LMFDB - Embedded newform 12.17.d.a.7.12

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			7.12
Root			$54.8669 - 95.0323i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.17.d.a.7.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(196.501 + 164.084i) q^{2} +3788.00i q^{3} +(11689.0 + 64485.1i) q^{4} -45026.4 q^{5} +(-621548. + 744344. i) q^{6} +3.24149e6i q^{7} +(-8.28406e6 + 1.45894e7i) q^{8} -1.43489e7 q^{9} +O(q^{10})$	\(q+(196.501 + 164.084i) q^{2} +3788.00i q^{3} +(11689.0 + 64485.1i) q^{4} -45026.4 q^{5} +(-621548. + 744344. i) q^{6} +3.24149e6i q^{7} +(-8.28406e6 + 1.45894e7i) q^{8} -1.43489e7 q^{9} +(-8.84773e6 - 7.38811e6i) q^{10} +2.75960e7i q^{11} +(-2.44269e8 + 4.42780e7i) q^{12} -6.92488e8 q^{13} +(-5.31875e8 + 6.36954e8i) q^{14} -1.70560e8i q^{15} +(-4.02170e9 + 1.50754e9i) q^{16} +2.60696e9 q^{17} +(-2.81957e9 - 2.35442e9i) q^{18} -1.17841e10i q^{19} +(-5.26316e8 - 2.90354e9i) q^{20} -1.22787e10 q^{21} +(-4.52806e9 + 5.42264e9i) q^{22} +3.87992e9i q^{23} +(-5.52644e10 - 3.13800e10i) q^{24} -1.50561e11 q^{25} +(-1.36074e11 - 1.13626e11i) q^{26} -5.43536e10i q^{27} +(-2.09028e11 + 3.78899e10i) q^{28} -6.46281e11 q^{29} +(2.79861e10 - 3.35151e10i) q^{30} +9.55575e11i q^{31} +(-1.03763e12 - 3.63663e11i) q^{32} -1.04534e11 q^{33} +(5.12270e11 + 4.27761e11i) q^{34} -1.45953e11i q^{35} +(-1.67725e11 - 9.25291e11i) q^{36} +6.34959e12 q^{37} +(1.93358e12 - 2.31558e12i) q^{38} -2.62314e12i q^{39} +(3.73002e11 - 6.56907e11i) q^{40} +1.16356e13 q^{41} +(-2.41278e12 - 2.01474e12i) q^{42} +1.79375e13i q^{43} +(-1.77953e12 + 3.22571e11i) q^{44} +6.46080e11 q^{45} +(-6.36633e11 + 7.62408e11i) q^{46} +3.29643e13i q^{47} +(-5.71055e12 - 1.52342e13i) q^{48} +2.27257e13 q^{49} +(-2.95852e13 - 2.47045e13i) q^{50} +9.87517e12i q^{51} +(-8.09452e12 - 4.46552e13i) q^{52} +5.59722e12 q^{53} +(8.91854e12 - 1.06805e13i) q^{54} -1.24255e12i q^{55} +(-4.72912e13 - 2.68527e13i) q^{56} +4.46381e13 q^{57} +(-1.26995e14 - 1.06044e14i) q^{58} +1.93936e14i q^{59} +(1.09986e13 - 1.99368e12i) q^{60} -1.41886e13 q^{61} +(-1.56794e14 + 1.87771e14i) q^{62} -4.65118e13i q^{63} +(-1.44224e14 - 2.41718e14i) q^{64} +3.11803e13 q^{65} +(-2.05409e13 - 1.71523e13i) q^{66} -3.51753e14i q^{67} +(3.04729e13 + 1.68110e14i) q^{68} -1.46971e13 q^{69} +(2.39484e13 - 2.86798e13i) q^{70} +8.84835e14i q^{71} +(1.18867e14 - 2.09341e14i) q^{72} +1.70546e14 q^{73} +(1.24770e15 + 1.04186e15i) q^{74} -5.70322e14i q^{75} +(7.59898e14 - 1.37745e14i) q^{76} -8.94522e13 q^{77} +(4.30415e14 - 5.15449e14i) q^{78} -1.50351e15i q^{79} +(1.81083e14 - 6.78791e13i) q^{80} +2.05891e14 q^{81} +(2.28641e15 + 1.90922e15i) q^{82} -4.88125e14i q^{83} +(-1.43527e14 - 7.91796e14i) q^{84} -1.17382e14 q^{85} +(-2.94326e15 + 3.52474e15i) q^{86} -2.44811e15i q^{87} +(-4.02609e14 - 2.28607e14i) q^{88} -7.27333e15 q^{89} +(1.26955e14 + 1.06011e14i) q^{90} -2.24469e15i q^{91} +(-2.50197e14 + 4.53526e13i) q^{92} -3.61972e15 q^{93} +(-5.40891e15 + 6.47752e15i) q^{94} +5.30595e14i q^{95} +(1.37755e15 - 3.93054e15i) q^{96} -1.59239e15 q^{97} +(4.46562e15 + 3.72892e15i) q^{98} -3.95973e14i 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 $

$2$	196.501	+	164.084i	0.767581	+	0.640952i
$2$	196.501	+	164.084i	0.767581	+	0.640952i
$3$			3788.00i			0.577350i
$3$			3788.00i			0.577350i
$4$	11689.0	+	64485.1i	0.178361	+	0.983965i
$5$	−45026.4			−0.115268			−0.0576338	−	0.998338i	$-0.518356\pi$
$5$	−45026.4			−0.115268			−0.0576338	+	0.998338i	$0.518356\pi$
$6$	−621548.	+	744344.i	−0.370054	+	0.443163i
$7$			3.24149e6i			0.562289i	0.959665	+	0.281145i	$0.0907141\pi$
$7$			3.24149e6i			0.562289i	−0.959665	+	0.281145i	$0.909286\pi$
$8$	−8.28406e6	+	1.45894e7i	−0.493768	+	0.869593i
$9$	−1.43489e7			−0.333333
$10$	−8.84773e6	−	7.38811e6i	−0.0884773	−	0.0738811i
$11$			2.75960e7i			0.128738i	0.997926	+	0.0643688i	$0.0205034\pi$
$11$			2.75960e7i			0.128738i	−0.997926	+	0.0643688i	$0.979497\pi$
$12$	−2.44269e8	+	4.42780e7i	−0.568093	+	0.102977i
$13$	−6.92488e8			−0.848917			−0.424459	−	0.905447i	$-0.639536\pi$
$13$	−6.92488e8			−0.848917			−0.424459	+	0.905447i	$0.639536\pi$
$14$	−5.31875e8	+	6.36954e8i	−0.360401	+	0.431602i
$15$		−	1.70560e8i		−	0.0665498i
$16$	−4.02170e9	+	1.50754e9i	−0.936375	+	0.351001i
$17$	2.60696e9			0.373718			0.186859	−	0.982387i	$-0.440169\pi$
$17$	2.60696e9			0.373718			0.186859	+	0.982387i	$0.440169\pi$
$18$	−2.81957e9	−	2.35442e9i	−0.255860	−	0.213651i
$19$		−	1.17841e10i		−	0.693852i	−0.937892	−	0.346926i	$-0.887225\pi$
$19$		−	1.17841e10i		−	0.693852i	0.937892	−	0.346926i	$-0.112775\pi$
$20$	−5.26316e8	−	2.90354e9i	−0.0205592	−	0.113419i
$21$	−1.22787e10			−0.324638
$22$	−4.52806e9	+	5.42264e9i	−0.0825146	+	0.0988165i
$23$			3.87992e9i			0.0495451i	0.999693	+	0.0247725i	$0.00788615\pi$
$23$			3.87992e9i			0.0495451i	−0.999693	+	0.0247725i	$0.992114\pi$
$24$	−5.52644e10	−	3.13800e10i	−0.502060	−	0.285077i
$25$	−1.50561e11			−0.986713
$26$	−1.36074e11	−	1.13626e11i	−0.651612	−	0.544115i
$27$		−	5.43536e10i		−	0.192450i
$28$	−2.09028e11	+	3.78899e10i	−0.553273	+	0.100290i
$29$	−6.46281e11			−1.29193			−0.645963	−	0.763369i	$-0.723544\pi$
$29$	−6.46281e11			−1.29193			−0.645963	+	0.763369i	$0.723544\pi$
$30$	2.79861e10	−	3.35151e10i	0.0426553	−	0.0510824i
$31$			9.55575e11i			1.12040i	0.828359	+	0.560198i	$0.189275\pi$
$31$			9.55575e11i			1.12040i	−0.828359	+	0.560198i	$0.810725\pi$
$32$	−1.03763e12	−	3.63663e11i	−0.943718	−	0.330750i
$33$	−1.04534e11			−0.0743267
$34$	5.12270e11	+	4.27761e11i	0.286859	+	0.239535i
$35$		−	1.45953e11i		−	0.0648138i
$36$	−1.67725e11	−	9.25291e11i	−0.0594535	−	0.327988i
$37$	6.34959e12			1.80772			0.903861	−	0.427826i	$-0.140720\pi$
$37$	6.34959e12			1.80772			0.903861	+	0.427826i	$0.140720\pi$
$38$	1.93358e12	−	2.31558e12i	0.444726	−	0.532588i
$39$		−	2.62314e12i		−	0.490123i
$40$	3.73002e11	−	6.56907e11i	0.0569156	−	0.100236i
$41$	1.16356e13			1.45720			0.728600	−	0.684939i	$-0.240171\pi$
$41$	1.16356e13			1.45720			0.728600	+	0.684939i	$0.240171\pi$
$42$	−2.41278e12	−	2.01474e12i	−0.249186	−	0.208077i
$43$			1.79375e13i			1.53467i	0.641246	+	0.767335i	$0.278418\pi$
$43$			1.79375e13i			1.53467i	−0.641246	+	0.767335i	$0.721582\pi$
$44$	−1.77953e12	+	3.22571e11i	−0.126673	+	0.0229617i
$45$	6.46080e11			0.0384226
$46$	−6.36633e11	+	7.62408e11i	−0.0317560	+	0.0380299i
$47$			3.29643e13i			1.38440i	0.721706	+	0.692200i	$0.243358\pi$
$47$			3.29643e13i			1.38440i	−0.721706	+	0.692200i	$0.756642\pi$
$48$	−5.71055e12	−	1.52342e13i	−0.202651	−	0.540616i
$49$	2.27257e13			0.683831
$50$	−2.95852e13	−	2.47045e13i	−0.757382	−	0.632436i
$51$			9.87517e12i			0.215766i
$52$	−8.09452e12	−	4.46552e13i	−0.151413	−	0.835305i
$53$	5.59722e12			0.0899013			0.0449506	−	0.998989i	$-0.485687\pi$
$53$	5.59722e12			0.0899013			0.0449506	+	0.998989i	$0.485687\pi$
$54$	8.91854e12	−	1.06805e13i	0.123351	−	0.147721i
$55$		−	1.24255e12i		−	0.0148393i
$56$	−4.72912e13	−	2.68527e13i	−0.488963	−	0.277641i
$57$	4.46381e13			0.400596
$58$	−1.26995e14	−	1.06044e14i	−0.991657	−	0.828062i
$59$			1.93936e14i			1.32082i	0.750906	+	0.660409i	$0.229617\pi$
$59$			1.93936e14i			1.32082i	−0.750906	+	0.660409i	$0.770383\pi$
$60$	1.09986e13	−	1.99368e12i	0.0654827	−	0.0118699i
$61$	−1.41886e13			−0.0740117			−0.0370058	−	0.999315i	$-0.511782\pi$
$61$	−1.41886e13			−0.0740117			−0.0370058	+	0.999315i	$0.511782\pi$
$62$	−1.56794e14	+	1.87771e14i	−0.718120	+	0.859994i
$63$		−	4.65118e13i		−	0.187430i
$64$	−1.44224e14	−	2.41718e14i	−0.512385	−	0.858756i
$65$	3.11803e13			0.0978527
$66$	−2.05409e13	−	1.71523e13i	−0.0570517	−	0.0476398i
$67$		−	3.51753e14i		−	0.866242i	−0.901336	−	0.433121i	$-0.857412\pi$
$67$		−	3.51753e14i		−	0.866242i	0.901336	−	0.433121i	$-0.142588\pi$
$68$	3.04729e13	+	1.68110e14i	0.0666565	+	0.367725i
$69$	−1.46971e13			−0.0286049
$70$	2.39484e13	−	2.86798e13i	0.0415425	−	0.0497498i
$71$			8.84835e14i			1.37024i	0.728432	+	0.685119i	$0.240250\pi$
$71$			8.84835e14i			1.37024i	−0.728432	+	0.685119i	$0.759750\pi$
$72$	1.18867e14	−	2.09341e14i	0.164589	−	0.289864i
$73$	1.70546e14			0.211475			0.105737	−	0.994394i	$-0.466280\pi$
$73$	1.70546e14			0.211475			0.105737	+	0.994394i	$0.466280\pi$
$74$	1.24770e15	+	1.04186e15i	1.38757	+	1.15866i
$75$		−	5.70322e14i		−	0.569679i
$76$	7.59898e14	−	1.37745e14i	0.682727	−	0.123756i
$77$	−8.94522e13			−0.0723878
