LMFDB - Embedded newform 12.17.d.a.7.13

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			7.13
Root			$-39.4461 + 68.3227i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.17.d.a.7.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(197.709 - 162.626i) q^{2} +3788.00i q^{3} +(12641.5 - 64305.2i) q^{4} +551815. q^{5} +(616027. + 748920. i) q^{6} +6.23463e6i q^{7} +(-7.95836e6 - 1.47695e7i) q^{8} -1.43489e7 q^{9} +O(q^{10})$	\(q+(197.709 - 162.626i) q^{2} +3788.00i q^{3} +(12641.5 - 64305.2i) q^{4} +551815. q^{5} +(616027. + 748920. i) q^{6} +6.23463e6i q^{7} +(-7.95836e6 - 1.47695e7i) q^{8} -1.43489e7 q^{9} +(1.09099e8 - 8.97395e7i) q^{10} +1.63591e8i q^{11} +(2.43588e8 + 4.78860e7i) q^{12} +6.83367e8 q^{13} +(1.01391e9 + 1.23264e9i) q^{14} +2.09027e9i q^{15} +(-3.97535e9 - 1.62583e9i) q^{16} +1.25977e10 q^{17} +(-2.83690e9 + 2.33351e9i) q^{18} -1.86745e10i q^{19} +(6.97577e9 - 3.54846e10i) q^{20} -2.36168e10 q^{21} +(2.66042e10 + 3.23434e10i) q^{22} +6.04622e10i q^{23} +(5.59470e10 - 3.01462e10i) q^{24} +1.51912e11 q^{25} +(1.35108e11 - 1.11133e11i) q^{26} -5.43536e10i q^{27} +(4.00919e11 + 7.88152e10i) q^{28} +5.51573e11 q^{29} +(3.39933e11 + 4.13265e11i) q^{30} -8.13840e11i q^{31} +(-1.05036e12 + 3.25055e11i) q^{32} -6.19683e11 q^{33} +(2.49067e12 - 2.04871e12i) q^{34} +3.44036e12i q^{35} +(-1.81392e11 + 9.22709e11i) q^{36} -3.30548e12 q^{37} +(-3.03697e12 - 3.69212e12i) q^{38} +2.58859e12i q^{39} +(-4.39154e12 - 8.15005e12i) q^{40} -1.01047e13 q^{41} +(-4.66924e12 + 3.84070e12i) q^{42} +8.88181e12i q^{43} +(1.05198e13 + 2.06804e12i) q^{44} -7.91794e12 q^{45} +(9.83274e12 + 1.19539e13i) q^{46} +4.48521e12i q^{47} +(6.15864e12 - 1.50586e13i) q^{48} -5.63771e12 q^{49} +(3.00342e13 - 2.47048e13i) q^{50} +4.77199e13i q^{51} +(8.63880e12 - 4.39441e13i) q^{52} -1.01910e14 q^{53} +(-8.83931e12 - 1.07462e13i) q^{54} +9.02720e13i q^{55} +(9.20827e13 - 4.96175e13i) q^{56} +7.07391e13 q^{57} +(1.09051e14 - 8.97001e13i) q^{58} -5.21747e13i q^{59} +(1.34415e14 + 2.64242e13i) q^{60} -3.28715e13 q^{61} +(-1.32352e14 - 1.60903e14i) q^{62} -8.94602e13i q^{63} +(-1.54804e14 + 2.35083e14i) q^{64} +3.77092e14 q^{65} +(-1.22517e14 + 1.00777e14i) q^{66} +7.59999e14i q^{67} +(1.59254e14 - 8.10095e14i) q^{68} -2.29031e14 q^{69} +(5.59493e14 + 6.80190e14i) q^{70} -7.87689e14i q^{71} +(1.14194e14 + 2.11927e14i) q^{72} -7.67875e14 q^{73} +(-6.53522e14 + 5.37557e14i) q^{74} +5.75440e14i q^{75} +(-1.20087e15 - 2.36075e14i) q^{76} -1.01993e15 q^{77} +(4.20972e14 + 5.11787e14i) q^{78} -2.52615e15i q^{79} +(-2.19366e15 - 8.97157e14i) q^{80} +2.05891e14 q^{81} +(-1.99780e15 + 1.64329e15i) q^{82} -2.72997e15i q^{83} +(-2.98552e14 + 1.51868e15i) q^{84} +6.95157e15 q^{85} +(1.44441e15 + 1.75601e15i) q^{86} +2.08936e15i q^{87} +(2.41617e15 - 1.30192e15i) q^{88} +5.91959e14 q^{89} +(-1.56545e15 + 1.28766e15i) q^{90} +4.26054e15i q^{91} +(3.88804e15 + 7.64335e14i) q^{92} +3.08282e15 q^{93} +(7.29412e14 + 8.86766e14i) q^{94} -1.03049e16i q^{95} +(-1.23131e15 - 3.97877e15i) q^{96} +6.86719e14 q^{97} +(-1.11463e15 + 9.16839e14i) q^{98} -2.34735e15i 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 $

$2$	197.709	−	162.626i	0.772300	−	0.635258i
$2$	197.709	−	162.626i	0.772300	−	0.635258i
$3$			3788.00i			0.577350i
$3$			3788.00i			0.577350i
$4$	12641.5	−	64305.2i	0.192894	−	0.981220i
$5$	551815.			1.41265			0.706323	−	0.707890i	$-0.250353\pi$
$5$	551815.			1.41265			0.706323	+	0.707890i	$0.250353\pi$
$6$	616027.	+	748920.i	0.366766	+	0.445888i
$7$			6.23463e6i			1.08150i	0.841183	+	0.540750i	$0.181860\pi$
$7$			6.23463e6i			1.08150i	−0.841183	+	0.540750i	$0.818140\pi$
$8$	−7.95836e6	−	1.47695e7i	−0.474355	−	0.880333i
$9$	−1.43489e7			−0.333333
$10$	1.09099e8	−	8.97395e7i	1.09099	−	0.897395i
$11$			1.63591e8i			0.763165i	0.924335	+	0.381582i	$0.124621\pi$
$11$			1.63591e8i			0.763165i	−0.924335	+	0.381582i	$0.875379\pi$
$12$	2.43588e8	+	4.78860e7i	0.566507	+	0.111368i
$13$	6.83367e8			0.837736			0.418868	−	0.908047i	$-0.362427\pi$
$13$	6.83367e8			0.837736			0.418868	+	0.908047i	$0.362427\pi$
$14$	1.01391e9	+	1.23264e9i	0.687032	+	0.835242i
$15$			2.09027e9i			0.815591i
$16$	−3.97535e9	−	1.62583e9i	−0.925584	−	0.378543i
$17$	1.25977e10			1.80592			0.902960	−	0.429724i	$-0.141389\pi$
$17$	1.25977e10			1.80592			0.902960	+	0.429724i	$0.141389\pi$
$18$	−2.83690e9	+	2.33351e9i	−0.257433	+	0.211753i
$19$		−	1.86745e10i		−	1.09957i	−0.835308	−	0.549783i	$-0.814710\pi$
$19$		−	1.86745e10i		−	1.09957i	0.835308	−	0.549783i	$-0.185290\pi$
$20$	6.97577e9	−	3.54846e10i	0.272491	−	1.38612i
$21$	−2.36168e10			−0.624404
$22$	2.66042e10	+	3.23434e10i	0.484807	+	0.589392i
$23$			6.04622e10i			0.772079i	0.922482	+	0.386039i	$0.126157\pi$
$23$			6.04622e10i			0.772079i	−0.922482	+	0.386039i	$0.873843\pi$
$24$	5.59470e10	−	3.01462e10i	0.508261	−	0.273869i
$25$	1.51912e11			0.995567
$26$	1.35108e11	−	1.11133e11i	0.646984	−	0.532179i
$27$		−	5.43536e10i		−	0.192450i
$28$	4.00919e11	+	7.88152e10i	1.06119	+	0.208615i
$29$	5.51573e11			1.10260			0.551301	−	0.834306i	$-0.314132\pi$
$29$	5.51573e11			1.10260			0.551301	+	0.834306i	$0.314132\pi$
$30$	3.39933e11	+	4.13265e11i	0.518111	+	0.629881i
$31$		−	8.13840e11i		−	0.954213i	−0.878845	−	0.477106i	$-0.841686\pi$
$31$		−	8.13840e11i		−	0.954213i	0.878845	−	0.477106i	$-0.158314\pi$
$32$	−1.05036e12	+	3.25055e11i	−0.955301	+	0.295636i
$33$	−6.19683e11			−0.440613
$34$	2.49067e12	−	2.04871e12i	1.39471	−	1.14723i
$35$			3.44036e12i			1.52778i
$36$	−1.81392e11	+	9.22709e11i	−0.0642981	+	0.327073i
$37$	−3.30548e12			−0.941066			−0.470533	−	0.882382i	$-0.655938\pi$
$37$	−3.30548e12			−0.941066			−0.470533	+	0.882382i	$0.655938\pi$
$38$	−3.03697e12	−	3.69212e12i	−0.698508	−	0.849195i
$39$			2.58859e12i			0.483667i
$40$	−4.39154e12	−	8.15005e12i	−0.670096	−	1.24360i
$41$	−1.01047e13			−1.26548			−0.632739	−	0.774365i	$-0.718069\pi$
$41$	−1.01047e13			−1.26548			−0.632739	+	0.774365i	$0.718069\pi$
$42$	−4.66924e12	+	3.84070e12i	−0.482227	+	0.396658i
$43$			8.88181e12i			0.759896i	0.925008	+	0.379948i	$0.124058\pi$
$43$			8.88181e12i			0.759896i	−0.925008	+	0.379948i	$0.875942\pi$
$44$	1.05198e13	+	2.06804e12i	0.748832	+	0.147210i
$45$	−7.91794e12			−0.470882
$46$	9.83274e12	+	1.19539e13i	0.490469	+	0.596276i
$47$			4.48521e12i			0.188365i	0.995555	+	0.0941825i	$0.0300237\pi$
$47$			4.48521e12i			0.188365i	−0.995555	+	0.0941825i	$0.969976\pi$
$48$	6.15864e12	−	1.50586e13i	0.218552	−	0.534386i
$49$	−5.63771e12			−0.169642
$50$	3.00342e13	−	2.47048e13i	0.768876	−	0.632442i
$51$			4.77199e13i			1.04265i
$52$	8.63880e12	−	4.39441e13i	0.161594	−	0.822003i
$53$	−1.01910e14			−1.63686			−0.818430	−	0.574607i	$-0.805155\pi$
$53$	−1.01910e14			−1.63686			−0.818430	+	0.574607i	$0.805155\pi$
$54$	−8.83931e12	−	1.07462e13i	−0.122255	−	0.148629i
$55$			9.02720e13i			1.07808i
$56$	9.20827e13	−	4.96175e13i	0.952081	−	0.513015i
$57$	7.07391e13			0.634835
$58$	1.09051e14	−	8.97001e13i	0.851540	−	0.700437i
$59$		−	5.21747e13i		−	0.355340i	−0.984090	−	0.177670i	$-0.943144\pi$
$59$		−	5.21747e13i		−	0.355340i	0.984090	−	0.177670i	$-0.0568559\pi$
$60$	1.34415e14	+	2.64242e13i	0.800274	+	0.157323i
$61$	−3.28715e13			−0.171467			−0.0857336	−	0.996318i	$-0.527323\pi$
$61$	−3.28715e13			−0.171467			−0.0857336	+	0.996318i	$0.527323\pi$
$62$	−1.32352e14	−	1.60903e14i	−0.606172	−	0.736939i
$63$		−	8.94602e13i		−	0.360500i
$64$	−1.54804e14	+	2.35083e14i	−0.549974	+	0.835182i
$65$	3.77092e14			1.18342
$66$	−1.22517e14	+	1.00777e14i	−0.340286	+	0.279903i
$67$			7.59999e14i			1.87161i	0.352522	+	0.935804i	$0.385324\pi$
$67$			7.59999e14i			1.87161i	−0.352522	+	0.935804i	$0.614676\pi$
$68$	1.59254e14	−	8.10095e14i	0.348352	−	1.77200i
$69$	−2.29031e14			−0.445760
$70$	5.59493e14	+	6.80190e14i	0.970532	+	1.17990i
$71$		−	7.87689e14i		−	1.21980i	−0.792479	−	0.609899i	$-0.791210\pi$
$71$		−	7.87689e14i		−	1.21980i	0.792479	−	0.609899i	$-0.208790\pi$
$72$	1.14194e14	+	2.11927e14i	0.158118	+	0.293444i
$73$	−7.67875e14			−0.952155			−0.476078	−	0.879403i	$-0.657942\pi$
$73$	−7.67875e14			−0.952155			−0.476078	+	0.879403i	$0.657942\pi$
$74$	−6.53522e14	+	5.37557e14i	−0.726786	+	0.597820i
$75$			5.75440e14i			0.574791i
$76$	−1.20087e15	−	2.36075e14i	−1.07892	−	0.212100i
$77$	−1.01993e15			−0.825363
