LMFDB - Embedded newform 177.10.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,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, 10, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
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:	$91.1613430010$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-18.1702 q^{2} +81.0000 q^{3} -181.842 q^{4} +1096.53 q^{5} -1471.79 q^{6} -2885.78 q^{7} +12607.3 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-18.1702 q^{2} +81.0000 q^{3} -181.842 q^{4} +1096.53 q^{5} -1471.79 q^{6} -2885.78 q^{7} +12607.3 q^{8} +6561.00 q^{9} -19924.2 q^{10} +1677.58 q^{11} -14729.2 q^{12} -12863.8 q^{13} +52435.4 q^{14} +88818.7 q^{15} -135974. q^{16} -100811. q^{17} -119215. q^{18} -509381. q^{19} -199395. q^{20} -233749. q^{21} -30482.0 q^{22} +2.00745e6 q^{23} +1.02119e6 q^{24} -750753. q^{25} +233738. q^{26} +531441. q^{27} +524758. q^{28} +1.00906e6 q^{29} -1.61386e6 q^{30} -9.60546e6 q^{31} -3.98425e6 q^{32} +135884. q^{33} +1.83177e6 q^{34} -3.16434e6 q^{35} -1.19307e6 q^{36} +1.57704e7 q^{37} +9.25558e6 q^{38} -1.04197e6 q^{39} +1.38242e7 q^{40} +1.77391e7 q^{41} +4.24727e6 q^{42} -3.57341e7 q^{43} -305054. q^{44} +7.19432e6 q^{45} -3.64759e7 q^{46} -142504. q^{47} -1.10139e7 q^{48} -3.20259e7 q^{49} +1.36414e7 q^{50} -8.16572e6 q^{51} +2.33918e6 q^{52} +6.97093e7 q^{53} -9.65641e6 q^{54} +1.83951e6 q^{55} -3.63819e7 q^{56} -4.12599e7 q^{57} -1.83349e7 q^{58} +1.21174e7 q^{59} -1.61510e7 q^{60} +7.35248e6 q^{61} +1.74534e8 q^{62} -1.89336e7 q^{63} +1.42013e8 q^{64} -1.41055e7 q^{65} -2.46904e6 q^{66} -1.33128e8 q^{67} +1.83318e7 q^{68} +1.62604e8 q^{69} +5.74969e7 q^{70} +2.69166e8 q^{71} +8.27164e7 q^{72} +2.14588e8 q^{73} -2.86551e8 q^{74} -6.08110e7 q^{75} +9.26270e7 q^{76} -4.84112e6 q^{77} +1.89328e7 q^{78} -6.11948e8 q^{79} -1.49099e8 q^{80} +4.30467e7 q^{81} -3.22323e8 q^{82} +4.77356e8 q^{83} +4.25054e7 q^{84} -1.10542e8 q^{85} +6.49297e8 q^{86} +8.17342e7 q^{87} +2.11497e7 q^{88} -7.71476e8 q^{89} -1.30722e8 q^{90} +3.71221e7 q^{91} -3.65040e8 q^{92} -7.78043e8 q^{93} +2.58934e6 q^{94} -5.58550e8 q^{95} -3.22724e8 q^{96} +1.38667e9 q^{97} +5.81917e8 q^{98} +1.10066e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * 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 $

$2$	−18.1702	−0.803019	−0.401509	−	0.915855i	$-0.631514\pi$
$2$	−18.1702	−0.803019	−0.401509	+	0.915855i	$0.631514\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−181.842	−0.355161
$5$	1096.53	0.784611	0.392306	−	0.919835i	$-0.371678\pi$
$5$	1096.53	0.784611	0.392306	+	0.919835i	$0.371678\pi$
$6$	−1471.79	−0.463623
$7$	−2885.78	−0.454279	−0.227140	−	0.973862i	$-0.572937\pi$
$7$	−2885.78	−0.454279	−0.227140	+	0.973862i	$0.572937\pi$
$8$	12607.3	1.08822
$9$	6561.00	0.333333
$10$	−19924.2	−0.630057
$11$	1677.58	0.0345474	0.0172737	−	0.999851i	$-0.494501\pi$
$11$	1677.58	0.0345474	0.0172737	+	0.999851i	$0.494501\pi$
$12$	−14729.2	−0.205052
$13$	−12863.8	−0.124918	−0.0624588	−	0.998048i	$-0.519894\pi$
$13$	−12863.8	−0.124918	−0.0624588	+	0.998048i	$0.519894\pi$
$14$	52435.4	0.364795
$15$	88818.7	0.452995
$16$	−135974.	−0.518700
$17$	−100811.	−0.292745	−0.146372	−	0.989230i	$-0.546760\pi$
$17$	−100811.	−0.292745	−0.146372	+	0.989230i	$0.546760\pi$
$18$	−119215.	−0.267673
$19$	−509381.	−0.896709	−0.448355	−	0.893856i	$-0.647990\pi$
$19$	−509381.	−0.896709	−0.448355	+	0.893856i	$0.647990\pi$
$20$	−199395.	−0.278663
$21$	−233749.	−0.262278
$22$	−30482.0	−0.0277422
$23$	2.00745e6	1.49579	0.747894	−	0.663818i	$-0.231065\pi$
$23$	2.00745e6	1.49579	0.747894	+	0.663818i	$0.231065\pi$
$24$	1.02119e6	0.628284
$25$	−750753.	−0.384385
$26$	233738.	0.100311
$27$	531441.	0.192450
$28$	524758.	0.161342
$29$	1.00906e6	0.264928	0.132464	−	0.991188i	$-0.457711\pi$
$29$	1.00906e6	0.264928	0.132464	+	0.991188i	$0.457711\pi$
$30$	−1.61386e6	−0.363764
$31$	−9.60546e6	−1.86806	−0.934030	−	0.357195i	$-0.883733\pi$
$31$	−9.60546e6	−1.86806	−0.934030	+	0.357195i	$0.883733\pi$
$32$	−3.98425e6	−0.671694
$33$	135884.	0.0199459
$34$	1.83177e6	0.235080
$35$	−3.16434e6	−0.356432
$36$	−1.19307e6	−0.118387
$37$	1.57704e7	1.38336	0.691678	−	0.722206i	$-0.256872\pi$
$37$	1.57704e7	1.38336	0.691678	+	0.722206i	$0.256872\pi$
$38$	9.25558e6	0.720074
$39$	−1.04197e6	−0.0721212
$40$	1.38242e7	0.853829
$41$	1.77391e7	0.980401	0.490200	−	0.871610i	$-0.336924\pi$
$41$	1.77391e7	0.980401	0.490200	+	0.871610i	$0.336924\pi$
$42$	4.24727e6	0.210614
$43$	−3.57341e7	−1.59395	−0.796975	−	0.604012i	$-0.793568\pi$
$43$	−3.57341e7	−1.59395	−0.796975	+	0.604012i	$0.793568\pi$
$44$	−305054.	−0.0122699
$45$	7.19432e6	0.261537
$46$	−3.64759e7	−1.20115
$47$	−142504.	−0.00425978	−0.00212989	−	0.999998i	$-0.500678\pi$
$47$	−142504.	−0.00425978	−0.00212989	+	0.999998i	$0.500678\pi$
$48$	−1.10139e7	−0.299472
$49$	−3.20259e7	−0.793631
$50$	1.36414e7	0.308669
$51$	−8.16572e6	−0.169016
$52$	2.33918e6	0.0443658
$53$	6.97093e7	1.21353	0.606764	−	0.794882i	$-0.292467\pi$
$53$	6.97093e7	1.21353	0.606764	+	0.794882i	$0.292467\pi$
$54$	−9.65641e6	−0.154541
$55$	1.83951e6	0.0271063
$56$	−3.63819e7	−0.494355
$57$	−4.12599e7	−0.517715
$58$	−1.83349e7	−0.212742
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−1.61510e7	−0.160886
$61$	7.35248e6	0.0679907	0.0339953	−	0.999422i	$-0.489177\pi$
$61$	7.35248e6	0.0679907	0.0339953	+	0.999422i	$0.489177\pi$
$62$	1.74534e8	1.50009
$63$	−1.89336e7	−0.151426
$64$	1.42013e8	1.05808
$65$	−1.41055e7	−0.0980117
$66$	−2.46904e6	−0.0160170
$67$	−1.33128e8	−0.807113	−0.403556	−	0.914955i	$-0.632226\pi$
$67$	−1.33128e8	−0.807113	−0.403556	+	0.914955i	$0.632226\pi$
$68$	1.83318e7	0.103971
$69$	1.62604e8	0.863594
$70$	5.74969e7	0.286222
$71$	2.69166e8	1.25707	0.628533	−	0.777783i	$-0.283656\pi$
$71$	2.69166e8	1.25707	0.628533	+	0.777783i	$0.283656\pi$
$72$	8.27164e7	0.362740
$73$	2.14588e8	0.884409	0.442205	−	0.896914i	$-0.354196\pi$
$73$	2.14588e8	0.884409	0.442205	+	0.896914i	$0.354196\pi$
$74$	−2.86551e8	−1.11086
$75$	−6.08110e7	−0.221925
