LMFDB - Embedded newform 177.10.a.a.1.5

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			1.5
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)

$f(q)$	$=$	$q-29.8118 q^{2} +81.0000 q^{3} +376.741 q^{4} +1198.15 q^{5} -2414.75 q^{6} +3753.28 q^{7} +4032.31 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-29.8118 q^{2} +81.0000 q^{3} +376.741 q^{4} +1198.15 q^{5} -2414.75 q^{6} +3753.28 q^{7} +4032.31 q^{8} +6561.00 q^{9} -35719.0 q^{10} +57581.4 q^{11} +30516.0 q^{12} -96612.2 q^{13} -111892. q^{14} +97050.2 q^{15} -313102. q^{16} +199617. q^{17} -195595. q^{18} -341838. q^{19} +451392. q^{20} +304015. q^{21} -1.71660e6 q^{22} -730028. q^{23} +326617. q^{24} -517560. q^{25} +2.88018e6 q^{26} +531441. q^{27} +1.41401e6 q^{28} -6.39864e6 q^{29} -2.89324e6 q^{30} -5.53055e6 q^{31} +7.26957e6 q^{32} +4.66410e6 q^{33} -5.95092e6 q^{34} +4.49699e6 q^{35} +2.47180e6 q^{36} -1.72095e7 q^{37} +1.01908e7 q^{38} -7.82559e6 q^{39} +4.83131e6 q^{40} -3.16553e7 q^{41} -9.06323e6 q^{42} +1.31337e7 q^{43} +2.16933e7 q^{44} +7.86107e6 q^{45} +2.17634e7 q^{46} -1.21817e7 q^{47} -2.53612e7 q^{48} -2.62665e7 q^{49} +1.54294e7 q^{50} +1.61689e7 q^{51} -3.63978e7 q^{52} +3.91644e7 q^{53} -1.58432e7 q^{54} +6.89912e7 q^{55} +1.51344e7 q^{56} -2.76889e7 q^{57} +1.90755e8 q^{58} +1.21174e7 q^{59} +3.65628e7 q^{60} -4.88904e7 q^{61} +1.64875e8 q^{62} +2.46252e7 q^{63} -5.64106e7 q^{64} -1.15756e8 q^{65} -1.39045e8 q^{66} +4.81274e7 q^{67} +7.52037e7 q^{68} -5.91322e7 q^{69} -1.34063e8 q^{70} -1.07918e7 q^{71} +2.64560e7 q^{72} +3.67275e8 q^{73} +5.13046e8 q^{74} -4.19224e7 q^{75} -1.28784e8 q^{76} +2.16119e8 q^{77} +2.33295e8 q^{78} +3.81830e8 q^{79} -3.75143e8 q^{80} +4.30467e7 q^{81} +9.43701e8 q^{82} -3.92397e8 q^{83} +1.14535e8 q^{84} +2.39171e8 q^{85} -3.91537e8 q^{86} -5.18290e8 q^{87} +2.32186e8 q^{88} -2.06771e8 q^{89} -2.34352e8 q^{90} -3.62612e8 q^{91} -2.75031e8 q^{92} -4.47974e8 q^{93} +3.63159e8 q^{94} -4.09573e8 q^{95} +5.88835e8 q^{96} -1.55606e9 q^{97} +7.83051e8 q^{98} +3.77792e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−29.8118	−1.31751	−0.658753	−	0.752359i	$-0.728916\pi$
$2$	−29.8118	−1.31751	−0.658753	+	0.752359i	$0.728916\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	376.741	0.735822
$5$	1198.15	0.857327	0.428663	−	0.903464i	$-0.358985\pi$
$5$	1198.15	0.857327	0.428663	+	0.903464i	$0.358985\pi$
$6$	−2414.75	−0.760662
$7$	3753.28	0.590839	0.295420	−	0.955368i	$-0.404541\pi$
$7$	3753.28	0.590839	0.295420	+	0.955368i	$0.404541\pi$
$8$	4032.31	0.348056
$9$	6561.00	0.333333
$10$	−35719.0	−1.12953
$11$	57581.4	1.18581	0.592905	−	0.805272i	$-0.297981\pi$
$11$	57581.4	1.18581	0.592905	+	0.805272i	$0.297981\pi$
$12$	30516.0	0.424827
$13$	−96612.2	−0.938182	−0.469091	−	0.883150i	$-0.655418\pi$
$13$	−96612.2	−0.938182	−0.469091	+	0.883150i	$0.655418\pi$
$14$	−111892.	−0.778434
$15$	97050.2	0.494978
$16$	−313102.	−1.19439
$17$	199617.	0.579664	0.289832	−	0.957078i	$-0.406401\pi$
$17$	199617.	0.579664	0.289832	+	0.957078i	$0.406401\pi$
$18$	−195595.	−0.439169
$19$	−341838.	−0.601768	−0.300884	−	0.953661i	$-0.597282\pi$
$19$	−341838.	−0.601768	−0.300884	+	0.953661i	$0.597282\pi$
$20$	451392.	0.630840
$21$	304015.	0.341121
$22$	−1.71660e6	−1.56231
$23$	−730028.	−0.543956	−0.271978	−	0.962303i	$-0.587678\pi$
$23$	−730028.	−0.543956	−0.271978	+	0.962303i	$0.587678\pi$
$24$	326617.	0.200950
$25$	−517560.	−0.264991
$26$	2.88018e6	1.23606
$27$	531441.	0.192450
$28$	1.41401e6	0.434753
$29$	−6.39864e6	−1.67995	−0.839976	−	0.542623i	$-0.817431\pi$
$29$	−6.39864e6	−1.67995	−0.839976	+	0.542623i	$0.817431\pi$
$30$	−2.89324e6	−0.652136
$31$	−5.53055e6	−1.07557	−0.537787	−	0.843081i	$-0.680740\pi$
$31$	−5.53055e6	−1.07557	−0.537787	+	0.843081i	$0.680740\pi$
$32$	7.26957e6	1.22556
$33$	4.66410e6	0.684628
$34$	−5.95092e6	−0.763711
$35$	4.49699e6	0.506542
$36$	2.47180e6	0.245274
$37$	−1.72095e7	−1.50960	−0.754798	−	0.655958i	$-0.772265\pi$
$37$	−1.72095e7	−1.50960	−0.754798	+	0.655958i	$0.772265\pi$
$38$	1.01908e7	0.792832
$39$	−7.82559e6	−0.541660
$40$	4.83131e6	0.298398
$41$	−3.16553e7	−1.74952	−0.874761	−	0.484555i	$-0.838982\pi$
$41$	−3.16553e7	−1.74952	−0.874761	+	0.484555i	$0.838982\pi$
$42$	−9.06323e6	−0.449429
$43$	1.31337e7	0.585838	0.292919	−	0.956137i	$-0.405373\pi$
$43$	1.31337e7	0.585838	0.292919	+	0.956137i	$0.405373\pi$
$44$	2.16933e7	0.872546
$45$	7.86107e6	0.285776
$46$	2.17634e7	0.716666
$47$	−1.21817e7	−0.364140	−0.182070	−	0.983286i	$-0.558280\pi$
$47$	−1.21817e7	−0.364140	−0.182070	+	0.983286i	$0.558280\pi$
$48$	−2.53612e7	−0.689580
$49$	−2.62665e7	−0.650909
$50$	1.54294e7	0.349127
$51$	1.61689e7	0.334669
$52$	−3.63978e7	−0.690335
$53$	3.91644e7	0.681789	0.340894	−	0.940102i	$-0.389270\pi$
$53$	3.91644e7	0.681789	0.340894	+	0.940102i	$0.389270\pi$
$54$	−1.58432e7	−0.253554
$55$	6.89912e7	1.01663
$56$	1.51344e7	0.205645
$57$	−2.76889e7	−0.347431
$58$	1.90755e8	2.21335
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	3.65628e7	0.364216
$61$	−4.88904e7	−0.452105	−0.226052	−	0.974115i	$-0.572582\pi$
$61$	−4.88904e7	−0.452105	−0.226052	+	0.974115i	$0.572582\pi$
$62$	1.64875e8	1.41708
$63$	2.46252e7	0.196946
$64$	−5.64106e7	−0.420291
$65$	−1.15756e8	−0.804329
$66$	−1.39045e8	−0.902002
$67$	4.81274e7	0.291780	0.145890	−	0.989301i	$-0.453395\pi$
$67$	4.81274e7	0.291780	0.145890	+	0.989301i	$0.453395\pi$
$68$	7.52037e7	0.426530
$69$	−5.91322e7	−0.314053
$70$	−1.34063e8	−0.667373
$71$	−1.07918e7	−0.0504001	−0.0252000	−	0.999682i	$-0.508022\pi$
$71$	−1.07918e7	−0.0504001	−0.0252000	+	0.999682i	$0.508022\pi$
$72$	2.64560e7	0.116019
$73$	3.67275e8	1.51369	0.756847	−	0.653592i	$-0.226739\pi$
$73$	3.67275e8	1.51369	0.756847	+	0.653592i	$0.226739\pi$
$74$	5.13046e8	1.98890
$75$	−4.19224e7	−0.152992
$76$	−1.28784e8	−0.442794
$77$	2.16119e8	0.700624
$78$	2.33295e8	0.713640
$79$	3.81830e8	1.10293	0.551466	−	0.834198i	$-0.314069\pi$
