LMFDB - Embedded newform 42.9.g.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,9,Mod(19,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("42.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	42.g (of order $6$, 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:	$17.1099016226$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 6683 x^{10} + 105006 x^{9} + 34690411 x^{8} + 548172728 x^{7} + \cdots + 30\!\cdots\!24 $ x^12 - 2x^11 + 6683x^10 + 105006x^9 + 34690411x^8 + 548172728x^7 + 69245553226x^6 + 2257669296800x^5 + 109555419264148x^4 + 2043640985398464x^3 + 35697604660076192x^2 + 112120335940899328*x + 305636965993402624
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{6}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$34.6228 + 59.9685i$ of defining polynomial
Character	$\chi$	$=$	42.31
Dual form			42.9.g.b.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65685 - 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(124.890 - 72.1052i) q^{5} +529.090i q^{6} +(1980.48 - 1357.39i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})$	\(q+(-5.65685 - 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(124.890 - 72.1052i) q^{5} +529.090i q^{6} +(1980.48 - 1357.39i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +(-1412.97 - 815.777i) q^{10} +(5721.83 - 9910.51i) q^{11} +(5184.00 - 2992.98i) q^{12} -16618.4i q^{13} +(-24502.9 - 11726.1i) q^{14} -6744.05 q^{15} +(-8192.00 - 14189.0i) q^{16} +(9252.26 + 5341.80i) q^{17} +(12371.5 - 21428.1i) q^{18} +(-107461. + 62042.5i) q^{19} +18458.9i q^{20} +(-111949. + 8665.43i) q^{21} -129470. q^{22} +(-167034. - 289312. i) q^{23} +(-58650.3 - 33861.7i) q^{24} +(-184914. + 320281. i) q^{25} +(-162827. + 94008.0i) q^{26} -102276. i q^{27} +(23717.9 + 306411. i) q^{28} -70689.7 q^{29} +(38150.1 + 66077.9i) q^{30} +(-1.24655e6 - 719697. i) q^{31} +(-92681.9 + 160530. i) q^{32} +(-463469. + 267584. i) q^{33} -120871. i q^{34} +(149467. - 312327. i) q^{35} -279936. q^{36} +(-1.32030e6 - 2.28683e6i) q^{37} +(1.21578e6 + 701931. i) q^{38} +(-388583. + 673046. i) q^{39} +(180860. - 104419. i) q^{40} +95248.5i q^{41} +(718181. + 1.04785e6i) q^{42} +396002. q^{43} +(732395. + 1.26854e6i) q^{44} +(273134. + 157694. i) q^{45} +(-1.88978e6 + 3.27319e6i) q^{46} +(5.72688e6 - 3.30642e6i) q^{47} +766204. i q^{48} +(2.07978e6 - 5.37656e6i) q^{49} +4.18413e6 q^{50} +(-249811. - 432685. i) q^{51} +(1.84217e6 + 1.06358e6i) q^{52} +(450942. - 781054. i) q^{53} +(-1.00209e6 + 578560. i) q^{54} -1.65030e6i q^{55} +(2.86804e6 - 1.96571e6i) q^{56} +5.80288e6 q^{57} +(399881. + 692615. i) q^{58} +(8.67216e6 + 5.00687e6i) q^{59} +(431619. - 747586. i) q^{60} +(-8.74012e6 + 5.04611e6i) q^{61} +1.62849e7i q^{62} +(4.73655e6 + 2.26671e6i) q^{63} +2.09715e6 q^{64} +(-1.19827e6 - 2.07547e6i) q^{65} +(5.24355e6 + 3.02736e6i) q^{66} +(1.77647e6 - 3.07694e6i) q^{67} +(-1.18429e6 + 683750. i) q^{68} +1.56228e7i q^{69} +(-3.90568e6 + 302320. i) q^{70} +3.99089e6 q^{71} +(1.58356e6 + 2.74280e6i) q^{72} +(-4.19536e7 - 2.42219e7i) q^{73} +(-1.49375e7 + 2.58725e7i) q^{74} +(1.49780e7 - 8.64758e6i) q^{75} -1.58829e7i q^{76} +(-2.12046e6 - 2.73943e7i) q^{77} +8.79264e6 q^{78} +(-2.60208e7 - 4.50694e7i) q^{79} +(-2.04619e6 - 1.18137e6i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(933241. - 538807. i) q^{82} +2.31059e7i q^{83} +(6.20415e6 - 1.29643e7i) q^{84} +1.54068e6 q^{85} +(-2.24013e6 - 3.88002e6i) q^{86} +(2.86293e6 + 1.65291e6i) q^{87} +(8.28610e6 - 1.43519e7i) q^{88} +(-4.42418e7 + 2.55430e7i) q^{89} -3.56821e6i q^{90} +(-2.25577e7 - 3.29124e7i) q^{91} +4.27608e7 q^{92} +(3.36569e7 + 5.82954e7i) q^{93} +(-6.47922e7 - 3.74078e7i) q^{94} +(-8.94717e6 + 1.54970e7i) q^{95} +(7.50723e6 - 4.33430e6i) q^{96} +2.33088e7i q^{97} +(-6.44444e7 + 1.00368e7i) q^{98} +2.50273e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 486 q^{3} - 768 q^{4} - 1122 q^{5} - 4434 q^{7} + 13122 q^{9}+O(q^{10}) $ 12 * q - 486 * q^3 - 768 * q^4 - 1122 * q^5 - 4434 * q^7 + 13122 * q^9	\( 12 q - 486 q^{3} - 768 q^{4} - 1122 q^{5} - 4434 q^{7} + 13122 q^{9} + 4224 q^{10} + 9606 q^{11} + 62208 q^{12} - 19968 q^{14} + 60588 q^{15} - 98304 q^{16} - 227388 q^{17} + 315408 q^{19} + 155358 q^{21} + 557568 q^{22} - 663480 q^{23} + 601008 q^{25} - 585984 q^{26} + 398592 q^{28} + 5944884 q^{29} - 114048 q^{30} - 3214278 q^{31} - 778086 q^{33} - 1019784 q^{35} - 3359232 q^{36} + 1607760 q^{37} - 986880 q^{38} + 903636 q^{39} - 540672 q^{40} + 2788992 q^{42} + 12627648 q^{43} + 1229568 q^{44} - 2453814 q^{45} - 4608768 q^{46} - 7830240 q^{47} + 16477242 q^{49} - 16565760 q^{50} + 6139476 q^{51} - 4283904 q^{52} - 33200358 q^{53} - 8110080 q^{56} - 17032032 q^{57} + 5576064 q^{58} - 29657382 q^{59} - 3877632 q^{60} + 58344096 q^{61} - 2886840 q^{63} + 25165824 q^{64} + 30909216 q^{65} - 22581504 q^{66} + 7977444 q^{67} + 29105664 q^{68} - 59774976 q^{70} + 117213264 q^{71} - 170286636 q^{73} - 80311296 q^{74} - 48681648 q^{75} - 3340686 q^{77} + 31643136 q^{78} + 35420490 q^{79} + 18382848 q^{80} - 28697814 q^{81} + 154232832 q^{82} - 26085888 q^{84} + 416634600 q^{85} - 71958528 q^{86} - 240767802 q^{87} - 35684352 q^{88} + 78064092 q^{89} + 335513292 q^{91} + 169850880 q^{92} + 86785506 q^{93} - 18456576 q^{94} - 250727796 q^{95} - 150533376 q^{98} + 42016644 q^{99}+O(q^{100}) \) 12 * q - 486 * q^3 - 768 * q^4 - 1122 * q^5 - 4434 * q^7 + 13122 * q^9 + 4224 * q^10 + 9606 * q^11 + 62208 * q^12 - 19968 * q^14 + 60588 * q^15 - 98304 * q^16 - 227388 * q^17 + 315408 * q^19 + 155358 * q^21 + 557568 * q^22 - 663480 * q^23 + 601008 * q^25 - 585984 * q^26 + 398592 * q^28 + 5944884 * q^29 - 114048 * q^30 - 3214278 * q^31 - 778086 * q^33 - 1019784 * q^35 - 3359232 * q^36 + 1607760 * q^37 - 986880 * q^38 + 903636 * q^39 - 540672 * q^40 + 2788992 * q^42 + 12627648 * q^43 + 1229568 * q^44 - 2453814 * q^45 - 4608768 * q^46 - 7830240 * q^47 + 16477242 * q^49 - 16565760 * q^50 + 6139476 * q^51 - 4283904 * q^52 - 33200358 * q^53 - 8110080 * q^56 - 17032032 * q^57 + 5576064 * q^58 - 29657382 * q^59 - 3877632 * q^60 + 58344096 * q^61 - 2886840 * q^63 + 25165824 * q^64 + 30909216 * q^65 - 22581504 * q^66 + 7977444 * q^67 + 29105664 * q^68 - 59774976 * q^70 + 117213264 * q^71 - 170286636 * q^73 - 80311296 * q^74 - 48681648 * q^75 - 3340686 * q^77 + 31643136 * q^78 + 35420490 * q^79 + 18382848 * q^80 - 28697814 * q^81 + 154232832 * q^82 - 26085888 * q^84 + 416634600 * q^85 - 71958528 * q^86 - 240767802 * q^87 - 35684352 * q^88 + 78064092 * q^89 + 335513292 * q^91 + 169850880 * q^92 + 86785506 * q^93 - 18456576 * q^94 - 250727796 * q^95 - 150533376 * q^98 + 42016644 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−5.65685	−	9.79796i	−0.353553	−	0.612372i
$2$	−5.65685	−	9.79796i	−0.353553	−	0.612372i
$3$	−40.5000	−	23.3827i	−0.500000	−	0.288675i
$3$	−40.5000	−	23.3827i	−0.500000	−	0.288675i
$4$	−64.0000	+	110.851i	−0.250000	+	0.433013i
$5$	124.890	−	72.1052i	0.199824	−	0.115368i	−0.396750	−	0.917927i	$-0.629862\pi$
$5$	124.890	−	72.1052i	0.199824	−	0.115368i	0.596573	+	0.802559i	$0.296529\pi$
$6$			529.090i			0.408248i
$7$	1980.48	−	1357.39i	0.824855	−	0.565344i
$7$	1980.48	−	1357.39i	0.824855	−	0.565344i
$8$	1448.15			0.353553
$9$	1093.50	+	1894.00i	0.166667	+	0.288675i
$10$	−1412.97	−	815.777i	−0.141297	−	0.0815777i
$11$	5721.83	−	9910.51i	0.390809	−	0.676901i	−0.601748	−	0.798686i	$-0.705529\pi$
$11$	5721.83	−	9910.51i	0.390809	−	0.676901i	0.992556	+	0.121785i	$0.0388620\pi$
$12$	5184.00	−	2992.98i	0.250000	−	0.144338i
$13$		−	16618.4i		−	0.581857i	−0.956745	−	0.290929i	$-0.906036\pi$
$13$		−	16618.4i		−	0.581857i	0.956745	−	0.290929i	$-0.0939642\pi$
$14$	−24502.9	−	11726.1i	−0.637831	−	0.305239i
$15$	−6744.05			−0.133216
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	9252.26	+	5341.80i	0.110778	+	0.0639575i	0.554365	−	0.832274i	$-0.312961\pi$
$17$	9252.26	+	5341.80i	0.110778	+	0.0639575i	−0.443587	+	0.896231i	$0.646294\pi$
$18$	12371.5	−	21428.1i	0.117851	−	0.204124i
$19$	−107461.	+	62042.5i	−0.824585	+	0.476074i	−0.851995	−	0.523550i	$-0.824607\pi$
$19$	−107461.	+	62042.5i	−0.824585	+	0.476074i	0.0274100	+	0.999624i	$0.491274\pi$
$20$			18458.9i			0.115368i
$21$	−111949.	+	8665.43i	−0.575628	+	0.0445567i
$22$	−129470.			−0.552687
$23$	−167034.	−	289312.i	−0.596890	−	1.03384i	−0.993277	−	0.115760i	$-0.963070\pi$
$23$	−167034.	−	289312.i	−0.596890	−	1.03384i	0.396387	−	0.918083i	$-0.370264\pi$
$24$	−58650.3	−	33861.7i	−0.176777	−	0.102062i
$25$	−184914.	+	320281.i	−0.473380	+	0.819919i
$26$	−162827.	+	94008.0i	−0.356313	+	0.205718i
$27$		−	102276.i		−	0.192450i
$28$	23717.9	+	306411.i	0.0385872	+	0.498509i
$29$	−70689.7			−0.0999457			−0.0499729	−	0.998751i	$-0.515913\pi$
$29$	−70689.7			−0.0999457			−0.0499729	+	0.998751i	$0.515913\pi$
$30$	38150.1	+	66077.9i	0.0470989	+	0.0815777i
$31$	−1.24655e6	−	719697.i	−1.34978	−	0.779297i	−0.361563	−	0.932348i	$-0.617757\pi$
$31$	−1.24655e6	−	719697.i	−1.34978	−	0.779297i	−0.988218	+	0.153051i	$0.951090\pi$
$32$	−92681.9	+	160530.i	−0.0883883	+	0.153093i
$33$	−463469.	+	267584.i	−0.390809	+	0.225634i
$34$		−	120871.i		−	0.0904496i
$35$	149467.	−	312327.i	0.0996029	−	0.208131i
$36$	−279936.			−0.166667
$37$	−1.32030e6	−	2.28683e6i	−0.704476	−	1.22019i	−0.966880	−	0.255231i	$-0.917849\pi$
$37$	−1.32030e6	−	2.28683e6i	−0.704476	−	1.22019i	0.262404	−	0.964958i	$-0.415485\pi$
$38$	1.21578e6	+	701931.i	0.583070	+	0.336635i
$39$	−388583.	+	673046.i	−0.167968	+	0.290929i
$40$	180860.	−	104419.i	0.0706484	−	0.0407888i
$41$			95248.5i			0.0337072i	0.999858	+	0.0168536i	$0.00536492\pi$
$41$			95248.5i			0.0337072i	−0.999858	+	0.0168536i	$0.994635\pi$
$42$	718181.	+	1.04785e6i	0.230801	+	0.336746i
$43$	396002.			0.115831			0.0579154	−	0.998321i	$-0.481555\pi$
$43$	396002.			0.115831			0.0579154	+	0.998321i	$0.481555\pi$
$44$	732395.	+	1.26854e6i	0.195404	+	0.338450i
$45$	273134.	+	157694.i	0.0666079	+	0.0384561i
