LMFDB - Embedded newform 177.8.a.a.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,8,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, 8, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
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:	$55.2921495107$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + \cdots - 23\!\cdots\!32 $ x^16 - 6x^15 - 1493x^14 + 8791x^13 + 890490x^12 - 5107725x^11 - 269092298x^10 + 1488374176x^9 + 42885295136x^8 - 226132003872x^7 - 3353576629440x^6 + 16796366777600x^5 + 99470801612800x^4 - 494039551757568x^3 - 493048066650624x^2 + 3193975642099712*x - 2385018853548032
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$1.05882$ of defining polynomial
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)

$f(q)$	$=$	$q-1.05882 q^{2} -27.0000 q^{3} -126.879 q^{4} +151.597 q^{5} +28.5880 q^{6} -1574.54 q^{7} +269.870 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-1.05882 q^{2} -27.0000 q^{3} -126.879 q^{4} +151.597 q^{5} +28.5880 q^{6} -1574.54 q^{7} +269.870 q^{8} +729.000 q^{9} -160.513 q^{10} +1597.23 q^{11} +3425.73 q^{12} +8756.36 q^{13} +1667.15 q^{14} -4093.12 q^{15} +15954.8 q^{16} +19841.7 q^{17} -771.876 q^{18} -4839.26 q^{19} -19234.5 q^{20} +42512.6 q^{21} -1691.17 q^{22} -30741.2 q^{23} -7286.48 q^{24} -55143.3 q^{25} -9271.37 q^{26} -19683.0 q^{27} +199776. q^{28} +14740.2 q^{29} +4333.86 q^{30} +72269.3 q^{31} -51436.5 q^{32} -43125.1 q^{33} -21008.7 q^{34} -238696. q^{35} -92494.7 q^{36} +357556. q^{37} +5123.88 q^{38} -236422. q^{39} +40911.4 q^{40} +562020. q^{41} -45013.0 q^{42} +682037. q^{43} -202654. q^{44} +110514. q^{45} +32549.3 q^{46} -1.24121e6 q^{47} -430778. q^{48} +1.65563e6 q^{49} +58386.6 q^{50} -535726. q^{51} -1.11100e6 q^{52} -1.94069e6 q^{53} +20840.7 q^{54} +242135. q^{55} -424921. q^{56} +130660. q^{57} -15607.1 q^{58} +205379. q^{59} +519331. q^{60} -2.48399e6 q^{61} -76519.8 q^{62} -1.14784e6 q^{63} -1.98775e6 q^{64} +1.32744e6 q^{65} +45661.5 q^{66} -1.19534e6 q^{67} -2.51749e6 q^{68} +830013. q^{69} +252735. q^{70} -5.50733e6 q^{71} +196735. q^{72} -1.03549e6 q^{73} -378585. q^{74} +1.48887e6 q^{75} +614000. q^{76} -2.51490e6 q^{77} +250327. q^{78} -1.05062e6 q^{79} +2.41869e6 q^{80} +531441. q^{81} -595075. q^{82} +8.29947e6 q^{83} -5.39395e6 q^{84} +3.00794e6 q^{85} -722151. q^{86} -397985. q^{87} +431043. q^{88} +1.51623e6 q^{89} -117014. q^{90} -1.37872e7 q^{91} +3.90041e6 q^{92} -1.95127e6 q^{93} +1.31421e6 q^{94} -733618. q^{95} +1.38878e6 q^{96} +1.02696e7 q^{97} -1.75301e6 q^{98} +1.16438e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9} - 3479 q^{10} + 898 q^{11} - 26298 q^{12} - 8172 q^{13} - 13315 q^{14} + 1836 q^{15} + 3138 q^{16} - 44985 q^{17} - 4374 q^{18} - 40137 q^{19} + 130657 q^{20} + 63261 q^{21} + 109394 q^{22} - 2833 q^{23} - 22113 q^{24} + 285746 q^{25} - 129420 q^{26} - 314928 q^{27} + 112890 q^{28} + 144375 q^{29} + 93933 q^{30} - 141759 q^{31} - 36224 q^{32} - 24246 q^{33} - 341332 q^{34} - 78859 q^{35} + 710046 q^{36} - 297971 q^{37} + 329075 q^{38} + 220644 q^{39} - 203048 q^{40} + 659077 q^{41} + 359505 q^{42} - 1431608 q^{43} + 254916 q^{44} - 49572 q^{45} + 873113 q^{46} - 1574073 q^{47} - 84726 q^{48} + 1893545 q^{49} + 302533 q^{50} + 1214595 q^{51} - 4972548 q^{52} + 587736 q^{53} + 118098 q^{54} - 4624036 q^{55} - 5798506 q^{56} + 1083699 q^{57} - 6991380 q^{58} + 3286064 q^{59} - 3527739 q^{60} - 6117131 q^{61} - 11570258 q^{62} - 1708047 q^{63} - 19063011 q^{64} - 5335514 q^{65} - 2953638 q^{66} - 16518710 q^{67} - 17284669 q^{68} + 76491 q^{69} - 39189486 q^{70} - 10882582 q^{71} + 597051 q^{72} - 21097441 q^{73} - 16717030 q^{74} - 7715142 q^{75} - 40864952 q^{76} - 3404601 q^{77} + 3494340 q^{78} - 3784458 q^{79} - 27466195 q^{80} + 8503056 q^{81} - 24990117 q^{82} - 1951425 q^{83} - 3048030 q^{84} - 23238675 q^{85} - 35910572 q^{86} - 3898125 q^{87} - 27843055 q^{88} + 10499443 q^{89} - 2536191 q^{90} + 699217 q^{91} - 20062766 q^{92} + 3827493 q^{93} - 59358988 q^{94} - 29236333 q^{95} + 978048 q^{96} - 25158976 q^{97} + 2120460 q^{98} + 654642 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9 - 3479 * q^10 + 898 * q^11 - 26298 * q^12 - 8172 * q^13 - 13315 * q^14 + 1836 * q^15 + 3138 * q^16 - 44985 * q^17 - 4374 * q^18 - 40137 * q^19 + 130657 * q^20 + 63261 * q^21 + 109394 * q^22 - 2833 * q^23 - 22113 * q^24 + 285746 * q^25 - 129420 * q^26 - 314928 * q^27 + 112890 * q^28 + 144375 * q^29 + 93933 * q^30 - 141759 * q^31 - 36224 * q^32 - 24246 * q^33 - 341332 * q^34 - 78859 * q^35 + 710046 * q^36 - 297971 * q^37 + 329075 * q^38 + 220644 * q^39 - 203048 * q^40 + 659077 * q^41 + 359505 * q^42 - 1431608 * q^43 + 254916 * q^44 - 49572 * q^45 + 873113 * q^46 - 1574073 * q^47 - 84726 * q^48 + 1893545 * q^49 + 302533 * q^50 + 1214595 * q^51 - 4972548 * q^52 + 587736 * q^53 + 118098 * q^54 - 4624036 * q^55 - 5798506 * q^56 + 1083699 * q^57 - 6991380 * q^58 + 3286064 * q^59 - 3527739 * q^60 - 6117131 * q^61 - 11570258 * q^62 - 1708047 * q^63 - 19063011 * q^64 - 5335514 * q^65 - 2953638 * q^66 - 16518710 * q^67 - 17284669 * q^68 + 76491 * q^69 - 39189486 * q^70 - 10882582 * q^71 + 597051 * q^72 - 21097441 * q^73 - 16717030 * q^74 - 7715142 * q^75 - 40864952 * q^76 - 3404601 * q^77 + 3494340 * q^78 - 3784458 * q^79 - 27466195 * q^80 + 8503056 * q^81 - 24990117 * q^82 - 1951425 * q^83 - 3048030 * q^84 - 23238675 * q^85 - 35910572 * q^86 - 3898125 * q^87 - 27843055 * q^88 + 10499443 * q^89 - 2536191 * q^90 + 699217 * q^91 - 20062766 * q^92 + 3827493 * q^93 - 59358988 * q^94 - 29236333 * q^95 + 978048 * q^96 - 25158976 * q^97 + 2120460 * q^98 + 654642 * 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 $

$2$	−1.05882	−0.0935869	−0.0467935	−	0.998905i	$-0.514900\pi$
$2$	−1.05882	−0.0935869	−0.0467935	+	0.998905i	$0.514900\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−126.879	−0.991241
$5$	151.597	0.542370	0.271185	−	0.962527i	$-0.412584\pi$
$5$	151.597	0.542370	0.271185	+	0.962527i	$0.412584\pi$
$6$	28.5880	0.0540324
$7$	−1574.54	−1.73504	−0.867522	−	0.497398i	$-0.834289\pi$
$7$	−1574.54	−1.73504	−0.867522	+	0.497398i	$0.834289\pi$
$8$	269.870	0.186354
$9$	729.000	0.333333
$10$	−160.513	−0.0507587
$11$	1597.23	0.361819	0.180910	−	0.983500i	$-0.442096\pi$
$11$	1597.23	0.361819	0.180910	+	0.983500i	$0.442096\pi$
$12$	3425.73	0.572294
$13$	8756.36	1.10541	0.552703	−	0.833378i	$-0.313596\pi$
$13$	8756.36	1.10541	0.552703	+	0.833378i	$0.313596\pi$
$14$	1667.15	0.162378
$15$	−4093.12	−0.313138
$16$	15954.8	0.973801
$17$	19841.7	0.979507	0.489754	−	0.871861i	$-0.337087\pi$
$17$	19841.7	0.979507	0.489754	+	0.871861i	$0.337087\pi$
$18$	−771.876	−0.0311956
