LMFDB - Embedded newform 177.8.a.b.1.2

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:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 $ x^17 - 2x^16 - 1639x^15 + 1625x^14 + 1070274x^13 - 274939x^12 - 357079564x^11 - 89298188x^10 + 64650816672x^9 + 33122051904x^8 - 6210397064704x^7 - 2735256748800x^6 + 288860762071040x^5 - 34502173230080x^4 - 5633463408885760x^3 + 4719471961341952x^2 + 37636623107620864x - 58321181718347776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-19.6388$ 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)

$f(q)$	$=$	$q-21.6388 q^{2} +27.0000 q^{3} +340.238 q^{4} -399.107 q^{5} -584.248 q^{6} -1780.57 q^{7} -4592.58 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-21.6388 q^{2} +27.0000 q^{3} +340.238 q^{4} -399.107 q^{5} -584.248 q^{6} -1780.57 q^{7} -4592.58 q^{8} +729.000 q^{9} +8636.21 q^{10} -204.067 q^{11} +9186.43 q^{12} +7466.22 q^{13} +38529.4 q^{14} -10775.9 q^{15} +55827.6 q^{16} +2070.83 q^{17} -15774.7 q^{18} +38611.6 q^{19} -135792. q^{20} -48075.4 q^{21} +4415.78 q^{22} -47604.4 q^{23} -124000. q^{24} +81161.6 q^{25} -161560. q^{26} +19683.0 q^{27} -605818. q^{28} +223646. q^{29} +233178. q^{30} +273826. q^{31} -620192. q^{32} -5509.82 q^{33} -44810.3 q^{34} +710639. q^{35} +248034. q^{36} -545039. q^{37} -835510. q^{38} +201588. q^{39} +1.83293e6 q^{40} -521804. q^{41} +1.04029e6 q^{42} +327902. q^{43} -69431.5 q^{44} -290949. q^{45} +1.03010e6 q^{46} -24173.5 q^{47} +1.50734e6 q^{48} +2.34689e6 q^{49} -1.75624e6 q^{50} +55912.4 q^{51} +2.54029e6 q^{52} -1.06061e6 q^{53} -425917. q^{54} +81444.8 q^{55} +8.17742e6 q^{56} +1.04251e6 q^{57} -4.83943e6 q^{58} -205379. q^{59} -3.66637e6 q^{60} +1.08933e6 q^{61} -5.92527e6 q^{62} -1.29804e6 q^{63} +6.27428e6 q^{64} -2.97982e6 q^{65} +119226. q^{66} -55751.2 q^{67} +704575. q^{68} -1.28532e6 q^{69} -1.53774e7 q^{70} -851859. q^{71} -3.34799e6 q^{72} +3.44512e6 q^{73} +1.17940e7 q^{74} +2.19136e6 q^{75} +1.31372e7 q^{76} +363356. q^{77} -4.36213e6 q^{78} -8.05252e6 q^{79} -2.22812e7 q^{80} +531441. q^{81} +1.12912e7 q^{82} +2.05020e6 q^{83} -1.63571e7 q^{84} -826483. q^{85} -7.09542e6 q^{86} +6.03843e6 q^{87} +937197. q^{88} -1.68320e6 q^{89} +6.29579e6 q^{90} -1.32941e7 q^{91} -1.61969e7 q^{92} +7.39330e6 q^{93} +523086. q^{94} -1.54102e7 q^{95} -1.67452e7 q^{96} +1.14133e7 q^{97} -5.07839e7 q^{98} -148765. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) $ 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9} - 6391 q^{10} - 8888 q^{11} + 31482 q^{12} - 12702 q^{13} - 17555 q^{14} - 28944 q^{15} + 139226 q^{16} - 36167 q^{17} - 23328 q^{18} - 71037 q^{19} - 274883 q^{20} - 64989 q^{21} - 325182 q^{22} - 269995 q^{23} - 179415 q^{24} + 97329 q^{25} - 336906 q^{26} + 334611 q^{27} - 901362 q^{28} - 543825 q^{29} - 172557 q^{30} - 633109 q^{31} - 837062 q^{32} - 239976 q^{33} - 529288 q^{34} - 287621 q^{35} + 850014 q^{36} - 867607 q^{37} - 1727169 q^{38} - 342954 q^{39} - 815662 q^{40} - 1428939 q^{41} - 473985 q^{42} - 477060 q^{43} - 1667926 q^{44} - 781488 q^{45} + 5305549 q^{46} - 1217849 q^{47} + 3759102 q^{48} + 4350738 q^{49} + 4561369 q^{50} - 976509 q^{51} + 4175994 q^{52} - 3487068 q^{53} - 629856 q^{54} - 960484 q^{55} - 5363196 q^{56} - 1917999 q^{57} - 3082906 q^{58} - 3491443 q^{59} - 7421841 q^{60} + 998917 q^{61} - 5742614 q^{62} - 1754703 q^{63} + 17531621 q^{64} - 6075816 q^{65} - 8779914 q^{66} - 356026 q^{67} - 16149231 q^{68} - 7289865 q^{69} - 548798 q^{70} - 12879428 q^{71} - 4844205 q^{72} - 6176157 q^{73} - 5971906 q^{74} + 2627883 q^{75} - 17624580 q^{76} + 239687 q^{77} - 9096462 q^{78} - 18886490 q^{79} - 70463349 q^{80} + 9034497 q^{81} - 19351611 q^{82} - 22824893 q^{83} - 24336774 q^{84} - 7973079 q^{85} - 27502196 q^{86} - 14683275 q^{87} - 62527651 q^{88} - 30609647 q^{89} - 4659039 q^{90} - 36301521 q^{91} - 41388548 q^{92} - 17093943 q^{93} + 1010176 q^{94} - 29303629 q^{95} - 22600674 q^{96} - 26249806 q^{97} - 93110852 q^{98} - 6479352 q^{99}+O(q^{100}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9 - 6391 * q^10 - 8888 * q^11 + 31482 * q^12 - 12702 * q^13 - 17555 * q^14 - 28944 * q^15 + 139226 * q^16 - 36167 * q^17 - 23328 * q^18 - 71037 * q^19 - 274883 * q^20 - 64989 * q^21 - 325182 * q^22 - 269995 * q^23 - 179415 * q^24 + 97329 * q^25 - 336906 * q^26 + 334611 * q^27 - 901362 * q^28 - 543825 * q^29 - 172557 * q^30 - 633109 * q^31 - 837062 * q^32 - 239976 * q^33 - 529288 * q^34 - 287621 * q^35 + 850014 * q^36 - 867607 * q^37 - 1727169 * q^38 - 342954 * q^39 - 815662 * q^40 - 1428939 * q^41 - 473985 * q^42 - 477060 * q^43 - 1667926 * q^44 - 781488 * q^45 + 5305549 * q^46 - 1217849 * q^47 + 3759102 * q^48 + 4350738 * q^49 + 4561369 * q^50 - 976509 * q^51 + 4175994 * q^52 - 3487068 * q^53 - 629856 * q^54 - 960484 * q^55 - 5363196 * q^56 - 1917999 * q^57 - 3082906 * q^58 - 3491443 * q^59 - 7421841 * q^60 + 998917 * q^61 - 5742614 * q^62 - 1754703 * q^63 + 17531621 * q^64 - 6075816 * q^65 - 8779914 * q^66 - 356026 * q^67 - 16149231 * q^68 - 7289865 * q^69 - 548798 * q^70 - 12879428 * q^71 - 4844205 * q^72 - 6176157 * q^73 - 5971906 * q^74 + 2627883 * q^75 - 17624580 * q^76 + 239687 * q^77 - 9096462 * q^78 - 18886490 * q^79 - 70463349 * q^80 + 9034497 * q^81 - 19351611 * q^82 - 22824893 * q^83 - 24336774 * q^84 - 7973079 * q^85 - 27502196 * q^86 - 14683275 * q^87 - 62527651 * q^88 - 30609647 * q^89 - 4659039 * q^90 - 36301521 * q^91 - 41388548 * q^92 - 17093943 * q^93 + 1010176 * q^94 - 29303629 * q^95 - 22600674 * q^96 - 26249806 * q^97 - 93110852 * q^98 - 6479352 * 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 $

$2$	−21.6388	−1.91262	−0.956309	−	0.292356i	$-0.905561\pi$
$2$	−21.6388	−1.91262	−0.956309	+	0.292356i	$0.905561\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	340.238	2.65811
$5$	−399.107	−1.42789	−0.713945	−	0.700202i	$-0.753093\pi$
$5$	−399.107	−1.42789	−0.713945	+	0.700202i	$0.753093\pi$
$6$	−584.248	−1.10425
$7$	−1780.57	−1.96208	−0.981039	−	0.193812i	$-0.937915\pi$
$7$	−1780.57	−1.96208	−0.981039	+	0.193812i	$0.937915\pi$
$8$	−4592.58	−3.17133
$9$	729.000	0.333333
$10$	8636.21	2.73101
$11$	−204.067	−0.0462274	−0.0231137	−	0.999733i	$-0.507358\pi$
$11$	−204.067	−0.0462274	−0.0231137	+	0.999733i	$0.507358\pi$
$12$	9186.43	1.53466
$13$	7466.22	0.942539	0.471269	−	0.881989i	$-0.343796\pi$
$13$	7466.22	0.942539	0.471269	+	0.881989i	$0.343796\pi$
$14$	38529.4	3.75271
$15$	−10775.9	−0.824392
$16$	55827.6	3.40744
$17$	2070.83	0.102229	0.0511144	−	0.998693i	$-0.483723\pi$
$17$	2070.83	0.102229	0.0511144	+	0.998693i	$0.483723\pi$
$18$	−15774.7	−0.637540
$19$	38611.6	1.29146	0.645729	−	0.763566i	$-0.276553\pi$
