LMFDB - Embedded newform 5.22.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,22,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	5.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$13.9738672144$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 1929606x^{2} - 743130000x + 239341586400 $ x^4 - x^3 - 1929606x^2 - 743130000x + 239341586400
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 5^{2}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-886.582$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2501.16 q^{2} -181393. q^{3} +4.15867e6 q^{4} +9.76562e6 q^{5} -4.53695e8 q^{6} +9.51907e8 q^{7} +5.15621e9 q^{8} +2.24432e10 q^{9} +O(q^{10})$	\(q+2501.16 q^{2} -181393. q^{3} +4.15867e6 q^{4} +9.76562e6 q^{5} -4.53695e8 q^{6} +9.51907e8 q^{7} +5.15621e9 q^{8} +2.24432e10 q^{9} +2.44254e10 q^{10} +6.26620e10 q^{11} -7.54356e11 q^{12} +3.65290e11 q^{13} +2.38088e12 q^{14} -1.77142e12 q^{15} +4.17515e12 q^{16} -4.06125e12 q^{17} +5.61342e13 q^{18} -3.33870e12 q^{19} +4.06121e13 q^{20} -1.72670e14 q^{21} +1.56728e14 q^{22} +1.41899e14 q^{23} -9.35302e14 q^{24} +9.53674e13 q^{25} +9.13651e14 q^{26} -2.17361e15 q^{27} +3.95867e15 q^{28} -2.13837e15 q^{29} -4.43061e15 q^{30} +2.75237e15 q^{31} -3.70604e14 q^{32} -1.13665e16 q^{33} -1.01579e16 q^{34} +9.29597e15 q^{35} +9.33340e16 q^{36} +3.43997e16 q^{37} -8.35063e15 q^{38} -6.62613e16 q^{39} +5.03536e16 q^{40} -1.12163e17 q^{41} -4.31875e17 q^{42} +4.13618e16 q^{43} +2.60591e17 q^{44} +2.19172e17 q^{45} +3.54913e17 q^{46} -5.44036e17 q^{47} -7.57345e17 q^{48} +3.47581e17 q^{49} +2.38530e17 q^{50} +7.36684e17 q^{51} +1.51912e18 q^{52} +1.34608e18 q^{53} -5.43656e18 q^{54} +6.11933e17 q^{55} +4.90823e18 q^{56} +6.05617e17 q^{57} -5.34841e18 q^{58} +7.47699e18 q^{59} -7.36676e18 q^{60} -1.07752e19 q^{61} +6.88413e18 q^{62} +2.13639e19 q^{63} -9.68287e18 q^{64} +3.56729e18 q^{65} -2.84294e19 q^{66} -1.74771e18 q^{67} -1.68894e19 q^{68} -2.57396e19 q^{69} +2.32507e19 q^{70} -2.17207e19 q^{71} +1.15722e20 q^{72} -1.65237e19 q^{73} +8.60394e19 q^{74} -1.72990e19 q^{75} -1.38845e19 q^{76} +5.96484e19 q^{77} -1.65730e20 q^{78} +7.06800e19 q^{79} +4.07730e19 q^{80} +1.59515e20 q^{81} -2.80539e20 q^{82} +1.53121e19 q^{83} -7.18077e20 q^{84} -3.96607e19 q^{85} +1.03453e20 q^{86} +3.87886e20 q^{87} +3.23098e20 q^{88} -1.94580e20 q^{89} +5.48185e20 q^{90} +3.47722e20 q^{91} +5.90113e20 q^{92} -4.99262e20 q^{93} -1.36072e21 q^{94} -3.26045e19 q^{95} +6.72251e19 q^{96} -7.93694e20 q^{97} +8.69358e20 q^{98} +1.40634e21 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2910 q^{2} + 83240 q^{3} + 9165268 q^{4} + 39062500 q^{5} - 158524712 q^{6} + 512613800 q^{7} + 5167363080 q^{8} + 21732888532 q^{9}+O(q^{10}) $ 4 * q + 2910 * q^2 + 83240 * q^3 + 9165268 * q^4 + 39062500 * q^5 - 158524712 * q^6 + 512613800 * q^7 + 5167363080 * q^8 + 21732888532 * q^9	$ 4 q + 2910 q^{2} + 83240 q^{3} + 9165268 q^{4} + 39062500 q^{5} - 158524712 q^{6} + 512613800 q^{7} + 5167363080 q^{8} + 21732888532 q^{9} + 28417968750 q^{10} + 33727076448 q^{11} - 142435377680 q^{12} + 863532165080 q^{13} + 2725405637616 q^{14} + 812890625000 q^{15} + 9168135122704 q^{16} + 17694691101480 q^{17} + 108219081471590 q^{18} + 65217596849840 q^{19} + 89504570312500 q^{20} - 248634744508992 q^{21} - 133302721028280 q^{22} + 306130984922520 q^{23} - 509427036802080 q^{24} + 381469726562500 q^{25} - 19\!\cdots\!12 q^{26}+ \cdots - 15\!\cdots\!16 q^{99}+O(q^{100}) $ 4 * q + 2910 * q^2 + 83240 * q^3 + 9165268 * q^4 + 39062500 * q^5 - 158524712 * q^6 + 512613800 * q^7 + 5167363080 * q^8 + 21732888532 * q^9 + 28417968750 * q^10 + 33727076448 * q^11 - 142435377680 * q^12 + 863532165080 * q^13 + 2725405637616 * q^14 + 812890625000 * q^15 + 9168135122704 * q^16 + 17694691101480 * q^17 + 108219081471590 * q^18 + 65217596849840 * q^19 + 89504570312500 * q^20 - 248634744508992 * q^21 - 133302721028280 * q^22 + 306130984922520 * q^23 - 509427036802080 * q^24 + 381469726562500 * q^25 - 1909802985226812 * q^26 - 3478503990916720 * q^27 - 2466701432057920 * q^28 - 1183867881941640 * q^29 - 1548092890625000 * q^30 + 8127647981305328 * q^31 + 6394106775900960 * q^32 - 27227776360130720 * q^33 + 32676043106528796 * q^34 + 5005994140625000 * q^35 + 132603401899613444 * q^36 + 50729262881561240 * q^37 + 35369554723756920 * q^38 - 90408012787467856 * q^39 + 50462530078125000 * q^40 - 151242912792059832 * q^41 - 584170109040328320 * q^42 + 195241056541629800 * q^43 - 614844690548787984 * q^44 + 212235239570312500 * q^45 - 156055372897688112 * q^46 - 461921266212226680 * q^47 - 268908035207420480 * q^48 + 348492786998301828 * q^49 + 277519226074218750 * q^50 + 3394366189837348048 * q^51 + 2124030127334250200 * q^52 + 1013253578565011640 * q^53 - 2325284713297481360 * q^54 + 329365980937500000 * q^55 + 3133890122325795840 * q^56 + 6889753607884864160 * q^57 - 15566576922395873820 * q^58 + 9994246603380823920 * q^59 - 1390970485156250000 * q^60 - 10817434481929098952 * q^61 + 3855611474231219520 * q^62 + 12245908869990535560 * q^63 - 45099981493147646912 * q^64 + 8432931299609375000 * q^65 - 81535658477725195744 * q^66 + 21966891437417653880 * q^67 - 2003292237110276760 * q^68 - 10872182089324606656 * q^69 + 26615289429843750000 * q^70 + 51295204524235287888 * q^71 + 203807399727091870440 * q^72 + 74737166154487034120 * q^73 - 95273704374004345644 * q^74 + 7938385009765625000 * q^75 + 33053497281514492880 * q^76 + 284152911785269322400 * q^77 - 411161554685929127600 * q^78 - 60935090437726582240 * q^79 + 89532569557656250000 * q^80 + 158163684388294667524 * q^81 + 209310572847889648620 * q^82 - 278730291142551479640 * q^83 - 1305319136534979185664 * q^84 + 172799717787890625000 * q^85 - 410177137146579139512 * q^86 + 180742525444629646640 * q^87 - 407444351717354555040 * q^88 - 323651892724949032920 * q^89 + 1056826967495996093750 * q^90 + 220855101702096981808 * q^91 + 2407334022772179833280 * q^92 + 193462123423446842880 * q^93 - 1285026294005215311264 * q^94 + 636890594236718750000 * q^95 - 20769436930632372352 * q^96 + 309141974076136362920 * q^97 + 746323122131488476270 * q^98 - 1516374777085318976416 * 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 $

$2$	2501.16	1.72714	0.863570	−	0.504230i	$-0.168223\pi$
$2$	2501.16	1.72714	0.863570	+	0.504230i	$0.168223\pi$
$3$	−181393.	−1.77357	−0.886785	−	0.462182i	$-0.847067\pi$
$3$	−181393.	−1.77357	−0.886785	+	0.462182i	$0.847067\pi$
$4$	4.15867e6	1.98301
$5$	9.76562e6	0.447214
$5$	9.76562e6	0.447214
$6$	−4.53695e8	−3.06320
$7$	9.51907e8	1.27369	0.636847	−	0.770990i	$-0.280238\pi$
$7$	9.51907e8	1.27369	0.636847	+	0.770990i	$0.280238\pi$
$8$	5.15621e9	1.69780
$9$	2.24432e10	2.14555
$10$	2.44254e10	0.772400
$11$	6.26620e10	0.728418	0.364209	−	0.931317i	$-0.381339\pi$
$11$	6.26620e10	0.728418	0.364209	+	0.931317i	$0.381339\pi$
$12$	−7.54356e11	−3.51701
$13$	3.65290e11	0.734908	0.367454	−	0.930042i	$-0.380230\pi$
