LMFDB - Embedded newform 177.10.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,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, 10, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
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:	$91.1613430010$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-36.0452 q^{2} -81.0000 q^{3} +787.255 q^{4} -242.182 q^{5} +2919.66 q^{6} +7611.77 q^{7} -9921.60 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-36.0452 q^{2} -81.0000 q^{3} +787.255 q^{4} -242.182 q^{5} +2919.66 q^{6} +7611.77 q^{7} -9921.60 q^{8} +6561.00 q^{9} +8729.49 q^{10} +17094.0 q^{11} -63767.6 q^{12} +68268.9 q^{13} -274368. q^{14} +19616.7 q^{15} -45448.5 q^{16} +321907. q^{17} -236492. q^{18} -803167. q^{19} -190659. q^{20} -616553. q^{21} -616155. q^{22} +995598. q^{23} +803650. q^{24} -1.89447e6 q^{25} -2.46076e6 q^{26} -531441. q^{27} +5.99240e6 q^{28} -4.98426e6 q^{29} -707089. q^{30} -3.39004e6 q^{31} +6.71806e6 q^{32} -1.38461e6 q^{33} -1.16032e7 q^{34} -1.84343e6 q^{35} +5.16518e6 q^{36} +2.66106e6 q^{37} +2.89503e7 q^{38} -5.52978e6 q^{39} +2.40283e6 q^{40} +2.95240e6 q^{41} +2.22238e7 q^{42} -4.26661e7 q^{43} +1.34573e7 q^{44} -1.58896e6 q^{45} -3.58865e7 q^{46} +2.32930e7 q^{47} +3.68132e6 q^{48} +1.75854e7 q^{49} +6.82866e7 q^{50} -2.60745e7 q^{51} +5.37450e7 q^{52} +6.00847e7 q^{53} +1.91559e7 q^{54} -4.13985e6 q^{55} -7.55210e7 q^{56} +6.50565e7 q^{57} +1.79658e8 q^{58} -1.21174e7 q^{59} +1.54434e7 q^{60} -7.21065e6 q^{61} +1.22195e8 q^{62} +4.99408e7 q^{63} -2.18884e8 q^{64} -1.65335e7 q^{65} +4.99085e7 q^{66} +2.28589e8 q^{67} +2.53423e8 q^{68} -8.06434e7 q^{69} +6.64469e7 q^{70} -5.89735e7 q^{71} -6.50956e7 q^{72} +1.06671e8 q^{73} -9.59183e7 q^{74} +1.53452e8 q^{75} -6.32297e8 q^{76} +1.30115e8 q^{77} +1.99322e8 q^{78} -3.06693e7 q^{79} +1.10068e7 q^{80} +4.30467e7 q^{81} -1.06420e8 q^{82} +2.84892e8 q^{83} -4.85384e8 q^{84} -7.79601e7 q^{85} +1.53791e9 q^{86} +4.03725e8 q^{87} -1.69599e8 q^{88} +7.19999e7 q^{89} +5.72742e7 q^{90} +5.19647e8 q^{91} +7.83789e8 q^{92} +2.74593e8 q^{93} -8.39599e8 q^{94} +1.94513e8 q^{95} -5.44163e8 q^{96} -8.66357e8 q^{97} -6.33870e8 q^{98} +1.12153e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * 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 $

$2$	−36.0452	−1.59299	−0.796493	−	0.604647i	$-0.793314\pi$
$2$	−36.0452	−1.59299	−0.796493	+	0.604647i	$0.793314\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	787.255	1.53761
$5$	−242.182	−0.173291	−0.0866456	−	0.996239i	$-0.527615\pi$
$5$	−242.182	−0.173291	−0.0866456	+	0.996239i	$0.527615\pi$
$6$	2919.66	0.919711
$7$	7611.77	1.19824	0.599121	−	0.800659i	$-0.295517\pi$
$7$	7611.77	1.19824	0.599121	+	0.800659i	$0.295517\pi$
$8$	−9921.60	−0.856401
$9$	6561.00	0.333333
$10$	8729.49	0.276051
$11$	17094.0	0.352027	0.176013	−	0.984388i	$-0.443680\pi$
$11$	17094.0	0.352027	0.176013	+	0.984388i	$0.443680\pi$
$12$	−63767.6	−0.887738
$13$	68268.9	0.662945	0.331473	−	0.943465i	$-0.392455\pi$
$13$	68268.9	0.662945	0.331473	+	0.943465i	$0.392455\pi$
$14$	−274368.	−1.90878
$15$	19616.7	0.100050
$16$	−45448.5	−0.173372
$17$	321907.	0.934783	0.467391	−	0.884051i	$-0.345194\pi$
$17$	321907.	0.934783	0.467391	+	0.884051i	$0.345194\pi$
$18$	−236492.	−0.530996
$19$	−803167.	−1.41389	−0.706943	−	0.707270i	$-0.749926\pi$
$19$	−803167.	−1.41389	−0.706943	+	0.707270i	$0.749926\pi$
$20$	−190659.	−0.266454
$21$	−616553.	−0.691805
$22$	−616155.	−0.560774
$23$	995598.	0.741837	0.370919	−	0.928665i	$-0.379043\pi$
$23$	995598.	0.741837	0.370919	+	0.928665i	$0.379043\pi$
$24$	803650.	0.494443
$25$	−1.89447e6	−0.969970
$26$	−2.46076e6	−1.05606
$27$	−531441.	−0.192450
$28$	5.99240e6	1.84242
$29$	−4.98426e6	−1.30861	−0.654304	−	0.756232i	$-0.727038\pi$
$29$	−4.98426e6	−1.30861	−0.654304	+	0.756232i	$0.727038\pi$
$30$	−707089.	−0.159378
$31$	−3.39004e6	−0.659291	−0.329645	−	0.944105i	$-0.606929\pi$
$31$	−3.39004e6	−0.659291	−0.329645	+	0.944105i	$0.606929\pi$
$32$	6.71806e6	1.13258
$33$	−1.38461e6	−0.203243
$34$	−1.16032e7	−1.48910
$35$	−1.84343e6	−0.207645
$36$	5.16518e6	0.512536
$37$	2.66106e6	0.233424	0.116712	−	0.993166i	$-0.462764\pi$
$37$	2.66106e6	0.233424	0.116712	+	0.993166i	$0.462764\pi$
$38$	2.89503e7	2.25230
$39$	−5.52978e6	−0.382752
$40$	2.40283e6	0.148407
$41$	2.95240e6	0.163173	0.0815865	−	0.996666i	$-0.474001\pi$
$41$	2.95240e6	0.163173	0.0815865	+	0.996666i	$0.474001\pi$
$42$	2.22238e7	1.10204
$43$	−4.26661e7	−1.90316	−0.951580	−	0.307401i	$-0.900541\pi$
$43$	−4.26661e7	−1.90316	−0.951580	+	0.307401i	$0.900541\pi$
$44$	1.34573e7	0.541279
$45$	−1.58896e6	−0.0577638
$46$	−3.58865e7	−1.18174
$47$	2.32930e7	0.696281	0.348141	−	0.937442i	$-0.386813\pi$
$47$	2.32930e7	0.696281	0.348141	+	0.937442i	$0.386813\pi$
$48$	3.68132e6	0.100096
$49$	1.75854e7	0.435783
$50$	6.82866e7	1.54515
$51$	−2.60745e7	−0.539697
$52$	5.37450e7	1.01935
$53$	6.00847e7	1.04598	0.522989	−	0.852340i	$-0.324817\pi$
$53$	6.00847e7	1.04598	0.522989	+	0.852340i	$0.324817\pi$
$54$	1.91559e7	0.306570
$55$	−4.13985e6	−0.0610031
$56$	−7.55210e7	−1.02617
$57$	6.50565e7	0.816308
$58$	1.79658e8	2.08459
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	1.54434e7	0.153837
$61$	−7.21065e6	−0.0666791	−0.0333396	−	0.999444i	$-0.510614\pi$
$61$	−7.21065e6	−0.0666791	−0.0333396	+	0.999444i	$0.510614\pi$
$62$	1.22195e8	1.05024
$63$	4.99408e7	0.399414
$64$	−2.18884e8	−1.63081
$65$	−1.65335e7	−0.114883
$66$	4.99085e7	0.323763
$67$	2.28589e8	1.38586	0.692929	−	0.721006i	$-0.256320\pi$
$67$	2.28589e8	1.38586	0.692929	+	0.721006i	$0.256320\pi$
$68$	2.53423e8	1.43733
$69$	−8.06434e7	−0.428300
$70$	6.64469e7	0.330775
$71$	−5.89735e7	−0.275419	−0.137710	−	0.990473i	$-0.543974\pi$
$71$	−5.89735e7	−0.275419	−0.137710	+	0.990473i	$0.543974\pi$
$72$	−6.50956e7	−0.285467
$73$	1.06671e8	0.439636	0.219818	−	0.975541i	$-0.429454\pi$
$73$	1.06671e8	0.439636	0.219818	+	0.975541i	$0.429454\pi$
$74$	−9.59183e7	−0.371842
$75$	1.53452e8	0.560013
