LMFDB - Embedded newform 45.9.g.a.28.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,9,Mod(28,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("45.28");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	45.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.3320374528$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} - 30x^{3} + 1089x^{2} - 3168x + 4608 $ x^6 - 2x^5 + 2x^4 - 30x^3 + 1089x^2 - 3168*x + 4608
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			28.3
Root			$3.70505 + 3.70505i$ of defining polynomial
Character	$\chi$	$=$	45.28
Dual form			45.9.g.a.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.8649 - 11.8649i) q^{2} -25.5528i q^{4} +(434.373 - 449.383i) q^{5} +(508.219 - 508.219i) q^{7} +(2734.24 + 2734.24i) q^{8} +O(q^{10})$	\(q+(11.8649 - 11.8649i) q^{2} -25.5528i q^{4} +(434.373 - 449.383i) q^{5} +(508.219 - 508.219i) q^{7} +(2734.24 + 2734.24i) q^{8} +(-178.084 - 10485.7i) q^{10} +7021.93 q^{11} +(-8073.75 - 8073.75i) q^{13} -12060.0i q^{14} +71424.6 q^{16} +(102958. - 102958. i) q^{17} -59599.0i q^{19} +(-11483.0 - 11099.5i) q^{20} +(83314.7 - 83314.7i) q^{22} +(-132866. - 132866. i) q^{23} +(-13264.5 - 390400. i) q^{25} -191589. q^{26} +(-12986.4 - 12986.4i) q^{28} +392047. i q^{29} -507883. q^{31} +(147482. - 147482. i) q^{32} -2.44319e6i q^{34} +(-7628.00 - 449141. i) q^{35} +(-61012.9 + 61012.9i) q^{37} +(-707137. - 707137. i) q^{38} +(2.41640e6 - 41038.9i) q^{40} +1.81765e6 q^{41} +(1.47723e6 + 1.47723e6i) q^{43} -179430. i q^{44} -3.15288e6 q^{46} +(1.79287e6 - 1.79287e6i) q^{47} +5.24823e6i q^{49} +(-4.78945e6 - 4.47468e6i) q^{50} +(-206307. + 206307. i) q^{52} +(5.66320e6 + 5.66320e6i) q^{53} +(3.05014e6 - 3.15553e6i) q^{55} +2.77918e6 q^{56} +(4.65161e6 + 4.65161e6i) q^{58} +1.74855e7i q^{59} -1.96459e7 q^{61} +(-6.02599e6 + 6.02599e6i) q^{62} +1.47850e7i q^{64} +(-7.13522e6 + 121181. i) q^{65} +(-1.12859e7 + 1.12859e7i) q^{67} +(-2.63088e6 - 2.63088e6i) q^{68} +(-5.41953e6 - 5.23852e6i) q^{70} -3.01001e7 q^{71} +(2.52645e7 + 2.52645e7i) q^{73} +1.44783e6i q^{74} -1.52292e6 q^{76} +(3.56868e6 - 3.56868e6i) q^{77} -8.14025e6i q^{79} +(3.10249e7 - 3.20970e7i) q^{80} +(2.15663e7 - 2.15663e7i) q^{82} +(1.99635e7 + 1.99635e7i) q^{83} +(-1.54533e6 - 9.09902e7i) q^{85} +3.50545e7 q^{86} +(1.91996e7 + 1.91996e7i) q^{88} -8.20905e7i q^{89} -8.20646e6 q^{91} +(-3.39509e6 + 3.39509e6i) q^{92} -4.25446e7i q^{94} +(-2.67827e7 - 2.58882e7i) q^{95} +(3.37379e7 - 3.37379e7i) q^{97} +(6.22698e7 + 6.22698e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 220 q^{5} - 2352 q^{7} + 8220 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 - 220 * q^5 - 2352 * q^7 + 8220 * q^8	$ 6 q + 2 q^{2} - 220 q^{5} - 2352 q^{7} + 8220 q^{8} + 30870 q^{10} - 23192 q^{11} - 119142 q^{13} + 218616 q^{16} + 265502 q^{17} - 412260 q^{20} - 35664 q^{22} - 28888 q^{23} - 340350 q^{25} + 801388 q^{26} + 1305192 q^{28} - 747648 q^{31} - 3033928 q^{32} + 4971680 q^{35} - 454002 q^{37} - 1443720 q^{38} + 2683500 q^{40} - 2489432 q^{41} + 792648 q^{43} - 3149928 q^{46} + 15313352 q^{47} - 29537650 q^{50} - 735732 q^{52} + 13509122 q^{53} + 4448040 q^{55} + 18454800 q^{56} - 23903520 q^{58} + 24111192 q^{61} - 53913416 q^{62} + 30943610 q^{65} - 32827752 q^{67} - 8118692 q^{68} - 44156280 q^{70} + 13992928 q^{71} + 111859638 q^{73} - 56470800 q^{76} - 26260136 q^{77} - 23045920 q^{80} + 38023056 q^{82} + 14768432 q^{83} - 19713030 q^{85} + 135560008 q^{86} - 44555040 q^{88} + 167542032 q^{91} - 69931048 q^{92} - 239661000 q^{95} - 186656202 q^{97} + 345959698 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 220 * q^5 - 2352 * q^7 + 8220 * q^8 + 30870 * q^10 - 23192 * q^11 - 119142 * q^13 + 218616 * q^16 + 265502 * q^17 - 412260 * q^20 - 35664 * q^22 - 28888 * q^23 - 340350 * q^25 + 801388 * q^26 + 1305192 * q^28 - 747648 * q^31 - 3033928 * q^32 + 4971680 * q^35 - 454002 * q^37 - 1443720 * q^38 + 2683500 * q^40 - 2489432 * q^41 + 792648 * q^43 - 3149928 * q^46 + 15313352 * q^47 - 29537650 * q^50 - 735732 * q^52 + 13509122 * q^53 + 4448040 * q^55 + 18454800 * q^56 - 23903520 * q^58 + 24111192 * q^61 - 53913416 * q^62 + 30943610 * q^65 - 32827752 * q^67 - 8118692 * q^68 - 44156280 * q^70 + 13992928 * q^71 + 111859638 * q^73 - 56470800 * q^76 - 26260136 * q^77 - 23045920 * q^80 + 38023056 * q^82 + 14768432 * q^83 - 19713030 * q^85 + 135560008 * q^86 - 44555040 * q^88 + 167542032 * q^91 - 69931048 * q^92 - 239661000 * q^95 - 186656202 * q^97 + 345959698 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	11.8649	−	11.8649i	0.741558	−	0.741558i	−0.231320	−	0.972878i	$-0.574304\pi$
$2$	11.8649	−	11.8649i	0.741558	−	0.741558i	0.972878	+	0.231320i	$0.0743044\pi$
$3$		0			0
$3$		0			0
$4$		−	25.5528i		−	0.0998158i
$5$	434.373	−	449.383i	0.694997	−	0.719012i
$5$	434.373	−	449.383i	0.694997	−	0.719012i
$6$		0			0
$7$	508.219	−	508.219i	0.211670	−	0.211670i	−0.593307	−	0.804976i	$-0.702178\pi$
$7$	508.219	−	508.219i	0.211670	−	0.211670i	0.804976	+	0.593307i	$0.202178\pi$
$8$	2734.24	+	2734.24i	0.667539	+	0.667539i
$9$		0			0
$10$	−178.084	−	10485.7i	−0.0178084	−	1.04857i
$11$	7021.93			0.479607			0.239804	−	0.970821i	$-0.422917\pi$
$11$	7021.93			0.479607			0.239804	+	0.970821i	$0.422917\pi$
$12$		0			0
$13$	−8073.75	−	8073.75i	−0.282684	−	0.282684i	0.551494	−	0.834179i	$-0.314058\pi$
$13$	−8073.75	−	8073.75i	−0.282684	−	0.282684i	−0.834179	+	0.551494i	$0.814058\pi$
$14$		−	12060.0i		−	0.313930i
$15$		0			0
$16$	71424.6			1.08985
$17$	102958.	−	102958.i	1.23273	−	1.23273i	0.269813	−	0.962913i	$-0.413038\pi$
$17$	102958.	−	102958.i	1.23273	−	1.23273i	0.962913	−	0.269813i	$-0.0869619\pi$
$18$		0			0
$19$		−	59599.0i		−	0.457324i	−0.973506	−	0.228662i	$-0.926565\pi$
$19$		−	59599.0i		−	0.457324i	0.973506	−	0.228662i	$-0.0734351\pi$
$20$	−11483.0	−	11099.5i	−0.0717688	−	0.0693717i
$21$		0			0
$22$	83314.7	−	83314.7i	0.355657	−	0.355657i
$23$	−132866.	−	132866.i	−0.474790	−	0.474790i	0.428671	−	0.903461i	$-0.358982\pi$
$23$	−132866.	−	132866.i	−0.474790	−	0.474790i	−0.903461	+	0.428671i	$0.858982\pi$
$24$		0			0
$25$	−13264.5	−	390400.i	−0.0339572	−	0.999423i
$26$	−191589.			−0.419254
$27$		0			0
$28$	−12986.4	−	12986.4i	−0.0211280	−	0.0211280i
$29$			392047.i			0.554302i	0.960826	+	0.277151i	$0.0893902\pi$
$29$			392047.i			0.554302i	−0.960826	+	0.277151i	$0.910610\pi$
$30$		0			0
$31$	−507883.			−0.549942			−0.274971	−	0.961453i	$-0.588668\pi$
$31$	−507883.			−0.549942			−0.274971	+	0.961453i	$0.588668\pi$
$32$	147482.	−	147482.i	0.140650	−	0.140650i
$33$		0			0
$34$		−	2.44319e6i		−	1.82827i
$35$	−7628.00	−	449141.i	−0.00508321	−	0.299303i
$36$		0			0
$37$	−61012.9	+	61012.9i	−0.0325548	+	0.0325548i	−0.723197	−	0.690642i	$-0.757328\pi$
$37$	−61012.9	+	61012.9i	−0.0325548	+	0.0325548i	0.690642	+	0.723197i	$0.257328\pi$
$38$	−707137.	−	707137.i	−0.339132	−	0.339132i
$39$		0			0
$40$	2.41640e6	−	41038.9i	0.943906	−	0.0160308i
$41$	1.81765e6			0.643242			0.321621	−	0.946868i	$-0.395772\pi$
$41$	1.81765e6			0.643242			0.321621	+	0.946868i	$0.395772\pi$
$42$		0			0
$43$	1.47723e6	+	1.47723e6i	0.432090	+	0.432090i	0.889339	−	0.457249i	$-0.151165\pi$
$43$	1.47723e6	+	1.47723e6i	0.432090	+	0.432090i	−0.457249	+	0.889339i	$0.651165\pi$
$44$		−	179430.i		−	0.0478724i
$45$		0			0
$46$	−3.15288e6			−0.704168
$47$	1.79287e6	−	1.79287e6i	0.367416	−	0.367416i	−0.499118	−	0.866534i	$-0.666343\pi$
$47$	1.79287e6	−	1.79287e6i	0.367416	−	0.367416i	0.866534	+	0.499118i	$0.166343\pi$
$48$		0			0
$49$			5.24823e6i			0.910392i
$50$	−4.78945e6	−	4.47468e6i	−0.766311	−	0.715949i
$51$		0			0
$52$	−206307.	+	206307.i	−0.0282164	+	0.0282164i
$53$	5.66320e6	+	5.66320e6i	0.717725	+	0.717725i	0.968139	−	0.250414i	$-0.0805666\pi$
