LMFDB - Embedded newform 29.15.c.a.12.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,15,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, 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:	$36.0554007641$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.13
Character	$\chi$	$=$	29.12
Dual form			29.15.c.a.17.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-55.9098 - 55.9098i) q^{2} +(1465.84 + 1465.84i) q^{3} -10132.2i q^{4} +40470.7i q^{5} -163909. i q^{6} +363644. q^{7} +(-1.48251e6 + 1.48251e6i) q^{8} -485606. i q^{9} +O(q^{10})$	\(q+(-55.9098 - 55.9098i) q^{2} +(1465.84 + 1465.84i) q^{3} -10132.2i q^{4} +40470.7i q^{5} -163909. i q^{6} +363644. q^{7} +(-1.48251e6 + 1.48251e6i) q^{8} -485606. i q^{9} +(2.26271e6 - 2.26271e6i) q^{10} +(-1.48788e7 - 1.48788e7i) q^{11} +(1.48522e7 - 1.48522e7i) q^{12} +8.87143e7i q^{13} +(-2.03312e7 - 2.03312e7i) q^{14} +(-5.93235e7 + 5.93235e7i) q^{15} -231610. q^{16} +(-2.71913e7 - 2.71913e7i) q^{17} +(-2.71501e7 + 2.71501e7i) q^{18} +(-7.19389e8 - 7.19389e8i) q^{19} +4.10057e8 q^{20} +(5.33043e8 + 5.33043e8i) q^{21} +1.66375e9i q^{22} +2.47785e9 q^{23} -4.34625e9 q^{24} +4.46564e9 q^{25} +(4.96000e9 - 4.96000e9i) q^{26} +(7.72288e9 - 7.72288e9i) q^{27} -3.68451e9i q^{28} +(-1.69505e10 - 3.19987e9i) q^{29} +6.63353e9 q^{30} +(-2.98856e10 - 2.98856e10i) q^{31} +(2.43025e10 + 2.43025e10i) q^{32} -4.36199e10i q^{33} +3.04052e9i q^{34} +1.47169e10i q^{35} -4.92025e9 q^{36} +(-9.85511e10 + 9.85511e10i) q^{37} +8.04418e10i q^{38} +(-1.30041e11 + 1.30041e11i) q^{39} +(-5.99984e10 - 5.99984e10i) q^{40} +(-2.59372e11 + 2.59372e11i) q^{41} -5.96046e10i q^{42} +(-2.71451e11 - 2.71451e11i) q^{43} +(-1.50755e11 + 1.50755e11i) q^{44} +1.96528e10 q^{45} +(-1.38536e11 - 1.38536e11i) q^{46} +(3.08804e11 - 3.08804e11i) q^{47} +(-3.39503e8 - 3.39503e8i) q^{48} -5.45986e11 q^{49} +(-2.49673e11 - 2.49673e11i) q^{50} -7.97161e10i q^{51} +8.98870e11 q^{52} -1.68665e12 q^{53} -8.63569e11 q^{54} +(6.02157e11 - 6.02157e11i) q^{55} +(-5.39107e11 + 5.39107e11i) q^{56} -2.10901e12i q^{57} +(7.68794e11 + 1.12660e12i) q^{58} -2.99910e12 q^{59} +(6.01077e11 + 6.01077e11i) q^{60} +(1.99267e12 + 1.99267e12i) q^{61} +3.34179e12i q^{62} -1.76588e11i q^{63} -2.71370e12i q^{64} -3.59033e12 q^{65} +(-2.43878e12 + 2.43878e12i) q^{66} -8.90196e12i q^{67} +(-2.75508e11 + 2.75508e11i) q^{68} +(3.63212e12 + 3.63212e12i) q^{69} +(8.22820e11 - 8.22820e11i) q^{70} -6.35956e12i q^{71} +(7.19918e11 + 7.19918e11i) q^{72} +(-5.63169e12 + 5.63169e12i) q^{73} +1.10199e13 q^{74} +(6.54590e12 + 6.54590e12i) q^{75} +(-7.28898e12 + 7.28898e12i) q^{76} +(-5.41060e12 - 5.41060e12i) q^{77} +1.45411e13 q^{78} +(-6.65488e9 - 6.65488e9i) q^{79} -9.37342e9i q^{80} +2.03183e13 q^{81} +2.90029e13 q^{82} +1.88963e12 q^{83} +(5.40089e12 - 5.40089e12i) q^{84} +(1.10045e12 - 1.10045e12i) q^{85} +3.03536e13i q^{86} +(-2.01562e13 - 2.95372e13i) q^{87} +4.41162e13 q^{88} +(9.87312e12 + 9.87312e12i) q^{89} +(-1.09879e12 - 1.09879e12i) q^{90} +3.22604e13i q^{91} -2.51060e13i q^{92} -8.76149e13i q^{93} -3.45303e13 q^{94} +(2.91142e13 - 2.91142e13i) q^{95} +7.12470e13i q^{96} +(-4.42602e13 + 4.42602e13i) q^{97} +(3.05260e13 + 3.05260e13i) q^{98} +(-7.22526e12 + 7.22526e12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 312 q^{2} - 2 q^{3} - 4 q^{7} - 689310 q^{8}+O(q^{10}) $ 68 * q - 312 * q^2 - 2 * q^3 - 4 * q^7 - 689310 * q^8	\( 68 q - 312 q^{2} - 2 q^{3} - 4 q^{7} - 689310 q^{8} + 23502846 q^{10} - 2993734 q^{11} - 76269906 q^{12} - 3845224 q^{14} + 277690070 q^{15} - 5490752792 q^{16} + 285786056 q^{17} + 5809842386 q^{18} - 1195066336 q^{19} + 1866268668 q^{20} - 8197524756 q^{21} + 2117392192 q^{23} + 8629372824 q^{24} - 73846917196 q^{25} - 16368356994 q^{26} + 33411191086 q^{27} + 48687460392 q^{29} + 128044102700 q^{30} + 73968522614 q^{31} - 2657032122 q^{32} - 259972090824 q^{36} + 95888936640 q^{37} - 571710579738 q^{39} + 977850700426 q^{40} - 57594847104 q^{41} + 48472463810 q^{43} + 1173476843650 q^{44} - 299491373708 q^{45} + 656204001636 q^{46} + 29961288922 q^{47} + 1808198535114 q^{48} + 9857850529980 q^{49} + 1443642384290 q^{50} - 11263919114280 q^{52} - 1993070689076 q^{53} + 2064324525592 q^{54} + 3054165001846 q^{55} + 8002123380864 q^{56} - 9170547007720 q^{58} - 8402401993912 q^{59} + 4455428077662 q^{60} - 4381209993964 q^{61} - 14884429709724 q^{65} - 5756218265814 q^{66} + 4595908790532 q^{68} + 51089269002600 q^{69} - 65383337180236 q^{70} + 101900024607216 q^{72} + 39493186331224 q^{73} - 152862151734316 q^{74} - 46335428712972 q^{75} + 46232026918072 q^{76} + 63231072283300 q^{77} + 111617680995888 q^{78} - 29034273461086 q^{79} - 345331621902328 q^{81} + 104609665443600 q^{82} - 2994621113016 q^{83} + 269240332456580 q^{84} + 11907997971872 q^{85} - 148747542169982 q^{87} + 186485775340436 q^{88} - 89923791148548 q^{89} + 103388070190448 q^{90} - 920451476162284 q^{94} - 393920660173420 q^{95} - 116095608365672 q^{97} + 24492650399928 q^{98} - 402079041111864 q^{99}+O(q^{100}) \) 68 * q - 312 * q^2 - 2 * q^3 - 4 * q^7 - 689310 * q^8 + 23502846 * q^10 - 2993734 * q^11 - 76269906 * q^12 - 3845224 * q^14 + 277690070 * q^15 - 5490752792 * q^16 + 285786056 * q^17 + 5809842386 * q^18 - 1195066336 * q^19 + 1866268668 * q^20 - 8197524756 * q^21 + 2117392192 * q^23 + 8629372824 * q^24 - 73846917196 * q^25 - 16368356994 * q^26 + 33411191086 * q^27 + 48687460392 * q^29 + 128044102700 * q^30 + 73968522614 * q^31 - 2657032122 * q^32 - 259972090824 * q^36 + 95888936640 * q^37 - 571710579738 * q^39 + 977850700426 * q^40 - 57594847104 * q^41 + 48472463810 * q^43 + 1173476843650 * q^44 - 299491373708 * q^45 + 656204001636 * q^46 + 29961288922 * q^47 + 1808198535114 * q^48 + 9857850529980 * q^49 + 1443642384290 * q^50 - 11263919114280 * q^52 - 1993070689076 * q^53 + 2064324525592 * q^54 + 3054165001846 * q^55 + 8002123380864 * q^56 - 9170547007720 * q^58 - 8402401993912 * q^59 + 4455428077662 * q^60 - 4381209993964 * q^61 - 14884429709724 * q^65 - 5756218265814 * q^66 + 4595908790532 * q^68 + 51089269002600 * q^69 - 65383337180236 * q^70 + 101900024607216 * q^72 + 39493186331224 * q^73 - 152862151734316 * q^74 - 46335428712972 * q^75 + 46232026918072 * q^76 + 63231072283300 * q^77 + 111617680995888 * q^78 - 29034273461086 * q^79 - 345331621902328 * q^81 + 104609665443600 * q^82 - 2994621113016 * q^83 + 269240332456580 * q^84 + 11907997971872 * q^85 - 148747542169982 * q^87 + 186485775340436 * q^88 - 89923791148548 * q^89 + 103388070190448 * q^90 - 920451476162284 * q^94 - 393920660173420 * q^95 - 116095608365672 * q^97 + 24492650399928 * q^98 - 402079041111864 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−55.9098	−	55.9098i	−0.436795	−	0.436795i	0.454137	−	0.890932i	$-0.349948\pi$
$2$	−55.9098	−	55.9098i	−0.436795	−	0.436795i	−0.890932	+	0.454137i	$0.849948\pi$
$3$	1465.84	+	1465.84i	0.670251	+	0.670251i	0.957774	−	0.287523i	$-0.0928318\pi$
$3$	1465.84	+	1465.84i	0.670251	+	0.670251i	−0.287523	+	0.957774i	$0.592832\pi$
$4$		−	10132.2i		−	0.618420i
$5$			40470.7i			0.518025i	0.965874	+	0.259012i	$0.0833971\pi$
$5$			40470.7i			0.518025i	−0.965874	+	0.259012i	$0.916603\pi$
$6$		−	163909.i		−	0.585525i
$7$	363644.			0.441560			0.220780	−	0.975324i	$-0.429140\pi$
$7$	363644.			0.441560			0.220780	+	0.975324i	$0.429140\pi$
$8$	−1.48251e6	+	1.48251e6i	−0.706918	+	0.706918i
$9$		−	485606.i		−	0.101528i
$10$	2.26271e6	−	2.26271e6i	0.226271	−	0.226271i
$11$	−1.48788e7	−	1.48788e7i	−0.763520	−	0.763520i	0.213437	−	0.976957i	$-0.431534\pi$
$11$	−1.48788e7	−	1.48788e7i	−0.763520	−	0.763520i	−0.976957	+	0.213437i	$0.931534\pi$
$12$	1.48522e7	−	1.48522e7i	0.414496	−	0.414496i
$13$			8.87143e7i			1.41381i	0.707310	+	0.706904i	$0.249909\pi$
$13$			8.87143e7i			1.41381i	−0.707310	+	0.706904i	$0.750091\pi$
$14$	−2.03312e7	−	2.03312e7i	−0.192871	−	0.192871i
$15$	−5.93235e7	+	5.93235e7i	−0.347207	+	0.347207i
$16$	−231610.			−0.000862815
$17$	−2.71913e7	−	2.71913e7i	−0.0662655	−	0.0662655i	0.673197	−	0.739463i	$-0.264920\pi$
$17$	−2.71913e7	−	2.71913e7i	−0.0662655	−	0.0662655i	−0.739463	+	0.673197i	$0.764920\pi$
$18$	−2.71501e7	+	2.71501e7i	−0.0443470	+	0.0443470i
$19$	−7.19389e8	−	7.19389e8i	−0.804801	−	0.804801i	0.179041	−	0.983842i	$-0.442701\pi$
$19$	−7.19389e8	−	7.19389e8i	−0.804801	−	0.804801i	−0.983842	+	0.179041i	$0.942701\pi$
$20$	4.10057e8			0.320357
$21$	5.33043e8	+	5.33043e8i	0.295956	+	0.295956i
$22$			1.66375e9i			0.667004i
$23$	2.47785e9			0.727745			0.363873	−	0.931449i	$-0.381454\pi$
$23$	2.47785e9			0.727745			0.363873	+	0.931449i	$0.381454\pi$
$24$	−4.34625e9			−0.947625
$25$	4.46564e9			0.731650
$26$	4.96000e9	−	4.96000e9i	0.617544	−	0.617544i
$27$	7.72288e9	−	7.72288e9i	0.738300	−	0.738300i
$28$		−	3.68451e9i		−	0.273070i
$29$	−1.69505e10	−	3.19987e9i	−0.982644	−	0.185501i
$29$	−1.69505e10	−	3.19987e9i	−0.982644	−	0.185501i
$30$	6.63353e9			0.303316
$31$	−2.98856e10	−	2.98856e10i	−1.08625	−	1.08625i	−0.995911	−	0.0903392i	$-0.971205\pi$
$31$	−2.98856e10	−	2.98856e10i	−1.08625	−	1.08625i	−0.0903392	−	0.995911i	$-0.528795\pi$
$32$	2.43025e10	+	2.43025e10i	0.707295	+	0.707295i
$33$		−	4.36199e10i		−	1.02350i
$34$			3.04052e9i			0.0578889i
$35$			1.47169e10i			0.228739i
$36$	−4.92025e9			−0.0627870
$37$	−9.85511e10	+	9.85511e10i	−1.03812	+	1.03812i	−0.0388806	+	0.999244i	$0.512379\pi$
$37$	−9.85511e10	+	9.85511e10i	−1.03812	+	1.03812i	−0.999244	+	0.0388806i	$0.987621\pi$
$38$			8.04418e10i			0.703066i
