LMFDB - Embedded newform 13.10.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,10,Mod(1,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("13.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	13.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:	$6.69546587013$
Analytic rank:	$1$
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} - 1602x^{2} + 1544x + 342272 $ x^4 - x^3 - 1602x^2 + 1544x + 342272
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-36.8028$ of defining polynomial
Character	$\chi$	$=$	13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+28.8028 q^{2} -204.594 q^{3} +317.603 q^{4} -258.914 q^{5} -5892.88 q^{6} -8862.28 q^{7} -5599.18 q^{8} +22175.6 q^{9} +O(q^{10})$	\(q+28.8028 q^{2} -204.594 q^{3} +317.603 q^{4} -258.914 q^{5} -5892.88 q^{6} -8862.28 q^{7} -5599.18 q^{8} +22175.6 q^{9} -7457.46 q^{10} +36087.9 q^{11} -64979.6 q^{12} -28561.0 q^{13} -255259. q^{14} +52972.2 q^{15} -323885. q^{16} +327405. q^{17} +638720. q^{18} +265525. q^{19} -82231.9 q^{20} +1.81317e6 q^{21} +1.03943e6 q^{22} -2.42458e6 q^{23} +1.14556e6 q^{24} -1.88609e6 q^{25} -822638. q^{26} -509973. q^{27} -2.81469e6 q^{28} +3.99178e6 q^{29} +1.52575e6 q^{30} -6.45220e6 q^{31} -6.46202e6 q^{32} -7.38336e6 q^{33} +9.43018e6 q^{34} +2.29457e6 q^{35} +7.04304e6 q^{36} -8.15498e6 q^{37} +7.64787e6 q^{38} +5.84340e6 q^{39} +1.44971e6 q^{40} -720241. q^{41} +5.22244e7 q^{42} -4.13245e7 q^{43} +1.14616e7 q^{44} -5.74158e6 q^{45} -6.98348e7 q^{46} +3.67369e7 q^{47} +6.62649e7 q^{48} +3.81864e7 q^{49} -5.43247e7 q^{50} -6.69850e7 q^{51} -9.07106e6 q^{52} +1.67334e7 q^{53} -1.46887e7 q^{54} -9.34367e6 q^{55} +4.96215e7 q^{56} -5.43248e7 q^{57} +1.14975e8 q^{58} -5.89865e7 q^{59} +1.68241e7 q^{60} +1.28785e8 q^{61} -1.85842e8 q^{62} -1.96527e8 q^{63} -2.02955e7 q^{64} +7.39484e6 q^{65} -2.12662e8 q^{66} -1.91470e8 q^{67} +1.03985e8 q^{68} +4.96054e8 q^{69} +6.60901e7 q^{70} +3.40865e8 q^{71} -1.24165e8 q^{72} +3.19890e8 q^{73} -2.34887e8 q^{74} +3.85882e8 q^{75} +8.43316e7 q^{76} -3.19821e8 q^{77} +1.68307e8 q^{78} +2.44328e8 q^{79} +8.38584e7 q^{80} -3.32145e8 q^{81} -2.07450e7 q^{82} -4.38630e8 q^{83} +5.75868e8 q^{84} -8.47697e7 q^{85} -1.19026e9 q^{86} -8.16693e8 q^{87} -2.02063e8 q^{88} -7.90342e8 q^{89} -1.65374e8 q^{90} +2.53116e8 q^{91} -7.70054e8 q^{92} +1.32008e9 q^{93} +1.05813e9 q^{94} -6.87481e7 q^{95} +1.32209e9 q^{96} -1.65696e8 q^{97} +1.09988e9 q^{98} +8.00272e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 33 q^{2} - 163 q^{3} + 1429 q^{4} + 471 q^{5} - 4529 q^{6} - 11241 q^{7} - 45543 q^{8} - 29953 q^{9}+O(q^{10}) $ 4 * q - 33 * q^2 - 163 * q^3 + 1429 * q^4 + 471 * q^5 - 4529 * q^6 - 11241 * q^7 - 45543 * q^8 - 29953 * q^9	\( 4 q - 33 q^{2} - 163 q^{3} + 1429 q^{4} + 471 q^{5} - 4529 q^{6} - 11241 q^{7} - 45543 q^{8} - 29953 q^{9} - 67831 q^{10} - 40140 q^{11} - 155479 q^{12} - 114244 q^{13} - 277653 q^{14} + 83307 q^{15} + 726609 q^{16} + 78717 q^{17} + 1691026 q^{18} + 209664 q^{19} + 870843 q^{20} + 1138431 q^{21} + 1364090 q^{22} - 4257444 q^{23} + 3561573 q^{24} - 2900157 q^{25} + 942513 q^{26} - 2077801 q^{27} + 4035181 q^{28} - 1647936 q^{29} - 744143 q^{30} - 11366002 q^{31} - 29458959 q^{32} - 14413222 q^{33} + 26257659 q^{34} - 13789797 q^{35} - 11587714 q^{36} + 4636891 q^{37} + 25172466 q^{38} + 4655443 q^{39} + 22536791 q^{40} + 13859538 q^{41} + 75564923 q^{42} - 33368081 q^{43} + 66489222 q^{44} - 17423928 q^{45} + 71369332 q^{46} - 3943005 q^{47} - 620787 q^{48} + 23294923 q^{49} - 4217748 q^{50} - 19664471 q^{51} - 40813669 q^{52} - 171019326 q^{53} - 64946915 q^{54} - 121160538 q^{55} - 281552967 q^{56} - 47829030 q^{57} + 79964734 q^{58} - 63389388 q^{59} + 37708135 q^{60} + 77050190 q^{61} - 95878740 q^{62} - 155695476 q^{63} + 768962465 q^{64} - 13452231 q^{65} - 42396374 q^{66} - 41174072 q^{67} - 717615423 q^{68} + 546642556 q^{69} + 409056389 q^{70} + 252460989 q^{71} + 562579254 q^{72} + 594415068 q^{73} - 957058539 q^{74} + 533318748 q^{75} - 326897170 q^{76} + 561950454 q^{77} + 129352769 q^{78} + 115998984 q^{79} - 509107233 q^{80} + 437803700 q^{81} - 875148240 q^{82} - 79577862 q^{83} + 108899441 q^{84} + 549463469 q^{85} - 589924887 q^{86} - 1087526510 q^{87} - 2327564370 q^{88} - 1152240276 q^{89} + 877550038 q^{90} + 321054201 q^{91} - 4213481460 q^{92} + 1618266556 q^{93} + 1859909503 q^{94} - 1273705170 q^{95} + 3171454029 q^{96} + 1049098084 q^{97} + 420532254 q^{98} + 2132181050 q^{99}+O(q^{100}) \) 4 * q - 33 * q^2 - 163 * q^3 + 1429 * q^4 + 471 * q^5 - 4529 * q^6 - 11241 * q^7 - 45543 * q^8 - 29953 * q^9 - 67831 * q^10 - 40140 * q^11 - 155479 * q^12 - 114244 * q^13 - 277653 * q^14 + 83307 * q^15 + 726609 * q^16 + 78717 * q^17 + 1691026 * q^18 + 209664 * q^19 + 870843 * q^20 + 1138431 * q^21 + 1364090 * q^22 - 4257444 * q^23 + 3561573 * q^24 - 2900157 * q^25 + 942513 * q^26 - 2077801 * q^27 + 4035181 * q^28 - 1647936 * q^29 - 744143 * q^30 - 11366002 * q^31 - 29458959 * q^32 - 14413222 * q^33 + 26257659 * q^34 - 13789797 * q^35 - 11587714 * q^36 + 4636891 * q^37 + 25172466 * q^38 + 4655443 * q^39 + 22536791 * q^40 + 13859538 * q^41 + 75564923 * q^42 - 33368081 * q^43 + 66489222 * q^44 - 17423928 * q^45 + 71369332 * q^46 - 3943005 * q^47 - 620787 * q^48 + 23294923 * q^49 - 4217748 * q^50 - 19664471 * q^51 - 40813669 * q^52 - 171019326 * q^53 - 64946915 * q^54 - 121160538 * q^55 - 281552967 * q^56 - 47829030 * q^57 + 79964734 * q^58 - 63389388 * q^59 + 37708135 * q^60 + 77050190 * q^61 - 95878740 * q^62 - 155695476 * q^63 + 768962465 * q^64 - 13452231 * q^65 - 42396374 * q^66 - 41174072 * q^67 - 717615423 * q^68 + 546642556 * q^69 + 409056389 * q^70 + 252460989 * q^71 + 562579254 * q^72 + 594415068 * q^73 - 957058539 * q^74 + 533318748 * q^75 - 326897170 * q^76 + 561950454 * q^77 + 129352769 * q^78 + 115998984 * q^79 - 509107233 * q^80 + 437803700 * q^81 - 875148240 * q^82 - 79577862 * q^83 + 108899441 * q^84 + 549463469 * q^85 - 589924887 * q^86 - 1087526510 * q^87 - 2327564370 * q^88 - 1152240276 * q^89 + 877550038 * q^90 + 321054201 * q^91 - 4213481460 * q^92 + 1618266556 * q^93 + 1859909503 * q^94 - 1273705170 * q^95 + 3171454029 * q^96 + 1049098084 * q^97 + 420532254 * q^98 + 2132181050 * 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 $

$2$	28.8028	1.27292	0.636459	−	0.771311i	$-0.280399\pi$
$2$	28.8028	1.27292	0.636459	+	0.771311i	$0.280399\pi$
$3$	−204.594	−1.45830	−0.729150	−	0.684354i	$-0.760084\pi$
$3$	−204.594	−1.45830	−0.729150	+	0.684354i	$0.760084\pi$
$4$	317.603	0.620318
$5$	−258.914	−0.185264	−0.0926319	−	0.995700i	$-0.529528\pi$
$5$	−258.914	−0.185264	−0.0926319	+	0.995700i	$0.529528\pi$
$6$	−5892.88	−1.85629
$7$	−8862.28	−1.39510	−0.697548	−	0.716538i	$-0.745726\pi$
$7$	−8862.28	−1.39510	−0.697548	+	0.716538i	$0.745726\pi$
$8$	−5599.18	−0.483303
$9$	22175.6	1.12664
$10$	−7457.46	−0.235825
$11$	36087.9	0.743181	0.371591	−	0.928397i	$-0.378812\pi$
$11$	36087.9	0.743181	0.371591	+	0.928397i	$0.378812\pi$
