LMFDB - Embedded newform 33.9.b.a.23.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,9,Mod(23,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("33.23");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	33.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.4434941320$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.18
Character	$\chi$	$=$	33.23
Dual form			33.9.b.a.23.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+12.0893i q^{2} +(-77.6992 + 22.8875i) q^{3} +109.849 q^{4} -288.931i q^{5} +(-276.694 - 939.329i) q^{6} +3024.09 q^{7} +4422.86i q^{8} +(5513.32 - 3556.68i) q^{9} +O(q^{10})$	\(q+12.0893i q^{2} +(-77.6992 + 22.8875i) q^{3} +109.849 q^{4} -288.931i q^{5} +(-276.694 - 939.329i) q^{6} +3024.09 q^{7} +4422.86i q^{8} +(5513.32 - 3556.68i) q^{9} +3492.97 q^{10} +4414.43i q^{11} +(-8535.16 + 2514.17i) q^{12} -9096.59 q^{13} +36559.2i q^{14} +(6612.91 + 22449.7i) q^{15} -25347.9 q^{16} +107300. i q^{17} +(42997.8 + 66652.2i) q^{18} -55815.2 q^{19} -31738.7i q^{20} +(-234970. + 69214.0i) q^{21} -53367.3 q^{22} +145256. i q^{23} +(-101228. - 343652. i) q^{24} +307144. q^{25} -109971. i q^{26} +(-346977. + 402537. i) q^{27} +332193. q^{28} +1.02612e6i q^{29} +(-271401. + 79945.4i) q^{30} +304251. q^{31} +825812. i q^{32} +(-101035. - 342997. i) q^{33} -1.29718e6 q^{34} -873754. i q^{35} +(605632. - 390697. i) q^{36} +2.96195e6 q^{37} -674767. i q^{38} +(706798. - 208198. i) q^{39} +1.27790e6 q^{40} -2.62933e6i q^{41} +(-836749. - 2.84062e6i) q^{42} -1.66848e6 q^{43} +484920. i q^{44} +(-1.02763e6 - 1.59297e6i) q^{45} -1.75605e6 q^{46} -4.65098e6i q^{47} +(1.96951e6 - 580151. i) q^{48} +3.38035e6 q^{49} +3.71316e6i q^{50} +(-2.45582e6 - 8.33709e6i) q^{51} -999250. q^{52} +4.33867e6i q^{53} +(-4.86640e6 - 4.19471e6i) q^{54} +1.27546e6 q^{55} +1.33751e7i q^{56} +(4.33680e6 - 1.27747e6i) q^{57} -1.24050e7 q^{58} +1.79174e7i q^{59} +(726420. + 2.46607e6i) q^{60} +1.96177e6 q^{61} +3.67818e6i q^{62} +(1.66728e7 - 1.07557e7i) q^{63} -1.64726e7 q^{64} +2.62829e6i q^{65} +(4.14660e6 - 1.22145e6i) q^{66} +2.34416e7 q^{67} +1.17867e7i q^{68} +(-3.32456e6 - 1.12863e7i) q^{69} +1.05631e7 q^{70} -2.05631e7i q^{71} +(1.57307e7 + 2.43846e7i) q^{72} -1.67837e7 q^{73} +3.58079e7i q^{74} +(-2.38648e7 + 7.02976e6i) q^{75} -6.13124e6 q^{76} +1.33496e7i q^{77} +(2.51697e6 + 8.54469e6i) q^{78} -7.34684e7 q^{79} +7.32380e6i q^{80} +(1.77468e7 - 3.92183e7i) q^{81} +3.17868e7 q^{82} +5.71837e7i q^{83} +(-2.58111e7 + 7.60307e6i) q^{84} +3.10022e7 q^{85} -2.01707e7i q^{86} +(-2.34853e7 - 7.97285e7i) q^{87} -1.95244e7 q^{88} -8.04561e7i q^{89} +(1.92579e7 - 1.24234e7i) q^{90} -2.75089e7 q^{91} +1.59563e7i q^{92} +(-2.36401e7 + 6.96355e6i) q^{93} +5.62271e7 q^{94} +1.61267e7i q^{95} +(-1.89008e7 - 6.41649e7i) q^{96} +3.68114e7 q^{97} +4.08660e7i q^{98} +(1.57007e7 + 2.43382e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9}+O(q^{10}) $ 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9} - 31836 q^{10} - 28900 q^{12} - 131624 q^{13} + 71041 q^{15} + 311972 q^{16} - 675394 q^{18} + 134608 q^{19} + 490306 q^{21} - 59088 q^{24} - 2324740 q^{25} + 2011426 q^{27} - 1996688 q^{28} - 324146 q^{30} + 964738 q^{31} - 512435 q^{33} + 9219648 q^{34} - 6887660 q^{36} - 5721542 q^{37} - 5782712 q^{39} + 8363496 q^{40} + 10350076 q^{42} + 4260820 q^{43} + 6595181 q^{45} - 39680292 q^{46} + 22674164 q^{48} + 20017254 q^{49} - 7985018 q^{51} + 48711952 q^{52} - 18774176 q^{54} - 4304454 q^{55} + 15476796 q^{57} - 16060008 q^{58} - 26730016 q^{60} + 58840 q^{61} - 42877282 q^{63} - 57365836 q^{64} - 10395110 q^{66} - 63186734 q^{67} + 100738079 q^{69} + 50969160 q^{70} + 48890880 q^{72} - 21879656 q^{73} - 122009926 q^{75} - 119289368 q^{76} - 123440744 q^{78} + 117211444 q^{79} + 138667019 q^{81} + 121755480 q^{82} - 28504816 q^{84} + 28880604 q^{85} + 14774868 q^{87} + 90481380 q^{88} + 189044834 q^{90} + 192183008 q^{91} - 113622071 q^{93} - 453996696 q^{94} + 11988416 q^{96} + 24314206 q^{97} - 57905155 q^{99}+O(q^{100}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9 - 31836 * q^10 - 28900 * q^12 - 131624 * q^13 + 71041 * q^15 + 311972 * q^16 - 675394 * q^18 + 134608 * q^19 + 490306 * q^21 - 59088 * q^24 - 2324740 * q^25 + 2011426 * q^27 - 1996688 * q^28 - 324146 * q^30 + 964738 * q^31 - 512435 * q^33 + 9219648 * q^34 - 6887660 * q^36 - 5721542 * q^37 - 5782712 * q^39 + 8363496 * q^40 + 10350076 * q^42 + 4260820 * q^43 + 6595181 * q^45 - 39680292 * q^46 + 22674164 * q^48 + 20017254 * q^49 - 7985018 * q^51 + 48711952 * q^52 - 18774176 * q^54 - 4304454 * q^55 + 15476796 * q^57 - 16060008 * q^58 - 26730016 * q^60 + 58840 * q^61 - 42877282 * q^63 - 57365836 * q^64 - 10395110 * q^66 - 63186734 * q^67 + 100738079 * q^69 + 50969160 * q^70 + 48890880 * q^72 - 21879656 * q^73 - 122009926 * q^75 - 119289368 * q^76 - 123440744 * q^78 + 117211444 * q^79 + 138667019 * q^81 + 121755480 * q^82 - 28504816 * q^84 + 28880604 * q^85 + 14774868 * q^87 + 90481380 * q^88 + 189044834 * q^90 + 192183008 * q^91 - 113622071 * q^93 - 453996696 * q^94 + 11988416 * q^96 + 24314206 * q^97 - 57905155 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$			12.0893i			0.755581i	0.925891	+	0.377791i	$0.123316\pi$
$2$			12.0893i			0.755581i	−0.925891	+	0.377791i	$0.876684\pi$
$3$	−77.6992	+	22.8875i	−0.959249	+	0.282562i
$3$	−77.6992	+	22.8875i	−0.959249	+	0.282562i
$4$	109.849			0.429097
$5$		−	288.931i		−	0.462289i	−0.972919	−	0.231145i	$-0.925753\pi$
$5$		−	288.931i		−	0.462289i	0.972919	−	0.231145i	$-0.0742471\pi$
$6$	−276.694	−	939.329i	−0.213498	−	0.724791i
$7$	3024.09			1.25951			0.629757	−	0.776792i	$-0.283154\pi$
$7$	3024.09			1.25951			0.629757	+	0.776792i	$0.283154\pi$
$8$			4422.86i			1.07980i
$9$	5513.32	−	3556.68i	0.840318	−	0.542094i
$10$	3492.97			0.349297
$11$			4414.43i			0.301511i
$11$			4414.43i			0.301511i
$12$	−8535.16	+	2514.17i	−0.411611	+	0.121246i
$13$	−9096.59			−0.318497			−0.159248	−	0.987239i	$-0.550907\pi$
$13$	−9096.59			−0.318497			−0.159248	+	0.987239i	$0.550907\pi$
$14$			36559.2i			0.951666i
$15$	6612.91	+	22449.7i	0.130625	+	0.443451i
$16$	−25347.9			−0.386779
$17$			107300.i			1.28470i	0.766411	+	0.642351i	$0.222041\pi$
$17$			107300.i			1.28470i	−0.766411	+	0.642351i	$0.777959\pi$
$18$	42997.8	+	66652.2i	0.409596	+	0.634928i
$19$	−55815.2			−0.428290			−0.214145	−	0.976802i	$-0.568697\pi$
$19$	−55815.2			−0.428290			−0.214145	+	0.976802i	$0.568697\pi$
$20$		−	31738.7i		−	0.198367i
$21$	−234970.	+	69214.0i	−1.20819	+	0.355891i
$22$	−53367.3			−0.227816
$23$			145256.i			0.519068i	0.965734	+	0.259534i	$0.0835689\pi$
$23$			145256.i			0.519068i	−0.965734	+	0.259534i	$0.916431\pi$
$24$	−101228.	−	343652.i	−0.305110	−	1.03580i
$25$	307144.			0.786288
$26$		−	109971.i		−	0.240650i
$27$	−346977.	+	402537.i	−0.652899	+	0.757445i
$28$	332193.			0.540454
$29$			1.02612e6i			1.45079i	0.688331	+	0.725396i	$0.258343\pi$
$29$			1.02612e6i			1.45079i	−0.688331	+	0.725396i	$0.741657\pi$
$30$	−271401.	+	79945.4i	−0.335063	+	0.0986981i
$31$	304251.			0.329447			0.164723	−	0.986340i	$-0.447327\pi$
$31$	304251.			0.329447			0.164723	+	0.986340i	$0.447327\pi$
$32$			825812.i			0.787556i
$33$	−101035.	−	342997.i	−0.0851956	−	0.289224i
$34$	−1.29718e6			−0.970697
$35$		−	873754.i		−	0.582260i
$36$	605632.	−	390697.i	0.360578	−	0.232611i
$37$	2.96195e6			1.58041			0.790207	−	0.612840i	$-0.209973\pi$
$37$	2.96195e6			1.58041			0.790207	+	0.612840i	$0.209973\pi$
$38$		−	674767.i		−	0.323608i
$39$	706798.	−	208198.i	0.305518	−	0.0899951i
$40$	1.27790e6			0.499180
$41$		−	2.62933e6i		−	0.930487i	−0.885183	−	0.465244i	$-0.845967\pi$
$41$		−	2.62933e6i		−	0.930487i	0.885183	−	0.465244i	$-0.154033\pi$
$42$	−836749.	−	2.84062e6i	−0.268904	−	0.912884i
$43$	−1.66848e6			−0.488030			−0.244015	−	0.969771i	$-0.578465\pi$
$43$	−1.66848e6			−0.488030			−0.244015	+	0.969771i	$0.578465\pi$
$44$			484920.i			0.129378i
$45$	−1.02763e6	−	1.59297e6i	−0.250604	−	0.388470i
$46$	−1.75605e6			−0.392198
$47$		−	4.65098e6i		−	0.953132i	−0.879139	−	0.476566i	$-0.841881\pi$
$47$		−	4.65098e6i		−	0.953132i	0.879139	−	0.476566i	$-0.158119\pi$
$48$	1.96951e6	−	580151.i	0.371017	−	0.109289i
$49$	3.38035e6			0.586377