$39$	−1.30041e11	+	1.30041e11i	−0.947605	+	0.947605i
$40$	−5.99984e10	−	5.99984e10i	−0.366201	−	0.366201i
$41$	−2.59372e11	+	2.59372e11i	−1.33179	+	1.33179i	−0.428026	+	0.903767i	$0.640791\pi$
$41$	−2.59372e11	+	2.59372e11i	−1.33179	+	1.33179i	−0.903767	+	0.428026i	$0.859209\pi$
$42$		−	5.96046e10i		−	0.258544i
$43$	−2.71451e11	−	2.71451e11i	−0.998649	−	0.998649i	0.00135041	−	0.999999i	$-0.499570\pi$
$43$	−2.71451e11	−	2.71451e11i	−0.998649	−	0.998649i	−0.999999	+	0.00135041i	$0.999570\pi$
$44$	−1.50755e11	+	1.50755e11i	−0.472176	+	0.472176i
$45$	1.96528e10			0.0525941
$46$	−1.38536e11	−	1.38536e11i	−0.317876	−	0.317876i
$47$	3.08804e11	−	3.08804e11i	0.609534	−	0.609534i	−0.333290	−	0.942824i	$-0.608159\pi$
$47$	3.08804e11	−	3.08804e11i	0.609534	−	0.609534i	0.942824	+	0.333290i	$0.108159\pi$
$48$	−3.39503e8	−	3.39503e8i	−0.000578302	−	0.000578302i
$49$	−5.45986e11			−0.805025
$50$	−2.49673e11	−	2.49673e11i	−0.319581	−	0.319581i
$51$		−	7.97161e10i		−	0.0888290i
$52$	8.98870e11			0.874327
$53$	−1.68665e12			−1.43580			−0.717901	−	0.696146i	$-0.754897\pi$
$53$	−1.68665e12			−1.43580			−0.717901	+	0.696146i	$0.754897\pi$
$54$	−8.63569e11			−0.644972
$55$	6.02157e11	−	6.02157e11i	0.395522	−	0.395522i
$56$	−5.39107e11	+	5.39107e11i	−0.312147	+	0.312147i
$57$		−	2.10901e12i		−	1.07884i
$58$	7.68794e11	+	1.12660e12i	0.348188	+	0.510240i
$59$	−2.99910e12			−1.20511			−0.602554	−	0.798078i	$-0.705850\pi$
$59$	−2.99910e12			−1.20511			−0.602554	+	0.798078i	$0.705850\pi$
$60$	6.01077e11	+	6.01077e11i	0.214719	+	0.214719i
$61$	1.99267e12	+	1.99267e12i	0.634054	+	0.634054i	0.949082	−	0.315028i	$-0.102014\pi$
$61$	1.99267e12	+	1.99267e12i	0.634054	+	0.634054i	−0.315028	+	0.949082i	$0.602014\pi$
$62$			3.34179e12i			0.948938i
$63$		−	1.76588e11i		−	0.0448308i
$64$		−	2.71370e12i		−	0.617023i
$65$	−3.59033e12			−0.732388
$66$	−2.43878e12	+	2.43878e12i	−0.447060	+	0.447060i
$67$		−	8.90196e12i		−	1.46880i	−0.678718	−	0.734399i	$-0.737464\pi$
$67$		−	8.90196e12i		−	1.46880i	0.678718	−	0.734399i	$-0.262536\pi$
$68$	−2.75508e11	+	2.75508e11i	−0.0409799	+	0.0409799i
$69$	3.63212e12	+	3.63212e12i	0.487772	+	0.487772i
$70$	8.22820e11	−	8.22820e11i	0.0999122	−	0.0999122i
$71$		−	6.35956e12i		−	0.699228i	−0.936894	−	0.349614i	$-0.886313\pi$
$71$		−	6.35956e12i		−	0.699228i	0.936894	−	0.349614i	$-0.113687\pi$
$72$	7.19918e11	+	7.19918e11i	0.0717721	+	0.0717721i
$73$	−5.63169e12	+	5.63169e12i	−0.509776	+	0.509776i	−0.914458	−	0.404682i	$-0.867382\pi$
$73$	−5.63169e12	+	5.63169e12i	−0.509776	+	0.509776i	0.404682	+	0.914458i	$0.367382\pi$
$74$	1.10199e13			0.906896
$75$	6.54590e12	+	6.54590e12i	0.490389	+	0.490389i
$76$	−7.28898e12	+	7.28898e12i	−0.497705	+	0.497705i
$77$	−5.41060e12	−	5.41060e12i	−0.337140	−	0.337140i
$78$	1.45411e13			0.827819
$79$	−6.65488e9	−	6.65488e9i	−0.000346538	−	0.000346538i	0.706933	−	0.707280i	$-0.250078\pi$
$79$	−6.65488e9	−	6.65488e9i	−0.000346538	−	0.000346538i	−0.707280	+	0.706933i	$0.750078\pi$
$80$		−	9.37342e9i		−	0.000446960i
$81$	2.03183e13			0.888164
$82$	2.90029e13			1.16344
$83$	1.88963e12			0.0696355			0.0348177	−	0.999394i	$-0.488915\pi$
$83$	1.88963e12			0.0696355			0.0348177	+	0.999394i	$0.488915\pi$
$84$	5.40089e12	−	5.40089e12i	0.183025	−	0.183025i
$85$	1.10045e12	−	1.10045e12i	0.0343272	−	0.0343272i
$86$			3.03536e13i			0.872410i
$87$	−2.01562e13	−	2.95372e13i	−0.534286	−	0.782950i
$88$	4.41162e13			1.07949
$89$	9.87312e12	+	9.87312e12i	0.223216	+	0.223216i	0.809851	−	0.586635i	$-0.199548\pi$
$89$	9.87312e12	+	9.87312e12i	0.223216	+	0.223216i	−0.586635	+	0.809851i	$0.699548\pi$
$90$	−1.09879e12	−	1.09879e12i	−0.0229729	−	0.0229729i
$91$			3.22604e13i			0.624281i
$92$		−	2.51060e13i		−	0.450052i
$93$		−	8.76149e13i		−	1.45612i
$94$	−3.45303e13			−0.532483
$95$	2.91142e13	−	2.91142e13i	0.416907	−	0.416907i
$96$			7.12470e13i			0.948130i
$97$	−4.42602e13	+	4.42602e13i	−0.547787	+	0.547787i	−0.925800	−	0.378013i	$-0.876607\pi$
$97$	−4.42602e13	+	4.42602e13i	−0.547787	+	0.547787i	0.378013	+	0.925800i	$0.376607\pi$
$98$	3.05260e13	+	3.05260e13i	0.351631	+	0.351631i
$99$	−7.22526e12	+	7.22526e12i	−0.0775188	+	0.0775188i
$100$		−	4.52467e13i		−	0.452467i
$101$	6.08562e13	+	6.08562e13i	0.567617	+	0.567617i	0.931460	−	0.363844i	$-0.118536\pi$
$101$	6.08562e13	+	6.08562e13i	0.567617	+	0.567617i	−0.363844	+	0.931460i	$0.618536\pi$
$102$	−4.45691e12	+	4.45691e12i	−0.0388001	+	0.0388001i
$103$	1.85735e14			1.51020			0.755098	−	0.655612i	$-0.227589\pi$
$103$	1.85735e14			1.51020			0.755098	+	0.655612i	$0.227589\pi$
$104$	−1.31520e14	−	1.31520e14i	−0.999446	−	0.999446i
$105$	−2.15726e13	+	2.15726e13i	−0.153313	+	0.153313i
$106$	9.43004e13	+	9.43004e13i	0.627151	+	0.627151i
$107$	−1.11894e14			−0.696821			−0.348411	−	0.937342i	$-0.613279\pi$
$107$	−1.11894e14			−0.696821			−0.348411	+	0.937342i	$0.613279\pi$
$108$	−7.82497e13	−	7.82497e13i	−0.456579	−	0.456579i
$109$		−	2.63339e14i		−	1.44056i	−0.693685	−	0.720278i	$-0.744014\pi$
$109$		−	2.63339e14i		−	1.44056i	0.693685	−	0.720278i	$-0.255986\pi$
$110$	−6.73330e13			−0.345525
$111$	−2.88920e14			−1.39161
$112$	−8.42236e10			−0.000380985
$113$	−1.10365e13	+	1.10365e13i	−0.0469118	+	0.0469118i	−0.730174	−	0.683262i	$-0.760561\pi$
$113$	−1.10365e13	+	1.10365e13i	−0.0469118	+	0.0469118i	0.683262	+	0.730174i	$0.260561\pi$
$114$	−1.17915e14	+	1.17915e14i	−0.471231	+	0.471231i
$115$			1.00280e14i			0.376990i
$116$	−3.24217e13	+	1.71746e14i	−0.114717	+	0.607687i
$117$	4.30802e13			0.143541
$118$	1.67679e14	+	1.67679e14i	0.526386	+	0.526386i
$119$	−9.88795e12	−	9.88795e12i	−0.0292602	−	0.0292602i
$120$		−	1.75896e14i		−	0.490893i
$121$			6.30101e13i			0.165925i
$122$		−	2.22819e14i		−	0.553903i
$123$	−7.60395e14			−1.78527
$124$	−3.02806e14	+	3.02806e14i	−0.671759	+	0.671759i
$125$			4.27741e14i			0.897038i
$126$	−9.87298e12	+	9.87298e12i	−0.0195819	+	0.0195819i
$127$	−1.82443e14	−	1.82443e14i	−0.342374	−	0.342374i	0.514885	−	0.857259i	$-0.327835\pi$
$127$	−1.82443e14	−	1.82443e14i	−0.342374	−	0.342374i	−0.857259	+	0.514885i	$0.827835\pi$
$128$	2.46449e14	−	2.46449e14i	0.437782	−	0.437782i
$129$		−	7.95807e14i		−	1.33869i
$130$	2.00735e14	+	2.00735e14i	0.319903	+	0.319903i
$131$	−4.23989e14	+	4.23989e14i	−0.640406	+	0.640406i	−0.950655	−	0.310249i	$-0.899587\pi$
$131$	−4.23989e14	+	4.23989e14i	−0.640406	+	0.640406i	0.310249	+	0.950655i	$0.399587\pi$
$132$	−4.41966e14			−0.632952
$133$	−2.61601e14	−	2.61601e14i	−0.355368	−	0.355368i
$134$	−4.97707e14	+	4.97707e14i	−0.641564	+	0.641564i
$135$	3.12550e14	+	3.12550e14i	0.382458	+	0.382458i
$136$	8.06230e13			0.0936886
$137$	1.63108e14	+	1.63108e14i	0.180065	+	0.180065i	0.791384	−	0.611319i	$-0.209361\pi$
$137$	1.63108e14	+	1.63108e14i	0.180065	+	0.180065i	−0.611319	+	0.791384i	$0.709361\pi$
$138$		−	4.06142e14i		−	0.426113i
$139$	1.29074e15			1.28746			0.643732	−	0.765251i	$-0.277385\pi$
$139$	1.29074e15			1.28746			0.643732	+	0.765251i	$0.277385\pi$
$140$	1.49115e14			0.141457
$141$	9.05313e14			0.817081
$142$	−3.55562e14	+	3.55562e14i	−0.305419	+	0.305419i
$143$	1.31997e15	−	1.31997e15i	1.07947	−	1.07947i
$144$			1.12471e11i			8.76000e-5i
$145$	1.29501e14	−	6.85998e14i	0.0960941	−	0.509034i
$146$	6.29734e14			0.445335
$147$	−8.00327e14	−	8.00327e14i	−0.539568	−	0.539568i
$148$	9.98538e14	+	9.98538e14i	0.641997	+	0.641997i
$149$			2.40175e15i			1.47307i	0.676398	+	0.736536i	$0.263540\pi$
$149$			2.40175e15i			1.47307i	−0.676398	+	0.736536i	$0.736460\pi$
$150$		−	7.31960e14i		−	0.428399i
$151$		−	1.70137e15i		−	0.950516i	−0.879847	−	0.475258i	$-0.842355\pi$
$151$		−	1.70137e15i		−	0.950516i	0.879847	−	0.475258i	$-0.157645\pi$
$152$	2.13301e15			1.13786
$153$	−1.32043e13	+	1.32043e13i	−0.00672782	+	0.00672782i
$154$			6.05011e14i			0.294522i
$155$	1.20949e15	−	1.20949e15i	0.562705	−	0.562705i
$156$	1.31760e15	+	1.31760e15i	0.586018	+	0.586018i
$157$	8.11260e14	−	8.11260e14i	0.345034	−	0.345034i	−0.513222	−	0.858256i	$-0.671548\pi$
$157$	8.11260e14	−	8.11260e14i	0.345034	−	0.345034i	0.858256	+	0.513222i	$0.171548\pi$
$158$			7.44146e11i			0.000302732i
$159$	−2.47236e15	−	2.47236e15i	−0.962347	−	0.962347i
$160$	−9.83538e14	+	9.83538e14i	−0.366396	+	0.366396i
$161$	9.01053e14			0.321343
$162$	−1.13599e15	−	1.13599e15i	−0.387946	−	0.387946i
$163$	1.03369e15	−	1.03369e15i	0.338124	−	0.338124i	−0.517537	−	0.855661i	$-0.673151\pi$
$163$	1.03369e15	−	1.03369e15i	0.338124	−	0.338124i	0.855661	+	0.517537i	$0.173151\pi$
$164$	2.62801e15	+	2.62801e15i	0.823607	+	0.823607i
$165$	1.76533e15			0.530198
$166$	−1.05649e14	−	1.05649e14i	−0.0304164	−	0.0304164i
$167$			4.56999e15i			1.26154i	0.775972	+	0.630768i	$0.217260\pi$
$167$			4.56999e15i			1.26154i	−0.775972	+	0.630768i	$0.782740\pi$
$168$	−1.58049e15			−0.418433
$169$	−3.93286e15			−0.998852
$170$	−1.23052e14			−0.0299879
$171$	−3.49340e14	+	3.49340e14i	−0.0817100	+	0.0817100i
$172$	−2.75040e15	+	2.75040e15i	−0.617584	+	0.617584i
$173$			4.98154e15i			1.07409i	0.843554	+	0.537045i	$0.180459\pi$
$173$			4.98154e15i			1.07409i	−0.843554	+	0.537045i	$0.819541\pi$
$174$	−5.24489e14	+	2.77834e15i	−0.108615	+	0.575362i
$175$	1.62390e15			0.323068
$176$	3.44609e12	+	3.44609e12i	0.000658776	+	0.000658776i
$177$	−4.39619e15	−	4.39619e15i	−0.807725	−	0.807725i
$178$		−	1.10401e15i		−	0.194999i
$179$		−	1.03293e16i		−	1.75429i	−0.480228	−	0.877144i	$-0.659446\pi$
$179$		−	1.03293e16i		−	1.75429i	0.480228	−	0.877144i	$-0.340554\pi$
$180$		−	1.99126e14i		−	0.0325253i
