LMFDB - Embedded newform 11.14.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,14,Mod(1,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("11.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	11.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:	$11.7954021847$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 1179x^{3} + 1520x^{2} + 251749x + 900864 $ x^5 - x^4 - 1179x^3 + 1520x^2 + 251749*x + 900864
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$20.4604$ of defining polynomial
Character	$\chi$	$=$	11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-93.8416 q^{2} +867.783 q^{3} +614.253 q^{4} -16509.6 q^{5} -81434.2 q^{6} +435884. q^{7} +711108. q^{8} -841275. q^{9} +O(q^{10})$	\(q-93.8416 q^{2} +867.783 q^{3} +614.253 q^{4} -16509.6 q^{5} -81434.2 q^{6} +435884. q^{7} +711108. q^{8} -841275. q^{9} +1.54929e6 q^{10} -1.77156e6 q^{11} +533039. q^{12} -2.78109e7 q^{13} -4.09041e7 q^{14} -1.43268e7 q^{15} -7.17635e7 q^{16} +1.26160e7 q^{17} +7.89466e7 q^{18} -2.24059e8 q^{19} -1.01411e7 q^{20} +3.78253e8 q^{21} +1.66246e8 q^{22} -8.42604e8 q^{23} +6.17088e8 q^{24} -9.48136e8 q^{25} +2.60982e9 q^{26} -2.11357e9 q^{27} +2.67743e8 q^{28} +3.25064e9 q^{29} +1.34445e9 q^{30} +4.27371e9 q^{31} +9.09008e8 q^{32} -1.53733e9 q^{33} -1.18391e9 q^{34} -7.19628e9 q^{35} -5.16756e8 q^{36} +6.57598e9 q^{37} +2.10260e10 q^{38} -2.41339e10 q^{39} -1.17401e10 q^{40} -2.16008e10 q^{41} -3.54959e10 q^{42} -5.32305e10 q^{43} -1.08819e9 q^{44} +1.38891e10 q^{45} +7.90713e10 q^{46} -2.53401e10 q^{47} -6.22752e10 q^{48} +9.31062e10 q^{49} +8.89746e10 q^{50} +1.09480e10 q^{51} -1.70829e10 q^{52} +1.16294e11 q^{53} +1.98341e11 q^{54} +2.92478e10 q^{55} +3.09961e11 q^{56} -1.94434e11 q^{57} -3.05045e11 q^{58} +1.65271e11 q^{59} -8.80026e9 q^{60} -5.75566e11 q^{61} -4.01052e11 q^{62} -3.66699e11 q^{63} +5.02584e11 q^{64} +4.59148e11 q^{65} +1.44266e11 q^{66} -7.20478e11 q^{67} +7.74944e9 q^{68} -7.31197e11 q^{69} +6.75311e11 q^{70} +1.13262e12 q^{71} -5.98238e11 q^{72} +3.93910e11 q^{73} -6.17100e11 q^{74} -8.22776e11 q^{75} -1.37629e11 q^{76} -7.72196e11 q^{77} +2.26476e12 q^{78} -3.75493e12 q^{79} +1.18479e12 q^{80} -4.92858e11 q^{81} +2.02706e12 q^{82} +6.73276e11 q^{83} +2.32343e11 q^{84} -2.08286e11 q^{85} +4.99524e12 q^{86} +2.82085e12 q^{87} -1.25977e12 q^{88} +8.55262e12 q^{89} -1.30338e12 q^{90} -1.21223e13 q^{91} -5.17572e11 q^{92} +3.70866e12 q^{93} +2.37796e12 q^{94} +3.69912e12 q^{95} +7.88822e11 q^{96} -2.42796e12 q^{97} -8.73723e12 q^{98} +1.49037e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 64 q^{2} + 480 q^{3} - 2400 q^{4} - 454 q^{5} + 79548 q^{6} - 313920 q^{7} - 255168 q^{8} + 1321749 q^{9}+O(q^{10}) $ 5 * q - 64 * q^2 + 480 * q^3 - 2400 * q^4 - 454 * q^5 + 79548 * q^6 - 313920 * q^7 - 255168 * q^8 + 1321749 * q^9	\( 5 q - 64 q^{2} + 480 q^{3} - 2400 q^{4} - 454 q^{5} + 79548 q^{6} - 313920 q^{7} - 255168 q^{8} + 1321749 q^{9} - 3535724 q^{10} - 8857805 q^{11} - 29768880 q^{12} - 36339498 q^{13} - 64558312 q^{14} - 162945300 q^{15} - 128942592 q^{16} - 309078454 q^{17} - 302859828 q^{18} - 147232948 q^{19} - 62530256 q^{20} - 859909128 q^{21} + 113379904 q^{22} + 677905444 q^{23} + 755940096 q^{24} + 1540265631 q^{25} + 1643160872 q^{26} + 5029885620 q^{27} + 6948937120 q^{28} + 2368825878 q^{29} + 7601916540 q^{30} - 83363076 q^{31} + 10024391680 q^{32} - 850349280 q^{33} + 7463914000 q^{34} + 591040520 q^{35} - 15037063632 q^{36} - 32935650382 q^{37} - 25107474384 q^{38} - 54599307000 q^{39} - 27853580928 q^{40} - 70273827286 q^{41} - 18264520200 q^{42} - 54501240436 q^{43} + 4251746400 q^{44} - 118334367738 q^{45} - 9391823524 q^{46} - 45017434472 q^{47} + 236995825920 q^{48} + 77867671053 q^{49} + 252640243516 q^{50} - 14973171168 q^{51} + 370262207008 q^{52} + 242684257518 q^{53} + 386371416420 q^{54} + 804288694 q^{55} + 508508098560 q^{56} - 78232137120 q^{57} + 338805253176 q^{58} - 384712501184 q^{59} + 607819216080 q^{60} - 795317095690 q^{61} + 567054167132 q^{62} - 1777323941640 q^{63} - 502608203776 q^{64} - 1104664950268 q^{65} - 140924134428 q^{66} - 1005952134296 q^{67} + 9188915584 q^{68} - 2334490276524 q^{69} - 50031562280 q^{70} - 1427050574148 q^{71} + 714622284864 q^{72} - 4111049036406 q^{73} + 2579474987436 q^{74} - 584109490620 q^{75} + 1028633987648 q^{76} + 556128429120 q^{77} + 4554998846160 q^{78} - 3666957194024 q^{79} + 1569918525184 q^{80} + 4090930814781 q^{81} + 4301648616232 q^{82} + 2718055516116 q^{83} + 8581863439392 q^{84} + 1506197091796 q^{85} + 6558172582872 q^{86} + 3556682104680 q^{87} + 452045677248 q^{88} + 7963494884214 q^{89} - 4671771563808 q^{90} - 604892444560 q^{91} + 6414213002576 q^{92} + 361484424660 q^{93} - 9832269652768 q^{94} - 5225122758984 q^{95} - 12178790559744 q^{96} - 13542719272730 q^{97} - 8557591646352 q^{98} - 2341558980189 q^{99}+O(q^{100}) \) 5 * q - 64 * q^2 + 480 * q^3 - 2400 * q^4 - 454 * q^5 + 79548 * q^6 - 313920 * q^7 - 255168 * q^8 + 1321749 * q^9 - 3535724 * q^10 - 8857805 * q^11 - 29768880 * q^12 - 36339498 * q^13 - 64558312 * q^14 - 162945300 * q^15 - 128942592 * q^16 - 309078454 * q^17 - 302859828 * q^18 - 147232948 * q^19 - 62530256 * q^20 - 859909128 * q^21 + 113379904 * q^22 + 677905444 * q^23 + 755940096 * q^24 + 1540265631 * q^25 + 1643160872 * q^26 + 5029885620 * q^27 + 6948937120 * q^28 + 2368825878 * q^29 + 7601916540 * q^30 - 83363076 * q^31 + 10024391680 * q^32 - 850349280 * q^33 + 7463914000 * q^34 + 591040520 * q^35 - 15037063632 * q^36 - 32935650382 * q^37 - 25107474384 * q^38 - 54599307000 * q^39 - 27853580928 * q^40 - 70273827286 * q^41 - 18264520200 * q^42 - 54501240436 * q^43 + 4251746400 * q^44 - 118334367738 * q^45 - 9391823524 * q^46 - 45017434472 * q^47 + 236995825920 * q^48 + 77867671053 * q^49 + 252640243516 * q^50 - 14973171168 * q^51 + 370262207008 * q^52 + 242684257518 * q^53 + 386371416420 * q^54 + 804288694 * q^55 + 508508098560 * q^56 - 78232137120 * q^57 + 338805253176 * q^58 - 384712501184 * q^59 + 607819216080 * q^60 - 795317095690 * q^61 + 567054167132 * q^62 - 1777323941640 * q^63 - 502608203776 * q^64 - 1104664950268 * q^65 - 140924134428 * q^66 - 1005952134296 * q^67 + 9188915584 * q^68 - 2334490276524 * q^69 - 50031562280 * q^70 - 1427050574148 * q^71 + 714622284864 * q^72 - 4111049036406 * q^73 + 2579474987436 * q^74 - 584109490620 * q^75 + 1028633987648 * q^76 + 556128429120 * q^77 + 4554998846160 * q^78 - 3666957194024 * q^79 + 1569918525184 * q^80 + 4090930814781 * q^81 + 4301648616232 * q^82 + 2718055516116 * q^83 + 8581863439392 * q^84 + 1506197091796 * q^85 + 6558172582872 * q^86 + 3556682104680 * q^87 + 452045677248 * q^88 + 7963494884214 * q^89 - 4671771563808 * q^90 - 604892444560 * q^91 + 6414213002576 * q^92 + 361484424660 * q^93 - 9832269652768 * q^94 - 5225122758984 * q^95 - 12178790559744 * q^96 - 13542719272730 * q^97 - 8557591646352 * q^98 - 2341558980189 * 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 $

$2$	−93.8416	−1.03681	−0.518407	−	0.855134i	$-0.673475\pi$
$2$	−93.8416	−1.03681	−0.518407	+	0.855134i	$0.673475\pi$
$3$	867.783	0.687263	0.343632	−	0.939105i	$-0.388343\pi$
$3$	867.783	0.687263	0.343632	+	0.939105i	$0.388343\pi$
