LMFDB - Embedded newform 207.7.d.e.91.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,7,Mod(91,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("207.91");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	207.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$47.6211953093$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.5
Character	$\chi$	$=$	207.91
Dual form			207.7.d.e.91.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.8996 q^{2} +54.8005 q^{4} -162.476i q^{5} -219.782i q^{7} +100.271 q^{8} +O(q^{10})$	\(q-10.8996 q^{2} +54.8005 q^{4} -162.476i q^{5} -219.782i q^{7} +100.271 q^{8} +1770.91i q^{10} -1606.67i q^{11} -3928.95 q^{13} +2395.53i q^{14} -4600.14 q^{16} -6864.44i q^{17} -1474.89i q^{19} -8903.75i q^{20} +17512.0i q^{22} +(-7766.67 - 9365.61i) q^{23} -10773.4 q^{25} +42823.9 q^{26} -12044.2i q^{28} -18555.6 q^{29} +27090.1 q^{31} +43722.2 q^{32} +74819.4i q^{34} -35709.2 q^{35} -74301.9i q^{37} +16075.6i q^{38} -16291.5i q^{40} +53361.4 q^{41} -68697.2i q^{43} -88046.5i q^{44} +(84653.4 + 102081. i) q^{46} +105757. q^{47} +69344.9 q^{49} +117425. q^{50} -215308. q^{52} -257751. i q^{53} -261045. q^{55} -22037.7i q^{56} +202248. q^{58} -158761. q^{59} -224111. i q^{61} -295270. q^{62} -182144. q^{64} +638359. i q^{65} +530212. i q^{67} -376175. i q^{68} +389215. q^{70} -458854. q^{71} +281567. q^{73} +809859. i q^{74} -80824.5i q^{76} -353118. q^{77} +253619. i q^{79} +747411. i q^{80} -581616. q^{82} -147594. i q^{83} -1.11530e6 q^{85} +748770. i q^{86} -161102. i q^{88} +260389. i q^{89} +863513. i q^{91} +(-425618. - 513240. i) q^{92} -1.15271e6 q^{94} -239633. q^{95} +1.39769e6i q^{97} -755829. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8}+O(q^{10}) $ 24 * q + 20 * q^2 + 816 * q^4 + 940 * q^8	$ 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8} + 384 q^{13} + 29544 q^{16} - 29336 q^{23} - 61272 q^{25} - 10088 q^{26} - 64672 q^{29} + 9696 q^{31} + 319620 q^{32} + 225744 q^{35} - 135280 q^{41} + 233232 q^{46} + 74336 q^{47} - 722136 q^{49} - 619324 q^{50} + 1059720 q^{52} - 1019328 q^{55} - 694344 q^{58} - 1057648 q^{59} + 488776 q^{62} - 273888 q^{64} + 2785512 q^{70} + 255392 q^{71} - 322560 q^{73} + 1002960 q^{77} - 5732712 q^{82} - 2704704 q^{85} + 1611444 q^{92} - 147720 q^{94} + 1672656 q^{95} - 9104212 q^{98}+O(q^{100}) $ 24 * q + 20 * q^2 + 816 * q^4 + 940 * q^8 + 384 * q^13 + 29544 * q^16 - 29336 * q^23 - 61272 * q^25 - 10088 * q^26 - 64672 * q^29 + 9696 * q^31 + 319620 * q^32 + 225744 * q^35 - 135280 * q^41 + 233232 * q^46 + 74336 * q^47 - 722136 * q^49 - 619324 * q^50 + 1059720 * q^52 - 1019328 * q^55 - 694344 * q^58 - 1057648 * q^59 + 488776 * q^62 - 273888 * q^64 + 2785512 * q^70 + 255392 * q^71 - 322560 * q^73 + 1002960 * q^77 - 5732712 * q^82 - 2704704 * q^85 + 1611444 * q^92 - 147720 * q^94 + 1672656 * q^95 - 9104212 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−10.8996			−1.36245			−0.681223	−	0.732076i	$-0.738551\pi$
$2$	−10.8996			−1.36245			−0.681223	+	0.732076i	$0.738551\pi$
$3$		0			0
$3$		0			0
$4$	54.8005			0.856258
$5$		−	162.476i		−	1.29981i	−0.760017	−	0.649903i	$-0.774810\pi$
$5$		−	162.476i		−	1.29981i	0.760017	−	0.649903i	$-0.225190\pi$
$6$		0			0
$7$		−	219.782i		−	0.640764i	−0.947288	−	0.320382i	$-0.896189\pi$
$7$		−	219.782i		−	0.640764i	0.947288	−	0.320382i	$-0.103811\pi$
$8$	100.271			0.195841
$9$		0			0
$10$			1770.91i			1.77091i
$11$		−	1606.67i		−	1.20712i	−0.797318	−	0.603559i	$-0.793749\pi$
$11$		−	1606.67i		−	1.20712i	0.797318	−	0.603559i	$-0.206251\pi$
$12$		0			0
$13$	−3928.95			−1.78833			−0.894163	−	0.447742i	$-0.852228\pi$
$13$	−3928.95			−1.78833			−0.894163	+	0.447742i	$0.852228\pi$
$14$			2395.53i			0.873006i
$15$		0			0
$16$	−4600.14			−1.12308
$17$		−	6864.44i		−	1.39720i	−0.715513	−	0.698599i	$-0.753807\pi$
$17$		−	6864.44i		−	1.39720i	0.715513	−	0.698599i	$-0.246193\pi$
$18$		0			0
$19$		−	1474.89i		−	0.215029i	−0.994203	−	0.107515i	$-0.965711\pi$
$19$		−	1474.89i		−	0.215029i	0.994203	−	0.107515i	$-0.0342893\pi$
$20$		−	8903.75i		−	1.11297i
$21$		0			0
$22$			17512.0i			1.64463i
$23$	−7766.67	−	9365.61i	−0.638339	−	0.769755i
$23$	−7766.67	−	9365.61i	−0.638339	−	0.769755i
$24$		0			0
$25$	−10773.4			−0.689496
$26$	42823.9			2.43650
$27$		0			0
$28$		−	12044.2i		−	0.548659i
$29$	−18555.6			−0.760819			−0.380409	−	0.924818i	$-0.624217\pi$
$29$	−18555.6			−0.760819			−0.380409	+	0.924818i	$0.624217\pi$
$30$		0			0
$31$	27090.1			0.909339			0.454670	−	0.890660i	$-0.349757\pi$
$31$	27090.1			0.909339			0.454670	+	0.890660i	$0.349757\pi$
$32$	43722.2			1.33429
$33$		0			0
$34$			74819.4i			1.90361i
$35$	−35709.2			−0.832869
$36$		0			0
$37$		−	74301.9i		−	1.46688i	−0.679754	−	0.733441i	$-0.737913\pi$
$37$		−	74301.9i		−	1.46688i	0.679754	−	0.733441i	$-0.262087\pi$
$38$			16075.6i			0.292966i
$39$		0			0
$40$		−	16291.5i		−	0.254555i
$41$	53361.4			0.774241			0.387120	−	0.922029i	$-0.373470\pi$
$41$	53361.4			0.774241			0.387120	+	0.922029i	$0.373470\pi$
$42$		0			0
$43$		−	68697.2i		−	0.864040i	−0.901864	−	0.432020i	$-0.857801\pi$
$43$		−	68697.2i		−	0.864040i	0.901864	−	0.432020i	$-0.142199\pi$
$44$		−	88046.5i		−	1.03360i
$45$		0			0
$46$	84653.4	+	102081.i	0.869702	+	1.04875i
$47$	105757.			1.01863			0.509316	−	0.860580i	$-0.329899\pi$
$47$	105757.			1.01863			0.509316	+	0.860580i	$0.329899\pi$
$48$		0			0
$49$	69344.9			0.589422
$50$	117425.			0.939400
$51$		0			0
$52$	−215308.			−1.53127
$53$		−	257751.i		−	1.73130i	−0.500650	−	0.865650i	$-0.666906\pi$
$53$		−	257751.i		−	1.73130i	0.500650	−	0.865650i	$-0.333094\pi$
$54$		0			0
$55$	−261045.			−1.56902
$56$		−	22037.7i		−	0.125488i
$57$		0			0
$58$	202248.			1.03657
$59$	−158761.			−0.773013			−0.386507	−	0.922287i	$-0.626318\pi$
$59$	−158761.			−0.773013			−0.386507	+	0.922287i	$0.626318\pi$
$60$		0			0
$61$		−	224111.i		−	0.987357i	−0.869644	−	0.493679i	$-0.835652\pi$
$61$		−	224111.i		−	0.987357i	0.869644	−	0.493679i	$-0.164348\pi$
$62$	−295270.			−1.23892
