LMFDB - Embedded newform 48.9.l.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,9,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.5541732829$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	48.19
Dual form			48.9.l.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.9603 - 1.12703i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(253.460 + 35.9753i) q^{4} +(156.665 - 156.665i) q^{5} +(565.044 - 490.507i) q^{6} -2214.37 q^{7} +(-4004.74 - 859.832i) q^{8} -2187.00i q^{9} +O(q^{10})$	\(q+(-15.9603 - 1.12703i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(253.460 + 35.9753i) q^{4} +(156.665 - 156.665i) q^{5} +(565.044 - 490.507i) q^{6} -2214.37 q^{7} +(-4004.74 - 859.832i) q^{8} -2187.00i q^{9} +(-2676.98 + 2323.85i) q^{10} +(17633.0 + 17633.0i) q^{11} +(-9571.07 + 7191.79i) q^{12} +(15142.0 + 15142.0i) q^{13} +(35341.9 + 2495.66i) q^{14} +10361.2i q^{15} +(62947.6 + 18236.6i) q^{16} -148379. q^{17} +(-2464.81 + 34905.1i) q^{18} +(103863. - 103863. i) q^{19} +(45344.4 - 34072.2i) q^{20} +(73225.1 - 73225.1i) q^{21} +(-261554. - 301300. i) q^{22} -198550. q^{23} +(160862. - 103996. i) q^{24} +341537. i q^{25} +(-224605. - 258736. i) q^{26} +(72320.0 + 72320.0i) q^{27} +(-561254. - 79662.7i) q^{28} +(-831508. - 831508. i) q^{29} +(11677.4 - 165368. i) q^{30} -1.08184e6i q^{31} +(-984106. - 362004. i) q^{32} -1.16618e6 q^{33} +(2.36816e6 + 167227. i) q^{34} +(-346915. + 346915. i) q^{35} +(78678.0 - 554316. i) q^{36} +(756487. - 756487. i) q^{37} +(-1.77473e6 + 1.54062e6i) q^{38} -1.00144e6 q^{39} +(-762108. + 492697. i) q^{40} -5.35660e6i q^{41} +(-1.25122e6 + 1.08616e6i) q^{42} +(-752131. - 752131. i) q^{43} +(3.83490e6 + 5.10361e6i) q^{44} +(-342627. - 342627. i) q^{45} +(3.16892e6 + 223772. i) q^{46} -2.04481e6i q^{47} +(-2.68461e6 + 1.47851e6i) q^{48} -861361. q^{49} +(384922. - 5.45102e6i) q^{50} +(4.90660e6 - 4.90660e6i) q^{51} +(3.29315e6 + 4.38263e6i) q^{52} +(-8.95789e6 + 8.95789e6i) q^{53} +(-1.07274e6 - 1.23575e6i) q^{54} +5.52495e6 q^{55} +(8.86797e6 + 1.90399e6i) q^{56} +6.86908e6i q^{57} +(1.23340e7 + 1.42082e7i) q^{58} +(-1.61116e6 - 1.61116e6i) q^{59} +(-372749. + 2.62616e6i) q^{60} +(-5.64933e6 - 5.64933e6i) q^{61} +(-1.21927e6 + 1.72665e7i) q^{62} +4.84283e6i q^{63} +(1.52986e7 + 6.88680e6i) q^{64} +4.74445e6 q^{65} +(1.86125e7 + 1.31432e6i) q^{66} +(5.04547e6 - 5.04547e6i) q^{67} +(-3.76080e7 - 5.33797e6i) q^{68} +(6.56569e6 - 6.56569e6i) q^{69} +(5.92783e6 - 5.14586e6i) q^{70} -2.68493e7 q^{71} +(-1.88045e6 + 8.75836e6i) q^{72} -5.97707e6i q^{73} +(-1.29263e7 + 1.12212e7i) q^{74} +(-1.12940e7 - 1.12940e7i) q^{75} +(3.00615e7 - 2.25885e7i) q^{76} +(-3.90460e7 - 3.90460e7i) q^{77} +(1.59832e7 + 1.12865e6i) q^{78} -5.23833e6i q^{79} +(1.27187e7 - 7.00465e6i) q^{80} -4.78297e6 q^{81} +(-6.03704e6 + 8.54927e7i) q^{82} +(2.72340e7 - 2.72340e7i) q^{83} +(2.11939e7 - 1.59253e7i) q^{84} +(-2.32457e7 + 2.32457e7i) q^{85} +(1.11565e7 + 1.28519e7i) q^{86} +5.49928e7 q^{87} +(-5.54541e7 - 8.57769e7i) q^{88} +4.38209e7i q^{89} +(5.08226e6 + 5.85456e6i) q^{90} +(-3.35301e7 - 3.35301e7i) q^{91} +(-5.03245e7 - 7.14292e6i) q^{92} +(3.57745e7 + 3.57745e7i) q^{93} +(-2.30456e6 + 3.26357e7i) q^{94} -3.25433e7i q^{95} +(4.45133e7 - 2.05717e7i) q^{96} +1.81696e7 q^{97} +(1.37475e7 + 970778. i) q^{98} +(3.85634e7 - 3.85634e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) $ 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−15.9603	−	1.12703i	−0.997516	−	0.0704393i
$2$	−15.9603	−	1.12703i	−0.997516	−	0.0704393i
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$4$	253.460	+	35.9753i	0.990077	+	0.140529i
$5$	156.665	−	156.665i	0.250664	−	0.250664i	−0.570579	−	0.821243i	$-0.693281\pi$
$5$	156.665	−	156.665i	0.250664	−	0.250664i	0.821243	+	0.570579i	$0.193281\pi$
$6$	565.044	−	490.507i	0.435991	−	0.378478i
$7$	−2214.37			−0.922270			−0.461135	−	0.887330i	$-0.652558\pi$
$7$	−2214.37			−0.922270			−0.461135	+	0.887330i	$0.652558\pi$
$8$	−4004.74	−	859.832i	−0.977719	−	0.209920i
$9$		−	2187.00i		−	0.333333i
$10$	−2676.98	+	2323.85i	−0.267698	+	0.232385i
$11$	17633.0	+	17633.0i	1.20436	+	1.20436i	0.972828	+	0.231530i	$0.0743730\pi$
$11$	17633.0	+	17633.0i	1.20436	+	1.20436i	0.231530	+	0.972828i	$0.425627\pi$
$12$	−9571.07	+	7191.79i	−0.461568	+	0.346827i
$13$	15142.0	+	15142.0i	0.530164	+	0.530164i	0.920621	−	0.390457i	$-0.127683\pi$
$13$	15142.0	+	15142.0i	0.530164	+	0.530164i	−0.390457	+	0.920621i	$0.627683\pi$
$14$	35341.9	+	2495.66i	0.919980	+	0.0649641i
$15$			10361.2i			0.204666i
$16$	62947.6	+	18236.6i	0.960503	+	0.278268i
$17$	−148379.			−1.77654			−0.888271	−	0.459320i	$-0.848093\pi$
$17$	−148379.			−1.77654			−0.888271	+	0.459320i	$0.848093\pi$
$18$	−2464.81	+	34905.1i	−0.0234798	+	0.332505i
$19$	103863.	−	103863.i	0.796975	−	0.796975i	−0.185642	−	0.982617i	$-0.559437\pi$
$19$	103863.	−	103863.i	0.796975	−	0.796975i	0.982617	+	0.185642i	$0.0594366\pi$
$20$	45344.4	−	34072.2i	0.283402	−	0.212951i
$21$	73225.1	−	73225.1i	0.376515	−	0.376515i
$22$	−261554.	−	301300.i	−1.11653	−	1.28620i
$23$	−198550.			−0.709512			−0.354756	−	0.934959i	$-0.615436\pi$
$23$	−198550.			−0.709512			−0.354756	+	0.934959i	$0.615436\pi$
$24$	160862.	−	103996.i	0.484851	−	0.313453i
$25$			341537.i			0.874335i
$26$	−224605.	−	258736.i	−0.491503	−	0.566192i
$27$	72320.0	+	72320.0i	0.136083	+	0.136083i
$28$	−561254.	−	79662.7i	−0.913118	−	0.129605i
$29$	−831508.	−	831508.i	−1.17564	−	1.17564i	−0.980844	−	0.194797i	$-0.937595\pi$
$29$	−831508.	−	831508.i	−1.17564	−	1.17564i	−0.194797	−	0.980844i	$-0.562405\pi$
$30$	11677.4	−	165368.i	0.0144166	−	0.204158i
$31$		−	1.08184e6i		−	1.17143i	−0.810516	−	0.585716i	$-0.800813\pi$
$31$		−	1.08184e6i		−	1.17143i	0.810516	−	0.585716i	$-0.199187\pi$
$32$	−984106.	−	362004.i	−0.938517	−	0.345234i
$33$	−1.16618e6			−0.983354
$34$	2.36816e6	+	167227.i	1.77213	+	0.125138i
$35$	−346915.	+	346915.i	−0.231180	+	0.231180i
$36$	78678.0	−	554316.i	0.0468429	−	0.330026i
$37$	756487.	−	756487.i	0.403641	−	0.403641i	−0.475873	−	0.879514i	$-0.657868\pi$
$37$	756487.	−	756487.i	0.403641	−	0.403641i	0.879514	+	0.475873i	$0.157868\pi$
$38$	−1.77473e6	+	1.54062e6i	−0.851134	+	0.738857i
$39$	−1.00144e6			−0.432877
$40$	−762108.	+	492697.i	−0.297698	+	0.192460i
$41$		−	5.35660e6i		−	1.89563i	−0.318819	−	0.947815i	$-0.603286\pi$
$41$		−	5.35660e6i		−	1.89563i	0.318819	−	0.947815i	$-0.396714\pi$
$42$	−1.25122e6	+	1.08616e6i	−0.402102	+	0.349059i
$43$	−752131.	−	752131.i	−0.219999	−	0.219999i	0.588499	−	0.808498i	$-0.299719\pi$
$43$	−752131.	−	752131.i	−0.219999	−	0.219999i	−0.808498	+	0.588499i	$0.799719\pi$
$44$	3.83490e6	+	5.10361e6i	1.02316	+	1.36165i
$45$	−342627.	−	342627.i	−0.0835547	−	0.0835547i
$46$	3.16892e6	+	223772.i	0.707749	+	0.0499775i
$47$		−	2.04481e6i		−	0.419047i	−0.977804	−	0.209523i	$-0.932809\pi$
$47$		−	2.04481e6i		−	0.419047i	0.977804	−	0.209523i	$-0.0671912\pi$
$48$	−2.68461e6	+	1.47851e6i	−0.505726	+	0.278521i
$49$	−861361.			−0.149417
$50$	384922.	−	5.45102e6i	0.0615875	−	0.872163i
$51$	4.90660e6	−	4.90660e6i	0.725270	−	0.725270i
$52$	3.29315e6	+	4.38263e6i	0.450400	+	0.599407i
$53$	−8.95789e6	+	8.95789e6i	−1.13528	+	1.13528i	−0.145992	+	0.989286i	$0.546637\pi$
$53$	−8.95789e6	+	8.95789e6i	−1.13528	+	1.13528i	−0.989286	+	0.145992i	$0.953363\pi$
$54$	−1.07274e6	−	1.23575e6i	−0.126159	−	0.145330i
$55$	5.52495e6			0.603778
$56$	8.86797e6	+	1.90399e6i	0.901721	+	0.193603i
$57$			6.86908e6i			0.650727i
$58$	1.23340e7	+	1.42082e7i	1.08991	+	1.25553i
$59$	−1.61116e6	−	1.61116e6i	−0.132963	−	0.132963i	0.637493	−	0.770456i	$-0.279971\pi$
$59$	−1.61116e6	−	1.61116e6i	−0.132963	−	0.132963i	−0.770456	+	0.637493i	$0.779971\pi$
$60$	−372749.	+	2.62616e6i	−0.0287615	+	0.202635i
$61$	−5.64933e6	−	5.64933e6i	−0.408017	−	0.408017i	0.473030	−	0.881046i	$-0.343160\pi$
$61$	−5.64933e6	−	5.64933e6i	−0.408017	−	0.408017i	−0.881046	+	0.473030i	$0.843160\pi$
$62$	−1.21927e6	+	1.72665e7i	−0.0825148	+	1.16852i
$63$			4.84283e6i			0.307423i
$64$	1.52986e7	+	6.88680e6i	0.911867	+	0.410485i
$65$	4.74445e6			0.265786
$66$	1.86125e7	+	1.31432e6i	0.980911	+	0.0692667i
$67$	5.04547e6	−	5.04547e6i	0.250382	−	0.250382i	−0.570745	−	0.821127i	$-0.693346\pi$
$67$	5.04547e6	−	5.04547e6i	0.250382	−	0.250382i	0.821127	+	0.570745i	$0.193346\pi$
$68$	−3.76080e7	−	5.33797e6i	−1.75891	−	0.249655i
$69$	6.56569e6	−	6.56569e6i	0.289657	−	0.289657i
$70$	5.92783e6	−	5.14586e6i	0.246890	−	0.214322i
$71$	−2.68493e7			−1.05657			−0.528286	−	0.849066i	$-0.677165\pi$
$71$	−2.68493e7			−1.05657			−0.528286	+	0.849066i	$0.677165\pi$
$72$	−1.88045e6	+	8.75836e6i	−0.0699733	+	0.325906i
$73$		−	5.97707e6i		−	0.210473i	−0.994447	−	0.105237i	$-0.966440\pi$
$73$		−	5.97707e6i		−	0.210473i	0.994447	−	0.105237i	$-0.0335600\pi$
$74$	−1.29263e7	+	1.12212e7i	−0.431070	+	0.374206i
$75$	−1.12940e7	−	1.12940e7i	−0.356946	−	0.356946i
$76$	3.00615e7	−	2.25885e7i	0.901064	−	0.677068i
$77$	−3.90460e7	−	3.90460e7i	−1.11074	−	1.11074i
$78$	1.59832e7	+	1.12865e6i	0.431802	+	0.0304916i
$79$		−	5.23833e6i		−	0.134488i	−0.997737	−	0.0672442i	$-0.978579\pi$
$79$		−	5.23833e6i		−	0.134488i	0.997737	−	0.0672442i	$-0.0214206\pi$
