LMFDB - Embedded newform 29.8.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,8,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	29.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:	$9.05916573904$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 1101 x^{8} - 1540 x^{7} + 405148 x^{6} + 870160 x^{5} - 54569376 x^{4} - 87078400 x^{3} + \cdots - 9372051456 $ x^10 - 1101x^8 - 1540x^7 + 405148x^6 + 870160x^5 - 54569376x^4 - 87078400x^3 + 2140673280x^2 - 1918315520x - 9372051456
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$22.0686$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.0686 q^{2} +73.8979 q^{3} +359.023 q^{4} +376.792 q^{5} -1630.82 q^{6} +647.379 q^{7} -5098.36 q^{8} +3273.90 q^{9} +O(q^{10})$	\(q-22.0686 q^{2} +73.8979 q^{3} +359.023 q^{4} +376.792 q^{5} -1630.82 q^{6} +647.379 q^{7} -5098.36 q^{8} +3273.90 q^{9} -8315.26 q^{10} -917.032 q^{11} +26531.1 q^{12} +5439.90 q^{13} -14286.7 q^{14} +27844.1 q^{15} +66558.6 q^{16} -23747.6 q^{17} -72250.4 q^{18} -29878.0 q^{19} +135277. q^{20} +47840.0 q^{21} +20237.6 q^{22} +34152.9 q^{23} -376758. q^{24} +63846.9 q^{25} -120051. q^{26} +80319.7 q^{27} +232424. q^{28} -24389.0 q^{29} -614481. q^{30} +215829. q^{31} -816266. q^{32} -67766.7 q^{33} +524076. q^{34} +243927. q^{35} +1.17541e6 q^{36} +61163.9 q^{37} +659365. q^{38} +401997. q^{39} -1.92102e6 q^{40} -202987. q^{41} -1.05576e6 q^{42} +436213. q^{43} -329236. q^{44} +1.23358e6 q^{45} -753706. q^{46} -1.14899e6 q^{47} +4.91854e6 q^{48} -404443. q^{49} -1.40901e6 q^{50} -1.75490e6 q^{51} +1.95305e6 q^{52} +237602. q^{53} -1.77254e6 q^{54} -345530. q^{55} -3.30057e6 q^{56} -2.20792e6 q^{57} +538231. q^{58} -1.56197e6 q^{59} +9.99668e6 q^{60} +2.82667e6 q^{61} -4.76303e6 q^{62} +2.11945e6 q^{63} +9.49434e6 q^{64} +2.04971e6 q^{65} +1.49552e6 q^{66} -1.28367e6 q^{67} -8.52593e6 q^{68} +2.52383e6 q^{69} -5.38313e6 q^{70} +3.48686e6 q^{71} -1.66915e7 q^{72} +68118.2 q^{73} -1.34980e6 q^{74} +4.71816e6 q^{75} -1.07269e7 q^{76} -593667. q^{77} -8.87151e6 q^{78} -770647. q^{79} +2.50787e7 q^{80} -1.22456e6 q^{81} +4.47963e6 q^{82} -3.66552e6 q^{83} +1.71756e7 q^{84} -8.94789e6 q^{85} -9.62660e6 q^{86} -1.80230e6 q^{87} +4.67535e6 q^{88} -322570. q^{89} -2.72233e7 q^{90} +3.52167e6 q^{91} +1.22617e7 q^{92} +1.59493e7 q^{93} +2.53566e7 q^{94} -1.12578e7 q^{95} -6.03203e7 q^{96} -2.17987e6 q^{97} +8.92550e6 q^{98} -3.00227e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9}+O(q^{10}) $ 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9} + 8496 q^{10} + 7384 q^{11} + 49720 q^{12} + 20820 q^{13} + 50976 q^{14} + 43516 q^{15} + 122082 q^{16} - 11620 q^{17} + 66060 q^{18} + 75068 q^{19} - 42914 q^{20} + 51480 q^{21} - 36950 q^{22} + 62040 q^{23} - 