LMFDB - Embedded newform 3.9.b.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,9,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	3.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.22213583018$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-14}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 14 $ x^2 + 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.1
Root			$-3.74166i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.9.b.a.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.4499i q^{2} +(45.0000 + 67.3498i) q^{3} -248.000 q^{4} +224.499i q^{5} +(1512.00 - 1010.25i) q^{6} -1750.00 q^{7} -179.600i q^{8} +(-2511.00 + 6061.48i) q^{9} +O(q^{10})$	\(q-22.4499i q^{2} +(45.0000 + 67.3498i) q^{3} -248.000 q^{4} +224.499i q^{5} +(1512.00 - 1010.25i) q^{6} -1750.00 q^{7} -179.600i q^{8} +(-2511.00 + 6061.48i) q^{9} +5040.00 q^{10} -6959.48i q^{11} +(-11160.0 - 16702.8i) q^{12} +25730.0 q^{13} +39287.4i q^{14} +(-15120.0 + 10102.5i) q^{15} -67520.0 q^{16} -74893.0i q^{17} +(136080. + 56371.8i) q^{18} +18938.0 q^{19} -55675.9i q^{20} +(-78750.0 - 117862. i) q^{21} -156240. q^{22} +470461. i q^{23} +(12096.0 - 8081.98i) q^{24} +340225. q^{25} -577637. i q^{26} +(-521235. + 103651. i) q^{27} +434000. q^{28} -460897. i q^{29} +(226800. + 339443. i) q^{30} -351478. q^{31} +1.46984e6i q^{32} +(468720. - 313177. i) q^{33} -1.68134e6 q^{34} -392874. i q^{35} +(622728. - 1.50325e6i) q^{36} +1.33517e6 q^{37} -425157. i q^{38} +(1.15785e6 + 1.73291e6i) q^{39} +40320.0 q^{40} -1.87547e6i q^{41} +(-2.64600e6 + 1.76793e6i) q^{42} -3.52615e6 q^{43} +1.72595e6i q^{44} +(-1.36080e6 - 563718. i) q^{45} +1.05618e7 q^{46} +4.08104e6i q^{47} +(-3.03840e6 - 4.54746e6i) q^{48} -2.70230e6 q^{49} -7.63803e6i q^{50} +(5.04403e6 - 3.37019e6i) q^{51} -6.38104e6 q^{52} +6.60177e6i q^{53} +(2.32697e6 + 1.17017e7i) q^{54} +1.56240e6 q^{55} +314299. i q^{56} +(852210. + 1.27547e6i) q^{57} -1.03471e7 q^{58} -1.37149e7i q^{59} +(3.74976e6 - 2.50541e6i) q^{60} +753602. q^{61} +7.89066e6i q^{62} +(4.39425e6 - 1.06076e7i) q^{63} +1.57128e7 q^{64} +5.77637e6i q^{65} +(-7.03080e6 - 1.05227e7i) q^{66} +2.26889e6 q^{67} +1.85735e7i q^{68} +(-3.16855e7 + 2.11707e7i) q^{69} -8.82000e6 q^{70} -1.70220e7i q^{71} +(1.08864e6 + 450974. i) q^{72} +2.76728e7 q^{73} -2.99745e7i q^{74} +(1.53101e7 + 2.29141e7i) q^{75} -4.69662e6 q^{76} +1.21791e7i q^{77} +(3.89038e7 - 2.59937e7i) q^{78} -2.29810e7 q^{79} -1.51582e7i q^{80} +(-3.04365e7 - 3.04408e7i) q^{81} -4.21042e7 q^{82} +4.63952e7i q^{83} +(1.95300e7 + 2.92298e7i) q^{84} +1.68134e7 q^{85} +7.91619e7i q^{86} +(3.10414e7 - 2.07404e7i) q^{87} -1.24992e6 q^{88} -7.26152e7i q^{89} +(-1.26554e7 + 3.05499e7i) q^{90} -4.50275e7 q^{91} -1.16674e8i q^{92} +(-1.58165e7 - 2.36720e7i) q^{93} +9.16191e7 q^{94} +4.25157e6i q^{95} +(-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	\( 2 q + 90 q^{3} - 496 q^{4} + 3024 q^{6} - 3500 q^{7} - 5022 q^{9} + 10080 q^{10} - 22320 q^{12} + 51460 q^{13} - 30240 q^{15} - 135040 q^{16} + 272160 q^{18} + 37876 q^{19} - 157500 q^{21} - 312480 q^{22} + 24192 q^{24} + 680450 q^{25} - 1042470 q^{27} + 868000 q^{28} + 453600 q^{30} - 702956 q^{31} + 937440 q^{33} - 3362688 q^{34} + 1245456 q^{36} + 2670340 q^{37} + 2315700 q^{39} + 80640 q^{40} - 5292000 q^{42} - 7052300 q^{43} - 2721600 q^{45} + 21123648 q^{46} - 6076800 q^{48} - 5404602 q^{49} + 10088064 q^{51} - 12762080 q^{52} + 4653936 q^{54} + 3124800 q^{55} + 1704420 q^{57} - 20694240 q^{58} + 7499520 q^{60} + 1507204 q^{61} + 8788500 q^{63} + 31425536 q^{64} - 14061600 q^{66} + 4537780 q^{67} - 63370944 q^{69} - 17640000 q^{70} + 2177280 q^{72} + 55345540 q^{73} + 30620250 q^{75} - 9393248 q^{76} + 77807520 q^{78} - 45961964 q^{79} - 60872958 q^{81} - 84208320 q^{82} + 39060000 q^{84} + 33626880 q^{85} + 62082720 q^{87} - 2499840 q^{88} - 25310880 q^{90} - 90055000 q^{91} - 31633020 q^{93} + 183238272 q^{94} - 197987328 q^{96} + 294542020 q^{97} + 84369600 q^{99}+O(q^{100}) \) 2 * q + 90 * q^3 - 496 * q^4 + 3024 * q^6 - 3500 * q^7 - 5022 * q^9 + 10080 * q^10 - 22320 * q^12 + 51460 * q^13 - 30240 * q^15 - 135040 * q^16 + 272160 * q^18 + 37876 * q^19 - 157500 * q^21 - 312480 * q^22 + 24192 * q^24 + 680450 * q^25 - 1042470 * q^27 + 868000 * q^28 + 453600 * q^30 - 702956 * q^31 + 937440 * q^33 - 3362688 * q^34 + 1245456 * q^36 + 2670340 * q^37 + 2315700 * q^39 + 80640 * q^40 - 5292000 * q^42 - 7052300 * q^43 - 2721600 * q^45 + 21123648 * q^46 - 6076800 * q^48 - 5404602 * q^49 + 10088064 * q^51 - 12762080 * q^52 + 4653936 * q^54 + 3124800 * q^55 + 1704420 * q^57 - 20694240 * q^58 + 7499520 * q^60 + 1507204 * q^61 + 8788500 * q^63 + 31425536 * q^64 - 14061600 * q^66 + 4537780 * q^67 - 63370944 * q^69 - 17640000 * q^70 + 2177280 * q^72 + 55345540 * q^73 + 30620250 * q^75 - 9393248 * q^76 + 77807520 * q^78 - 45961964 * q^79 - 60872958 * q^81 - 84208320 * q^82 + 39060000 * q^84 + 33626880 * q^85 + 62082720 * q^87 - 2499840 * q^88 - 25310880 * q^90 - 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 $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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
$5$			224.499i			0.359199i	0.983740	+	0.179600i	$0.0574802\pi$
$5$			224.499i			0.359199i	−0.983740	+	0.179600i	$0.942520\pi$
$6$	1512.00	−	1010.25i	1.16667	−	0.779512i
$7$	−1750.00			−0.728863			−0.364431	−	0.931230i	$-0.618737\pi$
$7$	−1750.00			−0.728863			−0.364431	+	0.931230i	$0.618737\pi$
$8$		−	179.600i		−	0.0438475i
$9$	−2511.00	+	6061.48i	−0.382716	+	0.923866i
$10$	5040.00			0.504000
$11$		−	6959.48i		−	0.475342i	−0.971346	−	0.237671i	$-0.923616\pi$
$11$		−	6959.48i		−	0.475342i	0.971346	−	0.237671i	$-0.0763840\pi$
$12$	−11160.0	−	16702.8i	−0.538194	−	0.805496i
$13$	25730.0			0.900879			0.450439	−	0.892807i	$-0.351267\pi$
$13$	25730.0			0.900879			0.450439	+	0.892807i	$0.351267\pi$
$14$			39287.4i			1.02268i
$15$	−15120.0	+	10102.5i	−0.298667	+	0.199555i
$16$	−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	$0.476852\pi$
$20$		−	55675.9i		−	0.347974i
$21$	−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
$25$	340225.			0.870976
$26$		−	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	$-0.894359\pi$
$29$		−	460897.i		−	0.651647i	0.945431	−	0.325823i	$-0.105641\pi$
$30$	226800.	+	339443.i	0.280000	+	0.419066i
$31$	−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