$50$			3.71316e6i			0.594105i
$51$	−2.45582e6	−	8.33709e6i	−0.363008	−	1.23235i
$52$	−999250.			−0.136666
$53$			4.33867e6i			0.549861i	0.961464	+	0.274930i	$0.0886548\pi$
$53$			4.33867e6i			0.549861i	−0.961464	+	0.274930i	$0.911345\pi$
$54$	−4.86640e6	−	4.19471e6i	−0.572311	−	0.493318i
$55$	1.27546e6			0.139386
$56$			1.33751e7i			1.36002i
$57$	4.33680e6	−	1.27747e6i	0.410837	−	0.121018i
$58$	−1.24050e7			−1.09619
$59$			1.79174e7i			1.47866i	0.673344	+	0.739329i	$0.264857\pi$
$59$			1.79174e7i			1.47866i	−0.673344	+	0.739329i	$0.735143\pi$
$60$	726420.	+	2.46607e6i	0.0560509	+	0.190283i
$61$	1.96177e6			0.141687			0.0708434	−	0.997487i	$-0.477431\pi$
$61$	1.96177e6			0.141687			0.0708434	+	0.997487i	$0.477431\pi$
$62$			3.67818e6i			0.248924i
$63$	1.66728e7	−	1.07557e7i	1.05839	−	0.682776i
$64$	−1.64726e7			−0.981841
$65$			2.62829e6i			0.147238i
$66$	4.14660e6	−	1.22145e6i	0.218533	−	0.0643722i
$67$	2.34416e7			1.16329			0.581646	−	0.813442i	$-0.302409\pi$
$67$	2.34416e7			1.16329			0.581646	+	0.813442i	$0.302409\pi$
$68$			1.17867e7i			0.551262i
$69$	−3.32456e6	−	1.12863e7i	−0.146669	−	0.497915i
$70$	1.05631e7			0.439945
$71$		−	2.05631e7i		−	0.809199i	−0.914494	−	0.404600i	$-0.867411\pi$
$71$		−	2.05631e7i		−	0.809199i	0.914494	−	0.404600i	$-0.132589\pi$
$72$	1.57307e7	+	2.43846e7i	0.585353	+	0.907374i
$73$	−1.67837e7			−0.591011			−0.295506	−	0.955341i	$-0.595488\pi$
$73$	−1.67837e7			−0.591011			−0.295506	+	0.955341i	$0.595488\pi$
$74$			3.58079e7i			1.19413i
$75$	−2.38648e7	+	7.02976e6i	−0.754247	+	0.222175i
$76$	−6.13124e6			−0.183778
$77$			1.33496e7i			0.379758i
$78$	2.51697e6	+	8.54469e6i	0.0679986	+	0.230844i
$79$	−7.34684e7			−1.88622			−0.943110	−	0.332482i	$-0.892114\pi$
$79$	−7.34684e7			−1.88622			−0.943110	+	0.332482i	$0.892114\pi$
$80$			7.32380e6i			0.178804i
$81$	1.77468e7	−	3.92183e7i	0.412268	−	0.911063i
$82$	3.17868e7			0.703059
$83$			5.71837e7i			1.20493i	0.798147	+	0.602463i	$0.205814\pi$
$83$			5.71837e7i			1.20493i	−0.798147	+	0.602463i	$0.794186\pi$
$84$	−2.58111e7	+	7.60307e6i	−0.518430	+	0.152712i
$85$	3.10022e7			0.593904
$86$		−	2.01707e7i		−	0.368746i
$87$	−2.34853e7	−	7.97285e7i	−0.409939	−	1.39167i
$88$	−1.95244e7			−0.325572
$89$		−	8.04561e7i		−	1.28233i	−0.767404	−	0.641164i	$-0.778452\pi$
$89$		−	8.04561e7i		−	1.28233i	0.767404	−	0.641164i	$-0.221548\pi$
$90$	1.92579e7	−	1.24234e7i	0.293521	−	0.189352i
$91$	−2.75089e7			−0.401151
$92$			1.59563e7i			0.222730i
$93$	−2.36401e7	+	6.96355e6i	−0.316022	+	0.0930891i
$94$	5.62271e7			0.720169
$95$			1.61267e7i			0.197994i
$96$	−1.89008e7	−	6.41649e7i	−0.222533	−	0.755462i
$97$	3.68114e7			0.415811			0.207905	−	0.978149i	$-0.433335\pi$
$97$	3.68114e7			0.415811			0.207905	+	0.978149i	$0.433335\pi$
$98$			4.08660e7i			0.443055i
$99$	1.57007e7	+	2.43382e7i	0.163448	+	0.253365i
$100$	3.37394e7			0.337394
$101$		−	1.65981e8i		−	1.59504i	−0.603292	−	0.797520i	$-0.706145\pi$
$101$		−	1.65981e8i		−	1.59504i	0.603292	−	0.797520i	$-0.293855\pi$
$102$	1.00790e8	−	2.96891e7i	0.931140	−	0.274282i
$103$	1.54289e8			1.37084			0.685421	−	0.728147i	$-0.259618\pi$
$103$	1.54289e8			1.37084			0.685421	+	0.728147i	$0.259618\pi$
$104$		−	4.02329e7i		−	0.343913i
$105$	1.99981e7	+	6.78900e7i	0.164525	+	0.558533i
$106$	−5.24514e7			−0.415464
$107$		−	7.37016e7i		−	0.562266i	−0.959669	−	0.281133i	$-0.909290\pi$
$107$		−	7.37016e7i		−	0.562266i	0.959669	−	0.281133i	$-0.0907102\pi$
$108$	−3.81150e7	+	4.42183e7i	−0.280157	+	0.325017i
$109$	1.70291e8			1.20638			0.603192	−	0.797596i	$-0.293895\pi$
$109$	1.70291e8			1.20638			0.603192	+	0.797596i	$0.293895\pi$
$110$			1.54195e7i			0.105317i
$111$	−2.30141e8	+	6.77917e7i	−1.51601	+	0.446565i
$112$	−7.66545e7			−0.487153
$113$		−	2.65009e8i		−	1.62535i	−0.582719	−	0.812673i	$-0.698011\pi$
$113$		−	2.65009e8i		−	1.62535i	0.582719	−	0.812673i	$-0.301989\pi$
$114$	1.54437e7	+	5.24288e7i	0.0914393	+	0.310421i
$115$	4.19691e7			0.239960
$116$			1.12718e8i			0.622531i
$117$	−5.01524e7	+	3.23537e7i	−0.267639	+	0.172655i
$118$	−2.16609e8			−1.11725
$119$			3.24484e8i			1.61810i
$120$	−9.92918e7	+	2.92479e7i	−0.478838	+	0.141049i
$121$	−1.94872e7			−0.0909091
$122$			2.37165e7i			0.107056i
$123$	6.01789e7	+	2.04297e8i	0.262920	+	0.892569i
$124$	3.34216e7			0.141365
$125$		−	2.01607e8i		−	0.825782i
$126$	1.30029e8	+	2.01563e8i	0.515892	+	0.799701i
$127$	−1.11160e8			−0.427299			−0.213650	−	0.976910i	$-0.568535\pi$
$127$	−1.11160e8			−0.427299			−0.213650	+	0.976910i	$0.568535\pi$
$128$			1.22662e7i			0.0456952i
$129$	1.29639e8	−	3.81873e7i	0.468143	−	0.137899i
$130$	−3.17741e7			−0.111250
$131$			2.78342e7i			0.0945135i	0.998883	+	0.0472567i	$0.0150479\pi$
$131$			2.78342e7i			0.0945135i	−0.998883	+	0.0472567i	$0.984952\pi$
$132$	−1.10986e7	−	3.76779e7i	−0.0365572	−	0.124105i
$133$	−1.68790e8			−0.539438
$134$			2.83393e8i			0.878961i
$135$	1.16305e8	+	1.00252e8i	0.350159	+	0.301828i
$136$	−4.74571e8			−1.38722
$137$		−	4.61369e8i		−	1.30968i	−0.755766	−	0.654841i	$-0.772735\pi$
$137$		−	4.61369e8i		−	1.30968i	0.755766	−	0.654841i	$-0.227265\pi$
$138$	1.36444e8	−	4.01916e7i	0.376216	−	0.110820i
$139$	−3.23476e8			−0.866528			−0.433264	−	0.901267i	$-0.642638\pi$
$139$	−3.23476e8			−0.866528			−0.433264	+	0.901267i	$0.642638\pi$
$140$		−	9.59809e7i		−	0.249846i
$141$	1.06449e8	+	3.61377e8i	0.269319	+	0.914291i
$142$	2.48594e8			0.611416
$143$		−	4.01562e7i		−	0.0960304i
$144$	−1.39751e8	+	9.01545e7i	−0.325017	+	0.209671i
$145$	2.96477e8			0.670686
$146$		−	2.02903e8i		−	0.446557i
$147$	−2.62650e8	+	7.73677e7i	−0.562482	+	0.165688i
$148$	3.25367e8			0.678151
$149$			4.91992e8i			0.998188i	0.866548	+	0.499094i	$0.166334\pi$
$149$			4.91992e8i			0.998188i	−0.866548	+	0.499094i	$0.833666\pi$
$150$	−8.49849e7	−	2.88509e8i	−0.167871	−	0.569895i
$151$	9.97334e8			1.91837			0.959186	−	0.282775i	$-0.0912549\pi$
$151$	9.97334e8			1.91837			0.959186	+	0.282775i	$0.0912549\pi$
$152$		−	2.46863e8i		−	0.462467i
$153$	3.81630e8	+	5.91577e8i	0.696430	+	1.07956i
$154$	−1.61388e8			−0.286938
$155$		−	8.79075e7i		−	0.152300i
$156$	7.76409e7	−	2.28703e7i	0.131097	−	0.0386166i
$157$	−5.11837e8			−0.842429			−0.421214	−	0.906961i	$-0.638396\pi$
$157$	−5.11837e8			−0.842429			−0.421214	+	0.906961i	$0.638396\pi$
$158$		−	8.88181e8i		−	1.42519i
$159$	−9.93012e7	−	3.37111e8i	−0.155370	−	0.527453i
$160$	2.38603e8			0.364079
$161$			4.39269e8i			0.653774i
$162$	4.74121e8	+	2.14546e8i	0.688382	+	0.311502i
$163$	−2.20655e8			−0.312581			−0.156291	−	0.987711i	$-0.549954\pi$
$163$	−2.20655e8			−0.312581			−0.156291	+	0.987711i	$0.549954\pi$
$164$		−	2.88829e8i		−	0.399269i
$165$	−9.91025e7	+	2.91922e7i	−0.133705	+	0.0393850i
$166$	−6.91311e8			−0.910419
$167$		−	4.76017e8i		−	0.612007i	−0.952030	−	0.306004i	$-0.901008\pi$
$167$		−	4.76017e8i		−	0.612007i	0.952030	−	0.306004i	$-0.0989920\pi$
$168$	−3.06123e8	−	1.03924e9i	−0.384290	−	1.30460i
$169$	−7.32983e8			−0.898560
$170$			3.74794e8i			0.448743i
$171$	−3.07727e8	+	1.98517e8i	−0.359900	+	0.232174i
$172$	−1.83280e8			−0.209412
$173$		−	1.15611e8i		−	0.129067i	−0.997916	−	0.0645335i	$-0.979444\pi$
$173$		−	1.15611e8i		−	0.129067i	0.997916	−	0.0645335i	$-0.0205559\pi$
$174$	9.63862e8	−	2.83921e8i	1.05152	−	0.309742i
$175$	9.28832e8			0.990342
$176$		−	1.11897e8i		−	0.116618i
$177$	−4.10085e8	−	1.39217e9i	−0.417812	−	1.41840i
$178$	9.72658e8			0.968902
$179$			1.21391e9i			1.18242i	0.806516	+	0.591212i	$0.201350\pi$
$179$			1.21391e9i			1.18242i	−0.806516	+	0.591212i	$0.798650\pi$
$180$	−1.12885e8	−	1.74986e8i	−0.107534	−	0.166691i
$181$	8.96371e7			0.0835168			0.0417584	−	0.999128i	$-0.486704\pi$
$181$	8.96371e7			0.0835168			0.0417584	+	0.999128i	$0.486704\pi$
$182$		−	3.32564e8i		−	0.303103i
$183$	−1.52428e8	+	4.49001e7i	−0.135913	+	0.0400353i
$184$	−6.42449e8			−0.560489
$185$		−	8.55799e8i		−	0.730609i
$186$	−8.41844e7	−	2.85792e8i	−0.0703364	−	0.238780i
$187$	−4.73666e8			−0.387352
$188$		−	5.10905e8i		−	0.408986i
$189$	−1.04929e9	+	1.21731e9i	−0.822336	+	0.954013i
$190$	−1.94961e8			−0.149601
$191$		−	5.21981e6i		−	0.00392212i	−0.999998	−	0.00196106i	$-0.999376\pi$
$191$		−	5.21981e6i		−	0.00392212i	0.999998	−	0.00196106i	$-0.000624226\pi$
