LMFDB - Embedded newform 12.17.d.a.7.6

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			7.6
Root			$-54.1541 - 93.7976i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.17.d.a.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-141.143 + 213.576i) q^{2} -3788.00i q^{3} +(-25693.4 - 60289.4i) q^{4} +110106. q^{5} +(809025. + 534648. i) q^{6} -7.35151e6i q^{7} +(1.65028e7 + 3.02193e6i) q^{8} -1.43489e7 q^{9} +O(q^{10})$	\(q+(-141.143 + 213.576i) q^{2} -3788.00i q^{3} +(-25693.4 - 60289.4i) q^{4} +110106. q^{5} +(809025. + 534648. i) q^{6} -7.35151e6i q^{7} +(1.65028e7 + 3.02193e6i) q^{8} -1.43489e7 q^{9} +(-1.55406e7 + 2.35159e7i) q^{10} +2.79666e8i q^{11} +(-2.28376e8 + 9.73265e7i) q^{12} +2.85853e7 q^{13} +(1.57011e9 + 1.03761e9i) q^{14} -4.17080e8i q^{15} +(-2.97467e9 + 3.09808e9i) q^{16} -6.15030e9 q^{17} +(2.02525e9 - 3.06458e9i) q^{18} -2.23587e10i q^{19} +(-2.82899e9 - 6.63821e9i) q^{20} -2.78475e10 q^{21} +(-5.97299e10 - 3.94728e10i) q^{22} -1.78982e10i q^{23} +(1.14471e10 - 6.25126e10i) q^{24} -1.40465e11 q^{25} +(-4.03462e9 + 6.10514e9i) q^{26} +5.43536e10i q^{27} +(-4.43218e11 + 1.88885e11i) q^{28} -4.59649e11 q^{29} +(8.90782e10 + 5.88678e10i) q^{30} +5.70578e11i q^{31} +(-2.41823e11 - 1.07259e12i) q^{32} +1.05937e12 q^{33} +(8.68071e11 - 1.31356e12i) q^{34} -8.09443e11i q^{35} +(3.68672e11 + 8.65088e11i) q^{36} -6.55720e12 q^{37} +(4.77529e12 + 3.15578e12i) q^{38} -1.08281e11i q^{39} +(1.81705e12 + 3.32732e11i) q^{40} +6.32978e12 q^{41} +(3.93047e12 - 5.94755e12i) q^{42} +1.18625e13i q^{43} +(1.68609e13 - 7.18557e12i) q^{44} -1.57990e12 q^{45} +(3.82262e12 + 2.52620e12i) q^{46} +2.75541e13i q^{47} +(1.17355e13 + 1.12680e13i) q^{48} -2.08118e13 q^{49} +(1.98256e13 - 2.99999e13i) q^{50} +2.32973e13i q^{51} +(-7.34454e11 - 1.72339e12i) q^{52} -1.04002e14 q^{53} +(-1.16086e13 - 7.67162e12i) q^{54} +3.07928e13i q^{55} +(2.22157e13 - 1.21321e14i) q^{56} -8.46948e13 q^{57} +(6.48761e13 - 9.81700e13i) q^{58} -1.51049e14i q^{59} +(-2.51455e13 + 1.07162e13i) q^{60} -2.11410e14 q^{61} +(-1.21862e14 - 8.05331e13i) q^{62} +1.05486e14i q^{63} +(2.63211e14 + 9.97407e13i) q^{64} +3.14741e12 q^{65} +(-1.49523e14 + 2.26257e14i) q^{66} +3.36308e14i q^{67} +(1.58022e14 + 3.70798e14i) q^{68} -6.77982e13 q^{69} +(1.72877e14 + 1.14247e14i) q^{70} -2.76524e14i q^{71} +(-2.36797e14 - 4.33614e13i) q^{72} +9.79291e14 q^{73} +(9.25502e14 - 1.40046e15i) q^{74} +5.32079e14i q^{75} +(-1.34800e15 + 5.74472e14i) q^{76} +2.05597e15 q^{77} +(2.31262e13 + 1.52831e13i) q^{78} -5.71801e14i q^{79} +(-3.27527e14 + 3.41116e14i) q^{80} +2.05891e14 q^{81} +(-8.93403e14 + 1.35189e15i) q^{82} -3.91206e15i q^{83} +(7.15496e14 + 1.67891e15i) q^{84} -6.77183e14 q^{85} +(-2.53354e15 - 1.67430e15i) q^{86} +1.74115e15i q^{87} +(-8.45131e14 + 4.61528e15i) q^{88} +2.27988e15 q^{89} +(2.22991e14 - 3.37428e14i) q^{90} -2.10145e14i q^{91} +(-1.07907e15 + 4.59865e14i) q^{92} +2.16135e15 q^{93} +(-5.88490e15 - 3.88907e15i) q^{94} -2.46182e15i q^{95} +(-4.06296e15 + 9.16024e14i) q^{96} -1.11049e16 q^{97} +(2.93743e15 - 4.44489e15i) q^{98} -4.01290e15i 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 $

$2$	−141.143	+	213.576i	−0.551339	+	0.834281i
$2$	−141.143	+	213.576i	−0.551339	+	0.834281i
$3$		−	3788.00i		−	0.577350i
$3$		−	3788.00i		−	0.577350i
$4$	−25693.4	−	60289.4i	−0.392050	−	0.919944i
$5$	110106.			0.281870			0.140935	−	0.990019i	$-0.454989\pi$
$5$	110106.			0.281870			0.140935	+	0.990019i	$0.454989\pi$
$6$	809025.	+	534648.i	0.481672	+	0.318316i
$7$		−	7.35151e6i		−	1.27524i	−0.770351	−	0.637620i	$-0.779919\pi$
$7$		−	7.35151e6i		−	1.27524i	0.770351	−	0.637620i	$-0.220081\pi$
$8$	1.65028e7	+	3.02193e6i	0.983644	+	0.180121i
$9$	−1.43489e7			−0.333333
$10$	−1.55406e7	+	2.35159e7i	−0.155406	+	0.235159i
$11$			2.79666e8i			1.30466i	0.757934	+	0.652331i	$0.226209\pi$
$11$			2.79666e8i			1.30466i	−0.757934	+	0.652331i	$0.773791\pi$
$12$	−2.28376e8	+	9.73265e7i	−0.531130	+	0.226350i
$13$	2.85853e7			0.0350426			0.0175213	−	0.999846i	$-0.494423\pi$
$13$	2.85853e7			0.0350426			0.0175213	+	0.999846i	$0.494423\pi$
$14$	1.57011e9	+	1.03761e9i	1.06391	+	0.703090i
$15$		−	4.17080e8i		−	0.162738i
$16$	−2.97467e9	+	3.09808e9i	−0.692593	+	0.721328i
$17$	−6.15030e9			−0.881668			−0.440834	−	0.897589i	$-0.645317\pi$
$17$	−6.15030e9			−0.881668			−0.440834	+	0.897589i	$0.645317\pi$
$18$	2.02525e9	−	3.06458e9i	0.183780	−	0.278094i
$19$		−	2.23587e10i		−	1.31649i	−0.752802	−	0.658247i	$-0.771298\pi$
$19$		−	2.23587e10i		−	1.31649i	0.752802	−	0.658247i	$-0.228702\pi$
$20$	−2.82899e9	−	6.63821e9i	−0.110507	−	0.259305i
$21$	−2.78475e10			−0.736261
$22$	−5.97299e10	−	3.94728e10i	−1.08846	−	0.719311i
$23$		−	1.78982e10i		−	0.228552i	−0.993449	−	0.114276i	$-0.963545\pi$
$23$		−	1.78982e10i		−	0.228552i	0.993449	−	0.114276i	$-0.0364549\pi$
$24$	1.14471e10	−	6.25126e10i	0.103993	−	0.567907i
$25$	−1.40465e11			−0.920549
$26$	−4.03462e9	+	6.10514e9i	−0.0193204	+	0.0292354i
$27$			5.43536e10i			0.192450i
$28$	−4.43218e11	+	1.88885e11i	−1.17315	+	0.499958i
$29$	−4.59649e11			−0.918845			−0.459422	−	0.888218i	$-0.651944\pi$
$29$	−4.59649e11			−0.918845			−0.459422	+	0.888218i	$0.651944\pi$
$30$	8.90782e10	+	5.88678e10i	0.135769	+	0.0897238i
$31$			5.70578e11i			0.668993i	0.942397	+	0.334497i	$0.108566\pi$
$31$			5.70578e11i			0.668993i	−0.942397	+	0.334497i	$0.891434\pi$
$32$	−2.41823e11	−	1.07259e12i	−0.219937	−	0.975514i
$33$	1.05937e12			0.753247
$34$	8.68071e11	−	1.31356e12i	0.486098	−	0.735559i
$35$		−	8.09443e11i		−	0.359453i
$36$	3.68672e11	+	8.65088e11i	0.130683	+	0.306648i
$37$	−6.55720e12			−1.86683			−0.933414	−	0.358800i	$-0.883186\pi$
$37$	−6.55720e12			−1.86683			−0.933414	+	0.358800i	$0.883186\pi$
$38$	4.77529e12	+	3.15578e12i	1.09833	+	0.725834i
$39$		−	1.08281e11i		−	0.0202319i
$40$	1.81705e12	+	3.32732e11i	0.277260	+	0.0507708i
$41$	6.32978e12			0.792716			0.396358	−	0.918096i	$-0.370274\pi$
$41$	6.32978e12			0.792716			0.396358	+	0.918096i	$0.370274\pi$
$42$	3.93047e12	−	5.94755e12i	0.405929	−	0.614248i
$43$			1.18625e13i			1.01491i	0.861678	+	0.507455i	$0.169414\pi$
$43$			1.18625e13i			1.01491i	−0.861678	+	0.507455i	$0.830586\pi$
$44$	1.68609e13	−	7.18557e12i	1.20022	−	0.511493i
$45$	−1.57990e12			−0.0939568
$46$	3.82262e12	+	2.52620e12i	0.190677	+	0.126010i
$47$			2.75541e13i			1.15719i	0.815616	+	0.578594i	$0.196398\pi$
$47$			2.75541e13i			1.15719i	−0.815616	+	0.578594i	$0.803602\pi$
$48$	1.17355e13	+	1.12680e13i	0.416459	+	0.399869i
$49$	−2.08118e13			−0.626239
$50$	1.98256e13	−	2.99999e13i	0.507535	−	0.767997i
$51$			2.32973e13i			0.509031i
$52$	−7.34454e11	−	1.72339e12i	−0.0137385	−	0.0322372i
$53$	−1.04002e14			−1.67046			−0.835228	−	0.549904i	$-0.814664\pi$
$53$	−1.04002e14			−1.67046			−0.835228	+	0.549904i	$0.814664\pi$
$54$	−1.16086e13	−	7.67162e12i	−0.160557	−	0.106105i
$55$			3.07928e13i			0.367746i
$56$	2.22157e13	−	1.21321e14i	0.229698	−	1.25438i
$57$	−8.46948e13			−0.760078
$58$	6.48761e13	−	9.81700e13i	0.506595	−	0.766575i
$59$		−	1.51049e14i		−	1.02873i	−0.857570	−	0.514367i	$-0.828027\pi$
$59$		−	1.51049e14i		−	1.02873i	0.857570	−	0.514367i	$-0.171973\pi$
$60$	−2.51455e13	+	1.07162e13i	−0.149710	+	0.0638014i
$61$	−2.11410e14			−1.10277			−0.551386	−	0.834250i	$-0.685901\pi$
$61$	−2.11410e14			−1.10277			−0.551386	+	0.834250i	$0.685901\pi$
$62$	−1.21862e14	−	8.05331e13i	−0.558129	−	0.368842i
$63$			1.05486e14i			0.425080i
$64$	2.63211e14	+	9.97407e13i	0.935113	+	0.354350i
$65$	3.14741e12			0.00987748
$66$	−1.49523e14	+	2.26257e14i	−0.415295	+	0.628420i
$67$			3.36308e14i			0.828206i	0.910230	+	0.414103i	$0.135905\pi$
$67$			3.36308e14i			0.828206i	−0.910230	+	0.414103i	$0.864095\pi$
$68$	1.58022e14	+	3.70798e14i	0.345658	+	0.811085i
$69$	−6.77982e13			−0.131955
$70$	1.72877e14	+	1.14247e14i	0.299885	+	0.198180i
$71$		−	2.76524e14i		−	0.428220i	−0.976810	−	0.214110i	$-0.931315\pi$
$71$		−	2.76524e14i		−	0.428220i	0.976810	−	0.214110i	$-0.0686851\pi$
$72$	−2.36797e14	−	4.33614e13i	−0.327881	−	0.0600404i
$73$	9.79291e14			1.21431			0.607154	−	0.794584i	$-0.292311\pi$
$73$	9.79291e14			1.21431			0.607154	+	0.794584i	$0.292311\pi$
$74$	9.25502e14	−	1.40046e15i	1.02926	−	1.55746i
$75$			5.32079e14i			0.531479i
$76$	−1.34800e15	+	5.74472e14i	−1.21110	+	0.516131i
$77$	2.05597e15			1.66376
