LMFDB - Embedded newform 83.13.b.c.82.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [83,13,Mod(82,83)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(83, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("83.82");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 83 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	83.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$75.8614868339$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			82.10
Character	$\chi$	$=$	83.82
Dual form			83.13.b.c.82.71

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-106.238i q^{2} -1381.89 q^{3} -7190.55 q^{4} +23413.1i q^{5} +146810. i q^{6} -193774. q^{7} +328759. i q^{8} +1.37818e6 q^{9} +O(q^{10})$	\(q-106.238i q^{2} -1381.89 q^{3} -7190.55 q^{4} +23413.1i q^{5} +146810. i q^{6} -193774. q^{7} +328759. i q^{8} +1.37818e6 q^{9} +2.48737e6 q^{10} -2.43332e6 q^{11} +9.93656e6 q^{12} -4.04428e6i q^{13} +2.05862e7i q^{14} -3.23544e7i q^{15} +5.47426e6 q^{16} +2.07432e7 q^{17} -1.46416e8i q^{18} -6.65061e7i q^{19} -1.68353e8i q^{20} +2.67775e8 q^{21} +2.58512e8i q^{22} +6.14611e7 q^{23} -4.54309e8i q^{24} -3.04034e8 q^{25} -4.29657e8 q^{26} -1.17011e9 q^{27} +1.39334e9 q^{28} +5.36412e8 q^{29} -3.43727e9 q^{30} +2.44503e7 q^{31} +7.65021e8i q^{32} +3.36259e9 q^{33} -2.20372e9i q^{34} -4.53686e9i q^{35} -9.90990e9 q^{36} +2.54516e9 q^{37} -7.06548e9 q^{38} +5.58876e9i q^{39} -7.69728e9 q^{40} -4.17502e9 q^{41} -2.84479e10i q^{42} +2.48273e9i q^{43} +1.74969e10 q^{44} +3.22676e10i q^{45} -6.52951e9i q^{46} -2.39842e9i q^{47} -7.56483e9 q^{48} +2.37072e10 q^{49} +3.23000e10i q^{50} -2.86649e10 q^{51} +2.90806e10i q^{52} -3.42712e10i q^{53} +1.24310e11i q^{54} -5.69717e10i q^{55} -6.37050e10i q^{56} +9.19042e10i q^{57} -5.69874e10i q^{58} +6.07879e10 q^{59} +2.32646e11i q^{60} -6.29250e10 q^{61} -2.59755e9i q^{62} -2.67057e11 q^{63} +1.03697e11 q^{64} +9.46894e10 q^{65} -3.57235e11i q^{66} +1.57099e10i q^{67} -1.49155e11 q^{68} -8.49326e10 q^{69} -4.81988e11 q^{70} -1.79565e11i q^{71} +4.53090e11i q^{72} +2.06534e11i q^{73} -2.70393e11i q^{74} +4.20142e11 q^{75} +4.78215e11i q^{76} +4.71516e11 q^{77} +5.93740e11 q^{78} -1.63933e11i q^{79} +1.28170e11i q^{80} +8.84539e11 q^{81} +4.43547e11i q^{82} +(1.18112e11 - 3.04860e11i) q^{83} -1.92545e12 q^{84} +4.85663e11i q^{85} +2.63761e11 q^{86} -7.41263e11 q^{87} -7.99977e11i q^{88} -5.24424e11i q^{89} +3.42805e12 q^{90} +7.83679e11i q^{91} -4.41939e11 q^{92} -3.37876e10 q^{93} -2.54804e11 q^{94} +1.55712e12 q^{95} -1.05718e12i q^{96} -7.53437e11i q^{97} -2.51861e12i q^{98} -3.35357e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9}+O(q^{10}) $ 80 * q + 918 * q^3 - 181150 * q^4 + 103918 * q^7 + 14902142 * q^9	\( 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9} + 1177482 q^{10} + 510406 q^{11} - 9260402 q^{12} + 203791850 q^{16} + 5571718 q^{17} + 46565862 q^{21} + 804389464 q^{23} - 4263713272 q^{25} + 18061794 q^{26} - 2326165338 q^{27} - 204811652 q^{28} + 1486960270 q^{29} - 2621683648 q^{30} - 665743010 q^{31} + 135224502 q^{33} - 54936709824 q^{36} - 280627202 q^{37} + 6646145310 q^{38} - 7119722058 q^{40} + 51318109072 q^{41} - 11512674650 q^{44} + 85368259738 q^{48} + 148785395094 q^{49} - 100143389562 q^{51} - 63584241050 q^{59} - 29216180978 q^{61} - 332932206620 q^{63} - 323596534090 q^{64} + 362112989184 q^{65} - 86115426752 q^{68} + 272383417100 q^{69} + 105630718656 q^{70} + 785418808326 q^{75} - 663355117738 q^{77} + 1483841884620 q^{78} + 2430778545148 q^{81} + 837315119192 q^{83} - 3013574788354 q^{84} + 452180651958 q^{86} - 682263689498 q^{87} - 499714512022 q^{90} + 997428187414 q^{92} - 1487992716298 q^{93} + 3169817690580 q^{94} + 1542762610848 q^{95} + 2021347267420 q^{99}+O(q^{100}) \) 80 * q + 918 * q^3 - 181150 * q^4 + 103918 * q^7 + 14902142 * q^9 + 1177482 * q^10 + 510406 * q^11 - 9260402 * q^12 + 203791850 * q^16 + 5571718 * q^17 + 46565862 * q^21 + 804389464 * q^23 - 4263713272 * q^25 + 18061794 * q^26 - 2326165338 * q^27 - 204811652 * q^28 + 1486960270 * q^29 - 2621683648 * q^30 - 665743010 * q^31 + 135224502 * q^33 - 54936709824 * q^36 - 280627202 * q^37 + 6646145310 * q^38 - 7119722058 * q^40 + 51318109072 * q^41 - 11512674650 * q^44 + 85368259738 * q^48 + 148785395094 * q^49 - 100143389562 * q^51 - 63584241050 * q^59 - 29216180978 * q^61 - 332932206620 * q^63 - 323596534090 * q^64 + 362112989184 * q^65 - 86115426752 * q^68 + 272383417100 * q^69 + 105630718656 * q^70 + 785418808326 * q^75 - 663355117738 * q^77 + 1483841884620 * q^78 + 2430778545148 * q^81 + 837315119192 * q^83 - 3013574788354 * q^84 + 452180651958 * q^86 - 682263689498 * q^87 - 499714512022 * q^90 + 997428187414 * q^92 - 1487992716298 * q^93 + 3169817690580 * q^94 + 1542762610848 * q^95 + 2021347267420 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/83\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	106.238i		−	1.65997i	−0.557785	−	0.829986i	$-0.688349\pi$
$2$		−	106.238i		−	1.65997i	0.557785	−	0.829986i	$-0.311651\pi$
$3$	−1381.89			−1.89560			−0.947800	−	0.318866i	$-0.896698\pi$
$3$	−1381.89			−1.89560			−0.947800	+	0.318866i	$0.896698\pi$
$4$	−7190.55			−1.75550
$5$			23413.1i			1.49844i	0.662321	+	0.749220i	$0.269572\pi$
$5$			23413.1i			1.49844i	−0.662321	+	0.749220i	$0.730428\pi$
$6$			146810.i			3.14664i
$7$	−193774.			−1.64705			−0.823527	−	0.567276i	$-0.807997\pi$
$7$	−193774.			−1.64705			−0.823527	+	0.567276i	$0.807997\pi$
$8$			328759.i			1.25412i
$9$	1.37818e6			2.59330
$10$	2.48737e6			2.48737
$11$	−2.43332e6			−1.37355			−0.686774	−	0.726871i	$-0.740974\pi$
$11$	−2.43332e6			−1.37355			−0.686774	+	0.726871i	$0.740974\pi$
$12$	9.93656e6			3.32773
$13$		−	4.04428e6i		−	0.837880i	−0.908014	−	0.418940i	$-0.862402\pi$
$13$		−	4.04428e6i		−	0.837880i	0.908014	−	0.418940i	$-0.137598\pi$
$14$			2.05862e7i			2.73406i
$15$		−	3.23544e7i		−	2.84044i
$16$	5.47426e6			0.326291
$17$	2.07432e7			0.859374			0.429687	−	0.902978i	$-0.358624\pi$
$17$	2.07432e7			0.859374			0.429687	+	0.902978i	$0.358624\pi$
$18$		−	1.46416e8i		−	4.30480i
$19$		−	6.65061e7i		−	1.41364i	−0.707392	−	0.706822i	$-0.750128\pi$
$19$		−	6.65061e7i		−	1.41364i	0.707392	−	0.706822i	$-0.249872\pi$
$20$		−	1.68353e8i		−	2.63052i
$21$	2.67775e8			3.12216
$22$			2.58512e8i			2.28005i
$23$	6.14611e7			0.415177			0.207588	−	0.978216i	$-0.433439\pi$
$23$	6.14611e7			0.415177			0.207588	+	0.978216i	$0.433439\pi$
$24$		−	4.54309e8i		−	2.37730i
$25$	−3.04034e8			−1.24532
$26$	−4.29657e8			−1.39086
$27$	−1.17011e9			−3.02025
$28$	1.39334e9			2.89141
$29$	5.36412e8			0.901800			0.450900	−	0.892574i	$-0.351103\pi$
$29$	5.36412e8			0.901800			0.450900	+	0.892574i	$0.351103\pi$
$30$	−3.43727e9			−4.71505
$31$	2.44503e7			0.0275495			0.0137747	−	0.999905i	$-0.495615\pi$
$31$	2.44503e7			0.0275495			0.0137747	+	0.999905i	$0.495615\pi$
$32$			7.65021e8i			0.712481i
$33$	3.36259e9			2.60370
$34$		−	2.20372e9i		−	1.42654i
$35$		−	4.53686e9i		−	2.46801i
$36$	−9.90990e9			−4.55254
$37$	2.54516e9			0.991982			0.495991	−	0.868328i	$-0.334805\pi$
$37$	2.54516e9			0.991982			0.495991	+	0.868328i	$0.334805\pi$
$38$	−7.06548e9			−2.34661
$39$			5.58876e9i			1.58828i
$40$	−7.69728e9			−1.87922
$41$	−4.17502e9			−0.878933			−0.439467	−	0.898259i	$-0.644833\pi$