$79$	3.81830e8	1.10293	0.551466	+	0.834198i	$0.314069\pi$
$80$	−3.75143e8	−1.02398
$81$	4.30467e7	0.111111
$82$	9.43701e8	2.30501
$83$	−3.92397e8	−0.907557	−0.453778	−	0.891115i	$-0.649924\pi$
$83$	−3.92397e8	−0.907557	−0.453778	+	0.891115i	$0.649924\pi$
$84$	1.14535e8	0.251005
$85$	2.39171e8	0.496961
$86$	−3.91537e8	−0.771845
$87$	−5.18290e8	−0.969921
$88$	2.32186e8	0.412728
$89$	−2.06771e8	−0.349329	−0.174665	−	0.984628i	$-0.555884\pi$
$89$	−2.06771e8	−0.349329	−0.174665	+	0.984628i	$0.555884\pi$
$90$	−2.34352e8	−0.376511
$91$	−3.62612e8	−0.554315
$92$	−2.75031e8	−0.400255
$93$	−4.47974e8	−0.620983
$94$	3.63159e8	0.479757
$95$	−4.09573e8	−0.515911
$96$	5.88835e8	0.707576
$97$	−1.55606e9	−1.78465	−0.892324	−	0.451396i	$-0.850926\pi$
$97$	−1.55606e9	−1.78465	−0.892324	+	0.451396i	$0.850926\pi$
$98$	7.83051e8	0.857576
$99$	3.77792e8	0.395270
$100$	−1.94986e8	−0.194986
$101$	3.34551e8	0.319901	0.159951	−	0.987125i	$-0.448867\pi$
$101$	3.34551e8	0.319901	0.159951	+	0.987125i	$0.448867\pi$
$102$	−4.82024e8	−0.440929
$103$	−5.05827e8	−0.442827	−0.221414	−	0.975180i	$-0.571067\pi$
$103$	−5.05827e8	−0.442827	−0.221414	+	0.975180i	$0.571067\pi$
$104$	−3.89570e8	−0.326540
$105$	3.64256e8	0.292452
$106$	−1.16756e9	−0.898261
$107$	1.20865e8	0.0891399	0.0445699	−	0.999006i	$-0.485808\pi$
$107$	1.20865e8	0.0891399	0.0445699	+	0.999006i	$0.485808\pi$
$108$	2.00216e8	0.141609
$109$	−4.83140e8	−0.327834	−0.163917	−	0.986474i	$-0.552413\pi$
$109$	−4.83140e8	−0.327834	−0.163917	+	0.986474i	$0.552413\pi$
$110$	−2.05675e9	−1.33941
$111$	−1.39397e9	−0.871565
$112$	−1.17516e9	−0.705691
$113$	2.71907e8	0.156880	0.0784399	−	0.996919i	$-0.475006\pi$
$113$	2.71907e8	0.156880	0.0784399	+	0.996919i	$0.475006\pi$
$114$	8.25453e8	0.457742
$115$	−8.74683e8	−0.466348
$116$	−2.41063e9	−1.23615
$117$	−6.33873e8	−0.312727
$118$	−3.61240e8	−0.171525
$119$	7.49216e8	0.342488
$120$	3.91336e8	0.172280
$121$	9.57675e8	0.406148
$122$	1.45751e9	0.595651
$123$	−2.56408e9	−1.01009
$124$	−2.08358e9	−0.791432
$125$	−2.96025e9	−1.08451
$126$	−7.34122e8	−0.259478
$127$	3.84542e9	1.31168	0.655839	−	0.754901i	$-0.272315\pi$
$127$	3.84542e9	1.31168	0.655839	+	0.754901i	$0.272315\pi$
$128$	−2.04032e9	−0.671821
$129$	1.06383e9	0.338234
$130$	3.45089e9	1.05971
$131$	1.21601e9	0.360759	0.180379	−	0.983597i	$-0.442267\pi$
$131$	1.21601e9	0.360759	0.180379	+	0.983597i	$0.442267\pi$
$132$	1.75716e9	0.503765
$133$	−1.28301e9	−0.355548
$134$	−1.43476e9	−0.384422
$135$	6.36746e8	0.164993
$136$	8.04916e8	0.201755
$137$	−1.94951e9	−0.472805	−0.236403	−	0.971655i	$-0.575968\pi$
$137$	−1.94951e9	−0.472805	−0.236403	+	0.971655i	$0.575968\pi$
$138$	1.76284e9	0.413767
$139$	−5.65775e9	−1.28552	−0.642758	−	0.766070i	$-0.722210\pi$
$139$	−5.65775e9	−1.28552	−0.642758	+	0.766070i	$0.722210\pi$
$140$	1.69420e9	0.372725
$141$	−9.86721e8	−0.210237
$142$	3.21722e8	0.0664024
$143$	−5.56307e9	−1.11251
$144$	−2.05426e9	−0.398129
$145$	−7.66654e9	−1.44027
$146$	−1.09491e10	−1.99430
$147$	−2.12759e9	−0.375802
$148$	−6.48352e9	−1.11079
$149$	−4.00709e9	−0.666025	−0.333013	−	0.942922i	$-0.608065\pi$
$149$	−4.00709e9	−0.666025	−0.333013	+	0.942922i	$0.608065\pi$
$150$	1.24978e9	0.201569
$151$	−5.01208e9	−0.784552	−0.392276	−	0.919848i	$-0.628312\pi$
$151$	−5.01208e9	−0.784552	−0.392276	+	0.919848i	$0.628312\pi$
$152$	−1.37840e9	−0.209449
$153$	1.30968e9	0.193221
$154$	−6.44289e9	−0.923076
$155$	−6.62643e9	−0.922119
$156$	−2.94822e9	−0.398565
$157$	−2.10960e9	−0.277109	−0.138555	−	0.990355i	$-0.544246\pi$
$157$	−2.10960e9	−0.277109	−0.138555	+	0.990355i	$0.544246\pi$
$158$	−1.13830e10	−1.45312
$159$	3.17231e9	0.393631
$160$	8.71004e9	1.05070
$161$	−2.74000e9	−0.321391
$162$	−1.28330e9	−0.146390
$163$	9.54943e9	1.05958	0.529789	−	0.848129i	$-0.322271\pi$
$163$	9.54943e9	1.05958	0.529789	+	0.848129i	$0.322271\pi$
$164$	−1.19259e10	−1.28734
$165$	5.58829e9	0.586950
$166$	1.16980e10	1.19571
$167$	2.24868e9	0.223720	0.111860	−	0.993724i	$-0.464319\pi$
$167$	2.24868e9	0.223720	0.111860	+	0.993724i	$0.464319\pi$
$168$	1.22588e9	0.118729
$169$	−1.27057e9	−0.119815
$170$	−7.13010e9	−0.654750
$171$	−2.24280e9	−0.200589
$172$	4.94799e9	0.431073
$173$	−1.94978e10	−1.65492	−0.827461	−	0.561523i	$-0.810216\pi$
$173$	−1.94978e10	−1.65492	−0.827461	+	0.561523i	$0.810216\pi$
$174$	1.54511e10	1.27788
$175$	−1.94255e9	−0.156567
$176$	−1.80288e10	−1.41632
$177$	9.81506e8	0.0751646
$178$	6.16421e9	0.460244
$179$	8.88715e9	0.647029	0.323515	−	0.946223i	$-0.395136\pi$
$179$	8.88715e9	0.647029	0.323515	+	0.946223i	$0.395136\pi$
$180$	2.96159e9	0.210280
$181$	−2.18779e9	−0.151514	−0.0757569	−	0.997126i	$-0.524137\pi$
$181$	−2.18779e9	−0.151514	−0.0757569	+	0.997126i	$0.524137\pi$
$182$	1.08101e10	0.730313
$183$	−3.96012e9	−0.261023
$184$	−2.94370e9	−0.189327
$185$	−2.06196e10	−1.29422
$186$	1.33549e10	0.818149
$187$	1.14942e10	0.687372
$188$	−4.58936e9	−0.267943
$189$	1.99465e9	0.113707
$190$	1.22101e10	0.679716
$191$	1.59262e10	0.865889	0.432945	−	0.901420i	$-0.357475\pi$
$191$	1.59262e10	0.865889	0.432945	+	0.901420i	$0.357475\pi$
$192$	−4.56926e9	−0.242655
$193$	2.85154e10	1.47935	0.739676	−	0.672963i	$-0.234979\pi$
$193$	2.85154e10	1.47935	0.739676	+	0.672963i	$0.234979\pi$
$194$	4.63888e10	2.35128
$195$	−9.37624e9	−0.464379
$196$	−9.89568e9	−0.478953
$197$	−1.07158e10	−0.506904	−0.253452	−	0.967348i	$-0.581566\pi$
$197$	−1.07158e10	−0.506904	−0.253452	+	0.967348i	$0.581566\pi$
$198$	−1.12626e10	−0.520771
$199$	1.84571e10	0.834306	0.417153	−	0.908836i	$-0.363028\pi$
$199$	1.84571e10	0.834306	0.417153	+	0.908836i	$0.363028\pi$
$200$	−2.08696e9	−0.0922316
$201$	3.89832e9	0.168459
$202$	−9.97355e9	−0.421472
$203$	−2.40159e10	−0.992582
$204$	6.09150e9	0.246257
$205$	−3.79278e10	−1.49991
$206$	1.50796e10	0.583428
$207$	−4.78971e9	−0.181319
$208$	3.02494e10	1.12055
$209$	−1.96835e10	−0.713583
$210$	−1.08591e10	−0.385308
$211$	5.31574e10	1.84626	0.923129	−	0.384491i	$-0.125623\pi$
