LMFDB - Embedded newform 177.8.a.b.1.3

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			1.3
Root			$-15.9892$ 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)

$f(q)$	$=$	$q-17.9892 q^{2} +27.0000 q^{3} +195.612 q^{4} -98.9095 q^{5} -485.709 q^{6} +159.201 q^{7} -1216.28 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-17.9892 q^{2} +27.0000 q^{3} +195.612 q^{4} -98.9095 q^{5} -485.709 q^{6} +159.201 q^{7} -1216.28 q^{8} +729.000 q^{9} +1779.30 q^{10} -4884.97 q^{11} +5281.52 q^{12} +11664.5 q^{13} -2863.90 q^{14} -2670.56 q^{15} -3158.35 q^{16} -10463.7 q^{17} -13114.1 q^{18} +14966.8 q^{19} -19347.9 q^{20} +4298.42 q^{21} +87876.7 q^{22} -88.0105 q^{23} -32839.6 q^{24} -68341.9 q^{25} -209835. q^{26} +19683.0 q^{27} +31141.6 q^{28} -102600. q^{29} +48041.2 q^{30} -287624. q^{31} +212500. q^{32} -131894. q^{33} +188233. q^{34} -15746.5 q^{35} +142601. q^{36} +566144. q^{37} -269240. q^{38} +314941. q^{39} +120302. q^{40} +296117. q^{41} -77325.3 q^{42} +740471. q^{43} -955557. q^{44} -72105.0 q^{45} +1583.24 q^{46} +958168. q^{47} -85275.4 q^{48} -798198. q^{49} +1.22942e6 q^{50} -282519. q^{51} +2.28171e6 q^{52} -732872. q^{53} -354082. q^{54} +483170. q^{55} -193633. q^{56} +404103. q^{57} +1.84569e6 q^{58} -205379. q^{59} -522392. q^{60} +2.28293e6 q^{61} +5.17412e6 q^{62} +116057. q^{63} -3.41844e6 q^{64} -1.15373e6 q^{65} +2.37267e6 q^{66} -4.29840e6 q^{67} -2.04681e6 q^{68} -2376.28 q^{69} +283267. q^{70} -4.99901e6 q^{71} -886670. q^{72} +3.66974e6 q^{73} -1.01845e7 q^{74} -1.84523e6 q^{75} +2.92768e6 q^{76} -777691. q^{77} -5.66554e6 q^{78} +3.18719e6 q^{79} +312391. q^{80} +531441. q^{81} -5.32690e6 q^{82} -4.43945e6 q^{83} +840822. q^{84} +1.03496e6 q^{85} -1.33205e7 q^{86} -2.77020e6 q^{87} +5.94150e6 q^{88} -1.07216e7 q^{89} +1.29711e6 q^{90} +1.85700e6 q^{91} -17215.9 q^{92} -7.76584e6 q^{93} -1.72367e7 q^{94} -1.48036e6 q^{95} +5.73751e6 q^{96} -4.05589e6 q^{97} +1.43590e7 q^{98} -3.56114e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−17.9892	−1.59004	−0.795018	−	0.606585i	$-0.792539\pi$
$2$	−17.9892	−1.59004	−0.795018	+	0.606585i	$0.792539\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	195.612	1.52822
$5$	−98.9095	−0.353869	−0.176935	−	0.984223i	$-0.556618\pi$
$5$	−98.9095	−0.353869	−0.176935	+	0.984223i	$0.556618\pi$
$6$	−485.709	−0.918008
$7$	159.201	0.175429	0.0877147	−	0.996146i	$-0.472044\pi$
$7$	159.201	0.175429	0.0877147	+	0.996146i	$0.472044\pi$
$8$	−1216.28	−0.839884
$9$	729.000	0.333333
$10$	1779.30	0.562665
$11$	−4884.97	−1.10659	−0.553296	−	0.832985i	$-0.686630\pi$
$11$	−4884.97	−1.10659	−0.553296	+	0.832985i	$0.686630\pi$
$12$	5281.52	0.882316
$13$	11664.5	1.47253	0.736265	−	0.676694i	$-0.236588\pi$
$13$	11664.5	1.47253	0.736265	+	0.676694i	$0.236588\pi$
$14$	−2863.90	−0.278939
$15$	−2670.56	−0.204307
$16$	−3158.35	−0.192770
$17$	−10463.7	−0.516550	−0.258275	−	0.966071i	$-0.583154\pi$
$17$	−10463.7	−0.516550	−0.258275	+	0.966071i	$0.583154\pi$
$18$	−13114.1	−0.530012
$19$	14966.8	0.500599	0.250300	−	0.968168i	$-0.419471\pi$
$19$	14966.8	0.500599	0.250300	+	0.968168i	$0.419471\pi$
$20$	−19347.9	−0.540789
$21$	4298.42	0.101284
$22$	87876.7	1.75952
$23$	−88.0105	−0.00150830	−0.000754148	−	1.00000i	$-0.500240\pi$
$23$	−88.0105	−0.00150830	−0.000754148		1.00000i	$0.500240\pi$
$24$	−32839.6	−0.484907
$25$	−68341.9	−0.874776
$26$	−209835.	−2.34138
$27$	19683.0	0.192450
$28$	31141.6	0.268094
$29$	−102600.	−0.781185	−0.390592	−	0.920564i	$-0.627730\pi$
$29$	−102600.	−0.781185	−0.390592	+	0.920564i	$0.627730\pi$
$30$	48041.2	0.324855
$31$	−287624.	−1.73404	−0.867019	−	0.498275i	$-0.833967\pi$
$31$	−287624.	−1.73404	−0.867019	+	0.498275i	$0.833967\pi$
$32$	212500.	1.14640
$33$	−131894.	−0.638891
$34$	188233.	0.821333
$35$	−15746.5	−0.0620791
$36$	142601.	0.509406
$37$	566144.	1.83747	0.918737	−	0.394870i	$-0.129210\pi$
$37$	566144.	1.83747	0.918737	+	0.394870i	$0.129210\pi$
$38$	−269240.	−0.795971
$39$	314941.	0.850165
$40$	120302.	0.297209
$41$	296117.	0.670995	0.335497	−	0.942041i	$-0.391096\pi$
$41$	296117.	0.670995	0.335497	+	0.942041i	$0.391096\pi$
$42$	−77325.3	−0.161046
$43$	740471.	1.42026	0.710131	−	0.704070i	$-0.248636\pi$
$43$	740471.	1.42026	0.710131	+	0.704070i	$0.248636\pi$
$44$	−955557.	−1.69111
$45$	−72105.0	−0.117956
$46$	1583.24	0.00239825
$47$	958168.	1.34617	0.673084	−	0.739566i	$-0.264969\pi$
$47$	958168.	1.34617	0.673084	+	0.739566i	$0.264969\pi$
$48$	−85275.4	−0.111296
$49$	−798198.	−0.969225
$50$	1.22942e6	1.39093
$51$	−282519.	−0.298230
$52$	2.28171e6	2.25034
$53$	−732872.	−0.676181	−0.338090	−	0.941114i	$-0.609781\pi$
$53$	−732872.	−0.676181	−0.338090	+	0.941114i	$0.609781\pi$
$54$	−354082.	−0.306003
$55$	483170.	0.391589
$56$	−193633.	−0.147340
$57$	404103.	0.289021
$58$	1.84569e6	1.24211
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−522392.	−0.312225
$61$	2.28293e6	1.28777	0.643884	−	0.765123i	$-0.277322\pi$
$61$	2.28293e6	1.28777	0.643884	+	0.765123i	$0.277322\pi$
$62$	5.17412e6	2.75718
$63$	116057.	0.0584765
$64$	−3.41844e6	−1.63004
$65$	−1.15373e6	−0.521083
$66$	2.37267e6	1.01586
$67$	−4.29840e6	−1.74600	−0.873001	−	0.487719i	$-0.837829\pi$
$67$	−4.29840e6	−1.74600	−0.873001	+	0.487719i	$0.837829\pi$
$68$	−2.04681e6	−0.789400
$69$	−2376.28	−0.000870816 0
$70$	283267.	0.0987080
$71$	−4.99901e6	−1.65760	−0.828800	−	0.559545i	$-0.810976\pi$
$71$	−4.99901e6	−1.65760	−0.828800	+	0.559545i	$0.810976\pi$
$72$	−886670.	−0.279961
$73$	3.66974e6	1.10409	0.552046	−	0.833814i	$-0.313847\pi$
$73$	3.66974e6	1.10409	0.552046	+	0.833814i	$0.313847\pi$
$74$	−1.01845e7	−2.92165
$75$	−1.84523e6	−0.505052
$76$	2.92768e6	0.765024
$77$	−777691.	−0.194129
$78$	−5.66554e6	−1.35179
$79$	3.18719e6	0.727300	0.363650	−	0.931536i	$-0.381530\pi$
$79$	3.18719e6	0.727300	0.363650	+	0.931536i	$0.381530\pi$
$80$	312391.	0.0682155