$41$	−4.17502e9			−0.878933			−0.439467	+	0.898259i	$0.644833\pi$
$42$		−	2.84479e10i		−	5.18269i
$43$			2.48273e9i			0.392752i	0.980529	+	0.196376i	$0.0629173\pi$
$43$			2.48273e9i			0.392752i	−0.980529	+	0.196376i	$0.937083\pi$
$44$	1.74969e10			2.41127
$45$			3.22676e10i			3.88590i
$46$		−	6.52951e9i		−	0.689182i
$47$		−	2.39842e9i		−	0.222504i	−0.993792	−	0.111252i	$-0.964514\pi$
$47$		−	2.39842e9i		−	0.222504i	0.993792	−	0.111252i	$-0.0354861\pi$
$48$	−7.56483e9			−0.618518
$49$	2.37072e10			1.71279
$50$			3.23000e10i			2.06720i
$51$	−2.86649e10			−1.62903
$52$			2.90806e10i			1.47090i
$53$		−	3.42712e10i		−	1.54623i	−0.634266	−	0.773115i	$-0.718697\pi$
$53$		−	3.42712e10i		−	1.54623i	0.634266	−	0.773115i	$-0.281303\pi$
$54$			1.24310e11i			5.01353i
$55$		−	5.69717e10i		−	2.05818i
$56$		−	6.37050e10i		−	2.06560i
$57$			9.19042e10i			2.67970i
$58$		−	5.69874e10i		−	1.49696i
$59$	6.07879e10			1.44114			0.720568	−	0.693384i	$-0.243881\pi$
$59$	6.07879e10			1.44114			0.720568	+	0.693384i	$0.243881\pi$
$60$			2.32646e11i			4.98641i
$61$	−6.29250e10			−1.22136			−0.610680	−	0.791877i	$-0.709104\pi$
$61$	−6.29250e10			−1.22136			−0.610680	+	0.791877i	$0.709104\pi$
$62$		−	2.59755e9i		−	0.0457313i
$63$	−2.67057e11			−4.27130
$64$	1.03697e11			1.50899
$65$	9.46894e10			1.25551
$66$		−	3.57235e11i		−	4.32206i
$67$			1.57099e10i			0.173669i	0.996223	+	0.0868347i	$0.0276752\pi$
$67$			1.57099e10i			0.173669i	−0.996223	+	0.0868347i	$0.972325\pi$
$68$	−1.49155e11			−1.50863
$69$	−8.49326e10			−0.787009
$70$	−4.81988e11			−4.09683
$71$		−	1.79565e11i		−	1.40176i	−0.713281	−	0.700879i	$-0.752791\pi$
$71$		−	1.79565e11i		−	1.40176i	0.713281	−	0.700879i	$-0.247209\pi$
$72$			4.53090e11i			3.25229i
$73$			2.06534e11i			1.36475i	0.731001	+	0.682376i	$0.239053\pi$
$73$			2.06534e11i			1.36475i	−0.731001	+	0.682376i	$0.760947\pi$
$74$		−	2.70393e11i		−	1.64666i
$75$	4.20142e11			2.36064
$76$			4.78215e11i			2.48166i
$77$	4.71516e11			2.26231
$78$	5.93740e11			2.63651
$79$		−	1.63933e11i		−	0.674377i	−0.941437	−	0.337189i	$-0.890524\pi$
$79$		−	1.63933e11i		−	0.674377i	0.941437	−	0.337189i	$-0.109476\pi$
$80$			1.28170e11i			0.488928i
$81$	8.84539e11			3.13189
$82$			4.43547e11i			1.45900i
$83$	1.18112e11	−	3.04860e11i	0.361265	−	0.932463i
$83$	1.18112e11	−	3.04860e11i	0.361265	−	0.932463i
$84$	−1.92545e12			−5.48096
$85$			4.85663e11i			1.28772i
$86$	2.63761e11			0.651957
$87$	−7.41263e11			−1.70945
$88$		−	7.99977e11i		−	1.72259i
$89$		−	5.24424e11i		−	1.05522i	−0.849487	−	0.527609i	$-0.823089\pi$
$89$		−	5.24424e11i		−	1.05522i	0.849487	−	0.527609i	$-0.176911\pi$
$90$	3.42805e12			6.45048
$91$			7.83679e11i			1.38003i
$92$	−4.41939e11			−0.728845
$93$	−3.37876e10			−0.0522228
$94$	−2.54804e11			−0.369350
$95$	1.55712e12			2.11826
$96$		−	1.05718e12i		−	1.35058i
$97$		−	7.53437e11i		−	0.904516i	−0.891887	−	0.452258i	$-0.850619\pi$
$97$		−	7.53437e11i		−	0.904516i	0.891887	−	0.452258i	$-0.149381\pi$
$98$		−	2.51861e12i		−	2.84318i
$99$	−3.35357e12			−3.56202
$100$	2.18617e12			2.18617
$101$		−	6.46366e10i		−	0.0608906i	−0.999536	−	0.0304453i	$-0.990307\pi$
$101$		−	6.46366e10i		−	0.0608906i	0.999536	−	0.0304453i	$-0.00969254\pi$
$102$			3.04530e12i			2.70414i
$103$			4.92174e11i			0.412188i	0.978532	+	0.206094i	$0.0660753\pi$
$103$			4.92174e11i			0.412188i	−0.978532	+	0.206094i	$0.933925\pi$
$104$	1.32959e12			1.05080
$105$			6.26946e12i			4.67837i
$106$	−3.64091e12			−2.56670
$107$			1.34542e12i			0.896512i	0.893905	+	0.448256i	$0.147955\pi$
$107$			1.34542e12i			0.896512i	−0.893905	+	0.448256i	$0.852045\pi$
$108$	8.41371e12			5.30207
$109$	4.93031e11			0.293978			0.146989	−	0.989138i	$-0.453042\pi$
$109$	4.93031e11			0.293978			0.146989	+	0.989138i	$0.453042\pi$
$110$	−6.05257e12			−3.41652
$111$	−3.51713e12			−1.88040
$112$	−1.06077e12			−0.537420
$113$	−1.13148e12			−0.543469			−0.271735	−	0.962372i	$-0.587597\pi$
$113$	−1.13148e12			−0.543469			−0.271735	+	0.962372i	$0.587597\pi$
$114$	9.76374e12			4.44823
$115$			1.43900e12i			0.622118i
$116$	−3.85709e12			−1.58311
$117$		−	5.57377e12i		−	2.17287i
$118$		−	6.45799e12i		−	2.39224i
$119$	−4.01950e12			−1.41544
$120$	1.06368e13			3.56224
$121$	2.78264e12			0.886634
$122$			6.68503e12i			2.02742i
$123$	5.76943e12			1.66611
$124$	−1.75811e11			−0.0483632
$125$		−	1.40230e12i		−	0.367603i
$126$			2.83716e13i			7.09024i
$127$	−5.36061e12			−1.27759			−0.638796	−	0.769377i	$-0.720567\pi$
$127$	−5.36061e12			−1.27759			−0.638796	+	0.769377i	$0.720567\pi$
$128$		−	7.88305e12i		−	1.79240i
$129$		−	3.43086e12i		−	0.744501i
$130$		−	1.00596e13i		−	2.08411i
$131$	3.43560e12			0.679791			0.339895	−	0.940463i	$-0.389608\pi$
$131$	3.43560e12			0.679791			0.339895	+	0.940463i	$0.389608\pi$
$132$	−2.41789e13			−4.57080
$133$			1.28872e13i			2.32835i
$134$	1.66899e12			0.288286
$135$		−	2.73959e13i		−	4.52567i
$136$			6.81951e12i			1.07775i
$137$			1.09718e13i			1.65941i	0.558200	+	0.829706i	$0.311492\pi$
$137$			1.09718e13i			1.65941i	−0.558200	+	0.829706i	$0.688508\pi$
$138$			9.02308e12i			1.30641i
$139$			2.82068e12i			0.391079i	0.980696	+	0.195540i	$0.0626458\pi$
$139$			2.82068e12i			0.391079i	−0.980696	+	0.195540i	$0.937354\pi$
$140$			3.26225e13i			4.33261i
$141$			3.31435e12i			0.421778i
$142$	−1.90767e13			−2.32688
$143$			9.84106e12i			1.15087i
$144$	7.54454e12			0.846170
$145$			1.25591e13i			1.35129i
$146$	2.19418e13			2.26545
$147$	−3.27608e13			−3.24676
$148$	−1.83011e13			−1.74143
$149$		−	1.26185e11i		−	0.0115316i	−0.999983	−	0.00576581i	$-0.998165\pi$
$149$		−	1.26185e11i		−	0.0115316i	0.999983	−	0.00576581i	$-0.00183532\pi$
$150$		−	4.46352e13i		−	3.91859i
$151$	−9.56240e10			−0.00806687			−0.00403344	−	0.999992i	$-0.501284\pi$
$151$	−9.56240e10			−0.00806687			−0.00403344	+	0.999992i	$0.501284\pi$
$152$	2.18645e13			1.77287
$153$	2.85879e13			2.22861
$154$		−	5.00930e13i		−	3.75537i
$155$			5.72457e11i			0.0412812i
$156$		−	4.01863e13i		−	2.78824i
$157$			5.70717e12i			0.381086i	0.981679	+	0.190543i	$0.0610248\pi$
$157$			5.70717e12i			0.381086i	−0.981679	+	0.190543i	$0.938975\pi$
$158$	−1.74159e13			−1.11945
$159$			4.73591e13i			2.93103i
$160$	−1.79115e13			−1.06761
$161$	−1.19096e13			−0.683819
$162$		−	9.39718e13i		−	5.19885i
$163$		−	7.71142e11i		−	0.0411158i	−0.999789	−	0.0205579i	$-0.993456\pi$
$163$		−	7.71142e11i		−	0.0411158i	0.999789	−	0.0205579i	$-0.00654424\pi$
$164$	3.00207e13			1.54297
$165$			7.87288e13i			3.90148i
$166$	−3.23877e13	−	1.25480e13i	−1.54786	−	0.599690i
$167$	1.43897e13			0.663365			0.331683	−	0.943391i	$-0.392384\pi$
$167$	1.43897e13			0.663365			0.331683	+	0.943391i	$0.392384\pi$
$168$			8.80335e13i			3.91554i
$169$	6.94185e12			0.297958
$170$	5.15960e13			2.13758
$171$		−	9.16577e13i		−	3.66600i
$172$		−	1.78522e13i		−	0.689478i
$173$	−2.32295e13			−0.866488			−0.433244	−	0.901277i	$-0.642631\pi$
$173$	−2.32295e13			−0.866488			−0.433244	+	0.901277i	$0.642631\pi$
$174$			7.87504e13i			2.83764i
$175$	5.89140e13			2.05112
$176$	−1.33206e13			−0.448177
$177$	−8.40023e13			−2.73182
$178$	−5.57138e13			−1.75163
$179$		−	4.36499e13i		−	1.32698i	−0.748184	−	0.663491i	$-0.769074\pi$
$179$		−	4.36499e13i		−	1.32698i	0.748184	−	0.663491i	$-0.230926\pi$
$180$		−	2.32022e14i		−	6.82172i
