LMFDB - Embedded newform 177.10.a.c.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:	$0$
Dimension:	$22$
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)

$f(q)$	$=$	$q-13.7066 q^{2} -81.0000 q^{3} -324.128 q^{4} -1287.82 q^{5} +1110.24 q^{6} +3218.96 q^{7} +11460.5 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-13.7066 q^{2} -81.0000 q^{3} -324.128 q^{4} -1287.82 q^{5} +1110.24 q^{6} +3218.96 q^{7} +11460.5 q^{8} +6561.00 q^{9} +17651.6 q^{10} -58323.1 q^{11} +26254.4 q^{12} +142785. q^{13} -44121.2 q^{14} +104313. q^{15} +8868.30 q^{16} -634613. q^{17} -89929.3 q^{18} +1.07010e6 q^{19} +417417. q^{20} -260736. q^{21} +799414. q^{22} -325370. q^{23} -928301. q^{24} -294653. q^{25} -1.95710e6 q^{26} -531441. q^{27} -1.04336e6 q^{28} -4.66165e6 q^{29} -1.42978e6 q^{30} -5.51199e6 q^{31} -5.98934e6 q^{32} +4.72417e6 q^{33} +8.69841e6 q^{34} -4.14543e6 q^{35} -2.12660e6 q^{36} +1.62950e7 q^{37} -1.46674e7 q^{38} -1.15656e7 q^{39} -1.47590e7 q^{40} -2.02347e7 q^{41} +3.57382e6 q^{42} -3.84725e7 q^{43} +1.89041e7 q^{44} -8.44936e6 q^{45} +4.45974e6 q^{46} -3.59866e6 q^{47} -718332. q^{48} -2.99919e7 q^{49} +4.03871e6 q^{50} +5.14036e7 q^{51} -4.62805e7 q^{52} +5.97566e7 q^{53} +7.28427e6 q^{54} +7.51094e7 q^{55} +3.68910e7 q^{56} -8.66778e7 q^{57} +6.38956e7 q^{58} +1.21174e7 q^{59} -3.38108e7 q^{60} +5.83430e7 q^{61} +7.55509e7 q^{62} +2.11196e7 q^{63} +7.75531e7 q^{64} -1.83881e8 q^{65} -6.47525e7 q^{66} +1.77772e7 q^{67} +2.05696e8 q^{68} +2.63550e7 q^{69} +5.68200e7 q^{70} -1.90982e8 q^{71} +7.51924e7 q^{72} -4.70490e8 q^{73} -2.23350e8 q^{74} +2.38669e7 q^{75} -3.46848e8 q^{76} -1.87740e8 q^{77} +1.58525e8 q^{78} -1.31253e8 q^{79} -1.14207e7 q^{80} +4.30467e7 q^{81} +2.77350e8 q^{82} -5.84868e7 q^{83} +8.45118e7 q^{84} +8.17265e8 q^{85} +5.27329e8 q^{86} +3.77594e8 q^{87} -6.68412e8 q^{88} +5.00612e8 q^{89} +1.15812e8 q^{90} +4.59619e8 q^{91} +1.05462e8 q^{92} +4.46471e8 q^{93} +4.93255e7 q^{94} -1.37809e9 q^{95} +4.85136e8 q^{96} +5.11624e8 q^{97} +4.11088e8 q^{98} -3.82658e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9} + 68441 q^{10} - 68033 q^{11} - 463158 q^{12} + 283817 q^{13} + 80285 q^{14} - 65448 q^{15} + 1067674 q^{16} + 436893 q^{17} + 236196 q^{18} + 1207580 q^{19} + 4209677 q^{20} - 1721169 q^{21} + 5460442 q^{22} + 2421966 q^{23} - 764235 q^{24} + 7441842 q^{25} - 2736526 q^{26} - 11691702 q^{27} + 4095246 q^{28} - 2320594 q^{29} - 5543721 q^{30} - 3178024 q^{31} - 20786874 q^{32} + 5510673 q^{33} - 13809336 q^{34} - 2630800 q^{35} + 37515798 q^{36} + 3981807 q^{37} - 24156377 q^{38} - 22989177 q^{39} - 29544450 q^{40} - 885225 q^{41} - 6503085 q^{42} + 12360835 q^{43} - 117711882 q^{44} + 5301288 q^{45} + 161066949 q^{46} + 75901252 q^{47} - 86481594 q^{48} + 170907951 q^{49} - 61318927 q^{50} - 35388333 q^{51} - 100762 q^{52} - 34790192 q^{53} - 19131876 q^{54} + 151773316 q^{55} - 417630344 q^{56} - 97813980 q^{57} - 432929294 q^{58} + 266581942 q^{59} - 340983837 q^{60} - 290555332 q^{61} + 158267098 q^{62} + 139414689 q^{63} - 131794443 q^{64} - 650690086 q^{65} - 442295802 q^{66} + 86645184 q^{67} + 62738541 q^{68} - 196179246 q^{69} + 429714610 q^{70} - 36567631 q^{71} + 61903035 q^{72} + 907807228 q^{73} - 171827242 q^{74} - 602789202 q^{75} + 1744504396 q^{76} - 310688725 q^{77} + 221658606 q^{78} + 2508604687 q^{79} + 3509441927 q^{80} + 947027862 q^{81} + 1759214793 q^{82} + 2185672083 q^{83} - 331714926 q^{84} + 2868860198 q^{85} + 2397001564 q^{86} + 187968114 q^{87} + 7683735877 q^{88} + 1320145942 q^{89} + 449041401 q^{90} + 3894639897 q^{91} + 3505964640 q^{92} + 257419944 q^{93} + 5406355552 q^{94} + 3093659122 q^{95} + 1683736794 q^{96} + 3904552980 q^{97} + 6137683116 q^{98} - 446364513 q^{99}+O(q^{100}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9 + 68441 * q^10 - 68033 * q^11 - 463158 * q^12 + 283817 * q^13 + 80285 * q^14 - 65448 * q^15 + 1067674 * q^16 + 436893 * q^17 + 236196 * q^18 + 1207580 * q^19 + 4209677 * q^20 - 1721169 * q^21 + 5460442 * q^22 + 2421966 * q^23 - 764235 * q^24 + 7441842 * q^25 - 2736526 * q^26 - 11691702 * q^27 + 4095246 * q^28 - 2320594 * q^29 - 5543721 * q^30 - 3178024 * q^31 - 20786874 * q^32 + 5510673 * q^33 - 13809336 * q^34 - 2630800 * q^35 + 37515798 * q^36 + 3981807 * q^37 - 24156377 * q^38 - 22989177 * q^39 - 29544450 * q^40 - 885225 * q^41 - 6503085 * q^42 + 12360835 * q^43 - 117711882 * q^44 + 5301288 * q^45 + 161066949 * q^46 + 75901252 * q^47 - 86481594 * q^48 + 170907951 * q^49 - 61318927 * q^50 - 35388333 * q^51 - 100762 * q^52 - 34790192 * q^53 - 19131876 * q^54 + 151773316 * q^55 - 417630344 * q^56 - 97813980 * q^57 - 432929294 * q^58 + 266581942 * q^59 - 340983837 * q^60 - 290555332 * q^61 + 158267098 * q^62 + 139414689 * q^63 - 131794443 * q^64 - 650690086 * q^65 - 442295802 * q^66 + 86645184 * q^67 + 62738541 * q^68 - 196179246 * q^69 + 429714610 * q^70 - 36567631 * q^71 + 61903035 * q^72 + 907807228 * q^73 - 171827242 * q^74 - 602789202 * q^75 + 1744504396 * q^76 - 310688725 * q^77 + 221658606 * q^78 + 2508604687 * q^79 + 3509441927 * q^80 + 947027862 * q^81 + 1759214793 * q^82 + 2185672083 * q^83 - 331714926 * q^84 + 2868860198 * q^85 + 2397001564 * q^86 + 187968114 * q^87 + 7683735877 * q^88 + 1320145942 * q^89 + 449041401 * q^90 + 3894639897 * q^91 + 3505964640 * q^92 + 257419944 * q^93 + 5406355552 * q^94 + 3093659122 * q^95 + 1683736794 * q^96 + 3904552980 * q^97 + 6137683116 * q^98 - 446364513 * 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 $

$2$	−13.7066	−0.605754	−0.302877	−	0.953030i	$-0.597947\pi$
$2$	−13.7066	−0.605754	−0.302877	+	0.953030i	$0.597947\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−324.128	−0.633062
$5$	−1287.82	−0.921487	−0.460743	−	0.887533i	$-0.652417\pi$
$5$	−1287.82	−0.921487	−0.460743	+	0.887533i	$0.652417\pi$
$6$	1110.24	0.349732
$7$	3218.96	0.506728	0.253364	−	0.967371i	$-0.418463\pi$
$7$	3218.96	0.506728	0.253364	+	0.967371i	$0.418463\pi$
$8$	11460.5	0.989234
$9$	6561.00	0.333333
$10$	17651.6	0.558194
$11$	−58323.1	−1.20108	−0.600542	−	0.799593i	$-0.705049\pi$
$11$	−58323.1	−1.20108	−0.600542	+	0.799593i	$0.705049\pi$
$12$	26254.4	0.365499
$13$	142785.	1.38655	0.693277	−	0.720671i	$-0.256166\pi$
$13$	142785.	1.38655	0.693277	+	0.720671i	$0.256166\pi$
$14$	−44121.2	−0.306952
$15$	104313.	0.532021
$16$	8868.30	0.0338299
$17$	−634613.	−1.84284	−0.921422	−	0.388563i	$-0.872972\pi$
$17$	−634613.	−1.84284	−0.921422	+	0.388563i	$0.872972\pi$
$18$	−89929.3	−0.201918
$19$	1.07010e6	1.88379	0.941894	−	0.335911i	$-0.109044\pi$
$19$	1.07010e6	1.88379	0.941894	+	0.335911i	$0.109044\pi$
$20$	417417.	0.583358
$21$	−260736.	−0.292560
$22$	799414.	0.727561
$23$	−325370.	−0.242439	−0.121220	−	0.992626i	$-0.538681\pi$
$23$	−325370.	−0.242439	−0.121220	+	0.992626i	$0.538681\pi$