$46$	−1.88978e6	+	3.27319e6i	−0.422065	+	0.731038i
$47$	5.72688e6	−	3.30642e6i	1.17362	−	0.677588i	0.219088	−	0.975705i	$-0.429692\pi$
$47$	5.72688e6	−	3.30642e6i	1.17362	−	0.677588i	0.954529	+	0.298117i	$0.0963584\pi$
$48$			766204.i			0.144338i
$49$	2.07978e6	−	5.37656e6i	0.360773	−	0.932654i
$50$	4.18413e6			0.669461
$51$	−249811.	−	432685.i	−0.0369259	−	0.0639575i
$52$	1.84217e6	+	1.06358e6i	0.251952	+	0.145464i
$53$	450942.	−	781054.i	0.0571501	−	0.0989869i	−0.836035	−	0.548676i	$-0.815132\pi$
$53$	450942.	−	781054.i	0.0571501	−	0.0989869i	0.893185	+	0.449689i	$0.148465\pi$
$54$	−1.00209e6	+	578560.i	−0.117851	+	0.0680414i
$55$		−	1.65030e6i		−	0.180348i
$56$	2.86804e6	−	1.96571e6i	0.291630	−	0.199879i
$57$	5.80288e6			0.549723
$58$	399881.	+	692615.i	0.0353361	+	0.0612040i
$59$	8.67216e6	+	5.00687e6i	0.715681	+	0.413198i	0.813161	−	0.582039i	$-0.197745\pi$
$59$	8.67216e6	+	5.00687e6i	0.715681	+	0.413198i	−0.0974802	+	0.995237i	$0.531078\pi$
$60$	431619.	−	747586.i	0.0333040	−	0.0576841i
$61$	−8.74012e6	+	5.04611e6i	−0.631245	+	0.364450i	−0.781234	−	0.624238i	$-0.785410\pi$
$61$	−8.74012e6	+	5.04611e6i	−0.631245	+	0.364450i	0.149989	+	0.988688i	$0.452076\pi$
$62$			1.62849e7i			1.10209i
$63$	4.73655e6	+	2.26671e6i	0.300677	+	0.143891i
$64$	2.09715e6			0.125000
$65$	−1.19827e6	−	2.07547e6i	−0.0671279	−	0.116269i
$66$	5.24355e6	+	3.02736e6i	0.276344	+	0.159547i
$67$	1.77647e6	−	3.07694e6i	0.0881576	−	0.152693i	−0.818575	−	0.574400i	$-0.805235\pi$
$67$	1.77647e6	−	3.07694e6i	0.0881576	−	0.152693i	0.906732	+	0.421707i	$0.138569\pi$
$68$	−1.18429e6	+	683750.i	−0.0553888	+	0.0319788i
$69$			1.56228e7i			0.689229i
$70$	−3.90568e6	+	302320.i	−0.162669	+	0.0125914i
$71$	3.99089e6			0.157050			0.0785248	−	0.996912i	$-0.474979\pi$
$71$	3.99089e6			0.157050			0.0785248	+	0.996912i	$0.474979\pi$
$72$	1.58356e6	+	2.74280e6i	0.0589256	+	0.102062i
$73$	−4.19536e7	−	2.42219e7i	−1.47733	−	0.852937i	−0.477658	−	0.878546i	$-0.658514\pi$
$73$	−4.19536e7	−	2.42219e7i	−1.47733	−	0.852937i	−0.999672	+	0.0256085i	$0.991848\pi$
$74$	−1.49375e7	+	2.58725e7i	−0.498140	+	0.862804i
$75$	1.49780e7	−	8.64758e6i	0.473380	−	0.273306i
$76$		−	1.58829e7i		−	0.476074i
$77$	−2.12046e6	−	2.73943e7i	−0.0603209	−	0.779287i
$78$	8.79264e6			0.237542
$79$	−2.60208e7	−	4.50694e7i	−0.668056	−	1.15711i	−0.978447	−	0.206498i	$-0.933793\pi$
$79$	−2.60208e7	−	4.50694e7i	−0.668056	−	1.15711i	0.310391	−	0.950609i	$-0.399540\pi$
$80$	−2.04619e6	−	1.18137e6i	−0.0499559	−	0.0288421i
$81$	−2.39148e6	+	4.14217e6i	−0.0555556	+	0.0962250i
$82$	933241.	−	538807.i	0.0206414	−	0.0119173i
$83$			2.31059e7i			0.486867i	0.969918	+	0.243433i	$0.0782737\pi$
$83$			2.31059e7i			0.486867i	−0.969918	+	0.243433i	$0.921726\pi$
$84$	6.20415e6	−	1.29643e7i	0.124613	−	0.260394i
$85$	1.54068e6			0.0295147
$86$	−2.24013e6	−	3.88002e6i	−0.0409524	−	0.0709316i
$87$	2.86293e6	+	1.65291e6i	0.0499729	+	0.0288518i
$88$	8.28610e6	−	1.43519e7i	0.138172	−	0.239321i
$89$	−4.42418e7	+	2.55430e7i	−0.705135	+	0.407110i	−0.809257	−	0.587455i	$-0.800130\pi$
$89$	−4.42418e7	+	2.55430e7i	−0.705135	+	0.407110i	0.104122	+	0.994565i	$0.466797\pi$
$90$		−	3.56821e6i		−	0.0543851i
$91$	−2.25577e7	−	3.29124e7i	−0.328949	−	0.479948i
$92$	4.27608e7			0.596890
$93$	3.36569e7	+	5.82954e7i	0.449927	+	0.779297i
$94$	−6.47922e7	−	3.74078e7i	−0.829873	−	0.479127i
$95$	−8.94717e6	+	1.54970e7i	−0.109848	+	0.190262i
$96$	7.50723e6	−	4.33430e6i	0.0883883	−	0.0510310i
$97$			2.33088e7i			0.263289i	0.991297	+	0.131645i	$0.0420258\pi$
$97$			2.33088e7i			0.263289i	−0.991297	+	0.131645i	$0.957974\pi$
$98$	−6.44444e7	+	1.00368e7i	−0.698684	+	0.108816i
$99$	2.50273e7			0.260539
$100$	−2.36690e7	−	4.09959e7i	−0.236690	−	0.409959i
$101$	−8.47998e7	−	4.89592e7i	−0.814909	−	0.470488i	0.0337486	−	0.999430i	$-0.489255\pi$
$101$	−8.47998e7	−	4.89592e7i	−0.814909	−	0.470488i	−0.848658	+	0.528942i	$0.822589\pi$
$102$	−2.82629e6	+	4.89528e6i	−0.0261105	+	0.0452248i
$103$	−3.42307e7	+	1.97631e7i	−0.304136	+	0.175593i	−0.644299	−	0.764773i	$-0.722851\pi$
$103$	−3.42307e7	+	1.97631e7i	−0.304136	+	0.175593i	0.340164	+	0.940366i	$0.389518\pi$
$104$		−	2.40661e7i		−	0.205718i
$105$	−1.33564e7	+	9.15431e6i	−0.109884	+	0.0753127i
$106$	−1.02037e7			−0.0808225
$107$	6.81792e7	+	1.18090e8i	0.520136	+	0.900901i	0.999726	+	0.0234088i	$0.00745192\pi$
$107$	6.81792e7	+	1.18090e8i	0.520136	+	0.900901i	−0.479590	+	0.877492i	$0.659215\pi$
$108$	1.13374e7	+	6.54566e6i	0.0833333	+	0.0481125i
$109$	−3.93809e7	+	6.82097e7i	−0.278984	+	0.483215i	−0.971133	−	0.238540i	$-0.923331\pi$
$109$	−3.93809e7	+	6.82097e7i	−0.278984	+	0.483215i	0.692148	+	0.721755i	$0.256664\pi$
$110$	−1.61695e7	+	9.33548e6i	−0.110440	+	0.0637626i
$111$			1.23489e8i			0.813459i
$112$	−3.54840e7	−	1.69812e7i	−0.225507	−	0.107918i
$113$	2.67287e8			1.63932			0.819660	−	0.572850i	$-0.194162\pi$
$113$	2.67287e8			1.63932			0.819660	+	0.572850i	$0.194162\pi$
$114$	−3.28260e7	−	5.68564e7i	−0.194357	−	0.336635i
$115$	−4.17218e7	−	2.40881e7i	−0.238546	−	0.137724i
$116$	4.52414e6	−	7.83604e6i	0.0249864	−	0.0432778i
$117$	3.14753e7	−	1.81722e7i	0.167968	−	0.0969762i
$118$		−	1.13293e8i		−	0.584351i
$119$	2.55748e7	−	1.97963e6i	0.127534	−	0.00987177i
$120$	−9.76643e6			−0.0470989
$121$	4.17007e7	+	7.22277e7i	0.194537	+	0.336948i
$122$	9.88832e7	+	5.70902e7i	0.446358	+	0.257705i
$123$	2.22717e6	−	3.85756e6i	0.00973043	−	0.0168536i
$124$	1.59559e8	−	9.21212e7i	0.674891	−	0.389648i
$125$			1.09665e8i			0.449189i
$126$	−4.58479e6	−	5.92310e7i	−0.0181902	−	0.234999i
$127$	4.24381e8			1.63133			0.815664	−	0.578526i	$-0.196372\pi$
$127$	4.24381e8			1.63133			0.815664	+	0.578526i	$0.196372\pi$
$128$	−1.18633e7	−	2.05478e7i	−0.0441942	−	0.0765466i
$129$	−1.60381e7	−	9.25960e6i	−0.0579154	−	0.0334375i
$130$	−1.35569e7	+	2.34813e7i	−0.0474666	+	0.0822145i
$131$	4.17185e8	−	2.40862e8i	1.41659	−	0.817867i	0.420589	−	0.907251i	$-0.361823\pi$
$131$	4.17185e8	−	2.40862e8i	1.41659	−	0.817867i	0.995997	+	0.0893844i	$0.0284900\pi$
$132$		−	6.85014e7i		−	0.225634i
$133$	−1.28608e8	+	2.68740e8i	−0.411018	+	0.858866i
$134$	−4.01970e7			−0.124674
$135$	−7.37462e6	−	1.27732e7i	−0.0222026	−	0.0384561i
$136$	1.33987e7	+	7.73575e6i	0.0391658	+	0.0226124i
$137$	2.39389e8	−	4.14634e8i	0.679552	−	1.17702i	−0.295564	−	0.955323i	$-0.595508\pi$
$137$	2.39389e8	−	4.14634e8i	0.679552	−	1.17702i	0.975116	−	0.221695i	$-0.0711590\pi$
$138$	1.53072e8	−	8.83761e7i	0.422065	−	0.243679i
$139$			4.78110e8i			1.28076i	0.768057	+	0.640382i	$0.221224\pi$
$139$			4.78110e8i			1.28076i	−0.768057	+	0.640382i	$0.778776\pi$
$140$	2.50560e7	+	3.65575e7i	0.0652227	+	0.0951621i
$141$	−3.09252e8			−0.782412
$142$	−2.25759e7	−	3.91026e7i	−0.0555254	−	0.0961729i
$143$	−1.64697e8	−	9.50879e7i	−0.393860	−	0.227395i
$144$	1.79159e7	−	3.10313e7i	0.0416667	−	0.0721688i
$145$	−8.82842e6	+	5.09709e6i	−0.0199715	+	0.0115306i
$146$			5.48079e8i			1.20624i
$147$	−2.09950e8	+	1.69120e8i	−0.449620	+	0.362181i
$148$	3.37997e8			0.704476
$149$	−4.31509e8	−	7.47396e8i	−0.875478	−	1.51637i	−0.856253	−	0.516557i	$-0.827213\pi$
$149$	−4.31509e8	−	7.47396e8i	−0.875478	−	1.51637i	−0.0192250	−	0.999815i	$-0.506120\pi$
$150$	−1.69457e8	−	9.78362e7i	−0.334730	−	0.193257i
$151$	3.77049e7	−	6.53067e7i	0.0725253	−	0.125617i	−0.827482	−	0.561492i	$-0.810228\pi$
$151$	3.77049e7	−	6.53067e7i	0.0725253	−	0.125617i	0.900007	+	0.435875i	$0.143561\pi$
$152$	−1.55620e8	+	8.98471e7i	−0.291535	+	0.168318i
$153$			2.33650e7i			0.0426383i
$154$	−2.56413e8	+	1.75742e8i	−0.455887	+	0.312458i
$155$	−2.07575e8			−0.359624
$156$	−4.97387e7	−	8.61499e7i	−0.0839839	−	0.145464i
$157$	−3.65569e8	−	2.11062e8i	−0.601688	−	0.347385i	0.168017	−	0.985784i	$-0.446264\pi$
$157$	−3.65569e8	−	2.11062e8i	−0.601688	−	0.347385i	−0.769705	+	0.638399i	$0.779597\pi$
$158$	−2.94392e8	+	5.09902e8i	−0.472387	+	0.818198i
$159$	−3.65263e7	+	2.10885e7i	−0.0571501	+	0.0329956i
$160$			2.67314e7i			0.0407888i
$161$	−7.23517e8	−	3.46245e8i	−1.07682	−	0.515323i
$162$	5.41131e7			0.0785674
$163$	−5.53458e7	−	9.58617e7i	−0.0784033	−	0.135798i	0.824158	−	0.566360i	$-0.191649\pi$
$163$	−5.53458e7	−	9.58617e7i	−0.0784033	−	0.135798i	−0.902561	+	0.430562i	$0.858316\pi$
$164$	−1.05584e7	−	6.09590e6i	−0.0145956	−	0.00842680i
$165$	−3.85883e7	+	6.68370e7i	−0.0520619	+	0.0901739i
$166$	2.26390e8	−	1.30707e8i	0.298144	−	0.172133i
$167$			3.68846e8i			0.474220i	0.971483	+	0.237110i	$0.0762001\pi$
$167$			3.68846e8i			0.474220i	−0.971483	+	0.237110i	$0.923800\pi$
$168$	−1.62119e8	+	1.25489e7i	−0.203515	+	0.0157532i
$169$	5.39559e8			0.661442
$170$	−8.71543e6	−	1.50956e7i	−0.0104350	−	0.0180740i
$171$	−2.35017e8	−	1.35687e8i	−0.274862	−	0.158691i
$172$	−2.53442e7	+	4.38974e7i	−0.0289577	+	0.0501562i
$173$	−1.04706e9	+	6.04523e8i	−1.16893	+	0.674882i	−0.953428	−	0.301621i	$-0.902472\pi$
$173$	−1.04706e9	+	6.04523e8i	−1.16893	+	0.674882i	−0.215503	+	0.976503i	$0.569139\pi$
$174$		−	3.74012e7i		−	0.0408027i
$175$	6.85277e7	+	8.85310e8i	0.0730657	+	0.943937i
$176$	−1.87493e8			−0.195404
$177$	−2.34148e8	−	4.05557e8i	−0.238560	−	0.413198i
$178$	5.00538e8	+	2.88986e8i	0.498606	+	0.287870i
$179$	9.13047e8	−	1.58144e9i	0.889367	−	1.54043i	0.0487411	−	0.998811i	$-0.484479\pi$
$179$	9.13047e8	−	1.58144e9i	0.889367	−	1.54043i	0.840626	−	0.541617i	$-0.182188\pi$
$180$	−3.49612e7	+	2.01848e7i	−0.0333040	+	0.0192280i
$181$			3.02300e8i			0.281659i	0.990034	+	0.140830i	$0.0449770\pi$
$181$			3.02300e8i			0.281659i	−0.990034	+	0.140830i	$0.955023\pi$
$182$	−1.94869e8	+	4.07200e8i	−0.177606	+	0.371127i
$183$	4.71967e8			0.420830
$184$	−2.41891e8	−	4.18968e8i	−0.211032	−	0.365519i
$185$	−3.29785e8	−	1.90401e8i	−0.281542	−	0.162548i
$186$	3.80784e8	−	6.59538e8i	0.318147	−	0.551046i
$187$	1.05880e8	−	6.11297e7i	0.0865858	−	0.0499903i
$188$			8.46442e8i			0.677588i
$189$	−1.38828e8	−	2.02555e8i	−0.108800	−	0.158743i
$190$	2.02451e8			0.155348