$181$		−	7.55085e12i		−	0.214746i	−0.994219	−	0.107373i	$-0.965756\pi$
$181$		−	7.55085e12i		−	0.214746i	0.994219	−	0.107373i	$-0.0342439\pi$
$182$	8.32566e13			2.29082
$183$	8.69555e13			2.31521
$184$			2.02059e13i			0.520680i
$185$			5.95901e13i			1.48643i
$186$			3.58953e12i			0.0866883i
$187$	−5.04749e13			−1.18039
$188$			1.72459e13i			0.390607i
$189$	2.26737e14			4.97452
$190$		−	1.65425e14i		−	3.51625i
$191$	3.12899e13			0.644471			0.322236	−	0.946659i	$-0.395566\pi$
$191$	3.12899e13			0.644471			0.322236	+	0.946659i	$0.395566\pi$
$192$	−1.43298e14			−2.86044
$193$	−3.64719e13			−0.705691			−0.352846	−	0.935682i	$-0.614786\pi$
$193$	−3.64719e13			−0.705691			−0.352846	+	0.935682i	$0.614786\pi$
$194$	−8.00437e13			−1.50147
$195$	−1.30850e14			−2.37995
$196$	−1.70468e14			−3.00681
$197$	−1.67320e13			−0.286253			−0.143127	−	0.989704i	$-0.545716\pi$
$197$	−1.67320e13			−0.286253			−0.143127	+	0.989704i	$0.545716\pi$
$198$			3.56277e14i			5.91285i
$199$	2.33453e13			0.375908			0.187954	−	0.982178i	$-0.439814\pi$
$199$	2.33453e13			0.375908			0.187954	+	0.982178i	$0.439814\pi$
$200$		−	9.99539e13i		−	1.56178i
$201$		−	2.17093e13i		−	0.329208i
$202$	−6.86688e12			−0.101077
$203$	−1.03943e14			−1.48531
$204$	2.06116e14			2.85977
$205$		−	9.77504e13i		−	1.31703i
$206$	5.22877e13			0.684221
$207$	8.47047e13			1.07668
$208$		−	2.21395e13i		−	0.273393i
$209$			1.61831e14i			1.94171i
$210$	6.66056e14			7.76595
$211$		−	1.15953e14i		−	1.31398i	−0.753901	−	0.656988i	$-0.771830\pi$
$211$		−	1.15953e14i		−	1.31398i	0.753901	−	0.656988i	$-0.228170\pi$
$212$			2.46429e14i			2.71441i
$213$			2.48140e14i			2.65717i
$214$	1.42935e14			1.48818
$215$	−5.81285e13			−0.588516
$216$		−	3.84683e14i		−	3.78775i
$217$	−4.73783e12			−0.0453755
$218$		−	5.23787e13i		−	0.487995i
$219$		−	2.85407e14i		−	2.58702i
$220$			4.09658e14i			3.61314i
$221$		−	8.38914e13i		−	0.720052i
$222$			3.73653e14i			3.12141i
$223$		−	1.34530e14i		−	1.09393i	−0.837155	−	0.546965i	$-0.815783\pi$
$223$		−	1.34530e14i		−	1.09393i	0.837155	−	0.546965i	$-0.184217\pi$
$224$		−	1.48241e14i		−	1.17350i
$225$	−4.19015e14			−3.22949
$226$			1.20206e14i			0.902143i
$227$	−1.74227e14			−1.27339			−0.636693	−	0.771117i	$-0.719698\pi$
$227$	−1.74227e14			−1.27339			−0.636693	+	0.771117i	$0.719698\pi$
$228$		−	6.60842e14i		−	4.70423i
$229$	−1.26599e14			−0.877843			−0.438922	−	0.898525i	$-0.644639\pi$
$229$	−1.26599e14			−0.877843			−0.438922	+	0.898525i	$0.644639\pi$
$230$	1.52876e14			1.03270
$231$	−6.51584e14			−4.28843
$232$			1.76350e14i			1.13096i
$233$		−	2.61820e14i		−	1.63632i	−0.574992	−	0.818159i	$-0.694995\pi$
$233$		−	2.61820e14i		−	1.63632i	0.574992	−	0.818159i	$-0.305005\pi$
$234$	−5.92147e14			−3.60690
$235$	5.61545e13			0.333409
$236$	−4.37098e14			−2.52992
$237$			2.26537e14i			1.27835i
$238$			4.27024e14i			2.34958i
$239$		−	2.30158e14i		−	1.23492i	−0.786603	−	0.617459i	$-0.788162\pi$
$239$		−	2.30158e14i		−	1.23492i	0.786603	−	0.617459i	$-0.211838\pi$
$240$		−	1.77116e14i		−	0.926812i
$241$	3.38033e14			1.72527			0.862635	−	0.505827i	$-0.168813\pi$
$241$	3.38033e14			1.72527			0.862635	+	0.505827i	$0.168813\pi$
$242$		−	2.95622e14i		−	1.47179i
$243$	−6.00494e14			−2.91656
$244$	4.52465e14			2.14410
$245$			5.55060e14i			2.56651i
$246$		−	6.12934e14i		−	2.76569i
$247$	−2.68970e14			−1.18446
$248$			8.03824e12i			0.0345502i
$249$	−1.63218e14	+	4.21283e14i	−0.684814	+	1.76758i
$250$	−1.48977e14			−0.610211
$251$			2.31480e13i			0.0925703i	0.998928	+	0.0462852i	$0.0147383\pi$
$251$			2.31480e13i			0.0925703i	−0.998928	+	0.0462852i	$0.985262\pi$
$252$	1.92028e15			7.49829
$253$	−1.49555e14			−0.570266
$254$			5.69501e14i			2.12076i
$255$		−	6.71134e14i		−	2.44100i
$256$	−4.12738e14			−1.46634
$257$		−	3.84106e14i		−	1.33307i	−0.745474	−	0.666534i	$-0.767777\pi$
$257$		−	3.84106e14i		−	1.33307i	0.745474	−	0.666534i	$-0.232223\pi$
$258$	−3.64489e14			−1.23585
$259$	−4.93186e14			−1.63385
$260$	−6.80868e14			−2.20406
$261$	7.39274e14			2.33864
$262$		−	3.64992e14i		−	1.12843i
$263$			4.32764e14i			1.30773i	0.756613	+	0.653863i	$0.226853\pi$
$263$			4.32764e14i			1.30773i	−0.756613	+	0.653863i	$0.773147\pi$
$264$			1.10548e15i			3.26534i
$265$	8.02396e14			2.31693
$266$	1.36911e15			3.86499
$267$			7.24697e14i			2.00027i
$268$		−	1.12962e14i		−	0.304877i
$269$			1.56346e14i			0.412643i	0.978484	+	0.206321i	$0.0661492\pi$
$269$			1.56346e14i			0.412643i	−0.978484	+	0.206321i	$0.933851\pi$
$270$	−2.91049e15			−7.51248
$271$			1.36163e14i			0.343750i	0.985119	+	0.171875i	$0.0549825\pi$
$271$			1.36163e14i			0.343750i	−0.985119	+	0.171875i	$0.945018\pi$
$272$	1.13554e14			0.280406
$273$		−	1.08296e15i		−	2.61599i
$274$	1.16562e15			2.75458
$275$	7.39814e14			1.71051
$276$	6.10712e14			1.38160
$277$	−1.45143e14			−0.321304			−0.160652	−	0.987011i	$-0.551360\pi$
$277$	−1.45143e14			−0.321304			−0.160652	+	0.987011i	$0.551360\pi$
$278$	2.99664e14			0.649181
$279$	3.36970e13			0.0714440
$280$	1.49153e15			3.09517
$281$			2.33651e13i			0.0474603i	0.999718	+	0.0237301i	$0.00755425\pi$
$281$			2.33651e13i			0.0474603i	−0.999718	+	0.0237301i	$0.992446\pi$
$282$	3.52111e14			0.700140
$283$		−	2.30838e14i		−	0.449353i	−0.974433	−	0.224677i	$-0.927867\pi$
$283$		−	2.30838e14i		−	0.449353i	0.974433	−	0.224677i	$-0.0721326\pi$
$284$			1.29117e15i			2.46079i
$285$	−2.15177e15			−4.01537
$286$	1.04550e15			1.91041
$287$	8.09013e14			1.44765
$288$			1.05434e15i			1.84768i
$289$	−1.52342e14			−0.261477
$290$	1.33425e15			2.24311
$291$			1.04117e15i			1.71460i
$292$		−	1.48509e15i		−	2.39583i
$293$	1.00193e15			1.58354			0.791771	−	0.610818i	$-0.209159\pi$
$293$	1.00193e15			1.58354			0.791771	+	0.610818i	$0.209159\pi$
$294$			3.48045e15i			5.38953i
$295$			1.42323e15i			2.15946i
$296$			8.36742e14i			1.24406i
$297$	2.84725e15			4.14846
$298$	−1.34057e13			−0.0191421
$299$		−	2.48566e14i		−	0.347868i
$300$	−3.02105e15			−4.14411
$301$		−	4.81089e14i		−	0.646884i
$302$			1.01589e13i			0.0133908i
$303$			8.93209e13i			0.115424i
$304$		−	3.64072e14i		−	0.461259i
$305$		−	1.47327e15i		−	1.83014i
$306$		−	3.03713e15i		−	3.69943i
$307$			7.43443e14i			0.888010i	0.896024	+	0.444005i	$0.146443\pi$
$307$			7.43443e14i			0.888010i	−0.896024	+	0.444005i	$0.853557\pi$
$308$	−3.39046e15			−3.97149
$309$		−	6.80132e14i		−	0.781344i
$310$	6.08168e13			0.0685257
$311$			1.49691e15i			1.65437i	0.561931	+	0.827184i	$0.310059\pi$
$311$			1.49691e15i			1.65437i	−0.561931	+	0.827184i	$0.689941\pi$
$312$	−1.83736e15			−1.99189
$313$	−1.07703e15			−1.14541			−0.572707	−	0.819760i	$-0.694107\pi$
$313$	−1.07703e15			−1.14541			−0.572707	+	0.819760i	$0.694107\pi$
$314$	6.06319e14			0.632591
$315$		−	6.25264e15i		−	6.40029i
$316$			1.17877e15i			1.18387i
$317$	−9.94300e14			−0.979855			−0.489927	−	0.871763i	$-0.662977\pi$
$317$	−9.94300e14			−0.979855			−0.489927	+	0.871763i	$0.662977\pi$
$318$	5.03134e15			4.86543
$319$	−1.30526e15			−1.23867
$320$			2.42787e15i			2.26113i
$321$		−	1.85923e15i		−	1.69943i
$322$			1.26525e15i			1.13512i
$323$		−	1.37955e15i		−	1.21485i
$324$	−6.36032e15			−5.49805
$325$			1.22960e15i			1.04343i
$326$	−8.19247e13			−0.0682510
$327$	−6.81315e14			−0.557265
$328$		−	1.37258e15i		−	1.10228i
$329$			4.64752e14i			0.366476i
