LMFDB - Embedded newform 48.9.l.a.43.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			43.18
Character	$\chi$	$=$	48.43
Dual form			48.9.l.a.19.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46245 - 15.9330i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-251.722 - 46.6024i) q^{4} +(-173.172 - 173.172i) q^{5} +(575.235 - 478.515i) q^{6} +3867.21 q^{7} +(-1110.65 + 3942.55i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(1.46245 - 15.9330i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-251.722 - 46.6024i) q^{4} +(-173.172 - 173.172i) q^{5} +(575.235 - 478.515i) q^{6} +3867.21 q^{7} +(-1110.65 + 3942.55i) q^{8} +2187.00i q^{9} +(-3012.41 + 2505.90i) q^{10} +(-6956.06 + 6956.06i) q^{11} +(-6782.93 - 9865.04i) q^{12} +(29126.1 - 29126.1i) q^{13} +(5655.60 - 61616.4i) q^{14} -11453.0i q^{15} +(61192.4 + 23461.8i) q^{16} +75850.6 q^{17} +(34845.5 + 3198.37i) q^{18} +(-164196. - 164196. i) q^{19} +(35521.1 + 51661.6i) q^{20} +(127881. + 127881. i) q^{21} +(100658. + 121004. i) q^{22} +249858. q^{23} +(-167100. + 93645.5i) q^{24} -330648. i q^{25} +(-421472. - 506662. i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(-973465. - 180222. i) q^{28} +(768677. - 768677. i) q^{29} +(-182480. - 16749.4i) q^{30} +358942. i q^{31} +(463308. - 940669. i) q^{32} -460047. q^{33} +(110928. - 1.20853e6i) q^{34} +(-669694. - 669694. i) q^{35} +(101920. - 550517. i) q^{36} +(-2.21375e6 - 2.21375e6i) q^{37} +(-2.85627e6 + 2.37601e6i) q^{38} +1.92629e6 q^{39} +(875074. - 490406. i) q^{40} +2.80901e6i q^{41} +(2.22456e6 - 1.85052e6i) q^{42} +(655665. - 655665. i) q^{43} +(2.07517e6 - 1.42683e6i) q^{44} +(378728. - 378728. i) q^{45} +(365404. - 3.98099e6i) q^{46} +2.55637e6i q^{47} +(1.24768e6 + 2.79935e6i) q^{48} +9.19054e6 q^{49} +(-5.26822e6 - 483555. i) q^{50} +(2.50824e6 + 2.50824e6i) q^{51} +(-8.68905e6 + 5.97435e6i) q^{52} +(1.00111e7 + 1.00111e7i) q^{53} +(1.04651e6 + 1.25804e6i) q^{54} +2.40919e6 q^{55} +(-4.29512e6 + 1.52467e7i) q^{56} -1.08593e7i q^{57} +(-1.11232e7 - 1.33715e7i) q^{58} +(6.95128e6 - 6.95128e6i) q^{59} +(-533736. + 2.88297e6i) q^{60} +(-1.15430e6 + 1.15430e6i) q^{61} +(5.71903e6 + 524934. i) q^{62} +8.45760e6i q^{63} +(-1.43101e7 - 8.75757e6i) q^{64} -1.00877e7 q^{65} +(-672795. + 7.32995e6i) q^{66} +(1.74804e7 + 1.74804e7i) q^{67} +(-1.90933e7 - 3.53482e6i) q^{68} +(8.26232e6 + 8.26232e6i) q^{69} +(-1.16497e7 + 9.69086e6i) q^{70} -678462. q^{71} +(-8.62235e6 - 2.42899e6i) q^{72} -5.75923e6i q^{73} +(-3.85092e7 + 3.20342e7i) q^{74} +(1.09339e7 - 1.09339e7i) q^{75} +(3.36799e7 + 4.89838e7i) q^{76} +(-2.69006e7 + 2.69006e7i) q^{77} +(2.81710e6 - 3.06916e7i) q^{78} -2.53504e6i q^{79} +(-6.53391e6 - 1.46598e7i) q^{80} -4.78297e6 q^{81} +(4.47560e7 + 4.10803e6i) q^{82} +(3.98881e7 + 3.98881e7i) q^{83} +(-2.62311e7 - 3.81502e7i) q^{84} +(-1.31352e7 - 1.31352e7i) q^{85} +(-9.48785e6 - 1.14056e7i) q^{86} +5.08374e7 q^{87} +(-1.96989e7 - 3.51503e7i) q^{88} -2.38798e7i q^{89} +(-5.48041e6 - 6.58815e6i) q^{90} +(1.12637e8 - 1.12637e8i) q^{91} +(-6.28948e7 - 1.16440e7i) q^{92} +(-1.18695e7 + 1.18695e7i) q^{93} +(4.07308e7 + 3.73856e6i) q^{94} +5.68684e7i q^{95} +(4.64268e7 - 1.57854e7i) q^{96} -3.94294e7 q^{97} +(1.34407e7 - 1.46433e8i) q^{98} +(-1.52129e7 - 1.52129e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) $ 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.46245	−	15.9330i	0.0914030	−	0.995814i
$2$	1.46245	−	15.9330i	0.0914030	−	0.995814i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$4$	−251.722	−	46.6024i	−0.983291	−	0.182041i
$5$	−173.172	−	173.172i	−0.277076	−	0.277076i	0.554865	−	0.831941i	$-0.312770\pi$
$5$	−173.172	−	173.172i	−0.277076	−	0.277076i	−0.831941	+	0.554865i	$0.812770\pi$
$6$	575.235	−	478.515i	0.443854	−	0.369224i
$7$	3867.21			1.61067			0.805334	−	0.592821i	$-0.201986\pi$
$7$	3867.21			1.61067			0.805334	+	0.592821i	$0.201986\pi$
$8$	−1110.65	+	3942.55i	−0.271154	+	0.962536i
$9$			2187.00i			0.333333i
$10$	−3012.41	+	2505.90i	−0.301241	+	0.250590i
$11$	−6956.06	+	6956.06i	−0.475108	+	0.475108i	−0.903563	−	0.428455i	$-0.859058\pi$
$11$	−6956.06	+	6956.06i	−0.475108	+	0.475108i	0.428455	+	0.903563i	$0.359058\pi$
$12$	−6782.93	−	9865.04i	−0.327109	−	0.475745i
$13$	29126.1	−	29126.1i	1.01979	−	1.01979i	0.0199860	−	0.999800i	$-0.493638\pi$
$13$	29126.1	−	29126.1i	1.01979	−	1.01979i	0.999800	−	0.0199860i	$-0.00636216\pi$
$14$	5655.60	−	61616.4i	0.147220	−	1.60393i
$15$		−	11453.0i		−	0.226231i
$16$	61192.4	+	23461.8i	0.933722	+	0.357998i
$17$	75850.6			0.908162			0.454081	−	0.890960i	$-0.349968\pi$
$17$	75850.6			0.908162			0.454081	+	0.890960i	$0.349968\pi$
$18$	34845.5	+	3198.37i	0.331938	+	0.0304677i
$19$	−164196.	−	164196.i	−1.25994	−	1.25994i	−0.951123	−	0.308813i	$-0.900068\pi$
$19$	−164196.	−	164196.i	−1.25994	−	1.25994i	−0.308813	−	0.951123i	$-0.599932\pi$
$20$	35521.1	+	51661.6i	0.222007	+	0.322885i
$21$	127881.	+	127881.i	0.657552	+	0.657552i
$22$	100658.	+	121004.i	0.429693	+	0.516546i
$23$	249858.			0.892856			0.446428	−	0.894820i	$-0.352696\pi$
$23$	249858.			0.892856			0.446428	+	0.894820i	$0.352696\pi$
$24$	−167100.	+	93645.5i	−0.503652	+	0.282255i
$25$		−	330648.i		−	0.846458i
$26$	−421472.	−	506662.i	−0.922306	−	1.10873i
$27$	−72320.0	+	72320.0i	−0.136083	+	0.136083i
$28$	−973465.	−	180222.i	−1.58376	−	0.293207i
$29$	768677.	−	768677.i	1.08681	−	1.08681i	0.0909510	−	0.995855i	$-0.471009\pi$
$29$	768677.	−	768677.i	1.08681	−	1.08681i	0.995855	−	0.0909510i	$-0.0289907\pi$
$30$	−182480.	−	16749.4i	−0.225284	−	0.0206782i
$31$			358942.i			0.388667i	0.980936	+	0.194333i	$0.0622543\pi$
$31$			358942.i			0.388667i	−0.980936	+	0.194333i	$0.937746\pi$
$32$	463308.	−	940669.i	0.441844	−	0.897092i
$33$	−460047.			−0.387924
$34$	110928.	−	1.20853e6i	0.0830087	−	0.904360i
$35$	−669694.	−	669694.i	−0.446277	−	0.446277i
$36$	101920.	−	550517.i	0.0606802	−	0.327764i
$37$	−2.21375e6	−	2.21375e6i	−1.18119	−	1.18119i	−0.979435	−	0.201758i	$-0.935334\pi$
$37$	−2.21375e6	−	2.21375e6i	−1.18119	−	1.18119i	−0.201758	−	0.979435i	$-0.564666\pi$
$38$	−2.85627e6	+	2.37601e6i	−1.36982	+	1.13950i
$39$	1.92629e6			0.832652
$40$	875074.	−	490406.i	0.341826	−	0.191565i
$41$			2.80901e6i			0.994072i	0.867730	+	0.497036i	$0.165578\pi$
$41$			2.80901e6i			0.994072i	−0.867730	+	0.497036i	$0.834422\pi$
$42$	2.22456e6	−	1.85052e6i	0.714902	−	0.594698i
$43$	655665.	−	655665.i	0.191782	−	0.191782i	−0.604684	−	0.796466i	$-0.706700\pi$
$43$	655665.	−	655665.i	0.191782	−	0.191782i	0.796466	+	0.604684i	$0.206700\pi$
$44$	2.07517e6	−	1.42683e6i	0.553659	−	0.380681i
$45$	378728.	−	378728.i	0.0923586	−	0.0923586i
$46$	365404.	−	3.98099e6i	0.0816097	−	0.889118i
$47$			2.55637e6i			0.523881i	0.965084	+	0.261941i	$0.0843625\pi$
$47$			2.55637e6i			0.523881i	−0.965084	+	0.261941i	$0.915638\pi$
$48$	1.24768e6	+	2.79935e6i	0.235038	+	0.527343i
$49$	9.19054e6			1.59425
$50$	−5.26822e6	−	483555.i	−0.842915	−	0.0773688i
$51$	2.50824e6	+	2.50824e6i	0.370756	+	0.370756i
$52$	−8.68905e6	+	5.97435e6i	−1.18839	+	0.817104i
$53$	1.00111e7	+	1.00111e7i	1.26876	+	1.26876i	0.946730	+	0.322029i	$0.104365\pi$
$53$	1.00111e7	+	1.00111e7i	1.26876	+	1.26876i	0.322029	+	0.946730i	$0.395635\pi$
$54$	1.04651e6	+	1.25804e6i	0.123075	+	0.147951i
$55$	2.40919e6			0.263282
$56$	−4.29512e6	+	1.52467e7i	−0.436740	+	1.55033i
$57$		−	1.08593e7i		−	1.02873i
$58$	−1.11232e7	−	1.33715e7i	−0.982920	−	1.18159i
$59$	6.95128e6	−	6.95128e6i	0.573662	−	0.573662i	−0.359487	−	0.933150i	$-0.617048\pi$
$59$	6.95128e6	−	6.95128e6i	0.573662	−	0.573662i	0.933150	+	0.359487i	$0.117048\pi$
$60$	−533736.	+	2.88297e6i	−0.0411833	+	0.222451i
$61$	−1.15430e6	+	1.15430e6i	−0.0833680	+	0.0833680i	−0.747561	−	0.664193i	$-0.768775\pi$
$61$	−1.15430e6	+	1.15430e6i	−0.0833680	+	0.0833680i	0.664193	+	0.747561i	$0.268775\pi$
$62$	5.71903e6	+	524934.i	0.387040	+	0.0355253i
$63$			8.45760e6i			0.536889i
$64$	−1.43101e7	−	8.75757e6i	−0.852951	−	0.521992i
$65$	−1.00877e7			−0.565116
$66$	−672795.	+	7.32995e6i	−0.0354574	+	0.386300i
$67$	1.74804e7	+	1.74804e7i	0.867466	+	0.867466i	0.992191	−	0.124726i	$-0.0398051\pi$
$67$	1.74804e7	+	1.74804e7i	0.867466	+	0.867466i	−0.124726	+	0.992191i	$0.539805\pi$
$68$	−1.90933e7	−	3.53482e6i	−0.892987	−	0.165322i
$69$	8.26232e6	+	8.26232e6i	0.364507	+	0.364507i
$70$	−1.16497e7	+	9.69086e6i	−0.485200	+	0.403618i
$71$	−678462.			−0.0266988			−0.0133494	−	0.999911i	$-0.504249\pi$
$71$	−678462.			−0.0266988			−0.0133494	+	0.999911i	$0.504249\pi$
$72$	−8.62235e6	−	2.42899e6i	−0.320845	−	0.0903848i
$73$		−	5.75923e6i		−	0.202802i	−0.994846	−	0.101401i	$-0.967667\pi$
$73$		−	5.75923e6i		−	0.202802i	0.994846	−	0.101401i	$-0.0323326\pi$
$74$	−3.85092e7	+	3.20342e7i	−1.28421	+	1.06828i
$75$	1.09339e7	−	1.09339e7i	0.345565	−	0.345565i
$76$	3.36799e7	+	4.89838e7i	1.00952	+	1.46824i
$77$	−2.69006e7	+	2.69006e7i	−0.765242	+	0.765242i
$78$	2.81710e6	−	3.06916e7i	0.0761069	−	0.829166i
$79$		−	2.53504e6i		−	0.0650843i	−0.999470	−	0.0325421i	$-0.989640\pi$
$79$		−	2.53504e6i		−	0.0650843i	0.999470	−	0.0325421i	$-0.0103603\pi$
$80$	−6.53391e6	−	1.46598e7i	−0.159519	−	0.357904i
$81$	−4.78297e6			−0.111111
