LMFDB - Embedded newform 12.17.d.a.7.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,17,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	12.d (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:	$19.4789452628$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 37115 x^{14} + 433616 x^{13} + 965822723 x^{12} + 11579264195 x^{11} + \cdots + 43\!\cdots\!49 $ x^16 - x^15 + 37115x^14 + 433616x^13 + 965822723x^12 + 11579264195x^11 + 12661863519850x^10 + 162120109773543x^9 + 120758933936870280x^8 + 1240343233445130327x^7 + 553297868296926315210x^6 + 3641854073469392130003x^5 + 1781463130185670341595803x^4 + 12984494303085096280528944x^3 + 125765846444242947670566147x^2 - 206760575884676576961270033x + 435779119237071236287541049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{106}\cdot 3^{51} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.10
Root			$-66.3279 - 114.883i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.17.d.a.7.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.3734 + 255.747i) q^{2} -3788.00i q^{3} +(-65277.3 + 5817.42i) q^{4} +86591.3 q^{5} +(968769. - 43082.3i) q^{6} +1.07917e7i q^{7} +(-2.23021e6 - 1.66283e7i) q^{8} -1.43489e7 q^{9} +O(q^{10})$	\(q+(11.3734 + 255.747i) q^{2} -3788.00i q^{3} +(-65277.3 + 5817.42i) q^{4} +86591.3 q^{5} +(968769. - 43082.3i) q^{6} +1.07917e7i q^{7} +(-2.23021e6 - 1.66283e7i) q^{8} -1.43489e7 q^{9} +(984836. + 2.21455e7i) q^{10} -3.08747e8i q^{11} +(2.20364e7 + 2.47270e8i) q^{12} -9.27660e8 q^{13} +(-2.75994e9 + 1.22738e8i) q^{14} -3.28007e8i q^{15} +(4.22728e9 - 7.59491e8i) q^{16} +1.04989e9 q^{17} +(-1.63196e8 - 3.66969e9i) q^{18} -2.14400e10i q^{19} +(-5.65245e9 + 5.03738e8i) q^{20} +4.08789e10 q^{21} +(7.89612e10 - 3.51149e9i) q^{22} -8.03506e10i q^{23} +(-6.29880e10 + 8.44803e9i) q^{24} -1.45090e11 q^{25} +(-1.05506e10 - 2.37247e11i) q^{26} +5.43536e10i q^{27} +(-6.27798e10 - 7.04452e11i) q^{28} +6.46948e10 q^{29} +(8.38870e10 - 3.73055e9i) q^{30} -1.00444e12i q^{31} +(2.42316e11 + 1.07248e12i) q^{32} -1.16953e12 q^{33} +(1.19408e10 + 2.68506e11i) q^{34} +9.34466e11i q^{35} +(9.36658e11 - 8.34736e10i) q^{36} +1.20118e12 q^{37} +(5.48323e12 - 2.43846e11i) q^{38} +3.51397e12i q^{39} +(-1.93117e11 - 1.43987e12i) q^{40} -1.21222e13 q^{41} +(4.64931e11 + 1.04547e13i) q^{42} -2.28614e12i q^{43} +(1.79611e12 + 2.01542e13i) q^{44} -1.24249e12 q^{45} +(2.05494e13 - 9.13858e11i) q^{46} +2.13186e13i q^{47} +(-2.87695e12 - 1.60129e13i) q^{48} -8.32276e13 q^{49} +(-1.65016e12 - 3.71063e13i) q^{50} -3.97697e12i q^{51} +(6.05551e13 - 5.39659e12i) q^{52} +1.37605e13 q^{53} +(-1.39008e13 + 6.18184e11i) q^{54} -2.67348e13i q^{55} +(1.79448e14 - 2.40678e13i) q^{56} -8.12148e13 q^{57} +(7.35799e11 + 1.65455e13i) q^{58} -1.78862e14i q^{59} +(1.90816e12 + 2.14114e13i) q^{60} -5.51686e13 q^{61} +(2.56884e14 - 1.14239e13i) q^{62} -1.54849e14i q^{63} +(-2.71527e14 + 7.41694e13i) q^{64} -8.03273e13 q^{65} +(-1.33015e13 - 2.99104e14i) q^{66} +2.57456e14i q^{67} +(-6.85338e13 + 6.10763e12i) q^{68} -3.04368e14 q^{69} +(-2.38987e14 + 1.06280e13i) q^{70} +4.05525e14i q^{71} +(3.20011e13 + 2.38598e14i) q^{72} -2.94670e14 q^{73} +(1.36615e13 + 3.07199e14i) q^{74} +5.49600e14i q^{75} +(1.24726e14 + 1.39955e15i) q^{76} +3.33190e15 q^{77} +(-8.98689e14 + 3.99657e13i) q^{78} +1.81169e14i q^{79} +(3.66046e14 - 6.57653e13i) q^{80} +2.05891e14 q^{81} +(-1.37870e14 - 3.10022e15i) q^{82} +1.39106e15i q^{83} +(-2.66846e15 + 2.37809e14i) q^{84} +9.09111e13 q^{85} +(5.84673e14 - 2.60011e13i) q^{86} -2.45064e14i q^{87} +(-5.13394e15 + 6.88571e14i) q^{88} +3.78150e15 q^{89} +(-1.41313e13 - 3.17764e14i) q^{90} -1.00110e16i q^{91} +(4.67433e14 + 5.24507e15i) q^{92} -3.80483e15 q^{93} +(-5.45219e15 + 2.42465e14i) q^{94} -1.85652e15i q^{95} +(4.06254e15 - 9.17892e14i) q^{96} +8.34786e15 q^{97} +(-9.46579e14 - 2.12852e16i) q^{98} +4.43018e15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9}+O(q^{10}) $ 16 * q - 186 * q^2 + 136588 * q^4 + 354144 * q^5 + 1561518 * q^6 + 14683680 * q^8 - 229582512 * q^9	\( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9} - 49800172 q^{10} + 425284020 q^{12} - 906419296 q^{13} - 806064072 q^{14} - 2108540816 q^{16} + 12240765600 q^{17} + 2668896702 q^{18} + 1002788712 q^{20} + 39806479296 q^{21} + 216706355928 q^{22} - 111931394832 q^{24} + 206381182512 q^{25} + 1054507182588 q^{26} - 1526063922288 q^{28} + 327679573728 q^{29} + 1192344308100 q^{30} - 5158730488416 q^{32} + 679591529280 q^{33} + 9473293385948 q^{34} - 1959888509316 q^{36} - 8149494749152 q^{37} + 23318999782920 q^{38} - 28671795971776 q^{40} - 25536724613472 q^{41} + 5103781482168 q^{42} - 11442227373552 q^{44} - 5081579320608 q^{45} + 9929654732736 q^{46} + 29246734238832 q^{48} - 93287012964080 q^{49} - 133601044957998 q^{50} + 302261844234872 q^{52} - 86928436629792 q^{53} - 22406076560826 q^{54} + 530930989929024 q^{56} + 48687411524544 q^{57} - 189801665049916 q^{58} + 268455359263896 q^{60} + 476028596468000 q^{61} - 419080420491096 q^{62} + 305944925720704 q^{64} - 12\!\cdots\!92 q^{65}+ \cdots - 33\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q - 186 * q^2 + 136588 * q^4 + 354144 * q^5 + 1561518 * q^6 + 14683680 * q^8 - 229582512 * q^9 - 49800172 * q^10 + 425284020 * q^12 - 906419296 * q^13 - 806064072 * q^14 - 2108540816 * q^16 + 12240765600 * q^17 + 2668896702 * q^18 + 1002788712 * q^20 + 39806479296 * q^21 + 216706355928 * q^22 - 111931394832 * q^24 + 206381182512 * q^25 + 1054507182588 * q^26 - 1526063922288 * q^28 + 327679573728 * q^29 + 1192344308100 * q^30 - 5158730488416 * q^32 + 679591529280 * q^33 + 9473293385948 * q^34 - 1959888509316 * q^36 - 8149494749152 * q^37 + 23318999782920 * q^38 - 28671795971776 * q^40 - 25536724613472 * q^41 + 5103781482168 * q^42 - 11442227373552 * q^44 - 5081579320608 * q^45 + 9929654732736 * q^46 + 29246734238832 * q^48 - 93287012964080 * q^49 - 133601044957998 * q^50 + 302261844234872 * q^52 - 86928436629792 * q^53 - 22406076560826 * q^54 + 530930989929024 * q^56 + 48687411524544 * q^57 - 189801665049916 * q^58 + 268455359263896 * q^60 + 476028596468000 * q^61 - 419080420491096 * q^62 + 305944925720704 * q^64 - 1276571708976192 * q^65 - 64815073701480 * q^66 - 1393626893610696 * q^68 + 384812600884992 * q^69 + 1815049064679696 * q^70 - 210694758737760 * q^72 - 368686901901280 * q^73 + 875633111941836 * q^74 - 4351002030861264 * q^76 - 81504772370688 * q^77 + 1907392409236620 * q^78 - 8190389938127328 * q^80 + 3294258113514384 * q^81 + 2390391408733340 * q^82 - 510964995024720 * q^84 + 10085047677398464 * q^85 - 894939801424296 * q^86 + 669091386916800 * q^88 - 5711067674201568 * q^89 + 714578036612004 * q^90 + 7708247605922304 * q^92 + 7132614781502016 * q^93 - 9487273535547696 * q^94 + 8786531038601952 * q^96 - 13564951560560608 * q^97 - 33011660914531290 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$1$	$-1$

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 $

$2$	11.3734	+	255.747i	0.0444273	+	0.999013i
$2$	11.3734	+	255.747i	0.0444273	+	0.999013i
$3$		−	3788.00i		−	0.577350i
$3$		−	3788.00i		−	0.577350i
$4$	−65277.3	+	5817.42i	−0.996052	+	0.0887668i
$5$	86591.3			0.221674			0.110837	−	0.993839i	$-0.464647\pi$
$5$	86591.3			0.221674			0.110837	+	0.993839i	$0.464647\pi$
$6$	968769.	−	43082.3i	0.576780	−	0.0256501i
$7$			1.07917e7i			1.87200i	0.352005	+	0.935998i	$0.385500\pi$
$7$			1.07917e7i			1.87200i	−0.352005	+	0.935998i	$0.614500\pi$
$8$	−2.23021e6	−	1.66283e7i	−0.132931	−	0.991125i
$9$	−1.43489e7			−0.333333
$10$	984836.	+	2.21455e7i	0.00984836	+	0.221455i
$11$		−	3.08747e8i		−	1.44033i	−0.693804	−	0.720163i	$-0.744067\pi$
$11$		−	3.08747e8i		−	1.44033i	0.693804	−	0.720163i	$-0.255933\pi$
$12$	2.20364e7	+	2.47270e8i	0.0512495	+	0.575071i
$13$	−9.27660e8			−1.13721			−0.568607	−	0.822609i	$-0.692517\pi$
$13$	−9.27660e8			−1.13721			−0.568607	+	0.822609i	$0.692517\pi$
$14$	−2.75994e9	+	1.22738e8i	−1.87015	+	0.0831677i
$15$		−	3.28007e8i		−	0.127983i
$16$	4.22728e9	−	7.59491e8i	0.984241	−	0.176833i
$17$	1.04989e9			0.150505			0.0752525	−	0.997165i	$-0.476024\pi$
$17$	1.04989e9			0.150505			0.0752525	+	0.997165i	$0.476024\pi$
$18$	−1.63196e8	−	3.66969e9i	−0.0148091	−	0.333004i
$19$		−	2.14400e10i		−	1.26240i	−0.775620	−	0.631200i	$-0.782563\pi$
$19$		−	2.14400e10i		−	1.26240i	0.775620	−	0.631200i	$-0.217437\pi$
$20$	−5.65245e9	+	5.03738e8i	−0.220799	+	0.0196773i
$21$	4.08789e10			1.08080
$22$	7.89612e10	−	3.51149e9i	1.43890	−	0.0639898i
$23$		−	8.03506e10i		−	1.02605i	−0.858375	−	0.513023i	$-0.828526\pi$
$23$		−	8.03506e10i		−	1.02605i	0.858375	−	0.513023i	$-0.171474\pi$
$24$	−6.29880e10	+	8.44803e9i	−0.572226	+	0.0767478i
$25$	−1.45090e11			−0.950861
$26$	−1.05506e10	−	2.37247e11i	−0.0505233	−	1.13609i
$27$			5.43536e10i			0.192450i
$28$	−6.27798e10	−	7.04452e11i	−0.166171	−	1.86461i
$29$	6.46948e10			0.129326			0.0646630	−	0.997907i	$-0.479403\pi$
$29$	6.46948e10			0.129326			0.0646630	+	0.997907i	$0.479403\pi$
$30$	8.38870e10	−	3.73055e9i	0.127857	−	0.00568595i
$31$		−	1.00444e12i		−	1.17769i	−0.808245	−	0.588846i	$-0.799582\pi$
$31$		−	1.00444e12i		−	1.17769i	0.808245	−	0.588846i	$-0.200418\pi$