$191$	−1.29731e9	−	2.24701e9i	−0.974791	−	1.68839i	−0.680622	−	0.732635i	$-0.738290\pi$
$191$	−1.29731e9	−	2.24701e9i	−0.974791	−	1.68839i	−0.294169	−	0.955753i	$-0.595043\pi$
$192$	−8.49347e7	−	4.90370e7i	−0.0625000	−	0.0360844i
$193$	3.95103e8	−	6.84338e8i	0.284761	−	0.493221i	−0.687790	−	0.725910i	$-0.741419\pi$
$193$	3.95103e8	−	6.84338e8i	0.284761	−	0.493221i	0.972551	+	0.232689i	$0.0747523\pi$
$194$	2.28379e8	−	1.31855e8i	0.161231	−	0.0930869i
$195$			1.12076e8i			0.0775126i
$196$	4.62893e8	+	5.74647e8i	0.313658	+	0.389383i
$197$	1.17701e9			0.781476			0.390738	−	0.920502i	$-0.372220\pi$
$197$	1.17701e9			0.781476			0.390738	+	0.920502i	$0.372220\pi$
$198$	−1.41576e8	−	2.45216e8i	−0.0921145	−	0.159547i
$199$	1.81959e9	+	1.05054e9i	1.16028	+	0.669887i	0.951371	−	0.308049i	$-0.0996759\pi$
$199$	1.81959e9	+	1.05054e9i	1.16028	+	0.669887i	0.208907	+	0.977935i	$0.433009\pi$
$200$	−2.67784e8	+	4.63816e8i	−0.167365	+	0.289885i
$201$	−1.43894e8	+	8.30775e7i	−0.0881576	+	0.0508978i
$202$			1.10782e9i			0.665371i
$203$	−1.39999e8	+	9.59535e7i	−0.0824407	+	0.0565037i
$204$	6.39516e7			0.0369259
$205$	6.86791e6	+	1.18956e7i	0.00388874	+	0.00673550i
$206$	3.87276e8	+	2.23594e8i	0.215056	+	0.124163i
$207$	3.65304e8	−	6.32725e8i	0.198963	−	0.344615i
$208$	−2.35798e8	+	1.36138e8i	−0.125976	+	0.0727322i
$209$			1.41999e9i			0.744216i
$210$	1.65249e8	+	7.90813e7i	0.0849692	+	0.0406627i
$211$	2.50774e9			1.26518			0.632592	−	0.774485i	$-0.281991\pi$
$211$	2.50774e9			1.26518			0.632592	+	0.774485i	$0.281991\pi$
$212$	5.77206e7	+	9.99750e7i	0.0285751	+	0.0494935i
$213$	−1.61631e8	−	9.33178e7i	−0.0785248	−	0.0453363i
$214$	7.71359e8	−	1.33603e9i	0.367791	−	0.637033i
$215$	4.94567e7	−	2.85538e7i	0.0231457	−	0.0133632i
$216$		−	1.48111e8i		−	0.0680414i
$217$	−3.44568e9	+	2.66714e8i	−1.55395	+	0.120284i
$218$	8.91088e8			0.394543
$219$	1.13275e9	+	1.96198e9i	0.492443	+	0.852937i
$220$	1.82937e8	+	1.05619e8i	0.0780929	+	0.0450870i
$221$	8.87722e7	−	1.53758e8i	0.0372141	−	0.0644568i
$222$	1.20994e9	−	6.98558e8i	0.498140	−	0.287601i
$223$			7.65190e8i			0.309421i	0.987960	+	0.154710i	$0.0494445\pi$
$223$			7.65190e8i			0.309421i	−0.987960	+	0.154710i	$0.950556\pi$
$224$	3.43471e7	+	4.43731e8i	0.0136426	+	0.176249i
$225$	−8.08815e8			−0.315587
$226$	−1.51200e9	−	2.61886e9i	−0.579587	−	1.00387i
$227$	3.94681e9	+	2.27869e9i	1.48643	+	0.858188i	0.999880	−	0.0154668i	$-0.00492344\pi$
$227$	3.94681e9	+	2.27869e9i	1.48643	+	0.858188i	0.486546	+	0.873655i	$0.338257\pi$
$228$	−3.71384e8	+	6.43256e8i	−0.137431	+	0.238037i
$229$	−5.15966e8	+	2.97893e8i	−0.187620	+	0.108322i	−0.590868	−	0.806768i	$-0.701215\pi$
$229$	−5.15966e8	+	2.97893e8i	−0.187620	+	0.108322i	0.403248	+	0.915091i	$0.367881\pi$
$230$			5.45051e8i			0.194772i
$231$	−5.54674e8	+	1.15905e9i	−0.194800	+	0.407057i
$232$	−1.02370e8			−0.0353361
$233$	−9.26162e8	−	1.60416e9i	−0.314241	−	0.544282i	0.665035	−	0.746813i	$-0.268417\pi$
$233$	−9.26162e8	−	1.60416e9i	−0.314241	−	0.544282i	−0.979276	+	0.202531i	$0.935083\pi$
$234$	−3.56102e8	−	2.05596e8i	−0.118771	−	0.0685725i
$235$	4.76819e8	−	8.25875e8i	0.156344	−	0.270796i
$236$	−1.11004e9	+	6.40880e8i	−0.357840	+	0.206599i
$237$			2.43375e9i			0.771404i
$238$	−1.64069e8	−	2.39382e8i	−0.0511351	−	0.0746078i
$239$	5.09785e9			1.56241			0.781206	−	0.624273i	$-0.214605\pi$
$239$	5.09785e9			1.56241			0.781206	+	0.624273i	$0.214605\pi$
$240$	5.52473e7	+	9.56911e7i	0.0166520	+	0.0288421i
$241$	−3.29429e9	−	1.90196e9i	−0.976548	−	0.563810i	−0.0753217	−	0.997159i	$-0.523998\pi$
$241$	−3.29429e9	−	1.90196e9i	−0.976548	−	0.563810i	−0.901226	+	0.433349i	$0.857332\pi$
$242$	4.71789e8	−	8.17163e8i	0.137558	−	0.238258i
$243$	1.93710e8	−	1.11839e8i	0.0555556	−	0.0320750i
$244$		−	1.29180e9i		−	0.364450i
$245$	−1.27934e8	−	8.21441e8i	−0.0355077	−	0.227988i
$246$	−5.03950e7			−0.0137609
$247$	1.03105e9	+	1.78583e9i	0.277007	+	0.479791i
$248$	−1.80520e9	−	1.04223e9i	−0.477220	−	0.275523i
$249$	5.40277e8	−	9.35788e8i	0.140546	−	0.243433i
$250$	1.07450e9	−	6.20360e8i	0.275071	−	0.158812i
$251$			1.93525e9i			0.487575i	0.969829	+	0.243788i	$0.0783900\pi$
$251$			1.93525e9i			0.487575i	−0.969829	+	0.243788i	$0.921610\pi$
$252$	−5.54407e8	+	3.79982e8i	−0.137476	+	0.0942240i
$253$	−3.82297e9			−0.933080
$254$	−2.40066e9	−	4.15807e9i	−0.576761	−	0.998980i
$255$	−6.23977e7	−	3.60253e7i	−0.0147573	−	0.00852015i
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	−3.23367e9	+	1.86696e9i	−0.741247	+	0.427959i	−0.822523	−	0.568732i	$-0.807434\pi$
$257$	−3.23367e9	+	1.86696e9i	−0.741247	+	0.427959i	0.0812753	+	0.996692i	$0.474101\pi$
$258$			2.09521e8i			0.0472877i
$259$	−5.71895e9	−	2.73685e9i	−1.27092	−	0.608208i
$260$	3.06758e8			0.0671279
$261$	−7.72992e7	−	1.33886e8i	−0.0166576	−	0.0288518i
$262$	−4.71991e9	−	2.72504e9i	−1.00168	−	0.578319i
$263$	−9.71287e8	+	1.68232e9i	−0.203013	+	0.351629i	−0.949498	−	0.313773i	$-0.898407\pi$
$263$	−9.71287e8	+	1.68232e9i	−0.203013	+	0.351629i	0.746485	+	0.665403i	$0.231740\pi$
$264$	−6.71174e8	+	3.87503e8i	−0.138172	+	0.0797735i
$265$		−	1.30061e8i		−	0.0263732i
$266$	3.36062e9	−	2.60130e8i	0.671263	−	0.0519593i
$267$	2.38906e9			0.470090
$268$	2.27389e8	+	3.93849e8i	0.0440788	+	0.0763467i
$269$	6.19505e7	+	3.57671e7i	0.0118314	+	0.00683085i	0.505904	−	0.862590i	$-0.331159\pi$
$269$	6.19505e7	+	3.57671e7i	0.0118314	+	0.00683085i	−0.494073	+	0.869421i	$0.664492\pi$
$270$	−8.34343e7	+	1.44512e8i	−0.0156996	+	0.0271926i
$271$	3.33129e9	−	1.92332e9i	0.617639	−	0.356594i	−0.158310	−	0.987389i	$-0.550605\pi$
$271$	3.33129e9	−	1.92332e9i	0.617639	−	0.356594i	0.775949	+	0.630795i	$0.217271\pi$
$272$		−	1.75040e8i		−	0.0319788i
$273$	1.44006e8	+	1.86041e9i	0.0259256	+	0.334934i
$274$	−5.41676e9			−0.961031
$275$	2.11610e9	+	3.66519e9i	0.370003	+	0.640863i
$276$	−1.73181e9	−	9.99862e8i	−0.298445	−	0.172307i
$277$	−1.22179e9	+	2.11621e9i	−0.207529	+	0.359451i	−0.950936	−	0.309389i	$-0.899875\pi$
$277$	−1.22179e9	+	2.11621e9i	−0.207529	+	0.359451i	0.743406	+	0.668840i	$0.233209\pi$
$278$	4.68451e9	−	2.70460e9i	0.784304	−	0.452818i
$279$		−	3.14795e9i		−	0.519531i
$280$	2.16451e8	−	4.52298e8i	0.0352150	−	0.0735855i
$281$	−6.22896e8			−0.0999058			−0.0499529	−	0.998752i	$-0.515907\pi$
$281$	−6.22896e8			−0.0999058			−0.0499529	+	0.998752i	$0.515907\pi$
$282$	1.74939e9	+	3.03003e9i	0.276624	+	0.479127i
$283$	−1.97237e9	−	1.13875e9i	−0.307498	−	0.177534i	0.338308	−	0.941035i	$-0.390145\pi$
$283$	−1.97237e9	−	1.13875e9i	−0.307498	−	0.177534i	−0.645806	+	0.763501i	$0.723479\pi$
$284$	−2.55417e8	+	4.42396e8i	−0.0392624	+	0.0680045i
$285$	7.24721e8	−	4.18418e8i	0.109848	−	0.0634206i
$286$			2.15159e9i			0.321585i
$287$	1.29289e8	+	1.88637e8i	0.0190562	+	0.0278036i
$288$	−4.05391e8			−0.0589256
$289$	−3.43081e9	−	5.94234e9i	−0.491819	−	0.851855i
$290$	9.98822e7	+	5.76670e7i	0.0141220	+	0.00815334i
$291$	5.45023e8	−	9.44007e8i	0.0760051	−	0.131645i
$292$	5.37006e9	−	3.10040e9i	0.738665	−	0.426469i
$293$			1.93090e9i			0.261992i	0.991383	+	0.130996i	$0.0418176\pi$
$293$			1.93090e9i			0.261992i	−0.991383	+	0.130996i	$0.958182\pi$
$294$	2.84468e9	+	1.10039e9i	0.380754	+	0.147285i
$295$	1.44409e9			0.190680
$296$	−1.91200e9	−	3.31168e9i	−0.249070	−	0.431402i
$297$	−1.01361e9	−	5.85205e8i	−0.130270	−	0.0752112i
$298$	−4.88197e9	+	8.45582e9i	−0.619056	+	1.07224i
$299$	−4.80791e9	+	2.77585e9i	−0.601549	+	0.347305i
$300$			2.21378e9i			0.273306i
$301$	7.84274e8	−	5.37530e8i	0.0955436	−	0.0654842i
$302$	−8.53163e8			−0.102566
$303$	2.28959e9	+	3.96569e9i	0.271636	+	0.470488i
$304$	1.76064e9	+	1.01650e9i	0.206146	+	0.119019i
$305$	−7.27702e8	+	1.26042e9i	−0.0840919	+	0.145651i
$306$	2.28929e8	−	1.32172e8i	0.0261105	−	0.0150749i
$307$		−	9.79849e9i		−	1.10308i	−0.834149	−	0.551538i	$-0.814041\pi$
$307$		−	9.79849e9i		−	1.10308i	0.834149	−	0.551538i	$-0.185959\pi$
$308$	3.17240e9	+	1.51818e9i	0.352521	+	0.168702i
$309$	1.84846e9			0.202757
$310$	1.17422e9	+	2.03382e9i	0.127146	+	0.220224i
$311$	−5.23031e9	−	3.01972e9i	−0.559096	−	0.322794i	0.193687	−	0.981063i	$-0.437955\pi$
$311$	−5.23031e9	−	3.01972e9i	−0.559096	−	0.322794i	−0.752782	+	0.658269i	$0.771289\pi$
$312$	−5.62729e8	+	9.74675e8i	−0.0593856	+	0.102859i
$313$	3.09906e9	−	1.78924e9i	0.322888	−	0.186420i	−0.329791	−	0.944054i	$-0.606978\pi$
$313$	3.09906e9	−	1.78924e9i	0.322888	−	0.186420i	0.652679	+	0.757634i	$0.273645\pi$
$314$			4.77578e9i			0.491276i
$315$	7.54988e8	−	5.84401e7i	0.0766828	−	0.00593566i
$316$	6.66133e9			0.668056
$317$	6.17510e9	+	1.06956e10i	0.611514	+	1.05917i	0.990985	+	0.133970i	$0.0427727\pi$
$317$	6.17510e9	+	1.06956e10i	0.611514	+	1.05917i	−0.379471	+	0.925204i	$0.623894\pi$
$318$	4.13248e8	+	2.38589e8i	0.0404112	+	0.0233314i
$319$	−4.04475e8	+	7.00571e8i	−0.0390597	+	0.0676533i
$320$	2.61913e8	−	1.51216e8i	0.0249780	−	0.0144210i
$321$		−	6.37685e9i		−	0.600601i
$322$	7.00336e8	+	9.04764e9i	0.0651452	+	0.841612i
$323$	−1.32567e9			−0.121794
$324$	−3.06110e8	−	5.30198e8i	−0.0277778	−	0.0481125i
$325$	5.32256e9	+	3.07298e9i	0.477076	+	0.275440i
$326$	−6.26166e8	+	1.08455e9i	−0.0554395	+	0.0960240i
$327$	3.18985e9	−	1.84166e9i	0.278984	−	0.161072i
$328$			1.37935e8i			0.0119173i
$329$	6.85386e9	−	1.43219e10i	0.584994	−	1.22241i
$330$	8.73154e8			0.0736267
$331$	1.16147e10	+	2.01172e10i	0.967600	+	1.67593i	0.702462	+	0.711721i	$0.252084\pi$
$331$	1.16147e10	+	2.01172e10i	0.967600	+	1.67593i	0.265138	+	0.964211i	$0.414583\pi$
$332$	−2.56131e9	−	1.47878e9i	−0.210819	−	0.121717i
$333$	2.88750e9	−	5.00130e9i	0.234825	−	0.406730i
$334$	3.61394e9	−	2.08651e9i	0.290399	−	0.167662i
$335$		−	5.12372e8i		−	0.0406824i
$336$	1.04004e9	+	1.51745e9i	0.0816004	+	0.119058i
$337$	1.15623e10			0.896450			0.448225	−	0.893921i	$-0.352056\pi$
$337$	1.15623e10			0.896450			0.448225	+	0.893921i	$0.352056\pi$
$338$	−3.05220e9	−	5.28657e9i	−0.233855	−	0.405049i
$339$	−1.08251e10	−	6.24988e9i	−0.819660	−	0.473231i