$78$	4.20972e14	+	5.11787e14i	0.307254	+	0.373536i
$79$		−	2.52615e15i		−	1.66511i	−0.553942	−	0.832555i	$-0.686877\pi$
$79$		−	2.52615e15i		−	1.66511i	0.553942	−	0.832555i	$-0.313123\pi$
$80$	−2.19366e15	−	8.97157e14i	−1.30752	−	0.534747i
$81$	2.05891e14			0.111111
$82$	−1.99780e15	+	1.64329e15i	−0.977328	+	0.803905i
$83$		−	2.72997e15i		−	1.21209i	−0.795432	−	0.606043i	$-0.792756\pi$
$83$		−	2.72997e15i		−	1.21209i	0.795432	−	0.606043i	$-0.207244\pi$
$84$	−2.98552e14	+	1.51868e15i	−0.120444	+	0.612678i
$85$	6.95157e15			2.55113
$86$	1.44441e15	+	1.75601e15i	0.482730	+	0.586867i
$87$			2.08936e15i			0.636588i
$88$	2.41617e15	−	1.30192e15i	0.671840	−	0.362011i
$89$	5.91959e14			0.150374			0.0751868	−	0.997169i	$-0.476045\pi$
$89$	5.91959e14			0.150374			0.0751868	+	0.997169i	$0.476045\pi$
$90$	−1.56545e15	+	1.28766e15i	−0.363662	+	0.299132i
$91$			4.26054e15i			0.906012i
$92$	3.88804e15	+	7.64335e14i	0.757579	+	0.148930i
$93$	3.08282e15			0.550915
$94$	7.29412e14	+	8.86766e14i	0.119660	+	0.145474i
$95$		−	1.03049e16i		−	1.55330i
$96$	−1.23131e15	−	3.97877e15i	−0.170685	−	0.551543i
$97$	6.86719e14			0.0876204			0.0438102	−	0.999040i	$-0.486050\pi$
$97$	6.86719e14			0.0876204			0.0438102	+	0.999040i	$0.486050\pi$
$98$	−1.11463e15	+	9.16839e14i	−0.131015	+	0.107767i
$99$		−	2.34735e15i		−	0.254388i
$100$	1.92039e15	−	9.76870e15i	0.192039	−	0.976870i
$101$	2.65050e15			0.244769			0.122385	−	0.992483i	$-0.460946\pi$
$101$	2.65050e15			0.244769			0.122385	+	0.992483i	$0.460946\pi$
$102$	7.76050e15	+	9.43464e15i	0.662351	+	0.805237i
$103$			1.92342e15i			0.151837i	0.997114	+	0.0759183i	$0.0241888\pi$
$103$			1.92342e15i			0.151837i	−0.997114	+	0.0759183i	$0.975811\pi$
$104$	−5.43848e15	−	1.00930e16i	−0.397385	−	0.737487i
$105$	−1.30321e16			−0.882062
$106$	−2.01486e16	+	1.65733e16i	−1.26415	+	1.03983i
$107$			1.63384e16i			0.950911i	0.879740	+	0.475455i	$0.157717\pi$
$107$			1.63384e16i			0.950911i	−0.879740	+	0.475455i	$0.842283\pi$
$108$	−3.49522e15	−	6.87112e14i	−0.188836	−	0.0371225i
$109$	−1.75593e16			−0.881240			−0.440620	−	0.897694i	$-0.645241\pi$
$109$	−1.75593e16			−0.881240			−0.440620	+	0.897694i	$0.645241\pi$
$110$	1.46806e16	+	1.78476e16i	0.684860	+	0.832602i
$111$		−	1.25211e16i		−	0.543325i
$112$	1.01365e16	−	2.47849e16i	0.409395	−	1.00102i
$113$	−2.89699e16			−1.08973			−0.544865	−	0.838524i	$-0.683419\pi$
$113$	−2.89699e16			−1.08973			−0.544865	+	0.838524i	$0.683419\pi$
$114$	1.39857e16	−	1.15040e16i	0.490283	−	0.403284i
$115$			3.33640e16i			1.09067i
$116$	6.97272e15	−	3.54690e16i	0.212686	−	1.08189i
$117$	−9.80557e15			−0.279245
$118$	−8.48496e15	−	1.03154e16i	−0.225732	−	0.274429i
$119$			7.85418e16i			1.95310i
$120$	3.08724e16	−	1.66351e16i	0.717992	−	0.386880i
$121$	1.91877e16			0.417579
$122$	−6.49899e15	+	5.34576e15i	−0.132424	+	0.108926i
$123$		−	3.82767e16i		−	0.730624i
$124$	−5.23341e16	−	1.02882e16i	−0.936292	−	0.184062i
$125$	−3.73240e14			−0.00626193
$126$	−1.45486e16	−	1.76871e16i	−0.229011	−	0.278414i
$127$			4.30379e16i			0.635948i	0.948099	+	0.317974i	$0.103002\pi$
$127$			4.30379e16i			0.635948i	−0.948099	+	0.317974i	$0.896998\pi$
$128$	7.62452e15	+	7.16531e16i	0.105811	+	0.994386i
$129$	−3.36443e16			−0.438726
$130$	7.45544e16	−	6.13250e16i	0.913958	−	0.751780i
$131$		−	1.23411e17i		−	1.42293i	−0.702724	−	0.711463i	$-0.748033\pi$
$131$		−	1.23411e17i		−	1.42293i	0.702724	−	0.711463i	$-0.251967\pi$
$132$	−7.83373e15	+	3.98488e16i	−0.0849918	+	0.432339i
$133$	1.16429e17			1.18918
$134$	1.23596e17	+	1.50259e17i	1.18895	+	1.44544i
$135$		−	2.99931e16i		−	0.271864i
$136$	−1.00257e17	−	1.86062e17i	−0.856648	−	1.58981i
$137$	−4.89372e16			−0.394343			−0.197172	−	0.980369i	$-0.563176\pi$
$137$	−4.89372e16			−0.394343			−0.197172	+	0.980369i	$0.563176\pi$
$138$	−4.52814e16	+	3.72464e16i	−0.344260	+	0.283173i
$139$		−	6.75988e16i		−	0.485088i	−0.970140	−	0.242544i	$-0.922018\pi$
$139$		−	6.75988e16i		−	0.485088i	0.970140	−	0.242544i	$-0.0779819\pi$
$140$	2.21233e17	+	4.34914e16i	1.49908	+	0.294699i
$141$	−1.69900e16			−0.108753
$142$	−1.28099e17	−	1.55733e17i	−0.774886	−	0.942049i
$143$			1.11793e17i			0.639331i
$144$	5.70419e16	+	2.33289e16i	0.308528	+	0.126181i
$145$	3.04366e17			1.55759
$146$	−1.51816e17	+	1.24877e17i	−0.735350	+	0.604864i
$147$		−	2.13556e16i		−	0.0979431i
$148$	−4.17862e16	+	2.12559e17i	−0.181526	+	0.923393i
$149$	1.11090e16			0.0457283			0.0228642	−	0.999739i	$-0.492721\pi$
$149$	1.11090e16			0.0457283			0.0228642	+	0.999739i	$0.492721\pi$
$150$	9.35816e16	+	1.13770e17i	0.365141	+	0.443911i
$151$		−	3.30474e16i		−	0.122271i	−0.998129	−	0.0611353i	$-0.980528\pi$
$151$		−	3.30474e16i		−	0.122271i	0.998129	−	0.0611353i	$-0.0194721\pi$
$152$	−2.75815e17	+	1.48619e17i	−0.967985	+	0.521585i
$153$	−1.80763e17			−0.601973
$154$	−2.01649e17	+	1.65867e17i	−0.637428	+	0.524318i
$155$		−	4.49089e17i		−	1.34796i
$156$	1.66460e17	+	3.27237e16i	0.474584	+	0.0932966i
$157$	3.42374e17			0.927477			0.463739	−	0.885972i	$-0.346508\pi$
$157$	3.42374e17			0.927477			0.463739	+	0.885972i	$0.346508\pi$
$158$	−4.10819e17	−	4.99443e17i	−1.05778	−	1.28596i
$159$		−	3.86036e17i		−	0.945041i
$160$	−5.79606e17	+	1.79370e17i	−1.34950	+	0.417628i
$161$	−3.76960e17			−0.835003
$162$	4.07065e16	−	3.34833e16i	0.0858111	−	0.0705842i
$163$			7.98548e17i			1.60251i	0.598325	+	0.801254i	$0.295833\pi$
$163$			7.98548e17i			1.60251i	−0.598325	+	0.801254i	$0.704167\pi$
$164$	−1.27739e17	+	6.49787e17i	−0.244103	+	1.24171i
$165$	−3.41950e17			−0.622431
$166$	−4.43965e17	−	5.39739e17i	−0.769988	−	0.936094i
$167$		−	4.20960e17i		−	0.695839i	−0.937524	−	0.347919i	$-0.886888\pi$
$167$		−	4.20960e17i		−	0.695839i	0.937524	−	0.347919i	$-0.113112\pi$
$168$	1.87951e17	+	3.48809e17i	0.296190	+	0.549684i
$169$	−1.98426e17			−0.298198
$170$	1.37439e18	−	1.13051e18i	1.97023	−	1.62062i
$171$			2.67959e17i			0.366522i
$172$	5.71147e17	+	1.12280e17i	0.745625	+	0.146580i
$173$	5.79494e17			0.722237			0.361119	−	0.932520i	$-0.382395\pi$
$173$	5.79494e17			0.722237			0.361119	+	0.932520i	$0.382395\pi$
$174$	3.39784e17	+	4.13084e17i	0.404397	+	0.491637i
$175$			9.47112e17i			1.07671i
$176$	2.65972e17	−	6.50332e17i	0.288891	−	0.706373i
$177$	1.97637e17			0.205155
$178$	1.17035e17	−	9.62680e16i	0.116134	−	0.0955260i
$179$		−	8.54530e17i		−	0.810780i	−0.914144	−	0.405390i	$-0.867136\pi$
$179$		−	8.54530e17i		−	0.810780i	0.914144	−	0.405390i	$-0.132864\pi$
$180$	−1.00095e17	+	5.09165e17i	−0.0908304	+	0.462038i
$181$	6.71619e17			0.583035			0.291518	−	0.956565i	$-0.405840\pi$
$181$	6.71619e17			0.583035			0.291518	+	0.956565i	$0.405840\pi$
$182$	6.92875e17	+	8.42347e17i	0.575551	+	0.699713i
$183$		−	1.24517e17i		−	0.0989966i
$184$	8.93000e17	−	4.81181e17i	0.679687	−	0.366240i
$185$	−1.82401e18			−1.32939
$186$	6.09501e17	−	5.01347e17i	0.425472	−	0.349973i
$187$			2.06087e18i			1.37822i
$188$	2.88422e17	+	5.66999e16i	0.184827	+	0.0363345i
$189$	3.38875e17			0.208135
$190$	−1.67584e18	−	2.03737e18i	−0.986744	−	1.19961i
$191$		−	6.78420e17i		−	0.383029i	−0.981490	−	0.191514i	$-0.938660\pi$
$191$		−	6.78420e17i		−	0.383029i	0.981490	−	0.191514i	$-0.0613399\pi$
$192$	−8.90493e17	−	5.86396e17i	−0.482193	−	0.317528i
$193$	2.71256e18			1.40903			0.704517	−	0.709687i	$-0.251164\pi$
$193$	2.71256e18			1.40903			0.704517	+	0.709687i	$0.251164\pi$
$194$	1.35770e17	−	1.11678e17i	0.0676692	−	0.0556615i
$195$			1.42842e18i			0.683250i
$196$	−7.12693e16	+	3.62534e17i	−0.0327230	+	0.166456i
$197$	−3.08272e18			−1.35895			−0.679476	−	0.733698i	$-0.737793\pi$
$197$	−3.08272e18			−1.35895			−0.679476	+	0.733698i	$0.737793\pi$
$198$	−3.81741e17	−	4.64093e17i	−0.161602	−	0.196464i
$199$		−	4.82688e17i		−	0.196264i	−0.995173	−	0.0981322i	$-0.968713\pi$
$199$		−	4.82688e17i		−	0.196264i	0.995173	−	0.0981322i	$-0.0312868\pi$
$200$	−1.20897e18	−	2.24366e18i	−0.472253	−	0.876431i
$201$	−2.87887e18			−1.08057
$202$	5.24028e17	−	4.31041e17i	0.189035	−	0.155492i
$203$			3.43885e18i			1.19246i
$204$	3.06864e18	+	6.03252e17i	1.02307	+	0.201121i
$205$	−5.57594e18			−1.78767
$206$	3.12798e17	+	3.80277e17i	0.0964554	+	0.117263i
$207$		−	8.67567e17i		−	0.257360i
$208$	−2.71662e18	−	1.11104e18i	−0.775395	−	0.317119i
$209$	3.05499e18			0.839150
$210$	−2.57656e18	+	2.11935e18i	−0.681216	+	0.560337i