$82$	4.47560e7	+	4.10803e6i	0.989910	+	0.0908611i
$83$	3.98881e7	+	3.98881e7i	0.840486	+	0.840486i	0.988922	−	0.148436i	$-0.0474239\pi$
$83$	3.98881e7	+	3.98881e7i	0.840486	+	0.840486i	−0.148436	+	0.988922i	$0.547424\pi$
$84$	−2.62311e7	−	3.81502e7i	−0.526864	−	0.766267i
$85$	−1.31352e7	−	1.31352e7i	−0.251630	−	0.251630i
$86$	−9.48785e6	−	1.14056e7i	−0.173450	−	0.208509i
$87$	5.08374e7			0.887374
$88$	−1.96989e7	−	3.51503e7i	−0.328481	−	0.586136i
$89$		−	2.38798e7i		−	0.380601i	−0.981726	−	0.190301i	$-0.939054\pi$
$89$		−	2.38798e7i		−	0.380601i	0.981726	−	0.190301i	$-0.0609463\pi$
$90$	−5.48041e6	−	6.58815e6i	−0.0835301	−	0.100414i
$91$	1.12637e8	−	1.12637e8i	1.64254	−	1.64254i
$92$	−6.28948e7	−	1.16440e7i	−0.877937	−	0.162536i
$93$	−1.18695e7	+	1.18695e7i	−0.158673	+	0.158673i
$94$	4.07308e7	+	3.73856e6i	0.521688	+	0.0478843i
$95$			5.68684e7i			0.698195i
$96$	4.64268e7	−	1.57854e7i	0.546618	−	0.185854i
$97$	−3.94294e7			−0.445382			−0.222691	−	0.974889i	$-0.571484\pi$
$97$	−3.94294e7			−0.445382			−0.222691	+	0.974889i	$0.571484\pi$
$98$	1.34407e7	−	1.46433e8i	0.145719	−	1.58758i
$99$	−1.52129e7	−	1.52129e7i	−0.158369	−	0.158369i
$100$	−1.54090e7	+	8.32315e7i	−0.154090	+	0.832315i
$101$	−9.04032e7	−	9.04032e7i	−0.868757	−	0.868757i	0.123578	−	0.992335i	$-0.460563\pi$
$101$	−9.04032e7	−	9.04032e7i	−0.868757	−	0.868757i	−0.992335	+	0.123578i	$0.960563\pi$
$102$	4.36319e7	−	3.62956e7i	0.403092	−	0.335315i
$103$	−8.95491e7			−0.795632			−0.397816	−	0.917465i	$-0.630232\pi$
$103$	−8.95491e7			−0.795632			−0.397816	+	0.917465i	$0.630232\pi$
$104$	8.24822e7	+	1.47180e8i	0.705061	+	1.25810i
$105$		−	4.42911e7i		−	0.364384i
$106$	1.74148e8	−	1.44867e8i	1.37942	−	1.14748i
$107$	−7.73852e7	+	7.73852e7i	−0.590368	+	0.590368i	−0.937731	−	0.347363i	$-0.887077\pi$
$107$	−7.73852e7	+	7.73852e7i	−0.590368	+	0.590368i	0.347363	+	0.937731i	$0.387077\pi$
$108$	2.15748e7	−	1.48343e7i	0.158582	−	0.109036i
$109$	3.80908e7	−	3.80908e7i	0.269845	−	0.269845i	−0.559193	−	0.829038i	$-0.688889\pi$
$109$	3.80908e7	−	3.80908e7i	0.269845	−	0.269845i	0.829038	+	0.559193i	$0.188889\pi$
$110$	3.52332e6	−	3.83857e7i	0.0240648	−	0.262180i
$111$		−	1.46409e8i		−	0.964441i
$112$	2.36644e8	+	9.07316e7i	1.50392	+	0.576616i
$113$	−2.93565e8			−1.80049			−0.900243	−	0.435387i	$-0.856612\pi$
$113$	−2.93565e8			−1.80049			−0.900243	+	0.435387i	$0.856612\pi$
$114$	−1.73022e8	−	1.58812e7i	−1.02443	−	0.0940293i
$115$	−4.32684e7	−	4.32684e7i	−0.247389	−	0.247389i
$116$	−2.29316e8	+	1.57671e8i	−1.26649	+	0.870804i
$117$	6.36988e7	+	6.36988e7i	0.339929	+	0.339929i
$118$	−1.00589e8	−	1.20921e8i	−0.518827	−	0.623696i
$119$	2.93330e8			1.46275
$120$	4.51538e7	+	1.27202e7i	0.217756	+	0.0613437i
$121$			1.17585e8i			0.548544i
$122$	1.67034e7	+	2.00796e7i	0.0753989	+	0.0906391i
$123$	−9.28886e7	+	9.28886e7i	−0.405828	+	0.405828i
$124$	1.67276e7	−	9.03537e7i	0.0707532	−	0.382172i
$125$	−1.24904e8	+	1.24904e8i	−0.511609	+	0.511609i
$126$	1.34755e8	+	1.23688e7i	0.534642	+	0.0490733i
$127$			2.86291e8i			1.10051i	0.834998	+	0.550253i	$0.185469\pi$
$127$			2.86291e8i			1.10051i	−0.834998	+	0.550253i	$0.814531\pi$
$128$	−1.60462e8	+	2.15196e8i	−0.597769	+	0.801668i
$129$	4.33632e7			0.156589
$130$	−1.47527e7	+	1.60727e8i	−0.0516533	+	0.562750i
$131$	−2.31325e7	−	2.31325e7i	−0.0785486	−	0.0785486i	0.666741	−	0.745290i	$-0.267689\pi$
$131$	−2.31325e7	−	2.31325e7i	−0.0785486	−	0.0785486i	−0.745290	+	0.666741i	$0.767689\pi$
$132$	1.15804e8	+	2.14393e7i	0.381442	+	0.0706180i
$133$	−6.34981e8	−	6.34981e8i	−2.02934	−	2.02934i
$134$	3.04080e8	−	2.52952e8i	0.943123	−	0.784545i
$135$	2.50476e7			0.0754105
$136$	−8.42434e7	+	2.99045e8i	−0.246252	+	0.874138i
$137$			4.57082e7i			0.129751i	0.997893	+	0.0648756i	$0.0206651\pi$
$137$			4.57082e7i			0.129751i	−0.997893	+	0.0648756i	$0.979335\pi$
$138$	1.43727e8	−	1.19561e8i	0.396298	−	0.329664i
$139$	3.36608e8	−	3.36608e8i	0.901706	−	0.901706i	−0.0938778	−	0.995584i	$-0.529926\pi$
$139$	3.36608e8	−	3.36608e8i	0.901706	−	0.901706i	0.995584	+	0.0938778i	$0.0299263\pi$
$140$	1.37368e8	+	1.99787e8i	0.357580	+	0.520061i
$141$	−8.45345e7	+	8.45345e7i	−0.213874	+	0.213874i
$142$	−992215.	+	1.08100e7i	−0.00244035	+	0.0265871i
$143$			4.05206e8i			0.969018i
$144$	−5.13109e7	+	1.33828e8i	−0.119333	+	0.311241i
$145$	−2.66227e8			−0.602255
$146$	−9.17620e7	−	8.42257e6i	−0.201953	−	0.0185367i
$147$	3.03914e8	+	3.03914e8i	0.650850	+	0.650850i
$148$	4.54084e8	+	6.60416e8i	0.946432	+	1.37648i
$149$	−4.76387e7	−	4.76387e7i	−0.0966529	−	0.0966529i	0.657127	−	0.753780i	$-0.271772\pi$
$149$	−4.76387e7	−	4.76387e7i	−0.0966529	−	0.0966529i	−0.753780	+	0.657127i	$0.771772\pi$
$150$	−1.58220e8	−	1.90200e8i	−0.312533	−	0.375704i
$151$	−4.87846e8			−0.938371			−0.469186	−	0.883100i	$-0.655452\pi$
$151$	−4.87846e8			−0.938371			−0.469186	+	0.883100i	$0.655452\pi$
$152$	8.29715e8	−	4.64987e8i	1.55437	−	0.871096i
$153$			1.65885e8i			0.302721i
$154$	3.89267e8	+	4.67948e8i	0.692093	+	0.831984i
$155$	6.21588e7	−	6.21588e7i	0.107690	−	0.107690i
$156$	−4.84891e8	−	8.97699e7i	−0.818739	−	0.151577i
$157$	−5.90509e8	+	5.90509e8i	−0.971915	+	0.971915i	−0.999616	−	0.0277017i	$-0.991181\pi$
$157$	−5.90509e8	+	5.90509e8i	−0.971915	+	0.971915i	0.0277017	+	0.999616i	$0.491181\pi$
$158$	−4.03908e7	−	3.70736e6i	−0.0648118	−	0.00594890i
$159$			6.62097e8i			1.03594i
$160$	−2.43130e8	+	8.26658e7i	−0.370987	+	0.126138i
$161$	9.66253e8			1.43809
$162$	−6.99484e6	+	7.62072e7i	−0.0101559	+	0.110646i
$163$	−1.48951e8	−	1.48951e8i	−0.211005	−	0.211005i	0.593689	−	0.804694i	$-0.297671\pi$
$163$	−1.48951e8	−	1.48951e8i	−0.211005	−	0.211005i	−0.804694	+	0.593689i	$0.797671\pi$
$164$	1.30907e8	−	7.07091e8i	0.180962	−	0.977462i
$165$	7.96675e7	+	7.96675e7i	0.107484	+	0.107484i
$166$	6.93871e8	−	5.77203e8i	0.913791	−	0.760145i
$167$	5.29734e8			0.681070			0.340535	−	0.940232i	$-0.389392\pi$
$167$	5.29734e8			0.681070			0.340535	+	0.940232i	$0.389392\pi$
$168$	−6.46210e8	+	3.62147e8i	−0.811216	+	0.454620i
$169$		−	8.80930e8i		−	1.07993i
$170$	−2.28493e8	+	1.90074e8i	−0.273576	+	0.227577i
$171$	3.59097e8	−	3.59097e8i	0.419979	−	0.419979i
$172$	−1.95601e8	+	1.34490e8i	−0.223490	+	0.153666i
$173$	−4.43112e7	+	4.43112e7i	−0.0494686	+	0.0494686i	−0.731408	−	0.681940i	$-0.761137\pi$
$173$	−4.43112e7	+	4.43112e7i	−0.0494686	+	0.0494686i	0.681940	+	0.731408i	$0.261137\pi$
$174$	7.43471e7	−	8.09994e8i	0.0811086	−	0.883659i
$175$		−	1.27869e9i		−	1.36336i
$176$	−5.88860e8	+	2.62457e8i	−0.613707	+	0.273531i
$177$	4.59731e8			0.468393
$178$	−3.80477e8	−	3.49229e7i	−0.379008	−	0.0347881i
$179$	3.51816e7	+	3.51816e7i	0.0342691	+	0.0342691i	0.724034	−	0.689765i	$-0.242286\pi$
$179$	3.51816e7	+	3.51816e7i	0.0342691	+	0.0342691i	−0.689765	+	0.724034i	$0.742286\pi$
$180$	−1.12984e8	+	7.76847e7i	−0.107628	+	0.0740023i
$181$	−4.90113e8	−	4.90113e8i	−0.456648	−	0.456648i	0.440905	−	0.897554i	$-0.354657\pi$
$181$	−4.90113e8	−	4.90113e8i	−0.456648	−	0.456648i	−0.897554	+	0.440905i	$0.854657\pi$
$182$	−1.62992e9	−	1.95937e9i	−1.48553	−	1.78579i
$183$	−7.63411e7			−0.0680697
$184$	−2.77504e8	+	9.85075e8i	−0.242102	+	0.859406i
$185$			7.66719e8i			0.654560i
$186$	1.71759e8	+	2.06476e8i	0.143505	+	0.172511i
$187$	−5.27621e8	+	5.27621e8i	−0.431475	+	0.431475i
$188$	1.19133e8	−	6.43497e8i	0.0953677	−	0.515128i
$189$	−2.79677e8	+	2.79677e8i	−0.219184	+	0.219184i
$190$	9.06086e8	+	8.31671e7i	0.695273	+	0.0638171i
$191$			9.18912e8i			0.690463i	0.938518	+	0.345231i	$0.112200\pi$
$191$			9.18912e8i			0.690463i	−0.938518	+	0.345231i	$0.887800\pi$
$192$	−1.83613e8	−	7.62805e8i	−0.135113	−	0.561318i
$193$	7.43886e8			0.536139			0.268069	−	0.963400i	$-0.413614\pi$
$193$	7.43886e8			0.536139			0.268069	+	0.963400i	$0.413614\pi$
$194$	−5.76634e7	+	6.28229e8i	−0.0407093	+	0.443518i
$195$	−3.33580e8	−	3.33580e8i	−0.230708	−	0.230708i
$196$	−2.31347e9	−	4.28302e8i	−1.56761	−	0.290219i
$197$	−1.28625e9	−	1.28625e9i	−0.854007	−	0.854007i	0.136617	−	0.990624i	$-0.456377\pi$
$197$	−1.28625e9	−	1.28625e9i	−0.854007	−	0.854007i	−0.990624	+	0.136617i	$0.956377\pi$
$198$	−2.64636e8	+	2.20139e8i	−0.172182	+	0.143231i
$199$	2.28993e9			1.46019			0.730096	−	0.683345i	$-0.239475\pi$
$199$	2.28993e9			1.46019			0.730096	+	0.683345i	$0.239475\pi$
$200$	1.30359e9	+	3.67233e8i	0.814746	+	0.229521i
$201$			1.15609e9i			0.708283i
$202$	−1.57261e9	+	1.30819e9i	−0.944527	+	0.785713i
$203$	2.97264e9	−	2.97264e9i	1.75048	−	1.75048i
$204$	−5.14489e8	−	7.48269e8i	−0.297068	−	0.432053i
$205$	4.86443e8	−	4.86443e8i	0.275433	−	0.275433i
$206$	−1.30961e8	+	1.42679e9i	−0.0727232	+	0.792302i
$207$			5.46439e8i			0.297619i
$208$	2.46565e9	−	1.09895e9i	1.31728	−	0.587116i
$209$	2.28432e9			1.19721
$210$	−7.05691e8	−	6.47734e7i	−0.362858	−	0.0333058i
$211$	−1.81831e9	−	1.81831e9i	−0.917355	−	0.917355i	0.0794816	−	0.996836i	$-0.474673\pi$
$211$	−1.81831e9	−	1.81831e9i	−0.917355	−	0.917355i	−0.996836	+	0.0794816i	$0.974673\pi$
$212$	−2.05348e9	−	2.98657e9i	−1.01659	−	1.47852i
$213$	−2.24355e7	−	2.24355e7i	−0.0108997	−	0.0108997i
$214$	1.11981e9	+	1.34615e9i	0.533935	+	0.641858i
$215$	−2.27086e8			−0.106276
$216$	−2.04803e8	−	3.65447e8i	−0.0940851	−	0.167884i