$76$	9.26270e7	0.318476
$77$	−4.84112e6	−0.0156942
$78$	1.89328e7	0.0579147
$79$	−6.11948e8	−1.76763	−0.883817	−	0.467832i	$-0.845035\pi$
$79$	−6.11948e8	−1.76763	−0.883817	+	0.467832i	$0.845035\pi$
$80$	−1.49099e8	−0.406978
$81$	4.30467e7	0.111111
$82$	−3.22323e8	−0.787280
$83$	4.77356e8	1.10405	0.552027	−	0.833826i	$-0.313854\pi$
$83$	4.77356e8	1.10405	0.552027	+	0.833826i	$0.313854\pi$
$84$	4.25054e7	0.0931509
$85$	−1.10542e8	−0.229691
$86$	6.49297e8	1.27997
$87$	8.17342e7	0.152956
$88$	2.11497e7	0.0375951
$89$	−7.71476e8	−1.30337	−0.651684	−	0.758490i	$-0.725937\pi$
$89$	−7.71476e8	−1.30337	−0.651684	+	0.758490i	$0.725937\pi$
$90$	−1.30722e8	−0.210019
$91$	3.71221e7	0.0567474
$92$	−3.65040e8	−0.531245
$93$	−7.78043e8	−1.07852
$94$	2.58934e6	0.00342069
$95$	−5.58550e8	−0.703568
$96$	−3.22724e8	−0.387803
$97$	1.38667e9	1.59038	0.795190	−	0.606361i	$-0.207371\pi$
$97$	1.38667e9	1.59038	0.795190	+	0.606361i	$0.207371\pi$
$98$	5.81917e8	0.637300
$99$	1.10066e7	0.0115158
$100$	1.36519e8	0.136519
$101$	−5.68775e8	−0.543869	−0.271934	−	0.962316i	$-0.587663\pi$
$101$	−5.68775e8	−0.543869	−0.271934	+	0.962316i	$0.587663\pi$
$102$	1.48373e8	0.135723
$103$	5.90682e7	0.0517114	0.0258557	−	0.999666i	$-0.491769\pi$
$103$	5.90682e7	0.0517114	0.0258557	+	0.999666i	$0.491769\pi$
$104$	−1.62177e8	−0.135938
$105$	−2.56312e8	−0.205786
$106$	−1.26664e9	−0.974485
$107$	−1.58696e8	−0.117041	−0.0585206	−	0.998286i	$-0.518638\pi$
$107$	−1.58696e8	−0.117041	−0.0585206	+	0.998286i	$0.518638\pi$
$108$	−9.66385e7	−0.0683507
$109$	−2.56370e9	−1.73959	−0.869797	−	0.493410i	$-0.835750\pi$
$109$	−2.56370e9	−1.73959	−0.869797	+	0.493410i	$0.835750\pi$
$110$	−3.34243e7	−0.0217668
$111$	1.27740e9	0.798681
$112$	3.92392e8	0.235635
$113$	−1.92831e8	−0.111256	−0.0556280	−	0.998452i	$-0.517716\pi$
$113$	−1.92831e8	−0.111256	−0.0556280	+	0.998452i	$0.517716\pi$
$114$	7.49702e8	0.415735
$115$	2.20123e9	1.17361
$116$	−1.83491e8	−0.0940920
$117$	−8.43992e7	−0.0416392
$118$	−2.20175e8	−0.104544
$119$	2.90920e8	0.132988
$120$	1.11976e9	0.492958
$121$	−2.35513e9	−0.998806
$122$	−1.33596e8	−0.0545978
$123$	1.43687e9	0.566035
$124$	1.74668e9	0.663461
$125$	−2.96488e9	−1.08620
$126$	3.44029e8	0.121598
$127$	−3.38046e9	−1.15308	−0.576539	−	0.817070i	$-0.695597\pi$
$127$	−3.38046e9	−1.15308	−0.576539	+	0.817070i	$0.695597\pi$
$128$	−5.40485e8	−0.177967
$129$	−2.89446e9	−0.920268
$130$	2.56300e8	0.0787052
$131$	−5.38013e9	−1.59614	−0.798071	−	0.602563i	$-0.794146\pi$
$131$	−5.38013e9	−1.59614	−0.798071	+	0.602563i	$0.794146\pi$
$132$	−2.47094e7	−0.00708402
$133$	1.46996e9	0.407356
$134$	2.41898e9	0.648127
$135$	5.82740e8	0.150998
$136$	−1.27096e9	−0.318571
$137$	−7.34840e9	−1.78218	−0.891088	−	0.453831i	$-0.850057\pi$
$137$	−7.34840e9	−1.78218	−0.891088	+	0.453831i	$0.850057\pi$
$138$	−2.95455e9	−0.693482
$139$	−6.11127e9	−1.38856	−0.694280	−	0.719705i	$-0.744277\pi$
$139$	−6.11127e9	−1.38856	−0.694280	+	0.719705i	$0.744277\pi$
$140$	5.75411e8	0.126591
$141$	−1.15428e7	−0.00245939
$142$	−4.89082e9	−1.00945
$143$	−2.15800e7	−0.00431557
$144$	−8.92126e8	−0.172900
$145$	1.10647e9	0.207865
$146$	−3.89912e9	−0.710197
$147$	−2.59409e9	−0.458203
$148$	−2.86772e9	−0.491314
$149$	−6.73461e9	−1.11937	−0.559686	−	0.828705i	$-0.689078\pi$
$149$	−6.73461e9	−1.11937	−0.559686	+	0.828705i	$0.689078\pi$
$150$	1.10495e9	0.178210
$151$	1.63533e9	0.255981	0.127991	−	0.991775i	$-0.459147\pi$
$151$	1.63533e9	0.255981	0.127991	+	0.991775i	$0.459147\pi$
$152$	−6.42191e9	−0.975816
$153$	−6.61423e8	−0.0975816
$154$	8.79644e7	0.0126027
$155$	−1.05327e10	−1.46570
$156$	1.89473e8	0.0256146
$157$	−6.72353e8	−0.0883179	−0.0441589	−	0.999025i	$-0.514061\pi$
$157$	−6.72353e8	−0.0883179	−0.0441589	+	0.999025i	$0.514061\pi$
$158$	1.11192e10	1.41944
$159$	5.64646e9	0.700630
$160$	−4.36883e9	−0.527018
$161$	−5.79308e9	−0.679505
$162$	−7.82169e8	−0.0892243
$163$	−1.02090e10	−1.13276	−0.566379	−	0.824145i	$-0.691656\pi$
$163$	−1.02090e10	−1.13276	−0.566379	+	0.824145i	$0.691656\pi$
$164$	−3.22572e9	−0.348200
$165$	1.49000e8	0.0156498
$166$	−8.67367e9	−0.886577
$167$	−8.98649e9	−0.894059	−0.447029	−	0.894519i	$-0.647518\pi$
$167$	−8.98649e9	−0.894059	−0.447029	+	0.894519i	$0.647518\pi$
$168$	−2.94693e9	−0.285416
$169$	−1.04390e10	−0.984396
$170$	2.00858e9	0.184446
$171$	−3.34205e9	−0.298903
$172$	6.49797e9	0.566109
$173$	1.26827e10	1.07648	0.538238	−	0.842793i	$-0.319090\pi$
$173$	1.26827e10	1.07648	0.538238	+	0.842793i	$0.319090\pi$
$174$	−1.48513e9	−0.122827
$175$	2.16651e9	0.174618
$176$	−2.28107e8	−0.0179197
$177$	9.81506e8	0.0751646
$178$	1.40179e10	1.04663
$179$	−1.31061e10	−0.954190	−0.477095	−	0.878852i	$-0.658310\pi$
$179$	−1.31061e10	−0.954190	−0.477095	+	0.878852i	$0.658310\pi$
$180$	−1.30823e9	−0.0928877
$181$	2.68008e10	1.85607	0.928034	−	0.372495i	$-0.121498\pi$
$181$	2.68008e10	1.85607	0.928034	+	0.372495i	$0.121498\pi$
$182$	−6.74517e8	−0.0455692
$183$	5.95551e8	0.0392544
$184$	2.53085e10	1.62775
$185$	1.72926e10	1.08540
$186$	1.41372e10	0.866076
$187$	−1.69119e8	−0.0101136
$188$	2.59133e7	0.00151291
$189$	−1.53362e9	−0.0874261
$190$	1.01490e10	0.564978
$191$	2.93131e9	0.159372	0.0796861	−	0.996820i	$-0.474608\pi$
$191$	2.93131e9	0.159372	0.0796861	+	0.996820i	$0.474608\pi$
$192$	1.15031e10	0.610884
$193$	−6.49197e9	−0.336797	−0.168399	−	0.985719i	$-0.553860\pi$
$193$	−6.49197e9	−0.336797	−0.168399	+	0.985719i	$0.553860\pi$
$194$	−2.51962e10	−1.27710
$195$	−1.14254e9	−0.0565871
$196$	5.82366e9	0.281866
$197$	−9.40339e9	−0.444822	−0.222411	−	0.974953i	$-0.571393\pi$
$197$	−9.40339e9	−0.444822	−0.222411	+	0.974953i	$0.571393\pi$
$198$	−1.99992e8	−0.00924740
$199$	2.14054e10	0.967575	0.483787	−	0.875186i	$-0.339261\pi$
$199$	2.14054e10	0.967575	0.483787	+	0.875186i	$0.339261\pi$
$200$	−9.46495e9	−0.418296
$201$	−1.07834e10	−0.465987
$202$	1.03348e10	0.436737
$203$	−2.91194e9	−0.120351
$204$	1.48487e9	0.0600280
$205$	1.94514e10	0.769233
$206$	−1.07328e9	−0.0415252
$207$	1.31709e10	0.498596
