LMFDB - Embedded newform 207.7.d.e.91.3

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			91.3
Character	$\chi$	$=$	207.91
Dual form			207.7.d.e.91.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-13.3624 q^{2} +114.554 q^{4} -40.7784i q^{5} +469.379i q^{7} -675.521 q^{8} +O(q^{10})$	\(q-13.3624 q^{2} +114.554 q^{4} -40.7784i q^{5} +469.379i q^{7} -675.521 q^{8} +544.897i q^{10} -1567.76i q^{11} +3791.51 q^{13} -6272.03i q^{14} +1695.14 q^{16} +9021.27i q^{17} +7102.08i q^{19} -4671.32i q^{20} +20949.1i q^{22} +(6001.12 - 10584.1i) q^{23} +13962.1 q^{25} -50663.7 q^{26} +53769.2i q^{28} +3651.94 q^{29} -27537.6 q^{31} +20582.2 q^{32} -120546. i q^{34} +19140.5 q^{35} -75148.6i q^{37} -94900.8i q^{38} +27546.7i q^{40} +1160.82 q^{41} -77082.8i q^{43} -179593. i q^{44} +(-80189.3 + 141429. i) q^{46} -128089. q^{47} -102668. q^{49} -186568. q^{50} +434333. q^{52} +149342. i q^{53} -63930.8 q^{55} -317076. i q^{56} -48798.7 q^{58} +55950.5 q^{59} +167059. i q^{61} +367968. q^{62} -383517. q^{64} -154612. i q^{65} -199627. i q^{67} +1.03342e6i q^{68} -255763. q^{70} -120126. q^{71} +659602. q^{73} +1.00417e6i q^{74} +813570. i q^{76} +735875. q^{77} -458548. i q^{79} -69125.1i q^{80} -15511.3 q^{82} +293064. i q^{83} +367873. q^{85} +1.03001e6i q^{86} +1.05906e6i q^{88} -43046.0i q^{89} +1.77966e6i q^{91} +(687451. - 1.21245e6i) q^{92} +1.71158e6 q^{94} +289611. q^{95} +856674. i q^{97} +1.37189e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−13.3624			−1.67030			−0.835150	−	0.550022i	$-0.814619\pi$
$2$	−13.3624			−1.67030			−0.835150	+	0.550022i	$0.814619\pi$
$3$		0			0
$3$		0			0
$4$	114.554			1.78990
$5$		−	40.7784i		−	0.326227i	−0.986607	−	0.163114i	$-0.947846\pi$
$5$		−	40.7784i		−	0.326227i	0.986607	−	0.163114i	$-0.0521537\pi$
$6$		0			0
$7$			469.379i			1.36845i	0.729270	+	0.684226i	$0.239860\pi$
$7$			469.379i			1.36845i	−0.729270	+	0.684226i	$0.760140\pi$
$8$	−675.521			−1.31938
$9$		0			0
$10$			544.897i			0.544897i
$11$		−	1567.76i		−	1.17788i	−0.808176	−	0.588941i	$-0.799545\pi$
$11$		−	1567.76i		−	1.17788i	0.808176	−	0.588941i	$-0.200455\pi$
$12$		0			0
$13$	3791.51			1.72577			0.862884	−	0.505401i	$-0.168656\pi$
$13$	3791.51			1.72577			0.862884	+	0.505401i	$0.168656\pi$
$14$		−	6272.03i		−	2.28573i
$15$		0			0
$16$	1695.14			0.413852
$17$			9021.27i			1.83620i	0.396343	+	0.918102i	$0.370279\pi$
$17$			9021.27i			1.83620i	−0.396343	+	0.918102i	$0.629721\pi$
$18$		0			0
$19$			7102.08i			1.03544i	0.855550	+	0.517720i	$0.173219\pi$
$19$			7102.08i			1.03544i	−0.855550	+	0.517720i	$0.826781\pi$
$20$		−	4671.32i		−	0.583915i
$21$		0			0
$22$			20949.1i			1.96742i
$23$	6001.12	−	10584.1i	0.493229	−	0.869900i
$23$	6001.12	−	10584.1i	0.493229	−	0.869900i
$24$		0			0
$25$	13962.1			0.893576
$26$	−50663.7			−2.88255
$27$		0			0
$28$			53769.2i			2.44940i
$29$	3651.94			0.149737			0.0748685	−	0.997193i	$-0.476146\pi$
$29$	3651.94			0.149737			0.0748685	+	0.997193i	$0.476146\pi$
$30$		0			0
$31$	−27537.6			−0.924359			−0.462180	−	0.886786i	$-0.652932\pi$
$31$	−27537.6			−0.924359			−0.462180	+	0.886786i	$0.652932\pi$
$32$	20582.2			0.628119
$33$		0			0
$34$		−	120546.i		−	3.06701i
$35$	19140.5			0.446426
$36$		0			0
$37$		−	75148.6i		−	1.48360i	−0.670623	−	0.741799i	$-0.733973\pi$
$37$		−	75148.6i		−	1.48360i	0.670623	−	0.741799i	$-0.266027\pi$
$38$		−	94900.8i		−	1.72949i
$39$		0			0
$40$			27546.7i			0.430417i
$41$	1160.82			0.0168427			0.00842136	−	0.999965i	$-0.497319\pi$
$41$	1160.82			0.0168427			0.00842136	+	0.999965i	$0.497319\pi$
$42$		0			0
$43$		−	77082.8i		−	0.969510i	−0.874650	−	0.484755i	$-0.838909\pi$
$43$		−	77082.8i		−	0.969510i	0.874650	−	0.484755i	$-0.161091\pi$
$44$		−	179593.i		−	2.10830i
$45$		0			0
$46$	−80189.3	+	141429.i	−0.823840	+	1.45299i
$47$	−128089.			−1.23372			−0.616862	−	0.787071i	$-0.711596\pi$
$47$	−128089.			−1.23372			−0.616862	+	0.787071i	$0.711596\pi$
$48$		0			0
$49$	−102668.			−0.872662
$50$	−186568.			−1.49254
$51$		0			0
$52$	434333.			3.08896
$53$			149342.i			1.00312i	0.865123	+	0.501560i	$0.167240\pi$
$53$			149342.i			1.00312i	−0.865123	+	0.501560i	$0.832760\pi$
$54$		0			0
$55$	−63930.8			−0.384257
$56$		−	317076.i		−	1.80550i
$57$		0			0
$58$	−48798.7			−0.250106
$59$	55950.5			0.272425			0.136213	−	0.990680i	$-0.456507\pi$
$59$	55950.5			0.272425			0.136213	+	0.990680i	$0.456507\pi$
$60$		0			0
$61$			167059.i			0.736003i	0.929825	+	0.368002i	$0.119958\pi$
$61$			167059.i			0.736003i	−0.929825	+	0.368002i	$0.880042\pi$
$62$	367968.			1.54396
$63$		0			0
$64$	−383517.			−1.46300
$65$		−	154612.i		−	0.562993i
$66$		0			0
$67$		−	199627.i		−	0.663735i	−0.943326	−	0.331868i	$-0.892321\pi$
$67$		−	199627.i		−	0.663735i	0.943326	−	0.331868i	$-0.107679\pi$
$68$			1.03342e6i			3.28663i
$69$		0			0
$70$	−255763.			−0.745666
$71$	−120126.			−0.335631			−0.167816	−	0.985818i	$-0.553671\pi$
$71$	−120126.			−0.335631			−0.167816	+	0.985818i	$0.553671\pi$
$72$		0			0
$73$	659602.			1.69556			0.847781	−	0.530347i	$-0.177938\pi$
$73$	659602.			1.69556			0.847781	+	0.530347i	$0.177938\pi$
$74$			1.00417e6i			2.47805i
$75$		0			0
$76$			813570.i			1.85334i
$77$	735875.			1.61188
$78$		0			0
$79$		−	458548.i		−	0.930045i	−0.885299	−	0.465022i	$-0.846046\pi$
$79$		−	458548.i		−	0.930045i	0.885299	−	0.465022i	$-0.153954\pi$
$80$		−	69125.1i		−	0.135010i
$81$		0			0
$82$	−15511.3			−0.0281324
$83$			293064.i			0.512541i	0.966605	+	0.256270i	$0.0824938\pi$
$83$			293064.i			0.512541i	−0.966605	+	0.256270i	$0.917506\pi$
$84$		0			0
$85$	367873.			0.599020
$86$			1.03001e6i			1.61937i
$87$		0			0
$88$			1.05906e6i			1.55407i
$89$		−	43046.0i		−	0.0610608i	−0.999534	−	0.0305304i	$-0.990280\pi$
