LMFDB - Embedded newform 7.10.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,10,Mod(1,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	7.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:	$3.60525085315$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 426x + 2016 $ x^3 - x^2 - 426*x + 2016
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$18.2745$ of defining polynomial
Character	$\chi$	$=$	7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-34.1627 q^{2} -79.6469 q^{3} +655.088 q^{4} +1423.70 q^{5} +2720.95 q^{6} +2401.00 q^{7} -4888.28 q^{8} -13339.4 q^{9} +O(q^{10})$	\(q-34.1627 q^{2} -79.6469 q^{3} +655.088 q^{4} +1423.70 q^{5} +2720.95 q^{6} +2401.00 q^{7} -4888.28 q^{8} -13339.4 q^{9} -48637.4 q^{10} +69354.4 q^{11} -52175.7 q^{12} +105959. q^{13} -82024.6 q^{14} -113393. q^{15} -168409. q^{16} +568267. q^{17} +455709. q^{18} -396405. q^{19} +932649. q^{20} -191232. q^{21} -2.36933e6 q^{22} -620765. q^{23} +389336. q^{24} +73796.7 q^{25} -3.61984e6 q^{26} +2.63013e6 q^{27} +1.57287e6 q^{28} +4.87652e6 q^{29} +3.87382e6 q^{30} -1.42482e6 q^{31} +8.25609e6 q^{32} -5.52386e6 q^{33} -1.94135e7 q^{34} +3.41830e6 q^{35} -8.73846e6 q^{36} +1.31092e7 q^{37} +1.35423e7 q^{38} -8.43931e6 q^{39} -6.95944e6 q^{40} -2.03049e7 q^{41} +6.53300e6 q^{42} -1.11768e7 q^{43} +4.54332e7 q^{44} -1.89913e7 q^{45} +2.12070e7 q^{46} -1.99352e7 q^{47} +1.34132e7 q^{48} +5.76480e6 q^{49} -2.52109e6 q^{50} -4.52607e7 q^{51} +6.94125e7 q^{52} +5.65007e7 q^{53} -8.98523e7 q^{54} +9.87398e7 q^{55} -1.17367e7 q^{56} +3.15725e7 q^{57} -1.66595e8 q^{58} -1.09340e8 q^{59} -7.42826e7 q^{60} +3.20008e7 q^{61} +4.86755e7 q^{62} -3.20278e7 q^{63} -1.95825e8 q^{64} +1.50854e8 q^{65} +1.88710e8 q^{66} +8.02869e7 q^{67} +3.72265e8 q^{68} +4.94420e7 q^{69} -1.16778e8 q^{70} +2.07893e8 q^{71} +6.52065e7 q^{72} -2.70274e8 q^{73} -4.47844e8 q^{74} -5.87768e6 q^{75} -2.59680e8 q^{76} +1.66520e8 q^{77} +2.88309e8 q^{78} -5.16196e8 q^{79} -2.39763e8 q^{80} +5.30772e7 q^{81} +6.93671e8 q^{82} -6.82693e8 q^{83} -1.25274e8 q^{84} +8.09042e8 q^{85} +3.81830e8 q^{86} -3.88400e8 q^{87} -3.39023e8 q^{88} -1.47150e8 q^{89} +6.48792e8 q^{90} +2.54408e8 q^{91} -4.06656e8 q^{92} +1.13482e8 q^{93} +6.81040e8 q^{94} -5.64362e8 q^{95} -6.57572e8 q^{96} +1.09643e9 q^{97} -1.96941e8 q^{98} -9.25144e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 14055 q^{8} - 26001 q^{9}+O(q^{10}) $ 3 * q + 21 * q^2 + 84 * q^3 + 1557 * q^4 + 1554 * q^5 + 4914 * q^6 + 7203 * q^7 + 14055 * q^8 - 26001 * q^9	\( 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 14055 q^{8} - 26001 q^{9} - 97860 q^{10} - 3444 q^{11} - 106386 q^{12} - 19782 q^{13} + 50421 q^{14} + 200304 q^{15} + 482961 q^{16} + 1016694 q^{17} - 273267 q^{18} + 222852 q^{19} - 1922088 q^{20} + 201684 q^{21} - 2847048 q^{22} + 1885632 q^{23} - 1449630 q^{24} + 3073221 q^{25} - 8785056 q^{26} + 551880 q^{27} + 3738357 q^{28} + 4081818 q^{29} + 8053200 q^{30} + 2869440 q^{31} + 25221951 q^{32} - 20259792 q^{33} - 3981642 q^{34} + 3731154 q^{35} - 35396379 q^{36} + 1395618 q^{37} + 43479870 q^{38} - 8990688 q^{39} - 82859280 q^{40} - 14420658 q^{41} + 11798514 q^{42} - 61631172 q^{43} + 97011984 q^{44} + 29774682 q^{45} + 89747664 q^{46} - 10368960 q^{47} + 16798782 q^{48} + 17294403 q^{49} + 73325055 q^{50} - 26146728 q^{51} - 80908044 q^{52} + 67502610 q^{53} - 117879300 q^{54} - 105823032 q^{55} + 33746055 q^{56} + 8471112 q^{57} - 159163830 q^{58} - 42590100 q^{59} - 179551008 q^{60} + 191746842 q^{61} - 46983468 q^{62} - 62428401 q^{63} + 7852161 q^{64} + 364283220 q^{65} - 8057952 q^{66} - 255175788 q^{67} + 743485806 q^{68} + 257903856 q^{69} - 234961860 q^{70} + 296514504 q^{71} - 609314265 q^{72} + 344213310 q^{73} - 690696462 q^{74} + 279031116 q^{75} + 728839986 q^{76} - 8269044 q^{77} + 280132776 q^{78} - 960412656 q^{79} - 1333333344 q^{80} - 35827677 q^{81} + 562675302 q^{82} - 1100517180 q^{83} - 255432786 q^{84} + 438179412 q^{85} - 880982256 q^{86} - 621821592 q^{87} + 1206124800 q^{88} + 506816478 q^{89} + 2303452620 q^{90} - 47496582 q^{91} + 691123488 q^{92} + 1693258512 q^{93} + 1388004828 q^{94} - 2203071072 q^{95} + 333385794 q^{96} - 647498250 q^{97} + 121060821 q^{98} - 1900979172 q^{99}+O(q^{100}) \) 3 * q + 21 * q^2 + 84 * q^3 + 1557 * q^4 + 1554 * q^5 + 4914 * q^6 + 7203 * q^7 + 14055 * q^8 - 26001 * q^9 - 97860 * q^10 - 3444 * q^11 - 106386 * q^12 - 19782 * q^13 + 50421 * q^14 + 200304 * q^15 + 482961 * q^16 + 1016694 * q^17 - 273267 * q^18 + 222852 * q^19 - 1922088 * q^20 + 201684 * q^21 - 2847048 * q^22 + 1885632 * q^23 - 1449630 * q^24 + 3073221 * q^25 - 8785056 * q^26 + 551880 * q^27 + 3738357 * q^28 + 4081818 * q^29 + 8053200 * q^30 + 2869440 * q^31 + 25221951 * q^32 - 20259792 * q^33 - 3981642 * q^34 + 3731154 * q^35 - 35396379 * q^36 + 1395618 * q^37 + 43479870 * q^38 - 8990688 * q^39 - 82859280 * q^40 - 14420658 * q^41 + 11798514 * q^42 - 61631172 * q^43 + 97011984 * q^44 + 29774682 * q^45 + 89747664 * q^46 - 10368960 * q^47 + 16798782 * q^48 + 17294403 * q^49 + 73325055 * q^50 - 26146728 * q^51 - 80908044 * q^52 + 67502610 * q^53 - 117879300 * q^54 - 105823032 * q^55 + 33746055 * q^56 + 8471112 * q^57 - 159163830 * q^58 - 42590100 * q^59 - 179551008 * q^60 + 191746842 * q^61 - 46983468 * q^62 - 62428401 * q^63 + 7852161 * q^64 + 364283220 * q^65 - 8057952 * q^66 - 255175788 * q^67 + 743485806 * q^68 + 257903856 * q^69 - 234961860 * q^70 + 296514504 * q^71 - 609314265 * q^72 + 344213310 * q^73 - 690696462 * q^74 + 279031116 * q^75 + 728839986 * q^76 - 8269044 * q^77 + 280132776 * q^78 - 960412656 * q^79 - 1333333344 * q^80 - 35827677 * q^81 + 562675302 * q^82 - 1100517180 * q^83 - 255432786 * q^84 + 438179412 * q^85 - 880982256 * q^86 - 621821592 * q^87 + 1206124800 * q^88 + 506816478 * q^89 + 2303452620 * q^90 - 47496582 * q^91 + 691123488 * q^92 + 1693258512 * q^93 + 1388004828 * q^94 - 2203071072 * q^95 + 333385794 * q^96 - 647498250 * q^97 + 121060821 * q^98 - 1900979172 * 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 $

$2$	−34.1627	−1.50979	−0.754896	−	0.655845i	$-0.772312\pi$
$2$	−34.1627	−1.50979	−0.754896	+	0.655845i	$0.772312\pi$
$3$	−79.6469	−0.567706	−0.283853	−	0.958868i	$-0.591613\pi$
$3$	−79.6469	−0.567706	−0.283853	+	0.958868i	$0.591613\pi$
$4$	655.088	1.27947
$5$	1423.70	1.01872	0.509358	−	0.860554i	$-0.329883\pi$
$5$	1423.70	1.01872	0.509358	+	0.860554i	$0.329883\pi$
$6$	2720.95	0.857117
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−4888.28	−0.421940
$9$	−13339.4	−0.677710
$10$	−48637.4	−1.53805
$11$	69354.4	1.42826	0.714129	−	0.700014i	$-0.246823\pi$
$11$	69354.4	1.42826	0.714129	+	0.700014i	$0.246823\pi$
$12$	−52175.7	−0.726362
$13$	105959.	1.02895	0.514473	−	0.857506i	$-0.327987\pi$
$13$	105959.	1.02895	0.514473	+	0.857506i	$0.327987\pi$
$14$	−82024.6	−0.570647
$15$	−113393.	−0.578331
$16$	−168409.	−0.642428
$17$	568267.	1.65018	0.825092	−	0.564998i	$-0.191123\pi$