$340$	−9.86038e7	+	1.70787e8i	−0.00737867	+	0.0127802i
$341$	−1.42651e10	+	8.23597e9i	−1.05501	+	0.609112i
$342$			3.07024e9i			0.224424i
$343$	−3.17913e9	−	1.34712e10i	−0.229685	−	0.973265i
$344$	5.73473e8			0.0409524
$345$	1.12649e9	+	1.95113e9i	0.0795152	+	0.137724i
$346$	1.18462e10	+	6.83939e9i	0.826559	+	0.477214i
$347$	7.19821e8	−	1.24677e9i	0.0496486	−	0.0859939i	−0.840133	−	0.542380i	$-0.817523\pi$
$347$	7.19821e8	−	1.24677e9i	0.0496486	−	0.0859939i	0.889782	+	0.456386i	$0.150857\pi$
$348$	−3.66455e8	+	2.11573e8i	−0.0249864	+	0.0144259i
$349$		−	2.11645e10i		−	1.42662i	−0.700850	−	0.713308i	$-0.747196\pi$
$349$		−	2.11645e10i		−	1.42662i	0.700850	−	0.713308i	$-0.252804\pi$
$350$	8.28658e9	−	5.67950e9i	0.552208	−	0.378476i
$351$	−1.69966e9			−0.111978
$352$	1.06062e9	+	1.83705e9i	0.0690859	+	0.119660i
$353$	8.93206e9	+	5.15693e9i	0.575245	+	0.332118i	0.759241	−	0.650809i	$-0.225570\pi$
$353$	8.93206e9	+	5.15693e9i	0.575245	+	0.332118i	−0.183997	+	0.982927i	$0.558904\pi$
$354$	−2.64909e9	+	4.58835e9i	−0.168688	+	0.292175i
$355$	4.98422e8	−	2.87764e8i	0.0313822	−	0.0181185i
$356$		−	6.53901e9i		−	0.407110i
$357$	−1.08207e9	−	5.17833e8i	−0.0666165	−	0.0318799i
$358$	−2.06599e10			−1.25775
$359$	−5.50652e9	−	9.53757e9i	−0.331512	−	0.574196i	0.651296	−	0.758823i	$-0.274225\pi$
$359$	−5.50652e9	−	9.53757e9i	−0.331512	−	0.574196i	−0.982809	+	0.184628i	$0.940892\pi$
$360$	3.95540e8	+	2.28365e8i	0.0235495	+	0.0135963i
$361$	−7.93242e8	+	1.37394e9i	−0.0467064	+	0.0808979i
$362$	2.96192e9	−	1.71007e9i	0.172480	−	0.0995815i
$363$		−	3.90030e9i		−	0.224632i
$364$	5.09208e9	−	3.94154e8i	0.290061	−	0.0224523i
$365$	−6.98610e9			−0.393608
$366$	−2.66985e9	−	4.62431e9i	−0.148786	−	0.257705i
$367$	1.71332e10	+	9.89188e9i	0.944441	+	0.545274i	0.891350	−	0.453316i	$-0.149759\pi$
$367$	1.71332e10	+	9.89188e9i	0.944441	+	0.545274i	0.0530916	+	0.998590i	$0.483092\pi$
$368$	−2.73669e9	+	4.74008e9i	−0.149222	+	0.258461i
$369$	−1.80400e8	+	1.04154e8i	−0.00973043	+	0.00561787i
$370$			4.30829e9i			0.229878i
$371$	−1.67115e8	−	2.15896e9i	−0.00882106	−	0.113959i
$372$	−8.61616e9			−0.449927
$373$	7.18091e9	+	1.24377e10i	0.370975	+	0.642547i	0.989716	−	0.143048i	$-0.0456904\pi$
$373$	7.18091e9	+	1.24377e10i	0.370975	+	0.642547i	−0.618741	+	0.785595i	$0.712357\pi$
$374$	−1.19789e9	−	6.91604e8i	−0.0612254	−	0.0353485i
$375$	2.56427e9	−	4.44144e9i	0.129670	−	0.224594i
$376$	8.29341e9	−	4.78820e9i	0.414936	−	0.239564i
$377$			1.17475e9i			0.0581541i
$378$	−1.19929e9	+	2.50606e9i	−0.0587434	+	0.122751i
$379$	−2.50167e10			−1.21248			−0.606239	−	0.795282i	$-0.707323\pi$
$379$	−2.50167e10			−1.21248			−0.606239	+	0.795282i	$0.707323\pi$
$380$	−1.14524e9	−	1.98361e9i	−0.0549239	−	0.0951309i
$381$	−1.71874e10	−	9.92317e9i	−0.815664	−	0.470924i
$382$	−1.46774e10	+	2.54221e10i	−0.689282	+	1.19387i
$383$	−3.37242e10	+	1.94707e10i	−1.56728	+	0.904869i	−0.570794	+	0.821093i	$0.693365\pi$
$383$	−3.37242e10	+	1.94707e10i	−1.56728	+	0.904869i	−0.996485	+	0.0837755i	$0.973302\pi$
$384$			1.10958e9i			0.0510310i
$385$	−2.24010e9	−	3.26837e9i	−0.101959	−	0.148761i
$386$	−8.94016e9			−0.402713
$387$	4.33029e8	+	7.50028e8i	0.0193051	+	0.0334375i
$388$	−2.58381e9	−	1.49176e9i	−0.114008	−	0.0658224i
$389$	5.95391e9	−	1.03125e10i	0.260018	−	0.450365i	−0.706228	−	0.707984i	$-0.749605\pi$
$389$	5.95391e9	−	1.03125e10i	0.260018	−	0.450365i	0.966246	+	0.257620i	$0.0829381\pi$
$390$	1.09811e9	−	6.33995e8i	0.0474666	−	0.0274048i
$391$		−	3.56905e9i		−	0.152702i
$392$	3.01185e9	−	7.78610e9i	0.127552	−	0.329743i
$393$	−2.25280e10			−0.944391
$394$	−6.65818e9	−	1.15323e10i	−0.276294	−	0.478554i
$395$	−6.49947e9	−	3.75247e9i	−0.266987	−	0.154145i
$396$	−1.60175e9	+	2.77431e9i	−0.0651348	+	0.112817i
$397$	−3.41629e10	+	1.97240e10i	−1.37529	+	0.794022i	−0.991588	−	0.129437i	$-0.958683\pi$
$397$	−3.41629e10	+	1.97240e10i	−1.37529	+	0.794022i	−0.383698	+	0.923458i	$0.625350\pi$
$398$		−	2.37711e10i		−	0.947363i
$399$	1.14925e10	−	7.87677e9i	0.453442	−	0.310783i
$400$	6.05927e9			0.236690
$401$	1.53782e10	+	2.66358e10i	0.594740	+	1.03012i	0.993583	+	0.113101i	$0.0360784\pi$
$401$	1.53782e10	+	2.66358e10i	0.594740	+	1.03012i	−0.398843	+	0.917019i	$0.630588\pi$
$402$	1.62798e9	+	9.39915e8i	0.0623368	+	0.0359902i
$403$	−1.19602e10	+	2.07157e10i	−0.453439	+	0.785380i
$404$	1.08544e10	−	6.26677e9i	0.407455	−	0.235244i
$405$			6.89754e8i			0.0256374i
$406$	1.73210e9	+	8.28913e8i	0.0637485	+	0.0305074i
$407$	−3.02182e10			−1.10126
$408$	−3.61765e8	−	6.26595e8i	−0.0130553	−	0.0226124i
$409$	4.47436e10	+	2.58327e10i	1.59896	+	0.923160i	0.991688	+	0.128666i	$0.0410695\pi$
$409$	4.47436e10	+	2.58327e10i	1.59896	+	0.923160i	0.607272	+	0.794494i	$0.292264\pi$
$410$	7.77015e7	−	1.34583e8i	0.00274976	−	0.00476272i
$411$	−1.93905e10	+	1.11951e10i	−0.679552	+	0.392339i
$412$		−	5.05936e9i		−	0.175593i
$413$	2.39713e10	−	1.85551e9i	0.823932	−	0.0637767i
$414$	−8.26588e9			−0.281377
$415$	1.66605e9	+	2.88569e9i	0.0561690	+	0.0972875i
$416$	2.66775e9	+	1.54023e9i	0.0890783	+	0.0514294i
$417$	1.11795e10	−	1.93635e10i	0.369725	−	0.640382i
$418$	1.39130e10	−	8.03266e9i	0.455738	−	0.263120i
$419$		−	3.58608e10i		−	1.16349i	−0.813370	−	0.581747i	$-0.802369\pi$
$419$		−	3.58608e10i		−	1.16349i	0.813370	−	0.581747i	$-0.197631\pi$
$420$	−1.59954e8	−	2.06645e9i	−0.00514043	−	0.0664093i
$421$	1.54748e10			0.492602			0.246301	−	0.969193i	$-0.420785\pi$
$421$	1.54748e10			0.492602			0.246301	+	0.969193i	$0.420785\pi$
$422$	−1.41859e10	−	2.45708e10i	−0.447310	−	0.774763i
$423$	1.25247e10	+	7.23113e9i	0.391206	+	0.225863i
$424$	6.53034e8	−	1.13109e9i	0.0202056	−	0.0349972i
$425$	−3.42175e9	+	1.97555e9i	−0.104880	+	0.0605525i
$426$			2.11154e9i			0.0641152i
$427$	−1.04601e10	+	2.18575e10i	−0.314647	+	0.657489i
$428$	−1.74539e10			−0.520136
$429$	4.44682e9	+	7.70212e9i	0.131287	+	0.227395i
$430$	−5.59538e8	−	3.23050e8i	−0.0163665	−	0.00944921i
$431$	2.60121e10	−	4.50542e10i	0.753817	−	1.30565i	−0.192144	−	0.981367i	$-0.561544\pi$
$431$	2.60121e10	−	4.50542e10i	0.753817	−	1.30565i	0.945960	−	0.324282i	$-0.105123\pi$
$432$	−1.45119e9	+	8.37844e8i	−0.0416667	+	0.0240563i
$433$		−	4.88075e10i		−	1.38846i	−0.719751	−	0.694232i	$-0.755744\pi$
$433$		−	4.88075e10i		−	1.38846i	0.719751	−	0.694232i	$-0.244256\pi$
$434$	2.21049e10	+	3.22518e10i	0.623061	+	0.909066i
$435$	4.76735e8			0.0133143
$436$	−5.04076e9	−	8.73085e9i	−0.139492	−	0.241608i
$437$	3.58992e10	+	2.07264e10i	0.984373	+	0.568328i
$438$	1.28156e10	−	2.21972e10i	0.348210	−	0.603118i
$439$	3.56355e10	−	2.05742e10i	0.959456	−	0.553942i	0.0634507	−	0.997985i	$-0.479789\pi$
$439$	3.56355e10	−	2.05742e10i	0.959456	−	0.553942i	0.896006	+	0.444043i	$0.146456\pi$
$440$		−	2.38988e9i		−	0.0637626i
$441$	1.24574e10	−	1.94017e9i	0.329363	−	0.0512962i
$442$	−2.00869e9			−0.0526288
$443$	2.29348e10	+	3.97242e10i	0.595497	+	1.03143i	0.993477	+	0.114037i	$0.0363782\pi$
$443$	2.29348e10	+	3.97242e10i	0.595497	+	1.03143i	−0.397979	+	0.917394i	$0.630288\pi$
$444$	−1.36889e10	−	7.90328e9i	−0.352238	−	0.203365i
$445$	−3.68356e9	+	6.38012e9i	−0.0939352	+	0.162700i
$446$	7.49730e9	−	4.32857e9i	0.189481	−	0.109397i
$447$			4.03594e10i			1.01091i
$448$	4.15336e9	−	2.84665e9i	0.103107	−	0.0706680i
$449$	3.59068e10			0.883468			0.441734	−	0.897146i	$-0.354363\pi$
$449$	3.59068e10			0.883468			0.441734	+	0.897146i	$0.354363\pi$
$450$	4.57535e9	+	7.92473e9i	0.111577	+	0.193257i
$451$	9.43961e8	+	5.44996e8i	0.0228164	+	0.0131731i
$452$	−1.71064e10	+	2.96291e10i	−0.409830	+	0.709846i
$453$	−3.05409e9	+	1.76328e9i	−0.0725253	+	0.0418725i
$454$		−	5.15610e10i		−	1.21366i
$455$	−5.19038e9	−	2.48390e9i	−0.121103	−	0.0579547i
$456$	8.40347e9			0.194357
$457$	8.72626e9	+	1.51143e10i	0.200061	+	0.346516i	0.948548	−	0.316633i	$-0.102553\pi$
$457$	8.72626e9	+	1.51143e10i	0.200061	+	0.346516i	−0.748487	+	0.663150i	$0.769219\pi$
$458$	5.83749e9	+	3.37028e9i	0.132667	+	0.0765956i
$459$	5.46337e8	−	9.46283e8i	0.0123086	−	0.0213192i
$460$	5.34038e9	−	3.08327e9i	0.119273	−	0.0688622i
$461$			8.24115e10i			1.82467i	0.409446	+	0.912334i	$0.365722\pi$
$461$			8.24115e10i			1.82467i	−0.409446	+	0.912334i	$0.634278\pi$
$462$	1.44940e10	−	1.12192e9i	0.318142	−	0.0246259i
$463$	−3.39786e9			−0.0739404			−0.0369702	−	0.999316i	$-0.511771\pi$
$463$	−3.39786e9			−0.0739404			−0.0369702	+	0.999316i	$0.511771\pi$
$464$	5.79090e8	+	1.00301e9i	0.0124932	+	0.0216389i
$465$	8.40681e9	+	4.85367e9i	0.179812	+	0.103815i
$466$	−1.04783e10	+	1.81490e10i	−0.222202	+	0.384865i
$467$	4.30438e9	−	2.48514e9i	0.0904990	−	0.0522496i	−0.454068	−	0.890967i	$-0.650028\pi$
$467$	4.30438e9	−	2.48514e9i	0.0904990	−	0.0522496i	0.544567	+	0.838718i	$0.316694\pi$
$468$			4.65210e9i			0.0969762i
$469$	−6.58347e8	−	8.50519e9i	−0.0136070	−	0.175789i
$470$	−1.07892e10			−0.221104
$471$	9.87038e9	+	1.70960e10i	0.200563	+	0.347385i
$472$	1.25586e10	+	7.25073e9i	0.253031	+	0.146088i
$473$	2.26586e9	−	3.92458e9i	0.0452677	−	0.0784060i
$474$	2.38458e10	−	1.37674e10i	0.472387	−	0.272733i
$475$		−	4.58901e10i		−	0.901457i
$476$	−1.41734e9	+	2.96169e9i	−0.0276088	+	0.0576916i
$477$	1.97242e9			0.0381001
$478$	−2.88378e10	−	4.99486e10i	−0.552396	−	0.956778i
$479$	−5.73910e10	−	3.31347e10i	−1.09019	−	0.629420i	−0.156562	−	0.987668i	$-0.550041\pi$
$479$	−5.73910e10	−	3.31347e10i	−1.09019	−	0.629420i	−0.933627	+	0.358248i	$0.883374\pi$
$480$	6.25051e8	−	1.08262e9i	0.0117747	−	0.0203944i
$481$	−3.80035e10	+	2.19413e10i	−0.709976	+	0.409905i
$482$			4.30364e10i			0.797348i
$483$	2.12063e10	+	3.09407e10i	0.389651	+	0.568514i
$484$	−1.06754e10			−0.194537
$485$	1.68069e9	+	2.91104e9i	0.0303753	+	0.0526115i
$486$	−2.19158e9	−	1.26531e9i	−0.0392837	−	0.0226805i
$487$	−3.04519e9	+	5.27443e9i	−0.0541376	+	0.0937691i	−0.891824	−	0.452382i	$-0.850574\pi$
$487$	−3.04519e9	+	5.27443e9i	−0.0541376	+	0.0937691i	0.837687	+	0.546151i	$0.183908\pi$
$488$	−1.26570e10	+	7.30755e9i	−0.223179	+	0.128852i
