LMFDB - Embedded newform 354.8.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,8,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, 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("354.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	354.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:	$110.584299021$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2 x^{6} - 77333 x^{5} - 3585829 x^{4} + 1295511138 x^{3} + 69321224657 x^{2} + \cdots - 316178833801950 $ x^7 - 2x^6 - 77333x^5 - 3585829x^4 + 1295511138x^3 + 69321224657x^2 - 5554636281450x - 316178833801950
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-75.1579$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -15.7693 q^{5} -216.000 q^{6} -472.852 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -15.7693 q^{5} -216.000 q^{6} -472.852 q^{7} -512.000 q^{8} +729.000 q^{9} +126.154 q^{10} -6307.22 q^{11} +1728.00 q^{12} +4052.85 q^{13} +3782.81 q^{14} -425.771 q^{15} +4096.00 q^{16} +6600.24 q^{17} -5832.00 q^{18} +19516.9 q^{19} -1009.23 q^{20} -12767.0 q^{21} +50457.8 q^{22} +70218.3 q^{23} -13824.0 q^{24} -77876.3 q^{25} -32422.8 q^{26} +19683.0 q^{27} -30262.5 q^{28} +148122. q^{29} +3406.17 q^{30} +91232.9 q^{31} -32768.0 q^{32} -170295. q^{33} -52801.9 q^{34} +7456.54 q^{35} +46656.0 q^{36} -241163. q^{37} -156135. q^{38} +109427. q^{39} +8073.88 q^{40} +315392. q^{41} +102136. q^{42} -285105. q^{43} -403662. q^{44} -11495.8 q^{45} -561746. q^{46} -120601. q^{47} +110592. q^{48} -599954. q^{49} +623011. q^{50} +178207. q^{51} +259382. q^{52} -174661. q^{53} -157464. q^{54} +99460.5 q^{55} +242100. q^{56} +526957. q^{57} -1.18498e6 q^{58} -205379. q^{59} -27249.3 q^{60} -2.80797e6 q^{61} -729863. q^{62} -344709. q^{63} +262144. q^{64} -63910.5 q^{65} +1.36236e6 q^{66} +4.23569e6 q^{67} +422416. q^{68} +1.89589e6 q^{69} -59652.3 q^{70} -4.68937e6 q^{71} -373248. q^{72} -4.25129e6 q^{73} +1.92931e6 q^{74} -2.10266e6 q^{75} +1.24908e6 q^{76} +2.98238e6 q^{77} -875415. q^{78} +4.14611e6 q^{79} -64591.0 q^{80} +531441. q^{81} -2.52313e6 q^{82} -6.08727e6 q^{83} -817087. q^{84} -104081. q^{85} +2.28084e6 q^{86} +3.99930e6 q^{87} +3.22930e6 q^{88} +3.19840e6 q^{89} +91966.5 q^{90} -1.91639e6 q^{91} +4.49397e6 q^{92} +2.46329e6 q^{93} +964811. q^{94} -307768. q^{95} -884736. q^{96} -2.79076e6 q^{97} +4.79964e6 q^{98} -4.59796e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9}+O(q^{10}) $ 7 * q - 56 * q^2 + 189 * q^3 + 448 * q^4 - 158 * q^5 - 1512 * q^6 - 581 * q^7 - 3584 * q^8 + 5103 * q^9	\( 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9} + 1264 q^{10} - 2201 q^{11} + 12096 q^{12} - 8421 q^{13} + 4648 q^{14} - 4266 q^{15} + 28672 q^{16} - 2425 q^{17} - 40824 q^{18} - 37084 q^{19} - 10112 q^{20} - 15687 q^{21} + 17608 q^{22} + 99364 q^{23} - 96768 q^{24} + 101361 q^{25} + 67368 q^{26} + 137781 q^{27} - 37184 q^{28} + 2498 q^{29} + 34128 q^{30} - 57962 q^{31} - 229376 q^{32} - 59427 q^{33} + 19400 q^{34} + 190586 q^{35} + 326592 q^{36} - 6497 q^{37} + 296672 q^{38} - 227367 q^{39} + 80896 q^{40} - 319165 q^{41} + 125496 q^{42} - 633743 q^{43} - 140864 q^{44} - 115182 q^{45} - 794912 q^{46} - 1626560 q^{47} + 774144 q^{48} - 3846354 q^{49} - 810888 q^{50} - 65475 q^{51} - 538944 q^{52} - 1215602 q^{53} - 1102248 q^{54} - 3329556 q^{55} + 297472 q^{56} - 1001268 q^{57} - 19984 q^{58} - 1437653 q^{59} - 273024 q^{60} - 3180086 q^{61} + 463696 q^{62} - 423549 q^{63} + 1835008 q^{64} + 544086 q^{65} + 475416 q^{66} - 5349632 q^{67} - 155200 q^{68} + 2682828 q^{69} - 1524688 q^{70} + 1752423 q^{71} - 2612736 q^{72} - 1843424 q^{73} + 51976 q^{74} + 2736747 q^{75} - 2373376 q^{76} - 3885063 q^{77} + 1818936 q^{78} - 4769243 q^{79} - 647168 q^{80} + 3720087 q^{81} + 2553320 q^{82} + 5154441 q^{83} - 1003968 q^{84} - 4594902 q^{85} + 5069944 q^{86} + 67446 q^{87} + 1126912 q^{88} + 20086462 q^{89} + 921456 q^{90} + 6733847 q^{91} + 6359296 q^{92} - 1564974 q^{93} + 13012480 q^{94} + 12936212 q^{95} - 6193152 q^{96} + 6244248 q^{97} + 30770832 q^{98} - 1604529 q^{99}+O(q^{100}) \) 7 * q - 56 * q^2 + 189 * q^3 + 448 * q^4 - 158 * q^5 - 1512 * q^6 - 581 * q^7 - 3584 * q^8 + 5103 * q^9 + 1264 * q^10 - 2201 * q^11 + 12096 * q^12 - 8421 * q^13 + 4648 * q^14 - 4266 * q^15 + 28672 * q^16 - 2425 * q^17 - 40824 * q^18 - 37084 * q^19 - 10112 * q^20 - 15687 * q^21 + 17608 * q^22 + 99364 * q^23 - 96768 * q^24 + 101361 * q^25 + 67368 * q^26 + 137781 * q^27 - 37184 * q^28 + 2498 * q^29 + 34128 * q^30 - 57962 * q^31 - 229376 * q^32 - 59427 * q^33 + 19400 * q^34 + 190586 * q^35 + 326592 * q^36 - 6497 * q^37 + 296672 * q^38 - 227367 * q^39 + 80896 * q^40 - 319165 * q^41 + 125496 * q^42 - 633743 * q^43 - 140864 * q^44 - 115182 * q^45 - 794912 * q^46 - 1626560 * q^47 + 774144 * q^48 - 3846354 * q^49 - 810888 * q^50 - 65475 * q^51 - 538944 * q^52 - 1215602 * q^53 - 1102248 * q^54 - 3329556 * q^55 + 297472 * q^56 - 1001268 * q^57 - 19984 * q^58 - 1437653 * q^59 - 273024 * q^60 - 3180086 * q^61 + 463696 * q^62 - 423549 * q^63 + 1835008 * q^64 + 544086 * q^65 + 475416 * q^66 - 5349632 * q^67 - 155200 * q^68 + 2682828 * q^69 - 1524688 * q^70 + 1752423 * q^71 - 2612736 * q^72 - 1843424 * q^73 + 51976 * q^74 + 2736747 * q^75 - 2373376 * q^76 - 3885063 * q^77 + 1818936 * q^78 - 4769243 * q^79 - 647168 * q^80 + 3720087 * q^81 + 2553320 * q^82 + 5154441 * q^83 - 1003968 * q^84 - 4594902 * q^85 + 5069944 * q^86 + 67446 * q^87 + 1126912 * q^88 + 20086462 * q^89 + 921456 * q^90 + 6733847 * q^91 + 6359296 * q^92 - 1564974 * q^93 + 13012480 * q^94 + 12936212 * q^95 - 6193152 * q^96 + 6244248 * q^97 + 30770832 * q^98 - 1604529 * 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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	64.0000	0.500000
$5$	−15.7693	−0.0564180	−0.0282090	−	0.999602i	$-0.508980\pi$
$5$	−15.7693	−0.0564180	−0.0282090	+	0.999602i	$0.508980\pi$
$6$	−216.000	−0.408248
$7$	−472.852	−0.521053	−0.260526	−	0.965467i	$-0.583896\pi$
$7$	−472.852	−0.521053	−0.260526	+	0.965467i	$0.583896\pi$
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	126.154	0.0398935
$11$	−6307.22	−1.42877	−0.714387	−	0.699751i	$-0.753294\pi$
$11$	−6307.22	−1.42877	−0.714387	+	0.699751i	$0.753294\pi$
$12$	1728.00	0.288675
$13$	4052.85	0.511633	0.255816	−	0.966725i	$-0.417656\pi$
$13$	4052.85	0.511633	0.255816	+	0.966725i	$0.417656\pi$
$14$	3782.81	0.368440
$15$	−425.771	−0.0325729
$16$	4096.00	0.250000
$17$	6600.24	0.325828	0.162914	−	0.986640i	$-0.447911\pi$
$17$	6600.24	0.325828	0.162914	+	0.986640i	$0.447911\pi$
$18$	−5832.00	−0.235702
$19$	19516.9	0.652791	0.326395	−	0.945233i	$-0.394166\pi$
$19$	19516.9	0.652791	0.326395	+	0.945233i	$0.394166\pi$