$78$	4.30415e14	−	5.15449e14i	0.314145	−	0.376209i
$79$		−	1.50351e15i		−	0.991037i	−0.868597	−	0.495519i	$-0.834978\pi$
$79$		−	1.50351e15i		−	0.991037i	0.868597	−	0.495519i	$-0.165022\pi$
$80$	1.81083e14	−	6.78791e13i	0.107934	−	0.0404591i
$81$	2.05891e14			0.111111
$82$	2.28641e15	+	1.90922e15i	1.11852	+	0.933996i
$83$		−	4.88125e14i		−	0.216724i	−0.994112	−	0.108362i	$-0.965439\pi$
$83$		−	4.88125e14i		−	0.216724i	0.994112	−	0.108362i	$-0.0345605\pi$
$84$	−1.43527e14	−	7.91796e14i	−0.0579026	−	0.319432i
$85$	−1.17382e14			−0.0430776
$86$	−2.94326e15	+	3.52474e15i	−0.983650	+	1.17798i
$87$		−	2.44811e15i		−	0.745893i
$88$	−4.02609e14	−	2.28607e14i	−0.111949	−	0.0635666i
$89$	−7.27333e15			−1.84762			−0.923811	−	0.382849i	$-0.874943\pi$
$89$	−7.27333e15			−1.84762			−0.923811	+	0.382849i	$0.874943\pi$
$90$	1.26955e14	+	1.06011e14i	0.0294924	+	0.0246270i
$91$		−	2.24469e15i		−	0.477337i
$92$	−2.50197e14	+	4.53526e13i	−0.0487506	+	0.00883689i
$93$	−3.61972e15			−0.646861
$94$	−5.40891e15	+	6.47752e15i	−0.887334	+	1.06264i
$95$			5.30595e14i			0.0799787i
$96$	1.37755e15	−	3.93054e15i	0.190958	−	0.544856i
$97$	−1.59239e15			−0.203178			−0.101589	−	0.994826i	$-0.532393\pi$
$97$	−1.59239e15			−0.203178			−0.101589	+	0.994826i	$0.532393\pi$
$98$	4.46562e15	+	3.72892e15i	0.524895	+	0.438303i
$99$		−	3.95973e14i		−	0.0429125i
$100$	−1.75991e15	−	9.70892e15i	−0.175991	−	0.970892i
$101$	7.05130e15			0.651176			0.325588	−	0.945512i	$-0.394438\pi$
$101$	7.05130e15			0.651176			0.325588	+	0.945512i	$0.394438\pi$
$102$	−1.62035e15	+	1.94048e15i	−0.138296	+	0.165618i
$103$		−	3.22497e15i		−	0.254582i	−0.991865	−	0.127291i	$-0.959372\pi$
$103$		−	3.22497e15i		−	0.254582i	0.991865	−	0.127291i	$-0.0406282\pi$
$104$	5.73661e15	−	1.01030e16i	0.419169	−	0.738213i
$105$	5.52868e14			0.0374203
$106$	1.09986e15	+	9.18414e14i	0.0690065	+	0.0576224i
$107$			1.41542e16i			0.823785i	0.911233	+	0.411892i	$0.135132\pi$
$107$			1.41542e16i			0.823785i	−0.911233	+	0.411892i	$0.864868\pi$
$108$	3.50500e15	−	6.35341e14i	0.189364	−	0.0343255i
$109$	2.21392e16			1.11109			0.555546	−	0.831486i	$-0.312509\pi$
$109$	2.21392e16			1.11109			0.555546	+	0.831486i	$0.312509\pi$
$110$	2.03883e14	−	2.44162e14i	0.00951127	−	0.0113903i
$111$			2.40522e16i			1.04369i
$112$	−4.88667e15	−	1.30363e16i	−0.197364	−	0.526514i
$113$	1.02991e16			0.387411			0.193705	−	0.981060i	$-0.437949\pi$
$113$	1.02991e16			0.387411			0.193705	+	0.981060i	$0.437949\pi$
$114$	8.77141e15	+	7.32438e15i	0.307490	+	0.256763i
$115$		−	1.74699e14i		−	0.00571095i
$116$	−7.55440e15	−	4.16755e16i	−0.230429	−	1.27121i
$117$	9.93644e15			0.282972
$118$	−3.18218e16	+	3.81086e16i	−0.846581	+	1.01383i
$119$			8.45044e15i			0.210138i
$120$	2.48836e15	+	1.41293e15i	0.0578713	+	0.0328602i
$121$	4.51882e16			0.983427
$122$	−2.78807e15	−	2.32812e15i	−0.0568099	−	0.0474379i
$123$			4.40757e16i			0.841315i
$124$	−6.16204e16	+	1.11698e16i	−1.10243	+	0.199834i
$125$	1.36497e16			0.229004
$126$	7.63183e15	−	9.13960e15i	0.120134	−	0.143867i
$127$			2.78419e15i			0.0411404i	0.999788	+	0.0205702i	$0.00654816\pi$
$127$			2.78419e15i			0.0411404i	−0.999788	+	0.0205702i	$0.993452\pi$
$128$	1.13220e16	−	7.11626e16i	0.157124	−	0.987579i
$129$	−6.79473e16			−0.886042
$130$	6.12694e15	+	5.11617e15i	0.0751099	+	0.0627189i
$131$		−	8.46988e16i		−	0.976577i	−0.872682	−	0.488289i	$-0.837621\pi$
$131$		−	8.46988e16i		−	0.976577i	0.872682	−	0.488289i	$-0.162379\pi$
$132$	−1.22190e15	−	6.74087e15i	−0.0132569	−	0.0731349i
$133$	3.81979e16			0.390146
$134$	5.77170e16	−	6.91197e16i	0.555220	−	0.664911i
$135$			2.44735e15i			0.0221833i
$136$	−2.15963e16	+	3.80339e16i	−0.184530	+	0.324983i
$137$	−1.59917e17			−1.28863			−0.644317	−	0.764758i	$-0.722858\pi$
$137$	−1.59917e17			−1.28863			−0.644317	+	0.764758i	$0.722858\pi$
$138$	−2.88800e15	−	2.41156e15i	−0.0219565	−	0.0183344i
$139$		−	4.46000e15i		−	0.0320049i	−0.999872	−	0.0160024i	$-0.994906\pi$
$139$		−	4.46000e15i		−	0.0320049i	0.999872	−	0.0160024i	$-0.00509395\pi$
$140$	9.41177e15	−	1.70605e15i	0.0637745	−	0.0115602i
$141$	−1.24869e17			−0.799284
$142$	−1.45187e17	+	1.73871e17i	−0.878256	+	1.05177i
$143$		−	1.91099e16i		−	0.109288i
$144$	5.77070e16	−	2.16315e16i	0.312125	−	0.117000i
$145$	2.90997e16			0.148917
$146$	3.35124e16	+	2.79838e16i	0.162324	+	0.135545i
$147$			8.60848e16i			0.394810i
$148$	7.42206e16	+	4.09454e17i	0.322426	+	1.77874i
$149$	−1.63558e17			−0.673259			−0.336629	−	0.941637i	$-0.609287\pi$
$149$	−1.63558e17			−0.673259			−0.336629	+	0.941637i	$0.609287\pi$
$150$	9.35807e16	−	1.12069e17i	0.365137	−	0.437275i
$151$		−	4.45986e17i		−	1.65008i	−0.565074	−	0.825041i	$-0.691152\pi$
$151$		−	4.45986e17i		−	1.65008i	0.565074	−	0.825041i	$-0.308848\pi$
$152$	1.71922e17	+	9.76201e16i	0.603369	+	0.342602i
$153$	−3.74071e16			−0.124573
$154$	−1.75774e16	−	1.46777e16i	−0.0555635	−	0.0463971i
$155$		−	4.30262e16i		−	0.129145i
$156$	1.69154e17	−	3.06620e16i	0.482263	−	0.0874185i
$157$	6.72606e17			1.82206			0.911031	−	0.412337i	$-0.135288\pi$
$157$	6.72606e17			1.82206			0.911031	+	0.412337i	$0.135288\pi$
$158$	2.46702e17	−	2.95441e17i	0.635208	−	0.760701i
$159$			2.12023e16i			0.0519045i
$160$	4.67208e16	+	1.63745e16i	0.108780	+	0.0381248i
$161$	−1.25767e16			−0.0278587
$162$	4.04577e16	+	3.37834e16i	0.0852868	+	0.0712169i
$163$		−	6.97357e17i		−	1.39944i	−0.714417	−	0.699720i	$-0.753308\pi$
$163$		−	6.97357e17i		−	1.39944i	0.714417	−	0.699720i	$-0.246692\pi$
$164$	1.36009e17	+	7.50326e17i	0.259907	+	1.43383i
$165$	4.70678e15			0.00856746
$166$	8.00934e16	−	9.59169e16i	0.138909	−	0.166353i
$167$			1.02388e18i			1.69246i	0.532818	+	0.846230i	$0.321133\pi$
$167$			1.02388e18i			1.69246i	−0.532818	+	0.846230i	$0.678867\pi$
$168$	1.01718e17	−	1.79139e17i	0.160296	−	0.282303i
$169$	−1.85877e17			−0.279340
$170$	−2.30657e16	−	1.92605e16i	−0.0330655	−	0.0276107i
$171$			1.69089e17i			0.231284i
$172$	−1.15670e18	+	2.09673e17i	−1.51006	+	0.273725i
$173$	−4.70521e17			−0.586423			−0.293211	−	0.956048i	$-0.594724\pi$
$173$	−4.70521e17			−0.586423			−0.293211	+	0.956048i	$0.594724\pi$
$174$	4.01695e17	−	4.81055e17i	0.478082	−	0.572533i
$175$		−	4.88040e17i		−	0.554818i
$176$	−4.16021e16	−	1.10983e17i	−0.0451870	−	0.120547i
$177$	−7.34630e17			−0.762575
$178$	−1.42921e18	−	1.19343e18i	−1.41820	−	1.18424i
$179$			1.41139e18i			1.33913i	0.742755	+	0.669564i	$0.233519\pi$
$179$			1.41139e18i			1.33913i	−0.742755	+	0.669564i	$0.766481\pi$
$180$	7.55206e15	+	4.16626e16i	0.00685307	+	0.0378065i
$181$	5.45235e17			0.473320			0.236660	−	0.971592i	$-0.423947\pi$
$181$	5.45235e17			0.473320			0.236660	+	0.971592i	$0.423947\pi$
$182$	3.68317e17	−	4.41083e17i	0.305950	−	0.366395i
$183$		−	5.37463e16i		−	0.0427307i
$184$	−5.66056e16	−	3.21415e16i	−0.0430841	−	0.0244638i
$185$	−2.85899e17			−0.208372
$186$	−7.11276e17	−	5.93936e17i	−0.496518	−	0.414607i
$187$			7.19419e16i			0.0481115i
$188$	−2.12571e18	+	3.85322e17i	−1.36220	+	0.246922i
$189$	1.76186e17			0.108213
$190$	−8.70621e16	+	1.04262e17i	−0.0512626	+	0.0613902i
$191$			5.83418e17i			0.329392i	0.986344	+	0.164696i	$0.0526643\pi$
$191$			5.83418e17i			0.329392i	−0.986344	+	0.164696i	$0.947336\pi$
$192$	9.15627e17	−	5.46319e17i	0.495803	−	0.295826i
$193$	3.06897e18			1.59417			0.797083	−	0.603870i	$-0.206375\pi$
$193$	3.06897e18			1.59417			0.797083	+	0.603870i	$0.206375\pi$
$194$	−3.12907e17	−	2.61286e17i	−0.155956	−	0.130227i
$195$			1.18111e17i			0.0564953i
$196$	2.65642e17	+	1.46547e18i	0.121968	+	0.672866i
$197$	1.15460e18			0.508982			0.254491	−	0.967075i	$-0.418092\pi$
$197$	1.15460e18			0.508982			0.254491	+	0.967075i	$0.418092\pi$
$198$	6.49728e16	−	7.78090e16i	0.0275049	−	0.0329388i
$199$			1.38254e18i			0.562149i	0.959686	+	0.281075i	$0.0906909\pi$
$199$			1.38254e18i			0.562149i	−0.959686	+	0.281075i	$0.909309\pi$
$200$	1.24725e18	−	2.19658e18i	0.487208	−	0.858039i
$201$	1.33244e18			0.500125
$202$	1.38559e18	+	1.15700e18i	0.499830	+	0.417373i
$203$		−	2.09491e18i		−	0.726436i
$204$	−6.36802e17	+	1.15431e17i	−0.212306	+	0.0384842i
$205$	−5.23911e17			−0.167968
$206$	5.29165e17	−	6.33709e17i	0.163175	−	0.195412i
$207$		−	5.56727e16i		−	0.0165150i
$208$	2.78498e18	−	1.04395e18i	0.794905	−	0.297971i
$209$	3.25194e17			0.0893249
$210$	1.08639e17	+	9.07166e16i	0.0287231	+	0.0239846i