$217$			1.38810e9i			0.626013i
$218$	−5.51196e8	−	6.62607e8i	−0.244051	−	0.293380i
$219$	1.90447e8	−	1.90447e8i	0.0827937	−	0.0827937i
$220$	−6.06448e8	−	1.12274e8i	−0.258883	−	0.0479280i
$221$	2.20923e9	−	2.20923e9i	0.926131	−	0.926131i
$222$	−2.33274e9	−	2.14115e8i	−0.960403	−	0.0881527i
$223$			2.99304e9i			1.21030i	0.796111	+	0.605151i	$0.206887\pi$
$223$			2.99304e9i			1.21030i	−0.796111	+	0.605151i	$0.793113\pi$
$224$	1.79171e9	−	3.63777e9i	0.711665	−	1.44492i
$225$	7.23126e8			0.282153
$226$	−4.29323e8	+	4.67737e9i	−0.164570	+	1.79295i
$227$	1.26992e9	+	1.26992e9i	0.478269	+	0.478269i	0.904578	−	0.426309i	$-0.140186\pi$
$227$	1.26992e9	+	1.26992e9i	0.478269	+	0.478269i	−0.426309	+	0.904578i	$0.640186\pi$
$228$	−5.06070e8	+	2.73353e9i	−0.187271	+	1.01154i
$229$	1.29695e9	+	1.29695e9i	0.471607	+	0.471607i	0.902434	−	0.430827i	$-0.141778\pi$
$229$	1.29695e9	+	1.29695e9i	0.471607	+	0.471607i	−0.430827	+	0.902434i	$0.641778\pi$
$230$	−7.52675e8	+	6.26119e8i	−0.268965	+	0.223741i
$231$	−1.77910e9			−0.624817
$232$	2.17682e9	+	3.88428e9i	0.751398	+	1.34078i
$233$			1.59746e9i			0.542010i	0.962578	+	0.271005i	$0.0873561\pi$
$233$			1.59746e9i			0.542010i	−0.962578	+	0.271005i	$0.912644\pi$
$234$	1.10807e9	−	9.21759e8i	0.369576	−	0.307435i
$235$	4.42693e8	−	4.42693e8i	0.145155	−	0.145155i
$236$	−2.07374e9	+	1.42585e9i	−0.668507	+	0.459647i
$237$	8.38289e7	−	8.38289e7i	0.0265705	−	0.0265705i
$238$	4.28980e8	−	4.67364e9i	0.133699	−	1.45662i
$239$			4.58713e9i			1.40588i	0.711247	+	0.702942i	$0.248131\pi$
$239$			4.58713e9i			1.40588i	−0.711247	+	0.702942i	$0.751869\pi$
$240$	2.68707e8	−	7.00835e8i	0.0809904	−	0.211237i
$241$	4.47492e9			1.32653			0.663265	−	0.748385i	$-0.269170\pi$
$241$	4.47492e9			1.32653			0.663265	+	0.748385i	$0.269170\pi$
$242$	1.87349e9	+	1.71962e8i	0.546248	+	0.0501386i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$	3.44357e8	−	2.36770e8i	0.0971514	−	0.0667986i
$245$	−1.59155e9	−	1.59155e9i	−0.441728	−	0.441728i
$246$	1.34415e9	+	1.61584e9i	0.367035	+	0.441223i
$247$	−9.56479e9			−2.56973
$248$	−1.41515e9	−	3.98658e8i	−0.374106	−	0.105389i
$249$			2.63804e9i			0.686254i
$250$	1.80744e9	+	2.17277e9i	0.462705	+	0.556230i
$251$	−4.08114e9	+	4.08114e9i	−1.02822	+	1.02822i	−0.0286314	+	0.999590i	$0.509115\pi$
$251$	−4.08114e9	+	4.08114e9i	−1.02822	+	1.02822i	−0.999590	+	0.0286314i	$0.990885\pi$
$252$	3.94145e8	−	2.12897e9i	0.0977357	−	0.527918i
$253$	−1.73802e9	+	1.73802e9i	−0.424203	+	0.424203i
$254$	4.56148e9	+	4.18685e8i	1.09590	+	0.100590i
$255$		−	8.68714e8i		−	0.205455i
$256$	3.19406e9	+	2.87136e9i	0.743675	+	0.668542i
$257$	2.37742e9			0.544971			0.272486	−	0.962160i	$-0.412154\pi$
$257$	2.37742e9			0.544971			0.272486	+	0.962160i	$0.412154\pi$
$258$	6.34164e7	−	6.90907e8i	0.0143127	−	0.155934i
$259$	−8.56103e9	−	8.56103e9i	−1.90251	−	1.90251i
$260$	2.53929e9	+	4.70110e8i	0.555674	+	0.102874i
$261$	1.68110e9	+	1.68110e9i	0.362269	+	0.362269i
$262$	−4.02402e8	+	3.34741e8i	−0.0853993	+	0.0710402i
$263$	−5.15504e9			−1.07748			−0.538740	−	0.842472i	$-0.681099\pi$
$263$	−5.15504e9			−1.07748			−0.538740	+	0.842472i	$0.681099\pi$
$264$	5.10951e8	−	1.81376e9i	0.105187	−	0.373391i
$265$		−	3.46730e9i		−	0.703085i
$266$	−1.10458e10	+	9.18855e9i	−2.20633	+	1.83536i
$267$	7.89659e8	−	7.89659e8i	0.155380	−	0.155380i
$268$	−3.58558e9	−	5.21484e9i	−0.695057	−	1.01089i
$269$	−5.95491e9	+	5.95491e9i	−1.13728	+	1.13728i	−0.148340	+	0.988936i	$0.547393\pi$
$269$	−5.95491e9	+	5.95491e9i	−1.13728	+	1.13728i	−0.988936	+	0.148340i	$0.952607\pi$
$270$	3.66309e7	−	3.99085e8i	0.00689274	−	0.0750948i
$271$		−	2.41682e9i		−	0.448093i	−0.974578	−	0.224046i	$-0.928073\pi$
$271$		−	2.41682e9i		−	0.448093i	0.974578	−	0.224046i	$-0.0719267\pi$
$272$	4.64148e9	+	1.77959e9i	0.847971	+	0.325120i
$273$	7.44938e9			1.34113
$274$	7.28269e8	+	6.68458e7i	0.129208	+	0.0118597i
$275$	2.30000e9	+	2.30000e9i	0.402159	+	0.402159i
$276$	−1.69477e9	−	2.46486e9i	−0.292061	−	0.424771i
$277$	1.43137e9	+	1.43137e9i	0.243127	+	0.243127i	0.818142	−	0.575016i	$-0.195004\pi$
$277$	1.43137e9	+	1.43137e9i	0.243127	+	0.243127i	−0.575016	+	0.818142i	$0.695004\pi$
$278$	−4.87091e9	−	5.85545e9i	−0.815513	−	0.980350i
$279$	−7.85006e8			−0.129556
$280$	3.38410e9	−	1.89651e9i	0.550568	−	0.308548i
$281$		−	1.14737e10i		−	1.84026i	−0.391613	−	0.920130i	$-0.628083\pi$
$281$		−	1.14737e10i		−	1.84026i	0.391613	−	0.920130i	$-0.371917\pi$
$282$	1.22326e9	+	1.47052e9i	0.193430	+	0.232527i
$283$	7.26379e9	−	7.26379e9i	1.13245	−	1.13245i	0.142677	−	0.989769i	$-0.454429\pi$
$283$	7.26379e9	−	7.26379e9i	1.13245	−	1.13245i	0.989769	−	0.142677i	$-0.0455711\pi$
$284$	1.70784e8	+	3.16180e7i	0.0262527	+	0.00486027i
$285$	−1.88053e9	+	1.88053e9i	−0.285037	+	0.285037i
$286$	6.45616e9	+	5.92593e8i	0.964961	+	0.0885711i
$287$			1.08630e10i			1.60112i
$288$	2.05724e9	+	1.01325e9i	0.299031	+	0.147281i
$289$	−1.22245e9			−0.175242
$290$	−3.89344e8	+	4.24181e9i	−0.0550479	+	0.599734i
$291$	−1.30385e9	−	1.30385e9i	−0.181827	−	0.181827i
$292$	−2.68394e8	+	1.44973e9i	−0.0369183	+	0.199414i
$293$	−5.60874e9	−	5.60874e9i	−0.761018	−	0.761018i	0.215489	−	0.976506i	$-0.430866\pi$
$293$	−5.60874e9	−	5.60874e9i	−0.761018	−	0.761018i	−0.976506	+	0.215489i	$0.930866\pi$
$294$	5.28672e9	−	4.39781e9i	0.707616	−	0.588636i
$295$	−2.40754e9			−0.317896
$296$	1.11865e10	−	6.26911e9i	1.45723	−	0.816655i
$297$		−	1.00612e9i		−	0.129308i
$298$	−8.28698e8	+	6.89359e8i	−0.105083	+	0.0874139i
$299$	7.27738e9	−	7.27738e9i	0.910522	−	0.910522i
$300$	−3.26185e9	+	2.24276e9i	−0.402698	+	0.276884i
$301$	2.53560e9	−	2.53560e9i	0.308897	−	0.308897i
$302$	−7.13449e8	+	7.77286e9i	−0.0857699	+	0.934443i
$303$		−	5.97892e9i		−	0.709337i
$304$	−6.19523e9	−	1.38999e10i	−0.725376	−	1.62748i
$305$	3.99786e8			0.0461985
$306$	2.64305e9	+	2.42599e8i	0.301453	+	0.0276696i
$307$	4.87950e9	+	4.87950e9i	0.549315	+	0.549315i	0.926243	−	0.376927i	$-0.123019\pi$
$307$	4.87950e9	+	4.87950e9i	0.549315	+	0.549315i	−0.376927	+	0.926243i	$0.623019\pi$
$308$	8.02511e9	−	5.51785e9i	0.891760	−	0.613150i
$309$	−2.96122e9	−	2.96122e9i	−0.324816	−	0.324816i
$310$	−8.99474e8	−	1.08128e9i	−0.0973961	−	0.117083i
$311$	−5.87046e9			−0.627525			−0.313762	−	0.949502i	$-0.601590\pi$
$311$	−5.87046e9			−0.627525			−0.313762	+	0.949502i	$0.601590\pi$
$312$	−2.13943e9	+	7.59449e9i	−0.225777	+	0.801457i
$313$			1.24393e10i			1.29604i	0.761625	+	0.648018i	$0.224402\pi$
$313$			1.24393e10i			1.29604i	−0.761625	+	0.648018i	$0.775598\pi$
$314$	8.54501e9	+	1.02722e10i	0.879010	+	1.05668i
$315$	1.46462e9	−	1.46462e9i	0.148759	−	0.148759i
$316$	−1.18139e8	+	6.38126e8i	−0.0118480	+	0.0639968i
$317$	−3.95200e9	+	3.95200e9i	−0.391363	+	0.391363i	−0.875173	−	0.483810i	$-0.839253\pi$
$317$	−3.95200e9	+	3.95200e9i	−0.391363	+	0.391363i	0.483810	+	0.875173i	$0.339253\pi$
$318$	1.05492e10	+	9.68283e8i	1.03160	+	0.0946878i
$319$			1.06939e10i			1.03270i
$320$	9.61551e8	+	3.99469e9i	0.0917006	+	0.380963i
$321$	−5.11797e9			−0.482034
$322$	1.41309e9	−	1.53953e10i	0.131446	−	1.43207i
$323$	−1.24544e10	−	1.24544e10i	−1.14423	−	1.14423i
$324$	1.20398e9	+	2.22898e8i	0.109255	+	0.0202267i
$325$	−9.63048e9	−	9.63048e9i	−0.863206	−	0.863206i
$326$	−2.59107e9	+	2.15541e9i	−0.229408	+	0.190835i
$327$	2.51918e9			0.220327
$328$	−1.10746e10	−	3.11982e9i	−0.956830	−	0.269547i
$329$			9.88604e9i			0.843799i
$330$	1.38585e9	−	1.15283e9i	0.116859	−	0.0972101i
$331$	−8.69387e8	+	8.69387e8i	−0.0724271	+	0.0724271i	−0.742392	−	0.669965i	$-0.766309\pi$
$331$	−8.69387e8	+	8.69387e8i	−0.0724271	+	0.0724271i	0.669965	+	0.742392i	$0.266309\pi$
$332$	−8.18184e9	−	1.18996e10i	−0.673440	−	0.979445i
$333$	4.84146e9	−	4.84146e9i	0.393731	−	0.393731i
$334$	7.74708e8	−	8.44026e9i	0.0622519	−	0.678219i
$335$		−	6.05425e9i		−	0.480707i
$336$	4.82505e9	+	1.08257e10i	0.378569	+	0.849374i
$337$	1.55974e10			1.20929			0.604646	−	0.796494i	$-0.293315\pi$
$337$	1.55974e10			1.20929			0.604646	+	0.796494i	$0.293315\pi$
$338$	−1.40359e10	−	1.28831e9i	−1.07541	−	0.0987086i
$339$	−9.70763e9	−	9.70763e9i	−0.735046	−	0.735046i
$340$	2.69430e9	+	3.91856e9i	0.201618	+	0.293232i
$341$	−2.49682e9	−	2.49682e9i	−0.184659	−	0.184659i
$342$	−5.19634e9	−	6.24666e9i	−0.379833	−	0.456608i
$343$	1.32481e10			0.957141
$344$	1.85678e9	+	3.31320e9i	0.132595	+	0.236600i
$345$		−	2.86161e9i		−	0.201992i
$346$	6.41209e8	+	7.70814e8i	0.0447399	+	0.0537831i
$347$	−1.03091e10	+	1.03091e10i	−0.711051	+	0.711051i	−0.966755	−	0.255704i	$-0.917693\pi$
$347$	−1.03091e10	+	1.03091e10i	−0.711051	+	0.711051i	0.255704	+	0.966755i	$0.417693\pi$
$348$	−1.27969e10	−	2.36915e9i	−0.872547	−	0.161538i
$349$	3.87981e9	−	3.87981e9i	0.261522	−	0.261522i	−0.564150	−	0.825672i	$-0.690796\pi$
$349$	3.87981e9	−	3.87981e9i	0.261522	−	0.261522i	0.825672	+	0.564150i	$0.190796\pi$
$350$	−2.03733e10	−	1.87001e9i	−1.35766	−	0.124615i
$351$			4.21280e9i			0.277551i
$352$	3.32055e9	+	9.76614e9i	0.216292	+	0.636140i
$353$	−6.63961e9			−0.427606			−0.213803	−	0.976877i	$-0.568585\pi$
$353$	−6.63961e9			−0.427606			−0.213803	+	0.976877i	$0.568585\pi$
$354$	6.72333e8	−	7.32491e9i	0.0428126	−	0.466433i
