LMFDB - Embedded newform 17.12.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,12,Mod(1,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	17.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:	$13.0618340695$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 8440x^{4} - 21100x^{3} + 19034528x^{2} + 24205632x - 12354600960 $ x^6 - 3x^5 - 8440x^4 - 21100x^3 + 19034528x^2 + 24205632*x - 12354600960
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$39.1370$ of defining polynomial
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+37.1370 q^{2} +473.718 q^{3} -668.845 q^{4} -9760.84 q^{5} +17592.4 q^{6} -83403.0 q^{7} -100895. q^{8} +47261.5 q^{9} +O(q^{10})$	\(q+37.1370 q^{2} +473.718 q^{3} -668.845 q^{4} -9760.84 q^{5} +17592.4 q^{6} -83403.0 q^{7} -100895. q^{8} +47261.5 q^{9} -362488. q^{10} +550925. q^{11} -316844. q^{12} +1.70757e6 q^{13} -3.09734e6 q^{14} -4.62388e6 q^{15} -2.37716e6 q^{16} +1.41986e6 q^{17} +1.75515e6 q^{18} +681176. q^{19} +6.52848e6 q^{20} -3.95095e7 q^{21} +2.04597e7 q^{22} -4.03648e7 q^{23} -4.77959e7 q^{24} +4.64458e7 q^{25} +6.34139e7 q^{26} -6.15291e7 q^{27} +5.57837e7 q^{28} +5.36234e7 q^{29} -1.71717e8 q^{30} -1.85677e8 q^{31} +1.18353e8 q^{32} +2.60983e8 q^{33} +5.27292e7 q^{34} +8.14083e8 q^{35} -3.16106e7 q^{36} -6.49851e6 q^{37} +2.52968e7 q^{38} +8.08905e8 q^{39} +9.84824e8 q^{40} -7.77386e8 q^{41} -1.46726e9 q^{42} -1.05577e9 q^{43} -3.68483e8 q^{44} -4.61312e8 q^{45} -1.49903e9 q^{46} -1.45067e9 q^{47} -1.12610e9 q^{48} +4.97874e9 q^{49} +1.72486e9 q^{50} +6.72611e8 q^{51} -1.14210e9 q^{52} -5.08243e9 q^{53} -2.28500e9 q^{54} -5.37749e9 q^{55} +8.41498e9 q^{56} +3.22685e8 q^{57} +1.99141e9 q^{58} +4.34382e9 q^{59} +3.09266e9 q^{60} -1.62659e9 q^{61} -6.89550e9 q^{62} -3.94175e9 q^{63} +9.26370e9 q^{64} -1.66673e10 q^{65} +9.69212e9 q^{66} +7.00277e9 q^{67} -9.49664e8 q^{68} -1.91215e10 q^{69} +3.02326e10 q^{70} +1.19236e10 q^{71} -4.76847e9 q^{72} -3.55028e9 q^{73} -2.41335e8 q^{74} +2.20022e10 q^{75} -4.55601e8 q^{76} -4.59488e10 q^{77} +3.00403e10 q^{78} +4.10490e10 q^{79} +2.32030e10 q^{80} -3.75196e10 q^{81} -2.88698e10 q^{82} -9.15064e9 q^{83} +2.64257e10 q^{84} -1.38590e10 q^{85} -3.92081e10 q^{86} +2.54024e10 q^{87} -5.55858e10 q^{88} +5.41496e10 q^{89} -1.71317e10 q^{90} -1.42416e11 q^{91} +2.69978e10 q^{92} -8.79587e10 q^{93} -5.38735e10 q^{94} -6.64885e9 q^{95} +5.60661e10 q^{96} +1.99620e10 q^{97} +1.84895e11 q^{98} +2.60376e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{2} - 476 q^{3} + 4613 q^{4} - 12884 q^{5} + 552 q^{6} - 23436 q^{7} + 74805 q^{8} + 296398 q^{9}+O(q^{10}) $ 6 * q - 9 * q^2 - 476 * q^3 + 4613 * q^4 - 12884 * q^5 + 552 * q^6 - 23436 * q^7 + 74805 * q^8 + 296398 * q^9	\( 6 q - 9 q^{2} - 476 q^{3} + 4613 q^{4} - 12884 q^{5} + 552 q^{6} - 23436 q^{7} + 74805 q^{8} + 296398 q^{9} - 676038 q^{10} - 962060 q^{11} - 2352344 q^{12} - 435268 q^{13} - 7990948 q^{14} - 9450288 q^{15} - 12496671 q^{16} + 8519142 q^{17} - 20195421 q^{18} - 26398480 q^{19} - 47202914 q^{20} - 56428792 q^{21} - 51774200 q^{22} - 99172772 q^{23} - 110557128 q^{24} + 66085866 q^{25} + 74451914 q^{26} + 105183712 q^{27} + 102848900 q^{28} + 165683964 q^{29} + 401475744 q^{30} - 199133468 q^{31} + 465766501 q^{32} + 518429376 q^{33} - 12778713 q^{34} + 804442912 q^{35} + 627274777 q^{36} - 785778644 q^{37} + 2174484940 q^{38} + 627357728 q^{39} + 657666206 q^{40} + 166444428 q^{41} + 652753248 q^{42} - 1110947880 q^{43} - 997577064 q^{44} - 1706447988 q^{45} - 1891667412 q^{46} - 5828211928 q^{47} - 2359114472 q^{48} - 1968801674 q^{49} - 126509183 q^{50} - 675851932 q^{51} - 6633403554 q^{52} - 9889898636 q^{53} - 1961072736 q^{54} - 10730153984 q^{55} + 5703448884 q^{56} - 13522850128 q^{57} + 14316796258 q^{58} + 204095112 q^{59} + 22313648592 q^{60} - 15864546948 q^{61} - 1838602020 q^{62} + 504344540 q^{63} + 6177095465 q^{64} + 12794774792 q^{65} + 56255165136 q^{66} + 17196640232 q^{67} + 6549800341 q^{68} + 2949266904 q^{69} + 52391765944 q^{70} + 8751653884 q^{71} + 38682669705 q^{72} - 13704156916 q^{73} - 9383651494 q^{74} - 15917467268 q^{75} + 59548672452 q^{76} - 12012382872 q^{77} + 35038956192 q^{78} - 89923384436 q^{79} + 25877503334 q^{80} - 152313828506 q^{81} + 57834669670 q^{82} - 26042106648 q^{83} + 3397466240 q^{84} - 18293437588 q^{85} + 29108045060 q^{86} - 195382431072 q^{87} - 228837945880 q^{88} + 53269579420 q^{89} - 10044062046 q^{90} - 226028668544 q^{91} - 9212077436 q^{92} - 62709484936 q^{93} + 83948222448 q^{94} - 170219637424 q^{95} + 116885663928 q^{96} - 106272517044 q^{97} + 132039821039 q^{98} - 10550584980 q^{99}+O(q^{100}) \) 6 * q - 9 * q^2 - 476 * q^3 + 4613 * q^4 - 12884 * q^5 + 552 * q^6 - 23436 * q^7 + 74805 * q^8 + 296398 * q^9 - 676038 * q^10 - 962060 * q^11 - 2352344 * q^12 - 435268 * q^13 - 7990948 * q^14 - 9450288 * q^15 - 12496671 * q^16 + 8519142 * q^17 - 20195421 * q^18 - 26398480 * q^19 - 47202914 * q^20 - 56428792 * q^21 - 51774200 * q^22 - 99172772 * q^23 - 110557128 * q^24 + 66085866 * q^25 + 74451914 * q^26 + 105183712 * q^27 + 102848900 * q^28 + 165683964 * q^29 + 401475744 * q^30 - 199133468 * q^31 + 465766501 * q^32 + 518429376 * q^33 - 12778713 * q^34 + 804442912 * q^35 + 627274777 * q^36 - 785778644 * q^37 + 2174484940 * q^38 + 627357728 * q^39 + 657666206 * q^40 + 166444428 * q^41 + 652753248 * q^42 - 1110947880 * q^43 - 997577064 * q^44 - 1706447988 * q^45 - 1891667412 * q^46 - 5828211928 * q^47 - 2359114472 * q^48 - 1968801674 * q^49 - 126509183 * q^50 - 675851932 * q^51 - 6633403554 * q^52 - 9889898636 * q^53 - 1961072736 * q^54 - 10730153984 * q^55 + 5703448884 * q^56 - 13522850128 * q^57 + 14316796258 * q^58 + 204095112 * q^59 + 22313648592 * q^60 - 15864546948 * q^61 - 1838602020 * q^62 + 504344540 * q^63 + 6177095465 * q^64 + 12794774792 * q^65 + 56255165136 * q^66 + 17196640232 * q^67 + 6549800341 * q^68 + 2949266904 * q^69 + 52391765944 * q^70 + 8751653884 * q^71 + 38682669705 * q^72 - 13704156916 * q^73 - 9383651494 * q^74 - 15917467268 * q^75 + 59548672452 * q^76 - 12012382872 * q^77 + 35038956192 * q^78 - 89923384436 * q^79 + 25877503334 * q^80 - 152313828506 * q^81 + 57834669670 * q^82 - 26042106648 * q^83 + 3397466240 * q^84 - 18293437588 * q^85 + 29108045060 * q^86 - 195382431072 * q^87 - 228837945880 * q^88 + 53269579420 * q^89 - 10044062046 * q^90 - 226028668544 * q^91 - 9212077436 * q^92 - 62709484936 * q^93 + 83948222448 * q^94 - 170219637424 * q^95 + 116885663928 * q^96 - 106272517044 * q^97 + 132039821039 * q^98 - 10550584980 * 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 $

$2$	37.1370	0.820619	0.410310	−	0.911946i	$-0.365421\pi$
$2$	37.1370	0.820619	0.410310	+	0.911946i	$0.365421\pi$
$3$	473.718	1.12552	0.562759	−	0.826621i	$-0.309740\pi$
$3$	473.718	1.12552	0.562759	+	0.826621i	$0.309740\pi$
$4$	−668.845	−0.326584
$5$	−9760.84	−1.39686	−0.698429	−	0.715680i	$-0.746117\pi$
$5$	−9760.84	−1.39686	−0.698429	+	0.715680i	$0.746117\pi$
$6$	17592.4	0.923622
$7$	−83403.0	−1.87561	−0.937805	−	0.347163i	$-0.887145\pi$