$13$	3.65290e11	0.734908	0.367454	+	0.930042i	$0.380230\pi$
$14$	2.38088e12	2.19985
$15$	−1.77142e12	−0.793165
$16$	4.17515e12	0.949320
$17$	−4.06125e12	−0.488592	−0.244296	−	0.969701i	$-0.578557\pi$
$17$	−4.06125e12	−0.488592	−0.244296	+	0.969701i	$0.578557\pi$
$18$	5.61342e13	3.70566
$19$	−3.33870e12	−0.124929	−0.0624646	−	0.998047i	$-0.519896\pi$
$19$	−3.33870e12	−0.124929	−0.0624646	+	0.998047i	$0.519896\pi$
$20$	4.06121e13	0.886829
$21$	−1.72670e14	−2.25899
$22$	1.56728e14	1.25808
$23$	1.41899e14	0.714230	0.357115	−	0.934060i	$-0.383760\pi$
$23$	1.41899e14	0.714230	0.357115	+	0.934060i	$0.383760\pi$
$24$	−9.35302e14	−3.01116
$25$	9.53674e13	0.200000
$26$	9.13651e14	1.26929
$27$	−2.17361e15	−2.03171
$28$	3.95867e15	2.52575
$29$	−2.13837e15	−0.943851	−0.471925	−	0.881638i	$-0.656441\pi$
$29$	−2.13837e15	−0.943851	−0.471925	+	0.881638i	$0.656441\pi$
$30$	−4.43061e15	−1.36991
$31$	2.75237e15	0.603128	0.301564	−	0.953446i	$-0.402491\pi$
$31$	2.75237e15	0.603128	0.301564	+	0.953446i	$0.402491\pi$
$32$	−3.70604e14	−0.0581883
$33$	−1.13665e16	−1.29190
$34$	−1.01579e16	−0.843866
$35$	9.29597e15	0.569613
$36$	9.33340e16	4.25465
$37$	3.43997e16	1.17608	0.588040	−	0.808832i	$-0.299900\pi$
$37$	3.43997e16	1.17608	0.588040	+	0.808832i	$0.299900\pi$
$38$	−8.35063e15	−0.215770
$39$	−6.62613e16	−1.30341
$40$	5.03536e16	0.759277
$41$	−1.12163e17	−1.30503	−0.652514	−	0.757777i	$-0.726286\pi$
$41$	−1.12163e17	−1.30503	−0.652514	+	0.757777i	$0.726286\pi$
$42$	−4.31875e17	−3.90158
$43$	4.13618e16	0.291864	0.145932	−	0.989295i	$-0.453382\pi$
$43$	4.13618e16	0.291864	0.145932	+	0.989295i	$0.453382\pi$
$44$	2.60591e17	1.44446
$45$	2.19172e17	0.959519
$46$	3.54913e17	1.23357
$47$	−5.44036e17	−1.50869	−0.754345	−	0.656479i	$-0.772045\pi$
$47$	−5.44036e17	−1.50869	−0.754345	+	0.656479i	$0.772045\pi$
$48$	−7.57345e17	−1.68369
$49$	3.47581e17	0.622296
$50$	2.38530e17	0.345428
$51$	7.36684e17	0.866552
$52$	1.51912e18	1.45733
$53$	1.34608e18	1.05724	0.528620	−	0.848859i	$-0.322710\pi$
$53$	1.34608e18	1.05724	0.528620	+	0.848859i	$0.322710\pi$
$54$	−5.43656e18	−3.50905
$55$	6.11933e17	0.325759
$56$	4.90823e18	2.16247
$57$	6.05617e17	0.221571
$58$	−5.34841e18	−1.63016
$59$	7.47699e18	1.90450	0.952249	−	0.305323i	$-0.0987643\pi$
$59$	7.47699e18	1.90450	0.952249	+	0.305323i	$0.0987643\pi$
$60$	−7.36676e18	−1.57285
$61$	−1.07752e19	−1.93402	−0.967010	−	0.254738i	$-0.918011\pi$
$61$	−1.07752e19	−1.93402	−0.967010	+	0.254738i	$0.918011\pi$
$62$	6.88413e18	1.04169
$63$	2.13639e19	2.73277
$64$	−9.68287e18	−1.04982
$65$	3.56729e18	0.328661
$66$	−2.84294e19	−2.23129
$67$	−1.74771e18	−0.117135	−0.0585673	−	0.998283i	$-0.518653\pi$
$67$	−1.74771e18	−0.117135	−0.0585673	+	0.998283i	$0.518653\pi$
$68$	−1.68894e19	−0.968883
$69$	−2.57396e19	−1.26674
$70$	2.32507e19	0.983802
$71$	−2.17207e19	−0.791885	−0.395942	−	0.918275i	$-0.629582\pi$
$71$	−2.17207e19	−0.791885	−0.395942	+	0.918275i	$0.629582\pi$
$72$	1.15722e20	3.64271
$73$	−1.65237e19	−0.450004	−0.225002	−	0.974358i	$-0.572239\pi$
$73$	−1.65237e19	−0.450004	−0.225002	+	0.974358i	$0.572239\pi$
$74$	8.60394e19	2.03125
$75$	−1.72990e19	−0.354714
$76$	−1.38845e19	−0.247736
$77$	5.96484e19	0.927782
$78$	−1.65730e20	−2.25117
$79$	7.06800e19	0.839870	0.419935	−	0.907554i	$-0.362053\pi$
$79$	7.06800e19	0.839870	0.419935	+	0.907554i	$0.362053\pi$
$80$	4.07730e19	0.424549
$81$	1.59515e20	1.45784
$82$	−2.80539e20	−2.25397
$83$	1.53121e19	0.108322	0.0541608	−	0.998532i	$-0.482752\pi$
$83$	1.53121e19	0.108322	0.0541608	+	0.998532i	$0.482752\pi$
$84$	−7.18077e20	−4.47959
$85$	−3.96607e19	−0.218505
$86$	1.03453e20	0.504091
$87$	3.87886e20	1.67399
$88$	3.23098e20	1.23671
$89$	−1.94580e20	−0.661461	−0.330730	−	0.943725i	$-0.607295\pi$
$89$	−1.94580e20	−0.661461	−0.330730	+	0.943725i	$0.607295\pi$
$90$	5.48185e20	1.65722
$91$	3.47722e20	0.936048
$92$	5.90113e20	1.41632
$93$	−4.99262e20	−1.06969
$94$	−1.36072e21	−2.60572
$95$	−3.26045e19	−0.0558701
$96$	6.72251e19	0.103201
$97$	−7.93694e20	−1.09282	−0.546412	−	0.837517i	$-0.684007\pi$
$97$	−7.93694e20	−1.09282	−0.546412	+	0.837517i	$0.684007\pi$
$98$	8.69358e20	1.07479
$99$	1.40634e21	1.56286
$100$	3.96602e20	0.396602
$101$	−2.12534e21	−1.91449	−0.957245	−	0.289278i	$-0.906585\pi$
$101$	−2.12534e21	−1.91449	−0.957245	+	0.289278i	$0.906585\pi$
$102$	1.84257e21	1.49666
$103$	−1.63004e20	−0.119511	−0.0597554	−	0.998213i	$-0.519032\pi$
$103$	−1.63004e20	−0.119511	−0.0597554	+	0.998213i	$0.519032\pi$
$104$	1.88351e21	1.24772
$105$	−1.68623e21	−1.01025
$106$	3.36676e21	1.82600
$107$	1.07977e21	0.530643	0.265321	−	0.964160i	$-0.414522\pi$
$107$	1.07977e21	0.530643	0.265321	+	0.964160i	$0.414522\pi$
$108$	−9.03935e21	−4.02891
$109$	−1.56726e21	−0.634109	−0.317055	−	0.948407i	$-0.602694\pi$
$109$	−1.56726e21	−0.634109	−0.317055	+	0.948407i	$0.602694\pi$
$110$	1.53055e21	0.562630
$111$	−6.23988e21	−2.08586
$112$	3.97436e21	1.20914
$113$	8.52628e20	0.236285	0.118142	−	0.992997i	$-0.462306\pi$
$113$	8.52628e20	0.236285	0.118142	+	0.992997i	$0.462306\pi$
$114$	1.51475e21	0.382684
$115$	1.38574e21	0.319413
$116$	−8.89277e21	−1.87167
$117$	8.19829e21	1.57678
$118$	1.87012e22	3.28933
$119$	−3.86593e21	−0.622317
$120$	−9.13381e21	−1.34663
$121$	−3.47373e21	−0.469407
$122$	−2.69505e22	−3.34032
$123$	2.03457e22	2.31456
$124$	1.14462e22	1.19601
$125$	9.31323e20	0.0894427
$126$	5.34345e22	4.71988
$127$	−4.36749e21	−0.355053	−0.177526	−	0.984116i	$-0.556809\pi$
$127$	−4.36749e21	−0.355053	−0.177526	+	0.984116i	$0.556809\pi$
$128$	−2.34412e22	−1.75500
$129$	−7.50277e21	−0.517642
$130$	8.92238e21	0.567643
$131$	−1.77816e22	−1.04381	−0.521906	−	0.853003i	$-0.674779\pi$
$131$	−1.77816e22	−1.04381	−0.521906	+	0.853003i	$0.674779\pi$
$132$	−4.72694e22	−2.56185
$133$	−3.17813e21	−0.159122
$134$	−4.37132e21	−0.202308
$135$	−2.12267e22	−0.908610
$136$	−2.09407e22	−0.829529
$137$	3.78261e22	1.38747	0.693737	−	0.720228i	$-0.255963\pi$
$137$	3.78261e22	1.38747	0.693737	+	0.720228i	$0.255963\pi$
$138$	−6.43790e22	−2.18783
$139$	2.43035e22	0.765619	0.382810	−	0.923827i	$-0.374957\pi$
$139$	2.43035e22	0.765619	0.382810	+	0.923827i	$0.374957\pi$
$140$	3.86589e22	1.12955
$141$	9.86845e22	2.67577
$142$	−5.43272e22	−1.36770
$143$	2.28898e22	0.535320
$144$	9.37039e22	2.03681
$145$	−2.08825e22	−0.422103
$146$	−4.13284e22	−0.777220
$147$	−6.30489e22	−1.10369
$148$	1.43057e23	2.33218
$149$	−1.63045e22	−0.247658	−0.123829	−	0.992304i	$-0.539517\pi$
$149$	−1.63045e22	−0.247658	−0.123829	+	0.992304i	$0.539517\pi$
$150$	−4.32677e22	−0.612641
$151$	−6.51277e22	−0.860019	−0.430009	−	0.902824i	$-0.641490\pi$
$151$	−6.51277e22	−0.860019	−0.430009	+	0.902824i	$0.641490\pi$
$152$	−1.72150e22	−0.212104
$153$	−9.11476e22	−1.04830
$154$	1.49190e23	1.60241
$155$	2.68786e22	0.269727
$156$	−2.75559e23	−2.58468
$157$	1.22612e23	1.07544	0.537720	−	0.843124i	$-0.319286\pi$
$157$	1.22612e23	1.07544	0.537720	+	0.843124i	$0.319286\pi$
$158$	1.76782e23	1.45057
$159$	−2.44170e23	−1.87509
$160$	−3.61918e21	−0.0260226
