LMFDB - Embedded newform 14.8.c.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,8,Mod(9,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("14.9");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	14.c (of order $3$, 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:	$4.37339035678$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{2389})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 598x^{2} + 597x + 356409 $ x^4 - x^3 + 598x^2 + 597x + 356409
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.2
Root			$-11.9693 + 20.7315i$ of defining polynomial
Character	$\chi$	$=$	14.11
Dual form			14.8.c.a.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 - 6.92820i) q^{2} +(38.4387 - 66.5778i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(10.6226 + 18.3989i) q^{5} -615.019 q^{6} +(-642.284 - 641.104i) q^{7} +512.000 q^{8} +(-1861.57 - 3224.33i) q^{9} +O(q^{10})$	\(q+(-4.00000 - 6.92820i) q^{2} +(38.4387 - 66.5778i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(10.6226 + 18.3989i) q^{5} -615.019 q^{6} +(-642.284 - 641.104i) q^{7} +512.000 q^{8} +(-1861.57 - 3224.33i) q^{9} +(84.9808 - 147.191i) q^{10} +(-1633.07 + 2828.56i) q^{11} +(2460.08 + 4260.98i) q^{12} +10238.0 q^{13} +(-1872.57 + 7014.29i) q^{14} +1633.28 q^{15} +(-2048.00 - 3547.24i) q^{16} +(18264.6 - 31635.1i) q^{17} +(-14892.5 + 25794.6i) q^{18} +(16200.6 + 28060.3i) q^{19} -1359.69 q^{20} +(-67371.9 + 18118.6i) q^{21} +26129.1 q^{22} +(-8370.58 - 14498.3i) q^{23} +(19680.6 - 34087.8i) q^{24} +(38836.8 - 67267.3i) q^{25} +(-40951.9 - 70930.7i) q^{26} -118094. q^{27} +(56086.7 - 15083.6i) q^{28} +43984.4 q^{29} +(-6533.10 - 11315.7i) q^{30} +(-66921.6 + 115912. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(125546. + 217452. i) q^{33} -292233. q^{34} +(4972.88 - 18627.5i) q^{35} +238281. q^{36} +(289939. + 502188. i) q^{37} +(129605. - 224482. i) q^{38} +(393534. - 681621. i) q^{39} +(5438.77 + 9420.23i) q^{40} -532967. q^{41} +(395017. + 394291. i) q^{42} -365375. q^{43} +(-104517. - 181028. i) q^{44} +(39549.4 - 68501.5i) q^{45} +(-66964.6 + 115986. i) q^{46} +(103432. + 179149. i) q^{47} -314890. q^{48} +(1513.36 + 823542. i) q^{49} -621389. q^{50} +(-1.40413e6 - 2.43203e6i) q^{51} +(-327615. + 567446. i) q^{52} +(544104. - 942416. i) q^{53} +(472376. + 818179. i) q^{54} -69389.9 q^{55} +(-328849. - 328245. i) q^{56} +2.49092e6 q^{57} +(-175938. - 304733. i) q^{58} +(-80826.2 + 139995. i) q^{59} +(-52264.8 + 90525.3i) q^{60} +(422154. + 731192. i) q^{61} +1.07075e6 q^{62} +(-871477. + 3.26439e6i) q^{63} +262144. q^{64} +(108754. + 188367. i) q^{65} +(1.00437e6 - 1.73962e6i) q^{66} +(-613923. + 1.06335e6i) q^{67} +(1.16893e6 + 2.02465e6i) q^{68} -1.28702e6 q^{69} +(-148947. + 40056.8i) q^{70} +1.10759e6 q^{71} +(-953122. - 1.65086e6i) q^{72} +(-819423. + 1.41928e6i) q^{73} +(2.31951e6 - 4.01751e6i) q^{74} +(-2.98567e6 - 5.17134e6i) q^{75} -2.07368e6 q^{76} +(2.86230e6 - 769770. i) q^{77} -6.29655e6 q^{78} +(2.49711e6 + 4.32512e6i) q^{79} +(43510.2 - 75361.8i) q^{80} +(-468133. + 810829. i) q^{81} +(2.13187e6 + 3.69251e6i) q^{82} -3.38355e6 q^{83} +(1.15166e6 - 4.31392e6i) q^{84} +776069. q^{85} +(1.46150e6 + 2.53139e6i) q^{86} +(1.69070e6 - 2.92838e6i) q^{87} +(-836132. + 1.44822e6i) q^{88} +(-3.26848e6 - 5.66118e6i) q^{89} -632790. q^{90} +(-6.57568e6 - 6.56361e6i) q^{91} +1.07143e6 q^{92} +(5.14476e6 + 8.91098e6i) q^{93} +(827454. - 1.43319e6i) q^{94} +(-344185. + 596146. i) q^{95} +(1.25956e6 + 2.18162e6i) q^{96} +1.35914e6 q^{97} +(5.69961e6 - 3.30465e6i) q^{98} +1.21603e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} + 56 q^{3} - 128 q^{4} + 238 q^{5} - 896 q^{6} + 168 q^{7} + 2048 q^{8} - 1972 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 + 56 * q^3 - 128 * q^4 + 238 * q^5 - 896 * q^6 + 168 * q^7 + 2048 * q^8 - 1972 * q^9	\( 4 q - 16 q^{2} + 56 q^{3} - 128 q^{4} + 238 q^{5} - 896 q^{6} + 168 q^{7} + 2048 q^{8} - 1972 q^{9} + 1904 q^{10} - 5848 q^{11} + 3584 q^{12} + 2632 q^{13} - 2016 q^{14} - 5784 q^{15} - 8192 q^{16} + 47642 q^{17} - 15776 q^{18} + 41048 q^{19} - 30464 q^{20} - 169582 q^{21} + 93568 q^{22} + 49316 q^{23} + 28672 q^{24} + 108816 q^{25} - 10528 q^{26} - 400624 q^{27} + 5376 q^{28} + 345640 q^{29} + 23136 q^{30} + 70252 q^{31} - 65536 q^{32} + 197190 q^{33} - 762272 q^{34} - 36904 q^{35} + 252416 q^{36} + 88166 q^{37} + 328384 q^{38} + 973336 q^{39} + 121856 q^{40} - 2312520 q^{41} + 1032640 q^{42} + 115088 q^{43} - 374272 q^{44} - 300468 q^{45} + 394528 q^{46} + 1412292 q^{47} - 458752 q^{48} + 465892 q^{49} - 1741056 q^{50} - 2576256 q^{51} - 84224 q^{52} + 2361174 q^{53} + 1602496 q^{54} - 1258040 q^{55} + 86016 q^{56} + 4620796 q^{57} - 1382560 q^{58} - 1842512 q^{59} + 185088 q^{60} - 1278242 q^{61} - 1124032 q^{62} - 2121448 q^{63} + 1048576 q^{64} - 1716372 q^{65} + 1577520 q^{66} + 2121480 q^{67} + 3049088 q^{68} - 5332236 q^{69} + 2595712 q^{70} + 7200320 q^{71} - 1009664 q^{72} + 1634682 q^{73} + 705328 q^{74} - 5321176 q^{75} - 5254144 q^{76} + 1416226 q^{77} - 15573376 q^{78} + 9192604 q^{79} + 974848 q^{80} - 3049498 q^{81} + 9250080 q^{82} - 56560 q^{83} + 2592128 q^{84} + 6369676 q^{85} - 460352 q^{86} + 691656 q^{87} - 2994176 q^{88} - 8936550 q^{89} + 4807488 q^{90} - 26111120 q^{91} - 6312448 q^{92} + 14550490 q^{93} + 11298336 q^{94} - 2562604 q^{95} + 1835008 q^{96} + 11748408 q^{97} + 20499248 q^{98} + 15278208 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 56 * q^3 - 128 * q^4 + 238 * q^5 - 896 * q^6 + 168 * q^7 + 2048 * q^8 - 1972 * q^9 + 1904 * q^10 - 5848 * q^11 + 3584 * q^12 + 2632 * q^13 - 2016 * q^14 - 5784 * q^15 - 8192 * q^16 + 47642 * q^17 - 15776 * q^18 + 41048 * q^19 - 30464 * q^20 - 169582 * q^21 + 93568 * q^22 + 49316 * q^23 + 28672 * q^24 + 108816 * q^25 - 10528 * q^26 - 400624 * q^27 + 5376 * q^28 + 345640 * q^29 + 23136 * q^30 + 70252 * q^31 - 65536 * q^32 + 197190 * q^33 - 762272 * q^34 - 36904 * q^35 + 252416 * q^36 + 88166 * q^37 + 328384 * q^38 + 973336 * q^39 + 121856 * q^40 - 2312520 * q^41 + 1032640 * q^42 + 115088 * q^43 - 374272 * q^44 - 300468 * q^45 + 394528 * q^46 + 1412292 * q^47 - 458752 * q^48 + 465892 * q^49 - 1741056 * q^50 - 2576256 * q^51 - 84224 * q^52 + 2361174 * q^53 + 1602496 * q^54 - 1258040 * q^55 + 86016 * q^56 + 4620796 * q^57 - 1382560 * q^58 - 1842512 * q^59 + 185088 * q^60 - 1278242 * q^61 - 1124032 * q^62 - 2121448 * q^63 + 1048576 * q^64 - 1716372 * q^65 + 1577520 * q^66 + 2121480 * q^67 + 3049088 * q^68 - 5332236 * q^69 + 2595712 * q^70 + 7200320 * q^71 - 1009664 * q^72 + 1634682 * q^73 + 705328 * q^74 - 5321176 * q^75 - 5254144 * q^76 + 1416226 * q^77 - 15573376 * q^78 + 9192604 * q^79 + 974848 * q^80 - 3049498 * q^81 + 9250080 * q^82 - 56560 * q^83 + 2592128 * q^84 + 6369676 * q^85 - 460352 * q^86 + 691656 * q^87 - 2994176 * q^88 - 8936550 * q^89 + 4807488 * q^90 - 26111120 * q^91 - 6312448 * q^92 + 14550490 * q^93 + 11298336 * q^94 - 2562604 * q^95 + 1835008 * q^96 + 11748408 * q^97 + 20499248 * q^98 + 15278208 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$3$	38.4387	−	66.5778i	0.821948	−	1.42366i	−0.0822818	−	0.996609i	$-0.526221\pi$
$3$	38.4387	−	66.5778i	0.821948	−	1.42366i	0.904230	−	0.427046i	$-0.140446\pi$
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	10.6226	+	18.3989i	0.0380046	+	0.0658259i	0.884402	−	0.466726i	$-0.154567\pi$
$5$	10.6226	+	18.3989i	0.0380046	+	0.0658259i	−0.846397	+	0.532552i	$0.821233\pi$
$6$	−615.019			−1.16241
$7$	−642.284	−	641.104i	−0.707756	−	0.706457i
$7$	−642.284	−	641.104i	−0.707756	−	0.706457i
$8$	512.000			0.353553
$9$	−1861.57	−	3224.33i	−0.851197	−	1.47432i
$10$	84.9808	−	147.191i	0.0268733	−	0.0465459i
$11$	−1633.07	+	2828.56i	−0.369939	+	0.640754i	−0.989556	−	0.144151i	$-0.953955\pi$
$11$	−1633.07	+	2828.56i	−0.369939	+	0.640754i	0.619616	+	0.784905i	$0.287288\pi$
$12$	2460.08	+	4260.98i	0.410974	+	0.711828i
$13$	10238.0			1.29245			0.646223	−	0.763149i	$-0.276348\pi$
$13$	10238.0			1.29245			0.646223	+	0.763149i	$0.276348\pi$
$14$	−1872.57	+	7014.29i	−0.182385	+	0.683181i
$15$	1633.28			0.124951
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	18264.6	−	31635.1i	0.901650	−	1.56170i	0.0762982	−	0.997085i	$-0.475690\pi$
$17$	18264.6	−	31635.1i	0.901650	−	1.56170i	0.825352	−	0.564619i	$-0.190977\pi$
$18$	−14892.5	+	25794.6i	−0.601887	+	1.04250i
$19$	16200.6	+	28060.3i	0.541868	+	0.938543i	0.998797	+	0.0490398i	$0.0156161\pi$
$19$	16200.6	+	28060.3i	0.541868	+	0.938543i	−0.456929	+	0.889503i	$0.651051\pi$
$20$	−1359.69			−0.0380046
$21$	−67371.9	+	18118.6i	−1.58749	+	0.426930i
$22$	26129.1			0.523173
$23$	−8370.58	−	14498.3i	−0.143452	−	0.248467i	0.785342	−	0.619062i	$-0.212487\pi$
$23$	−8370.58	−	14498.3i	−0.143452	−	0.248467i	−0.928795	+	0.370595i	$0.879154\pi$
$24$	19680.6	−	34087.8i	0.290602	−	0.503338i
$25$	38836.8	−	67267.3i	0.497111	−	0.861022i
$26$	−40951.9	−	70930.7i	−0.456948	−	0.791458i
$27$	−118094.			−1.15466
$28$	56086.7	−	15083.6i	0.482844	−	0.129853i
$29$	43984.4			0.334893			0.167446	−	0.985881i	$-0.446448\pi$
$29$	43984.4			0.334893			0.167446	+	0.985881i	$0.446448\pi$
$30$	−6533.10	−	11315.7i	−0.0441769	−	0.0765166i
$31$	−66921.6	+	115912.i	−0.403460	+	0.698813i	−0.994141	−	0.108092i	$-0.965526\pi$
$31$	−66921.6	+	115912.i	−0.403460	+	0.698813i	0.590681	+	0.806905i	$0.298859\pi$
$32$	−16384.0	+	28377.9i	−0.0883883	+	0.153093i
$33$	125546.	+	217452.i	0.608142	+	1.05333i
$34$	−292233.			−1.27513
$35$	4972.88	−	18627.5i	0.0196052	−	0.0734373i
$36$	238281.			0.851197
$37$	289939.	+	502188.i	0.941022	+	1.62990i	0.763526	+	0.645777i	$0.223466\pi$
$37$	289939.	+	502188.i	0.941022	+	1.62990i	0.177496	+	0.984122i	$0.443200\pi$
$38$	129605.	−	224482.i	0.383159	−	0.663650i
$39$	393534.	−	681621.i	1.06232	−	1.84000i
$40$	5438.77	+	9420.23i	0.0134366	+	0.0232730i