$63$		0			0
$64$	−182144.			−0.694824
$65$			638359.i			2.32448i
$66$		0			0
$67$			530212.i			1.76289i	0.472286	+	0.881445i	$0.343429\pi$
$67$			530212.i			1.76289i	−0.472286	+	0.881445i	$0.656571\pi$
$68$		−	376175.i		−	1.19636i
$69$		0			0
$70$	389215.			1.13474
$71$	−458854.			−1.28203			−0.641017	−	0.767526i	$-0.721487\pi$
$71$	−458854.			−1.28203			−0.641017	+	0.767526i	$0.721487\pi$
$72$		0			0
$73$	281567.			0.723791			0.361896	−	0.932219i	$-0.382130\pi$
$73$	281567.			0.723791			0.361896	+	0.932219i	$0.382130\pi$
$74$			809859.i			1.99855i
$75$		0			0
$76$		−	80824.5i		−	0.184121i
$77$	−353118.			−0.773477
$78$		0			0
$79$			253619.i			0.514399i	0.966358	+	0.257200i	$0.0827998\pi$
$79$			253619.i			0.514399i	−0.966358	+	0.257200i	$0.917200\pi$
$80$			747411.i			1.45979i
$81$		0			0
$82$	−581616.			−1.05486
$83$		−	147594.i		−	0.258127i	−0.991636	−	0.129063i	$-0.958803\pi$
$83$		−	147594.i		−	0.258127i	0.991636	−	0.129063i	$-0.0411971\pi$
$84$		0			0
$85$	−1.11530e6			−1.81609
$86$			748770.i			1.17721i
$87$		0			0
$88$		−	161102.i		−	0.236403i
$89$			260389.i			0.369362i	0.982799	+	0.184681i	$0.0591252\pi$
$89$			260389.i			0.369362i	−0.982799	+	0.184681i	$0.940875\pi$
$90$		0			0
$91$			863513.i			1.14589i
$92$	−425618.	−	513240.i	−0.546583	−	0.659109i
$93$		0			0
$94$	−1.15271e6			−1.38783
$95$	−239633.			−0.279497
$96$		0			0
$97$			1.39769e6i			1.53142i	0.643186	+	0.765710i	$0.277612\pi$
$97$			1.39769e6i			1.53142i	−0.643186	+	0.765710i	$0.722388\pi$
$98$	−755829.			−0.803055
$99$		0			0
$100$	−590386.			−0.590386
$101$	1.18689e6			1.15199			0.575993	−	0.817454i	$-0.304615\pi$
$101$	1.18689e6			1.15199			0.575993	+	0.817454i	$0.304615\pi$
$102$		0			0
$103$			607038.i			0.555526i	0.960650	+	0.277763i	$0.0895930\pi$
$103$			607038.i			0.555526i	−0.960650	+	0.277763i	$0.910407\pi$
$104$	−393958.			−0.350227
$105$		0			0
$106$			2.80937e6i			2.35880i
$107$		−	1.19097e6i		−	0.972184i	−0.873908	−	0.486092i	$-0.838422\pi$
$107$		−	1.19097e6i		−	0.972184i	0.873908	−	0.486092i	$-0.161578\pi$
$108$		0			0
$109$		−	1.52787e6i		−	1.17979i	−0.807478	−	0.589897i	$-0.799168\pi$
$109$		−	1.52787e6i		−	1.17979i	0.807478	−	0.589897i	$-0.200832\pi$
$110$	2.84528e6			2.13770
$111$		0			0
$112$			1.01103e6i			0.719629i
$113$			1.05493e6i			0.731117i	0.930788	+	0.365559i	$0.119122\pi$
$113$			1.05493e6i			0.731117i	−0.930788	+	0.365559i	$0.880878\pi$
$114$		0			0
$115$	−1.52168e6	+	1.26190e6i	−1.00053	+	0.829717i
$116$	−1.01686e6			−0.651457
$117$		0			0
$118$	1.73042e6			1.05319
$119$	−1.50868e6			−0.895274
$120$		0			0
$121$	−809839.			−0.457133
$122$			2.44272e6i			1.34522i
$123$		0			0
$124$	1.48455e6			0.778629
$125$		−	788273.i		−	0.403596i
$126$		0			0
$127$	−228919.			−0.111756			−0.0558779	−	0.998438i	$-0.517796\pi$
$127$	−228919.			−0.111756			−0.0558779	+	0.998438i	$0.517796\pi$
$128$	−812931.			−0.387636
$129$		0			0
$130$		−	6.95784e6i		−	3.16697i
$131$	2.04939e6			0.911614			0.455807	−	0.890079i	$-0.349351\pi$
$131$	2.04939e6			0.911614			0.455807	+	0.890079i	$0.349351\pi$
$132$		0			0
$133$	−324154.			−0.137783
$134$		−	5.77908e6i		−	2.40184i
$135$		0			0
$136$		−	688301.i		−	0.273629i
$137$		−	3.85440e6i		−	1.49898i	−0.662018	−	0.749488i	$-0.730300\pi$
$137$		−	3.85440e6i		−	1.49898i	0.662018	−	0.749488i	$-0.269700\pi$
$138$		0			0
$139$	−4.05743e6			−1.51080			−0.755400	−	0.655264i	$-0.772557\pi$
$139$	−4.05743e6			−1.51080			−0.755400	+	0.655264i	$0.772557\pi$
$140$	−1.95688e6			−0.713150
$141$		0			0
$142$	5.00131e6			1.74670
$143$			6.31254e6i			2.15872i
$144$		0			0
$145$			3.01484e6i			0.988917i
$146$	−3.06896e6			−0.986126
$147$		0			0
$148$		−	4.07178e6i		−	1.25603i
$149$			4.37188e6i			1.32163i	0.750550	+	0.660814i	$0.229789\pi$
$149$			4.37188e6i			1.32163i	−0.750550	+	0.660814i	$0.770211\pi$
$150$		0			0
$151$	−1.27442e6			−0.370153			−0.185076	−	0.982724i	$-0.559253\pi$
$151$	−1.27442e6			−0.370153			−0.185076	+	0.982724i	$0.559253\pi$
$152$		−	147888.i		−	0.0421116i
$153$		0			0
$154$	3.84883e6			1.05382
$155$		−	4.40149e6i		−	1.18196i
$156$		0			0
$157$			1.84958e6i			0.477941i	0.971027	+	0.238970i	$0.0768099\pi$
$157$			1.84958e6i			0.477941i	−0.971027	+	0.238970i	$0.923190\pi$
$158$		−	2.76434e6i		−	0.700841i
$159$		0			0
$160$		−	7.10379e6i		−	1.73432i
$161$	−2.05839e6	+	1.70697e6i	−0.493231	+	0.409025i
$162$		0			0
$163$	3.90418e6			0.901502			0.450751	−	0.892650i	$-0.351156\pi$
$163$	3.90418e6			0.901502			0.450751	+	0.892650i	$0.351156\pi$
$164$	2.92423e6			0.662949
$165$		0			0
$166$			1.60871e6i			0.351684i
$167$	1.57936e6			0.339103			0.169552	−	0.985521i	$-0.445768\pi$
$167$	1.57936e6			0.339103			0.169552	+	0.985521i	$0.445768\pi$
$168$		0			0
$169$	1.06099e7			2.19811
$170$	1.21563e7			2.47432
$171$		0			0
$172$		−	3.76464e6i		−	0.739841i
$173$	3.44019e6			0.664422			0.332211	−	0.943205i	$-0.392205\pi$
$173$	3.44019e6			0.664422			0.332211	+	0.943205i	$0.392205\pi$
$174$		0			0
$175$			2.36779e6i			0.441804i
$176$			7.39092e6i			1.35569i
$177$		0			0
$178$		−	2.83812e6i		−	0.503236i
$179$	6.13454e6			1.06960			0.534802	−	0.844977i	$-0.320386\pi$
$179$	6.13454e6			1.06960			0.534802	+	0.844977i	$0.320386\pi$
$180$		0			0
$181$		−	294540.i		−	0.0496717i	−0.999692	−	0.0248358i	$-0.992094\pi$
$181$		−	294540.i		−	0.0496717i	0.999692	−	0.0248358i	$-0.00790631\pi$
$182$		−	9.41191e6i		−	1.56122i
$183$		0			0
$184$	−778769.	−	939095.i	−0.125013	−	0.150750i
$185$	−1.20723e7			−1.90666
$186$		0			0
$187$	−1.10289e7			−1.68658
$188$	5.79556e6			0.872211
$189$		0			0
$190$	2.61190e6			0.380799
$191$		−	2.24501e6i		−	0.322194i	−0.986939	−	0.161097i	$-0.948497\pi$
$191$		−	2.24501e6i		−	0.322194i	0.986939	−	0.161097i	$-0.0515032\pi$
$192$		0			0
$193$	709667.			0.0987148			0.0493574	−	0.998781i	$-0.484283\pi$
$193$	709667.			0.0987148			0.0493574	+	0.998781i	$0.484283\pi$
$194$		−	1.52342e7i		−	2.08648i
$195$		0			0
$196$	3.80013e6			0.504697
$197$	2.48782e6			0.325403			0.162701	−	0.986675i	$-0.447979\pi$