$211$		−	7.12214e18i		−	1.81280i	−0.422415	−	0.906402i	$-0.638818\pi$
$211$		−	7.12214e18i		−	1.81280i	0.422415	−	0.906402i	$-0.361182\pi$
$212$	−1.28830e18	+	6.55337e18i	−0.315741	+	1.60612i
$213$	2.98376e18			0.704250
$214$	2.65705e18	+	3.23025e18i	0.604074	+	0.734388i
$215$			4.90112e18i			1.07346i
$216$	−8.02778e17	+	4.32566e17i	−0.169420	+	0.0912898i
$217$	5.07399e18			1.03198
$218$	−3.47162e18	+	2.85559e18i	−0.680582	+	0.559815i
$219$		−	2.90871e18i		−	0.549727i
$220$	5.80496e18	+	1.14118e18i	1.05783	+	0.207956i
$221$	8.60883e18			1.51288
$222$	−2.03626e18	−	2.47554e18i	−0.345152	−	0.419610i
$223$		−	2.96522e18i		−	0.484861i	−0.970169	−	0.242431i	$-0.922055\pi$
$223$		−	2.96522e18i		−	0.484861i	0.970169	−	0.242431i	$-0.0779447\pi$
$224$	−2.02660e18	−	6.54864e18i	−0.319730	−	1.03316i
$225$	−2.17976e18			−0.331856
$226$	−5.72760e18	+	4.71125e18i	−0.841598	+	0.692260i
$227$		−	9.80680e18i		−	1.39098i	−0.718536	−	0.695490i	$-0.755188\pi$
$227$		−	9.80680e18i		−	1.39098i	0.718536	−	0.695490i	$-0.244812\pi$
$228$	8.94250e17	−	4.54889e18i	0.122456	−	0.622912i
$229$	−1.24641e19			−1.64807			−0.824036	−	0.566537i	$-0.808283\pi$
$229$	−1.24641e19			−1.64807			−0.824036	+	0.566537i	$0.808283\pi$
$230$	5.42585e18	+	6.59635e18i	0.692859	+	0.842327i
$231$		−	3.86349e18i		−	0.476524i
$232$	−4.38962e18	−	8.14648e18i	−0.523025	−	0.970658i
$233$	7.98054e18			0.918724			0.459362	−	0.888249i	$-0.348078\pi$
$233$	7.98054e18			0.918724			0.459362	+	0.888249i	$0.348078\pi$
$234$	−1.93865e18	+	1.59464e18i	−0.215661	+	0.177393i
$235$			2.47501e18i			0.266093i
$236$	−3.35510e18	−	6.59567e17i	−0.348666	−	0.0685430i
$237$	9.56906e18			0.961352
$238$	1.27729e19	+	1.55284e19i	1.24072	+	1.50838i
$239$			1.32650e19i			1.24602i	0.782213	+	0.623011i	$0.214091\pi$
$239$			1.32650e19i			1.24602i	−0.782213	+	0.623011i	$0.785909\pi$
$240$	3.39843e18	−	8.30956e18i	0.308737	−	0.754898i
$241$	1.06974e19			0.940031			0.470015	−	0.882658i	$-0.344248\pi$
$241$	1.06974e19			0.940031			0.470015	+	0.882658i	$0.344248\pi$
$242$	3.79357e18	−	3.12041e18i	0.322496	−	0.265271i
$243$			7.79915e17i			0.0641500i
$244$	−4.15546e17	+	2.11381e18i	−0.0330750	+	0.168247i
$245$	−3.11097e18			−0.239645
$246$	−6.22479e18	−	7.56764e18i	−0.464135	−	0.564261i
$247$		−	1.27616e19i		−	0.921146i
$248$	−1.20200e19	+	6.47683e18i	−0.840026	+	0.452636i
$249$	1.03411e19			0.699798
$250$	−7.37929e16	+	6.06986e16i	−0.00483609	+	0.00397794i
$251$		−	1.26966e18i		−	0.0805933i	−0.999188	−	0.0402966i	$-0.987170\pi$
$251$		−	1.26966e18i		−	0.0805933i	0.999188	−	0.0402966i	$-0.0128303\pi$
$252$	−5.75275e18	−	1.13091e18i	−0.353730	−	0.0695384i
$253$	−9.89109e18			−0.589223
$254$	6.99909e18	+	8.50898e18i	0.403991	+	0.491143i
$255$			2.63325e19i			1.47289i
$256$	1.31601e19	+	1.29265e19i	0.713410	+	0.700747i
$257$	−2.93272e19			−1.54101			−0.770505	−	0.637434i	$-0.779996\pi$
$257$	−2.93272e19			−1.54101			−0.770505	+	0.637434i	$0.779996\pi$
$258$	−6.65177e18	+	5.47144e18i	−0.338828	+	0.278704i
$259$		−	2.06084e19i		−	1.01776i
$260$	4.76702e18	−	2.42490e19i	0.228276	−	1.16120i
$261$	−7.91447e18			−0.367534
$262$	−2.00698e19	−	2.43994e19i	−0.903925	−	1.09893i
$263$			7.63912e18i			0.333731i	0.985980	+	0.166866i	$0.0533646\pi$
$263$			7.63912e18i			0.333731i	−0.985980	+	0.166866i	$0.946635\pi$
$264$	4.93166e18	+	9.15243e18i	0.209007	+	0.387887i
$265$	−5.62356e19			−2.31230
$266$	2.30190e19	−	1.89344e19i	0.918404	−	0.755437i
$267$			2.24234e18i			0.0868182i
$268$	4.88719e19	+	9.60754e18i	1.83646	+	0.361022i
$269$	2.88691e19			1.05297			0.526484	−	0.850185i	$-0.323510\pi$
$269$	2.88691e19			1.05297			0.526484	+	0.850185i	$0.323510\pi$
$270$	−4.87766e18	−	5.92990e18i	−0.172704	−	0.209960i
$271$			4.69543e19i			1.61407i	0.590506	+	0.807033i	$0.298928\pi$
$271$			4.69543e19i			1.61407i	−0.590506	+	0.807033i	$0.701072\pi$
$272$	−5.00801e19	−	2.04817e19i	−1.67153	−	0.683619i
$273$	−1.61389e19			−0.523086
$274$	−9.67531e18	+	7.95846e18i	−0.304551	+	0.250510i
$275$			2.48514e19i			0.759782i
$276$	−2.89530e18	+	1.47279e19i	−0.0859845	+	0.437388i
$277$	−2.64632e19			−0.763493			−0.381746	−	0.924267i	$-0.624677\pi$
$277$	−2.64632e19			−0.763493			−0.381746	+	0.924267i	$0.624677\pi$
$278$	−1.09933e19	−	1.33649e19i	−0.308156	−	0.374634i
$279$			1.16777e19i			0.318071i
$280$	5.08126e19	−	2.73797e19i	1.34495	−	0.724709i
$281$	4.90965e18			0.126299			0.0631495	−	0.998004i	$-0.479885\pi$
$281$	4.90965e18			0.126299			0.0631495	+	0.998004i	$0.479885\pi$
$282$	−3.35906e18	+	2.76301e18i	−0.0839896	+	0.0690859i
$283$		−	2.08846e19i		−	0.507615i	−0.967255	−	0.253808i	$-0.918317\pi$
$283$		−	2.08846e19i		−	0.507615i	0.967255	−	0.253808i	$-0.0816830\pi$
$284$	−5.06525e19	−	9.95758e18i	−1.19689	−	0.235292i
$285$	3.90349e19			0.896796
$286$	1.81804e19	+	2.21024e19i	0.406140	+	0.493755i
$287$		−	6.29994e19i		−	1.36861i
$288$	1.50716e19	−	4.66418e18i	0.318434	−	0.0985452i
$289$	1.10040e20			2.26135
$290$	6.01758e19	−	4.94978e19i	1.20292	−	0.989469i
$291$			2.60129e18i			0.0505876i
$292$	−9.70711e18	+	4.93784e19i	−0.183665	+	0.934273i
$293$	2.60361e19			0.479330			0.239665	−	0.970856i	$-0.422962\pi$
$293$	2.60361e19			0.479330			0.239665	+	0.970856i	$0.422962\pi$
$294$	−3.47298e18	−	4.22220e18i	−0.0622191	−	0.0756414i
$295$		−	2.87908e19i		−	0.501969i
$296$	2.63062e19	+	4.88204e19i	0.446400	+	0.828452i
$297$	8.89177e18			0.146871
$298$	2.19635e18	−	1.80661e18i	0.0353160	−	0.0290493i
$299$			4.13179e19i			0.646798i
$300$	3.70038e19	+	7.27444e18i	0.563996	+	0.110874i
$301$	−5.53749e19			−0.821827
$302$	−5.37437e18	−	6.53377e18i	−0.0776734	−	0.0944296i
$303$			1.00401e19i			0.141318i
$304$	−3.03617e19	+	7.42379e19i	−0.416233	+	1.01774i
$305$	−1.81390e19			−0.242222
$306$	−3.57384e19	+	2.93967e19i	−0.464904	+	0.382409i
$307$			3.44548e17i			0.00436660i	0.999998	+	0.00218330i	$0.000694966\pi$
$307$			3.44548e17i			0.00436660i	−0.999998	+	0.00218330i	$0.999305\pi$
$308$	−1.28935e19	+	6.55869e19i	−0.159208	+	0.809862i
$309$	−7.28591e18			−0.0876629
$310$	−7.30335e19	−	8.87888e19i	−0.856305	−	1.04103i
$311$		−	9.70300e19i		−	1.10872i	−0.832276	−	0.554361i	$-0.812963\pi$
$311$		−	9.70300e19i		−	1.10872i	0.832276	−	0.554361i	$-0.187037\pi$
$312$	3.82323e19	−	2.06010e19i	0.425788	−	0.229430i
$313$	2.75499e19			0.299065			0.149532	−	0.988757i	$-0.452223\pi$
$313$	2.75499e19			0.299065			0.149532	+	0.988757i	$0.452223\pi$
$314$	6.76903e19	−	5.56789e19i	0.716291	−	0.589187i
$315$		−	4.93654e19i		−	0.509259i
$316$	−1.62445e20	−	3.19344e19i	−1.63384	−	0.321190i
$317$	−4.74309e19			−0.465144			−0.232572	−	0.972579i	$-0.574714\pi$
$317$	−4.74309e19			−0.465144			−0.232572	+	0.972579i	$0.574714\pi$
$318$	−6.27795e19	−	7.63227e19i	−0.600345	−	0.729855i
$319$			9.02324e19i			0.841467i
$320$	−8.54230e19	+	1.29722e20i	−0.776918	+	1.17982i
$321$	−6.18899e19			−0.549009
$322$	−7.45283e19	+	6.13035e19i	−0.644873	+	0.530443i
$323$		−	2.35256e20i		−	1.98573i
$324$	2.60278e18	−	1.32399e19i	0.0214327	−	0.109024i
$325$	1.03811e20			0.834023
$326$	1.29865e20	+	1.57880e20i	1.01801	+	1.23762i
$327$		−	6.65144e19i		−	0.508784i
$328$	8.04172e19	+	1.49242e20i	0.600286	+	1.11404i
$329$	−2.79636e19			−0.203717
$330$	−6.76065e19	+	5.56100e19i	−0.480703	+	0.395404i
$331$		−	3.49243e19i		−	0.242384i	−0.992629	−	0.121192i	$-0.961328\pi$
$331$		−	3.49243e19i		−	0.242384i	0.992629	−	0.121192i	$-0.0386716\pi$
$332$	−1.75551e20	−	3.45110e19i	−1.18932	−	0.233804i
$333$	4.74300e19			0.313689
$334$	−6.84590e19	−	8.32274e19i	−0.442037	−	0.537396i
$335$			4.19379e20i			2.64392i
$336$	9.38849e19	+	3.83969e19i	0.577938	+	0.236364i
$337$	−1.12357e19			−0.0675397			−0.0337698	−	0.999430i	$-0.510751\pi$
$337$	−1.12357e19			−0.0675397			−0.0337698	+	0.999430i	$0.510751\pi$
$338$	−3.92305e19	+	3.22692e19i	−0.230298	+	0.189433i
$339$		−	1.09738e20i		−	0.629156i
$340$	8.78785e19	−	4.47022e20i	0.492097	−	2.50321i
$341$	1.33137e20			0.728222
$342$	4.35772e19	+	5.29779e19i	0.232836	+	0.283065i
$343$			1.72046e20i			0.898032i
$344$	1.31180e20	−	7.06847e19i	0.668962	−	0.360461i
$345$	−1.26382e20			−0.629701
$346$	1.14571e20	−	9.42408e19i	0.557784	−	0.458807i
$347$			2.27278e20i			1.08124i	0.841267	+	0.540620i	$0.181810\pi$
$347$			2.27278e20i			1.08124i	−0.841267	+	0.540620i	$0.818190\pi$
$348$	1.34356e20	+	2.64126e19i	0.624632	+	0.122794i
