LMFDB - Embedded newform 11.14.a.a.1.1

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			1.1
Root			$28.2490$ 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)

$f(q)$	$=$	$q-124.996 q^{2} -1750.38 q^{3} +7432.04 q^{4} +27373.3 q^{5} +218790. q^{6} +75214.1 q^{7} +94992.6 q^{8} +1.46950e6 q^{9} +O(q^{10})$	\(q-124.996 q^{2} -1750.38 q^{3} +7432.04 q^{4} +27373.3 q^{5} +218790. q^{6} +75214.1 q^{7} +94992.6 q^{8} +1.46950e6 q^{9} -3.42156e6 q^{10} -1.77156e6 q^{11} -1.30089e7 q^{12} +1.16801e7 q^{13} -9.40148e6 q^{14} -4.79136e7 q^{15} -7.27569e7 q^{16} -1.25414e8 q^{17} -1.83681e8 q^{18} +2.18507e8 q^{19} +2.03439e8 q^{20} -1.31653e8 q^{21} +2.21438e8 q^{22} +9.99518e8 q^{23} -1.66273e8 q^{24} -4.71405e8 q^{25} -1.45997e9 q^{26} +2.18493e8 q^{27} +5.58994e8 q^{28} -1.29863e9 q^{29} +5.98902e9 q^{30} -6.48625e9 q^{31} +8.31616e9 q^{32} +3.10090e9 q^{33} +1.56763e10 q^{34} +2.05886e9 q^{35} +1.09214e10 q^{36} -2.98869e10 q^{37} -2.73125e10 q^{38} -2.04446e10 q^{39} +2.60026e9 q^{40} -2.41751e10 q^{41} +1.64561e10 q^{42} -3.77484e10 q^{43} -1.31663e10 q^{44} +4.02250e10 q^{45} -1.24936e11 q^{46} +8.20083e10 q^{47} +1.27352e11 q^{48} -9.12318e10 q^{49} +5.89238e10 q^{50} +2.19522e11 q^{51} +8.68072e10 q^{52} +1.37189e11 q^{53} -2.73108e10 q^{54} -4.84935e10 q^{55} +7.14479e9 q^{56} -3.82469e11 q^{57} +1.62323e11 q^{58} -2.62827e11 q^{59} -3.56096e11 q^{60} +7.10224e10 q^{61} +8.10757e11 q^{62} +1.10527e11 q^{63} -4.43463e11 q^{64} +3.19724e11 q^{65} -3.87600e11 q^{66} +8.31971e11 q^{67} -9.32082e11 q^{68} -1.74953e12 q^{69} -2.57349e11 q^{70} -1.74526e11 q^{71} +1.39591e11 q^{72} -2.21587e12 q^{73} +3.73575e12 q^{74} +8.25137e11 q^{75} +1.62395e12 q^{76} -1.33246e11 q^{77} +2.55550e12 q^{78} -3.44971e12 q^{79} -1.99160e12 q^{80} -2.72530e12 q^{81} +3.02179e12 q^{82} +1.50079e12 q^{83} -9.78450e11 q^{84} -3.43300e12 q^{85} +4.71840e12 q^{86} +2.27308e12 q^{87} -1.68285e11 q^{88} +2.74361e12 q^{89} -5.02797e12 q^{90} +8.78511e11 q^{91} +7.42845e12 q^{92} +1.13534e13 q^{93} -1.02507e13 q^{94} +5.98125e12 q^{95} -1.45564e13 q^{96} +4.96145e12 q^{97} +1.14036e13 q^{98} -2.60330e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−124.996	−1.38103	−0.690513	−	0.723320i	$-0.742615\pi$
$2$	−124.996	−1.38103	−0.690513	+	0.723320i	$0.742615\pi$
$3$	−1750.38	−1.38626	−0.693128	−	0.720815i	$-0.743768\pi$
$3$	−1750.38	−1.38626	−0.693128	+	0.720815i	$0.743768\pi$
$4$	7432.04	0.907231
$5$	27373.3	0.783470	0.391735	−	0.920078i	$-0.371875\pi$
$5$	27373.3	0.783470	0.391735	+	0.920078i	$0.371875\pi$
$6$	218790.	1.91445
$7$	75214.1	0.241636	0.120818	−	0.992675i	$-0.461448\pi$
$7$	75214.1	0.241636	0.120818	+	0.992675i	$0.461448\pi$
$8$	94992.6	0.128116
$9$	1.46950e6	0.921706
$10$	−3.42156e6	−1.08199
$11$	−1.77156e6	−0.301511
$11$	−1.77156e6	−0.301511
$12$	−1.30089e7	−1.25765
$13$	1.16801e7	0.671145	0.335572	−	0.942014i	$-0.391070\pi$
$13$	1.16801e7	0.671145	0.335572	+	0.942014i	$0.391070\pi$
$14$	−9.40148e6	−0.333706
$15$	−4.79136e7	−1.08609
$16$	−7.27569e7	−1.08416
$17$	−1.25414e8	−1.26017	−0.630084	−	0.776527i	$-0.716980\pi$
$17$	−1.25414e8	−1.26017	−0.630084	+	0.776527i	$0.716980\pi$
$18$	−1.83681e8	−1.27290
$19$	2.18507e8	1.06553	0.532766	−	0.846263i	$-0.321153\pi$
$19$	2.18507e8	1.06553	0.532766	+	0.846263i	$0.321153\pi$
$20$	2.03439e8	0.710788
$21$	−1.31653e8	−0.334970
$22$	2.21438e8	0.416395
$23$	9.99518e8	1.40786	0.703930	−	0.710269i	$-0.251427\pi$
$23$	9.99518e8	1.40786	0.703930	+	0.710269i	$0.251427\pi$
$24$	−1.66273e8	−0.177602
$25$	−4.71405e8	−0.386175
$26$	−1.45997e9	−0.926868
$27$	2.18493e8	0.108536
$28$	5.58994e8	0.219220
$29$	−1.29863e9	−0.405412	−0.202706	−	0.979240i	$-0.564974\pi$
$29$	−1.29863e9	−0.405412	−0.202706	+	0.979240i	$0.564974\pi$
$30$	5.98902e9	1.49992
$31$	−6.48625e9	−1.31263	−0.656316	−	0.754486i	$-0.727886\pi$
$31$	−6.48625e9	−1.31263	−0.656316	+	0.754486i	$0.727886\pi$
$32$	8.31616e9	1.36914
$33$	3.10090e9	0.417972
$34$	1.56763e10	1.74032
$35$	2.05886e9	0.189315
$36$	1.09214e10	0.836200
$37$	−2.98869e10	−1.91500	−0.957502	−	0.288428i	$-0.906867\pi$
$37$	−2.98869e10	−1.91500	−0.957502	+	0.288428i	$0.906867\pi$
$38$	−2.73125e10	−1.47153
$39$	−2.04446e10	−0.930378
$40$	2.60026e9	0.100375
$41$	−2.41751e10	−0.794828	−0.397414	−	0.917639i	$-0.630092\pi$
$41$	−2.41751e10	−0.794828	−0.397414	+	0.917639i	$0.630092\pi$
$42$	1.64561e10	0.462602
$43$	−3.77484e10	−0.910654	−0.455327	−	0.890324i	$-0.650478\pi$
$43$	−3.77484e10	−0.910654	−0.455327	+	0.890324i	$0.650478\pi$
$44$	−1.31663e10	−0.273540
$45$	4.02250e10	0.722128
$46$	−1.24936e11	−1.94429
$47$	8.20083e10	1.10974	0.554871	−	0.831936i	$-0.312768\pi$
$47$	8.20083e10	1.10974	0.554871	+	0.831936i	$0.312768\pi$
$48$	1.27352e11	1.50293
$49$	−9.12318e10	−0.941612
$50$	5.89238e10	0.533318
$51$	2.19522e11	1.74692
$52$	8.68072e10	0.608883
$53$	1.37189e11	0.850208	0.425104	−	0.905145i	$-0.360238\pi$
$53$	1.37189e11	0.850208	0.425104	+	0.905145i	$0.360238\pi$
$54$	−2.73108e10	−0.149891
$55$	−4.84935e10	−0.236225
$56$	7.14479e9	0.0309576
$57$	−3.82469e11	−1.47710
$58$	1.62323e11	0.559885
$59$	−2.62827e11	−0.811206	−0.405603	−	0.914049i	$-0.632938\pi$
$59$	−2.62827e11	−0.811206	−0.405603	+	0.914049i	$0.632938\pi$
$60$	−3.56096e11	−0.985334
$61$	7.10224e10	0.176503	0.0882513	−	0.996098i	$-0.471872\pi$
$61$	7.10224e10	0.176503	0.0882513	+	0.996098i	$0.471872\pi$
$62$	8.10757e11	1.81278
$63$	1.10527e11	0.222718
$64$	−4.43463e11	−0.806654
$65$	3.19724e11	0.525821
$66$	−3.87600e11	−0.577230
$67$	8.31971e11	1.12363	0.561813	−	0.827264i	$-0.310104\pi$
$67$	8.31971e11	1.12363	0.561813	+	0.827264i	$0.310104\pi$
$68$	−9.32082e11	−1.14326
$69$	−1.74953e12	−1.95166
$70$	−2.57349e11	−0.261448
$71$	−1.74526e11	−0.161689	−0.0808445	−	0.996727i	$-0.525762\pi$
$71$	−1.74526e11	−0.161689	−0.0808445	+	0.996727i	$0.525762\pi$
$72$	1.39591e11	0.118086
$73$	−2.21587e12	−1.71374	−0.856871	−	0.515532i	$-0.827595\pi$
$73$	−2.21587e12	−1.71374	−0.856871	+	0.515532i	$0.827595\pi$
$74$	3.73575e12	2.64467
$75$	8.25137e11	0.535338