$53$	5.66320e6	+	5.66320e6i	0.717725	+	0.717725i	−0.250414	+	0.968139i	$0.580567\pi$
$54$		0			0
$55$	3.05014e6	−	3.15553e6i	0.333326	−	0.344844i
$56$	2.77918e6			0.282595
$57$		0			0
$58$	4.65161e6	+	4.65161e6i	0.411047	+	0.411047i
$59$			1.74855e7i			1.44301i	0.692410	+	0.721504i	$0.256549\pi$
$59$			1.74855e7i			1.44301i	−0.692410	+	0.721504i	$0.743451\pi$
$60$		0			0
$61$	−1.96459e7			−1.41890			−0.709452	−	0.704754i	$-0.751057\pi$
$61$	−1.96459e7			−1.41890			−0.709452	+	0.704754i	$0.751057\pi$
$62$	−6.02599e6	+	6.02599e6i	−0.407814	+	0.407814i
$63$		0			0
$64$			1.47850e7i			0.881252i
$65$	−7.13522e6	+	121181.i	−0.399718	+	0.00678862i
$66$		0			0
$67$	−1.12859e7	+	1.12859e7i	−0.560061	+	0.560061i	−0.929325	−	0.369264i	$-0.879610\pi$
$67$	−1.12859e7	+	1.12859e7i	−0.560061	+	0.560061i	0.369264	+	0.929325i	$0.379610\pi$
$68$	−2.63088e6	−	2.63088e6i	−0.123045	−	0.123045i
$69$		0			0
$70$	−5.41953e6	−	5.23852e6i	−0.225720	−	0.218181i
$71$	−3.01001e7			−1.18450			−0.592249	−	0.805755i	$-0.701760\pi$
$71$	−3.01001e7			−1.18450			−0.592249	+	0.805755i	$0.701760\pi$
$72$		0			0
$73$	2.52645e7	+	2.52645e7i	0.889649	+	0.889649i	0.994489	−	0.104840i	$-0.0334331\pi$
$73$	2.52645e7	+	2.52645e7i	0.889649	+	0.889649i	−0.104840	+	0.994489i	$0.533433\pi$
$74$			1.44783e6i			0.0482825i
$75$		0			0
$76$	−1.52292e6			−0.0456482
$77$	3.56868e6	−	3.56868e6i	0.101518	−	0.101518i
$78$		0			0
$79$		−	8.14025e6i		−	0.208992i	−0.994525	−	0.104496i	$-0.966677\pi$
$79$		−	8.14025e6i		−	0.208992i	0.994525	−	0.104496i	$-0.0333229\pi$
$80$	3.10249e7	−	3.20970e7i	0.757445	−	0.783617i
$81$		0			0
$82$	2.15663e7	−	2.15663e7i	0.477001	−	0.477001i
$83$	1.99635e7	+	1.99635e7i	0.420652	+	0.420652i	0.885428	−	0.464776i	$-0.153865\pi$
$83$	1.99635e7	+	1.99635e7i	0.420652	+	0.420652i	−0.464776	+	0.885428i	$0.653865\pi$
$84$		0			0
$85$	−1.54533e6	−	9.09902e7i	−0.0296037	−	1.74309i
$86$	3.50545e7			0.640840
$87$		0			0
$88$	1.91996e7	+	1.91996e7i	0.320156	+	0.320156i
$89$		−	8.20905e7i		−	1.30838i	−0.756332	−	0.654189i	$-0.773010\pi$
$89$		−	8.20905e7i		−	1.30838i	0.756332	−	0.654189i	$-0.226990\pi$
$90$		0			0
$91$	−8.20646e6			−0.119671
$92$	−3.39509e6	+	3.39509e6i	−0.0473915	+	0.0473915i
$93$		0			0
$94$		−	4.25446e7i		−	0.544920i
$95$	−2.67827e7	−	2.58882e7i	−0.328822	−	0.317839i
$96$		0			0
$97$	3.37379e7	−	3.37379e7i	0.381093	−	0.381093i	−0.490403	−	0.871496i	$-0.663150\pi$
$97$	3.37379e7	−	3.37379e7i	0.381093	−	0.381093i	0.871496	+	0.490403i	$0.163150\pi$
$98$	6.22698e7	+	6.22698e7i	0.675108	+	0.675108i
$99$		0			0
$100$	−9.97582e6	+	338947.i	−0.0997582	+	0.00338947i
$101$	1.91592e7			0.184116			0.0920582	−	0.995754i	$-0.470655\pi$
$101$	1.91592e7			0.184116			0.0920582	+	0.995754i	$0.470655\pi$
$102$		0			0
$103$	−1.35177e8	−	1.35177e8i	−1.20103	−	1.20103i	−0.973854	−	0.227173i	$-0.927052\pi$
$103$	−1.35177e8	−	1.35177e8i	−1.20103	−	1.20103i	−0.227173	−	0.973854i	$-0.572948\pi$
$104$		−	4.41511e7i		−	0.377405i
$105$		0			0
$106$	1.34387e8			1.06447
$107$	−1.22825e8	+	1.22825e8i	−0.937029	+	0.937029i	−0.998132	−	0.0611024i	$-0.980538\pi$
$107$	−1.22825e8	+	1.22825e8i	−0.937029	+	0.937029i	0.0611024	+	0.998132i	$0.480538\pi$
$108$		0			0
$109$			1.66780e8i			1.18151i	0.806850	+	0.590757i	$0.201171\pi$
$109$			1.66780e8i			1.18151i	−0.806850	+	0.590757i	$0.798829\pi$
$110$	−1.25049e6	−	7.36298e7i	−0.00854104	−	0.502902i
$111$		0			0
$112$	3.62993e7	−	3.62993e7i	0.230689	−	0.230689i
$113$	−3.23356e7	−	3.23356e7i	−0.198320	−	0.198320i	0.600959	−	0.799280i	$-0.294785\pi$
$113$	−3.23356e7	−	3.23356e7i	−0.198320	−	0.198320i	−0.799280	+	0.600959i	$0.794785\pi$
$114$		0			0
$115$	−1.17421e8	+	1.99422e6i	−0.671357	+	0.0114020i
$116$	1.00179e7			0.0553281
$117$		0			0
$118$	2.07464e8	+	2.07464e8i	1.07007	+	1.07007i
$119$		−	1.04651e8i		−	0.521861i
$120$		0			0
$121$	−1.65051e8			−0.769977
$122$	−2.33097e8	+	2.33097e8i	−1.05220	+	1.05220i
$123$		0			0
$124$			1.29778e7i			0.0548929i
$125$	−1.81201e8	−	1.63618e8i	−0.742198	−	0.670181i
$126$		0			0
$127$	−2.93412e8	+	2.93412e8i	−1.12788	+	1.12788i	−0.137357	+	0.990522i	$0.543861\pi$
$127$	−2.93412e8	+	2.93412e8i	−1.12788	+	1.12788i	−0.990522	+	0.137357i	$0.956139\pi$
$128$	2.13178e8	+	2.13178e8i	0.794150	+	0.794150i
$129$		0			0
$130$	−8.32211e7	+	8.60967e7i	−0.291380	+	0.301448i
$131$	3.37671e8			1.14659			0.573295	−	0.819349i	$-0.305665\pi$
$131$	3.37671e8			1.14659			0.573295	+	0.819349i	$0.305665\pi$
$132$		0			0
$133$	−3.02893e7	−	3.02893e7i	−0.0968017	−	0.0968017i
$134$			2.67812e8i			0.830635i
$135$		0			0
$136$	5.63026e8			1.64578
$137$	−1.06123e8	+	1.06123e8i	−0.301249	+	0.301249i	−0.841502	−	0.540253i	$-0.818328\pi$
$137$	−1.06123e8	+	1.06123e8i	−0.301249	+	0.301249i	0.540253	+	0.841502i	$0.318328\pi$
$138$		0			0
$139$		−	5.86652e8i		−	1.57153i	−0.618528	−	0.785763i	$-0.712271\pi$
$139$		−	5.86652e8i		−	1.57153i	0.618528	−	0.785763i	$-0.287729\pi$
$140$	−1.14768e7	+	194917.i	−0.0298751	+	0.000507385i
$141$		0			0
$142$	−3.57135e8	+	3.57135e8i	−0.878373	+	0.878373i
$143$	−5.66933e7	−	5.66933e7i	−0.135577	−	0.135577i
$144$		0			0
$145$	1.76179e8	+	1.70295e8i	0.398550	+	0.385238i
$146$	5.99522e8			1.31945
$147$		0			0
$148$	1.55905e6	+	1.55905e6i	0.00324948	+	0.00324948i
$149$		−	5.45945e8i		−	1.10765i	−0.832632	−	0.553827i	$-0.813167\pi$
$149$		−	5.45945e8i		−	1.10765i	0.832632	−	0.553827i	$-0.186833\pi$
$150$		0			0
$151$	8.88293e7			0.170863			0.0854316	−	0.996344i	$-0.472773\pi$
$151$	8.88293e7			0.170863			0.0854316	+	0.996344i	$0.472773\pi$
$152$	1.62958e8	−	1.62958e8i	0.305282	−	0.305282i
$153$		0			0
$154$		−	8.46841e7i		−	0.150563i
$155$	−2.20611e8	+	2.28234e8i	−0.382208	+	0.395415i
$156$		0			0
$157$	−3.21072e8	+	3.21072e8i	−0.528450	+	0.528450i	−0.920110	−	0.391660i	$-0.871901\pi$
$157$	−3.21072e8	+	3.21072e8i	−0.528450	+	0.528450i	0.391660	+	0.920110i	$0.371901\pi$
$158$	−9.65834e7	−	9.65834e7i	−0.154979	−	0.154979i
$159$		0			0
$160$	−2.21360e6	−	1.30338e8i	−0.00337769	−	0.198881i
$161$	−1.35050e8			−0.200997
$162$		0			0
$163$	2.14053e8	+	2.14053e8i	0.303229	+	0.303229i	0.842276	−	0.539047i	$-0.181215\pi$
$163$	2.14053e8	+	2.14053e8i	0.303229	+	0.303229i	−0.539047	+	0.842276i	$0.681215\pi$
$164$		−	4.64461e7i		−	0.0642057i
$165$		0			0
$166$	4.73730e8			0.623876
$167$	−6.91005e8	+	6.91005e8i	−0.888414	+	0.888414i	−0.994371	−	0.105957i	$-0.966209\pi$
$167$	−6.91005e8	+	6.91005e8i	−0.888414	+	0.888414i	0.105957	+	0.994371i	$0.466209\pi$
$168$		0			0
$169$		−	6.85360e8i		−	0.840179i
$170$	−1.09793e9	−	1.06126e9i	−1.31455	−	1.27065i
$171$		0			0
$172$	3.77475e7	−	3.77475e7i	0.0431294	−	0.0431294i
$173$	3.40367e8	+	3.40367e8i	0.379982	+	0.379982i	0.871095	−	0.491114i	$-0.163410\pi$
$173$	3.40367e8	+	3.40367e8i	0.379982	+	0.379982i	−0.491114	+	0.871095i	$0.663410\pi$
$174$		0			0
$175$	−2.05150e8	−	1.91667e8i	−0.218735	−	0.204360i
$176$	5.01538e8			0.522701
$177$		0			0
$178$	−9.73998e8	−	9.73998e8i	−0.970237	−	0.970237i
$179$			7.51587e7i			0.0732094i	0.999330	+	0.0366047i	$0.0116542\pi$
$179$			7.51587e7i			0.0732094i	−0.999330	+	0.0366047i	$0.988346\pi$
$180$		0			0
$181$	1.46153e8			0.136174			0.0680870	−	0.997679i	$-0.478310\pi$
$181$	1.46153e8			0.136174			0.0680870	+	0.997679i	$0.478310\pi$
$182$	−9.73690e7	+	9.73690e7i	−0.0887432	+	0.0887432i
$183$		0			0
$184$		−	7.26573e8i		−	0.633881i
$185$	915760.	+	5.39205e7i	0.000781798	+	0.0460328i
$186$		0			0
$187$	7.22967e8	−	7.22967e8i	0.591224	−	0.591224i
$188$	−4.58130e7	−	4.58130e7i	−0.0366739	−	0.0366739i
$189$		0			0
$190$	−6.24937e8	+	1.06136e7i	−0.479537	+	0.00814421i
$191$	2.54450e9			1.91191			0.955957	−	0.293506i	$-0.0948222\pi$
$191$	2.54450e9			1.91191			0.955957	+	0.293506i	$0.0948222\pi$
$192$		0			0
$193$	9.46964e8	+	9.46964e8i	0.682503	+	0.682503i	0.960563	−	0.278061i	$-0.0896917\pi$