$32$	2.42316e11	+	1.07248e12i	0.220385	+	0.975413i
$33$	−1.16953e12			−0.831573
$34$	1.19408e10	+	2.68506e11i	0.00668653	+	0.150356i
$35$			9.34466e11i			0.414972i
$36$	9.36658e11	−	8.34736e10i	0.332017	−	0.0295889i
$37$	1.20118e12			0.341975			0.170988	−	0.985273i	$-0.445304\pi$
$37$	1.20118e12			0.341975			0.170988	+	0.985273i	$0.445304\pi$
$38$	5.48323e12	−	2.43846e11i	1.26115	−	0.0560849i
$39$			3.51397e12i			0.656571i
$40$	−1.93117e11	−	1.43987e12i	−0.0294673	−	0.219706i
$41$	−1.21222e13			−1.51814			−0.759068	−	0.651011i	$-0.774345\pi$
$41$	−1.21222e13			−1.51814			−0.759068	+	0.651011i	$0.774345\pi$
$42$	4.64931e11	+	1.04547e13i	0.0480169	+	1.07973i
$43$		−	2.28614e12i		−	0.195594i	−0.995206	−	0.0977968i	$-0.968820\pi$
$43$		−	2.28614e12i		−	0.195594i	0.995206	−	0.0977968i	$-0.0311795\pi$
$44$	1.79611e12	+	2.01542e13i	0.127853	+	1.43464i
$45$	−1.24249e12			−0.0738912
$46$	2.05494e13	−	9.13858e11i	1.02503	−	0.0455844i
$47$			2.13186e13i			0.895317i	0.894205	+	0.447658i	$0.147742\pi$
$47$			2.13186e13i			0.895317i	−0.894205	+	0.447658i	$0.852258\pi$
$48$	−2.87695e12	−	1.60129e13i	−0.102094	−	0.568252i
$49$	−8.32276e13			−2.50437
$50$	−1.65016e12	−	3.71063e13i	−0.0422441	−	0.949922i
$51$		−	3.97697e12i		−	0.0868942i
$52$	6.05551e13	−	5.39659e12i	1.13272	−	0.100947i
$53$	1.37605e13			0.221018			0.110509	−	0.993875i	$-0.464752\pi$
$53$	1.37605e13			0.221018			0.110509	+	0.993875i	$0.464752\pi$
$54$	−1.39008e13	+	6.18184e11i	−0.192260	+	0.00855003i
$55$		−	2.67348e13i		−	0.319283i
$56$	1.79448e14	−	2.40678e13i	1.85538	−	0.248846i
$57$	−8.12148e13			−0.728847
$58$	7.35799e11	+	1.65455e13i	0.00574560	+	0.129198i
$59$		−	1.78862e14i		−	1.21815i	−0.793112	−	0.609076i	$-0.791540\pi$
$59$		−	1.78862e14i		−	1.21815i	0.793112	−	0.609076i	$-0.208460\pi$
$60$	1.90816e12	+	2.14114e13i	0.0113607	+	0.127478i
$61$	−5.51686e13			−0.287775			−0.143888	−	0.989594i	$-0.545960\pi$
$61$	−5.51686e13			−0.287775			−0.143888	+	0.989594i	$0.545960\pi$
$62$	2.56884e14	−	1.14239e13i	1.17653	−	0.0523216i
$63$		−	1.54849e14i		−	0.623999i
$64$	−2.71527e14	+	7.41694e13i	−0.964659	+	0.263503i
$65$	−8.03273e13			−0.252090
$66$	−1.33015e13	−	2.99104e14i	−0.0369445	−	0.830752i
$67$			2.57456e14i			0.634021i	0.948422	+	0.317011i	$0.102679\pi$
$67$			2.57456e14i			0.634021i	−0.948422	+	0.317011i	$0.897321\pi$
$68$	−6.85338e13	+	6.10763e12i	−0.149911	+	0.0133599i
$69$	−3.04368e14			−0.592387
$70$	−2.38987e14	+	1.06280e13i	−0.414563	+	0.0184361i
$71$			4.05525e14i			0.627987i	0.949425	+	0.313993i	$0.101667\pi$
$71$			4.05525e14i			0.627987i	−0.949425	+	0.313993i	$0.898333\pi$
$72$	3.20011e13	+	2.38598e14i	0.0443103	+	0.330375i
$73$	−2.94670e14			−0.365387			−0.182693	−	0.983170i	$-0.558482\pi$
$73$	−2.94670e14			−0.365387			−0.182693	+	0.983170i	$0.558482\pi$
$74$	1.36615e13	+	3.07199e14i	0.0151930	+	0.341638i
$75$			5.49600e14i			0.548980i
$76$	1.24726e14	+	1.39955e15i	0.112059	+	1.25742i
$77$	3.33190e15			2.69629
$78$	−8.98689e14	+	3.99657e13i	−0.655922	+	0.0291696i
$79$			1.81169e14i			0.119417i	0.998216	+	0.0597085i	$0.0190171\pi$
$79$			1.81169e14i			0.119417i	−0.998216	+	0.0597085i	$0.980983\pi$
$80$	3.66046e14	−	6.57653e13i	0.218180	−	0.0391992i
$81$	2.05891e14			0.111111
$82$	−1.37870e14	−	3.10022e15i	−0.0674466	−	1.51664i
$83$			1.39106e15i			0.617620i	0.951124	+	0.308810i	$0.0999308\pi$
$83$			1.39106e15i			0.617620i	−0.951124	+	0.308810i	$0.900069\pi$
$84$	−2.66846e15	+	2.37809e14i	−1.07653	+	0.0959389i
$85$	9.09111e13			0.0333630
$86$	5.84673e14	−	2.60011e13i	0.195400	−	0.00868969i
$87$		−	2.45064e14i		−	0.0746664i
$88$	−5.13394e15	+	6.88571e14i	−1.42754	+	0.191464i
$89$	3.78150e15			0.960604			0.480302	−	0.877103i	$-0.340527\pi$
$89$	3.78150e15			0.960604			0.480302	+	0.877103i	$0.340527\pi$
$90$	−1.41313e13	−	3.17764e14i	−0.00328279	−	0.0738183i
$91$		−	1.00110e16i		−	2.12886i
$92$	4.67433e14	+	5.24507e15i	0.0910787	+	1.02199i
$93$	−3.80483e15			−0.679941
$94$	−5.45219e15	+	2.42465e14i	−0.894433	+	0.0397765i
$95$		−	1.85652e15i		−	0.279841i
$96$	4.06254e15	−	9.17892e14i	0.563155	−	0.127239i
$97$	8.34786e15			1.06513			0.532564	−	0.846390i	$-0.321229\pi$
$97$	8.34786e15			1.06513			0.532564	+	0.846390i	$0.321229\pi$
$98$	−9.46579e14	−	2.12852e16i	−0.111262	−	2.50190i
$99$			4.43018e15i			0.480109i
$100$	9.47107e15	−	8.44048e14i	0.947107	−	0.0844048i
$101$	−2.02699e15			−0.187189			−0.0935947	−	0.995610i	$-0.529836\pi$
$101$	−2.02699e15			−0.187189			−0.0935947	+	0.995610i	$0.529836\pi$
$102$	1.01710e15	−	4.52315e13i	0.0868084	−	0.00386047i
$103$			1.04678e16i			0.826342i	0.910654	+	0.413171i	$0.135579\pi$
$103$			1.04678e16i			0.826342i	−0.910654	+	0.413171i	$0.864421\pi$
$104$	2.06888e15	+	1.54254e16i	0.151171	+	1.12712i
$105$	3.53975e15			0.239584
$106$	1.56504e14	+	3.51922e15i	0.00981923	+	0.220800i
$107$			8.34371e15i			0.485612i	0.970075	+	0.242806i	$0.0780678\pi$
$107$			8.34371e15i			0.485612i	−0.970075	+	0.242806i	$0.921932\pi$
$108$	−3.16198e14	−	3.54806e15i	−0.0170832	−	0.191690i
$109$	−2.25395e16			−1.13118			−0.565591	−	0.824686i	$-0.691352\pi$
$109$	−2.25395e16			−1.13118			−0.565591	+	0.824686i	$0.691352\pi$
$110$	6.83735e15	−	3.04065e14i	0.318967	−	0.0141849i
$111$		−	4.55007e15i		−	0.197439i
$112$	8.19619e15	+	4.56195e16i	0.331030	+	1.84250i
$113$	−3.96494e16			−1.49145			−0.745726	−	0.666253i	$-0.767897\pi$
$113$	−3.96494e16			−1.49145			−0.745726	+	0.666253i	$0.767897\pi$
$114$	−9.23686e14	−	2.07705e16i	−0.0323807	−	0.728127i
$115$		−	6.95766e15i		−	0.227447i
$116$	−4.22310e15	+	3.76357e14i	−0.128815	+	0.0114798i
$117$	1.33109e16			0.379071
$118$	4.57434e16	−	2.03426e15i	1.21695	−	0.0541191i
$119$			1.13301e16i			0.281745i
$120$	−5.45421e15	+	7.31526e14i	−0.126848	+	0.0170130i
$121$	−4.93749e16			−1.07454
$122$	−6.27453e14	−	1.41092e16i	−0.0127851	−	0.287491i
$123$			4.59188e16i			0.876496i
$124$	5.84327e15	+	6.55673e16i	0.104540	+	1.17304i
$125$	−2.57763e16			−0.432455
$126$	3.96022e16	−	1.76116e15i	0.623383	−	0.0277226i
$127$		−	9.50930e16i		−	1.40514i	−0.711616	−	0.702569i	$-0.752036\pi$
$127$		−	9.50930e16i		−	1.40514i	0.711616	−	0.702569i	$-0.247964\pi$
$128$	−2.20568e16	−	6.85988e16i	−0.306100	−	0.952000i
$129$	−8.65988e15			−0.112926
$130$	−9.13593e14	−	2.05435e16i	−0.0111997	−	0.251841i
$131$		−	1.40724e16i		−	0.162254i	−0.996704	−	0.0811272i	$-0.974148\pi$
$131$		−	1.40724e16i		−	0.162254i	0.996704	−	0.0811272i	$-0.0258520\pi$
$132$	7.63439e16	−	6.80366e15i	0.828290	−	0.0738161i
$133$	2.31374e17			2.36321
$134$	−6.58436e16	+	2.92814e15i	−0.633395	+	0.0281678i
$135$			4.70655e15i			0.0426611i
$136$	−2.34147e15	−	1.74579e16i	−0.0200068	−	0.149169i
$137$	−1.77783e17			−1.43260			−0.716300	−	0.697793i	$-0.754166\pi$
$137$	−1.77783e17			−1.43260			−0.716300	+	0.697793i	$0.754166\pi$
$138$	−3.46169e15	−	7.78412e16i	−0.0263181	−	0.591802i
$139$		−	2.20734e17i		−	1.58398i	−0.610532	−	0.791992i	$-0.709044\pi$
$139$		−	2.20734e17i		−	1.58398i	0.610532	−	0.791992i	$-0.290956\pi$
$140$	−5.43618e15	−	6.09994e16i	−0.0368358	−	0.413334i
$141$	8.07549e16			0.516911
$142$	−1.03712e17	+	4.61219e15i	−0.627367	+	0.0278997i
$143$			2.86412e17i			1.63796i
$144$	−6.06569e16	+	1.08979e16i	−0.328080	+	0.0589442i
$145$	5.60201e15			0.0286682
$146$	−3.35139e15	−	7.53610e16i	−0.0162331	−	0.365026i
$147$			3.15266e17i			1.44590i
$148$	−7.84098e16	+	6.98777e15i	−0.340625	+	0.0303560i
$149$	3.42196e17			1.40859			0.704296	−	0.709906i	$-0.251263\pi$
$149$	3.42196e17			1.40859			0.704296	+	0.709906i	$0.251263\pi$
$150$	−1.40559e17	+	6.25080e15i	−0.548438	+	0.0243897i
$151$		−	3.61914e17i		−	1.33903i	−0.742799	−	0.669514i	$-0.766502\pi$
$151$		−	3.61914e17i		−	1.33903i	0.742799	−	0.669514i	$-0.233498\pi$
$152$	−3.56512e17	+	4.78158e16i	−1.25120	+	0.167812i
$153$	−1.50647e16			−0.0501684
$154$	3.78950e16	+	8.52124e17i	0.119789	+	2.69362i
$155$		−	8.69761e16i		−	0.261064i
$156$	−2.04422e16	−	2.29383e17i	−0.0582817	−	0.653979i
$157$	−1.92467e17			−0.521386			−0.260693	−	0.965422i	$-0.583951\pi$
$157$	−1.92467e17			−0.521386			−0.260693	+	0.965422i	$0.583951\pi$
$158$	−4.63334e16	+	2.06050e15i	−0.119299	+	0.00530537i
$159$		−	5.21248e16i		−	0.127605i
$160$	2.09825e16	+	9.28673e16i	0.0488536	+	0.216223i
$161$	8.67119e17			1.92075
$162$	2.34168e15	+	5.26561e16i	0.00493636	+	0.111001i
$163$			3.03025e17i			0.608103i	0.952656	+	0.304051i	$0.0983395\pi$
$163$			3.03025e17i			0.608103i	−0.952656	+	0.304051i	$0.901661\pi$
$164$	7.91305e17	−	7.05199e16i	1.51214	−	0.134760i
$165$	−1.01271e17			−0.184338
$166$	−3.55760e17	+	1.58211e16i	−0.617011	+	0.0274392i
$167$			9.25468e17i			1.52978i	0.644159	+	0.764891i	$0.277207\pi$
$167$			9.25468e17i			1.52978i	−0.644159	+	0.764891i	$0.722793\pi$
$168$	−9.11685e16	−	6.79747e17i	−0.143672	−	1.07121i
$169$	1.95137e17			0.293255
$170$	1.03397e15	+	2.32503e16i	0.00148223	+	0.0333301i
$171$			3.07641e17i			0.420800i
$172$	1.32994e16	+	1.49233e17i	0.0173622	+	0.194821i
$173$	−1.28458e18			−1.60100			−0.800502	−	0.599330i	$-0.795434\pi$
$173$	−1.28458e18			−1.60100			−0.800502	+	0.599330i	$0.795434\pi$
$174$	6.26744e16	−	2.78720e15i	0.0745926	−	0.00331722i
$175$		−	1.56576e18i		−	1.78001i
$176$	−2.34490e17	−	1.30516e18i	−0.254697	−	1.41763i