$78$	2.31262e13	+	1.52831e13i	0.0168791	+	0.0111546i
$79$		−	5.71801e14i		−	0.376902i	−0.982083	−	0.188451i	$-0.939653\pi$
$79$		−	5.71801e14i		−	0.376902i	0.982083	−	0.188451i	$-0.0603467\pi$
$80$	−3.27527e14	+	3.41116e14i	−0.195222	+	0.203321i
$81$	2.05891e14			0.111111
$82$	−8.93403e14	+	1.35189e15i	−0.437056	+	0.661348i
$83$		−	3.91206e15i		−	1.73693i	−0.495754	−	0.868463i	$-0.665108\pi$
$83$		−	3.91206e15i		−	1.73693i	0.495754	−	0.868463i	$-0.334892\pi$
$84$	7.15496e14	+	1.67891e15i	0.288651	+	0.677318i
$85$	−6.77183e14			−0.248516
$86$	−2.53354e15	−	1.67430e15i	−0.846720	−	0.559560i
$87$			1.74115e15i			0.530495i
$88$	−8.45131e14	+	4.61528e15i	−0.234997	+	1.28332i
$89$	2.27988e15			0.579152			0.289576	−	0.957155i	$-0.406486\pi$
$89$	2.27988e15			0.579152			0.289576	+	0.957155i	$0.406486\pi$
$90$	2.22991e14	−	3.37428e14i	0.0518021	−	0.0783864i
$91$		−	2.10145e14i		−	0.0446878i
$92$	−1.07907e15	+	4.59865e14i	−0.210255	+	0.0896040i
$93$	2.16135e15			0.386243
$94$	−5.88490e15	−	3.88907e15i	−0.965420	−	0.638003i
$95$		−	2.46182e15i		−	0.371080i
$96$	−4.06296e15	+	9.16024e14i	−0.563213	+	0.126980i
$97$	−1.11049e16			−1.41691			−0.708453	−	0.705758i	$-0.750607\pi$
$97$	−1.11049e16			−1.41691			−0.708453	+	0.705758i	$0.750607\pi$
$98$	2.93743e15	−	4.44489e15i	0.345270	−	0.522459i
$99$		−	4.01290e15i		−	0.434887i
$100$	3.60901e15	+	8.46853e15i	0.360901	+	0.846853i
$101$	3.75349e15			0.346628			0.173314	−	0.984867i	$-0.444552\pi$
$101$	3.75349e15			0.346628			0.173314	+	0.984867i	$0.444552\pi$
$102$	−4.97575e15	−	3.28825e15i	−0.424675	−	0.280649i
$103$		−	6.85010e15i		−	0.540753i	−0.962755	−	0.270376i	$-0.912852\pi$
$103$		−	6.85010e15i		−	0.540753i	0.962755	−	0.270376i	$-0.0871482\pi$
$104$	4.71739e14	+	8.63829e13i	0.0344695	+	0.00631191i
$105$	−3.06616e15			−0.207530
$106$	1.46791e16	−	2.22123e16i	0.920988	−	1.39363i
$107$			2.05356e16i			1.19519i	0.801797	+	0.597597i	$0.203878\pi$
$107$			2.05356e16i			1.19519i	−0.801797	+	0.597597i	$0.796122\pi$
$108$	3.27695e15	−	1.39653e15i	0.177043	−	0.0754501i
$109$	2.12953e16			1.06874			0.534369	−	0.845251i	$-0.320549\pi$
$109$	2.12953e16			1.06874			0.534369	+	0.845251i	$0.320549\pi$
$110$	−6.57660e15	−	4.34618e15i	−0.306803	−	0.202753i
$111$			2.48386e16i			1.07781i
$112$	2.27756e16	+	2.18683e16i	0.919867	+	0.883223i
$113$	−3.00062e16			−1.12871			−0.564357	−	0.825531i	$-0.690876\pi$
$113$	−3.00062e16			−1.12871			−0.564357	+	0.825531i	$0.690876\pi$
$114$	1.19541e16	−	1.80888e16i	0.419061	−	0.634118i
$115$		−	1.97069e15i		−	0.0644222i
$116$	1.18099e16	+	2.77120e16i	0.360233	+	0.845286i
$117$	−4.10168e14			−0.0116809
$118$	3.22605e16	+	2.13195e16i	0.858253	+	0.567181i
$119$			4.52140e16i			1.12434i
$120$	1.26039e15	−	6.88299e15i	0.0293125	−	0.160076i
$121$	−3.22633e16			−0.702144
$122$	2.98390e16	−	4.51520e16i	0.608002	−	0.920023i
$123$		−	2.39772e16i		−	0.457675i
$124$	3.43999e16	−	1.46601e16i	0.615436	−	0.262279i
$125$	−3.22667e16			−0.541346
$126$	−2.25293e16	−	1.48886e16i	−0.354636	−	0.234363i
$127$		−	1.03274e17i		−	1.52603i	−0.646381	−	0.763014i	$-0.723719\pi$
$127$		−	1.03274e17i		−	1.52603i	0.646381	−	0.763014i	$-0.276281\pi$
$128$	−5.84525e16	+	4.21378e16i	−0.811192	+	0.584780i
$129$	4.49350e16			0.585958
$130$	−4.44234e14	+	6.72210e14i	−0.00544584	+	0.00824059i
$131$			1.07452e17i			1.23892i	0.785027	+	0.619462i	$0.212649\pi$
$131$			1.07452e17i			1.23892i	−0.785027	+	0.619462i	$0.787351\pi$
$132$	−2.72189e16	−	6.38690e16i	−0.295311	−	0.692945i
$133$	−1.64371e17			−1.67885
$134$	−7.18273e16	−	4.74674e16i	−0.690957	−	0.456623i
$135$			5.98464e15i			0.0542460i
$136$	−1.01497e17	−	1.85858e16i	−0.867248	−	0.158807i
$137$	1.00063e17			0.806323			0.403161	−	0.915129i	$-0.367911\pi$
$137$	1.00063e17			0.806323			0.403161	+	0.915129i	$0.367911\pi$
$138$	9.56923e15	−	1.44801e16i	0.0727519	−	0.110087i
$139$		−	1.31938e17i		−	0.946784i	−0.880852	−	0.473392i	$-0.843029\pi$
$139$		−	1.31938e17i		−	0.946784i	0.880852	−	0.473392i	$-0.156971\pi$
$140$	−4.88008e16	+	2.07973e16i	−0.330676	+	0.140923i
$141$	1.04375e17			0.668103
$142$	5.90590e16	+	3.90294e16i	0.357256	+	0.236094i
$143$			7.99434e15i			0.0457188i
$144$	4.26832e16	−	4.44541e16i	0.230864	−	0.240443i
$145$	−5.06099e16			−0.258995
$146$	−1.38220e17	+	2.09153e17i	−0.669496	+	1.01307i
$147$			7.88348e16i			0.361559i
$148$	1.68477e17	+	3.95330e17i	0.731891	+	1.71738i
$149$	3.38569e17			1.39366			0.696830	−	0.717237i	$-0.254593\pi$
$149$	3.38569e17			1.39366			0.696830	+	0.717237i	$0.254593\pi$
$150$	−1.13639e17	−	7.50992e16i	−0.443403	−	0.293025i
$151$		−	2.91716e17i		−	1.07930i	−0.841888	−	0.539652i	$-0.818556\pi$
$151$		−	2.91716e17i		−	1.07930i	0.841888	−	0.539652i	$-0.181444\pi$
$152$	6.75666e16	−	3.68982e17i	0.237128	−	1.29496i
$153$	8.82501e16			0.293889
$154$	−2.90185e17	+	4.39105e17i	−0.917295	+	1.38804i
$155$			6.28239e16i			0.188569i
$156$	−6.52821e15	+	2.78211e15i	−0.0186122	+	0.00793190i
$157$	4.61806e17			1.25102			0.625508	−	0.780218i	$-0.284892\pi$
$157$	4.61806e17			1.25102			0.625508	+	0.780218i	$0.284892\pi$
$158$	1.22123e17	+	8.07057e16i	0.314442	+	0.207801i
$159$			3.93959e17i			0.964438i
$160$	−2.66261e16	−	1.18098e17i	−0.0619936	−	0.274969i
$161$	−1.31579e17			−0.291459
$162$	−2.90601e16	+	4.39734e16i	−0.0612599	+	0.0926979i
$163$		−	6.96960e17i		−	1.39864i	−0.714807	−	0.699321i	$-0.753486\pi$
$163$		−	6.96960e17i		−	1.39864i	0.714807	−	0.699321i	$-0.246514\pi$
$164$	−1.62634e17	−	3.81619e17i	−0.310785	−	0.729255i
$165$	1.16643e17			0.212318
$166$	8.35523e17	+	5.52160e17i	1.44908	+	0.957635i
$167$		−	5.64564e17i		−	0.933214i	−0.884465	−	0.466607i	$-0.845476\pi$
$167$		−	5.64564e17i		−	0.933214i	0.884465	−	0.466607i	$-0.154524\pi$
$168$	−4.59562e17	−	8.41531e16i	−0.724219	−	0.132616i
$169$	−6.64599e17			−0.998772
$170$	9.55795e16	−	1.44630e17i	0.137017	−	0.207332i
$171$			3.20824e17i			0.438831i
$172$	7.15182e17	−	3.04787e17i	0.933660	−	0.397896i
$173$	6.89996e17			0.859959			0.429979	−	0.902839i	$-0.358521\pi$
$173$	6.89996e17			0.859959			0.429979	+	0.902839i	$0.358521\pi$
$174$	−3.71867e17	−	2.45751e17i	−0.442582	−	0.292483i
$175$			1.03263e18i			1.17392i
$176$	−8.66428e17	−	8.31913e17i	−0.941090	−	0.903600i
$177$	−5.72174e17			−0.593940
$178$	−3.21789e17	+	4.86928e17i	−0.319309	+	0.483175i
$179$			1.44526e18i			1.37127i	0.727947	+	0.685634i	$0.240475\pi$
$179$			1.44526e18i			1.37127i	−0.727947	+	0.685634i	$0.759525\pi$
$180$	4.05929e16	+	9.52510e16i	0.0368358	+	0.0864350i
$181$	−2.25072e18			−1.95386			−0.976928	−	0.213570i	$-0.931491\pi$
$181$	−2.25072e18			−1.95386			−0.976928	+	0.213570i	$0.931491\pi$
$182$	4.48820e16	+	2.96605e16i	0.0372822	+	0.0246381i
$183$			8.00819e17i			0.636686i
$184$	5.40870e16	−	2.95370e17i	0.0411671	−	0.224814i
$185$	−7.21985e17			−0.526204
$186$	−3.05059e17	+	4.61612e17i	−0.212951	+	0.322236i
$187$		−	1.72003e18i		−	1.15028i
$188$	1.66122e18	−	7.07959e17i	1.06455	−	0.453676i
$189$	3.99581e17			0.245420
$190$	5.25786e17	+	3.47469e17i	0.309585	+	0.204591i
$191$		−	2.16038e18i		−	1.21973i	−0.792507	−	0.609863i	$-0.791224\pi$
$191$		−	2.16038e18i		−	1.21973i	0.792507	−	0.609863i	$-0.208776\pi$
$192$	3.77817e17	−	9.97041e17i	0.204584	−	0.539888i
$193$	−2.55966e17			−0.132961			−0.0664804	−	0.997788i	$-0.521177\pi$
$193$	−2.55966e17			−0.132961			−0.0664804	+	0.997788i	$0.521177\pi$
$194$	1.56738e18	−	2.37174e18i	0.781196	−	1.18210i
$195$		−	1.19224e16i		−	0.00570276i
$196$	5.34725e17	+	1.25473e18i	0.245517	+	0.576105i
$197$	−2.22754e18			−0.981964			−0.490982	−	0.871170i	$-0.663362\pi$
$197$	−2.22754e18			−0.981964			−0.490982	+	0.871170i	$0.663362\pi$
$198$	8.57059e17	+	5.66392e17i	0.362818	+	0.239770i
$199$			1.08784e18i			0.442323i	0.975237	+	0.221161i	$0.0709847\pi$
$199$			1.08784e18i			0.442323i	−0.975237	+	0.221161i	$0.929015\pi$
$200$	−2.31806e18	−	4.24474e17i	−0.905493	−	0.165810i
$201$	1.27393e18			0.478165
$202$	−5.29778e17	+	8.01655e17i	−0.191110	+	0.289185i
$203$			3.37911e18i			1.17175i
$204$	1.40458e18	−	5.98587e17i	0.468280	−	0.199566i
$205$	6.96945e17			0.223443
$206$	1.46302e18	+	9.66842e17i	0.451140	+	0.298138i
$207$			2.56819e17i			0.0761842i
$208$	−8.50318e16	+	8.85597e16i	−0.0242703	+	0.0252772i
$209$	6.25298e18			1.71758
$210$	4.32767e17	−	6.54859e17i	0.114419	−	0.173138i
