LMFDB - Embedded newform 177.9.c.a.58.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,9,Mod(58,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	177.c (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:	$72.1060139808$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.7
Character	$\chi$	$=$	177.58
Dual form			177.9.c.a.58.74

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-28.1432i q^{2} -46.7654 q^{3} -536.039 q^{4} -406.960 q^{5} +1316.13i q^{6} +2744.16 q^{7} +7881.18i q^{8} +2187.00 q^{9} +O(q^{10})$	\(q-28.1432i q^{2} -46.7654 q^{3} -536.039 q^{4} -406.960 q^{5} +1316.13i q^{6} +2744.16 q^{7} +7881.18i q^{8} +2187.00 q^{9} +11453.1i q^{10} -5707.50i q^{11} +25068.1 q^{12} -49047.0i q^{13} -77229.3i q^{14} +19031.6 q^{15} +84575.7 q^{16} -62224.1 q^{17} -61549.1i q^{18} +167552. q^{19} +218146. q^{20} -128332. q^{21} -160627. q^{22} -321556. i q^{23} -368567. i q^{24} -225009. q^{25} -1.38034e6 q^{26} -102276. q^{27} -1.47097e6 q^{28} -340144. q^{29} -535610. i q^{30} -822696. i q^{31} -362646. i q^{32} +266913. i q^{33} +1.75118e6i q^{34} -1.11676e6 q^{35} -1.17232e6 q^{36} -506510. i q^{37} -4.71543e6i q^{38} +2.29370e6i q^{39} -3.20732e6i q^{40} +2.70031e6 q^{41} +3.61166e6i q^{42} -2.76851e6i q^{43} +3.05944e6i q^{44} -890021. q^{45} -9.04960e6 q^{46} +71974.2i q^{47} -3.95521e6 q^{48} +1.76559e6 q^{49} +6.33247e6i q^{50} +2.90993e6 q^{51} +2.62911e7i q^{52} +2.39637e6 q^{53} +2.87837e6i q^{54} +2.32272e6i q^{55} +2.16272e7i q^{56} -7.83561e6 q^{57} +9.57275e6i q^{58} +(6.01191e6 - 1.05208e7i) q^{59} -1.02017e7 q^{60} -5.73423e6i q^{61} -2.31533e7 q^{62} +6.00147e6 q^{63} +1.14454e7 q^{64} +1.99601e7i q^{65} +7.51179e6 q^{66} -1.33867e7i q^{67} +3.33545e7 q^{68} +1.50377e7i q^{69} +3.14292e7i q^{70} -2.76871e7 q^{71} +1.72362e7i q^{72} +1.83891e6i q^{73} -1.42548e7 q^{74} +1.05226e7 q^{75} -8.98141e7 q^{76} -1.56623e7i q^{77} +6.45521e7 q^{78} -3.52171e7 q^{79} -3.44189e7 q^{80} +4.78297e6 q^{81} -7.59953e7i q^{82} +3.28542e7i q^{83} +6.87907e7 q^{84} +2.53227e7 q^{85} -7.79145e7 q^{86} +1.59070e7 q^{87} +4.49818e7 q^{88} +8.29411e7i q^{89} +2.50480e7i q^{90} -1.34593e8i q^{91} +1.72366e8i q^{92} +3.84737e7i q^{93} +2.02558e6 q^{94} -6.81867e7 q^{95} +1.69593e7i q^{96} -2.69493e6i q^{97} -4.96894e7i q^{98} -1.24823e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	28.1432i		−	1.75895i	−0.475946	−	0.879475i	$-0.657894\pi$
$2$		−	28.1432i		−	1.75895i	0.475946	−	0.879475i	$-0.342106\pi$
$3$	−46.7654			−0.577350
$3$	−46.7654			−0.577350
$4$	−536.039			−2.09390
$5$	−406.960			−0.651135			−0.325568	−	0.945519i	$-0.605555\pi$
$5$	−406.960			−0.651135			−0.325568	+	0.945519i	$0.605555\pi$
$6$			1316.13i			1.01553i
$7$	2744.16			1.14292			0.571461	−	0.820629i	$-0.306377\pi$
$7$	2744.16			1.14292			0.571461	+	0.820629i	$0.306377\pi$
$8$			7881.18i			1.92412i
$9$	2187.00			0.333333
$10$			11453.1i			1.14531i
$11$		−	5707.50i		−	0.389830i	−0.980820	−	0.194915i	$-0.937557\pi$
$11$		−	5707.50i		−	0.389830i	0.980820	−	0.194915i	$-0.0624431\pi$
$12$	25068.1			1.20891
$13$		−	49047.0i		−	1.71727i	−0.512586	−	0.858636i	$-0.671312\pi$
$13$		−	49047.0i		−	1.71727i	0.512586	−	0.858636i	$-0.328688\pi$
$14$		−	77229.3i		−	2.01034i
$15$	19031.6			0.375933
$16$	84575.7			1.29052
$17$	−62224.1			−0.745012			−0.372506	−	0.928030i	$-0.621501\pi$
$17$	−62224.1			−0.745012			−0.372506	+	0.928030i	$0.621501\pi$
$18$		−	61549.1i		−	0.586316i
$19$	167552.			1.28568			0.642842	−	0.765999i	$-0.277755\pi$
$19$	167552.			1.28568			0.642842	+	0.765999i	$0.277755\pi$
$20$	218146.			1.36341
$21$	−128332.			−0.659867
$22$	−160627.			−0.685691
$23$		−	321556.i		−	1.14907i	−0.818482	−	0.574533i	$-0.805184\pi$
$23$		−	321556.i		−	1.14907i	0.818482	−	0.574533i	$-0.194816\pi$
$24$		−	368567.i		−	1.11089i
$25$	−225009.			−0.576023
$26$	−1.38034e6			−3.02059
$27$	−102276.			−0.192450
$28$	−1.47097e6			−2.39317
$29$	−340144.			−0.480918			−0.240459	−	0.970659i	$-0.577298\pi$
$29$	−340144.			−0.480918			−0.240459	+	0.970659i	$0.577298\pi$
$30$		−	535610.i		−	0.661247i
$31$		−	822696.i		−	0.890825i	−0.895325	−	0.445413i	$-0.853057\pi$
$31$		−	822696.i		−	0.890825i	0.895325	−	0.445413i	$-0.146943\pi$
$32$		−	362646.i		−	0.345846i
$33$			266913.i			0.225068i
$34$			1.75118e6i			1.31044i
$35$	−1.11676e6			−0.744197
$36$	−1.17232e6			−0.697967
$37$		−	506510.i		−	0.270260i	−0.990828	−	0.135130i	$-0.956855\pi$
$37$		−	506510.i		−	0.270260i	0.990828	−	0.135130i	$-0.0431451\pi$
$38$		−	4.71543e6i		−	2.26145i
$39$			2.29370e6i			0.991467i
$40$		−	3.20732e6i		−	1.25286i
$41$	2.70031e6			0.955604			0.477802	−	0.878467i	$-0.341434\pi$
$41$	2.70031e6			0.955604			0.477802	+	0.878467i	$0.341434\pi$
$42$			3.61166e6i			1.16067i
$43$		−	2.76851e6i		−	0.809788i	−0.914364	−	0.404894i	$-0.867308\pi$
$43$		−	2.76851e6i		−	0.809788i	0.914364	−	0.404894i	$-0.132692\pi$
$44$			3.05944e6i			0.816265i
$45$	−890021.			−0.217045
$46$	−9.04960e6			−2.02115
$47$			71974.2i			0.0147498i	0.999973	+	0.00737489i	$0.00234752\pi$
$47$			71974.2i			0.0147498i	−0.999973	+	0.00737489i	$0.997652\pi$
$48$	−3.95521e6			−0.745084
$49$	1.76559e6			0.306271
$50$			6.33247e6i			1.01319i
$51$	2.90993e6			0.430133
$52$			2.62911e7i			3.59580i
$53$	2.39637e6			0.303704			0.151852	−	0.988403i	$-0.451476\pi$
$53$	2.39637e6			0.303704			0.151852	+	0.988403i	$0.451476\pi$
$54$			2.87837e6i			0.338510i
$55$			2.32272e6i			0.253832i
$56$			2.16272e7i			2.19912i
$57$	−7.83561e6			−0.742290
$58$			9.57275e6i			0.845911i
$59$	6.01191e6	−	1.05208e7i	0.496141	−	0.868242i
$59$	6.01191e6	−	1.05208e7i	0.496141	−	0.868242i
$60$	−1.02017e7			−0.787167
$61$		−	5.73423e6i		−	0.414148i	−0.978325	−	0.207074i	$-0.933606\pi$
$61$		−	5.73423e6i		−	0.414148i	0.978325	−	0.207074i	$-0.0663941\pi$
$62$	−2.31533e7			−1.56692
$63$	6.00147e6			0.380974
$64$	1.14454e7			0.682197
$65$			1.99601e7i			1.11818i
$66$	7.51179e6			0.395884
$67$		−	1.33867e7i		−	0.664315i	−0.943224	−	0.332157i	$-0.892223\pi$
$67$		−	1.33867e7i		−	0.664315i	0.943224	−	0.332157i	$-0.107777\pi$
$68$	3.33545e7			1.55998
$69$			1.50377e7i			0.663413i
$70$			3.14292e7i			1.30900i
$71$	−2.76871e7			−1.08954			−0.544771	−	0.838585i	$-0.683384\pi$
$71$	−2.76871e7			−1.08954			−0.544771	+	0.838585i	$0.683384\pi$
$72$			1.72362e7i			0.641372i
$73$			1.83891e6i			0.0647545i	0.999476	+	0.0323772i	$0.0103078\pi$
$73$			1.83891e6i			0.0647545i	−0.999476	+	0.0323772i	$0.989692\pi$
$74$	−1.42548e7			−0.475373
$75$	1.05226e7			0.332567
$76$	−8.98141e7			−2.69209
$77$		−	1.56623e7i		−	0.445545i
$78$	6.45521e7			1.74394
$79$	−3.52171e7			−0.904160			−0.452080	−	0.891977i	$-0.649318\pi$