$355$	1.17491e8	+	1.17491e8i	0.00739760	+	0.00739760i
$356$	−1.11286e9	+	6.01108e9i	−0.0692849	+	0.374242i
$357$	9.69988e9	+	9.69988e9i	0.597164	+	0.597164i
$358$	6.12000e8	−	5.09097e8i	0.0372580	−	0.0309934i
$359$	2.80624e10			1.68945			0.844727	−	0.535197i	$-0.179763\pi$
$359$	2.80624e10			1.68945			0.844727	+	0.535197i	$0.179763\pi$
$360$	1.07252e9	+	1.91379e9i	0.0638550	+	0.113942i
$361$			3.69371e10i			2.17488i
$362$	−8.52575e9	+	7.09222e9i	−0.496476	+	0.412998i
$363$	−3.88833e9	+	3.88833e9i	−0.223942	+	0.223942i
$364$	−3.36024e10	+	2.31041e10i	−1.91410	+	1.31608i
$365$	−9.97339e8	+	9.97339e8i	−0.0561916	+	0.0561916i
$366$	−1.11645e8	+	1.21634e9i	−0.00622177	+	0.0677848i
$367$			1.54020e10i			0.849008i	0.905426	+	0.424504i	$0.139551\pi$
$367$			1.54020e10i			0.849008i	−0.905426	+	0.424504i	$0.860449\pi$
$368$	1.52894e10	+	5.86210e9i	0.833679	+	0.319641i
$369$	−6.14330e9			−0.331357
$370$	1.22162e10	+	1.12129e9i	0.651820	+	0.0598288i
$371$	3.87151e10	+	3.87151e10i	2.04355	+	2.04355i
$372$	3.54098e9	−	2.43468e9i	0.184906	−	0.127136i
$373$	2.57851e9	+	2.57851e9i	0.133209	+	0.133209i	0.770567	−	0.637358i	$-0.219973\pi$
$373$	2.57851e9	+	2.57851e9i	0.133209	+	0.133209i	−0.637358	+	0.770567i	$0.719973\pi$
$374$	7.63498e9	+	9.17822e9i	0.390231	+	0.469107i
$375$	−8.26071e9			−0.417727
$376$	−1.00786e10	−	2.83923e9i	−0.504255	−	0.142053i
$377$		−	4.47772e10i		−	2.21662i
$378$	4.04708e9	+	4.86511e9i	0.198233	+	0.238301i
$379$	1.37457e10	−	1.37457e10i	0.666207	−	0.666207i	−0.290629	−	0.956836i	$-0.593865\pi$
$379$	1.37457e10	−	1.37457e10i	0.666207	−	0.666207i	0.956836	+	0.290629i	$0.0938646\pi$
$380$	2.65021e9	−	1.43151e10i	0.127100	−	0.686529i
$381$	−9.46710e9	+	9.46710e9i	−0.449280	+	0.449280i
$382$	1.46410e10	+	1.34386e9i	0.687573	+	0.0631104i
$383$			7.69303e9i			0.357521i	0.983893	+	0.178761i	$0.0572088\pi$
$383$			7.69303e9i			0.357521i	−0.983893	+	0.178761i	$0.942791\pi$
$384$	−1.24223e10	+	1.80995e9i	−0.571318	+	0.0832416i
$385$	9.31687e9			0.424060
$386$	1.08789e9	−	1.18524e10i	0.0490047	−	0.533895i
$387$	1.43394e9	+	1.43394e9i	0.0639274	+	0.0639274i
$388$	9.92526e9	+	1.83750e9i	0.437940	+	0.0810777i
$389$	−1.95449e10	−	1.95449e10i	−0.853561	−	0.853561i	0.137009	−	0.990570i	$-0.456251\pi$
$389$	−1.95449e10	−	1.95449e10i	−0.853561	−	0.853561i	−0.990570	+	0.137009i	$0.956251\pi$
$390$	−5.80279e9	+	4.82710e9i	−0.250829	+	0.208655i
$391$	1.89518e10			0.810858
$392$	−1.02075e10	+	3.62341e10i	−0.432288	+	1.53452i
$393$		−	1.52990e9i		−	0.0641346i
$394$	−2.23750e10	+	1.86128e10i	−0.928491	+	0.772374i
$395$	−4.38998e8	+	4.38998e8i	−0.0180333	+	0.0180333i
$396$	3.12047e9	+	4.53839e9i	0.126894	+	0.184553i
$397$	−4.41204e9	+	4.41204e9i	−0.177614	+	0.177614i	−0.790315	−	0.612701i	$-0.790083\pi$
$397$	−4.41204e9	+	4.41204e9i	−0.177614	+	0.177614i	0.612701	+	0.790315i	$0.290083\pi$
$398$	3.34890e9	−	3.64855e10i	0.133466	−	1.45408i
$399$		−	4.19953e10i		−	1.65695i
$400$	7.75758e9	−	2.02331e10i	0.303030	−	0.790357i
$401$	−2.66586e10			−1.03100			−0.515502	−	0.856888i	$-0.672395\pi$
$401$	−2.66586e10			−1.03100			−0.515502	+	0.856888i	$0.672395\pi$
$402$	1.84200e10	+	1.69072e9i	0.705318	+	0.0647392i
$403$	1.04546e10	+	1.04546e10i	0.396357	+	0.396357i
$404$	1.85435e10	+	2.69695e10i	0.696091	+	1.01239i
$405$	8.28278e8	+	8.28278e8i	0.0307862	+	0.0307862i
$406$	−4.30158e10	−	5.17105e10i	−1.58316	−	1.90316i
$407$	3.07979e10			1.12239
$408$	−1.26746e10	+	7.10307e9i	−0.457398	+	0.256333i
$409$			1.05358e10i			0.376508i	0.982120	+	0.188254i	$0.0602827\pi$
$409$			1.05358e10i			0.376508i	−0.982120	+	0.188254i	$0.939717\pi$
$410$	−7.03911e9	−	8.46190e9i	−0.249105	−	0.299456i
$411$	−1.51148e9	+	1.51148e9i	−0.0529707	+	0.0529707i
$412$	2.25415e10	+	4.17321e9i	0.782338	+	0.144838i
$413$	2.68821e10	−	2.68821e10i	0.923980	−	0.923980i
$414$	8.70642e9	+	7.99138e8i	0.296373	+	0.0272032i
$415$		−	1.38150e10i		−	0.465757i
$416$	−1.39037e10	−	4.08924e10i	−0.464255	−	1.36543i
$417$	2.22620e10			0.736240
$418$	3.34069e9	−	3.63960e10i	0.109429	−	1.19220i
$419$	1.89805e10	+	1.89805e10i	0.615816	+	0.615816i	0.944455	−	0.328640i	$-0.106590\pi$
$419$	1.89805e10	+	1.89805e10i	0.615816	+	0.615816i	−0.328640	+	0.944455i	$0.606590\pi$
$420$	−2.06407e9	+	1.11491e10i	−0.0663327	+	0.358295i
$421$	3.74379e10	+	3.74379e10i	1.19174	+	1.19174i	0.976578	+	0.215165i	$0.0690291\pi$
$421$	3.74379e10	+	3.74379e10i	1.19174	+	1.19174i	0.215165	+	0.976578i	$0.430971\pi$
$422$	−3.16303e10	+	2.63119e10i	−0.997364	+	0.829666i
$423$	−5.59079e9			−0.174627
$424$	−5.05881e10	+	2.83505e10i	−1.56526	+	0.877196i
$425$		−	2.50798e10i		−	0.768721i
$426$	−3.90275e8	+	3.24654e8i	−0.0118504	+	0.00985785i
$427$	−4.46393e9	+	4.46393e9i	−0.134278	+	0.134278i
$428$	2.30859e10	−	1.58733e10i	0.687975	−	0.473033i
$429$	−1.33994e10	+	1.33994e10i	−0.395600	+	0.395600i
$430$	−3.32102e8	+	3.61817e9i	−0.00971398	+	0.105832i
$431$			6.06882e9i			0.175871i	0.996126	+	0.0879357i	$0.0280270\pi$
$431$			6.06882e9i			0.175871i	−0.996126	+	0.0879357i	$0.971973\pi$
$432$	−6.12219e9	+	2.72868e9i	−0.175781	+	0.0783462i
$433$	−4.82856e10			−1.37362			−0.686809	−	0.726837i	$-0.740989\pi$
$433$	−4.82856e10			−1.37362			−0.686809	+	0.726837i	$0.740989\pi$
$434$	2.21167e10	+	2.03003e9i	0.623393	+	0.0572195i
$435$	−8.80364e9	−	8.80364e9i	−0.245870	−	0.245870i
$436$	−1.13634e10	+	7.81319e9i	−0.314459	+	0.216213i
$437$	−4.10256e10	−	4.10256e10i	−1.12494	−	1.12494i
$438$	−2.75588e9	−	3.31291e9i	−0.0748796	−	0.0900147i
$439$	−1.65738e10			−0.446236			−0.223118	−	0.974791i	$-0.571624\pi$
$439$	−1.65738e10			−0.446236			−0.223118	+	0.974791i	$0.571624\pi$
$440$	−2.67577e9	+	9.49836e9i	−0.0713901	+	0.253418i
$441$			2.00997e10i			0.531417i
$442$	−3.19689e10	−	3.84306e10i	−0.837603	−	1.00691i
$443$	1.72667e10	−	1.72667e10i	0.448327	−	0.448327i	−0.446471	−	0.894798i	$-0.647319\pi$
$443$	1.72667e10	−	1.72667e10i	0.448327	−	0.448327i	0.894798	+	0.446471i	$0.147319\pi$
$444$	−6.82301e9	+	3.68544e10i	−0.175567	+	0.948326i
$445$	−4.13532e9	+	4.13532e9i	−0.105455	+	0.105455i
$446$	4.76882e10	+	4.37717e9i	1.20524	+	0.110625i
$447$		−	3.15064e9i		−	0.0789167i
$448$	−5.53404e10	−	3.38674e10i	−1.37382	−	0.840755i
$449$	−2.16714e10			−0.533215			−0.266608	−	0.963805i	$-0.585903\pi$
$449$	−2.16714e10			−0.533215			−0.266608	+	0.963805i	$0.585903\pi$
$450$	1.05753e9	−	1.15216e10i	0.0257896	−	0.280972i
$451$	−1.95396e10	−	1.95396e10i	−0.472292	−	0.472292i
$452$	7.38968e10	+	1.36808e10i	1.77040	+	0.327762i
$453$	−1.61321e10	−	1.61321e10i	−0.383088	−	0.383088i
$454$	2.20908e10	−	1.83764e10i	0.519982	−	0.432552i
$455$	−3.90112e10			−0.910214
$456$	4.28133e10	+	1.20609e10i	0.990193	+	0.278946i
$457$		−	6.55610e10i		−	1.50307i	−0.659690	−	0.751537i	$-0.729313\pi$
$457$		−	6.55610e10i		−	1.50307i	0.659690	−	0.751537i	$-0.270687\pi$
$458$	2.25610e10	−	1.87676e10i	0.512739	−	0.426527i
$459$	−5.48551e9	+	5.48551e9i	−0.123585	+	0.123585i
$460$	8.87522e9	+	1.29081e10i	0.198220	+	0.288290i
$461$	2.69532e9	−	2.69532e9i	0.0596770	−	0.0596770i	−0.676638	−	0.736315i	$-0.736564\pi$
$461$	2.69532e9	−	2.69532e9i	0.0596770	−	0.0596770i	0.736315	+	0.676638i	$0.236564\pi$
$462$	−2.60184e9	+	2.83465e10i	−0.0571101	+	0.622202i
$463$		−	6.58039e9i		−	0.143195i	−0.997434	−	0.0715975i	$-0.977190\pi$
$463$		−	6.58039e9i		−	0.143195i	0.997434	−	0.0715975i	$-0.0228097\pi$
$464$	6.50718e10	−	2.90027e10i	1.40385	−	0.625701i
$465$	4.11095e9			0.0879286
$466$	2.54524e10	+	2.33621e9i	0.539742	+	0.0495414i
$467$	1.04374e10	+	1.04374e10i	0.219445	+	0.219445i	0.808265	−	0.588819i	$-0.200407\pi$
$467$	1.04374e10	+	1.04374e10i	0.219445	+	0.219445i	−0.588819	+	0.808265i	$0.700407\pi$
$468$	−1.30659e10	−	1.90029e10i	−0.272368	−	0.396130i
$469$	6.76005e10	+	6.76005e10i	1.39720	+	1.39720i
$470$	−6.40603e9	−	7.70086e9i	−0.131280	−	0.157815i
$471$	−3.90540e10			−0.793565
$472$	1.96853e10	+	3.51262e10i	0.396620	+	0.707722i
$473$			9.12169e9i			0.182235i
$474$	−1.21305e9	−	1.45824e9i	−0.0240307	−	0.0288879i
$475$	−5.42911e10	+	5.42911e10i	−1.06648	+	1.06648i
$476$	−7.38379e10	−	1.36699e10i	−1.43831	−	0.266280i
$477$	−2.18943e10	+	2.18943e10i	−0.422920	+	0.422920i
$478$	7.30869e10	+	6.70844e9i	1.40000	+	0.128502i
$479$		−	6.38680e10i		−	1.21322i	−0.794998	−	0.606612i	$-0.792528\pi$
$479$		−	6.38680e10i		−	1.21322i	0.794998	−	0.606612i	$-0.207472\pi$
$480$	−1.07734e10	−	5.30624e9i	−0.202950	−	0.0999591i
$481$	−1.28956e11			−2.40913
$482$	6.54433e9	−	7.12990e10i	0.121249	−	1.32098i
$483$	3.19522e10	+	3.19522e10i	0.587099	+	0.587099i
$484$	5.47976e9	−	2.95989e10i	0.0998574	−	0.539379i
$485$	6.82808e9	+	6.82808e9i	0.123405	+	0.123405i
$486$	−2.75133e9	+	2.28872e9i	−0.0493172	+	0.0410249i
$487$	5.08187e10			0.903457			0.451729	−	0.892155i	$-0.350808\pi$
$487$	5.08187e10			0.903457			0.451729	+	0.892155i	$0.350808\pi$
$488$	−3.26886e9	−	5.83290e9i	−0.0576391	−	0.102850i
$489$		−	9.85105e9i		−	0.172285i
$490$	−2.76857e10	+	2.30306e10i	−0.480255	+	0.399504i
$491$	−3.98846e10	+	3.98846e10i	−0.686246	+	0.686246i	−0.961400	−	0.275154i	$-0.911271\pi$
$491$	−3.98846e10	+	3.98846e10i	−0.686246	+	0.686246i	0.275154	+	0.961400i	$0.411271\pi$