$177$	−6.77527e17			−0.703300
$178$	4.30084e16	+	9.67108e17i	0.0426770	+	0.959655i
$179$		−	1.51930e18i		−	1.44152i	−0.693187	−	0.720758i	$-0.743794\pi$
$179$		−	1.51930e18i		−	1.44152i	0.693187	−	0.720758i	$-0.256206\pi$
$180$	8.11064e16	−	7.22809e15i	0.0735996	−	0.00655909i
$181$	−5.20028e17			−0.451438			−0.225719	−	0.974192i	$-0.572473\pi$
$181$	−5.20028e17			−0.451438			−0.225719	+	0.974192i	$0.572473\pi$
$182$	2.56029e18	−	1.13859e17i	2.12676	−	0.0945794i
$183$			2.08978e17i			0.166147i
$184$	−1.33610e18	+	1.79199e17i	−1.01694	+	0.136393i
$185$	1.04012e17			0.0758069
$186$	−4.32737e16	−	9.73074e17i	−0.0302079	−	0.679270i
$187$		−	3.24149e17i		−	0.216777i
$188$	−1.24020e17	−	1.39162e18i	−0.0794744	−	0.891783i
$189$	−5.86567e17			−0.360266
$190$	4.74800e17	−	2.11149e16i	0.279565	−	0.0124326i
$191$			2.42860e18i			1.37116i	0.727996	+	0.685582i	$0.240452\pi$
$191$			2.42860e18i			1.37116i	−0.727996	+	0.685582i	$0.759548\pi$
$192$	2.80953e17	+	1.02854e18i	0.152133	+	0.556946i
$193$	−2.42269e18			−1.25846			−0.629230	−	0.777219i	$-0.716630\pi$
$193$	−2.42269e18			−1.25846			−0.629230	+	0.777219i	$0.716630\pi$
$194$	9.49434e16	+	2.13494e18i	0.0473207	+	1.06408i
$195$			3.04279e17i			0.145544i
$196$	5.43287e18	−	4.84170e17i	2.49448	−	0.222305i
$197$	3.03655e18			1.33860			0.669300	−	0.742992i	$-0.266594\pi$
$197$	3.03655e18			1.33860			0.669300	+	0.742992i	$0.266594\pi$
$198$	−1.13301e18	+	5.03861e16i	−0.479635	+	0.0213299i
$199$		−	2.93148e18i		−	1.19196i	−0.802998	−	0.595981i	$-0.796763\pi$
$199$		−	2.93148e18i		−	1.19196i	0.802998	−	0.595981i	$-0.203237\pi$
$200$	3.23581e17	+	2.41260e18i	0.126399	+	0.942422i
$201$	9.75241e17			0.366052
$202$	−2.30538e16	−	5.18398e17i	−0.00831632	−	0.187005i
$203$			6.98166e17i			0.242098i
$204$	2.31357e16	+	2.59606e17i	0.00771331	+	0.0865511i
$205$	−1.04968e18			−0.336531
$206$	−2.67712e18	+	1.19055e17i	−0.825526	+	0.0367121i
$207$			1.15294e18i			0.342015i
$208$	−3.92148e18	+	7.04549e17i	−1.11929	+	0.201097i
$209$	−6.61955e18			−1.81827
$210$	4.02590e16	+	9.05282e17i	0.0106441	+	0.239348i
$211$			4.81806e18i			1.22634i	0.789950	+	0.613172i	$0.210107\pi$
$211$			4.81806e18i			1.22634i	−0.789950	+	0.613172i	$0.789893\pi$
$212$	−8.98250e17	+	8.00508e16i	−0.220146	+	0.0196191i
$213$	1.53613e18			0.362568
$214$	−2.13388e18	+	9.48962e16i	−0.485132	+	0.0215744i
$215$		−	1.97960e17i		−	0.0433580i
$216$	9.03809e17	−	1.21220e17i	0.190742	−	0.0255826i
$217$	1.08396e19			2.20464
$218$	−2.56350e17	−	5.76442e18i	−0.0502553	−	1.13006i
$219$			1.11621e18i			0.210956i
$220$	1.55528e17	+	1.74517e18i	0.0283417	+	0.318022i
$221$	−9.73938e17			−0.171156
$222$	1.16367e18	−	5.17496e16i	0.197245	−	0.00877169i
$223$			4.28116e18i			0.700039i	0.936742	+	0.350020i	$0.113825\pi$
$223$			4.28116e18i			0.700039i	−0.936742	+	0.350020i	$0.886175\pi$
$224$	−1.15738e19	+	2.61500e18i	−1.82597	+	0.412560i
$225$	2.08188e18			0.316954
$226$	−4.50948e17	−	1.01402e19i	−0.0662611	−	1.48998i
$227$		−	7.61610e18i		−	1.08025i	−0.841583	−	0.540127i	$-0.818376\pi$
$227$		−	7.61610e18i		−	1.08025i	0.841583	−	0.540127i	$-0.181624\pi$
$228$	5.30148e18	−	4.72460e17i	0.725970	−	0.0646974i
$229$	5.72737e18			0.757307			0.378653	−	0.925539i	$-0.376387\pi$
$229$	5.72737e18			0.757307			0.378653	+	0.925539i	$0.376387\pi$
$230$	1.77940e18	−	7.91321e16i	0.227223	−	0.0101049i
$231$		−	1.26212e19i		−	1.55670i
$232$	−1.44283e17	−	1.07577e18i	−0.0171914	−	0.128178i
$233$	9.31720e18			1.07260			0.536300	−	0.844027i	$-0.319822\pi$
$233$	9.31720e18			1.07260			0.536300	+	0.844027i	$0.319822\pi$
$234$	1.51390e17	+	3.40423e18i	0.0168411	+	0.378697i
$235$			1.84601e18i			0.198468i
$236$	1.04051e18	+	1.16756e19i	0.108131	+	1.21334i
$237$	6.86266e17			0.0689454
$238$	−2.89763e18	+	1.28861e17i	−0.281467	+	0.0125172i
$239$		−	1.10615e19i		−	1.03903i	−0.854460	−	0.519517i	$-0.826112\pi$
$239$		−	1.10615e19i		−	1.03903i	0.854460	−	0.519517i	$-0.173888\pi$
$240$	−2.49119e17	−	1.38658e18i	−0.0226317	−	0.125966i
$241$	−3.38785e18			−0.297707			−0.148853	−	0.988859i	$-0.547558\pi$
$241$	−3.38785e18			−0.297707			−0.148853	+	0.988859i	$0.547558\pi$
$242$	−5.61559e17	−	1.26275e19i	−0.0477389	−	1.07348i
$243$		−	7.79915e17i		−	0.0641500i
$244$	3.60126e18	−	3.20939e17i	0.286639	−	0.0255449i
$245$	−7.20679e18			−0.555153
$246$	−1.17436e19	+	5.22252e17i	−0.875631	+	0.0389403i
$247$			1.98891e19i			1.43562i
$248$	−1.67022e19	+	2.24012e18i	−1.16724	+	0.156552i
$249$	5.26934e18			0.356583
$250$	−2.93164e17	−	6.59222e18i	−0.0192128	−	0.432028i
$251$			8.87067e18i			0.563076i	0.959550	+	0.281538i	$0.0908445\pi$
$251$			8.87067e18i			0.563076i	−0.959550	+	0.281538i	$0.909156\pi$
$252$	9.00821e17	+	1.01081e19i	0.0553904	+	0.621536i
$253$	−2.48080e19			−1.47784
$254$	2.43198e19	−	1.08153e18i	1.40375	−	0.0624264i
$255$		−	3.44371e17i		−	0.0192622i
$256$	1.72931e19	−	6.42116e18i	0.937460	−	0.348092i
$257$	−2.60354e18			−0.136804			−0.0684021	−	0.997658i	$-0.521790\pi$
$257$	−2.60354e18			−0.136804			−0.0684021	+	0.997658i	$0.521790\pi$
$258$	−9.84920e16	−	2.21474e18i	−0.00501699	−	0.112815i
$259$			1.29628e19i			0.640176i
$260$	5.24355e18	−	4.67298e17i	0.251095	−	0.0223773i
$261$	−9.28300e17			−0.0431086
$262$	3.59897e18	−	1.60050e17i	0.162094	−	0.00720852i
$263$		−	1.18064e19i		−	0.515788i	−0.966173	−	0.257894i	$-0.916971\pi$
$263$		−	1.18064e19i		−	0.515788i	0.966173	−	0.257894i	$-0.0830285\pi$
$264$	2.60830e18	+	1.94473e19i	0.110542	+	0.824193i
$265$	1.19154e18			0.0489939
$266$	2.63151e18	+	5.91733e19i	0.104991	+	2.36087i
$267$		−	1.43243e19i		−	0.554605i
$268$	−1.49773e18	−	1.68060e19i	−0.0562800	−	0.631519i
$269$	−1.50417e19			−0.548628			−0.274314	−	0.961640i	$-0.588451\pi$
$269$	−1.50417e19			−0.548628			−0.274314	+	0.961640i	$0.588451\pi$
$270$	−1.20369e18	+	5.35293e16i	−0.0426190	+	0.00189532i
$271$			1.48927e19i			0.511941i	0.966685	+	0.255970i	$0.0823950\pi$
$271$			1.48927e19i			0.511941i	−0.966685	+	0.255970i	$0.917605\pi$
$272$	4.43817e18	−	7.97380e17i	0.148133	−	0.0266142i
$273$	−3.79217e19			−1.22910
$274$	−2.02199e18	−	4.54674e19i	−0.0636465	−	1.43118i
$275$			4.47960e19i			1.36955i
$276$	1.98683e19	−	1.77063e18i	0.590049	−	0.0525843i
$277$	5.25867e18			0.151718			0.0758592	−	0.997119i	$-0.475830\pi$
$277$	5.25867e18			0.151718			0.0758592	+	0.997119i	$0.475830\pi$
$278$	5.64521e19	−	2.51049e18i	1.58242	−	0.0703720i
$279$			1.44127e19i			0.392564i
$280$	1.55386e19	−	2.08406e18i	0.411290	−	0.0551627i
$281$	2.72271e19			0.700409			0.350204	−	0.936673i	$-0.386112\pi$
$281$	2.72271e19			0.700409			0.350204	+	0.936673i	$0.386112\pi$
$282$	9.18456e17	+	2.06529e19i	0.0229650	+	0.516401i
$283$		−	2.29628e19i		−	0.558128i	−0.960273	−	0.279064i	$-0.909976\pi$
$283$		−	2.29628e19i		−	0.558128i	0.960273	−	0.279064i	$-0.0900241\pi$
$284$	−2.35911e18	−	2.64716e19i	−0.0557444	−	0.625508i
$285$	−7.03249e18			−0.161566
$286$	−7.32491e19	+	3.25747e18i	−1.63634	+	0.0727700i
$287$		−	1.30819e20i		−	2.84195i
$288$	−3.47697e18	−	1.53889e19i	−0.0734618	−	0.325138i
$289$	−4.75589e19			−0.977348
$290$	6.37138e16	+	1.43270e18i	0.00127365	+	0.0286399i
$291$		−	3.16217e19i		−	0.614951i
$292$	1.92353e19	−	1.71422e18i	0.363945	−	0.0324342i
$293$	4.58027e19			0.843239			0.421619	−	0.906773i	$-0.361462\pi$
$293$	4.58027e19			0.843239			0.421619	+	0.906773i	$0.361462\pi$
$294$	−8.06283e19	+	3.58564e18i	−1.44447	+	0.0642373i
$295$		−	1.54879e19i		−	0.270032i
$296$	−2.67889e18	−	1.99736e19i	−0.0454591	−	0.338940i
$297$	1.67815e19			0.277191
$298$	3.89193e18	+	8.75158e19i	0.0625799	+	1.40720i
$299$			7.45380e19i			1.16683i
$300$	−3.19725e18	−	3.58764e19i	−0.0487312	−	0.546813i
$301$	2.46713e19			0.366150
$302$	9.25585e19	−	4.11619e18i	1.33771	−	0.0594894i
$303$			7.67824e18i			0.108074i
$304$	−1.62835e19	−	9.06331e19i	−0.223234	−	1.24251i
$305$	−4.77712e18			−0.0637922
$306$	−1.71337e17	−	3.85276e18i	−0.00222884	−	0.0501188i
$307$			7.08212e19i			0.897545i	0.893646	+	0.448773i	$0.148139\pi$
$307$			7.08212e19i			0.897545i	−0.893646	+	0.448773i	$0.851861\pi$
$308$	−2.17497e20	+	1.93831e19i	−2.68564	+	0.239341i
$309$	3.96522e19			0.477089
$310$	2.22439e19	−	9.89212e17i	0.260806	−	0.0115983i
$311$			6.64720e19i			0.759549i	0.925079	+	0.379774i	$0.123998\pi$
$311$			6.64720e19i			0.759549i	−0.925079	+	0.379774i	$0.876002\pi$
$312$	5.84315e19	−	7.83690e18i	0.650744	−	0.0872786i
$313$	2.79684e19			0.303608			0.151804	−	0.988411i	$-0.451492\pi$
$313$	2.79684e19			0.303608			0.151804	+	0.988411i	$0.451492\pi$
$314$	−2.18900e18	−	4.92229e19i	−0.0231638	−	0.520871i
$315$		−	1.34086e19i		−	0.138324i
$316$	−1.05393e18	−	1.18262e19i	−0.0106003	−	0.118946i
$317$	1.53397e20			1.50433			0.752165	−	0.658975i	$-0.229010\pi$
$317$	1.53397e20			1.50433			0.752165	+	0.658975i	$0.229010\pi$
$318$	1.33308e19	−	5.92835e17i	0.127479	−	0.00566914i
$319$		−	1.99743e19i		−	0.186272i
$320$	−2.35119e19	+	6.42242e18i	−0.213840	+	0.0584116i
$321$	3.16060e19			0.280368
$322$	9.86207e18	+	2.21763e20i	0.0853338	+	1.91886i
$323$		−	2.25096e19i		−	0.189998i
$324$	−1.34400e19	+	1.19776e18i	−0.110672	+	0.00986298i
$325$	1.34594e20			1.08133
$326$	−7.74977e19	+	3.44641e18i	−0.607502	+	0.0270163i
$327$			8.53795e19i			0.653088i