$4$	614.253	0.0749821
$5$	−16509.6	−0.472533	−0.236266	−	0.971688i	$-0.575924\pi$
$5$	−16509.6	−0.472533	−0.236266	+	0.971688i	$0.575924\pi$
$6$	−81434.2	−0.712564
$7$	435884.	1.40034	0.700171	−	0.713975i	$-0.253107\pi$
$7$	435884.	1.40034	0.700171	+	0.713975i	$0.253107\pi$
$8$	711108.	0.959071
$9$	−841275.	−0.527669
$10$	1.54929e6	0.489928
$11$	−1.77156e6	−0.301511
$11$	−1.77156e6	−0.301511
$12$	533039.	0.0515324
$13$	−2.78109e7	−1.59803	−0.799013	−	0.601314i	$-0.794644\pi$
$13$	−2.78109e7	−1.59803	−0.799013	+	0.601314i	$0.794644\pi$
$14$	−4.09041e7	−1.45189
$15$	−1.43268e7	−0.324754
$16$	−7.17635e7	−1.06936
$17$	1.26160e7	0.126767	0.0633833	−	0.997989i	$-0.479811\pi$
$17$	1.26160e7	0.126767	0.0633833	+	0.997989i	$0.479811\pi$
$18$	7.89466e7	0.547094
$19$	−2.24059e8	−1.09261	−0.546303	−	0.837588i	$-0.683965\pi$
$19$	−2.24059e8	−1.09261	−0.546303	+	0.837588i	$0.683965\pi$
$20$	−1.01411e7	−0.0354315
$21$	3.78253e8	0.962403
$22$	1.66246e8	0.312611
$23$	−8.42604e8	−1.18684	−0.593420	−	0.804893i	$-0.702223\pi$
$23$	−8.42604e8	−1.18684	−0.593420	+	0.804893i	$0.702223\pi$
$24$	6.17088e8	0.659134
$25$	−9.48136e8	−0.776713
$26$	2.60982e9	1.65685
$27$	−2.11357e9	−1.04991
$28$	2.67743e8	0.105001
$29$	3.25064e9	1.01480	0.507401	−	0.861710i	$-0.330606\pi$
$29$	3.25064e9	1.01480	0.507401	+	0.861710i	$0.330606\pi$
$30$	1.34445e9	0.336710
$31$	4.27371e9	0.864877	0.432439	−	0.901663i	$-0.357653\pi$
$31$	4.27371e9	0.864877	0.432439	+	0.901663i	$0.357653\pi$
$32$	9.09008e8	0.149656
$33$	−1.53733e9	−0.207218
$34$	−1.18391e9	−0.131433
$35$	−7.19628e9	−0.661707
$36$	−5.16756e8	−0.0395657
$37$	6.57598e9	0.421356	0.210678	−	0.977556i	$-0.432433\pi$
$37$	6.57598e9	0.421356	0.210678	+	0.977556i	$0.432433\pi$
$38$	2.10260e10	1.13283
$39$	−2.41339e10	−1.09826
$40$	−1.17401e10	−0.453192
$41$	−2.16008e10	−0.710191	−0.355096	−	0.934830i	$-0.615552\pi$
$41$	−2.16008e10	−0.710191	−0.355096	+	0.934830i	$0.615552\pi$
$42$	−3.54959e10	−0.997833
$43$	−5.32305e10	−1.28415	−0.642075	−	0.766642i	$-0.721926\pi$
$43$	−5.32305e10	−1.28415	−0.642075	+	0.766642i	$0.721926\pi$
$44$	−1.08819e9	−0.0226079
$45$	1.38891e10	0.249341
$46$	7.90713e10	1.23053
$47$	−2.53401e10	−0.342904	−0.171452	−	0.985192i	$-0.554846\pi$
$47$	−2.53401e10	−0.342904	−0.171452	+	0.985192i	$0.554846\pi$
$48$	−6.22752e10	−0.734932
$49$	9.31062e10	0.960957
$50$	8.89746e10	0.805306
$51$	1.09480e10	0.0871221
$52$	−1.70829e10	−0.119823
$53$	1.16294e11	0.720717	0.360358	−	0.932814i	$-0.382654\pi$
$53$	1.16294e11	0.720717	0.360358	+	0.932814i	$0.382654\pi$
$54$	1.98341e11	1.08856
$55$	2.92478e10	0.142474
$56$	3.09961e11	1.34303
$57$	−1.94434e11	−0.750908
$58$	−3.05045e11	−1.05216
$59$	1.65271e11	0.510105	0.255053	−	0.966927i	$-0.417907\pi$
$59$	1.65271e11	0.510105	0.255053	+	0.966927i	$0.417907\pi$
$60$	−8.80026e9	−0.0243508
$61$	−5.75566e11	−1.43038	−0.715190	−	0.698931i	$-0.753660\pi$
$61$	−5.75566e11	−1.43038	−0.715190	+	0.698931i	$0.753660\pi$
$62$	−4.01052e11	−0.896716
$63$	−3.66699e11	−0.738917
$64$	5.02584e11	0.914195
$65$	4.59148e11	0.755119
$66$	1.44266e11	0.214846
$67$	−7.20478e11	−0.973049	−0.486524	−	0.873667i	$-0.661736\pi$
$67$	−7.20478e11	−0.973049	−0.486524	+	0.873667i	$0.661736\pi$
$68$	7.74944e9	0.00950523
$69$	−7.31197e11	−0.815672
$70$	6.75311e11	0.686067
$71$	1.13262e12	1.04931	0.524656	−	0.851314i	$-0.324194\pi$
$71$	1.13262e12	1.04931	0.524656	+	0.851314i	$0.324194\pi$
$72$	−5.98238e11	−0.506072
$73$	3.93910e11	0.304648	0.152324	−	0.988331i	$-0.451324\pi$
$73$	3.93910e11	0.304648	0.152324	+	0.988331i	$0.451324\pi$
$74$	−6.17100e11	−0.436867
$75$	−8.22776e11	−0.533806
$76$	−1.37629e11	−0.0819258
$77$	−7.72196e11	−0.422219
$78$	2.26476e12	1.13870
$79$	−3.75493e12	−1.73790	−0.868952	−	0.494897i	$-0.835206\pi$
$79$	−3.75493e12	−1.73790	−0.868952	+	0.494897i	$0.835206\pi$
$80$	1.18479e12	0.505307
$81$	−4.92858e11	−0.193896
$82$	2.02706e12	0.736336
$83$	6.73276e11	0.226040	0.113020	−	0.993593i	$-0.463948\pi$
$83$	6.73276e11	0.226040	0.113020	+	0.993593i	$0.463948\pi$
$84$	2.32343e11	0.0721630
$85$	−2.08286e11	−0.0599014
$86$	4.99524e12	1.33142
$87$	2.82085e12	0.697437
$88$	−1.25977e12	−0.289171
$89$	8.55262e12	1.82417	0.912083	−	0.410007i	$-0.134474\pi$
$89$	8.55262e12	1.82417	0.912083	+	0.410007i	$0.134474\pi$
$90$	−1.30338e12	−0.258520
$91$	−1.21223e13	−2.23778
$92$	−5.17572e11	−0.0889917
$93$	3.70866e12	0.594398
$94$	2.37796e12	0.355527
$95$	3.69912e12	0.516292
$96$	7.88822e11	0.102853
$97$	−2.42796e12	−0.295955	−0.147977	−	0.988991i	$-0.547276\pi$
$97$	−2.42796e12	−0.295955	−0.147977	+	0.988991i	$0.547276\pi$
$98$	−8.73723e12	−0.996333
$99$	1.49037e12	0.159098
$100$	−5.82395e11	−0.0582395
$101$	−1.63005e13	−1.52796	−0.763978	−	0.645242i	$-0.776757\pi$
$101$	−1.63005e13	−1.52796	−0.763978	+	0.645242i	$0.776757\pi$
$102$	−1.02738e12	−0.0903293
$103$	−9.11493e11	−0.0752162	−0.0376081	−	0.999293i	$-0.511974\pi$
$103$	−9.11493e11	−0.0752162	−0.0376081	+	0.999293i	$0.511974\pi$
$104$	−1.97766e13	−1.53262
$105$	−6.24481e12	−0.454767
$106$	−1.09132e13	−0.747249
$107$	2.11737e13	1.36396	0.681980	−	0.731371i	$-0.261119\pi$
$107$	2.11737e13	1.36396	0.681980	+	0.731371i	$0.261119\pi$
$108$	−1.29827e12	−0.0787245
$109$	3.27226e13	1.86886	0.934428	−	0.356153i	$-0.115912\pi$
$109$	3.27226e13	1.86886	0.934428	+	0.356153i	$0.115912\pi$
$110$	−2.74466e12	−0.147719
$111$	5.70652e12	0.289582
$112$	−3.12806e13	−1.49747
$113$	8.05627e12	0.364019	0.182009	−	0.983297i	$-0.441740\pi$
$113$	8.05627e12	0.364019	0.182009	+	0.983297i	$0.441740\pi$
$114$	1.82460e13	0.778551
$115$	1.39111e13	0.560821
$116$	1.99671e12	0.0760920
$117$	2.33966e13	0.843229
$118$	−1.55093e13	−0.528884
$119$	5.49913e12	0.177517
$120$	−1.01879e13	−0.311462
$121$	3.13843e12	0.0909091
$122$	5.40121e13	1.48304
$123$	−1.87448e13	−0.488088
$124$	2.62514e12	0.0648503
$125$	3.58067e13	0.839555
$126$	3.44116e13	0.766119
$127$	5.17658e13	1.09476	0.547380	−	0.836884i	$-0.315625\pi$
$127$	5.17658e13	1.09476	0.547380	+	0.836884i	$0.315625\pi$
$128$	−5.46099e13	−1.09751
$129$	−4.61926e13	−0.882549
$130$	−4.30872e13	−0.782918
$131$	−8.17756e13	−1.41371	−0.706855	−	0.707358i	$-0.749887\pi$
$131$	−8.17756e13	−1.41371	−0.706855	+	0.707358i	$0.749887\pi$
$132$	−9.44310e11	−0.0155376
$133$	−9.76637e13	−1.53002
$134$	6.76109e13	1.00887
$135$	3.48942e13	0.496117
$136$	8.97137e12	0.121578
$137$	−3.61955e13	−0.467704	−0.233852	−	0.972272i	$-0.575133\pi$
$137$	−3.61955e13	−0.467704	−0.233852	+	0.972272i	$0.575133\pi$
$138$	6.86168e13	0.845700
$139$	−8.12263e13	−0.955214	−0.477607	−	0.878574i	$-0.658496\pi$
$139$	−8.12263e13	−0.955214	−0.477607	+	0.878574i	$0.658496\pi$
$140$	−4.42034e12	−0.0496162
$141$	−2.19897e13	−0.235665
$142$	−1.06287e14	−1.08794
$143$	4.92688e13	0.481823
$144$	6.03729e13	0.564268
$145$	−5.36668e13	−0.479527
$146$	−3.69652e13	−0.315863
$147$	8.07960e13	0.660430
$148$	4.03931e12	0.0315941
$149$	1.09989e14	0.823451	0.411726	−	0.911308i	$-0.364926\pi$
$149$	1.09989e14	0.823451	0.411726	+	0.911308i	$0.364926\pi$
$150$	7.72107e13	0.553457
$151$	9.41375e13	0.646268	0.323134	−	0.946353i	$-0.395264\pi$
$151$	9.41375e13	0.646268	0.323134	+	0.946353i	$0.395264\pi$
$152$	−1.59330e14	−1.04789
