LMFDB - Embedded newform 75.9.c.c.26.1

Newspace parameters

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.c (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-14}) $
Defining polynomial:	$ x^{2} + 14 $ x^2 + 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	no (minimal twist has level 3)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.1
Root			$-3.74166i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.9.c.c.26.2

$q$-expansion

$f(q)$	$=$	$q-22.4499i q^{2} +(-45.0000 + 67.3498i) q^{3} -248.000 q^{4} +(1512.00 + 1010.25i) q^{6} +1750.00 q^{7} -179.600i q^{8} +(-2511.00 - 6061.48i) q^{9} +O(q^{10})$	\(q-22.4499i q^{2} +(-45.0000 + 67.3498i) q^{3} -248.000 q^{4} +(1512.00 + 1010.25i) q^{6} +1750.00 q^{7} -179.600i q^{8} +(-2511.00 - 6061.48i) q^{9} +6959.48i q^{11} +(11160.0 - 16702.8i) q^{12} -25730.0 q^{13} -39287.4i q^{14} -67520.0 q^{16} -74893.0i q^{17} +(-136080. + 56371.8i) q^{18} +18938.0 q^{19} +(-78750.0 + 117862. i) q^{21} +156240. q^{22} +470461. i q^{23} +(12096.0 + 8081.98i) q^{24} +577637. i q^{26} +(521235. + 103651. i) q^{27} -434000. q^{28} +460897. i q^{29} -351478. q^{31} +1.46984e6i q^{32} +(-468720. - 313177. i) q^{33} -1.68134e6 q^{34} +(622728. + 1.50325e6i) q^{36} -1.33517e6 q^{37} -425157. i q^{38} +(1.15785e6 - 1.73291e6i) q^{39} +1.87547e6i q^{41} +(2.64600e6 + 1.76793e6i) q^{42} +3.52615e6 q^{43} -1.72595e6i q^{44} +1.05618e7 q^{46} +4.08104e6i q^{47} +(3.03840e6 - 4.54746e6i) q^{48} -2.70230e6 q^{49} +(5.04403e6 + 3.37019e6i) q^{51} +6.38104e6 q^{52} +6.60177e6i q^{53} +(2.32697e6 - 1.17017e7i) q^{54} -314299. i q^{56} +(-852210. + 1.27547e6i) q^{57} +1.03471e7 q^{58} +1.37149e7i q^{59} +753602. q^{61} +7.89066e6i q^{62} +(-4.39425e6 - 1.06076e7i) q^{63} +1.57128e7 q^{64} +(-7.03080e6 + 1.05227e7i) q^{66} -2.26889e6 q^{67} +1.85735e7i q^{68} +(-3.16855e7 - 2.11707e7i) q^{69} +1.70220e7i q^{71} +(-1.08864e6 + 450974. i) q^{72} -2.76728e7 q^{73} +2.99745e7i q^{74} -4.69662e6 q^{76} +1.21791e7i q^{77} +(-3.89038e7 - 2.59937e7i) q^{78} -2.29810e7 q^{79} +(-3.04365e7 + 3.04408e7i) q^{81} +4.21042e7 q^{82} +4.63952e7i q^{83} +(1.95300e7 - 2.92298e7i) q^{84} -7.91619e7i q^{86} +(-3.10414e7 - 2.07404e7i) q^{87} +1.24992e6 q^{88} +7.26152e7i q^{89} -4.50275e7 q^{91} -1.16674e8i q^{92} +(1.58165e7 - 2.36720e7i) q^{93} +9.16191e7 q^{94} +(-9.89937e7 - 6.61429e7i) q^{96} -1.47271e8 q^{97} +6.06665e7i q^{98} +(4.21848e7 - 1.74753e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 90 q^{3} - 496 q^{4} + 3024 q^{6} + 3500 q^{7} - 5022 q^{9}+O(q^{10}) $ 2 * q - 90 * q^3 - 496 * q^4 + 3024 * q^6 + 3500 * q^7 - 5022 * q^9	$ 2 q - 90 q^{3} - 496 q^{4} + 3024 q^{6} + 3500 q^{7} - 5022 q^{9} + 22320 q^{12} - 51460 q^{13} - 135040 q^{16} - 272160 q^{18} + 37876 q^{19} - 157500 q^{21} + 312480 q^{22} + 24192 q^{24} + 1042470 q^{27} - 868000 q^{28} - 702956 q^{31} - 937440 q^{33} - 3362688 q^{34} + 1245456 q^{36} - 2670340 q^{37} + 2315700 q^{39} + 5292000 q^{42} + 7052300 q^{43} + 21123648 q^{46} + 6076800 q^{48} - 5404602 q^{49} + 10088064 q^{51} + 12762080 q^{52} + 4653936 q^{54} - 1704420 q^{57} + 20694240 q^{58} + 1507204 q^{61} - 8788500 q^{63} + 31425536 q^{64} - 14061600 q^{66} - 4537780 q^{67} - 63370944 q^{69} - 2177280 q^{72} - 55345540 q^{73} - 9393248 q^{76} - 77807520 q^{78} - 45961964 q^{79} - 60872958 q^{81} + 84208320 q^{82} + 39060000 q^{84} - 62082720 q^{87} + 2499840 q^{88} - 90055000 q^{91} + 31633020 q^{93} + 183238272 q^{94} - 197987328 q^{96} - 294542020 q^{97} + 84369600 q^{99}+O(q^{100}) $ 2 * q - 90 * q^3 - 496 * q^4 + 3024 * q^6 + 3500 * q^7 - 5022 * q^9 + 22320 * q^12 - 51460 * q^13 - 135040 * q^16 - 272160 * q^18 + 37876 * q^19 - 157500 * q^21 + 312480 * q^22 + 24192 * q^24 + 1042470 * q^27 - 868000 * q^28 - 702956 * q^31 - 937440 * q^33 - 3362688 * q^34 + 1245456 * q^36 - 2670340 * q^37 + 2315700 * q^39 + 5292000 * q^42 + 7052300 * q^43 + 21123648 * q^46 + 6076800 * q^48 - 5404602 * q^49 + 10088064 * q^51 + 12762080 * q^52 + 4653936 * q^54 - 1704420 * q^57 + 20694240 * q^58 + 1507204 * q^61 - 8788500 * q^63 + 31425536 * q^64 - 14061600 * q^66 - 4537780 * q^67 - 63370944 * q^69 - 2177280 * q^72 - 55345540 * q^73 - 9393248 * q^76 - 77807520 * q^78 - 45961964 * q^79 - 60872958 * q^81 + 84208320 * q^82 + 39060000 * q^84 - 62082720 * q^87 + 2499840 * q^88 - 90055000 * q^91 + 31633020 * q^93 + 183238272 * q^94 - 197987328 * q^96 - 294542020 * q^97 + 84369600 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	22.4499i		−	1.40312i	−0.712610	−	0.701561i	$-0.752487\pi$
$2$		−	22.4499i		−	1.40312i	0.712610	−	0.701561i	$-0.247513\pi$
$3$	−45.0000	+	67.3498i	−0.555556	+	0.831479i
$3$	−45.0000	+	67.3498i	−0.555556	+	0.831479i
$4$	−248.000			−0.968750
$5$		0			0
$5$		0			0
$6$	1512.00	+	1010.25i	1.16667	+	0.779512i
$7$	1750.00			0.728863			0.364431	−	0.931230i	$-0.381263\pi$
$7$	1750.00			0.728863			0.364431	+	0.931230i	$0.381263\pi$
$8$		−	179.600i		−	0.0438475i
$9$	−2511.00	−	6061.48i	−0.382716	−	0.923866i
$10$		0			0
$11$			6959.48i			0.475342i	0.971346	+	0.237671i	$0.0763840\pi$
$11$			6959.48i			0.475342i	−0.971346	+	0.237671i	$0.923616\pi$
$12$	11160.0	−	16702.8i	0.538194	−	0.805496i
$13$	−25730.0			−0.900879			−0.450439	−	0.892807i	$-0.648733\pi$
$13$	−25730.0			−0.900879			−0.450439	+	0.892807i	$0.648733\pi$
$14$		−	39287.4i		−	1.02268i
$15$		0			0
$16$	−67520.0			−1.03027
$17$		−	74893.0i		−	0.896697i	−0.893859	−	0.448348i	$-0.852012\pi$
$17$		−	74893.0i		−	0.896697i	0.893859	−	0.448348i	$-0.147988\pi$
$18$	−136080.	+	56371.8i	−1.29630	+	0.536997i
$19$	18938.0			0.145318			0.0726590	−	0.997357i	$-0.476852\pi$
$19$	18938.0			0.145318			0.0726590	+	0.997357i	$0.476852\pi$
$20$		0			0
$21$	−78750.0	+	117862.i	−0.404924	+	0.606035i
$22$	156240.			0.666963
$23$			470461.i			1.68117i	0.541678	+	0.840586i	$0.317789\pi$
$23$			470461.i			1.68117i	−0.541678	+	0.840586i	$0.682211\pi$
$24$	12096.0	+	8081.98i	0.0364583	+	0.0243597i
$25$		0			0
$26$			577637.i			1.26404i
$27$	521235.	+	103651.i	0.980796	+	0.195038i
