LMFDB - Embedded newform 35.8.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,8,Mod(1,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("35.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	35.a (trivial)

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:	yes
Analytic conductor:	$10.9334758919$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 249x^{2} - 1008x + 3136 $ x^4 - 249x^2 - 1008x + 3136
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-11.9413$ of defining polynomial
Character	$\chi$	$=$	35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.25170 q^{2} -83.9745 q^{3} -122.930 q^{4} -125.000 q^{5} -189.085 q^{6} -343.000 q^{7} -565.018 q^{8} +4864.72 q^{9} +O(q^{10})$	\(q+2.25170 q^{2} -83.9745 q^{3} -122.930 q^{4} -125.000 q^{5} -189.085 q^{6} -343.000 q^{7} -565.018 q^{8} +4864.72 q^{9} -281.462 q^{10} -5400.28 q^{11} +10323.0 q^{12} +13114.2 q^{13} -772.332 q^{14} +10496.8 q^{15} +14462.8 q^{16} -22015.4 q^{17} +10953.9 q^{18} -43005.0 q^{19} +15366.2 q^{20} +28803.3 q^{21} -12159.8 q^{22} +54854.6 q^{23} +47447.1 q^{24} +15625.0 q^{25} +29529.2 q^{26} -224860. q^{27} +42164.9 q^{28} +102023. q^{29} +23635.6 q^{30} -129564. q^{31} +104888. q^{32} +453486. q^{33} -49572.0 q^{34} +42875.0 q^{35} -598019. q^{36} +20759.7 q^{37} -96834.1 q^{38} -1.10126e6 q^{39} +70627.2 q^{40} -441867. q^{41} +64856.2 q^{42} +591242. q^{43} +663856. q^{44} -608090. q^{45} +123516. q^{46} -269377. q^{47} -1.21450e6 q^{48} +117649. q^{49} +35182.7 q^{50} +1.84873e6 q^{51} -1.61213e6 q^{52} +753191. q^{53} -506316. q^{54} +675035. q^{55} +193801. q^{56} +3.61132e6 q^{57} +229724. q^{58} +2.41476e6 q^{59} -1.29037e6 q^{60} +1.00571e6 q^{61} -291740. q^{62} -1.66860e6 q^{63} -1.61506e6 q^{64} -1.63927e6 q^{65} +1.02111e6 q^{66} +3.75801e6 q^{67} +2.70635e6 q^{68} -4.60639e6 q^{69} +96541.5 q^{70} -989533. q^{71} -2.74865e6 q^{72} +532428. q^{73} +46744.6 q^{74} -1.31210e6 q^{75} +5.28660e6 q^{76} +1.85230e6 q^{77} -2.47970e6 q^{78} -3.39686e6 q^{79} -1.80785e6 q^{80} +8.24337e6 q^{81} -994951. q^{82} +2.31294e6 q^{83} -3.54078e6 q^{84} +2.75193e6 q^{85} +1.33130e6 q^{86} -8.56731e6 q^{87} +3.05125e6 q^{88} -4.08842e6 q^{89} -1.36923e6 q^{90} -4.49817e6 q^{91} -6.74327e6 q^{92} +1.08801e7 q^{93} -606554. q^{94} +5.37562e6 q^{95} -8.80792e6 q^{96} +1.03600e7 q^{97} +264910. q^{98} -2.62708e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 37 q^{3} + 280 q^{4} - 500 q^{5} + 1144 q^{6} - 1372 q^{7} + 1512 q^{8} + 2391 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 37 * q^3 + 280 * q^4 - 500 * q^5 + 1144 * q^6 - 1372 * q^7 + 1512 * q^8 + 2391 * q^9	\( 4 q - 2 q^{2} - 37 q^{3} + 280 q^{4} - 500 q^{5} + 1144 q^{6} - 1372 q^{7} + 1512 q^{8} + 2391 q^{9} + 250 q^{10} - 7225 q^{11} + 28500 q^{12} + 7957 q^{13} + 686 q^{14} + 4625 q^{15} + 51288 q^{16} + 64727 q^{17} + 96526 q^{18} - 37866 q^{19} - 35000 q^{20} + 12691 q^{21} + 59056 q^{22} + 111470 q^{23} + 209264 q^{24} + 62500 q^{25} - 336012 q^{26} - 192271 q^{27} - 96040 q^{28} + 218711 q^{29} - 143000 q^{30} + 219348 q^{31} + 103104 q^{32} + 253827 q^{33} - 229548 q^{34} + 171500 q^{35} - 450196 q^{36} - 212844 q^{37} - 1317920 q^{38} - 1647245 q^{39} - 189000 q^{40} - 1215338 q^{41} - 392392 q^{42} + 1074782 q^{43} - 2220924 q^{44} - 298875 q^{45} + 2026336 q^{46} + 110699 q^{47} + 78792 q^{48} + 470596 q^{49} - 31250 q^{50} + 3506861 q^{51} - 1359172 q^{52} + 3568154 q^{53} - 1503432 q^{54} + 903125 q^{55} - 518616 q^{56} + 774022 q^{57} + 2081468 q^{58} + 261488 q^{59} - 3562500 q^{60} + 5355426 q^{61} + 74592 q^{62} - 820113 q^{63} - 5693296 q^{64} - 994625 q^{65} - 517720 q^{66} + 10352960 q^{67} + 18065332 q^{68} - 2385378 q^{69} - 85750 q^{70} + 3607808 q^{71} + 4037080 q^{72} + 2787392 q^{73} - 5682108 q^{74} - 578125 q^{75} - 4421656 q^{76} + 2478175 q^{77} - 15138056 q^{78} - 735975 q^{79} - 6411000 q^{80} + 10831108 q^{81} - 11516292 q^{82} + 2001724 q^{83} - 9775500 q^{84} - 8090875 q^{85} - 8821416 q^{86} + 3525721 q^{87} + 21825008 q^{88} - 13872714 q^{89} - 12065750 q^{90} - 2729251 q^{91} - 15116664 q^{92} + 25033932 q^{93} - 45240712 q^{94} + 4733250 q^{95} - 1056352 q^{96} - 12763773 q^{97} - 235298 q^{98} - 26960042 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 37 * q^3 + 280 * q^4 - 500 * q^5 + 1144 * q^6 - 1372 * q^7 + 1512 * q^8 + 2391 * q^9 + 250 * q^10 - 7225 * q^11 + 28500 * q^12 + 7957 * q^13 + 686 * q^14 + 4625 * q^15 + 51288 * q^16 + 64727 * q^17 + 96526 * q^18 - 37866 * q^19 - 35000 * q^20 + 12691 * q^21 + 59056 * q^22 + 111470 * q^23 + 209264 * q^24 + 62500 * q^25 - 336012 * q^26 - 192271 * q^27 - 96040 * q^28 + 218711 * q^29 - 143000 * q^30 + 219348 * q^31 + 103104 * q^32 + 253827 * q^33 - 229548 * q^34 + 171500 * q^35 - 450196 * q^36 - 212844 * q^37 - 1317920 * q^38 - 1647245 * q^39 - 189000 * q^40 - 1215338 * q^41 - 392392 * q^42 + 1074782 * q^43 - 2220924 * q^44 - 298875 * q^45 + 2026336 * q^46 + 110699 * q^47 + 78792 * q^48 + 470596 * q^49 - 31250 * q^50 + 3506861 * q^51 - 1359172 * q^52 + 3568154 * q^53 - 1503432 * q^54 + 903125 * q^55 - 518616 * q^56 + 774022 * q^57 + 2081468 * q^58 + 261488 * q^59 - 3562500 * q^60 + 5355426 * q^61 + 74592 * q^62 - 820113 * q^63 - 5693296 * q^64 - 994625 * q^65 - 517720 * q^66 + 10352960 * q^67 + 18065332 * q^68 - 2385378 * q^69 - 85750 * q^70 + 3607808 * q^71 + 4037080 * q^72 + 2787392 * q^73 - 5682108 * q^74 - 578125 * q^75 - 4421656 * q^76 + 2478175 * q^77 - 15138056 * q^78 - 735975 * q^79 - 6411000 * q^80 + 10831108 * q^81 - 11516292 * q^82 + 2001724 * q^83 - 9775500 * q^84 - 8090875 * q^85 - 8821416 * q^86 + 3525721 * q^87 + 21825008 * q^88 - 13872714 * q^89 - 12065750 * q^90 - 2729251 * q^91 - 15116664 * q^92 + 25033932 * q^93 - 45240712 * q^94 + 4733250 * q^95 - 1056352 * q^96 - 12763773 * q^97 - 235298 * q^98 - 26960042 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	2.25170	0.199024	0.0995118	−	0.995036i	$-0.468272\pi$
$2$	2.25170	0.199024	0.0995118	+	0.995036i	$0.468272\pi$
$3$	−83.9745	−1.79566	−0.897828	−	0.440347i	$-0.854856\pi$
$3$	−83.9745	−1.79566	−0.897828	+	0.440347i	$0.854856\pi$
$4$	−122.930	−0.960390
$5$	−125.000	−0.447214
$5$	−125.000	−0.447214
$6$	−189.085	−0.357378
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−565.018	−0.390164
$9$	4864.72	2.22438
$10$	−281.462	−0.0890061
$11$	−5400.28	−1.22332	−0.611662	−	0.791119i	$-0.709499\pi$
$11$	−5400.28	−1.22332	−0.611662	+	0.791119i	$0.709499\pi$
$12$	10323.0	1.72453
$13$	13114.2	1.65554	0.827770	−	0.561067i	$-0.189609\pi$
$13$	13114.2	1.65554	0.827770	+	0.561067i	$0.189609\pi$
$14$	−772.332	−0.0752239
$15$	10496.8	0.803042
$16$	14462.8	0.882738
$17$	−22015.4	−1.08681	−0.543407	−	0.839469i	$-0.682866\pi$
$17$	−22015.4	−1.08681	−0.543407	+	0.839469i	$0.682866\pi$