$161$	1.35075e23	0.909710
$162$	3.98973e23	2.51789
$163$	2.09545e23	1.23968	0.619838	−	0.784730i	$-0.287198\pi$
$163$	2.09545e23	1.23968	0.619838	+	0.784730i	$0.287198\pi$
$164$	−4.66450e23	−2.58788
$165$	−1.11001e23	−0.577756
$166$	3.82981e22	0.187087
$167$	2.64805e23	1.21452	0.607258	−	0.794504i	$-0.292269\pi$
$167$	2.64805e23	1.21452	0.607258	+	0.794504i	$0.292269\pi$
$168$	−8.90321e23	−3.83530
$169$	−1.13627e23	−0.459910
$170$	−9.91979e22	−0.377388
$171$	−7.49311e22	−0.268042
$172$	1.72010e23	0.578770
$173$	1.29366e23	0.409578	0.204789	−	0.978806i	$-0.434349\pi$
$173$	1.29366e23	0.409578	0.204789	+	0.978806i	$0.434349\pi$
$174$	9.70166e23	2.89121
$175$	9.07809e22	0.254739
$176$	2.61623e23	0.691502
$177$	−1.35628e24	−3.37776
$178$	−4.86678e23	−1.14244
$179$	−6.05782e23	−1.34079	−0.670393	−	0.742006i	$-0.733874\pi$
$179$	−6.05782e23	−1.34079	−0.670393	+	0.742006i	$0.733874\pi$
$180$	9.11465e23	1.90274
$181$	9.41112e23	1.85360	0.926800	−	0.375555i	$-0.122548\pi$
$181$	9.41112e23	1.85360	0.926800	+	0.375555i	$0.122548\pi$
$182$	8.69711e23	1.61669
$183$	1.95455e24	3.43012
$184$	7.31662e23	1.21262
$185$	3.35935e23	0.525959
$186$	−1.24874e24	−1.84750
$187$	−2.54486e23	−0.355899
$188$	−2.26247e24	−2.99175
$189$	−2.06908e24	−2.58778
$190$	−8.15491e22	−0.0964954
$191$	−2.99512e23	−0.335401	−0.167700	−	0.985838i	$-0.553634\pi$
$191$	−2.99512e23	−0.335401	−0.167700	+	0.985838i	$0.553634\pi$
$192$	1.75641e24	1.86193
$193$	−1.10973e24	−1.11395	−0.556973	−	0.830530i	$-0.688037\pi$
$193$	−1.10973e24	−1.11395	−0.556973	+	0.830530i	$0.688037\pi$
$194$	−1.98516e24	−1.88746
$195$	−6.47083e23	−0.582903
$196$	1.44548e24	1.23402
$197$	−2.85158e23	−0.230776	−0.115388	−	0.993320i	$-0.536811\pi$
$197$	−2.85158e23	−0.230776	−0.115388	+	0.993320i	$0.536811\pi$
$198$	3.51748e24	2.69927
$199$	1.17364e24	0.854233	0.427116	−	0.904197i	$-0.359529\pi$
$199$	1.17364e24	0.854233	0.427116	+	0.904197i	$0.359529\pi$
$200$	4.91734e23	0.339559
$201$	3.17024e23	0.207746
$202$	−5.31582e24	−3.30659
$203$	−2.03553e24	−1.20218
$204$	3.06363e24	1.71838
$205$	−1.09534e24	−0.583626
$206$	−4.07700e23	−0.206412
$207$	3.18468e24	1.53242
$208$	1.52514e24	0.697663
$209$	−2.09209e23	−0.0910007
$210$	−4.21753e24	−1.74484
$211$	3.35865e24	1.32190	0.660950	−	0.750430i	$-0.270153\pi$
$211$	3.35865e24	1.32190	0.660950	+	0.750430i	$0.270153\pi$
$212$	5.59790e24	2.09652
$213$	3.94000e24	1.40446
$214$	2.70069e24	0.916494
$215$	4.03924e23	0.130526
$216$	−1.12076e25	−3.44944
$217$	2.62000e24	0.768200
$218$	−3.91999e24	−1.09520
$219$	2.99729e24	0.798114
$220$	2.54483e24	0.645983
$221$	−1.48354e24	−0.359070
$222$	−1.56070e25	−3.60257
$223$	−6.56226e23	−0.144495	−0.0722475	−	0.997387i	$-0.523017\pi$
$223$	−6.56226e23	−0.144495	−0.0722475	+	0.997387i	$0.523017\pi$
$224$	−3.52781e23	−0.0741140
$225$	2.14035e24	0.429110
$226$	2.13256e24	0.408097
$227$	5.40975e24	0.988338	0.494169	−	0.869366i	$-0.335472\pi$
$227$	5.40975e24	0.988338	0.494169	+	0.869366i	$0.335472\pi$
$228$	2.51857e24	0.439377
$229$	−4.26891e22	−0.00711286	−0.00355643	−	0.999994i	$-0.501132\pi$
$229$	−4.26891e22	−0.00711286	−0.00355643	+	0.999994i	$0.501132\pi$
$230$	3.46595e24	0.551671
$231$	−1.08198e25	−1.64549
$232$	−1.10259e25	−1.60247
$233$	4.66214e24	0.647662	0.323831	−	0.946115i	$-0.395029\pi$
$233$	4.66214e24	0.647662	0.323831	+	0.946115i	$0.395029\pi$
$234$	2.05053e25	2.72332
$235$	−5.31285e24	−0.674706
$236$	3.10944e25	3.77664
$237$	−1.28209e25	−1.48957
$238$	−9.66934e24	−1.07483
$239$	−4.94264e23	−0.0525752	−0.0262876	−	0.999654i	$-0.508369\pi$
$239$	−4.94264e23	−0.0525752	−0.0262876	+	0.999654i	$0.508369\pi$
$240$	−7.39595e24	−0.752967
$241$	−9.12434e24	−0.889247	−0.444623	−	0.895718i	$-0.646662\pi$
$241$	−9.12434e24	−0.889247	−0.444623	+	0.895718i	$0.646662\pi$
$242$	−8.68837e24	−0.810731
$243$	−6.19821e24	−0.553861
$244$	−4.48104e25	−3.83518
$245$	3.39435e24	0.278299
$246$	5.08879e25	3.99757
$247$	−1.21959e24	−0.0918115
$248$	1.41918e25	1.02399
$249$	−2.77752e24	−0.192116
$250$	2.32939e24	0.154480
$251$	−4.99422e24	−0.317610	−0.158805	−	0.987310i	$-0.550764\pi$
$251$	−4.99422e24	−0.317610	−0.158805	+	0.987310i	$0.550764\pi$
$252$	8.88453e25	5.41912
$253$	8.89169e24	0.520258
$254$	−1.09238e25	−0.613225
$255$	7.19418e24	0.387534
$256$	−3.83240e25	−1.98130
$257$	−2.40771e25	−1.19483	−0.597415	−	0.801932i	$-0.703805\pi$
$257$	−2.40771e25	−1.19483	−0.597415	+	0.801932i	$0.703805\pi$
$258$	−1.87657e25	−0.894040
$259$	3.27453e25	1.49797
$260$	1.48352e25	0.651738
$261$	−4.79918e25	−2.02508
$262$	−4.44747e25	−1.80281
$263$	1.57869e25	0.614840	0.307420	−	0.951574i	$-0.400534\pi$
$263$	1.57869e25	0.614840	0.307420	+	0.951574i	$0.400534\pi$
$264$	−5.86079e25	−2.19338
$265$	1.31453e25	0.472812
$266$	−7.94902e24	−0.274825
$267$	3.52956e25	1.17315
$268$	−7.26817e24	−0.232279
$269$	4.53399e24	0.139342	0.0696709	−	0.997570i	$-0.477805\pi$
$269$	4.53399e24	0.139342	0.0696709	+	0.997570i	$0.477805\pi$
$270$	−5.30914e25	−1.56930
$271$	3.06582e25	0.871705	0.435853	−	0.900018i	$-0.356447\pi$
$271$	3.06582e25	0.871705	0.435853	+	0.900018i	$0.356447\pi$
$272$	−1.69563e25	−0.463830
$273$	−6.30746e25	−1.66015
$274$	9.46092e25	2.39636
$275$	5.97591e24	0.145684
$276$	−1.07043e26	−2.51195
$277$	6.15385e25	1.39030	0.695151	−	0.718864i	$-0.255338\pi$
$277$	6.15385e25	1.39030	0.695151	+	0.718864i	$0.255338\pi$
$278$	6.07870e25	1.32233
$279$	6.17721e25	1.29404
$280$	4.79319e25	0.967087
$281$	−3.37635e25	−0.656192	−0.328096	−	0.944644i	$-0.606407\pi$
$281$	−3.37635e25	−0.656192	−0.328096	+	0.944644i	$0.606407\pi$
$282$	2.46826e26	4.62142
$283$	−5.76794e25	−1.04055	−0.520275	−	0.853999i	$-0.674170\pi$
$283$	−5.76794e25	−1.04055	−0.520275	+	0.853999i	$0.674170\pi$
$284$	−9.03295e25	−1.57032
$285$	5.91423e24	0.0990894
$286$	5.72512e25	0.924573
$287$	−1.06769e26	−1.66221
$288$	−8.31755e24	−0.124846
$289$	−5.25982e25	−0.761278
$290$	−5.22306e25	−0.729031
$291$	1.43971e26	1.93820
$292$	−6.87166e25	−0.892363
$293$	−8.91098e25	−1.11639	−0.558194	−	0.829710i	$-0.688506\pi$
$293$	−8.91098e25	−1.11639	−0.558194	+	0.829710i	$0.688506\pi$
$294$	−1.57696e26	−1.90622
$295$	7.30175e25	0.851717
$296$	1.77372e26	1.99674
$297$	−1.36203e26	−1.47994
$298$	−4.07803e25	−0.427740
$299$	5.18344e25	0.524893
$300$	−7.19410e25	−0.703402
$301$	3.93726e25	0.371746
$302$	−1.62895e26	−1.48537
$303$	3.85522e26	3.39548
$304$	−1.39396e25	−0.118598
$305$	−1.05226e26	−0.864920
$306$	−2.27975e26	−1.81056
$307$	−6.67571e25	−0.512324	−0.256162	−	0.966634i	$-0.582458\pi$
$307$	−6.67571e25	−0.512324	−0.256162	+	0.966634i	$0.582458\pi$
$308$	2.48058e26	1.83980
$309$	2.95678e25	0.211961
$310$	6.72279e25	0.465856
$311$	−1.31996e26	−0.884252	−0.442126	−	0.896953i	$-0.645776\pi$
$311$	−1.31996e26	−0.884252	−0.442126	+	0.896953i	$0.645776\pi$
$312$	−3.41657e26	−2.21293
$313$	7.17608e25	0.449440	0.224720	−	0.974423i	$-0.427853\pi$
$313$	7.17608e25	0.449440	0.224720	+	0.974423i	$0.427853\pi$
$314$	3.06672e26	1.85743
$315$	2.08631e26	1.22213