$193$	9.46964e8	+	9.46964e8i	0.682503	+	0.682503i	−0.278061	+	0.960563i	$0.589692\pi$
$194$		−	8.00595e8i		−	0.565205i
$195$		0			0
$196$	1.34107e8			0.0908715
$197$	−6.42356e8	+	6.42356e8i	−0.426492	+	0.426492i	−0.887432	−	0.460940i	$-0.847513\pi$
$197$	−6.42356e8	+	6.42356e8i	−0.426492	+	0.426492i	0.460940	+	0.887432i	$0.347513\pi$
$198$		0			0
$199$			3.47565e8i			0.221628i	0.993841	+	0.110814i	$0.0353457\pi$
$199$			3.47565e8i			0.221628i	−0.993841	+	0.110814i	$0.964654\pi$
$200$	1.03118e9	−	1.10371e9i	0.644486	−	0.689821i
$201$		0			0
$202$	2.27323e8	−	2.27323e8i	0.136533	−	0.136533i
$203$	1.99246e8	+	1.99246e8i	0.117329	+	0.117329i
$204$		0			0
$205$	7.89538e8	−	8.16820e8i	0.447052	−	0.462499i
$206$	−3.20772e9			−1.78126
$207$		0			0
$208$	−5.76664e8	−	5.76664e8i	−0.308084	−	0.308084i
$209$		−	4.18500e8i		−	0.219336i
$210$		0			0
$211$	−1.32439e9			−0.668168			−0.334084	−	0.942543i	$-0.608427\pi$
$211$	−1.32439e9			−0.668168			−0.334084	+	0.942543i	$0.608427\pi$
$212$	1.44711e8	−	1.44711e8i	0.0716403	−	0.0716403i
$213$		0			0
$214$			2.91463e9i			1.38972i
$215$	1.30551e9	−	2.21722e7i	0.610980	−	0.0103766i
$216$		0			0
$217$	−2.58115e8	+	2.58115e8i	−0.116406	+	0.116406i
$218$	1.97883e9	+	1.97883e9i	0.876160	+	0.876160i
$219$		0			0
$220$	−8.06328e7	−	7.79397e7i	−0.0344208	−	0.0332712i
$221$	−1.66252e9			−0.696945
$222$		0			0
$223$	2.96426e9	+	2.96426e9i	1.19866	+	1.19866i	0.974567	+	0.224096i	$0.0719429\pi$
$223$	2.96426e9	+	2.96426e9i	1.19866	+	1.19866i	0.224096	+	0.974567i	$0.428057\pi$
$224$		−	1.49906e8i		−	0.0595427i
$225$		0			0
$226$	−7.67318e8			−0.294132
$227$	8.37535e8	−	8.37535e8i	0.315428	−	0.315428i	−0.531580	−	0.847008i	$-0.678402\pi$
$227$	8.37535e8	−	8.37535e8i	0.315428	−	0.315428i	0.847008	+	0.531580i	$0.178402\pi$
$228$		0			0
$229$			2.66676e9i			0.969709i	0.874595	+	0.484854i	$0.161127\pi$
$229$			2.66676e9i			0.969709i	−0.874595	+	0.484854i	$0.838873\pi$
$230$	−1.36953e9	+	1.41685e9i	−0.489395	+	0.506305i
$231$		0			0
$232$	−1.07195e9	+	1.07195e9i	−0.370018	+	0.370018i
$233$	−9.91964e8	−	9.91964e8i	−0.336568	−	0.336568i	0.518506	−	0.855074i	$-0.326488\pi$
$233$	−9.91964e8	−	9.91964e8i	−0.336568	−	0.336568i	−0.855074	+	0.518506i	$0.826488\pi$
$234$		0			0
$235$	−2.69097e7	−	1.58446e9i	−0.00882343	−	0.519529i
$236$	4.46803e8			0.144035
$237$		0			0
$238$	−1.24167e9	−	1.24167e9i	−0.386990	−	0.386990i
$239$			1.26088e9i			0.386440i	0.981155	+	0.193220i	$0.0618931\pi$
$239$			1.26088e9i			0.386440i	−0.981155	+	0.193220i	$0.938107\pi$
$240$		0			0
$241$	−1.40173e9			−0.415524			−0.207762	−	0.978179i	$-0.566618\pi$
$241$	−1.40173e9			−0.415524			−0.207762	+	0.978179i	$0.566618\pi$
$242$	−1.95832e9	+	1.95832e9i	−0.570982	+	0.570982i
$243$		0			0
$244$			5.02009e8i			0.141629i
$245$	2.35846e9	+	2.27969e9i	0.654583	+	0.632720i
$246$		0			0
$247$	−4.81187e8	+	4.81187e8i	−0.129278	+	0.129278i
$248$	−1.38867e9	−	1.38867e9i	−0.367107	−	0.367107i
$249$		0			0
$250$	−4.09125e9	+	2.08612e8i	−1.04736	+	0.0534046i
$251$	−5.24024e9			−1.32025			−0.660126	−	0.751155i	$-0.729497\pi$
$251$	−5.24024e9			−1.32025			−0.660126	+	0.751155i	$0.729497\pi$
$252$		0			0
$253$	−9.32973e8	−	9.32973e8i	−0.227713	−	0.227713i
$254$			6.96261e9i			1.67277i
$255$		0			0
$256$	1.27373e9			0.296563
$257$	2.38954e9	−	2.38954e9i	0.547749	−	0.547749i	−0.378040	−	0.925789i	$-0.623402\pi$
$257$	2.38954e9	−	2.38954e9i	0.547749	−	0.547749i	0.925789	+	0.378040i	$0.123402\pi$
$258$		0			0
$259$			6.20158e7i			0.0137817i
$260$	3.09652e6	+	1.82325e8i	0.000677612	+	0.0398982i
$261$		0			0
$262$	4.00644e9	−	4.00644e9i	0.850263	−	0.850263i
$263$	1.29445e9	+	1.29445e9i	0.270559	+	0.270559i	0.829325	−	0.558766i	$-0.188725\pi$
$263$	1.29445e9	+	1.29445e9i	0.270559	+	0.270559i	−0.558766	+	0.829325i	$0.688725\pi$
$264$		0			0
$265$	5.00488e9	−	8.50005e7i	1.01487	−	0.0172361i
$266$	−7.18761e8			−0.143568
$267$		0			0
$268$	2.88386e8	+	2.88386e8i	0.0559029	+	0.0559029i
$269$		−	6.14346e9i		−	1.17329i	−0.809845	−	0.586643i	$-0.800449\pi$
$269$		−	6.14346e9i		−	1.17329i	0.809845	−	0.586643i	$-0.199551\pi$
$270$		0			0
$271$	−5.21208e9			−0.966349			−0.483174	−	0.875524i	$-0.660516\pi$
$271$	−5.21208e9			−0.966349			−0.483174	+	0.875524i	$0.660516\pi$
$272$	7.35377e9	−	7.35377e9i	1.34349	−	1.34349i
$273$		0			0
$274$			2.51828e9i			0.446787i
$275$	−9.31427e7	−	2.74136e9i	−0.0162861	−	0.479331i
$276$		0			0
$277$	5.42598e9	−	5.42598e9i	0.921635	−	0.921635i	−0.0755097	−	0.997145i	$-0.524058\pi$
$277$	5.42598e9	−	5.42598e9i	0.921635	−	0.921635i	0.997145	+	0.0755097i	$0.0240584\pi$
$278$	−6.96058e9	−	6.96058e9i	−1.16538	−	1.16538i
$279$		0			0
$280$	1.20720e9	−	1.24892e9i	0.196403	−	0.203189i
$281$	7.13397e9			1.14421			0.572106	−	0.820180i	$-0.306127\pi$
$281$	7.13397e9			1.14421			0.572106	+	0.820180i	$0.306127\pi$
$282$		0			0
$283$	2.63941e9	+	2.63941e9i	0.411492	+	0.411492i	0.882258	−	0.470766i	$-0.156022\pi$
$283$	2.63941e9	+	2.63941e9i	0.411492	+	0.411492i	−0.470766	+	0.882258i	$0.656022\pi$
$284$			7.69142e8i			0.118232i
$285$		0			0
$286$	−1.34532e9			−0.201077
$287$	9.23763e8	−	9.23763e8i	0.136155	−	0.136155i
$288$		0			0
$289$		−	1.42251e10i		−	2.03923i
$290$	4.11089e9	−	6.98173e7i	0.581224	−	0.00987123i
$291$		0			0
$292$	6.45579e8	−	6.45579e8i	0.0888010	−	0.0888010i
$293$	2.26873e9	+	2.26873e9i	0.307831	+	0.307831i	0.844068	−	0.536237i	$-0.180155\pi$
$293$	2.26873e9	+	2.26873e9i	0.307831	+	0.307831i	−0.536237	+	0.844068i	$0.680155\pi$
$294$		0			0
$295$	7.85766e9	+	7.59522e9i	1.03754	+	1.00289i
$296$	−3.33648e8			−0.0434631
$297$		0			0
$298$	−6.47760e9	−	6.47760e9i	−0.821390	−	0.821390i
$299$			2.14545e9i			0.268431i
$300$		0			0
$301$	1.50151e9			0.182921
$302$	1.05395e9	−	1.05395e9i	0.126705	−	0.126705i
$303$		0			0
$304$		−	4.25683e9i		−	0.498416i
$305$	−8.53366e9	+	8.82853e9i	−0.986134	+	1.02021i
$306$		0			0
$307$	−5.16937e9	+	5.16937e9i	−0.581948	+	0.581948i	−0.935438	−	0.353490i	$-0.884995\pi$
$307$	−5.16937e9	+	5.16937e9i	−0.581948	+	0.581948i	0.353490	+	0.935438i	$0.384995\pi$
$308$	−9.11898e7	−	9.11898e7i	−0.0101331	−	0.0101331i
$309$		0			0
$310$	9.04458e7	+	5.32550e9i	0.00979358	+	0.576652i
$311$	−1.32155e10			−1.41268			−0.706340	−	0.707873i	$-0.749655\pi$
$311$	−1.32155e10			−1.41268			−0.706340	+	0.707873i	$0.749655\pi$
$312$		0			0
$313$	−9.02814e9	−	9.02814e9i	−0.940635	−	0.940635i	0.0576992	−	0.998334i	$-0.481624\pi$
$313$	−9.02814e9	−	9.02814e9i	−0.940635	−	0.940635i	−0.998334	+	0.0576992i	$0.981624\pi$
$314$			7.61899e9i			0.783753i
$315$		0			0
$316$	−2.08006e8			−0.0208607
$317$	4.91807e9	−	4.91807e9i	0.487032	−	0.487032i	−0.420336	−	0.907369i	$-0.638088\pi$
$317$	4.91807e9	−	4.91807e9i	0.487032	−	0.487032i	0.907369	+	0.420336i	$0.138088\pi$
$318$		0			0
$319$			2.75293e9i			0.265847i
$320$	6.64410e9	+	6.42219e9i	0.633631	+	0.612468i
$321$		0			0
$322$	−1.60235e9	+	1.60235e9i	−0.149051	+	0.149051i
$323$	−6.13622e9	−	6.13622e9i	−0.563756	−	0.563756i
$324$		0			0
$325$	−3.04489e9	+	3.25908e9i	−0.272922	+	0.292121i
$326$	5.07944e9			0.449723
$327$		0			0
$328$	4.96989e9	+	4.96989e9i	0.429389	+	0.429389i
$329$		−	1.82234e9i		−	0.155541i
$330$		0			0
$331$	1.72045e9			0.143327			0.0716637	−	0.997429i	$-0.477169\pi$
$331$	1.72045e9			0.143327			0.0716637	+	0.997429i	$0.477169\pi$
$332$	5.10123e8	−	5.10123e8i	0.0419877	−	0.0419877i
$333$		0			0
$334$			1.63974e10i			1.31762i
$335$	1.69393e8	+	9.97394e9i	0.0134498	+	0.791932i
$336$		0			0
$337$	−5.92808e9	+	5.92808e9i	−0.459615	+	0.459615i	−0.898529	−	0.438914i	$-0.855363\pi$
$337$	−5.92808e9	+	5.92808e9i	−0.459615	+	0.459615i	0.438914	+	0.898529i	$0.355363\pi$
$338$	−8.13174e9	−	8.13174e9i	−0.623041	−	0.623041i
$339$		0			0
$340$	−2.32506e9	+	3.94876e7i	−0.173988	+	0.00295492i
