LMFDB - Embedded newform 7.18.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,18,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, 18, names="a")

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

chi := DirichletCharacter("7.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 18 $
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:	$12.8255461141$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 559376x^{3} + 70948970x^{2} + 30882981215x + 584478460232 $ x^5 - 2x^4 - 559376x^3 + 70948970x^2 + 30882981215x + 584478460232
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5}\cdot 3^{3}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-170.283$ 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)

$f(q)$	$=$	$q-51.2830 q^{2} +1738.66 q^{3} -128442. q^{4} +190715. q^{5} -89163.6 q^{6} +5.76480e6 q^{7} +1.33087e7 q^{8} -1.26117e8 q^{9} +O(q^{10})$	\(q-51.2830 q^{2} +1738.66 q^{3} -128442. q^{4} +190715. q^{5} -89163.6 q^{6} +5.76480e6 q^{7} +1.33087e7 q^{8} -1.26117e8 q^{9} -9.78045e6 q^{10} +8.49040e8 q^{11} -2.23317e8 q^{12} +3.73443e9 q^{13} -2.95637e8 q^{14} +3.31588e8 q^{15} +1.61526e10 q^{16} +3.16076e10 q^{17} +6.46768e9 q^{18} +5.89207e10 q^{19} -2.44958e10 q^{20} +1.00230e10 q^{21} -4.35413e10 q^{22} +1.00754e11 q^{23} +2.31392e10 q^{24} -7.26567e11 q^{25} -1.91513e11 q^{26} -4.43805e11 q^{27} -7.40443e11 q^{28} -4.00282e12 q^{29} -1.70048e10 q^{30} +6.91184e12 q^{31} -2.57275e12 q^{32} +1.47619e12 q^{33} -1.62093e12 q^{34} +1.09943e12 q^{35} +1.61988e13 q^{36} +1.60574e13 q^{37} -3.02163e12 q^{38} +6.49290e12 q^{39} +2.53816e12 q^{40} +2.32760e13 q^{41} -5.14010e11 q^{42} -2.01103e13 q^{43} -1.09052e14 q^{44} -2.40525e13 q^{45} -5.16698e12 q^{46} -1.16813e14 q^{47} +2.80839e13 q^{48} +3.32329e13 q^{49} +3.72606e13 q^{50} +5.49547e13 q^{51} -4.79658e14 q^{52} +2.19884e14 q^{53} +2.27597e13 q^{54} +1.61925e14 q^{55} +7.67218e13 q^{56} +1.02443e14 q^{57} +2.05277e14 q^{58} +1.86281e15 q^{59} -4.25899e13 q^{60} +8.63576e14 q^{61} -3.54460e14 q^{62} -7.27041e14 q^{63} -1.98522e15 q^{64} +7.12213e14 q^{65} -7.57034e13 q^{66} +3.23018e14 q^{67} -4.05974e15 q^{68} +1.75177e14 q^{69} -5.63824e13 q^{70} -4.28112e14 q^{71} -1.67845e15 q^{72} -1.32931e15 q^{73} -8.23470e14 q^{74} -1.26325e15 q^{75} -7.56790e15 q^{76} +4.89455e15 q^{77} -3.32976e14 q^{78} +8.04716e15 q^{79} +3.08055e15 q^{80} +1.55152e16 q^{81} -1.19367e15 q^{82} +2.14732e16 q^{83} -1.28738e15 q^{84} +6.02804e15 q^{85} +1.03132e15 q^{86} -6.95953e15 q^{87} +1.12996e16 q^{88} -5.68949e16 q^{89} +1.23348e15 q^{90} +2.15283e16 q^{91} -1.29411e16 q^{92} +1.20173e16 q^{93} +5.99051e15 q^{94} +1.12371e16 q^{95} -4.47313e15 q^{96} -1.50310e17 q^{97} -1.70429e15 q^{98} -1.07079e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 597 q^{2} - 1770 q^{3} + 534677 q^{4} + 1612824 q^{5} - 14383854 q^{6} + 28824005 q^{7} + 41916039 q^{8} + 552658077 q^{9}+O(q^{10}) $ 5 * q + 597 * q^2 - 1770 * q^3 + 534677 * q^4 + 1612824 * q^5 - 14383854 * q^6 + 28824005 * q^7 + 41916039 * q^8 + 552658077 * q^9	\( 5 q + 597 q^{2} - 1770 q^{3} + 534677 q^{4} + 1612824 q^{5} - 14383854 q^{6} + 28824005 q^{7} + 41916039 q^{8} + 552658077 q^{9} - 345084900 q^{10} + 765945912 q^{11} + 3634044078 q^{12} + 608204548 q^{13} + 3441586197 q^{14} + 41156724744 q^{15} + 116025034769 q^{16} + 8856152334 q^{17} + 90679358061 q^{18} + 18441763546 q^{19} + 784710030552 q^{20} - 10203697770 q^{21} - 140711201256 q^{22} - 218776878696 q^{23} - 3751889532894 q^{24} - 363036196609 q^{25} - 1677859982400 q^{26} - 4021274734668 q^{27} + 3082306504277 q^{28} + 2087156686674 q^{29} - 14802803892720 q^{30} - 12100718234660 q^{31} + 16029734494815 q^{32} + 6151440714912 q^{33} + 19542664353462 q^{34} + 9297609408024 q^{35} + 54957458168325 q^{36} + 16858800794026 q^{37} + 49131784416030 q^{38} + 74225922854496 q^{39} - 17226943156560 q^{40} - 32679617238786 q^{41} - 82920055923054 q^{42} + 2700646991248 q^{43} + 328390888489968 q^{44} - 89554636513368 q^{45} - 934408564817712 q^{46} + 72344569802340 q^{47} - 11\!\cdots\!62 q^{48}+ \cdots - 33\!\cdots\!92 q^{99}+O(q^{100}) \) 5 * q + 597 * q^2 - 1770 * q^3 + 534677 * q^4 + 1612824 * q^5 - 14383854 * q^6 + 28824005 * q^7 + 41916039 * q^8 + 552658077 * q^9 - 345084900 * q^10 + 765945912 * q^11 + 3634044078 * q^12 + 608204548 * q^13 + 3441586197 * q^14 + 41156724744 * q^15 + 116025034769 * q^16 + 8856152334 * q^17 + 90679358061 * q^18 + 18441763546 * q^19 + 784710030552 * q^20 - 10203697770 * q^21 - 140711201256 * q^22 - 218776878696 * q^23 - 3751889532894 * q^24 - 363036196609 * q^25 - 1677859982400 * q^26 - 4021274734668 * q^27 + 3082306504277 * q^28 + 2087156686674 * q^29 - 14802803892720 * q^30 - 12100718234660 * q^31 + 16029734494815 * q^32 + 6151440714912 * q^33 + 19542664353462 * q^34 + 9297609408024 * q^35 + 54957458168325 * q^36 + 16858800794026 * q^37 + 49131784416030 * q^38 + 74225922854496 * q^39 - 17226943156560 * q^40 - 32679617238786 * q^41 - 82920055923054 * q^42 + 2700646991248 * q^43 + 328390888489968 * q^44 - 89554636513368 * q^45 - 934408564817712 * q^46 + 72344569802340 * q^47 - 1114757827879362 * q^48 + 166164652848005 * q^49 - 1206805301442465 * q^50 + 93846313005588 * q^51 + 900407522478772 * q^52 + 1102150036344942 * q^53 + 425408583919932 * q^54 + 1762881466153488 * q^55 + 241637623543239 * q^56 + 2799346250520276 * q^57 + 15137889518826 * q^58 + 164356451065122 * q^59 + 1167267096771552 * q^60 + 3750393534081568 * q^61 - 7616424461183148 * q^62 + 3185963834947677 * q^63 + 6689352066227393 * q^64 + 7529870820155880 * q^65 - 14441400503014176 * q^66 - 3782791201197452 * q^67 - 26670706415203410 * q^68 + 4651070975625744 * q^69 - 1989345776604900 * q^70 - 3894420716406000 * q^71 - 11316579733409625 * q^72 + 5885320144516618 * q^73 + 11592671721146322 * q^74 + 6565928157933906 * q^75 - 25247751597093326 * q^76 + 4415525759443512 * q^77 - 40099299793127064 * q^78 + 43390368978234280 * q^79 + 72123460802732256 * q^80 + 16677438473389329 * q^81 - 12883198921542810 * q^82 + 35056612240074642 * q^83 + 20949540934898478 * q^84 - 72373519639835328 * q^85 + 66904881205136496 * q^86 + 103599288996180588 * q^87 + 110088558971776416 * q^88 - 58289826944373966 * q^89 - 71347471630924500 * q^90 + 3506178186514948 * q^91 - 16491269563372704 * q^92 - 16113403536918888 * q^93 - 85659528801383844 * q^94 - 5872171066415592 * q^95 - 772366271041943550 * q^96 + 47745465198885454 * q^97 + 19840059550051797 * q^98 - 330042831191860392 * 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 $

$2$	−51.2830	−0.141651	−0.0708254	−	0.997489i	$-0.522563\pi$
$2$	−51.2830	−0.141651	−0.0708254	+	0.997489i	$0.522563\pi$
$3$	1738.66	0.152997	0.0764985	−	0.997070i	$-0.475626\pi$
$3$	1738.66	0.152997	0.0764985	+	0.997070i	$0.475626\pi$
$4$	−128442.	−0.979935
$5$	190715.	0.218343	0.109172	−	0.994023i	$-0.465180\pi$
$5$	190715.	0.218343	0.109172	+	0.994023i	$0.465180\pi$
$6$	−89163.6	−0.0216721
$7$	5.76480e6	0.377964
$7$	5.76480e6	0.377964
$8$	1.33087e7	0.280459
$9$	−1.26117e8	−0.976592
$10$	−9.78045e6	−0.0309285