$35$		−	392874.i		−	0.261807i
$36$	622728.	−	1.50325e6i	0.370756	−	0.894995i
$37$	1.33517e6			0.712409			0.356205	−	0.934408i	$-0.384071\pi$
$37$	1.33517e6			0.712409			0.356205	+	0.934408i	$0.384071\pi$
$38$		−	425157.i		−	0.203899i
$39$	1.15785e6	+	1.73291e6i	0.500488	+	0.749062i
$40$	40320.0			0.0157500
$41$		−	1.87547e6i		−	0.663704i	−0.943331	−	0.331852i	$-0.892327\pi$
$41$		−	1.87547e6i		−	0.663704i	0.943331	−	0.331852i	$-0.107673\pi$
$42$	−2.64600e6	+	1.76793e6i	−0.850340	+	0.568157i
$43$	−3.52615e6			−1.03140			−0.515700	−	0.856769i	$-0.672468\pi$
$43$	−3.52615e6			−1.03140			−0.515700	+	0.856769i	$0.672468\pi$
$44$			1.72595e6i			0.460488i
$45$	−1.36080e6	−	563718.i	−0.331852	−	0.137471i
$46$	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
$50$		−	7.63803e6i		−	1.22209i
$51$	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
$55$	1.56240e6			0.170742
$56$			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	$-0.808521\pi$
$59$		−	1.37149e7i		−	1.13184i	0.824461	−	0.565919i	$-0.191479\pi$
$60$	3.74976e6	−	2.50541e6i	0.289333	−	0.193319i
$61$	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
$65$			5.77637e6i			0.323595i
$66$	−7.03080e6	−	1.05227e7i	−0.370535	−	0.554566i
$67$	2.26889e6			0.112594			0.0562969	−	0.998414i	$-0.482071\pi$
$67$	2.26889e6			0.112594			0.0562969	+	0.998414i	$0.482071\pi$
$68$			1.85735e7i			0.868675i
$69$	−3.16855e7	+	2.11707e7i	−1.39786	+	0.933985i
$70$	−8.82000e6			−0.367347
$71$		−	1.70220e7i		−	0.669849i	−0.942245	−	0.334925i	$-0.891289\pi$
$71$		−	1.70220e7i		−	0.669849i	0.942245	−	0.334925i	$-0.108711\pi$
$72$	1.08864e6	+	450974.i	0.0405093	+	0.0167812i
$73$	2.76728e7			0.974454			0.487227	−	0.873275i	$-0.338008\pi$
$73$	2.76728e7			0.974454			0.487227	+	0.873275i	$0.338008\pi$
$74$		−	2.99745e7i		−	0.999597i
$75$	1.53101e7	+	2.29141e7i	0.483876	+	0.724199i
$76$	−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	$0.595322\pi$
$80$		−	1.51582e7i		−	0.370073i
$81$	−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
$85$	1.68134e7			0.322093
$86$			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	$-0.803568\pi$
$89$		−	7.26152e7i		−	1.15736i	0.815555	−	0.578679i	$-0.196432\pi$
$90$	−1.26554e7	+	3.05499e7i	−0.192889	+	0.465628i
$91$	−4.50275e7			−0.656617
$92$		−	1.16674e8i		−	1.62864i
$93$	−1.58165e7	−	2.36720e7i	−0.211436	−	0.316448i
$94$	9.16191e7			1.17348
$95$			4.25157e6i			0.0521981i
$96$	−9.89937e7	+	6.61429e7i	−1.16553	+	0.778751i
$97$	1.47271e8			1.66353			0.831764	−	0.555129i	$-0.187331\pi$
$97$	1.47271e8			1.66353			0.831764	+	0.555129i	$0.187331\pi$
$98$			6.06665e7i			0.657726i
$99$	4.21848e7	+	1.74753e7i	0.439152	+	0.181921i
$100$	−8.43758e7			−0.843758
$101$			1.03545e8i			0.995045i	0.867451	+	0.497522i	$0.165757\pi$
$101$			1.03545e8i			0.995045i	−0.867451	+	0.497522i	$0.834243\pi$
$102$	−7.56605e7	−	1.13238e8i	−0.698986	−	1.04615i
$103$	−1.66064e8			−1.47545			−0.737726	−	0.675100i	$-0.764101\pi$
$103$	−1.66064e8			−1.47545			−0.737726	+	0.675100i	$0.764101\pi$
$104$		−	4.62110e6i		−	0.0395013i
$105$	2.64600e7	−	1.76793e7i	0.217687	−	0.145448i
$106$	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	$0.627368\pi$
$110$		−	3.50758e7i		−	0.239572i
$111$	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
$115$	−1.05618e8			−0.603876
$116$			1.14303e8i			0.631283i
$117$	−6.46080e7	+	1.55962e8i	−0.344781	+	0.832291i
$118$	−3.07899e8			−1.58811
$119$			1.31063e8i			0.653569i
$120$	1.81440e6	+	2.71555e6i	0.00875000	+	0.0130958i
$121$	1.65924e8			0.774050
$122$		−	1.69183e7i		−	0.0763692i
$123$	1.26312e8	−	8.43961e7i	0.551856	−	0.368724i
$124$	8.71665e7			0.368691
$125$			1.64075e8i			0.672053i
$126$	−2.38140e8	−	9.86507e7i	−0.944822	−	0.391397i
$127$	2.75994e8			1.06092			0.530462	−	0.847708i	$-0.322018\pi$
$127$	2.75994e8			1.06092			0.530462	+	0.847708i	$0.322018\pi$
$128$			2.35290e7i			0.0876523i
$129$	−1.58677e8	−	2.37486e8i	−0.573000	−	0.857588i
$130$	1.29679e8			0.454043
$131$		−	2.89118e8i		−	0.981725i	−0.871237	−	0.490862i	$-0.836682\pi$
$131$		−	2.89118e8i		−	0.981725i	0.871237	−	0.490862i	$-0.163318\pi$
$132$	−1.16243e8	+	7.76678e7i	−0.382886	+	0.255826i
$133$	−3.31415e7			−0.105917
$134$		−	5.09365e7i		−	0.157983i
$135$	−2.32697e7	−	1.17017e8i	−0.0700576	−	0.352301i
$136$	−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	$0.561202\pi$
$140$			9.74328e7i			0.253625i
$141$	−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
$145$	1.03471e8			0.234071
$146$		−	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	$0.312267\pi$
$149$			8.19236e8i			1.66213i	−0.556179	+	0.831063i	$0.687733\pi$
$150$	5.14420e8	−	3.43711e8i	1.01614	−	0.678936i
$151$	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
$155$		−	7.89066e7i		−	0.136706i
$156$	−2.87147e8	−	4.29762e8i	−0.484848	−	0.725654i
$157$	−7.59851e8			−1.25063			−0.625316	−	0.780371i	$-0.715030\pi$
$157$	−7.59851e8			−1.25063			−0.625316	+	0.780371i	$0.715030\pi$
$158$			5.15922e8i			0.827857i
$159$	−4.44628e8	+	2.97079e8i	−0.695678	+	0.464819i
$160$	−3.29979e8			−0.503508
$161$		−	8.23307e8i		−	1.22534i
$162$	−6.83394e8	+	6.83297e8i	−0.992227	+	0.992087i
$163$	6.68160e8			0.946520			0.473260	−	0.880923i	$-0.343077\pi$
$163$	6.68160e8			0.946520			0.473260	+	0.880923i	$0.343077\pi$
$164$			4.65116e8i			0.642963i
$165$	7.03080e7	+	1.05227e8i	0.0948569	+	0.141969i
$166$	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
$170$		−	3.77461e8i		−	0.451935i
$171$	−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
$175$	−5.95394e8			−0.634822
$176$			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	$0.216028\pi$
$179$			1.28895e9i			1.25552i	−0.778408	+	0.627759i	$0.783972\pi$
$180$	3.37478e8	+	1.39802e8i	0.321481	+	0.133175i
$181$	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
$185$			2.99745e8i			0.255897i
$186$	−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
$190$	9.54475e7			0.0732403
$191$			1.61787e8i			0.121565i	0.998151	+	0.0607827i	$0.0193597\pi$
$191$			1.61787e8i			0.121565i	−0.998151	+	0.0607827i	$0.980640\pi$
$192$	7.07075e8	+	1.05825e9i	0.520308	+	0.778725i
$193$	−1.58840e9			−1.14480			−0.572401	−	0.819974i	$-0.693988\pi$
$193$	−1.58840e9			−1.14480			−0.572401	+	0.819974i	$0.693988\pi$
$194$		−	3.30623e9i		−	2.33413i
$195$	−3.89038e8	+	2.59937e8i	−0.269062	+	0.179775i
$196$	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	$0.433803\pi$