$17$	568267.	1.65018	0.825092	+	0.564998i	$0.191123\pi$
$18$	455709.	1.02320
$19$	−396405.	−0.697828	−0.348914	−	0.937155i	$-0.613449\pi$
$19$	−396405.	−0.697828	−0.348914	+	0.937155i	$0.613449\pi$
$20$	932649.	1.30342
$21$	−191232.	−0.214573
$22$	−2.36933e6	−2.15637
$23$	−620765.	−0.462543	−0.231271	−	0.972889i	$-0.574288\pi$
$23$	−620765.	−0.462543	−0.231271	+	0.972889i	$0.574288\pi$
$24$	389336.	0.239538
$25$	73796.7	0.0377839
$26$	−3.61984e6	−1.55349
$27$	2.63013e6	0.952446
$28$	1.57287e6	0.483594
$29$	4.87652e6	1.28032	0.640161	−	0.768241i	$-0.278868\pi$
$29$	4.87652e6	1.28032	0.640161	+	0.768241i	$0.278868\pi$
$30$	3.87382e6	0.873159
$31$	−1.42482e6	−0.277096	−0.138548	−	0.990356i	$-0.544244\pi$
$31$	−1.42482e6	−0.277096	−0.138548	+	0.990356i	$0.544244\pi$
$32$	8.25609e6	1.39187
$33$	−5.52386e6	−0.810830
$34$	−1.94135e7	−2.49143
$35$	3.41830e6	0.385039
$36$	−8.73846e6	−0.867109
$37$	1.31092e7	1.14992	0.574960	−	0.818182i	$-0.305018\pi$
$37$	1.31092e7	1.14992	0.574960	+	0.818182i	$0.305018\pi$
$38$	1.35423e7	1.05357
$39$	−8.43931e6	−0.584139
$40$	−6.95944e6	−0.429837
$41$	−2.03049e7	−1.12221	−0.561105	−	0.827744i	$-0.689624\pi$
$41$	−2.03049e7	−1.12221	−0.561105	+	0.827744i	$0.689624\pi$
$42$	6.53300e6	0.323960
$43$	−1.11768e7	−0.498551	−0.249276	−	0.968433i	$-0.580193\pi$
$43$	−1.11768e7	−0.498551	−0.249276	+	0.968433i	$0.580193\pi$
$44$	4.54332e7	1.82741
$45$	−1.89913e7	−0.690395
$46$	2.12070e7	0.698343
$47$	−1.99352e7	−0.595909	−0.297955	−	0.954580i	$-0.596304\pi$
$47$	−1.99352e7	−0.595909	−0.297955	+	0.954580i	$0.596304\pi$
$48$	1.34132e7	0.364710
$49$	5.76480e6	0.142857
$50$	−2.52109e6	−0.0570458
$51$	−4.52607e7	−0.936819
$52$	6.94125e7	1.31651
$53$	5.65007e7	0.983586	0.491793	−	0.870712i	$-0.336342\pi$
$53$	5.65007e7	0.983586	0.491793	+	0.870712i	$0.336342\pi$
$54$	−8.98523e7	−1.43799
$55$	9.87398e7	1.45499
$56$	−1.17367e7	−0.159478
$57$	3.15725e7	0.396161
$58$	−1.66595e8	−1.93302
$59$	−1.09340e8	−1.17475	−0.587375	−	0.809315i	$-0.699839\pi$
$59$	−1.09340e8	−1.17475	−0.587375	+	0.809315i	$0.699839\pi$
$60$	−7.42826e7	−0.739957
$61$	3.20008e7	0.295921	0.147961	−	0.988993i	$-0.452729\pi$
$61$	3.20008e7	0.295921	0.147961	+	0.988993i	$0.452729\pi$
$62$	4.86755e7	0.418358
$63$	−3.20278e7	−0.256150
$64$	−1.95825e8	−1.45901
$65$	1.50854e8	1.04821
$66$	1.88710e8	1.22418
$67$	8.02869e7	0.486752	0.243376	−	0.969932i	$-0.421745\pi$
$67$	8.02869e7	0.486752	0.243376	+	0.969932i	$0.421745\pi$
$68$	3.72265e8	2.11136
$69$	4.94420e7	0.262588
$70$	−1.16778e8	−0.581328
$71$	2.07893e8	0.970906	0.485453	−	0.874263i	$-0.338655\pi$
$71$	2.07893e8	0.970906	0.485453	+	0.874263i	$0.338655\pi$
$72$	6.52065e7	0.285953
$73$	−2.70274e8	−1.11391	−0.556957	−	0.830541i	$-0.688031\pi$
$73$	−2.70274e8	−1.11391	−0.556957	+	0.830541i	$0.688031\pi$
$74$	−4.47844e8	−1.73614
$75$	−5.87768e6	−0.0214501
$76$	−2.59680e8	−0.892849
$77$	1.66520e8	0.539831
$78$	2.88309e8	0.881928
$79$	−5.16196e8	−1.49105	−0.745526	−	0.666477i	$-0.767802\pi$
$79$	−5.16196e8	−1.49105	−0.745526	+	0.666477i	$0.767802\pi$
$80$	−2.39763e8	−0.654452
$81$	5.30772e7	0.137002
$82$	6.93671e8	1.69430
$83$	−6.82693e8	−1.57897	−0.789486	−	0.613769i	$-0.789653\pi$
$83$	−6.82693e8	−1.57897	−0.789486	+	0.613769i	$0.789653\pi$
$84$	−1.25274e8	−0.274539
$85$	8.09042e8	1.68107
$86$	3.81830e8	0.752708
$87$	−3.88400e8	−0.726846
$88$	−3.39023e8	−0.602639
$89$	−1.47150e8	−0.248602	−0.124301	−	0.992245i	$-0.539669\pi$
$89$	−1.47150e8	−0.248602	−0.124301	+	0.992245i	$0.539669\pi$
$90$	6.48792e8	1.04235
$91$	2.54408e8	0.388905
$92$	−4.06656e8	−0.591809
$93$	1.13482e8	0.157309
$94$	6.81040e8	0.899699
$95$	−5.64362e8	−0.710889
$96$	−6.57572e8	−0.790174
$97$	1.09643e9	1.25750	0.628750	−	0.777608i	$-0.283567\pi$
$97$	1.09643e9	1.25750	0.628750	+	0.777608i	$0.283567\pi$
$98$	−1.96941e8	−0.215684
$99$	−9.25144e8	−0.967945
$100$	4.83433e7	0.0483433
$101$	2.08683e8	0.199545	0.0997727	−	0.995010i	$-0.468188\pi$
$101$	2.08683e8	0.199545	0.0997727	+	0.995010i	$0.468188\pi$
$102$	1.54623e9	1.41440
$103$	6.78194e8	0.593727	0.296863	−	0.954920i	$-0.404059\pi$
$103$	6.78194e8	0.593727	0.296863	+	0.954920i	$0.404059\pi$
$104$	−5.17957e8	−0.434154
$105$	−2.72257e8	−0.218589
$106$	−1.93021e9	−1.48501
$107$	−4.59542e8	−0.338921	−0.169461	−	0.985537i	$-0.554203\pi$
$107$	−4.59542e8	−0.338921	−0.169461	+	0.985537i	$0.554203\pi$
$108$	1.72297e9	1.21862
$109$	5.21086e8	0.353582	0.176791	−	0.984248i	$-0.443428\pi$
$109$	5.21086e8	0.353582	0.176791	+	0.984248i	$0.443428\pi$
$110$	−3.37322e9	−2.19673
$111$	−1.04410e9	−0.652816
$112$	−4.04349e8	−0.242815
$113$	4.45612e8	0.257101	0.128551	−	0.991703i	$-0.458968\pi$
$113$	4.45612e8	0.257101	0.128551	+	0.991703i	$0.458968\pi$
$114$	−1.07860e9	−0.598120
$115$	−8.83783e8	−0.471200
$116$	3.19455e9	1.63813
$117$	−1.41343e9	−0.697328
$118$	3.73535e9	1.77363
$119$	1.36441e9	0.623711
$120$	5.54298e8	0.244021
$121$	2.45208e9	1.03992
$122$	−1.09323e9	−0.446779
$123$	1.61723e9	0.637086
$124$	−9.33380e8	−0.354536
$125$	−2.67560e9	−0.980226
$126$	1.09416e9	0.386734
$127$	9.28626e8	0.316755	0.158378	−	0.987379i	$-0.449374\pi$
$127$	9.28626e8	0.316755	0.158378	+	0.987379i	$0.449374\pi$
$128$	2.46278e9	0.810925
$129$	8.90198e8	0.283030
$130$	−5.15357e9	−1.58257
$131$	2.57694e9	0.764509	0.382255	−	0.924057i	$-0.375148\pi$
$131$	2.57694e9	0.764509	0.382255	+	0.924057i	$0.375148\pi$
$132$	−3.61862e9	−1.03743
$133$	−9.51769e8	−0.263754
$134$	−2.74281e9	−0.734894
$135$	3.74452e9	0.970272
$136$	−2.77785e9	−0.696279
$137$	−4.44116e9	−1.07710	−0.538548	−	0.842595i	$-0.681027\pi$
$137$	−4.44116e9	−1.07710	−0.538548	+	0.842595i	$0.681027\pi$
$138$	−1.68907e9	−0.396453
$139$	−7.28389e9	−1.65499	−0.827497	−	0.561470i	$-0.810236\pi$
$139$	−7.28389e9	−1.65499	−0.827497	+	0.561470i	$0.810236\pi$
$140$	2.23929e9	0.492645
$141$	1.58778e9	0.338301
$142$	−7.10218e9	−1.46587
$143$	7.34872e9	1.46960
$144$	2.24647e9	0.435380
$145$	6.94270e9	1.30428
$146$	9.23328e9	1.68178
$147$	−4.59149e8	−0.0811008
$148$	8.58766e9	1.47129
$149$	4.87355e9	0.810042	0.405021	−	0.914307i	$-0.367264\pi$
$149$	4.87355e9	0.810042	0.405021	+	0.914307i	$0.367264\pi$
$150$	2.00797e8	0.0323852
$151$	−8.63776e9	−1.35209	−0.676044	−	0.736861i	$-0.736307\pi$
$151$	−8.63776e9	−1.35209	−0.676044	+	0.736861i	$0.736307\pi$
$152$	1.93774e9	0.294442
$153$	−7.58033e9	−1.11835
$154$	−5.68876e9	−0.815032
$155$	−2.02851e9	−0.282283
$156$	−5.52849e9	−0.747388
$157$	−9.34170e9	−1.22709	−0.613546	−	0.789659i	$-0.710258\pi$
$157$	−9.34170e9	−1.22709	−0.613546	+	0.789659i	$0.710258\pi$
$158$	1.76346e10	2.25118
$159$	−4.50010e9	−0.558387
$160$	1.17542e10	1.41792
$161$	−1.49046e9	−0.174825
$162$	−1.81326e9	−0.206844
$163$	−2.10680e9	−0.233765	−0.116883	−	0.993146i	$-0.537290\pi$
$163$	−2.10680e9	−0.233765	−0.116883	+	0.993146i	$0.537290\pi$
$164$	−1.33015e10	−1.43583
$165$	−7.86432e9	−0.826006
$166$	2.33226e10	2.38392
$167$	1.39800e10	1.39086	0.695431	−	0.718593i	$-0.255213\pi$
$167$	1.39800e10	1.39086	0.695431	+	0.718593i	$0.255213\pi$