$89$		−	43046.0i		−	0.0610608i	0.999534	−	0.0305304i	$-0.00971964\pi$
$90$		0			0
$91$			1.77966e6i			2.36163i
$92$	687451.	−	1.21245e6i	0.882832	−	1.55704i
$93$		0			0
$94$	1.71158e6			2.06069
$95$	289611.			0.337788
$96$		0			0
$97$			856674.i			0.938643i	0.883027	+	0.469321i	$0.155501\pi$
$97$			856674.i			0.938643i	−0.883027	+	0.469321i	$0.844499\pi$
$98$	1.37189e6			1.45761
$99$		0			0
$100$	1.59942e6			1.59942
$101$	292195.			0.283602			0.141801	−	0.989895i	$-0.454711\pi$
$101$	292195.			0.283602			0.141801	+	0.989895i	$0.454711\pi$
$102$		0			0
$103$			712314.i			0.651869i	0.945392	+	0.325934i	$0.105679\pi$
$103$			712314.i			0.651869i	−0.945392	+	0.325934i	$0.894321\pi$
$104$	−2.56125e6			−2.27694
$105$		0			0
$106$		−	1.99556e6i		−	1.67551i
$107$			562846.i			0.459450i	0.973256	+	0.229725i	$0.0737827\pi$
$107$			562846.i			0.459450i	−0.973256	+	0.229725i	$0.926217\pi$
$108$		0			0
$109$			2.02076e6i			1.56040i	0.625529	+	0.780201i	$0.284883\pi$
$109$			2.02076e6i			1.56040i	−0.625529	+	0.780201i	$0.715117\pi$
$110$	854269.			0.641825
$111$		0			0
$112$			795663.i			0.566337i
$113$			1.65496e6i			1.14697i	0.819217	+	0.573484i	$0.194409\pi$
$113$			1.65496e6i			1.14697i	−0.819217	+	0.573484i	$0.805591\pi$
$114$		0			0
$115$	−431601.	−	244716.i	−0.283785	−	0.160905i
$116$	418343.			0.268015
$117$		0			0
$118$	−747633.			−0.455032
$119$	−4.23440e6			−2.51276
$120$		0			0
$121$	−686316.			−0.387407
$122$		−	2.23231e6i		−	1.22935i
$123$		0			0
$124$	−3.15454e6			−1.65451
$125$		−	1.20652e6i		−	0.617736i
$126$		0			0
$127$	3.69029e6			1.80156			0.900781	−	0.434274i	$-0.142995\pi$
$127$	3.69029e6			1.80156			0.900781	+	0.434274i	$0.142995\pi$
$128$	3.80744e6			1.81553
$129$		0			0
$130$			2.06599e6i			0.940367i
$131$	337756.			0.150241			0.0751207	−	0.997174i	$-0.476066\pi$
$131$	337756.			0.150241			0.0751207	+	0.997174i	$0.476066\pi$
$132$		0			0
$133$	−3.33357e6			−1.41695
$134$			2.66750e6i			1.10864i
$135$		0			0
$136$		−	6.09406e6i		−	2.42265i
$137$		−	737585.i		−	0.286847i	−0.989661	−	0.143424i	$-0.954189\pi$
$137$		−	737585.i		−	0.286847i	0.989661	−	0.143424i	$-0.0458111\pi$
$138$		0			0
$139$	495563.			0.184525			0.0922624	−	0.995735i	$-0.470590\pi$
$139$	495563.			0.184525			0.0922624	+	0.995735i	$0.470590\pi$
$140$	2.19262e6			0.799060
$141$		0			0
$142$	1.60517e6			0.560605
$143$		−	5.94419e6i		−	2.03275i
$144$		0			0
$145$		−	148920.i		−	0.0488483i
$146$	−8.81387e6			−2.83210
$147$		0			0
$148$		−	8.60857e6i		−	2.65550i
$149$			3.68998e6i			1.11549i	0.830013	+	0.557744i	$0.188333\pi$
$149$			3.68998e6i			1.11549i	−0.830013	+	0.557744i	$0.811667\pi$
$150$		0			0
$151$	2.42810e6			0.705239			0.352619	−	0.935767i	$-0.385291\pi$
$151$	2.42810e6			0.705239			0.352619	+	0.935767i	$0.385291\pi$
$152$		−	4.79760e6i		−	1.36613i
$153$		0			0
$154$	−9.83305e6			−2.69232
$155$			1.12294e6i			0.301551i
$156$		0			0
$157$			3.65883e6i			0.945461i	0.881207	+	0.472730i	$0.156732\pi$
$157$			3.65883e6i			0.945461i	−0.881207	+	0.472730i	$0.843268\pi$
$158$			6.12731e6i			1.55345i
$159$		0			0
$160$		−	839309.i		−	0.204909i
$161$	4.96794e6	+	2.81680e6i	1.19042	+	0.674960i
$162$		0			0
$163$	−2.54229e6			−0.587032			−0.293516	−	0.955954i	$-0.594825\pi$
$163$	−2.54229e6			−0.587032			−0.293516	+	0.955954i	$0.594825\pi$
$164$	132976.			0.0301469
$165$		0			0
$166$		−	3.91604e6i		−	0.856097i
$167$	5.08973e6			1.09281			0.546406	−	0.837520i	$-0.315995\pi$
$167$	5.08973e6			1.09281			0.546406	+	0.837520i	$0.315995\pi$
$168$		0			0
$169$	9.54877e6			1.97828
$170$	−4.91567e6			−1.00054
$171$		0			0
$172$		−	8.83014e6i		−	1.73533i
$173$	−214344.			−0.0413975			−0.0206987	−	0.999786i	$-0.506589\pi$
$173$	−214344.			−0.0413975			−0.0206987	+	0.999786i	$0.506589\pi$
$174$		0			0
$175$			6.55353e6i			1.22282i
$176$		−	2.65758e6i		−	0.487470i
$177$		0			0
$178$			575198.i			0.101990i
$179$	9.94625e6			1.73420			0.867102	−	0.498131i	$-0.165980\pi$
$179$	9.94625e6			1.73420			0.867102	+	0.498131i	$0.165980\pi$
$180$		0			0
$181$		−	504979.i		−	0.0851604i	−0.999093	−	0.0425802i	$-0.986442\pi$
$181$		−	504979.i		−	0.0851604i	0.999093	−	0.0425802i	$-0.0135578\pi$
$182$		−	2.37805e7i		−	3.94464i
$183$		0			0
$184$	−4.05388e6	+	7.14976e6i	−0.650755	+	1.14773i
$185$	−3.06444e6			−0.483990
$186$		0			0
$187$	1.41432e7			2.16283
$188$	−1.46731e7			−2.20825
$189$		0			0
$190$	−3.86990e6			−0.564208
$191$			7.85205e6i			1.12689i	0.826152	+	0.563447i	$0.190525\pi$
$191$			7.85205e6i			1.12689i	−0.826152	+	0.563447i	$0.809475\pi$
$192$		0			0
$193$	−1.28145e7			−1.78250			−0.891248	−	0.453516i	$-0.850169\pi$
$193$	−1.28145e7			−1.78250			−0.891248	+	0.453516i	$0.850169\pi$
$194$		−	1.14472e7i		−	1.56782i
$195$		0			0
$196$	−1.17610e7			−1.56198
$197$	−1.12045e7			−1.46552			−0.732762	−	0.680485i	$-0.761769\pi$
$197$	−1.12045e7			−1.46552			−0.732762	+	0.680485i	$0.761769\pi$
$198$		0			0
$199$		−	8.48481e6i		−	1.07667i	−0.842731	−	0.538335i	$-0.819053\pi$
$199$		−	8.48481e6i		−	1.07667i	0.842731	−	0.538335i	$-0.180947\pi$
$200$	−9.43171e6			−1.17896
$201$		0			0
$202$	−3.90443e6			−0.473700
$203$			1.71414e6i			0.204908i
$204$		0			0
$205$		−	47336.3i		−	0.00549455i
$206$		−	9.51823e6i		−	1.08882i
$207$		0			0
$208$	6.42715e6			0.714214
$209$	1.11344e7			1.21963
$210$		0			0
$211$	−2.24487e6			−0.238971			−0.119485	−	0.992836i	$-0.538124\pi$
$211$	−2.24487e6			−0.238971			−0.119485	+	0.992836i	$0.538124\pi$
$212$			1.71077e7i			1.79549i
$213$		0			0
$214$		−	7.52098e6i		−	0.767420i
$215$	−3.14331e6			−0.316280
$216$		0			0
$217$		−	1.29256e7i		−	1.26494i
$218$		−	2.70023e7i		−	2.60634i
$219$		0			0
