LMFDB - Embedded newform 37.10.e.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,10,Mod(11,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("37.11");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	37.e (of order $6$, 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:	$19.0563259381$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	37.11
Dual form			37.10.e.a.27.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-17.2642 + 9.96751i) q^{2} +(-121.025 + 209.622i) q^{3} +(-57.2974 + 99.2421i) q^{4} +(-231.945 - 133.913i) q^{5} -4825.28i q^{6} +(-4145.43 + 7180.09i) q^{7} -12491.2i q^{8} +(-19452.7 - 33693.1i) q^{9} +O(q^{10})$	\(q+(-17.2642 + 9.96751i) q^{2} +(-121.025 + 209.622i) q^{3} +(-57.2974 + 99.2421i) q^{4} +(-231.945 - 133.913i) q^{5} -4825.28i q^{6} +(-4145.43 + 7180.09i) q^{7} -12491.2i q^{8} +(-19452.7 - 33693.1i) q^{9} +5339.13 q^{10} -42996.7 q^{11} +(-13868.9 - 24021.6i) q^{12} +(-35102.3 - 20266.3i) q^{13} -165278. i q^{14} +(56142.4 - 32413.8i) q^{15} +(95169.7 + 164839. i) q^{16} +(-582991. + 336590. i) q^{17} +(671673. + 387791. i) q^{18} +(932616. + 538446. i) q^{19} +(26579.7 - 15345.8i) q^{20} +(-1.00340e6 - 1.73794e6i) q^{21} +(742305. - 428570. i) q^{22} +346994. i q^{23} +(2.61843e6 + 1.51175e6i) q^{24} +(-940697. - 1.62933e6i) q^{25} +808019. q^{26} +4.65281e6 q^{27} +(-475044. - 822801. i) q^{28} +4.33075e6i q^{29} +(-646170. + 1.11920e6i) q^{30} +856931. i q^{31} +(2.25259e6 + 1.30053e6i) q^{32} +(5.20369e6 - 9.01305e6i) q^{33} +(6.70992e6 - 1.16219e7i) q^{34} +(1.92302e6 - 1.11026e6i) q^{35} +4.45837e6 q^{36} +(1.95694e6 + 1.12309e7i) q^{37} -2.14679e7 q^{38} +(8.49652e6 - 4.90547e6i) q^{39} +(-1.67274e6 + 2.89726e6i) q^{40} +(-8.81012e6 + 1.52596e7i) q^{41} +(3.46460e7 + 2.00029e7i) q^{42} +9.44902e6i q^{43} +(2.46360e6 - 4.26708e6i) q^{44} +1.04199e7i q^{45} +(-3.45866e6 - 5.99058e6i) q^{46} -4.92090e7 q^{47} -4.60718e7 q^{48} +(-1.41923e7 - 2.45818e7i) q^{49} +(3.24808e7 + 1.87528e7i) q^{50} -1.62943e8i q^{51} +(4.02254e6 - 2.32241e6i) q^{52} +(-2.33359e7 - 4.04189e7i) q^{53} +(-8.03272e7 + 4.63770e7i) q^{54} +(9.97286e6 + 5.75783e6i) q^{55} +(8.96878e7 + 5.17813e7i) q^{56} +(-2.25740e8 + 1.30331e8i) q^{57} +(-4.31668e7 - 7.47671e7i) q^{58} +(6.64512e6 - 3.83656e6i) q^{59} +7.42891e6i q^{60} +(1.25373e8 + 7.23839e7i) q^{61} +(-8.54147e6 - 1.47943e7i) q^{62} +3.22560e8 q^{63} -1.49306e8 q^{64} +(5.42786e6 + 9.40133e6i) q^{65} +2.07471e8i q^{66} +(-1.53147e7 + 2.65259e7i) q^{67} -7.71429e7i q^{68} +(-7.27375e7 - 4.19950e7i) q^{69} +(-2.21330e7 + 3.83354e7i) q^{70} +(1.32311e8 - 2.29170e8i) q^{71} +(-4.20867e8 + 2.42988e8i) q^{72} +6.11060e7 q^{73} +(-1.45729e8 - 1.74386e8i) q^{74} +4.55392e8 q^{75} +(-1.06873e8 + 6.17032e7i) q^{76} +(1.78240e8 - 3.08720e8i) q^{77} +(-9.77907e7 + 1.69378e8i) q^{78} +(3.04738e8 + 1.75940e8i) q^{79} -5.09780e7i q^{80} +(-1.80220e8 + 3.12150e8i) q^{81} -3.51260e8i q^{82} +(-8.46619e7 - 1.46639e8i) q^{83} +2.29970e8 q^{84} +1.80295e8 q^{85} +(-9.41832e7 - 1.63130e8i) q^{86} +(-9.07820e8 - 5.24130e8i) q^{87} +5.37080e8i q^{88} +(7.30862e8 - 4.21963e8i) q^{89} +(-1.03861e8 - 1.79892e8i) q^{90} +(2.91028e8 - 1.68025e8i) q^{91} +(-3.44363e7 - 1.98818e7i) q^{92} +(-1.79631e8 - 1.03710e8i) q^{93} +(8.49555e8 - 4.90491e8i) q^{94} +(-1.44210e8 - 2.49780e8i) q^{95} +(-5.45240e8 + 3.14795e8i) q^{96} -5.16564e8i q^{97} +(4.90038e8 + 2.82924e8i) q^{98} +(8.36403e8 + 1.44869e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 54 q^{2} - 75 q^{3} + 7082 q^{4} - 186 q^{5} - 4233 q^{7} - 173645 q^{9}+O(q^{10}) $ 56 * q - 54 * q^2 - 75 * q^3 + 7082 * q^4 - 186 * q^5 - 4233 * q^7 - 173645 * q^9	\( 56 q - 54 q^{2} - 75 q^{3} + 7082 q^{4} - 186 q^{5} - 4233 q^{7} - 173645 q^{9} + 97788 q^{10} - 239916 q^{11} + 184790 q^{12} - 16221 q^{13} + 385251 q^{15} - 1932502 q^{16} - 951654 q^{17} + 2811312 q^{18} - 1336047 q^{19} - 3977274 q^{20} + 1205555 q^{21} + 1410426 q^{22} - 4560318 q^{24} + 7900208 q^{25} + 6077964 q^{26} + 586098 q^{27} + 3406456 q^{28} - 12007340 q^{30} + 47328192 q^{32} + 8003280 q^{33} - 19428782 q^{34} - 4325523 q^{35} - 99800316 q^{36} + 38883015 q^{37} - 631920 q^{38} + 6587955 q^{39} + 25546036 q^{40} + 40335342 q^{41} - 91333530 q^{42} - 51286086 q^{44} - 92082750 q^{46} - 56174724 q^{47} + 388858084 q^{48} - 46172317 q^{49} - 250482252 q^{50} - 3706980 q^{52} - 197686869 q^{53} - 331423182 q^{54} + 339434874 q^{55} + 308799468 q^{56} + 360939639 q^{57} + 152139640 q^{58} + 26190393 q^{59} + 761586312 q^{61} + 443235042 q^{62} - 7358848 q^{63} - 2112154540 q^{64} - 76474689 q^{65} + 69911823 q^{67} + 1126766970 q^{69} + 788397646 q^{70} - 47291505 q^{71} + 1854440580 q^{72} - 1332048936 q^{73} - 1443954222 q^{74} - 1421404708 q^{75} - 1509740898 q^{76} + 1440770232 q^{77} - 58000938 q^{78} + 803079201 q^{79} - 1163206256 q^{81} + 231204831 q^{83} - 60315320 q^{84} - 822210144 q^{85} - 1325958588 q^{86} + 762221460 q^{87} + 2475878382 q^{89} - 4026498436 q^{90} + 2004728283 q^{91} + 183172434 q^{92} + 3380032662 q^{93} + 3222389442 q^{94} - 926002287 q^{95} - 14442188094 q^{96} + 2664119844 q^{98} + 3971333010 q^{99}+O(q^{100}) \) 56 * q - 54 * q^2 - 75 * q^3 + 7082 * q^4 - 186 * q^5 - 4233 * q^7 - 173645 * q^9 + 97788 * q^10 - 239916 * q^11 + 184790 * q^12 - 16221 * q^13 + 385251 * q^15 - 1932502 * q^16 - 951654 * q^17 + 2811312 * q^18 - 1336047 * q^19 - 3977274 * q^20 + 1205555 * q^21 + 1410426 * q^22 - 4560318 * q^24 + 7900208 * q^25 + 6077964 * q^26 + 586098 * q^27 + 3406456 * q^28 - 12007340 * q^30 + 47328192 * q^32 + 8003280 * q^33 - 19428782 * q^34 - 4325523 * q^35 - 99800316 * q^36 + 38883015 * q^37 - 631920 * q^38 + 6587955 * q^39 + 25546036 * q^40 + 40335342 * q^41 - 91333530 * q^42 - 51286086 * q^44 - 92082750 * q^46 - 56174724 * q^47 + 388858084 * q^48 - 46172317 * q^49 - 250482252 * q^50 - 3706980 * q^52 - 197686869 * q^53 - 331423182 * q^54 + 339434874 * q^55 + 308799468 * q^56 + 360939639 * q^57 + 152139640 * q^58 + 26190393 * q^59 + 761586312 * q^61 + 443235042 * q^62 - 7358848 * q^63 - 2112154540 * q^64 - 76474689 * q^65 + 69911823 * q^67 + 1126766970 * q^69 + 788397646 * q^70 - 47291505 * q^71 + 1854440580 * q^72 - 1332048936 * q^73 - 1443954222 * q^74 - 1421404708 * q^75 - 1509740898 * q^76 + 1440770232 * q^77 - 58000938 * q^78 + 803079201 * q^79 - 1163206256 * q^81 + 231204831 * q^83 - 60315320 * q^84 - 822210144 * q^85 - 1325958588 * q^86 + 762221460 * q^87 + 2475878382 * q^89 - 4026498436 * q^90 + 2004728283 * q^91 + 183172434 * q^92 + 3380032662 * q^93 + 3222389442 * q^94 - 926002287 * q^95 - 14442188094 * q^96 + 2664119844 * q^98 + 3971333010 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−17.2642	+	9.96751i	−0.762979	+	0.440506i	−0.830364	−	0.557221i	$-0.811868\pi$
$2$	−17.2642	+	9.96751i	−0.762979	+	0.440506i	0.0673855	+	0.997727i	$0.478534\pi$
$3$	−121.025	+	209.622i	−0.862642	+	1.49414i	0.00672812	+	0.999977i	$0.497858\pi$
$3$	−121.025	+	209.622i	−0.862642	+	1.49414i	−0.869370	+	0.494162i	$0.835475\pi$
$4$	−57.2974	+	99.2421i	−0.111909	+	0.193832i
$5$	−231.945	−	133.913i	−0.165966	−	0.0958206i	0.414716	−	0.909951i	$-0.363881\pi$
$5$	−231.945	−	133.913i	−0.165966	−	0.0958206i	−0.580682	+	0.814130i	$0.697214\pi$
$6$		−	4825.28i		−	1.52000i
$7$	−4145.43	+	7180.09i	−0.652571	+	1.13029i	0.329926	+	0.944007i	$0.392976\pi$
$7$	−4145.43	+	7180.09i	−0.652571	+	1.13029i	−0.982497	+	0.186280i	$0.940357\pi$
$8$		−	12491.2i		−	1.07820i
$9$	−19452.7	−	33693.1i	−0.988302	−	1.71179i
$10$	5339.13			0.168838
$11$	−42996.7			−0.885458			−0.442729	−	0.896655i	$-0.645990\pi$
$11$	−42996.7			−0.885458			−0.442729	+	0.896655i	$0.645990\pi$
$12$	−13868.9	−	24021.6i	−0.193075	−	0.334415i
$13$	−35102.3	−	20266.3i	−0.340871	−	0.196802i	0.319786	−	0.947490i	$-0.396389\pi$
$13$	−35102.3	−	20266.3i	−0.340871	−	0.196802i	−0.660657	+	0.750688i	$0.729722\pi$
$14$		−	165278.i		−	1.14985i
$15$	56142.4	−	32413.8i	0.286339	−	0.165318i
$16$	95169.7	+	164839.i	0.363044	+	0.628810i
$17$	−582991.	+	336590.i	−1.69294	+	0.977419i	−0.740814	+	0.671710i	$0.765560\pi$
$17$	−582991.	+	336590.i	−1.69294	+	0.977419i	−0.952125	+	0.305709i	$0.901106\pi$
$18$	671673.	+	387791.i	1.50811	+	0.870705i
$19$	932616.	+	538446.i	1.64177	+	0.947875i	0.980205	+	0.197986i	$0.0634401\pi$
$19$	932616.	+	538446.i	1.64177	+	0.947875i	0.661564	+	0.749889i	$0.269893\pi$
$20$	26579.7	−	15345.8i	0.0371462	−	0.0214464i
$21$	−1.00340e6	−	1.73794e6i	−1.12587	−	1.95006i
$22$	742305.	−	428570.i	0.675586	−	0.390049i
$23$			346994.i			0.258551i	0.991609	+	0.129275i	$0.0412651\pi$
$23$			346994.i			0.258551i	−0.991609	+	0.129275i	$0.958735\pi$
$24$	2.61843e6	+	1.51175e6i	1.61098	+	0.930099i
$25$	−940697.	−	1.62933e6i	−0.481637	−	0.834219i
$26$	808019.			0.346770
$27$	4.65281e6			1.68492
$28$	−475044.	−	822801.i	−0.146057	−	0.252979i
$29$			4.33075e6i			1.13703i	0.822673	+	0.568515i	$0.192482\pi$
$29$			4.33075e6i			1.13703i	−0.822673	+	0.568515i	$0.807518\pi$
$30$	−646170.	+	1.11920e6i	−0.145647	+	0.252268i
$31$			856931.i			0.166655i	0.996522	+	0.0833274i	$0.0265547\pi$
$31$			856931.i			0.166655i	−0.996522	+	0.0833274i	$0.973445\pi$
$32$	2.25259e6	+	1.30053e6i	0.379758	+	0.219253i
$33$	5.20369e6	−	9.01305e6i	0.763833	−	1.32300i
$34$	6.70992e6	−	1.16219e7i	0.861118	−	1.49150i
$35$	1.92302e6	−	1.11026e6i	0.216609	−	0.125060i
$36$	4.45837e6			0.442399
$37$	1.95694e6	+	1.12309e7i	0.171660	+	0.985156i
$37$	1.95694e6	+	1.12309e7i	0.171660	+	0.985156i
$38$	−2.14679e7			−1.67018
$39$	8.49652e6	−	4.90547e6i	0.588099	−	0.339539i
$40$	−1.67274e6	+	2.89726e6i	−0.103314	+	0.178944i
$41$	−8.81012e6	+	1.52596e7i	−0.486917	+	0.843365i	−0.999887	−	0.0150419i	$-0.995212\pi$
$41$	−8.81012e6	+	1.52596e7i	−0.486917	+	0.843365i	0.512970	+	0.858406i	$0.328545\pi$
$42$	3.46460e7	+	2.00029e7i	1.71803	+	0.991905i
$43$			9.44902e6i			0.421482i	0.977542	+	0.210741i	$0.0675876\pi$