$492$	2.77110e10	−	1.90533e10i	0.472924	−	0.325170i
$493$	5.83046e10	−	5.83046e10i	0.986996	−	0.986996i
$494$	−1.39880e10	+	1.52396e11i	−0.234881	+	2.55897i
$495$			5.26891e9i			0.0877606i
$496$	−8.42141e9	+	2.19645e10i	−0.139142	+	0.362907i
$497$	−2.62376e9			−0.0430029
$498$	4.20320e10	+	3.85800e9i	0.683381	+	0.0627257i
$499$	−7.30904e10	−	7.30904e10i	−1.17885	−	1.17885i	−0.980038	−	0.198811i	$-0.936292\pi$
$499$	−7.30904e10	−	7.30904e10i	−1.17885	−	1.17885i	−0.198811	−	0.980038i	$-0.563708\pi$
$500$	3.72621e10	−	2.56204e10i	0.596194	−	0.409927i
$501$	1.75173e10	+	1.75173e10i	0.278046	+	0.278046i
$502$	5.90565e10	+	7.09934e10i	0.929935	+	1.11790i
$503$	9.25242e10			1.44539			0.722693	−	0.691170i	$-0.242904\pi$
$503$	9.25242e10			1.44539			0.722693	+	0.691170i	$0.242904\pi$
$504$	−3.33445e10	−	9.39342e9i	−0.516775	−	0.145580i
$505$			3.13107e10i			0.481423i
$506$	2.51502e10	+	3.02338e10i	0.383654	+	0.461201i
$507$	2.91307e10	−	2.91307e10i	0.440879	−	0.440879i
$508$	1.33418e10	−	7.20658e10i	0.200337	−	1.08212i
$509$	−6.94091e10	+	6.94091e10i	−1.03406	+	1.03406i	−0.0346602	+	0.999399i	$0.511035\pi$
$509$	−6.94091e10	+	6.94091e10i	−1.03406	+	1.03406i	−0.999399	+	0.0346602i	$0.988965\pi$
$510$	−1.38412e10	−	1.27045e9i	−0.204595	−	0.0187792i
$511$		−	2.22722e10i		−	0.326647i
$512$	5.04207e10	−	4.66918e10i	0.733717	−	0.679455i
$513$	2.37493e10			0.342911
$514$	3.47686e9	−	3.78795e10i	0.0498120	−	0.542690i
$515$	1.55074e10	+	1.55074e10i	0.220450	+	0.220450i
$516$	−1.09155e10	−	2.02083e9i	−0.153973	−	0.0285057i
$517$	−1.77823e10	−	1.77823e10i	−0.248900	−	0.248900i
$518$	−1.48923e11	+	1.23883e11i	−2.06844	+	1.72065i
$519$	−2.93058e9			−0.0403909
$520$	1.12039e10	−	3.97711e10i	0.153234	−	0.543944i
$521$			2.84860e10i			0.386617i	0.981138	+	0.193309i	$0.0619219\pi$
$521$			2.84860e10i			0.386617i	−0.981138	+	0.193309i	$0.938078\pi$
$522$	2.92435e10	−	2.43265e10i	0.393865	−	0.327640i
$523$	−3.89497e10	+	3.89497e10i	−0.520591	+	0.520591i	−0.917750	−	0.397159i	$-0.869996\pi$
$523$	−3.89497e10	+	3.89497e10i	−0.520591	+	0.520591i	0.397159	+	0.917750i	$0.369996\pi$
$524$	4.74495e9	+	6.90102e9i	0.0629371	+	0.0915351i
$525$	4.22837e10	−	4.22837e10i	0.556591	−	0.556591i
$526$	−7.53898e9	+	8.21354e10i	−0.0984848	+	1.07297i
$527$			2.72260e10i			0.352972i
$528$	−2.81514e10	−	1.07935e10i	−0.362213	−	0.138876i
$529$	−1.58821e10			−0.202809
$530$	−5.52445e10	−	5.07074e9i	−0.700141	−	0.0642640i
$531$	1.52024e10	+	1.52024e10i	0.191221	+	0.191221i
$532$	1.30247e11	+	1.89431e11i	1.62601	+	2.36485i
$533$	8.18155e10	+	8.18155e10i	1.01374	+	1.01374i
$534$	−1.14268e10	−	1.37365e10i	−0.140527	−	0.168932i
$535$	2.68020e10			0.327153
$536$	−8.83319e10	+	4.95027e10i	−1.07018	+	0.599750i
$537$			2.32678e9i			0.0279806i
$538$	8.61710e10	+	1.03588e11i	1.02857	+	1.23647i
$539$	−6.39299e10	+	6.39299e10i	−0.757442	+	0.757442i
$540$	−6.30505e9	−	1.16728e9i	−0.0741504	−	0.0137278i
$541$	3.18217e10	−	3.18217e10i	0.371479	−	0.371479i	−0.496536	−	0.868016i	$-0.665395\pi$
$541$	3.18217e10	−	3.18217e10i	0.371479	−	0.371479i	0.868016	+	0.496536i	$0.165395\pi$
$542$	−3.85073e10	−	3.53448e9i	−0.446217	−	0.0409570i
$543$		−	3.24142e10i		−	0.372852i
$544$	3.51421e10	−	7.13503e10i	0.401266	−	0.814704i
$545$	−1.31925e10			−0.149535
$546$	1.08943e10	−	1.18691e11i	0.122583	−	1.33551i
$547$	1.31958e10	+	1.31958e10i	0.147396	+	0.147396i	0.776954	−	0.629558i	$-0.216764\pi$
$547$	1.31958e10	+	1.31958e10i	0.147396	+	0.147396i	−0.629558	+	0.776954i	$0.716764\pi$
$548$	2.13011e9	−	1.15058e10i	0.0236200	−	0.127583i
$549$	−2.52445e9	−	2.52445e9i	−0.0277893	−	0.0277893i
$550$	4.00097e10	−	3.32824e10i	0.437234	−	0.363717i
$551$	−2.52428e11			−2.73861
$552$	−4.17511e10	+	2.33980e10i	−0.449689	+	0.252013i
$553$		−	9.80353e9i		−	0.104829i
$554$	2.48994e10	−	2.07128e10i	0.264332	−	0.219887i
$555$	−2.53540e10	+	2.53540e10i	−0.267223	+	0.267223i
$556$	−1.00418e11	+	6.90450e10i	−1.05079	+	0.722492i
$557$	7.56493e10	−	7.56493e10i	0.785930	−	0.785930i	−0.194894	−	0.980824i	$-0.562436\pi$
$557$	7.56493e10	−	7.56493e10i	0.785930	−	0.785930i	0.980824	+	0.194894i	$0.0624364\pi$
$558$	−1.14803e9	+	1.25075e10i	−0.0118418	+	0.129013i
$559$		−	3.81940e10i		−	0.391154i
$560$	−2.52680e10	−	5.66924e10i	−0.256933	−	0.576465i
$561$	−3.48949e10			−0.352298
$562$	−1.82811e11	−	1.67797e10i	−1.83256	−	0.168205i
$563$	−1.78799e10	−	1.78799e10i	−0.177964	−	0.177964i	0.612504	−	0.790468i	$-0.290162\pi$
$563$	−1.78799e10	−	1.78799e10i	−0.177964	−	0.177964i	−0.790468	+	0.612504i	$0.790162\pi$
$564$	2.52187e10	−	1.73397e10i	0.249234	−	0.171366i
$565$	5.08373e10	+	5.08373e10i	0.498871	+	0.498871i
$566$	−1.05111e11	−	1.26357e11i	−1.02420	−	1.23122i
$567$	−1.84968e10			−0.178963
$568$	7.53533e8	−	2.67487e9i	0.00723950	−	0.0256986i
$569$		−	8.51803e10i		−	0.812625i	−0.913734	−	0.406313i	$-0.866814\pi$
$569$		−	8.51803e10i		−	0.812625i	0.913734	−	0.406313i	$-0.133186\pi$
$570$	2.72124e10	+	3.27127e10i	0.257791	+	0.309897i
$571$	1.18891e11	−	1.18891e11i	1.11842	−	1.11842i	0.126449	−	0.991973i	$-0.459642\pi$
$571$	1.18891e11	−	1.18891e11i	1.11842	−	1.11842i	0.991973	−	0.126449i	$-0.0403579\pi$
$572$	1.88836e10	−	1.01999e11i	0.176401	−	0.952826i
$573$	−3.03867e10	+	3.03867e10i	−0.281880	+	0.281880i
$574$	1.73081e11	+	1.58866e10i	1.59442	+	0.146347i
$575$		−	8.26148e10i		−	0.755765i
$576$	1.91528e10	−	3.12963e10i	0.173997	−	0.284317i
$577$	6.24358e10			0.563288			0.281644	−	0.959519i	$-0.409120\pi$
$577$	6.24358e10			0.563288			0.281644	+	0.959519i	$0.409120\pi$
$578$	−1.78776e9	+	1.94773e10i	−0.0160176	+	0.174508i
$579$	2.45989e10	+	2.45989e10i	0.218878	+	0.218878i
$580$	6.70154e10	+	1.24068e10i	0.592192	+	0.109635i
$581$	1.54256e11	+	1.54256e11i	1.35374	+	1.35374i
$582$	−2.26812e10	+	1.88675e10i	−0.197685	+	0.164446i
$583$	−1.39276e11			−1.20560
$584$	2.27060e10	+	6.39648e9i	0.195205	+	0.0549908i
$585$		−	2.20617e10i		−	0.188372i
$586$	−9.75667e10	+	8.11617e10i	−0.827391	+	0.688273i
$587$	−7.55708e10	+	7.55708e10i	−0.636504	+	0.636504i	−0.949691	−	0.313187i	$-0.898603\pi$
$587$	−7.55708e10	+	7.55708e10i	−0.636504	+	0.636504i	0.313187	+	0.949691i	$0.398603\pi$
$588$	−6.23388e10	−	9.06651e10i	−0.521494	−	0.758457i
$589$	5.89368e10	−	5.89368e10i	0.489695	−	0.489695i
$590$	−3.52090e9	+	3.83593e10i	−0.0290566	+	0.316565i
$591$		−	8.50680e10i		−	0.697294i
$592$	−8.35261e10	−	1.87403e11i	−0.680042	−	1.52577i
$593$	1.21041e11			0.978848			0.489424	−	0.872046i	$-0.337207\pi$
$593$	1.21041e11			0.978848			0.489424	+	0.872046i	$0.337207\pi$
$594$	−1.60306e10	−	1.47140e9i	−0.128767	−	0.0118191i
$595$	−5.07967e10	−	5.07967e10i	−0.405292	−	0.405292i
$596$	9.77165e9	+	1.42118e10i	0.0774431	+	0.112633i
$597$	7.57236e10	+	7.57236e10i	0.596121	+	0.596121i
$598$	−1.05308e11	−	1.26593e11i	−0.823486	−	0.989935i
$599$	1.45299e11			1.12864			0.564319	−	0.825557i	$-0.309139\pi$
$599$	1.45299e11			1.12864			0.564319	+	0.825557i	$0.309139\pi$
$600$	3.09637e10	+	5.52511e10i	0.238917	+	0.426320i
$601$		−	1.24287e9i		−	0.00952635i	−0.999989	−	0.00476317i	$-0.998484\pi$
$601$		−	1.24287e9i		−	0.00952635i	0.999989	−	0.00476317i	$-0.00151617\pi$
$602$	−3.66915e10	−	4.41079e10i	−0.279370	−	0.335838i
$603$	−3.82296e10	+	3.82296e10i	−0.289155	+	0.289155i
$604$	1.22802e11	+	2.27348e10i	0.922692	+	0.170822i
$605$	2.03625e10	−	2.03625e10i	0.151988	−	0.151988i
$606$	−9.52623e10	−	8.74386e9i	−0.706368	−	0.0648355i
$607$			4.13054e10i			0.304265i	0.988360	+	0.152133i	$0.0486141\pi$
$607$			4.13054e10i			0.304265i	−0.988360	+	0.152133i	$0.951386\pi$
$608$	−2.30527e11	+	7.83808e10i	−1.68697	+	0.573582i
$609$	1.96599e11			1.42926
$610$	5.84666e8	−	6.36980e9i	0.00422268	−	0.0460051i
$611$	7.44572e10	+	7.44572e10i	0.534247	+	0.534247i
$612$	7.73066e9	−	4.17570e10i	0.0551075	−	0.297662i
$613$	−3.17545e9	−	3.17545e9i	−0.0224887	−	0.0224887i	0.695773	−	0.718262i	$-0.255062\pi$
$613$	−3.17545e9	−	3.17545e9i	−0.0224887	−	0.0224887i	−0.718262	+	0.695773i	$0.755062\pi$
$614$	8.48812e10	−	7.06092e10i	0.597225	−	0.496807i
$615$	3.21715e10			0.224890
$616$	−7.61797e10	−	1.35934e11i	−0.529074	−	0.944071i
$617$			2.60113e9i			0.0179482i	0.999960	+	0.00897411i	$0.00285659\pi$
$617$			2.60113e9i			0.0179482i	−0.999960	+	0.00897411i	$0.997143\pi$
$618$	−5.15118e10	+	4.28506e10i	−0.353145	+	0.293767i
$619$	−1.10123e11	+	1.10123e11i	−0.750094	+	0.750094i	−0.974496	−	0.224403i	$-0.927957\pi$
$619$	−1.10123e11	+	1.10123e11i	−0.750094	+	0.750094i	0.224403	+	0.974496i	$0.427957\pi$
$620$	−1.85435e10	+	1.27500e10i	−0.125495	+	0.0862867i
$621$	−1.80697e10	+	1.80697e10i	−0.121502	+	0.121502i
$622$	−8.58524e9	+	9.35342e10i	−0.0573576	+	0.624898i
$623$		−	9.23482e10i		−	0.613022i
$624$	1.17874e11	+	4.51942e10i	0.777466	+	0.298088i
$625$	−8.58992e10			−0.562949
$626$	1.98195e11	+	1.81918e10i	1.29061	+	0.118462i
$627$	7.55380e10	+	7.55380e10i	0.488760	+	0.488760i
$628$	1.76164e11	−	1.21125e11i	1.13260	−	0.778747i
$629$	−1.67914e11	−	1.67914e11i	−1.07271	−	1.07271i
$630$	−2.11939e10	−	2.54778e10i	−0.134539	−	0.161733i
$631$	1.95217e11			1.23140			0.615701	−	0.787980i	$-0.288873\pi$
$631$	1.95217e11			1.23140			0.615701	+	0.787980i	$0.288873\pi$
$632$	9.99451e9	+	2.81554e9i	0.0626460	+	0.0176479i
