LMFDB - Embedded newform 177.9.c.a.58.12

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			58.12
Character	$\chi$	$=$	177.58
Dual form			177.9.c.a.58.69

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-24.0665i q^{2} -46.7654 q^{3} -323.199 q^{4} -984.641 q^{5} +1125.48i q^{6} -1144.76 q^{7} +1617.24i q^{8} +2187.00 q^{9} +O(q^{10})$	\(q-24.0665i q^{2} -46.7654 q^{3} -323.199 q^{4} -984.641 q^{5} +1125.48i q^{6} -1144.76 q^{7} +1617.24i q^{8} +2187.00 q^{9} +23696.9i q^{10} +25177.1i q^{11} +15114.5 q^{12} +6696.40i q^{13} +27550.5i q^{14} +46047.1 q^{15} -43817.4 q^{16} -891.553 q^{17} -52633.5i q^{18} -26924.9 q^{19} +318235. q^{20} +53535.4 q^{21} +605925. q^{22} -140383. i q^{23} -75630.9i q^{24} +578893. q^{25} +161159. q^{26} -102276. q^{27} +369987. q^{28} -177979. q^{29} -1.10820e6i q^{30} +1.04049e6i q^{31} +1.46855e6i q^{32} -1.17741e6i q^{33} +21456.6i q^{34} +1.12718e6 q^{35} -706836. q^{36} +116970. i q^{37} +647990. i q^{38} -313159. i q^{39} -1.59240e6i q^{40} +4.52564e6 q^{41} -1.28841e6i q^{42} -193497. i q^{43} -8.13719e6i q^{44} -2.15341e6 q^{45} -3.37854e6 q^{46} +2.11222e6i q^{47} +2.04914e6 q^{48} -4.45431e6 q^{49} -1.39320e7i q^{50} +41693.8 q^{51} -2.16427e6i q^{52} -1.23069e7 q^{53} +2.46143e6i q^{54} -2.47904e7i q^{55} -1.85136e6i q^{56} +1.25915e6 q^{57} +4.28334e6i q^{58} +(-1.18858e7 + 2.35778e6i) q^{59} -1.48824e7 q^{60} +1.29680e7i q^{61} +2.50410e7 q^{62} -2.50360e6 q^{63} +2.41256e7 q^{64} -6.59355e6i q^{65} -2.83363e7 q^{66} -1.51173e7i q^{67} +288149. q^{68} +6.56508e6i q^{69} -2.71274e7i q^{70} -1.88975e7 q^{71} +3.53691e6i q^{72} +4.52527e7i q^{73} +2.81506e6 q^{74} -2.70722e7 q^{75} +8.70210e6 q^{76} -2.88218e7i q^{77} -7.53667e6 q^{78} -3.05238e7 q^{79} +4.31445e7 q^{80} +4.78297e6 q^{81} -1.08917e8i q^{82} -6.98084e6i q^{83} -1.73026e7 q^{84} +877860. q^{85} -4.65680e6 q^{86} +8.32326e6 q^{87} -4.07174e7 q^{88} -7.29088e7i q^{89} +5.18252e7i q^{90} -7.66580e6i q^{91} +4.53718e7i q^{92} -4.86589e7i q^{93} +5.08339e7 q^{94} +2.65114e7 q^{95} -6.86772e7i q^{96} +5.68527e7i q^{97} +1.07200e8i q^{98} +5.50622e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	24.0665i		−	1.50416i	−0.659072	−	0.752080i	$-0.729051\pi$
$2$		−	24.0665i		−	1.50416i	0.659072	−	0.752080i	$-0.270949\pi$
$3$	−46.7654			−0.577350
$3$	−46.7654			−0.577350
$4$	−323.199			−1.26250
$5$	−984.641			−1.57543			−0.787713	−	0.616042i	$-0.788735\pi$
$5$	−984.641			−1.57543			−0.787713	+	0.616042i	$0.788735\pi$
$6$			1125.48i			0.868427i
$7$	−1144.76			−0.476787			−0.238393	−	0.971169i	$-0.576621\pi$
$7$	−1144.76			−0.476787			−0.238393	+	0.971169i	$0.576621\pi$
$8$			1617.24i			0.394835i
$9$	2187.00			0.333333
$10$			23696.9i			2.36969i
$11$			25177.1i			1.71963i	0.510608	+	0.859814i	$0.329420\pi$
$11$			25177.1i			1.71963i	−0.510608	+	0.859814i	$0.670580\pi$
$12$	15114.5			0.728902
$13$			6696.40i			0.234459i	0.993105	+	0.117230i	$0.0374014\pi$
$13$			6696.40i			0.234459i	−0.993105	+	0.117230i	$0.962599\pi$
$14$			27550.5i			0.717163i
$15$	46047.1			0.909573
$16$	−43817.4			−0.668601
$17$	−891.553			−0.0106746			−0.00533730	−	0.999986i	$-0.501699\pi$
$17$	−891.553			−0.0106746			−0.00533730	+	0.999986i	$0.501699\pi$
$18$		−	52633.5i		−	0.501386i
$19$	−26924.9			−0.206605			−0.103302	−	0.994650i	$-0.532941\pi$
$19$	−26924.9			−0.206605			−0.103302	+	0.994650i	$0.532941\pi$
$20$	318235.			1.98897
$21$	53535.4			0.275273
$22$	605925.			2.58659
$23$		−	140383.i		−	0.501654i	−0.968032	−	0.250827i	$-0.919297\pi$
$23$		−	140383.i		−	0.501654i	0.968032	−	0.250827i	$-0.0807026\pi$
$24$		−	75630.9i		−	0.227958i
$25$	578893.			1.48197
$26$	161159.			0.352664
$27$	−102276.			−0.192450
$28$	369987.			0.601941
$29$	−177979.			−0.251639			−0.125819	−	0.992053i	$-0.540156\pi$
$29$	−177979.			−0.251639			−0.125819	+	0.992053i	$0.540156\pi$
$30$		−	1.10820e6i		−	1.36814i
$31$			1.04049e6i			1.12666i	0.826234	+	0.563328i	$0.190479\pi$
$31$			1.04049e6i			1.12666i	−0.826234	+	0.563328i	$0.809521\pi$
$32$			1.46855e6i			1.40052i
$33$		−	1.17741e6i		−	0.992827i
$34$			21456.6i			0.0160563i
$35$	1.12718e6			0.751142
$36$	−706836.			−0.420832
$37$			116970.i			0.0624119i	0.999513	+	0.0312059i	$0.00993477\pi$
$37$			116970.i			0.0624119i	−0.999513	+	0.0312059i	$0.990065\pi$
$38$			647990.i			0.310766i
$39$		−	313159.i		−	0.135365i
$40$		−	1.59240e6i		−	0.622033i
$41$	4.52564e6			1.60157			0.800783	−	0.598954i	$-0.204417\pi$
$41$	4.52564e6			1.60157			0.800783	+	0.598954i	$0.204417\pi$
$42$		−	1.28841e6i		−	0.414054i
$43$		−	193497.i		−	0.0565979i	−0.999600	−	0.0282989i	$-0.990991\pi$
$43$		−	193497.i		−	0.0565979i	0.999600	−	0.0282989i	$-0.00900903\pi$
$44$		−	8.13719e6i		−	2.17102i
$45$	−2.15341e6			−0.525142
$46$	−3.37854e6			−0.754568
$47$			2.11222e6i			0.432861i	0.976298	+	0.216431i	$0.0694415\pi$
$47$			2.11222e6i			0.432861i	−0.976298	+	0.216431i	$0.930559\pi$
$48$	2.04914e6			0.386017
$49$	−4.45431e6			−0.772674
$50$		−	1.39320e7i		−	2.22911i
$51$	41693.8			0.00616298
$52$		−	2.16427e6i		−	0.296004i
$53$	−1.23069e7			−1.55971			−0.779855	−	0.625960i	$-0.784707\pi$
$53$	−1.23069e7			−1.55971			−0.779855	+	0.625960i	$0.784707\pi$
$54$			2.46143e6i			0.289476i
$55$		−	2.47904e7i		−	2.70915i
$56$		−	1.85136e6i		−	0.188252i
$57$	1.25915e6			0.119283
$58$			4.28334e6i			0.378505i
$59$	−1.18858e7	+	2.35778e6i	−0.980887	+	0.194579i
$59$	−1.18858e7	+	2.35778e6i	−0.980887	+	0.194579i
$60$	−1.48824e7			−1.14833
$61$			1.29680e7i			0.936603i	0.883569	+	0.468301i	$0.155134\pi$
$61$			1.29680e7i			0.936603i	−0.883569	+	0.468301i	$0.844866\pi$
$62$	2.50410e7			1.69467
$63$	−2.50360e6			−0.158929
$64$	2.41256e7			1.43800
$65$		−	6.59355e6i		−	0.369373i
$66$	−2.83363e7			−1.49337
$67$		−	1.51173e7i		−	0.750197i	−0.926985	−	0.375098i	$-0.877609\pi$
$67$		−	1.51173e7i		−	0.750197i	0.926985	−	0.375098i	$-0.122391\pi$
$68$	288149.			0.0134766
$69$			6.56508e6i			0.289630i
$70$		−	2.71274e7i		−	1.12984i
$71$	−1.88975e7			−0.743655			−0.371828	−	0.928302i	$-0.621269\pi$
$71$	−1.88975e7			−0.743655			−0.371828	+	0.928302i	$0.621269\pi$
$72$			3.53691e6i			0.131612i
$73$			4.52527e7i			1.59350i	0.604306	+	0.796752i	$0.293451\pi$
$73$			4.52527e7i			1.59350i	−0.604306	+	0.796752i	$0.706549\pi$
$74$	2.81506e6			0.0938774
$75$	−2.70722e7			−0.855614
$76$	8.70210e6			0.260837
$77$		−	2.88218e7i		−	0.819895i
$78$	−7.53667e6			−0.203611
$79$	−3.05238e7			−0.783666			−0.391833	−	0.920036i	$-0.628159\pi$
$79$	−3.05238e7			−0.783666			−0.391833	+	0.920036i	$0.628159\pi$
$80$	4.31445e7			1.05333
$81$	4.78297e6			0.111111
$82$		−	1.08917e8i		−	2.40901i