$153$	−1.06136e13	−0.0668909
$154$	7.24641e13	0.437762
$155$	−7.05574e13	−0.408683
$156$	−1.48243e13	−0.0823501
$157$	−1.42556e14	−0.759690	−0.379845	−	0.925050i	$-0.624023\pi$
$157$	−1.42556e14	−0.759690	−0.379845	+	0.925050i	$0.624023\pi$
$158$	3.52369e14	1.80188
$159$	1.00918e14	0.495322
$160$	−1.50074e13	−0.0707171
$161$	−3.67278e14	−1.66198
$162$	4.62506e13	0.201034
$163$	−2.72453e14	−1.13782	−0.568908	−	0.822401i	$-0.692634\pi$
$163$	−2.72453e14	−1.13782	−0.568908	+	0.822401i	$0.692634\pi$
$164$	−1.32684e13	−0.0532516
$165$	2.53807e13	0.0979171
$166$	−6.31813e13	−0.234361
$167$	3.62243e14	1.29224	0.646120	−	0.763235i	$-0.276390\pi$
$167$	3.62243e14	1.29224	0.646120	+	0.763235i	$0.276390\pi$
$168$	2.68979e14	0.923013
$169$	4.70573e14	1.55369
$170$	1.95459e13	0.0621066
$171$	1.88495e14	0.576534
$172$	−3.26970e13	−0.0962882
$173$	9.22643e13	0.261658	0.130829	−	0.991405i	$-0.458236\pi$
$173$	9.22643e13	0.261658	0.130829	+	0.991405i	$0.458236\pi$
$174$	−2.64713e14	−0.723112
$175$	−4.13278e14	−1.08766
$176$	1.27133e14	0.322424
$177$	1.43420e14	0.350577
$178$	−8.02592e14	−1.89132
$179$	5.13370e14	1.16650	0.583251	−	0.812292i	$-0.301780\pi$
$179$	5.13370e14	1.16650	0.583251	+	0.812292i	$0.301780\pi$
$180$	8.53144e12	0.0186961
$181$	−6.93076e14	−1.46511	−0.732555	−	0.680708i	$-0.761672\pi$
$181$	−6.93076e14	−1.46511	−0.732555	+	0.680708i	$0.761672\pi$
$182$	1.13758e15	2.32016
$183$	−4.99467e14	−0.983047
$184$	−5.99182e14	−1.13826
$185$	−1.08567e14	−0.199104
$186$	−3.48027e14	−0.616280
$187$	−2.23501e13	−0.0382216
$188$	−1.55652e13	−0.0257117
$189$	−9.21273e14	−1.47023
$190$	−3.47132e14	−0.535298
$191$	−2.31260e14	−0.344654	−0.172327	−	0.985040i	$-0.555129\pi$
$191$	−2.31260e14	−0.344654	−0.172327	+	0.985040i	$0.555129\pi$
$192$	4.36134e14	0.628293
$193$	2.58728e14	0.360347	0.180173	−	0.983635i	$-0.442334\pi$
$193$	2.58728e14	0.360347	0.180173	+	0.983635i	$0.442334\pi$
$194$	2.27844e14	0.306850
$195$	3.98441e14	0.518966
$196$	5.71907e13	0.0720545
$197$	−1.12023e15	−1.36545	−0.682724	−	0.730676i	$-0.739205\pi$
$197$	−1.12023e15	−1.36545	−0.682724	+	0.730676i	$0.739205\pi$
$198$	−1.39859e14	−0.164955
$199$	1.44472e15	1.64907	0.824534	−	0.565813i	$-0.191437\pi$
$199$	1.44472e15	1.64907	0.824534	+	0.565813i	$0.191437\pi$
$200$	−6.74227e14	−0.744923
$201$	−6.25219e14	−0.668741
$202$	1.52966e15	1.58421
$203$	1.41690e15	1.42107
$204$	6.72484e12	0.00653259
$205$	3.56621e14	0.335589
$206$	8.55360e13	0.0779852
$207$	7.08861e14	0.626259
$208$	1.99581e15	1.70886
$209$	3.96934e14	0.329433
$210$	5.86024e14	0.471509
$211$	−1.72354e15	−1.34458	−0.672290	−	0.740288i	$-0.734689\pi$
$211$	−1.72354e15	−1.34458	−0.672290	+	0.740288i	$0.734689\pi$
$212$	7.14340e13	0.0540408
$213$	9.82869e14	0.721154
$214$	−1.98697e15	−1.41417
$215$	8.78815e14	0.606803
$216$	−1.50298e15	−1.00694
$217$	1.86285e15	1.21112
$218$	−3.07074e15	−1.93765
$219$	3.41829e14	0.209373
$220$	1.79655e13	0.0106830
$221$	−3.50864e14	−0.202576
$222$	−5.35510e14	−0.300243
$223$	−1.68431e15	−0.917148	−0.458574	−	0.888656i	$-0.651640\pi$
$223$	−1.68431e15	−0.917148	−0.458574	+	0.888656i	$0.651640\pi$
$224$	3.96222e14	0.209569
$225$	7.97643e14	0.409847
$226$	−7.56013e14	−0.377420
$227$	9.80350e13	0.0475568	0.0237784	−	0.999717i	$-0.492430\pi$
$227$	9.80350e13	0.0475568	0.0237784	+	0.999717i	$0.492430\pi$
$228$	−1.19432e14	−0.0563046
$229$	1.53184e15	0.701911	0.350956	−	0.936392i	$-0.385857\pi$
$229$	1.53184e15	0.701911	0.350956	+	0.936392i	$0.385857\pi$
$230$	−1.30544e15	−0.581467
$231$	−6.70099e14	−0.290176
$232$	2.31156e15	0.973268
$233$	−1.66162e15	−0.680330	−0.340165	−	0.940366i	$-0.610483\pi$
$233$	−1.66162e15	−0.680330	−0.340165	+	0.940366i	$0.610483\pi$
$234$	−2.19558e15	−0.874271
$235$	4.18356e14	0.162033
$236$	1.01518e14	0.0382487
$237$	−3.25846e15	−1.19440
$238$	−5.16048e14	−0.184052
$239$	−2.29640e15	−0.797006	−0.398503	−	0.917167i	$-0.630470\pi$
$239$	−2.29640e15	−0.797006	−0.398503	+	0.917167i	$0.630470\pi$
$240$	1.02814e15	0.347279
$241$	1.03171e15	0.339191	0.169596	−	0.985514i	$-0.445754\pi$
$241$	1.03171e15	0.339191	0.169596	+	0.985514i	$0.445754\pi$
$242$	−2.94515e14	−0.0942558
$243$	2.94202e15	0.916653
$244$	−3.53543e14	−0.107253
$245$	−1.53715e15	−0.454084
$246$	1.75905e15	0.506057
$247$	6.23128e15	1.74601
$248$	3.03907e15	0.829479
$249$	5.84258e14	0.155349
$250$	−3.36016e15	−0.870462
$251$	1.43280e15	0.361664	0.180832	−	0.983514i	$-0.442121\pi$
$251$	1.43280e15	0.361664	0.180832	+	0.983514i	$0.442121\pi$
$252$	−2.25246e14	−0.0554055
$253$	1.49272e15	0.357846
$254$	−4.85779e15	−1.13506
$255$	−1.80747e14	−0.0411680
$256$	1.00751e15	0.223713
$257$	−5.73878e15	−1.24238	−0.621190	−	0.783660i	$-0.713350\pi$
$257$	−5.73878e15	−1.24238	−0.621190	+	0.783660i	$0.713350\pi$
$258$	4.33479e15	0.915039
$259$	2.86637e15	0.590042
$260$	2.82033e14	0.0566204
$261$	−2.73468e15	−0.535480
$262$	7.67396e15	1.46575
$263$	−2.32832e15	−0.433841	−0.216920	−	0.976189i	$-0.569601\pi$
$263$	−2.32832e15	−0.433841	−0.216920	+	0.976189i	$0.569601\pi$
$264$	−1.09321e15	−0.198736
$265$	−1.91997e15	−0.340562
$266$	9.16492e15	1.58635
$267$	7.42182e15	1.25368
$268$	−4.42556e14	−0.0729612
$269$	−1.05323e16	−1.69486	−0.847429	−	0.530909i	$-0.821851\pi$
$269$	−1.05323e16	−1.69486	−0.847429	+	0.530909i	$0.821851\pi$
$270$	−3.27453e15	−0.514381
$271$	9.98399e14	0.153110	0.0765551	−	0.997065i	$-0.475608\pi$
$271$	9.98399e14	0.153110	0.0765551	+	0.997065i	$0.475608\pi$
$272$	−9.05371e14	−0.135559
$273$	−1.05196e16	−1.53795
$274$	3.39664e15	0.484921
$275$	1.67968e15	0.234188
$276$	−4.49140e14	−0.0611608
$277$	5.32413e15	0.708158	0.354079	−	0.935216i	$-0.384794\pi$
$277$	5.32413e15	0.708158	0.354079	+	0.935216i	$0.384794\pi$
$278$	7.62241e15	0.990378
$279$	−3.59537e15	−0.456369
$280$	−5.11733e15	−0.634624
$281$	−1.10425e16	−1.33806	−0.669029	−	0.743236i	$-0.733290\pi$
$281$	−1.10425e16	−1.33806	−0.669029	+	0.743236i	$0.733290\pi$
$282$	2.06355e15	0.244341
$283$	1.59862e16	1.84984	0.924920	−	0.380162i	$-0.124132\pi$
$283$	1.59862e16	1.84984	0.924920	+	0.380162i	$0.124132\pi$
$284$	6.95715e14	0.0786796
$285$	3.21004e15	0.354828
$286$	−4.62346e15	−0.499560
$287$	−9.41546e15	−0.994510
$288$	−7.64726e14	−0.0789686
$289$	−9.74541e15	−0.983930
$290$	5.03618e15	0.497181
$291$	−2.10694e15	−0.203399
$292$	2.41960e14	0.0228431
$293$	−3.79157e15	−0.350090	−0.175045	−	0.984560i	$-0.556007\pi$
$293$	−3.79157e15	−0.350090	−0.175045	+	0.984560i	$0.556007\pi$
$294$	−7.58203e15	−0.684743
$295$	−2.72857e15	−0.241041
$296$	4.67623e15	0.404110
$297$	3.74432e15	0.316560
$298$	−1.03215e16	−0.853765
$299$	2.34336e16	1.89660
$300$	−5.05393e14	−0.0400259
$301$	−2.32024e16	−1.79825
$302$	−8.83401e15	−0.670059
$303$	−1.41453e16	−1.05011
$304$	1.60792e16	1.16839
$305$	9.50237e15	0.675901
$306$	9.95994e14	0.0693533
$307$	1.29807e13	0.000884907 0	0.000442453	−	1.00000i	$-0.499859\pi$
$307$	1.29807e13	0.000884907 0	0.000442453		1.00000i	$0.499859\pi$
$308$	−4.74324e14	−0.0316588
$309$	−7.90979e14	−0.0516933
$310$	6.62122e15	0.423728
$311$	1.26317e16	0.791627	0.395813	−	0.918331i	$-0.370463\pi$
$311$	1.26317e16	0.791627	0.395813	+	0.918331i	$0.370463\pi$
$312$	−1.71618e16	−1.05331