$18$	10953.9	0.442704
$19$	−43005.0	−1.43841	−0.719203	−	0.694800i	$-0.755493\pi$
$19$	−43005.0	−1.43841	−0.719203	+	0.694800i	$0.755493\pi$
$20$	15366.2	0.429499
$21$	28803.3	0.678694
$22$	−12159.8	−0.243471
$23$	54854.6	0.940082	0.470041	−	0.882645i	$-0.344239\pi$
$23$	54854.6	0.940082	0.470041	+	0.882645i	$0.344239\pi$
$24$	47447.1	0.700600
$25$	15625.0	0.200000
$26$	29529.2	0.329492
$27$	−224860.	−2.19856
$28$	42164.9	0.362993
$29$	102023.	0.776791	0.388396	−	0.921493i	$-0.373029\pi$
$29$	102023.	0.776791	0.388396	+	0.921493i	$0.373029\pi$
$30$	23635.6	0.159824
$31$	−129564.	−0.781124	−0.390562	−	0.920577i	$-0.627719\pi$
$31$	−129564.	−0.781124	−0.390562	+	0.920577i	$0.627719\pi$
$32$	104888.	0.565850
$33$	453486.	2.19667
$34$	−49572.0	−0.216302
$35$	42875.0	0.169031
$36$	−598019.	−2.13627
$37$	20759.7	0.0673776	0.0336888	−	0.999432i	$-0.489274\pi$
$37$	20759.7	0.0673776	0.0336888	+	0.999432i	$0.489274\pi$
$38$	−96834.1	−0.286277
$39$	−1.10126e6	−2.97278
$40$	70627.2	0.174487
$41$	−441867.	−1.00126	−0.500632	−	0.865660i	$-0.666899\pi$
$41$	−441867.	−1.00126	−0.500632	+	0.865660i	$0.666899\pi$
$42$	64856.2	0.135076
$43$	591242.	1.13403	0.567017	−	0.823706i	$-0.308097\pi$
$43$	591242.	1.13403	0.567017	+	0.823706i	$0.308097\pi$
$44$	663856.	1.17487
$45$	−608090.	−0.994773
$46$	123516.	0.187099
$47$	−269377.	−0.378458	−0.189229	−	0.981933i	$-0.560599\pi$
$47$	−269377.	−0.378458	−0.189229	+	0.981933i	$0.560599\pi$
$48$	−1.21450e6	−1.58509
$49$	117649.	0.142857
$50$	35182.7	0.0398047
$51$	1.84873e6	1.95155
$52$	−1.61213e6	−1.58996
$53$	753191.	0.694928	0.347464	−	0.937693i	$-0.387043\pi$
$53$	753191.	0.694928	0.347464	+	0.937693i	$0.387043\pi$
$54$	−506316.	−0.437566
$55$	675035.	0.547087
$56$	193801.	0.147468
$57$	3.61132e6	2.58288
$58$	229724.	0.154600
$59$	2.41476e6	1.53071	0.765355	−	0.643609i	$-0.222564\pi$
$59$	2.41476e6	1.53071	0.765355	+	0.643609i	$0.222564\pi$
$60$	−1.29037e6	−0.771233
$61$	1.00571e6	0.567306	0.283653	−	0.958927i	$-0.408454\pi$
$61$	1.00571e6	0.567306	0.283653	+	0.958927i	$0.408454\pi$
$62$	−291740.	−0.155462
$63$	−1.66860e6	−0.840736
$64$	−1.61506e6	−0.770120
$65$	−1.63927e6	−0.740380
$66$	1.02111e6	0.437189
$67$	3.75801e6	1.52650	0.763248	−	0.646106i	$-0.223603\pi$
$67$	3.75801e6	1.52650	0.763248	+	0.646106i	$0.223603\pi$
$68$	2.70635e6	1.04377
$69$	−4.60639e6	−1.68806
$70$	96541.5	0.0336411
$71$	−989533.	−0.328115	−0.164058	−	0.986451i	$-0.552458\pi$
$71$	−989533.	−0.328115	−0.164058	+	0.986451i	$0.552458\pi$
$72$	−2.74865e6	−0.867873
$73$	532428.	0.160188	0.0800941	−	0.996787i	$-0.474478\pi$
$73$	532428.	0.160188	0.0800941	+	0.996787i	$0.474478\pi$
$74$	46744.6	0.0134097
$75$	−1.31210e6	−0.359131
$76$	5.28660e6	1.38143
$77$	1.85230e6	0.462373
$78$	−2.47970e6	−0.591654
$79$	−3.39686e6	−0.775145	−0.387573	−	0.921839i	$-0.626686\pi$
$79$	−3.39686e6	−0.775145	−0.387573	+	0.921839i	$0.626686\pi$
$80$	−1.80785e6	−0.394772
$81$	8.24337e6	1.72348
$82$	−994951.	−0.199275
$83$	2.31294e6	0.444007	0.222004	−	0.975046i	$-0.428740\pi$
$83$	2.31294e6	0.444007	0.222004	+	0.975046i	$0.428740\pi$
$84$	−3.54078e6	−0.651811
$85$	2.75193e6	0.486038
$86$	1.33130e6	0.225699
$87$	−8.56731e6	−1.39485
$88$	3.05125e6	0.477297
$89$	−4.08842e6	−0.614739	−0.307369	−	0.951590i	$-0.599449\pi$
$89$	−4.08842e6	−0.614739	−0.307369	+	0.951590i	$0.599449\pi$
$90$	−1.36923e6	−0.197983
$91$	−4.49817e6	−0.625736
$92$	−6.74327e6	−0.902845
$93$	1.08801e7	1.40263
$94$	−606554.	−0.0753221
$95$	5.37562e6	0.643274
$96$	−8.80792e6	−1.01607
$97$	1.03600e7	1.15255	0.576273	−	0.817257i	$-0.304506\pi$
$97$	1.03600e7	1.15255	0.576273	+	0.817257i	$0.304506\pi$
$98$	264910.	0.0284320
$99$	−2.62708e7	−2.72114
$100$	−1.92078e6	−0.192078
$101$	−1.37030e7	−1.32340	−0.661699	−	0.749770i	$-0.730164\pi$
$101$	−1.37030e7	−1.32340	−0.661699	+	0.749770i	$0.730164\pi$
$102$	4.16279e6	0.388404
$103$	−4.10972e6	−0.370580	−0.185290	−	0.982684i	$-0.559323\pi$
$103$	−4.10972e6	−0.370580	−0.185290	+	0.982684i	$0.559323\pi$
$104$	−7.40975e6	−0.645932
$105$	−3.60041e6	−0.303521
$106$	1.69596e6	0.138307
$107$	−1.29399e7	−1.02115	−0.510574	−	0.859834i	$-0.670567\pi$
$107$	−1.29399e7	−1.02115	−0.510574	+	0.859834i	$0.670567\pi$
$108$	2.76420e7	2.11148
$109$	1.40565e7	1.03964	0.519822	−	0.854275i	$-0.325998\pi$
$109$	1.40565e7	1.03964	0.519822	+	0.854275i	$0.325998\pi$
$110$	1.51997e6	0.108883
$111$	−1.74329e6	−0.120987
$112$	−4.96073e6	−0.333643
$113$	8.11994e6	0.529393	0.264696	−	0.964332i	$-0.414728\pi$
$113$	8.11994e6	0.529393	0.264696	+	0.964332i	$0.414728\pi$
$114$	8.13160e6	0.514054
$115$	−6.85683e6	−0.420417
$116$	−1.25416e7	−0.746022
$117$	6.37968e7	3.68255
$118$	5.43732e6	0.304647
$119$	7.55129e6	0.410777
$120$	−5.93089e6	−0.313318
$121$	9.67584e6	0.496523
$122$	2.26455e6	0.112907
$123$	3.71056e7	1.79793
$124$	1.59273e7	0.750183
$125$	−1.95312e6	−0.0894427
$126$	−3.75718e6	−0.167326
$127$	−1.57352e7	−0.681645	−0.340823	−	0.940128i	$-0.610706\pi$
$127$	−1.57352e7	−0.681645	−0.340823	+	0.940128i	$0.610706\pi$
$128$	−1.70623e7	−0.719122
$129$	−4.96493e7	−2.03633
$130$	−3.69115e6	−0.147353
$131$	1.70480e7	0.662560	0.331280	−	0.943533i	$-0.392520\pi$
$131$	1.70480e7	0.662560	0.331280	+	0.943533i	$0.392520\pi$
$132$	−5.57469e7	−2.10966
$133$	1.47507e7	0.543666
$134$	8.46189e6	0.303809
$135$	2.81075e7	0.983227
$136$	1.24391e7	0.424036
$137$	2.23793e6	0.0743575	0.0371788	−	0.999309i	$-0.488163\pi$
$137$	2.23793e6	0.0743575	0.0371788	+	0.999309i	$0.488163\pi$
$138$	−1.03722e7	−0.335965
$139$	−3.28153e7	−1.03639	−0.518197	−	0.855261i	$-0.673397\pi$
$139$	−3.28153e7	−1.03639	−0.518197	+	0.855261i	$0.673397\pi$
$140$	−5.27062e6	−0.162335
$141$	2.26208e7	0.679580
$142$	−2.22813e6	−0.0653027
$143$	−7.08203e7	−2.02526
$144$	7.03573e7	1.96354
$145$	−1.27528e7	−0.347392
$146$	1.19887e6	0.0318813
$147$	−9.87952e6	−0.256522
$148$	−2.55199e6	−0.0647088
$149$	−2.47497e7	−0.612940	−0.306470	−	0.951880i	$-0.599148\pi$
$149$	−2.47497e7	−0.612940	−0.306470	+	0.951880i	$0.599148\pi$
$150$	−2.95445e6	−0.0714756
$151$	6.64346e6	0.157027	0.0785136	−	0.996913i	$-0.474983\pi$
$151$	6.64346e6	0.157027	0.0785136	+	0.996913i	$0.474983\pi$
$152$	2.42986e7	0.561214
$153$	−1.07099e8	−2.41749
$154$	4.17081e6	0.0920232
$155$	1.61956e7	0.349329
$156$	1.35377e8	2.85503
$157$	8.87783e7	1.83087	0.915437	−	0.402462i	$-0.131846\pi$
$157$	8.87783e7	1.83087	0.915437	+	0.402462i	$0.131846\pi$
$158$	−7.64870e6	−0.154272
$159$	−6.32488e7	−1.24785
$160$	−1.31110e7	−0.253056
$161$	−1.88151e7	−0.355318
$162$	1.85616e7	0.343014
$163$	2.61170e7	0.472352	0.236176	−	0.971710i	$-0.424106\pi$
$163$	2.61170e7	0.472352	0.236176	+	0.971710i	$0.424106\pi$
$164$	5.43187e7	0.961603
$165$	−5.66857e7	−0.982381
$166$	5.20803e6	0.0883680
$167$	−4.01729e7	−0.667460	−0.333730	−	0.942669i	$-0.608307\pi$