$79$	−3.52171e7			−0.904160			−0.452080	+	0.891977i	$0.649318\pi$
$80$	−3.44189e7			−0.840305
$81$	4.78297e6			0.111111
$82$		−	7.59953e7i		−	1.68086i
$83$			3.28542e7i			0.692275i	0.938184	+	0.346137i	$0.112507\pi$
$83$			3.28542e7i			0.692275i	−0.938184	+	0.346137i	$0.887493\pi$
$84$	6.87907e7			1.38170
$85$	2.53227e7			0.485103
$86$	−7.79145e7			−1.42438
$87$	1.59070e7			0.277658
$88$	4.49818e7			0.750078
$89$			8.29411e7i			1.32193i	0.750415	+	0.660967i	$0.229854\pi$
$89$			8.29411e7i			1.32193i	−0.750415	+	0.660967i	$0.770146\pi$
$90$			2.50480e7i			0.381771i
$91$		−	1.34593e8i		−	1.96271i
$92$			1.72366e8i			2.40603i
$93$			3.84737e7i			0.514318i
$94$	2.02558e6			0.0259441
$95$	−6.81867e7			−0.837154
$96$			1.69593e7i			0.199674i
$97$		−	2.69493e6i		−	0.0304411i	−0.999884	−	0.0152205i	$-0.995155\pi$
$97$		−	2.69493e6i		−	0.0304411i	0.999884	−	0.0152205i	$-0.00484503\pi$
$98$		−	4.96894e7i		−	0.538716i
$99$		−	1.24823e7i		−	0.129943i
$100$	1.20614e8			1.20614
$101$			8.66455e7i			0.832646i	0.909217	+	0.416323i	$0.136681\pi$
$101$			8.66455e7i			0.832646i	−0.909217	+	0.416323i	$0.863319\pi$
$102$		−	8.18948e7i		−	0.756581i
$103$		−	1.48893e8i		−	1.32290i	−0.749990	−	0.661449i	$-0.769942\pi$
$103$		−	1.48893e8i		−	1.32290i	0.749990	−	0.661449i	$-0.230058\pi$
$104$	3.86549e8			3.30423
$105$	5.22257e7			0.429662
$106$		−	6.74416e7i		−	0.534201i
$107$	−3.68069e7			−0.280798			−0.140399	−	0.990095i	$-0.544839\pi$
$107$	−3.68069e7			−0.280798			−0.140399	+	0.990095i	$0.544839\pi$
$108$	5.48238e7			0.402972
$109$		−	8.91124e7i		−	0.631295i	−0.948877	−	0.315647i	$-0.897778\pi$
$109$		−	8.91124e7i		−	0.631295i	0.948877	−	0.315647i	$-0.102222\pi$
$110$	6.53687e7			0.446477
$111$			2.36871e7i			0.156034i
$112$	2.32089e8			1.47497
$113$			3.04104e8i			1.86513i	0.361007	+	0.932563i	$0.382433\pi$
$113$			3.04104e8i			1.86513i	−0.361007	+	0.932563i	$0.617567\pi$
$114$			2.20519e8i			1.30565i
$115$			1.30860e8i			0.748197i
$116$	1.82331e8			1.00700
$117$		−	1.07266e8i		−	0.572424i
$118$	−2.96089e8	−	1.69194e8i	−1.52719	−	0.872686i
$119$	−1.70753e8			−0.851490
$120$			1.49992e8i			0.723340i
$121$	1.81783e8			0.848033
$122$	−1.61379e8			−0.728465
$123$	−1.26281e8			−0.551718
$124$			4.40997e8i			1.86530i
$125$	2.50538e8			1.02620
$126$		−	1.68900e8i		−	0.670114i
$127$	2.83628e8			1.09027			0.545135	−	0.838349i	$-0.316479\pi$
$127$	2.83628e8			1.09027			0.545135	+	0.838349i	$0.316479\pi$
$128$		−	4.14946e8i		−	1.54580i
$129$			1.29470e8i			0.467531i
$130$	5.61742e8			1.96682
$131$			2.19846e8i			0.746506i	0.927730	+	0.373253i	$0.121758\pi$
$131$			2.19846e8i			0.746506i	−0.927730	+	0.373253i	$0.878242\pi$
$132$		−	1.43076e8i		−	0.471271i
$133$	4.59788e8			1.46944
$134$	−3.76744e8			−1.16850
$135$	4.16221e7			0.125311
$136$		−	4.90400e8i		−	1.43349i
$137$	−1.43138e8			−0.406324			−0.203162	−	0.979145i	$-0.565122\pi$
$137$	−1.43138e8			−0.406324			−0.203162	+	0.979145i	$0.565122\pi$
$138$	4.23208e8			1.16691
$139$	1.34149e8			0.359358			0.179679	−	0.983725i	$-0.442494\pi$
$139$	1.34149e8			0.359358			0.179679	+	0.983725i	$0.442494\pi$
$140$	5.98627e8			1.55828
$141$		−	3.36590e6i		−	0.00851578i
$142$			7.79204e8i			1.91645i
$143$	−2.79936e8			−0.669444
$144$	1.84967e8			0.430174
$145$	1.38425e8			0.313143
$146$	5.17529e7			0.113900
$147$	−8.25687e7			−0.176826
$148$			2.71509e8i			0.565897i
$149$		−	2.11758e8i		−	0.429629i	−0.976655	−	0.214815i	$-0.931085\pi$
$149$		−	2.11758e8i		−	0.429629i	0.976655	−	0.214815i	$-0.0689147\pi$
$150$		−	2.96140e8i		−	0.584968i
$151$			9.10554e8i			1.75145i	0.482809	+	0.875726i	$0.339617\pi$
$151$			9.10554e8i			1.75145i	−0.482809	+	0.875726i	$0.660383\pi$
$152$			1.32050e9i			2.47381i
$153$	−1.36084e8			−0.248337
$154$	−4.40786e8			−0.783691
$155$			3.34804e8i			0.580048i
$156$		−	1.22951e9i		−	2.07604i
$157$		−	1.77008e8i		−	0.291337i	−0.989333	−	0.145668i	$-0.953467\pi$
$157$		−	1.77008e8i		−	0.291337i	0.989333	−	0.145668i	$-0.0465333\pi$
$158$			9.91121e8i			1.59037i
$159$	−1.12067e8			−0.175344
$160$			1.47582e8i			0.225193i
$161$		−	8.82399e8i		−	1.31329i
$162$		−	1.34608e8i		−	0.195439i
$163$	−9.70750e8			−1.37517			−0.687586	−	0.726103i	$-0.741330\pi$
$163$	−9.70750e8			−1.37517			−0.687586	+	0.726103i	$0.741330\pi$
$164$	−1.44747e9			−2.00094
$165$		−	1.08623e8i		−	0.146550i
$166$	9.24622e8			1.21768
$167$	−1.28578e9			−1.65311			−0.826556	−	0.562855i	$-0.809703\pi$
$167$	−1.28578e9			−1.65311			−0.826556	+	0.562855i	$0.809703\pi$
$168$		−	1.01140e9i		−	1.26966i
$169$	−1.58988e9			−1.94902
$170$		−	7.12661e8i		−	0.853272i
$171$	3.66435e8			0.428561
$172$			1.48403e9i			1.69562i
$173$			1.10174e9i			1.22997i	0.788539	+	0.614984i	$0.210838\pi$
$173$			1.10174e9i			1.22997i	−0.788539	+	0.614984i	$0.789162\pi$
$174$		−	4.47673e8i		−	0.488387i
$175$	−6.17460e8			−0.658349
$176$		−	4.82715e8i		−	0.503084i
$177$	−2.81149e8	+	4.92009e8i	−0.286447	+	0.501280i
$178$	2.33423e9			2.32521
$179$		−	2.16436e8i		−	0.210823i	−0.994429	−	0.105411i	$-0.966384\pi$
$179$		−	2.16436e8i		−	0.210823i	0.994429	−	0.105411i	$-0.0336159\pi$
$180$	4.77086e8			0.454471
$181$	−7.17258e8			−0.668284			−0.334142	−	0.942523i	$-0.608447\pi$
$181$	−7.17258e8			−0.668284			−0.334142	+	0.942523i	$0.608447\pi$
$182$	−3.78787e9			−3.45230
$183$			2.68163e8i			0.239108i
$184$	2.53424e9			2.21094
$185$			2.06129e8i			0.175976i
$186$	1.08277e9			0.904660
$187$			3.55144e8i			0.290428i
$188$		−	3.85810e7i		−	0.0308846i
$189$	−2.80661e8			−0.219956
$190$			1.91899e9i			1.47251i
$191$		−	8.84331e8i		−	0.664479i	−0.943195	−	0.332240i	$-0.892196\pi$
$191$		−	8.84331e8i		−	0.664479i	0.943195	−	0.332240i	$-0.107804\pi$
$192$	−5.35247e8			−0.393867
$193$	1.45097e9			1.04576			0.522878	−	0.852408i	$-0.324858\pi$
$193$	1.45097e9			1.04576			0.522878	+	0.852408i	$0.324858\pi$
$194$	−7.58438e7			−0.0535443
$195$		−	9.33444e8i		−	0.645579i
$196$	−9.46427e8			−0.641302
$197$	−2.08279e9			−1.38287			−0.691434	−	0.722440i	$-0.743021\pi$
$197$	−2.08279e9			−1.38287			−0.691434	+	0.722440i	$0.743021\pi$
$198$	−3.51292e8			−0.228564
$199$	1.28765e9			0.821078			0.410539	−	0.911843i	$-0.365341\pi$
$199$	1.28765e9			0.821078			0.410539	+	0.911843i	$0.365341\pi$
$200$		−	1.77334e9i		−	1.10834i
$201$			6.26033e8i			0.383542i
$202$	2.43848e9			1.46458
$203$	−9.33410e8			−0.549652
$204$	−1.55984e9			−0.900655
$205$	−1.09892e9			−0.622228
$206$	−4.19033e9			−2.32691
$207$		−	7.03242e8i		−	0.383022i
$208$		−	4.14818e9i		−	2.21618i
$209$		−	9.56300e8i		−	0.501198i
$210$		−	1.46980e9i		−	0.755754i
$211$			1.38402e9i			0.698253i	0.937076	+	0.349127i	$0.113522\pi$