$211$			1.48026e18i			0.376771i	0.982095	+	0.188385i	$0.0603254\pi$
$211$			1.48026e18i			0.376771i	−0.982095	+	0.188385i	$0.939675\pi$
$212$	6.54262e16	+	3.60938e17i	0.0160348	+	0.0884597i
$213$	−3.35175e18			−0.791107
$214$	−2.32247e18	+	2.78130e18i	−0.528007	+	0.632321i
$215$		−	8.07663e17i		−	0.176898i
$216$	7.92984e17	+	4.50268e17i	0.167353	+	0.0950258i
$217$	−3.09748e18			−0.629987
$218$	4.35037e18	+	3.63268e18i	0.852853	+	0.712157i
$219$			6.46027e17i			0.122095i
$220$	8.01261e16	−	1.45242e16i	0.0146013	−	0.00264674i
$221$	−1.80529e18			−0.317255
$222$	−3.94658e18	+	4.72627e18i	−0.668955	+	0.801116i
$223$		−	6.05000e17i		−	0.0989274i	−0.998776	−	0.0494637i	$-0.984249\pi$
$223$		−	6.05000e17i		−	0.0989274i	0.998776	−	0.0494637i	$-0.0157512\pi$
$224$	1.17881e18	−	3.36346e18i	0.185977	−	0.530643i
$225$	2.16038e18			0.328904
$226$	2.02378e18	+	1.68991e18i	0.297369	+	0.248312i
$227$		−	1.25176e19i		−	1.77547i	−0.460356	−	0.887734i	$-0.652278\pi$
$227$		−	1.25176e19i		−	1.77547i	0.460356	−	0.887734i	$-0.347722\pi$
$228$	5.21776e17	+	2.87849e18i	0.0714505	+	0.394172i
$229$	−1.23160e19			−1.62849			−0.814245	−	0.580521i	$-0.802849\pi$
$229$	−1.23160e19			−1.62849			−0.814245	+	0.580521i	$0.802849\pi$
$230$	2.86653e16	−	3.43285e16i	0.00366044	−	0.00438361i
$231$		−	3.38844e17i		−	0.0417931i
$232$	5.35383e18	−	9.42882e18i	0.637912	−	1.12345i
$233$	1.37425e18			0.158205			0.0791024	−	0.996866i	$-0.474795\pi$
$233$	1.37425e18			0.158205			0.0791024	+	0.996866i	$0.474795\pi$
$234$	1.95252e18	+	1.63041e18i	0.217204	+	0.181372i
$235$		−	1.48427e18i		−	0.159577i
$236$	−1.25060e19	+	2.26693e18i	−1.29964	+	0.235582i
$237$	5.69529e18			0.572176
$238$	−1.38658e18	+	1.66052e18i	−0.134688	+	0.161298i
$239$		−	9.58646e18i		−	0.900482i	−0.892907	−	0.450241i	$-0.851338\pi$
$239$		−	9.58646e18i		−	0.900482i	0.892907	−	0.450241i	$-0.148662\pi$
$240$	2.57126e17	+	6.85941e17i	0.0233591	+	0.0623156i
$241$	−8.84376e18			−0.777142			−0.388571	−	0.921419i	$-0.627031\pi$
$241$	−8.84376e18			−0.777142			−0.388571	+	0.921419i	$0.627031\pi$
$242$	8.87951e18	+	7.41465e18i	0.754859	+	0.630329i
$243$			7.79915e17i			0.0641500i
$244$	−1.65851e17	−	9.14953e17i	−0.0132008	−	0.0728249i
$245$	−1.02326e18			−0.0788236
$246$	−7.23211e18	+	8.66091e18i	−0.539243	+	0.645777i
$247$			8.16033e18i			0.589023i
$248$	−1.39412e19	−	7.91604e18i	−0.974289	−	0.553216i
$249$	1.84901e18			0.125125
$250$	2.68217e18	+	2.23969e18i	0.175779	+	0.146781i
$251$			1.29171e19i			0.819928i	0.912102	+	0.409964i	$0.134459\pi$
$251$			1.29171e19i			0.819928i	−0.912102	+	0.409964i	$0.865541\pi$
$252$	2.99932e18	−	5.43678e17i	0.184424	−	0.0334301i
$253$	−1.07071e17			−0.00637831
$254$	−4.56840e17	+	5.47095e17i	−0.0263690	+	0.0315786i
$255$		−	4.44644e17i		−	0.0248709i
$256$	1.39014e19	−	1.21257e19i	0.753596	−	0.657338i
$257$	2.12187e19			1.11495			0.557474	−	0.830195i	$-0.311771\pi$
$257$	2.12187e19			1.11495			0.557474	+	0.830195i	$0.311771\pi$
$258$	−1.33517e19	−	1.11490e19i	−0.680109	−	0.567911i
$259$			2.05821e19i			1.01646i
$260$	3.64467e17	+	2.01066e18i	0.0174531	+	0.0962837i
$261$	9.27343e18			0.430642
$262$	1.38977e19	−	1.66434e19i	0.625939	−	0.749602i
$263$			1.52461e19i			0.666060i	0.942916	+	0.333030i	$0.108071\pi$
$263$			1.52461e19i			0.666060i	−0.942916	+	0.333030i	$0.891929\pi$
$264$	8.65963e17	−	1.52508e18i	0.0367002	−	0.0646340i
$265$	−2.52023e17			−0.0103627
$266$	7.50592e18	+	6.26766e18i	0.299468	+	0.250065i
$267$		−	2.75513e19i		−	1.06672i
$268$	2.26828e19	−	4.11165e18i	0.852352	−	0.154503i
$269$	2.80251e19			1.02218			0.511092	−	0.859526i	$-0.329241\pi$
$269$	2.80251e19			1.02218			0.511092	+	0.859526i	$0.329241\pi$
$270$	−4.01570e17	+	4.80906e17i	−0.0142184	+	0.0170275i
$271$			4.19385e19i			1.44165i	0.693119	+	0.720824i	$0.256236\pi$
$271$			4.19385e19i			1.44165i	−0.693119	+	0.720824i	$0.743764\pi$
$272$	−1.04844e19	+	3.93010e18i	−0.349940	+	0.131175i
$273$	8.50287e18			0.275591
$274$	−3.14238e19	−	2.62398e19i	−0.989131	−	0.825953i
$275$		−	4.15487e18i		−	0.127027i
$276$	−1.71795e17	−	9.47747e17i	−0.00510198	−	0.0281462i
$277$	2.75902e19			0.796006			0.398003	−	0.917384i	$-0.369703\pi$
$277$	2.75902e19			0.796006			0.398003	+	0.917384i	$0.369703\pi$
$278$	7.31813e17	−	8.76393e17i	0.0205136	−	0.0245663i
$279$		−	1.37115e19i		−	0.373465i
$280$	2.12935e18	+	1.20908e18i	0.0563616	+	0.0320030i
$281$	−1.24012e19			−0.319017			−0.159508	−	0.987197i	$-0.550991\pi$
$281$	−1.24012e19			−0.319017			−0.159508	+	0.987197i	$0.550991\pi$
$282$	−2.45368e19	−	2.04889e19i	−0.613515	−	0.512303i
$283$		−	2.72260e19i		−	0.661748i	−0.943675	−	0.330874i	$-0.892656\pi$
$283$		−	2.72260e19i		−	0.661748i	0.943675	−	0.330874i	$-0.107344\pi$
$284$	−5.70587e19	+	1.03429e19i	−1.34827	+	0.244396i
$285$	−2.00989e18			−0.0461758
$286$	3.13563e18	−	3.75511e18i	0.0700481	−	0.0838870i
$287$			3.77167e19i			0.819368i
$288$	1.48888e19	+	5.21817e18i	0.314573	+	0.110250i
$289$	−4.18649e19			−0.860335
$290$	5.71812e18	+	4.77479e18i	0.114306	+	0.0954488i
$291$		−	6.03198e18i		−	0.117305i
$292$	1.99352e18	+	1.09977e19i	0.0377187	+	0.208084i
$293$	−7.20983e19			−1.32735			−0.663673	−	0.748023i	$-0.731003\pi$
$293$	−7.20983e19			−1.32735			−0.663673	+	0.748023i	$0.731003\pi$
$294$	−1.41251e19	+	1.69157e19i	−0.253054	+	0.303048i
$295$		−	8.73226e18i		−	0.152248i
$296$	−5.26004e19	+	9.26364e19i	−0.892596	+	1.57198i
$297$	1.49994e18			0.0247756
$298$	−3.21393e19	−	2.68372e19i	−0.516781	−	0.431527i
$299$		−	2.68680e18i		−	0.0420597i
$300$	3.67773e19	−	6.66652e18i	0.560545	−	0.101608i
$301$	−5.81443e19			−0.862929
$302$	7.31790e19	−	8.76365e19i	1.05762	−	1.26657i
$303$			2.67103e19i			0.375956i
$304$	1.77650e19	+	4.73921e19i	0.243543	+	0.649706i
$305$	6.38861e17			0.00853116
$306$	−7.35052e18	−	6.13790e18i	−0.0956195	−	0.0798451i
$307$		−	1.20412e20i		−	1.52603i	−0.646383	−	0.763013i	$-0.723719\pi$
$307$		−	1.20412e20i		−	1.52603i	0.646383	−	0.763013i	$-0.276281\pi$
$308$	−1.04561e18	−	5.76834e18i	−0.0129111	−	0.0712270i
$309$	1.22162e19			0.146983
$310$	7.05989e18	−	8.45467e18i	0.0827760	−	0.0991295i
$311$		−	5.06945e19i		−	0.579266i	−0.957138	−	0.289633i	$-0.906467\pi$
$311$		−	5.06945e19i		−	0.579266i	0.957138	−	0.289633i	$-0.0935332\pi$
$312$	3.82699e19	+	2.17303e19i	0.426207	+	0.242007i
$313$	4.30599e18			0.0467432			0.0233716	−	0.999727i	$-0.492560\pi$
$313$	4.30599e18			0.0467432			0.0233716	+	0.999727i	$0.492560\pi$
$314$	1.32167e20	+	1.10364e20i	1.39858	+	1.16785i
$315$			2.09426e18i			0.0216046i
$316$	9.69542e19	−	1.75746e19i	0.975146	−	0.176762i
$317$	9.98544e19			0.979249			0.489624	−	0.871934i	$-0.337134\pi$
$317$	9.98544e19			0.979249			0.489624	+	0.871934i	$0.337134\pi$
$318$	−3.47895e18	+	4.16626e18i	−0.0332683	+	0.0398409i
$319$		−	1.78348e19i		−	0.166319i
$320$	6.49388e18	+	1.08837e19i	0.0590615	+	0.0989868i
$321$	−5.36159e19			−0.475612
$322$	−2.47133e18	−	2.06364e18i	−0.0213838	−	0.0178561i
$323$		−	3.07207e19i		−	0.259305i
$324$	2.40667e18	+	1.32769e19i	0.0198178	+	0.109329i
$325$	1.04261e20			0.837638
$326$	1.14425e20	−	1.37031e20i	0.896975	−	1.07418i
$327$			8.38632e19i			0.641489i
$328$	−9.63903e19	+	1.69756e20i	−0.719520	+	1.26717i
$329$	−1.06853e20			−0.778433
$330$	9.24885e17	+	7.72306e17i	0.00657622	+	0.00549133i
$331$		−	3.89785e19i		−	0.270521i	−0.990810	−	0.135260i	$-0.956813\pi$
$331$		−	3.89785e19i		−	0.270521i	0.990810	−	0.135260i	$-0.0431871\pi$
$332$	3.14768e19	−	5.70571e18i	0.213249	−	0.0386550i
$333$	−9.11096e19			−0.602574
$334$	−1.68002e20	+	2.01194e20i	−1.08479	+	1.29910i
$335$			1.58382e19i			0.0998498i
$336$	4.93814e19	−	1.85107e19i	0.303983	−	0.113948i
$337$	1.58332e20			0.951767			0.475883	−	0.879508i	$-0.342128\pi$
$337$	1.58332e20			0.951767			0.475883	+	0.879508i	$0.342128\pi$
$338$	−3.65250e19	−	3.04994e19i	−0.214416	−	0.179043i
$339$			3.90129e19i			0.223672i
$340$	−1.37209e18	−	7.56942e18i	−0.00768334	−	0.0423868i
$341$	−2.63701e19			−0.144237
$342$	−2.77447e19	+	3.32261e19i	−0.148242	+	0.177529i
$343$			1.81389e20i			0.946800i
$344$	−2.61697e20	−	1.48596e20i	−1.33454	−	0.757772i
$345$	6.61760e17			0.00329722
$346$	−9.24578e19	−	7.72049e19i	−0.450127	−	0.375869i
$347$		−	3.30940e20i		−	1.57439i	−0.616701	−	0.787197i	$-0.711531\pi$
$347$		−	3.30940e20i		−	1.57439i	0.616701	−	0.787197i	$-0.288469\pi$
$348$	1.57867e20	−	2.86160e19i	0.733933	−	0.133038i