$28$	−434000.			−0.706086
$29$			460897.i			0.651647i	0.945431	+	0.325823i	$0.105641\pi$
$29$			460897.i			0.651647i	−0.945431	+	0.325823i	$0.894359\pi$
$30$		0			0
$31$	−351478.			−0.380585			−0.190292	−	0.981727i	$-0.560944\pi$
$31$	−351478.			−0.380585			−0.190292	+	0.981727i	$0.560944\pi$
$32$			1.46984e6i			1.40175i
$33$	−468720.	−	313177.i	−0.395237	−	0.264079i
$34$	−1.68134e6			−1.25817
$35$		0			0
$36$	622728.	+	1.50325e6i	0.370756	+	0.894995i
$37$	−1.33517e6			−0.712409			−0.356205	−	0.934408i	$-0.615929\pi$
$37$	−1.33517e6			−0.712409			−0.356205	+	0.934408i	$0.615929\pi$
$38$		−	425157.i		−	0.203899i
$39$	1.15785e6	−	1.73291e6i	0.500488	−	0.749062i
$40$		0			0
$41$			1.87547e6i			0.663704i	0.943331	+	0.331852i	$0.107673\pi$
$41$			1.87547e6i			0.663704i	−0.943331	+	0.331852i	$0.892327\pi$
$42$	2.64600e6	+	1.76793e6i	0.850340	+	0.568157i
$43$	3.52615e6			1.03140			0.515700	−	0.856769i	$-0.327532\pi$
$43$	3.52615e6			1.03140			0.515700	+	0.856769i	$0.327532\pi$
$44$		−	1.72595e6i		−	0.460488i
$45$		0			0
$46$	1.05618e7			2.35889
$47$			4.08104e6i			0.836333i	0.908370	+	0.418167i	$0.137327\pi$
$47$			4.08104e6i			0.836333i	−0.908370	+	0.418167i	$0.862673\pi$
$48$	3.03840e6	−	4.54746e6i	0.572374	−	0.856651i
$49$	−2.70230e6			−0.468759
$50$		0			0
$51$	5.04403e6	+	3.37019e6i	0.745585	+	0.498165i
$52$	6.38104e6			0.872726
$53$			6.60177e6i			0.836675i	0.908292	+	0.418337i	$0.137387\pi$
$53$			6.60177e6i			0.836675i	−0.908292	+	0.418337i	$0.862613\pi$
$54$	2.32697e6	−	1.17017e7i	0.273663	−	1.37618i
$55$		0			0
$56$		−	314299.i		−	0.0319589i
$57$	−852210.	+	1.27547e6i	−0.0807323	+	0.120829i
$58$	1.03471e7			0.914340
$59$			1.37149e7i			1.13184i	0.824461	+	0.565919i	$0.191479\pi$
$59$			1.37149e7i			1.13184i	−0.824461	+	0.565919i	$0.808521\pi$
$60$		0			0
$61$	753602.			0.0544280			0.0272140	−	0.999630i	$-0.491336\pi$
$61$	753602.			0.0544280			0.0272140	+	0.999630i	$0.491336\pi$
$62$			7.89066e6i			0.534007i
$63$	−4.39425e6	−	1.06076e7i	−0.278948	−	0.673372i
$64$	1.57128e7			0.936554
$65$		0			0
$66$	−7.03080e6	+	1.05227e7i	−0.370535	+	0.554566i
$67$	−2.26889e6			−0.112594			−0.0562969	−	0.998414i	$-0.517929\pi$
$67$	−2.26889e6			−0.112594			−0.0562969	+	0.998414i	$0.517929\pi$
$68$			1.85735e7i			0.868675i
$69$	−3.16855e7	−	2.11707e7i	−1.39786	−	0.933985i
$70$		0			0
$71$			1.70220e7i			0.669849i	0.942245	+	0.334925i	$0.108711\pi$
$71$			1.70220e7i			0.669849i	−0.942245	+	0.334925i	$0.891289\pi$
$72$	−1.08864e6	+	450974.i	−0.0405093	+	0.0167812i
$73$	−2.76728e7			−0.974454			−0.487227	−	0.873275i	$-0.661992\pi$
$73$	−2.76728e7			−0.974454			−0.487227	+	0.873275i	$0.661992\pi$
$74$			2.99745e7i			0.999597i
$75$		0			0
$76$	−4.69662e6			−0.140777
$77$			1.21791e7i			0.346459i
$78$	−3.89038e7	−	2.59937e7i	−1.05103	−	0.702246i
$79$	−2.29810e7			−0.590011			−0.295006	−	0.955496i	$-0.595322\pi$
$79$	−2.29810e7			−0.590011			−0.295006	+	0.955496i	$0.595322\pi$
$80$		0			0
$81$	−3.04365e7	+	3.04408e7i	−0.707057	+	0.707157i
$82$	4.21042e7			0.931257
$83$			4.63952e7i			0.977599i	0.872396	+	0.488799i	$0.162565\pi$
$83$			4.63952e7i			0.977599i	−0.872396	+	0.488799i	$0.837435\pi$
$84$	1.95300e7	−	2.92298e7i	0.392270	−	0.587096i
$85$		0			0
$86$		−	7.91619e7i		−	1.44718i
$87$	−3.10414e7	−	2.07404e7i	−0.541831	−	0.362026i
$88$	1.24992e6			0.0208426
$89$			7.26152e7i			1.15736i	0.815555	+	0.578679i	$0.196432\pi$
$89$			7.26152e7i			1.15736i	−0.815555	+	0.578679i	$0.803568\pi$
$90$		0			0
$91$	−4.50275e7			−0.656617
$92$		−	1.16674e8i		−	1.62864i
$93$	1.58165e7	−	2.36720e7i	0.211436	−	0.316448i
$94$	9.16191e7			1.17348
$95$		0			0
$96$	−9.89937e7	−	6.61429e7i	−1.16553	−	0.778751i
$97$	−1.47271e8			−1.66353			−0.831764	−	0.555129i	$-0.812669\pi$
$97$	−1.47271e8			−1.66353			−0.831764	+	0.555129i	$0.812669\pi$
$98$			6.06665e7i			0.657726i
$99$	4.21848e7	−	1.74753e7i	0.439152	−	0.181921i
$100$		0			0
$101$		−	1.03545e8i		−	0.995045i	−0.867451	−	0.497522i	$-0.834243\pi$
$101$		−	1.03545e8i		−	0.995045i	0.867451	−	0.497522i	$-0.165757\pi$
$102$	7.56605e7	−	1.13238e8i	0.698986	−	1.04615i
$103$	1.66064e8			1.47545			0.737726	−	0.675100i	$-0.235899\pi$
$103$	1.66064e8			1.47545			0.737726	+	0.675100i	$0.235899\pi$
$104$			4.62110e6i			0.0395013i
$105$		0			0
$106$	1.48209e8			1.17396
$107$			2.25540e7i			0.172063i	0.996292	+	0.0860316i	$0.0274186\pi$
$107$			2.25540e7i			0.172063i	−0.996292	+	0.0860316i	$0.972581\pi$
$108$	−1.29266e8	−	2.57055e7i	−0.950146	−	0.188943i
$109$	−1.09975e8			−0.779091			−0.389546	−	0.921007i	$-0.627368\pi$
$109$	−1.09975e8			−0.779091			−0.389546	+	0.921007i	$0.627368\pi$
$110$		0			0
$111$	6.00826e7	−	8.99235e7i	0.395783	−	0.592354i
$112$	−1.18160e8			−0.750928
$113$		−	2.87748e8i		−	1.76481i	−0.470490	−	0.882405i	$-0.655923\pi$
$113$		−	2.87748e8i		−	1.76481i	0.470490	−	0.882405i	$-0.344077\pi$
$114$	2.86343e7	+	1.91321e7i	0.169538	+	0.113277i
$115$		0			0
$116$		−	1.14303e8i		−	0.631283i
$117$	6.46080e7	+	1.55962e8i	0.344781	+	0.832291i
$118$	3.07899e8			1.58811
$119$		−	1.31063e8i		−	0.653569i
$120$		0			0
$121$	1.65924e8			0.774050
$122$		−	1.69183e7i		−	0.0763692i
$123$	−1.26312e8	−	8.43961e7i	−0.551856	−	0.368724i
$124$	8.71665e7			0.368691
$125$		0			0
$126$	−2.38140e8	+	9.86507e7i	−0.944822	+	0.391397i
$127$	−2.75994e8			−1.06092			−0.530462	−	0.847708i	$-0.677982\pi$
$127$	−2.75994e8			−1.06092			−0.530462	+	0.847708i	$0.677982\pi$
$128$			2.35290e7i			0.0876523i
$129$	−1.58677e8	+	2.37486e8i	−0.573000	+	0.857588i
$130$		0			0
$131$			2.89118e8i			0.981725i	0.871237	+	0.490862i	$0.163318\pi$
$131$			2.89118e8i			0.981725i	−0.871237	+	0.490862i	$0.836682\pi$
$132$	1.16243e8	+	7.76678e7i	0.382886	+	0.255826i
$133$	3.31415e7			0.105917
$134$			5.09365e7i			0.157983i
$135$		0			0
$136$	−1.34508e7			−0.0393180
$137$			2.07562e8i			0.589205i	0.955620	+	0.294602i	$0.0951872\pi$
$137$			2.07562e8i			0.589205i	−0.955620	+	0.294602i	$0.904813\pi$
$138$	−4.75282e8	+	7.11337e8i	−1.31049	+	1.96137i