$328$	2.70351e19	+	2.01572e20i	0.201807	+	1.50466i
$329$	−2.30064e20			−1.67603
$330$	−1.15180e18	−	2.58998e19i	−0.00818963	−	0.184156i
$331$		−	2.20271e19i		−	0.152874i	−0.997074	−	0.0764371i	$-0.975646\pi$
$331$		−	2.20271e19i		−	0.152874i	0.997074	−	0.0764371i	$-0.0243544\pi$
$332$	−8.09239e18	−	9.08047e19i	−0.0548242	−	0.615182i
$333$	−1.72356e19			−0.113992
$334$	−2.36686e20	+	1.05257e19i	−1.52827	+	0.0679641i
$335$			2.22934e19i			0.140546i
$336$	1.72806e20	−	3.10471e19i	1.06377	−	0.191120i
$337$	1.11783e20			0.671948			0.335974	−	0.941871i	$-0.390935\pi$
$337$	1.11783e20			0.671948			0.335974	+	0.941871i	$0.390935\pi$
$338$	2.21936e18	+	4.99057e19i	0.0130285	+	0.292965i
$339$			1.50192e20i			0.861090i
$340$	−5.93443e18	+	5.28868e17i	−0.0332313	+	0.00296153i
$341$	−3.10119e20			−1.69626
$342$	−7.86784e19	+	3.49892e18i	−0.420384	+	0.0186950i
$343$		−	5.39527e20i		−	2.81618i
$344$	−3.80146e19	+	5.09857e18i	−0.193858	+	0.0260005i
$345$	−2.63556e19			−0.131317
$346$	−1.46100e19	−	3.28528e20i	−0.0711282	−	1.59942i
$347$			2.52380e20i			1.20066i	0.799754	+	0.600328i	$0.204963\pi$
$347$			2.52380e20i			1.20066i	−0.799754	+	0.600328i	$0.795037\pi$
$348$	1.42564e18	+	1.59971e19i	0.00662789	+	0.0743716i
$349$	−1.31132e20			−0.595805			−0.297903	−	0.954596i	$-0.596287\pi$
$349$	−1.31132e20			−0.595805			−0.297903	+	0.954596i	$0.596287\pi$
$350$	4.00440e20	−	1.78080e19i	1.77825	−	0.0790809i
$351$		−	5.04217e19i		−	0.218857i
$352$	3.31124e20	−	7.48143e19i	1.40491	−	0.317427i
$353$	1.27633e20			0.529379			0.264690	−	0.964334i	$-0.414731\pi$
$353$	1.27633e20			0.529379			0.264690	+	0.964334i	$0.414731\pi$
$354$	−7.70578e18	−	1.73276e20i	−0.0312457	−	0.702606i
$355$			3.51149e19i			0.139208i
$356$	−2.46846e20	+	2.19986e19i	−0.956811	+	0.0852697i
$357$	4.29182e19			0.162666
$358$	3.88557e20	−	1.72796e19i	1.44009	−	0.0640426i
$359$		−	2.34814e20i		−	0.851075i	−0.904941	−	0.425537i	$-0.860085\pi$
$359$		−	2.34814e20i		−	0.851075i	0.904941	−	0.425537i	$-0.139915\pi$
$360$	2.77102e18	+	2.06605e19i	0.00982244	+	0.0732355i
$361$	−1.71234e20			−0.593653
$362$	−5.91448e18	−	1.32996e20i	−0.0200562	−	0.450992i
$363$			1.87032e20i			0.620387i
$364$	5.82383e19	+	6.53492e20i	0.188972	+	2.12046i
$365$	−2.55159e19			−0.0809967
$366$	−5.34456e19	+	2.37679e18i	−0.165983	+	0.00738145i
$367$		−	3.65051e20i		−	1.10924i	−0.832104	−	0.554619i	$-0.812864\pi$
$367$		−	3.65051e20i		−	1.10924i	0.832104	−	0.554619i	$-0.187136\pi$
$368$	−6.10255e19	−	3.39665e20i	−0.181438	−	1.00988i
$369$	1.73940e20			0.506045
$370$	1.18297e18	+	2.66007e19i	0.00336789	+	0.0757321i
$371$			1.48499e20i			0.413745i
$372$	2.48369e20	−	2.21343e19i	0.677257	−	0.0603562i
$373$	−4.99356e20			−1.33272			−0.666362	−	0.745629i	$-0.732149\pi$
$373$	−4.99356e20			−1.33272			−0.666362	+	0.745629i	$0.732149\pi$
$374$	8.29003e19	−	3.68667e18i	0.216562	−	0.00963079i
$375$			9.76405e19i			0.249678i
$376$	3.54493e20	−	4.75451e19i	0.887371	−	0.119015i
$377$	−6.00148e19			−0.147071
$378$	−6.67125e18	−	1.50013e20i	−0.0160056	−	0.359910i
$379$			2.81240e20i			0.660639i	0.943869	+	0.330319i	$0.107156\pi$
$379$			2.81240e20i			0.660639i	−0.943869	+	0.330319i	$0.892844\pi$
$380$	1.08002e19	+	1.21189e20i	0.0248406	+	0.278736i
$381$	−3.60212e20			−0.811256
$382$	−6.21108e20	+	2.76214e19i	−1.36981	+	0.0609170i
$383$			2.75719e20i			0.595492i	0.954645	+	0.297746i	$0.0962348\pi$
$383$			2.75719e20i			0.595492i	−0.954645	+	0.297746i	$0.903765\pi$
$384$	−2.59852e20	+	8.35510e19i	−0.549637	+	0.176727i
$385$	2.88514e20			0.597696
$386$	−2.75542e19	−	6.19597e20i	−0.0559099	−	1.25722i
$387$			3.28036e19i			0.0651979i
$388$	−5.44926e20	+	4.85630e19i	−1.06092	+	0.0945479i
$389$	−2.91955e20			−0.556826			−0.278413	−	0.960461i	$-0.589808\pi$
$389$	−2.91955e20			−0.556826			−0.278413	+	0.960461i	$0.589808\pi$
$390$	−7.78186e19	+	3.46068e18i	−0.145401	+	0.00646614i
$391$		−	8.43590e19i		−	0.154425i
$392$	1.85615e20	+	1.38394e21i	0.332909	+	2.48215i
$393$	−5.33060e19			−0.0936776
$394$	3.45358e19	+	7.76589e20i	0.0594703	+	1.33728i
$395$			1.56876e19i			0.0264716i
$396$	−2.57722e19	−	2.89190e20i	−0.0426177	−	0.478214i
$397$	6.92196e20			1.12177			0.560886	−	0.827893i	$-0.310460\pi$
$397$	6.92196e20			1.12177			0.560886	+	0.827893i	$0.310460\pi$
$398$	7.49719e20	−	3.33409e19i	1.19079	−	0.0529556i
$399$		−	8.76445e20i		−	1.36440i
$400$	−6.13336e20	+	1.10194e20i	−0.935876	+	0.168143i
$401$	1.00851e21			1.50844			0.754219	−	0.656623i	$-0.228016\pi$
$401$	1.00851e21			1.50844			0.754219	+	0.656623i	$0.228016\pi$
$402$	1.10918e19	+	2.49415e20i	0.0162627	+	0.365691i
$403$			9.31782e20i			1.33929i
$404$	1.32317e20	−	1.17919e19i	0.186451	−	0.0166162i
$405$	1.78284e19			0.0246304
$406$	−1.78554e20	+	7.94051e18i	−0.241859	+	0.0107557i
$407$		−	3.70861e20i		−	0.492556i
$408$	−6.61303e19	+	8.86948e18i	−0.0861230	+	0.0115509i
$409$	−1.90540e20			−0.243333			−0.121666	−	0.992571i	$-0.538824\pi$
$409$	−1.90540e20			−0.243333			−0.121666	+	0.992571i	$0.538824\pi$
$410$	−1.19384e19	−	2.68452e20i	−0.0149511	−	0.336199i
$411$			6.73440e20i			0.827112i
$412$	−6.08959e19	−	6.83313e20i	−0.0733517	−	0.823080i
$413$	1.93022e21			2.28038
$414$	−2.94862e20	+	1.31129e19i	−0.341677	+	0.0151948i
$415$			1.20454e20i			0.136910i
$416$	−2.24787e20	−	9.94895e20i	−0.250625	−	1.10925i
$417$	−8.36139e20			−0.914513
$418$	−7.52866e19	−	1.69293e21i	−0.0807807	−	1.81647i
$419$			6.02298e19i			0.0634015i	0.999497	+	0.0317007i	$0.0100923\pi$
$419$			6.02298e19i			0.0634015i	−0.999497	+	0.0317007i	$0.989908\pi$
$420$	−2.31066e20	+	2.05922e19i	−0.238639	+	0.0212671i
$421$	3.25175e20			0.329504			0.164752	−	0.986335i	$-0.447318\pi$
$421$	3.25175e20			0.329504			0.164752	+	0.986335i	$0.447318\pi$
$422$	−1.23220e21	+	5.47976e19i	−1.22513	+	0.0544831i
$423$		−	3.05899e20i		−	0.298439i
$424$	−3.06889e19	−	2.28814e20i	−0.0293802	−	0.219057i
$425$	−1.52328e20			−0.143109
$426$	1.74709e19	+	3.92860e20i	0.0161079	+	0.362210i
$427$		−	5.95362e20i		−	0.538714i
$428$	−4.85389e19	−	5.44655e20i	−0.0431062	−	0.483695i
$429$	1.08493e21			0.945676
$430$	5.06276e19	−	2.25147e18i	0.0433151	−	0.00192628i
$431$		−	1.23048e21i		−	1.03337i	−0.856174	−	0.516687i	$-0.827165\pi$
$431$		−	1.23048e21i		−	1.03337i	0.856174	−	0.516687i	$-0.172835\pi$
$432$	4.12811e19	+	2.29768e20i	0.0340315	+	0.189417i
$433$	−1.61953e21			−1.31065			−0.655324	−	0.755348i	$-0.727468\pi$
$433$	−1.61953e21			−1.31065			−0.655324	+	0.755348i	$0.727468\pi$
$434$	1.23283e20	+	2.77221e21i	0.0979459	+	2.20246i
$435$		−	2.12204e19i		−	0.0165516i
$436$	1.47132e21	−	1.31122e20i	1.12672	−	0.100411i
$437$	−1.72272e21			−1.29528
$438$	−2.85467e20	+	1.26951e19i	−0.210748	+	0.00937221i
$439$		−	7.38096e20i		−	0.535053i	−0.963551	−	0.267526i	$-0.913794\pi$
$439$		−	7.38096e20i		−	0.535053i	0.963551	−	0.267526i	$-0.0862063\pi$
$440$	−4.44555e20	+	5.96243e19i	−0.316449	+	0.0424426i
$441$	1.19422e21			0.834790
$442$	−1.10770e19	−	2.49082e20i	−0.00760401	−	0.170987i
$443$			5.24293e20i			0.353463i	0.984259	+	0.176732i	$0.0565525\pi$
$443$			5.24293e20i			0.353463i	−0.984259	+	0.176732i	$0.943448\pi$
$444$	2.64696e19	+	2.97016e20i	0.0175261	+	0.196660i
$445$	3.27445e20			0.212941
$446$	−1.09489e21	+	4.86912e19i	−0.699348	+	0.0311008i
$447$		−	1.29624e21i		−	0.813251i
$448$	−8.00413e20	−	2.93024e21i	−0.493276	−	1.80584i
$449$	−3.38302e20			−0.204802			−0.102401	−	0.994743i	$-0.532652\pi$
$449$	−3.38302e20			−0.204802			−0.102401	+	0.994743i	$0.532652\pi$
$450$	2.36780e19	+	5.32435e20i	0.0140814	+	0.316641i
$451$			3.74269e21i			2.18661i
$452$	2.58821e21	−	2.30657e20i	1.48556	−	0.132391i
$453$	−1.37093e21			−0.773089
$454$	1.94780e21	−	8.66208e19i	1.07919	−	0.0479927i
$455$		−	8.66867e20i		−	0.471912i
$456$	1.81126e20	+	1.35047e21i	0.0968863	+	0.722378i
$457$	2.94882e21			1.54995			0.774976	−	0.631991i	$-0.217762\pi$
$457$	2.94882e21			1.54995			0.774976	+	0.631991i	$0.217762\pi$
$458$	6.51396e19	+	1.46476e21i	0.0336451	+	0.756559i
$459$			5.70651e19i			0.0289647i
$460$	4.04756e19	+	4.54177e20i	0.0201898	+	0.226549i
$461$	−3.14872e21			−1.54357			−0.771785	−	0.635883i	$-0.780636\pi$
$461$	−3.14872e21			−1.54357			−0.771785	+	0.635883i	$0.780636\pi$
$462$	3.22784e21	−	1.43546e20i	1.55516	−	0.0691600i
$463$			7.56882e20i			0.358410i	0.983812	+	0.179205i	$0.0573526\pi$
$463$			7.56882e20i			0.358410i	−0.983812	+	0.179205i	$0.942647\pi$
$464$	2.73483e20	−	4.91351e19i	0.127288	−	0.0228691i
$465$	−3.29465e20			−0.150725
$466$	1.05968e20	+	2.38285e21i	0.0476527	+	1.07154i
$467$			3.65068e20i			0.161376i	0.996739	+	0.0806880i	$0.0257117\pi$
$467$			3.65068e20i			0.161376i	−0.996739	+	0.0806880i	$0.974288\pi$
$468$	−8.68900e20	+	7.74351e19i	−0.377575	+	0.0336489i
$469$	−2.77838e21			−1.18689
$470$	−4.72112e20	+	2.09954e19i	−0.198272	+	0.00881740i
$471$			7.29065e20i			0.301022i
$472$	−2.97417e21	+	3.98900e20i	−1.20734	+	0.161930i
$473$	−7.05838e20			−0.281719
$474$	7.80516e18	+	1.75511e20i	0.00306306	+	0.0688774i
$475$			3.11073e21i			1.20037i
$476$	−6.59117e19	−	7.39595e20i	−0.0250096	−	0.280633i
$477$	−1.97449e20			−0.0736727
$478$	2.82894e21	−	1.25806e20i	1.03801	−	0.0461614i
$479$		−	1.16860e21i		−	0.421678i	−0.977521	−	0.210839i	$-0.932380\pi$