$19$	38611.6	1.29146	0.645729	+	0.763566i	$0.276553\pi$
$20$	−135792.	−3.79549
$21$	−48075.4	−1.13281
$22$	4415.78	0.0884154
$23$	−47604.4	−0.815831	−0.407915	−	0.913020i	$-0.633744\pi$
$23$	−47604.4	−0.815831	−0.407915	+	0.913020i	$0.633744\pi$
$24$	−124000.	−1.83097
$25$	81161.6	1.03887
$26$	−161560.	−1.80272
$27$	19683.0	0.192450
$28$	−605818.	−5.21542
$29$	223646.	1.70282	0.851408	−	0.524505i	$-0.175749\pi$
$29$	223646.	1.70282	0.851408	+	0.524505i	$0.175749\pi$
$30$	233178.	1.57675
$31$	273826.	1.65085	0.825427	−	0.564508i	$-0.190934\pi$
$31$	273826.	1.65085	0.825427	+	0.564508i	$0.190934\pi$
$32$	−620192.	−3.34581
$33$	−5509.82	−0.0266894
$34$	−44810.3	−0.195525
$35$	710639.	2.80163
$36$	248034.	0.886037
$37$	−545039.	−1.76897	−0.884487	−	0.466565i	$-0.845491\pi$
$37$	−545039.	−1.76897	−0.884487	+	0.466565i	$0.845491\pi$
$38$	−835510.	−2.47007
$39$	201588.	0.544175
$40$	1.83293e6	4.52832
$41$	−521804.	−1.18240	−0.591200	−	0.806525i	$-0.701346\pi$
$41$	−521804.	−1.18240	−0.591200	+	0.806525i	$0.701346\pi$
$42$	1.04029e6	2.16663
$43$	327902.	0.628934	0.314467	−	0.949268i	$-0.398174\pi$
$43$	327902.	0.628934	0.314467	+	0.949268i	$0.398174\pi$
$44$	−69431.5	−0.122878
$45$	−290949.	−0.475963
$46$	1.03010e6	1.56037
$47$	−24173.5	−0.0339623	−0.0169811	−	0.999856i	$-0.505406\pi$
$47$	−24173.5	−0.0339623	−0.0169811	+	0.999856i	$0.505406\pi$
$48$	1.50734e6	1.96729
$49$	2.34689e6	2.84975
$50$	−1.75624e6	−1.98696
$51$	55912.4	0.0590218
$52$	2.54029e6	2.50537
$53$	−1.06061e6	−0.978570	−0.489285	−	0.872124i	$-0.662742\pi$
$53$	−1.06061e6	−0.978570	−0.489285	+	0.872124i	$0.662742\pi$
$54$	−425917.	−0.368084
$55$	81444.8	0.0660076
$56$	8.17742e6	6.22240
$57$	1.04251e6	0.745624
$58$	−4.83943e6	−3.25684
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−3.66637e6	−2.19133
$61$	1.08933e6	0.614475	0.307238	−	0.951633i	$-0.400595\pi$
$61$	1.08933e6	0.614475	0.307238	+	0.951633i	$0.400595\pi$
$62$	−5.92527e6	−3.15746
$63$	−1.29804e6	−0.654026
$64$	6.27428e6	2.99181
$65$	−2.97982e6	−1.34584
$66$	119226.	0.0510466
$67$	−55751.2	−0.0226461	−0.0113230	−	0.999936i	$-0.503604\pi$
$67$	−55751.2	−0.0226461	−0.0113230	+	0.999936i	$0.503604\pi$
$68$	704575.	0.271735
$69$	−1.28532e6	−0.471020
$70$	−1.53774e7	−5.35845
$71$	−851859.	−0.282464	−0.141232	−	0.989976i	$-0.545106\pi$
$71$	−851859.	−0.282464	−0.141232	+	0.989976i	$0.545106\pi$
$72$	−3.34799e6	−1.05711
$73$	3.44512e6	1.03651	0.518256	−	0.855225i	$-0.326581\pi$
$73$	3.44512e6	1.03651	0.518256	+	0.855225i	$0.326581\pi$
$74$	1.17940e7	3.38337
$75$	2.19136e6	0.599791
$76$	1.31372e7	3.43284
$77$	363356.	0.0907017
$78$	−4.36213e6	−1.04080
$79$	−8.05252e6	−1.83754	−0.918771	−	0.394791i	$-0.870817\pi$
$79$	−8.05252e6	−1.83754	−0.918771	+	0.394791i	$0.870817\pi$
$80$	−2.22812e7	−4.86545
$81$	531441.	0.111111
$82$	1.12912e7	2.26148
$83$	2.05020e6	0.393571	0.196785	−	0.980447i	$-0.436950\pi$
$83$	2.05020e6	0.393571	0.196785	+	0.980447i	$0.436950\pi$
$84$	−1.63571e7	−3.01112
$85$	−826483.	−0.145971
$86$	−7.09542e6	−1.20291
$87$	6.03843e6	0.983121
$88$	937197.	0.146602
$89$	−1.68320e6	−0.253087	−0.126544	−	0.991961i	$-0.540388\pi$
$89$	−1.68320e6	−0.253087	−0.126544	+	0.991961i	$0.540388\pi$
$90$	6.29579e6	0.910336
$91$	−1.32941e7	−1.84933
$92$	−1.61969e7	−2.16857
$93$	7.39330e6	0.953121
$94$	523086.	0.0649569
$95$	−1.54102e7	−1.84406
$96$	−1.67452e7	−1.93170
$97$	1.14133e7	1.26972	0.634861	−	0.772627i	$-0.281058\pi$
$97$	1.14133e7	1.26972	0.634861	+	0.772627i	$0.281058\pi$
$98$	−5.07839e7	−5.45048
$99$	−148765.	−0.0154091
$100$	2.76143e7	2.76143
$101$	7.19660e6	0.695029	0.347514	−	0.937675i	$-0.387026\pi$
$101$	7.19660e6	0.695029	0.347514	+	0.937675i	$0.387026\pi$
$102$	−1.20988e6	−0.112886
$103$	−2.77089e6	−0.249856	−0.124928	−	0.992166i	$-0.539870\pi$
$103$	−2.77089e6	−0.249856	−0.124928	+	0.992166i	$0.539870\pi$
$104$	−3.42893e7	−2.98911
$105$	1.91872e7	1.61752
$106$	2.29504e7	1.87163
$107$	−937525.	−0.0739843	−0.0369922	−	0.999316i	$-0.511778\pi$
$107$	−937525.	−0.0739843	−0.0369922	+	0.999316i	$0.511778\pi$
$108$	6.69691e6	0.511554
$109$	−1.52436e7	−1.12744	−0.563722	−	0.825965i	$-0.690631\pi$
$109$	−1.52436e7	−1.12744	−0.563722	+	0.825965i	$0.690631\pi$
$110$	−1.76237e6	−0.126247
$111$	−1.47161e7	−1.02132
$112$	−9.94049e7	−6.68567
$113$	−1.00374e7	−0.654402	−0.327201	−	0.944955i	$-0.606105\pi$
$113$	−1.00374e7	−0.654402	−0.327201	+	0.944955i	$0.606105\pi$
$114$	−2.25588e7	−1.42609
$115$	1.89993e7	1.16492
$116$	7.60928e7	4.52627
$117$	5.44288e6	0.314180
$118$	4.44416e6	0.249002
$119$	−3.68726e6	−0.200581
$120$	4.94892e7	2.61442
$121$	−1.94455e7	−0.997863
$122$	−2.35718e7	−1.17526
$123$	−1.40887e7	−0.682659
$124$	9.31661e7	4.38816
$125$	−1.21192e6	−0.0554993
$126$	2.80880e7	1.25090
$127$	9.06146e6	0.392541	0.196270	−	0.980550i	$-0.437117\pi$
$127$	9.06146e6	0.392541	0.196270	+	0.980550i	$0.437117\pi$
$128$	−5.63835e7	−2.37639
$129$	8.85336e6	0.363115
$130$	6.44799e7	2.57408
$131$	2.09570e7	0.814478	0.407239	−	0.913322i	$-0.366492\pi$
$131$	2.09570e7	0.814478	0.407239	+	0.913322i	$0.366492\pi$
$132$	−1.87465e6	−0.0709434
$133$	−6.87507e7	−2.53394
$134$	1.20639e6	0.0433133
$135$	−7.85563e6	−0.274797
$136$	−9.51046e6	−0.324202
$137$	2.19828e7	0.730399	0.365199	−	0.930929i	$-0.381001\pi$
$137$	2.19828e7	0.730399	0.365199	+	0.930929i	$0.381001\pi$
$138$	2.78128e7	0.900882
$139$	−6.44663e6	−0.203601	−0.101801	−	0.994805i	$-0.532460\pi$
$139$	−6.44663e6	−0.203601	−0.101801	+	0.994805i	$0.532460\pi$
$140$	2.41786e8	7.44704
$141$	−652684.	−0.0196081
$142$	1.84332e7	0.540247
$143$	−1.52361e6	−0.0435711
$144$	4.06983e7	1.13581
$145$	−8.92586e7	−2.43143
$146$	−7.45484e7	−1.98245
$147$	6.33660e7	1.64530
$148$	−1.85443e8	−4.70213
$149$	−3.38724e7	−0.838869	−0.419434	−	0.907786i	$-0.637772\pi$
$149$	−3.38724e7	−0.838869	−0.419434	+	0.907786i	$0.637772\pi$
$150$	−4.74185e7	−1.14717
$151$	−6.27255e7	−1.48260	−0.741301	−	0.671172i	$-0.765791\pi$
$151$	−6.27255e7	−1.48260	−0.741301	+	0.671172i	$0.765791\pi$
$152$	−1.77327e8	−4.09565
$153$	1.50963e6	0.0340762
$154$	−7.86260e6	−0.173478
$155$	−1.09286e8	−2.35724
$156$	6.85880e7	1.44648
$157$	4.72239e7	0.973898	0.486949	−	0.873430i	$-0.338110\pi$
$157$	4.72239e7	0.973898	0.486949	+	0.873430i	$0.338110\pi$
$158$	1.74247e8	3.51452
$159$	−2.86366e7	−0.564977
$160$	2.47523e8	4.77744
$161$	8.47631e7	1.60072
$162$	−1.14998e7	−0.212513
$163$	−2.85412e7	−0.516198	−0.258099	−	0.966119i	$-0.583096\pi$
$163$	−2.85412e7	−0.516198	−0.258099	+	0.966119i	$0.583096\pi$
$164$	−1.77538e8	−3.14295
$165$	2.19901e6	0.0381095
$166$	−4.43639e7	−0.752751
$167$	−6.05397e7	−1.00585	−0.502924	−	0.864331i	$-0.667742\pi$