$200$		−	6.11043e7i		−	0.0381902i
$201$	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
$205$	4.21042e8			0.238402
$206$			3.72812e9i			2.07024i
$207$	−2.85169e9	−	1.18133e9i	−1.55318	−	0.643412i
$208$	−1.73729e9			−0.928152
$209$		−	1.31799e8i		−	0.0690758i
$210$	−3.96900e8	−	5.94026e8i	−0.204082	−	0.305441i
$211$	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
$215$		−	7.91619e8i		−	0.370478i
$216$	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
$220$	−3.87475e8			−0.165407
$221$		−	1.92700e9i		−	0.807815i
$222$	2.01878e9	−	1.34885e9i	0.831144	−	0.555332i
$223$	4.40200e9			1.78004			0.890021	−	0.455920i	$-0.150690\pi$
$223$	4.40200e9			1.78004			0.890021	+	0.455920i	$0.150690\pi$
$224$		−	2.57222e9i		−	1.02168i
$225$	−8.54305e8	+	2.06227e9i	−0.333336	+	0.804665i
$226$	−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	$0.610160\pi$
$230$			2.37112e9i			0.847311i
$231$	−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
$235$	−9.16191e8			−0.300410
$236$			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	$0.113331\pi$
$239$			2.27461e9i			0.697132i	−0.937284	+	0.348566i	$0.886669\pi$
$240$	1.02090e9	−	6.82119e8i	0.307708	−	0.205596i
$241$	−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
$245$		−	6.06665e8i		−	0.168378i
$246$	−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
$250$	3.68348e9			0.942972
$251$		−	1.37549e9i		−	0.346547i	−0.984874	−	0.173274i	$-0.944566\pi$
$251$		−	1.37549e9i		−	0.346547i	0.984874	−	0.173274i	$-0.0554345\pi$
$252$	−1.08977e9	+	2.63068e9i	−0.270230	+	0.652329i
$253$	3.27417e9			0.799132
$254$		−	6.19605e9i		−	1.48861i
$255$	7.56605e8	+	1.13238e9i	0.178940	+	0.267813i
$256$	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
$260$		−	1.43254e9i		−	0.313483i
$261$	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
$265$	−1.48209e9			−0.300533
$266$			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	$-0.892394\pi$
$269$		−	3.47314e9i		−	0.663304i	0.943402	−	0.331652i	$-0.107606\pi$
$270$	−2.62702e9	+	5.22403e8i	−0.494321	+	0.0982993i
$271$	−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
$275$		−	2.36779e9i		−	0.414012i
$276$	7.85800e9	−	5.25035e9i	1.35418	−	0.904798i
$277$	3.38046e9			0.574192			0.287096	−	0.957902i	$-0.407310\pi$
$277$	3.38046e9			0.574192			0.287096	+	0.957902i	$0.407310\pi$
$278$			3.20289e9i			0.536245i
$279$	8.82561e8	−	2.13048e9i	0.145656	−	0.351609i
$280$	−7.05600e7			−0.0114796
$281$		−	4.02262e9i		−	0.645184i	−0.946538	−	0.322592i	$-0.895446\pi$
$281$		−	4.02262e9i		−	0.645184i	0.946538	−	0.322592i	$-0.104554\pi$
$282$	4.12286e9	+	6.17053e9i	0.651932	+	0.975722i
$283$	−1.04253e10			−1.62533			−0.812666	−	0.582730i	$-0.801984\pi$
$283$	−1.04253e10			−1.62533			−0.812666	+	0.582730i	$0.801984\pi$
$284$			4.22146e9i			0.648917i
$285$	−2.86343e8	+	1.91321e8i	−0.0434017	+	0.0289990i
$286$	−4.02006e9			−0.600853
$287$			3.28207e9i			0.483749i
$288$	−8.90943e9	−	3.69078e9i	−1.29503	−	0.536473i
$289$	1.36679e9			0.195935
$290$		−	2.32292e9i		−	0.328430i
$291$	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
$295$	3.07899e9			0.406555
$296$		−	2.39796e8i		−	0.0312374i
$297$	7.21360e8	+	3.62753e9i	0.0927099	+	0.466213i
$298$	1.83918e10			2.33216
$299$			1.21050e10i			1.51453i
$300$	−3.79691e9	−	5.68270e9i	−0.468754	−	0.701567i
$301$	6.17076e9			0.751749
$302$		−	9.51565e9i		−	1.14396i
$303$	−6.97372e9	+	4.65951e9i	−0.827359	+	0.552803i
$304$	−1.27869e9			−0.149717
$305$			1.69183e8i			0.0195505i
$306$	4.22185e9	−	1.01914e10i	0.481524	−	1.16238i
$307$	−2.99309e9			−0.336951			−0.168476	−	0.985706i	$-0.553884\pi$
$307$	−2.99309e9			−0.336951			−0.168476	+	0.985706i	$0.553884\pi$
$308$		−	3.02042e9i		−	0.335632i
$309$	−7.47286e9	−	1.11843e10i	−0.819696	−	1.22681i
$310$	−1.77145e9			−0.191815
$311$		−	6.44832e9i		−	0.689295i	−0.938732	−	0.344647i	$-0.887998\pi$
$311$		−	6.44832e9i		−	0.689295i	0.938732	−	0.344647i	$-0.112002\pi$
$312$	3.11230e8	−	2.07949e8i	0.0328445	−	0.0219452i
$313$	3.27737e7			0.00341467			0.00170733	−	0.999999i	$-0.499457\pi$
$313$	3.27737e7			0.00341467			0.00170733	+	0.999999i	$0.499457\pi$
$314$			1.70586e10i			1.75479i
$315$	2.38140e9	+	9.86507e8i	0.241875	+	0.100198i
$316$	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
$320$			3.52751e9i			0.336409i
$321$	−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
$325$	8.75399e9			0.784644
$326$		−	1.50002e10i		−	1.32808i
$327$	−4.94888e9	−	7.40680e9i	−0.432829	−	0.647798i
$328$	−3.36833e8			−0.0291018
$329$		−	7.14182e9i		−	0.609573i
$330$	2.36235e9	−	1.57841e9i	0.199200	−	0.133096i
$331$	−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
$335$			5.09365e8i			0.0404436i
$336$	5.31720e9	+	7.95806e9i	0.417182	+	0.624381i
$337$	1.59214e10			1.23441			0.617207	−	0.786801i	$-0.288264\pi$
$337$	1.59214e10			1.23441			0.617207	+	0.786801i	$0.288264\pi$
$338$			3.45051e9i			0.264372i
$339$	1.93798e10	−	1.29486e10i	1.46740	−	0.980451i
$340$	−4.16973e9			−0.312027
$341$			2.44611e9i			0.180908i
$342$	2.57708e9	+	1.06757e9i	0.188375	+	0.0780354i
$343$	1.48174e10			1.07052
$344$			6.33295e8i			0.0452243i
$345$	−4.75282e9	−	7.11337e9i	−0.335487	−	0.502110i
$346$	−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	$0.579079\pi$
$350$			1.33666e10i			0.890733i
$351$	−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
$355$	3.82143e9			0.240609
$356$			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	$-0.839940\pi$
$359$		−	1.60096e10i		−	0.963838i	0.876216	−	0.481919i	$-0.160060\pi$
$360$	−1.01244e8	+	2.44399e8i	−0.00602778	+	0.0145509i
$361$	−1.66249e10			−0.978883
$362$		−	1.05898e10i		−	0.616670i
$363$	7.46660e9	+	1.11750e10i	0.430028	+	0.643607i
$364$	1.11668e10			0.636098
$365$			6.21252e9i			0.350023i
$366$	1.13945e9	−	7.61325e8i	0.0634994	−	0.0424273i
$367$	1.36364e10			0.751686			0.375843	−	0.926683i	$-0.377353\pi$
$367$	1.36364e10			0.751686			0.375843	+	0.926683i	$0.377353\pi$
$368$		−	3.17655e10i		−	1.73207i
$369$	1.13681e10	+	4.70930e9i	0.613173	+	0.254010i
$370$	6.72926e9			0.359054
$371$		−	1.15531e10i		−	0.609821i
$372$	3.92249e9	+	5.87065e9i	0.204829	+	0.306559i
$373$	−2.44062e10			−1.26085			−0.630427	−	0.776248i	$-0.717120\pi$
$373$	−2.44062e10			−1.26085			−0.630427	+	0.776248i	$0.717120\pi$
$374$			1.17013e10i			0.598063i
$375$	−1.10505e10	+	7.38339e9i	−0.558798	+	0.373363i