$341$	−3.56632e9			−0.263756
$342$		0			0
$343$	5.59703e9	+	5.59703e9i	0.404372	+	0.404372i
$344$			8.07820e9i			0.576874i
$345$		0			0
$346$	8.07685e9			0.563557
$347$	−4.12838e9	+	4.12838e9i	−0.284749	+	0.284749i	−0.834999	−	0.550251i	$-0.814532\pi$
$347$	−4.12838e9	+	4.12838e9i	−0.284749	+	0.284749i	0.550251	+	0.834999i	$0.314532\pi$
$348$		0			0
$349$		−	3.79762e9i		−	0.255983i	−0.991775	−	0.127991i	$-0.959147\pi$
$349$		−	3.79762e9i		−	0.255983i	0.991775	−	0.127991i	$-0.0408530\pi$
$350$	−4.70820e9	+	1.59970e8i	−0.313749	+	0.0106602i
$351$		0			0
$352$	1.03561e9	−	1.03561e9i	0.0674568	−	0.0674568i
$353$	4.46363e9	+	4.46363e9i	0.287468	+	0.287468i	0.836078	−	0.548610i	$-0.184843\pi$
$353$	4.46363e9	+	4.46363e9i	0.287468	+	0.287468i	−0.548610	+	0.836078i	$0.684843\pi$
$354$		0			0
$355$	−1.30747e10	+	1.35265e10i	−0.823223	+	0.851668i
$356$	−2.09765e9			−0.130597
$357$		0			0
$358$	8.91752e8	+	8.91752e8i	0.0542890	+	0.0542890i
$359$		−	9.04307e8i		−	0.0544425i	−0.999629	−	0.0272213i	$-0.991334\pi$
$359$		−	9.04307e8i		−	0.0544425i	0.999629	−	0.0272213i	$-0.00866586\pi$
$360$		0			0
$361$	1.34315e10			0.790854
$362$	1.73410e9	−	1.73410e9i	0.100981	−	0.100981i
$363$		0			0
$364$			2.09698e8i			0.0119451i
$365$	2.23276e10	−	3.79201e8i	1.25797	−	0.0213648i
$366$		0			0
$367$	−9.88793e9	+	9.88793e9i	−0.545056	+	0.545056i	−0.925007	−	0.379951i	$-0.875941\pi$
$367$	−9.88793e9	+	9.88793e9i	−0.545056	+	0.545056i	0.379951	+	0.925007i	$0.375941\pi$
$368$	−9.48987e9	−	9.48987e9i	−0.517451	−	0.517451i
$369$		0			0
$370$	6.50628e8	+	6.28897e8i	0.0347157	+	0.0335562i
$371$	5.75629e9			0.303841
$372$		0			0
$373$	−1.56902e10	−	1.56902e10i	−0.810575	−	0.810575i	0.174145	−	0.984720i	$-0.444284\pi$
$373$	−1.56902e10	−	1.56902e10i	−0.810575	−	0.810575i	−0.984720	+	0.174145i	$0.944284\pi$
$374$		−	1.71559e10i		−	0.876854i
$375$		0			0
$376$	9.80428e9			0.490528
$377$	3.16529e9	−	3.16529e9i	0.156692	−	0.156692i
$378$		0			0
$379$			4.03797e8i			0.0195707i	0.999952	+	0.00978534i	$0.00311482\pi$
$379$			4.03797e8i			0.0195707i	−0.999952	+	0.00978534i	$0.996885\pi$
$380$	−6.61517e8	+	6.84375e8i	−0.0317254	+	0.0328216i
$381$		0			0
$382$	3.01903e10	−	3.01903e10i	1.41779	−	1.41779i
$383$	1.94253e10	+	1.94253e10i	0.902761	+	0.902761i	0.995674	−	0.0929130i	$-0.0296178\pi$
$383$	1.94253e10	+	1.94253e10i	0.902761	+	0.902761i	−0.0929130	+	0.995674i	$0.529618\pi$
$384$		0			0
$385$	−5.35633e7	−	3.15384e9i	−0.00243795	−	0.143548i
$386$	2.24713e10			1.01223
$387$		0			0
$388$	−8.62099e8	−	8.62099e8i	−0.0380391	−	0.0380391i
$389$		−	1.00547e10i		−	0.439109i	−0.975600	−	0.219555i	$-0.929540\pi$
$389$		−	1.00547e10i		−	0.439109i	0.975600	−	0.219555i	$-0.0704604\pi$
$390$		0			0
$391$	−2.73593e10			−1.17057
$392$	−1.43499e10	+	1.43499e10i	−0.607722	+	0.607722i
$393$		0			0
$394$			1.52430e10i			0.632537i
$395$	−3.65809e9	−	3.53591e9i	−0.150268	−	0.145249i
$396$		0			0
$397$	4.59921e9	−	4.59921e9i	0.185149	−	0.185149i	−0.608446	−	0.793595i	$-0.708207\pi$
$397$	4.59921e9	−	4.59921e9i	0.185149	−	0.185149i	0.793595	+	0.608446i	$0.208207\pi$
$398$	4.12383e9	+	4.12383e9i	0.164350	+	0.164350i
$399$		0			0
$400$	−9.47414e8	−	2.78841e10i	−0.0370084	−	1.08922i
$401$	−3.93282e10			−1.52099			−0.760496	−	0.649343i	$-0.775044\pi$
$401$	−3.93282e10			−1.52099			−0.760496	+	0.649343i	$0.775044\pi$
$402$		0			0
$403$	4.10052e9	+	4.10052e9i	0.155460	+	0.155460i
$404$		−	4.89572e8i		−	0.0183777i
$405$		0			0
$406$	4.72807e9			0.174012
$407$	−4.28428e8	+	4.28428e8i	−0.0156135	+	0.0156135i
$408$		0			0
$409$		−	3.53396e10i		−	1.26290i	−0.775417	−	0.631450i	$-0.782460\pi$
$409$		−	3.53396e10i		−	1.26290i	0.775417	−	0.631450i	$-0.217540\pi$
$410$	−3.23694e8	−	1.90593e10i	−0.0114551	−	0.674485i
$411$		0			0
$412$	−3.45415e9	+	3.45415e9i	−0.119881	+	0.119881i
$413$	8.88644e9	+	8.88644e9i	0.305441	+	0.305441i
$414$		0			0
$415$	1.76428e10	−	2.99637e8i	0.594806	−	0.0101019i
$416$	−2.38147e9			−0.0795191
$417$		0			0
$418$	−4.96547e9	−	4.96547e9i	−0.162650	−	0.162650i
$419$		−	1.65282e10i		−	0.536251i	−0.963384	−	0.268126i	$-0.913596\pi$
$419$		−	1.65282e10i		−	0.536251i	0.963384	−	0.268126i	$-0.0864042\pi$
$420$		0			0
$421$	−2.05277e10			−0.653449			−0.326725	−	0.945120i	$-0.605945\pi$
$421$	−2.05277e10			−0.653449			−0.326725	+	0.945120i	$0.605945\pi$
$422$	−1.57138e10	+	1.57138e10i	−0.495485	+	0.495485i
$423$		0			0
$424$			3.09691e10i			0.958219i
$425$	−4.15607e10	−	3.88293e10i	−1.27387	−	1.19015i
$426$		0			0
$427$	−9.98442e9	+	9.98442e9i	−0.300339	+	0.300339i
$428$	3.13854e9	+	3.13854e9i	0.0935303	+	0.0935303i
$429$		0			0
$430$	1.52267e10	−	1.57529e10i	0.445382	−	0.460772i
$431$	−2.06955e9			−0.0599745			−0.0299873	−	0.999550i	$-0.509547\pi$
$431$	−2.06955e9			−0.0599745			−0.0299873	+	0.999550i	$0.509547\pi$
$432$		0			0
$433$	2.90398e10	+	2.90398e10i	0.826118	+	0.826118i	0.986977	−	0.160860i	$-0.0514266\pi$
$433$	2.90398e10	+	2.90398e10i	0.826118	+	0.826118i	−0.160860	+	0.986977i	$0.551427\pi$
$434$			6.12504e9i			0.172643i
$435$		0			0
$436$	4.26171e9			0.117934
$437$	−7.91866e9	+	7.91866e9i	−0.217133	+	0.217133i
$438$		0			0
$439$		−	1.56289e10i		−	0.420795i	−0.977616	−	0.210398i	$-0.932524\pi$
$439$		−	1.56289e10i		−	0.420795i	0.977616	−	0.210398i	$-0.0674758\pi$
$440$	1.69678e10	−	2.88173e8i	0.452704	−	0.00768851i
$441$		0			0
$442$	−1.97257e10	+	1.97257e10i	−0.516825	+	0.516825i
$443$	−7.72628e9	−	7.72628e9i	−0.200611	−	0.200611i	0.599651	−	0.800262i	$-0.295306\pi$
$443$	−7.72628e9	−	7.72628e9i	−0.200611	−	0.200611i	−0.800262	+	0.599651i	$0.795306\pi$
$444$		0			0
$445$	−3.68901e10	−	3.56579e10i	−0.940739	−	0.909319i
$446$	7.03415e10			1.77776
$447$		0			0
$448$	7.51399e9	+	7.51399e9i	0.186534	+	0.186534i
$449$		−	1.21836e10i		−	0.299771i	−0.988703	−	0.149886i	$-0.952109\pi$
$449$		−	1.21836e10i		−	0.299771i	0.988703	−	0.149886i	$-0.0478905\pi$
$450$		0			0
$451$	1.27634e10			0.308504
$452$	−8.26266e8	+	8.26266e8i	−0.0197955	+	0.0197955i
$453$		0			0
$454$		−	1.98746e10i		−	0.467816i
$455$	−3.56467e9	+	3.68784e9i	−0.0831713	+	0.0860452i
$456$		0			0
$457$	4.53311e10	−	4.53311e10i	1.03928	−	1.03928i	0.0400801	−	0.999196i	$-0.487239\pi$
$457$	4.53311e10	−	4.53311e10i	1.03928	−	1.03928i	0.999196	−	0.0400801i	$-0.0127613\pi$
$458$	3.16409e10	+	3.16409e10i	0.719095	+	0.719095i
$459$		0			0
$460$	5.09579e7	+	3.00043e9i	0.00113810	+	0.0670120i
$461$	3.53353e9			0.0782357			0.0391178	−	0.999235i	$-0.487545\pi$
$461$	3.53353e9			0.0782357			0.0391178	+	0.999235i	$0.487545\pi$
$462$		0			0
$463$	1.72557e10	+	1.72557e10i	0.375499	+	0.375499i	0.869475	−	0.493976i	$-0.164457\pi$
$463$	1.72557e10	+	1.72557e10i	0.375499	+	0.375499i	−0.493976	+	0.869475i	$0.664457\pi$
$464$			2.80018e10i			0.604107i
$465$		0			0
$466$	−2.35392e10			−0.499169
$467$	2.45996e10	−	2.45996e10i	0.517203	−	0.517203i	−0.399521	−	0.916724i	$-0.630823\pi$
$467$	2.45996e10	−	2.45996e10i	0.517203	−	0.517203i	0.916724	+	0.399521i	$0.130823\pi$
$468$		0			0
$469$			1.14714e10i			0.237096i
$470$	−1.91188e10	−	1.84802e10i	−0.391804	−	0.378718i
$471$		0			0
$472$	−4.78094e10	+	4.78094e10i	−0.963264	+	0.963264i
$473$	1.03730e10	+	1.03730e10i	0.207234	+	0.207234i
$474$		0			0
$475$	−2.32674e10	+	7.90553e8i	−0.457061	+	0.0155295i
$476$	−2.67413e9			−0.0520900
$477$		0			0
$478$	1.49602e10	+	1.49602e10i	0.286568	+	0.286568i
$479$			7.37614e10i			1.40116i	0.713575	+	0.700579i	$0.247075\pi$
$479$			7.37614e10i			1.40116i	−0.713575	+	0.700579i	$0.752925\pi$
$480$		0			0
$481$	9.85206e8			0.0184055
$482$	−1.66314e10	+	1.66314e10i	−0.308135	+	0.308135i
$483$		0			0
$484$			4.21753e9i			0.0768558i
$485$	−5.06382e8	−	2.98161e10i	−0.00915189	−	0.538869i
$486$		0			0
$487$	−2.80441e10	+	2.80441e10i	−0.498569	+	0.498569i	−0.910992	−	0.412423i	$-0.864682\pi$