$192$	1.27990e9	−	3.77016e8i	0.941830	−	0.277431i
$193$	2.36333e9			1.70332			0.851660	−	0.524095i	$-0.175597\pi$
$193$	2.36333e9			1.70332			0.851660	+	0.524095i	$0.175597\pi$
$194$			4.45024e8i			0.314179i
$195$	−6.01549e7	−	2.04216e8i	−0.0416038	−	0.141238i
$196$	3.71327e8			0.251613
$197$			8.07745e8i			0.536302i	0.963377	+	0.268151i	$0.0864126\pi$
$197$			8.07745e8i			0.536302i	−0.963377	+	0.268151i	$0.913587\pi$
$198$	−2.94231e8	+	1.89811e8i	−0.191438	+	0.123498i
$199$	−2.92861e9			−1.86745			−0.933725	−	0.357992i	$-0.883462\pi$
$199$	−2.92861e9			−1.86745			−0.933725	+	0.357992i	$0.883462\pi$
$200$			1.35845e9i			0.849033i
$201$	−1.82139e9	+	5.36520e8i	−1.11589	+	0.328702i
$202$	2.00659e9			1.20518
$203$			3.10308e9i			1.82729i
$204$	−2.69769e8	−	9.15820e8i	−0.155766	−	0.528797i
$205$	−7.59696e8			−0.430154
$206$			1.86525e9i			1.03578i
$207$	5.16631e8	+	8.00846e8i	0.281384	+	0.436182i
$208$	2.30580e8			0.123188
$209$		−	2.46392e8i		−	0.129134i
$210$	−8.20742e8	+	2.41763e8i	−0.422017	+	0.124312i
$211$	3.16998e8			0.159929			0.0799645	−	0.996798i	$-0.474519\pi$
$211$	3.16998e8			0.159929			0.0799645	+	0.996798i	$0.474519\pi$
$212$			4.76597e8i			0.235944i
$213$	4.70638e8	+	1.59774e9i	0.228649	+	0.776224i
$214$	8.91000e8			0.424837
$215$			4.82075e8i			0.225611i
$216$	−1.78037e9	−	1.53463e9i	−0.817888	−	0.704999i
$217$	9.20084e8			0.414943
$218$			2.05870e9i			0.911521i
$219$	1.30408e9	−	3.84136e8i	0.566927	−	0.166997i
$220$	1.40108e8			0.0598099
$221$		−	9.76060e8i		−	0.409174i
$222$	−8.19554e8	−	2.78225e9i	−0.337416	−	1.14547i
$223$	−8.14859e7			−0.0329506			−0.0164753	−	0.999864i	$-0.505244\pi$
$223$	−8.14859e7			−0.0329506			−0.0164753	+	0.999864i	$0.505244\pi$
$224$			2.49733e9i			0.991938i
$225$	1.69338e9	−	1.09241e9i	0.660732	−	0.426243i
$226$	3.20377e9			1.22808
$227$		−	3.08538e9i		−	1.16200i	−0.813904	−	0.580999i	$-0.802662\pi$
$227$		−	3.08538e9i		−	1.16200i	0.813904	−	0.580999i	$-0.197338\pi$
$228$	4.76392e8	−	1.40329e8i	0.176289	−	0.0519287i
$229$	−1.94204e9			−0.706182			−0.353091	−	0.935589i	$-0.614869\pi$
$229$	−1.94204e9			−0.706182			−0.353091	+	0.935589i	$0.614869\pi$
$230$			5.07377e8i			0.181309i
$231$	−3.05540e8	−	1.03726e9i	−0.107305	−	0.364282i
$232$	−4.53837e9			−1.56656
$233$		−	3.68647e9i		−	1.25080i	−0.780305	−	0.625399i	$-0.784936\pi$
$233$		−	3.68647e9i		−	1.25080i	0.780305	−	0.625399i	$-0.215064\pi$
$234$	−3.91133e8	−	6.06308e8i	−0.130455	−	0.202223i
$235$	−1.34381e9			−0.440623
$236$			1.96821e9i			0.634488i
$237$	5.70843e9	−	1.68151e9i	1.80935	−	0.532974i
$238$	−3.92279e9			−1.22261
$239$			1.77521e9i			0.544075i	0.962287	+	0.272038i	$0.0876975\pi$
$239$			1.77521e9i			0.544075i	−0.962287	+	0.272038i	$0.912302\pi$
$240$	−1.67624e8	−	5.69053e8i	−0.0505231	−	0.171517i
$241$	−2.17160e8			−0.0643743			−0.0321871	−	0.999482i	$-0.510247\pi$
$241$	−2.17160e8			−0.0643743			−0.0321871	+	0.999482i	$0.510247\pi$
$242$		−	2.35586e8i		−	0.0686892i
$243$	−4.81301e8	+	3.45341e9i	−0.138036	+	0.990427i
$244$	2.15499e8			0.0607974
$245$		−	9.76687e8i		−	0.271076i
$246$	−2.46981e9	+	7.27521e8i	−0.674408	+	0.198658i
$247$	5.07728e8			0.136409
$248$			1.34566e9i			0.355736i
$249$	−1.30879e9	−	4.44313e9i	−0.340466	−	1.15582i
$250$	2.43729e9			0.623946
$251$		−	7.62141e9i		−	1.92017i	−0.279703	−	0.960087i	$-0.590236\pi$
$251$		−	7.62141e9i		−	1.92017i	0.279703	−	0.960087i	$-0.409764\pi$
$252$	1.83149e9	−	1.18151e9i	0.454153	−	0.292977i
$253$	−6.41224e8			−0.156505
$254$		−	1.34384e9i		−	0.322859i
$255$	−2.40884e9	+	7.09562e8i	−0.569702	+	0.167815i
$256$	−4.36527e9			−1.01637
$257$		−	1.71391e9i		−	0.392876i	−0.980516	−	0.196438i	$-0.937063\pi$
$257$		−	1.71391e9i		−	0.392876i	0.980516	−	0.196438i	$-0.0629374\pi$
$258$	4.61658e8	+	1.56725e9i	0.104194	+	0.353720i
$259$	8.95722e9			1.99056
$260$			2.88714e8i			0.0631793i
$261$	3.64957e9	+	5.65732e9i	0.786466	+	1.21913i
$262$	−3.36496e8			−0.0714126
$263$			1.42000e9i			0.296802i	0.988927	+	0.148401i	$0.0474126\pi$
$263$			1.42000e9i			0.296802i	−0.988927	+	0.148401i	$0.952587\pi$
$264$	1.51703e9	−	4.46864e8i	0.312304	−	0.0919941i
$265$	1.25357e9			0.254195
$266$		−	2.04056e9i		−	0.407589i
$267$	1.84144e9	+	6.25137e9i	0.362337	+	1.23007i
$268$	2.57503e9			0.499165
$269$		−	2.37499e9i		−	0.453580i	−0.973944	−	0.226790i	$-0.927177\pi$
$269$		−	2.37499e9i		−	0.453580i	0.973944	−	0.226790i	$-0.0728230\pi$
$270$	−1.21198e9	+	1.40605e9i	−0.228056	+	0.264573i
$271$	−8.98873e9			−1.66656			−0.833281	−	0.552850i	$-0.813540\pi$
$271$	−8.98873e9			−1.66656			−0.833281	+	0.552850i	$0.813540\pi$
$272$		−	2.71982e9i		−	0.496895i
$273$	2.13742e9	−	6.29611e8i	0.384804	−	0.113350i
$274$	5.57763e9			0.989572
$275$			1.35586e9i			0.237075i
$276$	−3.65199e8	−	1.23979e9i	−0.0629351	−	0.213654i
$277$	−5.42150e9			−0.920875			−0.460437	−	0.887692i	$-0.652307\pi$
$277$	−5.42150e9			−0.920875			−0.460437	+	0.887692i	$0.652307\pi$
$278$		−	3.91059e9i		−	0.654732i
$279$	1.67743e9	−	1.08212e9i	0.276840	−	0.178591i
$280$	3.86449e9			0.628724
$281$		−	3.12144e9i		−	0.500646i	−0.968162	−	0.250323i	$-0.919463\pi$
$281$		−	3.12144e9i		−	0.500646i	0.968162	−	0.250323i	$-0.0805367\pi$
$282$	−4.36880e9	+	1.28690e9i	−0.690821	+	0.203492i
$283$	6.08486e9			0.948648			0.474324	−	0.880350i	$-0.342693\pi$
$283$	6.08486e9			0.948648			0.474324	+	0.880350i	$0.342693\pi$
$284$		−	2.25883e9i		−	0.347225i
$285$	−3.69101e8	−	1.25303e9i	−0.0559456	−	0.189926i
$286$	4.85461e8			0.0725588
$287$		−	7.95136e9i		−	1.17196i
$288$	2.93715e9	+	4.55297e9i	0.426930	+	0.661797i
$289$	−4.53744e9			−0.650459
$290$			3.58420e9i			0.506758i
$291$	−2.86022e9	+	8.42522e8i	−0.398866	+	0.117492i
$292$	−1.84367e9			−0.253601
$293$			4.12562e9i			0.559781i	0.960032	+	0.279891i	$0.0902982\pi$
$293$			4.12562e9i			0.559781i	−0.960032	+	0.279891i	$0.909702\pi$
$294$	−9.35321e8	−	3.17526e9i	−0.125191	−	0.425001i
$295$	5.17690e9			0.683568
$296$			1.31003e10i			1.70653i
$297$	−1.77697e9	−	1.53171e9i	−0.228378	−	0.196856i
$298$	−5.94783e9			−0.754212
$299$		−	1.32134e9i		−	0.165322i
$300$	−2.62152e9	+	7.72211e8i	−0.323645	+	0.0953347i
$301$	−5.04564e9			−0.614681
$302$			1.20571e10i			1.44949i
$303$	3.79888e9	+	1.28966e10i	0.450697	+	1.53004i
$304$	1.41480e9			0.165654
$305$		−	5.66817e8i		−	0.0655003i
$306$	−7.15176e9	+	4.61364e9i	−0.815693	+	0.526209i
$307$	−1.44676e9			−0.162870			−0.0814351	−	0.996679i	$-0.525950\pi$
$307$	−1.44676e9			−0.162870			−0.0814351	+	0.996679i	$0.525950\pi$
$308$			1.46644e9i			0.162953i
$309$	−1.19882e10	+	3.53130e9i	−1.31498	+	0.387347i
$310$	1.06274e9			0.115075
$311$			6.21238e9i			0.664074i	0.943266	+	0.332037i	$0.107736\pi$
$311$			6.21238e9i			0.664074i	−0.943266	+	0.332037i	$0.892264\pi$
$312$	9.20831e8	+	3.12606e9i	0.0971766	+	0.329898i
$313$	1.17712e10			1.22643			0.613215	−	0.789916i	$-0.289876\pi$
$313$	1.17712e10			1.22643			0.613215	+	0.789916i	$0.289876\pi$
$314$		−	6.18775e9i		−	0.636523i
$315$	−3.10767e9	−	4.81729e9i	−0.315640	−	0.489284i
$316$	−8.07042e9			−0.809371
$317$		−	8.94887e9i		−	0.886198i	−0.896473	−	0.443099i	$-0.853879\pi$
$317$		−	8.94887e9i		−	0.886198i	0.896473	−	0.443099i	$-0.146121\pi$
$318$	4.07543e9	−	1.20048e9i	0.398534	−	0.117394i
$319$	−4.52972e9			−0.437430
$320$			4.75943e9i			0.453895i
$321$	1.68685e9	+	5.72655e9i	0.158875	+	0.539353i
$322$	−5.31046e9			−0.493979
$323$		−	5.98895e9i		−	0.550225i
$324$	1.94946e9	−	4.30808e9i	0.176903	−	0.390934i
$325$	−2.79396e9			−0.250430
$326$		−	2.66756e9i		−	0.236180i
$327$	−1.32315e10	+	3.89754e9i	−1.15722	+	0.340878i
$328$	1.16292e10			1.00474
$329$		−	1.40650e10i		−	1.20048i
$330$	−3.52913e8	−	1.19808e9i	−0.0297586	−	0.101025i
$331$	−1.45508e9			−0.121220			−0.0606100	−	0.998162i	$-0.519305\pi$
$331$	−1.45508e9			−0.121220			−0.0606100	+	0.998162i	$0.519305\pi$
$332$			6.28157e9i			0.517030i
$333$	1.63302e10	−	1.05347e10i	1.32805	−	0.856734i
$334$	5.75471e9			0.462421
$335$		−	6.77301e9i		−	0.537777i
$336$	5.95600e9	−	1.75443e9i	0.467302	−	0.137651i
$337$	1.82980e10			1.41868			0.709340	−	0.704866i	$-0.248993\pi$
$337$	1.82980e10			1.41868			0.709340	+	0.704866i	$0.248993\pi$
$338$		−	8.86125e9i		−	0.678935i
$339$	6.06538e9	+	2.05909e10i	0.459261	+	1.55911i
$340$	3.40555e9			0.254842