$24$	−928301.	−0.571134
$25$	−294653.	−0.150863
$26$	−1.95710e6	−0.839911
$27$	−531441.	−0.192450
$28$	−1.04336e6	−0.320790
$29$	−4.66165e6	−1.22391	−0.611954	−	0.790893i	$-0.709616\pi$
$29$	−4.66165e6	−1.22391	−0.611954	+	0.790893i	$0.709616\pi$
$30$	−1.42978e6	−0.322274
$31$	−5.51199e6	−1.07197	−0.535983	−	0.844229i	$-0.680059\pi$
$31$	−5.51199e6	−1.07197	−0.535983	+	0.844229i	$0.680059\pi$
$32$	−5.98934e6	−1.00973
$33$	4.72417e6	0.693446
$34$	8.69841e6	1.11631
$35$	−4.14543e6	−0.466943
$36$	−2.12660e6	−0.211021
$37$	1.62950e7	1.42938	0.714690	−	0.699442i	$-0.246568\pi$
$37$	1.62950e7	1.42938	0.714690	+	0.699442i	$0.246568\pi$
$38$	−1.46674e7	−1.14111
$39$	−1.15656e7	−0.800528
$40$	−1.47590e7	−0.911566
$41$	−2.02347e7	−1.11833	−0.559164	−	0.829057i	$-0.688878\pi$
$41$	−2.02347e7	−1.11833	−0.559164	+	0.829057i	$0.688878\pi$
$42$	3.57382e6	0.177219
$43$	−3.84725e7	−1.71610	−0.858050	−	0.513566i	$-0.828324\pi$
$43$	−3.84725e7	−1.71610	−0.858050	+	0.513566i	$0.828324\pi$
$44$	1.89041e7	0.760361
$45$	−8.44936e6	−0.307162
$46$	4.45974e6	0.146859
$47$	−3.59866e6	−0.107572	−0.0537861	−	0.998552i	$-0.517129\pi$
$47$	−3.59866e6	−0.107572	−0.0537861	+	0.998552i	$0.517129\pi$
$48$	−718332.	−0.0195317
$49$	−2.99919e7	−0.743227
$50$	4.03871e6	0.0913856
$51$	5.14036e7	1.06397
$52$	−4.62805e7	−0.877775
$53$	5.97566e7	1.04027	0.520133	−	0.854085i	$-0.325882\pi$
$53$	5.97566e7	1.04027	0.520133	+	0.854085i	$0.325882\pi$
$54$	7.28427e6	0.116577
$55$	7.51094e7	1.10678
$56$	3.68910e7	0.501272
$57$	−8.66778e7	−1.08761
$58$	6.38956e7	0.741388
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−3.38108e7	−0.336802
$61$	5.83430e7	0.539516	0.269758	−	0.962928i	$-0.413056\pi$
$61$	5.83430e7	0.539516	0.269758	+	0.962928i	$0.413056\pi$
$62$	7.55509e7	0.649347
$63$	2.11196e7	0.168909
$64$	7.75531e7	0.577816
$65$	−1.83881e8	−1.27769
$66$	−6.47525e7	−0.420058
$67$	1.77772e7	0.107777	0.0538884	−	0.998547i	$-0.482838\pi$
$67$	1.77772e7	0.107777	0.0538884	+	0.998547i	$0.482838\pi$
$68$	2.05696e8	1.16664
$69$	2.63550e7	0.139972
$70$	5.68200e7	0.282853
$71$	−1.90982e8	−0.891926	−0.445963	−	0.895051i	$-0.647139\pi$
$71$	−1.90982e8	−0.891926	−0.445963	+	0.895051i	$0.647139\pi$
$72$	7.51924e7	0.329745
$73$	−4.70490e8	−1.93909	−0.969544	−	0.244916i	$-0.921240\pi$
$73$	−4.70490e8	−1.93909	−0.969544	+	0.244916i	$0.921240\pi$
$74$	−2.23350e8	−0.865852
$75$	2.38669e7	0.0871005
$76$	−3.46848e8	−1.19255
$77$	−1.87740e8	−0.608623
$78$	1.58525e8	0.484923
$79$	−1.31253e8	−0.379131	−0.189565	−	0.981868i	$-0.560708\pi$
$79$	−1.31253e8	−0.379131	−0.189565	+	0.981868i	$0.560708\pi$
$80$	−1.14207e7	−0.0311738
$81$	4.30467e7	0.111111
$82$	2.77350e8	0.677431
$83$	−5.84868e7	−0.135271	−0.0676357	−	0.997710i	$-0.521546\pi$
$83$	−5.84868e7	−0.135271	−0.0676357	+	0.997710i	$0.521546\pi$
$84$	8.45118e7	0.185208
$85$	8.17265e8	1.69816
$86$	5.27329e8	1.03953
$87$	3.77594e8	0.706624
$88$	−6.68412e8	−1.18815
$89$	5.00612e8	0.845759	0.422879	−	0.906186i	$-0.361019\pi$
$89$	5.00612e8	0.845759	0.422879	+	0.906186i	$0.361019\pi$
$90$	1.15812e8	0.186065
$91$	4.59619e8	0.702606
$92$	1.05462e8	0.153479
$93$	4.46471e8	0.618899
$94$	4.93255e7	0.0651623
$95$	−1.37809e9	−1.73588
$96$	4.85136e8	0.582966
$97$	5.11624e8	0.586784	0.293392	−	0.955992i	$-0.405216\pi$
$97$	5.11624e8	0.586784	0.293392	+	0.955992i	$0.405216\pi$
$98$	4.11088e8	0.450213
$99$	−3.82658e8	−0.400361
$100$	9.55053e7	0.0955053
$101$	−1.61259e9	−1.54198	−0.770989	−	0.636848i	$-0.780238\pi$
$101$	−1.61259e9	−1.54198	−0.770989	+	0.636848i	$0.780238\pi$
$102$	−7.04572e8	−0.644502
$103$	−1.90647e8	−0.166903	−0.0834514	−	0.996512i	$-0.526594\pi$
$103$	−1.90647e8	−0.166903	−0.0834514	+	0.996512i	$0.526594\pi$
$104$	1.63639e9	1.37163
$105$	3.35780e8	0.269590
$106$	−8.19063e8	−0.630146
$107$	8.83809e7	0.0651826	0.0325913	−	0.999469i	$-0.489624\pi$
$107$	8.83809e7	0.0651826	0.0325913	+	0.999469i	$0.489624\pi$
$108$	1.72255e8	0.121833
$109$	2.73851e9	1.85821	0.929107	−	0.369812i	$-0.120578\pi$
$109$	2.73851e9	1.85821	0.929107	+	0.369812i	$0.120578\pi$
$110$	−1.02950e9	−0.670438
$111$	−1.31990e9	−0.825253
$112$	2.85467e7	0.0171425
$113$	1.25793e9	0.725779	0.362890	−	0.931832i	$-0.381790\pi$
$113$	1.25793e9	0.725779	0.362890	+	0.931832i	$0.381790\pi$
$114$	1.18806e9	0.658821
$115$	4.19018e8	0.223404
$116$	1.51097e9	0.774810
$117$	9.36811e8	0.462185
$118$	−1.66088e8	−0.0788624
$119$	−2.04280e9	−0.933821
$120$	1.19548e9	0.526293
$121$	1.04364e9	0.442603
$122$	−7.99687e8	−0.326814
$123$	1.63901e9	0.645666
$124$	1.78659e9	0.678621
$125$	2.89473e9	1.06050
$126$	−2.89479e8	−0.102317
$127$	−2.31195e9	−0.788608	−0.394304	−	0.918980i	$-0.629014\pi$
$127$	−2.31195e9	−0.788608	−0.394304	+	0.918980i	$0.629014\pi$
$128$	2.00355e9	0.659712
$129$	3.11627e9	0.990791
$130$	2.52039e9	0.773967
$131$	3.61228e9	1.07167	0.535834	−	0.844323i	$-0.319997\pi$
$131$	3.61228e9	1.07167	0.535834	+	0.844323i	$0.319997\pi$
$132$	−1.53124e9	−0.438995
$133$	3.44460e9	0.954568
$134$	−2.43665e8	−0.0652863
$135$	6.84399e8	0.177340
$136$	−7.27299e9	−1.82300
$137$	7.85703e7	0.0190553	0.00952765	−	0.999955i	$-0.496967\pi$
$137$	7.85703e7	0.0190553	0.00952765	+	0.999955i	$0.496967\pi$
$138$	−3.61239e8	−0.0847888
$139$	5.49642e9	1.24886	0.624430	−	0.781081i	$-0.285331\pi$
$139$	5.49642e9	1.24886	0.624430	+	0.781081i	$0.285331\pi$
$140$	1.34365e9	0.295604
$141$	2.91491e8	0.0621069
$142$	2.61772e9	0.540288
$143$	−8.32765e9	−1.66537
$144$	5.81849e7	0.0112766
$145$	6.00336e9	1.12782
$146$	6.44884e9	1.17461
$147$	2.42934e9	0.429102
$148$	−5.28167e9	−0.904886
$149$	−5.68911e9	−0.945596	−0.472798	−	0.881171i	$-0.656756\pi$
$149$	−5.68911e9	−0.945596	−0.472798	+	0.881171i	$0.656756\pi$
$150$	−3.27135e8	−0.0527615
$151$	−5.62546e8	−0.0880565	−0.0440283	−	0.999030i	$-0.514019\pi$
$151$	−5.62546e8	−0.0880565	−0.0440283	+	0.999030i	$0.514019\pi$
$152$	1.22639e10	1.86351
$153$	−4.16369e9	−0.614282
$154$	2.57328e9	0.368676
$155$	7.09843e9	0.987802
$156$	3.74872e9	0.506784
$157$	−7.75677e9	−1.01890	−0.509451	−	0.860500i	$-0.670151\pi$
$157$	−7.75677e9	−1.01890	−0.509451	+	0.860500i	$0.670151\pi$
$158$	1.79905e9	0.229660
$159$	−4.84029e9	−0.600598
$160$	7.71317e9	0.930449
$161$	−1.04736e9	−0.122851
$162$	−5.90026e8	−0.0673060
$163$	−1.46466e10	−1.62515	−0.812573	−	0.582859i	$-0.801934\pi$
$163$	−1.46466e10	−1.62515	−0.812573	+	0.582859i	$0.801934\pi$
$164$	6.55862e9	0.707971
$165$	−6.08387e9	−0.639001
$166$	8.01657e8	0.0819412
$167$	1.83446e10	1.82509	0.912547	−	0.408972i	$-0.134113\pi$
$167$	1.83446e10	1.82509	0.912547	+	0.408972i	$0.134113\pi$
$168$	−2.98817e9	−0.289410
$169$	9.78301e9	0.922534
$170$	−1.12020e10	−1.02867
$171$	7.02091e9	0.627929
$172$	1.24700e10	1.08640
$173$	3.91756e9	0.332513	0.166256	−	0.986083i	$-0.446832\pi$