$43$			9.44902e6i			0.421482i	−0.977542	+	0.210741i	$0.932412\pi$
$44$	2.46360e6	−	4.26708e6i	0.0990907	−	0.171630i
$45$			1.04199e7i			0.378799i
$46$	−3.45866e6	−	5.99058e6i	−0.113893	−	0.197269i
$47$	−4.92090e7			−1.47097			−0.735485	−	0.677541i	$-0.763046\pi$
$47$	−4.92090e7			−1.47097			−0.735485	+	0.677541i	$0.763046\pi$
$48$	−4.60718e7			−1.25271
$49$	−1.41923e7	−	2.45818e7i	−0.351698	−	0.609159i
$50$	3.24808e7	+	1.87528e7i	0.734957	+	0.424328i
$51$		−	1.62943e8i		−	3.37265i
$52$	4.02254e6	−	2.32241e6i	0.0762931	−	0.0440478i
$53$	−2.33359e7	−	4.04189e7i	−0.406240	−	0.703628i	0.588225	−	0.808697i	$-0.299827\pi$
$53$	−2.33359e7	−	4.04189e7i	−0.406240	−	0.703628i	−0.994465	+	0.105069i	$0.966494\pi$
$54$	−8.03272e7	+	4.63770e7i	−1.28556	+	0.742216i
$55$	9.97286e6	+	5.75783e6i	0.146956	+	0.0848451i
$56$	8.96878e7	+	5.17813e7i	1.21867	+	0.703601i
$57$	−2.25740e8	+	1.30331e8i	−2.83252	+	1.63535i
$58$	−4.31668e7	−	7.47671e7i	−0.500868	−	0.867530i
$59$	6.64512e6	−	3.83656e6i	0.0713951	−	0.0412200i	−0.463877	−	0.885899i	$-0.653542\pi$
$59$	6.64512e6	−	3.83656e6i	0.0713951	−	0.0412200i	0.535273	+	0.844679i	$0.320209\pi$
$60$			7.42891e6i			0.0740022i
$61$	1.25373e8	+	7.23839e7i	1.15936	+	0.669357i	0.951151	−	0.308727i	$-0.0999030\pi$
$61$	1.25373e8	+	7.23839e7i	1.15936	+	0.669357i	0.208210	+	0.978084i	$0.433236\pi$
$62$	−8.54147e6	−	1.47943e7i	−0.0734125	−	0.127154i
$63$	3.22560e8			2.57975
$64$	−1.49306e8			−1.11242
$65$	5.42786e6	+	9.40133e6i	0.0377154	+	0.0653249i
$66$			2.07471e8i			1.34589i
$67$	−1.53147e7	+	2.65259e7i	−0.0928481	+	0.160818i	−0.908708	−	0.417431i	$-0.862930\pi$
$67$	−1.53147e7	+	2.65259e7i	−0.0928481	+	0.160818i	0.815860	+	0.578249i	$0.196264\pi$
$68$		−	7.71429e7i		−	0.437528i
$69$	−7.27375e7	−	4.19950e7i	−0.386311	−	0.223037i
$70$	−2.21330e7	+	3.83354e7i	−0.110179	+	0.190836i
$71$	1.32311e8	−	2.29170e8i	0.617923	−	1.07027i	−0.371941	−	0.928256i	$-0.621308\pi$
$71$	1.32311e8	−	2.29170e8i	0.617923	−	1.07027i	0.989864	−	0.142018i	$-0.0453591\pi$
$72$	−4.20867e8	+	2.42988e8i	−1.84565	+	1.06559i
$73$	6.11060e7			0.251844			0.125922	−	0.992040i	$-0.459811\pi$
$73$	6.11060e7			0.251844			0.125922	+	0.992040i	$0.459811\pi$
$74$	−1.45729e8	−	1.74386e8i	−0.564940	−	0.676036i
$75$	4.55392e8			1.66192
$76$	−1.06873e8	+	6.17032e7i	−0.367457	+	0.212152i
$77$	1.78240e8	−	3.08720e8i	0.577824	−	1.00082i
$78$	−9.77907e7	+	1.69378e8i	−0.299138	+	0.518122i
$79$	3.04738e8	+	1.75940e8i	0.880247	+	0.508211i	0.870740	−	0.491744i	$-0.163640\pi$
$79$	3.04738e8	+	1.75940e8i	0.880247	+	0.508211i	0.00950708	+	0.999955i	$0.496974\pi$
$80$		−	5.09780e7i		−	0.139148i
$81$	−1.80220e8	+	3.12150e8i	−0.465178	+	0.805713i
$82$		−	3.51260e8i		−	0.857959i
$83$	−8.46619e7	−	1.46639e8i	−0.195811	−	0.339154i	0.751355	−	0.659898i	$-0.229401\pi$
$83$	−8.46619e7	−	1.46639e8i	−0.195811	−	0.339154i	−0.947166	+	0.320744i	$0.896067\pi$
$84$	2.29970e8			0.503980
$85$	1.80295e8			0.374628
$86$	−9.41832e7	−	1.63130e8i	−0.185665	−	0.321582i
$87$	−9.07820e8	−	5.24130e8i	−1.69888	−	0.980849i
$88$			5.37080e8i			0.954699i
$89$	7.30862e8	−	4.21963e8i	1.23475	−	0.712885i	0.266737	−	0.963769i	$-0.414055\pi$
$89$	7.30862e8	−	4.21963e8i	1.23475	−	0.712885i	0.968017	+	0.250884i	$0.0807213\pi$
$90$	−1.03861e8	−	1.79892e8i	−0.166863	−	0.289015i
$91$	2.91028e8	−	1.68025e8i	0.444885	−	0.256855i
$92$	−3.44363e7	−	1.98818e7i	−0.0501155	−	0.0289342i
$93$	−1.79631e8	−	1.03710e8i	−0.249006	−	0.143763i
$94$	8.49555e8	−	4.90491e8i	1.12232	−	0.647971i
$95$	−1.44210e8	−	2.49780e8i	−0.181652	−	0.314630i
$96$	−5.45240e8	+	3.14795e8i	−0.655190	+	0.378274i
$97$		−	5.16564e8i		−	0.592449i	−0.955118	−	0.296225i	$-0.904272\pi$
$97$		−	5.16564e8i		−	0.592449i	0.955118	−	0.296225i	$-0.0957277\pi$
$98$	4.90038e8	+	2.82924e8i	0.536677	+	0.309850i
$99$	8.36403e8	+	1.44869e9i	0.875099	+	1.51572i
$100$	2.15598e8			0.215598
$101$	1.16955e9			1.11833			0.559167	−	0.829055i	$-0.311121\pi$
$101$	1.16955e9			1.11833			0.559167	+	0.829055i	$0.311121\pi$
$102$	1.62414e9	+	2.81309e9i	1.48567	+	2.57326i
$103$		−	8.76631e8i		−	0.767448i	−0.923448	−	0.383724i	$-0.874641\pi$
$103$		−	8.76631e8i		−	0.767448i	0.923448	−	0.383724i	$-0.125359\pi$
$104$	−2.53150e8	+	4.38469e8i	−0.212192	+	0.367527i
$105$			5.37476e8i			0.431526i
$106$	8.05752e8	+	4.65201e8i	0.619905	+	0.357902i
$107$	−4.71134e8	+	8.16029e8i	−0.347470	+	0.601836i	−0.985799	−	0.167927i	$-0.946293\pi$
$107$	−4.71134e8	+	8.16029e8i	−0.347470	+	0.601836i	0.638329	+	0.769764i	$0.279626\pi$
$108$	−2.66594e8	+	4.61755e8i	−0.188557	+	0.326591i
$109$	−1.26971e8	+	7.33068e7i	−0.0861561	+	0.0497422i	−0.542459	−	0.840082i	$-0.682507\pi$
$109$	−1.26971e8	+	7.33068e7i	−0.0861561	+	0.0497422i	0.456303	+	0.889824i	$0.349173\pi$
$110$	−2.29565e8			−0.149499
$111$	−2.59107e9	−	9.48999e8i	−1.62004	−	0.593352i
$112$	−1.57808e9			−0.947647
$113$	−2.28914e9	+	1.32163e9i	−1.32075	+	0.762533i	−0.983847	−	0.179009i	$-0.942711\pi$
$113$	−2.28914e9	+	1.32163e9i	−1.32075	+	0.762533i	−0.336898	+	0.941541i	$0.609378\pi$
$114$	2.59816e9	−	4.50014e9i	1.44077	−	2.49548i
$115$	4.64671e7	−	8.04833e7i	0.0247745	−	0.0429107i
$116$	−4.29792e8	−	2.48141e8i	−0.220393	−	0.127244i
$117$			1.57694e9i			0.777999i
$118$	−7.64819e7	+	1.32471e8i	−0.0363153	+	0.0628999i
$119$		−	5.58123e9i		−	2.55134i
$120$	−4.04887e8	−	7.01285e8i	−0.178245	−	0.308730i
$121$	−5.09232e8			−0.215964
$122$	−2.88595e9			−1.17942
$123$	−2.13250e9	−	3.69359e9i	−0.840069	−	1.45504i
$124$	−8.50435e7	−	4.90999e7i	−0.0323031	−	0.0186502i
$125$			1.02699e9i			0.376244i
$126$	−5.56874e9	+	3.21512e9i	−1.96829	+	1.13639i
$127$	1.20758e9	+	2.09159e9i	0.411906	+	0.713442i	0.995098	−	0.0988920i	$-0.0315298\pi$
$127$	1.20758e9	+	2.09159e9i	0.411906	+	0.713442i	−0.583192	+	0.812334i	$0.698197\pi$
$128$	1.42433e9	−	8.22338e8i	0.468993	−	0.270773i
$129$	−1.98072e9	−	1.14357e9i	−0.629753	−	0.363588i
$130$	−1.87416e8	−	1.08204e8i	−0.0575521	−	0.0332277i
$131$	2.12336e9	−	1.22592e9i	0.629944	−	0.363699i	−0.150786	−	0.988566i	$-0.548180\pi$
$131$	2.12336e9	−	1.22592e9i	0.629944	−	0.363699i	0.780731	+	0.624868i	$0.214847\pi$
$132$	5.96316e8	+	1.03285e9i	0.170960	+	0.296111i
$133$	−7.73218e9	+	4.46418e9i	−2.14274	+	1.23711i
$134$		−	6.10600e8i		−	0.163601i
$135$	−1.07920e9	−	6.23074e8i	−0.279639	−	0.161450i
$136$	4.20440e9	+	7.28224e9i	1.05385	+	1.82532i
$137$	6.69944e6			0.00162479			0.000812393	−	1.00000i	$-0.499741\pi$
$137$	6.69944e6			0.00162479			0.000812393		1.00000i	$0.499741\pi$
$138$	1.67434e9			0.392996
$139$	1.57422e9	+	2.72663e9i	0.357683	+	0.619526i	0.987573	−	0.157159i	$-0.0502334\pi$
$139$	1.57422e9	+	2.72663e9i	0.357683	+	0.619526i	−0.629890	+	0.776684i	$0.716900\pi$
$140$			2.54459e8i			0.0559812i
$141$	5.95553e9	−	1.03153e10i	1.26892	−	2.19783i
$142$			5.27526e9i			1.08880i
$143$	1.50928e9	+	8.71384e8i	0.301827	+	0.174260i
$144$	3.70262e9	−	6.41313e9i	0.717593	−	1.24291i
$145$	5.79945e8	−	1.00449e9i	0.108951	−	0.188708i
$146$	−1.05495e9	+	6.09075e8i	−0.192151	+	0.110939i
$147$	6.87051e9			1.21356
$148$	−1.22670e9	−	4.49288e8i	−0.210165	−	0.0769746i
$149$	−7.10164e9			−1.18038			−0.590188	−	0.807266i	$-0.700947\pi$
$149$	−7.10164e9			−1.18038			−0.590188	+	0.807266i	$0.700947\pi$
$150$	−7.86200e9	+	4.53913e9i	−1.26801	+	0.732086i
$151$	−2.17454e9	+	3.76641e9i	−0.340385	+	0.589564i	−0.984504	−	0.175361i	$-0.943891\pi$
$151$	−2.17454e9	+	3.76641e9i	−0.340385	+	0.589564i	0.644119	+	0.764925i	$0.277224\pi$
$152$	6.72583e9	−	1.16495e10i	1.02200	−	1.77015i
$153$	2.26815e10	+	1.30952e10i	3.34627	+	1.93197i
$154$			7.10642e9i			1.01814i
$155$	1.14754e8	−	1.98761e8i	0.0159690	−	0.0276591i
$156$			1.12428e9i			0.151990i
$157$	−3.10088e9	−	5.37089e9i	−0.407321	−	0.705501i	0.587267	−	0.809393i	$-0.300204\pi$
$157$	−3.10088e9	−	5.37089e9i	−0.407321	−	0.705501i	−0.994589	+	0.103892i	$0.966870\pi$
$158$	−7.01476e9			−0.895479
$159$	1.12969e10			1.40176
$160$	−3.48317e8	−	6.03303e8i	−0.0420180	−	0.0727773i
$161$	−2.49144e9	−	1.43844e9i	−0.292237	−	0.168723i
$162$		−	7.18536e9i		−	0.819655i
$163$	9.25641e9	−	5.34419e9i	1.02707	−	0.592977i	0.110923	−	0.993829i	$-0.464619\pi$
$163$	9.25641e9	−	5.34419e9i	1.02707	−	0.592977i	0.916143	+	0.400852i	$0.131286\pi$
$164$	−1.00959e9	−	1.74867e9i	−0.108981	−	0.188760i
$165$	−2.41394e9	+	1.39369e9i	−0.253541	+	0.146382i
$166$	2.92325e9	+	1.68774e9i	0.298799	+	0.172512i
$167$	2.47748e9	+	1.43038e9i	0.246483	+	0.142307i	0.618153	−	0.786058i	$-0.287881\pi$
$167$	2.47748e9	+	1.43038e9i	0.246483	+	0.142307i	−0.371670	+	0.928365i	$0.621215\pi$
$168$	−2.17090e10	+	1.25337e10i	−2.10256	+	1.21391i
$169$	−4.48080e9	−	7.76098e9i	−0.422538	−	0.731857i
$170$	−3.11266e9	+	1.79710e9i	−0.285833	+	0.165026i
$171$		−	4.18970e10i		−	3.74715i
$172$	−9.37740e8	−	5.41405e8i	−0.0816967	−	0.0471676i
$173$	7.41266e9	+	1.28391e10i	0.629168	+	1.08975i	0.987719	+	0.156240i	$0.0499374\pi$
$173$	7.41266e9	+	1.28391e10i	0.629168	+	1.08975i	−0.358552	+	0.933510i	$0.616729\pi$
$174$	2.08971e10			1.72828
$175$	1.55984e10			1.25721
$176$	−4.09198e9	−	7.08752e9i	−0.321460	−	0.556785i
$177$			1.85728e9i			0.142232i
$178$	−8.41185e9	+	1.45698e10i	−0.628060	+	1.08783i
$179$		−	9.94165e9i		−	0.723802i	−0.932217	−	0.361901i	$-0.882128\pi$
$179$		−	9.94165e9i		−	0.723802i	0.932217	−	0.361901i	$-0.117872\pi$
$180$	−1.03409e9	−	5.97035e8i	−0.0734233	−	0.0423910i
$181$	−1.19466e10	+	2.06922e10i	−0.827356	+	1.43302i	0.0727492	+	0.997350i	$0.476823\pi$
$181$	−1.19466e10	+	2.06922e10i	−0.827356	+	1.43302i	−0.900105	+	0.435672i	$0.856511\pi$
$182$	−3.34958e9	+	5.80164e9i	−0.226292	+	0.391949i
$183$	−3.03465e10	+	1.75206e10i	−2.00023	+	1.15483i
$184$	4.33436e9			0.278769
$185$	1.05006e9	−	2.86700e9i	0.0659084	−	0.179951i
$186$	4.13493e9			0.253315
$187$	2.50667e10	−	1.44722e10i	1.49903	−	0.865463i
$188$	2.81955e9	−	4.88360e9i	0.164615	−	0.285121i
$189$	−1.92879e10	+	3.34076e10i	−1.09953	+	1.90444i