$341$			1.34309e9i			0.0993320i
$342$	−2.39993e9	−	3.72021e9i	−0.175426	−	0.271934i
$343$	−7.21082e9			−0.520964
$344$		−	7.37944e9i		−	0.526974i
$345$	−3.26096e9	+	9.60568e8i	−0.230181	+	0.0678034i
$346$	1.39766e9			0.0975205
$347$			1.17905e10i			0.813234i	0.913599	+	0.406617i	$0.133292\pi$
$347$			1.17905e10i			0.813234i	−0.913599	+	0.406617i	$0.866708\pi$
$348$	−2.57983e9	−	8.75809e9i	−0.175903	−	0.597162i
$349$	1.93748e10			1.30598			0.652988	−	0.757368i	$-0.273515\pi$
$349$	1.93748e10			1.30598			0.652988	+	0.757368i	$0.273515\pi$
$350$			1.12289e10i			0.748284i
$351$	3.15631e9	−	3.66172e9i	0.207946	−	0.241244i
$352$	−3.64549e9			−0.237457
$353$		−	2.55809e10i		−	1.64747i	−0.566977	−	0.823733i	$-0.691887\pi$
$353$		−	2.55809e10i		−	1.64747i	0.566977	−	0.823733i	$-0.308113\pi$
$354$	1.68304e10	−	4.95764e9i	1.07172	−	0.315691i
$355$	−5.94132e9			−0.374084
$356$		−	8.83801e9i		−	0.550243i
$357$	−7.42663e9	−	2.52121e10i	−0.457213	−	1.55216i
$358$	−1.46753e10			−0.893417
$359$			2.66400e10i			1.60382i	0.597445	+	0.801910i	$0.296183\pi$
$359$			2.66400e10i			1.60382i	−0.597445	+	0.801910i	$0.703817\pi$
$360$	7.04548e9	−	4.54508e9i	0.419469	−	0.270602i
$361$	−1.38682e10			−0.816568
$362$			1.08365e9i			0.0631037i
$363$	1.51414e9	−	4.46013e8i	0.0872045	−	0.0256874i
$364$	−3.02183e9			−0.172133
$365$			4.84932e9i			0.273218i
$366$	−5.42811e8	−	1.84275e9i	−0.0302499	−	0.102693i
$367$	−9.22091e9			−0.508288			−0.254144	−	0.967166i	$-0.581794\pi$
$367$	−9.22091e9			−0.508288			−0.254144	+	0.967166i	$0.581794\pi$
$368$		−	3.68195e9i		−	0.200764i
$369$	−9.35170e9	−	1.44964e10i	−0.504412	−	0.781905i
$370$	1.03460e10			0.552034
$371$			1.31205e10i			0.692558i
$372$	−2.59683e9	+	7.64938e8i	−0.135604	+	0.0399443i
$373$	−4.35860e9			−0.225171			−0.112585	−	0.993642i	$-0.535913\pi$
$373$	−4.35860e9			−0.225171			−0.112585	+	0.993642i	$0.535913\pi$
$374$		−	5.72629e9i		−	0.292676i
$375$	4.61428e9	+	1.56647e10i	0.233335	+	0.792131i
$376$	2.05706e10			1.02919
$377$		−	9.33417e9i		−	0.462073i
$378$	−1.47164e10	−	1.26852e10i	−0.720834	−	0.621341i
$379$	−2.44788e10			−1.18640			−0.593202	−	0.805053i	$-0.702137\pi$
$379$	−2.44788e10			−1.18640			−0.593202	+	0.805053i	$0.702137\pi$
$380$			1.77150e9i			0.0849586i
$381$	8.63701e9	−	2.54416e9i	0.409886	−	0.120738i
$382$	6.31039e7			0.00296348
$383$			2.29388e10i			1.06604i	0.846102	+	0.533022i	$0.178944\pi$
$383$			2.29388e10i			1.06604i	−0.846102	+	0.533022i	$0.821056\pi$
$384$	−2.80743e8	−	9.53074e8i	−0.0129117	−	0.0438331i
$385$	3.85713e9			0.175558
$386$			2.85711e10i			1.28700i
$387$	−9.19886e9	+	5.93424e9i	−0.410100	+	0.264558i
$388$	4.04369e9			0.178423
$389$		−	3.63015e10i		−	1.58536i	−0.609641	−	0.792678i	$-0.708686\pi$
$389$		−	3.63015e10i		−	1.58536i	0.609641	−	0.792678i	$-0.291314\pi$
$390$	2.46882e9	−	7.27231e8i	0.106717	−	0.0314350i
$391$	−1.55860e10			−0.666847
$392$			1.49508e10i			0.633169i
$393$	−6.37056e8	−	2.16270e9i	−0.0267059	−	0.0906620i
$394$	−9.76507e9			−0.405220
$395$			2.12273e10i			0.871979i
$396$	1.72470e9	+	2.67352e9i	0.0701349	+	0.108718i
$397$	1.69733e10			0.683290			0.341645	−	0.939829i	$-0.389016\pi$
$397$	1.69733e10			0.683290			0.341645	+	0.939829i	$0.389016\pi$
$398$		−	3.54048e10i		−	1.41101i
$399$	1.31149e10	−	3.86319e9i	0.517455	−	0.152425i
$400$	−7.78546e9			−0.304120
$401$			3.89763e10i			1.50738i	0.657230	+	0.753690i	$0.271728\pi$
$401$			3.89763e10i			1.50738i	−0.657230	+	0.753690i	$0.728272\pi$
$402$	−6.48615e9	−	2.20194e10i	−0.248361	−	0.843142i
$403$	−2.76765e9			−0.104928
$404$		−	1.82328e10i		−	0.684427i
$405$	−1.13314e10	−	5.12759e9i	−0.421175	−	0.190587i
$406$	−3.75140e10			−1.38067
$407$			1.30753e10i			0.476513i
$408$	3.68737e10	−	1.08617e10i	1.33069	−	0.391975i
$409$	1.22202e10			0.436702			0.218351	−	0.975870i	$-0.429932\pi$
$409$	1.22202e10			0.436702			0.218351	+	0.975870i	$0.429932\pi$
$410$		−	9.18419e9i		−	0.325017i
$411$	1.05596e10	+	3.58480e10i	0.370066	+	1.25631i
$412$	1.69485e10			0.588224
$413$			5.41840e10i			1.86239i
$414$	−9.68167e9	+	6.24571e9i	−0.329571	+	0.212608i
$415$	1.65222e10			0.557024
$416$		−	7.51208e9i		−	0.250834i
$417$	2.51338e10	−	7.40355e9i	0.831216	−	0.244848i
$418$	2.97871e9			0.0975715
$419$			1.98327e10i			0.643467i	0.946830	+	0.321734i	$0.104266\pi$
$419$			1.98327e10i			0.643467i	−0.946830	+	0.321734i	$0.895734\pi$
$420$	2.19676e9	+	7.45764e9i	0.0705970	+	0.239665i
$421$	−8.40602e9			−0.267585			−0.133793	−	0.991009i	$-0.542716\pi$
$421$	−8.40602e9			−0.267585			−0.133793	+	0.991009i	$0.542716\pi$
$422$			3.83229e9i			0.120839i
$423$	−1.65420e10	−	2.56424e10i	−0.516687	−	0.800934i
$424$	−1.91893e10			−0.593739
$425$			3.29564e10i			1.01015i
$426$	−1.93155e10	+	5.68969e9i	−0.586500	+	0.172763i
$427$	5.93259e9			0.178457
$428$		−	8.09603e9i		−	0.241267i
$429$	9.19076e8	+	3.12011e9i	0.0271345	+	0.0921171i
$430$	−5.82795e9			−0.170468
$431$			3.38236e10i			0.980192i	0.871668	+	0.490096i	$0.163038\pi$
$431$			3.38236e10i			0.980192i	−0.871668	+	0.490096i	$0.836962\pi$
$432$	8.79515e9	−	1.02035e10i	0.252527	−	0.292964i
$433$	4.38280e10			1.24681			0.623405	−	0.781899i	$-0.285749\pi$
$433$	4.38280e10			1.24681			0.623405	+	0.781899i	$0.285749\pi$
$434$			1.11232e10i			0.313523i
$435$	−2.30360e10	+	6.78562e9i	−0.643355	+	0.189510i
$436$	1.87063e10			0.517656
$437$		−	8.10752e9i		−	0.222312i
$438$	4.64394e9	+	1.57654e10i	0.126180	+	0.428359i
$439$	−2.04097e10			−0.549513			−0.274757	−	0.961514i	$-0.588597\pi$
$439$	−2.04097e10			−0.549513			−0.274757	+	0.961514i	$0.588597\pi$
$440$			5.64120e9i			0.150508i
$441$	1.86369e10	−	1.20228e10i	0.492743	−	0.317872i
$442$	1.17999e10			0.309164
$443$			2.67296e10i			0.694030i	0.937860	+	0.347015i	$0.112805\pi$
$443$			2.67296e10i			0.694030i	−0.937860	+	0.347015i	$0.887195\pi$
$444$	−2.52807e10	+	7.44684e9i	−0.650516	+	0.191620i
$445$	−2.32463e10			−0.592806
$446$		−	9.85107e8i		−	0.0248968i
$447$	−1.12605e10	−	3.82273e10i	−0.282050	−	0.957511i
$448$	−4.98146e10			−1.23664
$449$		−	6.99604e10i		−	1.72134i	−0.509163	−	0.860670i	$-0.670045\pi$
$449$		−	6.99604e10i		−	1.72134i	0.509163	−	0.860670i	$-0.329955\pi$
$450$	1.32065e10	+	2.04718e10i	0.322061	+	0.499237i
$451$	1.16070e10			0.280552
$452$		−	2.91109e10i		−	0.697432i
$453$	−7.74921e10	+	2.28265e10i	−1.84020	+	0.542059i
$454$	3.73001e10			0.877984
$455$			7.94818e9i			0.185448i
$456$	5.65007e9	+	1.91810e10i	0.130676	+	0.443621i
$457$	−7.59737e8			−0.0174180			−0.00870900	−	0.999962i	$-0.502772\pi$
$457$	−7.59737e8			−0.0174180			−0.00870900	+	0.999962i	$0.502772\pi$
$458$		−	2.34779e10i		−	0.533578i
$459$	−4.31921e10	−	3.72305e10i	−0.973091	−	0.838780i
$460$	4.61025e9			0.102966
$461$		−	4.80756e10i		−	1.06444i	−0.846607	−	0.532219i	$-0.821358\pi$
$461$		−	4.80756e10i		−	1.06444i	0.846607	−	0.532219i	$-0.178642\pi$
$462$	1.25397e10	−	3.69377e9i	0.275245	−	0.0810777i
$463$	7.87575e10			1.71383			0.856916	−	0.515456i	$-0.172378\pi$
$463$	7.87575e10			1.71383			0.856916	+	0.515456i	$0.172378\pi$
$464$		−	2.60100e10i		−	0.561136i
$465$	2.01198e9	+	6.83034e9i	0.0430341	+	0.146093i
$466$	4.45668e10			0.945079
$467$		−	7.63344e10i		−	1.60492i	−0.596708	−	0.802458i	$-0.703525\pi$
$467$		−	7.63344e10i		−	1.60492i	0.596708	−	0.802458i	$-0.296475\pi$
$468$	−5.50919e9	+	3.55401e9i	−0.114843	+	0.0740859i
$469$	7.08897e10			1.46518
$470$		−	1.62457e10i		−	0.332926i
$471$	3.97693e10	−	1.17147e10i	0.808099	−	0.238038i
$472$	−7.92462e10			−1.59665
$473$		−	7.36538e9i		−	0.147147i
$474$	2.03283e10	+	6.90110e10i	0.402705	+	1.36711i
$475$	−1.71433e10			−0.336760
$476$			3.56442e10i			0.694322i
$477$	1.54312e10	+	2.39205e10i	0.298076	+	0.462058i
$478$	−2.14611e10			−0.411093
$479$		−	8.37315e10i		−	1.59055i	−0.606250	−	0.795274i	$-0.707327\pi$
$479$		−	8.37315e10i		−	1.59055i	0.606250	−	0.795274i	$-0.292673\pi$
$480$	−1.85392e10	+	5.46102e9i	−0.349242	+	0.102875i
$481$	−2.69437e10			−0.503357
$482$		−	2.62532e9i		−	0.0486400i
$483$	−1.00538e10	−	3.41309e10i	−0.184731	−	0.627132i
$484$	−2.14064e9			−0.0390088
$485$		−	1.06360e10i		−	0.192225i
$486$	−4.17493e10	−	5.81859e9i	−0.748348	−	0.104297i
$487$	9.25576e9			0.164549			0.0822747	−	0.996610i	$-0.473782\pi$
$487$	9.25576e9			0.164549			0.0822747	+	0.996610i	$0.473782\pi$