$81$	531441.	0.111111
$82$	−5.32690e6	−1.06691
$83$	−4.43945e6	−0.852228	−0.426114	−	0.904670i	$-0.640118\pi$
$83$	−4.43945e6	−0.852228	−0.426114	+	0.904670i	$0.640118\pi$
$84$	840822.	0.154784
$85$	1.03496e6	0.182791
$86$	−1.33205e7	−2.25827
$87$	−2.77020e6	−0.451017
$88$	5.94150e6	0.929409
$89$	−1.07216e7	−1.61211	−0.806056	−	0.591839i	$-0.798402\pi$
$89$	−1.07216e7	−1.61211	−0.806056	+	0.591839i	$0.798402\pi$
$90$	1.29711e6	0.187555
$91$	1.85700e6	0.258325
$92$	−17215.9	−0.00230500
$93$	−7.76584e6	−1.00115
$94$	−1.72367e7	−2.14046
$95$	−1.48036e6	−0.177147
$96$	5.73751e6	0.661872
$97$	−4.05589e6	−0.451216	−0.225608	−	0.974218i	$-0.572437\pi$
$97$	−4.05589e6	−0.451216	−0.225608	+	0.974218i	$0.572437\pi$
$98$	1.43590e7	1.54110
$99$	−3.56114e6	−0.368864
$100$	−1.33685e7	−1.33685
$101$	−1.05360e7	−1.01754	−0.508768	−	0.860904i	$-0.669899\pi$
$101$	−1.05360e7	−1.01754	−0.508768	+	0.860904i	$0.669899\pi$
$102$	5.08229e6	0.474197
$103$	−9.49129e6	−0.855845	−0.427922	−	0.903816i	$-0.640754\pi$
$103$	−9.49129e6	−0.855845	−0.427922	+	0.903816i	$0.640754\pi$
$104$	−1.41873e7	−1.23675
$105$	−425155.	−0.0358414
$106$	1.31838e7	1.07515
$107$	−7.68612e6	−0.606547	−0.303273	−	0.952904i	$-0.598079\pi$
$107$	−7.68612e6	−0.606547	−0.303273	+	0.952904i	$0.598079\pi$
$108$	3.85023e6	0.294105
$109$	1.46696e7	1.08499	0.542494	−	0.840059i	$-0.317480\pi$
$109$	1.46696e7	1.08499	0.542494	+	0.840059i	$0.317480\pi$
$110$	−8.69185e6	−0.622641
$111$	1.52859e7	1.06087
$112$	−502812.	−0.0338176
$113$	−1.52191e7	−0.992234	−0.496117	−	0.868256i	$-0.665241\pi$
$113$	−1.52191e7	−0.992234	−0.496117	+	0.868256i	$0.665241\pi$
$114$	−7.26949e6	−0.459554
$115$	8705.07	0.000533740 0
$116$	−2.00697e7	−1.19382
$117$	8.50341e6	0.490843
$118$	3.69461e6	0.207005
$119$	−1.66582e6	−0.0906180
$120$	3.24815e6	0.171594
$121$	4.37575e6	0.224545
$122$	−4.10680e7	−2.04760
$123$	7.99515e6	0.387399
$124$	−5.62626e7	−2.64999
$125$	1.44870e7	0.663426
$126$	−2.08778e6	−0.0929797
$127$	1.49590e7	0.648021	0.324011	−	0.946053i	$-0.394969\pi$
$127$	1.49590e7	0.648021	0.324011	+	0.946053i	$0.394969\pi$
$128$	3.42951e7	1.44543
$129$	1.99927e7	0.819988
$130$	2.07547e7	0.828541
$131$	−2.82534e7	−1.09805	−0.549024	−	0.835807i	$-0.685000\pi$
$131$	−2.82534e7	−1.09805	−0.549024	+	0.835807i	$0.685000\pi$
$132$	−2.58000e7	−0.976364
$133$	2.38272e6	0.0878198
$134$	7.73248e7	2.77621
$135$	−1.94684e6	−0.0681022
$136$	1.27268e7	0.433842
$137$	4.47666e7	1.48741	0.743707	−	0.668506i	$-0.233066\pi$
$137$	4.47666e7	1.48741	0.743707	+	0.668506i	$0.233066\pi$
$138$	42747.4	0.00138463
$139$	−4.23885e7	−1.33874	−0.669370	−	0.742929i	$-0.733436\pi$
$139$	−4.23885e7	−1.33874	−0.669370	+	0.742929i	$0.733436\pi$
$140$	−3.08020e6	−0.0948703
$141$	2.58705e7	0.777210
$142$	8.99283e7	2.63565
$143$	−5.69807e7	−1.62949
$144$	−2.30244e6	−0.0642567
$145$	1.01481e7	0.276437
$146$	−6.60157e7	−1.75555
$147$	−2.15513e7	−0.559582
$148$	1.10744e8	2.80806
$149$	−3.46535e7	−0.858214	−0.429107	−	0.903254i	$-0.641172\pi$
$149$	−3.46535e7	−0.858214	−0.429107	+	0.903254i	$0.641172\pi$
$150$	3.31943e7	0.803052
$151$	−7.67555e7	−1.81422	−0.907110	−	0.420893i	$-0.861717\pi$
$151$	−7.67555e7	−1.81422	−0.907110	+	0.420893i	$0.861717\pi$
$152$	−1.82038e7	−0.420445
$153$	−7.62801e6	−0.172183
$154$	1.39901e7	0.308672
$155$	2.84487e7	0.613623
$156$	6.16062e7	1.29924
$157$	−6.08764e7	−1.25545	−0.627726	−	0.778434i	$-0.716014\pi$
$157$	−6.08764e7	−1.25545	−0.627726	+	0.778434i	$0.716014\pi$
$158$	−5.73351e7	−1.15643
$159$	−1.97875e7	−0.390393
$160$	−2.10183e7	−0.405675
$161$	−14011.3	−0.000264600 0
$162$	−9.56020e6	−0.176671
$163$	−9.26090e7	−1.67493	−0.837465	−	0.546491i	$-0.815963\pi$
$163$	−9.26090e7	−1.67493	−0.837465	+	0.546491i	$0.815963\pi$
$164$	5.79239e7	1.02543
$165$	1.30456e7	0.226084
$166$	7.98622e7	1.35507
$167$	6.05390e7	1.00584	0.502918	−	0.864334i	$-0.332260\pi$
$167$	6.05390e7	1.00584	0.502918	+	0.864334i	$0.332260\pi$
$168$	−5.22810e6	−0.0850670
$169$	7.33117e7	1.16834
$170$	−1.86180e7	−0.290645
$171$	1.09108e7	0.166866
$172$	1.44845e8	2.17047
$173$	6.39593e6	0.0939166	0.0469583	−	0.998897i	$-0.485047\pi$
$173$	6.39593e6	0.0939166	0.0469583	+	0.998897i	$0.485047\pi$
$174$	4.98336e7	0.717134
$175$	−1.08801e7	−0.153461
$176$	1.54284e7	0.213318
$177$	−5.54523e6	−0.0751646
$178$	1.92873e8	2.56332
$179$	−1.31141e8	−1.70904	−0.854519	−	0.519421i	$-0.826148\pi$
$179$	−1.31141e8	−1.70904	−0.854519	+	0.519421i	$0.826148\pi$
$180$	−1.41046e7	−0.180263
$181$	−3.39901e7	−0.426066	−0.213033	−	0.977045i	$-0.568334\pi$
$181$	−3.39901e7	−0.426066	−0.213033	+	0.977045i	$0.568334\pi$
$182$	−3.34059e7	−0.410746
$183$	6.16390e7	0.743493
$184$	107046.	0.00126679
$185$	−5.59971e7	−0.650226
$186$	1.39701e8	1.59186
$187$	5.11147e7	0.571610
$188$	1.87429e8	2.05724
$189$	3.13355e6	0.0337614
$190$	2.66304e7	0.281670
$191$	1.52054e8	1.57899	0.789497	−	0.613755i	$-0.210342\pi$
$191$	1.52054e8	1.57899	0.789497	+	0.613755i	$0.210342\pi$
$192$	−9.22980e7	−0.941105
$193$	5.77384e6	0.0578115	0.0289057	−	0.999582i	$-0.490798\pi$
$193$	5.77384e6	0.0578115	0.0289057	+	0.999582i	$0.490798\pi$
$194$	7.29622e7	0.717450
$195$	−3.11507e7	−0.300847
$196$	−1.56137e8	−1.48119
$197$	−1.02503e8	−0.955221	−0.477611	−	0.878572i	$-0.658497\pi$
$197$	−1.02503e8	−0.955221	−0.477611	+	0.878572i	$0.658497\pi$
$198$	6.40622e7	0.586507
$199$	8.62017e7	0.775408	0.387704	−	0.921784i	$-0.373268\pi$
$199$	8.62017e7	0.775408	0.387704	+	0.921784i	$0.373268\pi$
$200$	8.31230e7	0.734711
$201$	−1.16057e8	−1.00805
$202$	1.89534e8	1.61792
$203$	−1.63340e7	−0.137043
$204$	−5.52640e7	−0.455761
$205$	−2.92887e7	−0.237445
$206$	1.70741e8	1.36082
$207$	−64159.6	−0.000502766 0
$208$	−3.68405e7	−0.283860
$209$	−7.31122e7	−0.553959
$210$	7.64820e6	0.0569891
$211$	2.46914e7	0.180949	0.0904746	−	0.995899i	$-0.471162\pi$