$7$	−83403.0	−1.87561	−0.937805	+	0.347163i	$0.887145\pi$
$8$	−100895.	−1.08862
$9$	47261.5	0.266793
$10$	−362488.	−1.14629
$11$	550925.	1.03141	0.515707	−	0.856765i	$-0.327529\pi$
$11$	550925.	1.03141	0.515707	+	0.856765i	$0.327529\pi$
$12$	−316844.	−0.367577
$13$	1.70757e6	1.27553	0.637763	−	0.770233i	$-0.279860\pi$
$13$	1.70757e6	1.27553	0.637763	+	0.770233i	$0.279860\pi$
$14$	−3.09734e6	−1.53916
$15$	−4.62388e6	−1.57219
$16$	−2.37716e6	−0.566758
$17$	1.41986e6	0.242536
$17$	1.41986e6	0.242536
$18$	1.75515e6	0.218935
$19$	681176.	0.0631124	0.0315562	−	0.999502i	$-0.489954\pi$
$19$	681176.	0.0631124	0.0315562	+	0.999502i	$0.489954\pi$
$20$	6.52848e6	0.456192
$21$	−3.95095e7	−2.11103
$22$	2.04597e7	0.846397
$23$	−4.03648e7	−1.30767	−0.653837	−	0.756635i	$-0.726842\pi$
$23$	−4.03648e7	−1.30767	−0.653837	+	0.756635i	$0.726842\pi$
$24$	−4.77959e7	−1.22526
$25$	4.64458e7	0.951210
$26$	6.34139e7	1.04672
$27$	−6.15291e7	−0.825239
$28$	5.57837e7	0.612545
$29$	5.36234e7	0.485473	0.242737	−	0.970092i	$-0.421955\pi$
$29$	5.36234e7	0.485473	0.242737	+	0.970092i	$0.421955\pi$
$30$	−1.71717e8	−1.29017
$31$	−1.85677e8	−1.16485	−0.582425	−	0.812885i	$-0.697896\pi$
$31$	−1.85677e8	−1.16485	−0.582425	+	0.812885i	$0.697896\pi$
$32$	1.18353e8	0.623528
$33$	2.60983e8	1.16087
$34$	5.27292e7	0.199029
$35$	8.14083e8	2.61996
$36$	−3.16106e7	−0.0871303
$37$	−6.49851e6	−0.0154065	−0.00770326	−	0.999970i	$-0.502452\pi$
$37$	−6.49851e6	−0.0154065	−0.00770326	+	0.999970i	$0.502452\pi$
$38$	2.52968e7	0.0517912
$39$	8.08905e8	1.43563
$40$	9.84824e8	1.52065
$41$	−7.77386e8	−1.04791	−0.523957	−	0.851745i	$-0.675545\pi$
$41$	−7.77386e8	−1.04791	−0.523957	+	0.851745i	$0.675545\pi$
$42$	−1.46726e9	−1.73236
$43$	−1.05577e9	−1.09520	−0.547600	−	0.836740i	$-0.684458\pi$
$43$	−1.05577e9	−1.09520	−0.547600	+	0.836740i	$0.684458\pi$
$44$	−3.68483e8	−0.336843
$45$	−4.61312e8	−0.372671
$46$	−1.49903e9	−1.07310
$47$	−1.45067e9	−0.922636	−0.461318	−	0.887235i	$-0.652623\pi$
$47$	−1.45067e9	−0.922636	−0.461318	+	0.887235i	$0.652623\pi$
$48$	−1.12610e9	−0.637897
$49$	4.97874e9	2.51791
$50$	1.72486e9	0.780581
$51$	6.72611e8	0.272978
$52$	−1.14210e9	−0.416567
$53$	−5.08243e9	−1.66938	−0.834688	−	0.550723i	$-0.814352\pi$
$53$	−5.08243e9	−1.66938	−0.834688	+	0.550723i	$0.814352\pi$
$54$	−2.28500e9	−0.677207
$55$	−5.37749e9	−1.44074
$56$	8.41498e9	2.04183
$57$	3.22685e8	0.0710342
$58$	1.99141e9	0.398389
$59$	4.34382e9	0.791016	0.395508	−	0.918462i	$-0.370568\pi$
$59$	4.34382e9	0.791016	0.395508	+	0.918462i	$0.370568\pi$
$60$	3.09266e9	0.513452
$61$	−1.62659e9	−0.246584	−0.123292	−	0.992370i	$-0.539345\pi$
$61$	−1.62659e9	−0.246584	−0.123292	+	0.992370i	$0.539345\pi$
$62$	−6.89550e9	−0.955897
$63$	−3.94175e9	−0.500399
$64$	9.26370e9	1.07844
$65$	−1.66673e10	−1.78173
$66$	9.69212e9	0.952636
$67$	7.00277e9	0.633663	0.316831	−	0.948482i	$-0.397381\pi$
$67$	7.00277e9	0.633663	0.316831	+	0.948482i	$0.397381\pi$
$68$	−9.49664e8	−0.0792083
$69$	−1.91215e10	−1.47181
$70$	3.02326e10	2.14999
$71$	1.19236e10	0.784309	0.392155	−	0.919899i	$-0.371730\pi$
$71$	1.19236e10	0.784309	0.392155	+	0.919899i	$0.371730\pi$
$72$	−4.76847e9	−0.290436
$73$	−3.55028e9	−0.200441	−0.100220	−	0.994965i	$-0.531955\pi$
$73$	−3.55028e9	−0.200441	−0.100220	+	0.994965i	$0.531955\pi$
$74$	−2.41335e8	−0.0126429
$75$	2.20022e10	1.07061
$76$	−4.55601e8	−0.0206115
$77$	−4.59488e10	−1.93453
$78$	3.00403e10	1.17810
$79$	4.10490e10	1.50091	0.750454	−	0.660923i	$-0.229835\pi$
$79$	4.10490e10	1.50091	0.750454	+	0.660923i	$0.229835\pi$
$80$	2.32030e10	0.791681
$81$	−3.75196e10	−1.19561
$82$	−2.88698e10	−0.859938
$83$	−9.15064e9	−0.254989	−0.127495	−	0.991839i	$-0.540694\pi$
$83$	−9.15064e9	−0.254989	−0.127495	+	0.991839i	$0.540694\pi$
$84$	2.64257e10	0.689431
$85$	−1.38590e10	−0.338788
$86$	−3.92081e10	−0.898742
$87$	2.54024e10	0.546409
$88$	−5.55858e10	−1.12282
$89$	5.41496e10	1.02790	0.513949	−	0.857820i	$-0.328182\pi$
$89$	5.41496e10	1.02790	0.513949	+	0.857820i	$0.328182\pi$
$90$	−1.71317e10	−0.305821
$91$	−1.42416e11	−2.39239
$92$	2.69978e10	0.427066
$93$	−8.79587e10	−1.31106
$94$	−5.38735e10	−0.757132
$95$	−6.64885e9	−0.0881590
$96$	5.60661e10	0.701792
$97$	1.99620e10	0.236026	0.118013	−	0.993012i	$-0.462348\pi$
$97$	1.99620e10	0.236026	0.118013	+	0.993012i	$0.462348\pi$
$98$	1.84895e11	2.06625
$99$	2.60376e10	0.275174
$100$	−3.10650e10	−0.310650
$101$	−6.29881e10	−0.596335	−0.298168	−	0.954513i	$-0.596375\pi$
$101$	−6.29881e10	−0.596335	−0.298168	+	0.954513i	$0.596375\pi$
$102$	2.49788e10	0.224011
$103$	1.06050e11	0.901379	0.450689	−	0.892681i	$-0.351178\pi$
$103$	1.06050e11	0.901379	0.450689	+	0.892681i	$0.351178\pi$
$104$	−1.72286e11	−1.38856
$105$	3.85646e11	2.94881
$106$	−1.88746e11	−1.36992
$107$	−8.13250e10	−0.560548	−0.280274	−	0.959920i	$-0.590425\pi$
$107$	−8.13250e10	−0.560548	−0.280274	+	0.959920i	$0.590425\pi$
$108$	4.11534e10	0.269510
$109$	−3.42291e10	−0.213083	−0.106542	−	0.994308i	$-0.533978\pi$
$109$	−3.42291e10	−0.213083	−0.106542	+	0.994308i	$0.533978\pi$
$110$	−1.99704e11	−1.18230
$111$	−3.07846e9	−0.0173403
$112$	1.98262e11	1.06302
$113$	5.71150e10	0.291621	0.145810	−	0.989313i	$-0.453421\pi$
$113$	5.71150e10	0.291621	0.145810	+	0.989313i	$0.453421\pi$
$114$	1.19836e10	0.0582920
$115$	3.93994e11	1.82663
$116$	−3.58657e10	−0.158548
$117$	8.07022e10	0.340301
$118$	1.61316e11	0.649123
$119$	−1.18420e11	−0.454902
$120$	4.66528e11	1.71152
$121$	1.82066e10	0.0638131
$122$	−6.04067e10	−0.202351
$123$	−3.68262e11	−1.17945
$124$	1.24189e11	0.380421
$125$	2.32534e10	0.0681523
$126$	−1.46385e11	−0.410637
$127$	−5.63280e11	−1.51288	−0.756439	−	0.654064i	$-0.773063\pi$
$127$	−5.63280e11	−1.51288	−0.756439	+	0.654064i	$0.773063\pi$
$128$	1.01638e11	0.261458
$129$	−5.00137e11	−1.23267
$130$	−6.18972e11	−1.46212
$131$	6.02120e10	0.136361	0.0681806	−	0.997673i	$-0.478281\pi$
$131$	6.02120e10	0.136361	0.0681806	+	0.997673i	$0.478281\pi$
$132$	−1.74557e11	−0.379124
$133$	−5.68121e10	−0.118374
$134$	2.60062e11	0.519996
$135$	6.00575e11	1.15274
$136$	−1.43257e11	−0.264029
$137$	6.14846e11	1.08844	0.544219	−	0.838943i	$-0.316826\pi$
$137$	6.14846e11	1.08844	0.544219	+	0.838943i	$0.316826\pi$
$138$	−7.10116e11	−1.20780
$139$	−9.69611e11	−1.58495	−0.792476	−	0.609903i	$-0.791208\pi$
$139$	−9.69611e11	−1.58495	−0.792476	+	0.609903i	$0.791208\pi$
$140$	−5.44495e11	−0.855638
$141$	−6.87208e11	−1.03844
$142$	4.42807e11	0.643619
$143$	9.40741e11	1.31559
$144$	−1.12348e11	−0.151207
$145$	−5.23409e11	−0.678137
$146$	−1.31847e11	−0.164486
$147$	2.35852e12	2.83396
$148$	4.34650e9	0.00503153
$149$	6.77891e11	0.756197	0.378099	−	0.925765i	$-0.376578\pi$
$149$	6.77891e11	0.756197	0.378099	+	0.925765i	$0.376578\pi$
$150$	8.17096e11	0.878559
$151$	−4.14534e11	−0.429721	−0.214861	−	0.976645i	$-0.568930\pi$
$151$	−4.14534e11	−0.429721	−0.214861	+	0.976645i	$0.568930\pi$
$152$	−6.87275e10	−0.0687054
$153$	6.71046e10	0.0647067
$154$	−1.70640e12	−1.58751
$155$	1.81237e12	1.62713
$156$	−5.41032e11	−0.468854
$157$	−3.34061e11	−0.279497	−0.139749	−	0.990187i	$-0.544629\pi$