$20$	−1009.23	−0.0282090
$21$	−12767.0	−0.300830
$22$	50457.8	1.01030
$23$	70218.3	1.20338	0.601690	−	0.798730i	$-0.294494\pi$
$23$	70218.3	1.20338	0.601690	+	0.798730i	$0.294494\pi$
$24$	−13824.0	−0.204124
$25$	−77876.3	−0.996817
$26$	−32422.8	−0.361779
$27$	19683.0	0.192450
$28$	−30262.5	−0.260526
$29$	148122.	1.12779	0.563894	−	0.825847i	$-0.309303\pi$
$29$	148122.	1.12779	0.563894	+	0.825847i	$0.309303\pi$
$30$	3406.17	0.0230325
$31$	91232.9	0.550029	0.275014	−	0.961440i	$-0.411317\pi$
$31$	91232.9	0.550029	0.275014	+	0.961440i	$0.411317\pi$
$32$	−32768.0	−0.176777
$33$	−170295.	−0.824903
$34$	−52801.9	−0.230395
$35$	7456.54	0.0293967
$36$	46656.0	0.166667
$37$	−241163.	−0.782717	−0.391359	−	0.920238i	$-0.627995\pi$
$37$	−241163.	−0.782717	−0.391359	+	0.920238i	$0.627995\pi$
$38$	−156135.	−0.461593
$39$	109427.	0.295391
$40$	8073.88	0.0199468
$41$	315392.	0.714672	0.357336	−	0.933976i	$-0.383685\pi$
$41$	315392.	0.714672	0.357336	+	0.933976i	$0.383685\pi$
$42$	102136.	0.212719
$43$	−285105.	−0.546845	−0.273423	−	0.961894i	$-0.588156\pi$
$43$	−285105.	−0.546845	−0.273423	+	0.961894i	$0.588156\pi$
$44$	−403662.	−0.714387
$45$	−11495.8	−0.0188060
$46$	−561746.	−0.850918
$47$	−120601.	−0.169438	−0.0847188	−	0.996405i	$-0.526999\pi$
$47$	−120601.	−0.169438	−0.0847188	+	0.996405i	$0.526999\pi$
$48$	110592.	0.144338
$49$	−599954.	−0.728504
$50$	623011.	0.704856
$51$	178207.	0.188117
$52$	259382.	0.255816
$53$	−174661.	−0.161150	−0.0805749	−	0.996749i	$-0.525676\pi$
$53$	−174661.	−0.161150	−0.0805749	+	0.996749i	$0.525676\pi$
$54$	−157464.	−0.136083
$55$	99460.5	0.0806085
$56$	242100.	0.184220
$57$	526957.	0.376889
$58$	−1.18498e6	−0.797467
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−27249.3	−0.0162865
$61$	−2.80797e6	−1.58394	−0.791968	−	0.610563i	$-0.790943\pi$
$61$	−2.80797e6	−1.58394	−0.791968	+	0.610563i	$0.790943\pi$
$62$	−729863.	−0.388929
$63$	−344709.	−0.173684
$64$	262144.	0.125000
$65$	−63910.5	−0.0288653
$66$	1.36236e6	0.583295
$67$	4.23569e6	1.72053	0.860265	−	0.509847i	$-0.170298\pi$
$67$	4.23569e6	1.72053	0.860265	+	0.509847i	$0.170298\pi$
$68$	422416.	0.162914
$69$	1.89589e6	0.694772
$70$	−59652.3	−0.0207866
$71$	−4.68937e6	−1.55493	−0.777463	−	0.628928i	$-0.783494\pi$
$71$	−4.68937e6	−1.55493	−0.777463	+	0.628928i	$0.783494\pi$
$72$	−373248.	−0.117851
$73$	−4.25129e6	−1.27906	−0.639529	−	0.768767i	$-0.720871\pi$
$73$	−4.25129e6	−1.27906	−0.639529	+	0.768767i	$0.720871\pi$
$74$	1.92931e6	0.553465
$75$	−2.10266e6	−0.575513
$76$	1.24908e6	0.326395
$77$	2.98238e6	0.744467
$78$	−875415.	−0.208873
$79$	4.14611e6	0.946120	0.473060	−	0.881030i	$-0.343149\pi$
$79$	4.14611e6	0.946120	0.473060	+	0.881030i	$0.343149\pi$
$80$	−64591.0	−0.0141045
$81$	531441.	0.111111
$82$	−2.52313e6	−0.505349
$83$	−6.08727e6	−1.16855	−0.584277	−	0.811554i	$-0.698622\pi$
$83$	−6.08727e6	−1.16855	−0.584277	+	0.811554i	$0.698622\pi$
$84$	−817087.	−0.150415
$85$	−104081.	−0.0183826
$86$	2.28084e6	0.386678
$87$	3.99930e6	0.651129
$88$	3.22930e6	0.505148
$89$	3.19840e6	0.480914	0.240457	−	0.970660i	$-0.422703\pi$
$89$	3.19840e6	0.480914	0.240457	+	0.970660i	$0.422703\pi$
$90$	91966.5	0.0132978
$91$	−1.91639e6	−0.266588
$92$	4.49397e6	0.601690
$93$	2.46329e6	0.317559
$94$	964811.	0.119810
$95$	−307768.	−0.0368291
$96$	−884736.	−0.102062
$97$	−2.79076e6	−0.310472	−0.155236	−	0.987877i	$-0.549614\pi$
$97$	−2.79076e6	−0.310472	−0.155236	+	0.987877i	$0.549614\pi$
$98$	4.79964e6	0.515130
$99$	−4.59796e6	−0.476258
$100$	−4.98409e6	−0.498409
$101$	−1.07661e7	−1.03976	−0.519882	−	0.854238i	$-0.674024\pi$
$101$	−1.07661e7	−1.03976	−0.519882	+	0.854238i	$0.674024\pi$
$102$	−1.42565e6	−0.133019
$103$	3.75781e6	0.338848	0.169424	−	0.985543i	$-0.445809\pi$
$103$	3.75781e6	0.338848	0.169424	+	0.985543i	$0.445809\pi$
$104$	−2.07506e6	−0.180889
$105$	201326.	0.0169722
$106$	1.39729e6	0.113950
$107$	1.32015e6	0.104179	0.0520895	−	0.998642i	$-0.483412\pi$
$107$	1.32015e6	0.104179	0.0520895	+	0.998642i	$0.483412\pi$
$108$	1.25971e6	0.0962250
$109$	2.30887e7	1.70768	0.853842	−	0.520532i	$-0.174266\pi$
$109$	2.30887e7	1.70768	0.853842	+	0.520532i	$0.174266\pi$
$110$	−795684.	−0.0569988
$111$	−6.51141e6	−0.451902
$112$	−1.93680e6	−0.130263
$113$	2.77337e7	1.80815	0.904073	−	0.427378i	$-0.140563\pi$
$113$	2.77337e7	1.80815	0.904073	+	0.427378i	$0.140563\pi$
$114$	−4.21566e6	−0.266501
$115$	−1.10729e6	−0.0678922
$116$	9.47983e6	0.563894
$117$	2.95452e6	0.170544
$118$	1.64303e6	0.0920575
$119$	−3.12093e6	−0.169774
$120$	217995.	0.0115163
$121$	2.02939e7	1.04140
$122$	2.24637e7	1.12001
$123$	8.51557e6	0.412616
$124$	5.83890e6	0.275014
$125$	2.46003e6	0.112656
$126$	2.75767e6	0.122813
$127$	−3.89624e7	−1.68784	−0.843922	−	0.536465i	$-0.819759\pi$
$127$	−3.89624e7	−1.68784	−0.843922	+	0.536465i	$0.819759\pi$
$128$	−2.09715e6	−0.0883883
$129$	−7.69782e6	−0.315721
$130$	511284.	0.0204108
$131$	−2.94679e7	−1.14525	−0.572625	−	0.819818i	$-0.694075\pi$
$131$	−2.94679e7	−1.14525	−0.572625	+	0.819818i	$0.694075\pi$
$132$	−1.08989e7	−0.412452
$133$	−9.22861e6	−0.340138
$134$	−3.38855e7	−1.21660
$135$	−310387.	−0.0108576
$136$	−3.37932e6	−0.115198
$137$	−2.50620e7	−0.832708	−0.416354	−	0.909202i	$-0.636692\pi$
$137$	−2.50620e7	−0.832708	−0.416354	+	0.909202i	$0.636692\pi$
$138$	−1.51672e7	−0.491278
$139$	−4.73182e7	−1.49443	−0.747216	−	0.664581i	$-0.768610\pi$
$139$	−4.73182e7	−1.49443	−0.747216	+	0.664581i	$0.768610\pi$
$140$	477218.	0.0146984
$141$	−3.25624e6	−0.0978248
$142$	3.75149e7	1.09950
$143$	−2.55622e7	−0.731008
$144$	2.98598e6	0.0833333
$145$	−2.33579e6	−0.0636275
$146$	3.40103e7	0.904431
$147$	−1.61988e7	−0.420602
$148$	−1.54344e7	−0.391359
$149$	2.40779e7	0.596302	0.298151	−	0.954519i	$-0.403630\pi$
$149$	2.40779e7	0.596302	0.298151	+	0.954519i	$0.403630\pi$
$150$	1.68213e7	0.406949
$151$	−3.32051e7	−0.784847	−0.392423	−	0.919785i	$-0.628363\pi$
$151$	−3.32051e7	−0.784847	−0.392423	+	0.919785i	$0.628363\pi$
$152$	−9.99267e6	−0.230796
$153$	4.81158e6	0.108609
$154$	−2.38590e7	−0.526418
$155$	−1.43868e6	−0.0310315
$156$	7.00332e6	0.147696
$157$	−4.57004e7	−0.942478	−0.471239	−	0.882006i	$-0.656193\pi$
$157$	−4.57004e7	−0.942478	−0.471239	+	0.882006i	$0.656193\pi$
$158$	−3.31689e7	−0.669008
$159$	−4.71584e6	−0.0930399
$160$	516728.	0.00997338
$161$	−3.32028e7	−0.627025
$162$	−4.25153e6	−0.0785674
$163$	−5.99009e7	−1.08337	−0.541685	−	0.840582i	$-0.682213\pi$
$163$	−5.99009e7	−1.08337	−0.541685	+	0.840582i	$0.682213\pi$
$164$	2.01851e7	0.357336
$165$	2.68543e6	0.0465394
$166$	4.86982e7	0.826293
$167$	−2.91114e6	−0.0483677	−0.0241839	−	0.999708i	$-0.507699\pi$
$167$	−2.91114e6	−0.0483677	−0.0241839	+	0.999708i	$0.507699\pi$
$168$	6.53670e6	0.106359