205942 q^{24} + 261022 q^{25} - 201528 q^{26} - 28060 q^{27} - 24980 q^{28} - 243890 q^{29} - 1284894 q^{30} + 200600 q^{31} - 1761460 q^{32} - 1068000 q^{33} - 503932 q^{34} + 107528 q^{35} - 26300 q^{36} - 367740 q^{37} + 766880 q^{38} + 392692 q^{39} - 865000 q^{40} + 932764 q^{41} - 2058060 q^{42} + 1443560 q^{43} - 1325912 q^{44} + 4245684 q^{45} + 1760460 q^{46} - 286960 q^{47} + 3187120 q^{48} + 4713194 q^{49} - 3682652 q^{50} + 1451016 q^{51} + 2560210 q^{52} + 3953220 q^{53} - 3147534 q^{54} + 3981316 q^{55} + 2082464 q^{56} + 2050640 q^{57} + 6712320 q^{59} + 7476756 q^{60} + 1905196 q^{61} - 8048490 q^{62} + 3643800 q^{63} + 8445458 q^{64} + 4667544 q^{65} - 12425580 q^{66} - 2718200 q^{67} - 17699740 q^{68} + 1109064 q^{69} - 30441624 q^{70} + 3447736 q^{71} - 22466840 q^{72} - 2554460 q^{73} - 4214584 q^{74} + 1088084 q^{75} - 8294848 q^{76} - 3967800 q^{77} - 24809970 q^{78} + 4187744 q^{79} - 17715290 q^{80} + 5161402 q^{81} + 7020500 q^{82} + 3498720 q^{83} + 22947224 q^{84} + 1817072 q^{85} - 361638 q^{86} - 1951120 q^{87} + 15118470 q^{88} - 303268 q^{89} - 28959160 q^{90} + 27215080 q^{91} - 10783380 q^{92} + 1097360 q^{93} + 55641726 q^{94} - 8810536 q^{95} - 53327238 q^{96} + 4908620 q^{97} + 40120080 q^{98} - 14408716 q^{99}+O(q^{100}) \) 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9 + 8496 * q^10 + 7384 * q^11 + 49720 * q^12 + 20820 * q^13 + 50976 * q^14 + 43516 * q^15 + 122082 * q^16 - 11620 * q^17 + 66060 * q^18 + 75068 * q^19 - 42914 * q^20 + 51480 * q^21 - 36950 * q^22 + 62040 * q^23 - 205942 * q^24 + 261022 * q^25 - 201528 * q^26 - 28060 * q^27 - 24980 * q^28 - 243890 * q^29 - 1284894 * q^30 + 200600 * q^31 - 1761460 * q^32 - 1068000 * q^33 - 503932 * q^34 + 107528 * q^35 - 26300 * q^36 - 367740 * q^37 + 766880 * q^38 + 392692 * q^39 - 865000 * q^40 + 932764 * q^41 - 2058060 * q^42 + 1443560 * q^43 - 1325912 * q^44 + 4245684 * q^45 + 1760460 * q^46 - 286960 * q^47 + 3187120 * q^48 + 4713194 * q^49 - 3682652 * q^50 + 1451016 * q^51 + 2560210 * q^52 + 3953220 * q^53 - 3147534 * q^54 + 3981316 * q^55 + 2082464 * q^56 + 2050640 * q^57 + 6712320 * q^59 + 7476756 * q^60 + 1905196 * q^61 - 8048490 * q^62 + 3643800 * q^63 + 8445458 * q^64 + 4667544 * q^65 - 12425580 * q^66 - 2718200 * q^67 - 17699740 * q^68 + 1109064 * q^69 - 30441624 * q^70 + 3447736 * q^71 - 22466840 * q^72 - 2554460 * q^73 - 4214584 * q^74 + 1088084 * q^75 - 8294848 * q^76 - 3967800 * q^77 - 24809970 * q^78 + 4187744 * q^79 - 17715290 * q^80 + 5161402 * q^81 + 7020500 * q^82 + 3498720 * q^83 + 22947224 * q^84 + 1817072 * q^85 - 361638 * q^86 - 1951120 * q^87 + 15118470 * q^88 - 303268 * q^89 - 28959160 * q^90 + 27215080 * q^91 - 10783380 * q^92 + 1097360 * q^93 + 55641726 * q^94 - 8810536 * q^95 - 53327238 * q^96 + 4908620 * q^97 + 40120080 * q^98 - 14408716 * 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 $