$76$	−6.32297e8	−2.17400
$77$	1.30115e8	0.421813
$78$	1.99322e8	0.609718
$79$	−3.06693e7	−0.0885894	−0.0442947	−	0.999019i	$-0.514104\pi$
$79$	−3.06693e7	−0.0885894	−0.0442947	+	0.999019i	$0.514104\pi$
$80$	1.10068e7	0.0300439
$81$	4.30467e7	0.111111
$82$	−1.06420e8	−0.259932
$83$	2.84892e8	0.658913	0.329457	−	0.944171i	$-0.393134\pi$
$83$	2.84892e8	0.658913	0.329457	+	0.944171i	$0.393134\pi$
$84$	−4.85384e8	−1.06372
$85$	−7.79601e7	−0.161990
$86$	1.53791e9	3.03171
$87$	4.03725e8	0.755525
$88$	−1.69599e8	−0.301476
$89$	7.19999e7	0.121640	0.0608201	−	0.998149i	$-0.480628\pi$
$89$	7.19999e7	0.121640	0.0608201	+	0.998149i	$0.480628\pi$
$90$	5.72742e7	0.0920169
$91$	5.19647e8	0.794369
$92$	7.83789e8	1.14065
$93$	2.74593e8	0.380642
$94$	−8.39599e8	−1.10917
$95$	1.94513e8	0.245014
$96$	−5.44163e8	−0.653895
$97$	−8.66357e8	−0.993629	−0.496814	−	0.867857i	$-0.665497\pi$
$97$	−8.66357e8	−0.993629	−0.496814	+	0.867857i	$0.665497\pi$
$98$	−6.33870e8	−0.694197
$99$	1.12153e8	0.117342
$100$	−1.49143e9	−1.49143
$101$	−1.21040e9	−1.15740	−0.578698	−	0.815542i	$-0.696439\pi$
$101$	−1.21040e9	−1.15740	−0.578698	+	0.815542i	$0.696439\pi$
$102$	9.39860e8	0.859730
$103$	−2.40395e8	−0.210454	−0.105227	−	0.994448i	$-0.533557\pi$
$103$	−2.40395e8	−0.210454	−0.105227	+	0.994448i	$0.533557\pi$
$104$	−6.77337e8	−0.567747
$105$	1.49318e8	0.119884
$106$	−2.16576e9	−1.66623
$107$	−2.13921e9	−1.57771	−0.788854	−	0.614581i	$-0.789325\pi$
$107$	−2.13921e9	−1.57771	−0.788854	+	0.614581i	$0.789325\pi$
$108$	−4.18379e8	−0.295913
$109$	1.75721e9	1.19235	0.596175	−	0.802855i	$-0.296687\pi$
$109$	1.75721e9	1.19235	0.596175	+	0.802855i	$0.296687\pi$
$110$	1.49222e8	0.0971772
$111$	−2.15546e8	−0.134768
$112$	−3.45943e8	−0.207742
$113$	−2.26510e9	−1.30688	−0.653439	−	0.756979i	$-0.726674\pi$
$113$	−2.26510e9	−1.30688	−0.653439	+	0.756979i	$0.726674\pi$
$114$	−2.34497e9	−1.30037
$115$	−2.41116e8	−0.128554
$116$	−3.92388e9	−2.01212
$117$	4.47912e8	0.220982
$118$	4.36772e8	0.207389
$119$	2.45028e9	1.12010
$120$	−1.94629e8	−0.0856827
$121$	−2.06574e9	−0.876077
$122$	2.59909e8	0.106219
$123$	−2.39145e8	−0.0942080
$124$	−2.66882e9	−1.01373
$125$	9.31819e8	0.341379
$126$	−1.80013e9	−0.636261
$127$	−5.19361e9	−1.77155	−0.885774	−	0.464117i	$-0.846372\pi$
$127$	−5.19361e9	−1.77155	−0.885774	+	0.464117i	$0.846372\pi$
$128$	4.45007e9	1.46528
$129$	3.45596e9	1.09879
$130$	5.95952e8	0.183006
$131$	−4.53077e9	−1.34416	−0.672081	−	0.740478i	$-0.734599\pi$
$131$	−4.53077e9	−1.34416	−0.672081	+	0.740478i	$0.734599\pi$
$132$	−1.09004e9	−0.312507
$133$	−6.11352e9	−1.69418
$134$	−8.23953e9	−2.20765
$135$	1.28705e8	0.0333499
$136$	−3.19384e9	−0.800548
$137$	5.15763e9	1.25086	0.625428	−	0.780282i	$-0.284924\pi$
$137$	5.15763e9	1.25086	0.625428	+	0.780282i	$0.284924\pi$
$138$	2.90681e9	0.682276
$139$	1.20180e9	0.273064	0.136532	−	0.990636i	$-0.456404\pi$
$139$	1.20180e9	0.273064	0.136532	+	0.990636i	$0.456404\pi$
$140$	−1.45125e9	−0.319276
$141$	−1.88673e9	−0.401998
$142$	2.12571e9	0.438739
$143$	1.16699e9	0.233374
$144$	−2.98187e8	−0.0577907
$145$	1.20710e9	0.226770
$146$	−3.84497e9	−0.700334
$147$	−1.42442e9	−0.251600
$148$	2.09493e9	0.358915
$149$	7.95137e9	1.32161	0.660806	−	0.750557i	$-0.270215\pi$
$149$	7.95137e9	1.32161	0.660806	+	0.750557i	$0.270215\pi$
$150$	−5.53122e9	−0.892093
$151$	−4.03039e9	−0.630886	−0.315443	−	0.948945i	$-0.602153\pi$
$151$	−4.03039e9	−0.630886	−0.315443	+	0.948945i	$0.602153\pi$
$152$	7.96870e9	1.21085
$153$	2.11203e9	0.311594
$154$	−4.69003e9	−0.671943
$155$	8.21006e8	0.114249
$156$	−4.35334e9	−0.588522
$157$	4.48151e9	0.588675	0.294338	−	0.955702i	$-0.404901\pi$
$157$	4.48151e9	0.588675	0.294338	+	0.955702i	$0.404901\pi$
$158$	1.10548e9	0.141122
$159$	−4.86686e9	−0.603895
$160$	−1.62699e9	−0.196266
$161$	7.57826e9	0.888901
$162$	−1.55163e9	−0.176999
$163$	1.22081e10	1.35458	0.677288	−	0.735718i	$-0.263155\pi$
$163$	1.22081e10	1.35458	0.677288	+	0.735718i	$0.263155\pi$
$164$	2.32429e9	0.250896
$165$	3.35328e8	0.0352202
$166$	−1.02690e10	−1.04964
$167$	1.46186e9	0.145439	0.0727197	−	0.997352i	$-0.476832\pi$
$167$	1.46186e9	0.145439	0.0727197	+	0.997352i	$0.476832\pi$
$168$	6.11720e9	0.592462
$169$	−5.94386e9	−0.560504
$170$	2.81009e9	0.258047
$171$	−5.26958e9	−0.471296
$172$	−3.35891e10	−2.92631
$173$	1.06740e10	0.905982	0.452991	−	0.891515i	$-0.350357\pi$
$173$	1.06740e10	0.905982	0.452991	+	0.891515i	$0.350357\pi$
$174$	−1.45523e10	−1.20354
$175$	−1.44203e10	−1.16226
$176$	−7.76894e8	−0.0610316
$177$	9.81506e8	0.0751646
$178$	−2.59525e9	−0.193771
$179$	−1.20853e9	−0.0879872	−0.0439936	−	0.999032i	$-0.514008\pi$
$179$	−1.20853e9	−0.0879872	−0.0439936	+	0.999032i	$0.514008\pi$
$180$	−1.25091e9	−0.0888179
$181$	−1.40693e9	−0.0974358	−0.0487179	−	0.998813i	$-0.515514\pi$
$181$	−1.40693e9	−0.0974358	−0.0487179	+	0.998813i	$0.515514\pi$
$182$	−1.87308e10	−1.26542
$183$	5.84062e8	0.0384972
$184$	−9.87793e9	−0.635310
$185$	−6.44460e8	−0.0404504
$186$	−9.89776e9	−0.606357
$187$	5.50267e9	0.329068
$188$	1.83375e10	1.07061
$189$	−4.04521e9	−0.230602
$190$	−7.01124e9	−0.390304
$191$	−1.01040e10	−0.549343	−0.274672	−	0.961538i	$-0.588569\pi$
$191$	−1.01040e10	−0.549343	−0.274672	+	0.961538i	$0.588569\pi$
$192$	1.77296e10	0.941550
$193$	−3.13082e10	−1.62424	−0.812120	−	0.583490i	$-0.801687\pi$
$193$	−3.13082e10	−1.62424	−0.812120	+	0.583490i	$0.801687\pi$
$194$	3.12280e10	1.58284
$195$	1.33921e9	0.0663275
$196$	1.38442e10	0.670063
$197$	−4.34991e9	−0.205770	−0.102885	−	0.994693i	$-0.532807\pi$
$197$	−4.34991e9	−0.205770	−0.102885	+	0.994693i	$0.532807\pi$
$198$	−4.04259e9	−0.186925
$199$	−2.18718e10	−0.988657	−0.494328	−	0.869275i	$-0.664586\pi$
$199$	−2.18718e10	−0.988657	−0.494328	+	0.869275i	$0.664586\pi$
$200$	1.87962e10	0.830683
$201$	−1.85157e10	−0.800125
$202$	4.36290e10	1.84372
$203$	−3.79390e10	−1.56803
$204$	−2.05273e10	−0.829842
$205$	−7.15019e8	−0.0282765
$206$	8.66508e9	0.335251
$207$	6.53212e9	0.247279
$208$	−3.10272e9	−0.114936