$173$	3.91756e9	0.332513	0.166256	+	0.986083i	$0.446832\pi$
$174$	−5.17555e9	−0.428040
$175$	−9.48478e8	−0.0764462
$176$	−5.17227e8	−0.0406325
$177$	−9.81506e8	−0.0751646
$178$	−6.86172e9	−0.512322
$179$	6.82016e9	0.496542	0.248271	−	0.968691i	$-0.420138\pi$
$179$	6.82016e9	0.496542	0.248271	+	0.968691i	$0.420138\pi$
$180$	2.73867e9	0.194453
$181$	−6.85477e9	−0.474722	−0.237361	−	0.971422i	$-0.576282\pi$
$181$	−6.85477e9	−0.474722	−0.237361	+	0.971422i	$0.576282\pi$
$182$	−6.29984e9	−0.425606
$183$	−4.72578e9	−0.311490
$184$	−3.72891e9	−0.239829
$185$	−2.09850e10	−1.31715
$186$	−6.11962e9	−0.374901
$187$	3.70126e10	2.21341
$188$	1.16643e9	0.0680999
$189$	−1.71069e9	−0.0975198
$190$	1.88890e10	1.05152
$191$	3.27100e9	0.177840	0.0889201	−	0.996039i	$-0.471658\pi$
$191$	3.27100e9	0.177840	0.0889201	+	0.996039i	$0.471658\pi$
$192$	−6.28180e9	−0.333602
$193$	1.06930e10	0.554743	0.277371	−	0.960763i	$-0.410537\pi$
$193$	1.06930e10	0.554743	0.277371	+	0.960763i	$0.410537\pi$
$194$	−7.01265e9	−0.355446
$195$	1.48943e10	0.737676
$196$	9.72120e9	0.470509
$197$	6.60109e9	0.312261	0.156131	−	0.987736i	$-0.450098\pi$
$197$	6.60109e9	0.312261	0.156131	+	0.987736i	$0.450098\pi$
$198$	5.24496e9	0.242520
$199$	−3.54383e9	−0.160190	−0.0800949	−	0.996787i	$-0.525522\pi$
$199$	−3.54383e9	−0.160190	−0.0800949	+	0.996787i	$0.525522\pi$
$200$	−3.37688e9	−0.149238
$201$	−1.43995e9	−0.0622250
$202$	2.21032e10	0.934059
$203$	−1.50057e10	−0.620189
$204$	−1.66614e10	−0.673557
$205$	2.60585e10	1.03052
$206$	2.61314e9	0.101102
$207$	−2.13476e9	−0.0808131
$208$	1.26626e9	0.0469070
$209$	−6.24114e10	−2.26259
$210$	−4.60242e9	−0.163305
$211$	1.86373e10	0.647308	0.323654	−	0.946176i	$-0.395089\pi$
$211$	1.86373e10	0.647308	0.323654	+	0.946176i	$0.395089\pi$
$212$	−1.93688e10	−0.658553
$213$	1.54695e10	0.514954
$214$	−1.21141e9	−0.0394846
$215$	4.95456e10	1.58136
$216$	−6.09058e9	−0.190378
$217$	−1.77429e10	−0.543195
$218$	−3.75358e10	−1.12562
$219$	3.81097e10	1.11953
$220$	−2.43451e10	−0.700662
$221$	−9.06131e10	−2.55520
$222$	1.80914e10	0.499900
$223$	−4.63375e10	−1.25476	−0.627380	−	0.778713i	$-0.715873\pi$
$223$	−4.63375e10	−1.25476	−0.627380	+	0.778713i	$0.715873\pi$
$224$	−1.92795e10	−0.511657
$225$	−1.93322e9	−0.0502875
$226$	−1.72420e10	−0.439643
$227$	−1.44421e10	−0.361005	−0.180503	−	0.983575i	$-0.557772\pi$
$227$	−1.44421e10	−0.361005	−0.180503	+	0.983575i	$0.557772\pi$
$228$	2.80947e10	0.688522
$229$	−9.47681e9	−0.227721	−0.113860	−	0.993497i	$-0.536322\pi$
$229$	−9.47681e9	−0.227721	−0.113860	+	0.993497i	$0.536322\pi$
$230$	−5.74332e9	−0.135328
$231$	1.52069e10	0.351389
$232$	−5.34249e10	−1.21073
$233$	6.67568e9	0.148386	0.0741931	−	0.997244i	$-0.476362\pi$
$233$	6.67568e9	0.148386	0.0741931	+	0.997244i	$0.476362\pi$
$234$	−1.28405e10	−0.279970
$235$	4.63441e9	0.0991264
$236$	−3.92757e9	−0.0824177
$237$	1.06315e10	0.218891
$238$	2.79999e10	0.565666
$239$	−1.54044e10	−0.305389	−0.152695	−	0.988273i	$-0.548795\pi$
$239$	−1.54044e10	−0.305389	−0.152695	+	0.988273i	$0.548795\pi$
$240$	9.25080e8	0.0179982
$241$	8.37352e10	1.59894	0.799469	−	0.600707i	$-0.205114\pi$
$241$	8.37352e10	1.59894	0.799469	+	0.600707i	$0.205114\pi$
$242$	−1.43047e10	−0.268109
$243$	−3.48678e9	−0.0641500
$244$	−1.89106e10	−0.341547
$245$	3.86240e10	0.684874
$246$	−2.24653e10	−0.391115
$247$	1.52794e11	2.61197
$248$	−6.31702e10	−1.06042
$249$	4.73743e9	0.0780990
$250$	−3.96770e10	−0.642405
$251$	−1.74665e10	−0.277763	−0.138881	−	0.990309i	$-0.544351\pi$
$251$	−1.74665e10	−0.277763	−0.138881	+	0.990309i	$0.544351\pi$
$252$	−6.84546e9	−0.106930
$253$	1.89766e10	0.291190
$254$	3.16891e10	0.477703
$255$	−6.61985e10	−0.980431
$256$	−6.71691e10	−0.977439
$257$	−7.76557e10	−1.11039	−0.555194	−	0.831721i	$-0.687356\pi$
$257$	−7.76557e10	−1.11039	−0.555194	+	0.831721i	$0.687356\pi$
$258$	−4.27137e10	−0.600176
$259$	5.24531e10	0.724307
$260$	5.96008e10	0.808858
$261$	−3.05851e10	−0.407970
$262$	−4.95122e10	−0.649167
$263$	−1.93846e10	−0.249837	−0.124918	−	0.992167i	$-0.539867\pi$
$263$	−1.93846e10	−0.249837	−0.124918	+	0.992167i	$0.539867\pi$
$264$	5.41414e10	0.685981
$265$	−7.69556e10	−0.958592
$266$	−4.72140e10	−0.578233
$267$	−4.05496e10	−0.488299
$268$	−5.76207e9	−0.0682295
$269$	2.06615e10	0.240589	0.120294	−	0.992738i	$-0.461616\pi$
$269$	2.06615e10	0.240589	0.120294	+	0.992738i	$0.461616\pi$
$270$	−9.38081e9	−0.107425
$271$	−4.67978e10	−0.527064	−0.263532	−	0.964651i	$-0.584887\pi$
$271$	−4.67978e10	−0.527064	−0.263532	+	0.964651i	$0.584887\pi$
$272$	−5.62794e9	−0.0623432
$273$	−3.72292e10	−0.405650
$274$	−1.07694e9	−0.0115428
$275$	1.71851e10	0.181199
$276$	−8.54239e9	−0.0886112
$277$	−9.14024e10	−0.932821	−0.466411	−	0.884568i	$-0.654453\pi$
$277$	−9.14024e10	−0.932821	−0.466411	+	0.884568i	$0.654453\pi$
$278$	−7.53375e10	−0.756502
$279$	−3.61642e10	−0.357322
$280$	−4.75088e10	−0.461916
$281$	−1.31051e11	−1.25390	−0.626951	−	0.779059i	$-0.715697\pi$
$281$	−1.31051e11	−1.25390	−0.626951	+	0.779059i	$0.715697\pi$
$282$	−3.99537e9	−0.0376215
$283$	−1.84063e11	−1.70580	−0.852901	−	0.522073i	$-0.825159\pi$
$283$	−1.84063e11	−1.70580	−0.852901	+	0.522073i	$0.825159\pi$
$284$	6.19025e10	0.564645
$285$	1.11625e11	1.00221
$286$	1.14144e11	1.00880
$287$	−6.51347e10	−0.566688
$288$	−3.92960e10	−0.336575
$289$	2.84146e11	2.39608
$290$	−8.22859e10	−0.683179
$291$	−4.14415e10	−0.338780
$292$	1.52499e11	1.22756
$293$	3.58566e10	0.284227	0.142113	−	0.989850i	$-0.454610\pi$
$293$	3.58566e10	0.284227	0.142113	+	0.989850i	$0.454610\pi$
$294$	−3.32981e10	−0.259930
$295$	−1.56049e10	−0.119967
$296$	1.86749e11	1.41399
$297$	3.09953e10	0.231149
$298$	7.79786e10	0.572799
$299$	−4.64580e10	−0.336155
$300$	−7.73593e9	−0.0551400
$301$	−1.23842e11	−0.869596
$302$	7.71062e9	0.0533406
$303$	1.30620e11	0.890262
$304$	9.48994e9	0.0637283
$305$	−7.51351e10	−0.497157
$306$	5.70703e10	0.372103
$307$	2.81321e11	1.80750	0.903751	−	0.428059i	$-0.140802\pi$
$307$	2.81321e11	1.80750	0.903751	+	0.428059i	$0.140802\pi$
$308$	6.08517e10	0.385296
$309$	1.54424e10	0.0963614
$310$	−9.72957e10	−0.598365
$311$	2.77783e11	1.68377	0.841886	−	0.539655i	$-0.181445\pi$
$311$	2.77783e11	1.68377	0.841886	+	0.539655i	$0.181445\pi$
$312$	−1.32547e11	−0.791909
$313$	−1.15722e11	−0.681500	−0.340750	−	0.940154i	$-0.610681\pi$
$313$	−1.15722e11	−0.681500	−0.340750	+	0.940154i	$0.610681\pi$
$314$	1.06319e11	0.617204
$315$	−2.71982e10	−0.155648
$316$	4.25429e10	0.240013
$317$	2.98400e10	0.165971	0.0829855	−	0.996551i	$-0.473554\pi$
$317$	2.98400e10	0.165971	0.0829855	+	0.996551i	$0.473554\pi$
$318$	6.63441e10	0.363815
$319$	2.71882e11	1.47002
$320$	−9.98742e10	−0.532450
$321$	−7.15885e9	−0.0376332
$322$	1.43557e10	0.0744173
$323$	−6.79097e11	−3.47153
$324$	−1.39526e10	−0.0703402
$325$	−4.20720e10	−0.209179
$326$	2.00756e11	0.984439
$327$	−2.21820e11	−1.07284