$76$	1.62395e12	0.966683
$77$	−1.33246e11	−0.0728561
$78$	2.55550e12	1.28488
$79$	−3.44971e12	−1.59664	−0.798320	−	0.602233i	$-0.794278\pi$
$79$	−3.44971e12	−1.59664	−0.798320	+	0.602233i	$0.794278\pi$
$80$	−1.99160e12	−0.849409
$81$	−2.72530e12	−1.07216
$82$	3.02179e12	1.09768
$83$	1.50079e12	0.503864	0.251932	−	0.967745i	$-0.418934\pi$
$83$	1.50079e12	0.503864	0.251932	+	0.967745i	$0.418934\pi$
$84$	−9.78450e11	−0.303895
$85$	−3.43300e12	−0.987303
$86$	4.71840e12	1.25764
$87$	2.27308e12	0.562005
$88$	−1.68285e11	−0.0386286
$89$	2.74361e12	0.585178	0.292589	−	0.956238i	$-0.405483\pi$
$89$	2.74361e12	0.585178	0.292589	+	0.956238i	$0.405483\pi$
$90$	−5.02797e12	−0.997278
$91$	8.78511e11	0.162173
$92$	7.42845e12	1.27725
$93$	1.13534e13	1.81964
$94$	−1.02507e13	−1.53258
$95$	5.98125e12	0.834812
$96$	−1.45564e13	−1.89798
$97$	4.96145e12	0.604773	0.302387	−	0.953185i	$-0.402217\pi$
$97$	4.96145e12	0.604773	0.302387	+	0.953185i	$0.402217\pi$
$98$	1.14036e13	1.30039
$99$	−2.60330e12	−0.277905
$100$	−3.50350e12	−0.350350
$101$	−1.15222e13	−1.08006	−0.540030	−	0.841646i	$-0.681587\pi$
$101$	−1.15222e13	−1.08006	−0.540030	+	0.841646i	$0.681587\pi$
$102$	−2.74394e13	−2.41253
$103$	6.21518e12	0.512875	0.256437	−	0.966561i	$-0.417451\pi$
$103$	6.21518e12	0.512875	0.256437	+	0.966561i	$0.417451\pi$
$104$	1.10953e12	0.0859847
$105$	−3.60378e12	−0.262439
$106$	−1.71481e13	−1.17416
$107$	−2.59389e13	−1.67092	−0.835462	−	0.549548i	$-0.814800\pi$
$107$	−2.59389e13	−1.67092	−0.835462	+	0.549548i	$0.814800\pi$
$108$	1.62385e12	0.0984672
$109$	−1.90855e13	−1.09001	−0.545006	−	0.838432i	$-0.683473\pi$
$109$	−1.90855e13	−1.09001	−0.545006	+	0.838432i	$0.683473\pi$
$110$	6.06150e12	0.326233
$111$	5.23133e13	2.65468
$112$	−5.47235e12	−0.261973
$113$	1.15215e13	0.520592	0.260296	−	0.965529i	$-0.416180\pi$
$113$	1.15215e13	0.520592	0.260296	+	0.965529i	$0.416180\pi$
$114$	4.78071e13	2.03991
$115$	2.73601e13	1.10302
$116$	−9.65143e12	−0.367803
$117$	1.71639e13	0.618598
$118$	3.28523e13	1.12030
$119$	−9.43291e12	−0.304502
$120$	−4.55144e12	−0.139146
$121$	3.13843e12	0.0909091
$122$	−8.87752e12	−0.243755
$123$	4.23155e13	1.10184
$124$	−4.82061e13	−1.19086
$125$	−4.63186e13	−1.08603
$126$	−1.38154e13	−0.307579
$127$	−1.67593e13	−0.354431	−0.177215	−	0.984172i	$-0.556709\pi$
$127$	−1.67593e13	−0.354431	−0.177215	+	0.984172i	$0.556709\pi$
$128$	−1.26948e13	−0.255130
$129$	6.60739e13	1.26240
$130$	−3.99643e13	−0.726173
$131$	−4.85484e13	−0.839288	−0.419644	−	0.907689i	$-0.637845\pi$
$131$	−4.85484e13	−0.839288	−0.419644	+	0.907689i	$0.637845\pi$
$132$	2.30460e13	0.379197
$133$	1.64348e13	0.257471
$134$	−1.03993e14	−1.55176
$135$	5.98089e12	0.0850347
$136$	−1.19134e13	−0.161448
$137$	−9.21914e12	−0.119126	−0.0595631	−	0.998225i	$-0.518971\pi$
$137$	−9.21914e12	−0.119126	−0.0595631	+	0.998225i	$0.518971\pi$
$138$	2.18685e14	2.69529
$139$	−8.44601e13	−0.993243	−0.496622	−	0.867967i	$-0.665426\pi$
$139$	−8.44601e13	−0.993243	−0.496622	+	0.867967i	$0.665426\pi$
$140$	1.53015e13	0.171752
$141$	−1.43545e14	−1.53839
$142$	2.18151e13	0.223297
$143$	−2.06921e13	−0.202358
$144$	−1.06916e14	−0.999279
$145$	−3.55477e13	−0.317628
$146$	2.76975e14	2.36672
$147$	1.59690e14	1.30532
$148$	−2.22120e14	−1.73735
$149$	2.22606e14	1.66658	0.833290	−	0.552836i	$-0.186454\pi$
$149$	2.22606e14	1.66658	0.833290	+	0.552836i	$0.186454\pi$
$150$	−1.03139e14	−0.739315
$151$	−1.16327e14	−0.798604	−0.399302	−	0.916819i	$-0.630748\pi$
$151$	−1.16327e14	−0.798604	−0.399302	+	0.916819i	$0.630748\pi$
$152$	2.07565e13	0.136512
$153$	−1.84296e14	−1.16150
$154$	1.66553e13	0.100616
$155$	−1.77550e14	−1.02841
$156$	−1.51945e14	−0.844068
$157$	2.15822e14	1.15013	0.575065	−	0.818108i	$-0.304977\pi$
$157$	2.15822e14	1.15013	0.575065	+	0.818108i	$0.304977\pi$
$158$	4.31201e14	2.20500
$159$	−2.40132e14	−1.17861
$160$	2.27641e14	1.07268
$161$	7.51779e13	0.340190
$162$	3.40652e14	1.48069
$163$	−1.70041e14	−0.710123	−0.355061	−	0.934843i	$-0.615540\pi$
$163$	−1.70041e14	−0.710123	−0.355061	+	0.934843i	$0.615540\pi$
$164$	−1.79670e14	−0.721093
$165$	8.48819e13	0.327468
$166$	−1.87593e14	−0.695848
$167$	1.82418e14	0.650744	0.325372	−	0.945586i	$-0.394511\pi$
$167$	1.82418e14	0.650744	0.325372	+	0.945586i	$0.394511\pi$
$168$	−1.25061e13	−0.0429151
$169$	−1.66450e14	−0.549565
$170$	4.29112e14	1.36349
$171$	3.21095e14	0.982106
$172$	−2.80547e14	−0.826173
$173$	−7.96824e13	−0.225976	−0.112988	−	0.993596i	$-0.536042\pi$
$173$	−7.96824e13	−0.225976	−0.112988	+	0.993596i	$0.536042\pi$
$174$	−2.84127e14	−0.776144
$175$	−3.54563e13	−0.0933139
$176$	1.28893e14	0.326887
$177$	4.60046e14	1.12454
$178$	−3.42941e14	−0.808145
$179$	−1.16489e14	−0.264692	−0.132346	−	0.991204i	$-0.542251\pi$
$179$	−1.16489e14	−0.264692	−0.132346	+	0.991204i	$0.542251\pi$
$180$	2.98953e14	0.655137
$181$	−2.44894e14	−0.517687	−0.258844	−	0.965919i	$-0.583341\pi$
$181$	−2.44894e14	−0.517687	−0.258844	+	0.965919i	$0.583341\pi$
$182$	−1.09811e14	−0.223965
$183$	−1.24316e14	−0.244678
$184$	9.49468e13	0.180370
$185$	−8.18103e14	−1.50035
$186$	−1.41913e15	−2.51297
$187$	2.22179e14	0.379955
$188$	6.09489e14	1.00679
$189$	1.64338e13	0.0262262
$190$	−7.47633e14	−1.15290
$191$	9.84941e14	1.46789	0.733944	−	0.679210i	$-0.237677\pi$
$191$	9.84941e14	1.46789	0.733944	+	0.679210i	$0.237677\pi$
$192$	7.76227e14	1.11823
$193$	−5.36851e14	−0.747707	−0.373854	−	0.927488i	$-0.621964\pi$
$193$	−5.36851e14	−0.747707	−0.373854	+	0.927488i	$0.621964\pi$
$194$	−6.20162e14	−0.835207
$195$	−5.59637e14	−0.728923
$196$	−6.78038e14	−0.854259
$197$	9.19085e14	1.12028	0.560139	−	0.828399i	$-0.310748\pi$
$197$	9.19085e14	1.12028	0.560139	+	0.828399i	$0.310748\pi$
$198$	3.25403e14	0.383793
$199$	1.32503e15	1.51245	0.756224	−	0.654312i	$-0.227042\pi$
$199$	1.32503e15	1.51245	0.756224	+	0.654312i	$0.227042\pi$
$200$	−4.47800e13	−0.0494754
$201$	−1.45626e15	−1.55763
$202$	1.44024e15	1.49159
$203$	−9.76750e13	−0.0979623
$204$	1.63150e15	1.58486
$205$	−6.61752e14	−0.622724
$206$	−7.76873e14	−0.708293
$207$	1.46879e15	1.29763