$349$	1.03699e20			0.471164			0.235582	−	0.971854i	$-0.424300\pi$
$349$	1.03699e20			0.471164			0.235582	+	0.971854i	$0.424300\pi$
$350$	8.00794e19	−	9.59002e19i	0.355612	−	0.425868i
$351$			3.76392e19i			0.163374i
$352$	1.00357e19	−	2.86345e19i	0.0425799	−	0.121492i
$353$	−1.73945e20			−0.721465			−0.360733	−	0.932669i	$-0.617473\pi$
$353$	−1.73945e20			−0.721465			−0.360733	+	0.932669i	$0.617473\pi$
$354$	−1.44355e20	−	1.20541e20i	−0.585338	−	0.488774i
$355$		−	3.98410e19i		−	0.157944i
$356$	−8.50182e19	−	4.69022e20i	−0.329543	−	1.81800i
$357$	−3.20102e19			−0.121323
$358$	−2.31586e20	+	2.77339e20i	−0.858317	+	1.02789i
$359$			5.26548e20i			1.90846i	0.299079	+	0.954228i	$0.403321\pi$
$359$			5.26548e20i			1.90846i	−0.299079	+	0.954228i	$0.596679\pi$
$360$	−5.35217e18	+	9.42589e18i	−0.0189719	+	0.0334120i
$361$	1.49577e20			0.518569
$362$	1.07139e20	+	8.94642e19i	0.363312	+	0.303376i
$363$			1.71173e20i			0.567782i
$364$	1.44749e20	−	2.62383e19i	0.469683	−	0.0851381i
$365$	−7.67907e18			−0.0243762
$366$	8.81889e18	−	1.05612e19i	0.0273883	−	0.0327992i
$367$			1.15856e20i			0.352039i	0.984387	+	0.176019i	$0.0563222\pi$
$367$			1.15856e20i			0.352039i	−0.984387	+	0.176019i	$0.943678\pi$
$368$	−5.84914e18	−	1.56039e19i	−0.0173904	−	0.0463928i
$369$	−1.66959e20			−0.485733
$370$	−5.61794e19	−	4.69114e19i	−0.159942	−	0.133556i
$371$			1.81433e19i			0.0505505i
$372$	−4.23110e19	−	2.33418e20i	−0.115374	−	0.636488i
$373$	1.79070e20			0.477916			0.238958	−	0.971030i	$-0.423194\pi$
$373$	1.79070e20			0.477916			0.238958	+	0.971030i	$0.423194\pi$
$374$	−1.18045e19	+	1.41366e19i	−0.0308372	+	0.0369295i
$375$			5.17050e19i			0.132215i
$376$	−4.80929e20	−	2.73079e20i	−1.20387	−	0.683573i
$377$	4.47542e20			1.09674
$378$	3.46207e19	+	2.89093e19i	0.0830619	+	0.0693591i
$379$		−	5.63500e20i		−	1.32367i	−0.749649	−	0.661836i	$-0.769778\pi$
$379$		−	5.63500e20i		−	1.32367i	0.749649	−	0.661836i	$-0.230222\pi$
$380$	−3.42155e19	+	6.20215e18i	−0.0786963	+	0.0142651i
$381$	−1.05465e19			−0.0237524
$382$	−9.57294e19	+	1.14642e20i	−0.211124	+	0.252835i
$383$			3.70048e20i			0.799222i	0.916685	+	0.399611i	$0.130855\pi$
$383$			3.70048e20i			0.799222i	−0.916685	+	0.399611i	$0.869145\pi$
$384$	2.69563e20	+	4.28876e19i	0.570179	+	0.0907157i
$385$	4.02771e18			0.00834397
$386$	6.03054e20	+	5.03568e20i	1.22365	+	1.02178i
$387$		−	2.57384e20i		−	0.511557i
$388$	−1.86136e19	−	1.02686e20i	−0.0362390	−	0.199920i
$389$	−1.44538e20			−0.275666			−0.137833	−	0.990455i	$-0.544014\pi$
$389$	−1.44538e20			−0.275666			−0.137833	+	0.990455i	$0.544014\pi$
$390$	−1.93800e19	+	2.32088e19i	−0.0362108	+	0.0433647i
$391$			1.01148e19i			0.0185159i
$392$	−1.88261e20	+	3.31553e20i	−0.337654	+	0.594655i
$393$	3.20838e20			0.563827
$394$	2.26880e20	+	1.89451e20i	0.390685	+	0.326233i
$395$			6.76978e19i			0.114235i
$396$	2.55344e19	−	4.62854e18i	0.0422244	−	0.00765390i
$397$	−8.04793e19			−0.130425			−0.0652124	−	0.997871i	$-0.520772\pi$
$397$	−8.04793e19			−0.130425			−0.0652124	+	0.997871i	$0.520772\pi$
$398$	−2.26852e20	+	2.71669e20i	−0.360311	+	0.431495i
$399$			1.44694e20i			0.225251i
$400$	6.05509e20	−	2.26976e20i	0.923934	−	0.346338i
$401$	−1.41133e20			−0.211093			−0.105546	−	0.994414i	$-0.533659\pi$
$401$	−1.41133e20			−0.211093			−0.105546	+	0.994414i	$0.533659\pi$
$402$	2.61825e20	+	2.18632e20i	0.383887	+	0.320556i
$403$		−	6.61724e20i		−	0.951123i
$404$	8.24229e19	+	4.54704e20i	0.116144	+	0.640734i
$405$	−9.27054e18			−0.0128075
$406$	3.43741e20	−	4.11651e20i	0.465611	−	0.557598i
$407$			1.75223e20i			0.232722i
$408$	−1.44072e20	−	8.18065e19i	−0.187629	−	0.106538i
$409$	1.27269e20			0.162531			0.0812654	−	0.996693i	$-0.474104\pi$
$409$	1.27269e20			0.162531			0.0812654	+	0.996693i	$0.474104\pi$
$410$	−1.02949e20	−	8.59653e19i	−0.128929	−	0.107660i
$411$		−	6.05764e20i		−	0.743993i
$412$	2.07963e20	−	3.76968e19i	0.250500	−	0.0454074i
$413$	−6.28642e20			−0.742682
$414$	9.13498e18	−	1.09397e19i	0.0105853	−	0.0126766i
$415$			2.19785e19i			0.0249812i
$416$	7.18546e20	+	2.51832e20i	0.801139	+	0.280779i
$417$	1.68944e19			0.0184780
$418$	6.39009e19	+	5.33591e19i	0.0685641	+	0.0572530i
$419$		−	1.22983e21i		−	1.29459i	−0.762240	−	0.647295i	$-0.775900\pi$
$419$		−	1.22983e21i		−	1.29459i	0.762240	−	0.647295i	$-0.224100\pi$
$420$	6.46249e18	+	3.56517e19i	0.00667430	+	0.0368202i
$421$	−1.70492e21			−1.72762			−0.863810	−	0.503818i	$-0.831928\pi$
$421$	−1.70492e21			−1.72762			−0.863810	+	0.503818i	$0.831928\pi$
$422$	−2.42886e20	+	2.90871e20i	−0.241492	+	0.289202i
$423$		−	4.73002e20i		−	0.461467i
$424$	−4.63677e19	+	8.16599e19i	−0.0443904	+	0.0781775i
$425$	−3.92506e20			−0.368752
$426$	−6.58622e20	−	5.49968e20i	−0.607238	−	0.507062i
$427$		−	4.59921e19i		−	0.0416160i
$428$	−9.12733e20	+	1.65448e20i	−0.810575	+	0.146931i
$429$	7.23883e19			0.0630972
$430$	1.32524e20	−	1.58706e20i	0.113383	−	0.135783i
$431$			1.28885e21i			1.08239i	0.840896	+	0.541197i	$0.182029\pi$
$431$			1.28885e21i			1.08239i	−0.840896	+	0.541197i	$0.817971\pi$
$432$	8.19401e19	+	2.18594e20i	0.0675502	+	0.180205i
$433$	−1.15744e21			−0.936686			−0.468343	−	0.883547i	$-0.655149\pi$
$433$	−1.15744e21			−0.936686			−0.468343	+	0.883547i	$0.655149\pi$
$434$	−6.08658e20	−	5.08247e20i	−0.483566	−	0.403791i
$435$			1.10230e20i			0.0859774i
$436$	2.58786e20	+	1.42765e21i	0.198175	+	1.09328i
$437$	4.57214e19			0.0343770
$438$	−1.06002e20	+	1.26945e20i	−0.0782570	+	0.0937177i
$439$			2.49135e21i			1.80600i	0.429639	+	0.903001i	$0.358641\pi$
$439$			2.49135e21i			1.80600i	−0.429639	+	0.903001i	$0.641359\pi$
$440$	1.81280e19	+	1.02934e19i	0.0129041	+	0.00732717i
$441$	−3.26089e20			−0.227944
$442$	−3.54741e20	−	2.96219e20i	−0.243519	−	0.203346i
$443$		−	2.09067e21i		−	1.40947i	−0.709472	−	0.704734i	$-0.751066\pi$
$443$		−	2.09067e21i		−	1.40947i	0.709472	−	0.704734i	$-0.248934\pi$
$444$	−1.55101e21	+	2.81147e20i	−1.02695	+	0.186153i
$445$	3.27492e20			0.212971
$446$	9.92707e19	−	1.18883e20i	0.0634078	−	0.0759348i
$447$		−	6.19557e20i		−	0.388706i
$448$	7.83526e20	−	4.67499e20i	0.482869	−	0.288109i
$449$	2.29386e21			1.38866			0.694331	−	0.719656i	$-0.255700\pi$
$449$	2.29386e21			1.38866			0.694331	+	0.719656i	$0.255700\pi$
$450$	4.24516e20	+	3.54483e20i	0.252461	+	0.210812i
$451$			3.21097e20i			0.187596i
$452$	1.20386e20	+	6.64138e20i	0.0690988	+	0.381198i
$453$	1.68939e21			0.952675
$454$	2.05393e21	−	2.45971e21i	1.13799	−	1.36282i
$455$			1.01070e20i			0.0550215i
$456$	−3.69784e20	+	6.51240e20i	−0.197802	+	0.348355i
$457$	1.45139e21			0.762876			0.381438	−	0.924394i	$-0.375429\pi$
$457$	1.45139e21			0.762876			0.381438	+	0.924394i	$0.375429\pi$
$458$	−2.42010e21	−	2.02085e21i	−1.25000	−	1.04378i
$459$		−	1.41698e20i		−	0.0719220i
$460$	1.12655e19	−	2.04207e18i	0.00561937	−	0.00101861i
$461$	2.70680e21			1.32693			0.663466	−	0.748207i	$-0.269085\pi$
$461$	2.70680e21			1.32693			0.663466	+	0.748207i	$0.269085\pi$
$462$	5.55989e19	−	6.65832e19i	0.0267874	−	0.0320796i
$463$			2.77293e21i			1.31308i	0.754291	+	0.656540i	$0.227981\pi$
$463$			2.77293e21i			1.31308i	−0.754291	+	0.656540i	$0.772019\pi$
$464$	2.59915e21	−	9.74294e20i	1.20973	−	0.453467i
$465$	1.62983e20			0.0745621
$466$	2.70042e20	+	2.25493e20i	0.121435	+	0.101402i
$467$		−	1.65320e21i		−	0.730785i	−0.930853	−	0.365393i	$-0.880935\pi$
$467$		−	1.65320e21i		−	0.730785i	0.930853	−	0.365393i	$-0.119065\pi$
$468$	1.16147e20	+	6.40753e20i	0.0504711	+	0.278435i
$469$	1.14020e21			0.487079
$470$	2.43544e20	−	2.91660e20i	0.102281	−	0.122488i
$471$			2.54783e21i			1.05197i
$472$	−2.82941e21	−	1.60658e21i	−1.14857	−	0.652179i
$473$	−4.95005e20			−0.197570
$474$	1.11913e21	+	9.34505e20i	0.439191	+	0.366737i
$475$			1.77422e21i			0.684633i
$476$	−5.44928e20	+	9.87775e19i	−0.206768	+	0.0374803i
$477$	−8.03141e19			−0.0299671
$478$	1.57298e21	−	1.88375e21i	0.577166	−	0.691193i
$479$			9.34864e20i			0.337337i	0.985673	+	0.168669i	$0.0539468\pi$
$479$			9.34864e20i			0.337337i	−0.985673	+	0.168669i	$0.946053\pi$
$480$	−6.20264e19	+	1.76978e20i	−0.0220113	+	0.0628043i
$481$	−4.39701e21			−1.53461
$482$	−1.73780e21	−	1.45112e21i	−0.596520	−	0.498111i
$483$		−	4.76406e19i		−	0.0160842i
$484$	5.28206e20	+	2.91397e21i	0.175405	+	0.967658i
$485$	7.16999e19			0.0234199
$486$	−1.27971e20	+	1.53254e20i	−0.0411171	+	0.0492403i
$487$			1.25840e20i			0.0397729i	0.999802	+	0.0198864i	$0.00633047\pi$