$11$	8.49040e8	1.19424	0.597118	−	0.802153i	$-0.296312\pi$
$11$	8.49040e8	1.19424	0.597118	+	0.802153i	$0.296312\pi$
$12$	−2.23317e8	−0.149927
$13$	3.73443e9	1.26972	0.634858	−	0.772629i	$-0.281059\pi$
$13$	3.73443e9	1.26972	0.634858	+	0.772629i	$0.281059\pi$
$14$	−2.95637e8	−0.0535389
$15$	3.31588e8	0.0334059
$16$	1.61526e10	0.940208
$17$	3.16076e10	1.09894	0.549472	−	0.835512i	$-0.314829\pi$
$17$	3.16076e10	1.09894	0.549472	+	0.835512i	$0.314829\pi$
$18$	6.46768e9	0.138335
$19$	5.89207e10	0.795907	0.397953	−	0.917406i	$-0.369721\pi$
$19$	5.89207e10	0.795907	0.397953	+	0.917406i	$0.369721\pi$
$20$	−2.44958e10	−0.213962
$21$	1.00230e10	0.0578275
$22$	−4.35413e10	−0.169164
$23$	1.00754e11	0.268273	0.134136	−	0.990963i	$-0.457174\pi$
$23$	1.00754e11	0.268273	0.134136	+	0.990963i	$0.457174\pi$
$24$	2.31392e10	0.0429094
$25$	−7.26567e11	−0.952326
$26$	−1.91513e11	−0.179856
$27$	−4.43805e11	−0.302413
$28$	−7.40443e11	−0.370381
$29$	−4.00282e12	−1.48588	−0.742939	−	0.669359i	$-0.766569\pi$
$29$	−4.00282e12	−1.48588	−0.742939	+	0.669359i	$0.766569\pi$
$30$	−1.70048e10	−0.00473197
$31$	6.91184e12	1.45552	0.727762	−	0.685829i	$-0.240560\pi$
$31$	6.91184e12	1.45552	0.727762	+	0.685829i	$0.240560\pi$
$32$	−2.57275e12	−0.413640
$33$	1.47619e12	0.182715
$34$	−1.62093e12	−0.155666
$35$	1.09943e12	0.0825260
$36$	1.61988e13	0.956997
$37$	1.60574e13	0.751553	0.375776	−	0.926710i	$-0.377376\pi$
$37$	1.60574e13	0.751553	0.375776	+	0.926710i	$0.377376\pi$
$38$	−3.02163e12	−0.112741
$39$	6.49290e12	0.194263
$40$	2.53816e12	0.0612364
$41$	2.32760e13	0.455246	0.227623	−	0.973749i	$-0.426905\pi$
$41$	2.32760e13	0.455246	0.227623	+	0.973749i	$0.426905\pi$
$42$	−5.14010e11	−0.00819130
$43$	−2.01103e13	−0.262383	−0.131192	−	0.991357i	$-0.541880\pi$
$43$	−2.01103e13	−0.262383	−0.131192	+	0.991357i	$0.541880\pi$
$44$	−1.09052e14	−1.17027
$45$	−2.40525e13	−0.213232
$46$	−5.16698e12	−0.0380010
$47$	−1.16813e14	−0.715581	−0.357790	−	0.933802i	$-0.616470\pi$
$47$	−1.16813e14	−0.715581	−0.357790	+	0.933802i	$0.616470\pi$
$48$	2.80839e13	0.143849
$49$	3.32329e13	0.142857
$50$	3.72606e13	0.134898
$51$	5.49547e13	0.168135
$52$	−4.79658e14	−1.24424
$53$	2.19884e14	0.485119	0.242559	−	0.970137i	$-0.422013\pi$
$53$	2.19884e14	0.485119	0.242559	+	0.970137i	$0.422013\pi$
$54$	2.27597e13	0.0428370
$55$	1.61925e14	0.260754
$56$	7.67218e13	0.106004
$57$	1.02443e14	0.121771
$58$	2.05277e14	0.210476
$59$	1.86281e15	1.65168	0.825842	−	0.563901i	$-0.190700\pi$
$59$	1.86281e15	1.65168	0.825842	+	0.563901i	$0.190700\pi$
$60$	−4.25899e13	−0.0327356
$61$	8.63576e14	0.576763	0.288381	−	0.957516i	$-0.406883\pi$
$61$	8.63576e14	0.576763	0.288381	+	0.957516i	$0.406883\pi$
$62$	−3.54460e14	−0.206176
$63$	−7.27041e14	−0.369117
$64$	−1.98522e15	−0.881615
$65$	7.12213e14	0.277234
$66$	−7.57034e13	−0.0258817
$67$	3.23018e14	0.0971832	0.0485916	−	0.998819i	$-0.484527\pi$
$67$	3.23018e14	0.0971832	0.0485916	+	0.998819i	$0.484527\pi$
$68$	−4.05974e15	−1.07689
$69$	1.75177e14	0.0410450
$70$	−5.63824e13	−0.0116899
$71$	−4.28112e14	−0.0786794	−0.0393397	−	0.999226i	$-0.512525\pi$
$71$	−4.28112e14	−0.0786794	−0.0393397	+	0.999226i	$0.512525\pi$
$72$	−1.67845e15	−0.273894
$73$	−1.32931e15	−0.192923	−0.0964613	−	0.995337i	$-0.530752\pi$
$73$	−1.32931e15	−0.192923	−0.0964613	+	0.995337i	$0.530752\pi$
$74$	−8.23470e14	−0.106458
$75$	−1.26325e15	−0.145703
$76$	−7.56790e15	−0.779937
$77$	4.89455e15	0.451379
$78$	−3.32976e14	−0.0275175
$79$	8.04716e15	0.596778	0.298389	−	0.954444i	$-0.403551\pi$
$79$	8.04716e15	0.596778	0.298389	+	0.954444i	$0.403551\pi$
$80$	3.08055e15	0.205288
$81$	1.55152e16	0.930324
$82$	−1.19367e15	−0.0644859
$83$	2.14732e16	1.04649	0.523243	−	0.852184i	$-0.324722\pi$
$83$	2.14732e16	1.04649	0.523243	+	0.852184i	$0.324722\pi$
$84$	−1.28738e15	−0.0566672
$85$	6.02804e15	0.239947
$86$	1.03132e15	0.0371668
$87$	−6.95953e15	−0.227335
$88$	1.12996e16	0.334935
$89$	−5.68949e16	−1.53200	−0.765999	−	0.642842i	$-0.777755\pi$
$89$	−5.68949e16	−1.53200	−0.765999	+	0.642842i	$0.777755\pi$
$90$	1.23348e15	0.0302045
$91$	2.15283e16	0.479907
$92$	−1.29411e16	−0.262890
$93$	1.20173e16	0.222691
$94$	5.99051e15	0.101363
$95$	1.12371e16	0.173781
$96$	−4.47313e15	−0.0632858
$97$	−1.50310e17	−1.94728	−0.973642	−	0.228083i	$-0.926754\pi$
$97$	−1.50310e17	−1.94728	−0.973642	+	0.228083i	$0.926754\pi$
$98$	−1.70429e15	−0.0202358
$99$	−1.07079e17	−1.16628
$100$	9.33218e16	0.933218
$101$	1.50651e17	1.38433	0.692165	−	0.721740i	$-0.256657\pi$
$101$	1.50651e17	1.38433	0.692165	+	0.721740i	$0.256657\pi$
$102$	−2.81825e15	−0.0238165
$103$	−2.17868e17	−1.69464	−0.847321	−	0.531081i	$-0.821786\pi$
$103$	−2.17868e17	−1.69464	−0.847321	+	0.531081i	$0.821786\pi$
$104$	4.97003e16	0.356103
$105$	1.91154e15	0.0126262
$106$	−1.12763e16	−0.0687175
$107$	1.77330e17	0.997744	0.498872	−	0.866676i	$-0.333748\pi$
$107$	1.77330e17	0.997744	0.498872	+	0.866676i	$0.333748\pi$
$108$	5.70032e16	0.296345
$109$	2.00032e17	0.961553	0.480777	−	0.876843i	$-0.340355\pi$
$109$	2.00032e17	0.961553	0.480777	+	0.876843i	$0.340355\pi$
$110$	−8.30399e15	−0.0369359
$111$	2.79182e16	0.114985
$112$	9.31168e16	0.355365
$113$	−1.97388e17	−0.698481	−0.349240	−	0.937033i	$-0.613560\pi$
$113$	−1.97388e17	−0.698481	−0.349240	+	0.937033i	$0.613560\pi$
$114$	−5.25358e15	−0.0172490
$115$	1.92153e16	0.0585756
$116$	5.14130e17	1.45606
$117$	−4.70976e17	−1.23999
$118$	−9.55307e16	−0.233962
$119$	1.82211e17	0.415362
$120$	4.41300e15	0.00936900
$121$	2.15421e17	0.426200
$122$	−4.42868e16	−0.0816988
$123$	4.04690e16	0.0696513
$124$	−8.87771e17	−1.42632
$125$	−2.84071e17	−0.426278
$126$	3.72849e16	0.0522857
$127$	−6.24701e17	−0.819107	−0.409554	−	0.912286i	$-0.634316\pi$
$127$	−6.24701e17	−0.819107	−0.409554	+	0.912286i	$0.634316\pi$
$128$	4.39024e17	0.538522
$129$	−3.49649e16	−0.0401439
$130$	−3.65244e16	−0.0392704
$131$	−1.13132e18	−1.13967	−0.569833	−	0.821760i	$-0.692992\pi$
$131$	−1.13132e18	−1.13967	−0.569833	+	0.821760i	$0.692992\pi$
$132$	−1.89605e17	−0.179048
$133$	3.39666e17	0.300825
$134$	−1.65654e16	−0.0137661
$135$	−8.46403e16	−0.0660298
$136$	4.20655e17	0.308209
$137$	2.45559e18	1.69056	0.845281	−	0.534322i	$-0.179433\pi$
$137$	2.45559e18	1.69056	0.845281	+	0.534322i	$0.179433\pi$
$138$	−8.98361e15	−0.00581405
$139$	8.00889e17	0.487468	0.243734	−	0.969842i	$-0.421628\pi$
$139$	8.00889e17	0.487468	0.243734	+	0.969842i	$0.421628\pi$
$140$	−1.41214e17	−0.0808702
$141$	−2.03097e17	−0.109482
$142$	2.19549e16	0.0111450
$143$	3.17068e18	1.51634
$144$	−2.03713e18	−0.918199
$145$	−7.63398e17	−0.324432
$146$	6.81712e16	0.0273276
$147$	5.77807e16	0.0218567
$148$	−2.06244e18	−0.736473
$149$	4.29784e18	1.44933	0.724665	−	0.689102i	$-0.241995\pi$
$149$	4.29784e18	1.44933	0.724665	+	0.689102i	$0.241995\pi$
$150$	6.47834e16	0.0206390
$151$	−2.64003e17	−0.0794887	−0.0397444	−	0.999210i	$-0.512654\pi$
$151$	−2.64003e17	−0.0794887	−0.0397444	+	0.999210i	$0.512654\pi$
$152$	7.84156e17	0.223219
$153$	−3.98626e18	−1.07322
$154$	−2.51007e17	−0.0639381
$155$	1.31819e18	0.317804
$156$	−8.33961e17	−0.190365
$157$	−3.71964e18	−0.804182	−0.402091	−	0.915600i	$-0.631716\pi$