$328$	−2.31900e11	−1.10629
$329$	−1.15840e10	−0.0545099
$330$	8.33894e10	0.387078
$331$	−2.79768e10	−0.128107	−0.0640534	−	0.997946i	$-0.520403\pi$
$331$	−2.79768e10	−0.128107	−0.0640534	+	0.997946i	$0.520403\pi$
$332$	1.89572e10	0.0856352
$333$	1.06912e11	0.476460
$334$	−2.51444e11	−1.10556
$335$	−2.28937e10	−0.0993149
$336$	−2.31229e9	−0.00989725
$337$	1.18707e10	0.0501350	0.0250675	−	0.999686i	$-0.492020\pi$
$337$	1.18707e10	0.0501350	0.0250675	+	0.999686i	$0.492020\pi$
$338$	−1.34092e11	−0.558828
$339$	−1.01893e11	−0.419029
$340$	−2.64898e11	−1.07504
$341$	3.21476e11	1.28752
$342$	−9.62331e10	−0.380371
$343$	−2.26440e11	−0.883342
$344$	−4.40915e11	−1.69762
$345$	−3.39404e10	−0.128983
$346$	−5.36966e10	−0.201421
$347$	1.23258e11	0.456385	0.228193	−	0.973616i	$-0.426718\pi$
$347$	1.23258e11	0.456385	0.228193	+	0.973616i	$0.426718\pi$
$348$	−1.22389e11	−0.447337
$349$	1.27299e11	0.459314	0.229657	−	0.973272i	$-0.426239\pi$
$349$	1.27299e11	0.459314	0.229657	+	0.973272i	$0.426239\pi$
$350$	1.30005e10	0.0463076
$351$	−7.58817e10	−0.266843
$352$	3.49317e11	1.21277
$353$	3.18952e11	1.09330	0.546649	−	0.837362i	$-0.315903\pi$
$353$	3.18952e11	1.09330	0.546649	+	0.837362i	$0.315903\pi$
$354$	1.34532e10	0.0455313
$355$	2.45949e11	0.821898
$356$	−1.62262e11	−0.535418
$357$	1.65466e11	0.539142
$358$	−9.34815e10	−0.300782
$359$	8.68092e9	0.0275829	0.0137915	−	0.999905i	$-0.495610\pi$
$359$	8.68092e9	0.0275829	0.0137915	+	0.999905i	$0.495610\pi$
$360$	−9.68340e10	−0.303855
$361$	8.22420e11	2.54866
$362$	9.39559e10	0.287565
$363$	−8.45345e10	−0.255537
$364$	−1.48975e11	−0.444793
$365$	6.05905e11	1.78684
$366$	6.47746e10	0.188686
$367$	−2.06720e11	−0.594819	−0.297410	−	0.954750i	$-0.596123\pi$
$367$	−2.06720e11	−0.594819	−0.297410	+	0.954750i	$0.596123\pi$
$368$	−2.88548e9	−0.00820169
$369$	−1.32760e11	−0.372776
$370$	2.87634e11	0.797871
$371$	1.92354e11	0.527132
$372$	−1.44714e11	−0.391802
$373$	2.25859e11	0.604154	0.302077	−	0.953284i	$-0.402320\pi$
$373$	2.25859e11	0.604154	0.302077	+	0.953284i	$0.402320\pi$
$374$	−5.07318e11	−1.34078
$375$	−2.34473e11	−0.612282
$376$	−4.12425e10	−0.106414
$377$	−6.65613e11	−1.69702
$378$	2.34478e10	0.0590730
$379$	5.35540e11	1.33326	0.666630	−	0.745388i	$-0.267736\pi$
$379$	5.35540e11	1.33326	0.666630	+	0.745388i	$0.267736\pi$
$380$	4.46677e11	1.09892
$381$	1.87268e11	0.455303
$382$	−4.48344e10	−0.107727
$383$	−1.30230e11	−0.309256	−0.154628	−	0.987973i	$-0.549418\pi$
$383$	−1.30230e11	−0.309256	−0.154628	+	0.987973i	$0.549418\pi$
$384$	−1.62287e11	−0.380885
$385$	2.41775e11	0.560838
$386$	−1.46565e11	−0.336038
$387$	−2.52418e11	−0.572033
$388$	−1.65831e11	−0.371470
$389$	7.18519e11	1.59098	0.795491	−	0.605965i	$-0.207213\pi$
$389$	7.18519e11	1.59098	0.795491	+	0.605965i	$0.207213\pi$
$390$	−2.04151e11	−0.446850
$391$	2.06484e11	0.446778
$392$	−3.43722e11	−0.735225
$393$	−2.92594e11	−0.618728
$394$	−9.04789e10	−0.189153
$395$	1.69030e11	0.349364
$396$	1.24030e11	0.253454
$397$	6.32135e11	1.27718	0.638591	−	0.769546i	$-0.279518\pi$
$397$	6.32135e11	1.27718	0.638591	+	0.769546i	$0.279518\pi$
$398$	4.85741e10	0.0970356
$399$	−2.79013e11	−0.551120
$400$	−2.61307e9	−0.00510366
$401$	9.05543e11	1.74888	0.874438	−	0.485137i	$-0.161230\pi$
$401$	9.05543e11	1.74888	0.874438	+	0.485137i	$0.161230\pi$
$402$	1.97369e10	0.0376930
$403$	−7.87028e11	−1.48634
$404$	5.22686e11	0.976168
$405$	−5.54363e10	−0.102387
$406$	2.05678e11	0.375682
$407$	−9.50377e11	−1.71681
$408$	5.89112e11	1.05251
$409$	4.28566e11	0.757290	0.378645	−	0.925542i	$-0.376390\pi$
$409$	4.28566e11	0.757290	0.378645	+	0.925542i	$0.376390\pi$
$410$	−3.57175e11	−0.624244
$411$	−6.36420e9	−0.0110016
$412$	6.17941e10	0.105660
$413$	3.90053e10	0.0659704
$414$	2.92603e10	0.0489528
$415$	7.53202e10	0.124651
$416$	−8.55186e11	−1.40004
$417$	−4.45210e11	−0.721029
$418$	8.55450e11	1.37057
$419$	2.10147e11	0.333088	0.166544	−	0.986034i	$-0.446739\pi$
$419$	2.10147e11	0.333088	0.166544	+	0.986034i	$0.446739\pi$
$420$	−1.08836e11	−0.170667
$421$	5.69267e11	0.883174	0.441587	−	0.897218i	$-0.354416\pi$
$421$	5.69267e11	0.883174	0.441587	+	0.897218i	$0.354416\pi$
$422$	−2.55454e11	−0.392109
$423$	−2.36108e10	−0.0358574
$424$	6.84841e11	1.02907
$425$	1.86991e11	0.278016
$426$	−2.12035e11	−0.311935
$427$	1.87804e11	0.273388
$428$	−2.86467e10	−0.0412646
$429$	6.74540e11	0.961501
$430$	−6.79104e11	−0.957917
$431$	−1.13091e12	−1.57864	−0.789318	−	0.613985i	$-0.789566\pi$
$431$	−1.13091e12	−1.57864	−0.789318	+	0.613985i	$0.789566\pi$
$432$	−4.71298e9	−0.00651056
$433$	−7.03103e11	−0.961222	−0.480611	−	0.876934i	$-0.659585\pi$
$433$	−7.03103e11	−0.961222	−0.480611	+	0.876934i	$0.659585\pi$
$434$	2.43196e11	0.329042
$435$	−4.86272e11	−0.651145
$436$	−8.87628e11	−1.17636
$437$	−3.48178e11	−0.456704
$438$	−5.22356e11	−0.678162
$439$	1.82759e11	0.234849	0.117424	−	0.993082i	$-0.462536\pi$
$439$	1.82759e11	0.234849	0.117424	+	0.993082i	$0.462536\pi$
$440$	8.60793e11	1.09487
$441$	−1.96777e11	−0.247742
$442$	1.24200e12	1.54783
$443$	1.37003e12	1.69010	0.845050	−	0.534687i	$-0.179571\pi$
$443$	1.37003e12	1.69010	0.845050	+	0.534687i	$0.179571\pi$
$444$	4.27816e11	0.522436
$445$	−6.44697e11	−0.779356
$446$	6.35132e11	0.760076
$447$	4.60818e11	0.545940
$448$	2.49641e11	0.292795
$449$	5.34788e11	0.620973	0.310487	−	0.950578i	$-0.399508\pi$
$449$	5.34788e11	0.620973	0.310487	+	0.950578i	$0.399508\pi$
$450$	2.64980e10	0.0304619
$451$	1.18015e12	1.34320
$452$	−4.07731e11	−0.459463
$453$	4.55662e10	0.0508395
$454$	1.97953e11	0.218680
$455$	−5.91905e11	−0.647442
$456$	−9.93372e11	−1.07590
$457$	−5.62934e11	−0.603719	−0.301859	−	0.953352i	$-0.597607\pi$
$457$	−5.62934e11	−0.603719	−0.301859	+	0.953352i	$0.597607\pi$
$458$	1.29895e11	0.137943
$459$	3.37259e11	0.354656
$460$	−1.35815e11	−0.141429
$461$	−1.56743e11	−0.161635	−0.0808175	−	0.996729i	$-0.525753\pi$
$461$	−1.56743e11	−0.161635	−0.0808175	+	0.996729i	$0.525753\pi$
$462$	−2.08436e11	−0.212855
$463$	−2.23867e11	−0.226400	−0.113200	−	0.993572i	$-0.536110\pi$
$463$	−2.23867e11	−0.226400	−0.113200	+	0.993572i	$0.536110\pi$
$464$	−4.13409e10	−0.0414047
$465$	−5.74973e11	−0.570307
$466$	−9.15011e10	−0.0898856
$467$	−1.11895e12	−1.08865	−0.544323	−	0.838876i	$-0.683213\pi$
$467$	−1.11895e12	−1.08865	−0.544323	+	0.838876i	$0.683213\pi$
$468$	−3.03647e11	−0.292592
$469$	5.72240e10	0.0546136
$470$	−6.35223e10	−0.0600462
$471$	6.28298e11	0.588263
$472$	1.38871e11	0.128787
$473$	2.24384e12	2.06118
$474$	−1.45723e11	−0.132594
$475$	−3.15308e11	−0.284193
$476$	6.62127e11	0.591167
$477$	3.92063e11	0.346756
$478$	2.11142e11	0.184991
$479$	8.89411e11	0.771956	0.385978	−	0.922508i	$-0.373864\pi$
$479$	8.89411e11	0.771956	0.385978	+	0.922508i	$0.373864\pi$
$480$	−6.24766e11	−0.537195
$481$	2.32668e12	1.98191