$316$	2.93935e26	1.66547
$317$	−8.40594e25	−0.460749	−0.230374	−	0.973102i	$-0.573995\pi$
$317$	−8.40594e25	−0.460749	−0.230374	+	0.973102i	$0.573995\pi$
$318$	−6.10708e26	−3.23854
$319$	−1.33994e26	−0.687518
$320$	−9.45593e25	−0.469493
$321$	−1.95864e26	−0.941132
$322$	3.37845e26	1.57120
$323$	1.35593e25	0.0610394
$324$	6.63371e26	2.89090
$325$	3.48368e25	0.146982
$326$	5.24108e26	2.14109
$327$	2.84291e26	1.12464
$328$	−5.78337e26	−2.21567
$329$	−5.17871e26	−1.92161
$330$	−2.77631e26	−0.997864
$331$	−3.76918e26	−1.31236	−0.656180	−	0.754605i	$-0.727829\pi$
$331$	−3.76918e26	−1.31236	−0.656180	+	0.754605i	$0.727829\pi$
$332$	6.36781e25	0.214803
$333$	7.72040e26	2.52334
$334$	6.62321e26	2.09764
$335$	−1.70675e25	−0.0523842
$336$	−7.20922e26	−2.14450
$337$	1.53611e26	0.442901	0.221451	−	0.975172i	$-0.428921\pi$
$337$	1.53611e26	0.442901	0.221451	+	0.975172i	$0.428921\pi$
$338$	−2.84201e26	−0.794329
$339$	−1.54661e26	−0.419068
$340$	−1.64936e26	−0.433298
$341$	1.72469e26	0.439329
$342$	−1.87415e26	−0.462946
$343$	−2.00819e26	−0.481079
$344$	2.13270e26	0.495526
$345$	−2.51363e26	−0.566502
$346$	3.23566e26	0.707398
$347$	−6.04195e26	−1.28150	−0.640749	−	0.767750i	$-0.721376\pi$
$347$	−6.04195e26	−1.28150	−0.640749	+	0.767750i	$0.721376\pi$
$348$	1.61309e27	3.31953
$349$	7.19381e26	1.43645	0.718227	−	0.695809i	$-0.244954\pi$
$349$	7.19381e26	1.43645	0.718227	+	0.695809i	$0.244954\pi$
$350$	2.27058e26	0.439969
$351$	−7.94000e26	−1.49312
$352$	−2.32228e25	−0.0423854
$353$	−1.16904e26	−0.207107	−0.103554	−	0.994624i	$-0.533021\pi$
$353$	−1.16904e26	−0.207107	−0.103554	+	0.994624i	$0.533021\pi$
$354$	−3.39227e27	−5.83386
$355$	−2.12117e26	−0.354142
$356$	−8.09197e26	−1.31168
$357$	7.01255e26	1.10372
$358$	−1.51516e27	−2.31572
$359$	9.18825e25	0.136377	0.0681885	−	0.997672i	$-0.478278\pi$
$359$	9.18825e25	0.136377	0.0681885	+	0.997672i	$0.478278\pi$
$360$	1.13010e27	1.62907
$361$	−7.03063e26	−0.984393
$362$	2.35388e27	3.20143
$363$	6.30112e26	0.832526
$364$	1.44606e27	1.85619
$365$	−1.61364e26	−0.201248
$366$	4.88864e27	5.92430
$367$	3.25197e25	0.0382959	0.0191480	−	0.999817i	$-0.493905\pi$
$367$	3.25197e25	0.0382959	0.0191480	+	0.999817i	$0.493905\pi$
$368$	5.92451e26	0.678032
$369$	−2.51730e27	−2.80000
$370$	8.40228e26	0.908404
$371$	1.28134e27	1.34660
$372$	−2.07627e27	−2.12120
$373$	1.45809e27	1.44825	0.724123	−	0.689671i	$-0.242245\pi$
$373$	1.45809e27	1.44825	0.724123	+	0.689671i	$0.242245\pi$
$374$	−6.36511e26	−0.614688
$375$	−1.68936e26	−0.158633
$376$	−2.80516e27	−2.56145
$377$	−7.81125e26	−0.693644
$378$	−5.17510e27	−4.46946
$379$	2.13470e27	1.79318	0.896592	−	0.442858i	$-0.146035\pi$
$379$	2.13470e27	1.79318	0.896592	+	0.442858i	$0.146035\pi$
$380$	−1.35591e26	−0.110791
$381$	7.92234e26	0.629711
$382$	−7.49130e26	−0.579284
$383$	−6.17420e26	−0.464508	−0.232254	−	0.972655i	$-0.574610\pi$
$383$	−6.17420e26	−0.464508	−0.232254	+	0.972655i	$0.574610\pi$
$384$	4.25209e27	3.11261
$385$	5.82503e26	0.414917
$386$	−2.77561e27	−1.92394
$387$	9.28293e26	0.626210
$388$	−3.30071e27	−2.16708
$389$	−2.51202e27	−1.60529	−0.802643	−	0.596459i	$-0.796574\pi$
$389$	−2.51202e27	−1.60529	−0.802643	+	0.596459i	$0.796574\pi$
$390$	−1.61846e27	−1.00675
$391$	−5.76289e26	−0.348967
$392$	1.79220e27	1.05653
$393$	3.22546e27	1.85127
$394$	−7.13228e26	−0.398583
$395$	6.90235e26	0.375602
$396$	5.84849e27	3.09916
$397$	−4.11930e26	−0.212580	−0.106290	−	0.994335i	$-0.533897\pi$
$397$	−4.11930e26	−0.212580	−0.106290	+	0.994335i	$0.533897\pi$
$398$	2.93546e27	1.47538
$399$	5.76492e26	0.282213
$400$	3.98174e26	0.189864
$401$	−1.74526e27	−0.810672	−0.405336	−	0.914168i	$-0.632845\pi$
$401$	−1.74526e27	−0.810672	−0.405336	+	0.914168i	$0.632845\pi$
$402$	7.92929e26	0.358807
$403$	1.00541e27	0.443243
$404$	−8.83858e27	−3.79645
$405$	1.55776e27	0.651964
$406$	−5.09119e27	−2.07633
$407$	2.15555e27	0.856678
$408$	3.79850e27	1.47123
$409$	2.93183e27	1.10674	0.553368	−	0.832937i	$-0.313342\pi$
$409$	2.93183e27	1.10674	0.553368	+	0.832937i	$0.313342\pi$
$410$	−2.73964e27	−1.00800
$411$	−6.86140e27	−2.46078
$412$	−6.77880e26	−0.236991
$413$	7.11740e27	2.42575
$414$	7.96540e27	2.64670
$415$	1.49532e26	0.0484429
$416$	−1.35378e26	−0.0427630
$417$	−4.40849e27	−1.35788
$418$	−5.23267e26	−0.157171
$419$	6.55971e26	0.192149	0.0960744	−	0.995374i	$-0.469371\pi$
$419$	6.55971e26	0.192149	0.0960744	+	0.995374i	$0.469371\pi$
$420$	−7.01247e27	−2.00333
$421$	3.66653e27	1.02163	0.510815	−	0.859691i	$-0.329344\pi$
$421$	3.66653e27	1.02163	0.510815	+	0.859691i	$0.329344\pi$
$422$	8.40054e27	2.28311
$423$	−1.22099e28	−3.23697
$424$	6.94065e27	1.79498
$425$	−3.87311e26	−0.0977184
$426$	9.85459e27	2.42570
$427$	−1.02570e28	−2.46335
$428$	4.49042e27	1.05227
$429$	−4.15206e27	−0.949428
$430$	1.01028e27	0.225436
$431$	2.37476e27	0.517141	0.258570	−	0.965992i	$-0.416749\pi$
$431$	2.37476e27	0.517141	0.258570	+	0.965992i	$0.416749\pi$
$432$	−9.07516e27	−1.92875
$433$	−8.82058e27	−1.82968	−0.914838	−	0.403821i	$-0.867682\pi$
$433$	−8.82058e27	−1.82968	−0.914838	+	0.403821i	$0.867682\pi$
$434$	6.55305e27	1.32679
$435$	3.78795e27	0.748629
$436$	−6.51774e27	−1.25745
$437$	−4.73759e26	−0.0892282
$438$	7.49670e27	1.37845
$439$	6.12084e27	1.09884	0.549419	−	0.835547i	$-0.314849\pi$
$439$	6.12084e27	1.09884	0.549419	+	0.835547i	$0.314849\pi$
$440$	3.15525e27	0.553071
$441$	7.80084e27	1.33517
$442$	−3.71057e27	−0.620164
$443$	−5.81165e27	−0.948550	−0.474275	−	0.880377i	$-0.657290\pi$
$443$	−5.81165e27	−0.948550	−0.474275	+	0.880377i	$0.657290\pi$
$444$	−2.59496e28	−4.13628
$445$	−1.90020e27	−0.295814
$446$	−1.64133e27	−0.249563
$447$	2.95754e27	0.439239
$448$	−9.21719e27	−1.33715
$449$	1.90490e27	0.269952	0.134976	−	0.990849i	$-0.456904\pi$
$449$	1.90490e27	0.269952	0.134976	+	0.990849i	$0.456904\pi$
$450$	5.35337e27	0.741133
$451$	−7.02837e27	−0.950606
$452$	3.54580e27	0.468555
$453$	1.18137e28	1.52530
$454$	1.35307e28	1.70700
$455$	3.39573e27	0.418613
$456$	3.12269e27	0.376182
$457$	1.33265e28	1.56890	0.784450	−	0.620192i	$-0.212945\pi$
$457$	1.33265e28	1.56890	0.784450	+	0.620192i	$0.212945\pi$
$458$	−1.06772e26	−0.0122849
$459$	8.82759e27	0.992679
$460$	5.76282e27	0.633400
$461$	1.24822e28	1.34101	0.670503	−	0.741907i	$-0.266078\pi$
$461$	1.24822e28	1.34101	0.670503	+	0.741907i	$0.266078\pi$
$462$	−2.70622e28	−2.84198
$463$	−4.90917e27	−0.503974	−0.251987	−	0.967731i	$-0.581084\pi$
$463$	−4.90917e27	−0.503974	−0.251987	+	0.967731i	$0.581084\pi$
$464$	−8.92801e27	−0.896016
$465$	−4.87560e27	−0.478379
$466$	1.16608e28	1.11860
$467$	−1.62377e28	−1.52299	−0.761495	−	0.648171i	$-0.775534\pi$
$467$	−1.62377e28	−1.52299	−0.761495	+	0.648171i	$0.775534\pi$
$468$	3.40940e28	3.12678
$469$	−1.66366e27	−0.149194
$470$	−1.32883e28	−1.16531
$471$	−2.22410e28	−1.90737
$472$	3.85529e28	3.23345
$473$	2.59181e27	0.212599
$474$	−3.20672e28	−2.57269
$475$	−3.18403e26	−0.0249858
$476$	−1.60772e28	−1.23406
$477$	3.02103e28	2.26836
$478$	−1.23623e27	−0.0908046