$167$	−4.01729e7	−0.667460	−0.333730	+	0.942669i	$0.608307\pi$
$168$	−1.62744e7	−0.264802
$169$	1.09234e8	1.74081
$170$	6.19650e6	0.0967332
$171$	−2.09207e8	−3.19956
$172$	−7.26813e7	−1.08911
$173$	−2.89948e7	−0.425754	−0.212877	−	0.977079i	$-0.568283\pi$
$173$	−2.89948e7	−0.425754	−0.212877	+	0.977079i	$0.568283\pi$
$174$	−1.92910e7	−0.277608
$175$	−5.35938e6	−0.0755929
$176$	−7.81030e7	−1.07987
$177$	−2.02779e8	−2.74863
$178$	−9.20588e6	−0.122348
$179$	8.52441e7	1.11091	0.555455	−	0.831547i	$-0.312544\pi$
$179$	8.52441e7	1.11091	0.555455	+	0.831547i	$0.312544\pi$
$180$	7.47524e7	0.955369
$181$	3.60964e7	0.452470	0.226235	−	0.974073i	$-0.427358\pi$
$181$	3.60964e7	0.452470	0.226235	+	0.974073i	$0.427358\pi$
$182$	−1.01285e7	−0.124536
$183$	−8.44538e7	−1.01869
$184$	−3.09938e7	−0.366786
$185$	−2.59497e6	−0.0301322
$186$	2.44987e7	0.279156
$187$	1.18889e8	1.32953
$188$	3.31144e7	0.363467
$189$	7.71270e7	0.830979
$190$	1.21043e7	0.128027
$191$	1.27292e8	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$191$	1.27292e8	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$192$	1.35624e8	1.38287
$193$	1.34127e8	1.34297	0.671486	−	0.741017i	$-0.265656\pi$
$193$	1.34127e8	1.34297	0.671486	+	0.741017i	$0.265656\pi$
$194$	2.33275e7	0.229384
$195$	1.37657e8	1.32947
$196$	−1.44626e7	−0.137199
$197$	−6.57090e7	−0.612341	−0.306170	−	0.951977i	$-0.599048\pi$
$197$	−6.57090e7	−0.612341	−0.306170	+	0.951977i	$0.599048\pi$
$198$	−5.91539e7	−0.541571
$199$	1.55011e8	1.39437	0.697183	−	0.716894i	$-0.254437\pi$
$199$	1.55011e8	1.39437	0.697183	+	0.716894i	$0.254437\pi$
$200$	−8.82840e6	−0.0780328
$201$	−3.15577e8	−2.74106
$202$	−3.08550e7	−0.263388
$203$	−3.49938e7	−0.293599
$204$	−2.27265e8	−1.87424
$205$	5.52334e7	0.447779
$206$	−9.25385e6	−0.0737543
$207$	2.66852e8	2.09110
$208$	1.89668e8	1.46141
$209$	2.32239e8	1.75964
$210$	−8.10702e6	−0.0604079
$211$	9.70747e7	0.711406	0.355703	−	0.934599i	$-0.384241\pi$
$211$	9.70747e7	0.711406	0.355703	+	0.934599i	$0.384241\pi$
$212$	−9.25897e7	−0.667401
$213$	8.30956e7	0.589182
$214$	−2.91368e7	−0.203233
$215$	−7.39053e7	−0.507155
$216$	1.27050e8	0.857800
$217$	4.44406e7	0.295237
$218$	3.16510e7	0.206914
$219$	−4.47104e7	−0.287643
$220$	−8.29819e7	−0.525417
$221$	−2.88714e8	−1.79927
$222$	−3.92536e6	−0.0240793
$223$	6.99764e7	0.422556	0.211278	−	0.977426i	$-0.432237\pi$
$223$	6.99764e7	0.422556	0.211278	+	0.977426i	$0.432237\pi$
$224$	−3.59766e7	−0.213871
$225$	7.60112e7	0.444876
$226$	1.82836e7	0.105362
$227$	−3.16088e8	−1.79356	−0.896782	−	0.442472i	$-0.854102\pi$
$227$	−3.16088e8	−1.79356	−0.896782	+	0.442472i	$0.854102\pi$
$228$	−4.43939e8	−2.48057
$229$	1.48597e8	0.817686	0.408843	−	0.912605i	$-0.365932\pi$
$229$	1.48597e8	0.817686	0.408843	+	0.912605i	$0.365932\pi$
$230$	−1.54395e7	−0.0836730
$231$	−1.55546e8	−0.830263
$232$	−5.76447e7	−0.303076
$233$	1.09289e8	0.566018	0.283009	−	0.959117i	$-0.408667\pi$
$233$	1.09289e8	0.566018	0.283009	+	0.959117i	$0.408667\pi$
$234$	1.43651e8	0.732915
$235$	3.36721e7	0.169251
$236$	−2.96847e8	−1.47008
$237$	2.85250e8	1.39189
$238$	1.70032e7	0.0817544
$239$	3.80431e7	0.180253	0.0901267	−	0.995930i	$-0.471273\pi$
$239$	3.80431e7	0.180253	0.0901267	+	0.995930i	$0.471273\pi$
$240$	1.51813e8	0.708875
$241$	−3.11376e6	−0.0143293	−0.00716466	−	0.999974i	$-0.502281\pi$
$241$	−3.11376e6	−0.0143293	−0.00716466	+	0.999974i	$0.502281\pi$
$242$	2.17870e7	0.0988199
$243$	−2.00464e8	−0.896220
$244$	−1.23632e8	−0.544835
$245$	−1.47061e7	−0.0638877
$246$	8.35505e7	0.357830
$247$	−5.63976e8	−2.38134
$248$	7.32062e7	0.304766
$249$	−1.94228e8	−0.797284
$250$	−4.39784e6	−0.0178012
$251$	3.83469e8	1.53064	0.765318	−	0.643653i	$-0.222582\pi$
$251$	3.83469e8	1.53064	0.765318	+	0.643653i	$0.222582\pi$
$252$	2.05121e8	0.807434
$253$	−2.96230e8	−1.15003
$254$	−3.54308e7	−0.135664
$255$	−2.31092e8	−0.872758
$256$	1.68308e8	0.626998
$257$	1.74775e8	0.642263	0.321132	−	0.947035i	$-0.395937\pi$
$257$	1.74775e8	0.642263	0.321132	+	0.947035i	$0.395937\pi$
$258$	−1.11795e8	−0.405279
$259$	−7.12059e6	−0.0254664
$260$	2.01516e8	0.711053
$261$	4.96312e8	1.72788
$262$	3.83870e7	0.131865
$263$	−2.04900e8	−0.694540	−0.347270	−	0.937765i	$-0.612891\pi$
$263$	−2.04900e8	−0.694540	−0.347270	+	0.937765i	$0.612891\pi$
$264$	−2.56227e8	−0.857061
$265$	−9.41489e7	−0.310781
$266$	3.32141e7	0.108202
$267$	3.43323e8	1.10386
$268$	−4.61971e8	−1.46603
$269$	1.36801e8	0.428505	0.214253	−	0.976778i	$-0.431268\pi$
$269$	1.36801e8	0.428505	0.214253	+	0.976778i	$0.431268\pi$
$270$	6.32895e7	0.195686
$271$	1.87791e8	0.573170	0.286585	−	0.958055i	$-0.407480\pi$
$271$	1.87791e8	0.573170	0.286585	+	0.958055i	$0.407480\pi$
$272$	−3.18404e8	−0.959373
$273$	3.77731e8	1.12361
$274$	5.03914e6	0.0147989
$275$	−8.43794e7	−0.244665
$276$	5.66263e8	1.62120
$277$	−4.92433e8	−1.39209	−0.696046	−	0.717997i	$-0.745059\pi$
$277$	−4.92433e8	−1.39209	−0.696046	+	0.717997i	$0.745059\pi$
$278$	−7.38902e7	−0.206267
$279$	−6.30294e8	−1.73752
$280$	−2.42251e7	−0.0659497
$281$	4.05443e8	1.09008	0.545039	−	0.838411i	$-0.316515\pi$
$281$	4.05443e8	1.09008	0.545039	+	0.838411i	$0.316515\pi$
$282$	5.09351e7	0.135252
$283$	4.71836e8	1.23748	0.618741	−	0.785595i	$-0.287643\pi$
$283$	4.71836e8	1.23748	0.618741	+	0.785595i	$0.287643\pi$
$284$	1.21643e8	0.315118
$285$	−4.51415e8	−1.15510
$286$	−1.59466e8	−0.403075
$287$	1.51561e8	0.378442
$288$	5.10251e8	1.25866
$289$	7.43397e7	0.181167
$290$	−2.87155e7	−0.0691391
$291$	−8.69975e8	−2.06958
$292$	−6.54513e7	−0.153843
$293$	−3.02633e8	−0.702878	−0.351439	−	0.936211i	$-0.614308\pi$
$293$	−3.02633e8	−0.702878	−0.351439	+	0.936211i	$0.614308\pi$
$294$	−2.22457e7	−0.0510540
$295$	−3.01846e8	−0.684554
$296$	−1.17296e7	−0.0262883
$297$	1.21431e9	2.68956
$298$	−5.57288e7	−0.121990
$299$	7.19374e8	1.55634
$300$	1.61296e8	0.344906
$301$	−2.02796e8	−0.428624
$302$	1.49590e7	0.0312521
$303$	1.15070e9	2.37637
$304$	−6.21971e8	−1.26973
$305$	−1.25714e8	−0.253707
$306$	−2.41154e8	−0.481137
$307$	−4.34810e7	−0.0857660	−0.0428830	−	0.999080i	$-0.513654\pi$
$307$	−4.34810e7	−0.0857660	−0.0428830	+	0.999080i	$0.513654\pi$
$308$	−2.27702e8	−0.444058
$309$	3.45112e8	0.665435
$310$	3.64675e7	0.0695248
$311$	−9.64428e8	−1.81806	−0.909030	−	0.416730i	$-0.863176\pi$
$311$	−9.64428e8	−1.81806	−0.909030	+	0.416730i	$0.863176\pi$
$312$	6.22230e8	1.15987
$313$	1.77181e8	0.326597	0.163298	−	0.986577i	$-0.447787\pi$
$313$	1.77181e8	0.326597	0.163298	+	0.986577i	$0.447787\pi$
$314$	1.99902e8	0.364387
$315$	2.08575e8	0.375989
$316$	4.17576e8	0.744441
$317$	5.10443e8	0.899995	0.449998	−	0.893030i	$-0.351425\pi$
$317$	5.10443e8	0.899995	0.449998	+	0.893030i	$0.351425\pi$
$318$	−1.42417e8	−0.248352
$319$	−5.50952e8	−0.950268
$320$	2.01882e8	0.344408
$321$	1.08662e9	1.83363
