LMFDB - Embedded newform 33.9.b.a.23.20

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			23.20
Character	$\chi$	$=$	33.23
Dual form			33.9.b.a.23.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.2016i q^{2} +(-80.7607 + 6.22143i) q^{3} -6.49112 q^{4} +809.269i q^{5} +(-100.797 - 1308.45i) q^{6} -3530.96 q^{7} +4042.44i q^{8} +(6483.59 - 1004.89i) q^{9} +O(q^{10})$	\(q+16.2016i q^{2} +(-80.7607 + 6.22143i) q^{3} -6.49112 q^{4} +809.269i q^{5} +(-100.797 - 1308.45i) q^{6} -3530.96 q^{7} +4042.44i q^{8} +(6483.59 - 1004.89i) q^{9} -13111.4 q^{10} -4414.43i q^{11} +(524.228 - 40.3840i) q^{12} -10356.8 q^{13} -57207.1i q^{14} +(-5034.81 - 65357.2i) q^{15} -67155.6 q^{16} -92534.7i q^{17} +(16280.9 + 105044. i) q^{18} +184504. q^{19} -5253.06i q^{20} +(285163. - 21967.6i) q^{21} +71520.7 q^{22} -201854. i q^{23} +(-25149.7 - 326470. i) q^{24} -264291. q^{25} -167796. i q^{26} +(-517367. + 121493. i) q^{27} +22919.9 q^{28} +37264.0i q^{29} +(1.05889e6 - 81571.8i) q^{30} -1.26758e6 q^{31} -53162.6i q^{32} +(27464.0 + 356512. i) q^{33} +1.49921e6 q^{34} -2.85750e6i q^{35} +(-42085.8 + 6522.89i) q^{36} -2.14855e6 q^{37} +2.98925e6i q^{38} +(836419. - 64433.8i) q^{39} -3.27142e6 q^{40} +3.61216e6i q^{41} +(355910. + 4.62009e6i) q^{42} -2.62505e6 q^{43} +28654.6i q^{44} +(813230. + 5.24697e6i) q^{45} +3.27036e6 q^{46} -4.99275e6i q^{47} +(5.42353e6 - 417804. i) q^{48} +6.70286e6 q^{49} -4.28194e6i q^{50} +(575698. + 7.47317e6i) q^{51} +67227.0 q^{52} +1.16999e7i q^{53} +(-1.96838e6 - 8.38217e6i) q^{54} +3.57246e6 q^{55} -1.42737e7i q^{56} +(-1.49006e7 + 1.14788e6i) q^{57} -603736. q^{58} +417021. i q^{59} +(32681.6 + 424241. i) q^{60} +1.53477e7 q^{61} -2.05368e7i q^{62} +(-2.28933e7 + 3.54824e6i) q^{63} -1.63305e7 q^{64} -8.38140e6i q^{65} +(-5.77606e6 + 444961. i) q^{66} -8.02130e6 q^{67} +600654. i q^{68} +(1.25582e6 + 1.63019e7i) q^{69} +4.62959e7 q^{70} -3.66962e7i q^{71} +(4.06222e6 + 2.62095e7i) q^{72} -1.19377e7 q^{73} -3.48099e7i q^{74} +(2.13444e7 - 1.64427e6i) q^{75} -1.19764e6 q^{76} +1.55872e7i q^{77} +(1.04393e6 + 1.35513e7i) q^{78} -3.44849e7 q^{79} -5.43469e7i q^{80} +(4.10271e7 - 1.30306e7i) q^{81} -5.85227e7 q^{82} +6.78006e7i q^{83} +(-1.85103e6 + 142594. i) q^{84} +7.48855e7 q^{85} -4.25299e7i q^{86} +(-231835. - 3.00947e6i) q^{87} +1.78450e7 q^{88} -3.79929e6i q^{89} +(-8.50091e7 + 1.31756e7i) q^{90} +3.65693e7 q^{91} +1.31026e6i q^{92} +(1.02371e8 - 7.88617e6i) q^{93} +8.08904e7 q^{94} +1.49313e8i q^{95} +(330747. + 4.29345e6i) q^{96} -1.09278e8 q^{97} +1.08597e8i q^{98} +(-4.43603e6 - 2.86213e7i) 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 $

$2$			16.2016i			1.01260i	0.862358	+	0.506299i	$0.168987\pi$
$2$			16.2016i			1.01260i	−0.862358	+	0.506299i	$0.831013\pi$
$3$	−80.7607	+	6.22143i	−0.997046	+	0.0768077i
$3$	−80.7607	+	6.22143i	−0.997046	+	0.0768077i
$4$	−6.49112			−0.0253559
$5$			809.269i			1.29483i	0.762137	+	0.647415i	$0.224150\pi$
$5$			809.269i			1.29483i	−0.762137	+	0.647415i	$0.775850\pi$
$6$	−100.797	−	1308.45i	−0.0777754	−	1.00961i
$7$	−3530.96			−1.47062			−0.735310	−	0.677731i	$-0.762963\pi$
$7$	−3530.96			−1.47062			−0.735310	+	0.677731i	$0.762963\pi$
$8$			4042.44i			0.986923i
$9$	6483.59	−	1004.89i	0.988201	−	0.153162i
$10$	−13111.4			−1.31114
$11$		−	4414.43i		−	0.301511i
$11$		−	4414.43i		−	0.301511i
$12$	524.228	−	40.3840i	0.0252810	−	0.00194753i
$13$	−10356.8			−0.362619			−0.181309	−	0.983426i	$-0.558034\pi$
$13$	−10356.8			−0.362619			−0.181309	+	0.983426i	$0.558034\pi$
$14$		−	57207.1i		−	1.48915i
$15$	−5034.81	−	65357.2i	−0.0994530	−	1.29101i
$16$	−67155.6			−1.02471
$17$		−	92534.7i		−	1.10792i	−0.832543	−	0.553961i	$-0.813116\pi$
$17$		−	92534.7i		−	1.10792i	0.832543	−	0.553961i	$-0.186884\pi$
$18$	16280.9	+	105044.i	0.155091	+	1.00065i
$19$	184504.			1.41576			0.707881	−	0.706331i	$-0.249651\pi$
$19$	184504.			1.41576			0.707881	+	0.706331i	$0.249651\pi$
$20$		−	5253.06i		−	0.0328317i
$21$	285163.	−	21967.6i	1.46628	−	0.112955i
$22$	71520.7			0.305310
$23$		−	201854.i		−	0.721317i	−0.932698	−	0.360659i	$-0.882552\pi$
$23$		−	201854.i		−	0.721317i	0.932698	−	0.360659i	$-0.117448\pi$
$24$	−25149.7	−	326470.i	−0.0758033	−	0.984008i
$25$	−264291.			−0.676586
$26$		−	167796.i		−	0.367187i
$27$	−517367.	+	121493.i	−0.973518	+	0.228611i
$28$	22919.9			0.0372890
$29$			37264.0i			0.0526863i	0.999653	+	0.0263431i	$0.00838625\pi$
$29$			37264.0i			0.0526863i	−0.999653	+	0.0263431i	$0.991614\pi$
$30$	1.05889e6	−	81571.8i	1.30727	−	0.100706i
$31$	−1.26758e6			−1.37255			−0.686277	−	0.727341i	$-0.740756\pi$
$31$	−1.26758e6			−1.37255			−0.686277	+	0.727341i	$0.740756\pi$
$32$		−	53162.6i		−	0.0506998i
$33$	27464.0	+	356512.i	0.0231584	+	0.300621i
$34$	1.49921e6			1.12188
$35$		−	2.85750e6i		−	1.90420i
$36$	−42085.8	+	6522.89i	−0.0250568	+	0.00388356i
$37$	−2.14855e6			−1.14640			−0.573202	−	0.819414i	$-0.694299\pi$
$37$	−2.14855e6			−1.14640			−0.573202	+	0.819414i	$0.694299\pi$
$38$			2.98925e6i			1.43360i
$39$	836419.	−	64433.8i	0.361548	−	0.0278519i
$40$	−3.27142e6			−1.27790
$41$			3.61216e6i			1.27830i	0.769083	+	0.639148i	$0.220713\pi$
$41$			3.61216e6i			1.27830i	−0.769083	+	0.639148i	$0.779287\pi$
$42$	355910.	+	4.62009e6i	0.114378	+	1.48475i
$43$	−2.62505e6			−0.767827			−0.383913	−	0.923369i	$-0.625424\pi$
$43$	−2.62505e6			−0.767827			−0.383913	+	0.923369i	$0.625424\pi$
$44$			28654.6i			0.00764511i
$45$	813230.	+	5.24697e6i	0.198318	+	1.27955i
$46$	3.27036e6			0.730405
$47$		−	4.99275e6i		−	1.02317i	−0.859233	−	0.511585i	$-0.829058\pi$
$47$		−	4.99275e6i		−	1.02317i	0.859233	−	0.511585i	$-0.170942\pi$
$48$	5.42353e6	−	417804.i	1.02169	−	0.0787059i
$49$	6.70286e6			1.16272
$50$		−	4.28194e6i		−	0.685110i
$51$	575698.	+	7.47317e6i	0.0850970	+	1.10465i
$52$	67227.0			0.00919454
$53$			1.16999e7i			1.48279i	0.671069	+	0.741395i	$0.265835\pi$
$53$			1.16999e7i			1.48279i	−0.671069	+	0.741395i	$0.734165\pi$
$54$	−1.96838e6	−	8.38217e6i	−0.231491	−	0.985783i
$55$	3.57246e6			0.390406
$56$		−	1.42737e7i		−	1.45139i
$57$	−1.49006e7	+	1.14788e6i	−1.41158	+	0.108742i
$58$	−603736.			−0.0533500
$59$			417021.i			0.0344152i	0.999852	+	0.0172076i	$0.00547762\pi$
$59$			417021.i			0.0344152i	−0.999852	+	0.0172076i	$0.994522\pi$
$60$	32681.6	+	424241.i	0.00252173	+	0.0327347i
$61$	1.53477e7			1.10847			0.554236	−	0.832360i	$-0.313011\pi$
$61$	1.53477e7			1.10847			0.554236	+	0.832360i	$0.313011\pi$
$62$		−	2.05368e7i		−	1.38985i
$63$	−2.28933e7	+	3.54824e6i	−1.45327	+	0.225243i
$64$	−1.63305e7			−0.973375
$65$		−	8.38140e6i		−	0.469530i
$66$	−5.77606e6	+	444961.i	−0.304408	+	0.0234502i
$67$	−8.02130e6			−0.398057			−0.199029	−	0.979994i	$-0.563779\pi$
$67$	−8.02130e6			−0.398057			−0.199029	+	0.979994i	$0.563779\pi$
$68$			600654.i			0.0280924i
$69$	1.25582e6	+	1.63019e7i	0.0554028	+	0.719186i
$70$	4.62959e7			1.92819
$71$		−	3.66962e7i		−	1.44407i	−0.691857	−	0.722035i	$-0.743207\pi$
$71$		−	3.66962e7i		−	1.44407i	0.691857	−	0.722035i	$-0.256793\pi$
$72$	4.06222e6	+	2.62095e7i	0.151159	+	0.975279i
$73$	−1.19377e7			−0.420368			−0.210184	−	0.977662i	$-0.567406\pi$
$73$	−1.19377e7			−0.420368			−0.210184	+	0.977662i	$0.567406\pi$
$74$		−	3.48099e7i		−	1.16085i
$75$	2.13444e7	−	1.64427e6i	0.674587	−	0.0519670i
$76$	−1.19764e6			−0.0358980
$77$			1.55872e7i			0.443409i
$78$	1.04393e6	+	1.35513e7i	0.0282028	+	0.366103i
$79$	−3.44849e7			−0.885361			−0.442681	−	0.896679i	$-0.645972\pi$
$79$	−3.44849e7			−0.885361			−0.442681	+	0.896679i	$0.645972\pi$
$80$		−	5.43469e7i		−	1.32683i
$81$	4.10271e7	−	1.30306e7i	0.953083	−	0.302709i
$82$	−5.85227e7			−1.29440