$157$	−3.34061e11	−0.279497	−0.139749	+	0.990187i	$0.544629\pi$
$158$	1.52444e12	1.23167
$159$	−2.40764e12	−1.87891
$160$	−1.15523e12	−0.870979
$161$	3.36655e12	2.45269
$162$	−1.39337e12	−0.981144
$163$	5.03368e11	0.342653	0.171326	−	0.985214i	$-0.445195\pi$
$163$	5.03368e11	0.342653	0.171326	+	0.985214i	$0.445195\pi$
$164$	5.19951e11	0.342232
$165$	−2.54741e12	−1.62158
$166$	−3.39827e11	−0.209249
$167$	−1.06600e12	−0.635062	−0.317531	−	0.948248i	$-0.602854\pi$
$167$	−1.06600e12	−0.635062	−0.317531	+	0.948248i	$0.602854\pi$
$168$	3.98633e12	2.29812
$169$	1.12362e12	0.626966
$170$	−5.14681e11	−0.278016
$171$	3.21934e10	0.0168379
$172$	7.06147e11	0.357675
$173$	1.29537e11	0.0635536	0.0317768	−	0.999495i	$-0.489883\pi$
$173$	1.29537e11	0.0635536	0.0317768	+	0.999495i	$0.489883\pi$
$174$	9.43367e11	0.448394
$175$	−3.87372e12	−1.78410
$176$	−1.30964e12	−0.584562
$177$	2.05774e12	0.890304
$178$	2.01095e12	0.843513
$179$	3.26869e12	1.32948	0.664741	−	0.747074i	$-0.268542\pi$
$179$	3.26869e12	1.32948	0.664741	+	0.747074i	$0.268542\pi$
$180$	3.08546e11	0.121709
$181$	−3.18357e12	−1.21810	−0.609049	−	0.793132i	$-0.708449\pi$
$181$	−3.18357e12	−1.21810	−0.609049	+	0.793132i	$0.708449\pi$
$182$	−5.28891e12	−1.96324
$183$	−7.70545e11	−0.277535
$184$	4.07262e12	1.42356
$185$	6.34309e10	0.0215207
$186$	−3.26652e12	−1.07588
$187$	7.82235e11	0.250154
$188$	9.70272e11	0.301318
$189$	5.13171e12	1.54783
$190$	−2.46918e11	−0.0723449
$191$	2.58587e12	0.736077	0.368038	−	0.929811i	$-0.380030\pi$
$191$	2.58587e12	0.736077	0.368038	+	0.929811i	$0.380030\pi$
$192$	4.38838e12	1.21380
$193$	−3.90827e12	−1.05056	−0.525278	−	0.850931i	$-0.676039\pi$
$193$	−3.90827e12	−1.05056	−0.525278	+	0.850931i	$0.676039\pi$
$194$	7.41328e11	0.193687
$195$	−7.89559e12	−2.00537
$196$	−3.33000e12	−0.822311
$197$	−6.67356e12	−1.60248	−0.801241	−	0.598341i	$-0.795827\pi$
$197$	−6.67356e12	−1.60248	−0.801241	+	0.598341i	$0.795827\pi$
$198$	9.66956e11	0.225813
$199$	−8.38190e12	−1.90393	−0.951964	−	0.306209i	$-0.900939\pi$
$199$	−8.38190e12	−1.90393	−0.951964	+	0.306209i	$0.900939\pi$
$200$	−4.68617e12	−1.03551
$201$	3.31733e12	0.713199
$202$	−2.33919e12	−0.489364
$203$	−4.47235e12	−0.910558
$204$	−4.49873e11	−0.0891505
$205$	7.58794e12	1.46379
$206$	3.93839e12	0.739689
$207$	−1.90770e12	−0.348878
$208$	−4.05915e12	−0.722915
$209$	3.75277e11	0.0650949
$210$	1.43217e13	2.41985
$211$	−6.88158e12	−1.13275	−0.566376	−	0.824147i	$-0.691655\pi$
$211$	−6.88158e12	−1.13275	−0.566376	+	0.824147i	$0.691655\pi$
$212$	3.39936e12	0.545192
$213$	5.64843e12	0.882755
$214$	−3.02016e12	−0.459997
$215$	1.03052e13	1.52984
$216$	6.20800e12	0.898372
$217$	1.54861e13	2.18480
$218$	−1.27116e12	−0.174860
$219$	−1.68183e12	−0.225600
$220$	3.59670e12	0.470522
$221$	2.42450e12	0.309360
$222$	−1.14325e11	−0.0142298
$223$	−9.08403e12	−1.10307	−0.551534	−	0.834153i	$-0.685957\pi$
$223$	−9.08403e12	−1.10307	−0.551534	+	0.834153i	$0.685957\pi$
$224$	−9.87103e12	−1.16949
$225$	2.19510e12	0.253776
$226$	2.12108e12	0.239310
$227$	−1.65034e12	−0.181732	−0.0908662	−	0.995863i	$-0.528964\pi$
$227$	−1.65034e12	−0.181732	−0.0908662	+	0.995863i	$0.528964\pi$
$228$	−2.15826e11	−0.0231986
$229$	−1.55336e12	−0.162996	−0.0814980	−	0.996674i	$-0.525970\pi$
$229$	−1.55336e12	−0.162996	−0.0814980	+	0.996674i	$0.525970\pi$
$230$	1.46318e13	1.49897
$231$	−2.17668e13	−2.17735
$232$	−5.41035e12	−0.528496
$233$	−3.17619e12	−0.303005	−0.151502	−	0.988457i	$-0.548411\pi$
$233$	−3.17619e12	−0.303005	−0.151502	+	0.988457i	$0.548411\pi$
$234$	2.99704e12	0.279257
$235$	1.41597e13	1.28879
$236$	−2.90534e12	−0.258334
$237$	1.94457e13	1.68930
$238$	−4.39777e12	−0.373301
$239$	−3.96526e12	−0.328915	−0.164457	−	0.986384i	$-0.552587\pi$
$239$	−3.96526e12	−0.328915	−0.164457	+	0.986384i	$0.552587\pi$
$240$	1.09917e13	0.891051
$241$	1.17676e13	0.932380	0.466190	−	0.884685i	$-0.345626\pi$
$241$	1.17676e13	0.932380	0.466190	+	0.884685i	$0.345626\pi$
$242$	6.76139e11	0.0523662
$243$	−6.87404e12	−0.520448
$244$	1.08794e12	0.0805304
$245$	−4.85966e13	−3.51716
$246$	−1.36761e13	−0.967877
$247$	1.16315e12	0.0805015
$248$	1.87340e13	1.26808
$249$	−4.33482e12	−0.286995
$250$	8.63560e11	0.0559271
$251$	8.42143e12	0.533556	0.266778	−	0.963758i	$-0.414041\pi$
$251$	8.42143e12	0.533556	0.266778	+	0.963758i	$0.414041\pi$
$252$	2.63642e12	0.163422
$253$	−2.22380e13	−1.34875
$254$	−2.09185e13	−1.24150
$255$	−6.56525e12	−0.381312
$256$	−1.51975e13	−0.863879
$257$	8.86633e12	0.493301	0.246650	−	0.969105i	$-0.420670\pi$
$257$	8.86633e12	0.493301	0.246650	+	0.969105i	$0.420670\pi$
$258$	−1.85736e13	−1.01155
$259$	5.41996e11	0.0288966
$260$	1.11478e13	0.581884
$261$	2.53432e12	0.129521
$262$	2.23609e12	0.111901
$263$	1.06560e13	0.522202	0.261101	−	0.965312i	$-0.415914\pi$
$263$	1.06560e13	0.522202	0.261101	+	0.965312i	$0.415914\pi$
$264$	−2.63320e13	−1.26375
$265$	4.96088e13	2.33188
$266$	−2.10983e12	−0.0971401
$267$	2.56516e13	1.15692
$268$	−4.68376e12	−0.206944
$269$	−2.80933e12	−0.121609	−0.0608045	−	0.998150i	$-0.519367\pi$
$269$	−2.80933e12	−0.121609	−0.0608045	+	0.998150i	$0.519367\pi$
$270$	2.23035e13	0.945961
$271$	−2.06538e12	−0.0858360	−0.0429180	−	0.999079i	$-0.513665\pi$
$271$	−2.06538e12	−0.0858360	−0.0429180	+	0.999079i	$0.513665\pi$
$272$	−3.37522e12	−0.137459
$273$	−6.74651e13	−2.69268
$274$	2.28335e13	0.893192
$275$	2.55882e13	0.981091
$276$	1.27893e13	0.480671
$277$	4.01857e13	1.48058	0.740291	−	0.672286i	$-0.234688\pi$
$277$	4.01857e13	1.48058	0.740291	+	0.672286i	$0.234688\pi$
$278$	−3.60084e13	−1.30064
$279$	−8.77540e12	−0.310773
$280$	−8.21373e13	−2.85214
$281$	4.34049e13	1.47793	0.738966	−	0.673743i	$-0.235314\pi$
$281$	4.34049e13	1.47793	0.738966	+	0.673743i	$0.235314\pi$
$282$	−2.55208e13	−0.852167
$283$	3.62468e13	1.18698	0.593491	−	0.804841i	$-0.297749\pi$
$283$	3.62468e13	1.18698	0.593491	+	0.804841i	$0.297749\pi$
$284$	−7.97505e12	−0.256143
$285$	−3.14968e12	−0.0992246
$286$	3.49363e13	1.07960
$287$	6.48364e13	1.96548
$288$	5.59356e12	0.166353
$289$	2.01599e12	0.0588235
$290$	−1.94378e13	−0.556492
$291$	9.45635e12	0.265651
$292$	2.37458e12	0.0654609
$293$	2.58188e12	0.0698496	0.0349248	−	0.999390i	$-0.488881\pi$
$293$	2.58188e12	0.0698496	0.0349248	+	0.999390i	$0.488881\pi$
$294$	8.75881e13	2.32560
$295$	−4.23993e13	−1.10494
$296$	6.55670e11	0.0167718
$297$	−3.38979e13	−0.851162
$298$	2.51748e13	0.620550
$299$	−6.89256e13	−1.66797
$300$	−1.47161e13	−0.349643
$301$	8.80545e13	2.05417
$302$	−1.53945e13	−0.352637
$303$	−2.98386e13	−0.671187
$304$	−1.61926e12	−0.0357695
$305$	1.58769e13	0.344442
$306$	2.49206e12	0.0530996
$307$	−3.98448e13	−0.833894	−0.416947	−	0.908931i	$-0.636900\pi$
$307$	−3.98448e13	−0.833894	−0.416947	+	0.908931i	$0.636900\pi$
$308$	3.07326e13	0.631787
$309$	5.02379e13	1.01452
$310$	6.73058e13	1.33525
$311$	−5.69882e13	−1.11072	−0.555358	−	0.831612i	$-0.687419\pi$
$311$	−5.69882e13	−1.11072	−0.555358	+	0.831612i	$0.687419\pi$
$312$	−8.16148e13	−1.56285
$313$	−9.62973e13	−1.81184	−0.905921	−	0.423447i	$-0.860820\pi$
$313$	−9.62973e13	−1.81184	−0.905921	+	0.423447i	$0.860820\pi$
