LMFDB - Embedded newform 177.14.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	177.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:	$189.798744245$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.2942 q^{2} -729.000 q^{3} -7694.97 q^{4} -29584.7 q^{5} +16252.4 q^{6} -211098. q^{7} +354187. q^{8} +531441. q^{9} +O(q^{10})$	\(q-22.2942 q^{2} -729.000 q^{3} -7694.97 q^{4} -29584.7 q^{5} +16252.4 q^{6} -211098. q^{7} +354187. q^{8} +531441. q^{9} +659567. q^{10} +646871. q^{11} +5.60963e6 q^{12} +1.28962e7 q^{13} +4.70625e6 q^{14} +2.15673e7 q^{15} +5.51409e7 q^{16} +1.59397e8 q^{17} -1.18480e7 q^{18} +2.48218e8 q^{19} +2.27654e8 q^{20} +1.53890e8 q^{21} -1.44215e7 q^{22} -9.45900e8 q^{23} -2.58202e8 q^{24} -3.45446e8 q^{25} -2.87510e8 q^{26} -3.87420e8 q^{27} +1.62439e9 q^{28} -5.51968e9 q^{29} -4.80825e8 q^{30} +8.29003e9 q^{31} -4.13082e9 q^{32} -4.71569e8 q^{33} -3.55363e9 q^{34} +6.24528e9 q^{35} -4.08942e9 q^{36} +6.67944e9 q^{37} -5.53381e9 q^{38} -9.40133e9 q^{39} -1.04785e10 q^{40} +3.93601e10 q^{41} -3.43086e9 q^{42} -6.65126e10 q^{43} -4.97766e9 q^{44} -1.57225e10 q^{45} +2.10880e10 q^{46} -1.24471e11 q^{47} -4.01977e10 q^{48} -5.23267e10 q^{49} +7.70143e9 q^{50} -1.16201e11 q^{51} -9.92359e10 q^{52} +2.12436e11 q^{53} +8.63722e9 q^{54} -1.91375e10 q^{55} -7.47681e10 q^{56} -1.80951e11 q^{57} +1.23057e11 q^{58} +4.21805e10 q^{59} -1.65960e11 q^{60} -7.41487e10 q^{61} -1.84819e11 q^{62} -1.12186e11 q^{63} -3.59621e11 q^{64} -3.81531e11 q^{65} +1.05132e10 q^{66} +9.43989e11 q^{67} -1.22656e12 q^{68} +6.89561e11 q^{69} -1.39233e11 q^{70} -6.15028e11 q^{71} +1.88229e11 q^{72} -1.10346e12 q^{73} -1.48913e11 q^{74} +2.51830e11 q^{75} -1.91003e12 q^{76} -1.36553e11 q^{77} +2.09595e11 q^{78} +2.09592e12 q^{79} -1.63133e12 q^{80} +2.82430e11 q^{81} -8.77500e11 q^{82} +3.10329e12 q^{83} -1.18418e12 q^{84} -4.71573e12 q^{85} +1.48284e12 q^{86} +4.02385e12 q^{87} +2.29113e11 q^{88} -7.41037e11 q^{89} +3.50521e11 q^{90} -2.72236e12 q^{91} +7.27867e12 q^{92} -6.04343e12 q^{93} +2.77498e12 q^{94} -7.34347e12 q^{95} +3.01137e12 q^{96} -1.09886e13 q^{97} +1.16658e12 q^{98} +3.43774e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9}+O(q^{10}) $ 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9} + 6145337 q^{10} + 400846 q^{11} - 101457846 q^{12} + 9411686 q^{13} - 36368387 q^{14} - 1630044 q^{15} + 734877786 q^{16} + 228113833 q^{17} + 6377292 q^{18} + 524233755 q^{19} - 420745331 q^{20} - 544450005 q^{21} - 1844479318 q^{22} - 399937087 q^{23} + 534588093 q^{24} + 8617402914 q^{25} - 499433574 q^{26} - 12397455648 q^{27} + 12648993070 q^{28} - 225284149 q^{29} - 4479950673 q^{30} + 9454638761 q^{31} + 11648295118 q^{32} - 292216734 q^{33} + 39279537096 q^{34} + 17608963479 q^{35} + 73962769734 q^{36} + 37463929597 q^{37} + 65554547351 q^{38} - 6861119094 q^{39} + 144414252742 q^{40} + 22650227173 q^{41} + 26512554123 q^{42} + 96253617602 q^{43} - 132186868002 q^{44} + 1188302076 q^{45} + 327853892309 q^{46} + 239981844027 q^{47} - 535725905994 q^{48} + 286262776863 q^{49} - 671840368399 q^{50} - 166294984257 q^{51} - 952971648498 q^{52} - 47446514136 q^{53} - 4649045868 q^{54} - 474454082548 q^{55} - 1167728875984 q^{56} - 382166407395 q^{57} + 547596592762 q^{58} + 1349777076512 q^{59} + 306723346299 q^{60} + 661498471821 q^{61} + 555821093242 q^{62} + 396904053645 q^{63} + 3522679273173 q^{64} + 1269187682756 q^{65} + 1344625422822 q^{66} + 2838711491386 q^{67} + 1395029358261 q^{68} + 291554136423 q^{69} + 5677102514386 q^{70} + 1912914480734 q^{71} - 389714719797 q^{72} + 2403595726697 q^{73} - 742136417562 q^{74} - 6282086724306 q^{75} - 4020161987188 q^{76} - 4878303804101 q^{77} + 364087075446 q^{78} - 1705546365970 q^{79} - 4347383766449 q^{80} + 9037745167392 q^{81} - 6943720239935 q^{82} - 2549647313691 q^{83} - 9221115948030 q^{84} - 8455706309615 q^{85} - 33993832711012 q^{86} + 164232144621 q^{87} - 42970239360587 q^{88} - 17356719361241 q^{89} + 3265884040617 q^{90} - 30776775043291 q^{91} - 13184590997480 q^{92} - 6892431656769 q^{93} - 35604563339520 q^{94} + 219501126195 q^{95} - 8491607141022 q^{96} - 4427131429152 q^{97} - 32707332037060 q^{98} + 213025999086 q^{99}+O(q^{100}) \) 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9 + 6145337 * q^10 + 400846 * q^11 - 101457846 * q^12 + 9411686 * q^13 - 36368387 * q^14 - 1630044 * q^15 + 734877786 * q^16 + 228113833 * q^17 + 6377292 * q^18 + 524233755 * q^19 - 420745331 * q^20 - 544450005 * q^21 - 1844479318 * q^22 - 399937087 * q^23 + 534588093 * q^24 + 8617402914 * q^25 - 499433574 * q^26 - 12397455648 * q^27 + 12648993070 * q^28 - 225284149 * q^29 - 4479950673 * q^30 + 9454638761 * q^31 + 11648295118 * q^32 - 292216734 * q^33 + 39279537096 * q^34 + 17608963479 * q^35 + 73962769734 * q^36 + 37463929597 * q^37 + 65554547351 * q^38 - 6861119094 * q^39 + 144414252742 * q^40 + 22650227173 * q^41 + 26512554123 * q^42 + 96253617602 * q^43 - 132186868002 * q^44 + 1188302076 * q^45 + 327853892309 * q^46 + 239981844027 * q^47 - 535725905994 * q^48 + 286262776863 * q^49 - 671840368399 * q^50 - 166294984257 * q^51 - 952971648498 * q^52 - 47446514136 * q^53 - 4649045868 * q^54 - 474454082548 * q^55 - 1167728875984 * q^56 - 382166407395 * q^57 + 547596592762 * q^58 + 1349777076512 * q^59 + 306723346299 * q^60 + 661498471821 * q^61 + 555821093242 * q^62 + 396904053645 * q^63 + 3522679273173 * q^64 + 1269187682756 * q^65 + 1344625422822 * q^66 + 2838711491386 * q^67 + 1395029358261 * q^68 + 291554136423 * q^69 + 5677102514386 * q^70 + 1912914480734 * q^71 - 389714719797 * q^72 + 2403595726697 * q^73 - 742136417562 * q^74 - 6282086724306 * q^75 - 4020161987188 * q^76 - 4878303804101 * q^77 + 364087075446 * q^78 - 1705546365970 * q^79 - 4347383766449 * q^80 + 9037745167392 * q^81 - 6943720239935 * q^82 - 2549647313691 * q^83 - 9221115948030 * q^84 - 8455706309615 * q^85 - 33993832711012 * q^86 + 164232144621 * q^87 - 42970239360587 * q^88 - 17356719361241 * q^89 + 3265884040617 * q^90 - 30776775043291 * q^91 - 13184590997480 * q^92 - 6892431656769 * q^93 - 35604563339520 * q^94 + 219501126195 * q^95 - 8491607141022 * q^96 - 4427131429152 * q^97 - 32707332037060 * q^98 + 213025999086 * 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 $

$2$	−22.2942	−0.246318	−0.123159	−	0.992387i	$-0.539303\pi$
$2$	−22.2942	−0.246318	−0.123159	+	0.992387i	$0.539303\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−7694.97	−0.939327
$5$	−29584.7	−0.846765	−0.423382	−	0.905951i	$-0.639157\pi$
$5$	−29584.7	−0.846765	−0.423382	+	0.905951i	$0.639157\pi$
$6$	16252.4	0.142212
$7$	−211098.	−0.678183	−0.339091	−	0.940753i	$-0.610120\pi$
$7$	−211098.	−0.678183	−0.339091	+	0.940753i	$0.610120\pi$
$8$	354187.	0.477691
$9$	531441.	0.333333
$10$	659567.	0.208573
$11$	646871.	0.110094	0.0550472	−	0.998484i	$-0.482469\pi$
$11$	646871.	0.110094	0.0550472	+	0.998484i	$0.482469\pi$
$12$	5.60963e6	0.542321
$13$	1.28962e7	0.741020	0.370510	−	0.928828i	$-0.379183\pi$
