448.2i	−0.370873	+	1.06059i
$959$	−58425.3			−1.96731
$960$		0			0
$961$	25317.2			0.849829
$962$	−4307.25	+	12317.5i	−0.144357	+	0.412819i
$963$	284.115	−	284.115i	0.00950725	−	0.00950725i
$964$	−25316.9	−	20172.6i	−0.845853	−	0.673978i
$965$		0			0
$966$	−28893.9	−	59967.3i	−0.962366	−	1.99733i
$967$	19130.7	+	19130.7i	0.636195	+	0.636195i	0.949615	−	0.313420i	$-0.101475\pi$
$967$	19130.7	+	19130.7i	0.636195	+	0.636195i	−0.313420	+	0.949615i	$0.601475\pi$
$968$	−15003.2	+	9440.03i	−0.498164	+	0.313444i
$969$		−	367.505i		−	0.0121837i
$970$		0			0
$971$			37147.3i			1.22772i	0.789416	+	0.613859i	$0.210384\pi$
$971$			37147.3i			1.22772i	−0.789416	+	0.613859i	$0.789616\pi$
$972$	642.021	−	72.6050i	0.0211860	−	0.00239589i
$973$	−28690.5	−	28690.5i	−0.945298	−	0.945298i
$974$	−11381.5	+	5483.89i	−0.374420	+	0.180406i
$975$		0			0
$976$	7288.79	+	31814.0i	0.239046	+	1.04338i
$977$	4956.62	−	4956.62i	0.162310	−	0.162310i	−0.621279	−	0.783589i	$-0.713387\pi$
$977$	4956.62	−	4956.62i	0.162310	−	0.162310i	0.783589	+	0.621279i	$0.213387\pi$
$978$	−27613.8	−	9656.13i	−0.902854	−	0.315715i
$979$	−16020.4			−0.522998
$980$		0			0
$981$	−83.9804			−0.00273322
$982$	31586.4	+	11045.3i	1.02644	+	0.358931i
$983$	−20988.5	+	20988.5i	−0.681005	+	0.681005i	−0.960227	−	0.279222i	$-0.909924\pi$
$983$	−20988.5	+	20988.5i	−0.681005	+	0.681005i	0.279222	+	0.960227i	$0.409924\pi$
$984$	−7937.80	+	34876.6i	−0.257162	+	1.12990i
$985$		0			0
$986$	−381.927	+	184.023i	−0.0123357	+	0.00594370i
$987$	−7744.44	−	7744.44i	−0.249755	−	0.249755i
$988$	−4561.54	−	40336.2i	−0.146885	−	1.29885i
$989$			44404.0i			1.42767i
$990$		0			0
$991$		−	51558.7i		−	1.65269i	−0.563163	−	0.826346i	$-0.690416\pi$
$991$		−	51558.7i		−	1.65269i	0.563163	−	0.826346i	$-0.309584\pi$
$992$	1343.30	−	12032.9i	0.0429937	−	0.385127i
$993$	−33588.3	−	33588.3i	−1.07341	−	1.07341i
$994$	−19631.2	−	40743.2i	−0.626422	−	1.30010i
$995$		0			0
$996$	4588.82	−	5759.04i	0.145986	−	0.183215i
$997$	−7837.24	+	7837.24i	−0.248955	+	0.248955i	−0.820542	−	0.571587i	$-0.806328\pi$
$997$	−7837.24	+	7837.24i	−0.248955	+	0.248955i	0.571587	+	0.820542i	$0.306328\pi$
$998$	8252.95	−	23601.1i	0.261766	−	0.748576i
$999$	7236.06			0.229168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.e.f.43.7	yes	24
4.3	odd	2	inner	100.4.e.f.43.12	yes	24
5.2	odd	4	inner	100.4.e.f.7.12	yes	24
5.3	odd	4	inner	100.4.e.f.7.1	✓	24
5.4	even	2	inner	100.4.e.f.43.6	yes	24
20.3	even	4	inner	100.4.e.f.7.6	yes	24
20.7	even	4	inner	100.4.e.f.7.7	yes	24
20.19	odd	2	inner	100.4.e.f.43.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.e.f.7.1	✓	24	5.3	odd	4	inner
100.4.e.f.7.6	yes	24	20.3	even	4	inner
100.4.e.f.7.7	yes	24	20.7	even	4	inner
100.4.e.f.7.12	yes	24	5.2	odd	4	inner
100.4.e.f.43.1	yes	24	20.19	odd	2	inner
100.4.e.f.43.6	yes	24	5.4	even	2	inner
100.4.e.f.43.7	yes	24	1.1	even	1	trivial