$168$	9.34796e8	0.0905367
$169$	6.22820e8	0.0587316
$170$	−2.76390e10	−2.53806
$171$	5.28780e9	0.472925
$172$	−7.32180e9	−0.637881
$173$	−1.24435e10	−1.05618	−0.528088	−	0.849190i	$-0.677091\pi$
$173$	−1.24435e10	−1.05618	−0.528088	+	0.849190i	$0.677091\pi$
$174$	1.32688e10	1.09739
$175$	1.77186e8	0.0142810
$176$	−1.16799e10	−0.917553
$177$	8.70861e9	0.666913
$178$	5.02704e9	0.375338
$179$	7.30178e9	0.531606	0.265803	−	0.964027i	$-0.414363\pi$
$179$	7.30178e9	0.531606	0.265803	+	0.964027i	$0.414363\pi$
$180$	−1.24410e10	−0.883339
$181$	−1.27074e10	−0.880038	−0.440019	−	0.897988i	$-0.645028\pi$
$181$	−1.27074e10	−0.880038	−0.440019	+	0.897988i	$0.645028\pi$
$182$	−8.69125e9	−0.587166
$183$	−2.54876e9	−0.167996
$184$	3.03447e9	0.195165
$185$	1.86635e10	1.17144
$186$	−3.87685e9	−0.237504
$187$	3.94118e10	2.35689
$188$	−1.30593e10	−0.762448
$189$	6.31494e9	0.359991
$190$	1.92801e10	1.07329
$191$	1.61547e10	0.878311	0.439155	−	0.898411i	$-0.355278\pi$
$191$	1.61547e10	0.878311	0.439155	+	0.898411i	$0.355278\pi$
$192$	1.55968e10	0.828287
$193$	−1.52841e10	−0.792924	−0.396462	−	0.918051i	$-0.629762\pi$
$193$	−1.52841e10	−0.792924	−0.396462	+	0.918051i	$0.629762\pi$
$194$	−3.74570e10	−1.89856
$195$	−1.20150e10	−0.595072
$196$	3.77645e9	0.182781
$197$	2.33886e10	1.10639	0.553193	−	0.833053i	$-0.313409\pi$
$197$	2.33886e10	1.10639	0.553193	+	0.833053i	$0.313409\pi$
$198$	3.16054e10	1.46139
$199$	−2.53610e10	−1.14638	−0.573189	−	0.819423i	$-0.694294\pi$
$199$	−2.53610e10	−1.14638	−0.573189	+	0.819423i	$0.694294\pi$
$200$	−3.60738e8	−0.0159425
$201$	−6.39460e9	−0.276332
$202$	−7.12918e9	−0.301272
$203$	1.17085e10	0.483916
$204$	−2.96498e10	−1.19863
$205$	−2.89082e10	−1.14322
$206$	−2.31689e10	−0.896403
$207$	8.28061e9	0.313470
$208$	−1.78444e10	−0.661024
$209$	−2.74924e10	−0.996678
$210$	9.30104e9	0.330023
$211$	−9.23757e8	−0.0320838	−0.0160419	−	0.999871i	$-0.505107\pi$
$211$	−9.23757e8	−0.0320838	−0.0160419	+	0.999871i	$0.505107\pi$
$212$	3.70129e10	1.25847
$213$	−1.65580e10	−0.551189
$214$	1.56992e10	0.511700
$215$	−1.59124e10	−0.507883
$216$	−1.28568e10	−0.401875
$217$	−3.42098e9	−0.104733
$218$	−1.78017e10	−0.533835
$219$	2.15265e10	0.632375
$220$	6.46833e10	1.86162
$221$	6.02130e10	1.69795
$222$	3.56694e10	0.985615
$223$	6.68635e9	0.181058	0.0905290	−	0.995894i	$-0.471144\pi$
$223$	6.68635e9	0.181058	0.0905290	+	0.995894i	$0.471144\pi$
$224$	1.98229e10	0.526078
$225$	−9.84401e8	−0.0256065
$226$	−1.52233e10	−0.388169
$227$	−4.82876e10	−1.20703	−0.603516	−	0.797351i	$-0.706234\pi$
$227$	−4.82876e10	−1.20703	−0.603516	+	0.797351i	$0.706234\pi$
$228$	2.06827e10	0.506876
$229$	−2.34264e10	−0.562918	−0.281459	−	0.959573i	$-0.590818\pi$
$229$	−2.34264e10	−0.562918	−0.281459	+	0.959573i	$0.590818\pi$
$230$	3.01924e10	0.711413
$231$	−1.32628e10	−0.306465
$232$	−2.38378e10	−0.540219
$233$	−3.29140e10	−0.731609	−0.365805	−	0.930692i	$-0.619206\pi$
$233$	−3.29140e10	−0.731609	−0.365805	+	0.930692i	$0.619206\pi$
$234$	4.82864e10	1.05282
$235$	−2.83817e10	−0.607063
$236$	−7.16275e10	−1.50306
$237$	4.11134e10	0.846479
$238$	−4.66119e10	−0.941673
$239$	2.51973e10	0.499533	0.249766	−	0.968306i	$-0.419646\pi$
$239$	2.51973e10	0.499533	0.249766	+	0.968306i	$0.419646\pi$
$240$	1.90964e10	0.371536
$241$	7.00815e10	1.33822	0.669109	−	0.743165i	$-0.266676\pi$
$241$	7.00815e10	1.33822	0.669109	+	0.743165i	$0.266676\pi$
$242$	−8.37696e10	−1.57006
$243$	−5.59963e10	−1.03022
$244$	2.09633e10	0.378622
$245$	8.20735e9	0.145531
$246$	−5.52488e10	−0.961866
$247$	−4.20027e10	−0.718028
$248$	6.96489e9	0.116918
$249$	5.43744e10	0.896391
$250$	9.14056e10	1.47994
$251$	4.19681e10	0.667401	0.333701	−	0.942679i	$-0.391703\pi$
$251$	4.19681e10	0.667401	0.333701	+	0.942679i	$0.391703\pi$
$252$	−2.09811e10	−0.327737
$253$	−4.30527e10	−0.660630
$254$	−3.17243e10	−0.478235
$255$	−6.44377e10	−0.954353
$256$	1.61271e10	0.234680
$257$	8.37595e10	1.19766	0.598832	−	0.800875i	$-0.295632\pi$
$257$	8.37595e10	1.19766	0.598832	+	0.800875i	$0.295632\pi$
$258$	−3.04116e10	−0.427317
$259$	3.14751e10	0.434629
$260$	9.88226e10	1.34115
$261$	−6.50497e10	−0.867687
$262$	−8.80350e10	−1.15425
$263$	−2.34604e9	−0.0302367	−0.0151184	−	0.999886i	$-0.504813\pi$
$263$	−2.34604e9	−0.0302367	−0.0151184	+	0.999886i	$0.504813\pi$
$264$	2.70021e10	0.342122
$265$	8.04400e10	1.00200
$266$	3.25150e10	0.398214
$267$	1.17200e10	0.141133
$268$	5.25950e10	0.622784
$269$	−6.44659e10	−0.750663	−0.375332	−	0.926891i	$-0.622471\pi$
$269$	−6.44659e10	−0.750663	−0.375332	+	0.926891i	$0.622471\pi$
$270$	−1.27923e11	−1.46491
$271$	−1.40530e10	−0.158273	−0.0791365	−	0.996864i	$-0.525216\pi$
$271$	−1.40530e10	−0.158273	−0.0791365	+	0.996864i	$0.525216\pi$
$272$	−9.57011e10	−1.06012
$273$	−2.02628e10	−0.220784
$274$	1.51722e11	1.62619
$275$	5.11812e9	0.0539652
$276$	3.23889e10	0.335973
$277$	−7.52768e10	−0.768249	−0.384124	−	0.923281i	$-0.625497\pi$
$277$	−7.52768e10	−0.768249	−0.384124	+	0.923281i	$0.625497\pi$
$278$	2.48837e11	2.49870
$279$	1.90061e10	0.187791
$280$	−1.67096e10	−0.162463
$281$	9.56085e10	0.914783	0.457391	−	0.889266i	$-0.348784\pi$
$281$	9.56085e10	0.914783	0.457391	+	0.889266i	$0.348784\pi$
$282$	−5.42427e10	−0.510764
$283$	4.82806e10	0.447439	0.223719	−	0.974654i	$-0.428180\pi$
$283$	4.82806e10	0.447439	0.223719	+	0.974654i	$0.428180\pi$
$284$	1.36188e11	1.24224
$285$	4.49497e10	0.403576
$286$	−2.51052e11	−2.21879
$287$	−4.87522e10	−0.424156
$288$	−1.10131e11	−0.943286
$289$	2.04340e11	1.72311
$290$	−2.37181e11	−1.96920
$291$	−8.73272e10	−0.713890
$292$	−1.77053e11	−1.42522
$293$	−7.07439e10	−0.560770	−0.280385	−	0.959888i	$-0.590462\pi$
$293$	−7.07439e10	−0.560770	−0.280385	+	0.959888i	$0.590462\pi$
$294$	1.56857e10	0.122445
$295$	−1.55668e11	−1.19674
$296$	−6.40812e10	−0.485197
$297$	1.82411e11	1.36034
$298$	−1.66494e11	−1.22299
$299$	−6.57756e10	−0.475932
$300$	−3.85040e9	−0.0274448
$301$	−2.68355e10	−0.188435
$302$	2.95089e11	2.04137
$303$	−1.66210e10	−0.113283
$304$	6.67581e10	0.448304
$305$	4.55595e10	0.301460
$306$	2.58964e11	1.68847
$307$	1.30493e11	0.838429	0.419214	−	0.907887i	$-0.362306\pi$
$307$	1.30493e11	0.838429	0.419214	+	0.907887i	$0.362306\pi$
$308$	1.09085e11	0.690697
$309$	−5.40161e10	−0.337062
$310$	6.92993e10	0.426188
$311$	8.51715e10	0.516265	0.258132	−	0.966110i	$-0.416893\pi$
$311$	8.51715e10	0.516265	0.258132	+	0.966110i	$0.416893\pi$
$312$	4.12537e10	0.246472
$313$	−1.21745e11	−0.716969	−0.358484	−	0.933536i	$-0.616706\pi$
$313$	−1.21745e11	−0.716969	−0.358484	+	0.933536i	$0.616706\pi$
$314$	3.19137e11	1.85265
$315$	−4.55980e10	−0.260945
$316$	−3.38154e11	−1.90775
$317$	−2.14595e11	−1.19358	−0.596791	−	0.802397i	$-0.703558\pi$
$317$	−2.14595e11	−1.19358	−0.596791	+	0.802397i	$0.703558\pi$
$318$	1.53736e11	0.843048
$319$	3.38208e11	1.82863
$320$	−2.78796e11	−1.48632
$321$	3.66011e10	0.192407
$322$	5.09180e10	0.263949
$323$	−2.25264e11	−1.15154
$324$	3.47703e10	0.175289
$325$	7.81943e9	0.0388776
$326$	7.19740e10	0.352936