$488$			8.67664e9i			0.152993i
$489$	1.71447e10	−	5.05024e9i	0.299843	−	0.0883235i
$490$	1.18075e10			0.204820
$491$		−	4.12896e9i		−	0.0710420i	−0.999369	−	0.0355210i	$-0.988691\pi$
$491$		−	4.12896e9i		−	0.0710420i	0.999369	−	0.0355210i	$-0.0113091\pi$
$492$	6.61058e9	+	2.24418e10i	0.112818	+	0.382999i
$493$	−1.10102e11			−1.86384
$494$			6.13808e9i			0.103068i
$495$	7.03205e9	−	4.53642e9i	0.117128	−	0.0755601i
$496$	−7.71214e9			−0.127423
$497$		−	6.21848e10i		−	1.01920i
$498$	5.37143e10	−	1.58224e10i	0.873319	−	0.257250i
$499$	5.86503e10			0.945950			0.472975	−	0.881076i	$-0.343180\pi$
$499$	5.86503e10			0.945950			0.472975	+	0.881076i	$0.343180\pi$
$500$		−	2.21463e10i		−	0.354341i
$501$	1.08948e10	+	3.69861e10i	0.172930	+	0.587067i
$502$	9.21375e10			1.45085
$503$			1.14732e10i			0.179230i	0.995976	+	0.0896152i	$0.0285637\pi$
$503$			1.14732e10i			0.179230i	−0.995976	+	0.0896152i	$0.971436\pi$
$504$	4.75711e10	+	7.37415e10i	0.737260	+	1.14285i
$505$	−4.79569e10			−0.737370
$506$		−	7.75195e9i		−	0.118252i
$507$	5.69522e10	−	1.67761e10i	0.861943	−	0.253899i
$508$	−1.22107e10			−0.183353
$509$			5.97986e10i			0.890881i	0.895312	+	0.445440i	$0.146953\pi$
$509$			5.97986e10i			0.890881i	−0.895312	+	0.445440i	$0.853047\pi$
$510$	−8.57811e9	−	2.91212e10i	−0.126798	−	0.430456i
$511$	−5.07554e10			−0.744387
$512$		−	4.96329e10i		−	0.722253i
$513$	1.93666e10	−	2.24677e10i	0.279630	−	0.324406i
$514$	2.07200e10			0.296850
$515$		−	4.45790e10i		−	0.633725i
$516$	1.42407e10	−	4.19483e9i	0.200879	−	0.0591719i
$517$	2.05314e10			0.287380
$518$			1.08287e11i			1.50403i
$519$	2.64605e9	+	8.98288e9i	0.0364694	+	0.123807i
$520$	−1.16245e10			−0.158987
$521$			1.25170e11i			1.69882i	0.527730	+	0.849412i	$0.323043\pi$
$521$			1.25170e11i			1.69882i	−0.527730	+	0.849412i	$0.676957\pi$
$522$	−6.83931e10	+	4.41208e10i	−0.921149	+	0.594239i
$523$	−4.60203e10			−0.615095			−0.307548	−	0.951533i	$-0.599508\pi$
$523$	−4.60203e10			−0.615095			−0.307548	+	0.951533i	$0.599508\pi$
$524$			3.05756e9i			0.0405554i
$525$	−7.21695e10	+	2.12587e10i	−0.949984	+	0.279833i
$526$	−1.71669e10			−0.224258
$527$			3.26460e10i			0.423241i
$528$	2.56103e9	+	8.69427e9i	0.0329518	+	0.111866i
$529$	5.72115e10			0.730569
$530$			1.51548e10i			0.192065i
$531$	6.37266e10	+	9.87846e10i	0.801572	+	1.24254i
$532$	−1.85414e10			−0.231471
$533$			2.39180e10i			0.296357i
$534$	−7.55747e10	+	2.22617e10i	−0.929419	+	0.273775i
$535$	−2.12947e10			−0.259930
$536$			1.03679e11i			1.25612i
$537$	−2.77833e10	−	9.43195e10i	−0.334108	−	1.13424i
$538$	2.87120e10			0.342716
$539$			1.49223e10i			0.176799i
$540$	1.27760e10	+	1.10126e10i	0.150252	+	0.129514i
$541$	7.62294e10			0.889884			0.444942	−	0.895559i	$-0.353224\pi$
$541$	7.62294e10			0.889884			0.444942	+	0.895559i	$0.353224\pi$
$542$		−	1.08667e11i		−	1.25922i
$543$	−6.96473e9	+	2.05157e9i	−0.0801134	+	0.0235986i
$544$	−8.86093e10			−1.01177
$545$		−	4.92023e10i		−	0.557699i
$546$	7.61156e9	+	2.58399e10i	0.0856452	+	0.290751i
$547$	5.83750e10			0.652045			0.326022	−	0.945362i	$-0.394292\pi$
$547$	5.83750e10			0.652045			0.326022	+	0.945362i	$0.394292\pi$
$548$		−	5.06808e10i		−	0.561981i
$549$	1.08159e10	−	6.97740e9i	0.119062	−	0.0768076i
$550$	−1.63915e10			−0.179129
$551$		−	5.72730e10i		−	0.621360i
$552$	4.99177e10	−	1.47040e10i	0.537648	−	0.158373i
$553$	−2.22175e11			−2.37572
$554$		−	6.55422e10i		−	0.695796i
$555$	1.95871e10	+	6.64949e10i	0.206442	+	0.700836i
$556$	−3.55334e10			−0.371824
$557$			9.65542e9i			0.100311i	0.998741	+	0.0501557i	$0.0159718\pi$
$557$			9.65542e9i			0.100311i	−0.998741	+	0.0501557i	$0.984028\pi$
$558$	1.30821e10	+	2.02790e10i	0.134940	+	0.209175i
$559$	1.51775e10			0.155436
$560$			2.21479e10i			0.225206i
$561$	3.68035e10	−	1.08410e10i	0.371567	−	0.109451i
$562$	3.77361e10			0.378278
$563$		−	4.32026e10i		−	0.430007i	−0.976613	−	0.215004i	$-0.931024\pi$
$563$		−	4.32026e10i		−	0.430007i	0.976613	−	0.215004i	$-0.0689764\pi$
$564$	1.16933e10	+	3.96969e10i	0.115564	+	0.392319i
$565$	−7.65692e10			−0.751381
$566$			7.35617e10i			0.716780i
$567$	5.36679e10	−	1.18600e11i	0.519257	−	1.14750i
$568$	9.09477e10			0.873773
$569$		−	2.03534e10i		−	0.194173i	−0.995276	−	0.0970865i	$-0.969048\pi$
$569$		−	2.03534e10i		−	0.194173i	0.995276	−	0.0970865i	$-0.0309523\pi$
$570$	1.51483e10	−	4.46217e9i	0.143504	−	0.0422714i
$571$	−1.64922e11			−1.55144			−0.775718	−	0.631079i	$-0.782612\pi$
$571$	−1.64922e11			−1.55144			−0.775718	+	0.631079i	$0.782612\pi$
$572$		−	4.41112e9i		−	0.0412064i
$573$	1.19468e8	+	4.05575e8i	0.00110824	+	0.00376229i
$574$	9.61263e10			0.885513
$575$			4.46146e10i			0.408137i
$576$	−9.08186e10	+	5.85877e10i	−0.825059	+	0.532251i
$577$	1.34081e11			1.20966			0.604830	−	0.796355i	$-0.293241\pi$
$577$	1.34081e11			1.20966			0.604830	+	0.796355i	$0.293241\pi$
$578$		−	5.48545e10i		−	0.491474i
$579$	−1.83629e11	+	5.40908e10i	−1.63391	+	0.481293i
$580$	3.25677e10			0.287789
$581$			1.72929e11i			1.51762i
$582$	−1.01855e10	−	3.45780e10i	−0.0887750	−	0.301376i
$583$	−1.91527e10			−0.165789
$584$		−	7.42318e10i		−	0.638173i
$585$	9.34797e9	+	1.44906e10i	0.0798167	+	0.123726i
$586$	−4.98758e10			−0.422960
$587$		−	4.99106e10i		−	0.420378i	−0.977661	−	0.210189i	$-0.932592\pi$
$587$		−	4.99106e10i		−	0.420378i	0.977661	−	0.210189i	$-0.0674080\pi$
$588$	−2.88518e10	+	8.49875e9i	−0.241359	+	0.0710961i
$589$	−1.69818e10			−0.141099
$590$			6.25851e10i			0.516491i
$591$	−1.84873e10	−	6.27611e10i	−0.151538	−	0.514447i
$592$	−7.50793e10			−0.611271
$593$			1.06852e10i			0.0864098i	0.999066	+	0.0432049i	$0.0137568\pi$
$593$			1.06852e10i			0.0864098i	−0.999066	+	0.0432049i	$0.986243\pi$
$594$	1.85172e10	−	2.14823e10i	0.148741	−	0.172558i
$595$	9.37535e10			0.748031
$596$			5.40447e10i			0.428320i
$597$	2.27550e11	−	6.70285e10i	1.79135	−	0.527670i
$598$	1.59741e10			0.124914
$599$			1.03233e11i			0.801884i	0.916103	+	0.400942i	$0.131317\pi$
$599$			1.03233e11i			0.801884i	−0.916103	+	0.400942i	$0.868683\pi$
$600$	−3.10916e10	−	1.05551e11i	−0.239904	−	0.814435i
$601$	2.03937e11			1.56314			0.781571	−	0.623817i	$-0.214419\pi$
$601$	2.03937e11			1.56314			0.781571	+	0.623817i	$0.214419\pi$
$602$		−	6.09982e10i		−	0.464442i
$603$	1.29241e11	−	8.33744e10i	0.977534	−	0.630613i
$604$	1.09556e11			0.823168
$605$			5.63045e9i			0.0420263i
$606$	−1.55910e11	+	4.59258e10i	−1.15607	+	0.340539i
$607$	1.07455e11			0.791536			0.395768	−	0.918351i	$-0.370478\pi$
$607$	1.07455e11			0.791536			0.395768	+	0.918351i	$0.370478\pi$
$608$		−	4.60929e10i		−	0.337303i
$609$	−7.10217e10	−	2.41107e11i	−0.516324	−	1.75283i
$610$	6.85242e9			0.0494908
$611$			4.23081e10i			0.303570i
$612$	4.19216e10	+	6.49841e10i	0.298836	+	0.463235i
$613$	−8.14120e10			−0.576563			−0.288281	−	0.957546i	$-0.593084\pi$
$613$	−8.14120e10			−0.576563			−0.288281	+	0.957546i	$0.593084\pi$
$614$		−	1.74903e10i		−	0.123062i
$615$	5.90278e10	−	1.73875e10i	0.412625	−	0.121545i
$616$	−5.90436e10			−0.410062
$617$			2.64218e10i			0.182315i	0.995836	+	0.0911574i	$0.0290566\pi$
$617$			2.64218e10i			0.182315i	−0.995836	+	0.0911574i	$0.970943\pi$
$618$	−4.26909e10	−	1.44928e11i	−0.292672	−	0.993573i
$619$	−1.19674e11			−0.815152			−0.407576	−	0.913171i	$-0.633626\pi$
$619$	−1.19674e11			−0.815152			−0.407576	+	0.913171i	$0.633626\pi$
$620$		−	9.65654e9i		−	0.0653514i
$621$	−5.84712e10	−	5.04007e10i	−0.393165	−	0.338899i
$622$	−7.51034e10			−0.501762
$623$		−	2.43307e11i		−	1.61511i
$624$	−1.79159e10	+	5.27740e9i	−0.118168	+	0.0348082i
$625$	6.17276e10			0.404538
$626$			1.42305e11i			0.926667i
$627$	5.63930e9	+	1.91445e10i	0.0364884	+	0.123872i
$628$	−5.62247e10			−0.361484
$629$			3.17816e11i			2.03036i
$630$	5.82377e10	−	3.75695e10i	0.369694	−	0.238492i
$631$	2.68955e11			1.69653			0.848265	−	0.529572i	$-0.177648\pi$
$631$	2.68955e11			1.69653			0.848265	+	0.529572i	$0.177648\pi$
$632$		−	3.24940e11i		−	2.03674i
$633$	−2.46305e10	+	7.25530e9i	−0.153412	+	0.0451898i
$634$	1.08186e11			0.669595
$635$			3.21174e10i			0.197536i
$636$	−1.09081e10	−	3.70312e10i	−0.0666687	−	0.226329i
$637$	−3.07496e10			−0.186759
$638$		−	5.47612e10i		−	0.330514i
$639$	−7.31364e10	−	1.13371e11i	−0.438662	−	0.679985i