$209$	−1.37293e10	−0.497726
$210$	−5.38220e9	−0.190973
$211$	4.42064e10	1.53537	0.767686	−	0.640826i	$-0.221408\pi$
$211$	4.42064e10	1.53537	0.767686	+	0.640826i	$0.221408\pi$
$212$	4.73019e10	1.60830
$213$	4.77685e9	0.159013
$214$	7.71082e10	2.51327
$215$	1.03330e10	0.329801
$216$	5.27275e9	0.164814
$217$	−2.58042e10	−0.789990
$218$	−6.33388e10	−1.89940
$219$	−8.64034e9	−0.253824
$220$	−3.25911e9	−0.0937989
$221$	2.19762e10	0.619710
$222$	7.76938e9	0.214683
$223$	5.04420e10	1.36590	0.682952	−	0.730463i	$-0.260696\pi$
$223$	5.04420e10	1.36590	0.682952	+	0.730463i	$0.260696\pi$
$224$	5.11363e10	1.35710
$225$	−1.24296e10	−0.323323
$226$	8.16461e10	2.08184
$227$	−1.49660e10	−0.374101	−0.187050	−	0.982350i	$-0.559893\pi$
$227$	−1.49660e10	−0.374101	−0.187050	+	0.982350i	$0.559893\pi$
$228$	5.12161e10	1.25516
$229$	1.63674e10	0.393297	0.196648	−	0.980474i	$-0.436994\pi$
$229$	1.63674e10	0.393297	0.196648	+	0.980474i	$0.436994\pi$
$230$	8.69106e9	0.204785
$231$	−1.05393e10	−0.243534
$232$	4.94518e10	1.12069
$233$	2.72820e10	0.606421	0.303211	−	0.952924i	$-0.401941\pi$
$233$	2.72820e10	0.606421	0.303211	+	0.952924i	$0.401941\pi$
$234$	−1.61451e10	−0.352021
$235$	−5.64114e9	−0.120659
$236$	−9.53945e9	−0.200179
$237$	2.48421e9	0.0511471
$238$	−8.83209e10	−1.78430
$239$	3.93459e10	0.780026	0.390013	−	0.920809i	$-0.372471\pi$
$239$	3.93459e10	0.780026	0.390013	+	0.920809i	$0.372471\pi$
$240$	−8.91550e8	−0.0173458
$241$	−8.35801e10	−1.59598	−0.797988	−	0.602673i	$-0.794102\pi$
$241$	−8.35801e10	−1.59598	−0.797988	+	0.602673i	$0.794102\pi$
$242$	7.44601e10	1.39558
$243$	−3.48678e9	−0.0641500
$244$	−5.67662e9	−0.102526
$245$	−4.25887e9	−0.0755174
$246$	8.62001e9	0.150072
$247$	−5.48313e10	−0.937330
$248$	3.36346e10	0.564617
$249$	−2.30762e10	−0.380424
$250$	−3.35876e10	−0.543812
$251$	8.76618e10	1.39405	0.697025	−	0.717046i	$-0.254506\pi$
$251$	8.76618e10	1.39405	0.697025	+	0.717046i	$0.254506\pi$
$252$	3.93161e10	0.614142
$253$	1.70187e10	0.261147
$254$	1.87205e11	2.82205
$255$	6.31477e9	0.0935248
$256$	−4.83348e10	−0.703364
$257$	−6.46345e10	−0.924198	−0.462099	−	0.886828i	$-0.652904\pi$
$257$	−6.46345e10	−0.924198	−0.462099	+	0.886828i	$0.652904\pi$
$258$	−1.24571e11	−1.75036
$259$	2.02554e10	0.279699
$260$	−1.30161e10	−0.176644
$261$	−3.27017e10	−0.436203
$262$	1.63313e11	2.14123
$263$	8.56627e10	1.10406	0.552028	−	0.833826i	$-0.313854\pi$
$263$	8.56627e10	1.10406	0.552028	+	0.833826i	$0.313854\pi$
$264$	1.37376e10	0.174057
$265$	−1.45514e10	−0.181259
$266$	2.20363e11	2.69880
$267$	−5.83199e9	−0.0702290
$268$	1.79958e11	2.13090
$269$	1.25389e11	1.46007	0.730034	−	0.683410i	$-0.239504\pi$
$269$	1.25389e11	1.46007	0.730034	+	0.683410i	$0.239504\pi$
$270$	−4.63921e9	−0.0531260
$271$	−2.38301e10	−0.268389	−0.134194	−	0.990955i	$-0.542845\pi$
$271$	−2.38301e10	−0.268389	−0.134194	+	0.990955i	$0.542845\pi$
$272$	−1.46302e10	−0.162065
$273$	−4.20914e10	−0.458629
$274$	−1.85908e11	−1.99260
$275$	−3.23840e10	−0.341455
$276$	−6.34869e10	−0.658557
$277$	−1.00357e11	−1.02421	−0.512103	−	0.858924i	$-0.671133\pi$
$277$	−1.00357e11	−1.02421	−0.512103	+	0.858924i	$0.671133\pi$
$278$	−4.33189e10	−0.434987
$279$	−2.22420e10	−0.219764
$280$	1.82898e10	0.177827
$281$	−1.79252e11	−1.71508	−0.857542	−	0.514414i	$-0.828010\pi$
$281$	−1.79252e11	−1.71508	−0.857542	+	0.514414i	$0.828010\pi$
$282$	6.80075e10	0.640378
$283$	−2.07641e11	−1.92430	−0.962151	−	0.272517i	$-0.912144\pi$
$283$	−2.07641e11	−1.92430	−0.962151	+	0.272517i	$0.912144\pi$
$284$	−4.64272e10	−0.423486
$285$	−1.57555e10	−0.141459
$286$	−4.20642e10	−0.371762
$287$	2.24730e10	0.195521
$288$	4.40772e10	0.377527
$289$	−1.49636e10	−0.126181
$290$	−4.35100e10	−0.361242
$291$	7.01749e10	0.573672
$292$	8.39771e10	0.675987
$293$	−1.22646e11	−0.972182	−0.486091	−	0.873908i	$-0.661578\pi$
$293$	−1.22646e11	−0.972182	−0.486091	+	0.873908i	$0.661578\pi$
$294$	5.13435e10	0.400795
$295$	2.93461e9	0.0225606
$296$	−2.64020e10	−0.199905
$297$	−9.08443e9	−0.0677476
$298$	−2.86608e11	−2.10531
$299$	6.79684e10	0.491798
$300$	1.20806e11	0.861079
$301$	−3.24765e11	−2.28045
$302$	1.45276e11	1.00499
$303$	9.80422e10	0.668223
$304$	3.65027e10	0.245129
$305$	1.74629e9	0.0115549
$306$	−7.61286e10	−0.496365
$307$	1.93309e11	1.24202	0.621012	−	0.783801i	$-0.286722\pi$
$307$	1.93309e11	1.24202	0.621012	+	0.783801i	$0.286722\pi$
$308$	1.02434e11	0.648583
$309$	1.94720e10	0.121506
$310$	−2.95933e10	−0.181998
$311$	−1.41995e9	−0.00860702	−0.00430351	−	0.999991i	$-0.501370\pi$
$311$	−1.41995e9	−0.00860702	−0.00430351	+	0.999991i	$0.501370\pi$
$312$	5.48643e10	0.327789
$313$	−9.72842e9	−0.0572918	−0.0286459	−	0.999590i	$-0.509120\pi$
$313$	−9.72842e9	−0.0572918	−0.0286459	+	0.999590i	$0.509120\pi$
$314$	−1.61537e11	−0.937752
$315$	−1.20948e10	−0.0692149
$316$	−2.41446e10	−0.136216
$317$	−2.46412e10	−0.137055	−0.0685276	−	0.997649i	$-0.521830\pi$
$317$	−2.46412e10	−0.137055	−0.0685276	+	0.997649i	$0.521830\pi$
$318$	1.75427e11	0.961997
$319$	−8.52007e10	−0.460665
$320$	5.30097e10	0.282606
$321$	1.73276e11	0.910890
$322$	−2.73160e11	−1.41601
$323$	−2.58545e11	−1.32168
$324$	3.38887e10	0.170845
$325$	−1.29334e11	−0.643037
$326$	−4.40043e11	−2.15782
$327$	−1.42334e11	−0.688403
$328$	−2.92926e10	−0.139741
$329$	1.77301e11	0.834313
$330$	−1.20869e10	−0.0561053
$331$	−9.23716e10	−0.422973	−0.211486	−	0.977381i	$-0.567830\pi$
$331$	−9.23716e10	−0.422973	−0.211486	+	0.977381i	$0.567830\pi$
$332$	2.24282e11	1.01315
$333$	1.74592e10	0.0778082
$334$	−5.26931e10	−0.231683
$335$	−5.53601e10	−0.240157
$336$	2.80214e10	0.119940
$337$	−3.30308e11	−1.39503	−0.697516	−	0.716569i	$-0.745711\pi$
$337$	−3.30308e11	−1.39503	−0.697516	+	0.716569i	$0.745711\pi$
$338$	2.14247e11	0.892875
$339$	1.83473e11	0.754526
$340$	−6.13745e10	−0.249076
$341$	−5.79492e10	−0.232088
$342$	1.89943e11	0.750768
$343$	−1.73306e11	−0.676068
$344$	4.23317e11	1.62987
$345$	1.95304e10	0.0742207
$346$	−3.84746e11	−1.44322
$347$	−1.83796e10	−0.0680538	−0.0340269	−	0.999421i	$-0.510833\pi$