$157$	−3.71964e18	−0.804182	−0.402091	+	0.915600i	$0.631716\pi$
$158$	−4.12683e17	−0.0845340
$159$	3.82302e17	0.0742218
$160$	−4.90662e17	−0.0903156
$161$	5.80828e17	0.101398
$162$	−7.95665e17	−0.131781
$163$	−9.76784e18	−1.53534	−0.767669	−	0.640847i	$-0.778583\pi$
$163$	−9.76784e18	−1.53534	−0.767669	+	0.640847i	$0.778583\pi$
$164$	−2.98962e18	−0.446111
$165$	2.81531e17	0.0398945
$166$	−1.10121e18	−0.148235
$167$	9.45395e18	1.20927	0.604635	−	0.796503i	$-0.293319\pi$
$167$	9.45395e18	1.20927	0.604635	+	0.796503i	$0.293319\pi$
$168$	1.33393e17	0.0162182
$169$	5.29558e18	0.612176
$170$	−3.09136e17	−0.0339887
$171$	−7.43092e18	−0.777276
$172$	2.58301e18	0.257119
$173$	1.66020e19	1.57315	0.786574	−	0.617496i	$-0.211853\pi$
$173$	1.66020e19	1.57315	0.786574	+	0.617496i	$0.211853\pi$
$174$	3.56906e17	0.0322022
$175$	−4.18852e18	−0.359945
$176$	1.37142e19	1.12283
$177$	3.23879e18	0.252703
$178$	2.91774e18	0.217009
$179$	−1.51885e19	−1.07712	−0.538561	−	0.842586i	$-0.681032\pi$
$179$	−1.51885e19	−1.07712	−0.538561	+	0.842586i	$0.681032\pi$
$180$	3.08935e18	0.208954
$181$	−9.36942e18	−0.604567	−0.302284	−	0.953218i	$-0.597749\pi$
$181$	−9.36942e18	−0.604567	−0.302284	+	0.953218i	$0.597749\pi$
$182$	−1.10404e18	−0.0679792
$183$	1.50146e18	0.0882430
$184$	1.34090e18	0.0752396
$185$	3.06238e18	0.164097
$186$	−6.16285e17	−0.0315443
$187$	2.68361e19	1.31240
$188$	1.50037e19	0.701222
$189$	−2.55845e18	−0.114301
$190$	−5.76271e17	−0.0246162
$191$	−3.89256e19	−1.59020	−0.795100	−	0.606479i	$-0.792581\pi$
$191$	−3.89256e19	−1.59020	−0.795100	+	0.606479i	$0.792581\pi$
$192$	−3.45162e18	−0.134885
$193$	−3.40911e19	−1.27469	−0.637344	−	0.770580i	$-0.719967\pi$
$193$	−3.40911e19	−1.27469	−0.637344	+	0.770580i	$0.719967\pi$
$194$	7.70837e18	0.275834
$195$	1.23829e18	0.0424160
$196$	−4.26851e18	−0.139991
$197$	−9.30479e18	−0.292243	−0.146121	−	0.989267i	$-0.546679\pi$
$197$	−9.30479e18	−0.292243	−0.146121	+	0.989267i	$0.546679\pi$
$198$	5.49131e18	0.165205
$199$	−1.51791e19	−0.437517	−0.218758	−	0.975779i	$-0.570201\pi$
$199$	−1.51791e19	−0.437517	−0.218758	+	0.975779i	$0.570201\pi$
$200$	−9.66964e18	−0.267089
$201$	5.61618e17	0.0148687
$202$	−7.72583e18	−0.196091
$203$	−2.30755e19	−0.561609
$204$	−7.05850e18	−0.164762
$205$	4.43909e18	0.0994000
$206$	1.11730e19	0.240047
$207$	−1.27068e19	−0.261993
$208$	6.03210e19	1.19380
$209$	5.00260e19	0.950501
$210$	−9.80296e16	−0.00178852
$211$	5.65914e19	0.991630	0.495815	−	0.868428i	$-0.334869\pi$
$211$	5.65914e19	0.991630	0.495815	+	0.868428i	$0.334869\pi$
$212$	−2.82423e19	−0.475385
$213$	−7.44339e17	−0.0120377
$214$	−9.09400e18	−0.141331
$215$	−3.83534e18	−0.0572897
$216$	−5.90645e18	−0.0848145
$217$	3.98454e19	0.550137
$218$	−1.02582e19	−0.136205
$219$	−2.31122e18	−0.0295166
$220$	−2.07979e19	−0.255522
$221$	1.18036e20	1.39534
$222$	−1.43173e18	−0.0162878
$223$	−3.30739e19	−0.362155	−0.181077	−	0.983469i	$-0.557958\pi$
$223$	−3.30739e19	−0.362155	−0.181077	+	0.983469i	$0.557958\pi$
$224$	−1.48314e19	−0.156341
$225$	9.16326e19	0.930034
$226$	1.01227e19	0.0989403
$227$	−1.11864e20	−1.05310	−0.526551	−	0.850143i	$-0.676515\pi$
$227$	−1.11864e20	−1.05310	−0.526551	+	0.850143i	$0.676515\pi$
$228$	−1.31580e19	−0.119328
$229$	−4.72991e19	−0.413286	−0.206643	−	0.978416i	$-0.566254\pi$
$229$	−4.72991e19	−0.413286	−0.206643	+	0.978416i	$0.566254\pi$
$230$	−9.85422e17	−0.00829727
$231$	8.50993e18	0.0690596
$232$	−5.32722e19	−0.416728
$233$	1.33708e19	0.100840	0.0504198	−	0.998728i	$-0.483944\pi$
$233$	1.33708e19	0.100840	0.0504198	+	0.998728i	$0.483944\pi$
$234$	2.41531e19	0.175646
$235$	−2.22780e19	−0.156242
$236$	−2.39263e20	−1.61854
$237$	1.39913e19	0.0913052
$238$	−9.34435e18	−0.0588363
$239$	−2.82804e20	−1.71832	−0.859160	−	0.511707i	$-0.829013\pi$
$239$	−2.82804e20	−1.71832	−0.859160	+	0.511707i	$0.829013\pi$
$240$	5.35603e18	0.0314085
$241$	2.46167e20	1.39343	0.696715	−	0.717348i	$-0.254644\pi$
$241$	2.46167e20	1.39343	0.696715	+	0.717348i	$0.254644\pi$
$242$	−1.10475e19	−0.0603715
$243$	8.42886e19	0.444750
$244$	−1.10920e20	−0.565190
$245$	6.33802e18	0.0311919
$246$	−2.07537e18	−0.00986616
$247$	2.20035e20	1.01057
$248$	9.19875e19	0.408215
$249$	3.73346e19	0.160109
$250$	1.45680e19	0.0603825
$251$	−1.58711e20	−0.635887	−0.317943	−	0.948110i	$-0.602992\pi$
$251$	−1.58711e20	−0.635887	−0.317943	+	0.948110i	$0.602992\pi$
$252$	9.33826e19	0.361711
$253$	8.55443e19	0.320381
$254$	3.20366e19	0.116027
$255$	1.04807e19	0.0367112
$256$	2.37692e20	0.805333
$257$	−4.08656e20	−1.33945	−0.669725	−	0.742609i	$-0.733588\pi$
$257$	−4.08656e20	−1.33945	−0.669725	+	0.742609i	$0.733588\pi$
$258$	1.79311e18	0.00568641
$259$	9.25675e19	0.284060
$260$	−9.14781e19	−0.271671
$261$	5.04825e20	1.45110
$262$	5.80173e19	0.161435
$263$	8.19610e19	0.220792	0.110396	−	0.993888i	$-0.464788\pi$
$263$	8.19610e19	0.220792	0.110396	+	0.993888i	$0.464788\pi$
$264$	1.96461e19	0.0512440
$265$	4.19352e19	0.105923
$266$	−1.74191e19	−0.0426120
$267$	−9.89207e19	−0.234391
$268$	−4.14891e19	−0.0952332
$269$	2.37056e20	0.527177	0.263589	−	0.964635i	$-0.415094\pi$
$269$	2.37056e20	0.527177	0.263589	+	0.964635i	$0.415094\pi$
$270$	4.34061e18	0.00935318
$271$	−7.86494e20	−1.64231	−0.821157	−	0.570702i	$-0.806671\pi$
$271$	−7.86494e20	−1.64231	−0.821157	+	0.570702i	$0.806671\pi$
$272$	5.10546e20	1.03324
$273$	3.74303e19	0.0734244
$274$	−1.25930e20	−0.239469
$275$	−6.16884e20	−1.13730
$276$	−2.25001e19	−0.0402214
$277$	5.29661e20	0.918164	0.459082	−	0.888394i	$-0.348178\pi$
$277$	5.29661e20	0.918164	0.459082	+	0.888394i	$0.348178\pi$
$278$	−4.10720e19	−0.0690502
$279$	−8.71703e20	−1.42145
$280$	1.46320e19	0.0231452
$281$	−2.39151e20	−0.367002	−0.183501	−	0.983019i	$-0.558743\pi$
$281$	−2.39151e20	−0.367002	−0.183501	+	0.983019i	$0.558743\pi$
$282$	1.04154e19	0.0155082
$283$	−7.37199e20	−1.06512	−0.532562	−	0.846391i	$-0.678771\pi$
$283$	−7.37199e20	−1.06512	−0.532562	+	0.846391i	$0.678771\pi$
$284$	5.49875e19	0.0771007
$285$	1.95374e19	0.0265880
$286$	−1.62602e20	−0.214791
$287$	1.34182e20	0.172067
$288$	3.24468e20	0.403958
$289$	1.71798e20	0.207677
$290$	3.91494e19	0.0459560
$291$	−2.61338e20	−0.297929
$292$	1.70740e20	0.189052
$293$	9.86660e20	1.06119	0.530594	−	0.847626i	$-0.321969\pi$
$293$	9.86660e20	1.06119	0.530594	+	0.847626i	$0.321969\pi$
$294$	−2.96317e18	−0.00309602
$295$	3.55267e20	0.360634
$296$	2.13702e20	0.210780
$297$	−3.76808e20	−0.361152
$298$	−2.20406e20	−0.205299
$299$	3.76260e20	0.340630
$300$	1.62255e20	0.142780
$301$	−1.15932e20	−0.0991716
$302$	1.35389e19	0.0112596
$303$	2.61930e20	0.211798
$304$	9.51725e20	0.748318
$305$	1.64697e20	0.125932
$306$	2.04428e20	0.152022
$307$	−5.51578e20	−0.398961	−0.199481	−	0.979902i	$-0.563925\pi$
$307$	−5.51578e20	−0.398961	−0.199481	+	0.979902i	$0.563925\pi$
$308$	−6.28665e20	−0.442322
$309$	−3.78798e20	−0.259275
$310$	−6.76010e19	−0.0450172
$311$	1.45772e21	0.944520	0.472260	−	0.881459i	$-0.343438\pi$
$311$	1.45772e21	0.944520	0.472260	+	0.881459i	$0.343438\pi$
$312$	8.64118e19	0.0544828
$313$	3.09789e21	1.90081	0.950406	−	0.311011i	$-0.100668\pi$