$211$			7.95688e17i			0.202527i	0.994860	+	0.101264i	$0.0322885\pi$
$211$			7.95688e17i			0.202527i	−0.994860	+	0.101264i	$0.967711\pi$
$212$	2.67217e18	+	6.27022e18i	0.654902	+	1.53673i
$213$	−1.04747e18			−0.247233
$214$	−4.38592e18	−	2.89846e18i	−0.997127	−	0.658957i
$215$			1.30612e18i			0.286073i
$216$	−1.64253e17	+	8.96987e17i	−0.0346643	+	0.189302i
$217$	4.19461e18			0.853128
$218$	−3.00567e18	+	4.54816e18i	−0.589237	+	0.891628i
$219$		−	3.70955e18i		−	0.701081i
$220$	1.85648e18	−	7.91172e17i	0.338305	−	0.144175i
$221$	−1.75808e17			−0.0308959
$222$	−5.30494e18	−	3.50580e18i	−0.899200	−	0.594241i
$223$		−	3.63400e18i		−	0.594219i	−0.954843	−	0.297109i	$-0.903977\pi$
$223$		−	3.63400e18i		−	0.594219i	0.954843	−	0.297109i	$-0.0960226\pi$
$224$	−7.88515e18	+	1.77776e18i	−1.24402	+	0.280472i
$225$	2.01551e18			0.306850
$226$	4.23516e18	−	6.40861e18i	0.622304	−	0.941664i
$227$		−	4.77166e18i		−	0.676803i	−0.941002	−	0.338402i	$-0.890114\pi$
$227$		−	4.77166e18i		−	0.676803i	0.941002	−	0.338402i	$-0.109886\pi$
$228$	2.17610e18	+	5.10620e18i	0.297989	+	0.699229i
$229$	2.84610e18			0.376328			0.188164	−	0.982138i	$-0.439746\pi$
$229$	2.84610e18			0.376328			0.188164	+	0.982138i	$0.439746\pi$
$230$	4.20892e17	+	2.78149e17i	0.0537462	+	0.0355185i
$231$		−	7.78799e18i		−	0.960571i
$232$	−7.58550e18	−	1.38903e18i	−0.903817	−	0.165503i
$233$	−1.39954e19			−1.61115			−0.805577	−	0.592491i	$-0.798145\pi$
$233$	−1.39954e19			−1.61115			−0.805577	+	0.592491i	$0.798145\pi$
$234$	5.78923e16	−	8.76021e16i	0.00644012	−	0.00974513i
$235$			3.03387e18i			0.326177i
$236$	−9.10668e18	+	3.88097e18i	−0.946377	+	0.403315i
$237$	−2.16598e18			−0.217604
$238$	−9.65662e18	−	6.38163e18i	−0.938015	−	0.619892i
$239$		−	2.01239e18i		−	0.189029i	−0.995523	−	0.0945145i	$-0.969870\pi$
$239$		−	2.01239e18i		−	0.189029i	0.995523	−	0.0945145i	$-0.0301299\pi$
$240$	1.29215e18	+	1.24067e18i	0.117387	+	0.112711i
$241$	1.58633e19			1.39398			0.696991	−	0.717079i	$-0.254522\pi$
$241$	1.58633e19			1.39398			0.696991	+	0.717079i	$0.254522\pi$
$242$	4.55373e18	−	6.89067e18i	0.387119	−	0.585785i
$243$		−	7.79915e17i		−	0.0641500i
$244$	5.43183e18	+	1.27458e19i	0.432342	+	1.01449i
$245$	−2.29149e18			−0.176518
$246$	5.12095e18	+	3.38421e18i	0.381830	+	0.252334i
$247$		−	6.39132e17i		−	0.0461334i
$248$	−1.72425e18	+	9.41615e18i	−0.120500	+	0.658052i
$249$	−1.48189e19			−1.00281
$250$	4.55422e18	−	6.89140e18i	0.298465	−	0.451635i
$251$			1.07748e18i			0.0683941i	0.999415	+	0.0341971i	$0.0108874\pi$
$251$			1.07748e18i			0.0683941i	−0.999415	+	0.0341971i	$0.989113\pi$
$252$	6.35970e18	−	2.71030e18i	0.391050	−	0.166653i
$253$	5.00551e18			0.298184
$254$	2.20569e19	+	1.45764e19i	1.27314	+	0.841360i
$255$			2.56517e18i			0.143481i
$256$	−7.49470e17	−	1.84315e19i	−0.0406288	−	0.999174i
$257$	1.13768e19			0.597800			0.298900	−	0.954284i	$-0.403380\pi$
$257$	1.13768e19			0.597800			0.298900	+	0.954284i	$0.403380\pi$
$258$	−6.34225e18	+	9.59703e18i	−0.323062	+	0.488854i
$259$			4.82053e19i			2.38066i
$260$	−8.08676e16	−	1.89755e17i	−0.00387247	−	0.00908672i
$261$	6.59546e18			0.306282
$262$	−2.29492e19	−	1.51661e19i	−1.03361	−	0.683067i
$263$			5.57230e18i			0.243438i	0.992565	+	0.121719i	$0.0388407\pi$
$263$			5.57230e18i			0.243438i	−0.992565	+	0.121719i	$0.961159\pi$
$264$	1.74826e19	+	3.20135e18i	0.740927	+	0.135676i
$265$	−1.14512e19			−0.470852
$266$	2.31997e19	−	3.51056e19i	0.925613	−	1.40063i
$267$		−	8.63618e18i		−	0.334373i
$268$	2.02758e19	−	8.64089e18i	0.761903	−	0.324698i
$269$	−6.52002e18			−0.237810			−0.118905	−	0.992906i	$-0.537938\pi$
$269$	−6.52002e18			−0.237810			−0.118905	+	0.992906i	$0.537938\pi$
$270$	−1.27817e18	−	8.44689e17i	−0.0452564	−	0.0299079i
$271$			8.53618e18i			0.293433i	0.989179	+	0.146717i	$0.0468706\pi$
$271$			8.53618e18i			0.293433i	−0.989179	+	0.146717i	$0.953129\pi$
$272$	1.82951e19	−	1.90541e19i	0.610637	−	0.635972i
$273$	−7.96030e17			−0.0258005
$274$	−1.41232e19	+	2.13710e19i	−0.444557	+	0.672700i
$275$		−	3.92832e19i		−	1.20101i
$276$	1.74197e18	+	4.08751e18i	0.0517329	+	0.121391i
$277$	−3.90185e19			−1.12573			−0.562863	−	0.826551i	$-0.690300\pi$
$277$	−3.90185e19			−1.12573			−0.562863	+	0.826551i	$0.690300\pi$
$278$	2.81788e19	+	1.86221e19i	0.789884	+	0.521999i
$279$		−	8.18718e18i		−	0.222998i
$280$	2.44608e18	−	1.33581e19i	0.0647450	−	0.353574i
$281$	−2.75149e19			−0.707812			−0.353906	−	0.935281i	$-0.615147\pi$
$281$	−2.75149e19			−0.707812			−0.353906	+	0.935281i	$0.615147\pi$
$282$	−1.47318e19	+	2.22920e19i	−0.368351	+	0.557386i
$283$			4.31246e19i			1.04817i	0.851665	+	0.524087i	$0.175593\pi$
$283$			4.31246e19i			1.04817i	−0.851665	+	0.524087i	$0.824407\pi$
$284$	−1.66715e19	+	7.10485e18i	−0.393938	+	0.167884i
$285$	−9.32538e18			−0.214243
$286$	−1.70740e18	−	1.12834e18i	−0.0381423	−	0.0252066i
$287$		−	4.65334e19i		−	1.01090i
$288$	3.46989e18	+	1.53905e19i	0.0733122	+	0.325171i
$289$	−1.08350e19			−0.222662
$290$	7.14323e18	−	1.08091e19i	0.142794	−	0.216075i
$291$			4.20653e19i			0.818051i
$292$	−2.51613e19	−	5.90409e19i	−0.476070	−	1.11710i
$293$	3.11400e19			0.573294			0.286647	−	0.958036i	$-0.407459\pi$
$293$	3.11400e19			0.573294			0.286647	+	0.958036i	$0.407459\pi$
$294$	−1.68372e19	−	1.11270e19i	−0.301642	−	0.199342i
$295$		−	1.66314e19i		−	0.289970i
$296$	−1.08212e20	−	1.98154e19i	−1.83630	−	0.336255i
$297$	−1.52008e19			−0.251082
$298$	−4.77865e19	+	7.23101e19i	−0.768379	+	1.16270i
$299$		−	5.11625e17i		−	0.00800908i
$300$	3.20788e19	−	1.36709e19i	0.488931	−	0.208367i
$301$	8.72071e19			1.29425
$302$	6.23034e19	+	4.11736e19i	0.900444	+	0.595063i
$303$		−	1.42182e19i		−	0.200126i
$304$	6.92692e19	+	6.65098e19i	0.949624	+	0.911794i
$305$	−2.32774e19			−0.310839
$306$	−1.24559e19	+	1.88481e19i	−0.162033	+	0.245186i
$307$		−	7.14723e19i		−	0.905796i	−0.891562	−	0.452898i	$-0.850390\pi$
$307$		−	7.14723e19i		−	0.905796i	0.891562	−	0.452898i	$-0.149610\pi$
$308$	−5.28248e19	−	1.23953e20i	−0.652277	−	1.53056i
$309$	−2.59481e19			−0.312204
$310$	−1.34177e19	−	8.86714e18i	−0.157320	−	0.103966i
$311$			2.35492e19i			0.269087i	0.990908	+	0.134544i	$0.0429569\pi$
$311$			2.35492e19i			0.269087i	−0.990908	+	0.134544i	$0.957043\pi$
$312$	3.27218e17	−	1.78694e18i	0.00364418	−	0.0199010i
$313$	1.02937e20			1.11742			0.558711	−	0.829362i	$-0.311296\pi$
$313$	1.02937e20			1.11742			0.558711	+	0.829362i	$0.311296\pi$
$314$	−6.51807e19	+	9.86308e19i	−0.689734	+	1.04370i
$315$			1.16146e19i			0.119818i
$316$	−3.44736e19	+	1.46915e19i	−0.346729	+	0.147764i
$317$	6.09640e19			0.597860			0.298930	−	0.954275i	$-0.403370\pi$
$317$	6.09640e19			0.597860			0.298930	+	0.954275i	$0.403370\pi$
$318$	−8.41402e19	−	5.56045e19i	−0.804612	−	0.531732i
$319$		−	1.28548e20i		−	1.19878i
$320$	2.89810e19	+	1.09820e19i	0.263581	+	0.0998808i
$321$	7.77889e19			0.690045
$322$	1.85714e19	−	2.81020e19i	0.160693	−	0.243159i
$323$			1.37513e20i			1.16071i
$324$	−5.29004e18	−	1.24131e19i	−0.0435611	−	0.102216i
$325$	−4.01523e18			−0.0322584
$326$	1.48854e20	+	9.83709e19i	1.16686	+	0.771127i
$327$		−	8.06664e19i		−	0.617036i
$328$	1.04459e20	+	1.91282e19i	0.779751	+	0.142785i
$329$	2.02564e20			1.47569
$330$	−1.64633e19	+	2.49121e19i	−0.117059	+	0.177133i
$331$		−	1.80799e19i		−	0.125479i	−0.998030	−	0.0627397i	$-0.980016\pi$
$331$		−	1.80799e19i		−	0.125479i	0.998030	−	0.0627397i	$-0.0199838\pi$
$332$	−2.35856e20	+	1.00514e20i	−1.59787	+	0.680962i
$333$	9.40886e19			0.622276
$334$	1.20577e20	+	7.96841e19i	0.778563	+	0.514517i
$335$			3.70294e19i			0.233447i
$336$	8.28369e19	−	8.62738e19i	0.509929	−	0.531086i
$337$	−2.71714e20			−1.63332			−0.816662	−	0.577116i	$-0.804178\pi$
$337$	−2.71714e20			−1.63332			−0.816662	+	0.577116i	$0.804178\pi$
$338$	9.38035e19	−	1.41942e20i	0.550662	−	0.833257i
$339$			1.13663e20i			0.651663i
$340$	1.73991e19	+	4.08270e19i	0.0974308	+	0.228621i
$341$	−1.59571e20			−0.872810
$342$	−6.85202e19	−	4.52819e19i	−0.366108	−	0.241945i
$343$		−	9.13144e19i		−	0.476635i
$344$	−3.58476e19	+	1.95764e20i	−0.182807	+	0.998310i
$345$	−7.46496e18			−0.0371942
$346$	−9.73880e19	+	1.47367e20i	−0.474129	+	0.717448i
$347$			1.49773e20i			0.712523i	0.934386	+	0.356262i	$0.115949\pi$
$347$			1.49773e20i			0.712523i	−0.934386	+	0.356262i	$0.884051\pi$
$348$	1.04973e20	−	4.47360e19i	0.488026	−	0.207981i