$211$	2.46914e7	0.180949	0.0904746	+	0.995899i	$0.471162\pi$
$212$	−1.43358e8	−1.03335
$213$	−1.34973e8	−0.957016
$214$	1.38267e8	0.964431
$215$	−7.32396e7	−0.502587
$216$	−2.39401e7	−0.161636
$217$	−4.57899e7	−0.304201
$218$	−2.63894e8	−1.72517
$219$	9.90830e7	0.637448
$220$	9.45137e7	0.598433
$221$	−1.22053e8	−0.760635
$222$	−2.74981e8	−1.68682
$223$	4.55302e7	0.274936	0.137468	−	0.990506i	$-0.456104\pi$
$223$	4.55302e7	0.274936	0.137468	+	0.990506i	$0.456104\pi$
$224$	3.38302e7	0.201111
$225$	−4.98212e7	−0.291592
$226$	2.73780e8	1.57769
$227$	−2.56384e8	−1.45479	−0.727395	−	0.686219i	$-0.759269\pi$
$227$	−2.56384e8	−1.45479	−0.727395	+	0.686219i	$0.759269\pi$
$228$	7.90472e7	0.441687
$229$	−3.44709e8	−1.89683	−0.948415	−	0.317033i	$-0.897314\pi$
$229$	−3.44709e8	−1.89683	−0.948415	+	0.317033i	$0.897314\pi$
$230$	−156597.	−0.000848667 0
$231$	−2.09977e7	−0.112080
$232$	1.24790e8	0.656104
$233$	−1.44767e8	−0.749762	−0.374881	−	0.927073i	$-0.622316\pi$
$233$	−1.44767e8	−0.749762	−0.374881	+	0.927073i	$0.622316\pi$
$234$	−1.52970e8	−0.780458
$235$	−9.47720e7	−0.476368
$236$	−4.01745e7	−0.198957
$237$	8.60542e7	0.419907
$238$	2.99669e7	0.144086
$239$	−2.45941e8	−1.16530	−0.582650	−	0.812723i	$-0.697984\pi$
$239$	−2.45941e8	−1.16530	−0.582650	+	0.812723i	$0.697984\pi$
$240$	8.43455e6	0.0393842
$241$	2.54396e8	1.17071	0.585357	−	0.810775i	$-0.300954\pi$
$241$	2.54396e8	1.17071	0.585357	+	0.810775i	$0.300954\pi$
$242$	−7.87164e7	−0.357035
$243$	1.43489e7	0.0641500
$244$	4.46567e8	1.96799
$245$	7.89494e7	0.342979
$246$	−1.43826e8	−0.615979
$247$	1.74580e8	0.737147
$248$	3.49831e8	1.45639
$249$	−1.19865e8	−0.492034
$250$	−2.60609e8	−1.05487
$251$	3.25172e8	1.29794	0.648971	−	0.760813i	$-0.275200\pi$
$251$	3.25172e8	1.29794	0.648971	+	0.760813i	$0.275200\pi$
$252$	2.27022e7	0.0893647
$253$	429928.	0.00166907
$254$	−2.69100e8	−1.03038
$255$	2.79438e7	0.105535
$256$	−1.79381e8	−0.668245
$257$	2.54981e8	0.937003	0.468502	−	0.883463i	$-0.344794\pi$
$257$	2.54981e8	0.937003	0.468502	+	0.883463i	$0.344794\pi$
$258$	−3.59653e8	−1.30381
$259$	9.01307e7	0.322347
$260$	−2.25683e8	−0.796328
$261$	−7.47953e7	−0.260395
$262$	5.08256e8	1.74594
$263$	4.19400e8	1.42162	0.710809	−	0.703385i	$-0.248329\pi$
$263$	4.19400e8	1.42162	0.710809	+	0.703385i	$0.248329\pi$
$264$	1.60421e8	0.536594
$265$	7.24880e7	0.239280
$266$	−4.28633e7	−0.139637
$267$	−2.89484e8	−0.930754
$268$	−8.40817e8	−2.66827
$269$	−4.15320e8	−1.30092	−0.650459	−	0.759541i	$-0.725424\pi$
$269$	−4.15320e8	−1.30092	−0.650459	+	0.759541i	$0.725424\pi$
$270$	3.50220e7	0.108285
$271$	−5.50963e7	−0.168163	−0.0840814	−	0.996459i	$-0.526796\pi$
$271$	−5.50963e7	−0.168163	−0.0840814	+	0.996459i	$0.526796\pi$
$272$	3.30479e7	0.0995755
$273$	5.01389e7	0.149144
$274$	−8.05315e8	−2.36504
$275$	3.33848e8	0.968020
$276$	−464829.	−0.00133080
$277$	−2.16584e8	−0.612275	−0.306138	−	0.951987i	$-0.599037\pi$
$277$	−2.16584e8	−0.612275	−0.306138	+	0.951987i	$0.599037\pi$
$278$	7.62536e8	2.12865
$279$	−2.09678e8	−0.578013
$280$	1.91522e7	0.0521392
$281$	−1.30596e8	−0.351123	−0.175561	−	0.984468i	$-0.556174\pi$
$281$	−1.30596e8	−0.351123	−0.175561	+	0.984468i	$0.556174\pi$
$282$	−4.65391e8	−1.23579
$283$	4.03750e8	1.05891	0.529457	−	0.848337i	$-0.322396\pi$
$283$	4.03750e8	1.05891	0.529457	+	0.848337i	$0.322396\pi$
$284$	−9.77865e8	−2.53317
$285$	−3.99696e7	−0.102276
$286$	1.02504e9	2.59095
$287$	4.71420e7	0.117712
$288$	1.54913e8	0.382132
$289$	−3.00851e8	−0.733176
$290$	−1.82556e8	−0.439546
$291$	−1.09509e8	−0.260510
$292$	7.17844e8	1.68729
$293$	1.61200e8	0.374394	0.187197	−	0.982322i	$-0.440060\pi$
$293$	1.61200e8	0.374394	0.187197	+	0.982322i	$0.440060\pi$
$294$	3.87692e8	0.889756
$295$	2.03139e7	0.0460699
$296$	−6.88591e8	−1.54327
$297$	−9.61509e7	−0.212964
$298$	6.23390e8	1.36459
$299$	−1.02660e6	−0.00222101
$300$	−3.60949e8	−0.771830
$301$	1.17884e8	0.249156
$302$	1.38077e9	2.88468
$303$	−2.84471e8	−0.587474
$304$	−4.72702e7	−0.0965007
$305$	−2.25803e8	−0.455701
$306$	1.37222e8	0.273778
$307$	−7.32355e8	−1.44457	−0.722283	−	0.691597i	$-0.756907\pi$
$307$	−7.32355e8	−1.44457	−0.722283	+	0.691597i	$0.756907\pi$
$308$	−1.52126e8	−0.296671
$309$	−2.56265e8	−0.494122
$310$	−5.11770e8	−0.975683
$311$	1.98727e8	0.374624	0.187312	−	0.982300i	$-0.440022\pi$
$311$	1.98727e8	0.374624	0.187312	+	0.982300i	$0.440022\pi$
$312$	−3.83057e8	−0.714040
$313$	2.25644e8	0.415929	0.207964	−	0.978136i	$-0.433316\pi$
$313$	2.25644e8	0.415929	0.207964	+	0.978136i	$0.433316\pi$
$314$	1.09512e9	1.99622
$315$	−1.14792e7	−0.0206930
$316$	6.23453e8	1.11147
$317$	5.60321e8	0.987937	0.493968	−	0.869480i	$-0.335546\pi$
$317$	5.60321e8	0.987937	0.493968	+	0.869480i	$0.335546\pi$
$318$	3.55962e8	0.620739
$319$	5.01197e8	0.864452
$320$	3.38117e8	0.576822
$321$	−2.07525e8	−0.350190
$322$	252053.	0.000420723 0
$323$	−1.56607e8	−0.258585
$324$	1.03956e8	0.169802
$325$	−7.97173e8	−1.28813
$326$	1.66596e9	2.66320
$327$	3.96079e8	0.626419
$328$	−3.60161e8	−0.563558
$329$	1.52541e8	0.236157
$330$	−2.34680e8	−0.359482
$331$	4.88144e7	0.0739861	0.0369930	−	0.999316i	$-0.488222\pi$
$331$	4.88144e7	0.0739861	0.0369930	+	0.999316i	$0.488222\pi$
$332$	−8.68408e8	−1.30239
$333$	4.12719e8	0.612491
$334$	−1.08905e9	−1.59932
$335$	4.25152e8	0.617857
$336$	−1.35759e7	−0.0195246
$337$	−4.98448e8	−0.709439	−0.354720	−	0.934973i	$-0.615424\pi$
$337$	−4.98448e8	−0.709439	−0.354720	+	0.934973i	$0.615424\pi$
$338$	−1.31882e9	−1.85771
$339$	−4.10916e8	−0.572867
$340$	2.02449e8	0.279345
$341$	1.40503e9	1.91887
$342$	−1.96276e8	−0.265324
$343$	−2.58183e8	−0.345460
$344$	−9.00621e8	−1.19286
$345$	235037.	0.000308155 0
$346$	−1.15058e8	−0.149331
$347$	4.64305e8	0.596554	0.298277	−	0.954479i	$-0.403588\pi$
$347$	4.64305e8	0.596554	0.298277	+	0.954479i	$0.403588\pi$
$348$	−5.41883e8	−0.689252
$349$	−3.75860e8	−0.473301	−0.236651	−	0.971595i	$-0.576050\pi$