$169$	−4.63230e7	−0.738232
$170$	832649.	0.0129984
$171$	1.42278e7	0.217597
$172$	−1.82467e7	−0.273423
$173$	9.23115e7	1.35548	0.677742	−	0.735300i	$-0.262959\pi$
$173$	9.23115e7	1.35548	0.677742	+	0.735300i	$0.262959\pi$
$174$	−3.19944e7	−0.460418
$175$	3.68239e7	0.519394
$176$	−2.58344e7	−0.357194
$177$	−5.54523e6	−0.0751646
$178$	−2.55872e7	−0.340058
$179$	−9.77014e6	−0.127325	−0.0636627	−	0.997971i	$-0.520278\pi$
$179$	−9.77014e6	−0.127325	−0.0636627	+	0.997971i	$0.520278\pi$
$180$	−735732.	−0.00940299
$181$	−1.44851e8	−1.81571	−0.907854	−	0.419287i	$-0.862280\pi$
$181$	−1.44851e8	−1.81571	−0.907854	+	0.419287i	$0.862280\pi$
$182$	1.53312e7	0.188506
$183$	−7.58151e7	−0.914486
$184$	−3.59518e7	−0.425459
$185$	3.80297e6	0.0441593
$186$	−1.97063e7	−0.224548
$187$	−4.16292e7	−0.465535
$188$	−7.71849e6	−0.0847188
$189$	−9.30714e6	−0.100277
$190$	2.46215e6	0.0260421
$191$	−3.79012e7	−0.393582	−0.196791	−	0.980445i	$-0.563052\pi$
$191$	−3.79012e7	−0.393582	−0.196791	+	0.980445i	$0.563052\pi$
$192$	7.07789e6	0.0721688
$193$	−1.85813e8	−1.86049	−0.930243	−	0.366944i	$-0.880404\pi$
$193$	−1.85813e8	−1.86049	−0.930243	+	0.366944i	$0.880404\pi$
$194$	2.23261e7	0.219537
$195$	−1.72558e6	−0.0166654
$196$	−3.83971e7	−0.364252
$197$	1.43118e8	1.33371	0.666855	−	0.745187i	$-0.267640\pi$
$197$	1.43118e8	1.33371	0.666855	+	0.745187i	$0.267640\pi$
$198$	3.67837e7	0.336765
$199$	−1.08564e8	−0.976567	−0.488283	−	0.872685i	$-0.662377\pi$
$199$	−1.08564e8	−0.976567	−0.488283	+	0.872685i	$0.662377\pi$
$200$	3.98727e7	0.352428
$201$	1.14364e8	0.993348
$202$	8.61290e7	0.735224
$203$	−7.00399e7	−0.587637
$204$	1.14052e7	0.0940585
$205$	−4.97350e6	−0.0403203
$206$	−3.00625e7	−0.239602
$207$	5.11891e7	0.401127
$208$	1.66005e7	0.127908
$209$	−1.23098e8	−0.932691
$210$	−1.61061e6	−0.0120012
$211$	−1.42252e7	−0.104248	−0.0521241	−	0.998641i	$-0.516599\pi$
$211$	−1.42252e7	−0.104248	−0.0521241	+	0.998641i	$0.516599\pi$
$212$	−1.11783e7	−0.0805749
$213$	−1.26613e8	−0.897737
$214$	−1.05612e7	−0.0736657
$215$	4.49590e6	0.0308519
$216$	−1.00777e7	−0.0680414
$217$	−4.31396e7	−0.286594
$218$	−1.84710e8	−1.20752
$219$	−1.14785e8	−0.738465
$220$	6.36547e6	0.0403043
$221$	2.67498e7	0.166704
$222$	5.20912e7	0.319543
$223$	−5.02942e7	−0.303704	−0.151852	−	0.988403i	$-0.548524\pi$
$223$	−5.02942e7	−0.303704	−0.151852	+	0.988403i	$0.548524\pi$
$224$	1.54944e7	0.0921100
$225$	−5.67718e7	−0.332272
$226$	−2.21870e8	−1.27855
$227$	−2.01975e8	−1.14606	−0.573031	−	0.819534i	$-0.694232\pi$
$227$	−2.01975e8	−1.14606	−0.573031	+	0.819534i	$0.694232\pi$
$228$	3.37253e7	0.188444
$229$	3.34059e7	0.183823	0.0919115	−	0.995767i	$-0.470702\pi$
$229$	3.34059e7	0.183823	0.0919115	+	0.995767i	$0.470702\pi$
$230$	8.85835e6	0.0480071
$231$	8.05243e7	0.429818
$232$	−7.58386e7	−0.398733
$233$	−2.78191e8	−1.44078	−0.720389	−	0.693570i	$-0.756037\pi$
$233$	−2.78191e8	−1.44078	−0.720389	+	0.693570i	$0.756037\pi$
$234$	−2.36362e7	−0.120593
$235$	1.90180e6	0.00955932
$236$	−1.31443e7	−0.0650945
$237$	1.11945e8	0.546243
$238$	2.49675e7	0.120048
$239$	2.99950e8	1.42121	0.710603	−	0.703594i	$-0.248422\pi$
$239$	2.99950e8	1.42121	0.710603	+	0.703594i	$0.248422\pi$
$240$	−1.74396e6	−0.00814323
$241$	−5.02495e7	−0.231245	−0.115622	−	0.993293i	$-0.536886\pi$
$241$	−5.02495e7	−0.231245	−0.115622	+	0.993293i	$0.536886\pi$
$242$	−1.62351e8	−0.736379
$243$	1.43489e7	0.0641500
$244$	−1.79710e8	−0.791968
$245$	9.46086e6	0.0411007
$246$	−6.81246e7	−0.291763
$247$	7.90991e7	0.333989
$248$	−4.67112e7	−0.194465
$249$	−1.64356e8	−0.674666
$250$	−1.96802e7	−0.0796601
$251$	−2.45389e8	−0.979482	−0.489741	−	0.871868i	$-0.662909\pi$
$251$	−2.45389e8	−0.979482	−0.489741	+	0.871868i	$0.662909\pi$
$252$	−2.20614e7	−0.0868421
$253$	−4.42882e8	−1.71936
$254$	3.11699e8	1.19349
$255$	−2.81019e6	−0.0106132
$256$	1.67772e7	0.0625000
$257$	−2.17239e8	−0.798310	−0.399155	−	0.916883i	$-0.630697\pi$
$257$	−2.17239e8	−0.798310	−0.399155	+	0.916883i	$0.630697\pi$
$258$	6.15826e7	0.223249
$259$	1.14034e8	0.407837
$260$	−4.09027e6	−0.0144326
$261$	1.07981e8	0.375929
$262$	2.35743e8	0.809813
$263$	−9.96330e7	−0.337721	−0.168860	−	0.985640i	$-0.554009\pi$
$263$	−9.96330e7	−0.337721	−0.168860	+	0.985640i	$0.554009\pi$
$264$	8.71910e7	0.291647
$265$	2.75428e6	0.00909174
$266$	7.38289e7	0.240514
$267$	8.63567e7	0.277656
$268$	2.71084e8	0.860265
$269$	1.41804e7	0.0444176	0.0222088	−	0.999753i	$-0.492930\pi$
$269$	1.41804e7	0.0444176	0.0222088	+	0.999753i	$0.492930\pi$
$270$	2.48310e6	0.00767751
$271$	6.04494e8	1.84501	0.922507	−	0.385980i	$-0.126136\pi$
$271$	6.04494e8	1.84501	0.922507	+	0.385980i	$0.126136\pi$
$272$	2.70346e7	0.0814570
$273$	−5.17426e7	−0.153914
$274$	2.00496e8	0.588814
$275$	4.91183e8	1.42423
$276$	1.21337e8	0.347386
$277$	3.02734e8	0.855818	0.427909	−	0.903822i	$-0.359250\pi$
$277$	3.02734e8	0.855818	0.427909	+	0.903822i	$0.359250\pi$
$278$	3.78546e8	1.05672
$279$	6.65088e7	0.183343
$280$	−3.81775e6	−0.0103933
$281$	5.71181e8	1.53568	0.767841	−	0.640640i	$-0.221331\pi$
$281$	5.71181e8	1.53568	0.767841	+	0.640640i	$0.221331\pi$
$282$	2.60499e7	0.0691726
$283$	−5.09970e8	−1.33750	−0.668748	−	0.743489i	$-0.733169\pi$
$283$	−5.09970e8	−1.33750	−0.668748	+	0.743489i	$0.733169\pi$
$284$	−3.00119e8	−0.777463
$285$	−8.30975e6	−0.0212633
$286$	2.04498e8	0.516901
$287$	−1.49133e8	−0.372382
$288$	−2.38879e7	−0.0589256
$289$	−3.66775e8	−0.893836
$290$	1.86863e7	0.0449914
$291$	−7.53506e7	−0.179251
$292$	−2.72082e8	−0.639529
$293$	−5.27986e8	−1.22627	−0.613135	−	0.789978i	$-0.710092\pi$
$293$	−5.27986e8	−1.22627	−0.613135	+	0.789978i	$0.710092\pi$
$294$	1.29590e8	0.297411
$295$	3.23868e6	0.00734499
$296$	1.23476e8	0.276732
$297$	−1.24145e8	−0.274968
$298$	−1.92623e8	−0.421649
$299$	2.84584e8	0.615689
$300$	−1.34570e8	−0.287756
$301$	1.34812e8	0.284935
$302$	2.65640e8	0.554970
$303$	−2.90685e8	−0.600308
$304$	7.99414e7	0.163198
$305$	4.42797e7	0.0893624
$306$	−3.84926e7	−0.0767984
$307$	−5.67764e8	−1.11991	−0.559956	−	0.828522i	$-0.689182\pi$
$307$	−5.67764e8	−1.11991	−0.559956	+	0.828522i	$0.689182\pi$
$308$	1.90872e8	0.372233
$309$	1.01461e8	0.195634
$310$	1.15094e7	0.0219426
$311$	8.28775e8	1.56234	0.781170	−	0.624319i	$-0.214623\pi$
$311$	8.28775e8	1.56234	0.781170	+	0.624319i	$0.214623\pi$
$312$	−5.60265e7	−0.104437
$313$	−1.48016e8	−0.272837	−0.136418	−	0.990651i	$-0.543559\pi$
$313$	−1.48016e8	−0.272837	−0.136418	+	0.990651i	$0.543559\pi$
$314$	3.65603e8	0.666433
$315$	5.43582e6	0.00979891
$316$	2.65351e8	0.473060
$317$	−2.18062e8	−0.384478	−0.192239	−	0.981348i	$-0.561575\pi$
$317$	−2.18062e8	−0.384478	−0.192239	+	0.981348i	$0.561575\pi$
$318$	3.77267e7	0.0657891
$319$	−9.34241e8	−1.61136
$320$	−4.13383e6	−0.00705224
