LMFDB - Embedded newform 7.18.a.b.1.5

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			1.5
Root			$590.967$ 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)

$f(q)$	$=$	$q+709.967 q^{2} -14284.8 q^{3} +372981. q^{4} +630065. q^{5} -1.01417e7 q^{6} +5.76480e6 q^{7} +1.71747e8 q^{8} +7.49154e7 q^{9} +O(q^{10})$	\(q+709.967 q^{2} -14284.8 q^{3} +372981. q^{4} +630065. q^{5} -1.01417e7 q^{6} +5.76480e6 q^{7} +1.71747e8 q^{8} +7.49154e7 q^{9} +4.47325e8 q^{10} +7.22950e8 q^{11} -5.32795e9 q^{12} +1.48742e9 q^{13} +4.09282e9 q^{14} -9.00035e9 q^{15} +7.30473e10 q^{16} -3.31743e10 q^{17} +5.31874e10 q^{18} -5.09821e10 q^{19} +2.35002e11 q^{20} -8.23490e10 q^{21} +5.13270e11 q^{22} -3.22223e11 q^{23} -2.45337e12 q^{24} -3.65958e11 q^{25} +1.05602e12 q^{26} +7.74591e11 q^{27} +2.15016e12 q^{28} -4.72577e11 q^{29} -6.38995e12 q^{30} -6.40997e12 q^{31} +2.93499e13 q^{32} -1.03272e13 q^{33} -2.35526e13 q^{34} +3.63220e12 q^{35} +2.79420e13 q^{36} +7.94268e12 q^{37} -3.61956e13 q^{38} -2.12474e13 q^{39} +1.08212e14 q^{40} +2.30976e13 q^{41} -5.84651e13 q^{42} -3.43975e13 q^{43} +2.69646e14 q^{44} +4.72015e13 q^{45} -2.28767e14 q^{46} -5.66214e13 q^{47} -1.04347e15 q^{48} +3.32329e13 q^{49} -2.59818e14 q^{50} +4.73888e14 q^{51} +5.54777e14 q^{52} +1.72618e14 q^{53} +5.49933e14 q^{54} +4.55505e14 q^{55} +9.90087e14 q^{56} +7.28269e14 q^{57} -3.35514e14 q^{58} -1.00503e15 q^{59} -3.35695e15 q^{60} +2.46577e15 q^{61} -4.55086e15 q^{62} +4.31872e14 q^{63} +1.12630e16 q^{64} +9.37168e14 q^{65} -7.33196e15 q^{66} -9.75664e13 q^{67} -1.23734e16 q^{68} +4.60289e15 q^{69} +2.57874e15 q^{70} -8.90121e15 q^{71} +1.28665e16 q^{72} +5.24669e14 q^{73} +5.63903e15 q^{74} +5.22764e15 q^{75} -1.90153e16 q^{76} +4.16766e15 q^{77} -1.50850e16 q^{78} -8.29088e15 q^{79} +4.60245e16 q^{80} -2.07395e16 q^{81} +1.63985e16 q^{82} +7.79948e15 q^{83} -3.07146e16 q^{84} -2.09019e16 q^{85} -2.44211e16 q^{86} +6.75067e15 q^{87} +1.24164e17 q^{88} +4.84218e16 q^{89} +3.35115e16 q^{90} +8.57465e15 q^{91} -1.20183e17 q^{92} +9.15652e16 q^{93} -4.01993e16 q^{94} -3.21220e16 q^{95} -4.19258e17 q^{96} +1.05703e17 q^{97} +2.35943e16 q^{98} +5.41601e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	709.967	1.96102	0.980512	−	0.196459i	$-0.0629442\pi$
$2$	709.967	1.96102	0.980512	+	0.196459i	$0.0629442\pi$
$3$	−14284.8	−1.25702	−0.628512	−	0.777800i	$-0.716336\pi$
$3$	−14284.8	−1.25702	−0.628512	+	0.777800i	$0.716336\pi$
$4$	372981.	2.84562
$5$	630065.	0.721340	0.360670	−	0.932693i	$-0.382548\pi$
$5$	630065.	0.721340	0.360670	+	0.932693i	$0.382548\pi$
$6$	−1.01417e7	−2.46505
$7$	5.76480e6	0.377964
$7$	5.76480e6	0.377964
$8$	1.71747e8	3.61930
$9$	7.49154e7	0.580109
$10$	4.47325e8	1.41457
$11$	7.22950e8	1.01688	0.508441	−	0.861097i	$-0.330222\pi$
$11$	7.22950e8	1.01688	0.508441	+	0.861097i	$0.330222\pi$
$12$	−5.32795e9	−3.57701
$13$	1.48742e9	0.505724	0.252862	−	0.967502i	$-0.418628\pi$
$13$	1.48742e9	0.505724	0.252862	+	0.967502i	$0.418628\pi$
$14$	4.09282e9	0.741197
$15$	−9.00035e9	−0.906742
$16$	7.30473e10	4.25191
$17$	−3.31743e10	−1.15341	−0.576707	−	0.816951i	$-0.695663\pi$
$17$	−3.31743e10	−1.15341	−0.576707	+	0.816951i	$0.695663\pi$
$18$	5.31874e10	1.13761
$19$	−5.09821e10	−0.688672	−0.344336	−	0.938847i	$-0.611896\pi$
$19$	−5.09821e10	−0.688672	−0.344336	+	0.938847i	$0.611896\pi$
$20$	2.35002e11	2.05266
$21$	−8.23490e10	−0.475110
$22$	5.13270e11	1.99413
$23$	−3.22223e11	−0.857965	−0.428982	−	0.903313i	$-0.641128\pi$
$23$	−3.22223e11	−0.857965	−0.428982	+	0.903313i	$0.641128\pi$
$24$	−2.45337e12	−4.54954
$25$	−3.65958e11	−0.479668
$26$	1.05602e12	0.991737
$27$	7.74591e11	0.527813
$28$	2.15016e12	1.07554
$29$	−4.72577e11	−0.175424	−0.0877122	−	0.996146i	$-0.527956\pi$
$29$	−4.72577e11	−0.175424	−0.0877122	+	0.996146i	$0.527956\pi$
$30$	−6.38995e12	−1.77814
$31$	−6.40997e12	−1.34984	−0.674919	−	0.737892i	$-0.735821\pi$
$31$	−6.40997e12	−1.34984	−0.674919	+	0.737892i	$0.735821\pi$
$32$	2.93499e13	4.71881
$33$	−1.03272e13	−1.27824
$34$	−2.35526e13	−2.26187
$35$	3.63220e12	0.272641
$36$	2.79420e13	1.65077
$37$	7.94268e12	0.371751	0.185876	−	0.982573i	$-0.440488\pi$
$37$	7.94268e12	0.371751	0.185876	+	0.982573i	$0.440488\pi$
$38$	−3.61956e13	−1.35050
$39$	−2.12474e13	−0.635707
$40$	1.08212e14	2.61074
$41$	2.30976e13	0.451755	0.225878	−	0.974156i	$-0.427475\pi$
$41$	2.30976e13	0.451755	0.225878	+	0.974156i	$0.427475\pi$
$42$	−5.84651e13	−0.931703
$43$	−3.43975e13	−0.448792	−0.224396	−	0.974498i	$-0.572041\pi$
$43$	−3.43975e13	−0.448792	−0.224396	+	0.974498i	$0.572041\pi$
$44$	2.69646e14	2.89365
$45$	4.72015e13	0.418456
$46$	−2.28767e14	−1.68249
$47$	−5.66214e13	−0.346856	−0.173428	−	0.984847i	$-0.555484\pi$
$47$	−5.66214e13	−0.346856	−0.173428	+	0.984847i	$0.555484\pi$
$48$	−1.04347e15	−5.34475
$49$	3.32329e13	0.142857
$50$	−2.59818e14	−0.940641
$51$	4.73888e14	1.44987
$52$	5.54777e14	1.43910
$53$	1.72618e14	0.380840	0.190420	−	0.981703i	$-0.439015\pi$
$53$	1.72618e14	0.380840	0.190420	+	0.981703i	$0.439015\pi$
$54$	5.49933e14	1.03505
$55$	4.55505e14	0.733518
$56$	9.90087e14	1.36797
$57$	7.28269e14	0.865677
$58$	−3.35514e14	−0.344011
$59$	−1.00503e15	−0.891123	−0.445562	−	0.895251i	$-0.646996\pi$
$59$	−1.00503e15	−0.891123	−0.445562	+	0.895251i	$0.646996\pi$
$60$	−3.35695e15	−2.58024
$61$	2.46577e15	1.64683	0.823415	−	0.567439i	$-0.192066\pi$
$61$	2.46577e15	1.64683	0.823415	+	0.567439i	$0.192066\pi$
$62$	−4.55086e15	−2.64706
$63$	4.31872e14	0.219261
$64$	1.12630e16	5.00178
$65$	9.37168e14	0.364799
$66$	−7.33196e15	−2.50667
$67$	−9.75664e13	−0.0293538	−0.0146769	−	0.999892i	$-0.504672\pi$
$67$	−9.75664e13	−0.0293538	−0.0146769	+	0.999892i	$0.504672\pi$
$68$	−1.23734e16	−3.28217
$69$	4.60289e15	1.07848
$70$	2.57874e15	0.534655
$71$	−8.90121e15	−1.63589	−0.817943	−	0.575299i	$-0.804886\pi$
$71$	−8.90121e15	−1.63589	−0.817943	+	0.575299i	$0.804886\pi$
$72$	1.28665e16	2.09959
$73$	5.24669e14	0.0761450	0.0380725	−	0.999275i	$-0.487878\pi$
$73$	5.24669e14	0.0761450	0.0380725	+	0.999275i	$0.487878\pi$