$482$	−1.14773e12	−0.968563
$483$	8.48358e10	0.0709279
$484$	−3.38271e11	−0.280195
$485$	−6.58878e11	−0.540713
$486$	4.77921e10	0.0388591
$487$	9.69722e11	0.781209	0.390604	−	0.920559i	$-0.372266\pi$
$487$	9.69722e11	0.781209	0.390604	+	0.920559i	$0.372266\pi$
$488$	6.68640e11	0.533708
$489$	1.18637e12	0.938279
$490$	−5.29406e11	−0.414865
$491$	7.10876e11	0.551985	0.275992	−	0.961160i	$-0.410994\pi$
$491$	7.10876e11	0.551985	0.275992	+	0.961160i	$0.410994\pi$
$492$	−5.31248e11	−0.408747
$493$	2.95835e12	2.25547
$494$	−2.09429e12	−1.58221
$495$	4.92793e11	0.368928
$496$	−4.88820e10	−0.0362644
$497$	−6.14763e11	−0.451964
$498$	−6.49342e10	−0.0473088
$499$	1.54484e12	1.11540	0.557702	−	0.830041i	$-0.311683\pi$
$499$	1.54484e12	1.11540	0.557702	+	0.830041i	$0.311683\pi$
$500$	−9.38261e11	−0.671365
$501$	−1.48592e12	−1.05372
$502$	2.39407e11	0.168256
$503$	1.95247e12	1.35997	0.679983	−	0.733228i	$-0.261987\pi$
$503$	1.95247e12	1.35997	0.679983	+	0.733228i	$0.261987\pi$
$504$	2.42042e11	0.167091
$505$	2.07672e12	1.42091
$506$	−2.60106e11	−0.176389
$507$	−7.92424e11	−0.532625
$508$	7.49367e11	0.499238
$509$	−2.22432e12	−1.46882	−0.734409	−	0.678707i	$-0.762541\pi$
$509$	−2.22432e12	−1.46882	−0.734409	+	0.678707i	$0.762541\pi$
$510$	9.07359e11	0.593900
$511$	−1.51449e12	−0.982590
$512$	−1.05152e11	−0.0676246
$513$	−5.68693e11	−0.362535
$514$	1.06440e12	0.672621
$515$	2.45519e11	0.153799
$516$	−1.01007e12	−0.627232
$517$	2.09885e11	0.129203
$518$	−7.18957e11	−0.438752
$519$	−3.17322e11	−0.191976
$520$	−2.10737e12	−1.26394
$521$	−1.81361e12	−1.07839	−0.539193	−	0.842182i	$-0.681271\pi$
$521$	−1.81361e12	−1.07839	−0.539193	+	0.842182i	$0.681271\pi$
$522$	4.19219e11	0.247129
$523$	1.81150e12	1.05872	0.529361	−	0.848397i	$-0.322432\pi$
$523$	1.81150e12	1.05872	0.529361	+	0.848397i	$0.322432\pi$
$524$	−1.17084e12	−0.678432
$525$	7.68267e10	0.0441363
$526$	2.65698e11	0.151340
$527$	3.49798e12	1.97547
$528$	4.18954e10	0.0234592
$529$	−1.69529e12	−0.941223
$530$	1.05480e12	0.580671
$531$	7.95020e10	0.0433963
$532$	−1.11649e12	−0.604301
$533$	−2.88920e12	−1.55062
$534$	5.55799e11	0.295789
$535$	−1.13818e11	−0.0600649
$536$	2.03735e11	0.106617
$537$	−5.52433e11	−0.286678
$538$	−2.83199e11	−0.145738
$539$	1.74922e12	0.892678
$540$	−2.21833e11	−0.112267
$541$	1.59726e12	0.801657	0.400828	−	0.916153i	$-0.368722\pi$
$541$	1.59726e12	0.801657	0.400828	+	0.916153i	$0.368722\pi$
$542$	6.41440e11	0.319271
$543$	5.55236e11	0.274081
$544$	3.80091e12	1.86077
$545$	−3.52670e12	−1.71232
$546$	5.10287e11	0.245724
$547$	2.14748e12	1.02562	0.512810	−	0.858502i	$-0.328605\pi$
$547$	2.14748e12	1.02562	0.512810	+	0.858502i	$0.328605\pi$
$548$	−2.54668e10	−0.0120632
$549$	3.82788e11	0.179839
$550$	−2.35550e11	−0.109762
$551$	−4.98842e12	−2.30558
$552$	3.02042e11	0.138465
$553$	−4.22500e11	−0.192116
$554$	1.25282e12	0.565060
$555$	1.69979e12	0.760459
$556$	−1.78154e12	−0.790606
$557$	7.75058e11	0.341182	0.170591	−	0.985342i	$-0.445432\pi$
$557$	7.75058e11	0.341182	0.170591	+	0.985342i	$0.445432\pi$
$558$	4.95689e11	0.216449
$559$	−5.49329e12	−2.37947
$560$	−3.67630e10	−0.0157966
$561$	−2.99802e12	−1.27791
$562$	1.79628e12	0.759556
$563$	1.27236e12	0.533729	0.266865	−	0.963734i	$-0.414012\pi$
$563$	1.27236e12	0.533729	0.266865	+	0.963734i	$0.414012\pi$
$564$	−9.44805e10	−0.0393175
$565$	−1.61999e12	−0.668796
$566$	2.52289e12	1.03330
$567$	1.38566e11	0.0563031
$568$	−2.18875e12	−0.882324
$569$	−2.12273e12	−0.848963	−0.424482	−	0.905437i	$-0.639544\pi$
$569$	−2.12273e12	−0.848963	−0.424482	+	0.905437i	$0.639544\pi$
$570$	−1.53001e12	−0.607095
$571$	2.38084e12	0.937277	0.468639	−	0.883390i	$-0.344745\pi$
$571$	2.38084e12	0.937277	0.468639	+	0.883390i	$0.344745\pi$
$572$	2.69922e12	1.05428
$573$	−2.64951e11	−0.102676
$574$	8.92778e11	0.343273
$575$	9.58715e10	0.0365750
$576$	5.08826e11	0.192605
$577$	−4.36889e12	−1.64089	−0.820446	−	0.571724i	$-0.806275\pi$
$577$	−4.36889e12	−1.64089	−0.820446	+	0.571724i	$0.806275\pi$
$578$	−3.89468e12	−1.45143
$579$	−8.66133e11	−0.320281
$580$	−1.94585e12	−0.713977
$581$	−1.88267e11	−0.0685458
$582$	5.68024e11	0.205217
$583$	−3.48519e12	−1.24945
$584$	−5.39206e12	−1.91821
$585$	−1.20644e12	−0.425897
$586$	−4.91474e11	−0.172171
$587$	−2.04674e12	−0.711525	−0.355763	−	0.934576i	$-0.615779\pi$
$587$	−2.04674e12	−0.711525	−0.355763	+	0.934576i	$0.615779\pi$
$588$	−7.87417e11	−0.271648
$589$	−5.89836e12	−2.01935
$590$	2.13891e11	0.0726707
$591$	−5.34689e11	−0.180284
$592$	1.44509e11	0.0483557
$593$	4.09546e12	1.36005	0.680027	−	0.733187i	$-0.261968\pi$
$593$	4.09546e12	1.36005	0.680027	+	0.733187i	$0.261968\pi$
$594$	−4.24841e11	−0.140019
$595$	2.63075e12	0.860503
$596$	1.84400e12	0.598621
$597$	2.87051e11	0.0924856
$598$	6.36783e11	0.203627
$599$	2.90714e12	0.922666	0.461333	−	0.887227i	$-0.347371\pi$
$599$	2.90714e12	0.922666	0.461333	+	0.887227i	$0.347371\pi$
$600$	2.73527e11	0.0861628
$601$	1.56733e12	0.490034	0.245017	−	0.969519i	$-0.421207\pi$
$601$	1.56733e12	0.490034	0.245017	+	0.969519i	$0.421207\pi$
$602$	1.69745e12	0.526761
$603$	1.16636e11	0.0359256
$604$	1.82337e11	0.0557453
$605$	−1.34401e12	−0.407853
$606$	−1.79036e12	−0.539279
$607$	1.13643e12	0.339777	0.169889	−	0.985463i	$-0.445659\pi$
$607$	1.13643e12	0.339777	0.169889	+	0.985463i	$0.445659\pi$
$608$	−6.40917e12	−1.90211
$609$	1.21546e12	0.358066
$610$	1.02985e12	0.301155
$611$	−5.13834e11	−0.149155
$612$	1.34957e12	0.388878
$613$	−9.45096e11	−0.270336	−0.135168	−	0.990823i	$-0.543157\pi$
$613$	−9.45096e11	−0.270336	−0.135168	+	0.990823i	$0.543157\pi$
$614$	−3.85596e12	−1.09490
$615$	−2.11074e12	−0.594973
$616$	−2.15159e12	−0.602070
$617$	6.31900e12	1.75535	0.877677	−	0.479252i	$-0.159092\pi$
$617$	6.31900e12	1.75535	0.877677	+	0.479252i	$0.159092\pi$
$618$	−2.11664e11	−0.0583713
$619$	−6.28762e12	−1.72139	−0.860693	−	0.509125i	$-0.829969\pi$
$619$	−6.28762e12	−1.72139	−0.860693	+	0.509125i	$0.829969\pi$
$620$	−2.30080e12	−0.625340
$621$	1.72915e11	0.0466574
$622$	−3.80747e12	−1.01995
$623$	1.61145e12	0.428570
$624$	−1.02567e11	−0.0270818
$625$	−3.15238e12	−0.826378
$626$	1.58616e12	0.412821
$627$	5.05532e12	1.30631
$628$	2.51418e12	0.645028
$629$	−1.03410e13	−2.63412
$630$	3.72796e11	0.0942842
$631$	−7.30194e12	−1.83361	−0.916803	−	0.399340i	$-0.869239\pi$
$631$	−7.30194e12	−1.83361	−0.916803	+	0.399340i	$0.869239\pi$
$632$	−1.50423e12	−0.375049
$633$	−1.50962e12	−0.373723
$634$	−4.09007e11	−0.100538
$635$	2.97737e12	0.726692
$636$	1.56887e12	0.380216
$637$	−4.28239e12	−1.03052
$638$	−3.72659e12	−0.890469
$639$	−1.25303e12	−0.297309
$640$	−2.58020e12	−0.607916
$641$	2.82813e12	0.661665	0.330833	−	0.943689i	$-0.392670\pi$
$641$	2.82813e12	0.661665	0.330833	+	0.943689i	$0.392670\pi$
$642$	9.81239e10	0.0227964
$643$	1.81353e12	0.418384	0.209192	−	0.977875i	$-0.432917\pi$
