LMFDB - Embedded newform 207.7.d.e.91.11

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			91.11
Character	$\chi$	$=$	207.91
Dual form			207.7.d.e.91.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.368531 q^{2} -63.8642 q^{4} +113.928i q^{5} +569.901i q^{7} -47.1219 q^{8} +O(q^{10})$	\(q+0.368531 q^{2} -63.8642 q^{4} +113.928i q^{5} +569.901i q^{7} -47.1219 q^{8} +41.9859i q^{10} +814.298i q^{11} +3513.83 q^{13} +210.026i q^{14} +4069.94 q^{16} +7484.26i q^{17} +4283.93i q^{19} -7275.90i q^{20} +300.094i q^{22} +(-12048.1 - 1696.83i) q^{23} +2645.50 q^{25} +1294.96 q^{26} -36396.3i q^{28} +3314.46 q^{29} +34401.9 q^{31} +4515.70 q^{32} +2758.18i q^{34} -64927.5 q^{35} -7160.07i q^{37} +1578.76i q^{38} -5368.49i q^{40} -77969.3 q^{41} +113275. i q^{43} -52004.5i q^{44} +(-4440.10 - 625.334i) q^{46} +62809.9 q^{47} -207138. q^{49} +974.947 q^{50} -224408. q^{52} +135215. i q^{53} -92771.0 q^{55} -26854.8i q^{56} +1221.48 q^{58} +101668. q^{59} -38234.1i q^{61} +12678.2 q^{62} -258812. q^{64} +400322. i q^{65} +229273. i q^{67} -477976. i q^{68} -23927.8 q^{70} +64522.4 q^{71} -53631.6 q^{73} -2638.71i q^{74} -273590. i q^{76} -464069. q^{77} -458737. i q^{79} +463679. i q^{80} -28734.1 q^{82} -1.13063e6i q^{83} -852664. q^{85} +41745.4i q^{86} -38371.3i q^{88} +829443. i q^{89} +2.00254e6i q^{91} +(769442. + 108367. i) q^{92} +23147.4 q^{94} -488058. q^{95} -525418. i q^{97} -76337.0 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.368531			0.0460664			0.0230332	−	0.999735i	$-0.492668\pi$
$2$	0.368531			0.0460664			0.0230332	+	0.999735i	$0.492668\pi$
$3$		0			0
$3$		0			0
$4$	−63.8642			−0.997878
$5$			113.928i			0.911421i	0.890128	+	0.455711i	$0.150615\pi$
$5$			113.928i			0.911421i	−0.890128	+	0.455711i	$0.849385\pi$
$6$		0			0
$7$			569.901i			1.66152i	0.556631	+	0.830760i	$0.312094\pi$
$7$			569.901i			1.66152i	−0.556631	+	0.830760i	$0.687906\pi$
$8$	−47.1219			−0.0920350
$9$		0			0
$10$			41.9859i			0.0419859i
$11$			814.298i			0.611794i	0.952065	+	0.305897i	$0.0989563\pi$
$11$			814.298i			0.611794i	−0.952065	+	0.305897i	$0.901044\pi$
$12$		0			0
$13$	3513.83			1.59938			0.799689	−	0.600415i	$-0.204998\pi$
$13$	3513.83			1.59938			0.799689	+	0.600415i	$0.204998\pi$
$14$			210.026i			0.0765402i
$15$		0			0
$16$	4069.94			0.993638
$17$			7484.26i			1.52336i	0.647954	+	0.761679i	$0.275625\pi$
$17$			7484.26i			1.52336i	−0.647954	+	0.761679i	$0.724375\pi$
$18$		0			0
$19$			4283.93i			0.624571i	0.949988	+	0.312285i	$0.101095\pi$
$19$			4283.93i			0.624571i	−0.949988	+	0.312285i	$0.898905\pi$
$20$		−	7275.90i		−	0.909487i
$21$		0			0
$22$			300.094i			0.0281831i
$23$	−12048.1	−	1696.83i	−0.990227	−	0.139462i
$23$	−12048.1	−	1696.83i	−0.990227	−	0.139462i
$24$		0			0
$25$	2645.50			0.169312
$26$	1294.96			0.0736775
$27$		0			0
$28$		−	36396.3i		−	1.65799i
$29$	3314.46			0.135900			0.0679500	−	0.997689i	$-0.478354\pi$
$29$	3314.46			0.135900			0.0679500	+	0.997689i	$0.478354\pi$
$30$		0			0
$31$	34401.9			1.15478			0.577388	−	0.816470i	$-0.304072\pi$
$31$	34401.9			1.15478			0.577388	+	0.816470i	$0.304072\pi$
$32$	4515.70			0.137808
$33$		0			0
$34$			2758.18i			0.0701756i
$35$	−64927.5			−1.51434
$36$		0			0
$37$		−	7160.07i		−	0.141355i	−0.997499	−	0.0706776i	$-0.977484\pi$
$37$		−	7160.07i		−	0.141355i	0.997499	−	0.0706776i	$-0.0225162\pi$
$38$			1578.76i			0.0287717i
$39$		0			0
$40$		−	5368.49i		−	0.0838826i
$41$	−77969.3			−1.13129			−0.565643	−	0.824650i	$-0.691372\pi$
$41$	−77969.3			−1.13129			−0.565643	+	0.824650i	$0.691372\pi$
$42$		0			0
$43$			113275.i			1.42472i	0.701815	+	0.712359i	$0.252373\pi$
$43$			113275.i			1.42472i	−0.701815	+	0.712359i	$0.747627\pi$
$44$		−	52004.5i		−	0.610496i
$45$		0			0
$46$	−4440.10	−	625.334i	−0.0456162	−	0.00642449i
$47$	62809.9			0.604971			0.302485	−	0.953154i	$-0.402184\pi$
$47$	62809.9			0.604971			0.302485	+	0.953154i	$0.402184\pi$
$48$		0			0
$49$	−207138.			−1.76065
$50$	974.947			0.00779958
$51$		0			0
$52$	−224408.			−1.59598
$53$			135215.i			0.908235i	0.890942	+	0.454118i	$0.150045\pi$
$53$			135215.i			0.908235i	−0.890942	+	0.454118i	$0.849955\pi$
$54$		0			0
$55$	−92771.0			−0.557602
$56$		−	26854.8i		−	0.152918i
$57$		0			0
$58$	1221.48			0.00626042
$59$	101668.			0.495025			0.247513	−	0.968885i	$-0.420387\pi$
$59$	101668.			0.495025			0.247513	+	0.968885i	$0.420387\pi$
$60$		0			0
$61$		−	38234.1i		−	0.168446i	−0.996447	−	0.0842231i	$-0.973159\pi$
$61$		−	38234.1i		−	0.168446i	0.996447	−	0.0842231i	$-0.0268409\pi$
$62$	12678.2			0.0531963
$63$		0			0
$64$	−258812.			−0.987290
$65$			400322.i			1.45771i
$66$		0			0
$67$			229273.i			0.762306i	0.924512	+	0.381153i	$0.124473\pi$
$67$			229273.i			0.762306i	−0.924512	+	0.381153i	$0.875527\pi$
$68$		−	477976.i		−	1.52013i
$69$		0			0
$70$	−23927.8			−0.0697603
$71$	64522.4			0.180275			0.0901375	−	0.995929i	$-0.471269\pi$
$71$	64522.4			0.180275			0.0901375	+	0.995929i	$0.471269\pi$
$72$		0			0
$73$	−53631.6			−0.137864			−0.0689322	−	0.997621i	$-0.521959\pi$
$73$	−53631.6			−0.137864			−0.0689322	+	0.997621i	$0.521959\pi$
$74$		−	2638.71i		−	0.00651172i
$75$		0			0
$76$		−	273590.i		−	0.623245i
$77$	−464069.			−1.01651
$78$		0			0
$79$		−	458737.i		−	0.930427i	−0.885199	−	0.465213i	$-0.845978\pi$
$79$		−	458737.i		−	0.930427i	0.885199	−	0.465213i	$-0.154022\pi$
$80$			463679.i			0.905623i
$81$		0			0
$82$	−28734.1			−0.0521142
$83$		−	1.13063e6i		−	1.97736i	−0.150055	−	0.988678i	$-0.547945\pi$
$83$		−	1.13063e6i		−	1.97736i	0.150055	−	0.988678i	$-0.452055\pi$
$84$		0			0
$85$	−852664.			−1.38842
$86$			41745.4i			0.0656316i
$87$		0			0
$88$		−	38371.3i		−	0.0563065i
$89$			829443.i			1.17657i	0.808655	+	0.588284i	$0.200196\pi$