$139$	−1.42668e8			−0.382180			−0.191090	−	0.981573i	$-0.561202\pi$
$139$	−1.42668e8			−0.382180			−0.191090	+	0.981573i	$0.561202\pi$
$140$		0			0
$141$	−2.74857e8	−	1.83647e8i	−0.695394	−	0.464630i
$142$	3.82143e8			0.939880
$143$		−	1.79067e8i		−	0.428226i
$144$	1.69543e8	+	4.09271e8i	0.394302	+	0.951835i
$145$		0			0
$146$			6.21252e8i			1.36728i
$147$	1.21604e8	−	1.82000e8i	0.260422	−	0.389763i
$148$	3.31122e8			0.690147
$149$		−	8.19236e8i		−	1.66213i	−0.556179	−	0.831063i	$-0.687733\pi$
$149$		−	8.19236e8i		−	1.66213i	0.556179	−	0.831063i	$-0.312267\pi$
$150$		0			0
$151$	4.23861e8			0.815296			0.407648	−	0.913139i	$-0.366349\pi$
$151$	4.23861e8			0.815296			0.407648	+	0.913139i	$0.366349\pi$
$152$		−	3.40126e6i		−	0.00637184i
$153$	−4.53963e8	+	1.88056e8i	−0.828428	+	0.343180i
$154$	2.73420e8			0.486124
$155$		0			0
$156$	−2.87147e8	+	4.29762e8i	−0.484848	+	0.725654i
$157$	7.59851e8			1.25063			0.625316	−	0.780371i	$-0.284970\pi$
$157$	7.59851e8			1.25063			0.625316	+	0.780371i	$0.284970\pi$
$158$			5.15922e8i			0.827857i
$159$	−4.44628e8	−	2.97079e8i	−0.695678	−	0.464819i
$160$		0			0
$161$			8.23307e8i			1.22534i
$162$	6.83394e8	+	6.83297e8i	0.992227	+	0.992087i
$163$	−6.68160e8			−0.946520			−0.473260	−	0.880923i	$-0.656923\pi$
$163$	−6.68160e8			−0.946520			−0.473260	+	0.880923i	$0.656923\pi$
$164$		−	4.65116e8i		−	0.642963i
$165$		0			0
$166$	1.04157e9			1.37169
$167$		−	1.96306e8i		−	0.252387i	−0.992006	−	0.126194i	$-0.959724\pi$
$167$		−	1.96306e8i		−	0.252387i	0.992006	−	0.126194i	$-0.0402761\pi$
$168$	2.11680e7	+	1.41435e7i	0.0265731	+	0.0177549i
$169$	−1.53698e8			−0.188417
$170$		0			0
$171$	−4.75533e7	−	1.14792e8i	−0.0556156	−	0.134254i
$172$	−8.74485e8			−0.999168
$173$		−	1.02319e9i		−	1.14228i	−0.820852	−	0.571141i	$-0.806501\pi$
$173$		−	1.02319e9i		−	1.14228i	0.820852	−	0.571141i	$-0.193499\pi$
$174$	−4.65620e8	+	6.96877e8i	−0.507966	+	0.760255i
$175$		0			0
$176$		−	4.69904e8i		−	0.489732i
$177$	−9.23696e8	−	6.17170e8i	−0.941100	−	0.628799i
$178$	1.63021e9			1.62391
$179$		−	1.28895e9i		−	1.25552i	−0.778408	−	0.627759i	$-0.783972\pi$
$179$		−	1.28895e9i		−	1.25552i	0.778408	−	0.627759i	$-0.216028\pi$
$180$		0			0
$181$	4.71707e8			0.439499			0.219749	−	0.975556i	$-0.429476\pi$
$181$	4.71707e8			0.439499			0.219749	+	0.975556i	$0.429476\pi$
$182$			1.01086e9i			0.921314i
$183$	−3.39121e7	+	5.07550e7i	−0.0302378	+	0.0452558i
$184$	8.44946e7			0.0737153
$185$		0			0
$186$	−5.31435e8	−	3.55080e8i	−0.444016	−	0.296670i
$187$	5.21217e8			0.426238
$188$		−	1.01210e9i		−	0.810198i
$189$	9.12161e8	+	1.81390e8i	0.714866	+	0.142156i
$190$		0			0
$191$		−	1.61787e8i		−	0.121565i	−0.998151	−	0.0607827i	$-0.980640\pi$
$191$		−	1.61787e8i		−	0.121565i	0.998151	−	0.0607827i	$-0.0193597\pi$
$192$	−7.07075e8	+	1.05825e9i	−0.520308	+	0.778725i
$193$	1.58840e9			1.14480			0.572401	−	0.819974i	$-0.306012\pi$
$193$	1.58840e9			1.14480			0.572401	+	0.819974i	$0.306012\pi$
$194$			3.30623e9i			2.33413i
$195$		0			0
$196$	6.70171e8			0.454110
$197$			5.37769e8i			0.357052i	0.983935	+	0.178526i	$0.0571328\pi$
$197$			5.37769e8i			0.357052i	−0.983935	+	0.178526i	$0.942867\pi$
$198$	−3.92319e8	−	9.47046e8i	−0.255257	−	0.616184i
$199$	6.47586e8			0.412938			0.206469	−	0.978453i	$-0.433803\pi$
$199$	6.47586e8			0.412938			0.206469	+	0.978453i	$0.433803\pi$
$200$		0			0
$201$	1.02100e8	−	1.52809e8i	0.0625521	−	0.0936194i
$202$	−2.32457e9			−1.39617
$203$			8.06570e8i			0.474961i
$204$	−1.25092e9	−	8.35806e8i	−0.722285	−	0.482597i
$205$		0			0
$206$		−	3.72812e9i		−	2.07024i
$207$	2.85169e9	−	1.18133e9i	1.55318	−	0.643412i
$208$	1.73729e9			0.928152
$209$			1.31799e8i			0.0690758i
$210$		0			0
$211$	5.81104e7			0.0293173			0.0146586	−	0.999893i	$-0.495334\pi$
$211$	5.81104e7			0.0293173			0.0146586	+	0.999893i	$0.495334\pi$
$212$		−	1.63724e9i		−	0.810529i
$213$	−1.14643e9	−	7.65990e8i	−0.556966	−	0.372139i
$214$	5.06336e8			0.241426
$215$		0			0
$216$	1.86157e7	−	9.36136e7i	0.00855195	−	0.0430055i
$217$	−6.15086e8			−0.277394
$218$			2.46893e9i			1.09316i
$219$	1.24527e9	−	1.86376e9i	0.541363	−	0.810238i
$220$		0			0
$221$			1.92700e9i			0.807815i
$222$	−2.01878e9	−	1.34885e9i	−0.831144	−	0.555332i
$223$	−4.40200e9			−1.78004			−0.890021	−	0.455920i	$-0.849310\pi$
$223$	−4.40200e9			−1.78004			−0.890021	+	0.455920i	$0.849310\pi$
$224$			2.57222e9i			1.02168i
$225$		0			0
$226$	−6.45992e9			−2.47624
$227$		−	3.53592e9i		−	1.33168i	−0.746095	−	0.665839i	$-0.768074\pi$
$227$		−	3.53592e9i		−	1.33168i	0.746095	−	0.665839i	$-0.231926\pi$
$228$	2.11348e8	−	3.16317e8i	0.0782094	−	0.117053i
$229$	−1.86569e9			−0.678420			−0.339210	−	0.940711i	$-0.610160\pi$
$229$	−1.86569e9			−0.678420			−0.339210	+	0.940711i	$0.610160\pi$
$230$		0			0
$231$	−8.20260e8	−	5.48059e8i	−0.288074	−	0.192477i
$232$	8.27770e7			0.0285731
$233$			2.72132e9i			0.923328i	0.887055	+	0.461664i	$0.152747\pi$
$233$			2.72132e9i			0.923328i	−0.887055	+	0.461664i	$0.847253\pi$
$234$	3.50134e9	−	1.45045e9i	1.16781	−	0.483769i
$235$		0			0
$236$		−	3.40129e9i		−	1.09647i
$237$	1.03414e9	−	1.54777e9i	0.327784	−	0.490582i
$238$	−2.94235e9			−0.917037
$239$		−	2.27461e9i		−	0.697132i	−0.937284	−	0.348566i	$-0.886669\pi$
$239$		−	2.27461e9i		−	0.697132i	0.937284	−	0.348566i	$-0.113331\pi$
$240$		0			0
$241$	−1.74667e9			−0.517778			−0.258889	−	0.965907i	$-0.583356\pi$
$241$	−1.74667e9			−0.517778			−0.258889	+	0.965907i	$0.583356\pi$
$242$		−	3.72500e9i		−	1.08609i
$243$	−6.80540e8	−	3.41973e9i	−0.195177	−	0.980768i
$244$	−1.86893e8			−0.0527272
$245$		0			0
$246$	−1.89469e9	+	2.83571e9i	−0.517365	+	0.774321i
$247$	−4.87275e8			−0.130914
$248$			6.31253e7i			0.0166877i
$249$	−3.12471e9	−	2.08778e9i	−0.812853	−	0.543110i
$250$		0			0
$251$			1.37549e9i			0.346547i	0.984874	+	0.173274i	$0.0554345\pi$
$251$			1.37549e9i			0.346547i	−0.984874	+	0.173274i	$0.944566\pi$
$252$	1.08977e9	+	2.63068e9i	0.270230	+	0.652329i
$253$	−3.27417e9			−0.799132
$254$			6.19605e9i			1.48861i
$255$		0			0
$256$	4.55069e9			1.05954