$181$	6.16414e15			0.968552			0.484276	−	0.874915i	$-0.339083\pi$
$181$	6.16414e15			0.968552			0.484276	+	0.874915i	$0.339083\pi$
$182$	1.80367e15	−	1.80367e15i	0.272683	−	0.272683i
$183$			5.84186e15i			0.849950i
$184$	−3.67344e15	+	3.67344e15i	−0.514456	+	0.514456i
$185$	−3.98843e15	−	3.98843e15i	−0.537774	−	0.537774i
$186$	−4.89853e15	+	4.89853e15i	−0.636026	+	0.636026i
$187$			8.09151e14i			0.101190i
$188$	−3.12886e15	−	3.12886e15i	−0.376948	−	0.376948i
$189$	2.80838e15	−	2.80838e15i	0.326004	−	0.326004i
$190$	−3.25553e15			−0.364206
$191$	6.46062e15	+	6.46062e15i	0.696692	+	0.696692i	0.963695	−	0.267004i	$-0.0860336\pi$
$191$	6.46062e15	+	6.46062e15i	0.696692	+	0.696692i	−0.267004	+	0.963695i	$0.586034\pi$
$192$	3.97784e15	−	3.97784e15i	0.413560	−	0.413560i
$193$	−1.01540e16	−	1.01540e16i	−1.01797	−	1.01797i	−0.999836	−	0.0181321i	$-0.994228\pi$
$193$	−1.01540e16	−	1.01540e16i	−1.01797	−	1.01797i	−0.0181321	−	0.999836i	$-0.505772\pi$
$194$	4.94916e15			0.478541
$195$	−5.26284e15	−	5.26284e15i	−0.490883	−	0.490883i
$196$			5.53204e15i			0.497843i
$197$	4.67645e15			0.406118			0.203059	−	0.979166i	$-0.434912\pi$
$197$	4.67645e15			0.406118			0.203059	+	0.979166i	$0.434912\pi$
$198$	8.07925e14			0.0677197
$199$	−2.74212e15			−0.221879			−0.110939	−	0.993827i	$-0.535386\pi$
$199$	−2.74212e15			−0.221879			−0.110939	+	0.993827i	$0.535386\pi$
$200$	−6.62037e15	+	6.62037e15i	−0.517217	+	0.517217i
$201$	1.30488e16	−	1.30488e16i	0.984463	−	0.984463i
$202$		−	6.80491e15i		−	0.495864i
$203$	−6.16394e15	−	1.16361e15i	−0.433896	−	0.0819099i
$204$	−8.07699e14			−0.0549336
$205$	−1.04970e16	−	1.04970e16i	−0.689902	−	0.689902i
$206$	−1.03844e16	−	1.03844e16i	−0.659646	−	0.659646i
$207$		−	1.20326e15i		−	0.0738867i
$208$		−	2.05471e13i		−	0.00121985i
$209$			2.14073e16i			1.22896i
$210$	2.41224e15			0.133932
$211$	−2.24194e16	+	2.24194e16i	−1.20406	+	1.20406i	−0.231133	+	0.972922i	$0.574243\pi$
$211$	−2.24194e16	+	2.24194e16i	−1.20406	+	1.20406i	−0.972922	+	0.231133i	$0.925757\pi$
$212$			1.70895e16i			0.887928i
$213$	9.32209e15	−	9.32209e15i	0.468658	−	0.468658i
$214$	6.25599e15	+	6.25599e15i	0.304368	+	0.304368i
$215$	1.09858e16	−	1.09858e16i	0.517325	−	0.517325i
$216$			2.28986e16i			1.04384i
$217$	−1.08677e16	−	1.08677e16i	−0.479645	−	0.479645i
$218$	−1.47232e16	+	1.47232e16i	−0.629228	+	0.629228i
$219$	−1.65103e16			−0.683355
$220$	−6.10117e15	−	6.10117e15i	−0.244599	−	0.244599i
$221$	2.41226e15	−	2.41226e15i	0.0936867	−	0.0936867i
$222$	1.61535e16	+	1.61535e16i	0.607847	+	0.607847i
$223$	2.97431e16			1.08456			0.542279	−	0.840198i	$-0.317562\pi$
$223$	2.97431e16			1.08456			0.542279	+	0.840198i	$0.317562\pi$
$224$	8.83744e15	+	8.83744e15i	0.312313	+	0.312313i
$225$		−	2.16854e15i		−	0.0742831i
$226$	1.23410e15			0.0409817
$227$	−2.53198e16			−0.815227			−0.407614	−	0.913154i	$-0.633639\pi$
$227$	−2.53198e16			−0.815227			−0.407614	+	0.913154i	$0.633639\pi$
$228$	−2.13689e16			−0.667174
$229$	1.62799e16	−	1.62799e16i	0.492952	−	0.492952i	−0.416283	−	0.909235i	$-0.636668\pi$
$229$	1.62799e16	−	1.62799e16i	0.492952	−	0.492952i	0.909235	+	0.416283i	$0.136668\pi$
$230$	5.60664e15	−	5.60664e15i	0.164668	−	0.164668i
$231$		−	1.58621e16i		−	0.451937i
$232$	2.98732e16	−	2.03855e16i	0.825783	−	0.563515i
$233$	6.93483e16			1.86014			0.930068	−	0.367388i	$-0.119748\pi$
$233$	6.93483e16			1.86014			0.930068	+	0.367388i	$0.119748\pi$
$234$	−2.40861e15	−	2.40861e15i	−0.0626982	−	0.0626982i
$235$	1.24975e16	+	1.24975e16i	0.315754	+	0.315754i
$236$			3.03874e16i			0.745263i
$237$		−	1.95099e13i		−	0.000464534i
$238$			1.10567e15i			0.0255615i
$239$	−2.86352e16			−0.642859			−0.321429	−	0.946934i	$-0.604163\pi$
$239$	−2.86352e16			−0.642859			−0.321429	+	0.946934i	$0.604163\pi$
$240$	1.37399e13	−	1.37399e13i	0.000299575	−	0.000299575i
$241$		−	1.55634e16i		−	0.329599i	−0.986327	−	0.164800i	$-0.947302\pi$
$241$		−	1.55634e16i		−	0.329599i	0.986327	−	0.164800i	$-0.0526978\pi$
$242$	3.52288e15	−	3.52288e15i	0.0724754	−	0.0724754i
$243$	−7.15489e15	−	7.15489e15i	−0.143008	−	0.143008i
$244$	2.01901e16	−	2.01901e16i	0.392111	−	0.392111i
$245$		−	2.20964e16i		−	0.417023i
$246$	4.25136e16	+	4.25136e16i	0.779797	+	0.779797i
$247$	6.38201e16	−	6.38201e16i	1.13783	−	1.13783i
$248$	8.86116e16			1.53578
$249$	2.76989e15	+	2.76989e15i	0.0466732	+	0.0466732i
$250$	2.39149e16	−	2.39149e16i	0.391822	−	0.391822i
$251$	−1.27009e16	−	1.27009e16i	−0.202357	−	0.202357i	0.598652	−	0.801009i	$-0.295703\pi$
$251$	−1.27009e16	−	1.27009e16i	−0.202357	−	0.202357i	−0.801009	+	0.598652i	$0.795703\pi$
$252$	−1.78922e15			−0.0277243
$253$	−3.68675e16	−	3.68675e16i	−0.555648	−	0.555648i
$254$			2.04007e16i			0.299095i
$255$	3.22617e15			0.0460157
$256$	−7.20191e16			−0.999466
$257$	−2.27277e16			−0.306919			−0.153460	−	0.988155i	$-0.549041\pi$
$257$	−2.27277e16			−0.306919			−0.153460	+	0.988155i	$0.549041\pi$
$258$	−4.44934e16	+	4.44934e16i	−0.584733	+	0.584733i
$259$	−3.58375e16	+	3.58375e16i	−0.458394	+	0.458394i
$260$			3.63779e16i			0.452923i
$261$	−1.55388e15	+	8.23126e15i	−0.0188336	+	0.0997661i
$262$	4.74102e16			0.559452
$263$	1.46472e16	+	1.46472e16i	0.168292	+	0.168292i	0.786228	−	0.617936i	$-0.212031\pi$
$263$	1.46472e16	+	1.46472e16i	0.168292	+	0.168292i	−0.617936	+	0.786228i	$0.712031\pi$
$264$	6.46672e16	+	6.46672e16i	0.723530	+	0.723530i
$265$		−	6.82600e16i		−	0.743781i
$266$			2.92521e16i			0.310446i
$267$			2.89448e16i			0.299221i
$268$	−9.01964e16			−0.908334
$269$	4.31854e16	−	4.31854e16i	0.423712	−	0.423712i	−0.462768	−	0.886480i	$-0.653144\pi$
$269$	4.31854e16	−	4.31854e16i	0.423712	−	0.423712i	0.886480	+	0.462768i	$0.153144\pi$
$270$		−	3.49492e16i		−	0.334112i
$271$	−1.51595e17	+	1.51595e17i	−1.41221	+	1.41221i	−0.668525	+	0.743689i	$0.733074\pi$
$271$	−1.51595e17	+	1.51595e17i	−1.41221	+	1.41221i	−0.743689	+	0.668525i	$0.766926\pi$
$272$	6.29778e12	+	6.29778e12i	5.71749e−5	+	5.71749e-5i
$273$	−4.72885e16	+	4.72885e16i	−0.418425	+	0.418425i
$274$		−	1.82386e16i		−	0.157303i
$275$	−6.64435e16	−	6.64435e16i	−0.558629	−	0.558629i
$276$	3.68013e16	−	3.68013e16i	0.301648	−	0.301648i
$277$	4.44627e16			0.355335			0.177667	−	0.984091i	$-0.443145\pi$
$277$	4.44627e16			0.355335			0.177667	+	0.984091i	$0.443145\pi$
$278$	−7.21650e16	−	7.21650e16i	−0.562358	−	0.562358i
$279$	−1.45126e16	+	1.45126e16i	−0.110285	+	0.110285i
$280$	−2.18180e16	−	2.18180e16i	−0.161700	−	0.161700i
$281$	7.64568e16			0.552677			0.276339	−	0.961060i	$-0.410879\pi$
$281$	7.64568e16			0.552677			0.276339	+	0.961060i	$0.410879\pi$
$282$	−5.06159e16	−	5.06159e16i	−0.356897	−	0.356897i
$283$			1.50679e15i			0.0103645i	0.999987	+	0.00518223i	$0.00164956\pi$
$283$			1.50679e15i			0.0103645i	−0.999987	+	0.00518223i	$0.998350\pi$
$284$	−6.44363e16			−0.432416
$285$	8.53533e16			0.558864
$286$	−1.47598e17			−0.943015
$287$	−9.43191e16	+	9.43191e16i	−0.588066	+	0.588066i
$288$	1.18014e16	−	1.18014e16i	0.0718104	−	0.0718104i
$289$		−	1.66899e17i		−	0.991218i
$290$	−4.55944e16	+	3.11136e16i	−0.264317	+	0.180370i
$291$	−1.29757e17			−0.734309
$292$	5.70614e16	+	5.70614e16i	0.315255	+	0.315255i
$293$	7.54002e16	+	7.54002e16i	0.406724	+	0.406724i	0.880594	−	0.473871i	$-0.157144\pi$
$293$	7.54002e16	+	7.54002e16i	0.406724	+	0.406724i	−0.473871	+	0.880594i	$0.657144\pi$
$294$			8.94923e16i			0.471362i
$295$		−	1.21375e17i		−	0.624276i
$296$		−	2.92207e17i		−	1.46774i
$297$	−2.29815e17			−1.12741
$298$	1.34281e17	−	1.34281e17i	0.643431	−	0.643431i
$299$			2.19820e17i			1.02889i
$300$	6.63243e16	−	6.63243e16i	0.303266	−	0.303266i
$301$	−9.87116e16	−	9.87116e16i	−0.440963	−	0.440963i
$302$	−9.51230e16	+	9.51230e16i	−0.415181	+	0.415181i
$303$			1.78411e17i			0.760891i
$304$	1.66618e14	+	1.66618e14i	0.000694394	+	0.000694394i
$305$	−8.06447e16	+	8.06447e16i	−0.328456	+	0.328456i
$306$	1.47650e15			0.00587736
$307$	2.29355e17	+	2.29355e17i	0.892358	+	0.892358i	0.994745	−	0.102387i	$-0.0326479\pi$
$307$	2.29355e17	+	2.29355e17i	0.892358	+	0.892358i	−0.102387	+	0.994745i	$0.532648\pi$
$308$	−5.48212e16	+	5.48212e16i	−0.208494	+	0.208494i
$309$	2.72257e17	+	2.72257e17i	1.01221	+	1.01221i
$310$	−1.35245e17			−0.491574
$311$	4.03211e16	+	4.03211e16i	0.143288	+	0.143288i	0.775112	−	0.631824i	$-0.217693\pi$
$311$	4.03211e16	+	4.03211e16i	0.143288	+	0.143288i	−0.631824	+	0.775112i	$0.717693\pi$
$312$		−	3.85575e17i		−	1.33976i
$313$	5.96095e15			0.0202537			0.0101269	−	0.999949i	$-0.496776\pi$
$313$	5.96095e15			0.0202537			0.0101269	+	0.999949i	$0.496776\pi$
$314$	−9.07147e16			−0.301419
$315$	7.14663e15			0.0232235
$316$	−6.74285e13	+	6.74285e13i	−0.000214306	+	0.000214306i
$317$	1.06370e17	−	1.06370e17i	0.330678	−	0.330678i	−0.522166	−	0.852844i	$-0.674876\pi$
$317$	1.06370e17	−	1.06370e17i	0.330678	−	0.330678i	0.852844	+	0.522166i	$0.174876\pi$
$318$			2.76458e17i			0.840697i
$319$	2.04593e17	+	2.99814e17i	0.608635	+	0.891902i
$320$	1.09825e17			0.319633
$321$	−1.64019e17	−	1.64019e17i	−0.467045	−	0.467045i
$322$	−5.03777e16	−	5.03777e16i	−0.140361	−	0.140361i
$323$			3.91222e16i			0.106661i
$324$		−	2.05869e17i		−	0.549258i
$325$			3.96166e17i			1.03441i
$326$	−1.15586e17			−0.295382
$327$	3.86013e17	−	3.86013e17i	0.965534	−	0.965534i
$328$		−	7.69046e17i		−	1.88294i
$329$	1.12295e17	−	1.12295e17i	0.269146	−	0.269146i
$330$	−9.86992e16	−	9.86992e16i	−0.231588	−	0.231588i
$331$	−9.62814e16	+	9.62814e16i	−0.221180	+	0.221180i	−0.808995	−	0.587815i	$-0.799988\pi$