$330$	8.36400e15			6.47635
$331$		−	1.94740e15i		−	1.48077i	−0.672182	−	0.740386i	$-0.734643\pi$
$331$		−	1.94740e15i		−	1.48077i	0.672182	−	0.740386i	$-0.265357\pi$
$332$	−8.49291e14	+	2.19211e15i	−0.634203	+	1.63694i
$333$	3.50769e15			2.57251
$334$		−	1.52873e15i		−	1.10117i
$335$	−3.67817e14			−0.260233
$336$	1.46587e15			1.01873
$337$		−	1.45327e15i		−	0.992123i	−0.868287	−	0.496062i	$-0.834779\pi$
$337$		−	1.45327e15i		−	0.992123i	0.868287	−	0.496062i	$-0.165221\pi$
$338$		−	7.37489e14i		−	0.494601i
$339$	1.56358e15			1.03020
$340$		−	3.49218e15i		−	2.26060i
$341$	−5.94954e13			−0.0378405
$342$	−9.73754e15			−6.08545
$343$	−1.91176e15			−1.17400
$344$	−8.16219e14			−0.492557
$345$		−	1.98854e15i		−	1.17929i
$346$			2.46786e15i			1.43835i
$347$			1.47684e15i			0.845974i	0.906136	+	0.422987i	$0.139018\pi$
$347$			1.47684e15i			0.845974i	−0.906136	+	0.422987i	$0.860982\pi$
$348$	5.33009e15			3.00095
$349$	4.21993e14			0.233535			0.116768	−	0.993159i	$-0.462747\pi$
$349$	4.21993e14			0.233535			0.116768	+	0.993159i	$0.462747\pi$
$350$		−	6.25892e15i		−	3.40480i
$351$			4.73225e15i			2.53061i
$352$		−	1.86154e15i		−	0.978627i
$353$	2.79612e15			1.44513			0.722565	−	0.691303i	$-0.242963\pi$
$353$	2.79612e15			1.44513			0.722565	+	0.691303i	$0.242963\pi$
$354$			8.92425e15i			4.53474i
$355$	4.20419e15			2.10045
$356$			3.77089e15i			1.85244i
$357$	5.55451e15			2.68310
$358$	−4.63728e15			−2.20275
$359$	−1.04749e15			−0.489311			−0.244656	−	0.969610i	$-0.578675\pi$
$359$	−1.04749e15			−0.489311			−0.244656	+	0.969610i	$0.578675\pi$
$360$	−1.06083e16			−4.87337
$361$	−2.20975e15			−0.998387
$362$	−8.02189e14			−0.356472
$363$	−3.84531e15			−1.68070
$364$		−	5.63508e15i		−	2.42266i
$365$	−4.83560e15			−2.04500
$366$		−	9.23799e15i		−	3.84318i
$367$		−	2.48567e14i		−	0.101730i	−0.998706	−	0.0508649i	$-0.983802\pi$
$367$		−	2.48567e14i		−	0.101730i	0.998706	−	0.0508649i	$-0.0161978\pi$
$368$	3.36454e14			0.135469
$369$	−5.75395e15			−2.27933
$370$	6.33074e15			2.46743
$371$			6.64088e15i			2.54673i
$372$	2.42951e14			0.0916773
$373$	−8.23484e14			−0.305775			−0.152888	−	0.988244i	$-0.548857\pi$
$373$	−8.23484e14			−0.305775			−0.152888	+	0.988244i	$0.548857\pi$
$374$			5.36236e15i			1.95942i
$375$			1.93782e15i			0.696829i
$376$	7.88501e14			0.279046
$377$		−	2.16940e15i		−	0.755600i
$378$		−	2.40881e16i		−	8.25756i
$379$			1.88544e15i			0.636177i	0.948061	+	0.318088i	$0.103041\pi$
$379$			1.88544e15i			0.636177i	−0.948061	+	0.318088i	$0.896959\pi$
$380$	−1.11965e16			−3.71862
$381$	7.40778e15			2.42180
$382$		−	3.32418e15i		−	1.06980i
$383$	−1.86680e15			−0.591432			−0.295716	−	0.955276i	$-0.595558\pi$
$383$	−1.86680e15			−0.591432			−0.295716	+	0.955276i	$0.595558\pi$
$384$			1.08935e16i			3.39767i
$385$			1.10397e16i			3.38994i
$386$			3.87471e15i			1.17143i
$387$			3.42166e15i			1.01852i
$388$			5.41762e15i			1.58788i
$389$		−	6.04169e15i		−	1.74365i	−0.489813	−	0.871827i	$-0.662935\pi$
$389$		−	6.04169e15i		−	1.74365i	0.489813	−	0.871827i	$-0.337065\pi$
$390$			1.39013e16i			3.95065i
$391$	1.27490e15			0.356792
$392$			7.79396e15i			2.14804i
$393$	−4.74763e15			−1.28861
$394$			1.77758e15i			0.475172i
$395$	3.83818e15			1.01051
$396$	2.41140e16			6.25314
$397$	2.78415e15			0.711130			0.355565	−	0.934652i	$-0.384289\pi$
$397$	2.78415e15			0.711130			0.355565	+	0.934652i	$0.384289\pi$
$398$		−	2.48016e15i		−	0.623996i
$399$		−	1.78087e16i		−	4.41362i
$400$	−1.66436e15			−0.406338
$401$	2.81275e15			0.676495			0.338247	−	0.941057i	$-0.390166\pi$
$401$	2.81275e15			0.676495			0.338247	+	0.941057i	$0.390166\pi$
$402$	−2.30636e15			−0.546475
$403$		−	9.88838e13i		−	0.0230831i
$404$			4.64773e14i			0.106894i
$405$			2.07098e16i			4.69295i
$406$			1.10427e16i			2.46558i
$407$	−6.19319e15			−1.36254
$408$		−	9.42383e15i		−	2.04299i
$409$	1.16698e15			0.249301			0.124651	−	0.992201i	$-0.460219\pi$
$409$	1.16698e15			0.249301			0.124651	+	0.992201i	$0.460219\pi$
$410$	−1.03848e16			−2.18623
$411$		−	1.51618e16i		−	3.14558i
$412$		−	3.53900e15i		−	0.723598i
$413$	−1.17791e16			−2.37363
$414$		−	8.99887e15i		−	1.78725i
$415$	7.13772e15	+	2.76538e15i	1.39724	+	0.541334i
$416$	3.09396e15			0.596974
$417$		−	3.89787e15i		−	0.741330i
$418$	1.71926e16			3.22318
$419$	−8.14650e15			−1.50552			−0.752760	−	0.658295i	$-0.771278\pi$
$419$	−8.14650e15			−1.50552			−0.752760	+	0.658295i	$0.771278\pi$
$420$		−	4.50808e16i		−	8.21289i
$421$			4.40063e15i			0.790354i	0.918605	+	0.395177i	$0.129317\pi$
$421$			4.40063e15i			0.790354i	−0.918605	+	0.395177i	$0.870683\pi$
$422$	−1.23186e16			−2.18116
$423$		−	3.30546e15i		−	0.577019i
$424$	1.12670e16			1.93915
$425$	−6.30664e15			−1.07020
$426$	2.63619e16			4.41083
$427$	1.21932e16			2.01165
$428$		−	9.67433e15i		−	1.57383i
$429$		−	1.35993e16i		−	2.18158i
$430$			6.17546e15i			0.976919i
$431$	3.15832e15			0.492711			0.246355	−	0.969180i	$-0.420767\pi$
$431$	3.15832e15			0.492711			0.246355	+	0.969180i	$0.420767\pi$
$432$	−6.40547e15			−0.985482
$433$			1.04540e15i			0.158618i	0.996850	+	0.0793092i	$0.0252714\pi$
$433$			1.04540e15i			0.158618i	−0.996850	+	0.0793092i	$0.974729\pi$
$434$			5.03339e14i			0.0753220i
$435$		−	1.73553e16i		−	2.56151i
$436$	−3.54516e15			−0.516080
$437$		−	4.08754e15i		−	0.586912i
$438$	−3.03212e16			−4.29439
$439$			6.54330e15i			0.914134i	0.889432	+	0.457067i	$0.151100\pi$
$439$			6.54330e15i			0.914134i	−0.889432	+	0.457067i	$0.848900\pi$
$440$	1.87300e16			2.58120
$441$	3.26729e16			4.44177
$442$	−8.91247e15			−1.19527
$443$	−2.44043e15			−0.322883			−0.161441	−	0.986882i	$-0.551614\pi$
$443$	−2.44043e15			−0.322883			−0.161441	+	0.986882i	$0.551614\pi$
$444$	2.52901e16			3.30105
$445$	1.22784e16			1.58118
$446$	−1.42922e16			−1.81589
$447$			1.74374e14i			0.0218593i
$448$	−2.00938e16			−2.48539
$449$		−	8.52137e15i		−	1.04000i	−0.854168	−	0.519998i	$-0.825933\pi$
$449$		−	8.52137e15i		−	1.04000i	0.854168	−	0.519998i	$-0.174067\pi$
$450$			4.45154e16i			5.36087i
$451$	1.01592e16			1.20726
$452$	8.13593e15			0.954062
$453$	1.32142e14			0.0152916
$454$			1.85096e16i			2.11379i
$455$	−1.83484e16			−2.06790
$456$	−3.02143e16			−3.36066
$457$		−	1.25117e15i		−	0.137347i	−0.997639	−	0.0686733i	$-0.978123\pi$
$457$		−	1.25117e15i		−	0.137347i	0.997639	−	0.0686733i	$-0.0218766\pi$
$458$			1.34496e16i			1.45719i
$459$	−2.42718e16			−2.59553
$460$		−	1.03472e16i		−	1.09213i
$461$			3.09453e14i			0.0322396i	0.999870	+	0.0161198i	$0.00513131\pi$
$461$			3.09453e14i			0.0322396i	−0.999870	+	0.0161198i	$0.994869\pi$
$462$			6.92231e16i			7.11867i
$463$	−1.16502e16			−1.18262			−0.591311	−	0.806444i	$-0.701389\pi$
$463$	−1.16502e16			−1.18262			−0.591311	+	0.806444i	$0.701389\pi$
$464$	2.93646e15			0.294250
$465$		−	7.91074e14i		−	0.0782527i
$466$	−2.78153e16			−2.71624
$467$			5.84519e15i			0.563504i	0.959487	+	0.281752i	$0.0909155\pi$
$467$			5.84519e15i			0.563504i	−0.959487	+	0.281752i	$0.909084\pi$
$468$			4.00784e16i			3.81448i
$469$		−	3.04417e15i		−	0.286043i
$470$		−	5.96575e15i		−	0.553449i
$471$		−	7.88669e15i		−	0.722386i
$472$			1.99846e16i			1.80735i
$473$		−	6.04129e15i		−	0.539464i
$474$	2.40669e16			2.12202
$475$			2.02201e16i			1.76044i
$476$	2.89024e16			2.48480
$477$		−	4.72320e16i		−	4.00983i
$478$	−2.44515e16			−2.04993