$313$	3.09789e21	1.90081	0.950406	+	0.311011i	$0.100668\pi$
$314$	1.90755e20	0.113913
$315$	−1.38658e20	−0.0805943
$316$	−1.03359e21	−0.584803
$317$	−7.97629e20	−0.439336	−0.219668	−	0.975575i	$-0.570497\pi$
$317$	−7.97629e20	−0.439336	−0.219668	+	0.975575i	$0.570497\pi$
$318$	−1.96056e19	−0.0105136
$319$	−3.39855e21	−1.77449
$320$	−3.78612e20	−0.192495
$321$	3.08315e20	0.152652
$322$	−2.97866e19	−0.0143630
$323$	1.86234e21	0.874657
$324$	−1.99280e21	−0.911657
$325$	−2.71332e21	−1.20918
$326$	5.00925e20	0.217482
$327$	3.47786e20	0.147115
$328$	3.09773e20	0.127678
$329$	−6.73402e20	−0.270464
$330$	−1.44378e19	−0.00565109
$331$	−8.50736e20	−0.324531	−0.162266	−	0.986747i	$-0.551880\pi$
$331$	−8.50736e20	−0.324531	−0.162266	+	0.986747i	$0.551880\pi$
$332$	−2.75806e21	−1.02549
$333$	−2.02511e21	−0.733960
$334$	−4.84827e20	−0.171294
$335$	6.16045e19	0.0212193
$336$	1.61898e20	0.0543698
$337$	5.66654e21	1.85551	0.927757	−	0.373185i	$-0.121734\pi$
$337$	5.66654e21	1.85551	0.927757	+	0.373185i	$0.121734\pi$
$338$	−2.71573e20	−0.0867152
$339$	−3.43190e20	−0.106866
$340$	−7.74254e20	−0.235133
$341$	5.86843e21	1.73824
$342$	3.81080e20	0.110102
$343$	1.91581e20	0.0539949
$344$	−2.67641e20	−0.0735878
$345$	3.34089e19	0.00896189
$346$	−8.51403e20	−0.222837
$347$	2.33549e21	0.596454	0.298227	−	0.954495i	$-0.403605\pi$
$347$	2.33549e21	0.596454	0.298227	+	0.954495i	$0.403605\pi$
$348$	8.93896e20	0.222773
$349$	−2.30012e21	−0.559414	−0.279707	−	0.960085i	$-0.590237\pi$
$349$	−2.30012e21	−0.559414	−0.279707	+	0.960085i	$0.590237\pi$
$350$	2.14800e20	0.0509865
$351$	−1.65736e21	−0.383978
$352$	−2.18437e21	−0.493984
$353$	3.02456e21	0.667694	0.333847	−	0.942627i	$-0.391653\pi$
$353$	3.02456e21	0.667694	0.333847	+	0.942627i	$0.391653\pi$
$354$	−1.66095e20	−0.0357956
$355$	−8.16474e19	−0.0171791
$356$	7.30770e21	1.50126
$357$	3.16803e20	0.0635491
$358$	7.78914e20	0.152575
$359$	9.70555e20	0.185659	0.0928297	−	0.995682i	$-0.470409\pi$
$359$	9.70555e20	0.185659	0.0928297	+	0.995682i	$0.470409\pi$
$360$	−3.20106e20	−0.0598030
$361$	−2.00874e21	−0.366532
$362$	4.80492e20	0.0856374
$363$	3.74544e20	0.0652073
$364$	−2.76513e21	−0.470278
$365$	−2.53520e20	−0.0421234
$366$	−7.69996e19	−0.0124997
$367$	−1.62448e21	−0.257664	−0.128832	−	0.991666i	$-0.541123\pi$
$367$	−1.62448e21	−0.257664	−0.128832	+	0.991666i	$0.541123\pi$
$368$	1.62745e21	0.252232
$369$	−2.93551e21	−0.444590
$370$	−1.57048e20	−0.0232444
$371$	1.26759e21	0.183358
$372$	−1.54353e21	−0.218223
$373$	4.32215e21	0.597275	0.298638	−	0.954367i	$-0.403468\pi$
$373$	4.32215e21	0.597275	0.298638	+	0.954367i	$0.403468\pi$
$374$	−1.37624e21	−0.185902
$375$	−4.93903e20	−0.0652192
$376$	−1.55462e21	−0.200691
$377$	−1.49483e22	−1.88664
$378$	1.31205e20	0.0161909
$379$	−8.34315e21	−1.00669	−0.503346	−	0.864085i	$-0.667898\pi$
$379$	−8.34315e21	−1.00669	−0.503346	+	0.864085i	$0.667898\pi$
$380$	−1.44331e21	−0.170294
$381$	−1.08614e21	−0.125321
$382$	1.99622e21	0.225253
$383$	−1.83224e21	−0.202205	−0.101103	−	0.994876i	$-0.532237\pi$
$383$	−1.83224e21	−0.202205	−0.101103	+	0.994876i	$0.532237\pi$
$384$	7.63312e20	0.0823923
$385$	9.33464e20	0.0985556
$386$	1.74829e21	0.180560
$387$	2.53625e21	0.256241
$388$	1.93062e22	1.90821
$389$	−1.07749e22	−1.04194	−0.520968	−	0.853576i	$-0.674429\pi$
$389$	−1.07749e22	−1.04194	−0.520968	+	0.853576i	$0.674429\pi$
$390$	−6.35035e19	−0.00600825
$391$	3.18460e21	0.294817
$392$	4.42286e20	0.0400656
$393$	−1.96697e21	−0.174366
$394$	4.77178e20	0.0413964
$395$	1.53472e21	0.130302
$396$	1.37534e22	1.14288
$397$	−1.46435e22	−1.19104	−0.595518	−	0.803342i	$-0.703053\pi$
$397$	−1.46435e22	−1.19104	−0.595518	+	0.803342i	$0.703053\pi$
$398$	7.78430e20	0.0619746
$399$	5.90563e20	0.0460253
$400$	−1.17360e22	−0.895384
$401$	1.05677e22	0.789322	0.394661	−	0.918827i	$-0.370862\pi$
$401$	1.05677e22	0.789322	0.394661	+	0.918827i	$0.370862\pi$
$402$	−2.88015e19	−0.00210617
$403$	2.58118e22	1.84810
$404$	−1.93499e22	−1.35655
$405$	2.95898e21	0.203130
$406$	1.18338e21	0.0795523
$407$	1.36333e22	0.897532
$408$	7.31374e20	0.0471551
$409$	−1.22194e22	−0.771615	−0.385807	−	0.922579i	$-0.626077\pi$
$409$	−1.22194e22	−0.771615	−0.385807	+	0.922579i	$0.626077\pi$
$410$	−2.27650e20	−0.0140801
$411$	4.26943e21	0.258651
$412$	2.79835e22	1.66064
$413$	1.07387e22	0.624278
$414$	6.51645e20	0.0371115
$415$	4.09527e21	0.228493
$416$	−9.60777e21	−0.525205
$417$	1.39247e21	0.0745812
$418$	−2.56549e21	−0.134639
$419$	−3.66891e22	−1.88676	−0.943382	−	0.331708i	$-0.892375\pi$
$419$	−3.66891e22	−1.88676	−0.943382	+	0.331708i	$0.892375\pi$
$420$	−2.45522e20	−0.0123729
$421$	2.62711e21	0.129742	0.0648709	−	0.997894i	$-0.479336\pi$
$421$	2.62711e21	0.129742	0.0648709	+	0.997894i	$0.479336\pi$
$422$	−2.90218e21	−0.140465
$423$	1.47321e22	0.698830
$424$	2.92636e21	0.136056
$425$	−2.29650e22	−1.04655
$426$	3.81720e19	0.00170515
$427$	4.97835e21	0.217996
$428$	−2.27766e22	−0.977724
$429$	5.51273e21	0.231996
$430$	1.96688e20	0.00811513
$431$	−1.48704e22	−0.601541	−0.300771	−	0.953696i	$-0.597244\pi$
$431$	−1.48704e22	−0.601541	−0.300771	+	0.953696i	$0.597244\pi$
$432$	−7.16863e21	−0.284331
$433$	−1.76103e22	−0.684889	−0.342445	−	0.939538i	$-0.611255\pi$
$433$	−1.76103e22	−0.684889	−0.342445	+	0.939538i	$0.611255\pi$
$434$	−2.04339e21	−0.0779272
$435$	−1.32729e21	−0.0496371
$436$	−2.56925e22	−0.942260
$437$	5.93651e21	0.213520
$438$	1.18526e20	0.00418105
$439$	1.82200e22	0.630376	0.315188	−	0.949029i	$-0.397932\pi$
$439$	1.82200e22	0.630376	0.315188	+	0.949029i	$0.397932\pi$
$440$	2.15500e21	0.0731307
$441$	−4.19125e21	−0.139513
$442$	−6.05326e21	−0.197652
$443$	5.36820e22	1.71948	0.859740	−	0.510733i	$-0.170626\pi$
$443$	5.36820e22	1.71948	0.859740	+	0.510733i	$0.170626\pi$
$444$	−3.58588e21	−0.112678
$445$	−1.08507e22	−0.334502
$446$	1.69613e21	0.0512995
$447$	7.47247e21	0.221743
$448$	−1.14444e22	−0.333219
$449$	−1.10318e22	−0.315174	−0.157587	−	0.987505i	$-0.550372\pi$
$449$	−1.10318e22	−0.315174	−0.157587	+	0.987505i	$0.550372\pi$
$450$	−4.69920e21	−0.131740
$451$	1.97623e22	0.543671
$452$	2.53529e22	0.684466
$453$	−4.59011e20	−0.0121615
$454$	5.73673e21	0.149173
$455$	4.10577e21	0.104785
$456$	1.36338e21	0.0341519
$457$	1.46400e22	0.359959	0.179979	−	0.983670i	$-0.442397\pi$
$457$	1.46400e22	0.359959	0.179979	+	0.983670i	$0.442397\pi$
$458$	2.42564e21	0.0585423
$459$	−1.40276e22	−0.332335
$460$	−2.46806e21	−0.0574003
$461$	−1.47602e22	−0.337003	−0.168502	−	0.985701i	$-0.553893\pi$
$461$	−1.47602e22	−0.337003	−0.168502	+	0.985701i	$0.553893\pi$
$462$	−4.36415e20	−0.00978235
$463$	6.94572e22	1.52855	0.764273	−	0.644892i	$-0.223098\pi$
$463$	6.94572e22	1.52855	0.764273	+	0.644892i	$0.223098\pi$
$464$	−6.46561e22	−1.39703
$465$	2.29189e21	0.0486231
$466$	−6.85694e20	−0.0142840
$467$	7.70865e22	1.57683	0.788415	−	0.615143i	$-0.210902\pi$
$467$	7.70865e22	1.57683	0.788415	+	0.615143i	$0.210902\pi$
$468$	6.04932e22	1.21511
$469$	1.86214e21	0.0367318
$470$	1.14248e21	0.0221318
$471$	−6.46719e21	−0.123038
$472$	2.47916e22	0.463230
$473$	−1.70744e22	−0.313348
$474$	−7.17514e20	−0.0129335
$475$	−4.28098e22	−0.757963
$476$	−2.34036e22	−0.407027