$331$	−9.62814e16	+	9.62814e16i	−0.221180	+	0.221180i	0.587815	+	0.808995i	$0.299988\pi$
$332$		−	1.91461e16i		−	0.0430639i
$333$	4.78570e16	+	4.78570e16i	0.105399	+	0.105399i
$334$	2.55507e17	−	2.55507e17i	0.551033	−	0.551033i
$335$	3.60269e17			0.760874
$336$	−1.23458e14	−	1.23458e14i	−0.000255355	−	0.000255355i
$337$	6.54612e17	−	6.54612e17i	1.32610	−	1.32610i	0.417349	−	0.908746i	$-0.362959\pi$
$337$	6.54612e17	−	6.54612e17i	1.32610	−	1.32610i	0.908746	−	0.417349i	$-0.137041\pi$
$338$	2.19885e17	+	2.19885e17i	0.436294	+	0.436294i
$339$	−3.23554e16			−0.0628853
$340$	−1.11500e16	−	1.11500e16i	−0.0212286	−	0.0212286i
$341$			8.89326e17i			1.65875i
$342$	3.90630e16			0.0713811
$343$	−4.45176e17			−0.797027
$344$	8.04861e17			1.41193
$345$	−1.46994e17	+	1.46994e17i	−0.252678	+	0.252678i
$346$	2.78517e17	−	2.78517e17i	0.469157	−	0.469157i
$347$			1.36330e16i			0.0225054i	0.999937	+	0.0112527i	$0.00358191\pi$
$347$			1.36330e16i			0.0225054i	−0.999937	+	0.0112527i	$0.996418\pi$
$348$	−2.99276e17	+	2.04226e17i	−0.484192	+	0.330413i
$349$	−6.16114e16			−0.0976973			−0.0488487	−	0.998806i	$-0.515555\pi$
$349$	−6.16114e16			−0.0976973			−0.0488487	+	0.998806i	$0.515555\pi$
$350$	−9.07920e16	−	9.07920e16i	−0.141114	−	0.141114i
$351$	6.85130e17	+	6.85130e17i	1.04381	+	1.04381i
$352$		−	7.23185e17i		−	1.08007i
$353$			1.05169e18i			1.53980i	0.638164	+	0.769900i	$0.279694\pi$
$353$			1.05169e18i			1.53980i	−0.638164	+	0.769900i	$0.720306\pi$
$354$			4.91580e17i			0.705621i
$355$	2.57376e17			0.362217
$356$	1.00036e17	−	1.00036e17i	0.138041	−	0.138041i
$357$		−	2.89883e16i		−	0.0392234i
$358$	−5.77511e17	+	5.77511e17i	−0.766265	+	0.766265i
$359$	−9.73750e17	−	9.73750e17i	−1.26703	−	1.26703i	−0.947616	−	0.319413i	$-0.896514\pi$
$359$	−9.73750e17	−	9.73750e17i	−1.26703	−	1.26703i	−0.319413	−	0.947616i	$-0.603486\pi$
$360$	−2.91356e16	+	2.91356e16i	−0.0371797	+	0.0371797i
$361$			2.36034e17i			0.295409i
$362$	−3.44636e17	−	3.44636e17i	−0.423059	−	0.423059i
$363$	−9.23626e16	+	9.23626e16i	−0.111211	+	0.111211i
$364$	3.26869e17			0.386068
$365$	−2.27919e17	−	2.27919e17i	−0.264076	−	0.264076i
$366$	3.26617e17	−	3.26617e17i	0.371254	−	0.371254i
$367$	−7.49506e16	−	7.49506e16i	−0.0835820	−	0.0835820i	0.664080	−	0.747662i	$-0.268824\pi$
$367$	−7.49506e16	−	7.49506e16i	−0.0835820	−	0.0835820i	−0.747662	+	0.664080i	$0.768824\pi$
$368$	−5.73894e14			−0.000627910
$369$	1.25953e17	+	1.25953e17i	0.135214	+	0.135214i
$370$			4.45985e17i			0.469795i
$371$	−6.13340e17			−0.633993
$372$	−8.87730e17			−0.900493
$373$	2.09394e17			0.208451			0.104225	−	0.994554i	$-0.466764\pi$
$373$	2.09394e17			0.208451			0.104225	+	0.994554i	$0.466764\pi$
$374$	4.52394e16	−	4.52394e16i	0.0441994	−	0.0441994i
$375$	−6.26999e17	+	6.26999e17i	−0.601240	+	0.601240i
$376$			9.15613e17i			0.861781i
$377$	2.83874e17	−	1.50375e18i	0.262263	−	1.38927i
$378$	−3.14032e17			−0.284794
$379$	−8.28451e17	−	8.28451e17i	−0.737552	−	0.737552i	0.234552	−	0.972104i	$-0.424638\pi$
$379$	−8.28451e17	−	8.28451e17i	−0.737552	−	0.737552i	−0.972104	+	0.234552i	$0.924638\pi$
$380$	−2.94990e17	−	2.94990e17i	−0.257823	−	0.257823i
$381$		−	5.34864e17i		−	0.458953i
$382$		−	7.22424e17i		−	0.608623i
$383$			4.14869e17i			0.343178i	0.985169	+	0.171589i	$0.0548901\pi$
$383$			4.14869e17i			0.343178i	−0.985169	+	0.171589i	$0.945110\pi$
$384$	7.22510e17			0.586847
$385$	2.18971e17	−	2.18971e17i	0.174647	−	0.174647i
$386$			1.13541e18i			0.889287i
$387$	−1.31818e17	+	1.31818e17i	−0.101391	+	0.101391i
$388$	4.48453e17	+	4.48453e17i	0.338762	+	0.338762i
$389$	−1.58858e18	+	1.58858e18i	−1.17859	+	1.17859i	−0.198481	+	0.980105i	$0.563601\pi$
$389$	−1.58858e18	+	1.58858e18i	−1.17859	+	1.17859i	−0.980105	+	0.198481i	$0.936399\pi$
$390$			5.88489e17i			0.428831i
$391$	−6.73759e16	−	6.73759e16i	−0.0482244	−	0.0482244i
$392$	8.09433e17	−	8.09433e17i	0.569086	−	0.569086i
$393$	−1.24300e18			−0.858465
$394$	−2.61459e17	−	2.61459e17i	−0.177391	−	0.177391i
$395$	2.69327e14	−	2.69327e14i	0.000179515	−	0.000179515i
$396$	7.32077e16	+	7.32077e16i	0.0479392	+	0.0479392i
$397$	−1.03953e18			−0.668814			−0.334407	−	0.942429i	$-0.608536\pi$
$397$	−1.03953e18			−0.668814			−0.334407	+	0.942429i	$0.608536\pi$
$398$	1.53312e17	+	1.53312e17i	0.0969155	+	0.0969155i
$399$		−	7.66930e17i		−	0.476371i
$400$	−1.03429e15			−0.000631279
$401$	−1.12209e18			−0.673005			−0.336503	−	0.941683i	$-0.609244\pi$
$401$	−1.12209e18			−0.673005			−0.336503	+	0.941683i	$0.609244\pi$
$402$	−1.45912e18			−0.860018
$403$	2.65128e18	−	2.65128e18i	1.53575	−	1.53575i
$404$	6.16606e17	−	6.16606e17i	0.351025	−	0.351025i
$405$			8.22297e17i			0.460091i
$406$	2.79567e17	+	4.09682e17i	0.153746	+	0.225302i
$407$	2.93265e18			1.58526
$408$	1.18180e17	+	1.18180e17i	0.0627949	+	0.0627949i
$409$	−2.36487e18	−	2.36487e18i	−1.23522	−	1.23522i	−0.961933	−	0.273286i	$-0.911889\pi$
$409$	−2.36487e18	−	2.36487e18i	−1.23522	−	1.23522i	−0.273286	−	0.961933i	$-0.588111\pi$
$410$			1.17377e18i			0.602691i
$411$			4.78178e17i			0.241378i
$412$		−	1.88190e18i		−	0.933935i
$413$	−1.09060e18			−0.532128
$414$	−6.72739e16	+	6.72739e16i	−0.0322734	+	0.0322734i
$415$			7.64747e16i			0.0360729i
$416$	−2.15598e18	+	2.15598e18i	−0.999979	+	0.999979i
$417$	1.89202e18	+	1.89202e18i	0.862923	+	0.862923i
$418$	1.19688e18	−	1.19688e18i	0.536805	−	0.536805i
$419$		−	4.30646e17i		−	0.189942i	−0.995480	−	0.0949712i	$-0.969724\pi$
$419$		−	4.30646e17i		−	0.189942i	0.995480	−	0.0949712i	$-0.0302759\pi$
$420$	2.18578e17	+	2.18578e17i	0.0948115	+	0.0948115i
$421$	−2.06771e18	+	2.06771e18i	−0.882092	+	0.882092i	−0.993747	−	0.111655i	$-0.964385\pi$
$421$	−2.06771e18	+	2.06771e18i	−0.882092	+	0.882092i	0.111655	+	0.993747i	$0.464385\pi$
$422$	2.50693e18			1.05185
$423$	−1.49957e17	−	1.49957e17i	−0.0618849	−	0.0618849i
$424$	2.50049e18	−	2.50049e18i	1.01499	−	1.01499i
$425$	−1.21427e17	−	1.21427e17i	−0.0484832	−	0.0484832i
$426$	−1.04239e18			−0.409415
$427$	7.24621e17	+	7.24621e17i	0.279973	+	0.279973i
$428$			1.13373e18i			0.430928i
$429$	3.86971e18			1.44703
$430$	−1.22843e18			−0.451930
$431$	−2.20931e18			−0.799680			−0.399840	−	0.916585i	$-0.630934\pi$
$431$	−2.20931e18			−0.799680			−0.399840	+	0.916585i	$0.630934\pi$
$432$	−1.78870e15	+	1.78870e15i	−0.000637016	+	0.000637016i
$433$	−1.32251e17	+	1.32251e17i	−0.0463429	+	0.0463429i	−0.729898	−	0.683556i	$-0.760433\pi$
$433$	−1.32251e17	+	1.32251e17i	−0.0463429	+	0.0463429i	0.683556	+	0.729898i	$0.260433\pi$
$434$			1.21522e18i			0.419013i
$435$	1.19539e18	−	8.15735e17i	0.405588	−	0.276773i
$436$	−2.66820e18			−0.890868
$437$	−1.78253e18	−	1.78253e18i	−0.585690	−	0.585690i
$438$	9.23088e17	+	9.23088e17i	0.298486	+	0.298486i
$439$		−	1.99766e18i		−	0.635727i	−0.948137	−	0.317863i	$-0.897035\pi$
$439$		−	1.99766e18i		−	0.635727i	0.948137	−	0.317863i	$-0.102965\pi$
$440$			1.78541e18i			0.559204i
$441$			2.65134e17i			0.0817327i
$442$	−2.69738e17			−0.0818438
$443$	3.93023e17	−	3.93023e17i	0.117379	−	0.117379i	−0.645977	−	0.763357i	$-0.723550\pi$
$443$	3.93023e17	−	3.93023e17i	0.117379	−	0.117379i	0.763357	+	0.645977i	$0.223550\pi$
$444$			2.92739e18i			0.860597i
$445$	−3.99572e17	+	3.99572e17i	−0.115631	+	0.115631i
$446$	−1.66293e18	−	1.66293e18i	−0.473730	−	0.473730i
$447$	−3.52058e18	+	3.52058e18i	−0.987327	+	0.987327i
$448$		−	9.86819e17i		−	0.272453i
$449$	1.97483e18	+	1.97483e18i	0.536790	+	0.536790i	0.922585	−	0.385794i	$-0.126073\pi$
$449$	1.97483e18	+	1.97483e18i	0.536790	+	0.536790i	−0.385794	+	0.922585i	$0.626073\pi$
$450$	−1.21243e17	+	1.21243e17i	−0.0324465	+	0.0324465i
$451$	7.71832e18			2.03370
$452$	1.11824e17	+	1.11824e17i	0.0290112	+	0.0290112i
$453$	2.49393e18	−	2.49393e18i	0.637084	−	0.637084i
$454$	1.41562e18	+	1.41562e18i	0.356087	+	0.356087i
$455$	−1.30560e18			−0.323393
$456$	3.12665e18	+	3.12665e18i	0.762649	+	0.762649i
$457$			3.00662e18i			0.722214i	0.932524	+	0.361107i	$0.117601\pi$
$457$			3.00662e18i			0.722214i	−0.932524	+	0.361107i	$0.882399\pi$
$458$	−1.82042e18			−0.430638
$459$	−4.19990e17			−0.0978477
$460$	1.01606e18			0.233138
$461$	3.93536e18	−	3.93536e18i	0.889362	−	0.889362i	−0.105100	−	0.994462i	$-0.533516\pi$
$461$	3.93536e18	−	3.93536e18i	0.889362	−	0.889362i	0.994462	+	0.105100i	$0.0335163\pi$
$462$	−8.86848e17	+	8.86848e17i	−0.197404	+	0.197404i
$463$		−	6.27262e18i		−	1.37525i	−0.726066	−	0.687625i	$-0.758653\pi$
$463$		−	6.27262e18i		−	1.37525i	0.726066	−	0.687625i	$-0.241347\pi$
$464$	3.92591e15	+	7.41122e14i	0.000847840	+	0.000160053i
$465$	3.54583e18			0.754306
$466$	−3.87725e18	−	3.87725e18i	−0.812498	−	0.812498i
$467$	4.13430e18	+	4.13430e18i	0.853461	+	0.853461i	0.990558	−	0.137097i	$-0.0437772\pi$
$467$	4.13430e18	+	4.13430e18i	0.853461	+	0.853461i	−0.137097	+	0.990558i	$0.543777\pi$
$468$		−	4.36497e17i		−	0.0887688i
$469$		−	3.23714e18i		−	0.648563i
$470$		−	1.39747e18i		−	0.275839i
$471$	2.37835e18			0.462519
$472$	4.44620e18	−	4.44620e18i	0.851913	−	0.851913i
$473$			8.07776e18i			1.52498i
$474$	−1.09080e15	+	1.09080e15i	−0.000202906	+	0.000202906i
$475$	−3.21253e18	−	3.21253e18i	−0.588833	−	0.588833i
$476$	−1.00187e17	+	1.00187e17i	−0.0180951	+	0.0180951i
$477$			8.19049e17i			0.145774i
$478$	1.60099e18	+	1.60099e18i	0.280798	+	0.280798i
$479$	5.69452e18	−	5.69452e18i	0.984257	−	0.984257i	−0.0156208	−	0.999878i	$-0.504972\pi$
$479$	5.69452e18	−	5.69452e18i	0.984257	−	0.984257i	0.999878	+	0.0156208i	$0.00497244\pi$
$480$	−2.88341e18			−0.491155
$481$	−8.74289e18	−	8.74289e18i	−1.46771	−	1.46771i