$487$	−2.80441e10	+	2.80441e10i	−0.498569	+	0.498569i	0.412423	+	0.910992i	$0.364682\pi$
$488$	−5.37166e10	−	5.37166e10i	−0.947173	−	0.947173i
$489$		0			0
$490$	5.50313e10	−	9.34625e8i	0.954610	−	0.0162126i
$491$	1.16769e10			0.200911			0.100455	−	0.994942i	$-0.467970\pi$
$491$	1.16769e10			0.200911			0.100455	+	0.994942i	$0.467970\pi$
$492$		0			0
$493$	4.03646e10	+	4.03646e10i	0.683302	+	0.683302i
$494$			1.14185e10i			0.191735i
$495$		0			0
$496$	−3.62753e10			−0.599355
$497$	−1.52974e10	+	1.52974e10i	−0.250722	+	0.250722i
$498$		0			0
$499$			7.08522e10i			1.14275i	0.820689	+	0.571375i	$0.193590\pi$
$499$			7.08522e10i			1.14275i	−0.820689	+	0.571375i	$0.806410\pi$
$500$	−4.18091e9	+	4.63019e9i	−0.0668946	+	0.0740830i
$501$		0			0
$502$	−6.21751e10	+	6.21751e10i	−0.979043	+	0.979043i
$503$	7.32217e10	+	7.32217e10i	1.14385	+	1.14385i	0.987740	+	0.156107i	$0.0498944\pi$
$503$	7.32217e10	+	7.32217e10i	1.14385	+	1.14385i	0.156107	+	0.987740i	$0.450106\pi$
$504$		0			0
$505$	8.32225e9	−	8.60982e9i	0.127960	−	0.132382i
$506$	−2.21393e10			−0.337724
$507$		0			0
$508$	7.49750e9	+	7.49750e9i	0.112580	+	0.112580i
$509$		−	1.10598e11i		−	1.64769i	−0.566813	−	0.823846i	$-0.691824\pi$
$509$		−	1.10598e11i		−	1.64769i	0.566813	−	0.823846i	$-0.308176\pi$
$510$		0			0
$511$	2.56797e10			0.376623
$512$	−3.94608e10	+	3.94608e10i	−0.574231	+	0.574231i
$513$		0			0
$514$		−	5.67034e10i		−	0.812376i
$515$	−1.19463e11	+	2.02890e9i	−1.69826	+	0.0288425i
$516$		0			0
$517$	1.25894e10	−	1.25894e10i	0.176215	−	0.176215i
$518$	7.35813e8	+	7.35813e8i	0.0102199	+	0.0102199i
$519$		0			0
$520$	−1.98407e10	−	1.91781e10i	−0.271359	−	0.262296i
$521$	8.07216e10			1.09557			0.547783	−	0.836620i	$-0.315472\pi$
$521$	8.07216e10			1.09557			0.547783	+	0.836620i	$0.315472\pi$
$522$		0			0
$523$	−3.77792e10	−	3.77792e10i	−0.504948	−	0.504948i	0.408024	−	0.912971i	$-0.366218\pi$
$523$	−3.77792e10	−	3.77792e10i	−0.504948	−	0.504948i	−0.912971	+	0.408024i	$0.866218\pi$
$524$		−	8.62844e9i		−	0.114448i
$525$		0			0
$526$	3.07170e10			0.401270
$527$	−5.22908e10	+	5.22908e10i	−0.677927	+	0.677927i
$528$		0			0
$529$		−	4.30044e10i		−	0.549149i
$530$	5.83741e10	−	6.03911e10i	0.739804	−	0.765367i
$531$		0			0
$532$	−7.73978e8	+	7.73978e8i	−0.00966233	+	0.00966233i
$533$	−1.46752e10	−	1.46752e10i	−0.181835	−	0.181835i
$534$		0			0
$535$	1.84352e9	+	1.08548e11i	0.0225026	+	1.32497i
$536$	−6.17164e10			−0.747725
$537$		0			0
$538$	−7.28917e10	−	7.28917e10i	−0.870060	−	0.870060i
$539$			3.68527e10i			0.436631i
$540$		0			0
$541$	7.53948e10			0.880141			0.440071	−	0.897963i	$-0.354953\pi$
$541$	7.53948e10			0.880141			0.440071	+	0.897963i	$0.354953\pi$
$542$	−6.18409e10	+	6.18409e10i	−0.716604	+	0.716604i
$543$		0			0
$544$		−	3.03691e10i		−	0.346766i
$545$	7.49481e10	+	7.24449e10i	0.849522	+	0.821149i
$546$		0			0
$547$	2.20178e10	−	2.20178e10i	0.245937	−	0.245937i	−0.573364	−	0.819301i	$-0.694362\pi$
$547$	2.20178e10	−	2.20178e10i	0.245937	−	0.245937i	0.819301	+	0.573364i	$0.194362\pi$
$548$	2.71174e9	+	2.71174e9i	0.0300694	+	0.0300694i
$549$		0			0
$550$	−3.36312e10	−	3.14209e10i	−0.367529	−	0.343374i
$551$	2.33656e10			0.253496
$552$		0			0
$553$	−4.13703e9	−	4.13703e9i	−0.0442372	−	0.0442372i
$554$		−	1.28758e11i		−	1.36689i
$555$		0			0
$556$	−1.49906e10			−0.156863
$557$	1.03428e11	−	1.03428e11i	1.07453	−	1.07453i	0.0775357	−	0.996990i	$-0.475295\pi$
$557$	1.03428e11	−	1.03428e11i	1.07453	−	1.07453i	0.996990	−	0.0775357i	$-0.0247052\pi$
$558$		0			0
$559$		−	2.38536e10i		−	0.244290i
$560$	−5.44826e8	−	3.20797e10i	−0.00553995	−	0.326196i
$561$		0			0
$562$	8.46441e10	−	8.46441e10i	0.848499	−	0.848499i
$563$	7.70545e10	+	7.70545e10i	0.766945	+	0.766945i	0.977567	−	0.210623i	$-0.0675491\pi$
$563$	7.70545e10	+	7.70545e10i	0.766945	+	0.766945i	−0.210623	+	0.977567i	$0.567549\pi$
$564$		0			0
$565$	−2.85768e10	+	4.85334e8i	−0.280427	+	0.00476263i
$566$	6.26329e10			0.610290
$567$		0			0
$568$	−8.23008e10	−	8.23008e10i	−0.790698	−	0.790698i
$569$		−	6.19669e10i		−	0.591168i	−0.955317	−	0.295584i	$-0.904486\pi$
$569$		−	6.19669e10i		−	0.591168i	0.955317	−	0.295584i	$-0.0955142\pi$
$570$		0			0
$571$	2.38428e10			0.224292			0.112146	−	0.993692i	$-0.464228\pi$
$571$	2.38428e10			0.224292			0.112146	+	0.993692i	$0.464228\pi$
$572$	−1.44867e9	+	1.44867e9i	−0.0135328	+	0.0135328i
$573$		0			0
$574$		−	2.19208e10i		−	0.201933i
$575$	−5.01083e10	+	5.36331e10i	−0.458393	+	0.490638i
$576$		0			0
$577$	1.08821e11	−	1.08821e11i	0.981772	−	0.981772i	−0.0180652	−	0.999837i	$-0.505751\pi$
$577$	1.08821e11	−	1.08821e11i	0.981772	−	0.981772i	0.999837	+	0.0180652i	$0.00575065\pi$
$578$	−1.68780e11	−	1.68780e11i	−1.51220	−	1.51220i
$579$		0			0
$580$	4.35152e9	−	4.50188e9i	0.0384529	−	0.0397816i
$581$	2.02916e10			0.178079
$582$		0			0
$583$	3.97666e10	+	3.97666e10i	0.344226	+	0.344226i
$584$			1.38158e11i			1.18775i
$585$		0			0
$586$	5.38366e10			0.456549
$587$	9.61187e10	−	9.61187e10i	0.809572	−	0.809572i	−0.174997	−	0.984569i	$-0.555992\pi$
$587$	9.61187e10	−	9.61187e10i	0.809572	−	0.809572i	0.984569	+	0.174997i	$0.0559916\pi$
$588$		0			0
$589$			3.02693e10i			0.251502i
$590$	1.83347e11	−	3.11388e9i	1.51310	−	0.0256977i
$591$		0			0
$592$	−4.35782e9	+	4.35782e9i	−0.0354799	+	0.0354799i
$593$	−1.01154e10	−	1.01154e10i	−0.0818021	−	0.0818021i	0.665022	−	0.746824i	$-0.268422\pi$
$593$	−1.01154e10	−	1.01154e10i	−0.0818021	−	0.0818021i	−0.746824	+	0.665022i	$0.768422\pi$
$594$		0			0
$595$	−4.70283e10	−	4.54575e10i	−0.375225	−	0.362692i
$596$	−1.39505e10			−0.110561
$597$		0			0
$598$	2.54556e10	+	2.54556e10i	0.199057	+	0.199057i
$599$		−	1.61079e11i		−	1.25121i	−0.780139	−	0.625606i	$-0.784852\pi$
$599$		−	1.61079e11i		−	1.25121i	0.780139	−	0.625606i	$-0.215148\pi$
$600$		0			0
$601$	2.16088e11			1.65627			0.828137	−	0.560526i	$-0.189401\pi$
$601$	2.16088e11			1.65627			0.828137	+	0.560526i	$0.189401\pi$
$602$	1.78153e10	−	1.78153e10i	0.135646	−	0.135646i
$603$		0			0
$604$		−	2.26984e9i		−	0.0170548i
$605$	−7.16939e10	+	7.41712e10i	−0.535132	+	0.553623i
$606$		0			0
$607$	−8.94773e10	+	8.94773e10i	−0.659111	+	0.659111i	−0.955170	−	0.296059i	$-0.904327\pi$
$607$	−8.94773e10	+	8.94773e10i	−0.659111	+	0.659111i	0.296059	+	0.955170i	$0.404327\pi$
$608$	−8.78979e9	−	8.78979e9i	−0.0643227	−	0.0643227i
$609$		0			0
$610$	3.49862e9	+	2.06001e11i	0.0252684	+	1.48782i
$611$	−2.89504e10			−0.207725
$612$		0			0
$613$	−1.23726e11	−	1.23726e11i	−0.876229	−	0.876229i	0.116913	−	0.993142i	$-0.462700\pi$
$613$	−1.23726e11	−	1.23726e11i	−0.876229	−	0.876229i	−0.993142	+	0.116913i	$0.962700\pi$
$614$			1.22668e11i			0.863096i
$615$		0			0
$616$	1.95152e10			0.135535
$617$	−1.10854e11	+	1.10854e11i	−0.764908	+	0.764908i	−0.977205	−	0.212297i	$-0.931906\pi$
$617$	−1.10854e11	+	1.10854e11i	−0.764908	+	0.764908i	0.212297	+	0.977205i	$0.431906\pi$
$618$		0			0
$619$			1.30648e11i			0.889897i	0.895556	+	0.444949i	$0.146778\pi$
$619$			1.30648e11i			0.889897i	−0.895556	+	0.444949i	$0.853222\pi$
$620$	5.83202e9	+	5.63723e9i	0.0394686	+	0.0381504i
$621$		0			0
$622$	−1.56801e11	+	1.56801e11i	−1.04758	+	1.04758i
$623$	−4.17199e10	−	4.17199e10i	−0.276944	−	0.276944i
$624$		0			0
$625$	−1.52236e11	+	1.03569e10i	−0.997694	+	0.0678753i
$626$	−2.14236e11			−1.39507
$627$		0			0
$628$	8.20431e9	+	8.20431e9i	0.0527477	+	0.0527477i
$629$			1.25636e10i			0.0802622i
$630$		0			0
$631$	−2.21106e11			−1.39470			−0.697352	−	0.716729i	$-0.745639\pi$
$631$	−2.21106e11			−1.39470			−0.697352	+	0.716729i	$0.745639\pi$
$632$	2.22574e10	−	2.22574e10i	0.139510	−	0.139510i
$633$		0			0
$634$		−	1.16705e11i		−	0.722325i
$635$	4.40390e9	+	2.59304e11i	0.0270858	+	1.59483i
$636$		0			0