$477$	−2.77311e22	−0.473763
$478$	1.45031e22	0.243401
$479$	−9.51991e22	−1.56957	−0.784785	−	0.619768i	$-0.787227\pi$
$479$	−9.51991e22	−1.56957	−0.784785	+	0.619768i	$0.787227\pi$
$480$	−8.53094e20	−0.0138180
$481$	5.99652e22	0.954258
$482$	−1.26242e22	−0.197380
$483$	1.00986e21	0.0155135
$484$	−2.76692e22	−0.417648
$485$	−2.86665e22	−0.425177
$486$	−4.32258e21	−0.0629991
$487$	−1.05659e23	−1.51325	−0.756623	−	0.653852i	$-0.773152\pi$
$487$	−1.05659e23	−1.51325	−0.756623	+	0.653852i	$0.773152\pi$
$488$	1.14931e22	0.161758
$489$	−1.69829e22	−0.234902
$490$	−3.25033e20	−0.00441836
$491$	1.22685e23	1.63908	0.819538	−	0.573025i	$-0.194230\pi$
$491$	1.22685e23	1.63908	0.819538	+	0.573025i	$0.194230\pi$
$492$	−5.19792e21	−0.0682538
$493$	−1.26519e23	−1.63290
$494$	−1.12841e22	−0.143149
$495$	−2.04215e22	−0.254650
$496$	1.11645e23	1.36850
$497$	−2.46798e21	−0.0297380
$498$	−1.91463e21	−0.0226796
$499$	−1.39591e23	−1.62556	−0.812780	−	0.582571i	$-0.802047\pi$
$499$	−1.39591e23	−1.62556	−0.812780	+	0.582571i	$0.802047\pi$
$500$	3.64867e22	0.417724
$501$	1.64372e22	0.185015
$502$	8.13917e21	0.0900738
$503$	7.11940e22	0.774668	0.387334	−	0.921939i	$-0.373396\pi$
$503$	7.11940e22	0.774668	0.387334	+	0.921939i	$0.373396\pi$
$504$	−9.67595e21	−0.103522
$505$	2.87314e22	0.302259
$506$	−4.38697e21	−0.0453822
$507$	9.20719e21	0.0936612
$508$	8.02379e22	0.802672
$509$	9.92531e22	0.976434	0.488217	−	0.872722i	$-0.337647\pi$
$509$	9.92531e22	0.976434	0.488217	+	0.872722i	$0.337647\pi$
$510$	−5.37482e20	−0.00520017
$511$	−7.66322e21	−0.0729179
$512$	−6.97333e22	−0.652598
$513$	−2.61493e22	−0.240692
$514$	2.09571e22	0.189734
$515$	−4.15508e22	−0.370014
$516$	4.49096e21	0.0393384
$517$	−9.91787e22	−0.854572
$518$	−4.74714e21	−0.0402373
$519$	2.88652e22	0.240687
$520$	9.47861e21	0.0777528
$521$	1.06192e23	0.856982	0.428491	−	0.903546i	$-0.359045\pi$
$521$	1.06192e23	0.856982	0.428491	+	0.903546i	$0.359045\pi$
$522$	−2.58889e22	−0.205549
$523$	9.65971e22	0.754571	0.377285	−	0.926097i	$-0.376858\pi$
$523$	9.65971e22	0.754571	0.377285	+	0.926097i	$0.376858\pi$
$524$	1.45308e23	1.11680
$525$	−7.28239e21	−0.0550706
$526$	−4.20321e21	−0.0312754
$527$	2.18467e23	1.59954
$528$	2.38444e22	0.171790
$529$	−1.30899e23	−0.928030
$530$	−2.15056e21	−0.0150040
$531$	−2.34933e23	−1.61302
$532$	−4.36274e22	−0.294789
$533$	8.69228e22	0.578033
$534$	5.07295e21	0.0332017
$535$	3.38194e22	0.217851
$536$	4.29894e21	0.0272559
$537$	−2.64076e22	−0.164797
$538$	−1.21570e22	−0.0746750
$539$	2.82161e22	0.170605
$540$	1.08714e22	0.0647050
$541$	1.18301e23	0.693128	0.346564	−	0.938026i	$-0.387348\pi$
$541$	1.18301e23	0.693128	0.346564	+	0.938026i	$0.387348\pi$
$542$	4.03338e22	0.232635
$543$	−1.62902e22	−0.0924970
$544$	−8.13184e22	−0.454567
$545$	3.81490e22	0.209949
$546$	−1.91954e21	−0.0104006
$547$	−2.79654e23	−1.49187	−0.745933	−	0.666022i	$-0.767996\pi$
$547$	−2.79654e23	−1.49187	−0.745933	+	0.666022i	$0.767996\pi$
$548$	−3.15401e23	−1.65664
$549$	−1.08912e23	−0.563262
$550$	3.16357e22	0.161100
$551$	−2.35849e23	−1.18262
$552$	2.33137e21	0.0115114
$553$	4.63903e22	0.225561
$554$	−2.71626e22	−0.130059
$555$	5.32443e21	0.0251063
$556$	−1.02868e23	−0.477687
$557$	3.52964e23	1.61422	0.807108	−	0.590404i	$-0.201032\pi$
$557$	3.52964e23	1.61422	0.807108	+	0.590404i	$0.201032\pi$
$558$	4.47036e22	0.201350
$559$	−7.51005e22	−0.333152
$560$	1.77588e22	0.0775916
$561$	4.66587e22	0.200793
$562$	1.22644e22	0.0519862
$563$	−2.73110e22	−0.114029	−0.0570145	−	0.998373i	$-0.518158\pi$
$563$	−2.73110e22	−0.114029	−0.0570145	+	0.998373i	$0.518158\pi$
$564$	2.60862e22	0.107285
$565$	−3.76449e22	−0.152509
$566$	3.78058e22	0.150876
$567$	8.94419e22	0.351629
$568$	−5.69760e21	−0.0220664
$569$	2.16917e23	0.827635	0.413817	−	0.910360i	$-0.364195\pi$
$569$	2.16917e23	0.827635	0.413817	+	0.910360i	$0.364195\pi$
$570$	−1.00194e21	−0.00376621
$571$	1.22017e23	0.451870	0.225935	−	0.974142i	$-0.427456\pi$
$571$	1.22017e23	0.451870	0.225935	+	0.974142i	$0.427456\pi$
$572$	−4.07249e23	−1.48591
$573$	−6.76782e22	−0.243296
$574$	−6.88124e21	−0.0243734
$575$	−7.32047e22	−0.255483
$576$	2.50371e23	0.860978
$577$	2.96478e23	1.00461	0.502305	−	0.864691i	$-0.332485\pi$
$577$	2.96478e23	1.00461	0.502305	+	0.864691i	$0.332485\pi$
$578$	−8.81034e21	−0.0294175
$579$	−5.92727e22	−0.195023
$580$	9.80524e22	0.317922
$581$	1.23789e23	0.395534
$582$	1.34022e22	0.0422018
$583$	1.86690e23	0.579347
$584$	−1.76914e22	−0.0541069
$585$	−8.98223e22	−0.270744
$586$	−5.05989e22	−0.150318
$587$	−4.16005e22	−0.121808	−0.0609039	−	0.998144i	$-0.519398\pi$
$587$	−4.16005e22	−0.121808	−0.0609039	+	0.998144i	$0.519398\pi$
$588$	−7.42147e21	−0.0214182
$589$	4.07251e23	1.15846
$590$	−1.82191e22	−0.0510841
$591$	−1.61778e22	−0.0447123
$592$	2.59369e23	0.706616
$593$	7.92639e22	0.212868	0.106434	−	0.994320i	$-0.466057\pi$
$593$	7.92639e22	0.212868	0.106434	+	0.994320i	$0.466057\pi$
$594$	1.93239e22	0.0511575
$595$	3.47505e22	0.0906915
$596$	−5.52024e23	−1.42025
$597$	−2.63912e22	−0.0669388
$598$	−1.92958e22	−0.0482505
$599$	3.83971e23	0.946609	0.473304	−	0.880899i	$-0.343061\pi$
$599$	3.83971e23	0.946609	0.473304	+	0.880899i	$0.343061\pi$
$600$	−1.68122e22	−0.0408638
$601$	−1.66921e23	−0.400016	−0.200008	−	0.979794i	$-0.564097\pi$
$601$	−1.66921e23	−0.400016	−0.200008	+	0.979794i	$0.564097\pi$
$602$	5.94533e21	0.0140477
$603$	−4.07382e22	−0.0949083
$604$	3.39091e22	0.0778938
$605$	4.10841e22	0.0930579
$606$	−1.34326e22	−0.0300014
$607$	−7.24796e23	−1.59629	−0.798145	−	0.602465i	$-0.794185\pi$
$607$	−7.24796e23	−1.59629	−0.798145	+	0.602465i	$0.794185\pi$
$608$	−1.51588e23	−0.329219
$609$	−4.01203e22	−0.0859245
$610$	−8.44617e21	−0.0178384
$611$	−4.36230e23	−0.908583
$612$	5.12003e23	1.05169
$613$	−6.14887e23	−1.24561	−0.622803	−	0.782378i	$-0.714006\pi$
$613$	−6.14887e23	−1.24561	−0.622803	+	0.782378i	$0.714006\pi$
$614$	2.82866e22	0.0565131
$615$	7.71805e21	0.0152079
$616$	6.51399e22	0.126593
$617$	−3.90210e23	−0.747953	−0.373976	−	0.927438i	$-0.622006\pi$
$617$	−3.90210e23	−0.747953	−0.373976	+	0.927438i	$0.622006\pi$
$618$	1.94259e22	0.0367265
$619$	5.84219e22	0.108945	0.0544723	−	0.998515i	$-0.482652\pi$
$619$	5.84219e22	0.108945	0.0544723	+	0.998515i	$0.482652\pi$
$620$	−1.69311e23	−0.311427
$621$	−4.47152e22	−0.0811291
$622$	−7.47564e22	−0.133792
$623$	−3.27988e23	−0.579041
$624$	1.04877e23	0.182647
$625$	5.00150e23	0.859251
$626$	−1.58869e23	−0.269251
$627$	8.69781e22	0.145424
$628$	4.77759e23	0.788046
$629$	5.07534e23	0.825914
$630$	7.11079e21	0.0114162
$631$	−3.71042e23	−0.587724	−0.293862	−	0.955848i	$-0.594941\pi$
$631$	−3.71042e23	−0.587724	−0.293862	+	0.955848i	$0.594941\pi$
$632$	1.07097e23	0.167372
$633$	9.83931e22	0.151717
$634$	4.09048e22	0.0622323
$635$	−1.19140e23	−0.178847
$636$	−4.91037e22	−0.0727325
$637$	1.24106e23	0.181388
$638$	1.74288e23	0.251358
$639$	5.39923e22	0.0768377
$640$	8.37285e22	0.117583
$641$	1.98314e22	0.0274828	0.0137414	−	0.999906i	$-0.495626\pi$
$641$	1.98314e22	0.0274828	0.0137414	+	0.999906i	$0.495626\pi$
$642$	−1.58113e22	−0.0216233