$349$	−2.05223e20			−0.932446			−0.466223	−	0.884667i	$-0.654385\pi$
$349$	−2.05223e20			−0.932446			−0.466223	+	0.884667i	$0.654385\pi$
$350$	−2.20544e20	−	1.45748e20i	−0.979381	−	0.647229i
$351$			1.55372e18i			0.00674395i
$352$	2.99967e20	−	6.76296e19i	1.27272	−	0.286943i
$353$	−3.30812e20			−1.37209			−0.686047	−	0.727558i	$-0.740655\pi$
$353$	−3.30812e20			−1.37209			−0.686047	+	0.727558i	$0.740655\pi$
$354$	8.07583e19	−	1.22203e20i	0.327462	−	0.495513i
$355$		−	3.04469e19i		−	0.120702i
$356$	−5.85779e19	−	1.37453e20i	−0.227057	−	0.532787i
$357$	1.71270e20			0.649137
$358$	−3.08673e20	−	2.03988e20i	−1.14402	−	0.756034i
$359$		−	6.19789e19i		−	0.224641i	−0.993672	−	0.112320i	$-0.964172\pi$
$359$		−	6.19789e19i		−	0.224641i	0.993672	−	0.112320i	$-0.0358283\pi$
$360$	−2.60727e19	−	4.77433e18i	−0.0924201	−	0.0169236i
$361$	−2.11472e20			−0.733154
$362$	3.17673e20	−	4.80699e20i	1.07724	−	1.63006i
$363$			1.22213e20i			0.405383i
$364$	−1.26695e19	+	5.39935e18i	−0.0411102	+	0.0175198i
$365$	1.07825e20			0.342278
$366$	−1.71036e20	−	1.13030e20i	−0.531175	−	0.351030i
$367$		−	5.58418e20i		−	1.69680i	−0.529356	−	0.848400i	$-0.677566\pi$
$367$		−	5.58418e20i		−	1.69680i	0.529356	−	0.848400i	$-0.322434\pi$
$368$	5.54500e19	+	5.32411e19i	0.164861	+	0.158294i
$369$	−9.08255e19			−0.264239
$370$	1.01903e20	−	1.54199e20i	0.290117	−	0.439002i
$371$			7.64572e20i			2.13023i
$372$	−5.55324e19	−	1.30306e20i	−0.151427	−	0.355322i
$373$	−2.83522e19			−0.0756686			−0.0378343	−	0.999284i	$-0.512046\pi$
$373$	−2.83522e19			−0.0756686			−0.0378343	+	0.999284i	$0.512046\pi$
$374$	3.67357e20	+	2.42770e20i	0.959656	+	0.634194i
$375$			1.22226e20i			0.312546i
$376$	−8.32667e19	+	4.54721e20i	−0.208434	+	1.13826i
$377$	−1.31392e19			−0.0321987
$378$	−5.63980e19	+	8.53409e19i	−0.135310	+	0.204749i
$379$			5.05580e20i			1.18762i	0.804607	+	0.593808i	$0.202376\pi$
$379$			5.05580e20i			1.18762i	−0.804607	+	0.593808i	$0.797624\pi$
$380$	−1.48422e20	+	6.32526e19i	−0.341373	+	0.145482i
$381$	−3.91203e20			−0.881053
$382$	4.61405e20	+	3.04922e20i	1.01759	+	0.672483i
$383$		−	5.91288e20i		−	1.27705i	−0.769600	−	0.638527i	$-0.779544\pi$
$383$		−	5.91288e20i		−	1.27705i	0.769600	−	0.638527i	$-0.220456\pi$
$384$	1.59618e20	+	2.21418e20i	0.337623	+	0.468342i
$385$	2.26374e20			0.468964
$386$	3.61278e19	−	5.46682e19i	0.0733065	−	0.110927i
$387$		−	1.70213e20i		−	0.338303i
$388$	2.85323e20	+	6.69509e20i	0.555498	+	1.30347i
$389$	4.65626e20			0.888055			0.444028	−	0.896013i	$-0.353549\pi$
$389$	4.65626e20			0.888055			0.444028	+	0.896013i	$0.353549\pi$
$390$	2.54633e18	+	1.68276e18i	0.00475771	+	0.00314416i
$391$			1.10079e20i			0.201507i
$392$	−3.43453e20	−	6.28917e19i	−0.615996	−	0.112799i
$393$	4.07028e20			0.715293
$394$	3.14401e20	−	4.75749e20i	0.541395	−	0.819234i
$395$		−	6.29585e19i		−	0.106238i
$396$	−2.41936e20	+	1.03105e20i	−0.400072	+	0.170498i
$397$	4.60498e19			0.0746283			0.0373141	−	0.999304i	$-0.488120\pi$
$397$	4.60498e19			0.0746283			0.0373141	+	0.999304i	$0.488120\pi$
$398$	−2.32336e20	−	1.53540e20i	−0.369021	−	0.243870i
$399$			6.22635e20i			0.969282i
$400$	4.17835e20	−	4.35171e20i	0.637566	−	0.664018i
$401$	7.79341e20			1.16566			0.582831	−	0.812594i	$-0.301945\pi$
$401$	7.79341e20			1.16566			0.582831	+	0.812594i	$0.301945\pi$
$402$	−1.79806e20	+	2.72081e20i	−0.263631	+	0.398924i
$403$			1.63102e19i			0.0234433i
$404$	−9.64399e19	−	2.26296e20i	−0.135896	−	0.318879i
$405$	2.26698e19			0.0313189
$406$	−7.21697e20	−	4.76938e20i	−0.977568	−	0.646031i
$407$		−	1.83383e21i		−	2.43558i
$408$	−7.04028e19	+	3.84471e20i	−0.0916872	+	0.500706i
$409$	9.36081e20			1.19544			0.597719	−	0.801706i	$-0.296074\pi$
$409$	9.36081e20			1.19544			0.597719	+	0.801706i	$0.296074\pi$
$410$	−9.83687e19	+	1.48851e20i	−0.123193	+	0.186415i
$411$		−	3.79038e20i		−	0.465531i
$412$	−4.12988e20	+	1.76002e20i	−0.497462	+	0.212002i
$413$	−1.11044e21			−1.31188
$414$	−5.48504e19	−	3.62482e19i	−0.0635590	−	0.0420033i
$415$		−	4.30740e20i		−	0.489588i
$416$	−6.91259e18	−	3.06603e19i	−0.00770716	−	0.0341846i
$417$	−4.99780e20			−0.546626
$418$	−8.82563e20	+	1.33549e21i	−0.946969	+	1.43294i
$419$			5.47838e20i			0.576687i	0.957527	+	0.288343i	$0.0931045\pi$
$419$			5.47838e20i			0.576687i	−0.957527	+	0.288343i	$0.906896\pi$
$420$	7.87802e19	+	1.84857e20i	0.0813622	+	0.190916i
$421$	2.48756e19			0.0252067			0.0126034	−	0.999921i	$-0.495988\pi$
$421$	2.48756e19			0.0252067			0.0126034	+	0.999921i	$0.495988\pi$
$422$	−1.69940e20	−	1.12306e20i	−0.168964	−	0.111661i
$423$		−	3.95372e20i		−	0.385729i
$424$	−1.71633e21	−	3.14287e20i	−1.64313	−	0.300884i
$425$	8.63900e20			0.811618
$426$	1.47843e20	−	2.23715e20i	0.136309	−	0.206262i
$427$			1.55418e21i			1.40630i
$428$	1.23808e21	−	5.27631e20i	1.09951	−	0.468576i
$429$	3.02825e19			0.0263957
$430$	−2.78957e20	−	1.84350e20i	−0.238665	−	0.157723i
$431$		−	1.31218e20i		−	0.110199i	−0.998481	−	0.0550993i	$-0.982452\pi$
$431$		−	1.31218e20i		−	0.110199i	0.998481	−	0.0550993i	$-0.0175475\pi$
$432$	−1.68392e20	−	1.61684e20i	−0.138820	−	0.133290i
$433$	−4.09964e20			−0.331774			−0.165887	−	0.986145i	$-0.553049\pi$
$433$	−4.09964e20			−0.331774			−0.165887	+	0.986145i	$0.553049\pi$
$434$	−5.92040e20	+	8.95868e20i	−0.470363	+	0.711748i
$435$			1.91710e20i			0.149531i
$436$	−5.47148e20	−	1.28388e21i	−0.418999	−	0.983179i
$437$	−4.00181e20			−0.300888
$438$	7.92271e20	+	5.23576e20i	0.584899	+	0.386534i
$439$		−	2.96657e20i		−	0.215050i	−0.994202	−	0.107525i	$-0.965707\pi$
$439$		−	2.96657e20i		−	0.215050i	0.994202	−	0.107525i	$-0.0342925\pi$
$440$	−9.30537e19	+	5.08168e20i	−0.0662388	+	0.361731i
$441$	2.98626e20			0.208746
$442$	2.48141e19	−	3.75485e19i	0.0170341	−	0.0257759i
$443$		−	4.71887e20i		−	0.318133i	−0.987268	−	0.159066i	$-0.949152\pi$
$443$		−	4.71887e20i		−	0.318133i	0.987268	−	0.159066i	$-0.0508484\pi$
$444$	1.49751e21	−	6.38189e20i	0.991529	−	0.422557i
$445$	2.51028e20			0.163246
$446$	7.76136e20	+	5.12913e20i	0.495745	+	0.327616i
$447$		−	1.28250e21i		−	0.804630i
$448$	7.33245e20	−	1.93500e21i	0.451882	−	1.19249i
$449$	−1.42617e21			−0.863376			−0.431688	−	0.902023i	$-0.642082\pi$
$449$	−1.42617e21			−0.863376			−0.431688	+	0.902023i	$0.642082\pi$
$450$	−2.84475e20	+	4.30465e20i	−0.169178	+	0.255999i
$451$			1.77022e21i			1.03423i
$452$	7.70961e20	+	1.80906e21i	0.442512	+	1.03835i
$453$	−1.10502e21			−0.623137
$454$	1.01911e21	+	6.73485e20i	0.564644	+	0.373148i
$455$		−	2.31382e19i		−	0.0125962i
$456$	−1.39770e21	−	2.55942e20i	−0.747646	−	0.136906i
$457$	−7.28273e20			−0.382794			−0.191397	−	0.981513i	$-0.561302\pi$
$457$	−7.28273e20			−0.382794			−0.191397	+	0.981513i	$0.561302\pi$
$458$	−4.01707e20	+	6.07859e20i	−0.207485	+	0.313964i
$459$		−	3.34291e20i		−	0.169677i
$460$	−1.18812e20	+	5.06337e19i	−0.0592648	+	0.0252567i
$461$	9.05808e20			0.444047			0.222023	−	0.975041i	$-0.428734\pi$
$461$	9.05808e20			0.444047			0.222023	+	0.975041i	$0.428734\pi$
$462$	1.66333e21	+	1.09922e21i	0.801387	+	0.529601i
$463$		−	3.89319e20i		−	0.184356i	−0.995743	−	0.0921780i	$-0.970617\pi$
$463$		−	3.89319e20i		−	0.184356i	0.995743	−	0.0921780i	$-0.0293829\pi$
$464$	1.36730e21	−	1.42403e21i	0.636386	−	0.662789i
$465$	2.37977e20			0.108871
$466$	1.97535e21	−	2.98908e21i	0.888292	−	1.34416i
$467$			3.35721e21i			1.48403i	0.670382	+	0.742016i	$0.266130\pi$
$467$			3.35721e21i			1.48403i	−0.670382	+	0.742016i	$0.733870\pi$
$468$	1.05386e19	+	2.47288e19i	0.00457949	+	0.0107457i
$469$	2.47237e21			1.05616
$470$	−6.47961e20	−	4.28208e20i	−0.272123	−	0.179834i
$471$		−	1.74932e21i		−	0.722274i
$472$	4.56461e20	−	2.49274e21i	0.185297	−	1.01191i
$473$	−3.31753e21			−1.32411
$474$	3.05713e20	−	4.62601e20i	0.119974	−	0.181543i
$475$			3.14061e21i			1.21190i
$476$	2.72593e21	−	1.16170e21i	1.03433	−	0.440797i
$477$	1.49232e21			0.556818
$478$	4.29798e20	+	2.84034e20i	0.157703	+	0.104219i
$479$			7.80169e20i			0.281517i	0.990044	+	0.140758i	$0.0449541\pi$
$479$			7.80169e20i			0.281517i	−0.990044	+	0.140758i	$0.955046\pi$
$480$	−4.47355e20	+	1.00859e20i	−0.158753	+	0.0357920i
$481$	−1.87440e20			−0.0654186
$482$	−2.23899e21	+	3.38802e21i	−0.768557	+	1.16297i
$483$			4.98419e20i			0.168274i
$484$	8.28954e20	+	1.94514e21i	0.275275	+	0.645933i
$485$	−1.22271e21			−0.399384
$486$	1.66571e20	+	1.10079e20i	0.0535192	+	0.0353684i