$479$	−1.35391e16			−1.12092			−0.560461	−	0.828181i	$-0.689376\pi$
$479$	−1.35391e16			−1.12092			−0.560461	+	0.828181i	$0.689376\pi$
$480$	2.47518e16			2.02376
$481$		−	1.02933e16i		−	0.831162i
$482$		−	3.59120e16i		−	2.86390i
$483$	1.64578e16			1.29625
$484$	−2.00087e16			−1.55649
$485$	1.76403e16			1.35536
$486$			6.37953e16i			4.84140i
$487$			2.03508e16i			1.52548i	0.646702	+	0.762742i	$0.276148\pi$
$487$			2.03508e16i			1.52548i	−0.646702	+	0.762742i	$0.723852\pi$
$488$		−	2.06871e16i		−	1.53173i
$489$			1.06563e15i			0.0779390i
$490$	5.89686e16			4.26034
$491$		−	1.14308e16i		−	0.815807i	−0.913025	−	0.407903i	$-0.866260\pi$
$491$		−	1.14308e16i		−	0.815807i	0.913025	−	0.407903i	$-0.133740\pi$
$492$	−4.14854e16			−2.92485
$493$	1.11269e16			0.774983
$494$			2.85748e16i			1.96617i
$495$		−	7.85176e16i		−	5.33747i
$496$	1.33847e14			0.00898915
$497$			3.47952e16i			2.30877i
$498$	4.47564e16	+	1.73400e16i	2.93413	+	1.13677i
$499$	−1.22782e16			−0.795304			−0.397652	−	0.917536i	$-0.630175\pi$
$499$	−1.22782e16			−0.795304			−0.397652	+	0.917536i	$0.630175\pi$
$500$			1.00833e16i			0.645329i
$501$	−1.98850e16			−1.25747
$502$	2.45920e15			0.153664
$503$			9.61656e15i			0.593761i	0.954915	+	0.296881i	$0.0959463\pi$
$503$			9.61656e15i			0.593761i	−0.954915	+	0.296881i	$0.904054\pi$
$504$		−	8.77973e16i		−	5.35671i
$505$	1.51335e15			0.0912410
$506$			1.58884e16i			0.946624i
$507$	−9.59288e15			−0.564809
$508$	3.85457e16			2.24282
$509$	−2.57200e15			−0.147898			−0.0739492	−	0.997262i	$-0.523560\pi$
$509$	−2.57200e15			−0.147898			−0.0739492	+	0.997262i	$0.523560\pi$
$510$	−7.13000e16			−4.05199
$511$		−	4.00210e16i		−	2.24782i
$512$			1.15595e16i			0.641683i
$513$			7.78193e16i			4.26956i
$514$	−4.08067e16			−2.21286
$515$	−1.15233e16			−0.617640
$516$			2.46698e16i			1.30697i
$517$			5.83613e15i			0.305620i
$518$			5.23952e16i			2.71214i
$519$	3.21006e16			1.64251
$520$			3.11300e16i			1.57456i
$521$	3.25188e16			1.62596			0.812978	−	0.582295i	$-0.197845\pi$
$521$	3.25188e16			1.62596			0.812978	+	0.582295i	$0.197845\pi$
$522$		−	7.85391e16i		−	3.88207i
$523$	1.17650e16			0.574884			0.287442	−	0.957798i	$-0.407195\pi$
$523$	1.17650e16			0.574884			0.287442	+	0.957798i	$0.407195\pi$
$524$	−2.47039e16			−1.19338
$525$	−8.14128e16			−3.88810
$526$	4.59761e16			2.17079
$527$	5.07177e14			0.0236753
$528$	1.84077e16			0.849564
$529$	−1.81372e16			−0.827628
$530$		−	8.52451e16i		−	3.84604i
$531$	8.37769e16			3.73729
$532$		−	9.26658e16i		−	4.08743i
$533$			1.68850e16i			0.736440i
$534$	7.69905e16			3.32039
$535$	−3.15006e16			−1.34337
$536$	−5.16475e15			−0.217801
$537$			6.03194e16i			2.51543i
$538$	1.66100e16			0.684975
$539$	−5.76873e16			−2.35260
$540$			1.96991e17i			7.94483i
$541$		−	3.89020e16i		−	1.55163i	−0.630960	−	0.775815i	$-0.717339\pi$
$541$		−	3.89020e16i		−	1.55163i	0.630960	−	0.775815i	$-0.282661\pi$
$542$	1.44657e16			0.570614
$543$			1.04345e16i			0.407072i
$544$			1.58690e16i			0.612288i
$545$			1.15434e16i			0.440509i
$546$	−1.15052e17			−4.34247
$547$	1.43689e15			0.0536413			0.0268206	−	0.999640i	$-0.491462\pi$
$547$	1.43689e15			0.0536413			0.0268206	+	0.999640i	$0.491462\pi$
$548$		−	7.88932e16i		−	2.91311i
$549$	−8.67222e16			−3.16735
$550$		−	7.85964e16i		−	2.83940i
$551$		−	3.56747e16i		−	1.27482i
$552$		−	2.79223e16i		−	0.987000i
$553$			3.17660e16i			1.11074i
$554$			1.54197e16i			0.533355i
$555$		−	8.23470e16i		−	2.81767i
$556$		−	2.02822e16i		−	0.686542i
$557$	1.22864e16			0.411427			0.205713	−	0.978612i	$-0.434049\pi$
$557$	1.22864e16			0.411427			0.205713	+	0.978612i	$0.434049\pi$
$558$		−	3.57990e15i		−	0.118595i
$559$	1.00409e16			0.329079
$560$		−	2.48360e16i		−	0.805291i
$561$	6.97509e16			2.23755
$562$	2.48227e15			0.0787827
$563$	−5.97075e16			−1.87490			−0.937450	−	0.348119i	$-0.886821\pi$
$563$	−5.97075e16			−1.87490			−0.937450	+	0.348119i	$0.886821\pi$
$564$		−	2.38320e16i		−	0.740434i
$565$		−	2.64914e16i		−	0.814356i
$566$	−2.45238e16			−0.745914
$567$	−1.71401e17			−5.15840
$568$	5.90337e16			1.75797
$569$		−	3.05643e16i		−	0.900619i	−0.892872	−	0.450310i	$-0.851314\pi$
$569$		−	3.05643e16i		−	0.900619i	0.892872	−	0.450310i	$-0.148686\pi$
$570$			2.28600e17i			6.66540i
$571$			1.08853e16i			0.314069i	0.987593	+	0.157035i	$0.0501934\pi$
$571$			1.08853e16i			0.314069i	−0.987593	+	0.157035i	$0.949807\pi$
$572$		−	7.07626e16i		−	2.02035i
$573$	−4.32392e16			−1.22166
$574$		−	8.59480e16i		−	2.40306i
$575$	−1.86863e16			−0.517030
$576$	1.42914e17			3.91326
$577$			6.90950e16i			1.87237i	0.351507	+	0.936185i	$0.385669\pi$
$577$			6.90950e16i			1.87237i	−0.351507	+	0.936185i	$0.614331\pi$
$578$			1.61845e16i			0.434044i
$579$	5.04002e16			1.33771
$580$		−	9.03066e16i		−	2.37220i
$581$	−2.28871e16	+	5.90740e16i	−0.595024	+	1.53582i
$582$	1.10612e17			2.84619
$583$			8.33930e16i			2.12382i
$584$	−6.78998e16			−1.71156
$585$	1.30499e17			3.25592
$586$		−	1.06443e17i		−	2.62863i
$587$		−	4.11866e16i		−	1.00676i	−0.864064	−	0.503381i	$-0.832089\pi$
$587$		−	4.11866e16i		−	1.00676i	0.864064	−	0.503381i	$-0.167911\pi$
$588$	2.35568e17			5.69971
$589$		−	1.62609e15i		−	0.0389451i
$590$	1.51202e17			3.58464
$591$	2.31218e16			0.542621
$592$	1.39328e16			0.323675
$593$	−5.86269e16			−1.34824			−0.674122	−	0.738620i	$-0.735478\pi$
$593$	−5.86269e16			−1.34824			−0.674122	+	0.738620i	$0.735478\pi$
$594$		−	3.02487e17i		−	6.88633i
$595$		−	9.41091e16i		−	2.12095i
$596$			9.07339e14i			0.0202438i
$597$	−3.22607e16			−0.712571
$598$	−2.64072e16			−0.577451
$599$		−	3.62057e16i		−	0.783820i	−0.920004	−	0.391910i	$-0.871815\pi$
$599$		−	3.62057e16i		−	0.783820i	0.920004	−	0.391910i	$-0.128185\pi$
$600$			1.38126e17i			2.96051i
$601$		−	4.37601e15i		−	0.0928607i	−0.998922	−	0.0464303i	$-0.985215\pi$
$601$		−	4.37601e15i		−	0.0928607i	0.998922	−	0.0464303i	$-0.0147845\pi$
$602$	−5.11100e16			−1.07381
$603$			2.16511e16i			0.450376i
$604$	6.87589e14			0.0141614
$605$			6.51503e16i			1.32857i
$606$	9.48928e15			0.191601
$607$	8.50892e16			1.70115			0.850575	−	0.525855i	$-0.176254\pi$
$607$	8.50892e16			1.70115			0.850575	+	0.525855i	$0.176254\pi$
$608$	5.08786e16			1.00719
$609$	1.43638e17			2.81556
$610$	−1.56518e17			−3.03797
$611$	−9.69989e15			−0.186432
$612$	−2.05563e17			−3.91234
$613$		−	1.53299e16i		−	0.288920i	−0.989511	−	0.144460i	$-0.953856\pi$
$613$		−	1.53299e16i		−	0.288920i	0.989511	−	0.144460i	$-0.0461445\pi$
$614$	7.89821e16			1.47407
$615$			1.35080e17i			2.49656i
$616$			1.55015e17i			2.83720i
$617$	−9.51917e16			−1.72539			−0.862697	−	0.505721i	$-0.831226\pi$
$617$	−9.51917e16			−1.72539			−0.862697	+	0.505721i	$0.831226\pi$
$618$	−7.22559e16			−1.29701
$619$	3.16757e16			0.563097			0.281548	−	0.959547i	$-0.409152\pi$
$619$	3.16757e16			0.563097			0.281548	+	0.959547i	$0.409152\pi$
$620$		−	4.11628e15i		−	0.0724694i
$621$	−7.19161e16			−1.25394
$622$	1.59028e17			2.74620
$623$			1.01620e17i			1.73800i
$624$			3.05943e16i			0.518243i
$625$	−4.13950e16			−0.694492
$626$			1.14422e17i			1.90135i
$627$		−	2.23633e17i		−	3.68070i
$628$		−	4.10376e16i		−	0.668997i
$629$	5.27947e16			0.852484
$630$	−6.64269e17			−10.6243
$631$			9.93285e16i			1.57361i	0.617201	+	0.786806i	$0.288267\pi$
$631$			9.93285e16i			1.57361i	−0.617201	+	0.786806i	$0.711733\pi$