$80$	1.27187e7	−	7.00465e6i	0.310516	−	0.171012i
$81$	−4.78297e6			−0.111111
$82$	−6.03704e6	+	8.54927e7i	−0.133527	+	1.89092i
$83$	2.72340e7	−	2.72340e7i	0.573851	−	0.573851i	−0.359351	−	0.933202i	$-0.617002\pi$
$83$	2.72340e7	−	2.72340e7i	0.573851	−	0.573851i	0.933202	+	0.359351i	$0.117002\pi$
$84$	2.11939e7	−	1.59253e7i	0.425690	−	0.319868i
$85$	−2.32457e7	+	2.32457e7i	−0.445315	+	0.445315i
$86$	1.11565e7	+	1.28519e7i	0.203956	+	0.234949i
$87$	5.49928e7			0.959907
$88$	−5.54541e7	−	8.57769e7i	−0.924704	−	1.43034i
$89$			4.38209e7i			0.698428i	0.937043	+	0.349214i	$0.113551\pi$
$89$			4.38209e7i			0.698428i	−0.937043	+	0.349214i	$0.886449\pi$
$90$	5.08226e6	+	5.85456e6i	0.0774616	+	0.0892327i
$91$	−3.35301e7	−	3.35301e7i	−0.488955	−	0.488955i
$92$	−5.03245e7	−	7.14292e6i	−0.702471	−	0.0997067i
$93$	3.57745e7	+	3.57745e7i	0.478235	+	0.478235i
$94$	−2.30456e6	+	3.26357e7i	−0.0295173	+	0.418006i
$95$		−	3.25433e7i		−	0.399546i
$96$	4.45133e7	−	2.05717e7i	0.524089	−	0.242207i
$97$	1.81696e7			0.205238			0.102619	−	0.994721i	$-0.467278\pi$
$97$	1.81696e7			0.205238			0.102619	+	0.994721i	$0.467278\pi$
$98$	1.37475e7	+	970778.i	0.149046	+	0.0105248i
$99$	3.85634e7	−	3.85634e7i	0.401452	−	0.401452i
$100$	−1.22869e7	+	8.65659e7i	−0.122869	+	0.865659i
$101$	−6.02910e7	+	6.02910e7i	−0.579385	+	0.579385i	−0.934734	−	0.355349i	$-0.884362\pi$
$101$	−6.02910e7	+	6.02910e7i	−0.579385	+	0.579385i	0.355349	+	0.934734i	$0.384362\pi$
$102$	−8.38405e7	+	7.27807e7i	−0.774556	+	0.672381i
$103$	4.24328e7			0.377010			0.188505	−	0.982072i	$-0.439636\pi$
$103$	4.24328e7			0.377010			0.188505	+	0.982072i	$0.439636\pi$
$104$	−4.76202e7	−	7.36594e7i	−0.407059	−	0.629644i
$105$		−	2.29436e7i		−	0.188758i
$106$	1.53066e8	−	1.32874e8i	1.21243	−	1.05249i
$107$	−2.58816e7	−	2.58816e7i	−0.197449	−	0.197449i	0.601456	−	0.798906i	$-0.294587\pi$
$107$	−2.58816e7	−	2.58816e7i	−0.197449	−	0.197449i	−0.798906	+	0.601456i	$0.794587\pi$
$108$	1.57285e7	+	2.09319e7i	0.115609	+	0.153856i
$109$	−1.35469e8	−	1.35469e8i	−0.959697	−	0.959697i	0.0395215	−	0.999219i	$-0.487417\pi$
$109$	−1.35469e8	−	1.35469e8i	−0.959697	−	0.959697i	−0.999219	+	0.0395215i	$0.987417\pi$
$110$	−8.81796e7	−	6.22678e6i	−0.602279	−	0.0425297i
$111$			5.00312e7i			0.329571i
$112$	−1.39389e8	−	4.03826e7i	−0.885844	−	0.256639i
$113$	−1.90770e8			−1.17003			−0.585014	−	0.811023i	$-0.698911\pi$
$113$	−1.90770e8			−1.17003			−0.585014	+	0.811023i	$0.698911\pi$
$114$	7.74165e6	−	1.09632e8i	0.0458368	−	0.649111i
$115$	−3.11059e7	+	3.11059e7i	−0.177849	+	0.177849i
$116$	−1.80840e8	−	2.40668e8i	−0.998763	−	1.32919i
$117$	3.31156e7	−	3.31156e7i	0.176721	−	0.176721i
$118$	2.38987e7	+	2.75303e7i	0.123267	+	0.141998i
$119$	3.28565e8			1.63845
$120$	8.90892e6	−	4.14940e7i	0.0429635	−	0.200106i
$121$			4.07486e8i			1.90095i
$122$	8.37978e7	+	9.65318e7i	0.378263	+	0.435743i
$123$	1.77133e8	+	1.77133e8i	0.773888	+	0.773888i
$124$	3.89196e7	−	2.74203e8i	0.164620	−	1.15981i
$125$	1.14704e8	+	1.14704e8i	0.469829	+	0.469829i
$126$	5.45801e6	−	7.72928e7i	0.0216547	−	0.306660i
$127$		−	3.44808e8i		−	1.32545i	−0.748864	−	0.662723i	$-0.769401\pi$
$127$		−	3.44808e8i		−	1.32545i	0.748864	−	0.662723i	$-0.230599\pi$
$128$	−2.36408e8	−	1.27157e8i	−0.880688	−	0.473697i
$129$	4.97431e7			0.179628
$130$	−7.57227e7	−	5.34713e6i	−0.265126	−	0.0187218i
$131$	1.19049e8	−	1.19049e8i	0.404242	−	0.404242i	−0.475483	−	0.879725i	$-0.657727\pi$
$131$	1.19049e8	−	1.19049e8i	0.404242	−	0.404242i	0.879725	+	0.475483i	$0.157727\pi$
$132$	−2.95580e8	−	4.19537e7i	−0.973596	−	0.138189i
$133$	−2.29990e8	+	2.29990e8i	−0.735026	+	0.735026i
$134$	−8.62134e7	+	7.48406e7i	−0.267396	+	0.232123i
$135$	2.26600e7			0.0682221
$136$	5.94217e8	+	1.27581e8i	1.73696	+	0.372931i
$137$			2.33281e8i			0.662211i	0.943594	+	0.331106i	$0.107422\pi$
$137$			2.33281e8i			0.662211i	−0.943594	+	0.331106i	$0.892578\pi$
$138$	−1.12190e8	+	9.73904e7i	−0.309341	+	0.268534i
$139$	4.59460e8	+	4.59460e8i	1.23080	+	1.23080i	0.963656	+	0.267147i	$0.0860810\pi$
$139$	4.59460e8	+	4.59460e8i	1.23080	+	1.23080i	0.267147	+	0.963656i	$0.413919\pi$
$140$	−1.00409e8	+	7.54485e7i	−0.261373	+	0.196399i
$141$	6.76181e7	+	6.76181e7i	0.171075	+	0.171075i
$142$	4.28521e8	+	3.02599e7i	1.05395	+	0.0744242i
$143$			5.33999e8i			1.27701i
$144$	3.98834e7	−	1.37666e8i	0.0927561	−	0.320168i
$145$	−2.60537e8			−0.589382
$146$	−6.73633e6	+	9.53956e7i	−0.0148256	+	0.209951i
$147$	2.84836e7	−	2.84836e7i	0.0609993	−	0.0609993i
$148$	2.18954e8	−	1.64524e8i	0.456358	−	0.342912i
$149$	8.33726e6	−	8.33726e6i	0.0169152	−	0.0169152i	−0.698599	−	0.715514i	$-0.746193\pi$
$149$	8.33726e6	−	8.33726e6i	0.0169152	−	0.0169152i	0.715514	+	0.698599i	$0.246193\pi$
$150$	1.67526e8	+	1.92984e8i	0.330916	+	0.381202i
$151$	4.82778e8			0.928624			0.464312	−	0.885672i	$-0.346302\pi$
$151$	4.82778e8			0.928624			0.464312	+	0.885672i	$0.346302\pi$
$152$	−5.05246e8	+	3.26638e8i	−0.946518	+	0.611916i
$153$			3.24504e8i			0.592181i
$154$	5.79178e8	+	6.67190e8i	1.02974	+	1.18622i
$155$	−1.69487e8	−	1.69487e8i	−0.293636	−	0.293636i
$156$	−2.53824e8	−	3.60270e7i	−0.428582	−	0.0608317i
$157$	−3.33744e8	−	3.33744e8i	−0.549306	−	0.549306i	0.376934	−	0.926240i	$-0.376978\pi$
$157$	−3.33744e8	−	3.33744e8i	−0.549306	−	0.549306i	−0.926240	+	0.376934i	$0.876978\pi$
$158$	−5.90375e6	+	8.36051e7i	−0.00947326	+	0.134154i
$159$		−	5.92441e8i		−	0.926950i
$160$	−2.10888e8	+	9.74616e7i	−0.321790	+	0.148715i
$161$	4.39664e8			0.654362
$162$	7.63374e7	+	5.39054e6i	0.110835	+	0.00782659i
$163$	−2.08056e8	+	2.08056e8i	−0.294734	+	0.294734i	−0.838947	−	0.544213i	$-0.816828\pi$
$163$	−2.08056e8	+	2.08056e8i	−0.294734	+	0.294734i	0.544213	+	0.838947i	$0.316828\pi$
$164$	1.92705e8	−	1.35768e9i	0.266390	−	1.87682i
$165$	−1.82700e8	+	1.82700e8i	−0.246492	+	0.246492i
$166$	−4.65355e8	+	4.03968e8i	−0.612847	+	0.532004i
$167$	1.17457e9			1.51013			0.755063	−	0.655652i	$-0.227606\pi$
$167$	1.17457e9			1.51013			0.755063	+	0.655652i	$0.227606\pi$
$168$	−3.56208e8	+	2.30286e8i	−0.447164	+	0.289088i
$169$		−	3.57169e8i		−	0.437852i
$170$	3.97207e8	−	3.44809e8i	0.475577	−	0.412842i
$171$	−2.27147e8	−	2.27147e8i	−0.265658	−	0.265658i
$172$	−1.63577e8	−	2.17693e8i	−0.186899	−	0.248731i
$173$	−3.64925e8	−	3.64925e8i	−0.407399	−	0.407399i	0.473432	−	0.880831i	$-0.343015\pi$
$173$	−3.64925e8	−	3.64925e8i	−0.407399	−	0.407399i	−0.880831	+	0.473432i	$0.843015\pi$
$174$	−8.77700e8	−	6.19785e7i	−0.957522	−	0.0676151i
$175$		−	7.56290e8i		−	0.806373i
$176$	7.88388e8	+	1.43152e9i	0.821655	+	1.49192i
$177$	1.06556e8			0.108564
$178$	4.93874e7	−	6.99393e8i	0.0491967	−	0.696693i
$179$	−6.70515e8	+	6.70515e8i	−0.653125	+	0.653125i	−0.953744	−	0.300619i	$-0.902807\pi$
$179$	−6.70515e8	+	6.70515e8i	−0.653125	+	0.653125i	0.300619	+	0.953744i	$0.402807\pi$
$180$	−7.45159e7	−	9.91681e7i	−0.0709837	−	0.0944674i
$181$	−3.92064e8	+	3.92064e8i	−0.365294	+	0.365294i	−0.865758	−	0.500463i	$-0.833163\pi$
$181$	−3.92064e8	+	3.92064e8i	−0.365294	+	0.365294i	0.500463	+	0.865758i	$0.333163\pi$
$182$	4.97359e8	+	5.72938e8i	0.453299	+	0.522182i
$183$	3.73626e8			0.333144
$184$	7.95142e8	+	1.70720e8i	0.693703	+	0.148941i
$185$		−	2.37030e8i		−	0.202356i
$186$	−5.30651e8	−	6.11289e8i	−0.443361	−	0.510734i
$187$	−2.61636e9	−	2.61636e9i	−2.13959	−	2.13959i
$188$	7.35628e7	−	5.18278e8i	0.0588880	−	0.414888i
$189$	−1.60143e8	−	1.60143e8i	−0.125505	−	0.125505i
$190$	−3.66772e7	+	5.19399e8i	−0.0281437	+	0.398554i
$191$		−	1.64913e9i		−	1.23914i	−0.784940	−	0.619572i	$-0.787306\pi$
$191$		−	1.64913e9i		−	1.23914i	0.784940	−	0.619572i	$-0.212694\pi$
$192$	−7.33629e8	+	2.78162e8i	−0.539848	+	0.204688i
$193$	−2.45627e9			−1.77030			−0.885151	−	0.465304i	$-0.845945\pi$
$193$	−2.45627e9			−1.77030			−0.885151	+	0.465304i	$0.845945\pi$
$194$	−2.89992e8	−	2.04777e7i	−0.204729	−	0.0144568i
$195$	−1.56890e8	+	1.56890e8i	−0.108507	+	0.108507i
$196$	−2.18320e8	−	3.09877e7i	−0.147934	−	0.0209974i
$197$	1.67390e9	−	1.67390e9i	1.11139	−	1.11139i	0.118423	−	0.992963i	$-0.462216\pi$
$197$	1.67390e9	−	1.67390e9i	1.11139	−	1.11139i	0.992963	−	0.118423i	$-0.0377840\pi$
$198$	−6.58943e8	+	5.72019e8i	−0.428733	+	0.372177i
$199$	−2.24059e9			−1.42873			−0.714365	−	0.699773i	$-0.753284\pi$
$199$	−2.24059e9			−1.42873			−0.714365	+	0.699773i	$0.753284\pi$
$200$	2.93664e8	−	1.36777e9i	0.183540	−	0.854854i
$201$			3.33688e8i			0.204436i
$202$	1.03021e9	−	8.94310e8i	0.618757	−	0.537134i
$203$	1.84127e9	+	1.84127e9i	1.08426	+	1.08426i
$204$	1.42014e9	−	1.06711e9i	0.819994	−	0.616152i
$205$	−8.39192e8	−	8.39192e8i	−0.475167	−	0.475167i
$206$	−6.77238e8	−	4.78230e7i	−0.376073	−	0.0265563i
$207$			4.34230e8i			0.236504i
$208$	6.77014e8	+	1.22929e9i	0.361697	+	0.656753i
$209$	3.66282e9			1.91969
$210$	−2.58581e7	+	3.66186e8i	−0.0132960	+	0.188289i
$211$	−1.95649e9	+	1.95649e9i	−0.987067	+	0.987067i	−0.999917	−	0.0128502i	$-0.995910\pi$
$211$	−1.95649e9	+	1.95649e9i	−0.987067	+	0.987067i	0.0128502	+	0.999917i	$0.495910\pi$
$212$	−2.59273e9	+	1.94820e9i	−1.28355	+	0.964473i
$213$	8.87855e8	−	8.87855e8i	0.431344	−	0.431344i
$214$	3.83908e8	+	4.42246e8i	0.183051	+	0.210867i
$215$	−2.35665e8			−0.110291
