LMFDB - Embedded newform 177.8.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,8,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.4
Root			$15.0467$ 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)

$f(q)$	$=$	$q-15.0467 q^{2} -27.0000 q^{3} +98.4026 q^{4} +159.890 q^{5} +406.260 q^{6} +980.332 q^{7} +445.343 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-15.0467 q^{2} -27.0000 q^{3} +98.4026 q^{4} +159.890 q^{5} +406.260 q^{6} +980.332 q^{7} +445.343 q^{8} +729.000 q^{9} -2405.81 q^{10} -3390.91 q^{11} -2656.87 q^{12} -7169.91 q^{13} -14750.7 q^{14} -4317.03 q^{15} -19296.5 q^{16} -12242.5 q^{17} -10969.0 q^{18} +19577.3 q^{19} +15733.6 q^{20} -26469.0 q^{21} +51021.9 q^{22} +103217. q^{23} -12024.3 q^{24} -52560.2 q^{25} +107883. q^{26} -19683.0 q^{27} +96467.2 q^{28} -169076. q^{29} +64956.9 q^{30} -37743.0 q^{31} +233344. q^{32} +91554.5 q^{33} +184209. q^{34} +156745. q^{35} +71735.5 q^{36} -29517.3 q^{37} -294573. q^{38} +193588. q^{39} +71205.8 q^{40} +375081. q^{41} +398270. q^{42} +719695. q^{43} -333674. q^{44} +116560. q^{45} -1.55308e6 q^{46} -317727. q^{47} +521004. q^{48} +137507. q^{49} +790857. q^{50} +330547. q^{51} -705538. q^{52} +290607. q^{53} +296164. q^{54} -542172. q^{55} +436584. q^{56} -528586. q^{57} +2.54404e6 q^{58} +205379. q^{59} -424807. q^{60} -2.85898e6 q^{61} +567906. q^{62} +714662. q^{63} -1.04110e6 q^{64} -1.14640e6 q^{65} -1.37759e6 q^{66} +1.89394e6 q^{67} -1.20469e6 q^{68} -2.78687e6 q^{69} -2.35849e6 q^{70} +3.57204e6 q^{71} +324655. q^{72} -2.76466e6 q^{73} +444137. q^{74} +1.41913e6 q^{75} +1.92645e6 q^{76} -3.32421e6 q^{77} -2.91285e6 q^{78} -4.56707e6 q^{79} -3.08531e6 q^{80} +531441. q^{81} -5.64372e6 q^{82} -661014. q^{83} -2.60461e6 q^{84} -1.95745e6 q^{85} -1.08290e7 q^{86} +4.56506e6 q^{87} -1.51012e6 q^{88} -5.31858e6 q^{89} -1.75384e6 q^{90} -7.02889e6 q^{91} +1.01568e7 q^{92} +1.01906e6 q^{93} +4.78073e6 q^{94} +3.13021e6 q^{95} -6.30028e6 q^{96} -1.84545e6 q^{97} -2.06903e6 q^{98} -2.47197e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9} - 3479 q^{10} + 898 q^{11} - 26298 q^{12} - 8172 q^{13} - 13315 q^{14} + 1836 q^{15} + 3138 q^{16} - 44985 q^{17} - 4374 q^{18} - 40137 q^{19} + 130657 q^{20} + 63261 q^{21} + 109394 q^{22} - 2833 q^{23} - 22113 q^{24} + 285746 q^{25} - 129420 q^{26} - 314928 q^{27} + 112890 q^{28} + 144375 q^{29} + 93933 q^{30} - 141759 q^{31} - 36224 q^{32} - 24246 q^{33} - 341332 q^{34} - 78859 q^{35} + 710046 q^{36} - 297971 q^{37} + 329075 q^{38} + 220644 q^{39} - 203048 q^{40} + 659077 q^{41} + 359505 q^{42} - 1431608 q^{43} + 254916 q^{44} - 49572 q^{45} + 873113 q^{46} - 1574073 q^{47} - 84726 q^{48} + 1893545 q^{49} + 302533 q^{50} + 1214595 q^{51} - 4972548 q^{52} + 587736 q^{53} + 118098 q^{54} - 4624036 q^{55} - 5798506 q^{56} + 1083699 q^{57} - 6991380 q^{58} + 3286064 q^{59} - 3527739 q^{60} - 6117131 q^{61} - 11570258 q^{62} - 1708047 q^{63} - 19063011 q^{64} - 5335514 q^{65} - 2953638 q^{66} - 16518710 q^{67} - 17284669 q^{68} + 76491 q^{69} - 39189486 q^{70} - 10882582 q^{71} + 597051 q^{72} - 21097441 q^{73} - 16717030 q^{74} - 7715142 q^{75} - 40864952 q^{76} - 3404601 q^{77} + 3494340 q^{78} - 3784458 q^{79} - 27466195 q^{80} + 8503056 q^{81} - 24990117 q^{82} - 1951425 q^{83} - 3048030 q^{84} - 23238675 q^{85} - 35910572 q^{86} - 3898125 q^{87} - 27843055 q^{88} + 10499443 q^{89} - 2536191 q^{90} + 699217 q^{91} - 20062766 q^{92} + 3827493 q^{93} - 59358988 q^{94} - 29236333 q^{95} + 978048 q^{96} - 25158976 q^{97} + 2120460 q^{98} + 654642 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9 - 3479 * q^10 + 898 * q^11 - 26298 * q^12 - 8172 * q^13 - 13315 * q^14 + 1836 * q^15 + 3138 * q^16 - 44985 * q^17 - 4374 * q^18 - 40137 * q^19 + 130657 * q^20 + 63261 * q^21 + 109394 * q^22 - 2833 * q^23 - 22113 * q^24 + 285746 * q^25 - 129420 * q^26 - 314928 * q^27 + 112890 * q^28 + 144375 * q^29 + 93933 * q^30 - 141759 * q^31 - 36224 * q^32 - 24246 * q^33 - 341332 * q^34 - 78859 * q^35 + 710046 * q^36 - 297971 * q^37 + 329075 * q^38 + 220644 * q^39 - 203048 * q^40 + 659077 * q^41 + 359505 * q^42 - 1431608 * q^43 + 254916 * q^44 - 49572 * q^45 + 873113 * q^46 - 1574073 * q^47 - 84726 * q^48 + 1893545 * q^49 + 302533 * q^50 + 1214595 * q^51 - 4972548 * q^52 + 587736 * q^53 + 118098 * q^54 - 4624036 * q^55 - 5798506 * q^56 + 1083699 * q^57 - 6991380 * q^58 + 3286064 * q^59 - 3527739 * q^60 - 6117131 * q^61 - 11570258 * q^62 - 1708047 * q^63 - 19063011 * q^64 - 5335514 * q^65 - 2953638 * q^66 - 16518710 * q^67 - 17284669 * q^68 + 76491 * q^69 - 39189486 * q^70 - 10882582 * q^71 + 597051 * q^72 - 21097441 * q^73 - 16717030 * q^74 - 7715142 * q^75 - 40864952 * q^76 - 3404601 * q^77 + 3494340 * q^78 - 3784458 * q^79 - 27466195 * q^80 + 8503056 * q^81 - 24990117 * q^82 - 1951425 * q^83 - 3048030 * q^84 - 23238675 * q^85 - 35910572 * q^86 - 3898125 * q^87 - 27843055 * q^88 + 10499443 * q^89 - 2536191 * q^90 + 699217 * q^91 - 20062766 * q^92 + 3827493 * q^93 - 59358988 * q^94 - 29236333 * q^95 + 978048 * q^96 - 25158976 * q^97 + 2120460 * q^98 + 654642 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−15.0467	−1.32995	−0.664976	−	0.746865i	$-0.731558\pi$
$2$	−15.0467	−1.32995	−0.664976	+	0.746865i	$0.731558\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	98.4026	0.768770
$5$	159.890	0.572039	0.286020	−	0.958224i	$-0.407668\pi$
$5$	159.890	0.572039	0.286020	+	0.958224i	$0.407668\pi$
$6$	406.260	0.767848
$7$	980.332	1.08026	0.540132	−	0.841580i	$-0.318374\pi$
$7$	980.332	1.08026	0.540132	+	0.841580i	$0.318374\pi$
$8$	445.343	0.307524
$9$	729.000	0.333333
$10$	−2405.81	−0.760785
$11$	−3390.91	−0.768142	−0.384071	−	0.923304i	$-0.625478\pi$
$11$	−3390.91	−0.768142	−0.384071	+	0.923304i	$0.625478\pi$
$12$	−2656.87	−0.443850
$13$	−7169.91	−0.905132	−0.452566	−	0.891731i	$-0.649491\pi$
$13$	−7169.91	−0.905132	−0.452566	+	0.891731i	$0.649491\pi$
$14$	−14750.7	−1.43670
$15$	−4317.03	−0.330267
$16$	−19296.5	−1.17776
$17$	−12242.5	−0.604364	−0.302182	−	0.953250i	$-0.597715\pi$
$17$	−12242.5	−0.604364	−0.302182	+	0.953250i	$0.597715\pi$
$18$	−10969.0	−0.443317
$19$	19577.3	0.654808	0.327404	−	0.944884i	$-0.393826\pi$
$19$	19577.3	0.654808	0.327404	+	0.944884i	$0.393826\pi$
$20$	15733.6	0.439767
$21$	−26469.0	−0.623691
$22$	51021.9	1.02159
$23$	103217.	1.76891	0.884454	−	0.466628i	$-0.154531\pi$
$23$	103217.	1.76891	0.884454	+	0.466628i	$0.154531\pi$
$24$	−12024.3	−0.177549
$25$	−52560.2	−0.672771
$26$	107883.	1.20378
$27$	−19683.0	−0.192450
$28$	96467.2	0.830475
$29$	−169076.	−1.28733	−0.643665	−	0.765307i	$-0.722587\pi$