$83$			6.78006e7i			1.42863i	0.699822	+	0.714317i	$0.253263\pi$
$83$			6.78006e7i			1.42863i	−0.699822	+	0.714317i	$0.746737\pi$
$84$	−1.85103e6	+	142594.i	−0.0371788	+	0.00286408i
$85$	7.48855e7			1.43457
$86$		−	4.25299e7i		−	0.777500i
$87$	−231835.	−	3.00947e6i	−0.00404671	−	0.0525306i
$88$	1.78450e7			0.297569
$89$		−	3.79929e6i		−	0.0605540i	−0.999542	−	0.0302770i	$-0.990361\pi$
$89$		−	3.79929e6i		−	0.0605540i	0.999542	−	0.0302770i	$-0.00963894\pi$
$90$	−8.50091e7	+	1.31756e7i	−1.29567	+	0.200817i
$91$	3.65693e7			0.533274
$92$			1.31026e6i			0.0182897i
$93$	1.02371e8	−	7.88617e6i	1.36850	−	0.105423i
$94$	8.08904e7			1.03606
$95$			1.49313e8i			1.83317i
$96$	330747.	+	4.29345e6i	0.00389413	+	0.0505500i
$97$	−1.09278e8			−1.23437			−0.617184	−	0.786819i	$-0.711727\pi$
$97$	−1.09278e8			−1.23437			−0.617184	+	0.786819i	$0.711727\pi$
$98$			1.08597e8i			1.17737i
$99$	−4.43603e6	−	2.86213e7i	−0.0461800	−	0.297954i
$100$	1.71555e6			0.0171555
$101$			1.50287e8i			1.44423i	0.691773	+	0.722115i	$0.256830\pi$
$101$			1.50287e8i			1.44423i	−0.691773	+	0.722115i	$0.743170\pi$
$102$	−1.21077e8	+	9.32722e6i	−1.11857	+	0.0861691i
$103$	−1.26768e8			−1.12632			−0.563160	−	0.826348i	$-0.690415\pi$
$103$	−1.26768e8			−1.12632			−0.563160	+	0.826348i	$0.690415\pi$
$104$		−	4.18665e7i		−	0.357877i
$105$	1.77777e7	+	2.30773e8i	0.146258	+	1.89858i
$106$	−1.89557e8			−1.50147
$107$		−	2.33208e8i		−	1.77913i	−0.456809	−	0.889565i	$-0.651008\pi$
$107$		−	2.33208e8i		−	1.77913i	0.456809	−	0.889565i	$-0.348992\pi$
$108$	3.35829e6	−	788627.i	0.0246845	−	0.00579664i
$109$	−1.94192e8			−1.37571			−0.687853	−	0.725850i	$-0.741447\pi$
$109$	−1.94192e8			−1.37571			−0.687853	+	0.725850i	$0.741447\pi$
$110$			5.78795e7i			0.395325i
$111$	1.73518e8	−	1.33670e7i	1.14302	−	0.0880528i
$112$	2.37124e8			1.50696
$113$		−	2.70114e8i		−	1.65666i	−0.560239	−	0.828331i	$-0.689291\pi$
$113$		−	2.70114e8i		−	1.65666i	0.560239	−	0.828331i	$-0.310709\pi$
$114$	−1.85974e7	−	2.41414e8i	−0.110112	−	1.42936i
$115$	1.63354e8			0.933984
$116$		−	241885.i		−	0.00133591i
$117$	−6.71489e7	+	1.04074e7i	−0.358340	+	0.0555393i
$118$	−6.75640e6			−0.0348488
$119$			3.26736e8i			1.62933i
$120$	2.64202e8	−	2.03529e7i	1.27412	−	0.0981525i
$121$	−1.94872e7			−0.0909091
$122$			2.48657e8i			1.12244i
$123$	−2.24728e7	−	2.91721e8i	−0.0981831	−	1.27452i
$124$	8.22803e6			0.0348024
$125$			1.02238e8i			0.418766i
$126$	−5.74871e7	−	3.70907e8i	−0.228080	−	1.47158i
$127$	1.13356e8			0.435743			0.217872	−	0.975977i	$-0.430089\pi$
$127$	1.13356e8			0.435743			0.217872	+	0.975977i	$0.430089\pi$
$128$		−	2.78190e8i		−	1.03634i
$129$	2.12001e8	−	1.63315e7i	0.765558	−	0.0589750i
$130$	1.35792e8			0.475445
$131$		−	1.15367e8i		−	0.391738i	−0.980630	−	0.195869i	$-0.937247\pi$
$131$		−	1.15367e8i		−	0.391738i	0.980630	−	0.195869i	$-0.0627527\pi$
$132$	−178272.	−	2.31417e6i	−0.000587203	−	0.00762252i
$133$	−6.51475e8			−2.08205
$134$		−	1.29958e8i		−	0.403072i
$135$	−9.83206e7	−	4.18689e8i	−0.296012	−	1.26054i
$136$	3.74066e8			1.09343
$137$			3.94517e8i			1.11991i	0.828523	+	0.559955i	$0.189182\pi$
$137$			3.94517e8i			1.11991i	−0.828523	+	0.559955i	$0.810818\pi$
$138$	−2.64116e8	+	2.03463e7i	−0.728247	+	0.0561007i
$139$	1.85138e8			0.495949			0.247975	−	0.968767i	$-0.420235\pi$
$139$	1.85138e8			0.495949			0.247975	+	0.968767i	$0.420235\pi$
$140$			1.85483e7i			0.0482829i
$141$	3.10620e7	+	4.03218e8i	0.0785874	+	1.02015i
$142$	5.94537e8			1.46226
$143$			4.57191e7i			0.109334i
$144$	−4.35409e8	+	6.74842e7i	−1.01262	+	0.156947i
$145$	−3.01566e7			−0.0682198
$146$		−	1.93410e8i		−	0.425664i
$147$	−5.41328e8	+	4.17014e7i	−1.15929	+	0.0893061i
$148$	1.39465e7			0.0290682
$149$			2.46239e8i			0.499587i	0.968299	+	0.249794i	$0.0803628\pi$
$149$			2.46239e8i			0.499587i	−0.968299	+	0.249794i	$0.919637\pi$
$150$	2.66398e7	+	3.45812e8i	0.0526218	+	0.683086i
$151$	−2.67578e8			−0.514686			−0.257343	−	0.966320i	$-0.582847\pi$
$151$	−2.67578e8			−0.514686			−0.257343	+	0.966320i	$0.582847\pi$
$152$			7.45844e8i			1.39725i
$153$	−9.29876e7	−	5.99957e8i	−0.169691	−	1.09485i
$154$	−2.52537e8			−0.448995
$155$		−	1.02581e9i		−	1.77722i
$156$	−5.42930e6	+	418248.i	−0.00916738	+	0.000706212i
$157$	3.28157e8			0.540111			0.270056	−	0.962845i	$-0.412958\pi$
$157$	3.28157e8			0.540111			0.270056	+	0.962845i	$0.412958\pi$
$158$		−	5.58710e8i		−	0.896516i
$159$	−7.27902e7	−	9.44894e8i	−0.113890	−	1.47841i
$160$	4.30228e7			0.0656476
$161$			7.12738e8i			1.06078i
$162$	2.11117e8	+	6.64704e8i	0.306523	+	0.965091i
$163$	7.69943e8			1.09071			0.545354	−	0.838206i	$-0.316395\pi$
$163$	7.69943e8			1.09071			0.545354	+	0.838206i	$0.316395\pi$
$164$		−	2.34470e7i		−	0.0324124i
$165$	−2.88514e8	+	2.22258e7i	−0.389253	+	0.0299862i
$166$	−1.09848e9			−1.44663
$167$			1.06785e9i			1.37291i	0.727171	+	0.686457i	$0.240835\pi$
$167$			1.06785e9i			1.37291i	−0.727171	+	0.686457i	$0.759165\pi$
$168$	8.88026e7	+	1.15275e9i	0.111478	+	1.44710i
$169$	−7.08468e8			−0.868508
$170$			1.21326e9i			1.45264i
$171$	1.19625e9	−	1.85407e8i	1.39906	−	0.216841i
$172$	1.70395e7			0.0194690
$173$		−	3.17187e8i		−	0.354104i	−0.984201	−	0.177052i	$-0.943344\pi$
$173$		−	3.17187e8i		−	0.354104i	0.984201	−	0.177052i	$-0.0566561\pi$
$174$	4.87581e7	−	3.75610e6i	0.0531924	−	0.00409770i
$175$	9.33202e8			0.995001
$176$			2.96454e8i			0.308963i
$177$	−2.59447e6	−	3.36789e7i	−0.00264335	−	0.0343135i
$178$	6.15545e7			0.0613169
$179$			4.84139e6i			0.00471583i	0.999997	+	0.00235792i	$0.000750549\pi$
$179$			4.84139e6i			0.00471583i	−0.999997	+	0.00235792i	$0.999249\pi$
$180$	−5.27877e6	−	3.40587e7i	−0.00502855	−	0.0324443i
$181$	5.53185e8			0.515414			0.257707	−	0.966223i	$-0.417033\pi$
$181$	5.53185e8			0.515414			0.257707	+	0.966223i	$0.417033\pi$
$182$			5.92480e8i			0.539993i
$183$	−1.23949e9	+	9.54847e7i	−1.10520	+	0.0851392i
$184$	8.15983e8			0.711885
$185$		−	1.73875e9i		−	1.48440i
$186$	1.27768e8	+	1.65857e9i	0.106751	+	1.38574i
$187$	−4.08488e8			−0.334051
$188$			3.24085e7i			0.0259435i
$189$	1.82680e9	−	4.28987e8i	1.43167	−	0.336199i
$190$	−2.41911e9			−1.85627
$191$		−	3.13087e8i		−	0.235251i	−0.993058	−	0.117625i	$-0.962472\pi$
$191$		−	3.13087e8i		−	0.235251i	0.993058	−	0.117625i	$-0.0375282\pi$
$192$	1.31886e9	−	1.01599e8i	0.970499	−	0.0747627i
$193$	4.83543e8			0.348502			0.174251	−	0.984701i	$-0.444250\pi$
$193$	4.83543e8			0.348502			0.174251	+	0.984701i	$0.444250\pi$
$194$		−	1.77047e9i		−	1.24992i
$195$	5.21443e7	+	6.76888e8i	0.0360635	+	0.468143i
$196$	−4.35091e7			−0.0294819
$197$		−	8.26672e8i		−	0.548868i	−0.961606	−	0.274434i	$-0.911509\pi$
$197$		−	8.26672e8i		−	0.548868i	0.961606	−	0.274434i	$-0.0884905\pi$
$198$	4.63711e8	−	7.18707e7i	0.301708	−	0.0467618i
$199$	1.09074e8			0.0695520			0.0347760	−	0.999395i	$-0.488928\pi$
$199$	1.09074e8			0.0695520			0.0347760	+	0.999395i	$0.488928\pi$
$200$		−	1.06838e9i		−	0.667738i
$201$	6.47806e8	−	4.99039e7i	0.396881	−	0.0305739i
$202$	−2.43489e9			−1.46243
$203$		−	1.31578e8i		−	0.0774815i
$204$	−3.73693e6	−	4.85093e7i	−0.00215771	−	0.0280094i
$205$	−2.92321e9			−1.65518
$206$		−	2.05385e9i		−	1.14051i
$207$	−2.02842e8	−	1.30874e9i	−0.110478	−	0.712807i
$208$	6.95514e8			0.371580
$209$		−	8.14478e8i		−	0.426869i
$210$	−3.73889e9	+	2.88027e8i	−1.92250	+	0.148100i
$211$	−2.01418e9			−1.01617			−0.508086	−	0.861306i	$-0.669647\pi$
$211$	−2.01418e9			−1.01617			−0.508086	+	0.861306i	$0.669647\pi$
$212$		−	7.59456e7i		−	0.0375975i
$213$	2.28303e8	+	2.96361e9i	0.110916	+	1.43980i
$214$	3.77833e9			1.80154
$215$		−	2.12437e9i		−	0.994205i
$216$	−4.91128e8	−	2.09143e9i	−0.225621	−	0.960787i