$83$		−	6.98084e6i		−	0.147094i	−0.997292	−	0.0735470i	$-0.976568\pi$
$83$		−	6.98084e6i		−	0.147094i	0.997292	−	0.0735470i	$-0.0234319\pi$
$84$	−1.73026e7			−0.347531
$85$	877860.			0.0168170
$86$	−4.65680e6			−0.0851322
$87$	8.32326e6			0.145284
$88$	−4.07174e7			−0.678968
$89$		−	7.29088e7i		−	1.16204i	−0.813890	−	0.581018i	$-0.802654\pi$
$89$		−	7.29088e7i		−	1.16204i	0.813890	−	0.581018i	$-0.197346\pi$
$90$			5.18252e7i			0.789897i
$91$		−	7.66580e6i		−	0.111787i
$92$			4.53718e7i			0.633336i
$93$		−	4.86589e7i		−	0.650475i
$94$	5.08339e7			0.651092
$95$	2.65114e7			0.325490
$96$		−	6.86772e7i		−	0.808589i
$97$			5.68527e7i			0.642191i	0.947047	+	0.321095i	$0.104051\pi$
$97$			5.68527e7i			0.642191i	−0.947047	+	0.321095i	$0.895949\pi$
$98$			1.07200e8i			1.16223i
$99$			5.50622e7i			0.573209i
$100$	−1.87098e8			−1.87098
$101$		−	1.36115e8i		−	1.30804i	−0.756478	−	0.654019i	$-0.773082\pi$
$101$		−	1.36115e8i		−	1.30804i	0.756478	−	0.654019i	$-0.226918\pi$
$102$		−	1.00343e6i		−	0.00927011i
$103$			4.47854e7i			0.397912i	0.980008	+	0.198956i	$0.0637551\pi$
$103$			4.47854e7i			0.397912i	−0.980008	+	0.198956i	$0.936245\pi$
$104$	−1.08297e7			−0.0925727
$105$	−5.27131e7			−0.433672
$106$			2.96184e8i			2.34605i
$107$	−8.95949e7			−0.683516			−0.341758	−	0.939788i	$-0.611022\pi$
$107$	−8.95949e7			−0.683516			−0.341758	+	0.939788i	$0.611022\pi$
$108$	3.30554e7			0.242967
$109$			1.48038e8i			1.04874i	0.851492	+	0.524368i	$0.175698\pi$
$109$			1.48038e8i			1.04874i	−0.851492	+	0.524368i	$0.824302\pi$
$110$	−5.96619e8			−4.07499
$111$		−	5.47014e6i		−	0.0360335i
$112$	5.01607e7			0.318780
$113$			9.73838e7i			0.597273i	0.954367	+	0.298637i	$0.0965319\pi$
$113$			9.73838e7i			0.597273i	−0.954367	+	0.298637i	$0.903468\pi$
$114$		−	3.03035e7i		−	0.179421i
$115$			1.38227e8i			0.790319i
$116$	5.75227e7			0.317692
$117$			1.46450e7i			0.0781531i
$118$	5.67437e7	+	2.86049e8i	0.292678	+	1.47541i
$119$	1.02062e6			0.00508951
$120$			7.44693e7i			0.359131i
$121$	−4.19525e8			−1.95712
$122$	3.12096e8			1.40880
$123$	−2.11643e8			−0.924665
$124$		−	3.36285e8i		−	1.42240i
$125$	−1.85377e8			−0.759303
$126$			6.02530e7i			0.239054i
$127$	3.72172e8			1.43064			0.715318	−	0.698799i	$-0.246282\pi$
$127$	3.72172e8			1.43064			0.715318	+	0.698799i	$0.246282\pi$
$128$		−	2.04672e8i		−	0.762464i
$129$			9.04895e6i			0.0326768i
$130$	−1.58684e8			−0.555597
$131$		−	5.81434e8i		−	1.97431i	−0.159763	−	0.987155i	$-0.551073\pi$
$131$		−	5.81434e8i		−	1.97431i	0.159763	−	0.987155i	$-0.448927\pi$
$132$			3.80539e8i			1.25344i
$133$	3.08227e7			0.0985064
$134$	−3.63821e8			−1.12842
$135$	1.00705e8			0.303191
$136$		−	1.44186e6i		−	0.00421470i
$137$	−1.97317e8			−0.560121			−0.280061	−	0.959982i	$-0.590355\pi$
$137$	−1.97317e8			−0.560121			−0.280061	+	0.959982i	$0.590355\pi$
$138$	1.57999e8			0.435650
$139$	−5.92003e8			−1.58586			−0.792930	−	0.609313i	$-0.791445\pi$
$139$	−5.92003e8			−1.58586			−0.792930	+	0.609313i	$0.791445\pi$
$140$	−3.64304e8			−0.948313
$141$		−	9.87789e7i		−	0.249912i
$142$			4.54798e8i			1.11858i
$143$	−1.68596e8			−0.403183
$144$	−9.58287e7			−0.222867
$145$	1.75246e8			0.396438
$146$	1.08908e9			2.39689
$147$	2.08308e8			0.446104
$148$		−	3.78045e7i		−	0.0787947i
$149$		−	3.17764e8i		−	0.644703i	−0.946620	−	0.322352i	$-0.895527\pi$
$149$		−	3.17764e8i		−	0.644703i	0.946620	−	0.322352i	$-0.104473\pi$
$150$			6.51534e8i			1.28698i
$151$			2.09697e8i			0.403352i	0.979452	+	0.201676i	$0.0646388\pi$
$151$			2.09697e8i			0.403352i	−0.979452	+	0.201676i	$0.935361\pi$
$152$		−	4.35441e7i		−	0.0815747i
$153$	−1.94983e6			−0.00355820
$154$	−6.93642e8			−1.23325
$155$		−	1.02451e9i		−	1.77496i
$156$			1.01213e8i			0.170898i
$157$		−	1.88420e7i		−	0.0310119i	−0.999880	−	0.0155059i	$-0.995064\pi$
$157$		−	1.88420e7i		−	0.0310119i	0.999880	−	0.0155059i	$-0.00493589\pi$
$158$			7.34604e8i			1.17876i
$159$	5.75535e8			0.900499
$160$		−	1.44599e9i		−	2.20641i
$161$			1.60706e8i			0.239182i
$162$		−	1.15110e8i		−	0.167129i
$163$	5.12195e8			0.725580			0.362790	−	0.931871i	$-0.381824\pi$
$163$	5.12195e8			0.725580			0.362790	+	0.931871i	$0.381824\pi$
$164$	−1.46268e9			−2.02197
$165$			1.15933e9i			1.56413i
$166$	−1.68005e8			−0.221253
$167$	1.16176e9			1.49365			0.746827	−	0.665018i	$-0.231576\pi$
$167$	1.16176e9			1.49365			0.746827	+	0.665018i	$0.231576\pi$
$168$			8.65796e7i			0.108687i
$169$	7.70889e8			0.945029
$170$		−	2.11271e7i		−	0.0252955i
$171$	−5.88848e7			−0.0688682
$172$			6.25379e7i			0.0714545i
$173$		−	6.91440e8i		−	0.771916i	−0.922516	−	0.385958i	$-0.873871\pi$
$173$		−	6.91440e8i		−	0.771916i	0.922516	−	0.385958i	$-0.126129\pi$
$174$		−	2.00312e8i		−	0.218530i
$175$	−6.62697e8			−0.706582
$176$		−	1.10319e9i		−	1.14974i
$177$	5.55842e8	−	1.10263e8i	0.566315	−	0.112340i
$178$	−1.75466e9			−1.74789
$179$		−	1.64428e9i		−	1.60163i	−0.598911	−	0.800816i	$-0.704400\pi$
$179$		−	1.64428e9i		−	1.60163i	0.598911	−	0.800816i	$-0.295600\pi$
$180$	6.95980e8			0.662989
$181$	−4.32961e8			−0.403399			−0.201699	−	0.979447i	$-0.564646\pi$
$181$	−4.32961e8			−0.403399			−0.201699	+	0.979447i	$0.564646\pi$
$182$	−1.84489e8			−0.168146
$183$		−	6.06456e8i		−	0.540748i
$184$	2.27034e8			0.198070
$185$		−	1.15173e8i		−	0.0983253i
$186$	−1.17105e9			−0.978418
$187$		−	2.24467e7i		−	0.0183563i
$188$		−	6.82668e8i		−	0.546485i
$189$	1.17082e8			0.0917576
$190$		−	6.38038e8i		−	0.489589i
$191$		−	1.24938e9i		−	0.938773i	−0.882993	−	0.469386i	$-0.844475\pi$
$191$		−	1.24938e9i		−	0.938773i	0.882993	−	0.469386i	$-0.155525\pi$
$192$	−1.12824e9			−0.830230
$193$	−7.21573e8			−0.520057			−0.260028	−	0.965601i	$-0.583732\pi$
$193$	−7.21573e8			−0.520057			−0.260028	+	0.965601i	$0.583732\pi$
$194$	1.36825e9			0.965957
$195$			3.08350e8i			0.213258i
$196$	1.43963e9			0.975498
$197$	2.59760e9			1.72467			0.862336	−	0.506336i	$-0.169000\pi$
$197$	2.59760e9			1.72467			0.862336	+	0.506336i	$0.169000\pi$
$198$	1.32516e9			0.862198
$199$	2.46017e9			1.56875			0.784375	−	0.620288i	$-0.212984\pi$
$199$	2.46017e9			1.56875			0.784375	+	0.620288i	$0.212984\pi$
$200$			9.36211e8i			0.585132i
$201$			7.06966e8i			0.433126i
$202$	−3.27582e9			−1.96750
$203$	2.03744e8			0.119978
$204$	−1.34754e7			−0.00778074
$205$	−4.45614e9			−2.52315
$206$	1.07783e9			0.598524
$207$		−	3.07019e8i		−	0.167218i
$208$		−	2.93419e8i		−	0.156760i
$209$		−	6.77891e8i		−	0.355283i
$210$			1.26862e9i			0.652312i
$211$			1.09561e9i			0.552747i	0.961050	+	0.276374i	$0.0891327\pi$
$211$			1.09561e9i			0.552747i	−0.961050	+	0.276374i	$0.910867\pi$
$212$	3.97756e9			1.96913
$213$	8.83750e8			0.429349