$313$	−7.27786e15	−0.437487	−0.218744	−	0.975782i	$-0.570196\pi$
$313$	−7.27786e15	−0.437487	−0.218744	+	0.975782i	$0.570196\pi$
$314$	1.33777e16	0.787657
$315$	6.05405e15	0.349162
$316$	−2.30648e15	−0.130312
$317$	2.62181e16	1.45116	0.725582	−	0.688136i	$-0.241571\pi$
$317$	2.62181e16	1.45116	0.725582	+	0.688136i	$0.241571\pi$
$318$	−9.47032e15	−0.513557
$319$	−5.75870e15	−0.305975
$320$	−8.29747e15	−0.431987
$321$	1.83742e16	0.937400
$322$	3.44659e16	1.72317
$323$	−2.82673e15	−0.138506
$324$	−3.02739e14	−0.0145387
$325$	2.63685e16	1.24121
$326$	2.55674e16	1.17970
$327$	2.83961e16	1.28440
$328$	−1.53605e16	−0.681124
$329$	−1.10454e16	−0.480183
$330$	−2.38177e15	−0.101522
$331$	−7.69146e15	−0.321460	−0.160730	−	0.986998i	$-0.551385\pi$
$331$	−7.69146e15	−0.321460	−0.160730	+	0.986998i	$0.551385\pi$
$332$	4.13562e14	0.0169490
$333$	−5.53221e15	−0.222337
$334$	−3.39935e16	−1.33981
$335$	1.18948e16	0.459797
$336$	−2.71448e16	−1.02916
$337$	−3.94701e15	−0.146782	−0.0733912	−	0.997303i	$-0.523382\pi$
$337$	−3.94701e15	−0.146782	−0.0733912	+	0.997303i	$0.523382\pi$
$338$	−4.41593e16	−1.61088
$339$	6.99109e15	0.250177
$340$	−1.27940e14	−0.00449153
$341$	−7.57115e15	−0.260770
$342$	−1.76887e16	−0.597758
$343$	−1.64889e15	−0.0546737
$344$	−3.78527e16	−1.23159
$345$	1.20718e16	0.385432
$346$	−8.65823e15	−0.271291
$347$	−5.01319e16	−1.54160	−0.770801	−	0.637076i	$-0.780144\pi$
$347$	−5.01319e16	−1.54160	−0.770801	+	0.637076i	$0.780144\pi$
$348$	1.73272e15	0.0522952
$349$	−3.91013e16	−1.15831	−0.579157	−	0.815216i	$-0.696618\pi$
$349$	−3.91013e16	−1.15831	−0.579157	+	0.815216i	$0.696618\pi$
$350$	3.87826e16	1.12770
$351$	5.87804e16	1.67778
$352$	−1.61036e15	−0.0451228
$353$	4.39410e16	1.20874	0.604372	−	0.796702i	$-0.293424\pi$
$353$	4.39410e16	1.20874	0.604372	+	0.796702i	$0.293424\pi$
$354$	−1.34587e16	−0.363482
$355$	−1.86991e16	−0.495835
$356$	5.25347e15	0.136780
$357$	4.77206e15	0.122001
$358$	−4.81755e16	−1.20945
$359$	−5.44432e16	−1.34224	−0.671119	−	0.741350i	$-0.734186\pi$
$359$	−5.44432e16	−1.34224	−0.671119	+	0.741350i	$0.734186\pi$
$360$	9.87667e15	0.239136
$361$	8.14930e15	0.193787
$362$	6.50394e16	1.51905
$363$	2.72348e15	0.0624785
$364$	−7.44619e15	−0.167793
$365$	−6.50330e15	−0.143956
$366$	4.68708e16	1.01924
$367$	−1.42263e16	−0.303923	−0.151961	−	0.988386i	$-0.548559\pi$
$367$	−1.42263e16	−0.303923	−0.151961	+	0.988386i	$0.548559\pi$
$368$	6.04682e16	1.26916
$369$	1.81722e16	0.374746
$370$	1.01881e16	0.206434
$371$	5.06908e16	1.00925
$372$	2.27805e15	0.0445692
$373$	−1.90435e16	−0.366133	−0.183066	−	0.983101i	$-0.558602\pi$
$373$	−1.90435e16	−0.366133	−0.183066	+	0.983101i	$0.558602\pi$
$374$	2.09737e15	0.0396287
$375$	3.10724e16	0.576995
$376$	−1.80196e16	−0.328869
$377$	−9.04033e16	−1.62168
$378$	8.64537e16	1.52436
$379$	−1.15214e16	−0.199688	−0.0998438	−	0.995003i	$-0.531834\pi$
$379$	−1.15214e16	−0.199688	−0.0998438	+	0.995003i	$0.531834\pi$
$380$	2.27220e15	0.0387126
$381$	4.49215e16	0.752388
$382$	2.17018e16	0.357342
$383$	−6.36870e16	−1.03100	−0.515500	−	0.856890i	$-0.672394\pi$
$383$	−6.36870e16	−1.03100	−0.515500	+	0.856890i	$0.672394\pi$
$384$	−4.73896e16	−0.754275
$385$	1.27487e16	0.199512
$386$	−2.42794e16	−0.373612
$387$	4.47815e16	0.677606
$388$	−1.49138e15	−0.0221913
$389$	−1.04171e17	−1.52431	−0.762156	−	0.647393i	$-0.775859\pi$
$389$	−1.04171e17	−1.52431	−0.762156	+	0.647393i	$0.775859\pi$
$390$	−3.73903e16	−0.538071
$391$	−1.06303e16	−0.150452
$392$	6.62086e16	0.921626
$393$	−7.09635e16	−0.971591
$394$	1.05124e17	1.41572
$395$	6.19924e16	0.821216
$396$	9.15464e14	0.0119295
$397$	1.25018e17	1.60263	0.801316	−	0.598241i	$-0.204134\pi$
$397$	1.25018e17	1.60263	0.801316	+	0.598241i	$0.204134\pi$
$398$	−1.35575e17	−1.70978
$399$	−8.47509e16	−1.05153
$400$	6.80416e16	0.830585
$401$	1.28514e17	1.54351	0.771757	−	0.635918i	$-0.219378\pi$
$401$	1.28514e17	1.54351	0.771757	+	0.635918i	$0.219378\pi$
$402$	5.86716e16	0.693359
$403$	−1.18856e17	−1.38210
$404$	−1.00126e16	−0.114569
$405$	8.13689e15	0.0916222
$406$	−1.32964e17	−1.47339
$407$	−1.16497e16	−0.127044
$408$	7.78520e15	0.0835563
$409$	−2.45697e16	−0.259536	−0.129768	−	0.991544i	$-0.541423\pi$
$409$	−2.45697e16	−0.259536	−0.129768	+	0.991544i	$0.541423\pi$
$410$	−3.34659e16	−0.347943
$411$	−3.14098e16	−0.321436
$412$	−5.59888e14	−0.00563987
$413$	7.20392e16	0.714322
$414$	−6.65207e16	−0.649314
$415$	−1.11155e16	−0.106811
$416$	−2.52804e16	−0.239153
$417$	−7.04868e16	−0.656483
$418$	−3.72489e16	−0.341560
$419$	4.30242e16	0.388438	0.194219	−	0.980958i	$-0.437783\pi$
$419$	4.30242e16	0.388438	0.194219	+	0.980958i	$0.437783\pi$
$420$	−3.83590e15	−0.0340994
$421$	7.21078e16	0.631174	0.315587	−	0.948897i	$-0.397799\pi$
$421$	7.21078e16	0.631174	0.315587	+	0.948897i	$0.397799\pi$
$422$	1.61740e17	1.39408
$423$	2.13180e16	0.180940
$424$	8.26977e16	0.691218
$425$	−1.19617e16	−0.0984613
$426$	−9.22340e16	−0.747702
$427$	−2.50880e17	−2.00302
$428$	1.30060e16	0.102273
$429$	4.27546e16	0.331139
$430$	−8.24695e16	−0.629141
$431$	−1.69978e17	−1.27730	−0.638648	−	0.769499i	$-0.720506\pi$
$431$	−1.69978e17	−1.27730	−0.638648	+	0.769499i	$0.720506\pi$
$432$	1.51677e17	1.12273
$433$	1.32921e17	0.969221	0.484611	−	0.874730i	$-0.338961\pi$
$433$	1.32921e17	0.969221	0.484611	+	0.874730i	$0.338961\pi$
$434$	−1.74812e17	−1.25571
$435$	−4.65711e16	−0.329562
$436$	2.01000e16	0.140131
$437$	1.88793e17	1.29675
$438$	−3.20778e16	−0.217081
$439$	−7.27319e15	−0.0484959	−0.0242480	−	0.999706i	$-0.507719\pi$
$439$	−7.27319e15	−0.0484959	−0.0242480	+	0.999706i	$0.507719\pi$
$440$	2.07983e16	0.136643
$441$	−7.83279e16	−0.507067
$442$	3.29256e16	0.210034
$443$	1.57732e17	0.991506	0.495753	−	0.868463i	$-0.334892\pi$
$443$	1.57732e17	0.991506	0.495753	+	0.868463i	$0.334892\pi$
$444$	3.50525e15	0.0217135
$445$	−1.41200e17	−0.861978
$446$	1.58058e17	0.950911
$447$	9.54465e16	0.565928
$448$	2.19068e17	1.28019
$449$	−5.74947e16	−0.331152	−0.165576	−	0.986197i	$-0.552948\pi$
$449$	−5.74947e16	−0.331152	−0.165576	+	0.986197i	$0.552948\pi$
$450$	−7.48521e16	−0.424935
$451$	3.82672e16	0.214131
$452$	4.94859e15	0.0272949
$453$	8.16909e16	0.444156
$454$	−9.19976e15	−0.0493076
$455$	2.00135e17	1.05742
$456$	−1.38264e17	−0.720174
$457$	3.43309e17	1.76291	0.881454	−	0.472270i	$-0.156565\pi$
$457$	3.43309e17	1.76291	0.881454	+	0.472270i	$0.156565\pi$
$458$	−1.43750e17	−0.727751
$459$	−2.66649e16	−0.133094
$460$	8.54491e15	0.0420515
$461$	−6.40999e15	−0.0311029	−0.0155515	−	0.999879i	$-0.504950\pi$
$461$	−6.40999e15	−0.0311029	−0.0155515	+	0.999879i	$0.504950\pi$
$462$	6.28831e16	0.300858
$463$	−1.95384e17	−0.921747	−0.460873	−	0.887466i	$-0.652464\pi$
$463$	−1.95384e17	−0.921747	−0.460873	+	0.887466i	$0.652464\pi$
$464$	−2.33277e17	−1.08519
$465$	−6.12285e16	−0.280873
$466$	1.55930e17	0.705375
$467$	1.56780e17	0.699407	0.349703	−	0.936860i	$-0.386282\pi$
$467$	1.56780e17	0.699407	0.349703	+	0.936860i	$0.386282\pi$
$468$	1.43715e16	0.0632270
$469$	−3.14045e17	−1.36260
$470$	−3.92592e16	−0.167998
$471$	−1.23707e17	−0.522107
$472$	1.17526e17	0.489227
$473$	9.43011e16	0.387186
$474$	3.05780e17	1.23837
$475$	2.12438e17	0.848641
$476$	3.37786e15	0.0133106
$477$	−9.78353e16	−0.380300