$208$	1.74914e9	0.0647947
$209$	−8.54526e8	−0.0309790
$210$	4.65725e9	0.165250
$211$	−4.98106e10	−1.73002	−0.865009	−	0.501756i	$-0.832687\pi$
$211$	−4.98106e10	−1.73002	−0.865009	+	0.501756i	$0.832687\pi$
$212$	−1.26761e10	−0.430997
$213$	2.18025e10	0.725768
$214$	2.88354e9	0.0939862
$215$	−3.91834e10	−1.25063
$216$	6.70003e9	0.209428
$217$	2.77193e10	0.848620
$218$	4.65830e10	1.39693
$219$	1.73817e10	0.510614
$220$	−3.34500e8	−0.00962708
$221$	1.29681e9	0.0365690
$222$	−2.32107e10	−0.641356
$223$	8.74921e9	0.236917	0.118459	−	0.992959i	$-0.462205\pi$
$223$	8.74921e9	0.236917	0.118459	+	0.992959i	$0.462205\pi$
$224$	1.14977e10	0.305136
$225$	−4.92569e9	−0.128128
$226$	3.50378e9	0.0893406
$227$	3.86038e10	0.964969	0.482484	−	0.875905i	$-0.339735\pi$
$227$	3.86038e10	0.964969	0.482484	+	0.875905i	$0.339735\pi$
$228$	7.50279e9	0.183872
$229$	3.12351e10	0.750555	0.375278	−	0.926912i	$-0.377547\pi$
$229$	3.12351e10	0.750555	0.375278	+	0.926912i	$0.377547\pi$
$230$	−3.99968e10	−0.942432
$231$	−3.92131e8	−0.00906102
$232$	1.27216e10	0.288300
$233$	−5.00071e10	−1.11155	−0.555777	−	0.831332i	$-0.687579\pi$
$233$	−5.00071e10	−1.11155	−0.555777	+	0.831332i	$0.687579\pi$
$234$	1.53355e9	0.0334370
$235$	−1.56260e8	−0.00334227
$236$	−2.20345e9	−0.0462380
$237$	−4.95678e10	−1.02054
$238$	−5.28608e9	−0.106792
$239$	6.27521e10	1.24405	0.622025	−	0.782997i	$-0.286310\pi$
$239$	6.27521e10	1.24405	0.622025	+	0.782997i	$0.286310\pi$
$240$	−1.20770e10	−0.234969
$241$	5.35838e10	1.02319	0.511596	−	0.859226i	$-0.329055\pi$
$241$	5.35838e10	1.02319	0.511596	+	0.859226i	$0.329055\pi$
$242$	4.27933e10	0.802060
$243$	3.48678e9	0.0641500
$244$	−1.33699e9	−0.0241476
$245$	−3.51172e10	−0.622691
$246$	−2.61082e10	−0.454537
$247$	6.55256e9	0.112015
$248$	−1.21099e11	−2.03286
$249$	3.86658e10	0.637426
$250$	5.38725e10	0.872242
$251$	7.31890e10	1.16390	0.581948	−	0.813226i	$-0.302291\pi$
$251$	7.31890e10	1.16390	0.581948	+	0.813226i	$0.302291\pi$
$252$	3.44294e9	0.0537807
$253$	3.36766e9	0.0516756
$254$	6.14237e10	0.925943
$255$	−8.95393e9	−0.132612
$256$	−6.28902e10	−0.915172
$257$	−7.91834e10	−1.13223	−0.566115	−	0.824326i	$-0.691554\pi$
$257$	−7.91834e10	−1.13223	−0.566115	+	0.824326i	$0.691554\pi$
$258$	5.25931e10	0.738993
$259$	−4.55099e10	−0.628430
$260$	2.56497e9	0.0348099
$261$	6.62047e9	0.0883093
$262$	9.77582e10	1.28173
$263$	1.99558e10	0.257198	0.128599	−	0.991697i	$-0.458952\pi$
$263$	1.99558e10	0.257198	0.128599	+	0.991697i	$0.458952\pi$
$264$	1.71312e9	0.0217056
$265$	7.64382e10	0.952147
$266$	−2.67096e10	−0.327115
$267$	−6.24895e10	−0.752500
$268$	2.42084e10	0.286655
$269$	−1.24707e11	−1.45213	−0.726066	−	0.687625i	$-0.758653\pi$
$269$	−1.24707e11	−1.45213	−0.726066	+	0.687625i	$0.758653\pi$
$270$	−1.05885e10	−0.121255
$271$	−1.08239e11	−1.21905	−0.609525	−	0.792767i	$-0.708640\pi$
$271$	−1.08239e11	−1.21905	−0.609525	+	0.792767i	$0.708640\pi$
$272$	1.37077e10	0.151847
$273$	3.00689e9	0.0327631
$274$	1.33522e11	1.43112
$275$	−1.25945e9	−0.0132795
$276$	−2.95682e10	−0.306715
$277$	1.24654e11	1.27218	0.636090	−	0.771615i	$-0.280551\pi$
$277$	1.24654e11	1.27218	0.636090	+	0.771615i	$0.280551\pi$
$278$	1.11043e11	1.11504
$279$	−6.30214e10	−0.622686
$280$	−3.98938e10	−0.387877
$281$	1.22215e11	1.16936	0.584679	−	0.811265i	$-0.301220\pi$
$281$	1.22215e11	1.16936	0.584679	+	0.811265i	$0.301220\pi$
$282$	2.09736e8	0.00197493
$283$	−1.35737e11	−1.25794	−0.628969	−	0.777431i	$-0.716523\pi$
$283$	−1.35737e11	−1.25794	−0.628969	+	0.777431i	$0.716523\pi$
$284$	−4.89458e10	−0.446461
$285$	−4.52426e10	−0.406205
$286$	3.92113e8	0.00346549
$287$	−5.11912e10	−0.445376
$288$	−2.61406e10	−0.223898
$289$	−1.08425e11	−0.914300
$290$	−2.01048e10	−0.166920
$291$	1.12320e11	0.918206
$292$	−3.90212e10	−0.314108
$293$	7.79389e10	0.617803	0.308902	−	0.951094i	$-0.400039\pi$
$293$	7.79389e10	0.617803	0.308902	+	0.951094i	$0.400039\pi$
$294$	4.71353e10	0.367945
$295$	1.32870e10	0.102148
$296$	1.98821e11	1.50540
$297$	8.91533e8	0.00664865
$298$	1.22370e11	0.898877
$299$	−2.58234e10	−0.186850
$300$	1.10580e10	0.0788191
$301$	1.03121e11	0.724099
$302$	−2.97143e10	−0.205558
$303$	−4.60707e10	−0.314003
$304$	6.92626e10	0.465123
$305$	8.06219e9	0.0533462
$306$	1.20182e10	0.0783599
$307$	1.99796e11	1.28370	0.641850	−	0.766830i	$-0.278167\pi$
$307$	1.99796e11	1.28370	0.641850	+	0.766830i	$0.278167\pi$
$308$	8.80321e8	0.00557395
$309$	4.78453e9	0.0298556
$310$	1.91381e11	1.17698
$311$	2.73103e10	0.165541	0.0827703	−	0.996569i	$-0.473623\pi$
$311$	2.73103e10	0.165541	0.0827703	+	0.996569i	$0.473623\pi$
$312$	−1.31364e10	−0.0784837
$313$	−2.95243e11	−1.73872	−0.869362	−	0.494177i	$-0.835470\pi$
$313$	−2.95243e11	−1.73872	−0.869362	+	0.494177i	$0.835470\pi$
$314$	1.22168e10	0.0709209
$315$	−2.07612e10	−0.118811
$316$	1.11278e11	0.627794
$317$	−3.10967e11	−1.72961	−0.864805	−	0.502109i	$-0.832558\pi$
$317$	−3.10967e11	−1.72961	−0.864805	+	0.502109i	$0.832558\pi$
$318$	−1.02597e11	−0.562619
$319$	1.69278e9	0.00915257
$320$	1.55722e11	0.830183
$321$	−1.28544e10	−0.0675737
$322$	1.05262e11	0.545656
$323$	5.13514e10	0.262507
$324$	−7.82772e9	−0.0394623
$325$	9.65752e9	0.0480165
$326$	1.85499e11	0.909627
$327$	−2.07660e11	−1.00436
$328$	2.23642e11	1.06689
$329$	4.11237e8	0.00193513
$330$	−2.70737e9	−0.0125671
$331$	−2.95514e11	−1.35317	−0.676586	−	0.736364i	$-0.736541\pi$
$331$	−2.95514e11	−1.35317	−0.676586	+	0.736364i	$0.736541\pi$
$332$	−8.68035e10	−0.392117
$333$	1.03469e11	0.461119
$334$	1.63287e11	0.717946
$335$	−1.45979e11	−0.633270
$336$	3.17838e10	0.136044
$337$	6.54404e10	0.276383	0.138191	−	0.990406i	$-0.455871\pi$
$337$	6.54404e10	0.276383	0.138191	+	0.990406i	$0.455871\pi$
$338$	1.89680e11	0.790488
$339$	−1.56193e10	−0.0642336
$340$	2.01013e10	0.0815772
$341$	−1.61139e10	−0.0645366
$342$	6.07258e10	0.240025
$343$	2.08872e11	0.814809
$344$	−4.50510e11	−1.73457
$345$	1.78299e11	0.677585
$346$	−2.30448e11	−0.864431
$347$	−2.55074e11	−0.944459	−0.472230	−	0.881476i	$-0.656551\pi$