$321$	3.56441e7	0.0601478
$322$	2.65623e8	0.443373
$323$	1.28817e8	0.212698
$324$	3.40122e7	0.0555556
$325$	−3.15621e8	−0.510004
$326$	4.79207e8	0.766058
$327$	6.23396e8	0.985932
$328$	−1.61480e8	−0.252675
$329$	5.70265e7	0.0882859
$330$	−2.14835e7	−0.0329083
$331$	1.40448e8	0.212871	0.106436	−	0.994320i	$-0.466056\pi$
$331$	1.40448e8	0.212871	0.106436	+	0.994320i	$0.466056\pi$
$332$	−3.89585e8	−0.584277
$333$	−1.75808e8	−0.260906
$334$	2.32891e7	0.0342012
$335$	−6.67938e7	−0.0970688
$336$	−5.22936e7	−0.0752075
$337$	1.09586e9	1.55974	0.779869	−	0.625943i	$-0.215286\pi$
$337$	1.09586e9	1.55974	0.779869	+	0.625943i	$0.215286\pi$
$338$	3.70584e8	0.522009
$339$	7.48810e8	1.04393
$340$	−6.66120e6	−0.00919128
$341$	−5.75426e8	−0.785867
$342$	−1.13823e8	−0.153864
$343$	6.73103e8	0.900642
$344$	1.45974e8	0.193339
$345$	−2.98969e7	−0.0391976
$346$	−7.38492e8	−0.958472
$347$	−1.75535e8	−0.225533	−0.112767	−	0.993622i	$-0.535971\pi$
$347$	−1.75535e8	−0.225533	−0.112767	+	0.993622i	$0.535971\pi$
$348$	2.55955e8	0.325564
$349$	5.45220e8	0.686567	0.343284	−	0.939232i	$-0.388461\pi$
$349$	5.45220e8	0.686567	0.343284	+	0.939232i	$0.388461\pi$
$350$	−2.94592e8	−0.367267
$351$	7.97722e7	0.0984638
$352$	2.06675e8	0.252574
$353$	1.34805e9	1.63116	0.815578	−	0.578647i	$-0.196419\pi$
$353$	1.34805e9	1.63116	0.815578	+	0.578647i	$0.196419\pi$
$354$	4.43619e7	0.0531494
$355$	7.39480e7	0.0877258
$356$	2.04697e8	0.240457
$357$	−8.42652e7	−0.0980189
$358$	7.81611e7	0.0900326
$359$	−6.27049e8	−0.715271	−0.357636	−	0.933861i	$-0.616417\pi$
$359$	−6.27049e8	−0.715271	−0.357636	+	0.933861i	$0.616417\pi$
$360$	5.88586e6	0.00664892
$361$	−5.12961e8	−0.573864
$362$	1.15881e9	1.28390
$363$	5.47935e8	0.601251
$364$	−1.22649e8	−0.133294
$365$	6.70398e7	0.0721619
$366$	6.06521e8	0.646639
$367$	−1.66024e9	−1.75323	−0.876614	−	0.481194i	$-0.840203\pi$
$367$	−1.66024e9	−1.75323	−0.876614	+	0.481194i	$0.840203\pi$
$368$	2.87614e8	0.300845
$369$	2.29920e8	0.238224
$370$	−3.04238e7	−0.0312253
$371$	8.25886e7	0.0839675
$372$	1.57650e8	0.158780
$373$	−6.86864e8	−0.685315	−0.342657	−	0.939460i	$-0.611327\pi$
$373$	−6.86864e8	−0.685315	−0.342657	+	0.939460i	$0.611327\pi$
$374$	3.33034e8	0.329183
$375$	6.64208e7	0.0650422
$376$	6.17479e7	0.0599052
$377$	6.00317e8	0.577013
$378$	7.44571e7	0.0709063
$379$	1.77823e9	1.67784	0.838922	−	0.544251i	$-0.183186\pi$
$379$	1.77823e9	1.67784	0.838922	+	0.544251i	$0.183186\pi$
$380$	−1.96972e7	−0.0184146
$381$	−1.05198e9	−0.974478
$382$	3.03209e8	0.278305
$383$	−6.09943e8	−0.554745	−0.277372	−	0.960762i	$-0.589464\pi$
$383$	−6.09943e8	−0.554745	−0.277372	+	0.960762i	$0.589464\pi$
$384$	−5.66231e7	−0.0510310
$385$	−4.70300e7	−0.0420013
$386$	1.48651e9	1.31556
$387$	−2.07841e8	−0.182282
$388$	−1.78609e8	−0.155236
$389$	2.12855e9	1.83341	0.916707	−	0.399560i	$-0.130837\pi$
$389$	2.12855e9	1.83341	0.916707	+	0.399560i	$0.130837\pi$
$390$	1.38047e7	0.0117842
$391$	4.63458e8	0.392095
$392$	3.07177e8	0.257565
$393$	−7.95634e8	−0.661210
$394$	−1.14494e9	−0.943076
$395$	−6.53813e7	−0.0533781
$396$	−2.94270e8	−0.238129
$397$	2.12397e9	1.70366	0.851828	−	0.523821i	$-0.175494\pi$
$397$	2.12397e9	1.70366	0.851828	+	0.523821i	$0.175494\pi$
$398$	8.68516e8	0.690537
$399$	−2.49173e8	−0.196379
$400$	−3.18981e8	−0.249204
$401$	4.91592e8	0.380715	0.190357	−	0.981715i	$-0.439035\pi$
$401$	4.91592e8	0.380715	0.190357	+	0.981715i	$0.439035\pi$
$402$	−9.14909e8	−0.702403
$403$	3.69753e8	0.281413
$404$	−6.89032e8	−0.519882
$405$	−8.38045e6	−0.00626866
$406$	5.60319e8	0.415522
$407$	1.52107e9	1.11833
$408$	−9.12418e7	−0.0665094
$409$	−1.15110e9	−0.831923	−0.415961	−	0.909382i	$-0.636555\pi$
$409$	−1.15110e9	−0.831923	−0.415961	+	0.909382i	$0.636555\pi$
$410$	3.97880e7	0.0285108
$411$	−6.76673e8	−0.480764
$412$	2.40500e8	0.169424
$413$	9.71138e7	0.0678353
$414$	−4.09513e8	−0.283639
$415$	9.59919e7	0.0659275
$416$	−1.32804e8	−0.0904447
$417$	−1.27759e9	−0.862811
$418$	9.84781e8	0.659512
$419$	−1.27903e7	−0.00849437	−0.00424719	−	0.999991i	$-0.501352\pi$
$419$	−1.27903e7	−0.00849437	−0.00424719	+	0.999991i	$0.501352\pi$
$420$	1.28849e7	0.00848610
$421$	−9.10826e8	−0.594906	−0.297453	−	0.954737i	$-0.596137\pi$
$421$	−9.10826e8	−0.594906	−0.297453	+	0.954737i	$0.596137\pi$
$422$	1.13801e8	0.0737146
$423$	−8.79184e7	−0.0564792
$424$	8.94263e7	0.0569751
$425$	−5.14003e8	−0.324791
$426$	1.01290e9	0.634796
$427$	1.32775e9	0.825314
$428$	8.44897e7	0.0520895
$429$	−6.90179e8	−0.422048
$430$	−3.59672e7	−0.0218156
$431$	−9.57906e8	−0.576305	−0.288153	−	0.957585i	$-0.593041\pi$
$431$	−9.57906e8	−0.576305	−0.288153	+	0.957585i	$0.593041\pi$
$432$	8.06216e7	0.0481125
$433$	−1.59685e9	−0.945271	−0.472636	−	0.881258i	$-0.656697\pi$
$433$	−1.59685e9	−0.945271	−0.472636	+	0.881258i	$0.656697\pi$
$434$	3.45117e8	0.202653
$435$	−6.30662e7	−0.0367354
$436$	1.47768e9	0.853842
$437$	1.37045e9	0.785556
$438$	9.18278e8	0.522174
$439$	−2.08513e9	−1.17627	−0.588134	−	0.808763i	$-0.700137\pi$
$439$	−2.08513e9	−1.17627	−0.588134	+	0.808763i	$0.700137\pi$
$440$	−5.09238e7	−0.0284994
$441$	−4.37367e8	−0.242835
$442$	−2.13998e8	−0.117878
$443$	−1.14935e9	−0.628117	−0.314058	−	0.949404i	$-0.601689\pi$
$443$	−1.14935e9	−0.628117	−0.314058	+	0.949404i	$0.601689\pi$
$444$	−4.16730e8	−0.225951
$445$	−5.04365e7	−0.0271322
$446$	4.02353e8	0.214751
$447$	6.50102e8	0.344275
$448$	−1.23955e8	−0.0651316
$449$	−2.97757e9	−1.55239	−0.776194	−	0.630494i	$-0.782852\pi$
$449$	−2.97757e9	−1.55239	−0.776194	+	0.630494i	$0.782852\pi$
$450$	4.54175e8	0.234952
$451$	−1.98924e9	−1.02110
$452$	1.77496e9	0.904073
$453$	−8.96536e8	−0.453131
$454$	1.61580e9	0.810388
$455$	3.02202e7	0.0150403
$456$	−2.69802e8	−0.133250
$457$	−2.70358e9	−1.32505	−0.662525	−	0.749040i	$-0.730515\pi$
$457$	−2.70358e9	−1.32505	−0.662525	+	0.749040i	$0.730515\pi$
$458$	−2.67248e8	−0.129982
$459$	1.29913e8	0.0627057
$460$	−7.08668e7	−0.0339461
$461$	2.76446e8	0.131419	0.0657093	−	0.997839i	$-0.479069\pi$
$461$	2.76446e8	0.131419	0.0657093	+	0.997839i	$0.479069\pi$
$462$	−6.44194e8	−0.303927
$463$	5.13533e8	0.240456	0.120228	−	0.992746i	$-0.461638\pi$
$463$	5.13533e8	0.240456	0.120228	+	0.992746i	$0.461638\pi$
$464$	6.06709e8	0.281947
$465$	−3.88443e7	−0.0179160
$466$	2.22553e9	1.01878
$467$	4.17528e9	1.89704	0.948520	−	0.316719i	$-0.102581\pi$
$467$	4.17528e9	1.89704	0.948520	+	0.316719i	$0.102581\pi$
$468$	1.89090e8	0.0852721
$469$	−2.00285e9	−0.896487
$470$	−1.52144e7	−0.00675946
$471$	−1.23391e9	−0.544140
$472$	1.05154e8	0.0460287
$473$	1.79822e9	0.781319
$474$	−8.95560e8	−0.386252
$475$	−1.51991e9	−0.650713
$476$	−1.99740e8	−0.0848868
$477$	−1.27328e8	−0.0537166
$478$	−2.39960e9	−1.00494