$217$	4.47578e9			2.01850
$218$		−	3.14622e9i		−	1.39304i
$219$	9.64099e8	−	7.42696e7i	0.419126	−	0.0322875i
$220$	−2.31893e7			−0.00989912
$221$			9.58359e8i			0.401753i
$222$	2.16567e8	+	2.81127e9i	0.0891621	+	1.15742i
$223$	−3.24663e9			−1.31284			−0.656422	−	0.754394i	$-0.727931\pi$
$223$	−3.24663e9			−1.31284			−0.656422	+	0.754394i	$0.727931\pi$
$224$			1.87715e8i			0.0745601i
$225$	−1.71356e9	+	2.65585e8i	−0.668603	+	0.103627i
$226$	4.37628e9			1.67753
$227$			2.62037e9i			0.986868i	0.869783	+	0.493434i	$0.164259\pi$
$227$			2.62037e9i			0.986868i	−0.869783	+	0.493434i	$0.835741\pi$
$228$	9.67219e7	−	7.45100e6i	0.0357920	−	0.00275724i
$229$	−7.80560e8			−0.283834			−0.141917	−	0.989879i	$-0.545327\pi$
$229$	−7.80560e8			−0.283834			−0.141917	+	0.989879i	$0.545327\pi$
$230$			2.64660e9i			0.945751i
$231$	−9.69744e7	−	1.25883e9i	−0.0340572	−	0.442099i
$232$	−1.50637e8			−0.0519973
$233$		−	6.51126e8i		−	0.220923i	−0.993880	−	0.110462i	$-0.964767\pi$
$233$		−	6.51126e8i		−	0.220923i	0.993880	−	0.110462i	$-0.0352329\pi$
$234$	−1.68617e8	−	1.08792e9i	−0.0562390	−	0.362855i
$235$	4.04047e9			1.32483
$236$		−	2.70694e6i		−	0.000872630i
$237$	2.78503e9	−	2.14545e8i	0.882746	−	0.0680026i
$238$	−5.29364e9			−1.64986
$239$			3.98094e9i			1.22010i	0.792365	+	0.610048i	$0.208850\pi$
$239$			3.98094e9i			1.22010i	−0.792365	+	0.610048i	$0.791150\pi$
$240$	3.38116e8	+	4.38910e9i	0.101911	+	1.32291i
$241$	3.63924e9			1.07880			0.539402	−	0.842048i	$-0.318650\pi$
$241$	3.63924e9			1.07880			0.539402	+	0.842048i	$0.318650\pi$
$242$		−	3.15723e8i		−	0.0920544i
$243$	−3.23231e9	+	1.30761e9i	−0.927017	+	0.375019i
$244$	−9.96239e7			−0.0281063
$245$			5.42442e9i			1.50553i
$246$	4.72634e9	−	3.64095e8i	1.29058	−	0.0994201i
$247$	−1.91086e9			−0.513382
$248$		−	5.12412e9i		−	1.35460i
$249$	−4.21816e8	−	5.47562e9i	−0.109730	−	1.42441i
$250$	−1.65641e9			−0.424042
$251$		−	3.48706e9i		−	0.878546i	−0.898354	−	0.439273i	$-0.855236\pi$
$251$		−	3.48706e9i		−	0.878546i	0.898354	−	0.439273i	$-0.144764\pi$
$252$	1.48603e8	−	2.30320e7i	0.0368490	−	0.00571124i
$253$	−8.91071e8			−0.217485
$254$			1.83655e9i			0.441233i
$255$	−6.04781e9	+	4.65895e8i	−1.43033	+	0.110186i
$256$	3.26501e8			0.0760193
$257$			2.29937e9i			0.527079i	0.964649	+	0.263540i	$0.0848900\pi$
$257$			2.29937e9i			0.527079i	−0.964649	+	0.263540i	$0.915110\pi$
$258$	2.64597e8	+	3.43474e9i	0.0597180	+	0.775203i
$259$	7.58643e9			1.68593
$260$			5.44047e7i			0.0119054i
$261$	3.74464e7	+	2.41604e8i	0.00806952	+	0.0520646i
$262$	1.86912e9			0.396673
$263$			5.11934e9i			1.07002i	0.844846	+	0.535009i	$0.179692\pi$
$263$			5.11934e9i			1.07002i	−0.844846	+	0.535009i	$0.820308\pi$
$264$	−1.44118e9	+	1.11022e8i	−0.296690	+	0.0228556i
$265$	−9.46839e9			−1.91996
$266$		−	1.05549e10i		−	2.10828i
$267$	2.36370e7	+	3.06834e8i	0.00465101	+	0.0603751i
$268$	5.20672e7			0.0100931
$269$			6.95627e9i			1.32852i	0.747503	+	0.664259i	$0.231253\pi$
$269$			6.95627e9i			1.32852i	−0.747503	+	0.664259i	$0.768747\pi$
$270$	6.78343e9	−	1.59295e9i	1.27642	−	0.299742i
$271$	2.84996e9			0.528398			0.264199	−	0.964468i	$-0.414892\pi$
$271$	2.84996e9			0.528398			0.264199	+	0.964468i	$0.414892\pi$
$272$			6.21422e9i			1.13530i
$273$	−2.95336e9	+	2.27513e8i	−0.531699	+	0.0409596i
$274$	−6.39180e9			−1.13402
$275$			1.16670e9i			0.203998i
$276$	−8.15169e6	−	1.05818e8i	−0.00140479	−	0.0182357i
$277$	−4.15240e9			−0.705310			−0.352655	−	0.935753i	$-0.614721\pi$
$277$	−4.15240e9			−0.705310			−0.352655	+	0.935753i	$0.614721\pi$
$278$			2.99953e9i			0.502198i
$279$	−8.21848e9	+	1.27379e9i	−1.35636	+	0.210223i
$280$	1.15512e10			1.87930
$281$			5.80307e9i			0.930750i	0.885114	+	0.465375i	$0.154080\pi$
$281$			5.80307e9i			0.930750i	−0.885114	+	0.465375i	$0.845920\pi$
$282$	−6.53276e9	+	5.03253e8i	−1.03300	+	0.0795775i
$283$	2.54243e9			0.396372			0.198186	−	0.980164i	$-0.436495\pi$
$283$	2.54243e9			0.396372			0.198186	+	0.980164i	$0.436495\pi$
$284$			2.38200e8i			0.0366157i
$285$	−9.28940e8	−	1.20586e10i	−0.140802	−	1.82776i
$286$	−7.40722e8			−0.110711
$287$		−	1.27544e10i		−	1.87989i
$288$	−5.34227e7	−	3.44684e8i	−0.00776526	−	0.0501016i
$289$	−1.58692e9			−0.227490
$290$		−	4.88585e8i		−	0.0690793i
$291$	8.82535e9	−	6.79864e8i	1.23072	−	0.0948091i
$292$	7.74892e7			0.0106588
$293$			8.82254e9i			1.19708i	0.801093	+	0.598540i	$0.204252\pi$
$293$			8.82254e9i			1.19708i	−0.801093	+	0.598540i	$0.795748\pi$
$294$	−6.75628e8	−	8.77037e9i	−0.0904312	−	1.17389i
$295$	−3.37482e8			−0.0445618
$296$		−	8.68537e9i		−	1.13141i
$297$	5.36323e8	+	2.28388e9i	0.0689287	+	0.293527i
$298$	−3.98946e9			−0.505882
$299$			2.09055e9i			0.261563i
$300$	−1.38549e8	+	1.06732e7i	−0.0171048	+	0.00131767i
$301$	9.26893e9			1.12918
$302$		−	4.33518e9i		−	0.521170i
$303$	−9.35001e8	−	1.21373e10i	−0.110928	−	1.43996i
$304$	−1.23904e10			−1.45075
$305$			1.24204e10i			1.43528i
$306$	9.72025e9	−	1.50655e9i	1.10864	−	0.171829i
$307$	9.24765e9			1.04106			0.520532	−	0.853842i	$-0.325734\pi$
$307$	9.24765e9			1.04106			0.520532	+	0.853842i	$0.325734\pi$
$308$		−	1.01178e8i		−	0.0112430i
$309$	1.02379e10	−	7.88680e8i	1.12299	−	0.0865102i
$310$	1.66198e10			1.79961
$311$		−	1.50719e9i		−	0.161112i	−0.996750	−	0.0805559i	$-0.974330\pi$
$311$		−	1.50719e9i		−	0.161112i	0.996750	−	0.0805559i	$-0.0256696\pi$
$312$	2.60470e8	+	3.38117e9i	0.0274877	+	0.356820i
$313$	−1.37492e10			−1.43251			−0.716256	−	0.697837i	$-0.754146\pi$
$313$	−1.37492e10			−1.43251			−0.716256	+	0.697837i	$0.754146\pi$
$314$			5.31666e9i			0.546916i
$315$	−2.87148e9	−	1.85268e10i	−0.291651	−	1.88174i
$316$	2.23846e8			0.0224492
$317$		−	7.77092e9i		−	0.769548i	−0.923011	−	0.384774i	$-0.874279\pi$
$317$		−	7.77092e9i		−	0.769548i	0.923011	−	0.384774i	$-0.125721\pi$
$318$	1.53088e10	−	1.17932e9i	1.49704	−	0.115325i
$319$	1.64499e8			0.0158855
$320$		−	1.32158e10i		−	1.26036i
$321$	1.45088e9	+	1.88340e10i	0.136651	+	1.77387i
$322$	−1.15475e10			−1.07415
$323$		−	1.70730e10i		−	1.56855i
$324$	−2.66312e8	+	8.45834e7i	−0.0241663	+	0.00767548i
$325$	2.73720e9			0.245343
$326$			1.24743e10i			1.10445i
$327$	1.56831e10	−	1.20815e9i	1.37164	−	0.105665i
$328$	−1.46019e10			−1.26158
$329$			1.76292e10i			1.50469i
$330$	−3.60093e8	−	4.67439e9i	−0.0303640	−	0.394157i
$331$	−1.82116e10			−1.51718			−0.758590	−	0.651568i	$-0.774112\pi$
$331$	−1.82116e10			−1.51718			−0.758590	+	0.651568i	$0.774112\pi$
$332$		−	4.40102e8i		−	0.0362244i
$333$	−1.39303e10	+	2.15906e9i	−1.13288	+	0.175585i
$334$	−1.73008e10			−1.39021
$335$		−	6.49139e9i		−	0.515416i
$336$	−1.91503e10	+	1.47525e9i	−1.50251	+	0.115746i
$337$	1.08844e10			0.843891			0.421946	−	0.906621i	$-0.361347\pi$
$337$	1.08844e10			0.843891			0.421946	+	0.906621i	$0.361347\pi$
$338$		−	1.14783e10i		−	0.879450i
$339$	1.68050e9	+	2.18146e10i	0.127244	+	1.65177i
$340$	−4.86091e8			−0.0363749
$341$			5.59565e9i			0.413840i
$342$	3.00388e9	+	1.93811e10i	0.219573	+	1.41668i
$343$	−3.31226e9			−0.239303
$344$		−	1.06116e10i		−	0.757786i
$345$	−1.31926e10	+	1.01630e9i	−0.931225	+	0.0717372i
$346$	5.13893e9			0.358565
$347$			2.09393e10i			1.44426i	0.691759	+	0.722129i	$0.256836\pi$
$347$			2.09393e10i			1.44426i	−0.691759	+	0.722129i	$0.743164\pi$
$348$	1.50487e6	+	1.95348e7i	0.000102608	+	0.00133196i
$349$	1.07024e10			0.721409			0.360704	−	0.932680i	$-0.382536\pi$
$349$	1.07024e10			0.721409			0.360704	+	0.932680i	$0.382536\pi$
$350$			1.51193e10i			1.00754i
$351$	5.35825e9	−	1.25827e9i	0.353016	−	0.0828985i
$352$	−2.34682e8			−0.0152866
$353$			2.58306e10i			1.66355i	0.555115	+	0.831774i	$0.312674\pi$