$640$	3.54409e9			0.0211244
$641$			7.90714e10i			0.468368i	0.972192	+	0.234184i	$0.0752418\pi$
$641$			7.90714e10i			0.468368i	−0.972192	+	0.234184i	$0.924758\pi$
$642$	−6.92300e10	+	2.03928e10i	−0.407525	+	0.120043i
$643$	9.87009e10			0.577401			0.288700	−	0.957420i	$-0.406777\pi$
$643$	9.87009e10			0.577401			0.288700	+	0.957420i	$0.406777\pi$
$644$			4.82532e10i			0.280532i
$645$	−1.10335e10	−	3.74568e10i	−0.0637491	−	0.216417i
$646$	7.24022e10			0.415740
$647$			1.09583e11i			0.625353i	0.949860	+	0.312677i	$0.101226\pi$
$647$			1.09583e11i			0.625353i	−0.949860	+	0.312677i	$0.898774\pi$
$648$	1.73457e11	+	7.84914e10i	0.983765	+	0.445166i
$649$	−7.90952e10			−0.445832
$650$		−	3.37770e10i		−	0.189221i
$651$	−7.14898e10	+	2.10584e10i	−0.398034	+	0.117247i
$652$	−2.42387e10			−0.134128
$653$			2.25362e11i			1.23944i	0.784821	+	0.619722i	$0.212755\pi$
$653$			2.25362e11i			1.23944i	−0.784821	+	0.619722i	$0.787245\pi$
$654$	−4.71185e10	−	1.59959e11i	−0.257561	−	0.874376i
$655$	8.04216e9			0.0436926
$656$			6.66482e10i			0.359893i
$657$	−9.25338e10	+	5.96942e10i	−0.496637	+	0.320384i
$658$	1.70036e11			0.907063
$659$		−	3.65202e11i		−	1.93639i	−0.250206	−	0.968193i	$-0.580498\pi$
$659$		−	3.65202e11i		−	1.93639i	0.250206	−	0.968193i	$-0.419502\pi$
$660$	−1.08863e10	+	3.20673e9i	−0.0573726	+	0.0169000i
$661$	−2.13153e11			−1.11657			−0.558285	−	0.829649i	$-0.688540\pi$
$661$	−2.13153e11			−1.11657			−0.558285	+	0.829649i	$0.688540\pi$
$662$		−	1.75909e10i		−	0.0915916i
$663$	2.23396e10	+	7.58391e10i	0.115617	+	0.392499i
$664$	−2.52915e11			−1.30108
$665$			4.87688e10i			0.249376i
$666$	1.27357e11	+	1.97421e11i	0.647332	+	1.00345i
$667$	−1.49050e11			−0.753060
$668$		−	5.22899e10i		−	0.262610i
$669$	6.33139e9	−	1.86501e9i	0.0316078	−	0.00931057i
$670$	8.18809e10			0.406334
$671$			8.66011e9i			0.0427202i
$672$	−5.71578e10	−	1.94041e11i	−0.280284	−	0.951516i
$673$	−3.78188e11			−1.84352			−0.921759	−	0.387763i	$-0.873248\pi$
$673$	−3.78188e11			−1.84352			−0.921759	+	0.387763i	$0.873248\pi$
$674$			2.21210e11i			1.07193i
$675$	−1.06572e11	+	1.23637e11i	−0.513367	+	0.595570i
$676$	−8.05173e10			−0.385569
$677$			2.71560e11i			1.29274i	0.763024	+	0.646371i	$0.223714\pi$
$677$			2.71560e11i			1.29274i	−0.763024	+	0.646371i	$0.776286\pi$
$678$	−2.48930e11	+	7.33263e10i	−1.17804	+	0.347009i
$679$	1.11321e11			0.523720
$680$			1.37118e11i			0.641297i
$681$	7.06167e10	+	2.39732e11i	0.328336	+	1.11465i
$682$	−1.62371e10			−0.0750534
$683$			2.43241e11i			1.11778i	0.829243	+	0.558888i	$0.188772\pi$
$683$			2.43241e11i			1.11778i	−0.829243	+	0.558888i	$0.811228\pi$
$684$	−3.38035e10	+	2.18068e10i	−0.154432	+	0.0996250i
$685$	−1.33304e11			−0.605453
$686$		−	8.71737e10i		−	0.393631i
$687$	1.50895e11	−	4.44485e10i	0.677405	−	0.199540i
$688$	4.22925e10			0.188760
$689$		−	3.94671e10i		−	0.175129i
$690$	−1.16126e10	−	3.94228e10i	−0.0512310	−	0.173920i
$691$	−1.99275e11			−0.874061			−0.437030	−	0.899447i	$-0.643970\pi$
$691$	−1.99275e11			−0.874061			−0.437030	+	0.899447i	$0.643970\pi$
$692$		−	1.26997e10i		−	0.0553822i
$693$	4.74804e10	+	7.36009e10i	0.205865	+	0.319117i
$694$	−1.42539e11			−0.614464
$695$			9.34621e10i			0.400587i
$696$	3.52628e11	−	1.03872e11i	1.50273	−	0.442651i
$697$	2.82126e11			1.19540
$698$			2.34228e11i			0.986771i
$699$	8.43741e10	+	2.86436e11i	0.353427	+	1.19983i
$700$	1.02031e11			0.424953
$701$		−	5.28783e10i		−	0.218980i	−0.993988	−	0.109490i	$-0.965078\pi$
$701$		−	5.28783e10i		−	0.218980i	0.993988	−	0.109490i	$-0.0349218\pi$
$702$	4.42676e10	+	3.81576e10i	0.182279	+	0.157120i
$703$	−1.65322e11			−0.676876
$704$		−	7.27169e10i		−	0.296036i
$705$	1.04413e11	−	3.07565e10i	0.422667	−	0.124503i
$706$	3.09255e11			1.24480
$707$		−	5.01941e11i		−	2.00898i
$708$	−4.50474e10	−	1.52928e11i	−0.179282	−	0.608632i
$709$	4.08782e11			1.61773			0.808866	−	0.587993i	$-0.200082\pi$
$709$	4.08782e11			1.61773			0.808866	+	0.587993i	$0.200082\pi$
$710$		−	7.18264e10i		−	0.282651i
$711$	−4.05055e11	+	2.61304e11i	−1.58502	+	1.02251i
$712$	3.55846e11			1.38466
$713$			4.41944e10i			0.171005i
$714$	3.04797e11	−	8.97828e10i	1.17278	−	0.345462i
$715$	−1.16024e10			−0.0443939
$716$			1.33346e11i			0.507374i
$717$	−4.06302e10	−	1.37933e11i	−0.153735	−	0.521904i
$718$	−3.22058e11			−1.21182
$719$		−	3.15768e11i		−	1.18155i	−0.806835	−	0.590776i	$-0.798822\pi$
$719$		−	3.15768e11i		−	1.18155i	0.806835	−	0.590776i	$-0.201178\pi$
$720$	2.60484e10	+	4.03785e10i	0.0969285	+	0.150252i
$721$	4.66586e11			1.72659
$722$		−	1.67657e11i		−	0.616983i
$723$	1.68732e10	−	4.97026e9i	0.0617510	−	0.0181897i
$724$	9.84653e9			0.0358368
$725$			3.15166e11i			1.14074i
$726$	5.39198e9	+	1.83049e10i	0.0194089	+	0.0658901i
$727$	−4.33193e11			−1.55076			−0.775378	−	0.631497i	$-0.782441\pi$
$727$	−4.33193e11			−1.55076			−0.775378	+	0.631497i	$0.782441\pi$
$728$		−	1.21668e11i		−	0.433163i
$729$	−4.16432e10	−	2.79343e11i	−0.147446	−	0.989070i
$730$	−5.86249e10			−0.206439
$731$		−	1.79027e11i		−	0.626973i
$732$	−1.67441e10	+	4.93222e9i	−0.0583198	+	0.0171790i
$733$	−3.83767e11			−1.32939			−0.664695	−	0.747115i	$-0.731438\pi$
$733$	−3.83767e11			−1.32939			−0.664695	+	0.747115i	$0.731438\pi$
$734$		−	1.11474e11i		−	0.384053i
$735$	2.23539e10	+	7.58877e10i	0.0765957	+	0.260029i
$736$	−1.19955e11			−0.408795
$737$			1.03481e11i			0.350745i
$738$	1.75251e11	−	1.13056e11i	0.590793	−	0.381124i
$739$	1.24082e11			0.416036			0.208018	−	0.978125i	$-0.433299\pi$
$739$	1.24082e11			0.416036			0.208018	+	0.978125i	$0.433299\pi$
$740$		−	9.40086e10i		−	0.313502i
$741$	−3.94500e10	+	1.16206e10i	−0.130850	+	0.0385440i
$742$	−1.58618e11			−0.523284
$743$		−	1.57217e10i		−	0.0515875i	−0.999667	−	0.0257937i	$-0.991789\pi$
$743$		−	1.57217e10i		−	0.0515875i	0.999667	−	0.0257937i	$-0.00821131\pi$
$744$	−3.07988e10	−	1.04557e11i	−0.100518	−	0.341240i
$745$	1.42152e11			0.461452
$746$		−	5.26924e10i		−	0.170135i
$747$	2.03384e11	+	3.15273e11i	0.653183	+	1.01252i
$748$	−5.20317e10			−0.166212
$749$		−	2.22881e11i		−	0.708182i
$750$	−1.89375e11	+	5.57834e10i	−0.598519	+	0.176303i
$751$	−2.53140e11			−0.795793			−0.397897	−	0.917430i	$-0.630260\pi$
$751$	−2.53140e11			−0.795793			−0.397897	+	0.917430i	$0.630260\pi$
$752$			1.17893e11i			0.368651i
$753$	1.74435e11	+	5.92177e11i	0.542568	+	1.84192i
$754$	1.12844e11			0.349134
$755$		−	2.88161e11i		−	0.886843i
$756$	−1.15263e11	+	1.33720e11i	−0.352862	+	0.409364i
$757$	−5.52233e11			−1.68166			−0.840831	−	0.541298i	$-0.817933\pi$
$757$	−5.52233e11			−1.68166			−0.840831	+	0.541298i	$0.817933\pi$
$758$		−	2.95931e11i		−	0.896425i
$759$	4.98226e10	−	1.46760e10i	0.150127	−	0.0442223i
$760$	−7.13262e10			−0.213794
$761$		−	3.94928e11i		−	1.17755i	−0.808297	−	0.588776i	$-0.799610\pi$
$761$		−	3.94928e11i		−	1.17755i	0.808297	−	0.588776i	$-0.200390\pi$
$762$	3.07572e10	+	1.04415e11i	0.0912277	+	0.309702i
$763$	5.14976e11			1.51946
$764$		−	5.73390e8i		−	0.00168297i
$765$	1.70925e11	−	1.10265e11i	0.499068	−	0.321952i
$766$	−2.77314e11			−0.805482
$767$		−	1.62988e11i		−	0.470948i
$768$	3.39178e11	−	9.99101e10i	0.974950	−	0.287187i
$769$	−6.77887e10			−0.193844			−0.0969219	−	0.995292i	$-0.530900\pi$
$769$	−6.77887e10			−0.193844			−0.0969219	+	0.995292i	$0.530900\pi$
$770$			4.66299e10i			0.132648i
$771$	3.92271e10	+	1.33169e11i	0.111012	+	0.376866i
$772$	2.59610e11			0.730889
$773$		−	1.08276e11i		−	0.303258i	−0.988437	−	0.151629i	$-0.951548\pi$
$773$		−	1.08276e11i		−	0.303258i	0.988437	−	0.151629i	$-0.0484519\pi$
$774$	−7.17409e10	−	1.11208e11i	−0.199895	−	0.309864i
$775$	9.34489e10			0.259040
$776$			1.62812e11i			0.448992i
$777$	−6.95969e11	+	2.05008e11i	−1.90944	+	0.562455i
$778$	4.38860e11			1.19786
$779$			1.46757e11i			0.398519i
$780$	−6.60795e9	−	2.24328e10i	−0.0178520	−	0.0606047i
$781$	9.07744e10			0.243983
$782$		−	1.88423e11i		−	0.503857i
$783$	−4.13051e11	−	3.56040e11i	−1.09890	−	0.947221i
$784$	−8.56848e10			−0.226798
$785$			1.47886e11i			0.389446i
$786$	2.61455e10	−	7.70156e9i	0.0685025	−	0.0201785i
$787$	4.20493e11			1.09612			0.548062	−	0.836438i	$-0.315366\pi$
$787$	4.20493e11			1.09612			0.548062	+	0.836438i	$0.315366\pi$
$788$			8.87299e10i			0.230126i