$216$	−2.27439e8	−	3.51805e8i	−0.104484	−	0.161617i
$217$			2.39560e9i			1.08038i
$218$	2.00944e9	+	2.31480e9i	0.889713	+	1.02491i
$219$	1.97651e8	+	1.97651e8i	0.0859254	+	0.0859254i
$220$	1.40035e9	+	1.98762e8i	0.597787	+	0.0848482i
$221$	−2.24675e9	−	2.24675e9i	−0.941859	−	0.941859i
$222$	5.63866e7	−	7.98511e8i	0.0232148	−	0.328753i
$223$		−	9.08342e8i		−	0.367308i	−0.982991	−	0.183654i	$-0.941207\pi$
$223$		−	9.08342e8i		−	0.367308i	0.982991	−	0.183654i	$-0.0587926\pi$
$224$	2.17918e9	+	8.01612e8i	0.865566	+	0.318399i
$225$	7.46942e8			0.291445
$226$	3.04474e9	+	2.15003e8i	1.16712	+	0.0824159i
$227$	−2.36260e9	+	2.36260e9i	−0.889789	+	0.889789i	−0.994502	−	0.104714i	$-0.966607\pi$
$227$	−2.36260e9	+	2.36260e9i	−0.889789	+	0.889789i	0.104714	+	0.994502i	$0.466607\pi$
$228$	−2.47117e8	+	1.74103e9i	−0.0914458	+	0.644270i
$229$	2.55958e9	−	2.55958e9i	0.930738	−	0.930738i	−0.0670143	−	0.997752i	$-0.521347\pi$
$229$	2.55958e9	−	2.55958e9i	0.930738	−	0.930738i	0.997752	+	0.0670143i	$0.0213473\pi$
$230$	5.31516e8	−	4.61401e8i	0.189935	−	0.164880i
$231$	2.58236e9			0.906918
$232$	2.61501e9	+	4.04493e9i	0.902655	+	1.39624i
$233$			1.77202e9i			0.601236i	0.953745	+	0.300618i	$0.0971930\pi$
$233$			1.77202e9i			0.601236i	−0.953745	+	0.300618i	$0.902807\pi$
$234$	−5.65856e8	+	4.91211e8i	−0.188731	+	0.163834i
$235$	−3.20351e8	−	3.20351e8i	−0.105040	−	0.105040i
$236$	−3.50401e8	−	4.66325e8i	−0.112958	−	0.150328i
$237$	1.73222e8	+	1.73222e8i	0.0549046	+	0.0549046i
$238$	−5.24399e9	−	3.70302e8i	−1.63438	−	0.115411i
$239$			4.59510e8i			0.140833i	0.997518	+	0.0704164i	$0.0224328\pi$
$239$			4.59510e8i			0.140833i	−0.997518	+	0.0704164i	$0.977567\pi$
$240$	−1.88954e8	+	6.52215e8i	−0.0569522	+	0.196583i
$241$	1.61303e9			0.478161			0.239080	−	0.971000i	$-0.423154\pi$
$241$	1.61303e9			0.478161			0.239080	+	0.971000i	$0.423154\pi$
$242$	4.59249e8	−	6.50359e9i	0.133902	−	1.89623i
$243$	1.58164e8	−	1.58164e8i	0.0453609	−	0.0453609i
$244$	−1.22864e9	−	1.63511e9i	−0.346630	−	0.461306i
$245$	−1.34945e8	+	1.34945e8i	−0.0374535	+	0.0374535i
$246$	−2.62745e9	−	3.02672e9i	−0.717454	−	0.826478i
$247$	3.14538e9			0.845055
$248$	−9.30202e8	+	4.33249e9i	−0.245907	+	1.14533i
$249$			1.80115e9i			0.468548i
$250$	−1.70143e9	−	1.95998e9i	−0.435567	−	0.501756i
$251$	−2.03896e9	−	2.03896e9i	−0.513706	−	0.513706i	0.401954	−	0.915660i	$-0.368331\pi$
$251$	−2.03896e9	−	2.03896e9i	−0.513706	−	0.513706i	−0.915660	+	0.401954i	$0.868331\pi$
$252$	−1.74222e8	+	1.22746e9i	−0.0432018	+	0.304373i
$253$	−3.50104e9	−	3.50104e9i	−0.854506	−	0.854506i
$254$	−3.88608e8	+	5.50322e9i	−0.0933635	+	1.32215i
$255$		−	1.53739e9i		−	0.363598i
$256$	3.62982e9	+	2.29590e9i	0.845134	+	0.534555i
$257$	3.42454e9			0.785001			0.392500	−	0.919752i	$-0.371610\pi$
$257$	3.42454e9			0.785001			0.392500	+	0.919752i	$0.371610\pi$
$258$	−7.93913e8	−	5.60619e7i	−0.179182	−	0.0126529i
$259$	−1.67514e9	+	1.67514e9i	−0.372266	+	0.372266i
$260$	1.20253e9	+	1.70683e8i	0.263149	+	0.0373506i
$261$	−1.81851e9	+	1.81851e9i	−0.391880	+	0.391880i
$262$	−2.03423e9	+	1.76589e9i	−0.431713	+	0.374764i
$263$	5.58240e9			1.16680			0.583402	−	0.812184i	$-0.301721\pi$
$263$	5.58240e9			1.16680			0.583402	+	0.812184i	$0.301721\pi$
$264$	4.67024e9	+	1.00272e9i	0.961443	+	0.206425i
$265$			2.80678e9i			0.569147i
$266$	3.92991e9	−	3.41150e9i	0.784975	−	0.681426i
$267$	−1.44907e9	−	1.44907e9i	−0.285132	−	0.285132i
$268$	1.46034e9	−	1.09731e9i	0.283083	−	0.212711i
$269$	1.42926e8	+	1.42926e8i	0.0272961	+	0.0272961i	0.720623	−	0.693327i	$-0.243856\pi$
$269$	1.42926e8	+	1.42926e8i	0.0272961	+	0.0272961i	−0.693327	+	0.720623i	$0.743856\pi$
$270$	−3.61660e8	−	2.55385e7i	−0.0680527	−	0.00480552i
$271$			8.16306e9i			1.51348i	0.653718	+	0.756739i	$0.273208\pi$
$271$			8.16306e9i			1.51348i	−0.653718	+	0.756739i	$0.726792\pi$
$272$	−9.34007e9	−	2.70592e9i	−1.70637	−	0.494355i
$273$	2.21755e9			0.399230
$274$	2.62914e8	−	3.72322e9i	0.0466457	−	0.660566i
$275$	−6.02232e9	+	6.02232e9i	−1.05301	+	1.05301i
$276$	1.90034e9	−	1.42793e9i	0.327488	−	0.246077i
$277$	5.12840e8	−	5.12840e8i	0.0871089	−	0.0871089i	−0.662210	−	0.749319i	$-0.730381\pi$
$277$	5.12840e8	−	5.12840e8i	0.0871089	−	0.0871089i	0.749319	+	0.662210i	$0.230381\pi$
$278$	−6.81528e9	−	7.85092e9i	−1.14105	−	1.31444i
$279$	−2.36599e9			−0.390477
$280$	1.68759e9	−	1.09101e9i	0.274558	−	0.177500i
$281$		−	4.92693e9i		−	0.790225i	−0.918633	−	0.395113i	$-0.870706\pi$
$281$		−	4.92693e9i		−	0.790225i	0.918633	−	0.395113i	$-0.129294\pi$
$282$	−1.00299e9	−	1.15541e9i	−0.158600	−	0.182700i
$283$	8.15290e8	+	8.15290e8i	0.127106	+	0.127106i	0.767798	−	0.640692i	$-0.221352\pi$
$283$	8.15290e8	+	8.15290e8i	0.127106	+	0.127106i	−0.640692	+	0.767798i	$0.721352\pi$
$284$	−6.80521e9	−	9.65911e8i	−1.04609	−	0.148479i
$285$	1.07614e9	+	1.07614e9i	0.163114	+	0.163114i
$286$	6.01832e8	−	8.52275e9i	0.0899520	−	1.27384i
$287$			1.18615e10i			1.74828i
$288$	−7.91703e8	+	2.15224e9i	−0.115078	+	0.312839i
$289$	1.50404e10			2.15610
$290$	4.15823e9	+	2.93632e8i	0.587918	+	0.0415156i
$291$	−6.00834e8	+	6.00834e8i	−0.0837882	+	0.0837882i
$292$	2.15027e8	−	1.51495e9i	0.0295775	−	0.208385i
$293$	5.18980e9	−	5.18980e9i	0.704174	−	0.704174i	−0.261129	−	0.965304i	$-0.584095\pi$
$293$	5.18980e9	−	5.18980e9i	0.704174	−	0.704174i	0.965304	+	0.261129i	$0.0840949\pi$
$294$	−4.86707e8	+	4.22503e8i	−0.0651446	+	0.0565511i
$295$	−5.04824e8			−0.0666580
$296$	−3.67998e9	+	2.37908e9i	−0.479379	+	0.309915i
$297$			2.55044e9i			0.327785i
$298$	−1.42461e8	+	1.23668e8i	−0.0180647	+	0.0156817i
$299$	−3.00646e9	−	3.00646e9i	−0.376158	−	0.376158i
$300$	−2.45626e9	−	3.26887e9i	−0.303243	−	0.403565i
$301$	1.66550e9	+	1.66550e9i	0.202898	+	0.202898i
$302$	−7.70526e9	−	5.44105e8i	−0.926317	−	0.0654116i
$303$		−	3.98742e9i		−	0.473066i
$304$	8.43199e9	−	4.64380e9i	0.987270	−	0.543724i
$305$	−1.77011e9			−0.204550
$306$	3.65725e8	−	5.17917e9i	0.0417128	−	0.590710i
$307$	3.88759e9	−	3.88759e9i	0.437650	−	0.437650i	−0.453570	−	0.891220i	$-0.649850\pi$
$307$	3.88759e9	−	3.88759e9i	0.437650	−	0.437650i	0.891220	+	0.453570i	$0.149850\pi$
$308$	−8.49189e9	−	1.13013e10i	−0.943630	−	1.25581i
$309$	−1.40317e9	+	1.40317e9i	−0.153914	+	0.153914i
$310$	2.51404e9	+	2.89607e9i	0.272223	+	0.313590i
$311$	−9.36764e9			−1.00136			−0.500678	−	0.865633i	$-0.666916\pi$
$311$	−9.36764e9			−1.00136			−0.500678	+	0.865633i	$0.666916\pi$
$312$	4.01049e9	+	8.61067e8i	0.423232	+	0.0908696i
$313$			1.52837e10i			1.59240i	0.605033	+	0.796200i	$0.293160\pi$
$313$			1.52837e10i			1.59240i	−0.605033	+	0.796200i	$0.706840\pi$
$314$	4.95050e9	+	5.70277e9i	0.509249	+	0.586634i
$315$	7.58702e8	+	7.58702e8i	0.0770600	+	0.0770600i
$316$	1.88451e8	−	1.32771e9i	0.0188995	−	0.133154i
$317$	−1.13318e10	−	1.13318e10i	−1.12217	−	1.12217i	−0.991414	−	0.130761i	$-0.958258\pi$
$317$	−1.13318e10	−	1.13318e10i	−1.12217	−	1.12217i	−0.130761	−	0.991414i	$-0.541742\pi$
$318$	−6.67698e8	+	9.45551e9i	−0.0652937	+	0.924648i
$319$		−	2.93240e10i		−	2.83178i
$320$	3.47568e9	−	1.31784e9i	0.331466	−	0.125679i
$321$	1.71171e9			0.161217
$322$	−7.01716e9	−	4.95514e8i	−0.652736	−	0.0460928i
$323$	−1.54110e10	+	1.54110e10i	−1.41586	+	1.41586i
$324$	−1.21229e9	−	1.72069e8i	−0.110009	−	0.0156143i
$325$	−5.17156e9	+	5.17156e9i	−0.463541	+	0.463541i
$326$	3.55511e9	−	3.08614e9i	0.314763	−	0.273241i
$327$	8.95941e9			0.783590
$328$	−4.60577e9	+	2.14518e10i	−0.397931	+	1.85339i
$329$			4.52798e9i			0.386474i
$330$	3.12184e9	−	2.71003e9i	0.263242	−	0.228517i
$331$	4.13611e9	+	4.13611e9i	0.344572	+	0.344572i	0.858083	−	0.513511i	$-0.171655\pi$
$331$	4.13611e9	+	4.13611e9i	0.344572	+	0.344572i	−0.513511	+	0.858083i	$0.671655\pi$
$332$	7.88248e9	−	5.92297e9i	0.648799	−	0.487514i
$333$	−1.65444e9	−	1.65444e9i	−0.134547	−	0.134547i
$334$	−1.87464e10	−	1.32377e9i	−1.50637	−	0.106372i
$335$		−	1.58090e9i		−	0.125523i
$336$	5.94471e9	−	3.27396e9i	0.466417	−	0.256872i
$337$	−4.83515e9			−0.374878			−0.187439	−	0.982276i	$-0.560019\pi$
$337$	−4.83515e9			−0.374878			−0.187439	+	0.982276i	$0.560019\pi$
$338$	−4.02540e8	+	5.70051e9i	−0.0308420	+	0.436764i
$339$	6.30840e9	−	6.30840e9i	0.477662	−	0.477662i
$340$	−6.72813e9	+	5.05558e9i	−0.503476	+	0.378317i
$341$	1.90761e10	−	1.90761e10i	1.41082	−	1.41082i
$342$	3.36933e9	+	3.88133e9i	0.246286	+	0.283711i
$343$	1.46728e10			1.06007
$344$	2.36538e9	+	3.65879e9i	0.168915	+	0.261279i
$345$		−	2.05723e9i		−	0.145213i
$346$	5.41302e9	+	6.23559e9i	0.377690	+	0.435084i
$347$	7.33469e9	+	7.33469e9i	0.505899	+	0.505899i	0.913265	−	0.407366i	$-0.133553\pi$
$347$	7.33469e9	+	7.33469e9i	0.505899	+	0.505899i	−0.407366	+	0.913265i	$0.633553\pi$
$348$	1.39385e10	+	1.97838e9i	0.950381	+	0.134894i
$349$	4.25862e9	+	4.25862e9i	0.287056	+	0.287056i	0.835915	−	0.548859i	$-0.184938\pi$
$349$	4.25862e9	+	4.25862e9i	0.287056	+	0.287056i	−0.548859	+	0.835915i	$0.684938\pi$
$350$	−8.52360e8	+	1.20706e10i	−0.0568004	+	0.804370i
$351$			2.19014e9i			0.144292i
$352$	−1.09695e10	−	2.37360e10i	−0.714524	−	1.54609i
$353$	−2.05080e10			−1.32076			−0.660380	−	0.750932i	$-0.729605\pi$
$353$	−2.05080e10			−1.32076			−0.660380	+	0.750932i	$0.729605\pi$