$482$	−8.70149e17	+	8.70149e17i	−0.143967	+	0.143967i
$483$	1.32080e18	+	1.32080e18i	0.215381	+	0.215381i
$484$	6.38430e17			0.102611
$485$	−1.79124e18	−	1.79124e18i	−0.283767	−	0.283767i
$486$			8.00057e17i			0.124930i
$487$	6.57651e18			1.01226			0.506131	−	0.862457i	$-0.331075\pi$
$487$	6.57651e18			1.01226			0.506131	+	0.862457i	$0.331075\pi$
$488$	−5.90832e18			−0.896448
$489$	3.03043e18			0.453255
$490$	−1.23541e18	+	1.23541e18i	−0.182154	+	0.182154i
$491$	−7.94258e18	+	7.94258e18i	−1.15449	+	1.15449i	−0.168852	+	0.985641i	$0.554006\pi$
$491$	−7.94258e18	+	7.94258e18i	−1.15449	+	1.15449i	−0.985641	+	0.168852i	$0.945994\pi$
$492$			7.70447e18i			1.10405i
$493$	3.73897e17	+	5.47915e17i	0.0528231	+	0.0774078i
$494$	−7.13634e18			−0.994001
$495$	−2.92411e17	−	2.92411e17i	−0.0401567	−	0.0401567i
$496$	6.92180e15	+	6.92180e15i	0.000937233	+	0.000937233i
$497$		−	2.31261e18i		−	0.308751i
$498$		−	3.09728e17i		−	0.0407733i
$499$		−	1.20260e19i		−	1.56105i	−0.625124	−	0.780525i	$-0.714952\pi$
$499$		−	1.20260e19i		−	1.56105i	0.625124	−	0.780525i	$-0.285048\pi$
$500$	4.33395e18			0.554746
$501$	−6.69886e18	+	6.69886e18i	−0.845545	+	0.845545i
$502$			1.42021e18i			0.176777i
$503$	4.10535e18	−	4.10535e18i	0.503934	−	0.503934i	−0.408724	−	0.912658i	$-0.634026\pi$
$503$	4.10535e18	−	4.10535e18i	0.503934	−	0.503934i	0.912658	+	0.408724i	$0.134026\pi$
$504$	2.61794e17	+	2.61794e17i	0.0316917	+	0.0316917i
$505$	−2.46289e18	+	2.46289e18i	−0.294040	+	0.294040i
$506$			4.12251e18i			0.485409i
$507$	−5.76493e18	−	5.76493e18i	−0.669481	−	0.669481i
$508$	−1.84855e18	+	1.84855e18i	−0.211731	+	0.211731i
$509$	2.04850e18			0.231425			0.115713	−	0.993283i	$-0.463085\pi$
$509$	2.04850e18			0.231425			0.115713	+	0.993283i	$0.463085\pi$
$510$	−1.80374e17	−	1.80374e17i	−0.0200994	−	0.0200994i
$511$	−2.04793e18	+	2.04793e18i	−0.225097	+	0.225097i
$512$	−1.12544e16	−	1.12544e16i	−0.00122020	−	0.00122020i
$513$	−1.11115e19			−1.18837
$514$	1.27070e18	+	1.27070e18i	0.134061	+	0.134061i
$515$			7.51683e18i			0.782319i
$516$	−8.06327e18			−0.827872
$517$	−9.18929e18			−0.930782
$518$	4.00733e18			0.400449
$519$	−7.30213e18	+	7.30213e18i	−0.719909	+	0.719909i
$520$	5.32272e18	−	5.32272e18i	0.517738	−	0.517738i
$521$			5.88322e18i			0.564613i	0.959324	+	0.282307i	$0.0910995\pi$
$521$			5.88322e18i			0.564613i	−0.959324	+	0.282307i	$0.908900\pi$
$522$	5.47085e17	−	3.73331e17i	0.0518038	−	0.0353509i
$523$	−1.36436e19			−1.27473			−0.637364	−	0.770562i	$-0.719975\pi$
$523$	−1.36436e19			−1.27473			−0.637364	+	0.770562i	$0.719975\pi$
$524$	4.29593e18	+	4.29593e18i	0.396040	+	0.396040i
$525$	2.38038e18	+	2.38038e18i	0.216536	+	0.216536i
$526$		−	1.63784e18i		−	0.147019i
$527$			1.62526e18i			0.143962i
$528$			1.01028e16i			0.000883091i
$529$	−5.45311e18			−0.470387
$530$	−3.81640e18	+	3.81640e18i	−0.324880	+	0.324880i
$531$			1.45638e18i			0.122353i
$532$	−2.65059e18	+	2.65059e18i	−0.219767	+	0.219767i
$533$	−2.30100e19	−	2.30100e19i	−1.88290	−	1.88290i
$534$	1.61830e18	−	1.61830e18i	0.130698	−	0.130698i
$535$		−	4.52844e18i		−	0.360971i
$536$	1.31973e19	+	1.31973e19i	1.03832	+	1.03832i
$537$	1.51411e19	−	1.51411e19i	1.17581	−	1.17581i
$538$	−4.82897e18			−0.370151
$539$	8.12364e18	+	8.12364e18i	0.614652	+	0.614652i
$540$	3.16682e18	−	3.16682e18i	0.236519	−	0.236519i
$541$	−1.07263e19	−	1.07263e19i	−0.790805	−	0.790805i	0.190820	−	0.981625i	$-0.438885\pi$
$541$	−1.07263e19	−	1.07263e19i	−0.790805	−	0.790805i	−0.981625	+	0.190820i	$0.938885\pi$
$542$	1.69513e19			1.23370
$543$	9.03564e18	+	9.03564e18i	0.649172	+	0.649172i
$544$		−	1.32163e18i		−	0.0937386i
$545$	1.06575e19			0.746244
$546$	5.28779e18			0.365532
$547$	9.20832e18			0.628448			0.314224	−	0.949349i	$-0.398256\pi$
$547$	9.20832e18			0.628448			0.314224	+	0.949349i	$0.398256\pi$
$548$	1.65264e18	−	1.65264e18i	0.111356	−	0.111356i
$549$	9.67652e17	−	9.67652e17i	0.0643743	−	0.0643743i
$550$			7.42969e18i			0.488013i
$551$	9.89204e18	+	1.44959e19i	0.641541	+	0.940124i
$552$	−1.07693e19			−0.689629
$553$	−2.42000e15	−	2.42000e15i	−0.000153017	−	0.000153017i
$554$	−2.48590e18	−	2.48590e18i	−0.155209	−	0.155209i
$555$		−	1.16928e19i		−	0.720887i
$556$		−	1.30780e19i		−	0.796193i
$557$			1.64464e19i			0.988743i	0.869251	+	0.494372i	$0.164602\pi$
$557$			1.64464e19i			0.988743i	−0.869251	+	0.494372i	$0.835398\pi$
$558$	1.62280e18			0.0963440
$559$	2.40816e19	−	2.40816e19i	1.41190	−	1.41190i
$560$		−	3.40859e15i		−	0.000197360i
$561$	−1.18608e18	+	1.18608e18i	−0.0678227	+	0.0678227i
$562$	−4.27468e18	−	4.27468e18i	−0.241407	−	0.241407i
$563$	−1.00087e19	+	1.00087e19i	−0.558239	+	0.558239i	−0.928806	−	0.370566i	$-0.879164\pi$
$563$	−1.00087e19	+	1.00087e19i	−0.558239	+	0.558239i	0.370566	+	0.928806i	$0.379164\pi$
$564$		−	9.17280e18i		−	0.505299i
$565$	−4.46654e17	−	4.46654e17i	−0.0243015	−	0.0243015i
$566$	8.42442e16	−	8.42442e16i	0.00452715	−	0.00452715i
$567$	7.38864e18			0.392178
$568$	9.42814e18	+	9.42814e18i	0.494297	+	0.494297i
$569$	1.92855e19	−	1.92855e19i	0.998722	−	0.998722i	−0.00127682	−	0.999999i	$-0.500406\pi$
$569$	1.92855e19	−	1.92855e19i	0.998722	−	0.998722i	0.999999	+	0.00127682i	$0.000406425\pi$
$570$	−4.77209e18	−	4.77209e18i	−0.244109	−	0.244109i
$571$	−8.22624e16			−0.00415670			−0.00207835	−	0.999998i	$-0.500662\pi$
$571$	−8.22624e16			−0.00415670			−0.00207835	+	0.999998i	$0.500662\pi$
$572$	−1.33742e19	−	1.33742e19i	−0.667566	−	0.667566i
$573$			1.89404e19i			0.933916i
$574$	1.05467e19			0.513729
$575$	1.10652e19			0.532455
$576$	−1.31779e18			−0.0626453
$577$	2.99796e18	−	2.99796e18i	0.140797	−	0.140797i	−0.633195	−	0.773992i	$-0.718257\pi$
$577$	2.99796e18	−	2.99796e18i	0.140797	−	0.140797i	0.773992	+	0.633195i	$0.218257\pi$
$578$	−9.33129e18	+	9.33129e18i	−0.432959	+	0.432959i
$579$		−	2.97681e19i		−	1.36459i
$580$	−6.95066e18	−	1.31213e18i	−0.314797	−	0.0594265i
$581$	6.87153e17			0.0307482
$582$	7.25467e18	+	7.25467e18i	0.320743	+	0.320743i
$583$	2.50954e19	+	2.50954e19i	1.09626	+	1.09626i
$584$		−	1.66981e19i		−	0.720739i
$585$			1.74349e18i			0.0743580i
$586$		−	8.43122e18i		−	0.355310i
$587$	−1.00879e19			−0.420083			−0.210042	−	0.977692i	$-0.567360\pi$
$587$	−1.00879e19			−0.420083			−0.210042	+	0.977692i	$0.567360\pi$
$588$	−8.10907e18	+	8.10907e18i	−0.333680	+	0.333680i
$589$			4.29987e19i			1.74843i
$590$	−6.78608e18	+	6.78608e18i	−0.272681	+	0.272681i
$591$	6.85492e18	+	6.85492e18i	0.272201	+	0.272201i
$592$	2.28254e16	−	2.28254e16i	0.000895709	−	0.000895709i
$593$			3.95571e19i			1.53406i	0.641613	+	0.767029i	$0.278266\pi$
$593$			3.95571e19i			1.53406i	−0.641613	+	0.767029i	$0.721734\pi$
$594$	1.28489e19	+	1.28489e19i	0.492449	+	0.492449i
$595$	4.00172e17	−	4.00172e17i	0.0151575	−	0.0151575i
$596$	2.43350e19			0.910977
$597$	−4.01951e18	−	4.01951e18i	−0.148714	−	0.148714i
$598$	1.22901e19	−	1.22901e19i	0.449415	−	0.449415i
$599$	−7.53180e18	−	7.53180e18i	−0.272214	−	0.272214i	0.557777	−	0.829991i	$-0.311655\pi$
$599$	−7.53180e18	−	7.53180e18i	−0.272214	−	0.272214i	−0.829991	+	0.557777i	$0.811655\pi$
$600$	−1.94088e19			−0.693330
$601$	−6.11315e18	−	6.11315e18i	−0.215846	−	0.215846i	0.590899	−	0.806745i	$-0.298773\pi$
$601$	−6.11315e18	−	6.11315e18i	−0.215846	−	0.215846i	−0.806745	+	0.590899i	$0.798773\pi$
$602$			1.10379e19i			0.385222i
$603$	−4.32285e18			−0.149124
$604$	−1.72386e19			−0.587818
$605$	−2.55006e18			−0.0859534
$606$	9.97490e18	−	9.97490e18i	0.332353	−	0.332353i
$607$	−2.77624e19	+	2.77624e19i	−0.914399	+	0.914399i	−0.996615	−	0.0822159i	$-0.973800\pi$
$607$	−2.77624e19	+	2.77624e19i	−0.914399	+	0.914399i	0.0822159	+	0.996615i	$0.473800\pi$
$608$		−	3.49658e19i		−	1.13846i
$609$	−7.32967e18	−	1.07410e19i	−0.235919	−	0.345720i
$610$	9.01765e18			0.286936
$611$	2.73953e19	+	2.73953e19i	0.861763	+	0.861763i
$612$	1.33788e17	+	1.33788e17i	0.00416062	+	0.00416062i
$613$		−	2.20128e19i		−	0.676788i	−0.941004	−	0.338394i	$-0.890116\pi$
$613$		−	2.20128e19i		−	0.676788i	0.941004	−	0.338394i	$-0.109884\pi$
$614$		−	2.56464e19i		−	0.779556i
$615$		−	3.07737e19i		−	0.924814i
$616$	1.60426e19			0.476661
$617$	−3.42900e19	+	3.42900e19i	−1.00733	+	1.00733i	−0.00735522	+	0.999973i	$0.502341\pi$
$617$	−3.42900e19	+	3.42900e19i	−1.00733	+	1.00733i	−0.999973	+	0.00735522i	$0.997659\pi$
$618$		−	3.04437e19i		−	0.884257i
$619$	−7.27831e18	+	7.27831e18i	−0.209024	+	0.209024i	−0.803853	−	0.594829i	$-0.797220\pi$
$619$	−7.27831e18	+	7.27831e18i	−0.209024	+	0.209024i	0.594829	+	0.803853i	$0.297220\pi$
$620$	−1.22548e19	−	1.22548e19i	−0.347988	−	0.347988i
$621$	1.91361e19	−	1.91361e19i	0.537294	−	0.537294i
$622$		−	4.50868e18i		−	0.125175i
$623$	3.59030e18	+	3.59030e18i	0.0985631	+	0.0985631i
$624$	3.01188e16	−	3.01188e16i	0.000817608	−	0.000817608i
$625$	9.94512e18			0.266962
$626$	−3.33276e17	−	3.33276e17i	−0.00884674	−	0.00884674i
$627$	−3.13797e19	+	3.13797e19i	−0.823713	+	0.823713i
$628$	−8.21984e18	−	8.21984e18i	−0.213376	−	0.213376i
$629$	5.35947e18			0.137584
$630$	−3.99566e17	−	3.99566e17i	−0.0101439	−	0.0101439i
$631$			3.31342e19i			0.831899i	0.909388	+	0.415949i	$0.136551\pi$
$631$			3.31342e19i			0.831899i	−0.909388	+	0.415949i	$0.863449\pi$
$632$	1.97319e16			0.000489947
$633$	−6.57264e19			−1.61404
$634$	−1.18943e19			−0.288877
$635$	7.38360e18	−	7.38360e18i	0.177358	−	0.177358i
$636$	−2.50504e19	+	2.50504e19i	−0.595134	+	0.595134i
$637$		−	4.84368e19i		−	1.13815i
$638$	5.32377e18	−	2.82013e19i	0.123730	−	0.655427i