$13$	1.28962e7	0.741020	0.370510	+	0.928828i	$0.379183\pi$
$14$	4.70625e6	0.167049
$15$	2.15673e7	0.488880
$16$	5.51409e7	0.821663
$17$	1.59397e8	1.60163	0.800817	−	0.598910i	$-0.204399\pi$
$17$	1.59397e8	1.60163	0.800817	+	0.598910i	$0.204399\pi$
$18$	−1.18480e7	−0.0821060
$19$	2.48218e8	1.21042	0.605208	−	0.796067i	$-0.293090\pi$
$19$	2.48218e8	1.21042	0.605208	+	0.796067i	$0.293090\pi$
$20$	2.27654e8	0.795389
$21$	1.53890e8	0.391549
$22$	−1.44215e7	−0.0271182
$23$	−9.45900e8	−1.33234	−0.666169	−	0.745801i	$-0.732067\pi$
$23$	−9.45900e8	−1.33234	−0.666169	+	0.745801i	$0.732067\pi$
$24$	−2.58202e8	−0.275795
$25$	−3.45446e8	−0.282989
$26$	−2.87510e8	−0.182527
$27$	−3.87420e8	−0.192450
$28$	1.62439e9	0.637036
$29$	−5.51968e9	−1.72316	−0.861582	−	0.507618i	$-0.830526\pi$
$29$	−5.51968e9	−1.72316	−0.861582	+	0.507618i	$0.830526\pi$
$30$	−4.80825e8	−0.120420
$31$	8.29003e9	1.67766	0.838832	−	0.544390i	$-0.183239\pi$
$31$	8.29003e9	1.67766	0.838832	+	0.544390i	$0.183239\pi$
$32$	−4.13082e9	−0.680082
$33$	−4.71569e8	−0.0635631
$34$	−3.55363e9	−0.394511
$35$	6.24528e9	0.574261
$36$	−4.08942e9	−0.313109
$37$	6.67944e9	0.427985	0.213993	−	0.976835i	$-0.431353\pi$
$37$	6.67944e9	0.427985	0.213993	+	0.976835i	$0.431353\pi$
$38$	−5.53381e9	−0.298147
$39$	−9.40133e9	−0.427828
$40$	−1.04785e10	−0.404492
$41$	3.93601e10	1.29408	0.647039	−	0.762457i	$-0.276007\pi$
$41$	3.93601e10	1.29408	0.647039	+	0.762457i	$0.276007\pi$
$42$	−3.43086e9	−0.0964456
$43$	−6.65126e10	−1.60457	−0.802285	−	0.596941i	$-0.796383\pi$
$43$	−6.65126e10	−1.60457	−0.802285	+	0.596941i	$0.796383\pi$
$44$	−4.97766e9	−0.103415
$45$	−1.57225e10	−0.282255
$46$	2.10880e10	0.328179
$47$	−1.24471e11	−1.68435	−0.842175	−	0.539204i	$-0.818725\pi$
$47$	−1.24471e11	−1.68435	−0.842175	+	0.539204i	$0.818725\pi$
$48$	−4.01977e10	−0.474388
$49$	−5.23267e10	−0.540068
$50$	7.70143e9	0.0697054
$51$	−1.16201e11	−0.924703
$52$	−9.92359e10	−0.696061
$53$	2.12436e11	1.31654	0.658271	−	0.752781i	$-0.271288\pi$
$53$	2.12436e11	1.31654	0.658271	+	0.752781i	$0.271288\pi$
$54$	8.63722e9	0.0474039
$55$	−1.91375e10	−0.0932241
$56$	−7.47681e10	−0.323962
$57$	−1.80951e11	−0.698834
$58$	1.23057e11	0.424447
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	−1.65960e11	−0.459218
$61$	−7.41487e10	−0.184272	−0.0921360	−	0.995746i	$-0.529369\pi$
$61$	−7.41487e10	−0.184272	−0.0921360	+	0.995746i	$0.529369\pi$
$62$	−1.84819e11	−0.413239
$63$	−1.12186e11	−0.226061
$64$	−3.59621e11	−0.654147
$65$	−3.81531e11	−0.627470
$66$	1.05132e10	0.0156567
$67$	9.43989e11	1.27491	0.637457	−	0.770486i	$-0.279986\pi$
$67$	9.43989e11	1.27491	0.637457	+	0.770486i	$0.279986\pi$
$68$	−1.22656e12	−1.50446
$69$	6.89561e11	0.769225
$70$	−1.39233e11	−0.141451
$71$	−6.15028e11	−0.569791	−0.284895	−	0.958559i	$-0.591959\pi$
$71$	−6.15028e11	−0.569791	−0.284895	+	0.958559i	$0.591959\pi$
$72$	1.88229e11	0.159230
$73$	−1.10346e12	−0.853409	−0.426705	−	0.904391i	$-0.640326\pi$
$73$	−1.10346e12	−0.853409	−0.426705	+	0.904391i	$0.640326\pi$
$74$	−1.48913e11	−0.105420
$75$	2.51830e11	0.163384
$76$	−1.91003e12	−1.13698
$77$	−1.36553e11	−0.0746642
$78$	2.09595e11	0.105382
$79$	2.09592e12	0.970062	0.485031	−	0.874497i	$-0.338808\pi$
$79$	2.09592e12	0.970062	0.485031	+	0.874497i	$0.338808\pi$
$80$	−1.63133e12	−0.695756
$81$	2.82430e11	0.111111
$82$	−8.77500e11	−0.318755
$83$	3.10329e12	1.04187	0.520936	−	0.853596i	$-0.325583\pi$
$83$	3.10329e12	1.04187	0.520936	+	0.853596i	$0.325583\pi$
$84$	−1.18418e12	−0.367793
$85$	−4.71573e12	−1.35621
$86$	1.48284e12	0.395235
$87$	4.02385e12	0.994870
$88$	2.29113e11	0.0525912
$89$	−7.41037e11	−0.158054	−0.0790268	−	0.996872i	$-0.525181\pi$
$89$	−7.41037e11	−0.158054	−0.0790268	+	0.996872i	$0.525181\pi$
$90$	3.50521e11	0.0695245
$91$	−2.72236e12	−0.502547
$92$	7.27867e12	1.25150
$93$	−6.04343e12	−0.968600
$94$	2.77498e12	0.414886
$95$	−7.34347e12	−1.02494
$96$	3.01137e12	0.392645
$97$	−1.09886e13	−1.33945	−0.669727	−	0.742607i	$-0.733589\pi$
$97$	−1.09886e13	−1.33945	−0.669727	+	0.742607i	$0.733589\pi$
$98$	1.16658e12	0.133028
$99$	3.43774e11	0.0366981
$100$	2.65820e12	0.265820
$101$	−2.76989e12	−0.259641	−0.129820	−	0.991538i	$-0.541440\pi$
$101$	−2.76989e12	−0.259641	−0.129820	+	0.991538i	$0.541440\pi$
$102$	2.59060e12	0.227771
$103$	1.21571e13	1.00320	0.501602	−	0.865099i	$-0.332744\pi$
$103$	1.21571e13	1.00320	0.501602	+	0.865099i	$0.332744\pi$
$104$	4.56766e12	0.353979
$105$	−4.55281e12	−0.331550
$106$	−4.73608e12	−0.324288
$107$	−1.58637e13	−1.02190	−0.510951	−	0.859610i	$-0.670707\pi$
$107$	−1.58637e13	−1.02190	−0.510951	+	0.859610i	$0.670707\pi$
$108$	2.98119e12	0.180774
$109$	−3.21934e11	−0.0183863	−0.00919314	−	0.999958i	$-0.502926\pi$
$109$	−3.21934e11	−0.0183863	−0.00919314	+	0.999958i	$0.502926\pi$
$110$	4.26655e11	0.0229628
$111$	−4.86931e12	−0.247097
$112$	−1.16401e13	−0.557238
$113$	1.88941e13	0.853721	0.426861	−	0.904317i	$-0.359620\pi$
$113$	1.88941e13	0.853721	0.426861	+	0.904317i	$0.359620\pi$
$114$	4.03415e12	0.172136
$115$	2.79842e13	1.12818
$116$	4.24738e13	1.61862
$117$	6.85357e12	0.247007
$118$	−9.40380e11	−0.0320679
$119$	−3.36485e13	−1.08620
$120$	7.63884e12	0.233534
$121$	−3.41043e13	−0.987879
$122$	1.65308e12	0.0453895
$123$	−2.86935e13	−0.747137
$124$	−6.37915e13	−1.57588
$125$	4.63341e13	1.08639
$126$	2.50110e12	0.0556829
$127$	5.23481e13	1.10708	0.553538	−	0.832824i	$-0.313278\pi$
$127$	5.23481e13	1.10708	0.553538	+	0.832824i	$0.313278\pi$
$128$	4.18571e13	0.841210
$129$	4.84877e13	0.926399
$130$	8.50591e12	0.154557
$131$	−5.62228e13	−0.971962	−0.485981	−	0.873969i	$-0.661538\pi$
$131$	−5.62228e13	−0.971962	−0.485981	+	0.873969i	$0.661538\pi$
$132$	3.62871e12	0.0597065
$133$	−5.23983e13	−0.820884
$134$	−2.10455e13	−0.314034
$135$	1.14617e13	0.162960
$136$	5.64564e13	0.765086
$137$	1.41466e13	0.182797	0.0913983	−	0.995814i	$-0.470866\pi$
$137$	1.41466e13	0.182797	0.0913983	+	0.995814i	$0.470866\pi$
$138$	−1.53732e13	−0.189474
$139$	−8.31099e13	−0.977364	−0.488682	−	0.872462i	$-0.662522\pi$
$139$	−8.31099e13	−0.977364	−0.488682	+	0.872462i	$0.662522\pi$
$140$	−4.80572e13	−0.539420
$141$	9.07394e13	0.972460
$142$	1.37115e13	0.140350
$143$	8.34218e12	0.0815822
$144$	2.93041e13	0.273888
$145$	1.63298e14	1.45912
$146$	2.46007e13	0.210210
$147$	3.81461e13	0.311808
$148$	−5.13981e13	−0.402018
$149$	−1.76033e14	−1.31790	−0.658952	−	0.752185i	$-0.729000\pi$
$149$	−1.76033e14	−1.31790	−0.658952	+	0.752185i	$0.729000\pi$
$150$	−5.61434e12	−0.0402444
$151$	−5.29705e13	−0.363651	−0.181825	−	0.983331i	$-0.558201\pi$
$151$	−5.29705e13	−0.363651	−0.181825	+	0.983331i	$0.558201\pi$
$152$	8.79155e13	0.578206
$153$	8.47103e13	0.533878
$154$	3.04434e12	0.0183911
$155$	−2.45258e14	−1.42059
$156$	7.23430e13	0.401871
$157$	−2.04782e14	−1.09130	−0.545650	−	0.838013i	$-0.683717\pi$
$157$	−2.04782e14	−1.09130	−0.545650	+	0.838013i	$0.683717\pi$
$158$	−4.67269e13	−0.238944
$159$	−1.54866e14	−0.760106
$160$	1.22209e14	0.575869
$161$	1.99678e14	0.903568
$162$	−6.29653e12	−0.0273687
$163$	2.50697e13	0.104696	0.0523481	−	0.998629i	$-0.483329\pi$