$29$	−169076.	−1.28733	−0.643665	+	0.765307i	$0.722587\pi$
$30$	64956.9	0.439239
$31$	−37743.0	−0.227546	−0.113773	−	0.993507i	$-0.536294\pi$
$31$	−37743.0	−0.227546	−0.113773	+	0.993507i	$0.536294\pi$
$32$	233344.	1.25884
$33$	91554.5	0.443487
$34$	184209.	0.803774
$35$	156745.	0.617954
$36$	71735.5	0.256257
$37$	−29517.3	−0.0958011	−0.0479006	−	0.998852i	$-0.515253\pi$
$37$	−29517.3	−0.0958011	−0.0479006	+	0.998852i	$0.515253\pi$
$38$	−294573.	−0.870863
$39$	193588.	0.522578
$40$	71205.8	0.175916
$41$	375081.	0.849926	0.424963	−	0.905211i	$-0.360287\pi$
$41$	375081.	0.849926	0.424963	+	0.905211i	$0.360287\pi$
$42$	398270.	0.829478
$43$	719695.	1.38041	0.690206	−	0.723613i	$-0.257520\pi$
$43$	719695.	1.38041	0.690206	+	0.723613i	$0.257520\pi$
$44$	−333674.	−0.590525
$45$	116560.	0.190680
$46$	−1.55308e6	−2.35256
$47$	−317727.	−0.446387	−0.223193	−	0.974774i	$-0.571648\pi$
$47$	−317727.	−0.446387	−0.223193	+	0.974774i	$0.571648\pi$
$48$	521004.	0.679982
$49$	137507.	0.166970
$50$	790857.	0.894752
$51$	330547.	0.348929
$52$	−705538.	−0.695839
$53$	290607.	0.268127	0.134063	−	0.990973i	$-0.457197\pi$
$53$	290607.	0.268127	0.134063	+	0.990973i	$0.457197\pi$
$54$	296164.	0.255949
$55$	−542172.	−0.439407
$56$	436584.	0.332208
$57$	−528586.	−0.378054
$58$	2.54404e6	1.71209
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	−424807.	−0.253900
$61$	−2.85898e6	−1.61271	−0.806355	−	0.591432i	$-0.798563\pi$
$61$	−2.85898e6	−1.61271	−0.806355	+	0.591432i	$0.798563\pi$
$62$	567906.	0.302626
$63$	714662.	0.360088
$64$	−1.04110e6	−0.496436
$65$	−1.14640e6	−0.517771
$66$	−1.37759e6	−0.589816
$67$	1.89394e6	0.769316	0.384658	−	0.923059i	$-0.374319\pi$
$67$	1.89394e6	0.769316	0.384658	+	0.923059i	$0.374319\pi$
$68$	−1.20469e6	−0.464617
$69$	−2.78687e6	−1.02128
$70$	−2.35849e6	−0.821848
$71$	3.57204e6	1.18444	0.592218	−	0.805778i	$-0.298252\pi$
$71$	3.57204e6	1.18444	0.592218	+	0.805778i	$0.298252\pi$
$72$	324655.	0.102508
$73$	−2.76466e6	−0.831786	−0.415893	−	0.909413i	$-0.636531\pi$
$73$	−2.76466e6	−0.831786	−0.415893	+	0.909413i	$0.636531\pi$
$74$	444137.	0.127411
$75$	1.41913e6	0.388424
$76$	1.92645e6	0.503397
$77$	−3.32421e6	−0.829796
$78$	−2.91285e6	−0.695004
$79$	−4.56707e6	−1.04218	−0.521091	−	0.853501i	$-0.674475\pi$
$79$	−4.56707e6	−1.04218	−0.521091	+	0.853501i	$0.674475\pi$
$80$	−3.08531e6	−0.673727
$81$	531441.	0.111111
$82$	−5.64372e6	−1.13036
$83$	−661014.	−0.126893	−0.0634464	−	0.997985i	$-0.520209\pi$
$83$	−661014.	−0.126893	−0.0634464	+	0.997985i	$0.520209\pi$
$84$	−2.60461e6	−0.479475
$85$	−1.95745e6	−0.345720
$86$	−1.08290e7	−1.83588
$87$	4.56506e6	0.743241
$88$	−1.51012e6	−0.236222
$89$	−5.31858e6	−0.799707	−0.399853	−	0.916579i	$-0.630939\pi$
$89$	−5.31858e6	−0.799707	−0.399853	+	0.916579i	$0.630939\pi$
$90$	−1.75384e6	−0.253595
$91$	−7.02889e6	−0.977782
$92$	1.01568e7	1.35988
$93$	1.01906e6	0.131374
$94$	4.78073e6	0.593673
$95$	3.13021e6	0.374576
$96$	−6.30028e6	−0.726793
$97$	−1.84545e6	−0.205305	−0.102653	−	0.994717i	$-0.532733\pi$
$97$	−1.84545e6	−0.205305	−0.102653	+	0.994717i	$0.532733\pi$
$98$	−2.06903e6	−0.222062
$99$	−2.47197e6	−0.256047
$100$	−5.17206e6	−0.517206
$101$	4.95032e6	0.478088	0.239044	−	0.971009i	$-0.423166\pi$
$101$	4.95032e6	0.478088	0.239044	+	0.971009i	$0.423166\pi$
$102$	−4.97364e6	−0.464059
$103$	−2.16194e7	−1.94946	−0.974728	−	0.223393i	$-0.928287\pi$
$103$	−2.16194e7	−1.94946	−0.974728	+	0.223393i	$0.928287\pi$
$104$	−3.19307e6	−0.278350
$105$	−4.23212e6	−0.356776
$106$	−4.37267e6	−0.356595
$107$	−1.82441e6	−0.143973	−0.0719863	−	0.997406i	$-0.522934\pi$
$107$	−1.82441e6	−0.143973	−0.0719863	+	0.997406i	$0.522934\pi$
$108$	−1.93686e6	−0.147950
$109$	5.23038e6	0.386848	0.193424	−	0.981115i	$-0.438041\pi$
$109$	5.23038e6	0.386848	0.193424	+	0.981115i	$0.438041\pi$
$110$	8.15788e6	0.584390
$111$	796967.	0.0553108
$112$	−1.89169e7	−1.27229
$113$	2.44766e7	1.59579	0.797895	−	0.602796i	$-0.205947\pi$
$113$	2.44766e7	1.59579	0.797895	+	0.602796i	$0.205947\pi$
$114$	7.95346e6	0.502793
$115$	1.65034e7	1.01188
$116$	−1.66376e7	−0.989661
$117$	−5.22687e6	−0.301711
$118$	−3.09027e6	−0.173145
$119$	−1.20017e7	−0.652872
$120$	−1.92256e6	−0.101565
$121$	−7.98892e6	−0.409958
$122$	4.30181e7	2.14483
$123$	−1.01272e7	−0.490705
$124$	−3.71400e6	−0.174931
$125$	−2.08952e7	−0.956891
$126$	−1.07533e7	−0.478899
$127$	−2.70518e7	−1.17188	−0.585940	−	0.810355i	$-0.699275\pi$
$127$	−2.70518e7	−1.17188	−0.585940	+	0.810355i	$0.699275\pi$
$128$	−1.42029e7	−0.598606
$129$	−1.94318e7	−0.796981
$130$	1.72495e7	0.688611
$131$	1.34945e7	0.524454	0.262227	−	0.965006i	$-0.415543\pi$
$131$	1.34945e7	0.524454	0.262227	+	0.965006i	$0.415543\pi$
$132$	9.00920e6	0.340940
$133$	1.91922e7	0.707366
$134$	−2.84975e7	−1.02315
$135$	−3.14711e6	−0.110089
$136$	−5.45210e6	−0.185857
$137$	5.35174e7	1.77817	0.889084	−	0.457745i	$-0.151343\pi$
$137$	5.35174e7	1.77817	0.889084	+	0.457745i	$0.151343\pi$
$138$	4.19331e7	1.35825
$139$	1.33665e7	0.422149	0.211075	−	0.977470i	$-0.432304\pi$
$139$	1.33665e7	0.422149	0.211075	+	0.977470i	$0.432304\pi$
$140$	1.54241e7	0.475064
$141$	8.57863e6	0.257722
$142$	−5.37473e7	−1.57524
$143$	2.43125e7	0.695270
$144$	−1.40671e7	−0.392588
$145$	−2.70336e7	−0.736404
$146$	4.15990e7	1.10624
$147$	−3.71269e6	−0.0964003
$148$	−2.90458e6	−0.0736490
$149$	−1.60776e7	−0.398170	−0.199085	−	0.979982i	$-0.563797\pi$
$149$	−1.60776e7	−0.398170	−0.199085	+	0.979982i	$0.563797\pi$
$150$	−2.13531e7	−0.516586
$151$	−5.18108e7	−1.22462	−0.612310	−	0.790618i	$-0.709760\pi$
$151$	−5.18108e7	−1.22462	−0.612310	+	0.790618i	$0.709760\pi$
$152$	8.71859e6	0.201370
$153$	−8.92477e6	−0.201455
$154$	5.00184e7	1.10359
$155$	−6.03472e6	−0.130166
$156$	1.90495e7	0.401743
$157$	−8.16318e7	−1.68349	−0.841746	−	0.539874i	$-0.818472\pi$
$157$	−8.16318e7	−1.68349	−0.841746	+	0.539874i	$0.818472\pi$
$158$	6.87193e7	1.38605
$159$	−7.84638e6	−0.154803
$160$	3.73093e7	0.720107
$161$	1.01187e8	1.91089
$162$	−7.99642e6	−0.147772
$163$	8.91769e6	0.161286	0.0806428	−	0.996743i	$-0.474303\pi$
$163$	8.91769e6	0.161286	0.0806428	+	0.996743i	$0.474303\pi$
$164$	3.69089e7	0.653398
$165$	1.46386e7	0.253692
$166$	9.94606e6	0.168761
$167$	−3.21164e7	−0.533604	−0.266802	−	0.963751i	$-0.585967\pi$
$167$	−3.21164e7	−0.533604	−0.266802	+	0.963751i	$0.585967\pi$
$168$	−1.17878e7	−0.191800
$169$	−1.13409e7	−0.180736
$170$	2.94531e7	0.459790
$171$	1.42718e7	0.218269
$172$	7.08198e7	1.06122
$173$	−5.06027e7	−0.743040	−0.371520	−	0.928425i	$-0.621163\pi$
$173$	−5.06027e7	−0.743040	−0.371520	+	0.928425i	$0.621163\pi$
$174$	−6.86891e7	−0.988474