$376$	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	$0.659643\pi$
$380$		−	1.05439e9i		−	0.0505669i
$381$	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
$385$	−2.73420e9			−0.124448
$386$			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	$0.128572\pi$
$389$			1.79991e10i			0.786056i	−0.919527	+	0.393028i	$0.871428\pi$
$390$	5.83556e9	+	8.73387e9i	0.252246	+	0.377527i
$391$	3.52342e10			1.50750
$392$			4.85332e8i			0.0205539i
$393$	1.94720e10	−	1.30103e10i	0.816284	−	0.545403i
$394$	1.20729e10			0.500987
$395$		−	5.15922e9i		−	0.211931i
$396$	−1.04618e10	−	4.33386e9i	−0.425429	−	0.176236i
$397$	−2.35673e10			−0.948739			−0.474370	−	0.880326i	$-0.657324\pi$
$397$	−2.35673e10			−0.948739			−0.474370	+	0.880326i	$0.657324\pi$
$398$		−	1.45383e10i		−	0.579403i
$399$	−1.49137e9	−	2.23207e9i	−0.0588428	−	0.0880678i
$400$	−2.29720e10			−0.897343
$401$		−	1.37692e10i		−	0.532515i	−0.963902	−	0.266257i	$-0.914213\pi$
$401$		−	1.37692e10i		−	0.532515i	0.963902	−	0.266257i	$-0.0857871\pi$
$402$	3.43056e9	−	2.29214e9i	0.131359	−	0.0877682i
$403$	−9.04353e9			−0.342861
$404$		−	2.56791e10i		−	0.963950i
$405$	6.83394e9	−	6.83297e9i	0.254010	−	0.253974i
$406$	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	$0.278714\pi$
$410$		−	9.45236e9i		−	0.334507i
$411$	−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
$415$	−1.04157e10			−0.351153
$416$			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	$-0.881624\pi$
$419$		−	2.23996e10i		−	0.726750i	0.931643	−	0.363375i	$-0.118376\pi$
$420$	−6.56208e9	+	4.38447e9i	−0.210884	+	0.140903i
$421$	−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
$425$		−	2.54805e10i		−	0.781001i
$426$	−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
$430$	−1.77718e10			−0.519825
$431$			6.40436e10i			1.85595i	0.372640	+	0.927976i	$0.378453\pi$
$431$			6.40436e10i			1.85595i	−0.372640	+	0.927976i	$0.621547\pi$
$432$	3.51938e10	−	6.99854e9i	1.01049	−	0.200943i
$433$	−5.22954e9			−0.148769			−0.0743843	−	0.997230i	$-0.523699\pi$
$433$	−5.22954e9			−0.148769			−0.0743843	+	0.997230i	$0.523699\pi$
$434$		−	1.38087e10i		−	0.389218i
$435$	4.65620e9	+	6.96877e9i	0.130039	+	0.194625i
$436$	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	$0.300964\pi$
$440$		−	2.80606e8i		−	0.00748664i
$441$	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
$445$	1.63021e10			0.415722
$446$		−	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	$-0.881569\pi$
$449$		−	2.95505e10i		−	0.727076i	0.931579	−	0.363538i	$-0.118431\pi$
$450$	4.62978e10	+	1.91791e10i	1.12904	+	0.467712i
$451$	−1.30523e10			−0.315486
$452$			7.13614e10i			1.70966i
$453$	1.90737e10	+	2.85469e10i	0.452942	+	0.677902i
$454$	−7.93813e10			−1.86851
$455$		−	1.01086e10i		−	0.235856i
$456$	2.29074e8	−	1.53057e8i	0.00529806	−	0.00353991i
$457$	−2.02181e10			−0.463529			−0.231764	−	0.972772i	$-0.574450\pi$
$457$	−2.02181e10			−0.463529			−0.231764	+	0.972772i	$0.574450\pi$
$458$			4.18847e10i			0.951905i
$459$	7.76277e9	+	3.90369e10i	0.174890	+	0.879476i
$460$	2.61933e10			0.585005
$461$		−	7.01826e10i		−	1.55391i	−0.629556	−	0.776955i	$-0.716763\pi$
$461$		−	7.01826e10i		−	1.55391i	0.629556	−	0.776955i	$-0.283237\pi$
$462$	1.23039e10	+	1.84148e10i	0.270069	+	0.404202i
$463$	4.16009e9			0.0905271			0.0452635	−	0.998975i	$-0.485587\pi$
$463$	4.16009e9			0.0905271			0.0452635	+	0.998975i	$0.485587\pi$
$464$			3.11198e10i			0.671374i
$465$	5.31435e9	−	3.55080e9i	0.113668	−	0.0759476i
$466$	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
$470$			2.05684e10i			0.421512i
$471$	−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
$475$	6.44318e9			0.126569
$476$		−	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	$-0.860380\pi$
$479$		−	4.47149e10i		−	0.849395i	0.905335	−	0.424698i	$-0.139620\pi$
$480$	−1.48490e10	−	2.22240e10i	−0.279727	−	0.418656i
$481$	3.43539e10			0.641795
$482$			3.92127e10i			0.726505i
$483$	5.54496e10	−	3.70488e10i	1.01885	−	0.680747i
$484$	−4.11493e10			−0.749861
$485$			3.30623e10i			0.597538i
$486$	−7.67727e10	−	1.52781e10i	−1.37614	−	0.273857i
$487$	5.72836e10			1.01839			0.509195	−	0.860651i	$-0.329943\pi$
$487$	5.72836e10			1.01839			0.509195	+	0.860651i	$0.329943\pi$
$488$		−	1.35347e8i		−	0.00238654i
$489$	3.00672e10	+	4.50005e10i	0.525845	+	0.787012i
$490$	−1.36196e10			−0.236254
$491$			7.25262e10i			1.24787i	0.781477	+	0.623934i	$0.214467\pi$
$491$			7.25262e10i			1.24787i	−0.781477	+	0.623934i	$0.785533\pi$
$492$	−3.13255e10	+	2.09302e10i	−0.534611	+	0.357202i
$493$	−3.45180e10			−0.584330
$494$		−	1.09393e10i		−	0.183688i
$495$	−3.92319e9	+	9.47046e9i	−0.0653459	+	0.157743i
$496$	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	$0.568387\pi$
$500$		−	4.06907e10i		−	0.651051i
$501$	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
$505$	−2.32457e10			−0.357419
$506$		−	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	$0.159581\pi$
$509$			6.45184e10i			0.961197i	−0.876941	+	0.480599i	$0.840419\pi$
$510$	2.54219e10	−	1.69857e10i	0.375775	−	0.251075i
$511$	−4.84273e10			−0.710243
$512$		−	9.61394e10i		−	1.39901i
$513$	−9.87115e9	+	1.96295e9i	−0.142527	+	0.0283426i
$514$	1.78179e11			2.55272
$515$		−	3.72812e10i		−	0.529981i
$516$	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
$520$	1.03743e9			0.0141888
$521$			7.65146e10i			1.03847i	0.854632	+	0.519235i	$0.173783\pi$
$521$			7.65146e10i			1.03847i	−0.854632	+	0.519235i	$0.826217\pi$
$522$	2.59816e10	−	6.27189e10i	0.349932	−	0.844727i
$523$	−8.46771e10			−1.13177			−0.565886	−	0.824483i	$-0.691466\pi$
$523$	−8.46771e10			−1.13177			−0.565886	+	0.824483i	$0.691466\pi$
$524$			7.17012e10i			0.951046i
$525$	−2.67927e10	−	4.00997e10i	−0.352679	−	0.527842i
$526$	−7.24133e9			−0.0945966
$527$			2.63232e10i			0.341269i
$528$	−3.16480e10	+	2.11457e10i	−0.407202	+	0.272073i
$529$	−1.43023e11			−1.82634
$530$			3.32729e10i			0.421684i
$531$	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
$535$	−5.06336e9			−0.0618050
$536$		−	4.07492e8i		−	0.00493696i
$537$	−8.68104e10	+	5.80026e10i	−1.04394	+	0.697510i
$538$	−7.79717e10			−0.930696
$539$			1.88066e10i			0.222821i
$540$	5.77088e9	+	2.90202e10i	0.0678683	+	0.341292i
$541$	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
$545$		−	2.46893e10i		−	0.279849i
$546$	−6.80816e10	+	4.54889e10i	−0.766053	+	0.511841i
$547$	1.64171e11			1.83378			0.916892	−	0.399134i	$-0.130689\pi$