$347$	−2.55074e11	−0.944459	−0.472230	+	0.881476i	$0.656551\pi$
$348$	−1.48627e10	−0.0543240
$349$	−2.16864e11	−0.782479	−0.391240	−	0.920289i	$-0.627954\pi$
$349$	−2.16864e11	−0.782479	−0.391240	+	0.920289i	$0.627954\pi$
$350$	−3.93660e10	−0.140222
$351$	−6.83634e9	−0.0240404
$352$	−6.68388e9	−0.0232053
$353$	3.04446e11	1.04358	0.521789	−	0.853075i	$-0.325265\pi$
$353$	3.04446e11	1.04358	0.521789	+	0.853075i	$0.325265\pi$
$354$	−1.78342e10	−0.0603586
$355$	2.95148e11	0.986308
$356$	1.40287e11	0.462905
$357$	2.35645e10	0.0767806
$358$	2.38141e11	0.766233
$359$	−2.99907e11	−0.952932	−0.476466	−	0.879193i	$-0.658082\pi$
$359$	−2.99907e11	−0.952932	−0.476466	+	0.879193i	$0.658082\pi$
$360$	9.07008e10	0.284610
$361$	−6.32186e10	−0.195913
$362$	−4.86977e11	−1.49046
$363$	−1.90766e11	−0.576661
$364$	−6.75037e9	−0.0201545
$365$	2.35302e11	0.693917
$366$	−1.08213e10	−0.0315221
$367$	−1.37612e11	−0.395967	−0.197983	−	0.980205i	$-0.563439\pi$
$367$	−1.37612e11	−0.395967	−0.197983	+	0.980205i	$0.563439\pi$
$368$	−2.72962e11	−0.775865
$369$	1.16386e11	0.326800
$370$	−3.14211e11	−0.871594
$371$	−2.01166e11	−0.551280
$372$	1.41481e11	0.383050
$373$	5.96688e11	1.59609	0.798045	−	0.602598i	$-0.205868\pi$
$373$	5.96688e11	1.59609	0.798045	+	0.602598i	$0.205868\pi$
$374$	3.07293e9	0.00812139
$375$	−2.40155e11	−0.627120
$376$	−1.79659e9	−0.00463558
$377$	−1.29804e10	−0.0330941
$378$	2.78663e10	0.0702048
$379$	−4.36706e10	−0.108721	−0.0543604	−	0.998521i	$-0.517312\pi$
$379$	−4.36706e10	−0.108721	−0.0543604	+	0.998521i	$0.517312\pi$
$380$	1.01568e11	0.249880
$381$	−2.73817e11	−0.665730
$382$	−5.32627e10	−0.127979
$383$	7.11868e11	1.69046	0.845230	−	0.534403i	$-0.179463\pi$
$383$	7.11868e11	1.69046	0.845230	+	0.534403i	$0.179463\pi$
$384$	−4.37793e10	−0.102749
$385$	−5.30842e9	−0.0123138
$386$	1.17961e11	0.270454
$387$	−2.34452e11	−0.531317
$388$	−2.52156e11	−0.564840
$389$	6.46995e11	1.43261	0.716305	−	0.697787i	$-0.245832\pi$
$389$	6.46995e11	1.43261	0.716305	+	0.697787i	$0.245832\pi$
$390$	2.07603e10	0.0454405
$391$	−2.02374e11	−0.437884
$392$	−4.03759e11	−0.863644
$393$	−4.35790e11	−0.921534
$394$	1.70862e11	0.357200
$395$	−6.71017e11	−1.38691
$396$	−2.00146e9	−0.00408996
$397$	1.09495e11	0.221226	0.110613	−	0.993864i	$-0.464719\pi$
$397$	1.09495e11	0.221226	0.110613	+	0.993864i	$0.464719\pi$
$398$	−3.88941e11	−0.776981
$399$	1.19067e11	0.235187
$400$	1.02083e11	0.199381
$401$	−2.69349e11	−0.520194	−0.260097	−	0.965583i	$-0.583754\pi$
$401$	−2.69349e11	−0.520194	−0.260097	+	0.965583i	$0.583754\pi$
$402$	1.95937e11	0.374196
$403$	1.23563e11	0.233353
$404$	1.03427e11	0.193161
$405$	4.72019e10	0.0871790
$406$	5.29107e10	0.0966443
$407$	2.64560e10	0.0477913
$408$	−1.02948e11	−0.183927
$409$	−4.33340e10	−0.0765727	−0.0382863	−	0.999267i	$-0.512190\pi$
$409$	−4.33340e10	−0.0765727	−0.0382863	+	0.999267i	$0.512190\pi$
$410$	−3.53436e11	−0.617709
$411$	−5.95221e11	−1.02894
$412$	−1.07411e10	−0.0183659
$413$	−3.49681e10	−0.0591421
$414$	−2.39318e11	−0.400382
$415$	5.23434e11	0.866254
$416$	5.12525e10	0.0839063
$417$	−4.95013e11	−0.801685
$418$	1.55269e10	0.0248767
$419$	3.11457e11	0.493668	0.246834	−	0.969058i	$-0.420610\pi$
$419$	3.11457e11	0.493668	0.246834	+	0.969058i	$0.420610\pi$
$420$	4.66083e10	0.0730872
$421$	2.22481e11	0.345162	0.172581	−	0.984995i	$-0.444789\pi$
$421$	2.22481e11	0.345162	0.172581	+	0.984995i	$0.444789\pi$
$422$	9.05070e11	1.38924
$423$	−9.34970e8	−0.00141993
$424$	8.78845e11	1.32058
$425$	7.56844e10	0.112527
$426$	−3.96156e11	−0.582805
$427$	−2.12177e10	−0.0308867
$428$	2.88576e10	0.0415684
$429$	−1.74798e9	−0.00249160
$430$	7.11972e11	1.00428
$431$	−4.24757e11	−0.592916	−0.296458	−	0.955046i	$-0.595805\pi$
$431$	−4.24757e11	−0.592916	−0.296458	+	0.955046i	$0.595805\pi$
$432$	−7.22622e10	−0.0998239
$433$	1.33542e12	1.82567	0.912837	−	0.408325i	$-0.133887\pi$
$433$	1.33542e12	1.82567	0.912837	+	0.408325i	$0.133887\pi$
$434$	−5.03666e11	−0.681458
$435$	8.96238e10	0.120011
$436$	4.66189e11	0.617836
$437$	−1.02256e12	−1.34129
$438$	−3.15829e11	−0.410033
$439$	−1.39607e12	−1.79397	−0.896987	−	0.442057i	$-0.854249\pi$
$439$	−1.39607e12	−1.79397	−0.896987	+	0.442057i	$0.854249\pi$
$440$	2.31912e10	0.0294976
$441$	−2.10122e11	−0.264544
$442$	−2.35634e10	−0.0293656
$443$	5.81905e11	0.717852	0.358926	−	0.933366i	$-0.383143\pi$
$443$	5.81905e11	0.717852	0.358926	+	0.933366i	$0.383143\pi$
$444$	−2.32285e11	−0.283660
$445$	−8.45944e11	−1.02264
$446$	−1.58975e11	−0.190249
$447$	−5.45504e11	−0.646270
$448$	−4.09820e11	−0.480665
$449$	−5.29072e11	−0.614336	−0.307168	−	0.951655i	$-0.599381\pi$
$449$	−5.29072e11	−0.614336	−0.307168	+	0.951655i	$0.599381\pi$
$450$	8.95010e10	0.102890
$451$	2.97587e10	0.0338703
$452$	3.50648e10	0.0395137
$453$	1.32462e11	0.147791
$454$	−7.01439e11	−0.774888
$455$	4.07054e10	0.0445247
$456$	−5.20175e11	−0.563388
$457$	−1.28899e12	−1.38237	−0.691187	−	0.722676i	$-0.742912\pi$
$457$	−1.28899e12	−1.38237	−0.691187	+	0.722676i	$0.742912\pi$
$458$	−5.67549e11	−0.602710
$459$	−5.35753e10	−0.0563388
$460$	−4.00276e11	−0.416821
$461$	4.40656e11	0.454407	0.227204	−	0.973847i	$-0.427042\pi$
$461$	4.40656e11	0.454407	0.227204	+	0.973847i	$0.427042\pi$
$462$	7.12512e9	0.00727617
$463$	−4.52942e10	−0.0458066	−0.0229033	−	0.999738i	$-0.507291\pi$
$463$	−4.52942e10	−0.0458066	−0.0229033	+	0.999738i	$0.507291\pi$
$464$	−1.37207e11	−0.137418
$465$	−8.53145e11	−0.846222
$466$	9.08642e11	0.892598
$467$	9.95270e11	0.968311	0.484156	−	0.874982i	$-0.339127\pi$
$467$	9.95270e11	0.968311	0.484156	+	0.874982i	$0.339127\pi$
$468$	1.53474e10	0.0147886
$469$	3.84180e11	0.366654
$470$	2.83928e9	0.00268391
$471$	−5.44606e10	−0.0509904
$472$	1.52767e11	0.141674
$473$	−5.99467e10	−0.0550668
$474$	9.00658e11	0.819516
$475$	3.82419e11	0.344682
$476$	−5.29015e10	−0.0472321
$477$	4.57363e11	0.404509
$478$	−1.14022e12	−0.998996
$479$	2.36169e11	0.204981	0.102490	−	0.994734i	$-0.467319\pi$
$479$	2.36169e11	0.204981	0.102490	+	0.994734i	$0.467319\pi$
$480$	−3.53876e11	−0.304274