$478$	2.15498e17	0.826347
$479$	−2.22361e17	−0.841157	−0.420579	−	0.907256i	$-0.638173\pi$
$479$	−2.22361e17	−0.841157	−0.420579	+	0.907256i	$0.638173\pi$
$480$	−1.30231e16	−0.0486013
$481$	−1.82884e17	−0.673337
$482$	−9.68169e16	−0.351678
$483$	−3.18717e17	−1.14222
$484$	1.92779e15	0.00681655
$485$	4.00847e16	0.139848
$486$	−2.76084e17	−0.950398
$487$	−6.62312e16	−0.224970	−0.112485	−	0.993653i	$-0.535881\pi$
$487$	−6.62312e16	−0.224970	−0.112485	+	0.993653i	$0.535881\pi$
$488$	−4.09290e17	−1.37184
$489$	−2.36430e17	−0.781980
$490$	1.44248e17	0.470800
$491$	−2.65262e16	−0.0854370	−0.0427185	−	0.999087i	$-0.513602\pi$
$491$	−2.65262e16	−0.0854370	−0.0427185	+	0.999087i	$0.513602\pi$
$492$	−1.15141e16	−0.0365979
$493$	4.10102e16	0.128643
$494$	−5.84753e17	−1.81029
$495$	−2.46054e16	−0.0751791
$496$	−3.06697e17	−0.924865
$497$	4.93691e17	1.46940
$498$	−5.48277e16	−0.161068
$499$	3.87669e17	1.12411	0.562053	−	0.827101i	$-0.310012\pi$
$499$	3.87669e17	1.12411	0.562053	+	0.827101i	$0.310012\pi$
$500$	2.19944e16	0.0629516
$501$	3.14349e17	0.888110
$502$	−1.34456e17	−0.374978
$503$	−2.54261e17	−0.699983	−0.349991	−	0.936753i	$-0.613815\pi$
$503$	−2.54261e17	−0.699983	−0.349991	+	0.936753i	$0.613815\pi$
$504$	−2.60762e17	−0.708674
$505$	2.69114e17	0.722009
$506$	−1.40080e17	−0.371019
$507$	4.08355e17	1.06779
$508$	3.17973e16	0.0820873
$509$	−5.64615e15	−0.0143909	−0.00719543	−	0.999974i	$-0.502290\pi$
$509$	−5.64615e15	−0.0143909	−0.00719543	+	0.999974i	$0.502290\pi$
$510$	1.69616e16	0.0426836
$511$	1.71699e17	0.426611
$512$	3.52817e17	0.865556
$513$	4.73564e17	1.14714
$514$	5.38537e17	1.28812
$515$	1.50484e16	0.0355421
$516$	−2.83739e16	−0.0661754
$517$	4.48916e16	0.103389
$518$	−2.68984e17	−0.611764
$519$	8.00654e16	0.179828
$520$	3.26504e17	0.724213
$521$	6.08955e17	1.33395	0.666975	−	0.745080i	$-0.267589\pi$
$521$	6.08955e17	1.33395	0.666975	+	0.745080i	$0.267589\pi$
$522$	2.56627e17	0.555193
$523$	−7.89156e17	−1.68617	−0.843086	−	0.537779i	$-0.819263\pi$
$523$	−7.89156e17	−1.68617	−0.843086	+	0.537779i	$0.819263\pi$
$524$	−5.02309e16	−0.106003
$525$	−3.58635e17	−0.747511
$526$	2.18493e17	0.449812
$527$	5.39174e16	0.109638
$528$	1.10324e17	0.221590
$529$	2.05944e17	0.408590
$530$	1.80173e17	0.353099
$531$	−1.39039e17	−0.269167
$532$	−5.99902e16	−0.114724
$533$	6.00739e17	1.13490
$534$	−6.96476e17	−1.29983
$535$	−3.49569e17	−0.644516
$536$	−5.12338e17	−0.933223
$537$	4.45494e17	0.801694
$538$	9.88368e17	1.75725
$539$	−1.64943e17	−0.289739
$540$	2.14339e16	0.0371999
$541$	−8.69619e17	−1.49124	−0.745619	−	0.666372i	$-0.767846\pi$
$541$	−8.69619e17	−1.49124	−0.745619	+	0.666372i	$0.767846\pi$
$542$	−9.36914e16	−0.158747
$543$	−6.01440e17	−1.00692
$544$	1.14681e16	0.0189713
$545$	−5.40238e17	−0.883095
$546$	9.87174e17	1.59456
$547$	2.39588e16	0.0382426	0.0191213	−	0.999817i	$-0.493913\pi$
$547$	2.39588e16	0.0382426	0.0191213	+	0.999817i	$0.493913\pi$
$548$	−2.22332e16	−0.0350694
$549$	4.84209e17	0.754767
$550$	−1.57624e17	−0.242809
$551$	−7.28334e17	−1.10878
$552$	−5.19960e17	−0.782287
$553$	−1.63671e18	−2.43366
$554$	−4.99625e17	−0.734228
$555$	−9.42125e16	−0.136837
$556$	−4.98935e16	−0.0716239
$557$	−6.81762e17	−0.967329	−0.483664	−	0.875254i	$-0.660694\pi$
$557$	−6.81762e17	−0.967329	−0.483664	+	0.875254i	$0.660694\pi$
$558$	3.37395e17	0.473170
$559$	1.48039e18	2.05210
$560$	5.16430e17	0.707603
$561$	−1.93950e16	−0.0262683
$562$	1.03624e18	1.38732
$563$	3.21311e17	0.425227	0.212614	−	0.977136i	$-0.431802\pi$
$563$	3.21311e17	0.425227	0.212614	+	0.977136i	$0.431802\pi$
$564$	−1.35073e16	−0.0176707
$565$	−1.33006e17	−0.172011
$566$	−1.50017e18	−1.91794
$567$	−2.14829e17	−0.271521
$568$	8.05415e17	1.00637
$569$	5.39904e17	0.666940	0.333470	−	0.942761i	$-0.391780\pi$
$569$	5.39904e17	0.666940	0.333470	+	0.942761i	$0.391780\pi$
$570$	−3.01235e17	−0.367891
$571$	−7.09270e17	−0.856401	−0.428200	−	0.903684i	$-0.640852\pi$
$571$	−7.09270e17	−0.856401	−0.428200	+	0.903684i	$0.640852\pi$
$572$	3.02635e16	0.0361281
$573$	−2.00683e17	−0.236868
$574$	8.83562e17	1.03112
$575$	7.98903e17	0.921834
$576$	−4.22811e17	−0.482392
$577$	−3.15550e17	−0.355980	−0.177990	−	0.984032i	$-0.556959\pi$
$577$	−3.15550e17	−0.355980	−0.177990	+	0.984032i	$0.556959\pi$
$578$	9.14526e17	1.02015
$579$	2.24520e17	0.247653
$580$	−3.29650e16	−0.0359560
$581$	2.93470e17	0.316533
$582$	1.97719e17	0.210887
$583$	−2.06022e17	−0.217304
$584$	2.80113e17	0.292179
$585$	−3.86269e17	−0.398453
$586$	3.55807e17	0.362978
$587$	−1.86879e18	−1.88544	−0.942720	−	0.333586i	$-0.891741\pi$
$587$	−1.86879e18	−1.88544	−0.942720	+	0.333586i	$0.891741\pi$
$588$	4.96292e16	0.0495204
$589$	−9.57563e17	−0.944970
$590$	2.56053e17	0.249915
$591$	−9.72114e17	−0.938423
$592$	−4.71915e17	−0.450581
$593$	7.64722e17	0.722185	0.361092	−	0.932530i	$-0.382404\pi$
$593$	7.64722e17	0.722185	0.361092	+	0.932530i	$0.382404\pi$
$594$	−3.51373e17	−0.328214
$595$	−9.07886e16	−0.0838824
$596$	6.75610e16	0.0617441
$597$	1.25370e18	1.13334
$598$	−2.19905e18	−1.96642
$599$	2.02474e18	1.79100	0.895498	−	0.445065i	$-0.146819\pi$
$599$	2.02474e18	1.79100	0.895498	+	0.445065i	$0.146819\pi$
$600$	−5.85083e17	−0.511958
$601$	−4.89878e17	−0.424037	−0.212019	−	0.977266i	$-0.568004\pi$
$601$	−4.89878e17	−0.424037	−0.212019	+	0.977266i	$0.568004\pi$
$602$	2.17735e18	1.86445
$603$	6.06120e17	0.513448
$604$	5.78242e16	0.0484585
$605$	−5.18142e16	−0.0429575
$606$	1.32742e18	1.08877
$607$	1.59414e18	1.29360	0.646802	−	0.762658i	$-0.276106\pi$
$607$	1.59414e18	1.29360	0.646802	+	0.762658i	$0.276106\pi$
$608$	−2.03671e17	−0.163514
$609$	1.22956e18	0.976650
$610$	−8.91718e17	−0.700783
$611$	7.04732e17	0.547969
$612$	−6.51941e15	−0.00501561
$613$	−2.20425e18	−1.67790	−0.838952	−	0.544205i	$-0.816831\pi$
$613$	−2.20425e18	−1.67790	−0.838952	+	0.544205i	$0.816831\pi$
$614$	−1.21813e15	−0.000917483 0
$615$	3.09470e17	0.230638
$616$	−5.49115e17	−0.404938
$617$	−2.40120e18	−1.75216	−0.876082	−	0.482162i	$-0.839852\pi$
$617$	−2.40120e18	−1.75216	−0.876082	+	0.482162i	$0.839852\pi$
$618$	7.42267e16	0.0535964
$619$	−4.20881e17	−0.300725	−0.150363	−	0.988631i	$-0.548044\pi$
$619$	−4.20881e17	−0.300725	−0.150363	+	0.988631i	$0.548044\pi$
$620$	−4.33401e16	−0.0306439
$621$	1.78090e18	1.24608
$622$	−1.18538e18	−0.820769
$623$	3.72795e18	2.55445
$624$	1.73193e18	1.17444
$625$	5.66238e17	0.379996
$626$	6.82966e17	0.453592
$627$	3.44452e17	0.226407
$628$	−8.75652e16	−0.0569632
$629$	8.29628e16	0.0534139
$630$	−5.68122e17	−0.362016
$631$	2.01901e18	1.27335	0.636675	−	0.771132i	$-0.280309\pi$
$631$	2.01901e18	1.27335	0.636675	+	0.771132i	$0.280309\pi$
$632$	−2.67016e18	−1.66677
$633$	−1.49566e18	−0.924080
$634$	−2.46035e18	−1.50459
$635$	−8.54633e17	−0.517309
$636$	6.19892e16	0.0371403
$637$	−2.58937e18	−1.53563
$638$	5.40406e17	0.317239
$639$	−9.52845e17	−0.553690
$640$	9.01588e17	0.518607
$641$	1.90024e18	1.08201	0.541004	−	0.841020i	$-0.318044\pi$
$641$	1.90024e18	1.08201	0.541004	+	0.841020i	$0.318044\pi$
$642$	−1.72426e18	−0.971909
$643$	−9.90999e17	−0.552971	−0.276485	−	0.961018i	$-0.589170\pi$
$643$	−9.90999e17	−0.552971	−0.276485	+	0.961018i	$0.589170\pi$
$644$	−2.25601e17	−0.124619
$645$	7.62621e17	0.417033