$314$	−1.24060e13	−0.229361
$315$	3.84748e13	0.698986
$316$	−2.74554e13	−0.490173
$317$	−1.43934e13	−0.252544	−0.126272	−	0.991996i	$-0.540301\pi$
$317$	−1.43934e13	−0.252544	−0.126272	+	0.991996i	$0.540301\pi$
$318$	−8.94124e13	−1.54187
$319$	2.95425e13	0.500723
$320$	−9.04215e13	−1.50642
$321$	−3.85251e13	−0.630908
$322$	1.25023e14	2.01272
$323$	9.67172e11	0.0153070
$324$	2.50948e13	0.390469
$325$	7.93093e13	1.21329
$326$	1.86936e13	0.281187
$327$	−1.62149e13	−0.239829
$328$	7.84347e13	1.14078
$329$	1.20990e14	1.73050
$330$	−9.46032e13	−1.33070
$331$	−1.32817e14	−1.83738	−0.918692	−	0.394975i	$-0.870753\pi$
$331$	−1.32817e14	−1.83738	−0.918692	+	0.394975i	$0.870753\pi$
$332$	6.12036e12	0.0832755
$333$	−3.07130e11	−0.00411035
$334$	−3.95880e13	−0.521144
$335$	−6.83528e13	−0.885136
$336$	9.39203e13	1.19645
$337$	3.32318e13	0.416476	0.208238	−	0.978078i	$-0.433227\pi$
$337$	3.32318e13	0.416476	0.208238	+	0.978078i	$0.433227\pi$
$338$	4.17280e13	0.514500
$339$	2.70564e13	0.328225
$340$	9.26951e12	0.110643
$341$	−1.02294e14	−1.20144
$342$	1.19557e12	0.0138175
$343$	−2.50327e14	−2.84701
$344$	1.06522e14	1.19226
$345$	1.86642e14	2.05591
$346$	4.81061e12	0.0521533
$347$	−8.63526e13	−0.921432	−0.460716	−	0.887548i	$-0.652407\pi$
$347$	−8.63526e13	−0.921432	−0.460716	+	0.887548i	$0.652407\pi$
$348$	−1.69902e13	−0.178449
$349$	8.57753e13	0.886793	0.443397	−	0.896326i	$-0.353773\pi$
$349$	8.57753e13	0.886793	0.443397	+	0.896326i	$0.353773\pi$
$350$	−1.43858e14	−1.46407
$351$	−1.05065e14	−1.05261
$352$	6.52038e13	0.643115
$353$	8.38432e13	0.814155	0.407077	−	0.913394i	$-0.366548\pi$
$353$	8.38432e13	0.814155	0.407077	+	0.913394i	$0.366548\pi$
$354$	7.64184e13	0.730600
$355$	−1.16385e14	−1.09557
$356$	−3.62177e13	−0.335696
$357$	−5.60978e13	−0.512001
$358$	1.21389e14	1.09100
$359$	2.46768e13	0.218409	0.109204	−	0.994019i	$-0.465170\pi$
$359$	2.46768e13	0.218409	0.109204	+	0.994019i	$0.465170\pi$
$360$	4.65443e13	0.405698
$361$	−1.16026e14	−0.996017
$362$	−1.18228e14	−0.999595
$363$	8.62479e12	0.0718228
$364$	9.52543e13	0.781317
$365$	3.46537e13	0.279987
$366$	−2.86157e13	−0.227750
$367$	4.43460e13	0.347689	0.173845	−	0.984773i	$-0.444381\pi$
$367$	4.43460e13	0.347689	0.173845	+	0.984773i	$0.444381\pi$
$368$	9.59534e13	0.741135
$369$	−3.67405e13	−0.279576
$370$	2.35563e12	0.0176603
$371$	4.23890e14	3.13110
$372$	5.88307e13	0.428172
$373$	−2.07232e14	−1.48613	−0.743067	−	0.669217i	$-0.766630\pi$
$373$	−2.07232e14	−1.48613	−0.743067	+	0.669217i	$0.766630\pi$
$374$	2.90498e13	0.205281
$375$	1.10155e13	0.0767068
$376$	1.46366e14	1.00440
$377$	9.15655e13	0.619234
$378$	1.90576e14	1.27018
$379$	−6.54378e13	−0.429846	−0.214923	−	0.976631i	$-0.568950\pi$
$379$	−6.54378e13	−0.429846	−0.214923	+	0.976631i	$0.568950\pi$
$380$	4.44705e12	0.0287913
$381$	−2.66836e14	−1.70277
$382$	9.60314e13	0.604039
$383$	3.10686e14	1.92632	0.963161	−	0.268924i	$-0.0866680\pi$
$383$	3.10686e14	1.92632	0.963161	+	0.268924i	$0.0866680\pi$
$384$	4.81479e13	0.294276
$385$	4.48499e14	2.70226
$386$	−1.45141e14	−0.862106
$387$	−4.98973e13	−0.292191
$388$	−1.33515e13	−0.0770823
$389$	5.67606e13	0.323090	0.161545	−	0.986865i	$-0.448352\pi$
$389$	5.67606e13	0.323090	0.161545	+	0.986865i	$0.448352\pi$
$390$	−2.93218e14	−1.64564
$391$	−5.73122e13	−0.317158
$392$	−5.02332e14	−2.74105
$393$	2.85235e13	0.153477
$394$	−2.47836e14	−1.31503
$395$	−4.00673e14	−2.09655
$396$	−1.74151e13	−0.0898673
$397$	1.83719e14	0.934988	0.467494	−	0.883996i	$-0.345157\pi$
$397$	1.83719e14	0.934988	0.467494	+	0.883996i	$0.345157\pi$
$398$	−3.11279e14	−1.56240
$399$	−2.69129e13	−0.133232
$400$	−1.10409e14	−0.539106
$401$	−4.85421e13	−0.233789	−0.116895	−	0.993144i	$-0.537294\pi$
$401$	−4.85421e13	−0.233789	−0.116895	+	0.993144i	$0.537294\pi$
$402$	1.23196e14	0.585265
$403$	−3.17057e14	−1.48580
$404$	4.21292e13	0.194754
$405$	3.66223e14	1.67010
$406$	−1.66090e14	−0.747222
$407$	−3.58019e12	−0.0158905
$408$	−6.78634e13	−0.297170
$409$	3.55174e14	1.53449	0.767244	−	0.641355i	$-0.221628\pi$
$409$	3.55174e14	1.53449	0.767244	+	0.641355i	$0.221628\pi$
$410$	2.81793e14	1.20121
$411$	2.91264e14	1.22506
$412$	−7.09312e13	−0.294376
$413$	−3.62287e14	−1.48364
$414$	−7.08463e13	−0.286296
$415$	8.93179e13	0.356184
$416$	2.02096e14	0.795326
$417$	−4.59322e14	−1.78389
$418$	1.39366e13	0.0534181
$419$	−3.34129e14	−1.26397	−0.631986	−	0.774980i	$-0.717760\pi$
$419$	−3.34129e14	−1.26397	−0.631986	+	0.774980i	$0.717760\pi$
$420$	−2.57937e14	−0.963036
$421$	−3.52936e14	−1.30060	−0.650301	−	0.759677i	$-0.725357\pi$
$421$	−3.52936e14	−1.30060	−0.650301	+	0.759677i	$0.725357\pi$
$422$	−2.55561e14	−0.929557
$423$	−6.85608e13	−0.246152
$424$	5.12794e14	1.81732
$425$	6.59464e13	0.230702
$426$	2.09766e14	0.724405
$427$	1.35663e14	0.462495
$428$	5.43938e13	0.183066
$429$	4.45646e14	1.48073
$430$	3.82704e14	1.25541
$431$	−4.10453e14	−1.32935	−0.664673	−	0.747134i	$-0.731429\pi$
$431$	−4.10453e14	−1.32935	−0.664673	+	0.747134i	$0.731429\pi$
$432$	1.46264e14	0.467711
$433$	−9.60956e13	−0.303403	−0.151702	−	0.988426i	$-0.548475\pi$
$433$	−9.60956e13	−0.303403	−0.151702	+	0.988426i	$0.548475\pi$
$434$	5.75105e14	1.79289
$435$	−2.47948e14	−0.763256
$436$	2.28939e13	0.0695897
$437$	−2.74955e13	−0.0825304
$438$	−6.24580e13	−0.185132
$439$	1.59532e14	0.466974	0.233487	−	0.972360i	$-0.424986\pi$
$439$	1.59532e14	0.466974	0.233487	+	0.972360i	$0.424986\pi$
$440$	5.42564e14	1.56842
$441$	2.35303e14	0.671761
$442$	9.00386e13	0.253867
$443$	5.88114e14	1.63773	0.818863	−	0.573989i	$-0.194605\pi$
$443$	5.88114e14	1.63773	0.818863	+	0.573989i	$0.194605\pi$
$444$	2.05901e12	0.00566308
$445$	−5.28546e14	−1.43583
$446$	−3.37354e14	−0.905198
$447$	3.21129e14	0.851114
$448$	−7.72621e14	−2.02273
$449$	3.41090e14	0.882093	0.441046	−	0.897484i	$-0.354607\pi$
$449$	3.41090e14	0.882093	0.441046	+	0.897484i	$0.354607\pi$
$450$	8.15194e13	0.208253
$451$	−4.28281e14	−1.08083
$452$	−3.82010e13	−0.0952388
$453$	−1.96372e14	−0.483659
$454$	−6.12888e13	−0.149133
$455$	1.39010e15	3.34183
$456$	−3.25575e13	−0.0773292
$457$	−1.30043e14	−0.305175	−0.152587	−	0.988290i	$-0.548761\pi$
$457$	−1.30043e14	−0.305175	−0.152587	+	0.988290i	$0.548761\pi$
$458$	−5.76871e13	−0.133758
$459$	−8.73625e13	−0.200150
$460$	−2.63521e14	−0.596550
$461$	−2.89416e14	−0.647391	−0.323696	−	0.946161i	$-0.604925\pi$
$461$	−2.89416e14	−0.647391	−0.323696	+	0.946161i	$0.604925\pi$
$462$	−8.08352e14	−1.78677
$463$	6.06684e14	1.32516	0.662578	−	0.748993i	$-0.269462\pi$
$463$	6.06684e14	1.32516	0.662578	+	0.748993i	$0.269462\pi$
$464$	−1.27471e14	−0.275146
$465$	8.58550e14	1.83136
$466$	−1.17954e14	−0.248652
$467$	−4.17949e14	−0.870725	−0.435362	−	0.900255i	$-0.643380\pi$
$467$	−4.17949e14	−0.870725	−0.435362	+	0.900255i	$0.643380\pi$
$468$	−5.39772e13	−0.111137
$469$	−5.84052e14	−1.18850
$470$	5.25850e14	1.05761
$471$	−1.58251e14	−0.314579
$472$	−4.38271e14	−0.861117
$473$	−5.81651e14	−1.12960
$474$	7.22153e14	1.38627
$475$	3.16378e13	0.0600331
$476$	7.92048e13	0.148564
$477$	−2.40203e14	−0.445377
$478$	−1.47258e14	−0.269914