$643$	−2.64501e23	−0.356971	−0.178486	−	0.983942i	$-0.557120\pi$
$643$	−2.64501e23	−0.356971	−0.178486	+	0.983942i	$0.557120\pi$
$644$	−7.46027e22	−0.0993630
$645$	−6.66833e21	−0.00876515
$646$	−9.55065e22	−0.123896
$647$	−6.06129e23	−0.776030	−0.388015	−	0.921653i	$-0.626839\pi$
$647$	−6.06129e23	−0.776030	−0.388015	+	0.921653i	$0.626839\pi$
$648$	2.06486e23	0.260918
$649$	1.58160e24	1.97250
$650$	1.39147e23	0.171282
$651$	6.92775e22	0.0841693
$652$	1.25460e24	1.50453
$653$	−1.09975e24	−1.30176	−0.650880	−	0.759181i	$-0.725600\pi$
$653$	−1.09975e24	−1.30176	−0.650880	+	0.759181i	$0.725600\pi$
$654$	−1.78355e22	−0.0208389
$655$	−2.15759e23	−0.248839
$656$	3.75969e23	0.428026
$657$	1.67649e23	0.188407
$658$	3.45341e22	0.0383114
$659$	1.11521e24	1.22133	0.610663	−	0.791890i	$-0.290903\pi$
$659$	1.11521e24	1.22133	0.610663	+	0.791890i	$0.290903\pi$
$660$	−3.61605e22	−0.0390941
$661$	−7.56412e23	−0.807320	−0.403660	−	0.914909i	$-0.632262\pi$
$661$	−7.56412e23	−0.807320	−0.403660	+	0.914909i	$0.632262\pi$
$662$	4.36283e22	0.0459701
$663$	2.05225e23	0.213484
$664$	2.85780e23	0.293497
$665$	6.47795e22	0.0656831
$666$	1.03854e23	0.103966
$667$	−4.03301e23	−0.398620
$668$	−1.21428e24	−1.18501
$669$	−5.75042e22	−0.0554086
$670$	−3.15926e21	−0.00300573
$671$	7.33211e23	0.688791
$672$	−2.57867e22	−0.0239198
$673$	−1.01132e24	−0.926320	−0.463160	−	0.886275i	$-0.653284\pi$
$673$	−1.01132e24	−0.926320	−0.463160	+	0.886275i	$0.653284\pi$
$674$	−2.90598e23	−0.262835
$675$	3.22454e23	0.287996
$676$	−6.80175e23	−0.599893
$677$	−5.78847e23	−0.504150	−0.252075	−	0.967708i	$-0.581113\pi$
$677$	−5.78847e23	−0.504150	−0.252075	+	0.967708i	$0.581113\pi$
$678$	1.75998e22	0.0151376
$679$	−8.66509e23	−0.736004
$680$	8.02252e22	0.0672954
$681$	−1.94493e23	−0.161122
$682$	−3.00951e23	−0.246223
$683$	−1.42127e24	−1.14842	−0.574210	−	0.818708i	$-0.694691\pi$
$683$	−1.42127e24	−1.14842	−0.574210	+	0.818708i	$0.694691\pi$
$684$	9.54442e23	0.761680
$685$	4.68318e23	0.369123
$686$	−9.82487e21	−0.00764842
$687$	−8.22369e22	−0.0632316
$688$	−3.24834e23	−0.246695
$689$	8.21141e23	0.615963
$690$	−1.71331e21	−0.00126946
$691$	1.36113e24	0.996180	0.498090	−	0.867125i	$-0.334035\pi$
$691$	1.36113e24	0.996180	0.498090	+	0.867125i	$0.334035\pi$
$692$	−2.13240e24	−1.54158
$693$	−6.17286e23	−0.440813
$694$	−1.19771e23	−0.0844881
$695$	1.52742e23	0.106435
$696$	−9.26221e22	−0.0637582
$697$	7.35699e23	0.500290
$698$	1.17957e23	0.0792414
$699$	2.32472e22	0.0154282
$700$	5.37981e23	0.352723
$701$	1.50351e24	0.973872	0.486936	−	0.873438i	$-0.338114\pi$
$701$	1.50351e24	0.973872	0.486936	+	0.873438i	$0.338114\pi$
$702$	8.49945e22	0.0543908
$703$	9.46111e23	0.598166
$704$	−1.68553e24	−1.05286
$705$	−3.87337e22	−0.0239046
$706$	−1.55109e23	−0.0945794
$707$	8.68471e23	0.523227
$708$	−4.15997e23	−0.247632
$709$	−1.02666e24	−0.603858	−0.301929	−	0.953330i	$-0.597631\pi$
$709$	−1.02666e24	−0.603858	−0.301929	+	0.953330i	$0.597631\pi$
$710$	4.18713e21	0.00243344
$711$	−1.01489e24	−0.582808
$712$	−7.57195e23	−0.429663
$713$	6.96397e23	0.390478
$714$	−1.62466e22	−0.00900178
$715$	6.04697e23	0.331083
$716$	1.95085e24	1.05551
$717$	−4.91700e23	−0.262898
$718$	−4.97730e22	−0.0262988
$719$	3.40579e24	1.77837	0.889185	−	0.457548i	$-0.151272\pi$
$719$	3.40579e24	1.77837	0.889185	+	0.457548i	$0.151272\pi$
$720$	−3.88511e23	−0.200483
$721$	−1.25597e24	−0.640514
$722$	1.03014e23	0.0519196
$723$	4.28000e23	0.213191
$724$	1.20343e24	0.592437
$725$	2.90832e24	1.41504
$726$	−1.92078e22	−0.00923667
$727$	2.63583e24	1.25278	0.626390	−	0.779510i	$-0.284532\pi$
$727$	2.63583e24	1.25278	0.626390	+	0.779510i	$0.284532\pi$
$728$	2.86513e23	0.134594
$729$	−1.85708e24	−0.862278
$730$	1.30013e22	0.00596680
$731$	−6.35637e23	−0.288344
$732$	−1.92851e23	−0.0864724
$733$	−3.44835e24	−1.52837	−0.764184	−	0.644998i	$-0.776858\pi$
$733$	−3.44835e24	−1.52837	−0.764184	+	0.644998i	$0.776858\pi$
$734$	8.33085e22	0.0364983
$735$	1.10196e22	0.00477227
$736$	−2.59215e23	−0.110968
$737$	2.74255e23	0.116060
$738$	1.50542e23	0.0629764
$739$	7.48210e23	0.309418	0.154709	−	0.987960i	$-0.450556\pi$
$739$	7.48210e23	0.309418	0.154709	+	0.987960i	$0.450556\pi$
$740$	−3.93339e23	−0.160804
$741$	3.82566e23	0.154615
$742$	−6.50057e22	−0.0259728
$743$	3.81156e23	0.150556	0.0752779	−	0.997163i	$-0.476016\pi$
$743$	3.81156e23	0.150556	0.0752779	+	0.997163i	$0.476016\pi$
$744$	1.59935e23	0.0624558
$745$	8.19663e23	0.316452
$746$	−2.21653e23	−0.0846045
$747$	−2.70814e24	−1.02199
$748$	−3.44688e24	−1.28606
$749$	1.02227e24	0.377112
$750$	2.53288e22	0.00923835
$751$	−2.60063e24	−0.937863	−0.468932	−	0.883234i	$-0.655361\pi$
$751$	−2.60063e24	−0.937863	−0.468932	+	0.883234i	$0.655361\pi$
$752$	−1.88684e24	−0.672794
$753$	−2.75944e23	−0.0972888
$754$	7.66592e23	0.267244
$755$	−5.03495e22	−0.0173558
$756$	3.28612e23	0.112008
$757$	−5.46140e24	−1.84073	−0.920363	−	0.391065i	$-0.872107\pi$
$757$	−5.46140e24	−1.84073	−0.920363	+	0.391065i	$0.872107\pi$
$758$	4.27862e23	0.142599
$759$	1.48732e23	0.0490174
$760$	1.49550e23	0.0487385
$761$	−3.93343e24	−1.26766	−0.633828	−	0.773474i	$-0.718517\pi$
$761$	−3.93343e24	−1.26766	−0.633828	+	0.773474i	$0.718517\pi$
$762$	5.57006e22	0.0177518
$763$	1.15314e24	0.363433
$764$	4.99968e24	1.55829
$765$	−7.60240e23	−0.234330
$766$	9.39628e22	0.0286425
$767$	6.95655e24	2.09717
$768$	4.13266e23	0.123214
$769$	1.28744e23	0.0379624	0.0189812	−	0.999820i	$-0.493958\pi$
$769$	1.28744e23	0.0379624	0.0189812	+	0.999820i	$0.493958\pi$
$770$	−4.78709e22	−0.0139605
$771$	−7.10513e23	−0.204932
$772$	4.37873e24	1.24911
$773$	−2.80086e24	−0.790253	−0.395127	−	0.918627i	$-0.629299\pi$
$773$	−2.80086e24	−0.790253	−0.395127	+	0.918627i	$0.629299\pi$
$774$	−1.30067e23	−0.0362968
$775$	−5.02192e24	−1.38613
$776$	−2.00043e24	−0.546134
$777$	1.60943e23	0.0434604
$778$	5.52568e23	0.147591
$779$	1.37144e24	0.362333
$780$	−1.59049e23	−0.0415649
$781$	−3.63484e23	−0.0939618
$782$	−1.63316e23	−0.0417610
$783$	1.77647e24	0.449348
$784$	5.36800e23	0.134315
$785$	−7.09392e23	−0.175588
$786$	1.00872e23	0.0246990
$787$	6.01300e24	1.45648	0.728242	−	0.685320i	$-0.240338\pi$
$787$	6.01300e24	1.45648	0.728242	+	0.685320i	$0.240338\pi$
$788$	1.19513e24	0.286379
$789$	1.42502e23	0.0337806
$790$	−7.87049e22	−0.0184574
$791$	−1.13790e24	−0.264001
$792$	−1.42507e24	−0.327094
$793$	3.22497e24	0.732324
$794$	7.50962e23	0.168711
$795$	7.29108e22	0.0162058
$796$	1.94963e24	0.428738
$797$	−3.76960e23	−0.0820161	−0.0410080	−	0.999159i	$-0.513057\pi$
$797$	−3.76960e23	−0.0820161	−0.0410080	+	0.999159i	$0.513057\pi$
$798$	−3.02859e22	−0.00651951
$799$	−3.69217e24	−0.786382
$800$	1.86928e24	0.393921
$801$	7.17543e24	1.49614
$802$	−5.41945e23	−0.111808
$803$	−1.12864e24	−0.230395
$804$	−7.21354e22	−0.0145704
$805$	1.10773e23	0.0221395
$806$	−1.32371e24	−0.261785
$807$	4.12159e23	0.0806566
$808$	2.00496e24	0.388248
$809$	−3.60831e24	−0.691419	−0.345710	−	0.938342i	$-0.612362\pi$
$809$	−3.60831e24	−0.691419	−0.345710	+	0.938342i	$0.612362\pi$
$810$	−1.51745e23	−0.0287735
$811$	−9.30514e23	−0.174601	−0.0873003	−	0.996182i	$-0.527824\pi$
$811$	−9.30514e23	−0.174601	−0.0873003	+	0.996182i	$0.527824\pi$