$214$			2.15624e9i			1.02812i
$215$			1.90525e8i			0.0891658i
$216$		−	1.65405e8i		−	0.0759859i
$217$		−	1.19112e9i		−	0.537174i
$218$	3.56275e9			1.57747
$219$		−	2.11626e9i		−	0.920010i
$220$			8.01222e9i			3.42028i
$221$		−	5.97019e6i		−	0.00250276i
$222$	−1.31647e8			−0.0542001
$223$	−1.24794e8			−0.0504630			−0.0252315	−	0.999682i	$-0.508032\pi$
$223$	−1.24794e8			−0.0504630			−0.0252315	+	0.999682i	$0.508032\pi$
$224$		−	1.68114e9i		−	0.667748i
$225$	1.26604e9			0.493989
$226$	2.34369e9			0.898394
$227$		−	3.38194e9i		−	1.27369i	−0.770993	−	0.636844i	$-0.780240\pi$
$227$		−	3.38194e9i		−	1.27369i	0.770993	−	0.636844i	$-0.219760\pi$
$228$	−4.06957e8			−0.150595
$229$		−	2.52655e9i		−	0.918725i	−0.888249	−	0.459362i	$-0.848078\pi$
$229$		−	2.52655e9i		−	0.918725i	0.888249	−	0.459362i	$-0.151922\pi$
$230$	3.32665e9			1.18877
$231$			1.34786e9i			0.473367i
$232$		−	2.87835e8i		−	0.0993556i
$233$		−	4.38522e8i		−	0.148788i	−0.997229	−	0.0743940i	$-0.976298\pi$
$233$		−	4.38522e8i		−	0.148788i	0.997229	−	0.0743940i	$-0.0237022\pi$
$234$	3.52455e8			0.117555
$235$		−	2.07978e9i		−	0.681941i
$236$	3.84146e9	−	7.62033e8i	1.23836	−	0.245655i
$237$	1.42746e9			0.452450
$238$		−	2.45628e7i		−	0.00765543i
$239$	−1.05004e9			−0.321821			−0.160910	−	0.986969i	$-0.551443\pi$
$239$	−1.05004e9			−0.321821			−0.160910	+	0.986969i	$0.551443\pi$
$240$	−2.01767e9			−0.608141
$241$	−7.95562e8			−0.235834			−0.117917	−	0.993023i	$-0.537622\pi$
$241$	−7.95562e8			−0.235834			−0.117917	+	0.993023i	$0.537622\pi$
$242$			1.00965e10i			2.94382i
$243$	−2.23677e8			−0.0641500
$244$		−	4.19126e9i		−	1.18246i
$245$	4.38590e9			1.21729
$246$			5.09353e9i			1.39084i
$247$		−	1.80300e8i		−	0.0484404i
$248$	−1.68272e9			−0.444842
$249$			3.26461e8i			0.0849248i
$250$			4.46138e9i			1.14211i
$251$	−5.88382e9			−1.48240			−0.741199	−	0.671286i	$-0.765742\pi$
$251$	−5.88382e9			−1.48240			−0.741199	+	0.671286i	$0.765742\pi$
$252$	8.09161e8			0.200647
$253$	3.53444e9			0.862658
$254$		−	8.95690e9i		−	2.15190i
$255$	−4.10535e7			−0.00970932
$256$	1.25041e9			0.291133
$257$	−3.93418e9			−0.901823			−0.450912	−	0.892569i	$-0.648901\pi$
$257$	−3.93418e9			−0.901823			−0.450912	+	0.892569i	$0.648901\pi$
$258$	2.17777e8			0.0491511
$259$		−	1.33903e8i		−	0.0297572i
$260$			2.13103e9i			0.466332i
$261$	−3.89240e8			−0.0838795
$262$	−1.39931e10			−2.96968
$263$	3.00620e9			0.628340			0.314170	−	0.949367i	$-0.398274\pi$
$263$	3.00620e9			0.628340			0.314170	+	0.949367i	$0.398274\pi$
$264$	1.90416e9			0.392002
$265$	1.21179e10			2.45721
$266$		−	7.41796e8i		−	0.148169i
$267$			3.40961e9i			0.670902i
$268$			4.88589e9i			0.947119i
$269$			6.80415e9i			1.29947i	0.760162	+	0.649733i	$0.225119\pi$
$269$			6.80415e9i			1.29947i	−0.760162	+	0.649733i	$0.774881\pi$
$270$		−	2.42362e9i		−	0.456047i
$271$	2.05562e9			0.381124			0.190562	−	0.981675i	$-0.438969\pi$
$271$	2.05562e9			0.381124			0.190562	+	0.981675i	$0.438969\pi$
$272$	3.90656e7			0.00713705
$273$			3.58494e8i			0.0645403i
$274$			4.74874e9i			0.842512i
$275$			1.45748e10i			2.54843i
$276$		−	2.12183e9i		−	0.365657i
$277$	1.20555e9			0.204771			0.102385	−	0.994745i	$-0.467353\pi$
$277$	1.20555e9			0.204771			0.102385	+	0.994745i	$0.467353\pi$
$278$			1.42475e10i			2.38539i
$279$			2.27555e9i			0.375552i
$280$			1.82293e9i			0.296577i
$281$	9.91847e8			0.159081			0.0795407	−	0.996832i	$-0.474655\pi$
$281$	9.91847e8			0.159081			0.0795407	+	0.996832i	$0.474655\pi$
$282$	−2.37727e9			−0.375908
$283$		−	5.20924e9i		−	0.812135i	−0.913843	−	0.406068i	$-0.866900\pi$
$283$		−	5.20924e9i		−	0.812135i	0.913843	−	0.406068i	$-0.133100\pi$
$284$	6.10766e9			0.938861
$285$	−1.23982e9			−0.187922
$286$			4.05751e9i			0.606451i
$287$	−5.18080e9			−0.763606
$288$			3.21172e9i			0.466839i
$289$	−6.97496e9			−0.999886
$290$		−	4.21756e9i		−	0.596306i
$291$		−	2.65874e9i		−	0.370769i
$292$		−	1.46256e10i		−	2.01179i
$293$	−7.36969e9			−0.999952			−0.499976	−	0.866039i	$-0.666658\pi$
$293$	−7.36969e9			−0.999952			−0.499976	+	0.866039i	$0.666658\pi$
$294$		−	5.01325e9i		−	0.671011i
$295$	1.17032e10	−	2.32157e9i	1.54531	−	0.306545i
$296$	−1.89169e8			−0.0246424
$297$		−	2.57501e9i		−	0.330942i
$298$	−7.64749e9			−0.969736
$299$	9.40063e8			0.117618
$300$	8.74969e9			1.08021
$301$			2.21508e8i			0.0269851i
$302$	5.04668e9			0.606706
$303$			6.36546e9i			0.755196i
$304$	1.17978e9			0.138136
$305$		−	1.27689e10i		−	1.47555i
$306$			4.69256e7i			0.00535210i
$307$	1.38584e9			0.156012			0.0780061	−	0.996953i	$-0.475145\pi$
$307$	1.38584e9			0.156012			0.0780061	+	0.996953i	$0.475145\pi$
$308$			9.31517e9i			1.03511i
$309$		−	2.09441e9i		−	0.229735i
$310$	−2.46564e10			−2.66983
$311$	−7.57040e9			−0.809240			−0.404620	−	0.914485i	$-0.632596\pi$
$311$	−7.57040e9			−0.809240			−0.404620	+	0.914485i	$0.632596\pi$
$312$	5.06455e8			0.0534469
$313$		−	7.93693e9i		−	0.826942i	−0.910517	−	0.413471i	$-0.864316\pi$
$313$		−	7.93693e9i		−	0.826942i	0.910517	−	0.413471i	$-0.135684\pi$
$314$	−4.53462e8			−0.0466468
$315$	2.46515e9			0.250381
$316$	9.86527e9			0.989374
$317$	1.02666e10			1.01669			0.508347	−	0.861152i	$-0.330257\pi$
$317$	1.02666e10			1.01669			0.508347	+	0.861152i	$0.330257\pi$
$318$		−	1.38511e10i		−	1.35449i
$319$		−	4.48099e9i		−	0.432725i
$320$	−2.37551e10			−2.26546
$321$	4.18994e9			0.394628
$322$	3.86764e9			0.359768
$323$	2.40050e7			0.00220542
$324$	−1.54585e9			−0.140277
$325$			3.87650e9i			0.347461i
$326$		−	1.23268e10i		−	1.09139i
$327$		−	6.92303e9i		−	0.605488i
$328$			7.31906e9i			0.632354i
$329$		−	2.41800e9i		−	0.206382i
$330$	2.79011e10			2.35269
$331$	6.68667e9			0.557055			0.278527	−	0.960428i	$-0.410154\pi$
$331$	6.68667e9			0.557055			0.278527	+	0.960428i	$0.410154\pi$
$332$			2.25620e9i			0.185706i
$333$			2.55813e8i			0.0208040i
$334$		−	2.79595e10i		−	2.24669i
$335$			1.48851e10i			1.18188i
$336$	−2.34578e9			−0.184048
$337$			8.59323e9i			0.666249i	0.942883	+	0.333125i	$0.108103\pi$
$337$			8.59323e9i			0.666249i	−0.942883	+	0.333125i	$0.891897\pi$
$338$		−	1.85526e10i		−	1.42147i
$339$		−	4.55419e9i		−	0.344836i
$340$	−2.83723e8			−0.0212314
$341$	−2.61965e10			−1.93743
$342$			1.41715e9i			0.103589i
$343$	1.16985e10			0.845188
$344$	3.12931e8			0.0223468
$345$		−	6.46425e9i		−	0.456291i
$346$	−1.66406e10			−1.16108
$347$		−	1.27463e9i		−	0.0879160i	−0.999033	−	0.0439580i	$-0.986003\pi$
$347$		−	1.27463e9i		−	0.0879160i	0.999033	−	0.0439580i	$-0.0139968\pi$
$348$	−2.69007e9			−0.183420
$349$		−	1.23114e10i		−	0.829860i	−0.909853	−	0.414930i	$-0.863806\pi$
$349$		−	1.23114e10i		−	0.829860i	0.909853	−	0.414930i	$-0.136194\pi$