$220$	−7.32352e6			−0.687784
$221$			3.42043e7i			3.16886i
$222$		0			0
$223$	−7.16592e6			−0.646185			−0.323093	−	0.946367i	$-0.604723\pi$
$223$	−7.16592e6			−0.646185			−0.323093	+	0.946367i	$0.604723\pi$
$224$			9.66086e6i			0.859551i
$225$		0			0
$226$		−	2.21142e7i		−	1.91578i
$227$		−	6.95534e6i		−	0.594622i	−0.954781	−	0.297311i	$-0.903910\pi$
$227$		−	6.95534e6i		−	0.594622i	0.954781	−	0.297311i	$-0.0960898\pi$
$228$		0			0
$229$			2.26736e6i			0.188805i	0.995534	+	0.0944026i	$0.0300941\pi$
$229$			2.26736e6i			0.188805i	−0.995534	+	0.0944026i	$0.969906\pi$
$230$	5.76723e6	+	3.26999e6i	0.474006	+	0.268759i
$231$		0			0
$232$	−2.46696e6			−0.197560
$233$	8.37836e6			0.662356			0.331178	−	0.943568i	$-0.392554\pi$
$233$	8.37836e6			0.662356			0.331178	+	0.943568i	$0.392554\pi$
$234$		0			0
$235$			5.22326e6i			0.402474i
$236$	6.40934e6			0.487615
$237$		0			0
$238$	5.65817e7			4.19706
$239$	1.84843e7			1.35397			0.676986	−	0.735996i	$-0.263286\pi$
$239$	1.84843e7			1.35397			0.676986	+	0.735996i	$0.263286\pi$
$240$		0			0
$241$			1.13802e7i			0.813018i	0.913647	+	0.406509i	$0.133254\pi$
$241$			1.13802e7i			0.813018i	−0.913647	+	0.406509i	$0.866746\pi$
$242$	9.17083e6			0.647087
$243$		0			0
$244$			1.91372e7i			1.31738i
$245$			4.18663e6i			0.284686i
$246$		0			0
$247$			2.69276e7i			1.78693i
$248$	1.86022e7			1.21958
$249$		0			0
$250$			1.61219e7i			1.03180i
$251$			1.24948e7i			0.790149i	0.918649	+	0.395074i	$0.129281\pi$
$251$			1.24948e7i			0.790149i	−0.918649	+	0.395074i	$0.870719\pi$
$252$		0			0
$253$	−1.65933e7	−	9.40832e6i	−1.02464	−	0.580966i
$254$	−4.93111e7			−3.00915
$255$		0			0
$256$	−2.63315e7			−1.56948
$257$	2.74092e6			0.161472			0.0807360	−	0.996736i	$-0.474273\pi$
$257$	2.74092e6			0.161472			0.0807360	+	0.996736i	$0.474273\pi$
$258$		0			0
$259$	3.52732e7			2.03023
$260$		−	1.77114e7i		−	1.00770i
$261$		0			0
$262$	−4.51323e6			−0.250948
$263$			3.24876e7i			1.78587i	0.450181	+	0.892937i	$0.351359\pi$
$263$			3.24876e7i			1.78587i	−0.450181	+	0.892937i	$0.648641\pi$
$264$		0			0
$265$	6.08991e6			0.327245
$266$	4.45445e7			2.36673
$267$		0			0
$268$		−	2.28680e7i		−	1.18802i
$269$	−3.23907e7			−1.66404			−0.832020	−	0.554746i	$-0.812815\pi$
$269$	−3.23907e7			−1.66404			−0.832020	+	0.554746i	$0.812815\pi$
$270$		0			0
$271$	4.38123e6			0.220135			0.110067	−	0.993924i	$-0.464893\pi$
$271$	4.38123e6			0.220135			0.110067	+	0.993924i	$0.464893\pi$
$272$			1.52923e7i			0.759918i
$273$		0			0
$274$			9.85592e6i			0.479121i
$275$		−	2.18893e7i		−	1.05253i
$276$		0			0
$277$	−1.89203e7			−0.890203			−0.445102	−	0.895480i	$-0.646832\pi$
$277$	−1.89203e7			−0.890203			−0.445102	+	0.895480i	$0.646832\pi$
$278$	−6.62192e6			−0.308212
$279$		0			0
$280$	−1.29298e7			−0.589005
$281$			1.82191e7i			0.821124i	0.911833	+	0.410562i	$0.134667\pi$
$281$			1.82191e7i			0.821124i	−0.911833	+	0.410562i	$0.865333\pi$
$282$		0			0
$283$			1.04736e7i			0.462100i	0.972942	+	0.231050i	$0.0742162\pi$
$283$			1.04736e7i			0.462100i	−0.972942	+	0.231050i	$0.925784\pi$
$284$	−1.37609e7			−0.600748
$285$		0			0
$286$			7.94287e7i			3.39531i
$287$			544863.i			0.0230485i
$288$		0			0
$289$	−5.72458e7			−2.37165
$290$			1.98993e6i			0.0815913i
$291$		0			0
$292$	7.55600e7			3.03489
$293$		−	6.92202e6i		−	0.275188i	−0.990489	−	0.137594i	$-0.956063\pi$
$293$		−	6.92202e6i		−	0.275188i	0.990489	−	0.137594i	$-0.0439370\pi$
$294$		0			0
$295$		−	2.28157e6i		−	0.0888726i
$296$			5.07645e7i			1.95742i
$297$		0			0
$298$		−	4.93070e7i		−	1.86320i
$299$	2.27533e7	−	4.01296e7i	0.851199	−	1.50125i
$300$		0			0
$301$	3.61811e7			1.32673
$302$	−3.24453e7			−1.17796
$303$		0			0
$304$			1.20390e7i			0.428519i
$305$	6.81239e6			0.240104
$306$		0			0
$307$	−4.92649e6			−0.170264			−0.0851319	−	0.996370i	$-0.527131\pi$
$307$	−4.92649e6			−0.170264			−0.0851319	+	0.996370i	$0.527131\pi$
$308$	8.42973e7			2.88510
$309$		0			0
$310$		−	1.50052e7i		−	0.503681i
$311$	2.07147e7			0.688647			0.344323	−	0.938851i	$-0.388108\pi$
$311$	2.07147e7			0.688647			0.344323	+	0.938851i	$0.388108\pi$
$312$		0			0
$313$			2.78344e6i			0.0907712i	0.998970	+	0.0453856i	$0.0144517\pi$
$313$			2.78344e6i			0.0907712i	−0.998970	+	0.0453856i	$0.985548\pi$
$314$		−	4.88908e7i		−	1.57920i
$315$		0			0
$316$		−	5.25285e7i		−	1.66469i
$317$	−1.45950e7			−0.458171			−0.229085	−	0.973406i	$-0.573574\pi$
$317$	−1.45950e7			−0.458171			−0.229085	+	0.973406i	$0.573574\pi$
$318$		0			0
$319$		−	5.72537e6i		−	0.176373i
$320$			1.56392e7i			0.477270i
$321$		0			0
$322$	−6.63836e7	−	3.76392e7i	−1.98835	−	1.12739i
$323$	−6.40698e7			−1.90128
$324$		0			0
$325$	5.29376e7			1.54211
$326$	3.39711e7			0.980521
$327$		0			0
$328$	−784157.			−0.0222219
$329$		−	6.01223e7i		−	1.68829i
$330$		0			0
$331$	2.33621e6			0.0644211			0.0322105	−	0.999481i	$-0.489745\pi$
$331$	2.33621e6			0.0644211			0.0322105	+	0.999481i	$0.489745\pi$
$332$			3.35716e7i			0.917399i
$333$		0			0
$334$	−6.80111e7			−1.82533
$335$	−8.14047e6			−0.216528
$336$		0			0
$337$			1.06893e7i			0.279293i	0.990201	+	0.139647i	$0.0445967\pi$
$337$			1.06893e7i			0.279293i	−0.990201	+	0.139647i	$0.955403\pi$
$338$	−1.27595e8			−3.30432
$339$		0			0
$340$	4.21413e7			1.07219
$341$			4.31724e7i			1.08879i
$342$		0			0
$343$			7.03188e6i			0.174257i
$344$			5.20711e7i			1.27915i
$345$		0			0
$346$	2.86416e6			0.0691462
$347$	2.24727e7			0.537857			0.268929	−	0.963160i	$-0.413330\pi$
$347$	2.24727e7			0.537857			0.268929	+	0.963160i	$0.413330\pi$
$348$		0			0
$349$	4.55946e7			1.07260			0.536299	−	0.844028i	$-0.319822\pi$
$349$	4.55946e7			1.07260			0.536299	+	0.844028i	$0.319822\pi$
$350$		−	8.75709e7i		−	2.04247i