$2$	−22.0686	−1.95061	−0.975303	−	0.220869i	$-0.929111\pi$
$2$	−22.0686	−1.95061	−0.975303	+	0.220869i	$0.929111\pi$
$3$	73.8979	1.58018	0.790092	−	0.612988i	$-0.210033\pi$
$3$	73.8979	1.58018	0.790092	+	0.612988i	$0.210033\pi$
$4$	359.023	2.80487
$5$	376.792	1.34805	0.674025	−	0.738708i	$-0.264564\pi$
$5$	376.792	1.34805	0.674025	+	0.738708i	$0.264564\pi$
$6$	−1630.82	−3.08232
$7$	647.379	0.713371	0.356685	−	0.934225i	$-0.383907\pi$
$7$	647.379	0.713371	0.356685	+	0.934225i	$0.383907\pi$
$8$	−5098.36	−3.52059
$9$	3273.90	1.49698
$10$	−8315.26	−2.62952
$11$	−917.032	−0.207735	−0.103868	−	0.994591i	$-0.533122\pi$
$11$	−917.032	−0.207735	−0.103868	+	0.994591i	$0.533122\pi$
$12$	26531.1	4.43221
$13$	5439.90	0.686735	0.343367	−	0.939201i	$-0.388432\pi$
$13$	5439.90	0.686735	0.343367	+	0.939201i	$0.388432\pi$
$14$	−14286.7	−1.39151
$15$	27844.1	2.13017
$16$	66558.6	4.06241
$17$	−23747.6	−1.17233	−0.586163	−	0.810193i	$-0.699362\pi$
$17$	−23747.6	−1.17233	−0.586163	+	0.810193i	$0.699362\pi$
$18$	−72250.4	−2.92002
$19$	−29878.0	−0.999340	−0.499670	−	0.866216i	$-0.666545\pi$
$19$	−29878.0	−0.999340	−0.499670	+	0.866216i	$0.666545\pi$
$20$	135277.	3.78110
$21$	47840.0	1.12726
$22$	20237.6	0.405210
$23$	34152.9	0.585302	0.292651	−	0.956219i	$-0.405463\pi$
$23$	34152.9	0.585302	0.292651	+	0.956219i	$0.405463\pi$
$24$	−376758.	−5.56318
$25$	63846.9	0.817241
$26$	−120051.	−1.33955
$27$	80319.7	0.785324
$28$	232424.	2.00091
$29$	−24389.0	−0.185695
$29$	−24389.0	−0.185695
$30$	−614481.	−4.15512
$31$	215829.	1.30120	0.650598	−	0.759422i	$-0.274518\pi$
$31$	215829.	1.30120	0.650598	+	0.759422i	$0.274518\pi$
$32$	−816266.	−4.40359
$33$	−67766.7	−0.328260
$34$	524076.	2.28675
$35$	243927.	0.961660
$36$	1.17541e6	4.19884
$37$	61163.9	0.198513	0.0992565	−	0.995062i	$-0.468354\pi$
$37$	61163.9	0.198513	0.0992565	+	0.995062i	$0.468354\pi$
$38$	659365.	1.94932
$39$	401997.	1.08517
$40$	−1.92102e6	−4.74593
$41$	−202987.	−0.459964	−0.229982	−	0.973195i	$-0.573867\pi$
$41$	−202987.	−0.459964	−0.229982	+	0.973195i	$0.573867\pi$
$42$	−1.05576e6	−2.19884
$43$	436213.	0.836679	0.418339	−	0.908291i	$-0.362612\pi$
$43$	436213.	0.836679	0.418339	+	0.908291i	$0.362612\pi$
$44$	−329236.	−0.582670
$45$	1.23358e6	2.01801
$46$	−753706.	−1.14169
$47$	−1.14899e6	−1.61426	−0.807131	−	0.590372i	$-0.798981\pi$
$47$	−1.14899e6	−1.61426	−0.807131	+	0.590372i	$0.798981\pi$
$48$	4.91854e6	6.41936
$49$	−404443.	−0.491102
$50$	−1.40901e6	−1.59412
$51$	−1.75490e6	−1.85249
$52$	1.95305e6	1.92620
$53$	237602.	0.219222	0.109611	−	0.993975i	$-0.465040\pi$
$53$	237602.	0.219222	0.109611	+	0.993975i	$0.465040\pi$
