LMFDB - Embedded newform 22.13.d.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,13,Mod(7,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("22.7");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$N$	$=$	$22 = 2 \cdot 11$
Weight:	$k$	$=$	$13$
Character orbit:	$[\chi]$	$=$	22.d (of order $10$ , degree $4$ , 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:	$20.1078639801$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	22.17
Dual form			22.13.d.a.13.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-43.0399 + 13.9845i) q^{2} +(296.805 + 215.641i) q^{3} +(1656.87 - 1203.78i) q^{4} +(8358.15 - 25723.7i) q^{5} +(-15790.1 - 5130.51i) q^{6} +(-25261.8 - 34770.0i) q^{7} +(-54477.1 + 74981.2i) q^{8} +(-122632. - 377424. i) q^{9} +1.22403e6i q^{10} +(-579738. + 1.67402e6i) q^{11} +751351. q^{12} +(513841. - 166957. i) q^{13} +(1.57351e6 + 1.14322e6i) q^{14} +(8.02783e6 - 5.83256e6i) q^{15} +(1.29611e6 - 3.98902e6i) q^{16} +(-1.06737e7 - 3.46808e6i) q^{17} +(1.05562e7 + 1.45293e7i) q^{18} +(-3.35596e7 + 4.61908e7i) q^{19} +(-1.71175e7 - 5.26822e7i) q^{20} -1.57674e7i q^{21} +(1.54158e6 - 8.01569e7i) q^{22} -1.15205e8 q^{23} +(-3.23381e7 + 1.05073e7i) q^{24} +(-3.94338e8 - 2.86503e8i) q^{25} +(-1.97808e7 + 1.43716e7i) q^{26} +(1.05239e8 - 3.23893e8i) q^{27} +(-8.37110e7 - 2.71994e7i) q^{28} +(-5.32578e8 - 7.33031e8i) q^{29} +(-2.63952e8 + 3.63298e8i) q^{30} +(4.73842e7 + 1.45834e8i) q^{31} +1.89813e8i q^{32} +(-5.33056e8 + 3.71840e8i) q^{33} +5.07893e8 q^{34} +(-1.10556e9 + 3.59217e8i) q^{35} +(-6.57522e8 - 4.77718e8i) q^{36} +(2.13845e9 - 1.55367e9i) q^{37} +(7.98446e8 - 2.45736e9i) q^{38} +(1.88513e8 + 6.12516e7i) q^{39} +(1.47347e9 + 2.02806e9i) q^{40} +(-1.96727e9 + 2.70772e9i) q^{41} +(2.20499e8 + 6.78627e8i) q^{42} +3.28549e9i q^{43} +(1.05461e9 + 3.47150e9i) q^{44} -1.07337e10 q^{45} +(4.95841e9 - 1.61108e9i) q^{46} +(5.64374e9 + 4.10041e9i) q^{47} +(1.24489e9 - 9.04465e8i) q^{48} +(3.70640e9 - 1.14071e10i) q^{49} +(2.09789e10 + 6.81645e9i) q^{50} +(-2.42013e9 - 3.33102e9i) q^{51} +(6.50385e8 - 8.95179e8i) q^{52} +(-9.78871e9 - 3.01265e10i) q^{53} +1.54121e10i q^{54} +(3.82164e10 + 2.89047e10i) q^{55} +3.98328e9 q^{56} +(-1.99213e10 + 6.47282e9i) q^{57} +(3.31732e10 + 2.41017e10i) q^{58} +(-4.80211e10 + 3.48894e10i) q^{59} +(6.27990e9 - 1.93276e10i) q^{60} +(3.49034e10 + 1.13408e10i) q^{61} +(-4.07882e9 - 5.61402e9i) q^{62} +(-1.00251e10 + 1.37983e10i) q^{63} +(-2.65444e9 - 8.16951e9i) q^{64} -1.46133e10i q^{65} +(1.77427e10 - 2.34585e10i) q^{66} -1.46331e11 q^{67} +(-2.18596e10 + 7.10263e9i) q^{68} +(-3.41933e10 - 2.48429e10i) q^{69} +(4.25595e10 - 3.09213e10i) q^{70} +(6.00406e10 - 1.84786e11i) q^{71} +(3.49804e10 + 1.13658e10i) q^{72} +(-3.40511e10 - 4.68673e10i) q^{73} +(-7.03111e10 + 9.67750e10i) q^{74} +(-5.52594e10 - 1.70071e11i) q^{75} +1.16931e11i q^{76} +(7.28507e10 - 2.21313e10i) q^{77} -8.97016e9 q^{78} +(-3.22847e11 + 1.04899e11i) q^{79} +(-9.17794e10 - 6.66816e10i) q^{80} +(-6.95419e10 + 5.05252e10i) q^{81} +(4.68051e10 - 1.44051e11i) q^{82} +(7.18856e10 + 2.33571e10i) q^{83} +(-1.89805e10 - 2.61244e10i) q^{84} +(-1.78424e11 + 2.45580e11i) q^{85} +(-4.59460e10 - 1.41407e11i) q^{86} -3.32413e11i q^{87} +(-9.39374e10 - 1.34665e11i) q^{88} +6.46998e11 q^{89} +(4.61979e11 - 1.50106e11i) q^{90} +(-1.87856e10 - 1.36486e10i) q^{91} +(-1.90879e11 + 1.38682e11i) q^{92} +(-1.73839e10 + 5.35021e10i) q^{93} +(-3.00248e11 - 9.75565e10i) q^{94} +(9.07704e11 + 1.24935e12i) q^{95} +(-4.09314e10 + 5.63372e10i) q^{96} +(4.31897e11 + 1.32924e12i) q^{97} +5.42794e11i q^{98} +(7.02908e11 + 1.35184e10i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$48 q + 1240 q^{3} + 24576 q^{4} + 1440 q^{5} - 147200 q^{6} + 439200 q^{7} + 563348 q^{9} - 7317468 q^{11} + 737280 q^{12} + 13341600 q^{13} - 7524864 q^{14} - 29808888 q^{15} - 50331648 q^{16} + 29458800 q^{17}+ \cdots - 5181480396620 q^{99}+O(q^{100})$ 48 * q + 1240 * q^3 + 24576 * q^4 + 1440 * q^5 - 147200 * q^6 + 439200 * q^7 + 563348 * q^9 - 7317468 * q^11 + 737280 * q^12 + 13341600 * q^13 - 7524864 * q^14 - 29808888 * q^15 - 50331648 * q^16 + 29458800 * q^17 - 96857600 * q^18 + 59195700 * q^19 - 2949120 * q^20 - 147874560 * q^22 + 297521280 * q^23 - 301465600 * q^24 - 349772268 * q^25 + 603191808 * q^26 - 434593340 * q^27 - 981811200 * q^28 + 121665600 * q^29 + 3275650560 * q^30 - 1117400544 * q^31 - 13803991820 * q^33 - 2568870912 * q^34 + 1026283680 * q^35 + 7058374656 * q^36 + 11737565760 * q^37 + 4500864000 * q^38 - 23697921920 * q^39 - 7817134080 * q^40 + 4863244680 * q^41 + 12992468480 * q^42 - 18701991936 * q^44 + 29640403232 * q^45 + 33202391040 * q^46 + 8084031480 * q^47 + 5200936960 * q^48 + 593931516 * q^49 - 13593646080 * q^50 - 30011589660 * q^51 + 55099392000 * q^52 + 40815862920 * q^53 + 29310331992 * q^55 - 7285506048 * q^56 - 98665594300 * q^57 + 81900510720 * q^58 - 156541010940 * q^59 - 30685659136 * q^60 + 255357655680 * q^61 + 67163788800 * q^62 - 429459850400 * q^63 + 103079215104 * q^64 + 460708043264 * q^66 + 76186270200 * q^67 + 60331622400 * q^68 - 1054414688600 * q^69 - 352820375040 * q^70 + 60925955544 * q^71 + 95420416000 * q^72 + 363471756600 * q^73 + 378662860800 * q^74 - 57777629724 * q^75 + 326539185480 * q^77 - 1234846474240 * q^78 + 137547461520 * q^79 - 120795955200 * q^80 - 1017431491848 * q^81 + 613199754240 * q^82 + 715268672100 * q^83 - 354644459520 * q^84 + 1202406730800 * q^85 - 80499776256 * q^86 - 270225899520 * q^88 + 724193830584 * q^89 - 1005067351040 * q^90 + 1925501559192 * q^91 - 608833290240 * q^92 - 2466072811400 * q^93 + 300785049600 * q^94 + 6877125644400 * q^95 + 1350178653780 * q^97 - 5181480396620 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$ .

$n$	$13$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−43.0399	+	13.9845i	−0.672499	+	0.218508i
$2$	−43.0399	+	13.9845i	−0.672499	+	0.218508i
$3$	296.805	+	215.641i	0.407139	+	0.295804i	0.772443	−	0.635084i	$-0.219035\pi$
$3$	296.805	+	215.641i	0.407139	+	0.295804i	−0.365303	+	0.930889i	$0.619035\pi$
$4$	1656.87	−	1203.78i	0.404508	−	0.293893i
$5$	8358.15	−	25723.7i	0.534921	−	1.64632i	−0.208898	−	0.977938i	$-0.566988\pi$
$5$	8358.15	−	25723.7i	0.534921	−	1.64632i	0.743819	−	0.668381i	$-0.233012\pi$
$6$	−15790.1	−	5130.51i	−0.338436	−	0.109965i
$7$	−25261.8	−	34770.0i	−0.214722	−	0.295540i	0.688046	−	0.725667i	$-0.258469\pi$
$7$	−25261.8	−	34770.0i	−0.214722	−	0.295540i	−0.902768	+	0.430127i	$0.858469\pi$
$8$	−54477.1	+	74981.2i	−0.207813	+	0.286031i
$9$	−122632.	−	377424.i	−0.230755	−	0.710189i
$10$			1.22403e6i			1.22403i
$11$	−579738.	+	1.67402e6i	−0.327247	+	0.944939i
$11$	−579738.	+	1.67402e6i	−0.327247	+	0.944939i
$12$	751351.			0.251626
$13$	513841.	−	166957.i	0.106456	−	0.0345895i	−0.255305	−	0.966861i	$-0.582176\pi$
$13$	513841.	−	166957.i	0.106456	−	0.0345895i	0.361760	+	0.932271i	$0.382176\pi$
$14$	1.57351e6	+	1.14322e6i	0.208978	+	0.151832i
$15$	8.02783e6	−	5.83256e6i	0.704775	−	0.512049i
$16$	1.29611e6	−	3.98902e6i	0.0772542	−	0.237764i
$17$	−1.06737e7	−	3.46808e6i	−0.442201	−	0.143680i	0.0794499	−	0.996839i	$-0.474684\pi$
$17$	−1.06737e7	−	3.46808e6i	−0.442201	−	0.143680i	−0.521651	+	0.853159i	$0.674684\pi$
$18$	1.05562e7	+	1.45293e7i	0.310364	+	0.427180i
$19$	−3.35596e7	+	4.61908e7i	−0.713338	+	0.981825i	0.286381	+	0.958116i	$0.407548\pi$
$19$	−3.35596e7	+	4.61908e7i	−0.713338	+	0.981825i	−0.999719	+	0.0237093i	$0.992452\pi$
$20$	−1.71175e7	−	5.26822e7i	−0.267461	−	0.823159i
$21$		−	1.57674e7i		−	0.183842i
$22$	1.54158e6	−	8.01569e7i	0.0135966	−	0.706976i
$23$	−1.15205e8			−0.778222			−0.389111	−	0.921191i	$-0.627218\pi$
$23$	−1.15205e8			−0.778222			−0.389111	+	0.921191i	$0.627218\pi$
$24$	−3.23381e7	+	1.05073e7i	−0.169218	+	0.0549823i
$25$	−3.94338e8	−	2.86503e8i	−1.61521	−	1.17352i
$26$	−1.97808e7	+	1.43716e7i	−0.0640331	+	0.0465228i
$27$	1.05239e8	−	3.23893e8i	0.271641	−	0.836025i
$28$	−8.37110e7	−	2.71994e7i	−0.173714	−	0.0564431i
$29$	−5.32578e8	−	7.33031e8i	−0.895355	−	1.23235i	−0.971926	−	0.235286i	$-0.924397\pi$
$29$	−5.32578e8	−	7.33031e8i	−0.895355	−	1.23235i	0.0765713	−	0.997064i	$-0.475603\pi$
$30$	−2.63952e8	+	3.63298e8i	−0.362074	+	0.498352i
$31$	4.73842e7	+	1.45834e8i	0.0533904	+	0.164319i	0.974196	−	0.225702i	$-0.0724677\pi$
$31$	4.73842e7	+	1.45834e8i	0.0533904	+	0.164319i	−0.920806	+	0.390021i	$0.872468\pi$
$32$			1.89813e8i			0.176777i
$33$	−5.33056e8	+	3.71840e8i	−0.412752	+	0.287921i
$34$	5.07893e8			0.328775
$35$	−1.10556e9	+	3.59217e8i	−0.601412	+	0.195411i
$36$	−6.57522e8	−	4.77718e8i	−0.302062	−	0.219461i
$37$	2.13845e9	−	1.55367e9i	0.833466	−	0.605548i	−0.0870719	−	0.996202i	$-0.527751\pi$
$37$	2.13845e9	−	1.55367e9i	0.833466	−	0.605548i	0.920538	+	0.390654i	$0.127751\pi$
$38$	7.98446e8	−	2.45736e9i	0.265182	−	0.816146i
$39$	1.88513e8	+	6.12516e7i	0.0535740	+	0.0174072i
$40$	1.47347e9	+	2.02806e9i	0.359734	+	0.495131i
$41$	−1.96727e9	+	2.70772e9i	−0.414154	+	0.570034i	−0.964225	−	0.265084i	$-0.914600\pi$
$41$	−1.96727e9	+	2.70772e9i	−0.414154	+	0.570034i	0.550072	+	0.835117i	$0.314600\pi$
$42$	2.20499e8	+	6.78627e8i	0.0401709	+	0.123633i
$43$			3.28549e9i			0.519745i	0.965643	+	0.259872i	$0.0836805\pi$
$43$			3.28549e9i			0.519745i	−0.965643	+	0.259872i	$0.916320\pi$
$44$	1.05461e9	+	3.47150e9i	0.145336	+	0.478411i
$45$	−1.07337e10			−1.29263
$46$	4.95841e9	−	1.61108e9i	0.523353	−	0.170048i
$47$	5.64374e9	+	4.10041e9i	0.523576	+	0.380400i	0.817949	−	0.575290i	$-0.195111\pi$