$41$	−532967.			−1.20769			−0.603847	−	0.797100i	$-0.706366\pi$
$41$	−532967.			−1.20769			−0.603847	+	0.797100i	$0.706366\pi$
$42$	395017.	+	394291.i	0.822703	+	0.821192i
$43$	−365375.			−0.700809			−0.350404	−	0.936598i	$-0.613956\pi$
$43$	−365375.			−0.700809			−0.350404	+	0.936598i	$0.613956\pi$
$44$	−104517.	−	181028.i	−0.184970	−	0.320377i
$45$	39549.4	−	68501.5i	0.0646987	−	0.112062i
$46$	−66964.6	+	115986.i	−0.101436	+	0.175693i
$47$	103432.	+	179149.i	0.145315	+	0.251693i	0.929491	−	0.368846i	$-0.120247\pi$
$47$	103432.	+	179149.i	0.145315	+	0.251693i	−0.784175	+	0.620539i	$0.786914\pi$
$48$	−314890.			−0.410974
$49$	1513.36	+	823542.i	0.00183762	+	0.999998i
$50$	−621389.			−0.703022
$51$	−1.40413e6	−	2.43203e6i	−1.48222	−	2.56728i
$52$	−327615.	+	567446.i	−0.323111	+	0.559645i
$53$	544104.	−	942416.i	0.502015	−	0.869515i	−0.497982	−	0.867187i	$-0.665926\pi$
$53$	544104.	−	942416.i	0.502015	−	0.869515i	0.999997	−	0.00232824i	$-0.000741104\pi$
$54$	472376.	+	818179.i	0.408234	+	0.707083i
$55$	−69389.9			−0.0562376
$56$	−328849.	−	328245.i	−0.250230	−	0.249770i
$57$	2.49092e6			1.78155
$58$	−175938.	−	304733.i	−0.118402	−	0.205079i
$59$	−80826.2	+	139995.i	−0.0512354	+	0.0887423i	−0.890506	−	0.454972i	$-0.849649\pi$
$59$	−80826.2	+	139995.i	−0.0512354	+	0.0887423i	0.839270	+	0.543714i	$0.182983\pi$
$60$	−52264.8	+	90525.3i	−0.0312378	+	0.0541054i
$61$	422154.	+	731192.i	0.238131	+	0.412456i	0.960178	−	0.279389i	$-0.0901318\pi$
$61$	422154.	+	731192.i	0.238131	+	0.412456i	−0.722047	+	0.691844i	$0.756798\pi$
$62$	1.07075e6			0.570578
$63$	−871477.	+	3.26439e6i	−0.439101	+	1.64479i
$64$	262144.			0.125000
$65$	108754.	+	188367.i	0.0491188	+	0.0850763i
$66$	1.00437e6	−	1.73962e6i	0.430021	−	0.744819i
$67$	−613923.	+	1.06335e6i	−0.249375	+	0.431929i	−0.963352	−	0.268239i	$-0.913558\pi$
$67$	−613923.	+	1.06335e6i	−0.249375	+	0.431929i	0.713978	+	0.700168i	$0.246892\pi$
$68$	1.16893e6	+	2.02465e6i	0.450825	+	0.780852i
$69$	−1.28702e6			−0.471642
$70$	−148947.	+	40056.8i	−0.0519024	+	0.0139583i
$71$	1.10759e6			0.367259			0.183630	−	0.982995i	$-0.441215\pi$
$71$	1.10759e6			0.367259			0.183630	+	0.982995i	$0.441215\pi$
$72$	−953122.	−	1.65086e6i	−0.300943	−	0.521249i
$73$	−819423.	+	1.41928e6i	−0.246535	+	0.427011i	−0.962562	−	0.271062i	$-0.912625\pi$
$73$	−819423.	+	1.41928e6i	−0.246535	+	0.427011i	0.716027	+	0.698072i	$0.245959\pi$
$74$	2.31951e6	−	4.01751e6i	0.665403	−	1.15251i
$75$	−2.98567e6	−	5.17134e6i	−0.817199	−	1.41543i
$76$	−2.07368e6			−0.541868
$77$	2.86230e6	−	769770.i	0.714492	−	0.192151i
$78$	−6.29655e6			−1.50235
$79$	2.49711e6	+	4.32512e6i	0.569826	+	0.986968i	0.996583	+	0.0826011i	$0.0263227\pi$
$79$	2.49711e6	+	4.32512e6i	0.569826	+	0.986968i	−0.426757	+	0.904366i	$0.640344\pi$
$80$	43510.2	−	75361.8i	0.00950114	−	0.0164565i
$81$	−468133.	+	810829.i	−0.0978749	+	0.169524i
$82$	2.13187e6	+	3.69251e6i	0.426984	+	0.739559i
$83$	−3.38355e6			−0.649531			−0.324765	−	0.945795i	$-0.605285\pi$
$83$	−3.38355e6			−0.649531			−0.324765	+	0.945795i	$0.605285\pi$
$84$	1.15166e6	−	4.31392e6i	0.212006	−	0.794136i
$85$	776069.			0.137067
$86$	1.46150e6	+	2.53139e6i	0.247773	+	0.429156i
$87$	1.69070e6	−	2.92838e6i	0.275264	−	0.476772i
$88$	−836132.	+	1.44822e6i	−0.130793	+	0.226541i
$89$	−3.26848e6	−	5.66118e6i	−0.491452	−	0.851220i	0.508500	−	0.861062i	$-0.330200\pi$
$89$	−3.26848e6	−	5.66118e6i	−0.491452	−	0.851220i	−0.999952	+	0.00984263i	$0.996867\pi$
$90$	−632790.			−0.0914978
$91$	−6.57568e6	−	6.56361e6i	−0.914736	−	0.913057i
$92$	1.07143e6			0.143452
$93$	5.14476e6	+	8.91098e6i	0.663246	+	1.14878i
$94$	827454.	−	1.43319e6i	0.102753	−	0.177974i
$95$	−344185.	+	596146.i	−0.0411869	+	0.0713379i
$96$	1.25956e6	+	2.18162e6i	0.145301	+	0.251669i
$97$	1.35914e6			0.151204			0.0756022	−	0.997138i	$-0.475912\pi$
$97$	1.35914e6			0.151204			0.0756022	+	0.997138i	$0.475912\pi$
$98$	5.69961e6	−	3.30465e6i	0.611722	−	0.354678i
$99$	1.21603e7			1.25956
$100$	2.48556e6	+	4.30511e6i	0.248556	+	0.430511i
$101$	−5.84618e6	+	1.01259e7i	−0.564608	+	0.977930i	0.432478	+	0.901644i	$0.357639\pi$
$101$	−5.84618e6	+	1.01259e7i	−0.564608	+	0.977930i	−0.997086	+	0.0762853i	$0.975694\pi$
$102$	−1.12331e7	+	1.94562e7i	−1.04809	+	1.81534i
$103$	1.08658e6	+	1.88202e6i	0.0979790	+	0.169705i	0.910848	−	0.412742i	$-0.135429\pi$
$103$	1.08658e6	+	1.88202e6i	0.0979790	+	0.169705i	−0.812869	+	0.582447i	$0.802096\pi$
$104$	5.24184e6			0.456948
$105$	−1.04903e6	−	1.04710e6i	−0.0884349	−	0.0882726i
$106$	−8.70567e6			−0.709956
$107$	−5.38290e6	−	9.32345e6i	−0.424789	−	0.735756i	0.571612	−	0.820524i	$-0.306318\pi$
$107$	−5.38290e6	−	9.32345e6i	−0.424789	−	0.735756i	−0.996401	+	0.0847685i	$0.972985\pi$
$108$	3.77901e6	−	6.54543e6i	0.288665	−	0.499983i
$109$	6.18768e6	−	1.07174e7i	0.457652	−	0.792676i	−0.541185	−	0.840904i	$-0.682024\pi$
$109$	6.18768e6	−	1.07174e7i	0.457652	−	0.792676i	0.998836	+	0.0482280i	$0.0153574\pi$
$110$	277559.	+	480747.i	0.0198830	+	0.0344383i
$111$	4.45794e7			3.09388
$112$	−958754.	+	3.59132e6i	−0.0644829	+	0.241541i
$113$	−1.93909e7			−1.26422			−0.632112	−	0.774877i	$-0.717812\pi$
$113$	−1.93909e7			−1.26422			−0.632112	+	0.774877i	$0.717812\pi$
$114$	−9.96368e6	−	1.72576e7i	−0.629873	−	1.09097i
$115$	177835.	−	308019.i	0.0109037	−	0.0188858i
$116$	−1.40750e6	+	2.43786e6i	−0.0837232	+	0.145013i
$117$	−1.90587e7	−	3.30106e7i	−1.10013	−	1.90547i
$118$	1.29322e6			0.0724578
$119$	−3.20125e7	+	8.60925e6i	−1.74142	+	0.468329i
$120$	836237.			0.0441769
$121$	4.40974e6	+	7.63790e6i	0.226290	+	0.391945i
$122$	3.37723e6	−	5.84954e6i	0.168384	−	0.291650i
$123$	−2.04866e7	+	3.54838e7i	−0.992662	+	1.71934i
$124$	−4.28298e6	−	7.41834e6i	−0.201730	−	0.349406i
$125$	3.30997e6			0.151579
$126$	2.61023e7	−	7.01980e6i	1.16247	−	0.312628i
$127$	−1.41475e6			−0.0612868			−0.0306434	−	0.999530i	$-0.509756\pi$
$127$	−1.41475e6			−0.0612868			−0.0306434	+	0.999530i	$0.509756\pi$
$128$	−1.04858e6	−	1.81619e6i	−0.0441942	−	0.0765466i
$129$	−1.40446e7	+	2.43259e7i	−0.576028	+	0.997711i
$130$	870031.	−	1.50694e6i	0.0347323	−	0.0601580i
$131$	1.77615e7	+	3.07638e7i	0.690287	+	1.19561i	0.971744	+	0.236038i	$0.0758490\pi$
$131$	1.77615e7	+	3.07638e7i	0.690287	+	1.19561i	−0.281457	+	0.959574i	$0.590818\pi$
$132$	−1.60699e7			−0.608142
$133$	7.58418e6	−	2.84089e7i	0.279530	−	1.04707i
$134$	9.82277e6			0.352669
$135$	−1.25447e6	−	2.17280e6i	−0.0438824	−	0.0760066i
$136$	9.35146e6	−	1.61972e7i	0.318781	−	0.552146i
$137$	2.21508e7	−	3.83663e7i	0.735982	−	1.27476i	−0.218309	−	0.975880i	$-0.570054\pi$
$137$	2.21508e7	−	3.83663e7i	0.735982	−	1.27476i	0.954291	−	0.298878i	$-0.0966125\pi$
$138$	5.14807e6	+	8.91671e6i	0.166751	+	0.288820i
$139$	2.97789e7			0.940496			0.470248	−	0.882534i	$-0.344164\pi$
$139$	2.97789e7			0.940496			0.470248	+	0.882534i	$0.344164\pi$
$140$	873309.	+	871705.i	0.0268980	+	0.0268486i
$141$	1.59031e7			0.477766
$142$	−4.43034e6	−	7.67357e6i	−0.129846	−	0.224900i
$143$	−1.67193e7	+	2.89587e7i	−0.478126	+	0.828139i
$144$	−7.62498e6	+	1.32069e7i	−0.212799	+	0.368579i
$145$	467229.	+	809264.i	0.0127275	+	0.0220446i
$146$	1.31108e7			0.348653
$147$	5.48877e7	+	3.15551e7i	1.42516	+	0.819330i
$148$	−3.71121e7			−0.941022
$149$	2.04028e7	+	3.53387e7i	0.505286	+	0.875181i	0.999981	+	0.00611484i	$0.00194642\pi$
$149$	2.04028e7	+	3.53387e7i	0.505286	+	0.875181i	−0.494695	+	0.869067i	$0.664720\pi$
$150$	−2.38854e7	+	4.13707e7i	−0.577847	+	1.00086i
$151$	1.78291e7	−	3.08810e7i	0.421416	−	0.729914i	−0.574662	−	0.818391i	$-0.694867\pi$
$151$	1.78291e7	−	3.08810e7i	0.421416	−	0.729914i	0.996078	+	0.0884767i	$0.0281999\pi$
$152$	8.29471e6	+	1.43669e7i	0.191579	+	0.331825i
$153$	−1.36003e8			−3.06993
$154$	−1.67823e7	−	1.67515e7i	−0.370279	−	0.369599i
$155$	−2.84353e6			−0.0613333
$156$	2.51862e7	+	4.36238e7i	0.531161	+	0.919998i
$157$	2.60341e7	−	4.50923e7i	0.536899	−	0.929937i	−0.462169	−	0.886792i	$-0.652929\pi$
$157$	2.60341e7	−	4.50923e7i	0.536899	−	0.929937i	0.999069	−	0.0431455i	$-0.0137379\pi$
$158$	1.99769e7	−	3.46009e7i	0.402928	−	0.697891i
$159$	−4.18293e7	−	7.24505e7i	−0.825260	−	1.42939i
$160$	−696163.			−0.0134366
$161$	−3.91862e6	+	1.46784e7i	−0.0740018	+	0.277197i
$162$	7.49012e6			0.138416
$163$	−2.72230e7	−	4.71516e7i	−0.492356	−	0.852785i	0.507605	−	0.861590i	$-0.330531\pi$
$163$	−2.72230e7	−	4.71516e7i	−0.492356	−	0.852785i	−0.999961	+	0.00880425i	$0.997197\pi$
$164$	1.70550e7	−	2.95400e7i	0.301924	−	0.522947i
$165$	−2.66726e6	+	4.61982e6i	−0.0462244	+	0.0800629i
$166$	1.35342e7	+	2.34419e7i	0.229644	+	0.397755i
$167$	−3.69146e7			−0.613325			−0.306662	−	0.951818i	$-0.599212\pi$
$167$	−3.69146e7			−0.613325			−0.306662	+	0.951818i	$0.599212\pi$
$168$	−3.44944e7	+	9.27672e6i	−0.561262	+	0.150943i
$169$	4.20675e7			0.670414
$170$	−3.10427e6	−	5.37676e6i	−0.0484606	−	0.0839363i
$171$	6.03170e7	−	1.04472e8i	0.922473	−	1.59777i
$172$	1.16920e7	−	2.02512e7i	0.175202	−	0.303459i
$173$	3.84918e7	+	6.66697e7i	0.565206	+	0.978965i	0.997031	+	0.0770076i	$0.0245366\pi$
$173$	3.84918e7	+	6.66697e7i	0.565206	+	0.978965i	−0.431825	+	0.901958i	$0.642130\pi$
$174$	−2.70513e7			−0.389283
$175$	−6.80696e7	+	1.83063e7i	−0.960108	+	0.258206i
$176$	1.33781e7			0.184970
$177$	6.21371e6	+	1.07625e7i	0.0842256	+	0.145883i
$178$	−2.61478e7	+	4.52894e7i	−0.347509	+	0.601903i
$179$	−2.50183e7	+	4.33329e7i	−0.326041	+	0.564719i	−0.981722	−	0.190318i	$-0.939048\pi$
$179$	−2.50183e7	+	4.33329e7i	−0.326041	+	0.564719i	0.655682	+	0.755037i	$0.272381\pi$
$180$	2.53116e6	+	4.38410e6i	0.0323494	+	0.0560308i
$181$	1.63228e7			0.204606			0.102303	−	0.994753i	$-0.467379\pi$
$181$	1.63228e7			0.204606			0.102303	+	0.994753i	$0.467379\pi$
$182$	−1.91713e7	+	7.18121e7i	−0.235723	+	0.882973i
$183$	6.49082e7			0.782926
$184$	−4.28574e6	−	7.42311e6i	−0.0507181	−	0.0878463i
$185$	−6.15980e6	+	1.06691e7i	−0.0715263	+	0.123887i