$74$	5.63903e15	0.729013
$75$	5.22764e15	0.602955
$76$	−1.90153e16	−1.95969
$77$	4.16766e15	0.384345
$78$	−1.50850e16	−1.24664
$79$	−8.29088e15	−0.614852	−0.307426	−	0.951572i	$-0.599468\pi$
$79$	−8.29088e15	−0.614852	−0.307426	+	0.951572i	$0.599468\pi$
$80$	4.60245e16	3.06707
$81$	−2.07395e16	−1.24358
$82$	1.63985e16	0.885903
$83$	7.79948e15	0.380103	0.190052	−	0.981774i	$-0.439134\pi$
$83$	7.79948e15	0.380103	0.190052	+	0.981774i	$0.439134\pi$
$84$	−3.07146e16	−1.35198
$85$	−2.09019e16	−0.832004
$86$	−2.44211e16	−0.880091
$87$	6.75067e15	0.220513
$88$	1.24164e17	3.68040
$89$	4.84218e16	1.30384	0.651922	−	0.758286i	$-0.273963\pi$
$89$	4.84218e16	1.30384	0.651922	+	0.758286i	$0.273963\pi$
$90$	3.35115e16	0.820602
$91$	8.57465e15	0.191146
$92$	−1.20183e17	−2.44144
$93$	9.15652e16	1.69678
$94$	−4.01993e16	−0.680192
$95$	−3.21220e16	−0.496766
$96$	−4.19258e17	−5.93165
$97$	1.05703e17	1.36939	0.684697	−	0.728828i	$-0.259934\pi$
$97$	1.05703e17	1.36939	0.684697	+	0.728828i	$0.259934\pi$
$98$	2.35943e16	0.280146
$99$	5.41601e16	0.589902
$100$	−1.36495e17	−1.36495
$101$	−7.59274e16	−0.697697	−0.348848	−	0.937179i	$-0.613427\pi$
$101$	−7.59274e16	−0.697697	−0.348848	+	0.937179i	$0.613427\pi$
$102$	3.36444e17	2.84323
$103$	−1.86923e17	−1.45394	−0.726969	−	0.686670i	$-0.759072\pi$
$103$	−1.86923e17	−1.45394	−0.726969	+	0.686670i	$0.759072\pi$
$104$	2.55459e17	1.83037
$105$	−5.18852e16	−0.342716
$106$	1.22553e17	0.746835
$107$	−2.29258e17	−1.28992	−0.644960	−	0.764216i	$-0.723126\pi$
$107$	−2.29258e17	−1.28992	−0.644960	+	0.764216i	$0.723126\pi$
$108$	2.88907e17	1.50195
$109$	−1.36281e17	−0.655104	−0.327552	−	0.944833i	$-0.606224\pi$
$109$	−1.36281e17	−0.655104	−0.327552	+	0.944833i	$0.606224\pi$
$110$	3.23393e17	1.43845
$111$	−1.13460e17	−0.467300
$112$	4.21103e17	1.60707
$113$	−1.81639e16	−0.0642749	−0.0321375	−	0.999483i	$-0.510231\pi$
$113$	−1.81639e16	−0.0642749	−0.0321375	+	0.999483i	$0.510231\pi$
$114$	5.17047e17	1.69761
$115$	−2.03021e17	−0.618884
$116$	−1.76262e17	−0.499190
$117$	1.11430e17	0.293375
$118$	−7.13539e17	−1.74751
$119$	−1.91243e17	−0.435950
$120$	−1.54578e18	−3.28177
$121$	1.72096e16	0.0340483
$122$	1.75061e18	3.22947
$123$	−3.29944e17	−0.567867
$124$	−2.39079e18	−3.84112
$125$	−7.11278e17	−1.06734
$126$	3.06615e17	0.429975
$127$	1.35375e18	1.77503	0.887516	−	0.460777i	$-0.152429\pi$
$127$	1.35375e18	1.77503	0.887516	+	0.460777i	$0.152429\pi$
$128$	4.14941e18	5.08980
$129$	4.91361e17	0.564142
$130$	6.65358e17	0.715380
$131$	1.30520e17	0.131483	0.0657416	−	0.997837i	$-0.479059\pi$
$131$	1.30520e17	0.131483	0.0657416	+	0.997837i	$0.479059\pi$
$132$	−3.85184e18	−3.63739
$133$	−2.93902e17	−0.260293
$134$	−6.92689e16	−0.0575635
$135$	4.88042e17	0.380733
$136$	−5.69758e18	−4.17455
$137$	−2.94066e17	−0.202451	−0.101226	−	0.994863i	$-0.532276\pi$
$137$	−2.94066e17	−0.202451	−0.101226	+	0.994863i	$0.532276\pi$
$138$	3.26790e18	2.11493
$139$	2.18982e18	1.33286	0.666428	−	0.745570i	$-0.267823\pi$
$139$	2.18982e18	1.33286	0.666428	+	0.745570i	$0.267823\pi$
$140$	1.35474e18	0.775831
$141$	8.08825e17	0.436006
$142$	−6.31956e18	−3.20801
$143$	1.07533e18	0.514262
$144$	5.47236e18	2.46657
$145$	−2.97754e17	−0.126541
$146$	3.72498e17	0.149322
$147$	−4.74726e17	−0.179575
$148$	2.96246e18	1.05786
$149$	4.03478e18	1.36062	0.680309	−	0.732925i	$-0.261845\pi$
$149$	4.03478e18	1.36062	0.680309	+	0.732925i	$0.261845\pi$
$150$	3.71145e18	1.18241
$151$	2.50978e18	0.755668	0.377834	−	0.925873i	$-0.376669\pi$
$151$	2.50978e18	0.755668	0.377834	+	0.925873i	$0.376669\pi$
$152$	−8.75602e18	−2.49251
$153$	−2.48526e18	−0.669106
$154$	2.95890e18	0.753710
$155$	−4.03870e18	−0.973692
$156$	−7.92488e18	−1.80898
$157$	−2.69655e18	−0.582990	−0.291495	−	0.956572i	$-0.594153\pi$
$157$	−2.69655e18	−0.582990	−0.291495	+	0.956572i	$0.594153\pi$
$158$	−5.88625e18	−1.20574
$159$	−2.46582e18	−0.478724
$160$	1.84923e19	3.40386
$161$	−1.85755e18	−0.324280
$162$	−1.47243e19	−2.43870
$163$	8.26378e18	1.29892	0.649462	−	0.760394i	$-0.274994\pi$
$163$	8.26378e18	1.29892	0.649462	+	0.760394i	$0.274994\pi$
$164$	8.61494e18	1.28552
$165$	−6.50680e18	−0.922049
$166$	5.53737e18	0.745392
$167$	5.73008e18	0.732944	0.366472	−	0.930429i	$-0.380566\pi$
$167$	5.73008e18	0.732944	0.366472	+	0.930429i	$0.380566\pi$
$168$	−1.41432e19	−1.71957
$169$	−6.43801e18	−0.744243
$170$	−1.48397e19	−1.63158
$171$	−3.81934e18	−0.399505
$172$	−1.28296e19	−1.27709
$173$	1.19443e19	1.13180	0.565898	−	0.824475i	$-0.308530\pi$
$173$	1.19443e19	1.13180	0.565898	+	0.824475i	$0.308530\pi$
$174$	4.79275e18	0.432431
$175$	−2.10967e18	−0.181298
$176$	5.28095e19	4.32369
$177$	1.43567e19	1.12016
$178$	3.43778e19	2.55687
$179$	−1.66578e19	−1.18132	−0.590659	−	0.806922i	$-0.701132\pi$
$179$	−1.66578e19	−1.18132	−0.590659	+	0.806922i	$0.701132\pi$
$180$	1.76052e19	1.19076
$181$	3.00438e18	0.193859	0.0969297	−	0.995291i	$-0.469098\pi$
$181$	3.00438e18	0.193859	0.0969297	+	0.995291i	$0.469098\pi$
$182$	6.08772e18	0.374841
$183$	−3.52230e19	−2.07011
$184$	−5.53408e19	−3.10523
$185$	5.00440e18	0.268159
$186$	6.50082e19	3.32742
$187$	−2.39833e19	−1.17289
$188$	−2.11187e19	−0.987018
$189$	4.46536e18	0.199495
$190$	−2.28056e19	−0.974171
$191$	3.04433e18	0.124368	0.0621840	−	0.998065i	$-0.480193\pi$
$191$	3.04433e18	0.124368	0.0621840	+	0.998065i	$0.480193\pi$
$192$	−1.60890e20	−6.28736
$193$	9.84749e17	0.0368204	0.0184102	−	0.999831i	$-0.494140\pi$
$193$	9.84749e17	0.0368204	0.0184102	+	0.999831i	$0.494140\pi$
$194$	7.50458e19	2.68542
$195$	−1.33873e19	−0.458561
$196$	1.23952e19	0.406517
$197$	4.77172e19	1.49869	0.749345	−	0.662180i	$-0.230368\pi$
$197$	4.77172e19	1.49869	0.749345	+	0.662180i	$0.230368\pi$
$198$	3.84518e19	1.15681
$199$	5.07041e19	1.46148	0.730739	−	0.682657i	$-0.239176\pi$
$199$	5.07041e19	1.46148	0.730739	+	0.682657i	$0.239176\pi$
$200$	−6.28522e19	−1.73606
$201$	1.39372e18	0.0368984
$202$	−5.39059e19	−1.36820
$203$	−2.72432e18	−0.0663042
$204$	1.76751e20	4.12577
$205$	1.45530e19	0.325869
$206$	−1.32709e20	−2.85121
$207$	−2.41394e19	−0.497713