$19$	−4839.26	−0.161861	−0.0809304	−	0.996720i	$-0.525789\pi$
$19$	−4839.26	−0.161861	−0.0809304	+	0.996720i	$0.525789\pi$
$20$	−19234.5	−0.537620
$21$	42512.6	1.00173
$22$	−1691.17	−0.0338616
$23$	−30741.2	−0.526834	−0.263417	−	0.964682i	$-0.584849\pi$
$23$	−30741.2	−0.526834	−0.263417	+	0.964682i	$0.584849\pi$
$24$	−7286.48	−0.107592
$25$	−55143.3	−0.705835
$26$	−9271.37	−0.103452
$27$	−19683.0	−0.192450
$28$	199776.	1.71985
$29$	14740.2	0.112230	0.0561152	−	0.998424i	$-0.482129\pi$
$29$	14740.2	0.112230	0.0561152	+	0.998424i	$0.482129\pi$
$30$	4333.86	0.0293056
$31$	72269.3	0.435700	0.217850	−	0.975982i	$-0.430096\pi$
$31$	72269.3	0.435700	0.217850	+	0.975982i	$0.430096\pi$
$32$	−51436.5	−0.277489
$33$	−43125.1	−0.208897
$34$	−21008.7	−0.0916691
$35$	−238696.	−0.941036
$36$	−92494.7	−0.330414
$37$	357556.	1.16048	0.580240	−	0.814445i	$-0.302959\pi$
$37$	357556.	1.16048	0.580240	+	0.814445i	$0.302959\pi$
$38$	5123.88	0.0151480
$39$	−236422.	−0.638207
$40$	40911.4	0.101073
$41$	562020.	1.27353	0.636764	−	0.771059i	$-0.280273\pi$
$41$	562020.	1.27353	0.636764	+	0.771059i	$0.280273\pi$
$42$	−45013.0	−0.0937487
$43$	682037.	1.30818	0.654092	−	0.756415i	$-0.273051\pi$
$43$	682037.	1.30818	0.654092	+	0.756415i	$0.273051\pi$
$44$	−202654.	−0.358650
$45$	110514.	0.180790
$46$	32549.3	0.0493047
$47$	−1.24121e6	−1.74382	−0.871911	−	0.489665i	$-0.837119\pi$
$47$	−1.24121e6	−1.74382	−0.871911	+	0.489665i	$0.837119\pi$
$48$	−430778.	−0.562224
$49$	1.65563e6	2.01038
$50$	58386.6	0.0660569
$51$	−535726.	−0.565519
$52$	−1.11100e6	−1.09572
$53$	−1.94069e6	−1.79057	−0.895286	−	0.445493i	$-0.853028\pi$
$53$	−1.94069e6	−1.79057	−0.895286	+	0.445493i	$0.853028\pi$
$54$	20840.7	0.0180108
$55$	242135.	0.196240
$56$	−424921.	−0.323333
$57$	130660.	0.0934503
$58$	−15607.1	−0.0105033
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	519331.	0.310395
$61$	−2.48399e6	−1.40119	−0.700593	−	0.713561i	$-0.747081\pi$
$61$	−2.48399e6	−1.40119	−0.700593	+	0.713561i	$0.747081\pi$
$62$	−76519.8	−0.0407758
$63$	−1.14784e6	−0.578348
$64$	−1.98775e6	−0.947832
$65$	1.32744e6	0.599539
$66$	45661.5	0.0195500
$67$	−1.19534e6	−0.485546	−0.242773	−	0.970083i	$-0.578057\pi$
$67$	−1.19534e6	−0.485546	−0.242773	+	0.970083i	$0.578057\pi$
$68$	−2.51749e6	−0.970928
$69$	830013.	0.304168
$70$	252735.	0.0880687
$71$	−5.50733e6	−1.82615	−0.913076	−	0.407789i	$-0.866300\pi$
$71$	−5.50733e6	−1.82615	−0.913076	+	0.407789i	$0.866300\pi$
$72$	196735.	0.0621181
$73$	−1.03549e6	−0.311542	−0.155771	−	0.987793i	$-0.549786\pi$
$73$	−1.03549e6	−0.311542	−0.155771	+	0.987793i	$0.549786\pi$
$74$	−378585.	−0.108606
$75$	1.48887e6	0.407514
$76$	614000.	0.160443
$77$	−2.51490e6	−0.627773
$78$	250327.	0.0597278
$79$	−1.05062e6	−0.239745	−0.119873	−	0.992789i	$-0.538249\pi$
$79$	−1.05062e6	−0.239745	−0.119873	+	0.992789i	$0.538249\pi$
$80$	2.41869e6	0.528161
$81$	531441.	0.111111
$82$	−595075.	−0.119185
$83$	8.29947e6	1.59323	0.796613	−	0.604490i	$-0.206623\pi$
$83$	8.29947e6	1.59323	0.796613	+	0.604490i	$0.206623\pi$
$84$	−5.39395e6	−0.992955
$85$	3.00794e6	0.531256
$86$	−722151.	−0.122429
$87$	−397985.	−0.0647962
$88$	431043.	0.0674266
$89$	1.51623e6	0.227982	0.113991	−	0.993482i	$-0.463637\pi$
$89$	1.51623e6	0.227982	0.113991	+	0.993482i	$0.463637\pi$
$90$	−117014.	−0.0169196
$91$	−1.37872e7	−1.91793
$92$	3.90041e6	0.522219
$93$	−1.95127e6	−0.251552
$94$	1.31421e6	0.163199
$95$	−733618.	−0.0877884
$96$	1.38878e6	0.160208
$97$	1.02696e7	1.14249	0.571247	−	0.820778i	$-0.306460\pi$
$97$	1.02696e7	1.14249	0.571247	+	0.820778i	$0.306460\pi$
$98$	−1.75301e6	−0.188145
$99$	1.16438e6	0.120606
$100$	6.99653e6	0.699653
$101$	−1.21422e7	−1.17267	−0.586333	−	0.810070i	$-0.699429\pi$
$101$	−1.21422e7	−1.17267	−0.586333	+	0.810070i	$0.699429\pi$
$102$	567235.	0.0529252
$103$	−2.11994e7	−1.91159	−0.955793	−	0.294041i	$-0.905000\pi$
$103$	−2.11994e7	−1.91159	−0.955793	+	0.294041i	$0.905000\pi$
$104$	2.36308e6	0.205997
$105$	6.44478e6	0.543308
$106$	2.05484e6	0.167574
$107$	58058.2	0.00458163	0.00229082	−	0.999997i	$-0.499271\pi$
$107$	58058.2	0.00458163	0.00229082	+	0.999997i	$0.499271\pi$
$108$	2.49736e6	0.190765
$109$	1.06543e7	0.788011	0.394005	−	0.919108i	$-0.371089\pi$
$109$	1.06543e7	0.788011	0.394005	+	0.919108i	$0.371089\pi$
$110$	−256376.	−0.0183655
$111$	−9.65401e6	−0.670004
$112$	−2.51214e7	−1.68959
$113$	−4.86803e6	−0.317379	−0.158690	−	0.987329i	$-0.550727\pi$
$113$	−4.86803e6	−0.317379	−0.158690	+	0.987329i	$0.550727\pi$
$114$	−138345.	−0.00874573
$115$	−4.66028e6	−0.285739
$116$	−1.87022e6	−0.111247
$117$	6.38339e6	0.368469
$118$	−217458.	−0.0121840
$119$	−3.12416e7	−1.69949
$120$	−1.10461e6	−0.0583545
$121$	−1.69360e7	−0.869087
$122$	2.63009e6	0.131133
$123$	−1.51745e7	−0.735271
$124$	−9.16945e6	−0.431884
$125$	−2.02031e7	−0.925194
$126$	1.21535e6	0.0541258
$127$	−3.32597e7	−1.44081	−0.720403	−	0.693556i	$-0.756043\pi$
$127$	−3.32597e7	−1.44081	−0.720403	+	0.693556i	$0.756043\pi$
$128$	8.68852e6	0.366194
$129$	−1.84150e7	−0.755280
$130$	−1.40551e6	−0.0561090
$131$	3.81285e6	0.148184	0.0740918	−	0.997251i	$-0.476394\pi$
$131$	3.81285e6	0.148184	0.0740918	+	0.997251i	$0.476394\pi$
$132$	5.47166e6	0.207067
$133$	7.61961e6	0.280836
$134$	1.26565e6	0.0454407
$135$	−2.98388e6	−0.104379
$136$	5.35467e6	0.182535
$137$	4.60178e7	1.52899	0.764494	−	0.644630i	$-0.222989\pi$
$137$	4.60178e7	1.52899	0.764494	+	0.644630i	$0.222989\pi$
$138$	−878830.	−0.0284661
$139$	4.52736e7	1.42986	0.714930	−	0.699196i	$-0.246458\pi$
$139$	4.52736e7	1.42986	0.714930	+	0.699196i	$0.246458\pi$
$140$	3.02855e7	0.932794
$141$	3.35126e7	1.00680
$142$	5.83125e6	0.170904
$143$	1.39859e7	0.399957
$144$	1.16310e7	0.324600
$145$	2.23457e6	0.0608704
$146$	1.09639e6	0.0291562
$147$	−4.47021e7	−1.16069
$148$	−4.53663e7	−1.15032
$149$	2.55791e7	0.633481	0.316740	−	0.948512i	$-0.397412\pi$
$149$	2.55791e7	0.633481	0.316740	+	0.948512i	$0.397412\pi$
$150$	−1.57644e6	−0.0381380
$151$	2.20103e7	0.520243	0.260121	−	0.965576i	$-0.416237\pi$
$151$	2.20103e7	0.520243	0.260121	+	0.965576i	$0.416237\pi$
$152$	−1.30597e6	−0.0301634
$153$	1.44646e7	0.326502
$154$	2.66281e6	0.0587513
$155$	1.09558e7	0.236311
$156$	2.99969e7	0.632617
$157$	2.45776e7	0.506862	0.253431	−	0.967353i	$-0.418441\pi$
$157$	2.45776e7	0.506862	0.253431	+	0.967353i	$0.418441\pi$
$158$	1.11241e6	0.0224370
$159$	5.23987e7	1.03379
$160$	−7.79762e6	−0.150502
$161$	4.84033e7	0.914080
$162$	−562698.	−0.0103985
$163$	−7.12800e7	−1.28917	−0.644586	−	0.764532i	$-0.722970\pi$
$163$	−7.12800e7	−1.28917	−0.644586	+	0.764532i	$0.722970\pi$
$164$	−7.13085e7	−1.26237
$165$	−6.53764e6	−0.113299
$166$	−8.78761e6	−0.149105
$167$	1.72745e7	0.287010	0.143505	−	0.989650i	$-0.454163\pi$