$175$	−5.15265e7	−0.726770
$176$	6.54325e7	0.904689
$177$	−5.54523e6	−0.0751646
$178$	8.00270e7	1.06357
$179$	−6.22045e7	−0.810655	−0.405327	−	0.914172i	$-0.632843\pi$
$179$	−6.22045e7	−0.810655	−0.405327	+	0.914172i	$0.632843\pi$
$180$	1.14698e7	0.146589
$181$	6.29686e7	0.789313	0.394656	−	0.918829i	$-0.370864\pi$
$181$	6.29686e7	0.789313	0.394656	+	0.918829i	$0.370864\pi$
$182$	1.05761e8	1.30040
$183$	7.71924e7	0.931098
$184$	4.59671e7	0.543982
$185$	−4.71952e6	−0.0548020
$186$	−1.53335e7	−0.174721
$187$	4.15131e7	0.464237
$188$	−3.12651e7	−0.343169
$189$	−1.92959e7	−0.207897
$190$	−4.70992e7	−0.498168
$191$	−7.18839e7	−0.746474	−0.373237	−	0.927736i	$-0.621752\pi$
$191$	−7.18839e7	−0.746474	−0.373237	+	0.927736i	$0.621752\pi$
$192$	2.81098e7	0.286618
$193$	−3.68734e7	−0.369201	−0.184600	−	0.982814i	$-0.559099\pi$
$193$	−3.68734e7	−0.369201	−0.184600	+	0.982814i	$0.559099\pi$
$194$	2.77678e7	0.273046
$195$	3.09527e7	0.298935
$196$	1.35311e7	0.128362
$197$	1.75363e8	1.63420	0.817101	−	0.576495i	$-0.195580\pi$
$197$	1.75363e8	1.63420	0.817101	+	0.576495i	$0.195580\pi$
$198$	3.71950e7	0.340530
$199$	8.16489e7	0.734454	0.367227	−	0.930131i	$-0.380307\pi$
$199$	8.16489e7	0.734454	0.367227	+	0.930131i	$0.380307\pi$
$200$	−2.34073e7	−0.206893
$201$	−5.11364e7	−0.444165
$202$	−7.44858e7	−0.635834
$203$	−1.65751e8	−1.39066
$204$	3.25267e7	0.268247
$205$	5.99716e7	0.486191
$206$	3.25300e8	2.59268
$207$	7.52454e7	0.589636
$208$	1.38354e8	1.06603
$209$	−6.63846e7	−0.502986
$210$	6.36793e7	0.474494
$211$	1.04928e7	0.0768955	0.0384478	−	0.999261i	$-0.487759\pi$
$211$	1.04928e7	0.0768955	0.0384478	+	0.999261i	$0.487759\pi$
$212$	2.85965e7	0.206128
$213$	−9.64450e7	−0.683835
$214$	2.74513e7	0.191476
$215$	1.15072e8	0.789650
$216$	−8.76569e6	−0.0591831
$217$	−3.70006e7	−0.245810
$218$	−7.86998e7	−0.514489
$219$	7.46458e7	0.480232
$220$	−5.33511e7	−0.337803
$221$	8.77775e7	0.547029
$222$	−1.19917e7	−0.0735607
$223$	−2.52899e8	−1.52714	−0.763572	−	0.645723i	$-0.776556\pi$
$223$	−2.52899e8	−1.52714	−0.763572	+	0.645723i	$0.776556\pi$
$224$	2.28754e8	1.35988
$225$	−3.83164e7	−0.224257
$226$	−3.68291e8	−2.12232
$227$	457979.	0.00259869	0.00129935	−	0.999999i	$-0.499586\pi$
$227$	457979.	0.00259869	0.00129935	+	0.999999i	$0.499586\pi$
$228$	−5.20142e7	−0.290636
$229$	−1.85147e8	−1.01881	−0.509405	−	0.860527i	$-0.670135\pi$
$229$	−1.85147e8	−1.01881	−0.509405	+	0.860527i	$0.670135\pi$
$230$	−2.48321e8	−1.34576
$231$	8.97538e7	0.479083
$232$	−7.52970e7	−0.395886
$233$	−3.11021e8	−1.61081	−0.805404	−	0.592726i	$-0.798052\pi$
$233$	−3.11021e8	−1.61081	−0.805404	+	0.592726i	$0.798052\pi$
$234$	7.86470e7	0.401261
$235$	−5.08013e7	−0.255351
$236$	2.02098e7	0.100085
$237$	1.23311e8	0.601703
$238$	1.80586e8	0.868288
$239$	−1.44383e8	−0.684107	−0.342053	−	0.939680i	$-0.611122\pi$
$239$	−1.44383e8	−0.684107	−0.342053	+	0.939680i	$0.611122\pi$
$240$	8.33034e7	0.388976
$241$	−9.66758e7	−0.444896	−0.222448	−	0.974945i	$-0.571405\pi$
$241$	−9.66758e7	−0.444896	−0.222448	+	0.974945i	$0.571405\pi$
$242$	1.20207e8	0.545224
$243$	−1.43489e7	−0.0641500
$244$	−2.81331e8	−1.23980
$245$	2.19860e7	0.0955136
$246$	1.52380e8	0.652614
$247$	−1.40367e8	−0.592688
$248$	−1.68086e7	−0.0699761
$249$	1.78474e7	0.0732616
$250$	3.14404e8	1.27262
$251$	1.46912e8	0.586407	0.293203	−	0.956050i	$-0.405279\pi$
$251$	1.46912e8	0.586407	0.293203	+	0.956050i	$0.405279\pi$
$252$	7.03246e7	0.276825
$253$	−3.50000e8	−1.35877
$254$	4.07040e8	1.55854
$255$	5.28511e7	0.199601
$256$	3.46967e8	1.29255
$257$	−4.93706e8	−1.81427	−0.907136	−	0.420837i	$-0.861736\pi$
$257$	−4.93706e8	−1.81427	−0.907136	+	0.420837i	$0.861736\pi$
$258$	2.92384e8	1.05995
$259$	−2.89367e7	−0.103490
$260$	−1.12808e8	−0.398047
$261$	−1.23257e8	−0.429110
$262$	−2.03048e8	−0.697498
$263$	−1.94462e8	−0.659157	−0.329578	−	0.944128i	$-0.606907\pi$
$263$	−1.94462e8	−0.659157	−0.329578	+	0.944128i	$0.606907\pi$
$264$	4.07731e7	0.136383
$265$	4.64651e7	0.153379
$266$	−2.88779e8	−0.940762
$267$	1.43602e8	0.461711
$268$	1.86369e8	0.591427
$269$	−5.97880e7	−0.187275	−0.0936377	−	0.995606i	$-0.529850\pi$
$269$	−5.97880e7	−0.187275	−0.0936377	+	0.995606i	$0.529850\pi$
$270$	4.73536e7	0.146413
$271$	−5.18384e8	−1.58219	−0.791096	−	0.611693i	$-0.790489\pi$
$271$	−5.18384e8	−1.58219	−0.791096	+	0.611693i	$0.790489\pi$
$272$	2.36237e8	0.711797
$273$	1.89780e8	0.564523
$274$	−8.05258e8	−2.36488
$275$	1.78227e8	0.516783
$276$	−2.74235e8	−0.785129
$277$	2.35392e8	0.665444	0.332722	−	0.943025i	$-0.392033\pi$
$277$	2.35392e8	0.665444	0.332722	+	0.943025i	$0.392033\pi$
$278$	−2.01122e8	−0.561438
$279$	−2.75146e7	−0.0758488
$280$	6.98053e7	0.190036
$281$	−3.16518e8	−0.850994	−0.425497	−	0.904960i	$-0.639901\pi$
$281$	−3.16518e8	−0.850994	−0.425497	+	0.904960i	$0.639901\pi$
$282$	−1.29080e8	−0.342757
$283$	−2.45453e8	−0.643748	−0.321874	−	0.946782i	$-0.604313\pi$
$283$	−2.45453e8	−0.643748	−0.321874	+	0.946782i	$0.604313\pi$
$284$	3.51498e8	0.910559
$285$	−8.45155e7	−0.216262
$286$	−3.65822e8	−0.924675
$287$	3.67703e8	0.918144
$288$	1.70108e8	0.419614
$289$	−2.60460e8	−0.634745
$290$	4.06766e8	0.979381
$291$	4.98270e7	0.118533
$292$	−2.72050e8	−0.639452
$293$	1.97162e8	0.457916	0.228958	−	0.973436i	$-0.426468\pi$
$293$	1.97162e8	0.457916	0.228958	+	0.973436i	$0.426468\pi$
$294$	5.58637e7	0.128208
$295$	3.28380e7	0.0744732
$296$	−1.31453e7	−0.0294612
$297$	6.67432e7	0.147829
$298$	2.41914e8	0.529546
$299$	−7.40059e8	−1.60110
$300$	1.39646e8	0.298609
$301$	7.05540e8	1.49121
$302$	7.79581e8	1.62868
$303$	−1.33659e8	−0.276024
$304$	−3.77772e8	−0.771209
$305$	−4.57121e8	−0.922534
$306$	1.34288e8	0.267925
$307$	1.34184e7	0.0264677	0.0132339	−	0.999912i	$-0.495787\pi$
$307$	1.34184e7	0.0264677	0.0132339	+	0.999912i	$0.495787\pi$
$308$	−3.27111e8	−0.637922
$309$	5.83724e8	1.12552
$310$	9.08024e7	0.173114
$311$	−7.42366e8	−1.39945	−0.699724	−	0.714413i	$-0.746694\pi$
$311$	−7.42366e8	−1.39945	−0.699724	+	0.714413i	$0.746694\pi$
$312$	8.62129e7	0.160706
$313$	7.47946e8	1.37869	0.689343	−	0.724435i	$-0.257899\pi$
$313$	7.47946e8	1.37869	0.689343	+	0.724435i	$0.257899\pi$
$314$	1.22829e9	2.23896
$315$	1.14267e8	0.205985
$316$	−4.49412e8	−0.801198
$317$	−7.65404e8	−1.34953	−0.674766	−	0.738031i	$-0.735756\pi$
$317$	−7.65404e8	−1.34953	−0.674766	+	0.738031i	$0.735756\pi$
$318$	1.18062e8	0.205881
$319$	5.73323e8	0.988853
$320$	−1.66462e8	−0.283981
$321$	4.92591e7	0.0831226
$322$	−1.52253e9	−2.54139
$323$	−2.39674e8	−0.395742
$324$	5.22952e7	0.0854189
$325$	3.76852e8	0.608947
$326$	−1.34182e8	−0.214502
$327$	−1.41220e8	−0.223347
$328$	1.67039e8	0.261373