$211$	5.31574e10	1.84626	0.923129	+	0.384491i	$0.125623\pi$
$212$	1.47548e10	0.501675
$213$	−8.74135e8	−0.0290985
$214$	−3.60319e9	−0.117442
$215$	1.57361e10	0.502255
$216$	2.14293e9	0.0669834
$217$	−2.07577e10	−0.635492
$218$	1.44032e10	0.431923
$219$	2.97492e10	0.873932
$220$	2.59918e10	0.748057
$221$	−1.92854e10	−0.543830
$222$	4.15567e10	1.14829
$223$	−3.56353e10	−0.964958	−0.482479	−	0.875908i	$-0.660263\pi$
$223$	−3.56353e10	−0.964958	−0.482479	+	0.875908i	$0.660263\pi$
$224$	2.72847e10	0.724108
$225$	−3.39571e9	−0.0883302
$226$	−8.10602e9	−0.206690
$227$	3.84790e10	0.961851	0.480925	−	0.876762i	$-0.340301\pi$
$227$	3.84790e10	0.961851	0.480925	+	0.876762i	$0.340301\pi$
$228$	−1.04315e10	−0.255647
$229$	3.71856e10	0.893543	0.446772	−	0.894648i	$-0.352574\pi$
$229$	3.71856e10	0.893543	0.446772	+	0.894648i	$0.352574\pi$
$230$	2.60758e10	0.614417
$231$	1.75056e10	0.404505
$232$	−2.58013e10	−0.584717
$233$	−1.16087e10	−0.258037	−0.129019	−	0.991642i	$-0.541183\pi$
$233$	−1.16087e10	−0.258037	−0.129019	+	0.991642i	$0.541183\pi$
$234$	1.88969e10	0.412020
$235$	−1.45956e10	−0.312187
$236$	4.56511e9	0.0957959
$237$	3.09283e10	0.636778
$238$	−2.23354e10	−0.451230
$239$	−4.35010e10	−0.862401	−0.431200	−	0.902256i	$-0.641910\pi$
$239$	−4.35010e10	−0.862401	−0.431200	+	0.902256i	$0.641910\pi$
$240$	−3.03866e10	−0.591196
$241$	9.88603e10	1.88775	0.943876	−	0.330300i	$-0.107150\pi$
$241$	9.88603e10	1.88775	0.943876	+	0.330300i	$0.107150\pi$
$242$	−2.85500e10	−0.535102
$243$	3.48678e9	0.0641500
$244$	−1.84190e10	−0.332669
$245$	−3.14712e10	−0.558042
$246$	7.64398e10	1.33080
$247$	3.30257e10	0.564567
$248$	−2.23009e10	−0.374360
$249$	−3.17841e10	−0.523978
$250$	8.82503e10	1.42885
$251$	−2.80288e10	−0.445731	−0.222866	−	0.974849i	$-0.571541\pi$
$251$	−2.80288e10	−0.445731	−0.222866	+	0.974849i	$0.571541\pi$
$252$	9.27734e9	0.144918
$253$	−4.20361e10	−0.645030
$254$	−1.14639e11	−1.72814
$255$	1.93728e10	0.286921
$256$	8.97077e10	1.30542
$257$	1.25678e11	1.79705	0.898525	−	0.438921i	$-0.144639\pi$
$257$	1.25678e11	1.79705	0.898525	+	0.438921i	$0.144639\pi$
$258$	−3.17145e10	−0.445625
$259$	−6.45920e10	−0.891928
$260$	−4.36100e10	−0.591843
$261$	−4.19815e10	−0.559984
$262$	−3.62514e10	−0.475302
$263$	4.88379e10	0.629443	0.314721	−	0.949184i	$-0.398089\pi$
$263$	4.88379e10	0.629443	0.314721	+	0.949184i	$0.398089\pi$
$264$	1.88071e10	0.238289
$265$	4.69248e10	0.584516
$266$	3.82488e10	0.468437
$267$	−1.67485e10	−0.201685
$268$	1.81315e10	0.214698
$269$	−1.30250e11	−1.51668	−0.758338	−	0.651862i	$-0.773988\pi$
$269$	−1.30250e11	−1.51668	−0.758338	+	0.651862i	$0.773988\pi$
$270$	−1.89825e10	−0.217379
$271$	−1.48630e11	−1.67396	−0.836981	−	0.547232i	$-0.815682\pi$
$271$	−1.48630e11	−1.67396	−0.836981	+	0.547232i	$0.815682\pi$
$272$	−6.25003e10	−0.692344
$273$	−2.93716e10	−0.320034
$274$	5.81183e10	0.622924
$275$	−2.98019e10	−0.314229
$276$	−2.22775e10	−0.231087
$277$	−7.44131e10	−0.759435	−0.379717	−	0.925103i	$-0.623979\pi$
$277$	−7.44131e10	−0.759435	−0.379717	+	0.925103i	$0.623979\pi$
$278$	1.68668e11	1.69367
$279$	−3.62859e10	−0.358525
$280$	1.81333e10	0.176305
$281$	−7.52263e10	−0.719766	−0.359883	−	0.932997i	$-0.617183\pi$
$281$	−7.52263e10	−0.719766	−0.359883	+	0.932997i	$0.617183\pi$
$282$	2.94159e10	0.276988
$283$	1.70354e11	1.57875	0.789376	−	0.613910i	$-0.210404\pi$
$283$	1.70354e11	1.57875	0.789376	+	0.613910i	$0.210404\pi$
$284$	−4.06571e9	−0.0370855
$285$	−3.31754e10	−0.297862
$286$	1.65845e11	1.46573
$287$	−1.18811e11	−1.03369
$288$	4.76956e10	0.408519
$289$	−7.87411e10	−0.663990
$290$	2.28553e11	1.89756
$291$	−1.26041e11	−1.03037
$292$	1.38367e11	1.11381
$293$	−2.21986e11	−1.75963	−0.879817	−	0.475313i	$-0.842335\pi$
$293$	−2.21986e11	−1.75963	−0.879817	+	0.475313i	$0.842335\pi$
$294$	6.34271e10	0.495122
$295$	1.45184e10	0.111614
$296$	−6.93940e10	−0.525423
$297$	3.06011e10	0.228209
$298$	1.19458e11	0.877493
$299$	7.05296e10	0.510330
$300$	−1.57939e10	−0.112575
$301$	4.92942e10	0.346136
$302$	1.49419e11	1.03365
$303$	2.70986e10	0.184695
$304$	1.07030e11	0.718744
$305$	−5.85781e10	−0.387602
$306$	−3.90440e10	−0.254570
$307$	9.40822e10	0.604484	0.302242	−	0.953231i	$-0.402265\pi$
$307$	9.40822e10	0.604484	0.302242	+	0.953231i	$0.402265\pi$
$308$	8.14209e10	0.515535
$309$	−4.09720e10	−0.255667
$310$	1.97545e11	1.21490
$311$	−1.49871e11	−0.908442	−0.454221	−	0.890889i	$-0.650082\pi$
$311$	−1.49871e11	−0.908442	−0.454221	+	0.890889i	$0.650082\pi$
$312$	−3.15552e10	−0.188528
$313$	2.84656e9	0.0167637	0.00838187	−	0.999965i	$-0.497332\pi$
$313$	2.84656e9	0.0167637	0.00838187	+	0.999965i	$0.497332\pi$
$314$	6.28908e10	0.365093
$315$	2.95048e10	0.168847
$316$	1.43851e11	0.811562
$317$	2.45570e11	1.36587	0.682935	−	0.730479i	$-0.260703\pi$
$317$	2.45570e11	1.36587	0.682935	+	0.730479i	$0.260703\pi$
$318$	−9.45723e10	−0.518611
$319$	−3.68443e11	−1.99211
$320$	−6.75884e10	−0.360327
$321$	9.79003e9	0.0514649
$322$	8.16841e10	0.423434
$323$	−6.82365e10	−0.348823
$324$	1.62175e10	0.0817580
$325$	5.00026e10	0.248610
$326$	−2.84685e11	−1.39600
$327$	−3.91343e10	−0.189275
$328$	−1.27644e11	−0.608931
$329$	−4.57214e10	−0.215148
$330$	−1.66597e11	−0.773310
$331$	−2.49653e11	−1.14317	−0.571585	−	0.820543i	$-0.693671\pi$
$331$	−2.49653e11	−1.14317	−0.571585	+	0.820543i	$0.693671\pi$
$332$	−1.47832e11	−0.667800
$333$	−1.12912e11	−0.503198
$334$	−6.70372e10	−0.294752
$335$	5.76638e10	0.250151
$336$	−9.51877e10	−0.407431
$337$	6.41280e10	0.270840	0.135420	−	0.990788i	$-0.456762\pi$
$337$	6.41280e10	0.270840	0.135420	+	0.990788i	$0.456762\pi$
$338$	3.78781e10	0.157857
$339$	2.20245e10	0.0905746
$340$	9.01054e10	0.365675
$341$	−3.18457e11	−1.27543
$342$	6.68617e10	0.264277
$343$	−2.50044e11	−0.975422
$344$	5.29590e10	0.203904
$345$	−7.08493e10	−0.269246
$346$	5.81263e11	2.18037
$347$	−3.30945e11	−1.22539	−0.612693	−	0.790321i	$-0.709914\pi$
$347$	−3.30945e11	−1.22539	−0.612693	+	0.790321i	$0.709914\pi$