$197$	2.48782e6			0.325403			0.162701	+	0.986675i	$0.447979\pi$
$198$		0			0
$199$			1.47724e6i			0.187453i	0.995598	+	0.0937266i	$0.0298780\pi$
$199$			1.47724e6i			0.187453i	−0.995598	+	0.0937266i	$0.970122\pi$
$200$	−1.08025e6			−0.135031
$201$		0			0
$202$	−1.29366e7			−1.56952
$203$			4.07819e6i			0.487505i
$204$		0			0
$205$		−	8.66994e6i		−	1.00636i
$206$		−	6.61645e6i		−	0.756874i
$207$		0			0
$208$	1.80737e7			2.00843
$209$	−2.36966e6			−0.259566
$210$		0			0
$211$	7.31935e6			0.779157			0.389579	−	0.920993i	$-0.372621\pi$
$211$	7.31935e6			0.779157			0.389579	+	0.920993i	$0.372621\pi$
$212$		−	1.41249e7i		−	1.48244i
$213$		0			0
$214$			1.29810e7i			1.32455i
$215$	−1.11616e7			−1.12308
$216$		0			0
$217$		−	5.95392e6i		−	0.582671i
$218$			1.66531e7i			1.60741i
$219$		0			0
$220$	−1.43054e7			−1.34348
$221$			2.69700e7i			2.49865i
$222$		0			0
$223$	−703409.			−0.0634298			−0.0317149	−	0.999497i	$-0.510097\pi$
$223$	−703409.			−0.0634298			−0.0317149	+	0.999497i	$0.510097\pi$
$224$		−	9.60935e6i		−	0.854968i
$225$		0			0
$226$		−	1.14982e7i		−	0.996108i
$227$			9.48496e6i			0.810882i	0.914121	+	0.405441i	$0.132882\pi$
$227$			9.48496e6i			0.810882i	−0.914121	+	0.405441i	$0.867118\pi$
$228$		0			0
$229$		−	311688.i		−	0.0259546i	−0.999916	−	0.0129773i	$-0.995869\pi$
$229$		−	311688.i		−	0.0259546i	0.999916	−	0.0129773i	$-0.00413091\pi$
$230$	1.65857e7	−	1.37541e7i	1.36317	−	1.13044i
$231$		0			0
$232$	−1.86058e6			−0.148999
$233$	−1.56282e7			−1.23550			−0.617749	−	0.786375i	$-0.711955\pi$
$233$	−1.56282e7			−1.23550			−0.617749	+	0.786375i	$0.711955\pi$
$234$		0			0
$235$		−	1.71830e7i		−	1.32402i
$236$	−8.70016e6			−0.661899
$237$		0			0
$238$	1.64439e7			1.21976
$239$	2.63176e6			0.192776			0.0963879	−	0.995344i	$-0.469271\pi$
$239$	2.63176e6			0.192776			0.0963879	+	0.995344i	$0.469271\pi$
$240$		0			0
$241$			1.89669e7i			1.35502i	0.735513	+	0.677510i	$0.236941\pi$
$241$			1.89669e7i			1.35502i	−0.735513	+	0.677510i	$0.763059\pi$
$242$	8.82689e6			0.622819
$243$		0			0
$244$		−	1.22814e7i		−	0.845432i
$245$		−	1.12669e7i		−	0.766134i
$246$		0			0
$247$			5.79476e6i			0.384543i
$248$	2.71634e6			0.178086
$249$		0			0
$250$			8.59183e6i			0.549877i
$251$			6.64309e6i			0.420097i	0.977691	+	0.210048i	$0.0673621\pi$
$251$			6.64309e6i			0.420097i	−0.977691	+	0.210048i	$0.932638\pi$
$252$		0			0
$253$	−1.50475e7	+	1.24785e7i	−0.929185	+	0.770551i
$254$	2.49511e6			0.152261
$255$		0			0
$256$	2.05178e7			1.22296
$257$	−2.36926e7			−1.39577			−0.697886	−	0.716209i	$-0.745876\pi$
$257$	−2.36926e7			−1.39577			−0.697886	+	0.716209i	$0.745876\pi$
$258$		0			0
$259$	−1.63302e7			−0.939924
$260$			3.49824e7i			1.99035i
$261$		0			0
$262$	−2.23375e7			−1.24202
$263$		−	1.41309e7i		−	0.776788i	−0.921493	−	0.388394i	$-0.873030\pi$
$263$		−	1.41309e7i		−	0.776788i	0.921493	−	0.388394i	$-0.126970\pi$
$264$		0			0
$265$	−4.18782e7			−2.25035
$266$	3.53313e6			0.187722
$267$		0			0
$268$			2.90559e7i			1.50949i
$269$	−2.51521e7			−1.29216			−0.646082	−	0.763268i	$-0.723593\pi$
$269$	−2.51521e7			−1.29216			−0.646082	+	0.763268i	$0.723593\pi$
$270$		0			0
$271$	2.44564e7			1.22881			0.614405	−	0.788991i	$-0.289396\pi$
$271$	2.44564e7			1.22881			0.614405	+	0.788991i	$0.289396\pi$
$272$			3.15774e7i			1.56917i
$273$		0			0
$274$			4.20112e7i			2.04227i
$275$			1.73093e7i			0.832302i
$276$		0			0
$277$	3.06729e7			1.44316			0.721581	−	0.692330i	$-0.243416\pi$
$277$	3.06729e7			1.44316			0.721581	+	0.692330i	$0.243416\pi$
$278$	4.42242e7			2.05838
$279$		0			0
$280$	−3.58059e6			−0.163110
$281$			1.12468e7i			0.506885i	0.967350	+	0.253443i	$0.0815629\pi$
$281$			1.12468e7i			0.506885i	−0.967350	+	0.253443i	$0.918437\pi$
$282$		0			0
$283$			9.50856e6i			0.419523i	0.977753	+	0.209761i	$0.0672687\pi$
$283$			9.50856e6i			0.419523i	−0.977753	+	0.209761i	$0.932731\pi$
$284$	−2.51454e7			−1.09775
$285$		0			0
$286$		−	6.88040e7i		−	2.94114i
$287$		−	1.17279e7i		−	0.496105i
$288$		0			0
$289$	−2.29829e7			−0.952164
$290$		−	3.28604e7i		−	1.34735i
$291$		0			0
$292$	1.54300e7			0.619752
$293$		−	1.40459e7i		−	0.558400i	−0.960233	−	0.279200i	$-0.909931\pi$
$293$		−	1.40459e7i		−	0.558400i	0.960233	−	0.279200i	$-0.0900693\pi$
$294$		0			0
$295$			2.57948e7i			1.00477i
$296$		−	7.45030e6i		−	0.287275i
$297$		0			0
$298$		−	4.76515e7i		−	1.80065i
$299$	3.05149e7	+	3.67970e7i	1.14156	+	1.37657i
$300$		0			0
$301$	−1.50984e7			−0.553646
$302$	1.38906e7			0.504313
$303$		0			0
$304$			6.78468e6i			0.241495i
$305$	−3.64127e7			−1.28337
$306$		0			0
$307$	2.65536e7			0.917717			0.458859	−	0.888509i	$-0.348258\pi$
$307$	2.65536e7			0.917717			0.458859	+	0.888509i	$0.348258\pi$
$308$	−1.93510e7			−0.662296
$309$		0			0
$310$			4.79743e7i			1.61036i
$311$	1.35991e7			0.452093			0.226047	−	0.974116i	$-0.427420\pi$
$311$	1.35991e7			0.452093			0.226047	+	0.974116i	$0.427420\pi$
$312$		0			0
$313$		−	3.51071e7i		−	1.14489i	−0.819945	−	0.572443i	$-0.805996\pi$
$313$		−	3.51071e7i		−	1.14489i	0.819945	−	0.572443i	$-0.194004\pi$
$314$		−	2.01596e7i		−	0.651168i
$315$		0			0
$316$			1.38984e7i			0.440458i
$317$	1.10945e7			0.348282			0.174141	−	0.984721i	$-0.444285\pi$
$317$	1.10945e7			0.348282			0.174141	+	0.984721i	$0.444285\pi$
$318$		0			0
$319$			2.98128e7i			0.918398i
$320$			2.95940e7i			0.903136i
$321$		0			0
$322$	2.24356e7	−	1.86053e7i	0.672001	−	0.557274i
$323$	−1.01243e7			−0.300439
$324$		0			0
$325$	4.23280e7			1.23304
$326$	−4.25538e7			−1.22825
$327$		0			0
$328$	5.35058e6			0.151628
$329$		−	2.32436e7i		−	0.652702i
$330$		0			0
$331$	−2.25040e7			−0.620549			−0.310274	−	0.950647i	$-0.600421\pi$
$331$	−2.25040e7			−0.620549			−0.310274	+	0.950647i	$0.600421\pi$
$332$		−	8.08821e6i		−	0.221023i
$333$		0			0
$334$	−1.72143e7			−0.462010
$335$	8.61466e7			2.29142
$336$		0			0
$337$		−	3.28613e7i		−	0.858608i	−0.903160	−	0.429304i	$-0.858759\pi$
$337$		−	3.28613e7i		−	0.858608i	0.903160	−	0.429304i	$-0.141241\pi$
$338$	−1.15643e8			−2.99480