$489$			5.17653e9i			0.0905323i
$490$	−7.32474e9	+	5.90027e9i	−0.127060	+	0.102350i
$491$	−8.37867e10			−1.44161			−0.720807	−	0.693136i	$-0.756229\pi$
$491$	−8.37867e10			−1.44161			−0.720807	+	0.693136i	$0.756229\pi$
$492$	2.85077e8	+	4.93768e8i	0.00486521	+	0.00842680i
$493$	−6.54040e8	−	3.77610e8i	−0.0110718	−	0.00639228i
$494$	1.16650e10	−	2.02043e10i	0.195874	−	0.339263i
$495$	3.12566e9	−	1.80460e9i	0.0520619	−	0.0300580i
$496$			2.35830e10i			0.389648i
$497$	7.90388e9	−	5.41720e9i	0.129543	−	0.0887870i
$498$	−1.22251e10			−0.198762
$499$	−1.57841e10	−	2.73389e10i	−0.254577	−	0.440939i	0.710204	−	0.703996i	$-0.248603\pi$
$499$	−1.57841e10	−	2.73389e10i	−0.254577	−	0.440939i	−0.964780	+	0.263057i	$0.915269\pi$
$500$	−1.21565e10	−	7.01858e9i	−0.194504	−	0.112297i
$501$	8.62462e9	−	1.49383e10i	0.136895	−	0.237110i
$502$	1.89615e10	−	1.09474e10i	0.298578	−	0.172384i
$503$		−	6.33607e10i		−	0.989801i	−0.868950	−	0.494900i	$-0.835205\pi$
$503$		−	6.33607e10i		−	0.989801i	0.868950	−	0.494900i	$-0.164795\pi$
$504$	6.85925e9	+	3.28255e9i	0.106305	+	0.0508732i
$505$	−1.41208e10			−0.217118
$506$	2.16260e10	+	3.74573e10i	0.329893	+	0.571392i
$507$	−2.18521e10	−	1.26163e10i	−0.330721	−	0.190942i
$508$	−2.71604e10	+	4.70432e10i	−0.407832	+	0.706385i
$509$	8.59839e10	−	4.96429e10i	1.28099	−	0.739581i	0.303962	−	0.952684i	$-0.401690\pi$
$509$	8.59839e10	−	4.96429e10i	1.28099	−	0.739581i	0.977030	+	0.213104i	$0.0683572\pi$
$510$			8.15160e8i			0.0120493i
$511$	−1.15967e11	+	8.97644e9i	−1.70079	+	0.131650i
$512$	3.03700e9			0.0441942
$513$	6.34545e9	+	1.09906e10i	0.0916206	+	0.158691i
$514$	3.65848e10	+	2.11222e10i	0.524141	+	0.302613i
$515$	−2.85005e9	+	4.93642e9i	−0.0405157	+	0.0701752i
$516$	2.05288e9	−	1.18523e9i	0.0289577	−	0.0167187i
$517$		−	7.56750e10i		−	1.05923i
$518$	5.53572e9	+	7.15160e10i	0.0768873	+	0.993309i
$519$	5.65414e10			0.779287
$520$	−1.73529e9	−	3.00560e9i	−0.0237333	−	0.0411073i
$521$	−3.83954e10	−	2.21676e10i	−0.521109	−	0.300862i	0.216279	−	0.976332i	$-0.430608\pi$
$521$	−3.83954e10	−	2.21676e10i	−0.521109	−	0.300862i	−0.737388	+	0.675469i	$0.763941\pi$
$522$	−8.74540e8	+	1.51475e9i	−0.0117787	+	0.0204013i
$523$	−2.26513e10	+	1.30777e10i	−0.302751	+	0.174793i	−0.643678	−	0.765296i	$-0.722592\pi$
$523$	−2.26513e10	+	1.30777e10i	−0.302751	+	0.174793i	0.340927	+	0.940090i	$0.389259\pi$
$524$			6.16606e10i			0.817867i
$525$	1.79255e10	−	3.74574e10i	0.235958	−	0.493061i
$526$	2.19777e10			0.287104
$527$	−7.68895e9	−	1.33176e10i	−0.0996838	−	0.172657i
$528$	7.59347e9	+	4.38409e9i	0.0977022	+	0.0564084i
$529$	−1.66454e10	+	2.88307e10i	−0.212555	+	0.368156i
$530$	−1.27433e9	+	7.35736e8i	−0.0161502	+	0.00932435i
$531$			2.19001e10i			0.275466i
$532$	−2.15593e10	−	3.14557e10i	−0.269146	−	0.392692i
$533$	1.58288e9			0.0196128
$534$	−1.35145e10	−	2.34079e10i	−0.166202	−	0.287870i
$535$	1.70298e10	+	9.83214e9i	0.207871	+	0.120014i
$536$	2.57261e9	−	4.45589e9i	0.0311684	−	0.0539853i
$537$	−7.39568e10	+	4.26990e10i	−0.889367	+	0.513476i
$538$		−	8.09318e8i		−	0.00966029i
$539$	−4.13843e10	−	5.13755e10i	−0.490321	−	0.608697i
$540$	1.88790e9			0.0222026
$541$	−5.67065e10	−	9.82186e10i	−0.661979	−	1.14658i	−0.980095	−	0.198529i	$-0.936384\pi$
$541$	−5.67065e10	−	9.82186e10i	−0.661979	−	1.14658i	0.318116	−	0.948052i	$-0.396950\pi$
$542$	−3.76892e10	−	2.17599e10i	−0.436737	−	0.252150i
$543$	7.06859e9	−	1.22431e10i	0.0813080	−	0.140830i
$544$	−1.71503e9	+	9.90176e8i	−0.0195829	+	0.0113062i
$545$			1.13583e10i			0.128744i
$546$	1.74136e10	−	1.19350e10i	0.195938	−	0.134293i
$547$	5.43662e10			0.607267			0.303633	−	0.952789i	$-0.401800\pi$
$547$	5.43662e10			0.607267			0.303633	+	0.952789i	$0.401800\pi$
$548$	3.06418e10	+	5.30732e10i	0.339776	+	0.588509i
$549$	−1.91146e10	−	1.10358e10i	−0.210415	−	0.121483i
$550$	2.39409e10	−	4.14669e10i	0.261631	−	0.453159i
$551$	7.59637e9	−	4.38576e9i	0.0824137	−	0.0475816i
$552$			2.26243e10i			0.243679i
$553$	−1.12710e11	−	5.39385e10i	−1.20521	−	0.576764i
$554$	2.76460e10			0.293490
$555$	8.90418e9	+	1.54225e10i	0.0938474	+	0.162548i
$556$	−5.29991e10	−	3.05991e10i	−0.554587	−	0.320191i
$557$	7.26038e10	−	1.25754e11i	0.754291	−	1.30647i	−0.191435	−	0.981505i	$-0.561314\pi$
$557$	7.26038e10	−	1.25754e11i	0.754291	−	1.30647i	0.945726	−	0.324965i	$-0.105352\pi$
$558$	−3.08435e10	+	1.78075e10i	−0.318147	+	0.183682i
$559$		−	6.58094e9i		−	0.0673970i
$560$	−5.65603e9	+	4.37806e8i	−0.0575121	+	0.00445174i
$561$	−5.71751e9			−0.0577239
$562$	3.52363e9	+	6.10311e9i	0.0353220	+	0.0611795i
$563$	−1.02645e11	−	5.92621e10i	−1.02165	−	0.589853i	−0.107072	−	0.994251i	$-0.534148\pi$
$563$	−1.02645e11	−	5.92621e10i	−1.02165	−	0.589853i	−0.914583	+	0.404398i	$0.867481\pi$
$564$	1.97921e10	−	3.42809e10i	0.195603	−	0.338794i
$565$	3.33814e10	−	1.92728e10i	0.327575	−	0.189126i
$566$			2.57669e10i			0.251071i
$567$	8.86264e8	+	1.14497e10i	0.00857494	+	0.110780i
$568$	5.77943e9			0.0555254
$569$	4.16941e10	+	7.22163e10i	0.397764	+	0.688947i	0.993450	−	0.114270i	$-0.0364530\pi$
$569$	4.16941e10	+	7.22163e10i	0.397764	+	0.688947i	−0.595686	+	0.803217i	$0.703120\pi$
$570$	−8.19928e9	−	4.73386e9i	−0.0776741	−	0.0448452i
$571$	−8.47663e10	+	1.46820e11i	−0.797405	+	1.38115i	0.123896	+	0.992295i	$0.460461\pi$
$571$	−8.47663e10	+	1.46820e11i	−0.797405	+	1.38115i	−0.921301	+	0.388850i	$0.872872\pi$
$572$	2.10812e10	−	1.21712e10i	0.196930	−	0.113698i
$573$			1.21339e11i			1.12559i
$574$	1.11689e9	−	2.33387e9i	0.0102888	−	0.0214995i
$575$	1.23548e11			1.13022
$576$	2.29324e9	+	3.97200e9i	0.0208333	+	0.0360844i
$577$	1.24145e11	+	7.16753e10i	1.12002	+	0.646645i	0.941407	−	0.337274i	$-0.109505\pi$
$577$	1.24145e11	+	7.16753e10i	1.12002	+	0.646645i	0.178616	+	0.983919i	$0.442838\pi$
$578$	−3.88152e10	+	6.72299e10i	−0.347768	+	0.602353i
$579$	−3.20033e10	+	1.84771e10i	−0.284761	+	0.164407i
$580$		−	1.30486e9i		−	0.0115306i
$581$	3.13637e10	+	4.57607e10i	0.275247	+	0.401594i
$582$	−1.23325e10			−0.107487
$583$	−5.16043e9	−	8.93813e9i	−0.0446696	−	0.0773699i
$584$	−6.07553e10	−	3.50771e10i	−0.522315	−	0.301559i
$585$	2.62063e9	−	4.53906e9i	0.0223760	−	0.0387563i
$586$	1.89188e10	−	1.09228e10i	0.160437	−	0.0926283i
$587$			1.76771e11i			1.48888i	0.667692	+	0.744438i	$0.267283\pi$
$587$			1.76771e11i			1.48888i	−0.667692	+	0.744438i	$0.732717\pi$
$588$	−5.31037e9	−	3.40969e10i	−0.0444238	−	0.285236i
$589$	1.78607e11			1.48401
$590$	−8.16898e9	−	1.41491e10i	−0.0674155	−	0.116767i
$591$	−4.76690e10	−	2.75217e10i	−0.390738	−	0.225593i
$592$	−2.16318e10	+	3.74674e10i	−0.176119	+	0.305047i
$593$	2.24336e10	−	1.29520e10i	0.181418	−	0.104742i	−0.406541	−	0.913633i	$-0.633265\pi$
$593$	2.24336e10	−	1.29520e10i	0.181418	−	0.104742i	0.587959	+	0.808891i	$0.299932\pi$
$594$			1.32417e10i			0.106365i
$595$	3.05129e9	−	2.09131e9i	0.0243453	−	0.0166859i
$596$	1.10466e11			0.875478
$597$	−4.91290e10	−	8.50940e10i	−0.386759	−	0.669887i
$598$	5.43953e10	+	3.14051e10i	0.425360	+	0.245582i
$599$	1.11281e11	−	1.92744e11i	0.864399	−	1.49718i	−0.00324460	−	0.999995i	$-0.501033\pi$
$599$	1.11281e11	−	1.92744e11i	0.864399	−	1.49718i	0.867643	−	0.497187i	$-0.165634\pi$
$600$	2.16905e10	−	1.25230e10i	0.167365	−	0.0966284i
$601$			8.09548e10i			0.620504i	0.950654	+	0.310252i	$0.100413\pi$
$601$			8.09548e10i			0.620504i	−0.950654	+	0.310252i	$0.899587\pi$
$602$	−9.70322e9	−	4.64356e9i	−0.0738805	−	0.0353561i
$603$	7.77030e9			0.0587717
$604$	4.82622e9	+	8.35926e9i	0.0362626	+	0.0628087i
$605$	1.04160e10	+	6.01367e9i	0.0777461	+	0.0448867i
$606$	2.59038e10	−	4.48667e10i	0.192076	−	0.332685i
$607$	8.31275e10	−	4.79937e10i	0.612336	−	0.353532i	−0.161543	−	0.986866i	$-0.551647\pi$
$607$	8.31275e10	−	4.79937e10i	0.612336	−	0.353532i	0.773879	+	0.633333i	$0.218314\pi$
$608$		−	2.30009e10i		−	0.168318i
$609$	7.91363e9	−	6.12557e8i	0.0575316	−	0.00445325i
$610$	1.64660e10			0.118924
$611$	−5.49474e10	−	9.51717e10i	−0.394260	−	0.682878i
$612$	−2.59004e9	−	1.49536e9i	−0.0184629	−	0.0106596i
$613$	−1.40024e11	+	2.42528e11i	−0.991654	+	1.71760i	−0.384173	+	0.923261i	$0.625513\pi$
$613$	−1.40024e11	+	2.42528e11i	−0.991654	+	1.71760i	−0.607481	+	0.794334i	$0.707820\pi$
$614$	−9.60052e10	+	5.54287e10i	−0.675494	+	0.389997i
$615$		−	6.42361e8i		−	0.00449033i
$616$	−3.07076e9	−	3.96712e10i	−0.0213267	−	0.275519i
$617$	1.42078e11			0.980364			0.490182	−	0.871620i	$-0.336930\pi$
$617$	1.42078e11			0.980364			0.490182	+	0.871620i	$0.336930\pi$
$618$	−1.04565e10	−	1.81111e10i	−0.0716854	−	0.124163i
$619$	2.28357e11	+	1.31842e11i	1.55543	+	0.898031i	0.997684	+	0.0680221i	$0.0216688\pi$
$619$	2.28357e11	+	1.31842e11i	1.55543	+	0.898031i	0.557751	+	0.830008i	$0.311664\pi$
$620$	1.32848e10	−	2.30100e10i	0.0899061	−	0.155722i
$621$	−2.95896e10	+	1.70836e10i	−0.198963	+	0.114872i
$622$			6.83285e10i			0.456500i
$623$	−5.29480e10	+	1.10641e11i	−0.351477	+	0.734451i
$624$	1.27331e10			0.0839839
$625$	−6.43247e10	−	1.11414e11i	−0.421558	−	0.730160i
$626$	−3.50618e10	−	2.02430e10i	−0.228316	−	0.131819i
$627$	3.32031e10	−	5.75095e10i	0.214837	−	0.372108i
$628$	4.67929e10	−	2.70159e10i	0.300844	−	0.173692i
$629$		−	2.82111e10i		−	0.180226i
$630$	−4.84345e9	−	7.06676e9i	−0.0307463	−	0.0448599i
$631$	2.95798e11			1.86585			0.932926	−	0.360069i	$-0.117247\pi$
$631$	2.95798e11			1.86585			0.932926	+	0.360069i	$0.117247\pi$
$632$	−3.76822e10	−	6.52674e10i	−0.236193	−	0.409099i
$633$	−1.01564e11	−	5.86378e10i	−0.632592	−	0.365227i
$634$	6.98632e10	−	1.21007e11i	0.432406	−	0.748949i
$635$	5.30009e10	−	3.06001e10i	0.325978	−	0.188203i
$636$		−	5.39865e9i		−	0.0329956i
$637$	−8.93500e10	−	3.45627e10i	−0.542671	−	0.209918i
$638$	9.15222e9			0.0552387
$639$	4.36404e9	+	7.55874e9i	0.0261749	+	0.0453363i
$640$	−2.96321e9	−	1.71081e9i	−0.0176621	−	0.0101972i
$641$	−1.28368e11	+	2.22340e11i	−0.760369	+	1.31700i	0.182291	+	0.983245i	$0.441649\pi$