$208$	1.08652e20	2.15029
$209$	−3.68575e19	−0.700297
$210$	−3.68368e19	−0.672075
$211$	−7.04312e19	−1.23414	−0.617069	−	0.786909i	$-0.711680\pi$
$211$	−7.04312e19	−1.23414	−0.617069	+	0.786909i	$0.711680\pi$
$212$	6.43833e19	1.08372
$213$	1.27152e20	2.05635
$214$	−1.62766e20	−2.52956
$215$	−2.16726e19	−0.323731
$216$	1.33034e20	1.91031
$217$	−3.69522e19	−0.510191
$218$	−9.67550e19	−1.28468
$219$	−7.49479e18	−0.0957160
$220$	1.69895e20	2.08731
$221$	−4.93439e19	−0.583310
$222$	−8.05525e19	−0.916386
$223$	−1.46142e20	−1.60023	−0.800117	−	0.599845i	$-0.795229\pi$
$223$	−1.46142e20	−1.60023	−0.800117	+	0.599845i	$0.795229\pi$
$224$	1.69196e20	1.78354
$225$	−2.74159e19	−0.278260
$226$	−1.28957e19	−0.126045
$227$	1.36654e20	1.28648	0.643241	−	0.765663i	$-0.277589\pi$
$227$	1.36654e20	1.28648	0.643241	+	0.765663i	$0.277589\pi$
$228$	2.71630e20	2.46338
$229$	2.12650e19	0.185807	0.0929037	−	0.995675i	$-0.470385\pi$
$229$	2.12650e19	0.185807	0.0929037	+	0.995675i	$0.470385\pi$
$230$	−1.44138e20	−1.21365
$231$	−5.95342e19	−0.483131
$232$	−8.11637e19	−0.634913
$233$	1.12022e20	0.844849	0.422424	−	0.906398i	$-0.361179\pi$
$233$	1.12022e20	0.844849	0.422424	+	0.906398i	$0.361179\pi$
$234$	7.91117e19	0.575316
$235$	−3.56751e19	−0.250201
$236$	−3.74857e20	−2.53579
$237$	1.18434e20	0.772883
$238$	−1.35776e20	−0.854908
$239$	1.13315e20	0.688502	0.344251	−	0.938878i	$-0.388133\pi$
$239$	1.13315e20	0.688502	0.344251	+	0.938878i	$0.388133\pi$
$240$	−6.57451e20	−3.85539
$241$	7.40991e19	0.419439	0.209719	−	0.977762i	$-0.432745\pi$
$241$	7.40991e19	0.419439	0.209719	+	0.977762i	$0.432745\pi$
$242$	1.22182e19	0.0667695
$243$	1.96228e20	1.03540
$244$	9.19684e20	4.68625
$245$	2.09389e19	0.103049
$246$	−2.34249e20	−1.11360
$247$	−7.58316e19	−0.348278
$248$	−1.10089e21	−4.88546
$249$	−1.11414e20	−0.477799
$250$	−5.04984e20	−2.09309
$251$	−2.65281e20	−1.06287	−0.531434	−	0.847100i	$-0.678347\pi$
$251$	−2.65281e20	−1.06287	−0.531434	+	0.847100i	$0.678347\pi$
$252$	1.61080e20	0.623931
$253$	−2.32951e20	−0.872449
$254$	9.61116e20	3.48088
$255$	2.98580e20	1.04585
$256$	1.46967e21	4.97945
$257$	5.76755e20	1.89043	0.945213	−	0.326454i	$-0.105854\pi$
$257$	5.76755e20	1.89043	0.945213	+	0.326454i	$0.105854\pi$
$258$	3.48850e20	1.10630
$259$	4.57879e19	0.140509
$260$	3.49545e20	1.03808
$261$	−3.54033e19	−0.101765
$262$	9.26646e19	0.257842
$263$	2.60632e19	0.0702109	0.0351054	−	0.999384i	$-0.488823\pi$
$263$	2.60632e19	0.0702109	0.0351054	+	0.999384i	$0.488823\pi$
$264$	−1.77366e21	−4.62635
$265$	1.08761e20	0.274715
$266$	−2.08660e20	−0.510442
$267$	−6.91695e20	−1.63896
$268$	−3.63904e19	−0.0835296
$269$	6.85000e20	1.52334	0.761668	−	0.647967i	$-0.224381\pi$
$269$	6.85000e20	1.52334	0.761668	+	0.647967i	$0.224381\pi$
$270$	3.46494e20	0.746626
$271$	5.20567e19	0.108702	0.0543510	−	0.998522i	$-0.482691\pi$
$271$	5.20567e19	0.108702	0.0543510	+	0.998522i	$0.482691\pi$
$272$	−2.42329e21	−4.90422
$273$	−1.22487e20	−0.240275
$274$	−2.08777e20	−0.397012
$275$	−2.64569e20	−0.487766
$276$	1.71679e21	3.06895
$277$	−1.96473e20	−0.340585	−0.170292	−	0.985394i	$-0.554471\pi$
$277$	−1.96473e20	−0.340585	−0.170292	+	0.985394i	$0.554471\pi$
$278$	1.55470e21	2.61376
$279$	−4.80205e20	−0.783053
$280$	6.23819e20	0.986768
$281$	−6.64712e20	−1.02007	−0.510035	−	0.860154i	$-0.670367\pi$
$281$	−6.64712e20	−1.02007	−0.510035	+	0.860154i	$0.670367\pi$
$282$	5.74239e20	0.855018
$283$	−1.02256e21	−1.47743	−0.738713	−	0.674020i	$-0.764566\pi$
$283$	−1.02256e21	−1.47743	−0.738713	+	0.674020i	$0.764566\pi$
$284$	−3.31998e21	−4.65510
$285$	4.58857e20	0.624447
$286$	7.63446e20	1.00848
$287$	1.33153e20	0.170747
$288$	2.19876e21	2.73742
$289$	2.73292e20	0.330366
$290$	−2.11396e20	−0.248149
$291$	−1.50995e21	−1.72136
$292$	1.95691e20	0.216679
$293$	−8.21442e20	−0.883491	−0.441745	−	0.897140i	$-0.645641\pi$
$293$	−8.21442e20	−0.883491	−0.441745	+	0.897140i	$0.645641\pi$
$294$	−3.37039e20	−0.352151
$295$	−6.33235e20	−0.642803
$296$	1.36413e21	1.34548
$297$	5.59990e20	0.536723
$298$	2.86456e21	2.66821
$299$	−4.79279e20	−0.433894
$300$	1.94981e21	1.71578
$301$	−1.98295e20	−0.169627
$302$	1.78186e21	1.48188
$303$	1.08461e21	0.877022
$304$	−3.72410e21	−2.92817
$305$	1.55359e21	1.18793
$306$	−1.76445e21	−1.31213
$307$	−8.05962e20	−0.582960	−0.291480	−	0.956577i	$-0.594148\pi$
$307$	−8.05962e20	−0.582960	−0.291480	+	0.956577i	$0.594148\pi$
$308$	1.55446e21	1.09370
$309$	2.67015e21	1.82763
$310$	−2.86734e21	−1.90943
$311$	4.89401e20	0.317104	0.158552	−	0.987351i	$-0.449317\pi$
$311$	4.89401e20	0.317104	0.158552	+	0.987351i	$0.449317\pi$
$312$	−3.64918e21	−2.30081
$313$	−1.90315e21	−1.16774	−0.583869	−	0.811848i	$-0.698462\pi$
$313$	−1.90315e21	−1.16774	−0.583869	+	0.811848i	$0.698462\pi$
$314$	−1.91446e21	−1.14326
$315$	2.72107e20	0.158161
$316$	−3.09234e21	−1.74963
$317$	2.77933e21	1.53086	0.765431	−	0.643518i	$-0.222526\pi$
$317$	2.77933e21	1.53086	0.765431	+	0.643518i	$0.222526\pi$
$318$	−1.75065e21	−0.938790
$319$	−3.41650e20	−0.178386
$320$	7.09642e21	3.60798
$321$	3.27491e21	1.62146
$322$	−1.31880e21	−0.635921
$323$	1.69129e21	0.794324
$324$	−7.73541e21	−3.53876
$325$	−5.44331e20	−0.242580
$326$	5.86700e21	2.54722
$327$	1.94675e21	0.823482
$328$	3.96694e21	1.63504
$329$	−3.26411e20	−0.131099
$330$	−4.61961e21	−1.80816
$331$	−4.61116e21	−1.75902	−0.879512	−	0.475876i	$-0.842131\pi$
$331$	−4.61116e21	−1.75902	−0.879512	+	0.475876i	$0.842131\pi$
$332$	2.90905e21	1.08163
$333$	5.95028e20	0.215656
$334$	4.06816e21	1.43732
$335$	−6.14731e19	−0.0211741
$336$	−6.01537e21	−2.02013
$337$	4.16154e21	1.36270	0.681349	−	0.731958i	$-0.261393\pi$
$337$	4.16154e21	1.36270	0.681349	+	0.731958i	$0.261393\pi$
$338$	−4.57077e21	−1.45948
$339$	2.59467e20	0.0807951
$340$	−7.79601e21	−2.36756
$341$	−4.63409e21	−1.37263
$342$	−2.71161e21	−0.783438
$343$	1.91581e20	0.0539949
$344$	−5.90766e21	−1.62431
$345$	2.90012e21	0.777952
$346$	8.48004e21	2.21948
$347$	2.14002e20	0.0546534	0.0273267	−	0.999627i	$-0.491301\pi$
$347$	2.14002e20	0.0546534	0.0273267	+	0.999627i	$0.491301\pi$