$350$			1.59488e10i			1.06281i
$351$		−	6.84880e8i		−	0.0451217i
$352$	−3.69737e10			−2.40837
$353$			1.49416e9i			0.0962273i	0.998842	+	0.0481137i	$0.0153210\pi$
$353$			1.49416e9i			0.0962273i	−0.998842	+	0.0481137i	$0.984679\pi$
$354$	−2.65364e9	−	1.33772e10i	−0.168978	−	0.851828i
$355$	1.86073e10			1.17157
$356$			2.35640e10i			1.46707i
$357$	−4.77296e7			−0.00293843
$358$	−3.95721e10			−2.40911
$359$	1.96126e10			1.18075			0.590374	−	0.807130i	$-0.298980\pi$
$359$	1.96126e10			1.18075			0.590374	+	0.807130i	$0.298980\pi$
$360$		−	3.48259e9i		−	0.207344i
$361$	−1.62586e10			−0.957315
$362$			1.04199e10i			0.606776i
$363$	1.96193e10			1.12994
$364$			2.47758e9i			0.141131i
$365$		−	4.45577e10i		−	2.51045i
$366$	−1.45953e10			−0.813371
$367$		−	1.35978e10i		−	0.749559i	−0.927114	−	0.374779i	$-0.877718\pi$
$367$		−	1.35978e10i		−	0.749559i	0.927114	−	0.374779i	$-0.122282\pi$
$368$			6.15124e9i			0.335407i
$369$	9.89758e9			0.533856
$370$	−2.77183e9			−0.147897
$371$	1.40885e10			0.743649
$372$			1.57265e10i			0.821221i
$373$	−3.17309e10			−1.63926			−0.819628	−	0.572895i	$-0.805820\pi$
$373$	−3.17309e10			−1.63926			−0.819628	+	0.572895i	$0.805820\pi$
$374$	−5.40214e8			−0.0276108
$375$	8.66921e9			0.438384
$376$	−3.41598e9			−0.170908
$377$		−	1.19182e9i		−	0.0589990i
$378$		−	2.81776e9i		−	0.138018i
$379$	−2.76387e10			−1.33955			−0.669777	−	0.742563i	$-0.733610\pi$
$379$	−2.76387e10			−1.33955			−0.669777	+	0.742563i	$0.733610\pi$
$380$	−8.56845e9			−0.410930
$381$	−1.74048e10			−0.825978
$382$	−3.00682e10			−1.41206
$383$	8.72327e9			0.405400			0.202700	−	0.979241i	$-0.435028\pi$
$383$	8.72327e9			0.405400			0.202700	+	0.979241i	$0.435028\pi$
$384$			9.57157e9i			0.440209i
$385$			2.83791e10i			1.29168i
$386$			1.73658e10i			0.782249i
$387$		−	4.23178e8i		−	0.0188660i
$388$		−	1.83747e10i		−	0.810763i
$389$	2.74653e10			1.19946			0.599730	−	0.800203i	$-0.295275\pi$
$389$	2.74653e10			1.19946			0.599730	+	0.800203i	$0.295275\pi$
$390$	7.42091e9			0.320774
$391$			1.25159e8i			0.00535496i
$392$		−	7.20371e9i		−	0.305079i
$393$			2.71910e10i			1.13987i
$394$		−	6.25152e10i		−	2.59418i
$395$	3.00550e10			1.23461
$396$		−	1.77960e10i		−	0.723674i
$397$		−	2.85069e10i		−	1.14759i	−0.818997	−	0.573797i	$-0.805470\pi$
$397$		−	2.85069e10i		−	1.14759i	0.818997	−	0.573797i	$-0.194530\pi$
$398$		−	5.92079e10i		−	2.35965i
$399$	−1.44144e9			−0.0568727
$400$	−2.53656e10			−0.990845
$401$			1.91705e10i			0.741404i	0.928752	+	0.370702i	$0.120883\pi$
$401$			1.91705e10i			0.741404i	−0.928752	+	0.370702i	$0.879117\pi$
$402$	1.70142e10			0.651491
$403$	−6.96753e9			−0.264155
$404$			4.39922e10i			1.65139i
$405$	−4.70951e9			−0.175047
$406$		−	4.90342e9i		−	0.180466i
$407$	−2.94496e9			−0.107325
$408$			6.74290e7i			0.00243336i
$409$			1.83125e10i			0.654415i	0.944952	+	0.327208i	$0.106108\pi$
$409$			1.83125e10i			0.654415i	−0.944952	+	0.327208i	$0.893892\pi$
$410$			1.07244e11i			3.79522i
$411$	9.22760e9			0.323386
$412$		−	1.44746e10i		−	0.502362i
$413$	1.36064e10	−	2.69911e9i	0.467674	−	0.0927727i
$414$	−7.38888e9			−0.251523
$415$			6.87362e9i			0.231736i
$416$	−9.83398e9			−0.328364
$417$	2.76853e10			0.915597
$418$	−1.63145e10			−0.534402
$419$			5.56865e9i			0.180673i	0.995911	+	0.0903367i	$0.0287943\pi$
$419$			5.56865e9i			0.180673i	−0.995911	+	0.0903367i	$0.971206\pi$
$420$	1.70368e10			0.547509
$421$		−	2.41135e10i		−	0.767595i	−0.923417	−	0.383797i	$-0.874616\pi$
$421$		−	2.41135e10i		−	0.767595i	0.923417	−	0.383797i	$-0.125384\pi$
$422$	2.63676e10			0.831420
$423$			4.61943e9i			0.144287i
$424$		−	1.99032e10i		−	0.615828i
$425$	−5.16114e8			−0.0158194
$426$		−	2.12688e10i		−	0.645810i
$427$		−	1.48454e10i		−	0.446560i
$428$	2.89570e10			0.862935
$429$	7.88443e9			0.232778
$430$	4.58528e9			0.134119
$431$			5.54031e10i			1.60556i	0.596279	+	0.802778i	$0.296645\pi$
$431$			5.54031e10i			1.60556i	−0.596279	+	0.802778i	$0.703355\pi$
$432$	4.48147e9			0.128672
$433$	5.43575e10			1.54635			0.773175	−	0.634193i	$-0.218668\pi$
$433$	5.43575e10			1.54635			0.773175	+	0.634193i	$0.218668\pi$
$434$	−2.86661e10			−0.807996
$435$	−8.19543e9			−0.228884
$436$		−	4.78456e10i		−	1.32402i
$437$			3.77981e9i			0.103644i
$438$	−5.09311e10			−1.38384
$439$	1.48202e9			0.0399021			0.0199511	−	0.999801i	$-0.493649\pi$
$439$	1.48202e9			0.0399021			0.0199511	+	0.999801i	$0.493649\pi$
$440$	4.00920e10			1.06966
$441$	−9.74159e9			−0.257558
$442$	−1.43682e8			−0.00376455
$443$		−	4.92945e9i		−	0.127992i	−0.997950	−	0.0639961i	$-0.979615\pi$
$443$		−	4.92945e9i		−	0.127992i	0.997950	−	0.0639961i	$-0.0203845\pi$
$444$			1.76794e9i			0.0454921i
$445$			7.17890e10i			1.83070i
$446$			3.00335e9i			0.0759044i
$447$			1.48604e10i			0.372219i
$448$	−2.76182e10			−0.685619
$449$	−2.96211e10			−0.728812			−0.364406	−	0.931240i	$-0.618728\pi$
$449$	−2.96211e10			−0.728812			−0.364406	+	0.931240i	$0.618728\pi$
$450$		−	3.04692e10i		−	0.743038i
$451$			1.13942e11i			2.75410i
$452$		−	3.14743e10i		−	0.754055i
$453$		−	9.80656e9i		−	0.232875i
$454$	−8.13917e10			−1.91583
$455$			7.54806e9i			0.176112i
$456$			2.03636e9i			0.0470972i
$457$			4.73775e10i			1.08619i	0.839670	+	0.543097i	$0.182748\pi$
$457$			4.73775e10i			1.08619i	−0.839670	+	0.543097i	$0.817252\pi$
$458$	−6.08053e10			−1.38191
$459$	9.11844e7			0.00205433
$460$		−	4.46749e10i		−	0.997774i
$461$	3.64855e10			0.807823			0.403911	−	0.914798i	$-0.367650\pi$
$461$	3.64855e10			0.807823			0.403911	+	0.914798i	$0.367650\pi$
$462$	3.24384e10			0.712019
$463$			8.10218e10i			1.76310i	0.472086	+	0.881552i	$0.343501\pi$
$463$			8.10218e10i			1.76310i	−0.472086	+	0.881552i	$0.656499\pi$
$464$	7.79859e9			0.168246
$465$			4.79116e10i			1.02477i
$466$	−1.05537e10			−0.223801
$467$			5.32338e10i			1.11923i	0.828752	+	0.559616i	$0.189051\pi$
$467$			5.32338e10i			1.11923i	−0.828752	+	0.559616i	$0.810949\pi$
$468$		−	4.73325e9i		−	0.0986680i
$469$			1.73058e10i			0.357684i
$470$	−5.00532e10			−1.02575
$471$			8.81153e8i			0.0179047i
$472$	−3.81311e9	−	1.92222e10i	−0.0768265	−	0.387288i
$473$	4.87168e9			0.0973272
$474$		−	3.43540e10i		−	0.680556i
$475$	−1.55867e10			−0.306181
$476$	−3.29863e8			−0.00642548
$477$	−2.69151e10			−0.519904
$478$			2.52708e10i			0.484070i
$479$	7.39499e10			1.40474			0.702370	−	0.711812i	$-0.252125\pi$
$479$	7.39499e10			1.40474			0.702370	+	0.711812i	$0.252125\pi$
$480$			6.76224e10i			1.27387i
$481$	−7.83277e8			−0.0146331
$482$			1.91464e10i			0.354731i
$483$		−	7.51548e9i		−	0.138092i
$484$	1.35590e11			2.47085
$485$		−	5.59795e10i		−	1.01172i
$486$			5.38314e9i			0.0964919i