$257$			7.93672e9i			1.81932i	0.415356	+	0.909659i	$0.363657\pi$
$257$			7.93672e9i			1.81932i	−0.415356	+	0.909659i	$0.636343\pi$
$258$	5.33154e9	+	3.56228e9i	1.20330	+	0.803988i
$259$	−2.33655e9			−0.519249
$260$		0			0
$261$	2.79372e9	−	1.15731e9i	0.602034	−	0.249396i
$262$	6.49068e9			1.37748
$263$		−	3.22555e8i		−	0.0674187i	−0.999432	−	0.0337093i	$-0.989268\pi$
$263$		−	3.22555e8i		−	0.0674187i	0.999432	−	0.0337093i	$-0.0107320\pi$
$264$	−5.62464e7	+	8.41819e7i	−0.0115792	+	0.0173302i
$265$		0			0
$266$		−	7.44025e8i		−	0.148614i
$267$	−4.89062e9	−	3.26769e9i	−0.962319	−	0.642977i
$268$	5.62685e8			0.109075
$269$			3.47314e9i			0.663304i	0.943402	+	0.331652i	$0.107606\pi$
$269$			3.47314e9i			0.663304i	−0.943402	+	0.331652i	$0.892394\pi$
$270$		0			0
$271$	−1.44216e9			−0.267385			−0.133693	−	0.991023i	$-0.542683\pi$
$271$	−1.44216e9			−0.267385			−0.133693	+	0.991023i	$0.542683\pi$
$272$			5.05678e9i			0.923843i
$273$	2.02624e9	−	3.03259e9i	0.364787	−	0.545964i
$274$	4.65976e9			0.826726
$275$		0			0
$276$	7.85800e9	+	5.25035e9i	1.35418	+	0.904798i
$277$	−3.38046e9			−0.574192			−0.287096	−	0.957902i	$-0.592690\pi$
$277$	−3.38046e9			−0.574192			−0.287096	+	0.957902i	$0.592690\pi$
$278$			3.20289e9i			0.536245i
$279$	8.82561e8	+	2.13048e9i	0.145656	+	0.351609i
$280$		0			0
$281$			4.02262e9i			0.645184i	0.946538	+	0.322592i	$0.104554\pi$
$281$			4.02262e9i			0.645184i	−0.946538	+	0.322592i	$0.895446\pi$
$282$	−4.12286e9	+	6.17053e9i	−0.651932	+	0.975722i
$283$	1.04253e10			1.62533			0.812666	−	0.582730i	$-0.198016\pi$
$283$	1.04253e10			1.62533			0.812666	+	0.582730i	$0.198016\pi$
$284$		−	4.22146e9i		−	0.648917i
$285$		0			0
$286$	−4.02006e9			−0.600853
$287$			3.28207e9i			0.483749i
$288$	8.90943e9	−	3.69078e9i	1.29503	−	0.536473i
$289$	1.36679e9			0.195935
$290$		0			0
$291$	6.62720e9	−	9.91868e9i	0.924183	−	1.38319i
$292$	6.86285e9			0.944002
$293$		−	1.03927e10i		−	1.41012i	−0.709146	−	0.705061i	$-0.750919\pi$
$293$		−	1.03927e10i		−	1.41012i	0.709146	−	0.705061i	$-0.249081\pi$
$294$	−4.08588e9	−	2.72999e9i	−0.546885	−	0.365403i
$295$		0			0
$296$			2.39796e8i			0.0312374i
$297$	−7.21360e8	+	3.62753e9i	−0.0927099	+	0.466213i
$298$	−1.83918e10			−2.33216
$299$		−	1.21050e10i		−	1.51453i
$300$		0			0
$301$	6.17076e9			0.751749
$302$		−	9.51565e9i		−	1.14396i
$303$	6.97372e9	+	4.65951e9i	0.827359	+	0.552803i
$304$	−1.27869e9			−0.149717
$305$		0			0
$306$	4.22185e9	+	1.01914e10i	0.481524	+	1.16238i
$307$	2.99309e9			0.336951			0.168476	−	0.985706i	$-0.446116\pi$
$307$	2.99309e9			0.336951			0.168476	+	0.985706i	$0.446116\pi$
$308$		−	3.02042e9i		−	0.335632i
$309$	−7.47286e9	+	1.11843e10i	−0.819696	+	1.22681i
$310$		0			0
$311$			6.44832e9i			0.689295i	0.938732	+	0.344647i	$0.112002\pi$
$311$			6.44832e9i			0.689295i	−0.938732	+	0.344647i	$0.887998\pi$
$312$	−3.11230e8	−	2.07949e8i	−0.0328445	−	0.0219452i
$313$	−3.27737e7			−0.00341467			−0.00170733	−	0.999999i	$-0.500543\pi$
$313$	−3.27737e7			−0.00341467			−0.00170733	+	0.999999i	$0.500543\pi$
$314$		−	1.70586e10i		−	1.75479i
$315$		0			0
$316$	5.69928e9			0.571573
$317$			1.17797e10i			1.16653i	0.812282	+	0.583264i	$0.198225\pi$
$317$			1.17797e10i			1.16653i	−0.812282	+	0.583264i	$0.801775\pi$
$318$	−6.66942e9	+	9.98187e9i	−0.652198	+	0.976120i
$319$	−3.20761e9			−0.309755
$320$		0			0
$321$	−1.51901e9	−	1.01493e9i	−0.143067	−	0.0955907i
$322$	1.84832e10			1.71931
$323$		−	1.41832e9i		−	0.130306i
$324$	7.54825e9	−	7.54931e9i	0.684961	−	0.685058i
$325$		0			0
$326$			1.50002e10i			1.32808i
$327$	4.94888e9	−	7.40680e9i	0.432829	−	0.647798i
$328$	3.36833e8			0.0291018
$329$			7.14182e9i			0.609573i
$330$		0			0
$331$	−1.20100e10			−1.00053			−0.500265	−	0.865872i	$-0.666764\pi$
$331$	−1.20100e10			−1.00053			−0.500265	+	0.865872i	$0.666764\pi$
$332$		−	1.15060e10i		−	0.947049i
$333$	3.35261e9	+	8.09311e9i	0.272651	+	0.658171i
$334$	−4.40705e9			−0.354130
$335$		0			0
$336$	5.31720e9	−	7.95806e9i	0.417182	−	0.624381i
$337$	−1.59214e10			−1.23441			−0.617207	−	0.786801i	$-0.711736\pi$
$337$	−1.59214e10			−1.23441			−0.617207	+	0.786801i	$0.711736\pi$
$338$			3.45051e9i			0.264372i
$339$	1.93798e10	+	1.29486e10i	1.46740	+	0.980451i
$340$		0			0
$341$		−	2.44611e9i		−	0.180908i
$342$	−2.57708e9	+	1.06757e9i	−0.188375	+	0.0780354i
$343$	−1.48174e10			−1.07052
$344$		−	6.33295e8i		−	0.0452243i
$345$		0			0
$346$	−2.29706e10			−1.60276
$347$			4.94792e9i			0.341275i	0.985334	+	0.170638i	$0.0545828\pi$
$347$			4.94792e9i			0.341275i	−0.985334	+	0.170638i	$0.945417\pi$
$348$	7.69826e9	+	5.14361e9i	0.524899	+	0.350713i
$349$	−7.29567e9			−0.491772			−0.245886	−	0.969299i	$-0.579079\pi$
$349$	−7.29567e9			−0.491772			−0.245886	+	0.969299i	$0.579079\pi$
$350$		0			0
$351$	−1.34114e10	−	2.66695e9i	−0.883578	−	0.175706i
$352$	−1.02293e10			−0.666311
$353$			6.93875e9i			0.446871i	0.974719	+	0.223436i	$0.0717272\pi$
$353$			6.93875e9i			0.446871i	−0.974719	+	0.223436i	$0.928273\pi$
$354$	−1.38554e10	+	2.07369e10i	−0.882282	+	1.32048i
$355$		0			0
$356$		−	1.80086e10i		−	1.12119i
$357$	8.82706e9	+	5.89782e9i	0.543429	+	0.363094i
$358$	−2.89368e10			−1.76164
$359$			1.60096e10i			0.963838i	0.876216	+	0.481919i	$0.160060\pi$
$359$			1.60096e10i			0.963838i	−0.876216	+	0.481919i	$0.839940\pi$
$360$		0			0
$361$	−1.66249e10			−0.978883
$362$		−	1.05898e10i		−	0.616670i
$363$	−7.46660e9	+	1.11750e10i	−0.430028	+	0.643607i
$364$	1.11668e10			0.636098
$365$		0			0
$366$	1.13945e9	+	7.61325e8i	0.0634994	+	0.0424273i
$367$	−1.36364e10			−0.751686			−0.375843	−	0.926683i	$-0.622647\pi$
$367$	−1.36364e10			−0.751686			−0.375843	+	0.926683i	$0.622647\pi$
$368$		−	3.17655e10i		−	1.73207i
$369$	1.13681e10	−	4.70930e9i	0.613173	−	0.254010i
$370$		0			0
$371$			1.15531e10i			0.609821i
$372$	−3.92249e9	+	5.87065e9i	−0.204829	+	0.306559i
$373$	2.44062e10			1.26085			0.630427	−	0.776248i	$-0.282880\pi$
$373$	2.44062e10			1.26085			0.630427	+	0.776248i	$0.282880\pi$
$374$		−	1.17013e10i		−	0.598063i
$375$		0			0