$348$	2.51787e21	0.627494
$349$	−4.24495e21	−1.03242	−0.516210	−	0.856462i	$-0.672658\pi$
$349$	−4.24495e21	−1.03242	−0.516210	+	0.856462i	$0.672658\pi$
$350$	−1.49780e21	−0.355529
$351$	1.15214e21	0.266928
$352$	2.12185e22	4.79847
$353$	−6.49615e21	−1.43407	−0.717036	−	0.697036i	$-0.754502\pi$
$353$	−6.49615e21	−1.43407	−0.717036	+	0.697036i	$0.754502\pi$
$354$	1.01928e22	2.19667
$355$	−5.60834e21	−1.18003
$356$	1.80604e22	3.71024
$357$	2.73187e21	0.547999
$358$	−1.18265e22	−2.31659
$359$	2.32807e21	0.445342	0.222671	−	0.974894i	$-0.428522\pi$
$359$	2.32807e21	0.445342	0.222671	+	0.974894i	$0.428522\pi$
$360$	8.10672e21	1.51452
$361$	−2.88121e21	−0.525731
$362$	2.13301e21	0.380163
$363$	−2.45836e20	−0.0427995
$364$	3.19818e21	0.543927
$365$	3.30575e20	0.0549264
$366$	−2.50072e22	−4.05953
$367$	−6.28606e21	−0.997050	−0.498525	−	0.866875i	$-0.666125\pi$
$367$	−6.28606e21	−0.997050	−0.498525	+	0.866875i	$0.666125\pi$
$368$	−2.35375e22	−3.64799
$369$	1.73036e21	0.262067
$370$	3.55296e21	0.525866
$371$	9.95110e20	0.143944
$372$	3.41520e22	4.82838
$373$	2.77515e21	0.383496	0.191748	−	0.981444i	$-0.438584\pi$
$373$	2.77515e21	0.383496	0.191748	+	0.981444i	$0.438584\pi$
$374$	−1.70274e22	−2.30006
$375$	1.01605e22	1.34168
$376$	−9.72455e21	−1.25537
$377$	−7.02919e20	−0.0887164
$378$	3.17026e21	0.391214
$379$	1.36150e21	0.164280	0.0821402	−	0.996621i	$-0.473824\pi$
$379$	1.36150e21	0.164280	0.0821402	+	0.996621i	$0.473824\pi$
$380$	−1.19809e22	−1.41361
$381$	−1.93380e22	−2.23126
$382$	2.16138e21	0.243889
$383$	1.77336e22	1.95708	0.978539	−	0.206063i	$-0.0660652\pi$
$383$	1.77336e22	1.95708	0.978539	+	0.206063i	$0.0660652\pi$
$384$	−5.92734e22	−6.39801
$385$	2.62590e21	0.277244
$386$	6.99139e20	0.0722056
$387$	−2.57690e21	−0.260348
$388$	3.94252e22	3.89677
$389$	7.42340e20	0.0717846	0.0358923	−	0.999356i	$-0.488573\pi$
$389$	7.42340e20	0.0717846	0.0358923	+	0.999356i	$0.488573\pi$
$390$	−9.50450e21	−0.899250
$391$	1.06895e22	0.989589
$392$	5.70765e21	0.517042
$393$	−1.86445e21	−0.165277
$394$	3.38776e22	2.93897
$395$	−5.22379e21	−0.443517
$396$	2.02006e22	1.67863
$397$	−2.68397e21	−0.218302	−0.109151	−	0.994025i	$-0.534813\pi$
$397$	−2.68397e21	−0.218302	−0.109151	+	0.994025i	$0.534813\pi$
$398$	3.59982e22	2.86599
$399$	4.19833e21	0.327195
$400$	−2.67322e22	−2.03951
$401$	−2.24316e21	−0.167546	−0.0837728	−	0.996485i	$-0.526697\pi$
$401$	−2.24316e21	−0.167546	−0.0837728	+	0.996485i	$0.526697\pi$
$402$	9.89492e20	0.0723587
$403$	−9.53429e21	−0.682646
$404$	−2.83194e22	−1.98538
$405$	−1.30672e22	−0.897046
$406$	−1.93417e21	−0.130024
$407$	5.74216e21	0.378027
$408$	8.13888e22	5.24751
$409$	−8.51192e21	−0.537501	−0.268751	−	0.963210i	$-0.586611\pi$
$409$	−8.51192e21	−0.537501	−0.268751	+	0.963210i	$0.586611\pi$
$410$	1.03321e22	0.639037
$411$	4.20068e21	0.254486
$412$	−6.97186e22	−4.13735
$413$	−5.79381e21	−0.336813
$414$	−1.71382e22	−0.976027
$415$	4.91417e21	0.274184
$416$	4.36555e22	2.38641
$417$	−3.12812e22	−1.67543
$418$	−2.61676e22	−1.37330
$419$	−9.96885e21	−0.512656	−0.256328	−	0.966590i	$-0.582513\pi$
$419$	−9.96885e21	−0.512656	−0.256328	+	0.966590i	$0.582513\pi$
$420$	−1.93522e22	−0.975238
$421$	3.03130e22	1.49703	0.748517	−	0.663116i	$-0.230766\pi$
$421$	3.03130e22	1.49703	0.748517	+	0.663116i	$0.230766\pi$
$422$	−5.00038e22	−2.42018
$423$	−4.24181e21	−0.201214
$424$	2.96467e22	1.37837
$425$	1.21404e22	0.553257
$426$	9.02737e22	4.03255
$427$	1.42147e22	0.622444
$428$	−8.55089e22	−3.67062
$429$	−1.53608e22	−0.646439
$430$	−1.53868e22	−0.634845
$431$	3.91151e22	1.58229	0.791147	−	0.611626i	$-0.209484\pi$
$431$	3.91151e22	1.58229	0.791147	+	0.611626i	$0.209484\pi$
$432$	5.65817e22	2.24422
$433$	−1.26347e22	−0.491380	−0.245690	−	0.969349i	$-0.579014\pi$
$433$	−1.26347e22	−0.491380	−0.245690	+	0.969349i	$0.579014\pi$
$434$	−2.62348e22	−1.00050
$435$	4.25336e21	0.159065
$436$	−5.08302e22	−1.86418
$437$	1.64276e22	0.590856
$438$	−5.32105e21	−0.187701
$439$	7.31786e21	0.253184	0.126592	−	0.991955i	$-0.459596\pi$
$439$	7.31786e21	0.253184	0.126592	+	0.991955i	$0.459596\pi$
$440$	7.82316e22	2.65482
$441$	2.48966e21	0.0828727
$442$	−3.50325e22	−1.14388
$443$	−1.89320e22	−0.606407	−0.303203	−	0.952926i	$-0.598056\pi$
$443$	−1.89320e22	−0.606407	−0.303203	+	0.952926i	$0.598056\pi$
$444$	−4.23182e22	−1.32976
$445$	3.05088e22	0.940515
$446$	−1.03756e23	−3.13810
$447$	−5.76360e22	−1.71033
$448$	6.49290e22	1.89050
$449$	2.66778e22	0.762178	0.381089	−	0.924538i	$-0.375549\pi$
$449$	2.66778e22	0.762178	0.381089	+	0.924538i	$0.375549\pi$
$450$	−1.94644e22	−0.545674
$451$	1.66984e22	0.459382
$452$	−6.77477e21	−0.182902
$453$	−3.58516e22	−0.949892
$454$	9.70201e22	2.52282
$455$	5.40259e21	0.137881
$456$	1.25078e23	3.13314
$457$	−7.67130e21	−0.188617	−0.0943086	−	0.995543i	$-0.530064\pi$
$457$	−7.67130e21	−0.188617	−0.0943086	+	0.995543i	$0.530064\pi$
$458$	1.50974e22	0.364373
$459$	−2.56965e22	−0.608787
$460$	−7.57229e22	−1.76111
$461$	−2.54300e22	−0.580614	−0.290307	−	0.956934i	$-0.593757\pi$
$461$	−2.54300e22	−0.580614	−0.290307	+	0.956934i	$0.593757\pi$
$462$	−4.22673e22	−0.947432
$463$	1.48523e22	0.326856	0.163428	−	0.986555i	$-0.447745\pi$
$463$	1.48523e22	0.326856	0.163428	+	0.986555i	$0.447745\pi$
$464$	−3.45205e22	−0.745889
$465$	5.76920e22	1.22395
$466$	7.95320e22	1.65677
$467$	5.33564e22	1.09142	0.545711	−	0.837973i	$-0.316259\pi$
$467$	5.33564e22	1.09142	0.545711	+	0.837973i	$0.316259\pi$
$468$	4.15613e22	0.834833
$469$	−5.62451e20	−0.0110947
$470$	−2.53282e22	−0.490650
$471$	3.85197e22	0.732833
$472$	−1.72611e23	−3.22524
$473$	−2.48677e22	−0.456368
$474$	8.40839e22	1.51564
$475$	1.86573e22	0.330334
$476$	−7.13299e22	−1.24055
$477$	1.29318e22	0.220928
$478$	8.04498e22	1.35017
$479$	1.10027e22	0.181405	0.0907023	−	0.995878i	$-0.471089\pi$
$479$	1.10027e22	0.181405	0.0907023	+	0.995878i	$0.471089\pi$
$480$	−2.64159e23	−4.27874
$481$	1.18141e22	0.188004
$482$	5.26079e22	0.822529
$483$	2.65347e22	0.407628
$484$	6.41884e21	0.0968883
$485$	6.65999e22	0.987799
$486$	1.39315e23	2.03044