$89$			829443.i			1.17657i	−0.808655	+	0.588284i	$0.799804\pi$
$90$		0			0
$91$			2.00254e6i			2.65740i
$92$	769442.	+	108367.i	0.988126	+	0.139166i
$93$		0			0
$94$	23147.4			0.0278688
$95$	−488058.			−0.569247
$96$		0			0
$97$		−	525418.i		−	0.575691i	−0.957677	−	0.287846i	$-0.907061\pi$
$97$		−	525418.i		−	0.575691i	0.957677	−	0.287846i	$-0.0929390\pi$
$98$	−76337.0			−0.0811067
$99$		0			0
$100$	−168952.			−0.168952
$101$	−1.66810e6			−1.61904			−0.809521	−	0.587090i	$-0.800273\pi$
$101$	−1.66810e6			−1.61904			−0.809521	+	0.587090i	$0.800273\pi$
$102$		0			0
$103$		−	226535.i		−	0.207311i	−0.994613	−	0.103656i	$-0.966946\pi$
$103$		−	226535.i		−	0.207311i	0.994613	−	0.103656i	$-0.0330540\pi$
$104$	−165578.			−0.147199
$105$		0			0
$106$			49831.0i			0.0418391i
$107$			742387.i			0.606009i	0.952989	+	0.303004i	$0.0979897\pi$
$107$			742387.i			0.606009i	−0.952989	+	0.303004i	$0.902010\pi$
$108$		0			0
$109$		−	2.09107e6i		−	1.61469i	−0.590080	−	0.807344i	$-0.700904\pi$
$109$		−	2.09107e6i		−	1.61469i	0.590080	−	0.807344i	$-0.299096\pi$
$110$	−34189.0			−0.0256867
$111$		0			0
$112$			2.31947e6i			1.65095i
$113$		−	2.20924e6i		−	1.53111i	−0.643368	−	0.765557i	$-0.722464\pi$
$113$		−	2.20924e6i		−	1.53111i	0.643368	−	0.765557i	$-0.277536\pi$
$114$		0			0
$115$	193316.	−	1.37261e6i	0.127108	−	0.902514i
$116$	−211676.			−0.135612
$117$		0			0
$118$	37467.7			0.0228040
$119$	−4.26529e6			−2.53109
$120$		0			0
$121$	1.10848e6			0.625708
$122$		−	14090.5i		−	0.00775971i
$123$		0			0
$124$	−2.19705e6			−1.15232
$125$			2.08151e6i			1.06574i
$126$		0			0
$127$	−723004.			−0.352963			−0.176482	−	0.984304i	$-0.556472\pi$
$127$	−723004.			−0.352963			−0.176482	+	0.984304i	$0.556472\pi$
$128$	−384385.			−0.183289
$129$		0			0
$130$			147531.i			0.0671512i
$131$	3.35181e6			1.49096			0.745479	−	0.666529i	$-0.232221\pi$
$131$	3.35181e6			1.49096			0.745479	+	0.666529i	$0.232221\pi$
$132$		0			0
$133$	−2.44142e6			−1.03774
$134$			84494.3i			0.0351167i
$135$		0			0
$136$		−	352673.i		−	0.140202i
$137$			546016.i			0.212346i	0.994348	+	0.106173i	$0.0338597\pi$
$137$			546016.i			0.212346i	−0.994348	+	0.106173i	$0.966140\pi$
$138$		0			0
$139$	1.07985e6			0.402086			0.201043	−	0.979582i	$-0.435567\pi$
$139$	1.07985e6			0.402086			0.201043	+	0.979582i	$0.435567\pi$
$140$	4.14654e6			1.51113
$141$		0			0
$142$	23778.5			0.00830461
$143$			2.86131e6i			0.978489i
$144$		0			0
$145$			377609.i			0.123862i
$146$	−19764.9			−0.00635091
$147$		0			0
$148$			457272.i			0.141055i
$149$		−	4.51099e6i		−	1.36368i	−0.731501	−	0.681840i	$-0.761180\pi$
$149$		−	4.51099e6i		−	1.36368i	0.731501	−	0.681840i	$-0.238820\pi$
$150$		0			0
$151$	3.08008e6			0.894605			0.447302	−	0.894383i	$-0.352385\pi$
$151$	3.08008e6			0.894605			0.447302	+	0.894383i	$0.352385\pi$
$152$		−	201867.i		−	0.0574824i
$153$		0			0
$154$	−171024.			−0.0468268
$155$			3.91933e6i			1.05249i
$156$		0			0
$157$			5.92399e6i			1.53079i	0.643562	+	0.765394i	$0.277456\pi$
$157$			5.92399e6i			1.53079i	−0.643562	+	0.765394i	$0.722544\pi$
$158$		−	169059.i		−	0.0428614i
$159$		0			0
$160$			514463.i			0.125601i
$161$	967025.	−	6.86623e6i	0.231718	−	1.64528i
$162$		0			0
$163$	917099.			0.211765			0.105882	−	0.994379i	$-0.466233\pi$
$163$	917099.			0.211765			0.105882	+	0.994379i	$0.466233\pi$
$164$	4.97945e6			1.12888
$165$		0			0
$166$		−	416671.i		−	0.0910896i
$167$	7.58083e6			1.62767			0.813837	−	0.581094i	$-0.197375\pi$
$167$	7.58083e6			1.62767			0.813837	+	0.581094i	$0.197375\pi$
$168$		0			0
$169$	7.52020e6			1.55801
$170$	−314233.			−0.0639595
$171$		0			0
$172$		−	7.23422e6i		−	1.42169i
$173$	−5.62249e6			−1.08590			−0.542951	−	0.839765i	$-0.682693\pi$
$173$	−5.62249e6			−1.08590			−0.542951	+	0.839765i	$0.682693\pi$
$174$		0			0
$175$			1.50767e6i			0.281315i
$176$			3.31414e6i			0.607902i
$177$		0			0
$178$			305676.i			0.0542002i
$179$	−656490.			−0.114464			−0.0572320	−	0.998361i	$-0.518227\pi$
$179$	−656490.			−0.114464			−0.0572320	+	0.998361i	$0.518227\pi$
$180$		0			0
$181$		−	9.20126e6i		−	1.55171i	−0.630909	−	0.775857i	$-0.717318\pi$
$181$		−	9.20126e6i		−	1.55171i	0.630909	−	0.775857i	$-0.282682\pi$
$182$			737997.i			0.122417i
$183$		0			0
$184$	567729.	+	79957.9i	0.0911356	+	0.0128353i
$185$	815730.			0.128834
$186$		0			0
$187$	−6.09442e6			−0.931982
$188$	−4.01130e6			−0.603687
$189$		0			0
$190$	−179865.			−0.0262231
$191$		−	9.24960e6i		−	1.32746i	−0.747971	−	0.663732i	$-0.768972\pi$
$191$		−	9.24960e6i		−	1.32746i	0.747971	−	0.663732i	$-0.231028\pi$
$192$		0			0
$193$	−1.56196e6			−0.217269			−0.108634	−	0.994082i	$-0.534648\pi$
$193$	−1.56196e6			−0.217269			−0.108634	+	0.994082i	$0.534648\pi$
$194$		−	193633.i		−	0.0265200i
$195$		0			0
$196$	1.32287e7			1.75691
$197$	1.12002e7			1.46496			0.732482	−	0.680786i	$-0.238362\pi$
$197$	1.12002e7			1.46496			0.732482	+	0.680786i	$0.238362\pi$
$198$		0			0
$199$			4.87456e6i			0.618552i	0.950972	+	0.309276i	$0.100087\pi$
$199$			4.87456e6i			0.618552i	−0.950972	+	0.309276i	$0.899913\pi$
$200$	−124661.			−0.0155826
$201$		0			0
$202$	−614747.			−0.0745834
$203$			1.88892e6i			0.225800i
$204$		0			0
$205$		−	8.88286e6i		−	1.03108i
$206$		−	83485.1i		−	0.00955008i
$207$		0			0
$208$	1.43011e7			1.58920
$209$	−3.48840e6			−0.382109
$210$		0			0
$211$	1.01176e7			1.07704			0.538518	−	0.842614i	$-0.318984\pi$
$211$	1.01176e7			1.07704			0.538518	+	0.842614i	$0.318984\pi$
$212$		−	8.63542e6i		−	0.906308i
$213$		0			0
$214$			273593.i			0.0279166i
$215$	−1.29052e7			−1.29852
$216$		0			0
$217$			1.96057e7i			1.91868i
$218$		−	770624.i		−	0.0743829i
$219$		0			0
$220$	5.92475e6			0.556419