$190$	4.97936e9	+	2.87484e9i	0.277193	+	0.160038i
$191$		−	5.48131e9i		−	0.298012i	−0.988836	−	0.149006i	$-0.952393\pi$
$191$		−	5.48131e9i		−	0.298012i	0.988836	−	0.149006i	$-0.0476074\pi$
$192$	1.80698e10	−	3.12978e10i	0.959617	−	1.66211i
$193$			1.51088e7i			0.000783831i	1.00000		0.000391915i	$0.000124751\pi$
$193$			1.51088e7i			0.000783831i	−1.00000		0.000391915i	$0.999875\pi$
$194$	5.14885e9	+	8.91808e9i	0.260977	+	0.452026i
$195$	−2.62763e9			−0.130139
$196$	3.25273e9			0.157433
$197$	−5.58410e7	−	9.67194e7i	−0.00264153	−	0.00457526i	0.864702	−	0.502286i	$-0.167507\pi$
$197$	−5.58410e7	−	9.67194e7i	−0.00264153	−	0.00457526i	−0.867343	+	0.497711i	$0.834174\pi$
$198$	−2.88797e10	−	1.66737e10i	−1.33536	−	0.770973i
$199$			2.49640e10i			1.12843i	0.825627	+	0.564217i	$0.190822\pi$
$199$			2.49640e10i			1.12843i	−0.825627	+	0.564217i	$0.809178\pi$
$200$	−2.03523e10	+	1.17504e10i	−0.899454	+	0.519300i
$201$	−3.70694e9	−	6.42061e9i	−0.160189	−	0.277456i
$202$	−2.01913e10	+	1.16575e10i	−0.853264	+	0.492632i
$203$	−3.10951e10	−	1.79528e10i	−1.28517	−	0.741993i
$204$	1.61708e10	+	9.33624e9i	0.653728	+	0.377430i
$205$	4.08692e9	−	2.35959e9i	0.161623	−	0.0933133i
$206$	8.73783e9	+	1.51344e10i	0.338066	+	0.585547i
$207$	1.16913e10	−	6.74997e9i	0.442584	−	0.255526i
$208$		−	7.71496e9i		−	0.285791i
$209$	−4.00994e10	−	2.31514e10i	−1.45372	−	0.839304i
$210$	−5.35730e9	−	9.27911e9i	−0.190090	−	0.329245i
$211$	−1.07455e10			−0.373213			−0.186607	−	0.982435i	$-0.559749\pi$
$211$	−1.07455e10			−0.373213			−0.186607	+	0.982435i	$0.559749\pi$
$212$	5.34834e9			0.181848
$213$	3.20260e10	+	5.54707e10i	1.06609	+	1.84653i
$214$		−	1.87842e10i		−	0.612251i
$215$	1.26535e9	−	2.19165e9i	0.0403866	−	0.0699517i
$216$		−	5.81191e10i		−	1.81667i
$217$	−6.15284e9	−	3.55234e9i	−0.188368	−	0.108754i
$218$	1.46137e9	−	2.53117e9i	0.0438235	−	0.0759045i
$219$	−7.39538e9	+	1.28092e10i	−0.217251	+	0.376290i
$220$	−1.14284e9	+	6.59818e8i	−0.0328914	+	0.0189899i
$221$	2.72857e10			0.769432
$222$	5.41921e10	−	9.44280e9i	1.49743	−	0.260923i
$223$	−5.74242e10			−1.55497			−0.777487	−	0.628899i	$-0.783506\pi$
$223$	−5.74242e10			−1.55497			−0.777487	+	0.628899i	$0.783506\pi$
$224$	−1.86759e10	+	1.07825e10i	−0.495638	+	0.286157i
$225$	−3.65983e10	+	6.33901e10i	−0.952005	+	1.64892i
$226$	2.63468e10	−	4.56340e10i	0.671800	−	1.16359i
$227$	−4.36567e10	−	2.52052e10i	−1.09127	−	0.630048i	−0.157359	−	0.987541i	$-0.550298\pi$
$227$	−4.36567e10	−	2.52052e10i	−1.09127	−	0.630048i	−0.933916	+	0.357493i	$0.883631\pi$
$228$		−	2.98706e10i		−	0.732043i
$229$	1.86653e10	−	3.23292e10i	0.448513	−	0.776847i	−0.549777	−	0.835312i	$-0.685287\pi$
$229$	1.86653e10	−	3.23292e10i	0.448513	−	0.776847i	0.998289	+	0.0584647i	$0.0186205\pi$
$230$			1.85264e9i			0.0436533i
$231$	4.31430e10	+	7.47258e10i	0.996911	+	1.72670i
$232$	5.40962e10			1.22594
$233$	3.27108e10			0.727091			0.363546	−	0.931576i	$-0.381566\pi$
$233$	3.27108e10			0.727091			0.363546	+	0.931576i	$0.381566\pi$
$234$	−1.57182e10	−	2.72247e10i	−0.342713	−	0.593597i
$235$	1.14138e10	+	6.58974e9i	0.244131	+	0.140949i
$236$			8.79300e8i			0.0184516i
$237$	−7.37620e10	+	4.25865e10i	−1.51868	+	0.876808i
$238$	5.56310e10	+	9.63557e10i	1.12388	+	1.94662i
$239$	−3.17451e10	+	1.83281e10i	−0.629342	+	0.363351i	−0.780497	−	0.625159i	$-0.785034\pi$
$239$	−3.17451e10	+	1.83281e10i	−0.629342	+	0.363351i	0.151155	+	0.988510i	$0.451701\pi$
$240$	1.06861e10	+	6.16963e9i	0.207907	+	0.120035i
$241$	−1.26285e10	−	7.29105e9i	−0.241143	−	0.139224i	0.374559	−	0.927203i	$-0.377794\pi$
$241$	−1.26285e10	−	7.29105e9i	−0.241143	−	0.139224i	−0.615702	+	0.787979i	$0.711127\pi$
$242$	8.79151e9	−	5.07578e9i	0.164776	−	0.0951335i
$243$	2.16839e9	+	3.75575e9i	0.0398941	+	0.0690985i
$244$	−1.43671e10	+	8.29482e9i	−0.259486	+	0.149814i
$245$			7.60215e9i			0.134800i
$246$	7.36318e10	+	4.25114e10i	1.28191	+	0.740111i
$247$	−2.18246e10	−	3.78014e10i	−0.373088	−	0.646207i
$248$	1.07041e10			0.179687
$249$	4.09849e10			0.675658
$250$	−1.02365e10	−	1.77301e10i	−0.165738	−	0.287066i
$251$		−	9.85704e10i		−	1.56753i	−0.621060	−	0.783763i	$-0.713298\pi$
$251$		−	9.85704e10i		−	1.56753i	0.621060	−	0.783763i	$-0.286702\pi$
$252$	−1.84818e10	+	3.20115e10i	−0.288697	+	0.500038i
$253$		−	1.49196e10i		−	0.228936i
$254$	−4.16958e10	−	2.40731e10i	−0.628551	−	0.362894i
$255$	−2.18203e10	+	3.77939e10i	−0.323169	+	0.559746i
$256$	2.18290e10	−	3.78090e10i	0.317654	−	0.550193i
$257$	1.04357e11	−	6.02507e10i	1.49219	−	0.861516i	0.492229	−	0.870466i	$-0.336182\pi$
$257$	1.04357e11	−	6.02507e10i	1.49219	−	0.861516i	0.999960	+	0.00895038i	$0.00284903\pi$
$258$	4.55942e10			0.640650
$259$	−8.87509e10	−	3.25057e10i	−1.22553	−	0.448859i
$260$	−1.24401e9			−0.0168828
$261$	1.45916e11	−	8.42449e10i	1.94635	−	1.12373i
$262$	−2.44388e10	+	4.23292e10i	−0.320423	+	0.554989i
$263$	1.97081e10	−	3.41354e10i	0.254006	−	0.439951i	−0.710619	−	0.703577i	$-0.751585\pi$
$263$	1.97081e10	−	3.41354e10i	0.254006	−	0.439951i	0.964625	+	0.263626i	$0.0849185\pi$
$264$	−1.12584e11	−	6.50002e10i	−1.42645	−	0.823563i
$265$			1.24999e10i			0.155705i
$266$	8.89935e10	−	1.54141e11i	1.08991	−	1.88778i
$267$			2.04273e11i			2.45986i
$268$	−1.75499e9	−	3.03973e9i	−0.0207811	−	0.0359939i
$269$	−4.67989e10			−0.544942			−0.272471	−	0.962164i	$-0.587841\pi$
$269$	−4.67989e10			−0.544942			−0.272471	+	0.962164i	$0.587841\pi$
$270$	2.48420e10			0.284478
$271$	2.04416e10	+	3.54059e10i	0.230225	+	0.398762i	0.957874	−	0.287188i	$-0.0927203\pi$
$271$	2.04416e10	+	3.54059e10i	0.230225	+	0.398762i	−0.727649	+	0.685950i	$0.759387\pi$
$272$	−1.10966e11	−	6.40663e10i	−1.22922	−	0.709692i
$273$			8.13411e10i			0.886294i
$274$	−1.15661e8	+	6.67768e7i	−0.00123968	+	0.000715728i
$275$	4.04469e10	+	7.00560e10i	0.426469	+	0.738666i
$276$	8.33534e9	−	4.81241e9i	0.0864634	−	0.0499197i
$277$	3.99060e9	+	2.30398e9i	0.0407267	+	0.0235136i	0.520225	−	0.854029i	$-0.325848\pi$
$277$	3.99060e9	+	2.30398e9i	0.0407267	+	0.0235136i	−0.479498	+	0.877543i	$0.659181\pi$
$278$	−5.43554e10	−	3.13821e10i	−0.545810	−	0.315123i
$279$	2.88727e10	−	1.66696e10i	0.285278	−	0.164705i
$280$	−1.38684e10	−	2.40208e10i	−0.134839	−	0.233548i
$281$	−1.52440e11	+	8.80112e10i	−1.45855	+	0.842092i	−0.998940	−	0.0460310i	$-0.985343\pi$
$281$	−1.52440e11	+	8.80112e10i	−1.45855	+	0.842092i	−0.459606	+	0.888123i	$0.652009\pi$
$282$			2.37447e11i			2.23587i
$283$	1.57608e11	+	9.09952e10i	1.46063	+	0.843295i	0.999040	−	0.0437988i	$-0.0139461\pi$
$283$	1.57608e11	+	9.09952e10i	1.46063	+	0.843295i	0.461589	+	0.887094i	$0.347279\pi$
$284$	1.51622e10	+	2.62617e10i	0.138302	+	0.239547i
$285$	6.98124e10			0.626802
$286$	−3.47421e10			−0.307050
$287$	−7.30434e10	−	1.26515e11i	−0.635496	−	1.10071i
$288$		−	1.01196e11i		−	0.866754i
$289$	1.67291e11	−	2.89757e11i	1.41070	−	2.44340i
$290$			2.31224e10i			0.191974i
$291$	1.08283e11	+	6.25173e10i	0.885201	+	0.511071i
$292$	−3.50122e9	+	6.06429e9i	−0.0281836	+	0.0488154i
$293$	−2.80220e10	+	4.85355e10i	−0.222124	+	0.384730i	−0.955453	−	0.295144i	$-0.904632\pi$
$293$	−2.80220e10	+	4.85355e10i	−0.222124	+	0.384730i	0.733329	+	0.679874i	$0.237966\pi$
$294$	−1.18614e11	+	6.84819e10i	−0.925919	+	0.534580i
$295$	−2.05507e9			−0.0157989
$296$	1.40287e11	−	2.44445e10i	1.06219	−	0.185084i
$297$	−2.00056e11			−1.49192
$298$	1.22604e11	−	7.07857e10i	0.900602	−	0.519963i
$299$	7.03228e9	−	1.21803e10i	0.0508833	−	0.0881325i
$300$	−2.60928e10	+	4.51941e10i	−0.185984	+	0.322134i
$301$	−6.78448e10	−	3.91702e10i	−0.476395	−	0.275047i
$302$		−	8.66989e10i		−	0.599766i
$303$	−1.41545e11	+	2.45163e11i	−0.964721	+	1.67095i
$304$			2.04975e11i			1.37648i
$305$	−1.93864e10	−	3.35781e10i	−0.128276	−	0.222181i
$306$	−5.22106e11			−3.40418
$307$	2.25094e11			1.44624			0.723121	−	0.690722i	$-0.242707\pi$
$307$	2.25094e11			1.44624			0.723121	+	0.690722i	$0.242707\pi$
$308$	2.04253e10	+	3.53777e10i	0.129328	+	0.224002i
$309$	1.83761e11	+	1.06094e11i	1.14667	+	0.662033i
$310$			4.57527e9i			0.0281377i
$311$	1.15999e11	−	6.69722e10i	0.703126	−	0.405950i	−0.105385	−	0.994432i	$-0.533607\pi$
$311$	1.15999e11	−	6.69722e10i	0.703126	−	0.405950i	0.808511	+	0.588481i	$0.200274\pi$
$312$	−6.12751e10	−	1.06132e11i	−0.366091	−	0.634088i
$313$	−1.04407e11	+	6.02791e10i	−0.614863	+	0.354991i	−0.774866	−	0.632125i	$-0.782183\pi$
$313$	−1.04407e11	+	6.02791e10i	−0.614863	+	0.354991i	0.160003	+	0.987116i	$0.448849\pi$
$314$	1.07069e11	+	6.18162e10i	0.621555	+	0.358855i
$315$	−7.48160e10	−	4.31950e10i	−0.428151	−	0.247193i
$316$	−3.49214e10	+	2.01619e10i	−0.197015	+	0.113747i
$317$	−7.78211e10	−	1.34790e11i	−0.432844	−	0.749707i	0.564273	−	0.825588i	$-0.309156\pi$
$317$	−7.78211e10	−	1.34790e11i	−0.432844	−	0.749707i	−0.997117	+	0.0758810i	$0.975823\pi$
$318$	−1.95033e11	+	1.12602e11i	−1.06951	+	0.617483i
$319$		−	1.86208e11i		−	1.00679i
$320$	3.46308e10	+	1.99941e10i	0.184624	+	0.106592i
$321$	−1.14038e11	−	1.97520e11i	−0.599485	−	1.03834i
$322$	5.73505e10			0.297294
$323$	−7.24942e11			−3.70589
$324$	−2.06522e10	−	3.57707e10i	−0.104115	−	0.180333i
$325$			7.62578e10i			0.379148i
$326$	−1.06537e11	+	1.84527e11i	−0.522419	+	0.904857i
$327$		−	3.54879e10i		−	0.171639i
$328$	1.90610e11	+	1.10049e11i	0.909314	+	0.524993i
$329$	2.03992e11	−	3.53325e11i	0.959913	−	1.66262i
$330$	2.77832e10	−	4.81219e10i	0.128964	−	0.223373i
$331$	−1.14773e11	+	6.62640e10i	−0.525548	+	0.303425i	−0.739201	−	0.673484i	$-0.764797\pi$
$331$	−1.14773e11	+	6.62640e10i	−0.525548	+	0.303425i	0.213654	+	0.976909i	$0.431464\pi$
$332$	1.94036e10			0.0876520
$333$	3.40335e11	−	2.84406e11i	1.51673	−	1.26748i
$334$	−5.70291e10			−0.250748
$335$	7.10435e9	−	4.10170e9i	0.0308193	−	0.0177935i
$336$	1.90987e11	−	3.30799e11i	0.817480	−	1.41592i
$337$	−1.46822e11	+	2.54304e11i	−0.620094	+	1.07403i	0.369374	+	0.929281i	$0.379572\pi$
$337$	−1.46822e11	+	2.54304e11i	−0.620094	+	1.07403i	−0.989468	+	0.144753i	$0.953761\pi$