$348$	−1.95261e11	−0.713689
$349$	2.96053e11	1.06821	0.534103	−	0.845419i	$-0.320649\pi$
$349$	2.96053e11	1.06821	0.534103	+	0.845419i	$0.320649\pi$
$350$	5.79107e10	0.206278
$351$	−5.13437e10	−0.180553
$352$	4.18592e11	1.45328
$353$	4.89924e11	1.67936	0.839678	−	0.543084i	$-0.182744\pi$
$353$	4.89924e11	1.67936	0.839678	+	0.543084i	$0.182744\pi$
$354$	−2.92604e10	−0.0990298
$355$	−1.29302e10	−0.0432093
$356$	−7.78992e10	−0.257044
$357$	6.06865e10	0.197736
$358$	−2.64942e11	−0.852465
$359$	3.30923e10	0.105148	0.0525742	−	0.998617i	$-0.483257\pi$
$359$	3.30923e10	0.105148	0.0525742	+	0.998617i	$0.483257\pi$
$360$	3.16983e10	0.0994659
$361$	−2.05835e11	−0.637876
$362$	6.52219e10	0.199620
$363$	7.75717e10	0.234489
$364$	−1.36611e11	−0.407877
$365$	4.40050e11	1.29773
$366$	1.18058e11	0.343899
$367$	3.55123e11	1.02184	0.510918	−	0.859629i	$-0.329305\pi$
$367$	3.55123e11	1.02184	0.510918	+	0.859629i	$0.329305\pi$
$368$	2.28573e11	0.649695
$369$	−2.07691e11	−0.583174
$370$	6.14706e11	1.70514
$371$	1.46995e11	0.402828
$372$	−1.68770e11	−0.456933
$373$	−1.46968e11	−0.393128	−0.196564	−	0.980491i	$-0.562978\pi$
$373$	−1.46968e11	−0.393128	−0.196564	+	0.980491i	$0.562978\pi$
$374$	−3.42663e11	−0.905617
$375$	−2.39780e11	−0.626142
$376$	−4.91205e10	−0.126741
$377$	6.18187e11	1.57610
$378$	−5.94639e10	−0.149810
$379$	5.48957e11	1.36666	0.683332	−	0.730108i	$-0.260530\pi$
$379$	5.48957e11	1.36666	0.683332	+	0.730108i	$0.260530\pi$
$380$	−1.54303e11	−0.379619
$381$	3.11479e11	0.757298
$382$	−4.74788e11	−1.14081
$383$	−5.30270e11	−1.25922	−0.629611	−	0.776910i	$-0.716786\pi$
$383$	−5.30270e11	−1.25922	−0.629611	+	0.776910i	$0.716786\pi$
$384$	−1.65266e11	−0.387876
$385$	2.58943e11	0.600664
$386$	−8.50094e11	−1.94906
$387$	8.61699e10	0.195279
$388$	−5.86230e11	−1.31318
$389$	4.66846e11	1.03371	0.516857	−	0.856072i	$-0.327102\pi$
$389$	4.66846e11	1.03371	0.516857	+	0.856072i	$0.327102\pi$
$390$	2.79522e11	0.611823
$391$	−1.45726e11	−0.315312
$392$	−1.05915e11	−0.226553
$393$	9.84969e10	0.208284
$394$	3.19456e11	0.667849
$395$	4.57490e11	0.945573
$396$	1.42330e11	0.290849
$397$	1.89910e11	0.383699	0.191850	−	0.981424i	$-0.438551\pi$
$397$	1.89910e11	0.383699	0.191850	+	0.981424i	$0.438551\pi$
$398$	−5.50240e11	−1.09920
$399$	−1.03924e11	−0.205276
$400$	1.62049e11	0.316502
$401$	6.94730e11	1.34173	0.670867	−	0.741578i	$-0.265922\pi$
$401$	6.94730e11	1.34173	0.670867	+	0.741578i	$0.265922\pi$
$402$	−1.16216e11	−0.221946
$403$	5.34318e11	1.00908
$404$	1.26039e11	0.235390
$405$	5.15765e10	0.0952585
$406$	7.15956e11	1.30773
$407$	−9.90948e11	−1.79009
$408$	6.51982e10	0.116484
$409$	−1.08026e12	−1.90885	−0.954424	−	0.298454i	$-0.903529\pi$
$409$	−1.08026e12	−1.90885	−0.954424	+	0.298454i	$0.903529\pi$
$410$	1.13070e12	1.97614
$411$	−1.57910e11	−0.272974
$412$	−1.90566e11	−0.325842
$413$	4.54798e10	0.0769207
$414$	1.42790e11	0.238889
$415$	−4.70150e11	−0.778073
$416$	−7.02329e11	−1.14980
$417$	−4.58278e11	−0.742193
$418$	5.86800e11	0.940149
$419$	4.74824e11	0.752609	0.376304	−	0.926496i	$-0.377195\pi$
$419$	4.74824e11	0.752609	0.376304	+	0.926496i	$0.377195\pi$
$420$	1.37230e11	0.215193
$421$	4.95917e11	0.769378	0.384689	−	0.923046i	$-0.374309\pi$
$421$	4.95917e11	0.769378	0.384689	+	0.923046i	$0.374309\pi$
$422$	−1.58471e12	−2.43246
$423$	−7.99244e10	−0.121380
$424$	1.57923e11	0.237301
$425$	−1.03314e11	−0.153606
$426$	2.60595e10	0.0383374
$427$	−1.83499e11	−0.267121
$428$	4.55346e10	0.0655911
$429$	−4.50609e11	−0.642306
$430$	−4.69121e11	−0.661724
$431$	1.94411e11	0.271378	0.135689	−	0.990752i	$-0.456675\pi$
$431$	1.94411e11	0.271378	0.135689	+	0.990752i	$0.456675\pi$
$432$	−1.66395e11	−0.229860
$433$	−1.31522e12	−1.79805	−0.899027	−	0.437893i	$-0.855725\pi$
$433$	−1.31522e12	−1.79805	−0.899027	+	0.437893i	$0.855725\pi$
$434$	6.18823e11	0.837264
$435$	−6.20990e11	−0.831539
$436$	−1.82019e11	−0.241227
$437$	2.49551e11	0.327335
$438$	−8.86877e11	−1.15141
$439$	−6.36451e11	−0.817851	−0.408926	−	0.912568i	$-0.634096\pi$
$439$	−6.36451e11	−0.817851	−0.408926	+	0.912568i	$0.634096\pi$
$440$	2.78194e11	0.353843
$441$	−1.72335e11	−0.216970
$442$	5.74932e11	0.716500
$443$	4.80061e11	0.592215	0.296108	−	0.955155i	$-0.404311\pi$
$443$	4.80061e11	0.592215	0.296108	+	0.955155i	$0.404311\pi$
$444$	−5.25166e11	−0.641317
$445$	−2.47743e11	−0.299489
$446$	1.06235e12	1.27134
$447$	−3.24574e11	−0.384530
$448$	−2.11724e11	−0.248325
$449$	2.16718e11	0.251644	0.125822	−	0.992053i	$-0.459843\pi$
$449$	2.16718e11	0.251644	0.125822	+	0.992053i	$0.459843\pi$
$450$	1.01232e11	0.116376
$451$	−1.82276e12	−2.07460
$452$	1.02438e11	0.115436
$453$	−4.05978e11	−0.452961
$454$	−1.14713e12	−1.26724
$455$	−4.34464e11	−0.475229
$456$	−1.11650e11	−0.120925
$457$	−1.74336e12	−1.86966	−0.934832	−	0.355090i	$-0.884450\pi$
$457$	−1.74336e12	−1.86966	−0.934832	+	0.355090i	$0.884450\pi$
$458$	−1.10857e12	−1.17725
$459$	1.06084e11	0.111556
$460$	−3.29529e11	−0.343150
$461$	−1.17476e12	−1.21142	−0.605712	−	0.795684i	$-0.707112\pi$
$461$	−1.17476e12	−1.21142	−0.605712	+	0.795684i	$0.707112\pi$
$462$	−5.21874e11	−0.532938
$463$	5.26497e11	0.532453	0.266227	−	0.963910i	$-0.414223\pi$
$463$	5.26497e11	0.532453	0.266227	+	0.963910i	$0.414223\pi$
$464$	2.00343e12	2.00651
$465$	−5.36741e11	−0.532386
$466$	3.46076e11	0.339966
$467$	1.16256e11	0.113107	0.0565533	−	0.998400i	$-0.481989\pi$
$467$	1.16256e11	0.113107	0.0565533	+	0.998400i	$0.481989\pi$
$468$	−2.38806e11	−0.230112
$469$	1.80635e11	0.172395
$470$	4.35119e11	0.411309
$471$	−1.70877e11	−0.159989
$472$	4.88609e10	0.0453130
$473$	7.56255e11	0.694693
$474$	−9.22026e11	−0.838959
$475$	1.76922e11	0.159463
$476$	2.82260e11	0.252010
$477$	2.56957e11	0.227263
$478$	1.29684e12	1.13622
$479$	1.21539e12	1.05489	0.527443	−	0.849591i	$-0.323151\pi$
$479$	1.21539e12	1.05489	0.527443	+	0.849591i	$0.323151\pi$
$480$	7.05513e11	0.606624
$481$	1.66265e12	1.41628
$482$	−2.94720e12	−2.48713