$211$			1.38402e9i			0.698253i	−0.937076	+	0.349127i	$0.886478\pi$
$212$	−1.28455e9			−0.635927
$213$	1.29480e9			0.629048
$214$			1.03586e9i			0.493909i
$215$			1.12667e9i			0.527282i
$216$		−	8.06055e8i		−	0.370297i
$217$		−	2.25761e9i		−	1.01814i
$218$	−2.50791e9			−1.11042
$219$		−	8.59975e7i		−	0.0373860i
$220$		−	1.24507e9i		−	0.531499i
$221$			3.05191e9i			1.27939i
$222$	6.66631e8			0.274457
$223$	−4.49221e9			−1.81652			−0.908261	−	0.418403i	$-0.862590\pi$
$223$	−4.49221e9			−1.81652			−0.908261	+	0.418403i	$0.862590\pi$
$224$		−	9.95157e8i		−	0.395275i
$225$	−4.92094e8			−0.192008
$226$	8.55845e9			3.28066
$227$			2.37194e9i			0.893304i	0.894708	+	0.446652i	$0.147384\pi$
$227$			2.37194e9i			0.893304i	−0.894708	+	0.446652i	$0.852616\pi$
$228$	4.20019e9			1.55428
$229$			1.73293e9i			0.630142i	0.949068	+	0.315071i	$0.102028\pi$
$229$			1.73293e9i			0.630142i	−0.949068	+	0.315071i	$0.897972\pi$
$230$	3.68282e9			1.31604
$231$			7.32452e8i			0.257236i
$232$		−	2.68074e9i		−	0.925343i
$233$			9.85201e8i			0.334273i	0.985934	+	0.167136i	$0.0534520\pi$
$233$			9.85201e8i			0.334273i	−0.985934	+	0.167136i	$0.946548\pi$
$234$	−3.01880e9			−1.00686
$235$		−	2.92906e7i		−	0.00960410i
$236$	−3.22262e9	+	5.63956e9i	−1.03887	+	1.81801i
$237$	1.64694e9			0.522017
$238$			4.80553e9i			1.49773i
$239$	−1.03515e9			−0.317258			−0.158629	−	0.987338i	$-0.550707\pi$
$239$	−1.03515e9			−0.317258			−0.158629	+	0.987338i	$0.550707\pi$
$240$	1.60961e9			0.485150
$241$	−4.76332e9			−1.41202			−0.706012	−	0.708200i	$-0.749507\pi$
$241$	−4.76332e9			−1.41202			−0.706012	+	0.708200i	$0.749507\pi$
$242$		−	5.11596e9i		−	1.49165i
$243$	−2.23677e8			−0.0641500
$244$			3.07377e9i			0.867185i
$245$	−7.18525e8			−0.199424
$246$			3.55395e9i			0.970444i
$247$		−	8.21790e9i		−	2.20787i
$248$	6.48382e9			1.71405
$249$		−	1.53644e9i		−	0.399685i
$250$		−	7.05094e9i		−	1.80504i
$251$	7.08834e9			1.78587			0.892935	−	0.450186i	$-0.148642\pi$
$251$	7.08834e9			1.78587			0.892935	+	0.450186i	$0.148642\pi$
$252$	−3.21702e9			−0.797722
$253$	−1.83528e9			−0.447940
$254$		−	7.98219e9i		−	1.91773i
$255$	−1.18423e9			−0.280075
$256$	−8.74790e9			−2.03678
$257$	3.07457e9			0.704778			0.352389	−	0.935854i	$-0.385369\pi$
$257$	3.07457e9			0.704778			0.352389	+	0.935854i	$0.385369\pi$
$258$	3.64370e9			0.822364
$259$		−	1.38994e9i		−	0.308886i
$260$		−	1.06994e10i		−	2.34135i
$261$	−7.43896e8			−0.160306
$262$	6.18716e9			1.31307
$263$	−4.06444e9			−0.849527			−0.424764	−	0.905304i	$-0.639643\pi$
$263$	−4.06444e9			−0.849527			−0.424764	+	0.905304i	$0.639643\pi$
$264$	−2.10359e9			−0.433058
$265$	−9.75227e8			−0.197753
$266$		−	1.29399e10i		−	2.58466i
$267$		−	3.87877e9i		−	0.763219i
$268$			7.17578e9i			1.39101i
$269$			1.25437e9i			0.239562i	0.992800	+	0.119781i	$0.0382192\pi$
$269$			1.25437e9i			0.239562i	−0.992800	+	0.119781i	$0.961781\pi$
$270$		−	1.17138e9i		−	0.220416i
$271$	1.02476e10			1.89996			0.949981	−	0.312308i	$-0.101102\pi$
$271$	1.02476e10			1.89996			0.949981	+	0.312308i	$0.101102\pi$
$272$	−5.26265e9			−0.961454
$273$			6.29428e9i			1.13317i
$274$			4.02836e9i			0.714704i
$275$			1.28424e9i			0.224551i
$276$		−	8.06077e9i		−	1.38912i
$277$	−9.16453e9			−1.55665			−0.778325	−	0.627861i	$-0.783930\pi$
$277$	−9.16453e9			−1.55665			−0.778325	+	0.627861i	$0.783930\pi$
$278$		−	3.77538e9i		−	0.632093i
$279$		−	1.79924e9i		−	0.296942i
$280$		−	8.80140e9i		−	1.43192i
$281$	1.18401e10			1.89902			0.949511	−	0.313735i	$-0.101580\pi$
$281$	1.18401e10			1.89902			0.949511	+	0.313735i	$0.101580\pi$
$282$	−9.47271e7			−0.0149788
$283$		−	9.34560e9i		−	1.45701i	−0.685043	−	0.728503i	$-0.740217\pi$
$283$		−	9.34560e9i		−	1.45701i	0.685043	−	0.728503i	$-0.259783\pi$
$284$	1.48414e10			2.28140
$285$	3.18878e9			0.483331
$286$			7.87828e9i			1.17752i
$287$	7.41007e9			1.09218
$288$		−	7.93107e8i		−	0.115282i
$289$	−3.10392e9			−0.444958
$290$		−	3.89572e9i		−	0.550802i
$291$			1.26029e8i			0.0175752i
$292$		−	9.85729e8i		−	0.135590i
$293$	−4.31608e9			−0.585625			−0.292812	−	0.956170i	$-0.594591\pi$
$293$	−4.31608e9			−0.585625			−0.292812	+	0.956170i	$0.594591\pi$
$294$			2.32375e9i			0.311028i
$295$	−2.44661e9	+	4.28154e9i	−0.323055	+	0.565343i
$296$	3.99190e9			0.520011
$297$			5.83739e8i			0.0750228i
$298$	−5.95953e9			−0.755696
$299$	−1.57713e10			−1.97326
$300$	−5.64054e9			−0.696362
$301$		−	7.59721e9i		−	0.925525i
$302$	2.56259e10			3.08071
$303$		−	4.05201e9i		−	0.480728i
$304$	1.41708e10			1.65920
$305$			2.33360e9i			0.269666i
$306$			3.82984e9i			0.436812i
$307$	−3.72885e9			−0.419780			−0.209890	−	0.977725i	$-0.567311\pi$
$307$	−3.72885e9			−0.419780			−0.209890	+	0.977725i	$0.567311\pi$
$308$			8.39558e9i			0.932928i
$309$			6.96305e9i			0.763775i
$310$	9.42245e9			1.02027
$311$	−1.78526e10			−1.90835			−0.954177	−	0.299242i	$-0.903266\pi$
$311$	−1.78526e10			−1.90835			−0.954177	+	0.299242i	$0.903266\pi$
$312$	−1.80771e10			−1.90770
$313$			1.65765e10i			1.72710i	0.504266	+	0.863548i	$0.331763\pi$
$313$			1.65765e10i			1.72710i	−0.504266	+	0.863548i	$0.668237\pi$
$314$	−4.98158e9			−0.512447
$315$	−2.44236e9			−0.248066
$316$	1.88777e10			1.89322
$317$	−5.90897e9			−0.585160			−0.292580	−	0.956241i	$-0.594514\pi$
$317$	−5.90897e9			−0.585160			−0.292580	+	0.956241i	$0.594514\pi$
$318$			3.15393e9i			0.308421i
$319$			1.94137e9i			0.187476i
$320$	−4.65780e9			−0.444202
$321$	1.72129e9			0.162119
$322$	−2.48335e10			−2.31001
$323$	−1.04257e10			−0.957849
$324$	−2.56386e9			−0.232656
$325$			1.10360e10i			0.989188i
$326$			2.73200e10i			2.41886i
$327$			4.16738e9i			0.364478i
$328$			2.12816e10i			1.83869i
$329$			1.97508e8i			0.0168578i
$330$	−3.05699e9			−0.257774
$331$	8.74322e9			0.728382			0.364191	−	0.931324i	$-0.381345\pi$
$331$	8.74322e9			0.728382			0.364191	+	0.931324i	$0.381345\pi$
$332$		−	1.76111e10i		−	1.44955i
$333$		−	1.10774e9i		−	0.0900865i
$334$			3.61861e10i			2.90774i
$335$			5.44784e9i			0.432559i
$336$	−1.08537e10			−0.851573
$337$		−	9.50740e9i		−	0.737126i	−0.929603	−	0.368563i	$-0.879850\pi$
$337$		−	9.50740e9i		−	0.737126i	0.929603	−	0.368563i	$-0.120150\pi$
$338$			4.47442e10i			3.42823i
$339$		−	1.42215e10i		−	1.07683i
$340$	−1.35740e10			−1.01576
$341$	−4.69553e9			−0.347270
$342$		−	1.03127e10i		−	0.753817i
$343$	−1.09744e10			−0.792878
$344$	2.18191e10			1.55813
$345$		−	6.11972e9i		−	0.431972i
$346$	3.10064e10			2.16345
$347$		−	1.56359e10i		−	1.07846i	−0.842157	−	0.539232i	$-0.818714\pi$
$347$		−	1.56359e10i		−	1.07846i	0.842157	−	0.539232i	$-0.181286\pi$
$348$	−8.52676e9			−0.581389
$349$			1.05023e10i			0.707918i	0.935261	+	0.353959i	$0.115165\pi$