$351$		0			0
$352$		−	3.22680e7i		−	0.739851i
$353$	6.29900e7			1.43201			0.716007	−	0.698093i	$-0.245968\pi$
$353$	6.29900e7			1.43201			0.716007	+	0.698093i	$0.245968\pi$
$354$		0			0
$355$			4.89855e6i			0.109492i
$356$		−	4.93108e6i		−	0.109293i
$357$		0			0
$358$	−1.32906e8			−2.89664
$359$		−	6.83335e7i		−	1.47690i	−0.674309	−	0.738449i	$-0.735559\pi$
$359$		−	6.83335e7i		−	1.47690i	0.674309	−	0.738449i	$-0.264441\pi$
$360$		0			0
$361$	−3.39362e6			−0.0721342
$362$			6.74774e6i			0.142244i
$363$		0			0
$364$			2.03867e8i			4.22709i
$365$		−	2.68975e7i		−	0.553138i
$366$		0			0
$367$		−	7.33714e7i		−	1.48432i	−0.670221	−	0.742162i	$-0.733801\pi$
$367$		−	7.33714e7i		−	1.48432i	0.670221	−	0.742162i	$-0.266199\pi$
$368$	1.01727e7	−	1.79415e7i	0.204124	−	0.360010i
$369$		0			0
$370$	4.09483e7			0.808408
$371$	−7.00978e7			−1.37272
$372$		0			0
$373$			8.30679e7i			1.60069i	0.599541	+	0.800344i	$0.295350\pi$
$373$			8.30679e7i			1.60069i	−0.599541	+	0.800344i	$0.704650\pi$
$374$	−1.88987e8			−3.61258
$375$		0			0
$376$	8.65268e7			1.62775
$377$	1.38464e7			0.258412
$378$		0			0
$379$			6.89177e7i			1.26594i	0.774176	+	0.632970i	$0.218164\pi$
$379$			6.89177e7i			1.26594i	−0.774176	+	0.632970i	$0.781836\pi$
$380$	3.31761e7			0.604609
$381$		0			0
$382$		−	1.04922e8i		−	1.88225i
$383$		−	7.07466e7i		−	1.25924i	−0.776902	−	0.629621i	$-0.783210\pi$
$383$		−	7.07466e7i		−	1.25924i	0.776902	−	0.629621i	$-0.216790\pi$
$384$		0			0
$385$		−	3.00078e7i		−	0.525838i
$386$	1.71232e8			2.97730
$387$		0			0
$388$			9.81353e7i			1.68008i
$389$			1.19445e7i			0.202917i	0.994840	+	0.101458i	$0.0323509\pi$
$389$			1.19445e7i			0.202917i	−0.994840	+	0.101458i	$0.967649\pi$
$390$		0			0
$391$	9.54818e7	+	5.41377e7i	1.59731	+	0.905669i
$392$	6.93542e7			1.15137
$393$		0			0
$394$	1.49719e8			2.44787
$395$	−1.86989e7			−0.303406
$396$		0			0
$397$	−1.35684e7			−0.216849			−0.108425	−	0.994105i	$-0.534581\pi$
$397$	−1.35684e7			−0.216849			−0.108425	+	0.994105i	$0.534581\pi$
$398$			1.13377e8i			1.79836i
$399$		0			0
$400$	2.36677e7			0.369809
$401$		−	6.30703e7i		−	0.978119i	−0.872250	−	0.489059i	$-0.837340\pi$
$401$		−	6.30703e7i		−	0.978119i	0.872250	−	0.489059i	$-0.162660\pi$
$402$		0			0
$403$	−1.04409e8			−1.59523
$404$	3.34721e7			0.507620
$405$		0			0
$406$		−	2.29051e7i		−	0.342258i
$407$	−1.17815e8			−1.74750
$408$		0			0
$409$	6.92270e6			0.101183			0.0505913	−	0.998719i	$-0.483889\pi$
$409$	6.92270e6			0.101183			0.0505913	+	0.998719i	$0.483889\pi$
$410$			632526.i			0.00917756i
$411$		0			0
$412$			8.15984e7i			1.16678i
$413$			2.62620e7i			0.372801i
$414$		0			0
$415$	1.19507e7			0.167205
$416$	7.80377e7			1.08399
$417$		0			0
$418$	−1.48782e8			−2.03714
$419$			3.86181e7i			0.524987i	0.964934	+	0.262494i	$0.0845449\pi$
$419$			3.86181e7i			0.524987i	−0.964934	+	0.262494i	$0.915455\pi$
$420$		0			0
$421$			5.59677e7i			0.750052i	0.927014	+	0.375026i	$0.122366\pi$
$421$			5.59677e7i			0.750052i	−0.927014	+	0.375026i	$0.877634\pi$
$422$	2.99969e7			0.399153
$423$		0			0
$424$		−	1.00883e8i		−	1.32349i
$425$			1.25956e8i			1.64079i
$426$		0			0
$427$	−7.84139e7			−1.00719
$428$			6.44762e7i			0.822372i
$429$		0			0
$430$	4.20022e7			0.528283
$431$			9.77946e7i			1.22147i	0.791835	+	0.610735i	$0.209126\pi$
$431$			9.77946e7i			1.22147i	−0.791835	+	0.610735i	$0.790874\pi$
$432$		0			0
$433$		−	1.55568e8i		−	1.91627i	−0.286315	−	0.958136i	$-0.592430\pi$
$433$		−	1.55568e8i		−	1.91627i	0.286315	−	0.958136i	$-0.407570\pi$
$434$			1.72717e8i			2.11283i
$435$		0			0
$436$			2.31486e8i			2.79297i
$437$	7.51689e7	+	4.26204e7i	0.900728	+	0.510708i
$438$		0			0
$439$	1.32635e7			0.156770			0.0783851	−	0.996923i	$-0.475024\pi$
$439$	1.32635e7			0.156770			0.0783851	+	0.996923i	$0.475024\pi$
$440$	4.31866e7			0.506980
$441$		0			0
$442$		−	4.57052e8i		−	5.29296i
$443$	1.32324e6			0.0152205			0.00761023	−	0.999971i	$-0.497578\pi$
$443$	1.32324e6			0.0152205			0.00761023	+	0.999971i	$0.497578\pi$
$444$		0			0
$445$	−1.75535e6			−0.0199197
$446$	9.57539e7			1.07932
$447$		0			0
$448$		−	1.80015e8i		−	2.00205i
$449$	8.63709e7			0.954176			0.477088	−	0.878855i	$-0.341692\pi$
$449$	8.63709e7			0.954176			0.477088	+	0.878855i	$0.341692\pi$
$450$		0			0
$451$		−	1.81989e6i		−	0.0198388i
$452$			1.89582e8i			2.05296i
$453$		0			0
$454$			9.29401e7i			0.993197i
$455$	7.25716e7			0.770428
$456$		0			0
$457$			5.19478e7i			0.544275i	0.962258	+	0.272138i	$0.0877306\pi$
$457$			5.19478e7i			0.544275i	−0.962258	+	0.272138i	$0.912269\pi$
$458$		−	3.02974e7i		−	0.315362i
$459$		0			0
$460$	−4.94416e7	−	2.80331e7i	−0.507948	−	0.288004i
$461$	4.67094e7			0.476762			0.238381	−	0.971172i	$-0.423383\pi$
$461$	4.67094e7			0.476762			0.238381	+	0.971172i	$0.423383\pi$
$462$		0			0
$463$	5.63404e7			0.567646			0.283823	−	0.958877i	$-0.408397\pi$
$463$	5.63404e7			0.567646			0.283823	+	0.958877i	$0.408397\pi$
$464$	6.19054e6			0.0619690
$465$		0			0
$466$	−1.11955e8			−1.10633
$467$		−	1.36113e8i		−	1.33643i	−0.743966	−	0.668217i	$-0.767058\pi$
$467$		−	1.36113e8i		−	1.33643i	0.743966	−	0.668217i	$-0.232942\pi$
$468$		0			0
$469$	9.37008e7			0.908290
$470$		−	6.97953e7i		−	0.672253i
$471$		0			0
$472$	−3.77957e7			−0.359432
$473$	−1.20848e8			−1.14197
$474$		0			0
$475$			9.91601e7i			0.925243i
$476$	−4.85067e8			−4.49760
$477$		0			0
$478$	−2.46995e8			−2.26154
$479$		−	5.92042e7i		−	0.538699i	−0.963043	−	0.269349i	$-0.913191\pi$
$479$		−	5.92042e7i		−	0.538699i	0.963043	−	0.269349i	$-0.0868086\pi$
$480$		0			0
$481$		−	2.84927e8i		−	2.56035i
$482$		−	1.52067e8i		−	1.35798i
$483$		0			0
$484$	−7.86201e7			−0.693422
$485$	3.49338e7			0.306211
$486$		0			0