$487$			1.66474e21i			0.526157i	0.964774	+	0.263079i	$0.0847378\pi$
$487$			1.66474e21i			0.526157i	−0.964774	+	0.263079i	$0.915262\pi$
$488$	−3.48885e21	−	6.38865e20i	−1.08474	−	0.198633i
$489$	−2.64008e21			−0.807507
$490$	3.23428e20	−	4.89408e20i	0.0973214	−	0.147266i
$491$			3.23727e20i			0.0958358i	0.998851	+	0.0479179i	$0.0152586\pi$
$491$			3.23727e20i			0.0958358i	−0.998851	+	0.0479179i	$0.984741\pi$
$492$	−1.44557e21	+	6.16055e20i	−0.421035	+	0.179432i
$493$	2.82698e21			0.810116
$494$	1.36503e20	+	9.02089e19i	0.0384882	+	0.0254351i
$495$		−	4.41843e20i		−	0.122582i
$496$	−1.76770e21	−	1.69728e21i	−0.482564	−	0.463340i
$497$	−2.03287e21			−0.546083
$498$	2.09158e21	−	3.16496e21i	0.552891	−	0.836629i
$499$		−	5.40011e21i		−	1.40475i	−0.711808	−	0.702374i	$-0.752123\pi$
$499$		−	5.40011e21i		−	1.40475i	0.711808	−	0.702374i	$-0.247877\pi$
$500$	8.29042e20	+	1.94534e21i	0.212235	+	0.498008i
$501$	−2.13856e21			−0.538791
$502$	−2.30123e20	−	1.52078e20i	−0.0570599	−	0.0377083i
$503$		−	3.40969e21i		−	0.832092i	−0.909344	−	0.416046i	$-0.863415\pi$
$503$		−	3.40969e21i		−	0.832092i	0.909344	−	0.416046i	$-0.136585\pi$
$504$	−3.18772e20	+	1.74082e21i	−0.0765659	+	0.418128i
$505$	4.13280e20			0.0977043
$506$	−7.06492e20	+	1.06906e21i	−0.164400	+	0.248769i
$507$			2.51750e21i			0.576641i
$508$	−6.22635e21	+	2.65347e21i	−1.40386	+	0.598280i
$509$	2.83699e21			0.629675			0.314837	−	0.949146i	$-0.398050\pi$
$509$	2.83699e21			0.629675			0.314837	+	0.949146i	$0.398050\pi$
$510$	−5.47858e20	−	3.62055e20i	−0.119703	−	0.0791066i
$511$		−	7.19927e21i		−	1.54854i
$512$	4.04231e21	+	2.44141e21i	0.855993	+	0.516988i
$513$	1.21528e21			0.253359
$514$	−1.60576e21	+	2.42982e21i	−0.329591	+	0.498734i
$515$		−	7.54234e20i		−	0.152422i
$516$	−1.15453e21	−	2.70910e21i	−0.229725	−	0.539049i
$517$	−7.70595e21			−1.50974
$518$	−1.02955e22	−	6.80383e21i	−1.98614	−	1.31255i
$519$		−	2.61370e21i		−	0.496498i
$520$	5.19411e19	+	9.51124e18i	0.00971593	+	0.00177914i
$521$	9.01627e21			1.66083			0.830414	−	0.557146i	$-0.188104\pi$
$521$	9.01627e21			1.66083			0.830414	+	0.557146i	$0.188104\pi$
$522$	−9.30902e20	+	1.40863e21i	−0.168865	+	0.255525i
$523$			5.18747e21i			0.926705i	0.886174	+	0.463353i	$0.153354\pi$
$523$			5.18747e21i			0.926705i	−0.886174	+	0.463353i	$0.846646\pi$
$524$	6.47823e21	−	2.76081e21i	1.13974	−	0.485720i
$525$	3.91159e21			0.677764
$526$	−1.19011e21	−	7.86490e20i	−0.203096	−	0.134217i
$527$		−	3.50923e21i		−	0.589830i
$528$	−3.15128e21	+	3.28202e21i	−0.521694	+	0.543338i
$529$	5.81227e21			0.947764
$530$	1.61626e21	−	2.44570e21i	0.259599	−	0.392823i
$531$			2.16739e21i			0.342911i
$532$	4.22324e21	+	9.90981e21i	0.658192	+	1.54444i
$533$	1.80939e20			0.0277789
$534$	1.84448e21	+	1.21894e21i	0.278961	+	0.184353i
$535$			2.26109e21i			0.336890i
$536$	−1.01630e21	+	5.55003e21i	−0.149177	+	0.814661i
$537$	5.47464e21			0.791702
$538$	9.20253e20	−	1.39252e21i	0.131114	−	0.198401i
$539$		−	5.82034e21i		−	0.817030i
$540$	3.60810e20	−	1.53766e20i	0.0499033	−	0.0212671i
$541$	−4.52952e21			−0.617268			−0.308634	−	0.951181i	$-0.599872\pi$
$541$	−4.52952e21			−0.617268			−0.308634	+	0.951181i	$0.599872\pi$
$542$	−1.82312e21	−	1.20482e21i	−0.244806	−	0.161781i
$543$			8.52571e21i			1.12806i
$544$	1.48728e21	+	6.59675e21i	0.193911	+	0.860079i
$545$	2.34473e21			0.301246
$546$	1.12354e20	−	1.70013e20i	0.0142248	−	0.0215249i
$547$		−	4.00816e21i		−	0.500088i	−0.968235	−	0.250044i	$-0.919555\pi$
$547$		−	4.00816e21i		−	0.500088i	0.968235	−	0.250044i	$-0.0804450\pi$
$548$	−2.57096e21	−	6.03274e21i	−0.316119	−	0.741771i
$549$	3.03350e21			0.367591
$550$	8.38994e21	+	5.54454e21i	1.00198	+	0.662161i
$551$			1.02772e22i			1.20965i
$552$	−1.11886e21	−	2.04881e20i	−0.129797	−	0.0237678i
$553$	−4.20360e21			−0.480641
$554$	5.50718e21	−	8.33341e21i	0.620656	−	0.939171i
$555$			2.73487e21i			0.303804i
$556$	−7.95446e21	+	3.38993e21i	−0.870988	+	0.371187i
$557$	1.66572e22			1.79788			0.898939	−	0.438074i	$-0.144339\pi$
$557$	1.66572e22			1.79788			0.898939	+	0.438074i	$0.144339\pi$
$558$	1.74858e21	+	1.15556e21i	0.186043	+	0.122947i
$559$			3.39093e20i			0.0355651i
$560$	2.50772e21	+	2.40782e21i	0.259283	+	0.248955i
$561$	−6.51546e21			−0.664114
$562$	3.88353e21	−	5.87653e21i	0.390244	−	0.590514i
$563$		−	6.10315e20i		−	0.0604626i	−0.999543	−	0.0302313i	$-0.990376\pi$
$563$		−	6.10315e20i		−	0.0604626i	0.999543	−	0.0302313i	$-0.00962440\pi$
$564$	−2.68175e21	−	6.29271e21i	−0.261930	−	0.614617i
$565$	−3.30385e21			−0.318151
$566$	−9.21037e21	−	6.08673e21i	−0.874472	−	0.577899i
$567$		−	1.51361e21i		−	0.141693i
$568$	8.35637e20	−	4.56343e21i	0.0771314	−	0.421216i
$569$	−8.43853e21			−0.768013			−0.384006	−	0.923330i	$-0.625456\pi$
$569$	−8.43853e21			−0.768013			−0.384006	+	0.923330i	$0.625456\pi$
$570$	1.31621e21	−	1.99168e21i	0.118121	−	0.178739i
$571$		−	3.98249e21i		−	0.352424i	−0.984352	−	0.176212i	$-0.943616\pi$
$571$		−	3.98249e21i		−	0.352424i	0.984352	−	0.176212i	$-0.0563844\pi$
$572$	4.81975e20	−	2.05402e20i	0.0420587	−	0.0179241i
$573$	−8.18350e21			−0.704209
$574$	9.93843e21	+	6.56786e21i	0.843378	+	0.557351i
$575$			2.51406e21i			0.210394i
$576$	−3.77679e21	−	1.43117e21i	−0.311704	−	0.118117i
$577$	−1.92335e22			−1.56549			−0.782747	−	0.622340i	$-0.786182\pi$
$577$	−1.92335e22			−1.56549			−0.782747	+	0.622340i	$0.786182\pi$
$578$	1.52928e21	−	2.31409e21i	0.122762	−	0.185763i
$579$			9.69598e20i			0.0767650i
$580$	1.30034e21	+	3.05124e21i	0.101539	+	0.238261i
$581$	−2.87596e22			−2.21500
$582$	−8.98415e21	−	5.93722e21i	−0.682485	−	0.451024i
$583$		−	2.90858e22i		−	2.17938i
$584$	1.61611e22	+	2.95935e21i	1.19445	+	0.218722i
$585$	−4.51618e19			−0.00329249
$586$	−4.39518e21	+	6.65075e21i	−0.316079	+	0.478288i
$587$			3.06758e21i			0.217616i	0.994063	+	0.108808i	$0.0347034\pi$
$587$			3.06758e21i			0.217616i	−0.994063	+	0.108808i	$0.965297\pi$
$588$	4.75291e21	−	2.02553e21i	0.332614	−	0.141749i
$589$	1.27574e22			0.880725
$590$	3.55206e21	+	2.34740e21i	0.241916	+	0.159872i
$591$			8.43791e21i			0.566937i
$592$	1.95055e22	−	2.03147e22i	1.29295	−	1.34660i
$593$	−6.91134e21			−0.451986			−0.225993	−	0.974129i	$-0.572563\pi$
$593$	−6.91134e21			−0.451986			−0.225993	+	0.974129i	$0.572563\pi$
$594$	2.14549e21	−	3.24654e21i	0.138432	−	0.209473i
$595$			4.97832e21i			0.316918i
$596$	−8.69898e21	−	2.04121e22i	−0.546384	−	1.28209i
$597$	4.12072e21			0.255375
$598$	1.09271e20	+	7.22122e19i	0.00668182	+	0.00441572i
$599$			2.74806e22i			1.65811i	0.559170	+	0.829053i	$0.311120\pi$
$599$			2.74806e22i			1.65811i	−0.559170	+	0.829053i	$0.688880\pi$
$600$	−1.60791e21	+	8.78081e21i	−0.0957306	+	0.522787i
$601$	8.42505e21			0.494968			0.247484	−	0.968892i	$-0.420396\pi$
$601$	8.42505e21			0.494968			0.247484	+	0.968892i	$0.420396\pi$
$602$	−1.23087e22	+	1.86253e22i	−0.713573	+	1.07977i
$603$		−	4.82565e21i		−	0.276069i
$604$	−1.75874e22	+	7.49517e21i	−0.992900	+	0.423142i
$605$	−3.55237e21			−0.197914
$606$	3.03666e21	+	2.00680e21i	0.166961	+	0.110337i
$607$			3.45429e22i			1.87435i	0.348864	+	0.937173i	$0.386567\pi$
$607$			3.45429e22i			1.87435i	−0.348864	+	0.937173i	$0.613433\pi$
$608$	−2.39817e22	+	5.40686e21i	−1.28426	+	0.289545i
$609$	1.28001e22			0.676509
$610$	3.28544e21	−	4.97149e21i	0.171378	−	0.259327i
$611$			7.87644e20i			0.0405509i
$612$	−2.26744e21	−	5.32055e21i	−0.115219	−	0.270362i
$613$	−1.90775e22			−0.956838			−0.478419	−	0.878132i	$-0.658790\pi$
$613$	−1.90775e22			−0.956838			−0.478419	+	0.878132i	$0.658790\pi$
$614$	1.52648e22	+	1.00878e22i	0.755689	+	0.499401i
$615$		−	2.64002e21i		−	0.129005i
$616$	3.39292e22	+	6.21299e21i	1.63655	+	0.299678i
$617$	1.63854e22			0.780147			0.390074	−	0.920784i	$-0.372450\pi$
$617$	1.63854e22			0.780147			0.390074	+	0.920784i	$0.372450\pi$
$618$	3.66239e21	−	5.54190e21i	0.172130	−	0.260466i
$619$		−	2.17819e22i		−	1.01058i	−0.862950	−	0.505289i	$-0.831386\pi$
$619$		−	2.17819e22i		−	1.01058i	0.862950	−	0.505289i	$-0.168614\pi$
$620$	3.78762e21	−	1.61416e21i	0.173473	−	0.0739287i
$621$	9.72830e20			0.0439849
$622$	−5.02955e21	−	3.32380e21i	−0.224495	−	0.148358i
$623$		−	1.67606e22i		−	0.738558i
$624$	3.35464e20	+	3.22100e20i	0.0145938	+	0.0140125i
$625$	1.78805e22			0.767960
$626$	−1.45288e22	+	2.19849e22i	−0.616078	+	0.932244i
$627$		−	2.36863e22i		−	0.991645i