$349$			1.05023e10i			0.707918i	−0.935261	+	0.353959i	$0.884835\pi$
$350$			1.73773e10i			1.15800i
$351$			5.01633e9i			0.330489i
$352$	−2.06980e9			−0.134821
$353$		−	1.77402e10i		−	1.14251i	−0.820773	−	0.571254i	$-0.806457\pi$
$353$		−	1.77402e10i		−	1.14251i	0.820773	−	0.571254i	$-0.193543\pi$
$354$	1.38467e10	+	7.91244e9i	0.881726	+	0.503845i
$355$	1.12675e10			0.709440
$356$		−	4.44597e10i		−	2.76800i
$357$	7.98531e9			0.491608
$358$	−6.09119e9			−0.370826
$359$	−1.55105e10			−0.933787			−0.466894	−	0.884313i	$-0.654627\pi$
$359$	−1.55105e10			−0.933787			−0.466894	+	0.884313i	$0.654627\pi$
$360$		−	7.01442e9i		−	0.417620i
$361$	1.10900e10			0.652982
$362$			2.01859e10i			1.17548i
$363$	−8.50117e9			−0.489612
$364$			7.21469e10i			4.10972i
$365$		−	7.48363e8i		−	0.0421639i
$366$	7.54697e9			0.420579
$367$		−	3.08457e10i		−	1.70032i	−0.526527	−	0.850158i	$-0.676506\pi$
$367$		−	3.08457e10i		−	1.70032i	0.526527	−	0.850158i	$-0.323494\pi$
$368$		−	2.71958e10i		−	1.48289i
$369$	5.90558e9			0.318535
$370$	5.80113e9			0.309532
$371$	6.57603e9			0.347111
$372$		−	2.06234e10i		−	1.07693i
$373$	−1.50923e10			−0.779687			−0.389844	−	0.920881i	$-0.627471\pi$
$373$	−1.50923e10			−0.779687			−0.389844	+	0.920881i	$0.627471\pi$
$374$	9.99488e9			0.510847
$375$	−1.17165e10			−0.592479
$376$	−5.67242e8			−0.0283803
$377$			1.66831e10i			0.825868i
$378$			7.89869e9i			0.386891i
$379$	2.73541e10			1.32576			0.662882	−	0.748724i	$-0.269333\pi$
$379$	2.73541e10			1.32576			0.662882	+	0.748724i	$0.269333\pi$
$380$	3.65507e10			1.75292
$381$	−1.32640e10			−0.629467
$382$	−2.48879e10			−1.16879
$383$	1.55369e10			0.722053			0.361026	−	0.932556i	$-0.382426\pi$
$383$	1.55369e10			0.722053			0.361026	+	0.932556i	$0.382426\pi$
$384$			1.94051e10i			0.892466i
$385$			6.37391e9i			0.290110i
$386$		−	4.08350e10i		−	1.83943i
$387$		−	6.05472e9i		−	0.269929i
$388$			1.44459e9i			0.0637406i
$389$	−1.05981e10			−0.462840			−0.231420	−	0.972854i	$-0.574337\pi$
$389$	−1.05981e10			−0.462840			−0.231420	+	0.972854i	$0.574337\pi$
$390$	−2.62701e10			−1.13554
$391$			2.00085e10i			0.856067i
$392$			1.39150e10i			0.589302i
$393$		−	1.02812e10i		−	0.430995i
$394$			5.86163e10i			2.43239i
$395$	1.43319e10			0.588730
$396$			6.69099e9i			0.272088i
$397$		−	2.46311e10i		−	0.991565i	−0.868447	−	0.495783i	$-0.834881\pi$
$397$		−	2.46311e10i		−	0.991565i	0.868447	−	0.495783i	$-0.165119\pi$
$398$		−	3.62385e10i		−	1.44423i
$399$	−2.15021e10			−0.848379
$400$	−1.90303e10			−0.743370
$401$			3.11202e9i			0.120355i	0.998188	+	0.0601777i	$0.0191667\pi$
$401$			3.11202e9i			0.120355i	−0.998188	+	0.0601777i	$0.980833\pi$
$402$	1.76186e10			0.674631
$403$	−4.03508e10			−1.52979
$404$		−	4.64453e10i		−	1.74348i
$405$	−1.94648e9			−0.0723484
$406$			2.62691e10i			0.966810i
$407$	−2.89090e9			−0.105355
$408$			2.29337e10i			0.827626i
$409$		−	1.95746e10i		−	0.699521i	−0.936839	−	0.349760i	$-0.886263\pi$
$409$		−	1.95746e10i		−	0.699521i	0.936839	−	0.349760i	$-0.113737\pi$
$410$			3.09270e10i			1.09447i
$411$	6.69391e9			0.234592
$412$			7.98126e10i			2.77002i
$413$	1.64976e10	−	2.88707e10i	0.567050	−	0.992333i
$414$	−1.97915e10			−0.673716
$415$		−	1.33703e10i		−	0.450764i
$416$	−1.77867e10			−0.593912
$417$	−6.27352e9			−0.207476
$418$	−2.69133e10			−0.881581
$419$		−	5.13543e10i		−	1.66617i	−0.553142	−	0.833087i	$-0.686571\pi$
$419$		−	5.13543e10i		−	1.66617i	0.553142	−	0.833087i	$-0.313429\pi$
$420$	−2.79950e10			−0.899671
$421$			2.58050e10i			0.821439i	0.911762	+	0.410720i	$0.134722\pi$
$421$			2.58050e10i			0.821439i	−0.911762	+	0.410720i	$0.865278\pi$
$422$	3.89508e10			1.22819
$423$			1.57408e8i			0.00491659i
$424$			1.88863e10i			0.584363i
$425$	1.40010e10			0.429144
$426$		−	3.64397e10i		−	1.10646i
$427$		−	1.57356e10i		−	0.473339i
$428$	1.97299e10			0.587963
$429$	1.30913e10			0.386503
$430$	3.17081e10			0.927462
$431$		−	2.35267e10i		−	0.681793i	−0.940101	−	0.340897i	$-0.889269\pi$
$431$		−	2.35267e10i		−	0.681793i	0.940101	−	0.340897i	$-0.110731\pi$
$432$	−8.65005e9			−0.248361
$433$	2.29758e10			0.653612			0.326806	−	0.945091i	$-0.394028\pi$
$433$	2.29758e10			0.653612			0.326806	+	0.945091i	$0.394028\pi$
$434$	−6.35362e10			−1.79086
$435$	−6.47350e9			−0.180793
$436$			4.77677e10i			1.32187i
$437$		−	5.38771e10i		−	1.47733i
$438$	−2.42024e9			−0.0657601
$439$	4.42515e10			1.19143			0.595717	−	0.803194i	$-0.296868\pi$
$439$	4.42515e10			1.19143			0.595717	+	0.803194i	$0.296868\pi$
$440$	−1.83058e10			−0.488402
$441$	3.86135e9			0.102090
$442$	8.58904e10			2.25038
$443$		−	1.02222e9i		−	0.0265417i	−0.999912	−	0.0132708i	$-0.995776\pi$
$443$		−	1.02222e9i		−	0.0265417i	0.999912	−	0.0132708i	$-0.00422436\pi$
$444$		−	1.26972e10i		−	0.326721i
$445$		−	3.37537e10i		−	0.860758i
$446$			1.26425e11i			3.19517i
$447$			9.90292e9i			0.248047i
$448$	3.14079e10			0.779698
$449$	3.67444e10			0.904079			0.452039	−	0.891998i	$-0.350697\pi$
$449$	3.67444e10			0.904079			0.452039	+	0.891998i	$0.350697\pi$
$450$			1.38491e10i			0.337732i
$451$		−	1.54120e10i		−	0.372523i
$452$		−	1.63012e11i		−	3.90539i
$453$		−	4.25824e10i		−	1.01120i
$454$	6.67538e10			1.57128
$455$			5.47738e10i			1.27799i
$456$		−	6.17539e10i		−	1.42825i
$457$		−	4.00848e10i		−	0.918999i	−0.888178	−	0.459499i	$-0.848029\pi$
$457$		−	4.00848e10i		−	0.918999i	0.888178	−	0.459499i	$-0.151971\pi$
$458$	4.87701e10			1.10839
$459$	6.36403e9			0.143378
$460$		−	7.01461e10i		−	1.56665i
$461$	4.68445e10			1.03718			0.518591	−	0.855022i	$-0.326457\pi$
$461$	4.68445e10			1.03718			0.518591	+	0.855022i	$0.326457\pi$
$462$	2.06135e10			0.452464
$463$			2.50947e10i			0.546082i	0.962002	+	0.273041i	$0.0880294\pi$
$463$			2.50947e10i			0.546082i	−0.962002	+	0.273041i	$0.911971\pi$
$464$	−2.87679e10			−0.620636
$465$		−	1.56572e10i		−	0.334891i
$466$	2.77267e10			0.587969
$467$			2.89237e10i			0.608115i	0.952654	+	0.304058i	$0.0983416\pi$
$467$			2.89237e10i			0.608115i	−0.952654	+	0.304058i	$0.901658\pi$
$468$			5.74986e10i			1.19860i
$469$		−	3.67352e10i		−	0.759260i
$470$	−8.24330e8			−0.0168931
$471$			8.27787e9i			0.168203i
$472$	8.29164e10	+	4.73810e10i	1.67060	+	0.954633i
$473$	−1.58012e10			−0.315680
$474$		−	4.63502e10i		−	0.918201i
$475$	−3.77006e10			−0.740583
$476$	9.15301e10			1.78294
$477$	5.24087e9			0.101235
$478$			2.91324e10i			0.558040i
$479$	−6.00874e10			−1.14141			−0.570704	−	0.821156i	$-0.693330\pi$
$479$	−6.00874e10			−1.14141			−0.570704	+	0.821156i	$0.693330\pi$
$480$		−	6.90174e9i		−	0.130015i
$481$	−2.48428e10			−0.464109
$482$			1.34055e11i			2.48368i
$483$			4.12657e10i			0.758230i
$484$	−9.74429e10			−1.77570