$167$	−6.05397e7	−1.00585	−0.502924	+	0.864331i	$0.667742\pi$
$168$	2.20790e8	3.59251
$169$	−7.00401e6	−0.111620
$170$	1.78841e7	0.279188
$171$	2.81479e7	0.430486
$172$	1.11565e8	1.67178
$173$	−8.84147e7	−1.29826	−0.649132	−	0.760676i	$-0.724868\pi$
$173$	−8.84147e7	−1.29826	−0.649132	+	0.760676i	$0.724868\pi$
$174$	−1.30665e8	−1.88034
$175$	−1.44514e8	−2.03834
$176$	−1.13926e7	−0.157517
$177$	−5.54523e6	−0.0751646
$178$	3.64224e7	0.484059
$179$	9.25607e7	1.20626	0.603130	−	0.797643i	$-0.293920\pi$
$179$	9.25607e7	1.20626	0.603130	+	0.797643i	$0.293920\pi$
$180$	−9.89920e7	−1.26516
$181$	7.46139e6	0.0935287	0.0467644	−	0.998906i	$-0.485109\pi$
$181$	7.46139e6	0.0935287	0.0467644	+	0.998906i	$0.485109\pi$
$182$	2.87669e8	3.53707
$183$	2.94119e7	0.354767
$184$	2.18627e8	2.58727
$185$	2.17529e8	2.52590
$186$	−1.59982e8	−1.82296
$187$	−422589.	−0.00472577
$188$	−8.22475e6	−0.0902755
$189$	−3.50470e7	−0.377602
$190$	3.33458e8	3.52698
$191$	6.59363e7	0.684712	0.342356	−	0.939570i	$-0.388775\pi$
$191$	6.59363e7	0.684712	0.342356	+	0.939570i	$0.388775\pi$
$192$	1.69406e8	1.72732
$193$	1.34481e7	0.134651	0.0673257	−	0.997731i	$-0.478553\pi$
$193$	1.34481e7	0.134651	0.0673257	+	0.997731i	$0.478553\pi$
$194$	−2.46969e8	−2.42849
$195$	−8.04552e7	−0.777022
$196$	7.98502e8	7.57495
$197$	1.59146e7	0.148308	0.0741539	−	0.997247i	$-0.476374\pi$
$197$	1.59146e7	0.148308	0.0741539	+	0.997247i	$0.476374\pi$
$198$	3.21910e6	0.0294718
$199$	3.59450e7	0.323335	0.161668	−	0.986845i	$-0.448313\pi$
$199$	3.59450e7	0.323335	0.161668	+	0.986845i	$0.448313\pi$
$200$	−3.72741e8	−3.29460
$201$	−1.50528e6	−0.0130747
$202$	−1.55726e8	−1.32932
$203$	−3.98217e8	−3.34105
$204$	1.90235e7	0.156886
$205$	2.08256e8	1.68834
$206$	5.99588e7	0.477878
$207$	−3.47036e7	−0.271944
$208$	4.16821e8	3.21165
$209$	−7.87937e6	−0.0597007
$210$	−4.15189e8	−3.09370
$211$	−2.03281e8	−1.48973	−0.744866	−	0.667214i	$-0.767486\pi$
$211$	−2.03281e8	−1.48973	−0.744866	+	0.667214i	$0.767486\pi$
$212$	−3.60861e8	−2.60115
$213$	−2.30002e7	−0.163081
$214$	2.02869e7	0.141504
$215$	−1.30868e8	−0.898048
$216$	−9.03958e7	−0.610324
$217$	−4.87567e8	−3.23910
$218$	3.29853e8	2.15637
$219$	9.30183e7	0.598431
$220$	2.77106e7	0.175455
$221$	1.54613e7	0.0963546
$222$	3.18438e8	1.95339
$223$	−1.24671e8	−0.752830	−0.376415	−	0.926451i	$-0.622843\pi$
$223$	−1.24671e8	−0.752830	−0.376415	+	0.926451i	$0.622843\pi$
$224$	1.10429e9	6.56473
$225$	5.91668e7	0.346289
$226$	2.17196e8	1.25162
$227$	−1.63994e7	−0.0930547	−0.0465273	−	0.998917i	$-0.514815\pi$
$227$	−1.63994e7	−0.0930547	−0.0465273	+	0.998917i	$0.514815\pi$
$228$	3.54703e8	1.98195
$229$	−1.34148e8	−0.738179	−0.369089	−	0.929394i	$-0.620330\pi$
$229$	−1.34148e8	−0.738179	−0.369089	+	0.929394i	$0.620330\pi$
$230$	−4.11122e8	−2.22804
$231$	9.81062e6	0.0523666
$232$	−1.02711e9	−5.40020
$233$	−6.54300e7	−0.338869	−0.169434	−	0.985541i	$-0.554194\pi$
$233$	−6.54300e7	−0.338869	−0.169434	+	0.985541i	$0.554194\pi$
$234$	−1.17777e8	−0.600906
$235$	9.64781e6	0.0484944
$236$	−6.98778e7	−0.346057
$237$	−2.17418e8	−1.06091
$238$	7.97879e7	0.383634
$239$	−1.59121e8	−0.753936	−0.376968	−	0.926226i	$-0.623033\pi$
$239$	−1.59121e8	−0.753936	−0.376968	+	0.926226i	$0.623033\pi$
$240$	−6.01592e8	−2.80907
$241$	1.38094e8	0.635501	0.317750	−	0.948174i	$-0.397073\pi$
$241$	1.38094e8	0.635501	0.317750	+	0.948174i	$0.397073\pi$
$242$	4.20778e8	1.90853
$243$	1.43489e7	0.0641500
$244$	3.70631e8	1.63334
$245$	−9.36661e8	−4.06912
$246$	3.04863e8	1.30567
$247$	2.88283e8	1.21725
$248$	−1.25757e9	−5.23541
$249$	5.53554e7	0.227228
$250$	2.62244e7	0.106149
$251$	1.39109e8	0.555262	0.277631	−	0.960688i	$-0.410451\pi$
$251$	1.39109e8	0.555262	0.277631	+	0.960688i	$0.410451\pi$
$252$	−4.41642e8	−1.73847
$253$	9.71452e6	0.0377137
$254$	−1.96079e8	−0.750781
$255$	−2.23150e7	−0.0842766
$256$	4.16963e8	1.55331
$257$	4.09751e8	1.50575	0.752877	−	0.658162i	$-0.228666\pi$
$257$	4.09751e8	1.50575	0.752877	+	0.658162i	$0.228666\pi$
$258$	−1.91576e8	−0.694501
$259$	9.70480e8	3.47086
$260$	−1.01385e9	−3.57740
$261$	1.63038e8	0.567605
$262$	−4.53484e8	−1.55779
$263$	1.19894e8	0.406400	0.203200	−	0.979137i	$-0.434866\pi$
$263$	1.19894e8	0.406400	0.203200	+	0.979137i	$0.434866\pi$
$264$	2.53043e7	0.0846410
$265$	4.23299e8	1.39729
$266$	1.48768e9	4.84647
$267$	−4.54463e7	−0.146120
$268$	−1.89687e7	−0.0601958
$269$	−2.45594e8	−0.769282	−0.384641	−	0.923066i	$-0.625675\pi$
$269$	−2.45594e8	−0.769282	−0.384641	+	0.923066i	$0.625675\pi$
$270$	1.69986e8	0.525583
$271$	2.52445e8	0.770503	0.385252	−	0.922812i	$-0.374115\pi$
$271$	2.52445e8	0.770503	0.385252	+	0.922812i	$0.374115\pi$
$272$	1.15609e8	0.348339
$273$	−3.58942e8	−1.06771
$274$	−4.75681e8	−1.39697
$275$	−1.65624e7	−0.0480241
$276$	−4.37315e8	−1.25202
$277$	3.24074e8	0.916147	0.458074	−	0.888914i	$-0.348540\pi$
$277$	3.24074e8	0.916147	0.458074	+	0.888914i	$0.348540\pi$
$278$	1.39497e8	0.389412
$279$	1.99619e8	0.550285
$280$	−3.26367e9	−8.88491
$281$	−1.78256e8	−0.479260	−0.239630	−	0.970864i	$-0.577026\pi$
$281$	−1.78256e8	−0.479260	−0.239630	+	0.970864i	$0.577026\pi$
$282$	1.41233e7	0.0375029
$283$	−4.64602e8	−1.21851	−0.609254	−	0.792975i	$-0.708531\pi$
$283$	−4.64602e8	−1.21851	−0.609254	+	0.792975i	$0.708531\pi$
$284$	−2.89835e8	−0.750822
$285$	−4.16075e8	−1.06467
$286$	3.29692e7	0.0833349
$287$	9.29110e8	2.31996
$288$	−4.52120e8	−1.11527
$289$	−4.06050e8	−0.989549
$290$	1.93145e9	4.65040
$291$	3.08158e8	0.733074
$292$	1.17216e9	2.75517
$293$	−7.63943e8	−1.77429	−0.887145	−	0.461492i	$-0.847314\pi$
$293$	−7.63943e8	−1.77429	−0.887145	+	0.461492i	$0.847314\pi$
$294$	−1.37117e9	−3.14684
$295$	8.19682e7	0.185895
$296$	2.50314e9	5.61001
$297$	−4.01666e6	−0.00889646
$298$	7.32959e8	1.60444
$299$	−3.55425e8	−0.768952
$300$	7.45585e8	1.59431
$301$	−5.83853e8	−1.23402
$302$	1.35731e9	2.83565
$303$	1.94308e8	0.401275
$304$	2.15559e9	4.40057
$305$	−4.34759e8	−0.877402
$306$	−3.26667e7	−0.0651749
$307$	−5.34126e8	−1.05356	−0.526780	−	0.850001i	$-0.676601\pi$
$307$	−5.34126e8	−1.05356	−0.526780	+	0.850001i	$0.676601\pi$
$308$	1.23628e8	0.241095
$309$	−7.48140e7	−0.144254
$310$	2.36482e9	4.50850
$311$	7.32126e8	1.38014	0.690072	−	0.723741i	$-0.257579\pi$
$311$	7.32126e8	1.38014	0.690072	+	0.723741i	$0.257579\pi$
$312$	−9.25810e8	−1.72576
$313$	5.31534e8	0.979774	0.489887	−	0.871786i	$-0.337038\pi$
$313$	5.31534e8	0.979774	0.489887	+	0.871786i	$0.337038\pi$
$314$	−1.02187e9	−1.86270
$315$	5.18056e8	0.933876
$316$	−2.73978e9	−4.88439
$317$	1.07205e9	1.89020	0.945102	−	0.326775i	$-0.105962\pi$
$317$	1.07205e9	1.89020	0.945102	+	0.326775i	$0.105962\pi$
$318$	6.19662e8	1.08059
$319$	−4.56388e7	−0.0787167
$320$	−2.50411e9	−4.27197