$186$	4.11581e7	−	7.12878e7i	0.468986	−	0.812307i
$187$	5.96546e7	+	1.03325e8i	0.667112	+	1.15547i
$188$	−1.32393e7			−0.145315
$189$	7.58498e7	+	7.57106e7i	0.817219	+	0.815718i
$190$	5.50696e6			0.0582471
$191$	−7.45240e7	−	1.29079e8i	−0.773890	−	1.34042i	−0.935416	−	0.353549i	$-0.884975\pi$
$191$	−7.45240e7	−	1.29079e8i	−0.773890	−	1.34042i	0.161526	−	0.986869i	$-0.448359\pi$
$192$	1.00765e7	−	1.74530e7i	0.102743	−	0.177957i
$193$	−3.16993e7	+	5.49049e7i	−0.317395	+	0.549744i	−0.979944	−	0.199275i	$-0.936141\pi$
$193$	−3.16993e7	+	5.49049e7i	−0.317395	+	0.549744i	0.662549	+	0.749019i	$0.269475\pi$
$194$	−5.43658e6	−	9.41643e6i	−0.0534588	−	0.0925934i
$195$	1.67214e7			0.161492
$196$	−4.56937e7	−	2.62695e7i	−0.433471	−	0.249204i
$197$	2.93791e7			0.273783			0.136892	−	0.990586i	$-0.456289\pi$
$197$	2.93791e7			0.273783			0.136892	+	0.990586i	$0.456289\pi$
$198$	−4.86411e7	−	8.42489e7i	−0.445323	−	0.771323i
$199$	−2.45848e7	+	4.25821e7i	−0.221147	+	0.383037i	−0.955156	−	0.296102i	$-0.904313\pi$
$199$	−2.45848e7	+	4.25821e7i	−0.221147	+	0.383037i	0.734010	+	0.679139i	$0.237647\pi$
$200$	1.98845e7	−	3.44409e7i	0.175755	−	0.304417i
$201$	4.71968e7	+	8.17473e7i	0.409946	+	0.710047i
$202$	9.35388e7			0.798476
$203$	−2.82505e7	−	2.81986e7i	−0.237022	−	0.236587i
$204$	1.79729e8			1.48222
$205$	−5.66150e6	−	9.80600e6i	−0.0458979	−	0.0794975i
$206$	8.69268e6	−	1.50562e7i	0.0692816	−	0.119999i
$207$	−3.11648e7	+	5.39790e7i	−0.244213	+	0.422988i
$208$	−2.09674e7	−	3.63165e7i	−0.161556	−	0.279823i
$209$	−1.05827e8			−0.801834
$210$	−3.05842e6	+	1.14563e7i	−0.0227892	+	0.0853642i
$211$	−2.55314e8			−1.87105			−0.935526	−	0.353258i	$-0.885074\pi$
$211$	−2.55314e8			−1.87105			−0.935526	+	0.353258i	$0.885074\pi$
$212$	3.48227e7	+	6.03146e7i	0.251007	+	0.434758i
$213$	4.25741e7	−	7.37406e7i	0.301868	−	0.522851i
$214$	−4.30632e7	+	7.45876e7i	−0.300371	+	0.520258i
$215$	−3.88124e6	−	6.72250e6i	−0.0266339	−	0.0461314i
$216$	−6.04641e7			−0.408234
$217$	1.17294e8	−	3.15444e7i	0.779232	−	0.209562i
$218$	−9.90028e7			−0.647217
$219$	6.29951e7	+	1.09111e8i	0.405277	+	0.701961i
$220$	2.22048e6	−	3.84598e6i	0.0140594	−	0.0243516i
$221$	1.86992e8	−	3.23880e8i	1.16533	−	2.01842i
$222$	−1.78318e8	−	3.08855e8i	−1.09385	−	1.89461i
$223$	−3.35491e7			−0.202588			−0.101294	−	0.994857i	$-0.532298\pi$
$223$	−3.35491e7			−0.202588			−0.101294	+	0.994857i	$0.532298\pi$
$224$	2.87164e7	−	7.72282e6i	0.170711	−	0.0459100i
$225$	−2.89189e8			−1.69256
$226$	7.75638e7	+	1.34344e8i	0.446971	+	0.774177i
$227$	−7.55391e6	+	1.30838e7i	−0.0428629	+	0.0742407i	−0.886661	−	0.462420i	$-0.846981\pi$
$227$	−7.55391e6	+	1.30838e7i	−0.0428629	+	0.0742407i	0.843798	+	0.536661i	$0.180315\pi$
$228$	−7.97095e7	+	1.38061e8i	−0.445387	+	0.771434i
$229$	5.15808e7	+	8.93406e7i	0.283834	+	0.491615i	0.972326	−	0.233629i	$-0.0750603\pi$
$229$	5.15808e7	+	8.93406e7i	0.283834	+	0.491615i	−0.688492	+	0.725244i	$0.741727\pi$
$230$	−2.84535e6			−0.0154202
$231$	5.87734e7	−	2.20154e8i	0.313718	−	1.17513i
$232$	2.25200e7			0.118402
$233$	−5.19814e7	−	9.00345e7i	−0.269217	−	0.466298i	0.699443	−	0.714689i	$-0.253432\pi$
$233$	−5.19814e7	−	9.00345e7i	−0.269217	−	0.466298i	−0.968660	+	0.248391i	$0.920098\pi$
$234$	−1.52469e8	+	2.64085e8i	−0.777906	+	1.34737i
$235$	−2.19743e6	+	3.80606e6i	−0.0110453	+	0.0191310i
$236$	−5.17288e6	−	8.95968e6i	−0.0256177	−	0.0443711i
$237$	3.83942e8			1.87347
$238$	1.87696e8	+	1.87352e8i	0.902478	+	0.900821i
$239$	1.40545e8			0.665919			0.332960	−	0.942941i	$-0.391953\pi$
$239$	1.40545e8			0.665919			0.332960	+	0.942941i	$0.391953\pi$
$240$	−3.34495e6	−	5.79362e6i	−0.0156189	−	0.0270527i
$241$	−1.52501e8	+	2.64139e8i	−0.701798	+	1.21555i	0.266036	+	0.963963i	$0.414286\pi$
$241$	−1.52501e8	+	2.64139e8i	−0.701798	+	1.21555i	−0.967835	+	0.251587i	$0.919047\pi$
$242$	3.52780e7	−	6.11032e7i	0.160011	−	0.277147i
$243$	−9.31470e7	−	1.61335e8i	−0.416435	−	0.721286i
$244$	−5.40357e7			−0.238131
$245$	−1.51362e7	+	8.77600e6i	−0.0657559	+	0.0381255i
$246$	3.27785e8			1.40384
$247$	1.65861e8	+	2.87280e8i	0.700335	+	1.21302i
$248$	−3.42638e7	+	5.93467e7i	−0.142645	+	0.247068i
$249$	−1.30059e8	+	2.25269e8i	−0.533880	+	0.924708i
$250$	−1.32399e7	−	2.29322e7i	−0.0535913	−	0.0928229i
$251$	7.20544e7			0.287609			0.143804	−	0.989606i	$-0.454066\pi$
$251$	7.20544e7			0.287609			0.143804	+	0.989606i	$0.454066\pi$
$252$	−1.53044e8	−	1.52763e8i	−0.602440	−	0.601334i
$253$	5.46790e7			0.212275
$254$	5.65901e6	+	9.80169e6i	0.0216682	+	0.0375304i
$255$	2.98311e7	−	5.16689e7i	0.112662	−	0.195137i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	2.89343e6	+	5.01156e6i	0.0106328	+	0.0184165i	0.871293	−	0.490763i	$-0.163282\pi$
$257$	2.89343e6	+	5.01156e6i	0.0106328	+	0.0184165i	−0.860660	+	0.509180i	$0.829949\pi$
$258$	2.24713e8			0.814627
$259$	1.35732e8	−	5.08428e8i	0.485438	−	1.81836i
$260$	−1.39205e7			−0.0491188
$261$	−8.18799e7	−	1.41820e8i	−0.285060	−	0.493738i
$262$	1.42092e8	−	2.46110e8i	0.488106	−	0.845425i
$263$	−1.16636e8	+	2.02020e8i	−0.395356	+	0.684778i	−0.993147	−	0.116875i	$-0.962712\pi$
$263$	−1.16636e8	+	2.02020e8i	−0.395356	+	0.684778i	0.597790	+	0.801653i	$0.296046\pi$
$264$	6.42797e7	+	1.11336e8i	0.215011	+	0.372409i
$265$	2.31192e7			0.0763155
$266$	−2.27160e8	+	6.10910e7i	−0.740023	+	0.199018i
$267$	−5.02545e8			−1.61579
$268$	−3.92911e7	−	6.80542e7i	−0.124687	−	0.215965i
$269$	2.06500e8	−	3.57668e8i	0.646825	−	1.12033i	−0.337051	−	0.941486i	$-0.609430\pi$
$269$	2.06500e8	−	3.57668e8i	0.646825	−	1.12033i	0.983877	−	0.178848i	$-0.0572371\pi$
$270$	−1.00357e7	+	1.73824e7i	−0.0310296	+	0.0537448i
$271$	−1.45930e7	−	2.52758e7i	−0.0445401	−	0.0771457i	0.842896	−	0.538077i	$-0.180849\pi$
$271$	−1.45930e7	−	2.52758e7i	−0.0445401	−	0.0771457i	−0.887436	+	0.460931i	$0.847516\pi$
$272$	−1.49623e8			−0.450825
$273$	−6.89751e8	+	1.85498e8i	−2.05174	+	0.551784i
$274$	−3.54413e8			−1.04084
$275$	1.26847e8	+	2.19705e8i	0.367802	+	0.637052i
$276$	4.11845e7	−	7.13337e7i	0.117910	−	0.204227i
$277$	−3.26538e8	+	5.65581e8i	−0.923113	+	1.59888i	−0.128545	+	0.991704i	$0.541031\pi$
$277$	−3.26538e8	+	5.65581e8i	−0.923113	+	1.59888i	−0.794568	+	0.607175i	$0.792303\pi$
$278$	−1.19116e8	−	2.06314e8i	−0.332516	−	0.575934i
$279$	4.98316e8			1.37369
$280$	2.54612e6	−	9.53728e6i	0.00693147	−	0.0259640i
$281$	5.17554e8			1.39150			0.695750	−	0.718284i	$-0.255072\pi$
$281$	5.17554e8			1.39150			0.695750	+	0.718284i	$0.255072\pi$
$282$	−6.36125e7	−	1.10180e8i	−0.168916	−	0.292571i
$283$	−7.16532e6	+	1.24107e7i	−0.0187924	+	0.0325494i	−0.875269	−	0.483637i	$-0.839315\pi$
$283$	−7.16532e6	+	1.24107e7i	−0.0187924	+	0.0325494i	0.856476	+	0.516186i	$0.172649\pi$
$284$	−3.54427e7	+	6.13886e7i	−0.0918148	+	0.159028i
$285$	2.64601e7	+	4.58302e7i	0.0677070	+	0.117272i
$286$	2.67509e8			0.676173
$287$	3.42316e8	+	3.41688e8i	0.854753	+	0.853184i
$288$	1.22000e8			0.300943
$289$	−4.62019e8	−	8.00241e8i	−1.12595	−	1.95020i
$290$	3.73783e6	−	6.47411e6i	0.00899967	−	0.0155879i
$291$	5.22437e7	−	9.04888e7i	0.124282	−	0.215263i
$292$	−5.24431e7	−	9.08341e7i	−0.123267	−	0.213505i
$293$	−4.59597e8			−1.06743			−0.533716	−	0.845664i	$-0.679205\pi$
$293$	−4.59597e8			−1.06743			−0.533716	+	0.845664i	$0.679205\pi$
$294$	−930746.	−	5.06494e8i	−0.00213607	−	1.16241i
$295$	−3.43434e6			−0.00778872
$296$	1.48449e8	+	2.57120e8i	0.332702	+	0.576256i
$297$	1.92856e8	−	3.34036e8i	0.427155	−	0.739854i
$298$	1.63222e8	−	2.82709e8i	0.357291	−	0.618847i
$299$	−8.56977e7	−	1.48433e8i	−0.185404	−	0.321130i
$300$	3.82166e8			0.817199
$301$	2.34675e8	+	2.34244e8i	0.496002	+	0.495091i
$302$	−2.85266e8			−0.595972
$303$	4.49439e8	+	7.78451e8i	0.928157	+	1.60761i
$304$	6.63577e7	−	1.14935e8i	0.135467	−	0.234636i
$305$	−8.96875e6	+	1.55343e7i	−0.0181002	+	0.0313504i
$306$	5.44011e8	+	9.42255e8i	1.08538	+	1.87994i
$307$	−2.28161e8			−0.450046			−0.225023	−	0.974354i	$-0.572246\pi$
$307$	−2.28161e8			−0.450046			−0.225023	+	0.974354i	$0.572246\pi$
$308$	−4.89286e7	+	1.83277e8i	−0.0954190	+	0.357422i
$309$	1.67068e8			0.322135
$310$	1.13741e7	+	1.97005e7i	0.0216846	+	0.0375588i
$311$	−3.56536e8	+	6.17538e8i	−0.672112	+	1.16413i	0.305192	+	0.952291i	$0.401280\pi$
$311$	−3.56536e8	+	6.17538e8i	−0.672112	+	1.16413i	−0.977304	+	0.211842i	$0.932054\pi$
$312$	2.01490e8	−	3.48990e8i	0.375588	−	0.650537i
$313$	6.97714e7	+	1.20848e8i	0.128609	+	0.222758i	0.923138	−	0.384469i	$-0.125615\pi$
$313$	6.97714e7	+	1.20848e8i	0.128609	+	0.222758i	−0.794529	+	0.607226i	$0.792282\pi$
$314$	−4.16545e8			−0.759291
$315$	−6.93185e7	+	1.86421e7i	−0.124958	+	0.0336054i
$316$	−3.19630e8			−0.569826
$317$	7.69441e7	+	1.33271e8i	0.135665	+	0.234979i	0.925851	−	0.377888i	$-0.123350\pi$
$317$	7.69441e7	+	1.33271e8i	0.135665	+	0.234979i	−0.790186	+	0.612867i	$0.790016\pi$
$318$	−3.34635e8	+	5.79604e8i	−0.583547	+	1.01073i
$319$	−7.18297e7	+	1.24413e8i	−0.123890	+	0.214584i
$320$	2.78465e6	+	4.82316e6i	0.00475057	+	0.00822823i
$321$	−8.27646e8			−1.39662
$322$	1.17369e8	−	3.15647e7i	0.195911	−	0.0526873i
$323$	1.18359e9			1.95430
$324$	−2.99605e7	−	5.18931e7i	−0.0489374	−	0.0847621i
$325$	3.97610e8	−	6.88681e8i	0.642489	−	1.11282i
$326$	−2.17784e8	+	3.77213e8i	−0.348148	+	0.603010i
$327$	−4.75693e8	−	8.23924e8i	−0.752331	−	1.30308i
$328$	−2.72879e8			−0.426984
$329$	4.84207e7	−	1.81375e8i	0.0749627	−	0.280796i
$330$	4.26761e7			0.0653711
$331$	−6.99907e7	−	1.21227e8i	−0.106082	−	0.183740i	0.808098	−	0.589048i	$-0.200497\pi$
$331$	−6.99907e7	−	1.21227e8i	−0.106082	−	0.183740i	−0.914180	+	0.405309i	$0.867164\pi$
$332$	1.08274e8	−	1.87536e8i	0.162383	−	0.281255i
$333$	1.07948e9	−	1.86971e9i	1.60199	−	2.77473i
$334$	1.47658e8	+	2.55752e8i	0.216843	+	0.375583i
$335$	−2.60858e7			−0.0379095
$336$	2.02249e8	+	2.01877e8i	0.290869	+	0.290335i
$337$	−9.36806e7			−0.133335			−0.0666676	−	0.997775i	$-0.521237\pi$