$353$			2.58306e10i			1.66355i	−0.555115	+	0.831774i	$0.687326\pi$
$354$	5.45652e8	−	4.20345e7i	0.0347458	−	0.00267666i
$355$	2.96971e10			1.86982
$356$			2.46617e7i			0.00153540i
$357$	−2.03277e9	−	2.63875e10i	−0.125145	−	1.62452i
$358$	−7.84382e7			−0.00477525
$359$			7.97178e8i			0.0479930i	0.999712	+	0.0239965i	$0.00763905\pi$
$359$			7.97178e8i			0.0479930i	−0.999712	+	0.0239965i	$0.992361\pi$
$360$	−2.12105e10	+	3.28743e9i	−1.26282	+	0.195725i
$361$	1.70580e10			1.00438
$362$			8.96247e9i			0.521907i
$363$	1.57380e9	−	1.21238e8i	0.0906405	−	0.00698252i
$364$	−2.37376e8			−0.0135217
$365$		−	9.66083e9i		−	0.544306i
$366$	−1.54700e9	−	2.00817e10i	−0.0862118	−	1.11912i
$367$	−1.06670e10			−0.588002			−0.294001	−	0.955805i	$-0.594987\pi$
$367$	−1.06670e10			−0.588002			−0.294001	+	0.955805i	$0.594987\pi$
$368$			1.35556e10i			0.739143i
$369$	3.62984e9	+	2.34198e10i	0.195786	+	1.26321i
$370$	2.81705e10			1.50310
$371$		−	4.13119e10i		−	2.18062i
$372$	−6.64502e8	+	5.11901e7i	−0.0346996	+	0.00267309i
$373$	−2.59496e10			−1.34059			−0.670295	−	0.742095i	$-0.733832\pi$
$373$	−2.59496e10			−1.34059			−0.670295	+	0.742095i	$0.733832\pi$
$374$		−	6.61815e9i		−	0.338259i
$375$	−6.36065e8	−	8.25680e9i	−0.0321645	−	0.417529i
$376$	2.01829e10			1.00979
$377$		−	3.85934e8i		−	0.0191050i
$378$	6.95027e9	+	2.95971e10i	0.340435	+	1.44971i
$379$	−5.70570e9			−0.276536			−0.138268	−	0.990395i	$-0.544154\pi$
$379$	−5.70570e9			−0.276536			−0.138268	+	0.990395i	$0.544154\pi$
$380$		−	9.69209e8i		−	0.0464818i
$381$	−9.15474e9	+	7.05238e8i	−0.434456	+	0.0334685i
$382$	5.07250e9			0.238215
$383$		−	3.38835e10i		−	1.57468i	−0.616518	−	0.787341i	$-0.711457\pi$
$383$		−	3.38835e10i		−	1.57468i	0.616518	−	0.787341i	$-0.288543\pi$
$384$	1.73074e9	+	2.24668e10i	0.0795987	+	1.03328i
$385$	−1.26142e10			−0.574139
$386$			7.83416e9i			0.352893i
$387$	−1.70197e10	+	2.63789e9i	−0.758767	+	0.117602i
$388$	7.09335e8			0.0312986
$389$		−	2.22934e10i		−	0.973593i	−0.873515	−	0.486797i	$-0.838165\pi$
$389$		−	2.22934e10i		−	0.973593i	0.873515	−	0.486797i	$-0.161835\pi$
$390$	−1.09667e10	+	8.44820e8i	−0.474041	+	0.0365179i
$391$	−1.86785e10			−0.799163
$392$			2.70959e10i			1.14752i
$393$	7.17746e8	+	9.31711e9i	0.0300885	+	0.390581i
$394$	1.33934e10			0.555783
$395$		−	2.79076e10i		−	1.14639i
$396$	2.87948e7	+	1.85785e8i	0.00117094	+	0.00755490i
$397$	2.90338e10			1.16880			0.584402	−	0.811464i	$-0.301329\pi$
$397$	2.90338e10			1.16880			0.584402	+	0.811464i	$0.301329\pi$
$398$			1.76717e9i			0.0704283i
$399$	5.26136e10	−	4.05310e9i	2.07590	−	0.159917i
$400$	1.77486e10			0.693307
$401$		−	1.27430e10i		−	0.492828i	−0.969165	−	0.246414i	$-0.920748\pi$
$401$		−	1.27430e10i		−	0.492828i	0.969165	−	0.246414i	$-0.0792523\pi$
$402$	8.08522e8	+	1.04955e10i	0.0309590	+	0.401881i
$403$	1.31280e10			0.497714
$404$		−	9.75532e8i		−	0.0366198i
$405$	1.05453e10	+	3.32020e10i	0.391957	+	1.23408i
$406$	2.13176e9			0.0784576
$407$			9.48461e9i			0.345654i
$408$	−3.02098e10	+	2.32722e9i	−1.09020	+	0.0839842i
$409$	4.47008e9			0.159743			0.0798716	−	0.996805i	$-0.474549\pi$
$409$	4.47008e9			0.159743			0.0798716	+	0.996805i	$0.474549\pi$
$410$		−	4.73606e10i		−	1.67603i
$411$	−2.45446e9	−	3.18615e10i	−0.0860178	−	1.11660i
$412$	8.22869e8			0.0285589
$413$		−	1.47248e9i		−	0.0506117i
$414$	2.12036e10	−	3.28636e9i	0.721787	−	0.111870i
$415$	−5.48689e10			−1.84984
$416$			5.50592e8i			0.0183847i
$417$	−1.49519e10	+	1.15183e9i	−0.494484	+	0.0380928i
$418$	1.31958e10			0.432246
$419$		−	3.46876e10i		−	1.12543i	−0.826652	−	0.562714i	$-0.809757\pi$
$419$		−	3.46876e10i		−	1.12543i	0.826652	−	0.562714i	$-0.190243\pi$
$420$	−1.15397e8	−	1.49798e9i	−0.00370850	−	0.0481402i
$421$	−4.83823e10			−1.54013			−0.770066	−	0.637965i	$-0.779777\pi$
$421$	−4.83823e10			−1.54013			−0.770066	+	0.637965i	$0.779777\pi$
$422$		−	3.26328e10i		−	1.02897i
$423$	−5.01718e9	−	3.23709e10i	−0.156711	−	1.01110i
$424$	−4.72962e10			−1.46340
$425$			2.44561e10i			0.749604i
$426$	−4.80152e10	+	3.69887e9i	−1.45794	+	0.112313i
$427$	−5.41921e10			−1.63014
$428$			1.51378e9i			0.0451115i
$429$	−2.84438e8	−	3.69231e9i	−0.00839767	−	0.109011i
$430$	3.44181e10			1.00673
$431$		−	9.29263e9i		−	0.269296i	−0.990894	−	0.134648i	$-0.957010\pi$
$431$		−	9.29263e9i		−	0.269296i	0.990894	−	0.134648i	$-0.0429903\pi$
$432$	3.47441e10	−	8.15894e9i	0.997576	−	0.234260i
$433$	4.35080e10			1.23771			0.618854	−	0.785506i	$-0.287597\pi$
$433$	4.35080e10			1.23771			0.618854	+	0.785506i	$0.287597\pi$
$434$			7.25147e10i			2.04393i
$435$	2.43547e9	−	1.87617e8i	0.0680183	−	0.00523981i
$436$	1.26053e9			0.0348823
$437$		−	3.72428e10i		−	1.02121i
$438$	1.20329e9	+	1.56199e10i	0.0326943	+	0.424407i
$439$	−2.31745e10			−0.623955			−0.311977	−	0.950090i	$-0.600991\pi$
$439$	−2.31745e10			−0.623955			−0.311977	+	0.950090i	$0.600991\pi$
$440$			1.44414e10i			0.385301i
$441$	4.34586e10	−	6.73567e9i	1.14900	−	0.178085i
$442$	−1.55269e10			−0.406815
$443$			4.95067e10i			1.28543i	0.766105	+	0.642715i	$0.222192\pi$
$443$			4.95067e10i			1.28543i	−0.766105	+	0.642715i	$0.777808\pi$
$444$	−1.12633e9	+	8.67670e7i	−0.0289823	+	0.00223266i
$445$	3.07465e9			0.0784071
$446$		−	5.26005e10i		−	1.32938i
$447$	−1.53196e9	−	1.98864e10i	−0.0383722	−	0.498112i
$448$	5.76624e10			1.43146
$449$			1.14956e9i			0.0282844i	0.999900	+	0.0141422i	$0.00450175\pi$
$449$			1.14956e9i			0.0282844i	−0.999900	+	0.0141422i	$0.995498\pi$
$450$	−4.30289e9	−	2.77623e10i	−0.104933	−	0.677027i
$451$	1.59456e10			0.385421
$452$			1.75335e9i			0.0420062i
$453$	2.16098e10	−	1.66471e9i	0.513165	−	0.0395318i
$454$	−4.24541e10			−0.999301
$455$			2.95944e10i			0.690500i
$456$	−4.64022e9	−	6.02349e10i	−0.107320	−	1.39312i
$457$	4.36306e9			0.100029			0.0500146	−	0.998748i	$-0.484073\pi$
$457$	4.36306e9			0.100029			0.0500146	+	0.998748i	$0.484073\pi$
$458$		−	1.26463e10i		−	0.287410i
$459$	1.12423e10	+	4.78744e10i	0.253283	+	1.07858i
$460$	−1.06035e9			−0.0236820
$461$		−	4.28851e9i		−	0.0949516i	−0.998872	−	0.0474758i	$-0.984882\pi$
$461$		−	4.28851e9i		−	0.0949516i	0.998872	−	0.0474758i	$-0.0151177\pi$
$462$	2.03950e10	−	1.57114e9i	0.447668	−	0.0344863i
$463$	7.77760e10			1.69247			0.846236	−	0.532808i	$-0.178863\pi$
$463$	7.77760e10			1.69247			0.846236	+	0.532808i	$0.178863\pi$
$464$		−	2.50249e9i		−	0.0539883i
$465$	6.38203e9	+	8.28455e10i	0.136505	+	1.77197i
$466$	1.05493e10			0.223707
$467$			4.14374e10i			0.871214i	0.900137	+	0.435607i	$0.143466\pi$
$467$			4.14374e10i			0.871214i	−0.900137	+	0.435607i	$0.856534\pi$
$468$	4.35872e8	−	6.75560e7i	0.00908606	−	0.00140825i
$469$	2.83229e10			0.585391
$470$			6.54621e10i			1.34152i
$471$	−2.65022e10	+	2.04161e9i	−0.538516	+	0.0414847i
$472$	−1.68578e9			−0.0339651
$473$			1.15881e10i			0.231508i
$474$	3.47597e9	+	4.51218e10i	0.0688593	+	0.893867i
$475$	−4.87627e10			−0.957885
$476$		−	2.12088e9i		−	0.0413132i
$477$	1.17572e10	+	7.58575e10i	0.227107	+	1.46529i
$478$	−6.44975e10			−1.23547
$479$			8.91322e10i			1.69314i	0.532278	+	0.846570i	$0.321336\pi$
$479$			8.91322e10i			1.69314i	−0.532278	+	0.846570i	$0.678664\pi$
$480$	−3.47455e9	+	2.67663e8i	−0.0654537	+	0.00504224i
$481$	2.22520e10			0.415708
$482$			5.89615e10i			1.09240i
$483$	−4.43425e9	−	5.75613e10i	−0.0814764	−	1.05765i
$484$	1.26494e8			0.00230509
$485$		−	8.84351e10i		−	1.59830i
$486$	−2.11854e10	−	5.23685e10i	−0.379744	−	0.938696i
$487$	−3.32665e10			−0.591414			−0.295707	−	0.955279i	$-0.595555\pi$
$487$	−3.32665e10			−0.591414			−0.295707	+	0.955279i	$0.595555\pi$
$488$			6.20422e10i			1.09398i
$489$	−6.21812e10	+	4.79014e9i	−1.08749	+	0.0837748i