$321$	−2.53132e7	−0.0427149
$322$	−1.83417e9	−3.06157
$323$	7.99581e7	0.132024
$324$	1.80817e8	0.295346
$325$	6.05970e8	0.979174
$326$	6.17598e8	0.987289
$327$	−4.11577e8	−0.650930
$328$	2.39643e9	3.74979
$329$	4.30426e7	0.0666366
$330$	−4.75839e7	−0.0728889
$331$	−4.36057e7	−0.0660914	−0.0330457	−	0.999454i	$-0.510521\pi$
$331$	−4.36057e7	−0.0660914	−0.0330457	+	0.999454i	$0.510521\pi$
$332$	6.97556e8	1.04615
$333$	−3.97333e8	−0.589658
$334$	1.31001e9	1.92380
$335$	2.22507e7	0.0323361
$336$	−2.68393e9	−3.85997
$337$	−6.67140e8	−0.949538	−0.474769	−	0.880110i	$-0.657468\pi$
$337$	−6.67140e8	−0.949538	−0.474769	+	0.880110i	$0.657468\pi$
$338$	1.51559e8	0.213487
$339$	−2.71009e8	−0.377819
$340$	−2.81201e8	−0.388008
$341$	−5.58790e7	−0.0763147
$342$	−6.09087e8	−0.823356
$343$	−2.71243e9	−3.62935
$344$	−1.50592e9	−1.99456
$345$	5.12980e8	0.672565
$346$	1.91319e9	2.48308
$347$	3.15540e7	0.0405417	0.0202708	−	0.999795i	$-0.493547\pi$
$347$	3.15540e7	0.0405417	0.0202708	+	0.999795i	$0.493547\pi$
$348$	2.05451e9	2.61324
$349$	7.24543e8	0.912379	0.456189	−	0.889883i	$-0.349214\pi$
$349$	7.24543e8	0.912379	0.456189	+	0.889883i	$0.349214\pi$
$350$	3.12711e9	3.89857
$351$	1.46958e8	0.181392
$352$	1.26561e8	0.154668
$353$	9.26501e8	1.12107	0.560537	−	0.828129i	$-0.310595\pi$
$353$	9.26501e8	1.12107	0.560537	+	0.828129i	$0.310595\pi$
$354$	1.19992e8	0.143761
$355$	3.39983e8	0.403328
$356$	−5.72688e8	−0.672734
$357$	−9.95560e7	−0.115805
$358$	−2.00290e9	−2.30712
$359$	−1.08624e9	−1.23906	−0.619532	−	0.784971i	$-0.712678\pi$
$359$	−1.08624e9	−1.23906	−0.619532	+	0.784971i	$0.712678\pi$
$360$	1.33621e9	1.50944
$361$	5.96986e8	0.667866
$362$	−1.61456e8	−0.178885
$363$	−5.25029e8	−0.576116
$364$	−4.52318e9	−4.91574
$365$	−1.37497e9	−1.48003
$366$	−6.36438e8	−0.678535
$367$	8.58587e8	0.906678	0.453339	−	0.891338i	$-0.350233\pi$
$367$	8.58587e8	0.906678	0.453339	+	0.891338i	$0.350233\pi$
$368$	−2.65764e9	−2.77990
$369$	−3.80395e8	−0.394133
$370$	−4.70707e9	−4.83108
$371$	1.88850e9	1.92003
$372$	2.51548e9	2.53350
$373$	−1.80912e8	−0.180504	−0.0902518	−	0.995919i	$-0.528767\pi$
$373$	−1.80912e8	−0.180504	−0.0902518	+	0.995919i	$0.528767\pi$
$374$	9.14432e6	0.00903859
$375$	−3.27217e7	−0.0320425
$376$	1.11019e8	0.107706
$377$	1.66979e9	1.60497
$378$	7.58375e8	0.722209
$379$	−1.73658e9	−1.63854	−0.819270	−	0.573408i	$-0.805621\pi$
$379$	−1.73658e9	−1.63854	−0.819270	+	0.573408i	$0.805621\pi$
$380$	−5.24313e9	−4.90172
$381$	2.44659e8	0.226634
$382$	−1.42678e9	−1.30959
$383$	1.24471e9	1.13207	0.566035	−	0.824381i	$-0.308477\pi$
$383$	1.24471e9	1.13207	0.566035	+	0.824381i	$0.308477\pi$
$384$	−1.52235e9	−1.37201
$385$	−1.45018e8	−0.129512
$386$	−2.91001e8	−0.257537
$387$	2.39041e8	0.209645
$388$	3.88322e9	3.37506
$389$	−1.41664e9	−1.22021	−0.610106	−	0.792320i	$-0.708873\pi$
$389$	−1.41664e9	−1.22021	−0.610106	+	0.792320i	$0.708873\pi$
$390$	1.74096e9	1.48615
$391$	−9.85807e7	−0.0834014
$392$	−1.07783e10	−9.03750
$393$	5.65839e8	0.470239
$394$	−3.44373e8	−0.283656
$395$	3.21382e9	2.62381
$396$	−5.06156e7	−0.0409592
$397$	−1.99168e9	−1.59755	−0.798773	−	0.601633i	$-0.794517\pi$
$397$	−1.99168e9	−1.59755	−0.798773	+	0.601633i	$0.794517\pi$
$398$	−7.77808e8	−0.618417
$399$	−1.85627e9	−1.46297
$400$	4.53105e9	3.53988
$401$	−9.22799e8	−0.714664	−0.357332	−	0.933977i	$-0.616313\pi$
$401$	−9.22799e8	−0.714664	−0.357332	+	0.933977i	$0.616313\pi$
$402$	3.25725e7	0.0250069
$403$	2.04445e9	1.55599
$404$	2.44856e9	1.84746
$405$	−2.12102e8	−0.158654
$406$	8.61694e9	6.39017
$407$	1.11225e8	0.0817750
$408$	−2.56782e8	−0.187178
$409$	−3.58871e7	−0.0259362	−0.0129681	−	0.999916i	$-0.504128\pi$
$409$	−3.58871e7	−0.0259362	−0.0129681	+	0.999916i	$0.504128\pi$
$410$	−4.50641e9	−3.22914
$411$	5.93534e8	0.421696
$412$	−9.42763e8	−0.664144
$413$	3.65692e8	0.255441
$414$	7.50946e8	0.520124
$415$	−8.18249e8	−0.561975
$416$	−4.63049e9	−3.15355
$417$	−1.74059e8	−0.117549
$418$	1.70500e8	0.114185
$419$	−2.26805e8	−0.150627	−0.0753135	−	0.997160i	$-0.523996\pi$
$419$	−2.26805e8	−0.150627	−0.0753135	+	0.997160i	$0.523996\pi$
$420$	6.52823e9	4.29955
$421$	7.22132e8	0.471660	0.235830	−	0.971794i	$-0.424219\pi$
$421$	7.22132e8	0.471660	0.235830	+	0.971794i	$0.424219\pi$
$422$	4.39876e9	2.84929
$423$	−1.76225e7	−0.0113208
$424$	4.87096e9	3.10337
$425$	1.68072e8	0.106202
$426$	4.97697e8	0.311912
$427$	−1.93963e9	−1.20565
$428$	−3.18982e8	−0.196659
$429$	−4.11375e7	−0.0251558
$430$	2.83183e9	1.71762
$431$	2.37550e8	0.142917	0.0714586	−	0.997444i	$-0.477235\pi$
$431$	2.37550e8	0.142917	0.0714586	+	0.997444i	$0.477235\pi$
$432$	1.09885e9	0.655763
$433$	−2.62934e8	−0.155646	−0.0778231	−	0.996967i	$-0.524797\pi$
$433$	−2.62934e8	−0.155646	−0.0778231	+	0.996967i	$0.524797\pi$
$434$	1.05504e10	6.19517
$435$	−2.40998e9	−1.40379
$436$	−5.18645e9	−2.99687
$437$	−1.83809e9	−1.05361
$438$	−2.01281e9	−1.14457
$439$	9.64067e8	0.543853	0.271926	−	0.962318i	$-0.412339\pi$
$439$	9.64067e8	0.543853	0.271926	+	0.962318i	$0.412339\pi$
$440$	−3.74042e8	−0.209332
$441$	1.71088e9	0.949916
$442$	−3.34564e8	−0.184290
$443$	2.26896e9	1.23998	0.619989	−	0.784611i	$-0.287137\pi$
$443$	2.26896e9	1.23998	0.619989	+	0.784611i	$0.287137\pi$
$444$	−5.00696e9	−2.71478
$445$	6.71776e8	0.361380
$446$	2.69772e9	1.43988
$447$	−9.14555e8	−0.484321
$448$	−1.11718e10	−5.87016
$449$	−6.29447e8	−0.328168	−0.164084	−	0.986446i	$-0.552467\pi$
$449$	−6.29447e8	−0.328168	−0.164084	+	0.986446i	$0.552467\pi$
$450$	−1.28030e9	−0.662320
$451$	1.06483e8	0.0546592
$452$	−3.41509e9	−1.73947
$453$	−1.69359e9	−0.855981
$454$	3.54864e8	0.177978
$455$	5.30579e9	2.64064
$456$	−4.78783e9	−2.36462
$457$	−2.73973e9	−1.34277	−0.671383	−	0.741111i	$-0.734299\pi$
$457$	−2.73973e9	−1.34277	−0.671383	+	0.741111i	$0.734299\pi$
$458$	2.90281e9	1.41185
$459$	4.07601e7	0.0196739
$460$	6.46428e9	3.09648
$461$	1.50755e9	0.716668	0.358334	−	0.933593i	$-0.383345\pi$
$461$	1.50755e9	0.716668	0.358334	+	0.933593i	$0.383345\pi$
$462$	−2.12290e8	−0.100157
$463$	−7.07432e8	−0.331246	−0.165623	−	0.986189i	$-0.552964\pi$
$463$	−7.07432e8	−0.331246	−0.165623	+	0.986189i	$0.552964\pi$
$464$	1.24856e10	5.80225
$465$	−2.95072e9	−1.36095
$466$	1.41583e9	0.648126
$467$	−3.62529e9	−1.64715	−0.823575	−	0.567207i	$-0.808024\pi$
$467$	−3.62529e9	−1.64715	−0.823575	+	0.567207i	$0.808024\pi$
$468$	1.85188e9	0.835124
$469$	9.92690e7	0.0444333
$470$	−2.08767e8	−0.0927513
$471$	1.27505e9	0.562280
$472$	9.43220e8	0.412873
$473$	−6.69142e7	−0.0290740
$474$	4.70467e9	2.02911
$475$	3.13378e9	1.34166
$476$	−1.25455e9	−0.533166
$477$	−7.73188e8	−0.326190
$478$	3.44319e9	1.44199
$479$	1.79818e9	0.747580	0.373790	−	0.927513i	$-0.378058\pi$