$547$	1.64171e11			1.83378			0.916892	+	0.399134i	$0.130689\pi$
$548$		−	5.14755e10i		−	0.570792i
$549$	−1.89229e9	+	4.56795e9i	−0.0208305	+	0.0502842i
$550$	−5.31568e10			−0.580908
$551$		−	8.72847e9i		−	0.0946961i
$552$	3.80226e9	+	5.69070e9i	0.0409529	+	0.0612928i
$553$	4.02167e10			0.430037
$554$		−	7.58912e10i		−	0.805661i
$555$	−2.01878e10	+	1.34885e10i	−0.212773	+	0.142165i
$556$	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
$560$			2.65269e10i			0.269733i
$561$	−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
$565$	6.45992e10			0.633919
$566$			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	$0.185511\pi$
$569$			1.15380e11i			1.10073i	−0.834925	+	0.550364i	$0.814489\pi$
$570$	4.29514e9	+	6.42837e9i	0.0406891	+	0.0608978i
$571$	−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
$575$			1.60063e11i			1.46426i
$576$	−3.94548e10	+	9.52427e10i	−0.358434	+	0.865250i
$577$	7.42282e10			0.669678			0.334839	−	0.942275i	$-0.391318\pi$
$577$	7.42282e10			0.669678			0.334839	+	0.942275i	$0.391318\pi$
$578$		−	3.06844e10i		−	0.274920i
$579$	−7.14779e10	−	1.06978e11i	−0.636001	−	0.951879i
$580$	−2.56609e10			−0.226756
$581$		−	8.11916e10i		−	0.712535i
$582$	2.22674e11	−	1.48780e11i	1.94078	−	1.29674i
$583$	4.59449e10			0.397707
$584$		−	4.97002e9i		−	0.0427274i
$585$	−3.50134e10	−	1.45045e10i	−0.298958	−	0.123845i
$586$	−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
$590$		−	6.91231e10i		−	0.570447i
$591$	−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
$595$	−2.94235e10			−0.234761
$596$		−	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	$-0.962408\pi$
$599$		−	3.03370e10i		−	0.235649i	0.993034	−	0.117825i	$-0.0375921\pi$
$600$	4.11536e9	−	2.74969e9i	0.0317543	−	0.0212168i
$601$	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
$605$			3.72500e10i			0.278038i
$606$	1.04606e11	+	1.56560e11i	0.775649	+	1.16089i
$607$	−3.82366e10			−0.281660			−0.140830	−	0.990034i	$-0.544977\pi$
$607$	−3.82366e10			−0.281660			−0.140830	+	0.990034i	$0.544977\pi$
$608$			2.78359e10i			0.203700i
$609$	−5.43224e10	+	3.62957e10i	−0.394920	+	0.263867i
$610$	3.79815e9			0.0274317
$611$			1.05005e11i			0.753435i
$612$	−1.12583e11	−	4.66380e10i	−0.802539	−	0.332456i
$613$	1.08066e11			0.765330			0.382665	−	0.923887i	$-0.375006\pi$
$613$	1.08066e11			0.765330			0.382665	+	0.923887i	$0.375006\pi$
$614$			6.71948e10i			0.472783i
$615$	1.89469e10	+	2.83571e10i	0.132445	+	0.198226i
$616$	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	$0.475058\pi$
$620$			1.95688e10i			0.132434i
$621$	−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
$625$	9.60656e10			0.629575
$626$		−	7.35768e8i		−	0.00479119i
$627$	8.87662e9	−	5.93094e9i	0.0574351	−	0.0383754i
$628$	1.88443e11			1.21155
$629$		−	9.99949e10i		−	0.638815i
$630$	2.21470e10	−	5.34623e10i	0.140590	−	0.339379i
$631$	−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
$635$			6.19605e10i			0.381083i
$636$	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
$640$	−5.28224e9			−0.0314846
$641$		−	1.17803e11i		−	0.697791i	−0.937162	−	0.348896i	$-0.886557\pi$
$641$		−	1.17803e11i		−	0.697791i	0.937162	−	0.348896i	$-0.113443\pi$
$642$	2.27851e10	+	3.41016e10i	0.134125	+	0.200740i
$643$	−2.62680e10			−0.153668			−0.0768339	−	0.997044i	$-0.524481\pi$
$643$	−2.62680e10			−0.153668			−0.0768339	+	0.997044i	$0.524481\pi$
$644$			2.04180e11i			1.18705i
$645$	5.33154e10	−	3.56228e10i	0.308045	−	0.205821i
$646$	−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
$650$		−	1.96527e11i		−	1.10095i
$651$	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
$655$	6.49068e10			0.352635
$656$			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	$-0.968123\pi$
$659$		−	3.77120e10i		−	0.199957i	0.994990	−	0.0999787i	$-0.0318775\pi$
$660$	−1.74364e10	−	2.60964e10i	−0.0918926	−	0.137532i
$661$	−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
$665$		−	7.44025e9i		−	0.0380453i
$666$	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
$670$	1.14352e10			0.0567472
$671$		−	5.24468e9i		−	0.0258719i
$672$	1.73239e11	−	1.15750e11i	0.849510	−	0.567603i
$673$	−1.29783e11			−0.632642			−0.316321	−	0.948652i	$-0.602448\pi$
$673$	−1.29783e11			−0.632642			−0.316321	+	0.948652i	$0.602448\pi$
$674$		−	3.57434e11i		−	1.73203i
$675$	−1.77337e11	+	3.52648e10i	−0.854249	+	0.169874i
$676$	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
$680$		−	3.01969e9i		−	0.0141230i
$681$	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
$685$	−4.65976e10			−0.211642
$686$		−	3.32650e11i		−	1.50208i
$687$	−8.39562e10	−	1.25654e11i	−0.376900	−	0.564092i
$688$	2.38086e11			1.06262
$689$			1.69863e11i			0.753742i
$690$	−1.59695e11	+	1.06701e11i	−0.704522	+	0.470728i
$691$	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
$695$		−	3.20289e10i		−	0.137279i
$696$	−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
$700$	1.47658e11			0.614984
$701$			2.49323e11i			1.03250i	0.856438	+	0.516250i	$0.172673\pi$
$701$			2.49323e11i			1.03250i	−0.856438	+	0.516250i	$0.827327\pi$
$702$	5.98729e10	+	3.01085e11i	0.246537	+	1.23977i
$703$	2.52854e10			0.103526
$704$		−	1.09353e11i		−	0.445183i
$705$	−4.12286e10	−	6.17053e10i	−0.166895	−	0.249785i
$706$	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	$0.779482\pi$
$710$		−	8.57909e10i		−	0.337604i
$711$	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
$715$	4.02006e10			0.153818
$716$		−	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	$-0.979993\pi$
$719$		−	3.35735e10i		−	0.125626i	0.998025	−	0.0628132i	$-0.0200072\pi$
$720$	9.18812e10	+	3.80622e10i	0.341898	+	0.141633i
$721$	2.90611e11			1.07540
$722$			3.73228e11i			1.37349i
$723$	−7.86002e10	−	1.17638e11i	−0.287654	−	0.430521i
$724$	−1.16983e11			−0.425764
$725$		−	1.56809e11i		−	0.567569i
$726$	2.50878e11	−	1.67625e11i	0.903058	−	0.603381i
$727$	2.53113e11			0.906102			0.453051	−	0.891485i	$-0.350336\pi$
$727$	2.53113e11			0.906102			0.453051	+	0.891485i	$0.350336\pi$
$728$			8.08692e9i			0.0287911i
$729$	2.60942e11	−	1.08053e11i	0.923920	−	0.382586i
$730$	1.39471e11			0.491125
$731$			2.64084e11i			0.924853i
$732$	−8.41020e9	−	1.25872e10i	−0.0292929	−	0.0438416i
$733$	2.07602e11			0.719144			0.359572	−	0.933117i	$-0.382923\pi$
$733$	2.07602e11			0.719144			0.359572	+	0.933117i	$0.382923\pi$
$734$		−	3.06137e11i		−	1.05471i
$735$	4.08588e10	−	2.72999e10i	0.140003	−	0.0935432i