$487$	−1.88221e7			−0.162960			−0.0814798	−	0.996675i	$-0.525965\pi$
$487$	−1.88221e7			−0.162960			−0.0814798	+	0.996675i	$0.525965\pi$
$488$		−	1.12852e8i		−	0.971066i
$489$		0			0
$490$		−	5.59434e7i		−	0.475511i
$491$	−5.97827e7			−0.505046			−0.252523	−	0.967591i	$-0.581260\pi$
$491$	−5.97827e7			−0.505046			−0.252523	+	0.967591i	$0.581260\pi$
$492$		0			0
$493$			3.29451e7i			0.274948i
$494$		−	3.59818e8i		−	2.98471i
$495$		0			0
$496$	−4.66801e7			−0.382548
$497$		−	5.63847e7i		−	0.459296i
$498$		0			0
$499$	−7.60944e7			−0.612423			−0.306211	−	0.951964i	$-0.599061\pi$
$499$	−7.60944e7			−0.612423			−0.306211	+	0.951964i	$0.599061\pi$
$500$		−	1.38211e8i		−	1.10569i
$501$		0			0
$502$		−	1.66961e8i		−	1.31979i
$503$		−	1.17172e8i		−	0.920703i	−0.887737	−	0.460352i	$-0.847723\pi$
$503$		−	1.17172e8i		−	0.920703i	0.887737	−	0.460352i	$-0.152277\pi$
$504$		0			0
$505$		−	1.19152e7i		−	0.0925186i
$506$	2.21726e8	+	1.25718e8i	1.71146	+	0.970387i
$507$		0			0
$508$	4.22737e8			3.22462
$509$	−1.36371e8			−1.03412			−0.517059	−	0.855950i	$-0.672973\pi$
$509$	−1.36371e8			−1.03412			−0.517059	+	0.855950i	$0.672973\pi$
$510$		0			0
$511$			3.09604e8i			2.32030i
$512$	1.08176e8			0.805976
$513$		0			0
$514$	−3.66253e7			−0.269707
$515$	2.90470e7			0.212657
$516$		0			0
$517$			2.00813e8i			1.45318i
$518$	−4.71335e8			−3.39110
$519$		0			0
$520$			1.04444e8i			0.742799i
$521$			1.08762e8i			0.769068i	0.923111	+	0.384534i	$0.125638\pi$
$521$			1.08762e8i			0.769068i	−0.923111	+	0.384534i	$0.874362\pi$
$522$		0			0
$523$			1.00555e7i			0.0702908i	0.999382	+	0.0351454i	$0.0111894\pi$
$523$			1.00555e7i			0.0702908i	−0.999382	+	0.0351454i	$0.988811\pi$
$524$	3.86913e7			0.268918
$525$		0			0
$526$		−	4.34113e8i		−	2.98295i
$527$		−	2.48424e8i		−	1.69731i
$528$		0			0
$529$	−7.60091e7	−	1.27032e8i	−0.513451	−	0.858119i
$530$	−8.13758e7			−0.546598
$531$		0			0
$532$	−3.81873e8			−2.53620
$533$	4.40126e6			0.0290666
$534$		0			0
$535$	2.29520e7			0.149885
$536$			1.34852e8i			0.875717i
$537$		0			0
$538$	4.32818e8			2.77945
$539$			1.60959e8i			1.02789i
$540$		0			0
$541$	−1.74284e8			−1.10069			−0.550347	−	0.834936i	$-0.685505\pi$
$541$	−1.74284e8			−1.10069			−0.550347	+	0.834936i	$0.685505\pi$
$542$	−5.85438e7			−0.367691
$543$		0			0
$544$			1.85678e8i			1.15336i
$545$	8.24035e7			0.509045
$546$		0			0
$547$	−1.67420e8			−1.02293			−0.511465	−	0.859304i	$-0.670897\pi$
$547$	−1.67420e8			−1.02293			−0.511465	+	0.859304i	$0.670897\pi$
$548$		−	8.44933e7i		−	0.513429i
$549$		0			0
$550$			2.92493e8i			1.75804i
$551$			2.59363e7i			0.155044i
$552$		0			0
$553$	2.15233e8			1.27272
$554$	2.52821e8			1.48691
$555$		0			0
$556$	5.67687e7			0.330282
$557$			1.38029e8i			0.798736i	0.916791	+	0.399368i	$0.130770\pi$
$557$			1.38029e8i			0.798736i	−0.916791	+	0.399368i	$0.869230\pi$
$558$		0			0
$559$		−	2.92261e8i		−	1.67315i
$560$	3.24459e7			0.184755
$561$		0			0
$562$		−	2.43451e8i		−	1.37152i
$563$			3.21701e8i			1.80271i	0.433077	+	0.901357i	$0.357428\pi$
$563$			3.21701e8i			1.80271i	−0.433077	+	0.901357i	$0.642572\pi$
$564$		0			0
$565$	6.74865e7			0.374172
$566$		−	1.39952e8i		−	0.771847i
$567$		0			0
$568$	8.11478e7			0.442824
$569$		−	7.25247e7i		−	0.393685i	−0.980435	−	0.196843i	$-0.936931\pi$
$569$		−	7.25247e7i		−	0.393685i	0.980435	−	0.196843i	$-0.0630688\pi$
$570$		0			0
$571$			3.26457e8i			1.75355i	0.480903	+	0.876774i	$0.340309\pi$
$571$			3.26457e8i			1.75355i	−0.480903	+	0.876774i	$0.659691\pi$
$572$		−	6.80930e8i		−	3.63843i
$573$		0			0
$574$		−	7.28069e6i		−	0.0384979i
$575$	8.37883e7	−	1.47776e8i	0.440737	−	0.777321i
$576$		0			0
$577$	2.03247e8			1.05803			0.529014	−	0.848613i	$-0.322562\pi$
$577$	2.03247e8			1.05803			0.529014	+	0.848613i	$0.322562\pi$
$578$	7.64942e8			3.96136
$579$		0			0
$580$		−	1.70594e7i		−	0.0874337i
$581$	−1.37558e8			−0.701388
$582$		0			0
$583$	2.34132e8			1.18156
$584$	−4.45575e8			−2.23709
$585$		0			0
$586$			9.24948e7i			0.459647i
$587$	−3.41225e8			−1.68704			−0.843522	−	0.537094i	$-0.819522\pi$
$587$	−3.41225e8			−1.68704			−0.843522	+	0.537094i	$0.819522\pi$
$588$		0			0
$589$		−	1.95574e8i		−	0.957118i
$590$			3.04873e7i			0.148444i
$591$		0			0
$592$		−	1.27387e8i		−	0.613990i
$593$	4.85029e7			0.232597			0.116298	−	0.993214i	$-0.462897\pi$
$593$	4.85029e7			0.232597			0.116298	+	0.993214i	$0.462897\pi$
$594$		0			0
$595$			1.72672e8i			0.819730i
$596$			4.22701e8i			1.99662i
$597$		0			0
$598$	−3.04039e8	+	5.36229e8i	−1.42176	+	2.50753i
$599$	2.09120e8			0.973005			0.486502	−	0.873679i	$-0.338272\pi$
$599$	2.09120e8			0.973005			0.486502	+	0.873679i	$0.338272\pi$
$600$		0			0
$601$	−4.08234e8			−1.88056			−0.940278	−	0.340409i	$-0.889435\pi$
$601$	−4.08234e8			−1.88056			−0.940278	+	0.340409i	$0.889435\pi$
$602$	−4.83466e8			−2.21603
$603$		0			0
$604$	2.78149e8			1.26231
$605$			2.79869e7i			0.126383i
$606$		0			0
$607$	3.04590e8			1.36191			0.680957	−	0.732323i	$-0.261564\pi$
$607$	3.04590e8			1.36191			0.680957	+	0.732323i	$0.261564\pi$
$608$			1.46176e8i			0.650379i
$609$		0			0
$610$	−9.10299e7			−0.401046
$611$	−4.85651e8			−2.12912
$612$		0			0
$613$		−	5.70085e7i		−	0.247491i	−0.992314	−	0.123745i	$-0.960509\pi$
$613$		−	5.70085e7i		−	0.247491i	0.992314	−	0.123745i	$-0.0394906\pi$
$614$	6.58298e7			0.284392
$615$		0			0
$616$	−4.97099e8			−2.12667
$617$		−	3.77637e7i		−	0.160775i	−0.996764	−	0.0803877i	$-0.974384\pi$
$617$		−	3.77637e7i		−	0.160775i	0.996764	−	0.0803877i	$-0.0256158\pi$
$618$		0			0
$619$		−	3.40594e7i		−	0.143604i	−0.997419	−	0.0718018i	$-0.977125\pi$
$619$		−	3.40594e7i		−	0.143604i	0.997419	−	0.0718018i	$-0.0228749\pi$