$479$	1.79818e9	0.747580	0.373790	+	0.927513i	$0.378058\pi$
$480$	6.68312e9	2.75826
$481$	−4.06938e9	−1.66733
$482$	−2.98820e9	−1.21547
$483$	2.28860e9	0.924178
$484$	−6.61611e9	−2.65243
$485$	−4.55511e9	−1.81302
$486$	−3.10493e8	−0.122695
$487$	−1.58236e9	−0.620802	−0.310401	−	0.950606i	$-0.600463\pi$
$487$	−1.58236e9	−0.620802	−0.310401	+	0.950606i	$0.600463\pi$
$488$	−5.00283e9	−1.94871
$489$	−7.70613e8	−0.298027
$490$	2.02682e10	7.78268
$491$	−2.99676e8	−0.114253	−0.0571264	−	0.998367i	$-0.518194\pi$
$491$	−2.99676e8	−0.114253	−0.0571264	+	0.998367i	$0.518194\pi$
$492$	−4.79352e9	−1.81458
$493$	4.63132e8	0.174077
$494$	−6.23810e9	−2.32814
$495$	5.93732e7	0.0220025
$496$	1.52870e10	5.62520
$497$	1.51680e9	0.554217
$498$	−1.19782e9	−0.434601
$499$	1.35009e9	0.486419	0.243210	−	0.969974i	$-0.421800\pi$
$499$	1.35009e9	0.486419	0.243210	+	0.969974i	$0.421800\pi$
$500$	−4.12340e8	−0.147523
$501$	−1.63457e9	−0.580727
$502$	−3.01016e9	−1.06200
$503$	1.94191e9	0.680365	0.340183	−	0.940359i	$-0.389511\pi$
$503$	1.94191e9	0.680365	0.340183	+	0.940359i	$0.389511\pi$
$504$	5.96134e9	2.07413
$505$	−2.87222e9	−0.992424
$506$	−2.10211e8	−0.0721320
$507$	−1.89108e8	−0.0644441
$508$	3.08305e9	1.04342
$509$	−1.85092e9	−0.622120	−0.311060	−	0.950390i	$-0.600684\pi$
$509$	−1.85092e9	−0.622120	−0.311060	+	0.950390i	$0.600684\pi$
$510$	4.82871e8	0.161189
$511$	−6.13429e9	−2.03372
$512$	−1.80551e9	−0.594504
$513$	7.59993e8	0.248541
$514$	−8.86652e9	−2.87993
$515$	1.10588e9	0.356766
$516$	3.01225e9	0.965200
$517$	4.93302e6	0.00156999
$518$	−2.10000e10	−6.63844
$519$	−2.38720e9	−0.749553
$520$	1.36851e10	4.26811
$521$	2.35474e9	0.729475	0.364738	−	0.931110i	$-0.381159\pi$
$521$	2.35474e9	0.729475	0.364738	+	0.931110i	$0.381159\pi$
$522$	−3.52794e9	−1.08561
$523$	1.86850e9	0.571133	0.285566	−	0.958359i	$-0.407818\pi$
$523$	1.86850e9	0.571133	0.285566	+	0.958359i	$0.407818\pi$
$524$	7.13037e9	2.16497
$525$	−3.90188e9	−1.17684
$526$	−2.59437e9	−0.777288
$527$	5.67047e8	0.168765
$528$	−3.07600e8	−0.0909426
$529$	−1.13864e9	−0.334420
$530$	−9.15968e9	−2.67248
$531$	−1.49721e8	−0.0433963
$532$	−2.33916e10	−6.73550
$533$	−3.89591e9	−1.11446
$534$	9.83405e8	0.279472
$535$	3.74173e8	0.105641
$536$	2.56042e8	0.0718183
$537$	2.49914e9	0.696434
$538$	5.31437e9	1.47134
$539$	−4.78924e8	−0.131736
$540$	−2.67278e9	−0.730442
$541$	−1.58014e8	−0.0429046	−0.0214523	−	0.999770i	$-0.506829\pi$
$541$	−1.58014e8	−0.0429046	−0.0214523	+	0.999770i	$0.506829\pi$
$542$	−5.46261e9	−1.47368
$543$	2.01458e8	0.0539988
$544$	−1.28431e9	−0.342038
$545$	6.08383e9	1.60986
$546$	7.76707e9	2.04213
$547$	−4.19427e8	−0.109572	−0.0547862	−	0.998498i	$-0.517448\pi$
$547$	−4.19427e8	−0.109572	−0.0547862	+	0.998498i	$0.517448\pi$
$548$	7.47937e9	1.94148
$549$	7.94120e8	0.204825
$550$	3.58391e8	0.0918519
$551$	8.63532e9	2.19912
$552$	5.90294e9	1.49376
$553$	1.43381e10	3.60540
$554$	−7.01258e9	−1.75224
$555$	5.87328e9	1.45833
$556$	−2.19339e9	−0.541195
$557$	−7.37086e9	−1.80728	−0.903639	−	0.428295i	$-0.859114\pi$
$557$	−7.37086e9	−1.80728	−0.903639	+	0.428295i	$0.859114\pi$
$558$	−4.31952e9	−1.05249
$559$	2.44819e9	0.592795
$560$	3.96732e10	9.54640
$561$	−1.14099e7	−0.00272842
$562$	3.85724e9	0.916642
$563$	−5.40369e9	−1.27618	−0.638089	−	0.769963i	$-0.720275\pi$
$563$	−5.40369e9	−1.27618	−0.638089	+	0.769963i	$0.720275\pi$
$564$	−2.22068e8	−0.0521206
$565$	4.00598e9	0.934414
$566$	1.00534e10	2.33054
$567$	−9.46268e8	−0.218009
$568$	3.91224e9	0.895789
$569$	−2.39098e9	−0.544104	−0.272052	−	0.962283i	$-0.587702\pi$
$569$	−2.39098e9	−0.544104	−0.272052	+	0.962283i	$0.587702\pi$
$570$	9.00337e9	2.03631
$571$	−4.97857e9	−1.11912	−0.559562	−	0.828789i	$-0.689031\pi$
$571$	−4.97857e9	−1.11912	−0.559562	+	0.828789i	$0.689031\pi$
$572$	−5.18391e8	−0.115817
$573$	1.78028e9	0.395318
$574$	−2.01048e10	−4.43720
$575$	−3.86365e9	−0.847541
$576$	4.57395e9	0.997270
$577$	3.57830e9	0.775464	0.387732	−	0.921772i	$-0.373259\pi$
$577$	3.57830e9	0.775464	0.387732	+	0.921772i	$0.373259\pi$
$578$	8.78645e9	1.89263
$579$	3.63099e8	0.0777410
$580$	−3.03692e10	−6.46302
$581$	−3.65053e9	−0.772216
$582$	−6.66817e9	−1.40209
$583$	2.16437e8	0.0452367
$584$	−1.58220e10	−3.28713
$585$	−2.17229e9	−0.448614
$586$	1.65308e10	3.39354
$587$	−2.26324e9	−0.461845	−0.230923	−	0.972972i	$-0.574174\pi$
$587$	−2.26324e9	−0.461845	−0.230923	+	0.972972i	$0.574174\pi$
$588$	2.15595e10	4.37340
$589$	1.05729e10	2.13201
$590$	−1.77370e9	−0.355547
$591$	4.29694e8	0.0856255
$592$	−3.04282e10	−6.02768
$593$	2.71803e9	0.535257	0.267628	−	0.963522i	$-0.413760\pi$
$593$	2.71803e9	0.535257	0.267628	+	0.963522i	$0.413760\pi$
$594$	8.69157e7	0.0170155
$595$	1.47161e9	0.286407
$596$	−1.15247e10	−2.22981
$597$	9.70516e8	0.186678
$598$	7.69099e9	1.47071
$599$	5.48589e9	1.04293	0.521463	−	0.853274i	$-0.325386\pi$
$599$	5.48589e9	1.04293	0.521463	+	0.853274i	$0.325386\pi$
$600$	−1.00640e10	−1.90214
$601$	5.20845e9	0.978695	0.489348	−	0.872089i	$-0.337235\pi$
$601$	5.20845e9	0.978695	0.489348	+	0.872089i	$0.337235\pi$
$602$	1.26339e10	2.36020
$603$	−4.06427e7	−0.00754869
$604$	−2.13416e10	−3.94092
$605$	7.76085e9	1.42484
$606$	−4.20460e9	−0.767486
$607$	−8.43683e9	−1.53115	−0.765577	−	0.643345i	$-0.777546\pi$
$607$	−8.43683e9	−1.53115	−0.765577	+	0.643345i	$0.777546\pi$
$608$	−2.39466e10	−4.32097
$609$	−1.07519e10	−1.92896
$610$	9.40766e9	1.67814
$611$	−1.80485e8	−0.0320108
$612$	5.13635e8	0.0905785
$613$	−6.65621e9	−1.16712	−0.583560	−	0.812070i	$-0.698341\pi$
$613$	−6.65621e9	−1.16712	−0.583560	+	0.812070i	$0.698341\pi$
$614$	1.15579e10	2.01506
$615$	5.62291e9	0.974761
$616$	−1.66874e9	−0.287645
$617$	1.08431e10	1.85846	0.929231	−	0.369498i	$-0.120470\pi$
$617$	1.08431e10	1.85846	0.929231	+	0.369498i	$0.120470\pi$
$618$	1.61889e9	0.275903
$619$	−1.05882e10	−1.79434	−0.897172	−	0.441681i	$-0.854382\pi$
$619$	−1.05882e10	−1.79434	−0.897172	+	0.441681i	$0.854382\pi$
$620$	−3.71833e10	−6.26580
$621$	−9.36998e8	−0.157007
$622$	−1.58423e10	−2.63969
$623$	2.99705e9	0.496576
$624$	1.12542e10	1.85425
$625$	−5.85706e9	−0.959621
$626$	−1.15018e10	−1.87394
$627$	−2.12743e8	−0.0344682
$628$	1.60674e10	2.58873
$629$	−1.12868e9	−0.180840
$630$	−1.12101e10	−1.78615
$631$	9.06740e9	1.43675	0.718373	−	0.695658i	$-0.244887\pi$
$631$	9.06740e9	1.43675	0.718373	+	0.695658i	$0.244887\pi$
$632$	3.69819e10	5.82746
$633$	−5.48858e9	−0.860097
$634$	−2.31980e10	−3.61524
$635$	−3.61649e9	−0.560505
$636$	−9.74326e9	−1.50177
$637$	1.75224e10	2.68600
$638$	9.87569e8	0.150555
$639$	−6.21006e8	−0.0941548
$640$	2.25030e10	3.39322
$641$	−6.94011e9	−1.04079	−0.520395	−	0.853926i	$-0.674215\pi$
$641$	−6.94011e9	−1.04079	−0.520395	+	0.853926i	$0.674215\pi$