$221$			2.62984e7i			2.43642i
$222$		0			0
$223$	−1.27139e7			−1.14647			−0.573236	−	0.819390i	$-0.694312\pi$
$223$	−1.27139e7			−1.14647			−0.573236	+	0.819390i	$0.694312\pi$
$224$			2.57350e6i			0.228971i
$225$		0			0
$226$		−	814173.i		−	0.0705328i
$227$			1.69641e7i			1.45028i	0.688599	+	0.725142i	$0.258226\pi$
$227$			1.69641e7i			1.45028i	−0.688599	+	0.725142i	$0.741774\pi$
$228$		0			0
$229$		−	1.22935e7i		−	1.02369i	−0.859077	−	0.511847i	$-0.828962\pi$
$229$		−	1.22935e7i		−	1.02369i	0.859077	−	0.511847i	$-0.171038\pi$
$230$	71242.8	−	505850.i	0.00585542	−	0.0415756i
$231$		0			0
$232$	−156184.			−0.0125075
$233$	171237.			0.0135372			0.00676861	−	0.999977i	$-0.497845\pi$
$233$	171237.			0.0135372			0.00676861	+	0.999977i	$0.497845\pi$
$234$		0			0
$235$			7.15578e6i			0.551383i
$236$	−6.49293e6			−0.493975
$237$		0			0
$238$	−1.57189e6			−0.116598
$239$	543012.			0.0397755			0.0198877	−	0.999802i	$-0.493669\pi$
$239$	543012.			0.0397755			0.0198877	+	0.999802i	$0.493669\pi$
$240$		0			0
$241$		−	3.84804e6i		−	0.274909i	−0.990508	−	0.137455i	$-0.956108\pi$
$241$		−	3.84804e6i		−	0.274909i	0.990508	−	0.137455i	$-0.0438921\pi$
$242$	408509.			0.0288241
$243$		0			0
$244$			2.44179e6i			0.168089i
$245$		−	2.35988e7i		−	1.60469i
$246$		0			0
$247$			1.50530e7i			0.998924i
$248$	−1.62108e6			−0.106280
$249$		0			0
$250$			767103.i			0.0490946i
$251$		−	1.18733e7i		−	0.750845i	−0.926854	−	0.375422i	$-0.877498\pi$
$251$		−	1.18733e7i		−	0.750845i	0.926854	−	0.375422i	$-0.122502\pi$
$252$		0			0
$253$	1.38172e6	−	9.81074e6i	0.0853218	−	0.605815i
$254$	−266449.			−0.0162597
$255$		0			0
$256$	1.64223e7			0.978846
$257$	1.02407e7			0.603296			0.301648	−	0.953419i	$-0.402463\pi$
$257$	1.02407e7			0.603296			0.301648	+	0.953419i	$0.402463\pi$
$258$		0			0
$259$	4.08053e6			0.234865
$260$		−	2.55663e7i		−	1.45461i
$261$		0			0
$262$	1.23525e6			0.0686831
$263$		−	2.04038e6i		−	0.112162i	−0.998426	−	0.0560809i	$-0.982140\pi$
$263$		−	2.04038e6i		−	0.112162i	0.998426	−	0.0560809i	$-0.0178605\pi$
$264$		0			0
$265$	−1.54048e7			−0.827785
$266$	−899738.			−0.0478048
$267$		0			0
$268$		−	1.46424e7i		−	0.760688i
$269$	3.09947e7			1.59232			0.796161	−	0.605085i	$-0.206861\pi$
$269$	3.09947e7			1.59232			0.796161	+	0.605085i	$0.206861\pi$
$270$		0			0
$271$	−4.55560e6			−0.228896			−0.114448	−	0.993429i	$-0.536510\pi$
$271$	−4.55560e6			−0.228896			−0.114448	+	0.993429i	$0.536510\pi$
$272$			3.04605e7i			1.51367i
$273$		0			0
$274$			201224.i			0.00978200i
$275$			2.15422e6i			0.103584i
$276$		0			0
$277$	−1.18273e7			−0.556475			−0.278237	−	0.960512i	$-0.589750\pi$
$277$	−1.18273e7			−0.556475			−0.278237	+	0.960512i	$0.589750\pi$
$278$	397958.			0.0185226
$279$		0			0
$280$	3.05951e6			0.139373
$281$			1.70316e7i			0.767601i	0.923416	+	0.383801i	$0.125385\pi$
$281$			1.70316e7i			0.767601i	−0.923416	+	0.383801i	$0.874615\pi$
$282$		0			0
$283$		−	3.65196e7i		−	1.61126i	−0.592418	−	0.805631i	$-0.701826\pi$
$283$		−	3.65196e7i		−	1.61126i	0.592418	−	0.805631i	$-0.298174\pi$
$284$	−4.12067e6			−0.179892
$285$		0			0
$286$			1.05448e6i			0.0450755i
$287$		−	4.44348e7i		−	1.87965i
$288$		0			0
$289$	−3.18766e7			−1.32062
$290$			139161.i			0.00570588i
$291$		0			0
$292$	3.42514e6			0.137572
$293$			1.85690e7i			0.738220i	0.929386	+	0.369110i	$0.120337\pi$
$293$			1.85690e7i			0.738220i	−0.929386	+	0.369110i	$0.879663\pi$
$294$		0			0
$295$			1.15828e7i			0.451177i
$296$			337396.i			0.0130096i
$297$		0			0
$298$		−	1.66244e6i		−	0.0628198i
$299$	−4.23350e7	−	5.96237e6i	−1.58375	−	0.223052i
$300$		0			0
$301$	−6.45556e7			−2.36720
$302$	1.13511e6			0.0412112
$303$		0			0
$304$			1.74354e7i			0.620597i
$305$	4.35592e6			0.153525
$306$		0			0
$307$	−3.39160e7			−1.17217			−0.586084	−	0.810250i	$-0.699331\pi$
$307$	−3.39160e7			−1.17217			−0.586084	+	0.810250i	$0.699331\pi$
$308$	2.96374e7			1.01435
$309$		0			0
$310$			1.44439e6i			0.0484842i
$311$	3.91451e7			1.30136			0.650679	−	0.759353i	$-0.274484\pi$
$311$	3.91451e7			1.30136			0.650679	+	0.759353i	$0.274484\pi$
$312$		0			0
$313$			4.03448e7i			1.31569i	0.753152	+	0.657847i	$0.228533\pi$
$313$			4.03448e7i			1.31569i	−0.753152	+	0.657847i	$0.771467\pi$
$314$			2.18317e6i			0.0705179i
$315$		0			0
$316$			2.92968e7i			0.928452i
$317$	−3.59652e7			−1.12903			−0.564514	−	0.825423i	$-0.690937\pi$
$317$	−3.59652e7			−1.12903			−0.564514	+	0.825423i	$0.690937\pi$
$318$		0			0
$319$			2.69896e6i			0.0831428i
$320$		−	2.94858e7i		−	0.899837i
$321$		0			0
$322$	356379.	−	2.53042e6i	0.0106744	−	0.0757922i
$323$	−3.20621e7			−0.951445
$324$		0			0
$325$	9.29583e6			0.270793
$326$	337979.			0.00975523
$327$		0			0
$328$	3.67406e6			0.104118
$329$			3.57954e7i			1.00517i
$330$		0			0
$331$	−2.80276e7			−0.772863			−0.386431	−	0.922318i	$-0.626292\pi$
$331$	−2.80276e7			−0.772863			−0.386431	+	0.922318i	$0.626292\pi$
$332$			7.22065e7i			1.97316i
$333$		0			0
$334$	2.79377e6			0.0749810
$335$	−2.61206e7			−0.694781
$336$		0			0
$337$			3.06197e7i			0.800038i	0.916507	+	0.400019i	$0.130997\pi$
$337$			3.06197e7i			0.800038i	−0.916507	+	0.400019i	$0.869003\pi$
$338$	2.77143e6			0.0717717
$339$		0			0
$340$	5.44547e7			1.38547
$341$			2.80134e7i			0.706485i
$342$		0			0
$343$		−	5.10002e7i		−	1.26383i
$344$		−	5.33774e6i		−	0.131124i
$345$		0			0
$346$	−2.07206e6			−0.0500235
$347$	−7.04261e7			−1.68556			−0.842782	−	0.538255i	$-0.819084\pi$
$347$	−7.04261e7			−1.68556			−0.842782	+	0.538255i	$0.819084\pi$
$348$		0			0
$349$	−6.68006e7			−1.57146			−0.785731	−	0.618568i	$-0.787713\pi$
$349$	−6.68006e7			−1.57146			−0.785731	+	0.618568i	$0.787713\pi$
$350$			555624.i			0.0129592i
$351$		0			0