$483$	−2.21940e11	−0.185555
$484$	3.60795e11	0.298853
$485$	−1.86439e12	−1.53003
$486$	−1.03947e11	−0.0845181
$487$	1.78960e12	1.44170	0.720852	−	0.693089i	$-0.243751\pi$
$487$	1.78960e12	1.44170	0.720852	+	0.693089i	$0.243751\pi$
$488$	−1.97141e11	−0.157358
$489$	7.73504e11	0.611748
$490$	9.38213e11	0.735223
$491$	−7.13125e11	−0.553731	−0.276866	−	0.960909i	$-0.589296\pi$
$491$	−7.13125e11	−0.553731	−0.276866	+	0.960909i	$0.589296\pi$
$492$	−9.65994e11	−0.743244
$493$	−1.27728e12	−0.973808
$494$	−9.84554e11	−0.743821
$495$	4.52652e11	0.338876
$496$	1.73162e12	1.28465
$497$	−4.05046e10	−0.0297783
$498$	9.47541e11	0.690344
$499$	6.38235e11	0.460817	0.230408	−	0.973094i	$-0.425994\pi$
$499$	6.38235e11	0.460817	0.230408	+	0.973094i	$0.425994\pi$
$500$	−1.11525e12	−0.798007
$501$	1.82143e11	0.129165
$502$	8.35588e11	0.587254
$503$	2.65519e12	1.84944	0.924719	−	0.380651i	$-0.124300\pi$
$503$	2.65519e12	1.84944	0.924719	+	0.380651i	$0.124300\pi$
$504$	9.92966e10	0.0685484
$505$	4.00842e11	0.274260
$506$	1.25317e12	0.849830
$507$	−1.02917e11	−0.0691750
$508$	1.44873e12	0.965162
$509$	−1.39225e12	−0.919365	−0.459682	−	0.888083i	$-0.652037\pi$
$509$	−1.39225e12	−0.919365	−0.459682	+	0.888083i	$0.652037\pi$
$510$	−5.77538e11	−0.378020
$511$	1.37848e12	0.894350
$512$	−1.62970e12	−1.04808
$513$	−1.81667e11	−0.115810
$514$	−3.74668e12	−2.36763
$515$	−6.06057e11	−0.379648
$516$	4.00787e11	0.248880
$517$	−7.01442e11	−0.431802
$518$	1.92560e12	1.17512
$519$	−1.57932e12	−0.955470
$520$	−4.66764e11	−0.279951
$521$	−1.60344e12	−0.953418	−0.476709	−	0.879061i	$-0.658170\pi$
$521$	−1.60344e12	−0.953418	−0.476709	+	0.879061i	$0.658170\pi$
$522$	1.25154e12	0.737782
$523$	−1.88675e11	−0.110270	−0.0551350	−	0.998479i	$-0.517559\pi$
$523$	−1.88675e11	−0.110270	−0.0551350	+	0.998479i	$0.517559\pi$
$524$	4.58121e11	0.265454
$525$	−1.57346e11	−0.0903940
$526$	−1.45594e12	−0.829294
$527$	−1.10399e12	−0.623472
$528$	−1.46034e12	−0.817712
$529$	−1.26821e12	−0.704111
$530$	−1.39891e12	−0.770103
$531$	7.95020e10	0.0433963
$532$	−4.83363e11	−0.261620
$533$	3.05829e12	1.64137
$534$	4.99301e11	0.265722
$535$	1.44814e11	0.0764220
$536$	1.94064e11	0.101556
$537$	7.19859e11	0.373562
$538$	3.88298e12	1.99823
$539$	−1.51246e12	−0.771855
$540$	2.39888e11	0.121405
$541$	2.56290e12	1.28631	0.643153	−	0.765738i	$-0.277626\pi$
$541$	2.56290e12	1.28631	0.643153	+	0.765738i	$0.277626\pi$
$542$	4.43093e12	2.20546
$543$	−1.77211e11	−0.0874765
$544$	1.45113e12	0.710412
$545$	−5.78874e11	−0.281061
$546$	8.75619e11	0.421646
$547$	−7.77077e11	−0.371126	−0.185563	−	0.982632i	$-0.559411\pi$
$547$	−7.77077e11	−0.371126	−0.185563	+	0.982632i	$0.559411\pi$
$548$	−7.34460e11	−0.347901
$549$	−3.20770e11	−0.150702
$550$	8.88446e11	0.413999
$551$	2.18730e12	1.01094
$552$	−2.38440e11	−0.109308
$553$	1.43311e12	0.651655
$554$	2.21839e12	1.00056
$555$	−1.67019e12	−0.747216
$556$	−2.13151e12	−0.945911
$557$	1.02712e12	0.452139	0.226069	−	0.974111i	$-0.427412\pi$
$557$	1.02712e12	0.452139	0.226069	+	0.974111i	$0.427412\pi$
$558$	1.08175e12	0.472359
$559$	−1.26887e12	−0.549623
$560$	−1.40802e12	−0.605008
$561$	9.31031e11	0.396854
$562$	2.24263e12	0.948296
$563$	−5.35963e11	−0.224826	−0.112413	−	0.993662i	$-0.535858\pi$
$563$	−5.35963e11	−0.224826	−0.112413	+	0.993662i	$0.535858\pi$
$564$	−3.71738e11	−0.154697
$565$	3.25785e11	0.134497
$566$	−5.07856e12	−2.08002
$567$	1.61566e11	0.0656488
$568$	−4.35159e10	−0.0175420
$569$	−2.75925e12	−1.10353	−0.551766	−	0.833999i	$-0.686046\pi$
$569$	−2.75925e12	−1.10353	−0.551766	+	0.833999i	$0.686046\pi$
$570$	9.89018e11	0.392435
$571$	1.39378e12	0.548694	0.274347	−	0.961631i	$-0.411538\pi$
$571$	1.39378e12	0.548694	0.274347	+	0.961631i	$0.411538\pi$
$572$	−2.09584e12	−0.818607
$573$	1.29002e12	0.499921
$574$	3.54197e12	1.36189
$575$	3.77833e11	0.144143
$576$	−3.70110e11	−0.140097
$577$	−2.12754e12	−0.799073	−0.399536	−	0.916717i	$-0.630829\pi$
$577$	−2.12754e12	−0.799073	−0.399536	+	0.916717i	$0.630829\pi$
$578$	2.34741e12	0.874810
$579$	2.30975e12	0.854105
$580$	−2.88830e12	−1.05978
$581$	−1.47277e12	−0.536220
$582$	3.75749e12	1.35751
$583$	2.25514e12	0.808472
$584$	1.48096e12	0.526850
$585$	−7.59475e11	−0.268110
$586$	6.61781e12	2.31833
$587$	−3.82897e12	−1.33110	−0.665550	−	0.746353i	$-0.731803\pi$
$587$	−3.82897e12	−1.33110	−0.665550	+	0.746353i	$0.731803\pi$
$588$	−8.01550e11	−0.276524
$589$	1.89055e12	0.647246
$590$	−4.32820e11	−0.147053
$591$	−8.67977e11	−0.292661
$592$	5.38832e12	1.80304
$593$	4.08560e11	0.135678	0.0678390	−	0.997696i	$-0.478390\pi$
$593$	4.08560e11	0.135678	0.0678390	+	0.997696i	$0.478390\pi$
$594$	−9.12274e11	−0.300667
$595$	8.97674e11	0.293624
$596$	−1.50963e12	−0.490076
$597$	1.49503e12	0.481687
$598$	−2.10261e12	−0.672363
$599$	−8.44290e11	−0.267961	−0.133980	−	0.990984i	$-0.542776\pi$
$599$	−8.44290e11	−0.267961	−0.133980	+	0.990984i	$0.542776\pi$
$600$	−1.69044e11	−0.0532499
$601$	2.53159e12	0.791513	0.395756	−	0.918356i	$-0.370482\pi$
$601$	2.53159e12	0.791513	0.395756	+	0.918356i	$0.370482\pi$
$602$	−1.46955e12	−0.456036
$603$	3.15764e11	0.0972600
$604$	−1.88826e12	−0.577291
$605$	1.14744e12	0.348201
$606$	−8.07857e11	−0.243337
$607$	−5.34035e11	−0.159669	−0.0798345	−	0.996808i	$-0.525439\pi$
$607$	−5.34035e11	−0.159669	−0.0798345	+	0.996808i	$0.525439\pi$
$608$	−2.48501e12	−0.737501
$609$	−1.94529e12	−0.573067
$610$	1.74631e12	0.510668
$611$	1.17691e12	0.341630
$612$	4.93412e11	0.142177
$613$	3.77745e12	1.08050	0.540252	−	0.841504i	$-0.318329\pi$
$613$	3.77745e12	1.08050	0.540252	+	0.841504i	$0.318329\pi$
$614$	−2.80476e12	−0.796411
$615$	−3.07215e12	−0.865974
$616$	8.71459e11	0.243856
$617$	−2.81469e12	−0.781894	−0.390947	−	0.920413i	$-0.627852\pi$
$617$	−2.81469e12	−0.781894	−0.390947	+	0.920413i	$0.627852\pi$
$618$	1.22145e12	0.336842
$619$	2.92964e12	0.802059	0.401030	−	0.916065i	$-0.368652\pi$
$619$	2.92964e12	0.802059	0.401030	+	0.916065i	$0.368652\pi$