$642$	5.47747e8	0.0816973
$643$	−4.50631e9	−0.668471	−0.334235	−	0.942490i	$-0.608478\pi$
$643$	−4.50631e9	−0.668471	−0.334235	+	0.942490i	$0.608478\pi$
$644$	2.88396e10	4.25490
$645$	−3.53344e9	−0.518488
$646$	−1.73020e9	−0.252512
$647$	5.05823e9	0.734233	0.367116	−	0.930175i	$-0.380345\pi$
$647$	5.05823e9	0.734233	0.367116	+	0.930175i	$0.380345\pi$
$648$	−2.44069e9	−0.352371
$649$	4.19112e7	0.00601829
$650$	−1.31125e10	−1.87279
$651$	−1.31643e10	−1.87010
$652$	−9.71082e9	−1.37211
$653$	−3.31489e9	−0.465879	−0.232940	−	0.972491i	$-0.574834\pi$
$653$	−3.31489e9	−0.465879	−0.232940	+	0.972491i	$0.574834\pi$
$654$	8.90604e9	1.24498
$655$	−8.36409e9	−1.16298
$656$	−2.91311e10	−4.02896
$657$	2.51149e9	0.345504
$658$	−9.31391e8	−0.127450
$659$	−9.88658e9	−1.34570	−0.672849	−	0.739780i	$-0.734929\pi$
$659$	−9.88658e9	−1.34570	−0.672849	+	0.739780i	$0.734929\pi$
$660$	7.48187e8	0.101299
$661$	−1.76683e9	−0.237952	−0.118976	−	0.992897i	$-0.537961\pi$
$661$	−1.76683e9	−0.237952	−0.118976	+	0.992897i	$0.537961\pi$
$662$	9.43576e8	0.126408
$663$	4.17454e8	0.0556303
$664$	−9.41571e9	−1.24814
$665$	2.74389e10	3.61819
$666$	8.59782e9	1.12779
$667$	−1.06465e10	−1.38921
$668$	−2.05979e10	−2.67366
$669$	−3.36611e9	−0.434647
$670$	−4.81479e8	−0.0618466
$671$	−2.22296e8	−0.0284056
$672$	2.98160e10	3.79015
$673$	−8.78145e9	−1.11049	−0.555244	−	0.831688i	$-0.687375\pi$
$673$	−8.78145e9	−1.11049	−0.555244	+	0.831688i	$0.687375\pi$
$674$	1.44361e10	1.81610
$675$	1.59750e9	0.199930
$676$	−2.38303e9	−0.296699
$677$	1.26024e9	0.156096	0.0780482	−	0.996950i	$-0.475131\pi$
$677$	1.26024e9	0.156096	0.0780482	+	0.996950i	$0.475131\pi$
$678$	5.86430e9	0.722624
$679$	−2.03221e10	−2.49129
$680$	3.79569e9	0.462924
$681$	−4.42785e8	−0.0537251
$682$	1.20915e9	0.145961
$683$	1.20509e10	1.44726	0.723630	−	0.690188i	$-0.242472\pi$
$683$	1.20509e10	1.44726	0.723630	+	0.690188i	$0.242472\pi$
$684$	9.57698e9	1.14428
$685$	−8.77348e9	−1.04293
$686$	5.86937e10	6.94156
$687$	−3.62201e9	−0.426188
$688$	1.83060e10	2.14306
$689$	−7.91878e9	−0.922340
$690$	−1.11003e10	−1.28636
$691$	−1.63179e9	−0.188144	−0.0940720	−	0.995565i	$-0.529988\pi$
$691$	−1.63179e9	−0.188144	−0.0940720	+	0.995565i	$0.529988\pi$
$692$	−3.00820e10	−3.45093
$693$	2.64887e8	0.0302339
$694$	−6.82792e8	−0.0775408
$695$	2.57290e9	0.290720
$696$	−2.77320e10	−3.11781
$697$	−1.08057e9	−0.120875
$698$	−1.56782e10	−1.74503
$699$	−1.76661e9	−0.195646
$700$	−4.91692e10	−5.41813
$701$	−4.92646e9	−0.540159	−0.270080	−	0.962838i	$-0.587050\pi$
$701$	−4.92646e9	−0.540159	−0.270080	+	0.962838i	$0.587050\pi$
$702$	−3.17999e9	−0.346933
$703$	−2.10448e10	−2.28456
$704$	−1.28038e9	−0.138304
$705$	2.60491e8	0.0279982
$706$	−2.00484e10	−2.14419
$707$	−1.28141e10	−1.36370
$708$	−1.88670e9	−0.199796
$709$	1.23998e10	1.30663	0.653315	−	0.757087i	$-0.273378\pi$
$709$	1.23998e10	1.30663	0.653315	+	0.757087i	$0.273378\pi$
$710$	−7.35683e9	−0.771413
$711$	−5.87029e9	−0.612514
$712$	7.73022e9	0.802624
$713$	−1.30353e10	−1.34682
$714$	2.15427e9	0.221491
$715$	6.08085e8	0.0622147
$716$	3.14927e10	3.20637
$717$	−4.29627e9	−0.435285
$718$	2.35049e10	2.36986
$719$	−7.30887e9	−0.733329	−0.366665	−	0.930353i	$-0.619500\pi$
$719$	−7.30887e9	−0.733329	−0.366665	+	0.930353i	$0.619500\pi$
$720$	−1.62430e10	−1.62182
$721$	4.93377e9	0.490236
$722$	−1.29181e10	−1.27737
$723$	3.72854e9	0.366906
$724$	2.53865e9	0.248610
$725$	1.81514e10	1.76900
$726$	1.13610e10	1.10189
$727$	−1.04087e9	−0.100467	−0.0502337	−	0.998737i	$-0.515997\pi$
$727$	−1.04087e9	−0.100467	−0.0502337	+	0.998737i	$0.515997\pi$
$728$	6.10545e10	5.86486
$729$	3.87420e8	0.0370370
$730$	2.97528e10	2.83073
$731$	6.79030e8	0.0642951
$732$	1.00070e10	0.943011
$733$	1.03455e10	0.970262	0.485131	−	0.874441i	$-0.338772\pi$
$733$	1.03455e10	0.970262	0.485131	+	0.874441i	$0.338772\pi$
$734$	−1.85788e10	−1.73413
$735$	−2.52898e10	−2.34931
$736$	2.95239e10	2.72961
$737$	1.13770e7	0.00104687
$738$	8.23131e9	0.753827
$739$	−8.36230e9	−0.762203	−0.381101	−	0.924533i	$-0.624455\pi$
$739$	−8.36230e9	−0.762203	−0.381101	+	0.924533i	$0.624455\pi$
$740$	7.40117e10	6.71412
$741$	7.78364e9	0.702780
$742$	−4.08649e10	−3.67228
$743$	−1.24177e10	−1.11066	−0.555330	−	0.831630i	$-0.687408\pi$
$743$	−1.24177e10	−1.11066	−0.555330	+	0.831630i	$0.687408\pi$
$744$	−3.39544e10	−3.02267
$745$	1.35187e10	1.19781
$746$	3.91472e9	0.345235
$747$	1.49460e9	0.131190
$748$	−1.43781e8	−0.0125616
$749$	1.66933e9	0.145163
$750$	7.08059e8	0.0612851
$751$	−4.11718e9	−0.354699	−0.177349	−	0.984148i	$-0.556752\pi$
$751$	−4.11718e9	−0.354699	−0.177349	+	0.984148i	$0.556752\pi$
$752$	−1.34955e9	−0.115725
$753$	3.75595e9	0.320580
$754$	−3.61322e10	−3.06970
$755$	2.50342e10	2.11699
$756$	−1.19243e10	−1.00371
$757$	7.02287e9	0.588409	0.294204	−	0.955743i	$-0.404945\pi$
$757$	7.02287e9	0.588409	0.294204	+	0.955743i	$0.404945\pi$
$758$	3.75775e10	3.13390
$759$	2.62292e8	0.0217740
$760$	7.07725e10	5.84813
$761$	−3.65462e9	−0.300605	−0.150302	−	0.988640i	$-0.548025\pi$
$761$	−3.65462e9	−0.300605	−0.150302	+	0.988640i	$0.548025\pi$
$762$	−5.29414e9	−0.433464
$763$	2.71423e10	2.21213
$764$	2.24340e10	1.82004
$765$	−6.02506e8	−0.0486571
$766$	−2.69341e10	−2.16522
$767$	−1.53341e9	−0.122708
$768$	1.12580e10	0.896804
$769$	1.51627e10	1.20236	0.601179	−	0.799114i	$-0.294698\pi$
$769$	1.51627e10	1.20236	0.601179	+	0.799114i	$0.294698\pi$
$770$	3.13802e9	0.247707
$771$	1.10633e10	0.869347
$772$	4.57556e9	0.357918
$773$	1.27681e10	0.994253	0.497126	−	0.867678i	$-0.334388\pi$
$773$	1.27681e10	0.994253	0.497126	+	0.867678i	$0.334388\pi$
$774$	−5.17256e9	−0.400970
$775$	2.22242e10	1.71502
$776$	−5.24163e10	−4.02671
$777$	2.62030e10	2.00390
$778$	3.06543e10	2.33380
$779$	−2.01477e10	−1.52702
$780$	−2.73740e10	−2.06541
$781$	1.73837e8	0.0130576
$782$	2.13317e9	0.159515
$783$	4.40202e9	0.327707
$784$	1.31021e11	9.71036
$785$	−1.88474e10	−1.39062
$786$	−1.22441e10	−0.899388
$787$	−3.81227e9	−0.278787	−0.139394	−	0.990237i	$-0.544515\pi$
$787$	−3.81227e9	−0.278787	−0.139394	+	0.990237i	$0.544515\pi$
$788$	5.41476e9	0.394219
$789$	3.23715e9	0.234635
$790$	−6.95433e10	−5.01834
$791$	1.78722e10	1.28399
$792$	6.83216e8	0.0488675
$793$	8.13317e9	0.579167
$794$	4.30976e10	3.05550
$795$	1.14291e10	0.806725
$796$	1.22299e10	0.859461
$797$	−9.63179e9	−0.673911	−0.336956	−	0.941521i	$-0.609397\pi$
$797$	−9.63179e9	−0.673911	−0.336956	+	0.941521i	$0.609397\pi$
$798$	4.01675e10	2.79811
$799$	−5.00592e7	−0.00347192
$800$	−5.03357e10	−3.47585
$801$	−1.22705e9	−0.0843624
$802$	1.99683e10	1.36688
$803$	−7.03037e8	−0.0479153
$804$	−5.12155e8	−0.0347540
$805$	−3.38296e10	−2.28566
$806$	−4.42394e10	−2.97603