$487$	−8.13910e22	−1.16568	−0.582841	−	0.812586i	$-0.698059\pi$
$487$	−8.13910e22	−1.16568	−0.582841	+	0.812586i	$0.698059\pi$
$488$	4.23489e23	5.96037
$489$	−1.18046e23	−1.63278
$490$	1.48659e22	0.202081
$491$	−6.42302e22	−0.858118	−0.429059	−	0.903277i	$-0.641155\pi$
$491$	−6.42302e22	−0.858118	−0.429059	+	0.903277i	$0.641155\pi$
$492$	−1.23063e23	−1.61593
$493$	1.56774e22	0.202337
$494$	−5.38379e22	−0.682981
$495$	3.41243e22	0.425520
$496$	−4.68231e23	−5.73939
$497$	−5.13137e22	−0.618307
$498$	−7.91002e22	−0.936975
$499$	1.62074e23	1.88738	0.943689	−	0.330834i	$-0.107330\pi$
$499$	1.62074e23	1.88738	0.943689	+	0.330834i	$0.107330\pi$
$500$	−2.65293e23	−3.03725
$501$	−8.18530e22	−0.921328
$502$	−1.88341e23	−2.08431
$503$	−2.37847e22	−0.258803	−0.129401	−	0.991592i	$-0.541306\pi$
$503$	−2.37847e22	−0.258803	−0.129401	+	0.991592i	$0.541306\pi$
$504$	7.41727e22	0.793569
$505$	−4.78392e22	−0.503277
$506$	−1.65387e23	−1.71089
$507$	9.19657e22	0.935531
$508$	5.04922e23	5.05106
$509$	−1.28429e23	−1.26346	−0.631729	−	0.775190i	$-0.717654\pi$
$509$	−1.28429e23	−1.26346	−0.631729	+	0.775190i	$0.717654\pi$
$510$	2.11982e23	2.05094
$511$	3.02461e21	0.0287801
$512$	4.99549e23	4.67502
$513$	−3.94903e22	−0.363490
$514$	4.09477e23	3.70717
$515$	−1.17773e23	−1.04878
$516$	1.83268e23	1.60533
$517$	−4.09344e22	−0.352711
$518$	3.25079e22	0.275541
$519$	−1.70622e23	−1.42269
$520$	1.60956e23	1.32032
$521$	−1.16525e23	−0.940368	−0.470184	−	0.882568i	$-0.655813\pi$
$521$	−1.16525e23	−0.940368	−0.470184	+	0.882568i	$0.655813\pi$
$522$	−2.51352e22	−0.199564
$523$	7.65701e22	0.598129	0.299064	−	0.954233i	$-0.403325\pi$
$523$	7.65701e22	0.598129	0.299064	+	0.954233i	$0.403325\pi$
$524$	4.86813e22	0.374150
$525$	3.01363e22	0.227895
$526$	1.85040e22	0.137685
$527$	2.12646e23	1.55692
$528$	−7.54374e23	−5.43498
$529$	−3.72226e22	−0.263897
$530$	7.72165e22	0.538722
$531$	−7.52923e22	−0.516949
$532$	−1.09620e23	−0.740695
$533$	3.43557e22	0.228464
$534$	−4.91081e23	−3.21405
$535$	−1.44448e23	−0.930471
$536$	−1.67567e22	−0.106240
$537$	2.37953e23	1.48494
$538$	4.86327e23	2.98730
$539$	2.40257e22	0.145269
$540$	1.82030e23	1.08342
$541$	8.07011e22	0.472827	0.236414	−	0.971653i	$-0.424028\pi$
$541$	8.07011e22	0.472827	0.236414	+	0.971653i	$0.424028\pi$
$542$	3.69585e22	0.213167
$543$	−4.29170e22	−0.243686
$544$	−9.73662e23	−5.44274
$545$	−8.58659e22	−0.472553
$546$	−8.69618e22	−0.471185
$547$	−1.24574e23	−0.664562	−0.332281	−	0.943180i	$-0.607818\pi$
$547$	−1.24574e23	−0.664562	−0.332281	+	0.943180i	$0.607818\pi$
$548$	−1.09681e23	−0.576099
$549$	1.84724e23	0.955341
$550$	−1.87835e23	−0.956521
$551$	2.40930e22	0.120810
$552$	7.90532e23	3.90335
$553$	−4.77953e22	−0.232392
$554$	−1.39489e23	−0.667895
$555$	−7.14869e22	−0.337082
$556$	8.16761e23	3.79279
$557$	2.04647e23	0.935913	0.467956	−	0.883752i	$-0.344990\pi$
$557$	2.04647e23	0.935913	0.467956	+	0.883752i	$0.344990\pi$
$558$	−3.40930e23	−1.53559
$559$	−5.11633e22	−0.226965
$560$	2.65322e23	1.15925
$561$	3.42597e23	1.47435
$562$	−4.71923e23	−2.00038
$563$	1.04731e23	0.437274	0.218637	−	0.975806i	$-0.429839\pi$
$563$	1.04731e23	0.437274	0.218637	+	0.975806i	$0.429839\pi$
$564$	3.01676e23	1.24070
$565$	−1.14444e22	−0.0463641
$566$	−7.25986e23	−2.89727
$567$	−1.19559e23	−0.470030
$568$	−1.52876e24	−5.92076
$569$	4.16867e23	1.59053	0.795267	−	0.606259i	$-0.207331\pi$
$569$	4.16867e23	1.59053	0.795267	+	0.606259i	$0.207331\pi$
$570$	3.25773e23	1.22456
$571$	−8.38779e22	−0.310628	−0.155314	−	0.987865i	$-0.549639\pi$
$571$	−8.38779e22	−0.310628	−0.155314	+	0.987865i	$0.549639\pi$
$572$	4.01076e23	1.46339
$573$	−4.34877e22	−0.156334
$574$	9.45340e22	0.334840
$575$	1.17920e23	0.411539
$576$	8.43772e23	2.90158
$577$	5.09505e23	1.72645	0.863225	−	0.504820i	$-0.168441\pi$
$577$	5.09505e23	1.72645	0.863225	+	0.504820i	$0.168441\pi$
$578$	1.94028e23	0.647855
$579$	−1.40669e22	−0.0462841
$580$	−1.11057e23	−0.360086
$581$	4.49624e22	0.143666
$582$	−1.07201e24	−3.37563
$583$	1.24794e23	0.387269
$584$	9.01103e22	0.275591
$585$	7.02083e22	0.211623
$586$	−5.83196e23	−1.73255
$587$	3.95882e23	1.15915	0.579577	−	0.814917i	$-0.303218\pi$
$587$	3.95882e23	1.15915	0.579577	+	0.814917i	$0.303218\pi$
$588$	−1.77063e23	−0.511001
$589$	3.26794e23	0.929595
$590$	−4.49576e23	−1.26055
$591$	−6.81630e23	−1.88389
$592$	5.80191e23	1.58065
$593$	−7.92627e22	−0.212865	−0.106432	−	0.994320i	$-0.533943\pi$
$593$	−7.92627e22	−0.212865	−0.106432	+	0.994320i	$0.533943\pi$
$594$	3.97574e23	1.05253
$595$	−1.20495e23	−0.314468
$596$	1.50489e24	3.87180
$597$	−7.24298e23	−1.83711
$598$	−3.40272e23	−0.850876
$599$	−6.44290e23	−1.58838	−0.794188	−	0.607672i	$-0.792104\pi$
$599$	−6.44290e23	−1.58838	−0.794188	+	0.607672i	$0.792104\pi$
$600$	8.97831e23	2.18227
$601$	−4.31101e23	−1.03311	−0.516554	−	0.856255i	$-0.672785\pi$
$601$	−4.31101e23	−1.03311	−0.516554	+	0.856255i	$0.672785\pi$
$602$	−1.40783e23	−0.332643
$603$	−7.30922e21	−0.0170284
$604$	9.36098e23	2.15034
$605$	1.08432e22	0.0245604
$606$	7.70035e23	1.71986
$607$	−3.04833e23	−0.671363	−0.335682	−	0.941976i	$-0.608967\pi$
$607$	−3.04833e23	−0.671363	−0.335682	+	0.941976i	$0.608967\pi$
$608$	−1.49632e24	−3.24971
$609$	3.89163e22	0.0833460
$610$	1.10300e24	2.32955
$611$	−8.42195e22	−0.175413
$612$	−9.26954e23	−1.90402
$613$	−1.89474e22	−0.0383826	−0.0191913	−	0.999816i	$-0.506109\pi$
$613$	−1.89474e22	−0.0383826	−0.0191913	+	0.999816i	$0.506109\pi$
$614$	−5.72206e23	−1.14320
$615$	−2.07886e23	−0.409625
$616$	7.15783e23	1.39106
$617$	1.04160e24	1.99654	0.998270	−	0.0587990i	$-0.0187271\pi$
$617$	1.04160e24	1.99654	0.998270	+	0.0587990i	$0.0187271\pi$
$618$	1.89572e24	3.58404
$619$	−9.72503e23	−1.81351	−0.906756	−	0.421655i	$-0.861449\pi$
$619$	−9.72503e23	−1.81351	−0.906756	+	0.421655i	$0.861449\pi$
$620$	−1.50635e24	−2.77075
$621$	−2.49591e23	−0.452845
$622$	3.47458e23	0.621848
$623$	2.79142e23	0.492807
$624$	−1.55207e24	−2.70297
$625$	−1.68948e23	−0.290250
$626$	−1.35117e24	−2.28996
$627$	5.26502e23	0.880291
$628$	−1.00576e24	−1.65897