$736$	−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	$0.255071\pi$
$740$		−	7.43367e10i		−	0.247900i
$741$	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
$745$	−1.83918e11			−0.597034
$746$			5.47918e11i			1.76913i
$747$	−2.81224e11	−	1.16498e11i	−0.903170	−	0.374143i
$748$	1.29262e11			0.412918
$749$		−	3.94695e10i		−	0.125411i
$750$	1.65757e11	+	2.48082e11i	0.523873	+	0.784062i
$751$	−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
$755$			9.51565e10i			0.292854i
$756$	−2.26216e11	+	4.49847e10i	−0.692526	+	0.137714i
$757$	−8.95066e10			−0.272566			−0.136283	−	0.990670i	$-0.543516\pi$
$757$	−8.95066e10			−0.272566			−0.136283	+	0.990670i	$0.543516\pi$
$758$			4.45390e11i			1.34916i
$759$	1.47337e11	+	2.20514e11i	0.443962	+	0.664462i
$760$	7.63580e8			0.00228876
$761$		−	5.71473e11i		−	1.70395i	−0.523581	−	0.851976i	$-0.675404\pi$
$761$		−	5.71473e11i		−	1.70395i	0.523581	−	0.851976i	$-0.324596\pi$
$762$	4.17303e11	−	2.78822e11i	1.23775	−	0.827004i
$763$	1.92456e11			0.567851
$764$		−	4.01231e10i		−	0.117766i
$765$	−4.22185e10	+	1.01914e11i	−0.123270	+	0.297570i
$766$	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	$0.380625\pi$
$770$			6.13826e10i			0.174615i
$771$	−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
$775$	−1.19582e11			−0.331480
$776$		−	2.64498e10i		−	0.0729417i
$777$	−1.05145e11	−	1.57366e11i	−0.288472	−	0.431745i
$778$	4.04080e11			1.10293
$779$		−	3.55176e10i		−	0.0964482i
$780$	9.64813e10	−	6.44643e10i	0.260654	−	0.174157i
$781$	−1.18464e11			−0.318408
$782$		−	7.91007e11i		−	2.11521i
$783$	4.77727e10	+	2.40236e11i	0.127096	+	0.639132i
$784$	1.82459e11			0.482950
$785$		−	1.70586e11i		−	0.449226i
$786$	−2.92081e11	−	4.37146e11i	−0.765266	−	1.14535i
$787$	−2.15788e11			−0.562508			−0.281254	−	0.959633i	$-0.590750\pi$
$787$	−2.15788e11			−0.562508			−0.281254	+	0.959633i	$0.590750\pi$
$788$		−	1.33367e11i		−	0.345894i
$789$	2.17240e10	−	1.45150e10i	0.0560572	−	0.0374548i
$790$	−1.15824e11			−0.297366
$791$			5.03559e11i			1.28631i
$792$	3.13855e9	−	7.57637e9i	0.00797679	−	0.0192558i
$793$	1.93902e10			0.0490331
$794$			5.29083e11i			1.33120i
$795$	−6.66942e10	−	9.98187e10i	−0.166963	−	0.249887i
$796$	−1.60601e11			−0.400034
$797$			6.69766e11i			1.65993i	0.557815	+	0.829966i	$0.311640\pi$
$797$			6.69766e11i			1.65993i	−0.557815	+	0.829966i	$0.688360\pi$
$798$	−5.01099e10	+	3.34811e10i	−0.123570	+	0.0825636i
$799$	3.05641e11			0.749938
$800$			5.00077e11i			1.22089i
$801$	4.40156e11	+	1.82337e11i	1.06924	+	0.442940i
$802$	−3.09118e11			−0.747183
$803$		−	1.92588e11i		−	0.463199i
$804$	−2.53208e10	−	3.78967e10i	−0.0605973	−	0.0906938i
$805$	1.84832e11			0.440143
$806$			2.03027e11i			0.481075i
$807$	2.33915e11	−	1.56291e11i	0.551524	−	0.368502i
$808$	1.85966e10			0.0436303
$809$		−	9.93417e10i		−	0.231920i	−0.993254	−	0.115960i	$-0.963006\pi$
$809$		−	9.93417e10i		−	0.231920i	0.993254	−	0.115960i	$-0.0369944\pi$
$810$	−1.53400e11	−	1.53422e11i	−0.356357	−	0.356407i
$811$	−2.71549e11			−0.627718			−0.313859	−	0.949470i	$-0.601622\pi$
$811$	−2.71549e11			−0.627718			−0.313859	+	0.949470i	$0.601622\pi$
$812$		−	2.00029e11i		−	0.460119i
$813$	−6.48974e10	−	9.71295e10i	−0.148547	−	0.222325i
$814$	−2.08607e11			−0.475150
$815$			1.50002e11i			0.339989i
$816$	−3.40573e11	+	2.27555e11i	−0.768156	+	0.513246i
$817$	−6.67782e10			−0.149881
$818$		−	8.04785e11i		−	1.79749i
$819$	1.13064e11	−	2.72934e11i	0.251298	−	0.606626i
$820$	−1.04418e11			−0.230952
$821$		−	5.63227e11i		−	1.23968i	−0.784727	−	0.619842i	$-0.787197\pi$
$821$		−	5.63227e11i		−	1.23968i	0.784727	−	0.619842i	$-0.212803\pi$
$822$	2.09689e11	+	3.13834e11i	0.459292	+	0.687406i
$823$	−4.42272e11			−0.964028			−0.482014	−	0.876164i	$-0.660095\pi$
$823$	−4.42272e11			−0.964028			−0.482014	+	0.876164i	$0.660095\pi$
$824$			2.98249e10i			0.0646950i
$825$	1.59470e11	−	1.06551e11i	0.344242	−	0.230006i
$826$	5.38823e11			1.15751
$827$		−	4.54543e11i		−	0.971745i	−0.874030	−	0.485873i	$-0.838502\pi$
$827$		−	4.54543e11i		−	0.971745i	0.874030	−	0.485873i	$-0.161498\pi$
$828$	7.07220e11	+	2.92969e11i	1.50464	+	0.623305i
$829$	−1.32535e11			−0.280615			−0.140308	−	0.990108i	$-0.544809\pi$
$829$	−1.32535e11			−0.280615			−0.140308	+	0.990108i	$0.544809\pi$
$830$			2.33832e11i			0.492710i
$831$	1.52121e11	+	2.27674e11i	0.318996	+	0.477429i
$832$	4.04290e11			0.843722
$833$			2.02383e11i			0.420334i
$834$	−2.15714e11	+	1.44130e11i	−0.445877	+	0.297914i
$835$	4.40705e10			0.0906572
$836$			3.26861e10i			0.0669172i
$837$	1.83203e11	−	3.64312e10i	0.373276	−	0.0742286i
$838$	−5.02871e11			−1.01972
$839$		−	4.87205e10i		−	0.0983250i	−0.998791	−	0.0491625i	$-0.984345\pi$
$839$		−	4.87205e10i		−	0.0983250i	0.998791	−	0.0491625i	$-0.0156552\pi$
$840$	−3.17520e9	−	4.75220e9i	−0.00637755	−	0.00954504i
$841$	2.87820e11			0.575357
$842$			3.35705e11i			0.667897i
$843$	2.70923e11	−	1.81018e11i	0.536457	−	0.358435i
$844$	−1.44114e10			−0.0284011
$845$		−	3.45051e10i		−	0.0676793i
$846$	−2.30056e11	+	5.55348e11i	−0.449109	+	1.08414i
$847$	−2.90368e11			−0.564176
$848$		−	4.45751e11i		−	0.862004i
$849$	−4.69138e11	−	7.02141e11i	−0.902962	−	1.35143i
$850$	−5.72035e11			−1.09584
$851$			6.28145e11i			1.19768i
$852$	−2.84314e11	+	1.89965e11i	−0.539561	+	0.360509i
$853$	−7.24501e11			−1.36849			−0.684247	−	0.729250i	$-0.739869\pi$
$853$	−7.24501e11			−1.36849			−0.684247	+	0.729250i	$0.739869\pi$
$854$			2.96071e10i			0.0556626i
$855$	−2.57708e10	−	1.06757e10i	−0.0482241	−	0.0199771i
$856$	4.05068e9			0.00754455
$857$			4.16662e11i			0.772433i	0.922408	+	0.386216i	$0.126218\pi$
$857$			4.16662e11i			0.772433i	−0.922408	+	0.386216i	$0.873782\pi$
$858$	−1.80902e11	−	2.70750e11i	−0.333807	−	0.499597i
$859$	7.54443e11			1.38565			0.692826	−	0.721105i	$-0.256366\pi$
$859$	7.54443e11			1.38565			0.692826	+	0.721105i	$0.256366\pi$
$860$			1.96321e11i			0.358900i
$861$	−2.21047e11	+	1.47693e11i	−0.402227	+	0.268750i
$862$	1.43778e12			2.60413
$863$			2.06295e10i			0.0371916i	0.999827	+	0.0185958i	$0.00591957\pi$
$863$			2.06295e10i			0.0371916i	−0.999827	+	0.0185958i	$0.994080\pi$
$864$	−1.52351e11	−	7.66133e11i	−0.273395	−	1.37483i
$865$	2.29706e11			0.410306
$866$			1.17403e11i			0.208741i
$867$	6.15057e10	+	9.20533e10i	0.108853	+	0.162916i
$868$	−1.52541e11			−0.268726
$869$			1.59936e11i			0.280457i
$870$	1.56448e11	−	1.04532e11i	0.273083	−	0.182461i