$628$	−1.18654e22	−	2.78421e22i	−0.490461	−	1.15086i
$629$	4.03287e22			1.64592
$630$	−2.48060e21	−	1.63932e21i	−0.0999615	−	0.0660601i
$631$			1.30689e22i			0.520001i	0.965608	+	0.260001i	$0.0837228\pi$
$631$			1.30689e22i			0.520001i	−0.965608	+	0.260001i	$0.916277\pi$
$632$	1.72794e21	−	9.43633e21i	0.0678880	−	0.370738i
$633$	3.01406e21			0.116929
$634$	−8.60463e21	+	1.30204e22i	−0.329623	+	0.498783i
$635$		−	1.13711e22i		−	0.430142i
$636$	2.37516e22	−	1.01222e22i	0.887229	−	0.378108i
$637$	−5.94911e20			−0.0219450
$638$	2.74548e22	+	1.81436e22i	1.00012	+	0.660936i
$639$			3.96782e21i			0.142740i
$640$	−6.43595e21	+	4.63961e21i	−0.228651	+	0.164832i
$641$	−6.04230e21			−0.212001			−0.106000	−	0.994366i	$-0.533805\pi$
$641$	−6.04230e21			−0.212001			−0.106000	+	0.994366i	$0.533805\pi$
$642$	−1.09794e22	+	1.66138e22i	−0.380449	+	0.575692i
$643$		−	3.09480e22i		−	1.05912i	−0.848273	−	0.529559i	$-0.822357\pi$
$643$		−	3.09480e22i		−	1.05912i	0.848273	−	0.529559i	$-0.177643\pi$
$644$	3.38070e21	+	7.93280e21i	0.114267	+	0.268126i
$645$	4.94759e21			0.165164
$646$	−2.93695e22	−	1.94090e22i	−0.968358	−	0.639945i
$647$			1.03277e22i			0.336334i	0.985758	+	0.168167i	$0.0537848\pi$
$647$			1.03277e22i			0.336334i	−0.985758	+	0.168167i	$0.946215\pi$
$648$	3.39778e21	+	6.22189e20i	0.109294	+	0.0200135i
$649$	4.22434e22			1.34215
$650$	5.66721e20	−	8.57556e20i	0.0177853	−	0.0269126i
$651$		−	1.58892e22i		−	0.492553i
$652$	−4.20193e22	+	1.79073e22i	−1.28667	+	0.548338i
$653$	−2.19915e22			−0.665195			−0.332598	−	0.943069i	$-0.607925\pi$
$653$	−2.19915e22			−0.665195			−0.332598	+	0.943069i	$0.607925\pi$
$654$	1.72284e22	+	1.13855e22i	0.514782	+	0.340196i
$655$			1.18311e22i			0.349216i
$656$	−1.88290e22	+	1.96102e22i	−0.549030	+	0.571809i
$657$	−1.40518e22			−0.404769
$658$	−2.85905e22	+	4.32629e22i	−0.813607	+	1.23114i
$659$			2.47200e22i			0.694968i	0.937686	+	0.347484i	$0.112964\pi$
$659$			2.47200e22i			0.694968i	−0.937686	+	0.347484i	$0.887036\pi$
$660$	−2.99695e21	−	7.03234e21i	−0.0832393	−	0.195321i
$661$	8.06936e21			0.221426			0.110713	−	0.993852i	$-0.464687\pi$
$661$	8.06936e21			0.221426			0.110713	+	0.993852i	$0.464687\pi$
$662$	3.86143e21	+	2.55185e21i	0.104685	+	0.0691817i
$663$			6.65961e20i			0.0178378i
$664$	1.18220e22	−	6.45601e22i	0.312857	−	1.70852i
$665$	−1.80981e22			−0.473217
$666$	−1.32799e22	+	2.00951e22i	−0.343085	+	0.519153i
$667$			8.22687e21i			0.210004i
$668$	−3.40372e22	+	1.45056e22i	−0.858504	+	0.365867i
$669$	−1.37656e22			−0.343072
$670$	−7.90859e21	−	5.22643e21i	−0.194760	−	0.128708i
$671$		−	5.91241e22i		−	1.43875i
$672$	6.73416e21	+	2.98689e22i	0.161931	+	0.718233i
$673$	−4.46308e21			−0.106051			−0.0530254	−	0.998593i	$-0.516886\pi$
$673$	−4.46308e21			−0.106051			−0.0530254	+	0.998593i	$0.516886\pi$
$674$	3.83505e22	−	5.80315e22i	0.900516	−	1.36265i
$675$		−	7.63476e21i		−	0.177160i
$676$	1.70758e22	+	4.00683e22i	0.391569	+	0.918814i
$677$	1.59735e22			0.361985			0.180993	−	0.983484i	$-0.442069\pi$
$677$	1.59735e22			0.361985			0.180993	+	0.983484i	$0.442069\pi$
$678$	−2.42758e22	−	1.60428e22i	−0.543670	−	0.359287i
$679$			8.16378e22i			1.80690i
$680$	−1.11754e22	−	2.04640e21i	−0.244451	−	0.0447630i
$681$	−1.80750e22			−0.390752
$682$	2.25224e22	−	3.40806e22i	0.481215	−	0.728169i
$683$		−	6.33415e22i		−	1.33759i	−0.743447	−	0.668794i	$-0.766811\pi$
$683$		−	6.33415e22i		−	1.33759i	0.743447	−	0.668794i	$-0.233189\pi$
$684$	1.93423e22	−	8.24305e21i	0.403700	−	0.172044i
$685$	1.10175e22			0.227278
$686$	1.95026e22	+	1.28884e22i	0.397648	+	0.262788i
$687$		−	1.07810e22i		−	0.217273i
$688$	−3.67509e22	−	3.52869e22i	−0.732083	−	0.702920i
$689$	−2.97293e21			−0.0585371
$690$	1.05363e21	−	1.59434e21i	0.0205066	−	0.0310304i
$691$		−	2.24192e22i		−	0.431317i	−0.976469	−	0.215658i	$-0.930810\pi$
$691$		−	2.24192e22i		−	0.431317i	0.976469	−	0.215658i	$-0.0691897\pi$
$692$	−1.77283e22	−	4.15995e22i	−0.337147	−	0.791114i
$693$	−2.95009e22			−0.554586
$694$	−3.19880e22	−	2.11394e22i	−0.594445	−	0.392842i
$695$		−	1.45271e22i		−	0.266870i
$696$	−5.26163e21	+	2.87338e22i	−0.0955534	+	0.521819i
$697$	−3.89301e22			−0.698913
$698$	2.89658e22	−	4.38308e22i	0.514094	−	0.777922i
$699$			5.30144e22i			0.930200i
$700$	6.22565e22	−	2.65317e22i	1.07994	−	0.460236i
$701$	−7.77211e22			−1.33289			−0.666446	−	0.745553i	$-0.732185\pi$
$701$	−7.77211e22			−1.33289			−0.666446	+	0.745553i	$0.732185\pi$
$702$	−3.31836e20	−	2.19296e20i	−0.00562635	−	0.00371821i
$703$			1.46611e23i			2.45767i
$704$	−2.78941e22	+	7.36111e22i	−0.462307	+	1.22001i
$705$	1.14923e22			0.188318
$706$	4.66918e22	−	7.06535e22i	0.756489	−	1.14471i
$707$		−	2.75938e22i		−	0.442035i
$708$	1.47011e22	+	3.44961e22i	0.232854	+	0.546391i
$709$	7.62619e22			1.19437			0.597184	−	0.802105i	$-0.296286\pi$
$709$	7.62619e22			1.19437			0.597184	+	0.802105i	$0.296286\pi$
$710$	6.50273e21	+	4.29736e21i	0.100700	+	0.0665480i
$711$			8.20472e21i			0.125634i
$712$	3.76245e22	+	6.88965e21i	0.569679	+	0.104317i
$713$	1.02123e22			0.152900
$714$	−2.41736e22	+	3.65792e22i	−0.357895	+	0.541563i
$715$			8.80222e20i			0.0128868i
$716$	8.71340e22	−	3.71337e22i	1.26149	−	0.537606i
$717$	−7.62291e21			−0.109136
$718$	1.32372e22	+	8.74788e21i	0.187414	+	0.123853i
$719$			9.14698e22i			1.28070i	0.768084	+	0.640349i	$0.221210\pi$
$719$			9.14698e22i			1.28070i	−0.768084	+	0.640349i	$0.778790\pi$
$720$	4.69966e21	−	4.89464e21i	0.0650739	−	0.0677737i
$721$	−5.03585e22			−0.689590
$722$	2.98478e22	−	4.51653e22i	0.404217	−	0.611657i
$723$		−	6.00901e22i		−	0.804816i
$724$	5.78286e22	+	1.35695e23i	0.766009	+	1.79744i
$725$	6.45644e22			0.845842
$726$	−2.61018e22	−	1.72495e22i	−0.338203	−	0.223503i
$727$		−	9.03745e22i		−	1.15817i	−0.815269	−	0.579083i	$-0.803411\pi$
$727$		−	9.03745e22i		−	1.15817i	0.815269	−	0.579083i	$-0.196589\pi$
$728$	6.35045e20	−	3.46799e21i	0.00804921	−	0.0439569i
$729$	−2.95431e21			−0.0370370
$730$	−1.52188e22	+	2.30289e22i	−0.188711	+	0.285556i
$731$		−	7.29578e22i		−	0.894813i
$732$	4.82809e22	−	2.05758e22i	0.585716	−	0.249613i
$733$	−1.71201e22			−0.205435			−0.102717	−	0.994711i	$-0.532754\pi$
$733$	−1.71201e22			−0.205435			−0.102717	+	0.994711i	$0.532754\pi$
$734$	1.19265e23	+	7.88167e22i	1.41561	+	0.935512i
$735$			8.68016e21i			0.101913i
$736$	−1.91974e22	+	4.32819e21i	−0.222956	+	0.0502671i
$737$	−9.40539e22			−1.08053
$738$	1.28194e22	−	1.93981e22i	0.145685	−	0.220449i
$739$			7.93714e22i			0.892295i	0.894959	+	0.446147i	$0.147204\pi$
$739$			7.93714e22i			0.892295i	−0.894959	+	0.446147i	$0.852796\pi$
$740$	1.85502e22	+	4.35280e22i	0.206298	+	0.484078i
$741$	−2.42103e21			−0.0266351
$742$	−1.63294e23	−	1.07914e23i	−1.77721	−	1.17448i
$743$			1.40087e23i			1.50830i	0.656704	+	0.754148i	$0.271950\pi$
$743$			1.40087e23i			1.50830i	−0.656704	+	0.754148i	$0.728050\pi$
$744$	3.56683e22	+	6.53144e21i	0.379926	+	0.0695706i
$745$	3.72783e22			0.392831
$746$	4.00171e21	−	6.05535e21i	0.0417191	−	0.0631289i
$747$			5.61338e22i			0.578975i
$748$	−1.03700e23	+	4.41934e22i	−1.05819	+	0.450967i
$749$	1.50968e23			1.52416
$750$	−2.61046e22	−	1.72514e22i	−0.260751	−	0.172319i
$751$		−	6.44435e22i		−	0.636883i	−0.947943	−	0.318441i	$-0.896841\pi$
$751$		−	6.44435e22i		−	0.636883i	0.947943	−	0.318441i	$-0.103159\pi$
$752$	−8.53649e22	−	8.19643e22i	−0.834712	−	0.801461i
$753$	4.08148e21			0.0394874
$754$	1.85451e21	−	2.80622e21i	0.0177524	−	0.0268628i
$755$		−	3.21195e22i		−	0.304224i
$756$	−1.02666e22	−	2.40905e22i	−0.0962170	−	0.225773i
$757$	−1.09180e23			−1.01246			−0.506229	−	0.862399i	$-0.668961\pi$
$757$	−1.09180e23			−1.01246			−0.506229	+	0.862399i	$0.668961\pi$
$758$	−1.07980e23	−	7.13590e22i	−0.990806	−	0.654780i
$759$		−	1.89608e22i		−	0.172156i
$760$	7.43946e21	−	4.06270e22i	0.0668394	−	0.365011i
$761$	−3.15976e22			−0.280916			−0.140458	−	0.990087i	$-0.544858\pi$
$761$	−3.15976e22			−0.280916			−0.140458	+	0.990087i	$0.544858\pi$
$762$	5.52155e22	−	8.35515e22i	0.485759	−	0.735046i
$763$		−	1.56552e23i		−	1.36290i
$764$	−1.30248e23	+	5.55074e22i	−1.12208	+	0.478194i
$765$	9.71683e21			0.0828387
$766$	1.26285e23	+	8.34561e22i	1.06542	+	0.704089i
$767$		−	4.31780e21i		−	0.0360495i
$768$	−6.98185e22	+	2.83899e21i	−0.576874	+	0.0234571i
$769$	−4.62042e22			−0.377807			−0.188904	−	0.981996i	$-0.560493\pi$