$639$	−3.08824e18			−0.0709913
$640$	9.97398e18	+	9.97398e18i	0.226782	+	0.226782i
$641$	−2.65746e19	−	2.65746e19i	−0.597669	−	0.597669i	0.342022	−	0.939692i	$-0.388888\pi$
$641$	−2.65746e19	−	2.65746e19i	−0.597669	−	0.597669i	−0.939692	+	0.342022i	$0.888888\pi$
$642$			1.83405e19i			0.408006i
$643$			3.88493e19i			0.854882i	0.904043	+	0.427441i	$0.140585\pi$
$643$			3.88493e19i			0.854882i	−0.904043	+	0.427441i	$0.859415\pi$
$644$		−	9.12964e18i		−	0.198725i
$645$	3.22069e19			0.693475
$646$	2.18732e18	−	2.18732e18i	0.0465891	−	0.0465891i
$647$			8.83473e18i			0.186150i	0.995659	+	0.0930751i	$0.0296697\pi$
$647$			8.83473e18i			0.186150i	−0.995659	+	0.0930751i	$0.970330\pi$
$648$	−3.01222e19	+	3.01222e19i	−0.627859	+	0.627859i
$649$	4.46231e19	+	4.46231e19i	0.920125	+	0.920125i
$650$	2.21496e19	−	2.21496e19i	0.451827	−	0.451827i
$651$		−	3.18606e19i		−	0.642965i
$652$	−1.04735e19	−	1.04735e19i	−0.209102	−	0.209102i
$653$	−2.81840e19	+	2.81840e19i	−0.556686	+	0.556686i	−0.928362	−	0.371677i	$-0.878783\pi$
$653$	−2.81840e19	+	2.81840e19i	−0.556686	+	0.556686i	0.371677	+	0.928362i	$0.378783\pi$
$654$	−4.31638e19			−0.843481
$655$	−1.71591e19	−	1.71591e19i	−0.331746	−	0.331746i
$656$	6.00732e16	−	6.00732e16i	0.00114909	−	0.00114909i
$657$	2.73479e18	+	2.73479e18i	0.0517566	+	0.0517566i
$658$	−1.25567e19			−0.235123
$659$	−1.66198e18	−	1.66198e18i	−0.0307913	−	0.0307913i	0.691543	−	0.722335i	$-0.256931\pi$
$659$	−1.66198e18	−	1.66198e18i	−0.0307913	−	0.0307913i	−0.722335	+	0.691543i	$0.756931\pi$
$660$		−	1.78867e19i		−	0.327885i
$661$	−2.62056e19			−0.475318			−0.237659	−	0.971349i	$-0.576380\pi$
$661$	−2.62056e19			−0.475318			−0.237659	+	0.971349i	$0.576380\pi$
$662$	1.07661e19			0.193221
$663$	7.07196e18			0.125587
$664$	−2.80141e18	+	2.80141e18i	−0.0492266	+	0.0492266i
$665$	1.05872e19	−	1.05872e19i	0.184089	−	0.184089i
$666$		−	5.35135e18i		−	0.0920755i
$667$	−4.20007e19	−	7.92878e18i	−0.715115	−	0.134998i
$668$	4.63040e19			0.780159
$669$	4.35986e19	+	4.35986e19i	0.726926	+	0.726926i
$670$	−2.01425e19	−	2.01425e19i	−0.332346	−	0.332346i
$671$		−	5.92972e19i		−	0.968225i
$672$			2.59085e19i			0.418656i
$673$			9.47743e19i			1.51560i	0.652486	+	0.757801i	$0.273726\pi$
$673$			9.47743e19i			1.51560i	−0.652486	+	0.757801i	$0.726274\pi$
$674$	−7.31985e19			−1.15846
$675$	3.44876e19	−	3.44876e19i	0.540177	−	0.540177i
$676$			3.98484e19i			0.617710i
$677$	−2.40148e19	+	2.40148e19i	−0.368432	+	0.368432i	−0.866905	−	0.498473i	$-0.833894\pi$
$677$	−2.40148e19	+	2.40148e19i	−0.368432	+	0.368432i	0.498473	+	0.866905i	$0.333894\pi$
$678$	1.80898e18	+	1.80898e18i	0.0274680	+	0.0274680i
$679$	−1.60950e19	+	1.60950e19i	−0.241881	+	0.241881i
$680$			3.26287e18i			0.0485330i
$681$	−3.71147e19	−	3.71147e19i	−0.546407	−	0.546407i
$682$	4.97220e19	−	4.97220e19i	0.724533	−	0.724533i
$683$	−5.28610e19			−0.762414			−0.381207	−	0.924490i	$-0.624491\pi$
$683$	−5.28610e19			−0.762414			−0.381207	+	0.924490i	$0.624491\pi$
$684$	3.53958e18	+	3.53958e18i	0.0505311	+	0.0505311i
$685$	−6.60108e18	+	6.60108e18i	−0.0932783	+	0.0932783i
$686$	2.48897e19	+	2.48897e19i	0.348138	+	0.348138i
$687$	4.77275e19			0.660802
$688$	6.28709e16	+	6.28709e16i	0.000861649	+	0.000861649i
$689$		−	1.49630e20i		−	2.02995i
$690$	1.64369e19			0.220737
$691$	1.22774e19			0.163215			0.0816074	−	0.996665i	$-0.473995\pi$
$691$	1.22774e19			0.163215			0.0816074	+	0.996665i	$0.473995\pi$
$692$	5.04739e19			0.664238
$693$	−2.62742e18	+	2.62742e18i	−0.0342292	+	0.0342292i
$694$	7.62220e17	−	7.62220e17i	0.00983023	−	0.00983023i
$695$			5.22371e19i			0.666938i
$696$	7.36711e19	+	1.39074e19i	0.931178	+	0.175785i
$697$	1.41053e19			0.176504
$698$	3.44468e18	+	3.44468e18i	0.0426737	+	0.0426737i
$699$	1.01653e20	+	1.01653e20i	1.24676	+	1.24676i
$700$		−	1.64537e19i		−	0.199791i
$701$		−	1.51274e20i		−	1.81861i	−0.416134	−	0.909303i	$-0.636615\pi$
$701$		−	1.51274e20i		−	1.81861i	0.416134	−	0.909303i	$-0.363385\pi$
$702$		−	7.66110e19i		−	0.911866i
$703$	1.41793e20			1.67097
$704$	−4.03767e19	+	4.03767e19i	−0.471110	+	0.471110i
$705$			3.66386e19i			0.423268i
$706$	5.87997e19	−	5.87997e19i	0.672578	−	0.672578i
$707$	2.21300e19	+	2.21300e19i	0.250637	+	0.250637i
$708$	−4.45430e19	+	4.45430e19i	−0.499513	+	0.499513i
$709$			8.75829e19i			0.972513i	0.873816	+	0.486257i	$0.161638\pi$
$709$			8.75829e19i			0.972513i	−0.873816	+	0.486257i	$0.838362\pi$
$710$	−1.43898e19	−	1.43898e19i	−0.158215	−	0.158215i
$711$	−3.23165e15	+	3.23165e15i	−3.51833e−5	+	3.51833e-5i
$712$	−2.92741e19			−0.315590
$713$	−7.40519e19	−	7.40519e19i	−0.790514	−	0.790514i
$714$	−1.62073e18	+	1.62073e18i	−0.0171326	+	0.0171326i
$715$	5.34200e19	+	5.34200e19i	0.559192	+	0.559192i
$716$	−1.04659e20			−1.08489
$717$	−4.19746e19	−	4.19746e19i	−0.430876	−	0.430876i
$718$			1.08884e20i			1.10686i
$719$	8.89912e19			0.895870			0.447935	−	0.894066i	$-0.352160\pi$
$719$	8.89912e19			0.895870			0.447935	+	0.894066i	$0.352160\pi$
$720$	−4.55179e15			−4.53790e−5
$721$	6.75414e19			0.666842
$722$	1.31966e19	−	1.31966e19i	0.129033	−	0.129033i
$723$	2.28135e19	−	2.28135e19i	0.220914	−	0.220914i
$724$		−	6.24563e19i		−	0.598971i
$725$	−7.56948e19	−	1.42895e19i	−0.718952	−	0.135722i
$726$	1.03279e19			0.0971533
$727$	9.28182e19	+	9.28182e19i	0.864754	+	0.864754i	0.991886	−	0.127132i	$-0.0405772\pi$
$727$	9.28182e19	+	9.28182e19i	0.864754	+	0.864754i	−0.127132	+	0.991886i	$0.540577\pi$
$728$	−4.78265e19	−	4.78265e19i	−0.441316	−	0.441316i
$729$		−	1.18158e20i		−	1.07987i
$730$			2.54858e19i			0.230695i
$731$			1.47622e19i			0.132352i
$732$	5.91908e19			0.525626
$733$	−9.54452e19	+	9.54452e19i	−0.839511	+	0.839511i	−0.988794	−	0.149284i	$-0.952303\pi$
$733$	−9.54452e19	+	9.54452e19i	−0.839511	+	0.839511i	0.149284	+	0.988794i	$0.452303\pi$
$734$			8.38095e18i			0.0730165i
$735$	3.23898e19	−	3.23898e19i	0.279510	−	0.279510i
$736$	6.02178e19	+	6.02178e19i	0.514731	+	0.514731i
$737$	−1.32451e20	+	1.32451e20i	−1.12146	+	1.12146i
$738$		−	1.40840e19i		−	0.118122i
$739$	−6.01250e19	−	6.01250e19i	−0.499510	−	0.499510i	0.411775	−	0.911285i	$-0.364909\pi$
$739$	−6.01250e19	−	6.01250e19i	−0.499510	−	0.499510i	−0.911285	+	0.411775i	$0.864909\pi$
$740$	−4.04115e19	+	4.04115e19i	−0.332570	+	0.332570i
$741$	1.87100e20			1.52527
$742$	3.42917e19	+	3.42917e19i	0.276925	+	0.276925i
$743$	3.84282e19	−	3.84282e19i	0.307418	−	0.307418i	−0.536489	−	0.843907i	$-0.680250\pi$
$743$	3.84282e19	−	3.84282e19i	0.307418	−	0.307418i	0.843907	+	0.536489i	$0.180250\pi$
$744$	1.29890e20	+	1.29890e20i	1.02936	+	1.02936i
$745$	−9.72005e19			−0.763088
$746$	−1.17072e19	−	1.17072e19i	−0.0910502	−	0.0910502i
$747$		−	9.17617e17i		−	0.00706996i
$748$	8.19847e18			0.0625780
$749$	−4.06897e19			−0.307689
$750$	7.01108e19			0.525238
$751$	−7.68507e19	+	7.68507e19i	−0.570386	+	0.570386i	−0.932236	−	0.361851i	$-0.882145\pi$
$751$	−7.68507e19	+	7.68507e19i	−0.570386	+	0.570386i	0.361851	+	0.932236i	$0.382145\pi$
$752$	−7.15221e16	+	7.15221e16i	−0.000525915	+	0.000525915i
$753$		−	3.72350e19i		−	0.271260i
$754$	−9.99458e19	+	6.82031e19i	−0.721382	+	0.492271i
$755$	6.88555e19			0.492391
$756$	−2.84550e19	−	2.84550e19i	−0.201607	−	0.201607i
$757$	−9.47332e19	−	9.47332e19i	−0.665014	−	0.665014i	0.291543	−	0.956558i	$-0.405831\pi$
$757$	−9.47332e19	−	9.47332e19i	−0.665014	−	0.665014i	−0.956558	+	0.291543i	$0.905831\pi$
$758$			9.26371e19i			0.644318i
$759$		−	1.08084e20i		−	0.744847i
$760$			8.63244e19i			0.589438i
$761$	1.93172e20			1.30693			0.653465	−	0.756957i	$-0.273315\pi$
$761$	1.93172e20			1.30693			0.653465	+	0.756957i	$0.273315\pi$
$762$	−2.99041e19	+	2.99041e19i	−0.200469	+	0.200469i
$763$		−	9.57617e19i		−	0.636092i
$764$	6.54602e19	−	6.54602e19i	0.430848	−	0.430848i
$765$	−5.34386e17	−	5.34386e17i	−0.00348518	−	0.00348518i
$766$	2.31952e19	−	2.31952e19i	0.149898	−	0.149898i
$767$		−	2.66063e20i		−	1.70379i
$768$	−1.05568e20	−	1.05568e20i	−0.669892	−	0.669892i
$769$	−7.92081e19	+	7.92081e19i	−0.498064	+	0.498064i	−0.910835	−	0.412771i	$-0.864561\pi$
$769$	−7.92081e19	+	7.92081e19i	−0.498064	+	0.498064i	0.412771	+	0.910835i	$0.364561\pi$
$770$	−2.44852e19			−0.152570
$771$	−3.33151e19	−	3.33151e19i	−0.205713	−	0.205713i
$772$	−1.02882e20	+	1.02882e20i	−0.629531	+	0.629531i
$773$	−1.95017e20	−	1.95017e20i	−1.18254	−	1.18254i	−0.979084	−	0.203457i	$-0.934782\pi$
$773$	−1.95017e20	−	1.95017e20i	−1.18254	−	1.18254i	−0.203457	−	0.979084i	$-0.565218\pi$
$774$	1.47399e19			0.0885742
$775$	−1.33458e20	−	1.33458e20i	−0.794755	−	0.794755i
$776$		−	1.31233e20i		−	0.774481i
$777$	−1.05064e20			−0.614478
$778$	1.77634e20			1.02960
$779$	3.73179e20			2.14366
$780$	−5.33241e19	+	5.33241e19i	−0.303572	+	0.303572i
$781$	−9.46229e19	+	9.46229e19i	−0.533874	+	0.533874i
$782$			7.53394e18i			0.0421284i
$783$	−1.55619e20	+	1.06194e20i	−0.862441	+	0.588531i
$784$	1.26456e17			0.000694587
$785$	3.28322e19	+	3.28322e19i	0.178736	+	0.178736i
$786$	6.94957e19	+	6.94957e19i	0.374973	+	0.374973i
$787$		−	1.48755e20i		−	0.795514i	−0.917491	−	0.397757i	$-0.869789\pi$
$787$		−	1.48755e20i		−	0.795514i	0.917491	−	0.397757i	$-0.130211\pi$
$788$		−	4.73827e19i		−	0.251152i
$789$			4.29409e19i			0.225596i
$790$	−3.01161e16			−0.000156823
$791$	−4.01335e18	+	4.01335e18i	−0.0207144	+	0.0207144i
$792$		−	2.14231e19i		−	0.109599i
$793$	−1.76778e20	+	1.76778e20i	−0.896430	+	0.896430i
$794$	5.81201e19	+	5.81201e19i	0.292135	+	0.292135i
$795$	1.00058e20	−	1.00058e20i	0.498520	−	0.498520i