$485$			1.09673e9i			0.0198213i
$486$			6.29499e9i			0.112837i
$487$	8.08677e10			1.43767			0.718835	−	0.695181i	$-0.244676\pi$
$487$	8.08677e10			1.43767			0.718835	+	0.695181i	$0.244676\pi$
$488$	4.51925e10			0.796869
$489$	4.53975e10			0.793956
$490$			2.02216e10i			0.350777i
$491$	2.29280e9			0.0394493			0.0197247	−	0.999805i	$-0.493721\pi$
$491$	2.29280e9			0.0394493			0.0197247	+	0.999805i	$0.493721\pi$
$492$	6.76915e10			1.15524
$493$	2.11652e10			0.358290
$494$	−2.31278e11			−3.88353
$495$			5.07979e9i			0.0846106i
$496$		−	6.95801e10i		−	1.14963i
$497$	−7.59778e10			−1.24526
$498$	−4.32403e10			−0.703025
$499$	9.12096e10			1.47109			0.735544	−	0.677477i	$-0.236927\pi$
$499$	9.12096e10			1.47109			0.735544	+	0.677477i	$0.236927\pi$
$500$	−1.34298e11			−2.14877
$501$	6.01302e10			0.954424
$502$		−	1.99488e11i		−	3.14125i
$503$		−	4.30436e10i		−	0.672414i	−0.941788	−	0.336207i	$-0.890856\pi$
$503$		−	4.30436e10i		−	0.672414i	0.941788	−	0.336207i	$-0.109144\pi$
$504$			4.72987e10i			0.733039i
$505$		−	3.52612e10i		−	0.542165i
$506$			5.16505e10i			0.787903i
$507$	7.43512e10			1.12527
$508$	−1.52035e11			−2.28292
$509$			4.82412e10i			0.718699i	0.933203	+	0.359350i	$0.117001\pi$
$509$			4.82412e10i			0.718699i	−0.933203	+	0.359350i	$0.882999\pi$
$510$			3.33279e10i			0.492637i
$511$			5.04627e9i			0.0740093i
$512$			1.39967e11i			2.03679i
$513$	−1.71365e10			−0.247430
$514$		−	8.65282e10i		−	1.23967i
$515$			6.05936e10i			0.861386i
$516$		−	6.94010e10i		−	0.978965i
$517$	4.10792e8			0.00574990
$518$	−3.91174e10			−0.543314
$519$		−	5.15232e10i		−	0.710123i
$520$	−1.57310e11			−2.15150
$521$	−5.59642e10			−0.759555			−0.379777	−	0.925078i	$-0.623999\pi$
$521$	−5.59642e10			−0.759555			−0.379777	+	0.925078i	$0.623999\pi$
$522$			2.09356e10i			0.281970i
$523$	9.80172e10			1.31007			0.655037	−	0.755597i	$-0.272653\pi$
$523$	9.80172e10			1.31007			0.655037	+	0.755597i	$0.272653\pi$
$524$		−	1.17846e11i		−	1.56311i
$525$	2.88757e10			0.380098
$526$			1.14386e11i			1.49428i
$527$			5.11915e10i			0.663675i
$528$			2.25744e10i			0.290456i
$529$	−2.50870e10			−0.320350
$530$			2.74460e10i			0.347837i
$531$	1.31481e10	−	2.30090e10i	0.165380	−	0.289414i
$532$	−2.46464e11			−3.07686
$533$		−	1.32442e11i		−	1.64103i
$534$	−1.09161e11			−1.34246
$535$	1.49789e10			0.182837
$536$	1.05503e11			1.27822
$537$			1.01217e10i			0.121718i
$538$	3.53020e10			0.421377
$539$		−	1.00771e10i		−	0.119394i
$540$	−2.23111e10			−0.262389
$541$			8.07791e10i			0.942997i	0.881867	+	0.471498i	$0.156287\pi$
$541$			8.07791e10i			0.942997i	−0.881867	+	0.471498i	$0.843713\pi$
$542$		−	2.88400e11i		−	3.34194i
$543$	3.35429e10			0.385834
$544$			2.25653e10i			0.257659i
$545$			3.62652e10i			0.411058i
$546$	1.77141e11			1.99319
$547$	1.74965e9			0.0195435			0.00977176	−	0.999952i	$-0.496890\pi$
$547$	1.74965e9			0.0195435			0.00977176	+	0.999952i	$0.496890\pi$
$548$	7.67276e10			0.850803
$549$		−	1.25408e10i		−	0.138049i
$550$	3.61425e10			0.394973
$551$	−5.69917e10			−0.618309
$552$	−1.18515e11			−1.27648
$553$	−9.66412e10			−1.03338
$554$			2.57919e11i			2.73807i
$555$		−	9.63970e9i		−	0.101600i
$556$	−7.19090e10			−0.752461
$557$	−1.10540e11			−1.14841			−0.574207	−	0.818710i	$-0.694690\pi$
$557$	−1.10540e11			−1.14841			−0.574207	+	0.818710i	$0.694690\pi$
$558$	−5.06362e10			−0.522305
$559$	−1.35787e11			−1.39063
$560$	−9.44508e10			−0.960403
$561$		−	1.66084e10i		−	0.167678i
$562$		−	3.33218e11i		−	3.34028i
$563$			5.32954e10i			0.530464i	0.964185	+	0.265232i	$0.0854485\pi$
$563$			5.32954e10i			0.530464i	−0.964185	+	0.265232i	$0.914551\pi$
$564$			1.80425e9i			0.0178312i
$565$		−	1.23758e11i		−	1.21445i
$566$	−2.63015e11			−2.56280
$567$	1.31252e10			0.126991
$568$		−	2.18207e11i		−	2.09641i
$569$		−	5.27709e10i		−	0.503437i	−0.967800	−	0.251719i	$-0.919004\pi$
$569$		−	5.27709e10i		−	0.503437i	0.967800	−	0.251719i	$-0.0809957\pi$
$570$		−	8.97423e10i		−	0.850155i
$571$		−	8.72877e10i		−	0.821124i	−0.911833	−	0.410562i	$-0.865333\pi$
$571$		−	8.72877e10i		−	0.821124i	0.911833	−	0.410562i	$-0.134667\pi$
$572$	1.50056e11			1.40175
$573$			4.13561e10i			0.383637i
$574$		−	2.08543e11i		−	1.92109i
$575$			7.23529e10i			0.661888i
$576$	2.50310e10			0.227399
$577$	−7.68360e8			−0.00693205			−0.00346602	−	0.999994i	$-0.501103\pi$
$577$	−7.68360e8			−0.00693205			−0.00346602	+	0.999994i	$0.501103\pi$
$578$			8.73541e10i			0.782658i
$579$	−6.78553e10			−0.603768
$580$	−7.42012e10			−0.655691
$581$			9.01570e10i			0.791216i
$582$	3.54686e9			0.0309138
$583$		−	1.36773e10i		−	0.118393i
$584$	−1.44928e10			−0.124595
$585$			4.36528e10i			0.372725i
$586$			1.21468e11i			1.03008i
$587$		−	7.08101e10i		−	0.596407i	−0.954502	−	0.298203i	$-0.903613\pi$
$587$		−	7.08101e10i		−	0.596407i	0.954502	−	0.298203i	$-0.0963874\pi$
$588$	4.42600e10			0.370256
$589$		−	1.37844e11i		−	1.14532i
$590$	1.20496e11	+	6.88553e10i	0.994410	+	0.568237i
$591$	9.74024e10			0.798399
$592$		−	4.28384e10i		−	0.348776i
$593$	−7.38587e10			−0.597287			−0.298643	−	0.954365i	$-0.596534\pi$
$593$	−7.38587e10			−0.597287			−0.298643	+	0.954365i	$0.596534\pi$
$594$	1.64283e10			0.131961
$595$	6.94895e10			0.554435
$596$			1.13510e11i			0.899601i
$597$	−6.02173e10			−0.474050
$598$			4.43856e11i			3.47086i
$599$	−6.39782e10			−0.496963			−0.248482	−	0.968637i	$-0.579932\pi$
$599$	−6.39782e10			−0.496963			−0.248482	+	0.968637i	$0.579932\pi$
$600$			8.29307e10i			0.639898i
$601$		−	4.79700e10i		−	0.367682i	−0.982956	−	0.183841i	$-0.941147\pi$
$601$		−	4.79700e10i		−	0.367682i	0.982956	−	0.183841i	$-0.0588531\pi$
$602$	−2.13810e11			−1.62795
$603$		−	2.92767e10i		−	0.221438i
$604$		−	4.88093e11i		−	3.66737i
$605$	−7.39785e10			−0.552184
$606$	−1.14036e11			−0.845577
$607$	−1.76542e11			−1.30045			−0.650223	−	0.759743i	$-0.725325\pi$
$607$	−1.76542e11			−1.30045			−0.650223	+	0.759743i	$0.725325\pi$
$608$		−	6.07619e10i		−	0.444649i
$609$	4.36512e10			0.317342
$610$	6.56749e10			0.474329
$611$	3.53012e9			0.0253294
$612$	7.29464e10			0.519994
$613$			1.62572e11i			1.15134i	0.817681	+	0.575672i	$0.195259\pi$
$613$			1.62572e11i			1.15134i	−0.817681	+	0.575672i	$0.804741\pi$
$614$			1.04942e11i			0.738372i
$615$	5.13912e10			0.359243
$616$	1.23437e11			0.857281
$617$	−9.33035e10			−0.643809			−0.321905	−	0.946772i	$-0.604323\pi$
$617$	−9.33035e10			−0.643809			−0.321905	+	0.946772i	$0.604323\pi$
$618$	1.95962e11			1.34344
$619$	2.34361e11			1.59633			0.798165	−	0.602439i	$-0.205804\pi$
$619$	2.34361e11			1.59633			0.798165	+	0.602439i	$0.205804\pi$
$620$		−	1.79468e11i		−	1.21456i
$621$			3.28874e10i			0.221138i