$490$	−8.78842e10			−1.52450
$491$		−	6.09248e10i		−	1.04826i	−0.851639	−	0.524129i	$-0.824391\pi$
$491$		−	6.09248e10i		−	1.04826i	0.851639	−	0.524129i	$-0.175609\pi$
$492$	1.45874e8	+	1.89360e9i	0.00248953	+	0.0323167i
$493$	3.44821e9			0.0583723
$494$		−	3.09589e10i		−	0.519850i
$495$	2.31624e10	−	3.58994e9i	0.385800	−	0.0597953i
$496$	8.51252e10			1.40647
$497$			1.29573e11i			2.12368i
$498$	8.87138e10	−	6.83409e9i	1.44236	−	0.111113i
$499$	5.67884e9			0.0915920			0.0457960	−	0.998951i	$-0.485418\pi$
$499$	5.67884e9			0.0915920			0.0457960	+	0.998951i	$0.485418\pi$
$500$		−	6.63638e8i		−	0.0106182i
$501$	−6.64353e9	−	8.62401e10i	−0.105450	−	1.36886i
$502$	5.64959e10			0.889615
$503$			2.85420e10i			0.445874i	0.974833	+	0.222937i	$0.0715645\pi$
$503$			2.85420e10i			0.445874i	−0.974833	+	0.222937i	$0.928436\pi$
$504$	−1.43435e10	−	9.25446e10i	−0.222297	−	1.43426i
$505$	−1.21623e11			−1.87003
$506$		−	1.44367e10i		−	0.220225i
$507$	5.72164e10	−	4.40768e9i	0.865942	−	0.0667081i
$508$	−7.35810e8			−0.0110487
$509$		−	7.22096e9i		−	0.107578i	−0.998552	−	0.0537891i	$-0.982870\pi$
$509$		−	7.22096e9i		−	0.107578i	0.998552	−	0.0537891i	$-0.0171299\pi$
$510$	−7.54823e9	−	9.79840e10i	−0.111574	−	1.44835i
$511$	4.21516e10			0.618202
$512$		−	6.59267e10i		−	0.959360i
$513$	−9.54561e10	+	2.24159e10i	−1.37827	+	0.323659i
$514$	−3.72534e10			−0.533720
$515$		−	1.02590e11i		−	1.45839i
$516$	−1.37612e9	+	1.06010e8i	−0.0194115	+	0.00149537i
$517$	−2.20401e10			−0.308497
$518$			1.22912e11i			1.70717i
$519$	1.97336e9	+	2.56163e10i	0.0271979	+	0.353058i
$520$	3.38813e10			0.463390
$521$			3.82374e10i			0.518964i	0.965748	+	0.259482i	$0.0835518\pi$
$521$			3.82374e10i			0.518964i	−0.965748	+	0.259482i	$0.916448\pi$
$522$	−3.91437e9	+	6.06690e8i	−0.0527206	+	0.00817118i
$523$	9.92608e10			1.32670			0.663348	−	0.748311i	$-0.269135\pi$
$523$	9.92608e10			1.32670			0.663348	+	0.748311i	$0.269135\pi$
$524$			7.48860e8i			0.00993289i
$525$	−7.53661e10	+	5.80585e9i	−0.992062	+	0.0764238i
$526$	−8.29415e10			−1.08350
$527$			1.17295e11i			1.52068i
$528$	−1.84436e9	−	2.39418e10i	−0.0237307	−	0.308050i
$529$	3.75659e10			0.479701
$530$		−	1.53403e11i		−	1.94415i
$531$	4.19062e8	+	2.70379e9i	0.00527109	+	0.0340091i
$532$	4.22880e9			0.0527923
$533$		−	3.74103e10i		−	0.463534i
$534$	−4.97119e9	+	3.82957e8i	−0.0611357	+	0.00470961i
$535$	1.88728e11			2.30367
$536$		−	3.24256e10i		−	0.392852i
$537$	−3.01204e7	−	3.90995e8i	−0.000362212	−	0.00470190i
$538$	−1.12703e11			−1.34526
$539$		−	2.95893e10i		−	0.350574i
$540$	6.38211e8	+	2.71776e9i	0.00750567	+	0.0319622i
$541$	−6.98199e9			−0.0815061			−0.0407530	−	0.999169i	$-0.512976\pi$
$541$	−6.98199e9			−0.0815061			−0.0407530	+	0.999169i	$0.512976\pi$
$542$			4.61738e10i			0.535056i
$543$	−4.46756e10	+	3.44160e9i	−0.513891	+	0.0395878i
$544$	−4.91938e9			−0.0561714
$545$		−	1.57154e11i		−	1.78131i
$546$	−3.68607e9	−	4.78491e10i	−0.0414756	−	0.538398i
$547$	−9.06813e10			−1.01290			−0.506452	−	0.862268i	$-0.669043\pi$
$547$	−9.06813e10			−1.01290			−0.506452	+	0.862268i	$0.669043\pi$
$548$		−	2.56086e9i		−	0.0283964i
$549$	9.95083e10	−	1.54228e10i	1.09539	−	0.169775i
$550$	−1.89023e10			−0.206568
$551$			6.87534e9i			0.0745913i
$552$	−6.58994e10	+	5.07658e9i	−0.709782	+	0.0546783i
$553$	1.21765e11			1.30203
$554$		−	6.72754e10i		−	0.714196i
$555$	1.08175e10	+	1.40423e11i	0.114013	+	1.48001i
$556$	−1.20176e9			−0.0125753
$557$			4.46197e10i			0.463560i	0.972768	+	0.231780i	$0.0744549\pi$
$557$			4.46197e10i			0.463560i	−0.972768	+	0.231780i	$0.925545\pi$
$558$	−2.06373e10	−	1.33152e11i	−0.212871	−	1.37345i
$559$	2.71870e10			0.278428
$560$			1.91897e11i			1.95126i
$561$	3.29898e10	−	2.54138e9i	0.333064	−	0.0256577i
$562$	−9.40190e10			−0.942476
$563$		−	1.65656e10i		−	0.164882i	−0.996596	−	0.0824412i	$-0.973728\pi$
$563$		−	1.65656e10i		−	0.164882i	0.996596	−	0.0824412i	$-0.0262717\pi$
$564$	−2.01627e8	−	2.61734e9i	−0.00199266	−	0.0258668i
$565$	2.18595e11			2.14510
$566$			4.11914e10i			0.401366i
$567$	−1.44865e11	+	4.60106e10i	−1.40162	+	0.445170i
$568$	1.48342e11			1.42519
$569$		−	5.68477e10i		−	0.542330i	−0.962533	−	0.271165i	$-0.912591\pi$
$569$		−	5.68477e10i		−	0.542330i	0.962533	−	0.271165i	$-0.0874089\pi$
$570$	1.95369e11	−	1.50503e10i	1.85078	−	0.142576i
$571$	−2.85153e9			−0.0268246			−0.0134123	−	0.999910i	$-0.504269\pi$
$571$	−2.85153e9			−0.0268246			−0.0134123	+	0.999910i	$0.504269\pi$
$572$		−	2.96769e8i		−	0.00277226i
$573$	1.94785e9	+	2.52851e10i	0.0180691	+	0.234556i
$574$	2.06641e11			1.90357
$575$			5.33483e10i			0.488033i
$576$	−1.05880e11	+	1.64104e10i	−0.961890	+	0.149084i
$577$	−4.64151e10			−0.418751			−0.209376	−	0.977835i	$-0.567143\pi$
$577$	−4.64151e10			−0.418751			−0.209376	+	0.977835i	$0.567143\pi$
$578$		−	2.57105e10i		−	0.230356i
$579$	−3.90513e10	+	3.00833e9i	−0.347473	+	0.0267677i
$580$	1.95750e8			0.00172978
$581$		−	2.39401e11i		−	2.10098i
$582$	1.10149e10	+	1.42985e11i	0.0960035	+	1.24623i
$583$	5.16485e10			0.447078
$584$		−	4.82575e10i		−	0.414871i
$585$	−8.42242e9	−	5.43416e10i	−0.0719140	−	0.463990i
$586$	−1.42939e11			−1.21216
$587$			1.64956e11i			1.38937i	0.719316	+	0.694683i	$0.244455\pi$
$587$			1.64956e11i			1.38937i	−0.719316	+	0.694683i	$0.755545\pi$
$588$	3.51383e9	−	2.70689e8i	0.0293948	−	0.00226444i
$589$	−2.33873e11			−1.94321
$590$		−	5.46775e9i		−	0.0451233i
$591$	5.14308e9	+	6.67626e10i	0.0421573	+	0.547247i
$592$	1.44287e11			1.17474
$593$		−	1.90986e11i		−	1.54448i	−0.635329	−	0.772242i	$-0.719135\pi$
$593$		−	1.90986e11i		−	1.54448i	0.635329	−	0.772242i	$-0.280865\pi$
$594$	−3.70025e10	+	8.68927e9i	−0.297225	+	0.0697971i
$595$	−2.64417e11			−2.10971
$596$		−	1.59837e9i		−	0.0126675i
$597$	−8.80891e9	+	6.78597e8i	−0.0693465	+	0.00534213i
$598$	−3.38703e10			−0.264859
$599$		−	7.46362e10i		−	0.579752i	−0.957064	−	0.289876i	$-0.906386\pi$
$599$		−	7.46362e10i		−	0.579752i	0.957064	−	0.289876i	$-0.0936141\pi$
$600$	6.64686e9	+	8.62833e10i	0.0512875	+	0.665766i
$601$	−1.60386e11			−1.22933			−0.614663	−	0.788790i	$-0.710708\pi$
$601$	−1.60386e11			−1.22933			−0.614663	+	0.788790i	$0.710708\pi$
$602$			1.50171e11i			1.14341i
$603$	−5.20068e10	+	8.06055e9i	−0.393360	+	0.0609671i
$604$	1.73688e9			0.0130503
$605$		−	1.57704e10i		−	0.117712i
$606$	1.96643e11	−	1.51485e10i	1.45811	−	0.112326i
$607$	2.92518e10			0.215475			0.107738	−	0.994179i	$-0.465639\pi$
$607$	2.92518e10			0.215475			0.107738	+	0.994179i	$0.465639\pi$
$608$		−	9.80868e9i		−	0.0717788i
$609$	8.18601e8	+	1.06263e10i	0.00595118	+	0.0772526i
$610$	−2.01231e11			−1.45336
$611$			5.17086e10i			0.371021i
$612$	6.03594e8	+	3.89439e9i	0.00430268	+	0.0277609i
$613$	6.75531e10			0.478413			0.239207	−	0.970969i	$-0.423113\pi$
$613$	6.75531e10			0.478413			0.239207	+	0.970969i	$0.423113\pi$
$614$			1.49826e11i			1.05418i
$615$	2.36081e11	−	1.81865e10i	1.65029	−	0.127130i
$616$	−6.30101e10			−0.437610
$617$			1.42442e11i			0.982875i	0.870913	+	0.491437i	$0.163528\pi$
$617$			1.42442e11i			0.982875i	−0.870913	+	0.491437i	$0.836472\pi$
$618$	1.27779e10	+	1.65870e11i	0.0876001	+	1.13714i
$619$	−2.14085e11			−1.45823			−0.729113	−	0.684394i	$-0.760067\pi$
$619$	−2.14085e11			−1.45823			−0.729113	+	0.684394i	$0.760067\pi$
$620$			6.65869e9i			0.0450632i
$621$	2.45239e10	+	1.04433e11i	0.164901	+	0.702215i
$622$	2.44189e10			0.163142
$623$			1.34151e10i			0.0890519i
$624$	−5.61702e10	+	4.32709e9i	−0.370483	+	0.0285402i
$625$	−1.85977e11			−1.21882
$626$		−	2.22758e11i		−	1.45056i
$627$	5.06721e9	+	6.57778e10i	0.0327868	+	0.425608i
$628$	−2.13011e9			−0.0136950
$629$			1.98815e11i			1.27013i