100.4.e.f.43.12	yes	24	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.933623 - 2.66990i) q^{2} +(-3.69377 + 3.69377i) q^{3} +(-6.25670 - 4.98535i) q^{4} +(6.41339 + 13.3106i) q^{6} +(19.3489 + 19.3489i) q^{7} +(-19.1518 + 12.0503i) q^{8} -0.287847i q^{9} +O(q^{10})\)	\(q+(0.933623 - 2.66990i) q^{2} +(-3.69377 + 3.69377i) q^{3} +(-6.25670 - 4.98535i) q^{4} +(6.41339 + 13.3106i) q^{6} +(19.3489 + 19.3489i) q^{7} +(-19.1518 + 12.0503i) q^{8} -0.287847i q^{9} -23.4011i q^{11} +(41.5255 - 4.69604i) q^{12} +(62.9078 + 62.9078i) q^{13} +(69.7241 - 33.5950i) q^{14} +(14.2925 + 62.3837i) q^{16} +(-0.872206 + 0.872206i) q^{17} +(-0.768522 - 0.268741i) q^{18} +57.0354 q^{19} -142.941 q^{21} +(-62.4786 - 21.8479i) q^{22} +(-116.421 + 116.421i) q^{23} +(26.2312 - 115.253i) q^{24} +(226.690 - 109.225i) q^{26} +(-98.6685 - 98.6685i) q^{27} +(-24.5991 - 217.521i) q^{28} +121.516i q^{29} -66.8861i q^{31} +(179.902 + 20.0834i) q^{32} +(86.4384 + 86.4384i) q^{33} +(1.51439 + 3.14301i) q^{34} +(-1.43502 + 1.80097i) q^{36} +(-36.6685 + 36.6685i) q^{37} +(53.2496 - 152.279i) q^{38} -464.734 q^{39} -302.608 q^{41} +(-133.453 + 381.637i) q^{42} +(190.704 - 190.704i) q^{43} +(-116.663 + 146.414i) q^{44} +(202.139 + 419.526i) q^{46} +(54.1794 + 54.1794i) q^{47} +(-283.224 - 177.638i) q^{48} +405.760i q^{49} -6.44345i q^{51} +(-79.9774 - 707.213i) q^{52} +(-36.5947 - 36.5947i) q^{53} +(-355.554 + 171.316i) q^{54} +(-603.726 - 137.406i) q^{56} +(-210.676 + 210.676i) q^{57} +(324.436 + 113.451i) q^{58} +401.800 q^{59} +509.974 q^{61} +(-178.579 - 62.4464i) q^{62} +(5.56952 - 5.56952i) q^{63} +(221.581 - 461.569i) q^{64} +(311.483 - 150.081i) q^{66} +(187.627 + 187.627i) q^{67} +(9.80538 - 1.10887i) q^{68} -860.066i q^{69} -584.349i q^{71} +(3.46864 + 5.51278i) q^{72} +(-436.179 - 436.179i) q^{73} +(63.6666 + 132.136i) q^{74} +(-356.853 - 284.342i) q^{76} +(452.786 - 452.786i) q^{77} +(-433.886 + 1240.79i) q^{78} +608.649 q^{79} +736.689 q^{81} +(-282.522 + 807.933i) q^{82} +(124.596 - 124.596i) q^{83} +(894.337 + 712.610i) q^{84} +(-331.115 - 687.206i) q^{86} +(-448.853 - 448.853i) q^{87} +(281.991 + 448.174i) q^{88} -684.600i q^{89} +2434.39i q^{91} +(1308.81 - 148.011i) q^{92} +(247.062 + 247.062i) q^{93} +(195.237 - 94.0703i) q^{94} +(-738.699 + 590.332i) q^{96} +(384.093 - 384.093i) q^{97} +(1083.34 + 378.827i) q^{98} -6.73595 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 36 q^{6}+O(q^{10}) \) 24 * q + 36 * q^6	\( 24 q + 36 q^{6} - 676 q^{16} + 512 q^{21} + 2072 q^{26} - 4600 q^{36} - 392 q^{41} + 5016 q^{46} - 8224 q^{56} + 1088 q^{61} + 11140 q^{66} - 6700 q^{76} - 2424 q^{81} + 5216 q^{86} + 796 q^{96}+O(q^{100}) \) 24 * q + 36 * q^6 - 676 * q^16 + 512 * q^21 + 2072 * q^26 - 4600 * q^36 - 392 * q^41 + 5016 * q^46 - 8224 * q^56 + 1088 * q^61 + 11140 * q^66 - 6700 * q^76 - 2424 * q^81 + 5216 * q^86 + 796 * q^96

Introduction

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