$487$			1.25840e20i			0.0397729i	−0.999802	+	0.0198864i	$0.993670\pi$
$488$	1.17539e20	−	2.07002e20i	0.0365446	−	0.0643601i
$489$	2.64159e21			0.807968
$490$	−2.01071e20	−	1.67900e20i	−0.0605035	−	0.0505221i
$491$			1.35029e21i			0.399737i	0.979823	+	0.199868i	$0.0640515\pi$
$491$			1.35029e21i			0.399737i	−0.979823	+	0.199868i	$0.935949\pi$
$492$	−2.84223e21	+	5.15203e20i	−0.827825	+	0.150057i
$493$	−1.68483e21			−0.482815
$494$	−1.33898e21	+	1.60351e21i	−0.377536	+	0.452123i
$495$			1.78293e19i			0.00494643i
$496$	−1.44057e21	−	3.84304e21i	−0.393260	−	1.04911i
$497$	−2.86818e21			−0.770470
$498$	3.63333e20	+	3.03393e20i	0.0960439	+	0.0801994i
$499$		−	5.21112e21i		−	1.35559i	−0.735253	−	0.677793i	$-0.762937\pi$
$499$		−	5.21112e21i		−	1.35559i	0.735253	−	0.677793i	$-0.237063\pi$
$500$	1.59552e20	+	8.80202e20i	0.0408453	+	0.225332i
$501$	−3.87846e21			−0.977142
$502$	−2.11949e21	+	2.53822e21i	−0.525535	+	0.629361i
$503$		−	3.67581e21i		−	0.897036i	−0.893774	−	0.448518i	$-0.851952\pi$
$503$		−	3.67581e21i		−	0.897036i	0.893774	−	0.448518i	$-0.148048\pi$
$504$	6.78577e20	+	3.85306e20i	0.162988	+	0.0925469i
$505$	−3.17495e20			−0.0750595
$506$	−2.10394e19	−	1.75685e19i	−0.00489587	−	0.00408819i
$507$		−	7.04102e20i		−	0.161277i
$508$	−1.79539e20	+	3.25445e19i	−0.0404807	+	0.00733783i
$509$	3.70215e21			0.821698			0.410849	−	0.911703i	$-0.365232\pi$
$509$	3.70215e21			0.821698			0.410849	+	0.911703i	$0.365232\pi$
$510$	7.29588e19	−	8.73728e19i	0.0159410	−	0.0190904i
$511$			5.52822e20i			0.118910i
$512$	4.72127e21	−	1.01722e20i	0.999768	−	0.0215405i
$513$	−6.40507e20			−0.133532
$514$	4.16950e21	+	3.48165e21i	0.855812	+	0.714628i
$515$			1.45209e20i			0.0293451i
$516$	−7.94239e20	−	4.38159e21i	−0.158035	−	0.871835i
$517$	−9.09686e20			−0.178224
$518$	−3.37719e21	+	4.04440e21i	−0.651504	+	0.780217i
$519$		−	1.78233e21i		−	0.338571i
$520$	−2.58299e20	+	4.54900e20i	−0.0483166	+	0.0850921i
$521$	−4.65046e21			−0.856631			−0.428316	−	0.903629i	$-0.640893\pi$
$521$	−4.65046e21			−0.856631			−0.428316	+	0.903629i	$0.640893\pi$
$522$	1.82223e21	+	1.52162e21i	0.330552	+	0.276021i
$523$		−	7.31101e21i		−	1.30606i	−0.757331	−	0.653031i	$-0.773497\pi$
$523$		−	7.31101e21i		−	1.30606i	0.757331	−	0.653031i	$-0.226503\pi$
$524$	5.46181e21	−	9.90047e20i	0.960918	−	0.174183i
$525$	1.84869e21			0.320325
$526$	−2.50164e21	+	2.99587e21i	−0.426913	+	0.511255i
$527$			2.49115e21i			0.418712i
$528$	4.20403e20	−	1.57589e20i	0.0695976	−	0.0260888i
$529$	6.11756e21			0.997545
$530$	−4.95227e19	−	4.13529e19i	−0.00795422	−	0.00664200i
$531$		−	2.78277e21i		−	0.440273i
$532$	4.46497e20	+	2.46320e21i	0.0695866	+	0.383890i
$533$	−8.05753e21			−1.23704
$534$	4.52073e21	−	5.41385e21i	0.683720	−	0.818798i
$535$		−	6.37311e20i		−	0.0949557i
$536$	5.13185e21	+	2.91394e21i	0.753279	+	0.427723i
$537$	−5.34633e21			−0.773146
$538$	5.50696e21	+	4.59847e21i	0.784609	+	0.655171i
$539$			6.27139e20i			0.0880347i
$540$	−1.57818e20	+	2.86072e19i	−0.0218276	+	0.00395662i
$541$	8.52511e21			1.16178			0.580888	−	0.813984i	$-0.302706\pi$
$541$	8.52511e21			1.16178			0.580888	+	0.813984i	$0.302706\pi$
$542$	−6.88143e21	+	8.24095e21i	−0.924027	+	1.10658i
$543$			2.06535e21i			0.273272i
$544$	−2.70506e21	−	9.48057e20i	−0.352684	−	0.123607i
$545$	−9.96849e20			−0.128073
$546$	1.67082e21	+	1.39518e21i	0.211538	+	0.176640i
$547$			7.69610e21i			0.960223i	0.877208	+	0.480111i	$0.159404\pi$
$547$			7.69610e21i			0.960223i	−0.877208	+	0.480111i	$0.840596\pi$
$548$	−1.86927e21	−	1.03123e22i	−0.229842	−	1.26797i
$549$	2.03591e20			0.0246706
$550$	6.81747e20	−	8.16436e20i	0.0814183	−	0.0975036i
$551$			7.61583e21i			0.896405i
$552$	1.21752e20	−	2.14422e20i	0.0141242	−	0.0248746i
$553$	4.87361e21			0.557250
$554$	5.42149e21	+	4.52710e21i	0.610999	+	0.510202i
$555$		−	1.08299e21i		−	0.120304i
$556$	2.87604e20	−	5.21331e19i	0.0314917	−	0.00570841i
$557$	−4.62948e21			−0.499678			−0.249839	−	0.968287i	$-0.580378\pi$
$557$	−4.62948e21			−0.499678			−0.249839	+	0.968287i	$0.580378\pi$
$558$	2.24983e21	−	2.69431e21i	0.239373	−	0.286665i
$559$		−	1.24215e22i		−	1.30281i
$560$	2.20029e20	+	5.86977e20i	0.0227497	+	0.0606900i
$561$	−2.72516e20			−0.0277772
$562$	−2.43685e21	−	2.03484e21i	−0.244871	−	0.204475i
$563$			8.89108e21i			0.880820i	0.897797	+	0.440410i	$0.145167\pi$
$563$			8.89108e21i			0.880820i	−0.897797	+	0.440410i	$0.854833\pi$
$564$	−1.45960e21	−	8.05218e21i	−0.142561	−	0.786467i
$565$	−4.63731e20			−0.0446559
$566$	4.46735e21	−	5.34993e21i	0.424149	−	0.507945i
$567$			6.67393e20i			0.0624766i
$568$	−1.29092e22	−	7.33003e21i	−1.19155	−	0.676580i
$569$	1.92778e22			1.75452			0.877261	−	0.480014i	$-0.159368\pi$
$569$	1.92778e22			1.75452			0.877261	+	0.480014i	$0.159368\pi$
$570$	−3.94945e20	−	3.29791e20i	−0.0354436	−	0.0295964i
$571$		−	9.49922e21i		−	0.840619i	−0.907381	−	0.420309i	$-0.861922\pi$
$571$		−	9.49922e21i		−	0.840619i	0.907381	−	0.420309i	$-0.138078\pi$
$572$	1.23231e21	−	2.23377e20i	0.107535	−	0.0194926i
$573$	−2.20998e21			−0.190174
$574$	−6.18871e21	+	7.41137e21i	−0.525176	+	0.628931i
$575$		−	5.84163e20i		−	0.0488868i
$576$	2.06945e21	+	3.46839e21i	0.170795	+	0.286252i
$577$	3.93866e20			0.0320584			0.0160292	−	0.999872i	$-0.494898\pi$
$577$	3.93866e20			0.0320584			0.0160292	+	0.999872i	$0.494898\pi$
$578$	−8.22649e21	−	6.86935e21i	−0.660377	−	0.551434i
$579$			1.16252e22i			0.920392i
$580$	3.40148e20	+	1.87650e21i	0.0265610	+	0.146529i
$581$	1.58225e21			0.121861
$582$	9.89750e20	−	1.18529e21i	0.0751868	−	0.0900410i
$583$			1.54461e20i			0.0115737i
$584$	−1.41281e21	+	2.48815e21i	−0.104419	+	0.183897i
$585$	−4.47403e20			−0.0326176
$586$	−1.41674e22	−	1.18302e22i	−1.01885	−	0.850766i
$587$			1.14484e22i			0.812156i	0.913838	+	0.406078i	$0.133104\pi$
$587$			1.14484e22i			0.812156i	−0.913838	+	0.406078i	$0.866896\pi$
$588$	−5.55119e21	+	1.00625e21i	−0.388479	+	0.0704185i
$589$	1.12606e22			0.777389
$590$	1.43282e21	−	1.71590e21i	0.0975835	−	0.116862i
$591$			4.37363e21i			0.293861i
$592$	−2.55361e22	+	9.57225e21i	−1.69271	+	0.634513i
$593$	−2.05167e22			−1.34175			−0.670874	−	0.741572i	$-0.734081\pi$
$593$	−2.05167e22			−1.34175			−0.670874	+	0.741572i	$0.734081\pi$
$594$	2.94740e20	+	2.46116e20i	0.0190172	+	0.0158799i
$595$		−	3.80493e20i		−	0.0242221i
$596$	−1.91184e21	−	1.05471e22i	−0.120083	−	0.662463i
$597$	−5.23704e21			−0.324557
$598$	4.40860e20	−	5.27958e20i	0.0269582	−	0.0322842i
$599$			5.38868e20i			0.0325138i	0.999868	+	0.0162569i	$0.00517496\pi$
$599$			5.38868e20i			0.0325138i	−0.999868	+	0.0162569i	$0.994825\pi$
$600$	8.32064e21	+	4.72459e21i	0.495389	+	0.281290i
$601$	−5.44089e21			−0.319650			−0.159825	−	0.987145i	$-0.551093\pi$
$601$	−5.44089e21			−0.319650			−0.159825	+	0.987145i	$0.551093\pi$
$602$	−1.14254e22	−	9.54053e21i	−0.662368	−	0.553096i
$603$			5.04727e21i			0.288747i
$604$	2.87594e22	−	5.21314e21i	1.62362	−	0.294309i
$605$	−2.03466e21			−0.113357
$606$	−4.38272e21	+	5.24859e21i	−0.240970	+	0.288577i
$607$			5.75755e21i			0.312412i	0.987724	+	0.156206i	$0.0499264\pi$
$607$			5.75755e21i			0.312412i	−0.987724	+	0.156206i	$0.950074\pi$
$608$	−4.28544e21	+	1.22275e22i	−0.229492	+	0.654801i
$609$	7.93551e21			0.419408
$610$	1.25537e20	+	1.04827e20i	0.00654835	+	0.00546806i
$611$		−	2.28274e22i		−	1.17524i
$612$	−4.37253e20	−	2.41220e21i	−0.0222188	−	0.122575i
$613$	−9.14430e21			−0.458635			−0.229317	−	0.973352i	$-0.573649\pi$
$613$	−9.14430e21			−0.458635			−0.229317	+	0.973352i	$0.573649\pi$
$614$	1.97576e22	−	2.36610e22i	0.978109	−	1.17135i
$615$		−	1.98457e21i		−	0.0969764i
$616$	7.41027e20	−	1.30505e21i	0.0357428	−	0.0629479i
$617$	1.03301e22			0.491841			0.245920	−	0.969290i	$-0.420910\pi$
$617$	1.03301e22			0.491841			0.245920	+	0.969290i	$0.420910\pi$
$618$	2.40049e21	+	2.00448e21i	0.112821	+	0.0942092i
$619$			4.25685e22i			1.97498i	0.157681	+	0.987490i	$0.449598\pi$
$619$			4.25685e22i			1.97498i	−0.157681	+	0.987490i	$0.550402\pi$
$620$	2.77455e21	−	5.02934e20i	0.127075	−	0.0230345i
$621$	2.10888e20			0.00953496
$622$	8.31815e21	−	9.96151e21i	0.371282	−	0.444633i
$623$		−	2.35764e22i		−	1.03890i
$624$	3.95449e21	+	1.05495e22i	0.172034	+	0.458938i
$625$	2.23591e22			0.960317
$626$	8.46131e20	+	7.06544e20i	0.0358792	+	0.0299602i
$627$			1.23183e21i			0.0515717i
$628$	7.86211e21	+	4.33731e22i	0.324984	+	1.79285i