$630$	3.00164e11	−	4.65225e10i	1.90544	−	0.295325i
$631$	−1.41209e11			−0.890730			−0.445365	−	0.895349i	$-0.646926\pi$
$631$	−1.41209e11			−0.890730			−0.445365	+	0.895349i	$0.646926\pi$
$632$		−	1.39403e11i		−	0.873784i
$633$	1.62666e11	−	1.25310e10i	1.01317	−	0.0780499i
$634$	1.25901e11			0.779243
$635$			9.17358e10i			0.564214i
$636$	4.72490e8	+	6.13342e9i	0.00288778	+	0.0374865i
$637$	−6.94199e10			−0.421625
$638$			2.66515e9i			0.0160856i
$639$	−3.68758e10	−	2.37923e11i	−0.221176	−	1.42703i
$640$	2.25130e11			1.34188
$641$			4.87337e10i			0.288667i	0.989529	+	0.144334i	$0.0461038\pi$
$641$			4.87337e10i			0.288667i	−0.989529	+	0.144334i	$0.953896\pi$
$642$	−3.05141e11	+	2.35066e10i	−1.79622	+	0.138373i
$643$	3.24029e11			1.89557			0.947787	−	0.318905i	$-0.103315\pi$
$643$	3.24029e11			1.89557			0.947787	+	0.318905i	$0.103315\pi$
$644$		−	4.62647e9i		−	0.0268972i
$645$	1.32166e10	+	1.71566e11i	0.0763627	+	0.991268i
$646$	2.76609e11			1.58832
$647$			2.74581e11i			1.56694i	0.621427	+	0.783472i	$0.286553\pi$
$647$			2.74581e11i			1.56694i	−0.621427	+	0.783472i	$0.713447\pi$
$648$	5.26755e10	+	1.65849e11i	0.298751	+	0.940620i
$649$	1.84091e9			0.0103766
$650$			4.43470e10i			0.248434i
$651$	−3.61467e11	+	2.78457e10i	−2.01254	+	0.155037i
$652$	−4.99779e9			−0.0276559
$653$		−	3.19227e11i		−	1.75569i	−0.478949	−	0.877843i	$-0.658982\pi$
$653$		−	3.19227e11i		−	1.75569i	0.478949	−	0.877843i	$-0.341018\pi$
$654$	1.95740e10	+	2.54091e11i	0.106996	+	1.38892i
$655$	9.33628e10			0.507234
$656$		−	2.42577e11i		−	1.30989i
$657$	−7.73992e10	+	1.19961e10i	−0.415408	+	0.0643843i
$658$	−2.85620e11			−1.52365
$659$		−	1.43354e11i		−	0.760093i	−0.924967	−	0.380047i	$-0.875908\pi$
$659$		−	1.43354e11i		−	0.760093i	0.924967	−	0.380047i	$-0.124092\pi$
$660$	1.87278e9	−	1.44270e8i	0.00986987	−	0.000760329i
$661$	1.79340e11			0.939447			0.469724	−	0.882814i	$-0.344354\pi$
$661$	1.79340e11			0.939447			0.469724	+	0.882814i	$0.344354\pi$
$662$		−	2.95057e11i		−	1.53630i
$663$	−5.96236e9	−	7.73978e10i	−0.0308578	−	0.400566i
$664$	−2.74080e11			−1.40995
$665$		−	5.27218e11i		−	2.69590i
$666$	−3.49802e10	−	2.25693e11i	−0.177797	−	1.14715i
$667$	7.52189e9			0.0380035
$668$		−	6.93153e9i		−	0.0348115i
$669$	2.62200e11	−	2.01986e10i	1.30896	−	0.100837i
$670$	1.05171e11			0.521910
$671$		−	6.77514e10i		−	0.334217i
$672$	−1.16785e9	−	1.51600e10i	−0.00572679	−	0.0743398i
$673$	3.79005e11			1.84750			0.923750	−	0.382996i	$-0.125108\pi$
$673$	3.79005e11			1.84750			0.923750	+	0.382996i	$0.125108\pi$
$674$			1.76345e11i			0.854523i
$675$	1.36736e11	−	3.21096e10i	0.658669	−	0.154675i
$676$	4.59875e9			0.0220218
$677$			1.49714e11i			0.712702i	0.934352	+	0.356351i	$0.115979\pi$
$677$			1.49714e11i			0.712702i	−0.934352	+	0.356351i	$0.884021\pi$
$678$	−3.53431e11	+	2.72267e10i	−1.67258	+	0.128848i
$679$	3.85855e11			1.81529
$680$			3.02720e11i			1.41581i
$681$	−1.63024e10	−	2.11623e11i	−0.0757991	−	0.983953i
$682$	−9.06583e10			−0.419054
$683$		−	3.39483e11i		−	1.56004i	−0.625756	−	0.780019i	$-0.715210\pi$
$683$		−	3.39483e11i		−	1.56004i	0.625756	−	0.780019i	$-0.284790\pi$
$684$	−7.76497e9	+	1.20350e9i	−0.0354744	+	0.00549820i
$685$	−3.19270e11			−1.45009
$686$		−	5.36638e10i		−	0.242318i
$687$	6.30385e10	−	4.85619e9i	0.282995	−	0.0218006i
$688$	1.76287e11			0.786802
$689$		−	1.21173e11i		−	0.537687i
$690$	−1.64656e10	−	2.13741e11i	−0.0726410	−	0.942957i
$691$	1.70731e11			0.748858			0.374429	−	0.927256i	$-0.377839\pi$
$691$	1.70731e11			0.748858			0.374429	+	0.927256i	$0.377839\pi$
$692$			2.05890e9i			0.00897864i
$693$	1.56634e10	+	1.01061e11i	0.0679132	+	0.438177i
$694$	−3.39250e11			−1.46245
$695$			1.49827e11i			0.642170i
$696$	1.21656e10	−	9.37180e8i	0.0518437	−	0.00399380i
$697$	3.34250e11			1.41625
$698$			1.73397e11i			0.730497i
$699$	4.05093e9	+	5.25854e10i	0.0169686	+	0.220271i
$700$	−6.05753e9			−0.0252292
$701$		−	2.14649e10i		−	0.0888910i	−0.999012	−	0.0444455i	$-0.985848\pi$
$701$		−	2.14649e10i		−	0.0888910i	0.999012	−	0.0444455i	$-0.0141521\pi$
$702$	2.03860e10	+	8.68121e10i	0.0839430	+	0.357463i
$703$	−3.96415e11			−1.62304
$704$			7.20899e10i			0.293483i
$705$	−3.26312e11	+	2.51375e10i	−1.32092	+	0.101757i
$706$	−4.18496e11			−1.68451
$707$		−	5.30658e11i		−	2.12391i
$708$	1.68410e7	+	2.18614e8i	6.70247e−5	+	0.000870052i
$709$	−1.22807e11			−0.486003			−0.243001	−	0.970026i	$-0.578132\pi$
$709$	−1.22807e11			−0.486003			−0.243001	+	0.970026i	$0.578132\pi$
$710$			4.81140e11i			1.89338i
$711$	−2.23586e11	+	3.46537e10i	−0.874915	+	0.135603i
$712$	1.53584e10			0.0597621
$713$			2.55867e11i			0.990047i
$714$	4.27518e11	−	3.29340e10i	1.64498	−	0.126722i
$715$	−3.69991e10			−0.141569
$716$		−	3.14261e7i		−	0.000119574i
$717$	−2.47671e10	−	3.21503e11i	−0.0937128	−	1.21649i
$718$	−1.29155e10			−0.0485976
$719$		−	7.18957e10i		−	0.269022i	−0.990912	−	0.134511i	$-0.957054\pi$
$719$		−	7.18957e10i		−	0.269022i	0.990912	−	0.134511i	$-0.0429463\pi$
$720$	−5.46129e10	−	3.52363e11i	−0.203219	−	1.31117i
$721$	4.47614e11			1.65639
$722$			2.76367e11i			1.01704i
$723$	−2.93908e11	+	2.26413e10i	−1.07562	+	0.0828605i
$724$	−3.59079e9			−0.0130688
$725$		−	9.84856e9i		−	0.0356468i
$726$	1.96425e9	+	2.54980e10i	0.00707049	+	0.0917825i
$727$	1.79717e11			0.643357			0.321678	−	0.946849i	$-0.395753\pi$
$727$	1.79717e11			0.643357			0.321678	+	0.946849i	$0.395753\pi$
$728$			1.47829e11i			0.526301i
$729$	2.52908e11	−	1.25713e11i	0.895474	−	0.445113i
$730$	1.56521e11			0.551163
$731$			2.42908e11i			0.850692i
$732$	8.04570e9	−	6.19803e8i	0.0280233	−	0.00215878i
$733$	−3.78788e11			−1.31214			−0.656071	−	0.754699i	$-0.727783\pi$
$733$	−3.78788e11			−1.31214			−0.656071	+	0.754699i	$0.727783\pi$
$734$		−	1.72823e11i		−	0.595411i
$735$	−3.37476e10	−	4.38080e11i	−0.115636	−	1.50108i
$736$	−1.07311e10			−0.0365706
$737$			3.54094e10i			0.120019i
$738$	−3.79437e11	+	5.88091e10i	−1.27913	+	0.198253i
$739$	−2.12799e11			−0.713498			−0.356749	−	0.934200i	$-0.616115\pi$
$739$	−2.12799e11			−0.713498			−0.356749	+	0.934200i	$0.616115\pi$
$740$			1.12865e10i			0.0376384i
$741$	1.54322e11	−	1.18883e10i	0.511866	−	0.0394317i
$742$	6.69319e11			2.20809
$743$			4.70898e11i			1.54515i	0.634920	+	0.772577i	$0.281033\pi$
$743$			4.70898e11i			1.54515i	−0.634920	+	0.772577i	$0.718967\pi$
$744$	3.18793e10	+	4.13828e11i	0.104044	+	1.35060i
$745$	−1.99274e11			−0.646881
$746$		−	4.20425e11i		−	1.35748i
$747$	6.81324e10	+	4.39591e11i	0.218812	+	1.41178i
$748$	2.65154e9			0.00847018
$749$			8.23446e11i			2.61642i
$750$	1.33773e11	−	1.03053e10i	0.422789	−	0.0325697i
$751$	−4.36826e11			−1.37325			−0.686624	−	0.727013i	$-0.740908\pi$
$751$	−4.36826e11			−1.37325			−0.686624	+	0.727013i	$0.740908\pi$
$752$			3.35291e11i			1.04846i
$753$	2.16945e10	+	2.81618e11i	0.0674792	+	0.875951i
$754$	6.25274e9			0.0193457
$755$		−	2.16542e11i		−	0.666431i
$756$	−1.18580e10	+	2.78461e9i	−0.0363015	+	0.00852466i
$757$	−2.94690e11			−0.897392			−0.448696	−	0.893685i	$-0.648111\pi$
$757$	−2.94690e11			−0.897392			−0.448696	+	0.893685i	$0.648111\pi$
$758$		−	9.24414e10i		−	0.280020i
$759$	7.19635e10	−	5.54373e9i	0.216843	−	0.0167046i
$760$	−6.03589e11			−1.80920
$761$		−	1.65686e11i		−	0.494023i	−0.969012	−	0.247012i	$-0.920551\pi$
$761$		−	1.65686e11i		−	0.494023i	0.969012	−	0.247012i	$-0.0794486\pi$
$762$	−1.14260e10	−	1.48321e11i	−0.0338901	−	0.439930i
$763$	6.85685e11			2.02314
$764$			2.03229e9i			0.00596501i
$765$	4.85527e11	−	7.52520e10i	1.41764	−	0.219721i
$766$	5.48965e11			1.59452
$767$		−	4.31899e9i		−	0.0124796i
$768$	−2.63684e10	+	2.03130e9i	−0.0757948	+	0.00583887i