$620$			1.28637e8i			0.539747i
$621$		0			0
$622$	−2.76798e8			−1.15025
$623$	2.02049e7			0.0835588
$624$		0			0
$625$	1.68958e8			0.692054
$626$		−	3.71934e7i		−	0.151615i
$627$		0			0
$628$			4.19133e8i			1.69228i
$629$	6.77937e8			2.72419
$630$		0			0
$631$		−	2.37604e8i		−	0.945725i	−0.881136	−	0.472863i	$-0.843221\pi$
$631$		−	2.37604e8i		−	0.945725i	0.881136	−	0.472863i	$-0.156779\pi$
$632$			3.09759e8i			1.22708i
$633$		0			0
$634$	1.95025e8			0.765283
$635$		−	1.50484e8i		−	0.587718i
$636$		0			0
$637$	−3.89266e8			−1.50601
$638$			7.65047e7i			0.294595i
$639$		0			0
$640$		−	1.55261e8i		−	0.592275i
$641$			4.50113e8i			1.70902i	0.519433	+	0.854511i	$0.326143\pi$
$641$			4.50113e8i			1.70902i	−0.519433	+	0.854511i	$0.673857\pi$
$642$		0			0
$643$		−	1.93945e8i		−	0.729533i	−0.931099	−	0.364767i	$-0.881149\pi$
$643$		−	1.93945e8i		−	0.729533i	0.931099	−	0.364767i	$-0.118851\pi$
$644$	5.69097e8	+	3.22675e8i	2.13073	+	1.20811i
$645$		0			0
$646$	8.56126e8			3.17571
$647$	2.17106e8			0.801601			0.400800	−	0.916165i	$-0.368732\pi$
$647$	2.17106e8			0.801601			0.400800	+	0.916165i	$0.368732\pi$
$648$		0			0
$649$		−	8.77170e7i		−	0.320885i
$650$	−7.07373e8			−2.57578
$651$		0			0
$652$	−2.91229e8			−1.05073
$653$	4.36163e8			1.56642			0.783212	−	0.621755i	$-0.213580\pi$
$653$	4.36163e8			1.56642			0.783212	+	0.621755i	$0.213580\pi$
$654$		0			0
$655$		−	1.37732e7i		−	0.0490128i
$656$	1.96775e6			0.00697040
$657$		0			0
$658$			8.03378e8i			2.81996i
$659$			1.46383e8i			0.511486i	0.966745	+	0.255743i	$0.0823200\pi$
$659$			1.46383e8i			0.511486i	−0.966745	+	0.255743i	$0.917680\pi$
$660$		0			0
$661$			3.35799e8i			1.16272i	0.813647	+	0.581359i	$0.197479\pi$
$661$			3.35799e8i			1.16272i	−0.813647	+	0.581359i	$0.802521\pi$
$662$	−3.12174e7			−0.107603
$663$		0			0
$664$		−	1.97971e8i		−	0.676235i
$665$			1.35937e8i			0.462247i
$666$		0			0
$667$	2.19157e7	−	3.86523e7i	0.0738546	−	0.130256i
$668$	5.83049e8			1.95603
$669$		0			0
$670$	1.08776e8			0.361668
$671$	2.61908e8			0.866925
$672$		0			0
$673$	−1.42716e8			−0.468196			−0.234098	−	0.972213i	$-0.575214\pi$
$673$	−1.42716e8			−0.468196			−0.234098	+	0.972213i	$0.575214\pi$
$674$		−	1.42835e8i		−	0.466504i
$675$		0			0
$676$	1.09385e9			3.54093
$677$		−	4.50766e8i		−	1.45273i	−0.687308	−	0.726366i	$-0.741208\pi$
$677$		−	4.50766e8i		−	1.45273i	0.687308	−	0.726366i	$-0.258792\pi$
$678$		0			0
$679$	−4.02105e8			−1.28449
$680$	−2.48506e8			−0.790333
$681$		0			0
$682$		−	5.76887e8i		−	1.81860i
$683$	−2.27098e8			−0.712773			−0.356387	−	0.934339i	$-0.615991\pi$
$683$	−2.27098e8			−0.712773			−0.356387	+	0.934339i	$0.615991\pi$
$684$		0			0
$685$	−3.00775e7			−0.0935773
$686$		−	9.39628e7i		−	0.291061i
$687$		0			0
$688$		−	1.30666e8i		−	0.401234i
$689$			5.66231e8i			1.73115i
$690$		0			0
$691$	5.21427e8			1.58037			0.790186	−	0.612867i	$-0.209984\pi$
$691$	5.21427e8			1.58037			0.790186	+	0.612867i	$0.209984\pi$
$692$	−2.45540e7			−0.0740975
$693$		0			0
$694$	−3.00289e8			−0.898383
$695$		−	2.02083e7i		−	0.0601970i
$696$		0			0
$697$			1.04721e7i			0.0309267i
$698$	−6.09254e8			−1.79156
$699$		0			0
$700$			7.50732e8i			2.18872i
$701$			5.08788e7i			0.147701i	0.997269	+	0.0738503i	$0.0235287\pi$
$701$			5.08788e7i			0.147701i	−0.997269	+	0.0738503i	$0.976471\pi$
$702$		0			0
$703$	5.33711e8			1.53617
$704$			6.01263e8i			1.72324i
$705$		0			0
$706$	−8.41697e8			−2.39189
$707$			1.37150e8i			0.388096i
$708$		0			0
$709$		−	4.19730e8i		−	1.17769i	−0.808245	−	0.588846i	$-0.799583\pi$
$709$		−	4.19730e8i		−	1.17769i	0.808245	−	0.588846i	$-0.200417\pi$
$710$		−	6.54564e7i		−	0.182885i
$711$		0			0
$712$			2.90785e7i			0.0805622i
$713$	−1.65256e8	+	2.91460e8i	−0.455921	+	0.804100i
$714$		0			0
$715$	−2.42394e8			−0.663139
$716$	1.13938e9			3.10406
$717$		0			0
$718$			9.13100e8i			2.46686i
$719$	2.31060e8			0.621639			0.310820	−	0.950469i	$-0.399396\pi$
$719$	2.31060e8			0.621639			0.310820	+	0.950469i	$0.399396\pi$
$720$		0			0
$721$	−3.34346e8			−0.892051
$722$	4.53469e7			0.120486
$723$		0			0
$724$		−	5.78473e7i		−	0.152429i
$725$	5.09888e7			0.133801
$726$		0			0
$727$		−	6.06964e8i		−	1.57965i	−0.613335	−	0.789823i	$-0.710172\pi$
$727$		−	6.06964e8i		−	1.57965i	0.613335	−	0.789823i	$-0.289828\pi$
$728$		−	1.20220e9i		−	3.11588i
$729$		0			0
$730$			3.59415e8i			0.923907i
$731$	6.95385e8			1.78022
$732$		0			0
$733$			9.92159e7i			0.251924i	0.992035	+	0.125962i	$0.0402017\pi$
$733$			9.92159e7i			0.251924i	−0.992035	+	0.125962i	$0.959798\pi$
$734$			9.80418e8i			2.47927i
$735$		0			0
$736$	1.23516e8	−	2.17844e8i	0.309807	−	0.546401i
$737$	−3.12968e8			−0.781802
$738$		0			0
$739$	−9.18743e7			−0.227646			−0.113823	−	0.993501i	$-0.536310\pi$
$739$	−9.18743e7			−0.227646			−0.113823	+	0.993501i	$0.536310\pi$
$740$	−3.51043e8			−0.866295
$741$		0			0
$742$	9.36675e8			2.29286
$743$			6.62329e8i			1.61476i	0.590034	+	0.807379i	$0.299114\pi$
$743$			6.62329e8i			1.61476i	−0.590034	+	0.807379i	$0.700886\pi$
$744$		0			0
$745$	1.50471e8			0.363902
$746$		−	1.10999e9i		−	2.67363i
$747$		0			0
$748$	1.62016e9			3.87126
$749$	−2.64188e8			−0.628736
$750$		0			0
$751$		−	3.19510e8i		−	0.754335i	−0.926145	−	0.377167i	$-0.876898\pi$
$751$		−	3.19510e8i		−	0.754335i	0.926145	−	0.377167i	$-0.123102\pi$
$752$	−2.17129e8			−0.510580
$753$		0			0
$754$	−1.85021e8			−0.431625
$755$		−	9.90141e7i		−	0.230068i
$756$		0			0
$757$			5.19511e8i			1.19759i	0.800903	+	0.598794i	$0.204353\pi$
$757$			5.19511e8i			1.19759i	−0.800903	+	0.598794i	$0.795647\pi$
$758$		−	9.20906e8i		−	2.11450i
$759$		0			0
$760$	−1.95638e8			−0.445670
$761$	−3.04486e8			−0.690896			−0.345448	−	0.938438i	$-0.612273\pi$