$327$	−4.15029e10	−0.200731
$328$	9.92562e10	0.473506
$329$	−4.78644e10	−0.225233
$330$	2.68666e11	1.24710
$331$	−5.48000e10	−0.250931	−0.125466	−	0.992098i	$-0.540042\pi$
$331$	−5.48000e10	−0.250931	−0.125466	+	0.992098i	$0.540042\pi$
$332$	−4.47224e11	−2.02025
$333$	−1.74868e11	−0.779312
$334$	−4.77595e11	−2.09991
$335$	1.14304e11	0.495863
$336$	3.22051e10	0.137847
$337$	−2.34297e11	−0.989538	−0.494769	−	0.869025i	$-0.664747\pi$
$337$	−2.34297e11	−0.989538	−0.494769	+	0.869025i	$0.664747\pi$
$338$	−2.12772e10	−0.0886725
$339$	−3.54916e10	−0.145958
$340$	5.29994e11	2.15088
$341$	−9.88172e10	−0.395765
$342$	−1.80645e11	−0.714018
$343$	1.38413e10	0.0539949
$344$	5.46353e10	0.210359
$345$	7.03905e10	0.267503
$346$	4.25104e11	1.59460
$347$	3.43449e10	0.127169	0.0635843	−	0.997976i	$-0.479747\pi$
$347$	3.43449e10	0.127169	0.0635843	+	0.997976i	$0.479747\pi$
$348$	−2.54436e11	−0.929977
$349$	−2.13485e11	−0.770288	−0.385144	−	0.922856i	$-0.625848\pi$
$349$	−2.13485e11	−0.770288	−0.385144	+	0.922856i	$0.625848\pi$
$350$	−6.05314e9	−0.0215613
$351$	2.78686e11	0.980016
$352$	5.72595e11	1.98795
$353$	2.75882e11	0.945664	0.472832	−	0.881153i	$-0.343232\pi$
$353$	2.75882e11	0.945664	0.472832	+	0.881153i	$0.343232\pi$
$354$	−2.97509e11	−1.00690
$355$	2.95977e11	0.989079
$356$	−9.63962e10	−0.318079
$357$	−1.08671e11	−0.354084
$358$	−2.49448e11	−0.802614
$359$	−3.46238e11	−1.10015	−0.550073	−	0.835117i	$-0.685400\pi$
$359$	−3.46238e11	−1.10015	−0.550073	+	0.835117i	$0.685400\pi$
$360$	9.28345e10	0.291305
$361$	−1.65550e11	−0.513036
$362$	4.34117e11	1.32867
$363$	−1.95300e11	−0.590369
$364$	1.66659e11	0.497592
$365$	−3.84789e11	−1.13476
$366$	8.70725e10	0.253639
$367$	3.56842e11	1.02678	0.513391	−	0.858155i	$-0.328389\pi$
$367$	3.56842e11	1.02678	0.513391	+	0.858155i	$0.328389\pi$
$368$	1.04542e11	0.297150
$369$	2.70855e11	0.760534
$370$	−6.37596e11	−1.76863
$371$	1.35658e11	0.371760
$372$	7.43408e10	0.201272
$373$	6.73833e11	1.80245	0.901224	−	0.433354i	$-0.142670\pi$
$373$	6.73833e11	1.80245	0.901224	+	0.433354i	$0.142670\pi$
$374$	−1.34641e12	−3.55841
$375$	2.13103e11	0.556480
$376$	9.74487e10	0.251438
$377$	5.16711e11	1.31738
$378$	−2.15735e11	−0.543511
$379$	5.90163e11	1.46925	0.734625	−	0.678473i	$-0.237358\pi$
$379$	5.90163e11	1.46925	0.734625	+	0.678473i	$0.237358\pi$
$380$	−3.69707e11	−0.909561
$381$	−7.39622e10	−0.179824
$382$	−5.51887e11	−1.32607
$383$	−1.58931e11	−0.377412	−0.188706	−	0.982034i	$-0.560429\pi$
$383$	−1.58931e11	−0.377412	−0.188706	+	0.982034i	$0.560429\pi$
$384$	−1.96153e11	−0.460367
$385$	2.37074e11	0.549935
$386$	5.22145e11	1.19715
$387$	1.49092e11	0.337873
$388$	7.18258e11	1.60893
$389$	−3.75434e11	−0.831304	−0.415652	−	0.909524i	$-0.636447\pi$
$389$	−3.75434e11	−0.831304	−0.415652	+	0.909524i	$0.636447\pi$
$390$	4.10466e11	0.898435
$391$	−3.52760e11	−0.763280
$392$	−2.81799e10	−0.0602771
$393$	−2.05245e11	−0.434016
$394$	−7.99018e11	−1.67041
$395$	−7.34908e11	−1.51896
$396$	−6.06051e11	−1.23846
$397$	−4.33507e11	−0.875869	−0.437935	−	0.899007i	$-0.644290\pi$
$397$	−4.33507e11	−0.875869	−0.437935	+	0.899007i	$0.644290\pi$
$398$	8.66400e11	1.73079
$399$	7.58055e10	0.149735
$400$	−1.24280e10	−0.0242734
$401$	−1.77805e11	−0.343395	−0.171698	−	0.985150i	$-0.554925\pi$
$401$	−1.77805e11	−0.343395	−0.171698	+	0.985150i	$0.554925\pi$
$402$	2.18457e11	0.417203
$403$	−1.50972e11	−0.285118
$404$	1.36706e11	0.255312
$405$	7.55660e10	0.139566
$406$	−3.99994e11	−0.730612
$407$	9.09178e11	1.64238
$408$	2.21247e11	0.395281
$409$	−7.67870e11	−1.35685	−0.678427	−	0.734668i	$-0.737338\pi$
$409$	−7.67870e11	−1.35685	−0.678427	+	0.734668i	$0.737338\pi$
$410$	9.87580e11	1.72602
$411$	3.53725e11	0.611473
$412$	4.44277e11	0.759655
$413$	−2.62526e11	−0.444014
$414$	−2.82888e11	−0.473274
$415$	−9.71951e11	−1.60852
$416$	8.74807e11	1.43216
$417$	5.80139e11	0.939550
$418$	9.39215e11	1.50478
$419$	4.96552e11	0.787048	0.393524	−	0.919314i	$-0.371256\pi$
$419$	4.96552e11	0.787048	0.393524	+	0.919314i	$0.371256\pi$
$420$	−1.78353e11	−0.279677
$421$	−4.48514e11	−0.695835	−0.347917	−	0.937525i	$-0.613111\pi$
$421$	−4.48514e11	−0.695835	−0.347917	+	0.937525i	$0.613111\pi$
$422$	3.15580e10	0.0484399
$423$	2.65923e11	0.403854
$424$	−2.76191e11	−0.415014
$425$	4.19362e10	0.0623504
$426$	5.65667e11	0.832180
$427$	7.68338e10	0.111848
$428$	−3.01041e11	−0.433639
$429$	−5.85303e11	−0.834301
$430$	5.43611e11	0.766797
$431$	−1.65940e11	−0.231635	−0.115817	−	0.993271i	$-0.536949\pi$
$431$	−1.65940e11	−0.231635	−0.115817	+	0.993271i	$0.536949\pi$
$432$	−4.42936e11	−0.611878
$433$	−4.10674e11	−0.561438	−0.280719	−	0.959790i	$-0.590573\pi$
$433$	−4.10674e11	−0.561438	−0.280719	+	0.959790i	$0.590573\pi$
$434$	1.16870e11	0.158124
$435$	−5.52965e11	−0.740450
$436$	3.41358e11	0.452398
$437$	2.46074e11	0.322775
$438$	−7.35402e11	−0.954754
$439$	−3.29593e11	−0.423534	−0.211767	−	0.977320i	$-0.567922\pi$
$439$	−3.29593e11	−0.423534	−0.211767	+	0.977320i	$0.567922\pi$
$440$	−4.82667e11	−0.613919
$441$	−7.68988e10	−0.0968158
$442$	−2.05704e12	−2.56355
$443$	5.09091e11	0.628027	0.314014	−	0.949418i	$-0.398326\pi$
$443$	5.09091e11	0.628027	0.314014	+	0.949418i	$0.398326\pi$
$444$	−6.83981e11	−0.835258
$445$	−2.09497e11	−0.253255
$446$	−2.28424e11	−0.273360
$447$	−3.88163e11	−0.459865
$448$	−4.70175e11	−0.551453
$449$	1.49596e12	1.73705	0.868525	−	0.495646i	$-0.165069\pi$
$449$	1.49596e12	1.73705	0.868525	+	0.495646i	$0.165069\pi$
$450$	3.36298e10	0.0386605
$451$	−1.40824e12	−1.60281
$452$	2.91915e11	0.328953
$453$	6.87971e11	0.767588
$454$	1.64963e12	1.82237
$455$	3.62200e11	0.396184
$456$	−1.54335e11	−0.167156
$457$	1.43920e12	1.54347	0.771735	−	0.635944i	$-0.219389\pi$
$457$	1.43920e12	1.54347	0.771735	+	0.635944i	$0.219389\pi$
$458$	8.00307e11	0.849889
$459$	1.49462e12	1.57171
$460$	−5.78956e11	−0.602886
$461$	−1.37741e12	−1.42039	−0.710195	−	0.704005i	$-0.751393\pi$
$461$	−1.37741e12	−1.42039	−0.710195	+	0.704005i	$0.751393\pi$
$462$	4.53092e11	0.462698
$463$	1.76612e12	1.78610	0.893049	−	0.449960i	$-0.148562\pi$
$463$	1.76612e12	1.78610	0.893049	+	0.449960i	$0.148562\pi$
$464$	−8.21248e11	−0.822514
$465$	1.61565e11	0.160254
$466$	1.12443e12	1.10458
$467$	−1.17323e12	−1.14145	−0.570727	−	0.821140i	$-0.693339\pi$
$467$	−1.17323e12	−1.14145	−0.570727	+	0.821140i	$0.693339\pi$
$468$	−9.25919e11	−0.892209
$469$	1.92769e11	0.183975
$470$	9.69596e11	0.916538
$471$	7.44037e11	0.696627
$472$	5.34485e11	0.495674
$473$	−7.75161e11	−0.712060
$474$	−1.40454e12	−1.27801
$475$	−2.92534e10	−0.0263667
$476$	8.93808e11	0.798019
$477$	−7.53683e11	−0.666586
$478$	−8.60808e11	−0.754190
$479$	−1.98723e12	−1.72480	−0.862401	−	0.506225i	$-0.831040\pi$
$479$	−1.98723e12	−1.72480	−0.862401	+	0.506225i	$0.831040\pi$
$480$	−9.36185e11	−0.804963
$481$	1.38903e12	1.18321
$482$	−2.39417e12	−2.02043
$483$	1.18710e11	0.0992489
$484$	1.60633e12	1.33055
$485$	1.56099e12	1.28104
$486$	1.91298e12	1.55542
$487$	−1.23240e12	−0.992825	−0.496413	−	0.868087i	$-0.665350\pi$