$12$	−64979.6	−0.904610
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−255259.	−1.77584
$15$	52972.2	0.270170
$16$	−323885.	−1.23552
$17$	327405.	0.950747	0.475373	−	0.879784i	$-0.342313\pi$
$17$	327405.	0.950747	0.475373	+	0.879784i	$0.342313\pi$
$18$	638720.	1.43412
$19$	265525.	0.467428	0.233714	−	0.972305i	$-0.424912\pi$
$19$	265525.	0.467428	0.233714	+	0.972305i	$0.424912\pi$
$20$	−82231.9	−0.114923
$21$	1.81317e6	2.03447
$22$	1.03943e6	0.946008
$23$	−2.42458e6	−1.80660	−0.903299	−	0.429012i	$-0.858862\pi$
$23$	−2.42458e6	−1.80660	−0.903299	+	0.429012i	$0.858862\pi$
$24$	1.14556e6	0.704801
$25$	−1.88609e6	−0.965677
$26$	−822638.	−0.353044
$27$	−509973.	−0.184676
$28$	−2.81469e6	−0.865404
$29$	3.99178e6	1.04803	0.524017	−	0.851708i	$-0.324433\pi$
$29$	3.99178e6	1.04803	0.524017	+	0.851708i	$0.324433\pi$
$30$	1.52575e6	0.343904
$31$	−6.45220e6	−1.25482	−0.627408	−	0.778691i	$-0.715884\pi$
$31$	−6.45220e6	−1.25482	−0.627408	+	0.778691i	$0.715884\pi$
$32$	−6.46202e6	−1.08942
$33$	−7.38336e6	−1.08378
$34$	9.43018e6	1.21022
$35$	2.29457e6	0.258461
$36$	7.04304e6	0.698874
$37$	−8.15498e6	−0.715344	−0.357672	−	0.933847i	$-0.616429\pi$
$37$	−8.15498e6	−0.715344	−0.357672	+	0.933847i	$0.616429\pi$
$38$	7.64787e6	0.594997
$39$	5.84340e6	0.404460
$40$	1.44971e6	0.0895386
$41$	−720241.	−0.0398062	−0.0199031	−	0.999802i	$-0.506336\pi$
$41$	−720241.	−0.0398062	−0.0199031	+	0.999802i	$0.506336\pi$
$42$	5.22244e7	2.58971
$43$	−4.13245e7	−1.84332	−0.921658	−	0.388004i	$-0.873165\pi$
$43$	−4.13245e7	−1.84332	−0.921658	+	0.388004i	$0.873165\pi$
$44$	1.14616e7	0.461009
$45$	−5.74158e6	−0.208725
$46$	−6.98348e7	−2.29965
$47$	3.67369e7	1.09815	0.549076	−	0.835772i	$-0.314980\pi$
$47$	3.67369e7	1.09815	0.549076	+	0.835772i	$0.314980\pi$
$48$	6.62649e7	1.80176
$49$	3.81864e7	0.946295
$50$	−5.43247e7	−1.22923
$51$	−6.69850e7	−1.38647
$52$	−9.07106e6	−0.172045
$53$	1.67334e7	0.291302	0.145651	−	0.989336i	$-0.453472\pi$
$53$	1.67334e7	0.291302	0.145651	+	0.989336i	$0.453472\pi$
$54$	−1.46887e7	−0.235077
$55$	−9.34367e6	−0.137685
$56$	4.96215e7	0.674255
$57$	−5.43248e7	−0.681649
$58$	1.14975e8	1.33406
$59$	−5.89865e7	−0.633751	−0.316875	−	0.948467i	$-0.602634\pi$
$59$	−5.89865e7	−0.633751	−0.316875	+	0.948467i	$0.602634\pi$
$60$	1.68241e7	0.167591
$61$	1.28785e8	1.19091	0.595456	−	0.803388i	$-0.296971\pi$
$61$	1.28785e8	1.19091	0.595456	+	0.803388i	$0.296971\pi$
$62$	−1.85842e8	−1.59728
$63$	−1.96527e8	−1.57177
$64$	−2.02955e7	−0.151213
$65$	7.39484e6	0.0513829
$66$	−2.12662e8	−1.37956
$67$	−1.91470e8	−1.16082	−0.580410	−	0.814324i	$-0.697108\pi$
$67$	−1.91470e8	−1.16082	−0.580410	+	0.814324i	$0.697108\pi$
$68$	1.03985e8	0.589766
$69$	4.96054e8	2.63456
$70$	6.60901e7	0.328999
$71$	3.40865e8	1.59192	0.795958	−	0.605351i	$-0.206967\pi$
$71$	3.40865e8	1.59192	0.795958	+	0.605351i	$0.206967\pi$
$72$	−1.24165e8	−0.544508
$73$	3.19890e8	1.31840	0.659200	−	0.751968i	$-0.270895\pi$
$73$	3.19890e8	1.31840	0.659200	+	0.751968i	$0.270895\pi$
$74$	−2.34887e8	−0.910574
$75$	3.85882e8	1.40825
$76$	8.43316e7	0.289954
$77$	−3.19821e8	−1.03681
$78$	1.68307e8	0.514844
$79$	2.44328e8	0.705751	0.352876	−	0.935670i	$-0.385204\pi$
$79$	2.44328e8	0.705751	0.352876	+	0.935670i	$0.385204\pi$
$80$	8.38584e7	0.228898
$81$	−3.32145e8	−0.857325
$82$	−2.07450e7	−0.0506700
$83$	−4.38630e8	−1.01449	−0.507244	−	0.861802i	$-0.669336\pi$
$83$	−4.38630e8	−1.01449	−0.507244	+	0.861802i	$0.669336\pi$
$84$	5.75868e8	1.26202
$85$	−8.47697e7	−0.176139
$86$	−1.19026e9	−2.34639
$87$	−8.16693e8	−1.52835
$88$	−2.02063e8	−0.359182
$89$	−7.90342e8	−1.33524	−0.667621	−	0.744501i	$-0.732688\pi$
$89$	−7.90342e8	−1.33524	−0.667621	+	0.744501i	$0.732688\pi$
$90$	−1.65374e8	−0.265690
$91$	2.53116e8	0.386930
$92$	−7.70054e8	−1.12067
$93$	1.32008e9	1.82990
$94$	1.05813e9	1.39786
$95$	−6.87481e7	−0.0865974
$96$	1.32209e9	1.58869
$97$	−1.65696e8	−0.190037	−0.0950185	−	0.995476i	$-0.530291\pi$
$97$	−1.65696e8	−0.190037	−0.0950185	+	0.995476i	$0.530291\pi$
$98$	1.09988e9	1.20456
$99$	8.00272e8	0.837296
$100$	−5.99027e8	−0.599027
$101$	−7.41636e8	−0.709161	−0.354580	−	0.935026i	$-0.615376\pi$
$101$	−7.41636e8	−0.709161	−0.354580	+	0.935026i	$0.615376\pi$
$102$	−1.92936e9	−1.76487
$103$	1.42175e9	1.24467	0.622336	−	0.782750i	$-0.286184\pi$
$103$	1.42175e9	1.24467	0.622336	+	0.782750i	$0.286184\pi$
$104$	1.59918e8	0.134044
$105$	−4.69454e8	−0.376913
$106$	4.81970e8	0.370803
$107$	−1.44196e9	−1.06347	−0.531736	−	0.846910i	$-0.678460\pi$
$107$	−1.44196e9	−1.06347	−0.531736	+	0.846910i	$0.678460\pi$
$108$	−1.61969e8	−0.114558
$109$	−8.42758e7	−0.0571852	−0.0285926	−	0.999591i	$-0.509103\pi$
$109$	−8.42758e7	−0.0571852	−0.0285926	+	0.999591i	$0.509103\pi$
$110$	−2.69124e8	−0.175261
$111$	1.66846e9	1.04319
$112$	2.87036e9	1.72367
$113$	8.60241e8	0.496326	0.248163	−	0.968718i	$-0.420173\pi$
$113$	8.60241e8	0.496326	0.248163	+	0.968718i	$0.420173\pi$
$114$	−1.56471e9	−0.867683
$115$	6.27758e8	0.334697
$116$	1.26780e9	0.650115
$117$	−6.33358e8	−0.312473
$118$	−1.69898e9	−0.806712
$119$	−2.90155e9	−1.32638
$120$	−2.96601e8	−0.130574
$121$	−1.05561e9	−0.447681
$122$	3.70936e9	1.51593
$123$	1.47357e8	0.0580494
$124$	−2.04924e9	−0.778386
$125$	9.94026e8	0.364169
$126$	−5.66052e9	−2.00073
$127$	−1.44120e9	−0.491596	−0.245798	−	0.969321i	$-0.579050\pi$
$127$	−1.44120e9	−0.491596	−0.245798	+	0.969321i	$0.579050\pi$
$128$	2.72399e9	0.896934
$129$	8.45474e9	2.68811
$130$	2.12992e8	0.0654062
$131$	−4.54928e9	−1.34965	−0.674827	−	0.737976i	$-0.735782\pi$
$131$	−4.54928e9	−1.34965	−0.674827	+	0.737976i	$0.735782\pi$
$132$	−2.34498e9	−0.672289
$133$	−2.35316e9	−0.652107
$134$	−5.51489e9	−1.47763
$135$	1.32039e8	0.0342138
$136$	−1.83320e9	−0.459499
$137$	−1.99742e9	−0.484426	−0.242213	−	0.970223i	$-0.577873\pi$
$137$	−1.99742e9	−0.484426	−0.242213	+	0.970223i	$0.577873\pi$
$138$	1.42878e10	3.35358
$139$	3.55325e8	0.0807345	0.0403672	−	0.999185i	$-0.487147\pi$
$139$	3.55325e8	0.0807345	0.0403672	+	0.999185i	$0.487147\pi$
$140$	7.28762e8	0.160328
$141$	−7.51615e9	−1.60143
$142$	9.81789e9	2.02638
$143$	−1.03071e9	−0.206121
$144$	−7.18235e9	−1.39199
$145$	−1.03353e9	−0.194163
$146$	9.21372e9	1.67821
$147$	−7.81270e9	−1.37998
$148$	−2.59005e9	−0.443741
$149$	5.92546e9	0.984881	0.492440	−	0.870346i	$-0.336105\pi$
$149$	5.92546e9	0.984881	0.492440	+	0.870346i	$0.336105\pi$
$150$	1.11145e10	1.79258
$151$	−1.07568e10	−1.68378	−0.841891	−	0.539647i	$-0.818558\pi$
$151$	−1.07568e10	−1.68378	−0.841891	+	0.539647i	$0.818558\pi$
$152$	−1.48672e9	−0.225909
$153$	7.26040e9	1.07115
$154$	−9.21176e9	−1.31977
$155$	1.67056e9	0.232472
$156$	1.85588e9	0.250894
$157$	8.87634e9	1.16597	0.582983	−	0.812485i	$-0.301886\pi$
$157$	8.87634e9	1.16597	0.582983	+	0.812485i	$0.301886\pi$
$158$	7.03734e9	0.898363
$159$	−3.42355e9	−0.424805
$160$	1.67311e9	0.201829
$161$	2.14873e10	2.52038
$162$	−9.56672e9	−1.09130
$163$	2.75052e9	0.305190	0.152595	−	0.988289i	$-0.451237\pi$
$163$	2.75052e9	0.305190	0.152595	+	0.988289i	$0.451237\pi$