$54$	−1.77254e6	−1.53186
$55$	−345530.	−0.280038
$56$	−3.30057e6	−2.51148
$57$	−2.20792e6	−1.57914
$58$	538231.	0.362219
$59$	−1.56197e6	−0.990126	−0.495063	−	0.868857i	$-0.664855\pi$
$59$	−1.56197e6	−0.990126	−0.495063	+	0.868857i	$0.664855\pi$
$60$	9.99668e6	5.97484
$61$	2.82667e6	1.59449	0.797243	−	0.603659i	$-0.206291\pi$
$61$	2.82667e6	1.59449	0.797243	+	0.603659i	$0.206291\pi$
$62$	−4.76303e6	−2.53812
$63$	2.11945e6	1.06790
$64$	9.49434e6	4.52725
$65$	2.04971e6	0.925753
$66$	1.49552e6	0.640306
$67$	−1.28367e6	−0.521424	−0.260712	−	0.965417i	$-0.583957\pi$
$67$	−1.28367e6	−0.521424	−0.260712	+	0.965417i	$0.583957\pi$
$68$	−8.52593e6	−3.28822
$69$	2.52383e6	0.924884
$70$	−5.38313e6	−1.87582
$71$	3.48686e6	1.15619	0.578096	−	0.815969i	$-0.303796\pi$
$71$	3.48686e6	1.15619	0.578096	+	0.815969i	$0.303796\pi$
$72$	−1.66915e7	−5.27026
$73$	68118.2	0.0204943	0.0102472	−	0.999947i	$-0.496738\pi$
$73$	68118.2	0.0204943	0.0102472	+	0.999947i	$0.496738\pi$
$74$	−1.34980e6	−0.387221
$75$	4.71816e6	1.29139
$76$	−1.07269e7	−2.80302
$77$	−593667.	−0.148192
$78$	−8.87151e6	−2.11673
$79$	−770647.	−0.175857	−0.0879287	−	0.996127i	$-0.528025\pi$
$79$	−770647.	−0.175857	−0.0879287	+	0.996127i	$0.528025\pi$
$80$	2.50787e7	5.47634
$81$	−1.22456e6	−0.256026
$82$	4.47963e6	0.897209
$83$	−3.66552e6	−0.703658	−0.351829	−	0.936064i	$-0.614440\pi$
$83$	−3.66552e6	−0.703658	−0.351829	+	0.936064i	$0.614440\pi$
$84$	1.71756e7	3.16181
$85$	−8.94789e6	−1.58035
$86$	−9.62660e6	−1.63203
$87$	−1.80230e6	−0.293433
$88$	4.67535e6	0.731350
$89$	−322570.	−0.0485019	−0.0242509	−	0.999706i	$-0.507720\pi$
$89$	−322570.	−0.0485019	−0.0242509	+	0.999706i	$0.507720\pi$
$90$	−2.72233e7	−3.93634
$91$	3.52167e6	0.489897
$92$	1.22617e7	1.64169
$93$	1.59493e7	2.05613
$94$	2.53566e7	3.14879
$95$	−1.12578e7	−1.34716
$96$	−6.03203e7	−6.95848
$97$	−2.17987e6	−0.242510	−0.121255	−	0.992621i	$-0.538692\pi$
$97$	−2.17987e6	−0.242510	−0.121255	+	0.992621i	$0.538692\pi$
$98$	8.92550e6	0.957947
$99$	−3.00227e6	−0.310976
$100$	2.29225e7	2.29225
$101$	1.90852e7	1.84320	0.921598	−	0.388147i	$-0.126885\pi$
$101$	1.90852e7	1.84320	0.921598	+	0.388147i	$0.126885\pi$
$102$	3.87281e7	3.61348
$103$	−1.33432e7	−1.20317	−0.601587	−	0.798808i	$-0.705465\pi$
$103$	−1.33432e7	−1.20317	−0.601587	+	0.798808i	$0.705465\pi$
$104$	−2.77345e7	−2.41771
$105$	1.80257e7	1.51960
$106$	−5.24354e6	−0.427616
$107$	−6.92372e6	−0.546382	−0.273191	−	0.961960i	$-0.588079\pi$
$107$	−6.92372e6	−0.546382	−0.273191	+	0.961960i	$0.588079\pi$
$108$	2.88366e7	2.20273
$109$	−2.41593e7	−1.78686	−0.893432	−	0.449199i	$-0.851710\pi$
$109$	−2.41593e7	−1.78686	−0.893432	+	0.449199i	$0.851710\pi$
$110$	7.62536e6	0.546243
$111$	4.51988e6	0.313687
$112$	4.30886e7	2.89801