$479$	8.91775e14	1.61588	0.807942	−	0.589262i	$-0.200582\pi$
$479$	8.91775e14	1.61588	0.807942	+	0.589262i	$0.200582\pi$
$480$	−5.47252e14	−0.980303
$481$	−1.10966e13	−0.0196514
$482$	4.37012e14	0.765129
$483$	1.59479e15	2.76055
$484$	−1.21774e13	−0.0208403
$485$	−1.94846e14	−0.329694
$486$	−2.55281e14	−0.427089
$487$	−8.70872e14	−1.44061	−0.720303	−	0.693660i	$-0.755997\pi$
$487$	−8.70872e14	−1.44061	−0.720303	+	0.693660i	$0.755997\pi$
$488$	1.64116e14	0.268436
$489$	2.38454e14	0.385662
$490$	−1.80473e15	−2.88625
$491$	1.78098e14	0.281651	0.140825	−	0.990034i	$-0.455024\pi$
$491$	1.78098e14	0.281651	0.140825	+	0.990034i	$0.455024\pi$
$492$	2.46310e14	0.385189
$493$	7.61375e13	0.117745
$494$	4.31960e13	0.0660610
$495$	−2.54148e14	−0.384378
$496$	4.41384e14	0.660188
$497$	−9.94466e14	−1.47106
$498$	−1.60982e14	−0.235514
$499$	−9.90769e14	−1.43357	−0.716786	−	0.697293i	$-0.754387\pi$
$499$	−9.90769e14	−1.43357	−0.716786	+	0.697293i	$0.754387\pi$
$500$	−1.55529e13	−0.0222575
$501$	−5.04982e14	−0.714774
$502$	3.12746e14	0.437846
$503$	4.91559e14	0.680694	0.340347	−	0.940300i	$-0.389455\pi$
$503$	4.91559e14	0.680694	0.340347	+	0.940300i	$0.389455\pi$
$504$	3.97705e14	0.544745
$505$	6.14816e14	0.832996
$506$	−8.25851e14	−1.10681
$507$	5.32281e14	0.705662
$508$	3.76747e14	0.494082
$509$	2.03815e14	0.264417	0.132208	−	0.991222i	$-0.457793\pi$
$509$	2.03815e14	0.264417	0.132208	+	0.991222i	$0.457793\pi$
$510$	−2.43814e14	−0.312912
$511$	2.96104e14	0.375949
$512$	−7.72545e14	−0.970374
$513$	−4.19121e13	−0.0520828
$514$	3.29269e14	0.404812
$515$	−1.03514e15	−1.25910
$516$	3.34514e14	0.402570
$517$	−7.99210e14	−0.951618
$518$	2.01281e13	0.0237131
$519$	6.13639e13	0.0715307
$520$	1.68165e15	1.93962
$521$	3.76703e14	0.429924	0.214962	−	0.976622i	$-0.431037\pi$
$521$	3.76703e14	0.429924	0.214962	+	0.976622i	$0.431037\pi$
$522$	9.41171e13	0.106287
$523$	−3.77786e14	−0.422170	−0.211085	−	0.977468i	$-0.567700\pi$
$523$	−3.77786e14	−0.422170	−0.211085	+	0.977468i	$0.567700\pi$
$524$	−4.02724e13	−0.0445334
$525$	−1.83505e15	−2.00804
$526$	3.95732e14	0.428529
$527$	−2.63635e14	−0.282517
$528$	−6.20397e14	−0.657936
$529$	6.76507e14	0.710013
$530$	1.84232e15	1.91358
$531$	2.05295e14	0.211037
$532$	3.79985e13	0.0386592
$533$	−1.32744e15	−1.33664
$534$	9.52624e14	0.949390
$535$	7.93800e14	0.783006
$536$	−7.06547e14	−0.689818
$537$	1.54844e15	1.49636
$538$	−1.04330e14	−0.0997946
$539$	2.74291e15	2.59701
$540$	−4.01691e14	−0.376467
$541$	1.96416e15	1.82218	0.911092	−	0.412203i	$-0.135241\pi$
$541$	1.96416e15	1.82218	0.911092	+	0.412203i	$0.135241\pi$
$542$	−7.67021e13	−0.0704386
$543$	−1.50811e15	−1.37099
$544$	1.68045e14	0.151228
$545$	3.34104e14	0.297647
$546$	−2.50545e15	−2.20966
$547$	−8.43672e14	−0.736620	−0.368310	−	0.929703i	$-0.620064\pi$
$547$	−8.43672e14	−0.736620	−0.368310	+	0.929703i	$0.620064\pi$
$548$	−4.11237e14	−0.355466
$549$	−7.68752e13	−0.0657867
$550$	9.50267e14	0.805102
$551$	3.65270e13	0.0306394
$552$	1.92927e15	1.60224
$553$	−3.42361e15	−2.81512
$554$	1.49237e15	1.21499
$555$	3.00484e13	0.0242220
$556$	6.48519e14	0.517620
$557$	−8.45182e14	−0.667954	−0.333977	−	0.942581i	$-0.608391\pi$
$557$	−8.45182e14	−0.667954	−0.333977	+	0.942581i	$0.608391\pi$
$558$	−3.25892e14	−0.255026
$559$	−1.80280e15	−1.39696
$560$	−1.93520e15	−1.48488
$561$	3.70558e14	0.281554
$562$	1.61193e15	1.21282
$563$	3.14244e14	0.234137	0.117069	−	0.993124i	$-0.462650\pi$
$563$	3.14244e14	0.234137	0.117069	+	0.993124i	$0.462650\pi$
$564$	4.59635e14	0.339139
$565$	−5.57490e14	−0.407353
$566$	1.34610e15	0.974059
$567$	3.12925e15	2.24251
$568$	−1.20304e15	−0.853815
$569$	−2.42546e14	−0.170481	−0.0852405	−	0.996360i	$-0.527166\pi$
$569$	−2.42546e14	−0.170481	−0.0852405	+	0.996360i	$0.527166\pi$
$570$	−1.16970e14	−0.0814256
$571$	−4.71060e13	−0.0324772	−0.0162386	−	0.999868i	$-0.505169\pi$
$571$	−4.71060e13	−0.0324772	−0.0162386	+	0.999868i	$0.505169\pi$
$572$	−6.29210e14	−0.429652
$573$	1.22497e15	0.828468
$574$	2.40783e15	1.61291
$575$	−1.87478e15	−1.24387
$576$	4.37817e14	0.287719
$577$	2.50388e15	1.62984	0.814922	−	0.579570i	$-0.196780\pi$
$577$	2.50388e15	1.62984	0.814922	+	0.579570i	$0.196780\pi$
$578$	7.48679e13	0.0482717
$579$	−1.85141e15	−1.18242
$580$	3.50079e14	0.221469
$581$	7.63191e14	0.478261
$582$	3.51180e14	0.217999
$583$	−2.80004e15	−1.72182
$584$	3.58207e14	0.218204
$585$	−7.87721e14	−0.475352
$586$	9.58832e13	0.0573199
$587$	2.96841e15	1.75798	0.878991	−	0.476838i	$-0.158217\pi$
$587$	2.96841e15	1.75798	0.878991	+	0.476838i	$0.158217\pi$
$588$	−1.57748e15	−0.925526
$589$	−1.26479e14	−0.0735164
$590$	−1.57458e15	−0.906732
$591$	−3.16138e15	−1.80362
$592$	1.54480e13	0.00873177
$593$	−1.04860e15	−0.587233	−0.293616	−	0.955923i	$-0.594859\pi$
$593$	−1.04860e15	−0.587233	−0.293616	+	0.955923i	$0.594859\pi$
$594$	−1.25887e15	−0.698480
$595$	1.15588e15	0.635433
$596$	−4.53404e14	−0.246962
$597$	−3.97066e15	−2.14291
$598$	−2.55969e15	−1.36877
$599$	8.68326e14	0.460082	0.230041	−	0.973181i	$-0.426114\pi$
$599$	8.68326e14	0.460082	0.230041	+	0.973181i	$0.426114\pi$
$600$	−2.21992e15	−1.16548
$601$	−7.61650e14	−0.396228	−0.198114	−	0.980179i	$-0.563482\pi$
$601$	−7.61650e14	−0.396228	−0.198114	+	0.980179i	$0.563482\pi$
$602$	3.27008e15	1.68569
$603$	3.30961e14	0.169057
$604$	2.77259e14	0.140340
$605$	−1.77712e14	−0.0891377
$606$	−1.10811e15	−0.550789
$607$	2.15005e15	1.05904	0.529519	−	0.848298i	$-0.322373\pi$
$607$	2.15005e15	1.05904	0.529519	+	0.848298i	$0.322373\pi$
$608$	8.06195e13	0.0393523
$609$	−2.11863e15	−1.02485
$610$	5.89620e14	0.282656
$611$	−2.47711e15	−1.17685
$612$	−4.48826e13	−0.0211322
$613$	2.60698e15	1.21648	0.608239	−	0.793754i	$-0.291876\pi$
$613$	2.60698e15	1.21648	0.608239	+	0.793754i	$0.291876\pi$
$614$	−1.47972e15	−0.684309
$615$	3.59454e15	1.64752
$616$	4.63602e15	2.10597
$617$	6.03547e14	0.271733	0.135867	−	0.990727i	$-0.456618\pi$
$617$	6.03547e14	0.271733	0.135867	+	0.990727i	$0.456618\pi$
$618$	1.86569e15	0.832534
$619$	3.73734e15	1.65296	0.826482	−	0.562963i	$-0.190339\pi$
$619$	3.73734e15	1.65296	0.826482	+	0.562963i	$0.190339\pi$
$620$	−1.21219e15	−0.531394
$621$	2.48361e15	1.07914
$622$	−2.11637e15	−0.911474
$623$	−4.51624e15	−1.92794
$624$	−1.92289e15	−0.813654
$625$	−2.49483e15	−1.04641
$626$	−3.57619e15	−1.48683
$627$	1.77775e14	0.0732656
$628$	2.23435e14	0.0912794
$629$	−9.22696e12	−0.00373663
$630$	1.42884e15	0.573601
$631$	1.09948e15	0.437549	0.218774	−	0.975775i	$-0.429794\pi$
$631$	1.09948e15	0.437549	0.218774	+	0.975775i	$0.429794\pi$
$632$	−4.14166e15	−1.63392
$633$	−3.25993e15	−1.27493
$634$	−5.34527e14	−0.207243
$635$	5.49808e15	2.11327
$636$	1.61034e15	0.613624
$637$	8.50152e15	3.21166
$638$	1.09712e15	0.410903
$639$	5.63529e14	0.209248
$640$	−9.92075e14	−0.365220
$641$	−4.25383e15	−1.55261	−0.776303	−	0.630360i	$-0.782907\pi$
$641$	−4.25383e15	−1.55261	−0.776303	+	0.630360i	$0.782907\pi$
$642$	−1.43071e15	−0.517735
$643$	−5.90503e14	−0.211866	−0.105933	−	0.994373i	$-0.533783\pi$
$643$	−5.90503e14	−0.211866	−0.105933	+	0.994373i	$0.533783\pi$