$629$	1.65531e22			0.675578
$630$	−3.43634e20	+	4.11524e20i	−0.0138475	+	0.0165833i
$631$		−	2.86017e22i		−	1.13804i	−0.822324	−	0.569020i	$-0.807323\pi$
$631$		−	2.86017e22i		−	1.13804i	0.822324	−	0.569020i	$-0.192677\pi$
$632$	2.19353e22	+	1.24552e22i	0.861800	+	0.489343i
$633$	−5.60720e21			−0.217529
$634$	1.96215e22	+	1.63845e22i	0.751652	+	0.627651i
$635$		−	1.25362e20i		−	0.00474216i
$636$	−1.36723e21	+	2.47834e20i	−0.0510722	+	0.00925772i
$637$	−1.57373e22			−0.580516
$638$	2.92640e21	−	3.50455e21i	0.106603	−	0.127664i
$639$		−	1.26964e22i		−	0.456746i
$640$	−5.09789e20	+	3.20420e21i	−0.0181113	+	0.113836i
$641$	−5.68766e21			−0.199558			−0.0997791	−	0.995010i	$-0.531814\pi$
$641$	−5.68766e21			−0.199558			−0.0997791	+	0.995010i	$0.531814\pi$
$642$	−1.05356e22	−	8.79749e21i	−0.365071	−	0.304845i
$643$			9.58453e21i			0.328007i	0.986460	+	0.164003i	$0.0524408\pi$
$643$			9.58453e21i			0.328007i	−0.986460	+	0.164003i	$0.947559\pi$
$644$	−1.47010e20	−	8.11012e20i	−0.00496889	−	0.0274120i
$645$	3.05943e21			0.102132
$646$	5.04077e21	−	6.03664e21i	0.166202	−	0.199038i
$647$		−	4.46026e22i		−	1.45253i	−0.687414	−	0.726266i	$-0.741254\pi$
$647$		−	4.46026e22i		−	1.45253i	0.687414	−	0.726266i	$-0.258746\pi$
$648$	−1.70561e21	+	3.00382e21i	−0.0548632	+	0.0966215i
$649$	−5.35188e21			−0.170039
$650$	2.04874e22	+	1.71076e22i	0.642955	+	0.536886i
$651$		−	1.17333e22i		−	0.363723i
$652$	4.49692e22	−	8.15144e21i	1.37700	−	0.249605i
$653$	−4.48623e21			−0.135699			−0.0678494	−	0.997696i	$-0.521614\pi$
$653$	−4.48623e21			−0.135699			−0.0678494	+	0.997696i	$0.521614\pi$
$654$	−1.37606e22	+	1.64792e22i	−0.411164	+	0.492395i
$655$			3.81368e21i			0.112568i
$656$	−4.67950e22	+	1.75412e22i	−1.36449	+	0.511479i
$657$	−2.44715e21			−0.0704915
$658$	−2.09968e22	−	1.75329e22i	−0.597511	−	0.498939i
$659$			5.30196e21i			0.149057i	0.997219	+	0.0745286i	$0.0237452\pi$
$659$			5.30196e21i			0.149057i	−0.997219	+	0.0745286i	$0.976255\pi$
$660$	5.50177e19	+	3.03517e20i	0.00152810	+	0.00843009i
$661$	−5.01176e22			−1.37524			−0.687620	−	0.726070i	$-0.741345\pi$
$661$	−5.01176e22			−1.37524			−0.687620	+	0.726070i	$0.741345\pi$
$662$	6.39573e21	−	7.65929e21i	0.173391	−	0.207647i
$663$		−	6.83843e21i		−	0.183168i
$664$	7.12143e21	+	4.04366e21i	0.188461	+	0.107011i
$665$	−1.71992e21			−0.0449712
$666$	−1.79031e22	−	1.49496e22i	−0.462524	−	0.386221i
$667$		−	2.50752e21i		−	0.0640085i
$668$	−6.60252e22	+	1.19682e22i	−1.66532	+	0.301868i
$669$	2.29174e21			0.0571158
$670$	−2.59879e21	+	3.11221e21i	−0.0639989	+	0.0766428i
$671$		−	3.91549e20i		−	0.00952808i
$672$	1.27408e22	+	4.46532e21i	0.306367	+	0.107374i
$673$	−7.45742e22			−1.77202			−0.886009	−	0.463668i	$-0.846533\pi$
$673$	−7.45742e22			−1.77202			−0.886009	+	0.463668i	$0.846533\pi$
$674$	3.11124e22	+	2.59798e22i	0.730558	+	0.610037i
$675$			8.18350e21i			0.189893i
$676$	−2.17273e21	−	1.19863e22i	−0.0498232	−	0.274861i
$677$	−1.34138e22			−0.303979			−0.151989	−	0.988382i	$-0.548568\pi$
$677$	−1.34138e22			−0.303979			−0.151989	+	0.988382i	$0.548568\pi$
$678$	−6.40139e21	+	7.66606e21i	−0.143363	+	0.171686i
$679$		−	5.16172e21i		−	0.114245i
$680$	9.72402e20	−	1.71253e21i	0.0212704	−	0.0374600i
$681$	4.74165e22			1.02507
$682$	−5.18174e21	−	4.32691e21i	−0.110714	−	0.0924490i
$683$			6.68422e22i			1.41151i	0.708454	+	0.705757i	$0.249393\pi$
$683$			6.68422e22i			1.41151i	−0.708454	+	0.705757i	$0.750607\pi$
$684$	−1.09037e22	+	1.97648e21i	−0.227576	+	0.0412520i
$685$	7.20049e21			0.148538
$686$	−2.97630e22	+	3.56431e22i	−0.606854	+	0.726746i
$687$		−	4.66529e22i		−	0.940210i
$688$	−2.70415e22	−	7.21394e22i	−0.538671	−	1.43703i
$689$	−3.87601e21			−0.0763187
$690$	1.30036e20	+	1.08584e20i	0.00253088	+	0.00211336i
$691$			7.61674e22i			1.46536i	0.680572	+	0.732681i	$0.261731\pi$
$691$			7.61674e22i			1.46536i	−0.680572	+	0.732681i	$0.738269\pi$
$692$	−5.49994e21	−	3.03416e22i	−0.104595	−	0.577019i
$693$	1.28354e21			0.0241293
$694$	5.43019e22	−	6.50300e22i	1.00911	−	1.20848i
$695$			2.00818e20i			0.00368913i
$696$	3.57163e22	+	2.02803e22i	0.648624	+	0.368299i
$697$	3.03337e22			0.544582
$698$	2.03770e22	+	1.70154e22i	0.361657	+	0.301994i
$699$			5.20567e21i			0.0913396i
$700$	3.14713e22	−	5.70472e21i	0.545922	−	0.0989577i
$701$	6.67032e22			1.14394			0.571969	−	0.820275i	$-0.306180\pi$
$701$	6.67032e22			1.14394			0.571969	+	0.820275i	$0.306180\pi$
$702$	−6.17598e21	+	7.39613e21i	−0.104715	+	0.125403i
$703$		−	7.48241e22i		−	1.25429i
$704$	6.67047e21	−	3.98000e21i	0.110554	−	0.0659633i
$705$	5.62240e21			0.0921316
$706$	−3.41804e22	−	2.85416e22i	−0.553783	−	0.462425i
$707$			2.28567e22i			0.366149i
$708$	−8.58712e21	−	4.73727e22i	−0.136013	−	0.750347i
$709$	6.94725e22			1.08803			0.544017	−	0.839074i	$-0.316903\pi$
$709$	6.94725e22			1.08803			0.544017	+	0.839074i	$0.316903\pi$
$710$	6.53726e21	−	7.82878e21i	0.101235	−	0.121235i
$711$			2.15737e22i			0.330346i
$712$	6.02527e22	−	1.06113e23i	0.912297	−	1.60668i
$713$	−3.70756e21			−0.0555101
$714$	−6.29003e21	−	5.25236e21i	−0.0931252	−	0.0777622i
$715$			8.60452e20i			0.0125973i
$716$	−9.10135e22	+	1.64978e22i	−1.31766	+	0.238848i
$717$	3.63135e22			0.519894
$718$	−8.63980e22	+	1.03467e23i	−1.22323	+	1.46489i
$719$			7.93076e22i			1.11041i	0.831713	+	0.555205i	$0.187360\pi$
$719$			7.93076e22i			1.11041i	−0.831713	+	0.555205i	$0.812640\pi$
$720$	−2.59834e21	+	9.73991e20i	−0.0359779	+	0.0134864i
$721$	1.04537e22			0.143149
$722$	2.93919e22	+	2.45431e22i	0.398044	+	0.332378i
$723$		−	3.35001e22i		−	0.448683i
$724$	6.37327e21	+	3.51596e22i	0.0844217	+	0.465731i
$725$	9.73044e22			1.27476
$726$	−2.80866e22	+	3.36355e22i	−0.363921	+	0.435818i
$727$			1.18224e23i			1.51506i	0.652802	+	0.757528i	$0.273593\pi$
$727$			1.18224e23i			1.51506i	−0.652802	+	0.757528i	$0.726407\pi$
$728$	3.27486e22	+	1.85951e22i	0.415089	+	0.235694i
$729$	−2.95431e21			−0.0370370
$730$	−1.50894e21	−	1.26001e21i	−0.0187107	−	0.0156240i
$731$			4.67625e22i			0.573534i
$732$	3.46584e21	−	6.28242e20i	0.0420455	−	0.00762147i
$733$	−7.24896e22			−0.869849			−0.434925	−	0.900467i	$-0.643225\pi$
$733$	−7.24896e22			−0.869849			−0.434925	+	0.900467i	$0.643225\pi$
$734$	−1.90101e22	+	2.27658e22i	−0.225640	+	0.270218i
$735$		−	3.87609e21i		−	0.0455088i
$736$	1.41099e21	−	4.02592e21i	0.0163870	−	0.0467566i
$737$	9.70699e21			0.111518
$738$	−3.28075e22	−	2.73952e22i	−0.372840	−	0.311332i
$739$		−	4.36734e21i		−	0.0490978i	−0.999699	−	0.0245489i	$-0.992185\pi$
$739$		−	4.36734e21i		−	0.0490978i	0.999699	−	0.0245489i	$-0.00781494\pi$
$740$	−3.34189e21	−	1.84363e22i	−0.0371653	−	0.205031i
$741$	−3.09113e22			−0.340073
$742$	−2.97703e21	+	3.56518e21i	−0.0324005	+	0.0388016i
$743$		−	1.41363e23i		−	1.52204i	−0.648728	−	0.761020i	$-0.724699\pi$
$743$		−	1.41363e23i		−	1.52204i	0.648728	−	0.761020i	$-0.275301\pi$
$744$	2.99859e22	−	5.28093e22i	0.319399	−	0.562506i
$745$	7.36444e21			0.0776050
$746$	3.51873e22	+	2.93824e22i	0.366839	+	0.306321i
$747$			7.00406e21i			0.0722412i
$748$	−4.63918e21	+	8.40932e20i	−0.0473401	+	0.00858120i
$749$	−4.58805e22			−0.463205
$750$	−8.48395e21	+	1.01601e22i	−0.0847438	+	0.101486i
$751$		−	8.90798e22i		−	0.880358i	−0.897910	−	0.440179i	$-0.854915\pi$
$751$		−	8.90798e22i		−	0.880358i	0.897910	−	0.440179i	$-0.145085\pi$
$752$	−4.96950e22	−	1.32573e23i	−0.485926	−	1.29632i
$753$	−4.89300e22			−0.473386
$754$	8.79422e22	+	7.34343e22i	0.841835	+	0.702956i
$755$			2.00811e22i			0.190201i
$756$	2.05945e21	+	1.13614e22i	0.0193009	+	0.106477i
$757$	4.63034e22			0.429384			0.214692	−	0.976682i	$-0.431125\pi$
$757$	4.63034e22			0.429384			0.214692	+	0.976682i	$0.431125\pi$
$758$	9.24612e22	−	1.10728e23i	0.848410	−	1.01602i
$759$		−	4.05583e20i		−	0.00368252i
$760$	−7.74104e21	−	4.39548e21i	−0.0695490	−	0.0394910i
$761$	−1.56378e23			−1.39026			−0.695132	−	0.718882i	$-0.744654\pi$
$761$	−1.56378e23			−1.39026			−0.695132	+	0.718882i	$0.744654\pi$
$762$	−2.07239e21	−	1.73051e21i	−0.0182319	−	0.0152242i
$763$			7.17639e22i			0.624755i
$764$	−3.76218e22	+	6.81959e21i	−0.324110	+	0.0587505i
$765$	1.68431e21			0.0143592
$766$	−6.07188e22	+	7.27146e22i	−0.512263	+	0.613467i
$767$		−	1.34299e23i		−	1.12127i
$768$	4.59322e22	+	5.26584e22i	0.379514	+	0.435089i
$769$	2.59960e22			0.212567			0.106283	−	0.994336i	$-0.466105\pi$