$481$	−2.02866e11	−0.172805
$482$	−9.73631e11	−0.821642
$483$	−4.69239e11	−0.392313
$484$	4.28263e11	0.354737
$485$	1.52052e12	1.24783
$486$	−6.33557e10	−0.0515137
$487$	8.97688e11	0.723178	0.361589	−	0.932338i	$-0.382234\pi$
$487$	8.97688e11	0.723178	0.361589	+	0.932338i	$0.382234\pi$
$488$	9.26948e10	0.0739888
$489$	−8.26926e11	−0.653999
$490$	6.38088e11	0.500033
$491$	−1.38110e12	−1.07240	−0.536202	−	0.844090i	$-0.680141\pi$
$491$	−1.38110e12	−1.07240	−0.536202	+	0.844090i	$0.680141\pi$
$492$	−2.61283e11	−0.201033
$493$	−1.01725e11	−0.0775563
$494$	−1.19062e11	−0.0899499
$495$	1.20690e10	0.00903542
$496$	1.30609e12	0.968963
$497$	−7.76756e11	−0.571059
$498$	−7.02567e11	−0.511865
$499$	−2.23948e12	−1.61694	−0.808472	−	0.588535i	$-0.799705\pi$
$499$	−2.23948e12	−1.61694	−0.808472	+	0.588535i	$0.799705\pi$
$500$	5.39140e11	0.385777
$501$	−7.27906e11	−0.516185
$502$	−1.32986e12	−0.934630
$503$	−1.10093e12	−0.766840	−0.383420	−	0.923574i	$-0.625254\pi$
$503$	−1.10093e12	−0.766840	−0.383420	+	0.923574i	$0.625254\pi$
$504$	−2.38702e11	−0.164785
$505$	−6.23677e11	−0.426725
$506$	−6.11911e10	−0.0414965
$507$	−8.45561e11	−0.568341
$508$	6.14710e11	0.409528
$509$	1.30158e12	0.859492	0.429746	−	0.902950i	$-0.358603\pi$
$509$	1.30158e12	0.859492	0.429746	+	0.902950i	$0.358603\pi$
$510$	1.62695e11	0.106490
$511$	−6.19256e11	−0.401769
$512$	1.41946e12	0.912867
$513$	−2.70706e11	−0.172572
$514$	1.43878e12	0.909203
$515$	6.47699e10	0.0405733
$516$	5.26336e11	0.326843
$517$	−2.39062e8	−0.000147164 0
$518$	8.26925e11	0.504641
$519$	1.02730e12	0.621504
$520$	−1.77832e11	−0.106658
$521$	−2.03385e12	−1.20934	−0.604670	−	0.796476i	$-0.706695\pi$
$521$	−2.03385e12	−1.20934	−0.604670	+	0.796476i	$0.706695\pi$
$522$	−1.20296e11	−0.0709140
$523$	2.47262e12	1.44511	0.722554	−	0.691314i	$-0.242968\pi$
$523$	2.47262e12	1.44511	0.722554	+	0.691314i	$0.242968\pi$
$524$	9.78335e11	0.566887
$525$	1.75487e11	0.100816
$526$	−3.62602e11	−0.206535
$527$	9.68340e11	0.546865
$528$	−1.84767e10	−0.0103460
$529$	2.22871e12	1.23738
$530$	−1.38890e12	−0.764592
$531$	7.95020e10	0.0433963
$532$	−2.67302e11	−0.144677
$533$	−2.28192e11	−0.122469
$534$	1.13545e12	0.604272
$535$	−1.74014e11	−0.0918318
$536$	−1.67839e12	−0.878316
$537$	−1.06159e12	−0.550902
$538$	2.26596e12	1.16609
$539$	−5.37258e10	−0.0274179
$540$	−1.05967e11	−0.0536287
$541$	−3.02073e12	−1.51609	−0.758043	−	0.652205i	$-0.773844\pi$
$541$	−3.02073e12	−1.51609	−0.758043	+	0.652205i	$0.773844\pi$
$542$	1.96673e12	0.978921
$543$	2.17086e12	1.07160
$544$	4.01657e11	0.196635
$545$	−2.81117e12	−1.36490
$546$	−5.46359e10	−0.0263094
$547$	3.81968e12	1.82425	0.912124	−	0.409914i	$-0.134441\pi$
$547$	3.81968e12	1.82425	0.912124	+	0.409914i	$0.134441\pi$
$548$	1.33625e12	0.632959
$549$	4.82396e10	0.0226636
$550$	2.28844e10	0.0106637
$551$	−5.13998e11	−0.237563
$552$	2.04999e12	0.939780
$553$	1.76595e12	0.802999
$554$	−2.26500e12	−1.02158
$555$	1.40070e12	0.626654
$556$	1.11129e12	0.493162
$557$	8.89967e11	0.391765	0.195882	−	0.980627i	$-0.437243\pi$
$557$	8.89967e11	0.391765	0.195882	+	0.980627i	$0.437243\pi$
$558$	1.14511e12	0.500029
$559$	4.59676e11	0.199112
$560$	4.30269e11	0.184882
$561$	−1.36986e10	−0.00583907
$562$	−2.22068e12	−0.939017
$563$	7.76854e11	0.325875	0.162938	−	0.986636i	$-0.447903\pi$
$563$	7.76854e11	0.325875	0.162938	+	0.986636i	$0.447903\pi$
$564$	2.09898e9	0.000873478 0
$565$	−2.11444e11	−0.0872926
$566$	2.46637e12	1.01015
$567$	−1.24224e11	−0.0504755
$568$	3.39346e12	1.36796
$569$	−3.91130e12	−1.56429	−0.782143	−	0.623099i	$-0.785874\pi$
$569$	−3.91130e12	−1.56429	−0.782143	+	0.623099i	$0.785874\pi$
$570$	8.22068e11	0.326190
$571$	−1.32146e12	−0.520225	−0.260113	−	0.965578i	$-0.583760\pi$
$571$	−1.32146e12	−0.520225	−0.260113	+	0.965578i	$0.583760\pi$
$572$	3.92415e9	0.00153272
$573$	2.37437e11	0.0920135
$574$	9.30156e11	0.357645
$575$	−1.50710e12	−0.574959
$576$	9.31750e11	0.352694
$577$	9.16698e11	0.344298	0.172149	−	0.985071i	$-0.444929\pi$
$577$	9.16698e11	0.344298	0.172149	+	0.985071i	$0.444929\pi$
$578$	1.97011e12	0.734200
$579$	−5.25849e11	−0.194450
$580$	−2.01202e11	−0.0738256
$581$	−1.37755e12	−0.501549
$582$	−2.04089e12	−0.737337
$583$	1.16943e11	0.0419242
$584$	2.70538e12	0.962432
$585$	−9.25461e10	−0.0326706
$586$	−1.41617e12	−0.496108
$587$	7.25192e11	0.252105	0.126052	−	0.992024i	$-0.459769\pi$
$587$	7.25192e11	0.252105	0.126052	+	0.992024i	$0.459769\pi$
$588$	4.71716e11	0.162736
$589$	4.89284e12	1.67511
$590$	−2.41428e11	−0.0820265
$591$	−7.61674e11	−0.256818
$592$	−2.14436e12	−0.717547
$593$	−1.00706e12	−0.334434	−0.167217	−	0.985920i	$-0.553478\pi$
$593$	−1.00706e12	−0.334434	−0.167217	+	0.985920i	$0.553478\pi$
$594$	−1.61994e10	−0.00533899
$595$	3.19002e11	0.104344
$596$	1.22464e12	0.397557
$597$	1.73384e12	0.558630
$598$	4.69218e11	0.150044
$599$	−5.05825e12	−1.60539	−0.802694	−	0.596392i	$-0.796601\pi$
$599$	−5.05825e12	−1.60539	−0.802694	+	0.596392i	$0.796601\pi$
$600$	−7.66661e11	−0.241503
$601$	−4.20153e11	−0.131363	−0.0656814	−	0.997841i	$-0.520922\pi$
$601$	−4.20153e11	−0.131363	−0.0656814	+	0.997841i	$0.520922\pi$
$602$	−1.87373e12	−0.581465
$603$	−8.73456e11	−0.269038
$604$	−2.97372e11	−0.0909146
$605$	−2.58247e12	−0.783675
$606$	8.37116e11	0.252150
$607$	2.83924e12	0.848893	0.424446	−	0.905453i	$-0.360469\pi$
$607$	2.83924e12	0.848893	0.424446	+	0.905453i	$0.360469\pi$
$608$	2.02950e12	0.602314
$609$	−2.35867e11	−0.0694848
$610$	−1.46492e11	−0.0428380
$611$	1.83314e9	0.000532122 0
$612$	1.20275e11	0.0346572
$613$	4.68595e12	1.34037	0.670187	−	0.742193i	$-0.266214\pi$
$613$	4.68595e12	1.34037	0.670187	+	0.742193i	$0.266214\pi$
$614$	−3.63034e12	−1.03083
$615$	1.57556e12	0.444117
$616$	−6.10334e10	−0.0170787
$617$	6.26248e12	1.73966	0.869828	−	0.493355i	$-0.164230\pi$
$617$	6.26248e12	1.73966	0.869828	+	0.493355i	$0.164230\pi$
$618$	−8.69360e10	−0.0239746
$619$	−4.44051e12	−1.21569	−0.607847	−	0.794054i	$-0.707967\pi$
$619$	−4.44051e12	−1.21569	−0.607847	+	0.794054i	$0.707967\pi$