$352$			3.67713e6i			0.0843103i
$353$	7.85575e6			0.178593			0.0892963	−	0.996005i	$-0.471538\pi$
$353$	7.85575e6			0.178593			0.0892963	+	0.996005i	$0.471538\pi$
$354$		0			0
$355$			7.35088e6i			0.164306i
$356$		−	5.29717e7i		−	1.17407i
$357$		0			0
$358$	−241937.			−0.00527294
$359$			8.88485e6i			0.192029i	0.995380	+	0.0960145i	$0.0306095\pi$
$359$			8.88485e6i			0.192029i	−0.995380	+	0.0960145i	$0.969390\pi$
$360$		0			0
$361$	2.86938e7			0.609911
$362$		−	3.39095e6i		−	0.0714818i
$363$		0			0
$364$		−	1.27890e8i		−	2.65176i
$365$		−	6.11012e6i		−	0.125652i
$366$		0			0
$367$			8.43071e7i			1.70556i	0.522274	+	0.852778i	$0.325084\pi$
$367$			8.43071e7i			1.70556i	−0.522274	+	0.852778i	$0.674916\pi$
$368$	−4.90351e7	−	6.90600e6i	−0.983928	−	0.138574i
$369$		0			0
$370$	300622.			0.00593492
$371$	−7.70594e7			−1.50905
$372$		0			0
$373$			6.67702e7i			1.28664i	0.765599	+	0.643318i	$0.222443\pi$
$373$			6.67702e7i			1.28664i	−0.765599	+	0.643318i	$0.777557\pi$
$374$	−2.24598e6			−0.0429330
$375$		0			0
$376$	−2.95972e6			−0.0556785
$377$	1.16465e7			0.217355
$378$		0			0
$379$		−	5.19954e7i		−	0.955097i	−0.878605	−	0.477549i	$-0.841525\pi$
$379$		−	5.19954e7i		−	0.955097i	0.878605	−	0.477549i	$-0.158475\pi$
$380$	3.11694e7			0.568039
$381$		0			0
$382$		−	3.40876e6i		−	0.0611514i
$383$		−	3.43487e7i		−	0.611384i	−0.952130	−	0.305692i	$-0.901112\pi$
$383$		−	3.43487e7i		−	0.611384i	0.952130	−	0.305692i	$-0.0988878\pi$
$384$		0			0
$385$		−	5.28703e7i		−	0.926467i
$386$	−575629.			−0.0100088
$387$		0			0
$388$			3.35554e7i			0.574470i
$389$		−	7.76864e7i		−	1.31976i	−0.751369	−	0.659882i	$-0.770606\pi$
$389$		−	7.76864e7i		−	1.31976i	0.751369	−	0.659882i	$-0.229394\pi$
$390$		0			0
$391$	1.26995e7	−	9.01711e7i	0.212450	−	1.50847i
$392$	9.76076e6			0.162041
$393$		0			0
$394$	4.12762e6			0.0674856
$395$	5.22628e7			0.848011
$396$		0			0
$397$	−9.93649e7			−1.58804			−0.794020	−	0.607892i	$-0.792015\pi$
$397$	−9.93649e7			−1.58804			−0.794020	+	0.607892i	$0.792015\pi$
$398$			1.79643e6i			0.0284945i
$399$		0			0
$400$	1.07670e7			0.168235
$401$		−	3.38580e7i		−	0.525083i	−0.964921	−	0.262542i	$-0.915439\pi$
$401$		−	3.38580e7i		−	0.525083i	0.964921	−	0.262542i	$-0.0845607\pi$
$402$		0			0
$403$	1.20883e8			1.84692
$404$	1.06532e8			1.61561
$405$		0			0
$406$			696124.i			0.0104018i
$407$	5.83043e6			0.0864803
$408$		0			0
$409$	4.05687e7			0.592955			0.296477	−	0.955040i	$-0.404188\pi$
$409$	4.05687e7			0.592955			0.296477	+	0.955040i	$0.404188\pi$
$410$		−	3.27361e6i		−	0.0474980i
$411$		0			0
$412$			1.44675e7i			0.206871i
$413$			5.79406e7i			0.822494i
$414$		0			0
$415$	1.28810e8			1.80220
$416$	1.58674e7			0.220407
$417$		0			0
$418$	−1.28558e6			−0.0176024
$419$			8.70221e7i			1.18301i	0.806302	+	0.591504i	$0.201466\pi$
$419$			8.70221e7i			1.18301i	−0.806302	+	0.591504i	$0.798534\pi$
$420$		0			0
$421$			6.05889e7i			0.811983i	0.913877	+	0.405991i	$0.133074\pi$
$421$			6.05889e7i			0.811983i	−0.913877	+	0.405991i	$0.866926\pi$
$422$	3.72865e6			0.0496152
$423$		0			0
$424$		−	6.37161e6i		−	0.0835894i
$425$			1.97996e7i			0.257922i
$426$		0			0
$427$	2.17897e7			0.279877
$428$		−	4.74119e7i		−	0.604723i
$429$		0			0
$430$	−4.75595e6			−0.0598180
$431$			5.02127e7i			0.627165i	0.949561	+	0.313583i	$0.101529\pi$
$431$			5.02127e7i			0.627165i	−0.949561	+	0.313583i	$0.898471\pi$
$432$		0			0
$433$			1.09950e8i			1.35435i	0.735820	+	0.677177i	$0.236797\pi$
$433$			1.09950e8i			1.35435i	−0.735820	+	0.677177i	$0.763203\pi$
$434$			7.22531e6i			0.0883867i
$435$		0			0
$436$			1.33544e8i			1.61126i
$437$	7.26910e6	−	5.16132e7i	0.0871037	−	0.618467i
$438$		0			0
$439$	−3.55005e7			−0.419606			−0.209803	−	0.977744i	$-0.567282\pi$
$439$	−3.55005e7			−0.419606			−0.209803	+	0.977744i	$0.567282\pi$
$440$	4.37155e6			0.0513189
$441$		0			0
$442$			9.69179e6i			0.112237i
$443$	9.78683e7			1.12572			0.562861	−	0.826552i	$-0.309701\pi$
$443$	9.78683e7			1.12572			0.562861	+	0.826552i	$0.309701\pi$
$444$		0			0
$445$	−9.44965e7			−1.07235
$446$	−4.68546e6			−0.0528138
$447$		0			0
$448$		−	1.47497e8i		−	1.64040i
$449$	8.49424e7			0.938394			0.469197	−	0.883093i	$-0.344543\pi$
$449$	8.49424e7			0.938394			0.469197	+	0.883093i	$0.344543\pi$
$450$		0			0
$451$		−	6.34903e7i		−	0.692114i
$452$			1.41091e8i			1.52786i
$453$		0			0
$454$			6.25180e6i			0.0668093i
$455$	−2.28144e8			−2.42201
$456$		0			0
$457$		−	8.16735e7i		−	0.855722i	−0.903844	−	0.427861i	$-0.859267\pi$
$457$		−	8.16735e7i		−	0.855722i	0.903844	−	0.427861i	$-0.140733\pi$
$458$		−	4.53055e6i		−	0.0471579i
$459$		0			0
$460$	−1.23460e7	+	8.76607e7i	−0.126839	+	0.900599i
$461$	1.10947e8			1.13243			0.566215	−	0.824258i	$-0.308407\pi$
$461$	1.10947e8			1.13243			0.566215	+	0.824258i	$0.308407\pi$
$462$		0			0
$463$	1.53700e8			1.54857			0.774287	−	0.632835i	$-0.218109\pi$
$463$	1.53700e8			1.54857			0.774287	+	0.632835i	$0.218109\pi$
$464$	1.34897e7			0.135035
$465$		0			0
$466$	63106.1			0.000623611
$467$		−	2.80988e7i		−	0.275890i	−0.990440	−	0.137945i	$-0.955950\pi$
$467$		−	2.80988e7i		−	0.275890i	0.990440	−	0.137945i	$-0.0440498\pi$
$468$		0			0
$469$	−1.30663e8			−1.26659
$470$			2.63713e6i			0.0254002i
$471$		0			0
$472$	−4.79078e6			−0.0455597
$473$	−9.22396e7			−0.871634
$474$		0			0
$475$			1.13331e7i			0.105747i
$476$	2.72399e8			2.52572
$477$		0			0
$478$	200117.			0.00183231
$479$		−	2.05854e8i		−	1.87307i	−0.350578	−	0.936534i	$-0.614015\pi$
$479$		−	2.05854e8i		−	1.87307i	0.350578	−	0.936534i	$-0.385985\pi$
$480$		0			0
$481$		−	2.51593e7i		−	0.226080i
$482$		−	1.41812e6i		−	0.0126641i
$483$		0			0
$484$	−7.07922e7			−0.624380
$485$	5.98596e7			0.524697
$486$		0			0