$322$	−4.23660e7	−0.0707166
$323$	9.46773e8	1.56328
$324$	−1.01336e9	−1.65522
$325$	2.04909e8	0.331108
$326$	5.88075e7	0.0940093
$327$	−1.18039e9	−1.86684
$328$	2.49663e8	0.390657
$329$	9.23962e7	0.143044
$330$	−1.27639e8	−0.195517
$331$	−7.82727e8	−1.18635	−0.593175	−	0.805074i	$-0.702126\pi$
$331$	−7.82727e8	−1.18635	−0.593175	+	0.805074i	$0.702126\pi$
$332$	−2.84329e8	−0.426420
$333$	1.00990e8	0.149873
$334$	−9.04571e7	−0.132840
$335$	−4.69751e8	−0.682670
$336$	4.16575e8	0.599109
$337$	−7.46800e8	−1.06292	−0.531459	−	0.847084i	$-0.678356\pi$
$337$	−7.46800e8	−1.06292	−0.531459	+	0.847084i	$0.678356\pi$
$338$	2.45961e8	0.346463
$339$	−6.81868e8	−0.950607
$340$	−3.38294e8	−0.466786
$341$	6.99684e8	0.955568
$342$	−4.71071e8	−0.636788
$343$	−4.03536e7	−0.0539949
$344$	−3.34062e8	−0.442459
$345$	5.75799e8	0.754925
$346$	−6.52875e7	−0.0847352
$347$	−4.72014e8	−0.606459	−0.303229	−	0.952918i	$-0.598065\pi$
$347$	−4.72014e8	−0.606459	−0.303229	+	0.952918i	$0.598065\pi$
$348$	1.05318e9	1.33960
$349$	1.15536e9	1.45489	0.727443	−	0.686168i	$-0.240709\pi$
$349$	1.15536e9	1.45489	0.727443	+	0.686168i	$0.240709\pi$
$350$	−1.20677e7	−0.0150448
$351$	−2.94886e9	−3.63981
$352$	−5.66425e8	−0.692218
$353$	5.81965e7	0.0704183	0.0352091	−	0.999380i	$-0.488790\pi$
$353$	5.81965e7	0.0704183	0.0352091	+	0.999380i	$0.488790\pi$
$354$	−4.56596e8	−0.547042
$355$	1.23692e8	0.146738
$356$	5.02589e8	0.590388
$357$	−6.34116e8	−0.737615
$358$	1.91944e8	0.221097
$359$	−1.54744e9	−1.76515	−0.882576	−	0.470169i	$-0.844193\pi$
$359$	−1.54744e9	−1.76515	−0.882576	+	0.470169i	$0.844193\pi$
$360$	3.43581e8	0.388124
$361$	9.55557e8	1.06901
$362$	8.12782e7	0.0900522
$363$	−8.12524e8	−0.891585
$364$	5.52959e8	0.600950
$365$	−6.65535e7	−0.0716384
$366$	−1.90164e8	−0.202743
$367$	9.47485e8	1.00056	0.500278	−	0.865865i	$-0.333231\pi$
$367$	9.47485e8	1.00056	0.500278	+	0.865865i	$0.333231\pi$
$368$	7.93350e8	0.829846
$369$	−2.14956e9	−2.22719
$370$	−5.84308e6	−0.00599702
$371$	−2.58345e8	−0.262658
$372$	−1.33749e9	−1.34707
$373$	−5.87908e8	−0.586582	−0.293291	−	0.956023i	$-0.594750\pi$
$373$	−5.87908e8	−0.586582	−0.293291	+	0.956023i	$0.594750\pi$
$374$	2.67703e8	0.264607
$375$	1.64013e8	0.160608
$376$	1.52203e8	0.147661
$377$	1.33795e9	1.28601
$378$	1.73666e8	0.165384
$379$	1.69763e9	1.60179	0.800894	−	0.598806i	$-0.204358\pi$
$379$	1.69763e9	1.60179	0.800894	+	0.598806i	$0.204358\pi$
$380$	−6.60825e8	−0.617794
$381$	1.32135e9	1.22400
$382$	2.86622e8	0.263080
$383$	3.41934e8	0.310990	0.155495	−	0.987837i	$-0.450303\pi$
$383$	3.41934e8	0.310990	0.155495	+	0.987837i	$0.450303\pi$
$384$	1.43280e9	1.29130
$385$	−2.31537e8	−0.206780
$386$	3.02014e8	0.267283
$387$	2.87623e9	2.52252
$388$	−1.27355e9	−1.10689
$389$	7.33945e8	0.632179	0.316089	−	0.948729i	$-0.397630\pi$
$389$	7.33945e8	0.632179	0.316089	+	0.948729i	$0.397630\pi$
$390$	3.09962e8	0.264596
$391$	−1.20765e9	−1.02170
$392$	−6.64738e7	−0.0557377
$393$	−1.43160e9	−1.18973
$394$	−1.47957e8	−0.121870
$395$	4.24608e8	0.346655
$396$	3.22947e9	2.61335
$397$	−5.62681e6	−0.00451331	−0.00225666	−	0.999997i	$-0.500718\pi$
$397$	−5.62681e6	−0.00451331	−0.00225666	+	0.999997i	$0.500718\pi$
$398$	3.49037e8	0.277512
$399$	−1.23868e9	−0.976237
$400$	2.25981e8	0.176548
$401$	−1.14513e9	−0.886848	−0.443424	−	0.896312i	$-0.646236\pi$
$401$	−1.14513e9	−0.886848	−0.443424	+	0.896312i	$0.646236\pi$
$402$	−7.10583e8	−0.545536
$403$	−1.69913e9	−1.29318
$404$	1.68451e9	1.27098
$405$	−1.03042e9	−0.770765
$406$	−7.87954e7	−0.0584332
$407$	−1.12108e8	−0.0824247
$408$	−1.04457e9	−0.761423
$409$	−2.09582e9	−1.51468	−0.757341	−	0.653020i	$-0.773502\pi$
$409$	−2.09582e9	−1.51468	−0.757341	+	0.653020i	$0.773502\pi$
$410$	1.24369e8	0.0891186
$411$	−1.87929e8	−0.133520
$412$	5.05208e8	0.355902
$413$	−8.28264e8	−0.578554
$414$	6.00870e8	0.416178
$415$	−2.89117e8	−0.198566
$416$	1.37552e9	0.936787
$417$	2.75565e9	1.86101
$418$	5.22931e8	0.350209
$419$	−5.18817e8	−0.344560	−0.172280	−	0.985048i	$-0.555113\pi$
$419$	−5.18817e8	−0.344560	−0.172280	+	0.985048i	$0.555113\pi$
$420$	4.42598e8	0.291499
$421$	1.06945e9	0.698509	0.349254	−	0.937028i	$-0.386435\pi$
$421$	1.06945e9	0.698509	0.349254	+	0.937028i	$0.386435\pi$
$422$	2.18583e8	0.141587
$423$	−1.31044e9	−0.841834
$424$	−4.25566e8	−0.271136
$425$	−3.43991e8	−0.217363
$426$	1.87106e8	0.117261
$427$	−3.44958e8	−0.214422
$428$	1.59070e9	0.980700
$429$	5.94710e9	3.63668
$430$	−1.66412e8	−0.100936
$431$	−6.86019e8	−0.412730	−0.206365	−	0.978475i	$-0.566163\pi$
$431$	−6.86019e8	−0.412730	−0.206365	+	0.978475i	$0.566163\pi$
$432$	−3.25210e9	−1.94075
$433$	−2.94736e9	−1.74472	−0.872361	−	0.488863i	$-0.837412\pi$
$433$	−2.94736e9	−1.74472	−0.872361	+	0.488863i	$0.837412\pi$
$434$	1.00067e8	0.0587592
$435$	1.07091e9	0.623796
$436$	−1.72796e9	−0.998463
$437$	−2.35902e9	−1.35222
$438$	−1.00674e8	−0.0572478
$439$	1.50817e9	0.850796	0.425398	−	0.905006i	$-0.360134\pi$
$439$	1.50817e9	0.850796	0.425398	+	0.905006i	$0.360134\pi$
$440$	−3.81407e8	−0.213454
$441$	5.72329e8	0.317768
$442$	−6.50097e8	−0.358097
$443$	3.22444e9	1.76214	0.881071	−	0.472984i	$-0.156823\pi$
$443$	3.22444e9	1.76214	0.881071	+	0.472984i	$0.156823\pi$
$444$	2.14302e8	0.116195
$445$	5.11052e8	0.274919
$446$	1.57565e8	0.0840987
$447$	2.07834e9	1.10063
$448$	5.53965e8	0.291078
$449$	−3.36551e9	−1.75464	−0.877322	−	0.479901i	$-0.840672\pi$
$449$	−3.36551e9	−1.75464	−0.877322	+	0.479901i	$0.840672\pi$
$450$	1.71154e8	0.0885408
$451$	2.38621e9	1.22487
$452$	−9.98183e8	−0.508423
$453$	−5.57881e8	−0.281967
$454$	−7.11733e8	−0.356962
$455$	5.62271e8	0.279837
$456$	−2.04046e9	−1.00775
$457$	2.72839e9	1.33721	0.668605	−	0.743618i	$-0.266892\pi$
$457$	2.72839e9	1.33721	0.668605	+	0.743618i	$0.266892\pi$
$458$	3.34596e8	0.162739
$459$	4.95039e9	2.38943
$460$	8.42909e8	0.403765
$461$	−2.86319e9	−1.36112	−0.680561	−	0.732692i	$-0.738264\pi$
$461$	−2.86319e9	−1.36112	−0.680561	+	0.732692i	$0.738264\pi$
$462$	−3.50241e8	−0.165242
$463$	2.42271e9	1.13441	0.567203	−	0.823578i	$-0.308025\pi$
$463$	2.42271e9	1.13441	0.567203	+	0.823578i	$0.308025\pi$
$464$	1.47553e9	0.685703
$465$	−1.36001e9	−0.627275
$466$	2.46085e8	0.112651
$467$	2.32433e9	1.05606	0.528029	−	0.849226i	$-0.322931\pi$
$467$	2.32433e9	1.05606	0.528029	+	0.849226i	$0.322931\pi$
$468$	−7.84254e9	−3.53668
$469$	−1.28900e9	−0.576961
$470$	7.58193e7	0.0336851
$471$	−7.45512e9	−3.28762
$472$	−1.36438e9	−0.597228
$473$	−3.19287e9	−1.38729
$474$	6.42296e8	0.277020
$475$	−6.71953e8	−0.287681
$476$	−9.28279e8	−0.394506
$477$	3.66406e9	1.54578
$478$	8.56615e7	0.0358747
$479$	1.75061e9	0.727806	0.363903	−	0.931437i	$-0.381444\pi$
$479$	1.75061e9	0.727806	0.363903	+	0.931437i	$0.381444\pi$
$480$	1.10099e9	0.454401
$481$	2.72247e8	0.111546
$482$	−7.01124e6	−0.00285187