$208$	−8.49811e14	−0.727630
$209$	−3.87098e14	−0.321270
$210$	4.50459e14	0.362434
$211$	−2.30839e14	−0.180083	−0.0900416	−	0.995938i	$-0.528700\pi$
$211$	−2.30839e14	−0.180083	−0.0900416	+	0.995938i	$0.528700\pi$
$212$	1.01959e15	0.771335
$213$	3.05486e14	0.224142
$214$	3.24226e15	2.30759
$215$	−1.03330e15	−0.713470
$216$	2.07553e13	0.0139052
$217$	−4.87858e14	−0.317179
$218$	2.38561e15	1.50533
$219$	3.87860e15	2.37568
$220$	−3.60405e14	−0.214311
$221$	−1.46485e15	−0.845755
$222$	−6.53896e15	−3.66619
$223$	−8.62031e13	−0.0469398	−0.0234699	−	0.999725i	$-0.507471\pi$
$223$	−8.62031e13	−0.0469398	−0.0234699	+	0.999725i	$0.507471\pi$
$224$	6.25493e14	0.330834
$225$	−6.92728e14	−0.355940
$226$	−1.44014e15	−0.718951
$227$	−5.16573e14	−0.250590	−0.125295	−	0.992120i	$-0.539988\pi$
$227$	−5.16573e14	−0.250590	−0.125295	+	0.992120i	$0.539988\pi$
$228$	−2.84252e15	−1.34007
$229$	−2.65272e15	−1.21552	−0.607758	−	0.794123i	$-0.707931\pi$
$229$	−2.65272e15	−1.21552	−0.607758	+	0.794123i	$0.707931\pi$
$230$	−3.41991e15	−1.52329
$231$	2.33231e14	0.100997
$232$	−1.23360e14	−0.0519400
$233$	−3.37909e15	−1.38352	−0.691762	−	0.722126i	$-0.743165\pi$
$233$	−3.37909e15	−1.38352	−0.691762	+	0.722126i	$0.743165\pi$
$234$	−2.14542e15	−0.854299
$235$	2.24484e15	0.869449
$236$	−1.95334e15	−0.735951
$237$	6.03830e15	2.21335
$238$	1.17908e15	0.420525
$239$	5.40048e15	1.87433	0.937165	−	0.348886i	$-0.113440\pi$
$239$	5.40048e15	1.87433	0.937165	+	0.348886i	$0.113440\pi$
$240$	3.48605e15	1.17750
$241$	3.15905e15	1.03860	0.519298	−	0.854593i	$-0.326194\pi$
$241$	3.15905e15	1.03860	0.519298	+	0.854593i	$0.326194\pi$
$242$	−3.92291e14	−0.125548
$243$	4.42195e15	1.37776
$244$	5.27841e14	0.160129
$245$	−2.49732e15	−0.737724
$246$	−5.28928e15	−1.52166
$247$	2.55219e15	0.715126
$248$	−6.16146e14	−0.168170
$249$	−2.62695e15	−0.698484
$250$	5.78965e15	1.49983
$251$	−7.47962e15	−1.88799	−0.943996	−	0.329957i	$-0.892966\pi$
$251$	−7.47962e15	−1.88799	−0.943996	+	0.329957i	$0.892966\pi$
$252$	8.21440e14	0.202056
$253$	−1.77071e15	−0.424486
$254$	2.09485e15	0.489478
$255$	6.00904e15	1.36866
$256$	5.21965e15	1.15900
$257$	−6.79710e15	−1.47149	−0.735747	−	0.677257i	$-0.763169\pi$
$257$	−6.79710e15	−1.47149	−0.735747	+	0.677257i	$0.763169\pi$
$258$	−8.25898e15	−1.74341
$259$	−2.24792e15	−0.462734
$260$	2.37620e15	0.477041
$261$	−1.90833e15	−0.373671
$262$	6.06836e15	1.15908
$263$	−2.54205e15	−0.473666	−0.236833	−	0.971550i	$-0.576109\pi$
$263$	−2.54205e15	−0.473666	−0.236833	+	0.971550i	$0.576109\pi$
$264$	2.94563e14	0.0535491
$265$	3.75531e15	0.666112
$266$	−2.05428e15	−0.355574
$267$	−4.80236e15	−0.811206
$268$	6.18324e15	1.01939
$269$	−1.79024e15	−0.288085	−0.144042	−	0.989572i	$-0.546010\pi$
$269$	−1.79024e15	−0.288085	−0.144042	+	0.989572i	$0.546010\pi$
$270$	−7.47588e14	−0.117435
$271$	4.67251e15	0.716555	0.358278	−	0.933615i	$-0.383364\pi$
$271$	4.67251e15	0.716555	0.358278	+	0.933615i	$0.383364\pi$
$272$	9.12475e15	1.36623
$273$	−1.53773e15	−0.224813
$274$	1.15236e15	0.164516
$275$	8.35123e14	0.116436
$276$	−1.30026e16	−1.77060
$277$	8.46733e15	1.12623	0.563116	−	0.826378i	$-0.309602\pi$
$277$	8.46733e15	1.12623	0.563116	+	0.826378i	$0.309602\pi$
$278$	1.05572e16	1.37169
$279$	−9.53153e15	−1.20986
$280$	1.95576e14	0.0242543
$281$	−5.83307e15	−0.706815	−0.353408	−	0.935469i	$-0.614977\pi$
$281$	−5.83307e15	−0.706815	−0.353408	+	0.935469i	$0.614977\pi$
$282$	1.79426e16	2.12455
$283$	−1.06864e16	−1.23657	−0.618285	−	0.785954i	$-0.712172\pi$
$283$	−1.06864e16	−1.23657	−0.618285	+	0.785954i	$0.712172\pi$
$284$	−1.29708e15	−0.146689
$285$	−1.04694e16	−1.15726
$286$	2.58643e15	0.279461
$287$	−1.81831e15	−0.192059
$288$	1.22206e16	1.26194
$289$	5.82412e15	0.588023
$290$	4.44332e15	0.438653
$291$	−8.68441e15	−0.838370
$292$	−1.64684e16	−1.55476
$293$	−9.08667e15	−0.839006	−0.419503	−	0.907754i	$-0.637796\pi$
$293$	−9.08667e15	−0.839006	−0.419503	+	0.907754i	$0.637796\pi$
$294$	−1.99606e16	−1.80267
$295$	−7.19443e15	−0.635555
$296$	−2.83903e15	−0.245343
$297$	−3.87074e14	−0.0327248
$298$	−2.78249e16	−2.30159
$299$	1.16745e16	0.944878
$300$	6.13245e15	0.485675
$301$	−2.83921e15	−0.220047
$302$	1.45405e16	1.10289
$303$	2.01683e16	1.49724
$304$	−1.58979e16	−1.15521
$305$	1.94412e15	0.138285
$306$	2.30362e16	1.60407
$307$	1.01419e16	0.691387	0.345693	−	0.938347i	$-0.387644\pi$
$307$	1.01419e16	0.691387	0.345693	+	0.938347i	$0.387644\pi$
$308$	−9.90292e14	−0.0660973
$309$	−1.08789e16	−0.710976
$310$	2.21931e16	1.42026
$311$	2.15711e16	1.35186	0.675928	−	0.736967i	$-0.263743\pi$
$311$	2.15711e16	1.35186	0.675928	+	0.736967i	$0.263743\pi$
$312$	−1.94209e15	−0.119197
$313$	7.11443e15	0.427663	0.213832	−	0.976871i	$-0.431406\pi$
$313$	7.11443e15	0.427663	0.213832	+	0.976871i	$0.431406\pi$
$314$	−2.69769e16	−1.58836
$315$	3.02549e15	0.174492
$316$	−2.56384e16	−1.44852
$317$	1.06754e16	0.590881	0.295440	−	0.955361i	$-0.404534\pi$
$317$	1.06754e16	0.590881	0.295440	+	0.955361i	$0.404534\pi$
$318$	3.00156e16	1.62768
$319$	2.30059e15	0.122236
$320$	−1.21390e16	−0.631989
$321$	4.54028e16	2.31633
$322$	−9.39694e15	−0.469811
$323$	−2.74038e16	−1.34275
$324$	−2.02545e16	−0.972701
$325$	−5.50608e15	−0.259179
$326$	2.12544e16	0.980697
$327$	3.34068e16	1.51104
$328$	−2.29646e15	−0.101831
$329$	6.16819e15	0.268154
$330$	−1.06099e16	−0.452242
$331$	4.62412e16	1.93262	0.966312	−	0.257375i	$-0.0828574\pi$
$331$	4.62412e16	1.93262	0.966312	+	0.257375i	$0.0828574\pi$
$332$	1.11539e16	0.457121
$333$	−4.39187e16	−1.76507
$334$	−2.28015e16	−0.898693
$335$	2.27738e16	0.880327
$336$	9.57868e15	0.363162
$337$	−3.83483e16	−1.42611	−0.713053	−	0.701110i	$-0.752688\pi$
$337$	−3.83483e16	−1.42611	−0.713053	+	0.701110i	$0.752688\pi$
$338$	2.08056e16	0.758963
$339$	−2.01669e16	−0.721674
$340$	−2.55142e16	−0.895712
$341$	1.14908e16	0.395773
$342$	−4.01356e16	−1.35631
$343$	−1.41493e16	−0.469164
$344$	−3.58582e15	−0.116670
$345$	−4.78905e16	−1.52906
$346$	9.95999e15	0.312079
$347$	−3.12778e16	−0.961821	−0.480911	−	0.876770i	$-0.659694\pi$