$620$	−2.49645e12	−0.678515
$621$	−3.87967e11	−0.104684
$622$	4.46793e12	1.19688
$623$	−7.76070e11	−0.206398
$624$	2.45021e12	0.646952
$625$	−2.53597e12	−0.664789
$626$	−8.48610e10	−0.0220863
$627$	−1.59436e12	−0.411987
$628$	−7.94772e11	−0.203903
$629$	−3.43530e12	−0.875058
$630$	−8.79589e11	−0.222458
$631$	−2.11792e12	−0.531834	−0.265917	−	0.963996i	$-0.585675\pi$
$631$	−2.11792e12	−0.531834	−0.265917	+	0.963996i	$0.585675\pi$
$632$	1.53966e12	0.383882
$633$	4.30575e12	1.06594
$634$	−7.32089e12	−1.79954
$635$	4.60739e12	1.12454
$636$	1.19514e12	0.289642
$637$	2.53767e12	0.610671
$638$	1.09839e13	2.62461
$639$	−7.08050e10	−0.0168000
$640$	−2.44461e12	−0.575970
$641$	2.89567e12	0.677466	0.338733	−	0.940882i	$-0.390002\pi$
$641$	2.89567e12	0.677466	0.338733	+	0.940882i	$0.390002\pi$
$642$	−2.91858e11	−0.0678054
$643$	3.13182e11	0.0722517	0.0361258	−	0.999347i	$-0.488498\pi$
$643$	3.13182e11	0.0722517	0.0361258	+	0.999347i	$0.488498\pi$
$644$	−1.03227e12	−0.236487
$645$	1.27462e12	0.289977
$646$	2.03425e12	0.459576
$647$	5.41387e12	1.21461	0.607307	−	0.794467i	$-0.292250\pi$
$647$	5.41387e12	1.21461	0.607307	+	0.794467i	$0.292250\pi$
$648$	1.73578e11	0.0386729
$649$	6.97735e11	0.154379
$650$	−1.49067e12	−0.327545
$651$	−1.68137e12	−0.366901
$652$	3.59766e12	0.779661
$653$	−3.57083e12	−0.768528	−0.384264	−	0.923223i	$-0.625545\pi$
$653$	−3.57083e12	−0.768528	−0.384264	+	0.923223i	$0.625545\pi$
$654$	1.16666e12	0.249371
$655$	1.45696e12	0.309288
$656$	9.91133e12	2.08961
$657$	2.40969e12	0.504565
$658$	1.36304e12	0.283459
$659$	−4.34664e12	−0.897778	−0.448889	−	0.893588i	$-0.648180\pi$
$659$	−4.34664e12	−0.897778	−0.448889	+	0.893588i	$0.648180\pi$
$660$	2.10534e12	0.431891
$661$	−8.51008e11	−0.173391	−0.0866956	−	0.996235i	$-0.527631\pi$
$661$	−8.51008e11	−0.173391	−0.0866956	+	0.996235i	$0.527631\pi$
$662$	7.44260e12	1.50613
$663$	−1.56212e12	−0.313981
$664$	−1.58226e12	−0.315880
$665$	−1.53724e12	−0.304821
$666$	3.36609e12	0.662967
$667$	4.67119e12	0.913821
$668$	8.47171e11	0.164618
$669$	−2.88646e12	−0.557119
$670$	−1.71906e12	−0.329575
$671$	−2.81518e12	−0.536111
$672$	2.21006e12	0.418064
$673$	2.27797e12	0.428036	0.214018	−	0.976830i	$-0.431345\pi$
$673$	2.27797e12	0.428036	0.214018	+	0.976830i	$0.431345\pi$
$674$	−1.91177e12	−0.356834
$675$	−2.75053e11	−0.0509975
$676$	−4.78678e11	−0.0881623
$677$	−1.92066e12	−0.351400	−0.175700	−	0.984444i	$-0.556219\pi$
$677$	−1.92066e12	−0.351400	−0.175700	+	0.984444i	$0.556219\pi$
$678$	−6.56588e11	−0.119333
$679$	−5.84031e12	−1.05444
$680$	9.64410e11	0.172970
$681$	3.11680e12	0.555325
$682$	9.49376e12	1.68038
$683$	4.73681e12	0.832900	0.416450	−	0.909159i	$-0.363274\pi$
$683$	4.73681e12	0.832900	0.416450	+	0.909159i	$0.363274\pi$
$684$	−8.44954e11	−0.147598
$685$	−2.33580e12	−0.405349
$686$	7.45424e12	1.28512
$687$	3.01204e12	0.515887
$688$	−4.11217e12	−0.699718
$689$	−3.78376e12	−0.639642
$690$	2.11214e12	0.354734
$691$	−5.76580e12	−0.962074	−0.481037	−	0.876700i	$-0.659740\pi$
$691$	−5.76580e12	−0.962074	−0.481037	+	0.876700i	$0.659740\pi$
$692$	−7.34561e12	−1.21773
$693$	1.41796e12	0.233541
$694$	9.86604e12	1.61445
$695$	−6.77884e12	−1.10211
$696$	−2.08991e12	−0.337587
$697$	−6.31892e12	−1.01413
$698$	−8.82586e12	−1.40737
$699$	−9.40306e11	−0.148978
$700$	−7.31837e11	−0.115205
$701$	−4.93783e11	−0.0772334	−0.0386167	−	0.999254i	$-0.512295\pi$
$701$	−4.93783e11	−0.0772334	−0.0386167	+	0.999254i	$0.512295\pi$
$702$	1.53065e12	0.237880
$703$	5.88286e12	0.908426
$704$	−3.24820e12	−0.498386
$705$	−1.18224e12	−0.180241
$706$	−1.46055e13	−2.21256
$707$	1.25566e12	0.189010
$708$	3.69774e11	0.0553078
$709$	−1.04931e13	−1.55953	−0.779766	−	0.626071i	$-0.784662\pi$
$709$	−1.04931e13	−1.55953	−0.779766	+	0.626071i	$0.784662\pi$
$710$	3.85472e11	0.0569285
$711$	2.50519e12	0.367644
$712$	−8.33766e11	−0.121586
$713$	4.03745e12	0.585066
$714$	−1.80917e12	−0.260518
$715$	−6.66540e12	−0.953782
$716$	3.34815e12	0.476098
$717$	−3.52358e12	−0.497907
$718$	−9.86541e11	−0.138534
$719$	−3.92845e12	−0.548203	−0.274101	−	0.961701i	$-0.588380\pi$
$719$	−3.92845e12	−0.548203	−0.274101	+	0.961701i	$0.588380\pi$
$720$	−2.46131e12	−0.341327
$721$	−1.89851e12	−0.261640
$722$	6.13629e12	0.840405
$723$	8.00768e12	1.08989
$724$	−8.24230e11	−0.111487
$725$	3.31168e12	0.445172
$726$	−2.31255e12	−0.308941
$727$	−1.31532e13	−1.74633	−0.873167	−	0.487420i	$-0.837938\pi$
$727$	−1.31532e13	−1.74633	−0.873167	+	0.487420i	$0.837938\pi$
$728$	−1.46217e12	−0.192932
$729$	2.82430e11	0.0370370
$730$	−1.31187e13	−1.70977
$731$	2.62169e12	0.339589
$732$	−1.49194e12	−0.192066
$733$	−8.49071e12	−1.08637	−0.543183	−	0.839614i	$-0.682781\pi$
$733$	−8.49071e12	−1.08637	−0.543183	+	0.839614i	$0.682781\pi$
$734$	−1.05868e13	−1.34628
$735$	−2.54917e12	−0.322185
$736$	−5.30699e12	−0.666650
$737$	2.77124e12	0.345996
$738$	6.19162e12	0.768335
$739$	1.44722e13	1.78499	0.892496	−	0.451056i	$-0.148953\pi$
$739$	1.44722e13	1.78499	0.892496	+	0.451056i	$0.148953\pi$
$740$	−7.76824e12	−0.952313
$741$	2.67508e12	0.325953
$742$	−4.38217e12	−0.530728
$743$	−2.79119e11	−0.0336000	−0.0168000	−	0.999859i	$-0.505348\pi$
$743$	−2.79119e11	−0.0336000	−0.0168000	+	0.999859i	$0.505348\pi$
$744$	−1.80637e12	−0.216137
$745$	−4.80110e12	−0.571001
$746$	4.38139e12	0.517949
$747$	−2.57451e12	−0.302519
$748$	4.33034e12	0.505784
$749$	4.53638e11	0.0526673
$750$	7.14828e12	0.824946
$751$	−9.34249e12	−1.07172	−0.535862	−	0.844305i	$-0.680013\pi$
$751$	−9.34249e12	−1.07172	−0.535862	+	0.844305i	$0.680013\pi$
$752$	3.81412e12	0.434925
$753$	−2.27033e12	−0.257343
$754$	−1.84293e13	−2.07652
$755$	−6.00522e12	−0.672617
$756$	7.51465e11	0.0836682
$757$	−1.07230e13	−1.18682	−0.593410	−	0.804900i	$-0.702219\pi$
$757$	−1.07230e13	−1.18682	−0.593410	+	0.804900i	$0.702219\pi$
$758$	−1.63654e13	−1.80059
$759$	−3.40492e12	−0.372408
$760$	−1.65153e12	−0.179566
$761$	2.42453e12	0.262058	0.131029	−	0.991379i	$-0.458172\pi$