$167$	1.72745e7	0.287010	0.143505	+	0.989650i	$0.454163\pi$
$168$	1.14729e7	0.186676
$169$	1.39253e7	0.221923
$170$	−3.18486e6	−0.0497186
$171$	−3.52782e6	−0.0539536
$172$	−8.65361e7	−1.29673
$173$	−4.27240e7	−0.627351	−0.313676	−	0.949530i	$-0.601560\pi$
$173$	−4.27240e7	−0.627351	−0.313676	+	0.949530i	$0.601560\pi$
$174$	421393.	0.00606408
$175$	8.68254e7	1.22465
$176$	2.54833e7	0.352340
$177$	−5.54523e6	−0.0751646
$178$	−1.60541e6	−0.0213361
$179$	5.80252e7	0.756191	0.378095	−	0.925767i	$-0.376579\pi$
$179$	5.80252e7	0.756191	0.378095	+	0.925767i	$0.376579\pi$
$180$	−1.40219e7	−0.179207
$181$	−4.33616e7	−0.543539	−0.271769	−	0.962362i	$-0.587609\pi$
$181$	−4.33616e7	−0.543539	−0.271769	+	0.962362i	$0.587609\pi$
$182$	1.45981e7	0.179493
$183$	6.70678e7	0.808976
$184$	−8.29612e6	−0.0981777
$185$	5.42044e7	0.629410
$186$	2.06603e6	0.0235419
$187$	3.16917e7	0.354405
$188$	1.57483e8	1.72855
$189$	3.09917e7	0.333910
$190$	776766.	0.00821585
$191$	−6.93621e7	−0.720287	−0.360143	−	0.932897i	$-0.617272\pi$
$191$	−6.93621e7	−0.720287	−0.360143	+	0.932897i	$0.617272\pi$
$192$	5.36692e7	0.547231
$193$	3.17140e7	0.317541	0.158771	−	0.987315i	$-0.449247\pi$
$193$	3.17140e7	0.317541	0.158771	+	0.987315i	$0.449247\pi$
$194$	−1.08736e7	−0.106922
$195$	−3.58408e7	−0.346144
$196$	−2.10065e8	−1.99277
$197$	−1.33959e8	−1.24836	−0.624178	−	0.781282i	$-0.714566\pi$
$197$	−1.33959e8	−1.24836	−0.624178	+	0.781282i	$0.714566\pi$
$198$	−1.23286e6	−0.0112872
$199$	7.57957e7	0.681803	0.340902	−	0.940099i	$-0.389268\pi$
$199$	7.57957e7	0.681803	0.340902	+	0.940099i	$0.389268\pi$
$200$	−1.48815e7	−0.131535
$201$	3.22742e7	0.280330
$202$	1.28564e7	0.109746
$203$	−2.32090e7	−0.194725
$204$	6.79723e7	0.560566
$205$	8.52006e7	0.690723
$206$	2.24463e7	0.178899
$207$	−2.24103e7	−0.175611
$208$	1.39706e8	1.07645
$209$	−7.72939e6	−0.0585644
$210$	−6.82384e6	−0.0508465
$211$	−2.11972e8	−1.55343	−0.776713	−	0.629854i	$-0.783115\pi$
$211$	−2.11972e8	−1.55343	−0.776713	+	0.629854i	$0.783115\pi$
$212$	2.46233e8	1.77489
$213$	1.48698e8	1.05433
$214$	−61472.9	−0.000428781 0
$215$	1.03395e8	0.709519
$216$	−5.31184e6	−0.0358639
$217$	−1.13791e8	−0.755959
$218$	−1.12809e7	−0.0737475
$219$	2.79583e7	0.179869
$220$	−3.07218e7	−0.194521
$221$	1.73741e8	1.08275
$222$	1.02218e7	0.0627036
$223$	−1.80114e8	−1.08763	−0.543814	−	0.839206i	$-0.683020\pi$
$223$	−1.80114e8	−1.08763	−0.543814	+	0.839206i	$0.683020\pi$
$224$	8.09888e7	0.481456
$225$	−4.01995e7	−0.235278
$226$	5.15434e6	0.0297025
$227$	7.73940e7	0.439154	0.219577	−	0.975595i	$-0.429532\pi$
$227$	7.73940e7	0.439154	0.219577	+	0.975595i	$0.429532\pi$
$228$	−1.65780e7	−0.0926318
$229$	1.39410e8	0.767134	0.383567	−	0.923513i	$-0.374696\pi$
$229$	1.39410e8	0.767134	0.383567	+	0.923513i	$0.374696\pi$
$230$	4.93437e6	0.0267414
$231$	6.79022e7	0.362445
$232$	3.97793e6	0.0209146
$233$	1.24112e8	0.642787	0.321393	−	0.946946i	$-0.395849\pi$
$233$	1.24112e8	0.642787	0.321393	+	0.946946i	$0.395849\pi$
$234$	−6.75883e6	−0.0344839
$235$	−1.88163e8	−0.945796
$236$	−2.60583e7	−0.129049
$237$	2.83667e7	0.138417
$238$	3.30790e7	0.159050
$239$	−1.55356e8	−0.736096	−0.368048	−	0.929807i	$-0.619974\pi$
$239$	−1.55356e8	−0.736096	−0.368048	+	0.929807i	$0.619974\pi$
$240$	−6.53047e7	−0.304934
$241$	3.44462e8	1.58519	0.792597	−	0.609746i	$-0.208729\pi$
$241$	3.44462e8	1.58519	0.792597	+	0.609746i	$0.208729\pi$
$242$	1.79321e7	0.0813352
$243$	−1.43489e7	−0.0641500
$244$	3.15166e8	1.38891
$245$	2.50989e8	1.09037
$246$	1.60670e7	0.0688118
$247$	−4.23743e7	−0.178922
$248$	1.95033e7	0.0811945
$249$	−2.24086e8	−0.919849
$250$	2.13913e7	0.0865860
$251$	−4.67431e8	−1.86578	−0.932888	−	0.360166i	$-0.882720\pi$
$251$	−4.67431e8	−1.86578	−0.932888	+	0.360166i	$0.882720\pi$
$252$	1.45637e8	0.573283
$253$	−4.91007e7	−0.190619
$254$	3.52159e7	0.134841
$255$	−8.12145e7	−0.306721
$256$	2.45232e8	0.913561
$257$	−4.09247e8	−1.50390	−0.751952	−	0.659218i	$-0.770887\pi$
$257$	−4.09247e8	−1.50390	−0.751952	+	0.659218i	$0.770887\pi$
$258$	1.94981e7	0.0706843
$259$	−5.62986e8	−2.01349
$260$	−1.68424e8	−0.594288
$261$	1.07456e7	0.0374101
$262$	−4.03710e6	−0.0138680
$263$	1.04382e8	0.353818	0.176909	−	0.984227i	$-0.443390\pi$
$263$	1.04382e8	0.353818	0.176909	+	0.984227i	$0.443390\pi$
$264$	−1.16382e7	−0.0389287
$265$	−2.94204e8	−0.971152
$266$	−8.06776e6	−0.0262825
$267$	−4.09382e7	−0.131625
$268$	1.51664e8	0.481293
$269$	−1.95159e8	−0.611302	−0.305651	−	0.952144i	$-0.598874\pi$
$269$	−1.95159e8	−0.611302	−0.305651	+	0.952144i	$0.598874\pi$
$270$	3.15938e6	0.00976853
$271$	3.63467e8	1.10936	0.554681	−	0.832063i	$-0.312840\pi$
$271$	3.63467e8	1.10936	0.554681	+	0.832063i	$0.312840\pi$
$272$	3.16570e8	0.953845
$273$	3.72256e8	1.10732
$274$	−4.87244e7	−0.143093
$275$	−8.80763e7	−0.255385
$276$	−1.05311e8	−0.301504
$277$	−3.76920e8	−1.06554	−0.532771	−	0.846260i	$-0.678849\pi$
$277$	−3.76920e8	−1.06554	−0.532771	+	0.846260i	$0.678849\pi$
$278$	−4.79364e7	−0.133816
$279$	5.26843e7	0.145233
$280$	−6.44167e7	−0.175366
$281$	3.38642e8	0.910475	0.455238	−	0.890370i	$-0.349554\pi$
$281$	3.38642e8	0.910475	0.455238	+	0.890370i	$0.349554\pi$
$282$	−3.54837e7	−0.0942229
$283$	−2.79439e8	−0.732882	−0.366441	−	0.930441i	$-0.619424\pi$
$283$	−2.79439e8	−0.732882	−0.366441	+	0.930441i	$0.619424\pi$
$284$	6.98764e8	1.81016
$285$	1.98077e7	0.0506847
$286$	−1.48085e7	−0.0374308
$287$	−8.84923e8	−2.20963
$288$	−3.74972e7	−0.0924964
$289$	−1.66455e7	−0.0405653
$290$	−2.36600e6	−0.00569667
$291$	−2.77280e8	−0.659619
$292$	1.31382e8	0.308813
$293$	6.25978e8	1.45386	0.726930	−	0.686712i	$-0.240946\pi$
$293$	6.25978e8	1.45386	0.726930	+	0.686712i	$0.240946\pi$
$294$	4.73313e7	0.108626
$295$	3.11349e7	0.0706106
$296$	9.64935e7	0.216260
$297$	−3.14382e7	−0.0696322
$298$	−2.70836e7	−0.0592855
$299$	−2.69181e8	−0.582365
$300$	−1.88906e8	−0.403945
$301$	−1.07390e9	−2.26976
$302$	−2.33048e7	−0.0486879
$303$	3.27841e8	0.677039
$304$	−7.72092e7	−0.157620
$305$	−3.76566e8	−0.759962
$306$	−1.53153e7	−0.0305564
$307$	−2.80506e8	−0.553297	−0.276649	−	0.960971i	$-0.589224\pi$
$307$	−2.80506e8	−0.553297	−0.276649	+	0.960971i	$0.589224\pi$
$308$	3.19087e8	0.622275
$309$	5.72385e8	1.10365
$310$	−1.16002e7	−0.0221156
$311$	3.02914e8	0.571029	0.285515	−	0.958374i	$-0.407835\pi$
$311$	3.02914e8	0.571029	0.285515	+	0.958374i	$0.407835\pi$
$312$	−6.38030e7	−0.118932
$313$	−7.65931e8	−1.41184	−0.705918	−	0.708294i	$-0.749465\pi$
$313$	−7.65931e8	−1.41184	−0.705918	+	0.708294i	$0.749465\pi$
$314$	−2.60231e7	−0.0474357
$315$	−1.74009e8	−0.313679
$316$	1.33301e8	0.237645
$317$	−1.06128e9	−1.87120	−0.935601	−	0.353058i	$-0.885142\pi$
$317$	−1.06128e9	−1.87120	−0.935601	+	0.353058i	$0.885142\pi$