$347$	−1.83796e10	−0.0680538	−0.0340269	+	0.999421i	$0.510833\pi$
$348$	3.17834e11	1.16170
$349$	3.63360e11	1.31106	0.655530	−	0.755169i	$-0.272445\pi$
$349$	3.63360e11	1.31106	0.655530	+	0.755169i	$0.272445\pi$
$350$	5.19782e11	1.85146
$351$	−3.62809e10	−0.127584
$352$	1.14838e11	0.398698
$353$	−1.44721e11	−0.496073	−0.248036	−	0.968751i	$-0.579785\pi$
$353$	−1.44721e11	−0.496073	−0.248036	+	0.968751i	$0.579785\pi$
$354$	−3.53786e10	−0.119736
$355$	1.42823e10	0.0477277
$356$	5.66823e10	0.187035
$357$	−1.98473e11	−0.646688
$358$	4.35617e10	0.140162
$359$	−4.51872e11	−1.43579	−0.717894	−	0.696152i	$-0.754894\pi$
$359$	−4.51872e11	−1.43579	−0.717894	+	0.696152i	$0.754894\pi$
$360$	1.57650e10	0.0494689
$361$	3.22390e11	0.999076
$362$	5.07130e10	0.155214
$363$	1.67325e11	0.505803
$364$	4.09095e11	1.22143
$365$	−2.58337e10	−0.0761850
$366$	−2.10526e10	−0.0613256
$367$	−1.99239e11	−0.573294	−0.286647	−	0.958036i	$-0.592541\pi$
$367$	−1.99239e11	−0.573294	−0.286647	+	0.958036i	$0.592541\pi$
$368$	−4.52484e10	−0.128614
$369$	1.93707e10	0.0543910
$370$	2.32297e10	0.0644370
$371$	4.57351e11	1.25333
$372$	2.16175e11	0.585277
$373$	4.88966e11	1.30794	0.653972	−	0.756519i	$-0.273101\pi$
$373$	4.88966e11	1.30794	0.653972	+	0.756519i	$0.273101\pi$
$374$	−1.98345e11	−0.524202
$375$	−7.54773e10	−0.197095
$376$	−2.31104e11	−0.596295
$377$	−3.40270e11	−0.867535
$378$	1.45810e11	0.367346
$379$	2.52680e11	0.629063	0.314532	−	0.949247i	$-0.398153\pi$
$379$	2.52680e11	0.629063	0.314532	+	0.949247i	$0.398153\pi$
$380$	1.53131e11	0.376736
$381$	4.20683e11	1.02280
$382$	3.64201e11	0.875096
$383$	−7.44311e11	−1.76750	−0.883752	−	0.467956i	$-0.844990\pi$
$383$	−7.44311e11	−1.76750	−0.883752	+	0.467956i	$0.844990\pi$
$384$	−3.60455e11	−0.845982
$385$	−3.15116e10	−0.0730965
$386$	1.12851e12	2.58739
$387$	−2.79933e11	−0.634387
$388$	−6.82044e11	−1.52781
$389$	−6.06698e11	−1.34338	−0.671691	−	0.740831i	$-0.734432\pi$
$389$	−6.06698e11	−1.34338	−0.671691	+	0.740831i	$0.734432\pi$
$390$	−4.82721e10	−0.105659
$391$	3.20490e11	0.693457
$392$	−1.74476e11	−0.373205
$393$	3.66993e11	0.776052
$394$	1.56793e11	0.327789
$395$	7.42755e9	0.0153518
$396$	8.82933e10	0.180426
$397$	−1.25702e11	−0.253971	−0.126985	−	0.991905i	$-0.540530\pi$
$397$	−1.25702e11	−0.253971	−0.126985	+	0.991905i	$0.540530\pi$
$398$	7.88373e11	1.57492
$399$	4.95195e11	0.978134
$400$	8.61009e10	0.168166
$401$	4.96752e11	0.959378	0.479689	−	0.877439i	$-0.340750\pi$
$401$	4.96752e11	0.959378	0.479689	+	0.877439i	$0.340750\pi$
$402$	6.67402e11	1.27459
$403$	−2.31434e11	−0.437074
$404$	−9.52891e11	−1.77962
$405$	−1.04251e10	−0.0192546
$406$	1.36752e12	2.49785
$407$	4.54880e10	0.0821716
$408$	2.58701e11	0.462197
$409$	−8.77033e11	−1.54975	−0.774874	−	0.632116i	$-0.782187\pi$
$409$	−8.77033e11	−1.54975	−0.774874	+	0.632116i	$0.782187\pi$
$410$	2.57730e10	0.0450440
$411$	−4.17768e11	−0.722182
$412$	−1.89252e11	−0.323596
$413$	−9.22346e10	−0.155998
$414$	−2.35451e11	−0.393912
$415$	−6.89956e10	−0.114184
$416$	4.58634e11	0.750839
$417$	−9.73455e10	−0.157653
$418$	4.94875e11	0.792871
$419$	−1.30070e11	−0.206165	−0.103083	−	0.994673i	$-0.532871\pi$
$419$	−1.30070e11	−0.206165	−0.103083	+	0.994673i	$0.532871\pi$
$420$	1.17551e11	0.184334
$421$	−9.55911e11	−1.48302	−0.741512	−	0.670940i	$-0.765891\pi$
$421$	−9.55911e11	−1.48302	−0.741512	+	0.670940i	$0.765891\pi$
$422$	−1.59343e12	−2.44583
$423$	1.52825e11	0.232094
$424$	−5.96136e11	−0.895775
$425$	−6.09845e11	−0.906711
$426$	−1.72182e11	−0.253306
$427$	−5.48858e10	−0.0798977
$428$	−1.68410e12	−2.42589
$429$	−9.45258e10	−0.134739
$430$	−3.72454e11	−0.525369
$431$	5.09635e11	0.711396	0.355698	−	0.934601i	$-0.384243\pi$
$431$	5.09635e11	0.711396	0.355698	+	0.934601i	$0.384243\pi$
$432$	2.41532e10	0.0333655
$433$	−8.04193e10	−0.109942	−0.0549712	−	0.998488i	$-0.517507\pi$
$433$	−8.04193e10	−0.109942	−0.0549712	+	0.998488i	$0.517507\pi$
$434$	9.30117e11	1.25844
$435$	−9.77749e10	−0.130926
$436$	1.38337e12	1.83336
$437$	−7.99631e11	−1.04887
$438$	3.11443e11	0.404338
$439$	1.22947e11	0.157989	0.0789945	−	0.996875i	$-0.474829\pi$
$439$	1.22947e11	0.157989	0.0789945	+	0.996875i	$0.474829\pi$
$440$	4.10739e10	0.0522431
$441$	1.15378e11	0.145261
$442$	−7.92138e11	−0.987189
$443$	−9.69820e11	−1.19639	−0.598197	−	0.801349i	$-0.704116\pi$
$443$	−9.69820e11	−1.19639	−0.598197	+	0.801349i	$0.704116\pi$
$444$	−1.69689e11	−0.207220
$445$	−1.74371e10	−0.0210792
$446$	−1.81819e12	−2.17587
$447$	−6.44061e11	−0.763033
$448$	−1.66609e12	−1.95411
$449$	−8.84280e11	−1.02679	−0.513394	−	0.858153i	$-0.671612\pi$
$449$	−8.84280e11	−1.02679	−0.513394	+	0.858153i	$0.671612\pi$
$450$	4.48028e11	0.515050
$451$	5.04683e10	0.0574413
$452$	−1.78321e12	−2.00946
$453$	3.26461e11	0.364242
$454$	5.39451e11	0.595938
$455$	−1.25849e11	−0.137657
$456$	−6.45465e11	−0.699087
$457$	4.81205e11	0.516068	0.258034	−	0.966136i	$-0.416925\pi$
$457$	4.81205e11	0.516068	0.258034	+	0.966136i	$0.416925\pi$
$458$	−5.89966e11	−0.626517
$459$	−1.71075e11	−0.179899
$460$	−1.89820e11	−0.197665
$461$	1.38965e12	1.43301	0.716507	−	0.697580i	$-0.245740\pi$
$461$	1.38965e12	1.43301	0.716507	+	0.697580i	$0.245740\pi$
$462$	3.79892e11	0.387946
$463$	−4.35217e11	−0.440141	−0.220070	−	0.975484i	$-0.570629\pi$
$463$	−4.35217e11	−0.440141	−0.220070	+	0.975484i	$0.570629\pi$
$464$	2.26527e11	0.226876
$465$	−6.65015e10	−0.0659619
$466$	−9.83384e11	−0.966021
$467$	9.99032e10	0.0971971	0.0485985	−	0.998818i	$-0.484525\pi$
$467$	9.99032e10	0.0971971	0.0485985	+	0.998818i	$0.484525\pi$
$468$	3.52621e11	0.339783
$469$	1.73997e12	1.66059
$470$	2.03336e11	0.192209
$471$	−3.63002e11	−0.339872
$472$	1.20224e11	0.111494
$473$	−7.29333e11	−0.669963
$474$	−8.95439e10	−0.0814767
$475$	1.52158e12	1.37143
$476$	1.92900e12	1.72227
$477$	3.94215e11	0.348659
$478$	−1.41823e12	−1.24257
$479$	−1.44103e12	−1.25073	−0.625363	−	0.780334i	$-0.715049\pi$
$479$	−1.44103e12	−1.25073	−0.625363	+	0.780334i	$0.715049\pi$