$487$	−1.23240e12	−0.992825	−0.496413	+	0.868087i	$0.665350\pi$
$488$	−1.56428e11	−0.124861
$489$	1.67800e11	0.132710
$490$	−2.80385e11	−0.219721
$491$	−2.03763e12	−1.58219	−0.791095	−	0.611693i	$-0.790489\pi$
$491$	−2.03763e12	−1.58219	−0.791095	+	0.611693i	$0.790489\pi$
$492$	1.05943e12	0.815131
$493$	2.77117e12	2.11277
$494$	1.43493e12	1.08407
$495$	−1.31713e12	−0.986062
$496$	2.39951e11	0.178014
$497$	4.99151e11	0.366968
$498$	−1.85758e12	−1.35336
$499$	−3.26299e11	−0.235594	−0.117797	−	0.993038i	$-0.537583\pi$
$499$	−3.26299e11	−0.235594	−0.117797	+	0.993038i	$0.537583\pi$
$500$	−1.75275e12	−1.25417
$501$	−1.11347e12	−0.789601
$502$	−1.43374e12	−1.00764
$503$	−4.46869e11	−0.311261	−0.155630	−	0.987815i	$-0.549741\pi$
$503$	−4.46869e11	−0.311261	−0.155630	+	0.987815i	$0.549741\pi$
$504$	1.56561e11	0.108080
$505$	2.97103e11	0.203280
$506$	1.47080e12	0.997413
$507$	−4.96056e10	−0.0333423
$508$	6.08332e11	0.405279
$509$	1.34100e12	0.885523	0.442761	−	0.896639i	$-0.353999\pi$
$509$	1.34100e12	0.885523	0.442761	+	0.896639i	$0.353999\pi$
$510$	2.20136e12	1.44087
$511$	−6.48928e11	−0.421020
$512$	−1.81189e12	−1.16524
$513$	−1.04260e12	−0.664643
$514$	−2.86145e12	−1.80822
$515$	9.65545e11	0.604839
$516$	5.83158e11	0.362129
$517$	−1.38259e12	−0.851112
$518$	−1.07527e12	−0.656199
$519$	9.91089e11	0.599597
$520$	−7.37415e11	−0.442280
$521$	2.98523e12	1.77504	0.887520	−	0.460769i	$-0.152426\pi$
$521$	2.98523e12	1.77504	0.887520	+	0.460769i	$0.152426\pi$
$522$	2.22227e12	1.31003
$523$	1.64651e12	0.962289	0.481145	−	0.876641i	$-0.340221\pi$
$523$	1.64651e12	0.962289	0.481145	+	0.876641i	$0.340221\pi$
$524$	1.68812e12	0.978166
$525$	−1.41123e10	−0.00810739
$526$	8.01470e10	0.0456511
$527$	−8.09676e11	−0.457260
$528$	9.30265e11	0.520900
$529$	−1.41580e12	−0.786054
$530$	−2.74805e12	−1.51280
$531$	1.45853e12	0.796141
$532$	−6.23493e11	−0.337465
$533$	−2.15149e12	−1.15470
$534$	−4.00388e11	−0.213081
$535$	−6.54250e11	−0.345265
$536$	−3.92464e11	−0.205380
$537$	−5.81564e11	−0.301796
$538$	2.20233e12	1.13334
$539$	3.99814e11	0.204037
$540$	2.45299e12	1.24143
$541$	−4.57968e11	−0.229852	−0.114926	−	0.993374i	$-0.536663\pi$
$541$	−4.57968e11	−0.229852	−0.114926	+	0.993374i	$0.536663\pi$
$542$	4.80087e11	0.238959
$543$	1.01210e12	0.499603
$544$	4.69166e12	2.29684
$545$	7.41871e11	0.360200
$546$	6.92231e11	0.333337
$547$	2.39624e12	1.14443	0.572213	−	0.820105i	$-0.306085\pi$
$547$	2.39624e12	1.14443	0.572213	+	0.820105i	$0.306085\pi$
$548$	−2.90935e12	−1.37811
$549$	−4.26870e11	−0.200549
$550$	−1.74849e11	−0.0814761
$551$	−1.93308e12	−0.893444
$552$	−2.41686e11	−0.110796
$553$	−1.23939e12	−0.563565
$554$	2.57166e12	1.15990
$555$	−1.48649e12	−0.665034
$556$	−4.77159e12	−2.11751
$557$	1.07863e12	0.474814	0.237407	−	0.971410i	$-0.423702\pi$
$557$	1.07863e12	0.474814	0.237407	+	0.971410i	$0.423702\pi$
$558$	−6.49301e11	−0.283525
$559$	−1.18428e12	−0.512983
$560$	−5.75672e11	−0.247360
$561$	−3.13903e12	−1.33802
$562$	−3.26624e12	−1.38113
$563$	2.33140e11	0.0977976	0.0488988	−	0.998804i	$-0.484429\pi$
$563$	2.33140e11	0.0977976	0.0488988	+	0.998804i	$0.484429\pi$
$564$	1.04013e12	0.432846
$565$	6.34418e11	0.261913
$566$	−1.64939e12	−0.675539
$567$	1.27438e11	0.0517817
$568$	−1.01624e12	−0.409664
$569$	4.50535e11	0.180187	0.0900934	−	0.995933i	$-0.471283\pi$
$569$	4.50535e11	0.180187	0.0900934	+	0.995933i	$0.471283\pi$
$570$	−1.53560e12	−0.609315
$571$	−4.38839e12	−1.72760	−0.863800	−	0.503835i	$-0.831922\pi$
$571$	−4.38839e12	−1.72760	−0.863800	+	0.503835i	$0.831922\pi$
$572$	4.81406e12	1.88031
$573$	−1.28667e12	−0.498622
$574$	1.66550e12	0.640387
$575$	−4.58104e10	−0.0174767
$576$	2.61218e12	0.988785
$577$	3.13994e12	1.17932	0.589658	−	0.807653i	$-0.299263\pi$
$577$	3.13994e12	1.17932	0.589658	+	0.807653i	$0.299263\pi$
$578$	−6.98079e12	−2.60153
$579$	1.21733e12	0.450148
$580$	4.54808e12	1.66879
$581$	−1.63915e12	−0.596795
$582$	2.98333e12	1.07782
$583$	3.91857e12	1.40481
$584$	1.32117e12	0.470005
$585$	−2.01230e12	−0.710380
$586$	2.41680e12	0.846645
$587$	2.52512e12	0.877829	0.438915	−	0.898529i	$-0.355363\pi$
$587$	2.52512e12	0.877829	0.438915	+	0.898529i	$0.355363\pi$
$588$	−3.00783e11	−0.103766
$589$	5.64805e11	0.193366
$590$	5.31802e12	1.80682
$591$	−1.86283e12	−0.628102
$592$	−2.20770e12	−0.738740
$593$	−9.35417e11	−0.310641	−0.155321	−	0.987864i	$-0.549641\pi$
$593$	−9.35417e11	−0.310641	−0.155321	+	0.987864i	$0.549641\pi$
$594$	−6.23165e12	−2.05383
$595$	1.94251e12	0.635385
$596$	3.19261e12	1.03642
$597$	2.01993e12	0.650805
$598$	2.24707e12	0.718557
$599$	4.73586e12	1.50307	0.751534	−	0.659694i	$-0.229314\pi$
$599$	4.73586e12	1.50307	0.751534	+	0.659694i	$0.229314\pi$
$600$	2.87317e10	0.00905067
$601$	−5.99855e12	−1.87548	−0.937738	−	0.347344i	$-0.887084\pi$
$601$	−5.99855e12	−1.87548	−0.937738	+	0.347344i	$0.887084\pi$
$602$	9.16773e11	0.284497
$603$	−1.07098e12	−0.329877
$604$	−5.65850e12	−1.72995
$605$	3.49103e12	1.05938
$606$	5.67817e11	0.171034
$607$	3.43715e12	1.02766	0.513830	−	0.857892i	$-0.328226\pi$
$607$	3.43715e12	1.02766	0.513830	+	0.857892i	$0.328226\pi$
$608$	−3.27276e12	−0.971287
$609$	−9.32548e11	−0.274722
$610$	−1.55643e12	−0.455141
$611$	−2.11231e12	−0.613159
$612$	−4.96578e12	−1.43089
$613$	4.15273e12	1.18785	0.593925	−	0.804520i	$-0.297577\pi$
$613$	4.15273e12	1.18785	0.593925	+	0.804520i	$0.297577\pi$
$614$	−4.45801e12	−1.26585
$615$	2.30244e12	0.649010
$616$	−8.13995e11	−0.227776
$617$	−1.12196e12	−0.311669	−0.155834	−	0.987783i	$-0.549807\pi$
$617$	−1.12196e12	−0.311669	−0.155834	+	0.987783i	$0.549807\pi$
$618$	1.84533e12	0.508893
$619$	−5.98940e12	−1.63974	−0.819871	−	0.572549i	$-0.805955\pi$
$619$	−5.98940e12	−1.63974	−0.819871	+	0.572549i	$0.805955\pi$
$620$	−1.32885e12	−0.361172
$621$	−1.63269e12	−0.440547
$622$	−2.90969e12	−0.779452
$623$	−3.53307e11	−0.0939628
$624$	1.42125e12	0.375267
$625$	−3.95339e12	−1.03636
$626$	4.15912e12	1.08247
$627$	2.18969e12	0.565820
$628$	−6.11963e12	−1.57003
$629$	7.44951e12	1.89758
$630$	1.55775e12	0.393972
$631$	4.97135e12	1.24837	0.624184	−	0.781277i	$-0.285432\pi$
$631$	4.97135e12	1.24837	0.624184	+	0.781277i	$0.285432\pi$
$632$	2.52331e12	0.629134
$633$	7.35743e10	0.0182142
$634$	7.33113e12	1.80206
$635$	1.32208e12	0.322684
$636$	−2.94796e12	−0.714439
$637$	6.10833e11	0.146992
$638$	−1.15541e13	−2.76085
$639$	−2.77316e12	−0.657993
$640$	3.50626e12	0.826103
$641$	−2.41181e12	−0.564263	−0.282131	−	0.959376i	$-0.591041\pi$
$641$	−2.41181e12	−0.564263	−0.282131	+	0.959376i	$0.591041\pi$
$642$	−1.25039e12	−0.290495
$643$	6.86804e12	1.58447	0.792234	−	0.610217i	$-0.208918\pi$
$643$	6.86804e12	1.58447	0.792234	+	0.610217i	$0.208918\pi$
$644$	−9.76380e11	−0.223683
$645$	1.26738e12	0.288328
$646$	7.69562e12	1.73859
$647$	−1.73394e12	−0.389013	−0.194506	−	0.980901i	$-0.562310\pi$
$647$	−1.73394e12	−0.389013	−0.194506	+	0.980901i	$0.562310\pi$
$648$	−2.59456e11	−0.0578064
$649$	−7.58322e12	−1.67785