$643$	1.81353e12	0.418384	0.209192	+	0.977875i	$0.432917\pi$
$644$	3.39477e11	0.0777721
$645$	−4.01319e12	−0.913001
$646$	9.30815e12	2.10289
$647$	−3.84912e12	−0.863560	−0.431780	−	0.901979i	$-0.642114\pi$
$647$	−3.84912e12	−0.863560	−0.431780	+	0.901979i	$0.642114\pi$
$648$	4.93337e11	0.109915
$649$	−7.06722e11	−0.156368
$650$	5.76666e11	0.126711
$651$	1.43717e12	0.313614
$652$	4.74737e12	1.02882
$653$	6.98077e12	1.50243	0.751214	−	0.660058i	$-0.229469\pi$
$653$	6.98077e12	1.50243	0.751214	+	0.660058i	$0.229469\pi$
$654$	3.04040e12	0.649877
$655$	−4.65195e12	−0.987528
$656$	−1.79447e11	−0.0378329
$657$	−3.08689e12	−0.646363
$658$	1.58777e11	0.0330196
$659$	5.02751e12	1.03841	0.519205	−	0.854650i	$-0.326228\pi$
$659$	5.02751e12	1.03841	0.519205	+	0.854650i	$0.326228\pi$
$660$	1.97195e12	0.404528
$661$	7.25536e12	1.47827	0.739133	−	0.673560i	$-0.235236\pi$
$661$	7.25536e12	1.47827	0.739133	+	0.673560i	$0.235236\pi$
$662$	3.83468e11	0.0776012
$663$	7.33966e12	1.47525
$664$	−6.70288e11	−0.133815
$665$	−4.43602e12	−0.879621
$666$	−1.46540e12	−0.288617
$667$	1.51676e12	0.296723
$668$	−5.94601e12	−1.15540
$669$	3.75334e12	0.724436
$670$	3.13796e11	0.0601604
$671$	−3.40274e12	−0.648004
$672$	1.56164e12	0.295405
$673$	1.04093e13	1.95593	0.977964	−	0.208774i	$-0.0669473\pi$
$673$	1.04093e13	1.95593	0.977964	+	0.208774i	$0.0669473\pi$
$674$	−1.62707e11	−0.0303695
$675$	1.56591e11	0.0290335
$676$	−3.17095e12	−0.584021
$677$	−1.06163e11	−0.0194234	−0.00971171	−	0.999953i	$-0.503091\pi$
$677$	−1.06163e11	−0.0194234	−0.00971171	+	0.999953i	$0.503091\pi$
$678$	1.39661e12	0.253828
$679$	1.64690e12	0.297340
$680$	9.36627e12	1.67987
$681$	1.16981e12	0.208426
$682$	−4.40636e12	−0.779921
$683$	5.27750e12	0.927973	0.463986	−	0.885842i	$-0.346419\pi$
$683$	5.27750e12	0.927973	0.463986	+	0.885842i	$0.346419\pi$
$684$	−2.27567e12	−0.397518
$685$	−1.01184e11	−0.0175592
$686$	3.10373e12	0.535088
$687$	7.67621e11	0.131475
$688$	−3.41186e11	−0.0580555
$689$	8.53234e12	1.44239
$690$	4.65209e11	0.0781317
$691$	−6.28768e12	−1.04915	−0.524577	−	0.851363i	$-0.675777\pi$
$691$	−6.28768e12	−1.04915	−0.524577	+	0.851363i	$0.675777\pi$
$692$	−1.26979e12	−0.210501
$693$	−1.23176e12	−0.202874
$694$	−1.68945e12	−0.276457
$695$	−7.07839e12	−1.15081
$696$	4.32742e12	0.699016
$697$	1.28412e13	2.06090
$698$	−1.74484e12	−0.278232
$699$	−5.40730e11	−0.0856708
$700$	3.07428e11	0.0483952
$701$	1.18219e13	1.84908	0.924540	−	0.381086i	$-0.124450\pi$
$701$	1.18219e13	1.84908	0.924540	+	0.381086i	$0.124450\pi$
$702$	1.04008e12	0.161641
$703$	1.74373e13	2.69265
$704$	−4.52314e12	−0.694006
$705$	−3.75387e11	−0.0572307
$706$	−4.37176e12	−0.662270
$707$	−5.19087e12	−0.781363
$708$	3.18133e11	0.0475839
$709$	−4.92112e12	−0.731402	−0.365701	−	0.930732i	$-0.619171\pi$
$709$	−4.92112e12	−0.731402	−0.365701	+	0.930732i	$0.619171\pi$
$710$	−3.37114e12	−0.497868
$711$	−8.61154e11	−0.126377
$712$	5.73727e12	0.836653
$713$	1.79344e12	0.259886
$714$	−2.26799e12	−0.326587
$715$	1.07245e13	1.53462
$716$	−2.21060e12	−0.314342
$717$	1.24775e12	0.176316
$718$	−1.18986e11	−0.0167085
$719$	−3.96463e12	−0.553251	−0.276626	−	0.960978i	$-0.589216\pi$
$719$	−3.96463e12	−0.553251	−0.276626	+	0.960978i	$0.589216\pi$
$720$	−7.49315e10	−0.0103913
$721$	−6.13687e11	−0.0845743
$722$	−1.12726e13	−1.54386
$723$	−6.78255e12	−0.923147
$724$	2.22182e12	0.300529
$725$	1.37357e12	0.184642
$726$	1.15868e12	0.154793
$727$	3.63519e12	0.482638	0.241319	−	0.970446i	$-0.422420\pi$
$727$	3.63519e12	0.482638	0.241319	+	0.970446i	$0.422420\pi$
$728$	5.26747e12	0.695042
$729$	2.82430e11	0.0370370
$730$	−8.30493e12	−1.08239
$731$	2.44152e13	3.16251
$732$	1.53176e12	0.197192
$733$	−6.02702e12	−0.771143	−0.385572	−	0.922678i	$-0.625996\pi$
$733$	−6.02702e12	−0.771143	−0.385572	+	0.922678i	$0.625996\pi$
$734$	2.83344e12	0.360314
$735$	−3.12855e12	−0.395412
$736$	1.94875e12	0.244797
$737$	−1.03682e12	−0.129449
$738$	1.81969e12	0.225810
$739$	2.88139e12	0.355387	0.177694	−	0.984086i	$-0.443136\pi$
$739$	2.88139e12	0.355387	0.177694	+	0.984086i	$0.443136\pi$
$740$	6.80183e12	0.833840
$741$	−1.23763e13	−1.50802
$742$	−2.63653e12	−0.319312
$743$	−1.09604e13	−1.31940	−0.659700	−	0.751529i	$-0.729317\pi$
$743$	−1.09604e13	−1.31940	−0.659700	+	0.751529i	$0.729317\pi$
$744$	5.11679e12	0.612236
$745$	7.32653e12	0.871354
$746$	−3.09577e12	−0.365969
$747$	−3.83732e11	−0.0450905
$748$	−1.19968e13	−1.40123
$749$	2.84495e11	0.0330298
$750$	3.21384e12	0.370893
$751$	1.56238e12	0.179228	0.0896141	−	0.995977i	$-0.471437\pi$
$751$	1.56238e12	0.179228	0.0896141	+	0.995977i	$0.471437\pi$
$752$	−3.19140e10	−0.00363916
$753$	1.41479e12	0.160366
$754$	9.12333e12	1.02797
$755$	7.24456e11	0.0811429
$756$	5.54482e11	0.0617361
$757$	−1.08454e13	−1.20037	−0.600186	−	0.799860i	$-0.704907\pi$
$757$	−1.08454e13	−1.20037	−0.600186	+	0.799860i	$0.704907\pi$
$758$	−7.34045e12	−0.807628
$759$	−1.53711e12	−0.168119
$760$	−1.57936e13	−1.71720
$761$	1.50904e12	0.163106	0.0815530	−	0.996669i	$-0.474012\pi$
$761$	1.50904e12	0.163106	0.0815530	+	0.996669i	$0.474012\pi$
$762$	−2.56681e12	−0.275802
$763$	8.81517e12	0.941609
$764$	−1.06022e12	−0.112584
$765$	5.36208e12	0.566052
$766$	1.78502e12	0.187333
$767$	1.73018e12	0.180514
$768$	5.44070e12	0.564325
$769$	5.47095e12	0.564149	0.282075	−	0.959392i	$-0.408977\pi$
$769$	5.47095e12	0.564149	0.282075	+	0.959392i	$0.408977\pi$
$770$	−3.31392e12	−0.339730
$771$	6.29011e12	0.641082
$772$	−3.46590e12	−0.351187
$773$	9.29631e12	0.936489	0.468245	−	0.883599i	$-0.344887\pi$
$773$	9.29631e12	0.936489	0.468245	+	0.883599i	$0.344887\pi$
$774$	3.45981e12	0.346512
$775$	1.62413e12	0.161719
$776$	5.86347e12	0.580466
$777$	−4.24870e12	−0.418179
$778$	−9.84849e12	−0.963744
$779$	−2.16531e13	−2.10669
$780$	−4.82767e12	−0.466994
$781$	1.11386e13	1.07128
$782$	−2.83021e12	−0.270637
$783$	2.47739e12	0.235541
$784$	−2.65977e11	−0.0251433
$785$	9.98929e12	0.938904
$786$	4.01049e12	0.374797
$787$	−8.64096e12	−0.802926	−0.401463	−	0.915875i	$-0.631498\pi$
$787$	−8.64096e12	−0.802926	−0.401463	+	0.915875i	$0.631498\pi$
$788$	−2.13960e12	−0.197681
$789$	1.57015e12	0.144243
$790$	−2.31684e12	−0.211629
$791$	4.04924e12	0.367773
$792$	−4.38545e12	−0.396051
$793$	8.33049e12	0.748068
$794$	−8.66446e12	−0.773658
$795$	6.23340e12	0.553443
$796$	1.14866e12	0.101410
$797$	7.53539e12	0.661521	0.330760	−	0.943715i	$-0.392695\pi$
$797$	7.53539e12	0.661521	0.330760	+	0.943715i	$0.392695\pi$
$798$	3.82433e12	0.333843
$799$	2.28376e12	0.198239
$800$	1.76478e12	0.152330
$801$	3.28452e12	0.281920
$802$	−1.24120e13	−1.05939
$803$	2.74404e13	2.32901
$804$	4.66728e11	0.0393923
$805$	1.34880e12	0.113205
$806$	1.07875e13	0.900355
$807$	−1.67358e12	−0.138904
$808$	−1.84811e13	−1.52538
$809$	−4.53883e12	−0.372542	−0.186271	−	0.982498i	$-0.559640\pi$