$318$	−5.54806e7	−0.0967489
$319$	2.35434e7	0.0406071
$320$	−3.01337e8	−0.514076
$321$	−1.56757e6	−0.00264521
$322$	−5.12501e7	−0.0855459
$323$	−9.60192e7	−0.158544
$324$	−6.74287e7	−0.110138
$325$	−4.82855e8	−0.780234
$326$	7.54724e7	0.120650
$327$	−2.87666e8	−0.454958
$328$	1.51672e8	0.237327
$329$	1.95433e9	3.02561
$330$	6.92215e6	0.0106033
$331$	−3.08627e8	−0.467774	−0.233887	−	0.972264i	$-0.575145\pi$
$331$	−3.08627e8	−0.467774	−0.233887	+	0.972264i	$0.575145\pi$
$332$	−1.05303e9	−1.57927
$333$	2.60658e8	0.386827
$334$	−1.82905e7	−0.0268604
$335$	−1.81210e8	−0.263346
$336$	6.78278e8	0.975484
$337$	−7.55380e8	−1.07513	−0.537565	−	0.843222i	$-0.680656\pi$
$337$	−7.55380e8	−1.07513	−0.537565	+	0.843222i	$0.680656\pi$
$338$	−1.47443e7	−0.0207691
$339$	1.31437e8	0.183239
$340$	−3.81645e8	−0.526603
$341$	1.15430e8	0.157645
$342$	3.73531e6	0.00504935
$343$	−1.31016e9	−1.75306
$344$	1.84061e8	0.243785
$345$	1.25827e8	0.164971
$346$	4.52368e7	0.0587119
$347$	−2.59655e8	−0.333614	−0.166807	−	0.985990i	$-0.553346\pi$
$347$	−2.59655e8	−0.333614	−0.166807	+	0.985990i	$0.553346\pi$
$348$	5.04959e7	0.0642287
$349$	−4.22817e8	−0.532431	−0.266215	−	0.963914i	$-0.585773\pi$
$349$	−4.22817e8	−0.532431	−0.266215	+	0.963914i	$0.585773\pi$
$350$	−9.19321e7	−0.114612
$351$	−1.72351e8	−0.212736
$352$	−8.21556e7	−0.100401
$353$	1.55553e9	1.88221	0.941105	−	0.338116i	$-0.109790\pi$
$353$	1.55553e9	1.88221	0.941105	+	0.338116i	$0.109790\pi$
$354$	5.87138e6	0.00703442
$355$	−8.34895e8	−0.990450
$356$	−1.92378e8	−0.225985
$357$	8.43522e8	0.981201
$358$	−6.14380e7	−0.0707696
$359$	−7.61688e8	−0.868853	−0.434427	−	0.900707i	$-0.643049\pi$
$359$	−7.61688e8	−0.868853	−0.434427	+	0.900707i	$0.643049\pi$
$360$	2.98244e7	0.0336910
$361$	−8.70453e8	−0.973801
$362$	4.59119e7	0.0508681
$363$	4.57273e8	0.501767
$364$	1.74931e9	1.90113
$365$	−1.56977e8	−0.168971
$366$	−7.10124e7	−0.0757095
$367$	1.37332e8	0.145024	0.0725122	−	0.997368i	$-0.476898\pi$
$367$	1.37332e8	0.145024	0.0725122	+	0.997368i	$0.476898\pi$
$368$	−4.90469e8	−0.513031
$369$	4.09713e8	0.424509
$370$	−5.73924e7	−0.0589045
$371$	3.05570e9	3.10672
$372$	2.47575e8	0.249348
$373$	−2.94107e8	−0.293443	−0.146722	−	0.989178i	$-0.546872\pi$
$373$	−2.94107e8	−0.293443	−0.146722	+	0.989178i	$0.546872\pi$
$374$	−3.35556e7	−0.0331677
$375$	5.45483e8	0.534161
$376$	−3.34964e8	−0.324968
$377$	1.29070e8	0.124060
$378$	−3.28145e7	−0.0312496
$379$	6.95112e8	0.655870	0.327935	−	0.944700i	$-0.393647\pi$
$379$	6.95112e8	0.655870	0.327935	+	0.944700i	$0.393647\pi$
$380$	9.30806e7	0.0870195
$381$	8.98012e8	0.831850
$382$	7.34417e7	0.0674094
$383$	−5.22431e8	−0.475153	−0.237576	−	0.971369i	$-0.576353\pi$
$383$	−5.22431e8	−0.475153	−0.237576	+	0.971369i	$0.576353\pi$
$384$	−2.34590e8	−0.211422
$385$	−3.81251e8	−0.340485
$386$	−3.35792e7	−0.0297177
$387$	4.97205e8	0.436061
$388$	−1.30300e9	−1.13249
$389$	−1.26347e9	−1.08829	−0.544143	−	0.838993i	$-0.683145\pi$
$389$	−1.26347e9	−1.08829	−0.544143	+	0.838993i	$0.683145\pi$
$390$	3.79488e7	0.0323946
$391$	−6.09958e8	−0.516038
$392$	4.46806e8	0.374643
$393$	−1.02947e8	−0.0855538
$394$	1.41837e8	0.116830
$395$	−1.59271e8	−0.130031
$396$	−1.47735e8	−0.119550
$397$	7.32040e8	0.587175	0.293588	−	0.955932i	$-0.405151\pi$
$397$	7.32040e8	0.587175	0.293588	+	0.955932i	$0.405151\pi$
$398$	−8.02537e7	−0.0638079
$399$	−2.05730e8	−0.162141
$400$	−8.79799e8	−0.687343
$401$	−1.29683e9	−1.00434	−0.502168	−	0.864770i	$-0.667464\pi$
$401$	−1.29683e9	−1.00434	−0.502168	+	0.864770i	$0.667464\pi$
$402$	−3.41724e7	−0.0262352
$403$	6.32816e8	0.481626
$404$	1.54060e9	1.16240
$405$	8.05649e7	0.0602633
$406$	2.45741e7	0.0182237
$407$	5.71097e8	0.419884
$408$	−1.44576e8	−0.105387
$409$	2.56134e9	1.85113	0.925563	−	0.378594i	$-0.123592\pi$
$409$	2.56134e9	1.85113	0.925563	+	0.378594i	$0.123592\pi$
$410$	−9.02116e7	−0.0646426
$411$	−1.24248e9	−0.882762
$412$	2.68976e9	1.89484
$413$	−3.23378e8	−0.225884
$414$	2.37284e7	0.0164349
$415$	1.25818e9	0.864118
$416$	−4.50396e8	−0.306738
$417$	−1.22239e9	−0.825530
$418$	8.18400e6	0.00548086
$419$	−1.65931e9	−1.10199	−0.550995	−	0.834509i	$-0.685752\pi$
$419$	−1.65931e9	−1.10199	−0.550995	+	0.834509i	$0.685752\pi$
$420$	−8.17707e8	−0.538549
$421$	−2.44008e9	−1.59374	−0.796870	−	0.604151i	$-0.793512\pi$
$421$	−2.44008e9	−1.59374	−0.796870	+	0.604151i	$0.793512\pi$
$422$	2.24440e8	0.145380
$423$	−9.04840e8	−0.581274
$424$	−5.23734e8	−0.333680
$425$	−1.09414e9	−0.691370
$426$	−1.57444e8	−0.0986714
$427$	3.91115e9	2.43112
$428$	−7.36636e6	−0.00454150
$429$	−3.77619e8	−0.230916
$430$	−1.09476e8	−0.0664017
$431$	5.66963e8	0.341102	0.170551	−	0.985349i	$-0.445445\pi$
$431$	5.66963e8	0.341102	0.170551	+	0.985349i	$0.445445\pi$
$432$	−3.14038e8	−0.187408
$433$	−1.17068e9	−0.692996	−0.346498	−	0.938051i	$-0.612629\pi$
$433$	−1.17068e9	−0.692996	−0.346498	+	0.938051i	$0.612629\pi$
$434$	1.20484e8	0.0707479
$435$	−6.03334e7	−0.0351435
$436$	−1.35181e9	−0.781109
$437$	1.48765e8	0.0852737
$438$	−2.96026e7	−0.0168334
$439$	−1.09400e9	−0.617151	−0.308575	−	0.951200i	$-0.599852\pi$
$439$	−1.09400e9	−0.617151	−0.308575	+	0.951200i	$0.599852\pi$
$440$	6.53448e7	0.0365701
$441$	1.20696e9	0.670127
$442$	−1.83960e8	−0.101332
$443$	1.26000e8	0.0688584	0.0344292	−	0.999407i	$-0.489039\pi$
$443$	1.26000e8	0.0688584	0.0344292	+	0.999407i	$0.489039\pi$
$444$	1.22489e9	0.664135
$445$	2.29856e8	0.123650
$446$	1.90707e8	0.101788
$447$	−6.90636e8	−0.365740
$448$	3.12979e9	1.64453
$449$	−2.96820e8	−0.154750	−0.0773750	−	0.997002i	$-0.524654\pi$
$449$	−2.96820e8	−0.154750	−0.0773750	+	0.997002i	$0.524654\pi$
$450$	4.25638e7	0.0220190
$451$	8.97673e8	0.460787
$452$	6.17650e8	0.314599
$453$	−5.94277e8	−0.300362
$454$	−8.19459e7	−0.0410990
$455$	−2.09011e9	−1.04023
$456$	3.52612e7	0.0174149
$457$	2.03128e8	0.0995552	0.0497776	−	0.998760i	$-0.484149\pi$
$457$	2.03128e8	0.0995552	0.0497776	+	0.998760i	$0.484149\pi$
$458$	−1.47610e8	−0.0717937
$459$	−3.90544e8	−0.188506
$460$	5.91291e8	0.283236
$461$	−1.66300e9	−0.790567	−0.395283	−	0.918559i	$-0.629354\pi$
$461$	−1.66300e9	−0.790567	−0.395283	+	0.918559i	$0.629354\pi$
$462$	−7.18959e7	−0.0339201
$463$	−8.36357e8	−0.391614	−0.195807	−	0.980642i	$-0.562733\pi$
$463$	−8.36357e8	−0.391614	−0.195807	+	0.980642i	$0.562733\pi$
$464$	2.35176e8	0.109290
$465$	−2.95807e8	−0.136434
$466$	−1.31411e8	−0.0601564
$467$	−3.67614e9	−1.67026	−0.835129	−	0.550054i	$-0.814607\pi$
$467$	−3.67614e9	−1.67026	−0.835129	+	0.550054i	$0.814607\pi$
$468$	−8.09917e8	−0.365241
$469$	1.88211e9	0.842444
$470$	1.99230e8	0.0885142
$471$	−6.63594e8	−0.292637
$472$	5.54256e7	0.0242612
$473$	1.08937e9	0.473326
$474$	−3.00351e7	−0.0129540
$475$	2.66853e8	0.114247