$650$	−2.67132e11	−0.0586971
$651$	2.72471e11	0.0594573
$652$	−1.38014e12	−0.299095
$653$	2.86440e10	0.00616488	0.00308244	−	0.999995i	$-0.499019\pi$
$653$	2.86440e10	0.00616488	0.00308244	+	0.999995i	$0.499019\pi$
$654$	1.41785e12	0.303061
$655$	3.66878e12	0.778818
$656$	3.41953e12	0.720940
$657$	3.60529e12	0.754911
$658$	1.63518e12	0.340054
$659$	−6.31728e12	−1.30481	−0.652403	−	0.757872i	$-0.726239\pi$
$659$	−6.31728e12	−1.30481	−0.652403	+	0.757872i	$0.726239\pi$
$660$	−5.15182e12	−1.05685
$661$	−3.49558e12	−0.712217	−0.356109	−	0.934445i	$-0.615897\pi$
$661$	−3.49558e12	−0.712217	−0.356109	+	0.934445i	$0.615897\pi$
$662$	1.87212e12	0.378854
$663$	−4.79578e12	−0.963937
$664$	3.33719e12	0.666231
$665$	−1.35503e12	−0.268691
$666$	5.97396e12	1.17660
$667$	−3.02717e12	−0.592203
$668$	9.15816e12	1.77957
$669$	−5.32547e11	−0.102788
$670$	−3.90494e12	−0.748649
$671$	2.21939e12	0.422652
$672$	−1.57883e12	−0.298658
$673$	−8.02535e12	−1.50798	−0.753991	−	0.656885i	$-0.771874\pi$
$673$	−8.02535e12	−1.50798	−0.753991	+	0.656885i	$0.771874\pi$
$674$	8.00422e12	1.49400
$675$	1.94095e11	0.0359871
$676$	4.08002e11	0.0751453
$677$	1.17163e12	0.214358	0.107179	−	0.994240i	$-0.465818\pi$
$677$	1.17163e12	0.214358	0.107179	+	0.994240i	$0.465818\pi$
$678$	1.21249e12	0.220366
$679$	2.63253e12	0.475290
$680$	−3.95482e12	−0.709311
$681$	3.84596e12	0.685239
$682$	3.37586e12	0.597523
$683$	4.69754e12	0.825995	0.412997	−	0.910732i	$-0.364482\pi$
$683$	4.69754e12	0.825995	0.412997	+	0.910732i	$0.364482\pi$
$684$	3.46397e12	0.605093
$685$	−6.32288e12	−1.09726
$686$	−4.72855e11	−0.0815211
$687$	1.86584e12	0.319572
$688$	1.88227e12	0.320283
$689$	5.98676e12	1.01206
$690$	−2.40473e12	−0.403873
$691$	−7.83193e12	−1.30683	−0.653413	−	0.757001i	$-0.726664\pi$
$691$	−7.83193e12	−1.30683	−0.653413	+	0.757001i	$0.726664\pi$
$692$	−8.15161e12	−1.35134
$693$	−2.22127e12	−0.365849
$694$	−1.17332e12	−0.191998
$695$	−1.03701e13	−1.68597
$696$	1.89860e12	0.306685
$697$	−1.15386e13	−1.85185
$698$	7.29322e12	1.16297
$699$	2.62150e12	0.415339
$700$	1.16072e11	0.0182721
$701$	7.13243e12	1.11559	0.557797	−	0.829977i	$-0.311647\pi$
$701$	7.13243e12	1.11559	0.557797	+	0.829977i	$0.311647\pi$
$702$	−9.52066e12	−1.47962
$703$	−5.19655e12	−0.802446
$704$	−1.35813e13	−2.08384
$705$	2.26052e12	0.344633
$706$	−9.42486e12	−1.42776
$707$	5.01049e11	0.0754211
$708$	5.70491e12	0.853294
$709$	8.65274e12	1.28601	0.643007	−	0.765861i	$-0.277687\pi$
$709$	8.65274e12	1.28601	0.643007	+	0.765861i	$0.277687\pi$
$710$	−1.01114e13	−1.49330
$711$	6.88573e12	1.01050
$712$	7.19310e11	0.104895
$713$	8.84475e11	0.128169
$714$	3.71249e12	0.534593
$715$	1.04624e13	1.49711
$716$	4.78331e12	0.680174
$717$	−2.00689e12	−0.283588
$718$	1.18284e13	1.66099
$719$	4.58446e11	0.0639747	0.0319873	−	0.999488i	$-0.489816\pi$
$719$	4.58446e11	0.0639747	0.0319873	+	0.999488i	$0.489816\pi$
$720$	3.19829e12	0.443529
$721$	1.62834e12	0.224408
$722$	5.65565e12	0.774577
$723$	−5.58177e12	−0.759713
$724$	−8.32444e12	−1.12598
$725$	3.59871e11	0.0483755
$726$	6.67199e12	0.891334
$727$	−2.53850e12	−0.337033	−0.168517	−	0.985699i	$-0.553898\pi$
$727$	−2.53850e12	−0.337033	−0.168517	+	0.985699i	$0.553898\pi$
$728$	−1.24361e12	−0.164095
$729$	3.41521e12	0.447861
$730$	1.31454e13	1.71325
$731$	−6.35141e12	−0.822701
$732$	−1.66966e12	−0.214946
$733$	1.09361e13	1.39925	0.699624	−	0.714511i	$-0.253351\pi$
$733$	1.09361e13	1.39925	0.699624	+	0.714511i	$0.253351\pi$
$734$	−1.21907e13	−1.55023
$735$	−6.53690e11	−0.0826188
$736$	−5.12509e12	−0.643800
$737$	5.56824e12	0.695208
$738$	−9.25314e12	−1.14825
$739$	7.34996e12	0.906536	0.453268	−	0.891374i	$-0.350258\pi$
$739$	7.34996e12	0.906536	0.453268	+	0.891374i	$0.350258\pi$
$740$	1.22263e13	1.49882
$741$	3.34539e12	0.407628
$742$	−4.63444e12	−0.561281
$743$	−1.60813e12	−0.193584	−0.0967922	−	0.995305i	$-0.530858\pi$
$743$	−1.60813e12	−0.193584	−0.0967922	+	0.995305i	$0.530858\pi$
$744$	−5.54732e11	−0.0663751
$745$	6.93848e12	0.825203
$746$	−2.30199e13	−2.72132
$747$	9.10670e12	1.07009
$748$	2.58182e13	3.01557
$749$	−1.10336e12	−0.128100
$750$	−7.28018e12	−0.840168
$751$	−2.95903e12	−0.339446	−0.169723	−	0.985492i	$-0.554287\pi$
$751$	−2.95903e12	−0.339446	−0.169723	+	0.985492i	$0.554287\pi$
$752$	3.35726e12	0.382829
$753$	−3.34263e12	−0.378888
$754$	−1.76522e13	−1.98897
$755$	−1.22976e13	−1.37739
$756$	4.13684e12	0.460597
$757$	−4.83223e12	−0.534830	−0.267415	−	0.963581i	$-0.586170\pi$
$757$	−4.83223e12	−0.534830	−0.267415	+	0.963581i	$0.586170\pi$
$758$	−2.01616e13	−2.21826
$759$	3.42902e12	0.375043
$760$	2.75876e12	0.299953
$761$	3.15213e12	0.340701	0.170350	−	0.985384i	$-0.445510\pi$
$761$	3.15213e12	0.340701	0.170350	+	0.985384i	$0.445510\pi$
$762$	2.52675e12	0.271496
$763$	1.25113e12	0.133642
$764$	1.05827e13	1.12377
$765$	−1.07921e13	−1.13928
$766$	5.42952e12	0.569813
$767$	−1.15856e13	−1.20876
$768$	−1.28447e12	−0.133229
$769$	−6.87650e12	−0.709086	−0.354543	−	0.935040i	$-0.615364\pi$
$769$	−6.87650e12	−0.709086	−0.354543	+	0.935040i	$0.615364\pi$
$770$	−8.09909e12	−0.830286
$771$	−6.67118e12	−0.679920
$772$	−1.00124e13	−1.01452
$773$	1.16083e13	1.16939	0.584696	−	0.811253i	$-0.301214\pi$
$773$	1.16083e13	1.16939	0.584696	+	0.811253i	$0.301214\pi$
$774$	−5.09337e12	−0.510118
$775$	−1.05147e11	−0.0104698
$776$	−5.35965e12	−0.530590
$777$	−2.50690e12	−0.246741
$778$	1.28258e13	1.25510
$779$	8.04899e12	0.783110
$780$	−7.87091e12	−0.761376
$781$	1.44183e13	1.38670
$782$	1.20512e13	1.15239
$783$	1.28259e13	1.21944
$784$	−9.70842e11	−0.0917754
$785$	−1.32998e13	−1.25006
$786$	7.01171e12	0.655274
$787$	−2.50005e12	−0.232307	−0.116154	−	0.993231i	$-0.537057\pi$
$787$	−2.50005e12	−0.232307	−0.116154	+	0.993231i	$0.537057\pi$
$788$	1.53216e13	1.41559
$789$	1.86855e11	0.0171656
$790$	2.51064e13	2.29331
$791$	1.06991e12	0.0971751
$792$	4.52236e12	0.408415
$793$	3.39077e12	0.304487
$794$	1.48098e13	1.32238
$795$	−6.40680e12	−0.568838
$796$	−1.66137e13	−1.46675
$797$	2.77023e12	0.243194	0.121597	−	0.992580i	$-0.461198\pi$
$797$	2.77023e12	0.243194	0.121597	+	0.992580i	$0.461198\pi$
$798$	−2.58972e12	−0.226068
$799$	−1.13285e13	−0.983360
$800$	6.09272e11	0.0525904
$801$	1.96289e12	0.168480
$802$	6.07429e12	0.518455
$803$	−1.87447e13	−1.59096
$804$	−4.18903e12	−0.353558
$805$	−2.12196e12	−0.178097
$806$	5.15761e12	0.430468
$807$	5.13451e12	0.426156
$808$	−1.02010e12	−0.0841962
$809$	−2.96640e12	−0.243479	−0.121739	−	0.992562i	$-0.538847\pi$
$809$	−2.96640e12	−0.243479	−0.121739	+	0.992562i	$0.538847\pi$
$810$	−2.58154e12	−0.210715
$811$	−9.01447e12	−0.731722	−0.365861	−	0.930669i	$-0.619225\pi$
$811$	−9.01447e12	−0.731722	−0.365861	+	0.930669i	$0.619225\pi$
$812$	7.67012e12	0.619156
$813$	1.11928e12	0.0898524
$814$	−3.10599e13	−2.47965
$815$	−2.99946e12	−0.238140
$816$	7.62229e12	0.601838
$817$	4.43055e12	0.347903
$818$	2.62325e13	2.04857
$819$	−3.39364e12	−0.263565
$820$	−1.89374e13	−1.46271
$821$	1.25176e13	0.961563	0.480782	−	0.876840i	$-0.340353\pi$