$633$		−	1.20256e11i		−	0.749017i
$634$	5.71877e10	+	6.87469e10i	0.353953	+	0.425496i
$635$	4.95776e10	−	4.95776e10i	0.304924	−	0.304924i
$636$	3.08554e10	−	1.66665e11i	0.188583	−	1.01863i
$637$	2.67685e11	−	2.67685e11i	1.62580	−	1.62580i
$638$	1.70387e11	+	1.56393e10i	1.02838	+	0.0943920i
$639$		−	1.48380e9i		−	0.00889961i
$640$	6.50537e10	−	9.47839e9i	0.387750	−	0.0564956i
$641$	−4.92704e10			−0.291846			−0.145923	−	0.989296i	$-0.546615\pi$
$641$	−4.92704e10			−0.291846			−0.145923	+	0.989296i	$0.546615\pi$
$642$	−7.48476e9	+	8.15447e10i	−0.0440593	+	0.480016i
$643$	−1.33312e11	−	1.33312e11i	−0.779874	−	0.779874i	0.199935	−	0.979809i	$-0.435927\pi$
$643$	−1.33312e11	−	1.33312e11i	−0.779874	−	0.779874i	−0.979809	+	0.199935i	$0.935927\pi$
$644$	−2.43228e11	−	4.50297e10i	−1.41406	−	0.261792i
$645$	−7.50931e9	−	7.50931e9i	−0.0433871	−	0.0433871i
$646$	−2.16650e11	+	1.80222e11i	−1.24402	+	1.03485i
$647$	7.81289e9			0.0445856			0.0222928	−	0.999751i	$-0.492903\pi$
$647$	7.81289e9			0.0445856			0.0222928	+	0.999751i	$0.492903\pi$
$648$	5.31220e9	−	1.88571e10i	0.0301283	−	0.106948i
$649$			9.67070e10i			0.545103i
$650$	−1.67527e11	+	1.39359e11i	−0.938493	+	0.780693i
$651$	−4.59020e10	+	4.59020e10i	−0.255569	+	0.255569i
$652$	3.05528e10	+	4.44358e10i	0.169068	+	0.245891i
$653$	−2.33635e11	+	2.33635e11i	−1.28495	+	1.28495i	−0.347132	+	0.937816i	$0.612844\pi$
$653$	−2.33635e11	+	2.33635e11i	−1.28495	+	1.28495i	−0.937816	+	0.347132i	$0.887156\pi$
$654$	3.68417e9	−	4.01382e10i	0.0201386	−	0.219405i
$655$			8.01184e9i			0.0435278i
$656$	−6.59043e10	+	1.71890e11i	−0.355876	+	0.928187i
$657$	1.25954e10			0.0676008
$658$	1.57515e11	+	1.44578e10i	0.840267	+	0.0771257i
$659$	1.83980e11	+	1.83980e11i	0.975506	+	0.975506i	0.999707	−	0.0242007i	$-0.00770408\pi$
$659$	1.83980e11	+	1.83980e11i	0.975506	+	0.975506i	−0.0242007	+	0.999707i	$0.507704\pi$
$660$	−1.63414e10	−	2.37668e10i	−0.0861219	−	0.125255i
$661$	−1.54412e11	−	1.54412e11i	−0.808866	−	0.808866i	0.175596	−	0.984462i	$-0.443815\pi$
$661$	−1.54412e11	−	1.54412e11i	−0.808866	−	0.808866i	−0.984462	+	0.175596i	$0.943815\pi$
$662$	1.25805e10	+	1.51234e10i	0.0655039	+	0.0787440i
$663$	1.46110e11			0.756183
$664$	−2.01562e11	+	1.12959e11i	−1.03690	+	0.581096i
$665$			2.19922e11i			1.12456i
$666$	−7.00588e10	−	8.42196e10i	−0.356095	−	0.428071i
$667$	1.92060e11	−	1.92060e11i	0.970361	−	0.970361i
$668$	−1.33346e11	−	2.46869e10i	−0.669690	−	0.123983i
$669$	−9.89743e10	+	9.89743e10i	−0.494104	+	0.494104i
$670$	−9.64624e10	−	8.85402e9i	−0.478695	−	0.0439381i
$671$		−	1.60588e10i		−	0.0792176i
$672$	1.79543e11	−	6.10457e10i	0.880421	−	0.299349i
$673$	−3.53284e11			−1.72212			−0.861060	−	0.508504i	$-0.830199\pi$
$673$	−3.53284e11			−1.72212			−0.861060	+	0.508504i	$0.830199\pi$
$674$	2.28103e10	−	2.48513e11i	0.110533	−	1.20423i
$675$	2.39124e10	+	2.39124e10i	0.115188	+	0.115188i
$676$	−4.10535e10	+	2.21750e11i	−0.196591	+	1.06188i
$677$	1.94542e11	+	1.94542e11i	0.926101	+	0.926101i	0.997451	−	0.0713500i	$-0.0227307\pi$
$677$	1.94542e11	+	1.94542e11i	0.926101	+	0.926101i	−0.0713500	+	0.997451i	$0.522731\pi$
$678$	−1.68869e11	+	1.40475e11i	−0.799154	+	0.664783i
$679$	−1.52482e11			−0.717363
$680$	6.63749e10	−	3.71976e10i	0.310433	−	0.173972i
$681$			8.39876e10i			0.390505i
$682$	−4.34334e10	+	3.61304e10i	−0.200764	+	0.167007i
$683$	−2.05217e9	+	2.05217e9i	−0.00943042	+	0.00943042i	−0.711806	−	0.702376i	$-0.752123\pi$
$683$	−2.05217e9	+	2.05217e9i	−0.00943042	+	0.00943042i	0.702376	+	0.711806i	$0.252123\pi$
$684$	−1.07128e11	+	7.36580e10i	−0.489414	+	0.336508i
$685$	7.91539e9	−	7.91539e9i	0.0359509	−	0.0359509i
$686$	1.93746e10	−	2.11082e11i	0.0874856	−	0.953135i
$687$			8.57752e10i			0.385066i
$688$	5.55048e10	−	2.47387e10i	0.247729	−	0.110414i
$689$	5.83170e11			2.58773
$690$	−4.55941e10	−	4.18496e9i	−0.201146	−	0.0184627i
$691$	−2.90116e11	−	2.90116e11i	−1.27251	−	1.27251i	−0.944769	−	0.327736i	$-0.893714\pi$
$691$	−2.90116e11	−	2.90116e11i	−1.27251	−	1.27251i	−0.327736	−	0.944769i	$-0.606286\pi$
$692$	1.32191e10	−	9.08912e9i	0.0576473	−	0.0396367i
$693$	−5.88315e10	−	5.88315e10i	−0.255081	−	0.255081i
$694$	1.49178e11	+	1.79331e11i	0.643083	+	0.773067i
$695$	−1.16582e11			−0.499682
$696$	−5.64625e10	+	2.00429e11i	−0.240615	+	0.854129i
$697$			2.13065e11i			0.902778i
$698$	−5.61431e10	−	6.74911e10i	−0.236524	−	0.284331i
$699$	−5.28251e10	+	5.28251e10i	−0.221275	+	0.221275i
$700$	−5.95898e10	+	3.21874e11i	−0.248188	+	1.34058i
$701$	4.70381e10	−	4.70381e10i	0.194795	−	0.194795i	−0.602969	−	0.797764i	$-0.706016\pi$
$701$	4.70381e10	−	4.70381e10i	0.194795	−	0.194795i	0.797764	+	0.602969i	$0.206016\pi$
$702$	6.71226e10	+	6.16100e9i	0.276389	+	0.0253690i
$703$			7.26977e11i			2.97646i
$704$	1.60460e11	−	3.86240e10i	0.653246	−	0.157241i
$705$	2.92781e10			0.118518
$706$	−9.71009e9	+	1.05789e11i	−0.0390845	+	0.425816i
$707$	−3.49608e11	−	3.49608e11i	−1.39928	−	1.39928i
$708$	−1.15725e11	−	2.14246e10i	−0.460567	−	0.0852667i
$709$	−2.79548e11	−	2.79548e11i	−1.10630	−	1.10630i	−0.993633	−	0.112663i	$-0.964062\pi$
$709$	−2.79548e11	−	2.79548e11i	−1.10630	−	1.10630i	−0.112663	−	0.993633i	$-0.535938\pi$
$710$	2.04381e9	−	1.70016e9i	0.00804279	−	0.00669047i
$711$	5.54413e9			0.0216948
$712$	9.41471e10	+	2.65220e10i	0.366342	+	0.103202i
$713$			8.96844e10i			0.347023i
$714$	1.68734e11	−	1.40363e11i	0.649247	−	0.540082i
$715$	7.01705e10	−	7.01705e10i	0.268491	−	0.268491i
$716$	−7.21644e9	−	1.04955e10i	−0.0274581	−	0.0399349i
$717$	−1.51688e11	+	1.51688e11i	−0.573950	+	0.573950i
$718$	4.10397e10	−	4.47118e11i	0.154421	−	1.68238i
$719$		−	2.35652e11i		−	0.881771i	−0.897563	−	0.440886i	$-0.854664\pi$
$719$		−	2.35652e11i		−	0.881771i	0.897563	−	0.440886i	$-0.145336\pi$
$720$	3.20609e10	−	1.42897e10i	0.119301	−	0.0531731i
$721$	−3.46306e11			−1.28150
$722$	5.88520e11	+	5.40186e10i	2.16577	+	0.198790i
$723$	1.47977e11	+	1.47977e11i	0.541553	+	0.541553i
$724$	1.00532e11	+	1.46213e11i	0.365890	+	0.532147i
$725$	−2.54161e11	−	2.54161e11i	−0.919936	−	0.919936i
$726$	5.62663e10	+	6.76393e10i	0.202536	+	0.243474i
$727$	3.33213e11			1.19284			0.596422	−	0.802671i	$-0.296588\pi$
$727$	3.33213e11			1.19284			0.596422	+	0.802671i	$0.296588\pi$
$728$	3.18976e11	+	5.69176e11i	1.13562	+	2.02638i
$729$		−	1.04604e10i		−	0.0370370i
$730$	1.44321e10	+	1.73492e10i	0.0508203	+	0.0610925i
$731$	4.97326e10	−	4.97326e10i	0.174169	−	0.174169i
$732$	1.92168e10	+	3.55768e9i	0.0669323	+	0.0123915i
$733$	−1.19081e11	+	1.19081e11i	−0.412502	+	0.412502i	−0.882609	−	0.470107i	$-0.844215\pi$
$733$	−1.19081e11	+	1.19081e11i	−0.412502	+	0.412502i	0.470107	+	0.882609i	$0.344215\pi$
$734$	2.45400e11	+	2.25246e10i	0.845454	+	0.0776018i
$735$		−	1.05259e11i		−	0.360670i
$736$	1.15761e11	−	2.35033e11i	0.394503	−	0.800973i
$737$	−2.43189e11			−0.824280
$738$	−8.98426e9	+	9.78814e10i	−0.0302870	+	0.329970i
$739$	1.33783e11	+	1.33783e11i	0.448563	+	0.448563i	0.894877	−	0.446313i	$-0.147263\pi$
$739$	1.33783e11	+	1.33783e11i	0.448563	+	0.448563i	−0.446313	+	0.894877i	$0.647263\pi$
$740$	3.57310e10	−	1.93001e11i	0.119157	−	0.643623i
$741$	−3.16289e11	−	3.16289e11i	−1.04909	−	1.04909i
$742$	6.73468e11	−	5.60230e11i	2.22178	−	1.84821i
$743$	2.51026e11			0.823689			0.411844	−	0.911254i	$-0.364885\pi$
$743$	2.51026e11			0.823689			0.411844	+	0.911254i	$0.364885\pi$
$744$	−3.36133e10	−	5.99791e10i	−0.109703	−	0.195753i
$745$			1.64994e10i			0.0535603i
$746$	4.48544e10	−	3.73126e10i	0.144827	−	0.120476i
$747$	−8.72352e10	+	8.72352e10i	−0.280162	+	0.280162i
$748$	1.57403e11	−	1.08226e11i	0.502812	−	0.345720i
$749$	−2.99265e11	+	2.99265e11i	−0.950887	+	0.950887i
$750$	−1.20809e10	+	1.31618e11i	−0.0381815	+	0.415978i
$751$			4.97676e11i			1.56454i	0.622940	+	0.782270i	$0.285938\pi$
$751$			4.97676e11i			1.56454i	−0.622940	+	0.782270i	$0.714062\pi$
$752$	−5.99770e10	+	1.56431e11i	−0.187548	+	0.489160i
$753$	−2.69911e11			−0.839539
$754$	−7.13436e11	−	6.54843e10i	−2.20734	−	0.202606i
$755$	8.44814e10	+	8.44814e10i	0.260000	+	0.260000i
$756$	8.34345e10	−	5.73673e10i	0.255422	−	0.175621i
$757$	2.00160e11	+	2.00160e11i	0.609528	+	0.609528i	0.942823	−	0.333295i	$-0.108160\pi$
$757$	2.00160e11	+	2.00160e11i	0.609528	+	0.609528i	−0.333295	+	0.942823i	$0.608160\pi$
$758$	−1.98908e11	−	2.39112e11i	−0.602525	−	0.724311i
$759$	−1.14946e11			−0.346360
$760$	−2.24206e11	−	6.31609e10i	−0.672038	−	0.189319i
$761$		−	6.26569e11i		−	1.86823i	−0.356973	−	0.934115i	$-0.616191\pi$
$761$		−	6.26569e11i		−	1.86823i	0.356973	−	0.934115i	$-0.383809\pi$
$762$	1.36994e11	+	1.64685e11i	0.406334	+	0.488465i
$763$	1.47305e11	−	1.47305e11i	0.434630	−	0.434630i
$764$	4.28235e10	−	2.31311e11i	0.125692	−	0.678926i
$765$	2.87267e10	−	2.87267e10i	0.0838765	−	0.0838765i
$766$	1.22573e11	+	1.12506e10i	0.356025	+	0.0326785i
$767$		−	4.04927e11i		−	1.17003i
$768$	1.06709e10	+	2.00572e11i	0.0306730	+	0.576535i
$769$	2.89273e11			0.827184			0.413592	−	0.910462i	$-0.364274\pi$
$769$	2.89273e11			0.827184			0.413592	+	0.910462i	$0.364274\pi$
$770$	1.36254e10	−	1.48446e11i	0.0387603	−	0.422285i
$771$	7.86169e10	+	7.86169e10i	0.222484	+	0.222484i