$339$		0			0
$340$	−6.11192e7			−1.55504
$341$		−	4.35250e7i		−	1.09768i
$342$		0			0
$343$		−	4.10979e7i		−	1.01844i
$344$		−	6.88831e6i		−	0.169214i
$345$		0			0
$346$	−3.74966e7			−0.905239
$347$	4.39404e7			1.05166			0.525830	−	0.850590i	$-0.323755\pi$
$347$	4.39404e7			1.05166			0.525830	+	0.850590i	$0.323755\pi$
$348$		0			0
$349$	−6.13364e7			−1.44292			−0.721460	−	0.692456i	$-0.756529\pi$
$349$	−6.13364e7			−1.44292			−0.721460	+	0.692456i	$0.756529\pi$
$350$		−	2.58079e7i		−	0.601934i
$351$		0			0
$352$		−	7.02473e7i		−	1.61065i
$353$	2.62144e7			0.595957			0.297979	−	0.954573i	$-0.403688\pi$
$353$	2.62144e7			0.595957			0.297979	+	0.954573i	$0.403688\pi$
$354$		0			0
$355$			7.45527e7i			1.66640i
$356$			1.42694e7i			0.316269i
$357$		0			0
$358$	−6.68638e7			−1.45728
$359$		−	5.52959e7i		−	1.19512i	−0.801826	−	0.597558i	$-0.796138\pi$
$359$		−	5.52959e7i		−	1.19512i	0.801826	−	0.597558i	$-0.203862\pi$
$360$		0			0
$361$	4.48706e7			0.953762
$362$			3.21036e6i			0.0676750i
$363$		0			0
$364$			4.73209e7i			0.981181i
$365$		−	4.57478e7i		−	0.940788i
$366$		0			0
$367$			6.39160e7i			1.29304i	0.762898	+	0.646519i	$0.223776\pi$
$367$			6.39160e7i			1.29304i	−0.762898	+	0.646519i	$0.776224\pi$
$368$	3.57278e7	+	4.30831e7i	0.716906	+	0.864497i
$369$		0			0
$370$	1.31582e8			2.59772
$371$	−5.66489e7			−1.10935
$372$		0			0
$373$		−	1.00157e7i		−	0.192998i	−0.995333	−	0.0964992i	$-0.969235\pi$
$373$		−	1.00157e7i		−	0.192998i	0.995333	−	0.0964992i	$-0.0307645\pi$
$374$	1.20210e8			2.29788
$375$		0			0
$376$	1.06044e7			0.199490
$377$	7.29041e7			1.36059
$378$		0			0
$379$			3.47214e7i			0.637793i	0.947790	+	0.318897i	$0.103312\pi$
$379$			3.47214e7i			0.637793i	−0.947790	+	0.318897i	$0.896688\pi$
$380$	−1.31320e7			−0.239321
$381$		0			0
$382$			2.44696e7i			0.438972i
$383$			7.09421e6i			0.126272i	0.998005	+	0.0631361i	$0.0201102\pi$
$383$			7.09421e6i			0.126272i	−0.998005	+	0.0631361i	$0.979890\pi$
$384$		0			0
$385$			5.73731e7i			1.00537i
$386$	−7.73506e6			−0.134494
$387$		0			0
$388$			7.65939e7i			1.31129i
$389$			7.07860e7i			1.20254i	0.799047	+	0.601268i	$0.205338\pi$
$389$			7.07860e7i			1.20254i	−0.799047	+	0.601268i	$0.794662\pi$
$390$		0			0
$391$	−6.42897e7	+	5.33138e7i	−1.07550	+	0.891887i
$392$	6.95325e6			0.115433
$393$		0			0
$394$	−2.71162e7			−0.443343
$395$	4.12069e7			0.668619
$396$		0			0
$397$	4.69239e7			0.749933			0.374967	−	0.927038i	$-0.377654\pi$
$397$	4.69239e7			0.749933			0.374967	+	0.927038i	$0.377654\pi$
$398$		−	1.61013e7i		−	0.255395i
$399$		0			0
$400$	4.95590e7			0.774359
$401$			3.02762e7i			0.469535i	0.972052	+	0.234767i	$0.0754328\pi$
$401$			3.02762e7i			0.469535i	−0.972052	+	0.234767i	$0.924567\pi$
$402$		0			0
$403$	−1.06436e8			−1.62619
$404$	6.50423e7			0.986397
$405$		0			0
$406$		−	4.44505e7i		−	0.664199i
$407$	−1.19379e8			−1.77070
$408$		0			0
$409$	−7.70025e7			−1.12547			−0.562736	−	0.826637i	$-0.690251\pi$
$409$	−7.70025e7			−1.12547			−0.562736	+	0.826637i	$0.690251\pi$
$410$			9.44985e7i			1.37111i
$411$		0			0
$412$			3.32660e7i			0.475674i
$413$			3.48927e7i			0.495319i
$414$		0			0
$415$	−2.39804e7			−0.335515
$416$	−1.71782e8			−2.38615
$417$		0			0
$418$	2.58283e7			0.353644
$419$		−	1.00584e8i		−	1.36738i	−0.729775	−	0.683688i	$-0.760375\pi$
$419$		−	1.00584e8i		−	1.36738i	0.729775	−	0.683688i	$-0.239625\pi$
$420$		0			0
$421$		−	1.31330e8i		−	1.76002i	−0.474960	−	0.880008i	$-0.657537\pi$
$421$		−	1.31330e8i		−	1.76002i	0.474960	−	0.880008i	$-0.342463\pi$
$422$	−7.97777e7			−1.06156
$423$		0			0
$424$		−	2.58448e7i		−	0.339059i
$425$			7.39531e7i			0.963362i
$426$		0			0
$427$	−4.92556e7			−0.632663
$428$		−	6.52656e7i		−	0.832440i
$429$		0			0
$430$	1.21657e8			1.53014
$431$			1.07013e8i			1.33661i	0.743889	+	0.668303i	$0.232979\pi$
$431$			1.07013e8i			1.33661i	−0.743889	+	0.668303i	$0.767021\pi$
$432$		0			0
$433$			4.94367e7i			0.608956i	0.952519	+	0.304478i	$0.0984820\pi$
$433$			4.94367e7i			0.608956i	−0.952519	+	0.304478i	$0.901518\pi$
$434$			6.48951e7i			0.793858i
$435$		0			0
$436$		−	8.37279e7i		−	1.01021i
$437$	−1.38132e7	+	1.14550e7i	−0.165520	+	0.137262i
$438$		0			0
$439$	9.85699e7			1.16507			0.582533	−	0.812807i	$-0.302062\pi$
$439$	9.85699e7			1.16507			0.582533	+	0.812807i	$0.302062\pi$
$440$	−2.61752e7			−0.307278
$441$		0			0
$442$		−	2.93962e8i		−	3.40427i
$443$	−1.30585e8			−1.50204			−0.751022	−	0.660277i	$-0.770439\pi$
$443$	−1.30585e8			−1.50204			−0.751022	+	0.660277i	$0.770439\pi$
$444$		0			0
$445$	4.23069e7			0.480099
$446$	7.66685e6			0.0864196
$447$		0			0
$448$			4.00319e7i			0.445218i
$449$	−9.76580e7			−1.07887			−0.539435	−	0.842027i	$-0.681362\pi$
$449$	−9.76580e7			−1.07887			−0.539435	+	0.842027i	$0.681362\pi$
$450$		0			0
$451$		−	8.57344e7i		−	0.934599i
$452$			5.78105e7i			0.626025i
$453$		0			0
$454$		−	1.03382e8i		−	1.10478i
$455$	1.40300e8			1.48944
$456$		0			0
$457$		−	1.64688e8i		−	1.72549i	−0.505639	−	0.862745i	$-0.668743\pi$
$457$		−	1.64688e8i		−	1.72549i	0.505639	−	0.862745i	$-0.331257\pi$
$458$			3.39726e6i			0.0353617i
$459$		0			0
$460$	−8.33891e7	+	6.91525e7i	−0.856714	+	0.710452i
$461$	−8.62709e7			−0.880565			−0.440283	−	0.897859i	$-0.645122\pi$
$461$	−8.62709e7			−0.880565			−0.440283	+	0.897859i	$0.645122\pi$
$462$		0			0
$463$	7.86303e7			0.792222			0.396111	−	0.918203i	$-0.370360\pi$
$463$	7.86303e7			0.792222			0.396111	+	0.918203i	$0.370360\pi$
$464$	8.53583e7			0.854461
$465$		0			0
$466$	1.70341e8			1.68330
$467$		−	1.69346e8i		−	1.66274i	−0.555721	−	0.831369i	$-0.687558\pi$
$467$		−	1.69346e8i		−	1.66274i	0.555721	−	0.831369i	$-0.312442\pi$
$468$		0			0
$469$	1.16531e8			1.12960
$470$			1.87287e8i			1.80391i
$471$		0			0
$472$	−1.59190e7			−0.151388
$473$	−1.10374e8			−1.04300
$474$		0			0
$475$			1.58895e7i			0.148262i
$476$	−8.26764e7			−0.766586
$477$		0			0
$478$	−2.86850e7			−0.262646
$479$		−	1.31802e8i		−	1.19927i	−0.800275	−	0.599633i	$-0.795313\pi$