$646$	2.65265e17	0.143605
$647$	−1.86772e18	−1.00100	−0.500499	−	0.865737i	$-0.666850\pi$
$647$	−1.86772e18	−1.00100	−0.500499	+	0.865737i	$0.666850\pi$
$648$	−3.50475e17	−0.185960
$649$	−2.92788e17	−0.153802
$650$	−2.47447e18	−1.28690
$651$	1.61655e18	0.832361
$652$	−1.67355e17	−0.0853158
$653$	−2.53210e17	−0.127804	−0.0639020	−	0.997956i	$-0.520355\pi$
$653$	−2.53210e17	−0.127804	−0.0639020	+	0.997956i	$0.520355\pi$
$654$	−2.66474e18	−1.33168
$655$	1.35008e18	0.668024
$656$	1.55015e18	0.759450
$657$	−3.31387e17	−0.160753
$658$	1.03651e18	0.497860
$659$	1.81256e18	0.862058	0.431029	−	0.902338i	$-0.358151\pi$
$659$	1.81256e18	0.862058	0.431029	+	0.902338i	$0.358151\pi$
$660$	1.55902e16	0.00734203
$661$	−2.77298e18	−1.29311	−0.646557	−	0.762865i	$-0.723792\pi$
$661$	−2.77298e18	−1.29311	−0.646557	+	0.762865i	$0.723792\pi$
$662$	7.21779e17	0.333294
$663$	−3.04474e17	−0.139223
$664$	4.78772e17	0.216789
$665$	1.61239e18	0.722985
$666$	5.19151e17	0.230521
$667$	−2.73900e18	−1.20441
$668$	2.22509e17	0.0968949
$669$	−1.46161e18	−0.630322
$670$	−1.11623e18	−0.476724
$671$	1.01965e18	0.431276
$672$	3.43835e17	0.144029
$673$	2.92420e18	1.21313	0.606567	−	0.795032i	$-0.292546\pi$
$673$	2.92420e18	1.21313	0.606567	+	0.795032i	$0.292546\pi$
$674$	3.70394e17	0.152186
$675$	2.00395e18	0.815479
$676$	2.89051e17	0.116499
$677$	−1.34520e17	−0.0536981	−0.0268491	−	0.999639i	$-0.508547\pi$
$677$	−1.34520e17	−0.0536981	−0.0268491	+	0.999639i	$0.508547\pi$
$678$	−6.56056e17	−0.259387
$679$	−1.05831e18	−0.414438
$680$	−1.48114e17	−0.0574497
$681$	8.50731e16	0.0326841
$682$	7.10489e17	0.270370
$683$	2.27777e18	0.858569	0.429285	−	0.903169i	$-0.358766\pi$
$683$	2.27777e18	0.858569	0.429285	+	0.903169i	$0.358766\pi$
$684$	1.15784e17	0.0432297
$685$	5.97573e17	0.221005
$686$	1.54734e17	0.0566865
$687$	1.32930e18	0.482398
$688$	3.82001e18	1.37322
$689$	−3.23425e18	−1.15172
$690$	−1.13284e18	−0.399621
$691$	4.65812e18	1.62781	0.813904	−	0.580999i	$-0.197338\pi$
$691$	4.65812e18	1.62781	0.813904	+	0.580999i	$0.197338\pi$
$692$	5.66736e16	0.0196197
$693$	6.49629e17	0.222792
$694$	4.70446e18	1.59835
$695$	1.34102e18	0.451370
$696$	2.00593e18	0.668891
$697$	−2.72517e17	−0.0900286
$698$	3.66933e18	1.20096
$699$	−1.44193e18	−0.467566
$700$	−2.53857e17	−0.0815552
$701$	−3.50349e18	−1.11515	−0.557575	−	0.830126i	$-0.688268\pi$
$701$	−3.50349e18	−1.11515	−0.557575	+	0.830126i	$0.688268\pi$
$702$	−5.51605e18	−1.73955
$703$	−1.47340e18	−0.460376
$704$	−8.90358e17	−0.275640
$705$	3.63042e17	0.111360
$706$	−4.12350e18	−1.25324
$707$	−7.10512e18	−2.13966
$708$	8.80960e16	0.0262870
$709$	1.73604e18	0.513286	0.256643	−	0.966506i	$-0.417384\pi$
$709$	1.73604e18	0.513286	0.256643	+	0.966506i	$0.417384\pi$
$710$	1.75476e18	0.514088
$711$	3.15893e18	0.917038
$712$	6.08184e18	1.74950
$713$	−3.60105e18	−1.02647
$714$	−4.47818e17	−0.126492
$715$	−8.13408e17	−0.227677
$716$	3.15339e17	0.0874667
$717$	−1.99278e18	−0.547753
$718$	5.10904e18	1.39165
$719$	−5.97157e17	−0.161195	−0.0805973	−	0.996747i	$-0.525683\pi$
$719$	−5.97157e17	−0.161195	−0.0805973	+	0.996747i	$0.525683\pi$
$720$	−9.96733e17	−0.266635
$721$	−3.97306e17	−0.105328
$722$	−7.64744e17	−0.200921
$723$	8.95297e17	0.233114
$724$	−4.25724e17	−0.109857
$725$	−3.08205e18	−0.788210
$726$	−2.55575e17	−0.0647785
$727$	−2.81741e18	−0.707746	−0.353873	−	0.935294i	$-0.615135\pi$
$727$	−2.81741e18	−0.707746	−0.353873	+	0.935294i	$0.615135\pi$
$728$	−8.62030e18	−2.14619
$729$	3.33881e18	0.823878
$730$	6.10280e17	0.149256
$731$	−6.71558e17	−0.162787
$732$	−3.06799e17	−0.0737109
$733$	−7.79833e18	−1.85706	−0.928529	−	0.371260i	$-0.878926\pi$
$733$	−7.79833e18	−1.85706	−0.928529	+	0.371260i	$0.878926\pi$
$734$	1.33502e18	0.315111
$735$	−1.33391e18	−0.312075
$736$	−7.65933e17	−0.177617
$737$	1.27637e18	0.293385
$738$	−1.70531e18	−0.388542
$739$	2.59220e17	0.0585437	0.0292718	−	0.999571i	$-0.490681\pi$
$739$	2.59220e17	0.0585437	0.0292718	+	0.999571i	$0.490681\pi$
$740$	−6.66875e16	−0.0149293
$741$	5.40740e18	1.19997
$742$	−4.75691e18	−1.04640
$743$	2.00980e17	0.0438254	0.0219127	−	0.999760i	$-0.493024\pi$
$743$	2.00980e17	0.0438254	0.0219127	+	0.999760i	$0.493024\pi$
$744$	2.63726e18	0.570070
$745$	−1.81587e18	−0.389108
$746$	1.78707e18	0.379611
$747$	−5.66410e17	−0.119274
$748$	−1.37286e16	−0.00286593
$749$	9.22927e18	1.91001
$750$	−2.91589e18	−0.598236
$751$	−5.35138e18	−1.08844	−0.544222	−	0.838941i	$-0.683175\pi$
$751$	−5.35138e18	−1.08844	−0.544222	+	0.838941i	$0.683175\pi$
$752$	1.81850e18	0.366688
$753$	1.24336e18	0.248558
$754$	8.48359e18	1.68138
$755$	−1.55417e18	−0.305383
$756$	−5.65895e17	−0.110241
$757$	3.32154e18	0.641528	0.320764	−	0.947159i	$-0.396060\pi$
$757$	3.32154e18	0.641528	0.320764	+	0.947159i	$0.396060\pi$
$758$	1.08119e18	0.207039
$759$	1.29536e18	0.245934
$760$	2.63048e18	0.495160
$761$	−6.63532e18	−1.23840	−0.619201	−	0.785233i	$-0.712543\pi$
$761$	−6.63532e18	−1.23840	−0.619201	+	0.785233i	$0.712543\pi$
$762$	−4.21551e18	−0.780086
$763$	1.42633e19	2.61704
$764$	−1.42052e17	−0.0258429
$765$	1.75226e17	0.0316081
$766$	5.97649e18	1.06895
$767$	−4.59635e18	−0.815161
$768$	8.74304e17	0.153750
$769$	6.50871e18	1.13494	0.567471	−	0.823393i	$-0.307922\pi$
$769$	6.50871e18	1.13494	0.567471	+	0.823393i	$0.307922\pi$
$770$	−1.19635e18	−0.206857
$771$	−4.98002e18	−0.853842
$772$	1.58924e17	0.0270195
$773$	−5.94433e18	−1.00216	−0.501079	−	0.865401i	$-0.667064\pi$
$773$	−5.94433e18	−1.00216	−0.501079	+	0.865401i	$0.667064\pi$
$774$	−4.20237e18	−0.702551
$775$	−4.05206e18	−0.671761
$776$	−1.72654e18	−0.283841
$777$	2.48738e18	0.405514
$778$	9.77557e18	1.58043
$779$	4.83985e18	0.775959
$780$	2.44743e17	0.0389131
$781$	−2.00651e18	−0.316380
$782$	9.97567e17	0.155990
$783$	−6.87046e18	−1.06545
$784$	−6.68163e18	−1.02761
$785$	2.35354e18	0.358979
$786$	6.65933e18	1.00736
$787$	−2.22781e18	−0.334227	−0.167114	−	0.985938i	$-0.553445\pi$
$787$	−2.22781e18	−0.334227	−0.167114	+	0.985938i	$0.553445\pi$
$788$	−6.88102e17	−0.102384
$789$	−2.02048e18	−0.298163
$790$	−5.81747e18	−0.851448
$791$	3.51160e18	0.509751
$792$	1.05981e18	0.152587
$793$	1.60070e19	2.28578
$794$	−1.17319e19	−1.66163
$795$	−1.66612e18	−0.234056
$796$	8.87423e17	0.123650
$797$	7.23607e18	1.00005	0.500027	−	0.866010i	$-0.333323\pi$
$797$	7.23607e18	1.00005	0.500027	+	0.866010i	$0.333323\pi$
$798$	7.95316e18	1.09024
$799$	−3.19692e17	−0.0434688
$800$	−8.61863e17	−0.116239
$801$	−7.19511e18	−0.962556
$802$	−1.20599e19	−1.60034
$803$	−6.97836e17	−0.0918548
$804$	−3.84043e17	−0.0501436
$805$	6.06361e18	0.785341
$806$	1.11536e19	1.43298
$807$	−9.13975e18	−1.16481
$808$	−1.15914e19	−1.46542
$809$	−2.19463e18	−0.275230	−0.137615	−	0.990486i	$-0.543944\pi$
$809$	−2.19463e18	−0.275230	−0.137615	+	0.990486i	$0.543944\pi$
$810$	−7.63579e17	−0.0949952
$811$	−4.51729e18	−0.557497	−0.278749	−	0.960364i	$-0.589920\pi$
$811$	−4.51729e18	−0.557497	−0.278749	+	0.960364i	$0.589920\pi$
$812$	8.70337e17	0.106555
$813$	8.66394e17	0.105227
$814$	1.09323e18	0.131720
$815$	4.49809e18	0.537656
$816$	−7.85666e17	−0.0931648
$817$	1.19268e19	1.40307
$818$	2.30566e18	0.269091
$819$	1.01982e19	1.18081
$820$	2.19056e17	0.0251631