$337$	−9.36806e7			−0.133335			−0.0666676	+	0.997775i	$0.521237\pi$
$338$	−1.68270e8	−	2.91452e8i	−0.237027	−	0.410543i
$339$	−7.45363e8	+	1.29101e9i	−1.03913	+	1.79982i
$340$	−2.48342e7	+	4.30141e7i	−0.0342668	+	0.0593519i
$341$	−2.18575e8	−	3.78584e8i	−0.298511	−	0.517037i
$342$	−9.65072e8			−1.30457
$343$	5.27004e8	−	5.29917e8i	0.705155	−	0.709053i
$344$	−1.87072e8			−0.247773
$345$	−1.36715e7	−	2.36797e7i	−0.0179245	−	0.0310462i
$346$	3.07934e8	−	5.33358e8i	0.399661	−	0.692233i
$347$	2.85722e8	−	4.94886e8i	0.367106	−	0.635846i	−0.622006	−	0.783012i	$-0.713682\pi$
$347$	2.85722e8	−	4.94886e8i	0.367106	−	0.635846i	0.989112	+	0.147167i	$0.0470154\pi$
$348$	1.08205e8	+	1.87417e8i	0.137632	+	0.238386i
$349$	−2.32123e8			−0.292300			−0.146150	−	0.989262i	$-0.546688\pi$
$349$	−2.32123e8			−0.292300			−0.146150	+	0.989262i	$0.546688\pi$
$350$	3.99108e8	+	3.98375e8i	0.497568	+	0.496654i
$351$	−1.20904e9			−1.49234
$352$	−5.35125e7	−	9.26863e7i	−0.0653967	−	0.113270i
$353$	−5.79874e8	+	1.00437e9i	−0.701653	+	1.21530i	0.266233	+	0.963909i	$0.414221\pi$
$353$	−5.79874e8	+	1.00437e9i	−0.701653	+	1.21530i	−0.967886	+	0.251390i	$0.919112\pi$
$354$	4.97097e7	−	8.60996e7i	0.0595565	−	0.103155i
$355$	1.17654e7	+	2.03783e7i	0.0139575	+	0.0241752i
$356$	4.18366e8			0.491452
$357$	−6.57333e8	+	2.46225e9i	−0.764622	+	2.86413i
$358$	4.00292e8			0.461091
$359$	−4.85816e8	−	8.41458e8i	−0.554168	−	0.959847i	−0.997968	−	0.0637210i	$-0.979703\pi$
$359$	−4.85816e8	−	8.41458e8i	−0.554168	−	0.959847i	0.443800	−	0.896126i	$-0.353630\pi$
$360$	2.02493e7	−	3.50728e7i	0.0228745	−	0.0396197i
$361$	−7.79833e7	+	1.35071e8i	−0.0872421	+	0.151108i
$362$	−6.52911e7	−	1.13087e8i	−0.0723392	−	0.125295i
$363$	6.78019e8			0.743993
$364$	5.74214e8	−	1.54426e8i	0.624049	−	0.167828i
$365$	−3.48176e7			−0.0374778
$366$	−2.59633e8	−	4.49697e8i	−0.276806	−	0.479442i
$367$	8.51399e8	−	1.47467e9i	0.899088	−	1.55727i	0.0704252	−	0.997517i	$-0.477564\pi$
$367$	8.51399e8	−	1.47467e9i	0.899088	−	1.55727i	0.828663	−	0.559749i	$-0.189102\pi$
$368$	−3.42859e7	+	5.93849e7i	−0.0358631	+	0.0621167i
$369$	9.92154e8	+	1.71846e9i	1.02799	+	1.78052i
$370$	9.85569e7			0.101153
$371$	−9.53657e8	+	2.56471e8i	−0.969579	+	0.260753i
$372$	−6.58529e8			−0.663246
$373$	−1.88494e8	−	3.26481e8i	−0.188068	−	0.325744i	0.756538	−	0.653950i	$-0.226889\pi$
$373$	−1.88494e8	−	3.26481e8i	−0.188068	−	0.325744i	−0.944606	+	0.328206i	$0.893556\pi$
$374$	4.77237e8	−	8.26599e8i	0.471719	−	0.817042i
$375$	1.27231e8	−	2.20371e8i	0.124590	−	0.215797i
$376$	5.29570e7	+	9.17243e7i	0.0513767	+	0.0889870i
$377$	4.50311e8			0.432831
$378$	2.21139e8	−	8.28345e8i	0.210593	−	0.788842i
$379$	8.86999e8			0.836924			0.418462	−	0.908234i	$-0.362569\pi$
$379$	8.86999e8			0.836924			0.418462	+	0.908234i	$0.362569\pi$
$380$	−2.20278e7	−	3.81534e7i	−0.0205935	−	0.0356689i
$381$	−5.43812e7	+	9.41910e7i	−0.0503746	+	0.0872513i
$382$	−5.96192e8	+	1.03264e9i	−0.547223	+	0.947818i
$383$	2.17148e8	+	3.76111e8i	0.197497	+	0.342074i	0.947716	−	0.319115i	$-0.103386\pi$
$383$	2.17148e8	+	3.76111e8i	0.197497	+	0.342074i	−0.750220	+	0.661189i	$0.770052\pi$
$384$	−1.61224e8			−0.145301
$385$	4.45680e7	+	4.44861e7i	0.0398025	+	0.0397294i
$386$	5.07189e8			0.448864
$387$	6.80171e8	+	1.17809e9i	0.596526	+	1.03321i
$388$	−4.34926e7	+	7.53314e7i	−0.0378011	+	0.0654734i
$389$	−7.57986e7	+	1.31287e8i	−0.0652886	+	0.113083i	−0.896822	−	0.442392i	$-0.854130\pi$
$389$	−7.57986e7	+	1.31287e8i	−0.0652886	+	0.113083i	0.831533	+	0.555475i	$0.187463\pi$
$390$	−6.68857e7	−	1.15849e8i	−0.0570962	−	0.0988935i
$391$	−6.11540e8			−0.517376
$392$	774841.	+	4.21653e8i	0.000649697	+	0.353553i
$393$	2.73091e9			2.26952
$394$	−1.17517e8	−	2.03545e8i	−0.0967971	−	0.167657i
$395$	−5.30515e7	+	9.18880e7i	−0.0433120	+	0.0750186i
$396$	−3.89129e8	+	6.73991e8i	−0.314891	+	0.545408i
$397$	8.52585e8	+	1.47672e9i	0.683866	+	1.18449i	0.973792	+	0.227441i	$0.0730360\pi$
$397$	8.52585e8	+	1.47672e9i	0.683866	+	1.18449i	−0.289926	+	0.957049i	$0.593631\pi$
$398$	3.93357e8			0.312749
$399$	−1.59988e9	−	1.59694e9i	−1.26090	−	1.25859i
$400$	−3.18151e8			−0.248556
$401$	−5.75883e8	−	9.97459e8i	−0.445994	−	0.772484i	0.552127	−	0.833760i	$-0.313816\pi$
$401$	−5.75883e8	−	9.97459e8i	−0.445994	−	0.772484i	−0.998121	+	0.0612759i	$0.980483\pi$
$402$	3.77575e8	−	6.53978e8i	0.289876	−	0.502079i
$403$	−6.85141e8	+	1.18670e9i	−0.521450	+	0.903177i
$404$	−3.74155e8	−	6.48056e8i	−0.282304	−	0.488965i
$405$	−1.98911e7			−0.0148788
$406$	−8.23638e7	+	3.08519e8i	−0.0610795	+	0.228792i
$407$	−1.89396e9			−1.39248
$408$	−7.18916e8	−	1.24520e9i	−0.524043	−	0.907670i
$409$	−5.71985e8	+	9.90706e8i	−0.413383	+	0.716001i	−0.995257	−	0.0972783i	$-0.968986\pi$
$409$	−5.71985e8	+	9.90706e8i	−0.413383	+	0.716001i	0.581874	+	0.813279i	$0.302320\pi$
$410$	−4.52920e7	+	7.84480e7i	−0.0324547	+	0.0562132i
$411$	−1.70289e9	−	2.94950e9i	−1.20988	−	2.09557i
$412$	−1.39083e8			−0.0979790
$413$	1.41665e8	−	3.80985e7i	0.0989548	−	0.0266123i
$414$	4.98637e8			0.345369
$415$	−3.59421e7	−	6.22536e7i	−0.0246851	−	0.0427559i
$416$	−1.67739e8	+	2.90532e8i	−0.114237	+	0.197864i
$417$	1.14466e9	−	1.98261e9i	0.773039	−	1.33894i
$418$	4.23308e8	+	7.33191e8i	0.283491	+	0.491021i
$419$	1.72282e9			1.14417			0.572084	−	0.820195i	$-0.306135\pi$
$419$	1.72282e9			1.14417			0.572084	+	0.820195i	$0.306135\pi$
$420$	9.16050e7	−	2.46357e7i	0.0603319	−	0.0162253i
$421$	−2.50496e9			−1.63611			−0.818056	−	0.575139i	$-0.804948\pi$
$421$	−2.50496e9			−1.63611			−0.818056	+	0.575139i	$0.804948\pi$
$422$	1.02126e9	+	1.76887e9i	0.661517	+	1.14578i
$423$	3.85090e8	−	6.66996e8i	0.247384	−	0.428481i
$424$	2.78581e8	−	4.82517e8i	0.177489	−	0.307420i
$425$	−1.41868e9	−	2.45722e9i	−0.896441	−	1.55268i
$426$	−6.81186e8			−0.426906
$427$	1.97628e8	−	7.40278e8i	0.122843	−	0.460147i
$428$	6.89011e8			0.424789
$429$	1.28534e9	+	2.22627e9i	0.785990	+	1.36137i
$430$	−3.10499e7	+	5.37800e7i	−0.0188330	+	0.0326198i
$431$	−1.14303e9	+	1.97978e9i	−0.687679	+	1.19110i	0.284907	+	0.958555i	$0.408037\pi$
$431$	−1.14303e9	+	1.97978e9i	−0.687679	+	1.19110i	−0.972587	+	0.232541i	$0.925296\pi$
$432$	2.41857e8	+	4.18908e8i	0.144333	+	0.249992i
$433$	−2.07332e9			−1.22732			−0.613660	−	0.789570i	$-0.710303\pi$
$433$	−2.07332e9			−1.22732			−0.613660	+	0.789570i	$0.710303\pi$
$434$	−6.87722e8	−	6.86460e8i	−0.403830	−	0.403089i
$435$	7.18387e7			0.0418452
$436$	3.96011e8	+	6.85912e8i	0.228826	+	0.396338i
$437$	2.71217e8	−	4.69761e8i	0.155465	−	0.269273i
$438$	5.03961e8	−	8.72886e8i	0.286574	−	0.496361i
$439$	8.79323e8	+	1.52303e9i	0.496047	+	0.859178i	0.999990	−	0.00455873i	$-0.00145109\pi$
$439$	8.79323e8	+	1.52303e9i	0.496047	+	0.859178i	−0.503943	+	0.863737i	$0.668118\pi$
$440$	−3.55276e7			−0.0198830
$441$	2.65255e9	−	1.53796e9i	1.47275	−	0.853904i
$442$	−2.99187e9			−1.64803
$443$	9.64736e8	+	1.67097e9i	0.527224	+	0.913179i	0.999497	+	0.0317264i	$0.0101005\pi$
$443$	9.64736e8	+	1.67097e9i	0.527224	+	0.913179i	−0.472272	+	0.881453i	$0.656566\pi$
$444$	−1.42654e9	+	2.47084e9i	−0.773471	+	1.33969i
$445$	6.94395e7	−	1.20273e8i	0.0373548	−	0.0647005i
$446$	1.34196e8	+	2.32435e8i	0.0716257	+	0.124059i
$447$	3.13703e9			1.66128
$448$	−1.68371e8	−	1.68062e8i	−0.0884695	−	0.0883071i
$449$	3.29325e9			1.71697			0.858484	−	0.512840i	$-0.171407\pi$
$449$	3.29325e9			1.71697			0.858484	+	0.512840i	$0.171407\pi$
$450$	1.15676e9	+	2.00356e9i	0.598410	+	1.03648i
$451$	8.70373e8	−	1.50753e9i	0.446774	−	0.773835i
$452$	6.20510e8	−	1.07476e9i	0.316056	−	0.547425i
$453$	−1.37066e9	−	2.37405e9i	−0.692764	−	1.19990i
$454$	1.20863e8			0.0606172
$455$	5.09122e7	−	1.90708e8i	0.0253386	−	0.0949136i
$456$	1.27535e9			0.629873
$457$	9.57310e8	+	1.65811e9i	0.469187	+	0.812655i	0.999380	−	0.0352218i	$-0.0112138\pi$
$457$	9.57310e8	+	1.65811e9i	0.469187	+	0.812655i	−0.530193	+	0.847877i	$0.677880\pi$
$458$	4.12647e8	−	7.14725e8i	0.200701	−	0.347624i
$459$	−2.15694e9	+	3.73592e9i	−1.04110	+	1.80324i
$460$	1.13814e7	+	1.97132e7i	0.00545185	+	0.00944288i
$461$	−1.84068e9			−0.875032			−0.437516	−	0.899211i	$-0.644142\pi$
$461$	−1.84068e9			−0.875032			−0.437516	+	0.899211i	$0.644142\pi$
$462$	−1.76037e9	+	4.73423e8i	−0.830532	+	0.223359i
$463$	−1.67942e8			−0.0786367			−0.0393184	−	0.999227i	$-0.512519\pi$
$463$	−1.67942e8			−0.0786367			−0.0393184	+	0.999227i	$0.512519\pi$
$464$	−9.00801e7	−	1.56023e8i	−0.0418616	−	0.0725064i
$465$	−1.09301e8	+	1.89316e8i	−0.0504128	+	0.0873175i
$466$	−4.15852e8	+	7.20276e8i	−0.190365	+	0.329722i
$467$	−6.89538e8	−	1.19432e9i	−0.313292	−	0.542638i	0.665781	−	0.746147i	$-0.268099\pi$
$467$	−6.89538e8	−	1.19432e9i	−0.313292	−	0.542638i	−0.979073	+	0.203510i	$0.934765\pi$
$468$	2.43951e9			1.10013
$469$	1.07603e9	−	2.89381e8i	0.481636	−	0.129528i
$470$	3.51588e7			0.0156204
$471$	−2.00143e9	−	3.46658e9i	−0.882607	−	1.52872i
$472$	−4.13830e7	+	7.16775e7i	−0.0181144	+	0.0313751i
$473$	5.96684e8	−	1.03349e9i	0.259257	−	0.449046i
$474$	−1.53577e9	−	2.66003e9i	−0.662371	−	1.14726i
$475$	2.51672e9			1.07748
$476$	5.47226e8	−	2.04981e9i	0.232564	−	0.871141i
$477$	−4.05155e9			−1.70925
$478$	−5.62179e8	−	9.73722e8i	−0.235438	−	0.407791i
$479$	−2.26505e9	+	3.92318e9i	−0.941679	+	1.63104i	−0.179411	+	0.983774i	$0.557419\pi$
$479$	−2.26505e9	+	3.92318e9i	−0.941679	+	1.63104i	−0.762268	+	0.647261i	$0.775914\pi$
$480$	−2.67596e7	+	4.63490e7i	−0.0110442	+	0.0191292i
$481$	2.96838e9	+	5.14139e9i	1.21622	+	2.10655i
$482$	2.44001e9			0.992493
$483$	8.26630e8	+	8.25112e8i	0.333807	+	0.333195i
$484$	−5.64447e8			−0.226290
$485$	1.44376e7	+	2.50067e7i	0.00574646	+	0.00995316i
$486$	−7.45176e8	+	1.29068e9i	−0.294464	+	0.510026i
$487$	−7.69774e8	+	1.33329e9i	−0.302003	+	0.523085i	−0.976590	−	0.215111i	$-0.930989\pi$
$487$	−7.69774e8	+	1.33329e9i	−0.302003	+	0.523085i	0.674586	+	0.738196i	$0.264322\pi$