$329$	−3.11478e8	−0.482216
$330$	−2.20263e8	−0.337398
$331$	3.13126e8	0.474592	0.237296	−	0.971437i	$-0.423739\pi$
$331$	3.13126e8	0.474592	0.237296	+	0.971437i	$0.423739\pi$
$332$	−6.50455e7	−0.0975515
$333$	−2.15181e7	−0.0319337
$334$	4.83245e8	0.709667
$335$	3.02822e8	0.440079
$336$	5.10757e8	0.734560
$337$	1.30356e9	1.85535	0.927675	−	0.373388i	$-0.121804\pi$
$337$	1.30356e9	1.85535	0.927675	+	0.373388i	$0.121804\pi$
$338$	1.70643e8	0.240369
$339$	−6.60867e8	−0.921330
$340$	−1.92618e8	−0.265779
$341$	1.27983e8	0.174788
$342$	−2.14743e8	−0.290288
$343$	−6.72543e8	−0.899892
$344$	3.20511e8	0.424511
$345$	−4.45592e8	−0.584212
$346$	7.61402e8	0.988206
$347$	−2.10675e8	−0.270683	−0.135341	−	0.990799i	$-0.543213\pi$
$347$	−2.10675e8	−0.270683	−0.135341	+	0.990799i	$0.543213\pi$
$348$	4.49214e8	0.571381
$349$	6.27337e8	0.789972	0.394986	−	0.918687i	$-0.370749\pi$
$349$	6.27337e8	0.789972	0.394986	+	0.918687i	$0.370749\pi$
$350$	7.75302e8	0.966569
$351$	1.41125e8	0.174193
$352$	−7.91247e8	−0.966970
$353$	−8.10514e8	−0.980729	−0.490364	−	0.871517i	$-0.663136\pi$
$353$	−8.10514e8	−0.980729	−0.490364	+	0.871517i	$0.663136\pi$
$354$	8.34373e7	0.0999653
$355$	5.71133e8	0.677544
$356$	−5.23362e8	−0.614791
$357$	3.24046e8	0.376936
$358$	9.35971e8	1.07813
$359$	4.90257e8	0.559234	0.279617	−	0.960112i	$-0.409793\pi$
$359$	4.90257e8	0.559234	0.279617	+	0.960112i	$0.409793\pi$
$360$	5.19091e7	0.0586387
$361$	−5.10603e8	−0.571226
$362$	−9.47468e8	−1.04975
$363$	2.15701e8	0.236689
$364$	−6.91661e8	−0.751689
$365$	−4.42041e8	−0.475815
$366$	−1.16149e9	−1.23832
$367$	−6.65868e8	−0.703164	−0.351582	−	0.936157i	$-0.614356\pi$
$367$	−6.65868e8	−0.703164	−0.351582	+	0.936157i	$0.614356\pi$
$368$	−1.99173e9	−2.08335
$369$	2.73434e8	0.283309
$370$	7.10131e7	0.0728840
$371$	2.84891e8	0.289648
$372$	1.00278e8	0.100996
$373$	−1.50881e9	−1.50541	−0.752704	−	0.658360i	$-0.771251\pi$
$373$	−1.50881e9	−1.50541	−0.752704	+	0.658360i	$0.771251\pi$
$374$	−6.24635e8	−0.617412
$375$	5.64172e8	0.552461
$376$	−1.41497e8	−0.137275
$377$	1.21226e9	1.16520
$378$	2.90339e8	0.276493
$379$	−1.17501e9	−1.10868	−0.554339	−	0.832291i	$-0.687029\pi$
$379$	−1.17501e9	−1.10868	−0.554339	+	0.832291i	$0.687029\pi$
$380$	3.08020e8	0.287963
$381$	7.30398e8	0.676585
$382$	1.08161e9	0.992774
$383$	3.09605e8	0.281587	0.140794	−	0.990039i	$-0.455035\pi$
$383$	3.09605e8	0.281587	0.140794	+	0.990039i	$0.455035\pi$
$384$	3.83478e8	0.345606
$385$	−5.31508e8	−0.474676
$386$	5.54822e8	0.491019
$387$	5.24658e8	0.460137
$388$	−1.81597e8	−0.157833
$389$	−1.81950e9	−1.56721	−0.783606	−	0.621258i	$-0.786622\pi$
$389$	−1.81950e9	−1.56721	−0.783606	+	0.621258i	$0.786622\pi$
$390$	−4.65735e8	−0.397570
$391$	−1.26364e9	−1.06906
$392$	6.12379e7	0.0513474
$393$	−3.64352e8	−0.302794
$394$	−2.63863e9	−2.17341
$395$	−7.30229e8	−0.596169
$396$	−2.43248e8	−0.196842
$397$	6.58203e8	0.527950	0.263975	−	0.964529i	$-0.414966\pi$
$397$	6.58203e8	0.527950	0.263975	+	0.964529i	$0.414966\pi$
$398$	−1.22855e9	−0.976788
$399$	−5.18189e8	−0.408398
$400$	1.01423e9	0.792364
$401$	7.74197e8	0.599578	0.299789	−	0.954005i	$-0.403084\pi$
$401$	7.74197e8	0.599578	0.299789	+	0.954005i	$0.403084\pi$
$402$	7.69433e8	0.590717
$403$	2.70614e8	0.205960
$404$	4.87124e8	0.367540
$405$	8.49720e7	0.0635599
$406$	2.49400e9	1.84951
$407$	1.00090e8	0.0735889
$408$	1.47207e8	0.107304
$409$	1.08898e9	0.787022	0.393511	−	0.919320i	$-0.371260\pi$
$409$	1.08898e9	0.787022	0.393511	+	0.919320i	$0.371260\pi$
$410$	−9.02373e8	−0.646610
$411$	−1.44497e9	−1.02663
$412$	−2.12741e9	−1.49868
$413$	2.01340e8	0.140638
$414$	−1.13219e9	−0.784187
$415$	−1.05689e8	−0.0725877
$416$	−1.67305e9	−1.13942
$417$	−3.60896e8	−0.243728
$418$	9.98869e8	0.668946
$419$	1.86951e9	1.24159	0.620795	−	0.783973i	$-0.286810\pi$
$419$	1.86951e9	1.24159	0.620795	+	0.783973i	$0.286810\pi$
$420$	−4.16451e8	−0.274278
$421$	2.61169e9	1.70583	0.852913	−	0.522053i	$-0.174834\pi$
$421$	2.61169e9	1.70583	0.852913	+	0.522053i	$0.174834\pi$
$422$	−1.57881e8	−0.102267
$423$	−2.31623e8	−0.148796
$424$	1.29420e8	0.0824555
$425$	6.43468e8	0.406598
$426$	1.45118e9	0.909467
$427$	−2.80275e9	−1.74215
$428$	−1.79527e8	−0.110682
$429$	−6.56438e8	−0.401414
$430$	−1.73145e9	−1.05020
$431$	1.54835e9	0.931534	0.465767	−	0.884908i	$-0.345779\pi$
$431$	1.54835e9	0.931534	0.465767	+	0.884908i	$0.345779\pi$
$432$	3.79812e8	0.226661
$433$	−1.73247e9	−1.02555	−0.512776	−	0.858523i	$-0.671383\pi$
$433$	−1.73247e9	−1.02555	−0.512776	+	0.858523i	$0.671383\pi$
$434$	5.56736e8	0.326916
$435$	7.29908e8	0.425163
$436$	5.14683e8	0.297397
$437$	2.02071e9	1.15830
$438$	−1.12317e9	−0.638685
$439$	−3.14201e9	−1.77248	−0.886239	−	0.463227i	$-0.846691\pi$
$439$	−3.14201e9	−1.77248	−0.886239	+	0.463227i	$0.846691\pi$
$440$	−2.41452e8	−0.135129
$441$	1.00243e8	0.0556568
$442$	−1.32076e9	−0.727522
$443$	1.87980e9	1.02730	0.513651	−	0.857999i	$-0.328293\pi$
$443$	1.87980e9	1.02730	0.513651	+	0.857999i	$0.328293\pi$
$444$	7.84236e7	0.0425213
$445$	−8.50388e8	−0.457464
$446$	3.80529e9	2.03103
$447$	4.34094e8	0.229883
$448$	−1.02063e9	−0.536282
$449$	2.34987e9	1.22513	0.612564	−	0.790421i	$-0.290138\pi$
$449$	2.34987e9	1.22513	0.612564	+	0.790421i	$0.290138\pi$
$450$	5.76535e8	0.298251
$451$	−1.27186e9	−0.652864
$452$	2.40856e9	1.22680
$453$	1.39889e9	0.707035
$454$	−6.89106e6	−0.00345613
$455$	−1.12385e9	−0.559330
$456$	−2.35402e8	−0.116261
$457$	−1.89675e8	−0.0929615	−0.0464808	−	0.998919i	$-0.514801\pi$
$457$	−1.89675e8	−0.0929615	−0.0464808	+	0.998919i	$0.514801\pi$
$458$	2.78585e9	1.35497
$459$	2.40969e8	0.116310
$460$	1.62398e9	0.777907
$461$	−2.07603e9	−0.986919	−0.493459	−	0.869769i	$-0.664268\pi$
$461$	−2.07603e9	−0.986919	−0.493459	+	0.869769i	$0.664268\pi$
$462$	−1.35050e9	−0.637157
$463$	3.00869e9	1.40878	0.704392	−	0.709811i	$-0.251220\pi$
$463$	3.00869e9	1.40878	0.704392	+	0.709811i	$0.251220\pi$
$464$	3.26258e9	1.51617
$465$	1.62937e8	0.0751511
$466$	4.67983e9	2.14230
$467$	−1.33042e9	−0.604479	−0.302239	−	0.953232i	$-0.597734\pi$
$467$	−1.33042e9	−0.604479	−0.302239	+	0.953232i	$0.597734\pi$
$468$	−5.14337e8	−0.231946
$469$	1.85669e9	0.831064
$470$	7.64391e8	0.339604
$471$	2.20406e9	0.971964
$472$	9.14641e7	0.0400363
$473$	−2.44042e9	−1.06035
$474$	−1.85542e9	−0.800236
$475$	−1.02898e9	−0.440536
$476$	−1.18100e9	−0.501909
$477$	2.11852e8	0.0893756
$478$	2.17249e9	0.909829
$479$	2.48445e9	1.03290	0.516448	−	0.856318i	$-0.327254\pi$
$479$	2.48445e9	1.03290	0.516448	+	0.856318i	$0.327254\pi$
$480$	−1.00735e9	−0.415754
$481$	2.11636e8	0.0867127
$482$	1.45465e9	0.591689
$483$	−2.73205e9	−1.10325
$484$	−7.86130e8	−0.315163