$641$	−1.28368e11	+	2.22340e11i	−0.760369	+	1.31700i	−0.942660	+	0.333754i	$0.891685\pi$
$642$	−6.24801e10	+	3.60729e10i	−0.367791	+	0.212344i
$643$			2.31907e11i			1.35666i	0.734758	+	0.678329i	$0.237296\pi$
$643$			2.31907e11i			1.35666i	−0.734758	+	0.678329i	$0.762704\pi$
$644$	8.46867e10	−	5.80431e10i	0.492348	−	0.337448i
$645$	−2.67066e9			−0.0154305
$646$	7.49914e9	+	1.29889e10i	0.0430607	+	0.0745834i
$647$	−2.43215e11	−	1.40421e11i	−1.38795	−	0.801334i	−0.394867	−	0.918738i	$-0.629209\pi$
$647$	−2.43215e11	−	1.40421e11i	−1.38795	−	0.801334i	−0.993084	+	0.117405i	$0.962543\pi$
$648$	−3.46324e9	+	5.99851e9i	−0.0196419	+	0.0340207i
$649$	9.92413e10	−	5.72970e10i	0.559389	−	0.322963i
$650$		−	6.95337e10i		−	0.389531i
$651$	1.45786e11	+	6.97673e10i	0.811695	+	0.388444i
$652$	1.41685e10			0.0784033
$653$	−1.35508e10	−	2.34706e10i	−0.0745266	−	0.129084i	0.826354	−	0.563151i	$-0.190411\pi$
$653$	−1.35508e10	−	2.34706e10i	−0.0745266	−	0.129084i	−0.900880	+	0.434068i	$0.857078\pi$
$654$	−3.60891e10	−	2.08360e10i	−0.197272	−	0.113895i
$655$	3.47347e10	−	6.01623e10i	0.188712	−	0.326858i
$656$	1.35148e9	−	7.80276e8i	0.00729782	−	0.00421340i
$657$		−	1.05947e11i		−	0.568625i
$658$	−1.79097e11	+	1.38630e10i	−0.955397	+	0.0739528i
$659$	−1.61820e11			−0.858006			−0.429003	−	0.903303i	$-0.641135\pi$
$659$	−1.61820e11			−0.858006			−0.429003	+	0.903303i	$0.641135\pi$
$660$	−4.93931e9	−	8.55513e9i	−0.0260310	−	0.0450870i
$661$	−7.09023e10	−	4.09355e10i	−0.371411	−	0.214434i	0.302664	−	0.953097i	$-0.402124\pi$
$661$	−7.09023e10	−	4.09355e10i	−0.371411	−	0.214434i	−0.674075	+	0.738663i	$0.735457\pi$
$662$	1.31405e11	−	2.27601e11i	0.684196	−	1.18506i
$663$	−7.19055e9	+	4.15147e9i	−0.0372141	+	0.0214856i
$664$			3.34609e10i			0.172133i
$665$	3.31575e9	+	4.28362e10i	0.0169549	+	0.219040i
$666$	−6.53367e10			−0.332093
$667$	1.18076e10	+	2.04514e10i	0.0596566	+	0.103328i
$668$	−4.08871e10	−	2.36062e10i	−0.205343	−	0.118555i
$669$	1.78922e10	−	3.09902e10i	0.0893221	−	0.154710i
$670$	−5.02020e9	+	2.89841e9i	−0.0249128	+	0.0143834i
$671$			1.15492e11i			0.569721i
$672$	8.98457e9	−	1.87742e10i	0.0440575	−	0.0920630i
$673$	−1.98234e11			−0.966312			−0.483156	−	0.875534i	$-0.660510\pi$
$673$	−1.98234e11			−0.966312			−0.483156	+	0.875534i	$0.660510\pi$
$674$	−6.54064e10	−	1.13287e11i	−0.316943	−	0.548961i
$675$	3.27570e10	+	1.89123e10i	0.157793	+	0.0911021i
$676$	−3.45318e10	+	5.98108e10i	−0.165361	+	0.286413i
$677$	−1.25087e11	+	7.22188e10i	−0.595465	+	0.343792i	−0.767255	−	0.641342i	$-0.778378\pi$
$677$	−1.25087e11	+	7.22188e10i	−0.595465	+	0.343792i	0.171791	+	0.985133i	$0.445045\pi$
$678$			1.41419e11i			0.669250i
$679$	3.16392e10	+	4.61626e10i	0.148849	+	0.217176i
$680$	2.23115e9			0.0104350
$681$	−1.06564e11	−	1.84574e11i	−0.495475	−	0.858188i
$682$	1.61391e11	+	9.31794e10i	0.746007	+	0.430707i
$683$	1.04524e9	−	1.81041e9i	0.00480322	−	0.00831943i	−0.863614	−	0.504154i	$-0.831804\pi$
$683$	1.04524e9	−	1.81041e9i	0.00480322	−	0.00831943i	0.868417	+	0.495835i	$0.165138\pi$
$684$	3.00821e10	−	1.73679e10i	0.137431	−	0.0793457i
$685$		−	6.90448e10i		−	0.313595i
$686$	−1.14007e11	+	1.07354e11i	−0.514795	+	0.484754i
$687$	2.78622e10			0.125080
$688$	−3.24405e9	−	5.61886e9i	−0.0144788	−	0.0250781i
$689$	−1.29799e10	−	7.49394e9i	−0.0575963	−	0.0332532i
$690$	1.27448e10	−	2.20746e10i	0.0562257	−	0.0973858i
$691$	2.84000e10	−	1.63968e10i	0.124568	−	0.0719193i	−0.436421	−	0.899742i	$-0.643754\pi$
$691$	2.84000e10	−	1.63968e10i	0.124568	−	0.0719193i	0.560989	+	0.827823i	$0.310421\pi$
$692$		−	1.54758e11i		−	0.674882i
$693$	4.95660e10	−	3.39718e10i	0.214907	−	0.147294i
$694$	−1.62877e10			−0.0702137
$695$	3.44742e10	+	5.97111e10i	0.147760	+	0.255927i
$696$	4.14597e9	+	2.39368e9i	0.0176681	+	0.0102007i
$697$	−5.08798e8	+	8.81264e8i	−0.00215583	+	0.00373400i
$698$	−2.07369e11	+	1.19725e11i	−0.873621	+	0.504385i
$699$			8.66246e10i			0.362855i
$700$	−1.02523e11	−	4.90634e10i	−0.427003	−	0.204346i
$701$	−3.85237e11			−1.59535			−0.797675	−	0.603088i	$-0.793937\pi$
$701$	−3.85237e11			−1.59535			−0.797675	+	0.603088i	$0.793937\pi$
$702$	9.61475e9	+	1.66532e10i	0.0395904	+	0.0685725i
$703$	2.83761e11	+	1.63830e11i	1.16180	+	0.670766i
$704$	1.19996e10	−	2.07838e10i	0.0488511	−	0.0846126i
$705$	−3.86224e10	+	2.22986e10i	−0.156344	+	0.0902655i
$706$		−	1.16688e11i		−	0.469685i
$707$	−2.34401e11	+	1.81439e10i	−0.938170	+	0.0726193i
$708$	5.99420e10			0.238560
$709$	−1.40246e11	−	2.42913e11i	−0.555016	−	0.961315i	−0.997902	−	0.0647376i	$-0.979379\pi$
$709$	−1.40246e11	−	2.42913e11i	−0.555016	−	0.961315i	0.442887	−	0.896578i	$-0.353954\pi$
$710$	−5.63900e9	−	3.25568e9i	−0.0221906	−	0.0128117i
$711$	5.69075e10	−	9.85668e10i	0.222685	−	0.385702i
$712$	−6.40689e10	+	3.69902e10i	−0.249303	+	0.143935i
$713$			4.80856e11i			1.86062i
$714$	1.04740e9	+	1.35314e10i	0.00403013	+	0.0520654i
$715$	−2.74253e10			−0.104937
$716$	1.16870e11	+	2.02425e11i	0.444683	+	0.770214i
$717$	−2.06463e11	−	1.19202e11i	−0.781206	−	0.451030i
$718$	−6.22992e10	+	1.07905e11i	−0.234414	+	0.406018i
$719$	4.56523e11	−	2.63574e11i	1.70823	−	0.986249i	0.771485	−	0.636248i	$-0.219514\pi$
$719$	4.56523e11	−	2.63574e11i	1.70823	−	0.986249i	0.936749	−	0.350002i	$-0.113819\pi$
$720$		−	5.16732e9i		−	0.0192280i
$721$	−4.09669e10	+	8.56049e10i	−0.151598	+	0.316780i
$722$	1.79490e10			0.0660529
$723$	8.89458e10	+	1.54059e11i	0.325516	+	0.563810i
$724$	−3.35103e10	−	1.93472e10i	−0.121962	−	0.0704148i
$725$	1.30715e10	−	2.26405e10i	0.0473123	−	0.0819474i
$726$	−3.82149e10	+	2.20634e10i	−0.137558	+	0.0794193i
$727$		−	2.50961e11i		−	0.898399i	−0.893431	−	0.449200i	$-0.851709\pi$
$727$		−	2.50961e11i		−	0.898399i	0.893431	−	0.449200i	$-0.148291\pi$
$728$	−3.26670e10	−	4.76623e10i	−0.116301	−	0.169687i
$729$	−1.04604e10			−0.0370370
$730$	3.95194e10	+	6.84495e10i	0.139161	+	0.241034i
$731$	3.66392e9	+	2.11536e9i	0.0128315	+	0.00740825i
$732$	−3.02059e10	+	5.23181e10i	−0.105208	+	0.182225i
$733$	−3.86494e10	+	2.23143e10i	−0.133884	+	0.0772977i	−0.565446	−	0.824785i	$-0.691296\pi$
$733$	−3.86494e10	+	2.23143e10i	−0.133884	+	0.0772977i	0.431562	+	0.902083i	$0.357963\pi$
$734$		−	2.23828e11i		−	0.771133i
$735$	−1.40262e10	+	3.62598e10i	−0.0480606	+	0.124244i
$736$	6.19242e10			0.211032
$737$	−2.03294e10	−	3.52115e10i	−0.0689056	−	0.119348i
$738$	2.04100e9	+	1.17837e9i	0.00688045	+	0.00397243i
$739$	−4.99685e10	+	8.65479e10i	−0.167540	+	0.290188i	−0.937554	−	0.347839i	$-0.886916\pi$
$739$	−4.99685e10	+	8.65479e10i	−0.167540	+	0.290188i	0.770014	+	0.638026i	$0.220249\pi$
$740$	4.22124e10	−	2.43714e10i	0.140771	−	0.0812742i
$741$		−	9.64347e10i		−	0.319860i
$742$	−2.02081e10	+	1.38503e10i	−0.0666668	+	0.0456925i
$743$	1.57082e10			0.0515433			0.0257717	−	0.999668i	$-0.491796\pi$
$743$	1.57082e10			0.0515433			0.0257717	+	0.999668i	$0.491796\pi$
$744$	4.87404e10	+	8.44208e10i	0.159073	+	0.275523i
$745$	−1.07782e11	−	6.22281e10i	−0.349882	−	0.202005i
$746$	8.12427e10	−	1.40717e11i	0.262319	−	0.454349i
$747$	−4.37625e10	+	2.52663e10i	−0.140546	+	0.0811444i
$748$			1.56492e10i			0.0499903i
$749$	2.95321e11	+	1.41328e11i	0.938356	+	0.449058i
$750$	−5.80228e10			−0.183381
$751$	−1.67052e11	−	2.89343e11i	−0.525161	−	0.909606i	−0.999571	−	0.0293018i	$-0.990672\pi$
$751$	−1.67052e11	−	2.89343e11i	−0.525161	−	0.909606i	0.474409	−	0.880304i	$-0.342662\pi$
$752$	−9.38292e10	−	5.41723e10i	−0.293404	−	0.169397i
$753$	4.52513e10	−	7.83775e10i	0.140751	−	0.243788i
$754$	1.15102e10	−	6.64540e9i	0.0356120	−	0.0205606i
$755$		−	1.08749e10i		−	0.0334685i
$756$	3.13385e10	−	2.42577e9i	0.0959381	−	0.00742611i
$757$	−3.07832e11			−0.937410			−0.468705	−	0.883355i	$-0.655279\pi$
$757$	−3.07832e11			−0.937410			−0.468705	+	0.883355i	$0.655279\pi$
$758$	1.41516e11	+	2.45113e11i	0.428676	+	0.742488i
$759$	1.54830e11	+	8.93913e10i	0.466540	+	0.269357i
$760$	−1.29569e10	+	2.24420e10i	−0.0388370	+	0.0672677i
$761$	1.00743e10	−	5.81642e9i	0.0300385	−	0.0173427i	−0.484906	−	0.874567i	$-0.661146\pi$
$761$	1.00743e10	−	5.81642e9i	0.0300385	−	0.0173427i	0.514944	+	0.857224i	$0.327813\pi$
$762$			2.24536e11i			0.665987i
$763$	1.45942e10	+	1.88543e11i	0.0430609	+	0.556305i
$764$	3.32112e11			0.974791
$765$	1.68474e9	+	2.91805e9i	0.00491911	+	0.00852015i
$766$	3.81545e11	+	2.20285e11i	1.10823	+	0.639839i
$767$	8.32064e10	−	1.44118e11i	0.240422	−	0.416424i
$768$	1.08716e10	−	6.27674e9i	0.0312500	−	0.0180422i
$769$		−	6.63389e11i		−	1.89698i	−0.316807	−	0.948490i	$-0.602611\pi$
$769$		−	6.63389e11i		−	1.89698i	0.316807	−	0.948490i	$-0.397389\pi$
$770$	−1.93515e10	+	4.04371e10i	−0.0550493	+	0.115031i
$771$	1.74618e11			0.494165
$772$	5.05732e10	+	8.75953e10i	0.142381	+	0.246611i
$773$	5.28030e11	+	3.04859e11i	1.47891	+	0.853848i	0.999715	−	0.0238625i	$-0.00759640\pi$
$773$	5.28030e11	+	3.04859e11i	1.47891	+	0.853848i	0.479192	+	0.877710i	$0.340930\pi$
$774$	4.89916e9	−	8.48559e9i	0.0136508	−	0.0236439i
$775$	4.61010e11	−	2.66164e11i	1.27792	−	0.737807i
$776$			3.37548e10i			0.0930869i
$777$	1.67623e11	+	2.44567e11i	0.459884	+	0.670986i
$778$	−1.34722e11			−0.367721
$779$	−5.90945e9	−	1.02355e10i	−0.0160471	−	0.0277944i
$780$	−1.24237e10	−	7.17283e9i	−0.0335639	−	0.0193781i
$781$	2.28352e10	−	3.95518e10i	0.0613764	−	0.106307i
$782$	−3.49694e10	+	2.01896e10i	−0.0935107	+	0.0539884i
$783$			7.22985e9i			0.0192346i
$784$	−9.33254e10	+	1.45349e10i	−0.247022	+	0.0384721i
$785$	−6.08745e10			−0.160309
$786$	1.27437e11	+	2.20728e11i	0.333893	+	0.578319i
$787$	−3.98278e11	−	2.29946e11i	−1.03821	−	0.599413i	−0.118887	−	0.992908i	$-0.537933\pi$
$787$	−3.98278e11	−	2.29946e11i	−1.03821	−	0.599413i	−0.919327	+	0.393495i	$0.871266\pi$
$788$	−7.53287e10	+	1.30473e11i	−0.195369	+	0.338389i
$789$	7.86742e10	−	4.54226e10i	0.203013	−	0.117210i
$790$			8.49087e10i			0.217994i
$791$	5.29356e11	−	3.62813e11i	1.35220	−	0.926779i
$792$	3.62434e10			0.0921145
$793$	8.38584e10	+	1.45247e11i	0.212058	+	0.367295i