$483$	1.57999e9	0.638028
$484$	−1.18945e9	−0.476856
$485$	−1.29500e9	−0.515434
$486$	−4.51384e8	−0.178369
$487$	−4.46599e9	−1.75213	−0.876064	−	0.482194i	$-0.839840\pi$
$487$	−4.46599e9	−1.75213	−0.876064	+	0.482194i	$0.839840\pi$
$488$	−5.68243e8	−0.221342
$489$	−2.19316e9	−0.848182
$490$	−3.31137e7	−0.0127152
$491$	−2.00920e9	−0.766015	−0.383008	−	0.923745i	$-0.625112\pi$
$491$	−2.00920e9	−0.766015	−0.383008	+	0.923745i	$0.625112\pi$
$492$	−4.56139e9	−1.72671
$493$	−2.24607e9	−0.844228
$494$	−1.26990e9	−0.473943
$495$	3.28385e9	1.21693
$496$	−1.87386e9	−0.689527
$497$	3.39410e8	0.124016
$498$	−4.37341e8	−0.158678
$499$	3.18249e7	0.0114661	0.00573305	−	0.999984i	$-0.498175\pi$
$499$	3.18249e7	0.0114661	0.00573305	+	0.999984i	$0.498175\pi$
$500$	2.40097e8	0.0858999
$501$	3.37350e9	1.19853
$502$	8.63455e8	0.304633
$503$	4.34681e9	1.52294	0.761470	−	0.648201i	$-0.224478\pi$
$503$	4.34681e9	1.52294	0.761470	+	0.648201i	$0.224478\pi$
$504$	9.42788e8	0.328025
$505$	1.71287e9	0.591842
$506$	−6.67020e8	−0.228882
$507$	−9.17283e9	−3.12590
$508$	1.93432e9	0.654645
$509$	−4.54304e8	−0.152698	−0.0763492	−	0.997081i	$-0.524326\pi$
$509$	−4.54304e8	−0.152698	−0.0763492	+	0.997081i	$0.524326\pi$
$510$	−5.20348e8	−0.173699
$511$	−1.82623e8	−0.0605455
$512$	2.56295e9	0.843909
$513$	9.67010e9	3.16242
$514$	3.93540e8	0.127826
$515$	5.13716e8	0.165729
$516$	6.10338e9	1.95567
$517$	1.45471e9	0.462977
$518$	−1.60334e7	−0.00506841
$519$	2.43482e9	0.764508
$520$	9.26219e8	0.288870
$521$	−1.68316e9	−0.521425	−0.260713	−	0.965416i	$-0.583958\pi$
$521$	−1.68316e9	−0.521425	−0.260713	+	0.965416i	$0.583958\pi$
$522$	1.11754e9	0.343889
$523$	1.73091e9	0.529077	0.264539	−	0.964375i	$-0.414780\pi$
$523$	1.73091e9	0.529077	0.264539	+	0.964375i	$0.414780\pi$
$524$	−2.09571e9	−0.636315
$525$	4.50051e8	0.135739
$526$	−4.61373e8	−0.138230
$527$	2.85241e9	0.848937
$528$	6.55866e9	1.93908
$529$	−3.95797e8	−0.116246
$530$	−2.11995e8	−0.0618528
$531$	1.17471e10	3.40488
$532$	−1.81330e9	−0.522131
$533$	−5.79474e9	−1.65763
$534$	7.73059e8	0.219694
$535$	1.61749e9	0.456671
$536$	−2.12334e9	−0.595584
$537$	−7.15833e9	−1.99481
$538$	3.08034e8	0.0852827
$539$	−6.35337e8	−0.174761
$540$	−3.45525e9	−0.944281
$541$	1.49368e9	0.405572	0.202786	−	0.979223i	$-0.435000\pi$
$541$	1.49368e9	0.405572	0.202786	+	0.979223i	$0.435000\pi$
$542$	4.22849e8	0.114074
$543$	−3.03118e9	−0.812480
$544$	−2.30915e9	−0.614974
$545$	−1.75706e9	−0.464943
$546$	8.50536e8	0.223624
$547$	2.87217e8	0.0750333	0.0375167	−	0.999296i	$-0.488055\pi$
$547$	2.87217e8	0.0750333	0.0375167	+	0.999296i	$0.488055\pi$
$548$	−2.75109e8	−0.0714122
$549$	4.89249e9	1.26190
$550$	−1.89997e8	−0.0486941
$551$	−4.38749e9	−1.11734
$552$	2.60269e9	0.658622
$553$	1.16512e9	0.292977
$554$	−1.10881e9	−0.277059
$555$	2.17911e8	0.0541070
$556$	4.03399e9	0.995342
$557$	6.94330e9	1.70244	0.851222	−	0.524806i	$-0.175862\pi$
$557$	6.94330e9	1.70244	0.851222	+	0.524806i	$0.175862\pi$
$558$	−1.41923e9	−0.345807
$559$	7.75366e9	1.87744
$560$	6.20091e8	0.149210
$561$	−9.98367e9	−2.38737
$562$	9.12934e8	0.216951
$563$	−7.40630e9	−1.74913	−0.874565	−	0.484909i	$-0.838853\pi$
$563$	−7.40630e9	−1.74913	−0.874565	+	0.484909i	$0.838853\pi$
$564$	−2.78077e9	−0.652661
$565$	−1.01499e9	−0.236752
$566$	1.06243e9	0.246288
$567$	−2.82748e9	−0.651416
$568$	5.59104e8	0.128019
$569$	−4.25205e9	−0.967622	−0.483811	−	0.875172i	$-0.660748\pi$
$569$	−4.25205e9	−0.967622	−0.483811	+	0.875172i	$0.660748\pi$
$570$	−1.01645e9	−0.229892
$571$	6.25391e9	1.40581	0.702903	−	0.711286i	$-0.251887\pi$
$571$	6.25391e9	1.40581	0.702903	+	0.711286i	$0.251887\pi$
$572$	8.70593e9	1.94504
$573$	−1.06893e10	−2.37359
$574$	3.41268e8	0.0753190
$575$	8.57103e8	0.188016
$576$	−7.85681e9	−1.71304
$577$	8.10453e9	1.75636	0.878178	−	0.478334i	$-0.158759\pi$
$577$	8.10453e9	1.75636	0.878178	+	0.478334i	$0.158759\pi$
$578$	1.67390e8	0.0360565
$579$	−1.12633e10	−2.41151
$580$	1.56771e9	0.333631
$581$	−7.93337e8	−0.167819
$582$	−1.95892e9	−0.411895
$583$	−4.06744e9	−0.850122
$584$	−3.00831e8	−0.0624997
$585$	−7.97461e9	−1.64689
$586$	−6.81438e8	−0.139889
$587$	4.85213e9	0.990145	0.495073	−	0.868852i	$-0.335141\pi$
$587$	4.85213e9	0.990145	0.495073	+	0.868852i	$0.335141\pi$
$588$	1.21449e9	0.246361
$589$	5.57192e9	1.12357
$590$	−6.79664e8	−0.136242
$591$	5.51788e9	1.09955
$592$	3.00243e8	0.0594768
$593$	5.99686e9	1.18095	0.590476	−	0.807055i	$-0.298940\pi$
$593$	5.99686e9	1.18095	0.590476	+	0.807055i	$0.298940\pi$
$594$	2.73425e9	0.535286
$595$	−9.43911e8	−0.183705
$596$	3.04248e9	0.588661
$597$	−1.30170e10	−2.50380
$598$	1.61981e9	0.309749
$599$	−2.47057e9	−0.469681	−0.234840	−	0.972034i	$-0.575457\pi$
$599$	−2.47057e9	−0.469681	−0.234840	+	0.972034i	$0.575457\pi$
$600$	7.41361e8	0.140120
$601$	8.37526e9	1.57376	0.786879	−	0.617108i	$-0.211696\pi$
$601$	8.37526e9	1.57376	0.786879	+	0.617108i	$0.211696\pi$
$602$	−4.56635e8	−0.0853064
$603$	1.82816e10	3.39551
$604$	−8.16680e8	−0.150807
$605$	−1.20948e9	−0.222052
$606$	2.59103e9	0.472953
$607$	2.57508e9	0.467337	0.233668	−	0.972316i	$-0.424927\pi$
$607$	2.57508e9	0.467337	0.233668	+	0.972316i	$0.424927\pi$
$608$	−4.51071e9	−0.813921
$609$	2.93859e9	0.527203
$610$	−2.83069e8	−0.0504937
$611$	−3.53266e9	−0.626552
$612$	1.31656e10	2.32173
$613$	3.51849e9	0.616942	0.308471	−	0.951234i	$-0.400183\pi$
$613$	3.51849e9	0.616942	0.308471	+	0.951234i	$0.400183\pi$
$614$	−9.79060e7	−0.0170695
$615$	−4.63820e9	−0.804057
$616$	−1.04658e9	−0.180401
$617$	−3.16189e9	−0.541936	−0.270968	−	0.962588i	$-0.587344\pi$
$617$	−3.16189e9	−0.541936	−0.270968	+	0.962588i	$0.587344\pi$
$618$	7.77087e8	0.132437
$619$	−8.48781e9	−1.43840	−0.719198	−	0.694805i	$-0.755491\pi$
$619$	−8.48781e9	−1.43840	−0.719198	+	0.694805i	$0.755491\pi$
$620$	−1.99092e9	−0.335492
$621$	−1.23346e10	−2.06683
$622$	−2.17160e9	−0.361837
$623$	1.40233e9	0.232349
$624$	−1.59272e10	−2.62419
$625$	2.44141e8	0.0400000
$626$	3.98958e8	0.0650005
$627$	−1.95021e10	−3.15970
$628$	−1.09135e10	−1.75835
$629$	−4.57034e8	−0.0732270
$630$	4.69647e8	0.0748307
$631$	9.25057e9	1.46577	0.732885	−	0.680353i	$-0.238173\pi$
$631$	9.25057e9	1.46577	0.732885	+	0.680353i	$0.238173\pi$
$632$	1.91929e9	0.302434
$633$	−8.15180e9	−1.27744
$634$	1.14936e9	0.179120
$635$	1.96690e9	0.304841
$636$	7.77517e9	1.19842
$637$	1.54287e9	0.236506
$638$	−1.24058e9	−0.189126
$639$	−4.81380e9	−0.729852
$640$	2.13279e9	0.321601
$641$	6.98929e9	1.04817	0.524083	−	0.851667i	$-0.324408\pi$
$641$	6.98929e9	1.04817	0.524083	+	0.851667i	$0.324408\pi$
$642$	2.44675e9	0.364936
$643$	4.05980e9	0.602235	0.301118	−	0.953587i	$-0.402640\pi$
$643$	4.05980e9	0.602235	0.301118	+	0.953587i	$0.402640\pi$
$644$	2.31294e9	0.341243
$645$	6.20616e9	0.910676
$646$	2.13184e9	0.311130