$479$		−	1.31802e8i		−	1.19927i	0.800275	−	0.599633i	$-0.204687\pi$
$480$		0			0
$481$			2.91929e8i			2.62326i
$482$		−	2.06731e8i		−	1.84614i
$483$		0			0
$484$	−4.43796e7			−0.391424
$485$	2.27090e8			1.99055
$486$		0			0
$487$	1.02076e8			0.883761			0.441881	−	0.897074i	$-0.354311\pi$
$487$	1.02076e8			0.883761			0.441881	+	0.897074i	$0.354311\pi$
$488$		−	2.24718e7i		−	0.193365i
$489$		0			0
$490$			1.22804e8i			1.04382i
$491$	1.70391e8			1.43947			0.719733	−	0.694251i	$-0.244264\pi$
$491$	1.70391e8			1.43947			0.719733	+	0.694251i	$0.244264\pi$
$492$		0			0
$493$			1.27374e8i			1.06302i
$494$		−	6.31604e7i		−	0.523919i
$495$		0			0
$496$	−1.24618e8			−1.02126
$497$			1.00848e8i			0.821481i
$498$		0			0
$499$	−9.77836e7			−0.786981			−0.393491	−	0.919329i	$-0.628733\pi$
$499$	−9.77836e7			−0.786981			−0.393491	+	0.919329i	$0.628733\pi$
$500$		−	4.31977e7i		−	0.345582i
$501$		0			0
$502$		−	7.24068e7i		−	0.572359i
$503$			1.05813e8i			0.831446i	0.909491	+	0.415723i	$0.136471\pi$
$503$			1.05813e8i			0.831446i	−0.909491	+	0.415723i	$0.863529\pi$
$504$		0			0
$505$		−	1.92841e8i		−	1.49736i
$506$	1.64011e8	−	1.36010e8i	1.26596	−	1.04983i
$507$		0			0
$508$	−1.25449e7			−0.0956918
$509$	2.11018e8			1.60017			0.800085	−	0.599886i	$-0.204787\pi$
$509$	2.11018e8			1.60017			0.800085	+	0.599886i	$0.204787\pi$
$510$		0			0
$511$		−	6.18834e7i		−	0.463779i
$512$	−1.71607e8			−1.27858
$513$		0			0
$514$	2.58240e8			1.90166
$515$	9.86290e7			0.722076
$516$		0			0
$517$		−	1.69918e8i		−	1.22961i
$518$	1.77992e8			1.28060
$519$		0			0
$520$			6.40087e7i			0.455228i
$521$			6.93858e6i			0.0490634i	0.999699	+	0.0245317i	$0.00780947\pi$
$521$			6.93858e6i			0.0490634i	−0.999699	+	0.0245317i	$0.992191\pi$
$522$		0			0
$523$		−	1.77380e8i		−	1.23994i	−0.784626	−	0.619970i	$-0.787145\pi$
$523$		−	1.77380e8i		−	1.23994i	0.784626	−	0.619970i	$-0.212855\pi$
$524$	1.12308e8			0.780576
$525$		0			0
$526$			1.54021e8i			1.05833i
$527$		−	1.85958e8i		−	1.27053i
$528$		0			0
$529$	−2.73935e7	+	1.45479e8i	−0.185046	+	0.982730i
$530$	4.56454e8			3.06598
$531$		0			0
$532$	−1.77638e7			−0.117978
$533$	−2.09654e8			−1.38459
$534$		0			0
$535$	−1.93503e8			−1.26365
$536$			5.31647e7i			0.345246i
$537$		0			0
$538$	2.74147e8			1.76050
$539$		−	1.11415e8i		−	0.711501i
$540$		0			0
$541$	−1.01572e8			−0.641477			−0.320739	−	0.947168i	$-0.603931\pi$
$541$	−1.01572e8			−0.641477			−0.320739	+	0.947168i	$0.603931\pi$
$542$	−2.66564e8			−1.67419
$543$		0			0
$544$		−	3.00128e8i		−	1.86428i
$545$	−2.48241e8			−1.53350
$546$		0			0
$547$	−1.68367e7			−0.102871			−0.0514356	−	0.998676i	$-0.516380\pi$
$547$	−1.68367e7			−0.102871			−0.0514356	+	0.998676i	$0.516380\pi$
$548$		−	2.11223e8i		−	1.28351i
$549$		0			0
$550$		−	1.88664e8i		−	1.13397i
$551$			2.73674e7i			0.163598i
$552$		0			0
$553$	5.57409e7			0.329608
$554$	−3.34321e8			−1.96623
$555$		0			0
$556$	−2.22349e8			−1.29363
$557$		−	2.43652e8i		−	1.40995i	−0.709232	−	0.704975i	$-0.750958\pi$
$557$		−	2.43652e8i		−	1.40995i	0.709232	−	0.704975i	$-0.249042\pi$
$558$		0			0
$559$			2.69908e8i			1.54519i
$560$	1.64267e8			0.935378
$561$		0			0
$562$		−	1.22585e8i		−	0.690603i
$563$		−	2.01599e8i		−	1.12970i	−0.825193	−	0.564851i	$-0.808934\pi$
$563$		−	2.01599e8i		−	1.12970i	0.825193	−	0.564851i	$-0.191066\pi$
$564$		0			0
$565$	1.71400e8			0.950311
$566$		−	1.03639e8i		−	0.571577i
$567$		0			0
$568$	−4.60096e7			−0.251075
$569$			3.56375e8i			1.93451i	0.253810	+	0.967254i	$0.418316\pi$
$569$			3.56375e8i			1.93451i	−0.253810	+	0.967254i	$0.581684\pi$
$570$		0			0
$571$			1.34654e8i			0.723290i	0.932316	+	0.361645i	$0.117785\pi$
$571$			1.34654e8i			0.723290i	−0.932316	+	0.361645i	$0.882215\pi$
$572$			3.45930e8i			1.84842i
$573$		0			0
$574$			1.27829e8i			0.675916i
$575$	8.36732e7	+	1.00899e8i	0.440132	+	0.530743i
$576$		0			0
$577$	2.37855e8			1.23818			0.619092	−	0.785319i	$-0.287501\pi$
$577$	2.37855e8			1.23818			0.619092	+	0.785319i	$0.287501\pi$
$578$	2.50504e8			1.29727
$579$		0			0
$580$			1.65215e8i			0.846768i
$581$	−3.24384e7			−0.165398
$582$		0			0
$583$	−4.14121e8			−2.08988
$584$	2.82329e7			0.141748
$585$		0			0
$586$			1.53094e8i			0.760790i
$587$	1.33484e8			0.659954			0.329977	−	0.943989i	$-0.392959\pi$
$587$	1.33484e8			0.659954			0.329977	+	0.943989i	$0.392959\pi$
$588$		0			0
$589$		−	3.99549e7i		−	0.195535i
$590$		−	2.81152e8i		−	1.36894i
$591$		0			0
$592$			3.41799e8i			1.64743i
$593$	3.38405e8			1.62283			0.811414	−	0.584472i	$-0.198698\pi$
$593$	3.38405e8			1.62283			0.811414	+	0.584472i	$0.198698\pi$
$594$		0			0
$595$			2.45124e8i			1.16368i
$596$			2.39581e8i			1.13165i
$597$		0			0
$598$	−3.32599e8	−	4.01072e8i	−1.55531	−	1.87551i
$599$	−3.60443e8			−1.67709			−0.838544	−	0.544834i	$-0.816593\pi$
$599$	−3.60443e8			−1.67709			−0.838544	+	0.544834i	$0.816593\pi$
$600$		0			0
$601$	3.11612e7			0.143546			0.0717729	−	0.997421i	$-0.477134\pi$
$601$	3.11612e7			0.143546			0.0717729	+	0.997421i	$0.477134\pi$
$602$	1.64566e8			0.754312
$603$		0			0
$604$	−6.98387e7			−0.316946
$605$			1.31579e8i			0.594184i
$606$		0			0
$607$	3.01125e8			1.34642			0.673210	−	0.739451i	$-0.264915\pi$
$607$	3.01125e8			1.34642			0.673210	+	0.739451i	$0.264915\pi$
$608$		−	6.44853e7i		−	0.286913i
$609$		0			0
$610$	3.96882e8			1.74853
$611$	−4.15516e8			−1.82164
$612$		0			0
$613$			6.71266e7i			0.291416i	0.989328	+	0.145708i	$0.0465460\pi$
$613$			6.71266e7i			0.291416i	−0.989328	+	0.145708i	$0.953454\pi$
$614$	−2.89423e8			−1.25034
$615$		0			0
$616$	−3.54073e7			−0.151479
$617$			2.93868e8i			1.25111i	0.780178	+	0.625557i	$0.215128\pi$
$617$			2.93868e8i			1.25111i	−0.780178	+	0.625557i	$0.784872\pi$
$618$		0			0
$619$		−	3.23663e8i		−	1.36465i	−0.731049	−	0.682325i	$-0.760969\pi$
$619$		−	3.23663e8i		−	1.36465i	0.731049	−	0.682325i	$-0.239031\pi$
$620$		−	2.41204e8i		−	1.01207i
$621$		0			0
$622$	−1.48224e8			−0.615952
$623$	5.72287e7			0.236674
$624$		0			0
$625$	−2.96409e8			−1.21409
$626$			3.82652e8i			1.55984i
$627$		0			0