$620$	1.91528e12	0.520559
$621$	1.06684e12	0.287865
$622$	−4.96235e11	−0.132932
$623$	2.22631e12	0.592093
$624$	1.41680e11	0.0374093
$625$	−1.78475e12	−0.467862
$626$	5.36464e12	1.39623
$627$	−6.92166e10	−0.0178857
$628$	1.22262e11	0.0313670
$629$	−1.58983e12	−0.404970
$630$	3.77237e11	0.0954073
$631$	7.46084e12	1.87351	0.936755	−	0.349987i	$-0.113814\pi$
$631$	7.46084e12	1.87351	0.936755	+	0.349987i	$0.113814\pi$
$632$	−7.71500e12	−1.92357
$633$	−4.03466e12	−0.998826
$634$	5.65035e12	1.38891
$635$	−3.70676e12	−0.904718
$636$	−1.02676e12	−0.248836
$637$	4.11973e11	0.0991384
$638$	−3.07583e10	−0.00734968
$639$	1.76600e12	0.419022
$640$	−5.92656e11	−0.139635
$641$	6.49252e12	1.51898	0.759490	−	0.650519i	$-0.225449\pi$
$641$	6.49252e12	1.51898	0.759490	+	0.650519i	$0.225449\pi$
$642$	2.33567e11	0.0542630
$643$	−4.82725e12	−1.11365	−0.556827	−	0.830628i	$-0.687981\pi$
$643$	−4.82725e12	−1.11365	−0.556827	+	0.830628i	$0.687981\pi$
$644$	1.05343e12	0.241334
$645$	−3.17386e12	−0.722052
$646$	−9.33067e11	−0.210798
$647$	−1.71606e12	−0.385002	−0.192501	−	0.981297i	$-0.561660\pi$
$647$	−1.71606e12	−0.385002	−0.192501	+	0.981297i	$0.561660\pi$
$648$	5.42702e11	0.120913
$649$	2.03278e10	0.00449769
$650$	−1.75479e11	−0.0385581
$651$	2.24526e12	0.489951
$652$	1.85642e12	0.402311
$653$	5.54650e12	1.19374	0.596869	−	0.802338i	$-0.296411\pi$
$653$	5.54650e12	1.19374	0.596869	+	0.802338i	$0.296411\pi$
$654$	3.77323e12	0.806516
$655$	−5.89946e12	−1.25235
$656$	−2.41206e12	−0.508534
$657$	1.40791e12	0.294803
$658$	−7.47227e9	−0.00155395
$659$	5.59305e12	1.15522	0.577610	−	0.816313i	$-0.303985\pi$
$659$	5.59305e12	1.15522	0.577610	+	0.816313i	$0.303985\pi$
$660$	−2.70945e10	−0.00555820
$661$	−2.39528e12	−0.488033	−0.244017	−	0.969771i	$-0.578465\pi$
$661$	−2.39528e12	−0.488033	−0.244017	+	0.969771i	$0.578465\pi$
$662$	5.36957e12	1.08662
$663$	1.05042e11	0.0211131
$664$	6.01816e12	1.20145
$665$	1.61186e12	0.319616
$666$	−1.88006e12	−0.370287
$667$	2.02565e12	0.396276
$668$	1.63412e12	0.317535
$669$	7.08686e11	0.136784
$670$	2.65247e12	0.508527
$671$	1.23343e10	0.00234890
$672$	9.31312e11	0.176171
$673$	1.09679e12	0.206089	0.103045	−	0.994677i	$-0.467142\pi$
$673$	1.09679e12	0.206089	0.103045	+	0.994677i	$0.467142\pi$
$674$	−1.18907e12	−0.221941
$675$	−3.98981e11	−0.0739750
$676$	1.89826e12	0.349619
$677$	−2.91299e11	−0.0532954	−0.0266477	−	0.999645i	$-0.508483\pi$
$677$	−2.91299e11	−0.0532954	−0.0266477	+	0.999645i	$0.508483\pi$
$678$	2.83806e11	0.0515808
$679$	−4.00164e12	−0.722476
$680$	−1.39364e12	−0.249954
$681$	3.12690e12	0.557125
$682$	2.92793e11	0.0518241
$683$	−4.83319e12	−0.849847	−0.424924	−	0.905229i	$-0.639699\pi$
$683$	−4.83319e12	−0.849847	−0.424924	+	0.905229i	$0.639699\pi$
$684$	6.07726e11	0.106159
$685$	−8.05772e12	−1.39831
$686$	−3.79525e12	−0.654307
$687$	2.53004e12	0.433333
$688$	4.85891e12	0.826782
$689$	−8.96725e11	−0.151591
$690$	−3.23974e12	−0.544114
$691$	7.26763e12	1.21267	0.606333	−	0.795211i	$-0.292640\pi$
$691$	7.26763e12	1.21267	0.606333	+	0.795211i	$0.292640\pi$
$692$	−2.30625e12	−0.382322
$693$	−3.17626e10	−0.00523138
$694$	4.63475e12	0.758418
$695$	−6.70117e12	−1.08948
$696$	1.03045e12	0.166450
$697$	−1.78830e12	−0.287007
$698$	3.94047e12	0.628345
$699$	−4.05058e12	−0.641756
$700$	−3.93963e11	−0.0620176
$701$	1.24764e13	1.95146	0.975728	−	0.218985i	$-0.0702745\pi$
$701$	1.24764e13	1.95146	0.975728	+	0.218985i	$0.0702745\pi$
$702$	1.24218e11	0.0193049
$703$	−8.03312e12	−1.24047
$704$	2.38238e11	0.0365540
$705$	−1.26570e10	−0.00192966
$706$	−5.53187e12	−0.838012
$707$	1.64136e12	0.247068
$708$	−1.78479e11	−0.0266955
$709$	−9.20508e12	−1.36811	−0.684053	−	0.729433i	$-0.739784\pi$
$709$	−9.20508e12	−1.36811	−0.684053	+	0.729433i	$0.739784\pi$
$710$	−5.36292e12	−0.792024
$711$	−4.01499e12	−0.589211
$712$	−9.72621e12	−1.41835
$713$	−1.92825e13	−2.79422
$714$	−4.28173e11	−0.0616562
$715$	−2.36630e10	−0.00338605
$716$	2.38324e12	0.338891
$717$	5.08292e12	0.718253
$718$	5.44939e12	0.765222
$719$	5.25770e12	0.733696	0.366848	−	0.930281i	$-0.380437\pi$
$719$	5.25770e12	0.733696	0.366848	+	0.930281i	$0.380437\pi$
$720$	−9.78241e11	−0.135659
$721$	−1.70458e11	−0.0234914
$722$	1.14870e12	0.157322
$723$	4.34029e12	0.590740
$724$	−4.87352e12	−0.659203
$725$	−7.57558e11	−0.101834
$726$	3.46626e12	0.463070
$727$	−3.84442e12	−0.510418	−0.255209	−	0.966886i	$-0.582144\pi$
$727$	−3.84442e12	−0.510418	−0.255209	+	0.966886i	$0.582144\pi$
$728$	4.68009e11	0.0617537
$729$	2.82430e11	0.0370370
$730$	−4.27549e12	−0.557229
$731$	3.60240e12	0.466621
$732$	−1.08296e11	−0.0139416
$733$	−1.01488e13	−1.29852	−0.649259	−	0.760567i	$-0.724921\pi$
$733$	−1.01488e13	−1.29852	−0.649259	+	0.760567i	$0.724921\pi$
$734$	2.50044e12	0.317969
$735$	−2.84450e12	−0.359511
$736$	−7.99819e12	−1.00471
$737$	−2.23333e11	−0.0278836
$738$	−2.11476e12	−0.262427
$739$	8.01395e11	0.0988432	0.0494216	−	0.998778i	$-0.484262\pi$
$739$	8.01395e11	0.0988432	0.0494216	+	0.998778i	$0.484262\pi$
$740$	−3.14453e12	−0.385490
$741$	5.30758e11	0.0646717
$742$	3.65524e12	0.442688
$743$	−3.34243e12	−0.402358	−0.201179	−	0.979555i	$-0.564477\pi$
$743$	−3.34243e12	−0.402358	−0.201179	+	0.979555i	$0.564477\pi$
$744$	−9.80900e12	−1.17367
$745$	−7.38469e12	−0.878272
$746$	−1.08420e13	−1.28169
$747$	3.13193e12	0.368018
$748$	3.07529e10	0.00359194
$749$	4.57962e11	0.0531693
$750$	4.36367e12	0.503589
$751$	−1.86106e12	−0.213491	−0.106746	−	0.994286i	$-0.534043\pi$
$751$	−1.86106e12	−0.213491	−0.106746	+	0.994286i	$0.534043\pi$
$752$	1.93769e10	0.00220955
$753$	5.92831e12	0.671975
$754$	2.35857e11	0.0265752
$755$	1.79318e12	0.200846
$756$	2.78878e11	0.0310503
$757$	−1.12176e13	−1.24157	−0.620784	−	0.783982i	$-0.713185\pi$
$757$	−1.12176e13	−1.24157	−0.620784	+	0.783982i	$0.713185\pi$
$758$	7.93505e11	0.0873048
$759$	2.72780e11	0.0298349
$760$	−7.04180e12	−0.765636
$761$	−1.53092e13	−1.65471	−0.827354	−	0.561681i	$-0.810155\pi$
$761$	−1.53092e13	−1.65471	−0.827354	+	0.561681i	$0.810155\pi$