$647$	4.90361e9	0.711788	0.355894	−	0.934526i	$-0.384176\pi$
$647$	4.90361e9	0.711788	0.355894	+	0.934526i	$0.384176\pi$
$648$	−4.65765e9	−0.672441
$649$	−1.30404e10	−1.87255
$650$	4.61393e8	0.0658984
$651$	−3.73188e9	−0.530144
$652$	−3.21055e9	−0.453642
$653$	4.23630e9	0.595375	0.297687	−	0.954663i	$-0.403785\pi$
$653$	4.23630e9	0.595375	0.297687	+	0.954663i	$0.403785\pi$
$654$	−2.65787e9	−0.371546
$655$	−2.13101e9	−0.296306
$656$	−6.39063e9	−0.883853
$657$	2.59011e9	0.356319
$658$	2.08048e8	0.0284691
$659$	1.05946e10	1.44207	0.721034	−	0.692900i	$-0.243667\pi$
$659$	1.05946e10	1.44207	0.721034	+	0.692900i	$0.243667\pi$
$660$	6.96837e9	0.943468
$661$	−8.64100e9	−1.16375	−0.581874	−	0.813279i	$-0.697680\pi$
$661$	−8.64100e9	−1.16375	−0.581874	+	0.813279i	$0.697680\pi$
$662$	−1.76246e9	−0.236112
$663$	2.42446e10	3.23086
$664$	−1.30685e9	−0.173236
$665$	−1.84384e9	−0.243135
$666$	2.27399e8	0.0298284
$667$	5.59642e9	0.730247
$668$	4.93844e9	0.641021
$669$	−5.87623e9	−0.758765
$670$	−1.05774e9	−0.135867
$671$	−5.43110e9	−0.694000
$672$	3.02112e9	0.384039
$673$	6.03218e9	0.762819	0.381410	−	0.924406i	$-0.375439\pi$
$673$	6.03218e9	0.762819	0.381410	+	0.924406i	$0.375439\pi$
$674$	−1.68157e9	−0.211546
$675$	−3.51344e9	−0.439713
$676$	−1.34281e10	−1.67186
$677$	−1.09600e10	−1.35754	−0.678768	−	0.734353i	$-0.737486\pi$
$677$	−1.09600e10	−1.35754	−0.678768	+	0.734353i	$0.737486\pi$
$678$	−1.53536e9	−0.189193
$679$	−3.55348e9	−0.435621
$680$	−1.55489e9	−0.189635
$681$	2.65433e10	3.22063
$682$	1.57548e9	0.190181
$683$	−8.61765e9	−1.03494	−0.517471	−	0.855701i	$-0.673127\pi$
$683$	−8.61765e9	−1.03494	−0.517471	+	0.855701i	$0.673127\pi$
$684$	2.57178e10	3.07282
$685$	−2.79741e8	−0.0332537
$686$	−9.08641e7	−0.0107463
$687$	−1.24784e10	−1.46828
$688$	8.55100e9	1.00105
$689$	9.87749e9	1.15048
$690$	1.29652e9	0.150248
$691$	−1.89080e9	−0.218008	−0.109004	−	0.994041i	$-0.534766\pi$
$691$	−1.89080e9	−0.218008	−0.109004	+	0.994041i	$0.534766\pi$
$692$	3.56433e9	0.408890
$693$	9.01089e9	1.02849
$694$	−1.06283e9	−0.120700
$695$	4.10192e9	0.463490
$696$	4.84068e9	0.544220
$697$	9.72789e9	1.08819
$698$	2.60152e9	0.289557
$699$	−9.17748e9	−1.01637
$700$	6.58827e8	0.0725986
$701$	−5.36641e9	−0.588397	−0.294199	−	0.955744i	$-0.595053\pi$
$701$	−5.36641e9	−0.588397	−0.294199	+	0.955744i	$0.595053\pi$
$702$	−6.63993e9	−0.724409
$703$	−8.92772e8	−0.0969163
$704$	8.72177e9	0.942107
$705$	−2.82760e9	−0.303917
$706$	1.31041e8	0.0140149
$707$	4.70013e9	0.500197
$708$	2.49276e10	2.63975
$709$	−5.88817e9	−0.620466	−0.310233	−	0.950661i	$-0.600407\pi$
$709$	−5.88817e9	−0.620466	−0.310233	+	0.950661i	$0.600407\pi$
$710$	2.78516e8	0.0292042
$711$	−1.65248e10	−1.72422
$712$	2.31003e9	0.239849
$713$	−7.10721e9	−0.734320
$714$	−1.42784e9	−0.146803
$715$	8.85254e9	0.905725
$716$	−1.04790e10	−1.06691
$717$	−3.19465e9	−0.323673
$718$	−3.48436e9	−0.351307
$719$	4.02615e9	0.403961	0.201980	−	0.979390i	$-0.435262\pi$
$719$	4.02615e9	0.403961	0.201980	+	0.979390i	$0.435262\pi$
$720$	−8.79466e9	−0.878123
$721$	1.40964e9	0.140066
$722$	2.15162e9	0.212758
$723$	2.61476e8	0.0257305
$724$	−4.43733e9	−0.434547
$725$	1.59411e9	0.155358
$726$	−1.82956e9	−0.177447
$727$	−9.19346e9	−0.887378	−0.443689	−	0.896181i	$-0.646330\pi$
$727$	−9.19346e9	−0.887378	−0.443689	+	0.896181i	$0.646330\pi$
$728$	2.54154e9	0.244139
$729$	−1.19438e9	−0.114181
$730$	−1.49858e8	−0.0142577
$731$	−1.30164e10	−1.23248
$732$	1.03819e10	0.978336
$733$	−7.48176e9	−0.701681	−0.350840	−	0.936435i	$-0.614104\pi$
$733$	−7.48176e9	−0.701681	−0.350840	+	0.936435i	$0.614104\pi$
$734$	2.13345e9	0.199134
$735$	1.23494e9	0.114720
$736$	5.75359e9	0.531945
$737$	−2.02943e10	−1.86740
$738$	−4.84016e9	−0.443264
$739$	−1.01973e7	−0.000929455 0	−0.000464728	−	1.00000i	$-0.500148\pi$
$739$	−1.01973e7	−0.000929455 0	−0.000464728		1.00000i	$0.500148\pi$
$740$	3.18999e8	0.0289386
$741$	4.73596e10	4.27606
$742$	−5.81713e8	−0.0522752
$743$	−1.82814e10	−1.63512	−0.817559	−	0.575845i	$-0.804673\pi$
$743$	−1.82814e10	−1.63512	−0.817559	+	0.575845i	$0.804673\pi$
$744$	−6.14745e9	−0.547255
$745$	3.09371e9	0.274115
$746$	−1.32379e9	−0.116744
$747$	1.12518e10	0.987641
$748$	−1.46151e10	−1.27686
$749$	4.43840e9	0.385958
$750$	3.69307e8	0.0319649
$751$	7.58051e9	0.653068	0.326534	−	0.945185i	$-0.394119\pi$
$751$	7.58051e9	0.653068	0.326534	+	0.945185i	$0.394119\pi$
$752$	−3.89593e9	−0.334079
$753$	−3.22016e10	−2.74849
$754$	3.01265e9	0.255946
$755$	−8.30432e8	−0.0702247
$756$	−9.48121e9	−0.798063
$757$	−8.44446e9	−0.707516	−0.353758	−	0.935337i	$-0.615096\pi$
$757$	−8.44446e9	−0.707516	−0.353758	+	0.935337i	$0.615096\pi$
$758$	3.82254e9	0.318794
$759$	2.48758e10	2.06505
$760$	−3.03732e9	−0.250982
$761$	−8.70967e9	−0.716400	−0.358200	−	0.933645i	$-0.616609\pi$
$761$	−8.70967e9	−0.716400	−0.358200	+	0.933645i	$0.616609\pi$
$762$	2.97529e9	0.243605
$763$	−4.82138e9	−0.392948
$764$	−1.56479e10	−1.26949
$765$	1.33873e10	1.08113
$766$	7.69932e8	0.0618944
$767$	3.16677e10	2.53415
$768$	−1.41336e10	−1.12587
$769$	−2.09224e10	−1.65909	−0.829544	−	0.558442i	$-0.811399\pi$
$769$	−2.09224e10	−1.65909	−0.829544	+	0.558442i	$0.811399\pi$
$770$	−5.21351e8	−0.0411540
$771$	−1.46766e10	−1.15328
$772$	−1.64883e10	−1.28978
$773$	9.55003e9	0.743664	0.371832	−	0.928300i	$-0.378730\pi$
$773$	9.55003e9	0.743664	0.371832	+	0.928300i	$0.378730\pi$
$774$	6.47639e9	0.502041
$775$	−2.02444e9	−0.156225
$776$	−5.85358e9	−0.449682
$777$	5.97948e8	0.0457288
$778$	1.65262e9	0.125819
$779$	1.90025e10	1.44022
$780$	−1.69222e10	−1.27681
$781$	5.34376e9	0.401391
$782$	−2.71925e9	−0.203342
$783$	−2.29408e10	−1.70782
$784$	1.70153e9	0.126105
$785$	−1.10973e10	−0.818791
$786$	−3.22353e9	−0.236784
$787$	−2.18709e9	−0.159939	−0.0799695	−	0.996797i	$-0.525482\pi$
$787$	−2.18709e9	−0.159939	−0.0799695	+	0.996797i	$0.525482\pi$
$788$	8.07760e9	0.588086
$789$	1.72064e10	1.24715
$790$	9.56087e8	0.0689926
$791$	−2.78514e9	−0.200092
$792$	1.48435e10	1.06169
$793$	1.31891e10	0.939198
$794$	−1.26699e7	−0.000898256 0
$795$	7.90611e9	0.558056
$796$	−1.90555e10	−1.33913
$797$	1.56685e10	1.09628	0.548142	−	0.836385i	$-0.315335\pi$
$797$	1.56685e10	1.09628	0.548142	+	0.836385i	$0.315335\pi$
$798$	−2.78914e9	−0.194294
$799$	5.93044e9	0.411314
$800$	1.63888e9	0.113170
$801$	−1.98890e10	−1.36741
$802$	−2.57848e9	−0.176504
$803$	−2.87526e9	−0.195962
$804$	3.87938e10	2.63249
$805$	2.35189e9	0.158903
$806$	−3.82593e9	−0.257374
$807$	−1.14878e10	−0.769448
$808$	7.74243e9	0.516342
$809$	−9.81598e9	−0.651799	−0.325900	−	0.945404i	$-0.605667\pi$
$809$	−9.81598e9	−0.651799	−0.325900	+	0.945404i	$0.605667\pi$
$810$	−2.32020e9	−0.153401
$811$	1.43848e10	0.946960	0.473480	−	0.880804i	$-0.342998\pi$
$811$	1.43848e10	0.946960	0.473480	+	0.880804i	$0.342998\pi$
$812$	4.30179e9	0.281970