$47$	5.64374e9	+	4.10041e9i	0.523576	+	0.380400i	−0.294373	+	0.955690i	$0.595111\pi$
$48$	1.24489e9	−	9.04465e8i	0.101785	−	0.0739510i
$49$	3.70640e9	−	1.14071e10i	0.267779	−	0.824139i
$50$	2.09789e10	+	6.81645e9i	1.34265	+	0.436253i
$51$	−2.42013e9	−	3.33102e9i	−0.137536	−	0.189303i
$52$	6.50385e8	−	8.95179e8i	0.0328966	−	0.0452782i
$53$	−9.78871e9	−	3.01265e10i	−0.441642	−	1.35923i	−0.886125	−	0.463447i	$-0.846613\pi$
$53$	−9.78871e9	−	3.01265e10i	−0.441642	−	1.35923i	0.444483	−	0.895787i	$-0.353387\pi$
$54$			1.54121e10i			0.621582i
$55$	3.82164e10	+	2.89047e10i	1.38062	+	1.04422i
$56$	3.98328e9			0.129156
$57$	−1.99213e10	+	6.47282e9i	−0.580856	+	0.188731i
$58$	3.31732e10	+	2.41017e10i	0.871403	+	0.633111i
$59$	−4.80211e10	+	3.48894e10i	−1.13847	+	0.827144i	−0.986905	−	0.161304i	$-0.948430\pi$
$59$	−4.80211e10	+	3.48894e10i	−1.13847	+	0.827144i	−0.151561	+	0.988448i	$0.548430\pi$
$60$	6.27990e9	−	1.93276e10i	0.134600	−	0.414257i
$61$	3.49034e10	+	1.13408e10i	0.677469	+	0.220123i	0.627487	−	0.778627i	$-0.284084\pi$
$61$	3.49034e10	+	1.13408e10i	0.677469	+	0.220123i	0.0499818	+	0.998750i	$0.484084\pi$
$62$	−4.07882e9	−	5.61402e9i	−0.0718099	−	0.0988379i
$63$	−1.00251e10	+	1.37983e10i	−0.160341	+	0.220691i
$64$	−2.65444e9	−	8.16951e9i	−0.0386271	−	0.118882i
$65$		−	1.46133e10i		−	0.193762i
$66$	1.77427e10	−	2.34585e10i	0.214662	−	0.283816i
$67$	−1.46331e11			−1.61767			−0.808833	−	0.588038i	$-0.799900\pi$
$67$	−1.46331e11			−1.61767			−0.808833	+	0.588038i	$0.799900\pi$
$68$	−2.18596e10	+	7.10263e9i	−0.221100	+	0.0718399i
$69$	−3.41933e10	−	2.48429e10i	−0.316845	−	0.230201i
$70$	4.25595e10	−	3.09213e10i	0.361750	−	0.262827i
$71$	6.00406e10	−	1.84786e11i	0.468700	−	1.44251i	−0.385569	−	0.922679i	$-0.625995\pi$
$71$	6.00406e10	−	1.84786e11i	0.468700	−	1.44251i	0.854269	−	0.519831i	$-0.174005\pi$
$72$	3.49804e10	+	1.13658e10i	0.251090	+	0.0815840i
$73$	−3.40511e10	−	4.68673e10i	−0.225006	−	0.309694i	0.681557	−	0.731765i	$-0.261303\pi$
$73$	−3.40511e10	−	4.68673e10i	−0.225006	−	0.309694i	−0.906563	+	0.422071i	$0.861303\pi$
$74$	−7.03111e10	+	9.67750e10i	−0.428187	+	0.589349i
$75$	−5.52594e10	−	1.70071e11i	−0.310483	−	0.955570i
$76$			1.16931e11i			0.606801i
$77$	7.28507e10	−	2.21313e10i	0.349534	−	0.106185i
$78$	−8.97016e9			−0.0398320
$79$	−3.22847e11	+	1.04899e11i	−1.32811	+	0.431529i	−0.885273	−	0.465073i	$-0.846028\pi$
$79$	−3.22847e11	+	1.04899e11i	−1.32811	+	0.431529i	−0.442838	+	0.896602i	$0.646028\pi$
$80$	−9.17794e10	−	6.66816e10i	−0.350111	−	0.254370i
$81$	−6.95419e10	+	5.05252e10i	−0.246228	+	0.178895i
$82$	4.68051e10	−	1.44051e11i	0.153961	−	0.473843i
$83$	7.18856e10	+	2.33571e10i	0.219874	+	0.0714413i	0.416882	−	0.908960i	$-0.363123\pi$
$83$	7.18856e10	+	2.33571e10i	0.219874	+	0.0714413i	−0.197009	+	0.980402i	$0.563123\pi$
$84$	−1.89805e10	−	2.61244e10i	−0.0540297	−	0.0743655i
$85$	−1.78424e11	+	2.45580e11i	−0.473085	+	0.651146i
$86$	−4.59460e10	−	1.41407e11i	−0.113568	−	0.349528i
$87$		−	3.32413e11i		−	0.766588i
$88$	−9.39374e10	−	1.34665e11i	−0.202275	−	0.289974i
$89$	6.46998e11			1.30186			0.650928	−	0.759140i	$-0.274380\pi$
$89$	6.46998e11			1.30186			0.650928	+	0.759140i	$0.274380\pi$
$90$	4.61979e11	−	1.50106e11i	0.869294	−	0.282451i
$91$	−1.87856e10	−	1.36486e10i	−0.0330809	−	0.0240347i
$92$	−1.90879e11	+	1.38682e11i	−0.314798	+	0.228714i
$93$	−1.73839e10	+	5.35021e10i	−0.0268688	+	0.0826938i
$94$	−3.00248e11	−	9.75565e10i	−0.435224	−	0.141413i
$95$	9.07704e11	+	1.24935e12i	1.23482	+	1.69958i
$96$	−4.09314e10	+	5.63372e10i	−0.0522913	+	0.0719728i
$97$	4.31897e11	+	1.32924e12i	0.518501	+	1.59578i	0.776820	+	0.629723i	$0.216831\pi$
$97$	4.31897e11	+	1.32924e12i	0.518501	+	1.59578i	−0.258319	+	0.966060i	$0.583169\pi$
$98$			5.42794e11i			0.612744i
$99$	7.02908e11	+	1.35184e10i	0.746599	+	0.0143586i
$100$	−9.98253e11			−0.998253
$101$	1.45660e12	−	4.73277e11i	1.37218	−	0.445848i	0.472089	−	0.881551i	$-0.343500\pi$
$101$	1.45660e12	−	4.73277e11i	1.37218	−	0.445848i	0.900091	+	0.435702i	$0.143500\pi$
$102$	1.50745e11	+	1.09523e11i	0.133857	+	0.0972529i
$103$	−4.26455e11	+	3.09838e11i	−0.357149	+	0.259484i	−0.751862	−	0.659320i	$-0.770844\pi$
$103$	−4.26455e11	+	3.09838e11i	−0.357149	+	0.259484i	0.394713	+	0.918805i	$0.370844\pi$
$104$	−1.54739e10	+	4.76237e10i	−0.0122292	+	0.0376377i
$105$	−4.05596e11	−	1.31786e11i	−0.302662	−	0.0983408i
$106$	8.42610e11	+	1.15975e12i	0.594007	+	0.817580i
$107$	1.03819e12	−	1.42894e12i	0.691788	−	0.952165i	−0.308211	−	0.951318i	$-0.599730\pi$
$107$	1.03819e12	−	1.42894e12i	0.691788	−	0.952165i	1.00000		0.000846874i	$-0.000269568\pi$
$108$	−2.15530e11	−	6.63334e11i	−0.135821	−	0.418013i
$109$		−	1.76639e12i		−	1.05324i	−0.850100	−	0.526621i	$-0.823459\pi$
$109$		−	1.76639e12i		−	1.05324i	0.850100	−	0.526621i	$-0.176541\pi$
$110$	−2.04905e12	−	7.09618e11i	−1.15663	−	0.400561i
$111$	9.69736e11			0.518461
$112$	−1.71440e11	+	5.57043e10i	−0.0868569	+	0.0282215i
$113$	−1.54344e12	−	1.12137e12i	−0.741342	−	0.538616i	0.151789	−	0.988413i	$-0.451496\pi$
$113$	−1.54344e12	−	1.12137e12i	−0.741342	−	0.538616i	−0.893131	+	0.449797i	$0.851496\pi$
$114$	7.66891e11	−	5.57179e11i	0.349385	−	0.253843i
$115$	−9.62899e11	+	2.96350e12i	−0.416288	+	1.28120i
$116$	−1.76482e12	−	5.73425e11i	−0.724357	−	0.235358i
$117$	−1.26027e11	−	1.73461e11i	−0.0491302	−	0.0676219i
$118$	1.57891e12	−	2.17319e12i	0.584879	−	0.805017i
$119$	1.49051e11	+	4.58733e11i	0.0524873	+	0.161539i
$120$			9.19678e11i			0.307998i
$121$	−2.46624e12	−	1.94098e12i	−0.785819	−	0.618457i
$122$	−1.66084e12			−0.503695
$123$	−1.16779e12	+	3.79438e11i	−0.337237	+	0.109575i
$124$	2.54061e11	+	1.84586e11i	0.0698889	+	0.0507773i
$125$	−5.32360e12	+	3.86782e12i	−1.39555	+	1.01393i
$126$	2.38516e11	−	7.34075e11i	0.0596065	−	0.183450i
$127$	5.09935e12	+	1.65688e12i	1.21533	+	0.394883i	0.845378	−	0.534169i	$-0.179375\pi$
$127$	5.09935e12	+	1.65688e12i	1.21533	+	0.394883i	0.369948	+	0.929052i	$0.379375\pi$
$128$	2.28493e11	+	3.14494e11i	0.0519534	+	0.0715077i
$129$	−7.08488e11	+	9.75150e11i	−0.153743	+	0.211609i
$130$	2.04361e11	+	6.28957e11i	0.0423386	+	0.130305i
$131$		−	7.49282e12i		−	1.48258i	−0.671186	−	0.741289i	$-0.734215\pi$
$131$		−	7.49282e12i		−	1.48258i	0.671186	−	0.741289i	$-0.265785\pi$
$132$	−4.35587e11	+	1.25777e12i	−0.0823439	+	0.237771i
$133$	2.45383e12			0.443338
$134$	6.29809e12	−	2.04637e12i	1.08788	−	0.353473i
$135$	−7.45214e12	−	5.41430e12i	−1.23106	−	0.894416i
$136$	8.41510e11	−	6.11393e11i	0.132992	−	0.0966245i
$137$	2.23006e12	−	6.86341e12i	0.337281	−	1.03805i	−0.628306	−	0.777966i	$-0.716251\pi$
$137$	2.23006e12	−	6.86341e12i	0.337281	−	1.03805i	0.965587	−	0.260079i	$-0.0837486\pi$
$138$	1.81909e12	+	5.91059e11i	0.263379	+	0.0855769i
$139$	1.96111e12	+	2.69924e12i	0.271903	+	0.374242i	0.923031	−	0.384726i	$-0.125704\pi$
$139$	1.96111e12	+	2.69924e12i	0.271903	+	0.374242i	−0.651128	+	0.758968i	$0.725704\pi$
$140$	−1.39934e12	+	1.92602e12i	−0.185847	+	0.255796i
$141$	7.90869e11	+	2.43404e12i	0.100644	+	0.309752i
$142$			8.79281e12i			1.07250i
$143$	−1.84045e10	+	9.56969e11i	−0.00215232	+	0.111913i
$144$	−1.66450e12			−0.186684
$145$	−2.33076e13	+	7.57311e12i	−2.50779	+	0.814829i
$146$	2.12097e12	+	1.54098e12i	0.218987	+	0.159103i
$147$	3.55993e12	−	2.58644e12i	0.352807	−	0.256329i
$148$	1.67283e12	−	5.14845e12i	0.159178	−	0.489899i
$149$	7.50840e12	+	2.43963e12i	0.686167	+	0.222949i	0.631293	−	0.775544i	$-0.282524\pi$
$149$	7.50840e12	+	2.43963e12i	0.686167	+	0.222949i	0.0548737	+	0.998493i	$0.482524\pi$
$150$	4.75672e12	+	6.54706e12i	0.417599	+	0.574776i
$151$	3.07049e12	−	4.22616e12i	0.259027	−	0.356521i	−0.659620	−	0.751599i	$-0.729283\pi$
$151$	3.07049e12	−	4.22616e12i	0.259027	−	0.356521i	0.918647	+	0.395079i	$0.129283\pi$
$152$	−1.63522e12	−	5.03268e12i	−0.132591	−	0.408073i
$153$			4.45379e12i			0.347201i
$154$	−2.82599e12	+	1.97131e12i	−0.211859	+	0.147785i
$155$	4.14743e12			0.299081
$156$	3.86075e11	−	1.25443e11i	0.0267870	−	0.00870362i
$157$	1.04007e13	+	7.55652e12i	0.694485	+	0.504573i	0.878132	−	0.478419i	$-0.158790\pi$
$157$	1.04007e13	+	7.55652e12i	0.694485	+	0.504573i	−0.183646	+	0.982992i	$0.558790\pi$
$158$	1.24283e13	−	9.02972e12i	0.798860	−	0.580406i
$159$	3.59119e12	−	1.10526e13i	0.222257	−	0.684037i
$160$	4.88269e12	+	1.58648e12i	0.291031	+	0.0945616i
$161$	2.91029e12	+	4.00567e12i	0.167102	+	0.229996i
$162$	2.28651e12	−	3.14711e12i	0.126498	−	0.174109i
$163$	−3.60478e12	−	1.10944e13i	−0.192200	−	0.591531i	−0.999998	−	0.00207109i	$-0.999341\pi$
$163$	−3.60478e12	−	1.10944e13i	−0.192200	−	0.591531i	0.807798	−	0.589460i	$-0.200659\pi$
$164$			6.85450e12i			0.352300i
$165$	5.10976e12	+	1.68201e13i	0.253219	+	0.833536i
$166$	−3.42059e12			−0.163475
$167$	−1.26548e13	+	4.11178e12i	−0.583385	+	0.189553i	−0.585816	−	0.810444i	$-0.699226\pi$
$167$	−1.26548e13	+	4.11178e12i	−0.583385	+	0.189553i	0.00243164	+	0.999997i	$0.499226\pi$
$168$	1.18226e12	+	8.58960e11i	0.0525843	+	0.0382048i
$169$	−1.86124e13	+	1.35227e13i	−0.798881	+	0.580421i
$170$	4.24504e12	−	1.30649e13i	0.175869	−	0.541268i
$171$	2.15490e13	+	7.00170e12i	0.861888	+	0.280044i
$172$	3.95503e12	+	5.44363e12i	0.152749	+	0.210241i
$173$	1.89518e13	−	2.60849e13i	0.706927	−	0.973001i	−0.292931	−	0.956134i	$-0.594631\pi$
$173$	1.89518e13	−	2.60849e13i	0.706927	−	0.973001i	0.999858	−	0.0168675i	$-0.00536935\pi$
$174$	4.64863e12	+	1.43070e13i	0.167506	+	0.515529i
$175$			2.09487e13i			0.729338i
$176$	5.92628e12	+	4.48230e12i	0.199391	+	0.150808i
$177$	−2.17765e13			−0.708187