$637$	4.23729e10	−	4.23729e10i	0.257354	−	0.257354i
$638$	3.26633e10	+	3.26633e10i	0.197141	+	0.197141i
$639$		0			0
$640$	1.88397e11	−	3.19965e9i	1.12294	−	0.0190714i
$641$	−2.04377e11			−1.21060			−0.605298	−	0.795999i	$-0.706946\pi$
$641$	−2.04377e11			−1.21060			−0.605298	+	0.795999i	$0.706946\pi$
$642$		0			0
$643$	1.72443e11	+	1.72443e11i	1.00879	+	1.00879i	0.999961	+	0.00882849i	$0.00281023\pi$
$643$	1.72443e11	+	1.72443e11i	1.00879	+	1.00879i	0.00882849	+	0.999961i	$0.497190\pi$
$644$			3.45090e9i			0.0200627i
$645$		0			0
$646$	−1.45612e11			−0.836115
$647$	1.33246e11	−	1.33246e11i	0.760392	−	0.760392i	−0.216001	−	0.976393i	$-0.569301\pi$
$647$	1.33246e11	−	1.33246e11i	0.760392	−	0.760392i	0.976393	+	0.216001i	$0.0693014\pi$
$648$		0			0
$649$			1.22782e11i			0.692078i
$650$	2.54134e9	+	7.47962e10i	0.0142367	+	0.419012i
$651$		0			0
$652$	5.46966e9	−	5.46966e9i	0.0302670	−	0.0302670i
$653$	7.89023e10	+	7.89023e10i	0.433947	+	0.433947i	0.889969	−	0.456022i	$-0.150726\pi$
$653$	7.89023e10	+	7.89023e10i	0.433947	+	0.433947i	−0.456022	+	0.889969i	$0.650726\pi$
$654$		0			0
$655$	1.46675e11	−	1.51743e11i	0.796877	−	0.824412i
$656$	1.29825e11			0.701039
$657$		0			0
$658$	−2.16219e10	−	2.16219e10i	−0.115343	−	0.115343i
$659$			3.33275e11i			1.76710i	0.468339	+	0.883549i	$0.344853\pi$
$659$			3.33275e11i			1.76710i	−0.468339	+	0.883549i	$0.655147\pi$
$660$		0			0
$661$	−2.67623e11			−1.40190			−0.700951	−	0.713209i	$-0.747241\pi$
$661$	−2.67623e11			−1.40190			−0.700951	+	0.713209i	$0.747241\pi$
$662$	2.04130e10	−	2.04130e10i	0.106286	−	0.106286i
$663$		0			0
$664$			1.09170e11i			0.561603i
$665$	−2.67684e10	+	4.54621e8i	−0.136879	+	0.00232468i
$666$		0			0
$667$	5.20896e10	−	5.20896e10i	0.263177	−	0.263177i
$668$	1.76571e10	+	1.76571e10i	0.0886777	+	0.0886777i
$669$		0			0
$670$	1.20350e11	+	1.16330e11i	0.597237	+	0.577289i
$671$	−1.37952e11			−0.680517
$672$		0			0
$673$	−4.65870e10	−	4.65870e10i	−0.227093	−	0.227093i	0.584384	−	0.811477i	$-0.301336\pi$
$673$	−4.65870e10	−	4.65870e10i	−0.227093	−	0.227093i	−0.811477	+	0.584384i	$0.801336\pi$
$674$			1.40672e11i			0.681662i
$675$		0			0
$676$	−1.75129e10			−0.0838631
$677$	2.04905e11	−	2.04905e11i	0.975432	−	0.975432i	−0.0242736	−	0.999705i	$-0.507727\pi$
$677$	2.04905e11	−	2.04905e11i	0.975432	−	0.975432i	0.999705	+	0.0242736i	$0.00772728\pi$
$678$		0			0
$679$		−	3.42925e10i		−	0.161332i
$680$	2.44564e11	−	2.53014e11i	1.14382	−	1.18334i
$681$		0			0
$682$	−4.23141e10	+	4.23141e10i	−0.195590	+	0.195590i
$683$	−2.26392e11	−	2.26392e11i	−1.04035	−	1.04035i	−0.999151	−	0.0411961i	$-0.986883\pi$
$683$	−2.26392e11	−	2.26392e11i	−1.04035	−	1.04035i	−0.0411961	−	0.999151i	$-0.513117\pi$
$684$		0			0
$685$	1.59283e9	+	9.37866e10i	0.00723445	+	0.425969i
$686$	1.32817e11			0.599730
$687$		0			0
$688$	1.05511e11	+	1.05511e11i	0.470915	+	0.470915i
$689$		−	9.14465e10i		−	0.405779i
$690$		0			0
$691$	−1.15111e11			−0.504900			−0.252450	−	0.967610i	$-0.581236\pi$
$691$	−1.15111e11			−0.504900			−0.252450	+	0.967610i	$0.581236\pi$
$692$	8.69734e9	−	8.69734e9i	0.0379282	−	0.0379282i
$693$		0			0
$694$			9.79658e10i			0.422315i
$695$	−2.63631e11	−	2.54826e11i	−1.12995	−	1.09221i
$696$		0			0
$697$	1.87142e11	−	1.87142e11i	0.792941	−	0.792941i
$698$	−4.50585e10	−	4.50585e10i	−0.189826	−	0.189826i
$699$		0			0
$700$	−4.89764e9	+	5.24216e9i	−0.0203983	+	0.0218332i
$701$	−3.26439e10			−0.135185			−0.0675927	−	0.997713i	$-0.521532\pi$
$701$	−3.26439e10			−0.135185			−0.0675927	+	0.997713i	$0.521532\pi$
$702$		0			0
$703$	3.63631e9	+	3.63631e9i	0.0148881	+	0.0148881i
$704$			1.03819e11i			0.422655i
$705$		0			0
$706$	1.05921e11			0.426349
$707$	9.73707e9	−	9.73707e9i	0.0389718	−	0.0389718i
$708$		0			0
$709$		−	1.10106e11i		−	0.435737i	−0.975978	−	0.217869i	$-0.930090\pi$
$709$		−	1.10106e11i		−	0.435737i	0.975978	−	0.217869i	$-0.0699104\pi$
$710$	5.36034e9	+	3.15620e11i	0.0210940	+	1.24203i
$711$		0			0
$712$	2.24455e11	−	2.24455e11i	0.873392	−	0.873392i
$713$	6.74802e10	+	6.74802e10i	0.261107	+	0.261107i
$714$		0			0
$715$	−5.01030e10	+	8.50926e8i	−0.191708	+	0.00325587i
$716$	1.92052e9			0.00730746
$717$		0			0
$718$	−1.07295e10	−	1.07295e10i	−0.0403723	−	0.0403723i
$719$		−	2.80995e11i		−	1.05144i	−0.850658	−	0.525719i	$-0.823796\pi$
$719$		−	2.80995e11i		−	1.05144i	0.850658	−	0.525719i	$-0.176204\pi$
$720$		0			0
$721$	−1.37399e11			−0.508442
$722$	1.59364e11	−	1.59364e11i	0.586464	−	0.586464i
$723$		0			0
$724$		−	3.73463e9i		−	0.0135923i
$725$	1.53055e11	−	5.20033e9i	0.553982	−	0.0188226i
$726$		0			0
$727$	7.91155e10	−	7.91155e10i	0.283220	−	0.283220i	−0.551172	−	0.834392i	$-0.685819\pi$
$727$	7.91155e10	−	7.91155e10i	0.283220	−	0.283220i	0.834392	+	0.551172i	$0.185819\pi$
$728$	−2.24384e10	−	2.24384e10i	−0.0798853	−	0.0798853i
$729$		0			0
$730$	2.60416e11	−	2.69415e11i	0.917016	−	0.948702i
$731$	3.04187e11			1.06530
$732$		0			0
$733$	−1.00588e11	−	1.00588e11i	−0.348441	−	0.348441i	0.511088	−	0.859529i	$-0.329243\pi$
$733$	−1.00588e11	−	1.00588e11i	−0.348441	−	0.348441i	−0.859529	+	0.511088i	$0.829243\pi$
$734$			2.34639e11i			0.808381i
$735$		0			0
$736$	−3.91906e10			−0.133558
$737$	−7.92485e10	+	7.92485e10i	−0.268609	+	0.268609i
$738$		0			0
$739$		−	1.06947e11i		−	0.358584i	−0.983796	−	0.179292i	$-0.942619\pi$
$739$		−	1.06947e11i		−	0.358584i	0.983796	−	0.179292i	$-0.0573806\pi$
$740$	1.37782e9	−	2.34003e7i	0.00459480	−	7.80358e-5i
$741$		0			0
$742$	6.82979e10	−	6.82979e10i	0.225316	−	0.225316i
$743$	−5.96783e10	−	5.96783e10i	−0.195822	−	0.195822i	0.602384	−	0.798206i	$-0.294218\pi$
$743$	−5.96783e10	−	5.96783e10i	−0.195822	−	0.195822i	−0.798206	+	0.602384i	$0.794218\pi$
$744$		0			0
$745$	−2.45338e11	−	2.37144e11i	−0.796417	−	0.769817i
$746$	−3.72326e11			−1.20218
$747$		0			0
$748$	−1.84739e10	−	1.84739e10i	−0.0590135	−	0.0590135i
$749$			1.24844e11i			0.396681i
$750$		0			0
$751$	−2.90374e11			−0.912846			−0.456423	−	0.889763i	$-0.650870\pi$
$751$	−2.90374e11			−0.912846			−0.456423	+	0.889763i	$0.650870\pi$
$752$	1.28055e11	−	1.28055e11i	0.400429	−	0.400429i
$753$		0			0
$754$		−	7.51119e10i		−	0.232393i
$755$	3.85851e10	−	3.99184e10i	0.118750	−	0.122853i
$756$		0			0
$757$	−2.22407e11	+	2.22407e11i	−0.677274	+	0.677274i	−0.959383	−	0.282108i	$-0.908966\pi$
$757$	−2.22407e11	+	2.22407e11i	−0.677274	+	0.677274i	0.282108	+	0.959383i	$0.408966\pi$
$758$	4.79102e9	+	4.79102e9i	0.0145128	+	0.0145128i
$759$		0			0
$760$	−2.44588e9	−	1.44015e11i	−0.00733129	−	0.431671i
$761$	−5.59405e11			−1.66797			−0.833984	−	0.551788i	$-0.813946\pi$
$761$	−5.59405e11			−1.66797			−0.833984	+	0.551788i	$0.813946\pi$
$762$		0			0
$763$	8.47608e10	+	8.47608e10i	0.250090	+	0.250090i
$764$		−	6.50191e10i		−	0.190839i
$765$		0			0
$766$	4.60960e11			1.33890
$767$	1.41173e11	−	1.41173e11i	0.407916	−	0.407916i
$768$		0			0
$769$			3.07549e10i			0.0879446i	0.999033	+	0.0439723i	$0.0140013\pi$
$769$			3.07549e10i			0.0879446i	−0.999033	+	0.0439723i	$0.985999\pi$
$770$	−3.80556e10	−	3.67845e10i	−0.108257	−	0.104641i
$771$		0			0
$772$	2.41976e10	−	2.41976e10i	0.0681245	−	0.0681245i
$773$	1.21896e11	+	1.21896e11i	0.341405	+	0.341405i	0.856896	−	0.515490i	$-0.172390\pi$
$773$	1.21896e11	+	1.21896e11i	0.341405	+	0.341405i	−0.515490	+	0.856896i	$0.672390\pi$
$774$		0			0
$775$	6.73683e9	+	1.98277e11i	0.0186745	+	0.549625i
$776$	1.84495e11			0.508789
$777$		0			0
$778$	−1.19299e11	−	1.19299e11i	−0.325625	−	0.325625i
$779$		−	1.08330e11i		−	0.294170i
$780$		0			0
$781$	−2.11361e11			−0.568094
$782$	−3.24616e11	+	3.24616e11i	−0.868046	+	0.868046i
$783$		0			0
$784$			3.74853e11i			0.992193i
$785$	4.81906e9	+	2.83749e11i	0.0126906	+	0.747234i
$786$		0			0
$787$	−2.26235e9	+	2.26235e9i	−0.00589741	+	0.00589741i	−0.710049	−	0.704152i	$-0.751327\pi$