$163$	2.50697e13	0.104696	0.0523481	+	0.998629i	$0.483329\pi$
$164$	−3.02874e14	−1.21556
$165$	1.39513e13	0.0538230
$166$	−6.91852e13	−0.256632
$167$	−2.01757e14	−0.719734	−0.359867	−	0.933004i	$-0.617178\pi$
$167$	−2.01757e14	−0.719734	−0.359867	+	0.933004i	$0.617178\pi$
$168$	5.45060e13	0.187040
$169$	−1.36563e14	−0.450889
$170$	1.05133e14	0.334058
$171$	1.31913e14	0.403472
$172$	5.11812e14	1.50722
$173$	3.61780e14	1.02599	0.512997	−	0.858390i	$-0.328535\pi$
$173$	3.61780e14	1.02599	0.512997	+	0.858390i	$0.328535\pi$
$174$	−8.97083e13	−0.245054
$175$	7.29229e13	0.191918
$176$	3.56691e13	0.0904606
$177$	−3.07496e13	−0.0751646
$178$	1.65208e13	0.0389315
$179$	2.69481e14	0.612328	0.306164	−	0.951979i	$-0.400954\pi$
$179$	2.69481e14	0.612328	0.306164	+	0.951979i	$0.400954\pi$
$180$	1.20985e14	0.265130
$181$	5.96113e14	1.26014	0.630069	−	0.776539i	$-0.283027\pi$
$181$	5.96113e14	1.26014	0.630069	+	0.776539i	$0.283027\pi$
$182$	6.06928e13	0.123786
$183$	5.40544e13	0.106390
$184$	−3.35025e14	−0.636446
$185$	−1.97610e14	−0.362403
$186$	1.34733e14	0.238584
$187$	1.03110e14	0.176331
$188$	9.57801e14	1.58216
$189$	8.17837e13	0.130516
$190$	1.63716e14	0.252461
$191$	−2.32919e14	−0.347127	−0.173564	−	0.984823i	$-0.555528\pi$
$191$	−2.32919e14	−0.347127	−0.173564	+	0.984823i	$0.555528\pi$
$192$	2.62164e14	0.377672
$193$	1.81320e14	0.252536	0.126268	−	0.991996i	$-0.459700\pi$
$193$	1.81320e14	0.252536	0.126268	+	0.991996i	$0.459700\pi$
$194$	2.44983e14	0.329932
$195$	2.78136e14	0.362270
$196$	4.02652e14	0.507301
$197$	−3.05739e14	−0.372666	−0.186333	−	0.982487i	$-0.559660\pi$
$197$	−3.05739e14	−0.372666	−0.186333	+	0.982487i	$0.559660\pi$
$198$	−7.66415e12	−0.00903942
$199$	−1.18680e15	−1.35467	−0.677336	−	0.735674i	$-0.736866\pi$
$199$	−1.18680e15	−1.35467	−0.677336	+	0.735674i	$0.736866\pi$
$200$	−1.22352e14	−0.135182
$201$	−6.88168e14	−0.736072
$202$	6.17523e13	0.0639542
$203$	1.16519e15	1.16862
$204$	8.94161e14	0.868599
$205$	−1.16446e15	−1.09578
$206$	−2.71033e14	−0.247107
$207$	−5.02690e14	−0.444112
$208$	7.11108e14	0.608869
$209$	1.60565e14	0.133260
$210$	1.01501e14	0.0816668
$211$	1.24048e15	0.967726	0.483863	−	0.875144i	$-0.339233\pi$
$211$	1.24048e15	0.967726	0.483863	+	0.875144i	$0.339233\pi$
$212$	−1.63469e15	−1.23666
$213$	4.48355e14	0.328969
$214$	3.53667e14	0.251713
$215$	1.96776e15	1.35869
$216$	−1.37219e14	−0.0919317
$217$	−1.75001e15	−1.13776
$218$	7.17724e12	0.00452888
$219$	8.04421e14	0.492716
$220$	1.47263e14	0.0875680
$221$	2.05562e15	1.18684
$222$	1.08557e14	0.0608645
$223$	1.97639e15	1.07620	0.538098	−	0.842882i	$-0.319143\pi$
$223$	1.97639e15	1.07620	0.538098	+	0.842882i	$0.319143\pi$
$224$	8.72007e14	0.461220
$225$	−1.83584e14	−0.0943297
$226$	−4.21228e14	−0.210287
$227$	−2.58008e13	−0.0125160	−0.00625798	−	0.999980i	$-0.501992\pi$
$227$	−2.58008e13	−0.0125160	−0.00625798	+	0.999980i	$0.501992\pi$
$228$	1.39241e15	0.656434
$229$	1.42363e14	0.0652327	0.0326163	−	0.999468i	$-0.489616\pi$
$229$	1.42363e14	0.0652327	0.0326163	+	0.999468i	$0.489616\pi$
$230$	−6.23885e14	−0.277890
$231$	9.95473e13	0.0431074
$232$	−1.95500e15	−0.823141
$233$	−3.00500e15	−1.23036	−0.615179	−	0.788388i	$-0.710916\pi$
$233$	−3.00500e15	−1.23036	−0.615179	+	0.788388i	$0.710916\pi$
$234$	−1.52795e14	−0.0608422
$235$	3.68245e15	1.42625
$236$	−3.24578e14	−0.122290
$237$	−1.52793e15	−0.560066
$238$	7.50164e14	0.267551
$239$	−1.14734e15	−0.398203	−0.199102	−	0.979979i	$-0.563802\pi$
$239$	−1.14734e15	−0.398203	−0.199102	+	0.979979i	$0.563802\pi$
$240$	1.18924e15	0.401695
$241$	−8.41492e14	−0.276656	−0.138328	−	0.990387i	$-0.544173\pi$
$241$	−8.41492e14	−0.276656	−0.138328	+	0.990387i	$0.544173\pi$
$242$	7.60326e14	0.243332
$243$	−2.05891e14	−0.0641500
$244$	5.70572e14	0.173092
$245$	1.54807e15	0.457311
$246$	6.39697e14	0.184033
$247$	3.20107e15	0.896943
$248$	2.93622e15	0.801406
$249$	−2.26230e15	−0.601525
$250$	−1.03298e15	−0.267598
$251$	4.26827e15	1.07739	0.538695	−	0.842501i	$-0.318918\pi$
$251$	4.26827e15	1.07739	0.538695	+	0.842501i	$0.318918\pi$
$252$	8.63269e14	0.212345
$253$	−6.11875e14	−0.146683
$254$	−1.16706e15	−0.272693
$255$	3.43777e15	0.783006
$256$	2.01285e15	0.446942
$257$	1.76886e15	0.382937	0.191469	−	0.981499i	$-0.438675\pi$
$257$	1.76886e15	0.382937	0.191469	+	0.981499i	$0.438675\pi$
$258$	−1.08099e15	−0.228189
$259$	−1.41002e15	−0.290252
$260$	2.93587e15	0.589400
$261$	−2.93338e15	−0.574388
$262$	1.25344e15	0.239412
$263$	8.02597e15	1.49550	0.747748	−	0.663983i	$-0.231135\pi$
$263$	8.02597e15	1.49550	0.747748	+	0.663983i	$0.231135\pi$
$264$	−1.67024e14	−0.0303635
$265$	−6.28486e15	−1.11480
$266$	1.16818e15	0.202199
$267$	5.40216e14	0.0912523
$268$	−7.26397e15	−1.19756
$269$	4.70911e15	0.757791	0.378895	−	0.925439i	$-0.376304\pi$
$269$	4.70911e15	0.757791	0.378895	+	0.925439i	$0.376304\pi$
$270$	−2.55530e14	−0.0401400
$271$	−5.93737e14	−0.0910530	−0.0455265	−	0.998963i	$-0.514497\pi$
$271$	−5.93737e14	−0.0910530	−0.0455265	+	0.998963i	$0.514497\pi$
$272$	8.78931e15	1.31600
$273$	1.98460e15	0.290146
$274$	−3.15386e14	−0.0450261
$275$	−2.23459e14	−0.0311555
$276$	−5.30615e15	−0.722554
$277$	2.34491e15	0.311895	0.155947	−	0.987765i	$-0.450157\pi$
$277$	2.34491e15	0.311895	0.155947	+	0.987765i	$0.450157\pi$
$278$	1.85287e15	0.240742
$279$	4.40566e15	0.559221
$280$	2.21200e15	0.274320
$281$	1.42741e16	1.72964	0.864821	−	0.502080i	$-0.167432\pi$
$281$	1.42741e16	1.72964	0.864821	+	0.502080i	$0.167432\pi$
$282$	−2.02296e15	−0.239534
$283$	1.18379e16	1.36982	0.684908	−	0.728630i	$-0.259843\pi$
$283$	1.18379e16	1.36982	0.684908	+	0.728630i	$0.259843\pi$
$284$	4.73262e15	0.535220
$285$	5.35339e15	0.591748
$286$	−1.85982e14	−0.0200952
$287$	−8.30883e15	−0.877622
$288$	−2.19529e15	−0.226694
$289$	1.55029e16	1.56523
$290$	−3.64060e15	−0.359406
$291$	8.01072e15	0.773334
$292$	8.49108e15	0.801631
$293$	−1.31495e16	−1.21414	−0.607071	−	0.794647i	$-0.707656\pi$
$293$	−1.31495e16	−1.21414	−0.607071	+	0.794647i	$0.707656\pi$
$294$	−8.50436e14	−0.0768040
$295$	−1.24790e15	−0.110239
$296$	2.36577e15	0.204445
$297$	−2.50611e14	−0.0211877
$298$	3.92451e15	0.324624
$299$	−1.21985e16	−0.987289
$300$	−1.93782e15	−0.153471
$301$	1.40407e16	1.08819
$302$	1.18093e15	0.0895737
$303$	2.01925e15	0.149904
$304$	1.36870e16	0.994555
$305$	2.19367e15	0.156035
$306$	−1.88855e15	−0.131504
$307$	−7.32657e15	−0.499461	−0.249730	−	0.968315i	$-0.580342\pi$
$307$	−7.32657e15	−0.499461	−0.249730	+	0.968315i	$0.580342\pi$
$308$	1.05077e15	0.0701341
$309$	−8.86255e15	−0.579200
$310$	5.46783e15	0.349916
$311$	−2.51399e16	−1.57551	−0.787756	−	0.615987i	$-0.788757\pi$
$311$	−2.51399e16	−1.57551	−0.787756	+	0.615987i	$0.788757\pi$
$312$	−3.32983e15	−0.204370
$313$	−3.21315e16	−1.93149	−0.965745	−	0.259494i	$-0.916444\pi$
$313$	−3.21315e16	−1.93149	−0.965745	+	0.259494i	$0.916444\pi$
$314$	4.56545e15	0.268807
$315$	3.31900e15	0.191420
$316$	−1.61281e16	−0.911206
$317$	9.56293e15	0.529305	0.264652	−	0.964344i	$-0.414743\pi$
$317$	9.56293e15	0.529305	0.264652	+	0.964344i	$0.414743\pi$