$347$	−3.12778e16	−0.961821	−0.480911	+	0.876770i	$0.659694\pi$
$348$	1.68936e16	0.509869
$349$	2.44548e16	0.724435	0.362217	−	0.932094i	$-0.382020\pi$
$349$	2.44548e16	0.724435	0.362217	+	0.932094i	$0.382020\pi$
$350$	4.43191e15	0.128869
$351$	2.55203e15	0.0728434
$352$	−1.47326e16	−0.412811
$353$	7.13001e14	0.0196135	0.00980673	−	0.999952i	$-0.496878\pi$
$353$	7.13001e14	0.0196135	0.00980673	+	0.999952i	$0.496878\pi$
$354$	−5.75039e16	−1.55302
$355$	−4.77735e15	−0.126678
$356$	2.03906e16	0.530891
$357$	1.65112e16	0.422118
$358$	1.45607e16	0.365547
$359$	2.38313e16	0.587536	0.293768	−	0.955877i	$-0.405091\pi$
$359$	2.38313e16	0.587536	0.293768	+	0.955877i	$0.405091\pi$
$360$	3.82108e15	0.0925165
$361$	5.69217e15	0.135357
$362$	3.06108e16	0.714939
$363$	−5.49343e15	−0.126023
$364$	6.52913e15	0.147128
$365$	−6.06556e16	−1.34266
$366$	1.55390e16	0.337906
$367$	3.32196e16	0.709683	0.354842	−	0.934926i	$-0.384535\pi$
$367$	3.32196e16	0.709683	0.354842	+	0.934926i	$0.384535\pi$
$368$	−7.27219e16	−1.52635
$369$	−3.55252e16	−0.732597
$370$	1.02260e17	2.07202
$371$	1.03185e16	0.205441
$372$	8.43788e16	1.65084
$373$	3.42253e16	0.658022	0.329011	−	0.944326i	$-0.393285\pi$
$373$	3.42253e16	0.658022	0.329011	+	0.944326i	$0.393285\pi$
$374$	−2.77715e16	−0.524727
$375$	8.10750e16	1.50551
$376$	7.79019e15	0.142176
$377$	−1.51681e16	−0.272090
$378$	−2.05416e15	−0.0362191
$379$	−6.84810e16	−1.18690	−0.593452	−	0.804870i	$-0.702235\pi$
$379$	−6.84810e16	−1.18690	−0.593452	+	0.804870i	$0.702235\pi$
$380$	4.44529e16	0.757367
$381$	2.93351e16	0.491332
$382$	−1.23114e17	−2.02719
$383$	7.56208e16	1.22419	0.612096	−	0.790784i	$-0.290327\pi$
$383$	7.56208e16	1.22419	0.612096	+	0.790784i	$0.290327\pi$
$384$	2.22207e16	0.353676
$385$	−3.64739e15	−0.0570805
$386$	6.71043e16	1.03260
$387$	−5.54711e16	−0.839355
$388$	3.68737e16	0.548669
$389$	1.97946e16	0.289651	0.144826	−	0.989457i	$-0.453738\pi$
$389$	1.97946e16	0.289651	0.144826	+	0.989457i	$0.453738\pi$
$390$	6.99525e16	1.00666
$391$	−1.25354e17	−1.77414
$392$	−8.66635e15	−0.120636
$393$	8.49779e16	1.16347
$394$	−1.14882e17	−1.54713
$395$	−9.44301e16	−1.25092
$396$	−1.93478e16	−0.252124
$397$	4.89153e16	0.627056	0.313528	−	0.949579i	$-0.398489\pi$
$397$	4.89153e16	0.627056	0.313528	+	0.949579i	$0.398489\pi$
$398$	−1.65624e17	−2.08873
$399$	−2.87671e16	−0.356921
$400$	3.42980e16	0.418677
$401$	−1.39296e16	−0.167302	−0.0836511	−	0.996495i	$-0.526658\pi$
$401$	−1.39296e16	−0.167302	−0.0836511	+	0.996495i	$0.526658\pi$
$402$	1.82027e17	2.15113
$403$	−7.57603e16	−0.880966
$404$	−8.56337e16	−0.979864
$405$	−7.46004e16	−0.840008
$406$	1.22090e16	0.135288
$407$	5.29464e16	0.577395
$408$	2.08530e16	0.223809
$409$	4.21663e16	0.445415	0.222707	−	0.974885i	$-0.428511\pi$
$409$	4.21663e16	0.445415	0.222707	+	0.974885i	$0.428511\pi$
$410$	8.27165e16	0.859997
$411$	1.61370e16	0.165139
$412$	4.61914e16	0.465296
$413$	−1.97683e16	−0.196017
$414$	−1.83593e17	−1.79206
$415$	4.10816e16	0.394762
$416$	9.71338e16	0.918891
$417$	1.47837e17	1.37689
$418$	4.83857e16	0.443682
$419$	−1.37290e17	−1.23950	−0.619751	−	0.784798i	$-0.712767\pi$
$419$	−1.37290e17	−1.23950	−0.619751	+	0.784798i	$0.712767\pi$
$420$	−2.67834e16	−0.238092
$421$	−1.93638e17	−1.69495	−0.847475	−	0.530836i	$-0.821878\pi$
$421$	−1.93638e17	−1.69495	−0.847475	+	0.530836i	$0.821878\pi$
$422$	2.88540e16	0.248699
$423$	1.20511e17	1.02286
$424$	1.30319e16	0.108926
$425$	5.91209e16	0.486646
$426$	−3.81846e16	−0.309546
$427$	5.34189e15	0.0426495
$428$	−1.92779e17	−1.51591
$429$	3.62189e16	0.280520
$430$	1.29158e17	0.985320
$431$	4.32920e16	0.325316	0.162658	−	0.986683i	$-0.447993\pi$
$431$	4.32920e16	0.325316	0.162658	+	0.986683i	$0.447993\pi$
$432$	−1.58969e16	−0.117671
$433$	−1.04803e17	−0.764194	−0.382097	−	0.924122i	$-0.624798\pi$
$433$	−1.04803e17	−0.764194	−0.382097	+	0.924122i	$0.624798\pi$
$434$	6.09803e16	0.438033
$435$	6.22218e16	0.440314
$436$	−1.41844e17	−0.988893
$437$	2.18401e17	1.50012
$438$	−4.84811e17	−3.28088
$439$	−1.54229e17	−1.02837	−0.514183	−	0.857680i	$-0.671905\pi$
$439$	−1.54229e17	−1.02837	−0.514183	+	0.857680i	$0.671905\pi$
$440$	−4.60652e15	−0.0302643
$441$	−1.34065e17	−0.867889
$442$	1.83101e17	1.16801
$443$	−1.16533e17	−0.732528	−0.366264	−	0.930511i	$-0.619363\pi$
$443$	−1.16533e17	−0.732528	−0.366264	+	0.930511i	$0.619363\pi$
$444$	3.88794e17	2.40841
$445$	7.51017e16	0.458469
$446$	1.07751e16	0.0648251
$447$	−3.89645e17	−2.31031
$448$	−3.33547e16	−0.194917
$449$	1.72570e17	0.993948	0.496974	−	0.867765i	$-0.334444\pi$
$449$	1.72570e17	0.993948	0.496974	+	0.867765i	$0.334444\pi$
$450$	8.65884e16	0.491562
$451$	4.28277e16	0.239650
$452$	8.56279e16	0.472298
$453$	2.03617e17	1.10707
$454$	6.45696e16	0.346071
$455$	2.40478e16	0.127058
$456$	−3.63317e16	−0.189241
$457$	2.77306e17	1.42398	0.711990	−	0.702189i	$-0.247794\pi$
$457$	2.77306e17	1.42398	0.711990	+	0.702189i	$0.247794\pi$
$458$	3.31579e17	1.67866
$459$	−2.74022e16	−0.136774
$460$	2.03341e17	1.00069
$461$	−2.22963e17	−1.08187	−0.540936	−	0.841064i	$-0.681930\pi$
$461$	−2.22963e17	−1.08187	−0.540936	+	0.841064i	$0.681930\pi$
$462$	−2.91530e16	−0.139480
$463$	−9.50611e16	−0.448463	−0.224231	−	0.974536i	$-0.571987\pi$
$463$	−9.50611e16	−0.448463	−0.224231	+	0.974536i	$0.571987\pi$
$464$	9.44840e16	0.439533
$465$	3.10780e17	1.42564
$466$	4.22374e17	1.91068
$467$	1.46534e17	0.653699	0.326850	−	0.945076i	$-0.394013\pi$
$467$	1.46534e17	0.653699	0.326850	+	0.945076i	$0.394013\pi$
$468$	1.27563e17	0.561211
$469$	6.25760e16	0.271509
$470$	−2.80596e17	−1.20073
$471$	−3.77769e17	−1.59438
$472$	−2.49666e16	−0.103929
$473$	6.68736e16	0.274572
$474$	−7.54764e17	−3.05670
$475$	−1.03005e17	−0.411482
$476$	−7.01057e16	−0.276254
$477$	2.01598e17	0.783641
$478$	−6.75039e17	−2.58850
$479$	1.93976e17	0.733783	0.366891	−	0.930264i	$-0.380422\pi$
$479$	1.93976e17	0.733783	0.366891	+	0.930264i	$0.380422\pi$
$480$	−3.98457e17	−1.48701
$481$	−3.49083e17	−1.28524
$482$	−3.94870e17	−1.43433
$483$	−1.31590e17	−0.471591
$484$	2.33249e16	0.0824755