$338$	1.54715e11	+	8.93249e10i	0.644775	+	0.372261i
$339$		−	6.39805e11i		−	2.63117i
$340$	−1.03305e10	+	1.78929e10i	−0.0419242	+	0.0726148i
$341$		−	3.68452e10i		−	0.147566i
$342$	4.17609e11	+	7.23320e11i	1.65064	+	2.85899i
$343$	−9.92333e10			−0.387109
$344$	1.18029e11			0.454441
$345$	1.12474e10	+	1.94810e10i	0.0427430	+	0.0740331i
$346$	−2.55948e11	−	1.47771e11i	−0.960083	−	0.554304i
$347$			3.24752e11i			1.20246i	0.799078	+	0.601228i	$0.205322\pi$
$347$			3.24752e11i			1.20246i	−0.799078	+	0.601228i	$0.794678\pi$
$348$	1.04031e11	−	6.00626e10i	0.380240	−	0.219532i
$349$	−1.89675e11	−	3.28527e11i	−0.684378	−	1.18538i	−0.973632	−	0.228125i	$-0.926740\pi$
$349$	−1.89675e11	−	3.28527e11i	−0.684378	−	1.18538i	0.289254	−	0.957252i	$-0.406593\pi$
$350$	−2.69294e11	+	1.55477e11i	−0.959224	+	0.553808i
$351$	−1.63324e11	−	9.42953e10i	−0.574340	−	0.331595i
$352$	−9.68538e10	−	5.59186e10i	−0.336260	−	0.194140i
$353$	−6.78626e10	+	3.91805e10i	−0.232619	+	0.134302i	−0.611780	−	0.791028i	$-0.709546\pi$
$353$	−6.78626e10	+	3.91805e10i	−0.232619	+	0.134302i	0.379161	+	0.925331i	$0.376213\pi$
$354$	−1.85125e10	−	3.20646e10i	−0.0626542	−	0.108520i
$355$	−6.13778e10	+	3.54365e10i	−0.205109	+	0.118420i
$356$			9.67097e10i			0.319113i
$357$	1.16995e12	+	6.75470e11i	3.81206	+	2.20089i
$358$	9.90935e10	+	1.71635e11i	0.318839	+	0.552246i
$359$	3.09113e11			0.982183			0.491092	−	0.871108i	$-0.336598\pi$
$359$	3.09113e11			0.982183			0.491092	+	0.871108i	$0.336598\pi$
$360$	1.30157e11			0.408420
$361$	4.18505e11	+	7.24872e11i	1.29694	+	2.24636i
$362$		−	4.76313e11i		−	1.45782i
$363$	6.16300e10	−	1.06746e11i	0.186300	−	0.322681i
$364$			3.85096e10i			0.114977i
$365$	−1.41732e10	−	8.18292e9i	−0.0417976	−	0.0241318i
$366$	3.49273e11	−	6.04959e11i	1.01742	−	1.76222i
$367$	−2.00637e11	+	3.47513e11i	−0.577316	+	0.999941i	0.418470	+	0.908231i	$0.362567\pi$
$367$	−2.00637e11	+	3.47513e11i	−0.577316	+	0.999941i	−0.995786	+	0.0917099i	$0.970767\pi$
$368$	−5.71980e10	+	3.30233e10i	−0.162579	+	0.0938653i
$369$	6.85524e11			1.92488
$370$	1.04484e10	+	5.99630e10i	0.0289828	+	0.166332i
$371$	3.86948e11			1.06040
$372$	2.05848e10	−	1.18847e10i	0.0557319	−	0.0321769i
$373$	9.65433e10	−	1.67218e11i	0.258245	−	0.447294i	−0.707527	−	0.706687i	$-0.750189\pi$
$373$	9.65433e10	−	1.67218e11i	0.258245	−	0.447294i	0.965772	+	0.259393i	$0.0835224\pi$
$374$	−2.88505e11	+	4.99705e11i	−0.762484	+	1.32066i
$375$	−2.15279e11	−	1.24291e11i	−0.562161	−	0.324564i
$376$			6.14678e11i			1.58600i
$377$	8.77683e10	−	1.52019e11i	0.223770	−	0.387581i
$378$		−	7.69009e11i		−	1.93740i
$379$	−4.01425e10	−	6.95289e10i	−0.0999375	−	0.173097i	0.811721	−	0.584045i	$-0.198531\pi$
$379$	−4.01425e10	−	6.95289e10i	−0.0999375	−	0.173097i	−0.911659	+	0.410948i	$0.865198\pi$
$380$	3.30515e10			0.0813140
$381$	−5.84590e11			−1.42131
$382$	5.46350e10	+	9.46307e10i	0.131276	+	0.227377i
$383$	−2.47273e11	−	1.42763e11i	−0.587194	−	0.339017i	0.176793	−	0.984248i	$-0.443428\pi$
$383$	−2.47273e11	−	1.42763e11i	−0.587194	−	0.339017i	−0.763987	+	0.645231i	$0.776761\pi$
$384$			3.98095e11i			0.934320i
$385$	−8.26835e10	+	4.77373e10i	−0.191799	+	0.110735i
$386$	−1.50597e8	−	2.60842e8i	−0.000345282	−	0.000598046i
$387$	3.18367e11	−	1.83809e11i	0.721488	−	0.416551i
$388$	5.12648e10	+	2.95978e10i	0.114836	+	0.0663004i
$389$	−2.23394e11	−	1.28976e11i	−0.494649	−	0.285586i	0.231852	−	0.972751i	$-0.425522\pi$
$389$	−2.23394e11	−	1.28976e11i	−0.494649	−	0.285586i	−0.726501	+	0.687165i	$0.758855\pi$
$390$	4.53641e10	−	2.61910e10i	0.0992936	−	0.0573272i
$391$	−1.16794e11	−	2.02294e11i	−0.252713	−	0.437711i
$392$	−3.07056e11	+	1.77279e11i	−0.656795	+	0.379201i
$393$			5.93470e11i			1.25497i
$394$	1.92810e9	+	1.11319e9i	0.00403086	+	0.00232722i
$395$	−4.71216e10	−	8.16169e10i	−0.0973941	−	0.168692i
$396$	−1.91695e11			−0.391726
$397$	−7.42577e11			−1.50032			−0.750160	−	0.661256i	$-0.770024\pi$
$397$	−7.42577e11			−1.50032			−0.750160	+	0.661256i	$0.770024\pi$
$398$	−2.48829e11	−	4.30985e11i	−0.497082	−	0.860971i
$399$		−	2.16111e12i		−	4.26874i
$400$	1.79052e11	−	3.10127e11i	0.349710	−	0.605716i
$401$			2.52236e11i			0.487144i	0.969883	+	0.243572i	$0.0783192\pi$
$401$			2.52236e11i			0.487144i	−0.969883	+	0.243572i	$0.921681\pi$
$402$	1.27995e11	+	7.38980e10i	0.244442	+	0.141129i
$403$	1.73668e10	−	3.00802e10i	0.0327980	−	0.0568078i
$404$	−6.70120e10	+	1.16068e11i	−0.125152	+	0.216769i
$405$	8.36020e10	−	4.82676e10i	0.154408	−	0.0891473i
$406$	7.15779e11			1.30741
$407$	−8.41421e10	−	4.82890e11i	−0.151998	−	0.872314i
$408$	−2.03536e12			−3.63638
$409$	−6.77436e10	+	3.91118e10i	−0.119705	+	0.0691119i	−0.558657	−	0.829399i	$-0.688683\pi$
$409$	−6.77436e10	+	3.91118e10i	−0.119705	+	0.0691119i	0.438952	+	0.898511i	$0.355350\pi$
$410$	−4.70384e10	+	8.14729e10i	−0.0822101	+	0.142392i
$411$	−8.10802e8	+	1.40435e9i	−0.00140161	+	0.00242766i
$412$	8.69986e10	+	5.02287e10i	0.148756	+	0.0858844i
$413$			6.36167e10i			0.107596i
$414$	−1.34561e11	+	2.33066e11i	−0.225122	+	0.389922i
$415$			4.53494e10i			0.0750508i
$416$	−5.27140e10	−	9.13033e10i	−0.0862990	−	0.149474i
$417$	−7.62082e11			−1.23421
$418$	9.23048e11			1.47887
$419$	−7.30671e10	−	1.26556e11i	−0.115813	−	0.200595i	0.802291	−	0.596933i	$-0.203614\pi$
$419$	−7.30671e10	−	1.26556e11i	−0.115813	−	0.200595i	−0.918105	+	0.396338i	$0.870281\pi$
$420$	−5.33402e10	−	3.07960e10i	−0.0836437	−	0.0482917i
$421$			5.43956e11i			0.843906i	0.906618	+	0.421953i	$0.138655\pi$
$421$			5.43956e11i			0.843906i	−0.906618	+	0.421953i	$0.861345\pi$
$422$	1.85514e11	−	1.07106e11i	0.284754	−	0.164403i
$423$	9.57249e11	+	1.65800e12i	1.45376	+	2.51799i
$424$	−5.04880e11	+	2.91493e11i	−0.758651	+	0.438007i
$425$	1.09683e12	+	6.33258e11i	1.63076	+	0.941522i
$426$	−1.10581e12	−	6.38440e11i	−1.62681	−	0.939240i
$427$	−1.03945e12	+	6.00124e11i	−1.51313	+	0.873606i
$428$	−5.39896e10	−	9.35127e10i	−0.0777702	−	0.134702i
$429$	−3.65322e11	+	2.10919e11i	−0.520737	+	0.300648i
$430$			5.04496e10i			0.0711622i
$431$	1.12915e11	+	6.51913e10i	0.157617	+	0.0910002i	0.576734	−	0.816932i	$-0.304327\pi$
$431$	1.12915e11	+	6.51913e10i	0.157617	+	0.0910002i	−0.419117	+	0.907932i	$0.637660\pi$
$432$	4.42807e11	+	7.66964e11i	0.611699	+	1.05949i
$433$	1.02311e12			1.39871			0.699356	−	0.714774i	$-0.253470\pi$
$433$	1.02311e12			1.39871			0.699356	+	0.714774i	$0.253470\pi$
$434$	1.41632e11			0.191627
$435$	1.40376e11	+	2.43138e11i	0.187971	+	0.325576i
$436$		−	1.68012e10i		−	0.0222664i
$437$	−1.86837e11	+	3.23612e11i	−0.245074	+	0.424481i
$438$		−	2.94854e11i		−	0.382801i
$439$	−1.16942e12	−	6.75167e11i	−1.50273	−	0.867602i	−0.999995	−	0.00316272i	$-0.998993\pi$
$439$	−1.16942e12	−	6.75167e11i	−1.50273	−	0.867602i	−0.502736	−	0.864440i	$-0.667673\pi$
$440$	7.19221e10	−	1.24573e11i	0.0914799	−	0.158448i
$441$	−5.52158e11	+	9.56366e11i	−0.695168	+	1.20407i
$442$	−4.71067e11	+	2.71971e11i	−0.587060	+	0.338939i
$443$	−1.42435e11			−0.175711			−0.0878556	−	0.996133i	$-0.528001\pi$
$443$	−1.42435e11			−0.175711			−0.0878556	+	0.996133i	$0.528001\pi$
$444$	2.42642e11	−	2.02768e11i	0.296308	−	0.247615i
$445$	−2.26026e11			−0.273236
$446$	9.91385e11	−	5.72377e11i	1.18641	−	0.684975i
$447$	8.59478e11	−	1.48866e12i	1.01824	−	1.76365i
$448$	6.18937e11	−	1.07203e12i	0.725931	−	1.25735i
$449$	8.43716e11	+	4.87119e11i	0.979687	+	0.565623i	0.902176	−	0.431369i	$-0.141969\pi$
$449$	8.43716e11	+	4.87119e11i	0.979687	+	0.565623i	0.0775117	+	0.996991i	$0.475302\pi$
$450$		−	1.45917e12i		−	1.67746i
$451$	3.78806e11	−	6.56112e11i	0.431144	−	0.746764i
$452$		−	3.02905e11i		−	0.341337i
$453$	−5.26348e11	−	9.11661e11i	−0.587261	−	1.01717i
$454$	1.00493e12			1.11016
$455$	−9.00031e10			−0.0984479
$456$	1.62799e12	+	2.81976e12i	1.76324	+	3.05401i
$457$	−7.29182e11	−	4.20994e11i	−0.782012	−	0.451495i	0.0551312	−	0.998479i	$-0.482442\pi$
$457$	−7.29182e11	−	4.20994e11i	−0.782012	−	0.451495i	−0.837143	+	0.546985i	$0.815776\pi$
$458$			7.44186e11i			0.790290i
$459$	−2.71255e12	+	1.56609e12i	−2.85246	+	1.64687i
$460$	5.32489e9	+	9.22297e9i	0.00554498	+	0.00960419i
$461$	−3.42317e11	+	1.97637e11i	−0.353000	+	0.203804i	−0.666006	−	0.745947i	$-0.731997\pi$
$461$	−3.42317e11	+	1.97637e11i	−0.353000	+	0.203804i	0.313006	+	0.949751i	$0.398664\pi$
$462$	−1.48966e12	−	8.60056e11i	−1.52124	−	0.878290i
$463$	1.62396e12	+	9.37591e11i	1.64233	+	0.948198i	0.980004	+	0.198980i	$0.0637628\pi$
$463$	1.62396e12	+	9.37591e11i	1.64233	+	0.948198i	0.662323	+	0.749218i	$0.269570\pi$
$464$	−7.13875e11	+	4.12156e11i	−0.714976	+	0.412792i
$465$	2.77764e10	+	4.81101e10i	0.0275510	+	0.0477197i
$466$	−5.64726e11	+	3.26045e11i	−0.554755	+	0.320288i
$467$			3.78838e11i			0.368576i	0.982872	+	0.184288i	$0.0589979\pi$
$467$			3.78838e11i			0.368576i	−0.982872	+	0.184288i	$0.941002\pi$
$468$	−1.56499e11	−	9.03546e10i	−0.150801	−	0.0870651i
$469$	−1.26972e11	−	2.19922e11i	−0.121180	−	0.209890i
$470$	−2.62733e11			−0.248356
$471$	1.50114e12			1.40549
$472$	−4.79232e10	−	8.30054e10i	−0.0444433	−	0.0769781i
$473$		−	4.06277e11i		−	0.373204i
$474$	8.48963e11	−	1.47045e12i	0.772478	−	1.33797i
$475$		−	2.02606e12i		−	1.82613i
$476$	5.53893e11	+	3.19790e11i	0.494532	+	0.285518i
$477$	−9.07893e11	+	1.57252e12i	−0.802975	+	1.39079i
$478$	3.65370e11	−	6.32840e11i	0.320116	−	0.554458i
$479$	6.30579e11	−	3.64065e11i	0.547305	−	0.315987i	−0.200729	−	0.979647i	$-0.564331\pi$
$479$	6.30579e11	−	3.64065e11i	0.547305	−	0.315987i	0.748034	+	0.663660i	$0.230998\pi$
$480$	1.68621e11			0.144986
$481$	1.58915e11	−	4.33889e11i	0.135367	−	0.369594i
$482$	2.90694e11			0.245315
$483$	6.03055e11	−	3.48174e11i	0.504191	−	0.291095i
$484$	2.91777e10	−	5.05373e10i	0.0241683	−	0.0418608i
$485$	−6.91748e10	+	1.19814e11i	−0.0567688	+	0.0983265i
$486$	−7.48710e10	−	4.32268e10i	−0.0608766	−	0.0351471i
$487$		−	3.16731e11i		−	0.255159i	−0.991828	−	0.127579i	$-0.959279\pi$