$318$	3.45260e15	0.187228
$319$	−3.57052e15	−0.189711
$320$	1.06393e16	0.553909
$321$	1.15646e16	0.589995
$322$	−4.45164e15	−0.222565
$323$	3.95653e16	1.93864
$324$	−2.17329e15	−0.104370
$325$	−4.45494e15	−0.209701
$326$	−5.58909e14	−0.0257885
$327$	2.34690e14	0.0106153
$328$	1.39408e16	0.618170
$329$	2.62756e16	1.14230
$330$	−3.11032e14	−0.0132576
$331$	−2.83301e16	−1.18404	−0.592020	−	0.805923i	$-0.701669\pi$
$331$	−2.83301e16	−1.18404	−0.592020	+	0.805923i	$0.701669\pi$
$332$	−2.38797e16	−0.978659
$333$	3.54973e15	0.142662
$334$	4.49801e15	0.177283
$335$	−2.79277e16	−1.07955
$336$	8.48566e15	0.321722
$337$	4.43774e16	1.65032	0.825158	−	0.564902i	$-0.191086\pi$
$337$	4.43774e16	1.65032	0.825158	+	0.564902i	$0.191086\pi$
$338$	3.04456e15	0.111062
$339$	−1.37738e16	−0.492896
$340$	3.62874e16	1.27392
$341$	5.36258e15	0.184702
$342$	−2.94090e15	−0.0993825
$343$	3.14991e16	1.04445
$344$	−2.35579e16	−0.766490
$345$	−2.04005e16	−0.651353
$346$	−8.06559e15	−0.252721
$347$	−1.05564e16	−0.324620	−0.162310	−	0.986740i	$-0.551894\pi$
$347$	−1.05564e16	−0.324620	−0.162310	+	0.986740i	$0.551894\pi$
$348$	−3.09634e16	−0.934508
$349$	1.18454e16	0.350901	0.175451	−	0.984488i	$-0.443862\pi$
$349$	1.18454e16	0.350901	0.175451	+	0.984488i	$0.443862\pi$
$350$	−1.62576e15	−0.0472730
$351$	−4.99625e15	−0.142609
$352$	−2.67211e15	−0.0748732
$353$	−6.39399e16	−1.75888	−0.879441	−	0.476008i	$-0.842083\pi$
$353$	−6.39399e16	−1.75888	−0.879441	+	0.476008i	$0.842083\pi$
$354$	6.85537e14	0.0185144
$355$	1.81954e16	0.482479
$356$	5.70225e15	0.148464
$357$	2.45297e16	0.627118
$358$	−6.00786e15	−0.150827
$359$	1.47794e15	0.0364369	0.0182185	−	0.999834i	$-0.494201\pi$
$359$	1.47794e15	0.0364369	0.0182185	+	0.999834i	$0.494201\pi$
$360$	−5.56872e15	−0.134831
$361$	1.95592e16	0.465108
$362$	−1.32898e16	−0.310395
$363$	2.48620e16	0.570352
$364$	2.09485e16	0.472056
$365$	3.26455e16	0.722637
$366$	−1.20510e15	−0.0262057
$367$	2.39096e16	0.510790	0.255395	−	0.966837i	$-0.417795\pi$
$367$	2.39096e16	0.510790	0.255395	+	0.966837i	$0.417795\pi$
$368$	−5.21578e16	−1.09473
$369$	2.09175e16	0.431359
$370$	4.40554e15	0.0892664
$371$	−4.48448e16	−0.892856
$372$	4.65040e16	0.909832
$373$	6.34163e16	1.21925	0.609626	−	0.792689i	$-0.291320\pi$
$373$	6.34163e16	1.21925	0.609626	+	0.792689i	$0.291320\pi$
$374$	−2.29874e15	−0.0434335
$375$	−3.37776e16	−0.627228
$376$	−4.40860e16	−0.804600
$377$	−7.11829e16	−1.27690
$378$	−1.82330e15	−0.0321485
$379$	8.86925e16	1.53721	0.768603	−	0.639726i	$-0.220952\pi$
$379$	8.86925e16	1.53721	0.768603	+	0.639726i	$0.220952\pi$
$380$	5.65078e16	0.962753
$381$	−3.81618e16	−0.639170
$382$	5.19274e15	0.0855037
$383$	9.64597e16	1.56154	0.780771	−	0.624817i	$-0.214826\pi$
$383$	9.64597e16	1.56154	0.780771	+	0.624817i	$0.214826\pi$
$384$	−3.05138e16	−0.485673
$385$	4.03989e15	0.0632230
$386$	−4.04238e15	−0.0622042
$387$	−3.53475e16	−0.534857
$388$	8.45573e16	1.25819
$389$	−1.14991e17	−1.68264	−0.841321	−	0.540536i	$-0.818222\pi$
$389$	−1.14991e17	−1.68264	−0.841321	+	0.540536i	$0.818222\pi$
$390$	−6.20081e15	−0.0892336
$391$	−1.50774e17	−2.13392
$392$	−1.85334e16	−0.257986
$393$	4.09864e16	0.561162
$394$	6.81619e15	0.0917944
$395$	−6.20074e16	−0.821415
$396$	−2.64533e15	−0.0344716
$397$	−9.51365e16	−1.21958	−0.609788	−	0.792565i	$-0.708745\pi$
$397$	−9.51365e16	−1.21958	−0.609788	+	0.792565i	$0.708745\pi$
$398$	2.64588e16	0.333680
$399$	3.81984e16	0.473938
$400$	−1.90482e16	−0.232522
$401$	−2.78502e16	−0.334495	−0.167247	−	0.985915i	$-0.553488\pi$
$401$	−2.78502e16	−0.334495	−0.167247	+	0.985915i	$0.553488\pi$
$402$	1.53421e16	0.181308
$403$	1.06910e17	1.24318
$404$	2.13142e16	0.243888
$405$	−8.35561e15	−0.0940850
$406$	−2.59770e16	−0.287852
$407$	4.32074e15	0.0471188
$408$	−4.11567e16	−0.441723
$409$	1.31872e16	0.139300	0.0696501	−	0.997571i	$-0.477812\pi$
$409$	1.31872e16	0.139300	0.0696501	+	0.997571i	$0.477812\pi$
$410$	2.59606e16	0.269910
$411$	−1.03129e16	−0.105538
$412$	−9.35487e16	−0.942336
$413$	−8.90423e15	−0.0882919
$414$	1.12071e16	0.109393
$415$	−9.18100e16	−0.882221
$416$	−5.32719e16	−0.503954
$417$	6.05871e16	0.564282
$418$	−3.57966e15	−0.0328244
$419$	−1.09142e17	−0.985375	−0.492687	−	0.870206i	$-0.663985\pi$
$419$	−1.09142e17	−0.985375	−0.492687	+	0.870206i	$0.663985\pi$
$420$	3.50337e16	0.311434
$421$	−1.22179e17	−1.06946	−0.534729	−	0.845024i	$-0.679586\pi$
$421$	−1.22179e17	−1.06946	−0.534729	+	0.845024i	$0.679586\pi$
$422$	−2.76554e16	−0.238368
$423$	−6.61490e16	−0.561450
$424$	7.52419e16	0.628900
$425$	−5.50632e16	−0.453245
$426$	−9.99571e15	−0.0810310
$427$	1.56526e16	0.124970
$428$	1.22070e17	0.959900
$429$	−6.08145e15	−0.0471015
$430$	−4.38695e16	−0.334671
$431$	8.78433e16	0.660095	0.330048	−	0.943964i	$-0.392935\pi$
$431$	8.78433e16	0.660095	0.330048	+	0.943964i	$0.392935\pi$
$432$	−2.13627e16	−0.158129
$433$	−1.49721e17	−1.09172	−0.545859	−	0.837877i	$-0.683796\pi$
$433$	−1.49721e17	−1.09172	−0.545859	+	0.837877i	$0.683796\pi$
$434$	3.90150e16	0.280252
$435$	−1.19044e17	−0.842421
$436$	2.47727e15	0.0172707
$437$	−2.34789e17	−1.61268
$438$	−1.79339e16	−0.121365
$439$	1.16000e17	0.773461	0.386731	−	0.922193i	$-0.373604\pi$
$439$	1.16000e17	0.773461	0.386731	+	0.922193i	$0.373604\pi$
$440$	−6.77826e15	−0.0445324
$441$	−2.78085e16	−0.180023
$442$	−4.58283e16	−0.292341
$443$	−7.77720e16	−0.488876	−0.244438	−	0.969665i	$-0.578603\pi$
$443$	−7.77720e16	−0.488876	−0.244438	+	0.969665i	$0.578603\pi$
$444$	3.74692e16	0.232105
$445$	2.19234e16	0.133834
$446$	−4.40620e16	−0.265086
$447$	1.28328e17	0.760892
$448$	7.59153e16	0.443631
$449$	1.04155e17	0.599898	0.299949	−	0.953955i	$-0.403030\pi$
$449$	1.04155e17	0.599898	0.299949	+	0.953955i	$0.403030\pi$
$450$	4.09285e15	0.0232351
$451$	2.54609e16	0.142471
$452$	−1.45389e17	−0.801924
$453$	3.86155e16	0.209954
$454$	5.75206e14	0.00308291
$455$	8.05404e16	0.425539
$456$	−6.40904e16	−0.333827
$457$	−2.33789e17	−1.20052	−0.600260	−	0.799805i	$-0.704936\pi$
$457$	−2.33789e17	−1.20052	−0.600260	+	0.799805i	$0.704936\pi$
$458$	−3.17386e15	−0.0160680
$459$	−6.17538e16	−0.308234
$460$	−2.15338e17	−1.05973
$461$	1.75420e17	0.851184	0.425592	−	0.904915i	$-0.360066\pi$
$461$	1.75420e17	0.851184	0.425592	+	0.904915i	$0.360066\pi$
$462$	−2.21932e15	−0.0106181
$463$	2.97314e17	1.40262	0.701309	−	0.712857i	$-0.252599\pi$
$463$	2.97314e17	1.40262	0.701309	+	0.712857i	$0.252599\pi$
$464$	−3.04360e17	−1.41586
$465$	1.78793e17	0.820176
$466$	6.69940e16	0.303059
$467$	−2.06037e17	−0.919149	−0.459574	−	0.888139i	$-0.651998\pi$
$467$	−2.06037e17	−0.919149	−0.459574	+	0.888139i	$0.651998\pi$
$468$	−5.27380e16	−0.232020
$469$	−1.99274e17	−0.864625
$470$	−8.20971e16	−0.351311
$471$	1.49286e17	0.630063
$472$	1.49398e16	0.0621901
$473$	−4.30251e16	−0.176654
$474$	3.40639e16	0.137954
$475$	−8.57459e16	−0.342535
$476$	2.58924e17	1.02030
$477$	1.12897e17	0.438847
$478$	2.55789e16	0.0980846
$479$	3.75549e17	1.42064	0.710322	−	0.703876i	$-0.248549\pi$
$479$	3.75549e17	1.42064	0.710322	+	0.703876i	$0.248549\pi$