$488$	2.16143e8	+	3.74370e8i	0.0841921	+	0.145825i
$489$	−4.18566e9			−1.61876
$490$	1.21347e8	+	6.97625e7i	0.0465952	+	0.0267877i
$491$	−1.85780e9			−0.708295			−0.354148	−	0.935190i	$-0.615229\pi$
$491$	−1.85780e9			−0.708295			−0.354148	+	0.935190i	$0.615229\pi$
$492$	−1.31114e9	−	2.27096e9i	−0.496331	−	0.859670i
$493$	8.03356e8	−	1.39145e9i	0.301956	−	0.523003i
$494$	1.32689e9	−	2.29824e9i	0.495211	−	0.857731i
$495$	1.29174e8	+	2.23736e8i	0.0478692	+	0.0829119i
$496$	5.48222e8			0.201730
$497$	−7.11384e8	−	7.10078e8i	−0.259930	−	0.259453i
$498$	2.08095e9			0.755021
$499$	−2.67677e9	−	4.63630e9i	−0.964405	−	1.67040i	−0.711206	−	0.702983i	$-0.751851\pi$
$499$	−2.67677e9	−	4.63630e9i	−0.964405	−	1.67040i	−0.253198	−	0.967414i	$-0.581482\pi$
$500$	−1.05919e8	+	1.83457e8i	−0.0378948	+	0.0656357i
$501$	−1.41895e9	+	2.45769e9i	−0.504121	+	0.873163i
$502$	−2.88218e8	−	4.99207e8i	−0.101685	−	0.176124i
$503$	5.43979e9			1.90587			0.952936	−	0.303170i	$-0.0980450\pi$
$503$	5.43979e9			1.90587			0.952936	+	0.303170i	$0.0980450\pi$
$504$	−4.46196e8	+	1.67137e9i	−0.155246	+	0.581521i
$505$	−2.48406e8			−0.0858308
$506$	−2.18716e8	−	3.78827e8i	−0.0750505	−	0.129991i
$507$	1.61702e9	−	2.80076e9i	0.551046	−	0.954439i
$508$	4.52721e7	−	7.84135e7i	0.0153217	−	0.0265380i
$509$	−9.12084e8	−	1.57978e9i	−0.306565	−	0.530986i	0.671044	−	0.741418i	$-0.265846\pi$
$509$	−9.12084e8	−	1.57978e9i	−0.306565	−	0.530986i	−0.977609	+	0.210432i	$0.932513\pi$
$510$	−4.77297e8			−0.159328
$511$	1.43621e9	−	3.86246e8i	0.476151	−	0.128053i
$512$	1.34218e8			0.0441942
$513$	−1.91319e9	−	3.31375e9i	−0.625674	−	1.08370i
$514$	2.31474e7	−	4.00925e7i	0.00751850	−	0.0130224i
$515$	−2.30847e7	+	3.99839e7i	−0.00744730	+	0.0128991i
$516$	−8.98851e8	−	1.55686e9i	−0.288014	−	0.498855i
$517$	−6.75645e8			−0.215031
$518$	−4.06542e9	+	1.09333e9i	−1.28514	+	0.345619i
$519$	5.91830e9			1.85828
$520$	5.56820e7	+	9.64440e7i	0.0173661	+	0.0300790i
$521$	2.07430e8	−	3.59280e8i	0.0642599	−	0.111301i	−0.832106	−	0.554617i	$-0.812865\pi$
$521$	2.07430e8	−	3.59280e8i	0.0642599	−	0.111301i	0.896365	+	0.443316i	$0.146198\pi$
$522$	−6.55040e8	+	1.13456e9i	−0.201568	+	0.349125i
$523$	1.60836e9	+	2.78576e9i	0.491616	+	0.851505i	0.999953	−	0.00965354i	$-0.00307287\pi$
$523$	1.60836e9	+	2.78576e9i	0.491616	+	0.851505i	−0.508337	+	0.861158i	$0.669740\pi$
$524$	−2.27347e9			−0.690287
$525$	−1.39772e9	+	5.23559e9i	−0.421563	+	1.57910i
$526$	1.86618e9			0.559118
$527$	2.44459e9	+	4.23415e9i	0.727559	+	1.26017i
$528$	5.14237e8	−	8.90685e8i	0.152035	−	0.263333i
$529$	1.56228e9	−	2.70595e9i	0.458843	−	0.794739i
$530$	−9.24769e7	−	1.60175e8i	−0.0269816	−	0.0467335i
$531$	6.01853e8			0.174446
$532$	1.33189e9	+	1.32944e9i	0.383511	+	0.382806i
$533$	−5.45650e9			−1.56088
$534$	2.01018e9	+	3.48173e9i	0.571268	+	0.989466i
$535$	1.14361e8	−	1.98079e8i	0.0322878	−	0.0559242i
$536$	−3.14329e8	+	5.44433e8i	−0.0881672	+	0.152710i
$537$	1.92334e9	+	3.33132e9i	0.535977	+	0.928339i
$538$	−3.30400e9			−0.914749
$539$	−2.33191e9	−	1.34062e9i	−0.641433	−	0.368761i
$540$	1.60572e8			0.0438824
$541$	1.14907e9	+	1.99025e9i	0.312002	+	0.540403i	0.978796	−	0.204839i	$-0.0656672\pi$
$541$	1.14907e9	+	1.99025e9i	0.312002	+	0.540403i	−0.666794	+	0.745242i	$0.732334\pi$
$542$	−1.16744e8	+	2.02206e8i	−0.0314946	+	0.0545503i
$543$	6.27426e8	−	1.08673e9i	0.168176	−	0.291289i
$544$	5.98493e8	+	1.03662e9i	0.159391	+	0.276073i
$545$	2.62917e8			0.0695714
$546$	4.04417e9	+	4.03674e9i	1.06330	+	1.06135i
$547$	−6.33362e9			−1.65461			−0.827306	−	0.561752i	$-0.810128\pi$
$547$	−6.33362e9			−1.65461			−0.827306	+	0.561752i	$0.810128\pi$
$548$	1.41765e9	+	2.45544e9i	0.367991	+	0.637379i
$549$	1.57174e9	−	2.72233e9i	0.405393	−	0.702162i
$550$	1.01477e9	−	1.75764e9i	0.260075	−	0.450464i
$551$	7.12574e8	+	1.23421e9i	0.181468	+	0.314311i
$552$	−6.58952e8			−0.166751
$553$	1.16900e9	−	4.37886e9i	0.293952	−	1.10109i
$554$	5.22461e9			1.30548
$555$	4.73550e8	+	8.20212e8i	0.117582	+	0.203658i
$556$	−9.52925e8	+	1.65051e9i	−0.235124	+	0.407247i
$557$	3.75684e9	−	6.50705e9i	0.921149	−	1.59548i	0.123510	−	0.992343i	$-0.460585\pi$
$557$	3.75684e9	−	6.50705e9i	0.921149	−	1.59548i	0.797640	−	0.603134i	$-0.206082\pi$
$558$	−1.99326e9	−	3.45243e9i	−0.485674	−	0.841213i
$559$	−3.74070e9			−0.905757
$560$	−7.62607e7	+	2.05091e7i	−0.0183503	+	0.00493502i
$561$	9.17219e9			2.19332
$562$	−2.07022e9	−	3.58572e9i	−0.491970	−	0.852117i
$563$	−2.39314e9	+	4.14504e9i	−0.565183	+	0.978926i	0.431850	+	0.901946i	$0.357861\pi$
$563$	−2.39314e9	+	4.14504e9i	−0.565183	+	0.978926i	−0.997033	+	0.0769801i	$0.975472\pi$
$564$	−5.08900e8	+	8.81440e8i	−0.119442	+	0.206879i
$565$	−2.05982e8	−	3.56772e8i	−0.0480463	−	0.0832187i
$566$	1.14645e8			0.0265765
$567$	8.20500e8	−	2.20661e8i	0.189033	−	0.0508375i
$568$	5.67084e8			0.129846
$569$	−2.60548e9	−	4.51283e9i	−0.592919	−	1.02697i	−0.993837	−	0.110852i	$-0.964642\pi$
$569$	−2.60548e9	−	4.51283e9i	−0.592919	−	1.02697i	0.400918	−	0.916114i	$-0.368691\pi$
$570$	2.11680e8	−	3.66641e8i	0.0478761	−	0.0829238i
$571$	3.04516e9	−	5.27437e9i	0.684516	−	1.18562i	−0.289072	−	0.957307i	$-0.593347\pi$
$571$	3.04516e9	−	5.27437e9i	0.684516	−	1.18562i	0.973589	−	0.228310i	$-0.0733199\pi$
$572$	−1.07004e9	−	1.85336e9i	−0.239063	−	0.414070i
$573$	−1.14584e10			−2.54439
$574$	9.98017e8	−	3.73839e9i	0.220265	−	0.825073i
$575$	−1.30035e9			−0.285247
$576$	−4.87999e8	−	8.45238e8i	−0.106400	−	0.184289i
$577$	1.01575e9	−	1.75934e9i	0.220127	−	0.381271i	−0.734719	−	0.678371i	$-0.762686\pi$
$577$	1.01575e9	−	1.75934e9i	0.220127	−	0.381271i	0.954846	+	0.297100i	$0.0960195\pi$
$578$	−3.69615e9	+	6.40192e9i	−0.796164	+	1.37900i
$579$	2.43696e9	+	4.22094e9i	0.521764	+	0.903721i
$580$	−5.98053e7			−0.0127275
$581$	2.17320e9	+	2.16921e9i	0.459709	+	0.458865i
$582$	−8.35900e8			−0.175761
$583$	1.77712e9	+	3.07807e9i	0.371430	+	0.643336i
$584$	−4.19545e8	+	7.26673e8i	−0.0871632	+	0.150971i
$585$	4.04905e8	−	7.01317e8i	0.0836196	−	0.144833i
$586$	1.83839e9	+	3.18418e9i	0.377394	+	0.653666i
$587$	−7.84037e9			−1.59994			−0.799970	−	0.600041i	$-0.795151\pi$
$587$	−7.84037e9			−1.59994			−0.799970	+	0.600041i	$0.795151\pi$
$588$	−3.50537e9	+	2.03242e9i	−0.711071	+	0.412281i
$589$	−4.33668e9			−0.874488
$590$	1.37374e7	+	2.37938e7i	0.00275373	+	0.00476960i
$591$	1.12930e9	−	1.95600e9i	0.225036	−	0.389773i
$592$	1.18759e9	−	2.05696e9i	0.235256	−	0.407475i
$593$	7.96578e8	+	1.37971e9i	0.156869	+	0.271705i	0.933738	−	0.357957i	$-0.116527\pi$
$593$	7.96578e8	+	1.37971e9i	0.156869	+	0.271705i	−0.776869	+	0.629662i	$0.783193\pi$
$594$	−3.08569e9			−0.604088
$595$	−4.98456e8	−	4.97541e8i	−0.0970102	−	0.0968321i
$596$	−2.61156e9			−0.505286
$597$	1.89001e9	+	3.27360e9i	0.363542	+	0.629674i
$598$	−6.85582e8	+	1.18746e9i	−0.131101	+	0.227073i
$599$	−3.97790e8	+	6.88992e8i	−0.0756240	+	0.130985i	−0.901357	−	0.433076i	$-0.857428\pi$
$599$	−3.97790e8	+	6.88992e8i	−0.0756240	+	0.130985i	0.825733	+	0.564060i	$0.190762\pi$
$600$	−1.52866e9	−	2.64773e9i	−0.288924	−	0.500430i
$601$	6.44884e8			0.121177			0.0605886	−	0.998163i	$-0.480702\pi$
$601$	6.44884e8			0.121177			0.0605886	+	0.998163i	$0.480702\pi$
$602$	6.84190e8	−	2.56285e9i	0.127817	−	0.478779i
$603$	4.57144e9			0.849067
$604$	1.14106e9	+	1.97638e9i	0.210708	+	0.364957i
$605$	−9.36859e7	+	1.62269e8i	−0.0172001	+	0.0297914i
$606$	3.59551e9	−	6.22761e9i	0.656306	−	1.13676i
$607$	−1.62737e9	−	2.81869e9i	−0.295343	−	0.511549i	0.679721	−	0.733470i	$-0.262101\pi$
$607$	−1.62737e9	−	2.81869e9i	−0.295343	−	0.511549i	−0.975065	+	0.221921i	$0.928767\pi$
$608$	−1.06172e9			−0.191579
$609$	−2.96331e9	+	7.96936e8i	−0.531639	+	0.142976i
$610$	1.43500e8			0.0255975
$611$	1.05893e9	+	1.83412e9i	0.187812	+	0.325300i
$612$	4.35209e9	−	7.53804e9i	0.767482	−	1.32932i
$613$	−1.95906e9	+	3.39319e9i	−0.343508	+	0.594973i	−0.985081	−	0.172089i	$-0.944948\pi$
$613$	−1.95906e9	+	3.39319e9i	−0.343508	+	0.594973i	0.641574	+	0.767061i	$0.278282\pi$
$614$	9.12643e8	+	1.58074e9i	0.159115	+	0.275596i
$615$	−8.70483e8			−0.150903
$616$	1.46550e9	−	3.94122e8i	0.252611	−	0.0679357i
$617$	6.38504e9			1.09437			0.547187	−	0.837010i	$-0.315699\pi$
$617$	6.38504e9			1.09437			0.547187	+	0.837010i	$0.315699\pi$
$618$	−6.68270e8	−	1.15748e9i	−0.113892	−	0.197266i
$619$	5.48911e9	−	9.50741e9i	0.930217	−	1.61118i	0.147269	−	0.989096i	$-0.452952\pi$
$619$	5.48911e9	−	9.50741e9i	0.930217	−	1.61118i	0.782948	−	0.622087i	$-0.213715\pi$
$620$	9.09928e7	−	1.57604e8i	0.0153333	−	0.0265581i
$621$	9.88515e8	+	1.71216e9i	0.165639	+	0.286895i
$622$	5.70457e9			0.950510
$623$	−1.53011e9	+	5.73152e9i	−0.253522	+	0.949645i
$624$	−3.22383e9			−0.531161
$625$	−2.99897e9	−	5.19436e9i	−0.491351	−	0.851044i
$626$	5.58171e8	−	9.66780e8i	0.0909404	−	0.157513i
$627$	−4.06785e9	+	7.04572e9i	−0.659065	+	1.14153i
$628$	1.66618e9	+	2.88591e9i	0.268450	+	0.464969i
$629$	2.11824e10			3.39389
$630$	4.06431e8	+	4.05684e8i	0.0647582	+	0.0646393i
$631$	−6.75136e9			−1.06977			−0.534883	−	0.844926i	$-0.679644\pi$
$631$	−6.75136e9			−1.06977			−0.534883	+	0.844926i	$0.679644\pi$
$632$	1.27852e9	+	2.21446e9i	0.201464	+	0.348946i
$633$	−9.81393e9	+	1.69982e10i	−1.53791	+	2.66373i
$634$	6.15553e8	−	1.06617e9i	0.0959297	−	0.166155i
$635$	−1.50283e7	−	2.60299e7i	−0.00232918	−	0.00403426i
$636$	5.35415e9			0.825260
$637$	1.54937e7	+	8.43139e9i	0.00237503	+	1.29244i
$638$	1.14927e9			0.175207
$639$	−2.06184e9	−	3.57122e9i	−0.312610	−	0.541456i
$640$	2.22772e7	−	3.85853e7i	0.00335916	−	0.00581824i
$641$	−2.66451e9	+	4.61507e9i	−0.399590	+	0.692110i	−0.993675	−	0.112292i	$-0.964181\pi$
$641$	−2.66451e9	+	4.61507e9i	−0.399590	+	0.692110i	0.594085	+	0.804402i	$0.297514\pi$
$642$	3.31059e9	+	5.73410e9i	0.493779	+	0.855249i
$643$	3.64486e9			0.540683			0.270342	−	0.962764i	$-0.412863\pi$
$643$	3.64486e9			0.540683			0.270342	+	0.962764i	$0.412863\pi$