$354$	−1.70066e9	−	1.20091e8i	−0.108294	−	0.00764714i
$355$	−4.20634e9	+	4.20634e9i	−0.264845	+	0.264845i
$356$	−1.57647e9	+	1.11068e10i	−0.0981491	+	0.691497i
$357$	−1.08650e10	+	1.08650e10i	−0.668895	+	0.668895i
$358$	1.14573e10	−	9.94590e9i	0.697508	−	0.605497i
$359$	−4.00049e9			−0.240844			−0.120422	−	0.992723i	$-0.538425\pi$
$359$	−4.00049e9			−0.240844			−0.120422	+	0.992723i	$0.538425\pi$
$360$	1.07753e9	+	1.66673e9i	0.0641532	+	0.0992328i
$361$		−	4.59130e9i		−	0.270338i
$362$	6.69932e9	−	5.81558e9i	0.390118	−	0.338656i
$363$	−1.34748e10	−	1.34748e10i	−0.776061	−	0.776061i
$364$	−7.29226e9	−	9.70477e9i	−0.415391	−	0.552815i
$365$	−9.36399e8	−	9.36399e8i	−0.0527581	−	0.0527581i
$366$	−5.96316e9	−	4.21087e8i	−0.332317	−	0.0234664i
$367$		−	3.05584e9i		−	0.168448i	−0.996447	−	0.0842240i	$-0.973159\pi$
$367$		−	3.05584e9i		−	0.168448i	0.996447	−	0.0842240i	$-0.0268411\pi$
$368$	−1.24983e10	−	3.62088e9i	−0.681488	−	0.197435i
$369$	−1.17149e10			−0.631877
$370$	−2.67140e8	+	3.78307e9i	−0.0142538	+	0.201854i
$371$	1.98361e10	−	1.98361e10i	1.04703	−	1.04703i
$372$	7.78038e9	+	1.03544e10i	0.406284	+	0.540695i
$373$	−2.05293e9	+	2.05293e9i	−0.106057	+	0.106057i	−0.758144	−	0.652087i	$-0.773894\pi$
$373$	−2.05293e9	+	2.05293e9i	−0.106057	+	0.106057i	0.652087	+	0.758144i	$0.273894\pi$
$374$	3.88090e10	+	4.47065e10i	1.98357	+	2.28499i
$375$	−7.58611e9			−0.383613
$376$	−1.75820e9	+	8.18894e9i	−0.0879662	+	0.409710i
$377$		−	2.51814e10i		−	1.24657i
$378$	2.37544e9	+	2.73641e9i	0.116353	+	0.134034i
$379$	1.75012e9	+	1.75012e9i	0.0848226	+	0.0848226i	0.748245	−	0.663422i	$-0.230897\pi$
$379$	1.75012e9	+	1.75012e9i	0.0848226	+	0.0848226i	−0.663422	+	0.748245i	$0.730897\pi$
$380$	1.17076e9	−	8.24841e9i	0.0561477	−	0.395581i
$381$	1.14021e10	+	1.14021e10i	0.541111	+	0.541111i
$382$	−1.85862e9	+	2.63206e10i	−0.0872844	+	1.23607i
$383$			9.52508e9i			0.442663i	0.975199	+	0.221332i	$0.0710403\pi$
$383$			9.52508e9i			0.442663i	−0.975199	+	0.221332i	$0.928960\pi$
$384$	1.20224e10	−	3.61272e9i	0.552925	−	0.166153i
$385$	−1.22343e10			−0.556847
$386$	3.92027e10	+	2.76829e9i	1.76590	+	0.124699i
$387$	−1.64491e9	+	1.64491e9i	−0.0733328	+	0.0733328i
$388$	4.60526e9	+	6.53658e8i	0.203202	+	0.0288419i
$389$	−2.46644e10	+	2.46644e10i	−1.07714	+	1.07714i	−0.0803740	+	0.996765i	$0.525611\pi$
$389$	−2.46644e10	+	2.46644e10i	−1.07714	+	1.07714i	−0.996765	+	0.0803740i	$0.974389\pi$
$390$	2.68083e9	−	2.32719e9i	0.115880	−	0.100594i
$391$	2.94606e10			1.26048
$392$	3.44952e9	+	7.40625e8i	0.146088	+	0.0313656i
$393$			7.87347e9i			0.330062i
$394$	−2.86024e10	+	2.48294e10i	−1.18691	+	1.03034i
$395$	−8.20664e8	−	8.20664e8i	−0.0337114	−	0.0337114i
$396$	1.11616e10	−	8.38693e9i	0.453884	−	0.341053i
$397$	−1.00962e10	−	1.00962e10i	−0.406441	−	0.406441i	0.474055	−	0.880495i	$-0.342790\pi$
$397$	−1.00962e10	−	1.00962e10i	−0.406441	−	0.406441i	−0.880495	+	0.474055i	$0.842790\pi$
$398$	3.57604e10	+	2.52521e9i	1.42518	+	0.100639i
$399$		−	1.52107e10i		−	0.600147i
$400$	−6.22847e9	+	2.14989e10i	−0.243300	+	0.839802i
$401$	1.77965e10			0.688265			0.344133	−	0.938921i	$-0.388173\pi$
$401$	1.77965e10			0.688265			0.344133	+	0.938921i	$0.388173\pi$
$402$	3.76076e8	−	5.32575e9i	0.0144003	−	0.203928i
$403$	1.63813e10	−	1.63813e10i	0.621051	−	0.621051i
$404$	−1.74503e10	+	1.31123e10i	−0.655055	+	0.492215i
$405$	−7.49324e8	+	7.49324e8i	−0.0278516	+	0.0278516i
$406$	−2.73120e10	−	3.14623e10i	−1.00519	−	1.15794i
$407$	2.66783e10			0.972255
$408$	−2.38685e10	+	1.54308e10i	−0.861359	+	0.556862i
$409$			4.77242e10i			1.70548i	0.522338	+	0.852738i	$0.325060\pi$
$409$			4.77242e10i			1.70548i	−0.522338	+	0.852738i	$0.674940\pi$
$410$	1.24479e10	+	1.43395e10i	0.440516	+	0.507457i
$411$	−7.71415e9	−	7.71415e9i	−0.270347	−	0.270347i
$412$	1.07550e10	+	1.52653e9i	0.373269	+	0.0529807i
$413$	3.56770e9	+	3.56770e9i	0.122628	+	0.122628i
$414$	4.89389e8	−	6.93042e9i	0.0166592	−	0.235916i
$415$		−	8.53324e9i		−	0.287688i
$416$	−9.41988e9	−	2.03828e10i	−0.314537	−	0.680599i
$417$	−3.03870e10			−1.00495
$418$	−5.84595e10	−	4.12810e9i	−1.91492	−	0.135221i
$419$	−2.98751e10	+	2.98751e10i	−0.969290	+	0.969290i	−0.999542	−	0.0302522i	$-0.990369\pi$
$419$	−2.98751e10	+	2.98751e10i	−0.969290	+	0.969290i	0.0302522	+	0.999542i	$0.490369\pi$
$420$	8.25405e8	−	5.81528e9i	0.0265259	−	0.186885i
$421$	1.72971e10	−	1.72971e10i	0.550612	−	0.550612i	−0.376005	−	0.926618i	$-0.622703\pi$
$421$	1.72971e10	−	1.72971e10i	0.550612	−	0.550612i	0.926618	+	0.376005i	$0.122703\pi$
$422$	3.34310e10	−	2.90210e10i	1.05414	−	0.915087i
$423$	−4.47201e9			−0.139682
$424$	4.35762e10	−	2.81717e10i	1.34830	−	0.871665i
$425$		−	5.06768e10i		−	1.55329i
$426$	−1.51710e10	+	1.31698e10i	−0.460656	+	0.399889i
$427$	1.25097e10	+	1.25097e10i	0.376302	+	0.376302i
$428$	−5.62884e9	−	7.49104e9i	−0.167743	−	0.223237i
$429$	−1.76583e10	−	1.76583e10i	−0.521339	−	0.521339i
$430$	3.76128e9	+	2.65602e8i	0.110018	+	0.00776885i
$431$		−	1.31620e10i		−	0.381428i	−0.981646	−	0.190714i	$-0.938920\pi$
$431$		−	1.31620e10i		−	0.381428i	0.981646	−	0.190714i	$-0.0610803\pi$
$432$	3.23350e9	+	5.87123e9i	0.0928404	+	0.168575i
$433$	−3.63988e10			−1.03547			−0.517733	−	0.855542i	$-0.673224\pi$
$433$	−3.63988e10			−1.03547			−0.517733	+	0.855542i	$0.673224\pi$
$434$	2.69991e9	−	3.82344e10i	0.0761010	−	1.07769i
$435$	8.61546e9	−	8.61546e9i	0.240614	−	0.240614i
$436$	−2.94624e10	−	3.92095e10i	−0.815309	−	1.08504i
$437$	−2.06220e10	+	2.06220e10i	−0.565463	+	0.565463i
$438$	−2.93180e9	−	3.37731e9i	−0.0796594	−	0.0917645i
$439$	−6.89499e10			−1.85642			−0.928208	−	0.372061i	$-0.878651\pi$
$439$	−6.89499e10			−1.85642			−0.928208	+	0.372061i	$0.878651\pi$
$440$	−2.21260e10	−	4.75053e9i	−0.590325	−	0.126745i
$441$			1.88380e9i			0.0498057i
$442$	3.33266e10	+	3.83909e10i	0.873176	+	1.00586i
$443$	1.08623e10	+	1.08623e10i	0.282037	+	0.282037i	0.833921	−	0.551884i	$-0.186091\pi$
$443$	1.08623e10	+	1.08623e10i	0.282037	+	0.282037i	−0.551884	+	0.833921i	$0.686091\pi$
$444$	−1.79989e9	+	1.26809e10i	−0.0463142	+	0.326301i
$445$	6.86521e9	+	6.86521e9i	0.175071	+	0.175071i
$446$	−1.02373e9	+	1.44974e10i	−0.0258729	+	0.366395i
$447$			5.51395e8i			0.0138112i
$448$	−3.38768e10	−	1.52499e10i	−0.840988	−	0.378578i
$449$	−1.89946e9			−0.0467354			−0.0233677	−	0.999727i	$-0.507439\pi$
$449$	−1.89946e9			−0.0467354			−0.0233677	+	0.999727i	$0.507439\pi$
$450$	−1.19214e10	−	8.41825e8i	−0.290721	−	0.0205292i
$451$	9.44529e10	−	9.44529e10i	2.28302	−	2.28302i
$452$	−4.83525e10	−	6.86301e9i	−1.15842	−	0.164422i
$453$	−1.59646e10	+	1.59646e10i	−0.379109	+	0.379109i
$454$	4.03704e10	−	3.50450e10i	0.950255	−	0.824903i
$455$	−1.05060e10			−0.245127
$456$	5.90625e9	−	2.75088e10i	0.136601	−	0.636228i
$457$		−	2.18741e10i		−	0.501494i	−0.968053	−	0.250747i	$-0.919324\pi$
$457$		−	2.18741e10i		−	0.501494i	0.968053	−	0.250747i	$-0.0806762\pi$
$458$	−4.37363e10	+	3.79669e10i	−0.993986	+	0.862865i
$459$	−1.07307e10	−	1.07307e10i	−0.241757	−	0.241757i
$460$	−9.00314e9	+	6.76505e9i	−0.201077	+	0.151091i
$461$	1.40132e9	+	1.40132e9i	0.0310265	+	0.0310265i	0.722450	−	0.691423i	$-0.243016\pi$
$461$	1.40132e9	+	1.40132e9i	0.0310265	+	0.0310265i	−0.691423	+	0.722450i	$0.743016\pi$
$462$	−4.12151e10	−	2.91039e9i	−0.904665	−	0.0638827i
$463$			2.78405e10i			0.605833i	0.953017	+	0.302916i	$0.0979603\pi$
$463$			2.78405e10i			0.605833i	−0.953017	+	0.302916i	$0.902040\pi$
$464$	−3.71775e10	−	6.75053e10i	−0.802063	−	1.45635i
$465$	1.12092e10			0.239753
$466$	1.99712e9	−	2.82819e10i	0.0423507	−	0.599743i
$467$	2.39248e10	−	2.39248e10i	0.503015	−	0.503015i	−0.409359	−	0.912374i	$-0.634247\pi$
$467$	2.39248e10	−	2.39248e10i	0.503015	−	0.503015i	0.912374	+	0.409359i	$0.134247\pi$
$468$	9.58481e9	−	7.20212e9i	0.199802	−	0.150133i
$469$	−1.11725e10	+	1.11725e10i	−0.230920	+	0.230920i
$470$	4.75184e9	+	5.47393e9i	0.0973801	+	0.112178i
$471$	2.20725e10			0.448507
$472$	5.06693e9	+	7.83758e9i	0.102089	+	0.157912i
$473$		−	2.65247e10i		−	0.529914i
$474$	−2.56944e9	−	2.95989e9i	−0.0509008	−	0.0586357i
$475$	3.54729e10	+	3.54729e10i	0.696823	+	0.696823i
$476$	8.32780e10	+	1.18202e10i	1.62219	+	0.230249i
$477$	1.95909e10	+	1.95909e10i	0.378426	+	0.378426i
$478$	5.17881e8	−	7.33390e9i	0.00992016	−	0.140483i
$479$			7.33479e10i			1.39330i	0.717410	+	0.696651i	$0.245328\pi$
$479$			7.33479e10i			1.39330i	−0.717410	+	0.696651i	$0.754672\pi$
$480$	3.75081e9	−	1.01966e10i	0.0706579	−	0.192083i
$481$	2.29095e10			0.427992
$482$	−2.57443e10	−	1.81793e9i	−0.476973	−	0.0336813i
$483$	−1.45389e10	+	1.45389e10i	−0.267142	+	0.267142i
$484$	−1.46595e10	+	1.03281e11i	−0.267138	+	1.88209i
$485$	2.84654e9	−	2.84654e9i	0.0514459	−	0.0514459i
$486$	−2.70259e9	+	2.34608e9i	−0.0484434	+	0.0420531i
$487$	−8.20748e10			−1.45913			−0.729565	−	0.683911i	$-0.760278\pi$
$487$	−8.20748e10			−1.45913			−0.729565	+	0.683911i	$0.760278\pi$
$488$	1.77666e10	+	2.74816e10i	0.313275	+	0.484576i
$489$		−	1.37600e10i		−	0.240649i
$490$	2.30585e9	−	2.00167e9i	0.0399987	−	0.0347223i
$491$	1.36609e10	+	1.36609e10i	0.235046	+	0.235046i	0.814795	−	0.579749i	$-0.196849\pi$
$491$	1.36609e10	+	1.36609e10i	0.235046	+	0.235046i	−0.579749	+	0.814795i	$0.696849\pi$