$476$	3.96390e9	1.68460
$477$	−1.41477e9	−0.596857
$478$	1.64493e8	0.0688890
$479$	4.47354e9	1.85985	0.929924	−	0.367752i	$-0.119873\pi$
$479$	4.47354e9	1.85985	0.929924	+	0.367752i	$0.119873\pi$
$480$	2.10536e8	0.0868923
$481$	3.13089e9	1.28280
$482$	−3.64722e8	−0.148353
$483$	−1.30689e9	−0.527744
$484$	2.14883e9	0.861475
$485$	1.55685e9	0.619654
$486$	1.51928e7	0.00600360
$487$	5.90180e8	0.231544	0.115772	−	0.993276i	$-0.463066\pi$
$487$	5.90180e8	0.231544	0.115772	+	0.993276i	$0.463066\pi$
$488$	−6.70354e8	−0.261117
$489$	1.92456e9	0.744304
$490$	−2.65751e8	−0.102044
$491$	1.22115e9	0.465568	0.232784	−	0.972528i	$-0.425216\pi$
$491$	1.22115e9	0.465568	0.232784	+	0.972528i	$0.425216\pi$
$492$	1.92533e9	0.728831
$493$	2.92471e8	0.109930
$494$	4.48666e7	0.0167447
$495$	1.76516e8	0.0654133
$496$	1.15304e9	0.424285
$497$	8.67151e9	3.16846
$498$	2.37265e8	0.0860859
$499$	1.48542e9	0.535176	0.267588	−	0.963533i	$-0.413773\pi$
$499$	1.48542e9	0.535176	0.267588	+	0.963533i	$0.413773\pi$
$500$	2.56335e9	0.917090
$501$	−4.66411e8	−0.165705
$502$	4.94923e8	0.174612
$503$	−2.28973e9	−0.802224	−0.401112	−	0.916029i	$-0.631376\pi$
$503$	−2.28973e9	−0.802224	−0.401112	+	0.916029i	$0.631376\pi$
$504$	−3.09767e8	−0.107778
$505$	−1.84073e9	−0.636019
$506$	5.19885e7	0.0178394
$507$	−3.75984e8	−0.128127
$508$	4.21996e9	1.42819
$509$	−4.18910e9	−1.40802	−0.704009	−	0.710191i	$-0.748608\pi$
$509$	−4.18910e9	−1.40802	−0.704009	+	0.710191i	$0.748608\pi$
$510$	8.59911e7	0.0287050
$511$	1.63042e9	0.540539
$512$	−1.37179e9	−0.451691
$513$	9.52512e7	0.0311501
$514$	4.33317e8	0.140746
$515$	−3.21377e9	−1.03679
$516$	2.33648e9	0.748665
$517$	−1.98249e9	−0.630948
$518$	5.96098e8	0.188436
$519$	1.15355e9	0.362201
$520$	3.58235e8	0.111727
$521$	1.43063e9	0.443196	0.221598	−	0.975138i	$-0.428873\pi$
$521$	1.43063e9	0.443196	0.221598	+	0.975138i	$0.428873\pi$
$522$	−1.13776e7	−0.00350110
$523$	1.34628e9	0.411509	0.205755	−	0.978604i	$-0.434035\pi$
$523$	1.34628e9	0.411509	0.205755	+	0.978604i	$0.434035\pi$
$524$	−4.83770e8	−0.146886
$525$	−2.34429e9	−0.707055
$526$	−1.10521e8	−0.0331127
$527$	1.43395e9	0.426772
$528$	−6.88050e8	−0.203424
$529$	−2.45980e9	−0.722446
$530$	3.11507e8	0.0908871
$531$	1.49721e8	0.0433963
$532$	−9.66768e8	−0.278376
$533$	4.92125e9	1.40776
$534$	4.33460e7	0.0123184
$535$	8.80145e6	0.00248494
$536$	−3.22586e8	−0.0904835
$537$	−1.56668e9	−0.436587
$538$	2.06637e8	0.0572099
$539$	2.64442e9	0.727395
$540$	3.78592e8	0.103465
$541$	−3.77248e9	−1.02432	−0.512162	−	0.858889i	$-0.671155\pi$
$541$	−3.77248e9	−1.02432	−0.512162	+	0.858889i	$0.671155\pi$
$542$	−3.84845e8	−0.103822
$543$	1.17076e9	0.313812
$544$	−1.02059e9	−0.271803
$545$	1.61516e9	0.427393
$546$	−3.94150e8	−0.103630
$547$	1.81833e9	0.475026	0.237513	−	0.971384i	$-0.423668\pi$
$547$	1.81833e9	0.475026	0.237513	+	0.971384i	$0.423668\pi$
$548$	−5.83869e9	−1.51560
$549$	−1.81083e9	−0.467062
$550$	9.32566e7	0.0239007
$551$	−7.13317e7	−0.0181657
$552$	2.23995e8	0.0566829
$553$	1.65424e9	0.415969
$554$	3.99089e8	0.0997208
$555$	−1.46352e9	−0.363390
$556$	−5.74427e9	−1.41734
$557$	−5.99186e7	−0.0146916	−0.00734579	−	0.999973i	$-0.502338\pi$
$557$	−5.99186e7	−0.0146916	−0.00734579	+	0.999973i	$0.502338\pi$
$558$	−5.57829e7	−0.0135919
$559$	5.97216e9	1.44607
$560$	−3.80833e9	−0.916382
$561$	−8.55675e8	−0.204616
$562$	−3.58559e8	−0.0852086
$563$	−5.52477e9	−1.30477	−0.652386	−	0.757887i	$-0.726232\pi$
$563$	−5.52477e9	−1.30477	−0.652386	+	0.757887i	$0.726232\pi$
$564$	−4.25204e9	−0.997978
$565$	−7.37978e8	−0.172137
$566$	2.95874e8	0.0685882
$567$	−8.36775e8	−0.192783
$568$	−1.48626e9	−0.340311
$569$	−5.19237e9	−1.18161	−0.590803	−	0.806816i	$-0.701189\pi$
$569$	−5.19237e9	−1.18161	−0.590803	+	0.806816i	$0.701189\pi$
$570$	−2.09727e7	−0.00474342
$571$	1.98094e9	0.445293	0.222647	−	0.974899i	$-0.428530\pi$
$571$	1.98094e9	0.445293	0.222647	+	0.974899i	$0.428530\pi$
$572$	−1.77451e9	−0.396454
$573$	1.87278e9	0.415858
$574$	9.36970e8	0.206792
$575$	1.69517e9	0.371858
$576$	−1.44907e9	−0.315944
$577$	−3.25873e9	−0.706209	−0.353104	−	0.935584i	$-0.614874\pi$
$577$	−3.25873e9	−0.706209	−0.353104	+	0.935584i	$0.614874\pi$
$578$	1.76245e7	0.00379638
$579$	−8.56278e8	−0.183333
$580$	−2.83520e8	−0.0603372
$581$	−1.30679e10	−2.76432
$582$	2.93588e8	0.0617317
$583$	−3.09973e9	−0.647863
$584$	−2.79448e8	−0.0580571
$585$	9.67703e8	0.199846
$586$	−6.62795e8	−0.136062
$587$	−7.32754e8	−0.149529	−0.0747643	−	0.997201i	$-0.523820\pi$
$587$	−7.32754e8	−0.149529	−0.0747643	+	0.997201i	$0.523820\pi$
$588$	5.67176e9	1.15053
$589$	−3.49730e8	−0.0705227
$590$	−3.29661e7	−0.00660823
$591$	3.61688e9	0.720739
$592$	5.70472e9	1.13008
$593$	7.42096e9	1.46140	0.730699	−	0.682700i	$-0.239194\pi$
$593$	7.42096e9	1.46140	0.730699	+	0.682700i	$0.239194\pi$
$594$	3.32872e7	0.00651666
$595$	−4.73613e9	−0.921752
$596$	−3.24545e9	−0.627933
$597$	−2.04648e9	−0.393639
$598$	2.85013e8	0.0545018
$599$	−1.05376e9	−0.200331	−0.100165	−	0.994971i	$-0.531937\pi$
$599$	−1.05376e9	−0.200331	−0.100165	+	0.994971i	$0.531937\pi$
$600$	4.01801e8	0.0759419
$601$	−7.07267e9	−1.32899	−0.664496	−	0.747292i	$-0.731354\pi$
$601$	−7.07267e9	−1.32899	−0.664496	+	0.747292i	$0.731354\pi$
$602$	1.13706e9	0.212420
$603$	−8.71404e8	−0.161849
$604$	−2.79264e9	−0.515686
$605$	−2.56745e9	−0.471367
$606$	−3.47123e8	−0.0633620
$607$	4.55310e9	0.826317	0.413159	−	0.910659i	$-0.364426\pi$
$607$	4.55310e9	0.826317	0.413159	+	0.910659i	$0.364426\pi$
$608$	2.48914e8	0.0449146
$609$	6.26644e8	0.112424
$610$	3.98714e8	0.0711225
$611$	−1.08685e10	−1.92763
$612$	−1.83525e9	−0.323643
$613$	6.47628e9	1.13557	0.567785	−	0.823177i	$-0.307800\pi$
$613$	6.47628e9	1.13557	0.567785	+	0.823177i	$0.307800\pi$
$614$	2.97004e8	0.0517814
$615$	−2.30042e9	−0.398789
$616$	−6.78694e8	−0.116988
$617$	4.44035e9	0.761061	0.380531	−	0.924768i	$-0.375741\pi$
$617$	4.44035e9	0.761061	0.380531	+	0.924768i	$0.375741\pi$
$618$	−6.06049e8	−0.103288
$619$	2.96260e9	0.502060	0.251030	−	0.967979i	$-0.419231\pi$
$619$	2.96260e9	0.502060	0.251030	+	0.967979i	$0.419231\pi$
$620$	−1.39006e9	−0.234241
$621$	6.05079e8	0.101389
$622$	−3.20730e8	−0.0534409
$623$	−2.38737e9	−0.395559
$624$	−3.77205e9	−0.621486
$625$	1.24534e9	0.204037
$626$	8.10979e8	0.132129
$627$	2.08694e8	0.0338121
$628$	−3.11837e9	−0.502423
$629$	7.09452e9	1.13670
$630$	1.84244e8	0.0293562
$631$	1.60390e9	0.254142	0.127071	−	0.991894i	$-0.459442\pi$
$631$	1.60390e9	0.254142	0.127071	+	0.991894i	$0.459442\pi$
$632$	−2.83530e8	−0.0446775
$633$	5.72325e9	0.896871
$634$	1.12369e9	0.175120
$635$	−5.04207e9	−0.781450
$636$	−6.64830e9	−1.02473
$637$	1.44973e10	2.22229
$638$	−2.49281e7	−0.00380030
$639$	−4.01484e9	−0.608717