$485$	−2.95068e8	−0.117443
$486$	2.15903e8	0.0853164
$487$	−1.39919e9	−0.548940	−0.274470	−	0.961596i	$-0.588502\pi$
$487$	−1.39919e9	−0.548940	−0.274470	+	0.961596i	$0.588502\pi$
$488$	−1.27323e9	−0.495948
$489$	−2.40778e8	−0.0931183
$490$	−3.30816e8	−0.127028
$491$	1.98268e9	0.755907	0.377953	−	0.925825i	$-0.376628\pi$
$491$	1.98268e9	0.755907	0.377953	+	0.925825i	$0.376628\pi$
$492$	−9.96540e8	−0.377239
$493$	2.06992e9	0.778016
$494$	2.11206e9	0.788246
$495$	−3.95243e8	−0.146469
$496$	7.28305e8	0.267996
$497$	3.50178e9	1.27950
$498$	−2.68544e8	−0.0974344
$499$	3.50830e9	1.26400	0.631998	−	0.774970i	$-0.282235\pi$
$499$	3.50830e9	1.26400	0.631998	+	0.774970i	$0.282235\pi$
$500$	−2.05615e9	−0.735629
$501$	8.67143e8	0.308076
$502$	−2.21054e9	−0.779893
$503$	−3.10883e9	−1.08920	−0.544602	−	0.838694i	$-0.683319\pi$
$503$	−3.10883e9	−1.08920	−0.544602	+	0.838694i	$0.683319\pi$
$504$	3.18270e8	0.110736
$505$	7.91505e8	0.273485
$506$	5.26634e9	1.80710
$507$	3.06204e8	0.104348
$508$	−2.66197e9	−0.900906
$509$	2.98895e9	1.00463	0.502315	−	0.864685i	$-0.332482\pi$
$509$	2.98895e9	1.00463	0.502315	+	0.864685i	$0.332482\pi$
$510$	−7.95234e8	−0.265460
$511$	−2.71028e9	−0.898549
$512$	−3.40274e9	−1.12043
$513$	−3.85339e8	−0.126018
$514$	7.42864e9	2.41289
$515$	−3.45673e9	−1.11517
$516$	−1.91214e9	−0.612696
$517$	1.07738e9	0.342888
$518$	4.35402e8	0.137637
$519$	1.36627e9	0.428994
$520$	−5.10540e8	−0.159227
$521$	2.53744e8	0.0786075	0.0393037	−	0.999227i	$-0.487486\pi$
$521$	2.53744e8	0.0786075	0.0393037	+	0.999227i	$0.487486\pi$
$522$	1.85460e9	0.570696
$523$	2.79711e9	0.854975	0.427487	−	0.904021i	$-0.359399\pi$
$523$	2.79711e9	0.854975	0.427487	+	0.904021i	$0.359399\pi$
$524$	1.32789e9	0.403185
$525$	1.39121e9	0.419601
$526$	2.92600e9	0.876646
$527$	4.62067e8	0.137521
$528$	−1.76668e9	−0.522322
$529$	7.24899e9	2.12903
$530$	−6.99145e8	−0.203987
$531$	1.49721e8	0.0433963
$532$	1.88856e9	0.543802
$533$	−2.68929e9	−0.769295
$534$	−2.16073e9	−0.614053
$535$	−2.91705e8	−0.0823580
$536$	8.43453e8	0.236583
$537$	1.67952e9	0.468032
$538$	8.99610e8	0.249067
$539$	−4.66274e8	−0.128257
$540$	−3.09684e8	−0.0846332
$541$	−2.58195e9	−0.701064	−0.350532	−	0.936551i	$-0.613999\pi$
$541$	−2.58195e9	−0.701064	−0.350532	+	0.936551i	$0.613999\pi$
$542$	7.79996e9	2.10424
$543$	−1.70015e9	−0.455710
$544$	−2.85671e9	−0.760798
$545$	8.36284e8	0.221292
$546$	−2.85556e9	−0.750787
$547$	1.44486e9	0.377459	0.188730	−	0.982029i	$-0.439563\pi$
$547$	1.44486e9	0.377459	0.188730	+	0.982029i	$0.439563\pi$
$548$	5.26625e9	1.36700
$549$	−2.08419e9	−0.537570
$550$	−2.68172e9	−0.687297
$551$	−3.31005e9	−0.842955
$552$	−1.24111e9	−0.314068
$553$	−4.47725e9	−1.12583
$554$	−3.54186e9	−0.885008
$555$	1.27427e8	0.0316400
$556$	1.31530e9	0.324536
$557$	−4.77372e9	−1.17048	−0.585240	−	0.810860i	$-0.699000\pi$
$557$	−4.77372e9	−1.17048	−0.585240	+	0.810860i	$0.699000\pi$
$558$	4.14004e8	0.100875
$559$	−5.16015e9	−1.24946
$560$	−3.02463e9	−0.727803
$561$	−1.12085e9	−0.268027
$562$	4.76255e9	1.13178
$563$	−3.69151e9	−0.871816	−0.435908	−	0.899991i	$-0.643573\pi$
$563$	−3.69151e9	−0.871816	−0.435908	+	0.899991i	$0.643573\pi$
$564$	8.44159e8	0.198129
$565$	3.91356e9	0.912855
$566$	3.69326e9	0.856154
$567$	5.20988e8	0.120029
$568$	1.59078e9	0.364243
$569$	−2.15110e9	−0.489516	−0.244758	−	0.969584i	$-0.578709\pi$
$569$	−2.15110e9	−0.489516	−0.244758	+	0.969584i	$0.578709\pi$
$570$	1.27168e9	0.287617
$571$	5.63827e8	0.126742	0.0633709	−	0.997990i	$-0.479815\pi$
$571$	5.63827e8	0.126742	0.0633709	+	0.997990i	$0.479815\pi$
$572$	2.39241e9	0.534503
$573$	1.94087e9	0.430977
$574$	−5.53271e9	−1.22109
$575$	−5.42513e9	−1.19007
$576$	−7.58964e8	−0.165479
$577$	−3.12035e9	−0.676221	−0.338110	−	0.941106i	$-0.609788\pi$
$577$	−3.12035e9	−0.676221	−0.338110	+	0.941106i	$0.609788\pi$
$578$	3.91906e9	0.844179
$579$	9.95581e8	0.213158
$580$	−2.66018e9	−0.566125
$581$	−6.48013e8	−0.137078
$582$	−7.49732e8	−0.157643
$583$	−9.85420e8	−0.205959
$584$	−1.23122e9	−0.255795
$585$	−8.35723e8	−0.172590
$586$	−2.96663e9	−0.609006
$587$	−4.80777e9	−0.981094	−0.490547	−	0.871415i	$-0.663203\pi$
$587$	−4.80777e9	−0.981094	−0.490547	+	0.871415i	$0.663203\pi$
$588$	−3.65339e8	−0.0741097
$589$	−7.38903e8	−0.148999
$590$	−4.94103e8	−0.0990457
$591$	−4.73480e9	−0.943507
$592$	5.69579e8	0.112831
$593$	−4.97973e8	−0.0980651	−0.0490326	−	0.998797i	$-0.515614\pi$
$593$	−4.97973e8	−0.0980651	−0.0490326	+	0.998797i	$0.515614\pi$
$594$	−1.00426e9	−0.196605
$595$	−1.91895e9	−0.373469
$596$	−1.58207e9	−0.306101
$597$	−2.20452e9	−0.424037
$598$	1.11354e10	2.12938
$599$	−1.25174e9	−0.237968	−0.118984	−	0.992896i	$-0.537964\pi$
$599$	−1.25174e9	−0.237968	−0.118984	+	0.992896i	$0.537964\pi$
$600$	6.31998e8	0.119450
$601$	−3.57133e9	−0.671073	−0.335536	−	0.942027i	$-0.608918\pi$
$601$	−3.57133e9	−0.671073	−0.335536	+	0.942027i	$0.608918\pi$
$602$	−1.06160e10	−1.98324
$603$	1.38068e9	0.256439
$604$	−5.09832e9	−0.941451
$605$	−1.27735e9	−0.234512
$606$	2.01112e9	0.367099
$607$	−2.73915e9	−0.497113	−0.248556	−	0.968617i	$-0.579956\pi$
$607$	−2.73915e9	−0.497113	−0.248556	+	0.968617i	$0.579956\pi$
$608$	4.56823e9	0.824300
$609$	4.47528e9	0.802896
$610$	6.87816e9	1.22692
$611$	2.27807e9	0.404039
$612$	−8.78220e8	−0.154872
$613$	2.74148e9	0.480700	0.240350	−	0.970686i	$-0.422738\pi$
$613$	2.74148e9	0.480700	0.240350	+	0.970686i	$0.422738\pi$
$614$	−2.01903e8	−0.0352008
$615$	−1.61923e9	−0.280703
$616$	−1.48042e9	−0.255183
$617$	−9.78150e9	−1.67652	−0.838258	−	0.545274i	$-0.816425\pi$
$617$	−9.78150e9	−1.67652	−0.838258	+	0.545274i	$0.816425\pi$
$618$	−8.78311e9	−1.49689
$619$	8.34172e9	1.41364	0.706819	−	0.707394i	$-0.250130\pi$
$619$	8.34172e9	1.41364	0.706819	+	0.707394i	$0.250130\pi$
$620$	−5.93832e8	−0.100067
$621$	−2.03163e9	−0.340426
$622$	1.11701e10	1.86120
$623$	−5.21397e9	−0.863895
$624$	−3.73556e9	−0.615473
$625$	7.65329e8	0.125391
$626$	−1.12541e10	−1.83358
$627$	1.79239e9	0.290399
$628$	−8.03278e9	−1.29422
$629$	3.61365e8	0.0578987
$630$	−1.71934e9	−0.273949
$631$	−4.64175e7	−0.00735494	−0.00367747	−	0.999993i	$-0.501171\pi$
$631$	−4.64175e7	−0.00735494	−0.00367747	+	0.999993i	$0.501171\pi$
$632$	−2.03391e9	−0.320496
$633$	−2.83304e8	−0.0443956
$634$	1.15168e10	1.79481
$635$	−4.32531e9	−0.670361
$636$	−7.72104e8	−0.119008
$637$	−9.85914e8	−0.151130
$638$	−8.62660e9	−1.31513
$639$	2.60402e9	0.394812
$640$	−2.27090e9	−0.342426
$641$	−9.01725e9	−1.35229	−0.676147	−	0.736767i	$-0.736352\pi$
$641$	−9.01725e9	−1.35229	−0.676147	+	0.736767i	$0.736352\pi$
$642$	−7.41186e8	−0.110549