$762$	4.97532e12	0.534594
$763$	7.39828e12	0.790261
$764$	−5.33037e11	−0.0566027
$765$	−7.25269e11	−0.0765636
$766$	−1.29348e13	−1.35747
$767$	−1.55875e11	−0.0162629
$768$	−5.09410e12	−0.528375
$769$	−5.51350e12	−0.568537	−0.284269	−	0.958745i	$-0.591751\pi$
$769$	−5.51350e12	−0.568537	−0.284269	+	0.958745i	$0.591751\pi$
$770$	9.64554e10	0.00988822
$771$	−6.41385e12	−0.653694
$772$	1.18051e12	0.119617
$773$	1.48992e13	1.50091	0.750456	−	0.660921i	$-0.229834\pi$
$773$	1.48992e13	1.50091	0.750456	+	0.660921i	$0.229834\pi$
$774$	4.26004e12	0.426658
$775$	7.21133e12	0.718055
$776$	1.74822e13	1.73068
$777$	−3.68630e12	−0.362824
$778$	−1.17561e13	−1.15041
$779$	−9.03595e12	−0.879134
$780$	2.07763e11	0.0200975
$781$	4.51547e11	0.0434284
$782$	3.67718e12	0.351629
$783$	5.36258e11	0.0509854
$784$	4.35469e12	0.411656
$785$	−7.37253e11	−0.0692952
$786$	7.91842e12	0.740009
$787$	−6.16580e12	−0.572933	−0.286466	−	0.958090i	$-0.592481\pi$
$787$	−6.16580e12	−0.572933	−0.286466	+	0.958090i	$0.592481\pi$
$788$	1.70993e12	0.157983
$789$	1.61642e12	0.148494
$790$	1.21925e13	1.11371
$791$	5.56468e11	0.0505412
$792$	1.38763e11	0.0125317
$793$	−9.45806e10	−0.00849323
$794$	−1.98955e12	−0.177649
$795$	6.19149e12	0.549722
$796$	−3.89241e12	−0.343645
$797$	−2.00164e13	−1.75721	−0.878607	−	0.477546i	$-0.841526\pi$
$797$	−2.00164e13	−1.75721	−0.878607	+	0.477546i	$0.841526\pi$
$798$	−2.16348e12	−0.188860
$799$	1.43660e10	0.00124703
$800$	2.99118e12	0.258189
$801$	−5.06165e12	−0.434456
$802$	4.89413e12	0.417725
$803$	3.59988e11	0.0305540
$804$	1.96088e12	0.165500
$805$	−6.35227e12	−0.533147
$806$	−2.24516e12	−0.187387
$807$	−1.01013e13	−0.838389
$808$	−7.17070e12	−0.591848
$809$	1.58868e13	1.30398	0.651988	−	0.758230i	$-0.273935\pi$
$809$	1.58868e13	1.30398	0.651988	+	0.758230i	$0.273935\pi$
$810$	−8.57670e11	−0.0700064
$811$	−4.96216e12	−0.402789	−0.201394	−	0.979510i	$-0.564547\pi$
$811$	−4.96216e12	−0.402789	−0.201394	+	0.979510i	$0.564547\pi$
$812$	5.29514e11	0.0427440
$813$	−8.76735e12	−0.703819
$814$	−4.80712e11	−0.0383773
$815$	−1.11944e13	−0.888775
$816$	1.11033e12	0.0876688
$817$	1.82023e13	1.42931
$818$	7.87389e11	0.0614893
$819$	2.43558e11	0.0189158
$820$	−3.53708e12	−0.273202
$821$	−2.00520e13	−1.54033	−0.770164	−	0.637846i	$-0.779826\pi$
$821$	−2.00520e13	−1.54033	−0.770164	+	0.637846i	$0.779826\pi$
$822$	1.08153e13	0.826258
$823$	1.39355e13	1.05882	0.529410	−	0.848366i	$-0.322413\pi$
$823$	1.39355e13	1.05882	0.529410	+	0.848366i	$0.322413\pi$
$824$	7.44690e11	0.0562734
$825$	−1.02015e11	−0.00766693
$826$	6.35379e11	0.0474922
$827$	1.67616e13	1.24606	0.623031	−	0.782197i	$-0.285901\pi$
$827$	1.67616e13	1.24606	0.623031	+	0.782197i	$0.285901\pi$
$828$	−2.39503e12	−0.177082
$829$	−1.06490e13	−0.783095	−0.391548	−	0.920158i	$-0.628060\pi$
$829$	−1.06490e13	−0.783095	−0.391548	+	0.920158i	$0.628060\pi$
$830$	−9.51091e12	−0.695618
$831$	1.00970e13	0.734493
$832$	−1.82683e12	−0.132173
$833$	3.22857e12	0.232331
$834$	8.99450e12	0.643768
$835$	−9.85393e12	−0.701488
$836$	1.55389e11	0.0110025
$837$	−5.10474e12	−0.359508
$838$	−5.65925e12	−0.396425
$839$	2.13820e13	1.48977	0.744886	−	0.667192i	$-0.232504\pi$
$839$	2.13820e13	1.48977	0.744886	+	0.667192i	$0.232504\pi$
$840$	−3.23139e12	−0.223941
$841$	−1.34889e13	−0.929813
$842$	−4.04252e12	−0.277171
$843$	9.89945e12	0.675129
$844$	9.05767e12	0.614435
$845$	−1.14467e13	−0.772368
$846$	1.69886e10	0.00114023
$847$	6.79641e12	0.453737
$848$	−9.47867e12	−0.629457
$849$	−1.09947e13	−0.726271
$850$	−1.37520e12	−0.0903612
$851$	3.16583e13	2.06921
$852$	−3.96461e12	−0.257764
$853$	−1.06774e13	−0.690548	−0.345274	−	0.938502i	$-0.612214\pi$
$853$	−1.06774e13	−0.690548	−0.345274	+	0.938502i	$0.612214\pi$
$854$	3.85530e11	0.0248026
$855$	−3.66465e12	−0.234523
$856$	−2.00072e12	−0.127366
$857$	1.26338e13	0.800054	0.400027	−	0.916503i	$-0.369001\pi$
$857$	1.26338e13	0.800054	0.400027	+	0.916503i	$0.369001\pi$
$858$	3.17612e10	0.00200080
$859$	−2.64136e13	−1.65523	−0.827615	−	0.561296i	$-0.810303\pi$
$859$	−2.64136e13	−1.65523	−0.827615	+	0.561296i	$0.810303\pi$
$860$	7.12521e12	0.444175
$861$	−4.14648e12	−0.257138
$862$	7.71794e12	0.476122
$863$	2.48314e13	1.52388	0.761942	−	0.647645i	$-0.224246\pi$
$863$	2.48314e13	1.52388	0.761942	+	0.647645i	$0.224246\pi$
$864$	−2.11739e12	−0.129268
$865$	1.39069e13	0.844616
$866$	−2.42649e13	−1.46605
$867$	−8.78242e12	−0.527872
$868$	−5.04054e12	−0.301397
$869$	−1.02659e12	−0.0610671
$870$	−1.62849e12	−0.0963712
$871$	1.71253e12	0.100823
$872$	−3.23213e13	−1.89306
$873$	9.09795e12	0.530126
$874$	1.85801e13	1.07708
$875$	8.55599e12	0.493440
$876$	−3.16072e12	−0.181350
$877$	−1.05883e13	−0.604405	−0.302203	−	0.953244i	$-0.597722\pi$
$877$	−1.05883e13	−0.604405	−0.302203	+	0.953244i	$0.597722\pi$
$878$	2.53669e13	1.44059
$879$	6.31305e12	0.356689
$880$	−2.50125e11	−0.0140600
$881$	2.49573e13	1.39575	0.697874	−	0.716221i	$-0.254130\pi$
$881$	2.49573e13	1.39575	0.697874	+	0.716221i	$0.254130\pi$
$882$	3.81796e12	0.212433
$883$	−2.63084e13	−1.45637	−0.728184	−	0.685382i	$-0.759635\pi$
$883$	−2.63084e13	−1.45637	−0.728184	+	0.685382i	$0.759635\pi$
$884$	−2.35816e11	−0.0129879
$885$	1.07625e12	0.0589750
$886$	−1.05733e13	−0.576449
$887$	6.05761e12	0.328583	0.164291	−	0.986412i	$-0.447466\pi$
$887$	6.05761e12	0.328583	0.164291	+	0.986412i	$0.447466\pi$
$888$	1.61045e13	0.869140
$889$	9.75527e12	0.523819
$890$	1.53710e13	0.821197
$891$	7.22142e10	0.00383860
$892$	−1.59098e12	−0.0841437
$893$	7.25890e10	0.00381979
$894$	9.91193e12	0.518967
$895$	−1.43712e13	−0.748668
$896$	1.55972e12	0.0808465
$897$	−2.09170e12	−0.107878
$898$	9.61337e12	0.493324
$899$	−9.69253e12	−0.494901
$900$	8.95699e11	0.0455062
$901$	−7.02749e12	−0.355254
$902$	−5.40722e11	−0.0271985
$903$	8.35280e12	0.418059
$904$	−2.43107e12	−0.121071
$905$	2.93878e13	1.45629
$906$	−2.40686e12	−0.118679
$907$	4.24714e12	0.208384	0.104192	−	0.994557i	$-0.466774\pi$
$907$	4.24714e12	0.208384	0.104192	+	0.994557i	$0.466774\pi$