$349$	2.14999e20			0.976860			0.488430	−	0.872603i	$-0.337570\pi$
$349$	2.14999e20			0.976860			0.488430	+	0.872603i	$0.337570\pi$
$350$	1.54025e20	+	1.87252e20i	0.683986	+	0.831540i
$351$		−	3.71435e19i		−	0.161222i
$352$	−5.31761e19	−	1.71830e20i	−0.225619	−	0.729052i
$353$	−1.25150e20			−0.519080			−0.259540	−	0.965732i	$-0.583571\pi$
$353$	−1.25150e20			−0.519080			−0.259540	+	0.965732i	$0.583571\pi$
$354$	3.90747e19	−	3.21410e19i	0.158442	−	0.130327i
$355$		−	4.34658e20i		−	1.72314i
$356$	7.48326e18	−	3.80660e19i	0.0290062	−	0.147550i
$357$	−2.97516e20			−1.12762
$358$	−1.38969e20	−	1.68948e20i	−0.515054	−	0.626165i
$359$			8.80836e19i			0.319256i	0.987177	+	0.159628i	$0.0510295\pi$
$359$			8.80836e19i			0.319256i	−0.987177	+	0.159628i	$0.948970\pi$
$360$	6.30138e19	+	1.16944e20i	0.223365	+	0.414533i
$361$	−6.02974e19			−0.209045
$362$	1.32785e20	−	1.09223e20i	0.450278	−	0.370378i
$363$			7.26827e19i			0.241090i
$364$	2.73975e20	+	5.38597e19i	0.888996	+	0.174764i
$365$	−4.23725e20			−1.34506
$366$	−2.02497e19	−	2.46181e19i	−0.0628884	−	0.0764551i
$367$			4.92892e20i			1.49770i	0.662742	+	0.748848i	$0.269393\pi$
$367$			4.92892e20i			1.49770i	−0.662742	+	0.748848i	$0.730607\pi$
$368$	9.83014e19	−	2.40359e20i	0.292265	−	0.714623i
$369$	1.44992e20			0.421826
$370$	−3.60623e20	+	2.96632e20i	−1.02669	+	0.844508i
$371$		−	6.35374e20i		−	1.77026i
$372$	3.89715e19	−	1.98241e20i	0.106268	−	0.540569i
$373$	4.36182e20			1.16412			0.582059	−	0.813146i	$-0.302247\pi$
$373$	4.36182e20			1.16412			0.582059	+	0.813146i	$0.302247\pi$
$374$	3.35151e20	+	4.07451e20i	0.875522	+	1.06440i
$375$		−	1.41383e18i		−	0.00361533i
$376$	6.62445e19	−	3.56949e19i	0.165824	−	0.0893519i
$377$	3.76927e20			0.923690
$378$	6.69985e19	−	5.51099e19i	0.160742	−	0.132219i
$379$			4.57941e20i			1.07571i	0.843037	+	0.537855i	$0.180765\pi$
$379$			4.57941e20i			1.07571i	−0.843037	+	0.537855i	$0.819235\pi$
$380$	−6.62658e20	−	1.30269e20i	−1.52413	−	0.299622i
$381$	−1.63027e20			−0.367165
$382$	−1.10329e20	−	1.34130e20i	−0.243322	−	0.295813i
$383$			5.68585e20i			1.22802i	0.789299	+	0.614009i	$0.210444\pi$
$383$			5.68585e20i			1.22802i	−0.789299	+	0.614009i	$0.789556\pi$
$384$	−2.71422e20	+	2.88816e19i	−0.574109	+	0.0610903i
$385$	−5.62813e20			−1.16595
$386$	5.36297e20	−	4.41133e20i	1.08820	−	0.895100i
$387$		−	1.27444e20i		−	0.253299i
$388$	8.68117e18	−	4.41596e19i	0.0169015	−	0.0859748i
$389$	−5.68850e20			−1.08493			−0.542464	−	0.840079i	$-0.682509\pi$
$389$	−5.68850e20			−1.08493			−0.542464	+	0.840079i	$0.682509\pi$
$390$	2.32299e20	+	2.82412e20i	0.434040	+	0.527674i
$391$			7.61683e20i			1.39431i
$392$	4.48670e19	+	8.32665e19i	0.0804708	+	0.149342i
$393$	4.67479e20			0.821526
$394$	−6.09481e20	+	5.01330e20i	−1.04952	+	0.863285i
$395$		−	1.39397e21i		−	2.35221i
$396$	−1.50947e20	−	2.96741e19i	−0.249611	−	0.0490700i
$397$	−6.05280e19			−0.0980917			−0.0490458	−	0.998797i	$-0.515618\pi$
$397$	−6.05280e19			−0.0980917			−0.0490458	+	0.998797i	$0.515618\pi$
$398$	−7.84976e19	−	9.54316e19i	−0.124679	−	0.151575i
$399$			4.41032e20i			0.686574i
$400$	−6.03902e20	−	2.46982e20i	−0.921481	−	0.376865i
$401$	−6.39650e19			−0.0956725			−0.0478362	−	0.998855i	$-0.515233\pi$
$401$	−6.39650e19			−0.0956725			−0.0478362	+	0.998855i	$0.515233\pi$
$402$	−5.69179e20	+	4.68180e20i	−0.834526	+	0.686443i
$403$		−	5.56151e20i		−	0.799379i
$404$	3.35064e19	−	1.70441e20i	0.0472146	−	0.240173i
$405$	1.13614e20			0.156961
$406$	5.59247e20	+	6.79892e20i	0.757523	+	0.920940i
$407$		−	5.40747e20i		−	0.718189i
$408$	7.04801e20	−	3.79772e20i	0.917878	−	0.494586i
$409$	6.60017e20			0.842885			0.421443	−	0.906855i	$-0.361524\pi$
$409$	6.60017e20			0.842885			0.421443	+	0.906855i	$0.361524\pi$
$410$	−1.10241e21	+	9.06794e20i	−1.38062	+	1.13563i
$411$		−	1.85374e20i		−	0.227674i
$412$	1.23686e20	+	2.43149e19i	0.148985	+	0.0292884i
$413$	3.25290e20			0.384300
$414$	−1.41089e20	−	1.71526e20i	−0.163490	−	0.198759i
$415$		−	1.50644e21i		−	1.71225i
$416$	−7.17784e20	+	2.22132e20i	−0.800290	+	0.247665i
$417$	2.56064e20			0.280066
$418$	6.03999e20	−	4.96821e20i	0.648076	−	0.533077i
$419$			5.48782e18i			0.00577681i	0.999996	+	0.00288840i	$0.000919408\pi$
$419$			5.48782e18i			0.00577681i	−0.999996	+	0.00288840i	$0.999081\pi$
$420$	−1.64745e20	+	8.38030e20i	−0.170145	+	0.865496i
$421$	−1.66749e20			−0.168969			−0.0844845	−	0.996425i	$-0.526924\pi$
$421$	−1.66749e20			−0.168969			−0.0844845	+	0.996425i	$0.526924\pi$
$422$	−1.15825e21	−	1.40811e21i	−1.15160	−	1.40003i
$423$		−	6.43579e19i		−	0.0627883i
$424$	8.11040e20	+	1.50517e21i	0.776453	+	1.44098i
$425$	1.91373e21			1.79792
$426$	5.89916e20	−	4.85237e20i	0.543892	−	0.447381i
$427$		−	2.04942e20i		−	0.185442i
$428$	1.05065e21	+	2.06542e20i	0.933052	+	0.183425i
$429$	−4.23471e20			−0.369118
$430$	7.97049e20	+	9.68994e20i	0.681926	+	0.829036i
$431$			1.62505e21i			1.36473i	0.731010	+	0.682367i	$0.239049\pi$
$431$			1.62505e21i			1.36473i	−0.731010	+	0.682367i	$0.760951\pi$
$432$	−8.83697e19	+	2.16075e20i	−0.0728507	+	0.178129i
$433$	−7.82966e20			−0.633636			−0.316818	−	0.948486i	$-0.602614\pi$
$433$	−7.82966e20			−0.633636			−0.316818	+	0.948486i	$0.602614\pi$
$434$	1.00317e21	−	8.25163e20i	0.796999	−	0.655575i
$435$			1.15294e21i			0.899273i
$436$	−2.21976e20	+	1.12915e21i	−0.169986	+	0.864690i
$437$	1.12911e21			0.848951
$438$	−4.73032e20	−	5.75077e20i	−0.349219	−	0.424554i
$439$		−	7.42795e20i		−	0.538459i	−0.963076	−	0.269229i	$-0.913231\pi$
$439$		−	7.42795e20i		−	0.538459i	0.963076	−	0.269229i	$-0.0867690\pi$
$440$	1.33328e21	−	7.18418e20i	0.949071	−	0.511394i
$441$	8.08950e19			0.0565475
$442$	1.70204e21	−	1.40002e21i	1.16840	−	0.961072i
$443$			5.04300e19i			0.0339985i	0.999856	+	0.0169992i	$0.00541129\pi$
$443$			5.04300e19i			0.0339985i	−0.999856	+	0.0169992i	$0.994589\pi$
$444$	−8.05174e20	−	1.58286e20i	−0.533121	−	0.104804i
$445$	3.26652e20			0.212425
$446$	−4.82222e20	−	5.86249e20i	−0.308012	−	0.374458i
$447$			4.20809e19i			0.0264013i
$448$	−1.46566e21	−	9.65145e20i	−0.903249	−	0.594797i
$449$	−2.07764e21			−1.25777			−0.628883	−	0.777500i	$-0.716488\pi$
$449$	−2.07764e21			−1.25777			−0.628883	+	0.777500i	$0.716488\pi$
$450$	−4.30958e20	+	3.54486e20i	−0.256292	+	0.210814i
$451$		−	1.65305e21i		−	0.965768i
$452$	−3.66223e20	+	1.86291e21i	−0.210203	+	1.06926i
$453$	1.25183e20			0.0705930
$454$	−1.59484e21	−	1.93889e21i	−0.883631	−	1.07425i
$455$			2.35103e21i			1.27987i
$456$	−5.62968e20	−	1.04478e21i	−0.301137	−	0.558866i
$457$	−2.00990e21			−1.05644			−0.528220	−	0.849107i	$-0.677141\pi$
$457$	−2.00990e21			−1.05644			−0.528220	+	0.849107i	$0.677141\pi$
$458$	−2.46426e21	+	2.02698e21i	−1.27281	+	1.04695i
$459$		−	6.84728e20i		−	0.347550i
$460$	2.14548e21	+	4.21771e20i	1.07019	+	0.210385i
$461$	−8.59545e20			−0.421367			−0.210684	−	0.977554i	$-0.567569\pi$
$461$	−8.59545e20			−0.421367			−0.210684	+	0.977554i	$0.567569\pi$
$462$	−6.28305e20	−	7.63847e20i	−0.302715	−	0.368019i
$463$			2.49841e21i			1.18308i	0.806274	+	0.591542i	$0.201481\pi$
$463$			2.49841e21i			1.18308i	−0.806274	+	0.591542i	$0.798519\pi$
$464$	−2.19270e21	−	8.96764e20i	−1.02055	−	0.417383i
$465$	1.70115e21			0.778248
$466$	1.57782e21	−	1.29784e21i	0.709530	−	0.583627i
$467$			1.08871e21i			0.481257i	0.970617	+	0.240629i	$0.0773536\pi$
$467$			1.08871e21i			0.481257i	−0.970617	+	0.240629i	$0.922646\pi$
$468$	−1.23957e20	+	6.30549e20i	−0.0538648	+	0.274001i
$469$	−4.73832e21			−2.02414
$470$	4.02500e20	+	4.89330e20i	0.169038	+	0.205504i
$471$			1.29691e21i			0.535479i
$472$	−7.70596e20	+	4.15225e20i	−0.312817	+	0.168557i
$473$	−1.45299e21			−0.579926
$474$	1.89189e21	−	1.55618e21i	0.742452	−	0.610707i
$475$		−	2.83688e21i		−	1.09469i
$476$	5.05065e21	+	9.92888e20i	1.91642	+	0.376742i
$477$	1.46230e21			0.545620
$478$	2.15724e21	+	2.62262e21i	0.791545	+	0.962302i
$479$			1.80717e21i			0.652099i	0.945353	+	0.326050i	$0.105718\pi$
$479$			1.80717e21i			0.652099i	−0.945353	+	0.326050i	$0.894282\pi$
$480$	−6.79453e20	−	2.19555e21i	−0.241118	−	0.779135i
$481$	−2.25885e21			−0.788365
$482$	2.11497e21	−	1.73968e21i	0.725985	−	0.597162i
$483$		−	1.42792e21i		−	0.482089i
$484$	2.42561e20	−	1.23387e21i	0.0805486	−	0.409737i
$485$	3.78941e20			0.123777
$486$	1.26834e20	+	1.54196e20i	0.0407518	+	0.0495431i