$794$	3.86509e11	+	2.23151e11i	0.972474	+	0.561458i
$795$	−3.04118e9	+	5.26747e9i	−0.00761330	+	0.0131866i
$796$	−2.32908e11	+	1.34469e11i	−0.580139	+	0.334943i
$797$		−	1.78316e10i		−	0.0441935i	−0.999756	−	0.0220967i	$-0.992966\pi$
$797$		−	1.78316e10i		−	0.0441935i	0.999756	−	0.0220967i	$-0.00703418\pi$
$798$	−1.42188e11	−	6.80450e10i	−0.350631	−	0.167797i
$799$	7.06488e10			0.173348
$800$	−3.42764e10	−	5.93685e10i	−0.0836826	−	0.144943i
$801$	−9.67567e10	−	5.58625e10i	−0.235045	−	0.135703i
$802$	1.73984e11	−	3.01349e11i	0.420545	−	0.728405i
$803$	−4.80103e11	+	2.77188e11i	−1.15471	+	0.666671i
$804$		−	2.12678e10i		−	0.0508978i
$805$	−1.15326e11	+	8.92684e9i	−0.274627	+	0.0212576i
$806$	2.70629e11			0.641260
$807$	−1.67266e9	−	2.89714e9i	−0.00394380	−	0.00683085i
$808$	−1.22803e11	−	7.09005e10i	−0.288114	−	0.166343i
$809$	2.55304e11	−	4.42200e11i	0.596024	−	1.03234i	−0.397377	−	0.917655i	$-0.630079\pi$
$809$	2.55304e11	−	4.42200e11i	0.596024	−	1.03234i	0.993401	−	0.114689i	$-0.0365872\pi$
$810$	6.75818e9	−	3.90184e9i	0.0156996	−	0.00906419i
$811$		−	2.22379e11i		−	0.514057i	−0.966404	−	0.257028i	$-0.917257\pi$
$811$		−	2.22379e11i		−	0.514057i	0.966404	−	0.257028i	$-0.0827434\pi$
$812$	−1.67661e9	−	2.16601e10i	−0.00385663	−	0.0498238i
$813$	−1.79889e11			−0.411759
$814$	1.70940e11	+	2.96077e11i	0.389355	+	0.674383i
$815$	−1.38243e10	−	7.98144e9i	−0.0313337	−	0.0180905i
$816$	−4.09290e9	+	7.08912e9i	−0.00923147	+	0.0159894i
$817$	−4.25547e10	+	2.45690e10i	−0.0955123	+	0.0551441i
$818$		−	5.84528e11i		−	1.30555i
$819$	3.76692e10	−	7.87139e10i	0.0837242	−	0.174951i
$820$	−1.75818e9			−0.00388874
$821$	3.37908e11	+	5.85274e11i	0.743748	+	1.28821i	0.950778	+	0.309874i	$0.100287\pi$
$821$	3.37908e11	+	5.85274e11i	0.743748	+	1.28821i	−0.207030	+	0.978335i	$0.566380\pi$
$822$	2.19379e11	+	1.26658e11i	0.480516	+	0.277426i
$823$	−1.85716e11	+	3.21670e11i	−0.404810	+	0.701151i	−0.994299	−	0.106625i	$-0.965996\pi$
$823$	−1.85716e11	+	3.21670e11i	−0.404810	+	0.701151i	0.589490	+	0.807776i	$0.299329\pi$
$824$	−4.95714e10	+	2.86201e10i	−0.107528	+	0.0620814i
$825$		−	1.97920e11i		−	0.427242i
$826$	−1.53782e11	−	2.24374e11i	−0.330359	−	0.482005i
$827$	−4.71515e11			−1.00803			−0.504015	−	0.863695i	$-0.668144\pi$
$827$	−4.71515e11			−1.00803			−0.504015	+	0.863695i	$0.668144\pi$
$828$	4.67589e10	+	8.09888e10i	0.0994816	+	0.172307i
$829$	−1.67294e11	−	9.65875e10i	−0.354212	−	0.204504i	0.312327	−	0.949975i	$-0.398892\pi$
$829$	−1.67294e11	−	9.65875e10i	−0.354212	−	0.204504i	−0.666539	+	0.745470i	$0.732225\pi$
$830$	1.88492e10	−	3.26478e10i	0.0397174	−	0.0687926i
$831$	9.89653e10	−	5.71377e10i	0.207529	−	0.119817i
$832$		−	3.48514e10i		−	0.0727322i
$833$	4.79632e10	−	3.86356e10i	0.0996158	−	0.0802431i
$834$	−2.52963e11			−0.522870
$835$	2.65957e10	+	4.60651e10i	0.0547099	+	0.0947603i
$836$	−1.57407e11	−	9.08792e10i	−0.322255	−	0.186054i
$837$	−7.36076e10	+	1.27492e11i	−0.149976	+	0.259766i
$838$	−3.51363e11	+	2.02860e11i	−0.712492	+	0.411358i
$839$			4.35826e11i			0.879560i	0.898106	+	0.439780i	$0.144944\pi$
$839$			4.35826e11i			0.879560i	−0.898106	+	0.439780i	$0.855056\pi$
$840$	−1.93422e10	+	1.32569e10i	−0.0388498	+	0.0266271i
$841$	−4.95249e11			−0.990011
$842$	−8.75386e10	−	1.51621e11i	−0.174161	−	0.301656i
$843$	2.52273e10	+	1.45650e10i	0.0499529	+	0.0288403i
$844$	−1.60496e11	+	2.77987e11i	−0.316296	+	0.547840i
$845$	6.73854e10	−	3.89050e10i	0.132172	−	0.0763094i
$846$		−	1.63622e11i		−	0.319418i
$847$	1.80628e11	+	8.64412e10i	0.350956	+	0.167953i
$848$	−1.47765e10			−0.0285751
$849$	5.32540e10	+	9.22387e10i	0.102499	+	0.177534i
$850$	3.87127e10	+	2.23508e10i	0.0741613	+	0.0428171i
$851$	−4.41071e11	+	7.63958e11i	−0.840989	+	1.45664i
$852$	2.06888e10	−	1.19447e10i	0.0392624	−	0.0226682i
$853$		−	3.16582e11i		−	0.597984i	−0.954256	−	0.298992i	$-0.903350\pi$
$853$		−	3.16582e11i		−	0.597984i	0.954256	−	0.298992i	$-0.0966504\pi$
$854$	2.73330e11	−	2.11572e10i	0.513872	−	0.0397765i
$855$	−3.91349e10			−0.0732318
$856$	9.87340e10	+	1.71012e11i	0.183896	+	0.318517i
$857$	3.30546e10	+	1.90841e10i	0.0612785	+	0.0353792i	0.530326	−	0.847794i	$-0.322069\pi$
$857$	3.30546e10	+	1.90841e10i	0.0612785	+	0.0353792i	−0.469048	+	0.883173i	$0.655403\pi$
$858$	5.03100e10	−	8.71395e10i	0.0928336	−	0.160793i
$859$	−4.03458e11	+	2.32937e11i	−0.741013	+	0.427824i	−0.822437	−	0.568856i	$-0.807386\pi$
$859$	−4.03458e11	+	2.32937e11i	−0.741013	+	0.427824i	0.0814248	+	0.996679i	$0.474053\pi$
$860$			7.30978e9i			0.0133632i
$861$	−8.25369e8	−	1.06630e10i	−0.00150188	−	0.0194028i
$862$	−5.88586e11			−1.06606
$863$	−4.43856e11	−	7.68781e11i	−0.800200	−	1.38599i	−0.919484	−	0.393127i	$-0.871393\pi$
$863$	−4.43856e11	−	7.68781e11i	−0.800200	−	1.38599i	0.119284	−	0.992860i	$-0.461940\pi$
$864$	1.64183e10	+	9.47912e9i	0.0294628	+	0.0170103i
$865$	−8.71784e10	+	1.50997e11i	−0.155720	+	0.269715i
$866$	−4.78213e11	+	2.76097e11i	−0.850257	+	0.490896i
$867$			3.20886e11i			0.567904i
$868$	1.90958e11	−	3.99027e11i	0.336402	−	0.702949i
$869$	−5.95547e11			−1.04433
$870$	−2.69682e9	−	4.67103e9i	−0.00470733	−	0.00815334i
$871$	−5.11340e10	−	2.95222e10i	−0.0888458	−	0.0512951i
$872$	−5.70297e10	+	9.87783e10i	−0.0986359	+	0.170842i
$873$	−4.41469e10	+	2.54882e10i	−0.0760051	+	0.0438816i
$874$		−	4.68986e11i		−	0.803737i
$875$	1.48859e11	+	2.17190e11i	0.253946	+	0.370516i
$876$	−2.89983e11			−0.492443
$877$	1.26972e11	+	2.19921e11i	0.214639	+	0.371765i	0.953161	−	0.302464i	$-0.0978093\pi$
$877$	1.26972e11	+	2.19921e11i	0.214639	+	0.371765i	−0.738522	+	0.674229i	$0.764476\pi$
$878$	−4.03170e11	−	2.32770e11i	−0.678438	−	0.391696i
$879$	4.51496e10	−	7.82013e10i	0.0756307	−	0.130996i
$880$	−2.34160e10	+	1.35192e10i	−0.0390464	+	0.0225435i
$881$		−	1.78535e11i		−	0.296360i	−0.988960	−	0.148180i	$-0.952658\pi$
$881$		−	1.78535e11i		−	0.296360i	0.988960	−	0.148180i	$-0.0473415\pi$
$882$	−8.94796e10	−	1.11082e11i	−0.147860	−	0.183557i
$883$	9.62737e10			0.158367			0.0791836	−	0.996860i	$-0.474769\pi$
$883$	9.62737e10			0.158367			0.0791836	+	0.996860i	$0.474769\pi$
$884$	1.13628e10	+	1.96810e10i	0.0186071	+	0.0322284i
$885$	−5.84855e10	−	3.37666e10i	−0.0953400	−	0.0550446i
$886$	2.59477e11	−	4.49428e11i	0.421080	−	0.729332i
$887$	4.16296e11	−	2.40349e11i	0.672524	−	0.388282i	−0.124509	−	0.992219i	$-0.539735\pi$
$887$	4.16296e11	−	2.40349e11i	0.672524	−	0.388282i	0.797032	+	0.603937i	$0.206402\pi$
$888$			1.78831e11i			0.287601i
$889$	8.40477e11	−	5.76051e11i	1.34561	−	0.922261i
$890$	8.33495e10			0.132844
$891$	2.73674e10	+	4.74016e10i	0.0434232	+	0.0752112i
$892$	−8.48222e10	−	4.89721e10i	−0.133983	−	0.0773552i
$893$	−4.10276e11	+	7.10620e11i	−0.645165	+	1.11746i
$894$	3.95440e11	−	2.28307e11i	0.619056	−	0.357412i
$895$		−	2.63342e11i		−	0.410419i
$896$	−5.13864e10	−	2.45914e10i	−0.0797289	−	0.0381549i
$897$	2.59627e11			0.401033
$898$	−2.03119e11	−	3.51813e11i	−0.312353	−	0.541012i
$899$	8.81183e10	+	5.08752e10i	0.134905	+	0.0778874i
$900$	5.17641e10	−	8.96581e10i	0.0788967	−	0.136653i
$901$	8.34447e9	−	4.81768e9i	0.0126619	−	0.00731036i
$902$		−	1.23319e10i		−	0.0186295i
$903$	−4.43320e10	+	3.43153e9i	−0.0666755	+	0.00516104i
$904$	3.87073e11			0.579587
$905$	2.17974e10	+	3.77542e10i	0.0324945	+	0.0562822i
$906$	3.45531e10	+	1.99493e10i	0.0512831	+	0.0296083i
$907$	−2.80649e11	+	4.86099e11i	−0.414701	+	0.718282i	−0.995397	−	0.0958377i	$-0.969447\pi$
$907$	−2.80649e11	+	4.86099e11i	−0.414701	+	0.718282i	0.580696	+	0.814120i	$0.302780\pi$
$908$	−5.05192e11	+	2.91673e11i	−0.743213	+	0.429094i
$909$		−	2.14147e11i		−	0.313659i
$910$	5.02408e9	+	6.49062e10i	0.00732641	+	0.0946500i
$911$	−6.19584e11			−0.899553			−0.449776	−	0.893141i	$-0.648496\pi$
$911$	−6.19584e11			−0.899553			−0.449776	+	0.893141i	$0.648496\pi$
$912$	−4.75372e10	−	8.23368e10i	−0.0687154	−	0.119019i
$913$	2.28991e11	+	1.32208e11i	0.329560	+	0.190272i
$914$	9.87263e10	−	1.70999e11i	0.141465	−	0.245024i
$915$	5.89438e10	−	3.40312e10i	0.0840919	−	0.0485505i
$916$		−	7.62606e10i		−	0.108322i
$917$	4.99282e11	−	1.04330e12i	0.706103	−	1.47548i
$918$	−1.23622e10			−0.0174070
$919$	9.67495e10	+	1.67575e11i	0.135640	+	0.234935i	0.925842	−	0.377912i	$-0.123358\pi$
$919$	9.67495e10	+	1.67575e11i	0.135640	+	0.234935i	−0.790202	+	0.612847i	$0.790024\pi$
$920$	−6.04196e10	−	3.48832e10i	−0.0843386	−	0.0486929i
$921$	−2.29115e11	+	3.96839e11i	−0.318431	+	0.551538i
$922$	8.07464e11	−	4.66190e11i	1.11738	−	0.645118i
$923$		−	6.63224e10i		−	0.0913805i
$924$	−9.29832e10	−	1.35666e11i	−0.127561	−	0.186115i
$925$	9.76570e11			1.33394
$926$	1.92212e10	+	3.32921e10i	0.0261419	+	0.0452791i
$927$	−7.48626e10	−	4.32219e10i	−0.101379	−	0.0585309i
$928$	6.55166e9	−	1.13478e10i	0.00883404	−	0.0153010i
$929$	4.45439e11	−	2.57174e11i	0.598034	−	0.345275i	−0.170234	−	0.985404i	$-0.554452\pi$
$929$	4.45439e11	−	2.57174e11i	0.598034	−	0.345275i	0.768268	+	0.640129i	$0.221119\pi$
$930$		−	1.09826e11i		−	0.146816i
$931$	1.10080e11	+	7.06804e11i	0.146525	+	0.940807i
$932$	2.37097e11			0.314241
$933$	1.41218e11	+	2.44598e11i	0.186365	+	0.322794i
$934$	−4.86986e10	−	2.81161e10i	−0.0639924	−	0.0369460i
$935$	8.81554e9	−	1.52690e10i	0.0115346	−	0.0199785i
$936$	4.55810e10	−	2.63162e10i	0.0593856	−	0.0342863i
$937$			6.69971e11i			0.869156i	0.900634	+	0.434578i	$0.143102\pi$
$937$			6.69971e11i			0.869156i	−0.900634	+	0.434578i	$0.856898\pi$
$938$	−7.96093e10	+	5.45631e10i	−0.102838	+	0.0704835i
$939$	−1.67349e11			−0.215259
$940$	6.10329e10	+	1.05712e11i	0.0781722	+	0.135398i
$941$	3.05744e11	+	1.76521e11i	0.389941	+	0.225133i	0.682135	−	0.731227i	$-0.261052\pi$
$941$	3.05744e11	+	1.76521e11i	0.389941	+	0.225133i	−0.292193	+	0.956359i	$0.594385\pi$
$942$	1.11671e11	−	1.93419e11i	0.141819	−	0.245638i
$943$	2.75565e10	−	1.59098e10i	0.0348480	−	0.0201195i
$944$		−	1.64065e11i		−	0.206599i
$945$	−3.19435e10	−	1.52868e10i	−0.0400549	−	0.0191686i
$946$	−5.12706e10			−0.0640182