$479$		−	1.16860e21i		−	0.421678i	0.977521	−	0.210839i	$-0.0676196\pi$
$480$	3.51781e20	−	7.94815e19i	0.124837	−	0.0282057i
$481$	−1.11429e21			−0.388899
$482$	−3.85313e19	−	8.66434e20i	−0.0132263	−	0.297413i
$483$		−	3.28464e21i		−	1.10895i
$484$	3.22306e21	−	2.87234e20i	1.07030	−	0.0953836i
$485$	7.22852e20			0.236111
$486$	1.99461e20	−	8.87026e18i	0.0640867	−	0.00285001i
$487$		−	1.89144e21i		−	0.597808i	−0.954283	−	0.298904i	$-0.903379\pi$
$487$		−	1.89144e21i		−	0.597808i	0.954283	−	0.298904i	$-0.0966210\pi$
$488$	1.23038e20	+	9.17361e20i	0.0382542	+	0.285221i
$489$	1.14786e21			0.351088
$490$	−8.19655e19	−	1.84312e21i	−0.0246639	−	0.554605i
$491$			1.22609e21i			0.362969i	0.983394	+	0.181484i	$0.0580902\pi$
$491$			1.22609e21i			0.362969i	−0.983394	+	0.181484i	$0.941910\pi$
$492$	−2.67129e20	−	2.99746e21i	−0.0778037	−	0.873036i
$493$	6.79223e19			0.0194642
$494$	−5.08658e21	+	2.26206e20i	−1.43420	+	0.0637806i
$495$			3.83615e20i			0.106428i
$496$	−7.62866e20	−	4.24607e21i	−0.208255	−	1.15913i
$497$	−4.37630e21			−1.17559
$498$	5.99301e19	+	1.34762e21i	0.0158420	+	0.356231i
$499$			2.70150e21i			0.702750i	0.936235	+	0.351375i	$0.114286\pi$
$499$			2.70150e21i			0.702750i	−0.936235	+	0.351375i	$0.885714\pi$
$500$	1.68261e21	−	1.49952e20i	0.430747	−	0.0383876i
$501$	3.50567e21			0.883221
$502$	−2.26865e21	+	1.00889e20i	−0.562520	+	0.0250159i
$503$		−	5.65754e21i		−	1.38065i	−0.723499	−	0.690325i	$-0.757468\pi$
$503$		−	5.65754e21i		−	1.38065i	0.723499	−	0.690325i	$-0.242532\pi$
$504$	−2.57488e21	+	3.45346e20i	−0.618461	+	0.0829488i
$505$	−1.75520e20			−0.0414950
$506$	−2.82151e20	−	6.34458e21i	−0.0656564	−	1.47638i
$507$		−	7.39177e20i		−	0.169311i
$508$	5.53196e20	+	6.20741e21i	0.124730	+	1.39959i
$509$	7.61503e21			1.69017			0.845083	−	0.534635i	$-0.179551\pi$
$509$	7.61503e21			1.69017			0.845083	+	0.534635i	$0.179551\pi$
$510$	8.80719e19	−	3.91666e18i	0.0192431	−	0.000855765i
$511$		−	3.17999e21i		−	0.684003i
$512$	1.83888e21	+	4.34963e21i	0.389397	+	0.921070i
$513$	1.16534e21			0.242949
$514$	−2.96110e19	−	6.65848e20i	−0.00607783	−	0.136669i
$515$			9.06425e20i			0.183178i
$516$	5.65293e20	−	5.03781e19i	0.112480	−	0.0100241i
$517$	6.58207e21			1.28955
$518$	−3.31519e21	+	1.47430e20i	−0.639544	+	0.0284413i
$519$			4.86598e21i			0.924340i
$520$	1.79147e20	+	1.33571e21i	0.0335106	+	0.249853i
$521$	2.49450e21			0.459495			0.229748	−	0.973250i	$-0.426210\pi$
$521$	2.49450e21			0.459495			0.229748	+	0.973250i	$0.426210\pi$
$522$	−1.05579e19	−	2.37410e20i	−0.00191520	−	0.0430661i
$523$		−	9.64800e21i		−	1.72355i	−0.507291	−	0.861775i	$-0.669353\pi$
$523$		−	9.64800e21i		−	1.72355i	0.507291	−	0.861775i	$-0.330647\pi$
$524$	8.18648e19	+	9.18605e20i	0.0144028	+	0.161614i
$525$	−5.93111e21			−1.02769
$526$	3.01945e21	−	1.34279e20i	0.515279	−	0.0229150i
$527$		−	1.05455e21i		−	0.177249i
$528$	−4.94394e21	+	8.88248e20i	−0.818468	+	0.147049i
$529$	−3.23608e20			−0.0527684
$530$	1.35519e19	+	3.04734e20i	0.00217667	+	0.0489456i
$531$			2.56647e21i			0.406051i
$532$	−1.51035e22	+	1.34600e21i	−2.35388	+	0.209774i
$533$	1.12453e22			1.72644
$534$	3.66340e21	−	1.62916e20i	0.554057	−	0.0246396i
$535$			7.22493e20i			0.107647i
$536$	4.28106e21	−	5.74181e20i	0.628395	−	0.0842811i
$537$	−5.75510e21			−0.832259
$538$	−1.71075e20	−	3.84687e21i	−0.0243740	−	0.548086i
$539$			2.56963e22i			3.60711i
$540$	−2.73800e19	−	3.07231e20i	−0.00378689	−	0.0424927i
$541$	−1.85308e20			−0.0252532			−0.0126266	−	0.999920i	$-0.504019\pi$
$541$	−1.85308e20			−0.0252532			−0.0126266	+	0.999920i	$0.504019\pi$
$542$	−3.80877e21	+	1.69381e20i	−0.511435	+	0.0227441i
$543$			1.96986e21i			0.260638i
$544$	2.54405e20	+	1.12598e21i	0.0331691	+	0.146805i
$545$	−1.95173e21			−0.250753
$546$	−4.31298e20	−	9.69837e21i	−0.0546054	−	1.22788i
$547$		−	3.32896e21i		−	0.415346i	−0.978198	−	0.207673i	$-0.933411\pi$
$547$		−	3.32896e21i		−	0.415346i	0.978198	−	0.207673i	$-0.0665890\pi$
$548$	1.16052e22	−	1.03424e21i	1.42694	−	0.127167i
$549$	7.91609e20			0.0959250
$550$	−1.14565e22	+	5.09482e20i	−1.36820	+	0.0608454i
$551$		−	1.38706e21i		−	0.163261i
$552$	6.78804e20	+	5.06112e21i	0.0787466	+	0.587130i
$553$	−1.95511e21			−0.223548
$554$	5.98089e19	+	1.34489e21i	0.00674043	+	0.151569i
$555$		−	3.93996e20i		−	0.0437671i
$556$	1.28410e21	+	1.44089e22i	0.140605	+	1.57773i
$557$	−1.43792e22			−1.55201			−0.776003	−	0.630730i	$-0.782756\pi$
$557$	−1.43792e22			−1.55201			−0.776003	+	0.630730i	$0.782756\pi$
$558$	−3.68600e21	+	1.63921e20i	−0.392177	+	0.0174405i
$559$			2.12076e21i			0.222432i
$560$	7.09719e20	+	3.95025e21i	0.0733807	+	0.408433i
$561$	−1.22788e21			−0.125156
$562$	3.09665e20	+	6.96327e21i	0.0311172	+	0.699717i
$563$		−	1.86531e22i		−	1.84793i	−0.382483	−	0.923963i	$-0.624931\pi$
$563$		−	1.86531e22i		−	1.84793i	0.382483	−	0.923963i	$-0.375069\pi$
$564$	−5.27146e21	+	4.69785e20i	−0.514871	+	0.0458846i
$565$	−3.43329e21			−0.330616
$566$	5.87268e21	−	2.61165e20i	0.557577	−	0.0247961i
$567$			2.22191e21i			0.208000i
$568$	6.74320e21	−	9.04406e20i	0.622414	−	0.0834789i
$569$	1.93429e22			1.76045			0.880224	−	0.474558i	$-0.157392\pi$
$569$	1.93429e22			1.76045			0.880224	+	0.474558i	$0.157392\pi$
$570$	−7.99832e19	−	1.79854e21i	−0.00717794	−	0.161407i
$571$		−	1.79385e22i		−	1.58744i	−0.608281	−	0.793721i	$-0.708141\pi$
$571$		−	1.79385e22i		−	1.58744i	0.608281	−	0.793721i	$-0.291859\pi$
$572$	−1.66618e21	−	1.86962e22i	−0.145396	−	1.63149i
$573$	9.19953e21			0.791642
$574$	3.34566e22	−	1.48785e21i	2.83914	−	0.126260i
$575$			1.16581e22i			0.975626i
$576$	3.89612e21	−	1.06425e21i	0.321553	−	0.0878342i
$577$	−9.13899e21			−0.743861			−0.371930	−	0.928261i	$-0.621304\pi$
$577$	−9.13899e21			−0.743861			−0.371930	+	0.928261i	$0.621304\pi$
$578$	−5.40906e20	−	1.21631e22i	−0.0434209	−	0.976383i
$579$			9.17714e21i			0.726572i
$580$	−3.65684e20	+	3.25892e19i	−0.0285550	+	0.00254478i
$581$	−1.50119e22			−1.15618
$582$	8.08715e21	−	3.59645e20i	0.614344	−	0.0273206i
$583$		−	4.24852e21i		−	0.318339i
$584$	6.57177e20	+	4.89987e21i	0.0485712	+	0.362144i
$585$	1.15261e21			0.0840301
$586$	5.20932e20	+	1.17139e22i	0.0374628	+	0.842406i
$587$		−	6.18065e21i		−	0.438459i	−0.975673	−	0.219230i	$-0.929646\pi$
$587$		−	6.18065e21i		−	0.438459i	0.975673	−	0.219230i	$-0.0703544\pi$
$588$	−1.83403e21	−	2.05797e22i	−0.128348	−	1.44019i
$589$	−2.15353e22			−1.48672
$590$	3.96098e21	−	1.76149e20i	0.269766	−	0.0119968i
$591$		−	1.15024e22i		−	0.772841i
$592$	5.07773e21	−	9.12286e20i	0.336586	−	0.0604724i
$593$	−1.54453e22			−1.01009			−0.505045	−	0.863093i	$-0.668524\pi$
$593$	−1.54453e22			−1.01009			−0.505045	+	0.863093i	$0.668524\pi$
$594$	1.90862e20	+	4.29182e21i	0.0123148	+	0.276917i
$595$			9.81084e20i			0.0624555i
$596$	−2.23377e22	+	1.99070e21i	−1.40303	+	0.125036i
$597$	−1.11044e22			−0.688180
$598$	−1.90629e22	+	8.47749e20i	−1.16568	+	0.0518392i
$599$			2.88339e21i			0.173976i	0.996209	+	0.0869880i	$0.0277242\pi$
$599$			2.88339e21i			0.173976i	−0.996209	+	0.0869880i	$0.972276\pi$
$600$	9.13892e21	−	1.22572e21i	0.544108	−	0.0729764i
$601$	3.09120e22			1.81607			0.908033	−	0.418899i	$-0.137584\pi$
$601$	3.09120e22			1.81607			0.908033	+	0.418899i	$0.137584\pi$
$602$	2.80596e20	+	6.30961e21i	0.0162671	+	0.365789i
$603$		−	3.69421e21i		−	0.211340i
$604$	2.10541e21	+	2.36248e22i	0.118861	+	1.33374i
$605$	−4.27544e21			−0.238198
$606$	−1.96369e21	+	8.73276e19i	−0.107967	+	0.00480143i
$607$			5.21560e21i			0.283005i	0.989938	+	0.141503i	$0.0451934\pi$
$607$			5.21560e21i			0.283005i	−0.989938	+	0.141503i	$0.954807\pi$
$608$	2.29940e22	−	5.19527e21i	1.23136	−	0.278214i
$609$	2.64465e21			0.139775
$610$	−5.43320e19	−	1.22174e21i	−0.00283411	−	0.0637292i
$611$		−	1.97765e22i		−	1.01817i
$612$	9.83385e20	−	8.76379e19i	0.0499703	−	0.00445328i
$613$	−1.12100e22			−0.562239			−0.281119	−	0.959673i	$-0.590706\pi$
$613$	−1.12100e22			−0.562239			−0.281119	+	0.959673i	$0.590706\pi$
$614$	−1.81123e22	+	8.05476e20i	−0.896659	+	0.0398755i
$615$			3.97617e21i			0.194296i
$616$	−7.43084e21	−	5.54039e22i	−0.358420	−	2.67236i
$617$	−7.59471e21			−0.361601			−0.180801	−	0.983520i	$-0.557869\pi$
$617$	−7.59471e21			−0.361601			−0.180801	+	0.983520i	$0.557869\pi$
$618$	4.50979e20	+	1.01409e22i	0.0211957	+	0.476617i
$619$			1.37221e22i			0.636642i	0.947983	+	0.318321i	$0.103119\pi$
$619$			1.37221e22i			0.636642i	−0.947983	+	0.318321i	$0.896881\pi$
$620$	5.05976e20	+	5.67756e21i	0.0231738	+	0.260033i
$621$	4.36734e21			0.197462
$622$	−1.70000e22	+	7.56011e20i	−0.758799	+	0.0337447i
$623$			4.08088e22i			1.79825i
$624$	2.66883e21	+	1.48546e22i	0.116103	+	0.646224i
$625$	1.99069e22			0.854997
$626$	3.18096e20	+	7.15285e21i	0.0134885	+	0.303308i
$627$			2.50748e22i			1.04978i
$628$	1.25637e22	−	1.11966e21i	0.519328	−	0.0462818i
$629$	1.26110e21			0.0514690
$630$	3.42920e21	−	1.52501e20i	0.138188	−	0.00614536i
$631$			1.18843e22i			0.472865i	0.971648	+	0.236433i	$0.0759782\pi$
$631$			1.18843e22i			0.472865i	−0.971648	+	0.236433i	$0.924022\pi$
$632$	3.01253e21	−	4.04044e20i	0.118357	−	0.0158742i
$633$	1.82508e22			0.708030
$634$	1.74464e21	+	3.92309e22i	0.0668333	+	1.50284i