$479$	−1.58479e9	−0.658868	−0.329434	−	0.944179i	$-0.606858\pi$
$479$	−1.58479e9	−0.658868	−0.329434	+	0.944179i	$0.606858\pi$
$480$	1.39517e7	0.00575813
$481$	−9.77397e8	−0.400464
$482$	4.01996e8	0.163515
$483$	−8.96476e8	−0.362013
$484$	1.29881e9	0.520698
$485$	4.40084e7	0.0175162
$486$	−1.14791e8	−0.0453609
$487$	−9.40984e8	−0.369174	−0.184587	−	0.982816i	$-0.559095\pi$
$487$	−9.40984e8	−0.369174	−0.184587	+	0.982816i	$0.559095\pi$
$488$	1.43768e9	0.560006
$489$	−1.61732e9	−0.625484
$490$	−7.56869e7	−0.0290626
$491$	5.11490e8	0.195008	0.0975038	−	0.995235i	$-0.468914\pi$
$491$	5.11490e8	0.195008	0.0975038	+	0.995235i	$0.468914\pi$
$492$	5.44997e8	0.206308
$493$	9.77643e8	0.367465
$494$	−6.32793e8	−0.236166
$495$	7.25067e7	0.0268695
$496$	3.73690e8	0.137507
$497$	2.21737e9	0.810199
$498$	1.31485e9	0.477061
$499$	1.99424e9	0.718500	0.359250	−	0.933241i	$-0.383033\pi$
$499$	1.99424e9	0.718500	0.359250	+	0.933241i	$0.383033\pi$
$500$	1.57442e8	0.0563282
$501$	−7.86008e7	−0.0279251
$502$	1.96311e9	0.692598
$503$	−3.24980e7	−0.0113859	−0.00569296	−	0.999984i	$-0.501812\pi$
$503$	−3.24980e7	−0.0113859	−0.00569296	+	0.999984i	$0.501812\pi$
$504$	1.76491e8	0.0614067
$505$	1.69774e8	0.0586613
$506$	3.54306e9	1.21577
$507$	−1.25072e9	−0.426218
$508$	−2.49359e9	−0.843922
$509$	−6.09116e8	−0.204733	−0.102366	−	0.994747i	$-0.532641\pi$
$509$	−6.09116e8	−0.204733	−0.102366	+	0.994747i	$0.532641\pi$
$510$	2.24815e7	0.00750465
$511$	2.01023e9	0.666457
$512$	−1.34218e8	−0.0441942
$513$	3.84152e8	0.125630
$514$	1.73791e9	0.564491
$515$	−5.92581e7	−0.0191171
$516$	−4.92661e8	−0.157861
$517$	7.60660e8	0.242088
$518$	−9.12275e8	−0.288384
$519$	2.49241e9	0.782589
$520$	3.27222e7	0.0102054
$521$	7.38409e7	0.0228752	0.0114376	−	0.999935i	$-0.496359\pi$
$521$	7.38409e7	0.0228752	0.0114376	+	0.999935i	$0.496359\pi$
$522$	−8.63850e8	−0.265822
$523$	−3.35490e9	−1.02547	−0.512735	−	0.858547i	$-0.671368\pi$
$523$	−3.35490e9	−1.02547	−0.512735	+	0.858547i	$0.671368\pi$
$524$	−1.88595e9	−0.572625
$525$	9.94246e8	0.299872
$526$	7.97064e8	0.238805
$527$	6.02159e8	0.179215
$528$	−6.97528e8	−0.206226
$529$	1.52578e9	0.448124
$530$	−2.20342e7	−0.00642883
$531$	−1.49721e8	−0.0433963
$532$	−5.90631e8	−0.170069
$533$	1.27823e9	0.365649
$534$	−6.90854e8	−0.196332
$535$	−2.08179e7	−0.00587757
$536$	−2.16867e9	−0.608299
$537$	−2.63794e8	−0.0735113
$538$	−1.13443e8	−0.0314080
$539$	3.78405e9	1.04087
$540$	−1.98648e7	−0.00542882
$541$	−1.70701e9	−0.463494	−0.231747	−	0.972776i	$-0.574444\pi$
$541$	−1.70701e9	−0.463494	−0.231747	+	0.972776i	$0.574444\pi$
$542$	−4.83596e9	−1.30462
$543$	−3.91097e9	−1.04830
$544$	−2.16277e8	−0.0575988
$545$	−3.64093e8	−0.0963440
$546$	4.13941e8	0.108834
$547$	2.36938e9	0.618983	0.309492	−	0.950902i	$-0.399841\pi$
$547$	2.36938e9	0.618983	0.309492	+	0.950902i	$0.399841\pi$
$548$	−1.60397e9	−0.416354
$549$	−2.04701e9	−0.527979
$550$	−3.92947e9	−1.00708
$551$	2.89089e9	0.736210
$552$	−9.70698e8	−0.245639
$553$	−1.96050e9	−0.492978
$554$	−2.42187e9	−0.605155
$555$	1.02680e8	0.0254954
$556$	−3.02836e9	−0.747216
$557$	4.90835e9	1.20349	0.601744	−	0.798689i	$-0.294473\pi$
$557$	4.90835e9	1.20349	0.601744	+	0.798689i	$0.294473\pi$
$558$	−5.32070e8	−0.129643
$559$	−1.15548e9	−0.279784
$560$	3.05420e7	0.00734918
$561$	−1.12399e9	−0.268777
$562$	−4.56944e9	−1.08589
$563$	2.56618e9	0.606050	0.303025	−	0.952983i	$-0.402003\pi$
$563$	2.56618e9	0.606050	0.303025	+	0.952983i	$0.402003\pi$
$564$	−2.08399e8	−0.0489124
$565$	−4.37341e8	−0.102012
$566$	4.07976e9	0.945752
$567$	−2.51293e8	−0.0578947
$568$	2.40096e9	0.549750
$569$	−3.07860e9	−0.700583	−0.350292	−	0.936641i	$-0.613918\pi$
$569$	−3.07860e9	−0.700583	−0.350292	+	0.936641i	$0.613918\pi$
$570$	6.64780e7	0.0150354
$571$	−7.28186e9	−1.63688	−0.818439	−	0.574594i	$-0.805160\pi$
$571$	−7.28186e9	−1.63688	−0.818439	+	0.574594i	$0.805160\pi$
$572$	−1.63598e9	−0.365504
$573$	−1.02333e9	−0.227235
$574$	1.19307e9	0.263314
$575$	−5.46834e9	−1.19955
$576$	1.91103e8	0.0416667
$577$	8.63423e9	1.87115	0.935575	−	0.353129i	$-0.114882\pi$
$577$	8.63423e9	1.87115	0.935575	+	0.353129i	$0.114882\pi$
$578$	2.93420e9	0.632037
$579$	−5.01696e9	−1.07415
$580$	−1.49490e8	−0.0318138
$581$	2.87837e9	0.608879
$582$	6.02805e8	0.126749
$583$	1.10162e9	0.230247
$584$	2.17666e9	0.452216
$585$	−4.65908e7	−0.00962176
$586$	4.22389e9	0.867103
$587$	−7.46765e8	−0.152388	−0.0761939	−	0.997093i	$-0.524277\pi$
$587$	−7.46765e8	−0.152388	−0.0761939	+	0.997093i	$0.524277\pi$
$588$	−1.03672e9	−0.210301
$589$	1.78059e9	0.359054
$590$	−2.59095e7	−0.00519369
$591$	3.86418e9	0.770018
$592$	−9.87804e8	−0.195679
$593$	3.86581e9	0.761288	0.380644	−	0.924722i	$-0.375702\pi$
$593$	3.86581e9	0.761288	0.380644	+	0.924722i	$0.375702\pi$
$594$	9.93160e8	0.194432
$595$	4.92149e7	0.00957828
$596$	1.54098e9	0.298151
$597$	−2.93124e9	−0.563821
$598$	−2.27667e9	−0.435358
$599$	−2.24145e9	−0.426124	−0.213062	−	0.977039i	$-0.568344\pi$
$599$	−2.24145e9	−0.426124	−0.213062	+	0.977039i	$0.568344\pi$
$600$	1.07656e9	0.203474
$601$	5.53232e9	1.03955	0.519776	−	0.854302i	$-0.326015\pi$
$601$	5.53232e9	1.03955	0.519776	+	0.854302i	$0.326015\pi$
$602$	−1.07850e9	−0.201480
$603$	3.08782e9	0.573510
$604$	−2.12512e9	−0.392423
$605$	−3.20020e8	−0.0587535
$606$	2.32548e9	0.424482
$607$	6.45747e9	1.17193	0.585965	−	0.810336i	$-0.300716\pi$
$607$	6.45747e9	1.17193	0.585965	+	0.810336i	$0.300716\pi$
$608$	−6.39531e8	−0.115398
$609$	−1.89108e9	−0.339273
$610$	−3.54237e8	−0.0631888
$611$	−4.88779e8	−0.0866898
$612$	3.07941e8	0.0543047
$613$	−4.51411e9	−0.791518	−0.395759	−	0.918354i	$-0.629518\pi$
$613$	−4.51411e9	−0.791518	−0.395759	+	0.918354i	$0.629518\pi$
$614$	4.54212e9	0.791897
$615$	−1.34285e8	−0.0232789
$616$	−1.52698e9	−0.263209
$617$	−3.44760e8	−0.0590906	−0.0295453	−	0.999563i	$-0.509406\pi$
$617$	−3.44760e8	−0.0590906	−0.0295453	+	0.999563i	$0.509406\pi$
$618$	−8.11688e8	−0.138334
$619$	−9.76452e8	−0.165476	−0.0827378	−	0.996571i	$-0.526366\pi$
$619$	−9.76452e8	−0.165476	−0.0827378	+	0.996571i	$0.526366\pi$
$620$	−9.20754e7	−0.0155157
$621$	1.38211e9	0.231591
$622$	−6.63020e9	−1.10474
$623$	−1.51237e9	−0.250582
$624$	4.48212e8	0.0738478
$625$	6.04530e9	0.990461
$626$	1.18413e9	0.192925
$627$	−3.32364e9	−0.538489
$628$	−2.92483e9	−0.471239
$629$	−1.59174e9	−0.255031
$630$	−4.34865e7	−0.00692888
$631$	−6.68861e9	−1.05982	−0.529911	−	0.848053i	$-0.677775\pi$
$631$	−6.68861e9	−1.05982	−0.529911	+	0.848053i	$0.677775\pi$
$632$	−2.12281e9	−0.334504
$633$	−3.84079e8	−0.0601877
$634$	1.74449e9	0.271867
$635$	6.14409e8	0.0952248
$636$	−3.01814e8	−0.0465199
$637$	−2.43152e9	−0.372727
$638$	7.47392e9	1.13940
$639$	−3.41855e9	−0.518309
$640$	3.30706e7	0.00498669