$178$	−2.78467e13	+	9.04795e12i	−0.875496	+	0.284466i
$179$	−5.13705e12	−	3.73229e12i	−0.156169	−	0.113464i	0.506956	−	0.861972i	$-0.330771\pi$
$179$	−5.13705e12	−	3.73229e12i	−0.156169	−	0.113464i	−0.663126	+	0.748508i	$0.730771\pi$
$180$	−1.77844e13	+	1.29211e13i	−0.522881	+	0.379895i
$181$	−5.18293e11	+	1.59514e12i	−0.0147402	+	0.0453657i	−0.958156	−	0.286246i	$-0.907592\pi$
$181$	−5.18293e11	+	1.59514e12i	−0.0147402	+	0.0453657i	0.943416	+	0.331612i	$0.107592\pi$
$182$	9.99401e11	+	3.24725e11i	0.0274987	+	0.00893486i
$183$	7.91396e12	+	1.08926e13i	0.210711	+	0.290019i
$184$	6.27602e12	−	8.63820e12i	0.161725	−	0.222595i
$185$	−2.20928e13	−	6.79946e13i	−0.551087	−	1.69607i
$186$		−	2.54583e12i		−	0.0614825i
$187$	1.19936e13	−	1.58573e13i	0.280478	−	0.370834i
$188$	1.42869e13			0.323588
$189$	−1.39203e13	+	4.52298e12i	−0.305406	+	0.0992325i
$190$	−5.65390e13	−	4.10780e13i	−1.20178	−	0.873148i
$191$	2.34631e13	−	1.70469e13i	0.483265	−	0.351112i	−0.319324	−	0.947646i	$-0.603456\pi$
$191$	2.34631e13	−	1.70469e13i	0.483265	−	0.351112i	0.802588	+	0.596533i	$0.203456\pi$
$192$	9.73835e11	−	2.99716e12i	0.0194392	−	0.0598276i
$193$	−6.50095e13	−	2.11229e13i	−1.25786	−	0.408704i	−0.397131	−	0.917762i	$-0.629994\pi$
$193$	−6.50095e13	−	2.11229e13i	−1.25786	−	0.408704i	−0.860732	+	0.509058i	$0.829994\pi$
$194$	−3.71776e13	−	5.11706e13i	−0.697382	−	0.959865i
$195$	3.15124e12	−	4.33731e12i	0.0573157	−	0.0788883i
$196$	−7.59072e12	−	2.33618e13i	−0.133889	−	0.412069i
$197$			7.19775e13i			1.23140i	0.787980	+	0.615700i	$0.211127\pi$
$197$			7.19775e13i			1.23140i	−0.787980	+	0.615700i	$0.788873\pi$
$198$	−3.04422e13	+	9.24800e12i	−0.505224	+	0.153482i
$199$	8.44133e13			1.35923			0.679614	−	0.733570i	$-0.262147\pi$
$199$	8.44133e13			1.35923			0.679614	+	0.733570i	$0.262147\pi$
$200$	4.29647e13	−	1.39601e13i	0.671324	−	0.218126i
$201$	−4.34319e13	−	3.15551e13i	−0.658616	−	0.478512i
$202$	−5.60732e13	+	4.07396e13i	−0.825368	+	0.599665i
$203$	−1.20335e13	+	3.70354e13i	−0.171956	+	0.529226i
$204$	−8.01967e12	−	2.60575e12i	−0.111269	−	0.0361536i
$205$	5.32099e13	+	7.32371e13i	0.716917	+	0.986752i
$206$	1.40217e13	−	1.92992e13i	0.183483	−	0.252543i
$207$	1.41278e13	+	4.34810e13i	0.179578	+	0.552685i
$208$		−	2.26612e12i		−	0.0279835i
$209$	−5.78684e13	−	8.29579e13i	−0.694327	−	0.995360i
$210$	1.92998e13			0.225028
$211$	9.16071e13	−	2.97650e13i	1.03809	−	0.337295i	0.260105	−	0.965580i	$-0.416243\pi$
$211$	9.16071e13	−	2.97650e13i	1.03809	−	0.337295i	0.777983	+	0.628285i	$0.216243\pi$
$212$	−5.24845e13	−	3.81322e13i	−0.578117	−	0.420026i
$213$	5.76678e13	−	4.18981e13i	0.617527	−	0.448660i
$214$	−2.47004e13	+	7.60201e13i	−0.257171	+	0.791491i
$215$	8.45152e13	+	2.74606e13i	0.855665	+	0.278023i
$216$	1.85528e13	+	2.55357e13i	0.182678	+	0.251435i
$217$	3.87361e12	−	5.33157e12i	0.0370986	−	0.0510619i
$218$	2.47022e13	+	7.60254e13i	0.230142	+	0.708304i
$219$		−	2.12532e13i		−	0.192646i
$220$	9.81145e13	+	1.88694e12i	0.865361	+	0.0166426i
$221$	−6.06358e12			−0.0520446
$222$	−4.17374e13	+	1.35613e13i	−0.348664	+	0.113288i
$223$	−2.90630e13	−	2.11155e13i	−0.236326	−	0.171701i	0.463319	−	0.886191i	$-0.346658\pi$
$223$	−2.90630e13	−	2.11155e13i	−0.236326	−	0.171701i	−0.699645	+	0.714491i	$0.746658\pi$
$224$	6.59977e12	−	4.79502e12i	0.0522445	−	0.0379579i
$225$	−5.97745e13	+	1.83967e14i	−0.460703	+	1.41790i
$226$	8.21113e13	+	2.66796e13i	0.616243	+	0.200230i
$227$	6.38691e13	+	8.79083e13i	0.466805	+	0.642502i	0.975903	−	0.218207i	$-0.0700206\pi$
$227$	6.38691e13	+	8.79083e13i	0.466805	+	0.642502i	−0.509097	+	0.860709i	$0.670021\pi$
$228$	−2.52150e13	+	3.47055e13i	−0.179494	+	0.247053i
$229$	2.39451e13	+	7.36953e13i	0.166036	+	0.511007i	0.999111	−	0.0421531i	$-0.0134217\pi$
$229$	2.39451e13	+	7.36953e13i	0.166036	+	0.511007i	−0.833075	+	0.553160i	$0.813422\pi$
$230$		−	1.41014e14i		−	0.952569i
$231$	2.63949e13	+	9.14096e12i	0.173719	+	0.0601617i
$232$	8.39768e13			0.538557
$233$	−7.85866e13	+	2.55343e13i	−0.491149	+	0.159584i	−0.544112	−	0.839013i	$-0.683133\pi$
$233$	−7.85866e13	+	2.55343e13i	−0.491149	+	0.159584i	0.0529632	+	0.998596i	$0.483133\pi$
$234$	7.84996e12	+	5.70333e12i	0.0478159	+	0.0347403i
$235$	1.52649e14	−	1.10906e14i	0.906332	−	0.658488i
$236$	−3.75653e13	+	1.15614e14i	−0.217428	+	0.669173i
$237$	−1.18443e14	−	3.84845e13i	−0.668374	−	0.217168i
$238$	−1.28303e13	−	1.76594e13i	−0.0705952	−	0.0971660i
$239$	1.12498e14	−	1.54840e14i	0.603611	−	0.830799i	−0.392422	−	0.919785i	$-0.628363\pi$
$239$	1.12498e14	−	1.54840e14i	0.603611	−	0.830799i	0.996033	+	0.0889861i	$0.0283627\pi$
$240$	−1.28612e13	−	3.95828e13i	−0.0673001	−	0.207128i
$241$			3.11388e14i			1.58928i	0.607084	+	0.794638i	$0.292339\pi$
$241$			3.11388e14i			1.58928i	−0.607084	+	0.794638i	$0.707661\pi$
$242$	1.33290e14	+	4.90507e13i	0.663600	+	0.244204i
$243$	−2.12524e14			−1.03222
$244$	7.14822e13	−	2.32260e13i	0.338734	−	0.110061i
$245$	−2.62455e14	−	1.90685e14i	−1.21355	−	0.881699i
$246$	4.49554e13	−	3.26620e13i	0.202848	−	0.147378i
$247$	−9.53240e12	+	2.93377e13i	−0.0419779	+	0.129195i
$248$	−1.35161e13	−	4.39166e12i	−0.0580955	−	0.0188764i
$249$	1.62992e13	+	2.24340e13i	0.0683867	+	0.0941262i
$250$	1.75038e14	−	2.40918e14i	0.716954	−	0.986802i
$251$	−1.03574e14	−	3.18769e14i	−0.414200	−	1.27478i	−0.912964	−	0.408040i	$-0.866213\pi$
$251$	−1.03574e14	−	3.18769e14i	−0.414200	−	1.27478i	0.498764	−	0.866738i	$-0.333787\pi$
$252$			3.49301e13i			0.136394i
$253$	6.67887e13	−	1.92855e14i	0.254671	−	0.735372i
$254$	−2.42646e14			−0.903590
$255$	−1.05914e14	+	3.44136e13i	−0.385224	+	0.125167i
$256$	−1.42324e13	−	1.03404e13i	−0.0505636	−	0.0367366i
$257$	2.13872e14	−	1.55387e14i	0.742258	−	0.539282i	−0.151160	−	0.988509i	$-0.548301\pi$
$257$	2.13872e14	−	1.55387e14i	0.742258	−	0.539282i	0.893417	+	0.449228i	$0.148301\pi$
$258$	1.68563e13	−	5.18782e13i	0.0571535	−	0.175900i
$259$	−1.08042e14	−	3.51050e13i	−0.357927	−	0.116298i
$260$	−1.75913e13	−	2.42124e13i	−0.0569453	−	0.0783785i
$261$	−2.11352e14	+	2.90901e14i	−0.668595	+	0.920242i
$262$	1.04783e14	+	3.22490e14i	0.323955	+	0.997032i
$263$		−	5.84724e13i		−	0.176692i	−0.996090	−	0.0883459i	$-0.971842\pi$
$263$		−	5.84724e13i		−	0.176692i	0.996090	−	0.0883459i	$-0.0281581\pi$
$264$	1.15827e12	−	6.02260e13i	0.00342125	−	0.177894i
$265$	−8.56783e14			−2.47398
$266$	−1.05613e14	+	3.43156e13i	−0.298144	+	0.0968728i
$267$	1.92032e14	+	1.39519e14i	0.530037	+	0.385094i
$268$	−2.42452e14	+	1.76152e14i	−0.654360	+	0.475420i
$269$	3.11723e13	−	9.59385e13i	0.0822726	−	0.253209i	−0.901456	−	0.432871i	$-0.857500\pi$
$269$	3.11723e13	−	9.59385e13i	0.0822726	−	0.253209i	0.983728	+	0.179662i	$0.0575005\pi$
$270$	3.96456e14	+	1.28816e14i	1.02332	+	0.332497i
$271$	−2.54498e14	−	3.50286e14i	−0.642493	−	0.884315i	0.356253	−	0.934390i	$-0.384054\pi$
$271$	−2.54498e14	−	3.50286e14i	−0.642493	−	0.884315i	−0.998745	+	0.0500742i	$0.984054\pi$
$272$	−2.76685e13	+	3.80824e13i	−0.0683238	+	0.0940397i
$273$	−2.63247e12	−	8.10192e12i	−0.00635899	−	0.0195710i
$274$			3.26587e14i			0.771783i
$275$	7.08224e14	−	4.94031e14i	1.63747	−	1.14224i
$276$	−8.65593e13			−0.195821
$277$	−6.11381e14	+	1.98650e14i	−1.35342	+	0.439753i	−0.893842	−	0.448383i	$-0.852000\pi$
$277$	−6.11381e14	+	1.98650e14i	−1.35342	+	0.439753i	−0.459580	+	0.888136i	$0.652000\pi$
$278$	−1.22154e14	−	8.87499e13i	−0.264629	−	0.192264i
$279$	4.92302e13	−	3.57678e13i	0.104377	−	0.0758346i
$280$	3.32929e13	−	1.02465e14i	0.0690881	−	0.212631i
$281$	8.60444e14	+	2.79575e14i	1.74777	+	0.567885i	0.995820	−	0.0913341i	$-0.0291131\pi$
$281$	8.60444e14	+	2.79575e14i	1.74777	+	0.567885i	0.751951	+	0.659219i	$0.229113\pi$
$282$	−6.80778e13	−	9.37011e13i	−0.135366	−	0.186316i
$283$	2.17794e14	−	2.99768e14i	0.423963	−	0.583535i	−0.542592	−	0.839997i	$-0.682557\pi$
$283$	2.17794e14	−	2.99768e14i	0.423963	−	0.583535i	0.966554	+	0.256462i	$0.0825569\pi$
$284$	−1.22963e14	−	3.78442e14i	−0.234350	−	0.721255i
$285$			5.66551e14i			1.05723i
$286$	−1.25906e13	−	4.14452e13i	−0.0230065	−	0.0757318i
$287$	1.43844e14			0.257395
$288$	7.16398e13	−	2.32772e13i	0.125545	−	0.0407920i
$289$	−3.69452e14	−	2.68423e14i	−0.634119	−	0.460715i
$290$	8.97253e14	−	6.51892e14i	1.50844	−	1.09594i
$291$	−1.58450e14	+	4.87660e14i	−0.260937	+	0.803081i
$292$	−1.12836e14	−	3.66627e13i	−0.182033	−	0.0591463i
$293$	−2.50794e14	−	3.45188e14i	−0.396379	−	0.545569i	0.563451	−	0.826149i	$-0.309473\pi$
$293$	−2.50794e14	−	3.45188e14i	−0.396379	−	0.545569i	−0.959831	+	0.280580i	$0.909473\pi$
$294$	−1.17049e14	+	1.61104e14i	−0.181252	+	0.249472i
$295$	4.96117e14	+	1.52689e15i	0.752752	+	2.31673i
$296$			2.44983e14i			0.364238i
$297$	4.81192e14	+	3.63946e14i	0.701099	+	0.530271i
$298$	−3.57278e14			−0.510163
$299$	−5.91969e13	+	1.92342e13i	−0.0828461	+	0.0269183i
$300$	−2.96286e14	−	2.15264e14i	−0.406428	−	0.295287i
$301$	1.14237e14	−	8.29977e13i	0.153605	−	0.111601i
$302$	−7.30527e13	+	2.24833e14i	−0.0962929	+	0.296359i
$303$	5.34383e14	+	1.73632e14i	0.690553	+	0.224374i
$304$	1.40759e14	+	1.93738e14i	0.178334	+	0.245456i
$305$	5.83456e14	−	8.03058e14i	0.724785	−	0.997581i
$306$	−6.22841e13	−	1.91691e14i	−0.0758662	−	0.233492i
$307$			5.35111e14i			0.639165i	0.947558	+	0.319583i	$0.103543\pi$
$307$			5.35111e14i			0.639165i	−0.947558	+	0.319583i	$0.896457\pi$
$308$	9.40627e13	−	1.24365e14i	0.110183	−	0.145678i
$309$	−1.93388e14			−0.222166
$310$	−1.78505e14	+	5.79997e13i	−0.201131	+	0.0653515i
$311$	−9.03695e14	−	6.56573e14i	−0.998757	−	0.725639i	−0.0369354	−	0.999318i	$-0.511760\pi$