$487$		−	3.16731e11i		−	0.255159i	0.991828	−	0.127579i	$-0.0407207\pi$
$488$	9.04161e11	−	1.56605e12i	0.721700	−	1.25002i
$489$			2.58713e12i			2.04611i
$490$	−7.57746e10	−	1.31245e11i	−0.0593801	−	0.102849i
$491$	−1.87699e12			−1.45745			−0.728727	−	0.684805i	$-0.759887\pi$
$491$	−1.87699e12			−1.45745			−0.728727	+	0.684805i	$0.759887\pi$
$492$	4.88746e11			0.376045
$493$	−1.45769e12	−	2.52479e12i	−1.11135	−	1.92492i
$494$	7.53571e11	+	4.35075e11i	0.569316	+	0.328695i
$495$		−	4.48022e11i		−	0.335410i
$496$	−1.41255e11	+	8.15538e10i	−0.104794	+	0.0605030i
$497$	1.09697e12	+	1.90001e12i	0.806478	+	1.39686i
$498$	−7.07573e11	+	4.08518e11i	−0.515513	+	0.297631i
$499$	−2.19555e12	−	1.26760e12i	−1.58522	−	0.915228i	−0.994079	−	0.108662i	$-0.965343\pi$
$499$	−2.19555e12	−	1.26760e12i	−1.58522	−	0.915228i	−0.591144	−	0.806566i	$-0.701323\pi$
$500$	−1.01920e11	−	5.88437e10i	−0.0729282	−	0.0421051i
$501$	−5.99676e11	+	3.46223e11i	−0.425253	+	0.245520i
$502$	9.82502e11	+	1.70174e12i	0.690505	+	1.19599i
$503$	2.03493e12	−	1.17487e12i	1.41740	−	0.818337i	0.421331	−	0.906907i	$-0.361563\pi$
$503$	2.03493e12	−	1.17487e12i	1.41740	−	0.818337i	0.996070	+	0.0885699i	$0.0282297\pi$
$504$		−	4.02915e12i		−	2.78148i
$505$	−2.71270e11	−	1.56618e11i	−0.185605	−	0.107159i
$506$	1.48711e11	+	2.57575e11i	0.100848	+	0.174673i
$507$	2.16916e12			1.45800
$508$	−2.76764e11			−0.184384
$509$	1.25415e10	+	2.17225e10i	0.00828170	+	0.0143443i	0.870137	−	0.492811i	$-0.164030\pi$
$509$	1.25415e10	+	2.17225e10i	0.00828170	+	0.0143443i	−0.861855	+	0.507155i	$0.830697\pi$
$510$		−	8.69977e11i		−	0.569432i
$511$	−2.53311e11	+	4.38747e11i	−0.164346	+	0.284656i
$512$			1.71240e12i			1.10126i
$513$	4.33929e12	+	2.50529e12i	2.76624	+	1.59709i
$514$	−1.20110e12	+	2.08036e12i	−0.759005	+	1.31464i
$515$	−1.17393e11	+	2.03330e11i	−0.0735374	+	0.127370i
$516$	2.26981e11	−	1.31047e11i	0.140950	−	0.0813775i
$517$	2.11582e12			1.30248
$518$	1.85622e12	−	3.23440e11i	1.13278	−	0.197383i
$519$	−3.58847e12			−2.17098
$520$	1.17434e11	−	6.78004e10i	0.0704332	−	0.0406647i
$521$	−1.07862e12	+	1.86823e12i	−0.641358	+	1.11086i	0.343772	+	0.939053i	$0.388295\pi$
$521$	−1.07862e12	+	1.86823e12i	−0.641358	+	1.11086i	−0.985130	+	0.171811i	$0.945038\pi$
$522$	−1.67942e12	+	2.90885e12i	−0.990018	+	1.71476i
$523$	1.18340e12	+	6.83239e11i	0.691632	+	0.399314i	0.804223	−	0.594327i	$-0.202582\pi$
$523$	1.18340e12	+	6.83239e11i	0.691632	+	0.399314i	−0.112591	+	0.993641i	$0.535915\pi$
$524$			2.80968e11i			0.162805i
$525$	−1.88780e12	+	3.26976e12i	−1.08452	+	1.87845i
$526$			7.85762e11i			0.447564i
$527$	−2.88434e11	−	4.99582e11i	−0.162892	−	0.282137i
$528$	1.98093e12			1.10922
$529$	1.68075e12			0.933151
$530$	−1.24593e11	−	2.15802e11i	−0.0685888	−	0.118799i
$531$	−2.58531e11	−	1.49263e11i	−0.141120	−	0.0814756i
$532$		−	1.02314e12i		−	0.553776i
$533$	6.18511e11	−	3.57097e11i	0.331952	−	0.191652i
$534$	−2.03609e12	−	3.52662e12i	−1.08358	−	1.87682i
$535$	2.18554e11	−	1.26182e11i	0.115337	−	0.0665897i
$536$	3.31340e11	+	1.91299e11i	0.173393	+	0.100109i
$537$	2.08399e12	+	1.20319e12i	1.08146	+	0.624382i
$538$	8.07947e11	−	4.66469e11i	0.415779	−	0.240050i
$539$	6.10222e11	+	1.05694e12i	0.311414	+	0.539385i
$540$	1.23670e11	−	7.14010e10i	0.0625883	−	0.0361354i
$541$		−	3.65085e12i		−	1.83234i	−0.400790	−	0.916170i	$-0.631264\pi$
$541$		−	3.65085e12i		−	1.83234i	0.400790	−	0.916170i	$-0.368736\pi$
$542$	−7.05818e11	−	4.07504e11i	−0.351314	−	0.202831i
$543$	−2.89169e12	−	5.00856e12i	−1.42742	−	2.47237i
$544$	−1.75098e12			−0.857209
$545$	3.92671e10			0.0190653
$546$	−8.10768e11	−	1.40429e12i	−0.390418	−	0.676224i
$547$		−	9.49588e11i		−	0.453516i	−0.973951	−	0.226758i	$-0.927187\pi$
$547$		−	9.49588e11i		−	0.453516i	0.973951	−	0.226758i	$-0.0728126\pi$
$548$	−3.83861e8	+	6.64866e8i	−0.000181828	+	0.000314936i
$549$		−	5.63226e12i		−	2.64611i
$550$	−1.39657e12	−	8.06309e11i	−0.650774	−	0.375724i
$551$	−2.33188e12	+	4.03893e12i	−1.07776	+	1.86674i
$552$	−5.24567e11	+	9.08577e11i	−0.240478	+	0.416520i
$553$	−2.52654e12	+	1.45870e12i	−1.14885	+	0.663287i
$554$	−9.18596e10			−0.0414315
$555$	4.73902e11	+	5.67095e11i	0.212017	+	0.253710i
$556$	−3.60795e11			−0.160112
$557$	1.24615e12	−	7.19466e11i	0.548558	−	0.316710i	−0.199982	−	0.979800i	$-0.564088\pi$
$557$	1.24615e12	−	7.19466e11i	0.548558	−	0.316710i	0.748540	+	0.663090i	$0.230755\pi$
$558$	−3.32310e11	+	5.75577e11i	−0.145107	+	0.251333i
$559$	1.91497e11	−	3.31682e11i	0.0829485	−	0.143671i
$560$	3.66026e11	+	2.11325e11i	0.157277	+	0.0908042i
$561$			7.00603e12i			2.98634i
$562$	1.75451e12	−	3.03889e12i	0.741893	−	1.28500i
$563$		−	3.11463e12i		−	1.30653i	−0.757131	−	0.653264i	$-0.773399\pi$
$563$		−	3.11463e12i		−	1.30653i	0.757131	−	0.653264i	$-0.226601\pi$
$564$	6.82473e11	+	1.18208e12i	0.284007	+	0.491915i
$565$	7.07938e11			0.292265
$566$	−3.62798e12			−1.48591
$567$	−1.49417e12	−	2.58799e12i	−0.607124	−	1.05157i
$568$	−2.86260e12	−	1.65273e12i	−1.15397	−	0.666244i
$569$			6.93991e11i			0.277555i	0.990324	+	0.138777i	$0.0443172\pi$
$569$			6.93991e11i			0.277555i	−0.990324	+	0.138777i	$0.955683\pi$
$570$	−1.20526e12	+	6.95856e11i	−0.478237	+	0.276110i
$571$	−9.92035e11	−	1.71825e12i	−0.390539	−	0.676433i	0.601982	−	0.798510i	$-0.294378\pi$
$571$	−9.92035e11	−	1.71825e12i	−0.390539	−	0.676433i	−0.992521	+	0.122077i	$0.961045\pi$
$572$	−1.72956e11	+	9.98561e10i	−0.0675543	+	0.0390025i
$573$	1.14900e12	+	6.63377e11i	0.445272	+	0.257078i
$574$	2.52208e12	+	1.45612e12i	0.969739	+	0.559879i
$575$	5.65369e11	−	3.26416e11i	0.215688	−	0.124528i
$576$	2.90441e12	+	5.03059e12i	1.09940	+	1.90422i
$577$	−2.17973e12	+	1.25847e12i	−0.818674	+	0.472662i	−0.849959	−	0.526849i	$-0.823373\pi$
$577$	−2.17973e12	+	1.25847e12i	−0.818674	+	0.472662i	0.0312848	+	0.999511i	$0.490040\pi$
$578$			6.66992e12i			2.48568i
$579$	−3.16714e9	−	1.82855e9i	−0.00117115	−	0.000676165i
$580$	6.64587e10	+	1.15110e11i	0.0243852	+	0.0422364i
$581$	1.40384e12			0.511122
$582$	−2.49257e12			−0.900520
$583$	1.00337e12	+	1.73788e12i	0.359708	+	0.623033i
$584$		−	7.63287e11i		−	0.271538i
$585$	2.11173e11	−	3.65763e11i	0.0745483	−	0.129121i
$586$		−	1.11724e12i		−	0.391387i
$587$	−3.14605e11	−	1.81637e11i	−0.109369	−	0.0631442i	0.444318	−	0.895869i	$-0.353446\pi$
$587$	−3.14605e11	−	1.81637e11i	−0.109369	−	0.0631442i	−0.553687	+	0.832725i	$0.686779\pi$
$588$	−3.93662e11	+	6.81843e11i	−0.135808	+	0.235227i
$589$	−4.61411e11	+	7.99188e11i	−0.157968	+	0.273609i
$590$	3.54792e10	−	2.04839e10i	0.0120542	−	0.00695951i
$591$	2.70327e10			0.00911476
$592$	−1.66504e12	+	1.39142e12i	−0.557156	+	0.465597i
$593$	2.85038e12			0.946578			0.473289	−	0.880907i	$-0.343067\pi$
$593$	2.85038e12			0.946578			0.473289	+	0.880907i	$0.343067\pi$
$594$	3.45381e12	−	1.99406e12i	1.13831	−	0.657201i
$595$	−7.47401e11	+	1.29454e12i	−0.244471	+	0.423436i
$596$	4.06906e11	−	7.04782e11i	0.132095	−	0.228795i
$597$	−5.23301e12	−	3.02128e12i	−1.68604	−	0.973434i
$598$			2.80377e11i			0.0896576i
$599$	−2.04215e12	+	3.53711e12i	−0.648138	+	1.12261i	0.335430	+	0.942065i	$0.391119\pi$
$599$	−2.04215e12	+	3.53711e12i	−0.648138	+	1.12261i	−0.983567	+	0.180542i	$0.942215\pi$
$600$		−	5.68839e12i		−	1.79188i
$601$	−1.39555e12	−	2.41717e12i	−0.436326	−	0.755739i	0.561077	−	0.827764i	$-0.310387\pi$
$601$	−1.39555e12	−	2.41717e12i	−0.436326	−	0.755739i	−0.997403	+	0.0720250i	$0.977054\pi$
$602$	1.56172e12			0.484639
$603$	1.19166e12			0.367048
$604$	−2.49191e11	−	4.31611e11i	−0.0761843	−	0.131955i
$605$	1.18114e11	+	6.81930e10i	0.0358427	+	0.0206938i
$606$		−	5.64339e12i		−	1.69986i
$607$	2.91306e11	−	1.68185e11i	0.0870964	−	0.0502851i	−0.455819	−	0.890072i	$-0.650654\pi$
$607$	2.91306e11	−	1.68185e11i	0.0870964	−	0.0502851i	0.542916	+	0.839787i	$0.317320\pi$
$608$	1.40053e12	+	2.42580e12i	0.415650	+	0.719926i
$609$	7.52660e12	−	4.34548e12i	2.21728	−	1.28015i
$610$	6.69381e11	+	3.86467e11i	0.195744	+	0.113013i
$611$	1.72735e12	+	9.97284e11i	0.501411	+	0.289490i
$612$	−2.59919e12	+	1.50064e12i	−0.748955	+	0.432410i
$613$	−6.65701e11	−	1.15303e12i	−0.190418	−	0.329813i	0.754971	−	0.655758i	$-0.227651\pi$
$613$	−6.65701e11	−	1.15303e12i	−0.190418	−	0.329813i	−0.945389	+	0.325945i	$0.894318\pi$
$614$	−3.88607e12	+	2.24362e12i	−1.10345	+	0.637078i
$615$			1.14228e12i			0.321984i
$616$	−3.85628e12	−	2.22642e12i	−1.07908	−	0.623009i
$617$	3.27080e11	+	5.66520e11i	0.0908597	+	0.157374i	0.907873	−	0.419245i	$-0.137705\pi$
$617$	3.27080e11	+	5.66520e11i	0.0908597	+	0.157374i	−0.817013	+	0.576619i	$0.804372\pi$
$618$	−4.22999e12			−1.16652
$619$	2.34596e12			0.642263			0.321131	−	0.947035i	$-0.395937\pi$
$619$	2.34596e12			0.642263			0.321131	+	0.947035i	$0.395937\pi$
$620$	1.31503e10	+	2.27769e10i	0.00357414	+	0.00619060i
$621$			1.61450e12i			0.435637i
$622$	−1.33509e12	+	2.31245e12i	−0.357647	+	0.619463i
$623$			6.99687e12i			1.86083i
$624$	1.61722e12	+	9.33705e11i	0.427011	+	0.246535i
$625$	−1.69977e12	+	2.94409e12i	−0.445585	+	0.771776i
$626$	1.20167e12	−	2.08135e12i	0.312751	−	0.541701i
$627$	9.70609e12	−	5.60381e12i	2.50807	−	1.44804i
$628$	7.10691e11			0.182332
$629$	−4.92107e12	−	5.88880e12i	−1.25352	−	1.50003i
$630$	1.72219e12			0.435560
$631$	4.93020e11	−	2.84645e11i	0.123803	−	0.0714779i	−0.436819	−	0.899549i	$-0.643895\pi$
$631$	4.93020e11	−	2.84645e11i	0.123803	−	0.0714779i	0.560623	+	0.828071i	$0.310562\pi$
$632$	2.19770e12	−	3.80654e12i	0.547952	−	0.949081i
$633$	1.30048e12	−	2.25250e12i	0.321949	−	0.557633i
$634$	2.68705e12	+	1.55137e12i	0.660501	+	0.381340i
$635$		−	6.46843e11i		−	0.157876i
$636$	−6.47284e11	+	1.12113e12i	−0.156869	+	0.271706i
$637$			1.15050e12i			0.276860i
$638$	1.85603e12	+	3.21474e12i	0.443498	+	0.768161i
$639$	−1.02953e13			−2.44278
$640$	−4.40488e11			−0.103783
$641$	1.49988e12	+	2.59787e12i	0.350910	+	0.607794i	0.986409	−	0.164307i	$-0.0525389\pi$