$761$	−3.04486e8			−0.690896			−0.345448	+	0.938438i	$0.612273\pi$
$762$		0			0
$763$	−9.48505e8			−2.13533
$764$			8.99482e8i			2.01703i
$765$		0			0
$766$			9.45345e8i			2.10331i
$767$	2.12137e8			0.470143
$768$		0			0
$769$			1.99259e8i			0.438167i	0.975706	+	0.219083i	$0.0703067\pi$
$769$			1.99259e8i			0.438167i	−0.975706	+	0.219083i	$0.929693\pi$
$770$			4.00976e8i			0.878307i
$771$		0			0
$772$	−1.46795e9			−3.19050
$773$			3.83867e7i			0.0831079i	0.999136	+	0.0415539i	$0.0132308\pi$
$773$			3.83867e7i			0.0831079i	−0.999136	+	0.0415539i	$0.986769\pi$
$774$		0			0
$775$	−3.84483e8			−0.825985
$776$		−	5.78701e8i		−	1.23842i
$777$		0			0
$778$		−	1.59607e8i		−	0.338932i
$779$			8.24421e6i			0.0174396i
$780$		0			0
$781$			1.88329e8i			0.395334i
$782$	−1.27587e9	−	7.23410e8i	−2.66799	−	1.51274i
$783$		0			0
$784$	−1.74036e8			−0.361153
$785$	1.49201e8			0.308435
$786$		0			0
$787$		−	2.15211e7i		−	0.0441510i	−0.999756	−	0.0220755i	$-0.992973\pi$
$787$		−	2.15211e7i		−	0.0441510i	0.999756	−	0.0220755i	$-0.00702743\pi$
$788$	−1.28352e9			−2.62315
$789$		0			0
$790$	2.49862e8			0.506779
$791$	−7.76803e8			−1.56957
$792$		0			0
$793$			6.33406e8i			1.27017i
$794$	1.81307e8			0.362203
$795$		0			0
$796$		−	9.71968e8i		−	1.92714i
$797$		−	2.04730e8i		−	0.404396i	−0.979345	−	0.202198i	$-0.935191\pi$
$797$		−	2.04730e8i		−	0.404396i	0.979345	−	0.202198i	$-0.0648085\pi$
$798$		0			0
$799$		−	1.15553e9i		−	2.26537i
$800$	2.87371e8			0.561272
$801$		0			0
$802$			8.42771e8i			1.63375i
$803$		−	1.03410e9i		−	1.99717i
$804$		0			0
$805$	1.14864e8	−	2.02585e8i	0.220190	−	0.388346i
$806$	1.39516e9			2.66451
$807$		0			0
$808$	−1.97384e8			−0.374178
$809$	−2.79419e8			−0.527729			−0.263865	−	0.964560i	$-0.584997\pi$
$809$	−2.79419e8			−0.527729			−0.263865	+	0.964560i	$0.584997\pi$
$810$		0			0
$811$	1.40447e8			0.263299			0.131650	−	0.991296i	$-0.457973\pi$
$811$	1.40447e8			0.263299			0.131650	+	0.991296i	$0.457973\pi$
$812$			1.96362e8i			0.366766i
$813$		0			0
$814$	1.57429e9			2.91886
$815$			1.03670e8i			0.191506i
$816$		0			0
$817$	5.47448e8			1.00387
$818$	−9.25039e7			−0.169005
$819$		0			0
$820$		−	5.42255e6i		−	0.00983472i
$821$	−7.91944e8			−1.43108			−0.715542	−	0.698570i	$-0.753820\pi$
$821$	−7.91944e8			−1.43108			−0.715542	+	0.698570i	$0.753820\pi$
$822$		0			0
$823$	−4.21544e8			−0.756212			−0.378106	−	0.925762i	$-0.623424\pi$
$823$	−4.21544e8			−0.756212			−0.378106	+	0.925762i	$0.623424\pi$
$824$		−	4.81183e8i		−	0.860061i
$825$		0			0
$826$		−	3.50923e8i		−	0.622690i
$827$		−	6.25183e8i		−	1.10533i	−0.833404	−	0.552664i	$-0.813611\pi$
$827$		−	6.25183e8i		−	1.10533i	0.833404	−	0.552664i	$-0.186389\pi$
$828$		0			0
$829$	5.46404e8			0.959069			0.479535	−	0.877523i	$-0.340805\pi$
$829$	5.46404e8			0.959069			0.479535	+	0.877523i	$0.340805\pi$
$830$	−1.59690e8			−0.279282
$831$		0			0
$832$	−1.45411e9			−2.52480
$833$		−	9.26194e8i		−	1.60239i
$834$		0			0
$835$		−	2.07551e8i		−	0.356505i
$836$	1.27548e9			2.18301
$837$		0			0
$838$		−	5.16031e8i		−	0.876887i
$839$		−	5.10945e8i		−	0.865143i	−0.901600	−	0.432571i	$-0.857606\pi$
$839$		−	5.10945e8i		−	0.865143i	0.901600	−	0.432571i	$-0.142394\pi$
$840$		0			0
$841$	−5.81487e8			−0.977579
$842$		−	7.47863e8i		−	1.25281i
$843$		0			0
$844$	−2.57159e8			−0.427734
$845$		−	3.89383e8i		−	0.645368i
$846$		0			0
$847$		−	3.22142e8i		−	0.530149i
$848$			2.53155e8i			0.415144i
$849$		0			0
$850$		−	1.68308e9i		−	2.74061i
$851$	−7.95378e8	−	4.50976e8i	−1.29058	−	0.731753i
$852$		0			0
$853$	5.93821e8			0.956772			0.478386	−	0.878150i	$-0.341222\pi$
$853$	5.93821e8			0.956772			0.478386	+	0.878150i	$0.341222\pi$
$854$	1.04780e9			1.68230
$855$		0			0
$856$		−	3.80214e8i		−	0.606188i
$857$	−2.88254e8			−0.457965			−0.228983	−	0.973431i	$-0.573540\pi$
$857$	−2.88254e8			−0.457965			−0.228983	+	0.973431i	$0.573540\pi$
$858$		0			0
$859$	−6.27706e8			−0.990323			−0.495161	−	0.868801i	$-0.664891\pi$
$859$	−6.27706e8			−0.990323			−0.495161	+	0.868801i	$0.664891\pi$
$860$	−3.60079e8			−0.566112
$861$		0			0
$862$		−	1.30677e9i		−	2.04022i
$863$	7.29580e8			1.13512			0.567558	−	0.823333i	$-0.307888\pi$
$863$	7.29580e8			1.13512			0.567558	+	0.823333i	$0.307888\pi$
$864$		0			0
$865$			8.74062e6i			0.0135050i
$866$			2.07876e9i			3.20075i
$867$		0			0
$868$		−	1.48067e9i		−	2.26412i
$869$	−7.18894e8			−1.09548
$870$		0			0
$871$		−	7.56889e8i		−	1.14545i
$872$		−	1.36507e9i		−	2.05876i
$873$		0			0
$874$	−1.00444e9	−	5.69511e8i	−1.50449	−	0.853037i
$875$	5.66313e8			0.845342
$876$		0			0
$877$	2.96672e8			0.439822			0.219911	−	0.975520i	$-0.429423\pi$
$877$	2.96672e8			0.439822			0.219911	+	0.975520i	$0.429423\pi$
$878$	−1.77232e8			−0.261853
$879$		0			0
$880$	−1.08372e8			−0.159026
$881$		−	1.13251e8i		−	0.165621i	−0.996565	−	0.0828103i	$-0.973610\pi$
$881$		−	1.13251e8i		−	0.165621i	0.996565	−	0.0828103i	$-0.0263896\pi$
$882$		0			0
$883$	1.21809e8			0.176929			0.0884643	−	0.996079i	$-0.471804\pi$
$883$	1.21809e8			0.176929			0.0884643	+	0.996079i	$0.471804\pi$
$884$			3.91823e9i			5.67196i
$885$		0			0
$886$	−1.76817e7			−0.0254228
$887$	−4.35800e8			−0.624477			−0.312238	−	0.950004i	$-0.601079\pi$
$887$	−4.35800e8			−0.624477			−0.312238	+	0.950004i	$0.601079\pi$
$888$		0			0
$889$			1.73214e9i			2.46535i
$890$	2.34556e7			0.0332719
$891$		0			0
$892$	−8.20883e8			−1.15661
$893$		−	9.09698e8i		−	1.27745i
$894$		0			0
$895$		−	4.05592e8i		−	0.565744i
$896$			1.78714e9i			2.48447i
$897$		0			0
$898$	−1.15412e9			−1.59376
$899$	−1.00566e8			−0.138411
$900$		0			0
$901$	−1.34725e9			−1.84193
$902$			2.43180e7i			0.0331367i
$903$		0			0
$904$		−	1.11796e9i		−	1.51328i