$632$	5.38943e16			0.845747
$633$			1.60235e17i			2.49077i
$634$			1.05633e17i			1.62653i
$635$		−	1.25509e17i		−	1.91439i
$636$		−	3.40538e17i		−	5.14544i
$637$		−	9.58787e16i		−	1.43511i
$638$			1.38669e17i			2.05615i
$639$		−	2.47474e17i		−	3.63517i
$640$	1.84567e17			2.68580
$641$			6.23672e16i			0.899100i	0.893255	+	0.449550i	$0.148416\pi$
$641$			6.23672e16i			0.899100i	−0.893255	+	0.449550i	$0.851584\pi$
$642$	−1.97521e17			−2.82100
$643$			3.15179e16i			0.445955i	0.974824	+	0.222978i	$0.0715777\pi$
$643$			3.15179e16i			0.445955i	−0.974824	+	0.222978i	$0.928422\pi$
$644$	8.56364e16			1.20045
$645$	8.03273e16			1.11559
$646$	−1.46561e17			−2.01661
$647$			4.24073e16i			0.578116i	0.957312	+	0.289058i	$0.0933421\pi$
$647$			4.24073e16i			0.578116i	−0.957312	+	0.289058i	$0.906658\pi$
$648$			2.90800e17i			3.92775i
$649$	−1.47917e17			−1.97947
$650$	1.30631e17			1.73207
$651$	6.54717e15			0.0860138
$652$			5.54493e15i			0.0721789i
$653$		−	1.48570e16i		−	0.191625i	−0.995399	−	0.0958123i	$-0.969455\pi$
$653$		−	1.48570e16i		−	0.191625i	0.995399	−	0.0958123i	$-0.0305448\pi$
$654$			7.23817e16i			0.925043i
$655$			8.04383e16i			1.01863i
$656$	−2.28552e16			−0.286788
$657$			2.84642e17i			3.53921i
$658$	4.93744e16			0.608340
$659$	1.34760e17			1.64531			0.822656	−	0.568540i	$-0.192491\pi$
$659$	1.34760e17			1.64531			0.822656	+	0.568540i	$0.192491\pi$
$660$		−	5.66103e17i		−	6.84907i
$661$		−	1.40152e17i		−	1.68032i	−0.542339	−	0.840160i	$-0.682461\pi$
$661$		−	1.40152e17i		−	1.68032i	0.542339	−	0.840160i	$-0.317539\pi$
$662$	−2.06889e17			−2.45804
$663$			1.15929e17i			1.36493i
$664$	1.00225e17	+	3.88304e16i	1.16942	+	0.453068i
$665$	−3.01729e17			−3.48889
$666$		−	3.72651e17i		−	4.27028i
$667$	3.29685e16			0.374407
$668$	−1.03470e17			−1.16454
$669$			1.85906e17i			2.07365i
$670$			3.90762e16i			0.431980i
$671$	1.53117e17			1.67760
$672$			2.04854e17i			2.22448i
$673$	7.91646e16			0.852002			0.426001	−	0.904723i	$-0.359922\pi$
$673$	7.91646e16			0.852002			0.426001	+	0.904723i	$0.359922\pi$
$674$	−1.54392e17			−1.64690
$675$	3.55753e17			3.76119
$676$	−4.99157e16			−0.523066
$677$		−	1.42880e17i		−	1.48402i	−0.670388	−	0.742011i	$-0.733872\pi$
$677$		−	1.42880e17i		−	1.48402i	0.670388	−	0.742011i	$-0.266128\pi$
$678$		−	1.66112e17i		−	1.71010i
$679$			1.45997e17i			1.48979i
$680$	−1.59666e17			−1.61495
$681$	2.40763e17			2.41383
$682$			6.32068e15i			0.0628142i
$683$		−	1.60079e17i		−	1.57692i	−0.615083	−	0.788462i	$-0.710878\pi$
$683$		−	1.60079e17i		−	1.57692i	0.615083	−	0.788462i	$-0.289122\pi$
$684$			6.59069e17i			6.43567i
$685$	−2.56884e17			−2.48653
$686$			2.03102e17i			1.94881i
$687$	1.74946e17			1.66404
$688$			1.35911e16i			0.128152i
$689$	−1.38603e17			−1.29555
$690$	−2.11259e17			−1.95758
$691$	−4.77541e15			−0.0438674			−0.0219337	−	0.999759i	$-0.506982\pi$
$691$	−4.77541e15			−0.0438674			−0.0219337	+	0.999759i	$0.506982\pi$
$692$	1.67033e17			1.52112
$693$	6.49836e17			5.86684
$694$	1.56897e17			1.40429
$695$	−6.60409e16			−0.586009
$696$		−	2.43697e17i		−	2.14385i
$697$	−8.66033e16			−0.755332
$698$		−	4.48317e16i		−	0.387662i
$699$			3.61807e17i			3.10180i
$700$	−4.23624e17			−3.60074
$701$	5.70151e16			0.480487			0.240244	−	0.970713i	$-0.422773\pi$
$701$	5.70151e16			0.480487			0.240244	+	0.970713i	$0.422773\pi$
$702$	5.02745e17			4.20074
$703$		−	1.69268e17i		−	1.40231i
$704$	−2.52328e17			−2.07267
$705$	−7.75994e16			−0.632010
$706$		−	2.97054e17i		−	2.39887i
$707$			1.25249e16i			0.100290i
$708$	6.04022e17			4.79572
$709$		−	1.63753e17i		−	1.28918i	−0.764530	−	0.644588i	$-0.777029\pi$
$709$		−	1.63753e17i		−	1.28918i	0.764530	−	0.644588i	$-0.222971\pi$
$710$		−	4.46645e17i		−	3.48669i
$711$		−	2.25929e17i		−	1.74886i
$712$	1.72409e17			1.32337
$713$	1.50274e15			0.0114379
$714$		−	5.90101e17i		−	4.45387i
$715$	−2.30410e17			−1.72451
$716$			3.13867e17i			2.32952i
$717$			3.18053e17i			2.34091i
$718$			1.11284e17i			0.812243i
$719$			2.36075e17i			1.70874i	0.519663	+	0.854371i	$0.326058\pi$
$719$			2.36075e17i			1.70874i	−0.519663	+	0.854371i	$0.673942\pi$
$720$			1.76641e17i			1.26794i
$721$		−	9.53708e16i		−	0.678897i
$722$			2.34759e17i			1.65729i
$723$	−4.67125e17			−3.27042
$724$			5.42947e16i			0.376987i
$725$	−1.63088e17			−1.12303
$726$			4.08518e17i			2.78992i
$727$	−1.26500e17			−0.856809			−0.428404	−	0.903587i	$-0.640924\pi$
$727$	−1.26500e17			−0.856809			−0.428404	+	0.903587i	$0.640924\pi$
$728$	−2.57641e17			−1.73072
$729$	3.59737e17			2.39674
$730$			5.13726e17i			3.39464i
$731$			5.14997e16i			0.337521i
$732$	−6.25257e17			−4.06436
$733$	2.22957e17			1.43747			0.718734	−	0.695286i	$-0.244722\pi$
$733$	2.22957e17			1.43747			0.718734	+	0.695286i	$0.244722\pi$
$734$	−2.64073e16			−0.168868
$735$		−	7.67033e17i		−	4.86508i
$736$			4.70190e16i			0.295806i
$737$		−	3.82272e16i		−	0.238543i
$738$			6.11289e17i			3.78363i
$739$	5.14558e16			0.315913			0.157957	−	0.987446i	$-0.449509\pi$
$739$	5.14558e16			0.315913			0.157957	+	0.987446i	$0.449509\pi$
$740$		−	4.28485e17i		−	2.60943i
$741$	3.71687e17			2.24527
$742$	7.05515e17			4.22749
$743$			4.21882e16i			0.250760i	0.992109	+	0.125380i	$0.0400150\pi$
$743$			4.21882e16i			0.250760i	−0.992109	+	0.125380i	$0.959985\pi$
$744$		−	1.11080e16i		−	0.0654934i
$745$	2.95439e15			0.0172794
$746$			8.74854e16i			0.507578i
$747$	1.62780e17	−	4.20153e17i	0.936868	−	2.41815i
$748$	3.62942e17			2.07218
$749$		−	2.60709e17i		−	1.47661i
$750$	2.05871e17			1.15672
$751$	−1.42098e17			−0.792043			−0.396022	−	0.918241i	$-0.629609\pi$
$751$	−1.42098e17			−0.792043			−0.396022	+	0.918241i	$0.629609\pi$
$752$		−	1.31296e16i		−	0.0726011i
$753$		−	3.19881e16i		−	0.175476i
$754$	−2.30473e17			−1.25427
$755$		−	2.23886e15i		−	0.0120877i
$756$	−1.63036e18			−8.73279
$757$	−4.55834e16			−0.242232			−0.121116	−	0.992638i	$-0.538647\pi$
$757$	−4.55834e16			−0.242232			−0.121116	+	0.992638i	$0.538647\pi$
$758$	2.00306e17			1.05603
$759$	2.06669e17			1.08099
$760$			5.11916e17i			2.65654i
$761$			3.70781e17i			1.90902i	0.298182	+	0.954509i	$0.403620\pi$
$761$			3.70781e17i			1.90902i	−0.298182	+	0.954509i	$0.596380\pi$
$762$		−	7.86989e17i		−	4.02012i
$763$	−9.55367e16			−0.484198
$764$	−2.24991e17			−1.13137
$765$			6.69333e17i			3.33944i
$766$			1.98325e17i			0.981760i
$767$		−	2.45843e17i		−	1.20750i
$768$	5.70359e17			2.77959
$769$			1.45974e16i			0.0705860i	0.999377	+	0.0352930i	$0.0112364\pi$
$769$			1.45974e16i			0.0705860i	−0.999377	+	0.0352930i	$0.988764\pi$
$770$	1.17283e18			5.62720
$771$			5.30793e17i			2.52696i
$772$	2.62253e17			1.23884
$773$	−3.75320e17			−1.75924			−0.879619	−	0.475680i	$-0.842202\pi$
$773$	−3.75320e17			−1.75924			−0.879619	+	0.475680i	$0.842202\pi$
$774$	3.63511e17			1.69072
$775$	−7.43371e15			−0.0343080
$776$	2.47699e17			1.13437
$777$	6.81530e17			3.09712
$778$	−6.41858e17			−2.89442
$779$			2.77665e17i			1.24250i
$780$	9.40886e17			4.17801
$781$			4.36941e17i			1.92538i
$782$		−	1.35443e17i		−	0.592265i
$783$	−6.27660e17			−2.72366
$784$	1.29779e17			0.558868
$785$	−1.33623e17			−0.571034
$786$			5.04380e17i			2.13906i
$787$	−9.13785e16			−0.384588			−0.192294	−	0.981337i	$-0.561593\pi$
$787$	−9.13785e16			−0.384588			−0.192294	+	0.981337i	$0.561593\pi$