$311$	−9.03695e14	−	6.56573e14i	−0.998757	−	0.725639i	−0.961821	+	0.273679i	$0.911760\pi$
$312$	−1.48624e13	+	1.07981e13i	−0.0161124	+	0.0117063i
$313$	−3.32843e13	+	1.02439e14i	−0.0353976	+	0.108943i	−0.967194	−	0.254038i	$-0.918241\pi$
$313$	−3.32843e13	+	1.02439e14i	−0.0353976	+	0.108943i	0.931797	+	0.362981i	$0.118241\pi$
$314$	−5.53318e14	−	1.79784e14i	−0.577294	−	0.187574i
$315$	2.71154e14	+	3.73211e14i	0.277557	+	0.382025i
$316$	−4.08638e14	+	5.62442e14i	−0.410409	+	0.564879i
$317$	−1.61396e14	−	4.96725e14i	−0.159051	−	0.489509i	0.839498	−	0.543363i	$-0.182849\pi$
$317$	−1.61396e14	−	4.96725e14i	−0.159051	−	0.489509i	−0.998549	+	0.0538545i	$0.982849\pi$
$318$			5.25922e14i			0.508579i
$319$	1.53586e15	−	4.66578e14i	1.45750	−	0.442772i
$320$	−2.32337e14			−0.216380
$321$	6.16278e14	−	2.00241e14i	0.563309	−	0.183030i
$322$	−1.81276e14	−	1.31705e14i	−0.162631	−	0.118159i
$323$	5.18397e14	−	3.76638e14i	0.456507	−	0.331672i
$324$	−5.44003e13	+	1.67427e14i	−0.0470253	+	0.144729i
$325$	−2.50460e14	−	8.13795e13i	−0.212539	−	0.0690581i
$326$	3.10299e14	+	4.27090e14i	0.258508	+	0.355806i
$327$	3.80907e14	−	5.24274e14i	0.311554	−	0.428817i
$328$	−9.58569e13	−	2.95017e14i	−0.0769804	−	0.236921i
$329$		−	2.99816e14i		−	0.236418i
$330$	−4.55144e14	−	6.52477e14i	−0.352424	−	0.505222i
$331$	5.87865e14			0.447002			0.223501	−	0.974704i	$-0.428251\pi$
$331$	5.87865e14			0.447002			0.223501	+	0.974704i	$0.428251\pi$
$332$	1.47222e14	−	4.78353e13i	0.109937	−	0.0357207i
$333$	−8.48635e14	−	6.16570e14i	−0.622380	−	0.452186i
$334$	4.87158e14	−	3.53941e14i	0.350906	−	0.254948i
$335$	−1.22306e15	+	3.76419e15i	−0.865324	+	2.66319i
$336$	−6.28964e13	−	2.04363e13i	−0.0437109	−	0.0142025i
$337$	1.50181e15	+	2.06706e15i	1.02526	+	1.41115i	0.908448	+	0.417999i	$0.137268\pi$
$337$	1.50181e15	+	2.06706e15i	1.02526	+	1.41115i	0.116815	+	0.993154i	$0.462732\pi$
$338$	6.11967e14	−	8.42301e14i	0.410419	−	0.564894i
$339$	−2.16285e14	−	6.65658e14i	−0.142505	−	0.438584i
$340$			6.21676e14i			0.402431i
$341$	−2.71598e14	−	5.22338e12i	−0.172743	−	0.00332220i
$342$	−1.02538e15			−0.640810
$343$	−1.05601e15	+	3.43119e14i	−0.648492	+	0.210708i
$344$	−2.46350e14	−	1.78984e14i	−0.148663	−	0.108010i
$345$	−9.24845e14	+	6.71939e14i	−0.548472	+	0.398488i
$346$	−4.50899e14	+	1.38773e15i	−0.262799	+	0.808811i
$347$	−1.50425e15	−	4.88760e14i	−0.861674	−	0.279975i	−0.155346	−	0.987860i	$-0.549649\pi$
$347$	−1.50425e15	−	4.88760e14i	−0.861674	−	0.279975i	−0.706327	+	0.707885i	$0.749649\pi$
$348$	−4.00153e14	−	5.50764e14i	−0.225295	−	0.310091i
$349$	1.59086e15	−	2.18963e15i	0.880399	−	1.21176i	−0.0959115	−	0.995390i	$-0.530577\pi$
$349$	1.59086e15	−	2.18963e15i	0.880399	−	1.21176i	0.976310	−	0.216375i	$-0.0694234\pi$
$350$	−2.92957e14	−	9.01630e14i	−0.159366	−	0.490479i
$351$		−	1.84000e14i		−	0.0983955i
$352$	−3.17749e14	−	1.10042e14i	−0.167043	−	0.0578497i
$353$	2.20981e15			1.14211			0.571053	−	0.820913i	$-0.306535\pi$
$353$	2.20981e15			1.14211			0.571053	+	0.820913i	$0.306535\pi$
$354$	9.37257e14	−	3.04533e14i	0.476255	−	0.154744i
$355$	−4.25156e15	−	3.08894e15i	−2.12411	−	1.54326i
$356$	1.07199e15	−	7.78846e14i	0.526612	−	0.382606i
$357$	−5.46826e13	+	1.68296e14i	−0.0264143	+	0.0812949i
$358$	2.73292e14	+	8.87981e13i	0.129816	+	0.0421799i
$359$	−1.90639e15	−	2.62393e15i	−0.890525	−	1.22570i	−0.973393	−	0.229142i	$-0.926408\pi$
$359$	−1.90639e15	−	2.62393e15i	−0.890525	−	1.22570i	0.0828682	−	0.996561i	$-0.473592\pi$
$360$	5.84742e14	−	8.04828e14i	0.268627	−	0.369733i
$361$	−3.23394e14	−	9.95303e14i	−0.146113	−	0.449689i
$362$		−	7.59028e13i		−	0.0337292i
$363$	−3.13434e14	−	1.10791e15i	−0.136996	−	0.484247i
$364$	−4.75552e13			−0.0204451
$365$	−1.49021e15	+	4.84197e14i	−0.630215	+	0.204769i
$366$	−4.92944e14	−	3.58145e14i	−0.205074	−	0.148995i
$367$	−2.52901e14	+	1.83743e14i	−0.103503	+	0.0751994i	−0.638333	−	0.769760i	$-0.720376\pi$
$367$	−2.52901e14	+	1.83743e14i	−0.103503	+	0.0751994i	0.534830	+	0.844960i	$0.320376\pi$
$368$	−1.49318e14	+	4.59554e14i	−0.0601210	+	0.185033i
$369$	1.26321e15	+	4.10441e14i	0.500400	+	0.162590i
$370$	1.90174e15	+	2.61752e15i	0.741210	+	1.02019i
$371$	−8.00218e14	+	1.10141e15i	−0.306877	+	0.422380i
$372$	3.56022e13	+	1.09572e14i	0.0134344	+	0.0413469i
$373$			2.87774e15i			1.06856i	0.845308	+	0.534280i	$0.179417\pi$
$373$			2.87774e15i			1.06856i	−0.845308	+	0.534280i	$0.820583\pi$
$374$	−2.94445e14	+	8.50221e14i	−0.107591	+	0.310672i
$375$	−2.41413e15			−0.868106
$376$	−6.14908e14	+	1.99796e14i	−0.217612	+	0.0707065i
$377$	−3.96045e14	−	2.87743e14i	−0.137942	−	0.100221i
$378$	5.35877e14	−	3.89337e14i	0.183702	−	0.133467i
$379$	5.75587e14	−	1.77148e15i	0.194212	−	0.597723i	−0.805773	−	0.592225i	$-0.798250\pi$
$379$	5.75587e14	−	1.77148e15i	0.194212	−	0.597723i	0.999985	−	0.00549834i	$-0.00175018\pi$
$380$	3.00789e15	+	9.77323e14i	0.998988	+	0.324591i
$381$	1.15622e15	+	1.59140e15i	0.377999	+	0.520271i
$382$	−7.71456e14	+	1.06182e15i	−0.248274	+	0.341720i
$383$	6.38124e14	+	1.96395e15i	0.202168	+	0.622210i	0.999818	+	0.0190885i	$0.00607643\pi$
$383$	6.38124e14	+	1.96395e15i	0.202168	+	0.622210i	−0.797650	+	0.603121i	$0.793924\pi$
$384$			1.42616e14i			0.0444816i
$385$	3.95982e13	−	2.05897e15i	0.0121594	−	0.632245i
$386$	3.09340e15			0.935216
$387$	1.24002e15	−	4.02908e14i	0.369117	−	0.119933i
$388$	2.31572e15	+	1.68247e15i	0.678727	+	0.493124i
$389$	4.44051e14	−	3.22622e14i	0.128155	−	0.0931099i	−0.521861	−	0.853030i	$-0.674762\pi$
$389$	4.44051e14	−	3.22622e14i	0.128155	−	0.0931099i	0.650016	+	0.759920i	$0.274762\pi$
$390$	−7.49739e13	+	2.30746e14i	−0.0213070	+	0.0655762i
$391$	1.22966e15	+	3.99540e14i	0.344131	+	0.111815i
$392$	6.53407e14	+	8.99338e14i	0.180081	+	0.247860i
$393$	1.61576e15	−	2.22390e15i	0.438553	−	0.603616i
$394$	−1.00657e15	−	3.09790e15i	−0.269071	−	0.828115i
$395$			9.18159e15i			2.41733i
$396$	1.18090e15	−	8.23752e14i	0.306226	−	0.213612i
$397$	2.01614e15			0.514966			0.257483	−	0.966283i	$-0.417107\pi$
$397$	2.01614e15			0.514966			0.257483	+	0.966283i	$0.417107\pi$
$398$	−3.63314e15	+	1.18048e15i	−0.914079	+	0.297002i
$399$	7.28308e14	+	5.29147e14i	0.180500	+	0.131141i
$400$	−1.65397e15	+	1.20168e15i	−0.403802	+	0.293379i
$401$	1.81489e15	−	5.58565e15i	0.436499	−	1.34341i	−0.455043	−	0.890469i	$-0.650376\pi$
$401$	1.81489e15	−	5.58565e15i	0.436499	−	1.34341i	0.891542	−	0.452937i	$-0.149624\pi$
$402$	2.31059e15	+	7.50755e14i	0.547477	+	0.177886i
$403$	4.86958e13	+	6.70241e13i	0.0113674	+	0.0156459i
$404$	1.84366e15	−	2.53759e15i	0.424027	−	0.583623i
$405$	7.18454e14	+	2.21117e15i	0.162805	+	0.501064i
$406$		−	1.76228e15i		−	0.393477i
$407$	1.36113e15	+	4.48052e15i	0.299457	+	0.985738i
$408$	3.81606e14			0.0827283
$409$	−3.51622e15	+	1.14249e15i	−0.751167	+	0.244069i	−0.659483	−	0.751719i	$-0.729225\pi$
$409$	−3.51622e15	+	1.14249e15i	−0.751167	+	0.244069i	−0.0916840	+	0.995788i	$0.529225\pi$
$410$	−3.31433e15	−	2.40800e15i	−0.697739	−	0.506937i
$411$	2.14192e15	−	1.55620e15i	0.444379	−	0.322860i
$412$	−3.33601e14	+	1.02672e15i	−0.0682095	+	0.209927i
$413$	2.42620e15	+	7.88321e14i	0.488908	+	0.158856i
$414$	−1.21612e15	−	1.67385e15i	−0.241532	−	0.332441i
$415$	1.20166e15	−	1.65394e15i	0.235230	−	0.323767i
$416$	3.16905e13	+	9.75334e13i	0.00611462	+	0.0188189i
$417$			1.22404e15i			0.232799i
$418$	3.65078e15	+	2.76124e15i	0.684428	+	0.517662i
$419$	−5.26031e15			−0.972136			−0.486068	−	0.873921i	$-0.661569\pi$
$419$	−5.26031e15			−0.972136			−0.486068	+	0.873921i	$0.661569\pi$
$420$	−8.30660e14	+	2.69898e14i	−0.151331	+	0.0491704i
$421$	−3.55503e15	−	2.58288e15i	−0.638485	−	0.463886i	0.220845	−	0.975309i	$-0.429119\pi$
$421$	−3.55503e15	−	2.58288e15i	−0.638485	−	0.463886i	−0.859329	+	0.511423i	$0.829119\pi$
$422$	−3.52651e15	+	2.56216e15i	−0.624411	+	0.453661i
$423$	8.55489e14	−	2.63292e15i	0.149339	−	0.459617i
$424$	2.79219e15	+	9.07236e14i	0.480562	+	0.156144i
$425$	3.21541e15	+	4.42563e15i	0.545636	+	0.751003i
$426$	−1.89609e15	+	2.60975e15i	−0.317250	+	0.436657i
$427$	−4.87406e14	−	1.50008e15i	−0.0804125	−	0.247484i
$428$		−	3.61732e15i		−	0.588470i
$429$	−2.11824e14	+	2.80064e14i	−0.0339807	+	0.0449277i
$430$	−4.02155e15			−0.636184
$431$	−7.25981e15	+	2.35886e15i	−1.13256	+	0.367992i	−0.814549	−	0.580095i	$-0.803015\pi$
$431$	−7.25981e15	+	2.35886e15i	−1.13256	+	0.367992i	−0.318013	+	0.948086i	$0.603015\pi$
$432$	−1.15562e15	−	8.39604e14i	−0.177791	−	0.129173i
$433$	−9.56453e14	+	6.94904e14i	−0.145123	+	0.105438i	−0.657978	−	0.753037i	$-0.728588\pi$
$433$	−9.56453e14	+	6.94904e14i	−0.145123	+	0.105438i	0.512855	+	0.858475i	$0.328588\pi$
$434$	−9.21605e13	+	2.83641e14i	−0.0137913	+	0.0424454i
$435$	−8.55089e15	−	2.77835e15i	−1.26205	−	0.410064i
$436$	−2.12636e15	−	2.92668e15i	−0.309540	−	0.426046i
$437$	3.86623e15	−	5.32141e15i	0.555135	−	0.764078i
$438$	2.97216e14	+	9.14738e14i	0.0420947	+	0.129554i
$439$		−	1.10244e16i		−	1.54017i	−0.637939	−	0.770087i	$-0.720213\pi$
$439$		−	1.10244e16i		−	1.54017i	0.637939	−	0.770087i	$-0.279787\pi$
$440$	−4.24923e15	+	1.29087e15i	−0.585590	+	0.177896i
$441$	−4.75985e15			−0.647086
$442$	2.60976e14	−	8.47962e13i	0.0349999	−	0.0113722i
$443$	1.07394e16	+	7.80262e15i	1.42088	+	1.03233i	0.991626	+	0.129145i	$0.0412233\pi$
$443$	1.07394e16	+	7.80262e15i	1.42088	+	1.03233i	0.429253	+	0.903184i	$0.358777\pi$
$444$	1.60672e15	−	1.16735e15i	0.209722	−	0.152372i
$445$	5.40770e15	−	1.66432e16i	0.696390	−	2.14327i
$446$	1.54616e15	+	5.02377e14i	0.196447	+	0.0638294i