$641$	−9.99748e9	−1.49930	−0.749648	−	0.661836i	$-0.769777\pi$
$641$	−9.99748e9	−1.49930	−0.749648	+	0.661836i	$0.769777\pi$
$642$	−2.85153e8	−0.0425309
$643$	5.11669e9	0.759015	0.379508	−	0.925189i	$-0.376093\pi$
$643$	5.11669e9	0.759015	0.379508	+	0.925189i	$0.376093\pi$
$644$	−2.12498e9	−0.313512
$645$	1.21389e8	0.0178124
$646$	−1.03053e9	−0.150400
$647$	−3.21503e9	−0.466681	−0.233340	−	0.972395i	$-0.574966\pi$
$647$	−3.21503e9	−0.466681	−0.233340	+	0.972395i	$0.574966\pi$
$648$	−2.72098e8	−0.0392837
$649$	1.29537e9	0.186011
$650$	2.52497e9	0.360627
$651$	−1.16477e9	−0.165465
$652$	−3.83366e9	−0.541685
$653$	−4.18978e8	−0.0588837	−0.0294418	−	0.999566i	$-0.509373\pi$
$653$	−4.18978e8	−0.0588837	−0.0294418	+	0.999566i	$0.509373\pi$
$654$	−4.98717e9	−0.697159
$655$	4.64688e8	0.0646126
$656$	1.29184e9	0.178668
$657$	−3.09919e9	−0.426353
$658$	−4.56212e8	−0.0624276
$659$	6.47408e9	0.881209	0.440605	−	0.897701i	$-0.354764\pi$
$659$	6.47408e9	0.881209	0.440605	+	0.897701i	$0.354764\pi$
$660$	1.71868e8	0.0232697
$661$	−2.86345e8	−0.0385642	−0.0192821	−	0.999814i	$-0.506138\pi$
$661$	−2.86345e8	−0.0385642	−0.0192821	+	0.999814i	$0.506138\pi$
$662$	−1.12358e9	−0.150523
$663$	7.22244e8	0.0962468
$664$	3.11668e9	0.413147
$665$	1.45529e8	0.0191899
$666$	1.40646e9	0.184488
$667$	1.04009e10	1.35716
$668$	−1.86313e8	−0.0241839
$669$	−1.35794e9	−0.175344
$670$	5.34351e8	0.0686380
$671$	1.77105e10	2.26309
$672$	4.18349e8	0.0531797
$673$	−1.05188e10	−1.33019	−0.665095	−	0.746759i	$-0.731609\pi$
$673$	−1.05188e10	−1.33019	−0.665095	+	0.746759i	$0.731609\pi$
$674$	−8.76691e9	−1.10290
$675$	−1.53284e9	−0.191838
$676$	−2.96467e9	−0.369116
$677$	−3.65829e9	−0.453125	−0.226562	−	0.973997i	$-0.572749\pi$
$677$	−3.65829e9	−0.453125	−0.226562	+	0.973997i	$0.572749\pi$
$678$	−5.99048e9	−0.738173
$679$	1.31962e9	0.161772
$680$	5.32896e7	0.00649922
$681$	−5.45334e9	−0.661679
$682$	4.60341e9	0.555692
$683$	−1.13117e10	−1.35848	−0.679241	−	0.733916i	$-0.737691\pi$
$683$	−1.13117e10	−1.35848	−0.679241	+	0.733916i	$0.737691\pi$
$684$	9.10582e8	0.108798
$685$	3.95209e8	0.0469797
$686$	−5.38482e9	−0.636850
$687$	9.01961e8	0.106130
$688$	−1.16779e9	−0.136711
$689$	−7.07873e8	−0.0824495
$690$	2.39175e8	0.0277169
$691$	5.56257e9	0.641361	0.320680	−	0.947187i	$-0.396088\pi$
$691$	5.56257e9	0.641361	0.320680	+	0.947187i	$0.396088\pi$
$692$	5.90794e9	0.677742
$693$	2.17415e9	0.248156
$694$	1.40428e9	0.159476
$695$	7.46175e8	0.0843128
$696$	−2.04764e9	−0.230209
$697$	2.08166e9	0.232860
$698$	−4.36176e9	−0.485476
$699$	−7.51115e9	−0.831834
$700$	2.35673e9	0.259697
$701$	−7.81131e8	−0.0856468	−0.0428234	−	0.999083i	$-0.513635\pi$
$701$	−7.81131e8	−0.0856468	−0.0428234	+	0.999083i	$0.513635\pi$
$702$	−6.38177e8	−0.0696244
$703$	−4.70677e9	−0.510951
$704$	−1.65340e9	−0.178597
$705$	5.13486e7	0.00551908
$706$	−1.07844e10	−1.15340
$707$	5.09078e9	0.541771
$708$	−3.54895e8	−0.0375823
$709$	2.47802e9	0.261122	0.130561	−	0.991440i	$-0.458322\pi$
$709$	2.47802e9	0.261122	0.130561	+	0.991440i	$0.458322\pi$
$710$	−5.91584e8	−0.0620315
$711$	3.02252e9	0.315373
$712$	−1.63758e9	−0.170029
$713$	6.40622e9	0.661894
$714$	6.74122e8	0.0693098
$715$	4.03098e8	0.0412420
$716$	−6.25289e8	−0.0636627
$717$	8.09866e9	0.820533
$718$	5.01639e9	0.505773
$719$	−3.30612e8	−0.0331717	−0.0165858	−	0.999862i	$-0.505280\pi$
$719$	−3.30612e8	−0.0331717	−0.0165858	+	0.999862i	$0.505280\pi$
$720$	−4.70869e7	−0.00470150
$721$	−1.77689e9	−0.176558
$722$	4.10369e9	0.405783
$723$	−1.35674e9	−0.133509
$724$	−9.27045e9	−0.907854
$725$	−1.15352e10	−1.12420
$726$	−4.38348e9	−0.425148
$727$	−1.14138e9	−0.110169	−0.0550844	−	0.998482i	$-0.517543\pi$
$727$	−1.14138e9	−0.110169	−0.0550844	+	0.998482i	$0.517543\pi$
$728$	9.81194e8	0.0942530
$729$	3.87420e8	0.0370370
$730$	−5.36319e8	−0.0510262
$731$	−1.88176e9	−0.178178
$732$	−4.85217e9	−0.457243
$733$	−2.19466e9	−0.205828	−0.102914	−	0.994690i	$-0.532817\pi$
$733$	−2.19466e9	−0.205828	−0.102914	+	0.994690i	$0.532817\pi$
$734$	1.32819e10	1.23972
$735$	2.55443e8	0.0237295
$736$	−2.30091e9	−0.212730
$737$	−2.67154e10	−2.45825
$738$	−1.83936e9	−0.168450
$739$	−6.33410e9	−0.577337	−0.288669	−	0.957429i	$-0.593213\pi$
$739$	−6.33410e9	−0.577337	−0.288669	+	0.957429i	$0.593213\pi$
$740$	2.43390e8	0.0220797
$741$	2.13568e9	0.192829
$742$	−6.60709e8	−0.0593740
$743$	−2.20542e9	−0.197256	−0.0986280	−	0.995124i	$-0.531445\pi$
$743$	−2.20542e9	−0.197256	−0.0986280	+	0.995124i	$0.531445\pi$
$744$	−1.26120e9	−0.112274
$745$	−3.79691e8	−0.0336421
$746$	5.49491e9	0.484591
$747$	−4.43762e9	−0.389518
$748$	−2.66427e9	−0.232768
$749$	−6.24236e8	−0.0542828
$750$	−5.31367e8	−0.0459918
$751$	1.44573e10	1.24551	0.622753	−	0.782418i	$-0.286014\pi$
$751$	1.44573e10	1.24551	0.622753	+	0.782418i	$0.286014\pi$
$752$	−4.93983e8	−0.0423594
$753$	−6.62549e9	−0.565504
$754$	−4.80254e9	−0.408010
$755$	5.23620e8	0.0442794
$756$	−5.95657e8	−0.0501383
$757$	−1.22591e9	−0.102713	−0.0513563	−	0.998680i	$-0.516354\pi$
$757$	−1.22591e9	−0.102713	−0.0513563	+	0.998680i	$0.516354\pi$
$758$	−1.42259e10	−1.18642
$759$	−1.19578e10	−0.992672
$760$	1.57577e8	0.0130211
$761$	1.40724e10	1.15750	0.578752	−	0.815503i	$-0.303540\pi$
$761$	1.40724e10	1.15750	0.578752	+	0.815503i	$0.303540\pi$
$762$	8.41588e9	0.689060
$763$	−1.09175e10	−0.889794
$764$	−2.42567e9	−0.196791
$765$	−7.58752e7	−0.00612752
$766$	4.87954e9	0.392264
$767$	−8.32369e8	−0.0666089
$768$	4.52985e8	0.0360844
$769$	1.53138e10	1.21434	0.607172	−	0.794570i	$-0.292304\pi$
$769$	1.53138e10	1.21434	0.607172	+	0.794570i	$0.292304\pi$
$770$	3.76240e8	0.0296994
$771$	−5.86545e9	−0.460905
$772$	−1.18921e10	−0.930243
$773$	1.43334e10	1.11615	0.558073	−	0.829792i	$-0.311541\pi$
$773$	1.43334e10	1.11615	0.558073	+	0.829792i	$0.311541\pi$
$774$	1.66273e9	0.128893
$775$	−7.10488e9	−0.548278
$776$	1.42887e9	0.109768
$777$	3.07893e9	0.235465
$778$	−1.70284e10	−1.29642
$779$	6.15548e9	0.466531
$780$	−1.10437e8	−0.00833269
$781$	2.95769e10	2.22164
$782$	−3.70766e9	−0.277253
$783$	2.91549e9	0.217043
$784$	−2.45741e9	−0.182126
$785$	7.20663e8	0.0531727
$786$	6.36507e9	0.467546
$787$	−1.10112e10	−0.805237	−0.402619	−	0.915368i	$-0.631900\pi$
$787$	−1.10112e10	−0.805237	−0.402619	+	0.915368i	$0.631900\pi$
$788$	9.15953e9	0.666855
$789$	−2.69009e9	−0.194983
$790$	5.23050e8	0.0377440
$791$	−1.31139e10	−0.942139
$792$	2.35416e9	0.168383
$793$	−1.13803e10	−0.810393
$794$	−1.69918e10	−1.20467
$795$	7.43655e7	0.00524912
$796$	−6.94813e9	−0.488283
$797$	2.31380e10	1.61891	0.809454	−	0.587184i	$-0.199763\pi$
$797$	2.31380e10	1.61891	0.809454	+	0.587184i	$0.199763\pi$
$798$	1.99338e9	0.138861
$799$	−7.95998e8	−0.0552075
$800$	2.55185e9	0.176214
$801$	2.33163e9	0.160305