$487$			5.78185e21i			1.82740i	0.406384	+	0.913702i	$0.366790\pi$
$487$			5.78185e21i			1.82740i	−0.406384	+	0.913702i	$0.633210\pi$
$488$	2.61603e20	+	4.85497e20i	0.0813364	+	0.150948i
$489$	−3.02490e21			−0.925208
$490$	−6.15067e20	+	5.05925e20i	−0.185077	+	0.152236i
$491$		−	2.76420e21i		−	0.818309i	−0.912465	−	0.409155i	$-0.865824\pi$
$491$		−	2.76420e21i		−	0.818309i	0.912465	−	0.409155i	$-0.134176\pi$
$492$	−2.46139e21	−	4.83876e20i	−0.716902	−	0.140933i
$493$	6.94853e21			1.99121
$494$	−2.07536e21	−	2.52307e21i	−0.585166	−	0.711401i
$495$		−	1.29530e21i		−	0.359360i
$496$	−1.32317e21	+	3.23530e21i	−0.361211	+	0.883204i
$497$	4.91095e21			1.31921
$498$	2.04453e21	−	1.68174e21i	0.540454	−	0.444553i
$499$		−	3.77339e21i		−	0.981582i	−0.871277	−	0.490791i	$-0.836708\pi$
$499$		−	3.77339e21i		−	0.981582i	0.871277	−	0.490791i	$-0.163292\pi$
$500$	−4.71832e18	+	2.40013e19i	−0.00120789	+	0.00614433i
$501$	1.59459e21			0.401743
$502$	−2.06480e20	−	2.51024e20i	−0.0511975	−	0.0622422i
$503$			1.46692e21i			0.357984i	0.983851	+	0.178992i	$0.0572836\pi$
$503$			1.46692e21i			0.357984i	−0.983851	+	0.178992i	$0.942716\pi$
$504$	−1.32129e21	+	7.11957e20i	−0.317360	+	0.171005i
$505$	1.46259e21			0.345772
$506$	−1.95556e21	+	1.60855e21i	−0.455057	+	0.374309i
$507$		−	7.51636e20i		−	0.172165i
$508$	2.76756e21	+	5.44065e20i	0.624005	+	0.122671i
$509$	4.21015e21			0.934449			0.467225	−	0.884139i	$-0.345254\pi$
$509$	4.21015e21			0.934449			0.467225	+	0.884139i	$0.345254\pi$
$510$	4.28236e21	+	5.20617e21i	0.935667	+	1.13751i
$511$		−	4.78742e21i		−	1.02976i
$512$	4.70405e21	+	4.15508e20i	0.996122	+	0.0879871i
$513$	−1.01503e21			−0.211612
$514$	−5.79824e21	+	4.76937e21i	−1.19012	+	0.978939i
$515$			1.06137e21i			0.214491i
$516$	−4.25315e20	+	2.16350e21i	−0.0846277	+	0.430487i
$517$	−7.33741e20			−0.143754
$518$	−3.35147e21	−	4.07447e21i	−0.646543	−	0.786019i
$519$			2.19512e21i			0.416984i
$520$	−3.00104e21	−	5.56948e21i	−0.561364	−	1.04181i
$521$	3.74984e20			0.0690733			0.0345367	−	0.999403i	$-0.489004\pi$
$521$	3.74984e20			0.0690733			0.0345367	+	0.999403i	$0.489004\pi$
$522$	−1.56476e21	+	1.28710e21i	−0.283847	+	0.233479i
$523$		−	4.16131e21i		−	0.743389i	−0.928355	−	0.371695i	$-0.878777\pi$
$523$		−	4.16131e21i		−	0.743389i	0.928355	−	0.371695i	$-0.121223\pi$
$524$	−7.93595e21	−	1.56010e21i	−1.39620	−	0.274474i
$525$	−3.58766e21			−0.621637
$526$	1.24232e21	+	1.51032e21i	0.212006	+	0.257741i
$527$		−	1.02525e22i		−	1.72323i
$528$	2.46346e21	+	1.00750e21i	0.407825	+	0.166791i
$529$	2.47693e21			0.403894
$530$	−1.11183e22	+	9.14538e21i	−1.78579	+	1.46891i
$531$			7.48650e20i			0.118447i
$532$	1.47184e21	−	7.48699e21i	0.229386	−	1.16685i
$533$	−6.90525e21			−1.06014
$534$	3.64663e20	+	4.43330e20i	0.0551520	+	0.0670497i
$535$			9.01578e21i			1.34330i
$536$	1.12248e22	−	6.04835e21i	1.64764	−	0.887807i
$537$	3.23695e21			0.468104
$538$	5.70768e21	−	4.69487e21i	0.813207	−	0.668907i
$539$		−	9.22280e20i		−	0.129465i
$540$	−1.92871e21	−	3.79158e20i	−0.266758	−	0.0524410i
$541$	3.36486e21			0.458553			0.229276	−	0.973361i	$-0.426364\pi$
$541$	3.36486e21			0.458553			0.229276	+	0.973361i	$0.426364\pi$
$542$	7.63600e21	+	9.28328e21i	1.02535	+	1.24654i
$543$			2.54409e21i			0.336615i
$544$	−1.32321e22	+	4.09493e21i	−1.72520	+	0.533894i
$545$	−9.68946e21			−1.24488
$546$	−3.19081e21	+	2.62461e21i	−0.403979	+	0.332295i
$547$			8.64391e21i			1.07848i	0.842152	+	0.539240i	$0.181288\pi$
$547$			8.64391e21i			1.07848i	−0.842152	+	0.539240i	$0.818712\pi$
$548$	−6.18640e20	+	3.14691e21i	−0.0760665	+	0.386937i
$549$	4.71670e20			0.0571557
$550$	4.04148e21	+	4.91334e21i	0.482658	+	0.586780i
$551$		−	1.03004e22i		−	1.21238i
$552$	1.82271e21	+	3.38268e21i	0.211449	+	0.392417i
$553$	1.57496e22			1.80082
$554$	−5.23202e21	+	4.30361e21i	−0.589645	+	0.485015i
$555$		−	6.90934e21i		−	0.767526i
$556$	−4.34696e21	−	8.54552e20i	−0.475978	−	0.0935708i
$557$	−1.04692e21			−0.112999			−0.0564993	−	0.998403i	$-0.517994\pi$
$557$	−1.04692e21			−0.112999			−0.0564993	+	0.998403i	$0.517994\pi$
$558$	1.89910e21	+	2.30879e21i	0.202057	+	0.245646i
$559$			6.06954e21i			0.636592i
$560$	5.59345e21	−	1.36766e22i	0.578329	−	1.41408i
$561$	−7.80655e21			−0.795713
$562$	9.70681e20	−	7.98437e20i	0.0975407	−	0.0802325i
$563$		−	6.89681e21i		−	0.683252i	−0.939836	−	0.341626i	$-0.889022\pi$
$563$		−	6.89681e21i		−	0.683252i	0.939836	−	0.341626i	$-0.110978\pi$
$564$	−2.14779e20	+	1.09254e21i	−0.0209777	+	0.106710i
$565$	−1.59860e22			−1.53940
$566$	−3.39638e21	−	4.12907e21i	−0.322467	−	0.392031i
$567$			1.28366e21i			0.120167i
$568$	−1.16338e22	+	6.26871e21i	−1.07383	+	0.578618i
$569$	−1.48391e22			−1.35055			−0.675274	−	0.737567i	$-0.735975\pi$
$569$	−1.48391e22			−1.35055			−0.675274	+	0.737567i	$0.735975\pi$
$570$	7.71754e21	−	6.34809e21i	0.692596	−	0.569697i
$571$			1.05454e22i			0.933200i	0.884468	+	0.466600i	$0.154521\pi$
$571$			1.05454e22i			0.933200i	−0.884468	+	0.466600i	$0.845479\pi$
$572$	7.18886e21	+	1.41323e21i	0.627324	+	0.123323i
$573$	2.56985e21			0.221142
$574$	−1.02453e22	−	1.24555e22i	−0.869423	−	1.05698i
$575$			9.18491e21i			0.768656i
$576$	2.22127e21	−	3.37318e21i	0.183325	−	0.278394i
$577$	2.10843e22			1.71614			0.858071	−	0.513531i	$-0.171663\pi$
$577$	2.10843e22			1.71614			0.858071	+	0.513531i	$0.171663\pi$
$578$	2.17559e22	−	1.78954e22i	1.74644	−	1.43654i
$579$			1.02752e22i			0.813506i
$580$	3.84765e21	−	1.95723e22i	0.300449	−	1.52833i
$581$	1.70204e22			1.31087
$582$	4.23037e20	+	5.14297e20i	0.0321362	+	0.0390688i
$583$		−	1.66716e22i		−	1.24919i
$584$	6.11103e21	+	1.13412e22i	0.451660	+	0.838214i
$585$	−5.41086e21			−0.394475
$586$	5.14756e21	−	4.23415e21i	0.370187	−	0.304498i
$587$			1.40292e22i			0.995238i	0.867396	+	0.497619i	$0.165792\pi$
$587$			1.40292e22i			0.995238i	−0.867396	+	0.497619i	$0.834208\pi$
$588$	−1.37328e21	−	2.69968e20i	−0.0961037	−	0.0188927i
$589$	−1.51981e22			−1.04922
$590$	−4.68213e21	−	5.69218e21i	−0.318880	−	0.387671i
$591$		−	1.16773e22i		−	0.784591i
$592$	1.31404e22	+	5.37415e21i	0.871036	+	0.356234i
$593$	1.04825e21			0.0685532			0.0342766	−	0.999412i	$-0.489087\pi$
$593$	1.04825e21			0.0685532			0.0342766	+	0.999412i	$0.489087\pi$
$594$	1.75798e21	−	1.44603e21i	0.113429	−	0.0933011i
$595$			4.33405e22i			2.75904i
$596$	1.40435e20	−	7.14367e20i	0.00882073	−	0.0448695i
$597$	1.82842e21			0.113313
$598$	6.71937e21	+	8.16891e21i	0.410884	+	0.499522i
$599$			6.24002e21i			0.376506i	0.982121	+	0.188253i	$0.0602824\pi$
$599$			6.24002e21i			0.376506i	−0.982121	+	0.188253i	$0.939718\pi$
$600$	8.49899e21	−	4.57956e21i	0.506008	−	0.272655i
$601$	−3.51451e21			−0.206476			−0.103238	−	0.994657i	$-0.532920\pi$
$601$	−3.51451e21			−0.206476			−0.103238	+	0.994657i	$0.532920\pi$
$602$	−1.09481e22	+	9.00540e21i	−0.634697	+	0.522073i
$603$		−	1.09052e22i		−	0.623869i
$604$	−2.12512e21	−	4.17770e20i	−0.119974	−	0.0235853i
$605$	1.05880e22			0.589891
$606$	1.63278e21	+	1.98501e21i	0.0897732	+	0.109140i
$607$		−	2.32708e22i		−	1.26270i	−0.775497	−	0.631351i	$-0.782501\pi$
$607$		−	2.32708e22i		−	1.26270i	0.775497	−	0.631351i	$-0.217499\pi$
$608$	6.07025e21	+	1.96151e22i	0.325071	+	1.05042i
$609$	−1.30264e22			−0.688470
$610$	−3.58624e21	+	2.94987e21i	−0.187068	+	0.153874i
$611$			3.06505e21i			0.157800i
$612$	−2.28511e21	+	1.16240e22i	−0.116117	+	0.590668i
$613$	1.11962e22			0.561546			0.280773	−	0.959774i	$-0.409409\pi$
$613$	1.11962e22			0.561546			0.280773	+	0.959774i	$0.409409\pi$
$614$	5.60325e19	+	6.81202e19i	0.00277392	+	0.00337232i
$615$		−	2.11217e22i		−	1.03211i
$616$	8.11698e21	+	1.50639e22i	0.391515	+	0.726595i
$617$	2.41293e21			0.114885			0.0574425	−	0.998349i	$-0.481705\pi$
$617$	2.41293e21			0.114885			0.0574425	+	0.998349i	$0.481705\pi$
$618$	−1.44049e21	+	1.18488e21i	−0.0677020	+	0.0556886i
$619$		−	3.13705e22i		−	1.45544i	−0.685872	−	0.727722i	$-0.740579\pi$
$619$		−	3.13705e22i		−	1.45544i	0.685872	−	0.727722i	$-0.259421\pi$
$620$	−2.88787e22	−	5.67716e21i	−1.32265	−	0.260015i
$621$	3.28634e21			0.148587
$622$	−1.57796e22	−	1.91837e22i	−0.704325	−	0.856266i
$623$			3.69065e21i			0.162629i
$624$	4.20861e21	−	1.02906e22i	0.183089	−	0.447674i
$625$	−2.33858e22			−1.00441
$626$	5.44686e21	−	4.48033e21i	0.230968	−	0.189983i
$627$			1.15723e22i			0.484484i
$628$	4.32812e21	−	2.20164e22i	0.178905	−	0.910059i