$761$	2.42453e12	0.262058	0.131029	+	0.991379i	$0.458172\pi$
$762$	−9.28574e12	−0.997744
$763$	−1.81336e12	−0.193697
$764$	6.00006e12	0.637141
$765$	1.56920e12	0.165654
$766$	1.58083e13	1.65903
$767$	−1.17069e12	−0.122141
$768$	7.26633e12	0.753684
$769$	−2.80810e12	−0.289564	−0.144782	−	0.989464i	$-0.546248\pi$
$769$	−2.80810e12	−0.289564	−0.144782	+	0.989464i	$0.546248\pi$
$770$	−7.71955e12	−0.791378
$771$	1.01799e13	1.03753
$772$	1.07429e13	1.08854
$773$	−4.43601e12	−0.446874	−0.223437	−	0.974718i	$-0.571728\pi$
$773$	−4.43601e12	−0.446874	−0.223437	+	0.974718i	$0.571728\pi$
$774$	−2.56888e12	−0.257282
$775$	2.86239e12	0.285017
$776$	−6.27450e12	−0.621157
$777$	−5.23195e12	−0.514955
$778$	−1.39175e13	−1.36193
$779$	1.08210e13	1.05281
$780$	−3.53241e12	−0.341701
$781$	−6.21407e11	−0.0597649
$782$	4.34434e12	0.415425
$783$	−3.40050e12	−0.323307
$784$	8.22409e12	0.777438
$785$	−2.52761e12	−0.237573
$786$	−2.93637e12	−0.274416
$787$	−1.29011e13	−1.19878	−0.599390	−	0.800457i	$-0.704590\pi$
$787$	−1.29011e13	−1.19878	−0.599390	+	0.800457i	$0.704590\pi$
$788$	−4.03707e12	−0.372991
$789$	3.95587e12	0.363409
$790$	−1.36386e13	−1.24580
$791$	1.02054e12	0.0926908
$792$	1.52337e12	0.137576
$793$	4.72341e12	0.424157
$794$	−5.66156e12	−0.505526
$795$	3.80091e12	0.337470
$796$	6.95356e12	0.613901
$797$	−1.60038e13	−1.40495	−0.702475	−	0.711708i	$-0.747922\pi$
$797$	−1.60038e13	−1.40495	−0.702475	+	0.711708i	$0.747922\pi$
$798$	3.09816e12	0.270452
$799$	−2.43168e12	−0.211079
$800$	−3.76244e12	−0.324761
$801$	−1.35663e12	−0.116443
$802$	−2.07111e13	−1.76774
$803$	2.11482e13	1.79495
$804$	1.46866e12	0.123956
$805$	−3.28293e12	−0.275537
$806$	−1.59290e13	−1.32947
$807$	−1.05503e13	−0.875653
$808$	1.34901e12	0.111343
$809$	1.71444e13	1.40719	0.703595	−	0.710601i	$-0.251577\pi$
$809$	1.71444e13	1.40719	0.703595	+	0.710601i	$0.251577\pi$
$810$	−1.53758e12	−0.125504
$811$	−1.90092e13	−1.54302	−0.771509	−	0.636218i	$-0.780498\pi$
$811$	−1.90092e13	−1.54302	−0.771509	+	0.636218i	$0.780498\pi$
$812$	−9.04777e12	−0.730364
$813$	−1.20391e13	−0.966463
$814$	2.95419e13	2.35846
$815$	1.14417e13	0.908405
$816$	−5.06252e12	−0.399725
$817$	−4.48958e12	−0.352538
$818$	3.22043e13	2.51492
$819$	−2.37910e12	−0.184772
$820$	−1.42890e13	−1.10367
$821$	2.37312e13	1.82295	0.911477	−	0.411351i	$-0.134943\pi$
$821$	2.37312e13	1.82295	0.911477	+	0.411351i	$0.134943\pi$
$822$	4.70758e12	0.359645
$823$	8.15915e12	0.619934	0.309967	−	0.950747i	$-0.399682\pi$
$823$	8.15915e12	0.619934	0.309967	+	0.950747i	$0.399682\pi$
$824$	−2.03965e12	−0.154129
$825$	−2.41395e12	−0.181420
$826$	−1.35583e12	−0.101344
$827$	−8.76548e12	−0.651630	−0.325815	−	0.945434i	$-0.605639\pi$
$827$	−8.76548e12	−0.651630	−0.325815	+	0.945434i	$0.605639\pi$
$828$	−1.80448e12	−0.133418
$829$	1.34289e13	0.987521	0.493760	−	0.869598i	$-0.335622\pi$
$829$	1.34289e13	0.987521	0.493760	+	0.869598i	$0.335622\pi$
$830$	1.40160e13	1.02512
$831$	−6.02746e12	−0.438460
$832$	5.44995e12	0.394310
$833$	−5.24323e12	−0.377308
$834$	1.36621e13	0.977843
$835$	2.69426e12	0.191801
$836$	−7.41558e12	−0.525070
$837$	−2.93916e12	−0.206994
$838$	−1.41553e13	−0.991566
$839$	−9.77049e12	−0.680750	−0.340375	−	0.940290i	$-0.610554\pi$
$839$	−9.77049e12	−0.680750	−0.340375	+	0.940290i	$0.610554\pi$
$840$	1.46879e12	0.101790
$841$	2.64355e13	1.82224
$842$	−1.47842e13	−1.01366
$843$	−6.09333e12	−0.415557
$844$	2.00266e13	1.35852
$845$	−1.52234e12	−0.102720
$846$	2.38269e12	0.159919
$847$	3.59442e12	0.239968
$848$	−1.22624e13	−0.814320
$849$	1.37987e13	0.911493
$850$	3.07996e12	0.202376
$851$	1.25634e13	0.821154
$852$	−3.29323e11	−0.0214113
$853$	−1.40208e13	−0.906778	−0.453389	−	0.891313i	$-0.649785\pi$
$853$	−1.40208e13	−0.906778	−0.453389	+	0.891313i	$0.649785\pi$
$854$	5.47043e12	0.351934
$855$	−2.68721e12	−0.171970
$856$	4.87363e11	0.0310257
$857$	1.86132e12	0.117871	0.0589356	−	0.998262i	$-0.481229\pi$
$857$	1.86132e12	0.117871	0.0589356	+	0.998262i	$0.481229\pi$
$858$	1.34334e13	0.846242
$859$	−1.13968e12	−0.0714189	−0.0357095	−	0.999362i	$-0.511369\pi$
$859$	−1.13968e12	−0.0714189	−0.0357095	+	0.999362i	$0.511369\pi$
$860$	5.92843e12	0.369570
$861$	−9.62370e12	−0.596799
$862$	−5.79575e12	−0.357542
$863$	8.56652e12	0.525721	0.262861	−	0.964834i	$-0.415334\pi$
$863$	8.56652e12	0.525721	0.262861	+	0.964834i	$0.415334\pi$
$864$	3.86335e12	0.235859
$865$	−2.33613e13	−1.41881
$866$	3.92090e13	2.36895
$867$	−6.37803e12	−0.383355
$868$	−7.82027e12	−0.467609
$869$	2.19863e13	1.30787
$870$	1.85128e13	1.09556
$871$	−4.64969e12	−0.273743
$872$	−1.94817e12	−0.114104
$873$	−1.02093e13	−0.594882
$874$	−7.43956e12	−0.431266
$875$	−1.11106e13	−0.640771
$876$	1.12078e13	0.643058
$877$	−1.85029e13	−1.05619	−0.528096	−	0.849185i	$-0.677094\pi$
$877$	−1.85029e13	−1.05619	−0.528096	+	0.849185i	$0.677094\pi$
$878$	1.89737e13	1.07752
$879$	−1.79809e13	−1.01592
$880$	−2.16013e13	−1.21425
$881$	2.73534e12	0.152974	0.0764872	−	0.997071i	$-0.475630\pi$
$881$	2.73534e12	0.152974	0.0764872	+	0.997071i	$0.475630\pi$
$882$	5.13760e12	0.285859
$883$	1.11575e13	0.617652	0.308826	−	0.951118i	$-0.400064\pi$
$883$	1.11575e13	0.617652	0.308826	+	0.951118i	$0.400064\pi$
$884$	−7.26560e12	−0.400162
$885$	1.17599e12	0.0644406
$886$	−1.43115e13	−0.780247
$887$	2.87342e12	0.155863	0.0779316	−	0.996959i	$-0.475168\pi$
$887$	2.87342e12	0.155863	0.0779316	+	0.996959i	$0.475168\pi$
$888$	−5.62092e12	−0.303353
$889$	1.44329e13	0.774991
$890$	7.38566e12	0.394579
$891$	2.47869e12	0.131757
$892$	−1.34253e13	−0.710037
$893$	4.16418e12	0.219128
$894$	9.67613e12	0.506621
$895$	1.06481e13	0.554715
$896$	−7.65789e12	−0.396938
$897$	5.71290e12	0.294639
$898$	−6.46076e12	−0.331543
$899$	3.53880e13	1.80691
$900$	−1.27930e12	−0.0649954
$901$	7.81786e12	0.395208
$902$	5.43396e13	2.73330
$903$	3.99283e12	0.199842
$904$	1.09641e12	0.0546029
$905$	−2.62130e12	−0.129897
$906$	1.21029e13	0.596779
$907$	3.71918e13	1.82480	0.912398	−	0.409303i	$-0.134228\pi$