$796$			2.77837e19i			0.137214i
$797$	−6.34050e19	−	6.34050e19i	−0.310395	−	0.310395i	0.534667	−	0.845063i	$-0.320437\pi$
$797$	−6.34050e19	−	6.34050e19i	−0.310395	−	0.310395i	−0.845063	+	0.534667i	$0.820437\pi$
$798$	−4.28789e19	+	4.28789e19i	−0.208077	+	0.208077i
$799$	−1.67936e19			−0.0807822
$800$	1.08526e20	+	1.08526e20i	0.517492	+	0.517492i
$801$	4.79445e18	−	4.79445e18i	0.0226627	−	0.0226627i
$802$	6.27360e19	+	6.27360e19i	0.293966	+	0.293966i
$803$	1.67586e20			0.778448
$804$	−1.32213e20	−	1.32213e20i	−0.608811	−	0.608811i
$805$			3.64663e19i			0.166464i
$806$	−2.96465e20			−1.34162
$807$	1.26606e20			0.567986
$808$	−1.80440e20			−0.802517
$809$	−8.78014e19	+	8.78014e19i	−0.387134	+	0.387134i	−0.873664	−	0.486530i	$-0.838263\pi$
$809$	−8.78014e19	+	8.78014e19i	−0.387134	+	0.387134i	0.486530	+	0.873664i	$0.338263\pi$
$810$	4.59745e19	−	4.59745e19i	0.200966	−	0.200966i
$811$		−	1.88276e19i		−	0.0815923i	−0.999167	−	0.0407962i	$-0.987011\pi$
$811$		−	1.88276e19i		−	0.0815923i	0.999167	−	0.0407962i	$-0.0129894\pi$
$812$	−1.17899e19	+	6.24542e19i	−0.0506547	+	0.268330i
$813$	−4.44428e20			−1.89308
$814$	−1.63964e20	−	1.63964e20i	−0.692433	−	0.692433i
$815$	4.18340e19	+	4.18340e19i	0.175157	+	0.175157i
$816$			1.84631e16i			7.66430e-5i
$817$			3.90558e20i			1.60743i
$818$			2.64439e20i			1.07908i
$819$	1.56659e19			0.0633821
$820$	−1.06357e20	+	1.06357e20i	−0.426649	+	0.426649i
$821$		−	2.71807e20i		−	1.08108i	−0.841317	−	0.540542i	$-0.818219\pi$
$821$		−	2.71807e20i		−	1.08108i	0.841317	−	0.540542i	$-0.181781\pi$
$822$	2.67349e19	−	2.67349e19i	0.105433	−	0.105433i
$823$	2.27865e20	+	2.27865e20i	0.891002	+	0.891002i	0.994617	−	0.103616i	$-0.0330412\pi$
$823$	2.27865e20	+	2.27865e20i	0.891002	+	0.891002i	−0.103616	+	0.994617i	$0.533041\pi$
$824$	−2.75355e20	+	2.75355e20i	−1.06758	+	1.06758i
$825$		−	1.94791e20i		−	0.748843i
$826$	6.09754e19	+	6.09754e19i	0.232431	+	0.232431i
$827$	1.68390e20	−	1.68390e20i	0.636470	−	0.636470i	−0.313213	−	0.949683i	$-0.601405\pi$
$827$	1.68390e20	−	1.68390e20i	0.636470	−	0.636470i	0.949683	+	0.313213i	$0.101405\pi$
$828$	−1.21916e19			−0.0456930
$829$	−1.86105e20	−	1.86105e20i	−0.691633	−	0.691633i	0.270958	−	0.962591i	$-0.412660\pi$
$829$	−1.86105e20	−	1.86105e20i	−0.691633	−	0.691633i	−0.962591	+	0.270958i	$0.912660\pi$
$830$	4.27568e18	−	4.27568e18i	0.0157565	−	0.0157565i
$831$	6.51752e19	+	6.51752e19i	0.238163	+	0.238163i
$832$	2.40744e20			0.872352
$833$	1.48461e19	+	1.48461e19i	0.0533454	+	0.0533454i
$834$		−	2.11564e20i		−	0.753842i
$835$	−1.84950e20			−0.653507
$836$	2.16903e20			0.760015
$837$	−4.61605e20			−1.60396
$838$	−2.40773e19	+	2.40773e19i	−0.0829660	+	0.0829660i
$839$	−6.44495e19	+	6.44495e19i	−0.220235	+	0.220235i	−0.808597	−	0.588363i	$-0.799773\pi$
$839$	−6.44495e19	+	6.44495e19i	−0.220235	+	0.220235i	0.588363	+	0.808597i	$0.299773\pi$
$840$		−	6.39634e19i		−	0.216759i
$841$	2.77080e20	+	1.08479e20i	0.931179	+	0.364563i
$842$	2.31210e20			0.770587
$843$	1.12073e20	+	1.12073e20i	0.370432	+	0.370432i
$844$	2.27157e20	+	2.27157e20i	0.744612	+	0.744612i
$845$		−	1.59165e20i		−	0.517430i
$846$			1.67681e19i			0.0540620i
$847$			2.29132e19i			0.0732660i
$848$	3.90646e17			0.00123883
$849$	−2.20871e18	+	2.20871e18i	−0.00694679	+	0.00694679i
$850$			1.35779e19i			0.0423545i
$851$	−2.44194e20	+	2.44194e20i	−0.755490	+	0.755490i
$852$	−9.44531e19	−	9.44531e19i	−0.289827	−	0.289827i
$853$	3.40401e20	−	3.40401e20i	1.03597	−	1.03597i	0.0366436	−	0.999328i	$-0.488333\pi$
$853$	3.40401e20	−	3.40401e20i	1.03597	−	1.03597i	0.999328	−	0.0366436i	$-0.0116666\pi$
$854$		−	8.10269e19i		−	0.244582i
$855$	−1.41380e19	−	1.41380e19i	−0.0423278	−	0.0423278i
$856$	1.65885e20	−	1.65885e20i	0.492596	−	0.492596i
$857$	3.33451e20			0.982123			0.491062	−	0.871125i	$-0.336609\pi$
$857$	3.33451e20			0.982123			0.491062	+	0.871125i	$0.336609\pi$
$858$	−2.16355e20	−	2.16355e20i	−0.632056	−	0.632056i
$859$	1.73632e20	−	1.73632e20i	0.503126	−	0.503126i	−0.409282	−	0.912408i	$-0.634221\pi$
$859$	1.73632e20	−	1.73632e20i	0.503126	−	0.503126i	0.912408	+	0.409282i	$0.134221\pi$
$860$	−1.11310e20	−	1.11310e20i	−0.319924	−	0.319924i
$861$	−2.76513e20			−0.788304
$862$	1.23522e20	+	1.23522e20i	0.349296	+	0.349296i
$863$		−	5.05699e20i		−	1.41846i	−0.704979	−	0.709229i	$-0.749043\pi$
$863$		−	5.05699e20i		−	1.41846i	0.704979	−	0.709229i	$-0.250957\pi$
$864$	3.75370e20			1.04439
$865$	−2.01606e20			−0.556405
$866$	1.47882e19			0.0404847
$867$	2.44647e20	−	2.44647e20i	0.664364	−	0.664364i
$868$	−1.10114e20	+	1.10114e20i	−0.296622	+	0.296622i
$869$			1.98034e17i			0.000529177i
$870$	−1.12442e20	−	2.12264e19i	−0.298052	−	0.0562655i
$871$	7.89732e20			2.07660
$872$	3.90404e20	+	3.90404e20i	1.01836	+	1.01836i
$873$	2.14930e19	+	2.14930e19i	0.0556158	+	0.0556158i
$874$			1.99322e20i			0.511653i
$875$			1.55545e20i			0.396096i
$876$			1.67286e20i			0.422600i
$877$	2.34751e20			0.588316			0.294158	−	0.955757i	$-0.404961\pi$
$877$	2.34751e20			0.588316			0.294158	+	0.955757i	$0.404961\pi$
$878$	−1.11689e20	+	1.11689e20i	−0.277682	+	0.277682i
$879$			2.21049e20i			0.545214i
$880$	−1.39466e17	+	1.39466e17i	−0.000341263	+	0.000341263i
$881$	2.65463e20	+	2.65463e20i	0.644426	+	0.644426i	0.951640	−	0.307214i	$-0.0993968\pi$
$881$	2.65463e20	+	2.65463e20i	0.644426	+	0.644426i	−0.307214	+	0.951640i	$0.599397\pi$
$882$	1.48236e19	−	1.48236e19i	0.0357005	−	0.0357005i
$883$		−	1.24245e20i		−	0.296862i	−0.988923	−	0.148431i	$-0.952578\pi$
$883$		−	1.24245e20i		−	0.296862i	0.988923	−	0.148431i	$-0.0474223\pi$
$884$	−2.44415e19	−	2.44415e19i	−0.0579377	−	0.0579377i
$885$	1.77917e20	−	1.77917e20i	0.418422	−	0.418422i
$886$	−4.39476e19			−0.102541
$887$	1.14420e20	+	1.14420e20i	0.264872	+	0.264872i	0.827030	−	0.562158i	$-0.190029\pi$
$887$	1.14420e20	+	1.14420e20i	0.264872	+	0.264872i	−0.562158	+	0.827030i	$0.690029\pi$
$888$	4.28328e20	−	4.28328e20i	0.983752	−	0.983752i
$889$	−6.63443e19	−	6.63443e19i	−0.151179	−	0.151179i
$890$	4.46800e19			0.101014
$891$	−3.02313e20	−	3.02313e20i	−0.678131	−	0.678131i
$892$		−	3.01363e20i		−	0.670712i
$893$	−4.44300e20			−0.981107
$894$	3.93670e20			0.862520
$895$	4.18035e20			0.908765
$896$	8.96198e19	−	8.96198e19i	0.193307	−	0.193307i
$897$	−3.22221e20	+	3.22221e20i	−0.689615	+	0.689615i
$898$		−	2.20824e20i		−	0.468935i
$899$	4.10945e20	+	6.02205e20i	0.865897	+	1.26890i
$900$	−2.19721e19			−0.0459382
$901$	4.58623e19	+	4.58623e19i	0.0951441	+	0.0951441i
$902$	−4.31530e20	−	4.31530e20i	−0.888310	−	0.888310i
$903$		−	2.89390e20i		−	0.591112i
$904$		−	3.27235e19i		−	0.0663256i
$905$			2.49467e20i			0.501734i
$906$	−2.78870e20			−0.556550
$907$	−5.20847e20	+	5.20847e20i	−1.03148	+	1.03148i	−0.0319886	+	0.999488i	$0.510184\pi$
$907$	−5.20847e20	+	5.20847e20i	−1.03148	+	1.03148i	−0.999488	+	0.0319886i	$0.989816\pi$
$908$			2.56545e20i			0.504153i
$909$	2.95521e19	−	2.95521e19i	0.0576291	−	0.0576291i
$910$	7.29959e19	+	7.29959e19i	0.141257	+	0.141257i
$911$	2.68534e20	−	2.68534e20i	0.515669	−	0.515669i	−0.400589	−	0.916258i	$-0.631194\pi$
$911$	2.68534e20	−	2.68534e20i	0.515669	−	0.515669i	0.916258	+	0.400589i	$0.131194\pi$
$912$			4.88469e17i			0.000930836i
$913$	−2.81155e19	−	2.81155e19i	−0.0531681	−	0.0531681i
$914$	1.68100e20	−	1.68100e20i	0.315460	−	0.315460i
$915$	−2.36424e20			−0.440295
$916$	−1.64951e20	−	1.64951e20i	−0.304851	−	0.304851i
$917$	−1.54181e20	+	1.54181e20i	−0.282778	+	0.282778i
$918$	2.34816e19	+	2.34816e19i	0.0427394	+	0.0427394i
$919$	−3.52769e20			−0.637208			−0.318604	−	0.947888i	$-0.603214\pi$
$919$	−3.52769e20			−0.637208			−0.318604	+	0.947888i	$0.603214\pi$
$920$	−1.48667e20	−	1.48667e20i	−0.266501	−	0.266501i
$921$			6.72394e20i			1.19621i
$922$	−4.40051e20			−0.776938
$923$	5.64184e20			0.988574
$924$	−1.60718e20			−0.279487
$925$	−4.40094e20	+	4.40094e20i	−0.759544	+	0.759544i
$926$	−3.50701e20	+	3.50701e20i	−0.600703	+	0.600703i
$927$		−	9.01941e19i		−	0.153327i
$928$	−3.34174e20	−	4.89703e20i	−0.563815	−	0.826223i
$929$	−4.08969e20			−0.684826			−0.342413	−	0.939550i	$-0.611244\pi$
$929$	−4.08969e20			−0.684826			−0.342413	+	0.939550i	$0.611244\pi$
$930$	−1.98247e20	−	1.98247e20i	−0.329477	−	0.329477i
$931$	3.92776e20	+	3.92776e20i	0.647884	+	0.647884i
$932$		−	7.02650e20i		−	1.15034i
$933$			1.18208e20i			0.192077i
$934$		−	4.62295e20i		−	0.745575i
$935$	−3.27469e19			−0.0524190
$936$	−6.38671e19	+	6.38671e19i	−0.101472	+	0.101472i
$937$		−	5.60836e20i		−	0.884420i	−0.896912	−	0.442210i	$-0.854195\pi$
$937$		−	5.60836e20i		−	0.884420i	0.896912	−	0.442210i	$-0.145805\pi$
$938$	−1.80988e20	+	1.80988e20i	−0.283289	+	0.283289i
$939$	8.73779e18	+	8.73779e18i	0.0135751	+	0.0135751i
$940$	1.26627e20	−	1.26627e20i	0.195268	−	0.195268i
$941$			6.55071e20i			1.00268i	0.865251	+	0.501338i	$0.167159\pi$
$941$			6.55071e20i			1.00268i	−0.865251	+	0.501338i	$0.832841\pi$
$942$	−1.32973e20	−	1.32973e20i	−0.202026	−	0.202026i
$943$	−6.42684e20	+	6.42684e20i	−0.969206	+	0.969206i
$944$	6.94621e17			0.00103979
$945$	1.13657e20	+	1.13657e20i	0.168878	+	0.168878i
$946$	4.51626e20	−	4.51626e20i	0.666102	−	0.666102i
$947$	−7.68870e19	−	7.68870e19i	−0.112565	−	0.112565i	0.648581	−	0.761146i	$-0.275363\pi$
$947$	−7.68870e19	−	7.68870e19i	−0.112565	−	0.112565i	−0.761146	+	0.648581i	$0.775363\pi$
$948$	−1.97678e17			−0.000287277
$949$	−4.99612e20	−	4.99612e20i	−0.720725	−	0.720725i
$950$			3.59224e20i			0.514399i
$951$	3.11843e20			0.443274
$952$	2.93181e19			0.0413692