$485$	1.35811e17	0.473821
$486$	−5.52727e17	−1.90272
$487$	1.31492e17	0.446645	0.223322	−	0.974745i	$-0.428310\pi$
$487$	1.31492e17	0.446645	0.223322	+	0.974745i	$0.428310\pi$
$488$	6.74660e15	0.0226129
$489$	2.97635e17	0.984412
$490$	3.12155e17	1.01882
$491$	−2.12684e16	−0.0685024	−0.0342512	−	0.999413i	$-0.510905\pi$
$491$	−2.12684e16	−0.0685024	−0.0342512	+	0.999413i	$0.510905\pi$
$492$	3.14491e17	0.999619
$493$	1.62866e17	0.510888
$494$	−3.19014e17	−0.987607
$495$	−7.12610e16	−0.217730
$496$	4.71920e17	1.42311
$497$	−1.31268e16	−0.0390699
$498$	3.28359e17	0.964624
$499$	−1.41980e17	−0.411692	−0.205846	−	0.978584i	$-0.565995\pi$
$499$	−1.41980e17	−0.411692	−0.205846	+	0.978584i	$0.565995\pi$
$500$	−3.44241e17	−0.985277
$501$	−3.19300e17	−0.902097
$502$	9.34923e17	2.60736
$503$	1.05275e17	0.289824	0.144912	−	0.989445i	$-0.453710\pi$
$503$	1.05275e17	0.289824	0.144912	+	0.989445i	$0.453710\pi$
$504$	1.04992e16	0.0285338
$505$	−3.15402e17	−0.846194
$506$	2.21332e17	0.586226
$507$	2.91349e17	0.761838
$508$	−1.24556e17	−0.321551
$509$	2.97528e17	0.758336	0.379168	−	0.925328i	$-0.376210\pi$
$509$	2.97528e17	0.758336	0.379168	+	0.925328i	$0.376210\pi$
$510$	−7.51107e17	−1.89015
$511$	−1.66665e17	−0.414102
$512$	−5.48440e17	−1.34547
$513$	4.77423e16	0.115649
$514$	8.49611e17	2.03217
$515$	1.70130e17	0.401822
$516$	4.91064e17	1.14529
$517$	−1.45283e17	−0.334600
$518$	2.80981e17	0.639048
$519$	1.39474e17	0.313261
$520$	3.03714e16	0.0673664
$521$	−3.85362e17	−0.844157	−0.422079	−	0.906559i	$-0.638699\pi$
$521$	−3.85362e17	−0.844157	−0.422079	+	0.906559i	$0.638699\pi$
$522$	2.38533e17	0.516049
$523$	9.24639e16	0.197566	0.0987828	−	0.995109i	$-0.468505\pi$
$523$	9.24639e16	0.197566	0.0987828	+	0.995109i	$0.468505\pi$
$524$	−3.60813e17	−0.761428
$525$	6.20620e16	0.129357
$526$	3.17747e17	0.654145
$527$	8.13468e17	1.65414
$528$	−2.25612e17	−0.453150
$529$	4.95000e17	0.982072
$530$	−4.69399e17	−0.919918
$531$	−3.86223e17	−0.747693
$532$	1.22144e17	0.233586
$533$	−2.82368e17	−0.533445
$534$	6.00276e17	1.12030
$535$	−7.10033e17	−1.30912
$536$	7.90311e16	0.143955
$537$	2.03900e17	0.366931
$538$	2.23772e17	0.397852
$539$	1.61623e17	0.283907
$540$	4.44502e16	0.0771461
$541$	2.76497e17	0.474142	0.237071	−	0.971492i	$-0.423813\pi$
$541$	2.76497e17	0.474142	0.237071	+	0.971492i	$0.423813\pi$
$542$	−5.84045e17	−0.989581
$543$	4.28657e17	0.717647
$544$	−1.04296e18	−1.72535
$545$	−5.22433e17	−0.853992
$546$	1.92210e17	0.310473
$547$	−8.88416e17	−1.41807	−0.709037	−	0.705172i	$-0.750870\pi$
$547$	−8.88416e17	−1.41807	−0.709037	+	0.705172i	$0.750870\pi$
$548$	−6.85170e16	−0.108075
$549$	1.04367e17	0.162684
$550$	−1.04387e17	−0.160801
$551$	−2.83758e17	−0.431980
$552$	−1.66193e17	−0.250039
$553$	−2.59467e17	−0.385806
$554$	−1.05838e18	−1.55536
$555$	1.43199e18	2.07986
$556$	−6.27711e17	−0.901101
$557$	8.05652e17	1.14311	0.571556	−	0.820563i	$-0.306340\pi$
$557$	8.05652e17	1.14311	0.571556	+	0.820563i	$0.306340\pi$
$558$	1.19140e18	1.67085
$559$	−4.40906e17	−0.611180
$560$	−1.49796e17	−0.205248
$561$	−3.88897e17	−0.526715
$562$	7.29111e17	0.976129
$563$	−3.16606e17	−0.419001	−0.209500	−	0.977809i	$-0.567184\pi$
$563$	−3.16606e17	−0.419001	−0.209500	+	0.977809i	$0.567184\pi$
$564$	−1.06684e18	−1.39567
$565$	3.15381e17	0.407868
$566$	1.33576e18	1.70774
$567$	−2.04981e17	−0.259074
$568$	−1.65787e16	−0.0207150
$569$	−1.45703e18	−1.79986	−0.899930	−	0.436034i	$-0.856383\pi$
$569$	−1.45703e18	−1.79986	−0.899930	+	0.436034i	$0.856383\pi$
$570$	1.30864e18	1.59821
$571$	2.26991e17	0.274078	0.137039	−	0.990566i	$-0.456241\pi$
$571$	2.26991e17	0.274078	0.137039	+	0.990566i	$0.456241\pi$
$572$	−1.53784e17	−0.183585
$573$	−1.72402e18	−2.03487
$574$	2.27282e17	0.265239
$575$	−4.71178e17	−0.543681
$576$	−6.51667e17	−0.743498
$577$	−5.66700e15	−0.00639308	−0.00319654	−	0.999995i	$-0.501017\pi$
$577$	−5.66700e15	−0.00639308	−0.00319654	+	0.999995i	$0.501017\pi$
$578$	−7.27993e17	−0.812075
$579$	9.39692e17	1.03651
$580$	−2.64192e17	−0.288162
$581$	1.12881e17	0.121752
$582$	1.08552e18	1.15781
$583$	−2.43038e17	−0.256347
$584$	−2.10491e17	−0.219558
$585$	4.69833e17	0.484653
$586$	1.13580e18	1.15869
$587$	1.24814e18	1.25926	0.629632	−	0.776894i	$-0.283206\pi$
$587$	1.24814e18	1.25926	0.629632	+	0.776894i	$0.283206\pi$
$588$	1.18682e18	1.18422
$589$	−1.41729e18	−1.39865
$590$	8.99276e17	0.877718
$591$	−1.60875e18	−1.55299
$592$	2.17448e18	2.07618
$593$	6.30932e17	0.595837	0.297918	−	0.954591i	$-0.403708\pi$
$593$	6.30932e17	0.595837	0.297918	+	0.954591i	$0.403708\pi$
$594$	4.83828e16	0.0451938
$595$	−2.58210e17	−0.238568
$596$	1.65442e18	1.51197
$597$	−2.31930e18	−2.09664
$598$	−1.45927e18	−1.30490
$599$	−2.34714e17	−0.207618	−0.103809	−	0.994597i	$-0.533103\pi$
$599$	−2.34714e17	−0.207618	−0.103809	+	0.994597i	$0.533103\pi$
$600$	7.83819e16	0.0685856
$601$	−5.23105e17	−0.452799	−0.226399	−	0.974035i	$-0.572695\pi$
$601$	−5.23105e17	−0.452799	−0.226399	+	0.974035i	$0.572695\pi$
$602$	3.54890e17	0.303891
$603$	1.22258e18	1.03565
$604$	−8.64549e17	−0.724518
$605$	8.59092e16	0.0712245
$606$	−2.52096e18	−2.06773
$607$	−5.44056e17	−0.441486	−0.220743	−	0.975332i	$-0.570848\pi$
$607$	−5.44056e17	−0.441486	−0.220743	+	0.975332i	$0.570848\pi$
$608$	1.81714e18	1.45886
$609$	1.70968e17	0.135801
$610$	−2.43007e17	−0.190974
$611$	9.57868e17	0.744797
$612$	−1.36969e18	−1.05375
$613$	−3.03815e17	−0.231268	−0.115634	−	0.993292i	$-0.536890\pi$
$613$	−3.03815e17	−0.231268	−0.115634	+	0.993292i	$0.536890\pi$
$614$	−1.26770e18	−0.954823
$615$	1.15832e18	0.863254
$616$	−1.26574e16	−0.00933406
$617$	2.47875e18	1.80875	0.904377	−	0.426735i	$-0.140336\pi$
$617$	2.47875e18	1.80875	0.904377	+	0.426735i	$0.140336\pi$
$618$	1.35982e18	0.981876
$619$	1.87176e18	1.33740	0.668700	−	0.743532i	$-0.266851\pi$
$619$	1.87176e18	1.33740	0.668700	+	0.743532i	$0.266851\pi$
$620$	−1.31956e18	−0.933003
$621$	2.18388e17	0.152804
$622$	−2.69631e18	−1.86695
$623$	2.06358e17	0.141400
$624$	1.48749e18	1.00868
$625$	−6.92447e17	−0.464693
$626$	−8.89276e17	−0.590613