$769$	2.59960e22			0.212567			0.106283	+	0.994336i	$0.466105\pi$
$770$	7.91449e20	+	6.60882e20i	0.00640467	+	0.00534809i
$771$			8.03765e22i			0.643715i
$772$	3.58733e22	+	1.97903e23i	0.284336	+	1.56860i
$773$	−1.28175e23			−1.00546			−0.502732	−	0.864442i	$-0.667672\pi$
$773$	−1.28175e23			−1.00546			−0.502732	+	0.864442i	$0.667672\pi$
$774$	4.22325e22	−	5.05761e22i	0.327883	−	0.392661i
$775$		−	1.43872e23i		−	1.10551i
$776$	1.31915e22	−	2.32320e22i	0.100323	−	0.176682i
$777$	−7.79649e22			−0.586855
$778$	−2.84017e22	−	2.37163e22i	−0.211596	−	0.176689i
$779$		−	1.37115e23i		−	1.01108i
$780$	−7.61638e21	+	1.38060e21i	−0.0555894	+	0.0100765i
$781$	−2.44180e22			−0.176401
$782$	−1.65968e21	+	1.98757e21i	−0.0118678	+	0.0142124i
$783$			3.51277e22i			0.248631i
$784$	−9.13959e22	+	3.42599e22i	−0.640322	+	0.240025i
$785$	−3.02850e22			−0.210025
$786$	6.30450e22	+	5.26444e22i	0.432783	+	0.361386i
$787$		−	3.96418e22i		−	0.269374i	−0.990888	−	0.134687i	$-0.956997\pi$
$787$		−	3.96418e22i		−	0.269374i	0.990888	−	0.134687i	$-0.0430029\pi$
$788$	1.34962e22	+	7.44547e22i	0.0907823	+	0.500821i
$789$	−5.77523e22			−0.384550
$790$	−1.11081e22	+	1.33027e22i	−0.0732189	+	0.0876843i
$791$			3.33844e22i			0.217837i
$792$	5.77699e21	+	3.28026e21i	0.0373165	+	0.0211889i
$793$	9.82542e21			0.0628298
$794$	−1.58142e22	−	1.32054e22i	−0.100112	−	0.0835961i
$795$		−	9.54662e20i		−	0.00598291i
$796$	−8.91530e22	+	1.61605e22i	−0.553135	+	0.100265i
$797$	2.13798e21			0.0131322			0.00656609	−	0.999978i	$-0.497910\pi$
$797$	2.13798e21			0.0131322			0.00656609	+	0.999978i	$0.497910\pi$
$798$	−2.37419e22	+	2.84324e22i	−0.144375	+	0.172898i
$799$			8.59369e22i			0.517375i
$800$	1.56226e23	+	5.47533e22i	0.931180	+	0.326355i
$801$	1.04364e23			0.615874
$802$	−2.77327e22	−	2.31576e22i	−0.162031	−	0.135300i
$803$			4.70639e21i			0.0272247i
$804$	1.55749e22	+	8.59225e22i	0.0892026	+	0.492106i
$805$	5.66285e20			0.00321120
$806$	1.08578e23	−	1.30029e23i	0.609624	−	0.730064i
$807$			1.06159e23i			0.590158i
$808$	−5.84134e22	+	1.02874e23i	−0.321530	+	0.566258i
$809$	1.44463e23			0.787351			0.393675	−	0.919250i	$-0.371203\pi$
$809$	1.44463e23			0.787351			0.393675	+	0.919250i	$0.371203\pi$
$810$	−1.82167e21	−	1.52115e21i	−0.00983081	−	0.00820901i
$811$		−	3.08751e23i		−	1.64984i	−0.565249	−	0.824920i	$-0.691220\pi$
$811$		−	3.08751e23i		−	1.64984i	0.565249	−	0.824920i	$-0.308780\pi$
$812$	1.35091e23	−	2.44875e22i	0.714788	−	0.129568i
$813$	−1.58863e23			−0.832335
$814$	−2.87513e22	+	3.44315e22i	−0.149164	+	0.178633i
$815$			3.13995e22i			0.161310i
$816$	−1.48872e22	−	3.97150e22i	−0.0757342	−	0.202038i
$817$	2.11377e23			1.06483
$818$	2.50084e22	+	2.08827e22i	0.124755	+	0.104174i
$819$			3.22088e22i			0.159112i
$820$	−6.12402e21	−	3.37845e22i	−0.0299589	−	0.165275i
$821$	1.09914e23			0.532484			0.266242	−	0.963906i	$-0.414218\pi$
$821$	1.09914e23			0.532484			0.266242	+	0.963906i	$0.414218\pi$
$822$	9.93961e22	−	1.19033e23i	0.476864	−	0.571075i
$823$		−	7.16721e22i		−	0.340527i	−0.985399	−	0.170263i	$-0.945538\pi$
$823$		−	7.16721e22i		−	0.340527i	0.985399	−	0.170263i	$-0.0544618\pi$
$824$	4.70503e22	+	2.67159e22i	0.221383	+	0.125705i
$825$	1.57386e22			0.0733391
$826$	−1.23529e23	−	1.03150e23i	−0.570069	−	0.476024i
$827$			2.00338e23i			0.915628i	0.889048	+	0.457814i	$0.151367\pi$
$827$			2.00338e23i			0.915628i	−0.889048	+	0.457814i	$0.848633\pi$
$828$	3.59006e21	−	6.50760e20i	0.0162502	−	0.00294563i
$829$	1.46109e23			0.654999			0.327499	−	0.944851i	$-0.393794\pi$
$829$	1.46109e23			0.654999			0.327499	+	0.944851i	$0.393794\pi$
$830$	−3.60632e21	+	4.31880e21i	−0.0160118	+	0.0191751i
$831$			1.04511e23i			0.459574i
$832$	9.98731e22	+	1.67387e23i	0.434973	+	0.729012i
$833$	5.92451e22			0.255560
$834$	3.31977e21	+	2.77210e21i	0.0141834	+	0.0118435i
$835$		−	4.61018e22i		−	0.195086i
$836$	3.80121e21	+	2.09702e22i	0.0159320	+	0.0878926i
$837$	5.19390e22			0.215620
$838$	2.01795e23	−	2.41662e23i	0.829770	−	0.993702i
$839$			2.64414e23i			1.07693i	0.842647	+	0.538466i	$0.180996\pi$
$839$			2.64414e23i			1.07693i	−0.842647	+	0.538466i	$0.819004\pi$
$840$	−4.57999e21	+	8.06598e21i	−0.0184769	+	0.0325404i
$841$	1.67433e23			0.669071
$842$	−3.35019e23	−	2.79750e23i	−1.32609	−	1.10732i
$843$		−	4.69758e22i		−	0.184185i
$844$	−9.54545e22	+	1.73028e22i	−0.370729	+	0.0672011i
$845$	8.36939e21			0.0321988
$846$	7.76120e22	−	9.29453e22i	0.295778	−	0.354213i
$847$			1.46477e23i			0.552970i
$848$	−2.25104e22	+	8.43803e21i	−0.0841813	+	0.0315555i
$849$	1.03132e23			0.382060
$850$	−7.71277e22	−	6.44039e22i	−0.283047	−	0.236353i
$851$			2.46359e22i			0.0895637i
$852$	−3.91788e22	−	2.16138e23i	−0.141102	−	0.778422i
$853$	−1.71142e23			−0.610609			−0.305305	−	0.952255i	$-0.598758\pi$
$853$	−1.71142e23			−0.610609			−0.305305	+	0.952255i	$0.598758\pi$
$854$	7.54655e21	−	9.03748e21i	0.0266739	−	0.0319436i
$855$		−	7.61346e21i		−	0.0266596i
$856$	−2.06500e23	−	1.17254e23i	−0.716358	−	0.406759i
$857$	−4.71695e23			−1.62112			−0.810559	−	0.585657i	$-0.800836\pi$
$857$	−4.71695e23			−1.62112			−0.810559	+	0.585657i	$0.800836\pi$
$858$	1.42243e22	+	1.18777e22i	0.0484322	+	0.0404423i
$859$			1.89722e23i			0.639988i	0.947420	+	0.319994i	$0.103681\pi$
$859$			1.89722e23i			0.639988i	−0.947420	+	0.319994i	$0.896319\pi$
$860$	5.20823e22	−	9.44081e21i	0.174061	−	0.0315516i
$861$	−1.42871e23			−0.473062
$862$	−2.11480e23	+	2.53260e23i	−0.693762	+	0.830824i
$863$			1.25778e23i			0.408806i	0.978887	+	0.204403i	$0.0655254\pi$
$863$			1.25778e23i			0.408806i	−0.978887	+	0.204403i	$0.934475\pi$
$864$	−1.97664e22	+	5.63989e22i	−0.0636528	+	0.181619i
$865$	2.11859e22			0.0675956
$866$	−2.27437e23	−	1.89916e23i	−0.718982	−	0.600371i
$867$		−	1.58584e23i		−	0.496715i
$868$	−3.62066e22	−	1.99742e23i	−0.112365	−	0.619885i
$869$	4.14910e22			0.127584
$870$	−1.80869e22	+	2.16602e22i	−0.0551074	+	0.0659946i
$871$			2.43585e23i			0.735368i
$872$	−1.83402e23	+	3.22997e23i	−0.548622	+	0.966198i
$873$	2.28491e22			0.0677260
$874$	8.98428e21	+	7.50213e21i	0.0263871	+	0.0220340i
$875$			4.42453e22i			0.128766i
$876$	−4.16591e22	+	7.55143e21i	−0.120137	+	0.0217769i
$877$	−1.17923e22			−0.0336977			−0.0168489	−	0.999858i	$-0.505363\pi$
$877$	−1.17923e22			−0.0336977			−0.0168489	+	0.999858i	$0.505363\pi$
$878$	−4.08790e23	+	4.89551e23i	−1.15756	+	1.38625i
$879$		−	2.73108e23i		−	0.766344i
$880$	1.87319e21	+	4.99717e21i	0.00520861	+	0.0138951i
$881$	−3.20332e22			−0.0882661			−0.0441330	−	0.999026i	$-0.514053\pi$
$881$	−3.20332e22			−0.0882661			−0.0441330	+	0.999026i	$0.514053\pi$
$882$	−6.40767e22	−	5.35059e22i	−0.174965	−	0.146101i
$883$		−	1.83970e23i		−	0.497808i	−0.968528	−	0.248904i	$-0.919930\pi$
$883$		−	1.83970e23i		−	0.497808i	0.968528	−	0.248904i	$-0.0800704\pi$
$884$	−2.11021e22	−	1.16414e23i	−0.0565859	−	0.312168i
$885$	3.30778e22			0.0879002
$886$	3.43045e23	−	4.10818e23i	0.903401	−	1.08188i
$887$			1.11278e23i			0.290416i	0.989401	+	0.145208i	$0.0463851\pi$
$887$			1.11278e23i			0.290416i	−0.989401	+	0.145208i	$0.953615\pi$
$888$	−3.50906e23	−	1.99250e23i	−0.907585	−	0.515341i
$889$	−9.02490e21			−0.0231328
$890$	6.43524e22	+	5.37361e22i	0.163473	+	0.136504i
$891$			5.68178e21i			0.0143042i
$892$	3.90135e22	−	7.07187e21i	0.0973412	−	0.0176448i
$893$	3.88455e23			0.960569
$894$	1.01659e23	−	1.21743e23i	0.249142	−	0.298363i
$895$		−	6.35497e22i		−	0.154358i
$896$	2.30672e23	+	3.67001e22i	0.555305	+	0.0883492i
$897$	1.01776e22			0.0242832
$898$	4.50745e23	+	3.76386e23i	1.06591	+	0.890066i
$899$		−	6.17570e23i		−	1.44747i
$900$	2.52528e22	+	1.39312e23i	0.0586636	+	0.323631i
$901$	1.45918e22			0.0335977
$902$	−5.26869e22	+	6.30959e22i	−0.120240	+	0.143995i
$903$		−	2.20250e23i		−	0.498212i
$904$	−8.53183e22	+	1.50257e23i	−0.191291	+	0.336890i
$905$	−2.45500e22			−0.0545585
$906$	3.31967e23	+	2.77202e23i	0.731255	+	0.610619i
$907$		−	7.45124e22i		−	0.162693i	−0.996686	−	0.0813467i	$-0.974078\pi$
$907$		−	7.45124e22i		−	0.162693i	0.996686	−	0.0813467i	$-0.0259221\pi$
$908$	8.07197e23	−	1.46318e23i	1.74700	−	0.316674i
$909$	−1.01178e23			−0.217059
$910$	−1.65840e22	+	1.98604e22i	−0.0352662	+	0.0422335i
$911$			6.10002e23i			1.28583i	0.765936	+	0.642916i	$0.222276\pi$
$911$			6.10002e23i			1.28583i	−0.765936	+	0.642916i	$0.777724\pi$
$912$	−1.79521e23	+	6.72936e22i	−0.375108	+	0.140610i
$913$	1.34703e22			0.0279005