$164$	−2.28751e8	−0.0246925
$165$	1.91166e9	0.200785
$166$	−1.26338e10	−1.29136
$167$	−9.17849e9	−0.913160	−0.456580	−	0.889682i	$-0.650926\pi$
$167$	−9.17849e9	−0.913160	−0.456580	+	0.889682i	$0.650926\pi$
$168$	−1.01523e10	−0.983266
$169$	8.15731e8	0.0769231
$170$	−2.44161e9	−0.224210
$171$	5.88818e9	0.526622
$172$	−1.31248e10	−1.14344
$173$	9.75049e8	0.0827598	0.0413799	−	0.999143i	$-0.486825\pi$
$173$	9.75049e8	0.0827598	0.0413799	+	0.999143i	$0.486825\pi$
$174$	−2.35231e10	−1.94546
$175$	1.67150e10	1.34721
$176$	−1.16883e10	−0.918218
$177$	1.20683e10	0.924198
$178$	−2.27641e10	−1.69965
$179$	−8.88356e9	−0.646768	−0.323384	−	0.946268i	$-0.604820\pi$
$179$	−8.88356e9	−0.646768	−0.323384	+	0.946268i	$0.604820\pi$
$180$	−1.82354e9	−0.129476
$181$	−5.22791e9	−0.362055	−0.181028	−	0.983478i	$-0.557942\pi$
$181$	−5.22791e9	−0.362055	−0.181028	+	0.983478i	$0.557942\pi$
$182$	7.29045e9	0.492530
$183$	−2.63485e10	−1.73671
$184$	1.35757e10	0.873134
$185$	2.11144e9	0.132527
$186$	3.80220e10	2.32931
$187$	1.18154e10	0.706577
$188$	1.16678e10	0.681204
$189$	4.51952e9	0.257641
$190$	−1.98014e9	−0.110231
$191$	9.23471e9	0.502080	0.251040	−	0.967977i	$-0.419227\pi$
$191$	9.23471e9	0.502080	0.251040	+	0.967977i	$0.419227\pi$
$192$	4.15232e9	0.220514
$193$	1.07065e10	0.555441	0.277720	−	0.960662i	$-0.410421\pi$
$193$	1.07065e10	0.555441	0.277720	+	0.960662i	$0.410421\pi$
$194$	−4.77250e9	−0.241901
$195$	−1.51294e9	−0.0749317
$196$	1.21281e10	0.587004
$197$	−2.77001e10	−1.31034	−0.655169	−	0.755482i	$-0.727403\pi$
$197$	−2.77001e10	−1.31034	−0.655169	+	0.755482i	$0.727403\pi$
$198$	2.30501e10	1.06581
$199$	3.32299e10	1.50207	0.751035	−	0.660262i	$-0.229555\pi$
$199$	3.32299e10	1.50207	0.751035	+	0.660262i	$0.229555\pi$
$200$	1.05606e10	0.466715
$201$	3.91737e10	1.69282
$202$	−2.13612e10	−0.902703
$203$	−3.53763e10	−1.46211
$204$	−2.12746e10	−0.860055
$205$	1.86481e8	0.00737465
$206$	4.09503e10	1.58436
$207$	−5.37666e10	−2.03538
$208$	9.25048e9	0.342673
$209$	9.58225e9	0.347383
$210$	−1.35216e10	−0.479780
$211$	−1.49261e10	−0.518411	−0.259205	−	0.965822i	$-0.583461\pi$
$211$	−1.49261e10	−0.518411	−0.259205	+	0.965822i	$0.583461\pi$
$212$	5.31458e9	0.180700
$213$	−6.97389e10	−2.32149
$214$	−4.15325e10	−1.35371
$215$	1.06995e10	0.341500
$216$	2.85543e9	0.0892545
$217$	5.71812e10	1.75059
$218$	−2.42738e9	−0.0727920
$219$	−6.54474e10	−1.92262
$220$	−2.96758e9	−0.0854083
$221$	−9.35101e9	−0.263690
$222$	4.80563e10	1.32789
$223$	2.23373e10	0.604865	0.302433	−	0.953171i	$-0.402201\pi$
$223$	2.23373e10	0.604865	0.302433	+	0.953171i	$0.402201\pi$
$224$	5.72683e10	1.51984
$225$	−4.18252e10	−1.08797
$226$	2.47774e10	0.631782
$227$	5.20726e9	0.130165	0.0650824	−	0.997880i	$-0.479269\pi$
$227$	5.20726e9	0.130165	0.0650824	+	0.997880i	$0.479269\pi$
$228$	−1.72537e10	−0.422840
$229$	1.35573e10	0.325773	0.162887	−	0.986645i	$-0.447920\pi$
$229$	1.35573e10	0.325773	0.162887	+	0.986645i	$0.447920\pi$
$230$	1.80812e10	0.426042
$231$	6.54335e10	1.51198
$232$	−2.23507e10	−0.506518
$233$	2.06224e8	0.00458393	0.00229196	−	0.999997i	$-0.499270\pi$
$233$	2.06224e8	0.00458393	0.00229196	+	0.999997i	$0.499270\pi$
$234$	−1.82425e10	−0.397752
$235$	−9.51170e9	−0.203448
$236$	−1.87343e10	−0.393127
$237$	−4.99880e10	−1.02920
$238$	−8.35729e10	−1.68838
$239$	1.89887e10	0.376448	0.188224	−	0.982126i	$-0.439727\pi$
$239$	1.89887e10	0.376448	0.188224	+	0.982126i	$0.439727\pi$
$240$	−1.71569e10	−0.333801
$241$	−6.11533e10	−1.16773	−0.583866	−	0.811850i	$-0.698461\pi$
$241$	−6.11533e10	−1.16773	−0.583866	+	0.811850i	$0.698461\pi$
$242$	−3.04045e10	−0.569861
$243$	7.79927e10	1.43491
$244$	4.09024e10	0.738745
$245$	−9.88700e9	−0.175314
$246$	4.24430e9	0.0738920
$247$	−7.58366e9	−0.129641
$248$	3.61270e10	0.606457
$249$	8.97410e10	1.47943
$250$	2.86308e10	0.463557
$251$	−3.20685e9	−0.0509973	−0.0254986	−	0.999675i	$-0.508117\pi$
$251$	−3.20685e9	−0.0509973	−0.0254986	+	0.999675i	$0.508117\pi$
$252$	−6.24174e10	−0.974997
$253$	−8.74981e10	−1.34263
$254$	−4.15107e10	−0.625761
$255$	1.73433e10	0.256863
$256$	8.88499e10	1.29294
$257$	−2.80963e10	−0.401744	−0.200872	−	0.979617i	$-0.564378\pi$
$257$	−2.80963e10	−0.401744	−0.200872	+	0.979617i	$0.564378\pi$
$258$	2.43520e11	3.42174
$259$	7.22717e10	0.997975
$260$	2.34862e9	0.0318738
$261$	8.85201e10	1.18076
$262$	−1.31032e11	−1.71800
$263$	−1.25524e11	−1.61780	−0.808902	−	0.587944i	$-0.799938\pi$
$263$	−1.25524e11	−1.61780	−0.808902	+	0.587944i	$0.799938\pi$
$264$	4.13408e10	0.523795
$265$	−4.33252e9	−0.0539677
$266$	−6.77776e10	−0.830078
$267$	1.61699e11	1.94718
$268$	−6.08116e10	−0.720078
$269$	−1.78558e10	−0.207918	−0.103959	−	0.994582i	$-0.533151\pi$
$269$	−1.78558e10	−0.207918	−0.103959	+	0.994582i	$0.533151\pi$
$270$	3.80310e9	0.0435513
$271$	1.25204e11	1.41013	0.705063	−	0.709144i	$-0.250919\pi$
$271$	1.25204e11	1.41013	0.705063	+	0.709144i	$0.250919\pi$
$272$	−1.06041e11	−1.17467
$273$	−5.17859e10	−0.564260
$274$	−5.75314e10	−0.616634
$275$	−6.80650e10	−0.717673
$276$	1.57548e11	1.63427
$277$	−5.55594e10	−0.567020	−0.283510	−	0.958969i	$-0.591499\pi$
$277$	−5.55594e10	−0.567020	−0.283510	+	0.958969i	$0.591499\pi$
$278$	1.02344e10	0.102768
$279$	−1.43081e11	−1.41372
$280$	−1.28477e10	−0.124915
$281$	1.01237e11	0.968635	0.484317	−	0.874892i	$-0.339068\pi$
$281$	1.01237e11	0.968635	0.484317	+	0.874892i	$0.339068\pi$
$282$	−2.16486e11	−2.03849
$283$	−1.08041e11	−1.00127	−0.500635	−	0.865658i	$-0.666900\pi$
$283$	−1.08041e11	−1.00127	−0.500635	+	0.865658i	$0.666900\pi$
$284$	1.08260e11	0.987495
$285$	1.40654e10	0.126285
$286$	−2.96873e10	−0.262376
$287$	6.38298e9	0.0555335
$288$	−1.43299e11	−1.22738
$289$	−1.13940e10	−0.0960810
$290$	−2.97685e10	−0.247153
$291$	3.39003e10	0.277131
$292$	1.01598e11	0.817828
$293$	3.53224e9	0.0279992	0.0139996	−	0.999902i	$-0.495544\pi$
$293$	3.53224e9	0.0279992	0.0139996	+	0.999902i	$0.495544\pi$
$294$	−2.25028e11	−1.75660
$295$	1.52724e10	0.117411
$296$	4.56612e10	0.345728
$297$	−1.84039e10	−0.137248
$298$	1.70670e11	1.25367
$299$	6.92485e10	0.501060
$300$	1.22557e11	0.873562
$301$	3.66229e11	2.57160
$302$	−3.09826e11	−2.14332
$303$	1.51734e11	1.03417
$304$	−8.59996e10	−0.577518
$305$	−3.33441e10	−0.220633
$306$	2.09120e11	1.36348
$307$	−1.82031e11	−1.16956	−0.584781	−	0.811191i	$-0.698820\pi$
$307$	−1.82031e11	−1.16956	−0.584781	+	0.811191i	$0.698820\pi$
$308$	−1.01576e11	−0.643152
$309$	−2.90881e11	−1.81510
$310$	4.81170e10	0.295918
$311$	−1.51907e11	−0.920781	−0.460390	−	0.887717i	$-0.652291\pi$
$311$	−1.51907e11	−0.920781	−0.460390	+	0.887717i	$0.652291\pi$
$312$	−3.27183e10	−0.195477
$313$	6.10194e10	0.359351	0.179675	−	0.983726i	$-0.442495\pi$
$313$	6.10194e10	0.359351	0.179675	+	0.983726i	$0.442495\pi$
$314$	2.55664e11	1.48418
$315$	5.08835e10	0.291192
$316$	7.75994e10	0.437790
$317$	6.89227e10	0.383350	0.191675	−	0.981458i	$-0.438608\pi$
$317$	6.89227e10	0.383350	0.191675	+	0.981458i	$0.438608\pi$
$318$	−9.86080e10	−0.540742