$812$	2.96386e24	0.550340
$813$	−1.36744e24	−0.251269
$814$	−6.99159e23	−0.127136
$815$	−1.86287e24	−0.335231
$816$	8.87664e23	0.158082
$817$	−1.18491e24	−0.208833
$818$	6.26646e23	0.109300
$819$	−2.71509e24	−0.468673
$820$	−5.70166e23	−0.0974055
$821$	−5.51832e24	−0.933017	−0.466509	−	0.884517i	$-0.654488\pi$
$821$	−5.51832e24	−0.933017	−0.466509	+	0.884517i	$0.654488\pi$
$822$	−2.18949e23	−0.0366381
$823$	2.53726e24	0.420210	0.210105	−	0.977679i	$-0.432619\pi$
$823$	2.53726e24	0.420210	0.210105	+	0.977679i	$0.432619\pi$
$824$	−2.89954e24	−0.475278
$825$	−1.07255e24	−0.174004
$826$	−5.50715e23	−0.0884294
$827$	4.40692e23	0.0700388	0.0350194	−	0.999387i	$-0.488851\pi$
$827$	4.40692e23	0.0700388	0.0350194	+	0.999387i	$0.488851\pi$
$828$	1.63209e24	0.256736
$829$	−6.55025e24	−1.01987	−0.509934	−	0.860213i	$-0.670330\pi$
$829$	−6.55025e24	−1.01987	−0.509934	+	0.860213i	$0.670330\pi$
$830$	−2.10018e23	−0.0323662
$831$	9.20899e23	0.140476
$832$	−7.41368e24	−1.11940
$833$	1.05041e24	0.156992
$834$	−7.14101e22	−0.0105645
$835$	1.80301e24	0.264036
$836$	−6.42544e24	−0.931429
$837$	−3.06751e24	−0.440169
$838$	1.88153e24	0.267262
$839$	5.31103e24	0.746797	0.373398	−	0.927671i	$-0.378192\pi$
$839$	5.31103e24	0.746797	0.373398	+	0.927671i	$0.378192\pi$
$840$	2.54400e22	0.00354115
$841$	8.76541e24	1.20783
$842$	−1.34726e23	−0.0183780
$843$	−4.15802e23	−0.0561503
$844$	−7.26872e24	−0.971733
$845$	1.00995e24	0.133665
$846$	−7.55507e23	−0.0989898
$847$	1.24186e24	0.161088
$848$	3.55170e24	0.456113
$849$	−1.28174e24	−0.162961
$850$	1.17772e24	0.148245
$851$	1.61785e24	0.201621
$852$	9.56045e22	0.0117962
$853$	6.03409e24	0.737131	0.368566	−	0.929602i	$-0.379849\pi$
$853$	6.03409e24	0.737131	0.368566	+	0.929602i	$0.379849\pi$
$854$	−2.55305e23	−0.0308793
$855$	−1.41719e24	−0.169713
$856$	2.36002e24	0.279826
$857$	−3.48403e24	−0.409021	−0.204510	−	0.978864i	$-0.565560\pi$
$857$	−3.48403e24	−0.409021	−0.204510	+	0.978864i	$0.565560\pi$
$858$	−2.82709e23	−0.0328623
$859$	9.45723e24	1.08848	0.544242	−	0.838928i	$-0.316817\pi$
$859$	9.45723e24	1.08848	0.544242	+	0.838928i	$0.316817\pi$
$860$	4.92618e23	0.0561402
$861$	2.33296e23	0.0263257
$862$	7.62599e23	0.0852088
$863$	−1.62477e25	−1.79763	−0.898814	−	0.438329i	$-0.855570\pi$
$863$	−1.62477e25	−1.79763	−0.898814	+	0.438329i	$0.855570\pi$
$864$	1.14180e24	0.125090
$865$	3.16626e24	0.343486
$866$	9.03111e23	0.0970151
$867$	2.98698e23	0.0317739
$868$	−5.11783e24	−0.539098
$869$	6.83236e24	0.712693
$870$	6.80673e22	0.00703113
$871$	1.20629e24	0.123395
$872$	2.66215e24	0.269676
$873$	1.89567e25	1.90170
$874$	−3.04442e23	−0.0302453
$875$	−1.63762e24	−0.161118
$876$	2.96858e23	0.0289243
$877$	2.37177e24	0.228863	0.114432	−	0.993431i	$-0.463495\pi$
$877$	2.37177e24	0.228863	0.114432	+	0.993431i	$0.463495\pi$
$878$	−9.34376e23	−0.0892932
$879$	1.71546e24	0.162359
$880$	2.61551e24	0.245163
$881$	1.35967e25	1.26223	0.631117	−	0.775688i	$-0.282597\pi$
$881$	1.35967e25	1.26223	0.631117	+	0.775688i	$0.282597\pi$
$882$	2.14940e23	0.0197621
$883$	2.88795e24	0.262981	0.131490	−	0.991317i	$-0.458024\pi$
$883$	2.88795e24	0.262981	0.131490	+	0.991317i	$0.458024\pi$
$884$	−1.51608e25	−1.36735
$885$	6.17687e23	0.0551760
$886$	−2.75298e24	−0.243565
$887$	−8.98309e24	−0.787182	−0.393591	−	0.919286i	$-0.628767\pi$
$887$	−8.98309e24	−0.787182	−0.393591	+	0.919286i	$0.628767\pi$
$888$	3.71555e23	0.0322487
$889$	−3.60128e24	−0.309593
$890$	5.56458e23	0.0473824
$891$	1.31730e25	1.11103
$892$	4.24808e24	0.354888
$893$	−6.88269e24	−0.569535
$894$	−3.83211e23	−0.0314101
$895$	−2.89668e24	−0.235183
$896$	2.53088e24	0.203542
$897$	6.54187e23	0.0521154
$898$	5.65742e23	0.0446447
$899$	−2.76669e25	−2.16273
$900$	−1.17695e25	−0.911373
$901$	6.94999e24	0.533118
$902$	−1.01347e24	−0.0770114
$903$	−2.01566e23	−0.0151730
$904$	−2.62697e24	−0.195895
$905$	−1.78689e24	−0.132003
$906$	2.35395e22	0.00172269
$907$	−1.49853e25	−1.08643	−0.543216	−	0.839593i	$-0.682794\pi$
$907$	−1.49853e25	−1.08643	−0.543216	+	0.839593i	$0.682794\pi$
$908$	1.43680e25	1.03197
$909$	−1.89997e25	−1.35193
$910$	−2.10556e23	−0.0148428
$911$	−5.86880e24	−0.409867	−0.204934	−	0.978776i	$-0.565698\pi$
$911$	−5.86880e24	−0.409867	−0.204934	+	0.978776i	$0.565698\pi$
$912$	1.65472e24	0.114490
$913$	1.82316e25	1.24975
$914$	−7.50783e23	−0.0509884
$915$	2.86352e23	0.0192673
$916$	6.07519e24	0.404994
$917$	−6.52181e24	−0.430753
$918$	7.19378e23	0.0470754
$919$	−8.77378e24	−0.568859	−0.284430	−	0.958697i	$-0.591804\pi$
$919$	−8.77378e24	−0.568859	−0.284430	+	0.958697i	$0.591804\pi$
$920$	2.55731e23	0.0164281
$921$	−9.59004e23	−0.0610399
$922$	7.56948e23	0.0477368
$923$	−1.59875e24	−0.0999004
$924$	−1.09303e24	−0.0676740
$925$	−1.16668e25	−0.715723
$926$	−3.56198e24	−0.216520
$927$	2.74770e25	1.65497
$928$	1.02983e25	0.614619
$929$	−2.54460e24	−0.150483	−0.0752413	−	0.997165i	$-0.523973\pi$
$929$	−2.54460e24	−0.150483	−0.0752413	+	0.997165i	$0.523973\pi$
$930$	−1.17535e23	−0.00688750
$931$	1.95811e24	0.113701
$932$	−1.71737e24	−0.0988163
$933$	2.53448e24	0.144509
$934$	−3.95323e24	−0.223359
$935$	5.11805e24	0.286553
$936$	−6.26807e24	−0.347768
$937$	1.37040e24	0.0753462	0.0376731	−	0.999290i	$-0.488005\pi$
$937$	1.37040e24	0.0753462	0.0376731	+	0.999290i	$0.488005\pi$
$938$	−9.54960e22	−0.00520309
$939$	5.38617e24	0.290819
$940$	2.86143e24	0.153107
$941$	−1.89012e25	−1.00226	−0.501128	−	0.865373i	$-0.667081\pi$
$941$	−1.89012e25	−1.00226	−0.501128	+	0.865373i	$0.667081\pi$
$942$	3.31657e23	0.0174284
$943$	2.34516e24	0.122130
$944$	3.00894e25	1.55293
$945$	−4.87935e23	−0.0249569
$946$	8.75629e23	0.0443859
$947$	−5.10941e24	−0.256682	−0.128341	−	0.991730i	$-0.540965\pi$
$947$	−5.10941e24	−0.256682	−0.128341	+	0.991730i	$0.540965\pi$
$948$	−1.79707e24	−0.0894732
$949$	−4.96423e24	−0.244957
$950$	2.19542e24	0.107366
$951$	−1.38680e24	−0.0672172
$952$	2.42499e24	0.116492
$953$	3.72659e25	1.77428	0.887139	−	0.461502i	$-0.152689\pi$
$953$	3.72659e25	1.77428	0.887139	+	0.461502i	$0.152689\pi$
$954$	1.42214e24	0.0671089
$955$	−7.42370e24	−0.347210
$956$	3.63240e25	1.68384
$957$	−5.90892e24	−0.271492
$958$	4.88210e24	0.222331
$959$	1.41560e25	0.638973
$960$	−6.58276e23	−0.0294512
$961$	2.52235e25	1.11855
$962$	−3.07520e24	−0.135171
$963$	−2.23643e25	−0.974389
$964$	−3.16182e25	−1.36547
$965$	−6.50169e24	−0.278320
$966$	−5.17887e22	−0.00219750
$967$	−1.16711e25	−0.490892	−0.245446	−	0.969410i	$-0.578934\pi$
$967$	−1.16711e25	−0.490892	−0.245446	+	0.969410i	$0.578934\pi$
$968$	2.86697e24	0.119532
$969$	3.23797e24	0.133820
$970$	1.47010e24	0.0602266
$971$	−1.65948e25	−0.673922	−0.336961	−	0.941519i	$-0.609399\pi$
$971$	−1.65948e25	−0.673922	−0.336961	+	0.941519i	$0.609399\pi$
$972$	−1.08262e25	−0.435826
$973$	4.61696e24	0.184246
$974$	5.41850e24	0.214352
$975$	−4.71753e24	−0.185001
$976$	1.39490e25	0.542277
$977$	4.73931e25	1.82646	0.913232	−	0.407439i	$-0.133578\pi$
$977$	4.73931e25	1.82646	0.913232	+	0.407439i	$0.133578\pi$
$978$	8.70936e23	0.0332741
$979$	−4.83060e25	−1.82957
$980$	−8.14069e23	−0.0305661
$981$	−2.52274e25	−0.939045