$635$		−	8.23423e21i		−	0.311482i
$636$	3.03232e20	+	3.40257e21i	0.0113271	+	0.127101i
$637$	7.72069e22			2.84800
$638$	5.10838e21	−	2.27176e20i	0.186088	−	0.00827554i
$639$		−	5.81884e21i		−	0.209329i
$640$	−1.90993e21	−	5.94006e21i	−0.0678542	−	0.211033i
$641$	−1.01345e22			−0.355582			−0.177791	−	0.984068i	$-0.556895\pi$
$641$	−1.01345e22			−0.355582			−0.177791	+	0.984068i	$0.556895\pi$
$642$	3.59466e20	+	8.08313e21i	0.0124560	+	0.280091i
$643$		−	1.20343e22i		−	0.411845i	−0.978568	−	0.205922i	$-0.933981\pi$
$643$		−	1.20343e22i		−	0.411845i	0.978568	−	0.205922i	$-0.0660194\pi$
$644$	−5.66031e22	+	5.04439e21i	−1.91317	+	0.170499i
$645$	−7.49870e20			−0.0250327
$646$	5.75677e21	−	2.56010e20i	0.189810	−	0.00844107i
$647$			2.59972e21i			0.0846628i	0.999104	+	0.0423314i	$0.0134785\pi$
$647$			2.59972e21i			0.0846628i	−0.999104	+	0.0423314i	$0.986521\pi$
$648$	−4.59181e20	−	3.42362e21i	−0.0147701	−	0.110125i
$649$	−5.52230e22			−1.75454
$650$	1.53079e21	+	3.44221e22i	0.0480406	+	1.08026i
$651$		−	4.10605e22i		−	1.27285i
$652$	−1.76282e21	−	1.97806e22i	−0.0539793	−	0.605702i
$653$	4.59610e22			1.39022			0.695111	−	0.718903i	$-0.255355\pi$
$653$	4.59610e22			1.39022			0.695111	+	0.718903i	$0.255355\pi$
$654$	−2.18356e22	+	9.71054e20i	−0.652443	+	0.0290149i
$655$		−	1.21854e21i		−	0.0359675i
$656$	−5.12440e22	+	9.20670e21i	−1.49421	+	0.268456i
$657$	4.22819e21			0.121796
$658$	−2.61661e21	−	5.88383e22i	−0.0744614	−	1.67438i
$659$		−	4.92808e22i		−	1.38546i	−0.721196	−	0.692731i	$-0.756407\pi$
$659$		−	4.92808e22i		−	1.38546i	0.721196	−	0.692731i	$-0.243593\pi$
$660$	6.61071e21	−	5.89137e20i	0.183610	−	0.0163631i
$661$	−5.05160e22			−1.38617			−0.693086	−	0.720855i	$-0.743749\pi$
$661$	−5.05160e22			−1.38617			−0.693086	+	0.720855i	$0.743749\pi$
$662$	5.63338e21	−	2.50523e20i	0.152723	−	0.00679178i
$663$			3.68927e21i			0.0988172i
$664$	2.31310e22	−	3.10236e21i	0.612139	−	0.0821009i
$665$	2.00350e22			0.523861
$666$	−1.96027e20	−	4.40797e21i	−0.00506434	−	0.113879i
$667$		−	5.19827e21i		−	0.132694i
$668$	−5.38384e21	−	6.04121e22i	−0.135794	−	1.52374i
$669$	1.62170e22			0.404168
$670$	−5.70148e21	+	2.53551e20i	−0.140407	+	0.00624407i
$671$			1.70331e22i			0.414490i
$672$	9.90561e21	+	4.38417e22i	0.238192	+	1.05422i
$673$	3.85828e22			0.916797			0.458398	−	0.888747i	$-0.348423\pi$
$673$	3.85828e22			0.916797			0.458398	+	0.888747i	$0.348423\pi$
$674$	1.27135e21	+	2.85881e22i	0.0298528	+	0.671284i
$675$		−	7.88615e21i		−	0.182993i
$676$	−1.27380e22	+	1.13519e21i	−0.292097	+	0.0260313i
$677$	1.69357e21			0.0383790			0.0191895	−	0.999816i	$-0.493891\pi$
$677$	1.69357e21			0.0383790			0.0191895	+	0.999816i	$0.493891\pi$
$678$	−3.84111e22	+	1.70819e21i	−0.860240	+	0.0382559i
$679$			9.00875e22i			1.99391i
$680$	−2.02751e20	−	1.51170e21i	−0.00443498	−	0.0330669i
$681$	−2.88498e22			−0.623685
$682$	−3.52710e21	−	7.93120e22i	−0.0753603	−	1.69459i
$683$		−	5.11935e22i		−	1.08106i	−0.841326	−	0.540529i	$-0.818224\pi$
$683$		−	5.11935e22i		−	1.08106i	0.841326	−	0.540529i	$-0.181776\pi$
$684$	−1.78968e21	−	2.00820e22i	−0.0373530	−	0.419139i
$685$	−1.53944e22			−0.317570
$686$	1.37982e23	−	6.13624e21i	2.81340	−	0.125115i
$687$		−	2.16953e22i		−	0.437231i
$688$	−1.73630e21	−	9.66415e21i	−0.0345873	−	0.192511i
$689$	−1.27651e22			−0.251345
$690$	−2.99752e20	−	6.74037e21i	−0.00583404	−	0.131187i
$691$			5.80131e22i			1.11610i	0.829809	+	0.558048i	$0.188449\pi$
$691$			5.80131e22i			1.11610i	−0.829809	+	0.558048i	$0.811551\pi$
$692$	8.38539e22	−	7.47294e21i	1.59468	−	0.142116i
$693$	−4.78091e22			−0.898762
$694$	−6.45454e22	+	2.87041e21i	−1.19947	+	0.0533418i
$695$		−	1.91136e22i		−	0.351127i
$696$	−4.07500e21	+	5.46544e20i	−0.0740037	+	0.00992547i
$697$	−1.27269e22			−0.228487
$698$	−1.49141e21	−	3.35366e22i	−0.0264700	−	0.595217i
$699$		−	3.52935e22i		−	0.619266i
$700$	9.10871e21	+	1.02209e23i	0.158006	+	1.77298i
$701$	4.57259e22			0.784184			0.392092	−	0.919926i	$-0.371752\pi$
$701$	4.57259e22			0.784184			0.392092	+	0.919926i	$0.371752\pi$
$702$	1.28952e22	−	5.73465e20i	0.218641	−	0.00972321i
$703$		−	2.57534e22i		−	0.431709i
$704$	2.28996e22	+	8.38332e22i	0.379530	+	1.38942i
$705$	6.99268e21			0.114586
$706$	1.45162e21	+	3.26419e22i	0.0235189	+	0.528856i
$707$		−	2.18747e22i		−	0.350418i
$708$	4.42272e22	−	3.94146e21i	0.700524	−	0.0624297i
$709$	1.97438e21			0.0309215			0.0154607	−	0.999880i	$-0.495078\pi$
$709$	1.97438e21			0.0309215			0.0154607	+	0.999880i	$0.495078\pi$
$710$	−8.98054e21	+	3.99375e20i	−0.139071	+	0.00618464i
$711$		−	2.59957e21i		−	0.0398057i
$712$	−8.43355e21	−	6.28800e22i	−0.127694	−	0.952078i
$713$	−8.07076e22			−1.20837
$714$	4.88125e20	+	1.09762e22i	0.00722678	+	0.162505i
$715$			2.48008e22i			0.363093i
$716$	8.83840e21	+	9.91758e22i	0.127959	+	1.43582i
$717$	−4.19008e22			−0.599886
$718$	6.00529e22	−	2.67062e21i	0.850234	−	0.0378109i
$719$			1.09202e23i			1.52897i	0.644642	+	0.764485i	$0.277007\pi$
$719$			1.09202e23i			1.52897i	−0.644642	+	0.764485i	$0.722993\pi$
$720$	−5.25236e21	+	9.43660e20i	−0.0727268	+	0.0130664i
$721$	−1.12966e23			−1.54691
$722$	−1.94751e21	−	4.37926e22i	−0.0263744	−	0.593067i
$723$			1.28332e22i			0.171881i
$724$	3.39460e22	−	3.02522e21i	0.449656	−	0.0400727i
$725$	−9.38656e21			−0.122971
$726$	−4.78329e22	+	2.12718e21i	−0.619774	+	0.0275621i
$727$			6.91664e22i			0.886380i	0.896428	+	0.443190i	$0.146153\pi$
$727$			6.91664e22i			0.886380i	−0.896428	+	0.443190i	$0.853847\pi$
$728$	−1.66466e23	+	2.23267e22i	−2.10997	+	0.282992i
$729$	−2.95431e21			−0.0370370
$730$	−2.90201e20	−	6.52561e21i	−0.00359846	−	0.0809167i
$731$		−	2.40019e21i		−	0.0294378i
$732$	−1.21571e21	−	1.36415e22i	−0.0147483	−	0.165491i
$733$	−2.16381e22			−0.259649			−0.129825	−	0.991537i	$-0.541441\pi$
$733$	−2.16381e22			−0.259649			−0.129825	+	0.991537i	$0.541441\pi$
$734$	9.33608e22	−	4.15186e21i	1.10814	−	0.0492804i
$735$			2.72993e22i			0.320518i
$736$	8.61742e22	−	1.94702e22i	1.00082	−	0.226125i
$737$	7.94886e22			0.913198
$738$	1.97829e21	+	4.44848e22i	0.0224822	+	0.505546i
$739$		−	6.07196e22i		−	0.682612i	−0.939952	−	0.341306i	$-0.889131\pi$
$739$		−	6.07196e22i		−	0.682612i	0.939952	−	0.341306i	$-0.110869\pi$
$740$	−6.78961e21	+	6.05080e20i	−0.0755077	+	0.00672914i
$741$	7.53397e22			0.828854
$742$	−3.79783e22	+	1.68894e21i	−0.413337	+	0.0183816i
$743$		−	8.98422e22i		−	0.967319i	−0.875256	−	0.483660i	$-0.839307\pi$
$743$		−	8.98422e22i		−	0.967319i	0.875256	−	0.483660i	$-0.160693\pi$
$744$	8.48557e21	+	6.32679e22i	0.0903853	+	0.673907i
$745$	2.96312e22			0.312248
$746$	−5.67937e21	−	1.27709e23i	−0.0592092	−	1.33141i
$747$		−	1.99602e22i		−	0.205873i
$748$	1.88571e21	+	2.11596e22i	0.0192426	+	0.215921i
$749$	−9.00428e22			−0.909064
$750$	−2.49713e22	+	1.11050e21i	−0.249431	+	0.0110925i
$751$		−	8.45223e22i		−	0.835318i	−0.908604	−	0.417659i	$-0.862851\pi$
$751$		−	8.45223e22i		−	0.835318i	0.908604	−	0.417659i	$-0.137149\pi$
$752$	1.61913e22	+	9.01200e22i	0.158321	+	0.881208i
$753$	3.36021e22			0.325092
$754$	−6.82571e20	−	1.53486e22i	−0.00653397	−	0.146926i
$755$		−	3.13386e22i		−	0.296828i
$756$	3.82895e22	−	3.41231e21i	0.358844	−	0.0319796i
$757$	5.06405e21			0.0469603			0.0234802	−	0.999724i	$-0.492525\pi$
$757$	5.06405e21			0.0469603			0.0234802	+	0.999724i	$0.492525\pi$
$758$	−7.19265e22	+	3.19865e21i	−0.659986	+	0.0293504i
$759$			9.39726e22i			0.853231i
$760$	−3.08708e22	+	4.14044e21i	−0.277357	+	0.0371995i
$761$	2.94175e22			0.261534			0.130767	−	0.991413i	$-0.458256\pi$
$761$	2.94175e22			0.261534			0.130767	+	0.991413i	$0.458256\pi$
$762$	−4.09683e21	−	9.21232e22i	−0.0360419	−	0.810455i
$763$		−	2.43239e23i		−	2.11757i
$764$	−1.41282e22	−	1.58532e23i	−0.121714	−	1.36575i
$765$	−1.30447e21			−0.0111210
$766$	−7.05143e22	+	3.13585e21i	−0.594904	+	0.0264561i
$767$			1.65923e23i			1.38530i
$768$	−2.43233e22	−	6.55061e22i	−0.200971	−	0.541243i
$769$	1.97968e23			1.61877			0.809384	−	0.587280i	$-0.199801\pi$
$769$	1.97968e23			1.61877			0.809384	+	0.587280i	$0.199801\pi$
$770$	3.28137e21	+	7.37865e22i	0.0265540	+	0.597106i
$771$			9.86220e21i			0.0789839i
$772$	1.58147e23	−	1.40938e22i	1.25349	−	0.111709i
$773$	6.25457e22			0.490638			0.245319	−	0.969442i	$-0.421107\pi$
$773$	6.25457e22			0.490638			0.245319	+	0.969442i	$0.421107\pi$
$774$	−8.38942e21	+	3.73087e20i	−0.0651335	+	0.00289656i
$775$			1.45735e23i			1.11982i
$776$	−1.86175e22	−	1.38811e23i	−0.141588	−	1.05567i
$777$	4.91029e22			0.369606
$778$	−3.32052e21	−	7.46668e22i	−0.0247383	−	0.556276i
$779$			2.59901e23i			1.91649i
$780$	−1.77012e21	−	1.98625e22i	−0.0129195	−	0.144970i
$781$	1.25204e23			0.904506
$782$	2.15746e22	−	9.59447e20i	0.154273	−	0.00686068i
$783$			3.51640e21i			0.0248888i
$784$	−3.51827e23	+	6.32106e22i	−2.46490	+	0.442855i
$785$	−1.66660e22			−0.115578
$786$	−6.06269e20	−	1.36329e22i	−0.00416184	−	0.0935851i
$787$		−	2.18866e23i		−	1.48724i	−0.668603	−	0.743619i	$-0.733107\pi$
$787$		−	2.18866e23i		−	1.48724i	0.668603	−	0.743619i	$-0.266893\pi$
$788$	−1.98218e23	+	1.76649e22i	−1.33332	+	0.118823i
$789$	−4.47226e22			−0.297790
$790$	−4.01207e21	+	1.78421e20i	−0.0264455	+	0.00117606i
$791$		−	4.27884e23i		−	2.79199i