$492$	3.85236e10	+	5.12684e10i	0.657455	+	0.874962i
$493$	1.23378e11	+	1.23378e11i	2.08858	+	2.08858i
$494$	−5.02011e10	−	3.54493e9i	−0.842956	−	0.0595251i
$495$		−	1.20831e10i		−	0.201259i
$496$	1.97291e10	−	6.80993e10i	0.325972	−	1.12516i
$497$	5.94543e10			0.974445
$498$	2.02995e9	−	2.87469e10i	0.0330042	−	0.467384i
$499$	−4.19086e10	+	4.19086e10i	−0.675929	+	0.675929i	−0.959076	−	0.283148i	$-0.908621\pi$
$499$	−4.19086e10	+	4.19086e10i	−0.675929	+	0.675929i	0.283148	+	0.959076i	$0.408621\pi$
$500$	2.49464e10	+	3.31994e10i	0.399142	+	0.531191i
$501$	−3.88408e10	+	3.88408e10i	−0.616506	+	0.616506i
$502$	3.02444e10	+	3.48403e10i	0.476244	+	0.548615i
$503$	−1.00586e10			−0.157132			−0.0785660	−	0.996909i	$-0.525034\pi$
$503$	−1.00586e10			−0.157132			−0.0785660	+	0.996909i	$0.525034\pi$
$504$	4.16402e9	−	1.93943e10i	0.0645343	−	0.300574i
$505$			1.88910e10i			0.290462i
$506$	5.19317e10	+	5.98233e10i	0.792192	+	0.912574i
$507$	1.18109e10	+	1.18109e10i	0.178752	+	0.178752i
$508$	1.24046e10	−	8.73948e10i	0.186263	−	1.31229i
$509$	3.98221e10	+	3.98221e10i	0.593271	+	0.593271i	0.938513	−	0.345243i	$-0.112203\pi$
$509$	3.98221e10	+	3.98221e10i	0.593271	+	0.593271i	−0.345243	+	0.938513i	$0.612203\pi$
$510$	−1.73268e9	+	2.45371e10i	−0.0256116	+	0.362695i
$511$			1.32355e10i			0.194113i
$512$	−5.53453e10	−	4.07340e10i	−0.805381	−	0.592758i
$513$	1.50227e10			0.216909
$514$	−5.46566e10	−	3.85956e9i	−0.783051	−	0.0552949i
$515$	6.64774e9	−	6.64774e9i	0.0945029	−	0.0945029i
$516$	1.26079e10	+	1.78952e9i	0.177846	+	0.0252429i
$517$	3.60562e10	−	3.60562e10i	0.504682	−	0.504682i
$518$	2.86237e10	−	2.48478e10i	0.397563	−	0.345119i
$519$	2.41348e10			0.332640
$520$	−1.90003e10	−	4.07943e9i	−0.259864	−	0.0557938i
$521$			1.88714e9i			0.0256126i	0.999918	+	0.0128063i	$0.00407649\pi$
$521$			1.88714e9i			0.0256126i	−0.999918	+	0.0128063i	$0.995924\pi$
$522$	3.10734e10	−	2.69744e10i	0.418511	−	0.363303i
$523$	5.23015e9	+	5.23015e9i	0.0699049	+	0.0699049i	0.741195	−	0.671290i	$-0.234259\pi$
$523$	5.23015e9	+	5.23015e9i	0.0699049	+	0.0699049i	−0.671290	+	0.741195i	$0.734259\pi$
$524$	3.44570e10	−	2.58913e10i	0.457038	−	0.343423i
$525$	2.50091e10	+	2.50091e10i	0.329201	+	0.329201i
$526$	−8.90965e10	−	6.29152e9i	−1.16391	−	0.0821888i
$527$			1.60522e11i			2.08110i
$528$	−7.34082e10	−	2.12671e10i	−0.944515	−	0.273636i
$529$	−3.88887e10			−0.496593
$530$	3.16332e9	−	4.47969e10i	0.0400903	−	0.567733i
$531$	−3.52360e9	+	3.52360e9i	−0.0443209	+	0.0443209i
$532$	−6.65672e10	+	5.00193e10i	−0.831025	+	0.624440i
$533$	8.11098e10	−	8.11098e10i	1.00500	−	1.00500i
$534$	2.14945e10	+	2.47608e10i	0.264339	+	0.304508i
$535$	−8.10948e9			−0.0989870
$536$	−2.45440e10	+	1.58675e10i	−0.297363	+	0.192243i
$537$		−	4.43453e10i		−	0.533274i
$538$	−2.12005e9	−	2.44221e9i	−0.0253056	−	0.0291511i
$539$	−1.51884e10	−	1.51884e10i	−0.179952	−	0.179952i
$540$	5.74340e9	+	8.15202e8i	0.0675451	+	0.00958716i
$541$	−9.94355e10	−	9.94355e10i	−1.16079	−	1.16079i	−0.984304	−	0.176483i	$-0.943528\pi$
$541$	−9.94355e10	−	9.94355e10i	−1.16079	−	1.16079i	−0.176483	−	0.984304i	$-0.556472\pi$
$542$	9.20000e9	−	1.30285e11i	0.106608	−	1.50972i
$543$		−	2.59297e10i		−	0.298262i
$544$	1.46020e11	+	5.37137e10i	1.66731	+	0.613323i
$545$	−4.24466e10			−0.481123
$546$	−3.53927e10	−	2.49924e9i	−0.398238	−	0.0281215i
$547$	2.61262e10	−	2.61262e10i	0.291828	−	0.291828i	−0.545974	−	0.837802i	$-0.683840\pi$
$547$	2.61262e10	−	2.61262e10i	0.291828	−	0.291828i	0.837802	+	0.545974i	$0.183840\pi$
$548$	−8.39235e9	+	5.91272e10i	−0.0930596	+	0.655640i
$549$	−1.23551e10	+	1.23551e10i	−0.136006	+	0.136006i
$550$	1.02905e11	−	8.93305e10i	1.12457	−	0.976223i
$551$	−1.72725e11			−1.87391
$552$	−3.19392e10	+	2.06485e10i	−0.344008	+	0.222398i
$553$			1.15996e10i			0.124035i
$554$	−8.76304e9	+	7.60707e9i	−0.0930284	+	0.0807566i
$555$	7.83815e9	+	7.83815e9i	0.0826117	+	0.0826117i
$556$	9.99253e10	+	1.32984e11i	1.04563	+	1.39155i
$557$	1.63873e10	+	1.63873e10i	0.170250	+	0.170250i	0.787089	−	0.616839i	$-0.211587\pi$
$557$	1.63873e10	+	1.63873e10i	0.170250	+	0.170250i	−0.616839	+	0.787089i	$0.711587\pi$
$558$	3.77618e10	+	2.66654e9i	0.389507	+	0.0275049i
$559$		−	2.27776e10i		−	0.233271i
$560$	−2.81640e10	+	1.55109e10i	−0.286379	+	0.157719i
$561$	1.73036e11			1.74697
$562$	−5.55279e9	+	7.86350e10i	−0.0556629	+	0.788262i
$563$	−1.97783e10	+	1.97783e10i	−0.196859	+	0.196859i	−0.798652	−	0.601793i	$-0.794453\pi$
$563$	−1.97783e10	+	1.97783e10i	−0.196859	+	0.196859i	0.601793	+	0.798652i	$0.294453\pi$
$564$	1.47059e10	+	1.95710e10i	0.145336	+	0.193418i
$565$	−2.98870e10	+	2.98870e10i	−0.293284	+	0.293284i
$566$	−1.20934e10	−	1.39311e10i	−0.117837	−	0.135744i
$567$	1.05913e10			0.102474
$568$	1.07524e11	+	2.30859e10i	1.03303	+	0.221795i
$569$		−	1.97830e11i		−	1.88731i	−0.330936	−	0.943653i	$-0.607364\pi$
$569$		−	1.97830e11i		−	1.88731i	0.330936	−	0.943653i	$-0.392636\pi$
$570$	−1.59627e10	−	1.83884e10i	−0.151219	−	0.174198i
$571$	2.81032e10	+	2.81032e10i	0.264370	+	0.264370i	0.826827	−	0.562457i	$-0.190144\pi$
$571$	2.81032e10	+	2.81032e10i	0.264370	+	0.264370i	−0.562457	+	0.826827i	$0.690144\pi$
$572$	−1.92108e10	+	1.35347e11i	−0.179457	+	1.26434i
$573$	5.45337e10	+	5.45337e10i	0.505879	+	0.505879i
$574$	1.33683e10	−	1.89313e11i	0.123148	−	1.74394i
$575$		−	6.78123e10i		−	0.620351i
$576$	1.50614e10	−	3.34580e10i	0.136828	−	0.303956i
$577$	−6.70487e10			−0.604905			−0.302453	−	0.953164i	$-0.597805\pi$
$577$	−6.70487e10			−0.604905			−0.302453	+	0.953164i	$0.597805\pi$
$578$	−2.40049e11	−	1.69510e10i	−2.15075	−	0.151874i
$579$	8.12243e10	−	8.12243e10i	0.722723	−	0.722723i
$580$	−6.60355e10	−	9.37289e9i	−0.583533	−	0.0828250i
$581$	−6.03062e10	+	6.03062e10i	−0.529246	+	0.529246i
$582$	1.02666e10	−	8.91232e9i	0.0894821	−	0.0776781i
$583$	−3.15909e11			−2.73456
$584$	−5.13928e9	+	2.39366e10i	−0.0441825	+	0.205784i
$585$		−	1.03761e10i		−	0.0885955i
$586$	−8.86796e10	+	7.69815e10i	−0.752027	+	0.652824i
$587$	−1.20818e11	−	1.20818e11i	−1.01760	−	1.01760i	−0.999842	−	0.0177616i	$-0.994346\pi$
$587$	−1.20818e11	−	1.20818e11i	−1.01760	−	1.01760i	−0.0177616	−	0.999842i	$-0.505654\pi$
$588$	8.24414e9	−	6.19473e9i	0.0689662	−	0.0518219i
$589$	−1.12363e11	−	1.12363e11i	−0.933602	−	0.933602i
$590$	8.05712e9	+	5.68951e8i	0.0664924	+	0.00469534i
$591$			1.10706e11i			0.907443i
$592$	6.14148e10	−	3.38233e10i	0.500019	−	0.275378i
$593$	−8.11199e10			−0.656007			−0.328003	−	0.944677i	$-0.606376\pi$
$593$	−8.11199e10			−0.656007			−0.328003	+	0.944677i	$0.606376\pi$
$594$	2.87441e9	−	4.07056e10i	0.0230889	−	0.326970i
$595$	5.14747e10	−	5.14747e10i	0.410701	−	0.410701i
$596$	2.41309e9	−	1.81322e9i	0.0191245	−	0.0143703i
$597$	7.40921e10	−	7.40921e10i	0.583276	−	0.583276i
$598$	4.45954e10	+	5.13722e10i	0.348727	+	0.401720i
$599$	2.16087e11			1.67850			0.839249	−	0.543747i	$-0.182995\pi$
$599$	2.16087e11			1.67850			0.839249	+	0.543747i	$0.182995\pi$
$600$	3.55185e10	+	5.49404e10i	0.274062	+	0.423923i
$601$		−	4.77105e10i		−	0.365693i	−0.983142	−	0.182846i	$-0.941469\pi$
$601$		−	4.77105e10i		−	0.365693i	0.983142	−	0.182846i	$-0.0585311\pi$
$602$	−2.47047e10	−	2.84588e10i	−0.188102	−	0.216686i
$603$	−1.10344e10	−	1.10344e10i	−0.0834605	−	0.0834605i
$604$	1.22365e11	+	1.73681e10i	0.919409	+	0.130498i
$605$	6.38389e10	+	6.38389e10i	0.476501	+	0.476501i
$606$	−4.49394e9	+	6.36402e10i	−0.0333224	+	0.471891i
$607$		−	4.25857e10i		−	0.313696i	−0.987623	−	0.156848i	$-0.949867\pi$
$607$		−	4.25857e10i		−	0.313696i	0.987623	−	0.156848i	$-0.0501333\pi$
$608$	−1.39810e11	+	6.46131e10i	−1.02312	+	0.472831i
$609$	−1.21775e11			−0.885294
$610$	2.82514e10	+	1.99496e9i	0.204042	+	0.0144084i
$611$	3.09626e10	−	3.09626e10i	0.222164	−	0.222164i
$612$	−1.16741e10	+	8.22486e10i	−0.0832183	+	0.586304i
$613$	1.74903e11	−	1.74903e11i	1.23867	−	1.23867i	0.278120	−	0.960546i	$-0.410289\pi$
$613$	1.74903e11	−	1.74903e11i	1.23867	−	1.23867i	0.960546	−	0.278120i	$-0.0897111\pi$
$614$	−6.64284e10	+	5.76655e10i	−0.467391	+	0.405735i
$615$	5.55010e10			0.387972
$616$	1.22796e11	+	1.89942e11i	0.852827	+	1.31916i
$617$		−	1.02866e10i		−	0.0709793i	−0.999370	−	0.0354896i	$-0.988701\pi$
$617$		−	1.02866e10i		−	0.0709793i	0.999370	−	0.0354896i	$-0.0112991\pi$
$618$	2.39764e10	−	2.08136e10i	0.164373	−	0.142690i
$619$	−9.99336e9	−	9.99336e9i	−0.0680689	−	0.0680689i	0.672253	−	0.740322i	$-0.265327\pi$
$619$	−9.99336e9	−	9.99336e9i	−0.0680689	−	0.0680689i	−0.740322	+	0.672253i	$0.765327\pi$
$620$	−3.68607e10	−	4.90554e10i	−0.249458	−	0.331986i
$621$	−1.43592e10	−	1.43592e10i	−0.0965523	−	0.0965523i
$622$	1.49510e11	+	1.05576e10i	0.998869	+	0.0705348i
$623$		−	9.70358e10i		−	0.644139i
$624$	−6.30380e10	−	1.82628e10i	−0.415780	−	0.120456i
$625$	−9.74726e10			−0.638797
$626$	1.72252e10	−	2.43932e11i	0.112168	−	1.58845i
$627$	−1.21122e11	+	1.21122e11i	−0.783708	+	0.783708i
$628$	−7.25840e10	−	9.65971e10i	−0.466662	−	0.621048i
$629$	−1.12247e11	+	1.12247e11i	−0.717084	+	0.717084i
$630$	−1.12540e10	−	1.29642e10i	−0.0714406	−	0.0822967i
$631$	−5.29976e10			−0.334302			−0.167151	−	0.985931i	$-0.553457\pi$
$631$	−5.29976e10			−0.334302			−0.167151	+	0.985931i	$0.553457\pi$