$447$	1.70244e15	+	2.34321e15i	0.213416	+	0.293742i
$448$	−2.16998e14	+	2.98672e14i	−0.0268403	+	0.0369425i
$449$	−5.45164e14	−	1.67784e15i	−0.0665348	−	0.204773i	0.912262	−	0.409608i	$-0.134334\pi$
$449$	−5.45164e14	−	1.67784e15i	−0.0665348	−	0.204773i	−0.978797	+	0.204834i	$0.934334\pi$
$450$		−	8.75384e15i		−	1.05420i
$451$	−3.39226e15	−	4.86302e15i	−0.403116	−	0.577892i
$452$	−3.90716e15			−0.458174
$453$	1.82267e15	−	5.92221e14i	0.210921	−	0.0685322i
$454$	−3.97828e15	−	2.89039e15i	−0.454318	−	0.330081i
$455$	−5.08105e14	+	3.69160e14i	−0.0572645	+	0.0416051i
$456$	5.99913e14	−	1.84634e15i	0.0667267	−	0.205364i
$457$	5.54378e15	+	1.80128e15i	0.608567	+	0.197735i	0.597058	−	0.802198i	$-0.296336\pi$
$457$	5.54378e15	+	1.80128e15i	0.608567	+	0.197735i	0.0115095	+	0.999934i	$0.496336\pi$
$458$	−2.06119e15	−	2.83698e15i	−0.223318	−	0.307371i
$459$	−2.24658e15	+	3.09215e15i	−0.240240	+	0.330662i
$460$	1.97202e15	+	6.06924e15i	0.208144	+	0.640601i
$461$			1.76385e16i			1.83762i	0.394702	+	0.918809i	$0.370848\pi$
$461$			1.76385e16i			1.83762i	−0.394702	+	0.918809i	$0.629152\pi$
$462$	−1.26386e15	−	2.43067e13i	−0.129972	−	0.00249962i
$463$	−5.93942e15			−0.602918			−0.301459	−	0.953479i	$-0.597474\pi$
$463$	−5.93942e15			−0.602918			−0.301459	+	0.953479i	$0.597474\pi$
$464$	−3.61435e15	+	1.17437e15i	−0.362179	+	0.117679i
$465$	1.23098e15	+	8.94356e14i	0.121768	+	0.0884693i
$466$	3.02528e15	−	2.19799e15i	0.295427	−	0.214640i
$467$	−5.95934e15	+	1.83410e16i	−0.574509	+	1.76816i	0.0633353	+	0.997992i	$0.479826\pi$
$467$	−5.95934e15	+	1.83410e16i	−0.574509	+	1.76816i	−0.637845	+	0.770165i	$0.720174\pi$
$468$	−4.17620e14	−	1.35693e14i	−0.0397472	−	0.0129146i
$469$	3.69660e15	+	5.08794e15i	0.347349	+	0.478085i
$470$	−5.01904e15	+	6.90811e15i	−0.465622	+	0.640873i
$471$	1.45747e15	+	4.48562e15i	0.133498	+	0.410863i
$472$		−	5.50135e15i		−	0.497528i
$473$	−5.49997e15	−	1.90473e15i	−0.491127	−	0.170085i
$474$	5.63597e15			0.496934
$475$	2.64676e16	−	8.59985e15i	2.30438	−	0.748737i
$476$	7.99173e14	+	5.80633e14i	0.0687067	+	0.0499184i
$477$	−1.01701e16	+	7.38898e15i	−0.863403	+	0.627299i
$478$	−2.67654e15	+	8.23753e15i	−0.224391	+	0.690605i
$479$	−1.80824e16	−	5.87533e15i	−1.49707	−	0.486429i	−0.557912	−	0.829900i	$-0.688397\pi$
$479$	−1.80824e16	−	5.87533e15i	−1.49707	−	0.486429i	−0.939163	+	0.343471i	$0.888397\pi$
$480$	1.10709e15	+	1.52378e15i	0.0905184	+	0.124588i
$481$	8.39424e14	−	1.15537e15i	0.0677814	−	0.0932932i
$482$	−4.35460e15	−	1.34021e16i	−0.347269	−	1.06879i
$483$			1.81648e15i			0.143070i
$484$	−6.42275e15	−	2.47136e14i	−0.499630	−	0.0192249i
$485$	3.78029e16			2.90452
$486$	9.14702e15	−	2.97205e15i	0.694164	−	0.225547i
$487$	1.08861e16	+	7.90921e15i	0.816015	+	0.592870i	0.915568	−	0.402162i	$-0.131741\pi$
$487$	1.08861e16	+	7.90921e15i	0.816015	+	0.592870i	−0.0995530	+	0.995032i	$0.531741\pi$
$488$	−2.75178e15	+	1.99929e15i	−0.203749	+	0.148032i
$489$	1.32249e15	−	4.07020e15i	0.0967250	−	0.297689i
$490$	1.39627e16	+	4.53676e15i	1.00877	+	0.327770i
$491$	−1.01563e16	−	1.39789e16i	−0.724846	−	0.997665i	−0.999349	−	0.0360791i	$-0.988513\pi$
$491$	−1.01563e16	−	1.39789e16i	−0.724846	−	0.997665i	0.274503	−	0.961586i	$-0.411487\pi$
$492$	−1.47811e15	+	2.03445e15i	−0.104212	+	0.143435i
$493$	3.14234e15	+	9.67114e15i	0.218863	+	0.673591i
$494$		−	1.39600e15i		−	0.0960558i
$495$	6.22275e15	−	1.79684e16i	0.423011	−	1.22146i
$496$	6.43148e14			0.0431937
$497$	−7.94174e15	+	2.58043e15i	−0.526959	+	0.171219i
$498$	−1.01525e15	−	7.37620e14i	−0.0665573	−	0.0483567i
$499$	5.77151e15	−	4.19324e15i	0.373840	−	0.271611i	−0.384961	−	0.922933i	$-0.625785\pi$
$499$	5.77151e15	−	4.19324e15i	0.373840	−	0.271611i	0.758801	+	0.651322i	$0.225785\pi$
$500$	−4.16447e15	+	1.28169e16i	−0.266526	+	0.820283i
$501$	−4.64266e15	−	1.50849e15i	−0.293590	−	0.0953930i
$502$	8.91567e15	+	1.22714e16i	0.557098	+	0.766780i
$503$	−1.20920e16	+	1.66432e16i	−0.746602	+	1.02761i	0.251610	+	0.967829i	$0.419040\pi$
$503$	−1.20920e16	+	1.66432e16i	−0.746602	+	1.02761i	−0.998212	+	0.0597803i	$0.980960\pi$
$504$	−4.88480e14	−	1.50339e15i	−0.0298032	−	0.0917249i
$505$		−	4.14248e16i		−	2.49754i
$506$	−1.77597e14	+	9.23446e15i	−0.0105812	+	0.550185i
$507$	−8.44029e15			−0.496947
$508$	1.04435e16	−	3.39329e15i	0.607663	−	0.197442i
$509$	5.39074e14	+	3.91660e14i	0.0309986	+	0.0225218i	0.603177	−	0.797608i	$-0.293901\pi$
$509$	5.39074e14	+	3.91660e14i	0.0309986	+	0.0225218i	−0.572178	+	0.820129i	$0.693901\pi$
$510$	4.07728e15	−	2.96232e15i	0.231712	−	0.168349i
$511$	−7.69380e14	+	2.36791e15i	−0.0432131	+	0.132996i
$512$	7.57166e14	+	2.46018e14i	0.0420312	+	0.0136568i
$513$	1.14291e16	+	1.57308e16i	0.627059	+	0.863072i
$514$	−7.03201e15	+	9.67873e15i	−0.381330	+	0.524855i
$515$	4.40581e15	+	1.35597e16i	0.236147	+	0.726785i
$516$			2.46856e15i			0.130781i
$517$	−1.01361e16	+	7.07054e15i	−0.530793	+	0.370262i
$518$	5.14105e15			0.266117
$519$	1.12500e16	−	3.65534e15i	0.575636	−	0.187035i
$520$	1.09573e15	+	7.96092e14i	0.0554220	+	0.0402664i
$521$	−1.61301e16	+	1.17192e16i	−0.806512	+	0.585965i	−0.912817	−	0.408369i	$-0.866098\pi$
$521$	−1.61301e16	+	1.17192e16i	−0.806512	+	0.585965i	0.106306	+	0.994334i	$0.466098\pi$
$522$	5.02846e15	−	1.54760e16i	0.248549	−	0.764955i
$523$	−2.45625e16	−	7.98083e15i	−1.20022	−	0.389976i	−0.360380	−	0.932806i	$-0.617353\pi$
$523$	−2.45625e16	−	7.98083e15i	−1.20022	−	0.389976i	−0.839843	+	0.542830i	$0.817353\pi$
$524$	−9.01974e15	−	1.24146e16i	−0.435719	−	0.599715i
$525$	−4.51740e15	+	6.21767e15i	−0.215741	+	0.296942i
$526$	8.17708e14	+	2.51665e15i	0.0386086	+	0.118825i
$527$		−	1.72091e15i		−	0.0803330i
$528$	7.92379e14	+	2.60832e15i	0.0365704	+	0.120381i
$529$	−8.64247e15			−0.394370
$530$	3.68758e16	−	1.19817e16i	1.66374	−	0.540583i
$531$	1.90570e16	+	1.38457e16i	0.850135	+	0.617659i
$532$	4.06567e15	−	2.95388e15i	0.179334	−	0.130294i
$533$	−5.58792e14	+	1.71979e15i	−0.0243718	+	0.0750086i
$534$	−1.02162e16	−	3.31943e15i	−0.440595	−	0.143158i
$535$	−2.80804e16	−	3.86494e16i	−1.19751	−	1.64824i
$536$	7.97171e15	−	1.09721e16i	0.336173	−	0.462702i
$537$	−7.19866e14	−	2.21552e15i	−0.0300197	−	0.0923911i
$538$			4.56511e15i			0.188260i
$539$	1.69470e16	+	1.28177e16i	0.691131	+	0.522732i
$540$	−1.88648e16			−0.760835
$541$	−2.47246e16	+	8.03352e15i	−0.986158	+	0.320422i	−0.757321	−	0.653043i	$-0.773492\pi$
$541$	−2.47246e16	+	8.03352e15i	−0.986158	+	0.320422i	−0.228837	+	0.973465i	$0.573492\pi$
$542$	1.58521e16	+	1.15173e16i	0.625305	+	0.454311i
$543$	−4.97810e14	+	3.61680e14i	−0.0194207	+	0.0141100i
$544$	6.58285e14	−	2.02599e15i	0.0253992	−	0.0781708i
$545$	−4.54382e16	−	1.47638e16i	−1.73397	−	0.563402i
$546$	2.26603e14	+	3.11892e14i	0.00855282	+	0.0117719i
$547$	−9.13737e15	+	1.25765e16i	−0.341112	+	0.469501i	−0.944766	−	0.327746i	$-0.893711\pi$
$547$	−9.13737e15	+	1.25765e16i	−0.341112	+	0.469501i	0.603654	+	0.797247i	$0.293711\pi$
$548$	−4.56715e15	−	1.40563e16i	−0.168641	−	0.519023i
$549$		−	1.45641e16i		−	0.531925i
$550$	−2.35731e16	+	3.11672e16i	−0.851609	+	1.12596i
$551$	5.17324e16			1.84864
$552$	3.72550e15	−	1.21049e15i	0.131689	−	0.0427885i
$553$	1.18031e16	+	8.57542e15i	0.412709	+	0.299850i
$554$	2.35358e16	−	1.70997e16i	0.814084	−	0.591467i
$555$	8.10520e15	−	2.49452e16i	0.277336	−	0.853551i
$556$	6.49861e15	+	2.11153e15i	0.219974	+	0.0714739i
$557$	−2.72427e16	−	3.74963e16i	−0.912259	−	1.25562i	−0.966389	−	0.257083i	$-0.917239\pi$
$557$	−2.72427e16	−	3.74963e16i	−0.912259	−	1.25562i	0.0541300	−	0.998534i	$-0.482761\pi$
$558$	−1.61867e15	+	2.22790e15i	−0.0536232	+	0.0738059i
$559$	5.48536e14	+	1.68822e15i	0.0179777	+	0.0553297i
$560$			4.87567e15i			0.158091i
$561$	6.97923e15	−	2.12022e15i	0.223888	−	0.0680147i
$562$	−4.09431e16			−1.29946
$563$	−3.22221e16	+	1.04696e16i	−1.01182	+	0.328761i	−0.767579	−	0.640954i	$-0.778539\pi$
$563$	−3.22221e16	+	1.04696e16i	−1.01182	+	0.328761i	−0.244242	+	0.969714i	$0.578539\pi$
$564$	4.24043e15	+	3.08085e15i	0.131745	+	0.0957186i
$565$	−4.17462e16	+	3.03304e16i	−1.28329	+	0.932367i
$566$	−5.18173e15	+	1.59477e16i	−0.157607	+	0.485065i
$567$	3.51352e15	+	1.14161e15i	0.105741	+	0.0343573i
$568$	1.05846e16	+	1.45685e16i	0.315200	+	0.433836i
$569$	5.50724e14	−	7.58007e14i	0.0162278	−	0.0223357i	−0.800826	−	0.598897i	$-0.795606\pi$
$569$	5.50724e14	−	7.58007e14i	0.0162278	−	0.0223357i	0.817054	+	0.576561i	$0.195606\pi$
$570$	−7.92293e15	−	2.43843e16i	−0.231013	−	0.710986i
$571$		−	6.58960e15i		−	0.190126i	−0.995471	−	0.0950632i	$-0.969695\pi$
$571$		−	6.58960e15i		−	0.190126i	0.995471	−	0.0950632i	$-0.0303053\pi$
$572$	1.12149e15	+	1.60773e15i	0.0320199	+	0.0459024i
$573$	1.06400e16			0.300617
$574$	−6.19104e15	+	2.01159e15i	−0.173098	+	0.0562430i
$575$	4.54296e16	+	3.30065e16i	1.25699	+	0.913257i
$576$	−2.75785e15	+	2.00369e15i	−0.0755154	+	0.0548651i
$577$	2.02577e16	−	6.23468e16i	0.548954	−	1.68951i	−0.162446	−	0.986717i	$-0.551938\pi$
$577$	2.02577e16	−	6.23468e16i	0.548954	−	1.68951i	0.711399	−	0.702788i	$-0.248062\pi$
$578$	1.96549e16	+	6.38628e15i	0.527114	+	0.171270i
$579$	−1.47402e16	−	2.02881e16i	−0.391229	−	0.538481i
$580$	−2.95013e16	+	4.06050e16i	−0.774948	+	1.06662i
$581$	−1.00384e15	−	3.08950e15i	−0.0260980	−	0.0803215i
$582$		−	2.32047e16i		−	0.597087i
$583$	5.61072e16	+	1.07906e15i	1.42892	+	0.0274810i
$584$	5.36917e15			0.135341
$585$	−5.51542e15	+	1.79207e15i	−0.137608	+	0.0447116i
$586$	1.56214e16	+	1.13496e16i	0.385776	+	0.280283i
$587$	1.85609e16	−	1.34853e16i	0.453702	−	0.329634i	−0.337354	−	0.941378i	$-0.609532\pi$