$319$	1.44055e11	0.778880
$320$	5.25478e9	0.0280143
$321$	2.95016e11	1.55086
$322$	6.18896e11	3.20823
$323$	8.69341e10	0.444405
$324$	−1.05490e11	−0.531814
$325$	5.38686e10	0.267831
$326$	7.92227e10	0.388481
$327$	1.72423e10	0.0833931
$328$	4.03276e9	0.0192385
$329$	−3.25573e11	−1.53203
$330$	5.50611e10	0.255583
$331$	4.70422e10	0.215408	0.107704	−	0.994183i	$-0.465650\pi$
$331$	4.70422e10	0.215408	0.107704	+	0.994183i	$0.465650\pi$
$332$	−1.39310e11	−0.629306
$333$	−1.80842e11	−0.805934
$334$	−2.64366e11	−1.16238
$335$	4.95744e10	0.215058
$336$	−5.87258e11	−2.51363
$337$	−3.76711e11	−1.59101	−0.795507	−	0.605944i	$-0.792795\pi$
$337$	−3.76711e11	−1.59101	−0.795507	+	0.605944i	$0.792795\pi$
$338$	2.34954e10	0.0979167
$339$	−1.76000e11	−0.723792
$340$	−2.69231e10	−0.109262
$341$	−2.32846e11	−0.932556
$342$	1.69596e11	0.670346
$343$	1.92062e10	0.0749235
$344$	2.31383e11	0.890880
$345$	−1.28435e11	−0.488089
$346$	2.80842e10	0.105346
$347$	1.68331e11	0.623278	0.311639	−	0.950201i	$-0.399122\pi$
$347$	1.68331e11	0.623278	0.311639	+	0.950201i	$0.399122\pi$
$348$	−2.59384e11	−0.948062
$349$	−9.36126e10	−0.337769	−0.168884	−	0.985636i	$-0.554016\pi$
$349$	−9.36126e10	−0.337769	−0.168884	+	0.985636i	$0.554016\pi$
$350$	4.81441e11	1.71489
$351$	1.45653e10	0.0512199
$352$	−2.33201e11	−0.809634
$353$	−3.49043e11	−1.19644	−0.598222	−	0.801330i	$-0.704126\pi$
$353$	−3.49043e11	−1.19644	−0.598222	+	0.801330i	$0.704126\pi$
$354$	3.47600e11	1.17643
$355$	−8.82548e10	−0.294924
$356$	−2.51015e11	−0.828276
$357$	5.93640e11	1.93426
$358$	−2.55872e11	−0.823282
$359$	5.83173e11	1.85299	0.926493	−	0.376312i	$-0.122808\pi$
$359$	5.83173e11	1.85299	0.926493	+	0.376312i	$0.122808\pi$
$360$	3.21481e10	0.100878
$361$	−2.52184e11	−0.781512
$362$	−1.50579e11	−0.460866
$363$	2.15971e11	0.652854
$364$	8.03903e10	0.240020
$365$	−8.28239e10	−0.244252
$366$	−7.58912e11	−2.21068
$367$	5.28604e11	1.52101	0.760507	−	0.649329i	$-0.224950\pi$
$367$	5.28604e11	1.52101	0.760507	+	0.649329i	$0.224950\pi$
$368$	7.85286e11	2.23209
$369$	−1.59718e10	−0.0448472
$370$	6.08154e10	0.168696
$371$	−1.48296e11	−0.406394
$372$	4.19261e11	1.13512
$373$	−4.19405e11	−1.12187	−0.560937	−	0.827858i	$-0.689559\pi$
$373$	−4.19405e11	−1.12187	−0.560937	+	0.827858i	$0.689559\pi$
$374$	3.40316e11	0.899414
$375$	−2.03372e11	−0.531067
$376$	−2.05697e11	−0.530740
$377$	−1.14009e11	−0.290672
$378$	1.30175e11	0.327955
$379$	4.24128e11	1.05590	0.527948	−	0.849277i	$-0.322962\pi$
$379$	4.24128e11	1.05590	0.527948	+	0.849277i	$0.322962\pi$
$380$	−2.18346e10	−0.0537180
$381$	2.94861e11	0.716894
$382$	2.65986e11	0.639107
$383$	6.52696e10	0.154995	0.0774973	−	0.996993i	$-0.475307\pi$
$383$	6.52696e10	0.154995	0.0774973	+	0.996993i	$0.475307\pi$
$384$	−5.57311e11	−1.30800
$385$	8.28062e10	0.192083
$386$	3.08376e11	0.707030
$387$	−9.16396e11	−2.07675
$388$	−5.26254e10	−0.117883
$389$	−5.91803e11	−1.31040	−0.655200	−	0.755455i	$-0.727416\pi$
$389$	−5.91803e11	−1.31040	−0.655200	+	0.755455i	$0.727416\pi$
$390$	−4.35769e10	−0.0953819
$391$	−7.93819e11	−1.71762
$392$	−2.13813e11	−0.457347
$393$	9.30755e11	1.96820
$394$	−7.97842e11	−1.66795
$395$	−6.32600e10	−0.130750
$396$	2.54169e11	0.519390
$397$	−3.05131e11	−0.616495	−0.308248	−	0.951306i	$-0.599743\pi$
$397$	−3.05131e11	−0.616495	−0.308248	+	0.951306i	$0.599743\pi$
$398$	9.57115e11	1.91201
$399$	4.81441e11	0.950967
$400$	6.10876e11	1.19312
$401$	2.56722e11	0.495808	0.247904	−	0.968785i	$-0.420258\pi$
$401$	2.56722e11	0.495808	0.247904	+	0.968785i	$0.420258\pi$
$402$	1.12831e12	2.15483
$403$	1.84281e11	0.348023
$404$	−2.35546e11	−0.439906
$405$	8.59971e10	0.158831
$406$	−1.01894e12	−1.86114
$407$	−2.94296e11	−0.531631
$408$	3.75061e11	0.670087
$409$	−4.57003e11	−0.807540	−0.403770	−	0.914860i	$-0.632300\pi$
$409$	−4.57003e11	−0.807540	−0.403770	+	0.914860i	$0.632300\pi$
$410$	5.37117e9	0.00938732
$411$	4.08660e11	0.706438
$412$	4.51551e11	0.772093
$413$	5.22755e11	0.884144
$414$	−1.54863e12	−2.59087
$415$	1.13567e11	0.187948
$416$	1.84562e11	0.302150
$417$	−7.26973e10	−0.117735
$418$	2.75996e11	0.442190
$419$	−1.65068e11	−0.261637	−0.130818	−	0.991406i	$-0.541760\pi$
$419$	−1.65068e11	−0.261637	−0.130818	+	0.991406i	$0.541760\pi$
$420$	−1.49100e11	−0.233806
$421$	−9.10255e10	−0.141219	−0.0706096	−	0.997504i	$-0.522494\pi$
$421$	−9.10255e10	−0.141219	−0.0706096	+	0.997504i	$0.522494\pi$
$422$	−4.29913e11	−0.659894
$423$	8.14664e11	1.23722
$424$	−9.36935e10	−0.140787
$425$	−6.17514e11	−0.918114
$426$	−2.00868e12	−2.95507
$427$	−1.14133e12	−1.66144
$428$	−4.57971e11	−0.659691
$429$	2.10876e11	0.300587
$430$	3.08176e11	0.434701
$431$	7.94605e11	1.10918	0.554592	−	0.832122i	$-0.312874\pi$
$431$	7.94605e11	1.10918	0.554592	+	0.832122i	$0.312874\pi$
$432$	1.65173e11	0.228171
$433$	−8.26325e11	−1.12968	−0.564840	−	0.825200i	$-0.691062\pi$
$433$	−8.26325e11	−1.12968	−0.564840	+	0.825200i	$0.691062\pi$
$434$	1.64698e12	2.22836
$435$	2.11453e11	0.283148
$436$	−2.67662e10	−0.0354730
$437$	−6.43787e11	−0.844453
$438$	−1.88507e12	−2.44734
$439$	1.21562e12	1.56210	0.781050	−	0.624469i	$-0.214684\pi$
$439$	1.21562e12	1.56210	0.781050	+	0.624469i	$0.214684\pi$
$440$	5.23169e10	0.0665434
$441$	8.46807e11	1.06613
$442$	−2.69335e11	−0.335655
$443$	−8.73136e11	−1.07712	−0.538561	−	0.842586i	$-0.681032\pi$
$443$	−8.73136e11	−1.07712	−0.538561	+	0.842586i	$0.681032\pi$
$444$	5.29907e11	0.647108
$445$	2.04631e11	0.247372
$446$	6.43377e11	0.769943
$447$	−1.21231e12	−1.43625
$448$	1.79864e11	0.210957
$449$	1.22107e12	1.41785	0.708927	−	0.705282i	$-0.249179\pi$
$449$	1.22107e12	1.41785	0.708927	+	0.705282i	$0.249179\pi$
$450$	−1.20468e12	−1.38489
$451$	−2.59920e10	−0.0295832
$452$	2.73215e11	0.307880
$453$	2.20077e12	2.45546
$454$	1.49984e11	0.165689
$455$	−6.55352e10	−0.0716842
$456$	3.04174e11	0.329443
$457$	6.32643e11	0.678478	0.339239	−	0.940700i	$-0.389830\pi$
$457$	6.32643e11	0.678478	0.339239	+	0.940700i	$0.389830\pi$
$458$	3.90490e11	0.414682
$459$	−1.66968e11	−0.175580
$460$	1.99378e11	0.207619
$461$	8.09117e11	0.834367	0.417184	−	0.908822i	$-0.363017\pi$
$461$	8.09117e11	0.834367	0.417184	+	0.908822i	$0.363017\pi$
$462$	1.88467e12	1.92463
$463$	7.69685e11	0.778393	0.389196	−	0.921155i	$-0.372753\pi$
$463$	7.69685e11	0.778393	0.389196	+	0.921155i	$0.372753\pi$
$464$	−1.29288e12	−1.29487
$465$	−3.41787e11	−0.339014
$466$	5.93984e9	0.00583496
$467$	1.59708e12	1.55382	0.776909	−	0.629613i	$-0.216787\pi$
$467$	1.59708e12	1.55382	0.776909	+	0.629613i	$0.216787\pi$
$468$	−2.01156e11	−0.193833
$469$	1.69686e12	1.61946
$470$	−2.73964e11	−0.258972
$471$	−1.81604e12	−1.70033
$472$	3.30276e11	0.306294
$473$	−1.49132e12	−1.36992
$474$	−1.43980e12	−1.31008
$475$	−5.00804e11	−0.451384
$476$	−9.21542e11	−0.822780
$477$	3.71074e11	0.328192
$478$	5.46929e11	0.479187
$479$	1.61308e12	1.40006	0.700028	−	0.714115i	$-0.253171\pi$
$479$	1.61308e12	1.40006	0.700028	+	0.714115i	$0.253171\pi$
$480$	−3.42308e11	−0.294328
$481$	2.32914e11	0.198401