$821$	−6.90846e18	−0.787319	−0.393660	−	0.919256i	$-0.628791\pi$
$821$	−6.90846e18	−0.787319	−0.393660	+	0.919256i	$0.628791\pi$
$822$	2.94755e18	0.333269
$823$	−4.35677e18	−0.488726	−0.244363	−	0.969684i	$-0.578579\pi$
$823$	−4.35677e18	−0.488726	−0.244363	+	0.969684i	$0.578579\pi$
$824$	−6.48170e17	−0.0721377
$825$	1.45760e18	0.160949
$826$	−6.76028e18	−0.740618
$827$	1.14047e19	1.23965	0.619825	−	0.784740i	$-0.287204\pi$
$827$	1.14047e19	1.23965	0.619825	+	0.784740i	$0.287204\pi$
$828$	4.35420e17	0.0469582
$829$	−4.22267e18	−0.451838	−0.225919	−	0.974146i	$-0.572539\pi$
$829$	−4.22267e18	−0.451838	−0.225919	+	0.974146i	$0.572539\pi$
$830$	1.04310e18	0.110743
$831$	4.62019e18	0.486691
$832$	−1.39773e19	−1.46091
$833$	1.17463e18	0.121817
$834$	6.61460e18	0.680651
$835$	−5.98050e18	−0.610626
$836$	2.43818e17	0.0247016
$837$	−9.03280e18	−0.908044
$838$	−4.03746e18	−0.402737
$839$	−1.08584e19	−1.07476	−0.537381	−	0.843340i	$-0.680586\pi$
$839$	−1.08584e19	−1.07476	−0.537381	+	0.843340i	$0.680586\pi$
$840$	−4.44074e18	−0.436154
$841$	3.06021e17	0.0298247
$842$	−6.76672e18	−0.654409
$843$	−9.58247e18	−0.919598
$844$	−1.05869e18	−0.100819
$845$	−7.76897e18	−0.734167
$846$	−2.00052e18	−0.187601
$847$	1.36799e18	0.127304
$848$	−8.34567e18	−0.770705
$849$	1.38726e19	1.27133
$850$	1.12251e18	0.102086
$851$	−5.54094e18	−0.500082
$852$	6.03730e17	0.0540736
$853$	−1.70408e19	−1.51468	−0.757339	−	0.653022i	$-0.773501\pi$
$853$	−1.70408e19	−1.51468	−0.757339	+	0.653022i	$0.773501\pi$
$854$	2.35430e19	2.07676
$855$	−3.11198e18	−0.272431
$856$	1.50568e19	1.30813
$857$	1.16550e19	1.00493	0.502467	−	0.864596i	$-0.332426\pi$
$857$	1.16550e19	1.00493	0.502467	+	0.864596i	$0.332426\pi$
$858$	−4.01216e18	−0.343329
$859$	1.46183e18	0.124149	0.0620743	−	0.998072i	$-0.480228\pi$
$859$	1.46183e18	0.124149	0.0620743	+	0.998072i	$0.480228\pi$
$860$	5.39815e17	0.0454993
$861$	−8.17058e18	−0.683491
$862$	1.59511e19	1.32432
$863$	1.47779e19	1.21771	0.608853	−	0.793283i	$-0.291630\pi$
$863$	1.47779e19	1.21771	0.608853	+	0.793283i	$0.291630\pi$
$864$	−1.92125e18	−0.157125
$865$	−1.52325e18	−0.123642
$866$	−1.24735e19	−1.00490
$867$	−8.45691e18	−0.676219
$868$	1.14426e18	0.0908126
$869$	6.65209e18	0.523998
$870$	4.37031e18	0.341694
$871$	2.00372e19	1.55496
$872$	2.32693e19	1.79237
$873$	2.04258e18	0.156166
$874$	−1.77166e19	−1.34449
$875$	1.56076e19	1.17566
$876$	2.09969e17	0.0156993
$877$	5.43454e18	0.403335	0.201667	−	0.979454i	$-0.435364\pi$
$877$	5.43454e18	0.403335	0.201667	+	0.979454i	$0.435364\pi$
$878$	6.82528e17	0.0502812
$879$	−3.29026e18	−0.240604
$880$	−2.09892e18	−0.152356
$881$	−1.39490e19	−1.00508	−0.502539	−	0.864554i	$-0.667601\pi$
$881$	−1.39490e19	−1.00508	−0.502539	+	0.864554i	$0.667601\pi$
$882$	7.35042e18	0.525734
$883$	−2.32130e18	−0.164811	−0.0824055	−	0.996599i	$-0.526260\pi$
$883$	−2.32130e18	−0.164811	−0.0824055	+	0.996599i	$0.526260\pi$
$884$	−2.15519e17	−0.0151896
$885$	−2.36781e18	−0.165659
$886$	−1.48018e19	−1.02801
$887$	1.00797e19	0.694934	0.347467	−	0.937692i	$-0.387042\pi$
$887$	1.00797e19	0.694934	0.347467	+	0.937692i	$0.387042\pi$
$888$	4.05796e18	0.277730
$889$	2.25639e19	1.53304
$890$	1.32505e19	0.893710
$891$	8.73128e17	0.0584619
$892$	−1.03459e18	−0.0687696
$893$	5.67767e18	0.374659
$894$	−8.95686e18	−0.586762
$895$	−8.47554e18	−0.551210
$896$	−2.38036e19	−1.53688
$897$	2.03353e19	1.30346
$898$	5.39540e18	0.343342
$899$	1.38923e19	0.877680
$900$	4.89955e17	0.0307312
$901$	1.46717e18	0.0913628
$902$	−3.59106e18	−0.222014
$903$	−2.01346e19	−1.23587
$904$	5.72888e18	0.349120
$905$	1.14424e19	0.692312
$906$	−7.66601e18	−0.460507
$907$	−1.45005e19	−0.864840	−0.432420	−	0.901672i	$-0.642340\pi$
$907$	−1.45005e19	−0.864840	−0.432420	+	0.901672i	$0.642340\pi$
$908$	6.02183e16	0.00356591
$909$	1.37132e19	0.806256
$910$	−1.87810e19	−1.09635
$911$	−2.73569e19	−1.58561	−0.792807	−	0.609473i	$-0.791381\pi$
$911$	−2.73569e19	−1.58561	−0.792807	+	0.609473i	$0.791381\pi$
$912$	1.39533e19	0.802990
$913$	−1.19275e18	−0.0681537
$914$	−3.22166e19	−1.82781
$915$	8.24600e18	0.464522
$916$	9.40936e17	0.0526307
$917$	−3.56447e19	−1.97968
$918$	2.50228e18	0.137993
$919$	−2.94406e19	−1.61212	−0.806058	−	0.591837i	$-0.798403\pi$
$919$	−2.94406e19	−1.61212	−0.806058	+	0.591837i	$0.798403\pi$
$920$	9.89227e18	0.537867
$921$	1.12644e16	0.000608164 0
$922$	6.01524e17	0.0322479
$923$	−3.14992e19	−1.67683
$924$	−4.11610e17	−0.0217580
$925$	−6.23492e18	−0.327273
$926$	1.83351e19	0.955680
$927$	7.66817e17	0.0396893
$928$	2.95486e18	0.151871
$929$	1.44314e19	0.736555	0.368278	−	0.929716i	$-0.379948\pi$
$929$	1.44314e19	0.736555	0.368278	+	0.929716i	$0.379948\pi$
$930$	5.74578e18	0.291213
$931$	−2.08612e19	−1.04995
$932$	−1.02066e18	−0.0510125
$933$	1.09616e19	0.544056
$934$	−1.47125e19	−0.725154
$935$	3.68991e17	0.0180609
$936$	1.66375e19	0.808716
$937$	9.68227e18	0.467380	0.233690	−	0.972311i	$-0.424920\pi$
$937$	9.68227e18	0.467380	0.233690	+	0.972311i	$0.424920\pi$
$938$	2.94705e19	1.41276
$939$	−6.31560e18	−0.300669
$940$	2.56976e17	0.0121496
$941$	−2.56256e19	−1.20321	−0.601605	−	0.798794i	$-0.705472\pi$
$941$	−2.56256e19	−1.20321	−0.601605	+	0.798794i	$0.705472\pi$
$942$	1.16089e19	0.541328
$943$	1.82009e19	0.842884
$944$	−1.18605e19	−0.545486
$945$	1.52099e19	0.694734
$946$	−8.84937e18	−0.401439
$947$	2.69010e19	1.21197	0.605987	−	0.795475i	$-0.292778\pi$
$947$	2.69010e19	1.21197	0.605987	+	0.795475i	$0.292778\pi$
$948$	−2.00152e18	−0.0895584
$949$	−1.09550e19	−0.486835
$950$	−1.99355e19	−0.879882
$951$	2.27517e19	0.997332
$952$	3.91048e18	0.170251
$953$	−1.73815e18	−0.0751594	−0.0375797	−	0.999294i	$-0.511965\pi$
$953$	−1.73815e18	−0.0751594	−0.0375797	+	0.999294i	$0.511965\pi$
$954$	9.18103e18	0.394300
$955$	3.81801e18	0.162860
$956$	−1.41057e18	−0.0597612
$957$	−4.99731e18	−0.210285
$958$	2.08667e19	0.872123
$959$	−1.57770e19	−0.654945
$960$	−7.20040e18	−0.296889
$961$	−6.15291e18	−0.251987
$962$	1.71621e19	0.698125
$963$	−1.78129e19	−0.719720
$964$	6.33728e17	0.0254333
$965$	−4.27150e18	−0.170276
$966$	2.99090e19	1.18427
$967$	2.33708e18	0.0919183	0.0459591	−	0.998943i	$-0.485366\pi$
$967$	2.33708e18	0.0919183	0.0459591	+	0.998943i	$0.485366\pi$
$968$	2.23176e18	0.0871883
$969$	−2.45299e18	−0.0951900
$970$	−3.76161e18	−0.144996
$971$	−1.29089e18	−0.0494270	−0.0247135	−	0.999695i	$-0.507867\pi$
$971$	−1.29089e18	−0.0494270	−0.0247135	+	0.999695i	$0.507867\pi$
$972$	1.80715e18	0.0687326
$973$	−3.54053e19	−1.33763
$974$	6.21524e18	0.233252
$975$	2.28822e19	0.853036
$976$	4.13046e19	1.52959
$977$	4.06643e19	1.49589	0.747943	−	0.663763i	$-0.231041\pi$
$977$	4.06643e19	1.49589	0.747943	+	0.663763i	$0.231041\pi$
$978$	2.21870e19	0.810767
$979$	−1.51515e19	−0.550006
$980$	−9.44197e17	−0.0340481
$981$	−2.75287e19	−0.986137
$982$	2.48927e18	0.0885823
$983$	−1.49243e19	−0.527589	−0.263794	−	0.964579i	$-0.584974\pi$
$983$	−1.49243e19	−0.527589	−0.263794	+	0.964579i	$0.584974\pi$
$984$	−1.33296e19	−0.468111
$985$	1.84945e19	0.645219
$986$	−3.84846e18	−0.133379
$987$	−9.58498e18	−0.330012
$988$	3.82758e18	0.130920
$989$	4.48522e19	1.52408
$990$	2.30901e18	0.0779467
$991$	3.80367e19	1.27563	0.637814	−	0.770190i	$-0.279839\pi$