$479$	1.14107e28	0.819951	0.409976	−	0.912096i	$-0.365537\pi$
$479$	1.14107e28	0.819951	0.409976	+	0.912096i	$0.365537\pi$
$480$	6.56495e26	0.0461529
$481$	1.25659e28	0.864310
$482$	−2.28215e28	−1.53585
$483$	−2.45017e28	−1.61343
$484$	−1.44461e28	−0.930839
$485$	−7.75092e27	−0.488725
$486$	−1.55028e28	−0.956595
$487$	1.36964e28	0.827092	0.413546	−	0.910483i	$-0.364290\pi$
$487$	1.36964e28	0.827092	0.413546	+	0.910483i	$0.364290\pi$
$488$	−5.55590e28	−3.28357
$489$	−3.80102e28	−2.19865
$490$	8.48982e27	0.480662
$491$	1.48393e27	0.0822355	0.0411177	−	0.999154i	$-0.486908\pi$
$491$	1.48393e27	0.0822355	0.0411177	+	0.999154i	$0.486908\pi$
$492$	8.46110e28	4.58979
$493$	8.68445e27	0.461158
$494$	−3.05040e27	−0.158571
$495$	1.37337e28	0.698931
$496$	1.14916e28	0.572561
$497$	−2.06761e28	−1.00862
$498$	−6.94703e27	−0.331811
$499$	2.79992e28	1.30945	0.654726	−	0.755866i	$-0.272784\pi$
$499$	2.79992e28	1.30945	0.654726	+	0.755866i	$0.272784\pi$
$500$	3.87307e27	0.177366
$501$	−4.80339e28	−2.15403
$502$	−1.24914e28	−0.548556
$503$	3.52192e28	1.51466	0.757331	−	0.653031i	$-0.226503\pi$
$503$	3.52192e28	1.51466	0.757331	+	0.653031i	$0.226503\pi$
$504$	1.10156e29	4.63969
$505$	−2.07552e28	−0.856186
$506$	2.22396e28	0.898558
$507$	2.06113e28	0.815683
$508$	−1.81630e28	−0.704073
$509$	2.82365e28	1.07220	0.536098	−	0.844156i	$-0.319898\pi$
$509$	2.82365e28	1.07220	0.536098	+	0.844156i	$0.319898\pi$
$510$	1.79938e28	0.669325
$511$	−1.57290e28	−0.573168
$512$	−4.66947e28	−1.66699
$513$	7.25703e27	0.253820
$514$	−6.02208e28	−2.06364
$515$	−1.59184e27	−0.0534469
$516$	−3.12016e28	−1.02649
$517$	−3.40903e28	−1.09896
$518$	8.19015e28	2.58720
$519$	−2.34662e28	−0.726415
$520$	1.83937e28	0.557999
$521$	2.15474e28	0.640616	0.320308	−	0.947313i	$-0.396214\pi$
$521$	2.15474e28	0.640616	0.320308	+	0.947313i	$0.396214\pi$
$522$	−1.20036e29	−3.49760
$523$	1.77824e28	0.507835	0.253917	−	0.967226i	$-0.418281\pi$
$523$	1.77824e28	0.507835	0.253917	+	0.967226i	$0.418281\pi$
$524$	−7.39479e28	−2.06989
$525$	−1.64671e28	−0.451797
$526$	3.94857e28	1.06191
$527$	−1.11781e28	−0.294683
$528$	−4.74567e28	−1.22643
$529$	−1.93362e28	−0.489876
$530$	3.28785e28	0.816612
$531$	1.67808e29	4.08620
$532$	−1.32168e28	−0.315540
$533$	−4.09721e28	−0.959076
$534$	8.82802e28	2.02619
$535$	1.05446e28	0.237311
$536$	−9.01158e27	−0.198871
$537$	1.09885e29	2.37798
$538$	1.13403e28	0.240663
$539$	2.17801e28	0.453292
$540$	−8.82749e28	−1.80178
$541$	1.89901e28	0.380150	0.190075	−	0.981770i	$-0.439127\pi$
$541$	1.89901e28	0.380150	0.190075	+	0.981770i	$0.439127\pi$
$542$	7.66813e28	1.50556
$543$	−1.70711e29	−3.28749
$544$	1.50512e27	0.0284303
$545$	−1.53053e28	−0.283582
$546$	−1.57760e29	−2.86730
$547$	−5.64249e28	−1.00601	−0.503007	−	0.864283i	$-0.667773\pi$
$547$	−5.64249e28	−1.00601	−0.503007	+	0.864283i	$0.667773\pi$
$548$	1.57306e29	2.75138
$549$	−2.41830e29	−4.14954
$550$	1.49467e28	0.251616
$551$	7.13936e27	0.117915
$552$	−1.32719e29	−2.15066
$553$	6.72808e28	1.06974
$554$	1.53918e29	2.40124
$555$	−6.09363e28	−0.932825
$556$	1.01070e29	1.51823
$557$	−6.05036e28	−0.891870	−0.445935	−	0.895065i	$-0.647129\pi$
$557$	−6.05036e28	−0.891870	−0.445935	+	0.895065i	$0.647129\pi$
$558$	1.54502e29	2.23499
$559$	1.51091e28	0.214494
$560$	3.88121e28	0.540745
$561$	4.61621e28	0.631212
$562$	−8.44480e28	−1.13333
$563$	−3.00894e28	−0.396347	−0.198173	−	0.980167i	$-0.563501\pi$
$563$	−3.00894e28	−0.396347	−0.198173	+	0.980167i	$0.563501\pi$
$564$	4.10397e29	5.30607
$565$	8.32644e27	0.105670
$566$	−1.44266e29	−1.79717
$567$	1.51843e29	1.85684
$568$	−1.11997e29	−1.34446
$569$	1.42192e28	0.167570	0.0837848	−	0.996484i	$-0.473299\pi$
$569$	1.42192e28	0.167570	0.0837848	+	0.996484i	$0.473299\pi$
$570$	1.47925e28	0.171141
$571$	−4.34683e28	−0.493734	−0.246867	−	0.969049i	$-0.579401\pi$
$571$	−4.34683e28	−0.493734	−0.246867	+	0.969049i	$0.579401\pi$
$572$	9.51913e28	1.06155
$573$	5.43295e28	0.594857
$574$	−2.67047e29	−2.87086
$575$	1.35326e28	0.142846
$576$	−2.17315e29	−2.25244
$577$	−7.14601e28	−0.727306	−0.363653	−	0.931534i	$-0.618471\pi$
$577$	−7.14601e28	−0.727306	−0.363653	+	0.931534i	$0.618471\pi$
$578$	−1.31557e29	−1.31483
$579$	2.01297e29	1.97566
$580$	−8.68435e28	−0.837035
$581$	1.45757e28	0.137969
$582$	3.60095e29	3.34754
$583$	8.43479e28	0.770113
$584$	−8.51995e28	−0.764015
$585$	8.00614e28	0.705159
$586$	−2.22878e29	−1.92816
$587$	−1.41593e29	−1.20321	−0.601605	−	0.798793i	$-0.705472\pi$
$587$	−1.41593e29	−1.20321	−0.601605	+	0.798793i	$0.705472\pi$
$588$	−2.62200e29	−2.18862
$589$	−9.18933e27	−0.0753483
$590$	1.82629e29	1.47103
$591$	5.17259e28	0.409298
$592$	1.43624e29	1.11648
$593$	1.87360e26	0.00143088	0.000715441	−	1.00000i	$-0.499772\pi$
$593$	1.87360e26	0.00143088	0.000715441		1.00000i	$0.499772\pi$
$594$	−3.40666e29	−2.55606
$595$	−3.77533e28	−0.278308
$596$	−6.78053e28	−0.491109
$597$	−2.12890e29	−1.51504
$598$	1.29646e29	0.906564
$599$	−1.26640e29	−0.870140	−0.435070	−	0.900397i	$-0.643276\pi$
$599$	−1.26640e29	−0.870140	−0.435070	+	0.900397i	$0.643276\pi$
$600$	−8.91974e28	−0.602232
$601$	1.47366e29	0.977719	0.488859	−	0.872363i	$-0.337413\pi$
$601$	1.47366e29	0.977719	0.488859	+	0.872363i	$0.337413\pi$
$602$	9.84775e28	0.642057
$603$	−3.92243e28	−0.251318
$604$	−2.70845e29	−1.70543
$605$	−3.39231e28	−0.209925
$606$	9.64254e29	5.86447
$607$	2.99367e29	1.78946	0.894731	−	0.446606i	$-0.147368\pi$
$607$	2.99367e29	1.78946	0.894731	+	0.446606i	$0.147368\pi$
$608$	1.23733e27	0.00726942
$609$	3.69231e29	2.13215
$610$	−2.63188e29	−1.49384
$611$	−1.98731e29	−1.10875
$612$	−3.79053e29	−2.07879
$613$	6.89458e28	0.371683	0.185841	−	0.982580i	$-0.440499\pi$
$613$	6.89458e28	0.371683	0.185841	+	0.982580i	$0.440499\pi$
$614$	−1.66971e29	−0.884855
$615$	1.98688e29	1.03510
$616$	3.07559e29	1.57518
$617$	1.21954e29	0.614045	0.307023	−	0.951702i	$-0.400667\pi$
$617$	1.21954e29	0.614045	0.307023	+	0.951702i	$0.400667\pi$
$618$	7.39540e28	0.366086
$619$	1.98794e29	0.967500	0.483750	−	0.875206i	$-0.339274\pi$
$619$	1.98794e29	0.967500	0.483750	+	0.875206i	$0.339274\pi$
$620$	1.11779e29	0.534871
$621$	−3.08434e29	−1.45111
$622$	−3.30143e29	−1.52723
$623$	−1.85223e29	−0.842499
$624$	−2.76651e29	−1.23735
$625$	9.09495e27	0.0400000
$626$	1.79486e29	0.776245
$627$	3.79492e28	0.161396
$628$	5.09902e29	2.13261
$629$	−1.39706e29	−0.574623
$630$	5.21822e29	2.11080
$631$	1.51659e29	0.603337	0.301668	−	0.953413i	$-0.402456\pi$
$631$	1.51659e29	0.603337	0.301668	+	0.953413i	$0.402456\pi$
$632$	3.64441e29	1.42593
$633$	−6.09237e29	−2.34448
$634$	−2.10246e29	−0.795777
$635$	−4.26513e28	−0.158784
$636$	−1.01542e30	−3.71832
$637$	1.26968e29	0.457331
$638$	−3.35142e29	−1.18744
$639$	−4.87483e29	−1.69903
$640$	−2.28918e29	−0.784858
$641$	−1.59719e29	−0.538700	−0.269350	−	0.963042i	$-0.586809\pi$
$641$	−1.59719e29	−0.538700	−0.269350	+	0.963042i	$0.586809\pi$
$642$	−4.89887e29	−1.62547
$643$	4.89244e29	1.59702	0.798510	−	0.601982i	$-0.205622\pi$