$788$	1.20312e17			0.502519
$789$		−	5.98033e17i		−	2.47893i
$790$		−	4.07761e17i		−	1.67742i
$791$	2.19251e17			0.895124
$792$		−	1.10252e18i		−	4.46718i
$793$			2.54486e17i			1.02335i
$794$		−	2.95782e17i		−	1.18045i
$795$	−1.10882e18			−4.39198
$796$	−1.67866e17			−0.659908
$797$			3.34659e17i			1.30573i	0.757476	+	0.652863i	$0.226432\pi$
$797$			3.34659e17i			1.30573i	−0.757476	+	0.652863i	$0.773568\pi$
$798$	−1.89196e18			−7.32647
$799$		−	4.97509e16i		−	0.191214i
$800$		−	2.32593e17i		−	0.887270i
$801$		−	7.22753e17i		−	2.73649i
$802$		−	2.98821e17i		−	1.12296i
$803$		−	5.02564e17i		−	1.87455i
$804$			1.56102e17i			0.577925i
$805$		−	2.78841e17i		−	1.02466i
$806$	−1.05052e16			−0.0383174
$807$		−	2.16054e17i		−	0.782205i
$808$	2.12499e16			0.0763639
$809$		−	5.71747e16i		−	0.203945i	−0.994787	−	0.101973i	$-0.967485\pi$
$809$		−	5.71747e16i		−	0.203945i	0.994787	−	0.101973i	$-0.0325154\pi$
$810$	2.20017e18			7.79017
$811$	3.32007e17			1.16687			0.583435	−	0.812160i	$-0.301708\pi$
$811$	3.32007e17			1.16687			0.583435	+	0.812160i	$0.301708\pi$
$812$	7.47406e17			2.60748
$813$		−	1.88162e17i		−	0.651612i
$814$			6.57953e17i			2.26177i
$815$	1.80548e16			0.0616095
$816$	−1.56919e17			−0.531538
$817$	1.65117e17			0.555212
$818$		−	1.23978e17i		−	0.413833i
$819$			1.08005e18i			3.57884i
$820$			7.02879e17i			2.31205i
$821$			1.91579e17i			0.625590i	0.949821	+	0.312795i	$0.101265\pi$
$821$			1.91579e17i			0.625590i	−0.949821	+	0.312795i	$0.898735\pi$
$822$	−1.61077e18			−5.22158
$823$			2.71007e17i			0.872132i	0.899915	+	0.436066i	$0.143628\pi$
$823$			2.71007e17i			0.872132i	−0.899915	+	0.436066i	$0.856372\pi$
$824$	−1.61807e17			−0.516932
$825$	−1.02234e18			−3.24245
$826$			1.25139e18i			3.94016i
$827$			1.24672e17i			0.389705i	0.980833	+	0.194852i	$0.0624228\pi$
$827$			1.24672e17i			0.389705i	−0.980833	+	0.194852i	$0.937577\pi$
$828$	−6.09073e17			−1.89011
$829$		−	2.15343e17i		−	0.663444i	−0.943377	−	0.331722i	$-0.892370\pi$
$829$		−	2.15343e17i		−	0.663444i	0.943377	−	0.331722i	$-0.107630\pi$
$830$	2.93788e17	−	7.58299e17i	0.898599	−	2.31938i
$831$	2.00571e17			0.609064
$832$		−	4.19380e17i		−	1.26435i
$833$	4.91763e17			1.47193
$834$	−4.14103e17			−1.23059
$835$			3.36908e17i			0.994013i
$836$		−	1.16365e18i		−	3.40868i
$837$	−2.86094e16			−0.0832064
$838$			8.65469e17i			2.49912i
$839$	6.24359e17			1.79004			0.895020	−	0.446026i	$-0.147161\pi$
$839$	6.24359e17			1.79004			0.895020	+	0.446026i	$0.147161\pi$
$840$	−2.06114e18			−5.86721
$841$	−6.60772e16			−0.186756
$842$	4.67514e17			1.31197
$843$		−	3.22881e16i		−	0.0899657i
$844$			8.33766e17i			2.30669i
$845$			1.62530e17i			0.446472i
$846$	−3.51166e17			−0.957835
$847$	−5.39204e17			−1.46034
$848$		−	1.87609e17i		−	0.504521i
$849$			3.18993e17i			0.851794i
$850$			6.70006e17i			1.77650i
$851$	1.56428e17			0.411848
$852$		−	1.78426e18i		−	4.66467i
$853$	6.15974e17			1.59907			0.799537	−	0.600617i	$-0.205078\pi$
$853$	6.15974e17			1.59907			0.799537	+	0.600617i	$0.205078\pi$
$854$		−	1.29539e18i		−	3.33928i
$855$	2.14599e18			5.49328
$856$	−4.42320e17			−1.12433
$857$	2.70118e17			0.681819			0.340909	−	0.940096i	$-0.389265\pi$
$857$	2.70118e17			0.681819			0.340909	+	0.940096i	$0.389265\pi$
$858$	−1.44476e18			−3.62137
$859$	1.79763e17			0.447446			0.223723	−	0.974653i	$-0.428179\pi$
$859$	1.79763e17			0.447446			0.223723	+	0.974653i	$0.428179\pi$
$860$	4.17975e17			1.03314
$861$	−1.11797e18			−2.74417
$862$		−	3.35534e17i		−	0.817885i
$863$	6.39052e16			0.154693			0.0773466	−	0.997004i	$-0.475355\pi$
$863$	6.39052e16			0.154693			0.0773466	+	0.997004i	$0.475355\pi$
$864$		−	8.95157e17i		−	2.15187i
$865$		−	5.43875e17i		−	1.29838i
$866$	1.11061e17			0.263302
$867$	2.10520e17			0.495655
$868$	3.40676e16			0.0796569
$869$			3.98901e17i			0.926290i
$870$	−1.84379e18			−4.25204
$871$	6.35351e16			0.145514
$872$			1.62088e17i			0.368683i
$873$		−	1.03837e18i		−	2.34568i
$874$	−4.34252e17			−0.974257
$875$			2.71729e17i			0.605463i
$876$			2.05223e18i			4.54153i
$877$			5.06337e17i			1.11286i	0.830893	+	0.556432i	$0.187830\pi$
$877$			5.06337e17i			1.11286i	−0.830893	+	0.556432i	$0.812170\pi$
$878$	6.95148e17			1.51744
$879$	−1.38455e18			−3.00176
$880$		−	3.11878e17i		−	0.671566i
$881$	6.47225e16			0.138420			0.0692101	−	0.997602i	$-0.477952\pi$
$881$	6.47225e16			0.138420			0.0692101	+	0.997602i	$0.477952\pi$
$882$		−	3.47111e18i		−	7.37321i
$883$		−	3.42130e17i		−	0.721816i	−0.932601	−	0.360908i	$-0.882467\pi$
$883$		−	3.42130e17i		−	0.721816i	0.932601	−	0.360908i	$-0.117533\pi$
$884$			6.03225e17i			1.26405i
$885$		−	1.96676e18i		−	4.09346i
$886$			2.59267e17i			0.535976i
$887$			2.23283e17i			0.458473i	0.973371	+	0.229236i	$0.0736229\pi$
$887$			2.23283e17i			0.458473i	−0.973371	+	0.229236i	$0.926377\pi$
$888$		−	1.15629e18i		−	2.35824i
$889$	1.03875e18			2.10426
$890$		−	1.30444e18i		−	2.62472i
$891$	−2.15237e18			−4.30180
$892$			9.67343e17i			1.92040i
$893$	−1.59509e17			−0.314541
$894$	1.85252e16			0.0362858
$895$	1.02198e18			1.98840
$896$			1.52753e18i			2.95218i
$897$			3.43492e17i			0.659419i
$898$	−9.05295e17			−1.72636
$899$	1.31154e16			0.0248441
$900$	3.01295e18			5.66939
$901$		−	7.10894e17i		−	1.32879i
$902$		−	1.07929e18i		−	2.00401i
$903$			6.64813e17i			1.22623i
$904$		−	3.71983e17i		−	0.681573i
$905$	1.76789e17			0.321784
$906$		−	1.40385e16i		−	0.0253835i
$907$	8.49339e17			1.52559			0.762795	−	0.646641i	$-0.223827\pi$
$907$	8.49339e17			1.52559			0.762795	+	0.646641i	$0.223827\pi$
$908$	1.25279e18			2.23544
$909$		−	8.90812e16i		−	0.157908i
$910$			1.94930e18i			3.43265i
$911$	2.92527e16			0.0511748			0.0255874	−	0.999673i	$-0.491854\pi$
$911$	2.92527e16			0.0511748			0.0255874	+	0.999673i	$0.491854\pi$
$912$			5.03108e17i			0.874363i
$913$	−2.87405e17	+	7.41823e17i	−0.496215	+	1.28078i
$914$	−1.32922e17			−0.227991
$915$			2.03590e18i			3.46921i
$916$	9.10315e17			1.54106
$917$	−6.65732e17			−1.11965
$918$			2.57859e18i			4.30850i
$919$		−	5.14091e16i		−	0.0853388i	−0.999089	−	0.0426694i	$-0.986414\pi$
$919$		−	5.14091e16i		−	0.0853388i	0.999089	−	0.0426694i	$-0.0135862\pi$
$920$	−4.73083e17			−0.780208
$921$		−	1.02736e18i		−	1.68331i
$922$	3.28758e16			0.0535168
$923$	−7.26214e17			−1.17450
$924$	4.68524e18			7.52836
$925$	−7.73814e17			−1.23534
$926$			1.23769e18i			1.96312i
$927$			6.78307e17i			1.06893i
$928$			4.10366e17i			0.642516i
$929$	−1.01847e18			−1.58436			−0.792182	−	0.610285i	$-0.791055\pi$
$929$	−1.01847e18			−1.58436			−0.792182	+	0.610285i	$0.791055\pi$
$930$	−8.40422e16			−0.129897
$931$		−	1.57667e18i		−	2.42127i
$932$			1.88263e18i			2.87256i
$933$		−	2.06856e18i		−	3.13602i
$934$	6.20982e17			0.935400
$935$		−	1.18178e18i		−	1.76875i
$936$	1.83243e18			2.72503
$937$		−	5.71447e16i		−	0.0844381i	−0.999108	−	0.0422190i	$-0.986557\pi$
$937$		−	5.71447e16i		−	0.0844381i	0.999108	−	0.0422190i	$-0.0134427\pi$
$938$	−3.23407e17			−0.474823
$939$	1.48834e18			2.17124
$940$	−4.03781e17			−0.585301
$941$	7.45833e17			1.07425			0.537123	−	0.843504i	$-0.319511\pi$
$941$	7.45833e17			1.07425			0.537123	+	0.843504i	$0.319511\pi$
$942$	−8.37867e17			−1.19914
$943$	−2.56602e17			−0.364913
$944$	3.32769e17			0.470230
$945$			5.30862e18i			7.45402i