$871$	5.83785e10			0.101433
$872$			1.97515e10i			0.0341612i
$873$	−3.69798e11	+	8.92681e11i	−0.636659	+	1.53688i
$874$	2.00020e11			0.342789
$875$		−	2.87132e11i		−	0.489834i
$876$	−3.08828e11	−	4.62212e11i	−0.524446	−	0.784918i
$877$	5.98158e11			1.01115			0.505577	−	0.862782i	$-0.331280\pi$
$877$	5.98158e11			1.01115			0.505577	+	0.862782i	$0.331280\pi$
$878$		−	9.76126e11i		−	1.64259i
$879$	6.99945e11	−	4.67670e11i	1.17249	−	0.783401i
$880$	−1.05493e11			−0.175911
$881$		−	1.62306e11i		−	0.269420i	−0.990885	−	0.134710i	$-0.956990\pi$
$881$		−	1.62306e11i		−	0.269420i	0.990885	−	0.134710i	$-0.0430103\pi$
$882$	−3.67729e11	−	1.52334e11i	−0.607650	−	0.251722i
$883$	−6.06459e11			−0.997605			−0.498803	−	0.866716i	$-0.666227\pi$
$883$	−6.06459e11			−0.997605			−0.498803	+	0.866716i	$0.666227\pi$
$884$			4.77895e11i			0.782571i
$885$	1.38554e11	+	2.07369e11i	0.225864	+	0.338042i
$886$	8.50262e11			1.37981
$887$		−	4.65904e11i		−	0.752666i	−0.926484	−	0.376333i	$-0.877185\pi$
$887$		−	4.65904e11i		−	0.752666i	0.926484	−	0.376333i	$-0.122815\pi$
$888$	1.61502e10	−	1.07908e10i	0.0259733	−	0.0173541i
$889$	−4.82989e11			−0.773269
$890$		−	3.65981e11i		−	0.583308i
$891$	−2.11852e11	+	2.11822e11i	−0.336141	+	0.336094i
$892$	−1.09170e12			−1.72442
$893$			7.72867e10i			0.121534i
$894$	8.27631e11	+	1.23868e12i	1.29565	+	1.93915i
$895$	−2.89368e11			−0.450981
$896$		−	4.11757e10i		−	0.0638865i
$897$	−8.15267e11	+	5.44723e11i	−1.25930	+	0.841407i
$898$	−6.63408e11			−1.02018
$899$			1.61995e11i			0.248007i
$900$	2.11868e11	−	5.11443e11i	0.322920	−	0.779519i
$901$	4.94426e11			0.750243
$902$			2.93023e11i			0.442666i
$903$	2.77684e11	+	4.15600e11i	0.417638	+	0.625064i
$904$	−5.16794e10			−0.0773826
$905$			1.05898e11i			0.157868i
$906$	6.40877e11	−	4.28204e11i	0.951178	−	0.635533i
$907$	7.47111e11			1.10397			0.551983	−	0.833855i	$-0.313871\pi$
$907$	7.47111e11			1.10397			0.551983	+	0.833855i	$0.313871\pi$
$908$			8.76909e11i			1.29006i
$909$	−6.27635e11	−	2.60001e11i	−0.919288	−	0.380820i
$910$	−2.26939e11			−0.330935
$911$		−	9.01051e11i		−	1.30821i	−0.756406	−	0.654103i	$-0.773046\pi$
$911$		−	9.01051e11i		−	1.30821i	0.756406	−	0.654103i	$-0.226954\pi$
$912$	−5.75412e10	−	8.61198e10i	−0.0831763	−	0.124487i
$913$	3.22887e11			0.464694
$914$			4.53896e11i			0.650387i
$915$	−1.13945e10	+	7.61325e9i	−0.0162558	+	0.0108614i
$916$	4.62692e11			0.657219
$917$			5.05956e11i			0.715543i
$918$	8.76375e11	−	1.74274e11i	1.23401	−	0.245392i
$919$	−1.14699e12			−1.60804			−0.804021	−	0.594601i	$-0.797310\pi$
$919$	−1.14699e12			−1.60804			−0.804021	+	0.594601i	$0.797310\pi$
$920$			1.89690e10i			0.0264785i
$921$	−1.34689e11	−	2.01584e11i	−0.187195	−	0.280168i
$922$	−1.57560e12			−2.18032
$923$		−	4.37976e11i		−	0.603453i
$924$	2.03424e11	−	1.35919e11i	0.279071	−	0.186462i
$925$	4.54258e11			0.620492
$926$		−	9.33937e10i		−	0.127020i
$927$	4.16985e11	−	1.00659e12i	0.564679	−	1.36312i
$928$	6.77447e11			0.913447
$929$			4.36054e11i			0.585433i	0.956199	+	0.292716i	$0.0945592\pi$
$929$			4.36054e11i			0.585433i	−0.956199	+	0.292716i	$0.905441\pi$
$930$	−7.97152e10	−	1.19307e11i	−0.106564	−	0.159490i
$931$	−5.11762e10			−0.0681191
$932$		−	6.74887e11i		−	0.894474i
$933$	4.34293e11	−	2.90174e11i	0.573135	−	0.382942i
$934$	−6.46869e11			−0.850019
$935$		−	1.17013e11i		−	0.153104i
$936$	2.80107e10	+	1.16036e10i	0.0364939	+	0.0151178i
$937$	1.98881e11			0.258009			0.129004	−	0.991644i	$-0.458822\pi$
$937$	1.98881e11			0.258009			0.129004	+	0.991644i	$0.458822\pi$
$938$			8.91388e10i			0.115148i
$939$	1.47482e9	+	2.20731e9i	0.00189704	+	0.00283923i
$940$	2.27215e11			0.291022
$941$		−	1.28069e12i		−	1.63338i	−0.577079	−	0.816689i	$-0.695807\pi$
$941$		−	1.28069e12i		−	1.63338i	0.577079	−	0.816689i	$-0.304193\pi$
$942$	−1.14889e12	+	7.67637e11i	−1.45907	+	0.974883i
$943$	8.82335e11			1.11580
$944$			9.26030e11i			1.16610i
$945$	4.07219e10	+	2.04780e11i	0.0510624	+	0.256779i
$946$	5.50926e11			0.687905
$947$			1.35658e12i			1.68673i	0.537337	+	0.843367i	$0.319430\pi$
$947$			1.35658e12i			1.68673i	−0.537337	+	0.843367i	$0.680570\pi$
$948$	2.56468e11	+	3.83846e11i	0.317541	+	0.475251i
$949$	7.12020e11			0.877865
$950$		−	1.44649e11i		−	0.177591i
$951$	−7.93358e11	+	5.30084e11i	−0.969945	+	0.648072i
$952$	2.35388e10			0.0286574
$953$			5.01575e11i			0.608085i	0.952658	+	0.304042i	$0.0983365\pi$
$953$			5.01575e11i			0.608085i	−0.952658	+	0.304042i	$0.901664\pi$
$954$	−3.72153e11	+	8.98368e11i	−0.449292	+	1.08458i
$955$	−3.63211e10			−0.0436662
$956$		−	5.64103e11i		−	0.675347i
$957$	−1.44342e11	−	2.16032e11i	−0.172086	−	0.257555i
$958$	−1.00385e12			−1.19180
$959$		−	3.63234e11i		−	0.429450i
$960$	−2.37577e11	+	1.58738e11i	−0.279717	+	0.186894i
$961$	−7.29354e11			−0.855155
$962$		−	7.71244e11i		−	0.900516i
$963$	−1.36711e11	−	5.66330e10i	−0.158963	−	0.0658514i
$964$	4.33175e11			0.501597
$965$		−	3.56594e11i		−	0.411212i
$966$	−8.31744e11	−	1.24484e12i	−0.955171	−	1.42957i
$967$	1.10988e11			0.126932			0.0634661	−	0.997984i	$-0.479785\pi$
$967$	1.10988e11			0.126932			0.0634661	+	0.997984i	$0.479785\pi$
$968$		−	2.98000e10i		−	0.0339402i
$969$	9.55239e10	−	6.38246e10i	0.108347	−	0.0723924i
$970$	7.42246e11			0.838419
$971$			2.95380e11i			0.332280i	0.986102	+	0.166140i	$0.0531304\pi$
$971$			2.95380e11i			0.332280i	−0.986102	+	0.166140i	$0.946870\pi$
$972$	−1.68774e11	+	8.48092e11i	−0.189078	+	0.950119i
$973$	2.49669e11			0.278557
$974$		−	1.28601e12i		−	1.42892i
$975$	3.93930e11	+	5.89580e11i	0.435913	+	0.652415i
$976$	−5.08832e10			−0.0560758
$977$			6.09091e11i			0.668503i	0.942484	+	0.334252i	$0.108484\pi$
$977$			6.09091e11i			0.668503i	−0.942484	+	0.334252i	$0.891516\pi$
$978$	1.01026e12	−	6.75007e11i	1.10427	−	0.737824i
$979$	−5.05365e11			−0.550141
$980$			1.50453e11i			0.163116i
$981$	2.76147e11	−	6.66612e11i	0.298171	−	0.719776i
$982$	1.62821e12			1.75091
$983$			1.84012e12i			1.97076i	0.170384	+	0.985378i	$0.445499\pi$
$983$			1.84012e12i			1.97076i	−0.170384	+	0.985378i	$0.554501\pi$
$984$	−1.51575e10	−	2.26857e10i	−0.0161677	−	0.0241975i
$985$	−1.20729e11			−0.128253
$986$			7.74927e11i			0.819885i
$987$	4.81000e11	−	3.21382e11i	0.506847	−	0.338651i
$988$	−1.20844e11			−0.126823
$989$		−	1.65892e12i		−	1.73396i
$990$	2.12611e11	+	8.80753e10i	0.221333	+	0.0916882i
$991$	−5.72336e11			−0.593412			−0.296706	−	0.954969i	$-0.595888\pi$