$349$	−3.75860e8	−0.473301	−0.236651	+	0.971595i	$0.576050\pi$
$350$	1.95724e8	0.244009
$351$	2.29592e8	0.283388
$352$	−1.03806e9	−1.26859
$353$	−6.79230e8	−0.821874	−0.410937	−	0.911664i	$-0.634798\pi$
$353$	−6.79230e8	−0.821874	−0.410937	+	0.911664i	$0.634798\pi$
$354$	9.97544e7	0.119514
$355$	4.94450e8	0.586574
$356$	−2.09727e9	−2.46366
$357$	−4.49772e7	−0.0523184
$358$	2.35912e9	2.71743
$359$	4.73258e8	0.539843	0.269922	−	0.962882i	$-0.413002\pi$
$359$	4.73258e8	0.539843	0.269922	+	0.962882i	$0.413002\pi$
$360$	8.77001e7	0.0990698
$361$	−6.69868e8	−0.749400
$362$	6.11455e8	0.677461
$363$	1.18145e8	0.129641
$364$	3.63250e8	0.394776
$365$	−3.62972e8	−0.390704
$366$	−1.10884e9	−1.18218
$367$	1.29401e9	1.36649	0.683245	−	0.730189i	$-0.260568\pi$
$367$	1.29401e9	1.36649	0.683245	+	0.730189i	$0.260568\pi$
$368$	277968.	0.000290755 0
$369$	2.15869e8	0.223665
$370$	1.00734e9	1.03388
$371$	−1.16674e8	−0.118622
$372$	−1.51909e9	−1.52997
$373$	−6.91706e8	−0.690146	−0.345073	−	0.938576i	$-0.612146\pi$
$373$	−6.91706e8	−0.690146	−0.345073	+	0.938576i	$0.612146\pi$
$374$	−9.19512e8	−0.908881
$375$	3.91148e8	0.383029
$376$	−1.16540e9	−1.13062
$377$	−1.19677e9	−1.15032
$378$	−5.63701e7	−0.0536819
$379$	−9.69203e8	−0.914487	−0.457243	−	0.889342i	$-0.651163\pi$
$379$	−9.69203e8	−0.914487	−0.457243	+	0.889342i	$0.651163\pi$
$380$	−2.89575e8	−0.270719
$381$	4.03893e8	0.374135
$382$	−2.73533e9	−2.51066
$383$	−1.28084e9	−1.16493	−0.582465	−	0.812856i	$-0.697912\pi$
$383$	−1.28084e9	−1.16493	−0.582465	+	0.812856i	$0.697912\pi$
$384$	9.25967e8	0.834519
$385$	7.69211e7	0.0686962
$386$	−1.03867e8	−0.0919224
$387$	5.39803e8	0.473421
$388$	−7.93379e8	−0.689556
$389$	1.19302e9	1.02760	0.513802	−	0.857909i	$-0.328237\pi$
$389$	1.19302e9	1.02760	0.513802	+	0.857909i	$0.328237\pi$
$390$	5.60376e8	0.478359
$391$	920911.	0.000779111 0
$392$	9.70834e8	0.814036
$393$	−7.62842e8	−0.633958
$394$	1.84394e9	1.51884
$395$	−3.15244e8	−0.257369
$396$	−6.96601e8	−0.563704
$397$	−4.46557e7	−0.0358187	−0.0179094	−	0.999840i	$-0.505701\pi$
$397$	−4.46557e7	−0.0358187	−0.0179094	+	0.999840i	$0.505701\pi$
$398$	−1.55070e9	−1.23293
$399$	6.43335e7	0.0507028
$400$	2.15847e8	0.168631
$401$	5.52185e8	0.427641	0.213821	−	0.976873i	$-0.431409\pi$
$401$	5.52185e8	0.427641	0.213821	+	0.976873i	$0.431409\pi$
$402$	2.08777e9	1.60284
$403$	−3.35498e9	−2.55342
$404$	−2.06096e9	−1.55501
$405$	−5.25646e7	−0.0393188
$406$	2.93835e8	0.217903
$407$	−2.76560e9	−2.03333
$408$	3.43623e8	0.250479
$409$	8.01492e8	0.579252	0.289626	−	0.957140i	$-0.406469\pi$
$409$	8.01492e8	0.579252	0.289626	+	0.957140i	$0.406469\pi$
$410$	5.26881e8	0.377546
$411$	1.20870e9	0.858759
$412$	−1.85661e9	−1.30792
$413$	−3.26965e7	−0.0228390
$414$	1.15418e6	0.000799416 0
$415$	4.39104e8	0.301577
$416$	2.47871e9	1.68810
$417$	−1.14449e9	−0.772922
$418$	1.31523e9	0.880815
$419$	−3.06611e8	−0.203629	−0.101814	−	0.994803i	$-0.532465\pi$
$419$	−3.06611e8	−0.203629	−0.101814	+	0.994803i	$0.532465\pi$
$420$	−8.31653e7	−0.0547734
$421$	1.08219e9	0.706832	0.353416	−	0.935466i	$-0.385020\pi$
$421$	1.08219e9	0.706832	0.353416	+	0.935466i	$0.385020\pi$
$422$	−4.44178e8	−0.287716
$423$	6.98505e8	0.448723
$424$	8.91379e8	0.567913
$425$	7.15106e8	0.451866
$426$	2.42806e9	1.52169
$427$	3.63444e8	0.225912
$428$	−1.50350e9	−0.926935
$429$	−1.53848e9	−0.940786
$430$	1.31752e9	0.799132
$431$	1.67605e9	1.00836	0.504182	−	0.863597i	$-0.331794\pi$
$431$	1.67605e9	1.00836	0.504182	+	0.863597i	$0.331794\pi$
$432$	−6.21658e7	−0.0370986
$433$	2.51807e9	1.49060	0.745300	−	0.666730i	$-0.232306\pi$
$433$	2.51807e9	1.49060	0.745300	+	0.666730i	$0.232306\pi$
$434$	8.23725e8	0.483691
$435$	2.73999e8	0.159601
$436$	2.86954e9	1.65810
$437$	−1.31723e6	−0.000755053 0
$438$	−1.78242e9	−1.01357
$439$	−1.36932e9	−0.772465	−0.386232	−	0.922402i	$-0.626224\pi$
$439$	−1.36932e9	−0.772465	−0.386232	+	0.922402i	$0.626224\pi$
$440$	−5.87671e8	−0.328889
$441$	−5.81886e8	−0.323075
$442$	2.19564e9	1.20944
$443$	−3.62914e7	−0.0198331	−0.00991656	−	0.999951i	$-0.503157\pi$
$443$	−3.62914e7	−0.0198331	−0.00991656	+	0.999951i	$0.503157\pi$
$444$	2.99010e9	1.62123
$445$	1.06047e9	0.570477
$446$	−8.19052e8	−0.437159
$447$	−9.35646e8	−0.495490
$448$	−5.44219e8	−0.285957
$449$	−2.01372e9	−1.04987	−0.524937	−	0.851141i	$-0.675911\pi$
$449$	−2.01372e9	−1.04987	−0.524937	+	0.851141i	$0.675911\pi$
$450$	8.96245e8	0.463642
$451$	−1.44652e9	−0.742517
$452$	−2.97703e9	−1.51635
$453$	−2.07240e9	−1.04744
$454$	4.61214e9	2.31317
$455$	−1.83675e8	−0.0914133
$456$	−4.91503e8	−0.242744
$457$	−1.10905e8	−0.0543554	−0.0271777	−	0.999631i	$-0.508652\pi$
$457$	−1.10905e8	−0.0543554	−0.0271777	+	0.999631i	$0.508652\pi$
$458$	6.20104e9	3.01603
$459$	−2.05956e8	−0.0994101
$460$	1.70281e6	0.000815671 0
$461$	3.59226e9	1.70771	0.853856	−	0.520510i	$-0.174258\pi$
$461$	3.59226e9	1.70771	0.853856	+	0.520510i	$0.174258\pi$
$462$	3.77731e8	0.178212
$463$	−2.38603e9	−1.11723	−0.558614	−	0.829427i	$-0.688667\pi$
$463$	−2.38603e9	−1.11723	−0.558614	+	0.829427i	$0.688667\pi$
$464$	3.24046e8	0.150589
$465$	7.68115e8	0.354275
$466$	2.60424e9	1.19215
$467$	1.97044e9	0.895271	0.447636	−	0.894216i	$-0.352266\pi$
$467$	1.97044e9	0.895271	0.447636	+	0.894216i	$0.352266\pi$
$468$	1.66337e9	0.750115
$469$	−6.84308e8	−0.306300
$470$	1.70487e9	0.757442
$471$	−1.64366e9	−0.724836
$472$	2.49799e8	0.109344
$473$	−3.61718e9	−1.57165
$474$	−1.54805e9	−0.667667
$475$	−1.02286e9	−0.437913
$476$	−3.25855e8	−0.138484
$477$	−5.34264e8	−0.225394
$478$	4.42428e9	1.85287
$479$	4.56276e9	1.89694	0.948469	−	0.316869i	$-0.102632\pi$
$479$	4.56276e9	1.89694	0.948469	+	0.316869i	$0.102632\pi$
$480$	−5.67494e8	−0.234216
$481$	6.60378e9	2.70573
$482$	−4.57639e9	−1.86148
$483$	−378306.	−0.000152767 0
$484$	8.55949e8	0.343154
$485$	4.01166e8	0.159672
$486$	−2.58126e8	−0.102001