$487$	−2.15971e10			−0.383954			−0.191977	−	0.981399i	$-0.561490\pi$
$487$	−2.15971e10			−0.383954			−0.191977	+	0.981399i	$0.561490\pi$
$488$	−2.09725e10			−0.369803
$489$	−2.39530e10			−0.418914
$490$		−	1.05554e11i		−	1.83100i
$491$	−3.36314e10			−0.578653			−0.289327	−	0.957230i	$-0.593431\pi$
$491$	−3.36314e10			−0.578653			−0.289327	+	0.957230i	$0.593431\pi$
$492$	6.84029e10			1.16739
$493$	1.58678e8			0.00268614
$494$	−4.33920e9			−0.0728621
$495$		−	5.42165e10i		−	0.903048i
$496$		−	4.55916e10i		−	0.753283i
$497$	2.16332e10			0.354565
$498$	7.85680e9			0.127740
$499$	2.60087e10			0.419485			0.209743	−	0.977757i	$-0.432737\pi$
$499$	2.60087e10			0.419485			0.209743	+	0.977757i	$0.432737\pi$
$500$	5.99135e10			0.958617
$501$	−5.43301e10			−0.862361
$502$			1.41603e11i			2.22976i
$503$		−	4.32581e10i		−	0.675765i	−0.941188	−	0.337883i	$-0.890289\pi$
$503$		−	4.32581e10i		−	0.675765i	0.941188	−	0.337883i	$-0.109711\pi$
$504$		−	4.04893e9i		−	0.0627506i
$505$			1.34024e11i			2.06072i
$506$		−	8.50618e10i		−	1.29758i
$507$	−3.60509e10			−0.545613
$508$	−1.20286e11			−1.80617
$509$		−	1.16070e11i		−	1.72921i	−0.502454	−	0.864604i	$-0.667570\pi$
$509$		−	1.16070e11i		−	1.72921i	0.502454	−	0.864604i	$-0.332430\pi$
$510$			9.88015e8i			0.0146044i
$511$		−	5.18037e10i		−	0.759762i
$512$		−	8.24891e10i		−	1.20037i
$513$	2.75377e9			0.0397611
$514$			9.46821e10i			1.35649i
$515$		−	4.40975e10i		−	0.626881i
$516$		−	2.92461e9i		−	0.0412543i
$517$	−5.31796e10			−0.744360
$518$	−3.22258e9			−0.0447595
$519$			3.23354e10i			0.445666i
$520$	1.06634e10			0.145841
$521$	−5.76566e10			−0.782525			−0.391263	−	0.920279i	$-0.627962\pi$
$521$	−5.76566e10			−0.782525			−0.391263	+	0.920279i	$0.627962\pi$
$522$			9.36768e9i			0.126168i
$523$	6.75826e10			0.903291			0.451646	−	0.892197i	$-0.350837\pi$
$523$	6.75826e10			0.903291			0.451646	+	0.892197i	$0.350837\pi$
$524$			1.87919e11i			2.49256i
$525$	3.09913e10			0.407945
$526$		−	7.23489e10i		−	0.945124i
$527$		−	9.27652e8i		−	0.0120266i
$528$			5.15913e10i			0.663805i
$529$	5.86035e10			0.748343
$530$		−	2.91635e11i		−	3.69603i
$531$	−2.59942e10	+	5.15647e9i	−0.326962	+	0.0648597i
$532$	−9.96186e9			−0.124364
$533$			3.03055e10i			0.375502i
$534$	8.20575e10			1.00914
$535$	8.82189e10			1.07683
$536$	2.44483e10			0.296204
$537$			7.68952e10i			0.924702i
$538$	1.63752e11			1.95460
$539$		−	1.12147e11i		−	1.32871i
$540$	−3.25477e10			−0.382777
$541$			7.24724e10i			0.846026i	0.906124	+	0.423013i	$0.139028\pi$
$541$			7.24724e10i			0.846026i	−0.906124	+	0.423013i	$0.860972\pi$
$542$		−	4.94718e10i		−	0.573272i
$543$	2.02476e10			0.232902
$544$		−	1.30929e9i		−	0.0149500i
$545$		−	1.45764e11i		−	1.65221i
$546$	8.62771e9			0.0970789
$547$	8.38360e10			0.936443			0.468221	−	0.883611i	$-0.344895\pi$
$547$	8.38360e10			0.936443			0.468221	+	0.883611i	$0.344895\pi$
$548$	6.37726e10			0.707151
$549$			2.83611e10i			0.312201i
$550$	3.50766e11			3.83325
$551$	4.79208e9			0.0519897
$552$	−1.06173e10			−0.114356
$553$	3.49426e10			0.373641
$554$		−	2.90135e10i		−	0.308008i
$555$			5.38613e9i			0.0567681i
$556$	1.91335e11			2.00214
$557$	6.90382e10			0.717247			0.358624	−	0.933482i	$-0.383246\pi$
$557$	6.90382e10			0.717247			0.358624	+	0.933482i	$0.383246\pi$
$558$	5.47647e10			0.564890
$559$	1.29573e9			0.0132699
$560$	−4.93903e10			−0.502214
$561$			1.04973e9i			0.0105980i
$562$		−	2.38703e10i		−	0.239284i
$563$			1.10659e11i			1.10142i	0.834696	+	0.550712i	$0.185644\pi$
$563$			1.10659e11i			1.10142i	−0.834696	+	0.550712i	$0.814356\pi$
$564$			3.19252e10i			0.315513i
$565$		−	9.58881e10i		−	0.940960i
$566$	−1.25368e11			−1.22158
$567$	−5.47537e9			−0.0529763
$568$		−	3.05619e10i		−	0.293621i
$569$			1.65136e11i			1.57541i	0.616054	+	0.787704i	$0.288730\pi$
$569$			1.65136e11i			1.57541i	−0.616054	+	0.787704i	$0.711270\pi$
$570$			2.98381e10i			0.282665i
$571$		−	1.33371e11i		−	1.25463i	−0.778764	−	0.627317i	$-0.784153\pi$
$571$		−	1.33371e11i		−	1.25463i	0.778764	−	0.627317i	$-0.215847\pi$
$572$	5.44899e10			0.509016
$573$			5.84276e10i			0.542001i
$574$			1.24684e11i			1.14858i
$575$		−	8.12670e10i		−	0.743435i
$576$	5.27628e10			0.479333
$577$	−1.27540e10			−0.115065			−0.0575323	−	0.998344i	$-0.518323\pi$
$577$	−1.27540e10			−0.115065			−0.0575323	+	0.998344i	$0.518323\pi$
$578$			1.67863e11i			1.50399i
$579$	3.37446e10			0.300255
$580$	−5.66392e10			−0.500501
$581$			7.99142e9i			0.0701325i
$582$	−6.39866e10			−0.557696
$583$		−	3.09851e11i		−	2.68212i
$584$	−7.31846e10			−0.629171
$585$		−	1.44201e10i		−	0.123124i
$586$			1.77363e11i			1.50409i
$587$		−	1.33729e11i		−	1.12635i	−0.826337	−	0.563175i	$-0.809580\pi$
$587$		−	1.33729e11i		−	1.12635i	0.826337	−	0.563175i	$-0.190420\pi$
$588$	−6.73248e10			−0.563204
$589$		−	2.80151e10i		−	0.232772i
$590$	−5.58722e10	−	2.81656e11i	−0.461092	−	2.32440i
$591$	−1.21478e11			−0.995740
$592$		−	5.12532e9i		−	0.0417287i
$593$	1.74593e11			1.41192			0.705959	−	0.708253i	$-0.250516\pi$
$593$	1.74593e11			1.41192			0.705959	+	0.708253i	$0.250516\pi$
$594$	−6.19715e10			−0.497790
$595$	−1.00494e9			−0.00801814
$596$			1.02701e11i			0.813935i
$597$	−1.15051e11			−0.905718
$598$		−	2.26241e10i		−	0.176916i
$599$	−7.88184e10			−0.612238			−0.306119	−	0.951993i	$-0.599031\pi$
$599$	−7.88184e10			−0.612238			−0.306119	+	0.951993i	$0.599031\pi$
$600$		−	4.37822e10i		−	0.337826i
$601$		−	4.56479e10i		−	0.349883i	−0.984579	−	0.174942i	$-0.944026\pi$
$601$		−	4.56479e10i		−	0.349883i	0.984579	−	0.174942i	$-0.0559737\pi$
$602$	5.33094e9			0.0405899
$603$		−	3.30615e10i		−	0.250066i
$604$		−	6.77738e10i		−	0.509230i
$605$	4.13082e11			3.08329
$606$	1.53195e11			1.13593
$607$	−6.77809e10			−0.499290			−0.249645	−	0.968337i	$-0.580314\pi$
$607$	−6.77809e10			−0.499290			−0.249645	+	0.968337i	$0.580314\pi$
$608$		−	3.95406e10i		−	0.289353i
$609$	−9.52818e9			−0.0692693
$610$	−3.07303e11			−2.21946
$611$	−1.41443e10			−0.101488
$612$	6.30182e8			0.00449221
$613$			1.55090e11i			1.09835i	0.835707	+	0.549175i	$0.185058\pi$
$613$			1.55090e11i			1.09835i	−0.835707	+	0.549175i	$0.814942\pi$
$614$		−	3.33523e10i		−	0.234667i
$615$	2.08393e11			1.45674
$616$	4.66119e10			0.323723
$617$	−3.07611e10			−0.212257			−0.106128	−	0.994352i	$-0.533845\pi$
$617$	−3.07611e10			−0.212257			−0.106128	+	0.994352i	$0.533845\pi$
$618$	−5.04051e10			−0.345558
$619$	9.76912e10			0.665415			0.332708	−	0.943030i	$-0.392038\pi$
$619$	9.76912e10			0.665415			0.332708	+	0.943030i	$0.392038\pi$
$620$			3.31120e11i			2.24088i
$621$			1.43578e10i			0.0965434i
$622$			1.82193e11i			1.21723i
$623$			8.34634e10i			0.554044i