$643$	−6.73082e9	−0.998457	−0.499229	−	0.866470i	$-0.666383\pi$
$643$	−6.73082e9	−0.998457	−0.499229	+	0.866470i	$0.666383\pi$
$644$	9.95708e9	1.46903
$645$	−3.10694e9	−0.455905
$646$	3.60630e9	0.526318
$647$	1.43491e9	0.208286	0.104143	−	0.994562i	$-0.466790\pi$
$647$	1.43491e9	0.208286	0.104143	+	0.994562i	$0.466790\pi$
$648$	2.36674e8	0.0341694
$649$	−6.96421e8	−0.100004
$650$	−5.67037e9	−0.809869
$651$	9.99017e8	0.141919
$652$	8.77524e8	0.123992
$653$	3.13170e9	0.440133	0.220066	−	0.975485i	$-0.429373\pi$
$653$	3.13170e9	0.440133	0.220066	+	0.975485i	$0.429373\pi$
$654$	2.12489e9	0.297040
$655$	2.15763e9	0.300008
$656$	−7.23773e9	−1.00101
$657$	−2.01544e9	−0.277262
$658$	4.68671e9	0.641323
$659$	8.36231e9	1.13822	0.569111	−	0.822260i	$-0.307287\pi$
$659$	8.36231e9	1.13822	0.569111	+	0.822260i	$0.307287\pi$
$660$	1.44048e9	0.195031
$661$	1.18208e10	1.59200	0.795999	−	0.605298i	$-0.206946\pi$
$661$	1.18208e10	1.59200	0.795999	+	0.605298i	$0.206946\pi$
$662$	−4.71150e9	−0.631185
$663$	−2.36999e9	−0.315827
$664$	−2.94378e8	−0.0390227
$665$	3.06864e9	0.404641
$666$	3.23776e8	0.0424703
$667$	−1.74516e10	−2.27717
$668$	−3.16034e9	−0.410219
$669$	6.82827e9	0.881697
$670$	−4.55647e9	−0.585284
$671$	9.69452e9	1.23879
$672$	−6.17637e9	−0.785128
$673$	2.34562e9	0.296624	0.148312	−	0.988941i	$-0.452616\pi$
$673$	2.34562e9	0.296624	0.148312	+	0.988941i	$0.452616\pi$
$674$	−1.96142e10	−2.46753
$675$	1.03454e9	0.129475
$676$	−1.11597e9	−0.138944
$677$	−1.57414e10	−1.94977	−0.974884	−	0.222713i	$-0.928509\pi$
$677$	−1.57414e10	−1.94977	−0.974884	+	0.222713i	$0.928509\pi$
$678$	9.94386e9	1.22532
$679$	−1.80915e9	−0.221784
$680$	−8.71736e8	−0.106317
$681$	−1.23654e7	−0.00150036
$682$	−1.92572e9	−0.232459
$683$	−6.44477e9	−0.773989	−0.386994	−	0.922082i	$-0.626487\pi$
$683$	−6.44477e9	−0.773989	−0.386994	+	0.922082i	$0.626487\pi$
$684$	1.40438e9	0.167799
$685$	8.55688e9	1.01718
$686$	1.01195e10	1.19681
$687$	4.99898e9	0.588211
$688$	−1.38876e10	−1.62580
$689$	−2.08362e9	−0.242690
$690$	6.70468e9	0.776973
$691$	1.59645e10	1.84070	0.920349	−	0.391097i	$-0.127904\pi$
$691$	1.59645e10	1.84070	0.920349	+	0.391097i	$0.127904\pi$
$692$	−4.97943e9	−0.571227
$693$	−2.42335e9	−0.276599
$694$	3.16997e9	0.359995
$695$	2.13717e9	0.241486
$696$	2.03302e9	0.228565
$697$	−4.59192e9	−0.513664
$698$	−9.43933e9	−1.05062
$699$	8.39756e9	0.930001
$700$	−5.07034e9	−0.558719
$701$	1.28238e10	1.40606	0.703028	−	0.711162i	$-0.251831\pi$
$701$	1.28238e10	1.40606	0.703028	+	0.711162i	$0.251831\pi$
$702$	−2.12347e9	−0.231668
$703$	−5.77868e8	−0.0627314
$704$	3.53028e9	0.381333
$705$	1.37164e9	0.147427
$706$	1.21955e10	1.30432
$707$	4.85295e9	0.516462
$708$	−5.45665e8	−0.0577843
$709$	4.26207e8	0.0449117	0.0224558	−	0.999748i	$-0.492851\pi$
$709$	4.26207e8	0.0449117	0.0224558	+	0.999748i	$0.492851\pi$
$710$	−8.59365e9	−0.901101
$711$	−3.32940e9	−0.347394
$712$	−2.36859e9	−0.245929
$713$	−3.89573e9	−0.402509
$714$	−4.87581e9	−0.501306
$715$	3.88732e9	0.397722
$716$	−6.12108e9	−0.623207
$717$	3.89835e9	0.394969
$718$	−7.37674e9	−0.743754
$719$	9.93256e9	0.996576	0.498288	−	0.867012i	$-0.333962\pi$
$719$	9.93256e9	0.996576	0.498288	+	0.867012i	$0.333962\pi$
$720$	−2.24919e9	−0.224576
$721$	−2.11942e10	−2.10593
$722$	7.68288e9	0.759703
$723$	2.61025e9	0.256861
$724$	6.19627e9	0.606800
$725$	8.88670e9	0.866079
$726$	−3.24558e9	−0.314785
$727$	−7.03816e8	−0.0679342	−0.0339671	−	0.999423i	$-0.510814\pi$
$727$	−7.03816e8	−0.0679342	−0.0339671	+	0.999423i	$0.510814\pi$
$728$	−3.13027e9	−0.300692
$729$	3.87420e8	0.0370370
$730$	6.65125e9	0.632810
$731$	−8.81085e9	−0.834271
$732$	7.59593e9	0.715801
$733$	1.24906e10	1.17144	0.585718	−	0.810515i	$-0.300813\pi$
$733$	1.24906e10	1.17144	0.585718	+	0.810515i	$0.300813\pi$
$734$	1.00191e10	0.935174
$735$	−5.93622e8	−0.0551448
$736$	2.40851e10	2.22678
$737$	−6.42218e9	−0.590944
$738$	−4.11427e9	−0.376787
$739$	−8.92221e9	−0.813237	−0.406618	−	0.913598i	$-0.633292\pi$
$739$	−8.92221e9	−0.813237	−0.406618	+	0.913598i	$0.633292\pi$
$740$	−4.64413e8	−0.0421302
$741$	3.78991e9	0.342189
$742$	−4.28666e9	−0.385217
$743$	4.73069e9	0.423120	0.211560	−	0.977365i	$-0.432146\pi$
$743$	4.73069e9	0.423120	0.211560	+	0.977365i	$0.432146\pi$
$744$	4.53831e8	0.0404007
$745$	−2.57064e9	−0.227769
$746$	2.27026e10	2.00212
$747$	−4.81879e8	−0.0422976
$748$	4.08500e9	0.356892
$749$	−1.78853e9	−0.155528
$750$	−8.48891e9	−0.734746
$751$	6.35674e9	0.547640	0.273820	−	0.961781i	$-0.411713\pi$
$751$	6.35674e9	0.547640	0.273820	+	0.961781i	$0.411713\pi$
$752$	6.13100e9	0.525738
$753$	−3.96662e9	−0.338562
$754$	−1.82405e10	−1.54967
$755$	−8.28403e9	−0.700531
$756$	−1.89876e9	−0.159825
$757$	−3.90470e9	−0.327154	−0.163577	−	0.986531i	$-0.552303\pi$
$757$	−3.90470e9	−0.327154	−0.163577	+	0.986531i	$0.552303\pi$
$758$	1.76801e10	1.47449
$759$	9.45001e9	0.784487
$760$	1.39401e9	0.115191
$761$	2.13395e10	1.75525	0.877623	−	0.479351i	$-0.159128\pi$
$761$	2.13395e10	1.75525	0.877623	+	0.479351i	$0.159128\pi$
$762$	−1.09901e10	−0.899825
$763$	5.12750e9	0.417898
$764$	−7.07356e9	−0.573867
$765$	−1.42698e9	−0.115240
$766$	−4.65853e9	−0.374497
$767$	−1.47255e9	−0.117838
$768$	−9.36811e9	−0.746256
$769$	−1.05289e9	−0.0834910	−0.0417455	−	0.999128i	$-0.513292\pi$
$769$	−1.05289e9	−0.0834910	−0.0417455	+	0.999128i	$0.513292\pi$
$770$	7.99743e9	0.631296
$771$	1.33301e10	1.04747
$772$	−3.62844e9	−0.283830
$773$	5.93967e9	0.462524	0.231262	−	0.972891i	$-0.425715\pi$
$773$	5.93967e9	0.462524	0.231262	+	0.972891i	$0.425715\pi$
$774$	−7.89435e9	−0.611960
$775$	1.98378e9	0.153087
$776$	−8.21856e8	−0.0631364
$777$	7.81292e8	0.0597503
$778$	2.73774e10	2.08432
$779$	7.34305e9	0.556539
$780$	3.04583e9	0.229813
$781$	−1.21124e10	−0.909815
$782$	1.90135e10	1.42180
$783$	3.32793e9	0.247747
$784$	−2.65340e9	−0.196651
$785$	−1.30521e10	−0.963023
$786$	5.48228e9	0.402701
$787$	1.31636e10	0.962640	0.481320	−	0.876545i	$-0.340158\pi$
$787$	1.31636e10	0.962640	0.481320	+	0.876545i	$0.340158\pi$
$788$	1.72562e10	1.25633
$789$	5.25046e9	0.380564
$790$	1.09875e10	0.792875
$791$	2.39952e10	1.72388
$792$	−1.10087e9	−0.0787408
$793$	2.04986e10	1.45972
$794$	−9.90377e9	−0.702148
$795$	−1.25456e9	−0.0885535
$796$	8.03446e9	0.564626
$797$	−1.29607e10	−0.906825	−0.453412	−	0.891301i	$-0.649794\pi$
$797$	−1.29607e10	−0.906825	−0.453412	+	0.891301i	$0.649794\pi$
$798$	7.79703e9	0.543149
$799$	3.88977e9	0.269780
$800$	−1.22646e10	−0.846912
$801$	−3.87725e9	−0.266569
$802$	−1.16491e10	−0.797410
$803$	9.37471e9	0.638930
$804$	−5.03195e9	−0.341461
$805$	1.61788e10	1.09310
$806$	−4.07184e9	−0.273916
$807$	1.61427e9	0.108123