$905$	−2.05922e7			−0.0277816
$906$		0			0
$907$			2.67950e8i			0.359114i	0.983748	+	0.179557i	$0.0574664\pi$
$907$			2.67950e8i			0.359114i	−0.983748	+	0.179557i	$0.942534\pi$
$908$		−	7.96761e8i		−	1.06432i
$909$		0			0
$910$	−9.69731e8			−1.28685
$911$			2.28173e8i			0.301792i	0.988550	+	0.150896i	$0.0482159\pi$
$911$			2.28173e8i			0.301792i	−0.988550	+	0.150896i	$0.951784\pi$
$912$		0			0
$913$	4.59455e8			0.603713
$914$		−	6.94147e8i		−	0.909103i
$915$		0			0
$916$			2.59735e8i			0.337943i
$917$			1.58536e8i			0.205598i
$918$		0			0
$919$			1.06953e9i			1.37799i	0.724765	+	0.688996i	$0.241948\pi$
$919$			1.06953e9i			1.37799i	−0.724765	+	0.688996i	$0.758052\pi$
$920$	2.91556e8	+	1.65311e8i	0.374419	+	0.212294i
$921$		0			0
$922$	−6.24150e8			−0.796336
$923$	−4.55460e8			−0.579222
$924$		0			0
$925$		−	1.04923e9i		−	1.32571i
$926$	−7.52844e8			−0.948139
$927$		0			0
$928$	7.51649e7			0.0940527
$929$	9.78729e8			1.22072			0.610359	−	0.792125i	$-0.291025\pi$
$929$	9.78729e8			1.22072			0.610359	+	0.792125i	$0.291025\pi$
$930$		0			0
$931$		−	7.29154e8i		−	0.903588i
$932$	9.59773e8			1.18555
$933$		0			0
$934$			1.81879e9i			2.23225i
$935$		−	5.76737e8i		−	0.705575i
$936$		0			0
$937$			1.06425e9i			1.29367i	0.762629	+	0.646836i	$0.223908\pi$
$937$			1.06425e9i			1.29367i	−0.762629	+	0.646836i	$0.776092\pi$
$938$	−1.25207e9			−1.51712
$939$		0			0
$940$			5.98345e8i			0.720390i
$941$			2.04937e8i			0.245953i	0.992410	+	0.122976i	$0.0392439\pi$
$941$			2.04937e8i			0.245953i	−0.992410	+	0.122976i	$0.960756\pi$
$942$		0			0
$943$	6.96620e6	−	1.22862e7i	0.00830732	−	0.0146515i
$944$	9.48439e7			0.112744
$945$		0			0
$946$	1.61481e9			1.90743
$947$	1.19798e8			0.141059			0.0705296	−	0.997510i	$-0.477531\pi$
$947$	1.19798e8			0.141059			0.0705296	+	0.997510i	$0.477531\pi$
$948$		0			0
$949$	2.50089e9			2.92615
$950$		−	1.32502e9i		−	1.54543i
$951$		0			0
$952$	2.86042e9			3.31528
$953$		−	1.31168e8i		−	0.151548i	−0.997125	−	0.0757741i	$-0.975857\pi$
$953$		−	1.31168e8i		−	0.151548i	0.997125	−	0.0757741i	$-0.0241428\pi$
$954$		0			0
$955$	3.20194e8			0.367623
$956$	2.11745e9			2.42348
$957$		0			0
$958$			7.91110e8i			0.899789i
$959$	3.46207e8			0.392537
$960$		0			0
$961$	−1.29185e8			−0.145560
$962$			3.80731e9i			4.27655i
$963$		0			0
$964$			1.30365e9i			1.45522i
$965$			5.22553e8i			0.581498i
$966$		0			0
$967$	2.06255e8			0.228100			0.114050	−	0.993475i	$-0.463618\pi$
$967$	2.06255e8			0.228100			0.114050	+	0.993475i	$0.463618\pi$
$968$	4.63621e8			0.511137
$969$		0			0
$970$	−4.66799e8			−0.511464
$971$		−	3.50529e8i		−	0.382883i	−0.981504	−	0.191442i	$-0.938684\pi$
$971$		−	3.50529e8i		−	0.382883i	0.981504	−	0.191442i	$-0.0613162\pi$
$972$		0			0
$973$			2.32607e8i			0.252513i
$974$	2.51508e8			0.272192
$975$		0			0
$976$			2.83188e8i			0.304597i
$977$		−	6.80555e8i		−	0.729760i	−0.931055	−	0.364880i	$-0.881110\pi$
$977$		−	6.80555e8i		−	0.729760i	0.931055	−	0.364880i	$-0.118890\pi$
$978$		0			0
$979$	−6.74858e7			−0.0719224
$980$			4.79594e8i			0.509560i
$981$		0			0
$982$	7.98840e8			0.843578
$983$			9.28861e8i			0.977890i	0.872315	+	0.488945i	$0.162618\pi$
$983$			9.28861e8i			0.977890i	−0.872315	+	0.488945i	$0.837382\pi$
$984$		0			0
$985$			4.56901e8i			0.478094i
$986$		−	4.40226e8i		−	0.459246i
$987$		0			0
$988$			3.08466e9i			3.19843i
$989$	−8.15850e8	−	4.62583e8i	−0.843376	−	0.478190i
$990$		0			0
$991$	6.12594e8			0.629436			0.314718	−	0.949185i	$-0.398090\pi$
$991$	6.12594e8			0.629436			0.314718	+	0.949185i	$0.398090\pi$
$992$	−5.66784e8			−0.580608
$993$		0			0
$994$			7.53435e8i			0.767162i
$995$	−3.45997e8			−0.351239
$996$		0			0
$997$	−1.65349e8			−0.166846			−0.0834231	−	0.996514i	$-0.526585\pi$
$997$	−1.65349e8			−0.166846			−0.0834231	+	0.996514i	$0.526585\pi$
$998$	1.01680e9			1.02293
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.7.d.e.91.3		24
3.2	odd	2		69.7.d.a.22.22	yes	24
23.22	odd	2	inner	207.7.d.e.91.4		24
69.68	even	2		69.7.d.a.22.21	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.d.a.22.21	✓	24	69.68	even	2
69.7.d.a.22.22	yes	24	3.2	odd	2
207.7.d.e.91.3		24	1.1	even	1	trivial
207.7.d.e.91.4		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)

\(f(q)\)	\(=\)	\(q-13.3624 q^{2} +114.554 q^{4} -40.7784i q^{5} +469.379i q^{7} -675.521 q^{8} +O(q^{10})\)	\(q-13.3624 q^{2} +114.554 q^{4} -40.7784i q^{5} +469.379i q^{7} -675.521 q^{8} +544.897i q^{10} -1567.76i q^{11} +3791.51 q^{13} -6272.03i q^{14} +1695.14 q^{16} +9021.27i q^{17} +7102.08i q^{19} -4671.32i q^{20} +20949.1i q^{22} +(6001.12 - 10584.1i) q^{23} +13962.1 q^{25} -50663.7 q^{26} +53769.2i q^{28} +3651.94 q^{29} -27537.6 q^{31} +20582.2 q^{32} -120546. i q^{34} +19140.5 q^{35} -75148.6i q^{37} -94900.8i q^{38} +27546.7i q^{40} +1160.82 q^{41} -77082.8i q^{43} -179593. i q^{44} +(-80189.3 + 141429. i) q^{46} -128089. q^{47} -102668. q^{49} -186568. q^{50} +434333. q^{52} +149342. i q^{53} -63930.8 q^{55} -317076. i q^{56} -48798.7 q^{58} +55950.5 q^{59} +167059. i q^{61} +367968. q^{62} -383517. q^{64} -154612. i q^{65} -199627. i q^{67} +1.03342e6i q^{68} -255763. q^{70} -120126. q^{71} +659602. q^{73} +1.00417e6i q^{74} +813570. i q^{76} +735875. q^{77} -458548. i q^{79} -69125.1i q^{80} -15511.3 q^{82} +293064. i q^{83} +367873. q^{85} +1.03001e6i q^{86} +1.05906e6i q^{88} -43046.0i q^{89} +1.77966e6i q^{91} +(687451. - 1.21245e6i) q^{92} +1.71158e6 q^{94} +289611. q^{95} +856674. i q^{97} +1.37189e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{2} + 816 q^{4} + 940 q^{8}+O(q^{10}) \) 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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