$644$	−2.25170e15	−0.801009
$645$	4.88176e15	1.72186
$646$	3.59179e13	0.0125612
$647$	−1.08225e15	−0.375279	−0.187640	−	0.982238i	$-0.560084\pi$
$647$	−1.08225e15	−0.375279	−0.187640	+	0.982238i	$0.560084\pi$
$648$	3.78556e15	1.30157
$649$	2.39312e15	0.815865
$650$	2.94531e15	0.995652
$651$	7.33602e15	2.45904
$652$	−3.36675e14	−0.111905
$653$	2.07433e15	0.683683	0.341841	−	0.939758i	$-0.388949\pi$
$653$	2.07433e15	0.683683	0.341841	+	0.939758i	$0.388949\pi$
$654$	−6.02173e14	−0.196809
$655$	−5.87719e14	−0.190477
$656$	1.84797e15	0.593914
$657$	−1.67791e14	−0.0534762
$658$	4.49321e15	1.42008
$659$	−1.16049e15	−0.363724	−0.181862	−	0.983324i	$-0.558212\pi$
$659$	−1.16049e15	−0.363724	−0.181862	+	0.983324i	$0.558212\pi$
$660$	1.70382e15	0.529581
$661$	−2.13471e14	−0.0658006	−0.0329003	−	0.999459i	$-0.510474\pi$
$661$	−2.13471e14	−0.0658006	−0.0329003	+	0.999459i	$0.510474\pi$
$662$	−4.93242e15	−1.50779
$663$	1.14853e15	0.348191
$664$	9.23258e14	0.277587
$665$	5.54534e14	0.165352
$666$	−1.14059e13	−0.00337303
$667$	−2.16450e15	−0.634841
$668$	7.12987e14	0.207401
$669$	−4.30327e15	−1.24152
$670$	−2.53842e15	−0.726360
$671$	−8.96130e14	−0.254330
$672$	−4.67608e15	−1.31629
$673$	−5.89038e15	−1.64460	−0.822301	−	0.569053i	$-0.807310\pi$
$673$	−5.89038e15	−1.64460	−0.822301	+	0.569053i	$0.807310\pi$
$674$	1.23413e15	0.341768
$675$	−2.85777e15	−0.784975
$676$	−7.51530e14	−0.204757
$677$	3.62198e15	0.978833	0.489416	−	0.872050i	$-0.337210\pi$
$677$	3.62198e15	0.978833	0.489416	+	0.872050i	$0.337210\pi$
$678$	1.00479e15	0.269347
$679$	−1.66489e15	−0.442692
$680$	1.39831e15	0.368811
$681$	−7.81797e14	−0.204543
$682$	−3.79890e15	−0.985925
$683$	−2.95501e15	−0.760757	−0.380378	−	0.924831i	$-0.624206\pi$
$683$	−2.95501e15	−0.760757	−0.380378	+	0.924831i	$0.624206\pi$
$684$	−2.15324e13	−0.00549900
$685$	−6.00141e15	−1.52039
$686$	−9.29637e15	−2.33631
$687$	−7.35854e14	−0.183455
$688$	2.50973e15	0.620713
$689$	−8.67859e15	−2.12933
$690$	6.93132e15	1.68712
$691$	3.92191e15	0.947041	0.473520	−	0.880783i	$-0.342983\pi$
$691$	3.92191e15	0.947041	0.473520	+	0.880783i	$0.342983\pi$
$692$	−8.66400e13	−0.0207556
$693$	−2.17161e15	−0.516118
$694$	−3.20688e15	−0.756145
$695$	9.46421e15	2.21395
$696$	−2.56298e15	−0.594832
$697$	−1.10378e15	−0.254156
$698$	3.18544e15	0.727719
$699$	−1.50462e15	−0.341038
$700$	2.59092e15	0.582659
$701$	3.49877e15	0.780668	0.390334	−	0.920673i	$-0.372360\pi$
$701$	3.49877e15	0.780668	0.390334	+	0.920673i	$0.372360\pi$
$702$	−3.90180e15	−0.863794
$703$	−4.42663e12	−0.000972342 0
$704$	5.10361e15	1.11231
$705$	6.70772e15	1.45056
$706$	3.11368e15	0.668111
$707$	5.25339e15	1.11849
$708$	−1.37631e15	−0.290759
$709$	5.17383e15	1.08457	0.542285	−	0.840195i	$-0.317559\pi$
$709$	5.17383e15	1.08457	0.542285	+	0.840195i	$0.317559\pi$
$710$	−4.32217e15	−0.899044
$711$	1.94004e15	0.400431
$712$	−5.46345e15	−1.11899
$713$	7.49483e15	1.52324
$714$	−2.08330e15	−0.420158
$715$	−9.18242e15	−1.83770
$716$	−2.18625e15	−0.434188
$717$	−1.87842e15	−0.370200
$718$	9.16422e14	0.179230
$719$	−6.27676e15	−1.21822	−0.609112	−	0.793084i	$-0.708474\pi$
$719$	−6.27676e15	−1.21822	−0.609112	+	0.793084i	$0.708474\pi$
$720$	1.09661e15	0.211215
$721$	−8.84492e15	−1.69064
$722$	−4.30886e15	−0.817350
$723$	5.57451e15	1.04941
$724$	2.12931e15	0.397812
$725$	2.49058e15	0.461787
$726$	3.20299e14	0.0589392
$727$	5.94704e15	1.08608	0.543040	−	0.839707i	$-0.317273\pi$
$727$	5.94704e15	1.08608	0.543040	+	0.839707i	$0.317273\pi$
$728$	1.43691e16	2.60440
$729$	3.39014e15	0.609840
$730$	1.28693e15	0.229763
$731$	−1.49904e15	−0.265625
$732$	5.15375e14	0.0906384
$733$	2.61914e15	0.457179	0.228590	−	0.973523i	$-0.426589\pi$
$733$	2.61914e15	0.457179	0.228590	+	0.973523i	$0.426589\pi$
$734$	1.64688e15	0.285321
$735$	−2.30211e16	−3.95863
$736$	−4.77731e15	−0.815371
$737$	3.85800e15	0.653568
$738$	−1.36443e15	−0.229425
$739$	−8.44462e15	−1.40940	−0.704702	−	0.709503i	$-0.748919\pi$
$739$	−8.44462e15	−1.40940	−0.704702	+	0.709503i	$0.748919\pi$
$740$	−4.24254e13	−0.00702832
$741$	5.51006e14	0.0906059
$742$	1.57420e16	2.56944
$743$	−6.76393e15	−1.09587	−0.547937	−	0.836519i	$-0.684587\pi$
$743$	−6.76393e15	−1.09587	−0.547937	+	0.836519i	$0.684587\pi$
$744$	8.87463e15	1.42725
$745$	−6.61678e15	−1.05630
$746$	−7.69597e15	−1.21955
$747$	−4.32473e14	−0.0680293
$748$	−5.23193e14	−0.0816965
$749$	6.78275e15	1.05137
$750$	4.09084e14	0.0629470
$751$	5.39586e15	0.824216	0.412108	−	0.911135i	$-0.364793\pi$
$751$	5.39586e15	0.824216	0.412108	+	0.911135i	$0.364793\pi$
$752$	3.44847e15	0.522911
$753$	3.98938e15	0.600528
$754$	3.40047e15	0.508155
$755$	4.04620e15	0.600259
$756$	−3.43232e15	−0.505496
$757$	−1.17875e15	−0.172343	−0.0861714	−	0.996280i	$-0.527463\pi$
$757$	−1.17875e15	−0.172343	−0.0861714	+	0.996280i	$0.527463\pi$
$758$	−2.43016e15	−0.352740
$759$	−1.05345e16	−1.51805
$760$	6.70838e14	0.0959717
$761$	5.50198e15	0.781453	0.390727	−	0.920507i	$-0.372224\pi$
$761$	5.50198e15	0.781453	0.390727	+	0.920507i	$0.372224\pi$
$762$	−9.90947e15	−1.39733
$763$	2.85481e15	0.399661
$764$	−1.72954e15	−0.240391
$765$	−6.54997e14	−0.0903861
$766$	1.15380e16	1.58078
$767$	7.41736e15	1.00896
$768$	−7.19934e15	−0.972312
$769$	2.09401e15	0.280791	0.140395	−	0.990096i	$-0.455163\pi$
$769$	2.09401e15	0.280791	0.140395	+	0.990096i	$0.455163\pi$
$770$	1.66559e16	2.21753
$771$	4.20014e15	0.555219
$772$	2.61402e15	0.343095
$773$	−2.84149e15	−0.370305	−0.185153	−	0.982710i	$-0.559278\pi$
$773$	−2.84149e15	−0.370305	−0.185153	+	0.982710i	$0.559278\pi$
$774$	−1.85304e15	−0.239778
$775$	−8.62394e15	−1.10802
$776$	−2.01407e15	−0.256942
$777$	2.56753e14	0.0325237
$778$	2.10792e15	0.265134
$779$	−5.29537e14	−0.0661363
$780$	5.28092e15	0.654922
$781$	6.56902e15	0.808947
$782$	−2.12840e15	−0.260266
$783$	−3.29940e15	−0.400631
$784$	−1.18352e16	−1.42705
$785$	3.26071e15	0.390418
$786$	1.05928e15	0.125946
$787$	1.55887e15	0.184056	0.0920280	−	0.995756i	$-0.470665\pi$
$787$	1.55887e15	0.184056	0.0920280	+	0.995756i	$0.470665\pi$
$788$	4.46358e15	0.523346
$789$	5.04794e15	0.587748
$790$	−1.48798e16	−1.72047
$791$	−4.76356e15	−0.546967
$792$	−2.62707e15	−0.299559
$793$	−2.77751e15	−0.314524
$794$	6.82277e15	0.767269
$795$	2.35006e16	2.62457
$796$	5.60619e15	0.621793
$797$	−1.25364e16	−1.38086	−0.690431	−	0.723398i	$-0.742579\pi$
$797$	−1.25364e16	−1.38086	−0.690431	+	0.723398i	$0.742579\pi$
$798$	−9.99464e14	−0.109333
$799$	−2.05974e15	−0.223772
$800$	5.49702e15	0.593106
$801$	2.55919e15	0.274236
$802$	−1.80271e15	−0.191852
$803$	−1.95594e15	−0.206737
$804$	−2.21878e15	−0.232920
$805$	−3.28603e16	−3.42605
$806$	−1.17745e16	−1.21927
$807$	−1.33083e15	−0.136873
$808$	6.35521e15	0.649183
$809$	−1.22354e16	−1.24137	−0.620684	−	0.784061i	$-0.713145\pi$
$809$	−1.22354e16	−1.24137	−0.620684	+	0.784061i	$0.713145\pi$
$810$	1.36004e16	1.37052
$811$	−1.36973e16	−1.37094	−0.685472	−	0.728099i	$-0.740404\pi$
$811$	−1.36973e16	−1.37094	−0.685472	+	0.728099i	$0.740404\pi$
$812$	2.99131e15	0.297374
$813$	−9.78408e14	−0.0966100
$814$	−1.32958e14	−0.0130400