$808$	2.20459e9	0.147024
$809$	−1.62295e10	−1.07767	−0.538836	−	0.842411i	$-0.681136\pi$
$809$	−1.62295e10	−1.07767	−0.538836	+	0.842411i	$0.681136\pi$
$810$	−1.27855e9	−0.0845316
$811$	8.71515e9	0.573723	0.286861	−	0.957972i	$-0.407388\pi$
$811$	8.71515e9	0.573723	0.286861	+	0.957972i	$0.407388\pi$
$812$	−1.63103e10	−1.06910
$813$	1.39964e10	0.913478
$814$	−1.50603e9	−0.0978696
$815$	1.42585e9	0.0922618
$816$	−6.37839e9	−0.410956
$817$	1.40897e10	0.903906
$818$	−1.63855e10	−1.04670
$819$	−5.12406e9	−0.325927
$820$	5.90136e9	0.373769
$821$	2.43096e10	1.53312	0.766561	−	0.642171i	$-0.221966\pi$
$821$	2.43096e10	1.53312	0.766561	+	0.642171i	$0.221966\pi$
$822$	2.17420e10	1.36536
$823$	−1.50334e10	−0.940062	−0.470031	−	0.882650i	$-0.655757\pi$
$823$	−1.50334e10	−0.940062	−0.470031	+	0.882650i	$0.655757\pi$
$824$	−9.62805e9	−0.599506
$825$	−4.81212e9	−0.298365
$826$	−3.02949e9	−0.187042
$827$	−7.68810e9	−0.472661	−0.236331	−	0.971673i	$-0.575945\pi$
$827$	−7.68810e9	−0.472661	−0.236331	+	0.971673i	$0.575945\pi$
$828$	7.40434e9	0.453294
$829$	4.74776e9	0.289433	0.144716	−	0.989473i	$-0.453773\pi$
$829$	4.74776e9	0.289433	0.144716	+	0.989473i	$0.453773\pi$
$830$	1.59028e9	0.0965381
$831$	−6.35557e9	−0.384194
$832$	7.46461e9	0.449340
$833$	−1.68343e9	−0.100911
$834$	5.43028e9	0.324146
$835$	−5.13509e9	−0.305243
$836$	−6.53242e9	−0.386680
$837$	7.42895e8	0.0437913
$838$	−2.81299e10	−1.65125
$839$	−1.32986e10	−0.777391	−0.388696	−	0.921366i	$-0.627074\pi$
$839$	−1.32986e10	−0.777391	−0.388696	+	0.921366i	$0.627074\pi$
$840$	−1.88474e9	−0.109717
$841$	1.13370e10	0.657221
$842$	−3.92973e10	−2.26867
$843$	8.54599e9	0.491322
$844$	1.03251e9	0.0591150
$845$	−1.81329e9	−0.103388
$846$	3.48516e9	0.197891
$847$	−7.83179e9	−0.442863
$848$	−5.60768e9	−0.315790
$849$	6.62724e9	0.371668
$850$	−9.68205e9	−0.540756
$851$	−3.04670e9	−0.169463
$852$	−9.49044e9	−0.525712
$853$	5.80154e9	0.320053	0.160027	−	0.987113i	$-0.448842\pi$
$853$	5.80154e9	0.320053	0.160027	+	0.987113i	$0.448842\pi$
$854$	4.21720e10	2.31698
$855$	2.28192e9	0.124859
$856$	−8.12489e8	−0.0442751
$857$	−2.65557e10	−1.44120	−0.720601	−	0.693350i	$-0.756134\pi$
$857$	−2.65557e10	−1.44120	−0.720601	+	0.693350i	$0.756134\pi$
$858$	9.87721e9	0.533861
$859$	4.83329e9	0.260176	0.130088	−	0.991502i	$-0.458474\pi$
$859$	4.83329e9	0.260176	0.130088	+	0.991502i	$0.458474\pi$
$860$	1.13234e10	0.607060
$861$	−9.92799e9	−0.530091
$862$	−2.32975e10	−1.23889
$863$	9.78741e9	0.518358	0.259179	−	0.965829i	$-0.416548\pi$
$863$	9.78741e9	0.518358	0.259179	+	0.965829i	$0.416548\pi$
$864$	−4.59291e9	−0.242264
$865$	−8.09085e9	−0.425048
$866$	2.60679e10	1.36393
$867$	7.03243e9	0.366470
$868$	−3.64096e9	−0.188972
$869$	1.54865e10	0.800543
$870$	−1.09827e10	−0.565446
$871$	−1.35794e10	−0.696333
$872$	2.32931e9	0.118965
$873$	−1.34533e9	−0.0684351
$874$	−3.04050e10	−1.54048
$875$	−2.04843e10	−1.03369
$876$	7.34534e9	0.369188
$877$	−1.33028e10	−0.665956	−0.332978	−	0.942935i	$-0.608053\pi$
$877$	−1.33028e10	−0.665956	−0.332978	+	0.942935i	$0.608053\pi$
$878$	4.72767e10	2.35731
$879$	−5.32337e9	−0.264378
$880$	1.04620e10	0.517518
$881$	1.14650e10	0.564885	0.282443	−	0.959284i	$-0.408855\pi$
$881$	1.14650e10	0.564885	0.282443	+	0.959284i	$0.408855\pi$
$882$	−1.50832e9	−0.0740208
$883$	−1.56517e10	−0.765067	−0.382533	−	0.923942i	$-0.624948\pi$
$883$	−1.56517e10	−0.765067	−0.382533	+	0.923942i	$0.624948\pi$
$884$	8.63753e9	0.420540
$885$	−8.86627e8	−0.0429971
$886$	−2.82847e10	−1.36626
$887$	6.19771e9	0.298194	0.149097	−	0.988823i	$-0.452363\pi$
$887$	6.19771e9	0.298194	0.149097	+	0.988823i	$0.452363\pi$
$888$	3.54924e8	0.0170094
$889$	−2.65197e10	−1.26594
$890$	1.27955e10	0.608405
$891$	−1.80207e9	−0.0853491
$892$	−2.48859e10	−1.17402
$893$	−6.22022e9	−0.292298
$894$	−6.53167e9	−0.305734
$895$	−9.94587e9	−0.463727
$896$	−1.39235e10	−0.646653
$897$	1.99816e10	0.924393
$898$	−3.53577e10	−1.62936
$899$	6.38144e9	0.292927
$900$	−3.77043e9	−0.172402
$901$	−3.55775e9	−0.162046
$902$	1.91373e10	0.868277
$903$	−1.90496e10	−0.860950
$904$	1.09005e10	0.490745
$905$	1.00680e10	0.451518
$906$	−2.10487e10	−0.940322
$907$	−2.84672e10	−1.26683	−0.633417	−	0.773811i	$-0.718348\pi$
$907$	−2.84672e10	−1.26683	−0.633417	+	0.773811i	$0.718348\pi$
$908$	4.50663e7	0.00199780
$909$	3.60878e9	0.159363
$910$	1.69102e10	0.743881
$911$	1.41611e10	0.620558	0.310279	−	0.950646i	$-0.399578\pi$
$911$	1.41611e10	0.620558	0.310279	+	0.950646i	$0.399578\pi$
$912$	1.01998e10	0.445258
$913$	2.24144e9	0.0974717
$914$	2.85398e9	0.123634
$915$	1.23423e10	0.532625
$916$	−1.82190e10	−0.783231
$917$	1.32291e10	0.566549
$918$	−3.62578e9	−0.154686
$919$	1.43616e10	0.610379	0.305189	−	0.952292i	$-0.401280\pi$
$919$	1.43616e10	0.610379	0.305189	+	0.952292i	$0.401280\pi$
$920$	7.34968e9	0.311179
$921$	−3.62297e8	−0.0152812
$922$	3.12374e10	1.31255
$923$	−2.56112e10	−1.07207
$924$	8.83200e9	0.368305
$925$	1.55144e9	0.0644522
$926$	−4.52709e10	−1.87362
$927$	−1.57606e10	−0.649819
$928$	−3.94529e10	−1.62055
$929$	2.83698e10	1.16092	0.580458	−	0.814290i	$-0.302873\pi$
$929$	2.83698e10	1.16092	0.580458	+	0.814290i	$0.302873\pi$
$930$	−2.45167e9	−0.0999473
$931$	2.69201e9	0.109334
$932$	−3.06053e10	−1.23834
$933$	2.00439e10	0.807972
$934$	2.00185e10	0.803928
$935$	6.63753e9	0.265562
$936$	−2.32775e9	−0.0927834
$937$	−4.33315e10	−1.72074	−0.860370	−	0.509669i	$-0.829768\pi$
$937$	−4.33315e10	−1.72074	−0.860370	+	0.509669i	$0.829768\pi$
$938$	−2.79370e10	−1.10527
$939$	−2.01945e10	−0.795984
$940$	−4.99898e9	−0.196306
$941$	3.82084e10	1.49484	0.747421	−	0.664351i	$-0.231292\pi$
$941$	3.82084e10	1.49484	0.747421	+	0.664351i	$0.231292\pi$
$942$	−3.31638e10	−1.29266
$943$	3.87148e10	1.50344
$944$	−3.96309e9	−0.153332
$945$	−3.08521e9	−0.118925
$946$	3.67202e10	1.41022
$947$	1.03534e10	0.396148	0.198074	−	0.980187i	$-0.436531\pi$
$947$	1.03534e10	0.396148	0.198074	+	0.980187i	$0.436531\pi$
$948$	1.21341e10	0.462572
$949$	1.98224e10	0.752877
$950$	1.54828e10	0.585891
$951$	2.06659e10	0.779153
$952$	−5.34487e9	−0.200774
$953$	2.92299e10	1.09396	0.546981	−	0.837145i	$-0.315777\pi$
$953$	2.92299e10	1.09396	0.546981	+	0.837145i	$0.315777\pi$
$954$	−3.18767e9	−0.118865
$955$	−1.14935e10	−0.427013
$956$	−1.42077e10	−0.525921
$957$	−1.54797e10	−0.570914
$958$	−3.73828e10	−1.37370
$959$	5.24648e10	1.92089
$960$	4.49447e9	0.163957
$961$	−2.60881e10	−0.948223
$962$	−3.18443e9	−0.115324
$963$	−1.33000e9	−0.0479908
$964$	−9.51315e9	−0.342022
$965$	−5.89568e9	−0.211197
$966$	4.11084e10	1.46727
$967$	4.59588e9	0.163447	0.0817233	−	0.996655i	$-0.473958\pi$
$967$	4.59588e9	0.163447	0.0817233	+	0.996655i	$0.473958\pi$