$480$	1.31786e11	0.113314
$481$	1.81667e11	0.154748
$482$	3.01266e12	2.54237
$483$	−6.13839e11	−0.513207
$484$	−1.62627e12	−1.34706
$485$	2.09816e11	0.172187
$486$	1.25682e11	0.102190
$487$	1.91897e12	1.54593	0.772963	−	0.634452i	$-0.218774\pi$
$487$	1.91897e12	1.54593	0.772963	+	0.634452i	$0.218774\pi$
$488$	7.15412e10	0.0571041
$489$	−9.88855e11	−0.782065
$490$	1.53512e11	0.120298
$491$	2.21466e11	0.171965	0.0859827	−	0.996297i	$-0.472597\pi$
$491$	2.21466e11	0.171965	0.0859827	+	0.996297i	$0.472597\pi$
$492$	−1.88268e11	−0.144855
$493$	−1.60447e12	−1.22326
$494$	1.97640e12	1.49315
$495$	−2.71615e10	−0.0203344
$496$	1.54072e11	0.114303
$497$	−4.48893e11	−0.330019
$498$	8.31787e11	0.606010
$499$	−7.58060e11	−0.547332	−0.273666	−	0.961825i	$-0.588236\pi$
$499$	−7.58060e11	−0.547332	−0.273666	+	0.961825i	$0.588236\pi$
$500$	7.33579e11	0.524906
$501$	−1.18411e11	−0.0839695
$502$	−3.15978e12	−2.22070
$503$	4.35553e10	0.0303378	0.0151689	−	0.999885i	$-0.495171\pi$
$503$	4.35553e10	0.0303378	0.0151689	+	0.999885i	$0.495171\pi$
$504$	−4.95493e11	−0.342058
$505$	2.93136e11	0.200567
$506$	−6.13442e11	−0.416003
$507$	4.81453e11	0.323607
$508$	−4.08870e12	−2.72394
$509$	2.46695e12	1.62903	0.814516	−	0.580141i	$-0.197003\pi$
$509$	2.46695e12	1.62903	0.814516	+	0.580141i	$0.197003\pi$
$510$	−2.27617e11	−0.148984
$511$	8.11954e11	0.526790
$512$	−5.36197e11	−0.344834
$513$	4.26836e11	0.272103
$514$	2.32976e12	1.47224
$515$	5.82193e10	0.0364699
$516$	2.72072e12	1.68951
$517$	3.98169e11	0.245109
$518$	−7.30108e11	−0.445557
$519$	−8.64593e11	−0.523069
$520$	1.64039e11	0.0983855
$521$	−1.47965e12	−0.879809	−0.439905	−	0.898045i	$-0.644988\pi$
$521$	−1.47965e12	−0.879809	−0.439905	+	0.898045i	$0.644988\pi$
$522$	1.17874e12	0.694865
$523$	4.59042e9	0.00268284	0.00134142	−	0.999999i	$-0.499573\pi$
$523$	4.59042e9	0.00268284	0.00134142	+	0.999999i	$0.499573\pi$
$524$	−3.56687e12	−2.06679
$525$	1.16804e12	0.671030
$526$	−3.08773e12	−1.75875
$527$	−1.09128e12	−0.616294
$528$	6.29284e10	0.0352366
$529$	−8.09937e11	−0.449677
$530$	5.24508e11	0.288743
$531$	−7.95020e10	−0.0433963
$532$	−4.81290e12	−2.60498
$533$	2.01557e11	0.108175
$534$	2.10215e11	0.111874
$535$	5.18078e11	0.273403
$536$	−2.26797e12	−1.18685
$537$	9.78911e10	0.0507994
$538$	−4.51966e12	−2.32587
$539$	3.00605e11	0.153407
$540$	1.01324e11	0.0512791
$541$	−1.00252e12	−0.503157	−0.251579	−	0.967837i	$-0.580950\pi$
$541$	−1.00252e12	−0.503157	−0.251579	+	0.967837i	$0.580950\pi$
$542$	8.58960e11	0.427539
$543$	1.13961e11	0.0562546
$544$	2.16259e12	1.05872
$545$	−4.25564e11	−0.206624
$546$	1.51719e12	0.730590
$547$	2.37893e12	1.13616	0.568079	−	0.822974i	$-0.307687\pi$
$547$	2.37893e12	1.13616	0.568079	+	0.822974i	$0.307687\pi$
$548$	4.06036e12	1.92332
$549$	−4.73091e10	−0.0222264
$550$	1.16729e12	0.543934
$551$	4.00319e12	1.85022
$552$	8.00112e11	0.366796
$553$	−2.33448e11	−0.106152
$554$	3.61737e12	1.63155
$555$	5.22012e10	0.0233541
$556$	9.46119e11	0.419865
$557$	−2.81309e11	−0.123833	−0.0619164	−	0.998081i	$-0.519721\pi$
$557$	−2.81309e11	−0.123833	−0.0619164	+	0.998081i	$0.519721\pi$
$558$	8.01718e11	0.350081
$559$	−2.91277e12	−1.26169
$560$	8.37812e10	0.0359998
$561$	−4.45716e11	−0.189988
$562$	6.46117e12	2.73211
$563$	1.32901e12	0.557495	0.278748	−	0.960364i	$-0.410081\pi$
$563$	1.32901e12	0.557495	0.278748	+	0.960364i	$0.410081\pi$
$564$	−1.48534e12	−0.618115
$565$	5.48567e11	0.226471
$566$	7.48444e12	3.06539
$567$	3.27662e11	0.133138
$568$	5.85112e11	0.235869
$569$	−2.03849e12	−0.815273	−0.407636	−	0.913144i	$-0.633647\pi$
$569$	−2.03849e12	−0.815273	−0.407636	+	0.913144i	$0.633647\pi$
$570$	5.67910e11	0.225342
$571$	−2.71625e12	−1.06932	−0.534659	−	0.845068i	$-0.679560\pi$
$571$	−2.71625e12	−1.06932	−0.534659	+	0.845068i	$0.679560\pi$
$572$	9.18715e11	0.358838
$573$	8.18425e11	0.317163
$574$	−8.10044e11	−0.311462
$575$	−1.88613e12	−0.719560
$576$	−1.43610e12	−0.543604
$577$	1.61395e12	0.606175	0.303087	−	0.952963i	$-0.401983\pi$
$577$	1.61395e12	0.606175	0.303087	+	0.952963i	$0.401983\pi$
$578$	5.39365e11	0.201005
$579$	2.53597e12	0.937756
$580$	9.50293e11	0.348684
$581$	2.16853e12	0.789538
$582$	−2.52947e12	−0.913852
$583$	1.02708e12	0.368212
$584$	−1.05835e12	−0.376504
$585$	−1.08476e11	−0.0382942
$586$	4.42078e12	1.54867
$587$	−8.60925e11	−0.299291	−0.149646	−	0.988740i	$-0.547813\pi$
$587$	−8.60925e11	−0.299291	−0.149646	+	0.988740i	$0.547813\pi$
$588$	−1.12138e12	−0.386861
$589$	2.72277e12	0.932163
$590$	−1.05778e11	−0.0359387
$591$	3.52343e11	0.118802
$592$	−1.20941e11	−0.0404693
$593$	2.08900e11	0.0693732	0.0346866	−	0.999398i	$-0.488957\pi$
$593$	2.08900e11	0.0693732	0.0346866	+	0.999398i	$0.488957\pi$
$594$	3.27450e11	0.107921
$595$	−5.93414e11	−0.194103
$596$	6.25975e12	2.03212
$597$	1.77162e12	0.570801
$598$	−2.44993e12	−0.783427
$599$	−7.49045e11	−0.237732	−0.118866	−	0.992910i	$-0.537926\pi$
$599$	−7.49045e11	−0.237732	−0.118866	+	0.992910i	$0.537926\pi$
$600$	−1.52249e12	−0.479595
$601$	−2.92254e12	−0.913745	−0.456872	−	0.889532i	$-0.651030\pi$
$601$	−2.92254e12	−0.913745	−0.456872	+	0.889532i	$0.651030\pi$
$602$	1.17062e13	3.63272
$603$	1.49977e12	0.461952
$604$	−3.17294e12	−0.970054
$605$	5.00286e11	0.151817
$606$	−3.53395e12	−1.06447
$607$	−2.01355e12	−0.602024	−0.301012	−	0.953620i	$-0.597324\pi$
$607$	−2.01355e12	−0.602024	−0.301012	+	0.953620i	$0.597324\pi$
$608$	−5.39572e12	−1.60134
$609$	3.07306e12	0.905302
$610$	−6.29453e10	−0.0184068
$611$	1.59019e12	0.461596
$612$	1.66271e12	0.479109
$613$	3.83557e12	1.09713	0.548564	−	0.836109i	$-0.315175\pi$
$613$	3.83557e12	1.09713	0.548564	+	0.836109i	$0.315175\pi$
$614$	−6.96786e12	−1.97853
$615$	5.79165e10	0.0163254
$616$	−1.29095e12	−0.361241
$617$	4.53937e12	1.26099	0.630496	−	0.776192i	$-0.282851\pi$
$617$	4.53937e12	1.26099	0.630496	+	0.776192i	$0.282851\pi$
$618$	−7.01871e11	−0.193557
$619$	2.84541e11	0.0779000	0.0389500	−	0.999241i	$-0.487599\pi$
$619$	2.84541e11	0.0779000	0.0389500	+	0.999241i	$0.487599\pi$