$628$			1.01358e8i			0.409241i
$629$	−5.10041e8			−2.04952
$630$		0			0
$631$		−	3.09659e8i		−	1.23253i	−0.787541	−	0.616263i	$-0.788646\pi$
$631$		−	3.09659e8i		−	1.23253i	0.787541	−	0.616263i	$-0.211354\pi$
$632$			2.54305e7i			0.100740i
$633$		0			0
$634$	−1.20926e8			−0.474516
$635$			3.71937e7i			0.145261i
$636$		0			0
$637$	−2.72453e8			−1.05408
$638$		−	3.24947e8i		−	1.25127i
$639$		0			0
$640$			1.32082e8i			0.503851i
$641$		−	1.43431e8i		−	0.544590i	−0.962214	−	0.272295i	$-0.912217\pi$
$641$		−	1.43431e8i		−	0.544590i	0.962214	−	0.272295i	$-0.0877826\pi$
$642$		0			0
$643$			3.10636e7i			0.116847i	0.998292	+	0.0584237i	$0.0186074\pi$
$643$			3.10636e7i			0.116847i	−0.998292	+	0.0584237i	$0.981393\pi$
$644$	−1.12801e8	+	9.35431e7i	−0.422333	+	0.350230i
$645$		0			0
$646$	1.10350e8			0.409332
$647$	5.28652e8			1.95190			0.975949	−	0.218000i	$-0.0699532\pi$
$647$	5.28652e8			1.95190			0.975949	+	0.218000i	$0.0699532\pi$
$648$		0			0
$649$			2.55077e8i			0.933118i
$650$	−4.61357e8			−1.67995
$651$		0			0
$652$	2.13951e8			0.771918
$653$	−2.78700e8			−1.00091			−0.500457	−	0.865761i	$-0.666835\pi$
$653$	−2.78700e8			−1.00091			−0.500457	+	0.865761i	$0.666835\pi$
$654$		0			0
$655$		−	3.32976e8i		−	1.18492i
$656$	−2.45470e8			−0.869534
$657$		0			0
$658$			2.53345e8i			0.889271i
$659$			1.58187e8i			0.552733i	0.961052	+	0.276367i	$0.0891304\pi$
$659$			1.58187e8i			0.552733i	−0.961052	+	0.276367i	$0.910870\pi$
$660$		0			0
$661$			3.68083e7i			0.127450i	0.997967	+	0.0637252i	$0.0202981\pi$
$661$			3.68083e7i			0.127450i	−0.997967	+	0.0637252i	$0.979702\pi$
$662$	2.45284e8			0.845464
$663$		0			0
$664$		−	1.47993e7i		−	0.0505518i
$665$			5.26671e7i			0.179091i
$666$		0			0
$667$	1.44115e8	+	1.73785e8i	0.485660	+	0.585644i
$668$	8.65498e7			0.290360
$669$		0			0
$670$	−9.38961e8			−3.12193
$671$	−3.60074e8			−1.19186
$672$		0			0
$673$	3.37285e8			1.10650			0.553250	−	0.833015i	$-0.313387\pi$
$673$	3.37285e8			1.10650			0.553250	+	0.833015i	$0.313387\pi$
$674$			3.58174e8i			1.16981i
$675$		0			0
$676$	5.81425e8			1.88215
$677$		−	3.81974e8i		−	1.23103i	−0.788127	−	0.615513i	$-0.788949\pi$
$677$		−	3.81974e8i		−	1.23103i	0.788127	−	0.615513i	$-0.211051\pi$
$678$		0			0
$679$	3.07186e8			0.981278
$680$	−1.11832e8			−0.355664
$681$		0			0
$682$			4.74403e8i			1.49553i
$683$	4.48113e8			1.40645			0.703226	−	0.710966i	$-0.251742\pi$
$683$	4.48113e8			1.40645			0.703226	+	0.710966i	$0.251742\pi$
$684$		0			0
$685$	−6.26246e8			−1.94838
$686$			4.47949e8i			1.38757i
$687$		0			0
$688$			3.16017e8i			0.970387i
$689$			1.01269e9i			3.09613i
$690$		0			0
$691$	−7.90521e7			−0.239596			−0.119798	−	0.992798i	$-0.538225\pi$
$691$	−7.90521e7			−0.239596			−0.119798	+	0.992798i	$0.538225\pi$
$692$	1.88524e8			0.568917
$693$		0			0
$694$	−4.78931e8			−1.43283
$695$			6.59234e8i			1.96375i
$696$		0			0
$697$		−	3.66296e8i		−	1.08177i
$698$	6.68540e8			1.96590
$699$		0			0
$700$			1.29756e8i			0.378298i
$701$			5.04427e8i			1.46435i	0.681118	+	0.732174i	$0.261494\pi$
$701$			5.04427e8i			1.46435i	−0.681118	+	0.732174i	$0.738506\pi$
$702$		0			0
$703$	−1.09587e8			−0.315423
$704$			2.92646e8i			0.838734i
$705$		0			0
$706$	−2.85725e8			−0.811959
$707$		−	2.60858e8i		−	0.738151i
$708$		0			0
$709$		−	2.86560e8i		−	0.804038i	−0.915631	−	0.402019i	$-0.868309\pi$
$709$		−	2.86560e8i		−	0.804038i	0.915631	−	0.402019i	$-0.131691\pi$
$710$		−	8.12592e8i		−	2.27037i
$711$		0			0
$712$			2.61093e7i			0.0723362i
$713$	−2.10400e8	−	2.53716e8i	−0.580467	−	0.699968i
$714$		0			0
$715$	1.02564e9			2.80592
$716$	3.36176e8			0.915857
$717$		0			0
$718$			6.02702e8i			1.62828i
$719$	−6.86464e8			−1.84685			−0.923423	−	0.383783i	$-0.874621\pi$
$719$	−6.86464e8			−1.84685			−0.923423	+	0.383783i	$0.874621\pi$
$720$		0			0
$721$	1.33416e8			0.355961
$722$	−4.89070e8			−1.29945
$723$		0			0
$724$		−	1.61410e7i		−	0.0425318i
$725$	1.99906e8			0.524581
$726$		0			0
$727$		−	1.53301e8i		−	0.398972i	−0.979901	−	0.199486i	$-0.936073\pi$
$727$		−	1.53301e8i		−	0.398972i	0.979901	−	0.199486i	$-0.0639272\pi$
$728$			8.65849e7i			0.224413i
$729$		0			0
$730$			4.98631e8i			1.28177i
$731$	−4.71568e8			−1.20724
$732$		0			0
$733$			2.31274e8i			0.587240i	0.955922	+	0.293620i	$0.0948601\pi$
$733$			2.31274e8i			0.587240i	−0.955922	+	0.293620i	$0.905140\pi$
$734$		−	6.96657e8i		−	1.76169i
$735$		0			0
$736$	−3.39576e8	−	4.09485e8i	−0.851733	−	1.02708i
$737$	8.51878e8			2.12802
$738$		0			0
$739$	−2.62854e8			−0.651299			−0.325650	−	0.945491i	$-0.605583\pi$
$739$	−2.62854e8			−0.651299			−0.325650	+	0.945491i	$0.605583\pi$
$740$	−6.61566e8			−1.63259
$741$		0			0
$742$	6.17449e8			1.51143
$743$		−	3.46168e8i		−	0.843958i	−0.906606	−	0.421979i	$-0.861336\pi$
$743$		−	3.46168e8i		−	0.843958i	0.906606	−	0.421979i	$-0.138664\pi$
$744$		0			0
$745$	7.10324e8			1.71786
$746$			1.09166e8i			0.262950i
$747$		0			0
$748$	−6.04390e8			−1.44415
$749$	−2.61753e8			−0.622940
$750$		0			0
$751$			2.30256e8i			0.543615i	0.962352	+	0.271808i	$0.0876215\pi$
$751$			2.30256e8i			0.543615i	−0.962352	+	0.271808i	$0.912379\pi$
$752$	−4.86498e8			−1.14400
$753$		0			0
$754$	−7.94623e8			−1.85373
$755$			2.07062e8i			0.481127i
$756$		0			0
$757$		−	4.07649e8i		−	0.939721i	−0.882741	−	0.469860i	$-0.844304\pi$
$757$		−	4.07649e8i		−	0.939721i	0.882741	−	0.469860i	$-0.155696\pi$
$758$		−	3.78448e8i		−	0.868958i
$759$		0			0
$760$	−2.40282e7			−0.0547369
$761$	1.04973e8			0.238190			0.119095	−	0.992883i	$-0.462001\pi$
$761$	1.04973e8			0.238190			0.119095	+	0.992883i	$0.462001\pi$
$762$		0			0
$763$	−3.35798e8			−0.755969
$764$		−	1.23027e8i		−	0.275881i
$765$		0			0
$766$		−	7.73238e7i		−	0.172039i
$767$	6.23763e8			1.38240
$768$		0			0
$769$		−	5.72554e8i		−	1.25903i	−0.776986	−	0.629517i	$-0.783253\pi$
$769$		−	5.72554e8i		−	1.25903i	0.776986	−	0.629517i	$-0.216747\pi$
$770$		−	6.25342e8i		−	1.36976i
$771$		0			0
$772$	3.88901e7			0.0845253
$773$			1.70666e8i			0.369496i	0.982786	+	0.184748i	$0.0591469\pi$