$622$			5.02428e11i			3.35670i
$623$			2.27603e11i			1.51087i
$624$			1.93991e11i			1.27951i
$625$	−1.40648e10			−0.0921750
$626$	4.66517e11			3.03787
$627$			4.47217e10i			0.289367i
$628$			9.48834e10i			0.610031i
$629$			3.15171e10i			0.201346i
$630$			6.87357e10i			0.436335i
$631$	−4.43112e10			−0.279509			−0.139755	−	0.990186i	$-0.544631\pi$
$631$	−4.43112e10			−0.279509			−0.139755	+	0.990186i	$0.544631\pi$
$632$		−	2.77552e11i		−	1.73971i
$633$		−	6.47243e10i		−	0.403137i
$634$			1.66297e11i			1.02927i
$635$	−1.15425e11			−0.709913
$636$	6.00724e10			0.367153
$637$		−	8.65971e10i		−	0.525951i
$638$	5.46364e10			0.329761
$639$	−6.05517e10			−0.363181
$640$			1.68866e11i			1.00652i
$641$	−1.26538e11			−0.749528			−0.374764	−	0.927120i	$-0.622276\pi$
$641$	−1.26538e11			−0.749528			−0.374764	+	0.927120i	$0.622276\pi$
$642$		−	4.84425e10i		−	0.285159i
$643$	1.67234e11			0.978317			0.489158	−	0.872195i	$-0.337304\pi$
$643$	1.67234e11			0.978317			0.489158	+	0.872195i	$0.337304\pi$
$644$			4.73000e11i			2.74990i
$645$		−	5.26891e10i		−	0.304426i
$646$			2.93414e11i			1.68481i
$647$	1.60905e10			0.0918233			0.0459116	−	0.998946i	$-0.485381\pi$
$647$	1.60905e10			0.0918233			0.0459116	+	0.998946i	$0.485381\pi$
$648$			3.76955e10i			0.213791i
$649$	−6.00475e10	−	3.43130e10i	−0.338467	−	0.193410i
$650$	3.10589e11			1.73993
$651$			1.05578e11i			0.587826i
$652$	5.20360e11			2.87948
$653$	1.82713e11			1.00489			0.502444	−	0.864610i	$-0.332434\pi$
$653$	1.82713e11			1.00489			0.502444	+	0.864610i	$0.332434\pi$
$654$	1.17283e11			0.641099
$655$		−	8.94684e10i		−	0.486076i
$656$	2.28381e11			1.23323
$657$			4.02170e9i			0.0215848i
$658$	5.55852e9			0.0296521
$659$			1.16823e11i			0.619425i	0.950830	+	0.309712i	$0.100233\pi$
$659$			1.16823e11i			0.619425i	−0.950830	+	0.309712i	$0.899767\pi$
$660$			5.82261e10i			0.306861i
$661$	−2.78164e10			−0.145712			−0.0728560	−	0.997342i	$-0.523211\pi$
$661$	−2.78164e10			−0.145712			−0.0728560	+	0.997342i	$0.523211\pi$
$662$		−	2.46062e11i		−	1.28119i
$663$		−	1.42724e11i		−	0.738655i
$664$	−2.58930e11			−1.33202
$665$	−1.87115e11			−0.956802
$666$	−3.11752e10			−0.158458
$667$			1.09375e11i			0.552606i
$668$	6.89230e11			3.46145
$669$	2.10080e11			1.04877
$670$	1.53320e11			0.760849
$671$	−3.27281e10			−0.161447
$672$			4.65389e10i			0.228212i
$673$		−	1.70203e11i		−	0.829675i	−0.909896	−	0.414837i	$-0.863838\pi$
$673$		−	1.70203e11i		−	0.829675i	0.909896	−	0.414837i	$-0.136162\pi$
$674$	−2.67568e11			−1.29657
$675$	2.30130e10			0.110856
$676$	8.52236e11			4.08106
$677$	−1.60157e11			−0.762413			−0.381207	−	0.924490i	$-0.624491\pi$
$677$	−1.60157e11			−0.762413			−0.381207	+	0.924490i	$0.624491\pi$
$678$	−4.00239e11			−1.89409
$679$		−	7.39530e9i		−	0.0347918i
$680$			1.99573e11i			0.933396i
$681$		−	1.10924e11i		−	0.515749i
$682$			1.32147e11i			0.610831i
$683$		−	3.49843e11i		−	1.60765i	−0.594868	−	0.803823i	$-0.702796\pi$
$683$		−	3.49843e11i		−	1.60765i	0.594868	−	0.803823i	$-0.297204\pi$
$684$	−1.96424e11			−0.897365
$685$	5.82514e10			0.264572
$686$			3.08856e11i			1.39463i
$687$		−	8.10410e10i		−	0.363813i
$688$		−	2.34148e11i		−	1.04505i
$689$		−	1.17535e11i		−	0.521543i
$690$	−1.72228e11			−0.759816
$691$			1.43170e11i			0.627973i	0.949427	+	0.313987i	$0.101665\pi$
$691$			1.43170e11i			0.627973i	−0.949427	+	0.313987i	$0.898335\pi$
$692$		−	5.90575e11i		−	2.57543i
$693$		−	3.42534e10i		−	0.148515i
$694$	−4.40045e11			−1.89696
$695$	−5.45931e10			−0.233991
$696$			1.25366e11i			0.534247i
$697$	−1.68024e11			−0.711936
$698$	2.95568e11			1.24519
$699$		−	4.60733e10i		−	0.192992i
$700$	3.30982e11			1.37852
$701$		−	1.34207e11i		−	0.555781i	−0.960613	−	0.277891i	$-0.910365\pi$
$701$		−	1.34207e11i		−	0.555781i	0.960613	−	0.277891i	$-0.0896353\pi$
$702$	1.41175e11			0.581314
$703$		−	8.48665e10i		−	0.347468i
$704$		−	6.53244e10i		−	0.265941i
$705$			1.36978e9i			0.00554493i
$706$	−4.99265e11			−2.00961
$707$			2.37769e11i			0.951650i
$708$	1.50707e11	−	2.63736e11i	0.599792	−	1.04963i
$709$	2.30261e11			0.911245			0.455623	−	0.890173i	$-0.349417\pi$
$709$	2.30261e11			0.911245			0.455623	+	0.890173i	$0.349417\pi$
$710$		−	3.17104e11i		−	1.24787i
$711$	−7.70198e10			−0.301387
$712$	−6.53674e11			−2.54356
$713$	−2.64542e11			−1.02362
$714$		−	2.24732e11i		−	0.864714i
$715$	1.13922e11			0.435898
$716$			1.16018e11i			0.441442i
$717$	4.84092e10			0.183169
$718$			4.36515e11i			1.64248i
$719$			3.23619e11i			1.21093i	0.795873	+	0.605464i	$0.207012\pi$
$719$			3.23619e11i			1.21093i	−0.795873	+	0.605464i	$0.792988\pi$
$720$	−7.52741e10			−0.280102
$721$		−	4.08587e11i		−	1.51197i
$722$		−	3.12107e11i		−	1.14856i
$723$	2.22759e11			0.815232
$724$	3.84478e11			1.39932
$725$	7.65355e10			0.277020
$726$			2.39250e11i			0.861203i
$727$	−8.18255e10			−0.292921			−0.146461	−	0.989216i	$-0.546788\pi$
$727$	−8.18255e10			−0.292921			−0.146461	+	0.989216i	$0.546788\pi$
$728$	1.06075e12			3.77648
$729$	1.04604e10			0.0370370
$730$	−2.10613e10			−0.0741642
$731$			1.72268e11i			0.603302i
$732$		−	1.43746e11i		−	0.500669i
$733$	−5.06458e10			−0.175440			−0.0877198	−	0.996145i	$-0.527958\pi$
$733$	−5.06458e10			−0.175440			−0.0877198	+	0.996145i	$0.527958\pi$
$734$	−8.68095e11			−2.99077
$735$	3.36021e10			0.115138
$736$	−1.16611e11			−0.397400
$737$	−7.64045e10			−0.258970
$738$		−	1.66202e11i		−	0.560286i
$739$			2.40198e11i			0.805363i	0.915340	+	0.402682i	$0.131922\pi$
$739$			2.40198e11i			0.805363i	−0.915340	+	0.402682i	$0.868078\pi$
$740$		−	1.10493e11i		−	0.368475i
$741$			3.84313e11i			1.27471i
$742$		−	1.85070e11i		−	0.610550i
$743$	−7.18154e10			−0.235647			−0.117824	−	0.993035i	$-0.537592\pi$
$743$	−7.18154e10			−0.235647			−0.117824	+	0.993035i	$0.537592\pi$
$744$	−3.03218e11			−0.989609
$745$			8.61768e10i			0.279747i
$746$			4.24746e11i			1.37143i
$747$			7.18521e10i			0.230758i
$748$		−	1.90371e11i		−	0.608127i
$749$	−1.01004e11			−0.320930
$750$			3.29740e11i			1.04214i
$751$			2.61941e11i			0.823461i	0.911306	+	0.411731i	$0.135076\pi$
$751$			2.61941e11i			0.823461i	−0.911306	+	0.411731i	$0.864924\pi$
$752$			6.08727e9i			0.0190349i
$753$	−3.31489e11			−1.03107
$754$	4.69515e11			1.45266
$755$		−	3.70559e11i		−	1.14043i
$756$	1.50445e11			0.460565
$757$	−2.95970e11			−0.901290			−0.450645	−	0.892703i	$-0.648806\pi$
$757$	−2.95970e11			−0.901290			−0.450645	+	0.892703i	$0.648806\pi$
$758$		−	7.69832e11i		−	2.33195i
$759$	8.58274e10			0.258618
$760$		−	5.37392e11i		−	1.61078i
$761$	2.40603e11			0.717402			0.358701	−	0.933453i	$-0.383220\pi$
$761$	2.40603e11			0.717402			0.358701	+	0.933453i	$0.383220\pi$
$762$			3.73290e11i			1.10720i