$907$	3.71918e13	1.82480	0.912398	+	0.409303i	$0.134228\pi$
$908$	1.44966e13	0.707751
$909$	2.19499e12	0.106634
$910$	1.29521e13	0.626117
$911$	−1.53745e13	−0.739552	−0.369776	−	0.929121i	$-0.620566\pi$
$911$	−1.53745e13	−0.739552	−0.369776	+	0.929121i	$0.620566\pi$
$912$	8.66943e12	0.414967
$913$	−2.25948e13	−1.07619
$914$	5.19726e13	2.46329
$915$	−4.74482e12	−0.223782
$916$	1.40094e13	0.657489
$917$	4.56403e12	0.213150
$918$	−3.16256e12	−0.146976
$919$	−1.64189e13	−0.759317	−0.379659	−	0.925127i	$-0.623959\pi$
$919$	−1.64189e13	−0.759317	−0.379659	+	0.925127i	$0.623959\pi$
$920$	−3.52699e12	−0.162315
$921$	7.62066e12	0.348999
$922$	3.50217e13	1.59606
$923$	1.04262e12	0.0472844
$924$	6.59509e12	0.297644
$925$	8.90695e12	0.400029
$926$	−1.56958e13	−0.701511
$927$	−3.31873e12	−0.147609
$928$	−4.65154e13	−2.05888
$929$	6.63995e12	0.292479	0.146239	−	0.989249i	$-0.453283\pi$
$929$	6.63995e12	0.292479	0.146239	+	0.989249i	$0.453283\pi$
$930$	1.60012e13	0.701421
$931$	8.97889e12	0.391696
$932$	−4.37348e12	−0.189870
$933$	−1.21396e13	−0.524489
$934$	−3.46578e12	−0.149019
$935$	1.37718e13	0.589302
$936$	−2.55597e12	−0.108847
$937$	−4.04370e12	−0.171376	−0.0856881	−	0.996322i	$-0.527309\pi$
$937$	−4.04370e12	−0.171376	−0.0856881	+	0.996322i	$0.527309\pi$
$938$	−5.38506e12	−0.227132
$939$	2.30571e11	0.00967855
$940$	−5.49874e12	−0.229714
$941$	−9.70117e12	−0.403340	−0.201670	−	0.979454i	$-0.564637\pi$
$941$	−9.70117e12	−0.403340	−0.201670	+	0.979454i	$0.564637\pi$
$942$	5.09415e12	0.210787
$943$	2.31093e13	0.951664
$944$	−3.79397e12	−0.155496
$945$	2.38989e12	0.0974841
$946$	−2.25453e13	−0.915262
$947$	2.70375e11	0.0109243	0.00546213	−	0.999985i	$-0.498261\pi$
$947$	2.70375e11	0.0109243	0.00546213	+	0.999985i	$0.498261\pi$
$948$	1.16519e13	0.468555
$949$	−3.54832e13	−1.42012
$950$	−5.27434e12	−0.210093
$951$	1.98912e13	0.788586
$952$	3.02107e12	0.119205
$953$	−1.46064e13	−0.573622	−0.286811	−	0.957987i	$-0.592595\pi$
$953$	−1.46064e13	−0.573622	−0.286811	+	0.957987i	$0.592595\pi$
$954$	−7.66035e12	−0.299420
$955$	1.90820e13	0.742350
$956$	−1.63886e13	−0.634573
$957$	−2.98439e13	−1.15014
$958$	−3.62329e13	−1.38982
$959$	−7.31704e12	−0.279352
$960$	−5.47466e12	−0.208035
$961$	4.14733e12	0.156860
$962$	−4.95665e13	−1.86595
$963$	7.92992e11	0.0297133
$964$	3.72447e13	1.38905
$965$	3.41658e13	1.26829
$966$	6.61641e12	0.244470
$967$	−1.63067e13	−0.599717	−0.299859	−	0.953984i	$-0.596940\pi$
$967$	−1.63067e13	−0.599717	−0.299859	+	0.953984i	$0.596940\pi$
$968$	3.86164e12	0.141362
$969$	−5.52715e12	−0.201393
$970$	5.55807e13	2.01582
$971$	7.03233e12	0.253871	0.126935	−	0.991911i	$-0.459486\pi$
$971$	7.03233e12	0.253871	0.126935	+	0.991911i	$0.459486\pi$
$972$	1.31361e12	0.0472030
$973$	−2.12351e13	−0.759533
$974$	−5.33512e13	−1.89945
$975$	4.05021e12	0.143535
$976$	1.53077e13	0.539989
$977$	−5.02095e13	−1.76303	−0.881516	−	0.472155i	$-0.843476\pi$
$977$	−5.02095e13	−1.76303	−0.881516	+	0.472155i	$0.843476\pi$
$978$	−2.30595e13	−0.805982
$979$	−1.19062e13	−0.414239
$980$	−1.18565e13	−0.410619
$981$	−3.16988e12	−0.109278
$982$	2.12595e13	0.729544
$983$	3.28721e13	1.12289	0.561443	−	0.827515i	$-0.310246\pi$
$983$	3.28721e13	1.12289	0.561443	+	0.827515i	$0.310246\pi$
$984$	−1.03392e13	−0.351567
$985$	−1.28391e13	−0.434582
$986$	3.80778e13	1.28300
$987$	−3.70344e12	−0.124216
$988$	1.24421e13	0.415421
$989$	−9.58793e12	−0.318670
$990$	−1.34943e13	−0.446471
$991$	4.22004e13	1.38990	0.694952	−	0.719056i	$-0.255425\pi$
$991$	4.22004e13	1.38990	0.694952	+	0.719056i	$0.255425\pi$
$992$	−4.02047e13	−1.31818
$993$	−2.02219e13	−0.660010
$994$	1.20751e12	0.0392331
$995$	2.21144e13	0.715273
$996$	−1.19744e13	−0.385555
$997$	1.38251e13	0.443138	0.221569	−	0.975145i	$-0.428882\pi$
$997$	1.38251e13	0.443138	0.221569	+	0.975145i	$0.428882\pi$
$998$	−1.90269e13	−0.607129
$999$	−9.14584e12	−0.290522

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.5	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-29.8118 q^{2} +81.0000 q^{3} +376.741 q^{4} +1198.15 q^{5} -2414.75 q^{6} +3753.28 q^{7} +4032.31 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-29.8118 q^{2} +81.0000 q^{3} +376.741 q^{4} +1198.15 q^{5} -2414.75 q^{6} +3753.28 q^{7} +4032.31 q^{8} +6561.00 q^{9} -35719.0 q^{10} +57581.4 q^{11} +30516.0 q^{12} -96612.2 q^{13} -111892. q^{14} +97050.2 q^{15} -313102. q^{16} +199617. q^{17} -195595. q^{18} -341838. q^{19} +451392. q^{20} +304015. q^{21} -1.71660e6 q^{22} -730028. q^{23} +326617. q^{24} -517560. q^{25} +2.88018e6 q^{26} +531441. q^{27} +1.41401e6 q^{28} -6.39864e6 q^{29} -2.89324e6 q^{30} -5.53055e6 q^{31} +7.26957e6 q^{32} +4.66410e6 q^{33} -5.95092e6 q^{34} +4.49699e6 q^{35} +2.47180e6 q^{36} -1.72095e7 q^{37} +1.01908e7 q^{38} -7.82559e6 q^{39} +4.83131e6 q^{40} -3.16553e7 q^{41} -9.06323e6 q^{42} +1.31337e7 q^{43} +2.16933e7 q^{44} +7.86107e6 q^{45} +2.17634e7 q^{46} -1.21817e7 q^{47} -2.53612e7 q^{48} -2.62665e7 q^{49} +1.54294e7 q^{50} +1.61689e7 q^{51} -3.63978e7 q^{52} +3.91644e7 q^{53} -1.58432e7 q^{54} +6.89912e7 q^{55} +1.51344e7 q^{56} -2.76889e7 q^{57} +1.90755e8 q^{58} +1.21174e7 q^{59} +3.65628e7 q^{60} -4.88904e7 q^{61} +1.64875e8 q^{62} +2.46252e7 q^{63} -5.64106e7 q^{64} -1.15756e8 q^{65} -1.39045e8 q^{66} +4.81274e7 q^{67} +7.52037e7 q^{68} -5.91322e7 q^{69} -1.34063e8 q^{70} -1.07918e7 q^{71} +2.64560e7 q^{72} +3.67275e8 q^{73} +5.13046e8 q^{74} -4.19224e7 q^{75} -1.28784e8 q^{76} +2.16119e8 q^{77} +2.33295e8 q^{78} +3.81830e8 q^{79} -3.75143e8 q^{80} +4.30467e7 q^{81} +9.43701e8 q^{82} -3.92397e8 q^{83} +1.14535e8 q^{84} +2.39171e8 q^{85} -3.91537e8 q^{86} -5.18290e8 q^{87} +2.32186e8 q^{88} -2.06771e8 q^{89} -2.34352e8 q^{90} -3.62612e8 q^{91} -2.75031e8 q^{92} -4.47974e8 q^{93} +3.63159e8 q^{94} -4.09573e8 q^{95} +5.88835e8 q^{96} -1.55606e9 q^{97} +7.83051e8 q^{98} +3.77792e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more