$627$	6.77567e17	0.445362
$628$	1.60399e18	1.04343
$629$	3.74824e18	2.41323
$630$	−3.78174e17	−0.240978
$631$	1.32406e18	0.835060	0.417530	−	0.908663i	$-0.362896\pi$
$631$	1.32406e18	0.835060	0.417530	+	0.908663i	$0.362896\pi$
$632$	−3.27697e17	−0.204556
$633$	4.04055e17	0.249641
$634$	−1.33439e18	−0.816022
$635$	−4.58757e17	−0.277686
$636$	−1.78467e18	−1.06927
$637$	−1.06560e18	−0.631958
$638$	−2.87565e17	−0.168812
$639$	−2.56465e17	−0.149030
$640$	−3.47499e17	−0.199887
$641$	9.62465e17	0.548034	0.274017	−	0.961725i	$-0.411647\pi$
$641$	9.62465e17	0.548034	0.274017	+	0.961725i	$0.411647\pi$
$642$	−5.67518e18	−3.19891
$643$	−3.14406e18	−1.75436	−0.877181	−	0.480159i	$-0.840579\pi$
$643$	−3.14406e18	−1.75436	−0.877181	+	0.480159i	$0.840579\pi$
$644$	5.58725e17	0.308631
$645$	1.80866e18	0.989052
$646$	3.42537e18	1.85437
$647$	−1.35868e18	−0.728180	−0.364090	−	0.931364i	$-0.618620\pi$
$647$	−1.35868e18	−0.728180	−0.364090	+	0.931364i	$0.618620\pi$
$648$	−2.58883e17	−0.137362
$649$	4.65613e17	0.244588
$650$	6.88238e17	0.357933
$651$	8.53935e17	0.439692
$652$	−1.26375e18	−0.644245
$653$	1.22230e18	0.616941	0.308470	−	0.951234i	$-0.400183\pi$
$653$	1.22230e18	0.616941	0.308470	+	0.951234i	$0.400183\pi$
$654$	−4.17572e18	−2.08678
$655$	−1.32893e18	−0.657557
$656$	1.75891e18	0.861723
$657$	−3.25621e18	−1.57956
$658$	−7.70999e17	−0.370327
$659$	2.00210e18	0.952207	0.476103	−	0.879389i	$-0.342049\pi$
$659$	2.00210e18	0.952207	0.476103	+	0.879389i	$0.342049\pi$
$660$	6.30845e17	0.297089
$661$	−3.30484e18	−1.54114	−0.770568	−	0.637358i	$-0.780027\pi$
$661$	−3.30484e18	−1.54114	−0.770568	+	0.637358i	$0.780027\pi$
$662$	−5.77997e18	−2.66900
$663$	2.56405e18	1.17243
$664$	1.42564e17	0.0645532
$665$	4.49874e17	0.201721
$666$	5.48967e18	2.43761
$667$	−1.29800e18	−0.570764
$668$	1.35573e18	0.590375
$669$	1.50888e17	0.0650706
$670$	−2.84664e18	−1.21575
$671$	−1.25820e17	−0.0532176
$672$	−1.09485e18	−0.458621
$673$	3.92127e18	1.62678	0.813390	−	0.581718i	$-0.197619\pi$
$673$	3.92127e18	1.62678	0.813390	+	0.581718i	$0.197619\pi$
$674$	4.79339e18	1.96949
$675$	−1.02999e17	−0.0419139
$676$	−1.23706e18	−0.498582
$677$	−3.27152e18	−1.30594	−0.652970	−	0.757384i	$-0.726477\pi$
$677$	−3.27152e18	−1.30594	−0.652970	+	0.757384i	$0.726477\pi$
$678$	2.52079e18	0.996651
$679$	3.73171e17	0.146135
$680$	−3.26110e17	−0.126490
$681$	9.04198e17	0.347382
$682$	−1.43630e18	−0.546573
$683$	−4.39078e18	−1.65504	−0.827518	−	0.561439i	$-0.810248\pi$
$683$	−4.39078e18	−1.65504	−0.827518	+	0.561439i	$0.810248\pi$
$684$	2.38639e18	0.890997
$685$	−2.52358e17	−0.0933317
$686$	1.76861e18	0.647927
$687$	4.64326e18	1.68502
$688$	2.74646e18	0.987297
$689$	1.60238e18	0.570612
$690$	5.98613e18	2.11167
$691$	4.04721e18	1.41432	0.707161	−	0.707053i	$-0.249976\pi$
$691$	4.04721e18	1.41432	0.707161	+	0.707053i	$0.249976\pi$
$692$	−5.92202e17	−0.205013
$693$	−1.95805e17	−0.0671519
$694$	3.90960e18	1.32830
$695$	−2.31195e18	−0.778176
$696$	2.15926e17	0.0720021
$697$	3.03190e18	1.00162
$698$	−3.05676e18	−1.00046
$699$	5.91469e18	1.91792
$700$	−2.63513e17	−0.0846573
$701$	−2.44100e18	−0.776963	−0.388481	−	0.921457i	$-0.627000\pi$
$701$	−2.44100e18	−0.776963	−0.388481	+	0.921457i	$0.627000\pi$
$702$	−3.18994e17	−0.100599
$703$	−6.53048e18	−2.04050
$704$	7.85621e17	0.243215
$705$	−3.92931e18	−1.20528
$706$	−8.91223e16	−0.0270867
$707$	−8.66635e17	−0.260982
$708$	3.41907e18	1.02022
$709$	1.14621e18	0.338893	0.169447	−	0.985539i	$-0.445802\pi$
$709$	1.14621e18	0.338893	0.169447	+	0.985539i	$0.445802\pi$
$710$	5.97150e17	0.174946
$711$	−5.06934e18	−1.47163
$712$	2.60623e17	0.0749709
$713$	−6.48313e18	−1.84800
$714$	−2.06383e18	−0.582956
$715$	−5.66410e17	−0.158541
$716$	−8.65752e17	−0.240137
$717$	−9.45288e18	−2.59830
$718$	−2.97883e18	−0.811402
$719$	1.85638e18	0.501106	0.250553	−	0.968103i	$-0.419388\pi$
$719$	1.85638e18	0.501106	0.250553	+	0.968103i	$0.419388\pi$
$720$	−2.92665e18	−0.782905
$721$	4.67469e17	0.123929
$722$	−7.11499e17	−0.186932
$723$	−5.52954e18	−1.43976
$724$	−1.82006e18	−0.469662
$725$	6.12179e17	0.156560
$726$	6.86658e17	0.174041
$727$	6.71684e18	1.68730	0.843648	−	0.536897i	$-0.180404\pi$
$727$	6.71684e18	1.68730	0.843648	+	0.536897i	$0.180404\pi$
$728$	8.34521e16	0.0207770
$729$	−3.39507e18	−0.837761
$730$	7.58172e18	1.85425
$731$	4.73418e18	1.14758
$732$	−9.23920e17	−0.221979
$733$	−4.72136e18	−1.12432	−0.562162	−	0.827027i	$-0.690030\pi$
$733$	−4.72136e18	−1.12432	−0.562162	+	0.827027i	$0.690030\pi$
$734$	−4.15232e18	−0.980091
$735$	4.37125e18	1.02267
$736$	8.31215e18	1.92756
$737$	−1.47389e18	−0.338786
$738$	4.44052e18	1.01174
$739$	4.88018e18	1.10217	0.551083	−	0.834450i	$-0.314215\pi$
$739$	4.88018e18	1.10217	0.551083	+	0.834450i	$0.314215\pi$
$740$	−6.08017e18	−1.36116
$741$	−4.46729e18	−0.991347
$742$	−1.28978e18	−0.283719
$743$	−1.48252e18	−0.323276	−0.161638	−	0.986850i	$-0.551678\pi$
$743$	−1.48252e18	−0.323276	−0.161638	+	0.986850i	$0.551678\pi$
$744$	1.07849e18	0.233126
$745$	6.09346e18	1.30572
$746$	−4.27803e18	−0.908745
$747$	2.20541e18	0.464414
$748$	1.65124e18	0.344707
$749$	−1.95097e18	−0.403756
$750$	−1.01341e19	−2.07915
$751$	1.99680e18	0.406139	0.203070	−	0.979164i	$-0.434908\pi$
$751$	1.99680e18	0.406139	0.203070	+	0.979164i	$0.434908\pi$
$752$	−5.96668e18	−1.20314
$753$	1.30921e19	2.61724
$754$	1.89596e18	0.375764
$755$	−3.18426e18	−0.625682
$756$	1.22137e17	0.0237933
$757$	9.34746e18	1.80539	0.902693	−	0.430284i	$-0.141587\pi$
$757$	9.34746e18	1.80539	0.902693	+	0.430284i	$0.141587\pi$
$758$	8.55986e18	1.63914
$759$	3.09940e18	0.588446
$760$	5.68174e17	0.106953
$761$	2.13970e18	0.399349	0.199675	−	0.979862i	$-0.436012\pi$
$761$	2.13970e18	0.399349	0.199675	+	0.979862i	$0.436012\pi$
$762$	−3.66677e18	−0.678542
$763$	−1.43550e18	−0.263387
$764$	7.32011e18	1.33171
$765$	−5.04478e18	−0.910003
$766$	−9.45231e18	−1.69064
$767$	−3.06985e18	−0.544437
$768$	−9.13636e18	−1.60666
$769$	−1.00092e19	−1.74532	−0.872662	−	0.488325i	$-0.837608\pi$
$769$	−1.00092e19	−1.74532	−0.872662	+	0.488325i	$0.837608\pi$