$982$	−6.29166e24	−0.232176
$983$	−2.56899e25	−0.939849	−0.469925	−	0.882707i	$-0.655719\pi$
$983$	−2.56899e25	−0.939849	−0.469925	+	0.882707i	$0.655719\pi$
$984$	5.38589e23	0.0195344
$985$	−1.77456e24	−0.0638093
$986$	6.48830e24	0.231301
$987$	−1.17082e24	−0.0413802
$988$	−2.82618e25	−0.990298
$989$	−2.02620e24	−0.0703903
$990$	1.04728e24	0.0360713
$991$	−2.99102e25	−1.02139	−0.510697	−	0.859760i	$-0.670613\pi$
$991$	−2.99102e25	−1.02139	−0.510697	+	0.859760i	$0.670613\pi$
$992$	−1.77825e25	−0.602064
$993$	−1.47914e24	−0.0496524
$994$	1.26565e23	0.00421241
$995$	−2.89488e24	−0.0955289
$996$	−4.79533e24	−0.156897
$997$	3.62368e25	1.17555	0.587775	−	0.809024i	$-0.300004\pi$
$997$	3.62368e25	1.17555	0.587775	+	0.809024i	$0.300004\pi$
$998$	7.15865e24	0.230262
$999$	−7.12634e24	−0.227279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.18.a.b.1.2	✓	5
3.2	odd	2		63.18.a.e.1.4		5
4.3	odd	2		112.18.a.h.1.3		5
7.6	odd	2		49.18.a.d.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.18.a.b.1.2	✓	5	1.1	even	1	trivial
49.18.a.d.1.2		5	7.6	odd	2
63.18.a.e.1.4		5	3.2	odd	2
112.18.a.h.1.3		5	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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	7.a (trivial)

\(f(q)\)	\(=\)	\(q-51.2830 q^{2} +1738.66 q^{3} -128442. q^{4} +190715. q^{5} -89163.6 q^{6} +5.76480e6 q^{7} +1.33087e7 q^{8} -1.26117e8 q^{9} +O(q^{10})\)	\(q-51.2830 q^{2} +1738.66 q^{3} -128442. q^{4} +190715. q^{5} -89163.6 q^{6} +5.76480e6 q^{7} +1.33087e7 q^{8} -1.26117e8 q^{9} -9.78045e6 q^{10} +8.49040e8 q^{11} -2.23317e8 q^{12} +3.73443e9 q^{13} -2.95637e8 q^{14} +3.31588e8 q^{15} +1.61526e10 q^{16} +3.16076e10 q^{17} +6.46768e9 q^{18} +5.89207e10 q^{19} -2.44958e10 q^{20} +1.00230e10 q^{21} -4.35413e10 q^{22} +1.00754e11 q^{23} +2.31392e10 q^{24} -7.26567e11 q^{25} -1.91513e11 q^{26} -4.43805e11 q^{27} -7.40443e11 q^{28} -4.00282e12 q^{29} -1.70048e10 q^{30} +6.91184e12 q^{31} -2.57275e12 q^{32} +1.47619e12 q^{33} -1.62093e12 q^{34} +1.09943e12 q^{35} +1.61988e13 q^{36} +1.60574e13 q^{37} -3.02163e12 q^{38} +6.49290e12 q^{39} +2.53816e12 q^{40} +2.32760e13 q^{41} -5.14010e11 q^{42} -2.01103e13 q^{43} -1.09052e14 q^{44} -2.40525e13 q^{45} -5.16698e12 q^{46} -1.16813e14 q^{47} +2.80839e13 q^{48} +3.32329e13 q^{49} +3.72606e13 q^{50} +5.49547e13 q^{51} -4.79658e14 q^{52} +2.19884e14 q^{53} +2.27597e13 q^{54} +1.61925e14 q^{55} +7.67218e13 q^{56} +1.02443e14 q^{57} +2.05277e14 q^{58} +1.86281e15 q^{59} -4.25899e13 q^{60} +8.63576e14 q^{61} -3.54460e14 q^{62} -7.27041e14 q^{63} -1.98522e15 q^{64} +7.12213e14 q^{65} -7.57034e13 q^{66} +3.23018e14 q^{67} -4.05974e15 q^{68} +1.75177e14 q^{69} -5.63824e13 q^{70} -4.28112e14 q^{71} -1.67845e15 q^{72} -1.32931e15 q^{73} -8.23470e14 q^{74} -1.26325e15 q^{75} -7.56790e15 q^{76} +4.89455e15 q^{77} -3.32976e14 q^{78} +8.04716e15 q^{79} +3.08055e15 q^{80} +1.55152e16 q^{81} -1.19367e15 q^{82} +2.14732e16 q^{83} -1.28738e15 q^{84} +6.02804e15 q^{85} +1.03132e15 q^{86} -6.95953e15 q^{87} +1.12996e16 q^{88} -5.68949e16 q^{89} +1.23348e15 q^{90} +2.15283e16 q^{91} -1.29411e16 q^{92} +1.20173e16 q^{93} +5.99051e15 q^{94} +1.12371e16 q^{95} -4.47313e15 q^{96} -1.50310e17 q^{97} -1.70429e15 q^{98} -1.07079e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 597 q^{2} - 1770 q^{3} + 534677 q^{4} + 1612824 q^{5} - 14383854 q^{6} + 28824005 q^{7} + 41916039 q^{8} + 552658077 q^{9}+O(q^{10}) \) 5 * q + 597 * q^2 - 1770 * q^3 + 534677 * q^4 + 1612824 * q^5 - 14383854 * q^6 + 28824005 * q^7 + 41916039 * q^8 + 552658077 * q^9	\( 5 q + 597 q^{2} - 1770 q^{3} + 534677 q^{4} + 1612824 q^{5} - 14383854 q^{6} + 28824005 q^{7} + 41916039 q^{8} + 552658077 q^{9} - 345084900 q^{10} + 765945912 q^{11} + 3634044078 q^{12} + 608204548 q^{13} + 3441586197 q^{14} + 41156724744 q^{15} + 116025034769 q^{16} + 8856152334 q^{17} + 90679358061 q^{18} + 18441763546 q^{19} + 784710030552 q^{20} - 10203697770 q^{21} - 140711201256 q^{22} - 218776878696 q^{23} - 3751889532894 q^{24} - 363036196609 q^{25} - 1677859982400 q^{26} - 4021274734668 q^{27} + 3082306504277 q^{28} + 2087156686674 q^{29} - 14802803892720 q^{30} - 12100718234660 q^{31} + 16029734494815 q^{32} + 6151440714912 q^{33} + 19542664353462 q^{34} + 9297609408024 q^{35} + 54957458168325 q^{36} + 16858800794026 q^{37} + 49131784416030 q^{38} + 74225922854496 q^{39} - 17226943156560 q^{40} - 32679617238786 q^{41} - 82920055923054 q^{42} + 2700646991248 q^{43} + 328390888489968 q^{44} - 89554636513368 q^{45} - 934408564817712 q^{46} + 72344569802340 q^{47} - 11\!\cdots\!62 q^{48}+ \cdots - 33\!\cdots\!92 q^{99}+O(q^{100}) \) 5 * q + 597 * q^2 - 1770 * q^3 + 534677 * q^4 + 1612824 * q^5 - 14383854 * q^6 + 28824005 * q^7 + 41916039 * q^8 + 552658077 * q^9 - 345084900 * q^10 + 765945912 * q^11 + 3634044078 * q^12 + 608204548 * q^13 + 3441586197 * q^14 + 41156724744 * q^15 + 116025034769 * q^16 + 8856152334 * q^17 + 90679358061 * q^18 + 18441763546 * q^19 + 784710030552 * q^20 - 10203697770 * q^21 - 140711201256 * q^22 - 218776878696 * q^23 - 3751889532894 * q^24 - 363036196609 * q^25 - 1677859982400 * q^26 - 4021274734668 * q^27 + 3082306504277 * q^28 + 2087156686674 * q^29 - 14802803892720 * q^30 - 12100718234660 * q^31 + 16029734494815 * q^32 + 6151440714912 * q^33 + 19542664353462 * q^34 + 9297609408024 * q^35 + 54957458168325 * q^36 + 16858800794026 * q^37 + 49131784416030 * q^38 + 74225922854496 * q^39 - 17226943156560 * q^40 - 32679617238786 * q^41 - 82920055923054 * q^42 + 2700646991248 * q^43 + 328390888489968 * q^44 - 89554636513368 * q^45 - 934408564817712 * q^46 + 72344569802340 * q^47 - 1114757827879362 * q^48 + 166164652848005 * q^49 - 1206805301442465 * q^50 + 93846313005588 * q^51 + 900407522478772 * q^52 + 1102150036344942 * q^53 + 425408583919932 * q^54 + 1762881466153488 * q^55 + 241637623543239 * q^56 + 2799346250520276 * q^57 + 15137889518826 * q^58 + 164356451065122 * q^59 + 1167267096771552 * q^60 + 3750393534081568 * q^61 - 7616424461183148 * q^62 + 3185963834947677 * q^63 + 6689352066227393 * q^64 + 7529870820155880 * q^65 - 14441400503014176 * q^66 - 3782791201197452 * q^67 - 26670706415203410 * q^68 + 4651070975625744 * q^69 - 1989345776604900 * q^70 - 3894420716406000 * q^71 - 11316579733409625 * q^72 + 5885320144516618 * q^73 + 11592671721146322 * q^74 + 6565928157933906 * q^75 - 25247751597093326 * q^76 + 4415525759443512 * q^77 - 40099299793127064 * q^78 + 43390368978234280 * q^79 + 72123460802732256 * q^80 + 16677438473389329 * q^81 - 12883198921542810 * q^82 + 35056612240074642 * q^83 + 20949540934898478 * q^84 - 72373519639835328 * q^85 + 66904881205136496 * q^86 + 103599288996180588 * q^87 + 110088558971776416 * q^88 - 58289826944373966 * q^89 - 71347471630924500 * q^90 + 3506178186514948 * q^91 - 16491269563372704 * q^92 - 16113403536918888 * q^93 - 85659528801383844 * q^94 - 5872171066415592 * q^95 - 772366271041943550 * q^96 + 47745465198885454 * q^97 + 19840059550051797 * q^98 - 330042831191860392 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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