$643$	4.89244e29	1.59702	0.798510	+	0.601982i	$0.205622\pi$
$644$	5.61733e29	1.80396
$645$	−7.32692e28	−0.231497
$646$	3.39140e28	0.105424
$647$	1.47125e29	0.449979	0.224989	−	0.974361i	$-0.427765\pi$
$647$	1.47125e29	0.449979	0.224989	+	0.974361i	$0.427765\pi$
$648$	8.22492e29	2.47511
$649$	4.68523e29	1.38727
$650$	8.71326e28	0.253858
$651$	−4.75251e29	−1.36246
$652$	8.71431e29	2.45829
$653$	−5.34367e29	−1.48337	−0.741687	−	0.670746i	$-0.765974\pi$
$653$	−5.34367e29	−1.48337	−0.741687	+	0.670746i	$0.765974\pi$
$654$	7.11060e29	1.94241
$655$	−1.73648e29	−0.466807
$656$	−4.68298e29	−1.23889
$657$	−3.70844e29	−0.965507
$658$	−1.29528e30	−3.31889
$659$	5.88175e29	1.48323	0.741617	−	0.670824i	$-0.234059\pi$
$659$	5.88175e29	1.48323	0.741617	+	0.670824i	$0.234059\pi$
$660$	−4.61616e29	−1.14570
$661$	5.70060e29	1.39253	0.696266	−	0.717784i	$-0.254843\pi$
$661$	5.70060e29	1.39253	0.696266	+	0.717784i	$0.254843\pi$
$662$	−9.42734e29	−2.26663
$663$	2.69104e29	0.636836
$664$	7.89525e28	0.183908
$665$	−3.10364e28	−0.0711613
$666$	1.93100e30	4.35816
$667$	−3.03433e29	−0.674126
$668$	1.10124e30	2.40840
$669$	1.19035e29	0.256272
$670$	−4.26887e28	−0.0904747
$671$	−6.75194e29	−1.40878
$672$	6.39921e28	0.131446
$673$	−4.81923e29	−0.974584	−0.487292	−	0.873239i	$-0.662015\pi$
$673$	−4.81923e29	−0.974584	−0.487292	+	0.873239i	$0.662015\pi$
$674$	3.84205e29	0.764952
$675$	−2.07292e29	−0.406343
$676$	−4.72540e29	−0.912006
$677$	3.91881e29	0.744687	0.372343	−	0.928095i	$-0.378554\pi$
$677$	3.91881e29	0.744687	0.372343	+	0.928095i	$0.378554\pi$
$678$	−3.86833e29	−0.723788
$679$	−7.55523e29	−1.39192
$680$	−2.04499e29	−0.370977
$681$	−9.81292e29	−1.75289
$682$	4.31373e29	0.758783
$683$	9.73986e29	1.68708	0.843540	−	0.537067i	$-0.180468\pi$
$683$	9.73986e29	1.68708	0.843540	+	0.537067i	$0.180468\pi$
$684$	−3.11614e29	−0.531530
$685$	3.69395e29	0.620498
$686$	−5.02281e29	−0.830890
$687$	7.74352e27	0.0126152
$688$	1.72692e29	0.277073
$689$	4.91709e29	0.776974
$690$	−6.28701e29	−0.978427
$691$	3.02476e29	0.463630	0.231815	−	0.972760i	$-0.425534\pi$
$691$	3.02476e29	0.463630	0.231815	+	0.972760i	$0.425534\pi$
$692$	5.37991e29	0.812197
$693$	1.33870e30	1.99060
$694$	−1.51119e30	−2.21333
$695$	2.37339e29	0.342395
$696$	2.00002e30	2.84209
$697$	4.55523e29	0.637626
$698$	1.79929e30	2.48096
$699$	−8.45682e29	−1.14867
$700$	3.77528e29	0.505150
$701$	1.94176e29	0.255951	0.127976	−	0.991777i	$-0.459152\pi$
$701$	1.94176e29	0.255951	0.127976	+	0.991777i	$0.459152\pi$
$702$	−1.98592e30	−2.57883
$703$	−1.14850e29	−0.146927
$704$	−6.06748e29	−0.764707
$705$	9.63715e29	1.19664
$706$	−2.92397e29	−0.357703
$707$	−2.02312e30	−2.43847
$708$	−5.64031e30	−6.69813
$709$	1.18784e30	1.38987	0.694935	−	0.719073i	$-0.255433\pi$
$709$	1.18784e30	1.38987	0.694935	+	0.719073i	$0.255433\pi$
$710$	−5.30539e29	−0.611652
$711$	1.58629e30	1.80198
$712$	−1.00330e30	−1.12303
$713$	3.90559e29	0.430772
$714$	1.75395e30	1.90628
$715$	2.23533e29	0.239403
$716$	−2.51925e30	−2.65879
$717$	8.96562e28	0.0932457
$718$	2.29813e29	0.235542
$719$	−1.91789e30	−1.93718	−0.968592	−	0.248654i	$-0.920012\pi$
$719$	−1.91789e30	−1.93718	−0.968592	+	0.248654i	$0.920012\pi$
$720$	9.15077e29	0.910891
$721$	−1.55165e29	−0.152220
$722$	−1.75848e30	−1.70018
$723$	1.65509e30	1.57714
$724$	3.91378e30	3.67571
$725$	−2.03931e29	−0.188770
$726$	1.57601e30	1.43789
$727$	−4.61396e29	−0.414918	−0.207459	−	0.978244i	$-0.566519\pi$
$727$	−4.61396e29	−0.414918	−0.207459	+	0.978244i	$0.566519\pi$
$728$	1.79293e30	1.58922
$729$	−5.44268e29	−0.475525
$730$	−4.03598e29	−0.347583
$731$	−1.67981e29	−0.142603
$732$	8.12832e30	6.80196
$733$	9.05460e29	0.746926	0.373463	−	0.927645i	$-0.378170\pi$
$733$	9.05460e29	0.746926	0.373463	+	0.927645i	$0.378170\pi$
$734$	8.13371e28	0.0661424
$735$	−6.15712e29	−0.493583
$736$	−5.25884e28	−0.0415598
$737$	−1.09515e29	−0.0853229
$738$	−6.29619e30	−4.83600
$739$	−2.33471e30	−1.76793	−0.883967	−	0.467549i	$-0.845137\pi$
$739$	−2.33471e30	−1.76793	−0.883967	+	0.467549i	$0.845137\pi$
$740$	1.39704e30	1.04298
$741$	2.21226e29	0.162834
$742$	3.20484e30	2.32577
$743$	−1.72785e30	−1.23630	−0.618150	−	0.786061i	$-0.712117\pi$
$743$	−1.72785e30	−1.23630	−0.618150	+	0.786061i	$0.712117\pi$
$744$	−2.57430e30	−1.81611
$745$	−1.59224e29	−0.110756
$746$	3.64693e30	2.50132
$747$	3.43653e29	0.232410
$748$	−1.05832e30	−0.705752
$749$	1.02784e30	0.675877
$750$	−4.22536e29	−0.273981
$751$	−6.85837e29	−0.438532	−0.219266	−	0.975665i	$-0.570366\pi$
$751$	−6.85837e29	−0.438532	−0.219266	+	0.975665i	$0.570366\pi$
$752$	−2.27143e30	−1.43223
$753$	9.05919e29	0.563303
$754$	−1.95372e30	−1.19802
$755$	−6.36013e29	−0.384612
$756$	−8.60462e30	−5.13160
$757$	1.03811e30	0.610573	0.305287	−	0.952261i	$-0.401248\pi$
$757$	1.03811e30	0.610573	0.305287	+	0.952261i	$0.401248\pi$
$758$	5.33923e30	3.09708
$759$	−1.61289e30	−0.922714
$760$	−1.68115e29	−0.0948559
$761$	−1.31812e30	−0.733525	−0.366762	−	0.930315i	$-0.619534\pi$
$761$	−1.31812e30	−0.733525	−0.366762	+	0.930315i	$0.619534\pi$
$762$	1.98151e30	1.08760
$763$	−1.49189e30	−0.807661
$764$	−1.24557e30	−0.665104
$765$	−8.90113e29	−0.468813
$766$	−1.54427e30	−0.802271
$767$	2.73127e30	1.39963
$768$	6.95172e30	3.51398
$769$	2.39167e30	1.19254	0.596272	−	0.802782i	$-0.296648\pi$
$769$	2.39167e30	1.19254	0.596272	+	0.802782i	$0.296648\pi$
$770$	1.45694e30	0.716619
$771$	4.36742e30	2.11911
$772$	−4.61499e30	−2.20897
$773$	1.34403e30	0.634634	0.317317	−	0.948320i	$-0.397218\pi$
$773$	1.34403e30	0.634634	0.317317	+	0.948320i	$0.397218\pi$
$774$	2.32181e30	1.08155
$775$	2.62487e29	0.120626
$776$	−4.09245e30	−1.85539
$777$	−5.93979e30	−2.65675
$778$	−6.28298e30	−2.77255
$779$	3.74479e29	0.163036
$780$	−2.69101e30	−1.15590
$781$	−1.36106e30	−0.576823
$782$	−1.44139e30	−0.602714
$783$	4.64798e30	1.91764
$784$	1.45120e30	0.590758
$785$	1.19738e30	0.480951
$786$	8.06742e30	3.19741
$787$	1.44873e30	0.566567	0.283284	−	0.959036i	$-0.408576\pi$
$787$	1.44873e30	0.566567	0.283284	+	0.959036i	$0.408576\pi$
$788$	−1.18588e30	−0.457631
$789$	−2.86364e30	−1.09046
$790$	1.72639e30	0.648716
$791$	8.11622e29	0.300954
$792$	7.25136e30	2.65341
$793$	−3.93607e30	−1.42133
$794$	−1.03030e30	−0.367156
$795$	−2.38447e30	−0.838565
$796$	4.88077e30	1.69395
$797$	3.51473e30	1.20387	0.601936	−	0.798545i	$-0.294396\pi$
$797$	3.51473e30	1.20387	0.601936	+	0.798545i	$0.294396\pi$
$798$	1.44190e30	0.487422
$799$	2.20947e30	0.737133
$800$	−3.53436e28	−0.0116377
$801$	−4.36701e30	−1.41920
$802$	−4.36519e30	−1.40014
$803$	−1.03541e30	−0.327791
$804$	1.31840e30	0.411963
$805$	1.31909e30	0.406835
$806$	2.51471e30	0.765543
$807$	−8.22436e29	−0.247133
$808$	−1.09587e31	−3.25041
$809$	−2.11630e29	−0.0619610	−0.0309805	−	0.999520i	$-0.509863\pi$
$809$	−2.11630e29	−0.0619610	−0.0309805	+	0.999520i	$0.509863\pi$
$810$	3.89622e30	1.12603
$811$	−3.25295e30	−0.928024	−0.464012	−	0.885829i	$-0.653590\pi$
$811$	−3.25295e30	−0.928024	−0.464012	+	0.885829i	$0.653590\pi$
$812$	−8.46509e30	−2.38393