$789$	−3.25004e10	−	1.10333e11i	−0.0838649	−	0.284707i
$790$	−2.56623e11			−0.658851
$791$		−	8.01411e11i		−	2.04715i
$792$	−1.07644e11	+	6.94420e10i	−0.273584	+	0.176491i
$793$	−1.78454e10			−0.0451268
$794$			2.05196e11i			0.516281i
$795$	−9.74017e10	+	2.86912e10i	−0.243836	+	0.0718257i
$796$	−3.21704e11			−0.801317
$797$		−	5.60638e11i		−	1.38947i	−0.719265	−	0.694736i	$-0.755521\pi$
$797$		−	5.60638e11i		−	1.38947i	0.719265	−	0.694736i	$-0.244479\pi$
$798$	4.67033e10	+	1.58550e11i	0.115169	+	0.390979i
$799$	4.99048e11			1.22449
$800$			2.53643e11i			0.619246i
$801$	−2.86157e11	−	4.43581e11i	−0.695142	−	1.07756i
$802$	−4.71196e11			−1.13895
$803$		−	7.40903e10i		−	0.178197i
$804$	−2.00078e11	+	5.89361e10i	−0.478823	+	0.141045i
$805$	1.26918e11			0.302233
$806$		−	3.34589e10i		−	0.0792815i
$807$	5.43577e10	+	1.84535e11i	0.128164	+	0.435096i
$808$	7.34108e11			1.72232
$809$			5.67646e11i			1.32521i	0.748970	+	0.662603i	$0.230548\pi$
$809$			5.67646e11i			1.32521i	−0.748970	+	0.662603i	$0.769452\pi$
$810$	6.19890e10	−	1.36988e11i	0.144004	−	0.318232i
$811$	3.88871e11			0.898923			0.449462	−	0.893300i	$-0.351616\pi$
$811$	3.88871e11			0.898923			0.449462	+	0.893300i	$0.351616\pi$
$812$			3.40869e11i			0.784087i
$813$	6.98417e11	−	2.05730e11i	1.59865	−	0.470907i
$814$	−1.58071e11			−0.360044
$815$			6.37540e10i			0.144503i
$816$	6.22500e10	+	2.11328e11i	0.140404	+	0.476646i
$817$	9.31265e10			0.209019
$818$			1.47734e11i			0.329964i
$819$	−1.51666e11	+	9.78405e10i	−0.337095	+	0.217462i
$820$	−8.34517e10			−0.184578
$821$		−	4.86132e11i		−	1.06999i	−0.844854	−	0.534997i	$-0.820313\pi$
$821$		−	4.86132e11i		−	1.06999i	0.844854	−	0.534997i	$-0.179687\pi$
$822$	−4.33377e11	+	1.27658e11i	−0.949246	+	0.279615i
$823$	3.59285e11			0.783140			0.391570	−	0.920148i	$-0.371932\pi$
$823$	3.59285e11			0.783140			0.391570	+	0.920148i	$0.371932\pi$
$824$			6.82400e11i			1.48023i
$825$	−3.10324e10	−	1.05350e11i	−0.0669883	−	0.227414i
$826$	−6.55047e11			−1.40719
$827$		−	2.32417e10i		−	0.0496874i	−0.999691	−	0.0248437i	$-0.992091\pi$
$827$		−	2.32417e10i		−	0.0496874i	0.999691	−	0.0248437i	$-0.00790881\pi$
$828$	5.67513e10	+	8.79720e10i	0.120741	+	0.187164i
$829$	7.31109e11			1.54798			0.773988	−	0.633200i	$-0.218259\pi$
$829$	7.31109e11			1.54798			0.773988	+	0.633200i	$0.218259\pi$
$830$			1.99741e11i			0.420877i
$831$	4.21246e11	−	1.24085e11i	0.883348	−	0.260204i
$832$	1.49844e11			0.312713
$833$			3.62710e11i			0.753320i
$834$	8.95038e10	+	3.03850e11i	0.185002	+	0.628051i
$835$	−1.37536e11			−0.282924
$836$		−	2.70659e10i		−	0.0554112i
$837$	−1.05568e11	+	1.22472e11i	−0.215095	+	0.249538i
$838$	−2.39764e11			−0.486192
$839$		−	2.00560e11i		−	0.404760i	−0.979307	−	0.202380i	$-0.935132\pi$
$839$		−	2.00560e11i		−	0.404760i	0.979307	−	0.202380i	$-0.0648675\pi$
$840$	−3.00268e11	+	8.84485e10i	−0.603103	+	0.177653i
$841$	−5.52672e11			−1.10480
$842$		−	1.01623e11i		−	0.202182i
$843$	7.14421e10	+	2.42534e11i	0.141463	+	0.480244i
$844$	3.48219e10			0.0686250
$845$			2.11781e11i			0.415395i
$846$	3.09998e11	−	1.99982e11i	0.605170	−	0.390399i
$847$	−5.89310e10			−0.114501
$848$		−	1.09976e11i		−	0.212674i
$849$	−4.72789e11	+	1.39267e11i	−0.909989	+	0.268052i
$850$	−3.98420e11			−0.763248
$851$			4.30243e11i			0.820342i
$852$	5.16991e10	+	1.75510e11i	0.0981125	+	0.333075i
$853$	3.67449e11			0.694066			0.347033	−	0.937853i	$-0.387189\pi$
$853$	3.67449e11			0.694066			0.347033	+	0.937853i	$0.387189\pi$
$854$			7.17208e10i			0.134838i
$855$	5.73577e10	+	8.89119e10i	0.107331	+	0.166378i
$856$	3.25971e11			0.607134
$857$			9.09693e11i			1.68644i	0.537567	+	0.843221i	$0.319344\pi$
$857$			9.09693e11i			1.68644i	−0.537567	+	0.843221i	$0.680656\pi$
$858$	−3.77199e10	+	1.11110e10i	−0.0696019	+	0.0205023i
$859$	−5.49492e11			−1.00923			−0.504614	−	0.863345i	$-0.668365\pi$
$859$	−5.49492e11			−1.00923			−0.504614	+	0.863345i	$0.668365\pi$
$860$			5.29554e10i			0.0968091i
$861$	1.81987e11	+	6.17814e11i	0.331152	+	1.12420i
$862$	−4.08904e11			−0.740615
$863$		−	3.87633e11i		−	0.698840i	−0.936966	−	0.349420i	$-0.886379\pi$
$863$		−	3.87633e11i		−	0.698840i	0.936966	−	0.349420i	$-0.113621\pi$
$864$	−3.32420e11	−	2.86538e11i	−0.596531	−	0.514194i
$865$	−3.34036e10			−0.0596663
$866$			5.29850e11i			0.942067i
$867$	3.52556e11	−	1.03851e11i	0.623952	−	0.183795i
$868$	1.01070e11			0.178051
$869$		−	3.24321e11i		−	0.568717i
$870$	−8.20334e10	−	2.78490e11i	−0.143190	−	0.486107i
$871$	−2.13239e11			−0.370505
$872$			7.53172e11i			1.30265i
$873$	2.02953e11	−	1.30927e11i	0.349413	−	0.225409i
$874$	9.80142e10			0.167975
$875$		−	6.09679e11i		−	1.04008i
$876$	1.43251e11	−	4.21969e10i	0.243267	−	0.0716580i
$877$	−2.30189e11			−0.389122			−0.194561	−	0.980890i	$-0.562328\pi$
$877$	−2.30189e11			−0.389122			−0.194561	+	0.980890i	$0.562328\pi$
$878$		−	2.46739e11i		−	0.415202i
$879$	−9.44251e10	−	3.20557e11i	−0.158173	−	0.536970i
$880$	−3.23304e10			−0.0539114
$881$		−	1.72949e11i		−	0.287088i	−0.989644	−	0.143544i	$-0.954150\pi$
$881$		−	1.72949e11i		−	0.287088i	0.989644	−	0.143544i	$-0.0458499\pi$
$882$	1.45347e11	+	2.25308e11i	0.240178	+	0.372307i
$883$	−9.66785e11			−1.59033			−0.795165	−	0.606393i	$-0.792616\pi$
$883$	−9.66785e11			−1.59033			−0.795165	+	0.606393i	$0.792616\pi$
$884$		−	1.07219e11i		−	0.175575i
$885$	−4.02241e11	+	1.18486e11i	−0.655712	+	0.193150i
$886$	−3.23143e11			−0.524396
$887$			2.15715e11i			0.348486i	0.984703	+	0.174243i	$0.0557478\pi$
$887$			2.15715e11i			0.348486i	−0.984703	+	0.174243i	$0.944252\pi$
$888$	−2.99833e11	−	1.01788e12i	−0.482200	−	1.63699i
$889$	−3.36157e11			−0.538189
$890$		−	2.81031e11i		−	0.447913i
$891$	1.73126e11	+	7.83418e10i	0.274696	+	0.124303i
$892$	−8.95113e9			−0.0141390
$893$			2.59595e11i			0.408217i
$894$	4.62142e11	−	1.36131e11i	0.723478	−	0.213112i
$895$	3.50735e11			0.546622
$896$			3.70942e10i			0.0575537i
$897$	3.02421e10	+	1.02667e11i	0.0467135	+	0.158585i
$898$	8.45772e11			1.30061
$899$			3.12198e11i			0.477959i
$900$	1.86016e11	−	1.20000e11i	0.283518	−	0.182899i
$901$	−4.65537e11			−0.706407
$902$			1.40321e11i			0.211980i
$903$	3.92042e11	−	1.15482e11i	0.589632	−	0.173685i
$904$	1.17209e12			1.75505
$905$		−	2.58989e10i		−	0.0386089i
$906$	−2.75956e11	−	9.36825e11i	−0.409569	−	1.39042i
$907$	3.25292e11			0.480667			0.240333	−	0.970690i	$-0.422743\pi$
$907$	3.25292e11			0.480667			0.240333	+	0.970690i	$0.422743\pi$
$908$		−	3.38926e11i		−	0.498610i
$909$	−5.90340e11	−	9.15105e11i	−0.864662	−	1.34034i
$910$	−9.60880e10			−0.140121
$911$		−	1.03719e12i		−	1.50585i	−0.658104	−	0.752927i	$-0.728641\pi$
$911$		−	1.03719e12i		−	1.50585i	0.658104	−	0.752927i	$-0.271359\pi$
$912$	−1.09929e11	+	3.23812e10i	−0.158903	+	0.0468074i
$913$	−2.52434e11			−0.363299
$914$		−	9.18469e9i		−	0.0131607i
$915$	1.29730e10	+	4.40412e10i	0.0185079	+	0.0628311i
$916$	−2.13331e11			−0.303021
$917$			8.41733e10i			0.119041i
$918$	4.50091e11	−	5.22162e11i	0.633767	−	0.735249i
$919$	−2.16984e11			−0.304205			−0.152103	−	0.988365i	$-0.548604\pi$
$919$	−2.16984e11			−0.304205			−0.152103	+	0.988365i	$0.548604\pi$
$920$			1.85623e11i			0.259108i
$921$	1.12412e11	−	3.31126e10i	0.156233	−	0.0460209i
$922$	5.81200e11			0.804270
$923$			1.87054e11i			0.257727i
$924$	−3.35632e10	−	1.13941e11i	−0.0460443	−	0.156313i
$925$	9.09745e11			1.24266
$926$			9.52123e11i			1.29494i
$927$	8.50647e11	−	5.48758e11i	1.15194	−	0.743125i
$928$	−8.47381e11			−1.14258
$929$			9.82796e11i			1.31947i	0.751497	+	0.659736i	$0.229332\pi$
$929$			9.82796e11i			1.31947i	−0.751497	+	0.659736i	$0.770668\pi$
$930$	−8.25741e10	+	2.43235e10i	−0.110385	+	0.0325158i
$931$	−1.88675e11			−0.251140
$932$		−	4.04954e11i		−	0.536713i
$933$	−1.42186e11	−	4.82697e11i	−0.187642	−	0.637013i
$934$	9.22829e11			1.21265
$935$			1.36857e11i			0.179069i
$936$	−1.43096e11	−	2.21817e11i	−0.186433	−	0.288996i
$937$	1.41312e11			0.183324			0.0916621	−	0.995790i	$-0.470782\pi$
$937$	1.41312e11			0.183324			0.0916621	+	0.995790i	$0.470782\pi$
$938$			8.57006e11i			1.10706i
$939$	−9.14611e11	+	2.69413e11i	−1.17645	+	0.346542i
$940$	−1.47616e11			−0.189070
$941$		−	1.01179e12i		−	1.29042i	−0.764006	−	0.645210i	$-0.776770\pi$
$941$		−	1.01179e12i		−	1.29042i	0.764006	−	0.645210i	$-0.223230\pi$