$629$	−2.63492e23	−0.428783
$630$	1.93187e23	0.310158
$631$	−1.17487e24	−1.86097	−0.930486	−	0.366327i	$-0.880615\pi$
$631$	−1.17487e24	−1.86097	−0.930486	+	0.366327i	$0.880615\pi$
$632$	−1.42393e24	−2.22533
$633$	1.00610e24	1.55134
$634$	1.97323e24	3.00206
$635$	8.52949e23	1.28040
$636$	−9.19702e23	−1.36227
$637$	4.94312e22	0.0722463
$638$	−2.42560e23	−0.349819
$639$	−6.66837e23	−0.948992
$640$	2.61439e24	3.67148
$641$	2.37429e23	0.329033	0.164517	−	0.986374i	$-0.447394\pi$
$641$	2.37429e23	0.329033	0.164517	+	0.986374i	$0.447394\pi$
$642$	2.32508e24	3.17972
$643$	1.06039e24	1.43110	0.715551	−	0.698561i	$-0.246176\pi$
$643$	1.06039e24	1.43110	0.715551	+	0.698561i	$0.246176\pi$
$644$	−6.92830e23	−0.922777
$645$	3.09589e23	0.406938
$646$	1.20076e24	1.55769
$647$	−1.26845e23	−0.162400	−0.0811999	−	0.996698i	$-0.525875\pi$
$647$	−1.26845e23	−0.162400	−0.0811999	+	0.996698i	$0.525875\pi$
$648$	−3.56194e24	−4.50089
$649$	−7.26588e23	−0.906167
$650$	−3.86457e23	−0.475705
$651$	5.27855e23	0.641322
$652$	3.08223e24	3.69624
$653$	−2.89167e23	−0.342284	−0.171142	−	0.985246i	$-0.554746\pi$
$653$	−2.89167e23	−0.342284	−0.171142	+	0.985246i	$0.554746\pi$
$654$	1.38213e24	1.61487
$655$	8.22358e22	0.0948440
$656$	1.68721e24	1.92082
$657$	3.93058e22	0.0441724
$658$	−2.31741e23	−0.257088
$659$	−8.59245e23	−0.941003	−0.470501	−	0.882399i	$-0.655927\pi$
$659$	−8.59245e23	−0.941003	−0.470501	+	0.882399i	$0.655927\pi$
$660$	−2.42691e24	−2.62380
$661$	−1.53638e24	−1.63978	−0.819889	−	0.572523i	$-0.805965\pi$
$661$	−1.53638e24	−1.63978	−0.819889	+	0.572523i	$0.805965\pi$
$662$	−3.27377e24	−3.44949
$663$	7.04868e23	0.733234
$664$	1.33954e24	1.37571
$665$	−1.85177e23	−0.187760
$666$	4.22450e23	0.422907
$667$	1.52275e23	0.150508
$668$	2.13721e24	2.08568
$669$	2.08761e24	2.01153
$670$	−4.36439e22	−0.0415229
$671$	1.78263e24	1.67463
$672$	−2.41694e24	−2.24195
$673$	−7.69753e23	−0.705056	−0.352528	−	0.935801i	$-0.614678\pi$
$673$	−7.69753e23	−0.705056	−0.352528	+	0.935801i	$0.614678\pi$
$674$	2.95455e24	2.67229
$675$	−2.83468e23	−0.253175
$676$	−2.40125e24	−2.11783
$677$	−4.93312e23	−0.429653	−0.214827	−	0.976652i	$-0.568919\pi$
$677$	−4.93312e23	−0.429653	−0.214827	+	0.976652i	$0.568919\pi$
$678$	1.84213e23	0.158441
$679$	6.09358e23	0.517582
$680$	−3.58984e24	−3.01127
$681$	−1.95208e24	−1.61714
$682$	−3.29005e24	−2.69175
$683$	1.34954e24	1.09046	0.545229	−	0.838287i	$-0.316443\pi$
$683$	1.34954e24	1.09046	0.545229	+	0.838287i	$0.316443\pi$
$684$	−1.42454e24	−1.13684
$685$	−1.85281e23	−0.146036
$686$	1.36016e23	0.105885
$687$	−3.03766e23	−0.233564
$688$	−2.51264e24	−1.90822
$689$	2.56755e23	0.192600
$690$	2.05899e24	1.52558
$691$	−8.66512e23	−0.634178	−0.317089	−	0.948396i	$-0.602705\pi$
$691$	−8.66512e23	−0.634178	−0.317089	+	0.948396i	$0.602705\pi$
$692$	4.45498e24	3.22066
$693$	3.12222e23	0.222962
$694$	1.51934e23	0.107177
$695$	1.37973e24	0.961442
$696$	1.15941e24	0.798101
$697$	−7.66245e23	−0.521061
$698$	−3.01377e24	−2.02460
$699$	−1.60022e24	−1.06199
$700$	−7.86868e23	−0.515903
$701$	1.28038e24	0.829343	0.414671	−	0.909971i	$-0.363896\pi$
$701$	1.28038e24	0.829343	0.414671	+	0.909971i	$0.363896\pi$
$702$	8.17979e23	0.523452
$703$	−4.04934e23	−0.256014
$704$	8.14259e24	5.08622
$705$	5.09612e23	0.314508
$706$	−4.61205e24	−2.81225
$707$	−4.37706e23	−0.263705
$708$	5.35476e24	3.18755
$709$	−1.46968e24	−0.864427	−0.432214	−	0.901771i	$-0.642267\pi$
$709$	−1.46968e24	−0.864427	−0.432214	+	0.901771i	$0.642267\pi$
$710$	−3.98173e24	−2.31407
$711$	−6.21114e23	−0.356681
$712$	8.31629e24	4.71900
$713$	2.06544e24	1.15811
$714$	1.93954e24	1.07464
$715$	6.77525e23	0.370958
$716$	−6.21303e24	−3.36157
$717$	−1.61868e24	−0.865463
$718$	1.65285e24	0.873327
$719$	−6.66268e23	−0.347899	−0.173950	−	0.984755i	$-0.555653\pi$
$719$	−6.66268e23	−0.347899	−0.173950	+	0.984755i	$0.555653\pi$
$720$	3.44794e24	1.77924
$721$	−1.07757e24	−0.549537
$722$	−2.04556e24	−1.03097
$723$	−1.05849e24	−0.527244
$724$	1.12057e24	0.551649
$725$	1.72943e23	0.0841456
$726$	−1.74535e23	−0.0839308
$727$	1.52696e24	0.725749	0.362874	−	0.931838i	$-0.381795\pi$
$727$	1.52696e24	0.725749	0.362874	+	0.931838i	$0.381795\pi$
$728$	1.47267e24	0.691813
$729$	−1.24784e23	−0.0579396
$730$	2.34698e23	0.107712
$731$	1.14111e24	0.517643
$732$	−1.31375e25	−5.89072
$733$	−8.66982e23	−0.384261	−0.192131	−	0.981369i	$-0.561540\pi$
$733$	−8.66982e23	−0.384261	−0.192131	+	0.981369i	$0.561540\pi$
$734$	−4.46289e24	−1.95524
$735$	−2.99108e23	−0.129535
$736$	−9.45721e24	−4.04857
$737$	−7.05356e22	−0.0298493
$738$	1.22850e24	0.513920
$739$	1.00016e24	0.413613	0.206806	−	0.978382i	$-0.433693\pi$
$739$	1.00016e24	0.413613	0.206806	+	0.978382i	$0.433693\pi$
$740$	1.86654e24	0.763077
$741$	1.08324e24	0.437794
$742$	7.06495e23	0.282277
$743$	2.71721e24	1.07329	0.536647	−	0.843807i	$-0.319691\pi$
$743$	2.71721e24	1.07329	0.536647	+	0.843807i	$0.319691\pi$
$744$	1.57260e25	6.14114
$745$	2.54217e24	0.981469
$746$	1.97026e24	0.752046
$747$	5.84301e23	0.220501
$748$	−8.94532e24	−3.33758
$749$	−1.32163e24	−0.487544
$750$	7.21359e24	2.63106
$751$	4.37088e24	1.57626	0.788132	−	0.615506i	$-0.211048\pi$
$751$	4.37088e24	1.57626	0.788132	+	0.615506i	$0.211048\pi$
$752$	−4.13604e24	−1.47480
$753$	3.78949e24	1.33605
$754$	−4.99049e23	−0.173975
$755$	1.58132e24	0.545093
$756$	1.66549e24	0.567685
$757$	9.36154e23	0.315524	0.157762	−	0.987477i	$-0.449572\pi$
$757$	9.36154e23	0.315524	0.157762	+	0.987477i	$0.449572\pi$
$758$	9.66622e23	0.322158
$759$	3.32766e24	1.09669
$760$	−5.51686e24	−1.79795
$761$	−4.55578e24	−1.46823	−0.734113	−	0.679027i	$-0.762402\pi$
$761$	−4.55578e24	−1.46823	−0.734113	+	0.679027i	$0.762402\pi$
$762$	−1.37293e25	−4.37555
$763$	−7.85634e23	−0.247606
$764$	1.13548e24	0.353904
$765$	−1.56588e24	−0.482653
$766$	1.25903e25	3.83788
$767$	−1.49490e24	−0.450663
$768$	−2.09940e25	−6.25929
$769$	−1.70960e24	−0.504106	−0.252053	−	0.967713i	$-0.581106\pi$
$769$	−1.70960e24	−0.504106	−0.252053	+	0.967713i	$0.581106\pi$
$770$	1.86430e24	0.543681
$771$	−8.23883e24	−2.37631