$632$	−4.50408e9	+	2.09781e10i	−0.0282318	+	0.131492i
$633$		−	1.29395e11i		−	0.805937i
$634$	1.68087e11	+	1.93629e11i	1.04034	+	1.19843i
$635$	−5.40193e10	−	5.40193e10i	−0.332242	−	0.332242i
$636$	2.13133e10	−	1.50160e11i	0.130263	−	0.917752i
$637$	−1.30427e10	−	1.30427e10i	−0.0792157	−	0.0792157i
$638$	−3.30490e10	+	4.68018e11i	−0.199469	+	2.82475i
$639$			5.87194e10i			0.352191i
$640$	−5.69579e10	+	1.71158e10i	−0.339496	+	0.102018i
$641$	2.71775e11			1.60982			0.804909	−	0.593398i	$-0.202214\pi$
$641$	2.71775e11			1.60982			0.804909	+	0.593398i	$0.202214\pi$
$642$	−2.73193e10	−	1.92915e9i	−0.160816	−	0.0113560i
$643$	−2.29408e11	+	2.29408e11i	−1.34204	+	1.34204i	−0.448004	+	0.894032i	$0.647865\pi$
$643$	−2.29408e11	+	2.29408e11i	−1.34204	+	1.34204i	−0.894032	+	0.448004i	$0.852135\pi$
$644$	1.11437e11	+	1.58171e10i	0.647868	+	0.0919566i
$645$	7.79301e9	−	7.79301e9i	0.0450263	−	0.0450263i
$646$	2.63332e11	−	2.28595e11i	1.51207	−	1.31261i
$647$	−9.52693e9			−0.0543670			−0.0271835	−	0.999630i	$-0.508654\pi$
$647$	−9.52693e9			−0.0543670			−0.0271835	+	0.999630i	$0.508654\pi$
$648$	1.91545e10	+	4.11255e9i	0.108635	+	0.0233244i
$649$		−	5.68191e10i		−	0.320269i
$650$	8.83680e10	−	7.67110e10i	0.495041	−	0.429738i
$651$	−7.92180e10	−	7.92180e10i	−0.441062	−	0.441062i
$652$	−6.02187e10	+	4.52489e10i	−0.333228	+	0.250391i
$653$	3.73694e9	+	3.73694e9i	0.0205525	+	0.0205525i	0.717308	−	0.696756i	$-0.245374\pi$
$653$	3.73694e9	+	3.73694e9i	0.0205525	+	0.0205525i	−0.696756	+	0.717308i	$0.745374\pi$
$654$	−1.42995e11	−	1.00975e10i	−0.781643	−	0.0551955i
$655$		−	3.73017e10i		−	0.202658i
$656$	9.76861e10	−	3.37185e11i	0.527494	−	1.82076i
$657$	−1.30719e10			−0.0701578
$658$	5.10316e9	−	7.22677e10i	0.0272230	−	0.385514i
$659$	−8.41113e10	+	8.41113e10i	−0.445977	+	0.445977i	−0.894015	−	0.448038i	$-0.852123\pi$
$659$	−8.41113e10	+	8.41113e10i	−0.445977	+	0.445977i	0.448038	+	0.894015i	$0.352123\pi$
$660$	−5.28797e10	+	3.97343e10i	−0.278685	+	0.209406i
$661$	7.13768e10	−	7.13768e10i	0.373897	−	0.373897i	−0.494998	−	0.868894i	$-0.664831\pi$
$661$	7.13768e10	−	7.13768e10i	0.373897	−	0.373897i	0.868894	+	0.494998i	$0.164831\pi$
$662$	−6.13519e10	−	7.06750e10i	−0.319445	−	0.367988i
$663$	1.48592e11			0.769025
$664$	−1.32482e11	+	8.56483e10i	−0.681528	+	0.440602i
$665$			7.20629e10i			0.368490i
$666$	2.45407e10	+	2.82699e10i	0.124735	+	0.143690i
$667$	1.65096e11	+	1.65096e11i	0.834131	+	0.834131i
$668$	2.97706e11	+	4.22556e10i	1.49514	+	0.212216i
$669$	3.00372e10	+	3.00372e10i	0.149953	+	0.149953i
$670$	−1.78172e9	+	2.52315e10i	−0.00884178	+	0.125212i
$671$		−	1.99229e11i		−	0.982796i
$672$	−9.85690e10	+	4.55534e10i	−0.483352	+	0.223380i
$673$	7.06195e10			0.344242			0.172121	−	0.985076i	$-0.444938\pi$
$673$	7.06195e10			0.344242			0.172121	+	0.985076i	$0.444938\pi$
$674$	7.71702e10	+	5.44935e9i	0.373947	+	0.0264062i
$675$	−2.46999e10	+	2.46999e10i	−0.118982	+	0.118982i
$676$	1.28493e10	−	9.05279e10i	0.0615307	−	0.433507i
$677$	−1.97541e11	+	1.97541e11i	−0.940379	+	0.940379i	−0.998320	−	0.0579414i	$-0.981546\pi$
$677$	−1.97541e11	+	1.97541e11i	−0.940379	+	0.940379i	0.0579414	+	0.998320i	$0.481546\pi$
$678$	−1.07793e11	+	9.35739e10i	−0.510121	+	0.442829i
$679$	−4.02342e10			−0.189285
$680$	1.13080e11	−	7.31056e10i	0.528874	−	0.341913i
$681$		−	1.56253e11i		−	0.726510i
$682$	−3.25959e11	+	2.82960e11i	−1.50670	+	1.30794i
$683$	1.58883e11	+	1.58883e11i	0.730120	+	0.730120i	0.970643	−	0.240523i	$-0.0773190\pi$
$683$	1.58883e11	+	1.58883e11i	0.730120	+	0.730120i	−0.240523	+	0.970643i	$0.577319\pi$
$684$	−4.94010e10	−	6.57444e10i	−0.225689	−	0.300355i
$685$	3.65469e10	+	3.65469e10i	0.165993	+	0.165993i
$686$	−2.34181e11	−	1.65366e10i	−1.05744	−	0.0746708i
$687$			1.69281e11i			0.759944i
$688$	−3.36285e10	−	6.10611e10i	−0.150091	−	0.272528i
$689$	−2.71281e11			−1.20377
$690$	−2.31856e9	+	3.28339e10i	−0.0102287	+	0.144853i
$691$	2.89532e11	−	2.89532e11i	1.26994	−	1.26994i	0.323829	−	0.946116i	$-0.395030\pi$
$691$	2.89532e11	−	2.89532e11i	1.26994	−	1.26994i	0.946116	−	0.323829i	$-0.104970\pi$
$692$	−7.93655e10	−	1.05622e11i	−0.346105	−	0.460607i
$693$	−8.53936e10	+	8.53936e10i	−0.370248	+	0.370248i
$694$	−1.08797e11	−	1.25330e11i	−0.469007	−	0.540278i
$695$	1.43963e11			0.617036
$696$	−2.20232e11	−	4.72846e10i	−0.938519	−	0.201503i
$697$			7.94805e11i			3.36767i
$698$	−6.31691e10	−	7.27683e10i	−0.266123	−	0.306563i
$699$	−5.85974e10	−	5.85974e10i	−0.245454	−	0.245454i
$700$	2.72078e10	−	1.91689e11i	0.113319	−	0.798371i
$701$	2.09157e11	+	2.09157e11i	0.866163	+	0.866163i	0.992045	−	0.125882i	$-0.0401761\pi$
$701$	2.09157e11	+	2.09157e11i	0.866163	+	0.866163i	−0.125882	+	0.992045i	$0.540176\pi$
$702$	2.46835e9	−	3.49552e10i	0.0101639	−	0.143934i
$703$		−	1.57141e11i		−	0.643383i
$704$	1.48325e11	+	3.91195e11i	0.603843	+	1.59259i
$705$	2.11868e10			0.0857647
$706$	3.27312e11	+	2.31131e10i	1.31748	+	0.0930334i
$707$	1.33507e11	−	1.33507e11i	0.534349	−	0.534349i
$708$	2.70076e10	+	3.83338e9i	0.107486	+	0.0152563i
$709$	1.17973e11	−	1.17973e11i	0.466873	−	0.466873i	−0.434027	−	0.900900i	$-0.642908\pi$
$709$	1.17973e11	−	1.17973e11i	0.466873	−	0.466873i	0.900900	+	0.434027i	$0.142908\pi$
$710$	7.18750e10	−	6.23937e10i	0.282842	−	0.245531i
$711$	−1.14562e10			−0.0448294
$712$	3.76786e10	−	1.75491e11i	0.146614	−	0.682866i
$713$			2.14800e11i			0.831144i
$714$	1.85654e11	−	1.61163e11i	0.714350	−	0.620117i
$715$	8.36589e10	+	8.36589e10i	0.320102	+	0.320102i
$716$	−1.94070e11	+	1.45826e11i	−0.738426	+	0.554861i
$717$	−1.51951e10	−	1.51951e10i	−0.0574947	−	0.0574947i
$718$	6.38489e10	+	4.50867e9i	0.240246	+	0.0169649i
$719$		−	1.47736e11i		−	0.552803i	−0.961042	−	0.276401i	$-0.910858\pi$
$719$		−	1.47736e11i		−	0.552803i	0.961042	−	0.276401i	$-0.0891419\pi$
$720$	−1.53192e10	−	2.78158e10i	−0.0570040	−	0.103505i
$721$	−9.39620e10			−0.347705
$722$	−5.17453e9	+	7.32783e10i	−0.0190424	+	0.269666i
$723$	−5.33398e10	+	5.33398e10i	−0.195208	+	0.195208i
$724$	−1.13477e11	+	8.52678e10i	−0.413004	+	0.310335i
$725$	2.83991e11	−	2.83991e11i	1.02790	−	1.02790i
$726$	1.99875e11	+	2.30248e11i	0.719468	+	0.828799i
$727$	−1.66146e11			−0.594775			−0.297387	−	0.954757i	$-0.596115\pi$
$727$	−1.66146e11			−0.594775			−0.297387	+	0.954757i	$0.596115\pi$
$728$	1.05449e11	+	1.63109e11i	0.375419	+	0.580702i
$729$			1.04604e10i			0.0370370i
$730$	1.38898e10	+	1.60005e10i	0.0489108	+	0.0563433i
$731$	1.11600e11	+	1.11600e11i	0.390837	+	0.390837i
$732$	9.46990e10	+	1.34413e10i	0.329838	+	0.0468163i
$733$	−3.41230e11	−	3.41230e11i	−1.18204	−	1.18204i	−0.979215	−	0.202823i	$-0.934989\pi$
$733$	−3.41230e11	−	3.41230e11i	−1.18204	−	1.18204i	−0.202823	−	0.979215i	$-0.565011\pi$
$734$	−3.44401e9	+	4.87719e10i	−0.0118654	+	0.168030i
$735$		−	8.92476e9i		−	0.0305807i
$736$	1.95395e11	+	7.18761e10i	0.665888	+	0.244948i
$737$	1.77933e11			0.603098
$738$	1.86973e11	+	1.32030e10i	0.630307	+	0.0445090i
$739$	−2.85717e11	+	2.85717e11i	−0.957985	+	0.957985i	−0.999152	−	0.0411670i	$-0.986892\pi$
$739$	−2.85717e11	+	2.85717e11i	−0.957985	+	0.957985i	0.0411670	+	0.999152i	$0.486892\pi$
$740$	8.52725e9	−	6.00776e10i	0.0284369	−	0.200348i
$741$	−1.04012e11	+	1.04012e11i	−0.344992	+	0.344992i
$742$	−3.38945e11	+	2.94233e11i	−1.11818	+	0.970680i
$743$	5.52842e11			1.81403			0.907017	−	0.421094i	$-0.138354\pi$
$743$	5.52842e11			1.81403			0.907017	+	0.421094i	$0.138354\pi$
$744$	−1.12507e11	−	1.74027e11i	−0.367188	−	0.567970i
$745$		−	2.61231e9i		−	0.00848009i
$746$	3.50790e10	−	3.04516e10i	0.113264	−	0.0983229i
$747$	−5.95608e10	−	5.95608e10i	−0.191284	−	0.191284i
$748$	−5.69017e11	−	7.57266e11i	−1.81769	−	2.41903i
$749$	5.73115e10	+	5.73115e10i	0.182102	+	0.182102i
$750$	1.21076e11	+	8.54976e9i	0.382661	+	0.0270215i
$751$			1.14996e11i			0.361512i	0.983528	+	0.180756i	$0.0578545\pi$
$751$			1.14996e11i			0.361512i	−0.983528	+	0.180756i	$0.942145\pi$
$752$	3.72904e10	−	1.28716e11i	0.116607	−	0.402496i
$753$	1.34849e11			0.419439
$754$	−2.83802e10	+	4.01902e11i	−0.0878072	+	1.24347i
$755$	7.56345e10	−	7.56345e10i	0.232773	−	0.232773i
$756$	−3.48286e10	−	4.63511e10i	−0.106623	−	0.141897i
$757$	3.14721e10	−	3.14721e10i	0.0958390	−	0.0958390i	−0.657562	−	0.753401i	$-0.728412\pi$
$757$	3.14721e10	−	3.14721e10i	0.0958390	−	0.0958390i	0.753401	+	0.657562i	$0.228412\pi$
$758$	−2.59600e10	−	2.99048e10i	−0.0786371	−	0.0905868i
$759$	2.31546e11			0.697701
$760$	−2.79817e10	+	1.30327e11i	−0.0838727	+	0.390644i
$761$			3.65451e11i			1.08966i	0.838547	+	0.544829i	$0.183406\pi$
$761$			3.65451e11i			1.08966i	−0.838547	+	0.544829i	$0.816594\pi$
$762$	−1.69131e11	−	1.94832e11i	−0.501652	−	0.577883i
$763$	2.99979e11	+	2.99979e11i	0.885100	+	0.885100i
$764$	5.93281e10	−	4.17988e11i	0.174135	−	1.22685i
$765$	5.08384e10	+	5.08384e10i	0.148438	+	0.148438i
$766$	1.07350e10	−	1.52023e11i	0.0311809	−	0.441564i
$767$		−	4.87924e10i		−	0.140984i
$768$	−1.95952e11	+	4.41104e10i	−0.563256	+	0.126793i
$769$	1.60687e11			0.459490			0.229745	−	0.973251i	$-0.426211\pi$
$769$	1.60687e11			0.459490			0.229745	+	0.973251i	$0.426211\pi$
$770$	1.95262e11	+	1.37884e10i	0.555464	+	0.0392239i