$587$	1.85609e16	−	1.34853e16i	0.453702	−	0.329634i	0.791056	+	0.611744i	$0.209532\pi$
$588$	2.78481e15	−	8.57077e15i	0.0673801	−	0.207375i
$589$	−8.32636e15	−	2.70540e15i	−0.199418	−	0.0647947i
$590$	−4.27057e16	−	5.87793e16i	−1.01245	−	1.39352i
$591$	−1.55213e16	+	2.13633e16i	−0.364253	+	0.501352i
$592$	−3.42596e15	−	1.05440e16i	−0.0795889	−	0.244949i
$593$			1.86806e16i			0.429600i	0.976658	+	0.214800i	$0.0689099\pi$
$593$			1.86806e16i			0.429600i	−0.976658	+	0.214800i	$0.931090\pi$
$594$	−2.58000e16	−	8.93496e15i	−0.587357	−	0.203411i
$595$	1.30461e16			0.294022
$596$	1.53772e16	−	4.99636e15i	0.343084	−	0.111475i
$597$	2.50543e16	+	1.82030e16i	0.553395	+	0.402065i
$598$	2.27885e15	−	1.65568e15i	0.0498320	−	0.0362051i
$599$	1.69422e16	−	5.21428e16i	0.366784	−	1.12884i	−0.582073	−	0.813136i	$-0.697758\pi$
$599$	1.69422e16	−	5.21428e16i	0.366784	−	1.12884i	0.948857	−	0.315707i	$-0.102242\pi$
$600$	1.57625e16	+	5.12155e15i	0.337845	+	0.109772i
$601$	2.61591e16	+	3.60050e16i	0.555107	+	0.764039i	0.990694	−	0.136107i	$-0.0434592\pi$
$601$	2.61591e16	+	3.60050e16i	0.555107	+	0.764039i	−0.435587	+	0.900147i	$0.643459\pi$
$602$	−3.75605e15	+	5.16975e15i	−0.0789136	+	0.108615i
$603$	1.79450e16	+	5.52290e16i	0.373284	+	1.14885i
$604$		−	1.06984e16i		−	0.220342i
$605$	−7.05425e16	+	4.72177e16i	−1.43853	+	0.962882i
$606$	−2.54279e16			−0.513423
$607$	3.27104e16	−	1.06283e16i	0.653965	−	0.212486i	0.0368033	−	0.999323i	$-0.488283\pi$
$607$	3.27104e16	−	1.06283e16i	0.653965	−	0.212486i	0.617162	+	0.786836i	$0.288283\pi$
$608$	−8.76760e15	−	6.37003e15i	−0.173564	−	0.126101i
$609$	−1.15580e16	+	8.39736e15i	−0.226557	+	0.164603i
$610$	−1.38815e16	+	4.27229e16i	−0.269437	+	0.829243i
$611$	3.58457e15	+	1.16470e15i	0.0688954	+	0.0223855i
$612$	5.36140e15	+	7.37934e15i	0.102040	+	0.140446i
$613$	−2.61815e16	+	3.60358e16i	−0.493438	+	0.679159i	−0.981017	−	0.193920i	$-0.937880\pi$
$613$	−2.61815e16	+	3.60358e16i	−0.493438	+	0.679159i	0.487580	+	0.873079i	$0.337880\pi$
$614$	−7.48326e15	−	2.30311e16i	−0.139663	−	0.429838i
$615$			3.32114e16i			0.613813i
$616$	−2.30926e15	+	6.66809e15i	−0.0422658	+	0.122044i
$617$	9.51893e16			1.72535			0.862674	−	0.505760i	$-0.168788\pi$
$617$	9.51893e16			1.72535			0.862674	+	0.505760i	$0.168788\pi$
$618$	8.32339e15	−	2.70443e15i	0.149406	−	0.0485451i
$619$	4.95204e16	+	3.59787e16i	0.880319	+	0.639589i	0.933336	−	0.359005i	$-0.116884\pi$
$619$	4.95204e16	+	3.59787e16i	0.880319	+	0.639589i	−0.0530170	+	0.998594i	$0.516884\pi$
$620$	6.87173e15	−	4.99261e15i	0.120981	−	0.0878976i
$621$	−1.21241e16	+	3.73141e16i	−0.211397	+	0.650614i
$622$	4.80768e16	+	1.56211e16i	0.830220	+	0.269755i
$623$	−1.63444e16	−	2.24961e16i	−0.279537	−	0.384750i
$624$	4.88668e14	−	6.72594e14i	0.00827763	−	0.0113932i
$625$	1.82260e16	+	5.60938e16i	0.305781	+	0.941099i
$626$		−	4.87441e15i		−	0.0809983i
$627$	7.13530e14	−	3.71011e16i	0.0117437	−	0.610635i
$628$	2.63289e16			0.429215
$629$	−2.82133e16	+	9.16705e15i	−0.455565	+	0.148022i
$630$	−1.68896e16	−	1.22710e16i	−0.270132	−	0.196263i
$631$	3.84010e16	−	2.79000e16i	0.608368	−	0.442005i	−0.240471	−	0.970656i	$-0.577302\pi$
$631$	3.84010e16	−	2.79000e16i	0.608368	−	0.442005i	0.848839	+	0.528651i	$0.177302\pi$
$632$	9.72227e15	−	2.99221e16i	0.152569	−	0.469558i
$633$	3.36080e16	+	1.09199e16i	0.522420	+	0.169745i
$634$	1.38929e16	+	1.91220e16i	0.213923	+	0.294440i
$635$	8.52423e16	−	1.17326e17i	1.30021	−	1.78958i
$636$	−7.35476e15	−	2.26356e16i	−0.111129	−	0.342019i
$637$		−	6.48026e15i		−	0.0969965i
$638$	−5.95785e16	+	4.15598e16i	−0.883416	+	0.616239i
$639$	−7.71055e16			−1.13261
$640$	9.99974e15	−	3.24911e15i	0.145515	−	0.0472808i
$641$	3.34745e16	+	2.43207e16i	0.482577	+	0.350612i	0.802322	−	0.596891i	$-0.203598\pi$
$641$	3.34745e16	+	2.43207e16i	0.482577	+	0.350612i	−0.319746	+	0.947503i	$0.603598\pi$
$642$	−2.37243e16	+	1.72367e16i	−0.338831	+	0.246175i
$643$	−5.60326e15	+	1.72451e16i	−0.0792821	+	0.244005i	−0.982840	−	0.184461i	$-0.940946\pi$
$643$	−5.60326e15	+	1.72451e16i	−0.0792821	+	0.244005i	0.903558	+	0.428466i	$0.140946\pi$
$644$	9.64392e15	+	3.13350e15i	0.135188	+	0.0439253i
$645$	1.91629e16	+	2.63754e16i	0.266135	+	0.366303i
$646$	−1.70447e16	+	2.34600e16i	−0.234527	+	0.322799i
$647$	−7.81996e15	−	2.40674e16i	−0.106605	−	0.328097i	0.883499	−	0.468434i	$-0.155182\pi$
$647$	−7.81996e15	−	2.40674e16i	−0.106605	−	0.328097i	−0.990104	+	0.140337i	$0.955182\pi$
$648$		−	7.96680e15i		−	0.107605i
$649$	−3.05657e16	−	1.00615e17i	−0.409040	−	1.34646i
$650$	1.19178e16			0.158022
$651$	2.29941e15	−	7.47124e14i	0.0302086	−	0.00981538i
$652$	−1.93279e16	−	1.40425e16i	−0.251593	−	0.182793i
$653$	−2.86556e16	+	2.08195e16i	−0.369599	+	0.268529i	−0.757045	−	0.653363i	$-0.773357\pi$
$653$	−2.86556e16	+	2.08195e16i	−0.369599	+	0.268529i	0.387446	+	0.921892i	$0.373357\pi$
$654$	−9.06250e15	+	2.78915e16i	−0.115819	+	0.356456i
$655$	−1.92743e17	−	6.26261e16i	−2.44080	−	0.793063i
$656$	8.25134e15	+	1.13570e16i	0.103538	+	0.142508i
$657$	−1.35131e16	+	1.85991e16i	−0.168020	+	0.231260i
$658$	4.19279e15	+	1.29041e16i	0.0516592	+	0.158991i
$659$		−	1.13923e17i		−	1.39091i	−0.718570	−	0.695455i	$-0.755203\pi$
$659$		−	1.13923e17i		−	1.39091i	0.718570	−	0.695455i	$-0.244797\pi$
$660$	2.87140e16	+	2.17176e16i	0.347400	+	0.262753i
$661$	−6.56070e16			−0.786578			−0.393289	−	0.919415i	$-0.628663\pi$
$661$	−6.56070e16			−0.786578			−0.393289	+	0.919415i	$0.628663\pi$
$662$	−2.53017e16	+	8.22101e15i	−0.300608	+	0.0976736i
$663$	−1.79970e15	−	1.30756e15i	−0.0211894	−	0.0153950i
$664$	−5.66746e15	+	4.11765e15i	−0.0661272	+	0.0480442i
$665$	2.05095e16	−	6.31217e16i	0.237151	−	0.729875i
$666$	4.51476e16	+	1.46693e16i	0.517356	+	0.168099i
$667$	6.13556e16	+	8.44487e16i	0.696785	+	0.959042i
$668$	−1.60176e16	+	2.20463e16i	−0.180276	+	0.248128i
$669$	−4.07266e15	−	1.25343e16i	−0.0454277	−	0.139812i
$670$		−	1.79114e17i		−	1.98007i
$671$	−3.92196e16	+	5.18542e16i	−0.429702	+	0.568132i
$672$	2.99285e15			0.0324989
$673$	3.87959e16	−	1.26055e16i	0.417537	−	0.135666i	−0.0927113	−	0.995693i	$-0.529553\pi$
$673$	3.87959e16	−	1.26055e16i	0.417537	−	0.135666i	0.510249	+	0.860027i	$0.329553\pi$
$674$	−9.35445e16	−	6.79641e16i	−0.997836	−	0.724970i
$675$	−1.34296e17	+	9.75720e16i	−1.41985	+	1.03158i
$676$	−1.45598e16	+	4.48106e16i	−0.152573	+	0.469570i
$677$	−1.31558e17	−	4.27457e16i	−1.36642	−	0.443976i	−0.468238	−	0.883602i	$-0.655111\pi$
$677$	−1.31558e17	−	4.27457e16i	−1.36642	−	0.443976i	−0.898181	+	0.439626i	$0.855111\pi$
$678$	1.86178e16	+	2.56252e16i	0.191668	+	0.263809i
$679$	3.53072e16	−	4.85961e16i	0.360283	−	0.495887i
$680$	−8.69384e15	−	2.67569e16i	−0.0879343	−	0.270634i
$681$			3.98644e16i			0.399671i
$682$	1.17626e16	−	3.57335e15i	0.116895	−	0.0355116i
$683$	6.00987e16			0.592026			0.296013	−	0.955184i	$-0.404343\pi$
$683$	6.00987e16			0.592026			0.296013	+	0.955184i	$0.404343\pi$
$684$	4.41324e16	−	1.43395e16i	0.430944	−	0.140022i
$685$	−1.57913e17	−	1.14731e17i	−1.52853	−	1.11055i
$686$	4.06523e16	−	2.95356e16i	0.390068	−	0.283401i
$687$	−8.78474e15	+	2.70367e16i	−0.0835581	+	0.257165i
$688$	1.31059e16	+	4.25837e15i	0.123577	+	0.0401525i
$689$	−1.00597e16	−	1.38460e16i	−0.0940304	−	0.129422i
$690$	3.04085e16	−	4.18537e16i	0.281774	−	0.387828i
$691$	2.83499e16	+	8.72521e16i	0.260426	+	0.801508i	0.992712	+	0.120511i	$0.0384533\pi$
$691$	2.83499e16	+	8.72521e16i	0.260426	+	0.801508i	−0.732286	+	0.680997i	$0.761547\pi$
$692$		−	6.60332e16i		−	0.601348i
$693$	−1.72867e16	−	2.47816e16i	−0.156068	−	0.223733i
$694$	7.15778e16			0.640651
$695$	8.58259e16	−	2.78865e16i	0.761569	−	0.247449i
$696$	2.49247e16	+	1.81089e16i	0.219268	+	0.159307i
$697$	3.03886e16	−	2.20786e16i	0.265041	−	0.192564i
$698$	−3.78495e16	+	1.16489e17i	−0.327287	+	1.00728i
$699$	−2.88311e16	−	9.36781e15i	−0.247172	−	0.0803110i
$700$	2.52177e16	+	3.47092e16i	0.214347	+	0.295023i
$701$	5.43087e16	−	7.47495e16i	0.457679	−	0.629941i	−0.516346	−	0.856380i	$-0.672708\pi$
$701$	5.43087e16	−	7.47495e16i	0.457679	−	0.629941i	0.974025	+	0.226439i	$0.0727083\pi$
$702$	2.57315e15	+	7.91934e15i	0.0215002	+	0.0661708i
$703$			1.50917e17i			1.25028i
$704$	1.52148e16	+	2.92611e14i	0.124977	+	0.00240356i
$705$	6.92229e16			0.563787
$706$	−9.51099e16	+	3.09031e16i	−0.768064	+	0.249559i
$707$	−5.32521e16	−	3.86900e16i	−0.426403	−	0.309800i
$708$	−3.60807e16	+	2.62142e16i	−0.286468	+	0.208131i
$709$	6.03671e16	−	1.85791e17i	0.475251	−	1.46267i	−0.370368	−	0.928885i	$-0.620768\pi$
$709$	6.03671e16	−	1.85791e17i	0.475251	−	1.46267i	0.845619	−	0.533787i	$-0.179232\pi$
$710$	2.26184e17	+	7.34916e16i	1.76568	+	0.573704i
$711$	7.91830e16	+	1.08986e17i	0.612935	+	0.843633i
$712$	−3.52465e16	+	4.85127e16i	−0.270543	+	0.372371i
$713$	−5.45889e15	−	1.68007e16i	−0.0415496	−	0.127877i
$714$		−	8.00814e15i		−	0.0604425i
$715$	2.44630e16	+	8.47192e15i	0.183094	+	0.0634082i
$716$	−1.30043e16			−0.0965180
$717$	6.67798e16	−	2.16981e16i	0.491508	−	0.159701i
$718$	1.18745e17	+	8.62736e16i	0.866702	+	0.629696i
$719$	−2.96720e16	+	2.15580e16i	−0.214770	+	0.156040i	−0.689969	−	0.723839i	$-0.742376\pi$
$719$	−2.96720e16	+	2.15580e16i	−0.214770	+	0.156040i	0.475199	+	0.879878i	$0.342376\pi$
$720$	−1.39121e16	+	4.28171e16i	−0.0998614	+	0.307342i
$721$	2.15461e16	+	7.00075e15i	0.153376	+	0.0498348i
$722$	2.78377e16	+	3.83153e16i	0.196521	+	0.270488i
$723$	−6.71480e16	+	9.24213e16i	−0.470114	+	0.647057i
$724$	1.06146e15	+	3.26685e15i	0.00737011	+	0.0226829i
$725$			4.41647e17i			3.04121i