$376$	7.32953e8			0.0366712
$377$		−	1.18589e10i		−	0.587055i
$378$	4.07219e9	−	2.04780e10i	0.199463	−	1.00304i
$379$	−1.98392e10			−0.961542			−0.480771	−	0.876846i	$-0.659643\pi$
$379$	−1.98392e10			−0.961542			−0.480771	+	0.876846i	$0.659643\pi$
$380$		0			0
$381$	1.24197e10	−	1.85881e10i	0.589403	−	0.882137i
$382$	−3.63211e9			−0.170571
$383$			1.51133e10i			0.702366i	0.936307	+	0.351183i	$0.114220\pi$
$383$			1.51133e10i			0.702366i	−0.936307	+	0.351183i	$0.885780\pi$
$384$	−1.58467e9	−	1.05880e9i	−0.0728811	−	0.0486957i
$385$		0			0
$386$		−	3.56594e10i		−	1.60630i
$387$	−8.85416e9	−	2.13737e10i	−0.394733	−	0.952875i
$388$	3.65232e10			1.61154
$389$		−	1.79991e10i		−	0.786056i	−0.919527	−	0.393028i	$-0.871428\pi$
$389$		−	1.79991e10i		−	0.786056i	0.919527	−	0.393028i	$-0.128572\pi$
$390$		0			0
$391$	3.52342e10			1.50750
$392$			4.85332e8i			0.0205539i
$393$	−1.94720e10	−	1.30103e10i	−0.816284	−	0.545403i
$394$	1.20729e10			0.500987
$395$		0			0
$396$	−1.04618e10	+	4.33386e9i	−0.425429	+	0.176236i
$397$	2.35673e10			0.948739			0.474370	−	0.880326i	$-0.342676\pi$
$397$	2.35673e10			0.948739			0.474370	+	0.880326i	$0.342676\pi$
$398$		−	1.45383e10i		−	0.579403i
$399$	−1.49137e9	+	2.23207e9i	−0.0588428	+	0.0880678i
$400$		0			0
$401$			1.37692e10i			0.532515i	0.963902	+	0.266257i	$0.0857871\pi$
$401$			1.37692e10i			0.532515i	−0.963902	+	0.266257i	$0.914213\pi$
$402$	−3.43056e9	−	2.29214e9i	−0.131359	−	0.0877682i
$403$	9.04353e9			0.342861
$404$			2.56791e10i			0.963950i
$405$		0			0
$406$	1.81075e10			0.666428
$407$		−	9.29209e9i		−	0.338638i
$408$	6.05284e8	−	9.05906e8i	0.0218433	−	0.0326921i
$409$	3.58480e10			1.28107			0.640533	−	0.767931i	$-0.278714\pi$
$409$	3.58480e10			1.28107			0.640533	+	0.767931i	$0.278714\pi$
$410$		0			0
$411$	−1.39793e10	−	9.34031e9i	−0.489912	−	0.327336i
$412$	−4.11838e10			−1.42934
$413$			2.40011e10i			0.824955i
$414$	−2.65207e10	−	6.40203e10i	−0.902785	−	2.17930i
$415$		0			0
$416$		−	3.78191e10i		−	1.26281i
$417$	6.42007e9	−	9.60868e9i	0.212322	−	0.317775i
$418$	2.95887e9			0.0969217
$419$			2.23996e10i			0.726750i	0.931643	+	0.363375i	$0.118376\pi$
$419$			2.23996e10i			0.726750i	−0.931643	+	0.363375i	$0.881624\pi$
$420$		0			0
$421$	−1.49535e10			−0.476008			−0.238004	−	0.971264i	$-0.576493\pi$
$421$	−1.49535e10			−0.476008			−0.238004	+	0.971264i	$0.576493\pi$
$422$		−	1.30457e9i		−	0.0411357i
$423$	2.47372e10	−	1.02475e10i	0.772660	−	0.320078i
$424$	1.18567e9			0.0366861
$425$		0			0
$426$	−1.71964e10	+	2.57373e10i	−0.522156	+	0.781491i
$427$	1.31880e9			0.0396706
$428$		−	5.59339e9i		−	0.166686i
$429$	1.20602e10	+	8.05804e9i	0.356061	+	0.237903i
$430$		0			0
$431$		−	6.40436e10i		−	1.85595i	−0.372640	−	0.927976i	$-0.621547\pi$
$431$		−	6.40436e10i		−	1.85595i	0.372640	−	0.927976i	$-0.378453\pi$
$432$	−3.51938e10	−	6.99854e9i	−1.01049	−	0.200943i
$433$	5.22954e9			0.148769			0.0743843	−	0.997230i	$-0.476301\pi$
$433$	5.22954e9			0.148769			0.0743843	+	0.997230i	$0.476301\pi$
$434$			1.38087e10i			0.389218i
$435$		0			0
$436$	2.72738e10			0.754745
$437$			8.90959e9i			0.244305i
$438$	−4.18412e10	−	2.79563e10i	−1.13686	−	0.759598i
$439$	4.34801e10			1.17066			0.585332	−	0.810793i	$-0.300964\pi$
$439$	4.34801e10			1.17066			0.585332	+	0.810793i	$0.300964\pi$
$440$		0			0
$441$	6.78548e9	+	1.63800e10i	0.179402	+	0.433070i
$442$	4.32610e10			1.13346
$443$			3.78737e10i			0.983383i	0.870770	+	0.491691i	$0.163621\pi$
$443$			3.78737e10i			0.983383i	−0.870770	+	0.491691i	$0.836379\pi$
$444$	−1.49005e10	+	2.23010e10i	−0.383415	+	0.573843i
$445$		0			0
$446$			9.88246e10i			2.49761i
$447$	5.51754e10	+	3.68656e10i	1.38202	+	0.923403i
$448$	2.74973e10			0.682620
$449$			2.95505e10i			0.727076i	0.931579	+	0.363538i	$0.118431\pi$
$449$			2.95505e10i			0.727076i	−0.931579	+	0.363538i	$0.881569\pi$
$450$		0			0
$451$	−1.30523e10			−0.315486
$452$			7.13614e10i			1.70966i
$453$	−1.90737e10	+	2.85469e10i	−0.452942	+	0.677902i
$454$	−7.93813e10			−1.86851
$455$		0			0
$456$	2.29074e8	+	1.53057e8i	0.00529806	+	0.00353991i
$457$	2.02181e10			0.463529			0.231764	−	0.972772i	$-0.425550\pi$
$457$	2.02181e10			0.463529			0.231764	+	0.972772i	$0.425550\pi$
$458$			4.18847e10i			0.951905i
$459$	7.76277e9	−	3.90369e10i	0.174890	−	0.879476i
$460$		0			0
$461$			7.01826e10i			1.55391i	0.629556	+	0.776955i	$0.283237\pi$
$461$			7.01826e10i			1.55391i	−0.629556	+	0.776955i	$0.716763\pi$
$462$	−1.23039e10	+	1.84148e10i	−0.270069	+	0.404202i
$463$	−4.16009e9			−0.0905271			−0.0452635	−	0.998975i	$-0.514413\pi$
$463$	−4.16009e9			−0.0905271			−0.0452635	+	0.998975i	$0.514413\pi$
$464$		−	3.11198e10i		−	0.671374i
$465$		0			0
$466$	6.10935e10			1.29554
$467$		−	2.88138e10i		−	0.605806i	−0.953021	−	0.302903i	$-0.902044\pi$
$467$		−	2.88138e10i		−	0.605806i	0.953021	−	0.302903i	$-0.0979558\pi$
$468$	−1.60228e10	−	3.86786e10i	−0.334006	−	0.806282i
$469$	−3.97056e9			−0.0820654
$470$		0			0
$471$	−3.41933e10	+	5.11758e10i	−0.694796	+	1.03988i
$472$	2.46319e9			0.0496283
$473$			2.45402e10i			0.490268i
$474$	−3.47472e10	−	2.32165e10i	−0.688346	−	0.459921i
$475$		0			0
$476$			3.25036e10i			0.633145i
$477$	4.00165e10	−	1.65770e10i	0.772975	−	0.320209i
$478$	−5.10649e10			−0.978161
$479$			4.47149e10i			0.849395i	0.905335	+	0.424698i	$0.139620\pi$
$479$			4.47149e10i			0.849395i	−0.905335	+	0.424698i	$0.860380\pi$
$480$		0			0
$481$	3.43539e10			0.641795
$482$			3.92127e10i			0.726505i
$483$	−5.54496e10	−	3.70488e10i	−1.01885	−	0.680747i
$484$	−4.11493e10			−0.749861
$485$		0			0
$486$	−7.67727e10	+	1.52781e10i	−1.37614	+	0.273857i
$487$	−5.72836e10			−1.01839			−0.509195	−	0.860651i	$-0.670057\pi$
$487$	−5.72836e10			−1.01839			−0.509195	+	0.860651i	$0.670057\pi$
$488$		−	1.35347e8i		−	0.00238654i
$489$	3.00672e10	−	4.50005e10i	0.525845	−	0.787012i
$490$		0			0
$491$		−	7.25262e10i		−	1.24787i	−0.781477	−	0.623934i	$-0.785533\pi$
$491$		−	7.25262e10i		−	1.24787i	0.781477	−	0.623934i	$-0.214467\pi$
$492$	3.13255e10	+	2.09302e10i	0.534611	+	0.357202i