$487$	7.83541e7			0.678383			0.339191	−	0.940717i	$-0.389847\pi$
$487$	7.83541e7			0.678383			0.339191	+	0.940717i	$0.389847\pi$
$488$			1.80166e6i			0.0155029i
$489$		0			0
$490$		−	8.69689e6i		−	0.0739223i
$491$	9.63485e7			0.813955			0.406978	−	0.913438i	$-0.366583\pi$
$491$	9.63485e7			0.813955			0.406978	+	0.913438i	$0.366583\pi$
$492$		0			0
$493$			2.48063e7i			0.207024i
$494$			5.54750e6i			0.0460168i
$495$		0			0
$496$	1.40014e8			1.14743
$497$			3.67714e7i			0.299530i
$498$		0			0
$499$	−3.11543e7			−0.250736			−0.125368	−	0.992110i	$-0.540011\pi$
$499$	−3.11543e7			−0.250736			−0.125368	+	0.992110i	$0.540011\pi$
$500$		−	1.32934e8i		−	1.06347i
$501$		0			0
$502$		−	4.37568e6i		−	0.0345887i
$503$			5.43218e7i			0.426845i	0.976960	+	0.213423i	$0.0684611\pi$
$503$			5.43218e7i			0.426845i	−0.976960	+	0.213423i	$0.931539\pi$
$504$		0			0
$505$		−	1.90043e8i		−	1.47563i
$506$	509208.	−	3.61556e6i	0.00393047	−	0.0279077i
$507$		0			0
$508$	4.61740e7			0.352214
$509$	−2.23459e8			−1.69451			−0.847255	−	0.531187i	$-0.821746\pi$
$509$	−2.23459e8			−1.69451			−0.847255	+	0.531187i	$0.821746\pi$
$510$		0			0
$511$		−	3.05647e7i		−	0.229064i
$512$	3.06528e7			0.228381
$513$		0			0
$514$	3.77402e6			0.0277917
$515$	2.58086e7			0.188948
$516$		0			0
$517$			5.11459e7i			0.370117i
$518$	1.50380e6			0.0108194
$519$		0			0
$520$		−	1.88640e7i		−	0.134160i
$521$		−	1.32853e7i		−	0.0939415i	−0.998896	−	0.0469707i	$-0.985043\pi$
$521$		−	1.32853e7i		−	0.0939415i	0.998896	−	0.0469707i	$-0.0149568\pi$
$522$		0			0
$523$		−	9.24267e7i		−	0.646089i	−0.946384	−	0.323044i	$-0.895294\pi$
$523$		−	9.24267e7i		−	0.646089i	0.946384	−	0.323044i	$-0.104706\pi$
$524$	−2.14061e8			−1.48779
$525$		0			0
$526$		−	751945.i		−	0.00516689i
$527$			2.57473e8i			1.75914i
$528$		0			0
$529$	1.42277e8	+	4.08871e7i	0.961101	+	0.276197i
$530$	−5.67713e6			−0.0381330
$531$		0			0
$532$	1.55919e8			1.03553
$533$	−2.73971e8			−1.80935
$534$		0			0
$535$	−8.45784e7			−0.552329
$536$		−	1.08038e7i		−	0.0701588i
$537$		0			0
$538$	1.14225e7			0.0733525
$539$		−	1.68672e8i		−	1.07715i
$540$		0			0
$541$	5.01668e7			0.316829			0.158414	−	0.987373i	$-0.449362\pi$
$541$	5.01668e7			0.316829			0.158414	+	0.987373i	$0.449362\pi$
$542$	−1.67888e6			−0.0105444
$543$		0			0
$544$			3.37967e7i			0.209931i
$545$	2.38231e8			1.47166
$546$		0			0
$547$	8.48201e7			0.518247			0.259124	−	0.965844i	$-0.416566\pi$
$547$	8.48201e7			0.518247			0.259124	+	0.965844i	$0.416566\pi$
$548$		−	3.48709e7i		−	0.211895i
$549$		0			0
$550$			793897.i			0.00477173i
$551$			1.41989e7i			0.0848791i
$552$		0			0
$553$	2.61435e8			1.54592
$554$	−4.35872e6			−0.0256348
$555$		0			0
$556$	−6.89637e7			−0.401233
$557$		−	1.80275e8i		−	1.04321i	−0.853189	−	0.521603i	$-0.825334\pi$
$557$		−	1.80275e8i		−	1.04321i	0.853189	−	0.521603i	$-0.174666\pi$
$558$		0			0
$559$			3.98029e8i			2.27866i
$560$	−2.64251e8			−1.50471
$561$		0			0
$562$			6.27666e6i			0.0353606i
$563$			3.03781e8i			1.70230i	0.524925	+	0.851149i	$0.324093\pi$
$563$			3.03781e8i			1.70230i	−0.524925	+	0.851149i	$0.675907\pi$
$564$		0			0
$565$	2.51693e8			1.39549
$566$		−	1.34586e7i		−	0.0742250i
$567$		0			0
$568$	−3.04042e6			−0.0165916
$569$			1.02127e8i			0.554376i	0.960816	+	0.277188i	$0.0894025\pi$
$569$			1.02127e8i			0.554376i	−0.960816	+	0.277188i	$0.910598\pi$
$570$		0			0
$571$		−	2.29011e7i		−	0.123012i	−0.998107	−	0.0615059i	$-0.980410\pi$
$571$		−	2.29011e7i		−	0.123012i	0.998107	−	0.0615059i	$-0.0195903\pi$
$572$		−	1.82735e8i		−	0.976413i
$573$		0			0
$574$		−	1.63756e7i		−	0.0865888i
$575$	−3.18732e7	−	4.48895e6i	−0.167657	−	0.0236125i
$576$		0			0
$577$	−2.38699e8			−1.24257			−0.621287	−	0.783583i	$-0.713390\pi$
$577$	−2.38699e8			−1.24257			−0.621287	+	0.783583i	$0.713390\pi$
$578$	−1.17475e7			−0.0608362
$579$		0			0
$580$		−	2.41157e7i		−	0.123599i
$581$	6.44345e8			3.28541
$582$		0			0
$583$	−1.10106e8			−0.555653
$584$	2.52722e6			0.0126883
$585$		0			0
$586$			6.84325e6i			0.0340071i
$587$	−1.94478e8			−0.961514			−0.480757	−	0.876854i	$-0.659638\pi$
$587$	−1.94478e8			−0.961514			−0.480757	+	0.876854i	$0.659638\pi$
$588$		0			0
$589$			1.47375e8i			0.721239i
$590$			4.26861e6i			0.0207841i
$591$		0			0
$592$		−	2.91411e7i		−	0.140456i
$593$	−1.04386e8			−0.500586			−0.250293	−	0.968170i	$-0.580527\pi$
$593$	−1.04386e8			−0.500586			−0.250293	+	0.968170i	$0.580527\pi$
$594$		0			0
$595$		−	4.85934e8i		−	2.30689i
$596$			2.88091e8i			1.36079i
$597$		0			0
$598$	−1.56018e7	−	2.19732e6i	−0.0729575	−	0.0102752i
$599$	8.10305e7			0.377023			0.188512	−	0.982071i	$-0.439634\pi$
$599$	8.10305e7			0.377023			0.188512	+	0.982071i	$0.439634\pi$
$600$		0			0
$601$	−2.22644e7			−0.102562			−0.0512812	−	0.998684i	$-0.516330\pi$
$601$	−2.22644e7			−0.102562			−0.0512812	+	0.998684i	$0.516330\pi$
$602$	−2.37907e7			−0.109048
$603$		0			0
$604$	−1.96707e8			−0.892707
$605$			1.26286e8i			0.570283i
$606$		0			0
$607$	−3.25433e8			−1.45511			−0.727554	−	0.686050i	$-0.759343\pi$
$607$	−3.25433e8			−1.45511			−0.727554	+	0.686050i	$0.759343\pi$
$608$			1.93450e7i			0.0860710i
$609$		0			0
$610$	1.60529e6			0.00707236
$611$	2.20703e8			0.967576
$612$		0			0
$613$			5.64281e7i			0.244971i	0.992470	+	0.122485i	$0.0390864\pi$
$613$			5.64281e7i			0.244971i	−0.992470	+	0.122485i	$0.960914\pi$
$614$	−1.24991e7			−0.0539975
$615$		0			0
$616$	2.18678e7			0.0935543
$617$		−	1.30168e8i		−	0.554176i	−0.960845	−	0.277088i	$-0.910631\pi$
$617$		−	1.30168e8i		−	0.554176i	0.960845	−	0.277088i	$-0.0893694\pi$
$618$		0			0
$619$			9.93172e7i			0.418748i	0.977836	+	0.209374i	$0.0671426\pi$
$619$			9.93172e7i			0.418748i	−0.977836	+	0.209374i	$0.932857\pi$