$772$	3.67292e23	0.104777
$773$	2.10469e23	0.0593831	0.0296915	−	0.999559i	$-0.490547\pi$
$773$	2.10469e23	0.0593831	0.0296915	+	0.999559i	$0.490547\pi$
$774$	−1.82951e24	−0.510549
$775$	2.34578e24	0.647475
$776$	1.81542e25	4.95624
$777$	−6.54072e23	−0.176623
$778$	5.27037e23	0.140771
$779$	−1.17756e24	−0.311111
$780$	−4.99319e24	−1.30489
$781$	−6.43513e24	−1.66350
$782$	7.58919e24	1.94061
$783$	−3.66054e23	−0.0925913
$784$	2.42758e24	0.607416
$785$	−1.69900e24	−0.420534
$786$	−1.32370e24	−0.324113
$787$	−4.51369e24	−1.09332	−0.546659	−	0.837355i	$-0.684101\pi$
$787$	−4.51369e24	−1.09332	−0.546659	+	0.837355i	$0.684101\pi$
$788$	1.77976e25	4.26470
$789$	−3.72308e23	−0.0882568
$790$	−3.70872e24	−0.869748
$791$	−1.04711e23	−0.0242936
$792$	9.30182e24	2.13503
$793$	3.66762e24	0.832842
$794$	−1.90553e24	−0.428096
$795$	−1.55363e24	−0.345323
$796$	1.89117e25	4.15880
$797$	−2.24303e24	−0.488022	−0.244011	−	0.969773i	$-0.578463\pi$
$797$	−2.24303e24	−0.488022	−0.244011	+	0.969773i	$0.578463\pi$
$798$	2.98067e24	0.641637
$799$	1.87837e24	0.400068
$800$	−1.07408e25	−2.26346
$801$	3.62753e24	0.756372
$802$	−1.59257e24	−0.328561
$803$	3.79310e23	0.0774304
$804$	5.19829e23	0.104999
$805$	−1.17038e24	−0.233916
$806$	−6.76903e24	−1.33868
$807$	−9.78508e24	−1.91487
$808$	−1.30403e25	−2.52517
$809$	−5.63482e24	−1.07974	−0.539868	−	0.841749i	$-0.681526\pi$
$809$	−5.63482e24	−1.07974	−0.539868	+	0.841749i	$0.681526\pi$
$810$	−9.27727e24	−1.75913
$811$	9.57914e24	1.79742	0.898709	−	0.438544i	$-0.144506\pi$
$811$	9.57914e24	1.79742	0.898709	+	0.438544i	$0.144506\pi$
$812$	−1.01612e24	−0.188676
$813$	−7.43619e23	−0.136641
$814$	4.07674e24	0.741320
$815$	5.20671e24	0.936966
$816$	3.46162e25	6.16472
$817$	1.75366e24	0.309070
$818$	−6.04318e24	−1.05405
$819$	6.42373e23	0.110885
$820$	5.42797e24	0.927299
$821$	1.91099e24	0.323104	0.161552	−	0.986864i	$-0.448350\pi$
$821$	1.91099e24	0.323104	0.161552	+	0.986864i	$0.448350\pi$
$822$	2.98234e24	0.499053
$823$	3.84813e24	0.637311	0.318656	−	0.947871i	$-0.396769\pi$
$823$	3.84813e24	0.637311	0.318656	+	0.947871i	$0.396769\pi$
$824$	−3.21034e25	−5.26223
$825$	3.77932e24	0.613134
$826$	−4.11341e24	−0.660498
$827$	−9.04534e24	−1.43757	−0.718783	−	0.695234i	$-0.755301\pi$
$827$	−9.04534e24	−1.43757	−0.718783	+	0.695234i	$0.755301\pi$
$828$	−9.00353e24	−1.41630
$829$	−3.19994e24	−0.498229	−0.249114	−	0.968474i	$-0.580139\pi$
$829$	−3.19994e24	−0.498229	−0.249114	+	0.968474i	$0.580139\pi$
$830$	3.48890e24	0.537681
$831$	2.80658e24	0.428123
$832$	1.67528e25	2.52952
$833$	−1.10248e24	−0.164774
$834$	−2.22086e25	−3.28556
$835$	3.61032e24	0.528702
$836$	−1.37471e25	−1.99278
$837$	−4.96510e24	−0.712462
$838$	−7.07755e24	−1.00533
$839$	−8.58811e23	−0.120759	−0.0603797	−	0.998175i	$-0.519231\pi$
$839$	−8.58811e23	−0.120759	−0.0603797	+	0.998175i	$0.519231\pi$
$840$	−8.91113e24	−1.24039
$841$	−7.03382e24	−0.969226
$842$	2.15212e25	2.93572
$843$	9.49527e24	1.28225
$844$	−2.62694e25	−3.51188
$845$	−4.05636e24	−0.536852
$846$	−3.01154e24	−0.394585
$847$	9.92099e22	0.0128690
$848$	1.26093e25	1.61930
$849$	1.46071e25	1.85716
$850$	8.61927e24	1.08495
$851$	−2.55931e24	−0.318949
$852$	4.74252e25	5.85158
$853$	6.28681e24	0.768004	0.384002	−	0.923332i	$-0.374546\pi$
$853$	6.28681e24	0.768004	0.384002	+	0.923332i	$0.374546\pi$
$854$	1.00919e25	1.22063
$855$	−2.40643e24	−0.288179
$856$	−3.93744e25	−4.66860
$857$	4.27315e24	0.501661	0.250831	−	0.968031i	$-0.419296\pi$
$857$	4.27315e24	0.501661	0.250831	+	0.968031i	$0.419296\pi$
$858$	−1.09057e25	−1.26768
$859$	4.98450e24	0.573693	0.286847	−	0.957977i	$-0.407393\pi$
$859$	4.98450e24	0.573693	0.286847	+	0.957977i	$0.407393\pi$
$860$	−8.08347e24	−0.921215
$861$	−1.90206e24	−0.214634
$862$	2.77704e25	3.10292
$863$	9.04245e24	1.00045	0.500224	−	0.865896i	$-0.333251\pi$
$863$	9.04245e24	1.00045	0.500224	+	0.865896i	$0.333251\pi$
$864$	2.27342e25	2.49065
$865$	7.52567e24	0.816410
$866$	−8.97020e24	−0.963607
$867$	−3.90392e24	−0.415277
$868$	−1.37825e25	−1.45181
$869$	−5.99389e24	−0.625231
$870$	3.01974e24	0.311930
$871$	−1.45122e23	−0.0148449
$872$	−2.34059e25	−2.37102
$873$	7.91880e24	0.794398
$874$	1.16630e25	1.15868
$875$	−4.10038e24	−0.403418
$876$	−2.79541e24	−0.272371
$877$	−9.61731e24	−0.928019	−0.464010	−	0.885830i	$-0.653590\pi$
$877$	−9.61731e24	−0.928019	−0.464010	+	0.885830i	$0.653590\pi$
$878$	5.19544e24	0.496499
$879$	1.17341e25	1.11057
$880$	3.32734e25	3.11885
$881$	−1.16850e25	−1.08476	−0.542380	−	0.840133i	$-0.682477\pi$
$881$	−1.16850e25	−1.08476	−0.542380	+	0.840133i	$0.682477\pi$
$882$	1.76757e24	0.162515
$883$	8.90868e24	0.811236	0.405618	−	0.914043i	$-0.367056\pi$
$883$	8.90868e24	0.811236	0.405618	+	0.914043i	$0.367056\pi$
$884$	−1.84043e25	−1.65988
$885$	9.04564e24	0.808019
$886$	−1.34411e25	−1.18918
$887$	−9.81382e23	−0.0859978	−0.0429989	−	0.999075i	$-0.513691\pi$
$887$	−9.81382e23	−0.0859978	−0.0429989	+	0.999075i	$0.513691\pi$
$888$	−1.94863e25	−1.69130
$889$	7.80409e24	0.670899
$890$	2.16603e25	1.84437
$891$	−1.49936e25	−1.26458
$892$	−5.45081e25	−4.55365
$893$	2.88668e24	0.238870
$894$	−4.09196e25	−3.35400
$895$	−1.04955e25	−0.852131
$896$	2.39205e25	1.92377
$897$	6.84640e24	0.545414
$898$	1.89404e25	1.49465
$899$	3.02921e24	0.236795
$900$	−1.02256e25	−0.791821
$901$	−5.72649e24	−0.439266
$902$	1.18553e25	0.900859
$903$	2.83260e24	0.213226
$904$	−3.11959e24	−0.232630
$905$	1.89295e24	0.139839
$906$	−2.54535e25	−1.86276
$907$	5.98603e24	0.433987	0.216994	−	0.976173i	$-0.430375\pi$
$907$	5.98603e24	0.433987	0.216994	+	0.976173i	$0.430375\pi$
$908$	5.09694e25	3.66084
$909$	−5.68813e24	−0.404740
$910$	3.83566e24	0.270388
$911$	3.89447e24	0.271983	0.135992	−	0.990710i	$-0.456578\pi$
$911$	3.89447e24	0.271983	0.135992	+	0.990710i	$0.456578\pi$
$912$	5.31981e25	3.68078
$913$	5.63863e24	0.386520
$914$	−5.44637e24	−0.369883
$915$	−2.21928e25	−1.49325
$916$	7.93141e24	0.528736
$917$	7.52420e23	0.0496959
$918$	−1.82436e25	−1.19385
$919$	−2.21353e25	−1.43517	−0.717584	−	0.696472i	$-0.754752\pi$