$620$	6.46341e11	0.175671
$621$	−5.29102e11	−0.142767
$622$	5.11825e10	0.0137109
$623$	5.48047e11	0.145754
$624$	2.51320e11	0.0663585
$625$	3.47447e12	0.910812
$626$	3.50663e11	0.0912651
$627$	1.11207e12	0.287362
$628$	3.52809e12	0.905151
$629$	8.56614e11	0.218201
$630$	4.35958e11	0.110258
$631$	−1.03135e12	−0.258985	−0.129492	−	0.991580i	$-0.541335\pi$
$631$	−1.03135e12	−0.258985	−0.129492	+	0.991580i	$0.541335\pi$
$632$	3.04289e11	0.0758680
$633$	−3.58072e12	−0.886448
$634$	8.88198e11	0.218327
$635$	1.25780e12	0.306994
$636$	−3.83146e12	−0.928553
$637$	1.20054e12	0.288900
$638$	3.07107e12	0.733833
$639$	−3.86925e11	−0.0918064
$640$	−1.07773e12	−0.253921
$641$	−8.00081e11	−0.187186	−0.0935929	−	0.995611i	$-0.529835\pi$
$641$	−8.00081e11	−0.187186	−0.0935929	+	0.995611i	$0.529835\pi$
$642$	−6.24576e12	−1.45104
$643$	−4.85967e12	−1.12113	−0.560567	−	0.828109i	$-0.689417\pi$
$643$	−4.85967e12	−1.12113	−0.560567	+	0.828109i	$0.689417\pi$
$644$	5.96602e12	1.36678
$645$	−8.36970e11	−0.190411
$646$	9.31931e12	2.10541
$647$	−8.72956e11	−0.195850	−0.0979249	−	0.995194i	$-0.531220\pi$
$647$	−8.72956e11	−0.195850	−0.0979249	+	0.995194i	$0.531220\pi$
$648$	−4.27093e11	−0.0951556
$649$	−2.07134e11	−0.0458300
$650$	4.66185e12	1.02435
$651$	2.09014e12	0.456101
$652$	9.61087e12	2.08280
$653$	−4.17937e12	−0.899500	−0.449750	−	0.893155i	$-0.648487\pi$
$653$	−4.17937e12	−0.899500	−0.449750	+	0.893155i	$0.648487\pi$
$654$	5.13044e12	1.09662
$655$	1.09727e12	0.232932
$656$	−1.34182e11	−0.0282896
$657$	6.99867e11	0.146545
$658$	−6.39084e12	−1.32905
$659$	−4.28518e12	−0.885084	−0.442542	−	0.896748i	$-0.645923\pi$
$659$	−4.28518e12	−0.885084	−0.442542	+	0.896748i	$0.645923\pi$
$660$	2.63988e11	0.0541548
$661$	5.09397e12	1.03789	0.518943	−	0.854809i	$-0.326326\pi$
$661$	5.09397e12	1.03789	0.518943	+	0.854809i	$0.326326\pi$
$662$	3.32955e12	0.673790
$663$	−1.78008e12	−0.357790
$664$	−2.82658e12	−0.564294
$665$	1.48058e12	0.293586
$666$	−6.29320e11	−0.123947
$667$	−4.96232e12	−0.970774
$668$	1.15086e12	0.223629
$669$	−4.08580e12	−0.788605
$670$	1.99546e12	0.382567
$671$	−1.23259e11	−0.0234728
$672$	−4.14204e12	−0.783525
$673$	−1.75158e12	−0.329125	−0.164563	−	0.986367i	$-0.552621\pi$
$673$	−1.75158e12	−0.329125	−0.164563	+	0.986367i	$0.552621\pi$
$674$	1.19060e13	2.22227
$675$	1.00680e12	0.186671
$676$	−4.67933e12	−0.861834
$677$	1.69864e12	0.310780	0.155390	−	0.987853i	$-0.450337\pi$
$677$	1.69864e12	0.310780	0.155390	+	0.987853i	$0.450337\pi$
$678$	−6.61333e12	−1.20195
$679$	−6.59451e12	−1.19061
$680$	7.73489e11	0.138728
$681$	1.21224e12	0.215987
$682$	2.08879e12	0.369713
$683$	−7.96541e12	−1.40060	−0.700302	−	0.713847i	$-0.746951\pi$
$683$	−7.96541e12	−1.40060	−0.700302	+	0.713847i	$0.746951\pi$
$684$	−4.14850e12	−0.724667
$685$	−1.24908e12	−0.216762
$686$	6.24685e12	1.07697
$687$	−1.32576e12	−0.227070
$688$	1.93911e12	0.329955
$689$	4.10191e12	0.693426
$690$	−7.03976e11	−0.118233
$691$	−9.26701e12	−1.54628	−0.773140	−	0.634235i	$-0.781315\pi$
$691$	−9.26701e12	−1.54628	−0.773140	+	0.634235i	$0.781315\pi$
$692$	8.40315e12	1.39304
$693$	8.53686e11	0.140604
$694$	6.62494e11	0.108409
$695$	−2.91053e11	−0.0473196
$696$	−4.00560e12	−0.647032
$697$	9.50400e11	0.152531
$698$	−1.30974e13	−2.08850
$699$	−2.20984e12	−0.350118
$700$	−1.13524e13	−1.78710
$701$	−3.48399e12	−0.544937	−0.272469	−	0.962165i	$-0.587840\pi$
$701$	−3.48399e12	−0.544937	−0.272469	+	0.962165i	$0.587840\pi$
$702$	1.30775e12	0.203239
$703$	−2.13727e12	−0.330036
$704$	−3.74159e12	−0.574090
$705$	4.56932e11	0.0696627
$706$	5.21649e12	0.790237
$707$	−9.21327e12	−1.38684
$708$	7.72695e11	0.115574
$709$	3.47197e12	0.516022	0.258011	−	0.966142i	$-0.416933\pi$
$709$	3.47197e12	0.516022	0.258011	+	0.966142i	$0.416933\pi$
$710$	−5.14808e11	−0.0760297
$711$	−2.01221e11	−0.0295298
$712$	−7.14355e11	−0.104173
$713$	−3.37512e12	−0.489087
$714$	7.15399e12	1.03016
$715$	−2.82623e11	−0.0404417
$716$	−9.51422e11	−0.135290
$717$	−3.18702e12	−0.450348
$718$	1.62878e13	2.28719
$719$	−8.56963e12	−1.19587	−0.597933	−	0.801546i	$-0.704011\pi$
$719$	−8.56963e12	−1.19587	−0.597933	+	0.801546i	$0.704011\pi$
$720$	7.22156e10	0.0100146
$721$	−1.82983e12	−0.252175
$722$	−1.16206e13	−1.59151
$723$	6.76999e12	0.921437
$724$	−1.10761e12	−0.149818
$725$	9.44254e12	1.26931
$726$	−6.03127e12	−0.805738
$727$	1.77144e12	0.235191	0.117596	−	0.993062i	$-0.462481\pi$
$727$	1.77144e12	0.235191	0.117596	+	0.993062i	$0.462481\pi$
$728$	−5.15573e12	−0.680298
$729$	2.82430e11	0.0370370
$730$	9.31182e11	0.121362
$731$	−1.37345e13	−1.77904
$732$	4.59806e11	0.0591936
$733$	7.38789e12	0.945262	0.472631	−	0.881260i	$-0.343304\pi$
$733$	7.38789e12	0.945262	0.472631	+	0.881260i	$0.343304\pi$
$734$	7.18161e12	0.913250
$735$	3.44969e11	0.0436000
$736$	6.68849e12	0.840190
$737$	3.90749e12	0.487859
$738$	−6.98221e11	−0.0866442
$739$	−5.26699e12	−0.649624	−0.324812	−	0.945779i	$-0.605301\pi$
$739$	−5.26699e12	−0.649624	−0.324812	+	0.945779i	$0.605301\pi$
$740$	−5.07354e11	−0.0621968
$741$	4.44134e12	0.541168
$742$	−1.64853e13	−1.99654
$743$	8.11827e12	0.977269	0.488634	−	0.872489i	$-0.337495\pi$
$743$	8.11827e12	0.977269	0.488634	+	0.872489i	$0.337495\pi$
$744$	−2.72440e12	−0.325982
$745$	−1.92568e12	−0.229024
$746$	−1.76249e13	−2.08354
$747$	1.86917e12	0.219638
$748$	4.33200e12	0.505978
$749$	−1.62832e13	−1.89047
$750$	2.72059e12	0.313970
$751$	−6.42270e12	−0.736780	−0.368390	−	0.929671i	$-0.620091\pi$
$751$	−6.42270e12	−0.736780	−0.368390	+	0.929671i	$0.620091\pi$
$752$	−1.05863e12	−0.120716
$753$	−7.10061e12	−0.804856
$754$	1.22651e13	1.38197
$755$	9.76087e11	0.109327
$756$	−3.18461e12	−0.354575
$757$	−1.29515e13	−1.43347	−0.716736	−	0.697344i	$-0.754365\pi$
$757$	−1.29515e13	−1.43347	−0.716736	+	0.697344i	$0.754365\pi$
$758$	−9.10789e12	−1.00209
$759$	−1.37852e12	−0.150773
$760$	−1.92988e12	−0.209830
$761$	1.45543e13	1.57311	0.786556	−	0.617519i	$-0.211862\pi$
$761$	1.45543e13	1.57311	0.786556	+	0.617519i	$0.211862\pi$