$787$	−2.26235e9	+	2.26235e9i	−0.00589741	+	0.00589741i	0.704152	+	0.710049i	$0.251327\pi$
$788$	1.64140e10	+	1.64140e10i	0.0425706	+	0.0425706i
$789$		0			0
$790$	−8.53562e10	+	1.44965e9i	−0.219142	+	0.00372181i
$791$	−3.28671e10			−0.0839567
$792$		0			0
$793$	1.58616e11	+	1.58616e11i	0.401102	+	0.401102i
$794$		−	1.09139e11i		−	0.274597i
$795$		0			0
$796$	8.88127e9			0.0221219
$797$	−3.08554e11	+	3.08554e11i	−0.764711	+	0.764711i	−0.977170	−	0.212459i	$-0.931853\pi$
$797$	−3.08554e11	+	3.08554e11i	−0.764711	+	0.764711i	0.212459	+	0.977170i	$0.431853\pi$
$798$		0			0
$799$		−	3.69183e11i		−	0.905846i
$800$	−5.95333e10	−	5.56207e10i	−0.145345	−	0.135793i
$801$		0			0
$802$	−4.66626e11	+	4.66626e11i	−1.12790	+	1.12790i
$803$	1.77405e11	+	1.77405e11i	0.426682	+	0.426682i
$804$		0			0
$805$	−5.86619e10	+	6.06889e10i	−0.139692	+	0.144519i
$806$	9.73047e10			0.230565
$807$		0			0
$808$	5.23859e10	+	5.23859e10i	0.122905	+	0.122905i
$809$		−	3.71836e11i		−	0.868076i	−0.900895	−	0.434038i	$-0.857088\pi$
$809$		−	3.71836e11i		−	0.868076i	0.900895	−	0.434038i	$-0.142912\pi$
$810$		0			0
$811$	7.35802e11			1.70090			0.850448	−	0.526060i	$-0.176331\pi$
$811$	7.35802e11			1.70090			0.850448	+	0.526060i	$0.176331\pi$
$812$	5.09129e9	−	5.09129e9i	0.0117113	−	0.0117113i
$813$		0			0
$814$			1.01665e10i			0.0231566i
$815$	1.89170e11	−	3.21278e9i	0.428768	−	0.00728199i
$816$		0			0
$817$	8.80415e10	−	8.80415e10i	0.197606	−	0.197606i
$818$	−4.19302e11	−	4.19302e11i	−0.936513	−	0.936513i
$819$		0			0
$820$	−2.08721e10	−	2.01749e10i	−0.0461647	−	0.0446228i
$821$	5.89174e11			1.29679			0.648397	−	0.761303i	$-0.275440\pi$
$821$	5.89174e11			1.29679			0.648397	+	0.761303i	$0.275440\pi$
$822$		0			0
$823$	−6.93799e10	−	6.93799e10i	−0.151229	−	0.151229i	0.627438	−	0.778667i	$-0.284104\pi$
$823$	−6.93799e10	−	6.93799e10i	−0.151229	−	0.151229i	−0.778667	+	0.627438i	$0.784104\pi$
$824$		−	7.39211e11i		−	1.60346i
$825$		0			0
$826$	2.10874e11			0.453004
$827$	6.01415e10	−	6.01415e10i	0.128574	−	0.128574i	−0.639891	−	0.768465i	$-0.721021\pi$
$827$	6.01415e10	−	6.01415e10i	0.128574	−	0.128574i	0.768465	+	0.639891i	$0.221021\pi$
$828$		0			0
$829$			8.00261e11i			1.69439i	0.531282	+	0.847195i	$0.321711\pi$
$829$			8.00261e11i			1.69439i	−0.531282	+	0.847195i	$0.678289\pi$
$830$	2.05776e11	−	2.12886e11i	0.433592	−	0.448574i
$831$		0			0
$832$	1.19370e11	−	1.19370e11i	0.249116	−	0.249116i
$833$	5.40350e11	+	5.40350e11i	1.12226	+	1.12226i
$834$		0			0
$835$	1.03715e10	+	6.10680e11i	0.0213351	+	1.25623i
$836$	−1.06939e10			−0.0218932
$837$		0			0
$838$	−1.96105e11	−	1.96105e11i	−0.397661	−	0.397661i
$839$			6.08689e11i			1.22842i	0.789142	+	0.614211i	$0.210526\pi$
$839$			6.08689e11i			1.22842i	−0.789142	+	0.614211i	$0.789474\pi$
$840$		0			0
$841$	3.46545e11			0.692749
$842$	−2.43560e11	+	2.43560e11i	−0.484570	+	0.484570i
$843$		0			0
$844$			3.38419e10i			0.0666937i
$845$	−3.07989e11	−	2.97702e11i	−0.604099	−	0.583922i
$846$		0			0
$847$	−8.38822e10	+	8.38822e10i	−0.162981	+	0.162981i
$848$	4.04492e11	+	4.04492e11i	0.782215	+	0.782215i
$849$		0			0
$850$	−9.53820e11	+	3.24078e10i	−1.82722	+	0.0620831i
$851$	1.62130e10			0.0309134
$852$		0			0
$853$	3.37705e11	+	3.37705e11i	0.637883	+	0.637883i	0.950033	−	0.312150i	$-0.101049\pi$
$853$	3.37705e11	+	3.37705e11i	0.637883	+	0.637883i	−0.312150	+	0.950033i	$0.601049\pi$
$854$			2.36929e11i			0.445437i
$855$		0			0
$856$	−6.71668e11			−1.25101
$857$	−2.05118e11	+	2.05118e11i	−0.380260	+	0.380260i	−0.871196	−	0.490935i	$-0.836655\pi$
$857$	−2.05118e11	+	2.05118e11i	−0.380260	+	0.380260i	0.490935	+	0.871196i	$0.336655\pi$
$858$		0			0
$859$		−	1.00757e12i		−	1.85056i	−0.379281	−	0.925282i	$-0.623829\pi$
$859$		−	1.00757e12i		−	1.85056i	0.379281	−	0.925282i	$-0.376171\pi$
$860$	−5.66562e8	−	3.33595e10i	−0.00103575	−	0.0609855i
$861$		0			0
$862$	−2.45550e10	+	2.45550e10i	−0.0444746	+	0.0444746i
$863$	−1.70651e11	−	1.70651e11i	−0.307656	−	0.307656i	0.536344	−	0.844000i	$-0.319805\pi$
$863$	−1.70651e11	−	1.70651e11i	−0.307656	−	0.307656i	−0.844000	+	0.536344i	$0.819805\pi$
$864$		0			0
$865$	3.00801e11	−	5.10866e9i	0.537298	−	0.00912520i
$866$	6.89110e11			1.22523
$867$		0			0
$868$	6.59558e9	+	6.59558e9i	0.0116191	+	0.0116191i
$869$		−	5.71602e10i		−	0.100234i
$870$		0			0
$871$	1.82238e11			0.316641
$872$	−4.56017e11	+	4.56017e11i	−0.788706	+	0.788706i
$873$		0			0
$874$			1.87909e11i			0.322033i
$875$	−1.75243e11	+	8.93562e9i	−0.298958	+	0.0152438i
$876$		0			0
$877$	−1.79019e11	+	1.79019e11i	−0.302623	+	0.302623i	−0.842039	−	0.539416i	$-0.818645\pi$
$877$	−1.79019e11	+	1.79019e11i	−0.302623	+	0.302623i	0.539416	+	0.842039i	$0.318645\pi$
$878$	−1.85436e11	−	1.85436e11i	−0.312044	−	0.312044i
$879$		0			0
$880$	2.17855e11	−	2.25383e11i	0.363276	−	0.375829i
$881$	4.12168e10			0.0684180			0.0342090	−	0.999415i	$-0.489109\pi$
$881$	4.12168e10			0.0684180			0.0342090	+	0.999415i	$0.489109\pi$
$882$		0			0
$883$	−4.90367e11	−	4.90367e11i	−0.806638	−	0.806638i	0.177486	−	0.984123i	$-0.443204\pi$
$883$	−4.90367e11	−	4.90367e11i	−0.806638	−	0.806638i	−0.984123	+	0.177486i	$0.943204\pi$
$884$			4.24822e10i			0.0695661i
$885$		0			0
$886$	−1.83344e11			−0.297530
$887$	−5.99973e11	+	5.99973e11i	−0.969253	+	0.969253i	−0.999541	−	0.0302885i	$-0.990357\pi$
$887$	−5.99973e11	+	5.99973e11i	−0.969253	+	0.969253i	0.0302885	+	0.999541i	$0.490357\pi$
$888$		0			0
$889$			2.98235e11i			0.477475i
$890$	−8.60776e11	+	1.46190e10i	−1.37192	+	0.0233001i
$891$		0			0
$892$	7.57453e10	−	7.57453e10i	0.119645	−	0.119645i
$893$	−1.06853e11	−	1.06853e11i	−0.168028	−	0.168028i
$894$		0			0
$895$	3.37750e10	+	3.26469e10i	0.0526385	+	0.0508804i
$896$	2.16682e11			0.336195
$897$		0			0
$898$	−1.44557e11	−	1.44557e11i	−0.222298	−	0.222298i
$899$		−	1.99114e11i		−	0.304834i
$900$		0			0
$901$	1.16615e12			1.76952
$902$	1.51437e11	−	1.51437e11i	0.228773	−	0.228773i
$903$		0			0
$904$		−	1.76826e11i		−	0.264773i
$905$	6.34851e10	−	6.56787e10i	0.0946406	−	0.0979108i
$906$		0			0
$907$	−5.29755e11	+	5.29755e11i	−0.782791	+	0.782791i	−0.980301	−	0.197510i	$-0.936715\pi$
$907$	−5.29755e11	+	5.29755e11i	−0.782791	+	0.782791i	0.197510	+	0.980301i	$0.436715\pi$
$908$	−2.14014e10	−	2.14014e10i	−0.0314847	−	0.0314847i
$909$		0			0
$910$	1.46144e9	+	8.60505e10i	0.00213116	+	0.125484i
$911$	4.06858e11			0.590703			0.295351	−	0.955389i	$-0.404563\pi$
$911$	4.06858e11			0.590703			0.295351	+	0.955389i	$0.404563\pi$
$912$		0			0
$913$	1.40182e11	+	1.40182e11i	0.201748	+	0.201748i
$914$		−	1.07570e12i		−	1.54137i
$915$		0			0
$916$	6.81432e10			0.0967922
$917$	1.71611e11	−	1.71611e11i	0.242698	−	0.242698i
$918$		0			0
$919$		−	1.03523e12i		−	1.45135i	−0.688036	−	0.725676i	$-0.741527\pi$
$919$		−	1.03523e12i		−	1.45135i	0.688036	−	0.725676i	$-0.258473\pi$
$920$	−3.26509e11	−	3.15604e11i	−0.455768	−	0.440546i
$921$		0			0
$922$	4.19250e10	−	4.19250e10i	0.0580163	−	0.0580163i
$923$	2.43020e11	+	2.43020e11i	0.334839	+	0.334839i
$924$		0			0
$925$	2.46287e10	+	2.30101e10i	0.0336415	+	0.0314305i
$926$	4.09476e11			0.556909
$927$		0			0
$928$	5.78200e10	+	5.78200e10i	0.0779626	+	0.0779626i
$929$		−	5.10944e11i		−	0.685978i	−0.939339	−	0.342989i	$-0.888561\pi$
$929$		−	5.10944e11i		−	0.685978i	0.939339	−	0.342989i	$-0.111439\pi$
$930$		0			0
$931$	3.12789e11			0.416345
$932$	−2.53475e10	+	2.53475e10i	−0.0335948	+	0.0335948i
$933$		0			0
$934$		−	5.83746e11i		−	0.767072i
$935$	−1.08512e10	−	6.38927e11i	−0.0141982	−	0.835997i
$936$		0			0
$937$	−6.26235e11	+	6.26235e11i	−0.812417	+	0.812417i	−0.984996	−	0.172579i	$-0.944790\pi$
$937$	−6.26235e11	+	6.26235e11i	−0.812417	+	0.812417i	0.172579	+	0.984996i	$0.444790\pi$
$938$	1.36107e11	+	1.36107e11i	0.175820	+	0.175820i