$624$			1.37218e10i			0.0905053i
$625$	−4.36006e10			−0.285741
$626$	−1.91014e11			−1.24385
$627$			3.17018e10i			0.205123i
$628$			6.08971e9i			0.0391524i
$629$		−	1.04285e8i		−	0.000666222i
$630$		−	5.93276e10i		−	0.376612i
$631$	−2.20612e11			−1.39159			−0.695794	−	0.718241i	$-0.744947\pi$
$631$	−2.20612e11			−1.39159			−0.695794	+	0.718241i	$0.744947\pi$
$632$		−	4.93645e10i		−	0.309418i
$633$		−	5.12367e10i		−	0.319129i
$634$		−	2.47082e11i		−	1.52927i
$635$	−3.66456e11			−2.25386
$636$	−1.86012e11			−1.13688
$637$		−	2.98279e10i		−	0.181161i
$638$	−1.07842e11			−0.650887
$639$	−4.13289e10			−0.247885
$640$			2.01529e11i			1.20120i
$641$	1.03091e11			0.610646			0.305323	−	0.952249i	$-0.401236\pi$
$641$	1.03091e11			0.610646			0.305323	+	0.952249i	$0.401236\pi$
$642$		−	1.00837e11i		−	0.593583i
$643$	−2.79059e11			−1.63249			−0.816247	−	0.577702i	$-0.803949\pi$
$643$	−2.79059e11			−1.63249			−0.816247	+	0.577702i	$0.803949\pi$
$644$		−	5.19400e10i		−	0.301966i
$645$		−	8.90997e9i		−	0.0514799i
$646$		−	5.77718e8i		−	0.00331731i
$647$	−7.83016e10			−0.446842			−0.223421	−	0.974722i	$-0.571722\pi$
$647$	−7.83016e10			−0.446842			−0.223421	+	0.974722i	$0.571722\pi$
$648$			7.73522e9i			0.0438705i
$649$	−5.93621e10	−	2.99248e11i	−0.334603	−	1.68676i
$650$	9.32940e10			0.522637
$651$			5.57030e10i			0.310138i
$652$	−1.65541e11			−0.916041
$653$	1.77534e11			0.976402			0.488201	−	0.872731i	$-0.337653\pi$
$653$	1.77534e11			0.976402			0.488201	+	0.872731i	$0.337653\pi$
$654$	−1.66614e11			−0.910750
$655$			5.72504e11i			3.11038i
$656$	−1.98302e11			−1.07081
$657$			9.89677e10i			0.531168i
$658$	−5.81929e10			−0.310432
$659$			2.17806e11i			1.15486i	0.816440	+	0.577430i	$0.195944\pi$
$659$			2.17806e11i			1.15486i	−0.816440	+	0.577430i	$0.804056\pi$
$660$		−	3.74694e11i		−	1.97470i
$661$	−2.68055e11			−1.40416			−0.702081	−	0.712097i	$-0.747746\pi$
$661$	−2.68055e11			−1.40416			−0.702081	+	0.712097i	$0.747746\pi$
$662$		−	1.60925e11i		−	0.837899i
$663$			2.79198e8i			0.00144497i
$664$	1.12897e10			0.0580778
$665$	−3.03493e10			−0.155189
$666$	6.15654e9			0.0312925
$667$			2.49853e10i			0.126236i
$668$	−3.75479e11			−1.88573
$669$	5.83602e9			0.0291348
$670$	3.58233e11			1.77773
$671$	−3.26497e11			−1.61061
$672$			7.86193e10i			0.385524i
$673$			2.50768e11i			1.22239i	0.791478	+	0.611197i	$0.209312\pi$
$673$			2.50768e11i			1.22239i	−0.791478	+	0.611197i	$0.790688\pi$
$674$	2.06809e11			1.00215
$675$	−5.92068e10			−0.285205
$676$	−2.49150e11			−1.19309
$677$	8.82165e10			0.419948			0.209974	−	0.977707i	$-0.432662\pi$
$677$	8.82165e10			0.419948			0.209974	+	0.977707i	$0.432662\pi$
$678$	−1.09604e11			−0.518688
$679$		−	6.50830e10i		−	0.306188i
$680$			1.41971e9i			0.00663995i
$681$			1.58158e11i			0.735364i
$682$			6.30459e11i			2.91420i
$683$		−	2.38268e11i		−	1.09492i	−0.836832	−	0.547460i	$-0.815595\pi$
$683$		−	2.38268e11i		−	1.09492i	0.836832	−	0.547460i	$-0.184405\pi$
$684$	1.90315e10			0.0869458
$685$	1.94286e11			0.882430
$686$		−	2.81542e11i		−	1.27130i
$687$			1.18155e11i			0.530426i
$688$			8.47854e9i			0.0378414i
$689$		−	8.24117e10i		−	0.365689i
$690$	−1.55572e11			−0.686334
$691$		−	5.08258e10i		−	0.222932i	−0.993768	−	0.111466i	$-0.964445\pi$
$691$		−	5.08258e10i		−	0.222932i	0.993768	−	0.111466i	$-0.0355546\pi$
$692$			2.23472e11i			0.974540i
$693$		−	6.30333e10i		−	0.273298i
$694$	−3.06760e10			−0.132240
$695$	5.82911e11			2.49841
$696$			1.34607e10i			0.0573630i
$697$	−4.03485e9			−0.0170961
$698$	−2.96292e11			−1.24824
$699$			2.05077e10i			0.0859028i
$700$	2.14183e11			0.892056
$701$		−	3.96206e11i		−	1.64077i	−0.571810	−	0.820386i	$-0.693758\pi$
$701$		−	3.96206e11i		−	1.64077i	0.571810	−	0.820386i	$-0.306242\pi$
$702$	−1.64827e10			−0.0678703
$703$		−	3.14941e9i		−	0.0128946i
$704$			6.07412e11i			2.47282i
$705$			9.72618e10i			0.393719i
$706$	3.59593e10			0.144741
$707$			1.55820e11i			0.623655i
$708$	−1.79647e11	+	3.56367e10i	−0.714970	+	0.141829i
$709$	3.38316e11			1.33887			0.669433	−	0.742872i	$-0.266537\pi$
$709$	3.38316e11			1.33887			0.669433	+	0.742872i	$0.266537\pi$
$710$		−	4.47813e11i		−	1.76223i
$711$	−6.67556e10			−0.261222
$712$	1.17911e11			0.458812
$713$	1.46068e11			0.565191
$714$			1.14869e9i			0.00441986i
$715$	1.66006e11			0.635185
$716$			5.31428e11i			2.02205i
$717$	4.91055e10			0.185803
$718$		−	4.72007e11i		−	1.77603i
$719$		−	4.17322e11i		−	1.56155i	−0.624812	−	0.780775i	$-0.714824\pi$
$719$		−	4.17322e11i		−	1.56155i	0.624812	−	0.780775i	$-0.285176\pi$
$720$	9.43569e10			0.351111
$721$		−	5.12687e10i		−	0.189719i
$722$			3.91289e11i			1.43995i
$723$	3.72047e10			0.136159
$724$	1.39932e11			0.509289
$725$	−1.03031e11			−0.372920
$726$		−	4.72168e11i		−	1.69961i
$727$	3.81006e11			1.36394			0.681969	−	0.731381i	$-0.261124\pi$
$727$	3.81006e11			1.36394			0.681969	+	0.731381i	$0.261124\pi$
$728$	1.23975e10			0.0441374
$729$	1.04604e10			0.0370370
$730$	−1.07235e12			−3.77612
$731$			1.72513e8i			0.000604160i
$732$			1.96006e11i			0.682691i
$733$	1.16004e11			0.401842			0.200921	−	0.979607i	$-0.435606\pi$
$733$	1.16004e11			0.401842			0.200921	+	0.979607i	$0.435606\pi$
$734$	−3.27253e11			−1.12746
$735$	−2.05108e11			−0.702804
$736$	2.06160e11			0.702575
$737$	3.80609e11			1.29006
$738$		−	2.38201e11i		−	0.803004i
$739$		−	2.35296e11i		−	0.788926i	−0.918912	−	0.394463i	$-0.870931\pi$
$739$		−	2.35296e11i		−	0.788926i	0.918912	−	0.394463i	$-0.129069\pi$
$740$			3.72239e10i			0.124135i
$741$			8.43180e9i			0.0279671i
$742$		−	3.39061e11i		−	1.11857i
$743$	−3.67325e11			−1.20530			−0.602650	−	0.798006i	$-0.705888\pi$
$743$	−3.67325e11			−1.20530			−0.602650	+	0.798006i	$0.705888\pi$
$744$	7.86932e10			0.256830
$745$			3.12884e11i			1.01568i
$746$			7.63653e11i			2.46570i
$747$		−	1.52671e10i		−	0.0490314i
$748$			7.25474e9i			0.0231748i
$749$	1.02565e11			0.325891
$750$		−	2.08638e11i		−	0.659399i
$751$			6.38730e10i			0.200797i	0.994947	+	0.100399i	$0.0320118\pi$
$751$			6.38730e10i			0.200797i	−0.994947	+	0.100399i	$0.967988\pi$
$752$		−	9.25522e10i		−	0.289411i
$753$	2.75159e11			0.855862
$754$	−2.86830e10			−0.0887440
$755$		−	2.06476e11i		−	0.635451i
$756$	−3.78407e10			−0.115844
$757$	4.64224e11			1.41366			0.706828	−	0.707385i	$-0.250125\pi$
$757$	4.64224e11			1.41366			0.706828	+	0.707385i	$0.250125\pi$
$758$			6.65167e11i			2.01490i
$759$	−1.65289e11			−0.498056
$760$			4.28754e10i			0.128515i
$761$	1.03271e10			0.0307923			0.0153961	−	0.999881i	$-0.495099\pi$
$761$	1.03271e10			0.0307923			0.0153961	+	0.999881i	$0.495099\pi$
$762$			4.18873e11i			1.24240i
$763$		−	1.69468e11i		−	0.500023i