$620$		−	2.50305e8i		−	1.05025i
$621$		0			0
$622$	1.44262e7			0.0599488
$623$	−4.72701e8			−1.95489
$624$		0			0
$625$	−1.95806e8			−0.802022
$626$			1.48683e7i			0.0606092i
$627$		0			0
$628$		−	3.78331e8i		−	1.52754i
$629$	5.35878e7			0.215335
$630$		0			0
$631$			2.00601e8i			0.798444i	0.916854	+	0.399222i	$0.130720\pi$
$631$			2.00601e8i			0.798444i	−0.916854	+	0.399222i	$0.869280\pi$
$632$			2.16166e7i			0.0856318i
$633$		0			0
$634$	−1.32543e7			−0.0520103
$635$		−	8.23701e7i		−	0.321698i
$636$		0			0
$637$	−7.27850e8			−2.81594
$638$			994651.i			0.00383009i
$639$		0			0
$640$		−	4.37921e7i		−	0.167054i
$641$		−	4.64796e8i		−	1.76477i	−0.470528	−	0.882385i	$-0.655937\pi$
$641$		−	4.64796e8i		−	1.76477i	0.470528	−	0.882385i	$-0.344063\pi$
$642$		0			0
$643$			8.47536e7i			0.318805i	0.987214	+	0.159402i	$0.0509568\pi$
$643$			8.47536e7i			0.318805i	−0.987214	+	0.159402i	$0.949043\pi$
$644$	−6.17583e7	+	4.38506e8i	−0.231227	+	1.64179i
$645$		0			0
$646$	−1.18159e7			−0.0438296
$647$	1.91959e8			0.708752			0.354376	−	0.935103i	$-0.384693\pi$
$647$	1.91959e8			0.708752			0.354376	+	0.935103i	$0.384693\pi$
$648$		0			0
$649$			8.27879e7i			0.302854i
$650$	3.42580e6			0.0124745
$651$		0			0
$652$	−5.85698e7			−0.211315
$653$	1.15990e8			0.416564			0.208282	−	0.978069i	$-0.433213\pi$
$653$	1.15990e8			0.416564			0.208282	+	0.978069i	$0.433213\pi$
$654$		0			0
$655$			3.81864e8i			1.35889i
$656$	−3.17331e8			−1.12409
$657$		0			0
$658$			1.31917e7i			0.0463046i
$659$			1.84207e8i			0.643649i	0.946799	+	0.321824i	$0.104296\pi$
$659$			1.84207e8i			0.643649i	−0.946799	+	0.321824i	$0.895704\pi$
$660$		0			0
$661$			8.44401e6i			0.0292378i	0.999893	+	0.0146189i	$0.00465350\pi$
$661$			8.44401e6i			0.0292378i	−0.999893	+	0.0146189i	$0.995346\pi$
$662$	−1.03291e7			−0.0356030
$663$		0			0
$664$			5.32773e7i			0.181986i
$665$		−	2.78145e8i		−	0.945815i
$666$		0			0
$667$	−3.99330e7	−	5.62408e6i	−0.134572	−	0.0189528i
$668$	−4.84143e8			−1.62422
$669$		0			0
$670$	−9.62624e6			−0.0320061
$671$	3.11339e7			0.103054
$672$		0			0
$673$	−4.84325e8			−1.58888			−0.794441	−	0.607341i	$-0.792236\pi$
$673$	−4.84325e8			−1.58888			−0.794441	+	0.607341i	$0.792236\pi$
$674$			1.12843e7i			0.0368549i
$675$		0			0
$676$	−4.80272e8			−1.55470
$677$			2.68560e8i			0.865517i	0.901510	+	0.432759i	$0.142460\pi$
$677$			2.68560e8i			0.865517i	−0.901510	+	0.432759i	$0.857540\pi$
$678$		0			0
$679$	2.99436e8			0.956522
$680$	4.01792e7			0.127783
$681$		0			0
$682$			1.03238e7i			0.0325452i
$683$	4.25685e8			1.33606			0.668030	−	0.744134i	$-0.267138\pi$
$683$	4.25685e8			1.33606			0.668030	+	0.744134i	$0.267138\pi$
$684$		0			0
$685$	−6.22063e7			−0.193536
$686$		−	1.87951e7i		−	0.0582201i
$687$		0			0
$688$			4.61023e8i			1.41565i
$689$			4.75124e8i			1.45261i
$690$		0			0
$691$	1.62850e8			0.493577			0.246788	−	0.969069i	$-0.420625\pi$
$691$	1.62850e8			0.493577			0.246788	+	0.969069i	$0.420625\pi$
$692$	3.59076e8			1.08360
$693$		0			0
$694$	−2.59542e7			−0.0776478
$695$			1.23025e8i			0.366470i
$696$		0			0
$697$		−	5.83543e8i		−	1.72335i
$698$	−2.46181e7			−0.0723916
$699$		0			0
$700$		−	9.62862e7i		−	0.280718i
$701$		−	2.15840e7i		−	0.0626581i	−0.999509	−	0.0313291i	$-0.990026\pi$
$701$		−	2.15840e7i		−	0.0626581i	0.999509	−	0.0313291i	$-0.00997398\pi$
$702$		0			0
$703$	3.06732e7			0.0882864
$704$		−	2.10750e8i		−	0.604018i
$705$		0			0
$706$	2.89509e6			0.00822711
$707$		−	9.50653e8i		−	2.69007i
$708$		0			0
$709$		−	4.64513e8i		−	1.30334i	−0.758501	−	0.651672i	$-0.774068\pi$
$709$		−	4.64513e8i		−	1.30334i	0.758501	−	0.651672i	$-0.225932\pi$
$710$			2.70903e6i			0.00756900i
$711$		0			0
$712$		−	3.90850e7i		−	0.108285i
$713$	−4.14478e8	−	5.83742e7i	−1.14349	−	0.161047i
$714$		0			0
$715$	−3.25982e8			−0.891816
$716$	4.19262e7			0.114221
$717$		0			0
$718$			3.27434e6i			0.00884608i
$719$	3.55461e8			0.956324			0.478162	−	0.878272i	$-0.341303\pi$
$719$	3.55461e8			0.956324			0.478162	+	0.878272i	$0.341303\pi$
$720$		0			0
$721$	1.29102e8			0.344452
$722$	1.05746e7			0.0280964
$723$		0			0
$724$			5.87631e8i			1.54842i
$725$	8.76840e6			0.0230094
$726$		0			0
$727$		−	9.14852e7i		−	0.238094i	−0.992889	−	0.119047i	$-0.962016\pi$
$727$		−	9.14852e7i		−	0.238094i	0.992889	−	0.119047i	$-0.0379839\pi$
$728$		−	9.43634e7i		−	0.244573i
$729$		0			0
$730$		−	2.25177e6i		−	0.00578835i
$731$	−8.47780e8			−2.17036
$732$		0			0
$733$			5.88821e8i			1.49510i	0.664203	+	0.747552i	$0.268771\pi$
$733$			5.88821e8i			1.49510i	−0.664203	+	0.747552i	$0.731229\pi$
$734$			3.10698e7i			0.0785688i
$735$		0			0
$736$	−5.44056e7	−	7.66238e6i	−0.136462	−	0.0192190i
$737$	−1.86697e8			−0.466374
$738$		0			0
$739$	5.03241e8			1.24693			0.623466	−	0.781850i	$-0.285724\pi$
$739$	5.03241e8			1.24693			0.623466	+	0.781850i	$0.285724\pi$
$740$	−5.20959e7			−0.128561
$741$		0			0
$742$	−2.83988e7			−0.0695165
$743$			5.26147e8i			1.28275i	0.767230	+	0.641373i	$0.221635\pi$
$743$			5.26147e8i			1.28275i	−0.767230	+	0.641373i	$0.778365\pi$
$744$		0			0
$745$	5.13926e8			1.24289
$746$			2.46069e7i			0.0592707i
$747$		0			0
$748$	3.89215e8			0.930004
$749$	−4.23087e8			−1.00690
$750$		0			0
$751$		−	2.74856e8i		−	0.648911i	−0.945901	−	0.324456i	$-0.894819\pi$
$751$		−	2.74856e8i		−	0.648911i	0.945901	−	0.324456i	$-0.105181\pi$
$752$	2.55632e8			0.601122
$753$		0			0
$754$	4.29208e6			0.0100128
$755$			3.50906e8i			0.815362i
$756$		0			0
$757$		−	2.98024e8i		−	0.687010i	−0.939151	−	0.343505i	$-0.888386\pi$
$757$		−	2.98024e8i		−	0.687010i	0.939151	−	0.343505i	$-0.111614\pi$
$758$		−	1.91619e7i		−	0.0439979i
$759$		0			0
$760$	2.29982e7			0.0523906