$815$	−4.91329e15	−0.478637
$816$	−1.59890e15	−0.154713
$817$	−7.19166e14	−0.0691206
$818$	1.31901e16	1.25923
$819$	−6.73081e15	−0.638272
$820$	−5.07515e15	−0.478050
$821$	6.84674e15	0.640614	0.320307	−	0.947314i	$-0.396214\pi$
$821$	6.84674e15	0.640614	0.320307	+	0.947314i	$0.396214\pi$
$822$	1.08166e16	1.00530
$823$	7.44312e15	0.687157	0.343578	−	0.939124i	$-0.388361\pi$
$823$	7.44312e15	0.687157	0.343578	+	0.939124i	$0.388361\pi$
$824$	−1.07000e16	−0.981259
$825$	1.21216e16	1.10424
$826$	−1.34543e16	−1.21750
$827$	−1.54308e16	−1.38710	−0.693550	−	0.720408i	$-0.743954\pi$
$827$	−1.54308e16	−1.38710	−0.693550	+	0.720408i	$0.743954\pi$
$828$	1.27596e15	0.113938
$829$	−5.43293e15	−0.481931	−0.240965	−	0.970534i	$-0.577464\pi$
$829$	−5.43293e15	−0.481931	−0.240965	+	0.970534i	$0.577464\pi$
$830$	3.31700e15	0.292291
$831$	1.90367e16	1.66642
$832$	1.58184e16	1.37557
$833$	7.06909e15	0.610683
$834$	−1.70578e16	−1.46390
$835$	1.04050e16	0.887091
$836$	−2.51002e14	−0.0212590
$837$	1.14246e16	0.961279
$838$	−1.24085e16	−1.03724
$839$	−9.68334e15	−0.804145	−0.402072	−	0.915608i	$-0.631710\pi$
$839$	−9.68334e15	−0.804145	−0.402072	+	0.915608i	$0.631710\pi$
$840$	−3.89099e16	−3.21014
$841$	−9.32504e15	−0.764316
$842$	−1.31070e16	−1.06730
$843$	2.05617e16	1.66344
$844$	4.60271e15	0.369939
$845$	−1.09675e16	−0.875782
$846$	−2.54614e15	−0.201997
$847$	−1.51849e15	−0.119688
$848$	1.20817e16	0.946133
$849$	1.71707e16	1.33597
$850$	2.44905e15	0.189319
$851$	2.62311e14	0.0201467
$852$	−3.77792e15	−0.288294
$853$	8.63668e15	0.654828	0.327414	−	0.944881i	$-0.393823\pi$
$853$	8.63668e15	0.654828	0.327414	+	0.944881i	$0.393823\pi$
$854$	5.03810e15	0.379532
$855$	−3.14235e14	−0.0235202
$856$	8.20532e15	0.610224
$857$	8.09110e15	0.597878	0.298939	−	0.954272i	$-0.403367\pi$
$857$	8.09110e15	0.597878	0.298939	+	0.954272i	$0.403367\pi$
$858$	1.65499e16	1.21511
$859$	8.25551e14	0.0602256	0.0301128	−	0.999547i	$-0.490413\pi$
$859$	8.25551e14	0.0602256	0.0301128	+	0.999547i	$0.490413\pi$
$860$	−6.89258e15	−0.499621
$861$	3.07141e16	2.21218
$862$	−1.52430e16	−1.09089
$863$	−1.88827e16	−1.34278	−0.671391	−	0.741104i	$-0.734303\pi$
$863$	−1.88827e16	−1.34278	−0.671391	+	0.741104i	$0.734303\pi$
$864$	−7.28217e15	−0.514559
$865$	−1.26439e15	−0.0887752
$866$	−3.56870e15	−0.248978
$867$	9.55012e14	0.0662070
$868$	−1.03578e16	−0.713522
$869$	2.26149e16	1.54806
$870$	−9.20805e15	−0.626342
$871$	1.19577e16	0.808253
$872$	3.45356e15	0.231967
$873$	9.43434e14	0.0629699
$874$	−1.02110e15	−0.0677261
$875$	−1.93940e15	−0.127827
$876$	1.12488e15	0.0736774
$877$	6.41122e15	0.417295	0.208647	−	0.977991i	$-0.433094\pi$
$877$	6.41122e15	0.417295	0.208647	+	0.977991i	$0.433094\pi$
$878$	5.92454e15	0.383208
$879$	1.22308e15	0.0786171
$880$	1.27831e16	0.816550
$881$	2.93558e16	1.86349	0.931743	−	0.363118i	$-0.118288\pi$
$881$	2.93558e16	1.86349	0.931743	+	0.363118i	$0.118288\pi$
$882$	8.73843e15	0.551260
$883$	−3.15110e16	−1.97550	−0.987752	−	0.156029i	$-0.950131\pi$
$883$	−3.15110e16	−1.97550	−0.987752	+	0.156029i	$0.950131\pi$
$884$	−1.62161e15	−0.101032
$885$	−2.00853e16	−1.24363
$886$	2.18408e16	1.34395
$887$	1.71447e16	1.04845	0.524227	−	0.851579i	$-0.324354\pi$
$887$	1.71447e16	1.04845	0.524227	+	0.851579i	$0.324354\pi$
$888$	3.10603e14	0.0188770
$889$	4.69793e16	2.83757
$890$	−1.96286e16	−1.17827
$891$	−2.06705e16	−1.23317
$892$	6.07581e15	0.360244
$893$	−9.88161e14	−0.0582297
$894$	1.19258e16	0.698441
$895$	−3.19052e16	−1.85710
$896$	−8.47694e15	−0.490394
$897$	−3.26513e16	−1.87733
$898$	1.26671e16	0.723862
$899$	−9.95665e15	−0.565503
$900$	−1.46818e15	−0.0828792
$901$	−7.21632e15	−0.404883
$902$	−1.59051e16	−0.886952
$903$	4.17130e16	2.31200
$904$	−5.76264e15	−0.317464
$905$	3.10743e16	1.70151
$906$	−7.29266e15	−0.396900
$907$	−2.59385e16	−1.40315	−0.701575	−	0.712596i	$-0.747519\pi$
$907$	−2.59385e16	−1.40315	−0.701575	+	0.712596i	$0.747519\pi$
$908$	1.10382e15	0.0593509
$909$	−2.97691e15	−0.159098
$910$	5.16242e16	2.74237
$911$	−2.28485e16	−1.20644	−0.603222	−	0.797573i	$-0.706117\pi$
$911$	−2.28485e16	−1.20644	−0.603222	+	0.797573i	$0.706117\pi$
$912$	−7.67073e14	−0.0402592
$913$	−5.04132e15	−0.262999
$914$	−4.82941e15	−0.250432
$915$	7.52116e15	0.387676
$916$	1.03896e15	0.0532319
$917$	−5.02186e15	−0.255760
$918$	−3.24438e15	−0.164247
$919$	−1.18401e16	−0.595827	−0.297914	−	0.954593i	$-0.596291\pi$
$919$	−1.18401e16	−0.595827	−0.297914	+	0.954593i	$0.596291\pi$
$920$	−3.97522e16	−1.98851
$921$	−1.88752e16	−0.938564
$922$	−1.07480e16	−0.531262
$923$	2.03604e16	1.00041
$924$	1.45586e16	0.711088
$925$	−3.01829e14	−0.0146548
$926$	2.25304e16	1.08745
$927$	5.01210e15	0.240481
$928$	6.34651e15	0.302706
$929$	−6.80765e14	−0.0322783	−0.0161391	−	0.999870i	$-0.505137\pi$
$929$	−6.80765e14	−0.0322783	−0.0161391	+	0.999870i	$0.505137\pi$
$930$	3.18840e16	1.50285
$931$	3.39140e15	0.158911
$932$	2.12438e15	0.0989566
$933$	−2.69963e16	−1.25013
$934$	−1.55214e16	−0.714533
$935$	−7.63526e15	−0.349430
$936$	−8.14248e15	−0.370459
$937$	−2.20234e16	−0.996133	−0.498067	−	0.867139i	$-0.665956\pi$
$937$	−2.20234e16	−0.996133	−0.498067	+	0.867139i	$0.665956\pi$
$938$	−2.16899e16	−0.975309
$939$	−4.56177e16	−2.03926
$940$	−9.47067e15	−0.420899
$941$	4.32946e16	1.91289	0.956447	−	0.291906i	$-0.0942893\pi$
$941$	4.32946e16	1.91289	0.956447	+	0.291906i	$0.0942893\pi$
$942$	−5.87695e15	−0.258150
$943$	3.13790e16	1.37033
$944$	−1.03259e16	−0.448315
$945$	−5.00898e16	−2.16209
$946$	−2.16007e16	−0.926974
$947$	1.12925e16	0.481799	0.240900	−	0.970550i	$-0.422558\pi$
$947$	1.12925e16	0.481799	0.240900	+	0.970550i	$0.422558\pi$
$948$	−1.30061e16	−0.551699
$949$	−6.06233e15	−0.255668
$950$	1.17493e15	0.0492643
$951$	−6.81841e15	−0.284243
$952$	1.19481e16	0.495216
$953$	8.90629e15	0.367017	0.183508	−	0.983018i	$-0.441255\pi$
$953$	8.90629e15	0.367017	0.183508	+	0.983018i	$0.441255\pi$
$954$	−8.92043e15	−0.365485
$955$	−2.52402e16	−1.02819
$956$	2.65215e15	0.107418
$957$	1.39948e16	0.563574
$958$	3.31178e16	1.32602
$959$	−5.12800e16	−2.04148
$960$	−4.28343e16	−1.69551
$961$	9.06761e15	0.356873
$962$	−4.12096e14	−0.0161263
$963$	−3.84354e15	−0.149550
$964$	−7.87068e15	−0.304501
$965$	3.81479e16	1.46748
$966$	5.92258e16	2.26536
$967$	−9.20331e15	−0.350024	−0.175012	−	0.984566i	$-0.555996\pi$
$967$	−9.20331e15	−0.350024	−0.175012	+	0.984566i	$0.555996\pi$
$968$	−1.83696e15	−0.0694682
$969$	4.58167e14	0.0172283
$970$	−7.23598e15	−0.270553
$971$	2.07058e16	0.769815	0.384907	−	0.922955i	$-0.374233\pi$
$971$	2.07058e16	0.769815	0.384907	+	0.922955i	$0.374233\pi$
$972$	4.59766e15	0.169970
$973$	8.08685e16	2.97275
$974$	−3.23416e16	−1.18219
$975$	3.75702e16	1.36558
$976$	3.86666e15	0.139753
$977$	−2.57290e16	−0.924705	−0.462353	−	0.886696i	$-0.652995\pi$
$977$	−2.57290e16	−0.924705	−0.462353	+	0.886696i	$0.652995\pi$
$978$	8.85548e15	0.316481
$979$	2.98324e16	1.06019
$980$	3.25036e16	1.14865
$981$	−1.61772e15	−0.0568491
$982$	6.61403e15	0.231128
$983$	−5.38036e16	−1.86968	−0.934839	−	0.355073i	$-0.884456\pi$
$983$	−5.38036e16	−1.86968	−0.934839	+	0.355073i	$0.884456\pi$