$762$	−1.51636e13	−1.62931
$763$	1.33754e13	1.42872
$764$	−7.95443e12	−0.844674
$765$	−5.11496e11	−0.0539966
$766$	2.68288e13	2.81561
$767$	−8.27239e11	−0.0863081
$768$	3.91512e12	0.406087
$769$	−1.48958e13	−1.53601	−0.768006	−	0.640443i	$-0.778751\pi$
$769$	−1.48958e13	−1.53601	−0.768006	+	0.640443i	$0.778751\pi$
$770$	1.13584e12	0.116442
$771$	5.23539e12	0.533586
$772$	−2.46475e13	−2.49744
$773$	−1.43291e13	−1.44349	−0.721743	−	0.692162i	$-0.756659\pi$
$773$	−1.43291e13	−1.44349	−0.721743	+	0.692162i	$0.756659\pi$
$774$	1.00902e13	1.01057
$775$	6.42234e12	0.639492
$776$	8.59565e12	0.850944
$777$	−1.64068e12	−0.161484
$778$	2.18685e13	2.13999
$779$	−2.37127e12	−0.230708
$780$	1.05430e12	0.101986
$781$	−1.00809e12	−0.0969549
$782$	−1.15521e13	−1.10467
$783$	2.64884e12	0.251842
$784$	−7.99230e11	−0.0755527
$785$	−1.08534e12	−0.102012
$786$	−1.32283e13	−1.23624
$787$	1.13054e12	0.105051	0.0525255	−	0.998620i	$-0.483273\pi$
$787$	1.13054e12	0.105051	0.0525255	+	0.998620i	$0.483273\pi$
$788$	−3.42449e12	−0.316394
$789$	−6.93868e12	−0.637427
$790$	−2.67727e11	−0.0244552
$791$	−1.72414e13	−1.56596
$792$	−1.11274e12	−0.100492
$793$	−4.92263e11	−0.0442046
$794$	4.53094e12	0.404572
$795$	1.17866e12	0.104650
$796$	−1.72187e13	−1.52017
$797$	−2.22807e13	−1.95599	−0.977996	−	0.208622i	$-0.933102\pi$
$797$	−2.22807e13	−1.95599	−0.977996	+	0.208622i	$0.933102\pi$
$798$	−1.78494e13	−1.55815
$799$	7.49818e12	0.650871
$800$	−1.27272e13	−1.09857
$801$	4.72391e11	0.0405467
$802$	−1.79055e13	−1.52828
$803$	1.82343e12	0.154763
$804$	−1.45766e13	−1.23028
$805$	−1.83532e12	−0.154039
$806$	8.34209e12	0.696253
$807$	−1.01565e13	−0.842971
$808$	1.20091e13	0.991195
$809$	−7.94931e12	−0.652470	−0.326235	−	0.945289i	$-0.605780\pi$
$809$	−7.94931e12	−0.652470	−0.326235	+	0.945289i	$0.605780\pi$
$810$	3.75776e11	0.0306723
$811$	−5.75368e12	−0.467038	−0.233519	−	0.972352i	$-0.575024\pi$
$811$	−5.75368e12	−0.467038	−0.233519	+	0.972352i	$0.575024\pi$
$812$	−2.98677e13	−2.41101
$813$	1.93024e12	0.154954
$814$	−1.63962e12	−0.130898
$815$	−2.95658e12	−0.234736
$816$	1.18505e12	0.0935684
$817$	3.42680e13	2.69085
$818$	3.16128e13	2.46873
$819$	3.40940e12	0.264790
$820$	−5.62902e11	−0.0434781
$821$	3.18644e12	0.244772	0.122386	−	0.992483i	$-0.460945\pi$
$821$	3.18644e12	0.244772	0.122386	+	0.992483i	$0.460945\pi$
$822$	1.50585e13	1.15043
$823$	−9.54724e12	−0.725401	−0.362701	−	0.931906i	$-0.618145\pi$
$823$	−9.54724e12	−0.725401	−0.362701	+	0.931906i	$0.618145\pi$
$824$	2.38510e12	0.180233
$825$	2.62311e12	0.197139
$826$	3.32461e12	0.248502
$827$	−6.39294e12	−0.475254	−0.237627	−	0.971356i	$-0.576370\pi$
$827$	−6.39294e12	−0.475254	−0.237627	+	0.971356i	$0.576370\pi$
$828$	5.14244e12	0.380218
$829$	2.35682e13	1.73313	0.866563	−	0.499068i	$-0.166324\pi$
$829$	2.35682e13	1.73313	0.866563	+	0.499068i	$0.166324\pi$
$830$	2.48696e12	0.181893
$831$	8.12889e12	0.591325
$832$	−1.49430e13	−1.08114
$833$	5.66088e12	0.407363
$834$	3.50883e12	0.251140
$835$	−3.54037e11	−0.0252034
$836$	−1.08085e13	−0.765307
$837$	1.80161e12	0.126881
$838$	4.68841e12	0.328418
$839$	−6.86890e12	−0.478584	−0.239292	−	0.970948i	$-0.576915\pi$
$839$	−6.86890e12	−0.478584	−0.239292	+	0.970948i	$0.576915\pi$
$840$	−1.48147e12	−0.102669
$841$	1.03357e13	0.712454
$842$	3.44560e13	2.36244
$843$	1.45194e13	0.990204
$844$	3.48017e13	2.36080
$845$	1.43950e12	0.0971304
$846$	−5.50861e12	−0.369722
$847$	−1.57240e13	−1.04975
$848$	−2.73075e12	−0.181343
$849$	1.68189e13	1.11100
$850$	2.19820e13	1.44438
$851$	2.64934e12	0.173163
$852$	3.76060e12	0.244500
$853$	1.02548e13	0.663221	0.331610	−	0.943416i	$-0.392408\pi$
$853$	1.02548e13	0.663221	0.331610	+	0.943416i	$0.392408\pi$
$854$	1.97837e12	0.127276
$855$	1.27620e12	0.0816714
$856$	2.12244e13	1.35115
$857$	1.05349e13	0.667139	0.333570	−	0.942725i	$-0.391747\pi$
$857$	1.05349e13	0.667139	0.333570	+	0.942725i	$0.391747\pi$
$858$	3.40720e12	0.214637
$859$	9.86201e12	0.618011	0.309006	−	0.951060i	$-0.400004\pi$
$859$	9.86201e12	0.618011	0.309006	+	0.951060i	$0.400004\pi$
$860$	8.13468e12	0.507104
$861$	−1.82031e12	−0.112884
$862$	−1.83699e13	−1.13324
$863$	1.13582e13	0.697044	0.348522	−	0.937301i	$-0.386684\pi$
$863$	1.13582e13	0.697044	0.348522	+	0.937301i	$0.386684\pi$
$864$	−3.57025e12	−0.217965
$865$	−2.58505e12	−0.156999
$866$	2.89873e12	0.175137
$867$	1.21205e12	0.0728508
$868$	−2.03145e13	−1.21469
$869$	−5.24260e11	−0.0311858
$870$	3.52431e12	0.208563
$871$	1.56055e13	0.918747
$872$	−1.74343e13	−1.02113
$873$	−5.68417e12	−0.331210
$874$	2.88229e13	1.67084
$875$	7.09279e12	0.409054
$876$	−6.80215e12	−0.390281
$877$	−2.38147e12	−0.135940	−0.0679699	−	0.997687i	$-0.521652\pi$
$877$	−2.38147e12	−0.135940	−0.0679699	+	0.997687i	$0.521652\pi$
$878$	−4.43164e12	−0.251674
$879$	9.93429e12	0.561289
$880$	1.88150e11	0.0105762
$881$	−1.42926e13	−0.799321	−0.399660	−	0.916663i	$-0.630872\pi$
$881$	−1.42926e13	−0.799321	−0.399660	+	0.916663i	$0.630872\pi$
$882$	−4.15882e12	−0.231399
$883$	−2.73680e13	−1.51502	−0.757512	−	0.652822i	$-0.773585\pi$
$883$	−2.73680e13	−1.51502	−0.757512	+	0.652822i	$0.773585\pi$
$884$	1.73009e13	0.952870
$885$	−2.37703e11	−0.0130254
$886$	3.49573e13	1.90584
$887$	−2.10999e13	−1.14452	−0.572260	−	0.820072i	$-0.693933\pi$
$887$	−2.10999e13	−1.14452	−0.572260	+	0.820072i	$0.693933\pi$
$888$	2.13856e12	0.115415
$889$	−3.95326e13	−2.12274
$890$	6.28522e11	0.0335788
$891$	7.35839e11	0.0391141
$892$	3.97107e13	2.10022
$893$	−1.87081e13	−0.984463
$894$	2.32153e13	1.21550
$895$	2.92685e11	0.0152474
$896$	3.38729e13	1.75576
$897$	−5.50544e12	−0.283939
$898$	3.18740e13	1.63566
$899$	1.68968e13	0.862753
$900$	−9.78529e12	−0.497144
$901$	1.93417e13	0.977761
$902$	−1.81914e12	−0.0915032
$903$	2.63060e13	1.31662
$904$	2.24735e13	1.11921
$905$	3.40733e11	0.0168848
$906$	−1.17674e13	−0.580233
$907$	−1.82296e13	−0.894428	−0.447214	−	0.894427i	$-0.647584\pi$
$907$	−1.82296e13	−0.894428	−0.447214	+	0.894427i	$0.647584\pi$