$640$	1.31715e9	0.198613
$641$	−6.32307e8	−0.0948254	−0.0474127	−	0.998875i	$-0.515098\pi$
$641$	−6.32307e8	−0.0948254	−0.0474127	+	0.998875i	$0.515098\pi$
$642$	1.65977e6	0.000247557 0
$643$	−4.72453e9	−0.700842	−0.350421	−	0.936592i	$-0.613961\pi$
$643$	−4.72453e9	−0.700842	−0.350421	+	0.936592i	$0.613961\pi$
$644$	−6.14136e9	−0.906074
$645$	−2.79166e9	−0.409641
$646$	1.01667e8	0.0148376
$647$	−6.52515e9	−0.947165	−0.473582	−	0.880750i	$-0.657039\pi$
$647$	−6.52515e9	−0.947165	−0.473582	+	0.880750i	$0.657039\pi$
$648$	1.43420e8	0.0207060
$649$	3.28037e8	0.0471049
$650$	5.11254e8	0.0730197
$651$	3.07235e9	0.436453
$652$	9.04393e9	1.27788
$653$	−7.88114e9	−1.10762	−0.553812	−	0.832641i	$-0.686828\pi$
$653$	−7.88114e9	−1.10762	−0.553812	+	0.832641i	$0.686828\pi$
$654$	3.04585e8	0.0425781
$655$	5.78017e8	0.0803703
$656$	8.96689e9	1.24016
$657$	−7.54873e8	−0.103847
$658$	−2.06928e9	−0.283157
$659$	7.14701e9	0.972805	0.486402	−	0.873735i	$-0.338309\pi$
$659$	7.14701e9	0.972805	0.486402	+	0.873735i	$0.338309\pi$
$660$	8.29488e8	0.112307
$661$	−5.05842e9	−0.681255	−0.340627	−	0.940198i	$-0.610639\pi$
$661$	−5.05842e9	−0.681255	−0.340627	+	0.940198i	$0.610639\pi$
$662$	3.26779e8	0.0437776
$663$	−4.69101e9	−0.625128
$664$	2.23978e9	0.296904
$665$	1.15511e9	0.152317
$666$	−2.75989e8	−0.0362019
$667$	−4.53132e8	−0.0591267
$668$	−2.19177e9	−0.284496
$669$	4.86308e9	0.627942
$670$	1.91868e8	0.0246457
$671$	−3.96750e9	−0.506977
$672$	−2.18670e9	−0.277969
$673$	−1.46795e10	−1.85634	−0.928169	−	0.372158i	$-0.878618\pi$
$673$	−1.46795e10	−1.85634	−0.928169	+	0.372158i	$0.878618\pi$
$674$	7.99808e8	0.100618
$675$	1.08539e9	0.135838
$676$	−1.76683e9	−0.219979
$677$	8.90911e9	1.10350	0.551752	−	0.834008i	$-0.313959\pi$
$677$	8.90911e9	1.10350	0.551752	+	0.834008i	$0.313959\pi$
$678$	−1.39167e8	−0.0171488
$679$	−1.61700e10	−1.98228
$680$	8.11753e8	0.0990017
$681$	−2.08964e9	−0.253546
$682$	−1.22219e8	−0.0147535
$683$	−1.04640e10	−1.25668	−0.628338	−	0.777940i	$-0.716265\pi$
$683$	−1.04640e10	−1.25668	−0.628338	+	0.777940i	$0.716265\pi$
$684$	4.47606e8	0.0534810
$685$	6.97617e9	0.829278
$686$	1.38722e9	0.164063
$687$	−3.76408e9	−0.442905
$688$	1.08817e10	1.27391
$689$	−1.69934e10	−1.97931
$690$	−1.33228e8	−0.0154392
$691$	−9.56029e9	−1.10230	−0.551148	−	0.834408i	$-0.685810\pi$
$691$	−9.56029e9	−1.10230	−0.551148	+	0.834408i	$0.685810\pi$
$692$	5.42078e9	0.621857
$693$	−1.83336e9	−0.209258
$694$	2.74927e8	0.0312219
$695$	6.86335e9	0.775513
$696$	−1.07404e8	−0.0120750
$697$	1.11514e10	1.24743
$698$	4.47685e8	0.0498285
$699$	−3.35101e9	−0.371113
$700$	−1.10163e10	−1.21393
$701$	4.24136e9	0.465041	0.232521	−	0.972591i	$-0.425303\pi$
$701$	4.24136e9	0.465041	0.232521	+	0.972591i	$0.425303\pi$
$702$	1.82488e8	0.0199093
$703$	−1.73031e9	−0.187836
$704$	−3.17488e9	−0.342944
$705$	5.08041e9	0.546056
$706$	−1.64702e9	−0.176150
$707$	1.91185e10	2.03463
$708$	7.03573e8	0.0745063
$709$	1.04133e10	1.09730	0.548652	−	0.836051i	$-0.315141\pi$
$709$	1.04133e10	1.09730	0.548652	+	0.836051i	$0.315141\pi$
$710$	8.84000e8	0.0926932
$711$	−7.65900e8	−0.0799151
$712$	4.09184e8	0.0424853
$713$	−2.22164e9	−0.229542
$714$	−8.93134e8	−0.0918275
$715$	2.12022e9	0.216925
$716$	−7.36218e9	−0.749567
$717$	4.19460e9	0.424985
$718$	8.06487e8	0.0813133
$719$	−6.99544e9	−0.701882	−0.350941	−	0.936398i	$-0.614138\pi$
$719$	−6.99544e9	−0.701882	−0.350941	+	0.936398i	$0.614138\pi$
$720$	1.76323e9	0.176054
$721$	3.33794e10	3.31669
$722$	9.21649e8	0.0911351
$723$	−9.30049e9	−0.915212
$724$	5.50168e9	0.538778
$725$	−8.12824e8	−0.0792161
$726$	−4.84168e8	−0.0469589
$727$	1.85412e10	1.78965	0.894824	−	0.446418i	$-0.147301\pi$
$727$	1.85412e10	1.78965	0.894824	+	0.446418i	$0.147301\pi$
$728$	−3.72076e9	−0.357414
$729$	3.87420e8	0.0370370
$730$	1.66210e8	0.0158135
$731$	1.35328e10	1.28137
$732$	−8.50949e9	−0.801890
$733$	−7.68407e9	−0.720655	−0.360327	−	0.932826i	$-0.617335\pi$
$733$	−7.68407e9	−0.720655	−0.360327	+	0.932826i	$0.617335\pi$
$734$	−1.45409e8	−0.0135724
$735$	−6.77671e9	−0.629526
$736$	1.58122e9	0.146191
$737$	−1.90923e9	−0.175680
$738$	−4.33810e8	−0.0397285
$739$	−1.62766e9	−0.148357	−0.0741785	−	0.997245i	$-0.523633\pi$
$739$	−1.62766e9	−0.148357	−0.0741785	+	0.997245i	$0.523633\pi$
$740$	−6.87740e9	−0.623897
$741$	1.14411e9	0.103301
$742$	−3.23542e9	−0.290748
$743$	−1.23451e9	−0.110417	−0.0552084	−	0.998475i	$-0.517582\pi$
$743$	−1.23451e9	−0.110417	−0.0552084	+	0.998475i	$0.517582\pi$
$744$	−5.26589e8	−0.0468777
$745$	3.87772e9	0.343581
$746$	3.11405e8	0.0274625
$747$	6.05032e9	0.531075
$748$	−4.02101e9	−0.351301
$749$	−9.14149e7	−0.00794934
$750$	−5.77566e8	−0.0499905
$751$	1.87234e10	1.61304	0.806520	−	0.591206i	$-0.201348\pi$
$751$	1.87234e10	1.61304	0.806520	+	0.591206i	$0.201348\pi$
$752$	−1.98032e10	−1.69814
$753$	1.26206e10	1.07721
$754$	−1.36662e8	−0.0116104
$755$	3.33669e9	0.282164
$756$	−3.93219e9	−0.330985
$757$	−3.90822e9	−0.327449	−0.163724	−	0.986506i	$-0.552351\pi$
$757$	−3.90822e9	−0.327449	−0.163724	+	0.986506i	$0.552351\pi$
$758$	−7.35995e8	−0.0613809
$759$	1.32572e9	0.110054
$760$	−1.97981e8	−0.0163597
$761$	8.54296e9	0.702687	0.351344	−	0.936247i	$-0.385725\pi$
$761$	8.54296e9	0.702687	0.351344	+	0.936247i	$0.385725\pi$
$762$	−9.50829e8	−0.0778502
$763$	−1.67756e10	−1.36723
$764$	8.80059e9	0.713978
$765$	2.19279e9	0.177085
$766$	5.53158e8	0.0444681
$767$	1.79837e9	0.143912
$768$	−6.62127e9	−0.527445
$769$	−8.98742e9	−0.712677	−0.356338	−	0.934357i	$-0.615975\pi$
$769$	−8.98742e9	−0.712677	−0.356338	+	0.934357i	$0.615975\pi$
$770$	4.03674e8	0.0318650
$771$	1.10497e10	0.868279
$772$	−4.02384e9	−0.314760
$773$	7.14394e9	0.556301	0.278150	−	0.960538i	$-0.410279\pi$
$773$	7.14394e9	0.556301	0.278150	+	0.960538i	$0.410279\pi$
$774$	−5.26448e8	−0.0408096
$775$	−3.98517e9	−0.307532
$776$	2.77146e9	0.212908
$777$	1.52006e10	1.16249
$778$	1.33779e9	0.101849
$779$	−2.71976e9	−0.206134
$780$	4.54745e9	0.343112
$781$	−8.79645e9	−0.660737
$782$	6.45833e8	0.0482944
$783$	−2.90131e8	−0.0215987
$784$	2.64153e10	1.95771
$785$	3.72588e9	0.274907
$786$	1.09002e8	0.00800672
$787$	2.12694e9	0.155541	0.0777705	−	0.996971i	$-0.475220\pi$
$787$	2.12694e9	0.155541	0.0777705	+	0.996971i	$0.475220\pi$
$788$	1.69965e10	1.23742
$789$	−2.81831e9	−0.204277
$790$	1.68638e8	0.0121692
$791$	7.66490e9	0.550667
$792$	3.14230e8	0.0224755
$793$	−2.17507e10	−1.54888
$794$	−7.75095e8	−0.0549519
$795$	7.94349e9	0.560695
$796$	−9.61688e9	−0.675832
$797$	−7.00833e9	−0.490355	−0.245177	−	0.969478i	$-0.578846\pi$
$797$	−7.00833e9	−0.490355	−0.245177	+	0.969478i	$0.578846\pi$
$798$	2.17830e8	0.0151742
$799$	−2.46277e10	−1.70809
$800$	2.83638e9	0.195862
$801$	1.10533e9	0.0759939