$113$	5.03277e6	0.328120	0.164060	−	0.986450i	$-0.447541\pi$
$113$	5.03277e6	0.328120	0.164060	+	0.986450i	$0.447541\pi$
$114$	4.87257e7	3.08029
$115$	1.28685e7	0.789016
$116$	−8.75621e6	−0.520851
$117$	1.78097e7	1.02803
$118$	3.44705e7	1.93135
$119$	−1.53737e7	−0.836303
$120$	−1.41959e8	−7.49945
$121$	−1.86462e7	−0.956846
$122$	−6.23806e7	−3.11021
$123$	−1.50003e7	−0.726828
$124$	7.74874e7	3.64968
$125$	−5.37985e6	−0.246368
$126$	−4.67734e7	−2.08306
$127$	−2.20593e7	−0.955605	−0.477803	−	0.878467i	$-0.658567\pi$
$127$	−2.20593e7	−0.955605	−0.477803	+	0.878467i	$0.658567\pi$
$128$	−1.05045e8	−4.42730
$129$	3.22352e7	1.32211
$130$	−4.52342e7	−1.80578
$131$	4.21270e7	1.63723	0.818617	−	0.574340i	$-0.194741\pi$
$131$	4.21270e7	1.63723	0.818617	+	0.574340i	$0.194741\pi$
$132$	−2.43298e7	−0.920726
$133$	−1.93424e7	−0.712900
$134$	2.83288e7	1.01709
$135$	3.02638e7	1.05866
$136$	1.21074e8	4.12727
$137$	−1.07382e6	−0.0356789	−0.0178394	−	0.999841i	$-0.505679\pi$
$137$	−1.07382e6	−0.0356789	−0.0178394	+	0.999841i	$0.505679\pi$
$138$	−5.56973e7	−1.80409
$139$	7.04746e6	0.222577	0.111289	−	0.993788i	$-0.464502\pi$
$139$	7.04746e6	0.222577	0.111289	+	0.993788i	$0.464502\pi$
$140$	8.75754e7	2.69733
$141$	−8.49080e7	−2.55083
$142$	−7.69501e7	−2.25528
$143$	−4.98856e6	−0.142659
$144$	2.17906e8	6.08136
$145$	−9.18957e6	−0.250327
$146$	−1.50327e6	−0.0399763
$147$	−2.98875e7	−0.776031
$148$	2.19592e7	0.556803
$149$	2.10846e6	0.0522173	0.0261086	−	0.999659i	$-0.491688\pi$
$149$	2.10846e6	0.0522173	0.0261086	+	0.999659i	$0.491688\pi$
$150$	−1.04123e8	−2.51900
$151$	3.04554e7	0.719854	0.359927	−	0.932980i	$-0.382802\pi$
$151$	3.04554e7	0.719854	0.359927	+	0.932980i	$0.382802\pi$
$152$	1.52328e8	3.51827
$153$	−7.77472e7	−1.75495
$154$	1.31014e7	0.289065
$155$	8.13224e7	1.75408
$156$	1.44326e8	3.04375
$157$	−4.33834e7	−0.894694	−0.447347	−	0.894360i	$-0.647631\pi$
$157$	−4.33834e7	−0.894694	−0.447347	+	0.894360i	$0.647631\pi$
$158$	1.70071e7	0.343029
$159$	1.75583e7	0.346411
$160$	−3.07562e8	−5.93626
$161$	2.21098e7	0.417537
$162$	2.70244e7	0.499406
$163$	−6.67032e7	−1.20640	−0.603198	−	0.797591i	$-0.706107\pi$
$163$	−6.67032e7	−1.20640	−0.603198	+	0.797591i	$0.706107\pi$
$164$	−7.28769e7	−1.29014
$165$	−2.55339e7	−0.442511
$166$	8.08928e7	1.37256
$167$	6.05087e7	1.00533	0.502667	−	0.864480i	$-0.332352\pi$
$167$	6.05087e7	1.00533	0.502667	+	0.864480i	$0.332352\pi$
$168$	−2.43905e8	−3.96861
$169$	−3.31560e7	−0.528396
$170$	1.97467e8	3.08265
$171$	−9.78175e7	−1.49600
$172$	1.56610e8	2.34677
$173$	−1.01700e8	−1.49335	−0.746675	−	0.665189i	$-0.768351\pi$
$173$	−1.01700e8	−1.49335	−0.746675	+	0.665189i	$0.768351\pi$
$174$	3.97741e7	0.572372
$175$	4.13332e7	0.582996
$176$	−6.10364e7	−0.843907
$177$	−1.15426e8	−1.56458