$953$	−9.27169e20			−1.29870			−0.649349	−	0.760490i	$-0.724959\pi$
$953$	−9.27169e20			−1.29870			−0.649349	+	0.760490i	$0.724959\pi$
$954$	4.57928e19	−	4.57928e19i	0.0636735	−	0.0636735i
$955$	−2.61466e20	+	2.61466e20i	−0.360904	+	0.360904i
$956$			2.90138e20i			0.397557i
$957$	−1.39578e20	+	7.39379e20i	−0.189860	+	1.00574i
$958$	−6.36759e20			−0.859838
$959$	5.93130e19	+	5.93130e19i	0.0795097	+	0.0795097i
$960$	1.60986e20	+	1.60986e20i	0.214235	+	0.214235i
$961$			1.02935e21i			1.35988i
$962$			9.77627e20i			1.28218i
$963$			5.43366e19i			0.0707470i
$964$	−1.57692e20			−0.203831
$965$	4.10938e20	−	4.10938e20i	0.527333	−	0.527333i
$966$		−	1.47691e20i		−	0.188154i
$967$	9.26355e20	−	9.26355e20i	1.17164	−	1.17164i	0.189815	−	0.981820i	$-0.439211\pi$
$967$	9.26355e20	−	9.26355e20i	1.17164	−	1.17164i	0.981820	−	0.189815i	$-0.0607889\pi$
$968$	−9.34134e19	−	9.34134e19i	−0.117296	−	0.117296i
$969$	−5.73469e19	+	5.73469e19i	−0.0714897	+	0.0714897i
$970$			2.00296e20i			0.247896i
$971$	−9.31941e20	−	9.31941e20i	−1.14513	−	1.14513i	−0.987498	−	0.157630i	$-0.949615\pi$
$971$	−9.31941e20	−	9.31941e20i	−1.14513	−	1.14513i	−0.157630	−	0.987498i	$-0.550385\pi$
$972$	−7.24947e19	+	7.24947e19i	−0.0884387	+	0.0884387i
$973$	4.69369e20			0.568493
$974$	−3.67691e20	−	3.67691e20i	−0.442151	−	0.442151i
$975$	−5.80715e20	+	5.80715e20i	−0.693316	+	0.693316i
$976$	−4.61522e17	−	4.61522e17i	−0.000547071	−	0.000547071i
$977$	1.51037e21			1.77755			0.888774	−	0.458346i	$-0.151558\pi$
$977$	1.51037e21			1.77755			0.888774	+	0.458346i	$0.151558\pi$
$978$	−1.69431e20	−	1.69431e20i	−0.197980	−	0.197980i
$979$		−	2.93801e20i		−	0.340859i
$980$	−2.23885e20			−0.257895
$981$	−1.27879e20			−0.146257
$982$	8.88137e20			1.00855
$983$	4.35124e20	−	4.35124e20i	0.490612	−	0.490612i	−0.417887	−	0.908499i	$-0.637229\pi$
$983$	4.35124e20	−	4.35124e20i	0.490612	−	0.490612i	0.908499	+	0.417887i	$0.137229\pi$
$984$	1.12730e21	−	1.12730e21i	1.26204	−	1.26204i
$985$			1.89259e20i			0.210379i
$986$	9.72927e18	−	5.15383e19i	0.0107385	−	0.0568842i
$987$	3.29211e20			0.360790
$988$	−6.46637e20	−	6.46637e20i	−0.703659	−	0.703659i
$989$	−6.72615e20	−	6.72615e20i	−0.726762	−	0.726762i
$990$			3.26973e19i			0.0350805i
$991$		−	5.19970e20i		−	0.553940i	−0.960879	−	0.276970i	$-0.910670\pi$
$991$		−	5.19970e20i		−	0.553940i	0.960879	−	0.276970i	$-0.0893302\pi$
$992$		−	1.45259e21i		−	1.53660i
$993$	−2.82266e20			−0.296492
$994$	−1.29298e20	+	1.29298e20i	−0.134861	+	0.134861i
$995$		−	1.10976e20i		−	0.114939i
$996$	2.80651e19	−	2.80651e19i	0.0288636	−	0.0288636i
$997$	−8.17407e20	−	8.17407e20i	−0.834781	−	0.834781i	0.153386	−	0.988166i	$-0.450982\pi$
$997$	−8.17407e20	−	8.17407e20i	−0.834781	−	0.834781i	−0.988166	+	0.153386i	$0.950982\pi$
$998$	−6.72371e20	+	6.72371e20i	−0.681860	+	0.681860i
$999$			1.52220e21i			1.53289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.15.c.a.12.13	✓	68
29.17	odd	4	inner	29.15.c.a.17.13	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.15.c.a.12.13	✓	68	1.1	even	1	trivial
29.15.c.a.17.13	yes	68	29.17	odd	4	inner

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-55.9098 - 55.9098i) q^{2} +(1465.84 + 1465.84i) q^{3} -10132.2i q^{4} +40470.7i q^{5} -163909. i q^{6} +363644. q^{7} +(-1.48251e6 + 1.48251e6i) q^{8} -485606. i q^{9} +O(q^{10})\)	\(q+(-55.9098 - 55.9098i) q^{2} +(1465.84 + 1465.84i) q^{3} -10132.2i q^{4} +40470.7i q^{5} -163909. i q^{6} +363644. q^{7} +(-1.48251e6 + 1.48251e6i) q^{8} -485606. i q^{9} +(2.26271e6 - 2.26271e6i) q^{10} +(-1.48788e7 - 1.48788e7i) q^{11} +(1.48522e7 - 1.48522e7i) q^{12} +8.87143e7i q^{13} +(-2.03312e7 - 2.03312e7i) q^{14} +(-5.93235e7 + 5.93235e7i) q^{15} -231610. q^{16} +(-2.71913e7 - 2.71913e7i) q^{17} +(-2.71501e7 + 2.71501e7i) q^{18} +(-7.19389e8 - 7.19389e8i) q^{19} +4.10057e8 q^{20} +(5.33043e8 + 5.33043e8i) q^{21} +1.66375e9i q^{22} +2.47785e9 q^{23} -4.34625e9 q^{24} +4.46564e9 q^{25} +(4.96000e9 - 4.96000e9i) q^{26} +(7.72288e9 - 7.72288e9i) q^{27} -3.68451e9i q^{28} +(-1.69505e10 - 3.19987e9i) q^{29} +6.63353e9 q^{30} +(-2.98856e10 - 2.98856e10i) q^{31} +(2.43025e10 + 2.43025e10i) q^{32} -4.36199e10i q^{33} +3.04052e9i q^{34} +1.47169e10i q^{35} -4.92025e9 q^{36} +(-9.85511e10 + 9.85511e10i) q^{37} +8.04418e10i q^{38} +(-1.30041e11 + 1.30041e11i) q^{39} +(-5.99984e10 - 5.99984e10i) q^{40} +(-2.59372e11 + 2.59372e11i) q^{41} -5.96046e10i q^{42} +(-2.71451e11 - 2.71451e11i) q^{43} +(-1.50755e11 + 1.50755e11i) q^{44} +1.96528e10 q^{45} +(-1.38536e11 - 1.38536e11i) q^{46} +(3.08804e11 - 3.08804e11i) q^{47} +(-3.39503e8 - 3.39503e8i) q^{48} -5.45986e11 q^{49} +(-2.49673e11 - 2.49673e11i) q^{50} -7.97161e10i q^{51} +8.98870e11 q^{52} -1.68665e12 q^{53} -8.63569e11 q^{54} +(6.02157e11 - 6.02157e11i) q^{55} +(-5.39107e11 + 5.39107e11i) q^{56} -2.10901e12i q^{57} +(7.68794e11 + 1.12660e12i) q^{58} -2.99910e12 q^{59} +(6.01077e11 + 6.01077e11i) q^{60} +(1.99267e12 + 1.99267e12i) q^{61} +3.34179e12i q^{62} -1.76588e11i q^{63} -2.71370e12i q^{64} -3.59033e12 q^{65} +(-2.43878e12 + 2.43878e12i) q^{66} -8.90196e12i q^{67} +(-2.75508e11 + 2.75508e11i) q^{68} +(3.63212e12 + 3.63212e12i) q^{69} +(8.22820e11 - 8.22820e11i) q^{70} -6.35956e12i q^{71} +(7.19918e11 + 7.19918e11i) q^{72} +(-5.63169e12 + 5.63169e12i) q^{73} +1.10199e13 q^{74} +(6.54590e12 + 6.54590e12i) q^{75} +(-7.28898e12 + 7.28898e12i) q^{76} +(-5.41060e12 - 5.41060e12i) q^{77} +1.45411e13 q^{78} +(-6.65488e9 - 6.65488e9i) q^{79} -9.37342e9i q^{80} +2.03183e13 q^{81} +2.90029e13 q^{82} +1.88963e12 q^{83} +(5.40089e12 - 5.40089e12i) q^{84} +(1.10045e12 - 1.10045e12i) q^{85} +3.03536e13i q^{86} +(-2.01562e13 - 2.95372e13i) q^{87} +4.41162e13 q^{88} +(9.87312e12 + 9.87312e12i) q^{89} +(-1.09879e12 - 1.09879e12i) q^{90} +3.22604e13i q^{91} -2.51060e13i q^{92} -8.76149e13i q^{93} -3.45303e13 q^{94} +(2.91142e13 - 2.91142e13i) q^{95} +7.12470e13i q^{96} +(-4.42602e13 + 4.42602e13i) q^{97} +(3.05260e13 + 3.05260e13i) q^{98} +(-7.22526e12 + 7.22526e12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 312 q^{2} - 2 q^{3} - 4 q^{7} - 689310 q^{8}+O(q^{10}) \) 68 * q - 312 * q^2 - 2 * q^3 - 4 * q^7 - 689310 * q^8	\( 68 q - 312 q^{2} - 2 q^{3} - 4 q^{7} - 689310 q^{8} + 23502846 q^{10} - 2993734 q^{11} - 76269906 q^{12} - 3845224 q^{14} + 277690070 q^{15} - 5490752792 q^{16} + 285786056 q^{17} + 5809842386 q^{18} - 1195066336 q^{19} + 1866268668 q^{20} - 8197524756 q^{21} + 2117392192 q^{23} + 8629372824 q^{24} - 73846917196 q^{25} - 16368356994 q^{26} + 33411191086 q^{27} + 48687460392 q^{29} + 128044102700 q^{30} + 73968522614 q^{31} - 2657032122 q^{32} - 259972090824 q^{36} + 95888936640 q^{37} - 571710579738 q^{39} + 977850700426 q^{40} - 57594847104 q^{41} + 48472463810 q^{43} + 1173476843650 q^{44} - 299491373708 q^{45} + 656204001636 q^{46} + 29961288922 q^{47} + 1808198535114 q^{48} + 9857850529980 q^{49} + 1443642384290 q^{50} - 11263919114280 q^{52} - 1993070689076 q^{53} + 2064324525592 q^{54} + 3054165001846 q^{55} + 8002123380864 q^{56} - 9170547007720 q^{58} - 8402401993912 q^{59} + 4455428077662 q^{60} - 4381209993964 q^{61} - 14884429709724 q^{65} - 5756218265814 q^{66} + 4595908790532 q^{68} + 51089269002600 q^{69} - 65383337180236 q^{70} + 101900024607216 q^{72} + 39493186331224 q^{73} - 152862151734316 q^{74} - 46335428712972 q^{75} + 46232026918072 q^{76} + 63231072283300 q^{77} + 111617680995888 q^{78} - 29034273461086 q^{79} - 345331621902328 q^{81} + 104609665443600 q^{82} - 2994621113016 q^{83} + 269240332456580 q^{84} + 11907997971872 q^{85} - 148747542169982 q^{87} + 186485775340436 q^{88} - 89923791148548 q^{89} + 103388070190448 q^{90} - 920451476162284 q^{94} - 393920660173420 q^{95} - 116095608365672 q^{97} + 24492650399928 q^{98} - 402079041111864 q^{99}+O(q^{100}) \) 68 * q - 312 * q^2 - 2 * q^3 - 4 * q^7 - 689310 * q^8 + 23502846 * q^10 - 2993734 * q^11 - 76269906 * q^12 - 3845224 * q^14 + 277690070 * q^15 - 5490752792 * q^16 + 285786056 * q^17 + 5809842386 * q^18 - 1195066336 * q^19 + 1866268668 * q^20 - 8197524756 * q^21 + 2117392192 * q^23 + 8629372824 * q^24 - 73846917196 * q^25 - 16368356994 * q^26 + 33411191086 * q^27 + 48687460392 * q^29 + 128044102700 * q^30 + 73968522614 * q^31 - 2657032122 * q^32 - 259972090824 * q^36 + 95888936640 * q^37 - 571710579738 * q^39 + 977850700426 * q^40 - 57594847104 * q^41 + 48472463810 * q^43 + 1173476843650 * q^44 - 299491373708 * q^45 + 656204001636 * q^46 + 29961288922 * q^47 + 1808198535114 * q^48 + 9857850529980 * q^49 + 1443642384290 * q^50 - 11263919114280 * q^52 - 1993070689076 * q^53 + 2064324525592 * q^54 + 3054165001846 * q^55 + 8002123380864 * q^56 - 9170547007720 * q^58 - 8402401993912 * q^59 + 4455428077662 * q^60 - 4381209993964 * q^61 - 14884429709724 * q^65 - 5756218265814 * q^66 + 4595908790532 * q^68 + 51089269002600 * q^69 - 65383337180236 * q^70 + 101900024607216 * q^72 + 39493186331224 * q^73 - 152862151734316 * q^74 - 46335428712972 * q^75 + 46232026918072 * q^76 + 63231072283300 * q^77 + 111617680995888 * q^78 - 29034273461086 * q^79 - 345331621902328 * q^81 + 104609665443600 * q^82 - 2994621113016 * q^83 + 269240332456580 * q^84 + 11907997971872 * q^85 - 148747542169982 * q^87 + 186485775340436 * q^88 - 89923791148548 * q^89 + 103388070190448 * q^90 - 920451476162284 * q^94 - 393920660173420 * q^95 - 116095608365672 * q^97 + 24492650399928 * q^98 - 402079041111864 * q^99

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