$802$	1.37311e9	0.0939926
$803$	−1.65391e9	−0.112722
$804$	−4.09492e9	−0.277875
$805$	7.33780e9	0.495770
$806$	−6.70035e8	−0.0450739
$807$	5.26930e9	0.352935
$808$	−3.27682e9	−0.218531
$809$	2.24886e10	1.49329	0.746643	−	0.665225i	$-0.231665\pi$
$809$	2.24886e10	1.49329	0.746643	+	0.665225i	$0.231665\pi$
$810$	−8.53033e7	−0.00563986
$811$	−7.32750e9	−0.482373	−0.241186	−	0.970479i	$-0.577536\pi$
$811$	−7.32750e9	−0.482373	−0.241186	+	0.970479i	$0.577536\pi$
$812$	2.94474e9	0.193019
$813$	−9.81362e9	−0.640490
$814$	−6.04686e8	−0.0392957
$815$	−1.08058e10	−0.699209
$816$	−8.54738e9	−0.550703
$817$	−3.30056e9	−0.211743
$818$	−2.71199e9	−0.173241
$819$	−1.00509e10	−0.639310
$820$	−1.08102e10	−0.684673
$821$	−1.86005e10	−1.17307	−0.586534	−	0.809924i	$-0.699508\pi$
$821$	−1.86005e10	−1.17307	−0.586534	+	0.809924i	$0.699508\pi$
$822$	1.31556e9	0.0826150
$823$	−3.44677e9	−0.215532	−0.107766	−	0.994176i	$-0.534370\pi$
$823$	−3.44677e9	−0.215532	−0.107766	+	0.994176i	$0.534370\pi$
$824$	−5.72108e9	−0.356232
$825$	2.37806e9	0.147446
$826$	3.42397e8	0.0211398
$827$	5.34418e9	0.328558	0.164279	−	0.986414i	$-0.447470\pi$
$827$	5.34418e9	0.328558	0.164279	+	0.986414i	$0.447470\pi$
$828$	2.84340e9	0.174073
$829$	1.24427e10	0.758532	0.379266	−	0.925288i	$-0.376176\pi$
$829$	1.24427e10	0.758532	0.379266	+	0.925288i	$0.376176\pi$
$830$	−1.33218e9	−0.0808701
$831$	1.01769e10	0.615191
$832$	−1.74054e10	−1.04774
$833$	3.28506e10	1.96918
$834$	1.29428e9	0.0772588
$835$	2.61876e9	0.155666
$836$	9.80697e8	0.0580514
$837$	−1.42248e9	−0.0838505
$838$	1.75690e9	0.103132
$839$	2.08037e10	1.21611	0.608056	−	0.793894i	$-0.291950\pi$
$839$	2.08037e10	1.21611	0.608056	+	0.793894i	$0.291950\pi$
$840$	1.73925e9	0.101248
$841$	−1.70326e10	−0.987404
$842$	2.58360e9	0.149153
$843$	−9.14332e9	−0.525663
$844$	2.68948e10	1.53982
$845$	2.11104e9	0.120364
$846$	9.58059e8	0.0543996
$847$	2.66665e10	1.50790
$848$	−3.09633e10	−1.74366
$849$	7.54485e9	0.423130
$850$	1.15849e9	0.0647032
$851$	−1.09917e10	−0.611380
$852$	−1.88666e10	−1.04509
$853$	3.30134e10	1.82125	0.910623	−	0.413239i	$-0.135603\pi$
$853$	3.30134e10	1.82125	0.910623	+	0.413239i	$0.135603\pi$
$854$	−4.14118e9	−0.227521
$855$	−5.34807e8	−0.0292628
$856$	1.56681e7	0.000853806 0
$857$	7.37991e9	0.400515	0.200257	−	0.979743i	$-0.435822\pi$
$857$	7.37991e9	0.400515	0.200257	+	0.979743i	$0.435822\pi$
$858$	3.99829e8	0.0216107
$859$	8.66866e9	0.466633	0.233317	−	0.972401i	$-0.425042\pi$
$859$	8.66866e9	0.466633	0.233317	+	0.972401i	$0.425042\pi$
$860$	−1.31186e10	−0.703305
$861$	2.38929e10	1.27573
$862$	−6.00309e8	−0.0319227
$863$	−9.44417e8	−0.0500180	−0.0250090	−	0.999687i	$-0.507961\pi$
$863$	−9.44417e8	−0.0500180	−0.0250090	+	0.999687i	$0.507961\pi$
$864$	1.01242e9	0.0534028
$865$	−6.47684e9	−0.340257
$866$	1.23953e9	0.0648554
$867$	4.49429e8	0.0234204
$868$	1.44377e10	0.749338
$869$	−1.67807e9	−0.0867445
$870$	6.38819e7	0.00328898
$871$	−1.04668e10	−0.536725
$872$	2.87527e9	0.146849
$873$	7.48656e9	0.380831
$874$	−1.57514e8	−0.00798050
$875$	3.18106e10	1.60525
$876$	−3.54731e9	−0.178293
$877$	−1.94376e10	−0.973071	−0.486535	−	0.873661i	$-0.661740\pi$
$877$	−1.94376e10	−0.973071	−0.486535	+	0.873661i	$0.661740\pi$
$878$	1.15834e9	0.0577573
$879$	−1.69014e10	−0.839386
$880$	3.86320e9	0.191099
$881$	3.61733e10	1.78227	0.891134	−	0.453741i	$-0.149911\pi$
$881$	3.61733e10	1.78227	0.891134	+	0.453741i	$0.149911\pi$
$882$	−1.27795e9	−0.0627151
$883$	−2.10672e10	−1.02978	−0.514890	−	0.857256i	$-0.672167\pi$
$883$	−2.10672e10	−1.02978	−0.514890	+	0.857256i	$0.672167\pi$
$884$	−2.20441e10	−1.07327
$885$	−8.40641e8	−0.0407670
$886$	−1.33410e8	−0.00644424
$887$	3.08019e10	1.48199	0.740993	−	0.671512i	$-0.234355\pi$
$887$	3.08019e10	1.48199	0.740993	+	0.671512i	$0.234355\pi$
$888$	−2.60532e9	−0.124858
$889$	5.23688e10	2.49986
$890$	−2.43375e8	−0.0115721
$891$	8.48831e8	0.0402022
$892$	2.28527e10	1.07810
$893$	6.00653e9	0.282256
$894$	7.31256e8	0.0342285
$895$	8.79645e9	0.410135
$896$	−1.36804e10	−0.635363
$897$	7.26789e9	0.336229
$898$	3.14277e8	0.0144826
$899$	1.06526e9	0.0488988
$900$	5.10047e9	0.233218
$901$	−3.85067e10	−1.75388
$902$	−9.50469e8	−0.0431236
$903$	2.89952e10	1.31044
$904$	−1.31373e9	−0.0591449
$905$	−6.57349e9	−0.294799
$906$	6.29230e8	0.0281100
$907$	1.57628e10	0.701466	0.350733	−	0.936475i	$-0.385932\pi$
$907$	1.57628e10	0.701466	0.350733	+	0.936475i	$0.385932\pi$
$908$	−9.81966e9	−0.435307
$909$	−8.85170e9	−0.390889
$910$	2.21304e9	0.0973517
$911$	8.64623e9	0.378890	0.189445	−	0.981891i	$-0.439331\pi$
$911$	8.64623e9	0.378890	0.189445	+	0.981891i	$0.439331\pi$
$912$	2.08465e9	0.0910020
$913$	1.32561e10	0.576460
$914$	−2.15075e8	−0.00931706
$915$	1.01673e10	0.438764
$916$	−1.76883e10	−0.760415
$917$	−6.00348e9	−0.257105
$918$	4.13514e8	0.0176417
$919$	−1.72145e10	−0.731628	−0.365814	−	0.930688i	$-0.619209\pi$
$919$	−1.72145e10	−0.731628	−0.365814	+	0.930688i	$0.619209\pi$
$920$	−1.25767e9	−0.0532486
$921$	7.57367e9	0.319446
$922$	1.76081e9	0.0739867
$923$	−4.82242e10	−2.01864
$924$	−8.61536e9	−0.359270
$925$	−1.97168e10	−0.819107
$926$	8.85547e8	0.0366499
$927$	−1.54544e10	−0.637195
$928$	−7.58184e8	−0.0311427
$929$	2.13454e10	0.873471	0.436735	−	0.899590i	$-0.356135\pi$
$929$	2.13454e10	0.873471	0.436735	+	0.899590i	$0.356135\pi$
$930$	3.13205e8	0.0127684
$931$	−8.01205e9	−0.325402
$932$	−1.57472e10	−0.637157
$933$	−8.17868e9	−0.329684
$934$	3.89236e9	0.156314
$935$	4.80436e9	0.192219
$936$	1.72268e9	0.0686657
$937$	2.94917e9	0.117115	0.0585573	−	0.998284i	$-0.481350\pi$
$937$	2.94917e9	0.117115	0.0585573	+	0.998284i	$0.481350\pi$
$938$	−1.99281e9	−0.0788417
$939$	2.06801e10	0.815124
$940$	2.38740e10	0.937513
$941$	8.66911e9	0.339165	0.169582	−	0.985516i	$-0.445758\pi$
$941$	8.66911e9	0.339165	0.169582	+	0.985516i	$0.445758\pi$
$942$	7.02623e8	0.0273870
$943$	−1.72772e10	−0.670937
$944$	3.27677e9	0.126778
$945$	4.69825e9	0.181103
$946$	−1.15344e9	−0.0442971
$947$	1.86313e10	0.712884	0.356442	−	0.934317i	$-0.383990\pi$
$947$	1.86313e10	0.712884	0.356442	+	0.934317i	$0.383990\pi$
$948$	−3.59913e9	−0.137205
$949$	−9.06713e9	−0.344380
$950$	−2.82548e8	−0.0106920
$951$	2.86544e10	1.08034
$952$	−8.43115e9	−0.316707
$953$	3.78151e10	1.41527	0.707637	−	0.706576i	$-0.249761\pi$
$953$	3.78151e10	1.41527	0.707637	+	0.706576i	$0.249761\pi$
$954$	1.49798e9	0.0558580
$955$	−1.05151e10	−0.390662
$956$	1.97114e10	0.729649
$957$	−6.35672e8	−0.0234445
$958$	−4.73666e9	−0.174057
$959$	−7.24570e10	−2.65286
$960$	8.13609e9	0.296802
$961$	−2.22898e10	−0.810165
$962$	−3.31503e9	−0.120054
$963$	4.23244e7	0.00152721
$964$	−4.37050e10	−1.57131
$965$	4.80775e9	0.172225
$966$	1.38375e9	0.0493900