$991$	−5.72336e11			−0.593412			−0.296706	+	0.954969i	$0.595888\pi$
$992$		−	5.16617e11i		−	0.533485i
$993$	−5.40449e11	−	8.08870e11i	−0.555850	−	0.831920i
$994$	6.68750e11			0.685044
$995$			1.45383e11i			0.148327i
$996$	7.74928e11	−	5.17770e11i	0.787451	−	0.526138i
$997$	−1.44614e12			−1.46363			−0.731813	−	0.681505i	$-0.761326\pi$
$997$	−1.44614e12			−1.46363			−0.731813	+	0.681505i	$0.761326\pi$
$998$			5.93504e11i			0.598276i
$999$	−6.95937e11	+	1.38392e11i	−0.698728	+	0.138947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.9.b.a.2.1	✓	2
3.2	odd	2	inner	3.9.b.a.2.2	yes	2
4.3	odd	2		48.9.e.b.17.1		2
5.2	odd	4		75.9.d.b.74.3		4
5.3	odd	4		75.9.d.b.74.2		4
5.4	even	2		75.9.c.c.26.2		2
8.3	odd	2		192.9.e.f.65.2		2
8.5	even	2		192.9.e.e.65.1		2
9.2	odd	6		81.9.d.d.53.2		4
9.4	even	3		81.9.d.d.26.2		4
9.5	odd	6		81.9.d.d.26.1		4
9.7	even	3		81.9.d.d.53.1		4
12.11	even	2		48.9.e.b.17.2		2
15.2	even	4		75.9.d.b.74.1		4
15.8	even	4		75.9.d.b.74.4		4
15.14	odd	2		75.9.c.c.26.1		2
24.5	odd	2		192.9.e.e.65.2		2
24.11	even	2		192.9.e.f.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.9.b.a.2.1	✓	2	1.1	even	1	trivial
3.9.b.a.2.2	yes	2	3.2	odd	2	inner
48.9.e.b.17.1		2	4.3	odd	2
48.9.e.b.17.2		2	12.11	even	2
75.9.c.c.26.1		2	15.14	odd	2
75.9.c.c.26.2		2	5.4	even	2
75.9.d.b.74.1		4	15.2	even	4
75.9.d.b.74.2		4	5.3	odd	4
75.9.d.b.74.3		4	5.2	odd	4
75.9.d.b.74.4		4	15.8	even	4
81.9.d.d.26.1		4	9.5	odd	6
81.9.d.d.26.2		4	9.4	even	3
81.9.d.d.53.1		4	9.7	even	3
81.9.d.d.53.2		4	9.2	odd	6
192.9.e.e.65.1		2	8.5	even	2
192.9.e.e.65.2		2	24.5	odd	2
192.9.e.f.65.1		2	24.11	even	2
192.9.e.f.65.2		2	8.3	odd	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-22.4499i q^{2} +(45.0000 + 67.3498i) q^{3} -248.000 q^{4} +224.499i q^{5} +(1512.00 - 1010.25i) q^{6} -1750.00 q^{7} -179.600i q^{8} +(-2511.00 + 6061.48i) q^{9} +O(q^{10})\)	\(q-22.4499i q^{2} +(45.0000 + 67.3498i) q^{3} -248.000 q^{4} +224.499i q^{5} +(1512.00 - 1010.25i) q^{6} -1750.00 q^{7} -179.600i q^{8} +(-2511.00 + 6061.48i) q^{9} +5040.00 q^{10} -6959.48i q^{11} +(-11160.0 - 16702.8i) q^{12} +25730.0 q^{13} +39287.4i q^{14} +(-15120.0 + 10102.5i) q^{15} -67520.0 q^{16} -74893.0i q^{17} +(136080. + 56371.8i) q^{18} +18938.0 q^{19} -55675.9i q^{20} +(-78750.0 - 117862. i) q^{21} -156240. q^{22} +470461. i q^{23} +(12096.0 - 8081.98i) q^{24} +340225. q^{25} -577637. i q^{26} +(-521235. + 103651. i) q^{27} +434000. q^{28} -460897. i q^{29} +(226800. + 339443. i) q^{30} -351478. q^{31} +1.46984e6i q^{32} +(468720. - 313177. i) q^{33} -1.68134e6 q^{34} -392874. i q^{35} +(622728. - 1.50325e6i) q^{36} +1.33517e6 q^{37} -425157. i q^{38} +(1.15785e6 + 1.73291e6i) q^{39} +40320.0 q^{40} -1.87547e6i q^{41} +(-2.64600e6 + 1.76793e6i) q^{42} -3.52615e6 q^{43} +1.72595e6i q^{44} +(-1.36080e6 - 563718. i) q^{45} +1.05618e7 q^{46} +4.08104e6i q^{47} +(-3.03840e6 - 4.54746e6i) q^{48} -2.70230e6 q^{49} -7.63803e6i q^{50} +(5.04403e6 - 3.37019e6i) q^{51} -6.38104e6 q^{52} +6.60177e6i q^{53} +(2.32697e6 + 1.17017e7i) q^{54} +1.56240e6 q^{55} +314299. i q^{56} +(852210. + 1.27547e6i) q^{57} -1.03471e7 q^{58} -1.37149e7i q^{59} +(3.74976e6 - 2.50541e6i) q^{60} +753602. q^{61} +7.89066e6i q^{62} +(4.39425e6 - 1.06076e7i) q^{63} +1.57128e7 q^{64} +5.77637e6i q^{65} +(-7.03080e6 - 1.05227e7i) q^{66} +2.26889e6 q^{67} +1.85735e7i q^{68} +(-3.16855e7 + 2.11707e7i) q^{69} -8.82000e6 q^{70} -1.70220e7i q^{71} +(1.08864e6 + 450974. i) q^{72} +2.76728e7 q^{73} -2.99745e7i q^{74} +(1.53101e7 + 2.29141e7i) q^{75} -4.69662e6 q^{76} +1.21791e7i q^{77} +(3.89038e7 - 2.59937e7i) q^{78} -2.29810e7 q^{79} -1.51582e7i q^{80} +(-3.04365e7 - 3.04408e7i) q^{81} -4.21042e7 q^{82} +4.63952e7i q^{83} +(1.95300e7 + 2.92298e7i) q^{84} +1.68134e7 q^{85} +7.91619e7i q^{86} +(3.10414e7 - 2.07404e7i) q^{87} -1.24992e6 q^{88} -7.26152e7i q^{89} +(-1.26554e7 + 3.05499e7i) q^{90} -4.50275e7 q^{91} -1.16674e8i q^{92} +(-1.58165e7 - 2.36720e7i) q^{93} +9.16191e7 q^{94} +4.25157e6i q^{95} +(-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	\( 2 q + 90 q^{3} - 496 q^{4} + 3024 q^{6} - 3500 q^{7} - 5022 q^{9} + 10080 q^{10} - 22320 q^{12} + 51460 q^{13} - 30240 q^{15} - 135040 q^{16} + 272160 q^{18} + 37876 q^{19} - 157500 q^{21} - 312480 q^{22} + 24192 q^{24} + 680450 q^{25} - 1042470 q^{27} + 868000 q^{28} + 453600 q^{30} - 702956 q^{31} + 937440 q^{33} - 3362688 q^{34} + 1245456 q^{36} + 2670340 q^{37} + 2315700 q^{39} + 80640 q^{40} - 5292000 q^{42} - 7052300 q^{43} - 2721600 q^{45} + 21123648 q^{46} - 6076800 q^{48} - 5404602 q^{49} + 10088064 q^{51} - 12762080 q^{52} + 4653936 q^{54} + 3124800 q^{55} + 1704420 q^{57} - 20694240 q^{58} + 7499520 q^{60} + 1507204 q^{61} + 8788500 q^{63} + 31425536 q^{64} - 14061600 q^{66} + 4537780 q^{67} - 63370944 q^{69} - 17640000 q^{70} + 2177280 q^{72} + 55345540 q^{73} + 30620250 q^{75} - 9393248 q^{76} + 77807520 q^{78} - 45961964 q^{79} - 60872958 q^{81} - 84208320 q^{82} + 39060000 q^{84} + 33626880 q^{85} + 62082720 q^{87} - 2499840 q^{88} - 25310880 q^{90} - 90055000 q^{91} - 31633020 q^{93} + 183238272 q^{94} - 197987328 q^{96} + 294542020 q^{97} + 84369600 q^{99}+O(q^{100}) \) 2 * q + 90 * q^3 - 496 * q^4 + 3024 * q^6 - 3500 * q^7 - 5022 * q^9 + 10080 * q^10 - 22320 * q^12 + 51460 * q^13 - 30240 * q^15 - 135040 * q^16 + 272160 * q^18 + 37876 * q^19 - 157500 * q^21 - 312480 * q^22 + 24192 * q^24 + 680450 * q^25 - 1042470 * q^27 + 868000 * q^28 + 453600 * q^30 - 702956 * q^31 + 937440 * q^33 - 3362688 * q^34 + 1245456 * q^36 + 2670340 * q^37 + 2315700 * q^39 + 80640 * q^40 - 5292000 * q^42 - 7052300 * q^43 - 2721600 * q^45 + 21123648 * q^46 - 6076800 * q^48 - 5404602 * q^49 + 10088064 * q^51 - 12762080 * q^52 + 4653936 * q^54 + 3124800 * q^55 + 1704420 * q^57 - 20694240 * q^58 + 7499520 * q^60 + 1507204 * q^61 + 8788500 * q^63 + 31425536 * q^64 - 14061600 * q^66 + 4537780 * q^67 - 63370944 * q^69 - 17640000 * q^70 + 2177280 * q^72 + 55345540 * q^73 + 30620250 * q^75 - 9393248 * q^76 + 77807520 * q^78 - 45961964 * q^79 - 60872958 * q^81 - 84208320 * q^82 + 39060000 * q^84 + 33626880 * q^85 + 62082720 * q^87 - 2499840 * q^88 - 25310880 * q^90 - 90055000 * q^91 - 31633020 * q^93 + 183238272 * q^94 - 197987328 * q^96 + 294542020 * q^97 + 84369600 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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