$991$	3.80367e19	1.27563	0.637814	+	0.770190i	$0.279839\pi$
$992$	3.88484e18	0.129434
$993$	−6.67452e18	−0.220928
$994$	−4.63288e19	−1.52349
$995$	−2.38518e19	−0.779238
$996$	3.58882e17	0.0116484
$997$	−6.74110e18	−0.217376	−0.108688	−	0.994076i	$-0.534665\pi$
$997$	−6.74110e18	−0.217376	−0.108688	+	0.994076i	$0.534665\pi$
$998$	−3.63795e19	−1.16549
$999$	−1.38988e19	−0.442386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.14.a.a.1.2	✓	5
3.2	odd	2		99.14.a.e.1.4		5
4.3	odd	2		176.14.a.e.1.2		5
11.10	odd	2		121.14.a.b.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.14.a.a.1.2	✓	5	1.1	even	1	trivial
99.14.a.e.1.4		5	3.2	odd	2
121.14.a.b.1.4		5	11.10	odd	2
176.14.a.e.1.2		5	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)

\(f(q)\)	\(=\)	\(q-93.8416 q^{2} +867.783 q^{3} +614.253 q^{4} -16509.6 q^{5} -81434.2 q^{6} +435884. q^{7} +711108. q^{8} -841275. q^{9} +O(q^{10})\)	\(q-93.8416 q^{2} +867.783 q^{3} +614.253 q^{4} -16509.6 q^{5} -81434.2 q^{6} +435884. q^{7} +711108. q^{8} -841275. q^{9} +1.54929e6 q^{10} -1.77156e6 q^{11} +533039. q^{12} -2.78109e7 q^{13} -4.09041e7 q^{14} -1.43268e7 q^{15} -7.17635e7 q^{16} +1.26160e7 q^{17} +7.89466e7 q^{18} -2.24059e8 q^{19} -1.01411e7 q^{20} +3.78253e8 q^{21} +1.66246e8 q^{22} -8.42604e8 q^{23} +6.17088e8 q^{24} -9.48136e8 q^{25} +2.60982e9 q^{26} -2.11357e9 q^{27} +2.67743e8 q^{28} +3.25064e9 q^{29} +1.34445e9 q^{30} +4.27371e9 q^{31} +9.09008e8 q^{32} -1.53733e9 q^{33} -1.18391e9 q^{34} -7.19628e9 q^{35} -5.16756e8 q^{36} +6.57598e9 q^{37} +2.10260e10 q^{38} -2.41339e10 q^{39} -1.17401e10 q^{40} -2.16008e10 q^{41} -3.54959e10 q^{42} -5.32305e10 q^{43} -1.08819e9 q^{44} +1.38891e10 q^{45} +7.90713e10 q^{46} -2.53401e10 q^{47} -6.22752e10 q^{48} +9.31062e10 q^{49} +8.89746e10 q^{50} +1.09480e10 q^{51} -1.70829e10 q^{52} +1.16294e11 q^{53} +1.98341e11 q^{54} +2.92478e10 q^{55} +3.09961e11 q^{56} -1.94434e11 q^{57} -3.05045e11 q^{58} +1.65271e11 q^{59} -8.80026e9 q^{60} -5.75566e11 q^{61} -4.01052e11 q^{62} -3.66699e11 q^{63} +5.02584e11 q^{64} +4.59148e11 q^{65} +1.44266e11 q^{66} -7.20478e11 q^{67} +7.74944e9 q^{68} -7.31197e11 q^{69} +6.75311e11 q^{70} +1.13262e12 q^{71} -5.98238e11 q^{72} +3.93910e11 q^{73} -6.17100e11 q^{74} -8.22776e11 q^{75} -1.37629e11 q^{76} -7.72196e11 q^{77} +2.26476e12 q^{78} -3.75493e12 q^{79} +1.18479e12 q^{80} -4.92858e11 q^{81} +2.02706e12 q^{82} +6.73276e11 q^{83} +2.32343e11 q^{84} -2.08286e11 q^{85} +4.99524e12 q^{86} +2.82085e12 q^{87} -1.25977e12 q^{88} +8.55262e12 q^{89} -1.30338e12 q^{90} -1.21223e13 q^{91} -5.17572e11 q^{92} +3.70866e12 q^{93} +2.37796e12 q^{94} +3.69912e12 q^{95} +7.88822e11 q^{96} -2.42796e12 q^{97} -8.73723e12 q^{98} +1.49037e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 64 q^{2} + 480 q^{3} - 2400 q^{4} - 454 q^{5} + 79548 q^{6} - 313920 q^{7} - 255168 q^{8} + 1321749 q^{9}+O(q^{10}) \) 5 * q - 64 * q^2 + 480 * q^3 - 2400 * q^4 - 454 * q^5 + 79548 * q^6 - 313920 * q^7 - 255168 * q^8 + 1321749 * q^9	\( 5 q - 64 q^{2} + 480 q^{3} - 2400 q^{4} - 454 q^{5} + 79548 q^{6} - 313920 q^{7} - 255168 q^{8} + 1321749 q^{9} - 3535724 q^{10} - 8857805 q^{11} - 29768880 q^{12} - 36339498 q^{13} - 64558312 q^{14} - 162945300 q^{15} - 128942592 q^{16} - 309078454 q^{17} - 302859828 q^{18} - 147232948 q^{19} - 62530256 q^{20} - 859909128 q^{21} + 113379904 q^{22} + 677905444 q^{23} + 755940096 q^{24} + 1540265631 q^{25} + 1643160872 q^{26} + 5029885620 q^{27} + 6948937120 q^{28} + 2368825878 q^{29} + 7601916540 q^{30} - 83363076 q^{31} + 10024391680 q^{32} - 850349280 q^{33} + 7463914000 q^{34} + 591040520 q^{35} - 15037063632 q^{36} - 32935650382 q^{37} - 25107474384 q^{38} - 54599307000 q^{39} - 27853580928 q^{40} - 70273827286 q^{41} - 18264520200 q^{42} - 54501240436 q^{43} + 4251746400 q^{44} - 118334367738 q^{45} - 9391823524 q^{46} - 45017434472 q^{47} + 236995825920 q^{48} + 77867671053 q^{49} + 252640243516 q^{50} - 14973171168 q^{51} + 370262207008 q^{52} + 242684257518 q^{53} + 386371416420 q^{54} + 804288694 q^{55} + 508508098560 q^{56} - 78232137120 q^{57} + 338805253176 q^{58} - 384712501184 q^{59} + 607819216080 q^{60} - 795317095690 q^{61} + 567054167132 q^{62} - 1777323941640 q^{63} - 502608203776 q^{64} - 1104664950268 q^{65} - 140924134428 q^{66} - 1005952134296 q^{67} + 9188915584 q^{68} - 2334490276524 q^{69} - 50031562280 q^{70} - 1427050574148 q^{71} + 714622284864 q^{72} - 4111049036406 q^{73} + 2579474987436 q^{74} - 584109490620 q^{75} + 1028633987648 q^{76} + 556128429120 q^{77} + 4554998846160 q^{78} - 3666957194024 q^{79} + 1569918525184 q^{80} + 4090930814781 q^{81} + 4301648616232 q^{82} + 2718055516116 q^{83} + 8581863439392 q^{84} + 1506197091796 q^{85} + 6558172582872 q^{86} + 3556682104680 q^{87} + 452045677248 q^{88} + 7963494884214 q^{89} - 4671771563808 q^{90} - 604892444560 q^{91} + 6414213002576 q^{92} + 361484424660 q^{93} - 9832269652768 q^{94} - 5225122758984 q^{95} - 12178790559744 q^{96} - 13542719272730 q^{97} - 8557591646352 q^{98} - 2341558980189 q^{99}+O(q^{100}) \) 5 * q - 64 * q^2 + 480 * q^3 - 2400 * q^4 - 454 * q^5 + 79548 * q^6 - 313920 * q^7 - 255168 * q^8 + 1321749 * q^9 - 3535724 * q^10 - 8857805 * q^11 - 29768880 * q^12 - 36339498 * q^13 - 64558312 * q^14 - 162945300 * q^15 - 128942592 * q^16 - 309078454 * q^17 - 302859828 * q^18 - 147232948 * q^19 - 62530256 * q^20 - 859909128 * q^21 + 113379904 * q^22 + 677905444 * q^23 + 755940096 * q^24 + 1540265631 * q^25 + 1643160872 * q^26 + 5029885620 * q^27 + 6948937120 * q^28 + 2368825878 * q^29 + 7601916540 * q^30 - 83363076 * q^31 + 10024391680 * q^32 - 850349280 * q^33 + 7463914000 * q^34 + 591040520 * q^35 - 15037063632 * q^36 - 32935650382 * q^37 - 25107474384 * q^38 - 54599307000 * q^39 - 27853580928 * q^40 - 70273827286 * q^41 - 18264520200 * q^42 - 54501240436 * q^43 + 4251746400 * q^44 - 118334367738 * q^45 - 9391823524 * q^46 - 45017434472 * q^47 + 236995825920 * q^48 + 77867671053 * q^49 + 252640243516 * q^50 - 14973171168 * q^51 + 370262207008 * q^52 + 242684257518 * q^53 + 386371416420 * q^54 + 804288694 * q^55 + 508508098560 * q^56 - 78232137120 * q^57 + 338805253176 * q^58 - 384712501184 * q^59 + 607819216080 * q^60 - 795317095690 * q^61 + 567054167132 * q^62 - 1777323941640 * q^63 - 502608203776 * q^64 - 1104664950268 * q^65 - 140924134428 * q^66 - 1005952134296 * q^67 + 9188915584 * q^68 - 2334490276524 * q^69 - 50031562280 * q^70 - 1427050574148 * q^71 + 714622284864 * q^72 - 4111049036406 * q^73 + 2579474987436 * q^74 - 584109490620 * q^75 + 1028633987648 * q^76 + 556128429120 * q^77 + 4554998846160 * q^78 - 3666957194024 * q^79 + 1569918525184 * q^80 + 4090930814781 * q^81 + 4301648616232 * q^82 + 2718055516116 * q^83 + 8581863439392 * q^84 + 1506197091796 * q^85 + 6558172582872 * q^86 + 3556682104680 * q^87 + 452045677248 * q^88 + 7963494884214 * q^89 - 4671771563808 * q^90 - 604892444560 * q^91 + 6414213002576 * q^92 + 361484424660 * q^93 - 9832269652768 * q^94 - 5225122758984 * q^95 - 12178790559744 * q^96 - 13542719272730 * q^97 - 8557591646352 * q^98 - 2341558980189 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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