$769$	3.75635e11			1.07414			0.537070	−	0.843538i	$-0.319531\pi$
$769$	3.75635e11			1.07414			0.537070	+	0.843538i	$0.319531\pi$
$770$		−	2.04370e11i		−	0.581372i
$771$	−1.43053e10	−	1.85699e11i	−0.0404838	−	0.525522i
$772$	−3.13874e9			−0.00883661
$773$		−	3.33178e11i		−	0.933165i	−0.884478	−	0.466583i	$-0.845485\pi$
$773$		−	3.33178e11i		−	0.933165i	0.884478	−	0.466583i	$-0.154515\pi$
$774$	−4.27380e10	−	2.75746e11i	−0.119083	−	0.768327i
$775$	3.35011e11			0.928651
$776$		−	4.41749e11i		−	1.21823i
$777$	−6.12686e11	+	4.71984e10i	−1.68095	+	0.129492i
$778$	3.61188e11			0.985859
$779$			6.66457e11i			1.80977i
$780$	−3.38475e8	−	4.39376e9i	−0.000914425	−	0.0118702i
$781$	−1.61993e11			−0.435403
$782$		−	3.02621e11i		−	0.809231i
$783$	−4.52732e9	−	1.92792e10i	−0.0120446	−	0.0512910i
$784$	−4.50135e11			−1.19146
$785$			2.65567e11i			0.699353i
$786$	−1.50952e11	+	1.16286e10i	−0.395502	+	0.0304676i
$787$	1.92335e11			0.501371			0.250686	−	0.968069i	$-0.419344\pi$
$787$	1.92335e11			0.501371			0.250686	+	0.968069i	$0.419344\pi$
$788$			5.36603e9i			0.0139171i
$789$	−3.18496e10	−	4.13442e11i	−0.0821857	−	1.06686i
$790$	4.52147e11			1.16084
$791$			9.53762e11i			2.43632i
$792$	1.15700e11	−	1.79324e10i	0.294058	−	0.0455761i
$793$	−1.58953e11			−0.401952
$794$			4.70393e11i			1.18353i
$795$	7.64674e11	−	5.89069e10i	1.91429	−	0.147468i
$796$	−7.08014e8			−0.00176356
$797$		−	1.56629e11i		−	0.388186i	−0.980983	−	0.194093i	$-0.937824\pi$
$797$		−	1.56629e11i		−	0.388186i	0.980983	−	0.194093i	$-0.0621764\pi$
$798$	6.56666e10	+	8.52423e11i	0.161932	+	2.10205i
$799$	−4.62002e11			−1.13359
$800$			1.40504e10i			0.0343028i
$801$	−3.81788e9	−	2.46330e10i	−0.00927455	−	0.0598395i
$802$	2.06457e11			0.499037
$803$			5.26982e10i			0.126746i
$804$	−4.20499e9	+	3.23932e8i	−0.0100633	+	0.000775229i
$805$	−5.76797e11			−1.37353
$806$			2.12695e11i			0.503984i
$807$	−4.32779e10	−	5.61793e11i	−0.102040	−	1.32459i
$808$	−6.07527e11			−1.42534
$809$		−	1.57646e11i		−	0.368035i	−0.982923	−	0.184017i	$-0.941090\pi$
$809$		−	1.57646e11i		−	0.368035i	0.982923	−	0.184017i	$-0.0589102\pi$
$810$	−5.37924e11	+	1.70850e11i	−1.24963	+	0.396895i
$811$	3.97407e11			0.918655			0.459328	−	0.888267i	$-0.348090\pi$
$811$	3.97407e11			0.918655			0.459328	+	0.888267i	$0.348090\pi$
$812$			8.54086e8i			0.00196462i
$813$	−2.30165e11	+	1.77308e10i	−0.526838	+	0.0405851i
$814$	−1.53666e11			−0.350009
$815$			6.23091e11i			1.41228i
$816$	−3.86613e10	−	5.01865e11i	−0.0872000	−	1.13195i
$817$	−4.84331e11			−1.08706
$818$			7.24224e10i			0.161756i
$819$	2.37100e11	−	3.67482e10i	0.526982	−	0.0816772i
$820$	1.89749e10			0.0419686
$821$		−	2.55006e11i		−	0.561277i	−0.959814	−	0.280639i	$-0.909454\pi$
$821$		−	2.55006e11i		−	0.561277i	0.959814	−	0.280639i	$-0.0905462\pi$
$822$	5.16206e11	−	3.97661e10i	1.13067	−	0.0871015i
$823$	−8.74091e11			−1.90527			−0.952636	−	0.304112i	$-0.901640\pi$
$823$	−8.74091e11			−1.90527			−0.952636	+	0.304112i	$0.901640\pi$
$824$		−	5.12453e11i		−	1.11159i
$825$	−7.25851e9	−	9.42232e10i	−0.0156687	−	0.203396i
$826$	2.38566e10			0.0512493
$827$			5.32825e11i			1.13910i	0.821956	+	0.569551i	$0.192883\pi$
$827$			5.32825e11i			1.13910i	−0.821956	+	0.569551i	$0.807117\pi$
$828$	1.31667e9	+	8.49519e9i	0.00280128	+	0.0180739i
$829$	−3.51967e11			−0.745218			−0.372609	−	0.927988i	$-0.621537\pi$
$829$	−3.51967e11			−0.745218			−0.372609	+	0.927988i	$0.621537\pi$
$830$		−	8.88963e11i		−	1.87314i
$831$	3.35351e11	−	2.58338e10i	0.703226	−	0.0541733i
$832$	1.69131e11			0.352964
$833$		−	6.20248e11i		−	1.28821i
$834$	−1.86614e10	−	2.42245e11i	−0.0385727	−	0.500714i
$835$	−8.64176e11			−1.77769
$836$			5.28688e9i			0.0108237i
$837$	6.55806e11	−	1.54002e11i	1.33621	−	0.313780i
$838$	5.61993e11			1.13961
$839$			6.14265e11i			1.23968i	0.784730	+	0.619838i	$0.212802\pi$
$839$			6.14265e11i			1.23968i	−0.784730	+	0.619838i	$0.787198\pi$
$840$	−9.32887e11	+	7.18652e10i	−1.87375	+	0.144345i
$841$	4.98858e11			0.997224
$842$		−	7.83869e11i		−	1.55954i
$843$	−3.61034e10	−	4.68660e11i	−0.0714888	−	0.928000i
$844$	1.30743e10			0.0257660
$845$		−	5.73342e11i		−	1.12457i
$846$	5.24460e11	−	8.12862e10i	1.02384	−	0.158685i
$847$	6.88084e10			0.133693
$848$		−	7.85715e11i		−	1.51943i
$849$	−2.05328e11	+	1.58175e10i	−0.395201	+	0.0304445i
$850$	−3.96228e11			−0.759048
$851$			4.33693e11i			0.826922i
$852$	−1.48194e9	−	1.92372e10i	−0.00281237	−	0.0365076i
$853$	4.65175e11			0.878658			0.439329	−	0.898326i	$-0.355216\pi$
$853$	4.65175e11			0.878658			0.439329	+	0.898326i	$0.355216\pi$
$854$		−	8.77998e11i		−	1.65068i
$855$	1.50044e11	+	9.68084e11i	0.280772	+	1.81154i
$856$	9.42727e11			1.75586
$857$		−	6.55429e11i		−	1.21507i	−0.794292	−	0.607536i	$-0.792158\pi$
$857$		−	6.55429e11i		−	1.21507i	0.794292	−	0.607536i	$-0.207842\pi$
$858$	5.98213e10	−	4.60835e9i	0.110384	−	0.00850347i
$859$	−1.98501e11			−0.364578			−0.182289	−	0.983245i	$-0.558351\pi$
$859$	−1.98501e11			−0.364578			−0.182289	+	0.983245i	$0.558351\pi$
$860$			1.37895e10i			0.0252090i
$861$	7.93505e10	+	1.03005e12i	0.144390	+	1.87434i
$862$	1.50555e11			0.272688
$863$			5.33299e11i			0.961452i	0.876871	+	0.480726i	$0.159627\pi$
$863$			5.33299e11i			0.961452i	−0.876871	+	0.480726i	$0.840373\pi$
$864$	6.45889e9	+	2.75046e10i	0.0115905	+	0.0493571i
$865$	2.56690e11			0.458505
$866$			7.04899e11i			1.25330i
$867$	1.28161e11	−	9.87288e9i	0.226818	−	0.0174730i
$868$	−2.90528e10			−0.0511811
$869$			1.52231e11i			0.266947i
$870$	3.03969e9	+	3.94584e10i	0.00530582	+	0.0688752i
$871$	8.30746e10			0.144343
$872$		−	7.85010e11i		−	1.35772i
$873$	−7.08512e11	+	1.09813e11i	−1.21980	+	0.189058i
$874$	6.03392e11			1.03408
$875$		−	3.60998e11i		−	0.615846i
$876$	−6.25808e9	+	4.82093e8i	−0.0106273	+	0.000818681i
$877$	2.41745e9			0.00408656			0.00204328	−	0.999998i	$-0.499350\pi$
$877$	2.41745e9			0.00408656			0.00204328	+	0.999998i	$0.499350\pi$
$878$		−	3.75464e11i		−	0.631816i
$879$	−5.48888e10	−	7.12515e11i	−0.0919450	−	1.19354i
$880$	−2.39911e11			−0.400054
$881$		−	2.85057e11i		−	0.473182i	−0.971609	−	0.236591i	$-0.923970\pi$
$881$		−	2.85057e11i		−	0.473182i	0.971609	−	0.236591i	$-0.0760302\pi$
$882$	1.09128e11	+	7.04098e11i	0.180328	+	1.16348i
$883$	1.77513e11			0.292003			0.146001	−	0.989284i	$-0.453360\pi$
$883$	1.77513e11			0.292003			0.146001	+	0.989284i	$0.453360\pi$
$884$		−	6.22083e9i		−	0.0101868i
$885$	2.72553e10	−	2.09962e9i	0.0444302	−	0.00342269i
$886$	−8.02086e11			−1.30163
$887$		−	7.87339e8i		−	0.00127194i	−1.00000		0.000635971i	$-0.999798\pi$
$887$		−	7.87339e8i		−	0.00127194i	1.00000		0.000635971i	$-0.000202436\pi$
$888$	5.40354e10	+	7.01437e11i	0.0869013	+	1.12807i
$889$	−4.00256e11			−0.640813
$890$			4.98142e10i			0.0793949i
$891$	−5.75228e10	−	1.81111e11i	−0.0912702	−	0.287365i
$892$	2.10742e10			0.0332884
$893$		−	9.21180e11i		−	1.44857i
$894$	3.22192e11	−	2.48201e10i	0.504387	−	0.0388556i
$895$	−3.91799e9			−0.00610620
$896$			9.82276e11i			1.52406i
$897$	−1.30062e10	−	1.68835e11i	−0.0200901	−	0.260791i
$898$	−1.86247e10			−0.0286408
$899$		−	4.72352e10i		−	0.0723147i
$900$	1.11229e10	−	1.72394e9i	0.0169531	−	0.00262756i
$901$	1.08265e12			1.64281
$902$			2.58344e11i			0.390277i
$903$	−7.48565e11	+	5.76660e10i	−1.12585	+	0.0867298i
$904$	1.09192e12			1.63500
$905$			4.47676e11i			0.667374i
$906$	2.69710e10	+	3.50112e11i	0.0400299	+	0.519630i
$907$	−8.29322e11			−1.22545			−0.612723	−	0.790298i	$-0.709926\pi$
$907$	−8.29322e11			−1.22545			−0.612723	+	0.790298i	$0.709926\pi$
$908$		−	1.70091e10i		−	0.0250230i
$909$	1.51023e11	+	9.74400e11i	0.221201	+	1.42719i
$910$	−4.79476e11			−0.699199