$493$	3.45180e10			0.584330
$494$			1.09393e10i			0.183688i
$495$		0			0
$496$	2.37318e10			0.392106
$497$			2.97885e10i			0.488228i
$498$	−4.68706e10	+	7.01495e10i	−0.762050	+	1.14053i
$499$	−2.64368e10			−0.426389			−0.213195	−	0.977010i	$-0.568387\pi$
$499$	−2.64368e10			−0.426389			−0.213195	+	0.977010i	$0.568387\pi$
$500$		0			0
$501$	1.32212e10	+	8.83376e9i	0.209855	+	0.140215i
$502$	3.08797e10			0.486248
$503$		−	7.52828e10i		−	1.17604i	−0.808845	−	0.588022i	$-0.799907\pi$
$503$		−	7.52828e10i		−	1.17604i	0.808845	−	0.588022i	$-0.200093\pi$
$504$	−1.90512e9	+	7.89205e8i	−0.0295257	+	0.0122312i
$505$		0			0
$506$			7.35048e10i			1.12128i
$507$	6.91640e9	−	1.03515e10i	0.104676	−	0.156665i
$508$	6.84465e10			1.02777
$509$		−	6.45184e10i		−	0.961197i	−0.876941	−	0.480599i	$-0.840419\pi$
$509$		−	6.45184e10i		−	0.961197i	0.876941	−	0.480599i	$-0.159581\pi$
$510$		0			0
$511$	−4.84273e10			−0.710243
$512$		−	9.61394e10i		−	1.39901i
$513$	9.87115e9	+	1.96295e9i	0.142527	+	0.0283426i
$514$	1.78179e11			2.55272
$515$		0			0
$516$	3.93518e10	−	5.88964e10i	0.555094	−	0.830788i
$517$	−2.84019e10			−0.397544
$518$			5.24554e10i			0.728569i
$519$	6.89119e10	+	4.60437e10i	0.949783	+	0.634601i
$520$		0			0
$521$		−	7.65146e10i		−	1.03847i	−0.854632	−	0.519235i	$-0.826217\pi$
$521$		−	7.65146e10i		−	1.03847i	0.854632	−	0.519235i	$-0.173783\pi$
$522$	−2.59816e10	−	6.27189e10i	−0.349932	−	0.844727i
$523$	8.46771e10			1.13177			0.565886	−	0.824483i	$-0.308534\pi$
$523$	8.46771e10			1.13177			0.565886	+	0.824483i	$0.308534\pi$
$524$		−	7.17012e10i		−	0.951046i
$525$		0			0
$526$	−7.24133e9			−0.0945966
$527$			2.63232e10i			0.341269i
$528$	3.16480e10	+	2.11457e10i	0.407202	+	0.272073i
$529$	−1.43023e11			−1.82634
$530$		0			0
$531$	8.31326e10	−	3.44381e10i	1.04567	−	0.433173i
$532$	−8.21909e9			−0.102607
$533$		−	4.82558e10i		−	0.597917i
$534$	−7.33594e10	+	1.09794e11i	−0.902175	+	1.35025i
$535$		0			0
$536$			4.07492e8i			0.00493696i
$537$	8.68104e10	+	5.80026e10i	1.04394	+	0.697510i
$538$	7.79717e10			0.930696
$539$		−	1.88066e10i		−	0.222821i
$540$		0			0
$541$	1.43470e11			1.67483			0.837415	−	0.546568i	$-0.184066\pi$
$541$	1.43470e11			1.67483			0.837415	+	0.546568i	$0.184066\pi$
$542$			3.23765e10i			0.375174i
$543$	−2.12268e10	+	3.17694e10i	−0.244166	+	0.365434i
$544$	1.10081e11			1.25695
$545$		0			0
$546$	−6.80816e10	−	4.54889e10i	−0.766053	−	0.511841i
$547$	−1.64171e11			−1.83378			−0.916892	−	0.399134i	$-0.869311\pi$
$547$	−1.64171e11			−1.83378			−0.916892	+	0.399134i	$0.869311\pi$
$548$		−	5.14755e10i		−	0.570792i
$549$	−1.89229e9	−	4.56795e9i	−0.0208305	−	0.0502842i
$550$		0			0
$551$			8.72847e9i			0.0946961i
$552$	−3.80226e9	+	5.69070e9i	−0.0409529	+	0.0612928i
$553$	−4.02167e10			−0.430037
$554$			7.58912e10i			0.805661i
$555$		0			0
$556$	3.53817e10			0.370237
$557$		−	1.54420e11i		−	1.60429i	−0.597130	−	0.802145i	$-0.703692\pi$
$557$		−	1.54420e11i		−	1.60429i	0.597130	−	0.802145i	$-0.296308\pi$
$558$	4.78291e10	−	1.98135e10i	0.493351	−	0.204373i
$559$	−9.07278e10			−0.929166
$560$		0			0
$561$	−2.34547e10	+	3.51039e10i	−0.236799	+	0.354408i
$562$	9.03075e10			0.905271
$563$		−	1.54622e11i		−	1.53900i	−0.638646	−	0.769500i	$-0.720505\pi$
$563$		−	1.54622e11i		−	1.53900i	0.638646	−	0.769500i	$-0.279495\pi$
$564$	6.81646e10	+	4.55444e10i	0.673663	+	0.450110i
$565$		0			0
$566$		−	2.34047e11i		−	2.28054i
$567$	−5.32638e10	+	5.32714e10i	−0.515348	+	0.515420i
$568$	3.05714e9			0.0293712
$569$		−	1.15380e11i		−	1.10073i	−0.834925	−	0.550364i	$-0.814489\pi$
$569$		−	1.15380e11i		−	1.10073i	0.834925	−	0.550364i	$-0.185511\pi$
$570$		0			0
$571$	−1.63410e11			−1.53722			−0.768608	−	0.639720i	$-0.779050\pi$
$571$	−1.63410e11			−1.53722			−0.768608	+	0.639720i	$0.779050\pi$
$572$			4.44087e10i			0.414844i
$573$	1.08963e10	+	7.28041e9i	0.101079	+	0.0675363i
$574$	7.36823e10			0.678759
$575$		0			0
$576$	−3.94548e10	−	9.52427e10i	−0.358434	−	0.865250i
$577$	−7.42282e10			−0.669678			−0.334839	−	0.942275i	$-0.608682\pi$
$577$	−7.42282e10			−0.669678			−0.334839	+	0.942275i	$0.608682\pi$
$578$		−	3.06844e10i		−	0.274920i
$579$	−7.14779e10	+	1.06978e11i	−0.636001	+	0.951879i
$580$		0			0
$581$			8.11916e10i			0.712535i
$582$	−2.22674e11	−	1.48780e11i	−1.94078	−	1.29674i
$583$	−4.59449e10			−0.397707
$584$			4.97002e9i			0.0427274i
$585$		0			0
$586$	−2.33315e11			−1.97857
$587$			6.72877e10i			0.566739i	0.959011	+	0.283369i	$0.0914523\pi$
$587$			6.72877e10i			0.566739i	−0.959011	+	0.283369i	$0.908548\pi$
$588$	−3.01577e10	+	4.51359e10i	−0.252283	+	0.377583i
$589$	−6.65629e9			−0.0553059
$590$		0			0
$591$	−3.62187e10	−	2.41996e10i	−0.296881	−	0.198362i
$592$	9.01507e10			0.733977
$593$			2.36444e10i			0.191210i	0.995419	+	0.0956048i	$0.0304785\pi$
$593$			2.36444e10i			0.191210i	−0.995419	+	0.0956048i	$0.969521\pi$
$594$	8.14378e10	+	1.61945e10i	0.654154	+	0.130083i
$595$		0			0
$596$			2.03170e11i			1.61018i
$597$	−2.91414e10	+	4.36148e10i	−0.229410	+	0.343350i
$598$	−2.71756e11			−2.12507
$599$			3.03370e10i			0.235649i	0.993034	+	0.117825i	$0.0375921\pi$
$599$			3.03370e10i			0.235649i	−0.993034	+	0.117825i	$0.962408\pi$
$600$		0			0
$601$	3.37911e10			0.259003			0.129501	−	0.991579i	$-0.458662\pi$
$601$	3.37911e10			0.259003			0.129501	+	0.991579i	$0.458662\pi$
$602$		−	1.38533e11i		−	1.05480i
$603$	5.69718e9	+	1.37528e10i	0.0430914	+	0.104022i
$604$	−1.05117e11			−0.789818
$605$		0			0
$606$	1.04606e11	−	1.56560e11i	0.775649	−	1.16089i
$607$	3.82366e10			0.281660			0.140830	−	0.990034i	$-0.455023\pi$
$607$	3.82366e10			0.281660			0.140830	+	0.990034i	$0.455023\pi$
$608$			2.78359e10i			0.203700i
$609$	−5.43224e10	−	3.62957e10i	−0.394920	−	0.263867i
$610$		0			0
$611$		−	1.05005e11i		−	0.753435i
$612$	1.12583e11	−	4.66380e10i	0.802539	−	0.332456i
$613$	−1.08066e11			−0.765330			−0.382665	−	0.923887i	$-0.624994\pi$
$613$	−1.08066e11			−0.765330			−0.382665	+	0.923887i	$0.624994\pi$
$614$		−	6.71948e10i		−	0.472783i
$615$		0			0
$616$	2.18736e9			0.0151914