$968$	−3.55781e9	−0.126072
$969$	6.47120e9	0.228482
$970$	4.43980e9	0.156193
$971$	−5.52070e10	−1.93520	−0.967602	−	0.252481i	$-0.918753\pi$
$971$	−5.52070e10	−1.93520	−0.967602	+	0.252481i	$0.918753\pi$
$972$	−1.41197e9	−0.0493166
$973$	1.31036e10	0.456033
$974$	2.10531e10	0.730063
$975$	−1.01750e10	−0.351576
$976$	5.51681e10	1.89939
$977$	−4.44629e9	−0.152534	−0.0762671	−	0.997087i	$-0.524300\pi$
$977$	−4.44629e9	−0.152534	−0.0762671	+	0.997087i	$0.524300\pi$
$978$	3.62290e9	0.123843
$979$	1.80348e10	0.614288
$980$	2.16348e9	0.0734280
$981$	3.81294e9	0.128949
$982$	−2.98328e10	−1.00532
$983$	3.90750e10	1.31208	0.656041	−	0.754725i	$-0.272230\pi$
$983$	3.90750e10	1.31208	0.656041	+	0.754725i	$0.272230\pi$
$984$	−4.51007e9	−0.150904
$985$	2.80387e10	0.934828
$986$	−3.11454e10	−1.03472
$987$	8.40990e9	0.278407
$988$	−1.38125e10	−0.455641
$989$	7.42850e10	2.44182
$990$	5.94710e9	0.194797
$991$	−1.52795e10	−0.498713	−0.249357	−	0.968412i	$-0.580219\pi$
$991$	−1.52795e10	−0.498713	−0.249357	+	0.968412i	$0.580219\pi$
$992$	−8.80708e9	−0.286445
$993$	−8.45439e9	−0.274006
$994$	−5.26902e10	−1.70168
$995$	1.30548e10	0.420137
$996$	1.75623e9	0.0563214
$997$	1.22551e10	0.391637	0.195818	−	0.980640i	$-0.437264\pi$
$997$	1.22551e10	0.391637	0.195818	+	0.980640i	$0.437264\pi$
$998$	−5.27883e10	−1.68105
$999$	5.80989e8	0.0184369

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.a.1.4	✓	16
3.2	odd	2		531.8.a.b.1.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.4	✓	16	1.1	even	1	trivial
531.8.a.b.1.13		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-15.0467 q^{2} -27.0000 q^{3} +98.4026 q^{4} +159.890 q^{5} +406.260 q^{6} +980.332 q^{7} +445.343 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-15.0467 q^{2} -27.0000 q^{3} +98.4026 q^{4} +159.890 q^{5} +406.260 q^{6} +980.332 q^{7} +445.343 q^{8} +729.000 q^{9} -2405.81 q^{10} -3390.91 q^{11} -2656.87 q^{12} -7169.91 q^{13} -14750.7 q^{14} -4317.03 q^{15} -19296.5 q^{16} -12242.5 q^{17} -10969.0 q^{18} +19577.3 q^{19} +15733.6 q^{20} -26469.0 q^{21} +51021.9 q^{22} +103217. q^{23} -12024.3 q^{24} -52560.2 q^{25} +107883. q^{26} -19683.0 q^{27} +96467.2 q^{28} -169076. q^{29} +64956.9 q^{30} -37743.0 q^{31} +233344. q^{32} +91554.5 q^{33} +184209. q^{34} +156745. q^{35} +71735.5 q^{36} -29517.3 q^{37} -294573. q^{38} +193588. q^{39} +71205.8 q^{40} +375081. q^{41} +398270. q^{42} +719695. q^{43} -333674. q^{44} +116560. q^{45} -1.55308e6 q^{46} -317727. q^{47} +521004. q^{48} +137507. q^{49} +790857. q^{50} +330547. q^{51} -705538. q^{52} +290607. q^{53} +296164. q^{54} -542172. q^{55} +436584. q^{56} -528586. q^{57} +2.54404e6 q^{58} +205379. q^{59} -424807. q^{60} -2.85898e6 q^{61} +567906. q^{62} +714662. q^{63} -1.04110e6 q^{64} -1.14640e6 q^{65} -1.37759e6 q^{66} +1.89394e6 q^{67} -1.20469e6 q^{68} -2.78687e6 q^{69} -2.35849e6 q^{70} +3.57204e6 q^{71} +324655. q^{72} -2.76466e6 q^{73} +444137. q^{74} +1.41913e6 q^{75} +1.92645e6 q^{76} -3.32421e6 q^{77} -2.91285e6 q^{78} -4.56707e6 q^{79} -3.08531e6 q^{80} +531441. q^{81} -5.64372e6 q^{82} -661014. q^{83} -2.60461e6 q^{84} -1.95745e6 q^{85} -1.08290e7 q^{86} +4.56506e6 q^{87} -1.51012e6 q^{88} -5.31858e6 q^{89} -1.75384e6 q^{90} -7.02889e6 q^{91} +1.01568e7 q^{92} +1.01906e6 q^{93} +4.78073e6 q^{94} +3.13021e6 q^{95} -6.30028e6 q^{96} -1.84545e6 q^{97} -2.06903e6 q^{98} -2.47197e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9} - 3479 q^{10} + 898 q^{11} - 26298 q^{12} - 8172 q^{13} - 13315 q^{14} + 1836 q^{15} + 3138 q^{16} - 44985 q^{17} - 4374 q^{18} - 40137 q^{19} + 130657 q^{20} + 63261 q^{21} + 109394 q^{22} - 2833 q^{23} - 22113 q^{24} + 285746 q^{25} - 129420 q^{26} - 314928 q^{27} + 112890 q^{28} + 144375 q^{29} + 93933 q^{30} - 141759 q^{31} - 36224 q^{32} - 24246 q^{33} - 341332 q^{34} - 78859 q^{35} + 710046 q^{36} - 297971 q^{37} + 329075 q^{38} + 220644 q^{39} - 203048 q^{40} + 659077 q^{41} + 359505 q^{42} - 1431608 q^{43} + 254916 q^{44} - 49572 q^{45} + 873113 q^{46} - 1574073 q^{47} - 84726 q^{48} + 1893545 q^{49} + 302533 q^{50} + 1214595 q^{51} - 4972548 q^{52} + 587736 q^{53} + 118098 q^{54} - 4624036 q^{55} - 5798506 q^{56} + 1083699 q^{57} - 6991380 q^{58} + 3286064 q^{59} - 3527739 q^{60} - 6117131 q^{61} - 11570258 q^{62} - 1708047 q^{63} - 19063011 q^{64} - 5335514 q^{65} - 2953638 q^{66} - 16518710 q^{67} - 17284669 q^{68} + 76491 q^{69} - 39189486 q^{70} - 10882582 q^{71} + 597051 q^{72} - 21097441 q^{73} - 16717030 q^{74} - 7715142 q^{75} - 40864952 q^{76} - 3404601 q^{77} + 3494340 q^{78} - 3784458 q^{79} - 27466195 q^{80} + 8503056 q^{81} - 24990117 q^{82} - 1951425 q^{83} - 3048030 q^{84} - 23238675 q^{85} - 35910572 q^{86} - 3898125 q^{87} - 27843055 q^{88} + 10499443 q^{89} - 2536191 q^{90} + 699217 q^{91} - 20062766 q^{92} + 3827493 q^{93} - 59358988 q^{94} - 29236333 q^{95} + 978048 q^{96} - 25158976 q^{97} + 2120460 q^{98} + 654642 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9 - 3479 * q^10 + 898 * q^11 - 26298 * q^12 - 8172 * q^13 - 13315 * q^14 + 1836 * q^15 + 3138 * q^16 - 44985 * q^17 - 4374 * q^18 - 40137 * q^19 + 130657 * q^20 + 63261 * q^21 + 109394 * q^22 - 2833 * q^23 - 22113 * q^24 + 285746 * q^25 - 129420 * q^26 - 314928 * q^27 + 112890 * q^28 + 144375 * q^29 + 93933 * q^30 - 141759 * q^31 - 36224 * q^32 - 24246 * q^33 - 341332 * q^34 - 78859 * q^35 + 710046 * q^36 - 297971 * q^37 + 329075 * q^38 + 220644 * q^39 - 203048 * q^40 + 659077 * q^41 + 359505 * q^42 - 1431608 * q^43 + 254916 * q^44 - 49572 * q^45 + 873113 * q^46 - 1574073 * q^47 - 84726 * q^48 + 1893545 * q^49 + 302533 * q^50 + 1214595 * q^51 - 4972548 * q^52 + 587736 * q^53 + 118098 * q^54 - 4624036 * q^55 - 5798506 * q^56 + 1083699 * q^57 - 6991380 * q^58 + 3286064 * q^59 - 3527739 * q^60 - 6117131 * q^61 - 11570258 * q^62 - 1708047 * q^63 - 19063011 * q^64 - 5335514 * q^65 - 2953638 * q^66 - 16518710 * q^67 - 17284669 * q^68 + 76491 * q^69 - 39189486 * q^70 - 10882582 * q^71 + 597051 * q^72 - 21097441 * q^73 - 16717030 * q^74 - 7715142 * q^75 - 40864952 * q^76 - 3404601 * q^77 + 3494340 * q^78 - 3784458 * q^79 - 27466195 * q^80 + 8503056 * q^81 - 24990117 * q^82 - 1951425 * q^83 - 3048030 * q^84 - 23238675 * q^85 - 35910572 * q^86 - 3898125 * q^87 - 27843055 * q^88 + 10499443 * q^89 - 2536191 * q^90 + 699217 * q^91 - 20062766 * q^92 + 3827493 * q^93 - 59358988 * q^94 - 29236333 * q^95 + 978048 * q^96 - 25158976 * q^97 + 2120460 * q^98 + 654642 * q^99

Introduction

L-functions

Modular forms

Varieties

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