$807$	−6.63105e9	−0.444145
$808$	−3.30510e10	−2.20417
$809$	1.38532e9	0.0919878	0.0459939	−	0.998942i	$-0.485355\pi$
$809$	1.38532e9	0.0919878	0.0459939	+	0.998942i	$0.485355\pi$
$810$	4.58963e9	0.303445
$811$	1.41931e10	0.934339	0.467170	−	0.884168i	$-0.345274\pi$
$811$	1.41931e10	0.934339	0.467170	+	0.884168i	$0.345274\pi$
$812$	−1.35489e11	−8.88090
$813$	6.81602e9	0.444850
$814$	−2.40677e9	−0.156404
$815$	1.13910e10	0.737073
$816$	3.12145e9	0.201113
$817$	1.26608e10	0.812242
$818$	7.76554e8	0.0496061
$819$	−9.69143e9	−0.616445
$820$	7.08566e10	4.48778
$821$	−1.94897e10	−1.22915	−0.614573	−	0.788860i	$-0.710672\pi$
$821$	−1.94897e10	−1.22915	−0.614573	+	0.788860i	$0.710672\pi$
$822$	−1.28434e10	−0.806544
$823$	7.94309e9	0.496696	0.248348	−	0.968671i	$-0.420112\pi$
$823$	7.94309e9	0.496696	0.248348	+	0.968671i	$0.420112\pi$
$824$	1.27255e10	0.792376
$825$	−4.47186e8	−0.0277268
$826$	−7.91314e9	−0.488561
$827$	1.74454e10	1.07254	0.536268	−	0.844048i	$-0.319834\pi$
$827$	1.74454e10	1.07254	0.536268	+	0.844048i	$0.319834\pi$
$828$	−1.18075e10	−0.722856
$829$	2.55780e10	1.55929	0.779644	−	0.626223i	$-0.215400\pi$
$829$	2.55780e10	1.55929	0.779644	+	0.626223i	$0.215400\pi$
$830$	1.77059e10	1.07484
$831$	8.75000e9	0.528938
$832$	4.68452e10	2.81990
$833$	4.86001e9	0.291326
$834$	3.76643e9	0.224827
$835$	2.41618e10	1.43624
$836$	−2.68086e9	−0.158691
$837$	5.38972e9	0.317707
$838$	4.90778e9	0.288092
$839$	−7.34489e9	−0.429357	−0.214678	−	0.976685i	$-0.568870\pi$
$839$	−7.34489e9	−0.429357	−0.214678	+	0.976685i	$0.568870\pi$
$840$	−8.81190e10	−5.12970
$841$	3.27675e10	1.89958
$842$	−1.56261e10	−0.902106
$843$	−4.81290e9	−0.276701
$844$	−6.91639e10	−3.95987
$845$	2.79535e9	0.159382
$846$	3.81329e8	0.0216523
$847$	3.46241e10	1.95788
$848$	−5.92115e10	−3.33442
$849$	−1.25443e10	−0.703506
$850$	−3.63687e9	−0.203124
$851$	2.59463e10	1.44318
$852$	−7.82555e9	−0.433487
$853$	−3.22700e10	−1.78023	−0.890116	−	0.455734i	$-0.849377\pi$
$853$	−3.22700e10	−1.78023	−0.890116	+	0.455734i	$0.849377\pi$
$854$	4.19712e10	2.30594
$855$	−1.12340e10	−0.614687
$856$	4.30566e9	0.234629
$857$	−7.06953e9	−0.383670	−0.191835	−	0.981427i	$-0.561444\pi$
$857$	−7.06953e9	−0.383670	−0.191835	+	0.981427i	$0.561444\pi$
$858$	8.90168e8	0.0481134
$859$	−2.05380e10	−1.10556	−0.552779	−	0.833328i	$-0.686432\pi$
$859$	−2.05380e10	−1.10556	−0.552779	+	0.833328i	$0.686432\pi$
$860$	−4.45264e10	−2.38711
$861$	2.50860e10	1.33943
$862$	−5.14030e9	−0.273346
$863$	−3.50261e10	−1.85504	−0.927520	−	0.373773i	$-0.878064\pi$
$863$	−3.50261e10	−1.85504	−0.927520	+	0.373773i	$0.878064\pi$
$864$	−1.22072e10	−0.643901
$865$	3.52869e10	1.85378
$866$	5.68957e9	0.297692
$867$	−1.09634e10	−0.571317
$868$	−1.65889e11	−8.60990
$869$	1.64326e9	0.0849447
$870$	5.21492e10	2.68491
$871$	−4.16251e8	−0.0213448
$872$	7.00075e10	3.57550
$873$	8.32026e9	0.423240
$874$	3.97740e10	2.01516
$875$	2.15790e9	0.108894
$876$	3.16484e10	1.59070
$877$	2.05838e10	1.03045	0.515225	−	0.857055i	$-0.327708\pi$
$877$	2.05838e10	1.03045	0.515225	+	0.857055i	$0.327708\pi$
$878$	−2.08613e10	−1.04018
$879$	−2.06265e10	−1.02439
$880$	4.54686e9	0.224917
$881$	3.80144e9	0.187298	0.0936488	−	0.995605i	$-0.470147\pi$
$881$	3.80144e9	0.187298	0.0936488	+	0.995605i	$0.470147\pi$
$882$	−3.70215e10	−1.81683
$883$	−2.46327e10	−1.20406	−0.602032	−	0.798472i	$-0.705642\pi$
$883$	−2.46327e10	−1.20406	−0.602032	+	0.798472i	$0.705642\pi$
$884$	5.26052e9	0.256121
$885$	2.21314e9	0.107327
$886$	−4.90976e10	−2.37161
$887$	−2.28817e10	−1.10092	−0.550461	−	0.834861i	$-0.685548\pi$
$887$	−2.28817e10	−1.10092	−0.550461	+	0.834861i	$0.685548\pi$
$888$	6.75847e10	3.23894
$889$	−1.61346e10	−0.770196
$890$	−1.45364e10	−0.691183
$891$	−1.08450e8	−0.00513637
$892$	−4.24177e10	−2.00111
$893$	−9.33378e8	−0.0438609
$894$	1.97899e10	0.926322
$895$	−3.69416e10	−1.72241
$896$	1.00395e11	4.66265
$897$	−9.59649e9	−0.443955
$898$	1.36205e10	0.627661
$899$	6.12400e10	2.81110
$900$	2.01308e10	0.920476
$901$	−2.19635e9	−0.100038
$902$	−2.30417e9	−0.104542
$903$	−1.57640e10	−0.712460
$904$	4.60974e10	2.07533
$905$	−2.97790e9	−0.133549
$906$	3.66472e10	1.63717
$907$	2.43988e10	1.08578	0.542892	−	0.839802i	$-0.317329\pi$
$907$	2.43988e10	1.08578	0.542892	+	0.839802i	$0.317329\pi$
$908$	−5.57971e9	−0.247350
$909$	5.24632e9	0.231676
$910$	−1.14811e11	−5.05055
$911$	7.15550e9	0.313563	0.156782	−	0.987633i	$-0.449888\pi$
$911$	7.15550e9	0.313563	0.156782	+	0.987633i	$0.449888\pi$
$912$	5.82010e10	2.54067
$913$	−4.18379e8	−0.0181937
$914$	5.92844e10	2.56820
$915$	−1.17385e10	−0.506569
$916$	−4.56424e10	−1.96216
$917$	−3.73154e10	−1.59807
$918$	−8.82001e8	−0.0376287
$919$	−3.31022e10	−1.40687	−0.703433	−	0.710761i	$-0.748351\pi$
$919$	−3.31022e10	−1.40687	−0.703433	+	0.710761i	$0.748351\pi$
$920$	−8.72558e10	−3.69434
$921$	−1.44214e10	−0.608274
$922$	−3.26216e10	−1.37071
$923$	−6.36017e9	−0.266234
$924$	3.33795e9	0.139196
$925$	−4.42362e10	−1.83773
$926$	1.53080e10	0.633548
$927$	−2.01998e9	−0.0832852
$928$	−1.38703e11	−5.69729
$929$	4.50956e10	1.84535	0.922676	−	0.385577i	$-0.125997\pi$
$929$	4.50956e10	1.84535	0.922676	+	0.385577i	$0.125997\pi$
$930$	6.38501e10	2.60298
$931$	9.06172e10	3.68033
$932$	−2.22618e10	−0.900750
$933$	1.97674e10	0.796827
$934$	7.84469e10	3.15037
$935$	1.68658e8	0.00674787
$936$	−2.49969e10	−0.996369
$937$	2.71853e10	1.07956	0.539779	−	0.841807i	$-0.318508\pi$
$937$	2.71853e10	1.07956	0.539779	+	0.841807i	$0.318508\pi$
$938$	−2.14806e9	−0.0849840
$939$	1.43514e10	0.565673
$940$	3.28256e9	0.128903
$941$	−4.59907e10	−1.79931	−0.899655	−	0.436601i	$-0.856182\pi$
$941$	−4.59907e10	−1.79931	−0.899655	+	0.436601i	$0.856182\pi$
$942$	−2.75905e10	−1.07543
$943$	2.48402e10	0.964638
$944$	−1.14658e10	−0.443611
$945$	1.39875e10	0.539174
$946$	1.44794e9	0.0556074
$947$	4.47468e10	1.71213	0.856065	−	0.516868i	$-0.172902\pi$
$947$	4.47468e10	1.71213	0.856065	+	0.516868i	$0.172902\pi$
$948$	−7.39740e10	−2.82000
$949$	2.57221e10	0.976954
$950$	−6.78113e10	−2.56608
$951$	2.89454e10	1.09131
$952$	1.69340e10	0.636109
$953$	−6.72893e9	−0.251838	−0.125919	−	0.992041i	$-0.540188\pi$
$953$	−6.72893e9	−0.251838	−0.125919	+	0.992041i	$0.540188\pi$
$954$	1.67309e10	0.623877
$955$	−2.63156e10	−0.977692
$956$	−5.41390e10	−2.00405
$957$	−1.23225e9	−0.0454471
$958$	−3.89104e10	−1.42984
$959$	−3.91419e10	−1.43310
$960$	−6.76110e10	−2.46643
$961$	4.74681e10	1.72532
$962$	8.80566e10	3.18896
$963$	−6.83456e8	−0.0246614
$964$	4.69849e10	1.68923
$965$	−5.36724e9	−0.192267
$966$	−4.95227e10	−1.76760
$967$	−1.86690e9	−0.0663941	−0.0331970	−	0.999449i	$-0.510569\pi$
$967$	−1.86690e9	−0.0663941	−0.0331970	+	0.999449i	$0.510569\pi$