$772$	−1.87253e11	−	3.46669e10i	−0.527181	−	0.0975991i
$773$	1.41044e11	+	1.41044e11i	0.395035	+	0.395035i	0.876478	−	0.481443i	$-0.159887\pi$
$773$	1.41044e11	+	1.41044e11i	0.395035	+	0.395035i	−0.481443	+	0.876478i	$0.659887\pi$
$774$	2.49441e10	−	2.07499e10i	0.0695029	−	0.0578166i
$775$	1.18683e11			0.328990
$776$	4.37922e10	−	1.55452e11i	0.120767	−	0.428696i
$777$		−	5.66194e11i		−	1.55339i
$778$	−3.39992e11	+	2.82826e11i	−0.928006	+	0.771970i
$779$	4.61228e11	−	4.61228e11i	1.25247	−	1.25247i
$780$	6.84240e10	+	9.95153e10i	0.184855	+	0.268851i
$781$	4.71942e9	−	4.71942e9i	0.0126848	−	0.0126848i
$782$	2.77161e10	−	3.01960e11i	0.0741148	−	0.807463i
$783$			1.11181e11i			0.295791i
$784$	5.62392e11	+	2.15626e11i	1.48859	+	0.570739i
$785$	2.04520e11			0.538588
$786$	−2.43759e10	−	2.23740e9i	−0.0638662	−	0.00586210i
$787$	1.06170e11	+	1.06170e11i	0.276759	+	0.276759i	0.831814	−	0.555055i	$-0.187303\pi$
$787$	1.06170e11	+	1.06170e11i	0.276759	+	0.276759i	−0.555055	+	0.831814i	$0.687303\pi$
$788$	2.63836e11	+	3.83721e11i	0.684274	+	0.995202i
$789$	−1.70467e11	−	1.70467e11i	−0.439879	−	0.439879i
$790$	6.35256e9	+	7.63659e9i	0.0163095	+	0.0196061i
$791$	−1.13528e12			−2.89999
$792$	7.68738e10	−	4.30814e10i	0.195379	−	0.109494i
$793$			6.72406e10i			0.170035i
$794$	6.38448e10	+	7.67496e10i	0.160636	+	0.193105i
$795$	1.14657e11	−	1.14657e11i	0.287033	−	0.287033i
$796$	−5.76427e11	−	1.06716e11i	−1.43579	−	0.265814i
$797$	−2.14746e11	+	2.14746e11i	−0.532220	+	0.532220i	−0.921232	−	0.389013i	$-0.872816\pi$
$797$	−2.14746e11	+	2.14746e11i	−0.532220	+	0.532220i	0.389013	+	0.921232i	$0.372816\pi$
$798$	−6.69112e11	−	6.14159e10i	−1.65001	−	0.151450i
$799$			1.93902e11i			0.475769i
$800$	−3.11030e11	−	1.53192e11i	−0.759350	−	0.374003i
$801$	5.22251e10			0.126867
$802$	−3.89869e10	+	4.24753e11i	−0.0942369	+	1.02669i
$803$	4.00615e10	+	4.00615e10i	0.0963531	+	0.0963531i
$804$	5.38765e10	−	2.91013e11i	0.128936	−	0.696448i
$805$	−1.67328e11	−	1.67328e11i	−0.398461	−	0.398461i
$806$	1.81862e11	−	1.51284e11i	0.430926	−	0.358470i
$807$	−3.93835e11			−0.928583
$808$	4.56825e11	−	2.56013e11i	1.07178	−	0.600642i
$809$			3.41325e11i			0.796845i	0.917202	+	0.398423i	$0.130442\pi$
$809$			3.41325e11i			0.796845i	−0.917202	+	0.398423i	$0.869558\pi$
$810$	1.44083e10	−	1.19857e10i	0.0334713	−	0.0278434i
$811$	1.36819e11	−	1.36819e11i	0.316274	−	0.316274i	−0.531060	−	0.847334i	$-0.678206\pi$
$811$	1.36819e11	−	1.36819e11i	0.316274	−	0.316274i	0.847334	+	0.531060i	$0.178206\pi$
$812$	−8.86813e11	+	6.09748e11i	−2.03989	+	1.40258i
$813$	7.99198e10	−	7.99198e10i	0.182933	−	0.182933i
$814$	4.50403e10	−	4.90704e11i	0.102590	−	1.11769i
$815$			5.15884e10i			0.116929i
$816$	9.46374e10	+	2.12333e11i	0.213453	+	0.478912i
$817$	−2.15315e11			−0.483266
$818$	1.67867e11	+	1.54080e10i	0.374931	+	0.0344139i
$819$	2.46337e11	+	2.46337e11i	0.547512	+	0.547512i
$820$	−1.45118e11	+	9.97791e10i	−0.320971	+	0.220691i
$821$	−3.03338e11	−	3.03338e11i	−0.667658	−	0.667658i	0.289516	−	0.957173i	$-0.406506\pi$
$821$	−3.03338e11	−	3.03338e11i	−0.667658	−	0.667658i	−0.957173	+	0.289516i	$0.906506\pi$
$822$	2.18720e10	+	2.62930e10i	0.0479073	+	0.0575907i
$823$	2.56016e11			0.558043			0.279021	−	0.960285i	$-0.409990\pi$
$823$	2.56016e11			0.558043			0.279021	+	0.960285i	$0.409990\pi$
$824$	9.94576e10	−	3.53052e11i	0.215739	−	0.765825i
$825$			1.52114e11i			0.328362i
$826$	−3.88999e11	−	4.67626e11i	−0.835657	−	1.00457i
$827$	4.08888e11	−	4.08888e11i	0.874142	−	0.874142i	−0.118779	−	0.992921i	$-0.537898\pi$
$827$	4.08888e11	−	4.08888e11i	0.874142	−	0.874142i	0.992921	+	0.118779i	$0.0378979\pi$
$828$	2.54654e10	−	1.37551e11i	0.0541787	−	0.292646i
$829$	1.38500e11	−	1.38500e11i	0.293246	−	0.293246i	−0.545115	−	0.838361i	$-0.683514\pi$
$829$	1.38500e11	−	1.38500e11i	0.293246	−	0.293246i	0.838361	+	0.545115i	$0.183514\pi$
$830$	−2.20115e11	−	2.02037e10i	−0.463807	−	0.0425715i
$831$			9.46655e10i			0.198512i
$832$	−6.71873e11	+	1.61725e11i	−1.40215	+	0.337507i
$833$	6.97108e11			1.44784
$834$	3.25570e10	−	3.54700e11i	0.0672945	−	0.733158i
$835$	−9.17353e10	−	9.17353e10i	−0.188708	−	0.188708i
$836$	−5.75014e11	−	1.06455e11i	−1.17721	−	0.217941i
$837$	−2.59587e10	−	2.59587e10i	−0.0528908	−	0.0528908i
$838$	3.30174e11	−	2.74658e11i	0.669525	−	0.556951i
$839$	−6.59943e10			−0.133186			−0.0665930	−	0.997780i	$-0.521213\pi$
$839$	−6.59943e10			−0.133186			−0.0665930	+	0.997780i	$0.521213\pi$
$840$	1.74620e11	+	4.91918e10i	0.350732	+	0.0988043i
$841$		−	6.81484e11i		−	1.36230i
$842$	6.51249e11	−	5.41747e11i	1.29568	−	1.07783i
$843$	3.79414e11	−	3.79414e11i	0.751283	−	0.751283i
$844$	3.72971e11	+	5.42446e11i	0.735031	+	1.06902i
$845$	−1.52553e11	+	1.52553e11i	−0.299222	+	0.299222i
$846$	−8.17624e9	+	8.90782e10i	−0.0159614	+	0.173896i
$847$			4.54728e11i			0.883523i
$848$	3.77726e11	+	8.47483e11i	0.730455	+	1.63888i
$849$	4.80400e11			0.924639
$850$	−3.99597e11	−	3.66779e10i	−0.765503	−	0.0702634i
$851$	−5.53122e11	−	5.53122e11i	−1.05464	−	1.05464i
$852$	4.60196e9	+	6.69306e9i	0.00873343	+	0.0127018i
$853$	2.30642e11	+	2.30642e11i	0.435655	+	0.435655i	0.890547	−	0.454892i	$-0.150322\pi$
$853$	2.30642e11	+	2.30642e11i	0.435655	+	0.435655i	−0.454892	+	0.890547i	$0.650322\pi$
$854$	6.45956e10	+	7.76521e10i	0.121443	+	0.145990i
$855$	−1.24371e11			−0.232732
$856$	−2.19147e11	−	3.91043e11i	−0.408170	−	0.728331i
$857$			8.61467e11i			1.59704i	0.601969	+	0.798520i	$0.294383\pi$
$857$			8.61467e11i			1.59704i	−0.601969	+	0.798520i	$0.705617\pi$
$858$	1.93897e11	+	2.33089e11i	0.357785	+	0.430103i
$859$	−4.77315e11	+	4.77315e11i	−0.876663	+	0.876663i	−0.993188	−	0.116524i	$-0.962825\pi$
$859$	−4.77315e11	+	4.77315e11i	−0.876663	+	0.876663i	0.116524	+	0.993188i	$0.462825\pi$
$860$	5.71627e10	+	1.05828e10i	0.104501	+	0.0193466i
$861$	−3.59220e11	+	3.59220e11i	−0.653654	+	0.653654i
$862$	9.66947e10	+	8.87534e9i	0.175135	+	0.0160752i
$863$			9.62404e11i			1.73506i	0.497386	+	0.867529i	$0.334293\pi$
$863$			9.62404e11i			1.73506i	−0.497386	+	0.867529i	$0.665707\pi$
$864$	3.45227e10	+	1.01536e11i	0.0619513	+	0.182206i
$865$	1.53470e10			0.0274131
$866$	−7.06152e10	+	7.69336e11i	−0.125553	+	1.36787i
$867$	−4.04240e10	−	4.04240e10i	−0.0715422	−	0.0715422i
$868$	6.46891e10	−	3.49417e11i	0.113960	−	0.615553i
$869$	1.76339e10	+	1.76339e10i	0.0309221	+	0.0309221i
$870$	−1.53143e11	+	1.27394e11i	−0.267314	+	0.222367i
$871$	1.01827e12			1.76926
$872$	1.07869e11	+	1.92480e11i	0.186566	+	0.332905i
$873$		−	8.62320e10i		−	0.148461i
$874$	−7.13660e11	+	5.93665e11i	−1.22305	+	1.01741i
$875$	−4.83032e11	+	4.83032e11i	−0.824032	+	0.824032i
$876$	−5.68151e10	+	3.90645e10i	−0.0964822	+	0.0663385i
$877$	6.96107e11	−	6.96107e11i	1.17673	−	1.17673i	0.196161	−	0.980572i	$-0.437152\pi$
$877$	6.96107e11	−	6.96107e11i	1.17673	−	1.17673i	0.980572	−	0.196161i	$-0.0628475\pi$
$878$	−2.42384e10	+	2.64071e11i	−0.0407873	+	0.444368i
$879$		−	3.70941e11i		−	0.621368i
$880$	1.47424e11	+	5.65239e10i	0.245832	+	0.0942544i
$881$	4.26700e11			0.708302			0.354151	−	0.935188i	$-0.384770\pi$
$881$	4.26700e11			0.708302			0.354151	+	0.935188i	$0.384770\pi$
$882$	3.20249e11	+	2.93948e10i	0.529193	+	0.0485731i
$883$	3.44479e11	+	3.44479e11i	0.566656	+	0.566656i	0.931190	−	0.364534i	$-0.118772\pi$
$883$	3.44479e11	+	3.44479e11i	0.566656	+	0.566656i	−0.364534	+	0.931190i	$0.618772\pi$
$884$	−6.59069e11	+	4.53158e11i	−1.07925	+	0.742063i
$885$	−7.96127e10	−	7.96127e10i	−0.129780	−	0.129780i
$886$	−2.49859e11	−	3.00363e11i	−0.405472	−	0.487429i
$887$	4.99880e11			0.807554			0.403777	−	0.914857i	$-0.367697\pi$
$887$	4.99880e11			0.807554			0.403777	+	0.914857i	$0.367697\pi$
$888$	5.77224e11	+	1.62609e11i	0.928309	+	0.261512i
$889$			1.10715e12i			1.77255i
$890$	5.98404e10	+	7.19358e10i	0.0953750	+	0.114653i
$891$	3.32706e10	−	3.32706e10i	0.0527898	−	0.0527898i
$892$	1.39483e11	−	7.53417e11i	0.220324	−	1.19008i
$893$	4.19747e11	−	4.19747e11i	0.660057	−	0.660057i
$894$	−5.01993e10	−	4.60765e9i	−0.0785864	−	0.00721323i
$895$		−	1.21849e10i		−	0.0189903i
$896$	−6.20542e11	+	8.32210e11i	−0.962807	+	1.29122i
$897$	4.81299e11			0.743438
$898$	−3.16934e10	+	3.45292e11i	−0.0487375	+	0.530983i
$899$	2.75911e11	+	2.75911e11i	0.422405	+	0.422405i
$900$	−1.82027e11	−	3.36995e10i	−0.277438	−	0.0513633i
$901$	7.59349e11	+	7.59349e11i	1.15224	+	1.15224i
$902$	−3.39901e11	+	2.82750e11i	−0.513483	+	0.427146i
$903$	1.67695e11			0.252214
$904$	3.26047e11	−	1.15739e12i	0.488210	−	1.73303i
$905$			1.69748e11i			0.253052i
$906$	−2.80626e11	+	2.33441e11i	−0.416500	+	0.346469i
$907$	5.89250e11	−	5.89250e11i	0.870704	−	0.870704i	−0.121845	−	0.992549i	$-0.538881\pi$
$907$	5.89250e11	−	5.89250e11i	0.870704	−	0.870704i	0.992549	+	0.121845i	$0.0388811\pi$
$908$	−2.60486e11	−	3.78848e11i	−0.383213	−	0.557342i
$909$	1.97712e11	−	1.97712e11i	0.289586	−	0.289586i
$910$	−5.70518e10	+	6.21566e11i	−0.0831963	+	0.906404i
$911$		−	5.37608e11i		−	0.780534i	−0.920702	−	0.390267i	$-0.872383\pi$
$911$		−	5.37608e11i		−	0.780534i	0.920702	−	0.390267i	$-0.127617\pi$
$912$	2.54778e11	−	6.64507e11i	0.368284	−	0.960551i
$913$	−5.54927e11			−0.798643