$487$	2.91958e9	1.14543	0.572715	−	0.819754i	$-0.305890\pi$
$487$	2.91958e9	1.14543	0.572715	+	0.819754i	$0.305890\pi$
$488$	−2.77668e9	−1.08158
$489$	−2.50044e9	−0.967021
$490$	−1.42024e9	−0.545349
$491$	−8.15321e8	−0.310845	−0.155422	−	0.987848i	$-0.549674\pi$
$491$	−8.15321e8	−0.310845	−0.155422	+	0.987848i	$0.549674\pi$
$492$	1.56394e9	0.592030
$493$	1.07357e9	0.403521
$494$	−3.14055e9	−1.17209
$495$	3.52231e8	0.130530
$496$	9.08415e8	0.334271
$497$	−7.95847e8	−0.290792
$498$	2.15628e9	0.782352
$499$	−3.24554e9	−1.16932	−0.584662	−	0.811277i	$-0.698773\pi$
$499$	−3.24554e9	−1.16932	−0.584662	+	0.811277i	$0.698773\pi$
$500$	2.83382e9	1.01386
$501$	1.63455e9	0.580720
$502$	−5.84959e9	−2.06378
$503$	−4.45372e9	−1.56040	−0.780198	−	0.625532i	$-0.784882\pi$
$503$	−4.45372e9	−1.56040	−0.780198	+	0.625532i	$0.784882\pi$
$504$	−1.41159e8	−0.0491134
$505$	1.04211e9	0.360075
$506$	−7.73407e6	−0.00265388
$507$	1.97942e9	0.674542
$508$	2.92615e9	0.990317
$509$	4.82014e9	1.62012	0.810060	−	0.586347i	$-0.199435\pi$
$509$	4.82014e9	1.62012	0.810060	+	0.586347i	$0.199435\pi$
$510$	−5.02687e8	−0.167804
$511$	5.84226e8	0.193690
$512$	−1.16285e9	−0.382896
$513$	2.94591e8	0.0963404
$514$	−4.58690e9	−1.48987
$515$	9.38779e8	0.302857
$516$	3.91081e9	1.25312
$517$	−4.68062e9	−1.48966
$518$	−1.62138e9	−0.512543
$519$	1.72690e8	0.0542228
$520$	1.40326e9	0.437649
$521$	−3.16646e9	−0.980939	−0.490469	−	0.871458i	$-0.663175\pi$
$521$	−3.16646e9	−0.980939	−0.490469	+	0.871458i	$0.663175\pi$
$522$	1.34551e9	0.414037
$523$	−1.33084e9	−0.406790	−0.203395	−	0.979097i	$-0.565197\pi$
$523$	−1.33084e9	−0.406790	−0.203395	+	0.979097i	$0.565197\pi$
$524$	−5.52670e9	−1.67806
$525$	−2.93762e8	−0.0886010
$526$	−7.54467e9	−2.26042
$527$	3.00960e9	0.895717
$528$	4.16568e8	0.123159
$529$	−3.40482e9	−0.999998
$530$	−1.30400e9	−0.380463
$531$	−1.49721e8	−0.0433963
$532$	4.66088e8	0.134208
$533$	3.45405e9	0.988059
$534$	5.20758e9	1.47993
$535$	7.60231e8	0.214638
$536$	5.22806e9	1.46644
$537$	−3.54080e9	−0.986713
$538$	7.47128e9	2.06851
$539$	3.89917e9	1.07254
$540$	−3.80824e8	−0.104075
$541$	2.45311e8	0.0666081	0.0333040	−	0.999445i	$-0.489397\pi$
$541$	2.45311e8	0.0666081	0.0333040	+	0.999445i	$0.489397\pi$
$542$	9.91139e8	0.267385
$543$	−9.17732e8	−0.245990
$544$	−2.22353e9	−0.592171
$545$	−1.45096e9	−0.383944
$546$	−9.01959e8	−0.237144
$547$	1.35454e9	0.353865	0.176933	−	0.984223i	$-0.443383\pi$
$547$	1.35454e9	0.353865	0.176933	+	0.984223i	$0.443383\pi$
$548$	8.75687e9	2.27309
$549$	1.66425e9	0.429256
$550$	−6.00566e9	−1.53919
$551$	−1.53559e9	−0.391061
$552$	2.89023e6	0.000731384 0
$553$	5.07404e8	0.127590
$554$	3.89617e9	0.973540
$555$	−1.51192e9	−0.375408
$556$	−8.29169e9	−2.04589
$557$	−2.79389e9	−0.685041	−0.342520	−	0.939510i	$-0.611281\pi$
$557$	−2.79389e9	−0.685041	−0.342520	+	0.939510i	$0.611281\pi$
$558$	3.77194e9	0.919061
$559$	8.63721e9	2.09138
$560$	4.97329e7	0.0119670
$561$	1.38010e9	0.330019
$562$	2.34933e9	0.558298
$563$	1.29186e9	0.305095	0.152548	−	0.988296i	$-0.451252\pi$
$563$	1.29186e9	0.305095	0.152548	+	0.988296i	$0.451252\pi$
$564$	5.06058e9	1.18775
$565$	1.50531e9	0.351121
$566$	−7.26315e9	−1.68371
$567$	8.46059e7	0.0194922
$568$	6.08021e9	1.39219
$569$	2.83891e9	0.646040	0.323020	−	0.946392i	$-0.395302\pi$
$569$	2.83891e9	0.646040	0.323020	+	0.946392i	$0.395302\pi$
$570$	7.19022e8	0.162622
$571$	−2.52009e9	−0.566487	−0.283243	−	0.959048i	$-0.591410\pi$
$571$	−2.52009e9	−0.566487	−0.283243	+	0.959048i	$0.591410\pi$
$572$	−1.11461e10	−2.49021
$573$	4.10545e9	0.911632
$574$	−8.48048e8	−0.187167
$575$	6.01480e6	0.00131942
$576$	−2.49205e9	−0.543347
$577$	−7.41099e9	−1.60606	−0.803028	−	0.595941i	$-0.796779\pi$
$577$	−7.41099e9	−1.60606	−0.803028	+	0.595941i	$0.796779\pi$
$578$	5.41206e9	1.16578
$579$	1.55894e8	0.0333775
$580$	1.98509e9	0.422456
$581$	−7.06764e8	−0.149506
$582$	1.96998e9	0.414220
$583$	3.58006e9	0.748256
$584$	−4.46344e9	−0.927309
$585$	−8.41068e8	−0.173694
$586$	−2.89987e9	−0.595301
$587$	−2.54336e9	−0.519008	−0.259504	−	0.965742i	$-0.583559\pi$
$587$	−2.54336e9	−0.519008	−0.259504	+	0.965742i	$0.583559\pi$
$588$	−4.21570e9	−0.855163
$589$	−4.30480e9	−0.868058
$590$	−3.65432e8	−0.0732528
$591$	−2.76758e9	−0.551497
$592$	−1.78808e9	−0.354210
$593$	9.16399e9	1.80465	0.902326	−	0.431055i	$-0.141858\pi$
$593$	9.16399e9	1.80465	0.902326	+	0.431055i	$0.141858\pi$
$594$	1.72968e9	0.338620
$595$	1.64766e8	0.0320670
$596$	−6.77864e9	−1.31154
$597$	2.32745e9	0.447682
$598$	1.84677e7	0.00353149
$599$	−5.47291e9	−1.04046	−0.520229	−	0.854027i	$-0.674153\pi$
$599$	−5.47291e9	−1.04046	−0.520229	+	0.854027i	$0.674153\pi$
$600$	2.24432e9	0.424185
$601$	−4.19336e9	−0.787955	−0.393977	−	0.919120i	$-0.628901\pi$
$601$	−4.19336e9	−0.787955	−0.393977	+	0.919120i	$0.628901\pi$
$602$	−2.12063e9	−0.396167
$603$	−3.13353e9	−0.582001
$604$	−1.50143e10	−2.77252
$605$	−4.32804e8	−0.0794598
$606$	5.11741e9	0.934106
$607$	6.57768e9	1.19375	0.596874	−	0.802335i	$-0.296409\pi$
$607$	6.57768e9	1.19375	0.596874	+	0.802335i	$0.296409\pi$
$608$	3.18044e9	0.573885
$609$	−4.41018e8	−0.0791216
$610$	4.06202e9	0.724582
$611$	1.11765e10	1.98227
$612$	−1.49213e9	−0.263133
$613$	−7.04485e9	−1.23527	−0.617633	−	0.786467i	$-0.711908\pi$
$613$	−7.04485e9	−1.23527	−0.617633	+	0.786467i	$0.711908\pi$
$614$	1.31745e10	2.29691
$615$	−7.90796e8	−0.137089
$616$	9.45892e8	0.163046
$617$	−4.68870e9	−0.803627	−0.401813	−	0.915722i	$-0.631620\pi$
$617$	−4.68870e9	−0.803627	−0.401813	+	0.915722i	$0.631620\pi$
$618$	4.61000e9	0.785672
$619$	−6.66470e9	−1.12944	−0.564720	−	0.825282i	$-0.691016\pi$
$619$	−6.66470e9	−1.12944	−0.564720	+	0.825282i	$0.691016\pi$
$620$	5.56490e9	0.937749
$621$	−1.73231e6	−0.000290272 0
$622$	−3.57495e9	−0.595667
$623$	−1.70689e9	−0.282812
$624$	−9.94693e8	−0.163887
$625$	3.90631e9	0.640010