$482$	−1.76139e12	−1.48643
$483$	−4.39617e12	−3.67547
$484$	−3.35265e11	−0.277705
$485$	4.29009e10	0.0352070
$486$	2.24641e12	1.82653
$487$	9.29058e11	0.748449	0.374225	−	0.927338i	$-0.377909\pi$
$487$	9.29058e11	0.748449	0.374225	+	0.927338i	$0.377909\pi$
$488$	−7.21089e11	−0.575572
$489$	−5.62739e11	−0.445058
$490$	−2.84774e11	−0.223160
$491$	−2.30662e12	−1.79106	−0.895528	−	0.445005i	$-0.853202\pi$
$491$	−2.30662e12	−1.79106	−0.895528	+	0.445005i	$0.853202\pi$
$492$	4.68010e10	0.0360091
$493$	1.30693e12	0.996415
$494$	−2.18431e11	−0.165022
$495$	−2.07202e11	−0.155121
$496$	2.08977e12	1.55036
$497$	−3.02084e12	−2.22088
$498$	2.58480e12	1.88319
$499$	−1.31410e11	−0.0948800	−0.0474400	−	0.998874i	$-0.515106\pi$
$499$	−1.31410e11	−0.0948800	−0.0474400	+	0.998874i	$0.515106\pi$
$500$	3.15706e11	0.225901
$501$	1.87786e12	1.33166
$502$	−9.23664e10	−0.0649153
$503$	−1.88419e12	−1.31241	−0.656203	−	0.754584i	$-0.727838\pi$
$503$	−1.88419e12	−1.31241	−0.656203	+	0.754584i	$0.727838\pi$
$504$	1.10039e12	0.759641
$505$	1.92020e11	0.131382
$506$	−2.52019e12	−1.70906
$507$	−1.66893e11	−0.112177
$508$	−4.57730e11	−0.304946
$509$	−1.00390e11	−0.0662919	−0.0331459	−	0.999451i	$-0.510553\pi$
$509$	−1.00390e11	−0.0662919	−0.0331459	+	0.999451i	$0.510553\pi$
$510$	4.99537e11	0.326966
$511$	−2.83495e12	−1.83930
$512$	1.16445e12	0.748866
$513$	−1.35411e11	−0.0863226
$514$	−8.09252e11	−0.511387
$515$	−3.68110e11	−0.230593
$516$	2.68525e12	1.66748
$517$	1.32576e12	0.816126
$518$	2.08163e12	1.27034
$519$	−1.99489e11	−0.120689
$520$	−4.14051e10	−0.0248335
$521$	−1.04516e11	−0.0621462	−0.0310731	−	0.999517i	$-0.509892\pi$
$521$	−1.04516e11	−0.0621462	−0.0310731	+	0.999517i	$0.509892\pi$
$522$	2.54963e12	1.50300
$523$	1.17694e12	0.687855	0.343927	−	0.938996i	$-0.388243\pi$
$523$	1.17694e12	0.687855	0.343927	+	0.938996i	$0.388243\pi$
$524$	−1.44487e12	−0.837215
$525$	−3.41979e12	−1.96464
$526$	−3.61544e12	−2.05933
$527$	−2.11248e12	−1.19301
$528$	2.39136e12	1.33904
$529$	4.07744e12	2.26379
$530$	−1.24789e11	−0.0686964
$531$	−1.30806e12	−0.714008
$532$	−7.47370e11	−0.404514
$533$	2.05708e10	0.0110403
$534$	4.65739e12	2.47860
$535$	3.73343e11	0.197023
$536$	1.07208e12	0.561028
$537$	1.81752e12	0.943181
$538$	−5.14296e11	−0.264663
$539$	1.37807e12	0.703269
$540$	4.19360e10	0.0212234
$541$	−2.98502e12	−1.49817	−0.749083	−	0.662476i	$-0.769506\pi$
$541$	−2.98502e12	−1.49817	−0.749083	+	0.662476i	$0.769506\pi$
$542$	3.60624e12	1.79497
$543$	1.06960e12	0.527985
$544$	−2.11570e12	−1.03576
$545$	2.18202e10	0.0105943
$546$	−1.49158e12	−0.718257
$547$	3.78628e12	1.80830	0.904148	−	0.427219i	$-0.140507\pi$
$547$	3.78628e12	1.80830	0.904148	+	0.427219i	$0.140507\pi$
$548$	−6.34387e11	−0.300498
$549$	2.85588e12	1.34173
$550$	−1.96047e12	−0.913539
$551$	1.05992e12	0.489880
$552$	−2.77750e12	−1.27329
$553$	−2.16530e12	−0.984591
$554$	−1.60027e12	−0.721770
$555$	−4.31987e11	−0.193265
$556$	1.12852e11	0.0500811
$557$	1.00551e12	0.442627	0.221313	−	0.975203i	$-0.428966\pi$
$557$	1.00551e12	0.442627	0.221313	+	0.975203i	$0.428966\pi$
$558$	−4.12115e12	−1.79955
$559$	1.18027e12	0.511244
$560$	−7.43177e11	−0.319335
$561$	−2.41735e12	−1.03040
$562$	2.91591e12	1.23299
$563$	2.76515e11	0.115993	0.0579964	−	0.998317i	$-0.481529\pi$
$563$	2.76515e11	0.115993	0.0579964	+	0.998317i	$0.481529\pi$
$564$	−2.38715e12	−0.993399
$565$	−2.22728e11	−0.0919512
$566$	−3.11190e12	−1.27453
$567$	2.94356e12	1.19605
$568$	−1.90857e12	−0.769378
$569$	8.39220e11	0.335638	0.167819	−	0.985818i	$-0.446328\pi$
$569$	8.39220e11	0.335638	0.167819	+	0.985818i	$0.446328\pi$
$570$	4.05125e11	0.160750
$571$	−1.02285e11	−0.0402672	−0.0201336	−	0.999797i	$-0.506409\pi$
$571$	−1.02285e11	−0.0402672	−0.0201336	+	0.999797i	$0.506409\pi$
$572$	−3.27356e11	−0.127861
$573$	−1.88936e12	−0.732184
$574$	1.83848e11	0.0706896
$575$	4.57297e12	1.74459
$576$	−4.50064e11	−0.170362
$577$	−1.44021e12	−0.540921	−0.270461	−	0.962731i	$-0.587176\pi$
$577$	−1.44021e12	−0.540921	−0.270461	+	0.962731i	$0.587176\pi$
$578$	−3.28181e11	−0.122303
$579$	−2.19047e12	−0.809999
$580$	−3.28251e11	−0.120443
$581$	3.88726e12	1.41531
$582$	9.76424e11	0.352765
$583$	6.03874e11	0.216490
$584$	−1.79112e12	−0.637187
$585$	1.63985e11	0.0578899
$586$	1.01738e11	0.0356407
$587$	−2.13185e11	−0.0741116	−0.0370558	−	0.999313i	$-0.511798\pi$
$587$	−2.13185e11	−0.0741116	−0.0370558	+	0.999313i	$0.511798\pi$
$588$	−2.48134e12	−0.856028
$589$	−1.71322e12	−0.586536
$590$	4.39889e11	0.149455
$591$	5.66727e12	1.91087
$592$	2.64128e12	0.883825
$593$	−1.76049e12	−0.584640	−0.292320	−	0.956321i	$-0.594427\pi$
$593$	−1.76049e12	−0.584640	−0.292320	+	0.956321i	$0.594427\pi$
$594$	−5.30084e11	−0.174705
$595$	7.51253e11	0.245731
$596$	1.88194e12	0.610940
$597$	−6.79863e12	−2.19047
$598$	1.99455e12	0.637808
$599$	−2.06753e12	−0.656191	−0.328096	−	0.944644i	$-0.606407\pi$
$599$	−2.06753e12	−0.656191	−0.328096	+	0.944644i	$0.606407\pi$
$600$	−2.16062e12	−0.680610
$601$	−1.24403e12	−0.388951	−0.194476	−	0.980907i	$-0.562301\pi$
$601$	−1.24403e12	−0.388951	−0.194476	+	0.980907i	$0.562301\pi$
$602$	1.05484e13	3.27344
$603$	−4.24597e12	−1.30782
$604$	−3.41639e12	−1.04448
$605$	2.73312e11	0.0829391
$606$	4.37037e12	1.31641
$607$	−1.31511e12	−0.393200	−0.196600	−	0.980484i	$-0.562990\pi$
$607$	−1.31511e12	−0.393200	−0.196600	+	0.980484i	$0.562990\pi$
$608$	−1.71583e12	−0.509223
$609$	7.23776e12	2.13219
$610$	−9.60406e11	−0.280847
$611$	−1.04924e12	−0.304573
$612$	2.30593e12	0.664452
$613$	−3.08252e12	−0.881726	−0.440863	−	0.897574i	$-0.645328\pi$
$613$	−3.08252e12	−0.881726	−0.440863	+	0.897574i	$0.645328\pi$
$614$	−5.24301e12	−1.48876
$615$	−3.81528e10	−0.0107544
$616$	1.79074e12	0.501094
$617$	−2.29075e10	−0.00636348	−0.00318174	−	0.999995i	$-0.501013\pi$
$617$	−2.29075e10	−0.00636348	−0.00318174	+	0.999995i	$0.501013\pi$
$618$	−8.37818e12	−2.31048
$619$	−4.45350e12	−1.21925	−0.609626	−	0.792689i	$-0.708680\pi$
$619$	−4.45350e12	−1.21925	−0.609626	+	0.792689i	$0.708680\pi$
$620$	5.30576e11	0.144207
$621$	1.23647e12	0.333635
$622$	−4.37535e12	−1.17208
$623$	7.00424e12	1.86279
$624$	−1.89259e12	−0.499719
$625$	3.42640e12	0.898210
$626$	1.75753e12	0.457423
$627$	−1.96047e12	−0.506589
$628$	2.81915e12	0.723270
$629$	−2.66998e12	−0.680111
$630$	1.46559e12	0.370663
$631$	3.83831e12	0.963847	0.481923	−	0.876213i	$-0.339938\pi$
$631$	3.83831e12	0.963847	0.481923	+	0.876213i	$0.339938\pi$
$632$	−1.36804e12	−0.341092
$633$	3.05378e12	0.755998
$634$	1.98517e12	0.487973
$635$	3.73148e11	0.0910749
$636$	−1.08733e12	−0.263515
$637$	−1.09064e12	−0.262455
$638$	4.14919e12	0.991449
$639$	7.55890e12	1.79351
$640$	−7.05279e11	−0.166169
$641$	9.09238e11	0.212724	0.106362	−	0.994327i	$-0.466080\pi$
$641$	9.09238e11	0.212724	0.106362	+	0.994327i	$0.466080\pi$
$642$	8.49729e12	1.97412
$643$	8.23839e12	1.90061	0.950305	−	0.311321i	$-0.100771\pi$
$643$	8.23839e12	1.90061	0.950305	+	0.311321i	$0.100771\pi$
$644$	6.82444e12	1.56344
$645$	−2.18905e12	−0.498009