$641$	1.49988e12	+	2.59787e12i	0.350910	+	0.607794i	−0.635499	+	0.772102i	$0.719206\pi$
$642$	3.93757e12	+	2.27336e12i	0.914788	+	0.528153i
$643$		−	3.24482e12i		−	0.748585i	−0.927311	−	0.374293i	$-0.877886\pi$
$643$		−	3.24482e12i		−	0.748585i	0.927311	−	0.374293i	$-0.122114\pi$
$644$	2.85507e11	−	1.64837e11i	0.0654078	−	0.0377632i
$645$	3.06279e11	+	5.30490e11i	0.0696784	+	0.120687i
$646$	1.25156e13	−	7.22587e12i	2.82751	−	1.63246i
$647$	3.65084e12	+	2.10781e12i	0.819074	+	0.472893i	0.850097	−	0.526626i	$-0.176543\pi$
$647$	3.65084e12	+	2.10781e12i	0.819074	+	0.472893i	−0.0310231	+	0.999519i	$0.509877\pi$
$648$	3.89912e12	+	2.25116e12i	0.868718	+	0.501554i
$649$	−2.85718e11	+	1.64959e11i	−0.0632174	+	0.0364986i
$650$	−7.60101e11	−	1.31653e12i	−0.167017	−	0.289282i
$651$	1.48930e12	−	8.59846e11i	0.324988	−	0.187632i
$652$			1.22483e12i			0.265438i
$653$	−4.13511e12	−	2.38741e12i	−0.889975	−	0.513828i	−0.0160409	−	0.999871i	$-0.505106\pi$
$653$	−4.13511e12	−	2.38741e12i	−0.889975	−	0.513828i	−0.873934	+	0.486044i	$0.838440\pi$
$654$	3.53726e11	+	6.12672e11i	0.0756080	+	0.130957i
$655$	−6.56669e11			−0.139399
$656$	−3.35383e12			−0.707088
$657$	−1.18868e12	−	2.05885e12i	−0.248898	−	0.431103i
$658$			8.13317e12i			1.69139i
$659$	1.71763e12	−	2.97503e12i	0.354769	−	0.614478i	−0.632309	−	0.774716i	$-0.717893\pi$
$659$	1.71763e12	−	2.97503e12i	0.354769	−	0.614478i	0.987078	+	0.160238i	$0.0512262\pi$
$660$		−	3.19419e11i		−	0.0655258i
$661$	5.77130e12	+	3.33206e12i	1.17589	+	0.678901i	0.955061	−	0.296411i	$-0.0957897\pi$
$661$	5.77130e12	+	3.33206e12i	1.17589	+	0.678901i	0.220831	+	0.975312i	$0.429123\pi$
$662$	1.32097e12	−	2.28799e12i	0.267321	−	0.463014i
$663$	−3.30226e12	+	5.71969e12i	−0.663744	+	1.14964i
$664$	−1.83169e12	+	1.05753e12i	−0.365675	+	0.211123i
$665$	2.39125e12			0.474163
$666$	−3.04080e12	+	8.30235e12i	−0.598899	+	1.63519i
$667$	−1.50274e12			−0.293980
$668$	−2.83907e11	+	1.63914e11i	−0.0551673	+	0.0318508i
$669$	6.94978e12	−	1.20374e13i	1.34139	−	2.32335i
$670$	−8.17675e10	+	1.41625e11i	−0.0156763	+	0.0271522i
$671$	−5.39061e12	−	3.11227e12i	−1.02656	−	0.592688i
$672$		−	5.21983e12i		−	0.987403i
$673$	−4.96219e12	+	8.59476e12i	−0.932407	+	1.61498i	−0.153212	+	0.988193i	$0.548962\pi$
$673$	−4.96219e12	+	8.59476e12i	−0.932407	+	1.61498i	−0.779194	+	0.626783i	$0.784371\pi$
$674$		−	5.85381e12i		−	1.09262i
$675$	−4.37689e12	−	7.58099e12i	−0.811518	−	1.40559i
$676$	1.02695e12			0.189143
$677$	−3.71114e12			−0.678982			−0.339491	−	0.940609i	$-0.610255\pi$
$677$	−3.71114e12			−0.678982			−0.339491	+	0.940609i	$0.610255\pi$
$678$	6.37726e12	+	1.10457e13i	1.15905	+	2.00753i
$679$	3.70897e12	+	2.14138e12i	0.669637	+	0.386615i
$680$		−	2.25210e12i		−	0.403923i
$681$	1.05671e13	−	6.10093e12i	1.88276	−	1.08701i
$682$	3.67255e11	+	6.36104e11i	0.0650036	+	0.112590i
$683$	−3.99713e12	+	2.30775e12i	−0.702838	+	0.405784i	−0.808404	−	0.588629i	$-0.799668\pi$
$683$	−3.99713e12	+	2.30775e12i	−0.702838	+	0.405784i	0.105565	+	0.994412i	$0.466335\pi$
$684$	4.15795e12	+	2.40059e12i	0.726317	+	0.419340i
$685$	−1.55390e9	−	8.97145e8i	−0.000269659	−	0.000155688i
$686$	1.71319e12	−	9.89109e11i	0.295356	−	0.170524i
$687$	4.51794e12	+	7.82531e12i	0.773812	+	1.34028i
$688$	−1.55757e12	+	8.99261e11i	−0.265032	+	0.153016i
$689$			1.89173e12i			0.319795i
$690$	−3.88355e11	−	2.24217e11i	−0.0652241	−	0.0376571i
$691$	−3.22981e11	−	5.59419e11i	−0.0538922	−	0.0933439i	0.837821	−	0.545945i	$-0.183829\pi$
$691$	−3.22981e11	−	5.59419e11i	−0.0538922	−	0.0933439i	−0.891713	+	0.452601i	$0.850496\pi$
$692$	−1.69890e12			−0.281638
$693$	−1.38690e13			−2.28426
$694$	−3.23697e12	−	5.60659e12i	−0.529689	−	0.917448i
$695$		−	8.43236e11i		−	0.137094i
$696$	−6.54700e12	+	1.13397e13i	−1.05755	+	1.83173i
$697$		−	1.18616e13i		−	1.90369i
$698$	6.54920e12	+	3.78118e12i	1.04433	+	0.602945i
$699$	−3.95883e12	+	6.85689e12i	−0.627219	+	1.08638i
$700$	−8.93746e11	+	1.54801e12i	−0.140693	+	0.243688i
$701$	5.03021e12	−	2.90419e12i	0.786783	−	0.454249i	−0.0520458	−	0.998645i	$-0.516574\pi$
$701$	5.03021e12	−	2.90419e12i	0.786783	−	0.454249i	0.838829	+	0.544395i	$0.183241\pi$
$702$	3.75956e12			0.584278
$703$	−4.22214e12	+	1.15278e13i	−0.651979	+	1.78011i
$704$	6.41967e12			0.984998
$705$	−2.76271e12	+	1.59505e12i	−0.421196	+	0.243177i
$706$	7.81064e11	−	1.35284e12i	0.118322	−	0.204940i
$707$	−4.84827e12	+	8.39744e12i	−0.729792	+	1.26404i
$708$	−1.84321e11	−	1.06418e11i	−0.0275692	−	0.0159171i
$709$			5.14409e12i			0.764540i	0.924051	+	0.382270i	$0.124858\pi$
$709$			5.14409e12i			0.764540i	−0.924051	+	0.382270i	$0.875142\pi$
$710$	7.06428e11	−	1.22357e12i	0.104329	−	0.180703i
$711$		−	1.36901e13i		−	2.00906i
$712$	−5.27082e12	−	9.12933e12i	−0.768632	−	1.33131i
$713$	−2.97349e11			−0.0430888
$714$	−2.69310e13			−3.87803
$715$	−2.33380e11	−	4.04226e11i	−0.0333954	−	0.0578425i
$716$	9.86630e11	+	5.69631e11i	0.140296	+	0.0810000i
$717$		−	8.87264e12i		−	1.25377i
$718$	−5.33660e12	+	3.08109e12i	−0.749385	+	0.432657i
$719$	−4.16947e12	−	7.22173e12i	−0.581836	−	1.00777i	−0.995262	−	0.0972314i	$-0.969001\pi$
$719$	−4.16947e12	−	7.22173e12i	−0.581836	−	1.00777i	0.413426	−	0.910538i	$-0.364332\pi$
$720$	−1.71761e12	+	9.91662e11i	−0.238192	+	0.137520i
$721$	6.29428e12	+	3.63401e12i	0.867437	+	0.500815i
$722$	−1.44503e13	−	8.34291e12i	−1.97907	−	1.14262i
$723$	3.05673e12	−	1.76480e12i	0.416039	−	0.240200i
$724$	−1.36902e12	−	2.37122e12i	−0.185177	−	0.320736i
$725$	7.05624e12	−	4.07392e12i	0.948532	−	0.547635i
$726$			2.45719e12i			0.328265i
$727$	5.40308e12	+	3.11947e12i	0.717359	+	0.414168i	0.813780	−	0.581173i	$-0.197406\pi$
$727$	5.40308e12	+	3.11947e12i	0.717359	+	0.414168i	−0.0964208	+	0.995341i	$0.530739\pi$
$728$	−2.09883e12	−	3.63528e12i	−0.276940	−	0.479675i
$729$	−8.14424e12			−1.06801
$730$	3.26253e11			0.0425209
$731$	−3.18044e12	−	5.50869e12i	−0.411964	−	0.713543i
$732$		−	4.01553e12i		−	0.516944i
$733$	8.23714e11	−	1.42672e12i	0.105392	−	0.182545i	−0.808506	−	0.588488i	$-0.799724\pi$
$733$	8.23714e11	−	1.42672e12i	0.105392	−	0.182545i	0.913898	+	0.405943i	$0.133057\pi$
$734$		−	7.99940e12i		−	1.01724i
$735$	−1.59358e12	−	9.20053e11i	−0.201410	−	0.116284i
$736$	−4.51276e11	+	7.81633e11i	−0.0566881	+	0.0981867i
$737$	6.58483e11	−	1.14053e12i	0.0822131	−	0.142397i
$738$	−1.18351e13	+	6.83297e12i	−1.46864	+	0.847922i
$739$	5.27056e12			0.650065			0.325032	−	0.945703i	$-0.394625\pi$
$739$	5.27056e12			0.650065			0.325032	+	0.945703i	$0.394625\pi$
$740$	2.24361e11	+	2.68482e11i	0.0275046	+	0.0329133i
$741$	1.05653e13			1.28736
$742$	−6.68037e12	+	3.85691e12i	−0.809064	+	0.467113i
$743$	3.35967e12	−	5.81911e12i	0.404433	−	0.700498i	−0.589823	−	0.807533i	$-0.700802\pi$
$743$	3.35967e12	−	5.81911e12i	0.404433	−	0.700498i	0.994255	+	0.107035i	$0.0341356\pi$
$744$	−1.29546e12	+	2.24381e12i	−0.155005	+	0.268477i
$745$	1.64719e12	+	9.51005e11i	0.195903	+	0.113104i
$746$			3.84919e12i			0.455035i
$747$	−3.29381e12	+	5.70505e12i	−0.387040	+	0.670373i
$748$			3.31689e12i			0.387413i
$749$	−3.90611e12	−	6.76557e12i	−0.453498	−	0.785482i
$750$	4.95550e12			0.571889
$751$	1.40656e13			1.61354			0.806768	−	0.590868i	$-0.201215\pi$
$751$	1.40656e13			1.61354			0.806768	+	0.590868i	$0.201215\pi$
$752$	−4.68320e12	−	8.11155e12i	−0.534026	−	0.924961i
$753$	2.06625e13	+	1.19295e13i	2.34210	+	1.35221i
$754$			3.49932e12i			0.394288i
$755$	1.00874e12	−	5.82399e11i	0.112985	−	0.0652318i
$756$	−2.21029e12	−	3.82834e12i	−0.246094	−	0.426248i
$757$	−8.97908e12	+	5.18407e12i	−0.993803	+	0.573772i	−0.906409	−	0.422401i	$-0.861187\pi$
$757$	−8.97908e12	+	5.18407e12i	−0.993803	+	0.573772i	−0.0873941	+	0.996174i	$0.527854\pi$
$758$	1.38606e12	+	8.00242e11i	0.152500	+	0.0880461i
$759$	3.12747e12	+	1.80565e12i	0.342062	+	0.197490i
$760$	−3.12004e12	+	1.80136e12i	−0.339234	+	0.195857i
$761$	3.89131e12	+	6.73995e12i	0.420596	+	0.728494i	0.995998	−	0.0893773i	$-0.0284877\pi$
$761$	3.89131e12	+	6.73995e12i	0.420596	+	0.728494i	−0.575402	+	0.817871i	$0.695154\pi$
$762$	1.00925e13	−	5.82690e12i	1.08443	−	0.626095i
$763$		−	1.21555e12i		−	0.129841i
$764$	5.43977e11	+	3.14065e11i	0.0577644	+	0.0333503i
$765$	−3.50724e12	−	6.07472e12i	−0.370245	−	0.641283i
$766$	5.69197e12			0.597355
$767$	−3.11012e11			−0.0324487
$768$	5.28373e12	+	9.15169e12i	0.548044	+	0.949239i
$769$			6.12220e12i			0.631305i	0.948875	+	0.315652i	$0.102223\pi$
$769$			6.12220e12i			0.631305i	−0.948875	+	0.315652i	$0.897777\pi$
$770$	9.51645e11	−	1.64830e12i	0.0975588	−	0.168977i
$771$			2.91674e13i			2.97272i
$772$	−1.49943e9	−	8.65696e8i	−0.000151932	−	8.77178e-5i
$773$	1.67132e12	−	2.89481e12i	0.168365	−	0.291616i	−0.769480	−	0.638670i	$-0.779485\pi$
$773$	1.67132e12	−	2.89481e12i	0.168365	−	0.291616i	0.937845	+	0.347054i	$0.112818\pi$
$774$	−3.66424e12	+	6.34666e12i	−0.366986	+	0.635639i
$775$	1.39623e12	−	8.06112e11i	0.139027	−	0.0802671i
$776$	−6.45249e12			−0.638778
$777$	1.75550e13	−	1.46701e13i	1.72785	−	1.44391i
$778$	5.14229e12			0.503209
$779$	−1.64329e13	+	9.48756e12i	−1.59881	+	0.923073i
$780$	1.50557e11	−	2.60772e11i	0.0145638	−	0.0252252i
$781$	−5.68895e12	+	9.85355e12i	−0.547145	+	0.947683i
$782$	4.03273e12	+	2.32830e12i	0.385629	+	0.222643i
$783$			2.01502e13i			1.91580i
$784$	2.70135e12	−	4.67888e12i	0.255364	−	0.442303i
$785$			1.66100e12i			0.156119i
$786$	−5.91542e12	−	1.02458e13i	−0.552820	−	0.957513i
$787$	1.86123e10			0.00172947			0.000864736	−	1.00000i	$-0.499725\pi$
$787$	1.86123e10			0.00172947			0.000864736		1.00000i	$0.499725\pi$
$788$	1.27982e10			0.00118244
$789$	4.77035e12	+	8.26249e12i	0.438232	+	0.759040i
$790$	1.62704e12	+	9.39370e11i	0.148619	+	0.0858054i
$791$		−	2.19149e13i		−	1.99043i
$792$	1.80959e13	−	1.04477e13i	1.63424	−	0.943531i
$793$	−2.93391e12	−	5.08168e12i	−0.263462	−	0.456329i
$794$	1.28200e13	−	7.40164e12i	1.14471	−	0.660900i
$795$	−2.62026e12	−	1.51281e12i	−0.232644	−	0.134317i