$629$	−4.16413e22			−1.69949
$630$	−8.02811e21	−	9.75998e21i	−0.323511	−	0.393300i
$631$			1.54292e22i			0.613915i	0.951723	+	0.306958i	$0.0993110\pi$
$631$			1.54292e22i			0.613915i	−0.951723	+	0.306958i	$0.900689\pi$
$632$	−3.73101e22	+	2.01041e22i	−1.46585	+	0.789854i
$633$	2.69786e22			1.04662
$634$	−9.37751e21	+	7.71351e21i	−0.359231	+	0.295487i
$635$			2.37490e22i			0.898369i
$636$	−2.48241e22	−	4.88008e21i	−0.927293	−	0.182293i
$637$	−3.85263e21			−0.142116
$638$	1.46741e22	+	1.78397e22i	0.534549	+	0.649865i
$639$			1.13025e22i			0.406599i
$640$	4.20732e21	+	3.95392e22i	0.149474	+	1.40472i
$641$	1.58461e22			0.555977			0.277989	−	0.960584i	$-0.410332\pi$
$641$	1.58461e22			0.555977			0.277989	+	0.960584i	$0.410332\pi$
$642$	−1.22362e22	+	1.00649e22i	−0.423999	+	0.348762i
$643$		−	3.72434e22i		−	1.27456i	−0.770631	−	0.637282i	$-0.780059\pi$
$643$		−	3.72434e22i		−	1.27456i	0.770631	−	0.637282i	$-0.219941\pi$
$644$	−4.76534e21	+	2.42405e22i	−0.161067	+	0.819321i
$645$	−1.85654e22			−0.619764
$646$	−3.82587e22	−	4.65121e22i	−1.26145	−	1.53358i
$647$		−	1.60328e22i		−	0.522127i	−0.965322	−	0.261063i	$-0.915927\pi$
$647$		−	1.60328e22i		−	0.522127i	0.965322	−	0.261063i	$-0.0840731\pi$
$648$	−1.63856e21	−	3.04092e21i	−0.0527062	−	0.0978148i
$649$	8.53532e21			0.271183
$650$	2.05244e22	−	1.68824e22i	0.644116	−	0.529820i
$651$			1.92203e22i			0.595815i
$652$	5.13508e22	+	1.00949e22i	1.57241	+	0.309115i
$653$	3.30026e22			0.998257			0.499129	−	0.866528i	$-0.333654\pi$
$653$	3.30026e22			0.998257			0.499129	+	0.866528i	$0.333654\pi$
$654$	−1.08170e22	−	1.31505e22i	−0.323209	−	0.392934i
$655$		−	6.80998e22i		−	2.01009i
$656$	4.01699e22	+	1.64286e22i	1.17131	+	0.479038i
$657$	1.10182e22			0.317385
$658$	−5.52866e21	+	4.54762e21i	−0.157330	+	0.129413i
$659$		−	3.23306e22i		−	0.908929i	−0.890765	−	0.454465i	$-0.849831\pi$
$659$		−	3.23306e22i		−	0.908929i	0.890765	−	0.454465i	$-0.150169\pi$
$660$	−4.32277e21	+	2.19892e22i	−0.120063	+	0.610741i
$661$	3.72035e22			1.02087			0.510437	−	0.859915i	$-0.329484\pi$
$661$	3.72035e22			1.02087			0.510437	+	0.859915i	$0.329484\pi$
$662$	−5.67960e21	−	6.90484e21i	−0.153976	−	0.187193i
$663$			3.26102e22i			0.873464i
$664$	−4.03204e22	+	2.17261e22i	−1.06704	+	0.574960i
$665$	6.42472e22			1.67989
$666$	9.37732e21	−	7.71335e21i	0.242262	−	0.199273i
$667$			3.33493e22i			0.851296i
$668$	−2.70699e22	−	5.32157e21i	−0.682771	−	0.134223i
$669$	1.12322e22			0.279935
$670$	6.82019e22	+	8.29148e22i	1.67957	+	2.04190i
$671$		−	5.37749e21i		−	0.130858i
$672$	2.48062e22	−	7.67674e21i	0.596494	−	0.184596i
$673$	−1.03547e22			−0.246045			−0.123023	−	0.992404i	$-0.539259\pi$
$673$	−1.03547e22			−0.246045			−0.123023	+	0.992404i	$0.539259\pi$
$674$	−2.22139e21	+	1.82721e21i	−0.0521609	+	0.0429051i
$675$		−	8.25694e21i		−	0.191597i
$676$	−2.50840e21	+	1.27598e22i	−0.0575207	+	0.292598i
$677$	−1.82181e22			−0.412850			−0.206425	−	0.978462i	$-0.566183\pi$
$677$	−1.82181e22			−0.412850			−0.206425	+	0.978462i	$0.566183\pi$
$678$	−1.78462e22	−	2.16961e22i	−0.399676	−	0.485897i
$679$			4.28144e21i			0.0947614i
$680$	−5.53232e22	−	1.02672e23i	−1.21014	−	2.24584i
$681$	3.71481e22			0.803082
$682$	2.63224e22	−	2.16515e22i	0.562406	−	0.462609i
$683$			2.95751e22i			0.624540i	0.949993	+	0.312270i	$0.101089\pi$
$683$			2.95751e22i			0.624540i	−0.949993	+	0.312270i	$0.898911\pi$
$684$	1.72312e22	+	3.38741e21i	0.359639	+	0.0707000i
$685$	−2.70042e22			−0.557067
$686$	2.79792e22	+	3.40150e22i	0.570482	+	0.693550i
$687$		−	4.72139e22i		−	0.951515i
$688$	1.44403e22	−	3.53083e22i	0.287653	−	0.703347i
$689$	−6.96422e22			−1.37126
$690$	−2.49869e22	+	2.05531e22i	−0.486318	+	0.400022i
$691$			2.05008e22i			0.394410i	0.980362	+	0.197205i	$0.0631864\pi$
$691$			2.05008e22i			0.394410i	−0.980362	+	0.197205i	$0.936814\pi$
$692$	7.32568e21	−	3.72645e22i	0.139315	−	0.708674i
$693$	1.46349e22			0.275121
$694$	3.69614e22	+	4.49349e22i	0.686866	+	0.835041i
$695$		−	3.73020e22i		−	0.685258i
$696$	3.08588e22	−	1.66278e22i	0.560409	−	0.301969i
$697$	−1.27296e23			−2.28535
$698$	4.25071e22	−	3.49644e22i	0.754429	−	0.620558i
$699$			3.02303e22i			0.530425i
$700$	6.09043e22	+	1.19729e22i	1.05649	+	0.207690i
$701$	1.12569e21			0.0193051			0.00965257	−	0.999953i	$-0.496927\pi$
$701$	1.12569e21			0.0193051			0.00965257	+	0.999953i	$0.496927\pi$
$702$	−6.04049e21	−	7.34359e21i	−0.102418	−	0.124512i
$703$			6.17283e22i			1.03476i
$704$	−3.84575e22	−	2.53245e22i	−0.637382	−	0.419721i
$705$	−9.37531e21			−0.153629
$706$	−2.47433e22	+	2.03527e22i	−0.400886	+	0.329750i
$707$			1.65249e22i			0.264718i
$708$	2.49844e21	−	1.27091e22i	0.0395733	−	0.201303i
$709$	−7.16353e22			−1.12191			−0.560954	−	0.827847i	$-0.689566\pi$
$709$	−7.16353e22			−1.12191			−0.560954	+	0.827847i	$0.689566\pi$
$710$	−7.06867e22	−	8.59357e22i	−1.09464	−	1.33078i
$711$			3.62476e22i			0.555037i
$712$	−4.71103e21	−	8.74296e21i	−0.0713305	−	0.132379i
$713$	4.92066e22			0.736728
$714$	−5.88215e22	+	4.83839e22i	−0.870864	+	0.716333i
$715$			6.16889e22i			0.903148i
$716$	−5.49507e22	−	1.08026e22i	−0.795553	−	0.156395i
$717$	−5.02479e22			−0.719391
$718$	1.43247e22	+	1.74149e22i	0.202810	+	0.246562i
$719$			2.08266e22i			0.291600i	0.989314	+	0.145800i	$0.0465756\pi$
$719$			2.08266e22i			0.291600i	−0.989314	+	0.145800i	$0.953424\pi$
$720$	3.14766e22	+	1.28732e22i	0.435841	+	0.178249i
$721$	−1.19918e22			−0.164211
$722$	−1.19213e22	+	9.80592e21i	−0.161446	+	0.132798i
$723$			4.05217e22i			0.542727i
$724$	8.49029e21	−	4.31886e22i	0.112464	−	0.572085i
$725$	8.37903e22			1.09771
$726$	1.18201e22	+	1.43700e22i	0.153154	+	0.186193i
$727$		−	1.53743e23i		−	1.97025i	−0.171845	−	0.985124i	$-0.554973\pi$
$727$		−	1.53743e23i		−	1.97025i	0.171845	−	0.985124i	$-0.445027\pi$
$728$	6.29263e22	−	3.39070e22i	0.797592	−	0.429772i
$729$	−2.95431e21			−0.0370370
$730$	−8.37741e22	+	6.89087e22i	−1.03879	+	0.854459i
$731$			1.11890e23i			1.37231i
$732$	−8.00710e21	−	1.57409e21i	−0.0971374	−	0.0190959i
$733$	1.19532e23			1.43434			0.717169	−	0.696899i	$-0.245438\pi$
$733$	1.19532e23			1.43434			0.717169	+	0.696899i	$0.245438\pi$
$734$	8.01571e22	+	9.74491e22i	0.951423	+	1.15667i
$735$		−	1.17844e22i		−	0.138359i
$736$	−1.96535e22	−	6.35074e22i	−0.228254	−	0.737567i
$737$	−1.24329e23			−1.42835
$738$	2.86662e22	−	2.35795e22i	0.325776	−	0.267968i
$739$			5.95815e22i			0.669816i	0.942251	+	0.334908i	$0.108705\pi$
$739$			5.95815e22i			0.669816i	−0.942251	+	0.334908i	$0.891295\pi$
$740$	−2.30583e22	+	1.17293e23i	−0.256432	+	1.30443i
$741$	4.83408e22			0.531824
$742$	−1.03328e23	−	1.25619e23i	−1.12457	−	1.36717i
$743$		−	1.37140e23i		−	1.47657i	−0.674489	−	0.738285i	$-0.735636\pi$
$743$		−	1.37140e23i		−	1.47657i	0.674489	−	0.738285i	$-0.264364\pi$
$744$	−2.45342e22	−	4.55319e22i	−0.261330	−	0.484989i
$745$	6.13011e21			0.0645979
$746$	8.62370e22	−	7.09346e22i	0.899049	−	0.739516i
$747$			3.91721e22i			0.404029i
$748$	1.32524e23	+	2.60525e22i	1.35233	+	0.265850i
$749$	−1.01864e23			−1.02841
$750$	−2.29926e20	−	2.79527e20i	−0.00229667	−	0.00279212i
$751$			4.89019e22i			0.483288i	0.970365	+	0.241644i	$0.0776867\pi$
$751$			4.89019e22i			0.483288i	−0.970365	+	0.241644i	$0.922313\pi$
$752$	7.29220e21	−	1.78303e22i	0.0713043	−	0.174348i
$753$	4.80948e21			0.0465306
$754$	7.45217e22	−	6.12981e22i	0.713366	−	0.586781i
$755$		−	1.82361e22i		−	0.172725i
$756$	4.28389e21	−	2.17914e22i	0.0401480	−	0.204226i
$757$	7.21475e22			0.669043			0.334522	−	0.942388i	$-0.391425\pi$
$757$	7.21475e22			0.669043			0.334522	+	0.942388i	$0.391425\pi$
$758$	7.44731e22	+	9.05389e22i	0.683354	+	0.830771i
$759$		−	3.74674e22i		−	0.340188i
$760$	−1.52199e23	+	8.20101e22i	−1.36742	+	0.736815i
$761$	−9.65706e22			−0.858554			−0.429277	−	0.903173i	$-0.641232\pi$
$761$	−9.65706e22			−0.858554			−0.429277	+	0.903173i	$0.641232\pi$
$762$	−3.22320e22	+	2.65125e22i	−0.283561	+	0.233244i
$763$		−	1.09476e23i		−	0.953061i
$764$	−4.36259e22	−	8.57625e21i	−0.375835	−	0.0738841i
$765$	−9.97475e22			−0.850375
$766$	9.24667e22	+	1.12414e23i	0.780109	+	0.948399i
$767$		−	3.56545e22i		−	0.297681i
$768$	−4.89655e22	+	4.98504e22i	−0.404576	+	0.411887i
$769$	1.56033e23			1.27587			0.637936	−	0.770090i	$-0.279789\pi$
$769$	1.56033e23			1.27587			0.637936	+	0.770090i	$0.279789\pi$