$809$	−4.53883e12	−0.372542	−0.186271	+	0.982498i	$0.559640\pi$
$810$	7.59846e11	0.0620216
$811$	1.70530e13	1.38422	0.692112	−	0.721790i	$-0.256680\pi$
$811$	1.70530e13	1.38422	0.692112	+	0.721790i	$0.256680\pi$
$812$	4.86376e12	0.392618
$813$	3.79062e12	0.304300
$814$	1.30265e13	1.03996
$815$	1.88621e13	1.49755
$816$	4.55863e11	0.0359939
$817$	−4.11693e13	−3.23277
$818$	−5.87420e12	−0.458732
$819$	3.01556e12	0.234202
$820$	−8.44630e12	−0.652385
$821$	−2.05429e13	−1.57804	−0.789021	−	0.614367i	$-0.789412\pi$
$821$	−2.05429e13	−1.57804	−0.789021	+	0.614367i	$0.789412\pi$
$822$	8.72318e10	0.00666425
$823$	1.59691e13	1.21334	0.606670	−	0.794954i	$-0.292505\pi$
$823$	1.59691e13	1.21334	0.606670	+	0.794954i	$0.292505\pi$
$824$	−2.18492e12	−0.165106
$825$	−1.39199e12	−0.104615
$826$	−5.34632e11	−0.0399618
$827$	−1.00485e13	−0.747009	−0.373504	−	0.927628i	$-0.621844\pi$
$827$	−1.00485e13	−0.747009	−0.373504	+	0.927628i	$0.621844\pi$
$828$	6.91934e11	0.0511597
$829$	−1.76339e13	−1.29674	−0.648369	−	0.761326i	$-0.724549\pi$
$829$	−1.76339e13	−1.29674	−0.648369	+	0.761326i	$0.724549\pi$
$830$	−1.03239e12	−0.0755077
$831$	7.40359e12	0.538565
$832$	1.10734e13	0.801173
$833$	1.90332e13	1.36965
$834$	6.10234e12	0.436766
$835$	−2.36245e13	−1.68180
$836$	2.02293e13	1.43236
$837$	2.92930e12	0.206300
$838$	−2.88041e12	−0.201770
$839$	1.66900e13	1.16286	0.581429	−	0.813597i	$-0.302494\pi$
$839$	1.66900e13	1.16286	0.581429	+	0.813597i	$0.302494\pi$
$840$	3.84821e12	0.266687
$841$	7.22387e12	0.497953
$842$	−7.80274e12	−0.534986
$843$	1.06152e13	0.723941
$844$	−6.04085e12	−0.409786
$845$	−1.25987e13	−0.850102
$846$	3.23625e11	0.0217208
$847$	3.35942e12	0.224279
$848$	5.29940e11	0.0351921
$849$	1.49091e13	0.984845
$850$	−2.56302e12	−0.168409
$851$	−5.30192e12	−0.346538
$852$	−5.01410e12	−0.325998
$853$	−7.73139e12	−0.500019	−0.250010	−	0.968243i	$-0.580434\pi$
$853$	−7.73139e12	−0.500019	−0.250010	+	0.968243i	$0.580434\pi$
$854$	−2.57416e12	−0.165606
$855$	−9.04164e12	−0.578628
$856$	1.01289e12	0.0644808
$857$	2.47110e12	0.156486	0.0782432	−	0.996934i	$-0.475069\pi$
$857$	2.47110e12	0.156486	0.0782432	+	0.996934i	$0.475069\pi$
$858$	−9.24568e12	−0.582433
$859$	9.11844e11	0.0571415	0.0285707	−	0.999592i	$-0.490904\pi$
$859$	9.11844e11	0.0571415	0.0285707	+	0.999592i	$0.490904\pi$
$860$	−1.60591e13	−1.00110
$861$	5.27591e12	0.327177
$862$	1.55010e13	0.956265
$863$	1.90816e11	0.0117103	0.00585513	−	0.999983i	$-0.498136\pi$
$863$	1.90816e11	0.0117103	0.00585513	+	0.999983i	$0.498136\pi$
$864$	3.18298e12	0.194322
$865$	−5.04510e12	−0.306406
$866$	9.63719e12	0.582264
$867$	−2.30158e13	−1.38338
$868$	5.75096e12	0.343876
$869$	7.65511e12	0.455368
$870$	6.66516e12	0.394433
$871$	2.53831e12	0.149439
$872$	3.13848e13	1.83821
$873$	3.35676e12	0.195595
$874$	4.77235e12	0.276650
$875$	9.31802e12	0.537387
$876$	−1.23524e13	−0.708734
$877$	−2.11889e13	−1.20951	−0.604757	−	0.796410i	$-0.706730\pi$
$877$	−2.11889e13	−1.20951	−0.604757	+	0.796410i	$0.706730\pi$
$878$	−2.50501e12	−0.142261
$879$	−2.90438e12	−0.164098
$880$	6.66093e11	0.0374423
$881$	−1.88415e13	−1.05371	−0.526857	−	0.849954i	$-0.676630\pi$
$881$	−1.88415e13	−1.05371	−0.526857	+	0.849954i	$0.676630\pi$
$882$	2.69715e12	0.150071
$883$	−1.58998e13	−0.880175	−0.440088	−	0.897955i	$-0.645053\pi$
$883$	−1.58998e13	−0.880175	−0.440088	+	0.897955i	$0.645053\pi$
$884$	2.93702e13	1.61760
$885$	1.26400e12	0.0692632
$886$	−1.87785e13	−1.02378
$887$	1.82433e13	0.989570	0.494785	−	0.869016i	$-0.335247\pi$
$887$	1.82433e13	0.989570	0.494785	+	0.869016i	$0.335247\pi$
$888$	−1.51267e13	−0.816368
$889$	−7.44208e12	−0.399610
$890$	8.83663e12	0.472098
$891$	−2.51062e12	−0.133454
$892$	1.50193e13	0.794342
$893$	−3.85091e12	−0.202643
$894$	−6.31626e12	−0.330706
$895$	−8.78311e12	−0.457556
$896$	6.44934e12	0.334295
$897$	3.76310e12	0.194079
$898$	−7.33014e12	−0.376157
$899$	2.56950e13	1.31199
$900$	6.26611e11	0.0318351
$901$	−3.79223e13	−1.91705
$902$	−1.61759e13	−0.813652
$903$	1.00312e13	0.502061
$904$	1.44165e13	0.717965
$905$	8.82769e12	0.437450
$906$	−6.24560e11	−0.0307962
$907$	4.33489e12	0.212689	0.106345	−	0.994329i	$-0.466085\pi$
$907$	4.33489e12	0.212689	0.106345	+	0.994329i	$0.466085\pi$
$908$	4.68108e12	0.228539
$909$	−1.05802e13	−0.513993
$910$	8.11304e12	0.392191
$911$	2.18451e13	1.05080	0.525401	−	0.850854i	$-0.323915\pi$
$911$	2.18451e13	1.05080	0.525401	+	0.850854i	$0.323915\pi$
$912$	−7.68685e11	−0.0367935
$913$	3.41113e12	0.162472
$914$	7.71594e12	0.365705
$915$	6.08594e12	0.287034
$916$	3.07170e12	0.144161
$917$	1.16278e13	0.543044
$918$	−4.62269e12	−0.214834
$919$	−2.52060e13	−1.16569	−0.582845	−	0.812583i	$-0.698061\pi$
$919$	−2.52060e13	−1.16569	−0.582845	+	0.812583i	$0.698061\pi$
$920$	4.80215e12	0.220999
$921$	−2.27870e13	−1.04356
$922$	2.14843e12	0.0979110
$923$	−2.72693e13	−1.23670
$924$	−4.92899e12	−0.222451
$925$	−4.80139e12	−0.215640
$926$	3.06847e12	0.137143
$927$	−1.25084e12	−0.0556343
$928$	2.79202e13	1.23581
$929$	−6.09574e12	−0.268507	−0.134254	−	0.990947i	$-0.542864\pi$
$929$	−6.09574e12	−0.268507	−0.134254	+	0.990947i	$0.542864\pi$
$930$	7.88095e12	0.345466
$931$	−3.20942e13	−1.40008
$932$	−2.16377e12	−0.0939377
$933$	−2.25004e13	−0.972127
$934$	1.53371e13	0.659451
$935$	−4.76654e13	−2.03963
$936$	1.07363e13	0.457209
$937$	8.28034e12	0.350930	0.175465	−	0.984486i	$-0.443857\pi$
$937$	8.28034e12	0.350930	0.175465	+	0.984486i	$0.443857\pi$
$938$	−7.84349e11	−0.0330824
$939$	9.37347e12	0.393464
$940$	−1.50214e12	−0.0627532
$941$	−1.28286e13	−0.533368	−0.266684	−	0.963784i	$-0.585928\pi$
$941$	−1.28286e13	−0.533368	−0.266684	+	0.963784i	$0.585928\pi$
$942$	−8.61186e12	−0.356343
$943$	6.58376e12	0.271126
$944$	1.07460e11	0.00440427
$945$	2.20305e12	0.0898632
$946$	−3.07555e13	−1.24857
$947$	−4.37117e12	−0.176613	−0.0883066	−	0.996093i	$-0.528146\pi$
$947$	−4.37117e12	−0.176613	−0.0883066	+	0.996093i	$0.528146\pi$
$948$	−3.44598e12	−0.138572
$949$	−6.71789e13	−2.68865
$950$	4.32181e12	0.172151
$951$	−2.41704e12	−0.0958235
$952$	−2.34115e13	−0.923767
$953$	1.81879e13	0.714272	0.357136	−	0.934052i	$-0.383753\pi$
$953$	1.81879e13	0.714272	0.357136	+	0.934052i	$0.383753\pi$
$954$	−5.37387e12	−0.210049
$955$	−4.21244e12	−0.163877
$956$	4.99299e12	0.193330
$957$	−2.20224e13	−0.848715
$958$	−1.21908e13	−0.467616
$959$	2.52915e11	0.00965586
$960$	8.08981e12	0.307410
$961$	3.94240e12	0.149109
$962$	−3.18910e13	−1.20055
$963$	5.79867e11	0.0217275
$964$	−2.71409e13	−1.01223
$965$	−1.37706e13	−0.511188
$966$	−1.16281e12	−0.0429649
$967$	2.69067e13	0.989558	0.494779	−	0.869019i	$-0.335249\pi$
$967$	2.69067e13	0.989558	0.494779	+	0.869019i	$0.335249\pi$
$968$	1.19606e13	0.437838
$969$	5.50069e13	2.00429
$970$	9.03100e12	0.327539
$971$	2.98718e13	1.07839	0.539193	−	0.842182i	$-0.318729\pi$