$821$	1.25176e13	0.961563	0.480782	+	0.876840i	$0.340353\pi$
$822$	−1.20842e13	−0.923197
$823$	−1.50348e13	−1.14234	−0.571172	−	0.820830i	$-0.693511\pi$
$823$	−1.50348e13	−1.14234	−0.571172	+	0.820830i	$0.693511\pi$
$824$	−3.31520e12	−0.250517
$825$	−4.07642e11	−0.0306363
$826$	8.96858e12	0.670369
$827$	2.31522e13	1.72115	0.860574	−	0.509325i	$-0.170105\pi$
$827$	2.31522e13	1.72115	0.860574	+	0.509325i	$0.170105\pi$
$828$	5.42453e12	0.401075
$829$	4.88071e12	0.358912	0.179456	−	0.983766i	$-0.442566\pi$
$829$	4.88071e12	0.358912	0.179456	+	0.983766i	$0.442566\pi$
$830$	3.32044e13	2.42854
$831$	5.99556e12	0.436139
$832$	−2.07494e13	−1.50124
$833$	3.27595e12	0.235741
$834$	−1.98191e13	−1.41852
$835$	1.99034e13	1.41690
$836$	−1.80100e13	−1.27522
$837$	−3.74745e12	−0.263919
$838$	−1.69635e13	−1.18828
$839$	−1.18015e13	−0.822258	−0.411129	−	0.911577i	$-0.634865\pi$
$839$	−1.18015e13	−0.822258	−0.411129	+	0.911577i	$0.634865\pi$
$840$	1.33087e12	0.0922313
$841$	9.27330e12	0.639223
$842$	1.53224e13	1.05057
$843$	−7.61492e12	−0.519327
$844$	−6.05142e11	−0.0410503
$845$	8.86708e11	0.0598309
$846$	−9.08464e12	−0.609735
$847$	5.88744e12	0.393053
$848$	−9.51520e12	−0.631883
$849$	−3.84540e12	−0.254014
$850$	−1.43265e12	−0.0941361
$851$	−8.13771e12	−0.531887
$852$	−1.08470e13	−0.705229
$853$	−2.54707e13	−1.64729	−0.823646	−	0.567104i	$-0.808064\pi$
$853$	−2.54707e13	−1.64729	−0.823646	+	0.567104i	$0.808064\pi$
$854$	−2.62485e12	−0.168867
$855$	7.52824e12	0.481777
$856$	2.24637e12	0.143004
$857$	1.26584e13	0.801615	0.400807	−	0.916162i	$-0.368730\pi$
$857$	1.26584e13	0.801615	0.400807	+	0.916162i	$0.368730\pi$
$858$	1.99955e13	1.25962
$859$	2.01387e13	1.26201	0.631004	−	0.775779i	$-0.282643\pi$
$859$	2.01387e13	1.26201	0.631004	+	0.775779i	$0.282643\pi$
$860$	−1.04240e13	−0.649820
$861$	3.88296e12	0.240796
$862$	5.66896e12	0.349720
$863$	−1.44977e13	−0.889716	−0.444858	−	0.895601i	$-0.646746\pi$
$863$	−1.44977e13	−0.889716	−0.444858	+	0.895601i	$0.646746\pi$
$864$	2.17146e13	1.32568
$865$	−1.77159e13	−1.07594
$866$	1.40297e13	0.847655
$867$	−1.62750e13	−0.978217
$868$	−2.24104e12	−0.134002
$869$	−3.58004e13	−2.12961
$870$	1.88907e13	1.11792
$871$	8.50712e12	0.500842
$872$	−2.54721e12	−0.149191
$873$	−1.46257e13	−0.852221
$874$	−8.40656e12	−0.487323
$875$	−6.42411e12	−0.370490
$876$	1.41018e13	0.809104
$877$	1.83297e13	1.04630	0.523150	−	0.852241i	$-0.324757\pi$
$877$	1.83297e13	1.04630	0.523150	+	0.852241i	$0.324757\pi$
$878$	1.12598e13	0.639448
$879$	5.63453e12	0.318352
$880$	−1.66286e13	−0.934726
$881$	4.57369e12	0.255785	0.127892	−	0.991788i	$-0.459179\pi$
$881$	4.57369e12	0.255785	0.127892	+	0.991788i	$0.459179\pi$
$882$	2.62707e12	0.146172
$883$	3.07854e13	1.70420	0.852101	−	0.523377i	$-0.175328\pi$
$883$	3.07854e13	1.70420	0.852101	+	0.523377i	$0.175328\pi$
$884$	3.94448e13	2.17248
$885$	1.23984e13	0.679395
$886$	−1.73919e13	−0.948190
$887$	−2.58803e13	−1.40382	−0.701911	−	0.712264i	$-0.747670\pi$
$887$	−2.58803e13	−1.40382	−0.701911	+	0.712264i	$0.747670\pi$
$888$	5.10387e12	0.275449
$889$	2.22963e12	0.119722
$890$	7.15699e12	0.382363
$891$	3.68114e12	0.195674
$892$	4.38015e12	0.231658
$893$	7.90242e12	0.415842
$894$	1.32607e13	0.694301
$895$	1.03955e13	0.541556
$896$	5.91314e12	0.306501
$897$	5.23882e12	0.270189
$898$	−5.11061e13	−2.62258
$899$	−6.94814e12	−0.354773
$900$	−6.44870e11	−0.0327628
$901$	3.21075e13	1.62310
$902$	4.81091e13	2.41990
$903$	2.13737e12	0.106975
$904$	−2.17827e12	−0.108481
$905$	−1.80915e13	−0.896510
$906$	−2.35029e13	−1.15890
$907$	9.64118e12	0.473040	0.236520	−	0.971627i	$-0.423993\pi$
$907$	9.64118e12	0.473040	0.236520	+	0.971627i	$0.423993\pi$
$908$	−3.16326e13	−1.54436
$909$	−2.78371e12	−0.135234
$910$	−1.23737e13	−0.598156
$911$	7.28746e12	0.350545	0.175272	−	0.984520i	$-0.443919\pi$
$911$	7.28746e12	0.350545	0.175272	+	0.984520i	$0.443919\pi$
$912$	−5.31707e12	−0.254505
$913$	−4.73478e13	−2.25518
$914$	−4.91669e13	−2.33032
$915$	−3.62867e12	−0.171140
$916$	−1.53463e13	−0.720236
$917$	6.18722e12	0.288957
$918$	−5.10601e13	−2.37295
$919$	2.73276e13	1.26381	0.631906	−	0.775045i	$-0.282273\pi$
$919$	2.73276e13	1.26381	0.631906	+	0.775045i	$0.282273\pi$
$920$	4.32017e12	0.198818
$921$	−1.03934e13	−0.475981
$922$	4.70559e13	2.14449
$923$	2.20281e13	0.999011
$924$	−8.68829e12	−0.392112
$925$	9.67413e11	0.0434484
$926$	−6.03353e13	−2.69663
$927$	−9.04668e12	−0.402375
$928$	4.02610e13	1.78204
$929$	−7.21805e12	−0.317943	−0.158971	−	0.987283i	$-0.550818\pi$
$929$	−7.21805e12	−0.317943	−0.158971	+	0.987283i	$0.550818\pi$
$930$	−5.51948e12	−0.241949
$931$	−2.28520e12	−0.0996897
$932$	−2.15616e13	−0.936071
$933$	−6.78365e12	−0.293087
$934$	4.00808e13	1.72336
$935$	5.61106e13	2.40100
$936$	6.90922e12	0.294231
$937$	1.41988e13	0.601761	0.300880	−	0.953662i	$-0.402719\pi$
$937$	1.41988e13	0.601761	0.300880	+	0.953662i	$0.402719\pi$
$938$	−6.58550e12	−0.277764
$939$	9.69658e12	0.407027
$940$	−1.85925e13	−0.776718
$941$	−2.53242e13	−1.05289	−0.526445	−	0.850209i	$-0.676475\pi$
$941$	−2.53242e13	−1.05289	−0.526445	+	0.850209i	$0.676475\pi$
$942$	−2.54183e13	−1.05176
$943$	1.26046e13	0.519070
$944$	1.84138e13	0.754693
$945$	8.99058e12	0.366728
$946$	2.64816e13	1.07506
$947$	−1.37160e13	−0.554182	−0.277091	−	0.960844i	$-0.589370\pi$
$947$	−1.37160e13	−0.554182	−0.277091	+	0.960844i	$0.589370\pi$
$948$	2.69329e13	1.08304
$949$	−2.86380e13	−1.14616
$950$	9.99374e11	0.0398082
$951$	1.70918e13	0.677604
$952$	−6.66961e12	−0.263169
$953$	2.44096e13	0.958610	0.479305	−	0.877648i	$-0.340889\pi$
$953$	2.44096e13	0.958610	0.479305	+	0.877648i	$0.340889\pi$
$954$	2.57478e13	1.00641
$955$	2.29994e13	0.894750
$956$	1.65065e13	0.639137
$957$	−2.69372e13	−1.03812
$958$	6.78892e13	2.60409
$959$	−1.06632e13	−0.407104
$960$	2.22052e13	0.843790
$961$	−2.44095e13	−0.923218
$962$	−4.74531e13	−1.78639
$963$	6.13001e12	0.229690
$964$	4.59096e13	1.71221
$965$	−2.17600e13	−0.807765
$966$	−4.05546e12	−0.149845
$967$	−4.19850e13	−1.54410	−0.772049	−	0.635563i	$-0.780768\pi$
$967$	−4.19850e13	−1.54410	−0.772049	+	0.635563i	$0.780768\pi$
$968$	−1.19864e13	−0.438784
$969$	1.79416e13	0.653738
$970$	−5.33275e13	−1.93410
$971$	3.13254e12	0.113086	0.0565432	−	0.998400i	$-0.481992\pi$
$971$	3.13254e12	0.113086	0.0565432	+	0.998400i	$0.481992\pi$
$972$	−3.66825e13	−1.31814
$973$	−1.74886e13	−0.625529
$974$	4.21022e13	1.49896
$975$	−6.22793e11	−0.0220710
$976$	−5.38920e12	−0.190108
$977$	4.53124e13	1.59108	0.795539	−	0.605902i	$-0.207188\pi$
$977$	4.53124e13	1.59108	0.795539	+	0.605902i	$0.207188\pi$
$978$	−5.73251e12	−0.200364
$979$	−1.02055e13	−0.355068
$980$	5.37654e12	0.186202
$981$	−6.95097e12	−0.239626
$982$	6.96109e13	2.38878
$983$	−2.54481e13	−0.869290	−0.434645	−	0.900602i	$-0.643126\pi$
$983$	−2.54481e13	−0.869290	−0.434645	+	0.900602i	$0.643126\pi$
$984$	−7.90545e12	−0.268812
$985$	3.32984e13	1.12709
$986$	−9.46704e13	−3.18983
$987$	3.81225e12	0.127866
$988$	−2.75155e13	−0.918694