$626$	−4.05916e9	−0.661342
$627$	−1.97403e9	−0.319828
$628$	−1.19081e10	−1.91860
$629$	−5.92394e9	−0.949147
$630$	2.06502e8	0.0329027
$631$	6.09161e8	0.0965227	0.0482614	−	0.998835i	$-0.484632\pi$
$631$	6.09161e8	0.0965227	0.0482614	+	0.998835i	$0.484632\pi$
$632$	−3.87653e9	−0.610848
$633$	6.66667e8	0.104471
$634$	−1.00797e10	−1.57086
$635$	−1.47959e9	−0.229315
$636$	−3.87068e9	−0.596605
$637$	−9.31057e9	−1.42721
$638$	−9.01614e9	−1.37451
$639$	−3.64428e9	−0.552534
$640$	−3.39211e9	−0.511493
$641$	−3.31465e7	−0.00497089	−0.00248545	−	0.999997i	$-0.500791\pi$
$641$	−3.31465e7	−0.00497089	−0.00248545	+	0.999997i	$0.500791\pi$
$642$	3.73322e9	0.556815
$643$	−4.47226e9	−0.663421	−0.331710	−	0.943381i	$-0.607626\pi$
$643$	−4.47226e9	−0.663421	−0.331710	+	0.943381i	$0.607626\pi$
$644$	−2.74078e6	−0.000404366 0
$645$	−1.97747e9	−0.290169
$646$	2.81724e9	0.411159
$647$	−4.33561e9	−0.629340	−0.314670	−	0.949201i	$-0.601894\pi$
$647$	−4.33561e9	−0.629340	−0.314670	+	0.949201i	$0.601894\pi$
$648$	−6.46382e8	−0.0933205
$649$	1.00327e9	0.144066
$650$	1.43405e10	2.04818
$651$	−1.23633e9	−0.175631
$652$	−1.81154e10	−2.55966
$653$	−5.43227e9	−0.763458	−0.381729	−	0.924274i	$-0.624671\pi$
$653$	−5.43227e9	−0.763458	−0.381729	+	0.924274i	$0.624671\pi$
$654$	−7.12515e9	−0.996029
$655$	2.79453e9	0.388566
$656$	−9.35239e8	−0.129348
$657$	2.67524e9	0.368031
$658$	−2.74410e9	−0.375499
$659$	5.26358e9	0.716444	0.358222	−	0.933636i	$-0.383383\pi$
$659$	5.26358e9	0.716444	0.358222	+	0.933636i	$0.383383\pi$
$660$	2.55187e9	0.345505
$661$	1.51100e9	0.203497	0.101749	−	0.994810i	$-0.467556\pi$
$661$	1.51100e9	0.203497	0.101749	+	0.994810i	$0.467556\pi$
$662$	−8.78133e8	−0.117641
$663$	−3.29544e9	−0.439153
$664$	5.39962e9	0.715772
$665$	−2.35674e8	−0.0310768
$666$	−7.42449e9	−0.973884
$667$	9.02986e6	0.00117826
$668$	1.18421e10	1.53714
$669$	1.22931e9	0.158735
$670$	−7.64816e9	−0.982415
$671$	−1.11520e10	−1.42503
$672$	9.13416e8	0.116112
$673$	4.92429e8	0.0622717	0.0311359	−	0.999515i	$-0.490088\pi$
$673$	4.92429e8	0.0622717	0.0311359	+	0.999515i	$0.490088\pi$
$674$	8.96668e9	1.12803
$675$	−1.34517e9	−0.168351
$676$	1.43406e10	1.78548
$677$	1.38348e10	1.71361	0.856805	−	0.515640i	$-0.172446\pi$
$677$	1.38348e10	1.71361	0.856805	+	0.515640i	$0.172446\pi$
$678$	7.39205e9	0.910879
$679$	−6.45701e8	−0.0791566
$680$	−1.25880e9	−0.153523
$681$	−6.92236e9	−0.839923
$682$	−2.52754e10	−3.05108
$683$	8.01482e8	0.0962545	0.0481273	−	0.998841i	$-0.484675\pi$
$683$	8.01482e8	0.0962545	0.0481273	+	0.998841i	$0.484675\pi$
$684$	2.13428e9	0.255008
$685$	−4.42784e9	−0.526350
$686$	4.64450e9	0.549294
$687$	−9.30714e9	−1.09513
$688$	−2.33866e9	−0.273784
$689$	−8.54858e9	−0.995696
$690$	−4.22813e6	−0.000489978 0
$691$	−2.59241e9	−0.298903	−0.149452	−	0.988769i	$-0.547751\pi$
$691$	−2.59241e9	−0.298903	−0.149452	+	0.988769i	$0.547751\pi$
$692$	1.25112e9	0.143525
$693$	−5.66937e8	−0.0647096
$694$	−8.35247e9	−0.948543
$695$	4.19263e9	0.473739
$696$	3.36934e9	0.378802
$697$	−3.09846e9	−0.346602
$698$	6.76143e9	0.752566
$699$	−3.90871e9	−0.432876
$700$	−2.12827e9	−0.234522
$701$	1.40491e10	1.54040	0.770201	−	0.637801i	$-0.220156\pi$
$701$	1.40491e10	1.54040	0.770201	+	0.637801i	$0.220156\pi$
$702$	−4.13018e9	−0.450598
$703$	8.47335e9	0.919838
$704$	1.66990e10	1.80379
$705$	−2.55884e9	−0.275031
$706$	1.22188e10	1.30681
$707$	−1.67733e9	−0.178506
$708$	−1.08471e9	−0.114868
$709$	−9.39937e9	−0.990460	−0.495230	−	0.868762i	$-0.664916\pi$
$709$	−9.39937e9	−0.990460	−0.495230	+	0.868762i	$0.664916\pi$
$710$	−8.89476e9	−0.932675
$711$	2.32346e9	0.242433
$712$	1.30405e10	1.35399
$713$	2.53139e7	0.00261544
$714$	8.09105e8	0.0831881
$715$	5.63593e9	0.576626
$716$	−2.56526e10	−2.61178
$717$	−6.64040e9	−0.672786
$718$	−8.51354e9	−0.858371
$719$	1.11397e10	1.11769	0.558846	−	0.829272i	$-0.311244\pi$
$719$	1.11397e10	1.11769	0.558846	+	0.829272i	$0.311244\pi$
$720$	2.27733e8	0.0227385
$721$	−1.51102e9	−0.150140
$722$	1.20504e10	1.19157
$723$	6.86870e9	0.675912
$724$	−6.64886e9	−0.651122
$725$	7.01187e9	0.683362
$726$	−2.12534e9	−0.206134
$727$	−9.70625e9	−0.936874	−0.468437	−	0.883497i	$-0.655183\pi$
$727$	−9.70625e9	−0.936874	−0.468437	+	0.883497i	$0.655183\pi$
$728$	−2.25863e9	−0.216963
$729$	3.87420e8	0.0370370
$730$	6.52958e9	0.621234
$731$	−7.74803e9	−0.733636
$732$	1.20573e10	1.13622
$733$	4.02746e9	0.377718	0.188859	−	0.982004i	$-0.439521\pi$
$733$	4.02746e9	0.377718	0.188859	+	0.982004i	$0.439521\pi$
$734$	−2.32782e10	−2.17277
$735$	2.13163e9	0.198019
$736$	−1.87022e7	−0.00172911
$737$	2.09975e10	1.93211
$738$	−3.88331e9	−0.355635
$739$	1.14088e10	1.03989	0.519943	−	0.854201i	$-0.325953\pi$
$739$	1.14088e10	1.03989	0.519943	+	0.854201i	$0.325953\pi$
$740$	−1.09537e10	−0.993686
$741$	4.71365e9	0.425592
$742$	2.09887e9	0.188613
$743$	−3.48068e9	−0.311317	−0.155659	−	0.987811i	$-0.549750\pi$
$743$	−3.48068e9	−0.311317	−0.155659	+	0.987811i	$0.549750\pi$
$744$	9.44545e9	0.840848
$745$	3.42757e9	0.303696
$746$	1.24432e10	1.09736
$747$	−3.23636e9	−0.284076
$748$	9.99863e9	0.873544
$749$	−1.22364e9	−0.106406
$750$	−7.03645e9	−0.609031
$751$	−1.06375e10	−0.916433	−0.458217	−	0.888841i	$-0.651512\pi$
$751$	−1.06375e10	−0.916433	−0.458217	+	0.888841i	$0.651512\pi$
$752$	−3.02623e9	−0.259501
$753$	8.77965e9	0.749367
$754$	2.15290e10	1.82905
$755$	7.59185e9	0.641997
$756$	6.12959e8	0.0515947
$757$	2.08009e10	1.74279	0.871397	−	0.490578i	$-0.163214\pi$
$757$	2.08009e10	1.74279	0.871397	+	0.490578i	$0.163214\pi$
$758$	1.74352e10	1.45407
$759$	1.16081e7	0.000963637 0
$760$	1.80053e9	0.148783
$761$	1.33150e9	0.109521	0.0547604	−	0.998500i	$-0.482561\pi$
$761$	1.33150e9	0.109521	0.0547604	+	0.998500i	$0.482561\pi$
$762$	−7.26571e9	−0.594889
$763$	2.33541e9	0.190339
$764$	2.97435e10	2.41304
$765$	7.54483e8	0.0609304
$766$	2.30413e10	1.85228
$767$	−2.39564e9	−0.191707