$770$	−1.11273e23	+	9.15280e22i	−0.900459	+	0.740676i
$771$		−	1.11091e23i		−	0.889703i
$772$	3.42909e22	−	1.74432e23i	0.271794	−	1.38257i
$773$	1.93964e23			1.52155			0.760773	−	0.649018i	$-0.224820\pi$
$773$	1.93964e23			1.52155			0.760773	+	0.649018i	$0.224820\pi$
$774$	−2.07258e22	−	2.51969e22i	−0.160910	−	0.195622i
$775$		−	1.23632e23i		−	0.949983i
$776$	−5.46516e21	−	1.01425e22i	−0.0415632	−	0.0771351i
$777$	7.80646e22			0.587606
$778$	−1.12467e23	+	9.25099e22i	−0.837890	+	0.689210i
$779$			1.88701e23i			1.39148i
$780$	9.18550e22	+	1.80574e22i	0.670419	+	0.131795i
$781$	1.28859e23			0.930907
$782$	1.23870e23	+	1.50591e23i	0.885748	+	1.07683i
$783$		−	2.99800e22i		−	0.212196i
$784$	2.24119e22	+	9.16597e21i	0.157018	+	0.0642170i
$785$	1.88927e23			1.31020
$786$	9.24247e22	−	7.60243e22i	0.634465	−	0.521881i
$787$			5.67798e22i			0.385830i	0.981215	+	0.192915i	$0.0617942\pi$
$787$			5.67798e22i			0.385830i	−0.981215	+	0.192915i	$0.938206\pi$
$788$	−3.89702e22	+	1.98235e23i	−0.262134	+	1.33343i
$789$	−2.89369e22			−0.192680
$790$	−2.26696e23	−	2.75600e23i	−1.49426	−	1.81661i
$791$		−	1.80616e23i		−	1.17854i
$792$	−3.46694e22	+	1.86811e22i	−0.223947	+	0.120670i
$793$	−2.24633e22			−0.143644
$794$	−1.19669e22	+	9.84343e21i	−0.0757562	+	0.0623135i
$795$		−	2.13020e23i		−	1.33501i
$796$	−3.10393e22	−	6.10190e21i	−0.192578	−	0.0378583i
$797$	−4.74366e22			−0.291371			−0.145686	−	0.989331i	$-0.546539\pi$
$797$	−4.74366e22			−0.291371			−0.145686	+	0.989331i	$0.546539\pi$
$798$	7.17234e22	+	8.71960e22i	0.436152	+	0.530241i
$799$			5.65032e22i			0.340172i
$800$	−1.59562e23	+	4.93796e22i	−0.951066	+	0.294325i
$801$	−8.49396e21			−0.0501245
$802$	−1.26464e22	+	1.04024e22i	−0.0738879	+	0.0607767i
$803$		−	1.25618e23i		−	0.726652i
$804$	−3.63933e22	+	1.85127e23i	−0.208436	+	1.06028i
$805$	−2.08012e23			−1.17956
$806$	−9.04447e22	−	1.09956e23i	−0.507812	−	0.617360i
$807$			1.09356e23i			0.607931i
$808$	−2.10937e22	−	3.91467e22i	−0.116108	−	0.215479i
$809$	2.00157e22			0.109089			0.0545447	−	0.998511i	$-0.482629\pi$
$809$	2.00157e22			0.109089			0.0545447	+	0.998511i	$0.482629\pi$
$810$	2.24624e22	−	1.84766e22i	0.121221	−	0.0997105i
$811$			1.69910e23i			0.907930i	0.891020	+	0.453965i	$0.149991\pi$
$811$			1.69910e23i			0.907930i	−0.891020	+	0.453965i	$0.850009\pi$
$812$	2.21136e23	+	4.34723e22i	1.17007	+	0.230020i
$813$	−1.77863e23			−0.931881
$814$	−8.79395e22	−	1.06910e23i	−0.456235	−	0.554657i
$815$			4.40650e23i			2.26378i
$816$	7.75845e22	−	1.89703e23i	0.394688	−	0.965058i
$817$	1.65864e23			0.835556
$818$	1.30491e23	−	1.07336e23i	0.650960	−	0.535450i
$819$		−	6.11341e22i		−	0.302004i
$820$	−7.04884e22	+	3.58562e23i	−0.344831	+	1.75410i
$821$	−1.99595e23			−0.966952			−0.483476	−	0.875358i	$-0.660626\pi$
$821$	−1.99595e23			−0.966952			−0.483476	+	0.875358i	$0.660626\pi$
$822$	−3.01466e22	−	3.66500e22i	−0.144632	−	0.175833i
$823$			3.29793e23i			1.56690i	0.621453	+	0.783452i	$0.286543\pi$
$823$			3.29793e23i			1.56690i	−0.621453	+	0.783452i	$0.713457\pi$
$824$	2.84080e22	−	1.53073e22i	0.133667	−	0.0720245i
$825$	−9.41369e22			−0.438660
$826$	6.43127e22	−	5.29006e22i	0.296795	−	0.244130i
$827$		−	1.72298e23i		−	0.787476i	−0.919223	−	0.393738i	$-0.871182\pi$
$827$		−	1.72298e23i		−	0.787476i	0.919223	−	0.393738i	$-0.128818\pi$
$828$	−5.57891e22	−	1.09674e22i	−0.252526	−	0.0496432i
$829$	−9.37768e22			−0.420397			−0.210198	−	0.977659i	$-0.567411\pi$
$829$	−9.37768e22			−0.420397			−0.210198	+	0.977659i	$0.567411\pi$
$830$	−2.44986e23	−	2.97836e23i	−1.08772	−	1.32237i
$831$		−	1.00243e23i		−	0.440803i
$832$	−1.05788e23	+	1.60648e23i	−0.460733	+	0.699662i
$833$	−7.10220e22			−0.306361
$834$	5.06261e22	−	4.16427e22i	0.216295	−	0.177914i
$835$		−	2.32292e23i		−	0.982974i
$836$	3.86197e22	−	1.96452e23i	0.161867	−	0.823391i
$837$	−4.42351e22			−0.183638
$838$	8.92463e20	+	1.08499e21i	0.00366976	+	0.00446143i
$839$		−	4.12735e22i		−	0.168103i	−0.996461	−	0.0840516i	$-0.973214\pi$
$839$		−	4.12735e22i		−	0.168103i	0.996461	−	0.0840516i	$-0.0267860\pi$
$840$	1.03714e23	+	1.92478e23i	0.418411	+	0.776509i
$841$	5.39861e22			0.215732
$842$	−3.29678e22	+	2.71178e22i	−0.130495	+	0.107339i
$843$			1.85977e22i			0.0729188i
$844$	−4.57991e23	−	9.00347e22i	−1.77876	−	0.349680i
$845$	−1.09494e23			−0.421248
$846$	−1.04663e22	−	1.27241e22i	−0.0398868	−	0.0484914i
$847$			1.19628e23i			0.451612i
$848$	4.05129e23	+	1.65689e23i	1.51505	+	0.619622i
$849$	7.91108e22			0.293072
$850$	3.78361e23	−	3.11222e23i	1.38853	−	1.14214i
$851$		−	1.99857e23i		−	0.726577i
$852$	3.77193e22	−	1.91871e23i	0.135846	−	0.691024i
$853$	−1.03555e23			−0.369469			−0.184734	−	0.982788i	$-0.559142\pi$
$853$	−1.03555e23			−0.369469			−0.184734	+	0.982788i	$0.559142\pi$
$854$	−3.33289e22	−	4.05188e22i	−0.117803	−	0.143217i
$855$			1.47864e23i			0.517766i
$856$	2.41311e23	−	1.30027e23i	0.837119	−	0.451070i
$857$	−5.04122e23			−1.73256			−0.866282	−	0.499556i	$-0.833497\pi$
$857$	−5.04122e23			−1.73256			−0.866282	+	0.499556i	$0.833497\pi$
$858$	−8.37239e22	+	6.88674e22i	−0.285070	+	0.234485i
$859$		−	2.52990e22i		−	0.0853410i	−0.999089	−	0.0426705i	$-0.986413\pi$
$859$		−	2.52990e22i		−	0.0853410i	0.999089	−	0.0426705i	$-0.0135866\pi$
$860$	3.15167e23	+	6.19575e22i	1.05330	+	0.207065i
$861$	2.38641e23			0.790170
$862$	2.64275e23	+	3.21286e23i	0.866959	+	1.05398i
$863$		−	2.02291e23i		−	0.657493i	−0.944418	−	0.328746i	$-0.893374\pi$
$863$		−	2.02291e23i		−	0.657493i	0.944418	−	0.328746i	$-0.106626\pi$
$864$	1.76679e22	+	5.70911e22i	0.0568951	+	0.183848i
$865$	3.19773e23			1.02027
$866$	−1.54799e23	+	1.27331e23i	−0.489357	+	0.402522i
$867$			4.16831e23i			1.30559i
$868$	6.41430e22	−	3.26284e23i	0.199063	−	1.01260i
$869$	4.13257e23			1.27075
$870$	1.87498e23	+	2.27946e23i	0.571270	+	0.694508i
$871$			5.19358e23i			1.56791i
$872$	1.39743e23	+	2.59342e23i	0.418021	+	0.775785i
$873$	−9.85366e21			−0.0292068
$874$	2.23234e23	−	1.83622e23i	0.655645	−	0.539303i
$875$		−	2.32702e21i		−	0.00677228i
$876$	−1.87045e23	−	3.67705e22i	−0.539403	−	0.106039i
$877$	5.33238e23			1.52379			0.761894	−	0.647702i	$-0.224270\pi$
$877$	5.33238e23			1.52379			0.761894	+	0.647702i	$0.224270\pi$
$878$	−1.20798e23	−	1.46857e23i	−0.342060	−	0.415852i
$879$			9.86246e22i			0.276741i
$880$	1.46767e23	−	3.58863e23i	0.408100	−	0.997855i
$881$	−1.32750e23			−0.365785			−0.182893	−	0.983133i	$-0.558546\pi$
$881$	−1.32750e23			−0.365785			−0.182893	+	0.983133i	$0.558546\pi$
$882$	1.59937e22	−	1.31556e22i	0.0436716	−	0.0359222i
$883$		−	3.84763e22i		−	0.104114i	−0.998644	−	0.0520568i	$-0.983422\pi$
$883$		−	3.84763e22i		−	0.104114i	0.998644	−	0.0520568i	$-0.0165777\pi$
$884$	1.08829e23	−	5.53593e23i	0.291827	−	1.48447i
$885$	1.09059e23			0.289812
$886$	8.20124e21	+	9.97046e21i	0.0215978	+	0.0262570i
$887$			5.18795e23i			1.35396i	0.736001	+	0.676981i	$0.236712\pi$
$887$			5.18795e23i			1.35396i	−0.736001	+	0.676981i	$0.763288\pi$
$888$	−1.84931e23	+	9.96477e22i	−0.478307	+	0.257729i
$889$	−2.68326e23			−0.687778
$890$	6.45819e22	−	5.31221e22i	0.164055	−	0.134944i
$891$			3.36820e22i			0.0847961i
$892$	−1.90679e23	−	3.74848e22i	−0.475755	−	0.0935270i
$893$	8.37593e22			0.207120
$894$	6.84345e21	+	8.31976e21i	0.0167716	+	0.0203897i
$895$		−	4.71542e23i		−	1.14534i
$896$	−4.46731e23	+	4.75361e22i	−1.07543	+	0.114435i
$897$	−1.56512e23			−0.373429
$898$	−4.10768e23	+	3.37879e23i	−0.971373	+	0.799007i
$899$		−	4.48892e23i		−	1.05212i
$900$	−2.75555e22	+	1.40170e23i	−0.0640131	+	0.325623i
$901$	−1.28383e24			−2.95604
$902$	−2.68828e23	−	3.26822e23i	−0.613512	−	0.745862i
$903$		−	2.09760e23i		−	0.474482i
$904$	2.30553e23	+	4.27872e23i	0.516919	+	0.959326i
$905$	3.70609e23			0.823622
$906$	2.47499e22	−	2.03581e22i	0.0545189	−	0.0448448i
$907$		−	6.66102e23i		−	1.45440i	−0.686428	−	0.727198i	$-0.740822\pi$
$907$		−	6.66102e23i		−	1.45440i	0.686428	−	0.727198i	$-0.259178\pi$
$908$	−6.30629e23	−	1.23973e23i	−1.36486	−	0.268312i
$909$	−3.80318e22			−0.0815898
$910$	3.82339e23	+	4.64819e23i	0.813050	+	0.988446i
$911$		−	1.75935e23i		−	0.370856i	−0.982658	−	0.185428i	$-0.940633\pi$
$911$		−	1.75935e23i		−	0.370856i	0.982658	−	0.185428i	$-0.0593671\pi$
$912$	−2.81213e23	−	1.15010e23i	−0.587593	−	0.240312i
$913$	4.46599e23			0.925022
$914$	−3.97375e23	+	3.26862e23i	−0.815889	+	0.671113i