$764$			4.03798e11i			1.18520i
$765$	1.91988e9			0.00560568
$766$		−	2.09939e11i		−	0.609787i
$767$	−1.57887e10	−	7.95918e10i	−0.0456209	−	0.229978i
$768$	−5.84758e10			−0.168086
$769$		−	1.94833e11i		−	0.557131i	−0.960417	−	0.278565i	$-0.910141\pi$
$769$		−	1.94833e11i		−	0.557131i	0.960417	−	0.278565i	$-0.0898589\pi$
$770$	6.82988e11			1.94290
$771$	1.83983e11			0.520668
$772$	2.33211e11			0.656569
$773$		−	1.43747e11i		−	0.402606i	−0.979529	−	0.201303i	$-0.935482\pi$
$773$		−	1.43747e11i		−	0.402606i	0.979529	−	0.201303i	$-0.0645177\pi$
$774$	−1.01844e10			−0.0283774
$775$			6.02333e11i			1.66967i
$776$	−9.19446e10			−0.253559
$777$			6.26203e9i			0.0171803i
$778$		−	6.60994e11i		−	1.80418i
$779$	−1.21853e11			−0.330891
$780$		−	9.96582e10i		−	0.269237i
$781$		−	4.75784e11i		−	1.27881i
$782$	3.01215e9			0.00805471
$783$	1.82030e10			0.0484279
$784$	1.95177e11			0.516611
$785$			1.85526e10i			0.0488569i
$786$	6.54393e11			1.71454
$787$	6.52724e11			1.70149			0.850747	−	0.525575i	$-0.176150\pi$
$787$	6.52724e11			1.70149			0.850747	+	0.525575i	$0.176150\pi$
$788$	−8.39540e11			−2.17739
$789$	−1.40586e11			−0.362773
$790$		−	7.23321e11i		−	1.85705i
$791$		−	1.11482e11i		−	0.284772i
$792$	−8.90490e10			−0.226323
$793$	−8.68392e10			−0.219595
$794$	−6.86063e11			−1.72616
$795$	−5.66696e11			−1.41867
$796$	−7.95125e11			−1.98054
$797$		−	1.74045e11i		−	0.431348i	−0.976465	−	0.215674i	$-0.930805\pi$
$797$		−	1.74045e11i		−	0.431348i	0.976465	−	0.215674i	$-0.0691948\pi$
$798$			3.46904e10i			0.0855456i
$799$		−	1.88316e9i		−	0.00462062i
$800$			8.50133e11i			2.07552i
$801$		−	1.59452e11i		−	0.387346i
$802$	4.61367e11			1.11519
$803$	−1.13933e12			−2.74023
$804$		−	2.28491e11i		−	0.546820i
$805$		−	1.58238e11i		−	0.376814i
$806$			1.67684e11i			0.397331i
$807$		−	3.18199e11i		−	0.750247i
$808$	2.20131e11			0.516458
$809$		−	2.43870e11i		−	0.569330i	−0.958627	−	0.284665i	$-0.908118\pi$
$809$		−	2.43870e11i		−	0.569330i	0.958627	−	0.284665i	$-0.0918823\pi$
$810$			1.13342e11i			0.263299i
$811$		−	7.09347e11i		−	1.63974i	−0.572549	−	0.819870i	$-0.694045\pi$
$811$		−	7.09347e11i		−	1.63974i	0.572549	−	0.819870i	$-0.305955\pi$
$812$	−6.58499e10			−0.151472
$813$	−9.61320e10			−0.220042
$814$			7.08750e10i			0.161434i
$815$	−5.04328e11			−1.14310
$816$	−1.82692e9			−0.00412058
$817$			5.20989e9i			0.0116934i
$818$	4.40718e11			0.984345
$819$		−	1.67651e10i		−	0.0372624i
$820$	1.44022e12			3.18546
$821$		−	8.02571e10i		−	0.176649i	−0.996092	−	0.0883244i	$-0.971849\pi$
$821$		−	8.02571e10i		−	0.176649i	0.996092	−	0.0883244i	$-0.0281512\pi$
$822$		−	2.22077e11i		−	0.486424i
$823$			6.56148e11i			1.43022i	0.699013	+	0.715109i	$0.253623\pi$
$823$			6.56148e11i			1.43022i	−0.699013	+	0.715109i	$0.746377\pi$
$824$	−7.24288e10			−0.157110
$825$		−	6.81597e11i		−	1.47134i
$826$	−6.49582e10	−	3.27459e11i	−0.139545	−	0.703456i
$827$	−3.84202e11			−0.821367			−0.410683	−	0.911778i	$-0.634710\pi$
$827$	−3.84202e11			−0.821367			−0.410683	+	0.911778i	$0.634710\pi$
$828$			9.92280e10i			0.211112i
$829$	1.70431e11			0.360853			0.180427	−	0.983588i	$-0.442252\pi$
$829$	1.70431e11			0.360853			0.180427	+	0.983588i	$0.442252\pi$
$830$	1.65424e11			0.348568
$831$	−5.63782e10			−0.118224
$832$			1.61555e11i			0.337153i
$833$	3.97126e9			0.00824799
$834$		−	6.66289e11i		−	1.37720i
$835$	−1.14392e12			−2.35314
$836$			2.19093e11i			0.448543i
$837$		−	1.06417e11i		−	0.216825i
$838$	1.34018e11			0.271761
$839$		−	9.46766e11i		−	1.91071i	−0.295459	−	0.955355i	$-0.595473\pi$
$839$		−	9.46766e11i		−	1.91071i	0.295459	−	0.955355i	$-0.404527\pi$
$840$		−	8.52499e10i		−	0.171229i
$841$	−4.68570e11			−0.936678
$842$	−5.80329e11			−1.15458
$843$	−4.63841e10			−0.0918457
$844$		−	3.54100e11i		−	0.697841i
$845$	−7.59049e11			−1.48882
$846$	1.11174e11			0.217031
$847$	4.80258e11			0.933127
$848$	5.39256e11			1.04282
$849$			2.43612e11i			0.468886i
$850$			1.24211e10i			0.0237949i
$851$	1.64206e10			0.0313092
$852$	−2.85627e11			−0.542052
$853$	7.43531e11			1.40444			0.702220	−	0.711960i	$-0.252192\pi$
$853$	7.43531e11			1.40444			0.702220	+	0.711960i	$0.252192\pi$
$854$	−3.57277e11			−0.671697
$855$	5.79804e10			0.108497
$856$		−	1.44897e11i		−	0.269876i
$857$		−	5.26314e10i		−	0.0975713i	−0.998809	−	0.0487856i	$-0.984465\pi$
$857$		−	5.26314e10i		−	0.0975713i	0.998809	−	0.0487856i	$-0.0155351\pi$
$858$		−	1.89751e11i		−	0.350135i
$859$		−	1.52111e11i		−	0.279376i	−0.990196	−	0.139688i	$-0.955390\pi$
$859$		−	1.52111e11i		−	0.279376i	0.990196	−	0.139688i	$-0.0446099\pi$
$860$		−	6.15774e10i		−	0.112571i
$861$	2.42282e11			0.440868
$862$	1.33336e12			2.41501
$863$		−	2.75893e11i		−	0.497391i	−0.968582	−	0.248696i	$-0.919998\pi$
$863$		−	2.75893e11i		−	0.497391i	0.968582	−	0.248696i	$-0.0800019\pi$
$864$		−	1.50197e11i		−	0.269530i
$865$			6.80820e11i			1.21610i
$866$		−	1.30820e12i		−	2.32596i
$867$	3.26187e11			0.577284
$868$			3.84967e11i			0.678180i
$869$		−	7.68501e11i		−	1.34761i
$870$			1.97236e11i			0.344277i
$871$	1.01231e11			0.175891
$872$	−2.39413e11			−0.414077
$873$			1.24337e11i			0.214064i
$874$	9.09671e10			0.155897
$875$	2.12213e11			0.362026
$876$			6.83973e11i			1.16151i
$877$	5.09584e11			0.861425			0.430712	−	0.902489i	$-0.358262\pi$
$877$	5.09584e11			0.861425			0.430712	+	0.902489i	$0.358262\pi$
$878$		−	3.56671e10i		−	0.0600192i
$879$	3.44646e11			0.577322
$880$			1.08625e12i			1.81134i
$881$			6.07165e11i			1.00787i	0.863743	+	0.503933i	$0.168114\pi$
$881$			6.07165e11i			1.00787i	−0.863743	+	0.503933i	$0.831886\pi$
$882$			2.34446e11i			0.387408i
$883$	−9.62583e11			−1.58342			−0.791709	−	0.610899i	$-0.790808\pi$
$883$	−9.62583e11			−1.58342			−0.791709	+	0.610899i	$0.790808\pi$
$884$			1.92956e9i			0.00315972i
$885$	−5.47305e11	+	1.08569e11i	−0.892188	+	0.176984i
$886$	−1.18635e11			−0.192521
$887$			4.43748e11i			0.716873i	0.933554	+	0.358437i	$0.116690\pi$
$887$			4.43748e11i			0.716873i	−0.933554	+	0.358437i	$0.883310\pi$
$888$	8.84654e9			0.0142273
$889$	−4.26050e11			−0.682108
$890$	1.72771e12			2.75367
$891$			1.20421e11i			0.191070i
$892$	4.03332e10			0.0637093
$893$		−	5.68715e10i		−	0.0894311i
$894$	3.57637e11			0.559877
$895$			1.61902e12i			2.52325i
$896$			2.34302e11i			0.363532i
$897$	−4.39624e10			−0.0679065
$898$			7.12877e11i			1.09625i
$899$		−	1.85186e11i		−	0.283510i
$900$	−4.09182e11			−0.623659
$901$	1.09722e10			0.0166493
$902$	2.74220e12			4.14260
$903$		−	1.03589e10i		−	0.0155799i
$904$	−1.57493e11			−0.235824
$905$	4.26311e11			0.635525
$906$	−2.36010e11			−0.350282
$907$	−2.46384e11			−0.364069			−0.182035	−	0.983292i	$-0.558268\pi$