$967$	−3.55682e10	−1.26494	−0.632470	−	0.774585i	$-0.717959\pi$
$967$	−3.55682e10	−1.26494	−0.632470	+	0.774585i	$0.717959\pi$
$968$	−4.57052e9	−0.161958
$969$	2.59252e9	0.0915353
$970$	−1.64841e9	−0.0579915
$971$	2.79517e10	0.979806	0.489903	−	0.871777i	$-0.337032\pi$
$971$	2.79517e10	0.979806	0.489903	+	0.871777i	$0.337032\pi$
$972$	1.82057e9	0.0635882
$973$	−7.12852e10	−2.48087
$974$	−6.24891e8	−0.0216695
$975$	1.30371e10	0.450468
$976$	−3.96315e10	−1.36448
$977$	−6.61358e9	−0.226885	−0.113443	−	0.993545i	$-0.536188\pi$
$977$	−6.61358e9	−0.226885	−0.113443	+	0.993545i	$0.536188\pi$
$978$	−2.03775e9	−0.0696571
$979$	2.42176e9	0.0824882
$980$	−3.18453e10	−1.08082
$981$	7.76698e9	0.262670
$982$	−1.29297e9	−0.0435711
$983$	1.77476e10	0.595939	0.297970	−	0.954575i	$-0.403691\pi$
$983$	1.77476e10	0.595939	0.297970	+	0.954575i	$0.403691\pi$
$984$	−4.09515e9	−0.137021
$985$	−2.03077e10	−0.677071
$986$	−3.09672e8	−0.0102881
$987$	−5.27670e10	−1.74684
$988$	5.37641e9	0.177355
$989$	−2.09667e10	−0.689195
$990$	−1.86898e8	−0.00612183
$991$	−4.22116e9	−0.137776	−0.0688880	−	0.997624i	$-0.521945\pi$
$991$	−4.22116e9	−0.137776	−0.0688880	+	0.997624i	$0.521945\pi$
$992$	−3.71728e9	−0.120902
$993$	8.33294e9	0.270070
$994$	−9.18153e9	−0.296526
$995$	1.14904e10	0.369790
$996$	2.84318e10	0.911793
$997$	−2.02379e10	−0.646742	−0.323371	−	0.946272i	$-0.604816\pi$
$997$	−2.02379e10	−0.646742	−0.323371	+	0.946272i	$0.604816\pi$
$998$	−1.57278e9	−0.0500854
$999$	−7.03777e9	−0.223335

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.a.1.9	✓	16
3.2	odd	2		531.8.a.b.1.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.9	✓	16	1.1	even	1	trivial
531.8.a.b.1.8		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-1.05882 q^{2} -27.0000 q^{3} -126.879 q^{4} +151.597 q^{5} +28.5880 q^{6} -1574.54 q^{7} +269.870 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-1.05882 q^{2} -27.0000 q^{3} -126.879 q^{4} +151.597 q^{5} +28.5880 q^{6} -1574.54 q^{7} +269.870 q^{8} +729.000 q^{9} -160.513 q^{10} +1597.23 q^{11} +3425.73 q^{12} +8756.36 q^{13} +1667.15 q^{14} -4093.12 q^{15} +15954.8 q^{16} +19841.7 q^{17} -771.876 q^{18} -4839.26 q^{19} -19234.5 q^{20} +42512.6 q^{21} -1691.17 q^{22} -30741.2 q^{23} -7286.48 q^{24} -55143.3 q^{25} -9271.37 q^{26} -19683.0 q^{27} +199776. q^{28} +14740.2 q^{29} +4333.86 q^{30} +72269.3 q^{31} -51436.5 q^{32} -43125.1 q^{33} -21008.7 q^{34} -238696. q^{35} -92494.7 q^{36} +357556. q^{37} +5123.88 q^{38} -236422. q^{39} +40911.4 q^{40} +562020. q^{41} -45013.0 q^{42} +682037. q^{43} -202654. q^{44} +110514. q^{45} +32549.3 q^{46} -1.24121e6 q^{47} -430778. q^{48} +1.65563e6 q^{49} +58386.6 q^{50} -535726. q^{51} -1.11100e6 q^{52} -1.94069e6 q^{53} +20840.7 q^{54} +242135. q^{55} -424921. q^{56} +130660. q^{57} -15607.1 q^{58} +205379. q^{59} +519331. q^{60} -2.48399e6 q^{61} -76519.8 q^{62} -1.14784e6 q^{63} -1.98775e6 q^{64} +1.32744e6 q^{65} +45661.5 q^{66} -1.19534e6 q^{67} -2.51749e6 q^{68} +830013. q^{69} +252735. q^{70} -5.50733e6 q^{71} +196735. q^{72} -1.03549e6 q^{73} -378585. q^{74} +1.48887e6 q^{75} +614000. q^{76} -2.51490e6 q^{77} +250327. q^{78} -1.05062e6 q^{79} +2.41869e6 q^{80} +531441. q^{81} -595075. q^{82} +8.29947e6 q^{83} -5.39395e6 q^{84} +3.00794e6 q^{85} -722151. q^{86} -397985. q^{87} +431043. q^{88} +1.51623e6 q^{89} -117014. q^{90} -1.37872e7 q^{91} +3.90041e6 q^{92} -1.95127e6 q^{93} +1.31421e6 q^{94} -733618. q^{95} +1.38878e6 q^{96} +1.02696e7 q^{97} -1.75301e6 q^{98} +1.16438e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9} - 3479 q^{10} + 898 q^{11} - 26298 q^{12} - 8172 q^{13} - 13315 q^{14} + 1836 q^{15} + 3138 q^{16} - 44985 q^{17} - 4374 q^{18} - 40137 q^{19} + 130657 q^{20} + 63261 q^{21} + 109394 q^{22} - 2833 q^{23} - 22113 q^{24} + 285746 q^{25} - 129420 q^{26} - 314928 q^{27} + 112890 q^{28} + 144375 q^{29} + 93933 q^{30} - 141759 q^{31} - 36224 q^{32} - 24246 q^{33} - 341332 q^{34} - 78859 q^{35} + 710046 q^{36} - 297971 q^{37} + 329075 q^{38} + 220644 q^{39} - 203048 q^{40} + 659077 q^{41} + 359505 q^{42} - 1431608 q^{43} + 254916 q^{44} - 49572 q^{45} + 873113 q^{46} - 1574073 q^{47} - 84726 q^{48} + 1893545 q^{49} + 302533 q^{50} + 1214595 q^{51} - 4972548 q^{52} + 587736 q^{53} + 118098 q^{54} - 4624036 q^{55} - 5798506 q^{56} + 1083699 q^{57} - 6991380 q^{58} + 3286064 q^{59} - 3527739 q^{60} - 6117131 q^{61} - 11570258 q^{62} - 1708047 q^{63} - 19063011 q^{64} - 5335514 q^{65} - 2953638 q^{66} - 16518710 q^{67} - 17284669 q^{68} + 76491 q^{69} - 39189486 q^{70} - 10882582 q^{71} + 597051 q^{72} - 21097441 q^{73} - 16717030 q^{74} - 7715142 q^{75} - 40864952 q^{76} - 3404601 q^{77} + 3494340 q^{78} - 3784458 q^{79} - 27466195 q^{80} + 8503056 q^{81} - 24990117 q^{82} - 1951425 q^{83} - 3048030 q^{84} - 23238675 q^{85} - 35910572 q^{86} - 3898125 q^{87} - 27843055 q^{88} + 10499443 q^{89} - 2536191 q^{90} + 699217 q^{91} - 20062766 q^{92} + 3827493 q^{93} - 59358988 q^{94} - 29236333 q^{95} + 978048 q^{96} - 25158976 q^{97} + 2120460 q^{98} + 654642 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9 - 3479 * q^10 + 898 * q^11 - 26298 * q^12 - 8172 * q^13 - 13315 * q^14 + 1836 * q^15 + 3138 * q^16 - 44985 * q^17 - 4374 * q^18 - 40137 * q^19 + 130657 * q^20 + 63261 * q^21 + 109394 * q^22 - 2833 * q^23 - 22113 * q^24 + 285746 * q^25 - 129420 * q^26 - 314928 * q^27 + 112890 * q^28 + 144375 * q^29 + 93933 * q^30 - 141759 * q^31 - 36224 * q^32 - 24246 * q^33 - 341332 * q^34 - 78859 * q^35 + 710046 * q^36 - 297971 * q^37 + 329075 * q^38 + 220644 * q^39 - 203048 * q^40 + 659077 * q^41 + 359505 * q^42 - 1431608 * q^43 + 254916 * q^44 - 49572 * q^45 + 873113 * q^46 - 1574073 * q^47 - 84726 * q^48 + 1893545 * q^49 + 302533 * q^50 + 1214595 * q^51 - 4972548 * q^52 + 587736 * q^53 + 118098 * q^54 - 4624036 * q^55 - 5798506 * q^56 + 1083699 * q^57 - 6991380 * q^58 + 3286064 * q^59 - 3527739 * q^60 - 6117131 * q^61 - 11570258 * q^62 - 1708047 * q^63 - 19063011 * q^64 - 5335514 * q^65 - 2953638 * q^66 - 16518710 * q^67 - 17284669 * q^68 + 76491 * q^69 - 39189486 * q^70 - 10882582 * q^71 + 597051 * q^72 - 21097441 * q^73 - 16717030 * q^74 - 7715142 * q^75 - 40864952 * q^76 - 3404601 * q^77 + 3494340 * q^78 - 3784458 * q^79 - 27466195 * q^80 + 8503056 * q^81 - 24990117 * q^82 - 1951425 * q^83 - 3048030 * q^84 - 23238675 * q^85 - 35910572 * q^86 - 3898125 * q^87 - 27843055 * q^88 + 10499443 * q^89 - 2536191 * q^90 + 699217 * q^91 - 20062766 * q^92 + 3827493 * q^93 - 59358988 * q^94 - 29236333 * q^95 + 978048 * q^96 - 25158976 * q^97 + 2120460 * q^98 + 654642 * q^99

Introduction

L-functions

Modular forms

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