$914$	−1.04458e12	−	9.58795e10i	−1.49678	−	0.137386i
$915$	1.32202e10	+	1.32202e10i	0.0188605	+	0.0188605i
$916$	−2.66030e11	−	3.86912e11i	−0.377875	−	0.549579i
$917$	−8.94585e10	−	8.94585e10i	−0.126516	−	0.126516i
$918$	7.93785e10	+	9.54231e10i	0.111772	+	0.134364i
$919$	1.59541e11			0.223671			0.111836	−	0.993727i	$-0.464327\pi$
$919$	1.59541e11			0.223671			0.111836	+	0.993727i	$0.464327\pi$
$920$	2.18644e11	−	1.22532e11i	0.305201	−	0.171040i
$921$			3.22712e11i			0.448514i
$922$	−3.90029e10	−	4.68864e10i	−0.0539725	−	0.0648819i
$923$	−1.97610e10	+	1.97610e10i	−0.0272271	+	0.0272271i
$924$	4.47840e11	+	8.29105e10i	0.614377	+	0.113742i
$925$	−7.31970e11	+	7.31970e11i	−0.999831	+	0.999831i
$926$	−1.04846e11	−	9.62348e9i	−0.142596	−	0.0130884i
$927$		−	1.95844e11i		−	0.265211i
$928$	−3.66937e11	−	1.07920e12i	−0.494766	−	1.45516i
$929$	−1.04182e12			−1.39872			−0.699361	−	0.714769i	$-0.746532\pi$
$929$	−1.04182e12			−1.39872			−0.699361	+	0.714769i	$0.746532\pi$
$930$	6.01205e9	−	6.54998e10i	0.00803694	−	0.0875605i
$931$	−1.50905e12	−	1.50905e12i	−2.00865	−	2.00865i
$932$	7.44457e10	−	4.02118e11i	0.0986680	−	0.532954i
$933$	−1.94125e11	−	1.94125e11i	−0.256186	−	0.256186i
$934$	1.81564e11	−	1.51036e11i	0.238584	−	0.198469i
$935$	1.82739e11			0.239103
$936$	−3.21883e11	+	1.80389e11i	−0.419367	+	0.235020i
$937$			1.74717e11i			0.226660i	0.993557	+	0.113330i	$0.0361518\pi$
$937$			1.74717e11i			0.226660i	−0.993557	+	0.113330i	$0.963848\pi$
$938$	1.17594e12	−	9.78218e11i	1.51906	−	1.26364i
$939$	−4.11343e11	+	4.11343e11i	−0.529105	+	0.529105i
$940$	−1.32066e11	+	9.08053e10i	−0.169154	+	0.116305i
$941$	−4.95802e11	+	4.95802e11i	−0.632339	+	0.632339i	−0.948654	−	0.316315i	$-0.897554\pi$
$941$	−4.95802e11	+	4.95802e11i	−0.632339	+	0.632339i	0.316315	+	0.948654i	$0.397554\pi$
$942$	−5.71145e10	+	6.22249e11i	−0.0725342	+	0.790243i
$943$			7.01852e11i			0.887563i
$944$	5.88455e11	−	2.62276e11i	0.741011	−	0.330271i
$945$	9.68646e10			0.121461
$946$	1.45336e11	+	1.33400e10i	0.181472	+	0.0166568i
$947$	2.80233e11	+	2.80233e11i	0.348433	+	0.348433i	0.859526	−	0.511092i	$-0.170759\pi$
$947$	2.80233e11	+	2.80233e11i	0.348433	+	0.348433i	−0.511092	+	0.859526i	$0.670759\pi$
$948$	−2.50083e10	+	1.71950e10i	−0.0309635	+	0.0212897i
$949$	−1.67744e11	−	1.67744e11i	−0.206815	−	0.206815i
$950$	7.85623e11	+	9.44418e11i	0.964539	+	1.15950i
$951$	−2.61370e11			−0.319547
$952$	−3.25787e11	+	1.15647e12i	−0.396630	+	1.40795i
$953$		−	1.28443e12i		−	1.55718i	−0.627531	−	0.778592i	$-0.715934\pi$
$953$		−	1.28443e12i		−	1.55718i	0.627531	−	0.778592i	$-0.284066\pi$
$954$	3.16823e11	+	3.80862e11i	0.382493	+	0.459805i
$955$	1.59130e11	−	1.59130e11i	0.191311	−	0.191311i
$956$	2.13771e11	−	1.15468e12i	0.255928	−	1.38239i
$957$	−3.53628e11	+	3.53628e11i	−0.421598	+	0.421598i
$958$	−1.01761e12	−	9.34036e10i	−1.20815	−	0.110892i
$959$			1.76763e11i			0.208986i
$960$	−1.00300e11	+	1.63893e11i	−0.118091	+	0.192964i
$961$	7.24052e11			0.848938
$962$	−1.88591e11	+	2.05465e12i	−0.220202	+	2.39905i
$963$	−1.69241e11	−	1.69241e11i	−0.196789	−	0.196789i
$964$	−1.12644e12	−	2.08542e11i	−1.30436	−	0.241482i
$965$	−1.28821e11	−	1.28821e11i	−0.148551	−	0.148551i
$966$	5.55823e11	−	4.62366e11i	0.638304	−	0.530979i
$967$	−8.73470e11			−0.998947			−0.499473	−	0.866329i	$-0.666473\pi$
$967$	−8.73470e11			−0.998947			−0.499473	+	0.866329i	$0.666473\pi$
$968$	−4.63586e11	−	1.30596e11i	−0.527994	−	0.148740i
$969$		−	8.23685e11i		−	0.934256i
$970$	1.18778e11	−	9.88062e10i	0.134168	−	0.111608i
$971$	−6.07187e11	+	6.07187e11i	−0.683039	+	0.683039i	−0.960684	−	0.277645i	$-0.910446\pi$
$971$	−6.07187e11	+	6.07187e11i	−0.683039	+	0.683039i	0.277645	+	0.960684i	$0.410446\pi$
$972$	3.24426e10	+	4.71842e10i	0.0363454	+	0.0528605i
$973$	1.30173e12	−	1.30173e12i	1.45235	−	1.45235i
$974$	7.43197e10	−	8.09695e11i	0.0825787	−	0.899675i
$975$		−	6.36924e11i		−	0.704805i
$976$	−9.77163e10	+	4.35525e10i	−0.107688	+	0.0479970i
$977$	1.65874e12			1.82054			0.910269	−	0.414017i	$-0.135874\pi$
$977$	1.65874e12			1.82054			0.910269	+	0.414017i	$0.135874\pi$
$978$	−1.56957e11	−	1.44067e10i	−0.171564	−	0.0157474i
$979$	1.66109e11	+	1.66109e11i	0.180827	+	0.180827i
$980$	3.26458e11	+	4.74798e11i	0.353935	+	0.514760i
$981$	8.33046e10	+	8.33046e10i	0.0899483	+	0.0899483i
$982$	5.77154e11	+	6.93812e11i	0.620648	+	0.746098i
$983$	−1.55806e12			−1.66867			−0.834336	−	0.551256i	$-0.814149\pi$
$983$	−1.55806e12			−1.66867			−0.834336	+	0.551256i	$0.814149\pi$
$984$	−2.63051e11	−	4.69384e11i	−0.280582	−	0.500666i
$985$			4.45487e11i			0.473250i
$986$	−8.43702e11	−	1.01424e12i	−0.892650	−	1.07308i
$987$	−3.26913e11	+	3.26913e11i	−0.344479	+	0.344479i
$988$	2.40767e12	+	4.45742e11i	2.52679	+	0.467796i
$989$	1.63823e11	−	1.63823e11i	0.171234	−	0.171234i
$990$	8.39496e10	+	7.70550e9i	0.0873933	+	0.00802158i
$991$			9.44756e11i			0.979546i	0.871850	+	0.489773i	$0.162920\pi$
$991$			9.44756e11i			0.979546i	−0.871850	+	0.489773i	$0.837080\pi$
$992$	3.37645e11	+	1.66300e11i	0.348670	+	0.171730i
$993$	−5.74980e10			−0.0591365
$994$	−3.83711e9	+	4.18044e10i	−0.00393060	+	0.0428229i
$995$	−3.96552e11	−	3.96552e11i	−0.404584	−	0.404584i
$996$	1.22939e11	−	6.64055e11i	0.124926	−	0.674787i
$997$	−1.69255e11	−	1.69255e11i	−0.171302	−	0.171302i	0.616249	−	0.787551i	$-0.288651\pi$
$997$	−1.69255e11	−	1.69255e11i	−0.171302	−	0.171302i	−0.787551	+	0.616249i	$0.788651\pi$
$998$	−1.27144e12	+	1.05766e12i	−1.28166	+	1.06616i
$999$	3.20196e11			0.321480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.43.18	yes	64
4.3	odd	2		192.9.l.a.79.8		64
16.3	odd	4	inner	48.9.l.a.19.18	✓	64
16.13	even	4		192.9.l.a.175.8		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.18	✓	64	16.3	odd	4	inner
48.9.l.a.43.18	yes	64	1.1	even	1	trivial
192.9.l.a.79.8		64	4.3	odd	2
192.9.l.a.175.8		64	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.46245 - 15.9330i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-251.722 - 46.6024i) q^{4} +(-173.172 - 173.172i) q^{5} +(575.235 - 478.515i) q^{6} +3867.21 q^{7} +(-1110.65 + 3942.55i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(1.46245 - 15.9330i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-251.722 - 46.6024i) q^{4} +(-173.172 - 173.172i) q^{5} +(575.235 - 478.515i) q^{6} +3867.21 q^{7} +(-1110.65 + 3942.55i) q^{8} +2187.00i q^{9} +(-3012.41 + 2505.90i) q^{10} +(-6956.06 + 6956.06i) q^{11} +(-6782.93 - 9865.04i) q^{12} +(29126.1 - 29126.1i) q^{13} +(5655.60 - 61616.4i) q^{14} -11453.0i q^{15} +(61192.4 + 23461.8i) q^{16} +75850.6 q^{17} +(34845.5 + 3198.37i) q^{18} +(-164196. - 164196. i) q^{19} +(35521.1 + 51661.6i) q^{20} +(127881. + 127881. i) q^{21} +(100658. + 121004. i) q^{22} +249858. q^{23} +(-167100. + 93645.5i) q^{24} -330648. i q^{25} +(-421472. - 506662. i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(-973465. - 180222. i) q^{28} +(768677. - 768677. i) q^{29} +(-182480. - 16749.4i) q^{30} +358942. i q^{31} +(463308. - 940669. i) q^{32} -460047. q^{33} +(110928. - 1.20853e6i) q^{34} +(-669694. - 669694. i) q^{35} +(101920. - 550517. i) q^{36} +(-2.21375e6 - 2.21375e6i) q^{37} +(-2.85627e6 + 2.37601e6i) q^{38} +1.92629e6 q^{39} +(875074. - 490406. i) q^{40} +2.80901e6i q^{41} +(2.22456e6 - 1.85052e6i) q^{42} +(655665. - 655665. i) q^{43} +(2.07517e6 - 1.42683e6i) q^{44} +(378728. - 378728. i) q^{45} +(365404. - 3.98099e6i) q^{46} +2.55637e6i q^{47} +(1.24768e6 + 2.79935e6i) q^{48} +9.19054e6 q^{49} +(-5.26822e6 - 483555. i) q^{50} +(2.50824e6 + 2.50824e6i) q^{51} +(-8.68905e6 + 5.97435e6i) q^{52} +(1.00111e7 + 1.00111e7i) q^{53} +(1.04651e6 + 1.25804e6i) q^{54} +2.40919e6 q^{55} +(-4.29512e6 + 1.52467e7i) q^{56} -1.08593e7i q^{57} +(-1.11232e7 - 1.33715e7i) q^{58} +(6.95128e6 - 6.95128e6i) q^{59} +(-533736. + 2.88297e6i) q^{60} +(-1.15430e6 + 1.15430e6i) q^{61} +(5.71903e6 + 524934. i) q^{62} +8.45760e6i q^{63} +(-1.43101e7 - 8.75757e6i) q^{64} -1.00877e7 q^{65} +(-672795. + 7.32995e6i) q^{66} +(1.74804e7 + 1.74804e7i) q^{67} +(-1.90933e7 - 3.53482e6i) q^{68} +(8.26232e6 + 8.26232e6i) q^{69} +(-1.16497e7 + 9.69086e6i) q^{70} -678462. q^{71} +(-8.62235e6 - 2.42899e6i) q^{72} -5.75923e6i q^{73} +(-3.85092e7 + 3.20342e7i) q^{74} +(1.09339e7 - 1.09339e7i) q^{75} +(3.36799e7 + 4.89838e7i) q^{76} +(-2.69006e7 + 2.69006e7i) q^{77} +(2.81710e6 - 3.06916e7i) q^{78} -2.53504e6i q^{79} +(-6.53391e6 - 1.46598e7i) q^{80} -4.78297e6 q^{81} +(4.47560e7 + 4.10803e6i) q^{82} +(3.98881e7 + 3.98881e7i) q^{83} +(-2.62311e7 - 3.81502e7i) q^{84} +(-1.31352e7 - 1.31352e7i) q^{85} +(-9.48785e6 - 1.14056e7i) q^{86} +5.08374e7 q^{87} +(-1.96989e7 - 3.51503e7i) q^{88} -2.38798e7i q^{89} +(-5.48041e6 - 6.58815e6i) q^{90} +(1.12637e8 - 1.12637e8i) q^{91} +(-6.28948e7 - 1.16440e7i) q^{92} +(-1.18695e7 + 1.18695e7i) q^{93} +(4.07308e7 + 3.73856e6i) q^{94} +5.68684e7i q^{95} +(4.64268e7 - 1.57854e7i) q^{96} -3.94294e7 q^{97} +(1.34407e7 - 1.46433e8i) q^{98} +(-1.52129e7 - 1.52129e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) \) 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Introduction

L-functions

Modular forms

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