$919$	−2.21353e25	−1.43517	−0.717584	+	0.696472i	$0.754752\pi$
$920$	−3.48683e25	−2.23993
$921$	1.15130e25	0.732794
$922$	−1.80544e25	−1.13860
$923$	−1.32398e25	−0.827307
$924$	−2.22051e25	−1.37481
$925$	−2.90669e24	−0.178317
$926$	1.05447e25	0.640972
$927$	−1.40034e25	−0.843442
$928$	−1.38701e25	−0.827794
$929$	1.43522e25	0.848760	0.424380	−	0.905484i	$-0.360492\pi$
$929$	1.43522e25	0.848760	0.424380	+	0.905484i	$0.360492\pi$
$930$	4.09594e25	2.40020
$931$	−1.69428e24	−0.0983817
$932$	4.17821e25	2.40411
$933$	−6.99099e24	−0.398607
$934$	3.78813e25	2.14031
$935$	−1.51111e25	−0.846050
$936$	1.91378e25	1.06181
$937$	2.09421e25	1.15142	0.575710	−	0.817654i	$-0.304726\pi$
$937$	2.09421e25	1.15142	0.575710	+	0.817654i	$0.304726\pi$
$938$	−3.99321e23	−0.0217570
$939$	2.71861e25	1.46788
$940$	−1.33061e25	−0.711975
$941$	−2.57969e25	−1.36791	−0.683953	−	0.729526i	$-0.739741\pi$
$941$	−2.57969e25	−1.36791	−0.683953	+	0.729526i	$0.739741\pi$
$942$	2.73477e25	1.43710
$943$	−7.44256e24	−0.387590
$944$	−7.34149e25	−3.78898
$945$	2.81347e24	0.143903
$946$	−1.76552e25	−0.894949
$947$	−1.56112e25	−0.784262	−0.392131	−	0.919909i	$-0.628262\pi$
$947$	−1.56112e25	−0.784262	−0.392131	+	0.919909i	$0.628262\pi$
$948$	4.41734e25	2.19933
$949$	7.80401e23	0.0385083
$950$	1.32461e25	0.647793
$951$	−3.97021e25	−1.92433
$952$	−3.28454e25	−1.57783
$953$	1.05751e25	0.503496	0.251748	−	0.967793i	$-0.418995\pi$
$953$	1.05751e25	0.503496	0.251748	+	0.967793i	$0.418995\pi$
$954$	9.18112e24	0.433246
$955$	1.91813e24	0.0897116
$956$	4.22643e25	1.95921
$957$	4.88040e24	0.224235
$958$	7.81157e24	0.355739
$959$	−1.69523e24	−0.0765194
$960$	−1.01371e26	−4.53532
$961$	1.85376e25	0.822063
$962$	8.38759e24	0.368679
$963$	−1.71750e25	−0.748294
$964$	2.76375e25	1.19356
$965$	6.20455e23	0.0265600
$966$	1.88388e25	0.799368
$967$	5.82231e23	0.0244890	0.0122445	−	0.999925i	$-0.496102\pi$
$967$	5.82231e23	0.0244890	0.0122445	+	0.999925i	$0.496102\pi$
$968$	2.95570e24	0.123231
$969$	−2.41598e25	−0.998484
$970$	4.72837e25	1.93710
$971$	−1.26711e25	−0.514576	−0.257288	−	0.966335i	$-0.582829\pi$
$971$	−1.26711e25	−0.514576	−0.257288	+	0.966335i	$0.582829\pi$
$972$	7.31893e25	2.94635
$973$	1.26239e25	0.503772
$974$	−5.77849e25	−2.28593
$975$	7.77567e24	0.304929
$976$	1.80118e26	7.00218
$977$	1.34598e25	0.518724	0.259362	−	0.965780i	$-0.416488\pi$
$977$	1.34598e25	0.518724	0.259362	+	0.965780i	$0.416488\pi$
$978$	−8.38090e25	−3.20192
$979$	3.50065e25	1.32586
$980$	7.80980e24	0.293237
$981$	−1.02095e25	−0.380032
$982$	−4.56013e25	−1.68279
$983$	−1.33973e25	−0.490132	−0.245066	−	0.969506i	$-0.578810\pi$
$983$	−1.33973e25	−0.490132	−0.245066	+	0.969506i	$0.578810\pi$
$984$	−5.66669e25	−2.05528
$985$	3.00649e25	1.08107
$986$	1.11304e25	0.396788
$987$	4.66272e24	0.164795
$988$	−2.82837e25	−0.991065
$989$	1.10836e25	0.385047
$990$	2.42271e25	0.834455
$991$	−1.77063e25	−0.604646	−0.302323	−	0.953206i	$-0.597762\pi$
$991$	−1.77063e25	−0.604646	−0.302323	+	0.953206i	$0.597762\pi$
$992$	−1.88132e26	−6.36962
$993$	6.58695e25	2.21114
$994$	−3.64310e25	−1.21251
$995$	3.19469e25	1.05422
$996$	−4.15552e25	−1.35963
$997$	−1.38217e25	−0.448386	−0.224193	−	0.974545i	$-0.571975\pi$
$997$	−1.38217e25	−0.448386	−0.224193	+	0.974545i	$0.571975\pi$
$998$	1.15067e26	3.70119
$999$	6.15232e24	0.196215

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.18.a.b.1.5	✓	5
3.2	odd	2		63.18.a.e.1.1		5
4.3	odd	2		112.18.a.h.1.4		5
7.6	odd	2		49.18.a.d.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.18.a.b.1.5	✓	5	1.1	even	1	trivial
49.18.a.d.1.5		5	7.6	odd	2
63.18.a.e.1.1		5	3.2	odd	2
112.18.a.h.1.4		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)

\(f(q)\)	\(=\)	\(q+709.967 q^{2} -14284.8 q^{3} +372981. q^{4} +630065. q^{5} -1.01417e7 q^{6} +5.76480e6 q^{7} +1.71747e8 q^{8} +7.49154e7 q^{9} +O(q^{10})\)	\(q+709.967 q^{2} -14284.8 q^{3} +372981. q^{4} +630065. q^{5} -1.01417e7 q^{6} +5.76480e6 q^{7} +1.71747e8 q^{8} +7.49154e7 q^{9} +4.47325e8 q^{10} +7.22950e8 q^{11} -5.32795e9 q^{12} +1.48742e9 q^{13} +4.09282e9 q^{14} -9.00035e9 q^{15} +7.30473e10 q^{16} -3.31743e10 q^{17} +5.31874e10 q^{18} -5.09821e10 q^{19} +2.35002e11 q^{20} -8.23490e10 q^{21} +5.13270e11 q^{22} -3.22223e11 q^{23} -2.45337e12 q^{24} -3.65958e11 q^{25} +1.05602e12 q^{26} +7.74591e11 q^{27} +2.15016e12 q^{28} -4.72577e11 q^{29} -6.38995e12 q^{30} -6.40997e12 q^{31} +2.93499e13 q^{32} -1.03272e13 q^{33} -2.35526e13 q^{34} +3.63220e12 q^{35} +2.79420e13 q^{36} +7.94268e12 q^{37} -3.61956e13 q^{38} -2.12474e13 q^{39} +1.08212e14 q^{40} +2.30976e13 q^{41} -5.84651e13 q^{42} -3.43975e13 q^{43} +2.69646e14 q^{44} +4.72015e13 q^{45} -2.28767e14 q^{46} -5.66214e13 q^{47} -1.04347e15 q^{48} +3.32329e13 q^{49} -2.59818e14 q^{50} +4.73888e14 q^{51} +5.54777e14 q^{52} +1.72618e14 q^{53} +5.49933e14 q^{54} +4.55505e14 q^{55} +9.90087e14 q^{56} +7.28269e14 q^{57} -3.35514e14 q^{58} -1.00503e15 q^{59} -3.35695e15 q^{60} +2.46577e15 q^{61} -4.55086e15 q^{62} +4.31872e14 q^{63} +1.12630e16 q^{64} +9.37168e14 q^{65} -7.33196e15 q^{66} -9.75664e13 q^{67} -1.23734e16 q^{68} +4.60289e15 q^{69} +2.57874e15 q^{70} -8.90121e15 q^{71} +1.28665e16 q^{72} +5.24669e14 q^{73} +5.63903e15 q^{74} +5.22764e15 q^{75} -1.90153e16 q^{76} +4.16766e15 q^{77} -1.50850e16 q^{78} -8.29088e15 q^{79} +4.60245e16 q^{80} -2.07395e16 q^{81} +1.63985e16 q^{82} +7.79948e15 q^{83} -3.07146e16 q^{84} -2.09019e16 q^{85} -2.44211e16 q^{86} +6.75067e15 q^{87} +1.24164e17 q^{88} +4.84218e16 q^{89} +3.35115e16 q^{90} +8.57465e15 q^{91} -1.20183e17 q^{92} +9.15652e16 q^{93} -4.01993e16 q^{94} -3.21220e16 q^{95} -4.19258e17 q^{96} +1.05703e17 q^{97} +2.35943e16 q^{98} +5.41601e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 597 q^{2} - 1770 q^{3} + 534677 q^{4} + 1612824 q^{5} - 14383854 q^{6} + 28824005 q^{7} + 41916039 q^{8} + 552658077 q^{9}+O(q^{10}) \) 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

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Database

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