$968$	8.93052e10	3.16456
$969$	2.15887e9	0.0762242
$970$	9.85672e10	3.46762
$971$	2.50323e10	0.877471	0.438735	−	0.898616i	$-0.355427\pi$
$971$	2.50323e10	0.877471	0.438735	+	0.898616i	$0.355427\pi$
$972$	4.88205e9	0.170518
$973$	1.14787e10	0.399482
$974$	3.42403e10	1.18736
$975$	1.63612e10	0.565326
$976$	6.08145e10	2.09379
$977$	3.21353e10	1.10243	0.551216	−	0.834363i	$-0.314164\pi$
$977$	3.21353e10	1.10243	0.551216	+	0.834363i	$0.314164\pi$
$978$	1.66752e10	0.570012
$979$	3.43486e8	0.0116996
$980$	−3.18688e11	−10.8162
$981$	−1.11126e10	−0.375814
$982$	6.48464e9	0.218522
$983$	−2.52657e10	−0.848387	−0.424194	−	0.905572i	$-0.639442\pi$
$983$	−2.52657e10	−0.848387	−0.424194	+	0.905572i	$0.639442\pi$
$984$	6.47036e10	2.16494
$985$	−6.35163e9	−0.211767
$986$	−1.00216e10	−0.332942
$987$	1.16215e9	0.0384727
$988$	9.80849e10	3.23559
$989$	−1.56096e10	−0.513104
$990$	−1.28477e9	−0.0420824
$991$	−5.79422e10	−1.89120	−0.945600	−	0.325331i	$-0.894524\pi$
$991$	−5.79422e10	−1.89120	−0.945600	+	0.325331i	$0.894524\pi$
$992$	−1.69825e11	−5.52344
$993$	−1.17735e9	−0.0381579
$994$	−3.28217e10	−1.06001
$995$	−1.43459e10	−0.461687
$996$	1.88340e10	0.603998
$997$	−4.76882e10	−1.52398	−0.761988	−	0.647591i	$-0.775777\pi$
$997$	−4.76882e10	−1.52398	−0.761988	+	0.647591i	$0.775777\pi$
$998$	−2.92143e10	−0.930334
$999$	−1.07280e10	−0.340439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.b.1.2	✓	17
3.2	odd	2		531.8.a.d.1.16		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.2	✓	17	1.1	even	1	trivial
531.8.a.d.1.16		17	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)

\(f(q)\)	\(=\)	\(q-21.6388 q^{2} +27.0000 q^{3} +340.238 q^{4} -399.107 q^{5} -584.248 q^{6} -1780.57 q^{7} -4592.58 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-21.6388 q^{2} +27.0000 q^{3} +340.238 q^{4} -399.107 q^{5} -584.248 q^{6} -1780.57 q^{7} -4592.58 q^{8} +729.000 q^{9} +8636.21 q^{10} -204.067 q^{11} +9186.43 q^{12} +7466.22 q^{13} +38529.4 q^{14} -10775.9 q^{15} +55827.6 q^{16} +2070.83 q^{17} -15774.7 q^{18} +38611.6 q^{19} -135792. q^{20} -48075.4 q^{21} +4415.78 q^{22} -47604.4 q^{23} -124000. q^{24} +81161.6 q^{25} -161560. q^{26} +19683.0 q^{27} -605818. q^{28} +223646. q^{29} +233178. q^{30} +273826. q^{31} -620192. q^{32} -5509.82 q^{33} -44810.3 q^{34} +710639. q^{35} +248034. q^{36} -545039. q^{37} -835510. q^{38} +201588. q^{39} +1.83293e6 q^{40} -521804. q^{41} +1.04029e6 q^{42} +327902. q^{43} -69431.5 q^{44} -290949. q^{45} +1.03010e6 q^{46} -24173.5 q^{47} +1.50734e6 q^{48} +2.34689e6 q^{49} -1.75624e6 q^{50} +55912.4 q^{51} +2.54029e6 q^{52} -1.06061e6 q^{53} -425917. q^{54} +81444.8 q^{55} +8.17742e6 q^{56} +1.04251e6 q^{57} -4.83943e6 q^{58} -205379. q^{59} -3.66637e6 q^{60} +1.08933e6 q^{61} -5.92527e6 q^{62} -1.29804e6 q^{63} +6.27428e6 q^{64} -2.97982e6 q^{65} +119226. q^{66} -55751.2 q^{67} +704575. q^{68} -1.28532e6 q^{69} -1.53774e7 q^{70} -851859. q^{71} -3.34799e6 q^{72} +3.44512e6 q^{73} +1.17940e7 q^{74} +2.19136e6 q^{75} +1.31372e7 q^{76} +363356. q^{77} -4.36213e6 q^{78} -8.05252e6 q^{79} -2.22812e7 q^{80} +531441. q^{81} +1.12912e7 q^{82} +2.05020e6 q^{83} -1.63571e7 q^{84} -826483. q^{85} -7.09542e6 q^{86} +6.03843e6 q^{87} +937197. q^{88} -1.68320e6 q^{89} +6.29579e6 q^{90} -1.32941e7 q^{91} -1.61969e7 q^{92} +7.39330e6 q^{93} +523086. q^{94} -1.54102e7 q^{95} -1.67452e7 q^{96} +1.14133e7 q^{97} -5.07839e7 q^{98} -148765. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9} - 6391 q^{10} - 8888 q^{11} + 31482 q^{12} - 12702 q^{13} - 17555 q^{14} - 28944 q^{15} + 139226 q^{16} - 36167 q^{17} - 23328 q^{18} - 71037 q^{19} - 274883 q^{20} - 64989 q^{21} - 325182 q^{22} - 269995 q^{23} - 179415 q^{24} + 97329 q^{25} - 336906 q^{26} + 334611 q^{27} - 901362 q^{28} - 543825 q^{29} - 172557 q^{30} - 633109 q^{31} - 837062 q^{32} - 239976 q^{33} - 529288 q^{34} - 287621 q^{35} + 850014 q^{36} - 867607 q^{37} - 1727169 q^{38} - 342954 q^{39} - 815662 q^{40} - 1428939 q^{41} - 473985 q^{42} - 477060 q^{43} - 1667926 q^{44} - 781488 q^{45} + 5305549 q^{46} - 1217849 q^{47} + 3759102 q^{48} + 4350738 q^{49} + 4561369 q^{50} - 976509 q^{51} + 4175994 q^{52} - 3487068 q^{53} - 629856 q^{54} - 960484 q^{55} - 5363196 q^{56} - 1917999 q^{57} - 3082906 q^{58} - 3491443 q^{59} - 7421841 q^{60} + 998917 q^{61} - 5742614 q^{62} - 1754703 q^{63} + 17531621 q^{64} - 6075816 q^{65} - 8779914 q^{66} - 356026 q^{67} - 16149231 q^{68} - 7289865 q^{69} - 548798 q^{70} - 12879428 q^{71} - 4844205 q^{72} - 6176157 q^{73} - 5971906 q^{74} + 2627883 q^{75} - 17624580 q^{76} + 239687 q^{77} - 9096462 q^{78} - 18886490 q^{79} - 70463349 q^{80} + 9034497 q^{81} - 19351611 q^{82} - 22824893 q^{83} - 24336774 q^{84} - 7973079 q^{85} - 27502196 q^{86} - 14683275 q^{87} - 62527651 q^{88} - 30609647 q^{89} - 4659039 q^{90} - 36301521 q^{91} - 41388548 q^{92} - 17093943 q^{93} + 1010176 q^{94} - 29303629 q^{95} - 22600674 q^{96} - 26249806 q^{97} - 93110852 q^{98} - 6479352 q^{99}+O(q^{100}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9 - 6391 * q^10 - 8888 * q^11 + 31482 * q^12 - 12702 * q^13 - 17555 * q^14 - 28944 * q^15 + 139226 * q^16 - 36167 * q^17 - 23328 * q^18 - 71037 * q^19 - 274883 * q^20 - 64989 * q^21 - 325182 * q^22 - 269995 * q^23 - 179415 * q^24 + 97329 * q^25 - 336906 * q^26 + 334611 * q^27 - 901362 * q^28 - 543825 * q^29 - 172557 * q^30 - 633109 * q^31 - 837062 * q^32 - 239976 * q^33 - 529288 * q^34 - 287621 * q^35 + 850014 * q^36 - 867607 * q^37 - 1727169 * q^38 - 342954 * q^39 - 815662 * q^40 - 1428939 * q^41 - 473985 * q^42 - 477060 * q^43 - 1667926 * q^44 - 781488 * q^45 + 5305549 * q^46 - 1217849 * q^47 + 3759102 * q^48 + 4350738 * q^49 + 4561369 * q^50 - 976509 * q^51 + 4175994 * q^52 - 3487068 * q^53 - 629856 * q^54 - 960484 * q^55 - 5363196 * q^56 - 1917999 * q^57 - 3082906 * q^58 - 3491443 * q^59 - 7421841 * q^60 + 998917 * q^61 - 5742614 * q^62 - 1754703 * q^63 + 17531621 * q^64 - 6075816 * q^65 - 8779914 * q^66 - 356026 * q^67 - 16149231 * q^68 - 7289865 * q^69 - 548798 * q^70 - 12879428 * q^71 - 4844205 * q^72 - 6176157 * q^73 - 5971906 * q^74 + 2627883 * q^75 - 17624580 * q^76 + 239687 * q^77 - 9096462 * q^78 - 18886490 * q^79 - 70463349 * q^80 + 9034497 * q^81 - 19351611 * q^82 - 22824893 * q^83 - 24336774 * q^84 - 7973079 * q^85 - 27502196 * q^86 - 14683275 * q^87 - 62527651 * q^88 - 30609647 * q^89 - 4659039 * q^90 - 36301521 * q^91 - 41388548 * q^92 - 17093943 * q^93 + 1010176 * q^94 - 29303629 * q^95 - 22600674 * q^96 - 26249806 * q^97 - 93110852 * q^98 - 6479352 * q^99

Introduction

L-functions

Modular forms

Varieties

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