$802$	−3.93274e9	−0.269206
$803$	2.68138e10	1.82749
$804$	7.31927e9	0.496674
$805$	5.23585e8	0.0353754
$806$	−2.95802e9	−0.198989
$807$	3.82870e8	0.0256445
$808$	5.51225e9	0.367612
$809$	2.13480e10	1.41755	0.708773	−	0.705437i	$-0.249249\pi$
$809$	2.13480e10	1.41755	0.708773	+	0.705437i	$0.249249\pi$
$810$	6.70436e7	0.00443261
$811$	−2.34672e10	−1.54486	−0.772429	−	0.635102i	$-0.780958\pi$
$811$	−2.34672e10	−1.54486	−0.772429	+	0.635102i	$0.780958\pi$
$812$	−4.48255e9	−0.293819
$813$	1.63214e10	1.06522
$814$	−1.21686e10	−0.790776
$815$	9.44595e8	0.0611215
$816$	7.29934e8	0.0470292
$817$	−5.56437e9	−0.356976
$818$	9.20883e9	0.588258
$819$	−1.39705e9	−0.0888625
$820$	−3.18304e8	−0.0201602
$821$	−2.10502e10	−1.32757	−0.663783	−	0.747925i	$-0.731050\pi$
$821$	−2.10502e10	−1.32757	−0.663783	+	0.747925i	$0.731050\pi$
$822$	5.41338e9	0.339952
$823$	1.02642e10	0.641838	0.320919	−	0.947107i	$-0.396008\pi$
$823$	1.02642e10	0.641838	0.320919	+	0.947107i	$0.396008\pi$
$824$	−1.92400e9	−0.119801
$825$	1.32619e10	0.822278
$826$	−7.76910e8	−0.0479668
$827$	4.42662e8	0.0272146	0.0136073	−	0.999907i	$-0.495669\pi$
$827$	4.42662e8	0.0272146	0.0136073	+	0.999907i	$0.495669\pi$
$828$	3.27610e9	0.200563
$829$	1.26961e10	0.773983	0.386991	−	0.922083i	$-0.373514\pi$
$829$	1.26961e10	0.773983	0.386991	+	0.922083i	$0.373514\pi$
$830$	−7.67936e8	−0.0466178
$831$	8.17381e9	0.494107
$832$	1.06243e9	0.0639541
$833$	−3.95984e9	−0.237367
$834$	1.02207e10	0.610100
$835$	4.59067e7	0.00272881
$836$	−7.87825e9	−0.466345
$837$	1.79574e9	0.105853
$838$	1.02322e8	0.00600643
$839$	2.27019e9	0.132707	0.0663537	−	0.997796i	$-0.478863\pi$
$839$	2.27019e9	0.132707	0.0663537	+	0.997796i	$0.478863\pi$
$840$	−1.03079e8	−0.00600058
$841$	4.69036e9	0.271907
$842$	7.28661e9	0.420662
$843$	1.54219e10	0.886626
$844$	−9.10410e8	−0.0521241
$845$	7.30480e8	0.0416495
$846$	7.03347e8	0.0399368
$847$	−9.59599e9	−0.542623
$848$	−7.15410e8	−0.0402874
$849$	−1.37692e10	−0.772203
$850$	4.11202e9	0.229662
$851$	−1.69341e10	−0.941907
$852$	−8.10322e9	−0.448869
$853$	−1.47540e10	−0.813932	−0.406966	−	0.913443i	$-0.633413\pi$
$853$	−1.47540e10	−0.813932	−0.406966	+	0.913443i	$0.633413\pi$
$854$	−1.06220e10	−0.583585
$855$	−2.24363e8	−0.0122764
$856$	−6.75918e8	−0.0368329
$857$	2.61258e10	1.41787	0.708937	−	0.705272i	$-0.249175\pi$
$857$	2.61258e10	1.41787	0.708937	+	0.705272i	$0.249175\pi$
$858$	5.52143e9	0.298433
$859$	3.04468e9	0.163895	0.0819475	−	0.996637i	$-0.473886\pi$
$859$	3.04468e9	0.163895	0.0819475	+	0.996637i	$0.473886\pi$
$860$	2.87738e8	0.0154260
$861$	−4.02660e9	−0.214995
$862$	7.66325e9	0.407509
$863$	2.76581e10	1.46482	0.732410	−	0.680864i	$-0.238395\pi$
$863$	2.76581e10	1.46482	0.732410	+	0.680864i	$0.238395\pi$
$864$	−6.44973e8	−0.0340207
$865$	−1.45569e9	−0.0764736
$866$	1.27748e10	0.668408
$867$	−9.90294e9	−0.516056
$868$	−2.76093e9	−0.143297
$869$	−2.61504e10	−1.35179
$870$	5.04530e8	0.0259758
$871$	1.71666e10	0.880279
$872$	−1.18214e10	−0.603758
$873$	−2.03447e9	−0.103491
$874$	−1.09636e10	−0.555472
$875$	−1.16323e9	−0.0586999
$876$	−7.34623e9	−0.369232
$877$	2.43255e10	1.21776	0.608882	−	0.793261i	$-0.291618\pi$
$877$	2.43255e10	1.21776	0.608882	+	0.793261i	$0.291618\pi$
$878$	1.66810e10	0.831747
$879$	−1.42556e10	−0.707987
$880$	4.07390e8	0.0201521
$881$	1.39078e10	0.685238	0.342619	−	0.939474i	$-0.388686\pi$
$881$	1.39078e10	0.685238	0.342619	+	0.939474i	$0.388686\pi$
$882$	3.49893e9	0.171710
$883$	−2.86068e10	−1.39832	−0.699161	−	0.714964i	$-0.746443\pi$
$883$	−2.86068e10	−1.39832	−0.699161	+	0.714964i	$0.746443\pi$
$884$	1.71198e9	0.0833522
$885$	8.74444e7	0.00424063
$886$	9.19482e9	0.444146
$887$	−2.26550e10	−1.09001	−0.545007	−	0.838431i	$-0.683473\pi$
$887$	−2.26550e10	−1.09001	−0.545007	+	0.838431i	$0.683473\pi$
$888$	3.33384e9	0.159772
$889$	1.84234e10	0.879456
$890$	4.03492e8	0.0191853
$891$	−3.35192e9	−0.158753
$892$	−3.21883e9	−0.151852
$893$	−2.35377e9	−0.110607
$894$	−5.20082e9	−0.243439
$895$	1.54068e8	0.00718344
$896$	9.91642e8	0.0460550
$897$	7.68377e9	0.355468
$898$	2.38206e10	1.09770
$899$	1.35136e10	0.620316
$900$	−3.63340e9	−0.166136
$901$	−1.15280e9	−0.0525071
$902$	1.59140e10	0.722030
$903$	3.63993e9	0.164507
$904$	−1.41997e10	−0.639276
$905$	2.28420e9	0.102438
$906$	7.17229e9	0.320412
$907$	2.31390e10	1.02972	0.514860	−	0.857274i	$-0.327844\pi$
$907$	2.31390e10	1.02972	0.514860	+	0.857274i	$0.327844\pi$
$908$	−1.29264e10	−0.573031
$909$	−7.84850e9	−0.346588
$910$	−2.41762e8	−0.0106351
$911$	−4.37927e10	−1.91905	−0.959527	−	0.281615i	$-0.909130\pi$
$911$	−4.37927e10	−1.91905	−0.959527	+	0.281615i	$0.909130\pi$
$912$	2.15842e9	0.0942222
$913$	3.83938e10	1.66960
$914$	2.16286e10	0.936952
$915$	1.19555e9	0.0515934
$916$	2.13798e9	0.0919115
$917$	1.39340e10	0.596735
$918$	−1.03930e9	−0.0443396
$919$	4.04493e10	1.71912	0.859560	−	0.511034i	$-0.170737\pi$
$919$	4.04493e10	1.71912	0.859560	+	0.511034i	$0.170737\pi$
$920$	5.66934e8	0.0240035
$921$	−1.53296e10	−0.646581
$922$	−2.21157e9	−0.0929269
$923$	−1.90053e10	−0.795551
$924$	5.15355e9	0.214909
$925$	1.87809e10	0.780226
$926$	−4.10826e9	−0.170028
$927$	2.73945e9	0.112949
$928$	−4.85367e9	−0.199367
$929$	9.46378e7	0.00387266	0.00193633	−	0.999998i	$-0.499384\pi$
$929$	9.46378e7	0.00387266	0.00193633	+	0.999998i	$0.499384\pi$
$930$	3.10754e8	0.0126686
$931$	−1.17093e10	−0.475561
$932$	−1.78042e10	−0.720389
$933$	2.23769e10	0.902017
$934$	−3.34022e10	−1.34141
$935$	6.56463e8	0.0262645
$936$	−1.51272e9	−0.0602965
$937$	4.03496e10	1.60233	0.801163	−	0.598446i	$-0.204215\pi$
$937$	4.03496e10	1.60233	0.801163	+	0.598446i	$0.204215\pi$
$938$	1.60228e10	0.633912
$939$	−3.99643e9	−0.157522
$940$	1.21715e8	0.00477966
$941$	4.90264e9	0.191808	0.0959038	−	0.995391i	$-0.469426\pi$
$941$	4.90264e9	0.191808	0.0959038	+	0.995391i	$0.469426\pi$
$942$	9.87129e9	0.384765
$943$	2.21463e10	0.860022
$944$	−8.41232e8	−0.0325472
$945$	1.46767e8	0.00565740
$946$	−1.43857e10	−0.552476
$947$	4.48602e10	1.71647	0.858235	−	0.513256i	$-0.171561\pi$
$947$	4.48602e10	1.71647	0.858235	+	0.513256i	$0.171561\pi$
$948$	7.16448e9	0.273121
$949$	−1.72298e10	−0.654408
$950$	1.21593e10	0.460124
$951$	−5.88767e9	−0.221979
$952$	1.59792e9	0.0600241
$953$	2.64052e10	0.988245	0.494122	−	0.869392i	$-0.335489\pi$
$953$	2.64052e10	0.988245	0.494122	+	0.869392i	$0.335489\pi$
$954$	1.01862e9	0.0379834
$955$	5.97674e8	0.0222051
$956$	1.91968e10	0.710603
$957$	−2.52245e10	−0.930316
$958$	1.26783e10	0.465890
$959$	1.18506e10	0.433885
$960$	−1.11613e8	−0.00407161
$961$	−1.91892e10	−0.697468
$962$	7.81918e9	0.283171
$963$	9.62390e8	0.0347264
$964$	−3.21597e9	−0.115622
$965$	2.93015e9	0.104965
$966$	7.17181e9	0.255982