$480$	−8.90905e16	−0.332478
$481$	8.61394e16	0.317146
$482$	1.87604e16	0.0681453
$483$	−1.45565e17	−0.521675
$484$	2.62431e17	0.927942
$485$	3.25096e17	1.13420
$486$	4.59017e15	0.0158013
$487$	3.12931e17	1.06294	0.531472	−	0.847076i	$-0.321639\pi$
$487$	3.12931e17	1.06294	0.531472	+	0.847076i	$0.321639\pi$
$488$	−2.62625e16	−0.0880252
$489$	−1.82758e16	−0.0604463
$490$	−3.45129e16	−0.112644
$491$	2.37689e17	0.765560	0.382780	−	0.923840i	$-0.374967\pi$
$491$	2.37689e17	0.765560	0.382780	+	0.923840i	$0.374967\pi$
$492$	2.20795e17	0.701806
$493$	−8.79822e17	−2.75988
$494$	−7.13652e16	−0.220933
$495$	−1.01705e16	−0.0310747
$496$	4.57120e17	1.37848
$497$	1.29831e17	0.386422
$498$	5.04360e16	0.148167
$499$	−2.41112e17	−0.699141	−0.349571	−	0.936910i	$-0.613673\pi$
$499$	−2.41112e17	−0.699141	−0.349571	+	0.936910i	$0.613673\pi$
$500$	−3.56540e17	−1.02048
$501$	1.47081e17	0.415539
$502$	−9.51575e16	−0.265380
$503$	−5.89092e17	−1.62178	−0.810888	−	0.585201i	$-0.801016\pi$
$503$	−5.89092e17	−1.62178	−0.810888	+	0.585201i	$0.801016\pi$
$504$	−3.97348e16	−0.107987
$505$	8.19464e16	0.219855
$506$	1.36413e16	0.0361307
$507$	9.95545e16	0.260321
$508$	−4.02817e17	−1.03991
$509$	−4.33118e17	−1.10393	−0.551964	−	0.833868i	$-0.686121\pi$
$509$	−4.33118e17	−1.10393	−0.551964	+	0.833868i	$0.686121\pi$
$510$	−7.66422e16	−0.192869
$511$	2.32938e17	0.578767
$512$	−3.87768e17	−0.951300
$513$	−9.61647e16	−0.232945
$514$	−3.94352e16	−0.0943244
$515$	−3.59666e17	−0.849477
$516$	−3.73111e17	−0.870192
$517$	−8.05168e16	−0.185438
$518$	3.14351e16	0.0714944
$519$	−2.63738e17	−0.592358
$520$	−1.35133e17	−0.299737
$521$	−2.09186e17	−0.458235	−0.229118	−	0.973399i	$-0.573584\pi$
$521$	−2.09186e17	−0.458235	−0.229118	+	0.973399i	$0.573584\pi$
$522$	6.53973e16	0.141482
$523$	−5.23107e17	−1.11771	−0.558856	−	0.829265i	$-0.688760\pi$
$523$	−5.23107e17	−1.11771	−0.558856	+	0.829265i	$0.688760\pi$
$524$	4.32633e17	0.912990
$525$	−5.31608e16	−0.110804
$526$	−1.78932e17	−0.368367
$527$	1.32141e18	2.68700
$528$	−2.60027e16	−0.0522274
$529$	3.90690e17	0.775123
$530$	1.40116e17	0.274596
$531$	2.24165e16	0.0433963
$532$	4.03204e17	0.771079
$533$	5.07595e17	0.958938
$534$	−1.20437e16	−0.0224771
$535$	4.69323e17	0.865311
$536$	3.34349e17	0.609015
$537$	−1.96452e17	−0.353528
$538$	−1.04986e17	−0.186658
$539$	−3.38486e16	−0.0594585
$540$	−8.81977e16	−0.153073
$541$	8.07375e17	1.38450	0.692250	−	0.721658i	$-0.256620\pi$
$541$	8.07375e17	1.38450	0.692250	+	0.721658i	$0.256620\pi$
$542$	1.32369e16	0.0224280
$543$	−4.34567e17	−0.727541
$544$	−6.58441e17	−1.08924
$545$	9.52432e15	0.0155689
$546$	−4.42450e16	−0.0714681
$547$	−6.12909e17	−0.978314	−0.489157	−	0.872196i	$-0.662695\pi$
$547$	−6.12909e17	−0.978314	−0.489157	+	0.872196i	$0.662695\pi$
$548$	−1.08858e17	−0.171706
$549$	−3.94056e16	−0.0614240
$550$	4.98183e15	0.00767417
$551$	−1.37008e18	−2.08575
$552$	2.44233e17	0.367452
$553$	−4.42445e17	−0.657880
$554$	−5.22778e16	−0.0768253
$555$	1.44057e17	0.209233
$556$	6.39528e17	0.918065
$557$	−7.87487e17	−1.11734	−0.558669	−	0.829391i	$-0.688688\pi$
$557$	−7.87487e17	−1.11734	−0.558669	+	0.829391i	$0.688688\pi$
$558$	−9.82205e16	−0.137746
$559$	−8.57760e17	−1.18902
$560$	3.44370e17	0.471850
$561$	−7.51669e16	−0.101805
$562$	−3.18228e17	−0.426042
$563$	−9.62624e17	−1.27395	−0.636975	−	0.770885i	$-0.719814\pi$
$563$	−9.62624e17	−1.27395	−0.636975	+	0.770885i	$0.719814\pi$
$564$	−6.98237e17	−0.913458
$565$	−5.58977e17	−0.722901
$566$	−2.63916e17	−0.337410
$567$	−5.96203e16	−0.0753537
$568$	−2.17835e17	−0.272184
$569$	4.08005e17	0.504006	0.252003	−	0.967726i	$-0.418911\pi$
$569$	4.08005e17	0.504006	0.252003	+	0.967726i	$0.418911\pi$
$570$	−1.19349e17	−0.145758
$571$	1.26143e18	1.52310	0.761549	−	0.648107i	$-0.224439\pi$
$571$	1.26143e18	1.52310	0.761549	+	0.648107i	$0.224439\pi$
$572$	−6.41928e16	−0.0766324
$573$	1.69798e17	0.200414
$574$	1.85238e17	0.216174
$575$	3.26757e17	0.377037
$576$	−1.91117e17	−0.218049
$577$	8.72141e17	0.983884	0.491942	−	0.870628i	$-0.336287\pi$
$577$	8.72141e17	0.983884	0.491942	+	0.870628i	$0.336287\pi$
$578$	−3.45625e17	−0.385544
$579$	−1.32182e17	−0.145802
$580$	−1.25658e18	−1.37059
$581$	−6.55098e17	−0.706580
$582$	−1.78592e17	−0.190486
$583$	1.37419e17	0.144944
$584$	−3.90830e17	−0.407666
$585$	−2.02761e17	−0.209157
$586$	2.93157e17	0.299065
$587$	−4.56275e17	−0.460340	−0.230170	−	0.973150i	$-0.573928\pi$
$587$	−4.56275e17	−0.460340	−0.230170	+	0.973150i	$0.573928\pi$
$588$	−2.93533e17	−0.292890
$589$	2.05773e18	2.03067
$590$	2.78209e16	0.0271540
$591$	2.22884e17	0.215159
$592$	3.68310e17	0.351660
$593$	1.60494e18	1.51566	0.757831	−	0.652451i	$-0.226259\pi$
$593$	1.60494e18	1.51566	0.757831	+	0.652451i	$0.226259\pi$
$594$	5.58717e15	0.00521891
$595$	9.95481e17	0.919756
$596$	1.35457e18	1.23794
$597$	8.65180e17	0.782120
$598$	2.71956e17	0.243187
$599$	−1.11312e18	−0.984615	−0.492307	−	0.870421i	$-0.663846\pi$
$599$	−1.11312e18	−0.984615	−0.492307	+	0.870421i	$0.663846\pi$
$600$	8.91949e16	0.0780471
$601$	−2.13548e17	−0.184847	−0.0924235	−	0.995720i	$-0.529461\pi$
$601$	−2.13548e17	−0.184847	−0.0924235	+	0.995720i	$0.529461\pi$
$602$	−3.13025e17	−0.268041
$603$	5.01675e17	0.424971
$604$	4.07607e17	0.341587
$605$	1.00897e18	0.836501
$606$	−4.50174e16	−0.0369240
$607$	−3.12954e17	−0.253954	−0.126977	−	0.991906i	$-0.540527\pi$
$607$	−3.12954e17	−0.253954	−0.126977	+	0.991906i	$0.540527\pi$
$608$	−1.02534e18	−0.823182
$609$	−8.49426e17	−0.674703
$610$	−4.89060e16	−0.0384343
$611$	−1.60520e18	−1.24814
$612$	−6.51843e17	−0.501486
$613$	2.22352e18	1.69258	0.846288	−	0.532726i	$-0.178832\pi$
$613$	2.22352e18	1.69258	0.846288	+	0.532726i	$0.178832\pi$
$614$	1.63340e17	0.123026
$615$	8.48889e17	0.632649
$616$	−4.83653e16	−0.0356664
$617$	−1.27282e18	−0.928781	−0.464390	−	0.885631i	$-0.653726\pi$
$617$	−1.27282e18	−0.928781	−0.464390	+	0.885631i	$0.653726\pi$
$618$	1.97583e17	0.142667
$619$	2.09293e18	1.49543	0.747715	−	0.664020i	$-0.231151\pi$
$619$	2.09293e18	1.49543	0.747715	+	0.664020i	$0.231151\pi$
$620$	1.88726e18	1.33440
$621$	3.66461e17	0.256408
$622$	5.60474e17	0.388077
$623$	1.56431e17	0.107189
$624$	−5.18398e17	−0.351531
$625$	−9.49096e17	−0.636928
$626$	7.16344e17	0.475761
$627$	−1.17052e17	−0.0769378
$628$	1.57579e18	1.02509
$629$	1.06468e18	0.685475
$630$	−7.39943e16	−0.0471503
$631$	2.12560e18	1.34058	0.670288	−	0.742101i	$-0.266171\pi$
$631$	2.12560e18	1.34058	0.670288	+	0.742101i	$0.266171\pi$
$632$	7.42349e17	0.463390
$633$	−9.04307e17	−0.558717
$634$	−2.13197e17	−0.130377
$635$	−1.54871e18	−0.937432
$636$	1.19169e18	0.713988
$637$	−6.74815e17	−0.400201
$638$	7.96018e16	0.0467292
$639$	−3.26851e17	−0.189930
$640$	−1.23833e18	−0.712307
$641$	6.99801e17	0.398472	0.199236	−	0.979952i	$-0.436154\pi$
$641$	6.99801e17	0.398472	0.199236	+	0.979952i	$0.436154\pi$
$642$	−2.57823e17	−0.145327
$643$	3.40542e18	1.90020	0.950101	−	0.311944i	$-0.100980\pi$
$643$	3.40542e18	1.90020	0.950101	+	0.311944i	$0.100980\pi$
$644$	−1.53651e18	−0.848747
$645$	−1.43450e18	−0.784442