$946$	−6.41815e17			−0.895495
$947$			1.10354e18i			1.52999i	0.644039	+	0.764993i	$0.277257\pi$
$947$			1.10354e18i			1.52999i	−0.644039	+	0.764993i	$0.722743\pi$
$948$		−	1.62893e18i		−	2.24415i
$949$	8.35281e17			1.14350
$950$	2.14815e18			2.92229
$951$	1.37401e18			1.85741
$952$		−	1.32145e18i		−	1.77512i
$953$	−1.11064e18			−1.48258			−0.741288	−	0.671187i	$-0.765785\pi$
$953$	−1.11064e18			−1.48258			−0.741288	+	0.671187i	$0.765785\pi$
$954$	−5.01784e18			−6.65621
$955$			7.32594e17i			0.965702i
$956$			1.65496e18i			2.16790i
$957$	1.80373e18			2.34801
$958$			1.43836e18i			1.86070i
$959$		−	2.12605e18i		−	2.73314i
$960$		−	3.35506e18i		−	4.28620i
$961$	−7.87065e17			−0.999241
$962$	−1.09354e18			−1.37970
$963$			1.85424e18i			2.32492i
$964$	−2.43064e18			−3.02872
$965$		−	8.53922e17i		−	1.05744i
$966$		−	1.74844e18i		−	2.15173i
$967$			6.49512e17i			0.794381i	0.917736	+	0.397190i	$0.130015\pi$
$967$			6.49512e17i			0.794381i	−0.917736	+	0.397190i	$0.869985\pi$
$968$			9.14817e17i			1.11194i
$969$			1.90639e18i			2.30287i
$970$		−	1.87407e18i		−	2.24986i
$971$		−	3.35827e17i		−	0.400682i	−0.979726	−	0.200341i	$-0.935795\pi$
$971$		−	3.35827e17i		−	0.400682i	0.979726	−	0.200341i	$-0.0642051\pi$
$972$	4.31788e18			5.12003
$973$		−	5.46575e17i		−	0.644129i
$974$	2.16203e18			2.53226
$975$		−	1.69918e18i		−	1.97793i
$976$	−3.44468e17			−0.398519
$977$	−6.61233e17			−0.760304			−0.380152	−	0.924924i	$-0.624128\pi$
$977$	−6.61233e17			−0.760304			−0.380152	+	0.924924i	$0.624128\pi$
$978$	1.13211e17			0.129377
$979$			1.27609e18i			1.44939i
$980$		−	3.99119e18i		−	4.50553i
$981$	6.79487e17			0.762373
$982$	−1.21439e18			−1.35422
$983$	−1.08286e18			−1.20019			−0.600095	−	0.799929i	$-0.704871\pi$
$983$	−1.08286e18			−1.20019			−0.600095	+	0.799929i	$0.704871\pi$
$984$			1.89675e18i			2.08949i
$985$		−	3.91748e17i		−	0.428933i
$986$		−	1.18210e18i		−	1.28645i
$987$		−	6.42237e17i		−	0.694692i
$988$	1.93404e18			2.07933
$989$			1.52591e17i			0.163062i
$990$	−8.34156e18			−8.86005
$991$	−5.33287e17			−0.563014			−0.281507	−	0.959559i	$-0.590834\pi$
$991$	−5.33287e17			−0.563014			−0.281507	+	0.959559i	$0.590834\pi$
$992$			1.87050e16i			0.0196285i
$993$			2.69110e18i			2.80695i
$994$	3.69658e18			3.83249
$995$			5.46587e17i			0.563276i
$996$	1.17363e18	−	3.02926e18i	1.20219	−	3.10299i
$997$	−4.23107e17			−0.430803			−0.215402	−	0.976526i	$-0.569106\pi$
$997$	−4.23107e17			−0.430803			−0.215402	+	0.976526i	$0.569106\pi$
$998$			1.30442e18i			1.32018i
$999$	−2.97811e18			−2.99604

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	83.13.b.c.82.10	✓	80
83.82	odd	2	inner	83.13.b.c.82.71	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
83.13.b.c.82.10	✓	80	1.1	even	1	trivial
83.13.b.c.82.71	yes	80	83.82	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:	\( N \)	\(=\)	\( 83 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	83.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-106.238i q^{2} -1381.89 q^{3} -7190.55 q^{4} +23413.1i q^{5} +146810. i q^{6} -193774. q^{7} +328759. i q^{8} +1.37818e6 q^{9} +O(q^{10})\)	\(q-106.238i q^{2} -1381.89 q^{3} -7190.55 q^{4} +23413.1i q^{5} +146810. i q^{6} -193774. q^{7} +328759. i q^{8} +1.37818e6 q^{9} +2.48737e6 q^{10} -2.43332e6 q^{11} +9.93656e6 q^{12} -4.04428e6i q^{13} +2.05862e7i q^{14} -3.23544e7i q^{15} +5.47426e6 q^{16} +2.07432e7 q^{17} -1.46416e8i q^{18} -6.65061e7i q^{19} -1.68353e8i q^{20} +2.67775e8 q^{21} +2.58512e8i q^{22} +6.14611e7 q^{23} -4.54309e8i q^{24} -3.04034e8 q^{25} -4.29657e8 q^{26} -1.17011e9 q^{27} +1.39334e9 q^{28} +5.36412e8 q^{29} -3.43727e9 q^{30} +2.44503e7 q^{31} +7.65021e8i q^{32} +3.36259e9 q^{33} -2.20372e9i q^{34} -4.53686e9i q^{35} -9.90990e9 q^{36} +2.54516e9 q^{37} -7.06548e9 q^{38} +5.58876e9i q^{39} -7.69728e9 q^{40} -4.17502e9 q^{41} -2.84479e10i q^{42} +2.48273e9i q^{43} +1.74969e10 q^{44} +3.22676e10i q^{45} -6.52951e9i q^{46} -2.39842e9i q^{47} -7.56483e9 q^{48} +2.37072e10 q^{49} +3.23000e10i q^{50} -2.86649e10 q^{51} +2.90806e10i q^{52} -3.42712e10i q^{53} +1.24310e11i q^{54} -5.69717e10i q^{55} -6.37050e10i q^{56} +9.19042e10i q^{57} -5.69874e10i q^{58} +6.07879e10 q^{59} +2.32646e11i q^{60} -6.29250e10 q^{61} -2.59755e9i q^{62} -2.67057e11 q^{63} +1.03697e11 q^{64} +9.46894e10 q^{65} -3.57235e11i q^{66} +1.57099e10i q^{67} -1.49155e11 q^{68} -8.49326e10 q^{69} -4.81988e11 q^{70} -1.79565e11i q^{71} +4.53090e11i q^{72} +2.06534e11i q^{73} -2.70393e11i q^{74} +4.20142e11 q^{75} +4.78215e11i q^{76} +4.71516e11 q^{77} +5.93740e11 q^{78} -1.63933e11i q^{79} +1.28170e11i q^{80} +8.84539e11 q^{81} +4.43547e11i q^{82} +(1.18112e11 - 3.04860e11i) q^{83} -1.92545e12 q^{84} +4.85663e11i q^{85} +2.63761e11 q^{86} -7.41263e11 q^{87} -7.99977e11i q^{88} -5.24424e11i q^{89} +3.42805e12 q^{90} +7.83679e11i q^{91} -4.41939e11 q^{92} -3.37876e10 q^{93} -2.54804e11 q^{94} +1.55712e12 q^{95} -1.05718e12i q^{96} -7.53437e11i q^{97} -2.51861e12i q^{98} -3.35357e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9}+O(q^{10}) \) 80 * q + 918 * q^3 - 181150 * q^4 + 103918 * q^7 + 14902142 * q^9	\( 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9} + 1177482 q^{10} + 510406 q^{11} - 9260402 q^{12} + 203791850 q^{16} + 5571718 q^{17} + 46565862 q^{21} + 804389464 q^{23} - 4263713272 q^{25} + 18061794 q^{26} - 2326165338 q^{27} - 204811652 q^{28} + 1486960270 q^{29} - 2621683648 q^{30} - 665743010 q^{31} + 135224502 q^{33} - 54936709824 q^{36} - 280627202 q^{37} + 6646145310 q^{38} - 7119722058 q^{40} + 51318109072 q^{41} - 11512674650 q^{44} + 85368259738 q^{48} + 148785395094 q^{49} - 100143389562 q^{51} - 63584241050 q^{59} - 29216180978 q^{61} - 332932206620 q^{63} - 323596534090 q^{64} + 362112989184 q^{65} - 86115426752 q^{68} + 272383417100 q^{69} + 105630718656 q^{70} + 785418808326 q^{75} - 663355117738 q^{77} + 1483841884620 q^{78} + 2430778545148 q^{81} + 837315119192 q^{83} - 3013574788354 q^{84} + 452180651958 q^{86} - 682263689498 q^{87} - 499714512022 q^{90} + 997428187414 q^{92} - 1487992716298 q^{93} + 3169817690580 q^{94} + 1542762610848 q^{95} + 2021347267420 q^{99}+O(q^{100}) \) 80 * q + 918 * q^3 - 181150 * q^4 + 103918 * q^7 + 14902142 * q^9 + 1177482 * q^10 + 510406 * q^11 - 9260402 * q^12 + 203791850 * q^16 + 5571718 * q^17 + 46565862 * q^21 + 804389464 * q^23 - 4263713272 * q^25 + 18061794 * q^26 - 2326165338 * q^27 - 204811652 * q^28 + 1486960270 * q^29 - 2621683648 * q^30 - 665743010 * q^31 + 135224502 * q^33 - 54936709824 * q^36 - 280627202 * q^37 + 6646145310 * q^38 - 7119722058 * q^40 + 51318109072 * q^41 - 11512674650 * q^44 + 85368259738 * q^48 + 148785395094 * q^49 - 100143389562 * q^51 - 63584241050 * q^59 - 29216180978 * q^61 - 332932206620 * q^63 - 323596534090 * q^64 + 362112989184 * q^65 - 86115426752 * q^68 + 272383417100 * q^69 + 105630718656 * q^70 + 785418808326 * q^75 - 663355117738 * q^77 + 1483841884620 * q^78 + 2430778545148 * q^81 + 837315119192 * q^83 - 3013574788354 * q^84 + 452180651958 * q^86 - 682263689498 * q^87 - 499714512022 * q^90 + 997428187414 * q^92 - 1487992716298 * q^93 + 3169817690580 * q^94 + 1542762610848 * q^95 + 2021347267420 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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