$771$	−1.13243e11	+	1.13243e11i	−0.320475	+	0.320475i
$772$	−6.22566e11	−	8.83652e10i	−1.75273	−	0.248778i
$773$	−4.70343e11	+	4.70343e11i	−1.31734	+	1.31734i	−0.401460	+	0.915876i	$0.631497\pi$
$773$	−4.70343e11	+	4.70343e11i	−1.31734	+	1.31734i	−0.915876	+	0.401460i	$0.868503\pi$
$774$	2.81071e10	−	2.43993e10i	0.0783162	−	0.0679852i
$775$	3.69489e11			1.02422
$776$	−7.27645e10	−	1.56228e10i	−0.200665	−	0.0430836i
$777$		−	1.10788e11i		−	0.303954i
$778$	4.21447e11	−	3.65852e11i	1.15034	−	0.998590i
$779$	−5.56350e11	−	5.56350e11i	−1.51077	−	1.51077i
$780$	−4.54095e10	+	3.41211e10i	−0.122678	+	0.0921818i
$781$	−4.73433e11	−	4.73433e11i	−1.27249	−	1.27249i
$782$	−4.70199e11	−	3.32030e10i	−1.25735	−	0.0887871i
$783$		−	1.20269e11i		−	0.319969i
$784$	−5.42205e10	−	1.57083e10i	−0.143516	−	0.0415781i
$785$	−1.04572e11			−0.275383
$786$	8.87363e9	−	1.25663e11i	0.0232494	−	0.329243i
$787$	1.00923e11	−	1.00923e11i	0.263082	−	0.263082i	−0.563223	−	0.826305i	$-0.690439\pi$
$787$	1.00923e11	−	1.00923e11i	0.263082	−	0.263082i	0.826305	+	0.563223i	$0.190439\pi$
$788$	4.84486e11	−	3.64047e11i	1.25654	−	0.944176i
$789$	−1.84599e11	+	1.84599e11i	−0.476346	+	0.476346i
$790$	1.21731e10	+	1.40229e10i	0.0312531	+	0.0360023i
$791$	4.22435e11			1.07908
$792$	−1.87594e11	+	1.21278e11i	−0.476780	+	0.308235i
$793$		−	1.71085e11i		−	0.432632i
$794$	1.49760e11	+	1.72517e11i	0.376802	+	0.434061i
$795$	−9.28148e10	−	9.28148e10i	−0.232353	−	0.232353i
$796$	−5.67899e11	−	8.06060e10i	−1.41455	−	0.200777i
$797$	−4.91042e11	−	4.91042e11i	−1.21699	−	1.21699i	−0.968683	−	0.248303i	$-0.920127\pi$
$797$	−4.91042e11	−	4.91042e11i	−1.21699	−	1.21699i	−0.248303	−	0.968683i	$-0.579873\pi$
$798$	−1.71429e10	+	2.42766e11i	−0.0422739	+	0.598656i
$799$			3.03406e11i			0.744454i
$800$	1.23638e11	−	3.36109e11i	0.301850	−	0.820578i
$801$	9.58363e10			0.232809
$802$	−2.84036e11	−	2.00571e10i	−0.686556	−	0.0484809i
$803$	1.05394e11	−	1.05394e11i	0.253485	−	0.253485i
$804$	−1.20045e10	+	8.45765e10i	−0.0287291	+	0.202407i
$805$	6.88801e10	−	6.88801e10i	0.164025	−	0.164025i
$806$	−2.79912e11	+	2.42987e11i	−0.663255	+	0.575762i
$807$	−9.45257e9			−0.0222872
$808$	2.93290e11	−	1.89609e11i	0.688100	−	0.444851i
$809$			4.34749e11i			1.01495i	0.861667	+	0.507475i	$0.169421\pi$
$809$			4.34749e11i			1.01495i	−0.861667	+	0.507475i	$0.830579\pi$
$810$	1.28039e10	−	1.11149e10i	0.0297442	−	0.0258205i
$811$	−7.79576e10	−	7.79576e10i	−0.180208	−	0.180208i	0.611238	−	0.791447i	$-0.290672\pi$
$811$	−7.79576e10	−	7.79576e10i	−0.180208	−	0.180208i	−0.791447	+	0.611238i	$0.790672\pi$
$812$	4.00447e11	+	5.32927e11i	0.921130	+	1.22587i
$813$	−2.69937e11	−	2.69937e11i	−0.617875	−	0.617875i
$814$	−4.25792e11	−	3.00672e10i	−0.969840	−	0.0684850i
$815$			6.51903e10i			0.147758i
$816$	3.98338e11	−	2.19379e11i	0.898444	−	0.494805i
$817$	−1.56237e11			−0.350667
$818$	5.37866e10	−	7.61691e11i	0.120133	−	1.70124i
$819$	−7.33302e10	+	7.33302e10i	−0.162985	+	0.162985i
$820$	−1.82511e11	−	2.42892e11i	−0.403677	−	0.537226i
$821$	−3.90502e11	+	3.90502e11i	−0.859510	+	0.859510i	−0.991280	−	0.131770i	$-0.957934\pi$
$821$	−3.90502e11	+	3.90502e11i	−0.859510	+	0.859510i	0.131770	+	0.991280i	$0.457934\pi$
$822$	1.14426e11	+	1.31814e11i	0.250632	+	0.288718i
$823$	−1.27217e11			−0.277297			−0.138648	−	0.990342i	$-0.544276\pi$
$823$	−1.27217e11			−0.277297			−0.138648	+	0.990342i	$0.544276\pi$
$824$	−1.69932e11	−	3.64851e10i	−0.368610	−	0.0791419i
$825$		−	3.98294e11i		−	0.859781i
$826$	−5.29205e10	−	6.09623e10i	−0.113685	−	0.130961i
$827$	−4.50339e11	−	4.50339e11i	−0.962759	−	0.962759i	0.0365718	−	0.999331i	$-0.488356\pi$
$827$	−4.50339e11	−	4.50339e11i	−0.962759	−	0.962759i	−0.999331	+	0.0365718i	$0.988356\pi$
$828$	−1.56216e10	+	1.10060e11i	−0.0332356	+	0.234157i
$829$	3.38841e11	+	3.38841e11i	0.717427	+	0.717427i	0.968078	−	0.250651i	$-0.0806446\pi$
$829$	3.38841e11	+	3.38841e11i	0.717427	+	0.717427i	−0.250651	+	0.968078i	$0.580645\pi$
$830$	−9.61720e9	+	1.36193e11i	−0.0202645	+	0.286973i
$831$			3.39173e10i			0.0711241i
$832$	1.27372e11	+	3.35932e11i	0.265815	+	0.701064i
$833$	1.27807e11			0.265446
$834$	4.84984e11	+	3.42470e10i	1.00245	+	0.0707877i
$835$	1.84014e11	−	1.84014e11i	0.378534	−	0.378534i
$836$	9.28376e11	+	1.31771e11i	1.90064	+	0.269771i
$837$	7.82388e10	−	7.82388e10i	0.159412	−	0.159412i
$838$	5.10485e11	−	4.43145e11i	1.03516	−	0.898606i
$839$	4.79274e11			0.967244			0.483622	−	0.875277i	$-0.339321\pi$
$839$	4.79274e11			0.967244			0.483622	+	0.875277i	$0.339321\pi$
$840$	−1.97277e10	+	9.18832e10i	−0.0396240	+	0.184552i
$841$			8.82566e11i			1.76426i
$842$	−2.95561e11	+	2.56572e11i	−0.588029	+	0.510460i
$843$	1.62924e11	+	1.62924e11i	0.322608	+	0.322608i
$844$	−5.66275e11	+	4.25505e11i	−1.11598	+	0.838561i
$845$	−5.59559e10	−	5.59559e10i	−0.109754	−	0.109754i
$846$	7.13744e10	+	5.04008e9i	0.139335	+	0.00983911i
$847$		−	9.02326e11i		−	1.75319i
$848$	−7.27238e11	+	4.00516e11i	−1.40635	+	0.774526i
$849$	−5.39202e10			−0.103782
$850$	−5.71142e10	+	8.08814e11i	−0.109413	+	1.54943i
$851$	−1.50201e11	+	1.50201e11i	−0.286388	+	0.286388i
$852$	2.56976e11	−	1.93094e11i	0.487680	−	0.366447i
$853$	4.70031e11	−	4.70031e11i	0.887831	−	0.887831i	−0.106483	−	0.994314i	$-0.533959\pi$
$853$	4.70031e11	−	4.70031e11i	0.887831	−	0.887831i	0.994314	+	0.106483i	$0.0339590\pi$
$854$	−1.85560e11	−	2.13757e11i	−0.348860	−	0.401873i
$855$	−7.11721e10			−0.133182
$856$	8.13951e10	+	1.25903e11i	0.151601	+	0.234499i
$857$		−	3.64332e11i		−	0.675420i	−0.941250	−	0.337710i	$-0.890348\pi$
$857$		−	3.64332e11i		−	0.675420i	0.941250	−	0.337710i	$-0.109652\pi$
$858$	2.61930e11	+	3.01733e11i	0.483321	+	0.556767i
$859$	3.71572e11	+	3.71572e11i	0.682449	+	0.682449i	0.960551	−	0.278102i	$-0.0897054\pi$
$859$	3.71572e11	+	3.71572e11i	0.682449	+	0.682449i	−0.278102	+	0.960551i	$0.589705\pi$
$860$	−5.97317e10	−	8.47814e9i	−0.109197	−	0.0154991i
$861$	−3.92237e11	−	3.92237e11i	−0.713734	−	0.713734i
$862$	−1.48339e10	+	2.10069e11i	−0.0268675	+	0.380480i
$863$		−	2.41713e11i		−	0.435769i	−0.975975	−	0.217885i	$-0.930084\pi$
$863$		−	2.41713e11i		−	0.435769i	0.975975	−	0.217885i	$-0.0699156\pi$
$864$	−4.49904e10	−	9.73506e10i	−0.0807355	−	0.174696i
$865$	−1.14342e11			−0.204241
$866$	5.80934e11	+	4.10225e10i	1.03289	+	0.0729374i
$867$	−4.97359e11	+	4.97359e11i	−0.880225	+	0.880225i
$868$	−8.61825e10	+	6.07188e11i	−0.151824	+	1.06966i
$869$	9.23675e10	−	9.23675e10i	0.161972	−	0.161972i
$870$	−1.47215e11	+	1.27795e11i	−0.256965	+	0.223068i
$871$	1.52797e11			0.265487
$872$	4.26037e11	+	6.58999e11i	0.736854	+	1.13977i
$873$		−	3.97369e10i		−	0.0684128i
$874$	3.52373e11	−	3.05890e11i	0.603889	−	0.524228i
$875$	−2.53998e11	−	2.53998e11i	−0.433309	−	0.433309i
$876$	4.29859e10	+	5.72070e10i	0.0729977	+	0.0971477i
$877$	−9.18716e9	−	9.18716e9i	−0.0155304	−	0.0155304i	0.699299	−	0.714829i	$-0.253496\pi$
$877$	−9.18716e9	−	9.18716e9i	−0.0155304	−	0.0155304i	−0.714829	+	0.699299i	$0.753496\pi$
$878$	1.10046e12	+	7.77085e10i	1.85181	+	0.130765i
$879$			3.43234e11i			0.574956i
$880$	3.47782e11	+	1.00756e11i	0.579931	+	0.168012i
$881$	−9.87034e9			−0.0163843			−0.00819216	−	0.999966i	$-0.502608\pi$
$881$	−9.87034e9			−0.0163843			−0.00819216	+	0.999966i	$0.502608\pi$
$882$	2.12309e9	−	3.00659e10i	0.00350828	−	0.0496820i
$883$	3.36887e11	−	3.36887e11i	0.554168	−	0.554168i	−0.373473	−	0.927641i	$-0.621833\pi$
$883$	3.36887e11	−	3.36887e11i	0.554168	−	0.554168i	0.927641	+	0.373473i	$0.121833\pi$
$884$	−4.88633e11	−	6.50288e11i	−0.800155	−	1.06487i
$885$	1.66936e10	−	1.66936e10i	0.0272130	−	0.0272130i
$886$	−1.61123e11	−	1.85607e11i	−0.261470	−	0.301203i
$887$	−3.26209e11			−0.526989			−0.263495	−	0.964661i	$-0.584875\pi$
$887$	−3.26209e11			−0.526989			−0.263495	+	0.964661i	$0.584875\pi$
$888$	4.30184e10	−	2.00362e11i	0.0691835	−	0.322228i
$889$			7.63532e11i			1.22242i
$890$	−1.01833e11	−	1.17308e11i	−0.162304	−	0.186968i
$891$	−8.43381e10	−	8.43381e10i	−0.133817	−	0.133817i
$892$	3.26779e10	−	2.30228e11i	0.0516173	−	0.363663i
$893$	−2.12380e11	−	2.12380e11i	−0.333970	−	0.333970i
$894$	6.21437e8	−	8.80040e9i	0.000972853	−	0.0137769i
$895$			2.10092e11i			0.327430i
$896$	5.23495e11	+	2.81573e11i	0.812233	+	0.436877i
$897$	1.98836e11			0.307132
$898$	3.03159e10	+	2.14075e9i	0.0466193	+	0.00329201i
$899$	−8.99561e11	+	8.99561e11i	−1.37718	+	1.37718i
$900$	1.89320e11	+	2.68715e10i	0.288553	+	0.0409564i
$901$	1.32916e12	−	1.32916e12i	2.01687	−	2.01687i
$902$	−1.61394e12	+	1.40104e12i	−2.43816	+	2.11653i
$903$	−1.10150e11			−0.165666
$904$	7.63983e11	+	1.64030e11i	1.14396	+	0.245612i
$905$			1.22846e11i			0.183132i
$906$	2.72791e11	−	2.36806e11i	0.404872	−	0.351463i
$907$	6.89442e11	+	6.89442e11i	1.01875	+	1.01875i	0.999821	+	0.0189314i	$0.00602641\pi$
$907$	6.89442e11	+	6.89442e11i	1.01875	+	1.01875i	0.0189314	+	0.999821i	$0.493974\pi$
$908$	−6.83819e11	+	5.13829e11i	−1.00600	+	0.755918i
$909$	1.31856e11	+	1.31856e11i	0.193128	+	0.193128i
$910$	1.67678e11	+	1.18405e10i	0.244518	+	0.0172666i
$911$		−	6.22304e11i		−	0.903501i	−0.892144	−	0.451751i	$-0.850800\pi$
$911$		−	6.22304e11i		−	0.903501i	0.892144	−	0.451751i	$-0.149200\pi$