$792$	7.36665e22	−	9.88024e21i	0.475848	−	0.0638214i
$793$	5.11777e22			0.327262
$794$	7.87260e21	+	1.77027e23i	0.0498373	+	1.12067i
$795$		−	4.51356e21i		−	0.0282867i
$796$	1.70537e22	+	1.91359e23i	0.105807	+	1.18726i
$797$	−4.97106e22			−0.305339			−0.152669	−	0.988277i	$-0.548787\pi$
$797$	−4.97106e22			−0.305339			−0.152669	+	0.988277i	$0.548787\pi$
$798$	2.24148e23	−	9.96813e21i	1.36305	−	0.0606165i
$799$			2.23822e22i			0.134750i
$800$	−3.51576e22	−	1.55606e23i	−0.209556	−	0.927482i
$801$	−5.42604e22			−0.320201
$802$	1.14702e22	+	2.57925e23i	0.0670157	+	1.50695i
$803$			9.09784e22i			0.526277i
$804$	−6.36611e22	+	5.67338e21i	−0.364607	+	0.0324933i
$805$	7.50849e22			0.425780
$806$	−2.38301e23	+	1.05975e22i	−1.33797	+	0.0595009i
$807$			5.69778e22i			0.316751i
$808$	4.52063e21	+	3.37055e22i	0.0248833	+	0.185528i
$809$	−2.58507e23			−1.40891			−0.704455	−	0.709748i	$-0.748809\pi$
$809$	−2.58507e23			−1.40891			−0.704455	+	0.709748i	$0.748809\pi$
$810$	2.02769e20	+	4.55956e21i	0.00109426	+	0.0246061i
$811$			9.75187e22i			0.521100i	0.965460	+	0.260550i	$0.0839039\pi$
$811$			9.75187e22i			0.521100i	−0.965460	+	0.260550i	$0.916096\pi$
$812$	−4.06153e21	−	4.55744e22i	−0.0214902	−	0.241142i
$813$	5.64136e22			0.295569
$814$	9.48466e22	−	4.21794e21i	0.492070	−	0.0218829i
$815$			2.62393e22i			0.134800i
$816$	−3.02047e21	−	1.68118e22i	−0.0153657	−	0.0855248i
$817$	−4.90149e22			−0.246917
$818$	−2.16709e21	−	4.87302e22i	−0.0108106	−	0.243092i
$819$			1.43647e23i			0.709620i
$820$	6.85201e22	−	6.10641e21i	0.335202	−	0.0298728i
$821$	1.80543e23			0.874653			0.437327	−	0.899303i	$-0.355925\pi$
$821$	1.80543e23			0.874653			0.437327	+	0.899303i	$0.355925\pi$
$822$	−1.72230e23	+	7.65928e21i	−0.826295	+	0.0367463i
$823$			5.84547e22i			0.277729i	0.990311	+	0.138864i	$0.0443452\pi$
$823$			5.84547e22i			0.277729i	−0.990311	+	0.138864i	$0.955655\pi$
$824$	1.74063e23	−	2.33455e22i	0.819008	−	0.109846i
$825$	1.69687e23			0.790710
$826$	2.19531e22	+	4.93648e23i	0.101311	+	2.27812i
$827$			2.70285e23i			1.23532i	0.786446	+	0.617658i	$0.211919\pi$
$827$			2.70285e23i			1.23532i	−0.786446	+	0.617658i	$0.788081\pi$
$828$	−6.70715e21	−	7.52610e22i	−0.0303596	−	0.340665i
$829$	−3.13380e23			−1.40487			−0.702433	−	0.711749i	$-0.747903\pi$
$829$	−3.13380e23			−1.40487			−0.702433	+	0.711749i	$0.747903\pi$
$830$	−3.08057e22	+	1.36997e21i	−0.136775	+	0.00608255i
$831$		−	1.99198e22i		−	0.0875946i
$832$	2.51885e23	−	6.88040e22i	1.09702	−	0.299659i
$833$	−8.73796e22			−0.376921
$834$	−9.50972e21	−	2.13840e23i	−0.0406293	−	0.913610i
$835$			8.01375e22i			0.339113i
$836$	4.32106e23	−	3.85087e22i	1.81109	−	0.161402i
$837$	5.45951e22			0.226647
$838$	−1.54036e22	+	6.85016e20i	−0.0633389	+	0.00281675i
$839$			1.22175e23i			0.497608i	0.968554	+	0.248804i	$0.0800375\pi$
$839$			1.22175e23i			0.497608i	−0.968554	+	0.248804i	$0.919963\pi$
$840$	−7.89440e21	−	5.88602e22i	−0.0318482	−	0.237458i
$841$	−2.46061e23			−0.983275
$842$	3.69834e21	+	8.31627e22i	0.0146390	+	0.329179i
$843$		−	1.03136e23i		−	0.404381i
$844$	−2.80287e22	−	3.14510e23i	−0.108859	−	1.22150i
$845$	1.68971e22			0.0650069
$846$	7.82329e22	−	3.47911e21i	0.298144	−	0.0132588i
$847$		−	5.32838e23i		−	2.01154i
$848$	5.81696e22	−	1.04510e22i	0.217535	−	0.0390833i
$849$	−8.69830e22			−0.322235
$850$	−1.73248e21	−	3.89574e22i	−0.00635796	−	0.142968i
$851$		−	9.65156e22i		−	0.350882i
$852$	−1.00274e23	+	8.93629e21i	−0.361137	+	0.0321840i
$853$	1.08159e23			0.385896			0.192948	−	0.981209i	$-0.438195\pi$
$853$	1.08159e23			0.385896			0.192948	+	0.981209i	$0.438195\pi$
$854$	1.52262e23	−	6.77128e21i	0.538182	−	0.0239336i
$855$			2.66391e22i			0.0932803i
$856$	1.38742e23	−	1.86083e22i	0.481302	−	0.0645529i
$857$	2.22560e23			0.764894			0.382447	−	0.923977i	$-0.375081\pi$
$857$	2.22560e23			0.764894			0.382447	+	0.923977i	$0.375081\pi$
$858$	1.23393e22	+	2.77467e23i	0.0420138	+	0.944743i
$859$		−	6.15550e22i		−	0.207643i	−0.994596	−	0.103822i	$-0.966893\pi$
$859$		−	6.15550e22i		−	0.207643i	0.994596	−	0.103822i	$-0.0331071\pi$
$860$	1.15161e21	+	1.29223e22i	0.00384875	+	0.0431868i
$861$	−4.95542e23			−1.64080
$862$	3.14693e23	−	1.39947e22i	1.03235	−	0.0459100i
$863$		−	3.86238e22i		−	0.125536i	−0.998028	−	0.0627681i	$-0.980007\pi$
$863$		−	3.86238e22i		−	0.125536i	0.998028	−	0.0627681i	$-0.0199928\pi$
$864$	−5.82930e22	+	1.31708e22i	−0.187718	+	0.0424132i
$865$	−1.11233e23			−0.354900
$866$	−1.84195e22	−	4.14190e23i	−0.0582285	−	1.30935i
$867$			1.80153e23i			0.564272i
$868$	−7.07582e23	+	6.30587e22i	−2.19593	+	0.195698i
$869$	5.59352e22			0.171999
$870$	5.42705e21	−	2.41347e20i	0.0165352	−	0.000735341i
$871$		−	2.38831e23i		−	0.721018i
$872$	5.02679e22	+	3.74794e23i	0.150369	+	1.12114i
$873$	−1.19783e23			−0.355042
$874$	−1.95931e22	−	4.40581e23i	−0.0575457	−	1.29400i
$875$		−	2.78170e23i		−	0.809554i
$876$	−6.49345e21	−	7.28631e22i	−0.0187259	−	0.210123i
$877$	−6.96394e23			−1.99002			−0.995011	−	0.0997617i	$-0.968192\pi$
$877$	−6.96394e23			−1.99002			−0.995011	+	0.0997617i	$0.968192\pi$
$878$	1.88766e23	−	8.39465e21i	0.534525	−	0.0237709i
$879$		−	1.73501e23i		−	0.486844i
$880$	−2.03048e22	−	1.13016e23i	−0.0564596	−	0.314251i
$881$	−3.36202e23			−0.926388			−0.463194	−	0.886257i	$-0.653297\pi$
$881$	−3.36202e23			−0.926388			−0.463194	+	0.886257i	$0.653297\pi$
$882$	1.35824e22	+	3.05420e23i	0.0370874	+	0.833966i
$883$			4.48123e23i			1.21258i	0.795242	+	0.606292i	$0.207344\pi$
$883$			4.48123e23i			1.21258i	−0.795242	+	0.606292i	$0.792656\pi$
$884$	6.35761e22	−	5.66581e21i	0.170481	−	0.0151930i
$885$	−5.86680e22			−0.155903
$886$	−1.34086e23	+	5.96298e21i	−0.353114	+	0.0157034i
$887$		−	6.64749e21i		−	0.0173488i	−0.999962	−	0.00867439i	$-0.997239\pi$
$887$		−	6.64749e21i		−	0.0173488i	0.999962	−	0.00867439i	$-0.00276118\pi$
$888$	−7.56600e22	+	1.01476e22i	−0.195687	+	0.0262458i
$889$	1.02621e24			2.63041
$890$	3.72416e21	+	8.37432e22i	0.00946037	+	0.212730i
$891$		−	6.35682e22i		−	0.160036i
$892$	−2.49053e22	−	2.79462e23i	−0.0621402	−	0.697276i
$893$	4.57073e23			1.13025
$894$	3.31509e23	−	1.47426e22i	0.812448	−	0.0361305i
$895$		−	1.31558e23i		−	0.319546i
$896$	7.40297e23	−	2.38030e23i	1.78214	−	0.573017i
$897$	2.82350e23			0.673671
$898$	−3.84764e21	−	8.65198e22i	−0.00909878	−	0.204600i
$899$		−	6.49823e22i		−	0.152306i
$900$	−1.35900e23	+	1.21112e22i	−0.315702	+	0.0281349i
$901$	1.44470e22			0.0332644
$902$	−9.57183e23	+	4.25670e22i	−2.18445	+	0.0971452i
$903$		−	9.34547e22i		−	0.211397i
$904$	8.84266e22	+	6.59303e23i	0.198260	+	1.47822i
$905$	−4.50299e22			−0.100072
$906$	−1.55921e22	−	3.50611e23i	−0.0343462	−	0.772325i
$907$			4.63696e23i			1.01245i	0.862400	+	0.506227i	$0.168960\pi$
$907$			4.63696e23i			1.01245i	−0.862400	+	0.506227i	$0.831040\pi$
$908$	4.43061e22	+	4.97159e23i	0.0958907	+	1.07599i
$909$	2.90851e22			0.0623965
$910$	2.21699e23	−	9.85921e21i	0.471446	−	0.0209658i
$911$			5.45620e23i			1.15012i	0.818111	+	0.575060i	$0.195021\pi$
$911$			5.45620e23i			1.15012i	−0.818111	+	0.575060i	$0.804979\pi$
$912$	−3.43318e23	+	6.16819e22i	−0.717361	+	0.128884i
$913$	4.29486e23			0.889575
$914$	3.35380e22	+	7.54152e23i	0.0688601	+	1.54842i
$915$			1.80957e22i			0.0368304i
$916$	−3.73867e23	+	3.33185e22i	−0.754317	+	0.0672237i
$917$	1.51864e23			0.303740
$918$	−1.45942e22	+	6.49023e20i	−0.0289361	+	0.00128682i
$919$		−	3.81492e23i		−	0.749827i	−0.927060	−	0.374913i	$-0.877672\pi$
$919$		−	3.81492e23i		−	0.749827i	0.927060	−	0.374913i	$-0.122328\pi$
$920$	−1.15694e23	+	1.55171e22i	−0.225429	+	0.0302348i
$921$	2.68270e23			0.518198
$922$	−3.58116e22	−	8.05276e23i	−0.0685766	−	1.54205i
$923$		−	3.76189e23i		−	0.714155i
$924$	7.34229e22	+	8.23879e23i	0.138183	+	1.55056i
$925$	−1.74279e23			−0.325171
$926$	−1.93571e23	+	8.60831e21i	−0.358056	+	0.0159232i
$927$		−	1.50202e23i		−	0.275447i
$928$	1.56766e22	+	6.93838e22i	0.0285015	+	0.126146i
$929$	2.87790e23			0.518740			0.259370	−	0.965778i	$-0.416485\pi$
$929$	2.87790e23			0.518740			0.259370	+	0.965778i	$0.416485\pi$
$930$	−3.74713e21	−	8.42597e22i	−0.00669630	−	0.150576i
$931$			1.78440e24i			3.16152i
$932$	−6.08201e23	+	5.42020e22i	−1.06837	+	0.0952113i
$933$	2.51796e23			0.438526
$934$	−9.33651e22	+	4.15206e21i	−0.161217	+	0.00716949i
$935$		−	2.80685e22i		−	0.0480537i
$936$	−2.96862e22	−	2.21338e23i	−0.0503903	−	0.375707i
$937$	−9.03324e23			−1.52029			−0.760146	−	0.649753i	$-0.774872\pi$
$937$	−9.03324e23			−1.52029			−0.760146	+	0.649753i	$0.774872\pi$
$938$	−3.15996e22	−	7.10563e23i	−0.0527301	−	1.18571i
$939$		−	1.05944e23i		−	0.175288i
$940$	−1.07390e22	−	1.20503e23i	−0.0176174	−	0.197685i
$941$	3.62505e23			0.589653			0.294826	−	0.955551i	$-0.404738\pi$
$941$	3.62505e23			0.589653			0.294826	+	0.955551i	$0.404738\pi$
$942$	−1.86456e23	+	8.29193e21i	−0.300725	+	0.0133736i
$943$			9.74026e23i			1.55768i
$944$	−1.35844e23	−	7.56099e23i	−0.215409	−	1.19895i
$945$	−5.07916e22			−0.0798615
$946$	−8.02776e21	−	1.80516e23i	−0.0125160	−	0.281441i
$947$		−	2.76095e23i		−	0.426834i	−0.976961	−	0.213417i	$-0.931541\pi$
$947$		−	2.76095e23i		−	0.426834i	0.976961	−	0.213417i	$-0.0684593\pi$
$948$	−4.47976e22	+	3.99229e21i	−0.0686733	+	0.00612006i
$949$	2.73354e23			0.415523