$908$	−7.01980e12	−0.342719
$909$	−3.73173e12	−0.181290
$910$	−7.39627e11	−0.0357541
$911$	−2.80542e10	−0.00134948	−0.000674739	−	1.00000i	$-0.500215\pi$
$911$	−2.80542e10	−0.00134948	−0.000674739		1.00000i	$0.500215\pi$
$912$	5.61027e12	0.268539
$913$	8.00801e11	0.0381422
$914$	2.34212e13	1.11007
$915$	6.53038e11	0.0307995
$916$	−5.67986e12	−0.266568
$917$	1.55259e13	0.725094
$918$	9.73476e11	0.0452411
$919$	9.06347e12	0.419155	0.209578	−	0.977792i	$-0.432791\pi$
$919$	9.06347e12	0.419155	0.209578	+	0.977792i	$0.432791\pi$
$920$	2.77515e13	1.27715
$921$	1.61835e13	0.741144
$922$	−8.00682e12	−0.364898
$923$	−3.46250e12	−0.157030
$924$	7.13060e10	0.00321812
$925$	−1.18396e13	−0.531742
$926$	8.23007e11	0.0367836
$927$	3.87547e11	0.0172371
$928$	−4.02036e12	−0.177950
$929$	1.42413e13	0.627306	0.313653	−	0.949538i	$-0.398447\pi$
$929$	1.42413e13	0.627306	0.313653	+	0.949538i	$0.398447\pi$
$930$	1.55018e13	0.679532
$931$	1.63134e13	0.711656
$932$	9.09341e12	0.394780
$933$	2.21213e12	0.0955749
$934$	−1.80843e13	−0.777572
$935$	−1.85443e11	−0.00793522
$936$	−1.06405e12	−0.0453126
$937$	−1.79359e12	−0.0760142	−0.0380071	−	0.999277i	$-0.512101\pi$
$937$	−1.79359e12	−0.0760142	−0.0380071	+	0.999277i	$0.512101\pi$
$938$	−6.98064e12	−0.294430
$939$	−2.39147e13	−1.00385
$940$	2.84146e10	0.00118704
$941$	1.93549e13	0.804707	0.402354	−	0.915484i	$-0.368192\pi$
$941$	1.93549e13	0.804707	0.402354	+	0.915484i	$0.368192\pi$
$942$	9.89562e11	0.0409462
$943$	3.56104e13	1.46647
$944$	−1.64765e12	−0.0675290
$945$	−1.68166e12	−0.0685954
$946$	1.08925e12	0.0442197
$947$	8.51355e12	0.343982	0.171991	−	0.985099i	$-0.444980\pi$
$947$	8.51355e12	0.343982	0.171991	+	0.985099i	$0.444980\pi$
$948$	9.01352e12	0.362457
$949$	−2.76042e12	−0.110478
$950$	−6.94865e12	−0.276786
$951$	−2.51883e13	−0.998590
$952$	3.66771e12	0.144720
$953$	1.91350e12	0.0751469	0.0375734	−	0.999294i	$-0.488037\pi$
$953$	1.91350e12	0.0751469	0.0375734	+	0.999294i	$0.488037\pi$
$954$	−8.31040e12	−0.324828
$955$	3.21427e12	0.125045
$956$	−1.14110e13	−0.441838
$957$	1.37115e11	0.00528424
$958$	−4.29125e12	−0.164603
$959$	2.12059e13	0.809605
$960$	1.26135e13	0.479307
$961$	6.58253e13	2.48965
$962$	3.68613e12	0.138766
$963$	−1.04120e12	−0.0390137
$964$	−9.74381e12	−0.363398
$965$	−7.11862e12	−0.264255
$966$	8.52619e12	0.315034
$967$	−2.15966e13	−0.794268	−0.397134	−	0.917761i	$-0.629995\pi$
$967$	−2.15966e13	−0.794268	−0.397134	+	0.917761i	$0.629995\pi$
$968$	−2.96918e13	−1.08692
$969$	4.15946e12	0.151558
$970$	−2.76283e13	−1.00203
$971$	−2.99863e13	−1.08252	−0.541261	−	0.840854i	$-0.682053\pi$
$971$	−2.99863e13	−1.08252	−0.541261	+	0.840854i	$0.682053\pi$
$972$	−6.34045e11	−0.0227836
$973$	1.76358e13	0.630794
$974$	−1.63112e13	−0.580726
$975$	7.82259e11	0.0277223
$976$	−9.99746e11	−0.0352668
$977$	1.77038e13	0.621642	0.310821	−	0.950469i	$-0.399396\pi$
$977$	1.77038e13	0.621642	0.310821	+	0.950469i	$0.399396\pi$
$978$	1.50254e13	0.525173
$979$	−1.29421e12	−0.0450280
$980$	6.38580e12	0.221156
$981$	−1.68204e13	−0.579865
$982$	2.50949e13	0.861161
$983$	−2.82507e13	−0.965025	−0.482513	−	0.875889i	$-0.660276\pi$
$983$	−2.82507e13	−0.965025	−0.482513	+	0.875889i	$0.660276\pi$
$984$	1.81150e13	0.615970
$985$	−1.03111e13	−0.349012
$986$	1.84837e12	0.0622792
$987$	3.33102e10	0.00111725
$988$	−1.19153e12	−0.0397832
$989$	−7.17345e13	−2.38421
$990$	−2.19297e11	−0.00725561
$991$	−2.72770e13	−0.898391	−0.449196	−	0.893433i	$-0.648289\pi$
$991$	−2.72770e13	−0.898391	−0.449196	+	0.893433i	$0.648289\pi$
$992$	3.82705e13	1.25476
$993$	−2.39367e13	−0.781254
$994$	1.41138e13	0.458571
$995$	2.34716e13	0.759170
$996$	−7.03108e12	−0.226389
$997$	9.74389e12	0.312323	0.156162	−	0.987732i	$-0.450088\pi$
$997$	9.74389e12	0.312323	0.156162	+	0.987732i	$0.450088\pi$
$998$	4.06919e13	1.29844
$999$	8.38102e12	0.266227

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.8	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.8	✓	21	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-18.1702 q^{2} +81.0000 q^{3} -181.842 q^{4} +1096.53 q^{5} -1471.79 q^{6} -2885.78 q^{7} +12607.3 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-18.1702 q^{2} +81.0000 q^{3} -181.842 q^{4} +1096.53 q^{5} -1471.79 q^{6} -2885.78 q^{7} +12607.3 q^{8} +6561.00 q^{9} -19924.2 q^{10} +1677.58 q^{11} -14729.2 q^{12} -12863.8 q^{13} +52435.4 q^{14} +88818.7 q^{15} -135974. q^{16} -100811. q^{17} -119215. q^{18} -509381. q^{19} -199395. q^{20} -233749. q^{21} -30482.0 q^{22} +2.00745e6 q^{23} +1.02119e6 q^{24} -750753. q^{25} +233738. q^{26} +531441. q^{27} +524758. q^{28} +1.00906e6 q^{29} -1.61386e6 q^{30} -9.60546e6 q^{31} -3.98425e6 q^{32} +135884. q^{33} +1.83177e6 q^{34} -3.16434e6 q^{35} -1.19307e6 q^{36} +1.57704e7 q^{37} +9.25558e6 q^{38} -1.04197e6 q^{39} +1.38242e7 q^{40} +1.77391e7 q^{41} +4.24727e6 q^{42} -3.57341e7 q^{43} -305054. q^{44} +7.19432e6 q^{45} -3.64759e7 q^{46} -142504. q^{47} -1.10139e7 q^{48} -3.20259e7 q^{49} +1.36414e7 q^{50} -8.16572e6 q^{51} +2.33918e6 q^{52} +6.97093e7 q^{53} -9.65641e6 q^{54} +1.83951e6 q^{55} -3.63819e7 q^{56} -4.12599e7 q^{57} -1.83349e7 q^{58} +1.21174e7 q^{59} -1.61510e7 q^{60} +7.35248e6 q^{61} +1.74534e8 q^{62} -1.89336e7 q^{63} +1.42013e8 q^{64} -1.41055e7 q^{65} -2.46904e6 q^{66} -1.33128e8 q^{67} +1.83318e7 q^{68} +1.62604e8 q^{69} +5.74969e7 q^{70} +2.69166e8 q^{71} +8.27164e7 q^{72} +2.14588e8 q^{73} -2.86551e8 q^{74} -6.08110e7 q^{75} +9.26270e7 q^{76} -4.84112e6 q^{77} +1.89328e7 q^{78} -6.11948e8 q^{79} -1.49099e8 q^{80} +4.30467e7 q^{81} -3.22323e8 q^{82} +4.77356e8 q^{83} +4.25054e7 q^{84} -1.10542e8 q^{85} +6.49297e8 q^{86} +8.17342e7 q^{87} +2.11497e7 q^{88} -7.71476e8 q^{89} -1.30722e8 q^{90} +3.71221e7 q^{91} -3.65040e8 q^{92} -7.78043e8 q^{93} +2.58934e6 q^{94} -5.58550e8 q^{95} -3.22724e8 q^{96} +1.38667e9 q^{97} +5.81917e8 q^{98} +1.10066e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * q^99

Introduction

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