$911$			5.82338e11i			0.845476i	0.906252	+	0.422738i	$0.138931\pi$
$911$			5.82338e11i			0.845476i	−0.906252	+	0.422738i	$0.861069\pi$
$912$	1.00066e12	−	7.70863e10i	1.44646	−	0.111429i
$913$	2.99301e11			0.430749
$914$			7.06885e10i			0.101289i
$915$	−7.72728e10	−	1.00308e12i	−0.110241	−	1.43104i
$916$	5.06671e9			0.00719687
$917$			4.07355e11i			0.576098i
$918$	−7.75641e11	+	1.82144e11i	−1.09217	+	0.256474i
$919$	2.71867e11			0.381148			0.190574	−	0.981673i	$-0.438965\pi$
$919$	2.71867e11			0.381148			0.190574	+	0.981673i	$0.438965\pi$
$920$			6.60350e11i			0.921770i
$921$	−7.46847e11	+	5.75336e10i	−1.03799	+	0.0799618i
$922$	6.94806e10			0.0961479
$923$			3.80054e11i			0.523647i
$924$	6.29472e8	+	8.17122e9i	0.000863553	+	0.0112098i
$925$	5.67843e11			0.775642
$926$			1.26009e12i			1.71380i
$927$	−8.21914e11	+	1.27389e11i	−1.11303	+	0.172509i
$928$	1.98105e9			0.00267118
$929$			2.57259e11i			0.345388i	0.984976	+	0.172694i	$0.0552472\pi$
$929$			2.57259e11i			0.345388i	−0.984976	+	0.172694i	$0.944753\pi$
$930$	−1.34223e12	+	1.03399e11i	−1.79430	+	0.138224i
$931$	1.23670e12			1.64614
$932$			4.22654e9i			0.00560172i
$933$	9.37689e9	+	1.21722e11i	0.0123746	+	0.160636i
$934$	−6.71351e11			−0.882191
$935$		−	3.30577e11i		−	0.432539i
$936$	−4.20714e10	−	2.71445e11i	−0.0548130	−	0.353654i
$937$	−2.46466e11			−0.319742			−0.159871	−	0.987138i	$-0.551108\pi$
$937$	−2.46466e11			−0.319742			−0.159871	+	0.987138i	$0.551108\pi$
$938$			4.58875e11i			0.592766i
$939$	1.11039e12	−	8.55393e10i	1.42828	−	0.110028i
$940$	−2.62272e10			−0.0335924
$941$		−	1.14552e12i		−	1.46098i	−0.682922	−	0.730492i	$-0.739291\pi$
$941$		−	1.14552e12i		−	1.46098i	0.682922	−	0.730492i	$-0.260709\pi$
$942$	−3.30772e10	−	4.29378e11i	−0.0420074	−	0.545300i
$943$	7.29130e11			0.922058
$944$		−	2.80053e10i		−	0.0352657i
$945$	3.47166e11	+	1.47837e12i	0.435321	+	1.85378i
$946$	−1.87745e11			−0.234425
$947$		−	9.95921e11i		−	1.23830i	−0.785274	−	0.619149i	$-0.787478\pi$
$947$		−	9.95921e11i		−	1.23830i	0.785274	−	0.619149i	$-0.212522\pi$
$948$	−1.80779e10	+	1.39264e9i	−0.0223829	+	0.00172427i
$949$	1.23636e11			0.152433
$950$		−	7.90033e11i		−	0.969953i
$951$	4.83462e10	+	6.27585e11i	0.0591072	+	0.767275i
$952$	−1.32081e12			−1.60802
$953$		−	2.81088e11i		−	0.340777i	−0.985377	−	0.170389i	$-0.945498\pi$
$953$		−	2.81088e11i		−	0.340777i	0.985377	−	0.170389i	$-0.0545023\pi$
$954$	−1.22901e12	+	1.90485e11i	−1.48376	+	0.229968i
$955$	2.53372e11			0.304610
$956$		−	2.58408e10i		−	0.0309367i
$957$	−1.32851e10	+	1.02342e9i	−0.0158386	+	0.00122013i
$958$	−1.44408e12			−1.71447
$959$		−	1.39302e12i		−	1.64696i
$960$	8.22210e10	+	1.06732e12i	0.0968050	+	1.25663i
$961$	7.53873e11			0.883903
$962$			3.60517e11i			0.420945i
$963$	−2.34349e11	−	1.51202e12i	−0.272494	−	1.75814i
$964$	−2.36228e10			−0.0273541
$965$			3.91316e11i			0.451252i
$966$	9.32583e11	−	7.18419e10i	1.07097	−	0.0825029i
$967$	−1.59032e12			−1.81877			−0.909384	−	0.415957i	$-0.863447\pi$
$967$	−1.59032e12			−1.81877			−0.909384	+	0.415957i	$0.863447\pi$
$968$		−	7.87757e10i		−	0.0897203i
$969$	1.06218e11	+	1.37883e12i	0.120477	+	1.56392i
$970$	1.43279e12			1.61843
$971$		−	1.17604e11i		−	0.132296i	−0.997810	−	0.0661478i	$-0.978929\pi$
$971$		−	1.17604e11i		−	0.132296i	0.997810	−	0.0661478i	$-0.0210709\pi$
$972$	2.09813e10	−	8.48786e9i	0.0235054	−	0.00950896i
$973$	−6.53716e11			−0.729353
$974$		−	5.38970e11i		−	0.598865i
$975$	−2.21058e11	+	1.70293e10i	−0.244618	+	0.0188442i
$976$	−1.03068e12			−1.13586
$977$			2.45765e11i			0.269738i	0.990863	+	0.134869i	$0.0430613\pi$
$977$			2.45765e11i			0.269738i	−0.990863	+	0.134869i	$0.956939\pi$
$978$	−7.76079e10	−	1.00743e12i	−0.0848302	−	1.10119i
$979$	−1.67717e10			−0.0182577
$980$		−	3.52106e10i		−	0.0381741i
$981$	−1.25906e12	+	1.95143e11i	−1.35947	+	0.210706i
$982$	9.87078e11			1.06146
$983$		−	3.82073e11i		−	0.409197i	−0.978846	−	0.204598i	$-0.934411\pi$
$983$		−	3.82073e11i		−	0.409197i	0.978846	−	0.204598i	$-0.0655889\pi$
$984$	1.17926e12	−	9.08449e10i	1.25785	−	0.0968992i
$985$	6.69000e11			0.710691
$986$			5.58665e10i			0.0591077i
$987$	−1.09679e11	−	1.42374e12i	−0.115572	−	1.50025i
$988$	1.24036e10			0.0130173
$989$			5.29876e11i			0.553847i
$990$	5.81627e10	+	3.75267e11i	0.0605486	+	0.390660i
$991$	6.94513e11			0.720089			0.360044	−	0.932935i	$-0.382762\pi$
$991$	6.94513e11			0.720089			0.360044	+	0.932935i	$0.382762\pi$
$992$			6.73879e10i			0.0695881i
$993$	1.47079e12	−	1.13302e11i	1.51270	−	0.116531i
$994$	−2.09928e12			−2.15043
$995$			8.82704e10i			0.0900581i
$996$	2.73806e9	+	3.55429e10i	0.00278231	+	0.0361174i
$997$	5.41235e11			0.547778			0.273889	−	0.961761i	$-0.411690\pi$
$997$	5.41235e11			0.547778			0.273889	+	0.961761i	$0.411690\pi$
$998$			9.20062e10i			0.0927459i
$999$	1.11159e12	−	2.61034e11i	1.11605	−	0.262080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.9.b.a.23.20	yes	26
3.2	odd	2	inner	33.9.b.a.23.7	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.9.b.a.23.7	✓	26	3.2	odd	2	inner
33.9.b.a.23.20	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)

\(f(q)\)	\(=\)	\(q+16.2016i q^{2} +(-80.7607 + 6.22143i) q^{3} -6.49112 q^{4} +809.269i q^{5} +(-100.797 - 1308.45i) q^{6} -3530.96 q^{7} +4042.44i q^{8} +(6483.59 - 1004.89i) q^{9} +O(q^{10})\)	\(q+16.2016i q^{2} +(-80.7607 + 6.22143i) q^{3} -6.49112 q^{4} +809.269i q^{5} +(-100.797 - 1308.45i) q^{6} -3530.96 q^{7} +4042.44i q^{8} +(6483.59 - 1004.89i) q^{9} -13111.4 q^{10} -4414.43i q^{11} +(524.228 - 40.3840i) q^{12} -10356.8 q^{13} -57207.1i q^{14} +(-5034.81 - 65357.2i) q^{15} -67155.6 q^{16} -92534.7i q^{17} +(16280.9 + 105044. i) q^{18} +184504. q^{19} -5253.06i q^{20} +(285163. - 21967.6i) q^{21} +71520.7 q^{22} -201854. i q^{23} +(-25149.7 - 326470. i) q^{24} -264291. q^{25} -167796. i q^{26} +(-517367. + 121493. i) q^{27} +22919.9 q^{28} +37264.0i q^{29} +(1.05889e6 - 81571.8i) q^{30} -1.26758e6 q^{31} -53162.6i q^{32} +(27464.0 + 356512. i) q^{33} +1.49921e6 q^{34} -2.85750e6i q^{35} +(-42085.8 + 6522.89i) q^{36} -2.14855e6 q^{37} +2.98925e6i q^{38} +(836419. - 64433.8i) q^{39} -3.27142e6 q^{40} +3.61216e6i q^{41} +(355910. + 4.62009e6i) q^{42} -2.62505e6 q^{43} +28654.6i q^{44} +(813230. + 5.24697e6i) q^{45} +3.27036e6 q^{46} -4.99275e6i q^{47} +(5.42353e6 - 417804. i) q^{48} +6.70286e6 q^{49} -4.28194e6i q^{50} +(575698. + 7.47317e6i) q^{51} +67227.0 q^{52} +1.16999e7i q^{53} +(-1.96838e6 - 8.38217e6i) q^{54} +3.57246e6 q^{55} -1.42737e7i q^{56} +(-1.49006e7 + 1.14788e6i) q^{57} -603736. q^{58} +417021. i q^{59} +(32681.6 + 424241. i) q^{60} +1.53477e7 q^{61} -2.05368e7i q^{62} +(-2.28933e7 + 3.54824e6i) q^{63} -1.63305e7 q^{64} -8.38140e6i q^{65} +(-5.77606e6 + 444961. i) q^{66} -8.02130e6 q^{67} +600654. i q^{68} +(1.25582e6 + 1.63019e7i) q^{69} +4.62959e7 q^{70} -3.66962e7i q^{71} +(4.06222e6 + 2.62095e7i) q^{72} -1.19377e7 q^{73} -3.48099e7i q^{74} +(2.13444e7 - 1.64427e6i) q^{75} -1.19764e6 q^{76} +1.55872e7i q^{77} +(1.04393e6 + 1.35513e7i) q^{78} -3.44849e7 q^{79} -5.43469e7i q^{80} +(4.10271e7 - 1.30306e7i) q^{81} -5.85227e7 q^{82} +6.78006e7i q^{83} +(-1.85103e6 + 142594. i) q^{84} +7.48855e7 q^{85} -4.25299e7i q^{86} +(-231835. - 3.00947e6i) q^{87} +1.78450e7 q^{88} -3.79929e6i q^{89} +(-8.50091e7 + 1.31756e7i) q^{90} +3.65693e7 q^{91} +1.31026e6i q^{92} +(1.02371e8 - 7.88617e6i) q^{93} +8.08904e7 q^{94} +1.49313e8i q^{95} +(330747. + 4.29345e6i) q^{96} -1.09278e8 q^{97} +1.08597e8i q^{98} +(-4.43603e6 - 2.86213e7i) 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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