$769$	−4.62042e22			−0.377807			−0.188904	+	0.981996i	$0.560493\pi$
$770$	−3.19510e22	+	4.83479e22i	−0.258558	+	0.391248i
$771$		−	4.30954e22i		−	0.345140i
$772$	6.57664e21	+	1.54320e22i	0.0521273	+	0.122317i
$773$	−5.22077e22			−0.409542			−0.204771	−	0.978810i	$-0.565645\pi$
$773$	−5.22077e22			−0.409542			−0.204771	+	0.978810i	$0.565645\pi$
$774$	3.63535e22	+	2.40244e22i	0.282240	+	0.186520i
$775$		−	8.01461e22i		−	0.615841i
$776$	−1.83262e23	−	3.35583e22i	−1.39373	−	0.255215i
$777$	1.82601e23			1.37447
$778$	−6.57197e22	+	9.94465e22i	−0.489620	+	0.740888i
$779$		−	1.41526e23i		−	1.04361i
$780$	−7.18792e20	+	3.06326e20i	−0.00524622	+	0.00223577i
$781$	7.73345e22			0.558682
$782$	−2.35103e22	−	1.55369e22i	−0.168114	−	0.111099i
$783$		−	2.49836e22i		−	0.176832i
$784$	6.19080e22	−	6.44765e22i	0.433729	−	0.451724i
$785$	5.08475e22			0.352624
$786$	−5.74491e22	+	8.69314e22i	−0.394369	+	0.596756i
$787$		−	4.39285e22i		−	0.298503i	−0.988799	−	0.149252i	$-0.952314\pi$
$787$		−	4.39285e22i		−	0.298503i	0.988799	−	0.149252i	$-0.0476864\pi$
$788$	5.72331e22	+	1.34297e23i	0.384979	+	0.903352i
$789$	2.11078e22			0.140549
$790$	1.34464e22	+	8.88615e21i	0.0886320	+	0.0585729i
$791$			2.20591e23i			1.43938i
$792$	1.21267e22	−	6.62242e22i	0.0783324	−	0.427775i
$793$	−6.04322e21			−0.0386440
$794$	−6.49960e21	+	9.83513e21i	−0.0411455	+	0.0622610i
$795$			4.33771e22i			0.271847i
$796$	6.55851e22	−	2.79502e22i	0.406912	−	0.173413i
$797$	6.99666e22			0.429758			0.214879	−	0.976641i	$-0.431064\pi$
$797$	6.99666e22			0.429758			0.214879	+	0.976641i	$0.431064\pi$
$798$	−1.32980e23	−	8.78804e22i	−0.808654	−	0.534403i
$799$		−	1.69466e23i		−	1.02026i
$800$	3.39676e22	+	1.50661e23i	0.202463	+	0.898009i
$801$	−3.27138e22			−0.193051
$802$	−1.09998e23	+	1.66448e23i	−0.642675	+	0.972489i
$803$			2.73874e23i			1.58426i
$804$	−3.27317e22	−	7.68047e22i	−0.187465	−	0.439885i
$805$	−1.44875e22			−0.0821538
$806$	−3.48346e21	−	2.30206e21i	−0.0195583	−	0.0129252i
$807$			2.46978e22i			0.137300i
$808$	6.19431e22	+	1.13428e22i	0.340959	+	0.0624351i
$809$	7.47985e22			0.407666			0.203833	−	0.979006i	$-0.434660\pi$
$809$	7.47985e22			0.407666			0.203833	+	0.979006i	$0.434660\pi$
$810$	−3.19968e21	+	4.84172e21i	−0.0172674	+	0.0261288i
$811$			6.36111e22i			0.339912i	0.985452	+	0.169956i	$0.0543625\pi$
$811$			6.36111e22i			0.339912i	−0.985452	+	0.169956i	$0.945638\pi$
$812$	2.03725e23	−	8.68209e22i	1.07794	−	0.459384i
$813$	3.23350e22			0.169414
$814$	3.91661e23	+	2.58831e23i	2.03196	+	1.34283i
$815$		−	7.67392e22i		−	0.394236i
$816$	−7.21770e22	−	6.93017e22i	−0.367179	−	0.352552i
$817$	2.65230e23			1.33612
$818$	−1.32121e23	+	1.99924e23i	−0.659092	+	0.997331i
$819$			3.01536e21i			0.0148959i
$820$	−1.79069e22	−	4.20184e22i	−0.0876010	−	0.205555i
$821$	−1.14211e23			−0.553304			−0.276652	−	0.960970i	$-0.589225\pi$
$821$	−1.14211e23			−0.553304			−0.276652	+	0.960970i	$0.589225\pi$
$822$	8.09534e22	+	5.34985e22i	0.388383	+	0.256665i
$823$		−	2.46943e23i		−	1.17327i	−0.809852	−	0.586634i	$-0.800453\pi$
$823$		−	2.46943e23i		−	1.17327i	0.809852	−	0.586634i	$-0.199547\pi$
$824$	2.07005e22	−	1.13046e23i	0.0974010	−	0.531909i
$825$	−1.48804e23			−0.693401
$826$	1.56731e23	−	2.37163e23i	0.723292	−	1.09448i
$827$			4.05308e22i			0.185243i	0.995701	+	0.0926213i	$0.0295246\pi$
$827$			4.05308e22i			0.185243i	−0.995701	+	0.0926213i	$0.970475\pi$
$828$	1.54835e22	−	6.59856e21i	0.0700851	−	0.0298680i
$829$	−2.28590e23			−1.02476			−0.512379	−	0.858759i	$-0.671236\pi$
$829$	−2.28590e23			−1.02476			−0.512379	+	0.858759i	$0.671236\pi$
$830$	9.19958e22	+	6.07959e22i	0.408454	+	0.269929i
$831$			1.47802e23i			0.649938i
$832$	7.52397e21	+	2.85112e21i	0.0327688	+	0.0124174i
$833$	1.27999e23			0.552135
$834$	7.05404e22	−	1.06741e23i	0.301376	−	0.456040i
$835$		−	6.21616e22i		−	0.263045i
$836$	−1.60660e23	−	3.76989e23i	−0.673377	−	1.58008i
$837$	−3.10130e22			−0.128748
$838$	−1.17005e23	−	7.73234e22i	−0.481119	−	0.317950i
$839$		−	4.40484e22i		−	0.179405i	−0.995969	−	0.0897025i	$-0.971408\pi$
$839$		−	4.40484e22i		−	0.179405i	0.995969	−	0.0897025i	$-0.0285916\pi$
$840$	−5.06003e22	−	9.26574e21i	−0.204136	−	0.0373805i
$841$	−3.89694e22			−0.155724
$842$	−3.51101e21	+	5.31282e21i	−0.0138975	+	0.0210295i
$843$			1.04226e23i			0.408655i
$844$	4.79716e22	−	2.04439e22i	0.186314	−	0.0794008i
$845$	−7.31762e22			−0.281524
$846$	8.44419e22	+	5.58039e22i	0.321807	+	0.212668i
$847$			2.37184e23i			0.895402i
$848$	3.09371e23	−	3.22207e23i	1.15695	−	1.20495i
$849$	1.63356e23			0.605164
$850$	−1.21933e23	+	1.84508e23i	−0.447477	+	0.677118i
$851$			1.17362e23i			0.426668i
$852$	2.69131e22	+	6.31516e22i	0.0969276	+	0.227440i
$853$	−3.49514e23			−1.24702			−0.623508	−	0.781817i	$-0.714293\pi$
$853$	−3.49514e23			−1.24702			−0.623508	+	0.781817i	$0.714293\pi$
$854$	−3.31935e23	−	2.19361e23i	−1.17325	−	0.775349i
$855$			3.53245e22i			0.123693i
$856$	−6.20573e22	+	3.38896e23i	−0.215279	+	1.17565i
$857$	−4.09516e23			−1.40742			−0.703711	−	0.710486i	$-0.748475\pi$
$857$	−4.09516e23			−1.40742			−0.703711	+	0.710486i	$0.748475\pi$
$858$	−4.27416e21	+	6.46762e21i	−0.0145530	+	0.0220215i
$859$			3.17922e23i			1.07245i	0.844076	+	0.536223i	$0.180149\pi$
$859$			3.17922e23i			1.07245i	−0.844076	+	0.536223i	$0.819851\pi$
$860$	7.87455e22	−	3.35588e22i	0.263171	−	0.112155i
$861$	−1.76268e23			−0.583646
$862$	2.80251e22	+	1.85205e22i	0.0919366	+	0.0607568i
$863$		−	3.69823e23i		−	1.20201i	−0.799246	−	0.601004i	$-0.794768\pi$
$863$		−	3.69823e23i		−	1.20201i	0.799246	−	0.601004i	$-0.205232\pi$
$864$	5.82991e22	−	1.31439e22i	0.187738	−	0.0423268i
$865$	7.59724e22			0.242397
$866$	5.78634e22	−	8.75584e22i	0.182920	−	0.276793i
$867$			4.10429e22i			0.128554i
$868$	−1.07774e23	−	2.52891e23i	−0.334469	−	0.784829i
$869$	1.59913e23			0.491730
$870$	−4.09447e22	−	2.70585e22i	−0.124751	−	0.0824423i
$871$			9.61347e21i			0.0290225i
$872$	3.51432e23	+	6.43528e22i	1.05126	+	0.192502i
$873$	1.59343e23			0.472302
$874$	5.64826e22	−	8.54690e22i	0.165891	−	0.251025i
$875$			2.37209e23i			0.690346i
$876$	−2.23647e23	+	9.53109e22i	−0.644955	+	0.274859i
$877$	−3.95866e23			−1.13123			−0.565616	−	0.824669i	$-0.691361\pi$
$877$	−3.95866e23			−1.13123			−0.565616	+	0.824669i	$0.691361\pi$
$878$	6.33589e22	+	4.18711e22i	0.179412	+	0.118565i
$879$		−	1.17958e23i		−	0.330991i
$880$	−9.53986e22	−	9.15983e22i	−0.265265	−	0.254698i
$881$	−9.83780e22			−0.271076			−0.135538	−	0.990772i	$-0.543276\pi$
$881$	−9.83780e22			−0.271076			−0.135538	+	0.990772i	$0.543276\pi$
$882$	−4.21489e22	+	6.37793e22i	−0.115090	+	0.174153i
$883$			1.24652e22i			0.0337298i	0.999858	+	0.0168649i	$0.00536851\pi$
$883$			1.24652e22i			0.0337298i	−0.999858	+	0.0168649i	$0.994631\pi$
$884$	4.51712e21	+	1.05994e22i	0.0121128	+	0.0284225i
$885$	−6.29996e22			−0.167414
$886$	1.00784e23	+	6.66035e22i	0.265412	+	0.175399i
$887$		−	4.68255e23i		−	1.22206i	−0.791606	−	0.611031i	$-0.790755\pi$
$887$		−	4.68255e23i		−	1.22206i	0.791606	−	0.611031i	$-0.209245\pi$
$888$	−7.50606e22	+	4.09907e23i	−0.194137	+	1.06019i
$889$	−7.59222e23			−1.94605
$890$	−3.54308e22	+	5.36135e22i	−0.0900038	+	0.136193i
$891$			5.75807e22i			0.144962i
$892$	−2.19092e23	+	9.33699e22i	−0.546648	+	0.232964i
$893$	6.16076e23			1.52343
$894$	2.73910e23	+	1.81015e23i	0.671287	+	0.443624i
$895$			1.59131e23i			0.386520i
$896$	3.09777e23	+	4.29714e23i	0.745735	+	1.03447i
$897$	−1.93803e21			−0.00462404
$898$	2.01294e23	−	3.04595e23i	0.476013	−	0.720299i
$899$		−	2.62266e23i		−	0.614701i
$900$	−5.17854e22	−	1.21514e23i	−0.120300	−	0.282284i
$901$	6.39644e23			1.47279
$902$	−3.78077e23	−	2.49854e23i	−0.862836	−	0.570210i
$903$		−	3.30340e23i		−	0.747238i
$904$	−4.95187e23	−	9.06767e22i	−1.11025	−	0.203305i
$905$	−2.47817e23			−0.550734
$906$	1.55965e23	−	2.36005e23i	0.343560	−	0.519871i
$907$			5.34969e22i			0.116807i	0.998293	+	0.0584037i	$0.0186011\pi$
$907$			5.34969e22i			0.116807i	−0.998293	+	0.0584037i	$0.981399\pi$
$908$	−2.87681e23	+	1.22600e23i	−0.622621	+	0.265341i
$909$	−5.38584e22			−0.115543
$910$	4.94176e21	+	3.26579e21i	0.0105087	+	0.00694476i
$911$		−	1.96762e23i		−	0.414757i	−0.978261	−	0.207379i	$-0.933507\pi$
$911$		−	1.96762e23i		−	0.414757i	0.978261	−	0.207379i	$-0.0664932\pi$
$912$	2.51939e23	−	2.62391e23i	0.526425	−	0.548265i