$773$			1.70666e8i			0.369496i	−0.982786	+	0.184748i	$0.940853\pi$
$774$		0			0
$775$	−2.91852e8			−0.626985
$776$			1.40147e8i			0.299915i
$777$		0			0
$778$		−	7.71536e8i		−	1.63839i
$779$		−	7.87021e7i		−	0.166485i
$780$		0			0
$781$			7.37229e8i			1.54757i
$782$	7.00729e8	−	5.81098e8i	1.46531	−	1.21515i
$783$		0			0
$784$	−3.18996e8			−0.661968
$785$	3.00512e8			0.621230
$786$		0			0
$787$			1.62065e8i			0.332480i	0.986085	+	0.166240i	$0.0531626\pi$
$787$			1.62065e8i			0.332480i	−0.986085	+	0.166240i	$0.946837\pi$
$788$	1.36334e8			0.278628
$789$		0			0
$790$	−4.49137e8			−0.910957
$791$	2.31854e8			0.468473
$792$		0			0
$793$			8.80522e8i			1.76572i
$794$	−5.11450e8			−1.02174
$795$		0			0
$796$			8.09537e7i			0.160508i
$797$		−	3.21457e8i		−	0.634963i	−0.948264	−	0.317482i	$-0.897163\pi$
$797$		−	3.21457e8i		−	0.634963i	0.948264	−	0.317482i	$-0.102837\pi$
$798$		0			0
$799$		−	7.25965e8i		−	1.42323i
$800$	−4.71035e8			−0.919990
$801$		0			0
$802$		−	3.29997e8i		−	0.639715i
$803$		−	4.52386e8i		−	0.873701i
$804$		0			0
$805$	2.77342e8	+	3.34439e8i	0.531653	+	0.641105i
$806$	1.16010e9			2.21560
$807$		0			0
$808$	1.19010e8			0.225606
$809$	4.47863e8			0.845862			0.422931	−	0.906162i	$-0.361001\pi$
$809$	4.47863e8			0.845862			0.422931	+	0.906162i	$0.361001\pi$
$810$		0			0
$811$	9.94216e8			1.86388			0.931941	−	0.362610i	$-0.118114\pi$
$811$	9.94216e8			1.86388			0.931941	+	0.362610i	$0.118114\pi$
$812$			2.23487e8i			0.417430i
$813$		0			0
$814$	1.30118e9			2.41248
$815$		−	6.34334e8i		−	1.17178i
$816$		0			0
$817$	−1.01321e8			−0.185794
$818$	8.39294e8			1.53339
$819$		0			0
$820$		−	4.75117e8i		−	0.861706i
$821$	1.70550e8			0.308192			0.154096	−	0.988056i	$-0.450753\pi$
$821$	1.70550e8			0.308192			0.154096	+	0.988056i	$0.450753\pi$
$822$		0			0
$823$	−5.45105e8			−0.977869			−0.488934	−	0.872321i	$-0.662614\pi$
$823$	−5.45105e8			−0.977869			−0.488934	+	0.872321i	$0.662614\pi$
$824$			6.08681e7i			0.108795i
$825$		0			0
$826$		−	3.80316e8i		−	0.674845i
$827$		−	5.63227e8i		−	0.995788i	−0.867238	−	0.497894i	$-0.834107\pi$
$827$		−	5.63227e8i		−	0.995788i	0.867238	−	0.497894i	$-0.165893\pi$
$828$		0			0
$829$	4.00995e8			0.703843			0.351921	−	0.936030i	$-0.385528\pi$
$829$	4.00995e8			0.703843			0.351921	+	0.936030i	$0.385528\pi$
$830$	2.61376e8			0.457121
$831$		0			0
$832$	7.15634e8			1.24257
$833$		−	4.76014e8i		−	0.823539i
$834$		0			0
$835$		−	2.56608e8i		−	0.440768i
$836$	−1.29859e8			−0.222255
$837$		0			0
$838$			1.09632e9i			1.86297i
$839$		−	2.15528e8i		−	0.364937i	−0.983212	−	0.182468i	$-0.941591\pi$
$839$		−	2.15528e8i		−	0.364937i	0.983212	−	0.182468i	$-0.0584087\pi$
$840$		0			0
$841$	−2.50513e8			−0.421155
$842$			1.43144e9i			2.39792i
$843$		0			0
$844$	4.01104e8			0.667160
$845$		−	1.72384e9i		−	2.85711i
$846$		0			0
$847$			1.77988e8i			0.292914i
$848$			1.18569e9i			1.94439i
$849$		0			0
$850$		−	8.06057e8i		−	1.31253i
$851$	−6.95883e8	+	5.77079e8i	−1.12914	+	0.936368i
$852$		0			0
$853$	−1.76071e8			−0.283688			−0.141844	−	0.989889i	$-0.545303\pi$
$853$	−1.76071e8			−0.283688			−0.141844	+	0.989889i	$0.545303\pi$
$854$	5.36865e8			0.861968
$855$		0			0
$856$		−	1.19419e8i		−	0.190393i
$857$	−3.30301e7			−0.0524769			−0.0262384	−	0.999656i	$-0.508353\pi$
$857$	−3.30301e7			−0.0524769			−0.0262384	+	0.999656i	$0.508353\pi$
$858$		0			0
$859$	−1.49960e8			−0.236589			−0.118295	−	0.992979i	$-0.537743\pi$
$859$	−1.49960e8			−0.236589			−0.118295	+	0.992979i	$0.537743\pi$
$860$	−6.11663e8			−0.961650
$861$		0			0
$862$		−	1.16639e9i		−	1.82105i
$863$	8.36556e7			0.130156			0.0650778	−	0.997880i	$-0.479270\pi$
$863$	8.36556e7			0.130156			0.0650778	+	0.997880i	$0.479270\pi$
$864$		0			0
$865$		−	5.58948e8i		−	0.863620i
$866$		−	5.38839e8i		−	0.829669i
$867$		0			0
$868$		−	3.26278e8i		−	0.498917i
$869$	4.07483e8			0.620940
$870$		0			0
$871$		−	2.08318e9i		−	3.15262i
$872$		−	1.53200e8i		−	0.231052i
$873$		0			0
$874$	1.50558e8	−	1.24854e8i	0.225512	−	0.187012i
$875$	−1.73248e8			−0.258609
$876$		0			0
$877$	6.75754e8			1.00182			0.500910	−	0.865499i	$-0.332999\pi$
$877$	6.75754e8			1.00182			0.500910	+	0.865499i	$0.332999\pi$
$878$	−1.07437e9			−1.58734
$879$		0			0
$880$	1.20085e9			1.76213
$881$		−	4.95490e8i		−	0.724614i	−0.932059	−	0.362307i	$-0.881989\pi$
$881$		−	4.95490e8i		−	0.724614i	0.932059	−	0.362307i	$-0.118011\pi$
$882$		0			0
$883$	6.44084e8			0.935536			0.467768	−	0.883851i	$-0.345058\pi$
$883$	6.44084e8			0.935536			0.467768	+	0.883851i	$0.345058\pi$
$884$			1.47797e9i			2.13949i
$885$		0			0
$886$	1.42332e9			2.04645
$887$	8.93336e8			1.28010			0.640050	−	0.768333i	$-0.278914\pi$
$887$	8.93336e8			1.28010			0.640050	+	0.768333i	$0.278914\pi$
$888$		0			0
$889$			5.03122e7i			0.0716091i
$890$	−4.61126e8			−0.654109
$891$		0			0
$892$	−3.85472e7			−0.0543123
$893$		−	1.55980e8i		−	0.219036i
$894$		0			0
$895$		−	9.96714e8i		−	1.39028i
$896$			1.78667e8i			0.248383i
$897$		0			0
$898$	1.06443e9			1.46990
$899$	−5.02674e8			−0.691842
$900$		0			0
$901$	−1.76931e9			−2.41897
$902$			9.34468e8i			1.27334i
$903$		0			0
$904$			1.05778e8i			0.143183i
$905$	−4.78556e7			−0.0645636
$906$		0			0
$907$			1.50772e8i			0.202068i	0.994883	+	0.101034i	$0.0322151\pi$
$907$			1.50772e8i			0.202068i	−0.994883	+	0.101034i	$0.967785\pi$
$908$			5.19780e8i			0.694324i
$909$		0			0
$910$	−1.52921e9			−2.02928
$911$		−	1.18502e9i		−	1.56737i	−0.621159	−	0.783685i	$-0.713338\pi$
$911$		−	1.18502e9i		−	1.56737i	0.621159	−	0.783685i	$-0.286662\pi$
$912$		0			0
$913$	−2.37135e8			−0.311590
$914$			1.79502e9i			2.35089i
$915$		0			0
$916$		−	1.70807e7i		−	0.0222238i
$917$		−	4.50419e8i		−	0.584129i
$918$		0			0
$919$			7.20023e8i			0.927684i	0.885918	+	0.463842i	$0.153529\pi$
$919$			7.20023e8i			0.927684i	−0.885918	+	0.463842i	$0.846471\pi$
$920$	−1.52580e8	+	1.26531e8i	−0.195945	+	0.162493i
$921$		0			0
$922$	9.40315e8			1.19972
$923$	1.80282e9			2.29270
$924$		0			0
$925$			8.00482e8i			1.01141i