$644$	−6.88164e8	−	6.86901e8i	−0.101529	−	0.101343i
$645$	−5.96759e8			−0.0875669
$646$	−4.73435e9	−	8.20014e9i	−0.690950	−	1.19676i
$647$	4.98373e8	−	8.63207e8i	0.0723418	−	0.125300i	−0.827585	−	0.561340i	$-0.810286\pi$
$647$	4.98373e8	−	8.63207e8i	0.0723418	−	0.125300i	0.899927	+	0.436040i	$0.143619\pi$
$648$	−2.39684e8	+	4.15145e8i	−0.0346040	+	0.0599359i
$649$	−2.63990e8	−	4.57244e8i	−0.0379080	−	0.0656585i
$650$	−6.36176e9			−0.908617
$651$	2.40848e9	−	9.02170e9i	0.342144	−	1.28161i
$652$	3.48454e9			0.492356
$653$	−1.25807e9	−	2.17905e9i	−0.176811	−	0.306246i	0.763975	−	0.645245i	$-0.223245\pi$
$653$	−1.25807e9	−	2.17905e9i	−0.176811	−	0.306246i	−0.940787	+	0.338999i	$0.889912\pi$
$654$	−3.80554e9	+	6.59139e9i	−0.531979	+	0.921414i
$655$	−3.77346e8	+	6.53583e8i	−0.0524681	+	0.0908774i
$656$	1.09152e9	+	1.89056e9i	0.150962	+	0.261474i
$657$	6.10164e9			0.839398
$658$	−1.45029e9	+	3.90031e8i	−0.198455	+	0.0533714i
$659$	2.14485e9			0.291944			0.145972	−	0.989289i	$-0.453369\pi$
$659$	2.14485e9			0.291944			0.145972	+	0.989289i	$0.453369\pi$
$660$	−1.70704e8	−	2.95669e8i	−0.0231122	−	0.0400315i
$661$	2.15616e9	−	3.73457e9i	0.290386	−	0.502962i	−0.683515	−	0.729936i	$-0.739550\pi$
$661$	2.15616e9	−	3.73457e9i	0.290386	−	0.502962i	0.973901	+	0.226974i	$0.0728831\pi$
$662$	−5.59925e8	+	9.69819e8i	−0.0750114	+	0.129924i
$663$	−1.43755e10	−	2.48990e10i	−1.91569	−	3.31807i
$664$	−1.73238e9			−0.229644
$665$	6.03256e8	−	1.62236e8i	0.0795474	−	0.0213930i
$666$	−1.72717e10			−2.26556
$667$	−3.68175e8	−	6.37698e8i	−0.0480412	−	0.0832098i
$668$	1.18127e9	−	2.04601e9i	0.153331	−	0.265577i
$669$	−1.28958e9	+	2.23363e9i	−0.166517	+	0.288416i
$670$	1.04343e8	+	1.80728e8i	0.0134030	+	0.0232147i
$671$	−2.75763e9			−0.352377
$672$	5.89652e8	−	2.20873e9i	0.0749555	−	0.280769i
$673$	8.49626e9			1.07442			0.537211	−	0.843448i	$-0.319478\pi$
$673$	8.49626e9			1.07442			0.537211	+	0.843448i	$0.319478\pi$
$674$	3.74722e8	+	6.49038e8i	0.0471411	+	0.0816509i
$675$	−4.58640e9	+	7.94387e9i	−0.573995	+	0.994189i
$676$	−1.34616e9	+	2.33162e9i	−0.167604	+	0.290298i
$677$	−3.85081e9	−	6.66980e9i	−0.476971	−	0.826138i	0.522681	−	0.852528i	$-0.324932\pi$
$677$	−3.85081e9	−	6.66980e9i	−0.476971	−	0.826138i	−0.999652	+	0.0263906i	$0.991599\pi$
$678$	1.19258e10			1.46955
$679$	−8.72956e8	−	8.71353e8i	−0.107016	−	0.106819i
$680$	3.97347e8			0.0484606
$681$	5.80725e8	+	1.00584e9i	0.0704621	+	0.122044i
$682$	−1.74860e9	+	3.02867e9i	−0.211079	+	0.365600i
$683$	4.85022e9	−	8.40083e9i	0.582491	−	1.00890i	−0.412692	−	0.910871i	$-0.635412\pi$
$683$	4.85022e9	−	8.40083e9i	0.582491	−	1.00890i	0.995183	−	0.0980333i	$-0.0312552\pi$
$684$	3.86029e9	+	6.68622e9i	0.461236	+	0.798885i
$685$	9.41196e8			0.111883
$686$	−5.77939e9	−	1.53152e9i	−0.683515	−	0.181129i
$687$	7.93080e9			0.933186
$688$	7.48289e8	+	1.29607e9i	0.0876011	+	0.151730i
$689$	5.57052e9	−	9.64843e9i	0.648827	−	1.12380i
$690$	−1.09372e8	+	1.89437e8i	−0.0126746	+	0.0219530i
$691$	1.42444e9	+	2.46720e9i	0.164237	+	0.284466i	0.936384	−	0.350977i	$-0.114151\pi$
$691$	1.42444e9	+	2.46720e9i	0.164237	+	0.284466i	−0.772147	+	0.635444i	$0.780817\pi$
$692$	−4.92695e9			−0.565206
$693$	−7.81035e9	−	7.79601e9i	−0.891465	−	0.889828i
$694$	−4.57156e9			−0.519166
$695$	3.16329e8	+	5.47899e8i	0.0357432	+	0.0619090i
$696$	8.65640e8	−	1.49933e9i	0.0973207	−	0.168564i
$697$	−9.73441e9	+	1.68605e10i	−1.08892	+	1.88606i
$698$	9.28491e8	+	1.60819e9i	0.103344	+	0.178996i
$699$	−7.99240e9			−0.885130
$700$	1.16359e9	−	4.35860e9i	0.128221	−	0.480291i
$701$	−4.47816e9			−0.491006			−0.245503	−	0.969396i	$-0.578953\pi$
$701$	−4.47816e9			−0.491006			−0.245503	+	0.969396i	$0.578953\pi$
$702$	4.83617e9	+	8.37649e9i	0.527621	+	0.913866i
$703$	−9.39436e9	+	1.62715e10i	−1.01982	+	1.76638i
$704$	−4.28100e8	+	7.41490e8i	−0.0462424	+	0.0800942i
$705$	1.68933e8	+	2.92600e8i	0.0181573	+	0.0314494i
$706$	9.27799e9			0.992287
$707$	1.02466e10	−	2.75567e9i	1.09047	−	0.293265i
$708$	−7.95354e8			−0.0842256
$709$	4.19450e9	+	7.26510e9i	0.441997	+	0.765560i	0.997838	−	0.0657281i	$-0.0209370\pi$
$709$	4.19450e9	+	7.26510e9i	0.441997	+	0.765560i	−0.555841	+	0.831289i	$0.687604\pi$
$710$	9.41235e7	−	1.63027e8i	0.00986947	−	0.0170944i
$711$	9.29706e9	−	1.61030e10i	0.970068	−	1.68021i
$712$	−1.67346e9	−	2.89852e9i	−0.173754	−	0.300952i
$713$	2.24069e9			0.231509
$714$	1.96883e10	−	5.29485e9i	2.02425	−	0.544390i
$715$	−7.10411e8			−0.0726840
$716$	−1.60117e9	−	2.77331e9i	−0.163020	−	0.282360i
$717$	5.40235e9	−	9.35715e9i	0.547351	−	0.948040i
$718$	−3.88653e9	+	6.73167e9i	−0.391856	+	0.678714i
$719$	6.19091e8	+	1.07230e9i	0.0621160	+	0.107588i	0.895411	−	0.445240i	$-0.146882\pi$
$719$	6.19091e8	+	1.07230e9i	0.0621160	+	0.107588i	−0.833295	+	0.552829i	$0.813548\pi$
$720$	−3.23988e8			−0.0323494
$721$	5.08676e8	−	1.90540e9i	0.0505437	−	0.189327i
$722$	1.24773e9			0.123379
$723$	1.17239e10	+	2.03063e10i	1.15368	+	1.99824i
$724$	−5.22329e8	+	9.04700e8i	−0.0511516	+	0.0885971i
$725$	1.70821e9	−	2.95872e9i	0.166479	−	0.288350i
$726$	−2.71208e9	−	4.69746e9i	−0.263041	−	0.455601i
$727$	−3.52132e9			−0.339888			−0.169944	−	0.985454i	$-0.554359\pi$
$727$	−3.52132e9			−0.339888			−0.169944	+	0.985454i	$0.554359\pi$
$728$	−3.36675e9	−	3.36057e9i	−0.323408	−	0.322814i
$729$	−1.63694e10			−1.56490
$730$	1.39270e8	+	2.41224e8i	0.0132504	+	0.0229504i
$731$	−6.67342e9	+	1.15587e10i	−0.631884	+	1.09446i
$732$	−2.07706e9	+	3.59758e9i	−0.195732	+	0.339017i
$733$	−3.95436e9	−	6.84915e9i	−0.370862	−	0.642352i	0.618836	−	0.785520i	$-0.287604\pi$
$733$	−3.95436e9	−	6.84915e9i	−0.370862	−	0.642352i	−0.989698	+	0.143168i	$0.954271\pi$
$734$	−1.36224e10			−1.27150
$735$	2.47174e6	+	1.34507e9i	0.000229613	+	0.124951i
$736$	5.48574e8			0.0507181
$737$	−2.00516e9	−	3.47304e9i	−0.184507	−	0.319576i
$738$	7.93724e9	−	1.37477e10i	0.726895	−	1.25902i
$739$	−2.24356e9	+	3.88597e9i	−0.204495	+	0.354196i	−0.949972	−	0.312336i	$-0.898889\pi$
$739$	−2.24356e9	+	3.88597e9i	−0.204495	+	0.354196i	0.745477	+	0.666532i	$0.232222\pi$
$740$	−3.94227e8	−	6.82822e8i	−0.0357632	−	0.0619436i
$741$	2.55020e10			2.30255
$742$	5.59151e9	+	5.58124e9i	0.502476	+	0.501553i
$743$	−4.33508e9			−0.387736			−0.193868	−	0.981028i	$-0.562103\pi$
$743$	−4.33508e9			−0.387736			−0.193868	+	0.981028i	$0.562103\pi$
$744$	2.63412e9	+	4.56242e9i	0.234493	+	0.406153i
$745$	−4.33461e8	+	7.50777e8i	−0.0384064	+	0.0665218i
$746$	−1.50795e9	+	2.61185e9i	−0.132984	+	0.230336i
$747$	6.29871e9	+	1.09097e10i	0.552878	+	0.957613i
$748$	−7.63579e9			−0.667112
$749$	−2.51996e9	+	9.43930e9i	−0.219133	+	0.820830i
$750$	−2.03570e9			−0.176197
$751$	5.94199e9	+	1.02918e10i	0.511908	+	0.886651i	0.999905	+	0.0138052i	$0.00439447\pi$
$751$	5.94199e9	+	1.02918e10i	0.511908	+	0.886651i	−0.487997	+	0.872845i	$0.662272\pi$
$752$	4.23656e8	−	7.33794e8i	0.0363288	−	0.0629233i
$753$	2.76968e9	−	4.79722e9i	0.236400	−	0.409456i
$754$	−1.80124e9	−	3.11985e9i	−0.153029	−	0.265054i
$755$	7.57567e8			0.0640630
$756$	−6.62350e9	+	1.78129e9i	−0.557521	+	0.149937i
$757$	1.37796e10			1.15452			0.577260	−	0.816560i	$-0.304122\pi$
$757$	1.37796e10			1.15452			0.577260	+	0.816560i	$0.304122\pi$
$758$	−3.54799e9	−	6.14531e9i	−0.295897	−	0.512509i
$759$	2.10179e9	−	3.64041e9i	0.174479	−	0.302206i
$760$	−1.76223e8	+	3.05227e8i	−0.0145618	+	0.0252217i
$761$	−4.26500e9	−	7.38719e9i	−0.350810	−	0.607622i	0.635581	−	0.772034i	$-0.280761\pi$
$761$	−4.26500e9	−	7.38719e9i	−0.350810	−	0.607622i	−0.986392	+	0.164412i	$0.947427\pi$
$762$	8.70099e8			0.0712404
$763$	−1.08452e10	+	2.91664e9i	−0.883897	+	0.237710i
$764$	9.53907e9			0.773890
$765$	−1.44470e9	−	2.50230e9i	−0.116671	−	0.202081i
$766$	1.73718e9	−	3.00889e9i	0.139651	−	0.241883i
$767$	−8.27496e8	+	1.43327e9i	−0.0662189	+	0.114695i
$768$	6.44894e8	+	1.11699e9i	0.0513717	+	0.0889785i
$769$	−1.57605e10			−1.24976			−0.624881	−	0.780720i	$-0.714853\pi$
$769$	−1.57605e10			−1.24976			−0.624881	+	0.780720i	$0.714853\pi$
$770$	1.29937e8	−	4.86720e8i	0.0102569	−	0.0384204i
$771$	4.44878e8			0.0349583
$772$	−2.02876e9	−	3.51391e9i	−0.158697	−	0.274872i
$773$	1.87506e9	−	3.24770e9i	0.146011	−	0.252899i	−0.783738	−	0.621091i	$-0.786690\pi$
$773$	1.87506e9	−	3.24770e9i	0.146011	−	0.252899i	0.929750	+	0.368192i	$0.120023\pi$
$774$	5.44137e9	−	9.42472e9i	0.421808	−	0.730592i
$775$	5.19804e9	+	9.00327e9i	0.401129	+	0.694776i
$776$	6.95882e8			0.0534588
$777$	−2.86326e10	−	2.85801e10i	−2.18972	−	2.18570i
$778$	1.21278e9			0.0923320
$779$	−8.63439e9	−	1.49552e10i	−0.654411	−	1.13347i
$780$	−5.35086e8	+	9.26796e8i	−0.0403731	+	0.0699283i
$781$	−1.80876e9	+	3.13287e9i	−0.135864	+	0.235323i
$782$	2.44616e9	+	4.23687e9i	0.182920	+	0.316827i
$783$	−5.19430e9			−0.386688
$784$	2.91820e9	−	1.69198e9i	0.216276	−	0.125398i
$785$	1.10620e9			0.0816186
$786$	−1.09236e10	−	1.89203e10i	−0.802396	−	1.38979i
$787$	1.01205e10	−	1.75292e10i	0.740099	−	1.28189i	−0.212350	−	0.977194i	$-0.568112\pi$
$787$	1.01205e10	−	1.75292e10i	0.740099	−	1.28189i	0.952450	−	0.304696i	$-0.0985549\pi$
$788$	−9.40132e8	+	1.62836e9i	−0.0684459	+	0.118552i
$789$	8.96670e9	+	1.55308e10i	0.649925	+	1.12570i
$790$	8.48825e8			0.0612524
$791$	1.24545e10	+	1.24316e10i	0.894763	+	0.893120i
$792$	6.22607e9			0.445323
$793$	4.32200e9	+	7.48592e9i	0.307772	+	0.533076i
$794$	6.82068e9	−	1.18138e10i	0.483566	−	0.837561i
$795$	8.88673e8	−	1.53923e9i	0.0627273	−	0.108647i
$796$	−1.57343e9	−	2.72525e9i	−0.110573	−	0.191519i
$797$	−1.96658e10			−1.37597			−0.687983	−	0.725727i	$-0.741504\pi$
$797$	−1.96658e10			−1.37597			−0.687983	+	0.725727i	$0.741504\pi$
$798$	−4.66442e9	+	1.74720e10i	−0.324928	+	1.21712i
$799$	7.55654e9			0.524094
$800$	1.27260e9	+	2.20422e9i	0.0878777	+	0.152209i
$801$	−1.21690e10	+	2.10773e10i	−0.836644	+	1.44911i
$802$	−4.60706e9	+	7.97967e9i	−0.315365	+	0.546229i
$803$	−2.67635e9	−	4.63558e9i	−0.182406	−	0.315936i