$813$	−5.56120e30	−1.54603
$814$	5.39139e30	1.47960
$815$	2.04634e30	0.554400
$816$	3.07577e30	0.822635
$817$	−1.38095e29	−0.0364624
$818$	7.33299e30	1.91149
$819$	7.80401e30	2.00834
$820$	−4.55518e30	−1.15734
$821$	1.43191e30	0.359179	0.179590	−	0.983742i	$-0.442523\pi$
$821$	1.43191e30	0.359179	0.179590	+	0.983742i	$0.442523\pi$
$822$	−1.71615e31	−4.25012
$823$	2.77587e29	0.0678736	0.0339368	−	0.999424i	$-0.489196\pi$
$823$	2.77587e29	0.0678736	0.0339368	+	0.999424i	$0.489196\pi$
$824$	−8.40482e29	−0.202905
$825$	−1.08399e30	−0.258380
$826$	1.78018e31	4.18960
$827$	5.54220e30	1.28788	0.643938	−	0.765077i	$-0.277299\pi$
$827$	5.54220e30	1.28788	0.643938	+	0.765077i	$0.277299\pi$
$828$	1.32440e31	3.03880
$829$	−1.87387e30	−0.424537	−0.212269	−	0.977211i	$-0.568085\pi$
$829$	−1.87387e30	−0.424537	−0.212269	+	0.977211i	$0.568085\pi$
$830$	3.74005e29	0.0836677
$831$	−1.11627e31	−2.46580
$832$	−3.53706e30	−0.771521
$833$	−1.41161e30	−0.304049
$834$	−1.10264e31	−2.34525
$835$	2.58599e30	0.543148
$836$	−8.70033e29	−0.180455
$837$	−5.98259e30	−1.22538
$838$	1.64069e30	0.331868
$839$	−5.51808e30	−1.10227	−0.551134	−	0.834417i	$-0.685805\pi$
$839$	−5.51808e30	−1.10227	−0.551134	+	0.834417i	$0.685805\pi$
$840$	−8.69454e30	−1.71520
$841$	−5.60226e29	−0.109145
$842$	9.17060e30	1.76450
$843$	6.12447e30	1.16380
$844$	1.39675e31	2.62134
$845$	−1.10964e30	−0.205678
$846$	−3.05390e31	−5.59070
$847$	−3.30667e30	−0.597881
$848$	5.62008e30	1.00366
$849$	1.04627e31	1.84549
$850$	−9.68729e29	−0.168773
$851$	4.88129e30	0.839991
$852$	1.63852e31	2.78507
$853$	4.13486e30	0.694218	0.347109	−	0.937825i	$-0.387163\pi$
$853$	4.13486e30	0.694218	0.347109	+	0.937825i	$0.387163\pi$
$854$	−2.56544e31	−4.25455
$855$	−7.31749e29	−0.119872
$856$	5.56753e30	0.900923
$857$	6.80809e30	1.08825	0.544123	−	0.839006i	$-0.316863\pi$
$857$	6.80809e30	1.08825	0.544123	+	0.839006i	$0.316863\pi$
$858$	−1.03850e31	−1.63979
$859$	1.12597e30	0.175630	0.0878150	−	0.996137i	$-0.472012\pi$
$859$	1.12597e30	0.175630	0.0878150	+	0.996137i	$0.472012\pi$
$860$	1.67979e30	0.258834
$861$	1.93672e31	2.94804
$862$	5.93967e30	0.893174
$863$	−5.16076e30	−0.766655	−0.383327	−	0.923613i	$-0.625222\pi$
$863$	−5.16076e30	−0.766655	−0.383327	+	0.923613i	$0.625222\pi$
$864$	8.05550e29	0.118222
$865$	1.26334e30	0.183169
$866$	−2.20617e31	−3.16011
$867$	9.54096e30	1.35018
$868$	1.08957e31	1.52335
$869$	4.42895e30	0.611777
$870$	9.47428e30	1.29299
$871$	−6.38423e29	−0.0860831
$872$	−8.08114e30	−1.07659
$873$	−1.78130e31	−2.34471
$874$	−1.18495e30	−0.154109
$875$	8.86532e29	0.113923
$876$	1.24647e31	1.58267
$877$	8.16969e29	0.102497	0.0512484	−	0.998686i	$-0.483680\pi$
$877$	8.16969e29	0.102497	0.0512484	+	0.998686i	$0.483680\pi$
$878$	1.53092e31	1.89785
$879$	1.61639e31	1.97999
$880$	2.55491e30	0.309249
$881$	6.95439e30	0.831787	0.415893	−	0.909413i	$-0.363469\pi$
$881$	6.95439e30	0.831787	0.415893	+	0.909413i	$0.363469\pi$
$882$	1.95112e31	2.30602
$883$	−1.55336e31	−1.81419	−0.907096	−	0.420923i	$-0.861706\pi$
$883$	−1.55336e31	−1.81419	−0.907096	+	0.420923i	$0.861706\pi$
$884$	−6.16954e30	−0.712040
$885$	−1.32449e31	−1.51058
$886$	−1.45359e31	−1.63828
$887$	−1.06611e31	−1.18742	−0.593708	−	0.804681i	$-0.702336\pi$
$887$	−1.06611e31	−1.18742	−0.593708	+	0.804681i	$0.702336\pi$
$888$	−3.21741e31	−3.54136
$889$	−4.15744e30	−0.452228
$890$	−4.75271e30	−0.510913
$891$	9.99552e30	1.06191
$892$	−2.72903e30	−0.286535
$893$	1.81637e30	0.188479
$894$	7.39728e30	0.758627
$895$	−5.91584e30	−0.599618
$896$	−2.23139e31	−2.23533
$897$	−9.40243e30	−0.930935
$898$	4.76448e30	0.466245
$899$	−5.88558e30	−0.569263
$900$	8.90103e30	0.850930
$901$	−5.46676e30	−0.516559
$902$	−1.75791e31	−1.64183
$903$	−7.14194e30	−0.659317
$904$	4.39632e30	0.401163
$905$	9.19054e30	0.828955
$906$	2.95481e31	2.63441
$907$	1.06190e31	0.935854	0.467927	−	0.883767i	$-0.345001\pi$
$907$	1.06190e31	0.935854	0.467927	+	0.883767i	$0.345001\pi$
$908$	2.24974e31	1.95988
$909$	−4.76994e31	−4.10763
$910$	8.49327e30	0.723004
$911$	−2.19601e30	−0.184796	−0.0923979	−	0.995722i	$-0.529453\pi$
$911$	−2.19601e30	−0.184796	−0.0923979	+	0.995722i	$0.529453\pi$
$912$	2.52855e30	0.210342
$913$	9.59487e29	0.0789035
$914$	3.33317e31	2.70971
$915$	1.90874e31	1.53400
$916$	−1.77530e29	−0.0141049
$917$	−1.69264e31	−1.32950
$918$	2.20793e31	1.71449
$919$	1.43391e31	1.10081	0.550403	−	0.834899i	$-0.314474\pi$
$919$	1.43391e31	1.10081	0.550403	+	0.834899i	$0.314474\pi$
$920$	7.14514e30	0.542298
$921$	1.21093e31	0.908643
$922$	3.12200e31	2.31610
$923$	−7.93438e30	−0.581963
$924$	−4.49961e31	−3.26302
$925$	3.28061e30	0.235216
$926$	−1.22787e31	−0.870433
$927$	−3.65833e30	−0.256416
$928$	7.92488e29	0.0549210
$929$	5.45871e30	0.374046	0.187023	−	0.982356i	$-0.440116\pi$
$929$	5.45871e30	0.374046	0.187023	+	0.982356i	$0.440116\pi$
$930$	−1.21947e31	−0.826228
$931$	−1.16047e30	−0.0777430
$932$	1.93883e31	1.28432
$933$	2.39432e31	1.56828
$934$	−4.06132e31	−2.63042
$935$	−2.48521e30	−0.159163
$936$	4.22721e31	2.67705
$937$	1.97723e31	1.23820	0.619101	−	0.785311i	$-0.287497\pi$
$937$	1.97723e31	1.23820	0.619101	+	0.785311i	$0.287497\pi$
$938$	−4.16109e30	−0.257678
$939$	−1.30169e31	−0.797113
$940$	−2.20944e31	−1.33795
$941$	−1.20635e31	−0.722409	−0.361204	−	0.932487i	$-0.617634\pi$
$941$	−1.20635e31	−0.722409	−0.361204	+	0.932487i	$0.617634\pi$
$942$	−5.56283e31	−3.29429
$943$	−1.59159e31	−0.932090
$944$	3.12176e31	1.80798
$945$	−2.02058e31	−1.15729
$946$	6.48256e30	0.367189
$947$	−2.35722e31	−1.32046	−0.660231	−	0.751062i	$-0.729542\pi$
$947$	−2.35722e31	−1.32046	−0.660231	+	0.751062i	$0.729542\pi$
$948$	−5.33179e31	−2.95383
$949$	−6.03594e30	−0.330712
$950$	−7.96378e29	−0.0431540
$951$	1.52478e31	0.817170
$952$	−1.99336e31	−1.05657
$953$	3.37366e31	1.76858	0.884292	−	0.466934i	$-0.154642\pi$
$953$	3.37366e31	1.76858	0.884292	+	0.466934i	$0.154642\pi$
$954$	7.55610e31	3.91778
$955$	−2.92492e30	−0.149996
$956$	−2.05548e30	−0.104257
$957$	2.43057e31	1.21936
$958$	2.85400e31	1.41617
$959$	3.60069e31	1.76722
$960$	1.71524e31	0.832679
$961$	−1.32500e31	−0.636237
$962$	3.14293e31	1.49278
$963$	2.42336e31	1.13852
$964$	−3.79451e31	−1.76339
$965$	−1.08372e31	−0.498172
$966$	−6.12828e31	−2.78663
$967$	−9.90225e30	−0.445406	−0.222703	−	0.974886i	$-0.571488\pi$
$967$	−9.90225e30	−0.445406	−0.222703	+	0.974886i	$0.571488\pi$
$968$	−1.79113e31	−0.796957
$969$	−2.45957e30	−0.108258
$970$	−1.93863e31	−0.844097
$971$	1.63836e30	0.0705680	0.0352840	−	0.999377i	$-0.488766\pi$
$971$	1.63836e30	0.0705680	0.0352840	+	0.999377i	$0.488766\pi$
$972$	−2.57764e31	−1.09831
$973$	2.31346e31	0.975164
$974$	3.42571e31	1.42850
$975$	−6.31917e30	−0.260682
$976$	−4.49880e31	−1.83600
$977$	−5.02241e30	−0.202777	−0.101389	−	0.994847i	$-0.532329\pi$
$977$	−5.02241e30	−0.202777	−0.101389	+	0.994847i	$0.532329\pi$
$978$	−9.50697e31	−3.79738
$979$	−1.21928e31	−0.481820
$980$	1.41160e31	0.551871
$981$	−3.51745e31	−1.36051
$982$	3.71157e30	0.142032