$912$	−1.25269e11	+	4.32392e11i	−0.181077	+	0.625026i
$913$	9.60435e11			1.38224
$914$	−2.46528e10	+	3.49117e11i	−0.0353249	+	0.500248i
$915$	5.85341e10	−	5.85341e10i	0.0835073	−	0.0835073i
$916$	7.40833e11	−	5.56669e11i	1.05230	−	0.790706i
$917$	−2.63619e11	+	2.63619e11i	−0.372821	+	0.372821i
$918$	1.59171e11	+	1.83359e11i	0.224127	+	0.258185i
$919$	−9.92923e11			−1.39205			−0.696023	−	0.718020i	$-0.745049\pi$
$919$	−9.92923e11			−1.39205			−0.696023	+	0.718020i	$0.745049\pi$
$920$	1.51317e11	−	9.78251e10i	0.211220	−	0.136552i
$921$			2.57111e11i			0.357340i
$922$	−2.07861e10	−	2.39447e10i	−0.0287640	−	0.0331349i
$923$	−4.06552e11	−	4.06552e11i	−0.560157	−	0.560157i
$924$	6.54523e11	+	9.29011e10i	0.897918	+	0.127448i
$925$	2.58369e11	+	2.58369e11i	0.352917	+	0.352917i
$926$	3.13770e10	−	4.44341e11i	0.0426744	−	0.604328i
$927$		−	9.28005e10i		−	0.125670i
$928$	5.17283e11	+	1.11930e12i	0.697487	+	1.50923i
$929$	−4.47891e11			−0.601326			−0.300663	−	0.953730i	$-0.597208\pi$
$929$	−4.47891e11			−0.601326			−0.300663	+	0.953730i	$0.597208\pi$
$930$	−1.78902e11	−	1.26331e10i	−0.239157	−	0.0168880i
$931$	−8.94631e10	+	8.94631e10i	−0.119082	+	0.119082i
$932$	−6.37490e10	+	4.49136e11i	−0.0844909	+	0.595270i
$933$	3.09770e11	−	3.09770e11i	0.408802	−	0.408802i
$934$	−4.08810e11	+	3.54882e11i	−0.537198	+	0.466334i
$935$	−8.19784e11			−1.07264
$936$	−1.61093e11	+	1.04145e11i	−0.209881	+	0.135686i
$937$		−	7.44085e11i		−	0.965304i	−0.875812	−	0.482652i	$-0.839674\pi$
$937$		−	7.44085e11i		−	0.965304i	0.875812	−	0.482652i	$-0.160326\pi$
$938$	1.90908e11	−	1.65725e11i	0.246612	−	0.214080i
$939$	−5.05404e11	−	5.05404e11i	−0.650095	−	0.650095i
$940$	−6.96713e10	−	9.27207e10i	−0.0892365	−	0.118759i
$941$	2.93951e11	+	2.93951e11i	0.374901	+	0.374901i	0.869258	−	0.494358i	$-0.164597\pi$
$941$	2.93951e11	+	2.93951e11i	0.374901	+	0.374901i	−0.494358	+	0.869258i	$0.664597\pi$
$942$	−3.52283e11	−	2.48764e10i	−0.447392	−	0.0315925i
$943$			1.06356e12i			1.34497i
$944$	−7.20364e10	−	1.30800e11i	−0.0907118	−	0.164710i
$945$	−5.01777e10			−0.0629193
$946$	−2.98940e10	+	4.23340e11i	−0.0373267	+	0.528597i
$947$	3.07708e11	−	3.07708e11i	0.382595	−	0.382595i	−0.489441	−	0.872036i	$-0.662799\pi$
$947$	3.07708e11	−	3.07708e11i	0.382595	−	0.382595i	0.872036	+	0.489441i	$0.162799\pi$
$948$	3.76730e10	+	5.01364e10i	0.0466441	+	0.0620755i
$949$	9.05050e10	−	9.05050e10i	0.111585	−	0.111585i
$950$	−5.26178e11	−	6.06136e11i	−0.646008	−	0.744176i
$951$	7.49440e11			0.916252
$952$	−1.31582e12	−	2.82511e11i	−1.60195	−	0.343944i
$953$		−	6.85820e11i		−	0.831455i	−0.909489	−	0.415727i	$-0.863527\pi$
$953$		−	6.85820e11i		−	0.831455i	0.909489	−	0.415727i	$-0.136473\pi$
$954$	−2.90596e11	−	3.34755e11i	−0.350830	−	0.404142i
$955$	−2.58361e11	−	2.58361e11i	−0.310609	−	0.310609i
$956$	−1.65310e10	+	1.16467e11i	−0.0197910	+	0.139435i
$957$	9.69688e11	+	9.69688e11i	1.15607	+	1.15607i
$958$	8.26652e10	−	1.17065e12i	0.0981433	−	1.38984i
$959$		−	5.16570e11i		−	0.610738i
$960$	−7.13557e10	+	1.58512e11i	−0.0840125	+	0.186629i
$961$	−3.17491e11			−0.372252
$962$	−3.65642e11	−	2.58197e10i	−0.426929	−	0.0301474i
$963$	−5.66030e10	+	5.66030e10i	−0.0658165	+	0.0658165i
$964$	4.08838e11	+	5.80292e10i	0.473416	+	0.0671953i
$965$	−3.84812e11	+	3.84812e11i	−0.443751	+	0.443751i
$966$	2.48430e11	−	2.15658e11i	0.285296	−	0.247661i
$967$	−1.02247e11			−0.116936			−0.0584678	−	0.998289i	$-0.518621\pi$
$967$	−1.02247e11			−0.116936			−0.0584678	+	0.998289i	$0.518621\pi$
$968$	3.50370e11	−	1.63187e12i	0.399048	−	1.85860i
$969$		−	1.01922e12i		−	1.15604i
$970$	−4.86397e10	+	4.22234e10i	−0.0549419	+	0.0476943i
$971$	1.47173e11	+	1.47173e11i	0.165558	+	0.165558i	0.785024	−	0.619466i	$-0.212651\pi$
$971$	1.47173e11	+	1.47173e11i	0.165558	+	0.165558i	−0.619466	+	0.785024i	$0.712651\pi$
$972$	4.57781e10	−	3.43981e10i	0.0512853	−	0.0385363i
$973$	−1.01742e12	−	1.01742e12i	−1.13513	−	1.13513i
$974$	1.30994e12	+	9.25007e10i	1.45551	+	0.102780i
$975$		−	3.42028e11i		−	0.378480i
$976$	−2.52587e11	−	4.58636e11i	−0.278363	−	0.505439i
$977$	5.20634e11			0.571418			0.285709	−	0.958316i	$-0.407771\pi$
$977$	5.20634e11			0.571418			0.285709	+	0.958316i	$0.407771\pi$
$978$	−1.55080e10	+	2.19614e11i	−0.0169512	+	0.240051i
$979$	−7.72694e11	+	7.72694e11i	−0.841157	+	0.841157i
$980$	−3.90578e10	+	2.93484e10i	−0.0423452	+	0.0318186i
$981$	−2.96271e11	+	2.96271e11i	−0.319899	+	0.319899i
$982$	−2.02635e11	−	2.33428e11i	−0.217906	−	0.251019i
$983$	−6.78607e11			−0.726782			−0.363391	−	0.931637i	$-0.618381\pi$
$983$	−6.78607e11			−0.726782			−0.363391	+	0.931637i	$0.618381\pi$
$984$	−5.57065e11	−	8.61674e11i	−0.594190	−	0.919099i
$985$		−	5.24484e11i		−	0.557170i
$986$	−1.83009e12	−	2.10820e12i	−1.93627	−	2.23050i
$987$	−1.49732e11	−	1.49732e11i	−0.157777	−	0.157777i
$988$	7.97226e11	+	1.13156e11i	0.836669	+	0.118754i
$989$	1.49336e11	+	1.49336e11i	0.156092	+	0.156092i
$990$	−1.36180e10	+	1.92849e11i	−0.0141766	+	0.200760i
$991$		−	1.30297e12i		−	1.35095i	−0.737381	−	0.675477i	$-0.763938\pi$
$991$		−	1.30297e12i		−	1.35095i	0.737381	−	0.675477i	$-0.236062\pi$
$992$	−3.91631e11	+	1.06465e12i	−0.404418	+	1.09941i
$993$	−2.73547e11			−0.281342
$994$	−9.48905e11	−	6.70066e10i	−0.972025	−	0.0686392i
$995$	−3.51022e11	+	3.51022e11i	−0.358131	+	0.358131i
$996$	−6.47971e10	+	4.56520e11i	−0.0658443	+	0.463898i
$997$	−8.97732e11	+	8.97732e11i	−0.908586	+	0.908586i	−0.996158	−	0.0875721i	$-0.972089\pi$
$997$	−8.97732e11	+	8.97732e11i	−0.908586	+	0.908586i	0.0875721	+	0.996158i	$0.472089\pi$
$998$	7.16104e11	−	6.21640e11i	0.721862	−	0.626638i
$999$	1.09418e11			0.109857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.19.1	✓	64
4.3	odd	2		192.9.l.a.175.26		64
16.5	even	4		192.9.l.a.79.26		64
16.11	odd	4	inner	48.9.l.a.43.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.1	✓	64	1.1	even	1	trivial
48.9.l.a.43.1	yes	64	16.11	odd	4	inner
192.9.l.a.79.26		64	16.5	even	4
192.9.l.a.175.26		64	4.3	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.9603 - 1.12703i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(253.460 + 35.9753i) q^{4} +(156.665 - 156.665i) q^{5} +(565.044 - 490.507i) q^{6} -2214.37 q^{7} +(-4004.74 - 859.832i) q^{8} -2187.00i q^{9} +O(q^{10})\)	\(q+(-15.9603 - 1.12703i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(253.460 + 35.9753i) q^{4} +(156.665 - 156.665i) q^{5} +(565.044 - 490.507i) q^{6} -2214.37 q^{7} +(-4004.74 - 859.832i) q^{8} -2187.00i q^{9} +(-2676.98 + 2323.85i) q^{10} +(17633.0 + 17633.0i) q^{11} +(-9571.07 + 7191.79i) q^{12} +(15142.0 + 15142.0i) q^{13} +(35341.9 + 2495.66i) q^{14} +10361.2i q^{15} +(62947.6 + 18236.6i) q^{16} -148379. q^{17} +(-2464.81 + 34905.1i) q^{18} +(103863. - 103863. i) q^{19} +(45344.4 - 34072.2i) q^{20} +(73225.1 - 73225.1i) q^{21} +(-261554. - 301300. i) q^{22} -198550. q^{23} +(160862. - 103996. i) q^{24} +341537. i q^{25} +(-224605. - 258736. i) q^{26} +(72320.0 + 72320.0i) q^{27} +(-561254. - 79662.7i) q^{28} +(-831508. - 831508. i) q^{29} +(11677.4 - 165368. i) q^{30} -1.08184e6i q^{31} +(-984106. - 362004. i) q^{32} -1.16618e6 q^{33} +(2.36816e6 + 167227. i) q^{34} +(-346915. + 346915. i) q^{35} +(78678.0 - 554316. i) q^{36} +(756487. - 756487. i) q^{37} +(-1.77473e6 + 1.54062e6i) q^{38} -1.00144e6 q^{39} +(-762108. + 492697. i) q^{40} -5.35660e6i q^{41} +(-1.25122e6 + 1.08616e6i) q^{42} +(-752131. - 752131. i) q^{43} +(3.83490e6 + 5.10361e6i) q^{44} +(-342627. - 342627. i) q^{45} +(3.16892e6 + 223772. i) q^{46} -2.04481e6i q^{47} +(-2.68461e6 + 1.47851e6i) q^{48} -861361. q^{49} +(384922. - 5.45102e6i) q^{50} +(4.90660e6 - 4.90660e6i) q^{51} +(3.29315e6 + 4.38263e6i) q^{52} +(-8.95789e6 + 8.95789e6i) q^{53} +(-1.07274e6 - 1.23575e6i) q^{54} +5.52495e6 q^{55} +(8.86797e6 + 1.90399e6i) q^{56} +6.86908e6i q^{57} +(1.23340e7 + 1.42082e7i) q^{58} +(-1.61116e6 - 1.61116e6i) q^{59} +(-372749. + 2.62616e6i) q^{60} +(-5.64933e6 - 5.64933e6i) q^{61} +(-1.21927e6 + 1.72665e7i) q^{62} +4.84283e6i q^{63} +(1.52986e7 + 6.88680e6i) q^{64} +4.74445e6 q^{65} +(1.86125e7 + 1.31432e6i) q^{66} +(5.04547e6 - 5.04547e6i) q^{67} +(-3.76080e7 - 5.33797e6i) q^{68} +(6.56569e6 - 6.56569e6i) q^{69} +(5.92783e6 - 5.14586e6i) q^{70} -2.68493e7 q^{71} +(-1.88045e6 + 8.75836e6i) q^{72} -5.97707e6i q^{73} +(-1.29263e7 + 1.12212e7i) q^{74} +(-1.12940e7 - 1.12940e7i) q^{75} +(3.00615e7 - 2.25885e7i) q^{76} +(-3.90460e7 - 3.90460e7i) q^{77} +(1.59832e7 + 1.12865e6i) q^{78} -5.23833e6i q^{79} +(1.27187e7 - 7.00465e6i) q^{80} -4.78297e6 q^{81} +(-6.03704e6 + 8.54927e7i) q^{82} +(2.72340e7 - 2.72340e7i) q^{83} +(2.11939e7 - 1.59253e7i) q^{84} +(-2.32457e7 + 2.32457e7i) q^{85} +(1.11565e7 + 1.28519e7i) q^{86} +5.49928e7 q^{87} +(-5.54541e7 - 8.57769e7i) q^{88} +4.38209e7i q^{89} +(5.08226e6 + 5.85456e6i) q^{90} +(-3.35301e7 - 3.35301e7i) q^{91} +(-5.03245e7 - 7.14292e6i) q^{92} +(3.57745e7 + 3.57745e7i) q^{93} +(-2.30456e6 + 3.26357e7i) q^{94} -3.25433e7i q^{95} +(4.45133e7 - 2.05717e7i) q^{96} +1.81696e7 q^{97} +(1.37475e7 + 970778. i) q^{98} +(3.85634e7 - 3.85634e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) \) 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more