$915$		−	6.87104e22i		−	0.139847i
$916$	−1.57565e23	+	8.01505e23i	−0.317904	+	1.61712i
$917$	7.69420e23			1.53889
$918$	−1.11355e23	−	1.35377e23i	−0.220784	−	0.268412i
$919$			1.49598e21i			0.00294037i	0.999999	+	0.00147018i	$0.000467974\pi$
$919$			1.49598e21i			0.00294037i	−0.999999	+	0.00147018i	$0.999532\pi$
$920$	4.92770e23	−	2.65522e23i	0.960156	−	0.517367i
$921$	−1.30515e21			−0.00252106
$922$	−1.69940e23	+	1.39784e23i	−0.325422	+	0.267677i
$923$		−	5.38280e23i		−	1.02187i
$924$	−2.48443e23	−	4.88404e22i	−0.467574	−	0.0919186i
$925$	−5.02140e23			−0.936895
$926$	4.06306e23	+	4.93957e23i	0.751563	+	0.913695i
$927$		−	2.75990e22i		−	0.0506122i
$928$	−5.79352e23	+	1.79291e23i	−1.05332	+	0.325968i
$929$	−6.27962e23			−1.13190			−0.565950	−	0.824440i	$-0.691490\pi$
$929$	−6.27962e23			−1.13190			−0.565950	+	0.824440i	$0.691490\pi$
$930$	3.36331e23	−	2.76651e23i	0.601041	−	0.494388i
$931$			1.05282e23i			0.186533i
$932$	1.00886e23	−	5.13190e23i	0.177217	−	0.901470i
$933$	3.67549e23			0.640121
$934$	1.77053e23	+	2.15248e23i	0.305723	+	0.371675i
$935$			1.13722e24i			1.94693i
$936$	7.80363e22	+	1.44824e23i	0.132462	+	0.245829i
$937$	4.30017e23			0.723717			0.361858	−	0.932233i	$-0.382142\pi$
$937$	4.30017e23			0.723717			0.361858	+	0.932233i	$0.382142\pi$
$938$	−9.36807e23	+	7.70574e23i	−1.56325	+	1.28585i
$939$			1.04359e23i			0.172665i
$940$	1.59156e23	+	3.12878e22i	0.261096	+	0.0513278i
$941$	3.93278e23			0.639709			0.319854	−	0.947467i	$-0.396366\pi$
$941$	3.93278e23			0.639709			0.319854	+	0.947467i	$0.396366\pi$
$942$	2.10911e23	+	2.56411e23i	0.340168	+	0.413551i
$943$		−	6.10955e23i		−	0.977048i
$944$	−8.48272e22	+	2.07413e23i	−0.134511	+	0.328897i
$945$	1.86996e23			0.294021
$946$	−2.87268e23	+	2.36294e23i	−0.447877	+	0.368403i
$947$			6.23885e23i			0.964506i	0.876032	+	0.482253i	$0.160181\pi$
$947$			6.23885e23i			0.964506i	−0.876032	+	0.482253i	$0.839819\pi$
$948$	1.20967e23	−	6.15340e23i	0.185439	−	0.943298i
$949$	−5.24741e23			−0.797655
$950$	−4.61350e23	−	5.60876e23i	−0.695412	−	0.845430i
$951$		−	1.79668e23i		−	0.268551i
$952$	1.16003e24	−	6.25064e23i	1.71938	−	0.926465i
$953$	−3.44977e23			−0.507046			−0.253523	−	0.967329i	$-0.581589\pi$
$953$	−3.44977e23			−0.507046			−0.253523	+	0.967329i	$0.581589\pi$
$954$	2.89110e23	−	2.37808e23i	0.421382	−	0.346609i
$955$		−	3.74362e23i		−	0.541084i
$956$	8.53011e23	+	1.67690e23i	1.22262	+	0.240350i
$957$	−3.41800e23			−0.485821
$958$	2.93892e23	+	3.57292e23i	0.414251	+	0.503616i
$959$		−	3.05105e23i		−	0.426482i
$960$	−4.91387e23	−	3.23582e23i	−0.681167	−	0.448554i
$961$	6.50881e22			0.0894776
$962$	−4.46595e23	+	3.67349e23i	−0.608855	+	0.500816i
$963$		−	2.34438e23i		−	0.316970i
$964$	1.35231e23	−	6.87899e23i	0.181326	−	0.922376i
$965$	1.49683e24			1.99046
$966$	−2.32217e23	−	2.82313e23i	−0.306251	−	0.372318i
$967$		−	3.59607e23i		−	0.470344i	−0.971954	−	0.235172i	$-0.924435\pi$
$967$		−	3.59607e23i		−	0.470344i	0.971954	−	0.235172i	$-0.0755654\pi$
$968$	−1.52702e23	−	2.83393e23i	−0.198081	−	0.367609i
$969$	8.91147e23			1.14646
$970$	7.49201e22	−	6.16258e22i	0.0955926	−	0.0786300i
$971$			1.75593e23i			0.222205i	0.993809	+	0.111102i	$0.0354381\pi$
$971$			1.75593e23i			0.222205i	−0.993809	+	0.111102i	$0.964562\pi$
$972$	5.01526e22	+	9.85930e21i	0.0629453	+	0.0123742i
$973$	4.21454e23			0.524623
$974$	9.40279e23	+	1.14312e24i	1.16087	+	1.41130i
$975$			3.93237e23i			0.481523i
$976$	1.30676e23	+	5.34435e22i	0.158707	+	0.0649077i
$977$	−2.99858e23			−0.361210			−0.180605	−	0.983556i	$-0.557806\pi$
$977$	−2.99858e23			−0.361210			−0.180605	+	0.983556i	$0.557806\pi$
$978$	−5.98048e23	+	4.91927e23i	−0.714538	+	0.587746i
$979$			9.68393e22i			0.114760i
$980$	−3.93274e22	+	2.00052e23i	−0.0462261	+	0.235144i
$981$	2.51956e23			0.293747
$982$	−4.49531e23	−	5.46507e23i	−0.519838	−	0.631980i
$983$			4.49857e22i			0.0515996i	0.999667	+	0.0257998i	$0.00821324\pi$
$983$			4.49857e22i			0.0515996i	−0.999667	+	0.0257998i	$0.991787\pi$
$984$	−5.65330e23	+	3.04620e23i	−0.643192	+	0.346575i
$985$	−1.70109e24			−1.91972
$986$	1.37378e24	−	1.13001e24i	1.53781	−	1.26493i
$987$		−	1.05926e23i		−	0.117616i
$988$	−8.20636e23	−	1.61326e23i	−0.903847	−	0.177684i
$989$	−5.37014e23			−0.586699
$990$	−2.10650e23	−	2.56093e23i	−0.228287	−	0.277534i
$991$			1.06835e24i			1.14848i	0.818687	+	0.574241i	$0.194703\pi$
$991$			1.06835e24i			1.14848i	−0.818687	+	0.574241i	$0.805297\pi$
$992$	2.64542e23	+	8.54828e23i	0.282099	+	0.911560i
$993$	1.32293e23			0.139940
$994$	9.70938e23	−	7.98648e23i	1.01883	−	0.838040i
$995$		−	2.66354e23i		−	0.277252i
$996$	1.30727e23	−	6.64988e23i	0.134987	−	0.686656i
$997$	3.63390e23			0.372230			0.186115	−	0.982528i	$-0.440410\pi$
$997$	3.63390e23			0.372230			0.186115	+	0.982528i	$0.440410\pi$
$998$	−6.13651e23	−	7.46031e23i	−0.623558	−	0.758076i
$999$			1.79665e23i			0.181108i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.17.d.a.7.13	✓	16
3.2	odd	2		36.17.d.d.19.4		16
4.3	odd	2	inner	12.17.d.a.7.14	yes	16
12.11	even	2		36.17.d.d.19.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.17.d.a.7.13	✓	16	1.1	even	1	trivial
12.17.d.a.7.14	yes	16	4.3	odd	2	inner
36.17.d.d.19.3		16	12.11	even	2
36.17.d.d.19.4		16	3.2	odd	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)

\(f(q)\)	\(=\)	\(q+(197.709 - 162.626i) q^{2} +3788.00i q^{3} +(12641.5 - 64305.2i) q^{4} +551815. q^{5} +(616027. + 748920. i) q^{6} +6.23463e6i q^{7} +(-7.95836e6 - 1.47695e7i) q^{8} -1.43489e7 q^{9} +O(q^{10})\)	\(q+(197.709 - 162.626i) q^{2} +3788.00i q^{3} +(12641.5 - 64305.2i) q^{4} +551815. q^{5} +(616027. + 748920. i) q^{6} +6.23463e6i q^{7} +(-7.95836e6 - 1.47695e7i) q^{8} -1.43489e7 q^{9} +(1.09099e8 - 8.97395e7i) q^{10} +1.63591e8i q^{11} +(2.43588e8 + 4.78860e7i) q^{12} +6.83367e8 q^{13} +(1.01391e9 + 1.23264e9i) q^{14} +2.09027e9i q^{15} +(-3.97535e9 - 1.62583e9i) q^{16} +1.25977e10 q^{17} +(-2.83690e9 + 2.33351e9i) q^{18} -1.86745e10i q^{19} +(6.97577e9 - 3.54846e10i) q^{20} -2.36168e10 q^{21} +(2.66042e10 + 3.23434e10i) q^{22} +6.04622e10i q^{23} +(5.59470e10 - 3.01462e10i) q^{24} +1.51912e11 q^{25} +(1.35108e11 - 1.11133e11i) q^{26} -5.43536e10i q^{27} +(4.00919e11 + 7.88152e10i) q^{28} +5.51573e11 q^{29} +(3.39933e11 + 4.13265e11i) q^{30} -8.13840e11i q^{31} +(-1.05036e12 + 3.25055e11i) q^{32} -6.19683e11 q^{33} +(2.49067e12 - 2.04871e12i) q^{34} +3.44036e12i q^{35} +(-1.81392e11 + 9.22709e11i) q^{36} -3.30548e12 q^{37} +(-3.03697e12 - 3.69212e12i) q^{38} +2.58859e12i q^{39} +(-4.39154e12 - 8.15005e12i) q^{40} -1.01047e13 q^{41} +(-4.66924e12 + 3.84070e12i) q^{42} +8.88181e12i q^{43} +(1.05198e13 + 2.06804e12i) q^{44} -7.91794e12 q^{45} +(9.83274e12 + 1.19539e13i) q^{46} +4.48521e12i q^{47} +(6.15864e12 - 1.50586e13i) q^{48} -5.63771e12 q^{49} +(3.00342e13 - 2.47048e13i) q^{50} +4.77199e13i q^{51} +(8.63880e12 - 4.39441e13i) q^{52} -1.01910e14 q^{53} +(-8.83931e12 - 1.07462e13i) q^{54} +9.02720e13i q^{55} +(9.20827e13 - 4.96175e13i) q^{56} +7.07391e13 q^{57} +(1.09051e14 - 8.97001e13i) q^{58} -5.21747e13i q^{59} +(1.34415e14 + 2.64242e13i) q^{60} -3.28715e13 q^{61} +(-1.32352e14 - 1.60903e14i) q^{62} -8.94602e13i q^{63} +(-1.54804e14 + 2.35083e14i) q^{64} +3.77092e14 q^{65} +(-1.22517e14 + 1.00777e14i) q^{66} +7.59999e14i q^{67} +(1.59254e14 - 8.10095e14i) q^{68} -2.29031e14 q^{69} +(5.59493e14 + 6.80190e14i) q^{70} -7.87689e14i q^{71} +(1.14194e14 + 2.11927e14i) q^{72} -7.67875e14 q^{73} +(-6.53522e14 + 5.37557e14i) q^{74} +5.75440e14i q^{75} +(-1.20087e15 - 2.36075e14i) q^{76} -1.01993e15 q^{77} +(4.20972e14 + 5.11787e14i) q^{78} -2.52615e15i q^{79} +(-2.19366e15 - 8.97157e14i) q^{80} +2.05891e14 q^{81} +(-1.99780e15 + 1.64329e15i) q^{82} -2.72997e15i q^{83} +(-2.98552e14 + 1.51868e15i) q^{84} +6.95157e15 q^{85} +(1.44441e15 + 1.75601e15i) q^{86} +2.08936e15i q^{87} +(2.41617e15 - 1.30192e15i) q^{88} +5.91959e14 q^{89} +(-1.56545e15 + 1.28766e15i) q^{90} +4.26054e15i q^{91} +(3.88804e15 + 7.64335e14i) q^{92} +3.08282e15 q^{93} +(7.29412e14 + 8.86766e14i) q^{94} -1.03049e16i q^{95} +(-1.23131e15 - 3.97877e15i) q^{96} +6.86719e14 q^{97} +(-1.11463e15 + 9.16839e14i) q^{98} -2.34735e15i 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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