$983$	−2.84513e31	−1.07719	−0.538593	−	0.842566i	$-0.681044\pi$
$983$	−2.84513e31	−1.07719	−0.538593	+	0.842566i	$0.681044\pi$
$984$	1.04906e32	3.92965
$985$	−2.78475e30	−0.103206
$986$	2.17212e31	0.796484
$987$	9.39384e31	3.40811
$988$	−5.07189e30	−0.182063
$989$	5.86922e30	0.208458
$990$	3.43504e31	1.20715
$991$	2.50375e31	0.870597	0.435298	−	0.900286i	$-0.356643\pi$
$991$	2.50375e31	0.870597	0.435298	+	0.900286i	$0.356643\pi$
$992$	−1.02004e30	−0.0350949
$993$	6.83704e31	2.32756
$994$	−5.17144e31	−1.74203
$995$	1.14613e31	0.382025
$996$	−1.15508e31	−0.380968
$997$	−4.42681e31	−1.44475	−0.722374	−	0.691503i	$-0.756949\pi$
$997$	−4.42681e31	−1.44475	−0.722374	+	0.691503i	$0.756949\pi$
$998$	7.00306e31	2.26161
$999$	−7.47716e31	−2.38946

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.22.a.b.1.4	✓	4
3.2	odd	2		45.22.a.f.1.1		4
4.3	odd	2		80.22.a.g.1.4		4
5.2	odd	4		25.22.b.c.24.8		8
5.3	odd	4		25.22.b.c.24.1		8
5.4	even	2		25.22.a.c.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.22.a.b.1.4	✓	4	1.1	even	1	trivial
25.22.a.c.1.1		4	5.4	even	2
25.22.b.c.24.1		8	5.3	odd	4
25.22.b.c.24.8		8	5.2	odd	4
45.22.a.f.1.1		4	3.2	odd	2
80.22.a.g.1.4		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q+2501.16 q^{2} -181393. q^{3} +4.15867e6 q^{4} +9.76562e6 q^{5} -4.53695e8 q^{6} +9.51907e8 q^{7} +5.15621e9 q^{8} +2.24432e10 q^{9} +O(q^{10})\)	\(q+2501.16 q^{2} -181393. q^{3} +4.15867e6 q^{4} +9.76562e6 q^{5} -4.53695e8 q^{6} +9.51907e8 q^{7} +5.15621e9 q^{8} +2.24432e10 q^{9} +2.44254e10 q^{10} +6.26620e10 q^{11} -7.54356e11 q^{12} +3.65290e11 q^{13} +2.38088e12 q^{14} -1.77142e12 q^{15} +4.17515e12 q^{16} -4.06125e12 q^{17} +5.61342e13 q^{18} -3.33870e12 q^{19} +4.06121e13 q^{20} -1.72670e14 q^{21} +1.56728e14 q^{22} +1.41899e14 q^{23} -9.35302e14 q^{24} +9.53674e13 q^{25} +9.13651e14 q^{26} -2.17361e15 q^{27} +3.95867e15 q^{28} -2.13837e15 q^{29} -4.43061e15 q^{30} +2.75237e15 q^{31} -3.70604e14 q^{32} -1.13665e16 q^{33} -1.01579e16 q^{34} +9.29597e15 q^{35} +9.33340e16 q^{36} +3.43997e16 q^{37} -8.35063e15 q^{38} -6.62613e16 q^{39} +5.03536e16 q^{40} -1.12163e17 q^{41} -4.31875e17 q^{42} +4.13618e16 q^{43} +2.60591e17 q^{44} +2.19172e17 q^{45} +3.54913e17 q^{46} -5.44036e17 q^{47} -7.57345e17 q^{48} +3.47581e17 q^{49} +2.38530e17 q^{50} +7.36684e17 q^{51} +1.51912e18 q^{52} +1.34608e18 q^{53} -5.43656e18 q^{54} +6.11933e17 q^{55} +4.90823e18 q^{56} +6.05617e17 q^{57} -5.34841e18 q^{58} +7.47699e18 q^{59} -7.36676e18 q^{60} -1.07752e19 q^{61} +6.88413e18 q^{62} +2.13639e19 q^{63} -9.68287e18 q^{64} +3.56729e18 q^{65} -2.84294e19 q^{66} -1.74771e18 q^{67} -1.68894e19 q^{68} -2.57396e19 q^{69} +2.32507e19 q^{70} -2.17207e19 q^{71} +1.15722e20 q^{72} -1.65237e19 q^{73} +8.60394e19 q^{74} -1.72990e19 q^{75} -1.38845e19 q^{76} +5.96484e19 q^{77} -1.65730e20 q^{78} +7.06800e19 q^{79} +4.07730e19 q^{80} +1.59515e20 q^{81} -2.80539e20 q^{82} +1.53121e19 q^{83} -7.18077e20 q^{84} -3.96607e19 q^{85} +1.03453e20 q^{86} +3.87886e20 q^{87} +3.23098e20 q^{88} -1.94580e20 q^{89} +5.48185e20 q^{90} +3.47722e20 q^{91} +5.90113e20 q^{92} -4.99262e20 q^{93} -1.36072e21 q^{94} -3.26045e19 q^{95} +6.72251e19 q^{96} -7.93694e20 q^{97} +8.69358e20 q^{98} +1.40634e21 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2910 q^{2} + 83240 q^{3} + 9165268 q^{4} + 39062500 q^{5} - 158524712 q^{6} + 512613800 q^{7} + 5167363080 q^{8} + 21732888532 q^{9}+O(q^{10}) \) 4 * q + 2910 * q^2 + 83240 * q^3 + 9165268 * q^4 + 39062500 * q^5 - 158524712 * q^6 + 512613800 * q^7 + 5167363080 * q^8 + 21732888532 * q^9	\( 4 q + 2910 q^{2} + 83240 q^{3} + 9165268 q^{4} + 39062500 q^{5} - 158524712 q^{6} + 512613800 q^{7} + 5167363080 q^{8} + 21732888532 q^{9} + 28417968750 q^{10} + 33727076448 q^{11} - 142435377680 q^{12} + 863532165080 q^{13} + 2725405637616 q^{14} + 812890625000 q^{15} + 9168135122704 q^{16} + 17694691101480 q^{17} + 108219081471590 q^{18} + 65217596849840 q^{19} + 89504570312500 q^{20} - 248634744508992 q^{21} - 133302721028280 q^{22} + 306130984922520 q^{23} - 509427036802080 q^{24} + 381469726562500 q^{25} - 19\!\cdots\!12 q^{26}+ \cdots - 15\!\cdots\!16 q^{99}+O(q^{100}) \) 4 * q + 2910 * q^2 + 83240 * q^3 + 9165268 * q^4 + 39062500 * q^5 - 158524712 * q^6 + 512613800 * q^7 + 5167363080 * q^8 + 21732888532 * q^9 + 28417968750 * q^10 + 33727076448 * q^11 - 142435377680 * q^12 + 863532165080 * q^13 + 2725405637616 * q^14 + 812890625000 * q^15 + 9168135122704 * q^16 + 17694691101480 * q^17 + 108219081471590 * q^18 + 65217596849840 * q^19 + 89504570312500 * q^20 - 248634744508992 * q^21 - 133302721028280 * q^22 + 306130984922520 * q^23 - 509427036802080 * q^24 + 381469726562500 * q^25 - 1909802985226812 * q^26 - 3478503990916720 * q^27 - 2466701432057920 * q^28 - 1183867881941640 * q^29 - 1548092890625000 * q^30 + 8127647981305328 * q^31 + 6394106775900960 * q^32 - 27227776360130720 * q^33 + 32676043106528796 * q^34 + 5005994140625000 * q^35 + 132603401899613444 * q^36 + 50729262881561240 * q^37 + 35369554723756920 * q^38 - 90408012787467856 * q^39 + 50462530078125000 * q^40 - 151242912792059832 * q^41 - 584170109040328320 * q^42 + 195241056541629800 * q^43 - 614844690548787984 * q^44 + 212235239570312500 * q^45 - 156055372897688112 * q^46 - 461921266212226680 * q^47 - 268908035207420480 * q^48 + 348492786998301828 * q^49 + 277519226074218750 * q^50 + 3394366189837348048 * q^51 + 2124030127334250200 * q^52 + 1013253578565011640 * q^53 - 2325284713297481360 * q^54 + 329365980937500000 * q^55 + 3133890122325795840 * q^56 + 6889753607884864160 * q^57 - 15566576922395873820 * q^58 + 9994246603380823920 * q^59 - 1390970485156250000 * q^60 - 10817434481929098952 * q^61 + 3855611474231219520 * q^62 + 12245908869990535560 * q^63 - 45099981493147646912 * q^64 + 8432931299609375000 * q^65 - 81535658477725195744 * q^66 + 21966891437417653880 * q^67 - 2003292237110276760 * q^68 - 10872182089324606656 * q^69 + 26615289429843750000 * q^70 + 51295204524235287888 * q^71 + 203807399727091870440 * q^72 + 74737166154487034120 * q^73 - 95273704374004345644 * q^74 + 7938385009765625000 * q^75 + 33053497281514492880 * q^76 + 284152911785269322400 * q^77 - 411161554685929127600 * q^78 - 60935090437726582240 * q^79 + 89532569557656250000 * q^80 + 158163684388294667524 * q^81 + 209310572847889648620 * q^82 - 278730291142551479640 * q^83 - 1305319136534979185664 * q^84 + 172799717787890625000 * q^85 - 410177137146579139512 * q^86 + 180742525444629646640 * q^87 - 407444351717354555040 * q^88 - 323651892724949032920 * q^89 + 1056826967495996093750 * q^90 + 220855101702096981808 * q^91 + 2407334022772179833280 * q^92 + 193462123423446842880 * q^93 - 1285026294005215311264 * q^94 + 636890594236718750000 * q^95 - 20769436930632372352 * q^96 + 309141974076136362920 * q^97 + 746323122131488476270 * q^98 - 1516374777085318976416 * q^99

Introduction

L-functions

Modular forms

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