$726$	2.89838e16	+	4.33013e16i	0.197941	+	0.295721i
$727$	−9.56106e16			−0.647589			−0.323795	−	0.946127i	$-0.604959\pi$
$727$	−9.56106e16			−0.647589			−0.323795	+	0.946127i	$0.604959\pi$
$728$	2.04677e15	−	6.65037e14i	0.0137493	−	0.00446743i
$729$	−2.61207e16	−	1.89778e16i	−0.174028	−	0.126439i
$730$	5.73670e16	−	4.16796e16i	0.379075	−	0.275414i
$731$	1.13944e16	−	3.50682e16i	0.0746768	−	0.229832i
$732$	2.62247e16	+	8.52093e15i	0.170469	+	0.0553886i
$733$	4.96626e16	+	6.83547e16i	0.320188	+	0.440701i	0.938525	−	0.345212i	$-0.112193\pi$
$733$	4.96626e16	+	6.83547e16i	0.320188	+	0.440701i	−0.618336	+	0.785914i	$0.712193\pi$
$734$	8.31526e15	−	1.14450e16i	0.0531740	−	0.0731878i
$735$	−3.67785e16	−	1.13192e17i	−0.233276	−	0.717949i
$736$		−	2.18673e16i		−	0.137572i
$737$	8.48340e16	−	2.44961e17i	0.529377	−	1.52860i
$738$	−6.01082e16			−0.372045
$739$	−2.42969e17	+	7.89455e16i	−1.49171	+	0.484686i	−0.937588	−	0.347749i	$-0.886946\pi$
$739$	−2.42969e17	+	7.89455e16i	−1.49171	+	0.484686i	−0.554123	+	0.832435i	$0.686946\pi$
$740$	−1.18456e17	−	8.60631e16i	−0.721382	−	0.524115i
$741$	−9.15569e15	+	6.65199e15i	−0.0553072	+	0.0401830i
$742$	1.90387e16	−	5.85950e16i	0.114081	−	0.351105i
$743$	2.56902e17	+	8.34726e16i	1.52699	+	0.496148i	0.947750	−	0.319013i	$-0.103351\pi$
$743$	2.56902e17	+	8.34726e16i	1.52699	+	0.496148i	0.579235	+	0.815160i	$0.303351\pi$
$744$	−3.06463e15	−	4.21810e15i	−0.0180692	−	0.0248702i
$745$	1.25513e17	−	1.72753e17i	0.734091	−	1.01039i
$746$	−4.02438e16	−	1.23858e17i	−0.233489	−	0.718605i
$747$		−	2.99957e16i		−	0.172637i
$748$	7.82957e14	−	4.07111e16i	0.00447021	−	0.232436i
$749$	−7.59108e16			−0.429945
$750$	1.03904e17	−	3.37604e16i	0.583800	−	0.189688i
$751$	1.61445e16	+	1.17297e16i	0.0899883	+	0.0653803i	0.631870	−	0.775075i	$-0.282288\pi$
$751$	1.61445e16	+	1.17297e16i	0.0899883	+	0.0653803i	−0.541881	+	0.840455i	$0.682288\pi$
$752$	2.36715e16	−	1.71984e16i	0.130894	−	0.0951000i
$753$	3.79984e16	−	1.16947e17i	0.208447	−	0.641534i
$754$	2.10697e16	+	6.84595e15i	0.114665	+	0.0372568i
$755$	−8.30491e16	−	1.14307e17i	−0.448387	−	0.617152i
$756$	−1.76194e16	+	2.42510e16i	−0.0943757	+	0.129897i
$757$	9.83060e16	+	3.02555e17i	0.522402	+	1.60779i	0.769397	+	0.638771i	$0.220557\pi$
$757$	9.83060e16	+	3.02555e17i	0.522402	+	1.60779i	−0.246995	+	0.969017i	$0.579443\pi$
$758$			8.42935e16i			0.444405i
$759$	6.14106e16	−	4.28378e16i	0.321213	−	0.224066i
$760$	−1.43127e17			−0.742744
$761$	−1.20075e17	+	3.90147e16i	−0.618222	+	0.200873i	−0.601351	−	0.798985i	$-0.705371\pi$
$761$	−1.20075e17	+	3.90147e16i	−0.618222	+	0.200873i	−0.0168713	+	0.999858i	$0.505371\pi$
$762$	−7.20186e16	−	5.23245e16i	−0.367887	−	0.267286i
$763$	−6.14174e16	+	4.46224e16i	−0.311275	+	0.226155i
$764$	1.83544e16	−	5.64890e16i	0.0922954	−	0.284056i
$765$	1.14568e17	+	3.72254e16i	0.571604	+	0.185725i
$766$	−5.49296e16	−	7.56042e16i	−0.271916	−	0.374260i
$767$	−1.88502e16	+	2.59450e16i	−0.0925855	+	0.127433i
$768$	−1.99441e15	−	6.13817e15i	−0.00971959	−	0.0299138i
$769$			3.83835e16i			0.185604i	0.995685	+	0.0928019i	$0.0295823\pi$
$769$			3.83835e16i			0.185604i	−0.995685	+	0.0928019i	$0.970418\pi$
$770$	2.70894e16	+	8.91716e16i	0.129973	+	0.427841i
$771$	9.69860e16			0.461724
$772$	−1.33140e17	+	4.32597e16i	−0.628931	+	0.204352i
$773$	7.08237e16	+	5.14564e16i	0.331972	+	0.241192i	0.741267	−	0.671210i	$-0.234225\pi$
$773$	7.08237e16	+	5.14564e16i	0.331972	+	0.241192i	−0.409295	+	0.912402i	$0.634225\pi$
$774$	−4.77360e16	+	3.46823e16i	−0.222024	+	0.161310i
$775$	2.30964e16	−	7.10834e16i	0.106594	−	0.328063i
$776$	−1.23197e17	−	4.00290e16i	−0.564194	−	0.183318i
$777$	−2.44973e16	−	3.37177e16i	−0.111325	−	0.153226i
$778$	−1.46002e16	+	2.00954e16i	−0.0658386	+	0.0906191i
$779$	−5.90509e16	−	1.81740e17i	−0.264242	−	0.813253i
$780$		−	1.09798e16i		−	0.0487557i
$781$	2.74527e17	+	2.07637e17i	1.20970	+	0.914950i
$782$	−5.85117e16			−0.255860
$783$	−2.93472e17	+	9.53548e16i	−1.27349	+	0.413782i
$784$	−4.06994e16	−	2.95698e16i	−0.175264	−	0.127336i
$785$	2.81312e17	−	2.04385e17i	1.20218	−	0.873437i
$786$	−3.84420e16	+	1.18312e17i	−0.163031	+	0.501758i
$787$	−2.36015e16	−	7.66858e15i	−0.0993323	−	0.0322750i	0.258929	−	0.965896i	$-0.416630\pi$
$787$	−2.36015e16	−	7.66858e15i	−0.0993323	−	0.0322750i	−0.358261	+	0.933621i	$0.616630\pi$
$788$	8.66454e16	+	1.19257e17i	0.361900	+	0.498112i
$789$	1.26091e16	−	1.73549e16i	0.0522662	−	0.0719382i
$790$	−1.28400e17	−	3.95175e17i	−0.528205	−	1.62565i
$791$			8.19932e16i			0.334749i
$792$	−3.93060e16	+	5.19685e16i	−0.159260	+	0.210566i
$793$	1.98282e16			0.0797342
$794$	−8.67747e16	+	2.81948e16i	−0.346314	+	0.112524i
$795$	−2.54297e17	−	1.84758e17i	−1.00725	−	0.731812i
$796$	1.39862e17	−	1.01615e17i	0.549819	−	0.399467i
$797$	−1.35390e17	+	4.16688e17i	−0.528247	+	1.62578i	0.229558	+	0.973295i	$0.426272\pi$
$797$	−1.35390e17	+	4.16688e17i	−0.528247	+	1.62578i	−0.757805	+	0.652482i	$0.773728\pi$
$798$	−3.87462e16	−	1.25894e16i	−0.150042	−	0.0487515i
$799$	−4.60187e16	−	6.33393e16i	−0.176870	−	0.243441i
$800$	5.43819e16	−	7.48502e16i	0.207450	−	0.285531i
$801$	−7.93429e16	−	2.44192e17i	−0.300409	−	0.924564i
$802$			2.65786e17i			0.998818i
$803$	9.81973e16	−	2.98313e16i	0.366274	−	0.111270i
$804$	−1.09946e17			−0.407047
$805$	1.27365e17	−	4.13835e16i	0.468032	−	0.152073i
$806$	−3.03316e15	−	2.20372e15i	−0.0110633	−	0.00803797i
$807$	2.99404e16	−	2.17530e16i	0.108397	−	0.0787548i
$808$	−4.38642e16	+	1.35000e17i	−0.157631	+	0.485139i
$809$	−8.69098e16	−	2.82387e16i	−0.310011	−	0.100729i	0.149879	−	0.988704i	$-0.452111\pi$
$809$	−8.69098e16	−	2.82387e16i	−0.310011	−	0.100729i	−0.459891	+	0.887976i	$0.652111\pi$
$810$	−6.18444e16	−	8.51215e16i	−0.218973	−	0.301390i
$811$	2.71276e17	−	3.73379e17i	0.953423	−	1.31227i	0.00343282	−	0.999994i	$-0.498907\pi$
$811$	2.71276e17	−	3.73379e17i	0.953423	−	1.31227i	0.949990	−	0.312280i	$-0.101093\pi$
$812$	2.46447e16	+	7.58485e16i	0.0859779	+	0.264613i
$813$		−	1.58847e17i		−	0.550092i
$814$	−1.21241e17	−	1.73806e17i	−0.416776	−	0.597474i
$815$	−3.15518e17			−1.07666
$816$	−1.64243e16	+	5.33657e15i	−0.0556346	+	0.0180768i
$817$	−1.51760e17	−	1.10260e17i	−0.510298	−	0.370753i
$818$	1.35361e17	−	9.83454e16i	0.451828	−	0.328272i
$819$	−2.84757e15	+	8.76391e15i	−0.00943562	+	0.0290398i
$820$	1.76323e17	+	5.72909e16i	0.579998	+	0.188453i
$821$	−7.60057e16	−	1.04613e17i	−0.248192	−	0.341607i	0.666685	−	0.745339i	$-0.267713\pi$
$821$	−7.60057e16	−	1.04613e17i	−0.248192	−	0.341607i	−0.914877	+	0.403733i	$0.867713\pi$
$822$	−7.04255e16	+	9.69324e16i	−0.228297	+	0.314223i
$823$	1.28591e17	+	3.95761e17i	0.413819	+	1.27360i	0.913303	+	0.407280i	$0.133523\pi$
$823$	1.28591e17	+	3.95761e17i	0.413819	+	1.27360i	−0.499485	+	0.866323i	$0.666477\pi$
$824$		−	4.88552e16i		−	0.156080i
$825$	3.16738e17	+	6.09151e15i	1.00456	+	0.0193197i
$826$	−1.15448e17			−0.363501
$827$	−1.51591e17	+	4.92548e16i	−0.473848	+	0.153963i	−0.536199	−	0.844092i	$-0.680140\pi$
$827$	−1.51591e17	+	4.92548e16i	−0.473848	+	0.153963i	0.0623507	+	0.998054i	$0.480140\pi$
$828$	7.57498e16	+	5.50354e16i	0.235071	+	0.170789i
$829$	1.90431e17	−	1.38356e17i	0.586691	−	0.426256i	−0.254439	−	0.967089i	$-0.581891\pi$
$829$	1.90431e17	−	1.38356e17i	0.586691	−	0.426256i	0.841130	+	0.540833i	$0.181891\pi$
$830$	−2.85898e16	+	8.79903e16i	−0.0874464	+	0.269132i
$831$	−2.24298e17	−	7.28788e16i	−0.681112	−	0.221307i
$832$	−2.72791e15	−	3.75465e15i	−0.00822414	−	0.0113196i
$833$	−7.91218e16	+	1.08902e17i	−0.236824	+	0.325960i
$834$	−1.71177e16	−	5.26828e16i	−0.0508684	−	0.156557i
$835$			3.59894e17i			1.06183i
$836$	−1.95744e17	−	6.77891e16i	−0.573390	−	0.198574i
$837$	5.22212e16			0.151878
$838$	2.26403e17	−	7.35628e16i	0.653760	−	0.212420i
$839$	−2.52121e17	−	1.83177e17i	−0.722833	−	0.525169i	0.164455	−	0.986385i	$-0.447413\pi$
$839$	−2.52121e17	−	1.83177e17i	−0.722833	−	0.525169i	−0.887288	+	0.461216i	$0.847413\pi$
$840$	3.19771e16	−	2.32328e16i	0.0910257	−	0.0661340i
$841$	−1.44360e17	+	4.44294e17i	−0.408010	+	1.25572i
$842$	1.89128e17	+	6.14515e16i	0.530743	+	0.172449i
$843$	1.95096e17	+	2.68526e17i	0.543604	+	0.748206i
$844$	1.15950e17	−	1.59592e17i	0.320787	−	0.441525i
$845$	1.92289e17	+	5.91805e17i	0.528219	+	1.62569i
$846$			1.25284e17i			0.341723i
$847$	−5.18625e15	+	1.34784e17i	−0.0140460	+	0.365037i
$848$	−1.32863e17			−0.357296
$849$	1.29285e17	−	4.20071e16i	0.345224	−	0.112170i
$850$	−2.00281e17	−	1.45513e17i	−0.531039	−	0.385823i
$851$	−2.46359e17	+	1.78990e17i	−0.648622	+	0.471251i
$852$	4.51116e16	−	1.38839e17i	0.117937	−	0.362973i
$853$	3.85624e16	+	1.25297e16i	0.100108	+	0.0325271i	0.358643	−	0.933475i	$-0.383240\pi$
$853$	3.85624e16	+	1.25297e16i	0.100108	+	0.0325271i	−0.258535	+	0.966002i	$0.583240\pi$
$854$	4.19558e16	+	5.77472e16i	0.108155	+	0.148862i
$855$	3.60220e17	−	4.95800e17i	0.922084	−	1.26914i
$856$	5.05865e16	+	1.55689e17i	0.128585	+	0.395745i
$857$		−	4.14782e17i		−	1.04697i	−0.852035	−	0.523485i	$-0.824632\pi$
$857$		−	4.14782e17i		−	1.04697i	0.852035	−	0.523485i	$-0.175368\pi$
$858$	5.20035e15	−	1.50162e16i	0.0130349	−	0.0376388i
$859$	3.10481e17			0.772815			0.386407	−	0.922328i	$-0.373716\pi$
$859$	3.10481e17			0.772815			0.386407	+	0.922328i	$0.373716\pi$
$860$	1.73087e17	−	5.62394e16i	0.427833	−	0.139011i
$861$	4.26936e16	+	3.10187e16i	0.104796	+	0.0761387i
$862$	2.79474e17	−	2.03050e17i	0.681237	−	0.494948i
$863$	−1.73504e17	+	5.33989e17i	−0.419994	+	1.29261i	0.487712	+	0.873004i	$0.337832\pi$