$646$	−8.82075e17	−0.477523
$647$	1.47821e18	0.792245	0.396123	−	0.918198i	$-0.370356\pi$
$647$	1.47821e18	0.792245	0.396123	+	0.918198i	$0.370356\pi$
$648$	1.00033e17	0.0530768
$649$	2.72854e16	0.0143331
$650$	9.93192e16	0.0516531
$651$	1.27576e18	0.656888
$652$	−1.92911e17	−0.0983439
$653$	2.47207e18	1.24774	0.623870	−	0.781528i	$-0.285559\pi$
$653$	2.47207e18	1.24774	0.623870	+	0.781528i	$0.285559\pi$
$654$	−5.23221e15	−0.00261475
$655$	1.66334e18	0.823023
$656$	2.17035e18	1.06330
$657$	−5.86423e17	−0.284470
$658$	−5.85793e17	−0.281369
$659$	−1.47599e18	−0.701987	−0.350993	−	0.936378i	$-0.614156\pi$
$659$	−1.47599e18	−0.701987	−0.350993	+	0.936378i	$0.614156\pi$
$660$	−1.07354e17	−0.0505574
$661$	−8.95513e17	−0.417602	−0.208801	−	0.977958i	$-0.566956\pi$
$661$	−8.95513e17	−0.417602	−0.208801	+	0.977958i	$0.566956\pi$
$662$	6.31596e17	0.291650
$663$	−1.49855e18	−0.685224
$664$	1.09914e18	0.497694
$665$	1.55019e18	0.695096
$666$	−7.91382e16	−0.0351402
$667$	5.22106e18	2.29584
$668$	1.55252e18	0.676066
$669$	−1.44079e18	−0.621342
$670$	6.22624e17	0.265913
$671$	−4.79646e16	−0.0202873
$672$	−6.35693e17	−0.266285
$673$	4.98023e17	0.206610	0.103305	−	0.994650i	$-0.467058\pi$
$673$	4.98023e17	0.206610	0.103305	+	0.994650i	$0.467058\pi$
$674$	−9.89356e17	−0.406503
$675$	1.33833e17	0.0544613
$676$	1.05085e18	0.423532
$677$	3.21204e18	1.28220	0.641098	−	0.767459i	$-0.278479\pi$
$677$	3.21204e18	1.28220	0.641098	+	0.767459i	$0.278479\pi$
$678$	3.07075e17	0.121409
$679$	2.31968e18	0.908395
$680$	−1.67025e18	−0.647848
$681$	1.88088e16	0.00722610
$682$	−1.19554e17	−0.0454953
$683$	−1.08598e18	−0.409343	−0.204672	−	0.978831i	$-0.565613\pi$
$683$	−1.08598e18	−0.409343	−0.204672	+	0.978831i	$0.565613\pi$
$684$	−1.01507e18	−0.378993
$685$	−4.18523e17	−0.154786
$686$	−7.02247e17	−0.257266
$687$	−1.03782e17	−0.0376621
$688$	−3.66756e18	−1.31842
$689$	2.73961e18	0.975584
$690$	4.54812e17	0.160440
$691$	1.83985e18	0.642946	0.321473	−	0.946919i	$-0.395822\pi$
$691$	1.83985e18	0.642946	0.321473	+	0.946919i	$0.395822\pi$
$692$	−2.78389e18	−0.963745
$693$	−7.25700e16	−0.0248881
$694$	2.35347e17	0.0799598
$695$	2.45879e18	0.827598
$696$	1.42519e18	0.475241
$697$	6.27389e18	2.07264
$698$	−2.64084e17	−0.0864333
$699$	2.19065e18	0.710347
$700$	−5.61140e17	−0.180274
$701$	−2.35387e18	−0.749230	−0.374615	−	0.927181i	$-0.622225\pi$
$701$	−2.35387e18	−0.749230	−0.374615	+	0.927181i	$0.622225\pi$
$702$	1.11387e17	0.0351273
$703$	1.65796e18	0.518040
$704$	−2.32629e17	−0.0720179
$705$	−2.68450e18	−0.823445
$706$	1.42549e18	0.433244
$707$	5.84717e17	0.176084
$708$	2.36617e17	0.0706042
$709$	6.61737e18	1.95652	0.978261	−	0.207376i	$-0.0664924\pi$
$709$	6.61737e18	1.95652	0.978261	+	0.207376i	$0.0664924\pi$
$710$	−4.05652e17	−0.118843
$711$	1.11386e18	0.323354
$712$	−2.62465e17	−0.0755009
$713$	−7.84154e18	−2.23521
$714$	−5.46870e17	−0.154471
$715$	−2.46801e17	−0.0690809
$716$	−2.07365e18	−0.575176
$717$	8.36409e17	0.229903
$718$	−3.29493e16	−0.00897507
$719$	3.05598e18	0.824922	0.412461	−	0.910975i	$-0.364669\pi$
$719$	3.05598e18	0.824922	0.412461	+	0.910975i	$0.364669\pi$
$720$	−8.66955e17	−0.231919
$721$	−2.56635e18	−0.680355
$722$	−4.36056e17	−0.114565
$723$	6.13448e17	0.159727
$724$	−4.58707e18	−1.18368
$725$	1.90675e18	0.487637
$726$	−5.54278e17	−0.140488
$727$	4.53502e18	1.13922	0.569608	−	0.821917i	$-0.307095\pi$
$727$	4.53502e18	1.13922	0.569608	+	0.821917i	$0.307095\pi$
$728$	−9.64225e17	−0.240062
$729$	1.50095e17	0.0370370
$730$	−7.27805e17	−0.177999
$731$	−1.06019e19	−2.56993
$732$	−4.15947e17	−0.0999346
$733$	1.74021e18	0.414406	0.207203	−	0.978298i	$-0.433564\pi$
$733$	1.74021e18	0.414406	0.207203	+	0.978298i	$0.433564\pi$
$734$	−5.33044e17	−0.125817
$735$	−1.12854e18	−0.264028
$736$	3.90734e18	0.906098
$737$	6.10640e17	0.140361
$738$	−4.66339e17	−0.106252
$739$	−5.99849e18	−1.35473	−0.677366	−	0.735646i	$-0.736879\pi$
$739$	−5.99849e18	−1.35473	−0.677366	+	0.735646i	$0.736879\pi$
$740$	1.52060e18	0.340415
$741$	−2.33358e18	−0.517850
$742$	9.99777e17	0.219927
$743$	−4.85927e18	−1.05960	−0.529802	−	0.848122i	$-0.677734\pi$
$743$	−4.85927e18	−1.05960	−0.529802	+	0.848122i	$0.677734\pi$
$744$	−2.14050e18	−0.462692
$745$	5.20790e18	1.11596
$746$	−1.41381e18	−0.300324
$747$	1.64921e18	0.347291
$748$	−7.93425e17	−0.165632
$749$	3.34879e18	0.693036
$750$	7.53043e17	0.154498
$751$	2.09774e18	0.426671	0.213335	−	0.976979i	$-0.431567\pi$
$751$	2.09774e18	0.426671	0.213335	+	0.976979i	$0.431567\pi$
$752$	−6.86345e18	−1.38397
$753$	−3.11157e18	−0.622031
$754$	1.58696e18	0.314523
$755$	1.56712e18	0.307927
$756$	−6.29323e17	−0.122598
$757$	−4.39866e18	−0.849566	−0.424783	−	0.905295i	$-0.639650\pi$
$757$	−4.39866e18	−0.849566	−0.424783	+	0.905295i	$0.639650\pi$
$758$	−1.97733e18	−0.378642
$759$	4.46057e17	0.0846874
$760$	−2.60096e18	−0.489604
$761$	−3.68185e18	−0.687173	−0.343586	−	0.939121i	$-0.611642\pi$
$761$	−3.68185e18	−0.687173	−0.343586	+	0.939121i	$0.611642\pi$
$762$	8.50785e17	0.157439
$763$	6.79595e16	0.0124693
$764$	1.79231e18	0.326066
$765$	−2.50613e18	−0.452069
$766$	−2.15049e18	−0.384636
$767$	5.43969e17	0.0964726
$768$	−1.46737e18	−0.258042
$769$	−1.53489e18	−0.267643	−0.133821	−	0.991005i	$-0.542725\pi$
$769$	−1.53489e18	−0.267643	−0.133821	+	0.991005i	$0.542725\pi$
$770$	−9.00660e16	−0.0155730
$771$	−1.28950e18	−0.221089
$772$	−1.39525e18	−0.237214
$773$	−2.39398e18	−0.403602	−0.201801	−	0.979427i	$-0.564679\pi$
$773$	−2.39398e18	−0.403602	−0.201801	+	0.979427i	$0.564679\pi$
$774$	7.88043e17	0.131745
$775$	−2.86376e18	−0.474761
$776$	−3.89203e18	−0.639846
$777$	1.02790e18	0.167577
$778$	2.56363e18	0.414465
$779$	9.76987e18	1.56637
$780$	−2.14025e18	−0.340290
$781$	−3.97844e17	−0.0627308
$782$	3.36138e18	0.525622
$783$	2.13844e18	0.331623
$784$	−2.88534e18	−0.443754
$785$	6.05843e18	0.924075
$786$	−9.13758e17	−0.138224
$787$	1.83271e18	0.274953	0.137477	−	0.990505i	$-0.456101\pi$
$787$	1.83271e18	0.274953	0.137477	+	0.990505i	$0.456101\pi$
$788$	2.35265e18	0.350056
$789$	−5.85093e18	−0.863425
$790$	1.38240e18	0.202329
$791$	−3.98850e18	−0.578979
$792$	1.21760e17	0.0175304
$793$	−9.56236e17	−0.136549
$794$	2.12099e18	0.300404
$795$	4.58166e18	0.643631
$796$	9.13242e18	1.27248
$797$	9.59167e18	1.32561	0.662804	−	0.748793i	$-0.269366\pi$
$797$	9.59167e18	1.32561	0.662804	+	0.748793i	$0.269366\pi$
$798$	−8.51601e17	−0.116739
$799$	−1.98404e19	−2.69771
$800$	1.42697e18	0.192456
$801$	−3.93817e17	−0.0526846
$802$	6.20896e17	0.0823921
$803$	−7.13795e17	−0.0939556
$804$	5.29543e18	0.691413
$805$	−5.90741e18	−0.765110
$806$	−2.38347e18	−0.306218
$807$	−3.43294e18	−0.437511
$808$	−9.81057e17	−0.124028
$809$	4.77674e18	0.599054	0.299527	−	0.954088i	$-0.403171\pi$
$809$	4.77674e18	0.599054	0.299527	+	0.954088i	$0.403171\pi$
$810$	1.86281e17	0.0231748
$811$	−1.04815e19	−1.29357	−0.646785	−	0.762672i	$-0.723887\pi$
$811$	−1.04815e19	−1.29357	−0.646785	+	0.762672i	$0.723887\pi$
$812$	−8.96612e18	−1.09772
$813$	4.32835e17	0.0525695
$814$	−9.63272e16	−0.0116062