$763$		−	2.44538e11i		−	0.721521i
$764$			4.74036e11i			1.39135i
$765$	5.53807e10			0.161701
$766$		−	4.37258e11i		−	1.27005i
$767$	−5.16014e11	−	2.94866e11i	−1.49101	−	0.852008i
$768$	4.09099e11			1.17593
$769$		−	5.22952e11i		−	1.49540i	−0.664038	−	0.747699i	$-0.731159\pi$
$769$		−	5.22952e11i		−	1.49540i	0.664038	−	0.747699i	$-0.268841\pi$
$770$	1.79382e11			0.510289
$771$	−1.43784e11			−0.406904
$772$	−7.77778e11			−2.18971
$773$		−	2.34322e11i		−	0.656289i	−0.944628	−	0.328144i	$-0.893577\pi$
$773$		−	2.34322e11i		−	0.656289i	0.944628	−	0.328144i	$-0.106423\pi$
$774$	−1.70399e11			−0.474792
$775$			1.85114e11i			0.513136i
$776$	2.12392e10			0.0585722
$777$			6.50012e10i			0.178335i
$778$			2.98265e11i			0.814111i
$779$	4.52441e11			1.22860
$780$			5.00362e11i			1.35178i
$781$			1.58024e11i			0.424736i
$782$	5.63103e11			1.50578
$783$	3.47886e10			0.0925528
$784$	1.49326e11			0.395250
$785$			7.20353e10i			0.189700i
$786$	−2.89345e11			−0.758099
$787$	−6.84094e11			−1.78327			−0.891635	−	0.452756i	$-0.850441\pi$
$787$	−6.84094e11			−1.78327			−0.891635	+	0.452756i	$0.850441\pi$
$788$	1.11646e12			2.89559
$789$	1.90075e11			0.490475
$790$		−	4.03346e11i		−	1.03555i
$791$			8.34509e11i			2.13169i
$792$	9.83753e10			0.250026
$793$	−2.81247e11			−0.711205
$794$	−6.93197e11			−1.74411
$795$	4.56069e10			0.114173
$796$	−6.90229e11			−1.71926
$797$			4.90056e11i			1.21454i	0.794495	+	0.607270i	$0.207736\pi$
$797$			4.90056e11i			1.21454i	−0.794495	+	0.607270i	$0.792264\pi$
$798$			6.05139e11i			1.49226i
$799$		−	4.47853e9i		−	0.0109888i
$800$			8.15986e10i			0.199215i
$801$			1.81392e11i			0.440645i
$802$	8.75823e10			0.211699
$803$	1.04956e10			0.0252432
$804$		−	3.35578e11i		−	0.803100i
$805$			3.59101e11i			0.855131i
$806$			1.13560e12i			2.69082i
$807$		−	5.86612e10i		−	0.138311i
$808$	−6.82869e11			−1.60211
$809$			7.40132e11i			1.72789i	0.503589	+	0.863943i	$0.332013\pi$
$809$			7.40132e11i			1.72789i	−0.503589	+	0.863943i	$0.667987\pi$
$810$			5.47800e10i			0.127257i
$811$			5.04910e11i			1.16716i	0.812056	+	0.583580i	$0.198348\pi$
$811$			5.04910e11i			1.16716i	−0.812056	+	0.583580i	$0.801652\pi$
$812$	5.00344e11			1.15092
$813$	−4.79233e11			−1.09694
$814$			8.13592e10i			0.185314i
$815$	3.95056e11			0.895423
$816$	2.46110e11			0.555096
$817$		−	4.63867e11i		−	1.04113i
$818$	−5.50893e11			−1.23042
$819$		−	2.94354e11i		−	0.654236i
$820$	5.89062e11			1.30288
$821$			4.65143e11i			1.02380i	0.859046	+	0.511898i	$0.171057\pi$
$821$			4.65143e11i			1.02380i	−0.859046	+	0.511898i	$0.828943\pi$
$822$		−	1.88388e11i		−	0.412635i
$823$			4.75117e11i			1.03562i	0.855495	+	0.517811i	$0.173253\pi$
$823$			4.75117e11i			1.03562i	−0.855495	+	0.517811i	$0.826747\pi$
$824$	1.17346e12			2.54541
$825$		−	6.00578e10i		−	0.129644i
$826$	−8.12514e11	−	4.64296e11i	−1.74546	−	0.997412i
$827$	−3.93701e11			−0.841675			−0.420838	−	0.907136i	$-0.638264\pi$
$827$	−3.93701e11			−0.841675			−0.420838	+	0.907136i	$0.638264\pi$
$828$			3.76965e11i			0.802010i
$829$	−2.28295e11			−0.483368			−0.241684	−	0.970355i	$-0.577700\pi$
$829$	−2.28295e11			−0.483368			−0.241684	+	0.970355i	$0.577700\pi$
$830$	−3.76284e11			−0.792872
$831$	4.28583e11			0.898732
$832$		−	5.61361e11i		−	1.17152i
$833$	−1.09863e11			−0.228176
$834$			1.76557e11i			0.364939i
$835$	5.23262e11			1.07640
$836$			5.12614e11i			1.04946i
$837$			8.41419e10i			0.171439i
$838$	−1.44527e12			−2.93072
$839$		−	7.99134e11i		−	1.61277i	−0.591392	−	0.806384i	$-0.701421\pi$
$839$		−	7.99134e11i		−	1.61277i	0.591392	−	0.806384i	$-0.298579\pi$
$840$			4.11601e11i			0.826721i
$841$	−3.84548e11			−0.768718
$842$	7.26235e11			1.44487
$843$	−5.53706e11			−1.09640
$844$		−	7.41889e11i		−	1.46207i
$845$	6.47016e11			1.26908
$846$	4.42995e9			0.00864803
$847$	4.98842e11			0.969236
$848$	2.02675e11			0.391937
$849$			4.37050e11i			0.841203i
$850$		−	3.94032e11i		−	0.754842i
$851$	−1.62871e11			−0.310546
$852$	−6.94062e11			−1.31716
$853$	3.39922e11			0.642072			0.321036	−	0.947067i	$-0.395969\pi$
$853$	3.39922e11			0.642072			0.321036	+	0.947067i	$0.395969\pi$
$854$	−4.42850e11			−0.832579
$855$	−1.49124e11			−0.279051
$856$		−	2.90082e11i		−	0.540288i
$857$		−	5.65338e11i		−	1.04806i	−0.851701	−	0.524029i	$-0.824428\pi$
$857$		−	5.65338e11i		−	1.04806i	0.851701	−	0.524029i	$-0.175572\pi$
$858$		−	3.68431e11i		−	0.679840i
$859$			9.28491e11i			1.70532i	0.522468	+	0.852659i	$0.325011\pi$
$859$			9.28491e11i			1.70532i	−0.522468	+	0.852659i	$0.674989\pi$
$860$		−	6.03939e11i		−	1.10408i
$861$	−3.46535e11			−0.630571
$862$	−6.62118e11			−1.19924
$863$			9.50068e11i			1.71282i	0.516297	+	0.856410i	$0.327310\pi$
$863$			9.50068e11i			1.71282i	−0.516297	+	0.856410i	$0.672690\pi$
$864$			3.70899e10i			0.0665581i
$865$		−	4.48363e11i		−	0.800876i
$866$		−	6.46613e11i		−	1.14967i
$867$	1.45156e11			0.256896
$868$			1.21016e12i			2.13189i
$869$			2.01001e11i			0.352468i
$870$			1.82185e11i			0.318006i
$871$	−6.56577e11			−1.14081
$872$	7.02311e11			1.21469
$873$		−	5.89380e9i		−	0.0101470i
$874$	−1.51627e12			−2.59856
$875$	6.87516e11			1.17287
$876$			4.60980e10i			0.0782826i
$877$	5.13352e11			0.867795			0.433898	−	0.900962i	$-0.357138\pi$
$877$	5.13352e11			0.867795			0.433898	+	0.900962i	$0.357138\pi$
$878$		−	1.24538e12i		−	2.09567i
$879$	2.01843e11			0.338111
$880$			1.96446e11i			0.327576i
$881$		−	2.13360e11i		−	0.354168i	−0.984196	−	0.177084i	$-0.943334\pi$
$881$		−	2.13360e11i		−	0.354168i	0.984196	−	0.177084i	$-0.0566665\pi$
$882$		−	1.08671e11i		−	0.179572i
$883$	−1.11489e12			−1.83396			−0.916979	−	0.398936i	$-0.869380\pi$
$883$	−1.11489e12			−1.83396			−0.916979	+	0.398936i	$0.869380\pi$
$884$		−	1.63594e12i		−	2.67891i
$885$	1.14416e11	−	2.00228e11i	0.186516	−	0.326401i
$886$	−2.87684e10			−0.0466854
$887$		−	2.59056e10i		−	0.0418504i	−0.999781	−	0.0209252i	$-0.993339\pi$
$887$		−	2.59056e10i		−	0.0418504i	0.999781	−	0.0209252i	$-0.00666119\pi$
$888$	−1.86683e11			−0.300228
$889$	7.78319e11			1.24609
$890$	−9.49936e11			−1.51403
$891$		−	2.72988e10i		−	0.0433144i
$892$	2.40800e12			3.80362
$893$			1.20594e10i			0.0189635i
$894$	2.78700e11			0.436301
$895$			8.80806e10i			0.137274i
$896$		−	1.13868e12i		−	1.76672i
$897$	7.37552e11			1.13926
$898$		−	1.03411e12i		−	1.59023i
$899$			2.79835e11i			0.428414i
$900$	2.63782e11			0.402045
$901$	−1.49112e11			−0.226263
$902$	−4.33743e11			−0.655249
$903$			3.55286e11i			0.534352i
$904$	−2.39670e12			−3.58872
$905$	2.91895e11			0.435144
$906$	−1.19840e12			−1.77865
$907$	1.30006e12			1.92103			0.960516	−	0.278224i	$-0.0897458\pi$
$907$	1.30006e12			1.92103			0.960516	+	0.278224i	$0.0897458\pi$