$770$	4.55910e17	0.0788297
$771$	1.18975e19	2.03987
$772$	−3.98990e18	−0.678343
$773$	−9.53131e18	−1.60689	−0.803444	−	0.595380i	$-0.797002\pi$
$773$	−9.53131e18	−1.60689	−0.803444	+	0.595380i	$0.797002\pi$
$774$	6.93368e18	1.15917
$775$	3.05765e18	0.506906
$776$	4.71301e17	0.0774814
$777$	3.93470e18	0.641468
$778$	−2.47425e18	−0.400016
$779$	−5.28242e18	−0.846914
$780$	−4.15924e18	−0.661302
$781$	3.09183e17	0.0487511
$782$	1.56687e19	2.45013
$783$	−2.83741e17	−0.0440018
$784$	6.63775e18	1.02086
$785$	5.90775e18	0.901092
$786$	−1.06219e19	−1.60678
$787$	−7.63610e18	−1.14561	−0.572803	−	0.819693i	$-0.694144\pi$
$787$	−7.63610e18	−1.14561	−0.572803	+	0.819693i	$0.694144\pi$
$788$	6.83068e18	1.01635
$789$	4.44955e18	0.656623
$790$	1.18034e19	1.72755
$791$	8.66577e17	0.125794
$792$	−2.47295e17	−0.0356042
$793$	8.29551e17	0.118459
$794$	−6.11422e18	−0.865980
$795$	−6.57320e18	−0.923402
$796$	9.84767e18	1.37214
$797$	5.06965e17	0.0700647	0.0350323	−	0.999386i	$-0.488847\pi$
$797$	5.06965e17	0.0700647	0.0350323	+	0.999386i	$0.488847\pi$
$798$	3.59577e18	0.492917
$799$	−1.02850e19	−1.39846
$800$	−3.92028e18	−0.528728
$801$	4.03173e18	0.539362
$802$	1.74115e18	0.231048
$803$	3.92554e18	0.516712
$804$	−1.08230e19	−1.41313
$805$	2.05787e18	0.266529
$806$	9.46975e18	1.21664
$807$	3.13359e18	0.399359
$808$	−1.09453e18	−0.138373
$809$	1.14892e19	1.44087	0.720435	−	0.693522i	$-0.243942\pi$
$809$	1.14892e19	1.44087	0.720435	+	0.693522i	$0.243942\pi$
$810$	9.32476e18	1.16007
$811$	−1.25201e19	−1.54516	−0.772580	−	0.634917i	$-0.781034\pi$
$811$	−1.25201e19	−1.54516	−0.772580	+	0.634917i	$0.781034\pi$
$812$	−7.25924e17	−0.0888745
$813$	−8.17865e18	−0.993329
$814$	−6.61810e18	−0.797397
$815$	−4.65457e18	−0.556360
$816$	−1.59717e19	−1.89394
$817$	−8.24827e18	−0.970330
$818$	−5.27063e18	−0.615129
$819$	1.29097e18	0.149476
$820$	−4.91817e18	−0.564954
$821$	6.89534e18	0.785824	0.392912	−	0.919576i	$-0.371468\pi$
$821$	6.89534e18	0.785824	0.392912	+	0.919576i	$0.371468\pi$
$822$	−2.01706e18	−0.228062
$823$	7.63121e18	0.856041	0.428020	−	0.903769i	$-0.359211\pi$
$823$	7.63121e18	0.856041	0.428020	+	0.903769i	$0.359211\pi$
$824$	5.90396e17	0.0657077
$825$	−1.46178e18	−0.161410
$826$	2.47096e18	0.270704
$827$	−1.09826e19	−1.19376	−0.596882	−	0.802329i	$-0.703594\pi$
$827$	−1.09826e19	−1.19376	−0.596882	+	0.802329i	$0.703594\pi$
$828$	1.09161e19	1.17725
$829$	9.92701e18	1.06222	0.531109	−	0.847303i	$-0.321775\pi$
$829$	9.92701e18	1.06222	0.531109	+	0.847303i	$0.321775\pi$
$830$	−5.13505e18	−0.545176
$831$	−1.48210e19	−1.56125
$832$	−5.17971e18	−0.541382
$833$	1.14418e19	1.18659
$834$	−1.84791e19	−1.90152
$835$	4.99338e18	0.509838
$836$	−2.87692e18	−0.291466
$837$	−1.41720e18	−0.142468
$838$	1.71607e19	1.71178
$839$	1.10351e19	1.09225	0.546127	−	0.837702i	$-0.316102\pi$
$839$	1.10351e19	1.09225	0.546127	+	0.837702i	$0.316102\pi$
$840$	−3.42332e17	−0.0336227
$841$	−8.57420e18	−0.835641
$842$	2.42040e19	2.34077
$843$	1.02101e19	0.979827
$844$	−1.71560e18	−0.163377
$845$	−4.55627e18	−0.430568
$846$	−1.50634e19	−1.41259
$847$	2.36054e17	0.0219669
$848$	−9.98143e18	−0.921764
$849$	1.87052e19	1.71420
$850$	−7.38988e18	−0.672070
$851$	−2.98725e19	−2.69606
$852$	2.27038e18	0.203349
$853$	6.11972e18	0.543955	0.271977	−	0.962304i	$-0.412322\pi$
$853$	6.11972e18	0.543955	0.271977	+	0.962304i	$0.412322\pi$
$854$	−6.67715e17	−0.0589000
$855$	8.78942e18	0.769451
$856$	−2.46400e18	−0.214073
$857$	1.45653e19	1.25586	0.627932	−	0.778268i	$-0.283902\pi$
$857$	1.45653e19	1.25586	0.627932	+	0.778268i	$0.283902\pi$
$858$	−4.52723e18	−0.387405
$859$	−1.49522e19	−1.26985	−0.634923	−	0.772576i	$-0.718968\pi$
$859$	−1.49522e19	−1.26985	−0.634923	+	0.772576i	$0.718968\pi$
$860$	−7.67951e18	−0.647282
$861$	3.18273e18	0.266243
$862$	−5.41133e18	−0.449270
$863$	−3.31070e18	−0.272803	−0.136402	−	0.990654i	$-0.543554\pi$
$863$	−3.31070e18	−0.272803	−0.136402	+	0.990654i	$0.543554\pi$
$864$	1.81703e18	0.148601
$865$	−2.18117e18	−0.177045
$866$	1.31000e19	1.05537
$867$	−1.01944e19	−0.815151
$868$	−3.62578e18	−0.287755
$869$	6.11138e18	0.481405
$870$	−7.77749e18	−0.608085
$871$	9.71753e18	0.754116
$872$	−1.81298e18	−0.139649
$873$	7.29084e18	0.557423
$874$	−2.72993e19	−2.07170
$875$	−3.48381e18	−0.262423
$876$	2.88259e19	2.15529
$877$	1.81816e19	1.34938	0.674692	−	0.738099i	$-0.264277\pi$
$877$	1.81816e19	1.34938	0.674692	+	0.738099i	$0.264277\pi$
$878$	1.92781e19	1.42020
$879$	1.59051e19	1.16308
$880$	3.52824e18	0.256106
$881$	1.25538e18	0.0904552	0.0452276	−	0.998977i	$-0.485599\pi$
$881$	1.25538e18	0.0904552	0.0452276	+	0.998977i	$0.485599\pi$
$882$	1.67576e19	1.19858
$883$	−1.42638e18	−0.101273	−0.0506363	−	0.998717i	$-0.516125\pi$
$883$	−1.42638e18	−0.101273	−0.0506363	+	0.998717i	$0.516125\pi$
$884$	−1.08868e19	−0.767295
$885$	1.25930e19	0.881042
$886$	1.45662e19	1.01164
$887$	−1.84592e19	−1.27265	−0.636325	−	0.771421i	$-0.719546\pi$
$887$	−1.84592e19	−1.27265	−0.636325	+	0.771421i	$0.719546\pi$
$888$	4.96938e18	0.340109
$889$	−1.26054e18	−0.0856433
$890$	−9.38743e18	−0.633157
$891$	4.82803e18	0.323270
$892$	−6.40665e17	−0.0425853
$893$	1.79194e19	1.18246
$894$	4.87041e19	3.19059
$895$	−3.18870e18	−0.207378
$896$	−9.54830e17	−0.0616487
$897$	−2.04348e19	−1.30984
$898$	−2.15706e19	−1.37267
$899$	8.42321e18	0.532157
$900$	−5.14838e18	−0.322920
$901$	−1.72054e19	−1.07140
$902$	−5.35329e18	−0.330962
$903$	4.96969e18	0.305042
$904$	1.09445e18	0.0666965
$905$	−6.70356e18	−0.405592
$906$	−2.54513e19	−1.52889
$907$	−9.01687e18	−0.537785	−0.268892	−	0.963170i	$-0.586658\pi$
$907$	−9.01687e18	−0.537785	−0.268892	+	0.963170i	$0.586658\pi$
$908$	−3.83919e18	−0.227343
$909$	−1.69319e19	−0.995498
$910$	−3.00588e18	−0.175470
$911$	4.17896e18	0.242214	0.121107	−	0.992639i	$-0.461356\pi$
$911$	4.17896e18	0.242214	0.121107	+	0.992639i	$0.461356\pi$
$912$	2.78273e19	1.60142
$913$	−2.65874e18	−0.151921
$914$	−3.46622e19	−1.96655
$915$	−3.40294e18	−0.191698
$916$	−1.97151e19	−1.10275
$917$	−3.65152e18	−0.202803