$984$	3.71559e16	1.28397
$985$	6.51395e16	2.23844
$986$	2.82752e15	0.0966234
$987$	5.73152e16	1.94772
$988$	−7.77969e14	−0.0262905
$989$	4.26160e16	1.43216
$990$	−9.43830e15	−0.315428
$991$	−1.19840e16	−0.398288	−0.199144	−	0.979970i	$-0.563816\pi$
$991$	−1.19840e16	−0.398288	−0.199144	+	0.979970i	$0.563816\pi$
$992$	−2.19755e16	−0.726316
$993$	−6.29178e16	−2.06801
$994$	−3.69315e16	−1.20718
$995$	8.18144e16	2.65952
$996$	2.89932e15	0.0937282
$997$	−4.39641e16	−1.41343	−0.706715	−	0.707498i	$-0.749824\pi$
$997$	−4.39641e16	−1.41343	−0.706715	+	0.707498i	$0.749824\pi$
$998$	−3.67942e16	−1.17642
$999$	3.99847e14	0.0127141

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.a.a.1.5	✓	6
3.2	odd	2		153.12.a.a.1.2		6
4.3	odd	2		272.12.a.f.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.a.a.1.5	✓	6	1.1	even	1	trivial
153.12.a.a.1.2		6	3.2	odd	2
272.12.a.f.1.2		6	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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q+37.1370 q^{2} +473.718 q^{3} -668.845 q^{4} -9760.84 q^{5} +17592.4 q^{6} -83403.0 q^{7} -100895. q^{8} +47261.5 q^{9} +O(q^{10})\)	\(q+37.1370 q^{2} +473.718 q^{3} -668.845 q^{4} -9760.84 q^{5} +17592.4 q^{6} -83403.0 q^{7} -100895. q^{8} +47261.5 q^{9} -362488. q^{10} +550925. q^{11} -316844. q^{12} +1.70757e6 q^{13} -3.09734e6 q^{14} -4.62388e6 q^{15} -2.37716e6 q^{16} +1.41986e6 q^{17} +1.75515e6 q^{18} +681176. q^{19} +6.52848e6 q^{20} -3.95095e7 q^{21} +2.04597e7 q^{22} -4.03648e7 q^{23} -4.77959e7 q^{24} +4.64458e7 q^{25} +6.34139e7 q^{26} -6.15291e7 q^{27} +5.57837e7 q^{28} +5.36234e7 q^{29} -1.71717e8 q^{30} -1.85677e8 q^{31} +1.18353e8 q^{32} +2.60983e8 q^{33} +5.27292e7 q^{34} +8.14083e8 q^{35} -3.16106e7 q^{36} -6.49851e6 q^{37} +2.52968e7 q^{38} +8.08905e8 q^{39} +9.84824e8 q^{40} -7.77386e8 q^{41} -1.46726e9 q^{42} -1.05577e9 q^{43} -3.68483e8 q^{44} -4.61312e8 q^{45} -1.49903e9 q^{46} -1.45067e9 q^{47} -1.12610e9 q^{48} +4.97874e9 q^{49} +1.72486e9 q^{50} +6.72611e8 q^{51} -1.14210e9 q^{52} -5.08243e9 q^{53} -2.28500e9 q^{54} -5.37749e9 q^{55} +8.41498e9 q^{56} +3.22685e8 q^{57} +1.99141e9 q^{58} +4.34382e9 q^{59} +3.09266e9 q^{60} -1.62659e9 q^{61} -6.89550e9 q^{62} -3.94175e9 q^{63} +9.26370e9 q^{64} -1.66673e10 q^{65} +9.69212e9 q^{66} +7.00277e9 q^{67} -9.49664e8 q^{68} -1.91215e10 q^{69} +3.02326e10 q^{70} +1.19236e10 q^{71} -4.76847e9 q^{72} -3.55028e9 q^{73} -2.41335e8 q^{74} +2.20022e10 q^{75} -4.55601e8 q^{76} -4.59488e10 q^{77} +3.00403e10 q^{78} +4.10490e10 q^{79} +2.32030e10 q^{80} -3.75196e10 q^{81} -2.88698e10 q^{82} -9.15064e9 q^{83} +2.64257e10 q^{84} -1.38590e10 q^{85} -3.92081e10 q^{86} +2.54024e10 q^{87} -5.55858e10 q^{88} +5.41496e10 q^{89} -1.71317e10 q^{90} -1.42416e11 q^{91} +2.69978e10 q^{92} -8.79587e10 q^{93} -5.38735e10 q^{94} -6.64885e9 q^{95} +5.60661e10 q^{96} +1.99620e10 q^{97} +1.84895e11 q^{98} +2.60376e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{2} - 476 q^{3} + 4613 q^{4} - 12884 q^{5} + 552 q^{6} - 23436 q^{7} + 74805 q^{8} + 296398 q^{9}+O(q^{10}) \) 6 * q - 9 * q^2 - 476 * q^3 + 4613 * q^4 - 12884 * q^5 + 552 * q^6 - 23436 * q^7 + 74805 * q^8 + 296398 * q^9	\( 6 q - 9 q^{2} - 476 q^{3} + 4613 q^{4} - 12884 q^{5} + 552 q^{6} - 23436 q^{7} + 74805 q^{8} + 296398 q^{9} - 676038 q^{10} - 962060 q^{11} - 2352344 q^{12} - 435268 q^{13} - 7990948 q^{14} - 9450288 q^{15} - 12496671 q^{16} + 8519142 q^{17} - 20195421 q^{18} - 26398480 q^{19} - 47202914 q^{20} - 56428792 q^{21} - 51774200 q^{22} - 99172772 q^{23} - 110557128 q^{24} + 66085866 q^{25} + 74451914 q^{26} + 105183712 q^{27} + 102848900 q^{28} + 165683964 q^{29} + 401475744 q^{30} - 199133468 q^{31} + 465766501 q^{32} + 518429376 q^{33} - 12778713 q^{34} + 804442912 q^{35} + 627274777 q^{36} - 785778644 q^{37} + 2174484940 q^{38} + 627357728 q^{39} + 657666206 q^{40} + 166444428 q^{41} + 652753248 q^{42} - 1110947880 q^{43} - 997577064 q^{44} - 1706447988 q^{45} - 1891667412 q^{46} - 5828211928 q^{47} - 2359114472 q^{48} - 1968801674 q^{49} - 126509183 q^{50} - 675851932 q^{51} - 6633403554 q^{52} - 9889898636 q^{53} - 1961072736 q^{54} - 10730153984 q^{55} + 5703448884 q^{56} - 13522850128 q^{57} + 14316796258 q^{58} + 204095112 q^{59} + 22313648592 q^{60} - 15864546948 q^{61} - 1838602020 q^{62} + 504344540 q^{63} + 6177095465 q^{64} + 12794774792 q^{65} + 56255165136 q^{66} + 17196640232 q^{67} + 6549800341 q^{68} + 2949266904 q^{69} + 52391765944 q^{70} + 8751653884 q^{71} + 38682669705 q^{72} - 13704156916 q^{73} - 9383651494 q^{74} - 15917467268 q^{75} + 59548672452 q^{76} - 12012382872 q^{77} + 35038956192 q^{78} - 89923384436 q^{79} + 25877503334 q^{80} - 152313828506 q^{81} + 57834669670 q^{82} - 26042106648 q^{83} + 3397466240 q^{84} - 18293437588 q^{85} + 29108045060 q^{86} - 195382431072 q^{87} - 228837945880 q^{88} + 53269579420 q^{89} - 10044062046 q^{90} - 226028668544 q^{91} - 9212077436 q^{92} - 62709484936 q^{93} + 83948222448 q^{94} - 170219637424 q^{95} + 116885663928 q^{96} - 106272517044 q^{97} + 132039821039 q^{98} - 10550584980 q^{99}+O(q^{100}) \) 6 * q - 9 * q^2 - 476 * q^3 + 4613 * q^4 - 12884 * q^5 + 552 * q^6 - 23436 * q^7 + 74805 * q^8 + 296398 * q^9 - 676038 * q^10 - 962060 * q^11 - 2352344 * q^12 - 435268 * q^13 - 7990948 * q^14 - 9450288 * q^15 - 12496671 * q^16 + 8519142 * q^17 - 20195421 * q^18 - 26398480 * q^19 - 47202914 * q^20 - 56428792 * q^21 - 51774200 * q^22 - 99172772 * q^23 - 110557128 * q^24 + 66085866 * q^25 + 74451914 * q^26 + 105183712 * q^27 + 102848900 * q^28 + 165683964 * q^29 + 401475744 * q^30 - 199133468 * q^31 + 465766501 * q^32 + 518429376 * q^33 - 12778713 * q^34 + 804442912 * q^35 + 627274777 * q^36 - 785778644 * q^37 + 2174484940 * q^38 + 627357728 * q^39 + 657666206 * q^40 + 166444428 * q^41 + 652753248 * q^42 - 1110947880 * q^43 - 997577064 * q^44 - 1706447988 * q^45 - 1891667412 * q^46 - 5828211928 * q^47 - 2359114472 * q^48 - 1968801674 * q^49 - 126509183 * q^50 - 675851932 * q^51 - 6633403554 * q^52 - 9889898636 * q^53 - 1961072736 * q^54 - 10730153984 * q^55 + 5703448884 * q^56 - 13522850128 * q^57 + 14316796258 * q^58 + 204095112 * q^59 + 22313648592 * q^60 - 15864546948 * q^61 - 1838602020 * q^62 + 504344540 * q^63 + 6177095465 * q^64 + 12794774792 * q^65 + 56255165136 * q^66 + 17196640232 * q^67 + 6549800341 * q^68 + 2949266904 * q^69 + 52391765944 * q^70 + 8751653884 * q^71 + 38682669705 * q^72 - 13704156916 * q^73 - 9383651494 * q^74 - 15917467268 * q^75 + 59548672452 * q^76 - 12012382872 * q^77 + 35038956192 * q^78 - 89923384436 * q^79 + 25877503334 * q^80 - 152313828506 * q^81 + 57834669670 * q^82 - 26042106648 * q^83 + 3397466240 * q^84 - 18293437588 * q^85 + 29108045060 * q^86 - 195382431072 * q^87 - 228837945880 * q^88 + 53269579420 * q^89 - 10044062046 * q^90 - 226028668544 * q^91 - 9212077436 * q^92 - 62709484936 * q^93 + 83948222448 * q^94 - 170219637424 * q^95 + 116885663928 * q^96 - 106272517044 * q^97 + 132039821039 * q^98 - 10550584980 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more