$815$	−7.41682e17	−0.0886530
$816$	−6.40741e18	−0.759795
$817$	−1.65096e19	−1.94220
$818$	−2.93998e17	−0.0343122
$819$	−1.44677e18	−0.167516
$820$	8.96046e18	1.02930
$821$	−5.98950e18	−0.682590	−0.341295	−	0.939956i	$-0.610866\pi$
$821$	−5.98950e18	−0.682590	−0.341295	+	0.939956i	$0.610866\pi$
$822$	2.29917e17	0.0259958
$823$	7.33979e18	0.823350	0.411675	−	0.911331i	$-0.364944\pi$
$823$	7.33979e18	0.823350	0.411675	+	0.911331i	$0.364944\pi$
$824$	4.30589e18	0.479222
$825$	1.62902e17	0.0179877
$826$	1.98512e17	0.0217479
$827$	9.25792e18	1.00630	0.503150	−	0.864199i	$-0.332174\pi$
$827$	9.25792e18	1.00630	0.503150	+	0.864199i	$0.332174\pi$
$828$	3.86818e18	0.417167
$829$	1.47373e19	1.57693	0.788467	−	0.615077i	$-0.210875\pi$
$829$	1.47373e19	1.57693	0.788467	+	0.615077i	$0.210875\pi$
$830$	2.04683e18	0.217307
$831$	−1.70944e18	−0.180072
$832$	−4.63775e18	−0.484736
$833$	−8.34073e18	−0.864991
$834$	−1.35074e18	−0.138993
$835$	5.96894e18	0.609445
$836$	−1.23554e18	−0.125175
$837$	−3.21173e18	−0.322867
$838$	2.43323e18	0.242716
$839$	−1.99996e19	−1.97956	−0.989779	−	0.142612i	$-0.954450\pi$
$839$	−1.99996e19	−1.97956	−0.989779	+	0.142612i	$0.954450\pi$
$840$	−1.61254e18	−0.158379
$841$	2.02062e19	1.96930
$842$	2.72388e18	0.263427
$843$	−1.04058e19	−0.998610
$844$	−9.54542e18	−0.909011
$845$	4.04018e18	0.381797
$846$	1.47474e18	0.138295
$847$	7.19934e18	0.669963
$848$	1.17139e19	1.08175
$849$	−8.62981e18	−0.790863
$850$	1.22759e18	0.111642
$851$	−6.31808e18	−0.570221
$852$	−3.45008e18	−0.309009
$853$	2.42111e18	0.215202	0.107601	−	0.994194i	$-0.465683\pi$
$853$	2.42111e18	0.215202	0.107601	+	0.994194i	$0.465683\pi$
$854$	−3.48962e17	−0.0307824
$855$	−3.90262e18	−0.341646
$856$	−5.61870e18	−0.488154
$857$	2.24309e19	1.93407	0.967035	−	0.254642i	$-0.0819578\pi$
$857$	2.24309e19	1.93407	0.967035	+	0.254642i	$0.0819578\pi$
$858$	1.35581e17	0.0116020
$859$	1.46709e19	1.24595	0.622975	−	0.782242i	$-0.285924\pi$
$859$	1.46709e19	1.24595	0.622975	+	0.782242i	$0.285924\pi$
$860$	−1.51418e19	−1.27626
$861$	6.05714e18	0.506695
$862$	−1.95839e18	−0.162593
$863$	1.40414e19	1.15702	0.578508	−	0.815677i	$-0.303635\pi$
$863$	1.40414e19	1.15702	0.578508	+	0.815677i	$0.303635\pi$
$864$	1.60036e18	0.130882
$865$	−1.07032e19	−0.868776
$866$	3.33790e18	0.268910
$867$	−1.13016e19	−0.903686
$868$	1.34663e19	1.06873
$869$	1.35579e18	0.106798
$870$	2.65400e18	0.207503
$871$	1.21739e19	0.944737
$872$	−1.14025e17	−0.00878297
$873$	−5.83982e18	−0.446485
$874$	5.23443e18	0.397233
$875$	−9.78104e18	−0.736771
$876$	−6.19000e18	−0.462822
$877$	2.55638e19	1.89726	0.948631	−	0.316384i	$-0.102469\pi$
$877$	2.55638e19	1.89726	0.948631	+	0.316384i	$0.102469\pi$
$878$	−2.58612e18	−0.190517
$879$	9.58599e18	0.700986
$880$	−1.05526e18	−0.0765988
$881$	−1.57648e18	−0.113591	−0.0567957	−	0.998386i	$-0.518088\pi$
$881$	−1.57648e18	−0.113591	−0.0567957	+	0.998386i	$0.518088\pi$
$882$	6.19968e17	0.0443428
$883$	7.16353e17	0.0508607	0.0254304	−	0.999677i	$-0.491904\pi$
$883$	7.16353e17	0.0508607	0.0254304	+	0.999677i	$0.491904\pi$
$884$	−1.58179e19	−1.11483
$885$	9.09719e17	0.0636467
$886$	1.73386e18	0.120419
$887$	1.38829e19	0.957141	0.478571	−	0.878049i	$-0.341155\pi$
$887$	1.38829e19	0.957141	0.478571	+	0.878049i	$0.341155\pi$
$888$	−1.72465e18	−0.118036
$889$	−1.10506e19	−0.750799
$890$	−4.88763e17	−0.0329658
$891$	1.82696e17	0.0122327
$892$	−1.52083e19	−1.01090
$893$	−3.08960e19	−2.03877
$894$	−2.86097e18	−0.187422
$895$	−7.97254e18	−0.518498
$896$	−8.83595e18	−0.570494
$897$	8.89272e18	0.570012
$898$	−2.32204e18	−0.147766
$899$	−4.57583e19	−2.89089
$900$	1.41267e18	0.0886065
$901$	3.38617e19	2.10862
$902$	−5.67629e17	−0.0350931
$903$	−1.02356e19	−0.628268
$904$	6.69203e18	0.407815
$905$	−1.76359e19	−1.06704
$906$	−8.60901e17	−0.0517154
$907$	−5.04050e18	−0.300626	−0.150313	−	0.988638i	$-0.548028\pi$
$907$	−5.04050e18	−0.300626	−0.150313	+	0.988638i	$0.548028\pi$
$908$	1.98536e17	0.0117566
$909$	−1.47203e18	−0.0865470
$910$	−1.79558e18	−0.104818
$911$	−1.16890e19	−0.677496	−0.338748	−	0.940877i	$-0.610003\pi$
$911$	−1.16890e19	−0.677496	−0.338748	+	0.940877i	$0.610003\pi$
$912$	−9.97780e18	−0.574207
$913$	2.00743e18	0.114704
$914$	5.21214e18	0.295710
$915$	−1.59919e18	−0.0900869
$916$	−1.09548e18	−0.0612749
$917$	1.18685e19	0.659168
$918$	1.37675e18	0.0759237
$919$	−2.74914e19	−1.50538	−0.752690	−	0.658375i	$-0.771244\pi$
$919$	−2.74914e19	−1.50538	−0.752690	+	0.658375i	$0.771244\pi$
$920$	9.91163e18	0.538920
$921$	5.34107e18	0.288364
$922$	−3.91085e18	−0.209662
$923$	−7.93152e18	−0.422226
$924$	−7.66014e17	−0.0404919
$925$	−2.30738e18	−0.121115
$926$	−6.62838e18	−0.345490
$927$	6.46080e18	0.334401
$928$	2.28008e19	1.17189
$929$	−1.47974e19	−0.755235	−0.377618	−	0.925962i	$-0.623257\pi$
$929$	−1.47974e19	−0.755235	−0.377618	+	0.925962i	$0.623257\pi$
$930$	−3.98605e18	−0.202024
$931$	−1.29884e19	−0.653707
$932$	2.31234e19	1.15571
$933$	1.83270e19	0.909622
$934$	4.59343e18	0.226403
$935$	−3.05047e18	−0.149311
$936$	2.42744e18	0.117993
$937$	−1.32380e19	−0.639020	−0.319510	−	0.947583i	$-0.603518\pi$
$937$	−1.32380e19	−0.639020	−0.319510	+	0.947583i	$0.603518\pi$
$938$	4.44265e18	0.212973
$939$	2.34238e19	1.11515
$940$	−2.83363e19	−1.33971
$941$	−3.52473e19	−1.65498	−0.827491	−	0.561478i	$-0.810233\pi$
$941$	−3.52473e19	−1.65498	−0.827491	+	0.561478i	$0.810233\pi$
$942$	−3.32821e18	−0.155196
$943$	−3.72307e19	−1.72415
$944$	2.32587e18	0.106971
$945$	−2.41955e18	−0.110517
$946$	9.59208e17	0.0435131
$947$	−1.11020e19	−0.500179	−0.250090	−	0.968223i	$-0.580460\pi$
$947$	−1.11020e19	−0.500179	−0.250090	+	0.968223i	$0.580460\pi$
$948$	1.17574e19	0.526085
$949$	−1.42304e19	−0.632393
$950$	1.91163e18	0.0843725
$951$	−6.97137e18	−0.305594
$952$	−1.19178e19	−0.518869
$953$	−1.34067e19	−0.579719	−0.289860	−	0.957069i	$-0.593609\pi$
$953$	−1.34067e19	−0.579719	−0.289860	+	0.957069i	$0.593609\pi$
$954$	−2.51695e18	−0.108096
$955$	6.89086e18	0.293935
$956$	8.82873e18	0.374043
$957$	2.60291e18	0.109530
$958$	−8.37255e18	−0.349930
$959$	−2.98632e18	−0.123969
$960$	−7.75605e18	−0.319799
$961$	4.43070e19	1.81456
$962$	−1.92041e18	−0.0781187
$963$	−8.43061e18	−0.340634
$964$	6.47526e18	0.259870
$965$	−5.36431e18	−0.213839
$966$	3.24525e18	0.128498
$967$	2.98620e19	1.17449	0.587243	−	0.809411i	$-0.300213\pi$
$967$	2.98620e19	1.17449	0.587243	+	0.809411i	$0.300213\pi$
$968$	−1.20793e19	−0.471901
$969$	−2.88431e19	−1.11928
$970$	−7.24775e18	−0.279375
$971$	−4.14106e18	−0.158557	−0.0792787	−	0.996852i	$-0.525262\pi$
$971$	−4.14106e18	−0.158557	−0.0792787	+	0.996852i	$0.525262\pi$
$972$	1.58433e18	0.0602579
$973$	1.75443e19	0.662832
$974$	−6.97654e18	−0.261822
$975$	3.24765e18	0.121071
$976$	−4.08862e18	−0.151410
$977$	−4.94949e19	−1.82073	−0.910366	−	0.413803i	$-0.864200\pi$
$977$	−4.94949e19	−1.82073	−0.910366	+	0.413803i	$0.864200\pi$
$978$	4.07445e17	0.0148890
$979$	−4.79355e17	−0.0174008
$980$	−1.19124e19	−0.429564
$981$	−1.71089e17	−0.00612876
$982$	−5.29908e18	−0.188571