$971$	2.98718e13	1.07839	0.539193	+	0.842182i	$0.318729\pi$
$972$	1.13016e12	0.0406110
$973$	1.76928e13	0.632832
$974$	−1.32916e13	−0.473220
$975$	3.40783e12	0.120770
$976$	5.17403e11	0.0182518
$977$	−1.14354e13	−0.401536	−0.200768	−	0.979639i	$-0.564344\pi$
$977$	−1.14354e13	−0.401536	−0.200768	+	0.979639i	$0.564344\pi$
$978$	−1.62612e13	−0.568366
$979$	−2.91973e13	−1.01583
$980$	−1.25191e13	−0.433568
$981$	1.79674e13	0.619404
$982$	−9.74372e12	−0.334367
$983$	−1.66845e13	−0.569932	−0.284966	−	0.958538i	$-0.591982\pi$
$983$	−1.66845e13	−0.569932	−0.284966	+	0.958538i	$0.591982\pi$
$984$	1.87839e13	0.638715
$985$	−8.50100e12	−0.287744
$986$	−4.05490e13	−1.36626
$987$	9.38300e11	0.0314713
$988$	−4.95247e13	−1.65354
$989$	1.25178e13	0.416050
$990$	−6.75454e12	−0.223479
$991$	4.04049e13	1.33077	0.665384	−	0.746501i	$-0.268268\pi$
$991$	4.04049e13	1.33077	0.665384	+	0.746501i	$0.268268\pi$
$992$	3.30131e13	1.08239
$993$	2.26612e12	0.0739625
$994$	8.42634e12	0.273779
$995$	4.56381e12	0.147613
$996$	−1.53553e12	−0.0494415
$997$	−3.04999e13	−0.977620	−0.488810	−	0.872390i	$-0.662569\pi$
$997$	−3.04999e13	−0.977620	−0.488810	+	0.872390i	$0.662569\pi$
$998$	−2.11746e13	−0.675660
$999$	−8.65985e12	−0.275084

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.c.1.8	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.c.1.8	✓	22	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)

\(f(q)\)	\(=\)	\(q-13.7066 q^{2} -81.0000 q^{3} -324.128 q^{4} -1287.82 q^{5} +1110.24 q^{6} +3218.96 q^{7} +11460.5 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-13.7066 q^{2} -81.0000 q^{3} -324.128 q^{4} -1287.82 q^{5} +1110.24 q^{6} +3218.96 q^{7} +11460.5 q^{8} +6561.00 q^{9} +17651.6 q^{10} -58323.1 q^{11} +26254.4 q^{12} +142785. q^{13} -44121.2 q^{14} +104313. q^{15} +8868.30 q^{16} -634613. q^{17} -89929.3 q^{18} +1.07010e6 q^{19} +417417. q^{20} -260736. q^{21} +799414. q^{22} -325370. q^{23} -928301. q^{24} -294653. q^{25} -1.95710e6 q^{26} -531441. q^{27} -1.04336e6 q^{28} -4.66165e6 q^{29} -1.42978e6 q^{30} -5.51199e6 q^{31} -5.98934e6 q^{32} +4.72417e6 q^{33} +8.69841e6 q^{34} -4.14543e6 q^{35} -2.12660e6 q^{36} +1.62950e7 q^{37} -1.46674e7 q^{38} -1.15656e7 q^{39} -1.47590e7 q^{40} -2.02347e7 q^{41} +3.57382e6 q^{42} -3.84725e7 q^{43} +1.89041e7 q^{44} -8.44936e6 q^{45} +4.45974e6 q^{46} -3.59866e6 q^{47} -718332. q^{48} -2.99919e7 q^{49} +4.03871e6 q^{50} +5.14036e7 q^{51} -4.62805e7 q^{52} +5.97566e7 q^{53} +7.28427e6 q^{54} +7.51094e7 q^{55} +3.68910e7 q^{56} -8.66778e7 q^{57} +6.38956e7 q^{58} +1.21174e7 q^{59} -3.38108e7 q^{60} +5.83430e7 q^{61} +7.55509e7 q^{62} +2.11196e7 q^{63} +7.75531e7 q^{64} -1.83881e8 q^{65} -6.47525e7 q^{66} +1.77772e7 q^{67} +2.05696e8 q^{68} +2.63550e7 q^{69} +5.68200e7 q^{70} -1.90982e8 q^{71} +7.51924e7 q^{72} -4.70490e8 q^{73} -2.23350e8 q^{74} +2.38669e7 q^{75} -3.46848e8 q^{76} -1.87740e8 q^{77} +1.58525e8 q^{78} -1.31253e8 q^{79} -1.14207e7 q^{80} +4.30467e7 q^{81} +2.77350e8 q^{82} -5.84868e7 q^{83} +8.45118e7 q^{84} +8.17265e8 q^{85} +5.27329e8 q^{86} +3.77594e8 q^{87} -6.68412e8 q^{88} +5.00612e8 q^{89} +1.15812e8 q^{90} +4.59619e8 q^{91} +1.05462e8 q^{92} +4.46471e8 q^{93} +4.93255e7 q^{94} -1.37809e9 q^{95} +4.85136e8 q^{96} +5.11624e8 q^{97} +4.11088e8 q^{98} -3.82658e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9} + 68441 q^{10} - 68033 q^{11} - 463158 q^{12} + 283817 q^{13} + 80285 q^{14} - 65448 q^{15} + 1067674 q^{16} + 436893 q^{17} + 236196 q^{18} + 1207580 q^{19} + 4209677 q^{20} - 1721169 q^{21} + 5460442 q^{22} + 2421966 q^{23} - 764235 q^{24} + 7441842 q^{25} - 2736526 q^{26} - 11691702 q^{27} + 4095246 q^{28} - 2320594 q^{29} - 5543721 q^{30} - 3178024 q^{31} - 20786874 q^{32} + 5510673 q^{33} - 13809336 q^{34} - 2630800 q^{35} + 37515798 q^{36} + 3981807 q^{37} - 24156377 q^{38} - 22989177 q^{39} - 29544450 q^{40} - 885225 q^{41} - 6503085 q^{42} + 12360835 q^{43} - 117711882 q^{44} + 5301288 q^{45} + 161066949 q^{46} + 75901252 q^{47} - 86481594 q^{48} + 170907951 q^{49} - 61318927 q^{50} - 35388333 q^{51} - 100762 q^{52} - 34790192 q^{53} - 19131876 q^{54} + 151773316 q^{55} - 417630344 q^{56} - 97813980 q^{57} - 432929294 q^{58} + 266581942 q^{59} - 340983837 q^{60} - 290555332 q^{61} + 158267098 q^{62} + 139414689 q^{63} - 131794443 q^{64} - 650690086 q^{65} - 442295802 q^{66} + 86645184 q^{67} + 62738541 q^{68} - 196179246 q^{69} + 429714610 q^{70} - 36567631 q^{71} + 61903035 q^{72} + 907807228 q^{73} - 171827242 q^{74} - 602789202 q^{75} + 1744504396 q^{76} - 310688725 q^{77} + 221658606 q^{78} + 2508604687 q^{79} + 3509441927 q^{80} + 947027862 q^{81} + 1759214793 q^{82} + 2185672083 q^{83} - 331714926 q^{84} + 2868860198 q^{85} + 2397001564 q^{86} + 187968114 q^{87} + 7683735877 q^{88} + 1320145942 q^{89} + 449041401 q^{90} + 3894639897 q^{91} + 3505964640 q^{92} + 257419944 q^{93} + 5406355552 q^{94} + 3093659122 q^{95} + 1683736794 q^{96} + 3904552980 q^{97} + 6137683116 q^{98} - 446364513 q^{99}+O(q^{100}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9 + 68441 * q^10 - 68033 * q^11 - 463158 * q^12 + 283817 * q^13 + 80285 * q^14 - 65448 * q^15 + 1067674 * q^16 + 436893 * q^17 + 236196 * q^18 + 1207580 * q^19 + 4209677 * q^20 - 1721169 * q^21 + 5460442 * q^22 + 2421966 * q^23 - 764235 * q^24 + 7441842 * q^25 - 2736526 * q^26 - 11691702 * q^27 + 4095246 * q^28 - 2320594 * q^29 - 5543721 * q^30 - 3178024 * q^31 - 20786874 * q^32 + 5510673 * q^33 - 13809336 * q^34 - 2630800 * q^35 + 37515798 * q^36 + 3981807 * q^37 - 24156377 * q^38 - 22989177 * q^39 - 29544450 * q^40 - 885225 * q^41 - 6503085 * q^42 + 12360835 * q^43 - 117711882 * q^44 + 5301288 * q^45 + 161066949 * q^46 + 75901252 * q^47 - 86481594 * q^48 + 170907951 * q^49 - 61318927 * q^50 - 35388333 * q^51 - 100762 * q^52 - 34790192 * q^53 - 19131876 * q^54 + 151773316 * q^55 - 417630344 * q^56 - 97813980 * q^57 - 432929294 * q^58 + 266581942 * q^59 - 340983837 * q^60 - 290555332 * q^61 + 158267098 * q^62 + 139414689 * q^63 - 131794443 * q^64 - 650690086 * q^65 - 442295802 * q^66 + 86645184 * q^67 + 62738541 * q^68 - 196179246 * q^69 + 429714610 * q^70 - 36567631 * q^71 + 61903035 * q^72 + 907807228 * q^73 - 171827242 * q^74 - 602789202 * q^75 + 1744504396 * q^76 - 310688725 * q^77 + 221658606 * q^78 + 2508604687 * q^79 + 3509441927 * q^80 + 947027862 * q^81 + 1759214793 * q^82 + 2185672083 * q^83 - 331714926 * q^84 + 2868860198 * q^85 + 2397001564 * q^86 + 187968114 * q^87 + 7683735877 * q^88 + 1320145942 * q^89 + 449041401 * q^90 + 3894639897 * q^91 + 3505964640 * q^92 + 257419944 * q^93 + 5406355552 * q^94 + 3093659122 * q^95 + 1683736794 * q^96 + 3904552980 * q^97 + 6137683116 * q^98 - 446364513 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more