$804$	−6.04119e9			−0.409946
$805$	−3.11692e8	+	8.38247e7i	−0.0210591	+	0.00566352i
$806$	1.09623e10			0.737441
$807$	−1.58752e10	−	2.74966e10i	−1.06331	−	1.84171i
$808$	−2.99324e9	+	5.18445e9i	−0.199619	+	0.345750i
$809$	−2.91367e9	+	5.04662e9i	−0.193473	+	0.335105i	−0.946399	−	0.323000i	$-0.895308\pi$
$809$	−2.91367e9	+	5.04662e9i	−0.193473	+	0.335105i	0.752926	+	0.658105i	$0.228642\pi$
$810$	7.95646e7	+	1.37810e8i	0.00526044	+	0.00911135i
$811$	1.13903e10			0.749829			0.374914	−	0.927059i	$-0.377672\pi$
$811$	1.13903e10			0.749829			0.374914	+	0.927059i	$0.377672\pi$
$812$	2.46694e9	−	6.63445e8i	0.161701	−	0.0434869i
$813$	−2.24374e9			−0.146439
$814$	7.57584e9	+	1.31217e10i	0.492318	+	0.852719i
$815$	5.78358e8	−	1.00175e9i	0.0374236	−	0.0648195i
$816$	−5.75132e9	+	9.96159e9i	−0.370555	+	0.641820i
$817$	−5.91930e9	−	1.02525e10i	−0.379746	−	0.657739i
$818$	9.15175e9			0.584612
$819$	−8.92216e9	+	3.34207e10i	−0.567514	+	2.12580i
$820$	7.24672e8			0.0458979
$821$	−5.98364e9	−	1.03640e10i	−0.377367	−	0.653619i	0.613311	−	0.789841i	$-0.289837\pi$
$821$	−5.98364e9	−	1.03640e10i	−0.377367	−	0.653619i	−0.990678	+	0.136222i	$0.956504\pi$
$822$	−1.36232e10	+	2.35960e10i	−0.855513	+	1.48179i
$823$	1.24348e10	−	2.15376e10i	0.777568	−	1.34679i	−0.155772	−	0.987793i	$-0.549787\pi$
$823$	1.24348e10	−	2.15376e10i	0.777568	−	1.34679i	0.933340	−	0.358994i	$-0.116880\pi$
$824$	5.56331e8	+	9.63594e8i	0.0346408	+	0.0599997i
$825$	1.95033e10			1.20926
$826$	−8.30613e8	−	8.29088e8i	−0.0512824	−	0.0511883i
$827$	1.05586e10			0.649137			0.324569	−	0.945862i	$-0.394781\pi$
$827$	1.05586e10			0.649137			0.324569	+	0.945862i	$0.394781\pi$
$828$	−1.99455e9	−	3.45466e9i	−0.122106	−	0.211494i
$829$	5.93269e9	−	1.02757e10i	0.361668	−	0.626428i	−0.626567	−	0.779367i	$-0.715541\pi$
$829$	5.93269e9	−	1.02757e10i	0.361668	−	0.626428i	0.988236	+	0.152939i	$0.0488739\pi$
$830$	−2.87537e8	+	4.98029e8i	−0.0174550	+	0.0302330i
$831$	2.51034e10	+	4.34804e10i	1.51750	+	2.62839i
$832$	2.68382e9			0.161556
$833$	2.60805e10	+	1.49938e10i	1.56336	+	0.898779i
$834$	−1.83146e10			−1.09324
$835$	−3.92129e8	−	6.79188e8i	−0.0233092	−	0.0403726i
$836$	3.38646e9	−	5.86552e9i	0.200458	−	0.347204i
$837$	7.90304e9	−	1.36885e10i	0.465859	−	0.806892i
$838$	−6.89127e9	−	1.19360e10i	−0.404525	−	0.700657i
$839$	4.68285e9			0.273743			0.136872	−	0.990589i	$-0.456295\pi$
$839$	4.68285e9			0.273743			0.136872	+	0.990589i	$0.456295\pi$
$840$	−5.37102e8	−	5.36115e8i	−0.0312665	−	0.0312091i
$841$	−1.53152e10			−0.887847
$842$	1.00198e10	+	1.73548e10i	0.578453	+	1.00191i
$843$	1.98941e10	−	3.44576e10i	1.14374	−	1.98102i
$844$	8.17004e9	−	1.41509e10i	0.467763	−	0.810189i
$845$	4.46866e8	+	7.73995e8i	0.0254788	+	0.0441306i
$846$	−6.16144e9			−0.349853
$847$	2.06439e9	−	7.73280e9i	0.116734	−	0.437265i
$848$	−4.45730e9			−0.251007
$849$	5.50851e8	+	9.54102e8i	0.0308928	+	0.0535079i
$850$	−1.13494e10	+	1.96577e10i	−0.633879	+	1.09791i
$851$	4.85391e9	−	8.40721e9i	0.269984	−	0.467626i
$852$	2.72474e9	+	4.71940e9i	0.150934	+	0.261425i
$853$	−5.76473e9			−0.318022			−0.159011	−	0.987277i	$-0.550831\pi$
$853$	−5.76473e9			−0.318022			−0.159011	+	0.987277i	$0.550831\pi$
$854$	−5.91930e9	+	1.59190e9i	−0.325213	+	0.0874610i
$855$	2.56290e9			0.140233
$856$	−2.75604e9	−	4.77361e9i	−0.150185	−	0.260129i
$857$	−1.23111e10	+	2.13235e10i	−0.668135	+	1.15724i	0.310290	+	0.950642i	$0.399574\pi$
$857$	−1.23111e10	+	2.13235e10i	−0.668135	+	1.15724i	−0.978425	+	0.206602i	$0.933759\pi$
$858$	1.02827e10	−	1.78102e10i	0.555779	−	0.962637i
$859$	−1.49943e10	−	2.59709e10i	−0.807144	−	1.39801i	−0.914834	−	0.403829i	$-0.867679\pi$
$859$	−1.49943e10	−	2.59709e10i	−0.807144	−	1.39801i	0.107691	−	0.994184i	$-0.465654\pi$
$860$	4.96798e8			0.0266339
$861$	3.59070e10	−	9.65662e9i	1.91720	−	0.515601i
$862$	1.82884e10			0.972526
$863$	−4.28994e8	−	7.43040e8i	−0.0227203	−	0.0393527i	0.854442	−	0.519547i	$-0.173899\pi$
$863$	−4.28994e8	−	7.43040e8i	−0.0227203	−	0.0393527i	−0.877162	+	0.480195i	$0.840566\pi$
$864$	1.93485e9	−	3.35126e9i	0.102059	−	0.176771i
$865$	−8.17766e8	+	1.41641e9i	−0.0429608	+	0.0744103i
$866$	8.29326e9	+	1.43644e10i	0.433923	+	0.751577i
$867$	−7.10377e10			−3.70187
$868$	−2.00504e9	+	7.51052e9i	−0.104065	+	0.389808i
$869$	−1.63118e10			−0.843204
$870$	−2.87355e8	−	4.97713e8i	−0.0147945	−	0.0256249i
$871$	−6.28533e9	+	1.08865e10i	−0.322303	+	0.558245i
$872$	3.16809e9	−	5.48729e9i	0.161804	−	0.280253i
$873$	−2.53014e9	−	4.38233e9i	−0.128705	−	0.222923i
$874$	−4.33947e9			−0.219860
$875$	−2.12594e9	−	2.12204e9i	−0.107281	−	0.107084i
$876$	−8.06337e9			−0.405277
$877$	2.82487e9	+	4.89282e9i	0.141416	+	0.244940i	0.928030	−	0.372505i	$-0.121501\pi$
$877$	2.82487e9	+	4.89282e9i	0.141416	+	0.244940i	−0.786614	+	0.617445i	$0.788168\pi$
$878$	7.03459e9	−	1.21843e10i	0.350758	−	0.607531i
$879$	−1.76663e10	+	3.05989e10i	−0.877373	+	1.51966i
$880$	1.42110e8	+	2.46142e8i	0.00702970	+	0.0121758i
$881$	−2.87116e10			−1.41462			−0.707312	−	0.706902i	$-0.750092\pi$
$881$	−2.87116e10			−1.41462			−0.707312	+	0.706902i	$0.750092\pi$
$882$	−2.12655e10	−	1.22256e10i	−1.04360	−	0.599970i
$883$	1.38023e10			0.674668			0.337334	−	0.941385i	$-0.390475\pi$
$883$	1.38023e10			0.674668			0.337334	+	0.941385i	$0.390475\pi$
$884$	1.19675e10	+	2.07283e10i	0.582667	+	1.00921i
$885$	−1.32011e8	+	2.28651e8i	−0.00640192	+	0.0110884i
$886$	7.71789e9	−	1.33678e10i	0.372804	−	0.645715i
$887$	1.86125e10	+	3.22378e10i	0.895513	+	1.55107i	0.833168	+	0.553020i	$0.186525\pi$
$887$	1.86125e10	+	3.22378e10i	0.895513	+	1.55107i	0.0623449	+	0.998055i	$0.480142\pi$
$888$	2.28247e10			1.09385
$889$	9.08672e8	+	9.07003e8i	0.0433761	+	0.0432965i
$890$	−1.11103e9			−0.0528277
$891$	−1.52899e9	−	2.64828e9i	−0.0724156	−	0.125427i
$892$	1.07357e9	−	1.85948e9i	0.0506470	−	0.0877232i
$893$	−3.35131e9	+	5.80464e9i	−0.157483	+	0.272769i
$894$	−1.25481e10	−	2.17340e10i	−0.587350	−	1.01732i
$895$	−1.06304e9			−0.0495642
$896$	−4.90882e8	+	1.83875e9i	−0.0227981	+	0.0853976i
$897$	−1.31764e10			−0.609571
$898$	−1.31730e10	−	2.28163e10i	−0.607040	−	1.05142i
$899$	−2.94351e9	+	5.09830e9i	−0.135116	+	0.234027i
$900$	9.25406e9	−	1.60285e10i	0.423139	−	0.732899i
$901$	−1.98757e10	−	3.44256e10i	−0.905284	−	1.56800i
$902$	−1.39260e10			−0.631834
$903$	2.46160e10	−	6.62009e9i	1.11253	−	0.299197i
$904$	−9.92816e9			−0.446971
$905$	1.73390e8	+	3.00321e8i	0.00777597	+	0.0134684i
$906$	−1.09653e10	+	1.89924e10i	−0.489858	+	0.848459i
$907$	2.80129e9	−	4.85198e9i	0.124662	−	0.215920i	−0.796939	−	0.604060i	$-0.793549\pi$
$907$	2.80129e9	−	4.85198e9i	0.124662	−	0.215920i	0.921601	+	0.388139i	$0.126882\pi$
$908$	−4.83450e8	−	8.37360e8i	−0.0214314	−	0.0371203i
$909$	4.35322e10			1.92237
$910$	−1.52491e9	+	4.10101e8i	−0.0670810	+	0.0180404i
$911$	−3.57046e10			−1.56462			−0.782312	−	0.622886i	$-0.785960\pi$
$911$	−3.57046e10			−1.56462			−0.782312	+	0.622886i	$0.785960\pi$
$912$	−5.10141e9	−	8.83589e9i	−0.222694	−	0.385717i
$913$	5.52558e9	−	9.57059e9i	0.240287	−	0.416189i
$914$	7.65848e9	−	1.32649e10i	0.331765	−	0.574634i
$915$	6.89494e8	+	1.19424e9i	0.0297548	+	0.0515368i
$916$	−6.60235e9			−0.283834
$917$	8.31489e9	−	3.11460e10i	0.356093	−	1.33386i
$918$	3.45110e10			1.47234
$919$	−2.19020e9	−	3.79354e9i	−0.0930850	−	0.161228i	0.815723	−	0.578443i	$-0.196340\pi$
$919$	−2.19020e9	−	3.79354e9i	−0.0930850	−	0.161228i	−0.908808	+	0.417215i	$0.863006\pi$
$920$	9.10513e7	−	1.57706e8i	0.00385504	−	0.00667713i
$921$	−8.77020e9	+	1.51904e10i	−0.369914	+	0.640710i
$922$	7.36270e9	+	1.27526e10i	0.309371	+	0.535845i
$923$	1.13394e10			0.474663
$924$	1.03214e10	+	1.03025e10i	0.430416	+	0.429626i
$925$	4.50412e10			1.87117
$926$	6.71767e8	+	1.16353e9i	0.0278023	+	0.0481550i
$927$	4.04550e9	−	7.00701e9i	0.166799	−	0.288904i
$928$	−7.20641e8	+	1.24819e9i	−0.0296006	+	0.0512698i
$929$	9.08246e9	+	1.57313e10i	0.371662	+	0.643738i	0.989821	−	0.142315i	$-0.0454546\pi$
$929$	9.08246e9	+	1.57313e10i	0.371662	+	0.643738i	−0.618159	+	0.786053i	$0.712121\pi$
$930$	1.74882e9			0.0712944
$931$	−2.30843e10	+	1.33843e10i	−0.937546	+	0.543592i
$932$	6.65362e9			0.269217
$933$	2.74096e10	+	4.74747e10i	1.10488	+	1.91371i
$934$	−5.51631e9	+	9.55452e9i	−0.221531	+	0.383703i
$935$	−1.26738e9	+	2.19516e9i	−0.0507066	+	0.0878264i
$936$	−9.75804e9	−	1.69014e10i	−0.388953	−	0.673686i
$937$	2.55925e10			1.01631			0.508153	−	0.861267i	$-0.330328\pi$
$937$	2.55925e10			1.01631			0.508153	+	0.861267i	$0.330328\pi$
$938$	−6.30900e9	−	6.29742e9i	−0.249604	−	0.249145i
$939$	1.07277e10			0.422840
$940$	−1.40635e8	−	2.43588e8i	−0.00552264	−	0.00956550i
$941$	−1.53193e10	+	2.65338e10i	−0.599343	+	1.03809i	0.393576	+	0.919292i	$0.371238\pi$
$941$	−1.53193e10	+	2.65338e10i	−0.599343	+	1.03809i	−0.992918	+	0.118800i	$0.962095\pi$
$942$	−1.60114e10	+	2.77326e10i	−0.624097	+	1.08097i
$943$	4.46124e9	+	7.72710e9i	0.173247	+	0.300072i
$944$	6.62128e8			0.0256177
$945$	−5.87268e8	+	2.19980e9i	−0.0226373	+	0.0847952i
$946$	−9.54694e9			−0.366645
$947$	−1.13440e10	−	1.96484e10i	−0.434052	−	0.751800i	0.563166	−	0.826344i	$-0.309583\pi$
$947$	−1.13440e10	−	1.96484e10i	−0.434052	−	0.751800i	−0.997218	+	0.0745437i	$0.976250\pi$
$948$	−1.22861e10	+	2.12802e10i	−0.468367	+	0.811236i
$949$	−8.38923e9	+	1.45306e10i	−0.318633	+	0.551888i
$950$	−1.00669e10	−	1.74363e10i	−0.380945	−	0.659816i
$951$	1.18305e10			0.446038
$952$	−1.63904e10	+	4.40793e9i	−0.615687	+	0.165579i
$953$	−2.31130e10			−0.865030			−0.432515	−	0.901627i	$-0.642374\pi$
$953$	−2.31130e10			−0.865030			−0.432515	+	0.901627i	$0.642374\pi$
$954$	1.62062e10	+	2.80699e10i	0.604313	+	1.04670i
$955$	1.58328e9	−	2.74232e9i	0.0588228	−	0.101884i
$956$	−4.49743e9	+	7.78977e9i	−0.166480	+	0.288352i
$957$	5.52208e9	+	9.56452e9i	0.203662	+	0.352754i
$958$	3.62407e10			1.33173