$908$	−1.17820e13	−0.575220
$909$	−7.94142e12	−0.385799
$910$	4.53625e12	0.219286
$911$	−2.40842e13	−1.15851	−0.579256	−	0.815146i	$-0.696657\pi$
$911$	−2.40842e13	−1.15851	−0.579256	+	0.815146i	$0.696657\pi$
$912$	−2.95672e12	−0.141525
$913$	4.86993e12	0.231955
$914$	−1.73451e13	−0.822089
$915$	−1.41449e11	−0.00667123
$916$	1.28853e13	0.604736
$917$	−3.44872e13	−1.61063
$918$	6.16642e12	0.286577
$919$	2.76663e13	1.27947	0.639737	−	0.768594i	$-0.279043\pi$
$919$	2.76663e13	1.27947	0.639737	+	0.768594i	$0.279043\pi$
$920$	2.39226e12	0.110094
$921$	−1.56580e13	−0.717083
$922$	−5.00901e13	−2.28277
$923$	−4.02605e12	−0.182588
$924$	−8.29714e12	−0.374459
$925$	−5.04130e12	−0.226415
$926$	1.56875e13	0.701139
$927$	−1.57723e12	−0.0701514
$928$	−3.34845e13	−1.48210
$929$	2.01602e13	0.888024	0.444012	−	0.896021i	$-0.353555\pi$
$929$	2.01602e13	0.888024	0.444012	+	0.896021i	$0.353555\pi$
$930$	2.39706e12	0.105076
$931$	−1.41240e13	−0.616148
$932$	2.14779e13	0.932438
$933$	1.15016e11	0.00496926
$934$	−3.60103e12	−0.154834
$935$	−1.33265e12	−0.0570247
$936$	−4.44401e12	−0.189249
$937$	1.74977e13	0.741569	0.370785	−	0.928719i	$-0.379089\pi$
$937$	1.74977e13	0.741569	0.370785	+	0.928719i	$0.379089\pi$
$938$	−6.27174e13	−2.64530
$939$	7.88002e11	0.0330775
$940$	−4.44101e12	−0.185527
$941$	6.82182e12	0.283627	0.141813	−	0.989893i	$-0.454707\pi$
$941$	6.82182e12	0.283627	0.141813	+	0.989893i	$0.454707\pi$
$942$	1.30845e13	0.541411
$943$	2.93941e12	0.121048
$944$	5.50715e11	0.0225711
$945$	9.79676e11	0.0399613
$946$	2.62890e13	1.06724
$947$	−1.82410e13	−0.737011	−0.368506	−	0.929625i	$-0.620131\pi$
$947$	−1.82410e13	−0.737011	−0.368506	+	0.929625i	$0.620131\pi$
$948$	1.95571e12	0.0786442
$949$	7.28230e12	0.291454
$950$	−5.48456e13	−2.18467
$951$	1.99594e12	0.0791289
$952$	−2.43107e13	−0.959250
$953$	3.07532e12	0.120774	0.0603868	−	0.998175i	$-0.480767\pi$
$953$	3.07532e12	0.120774	0.0603868	+	0.998175i	$0.480767\pi$
$954$	−1.42096e13	−0.555409
$955$	2.44701e12	0.0951964
$956$	3.09752e13	1.19937
$957$	6.90126e12	0.265965
$958$	5.19421e13	1.99239
$959$	3.92587e13	1.49883
$960$	−4.29379e12	−0.163162
$961$	−1.49473e13	−0.565335
$962$	−6.54823e12	−0.246511
$963$	−1.40354e13	−0.525902
$964$	−6.57989e13	−2.45398
$965$	7.58228e12	0.281467
$966$	2.21259e13	0.817532
$967$	−3.97010e12	−0.146010	−0.0730049	−	0.997332i	$-0.523259\pi$
$967$	−3.97010e12	−0.146010	−0.0730049	+	0.997332i	$0.523259\pi$
$968$	2.04955e13	0.750273
$969$	2.09422e13	0.763071
$970$	−7.56285e12	−0.274292
$971$	4.95697e12	0.178949	0.0894746	−	0.995989i	$-0.471481\pi$
$971$	4.95697e12	0.178949	0.0894746	+	0.995989i	$0.471481\pi$
$972$	−2.74499e12	−0.0986375
$973$	9.14779e12	0.327196
$974$	−6.91697e13	−2.46264
$975$	1.04760e13	0.371258
$976$	3.27713e11	0.0115603
$977$	2.85651e13	1.00302	0.501510	−	0.865152i	$-0.332778\pi$
$977$	2.85651e13	1.00302	0.501510	+	0.865152i	$0.332778\pi$
$978$	3.56434e13	1.24582
$979$	1.23076e12	0.0428206
$980$	−3.35282e12	−0.116116
$981$	1.15290e13	0.397450
$982$	−7.98279e12	−0.273938
$983$	7.23756e12	0.247230	0.123615	−	0.992330i	$-0.460551\pi$
$983$	7.23756e12	0.247230	0.123615	+	0.992330i	$0.460551\pi$
$984$	2.37270e12	0.0806798
$985$	1.05347e12	0.0356582
$986$	5.78334e13	1.94864
$987$	−1.43614e13	−0.481691
$988$	−4.31662e13	−1.44124
$989$	−4.24783e13	−1.41184
$990$	9.79042e11	0.0323924
$991$	−2.56375e13	−0.844393	−0.422196	−	0.906504i	$-0.638741\pi$
$991$	−2.56375e13	−0.844393	−0.422196	+	0.906504i	$0.638741\pi$
$992$	−2.27745e13	−0.746700
$993$	7.48210e12	0.244204
$994$	1.61804e13	0.525716
$995$	5.29695e12	0.171326
$996$	−1.81669e13	−0.584942
$997$	9.24324e12	0.296276	0.148138	−	0.988967i	$-0.452672\pi$
$997$	9.24324e12	0.296276	0.148138	+	0.988967i	$0.452672\pi$
$998$	2.73244e13	0.871893
$999$	−1.41419e12	−0.0449226

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.3	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.3	✓	21	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-36.0452 q^{2} -81.0000 q^{3} +787.255 q^{4} -242.182 q^{5} +2919.66 q^{6} +7611.77 q^{7} -9921.60 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-36.0452 q^{2} -81.0000 q^{3} +787.255 q^{4} -242.182 q^{5} +2919.66 q^{6} +7611.77 q^{7} -9921.60 q^{8} +6561.00 q^{9} +8729.49 q^{10} +17094.0 q^{11} -63767.6 q^{12} +68268.9 q^{13} -274368. q^{14} +19616.7 q^{15} -45448.5 q^{16} +321907. q^{17} -236492. q^{18} -803167. q^{19} -190659. q^{20} -616553. q^{21} -616155. q^{22} +995598. q^{23} +803650. q^{24} -1.89447e6 q^{25} -2.46076e6 q^{26} -531441. q^{27} +5.99240e6 q^{28} -4.98426e6 q^{29} -707089. q^{30} -3.39004e6 q^{31} +6.71806e6 q^{32} -1.38461e6 q^{33} -1.16032e7 q^{34} -1.84343e6 q^{35} +5.16518e6 q^{36} +2.66106e6 q^{37} +2.89503e7 q^{38} -5.52978e6 q^{39} +2.40283e6 q^{40} +2.95240e6 q^{41} +2.22238e7 q^{42} -4.26661e7 q^{43} +1.34573e7 q^{44} -1.58896e6 q^{45} -3.58865e7 q^{46} +2.32930e7 q^{47} +3.68132e6 q^{48} +1.75854e7 q^{49} +6.82866e7 q^{50} -2.60745e7 q^{51} +5.37450e7 q^{52} +6.00847e7 q^{53} +1.91559e7 q^{54} -4.13985e6 q^{55} -7.55210e7 q^{56} +6.50565e7 q^{57} +1.79658e8 q^{58} -1.21174e7 q^{59} +1.54434e7 q^{60} -7.21065e6 q^{61} +1.22195e8 q^{62} +4.99408e7 q^{63} -2.18884e8 q^{64} -1.65335e7 q^{65} +4.99085e7 q^{66} +2.28589e8 q^{67} +2.53423e8 q^{68} -8.06434e7 q^{69} +6.64469e7 q^{70} -5.89735e7 q^{71} -6.50956e7 q^{72} +1.06671e8 q^{73} -9.59183e7 q^{74} +1.53452e8 q^{75} -6.32297e8 q^{76} +1.30115e8 q^{77} +1.99322e8 q^{78} -3.06693e7 q^{79} +1.10068e7 q^{80} +4.30467e7 q^{81} -1.06420e8 q^{82} +2.84892e8 q^{83} -4.85384e8 q^{84} -7.79601e7 q^{85} +1.53791e9 q^{86} +4.03725e8 q^{87} -1.69599e8 q^{88} +7.19999e7 q^{89} +5.72742e7 q^{90} +5.19647e8 q^{91} +7.83789e8 q^{92} +2.74593e8 q^{93} -8.39599e8 q^{94} +1.94513e8 q^{95} -5.44163e8 q^{96} -8.66357e8 q^{97} -6.33870e8 q^{98} +1.12153e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * q^99

Introduction

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