$908$		−	1.27145e12i		−	1.87049i
$909$			1.89494e11i			0.277549i
$910$	1.54151e12			2.24792
$911$	−1.22667e12			−1.78096			−0.890478	−	0.455026i	$-0.849630\pi$
$911$	−1.22667e12			−1.78096			−0.890478	+	0.455026i	$0.849630\pi$
$912$	−6.62702e11			−0.957942
$913$	1.87515e11			0.269869
$914$	−1.12811e12			−1.61647
$915$		−	1.09132e11i		−	0.155692i
$916$		−	9.28917e11i		−	1.31946i
$917$			6.03291e11i			0.853198i
$918$		−	1.79104e11i		−	0.252194i
$919$		−	1.29291e12i		−	1.81262i	−0.422618	−	0.906308i	$-0.638889\pi$
$919$		−	1.29291e12i		−	1.81262i	0.422618	−	0.906308i	$-0.361111\pi$
$920$	−1.03133e12			−1.43962
$921$	1.74381e11			0.242360
$922$		−	1.31835e12i		−	1.82435i
$923$			1.35797e12i			1.87104i
$924$		−	3.92622e11i		−	0.538626i
$925$			1.13969e11i			0.155676i
$926$	7.06244e11			0.960530
$927$		−	3.25630e11i		−	0.440966i
$928$			1.23352e11i			0.166324i
$929$			5.20893e11i			0.699336i	0.936874	+	0.349668i	$0.113706\pi$
$929$			5.20893e11i			0.699336i	−0.936874	+	0.349668i	$0.886294\pi$
$930$	−4.40644e11			−0.589056
$931$	2.95828e11			0.393768
$932$		−	5.28106e11i		−	0.699934i
$933$	8.34882e11			1.10179
$934$	8.14004e11			1.06964
$935$		−	1.44529e11i		−	0.189108i
$936$	8.45382e11			1.10141
$937$		−	1.15219e12i		−	1.49474i	−0.664408	−	0.747370i	$-0.731316\pi$
$937$		−	1.15219e12i		−	1.49474i	0.664408	−	0.747370i	$-0.268684\pi$
$938$	−1.03384e12			−1.33550
$939$		−	7.75208e11i		−	0.997140i
$940$			1.57009e10i			0.0201100i
$941$		−	2.92866e11i		−	0.373518i	−0.982406	−	0.186759i	$-0.940202\pi$
$941$		−	2.92866e11i		−	0.373518i	0.982406	−	0.186759i	$-0.0597983\pi$
$942$	2.32966e11			0.295861
$943$		−	8.68299e11i		−	1.09805i
$944$	5.08462e11	−	8.89804e11i	0.640281	−	1.12049i
$945$	1.14218e11			0.143221
$946$			4.44697e11i			0.555264i
$947$	1.73015e11			0.215121			0.107560	−	0.994199i	$-0.465696\pi$
$947$	1.73015e11			0.215121			0.107560	+	0.994199i	$0.465696\pi$
$948$	−8.82824e11			−1.09305
$949$	9.01932e10			0.111201
$950$			1.06101e12i			1.30265i
$951$	2.76335e11			0.337842
$952$		−	1.34573e12i		−	1.63837i
$953$	8.31729e11			1.00835			0.504174	−	0.863602i	$-0.331797\pi$
$953$	8.31729e11			1.00835			0.504174	+	0.863602i	$0.331797\pi$
$954$		−	1.47495e11i		−	0.178067i
$955$			3.59887e11i			0.432666i
$956$	5.54881e11			0.664306
$957$		−	9.07890e10i		−	0.108239i
$958$			1.69105e12i			2.00768i
$959$	−3.92793e11			−0.464397
$960$	2.17824e11			0.256460
$961$	1.76062e11			0.206430
$962$			6.99155e11i			0.816344i
$963$	−8.04966e10			−0.0935993
$964$	2.55333e12			2.95664
$965$	−5.90488e11			−0.680929
$966$	1.16135e12			1.33369
$967$		−	2.17787e11i		−	0.249073i	−0.992215	−	0.124537i	$-0.960256\pi$
$967$		−	2.17787e11i		−	0.249073i	0.992215	−	0.124537i	$-0.0397444\pi$
$968$			1.43267e12i			1.63171i
$969$	4.87564e11			0.553014
$970$	3.08654e10			0.0348646
$971$	2.95639e11			0.332571			0.166286	−	0.986078i	$-0.446823\pi$
$971$	2.95639e11			0.332571			0.166286	+	0.986078i	$0.446823\pi$
$972$	1.19900e11			0.134324
$973$	3.68125e11			0.410719
$974$		−	2.27587e12i		−	2.52879i
$975$		−	5.16103e11i		−	0.571108i
$976$		−	4.84976e11i		−	0.534467i
$977$		−	6.13007e11i		−	0.672801i	−0.941719	−	0.336401i	$-0.890790\pi$
$977$		−	6.13007e11i		−	0.672801i	0.941719	−	0.336401i	$-0.109210\pi$
$978$		−	1.27763e12i		−	1.39653i
$979$	4.73386e11			0.515329
$980$	3.85158e11			0.417575
$981$		−	1.94889e11i		−	0.210432i
$982$		−	6.45266e10i		−	0.0693894i
$983$			1.50377e11i			0.161053i	0.996752	+	0.0805263i	$0.0256601\pi$
$983$			1.50377e11i			0.161053i	−0.996752	+	0.0805263i	$0.974340\pi$
$984$		−	9.95244e11i		−	1.06157i
$985$	8.47611e11			0.900434
$986$		−	5.95656e11i		−	0.630213i
$987$		−	9.23655e9i		−	0.00973288i
$988$			4.40511e12i			4.62306i
$989$	−8.90228e11			−0.930499
$990$	1.42961e11			0.148826
$991$		−	3.90397e11i		−	0.404773i	−0.979306	−	0.202387i	$-0.935130\pi$
$991$		−	3.90397e11i		−	0.404773i	0.979306	−	0.202387i	$-0.0648698\pi$
$992$	−2.98347e11			−0.308089
$993$	−4.08880e11			−0.420532
$994$			2.13826e12i			2.19035i
$995$	−5.24020e11			−0.534633
$996$			8.23591e11i			0.836901i
$997$	2.66999e11			0.270227			0.135113	−	0.990830i	$-0.456860\pi$
$997$	2.66999e11			0.270227			0.135113	+	0.990830i	$0.456860\pi$
$998$		−	2.56693e12i		−	2.58757i
$999$			5.18037e10i			0.0520115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.9.c.a.58.7	✓	80
59.58	odd	2	inner	177.9.c.a.58.74	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.9.c.a.58.7	✓	80	1.1	even	1	trivial
177.9.c.a.58.74	yes	80	59.58	odd	2	inner

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-28.1432i q^{2} -46.7654 q^{3} -536.039 q^{4} -406.960 q^{5} +1316.13i q^{6} +2744.16 q^{7} +7881.18i q^{8} +2187.00 q^{9} +O(q^{10})\)	\(q-28.1432i q^{2} -46.7654 q^{3} -536.039 q^{4} -406.960 q^{5} +1316.13i q^{6} +2744.16 q^{7} +7881.18i q^{8} +2187.00 q^{9} +11453.1i q^{10} -5707.50i q^{11} +25068.1 q^{12} -49047.0i q^{13} -77229.3i q^{14} +19031.6 q^{15} +84575.7 q^{16} -62224.1 q^{17} -61549.1i q^{18} +167552. q^{19} +218146. q^{20} -128332. q^{21} -160627. q^{22} -321556. i q^{23} -368567. i q^{24} -225009. q^{25} -1.38034e6 q^{26} -102276. q^{27} -1.47097e6 q^{28} -340144. q^{29} -535610. i q^{30} -822696. i q^{31} -362646. i q^{32} +266913. i q^{33} +1.75118e6i q^{34} -1.11676e6 q^{35} -1.17232e6 q^{36} -506510. i q^{37} -4.71543e6i q^{38} +2.29370e6i q^{39} -3.20732e6i q^{40} +2.70031e6 q^{41} +3.61166e6i q^{42} -2.76851e6i q^{43} +3.05944e6i q^{44} -890021. q^{45} -9.04960e6 q^{46} +71974.2i q^{47} -3.95521e6 q^{48} +1.76559e6 q^{49} +6.33247e6i q^{50} +2.90993e6 q^{51} +2.62911e7i q^{52} +2.39637e6 q^{53} +2.87837e6i q^{54} +2.32272e6i q^{55} +2.16272e7i q^{56} -7.83561e6 q^{57} +9.57275e6i q^{58} +(6.01191e6 - 1.05208e7i) q^{59} -1.02017e7 q^{60} -5.73423e6i q^{61} -2.31533e7 q^{62} +6.00147e6 q^{63} +1.14454e7 q^{64} +1.99601e7i q^{65} +7.51179e6 q^{66} -1.33867e7i q^{67} +3.33545e7 q^{68} +1.50377e7i q^{69} +3.14292e7i q^{70} -2.76871e7 q^{71} +1.72362e7i q^{72} +1.83891e6i q^{73} -1.42548e7 q^{74} +1.05226e7 q^{75} -8.98141e7 q^{76} -1.56623e7i q^{77} +6.45521e7 q^{78} -3.52171e7 q^{79} -3.44189e7 q^{80} +4.78297e6 q^{81} -7.59953e7i q^{82} +3.28542e7i q^{83} +6.87907e7 q^{84} +2.53227e7 q^{85} -7.79145e7 q^{86} +1.59070e7 q^{87} +4.49818e7 q^{88} +8.29411e7i q^{89} +2.50480e7i q^{90} -1.34593e8i q^{91} +1.72366e8i q^{92} +3.84737e7i q^{93} +2.02558e6 q^{94} -6.81867e7 q^{95} +1.69593e7i q^{96} -2.69493e6i q^{97} -4.96894e7i q^{98} -1.24823e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Introduction

L-functions

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