$617$			4.72538e9i			0.0326059i	0.999867	+	0.0163029i	$0.00518962\pi$
$617$			4.72538e9i			0.0326059i	−0.999867	+	0.0163029i	$0.994810\pi$
$618$	2.51088e11	+	1.67765e11i	1.72136	+	1.15013i
$619$	2.29845e10			0.156557			0.0782786	−	0.996932i	$-0.475058\pi$
$619$	2.29845e10			0.156557			0.0782786	+	0.996932i	$0.475058\pi$
$620$		0			0
$621$	−4.87639e10	+	2.45221e11i	−0.327893	+	1.64889i
$622$	1.44764e11			0.967165
$623$			1.27077e11i			0.843555i
$624$	−7.81780e10	+	1.17006e11i	−0.515640	+	0.771739i
$625$		0			0
$626$			7.35768e8i			0.00479119i
$627$	−8.87662e9	−	5.93094e9i	−0.0574351	−	0.0383754i
$628$	−1.88443e11			−1.21155
$629$			9.99949e10i			0.638815i
$630$		0			0
$631$	−1.01892e11			−0.642722			−0.321361	−	0.946957i	$-0.604140\pi$
$631$	−1.01892e11			−0.642722			−0.321361	+	0.946957i	$0.604140\pi$
$632$			4.12737e9i			0.0258705i
$633$	−2.61497e9	+	3.91372e9i	−0.0162874	+	0.0243767i
$634$	2.64453e11			1.63678
$635$		0			0
$636$	1.10268e11	+	7.36757e10i	0.673938	+	0.450294i
$637$	6.95302e10			0.422295
$638$			7.20106e10i			0.434624i
$639$	1.03179e11	−	4.27422e10i	0.618851	−	0.256362i
$640$		0			0
$641$			1.17803e11i			0.697791i	0.937162	+	0.348896i	$0.113443\pi$
$641$			1.17803e11i			0.697791i	−0.937162	+	0.348896i	$0.886557\pi$
$642$	−2.27851e10	+	3.41016e10i	−0.134125	+	0.200740i
$643$	2.62680e10			0.153668			0.0768339	−	0.997044i	$-0.475519\pi$
$643$	2.62680e10			0.153668			0.0768339	+	0.997044i	$0.475519\pi$
$644$		−	2.04180e11i		−	1.18705i
$645$		0			0
$646$	−3.18413e10			−0.182836
$647$		−	3.10527e11i		−	1.77208i	−0.463612	−	0.886038i	$-0.653447\pi$
$647$		−	3.10527e11i		−	1.77208i	0.463612	−	0.886038i	$-0.346553\pi$
$648$	5.46715e9	+	5.46638e9i	0.0310071	+	0.0310027i
$649$	−9.54486e10			−0.538010
$650$		0			0
$651$	2.76789e10	−	4.14260e10i	0.154108	−	0.230648i
$652$	1.65704e11			0.916942
$653$		−	3.48345e10i		−	0.191583i	−0.995401	−	0.0957914i	$-0.969462\pi$
$653$		−	3.48345e10i		−	0.191583i	0.995401	−	0.0957914i	$-0.0305382\pi$
$654$	−1.66282e11	−	1.11102e11i	−0.908940	−	0.607311i
$655$		0			0
$656$		−	1.26632e11i		−	0.683796i
$657$	6.94863e10	+	1.67738e11i	0.372939	+	0.900265i
$658$	1.60333e11			0.855304
$659$			3.77120e10i			0.199957i	0.994990	+	0.0999787i	$0.0318775\pi$
$659$			3.77120e10i			0.199957i	−0.994990	+	0.0999787i	$0.968123\pi$
$660$		0			0
$661$	−1.39619e11			−0.731372			−0.365686	−	0.930738i	$-0.619166\pi$
$661$	−1.39619e11			−0.731372			−0.365686	+	0.930738i	$0.619166\pi$
$662$			2.69623e11i			1.40386i
$663$	−1.29783e11	−	8.67149e10i	−0.671682	−	0.448786i
$664$	8.33256e9			0.0428653
$665$		0			0
$666$	1.81690e11	−	7.52659e10i	0.923494	−	0.382562i
$667$	−2.16834e11			−1.09553
$668$			4.86838e10i			0.244500i
$669$	1.98090e11	−	2.96474e11i	0.988912	−	1.48007i
$670$		0			0
$671$			5.24468e9i			0.0258719i
$672$	−1.73239e11	−	1.15750e11i	−0.849510	−	0.567603i
$673$	1.29783e11			0.632642			0.316321	−	0.948652i	$-0.397552\pi$
$673$	1.29783e11			0.632642			0.316321	+	0.948652i	$0.397552\pi$
$674$			3.57434e11i			1.73203i
$675$		0			0
$676$	3.81171e10			0.182529
$677$			3.40648e11i			1.62163i	0.585306	+	0.810813i	$0.300975\pi$
$677$			3.40648e11i			1.62163i	−0.585306	+	0.810813i	$0.699025\pi$
$678$	2.90696e11	−	4.35075e11i	1.37569	−	2.05895i
$679$	−2.57724e11			−1.21248
$680$		0			0
$681$	2.38144e11	+	1.59117e11i	1.10726	+	0.739821i
$682$	−5.49149e10			−0.253836
$683$		−	1.02876e11i		−	0.472750i	−0.971662	−	0.236375i	$-0.924041\pi$
$683$		−	1.02876e11i		−	0.472750i	0.971662	−	0.236375i	$-0.0759593\pi$
$684$	1.17932e10	+	2.84685e10i	0.0538776	+	0.130059i
$685$		0			0
$686$			3.32650e11i			1.50208i
$687$	8.39562e10	−	1.25654e11i	0.376900	−	0.564092i
$688$	−2.38086e11			−1.06262
$689$		−	1.69863e11i		−	0.753742i
$690$		0			0
$691$	3.58259e11			1.57140			0.785698	−	0.618611i	$-0.212304\pi$
$691$	3.58259e11			1.57140			0.785698	+	0.618611i	$0.212304\pi$
$692$			2.53752e11i			1.10659i
$693$	7.38234e10	−	3.05817e10i	0.320082	−	0.132595i
$694$	1.11081e11			0.478851
$695$		0			0
$696$	−3.72496e9	+	5.57501e9i	−0.0158740	+	0.0237580i
$697$	1.40459e11			0.595141
$698$			1.63787e11i			0.690016i
$699$	−1.83280e11	−	1.22459e11i	−0.767728	−	0.512960i
$700$		0			0
$701$		−	2.49323e11i		−	1.03250i	−0.856438	−	0.516250i	$-0.827327\pi$
$701$		−	2.49323e11i		−	1.03250i	0.856438	−	0.516250i	$-0.172673\pi$
$702$	−5.98729e10	+	3.01085e11i	−0.246537	+	1.23977i
$703$	−2.52854e10			−0.103526
$704$			1.09353e11i			0.445183i
$705$		0			0
$706$	1.55775e11			0.627015
$707$		−	1.81203e11i		−	0.725251i
$708$	2.29077e11	+	1.53058e11i	0.911691	+	0.609149i
$709$	−3.88874e11			−1.53895			−0.769474	−	0.638678i	$-0.779482\pi$
$709$	−3.88874e11			−1.53895			−0.769474	+	0.638678i	$0.779482\pi$
$710$		0			0
$711$	5.77052e10	+	1.39299e11i	0.225807	+	0.545091i
$712$	1.30417e10			0.0507473
$713$		−	1.65357e11i		−	0.639829i
$714$	1.32406e11	−	1.98167e11i	0.509465	−	0.762497i
$715$		0			0
$716$			3.19659e11i			1.21628i
$717$	1.53195e11	+	1.02357e11i	0.579651	+	0.387296i
$718$	3.59416e11			1.35238
$719$			3.35735e10i			0.125626i	0.998025	+	0.0628132i	$0.0200072\pi$
$719$			3.35735e10i			0.125626i	−0.998025	+	0.0628132i	$0.979993\pi$
$720$		0			0
$721$	2.90611e11			1.07540
$722$			3.73228e11i			1.37349i
$723$	7.86002e10	−	1.17638e11i	0.287654	−	0.430521i
$724$	−1.16983e11			−0.425764
$725$		0			0
$726$	2.50878e11	+	1.67625e11i	0.903058	+	0.603381i
$727$	−2.53113e11			−0.906102			−0.453051	−	0.891485i	$-0.649664\pi$
$727$	−2.53113e11			−0.906102			−0.453051	+	0.891485i	$0.649664\pi$
$728$			8.08692e9i			0.0287911i
$729$	2.60942e11	+	1.08053e11i	0.923920	+	0.382586i
$730$		0			0
$731$		−	2.64084e11i		−	0.924853i
$732$	8.41020e9	−	1.25872e10i	0.0292929	−	0.0438416i
$733$	−2.07602e11			−0.719144			−0.359572	−	0.933117i	$-0.617077\pi$
$733$	−2.07602e11			−0.719144			−0.359572	+	0.933117i	$0.617077\pi$
$734$			3.06137e11i			1.05471i
$735$		0			0
$736$	−6.91504e11			−2.35659
$737$		−	1.57903e10i		−	0.0535205i
$738$	−1.05724e11	−	2.55214e11i	−0.356407	−	0.860357i