$813$	−1.57697e10	−1.02922
$814$	−2.52434e8	−0.0164045
$815$	−3.26462e9	−0.211242
$816$	2.67378e10	1.72270
$817$	−2.54264e10	−1.63120
$818$	−4.71914e9	−0.301458
$819$	−2.18823e10	−1.39187
$820$	−6.78984e9	−0.430042
$821$	1.02959e10	0.649325	0.324663	−	0.945830i	$-0.394749\pi$
$821$	1.02959e10	0.649325	0.324663	+	0.945830i	$0.394749\pi$
$822$	−4.23159e8	−0.0265737
$823$	2.30875e10	1.44370	0.721851	−	0.692049i	$-0.243292\pi$
$823$	2.30875e10	1.44370	0.721851	+	0.692049i	$0.243292\pi$
$824$	2.32207e9	0.144587
$825$	7.08571e9	0.439334
$826$	−1.86500e9	−0.115146
$827$	1.18121e10	0.726202	0.363101	−	0.931750i	$-0.381718\pi$
$827$	1.18121e10	0.726202	0.363101	+	0.931750i	$0.381718\pi$
$828$	−3.28041e10	−2.00827
$829$	2.76192e10	1.68372	0.841859	−	0.539697i	$-0.181461\pi$
$829$	2.76192e10	1.68372	0.841859	+	0.539697i	$0.181461\pi$
$830$	−6.51003e8	−0.0395194
$831$	4.13518e10	2.49972
$832$	−2.11802e10	−1.27497
$833$	−2.59009e9	−0.155259
$834$	6.20489e9	0.370385
$835$	5.02161e9	0.298497
$836$	−2.85491e10	−1.68994
$837$	2.91339e10	1.71735
$838$	−1.16822e9	−0.0685757
$839$	1.39121e10	0.813252	0.406626	−	0.913595i	$-0.366705\pi$
$839$	1.39121e10	0.813252	0.406626	+	0.913595i	$0.366705\pi$
$840$	2.03429e9	0.118423
$841$	−6.84123e9	−0.396596
$842$	2.40807e9	0.139020
$843$	−3.40469e10	−1.95740
$844$	−1.19334e10	−0.683227
$845$	−1.36542e10	−0.778516
$846$	−2.95072e9	−0.167545
$847$	−3.31881e9	−0.187668
$848$	1.08932e10	0.613439
$849$	−3.96222e10	−2.22209
$850$	−7.74563e8	−0.0432604
$851$	1.13877e9	0.0633405
$852$	−1.02149e10	−0.565844
$853$	−1.59256e10	−0.878565	−0.439283	−	0.898349i	$-0.644767\pi$
$853$	−1.59256e10	−0.878565	−0.439283	+	0.898349i	$0.644767\pi$
$854$	−7.76740e8	−0.0426750
$855$	2.61509e10	1.43089
$856$	7.31129e9	0.398415
$857$	2.84395e10	1.54344	0.771719	−	0.635964i	$-0.219397\pi$
$857$	2.84395e10	1.54344	0.771719	+	0.635964i	$0.219397\pi$
$858$	1.33911e10	0.723785
$859$	9.80898e9	0.528017	0.264008	−	0.964520i	$-0.414955\pi$
$859$	9.80898e9	0.528017	0.264008	+	0.964520i	$0.414955\pi$
$860$	9.08517e9	0.487067
$861$	−1.27272e10	−0.679552
$862$	−1.54471e9	−0.0821430
$863$	5.18908e9	0.274823	0.137411	−	0.990514i	$-0.456122\pi$
$863$	5.18908e9	0.274823	0.137411	+	0.990514i	$0.456122\pi$
$864$	−2.35851e10	−1.24406
$865$	3.62435e9	0.190403
$866$	−6.63657e9	−0.347241
$867$	−6.24264e9	−0.325313
$868$	−5.46308e9	−0.283543
$869$	1.83440e10	0.948254
$870$	2.41137e9	0.124150
$871$	4.92832e10	2.52718
$872$	−7.94217e9	−0.405631
$873$	5.03984e10	2.56370
$874$	−5.31180e9	−0.269124
$875$	6.69922e8	0.0338062
$876$	5.49624e9	0.276249
$877$	−1.44992e10	−0.725847	−0.362923	−	0.931819i	$-0.618221\pi$
$877$	−1.44992e10	−0.725847	−0.362923	+	0.931819i	$0.618221\pi$
$878$	3.39595e9	0.169329
$879$	2.54135e10	1.26213
$880$	9.76288e9	0.482935
$881$	8.32527e9	0.410187	0.205094	−	0.978742i	$-0.434250\pi$
$881$	8.32527e9	0.410187	0.205094	+	0.978742i	$0.434250\pi$
$882$	1.28871e9	0.0632434
$883$	−1.04363e10	−0.510132	−0.255066	−	0.966924i	$-0.582097\pi$
$883$	−1.04363e10	−0.510132	−0.255066	+	0.966924i	$0.582097\pi$
$884$	3.54916e10	1.72800
$885$	2.53473e10	1.22922
$886$	7.26045e9	0.350708
$887$	1.87211e10	0.900740	0.450370	−	0.892842i	$-0.351292\pi$
$887$	1.87211e10	0.900740	0.450370	+	0.892842i	$0.351292\pi$
$888$	9.84989e8	0.0472048
$889$	5.39716e9	0.257638
$890$	1.15073e9	0.0547155
$891$	−4.45165e10	−2.10838
$892$	−8.60219e9	−0.405818
$893$	1.15845e10	0.544376
$894$	4.67980e9	0.219051
$895$	−1.06555e10	−0.496814
$896$	5.85237e9	0.271802
$897$	−6.04091e10	−2.79466
$898$	−7.57811e9	−0.349216
$899$	−1.32185e10	−0.606770
$900$	−9.34405e9	−0.427254
$901$	−1.65818e10	−0.755258
$902$	5.37301e9	0.243778
$903$	1.70297e10	0.769662
$904$	−4.58791e9	−0.206550
$905$	−4.51206e9	−0.202351
$906$	−1.25618e9	−0.0561181
$907$	−8.88710e9	−0.395489	−0.197745	−	0.980254i	$-0.563362\pi$
$907$	−8.88710e9	−0.395489	−0.197745	+	0.980254i	$0.563362\pi$
$908$	3.88566e10	1.72252
$909$	−6.66612e10	−2.94374
$910$	1.26606e9	0.0556943
$911$	−3.31567e10	−1.45297	−0.726487	−	0.687181i	$-0.758848\pi$
$911$	−3.31567e10	−1.45297	−0.726487	+	0.687181i	$0.758848\pi$
$912$	5.22297e10	2.28001
$913$	−1.24905e10	−0.543165
$914$	6.14350e9	0.266136
$915$	1.05567e10	0.455571
$916$	−1.82670e10	−0.785297
$917$	−5.84748e9	−0.250424
$918$	1.11468e10	0.475553
$919$	−2.43344e10	−1.03423	−0.517115	−	0.855916i	$-0.672994\pi$
$919$	−2.43344e10	−1.03423	−0.517115	+	0.855916i	$0.672994\pi$
$920$	3.87423e9	0.164032
$921$	3.65130e9	0.154006
$922$	−6.44703e9	−0.270895
$923$	−1.29769e10	−0.543208
$924$	1.91212e10	0.797376
$925$	3.24371e8	0.0134755
$926$	5.45522e9	0.225774
$927$	−1.99926e10	−0.824311
$928$	1.07010e10	0.439547
$929$	−3.59225e10	−1.46998	−0.734990	−	0.678078i	$-0.762813\pi$
$929$	−3.59225e10	−1.46998	−0.734990	+	0.678078i	$0.762813\pi$
$930$	−3.06234e9	−0.124843
$931$	−5.05949e9	−0.205486
$932$	−1.34349e10	−0.543598
$933$	8.09873e10	3.26461
$934$	5.23367e9	0.210181
$935$	−1.48612e10	−0.594583
$936$	−3.60463e10	−1.43680
$937$	−1.59065e10	−0.631663	−0.315831	−	0.948815i	$-0.602283\pi$
$937$	−1.59065e10	−0.631663	−0.315831	+	0.948815i	$0.602283\pi$
$938$	−2.90243e9	−0.114829
$939$	−1.48787e10	−0.586455
$940$	−4.13930e9	−0.162547
$941$	−1.08171e10	−0.423203	−0.211602	−	0.977356i	$-0.567868\pi$
$941$	−1.08171e10	−0.423203	−0.211602	+	0.977356i	$0.567868\pi$
$942$	−1.67867e10	−0.654314
$943$	−2.42385e10	−0.941270
$944$	3.49242e10	1.35121
$945$	−9.64087e9	−0.371625
$946$	−7.18938e9	−0.276104
$947$	4.16267e10	1.59275	0.796373	−	0.604806i	$-0.206749\pi$
$947$	4.16267e10	1.59275	0.796373	+	0.604806i	$0.206749\pi$
$948$	−3.50657e10	−1.33676
$949$	6.98236e9	0.265198
$950$	−1.51303e9	−0.0572553
$951$	−4.28642e10	−1.61608
$952$	−4.26661e9	−0.160271
$953$	2.52566e9	0.0945257	0.0472629	−	0.998882i	$-0.484950\pi$
$953$	2.52566e9	0.0945257	0.0472629	+	0.998882i	$0.484950\pi$
$954$	8.25035e9	0.307647
$955$	−1.59115e10	−0.591151
$956$	−4.67663e9	−0.173113
$957$	4.62659e10	1.70635
$958$	3.94184e9	0.144851
$959$	−7.67611e8	−0.0281045
$960$	−1.69530e10	−0.618439
$961$	−1.07257e10	−0.389846
$962$	6.13018e8	0.0222004
$963$	−6.29491e10	−2.27142
$964$	3.82774e8	0.0137617
$965$	−1.67659e10	−0.600595
$966$	3.55766e9	0.126983
$967$	3.55623e10	1.26473	0.632365	−	0.774671i	$-0.282084\pi$
$967$	3.55623e10	1.26473	0.632365	+	0.774671i	$0.282084\pi$
$968$	−5.46702e9	−0.193726
$969$	−7.95048e10	−2.80711
$970$	−2.91594e9	−0.102584
$971$	3.90352e10	1.36832	0.684162	−	0.729330i	$-0.260168\pi$
$971$	3.90352e10	1.36832	0.684162	+	0.729330i	$0.260168\pi$
$972$	2.46430e10	0.860720
$973$	1.12557e10	0.391720
$974$	−1.00560e10	−0.348715
$975$	−1.72072e10	−0.594556
$976$	1.45453e10	0.500783
$977$	−2.68391e10	−0.920740	−0.460370	−	0.887727i	$-0.652283\pi$
$977$	−2.68391e10	−0.920740	−0.460370	+	0.887727i	$0.652283\pi$