$646$	2.50395e12	0.565691
$647$	−8.73559e12	−1.95985	−0.979925	−	0.199365i	$-0.936112\pi$
$647$	−8.73559e12	−1.95985	−0.979925	+	0.199365i	$0.936112\pi$
$648$	1.85974e12	0.414348
$649$	−2.12870e12	−0.470992
$650$	1.55157e12	0.340926
$651$	−1.16989e13	−2.55289
$652$	8.73573e11	0.189315
$653$	−6.13232e11	−0.131982	−0.0659911	−	0.997820i	$-0.521021\pi$
$653$	−6.13232e11	−0.131982	−0.0659911	+	0.997820i	$0.521021\pi$
$654$	4.96627e11	0.106153
$655$	1.17787e12	0.250042
$656$	2.33275e11	0.0491815
$657$	7.09375e12	1.48536
$658$	−9.37742e12	−1.95015
$659$	−8.83233e12	−1.82428	−0.912139	−	0.409882i	$-0.865570\pi$
$659$	−8.83233e12	−1.82428	−0.912139	+	0.409882i	$0.865570\pi$
$660$	6.07148e11	0.124551
$661$	−5.61801e12	−1.14466	−0.572329	−	0.820024i	$-0.693960\pi$
$661$	−5.61801e12	−1.14466	−0.572329	+	0.820024i	$0.693960\pi$
$662$	1.35495e12	0.274196
$663$	1.91316e12	0.384539
$664$	2.45597e12	0.490306
$665$	6.09265e11	0.120812
$666$	−5.20875e12	−1.02589
$667$	−9.67839e12	−1.89338
$668$	−2.91511e12	−0.566450
$669$	−4.57007e12	−0.882075
$670$	1.42788e12	0.273751
$671$	4.64757e12	0.885064
$672$	−1.17167e13	−2.21638
$673$	4.50151e12	0.845844	0.422922	−	0.906166i	$-0.361004\pi$
$673$	4.50151e12	0.845844	0.422922	+	0.906166i	$0.361004\pi$
$674$	−1.08503e13	−2.02523
$675$	9.61854e11	0.178337
$676$	2.59079e11	0.0477168
$677$	4.33098e12	0.792387	0.396193	−	0.918167i	$-0.370331\pi$
$677$	4.33098e12	0.792387	0.396193	+	0.918167i	$0.370331\pi$
$678$	−5.06929e12	−0.921327
$679$	1.46844e12	0.265120
$680$	4.74641e11	0.0851285
$681$	−1.06537e12	−0.189819
$682$	−6.70664e12	−1.18707
$683$	6.25107e12	1.09916	0.549580	−	0.835441i	$-0.314788\pi$
$683$	6.25107e12	1.09916	0.549580	+	0.835441i	$0.314788\pi$
$684$	1.87010e12	0.326673
$685$	5.17161e11	0.0897466
$686$	5.53193e11	0.0953715
$687$	−2.77375e12	−0.475075
$688$	1.33844e13	2.27746
$689$	−4.77923e11	−0.0807926
$690$	−3.69930e12	−0.621296
$691$	7.34082e12	1.22488	0.612440	−	0.790517i	$-0.290188\pi$
$691$	7.34082e12	1.22488	0.612440	+	0.790517i	$0.290188\pi$
$692$	3.09679e11	0.0513374
$693$	−7.09223e12	−1.16811
$694$	4.84841e12	0.793381
$695$	−9.19986e10	−0.0149572
$696$	4.57281e12	0.738656
$697$	−2.35810e11	−0.0378456
$698$	−2.69631e12	−0.429952
$699$	−4.21922e10	−0.00668474
$700$	5.30875e12	0.835701
$701$	−1.71509e11	−0.0268259	−0.0134130	−	0.999910i	$-0.504270\pi$
$701$	−1.71509e11	−0.0268259	−0.0134130	+	0.999910i	$0.504270\pi$
$702$	4.19523e11	0.0651987
$703$	−2.16535e12	−0.334372
$704$	−7.32421e11	−0.112379
$705$	1.94604e12	0.296688
$706$	−1.00534e13	−1.52297
$707$	6.57259e12	0.989348
$708$	3.83292e12	0.573297
$709$	−1.00896e13	−1.49956	−0.749780	−	0.661687i	$-0.769841\pi$
$709$	−1.00896e13	−1.49956	−0.749780	+	0.661687i	$0.769841\pi$
$710$	−2.54199e12	−0.375414
$711$	5.41813e12	0.795126
$712$	4.42527e12	0.645327
$713$	1.56439e13	2.26695
$714$	1.70985e13	2.46216
$715$	2.66865e11	0.0381868
$716$	−2.82145e12	−0.401202
$717$	−3.88497e12	−0.548974
$718$	1.67970e13	2.35870
$719$	8.18068e12	1.14159	0.570794	−	0.821093i	$-0.306635\pi$
$719$	8.18068e12	1.14159	0.570794	+	0.821093i	$0.306635\pi$
$720$	1.85961e12	0.257885
$721$	−1.25999e13	−1.73644
$722$	−7.26362e12	−0.994800
$723$	1.25116e13	1.70290
$724$	−1.66040e12	−0.224589
$725$	−7.52885e12	−1.01206
$726$	6.22058e12	0.831029
$727$	−9.98421e11	−0.132559	−0.0662795	−	0.997801i	$-0.521113\pi$
$727$	−9.98421e11	−0.132559	−0.0662795	+	0.997801i	$0.521113\pi$
$728$	−1.41724e12	−0.187005
$729$	−9.41920e12	−1.23521
$730$	−2.38556e12	−0.310912
$731$	−1.35298e13	−1.75253
$732$	−8.36837e12	−1.07731
$733$	−2.10457e12	−0.269274	−0.134637	−	0.990895i	$-0.542987\pi$
$733$	−2.10457e12	−0.269274	−0.134637	+	0.990895i	$0.542987\pi$
$734$	1.52253e13	1.93613
$735$	2.02282e12	0.255661
$736$	1.56677e13	1.96814
$737$	−6.90977e12	−0.862700
$738$	−4.60033e11	−0.0570867
$739$	−1.28931e13	−1.59023	−0.795113	−	0.606461i	$-0.792588\pi$
$739$	−1.28931e13	−1.59023	−0.795113	+	0.606461i	$0.792588\pi$
$740$	6.70599e11	0.0822092
$741$	1.55157e12	0.189056
$742$	−4.27135e12	−0.517306
$743$	2.72357e11	0.0327861	0.0163930	−	0.999866i	$-0.494782\pi$
$743$	2.72357e11	0.0327861	0.0163930	+	0.999866i	$0.494782\pi$
$744$	−7.39137e12	−0.884396
$745$	−1.53418e12	−0.182463
$746$	−1.20801e13	−1.42805
$747$	−9.72689e12	−1.14296
$748$	3.75259e12	0.438303
$749$	1.27790e13	1.48365
$750$	−5.85768e12	−0.676005
$751$	−1.40530e13	−1.61209	−0.806045	−	0.591855i	$-0.798396\pi$
$751$	−1.40530e13	−1.61209	−0.806045	+	0.591855i	$0.798396\pi$
$752$	−1.18985e13	−1.35679
$753$	6.56102e11	0.0743693
$754$	−3.28379e12	−0.370002
$755$	2.78508e12	0.311944
$756$	1.43541e12	0.159819
$757$	8.53220e12	0.944342	0.472171	−	0.881507i	$-0.343470\pi$
$757$	8.53220e12	0.944342	0.472171	+	0.881507i	$0.343470\pi$
$758$	1.22161e13	1.34407
$759$	1.79016e13	1.95796
$760$	3.84933e11	0.0418528
$761$	1.13835e13	1.23039	0.615197	−	0.788373i	$-0.289076\pi$
$761$	1.13835e13	1.23039	0.615197	+	0.788373i	$0.289076\pi$
$762$	8.49283e12	0.912547
$763$	7.46876e11	0.0797789
$764$	2.93297e12	0.311450
$765$	−1.87982e12	−0.198445
$766$	1.87995e12	0.197295
$767$	1.68471e12	0.175771
$768$	−1.81781e13	−1.88549
$769$	1.94858e12	0.200933	0.100466	−	0.994940i	$-0.467967\pi$
$769$	1.94858e12	0.200933	0.100466	+	0.994940i	$0.467967\pi$
$770$	2.38505e12	0.244506
$771$	5.74832e12	0.585864
$772$	3.40040e12	0.344550
$773$	−1.09355e13	−1.10161	−0.550807	−	0.834633i	$-0.685680\pi$
$773$	−1.09355e13	−1.10161	−0.550807	+	0.834633i	$0.685680\pi$
$774$	−2.63948e13	−2.64353
$775$	1.21694e13	1.21175
$776$	9.27760e11	0.0918455
$777$	−1.47863e13	−1.45535
$778$	−1.70456e13	−1.66803
$779$	−1.91242e11	−0.0186065
$780$	−4.80514e11	−0.0464815
$781$	1.23011e13	1.18308
$782$	−2.28642e13	−2.18638
$783$	−2.03570e12	−0.193547
$784$	−1.23680e13	−1.16917
$785$	−2.29821e12	−0.216011
$786$	2.68084e13	2.50535
$787$	7.50366e12	0.697247	0.348623	−	0.937263i	$-0.386649\pi$
$787$	7.50366e12	0.697247	0.348623	+	0.937263i	$0.386649\pi$
$788$	−8.79764e12	−0.812827
$789$	2.56814e13	2.35924
$790$	−1.82207e12	−0.166434
$791$	−7.62369e12	−0.692423
$792$	−4.48087e12	−0.404668
$793$	−3.67822e12	−0.330300
$794$	−8.78865e12	−0.784747
$795$	8.86406e11	0.0787011
$796$	1.05539e13	0.931762
$797$	1.65844e12	0.145592	0.0727962	−	0.997347i	$-0.476808\pi$
$797$	1.65844e12	0.145592	0.0727962	+	0.997347i	$0.476808\pi$
$798$	1.38669e13	1.21050
$799$	1.20278e13	1.04406
$800$	1.21880e13	1.05202
$801$	−1.75263e13	−1.50434
$802$	7.39433e12	0.631123
$803$	1.15441e13	0.979810
$804$	1.24417e13	1.05009
$805$	−5.56337e12	−0.466935
$806$	5.30782e12	0.443005
$807$	3.65318e12	0.303207
$808$	4.15256e12	0.342740
$809$	−7.07921e12	−0.581054	−0.290527	−	0.956867i	$-0.593831\pi$
$809$	−7.07921e12	−0.581054	−0.290527	+	0.956867i	$0.593831\pi$
$810$	2.47696e12	0.202179
$811$	−1.84596e13	−1.49840	−0.749201	−	0.662343i	$-0.769562\pi$
$811$	−1.84596e13	−1.49840	−0.749201	+	0.662343i	$0.769562\pi$
$812$	−1.12356e13	−0.906973
$813$	−2.56161e13	−2.05639
$814$	−8.47657e12	−0.676722
$815$	−7.12147e11	−0.0565406