$796$	−2.47748e12	−	1.43038e12i	−0.218727	−	0.126282i
$797$	7.47420e11	−	4.31523e11i	0.0656149	−	0.0378828i	−0.466834	−	0.884345i	$-0.654605\pi$
$797$	7.47420e11	−	4.31523e11i	0.0656149	−	0.0378828i	0.532449	+	0.846462i	$0.321272\pi$
$798$	2.15409e13	+	3.73100e13i	1.88040	+	3.25696i
$799$	2.86884e13	−	1.65632e13i	2.49026	−	1.43775i
$800$		−	4.89363e12i		−	0.422402i
$801$	−2.84345e13	−	1.64167e13i	−2.44062	−	1.40909i
$802$	−2.51417e12	−	4.35466e12i	−0.214590	−	0.371681i
$803$	−2.62736e12			−0.222997
$804$	8.49593e11			0.0717065
$805$	3.85252e11	+	6.67275e11i	0.0323343	+	0.0560046i
$806$			6.92416e11i			0.0577909i
$807$	5.66385e12	−	9.81007e12i	0.470090	−	0.814219i
$808$		−	1.46090e13i		−	1.20579i
$809$	−1.24002e13	−	7.15924e12i	−1.01779	−	0.587623i	−0.104329	−	0.994543i	$-0.533270\pi$
$809$	−1.24002e13	−	7.15924e12i	−1.01779	−	0.587623i	−0.913464	+	0.406920i	$0.866603\pi$
$810$	−9.62216e11	+	1.66661e12i	−0.0785399	+	0.136035i
$811$	−8.52977e11	+	1.47740e12i	−0.0692379	+	0.119924i	−0.898566	−	0.438838i	$-0.855390\pi$
$811$	−8.52977e11	+	1.47740e12i	−0.0692379	+	0.119924i	0.829328	+	0.558762i	$0.188723\pi$
$812$	3.56334e12	−	2.05730e12i	0.287644	−	0.166071i
$813$	−9.89581e12			−0.794408
$814$	6.26586e12	+	7.49803e12i	0.500231	+	0.598601i
$815$	−2.86263e12			−0.227277
$816$	2.68594e13	−	1.55073e13i	2.12076	−	1.22442i
$817$	−5.08779e12	+	8.81231e12i	−0.399512	+	0.691975i
$818$	7.79695e11	−	1.35047e12i	0.0608884	−	0.105462i
$819$	−1.13226e13	−	6.53709e12i	−0.879362	−	0.507700i
$820$			5.40793e11i			0.0417704i
$821$	−9.35275e12	+	1.61994e13i	−0.718448	+	1.24439i	0.243167	+	0.969984i	$0.421814\pi$
$821$	−9.35275e12	+	1.61994e13i	−0.718448	+	1.24439i	−0.961615	+	0.274404i	$0.911520\pi$
$822$		−	3.23267e10i		−	0.00246967i
$823$	7.41502e11	+	1.28432e12i	0.0563395	+	0.0975829i	0.892820	−	0.450414i	$-0.148724\pi$
$823$	7.41502e11	+	1.28432e12i	0.0563395	+	0.0975829i	−0.836480	+	0.547997i	$0.815390\pi$
$824$	−1.09502e13			−0.827461
$825$	−1.95804e13			−1.47156
$826$	−6.34100e11	−	1.09829e12i	−0.0473966	−	0.0820934i
$827$	4.94462e12	+	2.85478e12i	0.367585	+	0.212225i	0.672403	−	0.740185i	$-0.265262\pi$
$827$	4.94462e12	+	2.85478e12i	0.367585	+	0.212225i	−0.304818	+	0.952411i	$0.598596\pi$
$828$			1.54702e12i			0.114383i
$829$	−1.84885e13	+	1.06743e13i	−1.35959	+	0.784957i	−0.989568	−	0.144068i	$-0.953982\pi$
$829$	−1.84885e13	+	1.06743e13i	−1.35959	+	0.784957i	−0.370018	+	0.929025i	$0.620648\pi$
$830$	−4.52021e11	−	7.82924e11i	−0.0330603	−	0.0572622i
$831$	−9.65928e11	+	5.57679e11i	−0.0702651	+	0.0405676i
$832$	5.24098e12	+	3.02588e12i	0.379191	+	0.218926i
$833$	1.65480e13	+	9.55396e12i	1.19081	+	0.687513i
$834$	1.31568e13	−	7.59606e12i	0.941676	−	0.543677i
$835$	−3.83093e11	−	6.63536e11i	−0.0272719	−	0.0472362i
$836$	4.59519e12	−	2.65303e12i	0.325368	−	0.187851i
$837$			3.98714e12i			0.280800i
$838$	2.52290e12	+	1.45659e12i	0.176726	+	0.102033i
$839$	7.08233e12	+	1.22670e13i	0.493455	+	0.854689i	0.999972	−	0.00754142i	$-0.00240053\pi$
$839$	7.08233e12	+	1.22670e13i	0.493455	+	0.854689i	−0.506517	+	0.862230i	$0.669067\pi$
$840$	6.71371e12			0.465271
$841$	−4.24823e12			−0.292837
$842$	−5.42188e12	−	9.39098e12i	−0.371746	−	0.643882i
$843$		−	4.26063e13i		−	2.90569i
$844$	6.15692e11	−	1.06641e12i	0.0417659	−	0.0723407i
$845$			2.40016e12i			0.161951i
$846$	−3.30524e13	−	1.90828e13i	−2.21838	−	1.28078i
$847$	2.11098e12	−	3.65633e12i	0.140932	−	0.244101i
$848$	4.44174e12	−	7.69331e12i	0.294966	−	0.510895i
$849$	−3.81492e13	+	2.20254e13i	−2.52000	+	1.45492i
$850$	−2.52480e13			−1.65898
$851$	−3.89703e12	+	6.79046e11i	−0.254713	+	0.0443830i
$852$	−7.34004e12			−0.477222
$853$	1.45007e13	−	8.37199e12i	0.937818	−	0.541449i	0.0485422	−	0.998821i	$-0.484542\pi$
$853$	1.45007e13	−	8.37199e12i	0.937818	−	0.541449i	0.889276	+	0.457372i	$0.151209\pi$
$854$	1.19635e13	−	2.07214e13i	0.769658	−	1.33309i
$855$	−5.61057e12	+	9.71780e12i	−0.359054	+	0.621900i
$856$	1.01932e13	+	5.88503e12i	0.648899	+	0.374642i
$857$			9.38124e11i			0.0594082i	0.999559	+	0.0297041i	$0.00945650\pi$
$857$			9.38124e11i			0.0594082i	−0.999559	+	0.0297041i	$0.990543\pi$
$858$	4.20468e12	−	7.28271e12i	0.264874	−	0.458776i
$859$		−	3.02976e12i		−	0.189863i	−0.995484	−	0.0949313i	$-0.969737\pi$
$859$		−	3.02976e12i		−	0.189863i	0.995484	−	0.0949313i	$-0.0302631\pi$
$860$	1.45003e11	+	2.51152e11i	0.00903926	+	0.0156565i
$861$	3.53604e13			2.19282
$862$	−2.59918e12			−0.160344
$863$	8.80284e12	+	1.52470e13i	0.540224	+	0.935696i	0.998891	+	0.0470873i	$0.0149939\pi$
$863$	8.80284e12	+	1.52470e13i	0.540224	+	0.935696i	−0.458667	+	0.888608i	$0.651673\pi$
$864$	1.04809e13	+	6.05113e12i	0.639861	+	0.369424i
$865$		−	3.97061e12i		−	0.241149i
$866$	−1.76633e13	+	1.01979e13i	−1.06719	+	0.616141i
$867$	4.04930e13	+	7.01359e13i	2.43385	+	4.21555i
$868$	7.05083e11	−	4.07080e11i	0.0421601	−	0.0243411i
$869$	−1.31027e13	−	7.56486e12i	−0.779422	−	0.449999i
$870$	−4.84697e12	−	2.79840e12i	−0.286836	−	0.165605i
$871$	1.07516e12	−	6.20747e11i	0.0632985	−	0.0365454i
$872$	9.15689e11	+	1.58602e12i	0.0536320	+	0.0928933i
$873$	−1.74046e13	+	1.00486e13i	−1.01415	+	0.585518i
$874$		−	7.44922e12i		−	0.431826i
$875$	−7.37385e12	−	4.25730e12i	−0.425264	−	0.245526i
$876$	−8.47472e11	−	1.46786e12i	−0.0486247	−	0.0842204i
$877$	5.17368e12			0.295326			0.147663	−	0.989038i	$-0.452825\pi$
$877$	5.17368e12			0.295326			0.147663	+	0.989038i	$0.452825\pi$
$878$	2.69189e13			1.52874
$879$	−6.78274e12	−	1.17481e13i	−0.383226	−	0.663768i
$880$			2.19189e12i			0.123210i
$881$	−6.96160e12	+	1.20578e13i	−0.389329	+	0.674338i	−0.992359	−	0.123380i	$-0.960627\pi$
$881$	−6.96160e12	+	1.20578e13i	−0.389329	+	0.674338i	0.603030	+	0.797718i	$0.293960\pi$
$882$		−	2.20146e13i		−	1.22490i
$883$	9.38314e12	+	5.41736e12i	0.519428	+	0.299892i	0.736701	−	0.676219i	$-0.236383\pi$
$883$	9.38314e12	+	5.41736e12i	0.519428	+	0.299892i	−0.217273	+	0.976111i	$0.569716\pi$
$884$	−1.56340e12	+	2.70789e12i	−0.0861064	+	0.149141i
$885$	2.48715e11	−	4.30787e11i	0.0136288	−	0.0236058i
$886$	2.45903e12	−	1.41972e12i	0.134064	−	0.0774018i
$887$	9.34329e11			0.0506808			0.0253404	−	0.999679i	$-0.491933\pi$
$887$	9.34329e11			0.0506808			0.0253404	+	0.999679i	$0.491933\pi$
$888$	−1.18541e13	+	3.23656e13i	−0.639751	+	1.74673i
$889$	−2.00237e13			−1.07519
$890$	3.90217e12	−	2.25292e12i	0.208474	−	0.120362i
$891$	7.74885e12	−	1.34214e13i	0.411896	−	0.713425i
$892$	3.29026e12	−	5.69890e12i	0.174016	−	0.301404i
$893$	−4.58931e13	−	2.64964e13i	−2.41499	−	1.39430i
$894$			3.42674e13i			1.79417i
$895$	−1.33132e12	+	2.30591e12i	−0.0693552	+	0.120127i
$896$			1.36358e13i			0.706795i
$897$	1.70217e12	+	2.94824e12i	0.0877882	+	0.152054i
$898$	−1.94215e13			−0.996641
$899$	−3.71115e12			−0.189492
$900$	−4.19397e12	−	7.26417e12i	−0.213076	−	0.369058i
$901$	2.72092e13	+	1.57092e13i	1.37548	+	0.794133i
$902$			1.51030e13i			0.759686i
$903$	1.64219e13	−	9.48117e12i	0.821917	−	0.474534i
$904$	1.65088e13	+	2.85940e13i	0.822161	+	1.42403i
$905$	5.54192e12	−	3.19963e12i	0.274626	−	0.158556i
$906$	1.81740e13	+	1.04928e13i	0.896135	+	0.517384i
$907$	−3.57519e12	−	2.06414e12i	−0.175415	−	0.101276i	0.409722	−	0.912211i	$-0.365626\pi$
$907$	−3.57519e12	−	2.06414e12i	−0.175415	−	0.101276i	−0.585137	+	0.810935i	$0.698959\pi$
$908$	5.00283e12	−	2.88838e12i	0.244247	−	0.141016i
$909$	−2.27509e13	−	3.94057e13i	−1.10525	−	1.91435i
$910$	1.55384e12	−	8.97107e11i	0.0751136	−	0.0433669i
$911$		−	1.68182e13i		−	0.808995i	−0.914539	−	0.404498i	$-0.867446\pi$
$911$		−	1.68182e13i		−	0.808995i	0.914539	−	0.404498i	$-0.132554\pi$
$912$	−4.29673e13	−	2.48072e13i	−2.05665	−	1.18741i
$913$	3.64018e12	+	6.30498e12i	0.173382	+	0.300307i
$914$	1.67850e13			0.795544
$915$	9.38495e12			0.442626
$916$	2.13895e12	+	3.70476e12i	0.100385	+	0.173872i
$917$			2.03279e13i			0.949357i
$918$	3.12200e13	−	5.40747e13i	1.45091	−	2.51305i
$919$		−	1.15667e13i		−	0.534921i	−0.963569	−	0.267460i	$-0.913816\pi$
$919$		−	1.15667e13i		−	0.534921i	0.963569	−	0.267460i	$-0.0861845\pi$
$920$	−1.00533e12	−	5.80429e11i	−0.0462662	−	0.0267118i
$921$	−2.72420e13	+	4.71846e13i	−1.24759	+	2.16089i
$922$	3.93990e12	−	6.82410e12i	0.179554	−	0.310997i
$923$	−9.28886e12	+	5.36292e12i	−0.421264	+	0.243217i
$924$	−9.88793e12			−0.446253
$925$	1.64579e13	−	1.37533e13i	0.739158	−	0.617690i
$926$	−3.73818e13			−1.67075
$927$	−2.95364e13	+	1.70529e13i	−1.31371	+	0.758470i
$928$	−5.63228e12	+	9.75539e12i	−0.249298	+	0.431796i
$929$	6.84493e12	−	1.18558e13i	0.301507	−	0.522226i	−0.674970	−	0.737845i	$-0.735844\pi$
$929$	6.84493e12	−	1.18558e13i	0.301507	−	0.522226i	0.976478	+	0.215619i	$0.0691768\pi$
$930$	−9.59076e11	−	5.53723e11i	−0.0420417	−	0.0242728i
$931$		−	3.05672e13i		−	1.33346i
$932$	−1.87424e12	+	3.24628e12i	−0.0813681	+	0.140934i
$933$			3.24213e13i			1.40076i
$934$	−3.77607e12	−	6.54034e12i	−0.162360	−	0.281216i
$935$	−7.75211e12			−0.331717
$936$	1.96979e13			0.838837
$937$	−1.84016e13	−	3.18725e13i	−0.779880	−	1.35079i	−0.932011	−	0.362431i	$-0.881947\pi$
$937$	−1.84016e13	−	3.18725e13i	−0.779880	−	1.35079i	0.152131	−	0.988360i	$-0.451386\pi$
$938$	4.38416e12	+	2.53120e12i	0.184916	+	0.106761i
$939$		−	2.91812e13i		−	1.22492i
$940$	−1.30796e12	+	7.55150e11i	−0.0546410	+	0.0315470i
$941$	−1.88265e13	−	3.26084e13i	−0.782738	−	1.35574i	−0.930341	−	0.366695i	$-0.880489\pi$
$941$	−1.88265e13	−	3.26084e13i	−0.782738	−	1.35574i	0.147604	−	0.989047i	$-0.452844\pi$
$942$	−2.59161e13	+	1.49626e13i	−1.07236	+	0.619126i
$943$	−5.29498e12	−	3.05706e12i	−0.218053	−	0.125893i
$944$	1.26483e12	+	7.30249e11i	0.0518391	+	0.0299293i
$945$	8.94745e12	−	5.16581e12i	0.364969	−	0.210715i
$946$	4.04957e12	+	7.01406e12i	0.164399	+	0.284747i
$947$	−2.77225e13	+	1.60056e13i	−1.12010	+	0.646690i	−0.941426	−	0.337219i	$-0.890514\pi$
$947$	−2.77225e13	+	1.60056e13i	−1.12010	+	0.646690i	−0.178673	+	0.983908i	$0.557181\pi$