$739$	4.15014e11			1.39151			0.695753	−	0.718281i	$-0.255071\pi$
$739$	4.15014e11			1.39151			0.695753	+	0.718281i	$0.255071\pi$
$740$		0			0
$741$	2.19274e10	−	3.28179e10i	0.0727300	−	0.108852i
$742$	2.59366e11			0.855653
$743$			3.30690e11i			1.08509i	0.840027	+	0.542545i	$0.182539\pi$
$743$			3.30690e11i			1.08509i	−0.840027	+	0.542545i	$0.817461\pi$
$744$	−4.25148e9	−	2.84064e9i	−0.0138755	−	0.00927095i
$745$		0			0
$746$		−	5.47918e11i		−	1.76913i
$747$	2.81224e11	−	1.16498e11i	0.903170	−	0.374143i
$748$	−1.29262e11			−0.412918
$749$			3.94695e10i			0.125411i
$750$		0			0
$751$	−4.77978e11			−1.50262			−0.751308	−	0.659952i	$-0.770577\pi$
$751$	−4.77978e11			−1.50262			−0.751308	+	0.659952i	$0.770577\pi$
$752$		−	2.75552e11i		−	0.861652i
$753$	−9.26390e10	−	6.18970e10i	−0.288147	−	0.192526i
$754$	−2.66231e11			−0.823709
$755$		0			0
$756$	−2.26216e11	−	4.49847e10i	−0.692526	−	0.137714i
$757$	8.95066e10			0.272566			0.136283	−	0.990670i	$-0.456484\pi$
$757$	8.95066e10			0.272566			0.136283	+	0.990670i	$0.456484\pi$
$758$			4.45390e11i			1.34916i
$759$	1.47337e11	−	2.20514e11i	0.443962	−	0.664462i
$760$		0			0
$761$			5.71473e11i			1.70395i	0.523581	+	0.851976i	$0.324596\pi$
$761$			5.71473e11i			1.70395i	−0.523581	+	0.851976i	$0.675404\pi$
$762$	−4.17303e11	−	2.78822e11i	−1.23775	−	0.827004i
$763$	−1.92456e11			−0.567851
$764$			4.01231e10i			0.117766i
$765$		0			0
$766$	3.39292e11			0.985504
$767$		−	3.52884e11i		−	1.01965i
$768$	−2.04781e11	+	3.06488e11i	−0.588634	+	0.880986i
$769$	2.56194e11			0.732596			0.366298	−	0.930498i	$-0.380625\pi$
$769$	2.56194e11			0.732596			0.366298	+	0.930498i	$0.380625\pi$
$770$		0			0
$771$	−5.34537e11	−	3.57152e11i	−1.51273	−	1.01073i
$772$	−3.93923e11			−1.10903
$773$			1.00523e11i			0.281543i	0.990042	+	0.140772i	$0.0449584\pi$
$773$			1.00523e11i			0.281543i	−0.990042	+	0.140772i	$0.955042\pi$
$774$	−4.79838e11	+	1.98775e11i	−1.33700	+	0.553859i

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-22.4499i q^{2} +(-45.0000 + 67.3498i) q^{3} -248.000 q^{4} +(1512.00 + 1010.25i) q^{6} +1750.00 q^{7} -179.600i q^{8} +(-2511.00 - 6061.48i) q^{9} +O(q^{10})\)	\(q-22.4499i q^{2} +(-45.0000 + 67.3498i) q^{3} -248.000 q^{4} +(1512.00 + 1010.25i) q^{6} +1750.00 q^{7} -179.600i q^{8} +(-2511.00 - 6061.48i) q^{9} +6959.48i q^{11} +(11160.0 - 16702.8i) q^{12} -25730.0 q^{13} -39287.4i q^{14} -67520.0 q^{16} -74893.0i q^{17} +(-136080. + 56371.8i) q^{18} +18938.0 q^{19} +(-78750.0 + 117862. i) q^{21} +156240. q^{22} +470461. i q^{23} +(12096.0 + 8081.98i) q^{24} +577637. i q^{26} +(521235. + 103651. i) q^{27} -434000. q^{28} +460897. i q^{29} -351478. q^{31} +1.46984e6i q^{32} +(-468720. - 313177. i) q^{33} -1.68134e6 q^{34} +(622728. + 1.50325e6i) q^{36} -1.33517e6 q^{37} -425157. i q^{38} +(1.15785e6 - 1.73291e6i) q^{39} +1.87547e6i q^{41} +(2.64600e6 + 1.76793e6i) q^{42} +3.52615e6 q^{43} -1.72595e6i q^{44} +1.05618e7 q^{46} +4.08104e6i q^{47} +(3.03840e6 - 4.54746e6i) q^{48} -2.70230e6 q^{49} +(5.04403e6 + 3.37019e6i) q^{51} +6.38104e6 q^{52} +6.60177e6i q^{53} +(2.32697e6 - 1.17017e7i) q^{54} -314299. i q^{56} +(-852210. + 1.27547e6i) q^{57} +1.03471e7 q^{58} +1.37149e7i q^{59} +753602. q^{61} +7.89066e6i q^{62} +(-4.39425e6 - 1.06076e7i) q^{63} +1.57128e7 q^{64} +(-7.03080e6 + 1.05227e7i) q^{66} -2.26889e6 q^{67} +1.85735e7i q^{68} +(-3.16855e7 - 2.11707e7i) q^{69} +1.70220e7i q^{71} +(-1.08864e6 + 450974. i) q^{72} -2.76728e7 q^{73} +2.99745e7i q^{74} -4.69662e6 q^{76} +1.21791e7i q^{77} +(-3.89038e7 - 2.59937e7i) q^{78} -2.29810e7 q^{79} +(-3.04365e7 + 3.04408e7i) q^{81} +4.21042e7 q^{82} +4.63952e7i q^{83} +(1.95300e7 - 2.92298e7i) q^{84} -7.91619e7i q^{86} +(-3.10414e7 - 2.07404e7i) q^{87} +1.24992e6 q^{88} +7.26152e7i q^{89} -4.50275e7 q^{91} -1.16674e8i q^{92} +(1.58165e7 - 2.36720e7i) q^{93} +9.16191e7 q^{94} +(-9.89937e7 - 6.61429e7i) q^{96} -1.47271e8 q^{97} +6.06665e7i q^{98} +(4.21848e7 - 1.74753e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 90 q^{3} - 496 q^{4} + 3024 q^{6} + 3500 q^{7} - 5022 q^{9}+O(q^{10}) \) 2 * q - 90 * q^3 - 496 * q^4 + 3024 * q^6 + 3500 * q^7 - 5022 * q^9	\( 2 q - 90 q^{3} - 496 q^{4} + 3024 q^{6} + 3500 q^{7} - 5022 q^{9} + 22320 q^{12} - 51460 q^{13} - 135040 q^{16} - 272160 q^{18} + 37876 q^{19} - 157500 q^{21} + 312480 q^{22} + 24192 q^{24} + 1042470 q^{27} - 868000 q^{28} - 702956 q^{31} - 937440 q^{33} - 3362688 q^{34} + 1245456 q^{36} - 2670340 q^{37} + 2315700 q^{39} + 5292000 q^{42} + 7052300 q^{43} + 21123648 q^{46} + 6076800 q^{48} - 5404602 q^{49} + 10088064 q^{51} + 12762080 q^{52} + 4653936 q^{54} - 1704420 q^{57} + 20694240 q^{58} + 1507204 q^{61} - 8788500 q^{63} + 31425536 q^{64} - 14061600 q^{66} - 4537780 q^{67} - 63370944 q^{69} - 2177280 q^{72} - 55345540 q^{73} - 9393248 q^{76} - 77807520 q^{78} - 45961964 q^{79} - 60872958 q^{81} + 84208320 q^{82} + 39060000 q^{84} - 62082720 q^{87} + 2499840 q^{88} - 90055000 q^{91} + 31633020 q^{93} + 183238272 q^{94} - 197987328 q^{96} - 294542020 q^{97} + 84369600 q^{99}+O(q^{100}) \) 2 * q - 90 * q^3 - 496 * q^4 + 3024 * q^6 + 3500 * q^7 - 5022 * q^9 + 22320 * q^12 - 51460 * q^13 - 135040 * q^16 - 272160 * q^18 + 37876 * q^19 - 157500 * q^21 + 312480 * q^22 + 24192 * q^24 + 1042470 * q^27 - 868000 * q^28 - 702956 * q^31 - 937440 * q^33 - 3362688 * q^34 + 1245456 * q^36 - 2670340 * q^37 + 2315700 * q^39 + 5292000 * q^42 + 7052300 * q^43 + 21123648 * q^46 + 6076800 * q^48 - 5404602 * q^49 + 10088064 * q^51 + 12762080 * q^52 + 4653936 * q^54 - 1704420 * q^57 + 20694240 * q^58 + 1507204 * q^61 - 8788500 * q^63 + 31425536 * q^64 - 14061600 * q^66 - 4537780 * q^67 - 63370944 * q^69 - 2177280 * q^72 - 55345540 * q^73 - 9393248 * q^76 - 77807520 * q^78 - 45961964 * q^79 - 60872958 * q^81 + 84208320 * q^82 + 39060000 * q^84 - 62082720 * q^87 + 2499840 * q^88 - 90055000 * q^91 + 31633020 * q^93 + 183238272 * q^94 - 197987328 * q^96 - 294542020 * q^97 + 84369600 * q^99

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