$914$	2.85199e23	+	2.38149e23i	0.585569	+	0.488967i
$915$			2.42000e21i			0.00492546i
$916$	−1.43962e23	−	7.94198e23i	−0.290459	−	1.60238i
$917$	2.74550e23			0.549119
$918$	2.32503e22	−	2.78437e22i	0.0460986	−	0.0552060i
$919$			2.84863e23i			0.559901i	0.960014	+	0.279951i	$0.0903181\pi$
$919$			2.84863e23i			0.559901i	−0.960014	+	0.279951i	$0.909682\pi$
$920$	2.54875e21	+	1.44722e21i	0.00496620	+	0.00281989i
$921$	4.56119e23			0.881051
$922$	5.31888e23	+	4.44142e23i	1.01853	+	0.850499i
$923$		−	6.12738e23i		−	1.16322i
$924$	2.18504e22	−	3.96077e21i	0.0411230	−	0.00745424i
$925$	−9.55997e23			−1.78370
$926$	−4.54993e23	+	5.44883e23i	−0.841621	+	1.00789i
$927$			4.62748e22i			0.0848607i
$928$	6.70600e23	+	2.35029e23i	1.21921	+	0.427304i
$929$	−2.66657e23			−0.480649			−0.240324	−	0.970693i	$-0.577254\pi$
$929$	−2.66657e23			−0.480649			−0.240324	+	0.970693i	$0.577254\pi$
$930$	3.20262e22	+	2.67428e22i	0.0572325	+	0.0477908i
$931$		−	2.67802e23i		−	0.474478i
$932$	1.60637e22	+	8.86190e22i	0.0282175	+	0.155668i
$933$	1.92031e23			0.334439
$934$	2.71263e23	−	3.24854e23i	0.468398	−	0.560937i
$935$		−	3.23929e21i		−	0.00554570i
$936$	−8.23141e22	+	1.44966e23i	−0.139723	+	0.246071i
$937$	−6.92827e23			−1.16603			−0.583013	−	0.812463i	$-0.698126\pi$
$937$	−6.92827e23			−1.16603			−0.583013	+	0.812463i	$0.698126\pi$
$938$	2.24051e23	+	1.87089e23i	0.373872	+	0.312194i
$939$			1.63111e22i			0.0269872i
$940$	9.57132e22	−	1.73497e22i	0.157018	−	0.0284622i
$941$	5.28516e23			0.859689			0.429845	−	0.902903i	$-0.358568\pi$
$941$	5.28516e23			0.859689			0.429845	+	0.902903i	$0.358568\pi$
$942$	−4.18057e23	+	5.00650e23i	−0.674261	+	0.807471i
$943$			4.51454e22i			0.0721971i
$944$	−2.92367e23	−	7.79954e23i	−0.463609	−	1.23678i
$945$	−7.93305e21			−0.0124734
$946$	−9.72688e22	−	8.12223e22i	−0.151651	−	0.126633i
$947$		−	6.74753e23i		−	1.04315i	−0.853207	−	0.521573i	$-0.825345\pi$
$947$		−	6.74753e23i		−	1.04315i	0.853207	−	0.521573i	$-0.174655\pi$
$948$	6.65725e22	+	3.67262e23i	0.102054	+	0.563001i
$949$	−1.18101e23			−0.179524
$950$	−2.91120e23	+	3.48635e23i	−0.438817	+	0.525511i
$951$			3.78248e23i			0.565369i
$952$	−1.23286e23	−	7.00040e22i	−0.182734	−	0.103759i
$953$	−7.56472e23			−1.11186			−0.555929	−	0.831229i	$-0.687638\pi$
$953$	−7.56472e23			−1.11186			−0.555929	+	0.831229i	$0.687638\pi$
$954$	−1.57818e22	−	1.31782e22i	−0.0230022	−	0.0192075i
$955$		−	2.62692e22i		−	0.0379682i
$956$	6.18185e23	−	1.12057e23i	0.886043	−	0.160611i
$957$	6.75581e22			0.0960245
$958$	−1.53396e23	+	1.83701e23i	−0.216217	+	0.258934i
$959$		−	5.18368e23i		−	0.724585i
$960$	−4.12274e22	+	2.45988e22i	−0.0571500	+	0.0340992i
$961$	−1.85701e23			−0.255286
$962$	−8.64016e23	−	7.21478e23i	−1.17793	−	0.983609i
$963$		−	2.03097e23i		−	0.274595i
$964$	−1.03375e23	−	5.70291e23i	−0.138612	−	0.764681i
$965$	−1.38185e23			−0.183756
$966$	7.81704e21	−	9.36140e21i	0.0103092	−	0.0123459i
$967$			1.04571e24i			1.36773i	0.729608	+	0.683866i	$0.239703\pi$
$967$			1.04571e24i			1.36773i	−0.729608	+	0.683866i	$0.760297\pi$
$968$	−3.74342e23	+	6.59267e23i	−0.485585	+	0.855181i
$969$	1.16370e23			0.149710
$970$	1.40891e22	+	1.17648e22i	0.0179766	+	0.0150110i
$971$		−	1.34646e23i		−	0.170388i	−0.996364	−	0.0851941i	$-0.972849\pi$
$971$		−	1.34646e23i		−	0.170388i	0.996364	−	0.0851941i	$-0.0271510\pi$
$972$	−5.02929e22	+	9.11645e21i	−0.0631214	+	0.0114418i
$973$	1.44570e22			0.0179960
$974$	−2.06483e22	+	2.47277e22i	−0.0254925	+	0.0305289i
$975$			3.94941e23i			0.483610i
$976$	5.70622e22	−	2.13898e22i	0.0693027	−	0.0259782i
$977$	1.14732e24			1.38207			0.691034	−	0.722822i	$-0.257156\pi$
$977$	1.14732e24			1.38207			0.691034	+	0.722822i	$0.257156\pi$
$978$	5.19074e23	+	4.33441e23i	0.620180	+	0.517869i
$979$		−	2.00715e23i		−	0.237858i
$980$	−1.19609e22	−	6.59849e22i	−0.0140590	−	0.0775597i
$981$	−3.17673e23			−0.370364
$982$	−2.21560e23	+	2.65332e23i	−0.256212	+	0.306830i
$983$		−	1.23621e23i		−	0.141796i	−0.997484	−	0.0708980i	$-0.977414\pi$
$983$		−	1.23621e23i		−	0.141796i	0.997484	−	0.0708980i	$-0.0225865\pi$
$984$	−6.43036e23	−	3.65126e23i	−0.731602	−	0.415415i
$985$	−5.19876e22			−0.0586692
$986$	−3.31071e23	−	2.76454e23i	−0.370600	−	0.309462i
$987$		−	4.04760e23i		−	0.449429i
$988$	−5.26220e23	+	9.53865e22i	−0.579578	+	0.105058i
$989$	−6.95963e22			−0.0760354
$990$	−2.92549e21	+	3.50346e21i	−0.00317042	+	0.00379678i
$991$			1.00814e24i			1.08376i	0.840456	+	0.541879i	$0.182287\pi$
$991$			1.00814e24i			1.08376i	−0.840456	+	0.541879i	$0.817713\pi$
$992$	3.47508e23	−	9.91533e23i	0.370571	−	1.05734i
$993$	1.47650e23			0.156185
$994$	−5.63600e23	−	4.70622e23i	−0.591398	−	0.493834i
$995$		−	6.22506e22i		−	0.0647976i
$996$	2.16132e22	+	1.19234e23i	0.0223174	+	0.123119i
$997$	9.03998e23			0.925990			0.462995	−	0.886361i	$-0.346775\pi$
$997$	9.03998e23			0.925990			0.462995	+	0.886361i	$0.346775\pi$
$998$	8.55060e23	−	1.02399e24i	0.868865	−	1.04052i
$999$		−	3.45123e23i		−	0.347896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.17.d.a.7.12	yes	16
3.2	odd	2		36.17.d.d.19.5		16
4.3	odd	2	inner	12.17.d.a.7.11	✓	16
12.11	even	2		36.17.d.d.19.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.17.d.a.7.11	✓	16	4.3	odd	2	inner
12.17.d.a.7.12	yes	16	1.1	even	1	trivial
36.17.d.d.19.5		16	3.2	odd	2
36.17.d.d.19.6		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)

\(f(q)\)	\(=\)	\(q+(196.501 + 164.084i) q^{2} +3788.00i q^{3} +(11689.0 + 64485.1i) q^{4} -45026.4 q^{5} +(-621548. + 744344. i) q^{6} +3.24149e6i q^{7} +(-8.28406e6 + 1.45894e7i) q^{8} -1.43489e7 q^{9} +O(q^{10})\)	\(q+(196.501 + 164.084i) q^{2} +3788.00i q^{3} +(11689.0 + 64485.1i) q^{4} -45026.4 q^{5} +(-621548. + 744344. i) q^{6} +3.24149e6i q^{7} +(-8.28406e6 + 1.45894e7i) q^{8} -1.43489e7 q^{9} +(-8.84773e6 - 7.38811e6i) q^{10} +2.75960e7i q^{11} +(-2.44269e8 + 4.42780e7i) q^{12} -6.92488e8 q^{13} +(-5.31875e8 + 6.36954e8i) q^{14} -1.70560e8i q^{15} +(-4.02170e9 + 1.50754e9i) q^{16} +2.60696e9 q^{17} +(-2.81957e9 - 2.35442e9i) q^{18} -1.17841e10i q^{19} +(-5.26316e8 - 2.90354e9i) q^{20} -1.22787e10 q^{21} +(-4.52806e9 + 5.42264e9i) q^{22} +3.87992e9i q^{23} +(-5.52644e10 - 3.13800e10i) q^{24} -1.50561e11 q^{25} +(-1.36074e11 - 1.13626e11i) q^{26} -5.43536e10i q^{27} +(-2.09028e11 + 3.78899e10i) q^{28} -6.46281e11 q^{29} +(2.79861e10 - 3.35151e10i) q^{30} +9.55575e11i q^{31} +(-1.03763e12 - 3.63663e11i) q^{32} -1.04534e11 q^{33} +(5.12270e11 + 4.27761e11i) q^{34} -1.45953e11i q^{35} +(-1.67725e11 - 9.25291e11i) q^{36} +6.34959e12 q^{37} +(1.93358e12 - 2.31558e12i) q^{38} -2.62314e12i q^{39} +(3.73002e11 - 6.56907e11i) q^{40} +1.16356e13 q^{41} +(-2.41278e12 - 2.01474e12i) q^{42} +1.79375e13i q^{43} +(-1.77953e12 + 3.22571e11i) q^{44} +6.46080e11 q^{45} +(-6.36633e11 + 7.62408e11i) q^{46} +3.29643e13i q^{47} +(-5.71055e12 - 1.52342e13i) q^{48} +2.27257e13 q^{49} +(-2.95852e13 - 2.47045e13i) q^{50} +9.87517e12i q^{51} +(-8.09452e12 - 4.46552e13i) q^{52} +5.59722e12 q^{53} +(8.91854e12 - 1.06805e13i) q^{54} -1.24255e12i q^{55} +(-4.72912e13 - 2.68527e13i) q^{56} +4.46381e13 q^{57} +(-1.26995e14 - 1.06044e14i) q^{58} +1.93936e14i q^{59} +(1.09986e13 - 1.99368e12i) q^{60} -1.41886e13 q^{61} +(-1.56794e14 + 1.87771e14i) q^{62} -4.65118e13i q^{63} +(-1.44224e14 - 2.41718e14i) q^{64} +3.11803e13 q^{65} +(-2.05409e13 - 1.71523e13i) q^{66} -3.51753e14i q^{67} +(3.04729e13 + 1.68110e14i) q^{68} -1.46971e13 q^{69} +(2.39484e13 - 2.86798e13i) q^{70} +8.84835e14i q^{71} +(1.18867e14 - 2.09341e14i) q^{72} +1.70546e14 q^{73} +(1.24770e15 + 1.04186e15i) q^{74} -5.70322e14i q^{75} +(7.59898e14 - 1.37745e14i) q^{76} -8.94522e13 q^{77} +(4.30415e14 - 5.15449e14i) q^{78} -1.50351e15i q^{79} +(1.81083e14 - 6.78791e13i) q^{80} +2.05891e14 q^{81} +(2.28641e15 + 1.90922e15i) q^{82} -4.88125e14i q^{83} +(-1.43527e14 - 7.91796e14i) q^{84} -1.17382e14 q^{85} +(-2.94326e15 + 3.52474e15i) q^{86} -2.44811e15i q^{87} +(-4.02609e14 - 2.28607e14i) q^{88} -7.27333e15 q^{89} +(1.26955e14 + 1.06011e14i) q^{90} -2.24469e15i q^{91} +(-2.50197e14 + 4.53526e13i) q^{92} -3.61972e15 q^{93} +(-5.40891e15 + 6.47752e15i) q^{94} +5.30595e14i q^{95} +(1.37755e15 - 3.93054e15i) q^{96} -1.59239e15 q^{97} +(4.46562e15 + 3.72892e15i) q^{98} -3.95973e14i 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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