$768$	−4.84328e9	−0.385811
$769$	−2.19213e10	−1.73830	−0.869148	−	0.494553i	$-0.835332\pi$
$769$	−2.19213e10	−1.73830	−0.869148	+	0.494553i	$0.835332\pi$
$770$	−1.38375e9	−0.109230
$771$	6.88448e9	0.540979
$772$	1.12943e9	0.0883485
$773$	3.83517e9	0.298646	0.149323	−	0.988788i	$-0.452291\pi$
$773$	3.83517e9	0.298646	0.149323	+	0.988788i	$0.452291\pi$
$774$	−9.71064e9	−0.752756
$775$	1.96567e10	1.51690
$776$	4.93310e9	0.378969
$777$	2.43353e9	0.186107
$778$	−2.14616e10	−1.63393
$779$	4.43191e9	0.335900
$780$	−6.09344e9	−0.459760
$781$	2.44200e10	1.83429
$782$	−1.65665e7	−0.00123881
$783$	−2.01947e9	−0.150339
$784$	2.52099e9	0.186838
$785$	6.02126e9	0.444266
$786$	1.37229e10	1.00802
$787$	1.79274e10	1.31101	0.655504	−	0.755192i	$-0.272456\pi$
$787$	1.79274e10	1.31101	0.655504	+	0.755192i	$0.272456\pi$
$788$	−2.00508e10	−1.45979
$789$	1.13238e10	0.820771
$790$	5.67099e9	0.409227
$791$	−2.42289e9	−0.174067
$792$	4.33135e9	0.309803
$793$	2.66292e10	1.89627
$794$	8.03321e8	0.0569531
$795$	1.95718e9	0.138148
$796$	1.68621e10	1.18499
$797$	−5.47185e9	−0.382851	−0.191426	−	0.981507i	$-0.561311\pi$
$797$	−5.47185e9	−0.382851	−0.191426	+	0.981507i	$0.561311\pi$
$798$	−1.15731e9	−0.0806193
$799$	−1.00259e10	−0.695363
$800$	−1.45227e10	−1.00284
$801$	−7.81606e9	−0.537371
$802$	−9.93338e9	−0.679965
$803$	−1.79266e10	−1.22178
$804$	−2.27021e10	−1.54053
$805$	1.38586e6	9.36337e−5 0
$806$	6.03535e10	4.06003
$807$	−1.12136e10	−0.751086
$808$	1.28147e10	0.854612
$809$	2.20226e9	0.146234	0.0731171	−	0.997323i	$-0.476705\pi$
$809$	2.20226e9	0.146234	0.0731171	+	0.997323i	$0.476705\pi$
$810$	9.45595e8	0.0625184
$811$	−5.11433e9	−0.336679	−0.168339	−	0.985729i	$-0.553840\pi$
$811$	−5.11433e9	−0.336679	−0.168339	+	0.985729i	$0.553840\pi$
$812$	−3.19512e9	−0.209431
$813$	−1.48760e9	−0.0970889
$814$	4.97509e10	3.23307
$815$	9.15991e9	0.592707
$816$	8.92293e8	0.0574899
$817$	1.10825e10	0.710982
$818$	−1.44182e10	−0.921032
$819$	1.35375e9	0.0861083
$820$	−5.72922e9	−0.362867
$821$	−4.81471e9	−0.303647	−0.151824	−	0.988408i	$-0.548515\pi$
$821$	−4.81471e9	−0.303647	−0.151824	+	0.988408i	$0.548515\pi$
$822$	−2.17435e10	−1.36546
$823$	−2.90096e10	−1.81402	−0.907011	−	0.421107i	$-0.861642\pi$
$823$	−2.90096e10	−1.81402	−0.907011	+	0.421107i	$0.861642\pi$
$824$	1.15441e10	0.718810
$825$	9.01390e9	0.558887
$826$	5.88185e8	0.0363148
$827$	5.95215e9	0.365936	0.182968	−	0.983119i	$-0.441430\pi$
$827$	5.95215e9	0.365936	0.182968	+	0.983119i	$0.441430\pi$
$828$	−1.25504e7	−0.000768335 0
$829$	1.00332e10	0.611643	0.305821	−	0.952089i	$-0.401069\pi$
$829$	1.00332e10	0.611643	0.305821	+	0.952089i	$0.401069\pi$
$830$	−7.89913e9	−0.479519
$831$	−5.84776e9	−0.353497
$832$	−3.98744e10	−2.40028
$833$	8.35207e9	0.500653
$834$	2.05885e10	1.22897
$835$	−5.98788e9	−0.355935
$836$	−1.43016e10	−0.846570
$837$	−5.66130e9	−0.333716
$838$	5.51569e9	0.323777
$839$	7.75973e9	0.453607	0.226803	−	0.973941i	$-0.427173\pi$
$839$	7.75973e9	0.453607	0.226803	+	0.973941i	$0.427173\pi$
$840$	5.17108e8	0.0301026
$841$	−6.72315e9	−0.389751
$842$	−1.94677e10	−1.12389
$843$	−3.52610e9	−0.202721
$844$	4.82992e9	0.276529
$845$	−7.25123e9	−0.413441
$846$	−1.25655e10	−0.713485
$847$	6.96624e8	0.0393919
$848$	2.31466e9	0.130347
$849$	1.09013e10	0.611364
$850$	−1.28642e10	−0.718483
$851$	−4.98266e7	−0.00277146
$852$	−2.64024e10	−1.46253
$853$	3.15852e10	1.74246	0.871229	−	0.490877i	$-0.163324\pi$
$853$	3.15852e10	1.74246	0.871229	+	0.490877i	$0.163324\pi$
$854$	−6.53807e9	−0.359209
$855$	−1.07918e9	−0.0590490
$856$	9.34849e9	0.509429
$857$	−1.81369e10	−0.984304	−0.492152	−	0.870509i	$-0.663790\pi$
$857$	−1.81369e10	−0.984304	−0.492152	+	0.870509i	$0.663790\pi$
$858$	2.76760e10	1.49588
$859$	2.80979e10	1.51251	0.756253	−	0.654279i	$-0.227028\pi$
$859$	2.80979e10	1.51251	0.756253	+	0.654279i	$0.227028\pi$
$860$	−1.43265e10	−0.768062
$861$	1.27283e9	0.0679612
$862$	−3.01509e10	−1.60334
$863$	−1.12434e10	−0.595467	−0.297734	−	0.954649i	$-0.596231\pi$
$863$	−1.12434e10	−0.595467	−0.297734	+	0.954649i	$0.596231\pi$
$864$	4.18264e9	0.220624
$865$	−6.32618e8	−0.0332342
$866$	−4.52982e10	−2.37011
$867$	−8.12296e9	−0.423299
$868$	−8.95705e9	−0.464885
$869$	−1.55693e10	−0.804824
$870$	−4.92902e9	−0.253772
$871$	−5.01386e10	−2.57104
$872$	−1.78424e10	−0.911265
$873$	−2.95674e9	−0.150405
$874$	2.36960e7	0.00120056
$875$	2.30634e9	0.116384
$876$	1.93818e10	0.974158
$877$	−1.39725e10	−0.699481	−0.349740	−	0.936847i	$-0.613730\pi$
$877$	−1.39725e10	−0.699481	−0.349740	+	0.936847i	$0.613730\pi$
$878$	2.46330e10	1.22825
$879$	4.35241e9	0.216157
$880$	−1.52602e9	−0.0754867
$881$	−1.05370e10	−0.519158	−0.259579	−	0.965722i	$-0.583584\pi$
$881$	−1.05370e10	−0.519158	−0.259579	+	0.965722i	$0.583584\pi$
$882$	1.04677e10	0.513701
$883$	2.48119e10	1.21282	0.606412	−	0.795151i	$-0.292608\pi$
$883$	2.48119e10	1.21282	0.606412	+	0.795151i	$0.292608\pi$
$884$	−2.38750e10	−1.16242
$885$	5.48476e8	0.0265985
$886$	6.52854e8	0.0315354
$887$	3.02069e10	1.45336	0.726680	−	0.686976i	$-0.241062\pi$
$887$	3.02069e10	1.45336	0.726680	+	0.686976i	$0.241062\pi$
$888$	−1.85920e10	−0.891005
$889$	2.38148e9	0.113682
$890$	−1.90770e10	−0.907080
$891$	−2.59607e9	−0.122955
$892$	8.90624e9	0.420162
$893$	1.43407e10	0.673891
$894$	1.68315e10	0.787848
$895$	1.29711e10	0.604776
$896$	5.45981e9	0.253571
$897$	−2.77181e7	−0.00128230
$898$	3.62253e10	1.66934
$899$	2.95101e10	1.35460
$900$	−9.74562e9	−0.445616
$901$	7.66853e9	0.349281
$902$	2.60218e10	1.18063
$903$	3.18286e9	0.143850
$904$	1.85107e10	0.833362
$905$	3.36194e9	0.150772
$906$	3.72808e10	1.66547
$907$	1.15712e10	0.514937	0.257468	−	0.966287i	$-0.417112\pi$
$907$	1.15712e10	0.514937	0.257468	+	0.966287i	$0.417112\pi$
$908$	−5.01517e10	−2.22323
$909$	−7.68072e9	−0.339178
$910$	3.30416e9	0.145350
$911$	−1.60273e10	−0.702338	−0.351169	−	0.936312i	$-0.614216\pi$