$863$	−1.73504e17	+	5.33989e17i	−0.419994	+	1.29261i	−0.907707	+	0.419605i	$0.862168\pi$
$864$	6.14790e16	+	1.99757e16i	0.147790	+	0.0480198i
$865$	−5.12600e17	−	7.05533e17i	−1.22372	−	1.68431i
$866$	3.14478e16	−	4.32841e16i	0.0745560	−	0.102617i
$867$	−5.17721e16	−	1.59338e17i	−0.121894	−	0.375150i
$868$		−	1.34967e16i		−	0.0315580i
$869$	1.15636e16	−	6.01265e17i	0.0268518	−	1.39620i
$870$	4.06884e17			0.938328
$871$	−7.51910e16	+	2.44311e16i	−0.172210	+	0.0559543i
$872$	1.32446e17	+	9.62279e16i	0.301260	+	0.218878i
$873$	4.48723e17	−	3.26016e17i	1.01366	−	0.736468i
$874$	−9.19848e16	+	2.83100e17i	−0.206370	+	0.635143i
$875$	2.68968e17	+	8.73929e16i	0.599311	+	0.194728i
$876$	−2.55843e16	−	3.52138e16i	−0.0566173	−	0.0779270i
$877$	−3.18250e17	+	4.38033e17i	−0.699473	+	0.962742i	0.300487	+	0.953786i	$0.402851\pi$
$877$	−3.18250e17	+	4.38033e17i	−0.699473	+	0.962742i	−0.999960	+	0.00895574i	$0.997149\pi$
$878$	1.54172e17	+	4.74491e17i	0.336540	+	1.03576i
$879$		−	1.56535e17i		−	0.339374i
$880$	1.64834e17	−	1.14982e17i	0.354937	−	0.247591i
$881$	5.23209e17			1.11897			0.559486	−	0.828840i	$-0.310998\pi$
$881$	5.23209e17			1.11897			0.559486	+	0.828840i	$0.310998\pi$
$882$	2.04864e17	−	6.65642e16i	0.435164	−	0.141393i
$883$	−3.49433e17	−	2.53878e17i	−0.737224	−	0.535625i	0.154617	−	0.987975i	$-0.450586\pi$
$883$	−3.49433e17	−	2.53878e17i	−0.737224	−	0.535625i	−0.891841	+	0.452350i	$0.850586\pi$
$884$	−1.00465e16	+	7.29924e15i	−0.0210525	+	0.0152955i
$885$	−1.82011e17	+	5.60172e17i	−0.378824	+	1.16590i
$886$	−5.71338e17	−	1.85639e17i	−1.18111	−	0.383766i
$887$	4.52647e17	+	6.23015e17i	0.929433	+	1.27925i	0.960080	+	0.279724i	$0.0902429\pi$
$887$	4.52647e17	+	6.23015e17i	0.929433	+	1.27925i	−0.0306479	+	0.999530i	$0.509757\pi$
$888$	−5.28284e16	+	7.27120e16i	−0.107743	+	0.148296i
$889$	−7.12094e16	−	2.19160e17i	−0.144254	−	0.443967i
$890$			7.91946e17i			1.59351i
$891$	−4.42639e16	−	1.45706e17i	−0.0884673	−	0.291213i
$892$	−7.35719e16			−0.146057
$893$	−3.78803e17	+	1.23081e17i	−0.746973	+	0.242706i
$894$	−1.06042e17	−	7.70438e16i	−0.207707	−	0.150908i
$895$	−1.38945e17	+	1.00949e17i	−0.270336	+	0.196410i
$896$	5.16278e15	−	1.58894e16i	0.00997782	−	0.0307086i
$897$	−2.17176e16	−	7.05648e15i	−0.0416925	−	0.0135467i
$898$	4.69276e16	+	6.45903e16i	0.0894892	+	0.123171i
$899$	8.16647e16	−	1.12402e17i	0.154695	−	0.212919i
$900$	1.22418e17	+	3.76764e17i	0.230351	+	0.708949i
$901$			3.55508e17i			0.664510i
$902$	2.14010e17	+	1.61865e17i	0.397369	+	0.300547i
$903$	5.18037e16			0.0955507
$904$	1.68164e17	−	5.46398e16i	0.308122	−	0.100115i
$905$	3.67010e16	+	2.66648e16i	0.0668016	+	0.0485342i
$906$	−7.01656e16	+	5.09783e16i	−0.126869	+	0.0921757i
$907$	−3.67937e16	+	1.13239e17i	−0.0660891	+	0.203401i	−0.978648	−	0.205544i	$-0.934103\pi$
$907$	−3.67937e16	+	1.13239e17i	−0.0660891	+	0.203401i	0.912559	+	0.408946i	$0.134103\pi$
$908$	2.11645e17	+	6.87677e16i	0.377653	+	0.122707i
$909$	−3.57252e17	−	4.91715e17i	−0.633274	−	0.871626i
$910$	1.67063e16	−	2.29942e16i	0.0294192	−	0.0404921i
$911$	−3.12061e16	−	9.60426e16i	−0.0545921	−	0.168017i	0.920043	−	0.391818i	$-0.128154\pi$
$911$	−3.12061e16	−	9.60426e16i	−0.0545921	−	0.168017i	−0.974635	+	0.223800i	$0.928154\pi$
$912$			8.78559e16i			0.152687i
$913$	−8.07750e16	+	1.06797e17i	−0.139461	+	0.184388i
$914$	−2.63794e17			−0.452467
$915$	3.46345e17	−	1.12534e17i	0.590177	−	0.191760i
$916$	1.28387e17	+	9.32786e16i	0.217344	+	0.157910i
$917$	−2.60525e17	+	1.89283e17i	−0.438161	+	0.318342i
$918$	5.34503e16	−	1.64503e17i	0.0893087	−	0.274864i
$919$	−2.19744e17	−	7.13993e16i	−0.364775	−	0.118523i	0.120894	−	0.992665i	$-0.461424\pi$
$919$	−2.19744e17	−	7.13993e16i	−0.364775	−	0.118523i	−0.485669	+	0.874143i	$0.661424\pi$
$920$	−1.69751e17	−	2.33642e17i	−0.279953	−	0.385322i
$921$	−1.15392e17	+	1.58823e17i	−0.189068	+	0.260230i
$922$	−2.46665e17	−	7.59158e17i	−0.401534	−	1.23580i
$923$		−	1.04975e17i		−	0.169775i
$924$	5.47365e16	−	1.66284e16i	0.0879519	−	0.0267188i
$925$	−1.28840e18			−2.05684
$926$	2.55632e17	−	8.30600e16i	0.405462	−	0.131742i
$927$	1.69237e17	+	1.22958e17i	0.266697	+	0.193767i
$928$	1.39138e17	−	1.01090e17i	0.217851	−	0.158278i
$929$	2.95498e17	−	9.09449e17i	0.459685	−	1.41476i	−0.405862	−	0.913935i	$-0.633029\pi$
$929$	2.95498e17	−	9.09449e17i	0.459685	−	1.41476i	0.865546	−	0.500829i	$-0.166971\pi$
$930$	−6.54882e16	−	2.12784e16i	−0.101220	−	0.0328883i
$931$	4.02520e17	+	5.54021e17i	0.618143	+	0.850801i
$932$	−9.94698e16	+	1.36908e17i	−0.151773	+	0.208898i
$933$	−1.26637e17	−	3.89748e17i	−0.191986	−	0.590873i
$934$		−	8.72732e17i		−	1.31462i
$935$	−3.07665e17	−	4.41057e17i	−0.460477	−	0.660123i
$936$	1.98719e16			0.0295519
$937$	4.98726e17	−	1.62046e17i	0.736927	−	0.239442i	0.0835802	−	0.996501i	$-0.473365\pi$
$937$	4.98726e17	−	1.62046e17i	0.736927	−	0.239442i	0.653346	+	0.757059i	$0.273365\pi$
$938$	−2.30254e17	−	1.67289e17i	−0.338057	−	0.245613i
$939$	−3.19689e16	+	2.32268e16i	−0.0466374	+	0.0338840i
$940$	1.19412e17	−	3.67513e17i	0.173094	−	0.532728i
$941$	−5.68862e16	−	1.84834e16i	−0.0819349	−	0.0266223i	0.267763	−	0.963485i	$-0.413716\pi$
$941$	−5.68862e16	−	1.84834e16i	−0.0819349	−	0.0266223i	−0.349698	+	0.936863i	$0.613716\pi$
$942$	−1.25458e17	−	1.72679e17i	−0.179554	−	0.247135i
$943$	2.26639e17	−	3.11942e17i	0.322304	−	0.443613i
$944$	7.69337e16	+	2.36778e17i	0.108714	+	0.334587i
$945$			3.95886e17i			0.555877i
$946$	2.63355e17	+	5.06485e15i	0.367447	+	0.00706675i
$947$	−1.13181e18			−1.56919			−0.784594	−	0.620010i	$-0.787128\pi$
$947$	−1.13181e18			−1.56919			−0.784594	+	0.620010i	$0.787128\pi$
$948$	−2.42571e17	+	7.88163e16i	−0.334187	+	0.108584i
$949$	−2.53216e16	−	1.83972e16i	−0.0346653	−	0.0251858i
$950$	−1.01890e18	+	7.40274e17i	−1.38608	+	1.00705i
$951$	5.92114e16	−	1.82234e17i	0.0800427	−	0.246346i
$952$	−4.25162e16	−	1.38144e16i	−0.0571127	−	0.0185571i
$953$	−7.63813e16	−	1.05130e17i	−0.101960	−	0.140336i	0.754988	−	0.655738i	$-0.227642\pi$
$953$	−7.63813e16	−	1.05130e17i	−0.101960	−	0.140336i	−0.856948	+	0.515402i	$0.827642\pi$
$954$	3.34387e17	−	4.60245e17i	0.443567	−	0.610518i
$955$	−2.42403e17	−	7.46039e17i	−0.319534	−	0.983425i
$956$		−	3.91973e17i		−	0.513462i
$957$	5.56464e17	+	1.92712e17i	0.724379	+	0.250864i
$958$	8.60429e17			1.11307
$959$	−2.94976e17	+	9.58434e16i	−0.379205	+	0.123211i
$960$	−6.89586e16	−	5.01013e16i	−0.0880969	−	0.0640062i
$961$	6.18210e17	−	4.49156e17i	0.784867	−	0.570239i
$962$	−1.99715e16	+	6.14659e16i	−0.0251976	+	0.0775503i
$963$	−6.66632e17	−	2.16602e17i	−0.835851	−	0.271584i
$964$	3.74844e17	+	5.15928e17i	0.467076	+	0.642875i
$965$	−1.08672e18	+	1.49574e18i	−1.34572	+	1.85222i
$966$	−2.54026e16	−	7.81811e16i	−0.0312619	−	0.0962141i
$967$		−	4.42357e17i		−	0.541020i	−0.962717	−	0.270510i	$-0.912808\pi$
$967$		−	4.42357e17i		−	0.541020i	0.962717	−	0.270510i	$-0.0871924\pi$
$968$	2.79891e17	−	7.91823e16i	0.340201	−	0.0962445i
$969$	2.35081e17			0.283972
$970$	−1.62703e18	+	5.28655e17i	−1.95329	+	0.634662i
$971$	9.84263e17	+	7.15109e17i	1.17435	+	0.853212i	0.991523	−	0.129934i	$-0.0414765\pi$
$971$	9.84263e17	+	7.15109e17i	1.17435	+	0.853212i	0.182823	+	0.983146i	$0.441477\pi$
$972$	−3.52124e17	+	2.55833e17i	−0.417540	+	0.303361i
$973$	4.43112e16	−	1.36376e17i	0.0522199	−	0.160716i
$974$	−5.79143e17	−	1.88175e17i	−0.678316	−	0.220398i
$975$	−5.67890e16	−	7.81634e16i	−0.0661054	−	0.0909862i
$976$	9.04775e16	−	1.24532e17i	0.104675	−	0.144072i
$977$	1.07613e17	+	3.31199e17i	0.123737	+	0.380822i	0.993669	−	0.112349i	$-0.0358376\pi$
$977$	1.07613e17	+	3.31199e17i	0.123737	+	0.380822i	−0.869932	+	0.493171i	$0.835838\pi$
$978$			1.93675e17i			0.221331i
$979$	−3.75090e17	+	1.08309e18i	−0.426029	+	1.23017i
$980$	−6.64397e17			−0.750018
$981$	−6.66679e17	+	2.16617e17i	−0.748002	+	0.243041i
$982$	6.32614e17	+	4.59621e17i	0.705456	+	0.512544i
$983$	7.69582e17	−	5.59134e17i	0.852970	−	0.619719i	−0.0729930	−	0.997332i	$-0.523255\pi$
$983$	7.69582e17	−	5.59134e17i	0.852970	−	0.619719i	0.925963	+	0.377613i	$0.123255\pi$
$984$	3.51671e16	−	1.08233e17i	0.0387405	−	0.119231i
$985$	1.85153e18	+	6.01598e17i	2.02728	+	0.658702i
$986$	−2.70492e17	−	3.72301e17i	−0.294370	−	0.405166i
$987$	6.46528e16	−	8.89869e16i	0.0699334	−	0.0962550i
$988$	1.95224e16	+	6.00837e16i	0.0209890	+	0.0645974i
$989$		−	3.78505e17i		−	0.404477i
$990$	−1.65469e16	+	8.60382e17i	−0.0175754	+	0.913861i
$991$	9.46580e17			0.999344			0.499672	−	0.866215i	$-0.333454\pi$
$991$	9.46580e17			0.999344			0.499672	+	0.866215i	$0.333454\pi$
$992$	−2.76810e16	+	8.99411e15i	−0.0290477	+	0.00943818i
$993$	1.74481e17	+	1.26768e17i	0.181992	+	0.132225i
$994$	3.05726e17	−	2.22123e17i	0.316967	−	0.230290i
$995$	7.05538e17	−	2.17142e18i	0.727080	−	2.23772i
$996$	5.40114e16	+	1.75494e16i	0.0553260	+	0.0179765i
$997$	3.09044e17	+	4.25363e17i	0.314666	+	0.433100i	0.936829	−	0.349787i	$-0.113746\pi$
$997$	3.09044e17	+	4.25363e17i	0.314666	+	0.433100i	−0.622163	+	0.782887i	$0.713746\pi$
$998$	−1.89765e17	+	2.61189e17i	−0.192058	+	0.264345i
$999$	−2.78175e17	−	8.56136e17i	−0.279850	−	0.861291i

Display

a_p

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.13.d.a.17.4	yes	48
11.2	odd	10	inner	22.13.d.a.13.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.13.d.a.13.4	✓	48	11.2	odd	10	inner
22.13.d.a.17.4	yes	48	1.1	even	1	trivial

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	22.13.d.a.17.4

Level	$22$
Weight	$13$
Character	22.17
Analytic conductor	$20.108$
Analytic rank	$0$
Dimension	$48$
Inner twists	$2$