$907$	−2.46384e11			−0.364069			−0.182035	+	0.983292i	$0.558268\pi$
$908$			1.09304e12i			1.60802i
$909$		−	2.97683e11i		−	0.436012i
$910$	1.81656e11			0.264901
$911$	−3.98299e11			−0.578277			−0.289138	−	0.957287i	$-0.593369\pi$
$911$	−3.98299e11			−0.578277			−0.289138	+	0.957287i	$0.593369\pi$
$912$	−5.51729e10			−0.0797529
$913$	1.75757e11			0.252947
$914$	1.14021e12			1.63381
$915$			5.97141e11i			0.851908i
$916$			8.16577e11i			1.15989i
$917$			6.65606e11i			0.941325i
$918$		−	2.19449e9i		−	0.00309004i
$919$		−	6.97622e11i		−	0.978044i	−0.872272	−	0.489022i	$-0.837354\pi$
$919$		−	6.97622e11i		−	0.978044i	0.872272	−	0.489022i	$-0.162646\pi$
$920$	−2.23547e11			−0.312045
$921$	−6.48092e10			−0.0900737
$922$		−	8.78079e11i		−	1.21509i
$923$		−	1.26545e11i		−	0.174357i
$924$		−	4.35628e11i		−	0.597623i
$925$			6.77131e10i			0.0924923i
$926$	1.94992e12			2.65199
$927$			9.79456e10i			0.132637i
$928$		−	2.61371e11i		−	0.352424i
$929$			1.22783e12i			1.64845i	0.566264	+	0.824224i	$0.308388\pi$
$929$			1.22783e12i			1.64845i	−0.566264	+	0.824224i	$0.691612\pi$
$930$	1.15307e12			1.54142
$931$	1.19932e11			0.159638
$932$			1.41730e11i			0.187844i
$933$	3.54033e11			0.467215
$934$	1.28115e12			1.68350
$935$			2.21019e10i			0.0289190i
$936$	−2.36845e10			−0.0308576
$937$			6.25346e11i			0.811263i	0.914037	+	0.405632i	$0.132948\pi$
$937$			6.25346e11i			0.811263i	−0.914037	+	0.405632i	$0.867052\pi$
$938$	4.16490e11			0.538013
$939$			3.71173e11i			0.477435i
$940$			6.72183e11i			0.860947i
$941$			8.46234e11i			1.07927i	0.841898	+	0.539637i	$0.181439\pi$
$941$			8.46234e11i			1.07927i	−0.841898	+	0.539637i	$0.818561\pi$
$942$	2.12063e10			0.0269316
$943$		−	6.35326e11i		−	0.803433i
$944$	5.20804e11	−	1.03312e11i	0.655822	−	0.130096i
$945$	−1.15284e11			−0.144557
$946$		−	1.17245e11i		−	0.146396i
$947$	−1.06021e12			−1.31824			−0.659118	−	0.752039i	$-0.729070\pi$
$947$	−1.06021e12			−1.31824			−0.659118	+	0.752039i	$0.729070\pi$
$948$	−4.61353e11			−0.571215
$949$	−3.03030e11			−0.373612
$950$			3.75117e11i			0.460545i
$951$	−4.80122e11			−0.586988
$952$			1.65059e9i			0.00200951i
$953$	−4.84868e11			−0.587831			−0.293915	−	0.955831i	$-0.594958\pi$
$953$	−4.84868e11			−0.587831			−0.293915	+	0.955831i	$0.594958\pi$
$954$			6.47754e11i			0.782018i
$955$			1.23019e12i			1.47897i
$956$	3.39372e11			0.406297
$957$			2.09555e11i			0.249834i
$958$		−	1.77972e12i		−	2.11295i
$959$	2.25882e11			0.267058
$960$	1.11092e12			1.30797
$961$	−2.29728e11			−0.269352
$962$			1.88508e10i			0.0220104i
$963$	−1.95944e11			−0.227839
$964$	2.57124e11			0.297739
$965$	7.10490e11			0.819311
$966$	−1.80872e11			−0.207712
$967$		−	4.71254e11i		−	0.538951i	−0.963007	−	0.269475i	$-0.913150\pi$
$967$		−	4.71254e11i		−	0.538951i	0.963007	−	0.269475i	$-0.0868503\pi$
$968$		−	6.78474e11i		−	0.772737i
$969$	−1.12260e9			−0.00127330
$970$	−1.34723e12			−1.52179
$971$	−1.38722e12			−1.56052			−0.780259	−	0.625457i	$-0.784913\pi$
$971$	−1.38722e12			−1.56052			−0.780259	+	0.625457i	$0.784913\pi$
$972$	7.22922e10			0.0809891
$973$	6.77705e11			0.756117
$974$			5.19768e11i			0.577529i
$975$		−	1.81286e11i		−	0.200607i
$976$		−	5.68227e11i		−	0.626213i
$977$		−	9.75949e11i		−	1.07115i	−0.844489	−	0.535573i	$-0.820096\pi$
$977$		−	9.75949e11i		−	1.07115i	0.844489	−	0.535573i	$-0.179904\pi$
$978$			5.76466e11i			0.630113i
$979$	1.83563e12			1.99827
$980$	−1.41752e12			−1.53682
$981$			3.23758e11i			0.349579i
$982$			8.09391e11i			0.870387i
$983$		−	1.62338e12i		−	1.73863i	−0.494261	−	0.869313i	$-0.664561\pi$
$983$		−	1.62338e12i		−	1.73863i	0.494261	−	0.869313i	$-0.335439\pi$
$984$		−	3.42279e11i		−	0.365090i
$985$	−2.55770e12			−2.71709
$986$		−	3.81883e9i		−	0.00404038i
$987$			1.13079e11i			0.119155i
$988$			5.82727e10i			0.0611558i
$989$	−2.71638e10			−0.0283926
$990$	−1.30480e12			−1.35833
$991$		−	1.93304e11i		−	0.200423i	−0.994966	−	0.100211i	$-0.968048\pi$
$991$		−	1.93304e11i		−	0.200423i	0.994966	−	0.100211i	$-0.0319519\pi$
$992$	−1.52801e12			−1.57790
$993$	−3.12704e11			−0.321616
$994$		−	5.20637e11i		−	0.533322i
$995$	−2.42239e12			−2.47145
$996$		−	1.05512e11i		−	0.107217i
$997$	−9.71652e11			−0.983399			−0.491700	−	0.870765i	$-0.663624\pi$
$997$	−9.71652e11			−0.983399			−0.491700	+	0.870765i	$0.663624\pi$
$998$		−	6.25940e11i		−	0.630973i
$999$		−	1.19632e10i		−	0.0120112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.9.c.a.58.12	✓	80
59.58	odd	2	inner	177.9.c.a.58.69	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.9.c.a.58.12	✓	80	1.1	even	1	trivial
177.9.c.a.58.69	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)

\(f(q)\)	\(=\)	\(q-24.0665i q^{2} -46.7654 q^{3} -323.199 q^{4} -984.641 q^{5} +1125.48i q^{6} -1144.76 q^{7} +1617.24i q^{8} +2187.00 q^{9} +O(q^{10})\)	\(q-24.0665i q^{2} -46.7654 q^{3} -323.199 q^{4} -984.641 q^{5} +1125.48i q^{6} -1144.76 q^{7} +1617.24i q^{8} +2187.00 q^{9} +23696.9i q^{10} +25177.1i q^{11} +15114.5 q^{12} +6696.40i q^{13} +27550.5i q^{14} +46047.1 q^{15} -43817.4 q^{16} -891.553 q^{17} -52633.5i q^{18} -26924.9 q^{19} +318235. q^{20} +53535.4 q^{21} +605925. q^{22} -140383. i q^{23} -75630.9i q^{24} +578893. q^{25} +161159. q^{26} -102276. q^{27} +369987. q^{28} -177979. q^{29} -1.10820e6i q^{30} +1.04049e6i q^{31} +1.46855e6i q^{32} -1.17741e6i q^{33} +21456.6i q^{34} +1.12718e6 q^{35} -706836. q^{36} +116970. i q^{37} +647990. i q^{38} -313159. i q^{39} -1.59240e6i q^{40} +4.52564e6 q^{41} -1.28841e6i q^{42} -193497. i q^{43} -8.13719e6i q^{44} -2.15341e6 q^{45} -3.37854e6 q^{46} +2.11222e6i q^{47} +2.04914e6 q^{48} -4.45431e6 q^{49} -1.39320e7i q^{50} +41693.8 q^{51} -2.16427e6i q^{52} -1.23069e7 q^{53} +2.46143e6i q^{54} -2.47904e7i q^{55} -1.85136e6i q^{56} +1.25915e6 q^{57} +4.28334e6i q^{58} +(-1.18858e7 + 2.35778e6i) q^{59} -1.48824e7 q^{60} +1.29680e7i q^{61} +2.50410e7 q^{62} -2.50360e6 q^{63} +2.41256e7 q^{64} -6.59355e6i q^{65} -2.83363e7 q^{66} -1.51173e7i q^{67} +288149. q^{68} +6.56508e6i q^{69} -2.71274e7i q^{70} -1.88975e7 q^{71} +3.53691e6i q^{72} +4.52527e7i q^{73} +2.81506e6 q^{74} -2.70722e7 q^{75} +8.70210e6 q^{76} -2.88218e7i q^{77} -7.53667e6 q^{78} -3.05238e7 q^{79} +4.31445e7 q^{80} +4.78297e6 q^{81} -1.08917e8i q^{82} -6.98084e6i q^{83} -1.73026e7 q^{84} +877860. q^{85} -4.65680e6 q^{86} +8.32326e6 q^{87} -4.07174e7 q^{88} -7.29088e7i q^{89} +5.18252e7i q^{90} -7.66580e6i q^{91} +4.53718e7i q^{92} -4.86589e7i q^{93} +5.08339e7 q^{94} +2.65114e7 q^{95} -6.86772e7i q^{96} +5.68527e7i q^{97} +1.07200e8i q^{98} +5.50622e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more