$918$	3.42516e18	0.188888
$919$	4.46585e18	0.244542	0.122271	−	0.992497i	$-0.460982\pi$
$919$	4.46585e18	0.244542	0.122271	+	0.992497i	$0.460982\pi$
$920$	2.59901e18	0.141315
$921$	−1.77522e19	−0.958439
$922$	2.78695e19	1.49409
$923$	−2.03849e18	−0.108517
$924$	1.73338e18	0.0916278
$925$	1.40888e19	0.739527
$926$	1.18823e19	0.619339
$927$	9.13318e18	0.472720
$928$	−1.07996e19	−0.555066
$929$	3.53217e18	0.180277	0.0901383	−	0.995929i	$-0.471269\pi$
$929$	3.53217e18	0.180277	0.0901383	+	0.995929i	$0.471269\pi$
$930$	−3.88463e19	−1.96884
$931$	−1.99348e19	−1.00332
$932$	−2.51135e19	−1.25518
$933$	−3.77576e19	−1.87402
$934$	−1.83161e19	−0.902775
$935$	6.08177e18	0.297683
$936$	1.63045e18	0.0792525
$937$	2.76825e19	1.33628	0.668140	−	0.744035i	$-0.267091\pi$
$937$	2.76825e19	1.33628	0.668140	+	0.744035i	$0.267091\pi$
$938$	−7.82175e18	−0.374961
$939$	−1.24529e19	−0.592850
$940$	1.66837e19	0.788791
$941$	−1.10839e19	−0.520428	−0.260214	−	0.965551i	$-0.583793\pi$
$941$	−1.10839e19	−0.520428	−0.260214	+	0.965551i	$0.583793\pi$
$942$	4.72197e19	2.20187
$943$	−2.41634e19	−1.11901
$944$	1.91225e19	0.879480
$945$	4.49847e17	0.0205475
$946$	−8.35894e18	−0.379192
$947$	−1.47334e19	−0.663787	−0.331893	−	0.943317i	$-0.607687\pi$
$947$	−1.47334e19	−0.663787	−0.331893	+	0.943317i	$0.607687\pi$
$948$	4.48769e19	2.00802
$949$	−2.58816e19	−1.15017
$950$	1.28753e19	0.568267
$951$	−1.86860e19	−0.819112
$952$	−8.96057e17	−0.0390118
$953$	4.60762e19	1.99238	0.996191	−	0.0871989i	$-0.0277916\pi$
$953$	4.60762e19	1.99238	0.996191	+	0.0871989i	$0.0277916\pi$
$954$	−2.51990e19	−1.08223
$955$	2.69611e19	1.15005
$956$	4.01366e19	1.70045
$957$	−4.02691e18	−0.169451
$958$	−2.42463e19	−1.01337
$959$	−6.93410e17	−0.0287852
$960$	2.12479e19	0.876099
$961$	1.76539e19	0.723002
$962$	4.36340e19	1.77495
$963$	−3.81171e19	−1.54010
$964$	2.34782e19	0.942246
$965$	−1.46954e19	−0.585806
$966$	1.64482e19	0.651279
$967$	3.14163e19	1.23561	0.617807	−	0.786330i	$-0.288021\pi$
$967$	3.14163e19	1.23561	0.617807	+	0.786330i	$0.288021\pi$
$968$	2.98127e17	0.0116469
$969$	4.79670e19	1.86139
$970$	−1.69759e19	−0.654359
$971$	4.09090e19	1.56637	0.783185	−	0.621789i	$-0.213594\pi$
$971$	4.09090e19	1.56637	0.783185	+	0.621789i	$0.213594\pi$
$972$	3.28641e19	1.24994
$973$	−6.35260e18	−0.240004
$974$	−1.64360e19	−0.616827
$975$	9.63771e18	0.359289
$976$	−5.16737e18	−0.191358
$977$	−2.04330e19	−0.751653	−0.375826	−	0.926690i	$-0.622641\pi$
$977$	−2.04330e19	−0.751653	−0.375826	+	0.926690i	$0.622641\pi$
$978$	−3.72033e19	−1.35950
$979$	−4.86048e18	−0.176438
$980$	−1.85602e19	−0.669286
$981$	−2.80461e19	−1.00467
$982$	2.65847e18	0.0946035
$983$	−4.09270e18	−0.144681	−0.0723406	−	0.997380i	$-0.523047\pi$
$983$	−4.09270e18	−0.144681	−0.0723406	+	0.997380i	$0.523047\pi$
$984$	4.01966e18	0.141163
$985$	2.51584e19	0.877703
$986$	−2.03576e19	−0.705549
$987$	−1.07966e19	−0.371730
$988$	1.89679e19	0.648784
$989$	−3.77302e19	−1.28207
$990$	8.90735e18	0.300691
$991$	2.05578e19	0.689441	0.344721	−	0.938705i	$-0.387974\pi$
$991$	2.05578e19	0.689441	0.344721	+	0.938705i	$0.387974\pi$
$992$	−5.39407e19	−1.79718
$993$	−8.09395e19	−2.67911
$994$	1.64080e18	0.0539566
$995$	3.62704e19	1.18496
$996$	−1.95236e19	−0.633686
$997$	−2.04486e19	−0.659393	−0.329697	−	0.944087i	$-0.606947\pi$
$997$	−2.04486e19	−0.659393	−0.329697	+	0.944087i	$0.606947\pi$
$998$	1.77469e19	0.568557
$999$	−6.53009e18	−0.207847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.14.a.a.1.1	✓	5
3.2	odd	2		99.14.a.e.1.5		5
4.3	odd	2		176.14.a.e.1.5		5
11.10	odd	2		121.14.a.b.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.14.a.a.1.1	✓	5	1.1	even	1	trivial
99.14.a.e.1.5		5	3.2	odd	2
121.14.a.b.1.5		5	11.10	odd	2
176.14.a.e.1.5		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)

\(f(q)\)	\(=\)	\(q-124.996 q^{2} -1750.38 q^{3} +7432.04 q^{4} +27373.3 q^{5} +218790. q^{6} +75214.1 q^{7} +94992.6 q^{8} +1.46950e6 q^{9} +O(q^{10})\)	\(q-124.996 q^{2} -1750.38 q^{3} +7432.04 q^{4} +27373.3 q^{5} +218790. q^{6} +75214.1 q^{7} +94992.6 q^{8} +1.46950e6 q^{9} -3.42156e6 q^{10} -1.77156e6 q^{11} -1.30089e7 q^{12} +1.16801e7 q^{13} -9.40148e6 q^{14} -4.79136e7 q^{15} -7.27569e7 q^{16} -1.25414e8 q^{17} -1.83681e8 q^{18} +2.18507e8 q^{19} +2.03439e8 q^{20} -1.31653e8 q^{21} +2.21438e8 q^{22} +9.99518e8 q^{23} -1.66273e8 q^{24} -4.71405e8 q^{25} -1.45997e9 q^{26} +2.18493e8 q^{27} +5.58994e8 q^{28} -1.29863e9 q^{29} +5.98902e9 q^{30} -6.48625e9 q^{31} +8.31616e9 q^{32} +3.10090e9 q^{33} +1.56763e10 q^{34} +2.05886e9 q^{35} +1.09214e10 q^{36} -2.98869e10 q^{37} -2.73125e10 q^{38} -2.04446e10 q^{39} +2.60026e9 q^{40} -2.41751e10 q^{41} +1.64561e10 q^{42} -3.77484e10 q^{43} -1.31663e10 q^{44} +4.02250e10 q^{45} -1.24936e11 q^{46} +8.20083e10 q^{47} +1.27352e11 q^{48} -9.12318e10 q^{49} +5.89238e10 q^{50} +2.19522e11 q^{51} +8.68072e10 q^{52} +1.37189e11 q^{53} -2.73108e10 q^{54} -4.84935e10 q^{55} +7.14479e9 q^{56} -3.82469e11 q^{57} +1.62323e11 q^{58} -2.62827e11 q^{59} -3.56096e11 q^{60} +7.10224e10 q^{61} +8.10757e11 q^{62} +1.10527e11 q^{63} -4.43463e11 q^{64} +3.19724e11 q^{65} -3.87600e11 q^{66} +8.31971e11 q^{67} -9.32082e11 q^{68} -1.74953e12 q^{69} -2.57349e11 q^{70} -1.74526e11 q^{71} +1.39591e11 q^{72} -2.21587e12 q^{73} +3.73575e12 q^{74} +8.25137e11 q^{75} +1.62395e12 q^{76} -1.33246e11 q^{77} +2.55550e12 q^{78} -3.44971e12 q^{79} -1.99160e12 q^{80} -2.72530e12 q^{81} +3.02179e12 q^{82} +1.50079e12 q^{83} -9.78450e11 q^{84} -3.43300e12 q^{85} +4.71840e12 q^{86} +2.27308e12 q^{87} -1.68285e11 q^{88} +2.74361e12 q^{89} -5.02797e12 q^{90} +8.78511e11 q^{91} +7.42845e12 q^{92} +1.13534e13 q^{93} -1.02507e13 q^{94} +5.98125e12 q^{95} -1.45564e13 q^{96} +4.96145e12 q^{97} +1.14036e13 q^{98} -2.60330e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 64 q^{2} + 480 q^{3} - 2400 q^{4} - 454 q^{5} + 79548 q^{6} - 313920 q^{7} - 255168 q^{8} + 1321749 q^{9}+O(q^{10}) \) 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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