$911$	−1.60273e10	−0.702338	−0.351169	+	0.936312i	$0.614216\pi$
$912$	−1.27630e9	−0.0557147
$913$	2.16866e10	0.943068
$914$	1.99509e9	0.0864271
$915$	−6.09668e9	−0.263099
$916$	−6.74291e10	−2.89877
$917$	−4.49797e9	−0.192630
$918$	3.70499e9	0.158066
$919$	9.52685e9	0.404897	0.202449	−	0.979293i	$-0.435110\pi$
$919$	9.52685e9	0.404897	0.202449	+	0.979293i	$0.435110\pi$
$920$	−1.05878e7	−0.000448280 0
$921$	−1.97736e10	−0.834021
$922$	−6.46219e10	−2.71532
$923$	−5.83109e10	−2.44086
$924$	−4.10739e9	−0.171283
$925$	−3.86914e10	−1.60738
$926$	4.29228e10	1.77643
$927$	−6.91915e9	−0.285282
$928$	−2.18025e10	−0.895547
$929$	7.62148e9	0.311878	0.155939	−	0.987767i	$-0.450160\pi$
$929$	7.62148e9	0.311878	0.155939	+	0.987767i	$0.450160\pi$
$930$	−1.38178e10	−0.563311
$931$	−1.19464e10	−0.485193
$932$	−2.83181e10	−1.14580
$933$	5.36564e9	0.216290
$934$	−3.54467e10	−1.42351
$935$	−5.05573e9	−0.202275
$936$	−1.03425e10	−0.412251
$937$	2.55429e9	0.101434	0.0507168	−	0.998713i	$-0.483849\pi$
$937$	2.55429e9	0.101434	0.0507168	+	0.998713i	$0.483849\pi$
$938$	1.23102e10	0.487028
$939$	6.09239e9	0.240137
$940$	−1.85385e10	−0.727993
$941$	−1.11902e10	−0.437797	−0.218898	−	0.975748i	$-0.570246\pi$
$941$	−1.11902e10	−0.437797	−0.218898	+	0.975748i	$0.570246\pi$
$942$	2.95682e10	1.15252
$943$	−2.60613e7	−0.00101206
$944$	6.48658e8	0.0250965
$945$	−3.09938e8	−0.0119471
$946$	6.50702e10	2.49898
$947$	2.91042e10	1.11361	0.556803	−	0.830645i	$-0.312028\pi$
$947$	2.91042e10	1.11361	0.556803	+	0.830645i	$0.312028\pi$
$948$	1.68332e10	0.641709
$949$	4.28056e10	1.62581
$950$	1.84004e10	0.696297
$951$	1.51287e10	0.570386
$952$	2.02611e9	0.0761087
$953$	1.18538e10	0.443643	0.221821	−	0.975087i	$-0.428800\pi$
$953$	1.18538e10	0.443643	0.221821	+	0.975087i	$0.428800\pi$
$954$	9.61099e9	0.358384
$955$	−1.50396e10	−0.558758
$956$	−4.81089e10	−1.78083
$957$	1.35323e10	0.499092
$958$	−8.20804e10	−3.01620
$959$	7.12688e9	0.260936
$960$	9.12915e9	0.333028
$961$	5.52147e10	2.00689
$962$	−1.18797e11	−4.30222
$963$	−5.60318e9	−0.202182
$964$	4.97629e10	1.78911
$965$	−5.71088e8	−0.0204577
$966$	6.80543e6	0.000242905 0
$967$	−3.91605e10	−1.39269	−0.696347	−	0.717705i	$-0.745193\pi$
$967$	−3.91605e10	−1.39269	−0.696347	+	0.717705i	$0.745193\pi$
$968$	−5.32215e9	−0.188592
$969$	−4.22839e9	−0.149294
$970$	−7.21666e9	−0.253884
$971$	4.49711e10	1.57640	0.788200	−	0.615419i	$-0.211013\pi$
$971$	4.49711e10	1.57640	0.788200	+	0.615419i	$0.211013\pi$
$972$	2.80681e9	0.0980352
$973$	−6.74829e9	−0.234854
$974$	−5.25209e10	−1.82128
$975$	−2.15237e10	−0.743704
$976$	−7.21027e9	−0.248243
$977$	−3.26239e10	−1.11919	−0.559597	−	0.828765i	$-0.689044\pi$
$977$	−3.26239e10	−1.11919	−0.559597	+	0.828765i	$0.689044\pi$
$978$	4.49810e10	1.53760
$979$	5.23748e10	1.78395
$980$	1.54434e10	0.524146
$981$	1.06941e10	0.361663
$982$	1.46670e10	0.494254
$983$	−4.19068e10	−1.40717	−0.703585	−	0.710611i	$-0.748419\pi$
$983$	−4.19068e10	−1.40717	−0.703585	+	0.710611i	$0.748419\pi$
$984$	−9.72435e9	−0.325370
$985$	1.01385e10	0.338024
$986$	−1.93127e10	−0.641613
$987$	4.11861e9	0.136346
$988$	3.41498e10	1.12652
$989$	−6.51692e7	−0.00214218
$990$	−6.33636e9	−0.207547
$991$	1.39919e10	0.456687	0.228343	−	0.973581i	$-0.426669\pi$
$991$	1.39919e10	0.456687	0.228343	+	0.973581i	$0.426669\pi$
$992$	−6.11201e10	−1.98789
$993$	1.31799e9	0.0427159
$994$	1.43167e10	0.462370
$995$	−8.52617e9	−0.274393
$996$	−2.34470e10	−0.751934
$997$	5.75080e10	1.83779	0.918893	−	0.394506i	$-0.129084\pi$
$997$	5.75080e10	1.83779	0.918893	+	0.394506i	$0.129084\pi$
$998$	5.83846e10	1.85927
$999$	1.11434e10	0.353622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.b.1.3	✓	17
3.2	odd	2		531.8.a.d.1.15		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.3	✓	17	1.1	even	1	trivial
531.8.a.d.1.15		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)

\(f(q)\)	\(=\)	\(q-17.9892 q^{2} +27.0000 q^{3} +195.612 q^{4} -98.9095 q^{5} -485.709 q^{6} +159.201 q^{7} -1216.28 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-17.9892 q^{2} +27.0000 q^{3} +195.612 q^{4} -98.9095 q^{5} -485.709 q^{6} +159.201 q^{7} -1216.28 q^{8} +729.000 q^{9} +1779.30 q^{10} -4884.97 q^{11} +5281.52 q^{12} +11664.5 q^{13} -2863.90 q^{14} -2670.56 q^{15} -3158.35 q^{16} -10463.7 q^{17} -13114.1 q^{18} +14966.8 q^{19} -19347.9 q^{20} +4298.42 q^{21} +87876.7 q^{22} -88.0105 q^{23} -32839.6 q^{24} -68341.9 q^{25} -209835. q^{26} +19683.0 q^{27} +31141.6 q^{28} -102600. q^{29} +48041.2 q^{30} -287624. q^{31} +212500. q^{32} -131894. q^{33} +188233. q^{34} -15746.5 q^{35} +142601. q^{36} +566144. q^{37} -269240. q^{38} +314941. q^{39} +120302. q^{40} +296117. q^{41} -77325.3 q^{42} +740471. q^{43} -955557. q^{44} -72105.0 q^{45} +1583.24 q^{46} +958168. q^{47} -85275.4 q^{48} -798198. q^{49} +1.22942e6 q^{50} -282519. q^{51} +2.28171e6 q^{52} -732872. q^{53} -354082. q^{54} +483170. q^{55} -193633. q^{56} +404103. q^{57} +1.84569e6 q^{58} -205379. q^{59} -522392. q^{60} +2.28293e6 q^{61} +5.17412e6 q^{62} +116057. q^{63} -3.41844e6 q^{64} -1.15373e6 q^{65} +2.37267e6 q^{66} -4.29840e6 q^{67} -2.04681e6 q^{68} -2376.28 q^{69} +283267. q^{70} -4.99901e6 q^{71} -886670. q^{72} +3.66974e6 q^{73} -1.01845e7 q^{74} -1.84523e6 q^{75} +2.92768e6 q^{76} -777691. q^{77} -5.66554e6 q^{78} +3.18719e6 q^{79} +312391. q^{80} +531441. q^{81} -5.32690e6 q^{82} -4.43945e6 q^{83} +840822. q^{84} +1.03496e6 q^{85} -1.33205e7 q^{86} -2.77020e6 q^{87} +5.94150e6 q^{88} -1.07216e7 q^{89} +1.29711e6 q^{90} +1.85700e6 q^{91} -17215.9 q^{92} -7.76584e6 q^{93} -1.72367e7 q^{94} -1.48036e6 q^{95} +5.73751e6 q^{96} -4.05589e6 q^{97} +1.43590e7 q^{98} -3.56114e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) \) 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

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