$947$	−2.55232e11	−	4.42074e11i	−0.317347	−	0.549661i	0.662587	−	0.748985i	$-0.269459\pi$
$947$	−2.55232e11	−	4.42074e11i	−0.317347	−	0.549661i	−0.979934	+	0.199324i	$0.936125\pi$
$948$	−2.69784e11	−	1.55760e11i	−0.334028	−	0.192851i
$949$	−4.02530e11	+	6.97203e11i	−0.496288	+	0.859595i
$950$	−4.49630e11	+	2.59594e11i	−0.552027	+	0.318713i
$951$		−	5.77561e11i		−	0.706116i
$952$	3.70363e10	−	2.86680e9i	0.0450899	−	0.00349020i
$953$	1.54713e11			0.187567			0.0937835	−	0.995593i	$-0.470104\pi$
$953$	1.54713e11			0.187567			0.0937835	+	0.995593i	$0.470104\pi$
$954$	−1.11577e10	−	1.93257e10i	−0.0134704	−	0.0233314i
$955$	−3.24043e11	−	1.87086e11i	−0.389573	−	0.224920i
$956$	−3.26263e11	+	5.65103e11i	−0.390603	+	0.676544i
$957$	3.27624e10	−	1.89154e10i	0.0390597	−	0.0225511i
$958$			7.49752e11i			0.890135i
$959$	−8.87157e10	−	1.14612e12i	−0.104888	−	1.35505i
$960$	−1.41433e10			−0.0166520
$961$	6.09482e11	+	1.05565e12i	0.714607	+	1.23774i
$962$	4.29961e11	+	2.48238e11i	0.502029	+	0.289846i
$963$	−1.49108e11	+	2.58262e11i	−0.173379	+	0.300300i
$964$	4.21669e11	−	2.43451e11i	0.488274	−	0.281905i
$965$		−	1.13956e11i		−	0.131410i
$966$	1.83195e11	−	3.82805e11i	0.210380	−	0.439612i
$967$	3.41751e11			0.390845			0.195422	−	0.980719i	$-0.437392\pi$
$967$	3.41751e11			0.390845			0.195422	+	0.980719i	$0.437392\pi$
$968$	6.03890e10	+	1.04597e11i	0.0687791	+	0.119129i
$969$	5.36898e10	+	3.09978e10i	0.0608971	+	0.0351589i
$970$	1.90148e10	−	3.29346e10i	0.0214785	−	0.0372019i
$971$	−7.00612e11	+	4.04498e11i	−0.788135	+	0.455030i	−0.839306	−	0.543660i	$-0.817038\pi$
$971$	−7.00612e11	+	4.04498e11i	−0.788135	+	0.455030i	0.0511707	+	0.998690i	$0.483705\pi$
$972$			2.86307e10i			0.0320750i
$973$	6.48983e11	+	9.46887e11i	0.724072	+	1.05644i
$974$	6.89049e10			0.0765621
$975$	−1.43709e11	−	2.48912e11i	−0.159025	−	0.275440i
$976$	1.43198e11	+	8.26755e10i	0.157811	+	0.0911124i
$977$	−1.06728e11	+	1.84858e11i	−0.117138	+	0.202889i	−0.918632	−	0.395113i	$-0.870705\pi$
$977$	−1.06728e11	+	1.84858e11i	−0.117138	+	0.202889i	0.801494	+	0.598003i	$0.204039\pi$
$978$	5.07195e10	−	2.92829e10i	0.0554395	−	0.0320080i
$979$			5.84611e11i			0.636409i
$980$	9.92456e10	+	3.83906e10i	0.107599	+	0.0416217i
$981$	−1.72252e11			−0.185990
$982$	4.73969e11	+	8.20938e11i	0.509687	+	0.882805i
$983$	6.78356e11	+	3.91649e11i	0.726514	+	0.419453i	0.817145	−	0.576432i	$-0.195555\pi$
$983$	6.78356e11	+	3.91649e11i	0.726514	+	0.419453i	−0.0906316	+	0.995884i	$0.528889\pi$
$984$	3.22528e9	−	5.58635e9i	0.00344023	−	0.00595865i
$985$	1.46997e11	−	8.48686e10i	0.156157	−	0.0901576i
$986$			8.54434e9i			0.00904005i
$987$	−6.12466e11	+	4.19775e11i	−0.645377	+	0.442332i
$988$	−2.63948e11			−0.277007
$989$	−6.61460e10	−	1.14568e11i	−0.0691382	−	0.119751i
$990$	−3.53628e10	−	2.04167e10i	−0.0368133	−	0.0212542i
$991$	7.39571e11	−	1.28097e12i	0.766805	−	1.32815i	−0.172482	−	0.985013i	$-0.555179\pi$
$991$	7.39571e11	−	1.28097e12i	0.766805	−	1.32815i	0.939287	−	0.343133i	$-0.111488\pi$
$992$	2.31066e11	−	1.33406e11i	0.238610	−	0.137761i
$993$		−	1.08633e12i		−	1.11729i
$994$	−9.77886e10	−	4.67975e10i	−0.100171	−	0.0479377i
$995$	3.02998e11			0.309135
$996$	6.91555e10	+	1.19781e11i	0.0702731	+	0.121717i
$997$	6.74829e11	+	3.89613e11i	0.682988	+	0.394324i	0.800980	−	0.598691i	$-0.204312\pi$
$997$	6.74829e11	+	3.89613e11i	0.682988	+	0.394324i	−0.117992	+	0.993015i	$0.537646\pi$
$998$	−1.78577e11	+	3.09304e11i	−0.180013	+	0.311791i
$999$	−2.33888e11	+	1.35035e11i	−0.234825	+	0.135577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.9.g.b.31.2	yes	12
3.2	odd	2		126.9.n.c.73.5		12
7.3	odd	6		294.9.c.b.97.8		12
7.4	even	3		294.9.c.b.97.11		12
7.5	odd	6	inner	42.9.g.b.19.2	✓	12
21.5	even	6		126.9.n.c.19.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.9.g.b.19.2	✓	12	7.5	odd	6	inner
42.9.g.b.31.2	yes	12	1.1	even	1	trivial
126.9.n.c.19.5		12	21.5	even	6
126.9.n.c.73.5		12	3.2	odd	2
294.9.c.b.97.8		12	7.3	odd	6
294.9.c.b.97.11		12	7.4	even	3

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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	42.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(124.890 - 72.1052i) q^{5} +529.090i q^{6} +(1980.48 - 1357.39i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(124.890 - 72.1052i) q^{5} +529.090i q^{6} +(1980.48 - 1357.39i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +(-1412.97 - 815.777i) q^{10} +(5721.83 - 9910.51i) q^{11} +(5184.00 - 2992.98i) q^{12} -16618.4i q^{13} +(-24502.9 - 11726.1i) q^{14} -6744.05 q^{15} +(-8192.00 - 14189.0i) q^{16} +(9252.26 + 5341.80i) q^{17} +(12371.5 - 21428.1i) q^{18} +(-107461. + 62042.5i) q^{19} +18458.9i q^{20} +(-111949. + 8665.43i) q^{21} -129470. q^{22} +(-167034. - 289312. i) q^{23} +(-58650.3 - 33861.7i) q^{24} +(-184914. + 320281. i) q^{25} +(-162827. + 94008.0i) q^{26} -102276. i q^{27} +(23717.9 + 306411. i) q^{28} -70689.7 q^{29} +(38150.1 + 66077.9i) q^{30} +(-1.24655e6 - 719697. i) q^{31} +(-92681.9 + 160530. i) q^{32} +(-463469. + 267584. i) q^{33} -120871. i q^{34} +(149467. - 312327. i) q^{35} -279936. q^{36} +(-1.32030e6 - 2.28683e6i) q^{37} +(1.21578e6 + 701931. i) q^{38} +(-388583. + 673046. i) q^{39} +(180860. - 104419. i) q^{40} +95248.5i q^{41} +(718181. + 1.04785e6i) q^{42} +396002. q^{43} +(732395. + 1.26854e6i) q^{44} +(273134. + 157694. i) q^{45} +(-1.88978e6 + 3.27319e6i) q^{46} +(5.72688e6 - 3.30642e6i) q^{47} +766204. i q^{48} +(2.07978e6 - 5.37656e6i) q^{49} +4.18413e6 q^{50} +(-249811. - 432685. i) q^{51} +(1.84217e6 + 1.06358e6i) q^{52} +(450942. - 781054. i) q^{53} +(-1.00209e6 + 578560. i) q^{54} -1.65030e6i q^{55} +(2.86804e6 - 1.96571e6i) q^{56} +5.80288e6 q^{57} +(399881. + 692615. i) q^{58} +(8.67216e6 + 5.00687e6i) q^{59} +(431619. - 747586. i) q^{60} +(-8.74012e6 + 5.04611e6i) q^{61} +1.62849e7i q^{62} +(4.73655e6 + 2.26671e6i) q^{63} +2.09715e6 q^{64} +(-1.19827e6 - 2.07547e6i) q^{65} +(5.24355e6 + 3.02736e6i) q^{66} +(1.77647e6 - 3.07694e6i) q^{67} +(-1.18429e6 + 683750. i) q^{68} +1.56228e7i q^{69} +(-3.90568e6 + 302320. i) q^{70} +3.99089e6 q^{71} +(1.58356e6 + 2.74280e6i) q^{72} +(-4.19536e7 - 2.42219e7i) q^{73} +(-1.49375e7 + 2.58725e7i) q^{74} +(1.49780e7 - 8.64758e6i) q^{75} -1.58829e7i q^{76} +(-2.12046e6 - 2.73943e7i) q^{77} +8.79264e6 q^{78} +(-2.60208e7 - 4.50694e7i) q^{79} +(-2.04619e6 - 1.18137e6i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(933241. - 538807. i) q^{82} +2.31059e7i q^{83} +(6.20415e6 - 1.29643e7i) q^{84} +1.54068e6 q^{85} +(-2.24013e6 - 3.88002e6i) q^{86} +(2.86293e6 + 1.65291e6i) q^{87} +(8.28610e6 - 1.43519e7i) q^{88} +(-4.42418e7 + 2.55430e7i) q^{89} -3.56821e6i q^{90} +(-2.25577e7 - 3.29124e7i) q^{91} +4.27608e7 q^{92} +(3.36569e7 + 5.82954e7i) q^{93} +(-6.47922e7 - 3.74078e7i) q^{94} +(-8.94717e6 + 1.54970e7i) q^{95} +(7.50723e6 - 4.33430e6i) q^{96} +2.33088e7i q^{97} +(-6.44444e7 + 1.00368e7i) q^{98} +2.50273e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 486 q^{3} - 768 q^{4} - 1122 q^{5} - 4434 q^{7} + 13122 q^{9}+O(q^{10}) \) 12 * q - 486 * q^3 - 768 * q^4 - 1122 * q^5 - 4434 * q^7 + 13122 * q^9	\( 12 q - 486 q^{3} - 768 q^{4} - 1122 q^{5} - 4434 q^{7} + 13122 q^{9} + 4224 q^{10} + 9606 q^{11} + 62208 q^{12} - 19968 q^{14} + 60588 q^{15} - 98304 q^{16} - 227388 q^{17} + 315408 q^{19} + 155358 q^{21} + 557568 q^{22} - 663480 q^{23} + 601008 q^{25} - 585984 q^{26} + 398592 q^{28} + 5944884 q^{29} - 114048 q^{30} - 3214278 q^{31} - 778086 q^{33} - 1019784 q^{35} - 3359232 q^{36} + 1607760 q^{37} - 986880 q^{38} + 903636 q^{39} - 540672 q^{40} + 2788992 q^{42} + 12627648 q^{43} + 1229568 q^{44} - 2453814 q^{45} - 4608768 q^{46} - 7830240 q^{47} + 16477242 q^{49} - 16565760 q^{50} + 6139476 q^{51} - 4283904 q^{52} - 33200358 q^{53} - 8110080 q^{56} - 17032032 q^{57} + 5576064 q^{58} - 29657382 q^{59} - 3877632 q^{60} + 58344096 q^{61} - 2886840 q^{63} + 25165824 q^{64} + 30909216 q^{65} - 22581504 q^{66} + 7977444 q^{67} + 29105664 q^{68} - 59774976 q^{70} + 117213264 q^{71} - 170286636 q^{73} - 80311296 q^{74} - 48681648 q^{75} - 3340686 q^{77} + 31643136 q^{78} + 35420490 q^{79} + 18382848 q^{80} - 28697814 q^{81} + 154232832 q^{82} - 26085888 q^{84} + 416634600 q^{85} - 71958528 q^{86} - 240767802 q^{87} - 35684352 q^{88} + 78064092 q^{89} + 335513292 q^{91} + 169850880 q^{92} + 86785506 q^{93} - 18456576 q^{94} - 250727796 q^{95} - 150533376 q^{98} + 42016644 q^{99}+O(q^{100}) \) 12 * q - 486 * q^3 - 768 * q^4 - 1122 * q^5 - 4434 * q^7 + 13122 * q^9 + 4224 * q^10 + 9606 * q^11 + 62208 * q^12 - 19968 * q^14 + 60588 * q^15 - 98304 * q^16 - 227388 * q^17 + 315408 * q^19 + 155358 * q^21 + 557568 * q^22 - 663480 * q^23 + 601008 * q^25 - 585984 * q^26 + 398592 * q^28 + 5944884 * q^29 - 114048 * q^30 - 3214278 * q^31 - 778086 * q^33 - 1019784 * q^35 - 3359232 * q^36 + 1607760 * q^37 - 986880 * q^38 + 903636 * q^39 - 540672 * q^40 + 2788992 * q^42 + 12627648 * q^43 + 1229568 * q^44 - 2453814 * q^45 - 4608768 * q^46 - 7830240 * q^47 + 16477242 * q^49 - 16565760 * q^50 + 6139476 * q^51 - 4283904 * q^52 - 33200358 * q^53 - 8110080 * q^56 - 17032032 * q^57 + 5576064 * q^58 - 29657382 * q^59 - 3877632 * q^60 + 58344096 * q^61 - 2886840 * q^63 + 25165824 * q^64 + 30909216 * q^65 - 22581504 * q^66 + 7977444 * q^67 + 29105664 * q^68 - 59774976 * q^70 + 117213264 * q^71 - 170286636 * q^73 - 80311296 * q^74 - 48681648 * q^75 - 3340686 * q^77 + 31643136 * q^78 + 35420490 * q^79 + 18382848 * q^80 - 28697814 * q^81 + 154232832 * q^82 - 26085888 * q^84 + 416634600 * q^85 - 71958528 * q^86 - 240767802 * q^87 - 35684352 * q^88 + 78064092 * q^89 + 335513292 * q^91 + 169850880 * q^92 + 86785506 * q^93 - 18456576 * q^94 - 250727796 * q^95 - 150533376 * q^98 + 42016644 * q^99

Introduction

L-functions

Modular forms

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Database

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