$950$	−7.95561e23	+	3.53795e22i	−1.19918	+	0.0533290i
$951$		−	5.81068e23i		−	0.868525i
$952$	1.88400e23	−	2.52684e22i	0.279245	−	0.0374526i
$953$	−2.33311e23			−0.342919			−0.171459	−	0.985191i	$-0.554848\pi$
$953$	−2.33311e23			−0.342919			−0.171459	+	0.985191i	$0.554848\pi$
$954$	−2.24566e21	−	5.04969e22i	−0.00327308	−	0.0736000i
$955$			2.10296e23i			0.303951i
$956$	6.43492e22	+	7.22063e23i	0.0922316	+	1.03493i
$957$	−7.56626e22			−0.107544
$958$	2.98866e23	−	1.32909e22i	0.421262	−	0.0187340i
$959$		−	1.91857e24i		−	2.68182i
$960$	2.43281e22	+	8.90630e22i	0.0337240	+	0.123460i
$961$	−2.81483e23			−0.386960
$962$	−1.26732e22	−	2.84976e23i	−0.0172777	−	0.388515i
$963$		−	1.19723e23i		−	0.161871i
$964$	2.21150e23	−	1.97086e22i	0.296531	−	0.0264264i
$965$	−2.09784e23			−0.278968
$966$	8.40038e23	−	3.73575e22i	1.10785	−	0.0492675i
$967$		−	1.41945e24i		−	1.85656i	−0.371879	−	0.928281i	$-0.621286\pi$
$967$		−	1.41945e24i		−	1.85656i	0.371879	−	0.928281i	$-0.378714\pi$
$968$	1.10116e23	+	8.21022e23i	0.142840	+	1.06501i
$969$	−8.52663e22			−0.109695
$970$	8.22127e21	+	1.84867e23i	0.0104898	+	0.235878i
$971$			1.02803e24i			1.30092i	0.759539	+	0.650462i	$0.225425\pi$
$971$			1.02803e24i			1.30092i	−0.759539	+	0.650462i	$0.774575\pi$
$972$	4.53709e21	+	5.09107e22i	0.00569439	+	0.0638968i
$973$	2.38209e24			2.96521
$974$	4.83731e23	−	2.15121e22i	0.597218	−	0.0265590i
$975$		−	5.09842e23i		−	0.624307i
$976$	−2.33213e23	+	4.19000e22i	−0.283240	+	0.0508880i
$977$	−1.25942e24			−1.51710			−0.758549	−	0.651615i	$-0.774092\pi$
$977$	−1.25942e24			−1.51710			−0.758549	+	0.651615i	$0.774092\pi$
$978$	1.30550e22	+	2.93561e23i	0.0155979	+	0.350742i
$979$		−	1.16753e24i		−	1.38358i
$980$	4.70439e23	−	4.19249e22i	0.552962	−	0.0492792i
$981$	3.23417e23			0.377061
$982$	−3.13568e23	+	1.39448e22i	−0.362610	+	0.0161257i
$983$			5.44196e23i			0.624205i	0.950048	+	0.312103i	$0.101033\pi$
$983$			5.44196e23i			0.624205i	−0.950048	+	0.312103i	$0.898967\pi$
$984$	7.63553e23	−	1.02409e23i	0.868718	−	0.116514i
$985$	2.62939e23			0.296732
$986$	7.72505e20	+	1.73709e22i	0.000864741	+	0.0194450i
$987$			8.71482e23i			0.967656i
$988$	−1.15703e23	−	1.29830e24i	−0.127435	−	1.42995i
$989$	−1.83692e23			−0.200688
$990$	−9.81085e22	+	4.36300e21i	−0.106322	+	0.00472828i
$991$			1.42399e24i			1.53080i	0.643553	+	0.765401i	$0.277459\pi$
$991$			1.42399e24i			1.53080i	−0.643553	+	0.765401i	$0.722541\pi$
$992$	1.07724e24	−	2.43393e23i	1.14874	−	0.259546i
$993$	−8.34387e22			−0.0882620
$994$	−4.97733e22	−	1.11923e24i	−0.0522282	−	1.17443i
$995$		−	2.53841e23i		−	0.264227i
$996$	−3.43968e23	+	3.06539e22i	−0.355176	+	0.0316528i
$997$	−1.83119e24			−1.87574			−0.937869	−	0.346989i	$-0.887204\pi$
$997$	−1.83119e24			−1.87574			−0.937869	+	0.346989i	$0.887204\pi$
$998$	−6.90902e23	+	3.07252e22i	−0.702056	+	0.0312213i
$999$			6.52885e22i			0.0658132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.17.d.a.7.10	yes	16
3.2	odd	2		36.17.d.d.19.7		16
4.3	odd	2	inner	12.17.d.a.7.9	✓	16
12.11	even	2		36.17.d.d.19.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.17.d.a.7.9	✓	16	4.3	odd	2	inner
12.17.d.a.7.10	yes	16	1.1	even	1	trivial
36.17.d.d.19.7		16	3.2	odd	2
36.17.d.d.19.8		16	12.11	even	2

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(11.3734 + 255.747i) q^{2} -3788.00i q^{3} +(-65277.3 + 5817.42i) q^{4} +86591.3 q^{5} +(968769. - 43082.3i) q^{6} +1.07917e7i q^{7} +(-2.23021e6 - 1.66283e7i) q^{8} -1.43489e7 q^{9} +O(q^{10})\)	\(q+(11.3734 + 255.747i) q^{2} -3788.00i q^{3} +(-65277.3 + 5817.42i) q^{4} +86591.3 q^{5} +(968769. - 43082.3i) q^{6} +1.07917e7i q^{7} +(-2.23021e6 - 1.66283e7i) q^{8} -1.43489e7 q^{9} +(984836. + 2.21455e7i) q^{10} -3.08747e8i q^{11} +(2.20364e7 + 2.47270e8i) q^{12} -9.27660e8 q^{13} +(-2.75994e9 + 1.22738e8i) q^{14} -3.28007e8i q^{15} +(4.22728e9 - 7.59491e8i) q^{16} +1.04989e9 q^{17} +(-1.63196e8 - 3.66969e9i) q^{18} -2.14400e10i q^{19} +(-5.65245e9 + 5.03738e8i) q^{20} +4.08789e10 q^{21} +(7.89612e10 - 3.51149e9i) q^{22} -8.03506e10i q^{23} +(-6.29880e10 + 8.44803e9i) q^{24} -1.45090e11 q^{25} +(-1.05506e10 - 2.37247e11i) q^{26} +5.43536e10i q^{27} +(-6.27798e10 - 7.04452e11i) q^{28} +6.46948e10 q^{29} +(8.38870e10 - 3.73055e9i) q^{30} -1.00444e12i q^{31} +(2.42316e11 + 1.07248e12i) q^{32} -1.16953e12 q^{33} +(1.19408e10 + 2.68506e11i) q^{34} +9.34466e11i q^{35} +(9.36658e11 - 8.34736e10i) q^{36} +1.20118e12 q^{37} +(5.48323e12 - 2.43846e11i) q^{38} +3.51397e12i q^{39} +(-1.93117e11 - 1.43987e12i) q^{40} -1.21222e13 q^{41} +(4.64931e11 + 1.04547e13i) q^{42} -2.28614e12i q^{43} +(1.79611e12 + 2.01542e13i) q^{44} -1.24249e12 q^{45} +(2.05494e13 - 9.13858e11i) q^{46} +2.13186e13i q^{47} +(-2.87695e12 - 1.60129e13i) q^{48} -8.32276e13 q^{49} +(-1.65016e12 - 3.71063e13i) q^{50} -3.97697e12i q^{51} +(6.05551e13 - 5.39659e12i) q^{52} +1.37605e13 q^{53} +(-1.39008e13 + 6.18184e11i) q^{54} -2.67348e13i q^{55} +(1.79448e14 - 2.40678e13i) q^{56} -8.12148e13 q^{57} +(7.35799e11 + 1.65455e13i) q^{58} -1.78862e14i q^{59} +(1.90816e12 + 2.14114e13i) q^{60} -5.51686e13 q^{61} +(2.56884e14 - 1.14239e13i) q^{62} -1.54849e14i q^{63} +(-2.71527e14 + 7.41694e13i) q^{64} -8.03273e13 q^{65} +(-1.33015e13 - 2.99104e14i) q^{66} +2.57456e14i q^{67} +(-6.85338e13 + 6.10763e12i) q^{68} -3.04368e14 q^{69} +(-2.38987e14 + 1.06280e13i) q^{70} +4.05525e14i q^{71} +(3.20011e13 + 2.38598e14i) q^{72} -2.94670e14 q^{73} +(1.36615e13 + 3.07199e14i) q^{74} +5.49600e14i q^{75} +(1.24726e14 + 1.39955e15i) q^{76} +3.33190e15 q^{77} +(-8.98689e14 + 3.99657e13i) q^{78} +1.81169e14i q^{79} +(3.66046e14 - 6.57653e13i) q^{80} +2.05891e14 q^{81} +(-1.37870e14 - 3.10022e15i) q^{82} +1.39106e15i q^{83} +(-2.66846e15 + 2.37809e14i) q^{84} +9.09111e13 q^{85} +(5.84673e14 - 2.60011e13i) q^{86} -2.45064e14i q^{87} +(-5.13394e15 + 6.88571e14i) q^{88} +3.78150e15 q^{89} +(-1.41313e13 - 3.17764e14i) q^{90} -1.00110e16i q^{91} +(4.67433e14 + 5.24507e15i) q^{92} -3.80483e15 q^{93} +(-5.45219e15 + 2.42465e14i) q^{94} -1.85652e15i q^{95} +(4.06254e15 - 9.17892e14i) q^{96} +8.34786e15 q^{97} +(-9.46579e14 - 2.12852e16i) q^{98} +4.43018e15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9}+O(q^{10}) \) 16 * q - 186 * q^2 + 136588 * q^4 + 354144 * q^5 + 1561518 * q^6 + 14683680 * q^8 - 229582512 * q^9	\( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9} - 49800172 q^{10} + 425284020 q^{12} - 906419296 q^{13} - 806064072 q^{14} - 2108540816 q^{16} + 12240765600 q^{17} + 2668896702 q^{18} + 1002788712 q^{20} + 39806479296 q^{21} + 216706355928 q^{22} - 111931394832 q^{24} + 206381182512 q^{25} + 1054507182588 q^{26} - 1526063922288 q^{28} + 327679573728 q^{29} + 1192344308100 q^{30} - 5158730488416 q^{32} + 679591529280 q^{33} + 9473293385948 q^{34} - 1959888509316 q^{36} - 8149494749152 q^{37} + 23318999782920 q^{38} - 28671795971776 q^{40} - 25536724613472 q^{41} + 5103781482168 q^{42} - 11442227373552 q^{44} - 5081579320608 q^{45} + 9929654732736 q^{46} + 29246734238832 q^{48} - 93287012964080 q^{49} - 133601044957998 q^{50} + 302261844234872 q^{52} - 86928436629792 q^{53} - 22406076560826 q^{54} + 530930989929024 q^{56} + 48687411524544 q^{57} - 189801665049916 q^{58} + 268455359263896 q^{60} + 476028596468000 q^{61} - 419080420491096 q^{62} + 305944925720704 q^{64} - 12\!\cdots\!92 q^{65}+ \cdots - 33\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q - 186 * q^2 + 136588 * q^4 + 354144 * q^5 + 1561518 * q^6 + 14683680 * q^8 - 229582512 * q^9 - 49800172 * q^10 + 425284020 * q^12 - 906419296 * q^13 - 806064072 * q^14 - 2108540816 * q^16 + 12240765600 * q^17 + 2668896702 * q^18 + 1002788712 * q^20 + 39806479296 * q^21 + 216706355928 * q^22 - 111931394832 * q^24 + 206381182512 * q^25 + 1054507182588 * q^26 - 1526063922288 * q^28 + 327679573728 * q^29 + 1192344308100 * q^30 - 5158730488416 * q^32 + 679591529280 * q^33 + 9473293385948 * q^34 - 1959888509316 * q^36 - 8149494749152 * q^37 + 23318999782920 * q^38 - 28671795971776 * q^40 - 25536724613472 * q^41 + 5103781482168 * q^42 - 11442227373552 * q^44 - 5081579320608 * q^45 + 9929654732736 * q^46 + 29246734238832 * q^48 - 93287012964080 * q^49 - 133601044957998 * q^50 + 302261844234872 * q^52 - 86928436629792 * q^53 - 22406076560826 * q^54 + 530930989929024 * q^56 + 48687411524544 * q^57 - 189801665049916 * q^58 + 268455359263896 * q^60 + 476028596468000 * q^61 - 419080420491096 * q^62 + 305944925720704 * q^64 - 1276571708976192 * q^65 - 64815073701480 * q^66 - 1393626893610696 * q^68 + 384812600884992 * q^69 + 1815049064679696 * q^70 - 210694758737760 * q^72 - 368686901901280 * q^73 + 875633111941836 * q^74 - 4351002030861264 * q^76 - 81504772370688 * q^77 + 1907392409236620 * q^78 - 8190389938127328 * q^80 + 3294258113514384 * q^81 + 2390391408733340 * q^82 - 510964995024720 * q^84 + 10085047677398464 * q^85 - 894939801424296 * q^86 + 669091386916800 * q^88 - 5711067674201568 * q^89 + 714578036612004 * q^90 + 7708247605922304 * q^92 + 7132614781502016 * q^93 - 9487273535547696 * q^94 + 8786531038601952 * q^96 - 13564951560560608 * q^97 - 33011660914531290 * q^98

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