$761$	1.44743e8			0.328431			0.164216	−	0.986424i	$-0.447491\pi$
$761$	1.44743e8			0.328431			0.164216	+	0.986424i	$0.447491\pi$
$762$		0			0
$763$	1.19170e9			2.68284
$764$			5.90718e8i			1.32465i
$765$		0			0
$766$		−	1.26586e7i		−	0.0281642i
$767$	3.57244e8			0.791732
$768$		0			0
$769$		−	4.15230e8i		−	0.913082i	−0.889702	−	0.456541i	$-0.849088\pi$
$769$		−	4.15230e8i		−	0.913082i	0.889702	−	0.456541i	$-0.150912\pi$
$770$		−	1.94844e7i		−	0.0426790i
$771$		0			0
$772$	9.97530e7			0.216807
$773$		−	3.40961e7i		−	0.0738187i	−0.999319	−	0.0369094i	$-0.988249\pi$
$773$		−	3.40961e7i		−	0.0738187i	0.999319	−	0.0369094i	$-0.0117513\pi$
$774$		0			0
$775$	9.10101e7			0.195517
$776$			2.47587e7i			0.0529837i
$777$		0			0
$778$		−	2.86299e7i		−	0.0607968i
$779$		−	3.34015e8i		−	0.706568i
$780$		0			0
$781$			5.25404e7i			0.110291i
$782$	4.68016e6	−	3.32308e7i	0.00978680	−	0.0694898i
$783$		0			0
$784$	−8.43042e8			−1.74945
$785$	−6.74906e8			−1.39519
$786$		0			0
$787$		−	6.07623e8i		−	1.24655i	−0.782003	−	0.623275i	$-0.785802\pi$
$787$		−	6.07623e8i		−	1.24655i	0.782003	−	0.623275i	$-0.214198\pi$
$788$	−7.15292e8			−1.46186
$789$		0			0
$790$	1.92605e7			0.0390648
$791$	1.25905e9			2.54398
$792$		0			0
$793$		−	1.34348e8i		−	0.269409i
$794$	−3.66190e7			−0.0731552
$795$		0			0
$796$		−	3.11310e8i		−	0.617240i
$797$		−	2.55908e8i		−	0.505485i	−0.967534	−	0.252743i	$-0.918667\pi$
$797$		−	2.55908e8i		−	0.505485i	0.967534	−	0.252743i	$-0.0813326\pi$
$798$		0			0
$799$			4.70085e8i			0.921587i
$800$	1.19463e7			0.0233326
$801$		0			0
$802$		−	1.24777e7i		−	0.0241887i
$803$		−	4.36721e7i		−	0.0843446i
$804$		0			0
$805$	7.82253e8	+	1.10171e8i	1.49955	+	0.211193i
$806$	4.45490e7			0.0850810
$807$		0			0
$808$	7.86041e7			0.149009
$809$	1.94709e8			0.367740			0.183870	−	0.982951i	$-0.441138\pi$
$809$	1.94709e8			0.367740			0.183870	+	0.982951i	$0.441138\pi$
$810$		0			0
$811$	4.20154e8			0.787674			0.393837	−	0.919180i	$-0.371148\pi$
$811$	4.20154e8			0.787674			0.393837	+	0.919180i	$0.371148\pi$
$812$		−	1.20634e8i		−	0.225321i
$813$		0			0
$814$	2.14869e6			0.00398383
$815$			1.04483e8i			0.193007i
$816$		0			0
$817$	−4.85263e8			−0.889837
$818$	1.49508e7			0.0273153
$819$		0			0
$820$			5.67297e8i			1.02889i
$821$	5.01126e8			0.905560			0.452780	−	0.891622i	$-0.350432\pi$
$821$	5.01126e8			0.905560			0.452780	+	0.891622i	$0.350432\pi$
$822$		0			0
$823$	8.26839e8			1.48327			0.741637	−	0.670801i	$-0.234050\pi$
$823$	8.26839e8			1.48327			0.741637	+	0.670801i	$0.234050\pi$
$824$			1.06748e7i			0.0190799i
$825$		0			0
$826$			2.13529e7i			0.0378893i
$827$		−	3.01216e8i		−	0.532551i	−0.963897	−	0.266276i	$-0.914207\pi$
$827$		−	3.01216e8i		−	0.532551i	0.963897	−	0.266276i	$-0.0857931\pi$
$828$		0			0
$829$	4.68607e8			0.822517			0.411259	−	0.911519i	$-0.365089\pi$
$829$	4.68607e8			0.822517			0.411259	+	0.911519i	$0.365089\pi$
$830$	4.74703e7			0.0830210
$831$		0			0
$832$	−9.09422e8			−1.57905
$833$		−	1.55028e9i		−	2.68210i
$834$		0			0
$835$			8.63666e8i			1.48350i
$836$	2.22784e8			0.381298
$837$		0			0
$838$			3.20704e7i			0.0544969i
$839$			1.01082e9i			1.71154i	0.517353	+	0.855772i	$0.326918\pi$
$839$			1.01082e9i			1.71154i	−0.517353	+	0.855772i	$0.673082\pi$
$840$		0			0
$841$	−5.83838e8			−0.981531
$842$			2.23289e7i			0.0374051i
$843$		0			0
$844$	−6.46153e8			−1.07475
$845$			8.56759e8i			1.42000i
$846$		0			0
$847$			6.31724e8i			1.03963i
$848$			5.50319e8i			0.902457i
$849$		0			0
$850$			7.29676e6i			0.0118816i
$851$	−1.21494e7	+	8.62652e7i	−0.0197136	+	0.139974i
$852$		0			0
$853$	1.99330e8			0.321163			0.160581	−	0.987023i	$-0.448663\pi$
$853$	1.99330e8			0.321163			0.160581	+	0.987023i	$0.448663\pi$
$854$	8.03017e6			0.0128929
$855$		0			0
$856$		−	3.49827e7i		−	0.0557740i
$857$	−6.74308e8			−1.07131			−0.535656	−	0.844437i	$-0.679935\pi$
$857$	−6.74308e8			−1.07131			−0.535656	+	0.844437i	$0.679935\pi$
$858$		0			0
$859$	−2.08702e8			−0.329266			−0.164633	−	0.986355i	$-0.552644\pi$
$859$	−2.08702e8			−0.329266			−0.164633	+	0.986355i	$0.552644\pi$
$860$	8.24177e8			1.29576
$861$		0			0
$862$			1.85049e7i			0.0288912i
$863$	8.99089e8			1.39885			0.699424	−	0.714707i	$-0.253440\pi$
$863$	8.99089e8			1.39885			0.699424	+	0.714707i	$0.253440\pi$
$864$		0			0
$865$		−	6.40557e8i		−	0.989713i
$866$			4.05200e7i			0.0623902i
$867$		0			0
$868$		−	1.25210e9i		−	1.91461i
$869$	3.73548e8			0.569230
$870$		0			0
$871$			8.05628e8i			1.21921i
$872$			9.85352e7i			0.148608i
$873$		0			0
$874$	2.67889e6	−	1.90211e7i	0.00401255	−	0.0284905i
$875$	−1.18626e9			−1.77074
$876$		0			0
$877$	3.34022e8			0.495195			0.247598	−	0.968863i	$-0.420359\pi$
$877$	3.34022e8			0.495195			0.247598	+	0.968863i	$0.420359\pi$
$878$	−1.30831e7			−0.0193297
$879$		0			0
$880$	−3.77573e8			−0.554055
$881$		−	3.45526e8i		−	0.505304i	−0.967557	−	0.252652i	$-0.918697\pi$
$881$		−	3.45526e8i		−	0.505304i	0.967557	−	0.252652i	$-0.0813028\pi$
$882$		0			0
$883$	7.01907e7			0.101952			0.0509762	−	0.998700i	$-0.483767\pi$
$883$	7.01907e7			0.101952			0.0509762	+	0.998700i	$0.483767\pi$
$884$		−	1.67953e9i		−	2.43125i
$885$		0			0
$886$	3.60675e7			0.0518579
$887$	5.64947e8			0.809537			0.404769	−	0.914419i	$-0.367352\pi$
$887$	5.64947e8			0.809537			0.404769	+	0.914419i	$0.367352\pi$
$888$		0			0
$889$		−	4.12041e8i		−	0.586455i
$890$	−3.48249e7			−0.0493992
$891$		0			0
$892$	8.11962e8			1.14404
$893$			2.69073e8i			0.377847i
$894$		0			0
$895$		−	7.47924e7i		−	0.104325i
$896$		−	2.19062e8i		−	0.304539i
$897$		0			0
$898$	3.13039e7			0.0432284
$899$	1.14024e8			0.156934
$900$		0			0
$901$	−1.01199e9			−1.38357
$902$		−	2.33981e7i		−	0.0318832i
$903$		0			0
$904$			1.04104e8i			0.140916i