$967$	1.30518e10	0.464172	0.232086	−	0.972695i	$-0.425445\pi$
$967$	1.30518e10	0.464172	0.232086	+	0.972695i	$0.425445\pi$
$968$	−1.03905e10	−0.368189
$969$	3.47805e9	0.122801
$970$	−3.52067e8	−0.0123858
$971$	4.06303e10	1.42424	0.712119	−	0.702059i	$-0.247736\pi$
$971$	4.06303e10	1.42424	0.712119	+	0.702059i	$0.247736\pi$
$972$	9.18330e8	0.0320750
$973$	2.23745e10	0.778678
$974$	7.52787e9	0.261045
$975$	−8.52176e9	−0.294451
$976$	−1.15014e10	−0.395984
$977$	5.93854e9	0.203727	0.101864	−	0.994798i	$-0.467520\pi$
$977$	5.93854e9	0.203727	0.101864	+	0.994798i	$0.467520\pi$
$978$	1.29386e10	0.442284
$979$	−2.01730e10	−0.687118
$980$	6.05495e8	0.0205504
$981$	1.68317e10	0.569228
$982$	−4.09192e9	−0.137891
$983$	−4.88730e10	−1.64109	−0.820543	−	0.571585i	$-0.806329\pi$
$983$	−4.88730e10	−1.64109	−0.820543	+	0.571585i	$0.806329\pi$
$984$	−4.35997e9	−0.145882
$985$	−2.25687e9	−0.0752452
$986$	−7.82115e9	−0.259837
$987$	1.53972e9	0.0509719
$988$	5.06234e9	0.166995
$989$	−2.00196e10	−0.658063
$990$	−5.80053e8	−0.0189996
$991$	1.69551e9	0.0553405	0.0276702	−	0.999617i	$-0.491191\pi$
$991$	1.69551e9	0.0553405	0.0276702	+	0.999617i	$0.491191\pi$
$992$	−2.98952e9	−0.0972323
$993$	3.79209e9	0.122901
$994$	−1.77390e10	−0.572897
$995$	1.71199e9	0.0550959
$996$	−1.05188e10	−0.337333
$997$	−3.42837e10	−1.09561	−0.547803	−	0.836608i	$-0.684536\pi$
$997$	−3.42837e10	−1.09561	−0.547803	+	0.836608i	$0.684536\pi$
$998$	−1.59540e10	−0.508056
$999$	−4.74681e9	−0.150634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.8.a.c.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.8.a.c.1.4	✓	7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -15.7693 q^{5} -216.000 q^{6} -472.852 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -15.7693 q^{5} -216.000 q^{6} -472.852 q^{7} -512.000 q^{8} +729.000 q^{9} +126.154 q^{10} -6307.22 q^{11} +1728.00 q^{12} +4052.85 q^{13} +3782.81 q^{14} -425.771 q^{15} +4096.00 q^{16} +6600.24 q^{17} -5832.00 q^{18} +19516.9 q^{19} -1009.23 q^{20} -12767.0 q^{21} +50457.8 q^{22} +70218.3 q^{23} -13824.0 q^{24} -77876.3 q^{25} -32422.8 q^{26} +19683.0 q^{27} -30262.5 q^{28} +148122. q^{29} +3406.17 q^{30} +91232.9 q^{31} -32768.0 q^{32} -170295. q^{33} -52801.9 q^{34} +7456.54 q^{35} +46656.0 q^{36} -241163. q^{37} -156135. q^{38} +109427. q^{39} +8073.88 q^{40} +315392. q^{41} +102136. q^{42} -285105. q^{43} -403662. q^{44} -11495.8 q^{45} -561746. q^{46} -120601. q^{47} +110592. q^{48} -599954. q^{49} +623011. q^{50} +178207. q^{51} +259382. q^{52} -174661. q^{53} -157464. q^{54} +99460.5 q^{55} +242100. q^{56} +526957. q^{57} -1.18498e6 q^{58} -205379. q^{59} -27249.3 q^{60} -2.80797e6 q^{61} -729863. q^{62} -344709. q^{63} +262144. q^{64} -63910.5 q^{65} +1.36236e6 q^{66} +4.23569e6 q^{67} +422416. q^{68} +1.89589e6 q^{69} -59652.3 q^{70} -4.68937e6 q^{71} -373248. q^{72} -4.25129e6 q^{73} +1.92931e6 q^{74} -2.10266e6 q^{75} +1.24908e6 q^{76} +2.98238e6 q^{77} -875415. q^{78} +4.14611e6 q^{79} -64591.0 q^{80} +531441. q^{81} -2.52313e6 q^{82} -6.08727e6 q^{83} -817087. q^{84} -104081. q^{85} +2.28084e6 q^{86} +3.99930e6 q^{87} +3.22930e6 q^{88} +3.19840e6 q^{89} +91966.5 q^{90} -1.91639e6 q^{91} +4.49397e6 q^{92} +2.46329e6 q^{93} +964811. q^{94} -307768. q^{95} -884736. q^{96} -2.79076e6 q^{97} +4.79964e6 q^{98} -4.59796e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9}+O(q^{10}) \) 7 * q - 56 * q^2 + 189 * q^3 + 448 * q^4 - 158 * q^5 - 1512 * q^6 - 581 * q^7 - 3584 * q^8 + 5103 * q^9	\( 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9} + 1264 q^{10} - 2201 q^{11} + 12096 q^{12} - 8421 q^{13} + 4648 q^{14} - 4266 q^{15} + 28672 q^{16} - 2425 q^{17} - 40824 q^{18} - 37084 q^{19} - 10112 q^{20} - 15687 q^{21} + 17608 q^{22} + 99364 q^{23} - 96768 q^{24} + 101361 q^{25} + 67368 q^{26} + 137781 q^{27} - 37184 q^{28} + 2498 q^{29} + 34128 q^{30} - 57962 q^{31} - 229376 q^{32} - 59427 q^{33} + 19400 q^{34} + 190586 q^{35} + 326592 q^{36} - 6497 q^{37} + 296672 q^{38} - 227367 q^{39} + 80896 q^{40} - 319165 q^{41} + 125496 q^{42} - 633743 q^{43} - 140864 q^{44} - 115182 q^{45} - 794912 q^{46} - 1626560 q^{47} + 774144 q^{48} - 3846354 q^{49} - 810888 q^{50} - 65475 q^{51} - 538944 q^{52} - 1215602 q^{53} - 1102248 q^{54} - 3329556 q^{55} + 297472 q^{56} - 1001268 q^{57} - 19984 q^{58} - 1437653 q^{59} - 273024 q^{60} - 3180086 q^{61} + 463696 q^{62} - 423549 q^{63} + 1835008 q^{64} + 544086 q^{65} + 475416 q^{66} - 5349632 q^{67} - 155200 q^{68} + 2682828 q^{69} - 1524688 q^{70} + 1752423 q^{71} - 2612736 q^{72} - 1843424 q^{73} + 51976 q^{74} + 2736747 q^{75} - 2373376 q^{76} - 3885063 q^{77} + 1818936 q^{78} - 4769243 q^{79} - 647168 q^{80} + 3720087 q^{81} + 2553320 q^{82} + 5154441 q^{83} - 1003968 q^{84} - 4594902 q^{85} + 5069944 q^{86} + 67446 q^{87} + 1126912 q^{88} + 20086462 q^{89} + 921456 q^{90} + 6733847 q^{91} + 6359296 q^{92} - 1564974 q^{93} + 13012480 q^{94} + 12936212 q^{95} - 6193152 q^{96} + 6244248 q^{97} + 30770832 q^{98} - 1604529 q^{99}+O(q^{100}) \) 7 * q - 56 * q^2 + 189 * q^3 + 448 * q^4 - 158 * q^5 - 1512 * q^6 - 581 * q^7 - 3584 * q^8 + 5103 * q^9 + 1264 * q^10 - 2201 * q^11 + 12096 * q^12 - 8421 * q^13 + 4648 * q^14 - 4266 * q^15 + 28672 * q^16 - 2425 * q^17 - 40824 * q^18 - 37084 * q^19 - 10112 * q^20 - 15687 * q^21 + 17608 * q^22 + 99364 * q^23 - 96768 * q^24 + 101361 * q^25 + 67368 * q^26 + 137781 * q^27 - 37184 * q^28 + 2498 * q^29 + 34128 * q^30 - 57962 * q^31 - 229376 * q^32 - 59427 * q^33 + 19400 * q^34 + 190586 * q^35 + 326592 * q^36 - 6497 * q^37 + 296672 * q^38 - 227367 * q^39 + 80896 * q^40 - 319165 * q^41 + 125496 * q^42 - 633743 * q^43 - 140864 * q^44 - 115182 * q^45 - 794912 * q^46 - 1626560 * q^47 + 774144 * q^48 - 3846354 * q^49 - 810888 * q^50 - 65475 * q^51 - 538944 * q^52 - 1215602 * q^53 - 1102248 * q^54 - 3329556 * q^55 + 297472 * q^56 - 1001268 * q^57 - 19984 * q^58 - 1437653 * q^59 - 273024 * q^60 - 3180086 * q^61 + 463696 * q^62 - 423549 * q^63 + 1835008 * q^64 + 544086 * q^65 + 475416 * q^66 - 5349632 * q^67 - 155200 * q^68 + 2682828 * q^69 - 1524688 * q^70 + 1752423 * q^71 - 2612736 * q^72 - 1843424 * q^73 + 51976 * q^74 + 2736747 * q^75 - 2373376 * q^76 - 3885063 * q^77 + 1818936 * q^78 - 4769243 * q^79 - 647168 * q^80 + 3720087 * q^81 + 2553320 * q^82 + 5154441 * q^83 - 1003968 * q^84 - 4594902 * q^85 + 5069944 * q^86 + 67446 * q^87 + 1126912 * q^88 + 20086462 * q^89 + 921456 * q^90 + 6733847 * q^91 + 6359296 * q^92 - 1564974 * q^93 + 13012480 * q^94 + 12936212 * q^95 - 6193152 * q^96 + 6244248 * q^97 + 30770832 * q^98 - 1604529 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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