$959$	−3.88239e10	+	1.04411e10i	−1.42146	+	0.382278i
$960$	4.28154e8			0.0156189
$961$	4.79931e9	+	8.31265e9i	0.174440	+	0.302140i
$962$	2.37471e10	−	4.11311e10i	0.859997	−	1.48956i
$963$	−2.00413e10	+	3.47125e10i	−0.723157	+	1.25255i
$964$	−9.76005e9	−	1.69049e10i	−0.350899	−	0.607775i
$965$	−1.34692e9			−0.0482498
$966$	2.41002e9	−	9.02751e9i	0.0860204	−	0.322217i
$967$	1.63381e10			0.581043			0.290521	−	0.956868i	$-0.406171\pi$
$967$	1.63381e10			0.581043			0.290521	+	0.956868i	$0.406171\pi$
$968$	2.25779e9	+	3.91061e9i	0.0800055	+	0.138574i
$969$	4.54956e10	−	7.88006e10i	1.60633	−	2.78225i
$970$	1.15501e8	−	2.00054e8i	0.00406336	−	0.00703795i
$971$	2.36893e9	+	4.10311e9i	0.0830396	+	0.143829i	0.904554	−	0.426359i	$-0.140204\pi$
$971$	2.36893e9	+	4.10311e9i	0.0830396	+	0.143829i	−0.821515	+	0.570188i	$0.806871\pi$
$972$	1.19228e10			0.416435
$973$	−1.91265e10	−	1.90914e10i	−0.665642	−	0.664420i
$974$	1.23164e10			0.427097
$975$	−3.05672e10	−	5.29440e10i	−1.05619	−	1.82937i
$976$	1.72914e9	−	2.99496e9i	0.0595328	−	0.103114i
$977$	−8.57370e9	+	1.48501e10i	−0.294129	+	0.509446i	−0.974782	−	0.223160i	$-0.928363\pi$
$977$	−8.57370e9	+	1.48501e10i	−0.294129	+	0.509446i	0.680653	+	0.732606i	$0.261696\pi$
$978$	1.67427e10	+	2.89991e10i	0.572319	+	0.991286i
$979$	2.13506e10			0.727230
$980$	−2.05771e6	−	1.11976e9i	−6.98380e−5	−	0.0380045i
$981$	−4.60751e10			−1.55821
$982$	7.43121e9	+	1.28712e10i	0.250420	+	0.433741i
$983$	2.27209e10	−	3.93537e10i	0.762935	−	1.32144i	−0.178397	−	0.983959i	$-0.557091\pi$
$983$	2.27209e10	−	3.93537e10i	0.762935	−	1.32144i	0.941332	−	0.337483i	$-0.109575\pi$
$984$	−1.04891e10	+	1.81677e10i	−0.350959	+	0.607879i
$985$	3.12083e8	+	5.40543e8i	0.0104050	+	0.0180220i
$986$	−1.28537e10			−0.427030
$987$	−1.02143e10	−	1.01956e10i	−0.338142	−	0.337521i
$988$	−2.12302e10			−0.700335
$989$	3.05840e9	+	5.29731e9i	0.100533	+	0.174128i
$990$	1.03339e9	−	1.78989e9i	0.0338487	−	0.0586276i
$991$	1.63460e10	−	2.83122e10i	0.533525	−	0.924092i	−0.465708	−	0.884938i	$-0.654200\pi$
$991$	1.63460e10	−	2.83122e10i	0.533525	−	0.924092i	0.999233	−	0.0391537i	$-0.0124662\pi$
$992$	−2.19289e9	−	3.79819e9i	−0.0713223	−	0.123534i
$993$	−1.07614e10			−0.348776
$994$	−2.07403e9	+	7.76892e9i	−0.0669826	+	0.250904i
$995$	−1.04462e9			−0.0336184
$996$	−8.32380e9	−	1.44172e10i	−0.266940	−	0.462354i
$997$	−2.70222e10	+	4.68038e10i	−0.863550	+	1.49571i	0.00493036	+	0.999988i	$0.498431\pi$
$997$	−2.70222e10	+	4.68038e10i	−0.863550	+	1.49571i	−0.868480	+	0.495724i	$0.834903\pi$
$998$	−2.14142e10	+	3.70904e10i	−0.681937	+	1.18115i
$999$	−3.42400e10	−	5.93054e10i	−1.08656	−	1.88198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.8.c.a.11.2	yes	4
3.2	odd	2		126.8.g.e.109.2		4
4.3	odd	2		112.8.i.a.81.1		4
7.2	even	3	inner	14.8.c.a.9.2	✓	4
7.3	odd	6		98.8.a.k.1.2		2
7.4	even	3		98.8.a.h.1.1		2
7.5	odd	6		98.8.c.h.79.1		4
7.6	odd	2		98.8.c.h.67.1		4
21.2	odd	6		126.8.g.e.37.2		4
28.23	odd	6		112.8.i.a.65.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.8.c.a.9.2	✓	4	7.2	even	3	inner
14.8.c.a.11.2	yes	4	1.1	even	1	trivial
98.8.a.h.1.1		2	7.4	even	3
98.8.a.k.1.2		2	7.3	odd	6
98.8.c.h.67.1		4	7.6	odd	2
98.8.c.h.79.1		4	7.5	odd	6
112.8.i.a.65.1		4	28.23	odd	6
112.8.i.a.81.1		4	4.3	odd	2
126.8.g.e.37.2		4	21.2	odd	6
126.8.g.e.109.2		4	3.2	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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 6.92820i) q^{2} +(38.4387 - 66.5778i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(10.6226 + 18.3989i) q^{5} -615.019 q^{6} +(-642.284 - 641.104i) q^{7} +512.000 q^{8} +(-1861.57 - 3224.33i) q^{9} +O(q^{10})\)	\(q+(-4.00000 - 6.92820i) q^{2} +(38.4387 - 66.5778i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(10.6226 + 18.3989i) q^{5} -615.019 q^{6} +(-642.284 - 641.104i) q^{7} +512.000 q^{8} +(-1861.57 - 3224.33i) q^{9} +(84.9808 - 147.191i) q^{10} +(-1633.07 + 2828.56i) q^{11} +(2460.08 + 4260.98i) q^{12} +10238.0 q^{13} +(-1872.57 + 7014.29i) q^{14} +1633.28 q^{15} +(-2048.00 - 3547.24i) q^{16} +(18264.6 - 31635.1i) q^{17} +(-14892.5 + 25794.6i) q^{18} +(16200.6 + 28060.3i) q^{19} -1359.69 q^{20} +(-67371.9 + 18118.6i) q^{21} +26129.1 q^{22} +(-8370.58 - 14498.3i) q^{23} +(19680.6 - 34087.8i) q^{24} +(38836.8 - 67267.3i) q^{25} +(-40951.9 - 70930.7i) q^{26} -118094. q^{27} +(56086.7 - 15083.6i) q^{28} +43984.4 q^{29} +(-6533.10 - 11315.7i) q^{30} +(-66921.6 + 115912. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(125546. + 217452. i) q^{33} -292233. q^{34} +(4972.88 - 18627.5i) q^{35} +238281. q^{36} +(289939. + 502188. i) q^{37} +(129605. - 224482. i) q^{38} +(393534. - 681621. i) q^{39} +(5438.77 + 9420.23i) q^{40} -532967. q^{41} +(395017. + 394291. i) q^{42} -365375. q^{43} +(-104517. - 181028. i) q^{44} +(39549.4 - 68501.5i) q^{45} +(-66964.6 + 115986. i) q^{46} +(103432. + 179149. i) q^{47} -314890. q^{48} +(1513.36 + 823542. i) q^{49} -621389. q^{50} +(-1.40413e6 - 2.43203e6i) q^{51} +(-327615. + 567446. i) q^{52} +(544104. - 942416. i) q^{53} +(472376. + 818179. i) q^{54} -69389.9 q^{55} +(-328849. - 328245. i) q^{56} +2.49092e6 q^{57} +(-175938. - 304733. i) q^{58} +(-80826.2 + 139995. i) q^{59} +(-52264.8 + 90525.3i) q^{60} +(422154. + 731192. i) q^{61} +1.07075e6 q^{62} +(-871477. + 3.26439e6i) q^{63} +262144. q^{64} +(108754. + 188367. i) q^{65} +(1.00437e6 - 1.73962e6i) q^{66} +(-613923. + 1.06335e6i) q^{67} +(1.16893e6 + 2.02465e6i) q^{68} -1.28702e6 q^{69} +(-148947. + 40056.8i) q^{70} +1.10759e6 q^{71} +(-953122. - 1.65086e6i) q^{72} +(-819423. + 1.41928e6i) q^{73} +(2.31951e6 - 4.01751e6i) q^{74} +(-2.98567e6 - 5.17134e6i) q^{75} -2.07368e6 q^{76} +(2.86230e6 - 769770. i) q^{77} -6.29655e6 q^{78} +(2.49711e6 + 4.32512e6i) q^{79} +(43510.2 - 75361.8i) q^{80} +(-468133. + 810829. i) q^{81} +(2.13187e6 + 3.69251e6i) q^{82} -3.38355e6 q^{83} +(1.15166e6 - 4.31392e6i) q^{84} +776069. q^{85} +(1.46150e6 + 2.53139e6i) q^{86} +(1.69070e6 - 2.92838e6i) q^{87} +(-836132. + 1.44822e6i) q^{88} +(-3.26848e6 - 5.66118e6i) q^{89} -632790. q^{90} +(-6.57568e6 - 6.56361e6i) q^{91} +1.07143e6 q^{92} +(5.14476e6 + 8.91098e6i) q^{93} +(827454. - 1.43319e6i) q^{94} +(-344185. + 596146. i) q^{95} +(1.25956e6 + 2.18162e6i) q^{96} +1.35914e6 q^{97} +(5.69961e6 - 3.30465e6i) q^{98} +1.21603e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 56 q^{3} - 128 q^{4} + 238 q^{5} - 896 q^{6} + 168 q^{7} + 2048 q^{8} - 1972 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 + 56 * q^3 - 128 * q^4 + 238 * q^5 - 896 * q^6 + 168 * q^7 + 2048 * q^8 - 1972 * q^9	\( 4 q - 16 q^{2} + 56 q^{3} - 128 q^{4} + 238 q^{5} - 896 q^{6} + 168 q^{7} + 2048 q^{8} - 1972 q^{9} + 1904 q^{10} - 5848 q^{11} + 3584 q^{12} + 2632 q^{13} - 2016 q^{14} - 5784 q^{15} - 8192 q^{16} + 47642 q^{17} - 15776 q^{18} + 41048 q^{19} - 30464 q^{20} - 169582 q^{21} + 93568 q^{22} + 49316 q^{23} + 28672 q^{24} + 108816 q^{25} - 10528 q^{26} - 400624 q^{27} + 5376 q^{28} + 345640 q^{29} + 23136 q^{30} + 70252 q^{31} - 65536 q^{32} + 197190 q^{33} - 762272 q^{34} - 36904 q^{35} + 252416 q^{36} + 88166 q^{37} + 328384 q^{38} + 973336 q^{39} + 121856 q^{40} - 2312520 q^{41} + 1032640 q^{42} + 115088 q^{43} - 374272 q^{44} - 300468 q^{45} + 394528 q^{46} + 1412292 q^{47} - 458752 q^{48} + 465892 q^{49} - 1741056 q^{50} - 2576256 q^{51} - 84224 q^{52} + 2361174 q^{53} + 1602496 q^{54} - 1258040 q^{55} + 86016 q^{56} + 4620796 q^{57} - 1382560 q^{58} - 1842512 q^{59} + 185088 q^{60} - 1278242 q^{61} - 1124032 q^{62} - 2121448 q^{63} + 1048576 q^{64} - 1716372 q^{65} + 1577520 q^{66} + 2121480 q^{67} + 3049088 q^{68} - 5332236 q^{69} + 2595712 q^{70} + 7200320 q^{71} - 1009664 q^{72} + 1634682 q^{73} + 705328 q^{74} - 5321176 q^{75} - 5254144 q^{76} + 1416226 q^{77} - 15573376 q^{78} + 9192604 q^{79} + 974848 q^{80} - 3049498 q^{81} + 9250080 q^{82} - 56560 q^{83} + 2592128 q^{84} + 6369676 q^{85} - 460352 q^{86} + 691656 q^{87} - 2994176 q^{88} - 8936550 q^{89} + 4807488 q^{90} - 26111120 q^{91} - 6312448 q^{92} + 14550490 q^{93} + 11298336 q^{94} - 2562604 q^{95} + 1835008 q^{96} + 11748408 q^{97} + 20499248 q^{98} + 15278208 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 56 * q^3 - 128 * q^4 + 238 * q^5 - 896 * q^6 + 168 * q^7 + 2048 * q^8 - 1972 * q^9 + 1904 * q^10 - 5848 * q^11 + 3584 * q^12 + 2632 * q^13 - 2016 * q^14 - 5784 * q^15 - 8192 * q^16 + 47642 * q^17 - 15776 * q^18 + 41048 * q^19 - 30464 * q^20 - 169582 * q^21 + 93568 * q^22 + 49316 * q^23 + 28672 * q^24 + 108816 * q^25 - 10528 * q^26 - 400624 * q^27 + 5376 * q^28 + 345640 * q^29 + 23136 * q^30 + 70252 * q^31 - 65536 * q^32 + 197190 * q^33 - 762272 * q^34 - 36904 * q^35 + 252416 * q^36 + 88166 * q^37 + 328384 * q^38 + 973336 * q^39 + 121856 * q^40 - 2312520 * q^41 + 1032640 * q^42 + 115088 * q^43 - 374272 * q^44 - 300468 * q^45 + 394528 * q^46 + 1412292 * q^47 - 458752 * q^48 + 465892 * q^49 - 1741056 * q^50 - 2576256 * q^51 - 84224 * q^52 + 2361174 * q^53 + 1602496 * q^54 - 1258040 * q^55 + 86016 * q^56 + 4620796 * q^57 - 1382560 * q^58 - 1842512 * q^59 + 185088 * q^60 - 1278242 * q^61 - 1124032 * q^62 - 2121448 * q^63 + 1048576 * q^64 - 1716372 * q^65 + 1577520 * q^66 + 2121480 * q^67 + 3049088 * q^68 - 5332236 * q^69 + 2595712 * q^70 + 7200320 * q^71 - 1009664 * q^72 + 1634682 * q^73 + 705328 * q^74 - 5321176 * q^75 - 5254144 * q^76 + 1416226 * q^77 - 15573376 * q^78 + 9192604 * q^79 + 974848 * q^80 - 3049498 * q^81 + 9250080 * q^82 - 56560 * q^83 + 2592128 * q^84 + 6369676 * q^85 - 460352 * q^86 + 691656 * q^87 - 2994176 * q^88 - 8936550 * q^89 + 4807488 * q^90 - 26111120 * q^91 - 6312448 * q^92 + 14550490 * q^93 + 11298336 * q^94 - 2562604 * q^95 + 1835008 * q^96 + 11748408 * q^97 + 20499248 * q^98 + 15278208 * q^99

Introduction

L-functions

Modular forms

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