$816$	2.16954e13	1.71302
$817$	−1.09727e13	−0.861616
$818$	−1.31630e13	−1.02793
$819$	5.61299e12	0.435930
$820$	5.92268e10	0.00457463
$821$	2.40377e13	1.84650	0.923250	−	0.384200i	$-0.125523\pi$
$821$	2.40377e13	1.84650	0.923250	+	0.384200i	$0.125523\pi$
$822$	1.17706e13	0.899237
$823$	−1.26494e12	−0.0961104	−0.0480552	−	0.998845i	$-0.515302\pi$
$823$	−1.26494e12	−0.0961104	−0.0480552	+	0.998845i	$0.515302\pi$
$824$	−7.96062e12	−0.601554
$825$	1.39257e13	1.04658
$826$	1.50568e13	1.12544
$827$	−9.81229e12	−0.729450	−0.364725	−	0.931115i	$-0.618837\pi$
$827$	−9.81229e12	−0.729450	−0.364725	+	0.931115i	$0.618837\pi$
$828$	−1.70764e13	−1.26258
$829$	1.26128e13	0.927504	0.463752	−	0.885965i	$-0.346503\pi$
$829$	1.26128e13	0.927504	0.463752	+	0.885965i	$0.346503\pi$
$830$	3.27107e12	0.239242
$831$	1.13671e13	0.826886
$832$	5.79658e11	0.0419389
$833$	1.25024e13	0.899687
$834$	−2.09389e12	−0.149867
$835$	2.37644e12	0.169175
$836$	3.04335e12	0.215488
$837$	3.29045e12	0.231734
$838$	−4.75441e12	−0.333042
$839$	−8.53632e12	−0.594760	−0.297380	−	0.954759i	$-0.596113\pi$
$839$	−8.53632e12	−0.594760	−0.297380	+	0.954759i	$0.596113\pi$
$840$	2.62856e12	0.182163
$841$	1.42715e12	0.0983759
$842$	−2.62179e12	−0.179760
$843$	−2.07124e13	−1.41256
$844$	−4.74056e12	−0.321580
$845$	−2.11204e11	−0.0142511
$846$	2.34646e13	1.57488
$847$	9.35511e12	0.624559
$848$	−5.41970e12	−0.359910
$849$	2.21046e13	1.46015
$850$	−1.77862e13	−1.16868
$851$	1.97724e13	1.29234
$852$	−2.21493e13	−1.44006
$853$	−1.12025e13	−0.724507	−0.362254	−	0.932080i	$-0.617993\pi$
$853$	−1.12025e13	−0.724507	−0.362254	+	0.932080i	$0.617993\pi$
$854$	−3.28734e13	−2.11487
$855$	−1.52453e12	−0.0975639
$856$	8.07379e12	0.513979
$857$	−2.23241e13	−1.41371	−0.706856	−	0.707357i	$-0.749887\pi$
$857$	−2.23241e13	−1.41371	−0.706856	+	0.707357i	$0.749887\pi$
$858$	6.07383e12	0.382622
$859$	−2.11323e13	−1.32428	−0.662138	−	0.749382i	$-0.730351\pi$
$859$	−2.11323e13	−1.32428	−0.662138	+	0.749382i	$0.730351\pi$
$860$	3.39819e12	0.211838
$861$	−1.30592e12	−0.0809845
$862$	2.28869e13	1.41190
$863$	1.17061e13	0.718395	0.359197	−	0.933262i	$-0.383050\pi$
$863$	1.17061e13	0.718395	0.359197	+	0.933262i	$0.383050\pi$
$864$	3.29546e12	0.201189
$865$	−2.52454e11	−0.0153324
$866$	−2.38005e13	−1.43799
$867$	2.33115e12	0.140115
$868$	1.81609e13	1.08592
$869$	8.81730e12	0.524501
$870$	6.09045e12	0.360423
$871$	5.46859e12	0.321954
$872$	4.71876e11	0.0276378
$873$	−3.67440e12	−0.214103
$874$	−1.85429e13	−1.07492
$875$	−8.80934e12	−0.508051
$876$	−2.07863e13	−1.19264
$877$	1.17836e13	0.672638	0.336319	−	0.941748i	$-0.390818\pi$
$877$	1.17836e13	0.672638	0.336319	+	0.941748i	$0.390818\pi$
$878$	3.50134e13	1.98842
$879$	−7.22674e11	−0.0408312
$880$	3.02627e12	0.170113
$881$	−1.93741e13	−1.08350	−0.541751	−	0.840539i	$-0.682238\pi$
$881$	−1.93741e13	−1.08350	−0.541751	+	0.840539i	$0.682238\pi$
$882$	2.43904e13	1.35710
$883$	−1.50199e13	−0.831466	−0.415733	−	0.909487i	$-0.636475\pi$
$883$	−1.50199e13	−0.831466	−0.415733	+	0.909487i	$0.636475\pi$
$884$	−2.96991e12	−0.163572
$885$	−3.12464e12	−0.171220
$886$	−2.51488e13	−1.37109
$887$	1.23661e13	0.670776	0.335388	−	0.942080i	$-0.391133\pi$
$887$	1.23661e13	0.670776	0.335388	+	0.942080i	$0.391133\pi$
$888$	−9.34200e12	−0.504175
$889$	1.27723e13	0.685824
$890$	5.89394e12	0.314884
$891$	−1.19864e13	−0.637148
$892$	7.09439e12	0.375209
$893$	9.75457e12	0.513306
$894$	−3.49180e13	−1.82823
$895$	2.30008e12	0.119823
$896$	−2.41408e13	−1.25131
$897$	−1.41678e13	−0.730696
$898$	3.51702e13	1.80481
$899$	−2.57558e13	−1.31509
$900$	−1.32838e13	−0.674887
$901$	5.47860e12	0.276954
$902$	−7.48644e11	−0.0376570
$903$	−7.49283e13	−3.75017
$904$	−4.81664e12	−0.239876
$905$	1.35358e12	0.0670757
$906$	6.33884e13	3.12560
$907$	9.76708e12	0.479217	0.239608	−	0.970870i	$-0.422981\pi$
$907$	9.76708e12	0.479217	0.239608	+	0.970870i	$0.422981\pi$
$908$	1.65384e12	0.0807436
$909$	−1.64462e13	−0.798967
$910$	−1.88760e12	−0.0912480
$911$	−1.91556e13	−0.921430	−0.460715	−	0.887548i	$-0.652407\pi$
$911$	−1.91556e13	−0.921430	−0.460715	+	0.887548i	$0.652407\pi$
$912$	1.75950e13	0.842194
$913$	−1.58293e13	−0.753949
$914$	1.82219e13	0.863647
$915$	6.82200e12	0.321749
$916$	4.30586e12	0.202083
$917$	4.03170e13	1.88290
$918$	−4.80914e12	−0.223499
$919$	−2.82464e13	−1.30630	−0.653150	−	0.757229i	$-0.726553\pi$
$919$	−2.82464e13	−1.30630	−0.653150	+	0.757229i	$0.726553\pi$
$920$	−3.51493e12	−0.161760
$921$	3.72425e13	1.70557
$922$	2.33049e13	1.06208
$923$	−9.73546e12	−0.441518
$924$	2.07819e13	0.937909
$925$	1.53810e13	0.690792
$926$	2.21691e13	0.990830
$927$	3.15281e13	1.40229
$928$	−2.57950e13	−1.14175
$929$	1.81017e13	0.797348	0.398674	−	0.917093i	$-0.369471\pi$
$929$	1.81017e13	0.797348	0.398674	+	0.917093i	$0.369471\pi$
$930$	−9.84444e12	−0.431537
$931$	1.01395e13	0.442324
$932$	6.54974e10	0.00284350
$933$	3.10792e13	1.34277
$934$	4.60004e13	1.97788
$935$	−3.05916e12	−0.130903
$936$	3.54629e12	0.151019
$937$	2.51202e13	1.06462	0.532310	−	0.846550i	$-0.321324\pi$
$937$	2.51202e13	1.06462	0.532310	+	0.846550i	$0.321324\pi$
$938$	4.88745e13	2.06143
$939$	−1.24842e13	−0.524041
$940$	−3.02095e12	−0.126202
$941$	8.09156e11	0.0336418	0.0168209	−	0.999859i	$-0.494645\pi$
$941$	8.09156e11	0.0336418	0.0168209	+	0.999859i	$0.494645\pi$
$942$	−5.23072e13	−2.16438
$943$	1.74628e12	0.0719138
$944$	1.91048e13	0.783014
$945$	−1.17017e12	−0.0477315
$946$	−4.29541e13	−1.74379
$947$	−1.25569e13	−0.507349	−0.253675	−	0.967290i	$-0.581639\pi$
$947$	−1.25569e13	−0.507349	−0.253675	+	0.967290i	$0.581639\pi$
$948$	−1.58763e13	−0.638430
$949$	−9.13636e12	−0.365658
$950$	−1.44246e13	−0.574575
$951$	−1.41012e13	−0.559040
$952$	1.62463e13	0.641045
$953$	−3.64201e13	−1.43029	−0.715144	−	0.698977i	$-0.753639\pi$
$953$	−3.64201e13	−1.43029	−0.715144	+	0.698977i	$0.753639\pi$
$954$	1.06880e13	0.417761
$955$	−2.39100e12	−0.0930173
$956$	6.03087e12	0.233518
$957$	−2.94728e13	−1.13584
$958$	4.64612e13	1.78216
$959$	1.77017e13	0.675821
$960$	−1.07509e12	−0.0408532
$961$	1.51913e13	0.574564
$962$	6.70859e12	0.252548
$963$	−3.19763e13	−1.19815
$964$	−1.94225e13	−0.724366
$965$	−2.77205e12	−0.102903
$966$	−1.26622e14	−4.67857
$967$	2.96691e13	1.09115	0.545575	−	0.838062i	$-0.316311\pi$
$967$	2.96691e13	1.09115	0.545575	+	0.838062i	$0.316311\pi$
$968$	5.91055e12	0.216366
$969$	−1.77862e13	−0.648076
$970$	1.23567e12	0.0448156
$971$	−1.05417e13	−0.380563	−0.190281	−	0.981730i	$-0.560940\pi$
$971$	−1.05417e13	−0.380563	−0.190281	+	0.981730i	$0.560940\pi$
$972$	2.47707e13	0.890103
$973$	−3.14899e12	−0.112632
$974$	2.67595e13	0.952714
$975$	−1.10212e13	−0.390577
$976$	−4.17114e13	−1.47140
$977$	−2.40729e13	−0.845285	−0.422643	−	0.906296i	$-0.638897\pi$
$977$	−2.40729e13	−0.845285	−0.422643	+	0.906296i	$0.638897\pi$
$978$	−1.62085e13	−0.566522
$979$	−2.85218e13	−0.992328
$980$	−3.14014e12	−0.108751
$981$	−1.86887e12	−0.0644270
$982$	−6.64372e13	−2.27987
$983$	−3.57135e13	−1.21995	−0.609974	−	0.792421i	$-0.708820\pi$