$983$	2.74605e19	0.970759	0.485379	−	0.874304i	$-0.338681\pi$
$983$	2.74605e19	0.970759	0.485379	+	0.874304i	$0.338681\pi$
$984$	−1.01628e19	−0.356901
$985$	9.04521e18	0.315561
$986$	1.96149e19	0.679808
$987$	−1.91549e19	−0.659506
$988$	−2.46321e19	−0.842523
$989$	6.29142e19	2.13783
$990$	2.26742e17	0.00765426
$991$	3.83927e19	1.28757	0.643784	−	0.765207i	$-0.277364\pi$
$991$	3.83927e19	1.28757	0.643784	+	0.765207i	$0.277364\pi$
$992$	−3.42446e19	−1.14095
$993$	2.06526e19	0.683605
$994$	−2.89448e18	−0.0951828
$995$	3.51113e19	1.14709
$996$	1.74083e19	0.565029
$997$	3.98135e19	1.28384	0.641922	−	0.766770i	$-0.278137\pi$
$997$	3.98135e19	1.28384	0.641922	+	0.766770i	$0.278137\pi$
$998$	5.37539e18	0.172211
$999$	−2.58775e18	−0.0823658

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.d.1.15	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.d.1.15	✓	32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-22.2942 q^{2} -729.000 q^{3} -7694.97 q^{4} -29584.7 q^{5} +16252.4 q^{6} -211098. q^{7} +354187. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-22.2942 q^{2} -729.000 q^{3} -7694.97 q^{4} -29584.7 q^{5} +16252.4 q^{6} -211098. q^{7} +354187. q^{8} +531441. q^{9} +659567. q^{10} +646871. q^{11} +5.60963e6 q^{12} +1.28962e7 q^{13} +4.70625e6 q^{14} +2.15673e7 q^{15} +5.51409e7 q^{16} +1.59397e8 q^{17} -1.18480e7 q^{18} +2.48218e8 q^{19} +2.27654e8 q^{20} +1.53890e8 q^{21} -1.44215e7 q^{22} -9.45900e8 q^{23} -2.58202e8 q^{24} -3.45446e8 q^{25} -2.87510e8 q^{26} -3.87420e8 q^{27} +1.62439e9 q^{28} -5.51968e9 q^{29} -4.80825e8 q^{30} +8.29003e9 q^{31} -4.13082e9 q^{32} -4.71569e8 q^{33} -3.55363e9 q^{34} +6.24528e9 q^{35} -4.08942e9 q^{36} +6.67944e9 q^{37} -5.53381e9 q^{38} -9.40133e9 q^{39} -1.04785e10 q^{40} +3.93601e10 q^{41} -3.43086e9 q^{42} -6.65126e10 q^{43} -4.97766e9 q^{44} -1.57225e10 q^{45} +2.10880e10 q^{46} -1.24471e11 q^{47} -4.01977e10 q^{48} -5.23267e10 q^{49} +7.70143e9 q^{50} -1.16201e11 q^{51} -9.92359e10 q^{52} +2.12436e11 q^{53} +8.63722e9 q^{54} -1.91375e10 q^{55} -7.47681e10 q^{56} -1.80951e11 q^{57} +1.23057e11 q^{58} +4.21805e10 q^{59} -1.65960e11 q^{60} -7.41487e10 q^{61} -1.84819e11 q^{62} -1.12186e11 q^{63} -3.59621e11 q^{64} -3.81531e11 q^{65} +1.05132e10 q^{66} +9.43989e11 q^{67} -1.22656e12 q^{68} +6.89561e11 q^{69} -1.39233e11 q^{70} -6.15028e11 q^{71} +1.88229e11 q^{72} -1.10346e12 q^{73} -1.48913e11 q^{74} +2.51830e11 q^{75} -1.91003e12 q^{76} -1.36553e11 q^{77} +2.09595e11 q^{78} +2.09592e12 q^{79} -1.63133e12 q^{80} +2.82430e11 q^{81} -8.77500e11 q^{82} +3.10329e12 q^{83} -1.18418e12 q^{84} -4.71573e12 q^{85} +1.48284e12 q^{86} +4.02385e12 q^{87} +2.29113e11 q^{88} -7.41037e11 q^{89} +3.50521e11 q^{90} -2.72236e12 q^{91} +7.27867e12 q^{92} -6.04343e12 q^{93} +2.77498e12 q^{94} -7.34347e12 q^{95} +3.01137e12 q^{96} -1.09886e13 q^{97} +1.16658e12 q^{98} +3.43774e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9}+O(q^{10}) \) 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9} + 6145337 q^{10} + 400846 q^{11} - 101457846 q^{12} + 9411686 q^{13} - 36368387 q^{14} - 1630044 q^{15} + 734877786 q^{16} + 228113833 q^{17} + 6377292 q^{18} + 524233755 q^{19} - 420745331 q^{20} - 544450005 q^{21} - 1844479318 q^{22} - 399937087 q^{23} + 534588093 q^{24} + 8617402914 q^{25} - 499433574 q^{26} - 12397455648 q^{27} + 12648993070 q^{28} - 225284149 q^{29} - 4479950673 q^{30} + 9454638761 q^{31} + 11648295118 q^{32} - 292216734 q^{33} + 39279537096 q^{34} + 17608963479 q^{35} + 73962769734 q^{36} + 37463929597 q^{37} + 65554547351 q^{38} - 6861119094 q^{39} + 144414252742 q^{40} + 22650227173 q^{41} + 26512554123 q^{42} + 96253617602 q^{43} - 132186868002 q^{44} + 1188302076 q^{45} + 327853892309 q^{46} + 239981844027 q^{47} - 535725905994 q^{48} + 286262776863 q^{49} - 671840368399 q^{50} - 166294984257 q^{51} - 952971648498 q^{52} - 47446514136 q^{53} - 4649045868 q^{54} - 474454082548 q^{55} - 1167728875984 q^{56} - 382166407395 q^{57} + 547596592762 q^{58} + 1349777076512 q^{59} + 306723346299 q^{60} + 661498471821 q^{61} + 555821093242 q^{62} + 396904053645 q^{63} + 3522679273173 q^{64} + 1269187682756 q^{65} + 1344625422822 q^{66} + 2838711491386 q^{67} + 1395029358261 q^{68} + 291554136423 q^{69} + 5677102514386 q^{70} + 1912914480734 q^{71} - 389714719797 q^{72} + 2403595726697 q^{73} - 742136417562 q^{74} - 6282086724306 q^{75} - 4020161987188 q^{76} - 4878303804101 q^{77} + 364087075446 q^{78} - 1705546365970 q^{79} - 4347383766449 q^{80} + 9037745167392 q^{81} - 6943720239935 q^{82} - 2549647313691 q^{83} - 9221115948030 q^{84} - 8455706309615 q^{85} - 33993832711012 q^{86} + 164232144621 q^{87} - 42970239360587 q^{88} - 17356719361241 q^{89} + 3265884040617 q^{90} - 30776775043291 q^{91} - 13184590997480 q^{92} - 6892431656769 q^{93} - 35604563339520 q^{94} + 219501126195 q^{95} - 8491607141022 q^{96} - 4427131429152 q^{97} - 32707332037060 q^{98} + 213025999086 q^{99}+O(q^{100}) \) 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9 + 6145337 * q^10 + 400846 * q^11 - 101457846 * q^12 + 9411686 * q^13 - 36368387 * q^14 - 1630044 * q^15 + 734877786 * q^16 + 228113833 * q^17 + 6377292 * q^18 + 524233755 * q^19 - 420745331 * q^20 - 544450005 * q^21 - 1844479318 * q^22 - 399937087 * q^23 + 534588093 * q^24 + 8617402914 * q^25 - 499433574 * q^26 - 12397455648 * q^27 + 12648993070 * q^28 - 225284149 * q^29 - 4479950673 * q^30 + 9454638761 * q^31 + 11648295118 * q^32 - 292216734 * q^33 + 39279537096 * q^34 + 17608963479 * q^35 + 73962769734 * q^36 + 37463929597 * q^37 + 65554547351 * q^38 - 6861119094 * q^39 + 144414252742 * q^40 + 22650227173 * q^41 + 26512554123 * q^42 + 96253617602 * q^43 - 132186868002 * q^44 + 1188302076 * q^45 + 327853892309 * q^46 + 239981844027 * q^47 - 535725905994 * q^48 + 286262776863 * q^49 - 671840368399 * q^50 - 166294984257 * q^51 - 952971648498 * q^52 - 47446514136 * q^53 - 4649045868 * q^54 - 474454082548 * q^55 - 1167728875984 * q^56 - 382166407395 * q^57 + 547596592762 * q^58 + 1349777076512 * q^59 + 306723346299 * q^60 + 661498471821 * q^61 + 555821093242 * q^62 + 396904053645 * q^63 + 3522679273173 * q^64 + 1269187682756 * q^65 + 1344625422822 * q^66 + 2838711491386 * q^67 + 1395029358261 * q^68 + 291554136423 * q^69 + 5677102514386 * q^70 + 1912914480734 * q^71 - 389714719797 * q^72 + 2403595726697 * q^73 - 742136417562 * q^74 - 6282086724306 * q^75 - 4020161987188 * q^76 - 4878303804101 * q^77 + 364087075446 * q^78 - 1705546365970 * q^79 - 4347383766449 * q^80 + 9037745167392 * q^81 - 6943720239935 * q^82 - 2549647313691 * q^83 - 9221115948030 * q^84 - 8455706309615 * q^85 - 33993832711012 * q^86 + 164232144621 * q^87 - 42970239360587 * q^88 - 17356719361241 * q^89 + 3265884040617 * q^90 - 30776775043291 * q^91 - 13184590997480 * q^92 - 6892431656769 * q^93 - 35604563339520 * q^94 + 219501126195 * q^95 - 8491607141022 * q^96 - 4427131429152 * q^97 - 32707332037060 * q^98 + 213025999086 * q^99

Introduction

L-functions

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