$939$		0			0
$940$	−4.04875e10	+	6.87620e8i	−0.0518572	+	0.000880718i
$941$	−5.32097e11			−0.678628			−0.339314	−	0.940673i	$-0.610195\pi$
$941$	−5.32097e11			−0.678628			−0.339314	+	0.940673i	$0.610195\pi$
$942$		0			0
$943$	−2.41503e11	−	2.41503e11i	−0.305405	−	0.305405i
$944$			1.24889e12i			1.57267i
$945$		0			0
$946$	2.46150e11			0.307352
$947$	6.94903e11	−	6.94903e11i	0.864021	−	0.864021i	−0.127781	−	0.991802i	$-0.540786\pi$
$947$	6.94903e11	−	6.94903e11i	0.864021	−	0.864021i	0.991802	+	0.127781i	$0.0407855\pi$
$948$		0			0
$949$		−	4.07958e11i		−	0.502980i
$950$	−2.66686e11	+	2.85446e11i	−0.327421	+	0.350453i
$951$		0			0
$952$	2.86140e11	−	2.86140e11i	0.348362	−	0.348362i
$953$	−1.46903e11	−	1.46903e11i	−0.178098	−	0.178098i	0.612428	−	0.790526i	$-0.290193\pi$
$953$	−1.46903e11	−	1.46903e11i	−0.178098	−	0.178098i	−0.790526	+	0.612428i	$0.790193\pi$
$954$		0			0
$955$	1.10526e12	−	1.14345e12i	1.32878	−	1.37469i
$956$	3.22191e10			0.0385728
$957$		0			0
$958$	8.75174e11	+	8.75174e11i	1.03904	+	1.03904i
$959$			1.07867e11i			0.127531i
$960$		0			0
$961$	−5.94946e11			−0.697564
$962$	1.16894e10	−	1.16894e10i	0.0136487	−	0.0136487i
$963$		0			0
$964$			3.58182e10i			0.0414758i
$965$	8.36885e11	−	1.42132e10i	0.965065	−	0.0163902i
$966$		0			0
$967$	8.32464e11	−	8.32464e11i	0.952050	−	0.952050i	−0.0468522	−	0.998902i	$-0.514919\pi$
$967$	8.32464e11	−	8.32464e11i	0.952050	−	0.952050i	0.998902	+	0.0468522i	$0.0149190\pi$
$968$	−4.51290e11	−	4.51290e11i	−0.513989	−	0.513989i
$969$		0			0
$970$	−3.59774e11	−	3.47757e11i	−0.406389	−	0.392816i
$971$	−1.00239e11			−0.112761			−0.0563804	−	0.998409i	$-0.517956\pi$
$971$	−1.00239e11			−0.112761			−0.0563804	+	0.998409i	$0.517956\pi$
$972$		0			0
$973$	−2.98148e11	−	2.98148e11i	−0.332644	−	0.332644i
$974$			6.65481e11i			0.739435i
$975$		0			0
$976$	−1.40320e12			−1.54640
$977$	1.07451e11	−	1.07451e11i	0.117932	−	0.117932i	−0.645678	−	0.763610i	$-0.723425\pi$
$977$	1.07451e11	−	1.07451e11i	0.117932	−	0.117932i	0.763610	+	0.645678i	$0.223425\pi$
$978$		0			0
$979$		−	5.76434e11i		−	0.627507i
$980$	5.82526e10	−	6.02654e10i	0.0631554	−	0.0653377i
$981$		0			0
$982$	1.38546e11	−	1.38546e11i	0.148987	−	0.148987i
$983$	−5.36756e10	−	5.36756e10i	−0.0574861	−	0.0574861i	0.677779	−	0.735265i	$-0.262942\pi$
$983$	−5.36756e10	−	5.36756e10i	−0.0574861	−	0.0574861i	−0.735265	+	0.677779i	$0.762942\pi$
$984$		0			0
$985$	9.64130e9	+	5.67686e11i	0.0102421	+	0.603064i
$986$	9.57846e11			1.01342
$987$		0			0
$988$	1.22957e10	+	1.22957e10i	0.0129040	+	0.0129040i
$989$		−	3.92547e11i		−	0.410304i
$990$		0			0
$991$	−1.54321e12			−1.60004			−0.800019	−	0.599974i	$-0.795177\pi$
$991$	−1.54321e12			−1.60004			−0.800019	+	0.599974i	$0.795177\pi$
$992$	−7.49037e10	+	7.49037e10i	−0.0773493	+	0.0773493i
$993$		0			0
$994$			3.63005e11i			0.371850i
$995$	1.56190e11	+	1.50973e11i	0.159353	+	0.154031i
$996$		0			0
$997$	−7.69594e11	+	7.69594e11i	−0.778898	+	0.778898i	−0.979644	−	0.200745i	$-0.935664\pi$
$997$	−7.69594e11	+	7.69594e11i	−0.778898	+	0.778898i	0.200745	+	0.979644i	$0.435664\pi$
$998$	8.40656e11	+	8.40656e11i	0.847415	+	0.847415i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.9.g.a.28.3		6
3.2	odd	2		5.9.c.a.3.1	yes	6
5.2	odd	4	inner	45.9.g.a.37.3		6
12.11	even	2		80.9.p.c.33.3		6
15.2	even	4		5.9.c.a.2.1	✓	6
15.8	even	4		25.9.c.b.7.3		6
15.14	odd	2		25.9.c.b.18.3		6
60.47	odd	4		80.9.p.c.17.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.9.c.a.2.1	✓	6	15.2	even	4
5.9.c.a.3.1	yes	6	3.2	odd	2
25.9.c.b.7.3		6	15.8	even	4
25.9.c.b.18.3		6	15.14	odd	2
45.9.g.a.28.3		6	1.1	even	1	trivial
45.9.g.a.37.3		6	5.2	odd	4	inner
80.9.p.c.17.3		6	60.47	odd	4
80.9.p.c.33.3		6	12.11	even	2

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	45.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(11.8649 - 11.8649i) q^{2} -25.5528i q^{4} +(434.373 - 449.383i) q^{5} +(508.219 - 508.219i) q^{7} +(2734.24 + 2734.24i) q^{8} +O(q^{10})\)	\(q+(11.8649 - 11.8649i) q^{2} -25.5528i q^{4} +(434.373 - 449.383i) q^{5} +(508.219 - 508.219i) q^{7} +(2734.24 + 2734.24i) q^{8} +(-178.084 - 10485.7i) q^{10} +7021.93 q^{11} +(-8073.75 - 8073.75i) q^{13} -12060.0i q^{14} +71424.6 q^{16} +(102958. - 102958. i) q^{17} -59599.0i q^{19} +(-11483.0 - 11099.5i) q^{20} +(83314.7 - 83314.7i) q^{22} +(-132866. - 132866. i) q^{23} +(-13264.5 - 390400. i) q^{25} -191589. q^{26} +(-12986.4 - 12986.4i) q^{28} +392047. i q^{29} -507883. q^{31} +(147482. - 147482. i) q^{32} -2.44319e6i q^{34} +(-7628.00 - 449141. i) q^{35} +(-61012.9 + 61012.9i) q^{37} +(-707137. - 707137. i) q^{38} +(2.41640e6 - 41038.9i) q^{40} +1.81765e6 q^{41} +(1.47723e6 + 1.47723e6i) q^{43} -179430. i q^{44} -3.15288e6 q^{46} +(1.79287e6 - 1.79287e6i) q^{47} +5.24823e6i q^{49} +(-4.78945e6 - 4.47468e6i) q^{50} +(-206307. + 206307. i) q^{52} +(5.66320e6 + 5.66320e6i) q^{53} +(3.05014e6 - 3.15553e6i) q^{55} +2.77918e6 q^{56} +(4.65161e6 + 4.65161e6i) q^{58} +1.74855e7i q^{59} -1.96459e7 q^{61} +(-6.02599e6 + 6.02599e6i) q^{62} +1.47850e7i q^{64} +(-7.13522e6 + 121181. i) q^{65} +(-1.12859e7 + 1.12859e7i) q^{67} +(-2.63088e6 - 2.63088e6i) q^{68} +(-5.41953e6 - 5.23852e6i) q^{70} -3.01001e7 q^{71} +(2.52645e7 + 2.52645e7i) q^{73} +1.44783e6i q^{74} -1.52292e6 q^{76} +(3.56868e6 - 3.56868e6i) q^{77} -8.14025e6i q^{79} +(3.10249e7 - 3.20970e7i) q^{80} +(2.15663e7 - 2.15663e7i) q^{82} +(1.99635e7 + 1.99635e7i) q^{83} +(-1.54533e6 - 9.09902e7i) q^{85} +3.50545e7 q^{86} +(1.91996e7 + 1.91996e7i) q^{88} -8.20905e7i q^{89} -8.20646e6 q^{91} +(-3.39509e6 + 3.39509e6i) q^{92} -4.25446e7i q^{94} +(-2.67827e7 - 2.58882e7i) q^{95} +(3.37379e7 - 3.37379e7i) q^{97} +(6.22698e7 + 6.22698e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 220 q^{5} - 2352 q^{7} + 8220 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 - 220 * q^5 - 2352 * q^7 + 8220 * q^8	\( 6 q + 2 q^{2} - 220 q^{5} - 2352 q^{7} + 8220 q^{8} + 30870 q^{10} - 23192 q^{11} - 119142 q^{13} + 218616 q^{16} + 265502 q^{17} - 412260 q^{20} - 35664 q^{22} - 28888 q^{23} - 340350 q^{25} + 801388 q^{26} + 1305192 q^{28} - 747648 q^{31} - 3033928 q^{32} + 4971680 q^{35} - 454002 q^{37} - 1443720 q^{38} + 2683500 q^{40} - 2489432 q^{41} + 792648 q^{43} - 3149928 q^{46} + 15313352 q^{47} - 29537650 q^{50} - 735732 q^{52} + 13509122 q^{53} + 4448040 q^{55} + 18454800 q^{56} - 23903520 q^{58} + 24111192 q^{61} - 53913416 q^{62} + 30943610 q^{65} - 32827752 q^{67} - 8118692 q^{68} - 44156280 q^{70} + 13992928 q^{71} + 111859638 q^{73} - 56470800 q^{76} - 26260136 q^{77} - 23045920 q^{80} + 38023056 q^{82} + 14768432 q^{83} - 19713030 q^{85} + 135560008 q^{86} - 44555040 q^{88} + 167542032 q^{91} - 69931048 q^{92} - 239661000 q^{95} - 186656202 q^{97} + 345959698 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 220 * q^5 - 2352 * q^7 + 8220 * q^8 + 30870 * q^10 - 23192 * q^11 - 119142 * q^13 + 218616 * q^16 + 265502 * q^17 - 412260 * q^20 - 35664 * q^22 - 28888 * q^23 - 340350 * q^25 + 801388 * q^26 + 1305192 * q^28 - 747648 * q^31 - 3033928 * q^32 + 4971680 * q^35 - 454002 * q^37 - 1443720 * q^38 + 2683500 * q^40 - 2489432 * q^41 + 792648 * q^43 - 3149928 * q^46 + 15313352 * q^47 - 29537650 * q^50 - 735732 * q^52 + 13509122 * q^53 + 4448040 * q^55 + 18454800 * q^56 - 23903520 * q^58 + 24111192 * q^61 - 53913416 * q^62 + 30943610 * q^65 - 32827752 * q^67 - 8118692 * q^68 - 44156280 * q^70 + 13992928 * q^71 + 111859638 * q^73 - 56470800 * q^76 - 26260136 * q^77 - 23045920 * q^80 + 38023056 * q^82 + 14768432 * q^83 - 19713030 * q^85 + 135560008 * q^86 - 44555040 * q^88 + 167542032 * q^91 - 69931048 * q^92 - 239661000 * q^95 - 186656202 * q^97 + 345959698 * q^98

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