$948$		−	9.76039e12i		−	0.392491i
$949$	−2.14496e12	−	1.23839e12i	−0.0858463	−	0.0495634i
$950$	2.01948e13	+	3.49784e13i	0.804420	+	1.39330i
$951$	3.76733e13			1.49356
$952$	−6.97162e13			−2.75085
$953$	5.68918e12	+	9.85395e12i	0.223425	+	0.386983i	0.955846	−	0.293869i	$-0.0949429\pi$
$953$	5.68918e12	+	9.85395e12i	0.223425	+	0.386983i	−0.732421	+	0.680852i	$0.761610\pi$
$954$		−	3.61977e13i		−	1.41486i
$955$	−7.34021e11	+	1.27136e12i	−0.0285557	+	0.0494600i
$956$		−	4.20060e12i		−	0.162649i
$957$	3.90332e13	+	2.25359e13i	1.50429	+	0.868501i
$958$	−7.25764e12	+	1.25706e13i	−0.278388	+	0.482183i
$959$	−2.77720e10	+	4.81026e10i	−0.00106029	+	0.00183647i
$960$	−8.38240e12	+	4.83958e12i	−0.318528	+	0.183902i
$961$	2.57053e13			0.972226
$962$	1.58125e12	+	9.07474e12i	0.0595267	+	0.341622i
$963$	3.66594e13			1.37362
$964$	1.44716e12	−	8.35516e11i	0.0539721	−	0.0311608i
$965$	2.02327e9	−	3.50441e9i	7.51072e−5	−	0.000130089i
$966$	−6.94086e12	+	1.20219e13i	−0.256458	+	0.444198i
$967$	4.23262e12	+	2.44370e12i	0.155665	+	0.0898730i	0.575809	−	0.817584i	$-0.304687\pi$
$967$	4.23262e12	+	2.44370e12i	0.155665	+	0.0898730i	−0.420144	+	0.907457i	$0.638021\pi$
$968$			6.36091e12i			0.232852i
$969$	8.77363e13	−	1.51964e14i	3.19685	−	5.53711i
$970$		−	2.75800e12i		−	0.100028i
$971$	2.59569e13	+	4.49588e13i	0.937059	+	1.62303i	0.770920	+	0.636932i	$0.219797\pi$
$971$	2.59569e13	+	4.49588e13i	0.937059	+	1.62303i	0.166139	+	0.986102i	$0.446870\pi$
$972$	−4.96972e11			−0.0178580
$973$	−2.61032e13			−0.933656
$974$	3.15702e12	+	5.46812e12i	0.112399	+	0.194681i
$975$	−1.59853e13	−	9.22912e12i	−0.566500	−	0.327069i
$976$			2.75550e13i			0.972023i
$977$	1.64726e13	−	9.51046e12i	0.578411	−	0.333946i	−0.182091	−	0.983282i	$-0.558286\pi$
$977$	1.64726e13	−	9.51046e12i	0.578411	−	0.333946i	0.760502	+	0.649336i	$0.224953\pi$
$978$	−2.57872e13	−	4.46648e13i	−0.901322	−	1.56113i
$979$	−3.14246e13	+	1.81430e13i	−1.09332	+	0.631230i
$980$	−7.54453e11	−	4.35584e11i	−0.0261285	−	0.0150853i
$981$	4.93987e12	+	2.85204e12i	0.170296	+	0.0983207i
$982$	3.24048e13	−	1.87089e13i	1.11201	−	0.642017i
$983$	−9.46655e9	−	1.63965e10i	−0.000323371	−	0.000560095i	0.865864	−	0.500280i	$-0.166770\pi$
$983$	−9.46655e9	−	1.63965e10i	−0.000323371	−	0.000560095i	−0.866187	+	0.499720i	$0.833436\pi$
$984$	−4.61373e13	+	2.66374e13i	−1.56882	+	0.905761i
$985$			2.99114e10i			0.00101245i
$986$	5.03316e13	+	2.90590e13i	1.69588	+	0.979117i
$987$	4.93764e13	+	8.55224e13i	1.65612	+	2.86849i
$988$	5.00198e12			0.167007
$989$	−3.27875e12			−0.108975
$990$	4.46567e12	+	7.73476e12i	0.147750	+	0.255911i
$991$			2.49226e13i			0.820847i	0.911895	+	0.410423i	$0.134619\pi$
$991$			2.49226e13i			0.820847i	−0.911895	+	0.410423i	$0.865381\pi$
$992$	−1.11447e12	+	1.93031e12i	−0.0365396	+	0.0632885i
$993$		−	3.20785e13i		−	1.04699i
$994$	−3.78768e13	−	2.18682e13i	−1.23065	−	0.710516i
$995$	3.34302e12	−	5.79028e12i	0.108127	−	0.187282i
$996$	−2.34833e12	+	4.06743e12i	−0.0756123	+	0.130964i
$997$	−1.57904e13	+	9.11662e12i	−0.506135	+	0.292217i	−0.731243	−	0.682117i	$-0.761060\pi$
$997$	−1.57904e13	+	9.11662e12i	−0.506135	+	0.292217i	0.225109	+	0.974334i	$0.427726\pi$
$998$	5.05392e13			1.61265
$999$	9.10529e12	+	5.22551e13i	0.289234	+	1.65991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.e.a.11.9	✓	56
37.27	even	6	inner	37.10.e.a.27.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.e.a.11.9	✓	56	1.1	even	1	trivial
37.10.e.a.27.9	yes	56	37.27	even	6	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	37.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-17.2642 + 9.96751i) q^{2} +(-121.025 + 209.622i) q^{3} +(-57.2974 + 99.2421i) q^{4} +(-231.945 - 133.913i) q^{5} -4825.28i q^{6} +(-4145.43 + 7180.09i) q^{7} -12491.2i q^{8} +(-19452.7 - 33693.1i) q^{9} +O(q^{10})\)	\(q+(-17.2642 + 9.96751i) q^{2} +(-121.025 + 209.622i) q^{3} +(-57.2974 + 99.2421i) q^{4} +(-231.945 - 133.913i) q^{5} -4825.28i q^{6} +(-4145.43 + 7180.09i) q^{7} -12491.2i q^{8} +(-19452.7 - 33693.1i) q^{9} +5339.13 q^{10} -42996.7 q^{11} +(-13868.9 - 24021.6i) q^{12} +(-35102.3 - 20266.3i) q^{13} -165278. i q^{14} +(56142.4 - 32413.8i) q^{15} +(95169.7 + 164839. i) q^{16} +(-582991. + 336590. i) q^{17} +(671673. + 387791. i) q^{18} +(932616. + 538446. i) q^{19} +(26579.7 - 15345.8i) q^{20} +(-1.00340e6 - 1.73794e6i) q^{21} +(742305. - 428570. i) q^{22} +346994. i q^{23} +(2.61843e6 + 1.51175e6i) q^{24} +(-940697. - 1.62933e6i) q^{25} +808019. q^{26} +4.65281e6 q^{27} +(-475044. - 822801. i) q^{28} +4.33075e6i q^{29} +(-646170. + 1.11920e6i) q^{30} +856931. i q^{31} +(2.25259e6 + 1.30053e6i) q^{32} +(5.20369e6 - 9.01305e6i) q^{33} +(6.70992e6 - 1.16219e7i) q^{34} +(1.92302e6 - 1.11026e6i) q^{35} +4.45837e6 q^{36} +(1.95694e6 + 1.12309e7i) q^{37} -2.14679e7 q^{38} +(8.49652e6 - 4.90547e6i) q^{39} +(-1.67274e6 + 2.89726e6i) q^{40} +(-8.81012e6 + 1.52596e7i) q^{41} +(3.46460e7 + 2.00029e7i) q^{42} +9.44902e6i q^{43} +(2.46360e6 - 4.26708e6i) q^{44} +1.04199e7i q^{45} +(-3.45866e6 - 5.99058e6i) q^{46} -4.92090e7 q^{47} -4.60718e7 q^{48} +(-1.41923e7 - 2.45818e7i) q^{49} +(3.24808e7 + 1.87528e7i) q^{50} -1.62943e8i q^{51} +(4.02254e6 - 2.32241e6i) q^{52} +(-2.33359e7 - 4.04189e7i) q^{53} +(-8.03272e7 + 4.63770e7i) q^{54} +(9.97286e6 + 5.75783e6i) q^{55} +(8.96878e7 + 5.17813e7i) q^{56} +(-2.25740e8 + 1.30331e8i) q^{57} +(-4.31668e7 - 7.47671e7i) q^{58} +(6.64512e6 - 3.83656e6i) q^{59} +7.42891e6i q^{60} +(1.25373e8 + 7.23839e7i) q^{61} +(-8.54147e6 - 1.47943e7i) q^{62} +3.22560e8 q^{63} -1.49306e8 q^{64} +(5.42786e6 + 9.40133e6i) q^{65} +2.07471e8i q^{66} +(-1.53147e7 + 2.65259e7i) q^{67} -7.71429e7i q^{68} +(-7.27375e7 - 4.19950e7i) q^{69} +(-2.21330e7 + 3.83354e7i) q^{70} +(1.32311e8 - 2.29170e8i) q^{71} +(-4.20867e8 + 2.42988e8i) q^{72} +6.11060e7 q^{73} +(-1.45729e8 - 1.74386e8i) q^{74} +4.55392e8 q^{75} +(-1.06873e8 + 6.17032e7i) q^{76} +(1.78240e8 - 3.08720e8i) q^{77} +(-9.77907e7 + 1.69378e8i) q^{78} +(3.04738e8 + 1.75940e8i) q^{79} -5.09780e7i q^{80} +(-1.80220e8 + 3.12150e8i) q^{81} -3.51260e8i q^{82} +(-8.46619e7 - 1.46639e8i) q^{83} +2.29970e8 q^{84} +1.80295e8 q^{85} +(-9.41832e7 - 1.63130e8i) q^{86} +(-9.07820e8 - 5.24130e8i) q^{87} +5.37080e8i q^{88} +(7.30862e8 - 4.21963e8i) q^{89} +(-1.03861e8 - 1.79892e8i) q^{90} +(2.91028e8 - 1.68025e8i) q^{91} +(-3.44363e7 - 1.98818e7i) q^{92} +(-1.79631e8 - 1.03710e8i) q^{93} +(8.49555e8 - 4.90491e8i) q^{94} +(-1.44210e8 - 2.49780e8i) q^{95} +(-5.45240e8 + 3.14795e8i) q^{96} -5.16564e8i q^{97} +(4.90038e8 + 2.82924e8i) q^{98} +(8.36403e8 + 1.44869e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 54 q^{2} - 75 q^{3} + 7082 q^{4} - 186 q^{5} - 4233 q^{7} - 173645 q^{9}+O(q^{10}) \) 56 * q - 54 * q^2 - 75 * q^3 + 7082 * q^4 - 186 * q^5 - 4233 * q^7 - 173645 * q^9	\( 56 q - 54 q^{2} - 75 q^{3} + 7082 q^{4} - 186 q^{5} - 4233 q^{7} - 173645 q^{9} + 97788 q^{10} - 239916 q^{11} + 184790 q^{12} - 16221 q^{13} + 385251 q^{15} - 1932502 q^{16} - 951654 q^{17} + 2811312 q^{18} - 1336047 q^{19} - 3977274 q^{20} + 1205555 q^{21} + 1410426 q^{22} - 4560318 q^{24} + 7900208 q^{25} + 6077964 q^{26} + 586098 q^{27} + 3406456 q^{28} - 12007340 q^{30} + 47328192 q^{32} + 8003280 q^{33} - 19428782 q^{34} - 4325523 q^{35} - 99800316 q^{36} + 38883015 q^{37} - 631920 q^{38} + 6587955 q^{39} + 25546036 q^{40} + 40335342 q^{41} - 91333530 q^{42} - 51286086 q^{44} - 92082750 q^{46} - 56174724 q^{47} + 388858084 q^{48} - 46172317 q^{49} - 250482252 q^{50} - 3706980 q^{52} - 197686869 q^{53} - 331423182 q^{54} + 339434874 q^{55} + 308799468 q^{56} + 360939639 q^{57} + 152139640 q^{58} + 26190393 q^{59} + 761586312 q^{61} + 443235042 q^{62} - 7358848 q^{63} - 2112154540 q^{64} - 76474689 q^{65} + 69911823 q^{67} + 1126766970 q^{69} + 788397646 q^{70} - 47291505 q^{71} + 1854440580 q^{72} - 1332048936 q^{73} - 1443954222 q^{74} - 1421404708 q^{75} - 1509740898 q^{76} + 1440770232 q^{77} - 58000938 q^{78} + 803079201 q^{79} - 1163206256 q^{81} + 231204831 q^{83} - 60315320 q^{84} - 822210144 q^{85} - 1325958588 q^{86} + 762221460 q^{87} + 2475878382 q^{89} - 4026498436 q^{90} + 2004728283 q^{91} + 183172434 q^{92} + 3380032662 q^{93} + 3222389442 q^{94} - 926002287 q^{95} - 14442188094 q^{96} + 2664119844 q^{98} + 3971333010 q^{99}+O(q^{100}) \) 56 * q - 54 * q^2 - 75 * q^3 + 7082 * q^4 - 186 * q^5 - 4233 * q^7 - 173645 * q^9 + 97788 * q^10 - 239916 * q^11 + 184790 * q^12 - 16221 * q^13 + 385251 * q^15 - 1932502 * q^16 - 951654 * q^17 + 2811312 * q^18 - 1336047 * q^19 - 3977274 * q^20 + 1205555 * q^21 + 1410426 * q^22 - 4560318 * q^24 + 7900208 * q^25 + 6077964 * q^26 + 586098 * q^27 + 3406456 * q^28 - 12007340 * q^30 + 47328192 * q^32 + 8003280 * q^33 - 19428782 * q^34 - 4325523 * q^35 - 99800316 * q^36 + 38883015 * q^37 - 631920 * q^38 + 6587955 * q^39 + 25546036 * q^40 + 40335342 * q^41 - 91333530 * q^42 - 51286086 * q^44 - 92082750 * q^46 - 56174724 * q^47 + 388858084 * q^48 - 46172317 * q^49 - 250482252 * q^50 - 3706980 * q^52 - 197686869 * q^53 - 331423182 * q^54 + 339434874 * q^55 + 308799468 * q^56 + 360939639 * q^57 + 152139640 * q^58 + 26190393 * q^59 + 761586312 * q^61 + 443235042 * q^62 - 7358848 * q^63 - 2112154540 * q^64 - 76474689 * q^65 + 69911823 * q^67 + 1126766970 * q^69 + 788397646 * q^70 - 47291505 * q^71 + 1854440580 * q^72 - 1332048936 * q^73 - 1443954222 * q^74 - 1421404708 * q^75 - 1509740898 * q^76 + 1440770232 * q^77 - 58000938 * q^78 + 803079201 * q^79 - 1163206256 * q^81 + 231204831 * q^83 - 60315320 * q^84 - 822210144 * q^85 - 1325958588 * q^86 + 762221460 * q^87 + 2475878382 * q^89 - 4026498436 * q^90 + 2004728283 * q^91 + 183172434 * q^92 + 3380032662 * q^93 + 3222389442 * q^94 - 926002287 * q^95 - 14442188094 * q^96 + 2664119844 * q^98 + 3971333010 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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