$913$	1.09407e24			2.26610
$914$	1.02791e23	−	1.55542e23i	0.211049	−	0.319358i
$915$			8.81746e22i			0.179463i
$916$	−7.31261e22	−	1.71590e23i	−0.147540	−	0.346201i
$917$	7.89935e23			1.57993
$918$	7.13965e22	+	4.71828e22i	0.141558	+	0.0935496i
$919$			8.95479e22i			0.176008i	0.996120	+	0.0880038i	$0.0280488\pi$
$919$			8.95479e22i			0.176008i	−0.996120	+	0.0880038i	$0.971951\pi$
$920$	5.95529e21	−	3.25219e22i	0.0116038	−	0.0633685i
$921$	−2.70737e23			−0.522962
$922$	−1.27848e23	+	1.93459e23i	−0.244820	+	0.370460i
$923$		−	7.90454e21i		−	0.0150059i
$924$	−4.69534e23	+	2.00100e23i	−0.883672	+	0.376592i
$925$	9.21054e23			1.71851
$926$	8.31491e22	+	5.49495e22i	0.153805	+	0.101643i
$927$			9.82914e22i			0.180251i
$928$	1.11154e23	+	4.93014e23i	0.202088	+	0.896346i
$929$	−2.47553e23			−0.446212			−0.223106	−	0.974794i	$-0.571620\pi$
$929$	−2.47553e23			−0.446212			−0.223106	+	0.974794i	$0.571620\pi$
$930$	−3.35887e22	+	5.08261e22i	−0.0600246	+	0.0908287i
$931$			4.65325e23i			0.824439i
$932$	3.59589e23	+	8.43773e23i	0.631653	+	1.48217i
$933$	8.92043e22			0.155358
$934$	−7.17019e23	−	4.73846e23i	−1.23810	−	0.818205i
$935$		−	1.89385e23i		−	0.324230i
$936$	−6.76893e21	−	1.23950e21i	−0.0114898	−	0.00210397i
$937$	4.39368e23			0.739455			0.369728	−	0.929140i	$-0.379451\pi$
$937$	4.39368e23			0.739455			0.369728	+	0.929140i	$0.379451\pi$
$938$	−3.48957e23	+	5.28039e23i	−0.582304	+	0.881137i
$939$		−	3.89925e23i		−	0.645144i
$940$	1.82910e23	−	7.79503e22i	0.300065	−	0.127878i
$941$	−9.97408e23			−1.62239			−0.811196	−	0.584774i	$-0.801183\pi$
$941$	−9.97408e23			−1.62239			−0.811196	+	0.584774i	$0.801183\pi$
$942$	3.73613e23	+	2.46904e23i	0.602580	+	0.398218i
$943$		−	1.13292e23i		−	0.181177i
$944$	4.67963e23	+	4.49321e23i	0.742054	+	0.712494i
$945$	4.39961e22			0.0691767
$946$	4.68245e23	−	7.08544e23i	0.730036	−	1.10468i
$947$			1.16027e24i			1.79374i	0.442292	+	0.896871i	$0.354166\pi$
$947$			1.16027e24i			1.79374i	−0.442292	+	0.896871i	$0.645834\pi$
$948$	5.56514e22	+	1.30586e23i	0.0853119	+	0.200184i
$949$	2.79934e22			0.0425525
$950$	−6.70759e23	−	4.43275e23i	−1.01106	−	0.668166i
$951$		−	2.30931e23i		−	0.345174i
$952$	−1.36634e23	+	7.46158e23i	−0.202517	+	1.10595i
$953$	2.14806e22			0.0315721			0.0157861	−	0.999875i	$-0.494975\pi$
$953$	2.14806e22			0.0315721			0.0157861	+	0.999875i	$0.494975\pi$
$954$	−2.10630e23	+	3.18723e23i	−0.306996	+	0.464543i
$955$		−	2.37870e23i		−	0.343805i
$956$	−1.21326e23	+	5.17051e22i	−0.173896	+	0.0741088i
$957$	−4.86940e23			−0.692117
$958$	−1.66625e23	−	1.10115e23i	−0.234864	−	0.155211i
$959$		−	7.35614e23i		−	1.02826i
$960$	4.15998e22	−	1.09780e23i	0.0576662	−	0.152178i
$961$	4.01863e23			0.552448
$962$	2.64558e22	−	4.00326e22i	0.0360678	−	0.0545775i
$963$		−	2.94664e23i		−	0.398398i
$964$	−4.07582e23	−	9.56390e23i	−0.546511	−	1.28239i
$965$	−2.81833e22			−0.0374777
$966$	−1.06450e23	−	7.03483e22i	−0.140388	−	0.0927762i
$967$		−	2.61935e23i		−	0.342596i	−0.985219	−	0.171298i	$-0.945204\pi$
$967$		−	2.61935e23i		−	0.342596i	0.985219	−	0.171298i	$-0.0547961\pi$
$968$	−5.32435e23	−	9.74975e22i	−0.690660	−	0.126471i
$969$	5.20899e23			0.670136
$970$	1.72577e23	−	2.61142e23i	0.220196	−	0.333199i
$971$			5.64518e23i			0.714371i	0.934033	+	0.357186i	$0.116264\pi$
$971$			5.64518e23i			0.714371i	−0.934033	+	0.357186i	$0.883736\pi$
$972$	−4.70206e22	+	2.00387e22i	−0.0590144	+	0.0251500i
$973$	−9.69942e23			−1.20738
$974$	−3.55549e23	−	2.34966e23i	−0.438963	−	0.290091i
$975$			1.52097e22i			0.0186244i
$976$	6.28873e23	−	6.54964e23i	0.763773	−	0.795461i
$977$	−1.17805e24			−1.41908			−0.709541	−	0.704664i	$-0.751098\pi$
$977$	−1.17805e24			−1.41908			−0.709541	+	0.704664i	$0.751098\pi$
$978$	3.72628e23	−	5.63858e23i	0.445210	−	0.673688i
$979$			6.37605e23i			0.755597i
$980$	5.88762e22	+	1.38153e23i	0.0692040	+	0.162387i
$981$	−3.05564e23			−0.356246
$982$	−6.91404e22	−	4.56918e22i	−0.0799540	−	0.0528380i
$983$		−	1.17240e24i		−	1.34477i	−0.740201	−	0.672386i	$-0.765269\pi$
$983$		−	1.17240e24i		−	1.34477i	0.740201	−	0.672386i	$-0.234731\pi$
$984$	7.24574e22	−	3.95691e23i	0.0824369	−	0.450190i
$985$	−2.45265e23			−0.276787
$986$	−3.99008e23	+	6.03775e23i	−0.446649	+	0.675864i
$987$		−	7.67313e23i		−	0.851992i
$988$	−3.85329e22	+	1.64215e22i	−0.0424401	+	0.0180866i
$989$	2.12316e23			0.231960
$990$	9.43670e22	+	6.23630e22i	0.102268	+	0.0675842i
$991$		−	2.61631e23i		−	0.281255i	−0.990063	−	0.140627i	$-0.955088\pi$
$991$		−	2.61631e23i		−	0.281255i	0.990063	−	0.140627i	$-0.0449119\pi$
$992$	6.11996e23	−	1.37979e23i	0.652612	−	0.147136i
$993$	−6.84866e22			−0.0724455
$994$	2.86925e23	−	4.34173e23i	0.301077	−	0.455587i
$995$			1.19777e23i			0.124678i
$996$	3.80747e23	+	8.93422e23i	0.393154	+	0.922533i
$997$	−1.45062e24			−1.48591			−0.742957	−	0.669339i	$-0.766577\pi$
$997$	−1.45062e24			−1.48591			−0.742957	+	0.669339i	$0.766577\pi$
$998$	1.15333e24	+	7.62187e23i	1.17195	+	0.774493i
$999$		−	3.56407e23i		−	0.359271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.17.d.a.7.6	yes	16
3.2	odd	2		36.17.d.d.19.11		16
4.3	odd	2	inner	12.17.d.a.7.5	✓	16
12.11	even	2		36.17.d.d.19.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.17.d.a.7.5	✓	16	4.3	odd	2	inner
12.17.d.a.7.6	yes	16	1.1	even	1	trivial
36.17.d.d.19.11		16	3.2	odd	2
36.17.d.d.19.12		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)

\(f(q)\)	\(=\)	\(q+(-141.143 + 213.576i) q^{2} -3788.00i q^{3} +(-25693.4 - 60289.4i) q^{4} +110106. q^{5} +(809025. + 534648. i) q^{6} -7.35151e6i q^{7} +(1.65028e7 + 3.02193e6i) q^{8} -1.43489e7 q^{9} +O(q^{10})\)	\(q+(-141.143 + 213.576i) q^{2} -3788.00i q^{3} +(-25693.4 - 60289.4i) q^{4} +110106. q^{5} +(809025. + 534648. i) q^{6} -7.35151e6i q^{7} +(1.65028e7 + 3.02193e6i) q^{8} -1.43489e7 q^{9} +(-1.55406e7 + 2.35159e7i) q^{10} +2.79666e8i q^{11} +(-2.28376e8 + 9.73265e7i) q^{12} +2.85853e7 q^{13} +(1.57011e9 + 1.03761e9i) q^{14} -4.17080e8i q^{15} +(-2.97467e9 + 3.09808e9i) q^{16} -6.15030e9 q^{17} +(2.02525e9 - 3.06458e9i) q^{18} -2.23587e10i q^{19} +(-2.82899e9 - 6.63821e9i) q^{20} -2.78475e10 q^{21} +(-5.97299e10 - 3.94728e10i) q^{22} -1.78982e10i q^{23} +(1.14471e10 - 6.25126e10i) q^{24} -1.40465e11 q^{25} +(-4.03462e9 + 6.10514e9i) q^{26} +5.43536e10i q^{27} +(-4.43218e11 + 1.88885e11i) q^{28} -4.59649e11 q^{29} +(8.90782e10 + 5.88678e10i) q^{30} +5.70578e11i q^{31} +(-2.41823e11 - 1.07259e12i) q^{32} +1.05937e12 q^{33} +(8.68071e11 - 1.31356e12i) q^{34} -8.09443e11i q^{35} +(3.68672e11 + 8.65088e11i) q^{36} -6.55720e12 q^{37} +(4.77529e12 + 3.15578e12i) q^{38} -1.08281e11i q^{39} +(1.81705e12 + 3.32732e11i) q^{40} +6.32978e12 q^{41} +(3.93047e12 - 5.94755e12i) q^{42} +1.18625e13i q^{43} +(1.68609e13 - 7.18557e12i) q^{44} -1.57990e12 q^{45} +(3.82262e12 + 2.52620e12i) q^{46} +2.75541e13i q^{47} +(1.17355e13 + 1.12680e13i) q^{48} -2.08118e13 q^{49} +(1.98256e13 - 2.99999e13i) q^{50} +2.32973e13i q^{51} +(-7.34454e11 - 1.72339e12i) q^{52} -1.04002e14 q^{53} +(-1.16086e13 - 7.67162e12i) q^{54} +3.07928e13i q^{55} +(2.22157e13 - 1.21321e14i) q^{56} -8.46948e13 q^{57} +(6.48761e13 - 9.81700e13i) q^{58} -1.51049e14i q^{59} +(-2.51455e13 + 1.07162e13i) q^{60} -2.11410e14 q^{61} +(-1.21862e14 - 8.05331e13i) q^{62} +1.05486e14i q^{63} +(2.63211e14 + 9.97407e13i) q^{64} +3.14741e12 q^{65} +(-1.49523e14 + 2.26257e14i) q^{66} +3.36308e14i q^{67} +(1.58022e14 + 3.70798e14i) q^{68} -6.77982e13 q^{69} +(1.72877e14 + 1.14247e14i) q^{70} -2.76524e14i q^{71} +(-2.36797e14 - 4.33614e13i) q^{72} +9.79291e14 q^{73} +(9.25502e14 - 1.40046e15i) q^{74} +5.32079e14i q^{75} +(-1.34800e15 + 5.74472e14i) q^{76} +2.05597e15 q^{77} +(2.31262e13 + 1.52831e13i) q^{78} -5.71801e14i q^{79} +(-3.27527e14 + 3.41116e14i) q^{80} +2.05891e14 q^{81} +(-8.93403e14 + 1.35189e15i) q^{82} -3.91206e15i q^{83} +(7.15496e14 + 1.67891e15i) q^{84} -6.77183e14 q^{85} +(-2.53354e15 - 1.67430e15i) q^{86} +1.74115e15i q^{87} +(-8.45131e14 + 4.61528e15i) q^{88} +2.27988e15 q^{89} +(2.22991e14 - 3.37428e14i) q^{90} -2.10145e14i q^{91} +(-1.07907e15 + 4.59865e14i) q^{92} +2.16135e15 q^{93} +(-5.88490e15 - 3.88907e15i) q^{94} -2.46182e15i q^{95} +(-4.06296e15 + 9.16024e14i) q^{96} -1.11049e16 q^{97} +(2.93743e15 - 4.44489e15i) q^{98} -4.01290e15i 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more