$905$	1.04828e9			1.41426
$906$		0			0
$907$		−	6.29881e8i		−	0.844184i	−0.906553	−	0.422092i	$-0.861296\pi$
$907$		−	6.29881e8i		−	0.844184i	0.906553	−	0.422092i	$-0.138704\pi$
$908$		−	1.08340e9i		−	1.44721i
$909$		0			0
$910$	−8.40782e7			−0.111573
$911$		−	4.77257e8i		−	0.631244i	−0.948885	−	0.315622i	$-0.897787\pi$
$911$		−	4.77257e8i		−	0.631244i	0.948885	−	0.315622i	$-0.102213\pi$
$912$		0			0
$913$	9.20666e8			1.20973
$914$		−	3.00992e7i		−	0.0394200i
$915$		0			0
$916$			7.85116e8i			1.02152i
$917$			1.91020e9i			2.47726i
$918$		0			0
$919$		−	1.23534e9i		−	1.59163i	−0.605541	−	0.795814i	$-0.707043\pi$
$919$		−	1.23534e9i		−	1.59163i	0.605541	−	0.795814i	$-0.292957\pi$
$920$	−9.10941e6	+	6.46801e7i	−0.0116984	+	0.0830629i
$921$		0			0
$922$	4.08872e7			0.0521669
$923$	2.26721e8			0.288328
$924$		0			0
$925$		−	1.89419e7i		−	0.0239331i
$926$	5.66434e7			0.0713372
$927$		0			0
$928$	1.49671e7			0.0187281
$929$	−5.67410e8			−0.707701			−0.353850	−	0.935302i	$-0.615128\pi$
$929$	−5.67410e8			−0.707701			−0.353850	+	0.935302i	$0.615128\pi$
$930$		0			0
$931$		−	8.87367e8i		−	1.09965i
$932$	−1.09359e7			−0.0135085
$933$		0			0
$934$		−	1.03553e7i		−	0.0127093i
$935$		−	6.94322e8i		−	0.849428i
$936$		0			0
$937$			1.36840e9i			1.66339i	0.555237	+	0.831693i	$0.312628\pi$
$937$			1.36840e9i			1.66339i	−0.555237	+	0.831693i	$0.687372\pi$
$938$	−4.81534e7			−0.0583470
$939$		0			0
$940$		−	4.56998e8i		−	0.550213i
$941$			6.47091e8i			0.776599i	0.921533	+	0.388299i	$0.126937\pi$
$941$			6.47091e8i			0.776599i	−0.921533	+	0.388299i	$0.873063\pi$
$942$		0			0
$943$	9.39382e8	+	1.32301e8i	1.12023	+	0.157771i
$944$	4.13782e8			0.491876
$945$		0			0
$946$	−3.39932e7			−0.0401530
$947$	1.95225e8			0.229871			0.114936	−	0.993373i	$-0.463334\pi$
$947$	1.95225e8			0.229871			0.114936	+	0.993373i	$0.463334\pi$
$948$		0			0
$949$	−1.88452e8			−0.220497
$950$			4.17661e6i			0.00487139i
$951$		0			0
$952$	2.00989e8			0.232949
$953$			5.88380e8i			0.679797i	0.940462	+	0.339898i	$0.110393\pi$
$953$			5.88380e8i			0.679797i	−0.940462	+	0.339898i	$0.889607\pi$
$954$		0			0
$955$	1.05378e9			1.20988
$956$	−3.46790e7			−0.0396911
$957$		0			0
$958$		−	7.58637e7i		−	0.0862854i
$959$	−3.11175e8			−0.352817
$960$		0			0
$961$	2.95988e8			0.333506
$962$		−	9.27197e6i		−	0.0104147i
$963$		0			0
$964$			2.45752e8i			0.274326i
$965$		−	1.77950e8i		−	0.198023i
$966$		0			0
$967$	−1.85929e8			−0.205621			−0.102811	−	0.994701i	$-0.532784\pi$
$967$	−1.85929e8			−0.205621			−0.102811	+	0.994701i	$0.532784\pi$
$968$	−5.22337e7			−0.0575870
$969$		0			0
$970$	2.20601e7			0.0241709
$971$		−	2.12025e8i		−	0.231595i	−0.993273	−	0.115798i	$-0.963058\pi$
$971$		−	2.12025e8i		−	0.231595i	0.993273	−	0.115798i	$-0.0369424\pi$
$972$		0			0
$973$			6.15408e8i			0.668074i
$974$	2.88759e7			0.0312506
$975$		0			0
$976$		−	1.55611e8i		−	0.167375i
$977$		−	4.00645e8i		−	0.429612i	−0.976657	−	0.214806i	$-0.931088\pi$
$977$		−	4.00645e8i		−	0.429612i	0.976657	−	0.214806i	$-0.0689119\pi$
$978$		0			0
$979$	−6.75414e8			−0.719817
$980$			1.50712e9i			1.60129i
$981$		0			0
$982$	3.55074e7			0.0374960
$983$			1.40422e9i			1.47834i	0.673517	+	0.739172i	$0.264783\pi$
$983$			1.40422e9i			1.47834i	−0.673517	+	0.739172i	$0.735217\pi$
$984$		0			0
$985$			1.27601e9i			1.33520i
$986$			9.14189e6i			0.00953686i
$987$		0			0
$988$		−	9.61348e8i		−	0.996804i
$989$	1.92208e8	−	1.36475e9i	0.198693	−	1.41079i
$990$		0			0
$991$	−1.62423e8			−0.166888			−0.0834441	−	0.996512i	$-0.526592\pi$
$991$	−1.62423e8			−0.166888			−0.0834441	+	0.996512i	$0.526592\pi$
$992$	1.55349e8			0.159138
$993$		0			0
$994$			1.35514e7i			0.0137983i
$995$	−5.55347e8			−0.563761
$996$		0			0
$997$	1.73006e9			1.74572			0.872861	−	0.487970i	$-0.162262\pi$
$997$	1.73006e9			1.74572			0.872861	+	0.487970i	$0.162262\pi$
$998$	−1.14813e7			−0.0115505
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.7.d.e.91.11		24
3.2	odd	2		69.7.d.a.22.13	✓	24
23.22	odd	2	inner	207.7.d.e.91.12		24
69.68	even	2		69.7.d.a.22.14	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.d.a.22.13	✓	24	3.2	odd	2
69.7.d.a.22.14	yes	24	69.68	even	2
207.7.d.e.91.11		24	1.1	even	1	trivial
207.7.d.e.91.12		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)

\(f(q)\)	\(=\)	\(q+0.368531 q^{2} -63.8642 q^{4} +113.928i q^{5} +569.901i q^{7} -47.1219 q^{8} +O(q^{10})\)	\(q+0.368531 q^{2} -63.8642 q^{4} +113.928i q^{5} +569.901i q^{7} -47.1219 q^{8} +41.9859i q^{10} +814.298i q^{11} +3513.83 q^{13} +210.026i q^{14} +4069.94 q^{16} +7484.26i q^{17} +4283.93i q^{19} -7275.90i q^{20} +300.094i q^{22} +(-12048.1 - 1696.83i) q^{23} +2645.50 q^{25} +1294.96 q^{26} -36396.3i q^{28} +3314.46 q^{29} +34401.9 q^{31} +4515.70 q^{32} +2758.18i q^{34} -64927.5 q^{35} -7160.07i q^{37} +1578.76i q^{38} -5368.49i q^{40} -77969.3 q^{41} +113275. i q^{43} -52004.5i q^{44} +(-4440.10 - 625.334i) q^{46} +62809.9 q^{47} -207138. q^{49} +974.947 q^{50} -224408. q^{52} +135215. i q^{53} -92771.0 q^{55} -26854.8i q^{56} +1221.48 q^{58} +101668. q^{59} -38234.1i q^{61} +12678.2 q^{62} -258812. q^{64} +400322. i q^{65} +229273. i q^{67} -477976. i q^{68} -23927.8 q^{70} +64522.4 q^{71} -53631.6 q^{73} -2638.71i q^{74} -273590. i q^{76} -464069. q^{77} -458737. i q^{79} +463679. i q^{80} -28734.1 q^{82} -1.13063e6i q^{83} -852664. q^{85} +41745.4i q^{86} -38371.3i q^{88} +829443. i q^{89} +2.00254e6i q^{91} +(769442. + 108367. i) q^{92} +23147.4 q^{94} -488058. q^{95} -525418. i q^{97} -76337.0 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8}+O(q^{10}) \) 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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