$989$	6.93817e12	0.230601
$990$	4.49966e13	1.48875
$991$	−5.41691e13	−1.78410	−0.892052	−	0.451933i	$-0.850734\pi$
$991$	−5.41691e13	−1.78410	−0.892052	+	0.451933i	$0.850734\pi$
$992$	−1.17634e13	−0.385683
$993$	4.36465e12	0.142455
$994$	−1.70523e13	−0.554045
$995$	−3.61065e13	−1.16783
$996$	3.56200e13	1.14690
$997$	−4.29329e13	−1.37614	−0.688069	−	0.725646i	$-0.741541\pi$
$997$	−4.29329e13	−1.37614	−0.688069	+	0.725646i	$0.741541\pi$
$998$	1.11473e13	0.355697
$999$	3.44788e13	1.09524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.10.a.b.1.1	✓	3
3.2	odd	2		63.10.a.e.1.3		3
4.3	odd	2		112.10.a.h.1.3		3
5.2	odd	4		175.10.b.d.99.2		6
5.3	odd	4		175.10.b.d.99.5		6
5.4	even	2		175.10.a.d.1.3		3
7.2	even	3		49.10.c.d.18.3		6
7.3	odd	6		49.10.c.e.30.3		6
7.4	even	3		49.10.c.d.30.3		6
7.5	odd	6		49.10.c.e.18.3		6
7.6	odd	2		49.10.a.c.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.b.1.1	✓	3	1.1	even	1	trivial
49.10.a.c.1.1		3	7.6	odd	2
49.10.c.d.18.3		6	7.2	even	3
49.10.c.d.30.3		6	7.4	even	3
49.10.c.e.18.3		6	7.5	odd	6
49.10.c.e.30.3		6	7.3	odd	6
63.10.a.e.1.3		3	3.2	odd	2
112.10.a.h.1.3		3	4.3	odd	2
175.10.a.d.1.3		3	5.4	even	2
175.10.b.d.99.2		6	5.2	odd	4
175.10.b.d.99.5		6	5.3	odd	4

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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	7.a (trivial)

\(f(q)\)	\(=\)	\(q-34.1627 q^{2} -79.6469 q^{3} +655.088 q^{4} +1423.70 q^{5} +2720.95 q^{6} +2401.00 q^{7} -4888.28 q^{8} -13339.4 q^{9} +O(q^{10})\)	\(q-34.1627 q^{2} -79.6469 q^{3} +655.088 q^{4} +1423.70 q^{5} +2720.95 q^{6} +2401.00 q^{7} -4888.28 q^{8} -13339.4 q^{9} -48637.4 q^{10} +69354.4 q^{11} -52175.7 q^{12} +105959. q^{13} -82024.6 q^{14} -113393. q^{15} -168409. q^{16} +568267. q^{17} +455709. q^{18} -396405. q^{19} +932649. q^{20} -191232. q^{21} -2.36933e6 q^{22} -620765. q^{23} +389336. q^{24} +73796.7 q^{25} -3.61984e6 q^{26} +2.63013e6 q^{27} +1.57287e6 q^{28} +4.87652e6 q^{29} +3.87382e6 q^{30} -1.42482e6 q^{31} +8.25609e6 q^{32} -5.52386e6 q^{33} -1.94135e7 q^{34} +3.41830e6 q^{35} -8.73846e6 q^{36} +1.31092e7 q^{37} +1.35423e7 q^{38} -8.43931e6 q^{39} -6.95944e6 q^{40} -2.03049e7 q^{41} +6.53300e6 q^{42} -1.11768e7 q^{43} +4.54332e7 q^{44} -1.89913e7 q^{45} +2.12070e7 q^{46} -1.99352e7 q^{47} +1.34132e7 q^{48} +5.76480e6 q^{49} -2.52109e6 q^{50} -4.52607e7 q^{51} +6.94125e7 q^{52} +5.65007e7 q^{53} -8.98523e7 q^{54} +9.87398e7 q^{55} -1.17367e7 q^{56} +3.15725e7 q^{57} -1.66595e8 q^{58} -1.09340e8 q^{59} -7.42826e7 q^{60} +3.20008e7 q^{61} +4.86755e7 q^{62} -3.20278e7 q^{63} -1.95825e8 q^{64} +1.50854e8 q^{65} +1.88710e8 q^{66} +8.02869e7 q^{67} +3.72265e8 q^{68} +4.94420e7 q^{69} -1.16778e8 q^{70} +2.07893e8 q^{71} +6.52065e7 q^{72} -2.70274e8 q^{73} -4.47844e8 q^{74} -5.87768e6 q^{75} -2.59680e8 q^{76} +1.66520e8 q^{77} +2.88309e8 q^{78} -5.16196e8 q^{79} -2.39763e8 q^{80} +5.30772e7 q^{81} +6.93671e8 q^{82} -6.82693e8 q^{83} -1.25274e8 q^{84} +8.09042e8 q^{85} +3.81830e8 q^{86} -3.88400e8 q^{87} -3.39023e8 q^{88} -1.47150e8 q^{89} +6.48792e8 q^{90} +2.54408e8 q^{91} -4.06656e8 q^{92} +1.13482e8 q^{93} +6.81040e8 q^{94} -5.64362e8 q^{95} -6.57572e8 q^{96} +1.09643e9 q^{97} -1.96941e8 q^{98} -9.25144e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 14055 q^{8} - 26001 q^{9}+O(q^{10}) \) 3 * q + 21 * q^2 + 84 * q^3 + 1557 * q^4 + 1554 * q^5 + 4914 * q^6 + 7203 * q^7 + 14055 * q^8 - 26001 * q^9	\( 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 14055 q^{8} - 26001 q^{9} - 97860 q^{10} - 3444 q^{11} - 106386 q^{12} - 19782 q^{13} + 50421 q^{14} + 200304 q^{15} + 482961 q^{16} + 1016694 q^{17} - 273267 q^{18} + 222852 q^{19} - 1922088 q^{20} + 201684 q^{21} - 2847048 q^{22} + 1885632 q^{23} - 1449630 q^{24} + 3073221 q^{25} - 8785056 q^{26} + 551880 q^{27} + 3738357 q^{28} + 4081818 q^{29} + 8053200 q^{30} + 2869440 q^{31} + 25221951 q^{32} - 20259792 q^{33} - 3981642 q^{34} + 3731154 q^{35} - 35396379 q^{36} + 1395618 q^{37} + 43479870 q^{38} - 8990688 q^{39} - 82859280 q^{40} - 14420658 q^{41} + 11798514 q^{42} - 61631172 q^{43} + 97011984 q^{44} + 29774682 q^{45} + 89747664 q^{46} - 10368960 q^{47} + 16798782 q^{48} + 17294403 q^{49} + 73325055 q^{50} - 26146728 q^{51} - 80908044 q^{52} + 67502610 q^{53} - 117879300 q^{54} - 105823032 q^{55} + 33746055 q^{56} + 8471112 q^{57} - 159163830 q^{58} - 42590100 q^{59} - 179551008 q^{60} + 191746842 q^{61} - 46983468 q^{62} - 62428401 q^{63} + 7852161 q^{64} + 364283220 q^{65} - 8057952 q^{66} - 255175788 q^{67} + 743485806 q^{68} + 257903856 q^{69} - 234961860 q^{70} + 296514504 q^{71} - 609314265 q^{72} + 344213310 q^{73} - 690696462 q^{74} + 279031116 q^{75} + 728839986 q^{76} - 8269044 q^{77} + 280132776 q^{78} - 960412656 q^{79} - 1333333344 q^{80} - 35827677 q^{81} + 562675302 q^{82} - 1100517180 q^{83} - 255432786 q^{84} + 438179412 q^{85} - 880982256 q^{86} - 621821592 q^{87} + 1206124800 q^{88} + 506816478 q^{89} + 2303452620 q^{90} - 47496582 q^{91} + 691123488 q^{92} + 1693258512 q^{93} + 1388004828 q^{94} - 2203071072 q^{95} + 333385794 q^{96} - 647498250 q^{97} + 121060821 q^{98} - 1900979172 q^{99}+O(q^{100}) \) 3 * q + 21 * q^2 + 84 * q^3 + 1557 * q^4 + 1554 * q^5 + 4914 * q^6 + 7203 * q^7 + 14055 * q^8 - 26001 * q^9 - 97860 * q^10 - 3444 * q^11 - 106386 * q^12 - 19782 * q^13 + 50421 * q^14 + 200304 * q^15 + 482961 * q^16 + 1016694 * q^17 - 273267 * q^18 + 222852 * q^19 - 1922088 * q^20 + 201684 * q^21 - 2847048 * q^22 + 1885632 * q^23 - 1449630 * q^24 + 3073221 * q^25 - 8785056 * q^26 + 551880 * q^27 + 3738357 * q^28 + 4081818 * q^29 + 8053200 * q^30 + 2869440 * q^31 + 25221951 * q^32 - 20259792 * q^33 - 3981642 * q^34 + 3731154 * q^35 - 35396379 * q^36 + 1395618 * q^37 + 43479870 * q^38 - 8990688 * q^39 - 82859280 * q^40 - 14420658 * q^41 + 11798514 * q^42 - 61631172 * q^43 + 97011984 * q^44 + 29774682 * q^45 + 89747664 * q^46 - 10368960 * q^47 + 16798782 * q^48 + 17294403 * q^49 + 73325055 * q^50 - 26146728 * q^51 - 80908044 * q^52 + 67502610 * q^53 - 117879300 * q^54 - 105823032 * q^55 + 33746055 * q^56 + 8471112 * q^57 - 159163830 * q^58 - 42590100 * q^59 - 179551008 * q^60 + 191746842 * q^61 - 46983468 * q^62 - 62428401 * q^63 + 7852161 * q^64 + 364283220 * q^65 - 8057952 * q^66 - 255175788 * q^67 + 743485806 * q^68 + 257903856 * q^69 - 234961860 * q^70 + 296514504 * q^71 - 609314265 * q^72 + 344213310 * q^73 - 690696462 * q^74 + 279031116 * q^75 + 728839986 * q^76 - 8269044 * q^77 + 280132776 * q^78 - 960412656 * q^79 - 1333333344 * q^80 - 35827677 * q^81 + 562675302 * q^82 - 1100517180 * q^83 - 255432786 * q^84 + 438179412 * q^85 - 880982256 * q^86 - 621821592 * q^87 + 1206124800 * q^88 + 506816478 * q^89 + 2303452620 * q^90 - 47496582 * q^91 + 691123488 * q^92 + 1693258512 * q^93 + 1388004828 * q^94 - 2203071072 * q^95 + 333385794 * q^96 - 647498250 * q^97 + 121060821 * q^98 - 1900979172 * q^99

Introduction

L-functions

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