$978$	−4.93833e9	−0.168808
$979$	2.20786e10	0.752025
$980$	1.80782e9	0.0613570
$981$	6.83809e10	2.31256
$982$	−4.52410e9	−0.152455
$983$	6.49160e9	0.217979	0.108989	−	0.994043i	$-0.465239\pi$
$983$	6.49160e9	0.217979	0.108989	+	0.994043i	$0.465239\pi$
$984$	−2.09653e10	−0.701486
$985$	8.21363e9	0.273847
$986$	−5.05748e9	−0.168021
$987$	−7.75893e9	−0.256857
$988$	6.93295e10	2.28701
$989$	3.24324e10	1.06608
$990$	7.39424e9	0.242198
$991$	3.62645e10	1.18365	0.591826	−	0.806066i	$-0.298407\pi$
$991$	3.62645e10	1.18365	0.591826	+	0.806066i	$0.298407\pi$
$992$	−1.35898e10	−0.441999
$993$	6.57291e10	2.13027
$994$	7.64248e8	0.0246821
$995$	−1.93764e10	−0.623579
$996$	2.38764e10	0.765704
$997$	1.30595e10	0.417343	0.208671	−	0.977986i	$-0.433086\pi$
$997$	1.30595e10	0.417343	0.208671	+	0.977986i	$0.433086\pi$
$998$	7.16601e7	0.00228203
$999$	−4.66803e9	−0.148134

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.8.a.c.1.3	✓	4
3.2	odd	2		315.8.a.j.1.2		4
4.3	odd	2		560.8.a.p.1.4		4
5.2	odd	4		175.8.b.e.99.5		8
5.3	odd	4		175.8.b.e.99.4		8
5.4	even	2		175.8.a.e.1.2		4
7.6	odd	2		245.8.a.e.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.8.a.c.1.3	✓	4	1.1	even	1	trivial
175.8.a.e.1.2		4	5.4	even	2
175.8.b.e.99.4		8	5.3	odd	4
175.8.b.e.99.5		8	5.2	odd	4
245.8.a.e.1.3		4	7.6	odd	2
315.8.a.j.1.2		4	3.2	odd	2
560.8.a.p.1.4		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	35.a (trivial)

\(f(q)\)	\(=\)	\(q+2.25170 q^{2} -83.9745 q^{3} -122.930 q^{4} -125.000 q^{5} -189.085 q^{6} -343.000 q^{7} -565.018 q^{8} +4864.72 q^{9} +O(q^{10})\)	\(q+2.25170 q^{2} -83.9745 q^{3} -122.930 q^{4} -125.000 q^{5} -189.085 q^{6} -343.000 q^{7} -565.018 q^{8} +4864.72 q^{9} -281.462 q^{10} -5400.28 q^{11} +10323.0 q^{12} +13114.2 q^{13} -772.332 q^{14} +10496.8 q^{15} +14462.8 q^{16} -22015.4 q^{17} +10953.9 q^{18} -43005.0 q^{19} +15366.2 q^{20} +28803.3 q^{21} -12159.8 q^{22} +54854.6 q^{23} +47447.1 q^{24} +15625.0 q^{25} +29529.2 q^{26} -224860. q^{27} +42164.9 q^{28} +102023. q^{29} +23635.6 q^{30} -129564. q^{31} +104888. q^{32} +453486. q^{33} -49572.0 q^{34} +42875.0 q^{35} -598019. q^{36} +20759.7 q^{37} -96834.1 q^{38} -1.10126e6 q^{39} +70627.2 q^{40} -441867. q^{41} +64856.2 q^{42} +591242. q^{43} +663856. q^{44} -608090. q^{45} +123516. q^{46} -269377. q^{47} -1.21450e6 q^{48} +117649. q^{49} +35182.7 q^{50} +1.84873e6 q^{51} -1.61213e6 q^{52} +753191. q^{53} -506316. q^{54} +675035. q^{55} +193801. q^{56} +3.61132e6 q^{57} +229724. q^{58} +2.41476e6 q^{59} -1.29037e6 q^{60} +1.00571e6 q^{61} -291740. q^{62} -1.66860e6 q^{63} -1.61506e6 q^{64} -1.63927e6 q^{65} +1.02111e6 q^{66} +3.75801e6 q^{67} +2.70635e6 q^{68} -4.60639e6 q^{69} +96541.5 q^{70} -989533. q^{71} -2.74865e6 q^{72} +532428. q^{73} +46744.6 q^{74} -1.31210e6 q^{75} +5.28660e6 q^{76} +1.85230e6 q^{77} -2.47970e6 q^{78} -3.39686e6 q^{79} -1.80785e6 q^{80} +8.24337e6 q^{81} -994951. q^{82} +2.31294e6 q^{83} -3.54078e6 q^{84} +2.75193e6 q^{85} +1.33130e6 q^{86} -8.56731e6 q^{87} +3.05125e6 q^{88} -4.08842e6 q^{89} -1.36923e6 q^{90} -4.49817e6 q^{91} -6.74327e6 q^{92} +1.08801e7 q^{93} -606554. q^{94} +5.37562e6 q^{95} -8.80792e6 q^{96} +1.03600e7 q^{97} +264910. q^{98} -2.62708e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 37 q^{3} + 280 q^{4} - 500 q^{5} + 1144 q^{6} - 1372 q^{7} + 1512 q^{8} + 2391 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 37 * q^3 + 280 * q^4 - 500 * q^5 + 1144 * q^6 - 1372 * q^7 + 1512 * q^8 + 2391 * q^9	\( 4 q - 2 q^{2} - 37 q^{3} + 280 q^{4} - 500 q^{5} + 1144 q^{6} - 1372 q^{7} + 1512 q^{8} + 2391 q^{9} + 250 q^{10} - 7225 q^{11} + 28500 q^{12} + 7957 q^{13} + 686 q^{14} + 4625 q^{15} + 51288 q^{16} + 64727 q^{17} + 96526 q^{18} - 37866 q^{19} - 35000 q^{20} + 12691 q^{21} + 59056 q^{22} + 111470 q^{23} + 209264 q^{24} + 62500 q^{25} - 336012 q^{26} - 192271 q^{27} - 96040 q^{28} + 218711 q^{29} - 143000 q^{30} + 219348 q^{31} + 103104 q^{32} + 253827 q^{33} - 229548 q^{34} + 171500 q^{35} - 450196 q^{36} - 212844 q^{37} - 1317920 q^{38} - 1647245 q^{39} - 189000 q^{40} - 1215338 q^{41} - 392392 q^{42} + 1074782 q^{43} - 2220924 q^{44} - 298875 q^{45} + 2026336 q^{46} + 110699 q^{47} + 78792 q^{48} + 470596 q^{49} - 31250 q^{50} + 3506861 q^{51} - 1359172 q^{52} + 3568154 q^{53} - 1503432 q^{54} + 903125 q^{55} - 518616 q^{56} + 774022 q^{57} + 2081468 q^{58} + 261488 q^{59} - 3562500 q^{60} + 5355426 q^{61} + 74592 q^{62} - 820113 q^{63} - 5693296 q^{64} - 994625 q^{65} - 517720 q^{66} + 10352960 q^{67} + 18065332 q^{68} - 2385378 q^{69} - 85750 q^{70} + 3607808 q^{71} + 4037080 q^{72} + 2787392 q^{73} - 5682108 q^{74} - 578125 q^{75} - 4421656 q^{76} + 2478175 q^{77} - 15138056 q^{78} - 735975 q^{79} - 6411000 q^{80} + 10831108 q^{81} - 11516292 q^{82} + 2001724 q^{83} - 9775500 q^{84} - 8090875 q^{85} - 8821416 q^{86} + 3525721 q^{87} + 21825008 q^{88} - 13872714 q^{89} - 12065750 q^{90} - 2729251 q^{91} - 15116664 q^{92} + 25033932 q^{93} - 45240712 q^{94} + 4733250 q^{95} - 1056352 q^{96} - 12763773 q^{97} - 235298 q^{98} - 26960042 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 37 * q^3 + 280 * q^4 - 500 * q^5 + 1144 * q^6 - 1372 * q^7 + 1512 * q^8 + 2391 * q^9 + 250 * q^10 - 7225 * q^11 + 28500 * q^12 + 7957 * q^13 + 686 * q^14 + 4625 * q^15 + 51288 * q^16 + 64727 * q^17 + 96526 * q^18 - 37866 * q^19 - 35000 * q^20 + 12691 * q^21 + 59056 * q^22 + 111470 * q^23 + 209264 * q^24 + 62500 * q^25 - 336012 * q^26 - 192271 * q^27 - 96040 * q^28 + 218711 * q^29 - 143000 * q^30 + 219348 * q^31 + 103104 * q^32 + 253827 * q^33 - 229548 * q^34 + 171500 * q^35 - 450196 * q^36 - 212844 * q^37 - 1317920 * q^38 - 1647245 * q^39 - 189000 * q^40 - 1215338 * q^41 - 392392 * q^42 + 1074782 * q^43 - 2220924 * q^44 - 298875 * q^45 + 2026336 * q^46 + 110699 * q^47 + 78792 * q^48 + 470596 * q^49 - 31250 * q^50 + 3506861 * q^51 - 1359172 * q^52 + 3568154 * q^53 - 1503432 * q^54 + 903125 * q^55 - 518616 * q^56 + 774022 * q^57 + 2081468 * q^58 + 261488 * q^59 - 3562500 * q^60 + 5355426 * q^61 + 74592 * q^62 - 820113 * q^63 - 5693296 * q^64 - 994625 * q^65 - 517720 * q^66 + 10352960 * q^67 + 18065332 * q^68 - 2385378 * q^69 - 85750 * q^70 + 3607808 * q^71 + 4037080 * q^72 + 2787392 * q^73 - 5682108 * q^74 - 578125 * q^75 - 4421656 * q^76 + 2478175 * q^77 - 15138056 * q^78 - 735975 * q^79 - 6411000 * q^80 + 10831108 * q^81 - 11516292 * q^82 + 2001724 * q^83 - 9775500 * q^84 - 8090875 * q^85 - 8821416 * q^86 + 3525721 * q^87 + 21825008 * q^88 - 13872714 * q^89 - 12065750 * q^90 - 2729251 * q^91 - 15116664 * q^92 + 25033932 * q^93 - 45240712 * q^94 + 4733250 * q^95 - 1056352 * q^96 - 12763773 * q^97 - 235298 * q^98 - 26960042 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more