$983$	−3.57135e13	−1.21995	−0.609974	+	0.792421i	$0.708820\pi$
$984$	−8.25078e11	−0.0280555
$985$	7.17195e12	0.242758
$986$	3.76432e13	1.26835
$987$	6.66102e13	2.23416
$988$	−2.40859e12	−0.0804187
$989$	1.00195e14	3.33013
$990$	−5.96799e12	−0.197456
$991$	2.48780e13	0.819376	0.409688	−	0.912226i	$-0.365638\pi$
$991$	2.48780e13	0.819376	0.409688	+	0.912226i	$0.365638\pi$
$992$	4.16943e13	1.36702
$993$	−9.62454e12	−0.314129
$994$	−8.70089e13	−2.82699
$995$	−8.60369e12	−0.278279
$996$	2.85020e13	0.917717
$997$	−3.31717e13	−1.06326	−0.531630	−	0.846977i	$-0.678420\pi$
$997$	−3.31717e13	−1.06326	−0.531630	+	0.846977i	$0.678420\pi$
$998$	−3.78497e12	−0.120774
$999$	4.15882e12	0.132107

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.10.a.a.1.4	✓	4
3.2	odd	2		117.10.a.c.1.1		4
4.3	odd	2		208.10.a.g.1.4		4
5.4	even	2		325.10.a.a.1.1		4
13.12	even	2		169.10.a.a.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.a.1.4	✓	4	1.1	even	1	trivial
117.10.a.c.1.1		4	3.2	odd	2
169.10.a.a.1.1		4	13.12	even	2
208.10.a.g.1.4		4	4.3	odd	2
325.10.a.a.1.1		4	5.4	even	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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	13.a (trivial)

\(f(q)\)	\(=\)	\(q+28.8028 q^{2} -204.594 q^{3} +317.603 q^{4} -258.914 q^{5} -5892.88 q^{6} -8862.28 q^{7} -5599.18 q^{8} +22175.6 q^{9} +O(q^{10})\)	\(q+28.8028 q^{2} -204.594 q^{3} +317.603 q^{4} -258.914 q^{5} -5892.88 q^{6} -8862.28 q^{7} -5599.18 q^{8} +22175.6 q^{9} -7457.46 q^{10} +36087.9 q^{11} -64979.6 q^{12} -28561.0 q^{13} -255259. q^{14} +52972.2 q^{15} -323885. q^{16} +327405. q^{17} +638720. q^{18} +265525. q^{19} -82231.9 q^{20} +1.81317e6 q^{21} +1.03943e6 q^{22} -2.42458e6 q^{23} +1.14556e6 q^{24} -1.88609e6 q^{25} -822638. q^{26} -509973. q^{27} -2.81469e6 q^{28} +3.99178e6 q^{29} +1.52575e6 q^{30} -6.45220e6 q^{31} -6.46202e6 q^{32} -7.38336e6 q^{33} +9.43018e6 q^{34} +2.29457e6 q^{35} +7.04304e6 q^{36} -8.15498e6 q^{37} +7.64787e6 q^{38} +5.84340e6 q^{39} +1.44971e6 q^{40} -720241. q^{41} +5.22244e7 q^{42} -4.13245e7 q^{43} +1.14616e7 q^{44} -5.74158e6 q^{45} -6.98348e7 q^{46} +3.67369e7 q^{47} +6.62649e7 q^{48} +3.81864e7 q^{49} -5.43247e7 q^{50} -6.69850e7 q^{51} -9.07106e6 q^{52} +1.67334e7 q^{53} -1.46887e7 q^{54} -9.34367e6 q^{55} +4.96215e7 q^{56} -5.43248e7 q^{57} +1.14975e8 q^{58} -5.89865e7 q^{59} +1.68241e7 q^{60} +1.28785e8 q^{61} -1.85842e8 q^{62} -1.96527e8 q^{63} -2.02955e7 q^{64} +7.39484e6 q^{65} -2.12662e8 q^{66} -1.91470e8 q^{67} +1.03985e8 q^{68} +4.96054e8 q^{69} +6.60901e7 q^{70} +3.40865e8 q^{71} -1.24165e8 q^{72} +3.19890e8 q^{73} -2.34887e8 q^{74} +3.85882e8 q^{75} +8.43316e7 q^{76} -3.19821e8 q^{77} +1.68307e8 q^{78} +2.44328e8 q^{79} +8.38584e7 q^{80} -3.32145e8 q^{81} -2.07450e7 q^{82} -4.38630e8 q^{83} +5.75868e8 q^{84} -8.47697e7 q^{85} -1.19026e9 q^{86} -8.16693e8 q^{87} -2.02063e8 q^{88} -7.90342e8 q^{89} -1.65374e8 q^{90} +2.53116e8 q^{91} -7.70054e8 q^{92} +1.32008e9 q^{93} +1.05813e9 q^{94} -6.87481e7 q^{95} +1.32209e9 q^{96} -1.65696e8 q^{97} +1.09988e9 q^{98} +8.00272e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 33 q^{2} - 163 q^{3} + 1429 q^{4} + 471 q^{5} - 4529 q^{6} - 11241 q^{7} - 45543 q^{8} - 29953 q^{9}+O(q^{10}) \) 4 * q - 33 * q^2 - 163 * q^3 + 1429 * q^4 + 471 * q^5 - 4529 * q^6 - 11241 * q^7 - 45543 * q^8 - 29953 * q^9	\( 4 q - 33 q^{2} - 163 q^{3} + 1429 q^{4} + 471 q^{5} - 4529 q^{6} - 11241 q^{7} - 45543 q^{8} - 29953 q^{9} - 67831 q^{10} - 40140 q^{11} - 155479 q^{12} - 114244 q^{13} - 277653 q^{14} + 83307 q^{15} + 726609 q^{16} + 78717 q^{17} + 1691026 q^{18} + 209664 q^{19} + 870843 q^{20} + 1138431 q^{21} + 1364090 q^{22} - 4257444 q^{23} + 3561573 q^{24} - 2900157 q^{25} + 942513 q^{26} - 2077801 q^{27} + 4035181 q^{28} - 1647936 q^{29} - 744143 q^{30} - 11366002 q^{31} - 29458959 q^{32} - 14413222 q^{33} + 26257659 q^{34} - 13789797 q^{35} - 11587714 q^{36} + 4636891 q^{37} + 25172466 q^{38} + 4655443 q^{39} + 22536791 q^{40} + 13859538 q^{41} + 75564923 q^{42} - 33368081 q^{43} + 66489222 q^{44} - 17423928 q^{45} + 71369332 q^{46} - 3943005 q^{47} - 620787 q^{48} + 23294923 q^{49} - 4217748 q^{50} - 19664471 q^{51} - 40813669 q^{52} - 171019326 q^{53} - 64946915 q^{54} - 121160538 q^{55} - 281552967 q^{56} - 47829030 q^{57} + 79964734 q^{58} - 63389388 q^{59} + 37708135 q^{60} + 77050190 q^{61} - 95878740 q^{62} - 155695476 q^{63} + 768962465 q^{64} - 13452231 q^{65} - 42396374 q^{66} - 41174072 q^{67} - 717615423 q^{68} + 546642556 q^{69} + 409056389 q^{70} + 252460989 q^{71} + 562579254 q^{72} + 594415068 q^{73} - 957058539 q^{74} + 533318748 q^{75} - 326897170 q^{76} + 561950454 q^{77} + 129352769 q^{78} + 115998984 q^{79} - 509107233 q^{80} + 437803700 q^{81} - 875148240 q^{82} - 79577862 q^{83} + 108899441 q^{84} + 549463469 q^{85} - 589924887 q^{86} - 1087526510 q^{87} - 2327564370 q^{88} - 1152240276 q^{89} + 877550038 q^{90} + 321054201 q^{91} - 4213481460 q^{92} + 1618266556 q^{93} + 1859909503 q^{94} - 1273705170 q^{95} + 3171454029 q^{96} + 1049098084 q^{97} + 420532254 q^{98} + 2132181050 q^{99}+O(q^{100}) \) 4 * q - 33 * q^2 - 163 * q^3 + 1429 * q^4 + 471 * q^5 - 4529 * q^6 - 11241 * q^7 - 45543 * q^8 - 29953 * q^9 - 67831 * q^10 - 40140 * q^11 - 155479 * q^12 - 114244 * q^13 - 277653 * q^14 + 83307 * q^15 + 726609 * q^16 + 78717 * q^17 + 1691026 * q^18 + 209664 * q^19 + 870843 * q^20 + 1138431 * q^21 + 1364090 * q^22 - 4257444 * q^23 + 3561573 * q^24 - 2900157 * q^25 + 942513 * q^26 - 2077801 * q^27 + 4035181 * q^28 - 1647936 * q^29 - 744143 * q^30 - 11366002 * q^31 - 29458959 * q^32 - 14413222 * q^33 + 26257659 * q^34 - 13789797 * q^35 - 11587714 * q^36 + 4636891 * q^37 + 25172466 * q^38 + 4655443 * q^39 + 22536791 * q^40 + 13859538 * q^41 + 75564923 * q^42 - 33368081 * q^43 + 66489222 * q^44 - 17423928 * q^45 + 71369332 * q^46 - 3943005 * q^47 - 620787 * q^48 + 23294923 * q^49 - 4217748 * q^50 - 19664471 * q^51 - 40813669 * q^52 - 171019326 * q^53 - 64946915 * q^54 - 121160538 * q^55 - 281552967 * q^56 - 47829030 * q^57 + 79964734 * q^58 - 63389388 * q^59 + 37708135 * q^60 + 77050190 * q^61 - 95878740 * q^62 - 155695476 * q^63 + 768962465 * q^64 - 13452231 * q^65 - 42396374 * q^66 - 41174072 * q^67 - 717615423 * q^68 + 546642556 * q^69 + 409056389 * q^70 + 252460989 * q^71 + 562579254 * q^72 + 594415068 * q^73 - 957058539 * q^74 + 533318748 * q^75 - 326897170 * q^76 + 561950454 * q^77 + 129352769 * q^78 + 115998984 * q^79 - 509107233 * q^80 + 437803700 * q^81 - 875148240 * q^82 - 79577862 * q^83 + 108899441 * q^84 + 549463469 * q^85 - 589924887 * q^86 - 1087526510 * q^87 - 2327564370 * q^88 - 1152240276 * q^89 + 877550038 * q^90 + 321054201 * q^91 - 4213481460 * q^92 + 1618266556 * q^93 + 1859909503 * q^94 - 1273705170 * q^95 + 3171454029 * q^96 + 1049098084 * q^97 + 420532254 * q^98 + 2132181050 * q^99

Introduction

L-functions

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