$926$	−8.57035e8			−1.07936
$927$		0			0
$928$	−8.11292e8			−1.01516
$929$	8.30705e7			0.103609			0.0518047	−	0.998657i	$-0.483503\pi$
$929$	8.30705e7			0.103609			0.0518047	+	0.998657i	$0.483503\pi$
$930$		0			0
$931$		−	1.02276e8i		−	0.126743i
$932$	−8.56435e8			−1.05791
$933$		0			0
$934$			1.84580e9i			2.26539i
$935$			1.79193e9i			2.19223i
$936$		0			0
$937$			1.17181e8i			0.142442i	0.997461	+	0.0712209i	$0.0226895\pi$
$937$			1.17181e8i			0.142442i	−0.997461	+	0.0712209i	$0.977310\pi$
$938$	−1.27014e9			−1.53901
$939$		0			0
$940$		−	9.41637e8i		−	1.13370i
$941$			1.60300e8i			0.192382i	0.995363	+	0.0961908i	$0.0306659\pi$
$941$			1.60300e8i			0.192382i	−0.995363	+	0.0961908i	$0.969334\pi$
$942$		0			0
$943$	−4.14441e8	−	4.99762e8i	−0.494228	−	0.595976i
$944$	7.30321e8			0.868156
$945$		0			0
$946$	1.20303e9			1.42103
$947$	−2.05644e7			−0.0242139			−0.0121070	−	0.999927i	$-0.503854\pi$
$947$	−2.05644e7			−0.0242139			−0.0121070	+	0.999927i	$0.503854\pi$
$948$		0			0
$949$	−1.10626e9			−1.29437
$950$		−	1.73189e8i		−	0.201999i
$951$		0			0
$952$	−1.51276e8			−0.175331
$953$		−	3.96103e8i		−	0.457645i	−0.973468	−	0.228823i	$-0.926512\pi$
$953$		−	3.96103e8i		−	0.457645i	0.973468	−	0.228823i	$-0.0734876\pi$
$954$		0			0
$955$	−3.64759e8			−0.418789
$956$	1.44222e8			0.165066
$957$		0			0
$958$			1.43658e9i			1.63393i
$959$	−8.47127e8			−0.960489
$960$		0			0
$961$	−1.53629e8			−0.173102
$962$		−	3.18190e9i		−	3.57405i
$963$		0			0
$964$			1.03940e9i			1.16025i
$965$		−	1.15304e8i		−	0.128310i
$966$		0			0
$967$	1.37417e9			1.51971			0.759855	−	0.650092i	$-0.225270\pi$
$967$	1.37417e9			1.51971			0.759855	+	0.650092i	$0.225270\pi$
$968$	−8.12030e7			−0.0895254
$969$		0			0
$970$	−2.47518e9			−2.71201
$971$			8.46449e7i			0.0924577i	0.998931	+	0.0462289i	$0.0147203\pi$
$971$			8.46449e7i			0.0924577i	−0.998931	+	0.0462289i	$0.985280\pi$
$972$		0			0
$973$			8.91750e8i			0.968066i
$974$	−1.11258e9			−1.20408
$975$		0			0
$976$			1.03094e9i			1.10888i
$977$		−	7.26228e8i		−	0.778734i	−0.921083	−	0.389367i	$-0.872694\pi$
$977$		−	7.26228e8i		−	0.778734i	0.921083	−	0.389367i	$-0.127306\pi$
$978$		0			0
$979$	4.18360e8			0.445863
$980$		−	6.17430e8i		−	0.656008i
$981$		0			0
$982$	−1.85718e9			−1.96119
$983$			1.23399e9i			1.29913i	0.760306	+	0.649565i	$0.225049\pi$
$983$			1.23399e9i			1.29913i	−0.760306	+	0.649565i	$0.774951\pi$
$984$		0			0
$985$		−	4.04211e8i		−	0.422960i
$986$		−	1.38832e9i		−	1.44830i
$987$		0			0
$988$			3.17556e8i			0.329268i
$989$	−6.43392e8	+	5.33549e8i	−0.665099	+	0.551551i
$990$		0			0
$991$	1.54592e9			1.58842			0.794211	−	0.607642i	$-0.207884\pi$
$991$	1.54592e9			1.58842			0.794211	+	0.607642i	$0.207884\pi$
$992$	1.18444e9			1.21333
$993$		0			0
$994$		−	1.09920e9i		−	1.11922i
$995$	2.40016e8			0.243653
$996$		0			0
$997$	−1.06995e9			−1.07964			−0.539818	−	0.841782i	$-0.681507\pi$
$997$	−1.06995e9			−1.07964			−0.539818	+	0.841782i	$0.681507\pi$
$998$	1.06580e9			1.07222
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.7.d.e.91.5		24
3.2	odd	2		69.7.d.a.22.20	yes	24
23.22	odd	2	inner	207.7.d.e.91.6		24
69.68	even	2		69.7.d.a.22.19	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.d.a.22.19	✓	24	69.68	even	2
69.7.d.a.22.20	yes	24	3.2	odd	2
207.7.d.e.91.5		24	1.1	even	1	trivial
207.7.d.e.91.6		24	23.22	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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	207.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-10.8996 q^{2} +54.8005 q^{4} -162.476i q^{5} -219.782i q^{7} +100.271 q^{8} +O(q^{10})\)	\(q-10.8996 q^{2} +54.8005 q^{4} -162.476i q^{5} -219.782i q^{7} +100.271 q^{8} +1770.91i q^{10} -1606.67i q^{11} -3928.95 q^{13} +2395.53i q^{14} -4600.14 q^{16} -6864.44i q^{17} -1474.89i q^{19} -8903.75i q^{20} +17512.0i q^{22} +(-7766.67 - 9365.61i) q^{23} -10773.4 q^{25} +42823.9 q^{26} -12044.2i q^{28} -18555.6 q^{29} +27090.1 q^{31} +43722.2 q^{32} +74819.4i q^{34} -35709.2 q^{35} -74301.9i q^{37} +16075.6i q^{38} -16291.5i q^{40} +53361.4 q^{41} -68697.2i q^{43} -88046.5i q^{44} +(84653.4 + 102081. i) q^{46} +105757. q^{47} +69344.9 q^{49} +117425. q^{50} -215308. q^{52} -257751. i q^{53} -261045. q^{55} -22037.7i q^{56} +202248. q^{58} -158761. q^{59} -224111. i q^{61} -295270. q^{62} -182144. q^{64} +638359. i q^{65} +530212. i q^{67} -376175. i q^{68} +389215. q^{70} -458854. q^{71} +281567. q^{73} +809859. i q^{74} -80824.5i q^{76} -353118. q^{77} +253619. i q^{79} +747411. i q^{80} -581616. q^{82} -147594. i q^{83} -1.11530e6 q^{85} +748770. i q^{86} -161102. i q^{88} +260389. i q^{89} +863513. i q^{91} +(-425618. - 513240. i) q^{92} -1.15271e6 q^{94} -239633. q^{95} +1.39769e6i q^{97} -755829. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8}+O(q^{10}) \) 24 * q + 20 * q^2 + 816 * q^4 + 940 * q^8	\( 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8} + 384 q^{13} + 29544 q^{16} - 29336 q^{23} - 61272 q^{25} - 10088 q^{26} - 64672 q^{29} + 9696 q^{31} + 319620 q^{32} + 225744 q^{35} - 135280 q^{41} + 233232 q^{46} + 74336 q^{47} - 722136 q^{49} - 619324 q^{50} + 1059720 q^{52} - 1019328 q^{55} - 694344 q^{58} - 1057648 q^{59} + 488776 q^{62} - 273888 q^{64} + 2785512 q^{70} + 255392 q^{71} - 322560 q^{73} + 1002960 q^{77} - 5732712 q^{82} - 2704704 q^{85} + 1611444 q^{92} - 147720 q^{94} + 1672656 q^{95} - 9104212 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 + 816 * q^4 + 940 * q^8 + 384 * q^13 + 29544 * q^16 - 29336 * q^23 - 61272 * q^25 - 10088 * q^26 - 64672 * q^29 + 9696 * q^31 + 319620 * q^32 + 225744 * q^35 - 135280 * q^41 + 233232 * q^46 + 74336 * q^47 - 722136 * q^49 - 619324 * q^50 + 1059720 * q^52 - 1019328 * q^55 - 694344 * q^58 - 1057648 * q^59 + 488776 * q^62 - 273888 * q^64 + 2785512 * q^70 + 255392 * q^71 - 322560 * q^73 + 1002960 * q^77 - 5732712 * q^82 - 2704704 * q^85 + 1611444 * q^92 - 147720 * q^94 + 1672656 * q^95 - 9104212 * q^98

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