$942$	1.41622e11	+	4.80783e11i	0.179857	+	0.610584i
$943$	3.81928e11			0.482986
$944$		−	4.54170e11i		−	0.571914i
$945$	3.51719e11	+	3.03173e11i	0.441030	+	0.380157i
$946$	8.90422e10			0.111181
$947$			1.81833e11i			0.226086i	0.993590	+	0.113043i	$0.0360597\pi$
$947$			1.81833e11i			0.226086i	−0.993590	+	0.113043i	$0.963940\pi$
$948$	6.27065e11	−	1.84712e11i	0.776388	−	0.228697i
$949$	1.52674e11			0.188235
$950$		−	2.07251e11i		−	0.254449i
$951$	2.04817e11	+	6.95320e11i	0.250406	+	0.850085i
$952$	−1.43515e12			−1.74722
$953$			8.23641e11i			0.998542i	0.866446	+	0.499271i	$0.166399\pi$
$953$			8.23641e11i			0.998542i	−0.866446	+	0.499271i	$0.833601\pi$
$954$	−2.89182e11	+	1.86553e11i	−0.349122	+	0.225221i
$955$	−1.50816e9			−0.00181316
$956$			1.95005e11i			0.233461i
$957$	3.51956e11	−	1.03674e11i	0.419605	−	0.123601i
$958$	1.01226e12			1.20179
$959$		−	1.39522e12i		−	1.64956i
$960$	−1.08932e11	−	3.69804e11i	−0.128253	−	0.435398i
$961$	−7.60322e11			−0.891465
$962$		−	3.25730e11i		−	0.380327i
$963$	−2.62133e11	−	4.06341e11i	−0.304801	−	0.472482i
$964$	−2.38548e10			−0.0276228
$965$		−	6.82840e11i		−	0.787426i
$966$	4.12618e11	−	1.21543e11i	0.473849	−	0.139580i
$967$	−1.10952e12			−1.26890			−0.634451	−	0.772963i	$-0.718774\pi$
$967$	−1.10952e12			−1.26890			−0.634451	+	0.772963i	$0.718774\pi$
$968$		−	8.61890e10i		−	0.0981635i
$969$	1.37072e11	+	4.65336e11i	0.155473	+	0.527803i
$970$	1.28581e11			0.145242
$971$			5.41910e11i			0.609608i	0.952415	+	0.304804i	$0.0985909\pi$
$971$			5.41910e11i			0.609608i	−0.952415	+	0.304804i	$0.901409\pi$
$972$	−5.28703e10	+	3.79353e11i	−0.0592307	+	0.424989i
$973$	−9.78221e11			−1.09140
$974$			1.11896e11i			0.124330i
$975$	2.17089e11	−	6.39468e10i	0.240225	−	0.0707621i
$976$	−4.97269e10			−0.0548015
$977$			6.42355e11i			0.705013i	0.935809	+	0.352506i	$0.114671\pi$
$977$			6.42355e11i			0.705013i	−0.935809	+	0.352506i	$0.885329\pi$
$978$	6.10538e10	+	2.07267e11i	0.0667356	+	0.226556i
$979$	3.55168e11			0.386636
$980$		−	1.07288e11i		−	0.116318i
$981$	9.38869e11	−	6.05671e11i	1.01375	−	0.653974i
$982$	4.99163e10			0.0536780
$983$		−	1.02977e11i		−	0.110287i	−0.998478	−	0.0551436i	$-0.982438\pi$
$983$		−	1.02977e11i		−	0.110287i	0.998478	−	0.0551436i	$-0.0175617\pi$
$984$	−9.03577e11	+	2.66163e11i	−0.963795	+	0.283901i
$985$	2.33383e11			0.247927
$986$		−	1.33106e12i		−	1.40828i
$987$	3.21913e11	+	1.09284e12i	0.339211	+	1.15156i
$988$	5.57733e10			0.0585327
$989$		−	2.42357e11i		−	0.253321i
$990$	5.48421e10	+	8.50126e10i	0.0570918	+	0.0884998i
$991$	3.42425e11			0.355034			0.177517	−	0.984118i	$-0.443193\pi$
$991$	3.42425e11			0.355034			0.177517	+	0.984118i	$0.443193\pi$
$992$			2.51254e11i			0.259458i
$993$	1.13058e11	−	3.33031e10i	0.116280	−	0.0342521i
$994$	7.51771e11			0.770087
$995$			8.46165e11i			0.863302i
$996$	−1.43769e11	−	4.88073e11i	−0.146093	−	0.495961i
$997$	1.26844e12			1.28378			0.641889	−	0.766797i	$-0.278151\pi$
$997$	1.26844e12			1.28378			0.641889	+	0.766797i	$0.278151\pi$
$998$			7.09041e11i			0.714742i
$999$	−1.02773e12	+	1.19230e12i	−1.03185	+	1.19708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.9.b.a.23.18	yes	26
3.2	odd	2	inner	33.9.b.a.23.9	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.9.b.a.23.9	✓	26	3.2	odd	2	inner
33.9.b.a.23.18	yes	26	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	33.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+12.0893i q^{2} +(-77.6992 + 22.8875i) q^{3} +109.849 q^{4} -288.931i q^{5} +(-276.694 - 939.329i) q^{6} +3024.09 q^{7} +4422.86i q^{8} +(5513.32 - 3556.68i) q^{9} +O(q^{10})\)	\(q+12.0893i q^{2} +(-77.6992 + 22.8875i) q^{3} +109.849 q^{4} -288.931i q^{5} +(-276.694 - 939.329i) q^{6} +3024.09 q^{7} +4422.86i q^{8} +(5513.32 - 3556.68i) q^{9} +3492.97 q^{10} +4414.43i q^{11} +(-8535.16 + 2514.17i) q^{12} -9096.59 q^{13} +36559.2i q^{14} +(6612.91 + 22449.7i) q^{15} -25347.9 q^{16} +107300. i q^{17} +(42997.8 + 66652.2i) q^{18} -55815.2 q^{19} -31738.7i q^{20} +(-234970. + 69214.0i) q^{21} -53367.3 q^{22} +145256. i q^{23} +(-101228. - 343652. i) q^{24} +307144. q^{25} -109971. i q^{26} +(-346977. + 402537. i) q^{27} +332193. q^{28} +1.02612e6i q^{29} +(-271401. + 79945.4i) q^{30} +304251. q^{31} +825812. i q^{32} +(-101035. - 342997. i) q^{33} -1.29718e6 q^{34} -873754. i q^{35} +(605632. - 390697. i) q^{36} +2.96195e6 q^{37} -674767. i q^{38} +(706798. - 208198. i) q^{39} +1.27790e6 q^{40} -2.62933e6i q^{41} +(-836749. - 2.84062e6i) q^{42} -1.66848e6 q^{43} +484920. i q^{44} +(-1.02763e6 - 1.59297e6i) q^{45} -1.75605e6 q^{46} -4.65098e6i q^{47} +(1.96951e6 - 580151. i) q^{48} +3.38035e6 q^{49} +3.71316e6i q^{50} +(-2.45582e6 - 8.33709e6i) q^{51} -999250. q^{52} +4.33867e6i q^{53} +(-4.86640e6 - 4.19471e6i) q^{54} +1.27546e6 q^{55} +1.33751e7i q^{56} +(4.33680e6 - 1.27747e6i) q^{57} -1.24050e7 q^{58} +1.79174e7i q^{59} +(726420. + 2.46607e6i) q^{60} +1.96177e6 q^{61} +3.67818e6i q^{62} +(1.66728e7 - 1.07557e7i) q^{63} -1.64726e7 q^{64} +2.62829e6i q^{65} +(4.14660e6 - 1.22145e6i) q^{66} +2.34416e7 q^{67} +1.17867e7i q^{68} +(-3.32456e6 - 1.12863e7i) q^{69} +1.05631e7 q^{70} -2.05631e7i q^{71} +(1.57307e7 + 2.43846e7i) q^{72} -1.67837e7 q^{73} +3.58079e7i q^{74} +(-2.38648e7 + 7.02976e6i) q^{75} -6.13124e6 q^{76} +1.33496e7i q^{77} +(2.51697e6 + 8.54469e6i) q^{78} -7.34684e7 q^{79} +7.32380e6i q^{80} +(1.77468e7 - 3.92183e7i) q^{81} +3.17868e7 q^{82} +5.71837e7i q^{83} +(-2.58111e7 + 7.60307e6i) q^{84} +3.10022e7 q^{85} -2.01707e7i q^{86} +(-2.34853e7 - 7.97285e7i) q^{87} -1.95244e7 q^{88} -8.04561e7i q^{89} +(1.92579e7 - 1.24234e7i) q^{90} -2.75089e7 q^{91} +1.59563e7i q^{92} +(-2.36401e7 + 6.96355e6i) q^{93} +5.62271e7 q^{94} +1.61267e7i q^{95} +(-1.89008e7 - 6.41649e7i) q^{96} +3.68114e7 q^{97} +4.08660e7i q^{98} +(1.57007e7 + 2.43382e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9}+O(q^{10}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9} - 31836 q^{10} - 28900 q^{12} - 131624 q^{13} + 71041 q^{15} + 311972 q^{16} - 675394 q^{18} + 134608 q^{19} + 490306 q^{21} - 59088 q^{24} - 2324740 q^{25} + 2011426 q^{27} - 1996688 q^{28} - 324146 q^{30} + 964738 q^{31} - 512435 q^{33} + 9219648 q^{34} - 6887660 q^{36} - 5721542 q^{37} - 5782712 q^{39} + 8363496 q^{40} + 10350076 q^{42} + 4260820 q^{43} + 6595181 q^{45} - 39680292 q^{46} + 22674164 q^{48} + 20017254 q^{49} - 7985018 q^{51} + 48711952 q^{52} - 18774176 q^{54} - 4304454 q^{55} + 15476796 q^{57} - 16060008 q^{58} - 26730016 q^{60} + 58840 q^{61} - 42877282 q^{63} - 57365836 q^{64} - 10395110 q^{66} - 63186734 q^{67} + 100738079 q^{69} + 50969160 q^{70} + 48890880 q^{72} - 21879656 q^{73} - 122009926 q^{75} - 119289368 q^{76} - 123440744 q^{78} + 117211444 q^{79} + 138667019 q^{81} + 121755480 q^{82} - 28504816 q^{84} + 28880604 q^{85} + 14774868 q^{87} + 90481380 q^{88} + 189044834 q^{90} + 192183008 q^{91} - 113622071 q^{93} - 453996696 q^{94} + 11988416 q^{96} + 24314206 q^{97} - 57905155 q^{99}+O(q^{100}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9 - 31836 * q^10 - 28900 * q^12 - 131624 * q^13 + 71041 * q^15 + 311972 * q^16 - 675394 * q^18 + 134608 * q^19 + 490306 * q^21 - 59088 * q^24 - 2324740 * q^25 + 2011426 * q^27 - 1996688 * q^28 - 324146 * q^30 + 964738 * q^31 - 512435 * q^33 + 9219648 * q^34 - 6887660 * q^36 - 5721542 * q^37 - 5782712 * q^39 + 8363496 * q^40 + 10350076 * q^42 + 4260820 * q^43 + 6595181 * q^45 - 39680292 * q^46 + 22674164 * q^48 + 20017254 * q^49 - 7985018 * q^51 + 48711952 * q^52 - 18774176 * q^54 - 4304454 * q^55 + 15476796 * q^57 - 16060008 * q^58 - 26730016 * q^60 + 58840 * q^61 - 42877282 * q^63 - 57365836 * q^64 - 10395110 * q^66 - 63186734 * q^67 + 100738079 * q^69 + 50969160 * q^70 + 48890880 * q^72 - 21879656 * q^73 - 122009926 * q^75 - 119289368 * q^76 - 123440744 * q^78 + 117211444 * q^79 + 138667019 * q^81 + 121755480 * q^82 - 28504816 * q^84 + 28880604 * q^85 + 14774868 * q^87 + 90481380 * q^88 + 189044834 * q^90 + 192183008 * q^91 - 113622071 * q^93 - 453996696 * q^94 + 11988416 * q^96 + 24314206 * q^97 - 57905155 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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