$178$	7.11866e6	0.0946081
$179$	3.98101e7	0.518809	0.259405	−	0.965769i	$-0.416474\pi$
$179$	3.98101e7	0.518809	0.259405	+	0.965769i	$0.416474\pi$
$180$	4.42883e8	5.66025
$181$	5.63538e7	0.706396	0.353198	−	0.935549i	$-0.385094\pi$
$181$	5.63538e7	0.706396	0.353198	+	0.935549i	$0.385094\pi$
$182$	−7.77184e7	−0.955596
$183$	2.08885e8	2.51958
$184$	−1.74123e8	−2.06061
$185$	2.30460e7	0.267606
$186$	−3.51978e8	−4.01070
$187$	2.17773e7	0.243533
$188$	−4.12514e8	−4.52779
$189$	5.19973e7	0.560227
$190$	2.48443e8	2.62778
$191$	1.79471e7	0.186370	0.0931851	−	0.995649i	$-0.470295\pi$
$191$	1.79471e7	0.186370	0.0931851	+	0.995649i	$0.470295\pi$
$192$	7.01612e8	7.15389
$193$	−8.66641e7	−0.867738	−0.433869	−	0.900976i	$-0.642852\pi$
$193$	−8.66641e7	−0.867738	−0.433869	+	0.900976i	$0.642852\pi$
$194$	4.81068e7	0.473042
$195$	1.51469e8	1.46286
$196$	−1.45205e8	−1.37748
$197$	−1.48231e8	−1.38136	−0.690681	−	0.723159i	$-0.742689\pi$
$197$	−1.48231e8	−1.38136	−0.690681	+	0.723159i	$0.742689\pi$
$198$	6.62559e7	0.606592
$199$	1.80493e8	1.62358	0.811791	−	0.583948i	$-0.198493\pi$
$199$	1.80493e8	1.62358	0.811791	+	0.583948i	$0.198493\pi$
$200$	−3.25514e8	−2.87717
$201$	−9.48604e7	−0.823946
$202$	−4.21183e8	−3.59535
$203$	−1.57889e7	−0.132470
$204$	−6.30048e8	−5.19599
$205$	−7.64837e7	−0.620055
$206$	2.94465e8	2.34692
$207$	1.11813e8	0.876186
$208$	3.62072e8	2.78980
$209$	2.73991e7	0.207598
$210$	−3.97802e8	−2.96414
$211$	1.01529e8	0.744049	0.372024	−	0.928223i	$-0.378664\pi$
$211$	1.01529e8	0.744049	0.372024	+	0.928223i	$0.378664\pi$
$212$	8.53045e7	0.614888
$213$	2.57672e8	1.82700
$214$	1.52797e8	1.06578
$215$	1.64361e8	1.12789
$216$	−4.09498e8	−2.76480
$217$	1.39723e8	0.928236
$218$	5.33162e8	3.48547
$219$	5.03379e6	0.0323848
$220$	−1.24053e8	−0.785468
$221$	−1.29184e8	−0.805077
$222$	−9.97475e7	−0.611880
$223$	9.90258e7	0.597973	0.298986	−	0.954257i	$-0.403351\pi$
$223$	9.90258e7	0.597973	0.298986	+	0.954257i	$0.403351\pi$
$224$	−5.28433e8	−3.14139
$225$	2.09029e8	1.22340
$226$	−1.11066e8	−0.640033
$227$	−7.06827e7	−0.401072	−0.200536	−	0.979686i	$-0.564268\pi$
$227$	−7.06827e7	−0.401072	−0.200536	+	0.979686i	$0.564268\pi$
$228$	−7.92694e8	−4.42928
$229$	7.97463e7	0.438820	0.219410	−	0.975633i	$-0.429587\pi$
$229$	7.97463e7	0.438820	0.219410	+	0.975633i	$0.429587\pi$
$230$	−2.83990e8	−1.53906
$231$	−4.38708e7	−0.234171
$232$	1.24344e8	0.653757
$233$	2.78555e8	1.44266	0.721332	−	0.692590i	$-0.243530\pi$
$233$	2.78555e8	1.44266	0.721332	+	0.692590i	$0.243530\pi$
$234$	−3.93035e8	−2.00528
$235$	−4.32930e8	−2.17611
$236$	−5.60783e8	−2.77717
$237$	−5.69492e7	−0.277887
$238$	3.39276e8	1.63130
$239$	3.03984e8	1.44032	0.720159	−	0.693809i	$-0.244069\pi$
$239$	3.03984e8	1.44032	0.720159	+	0.693809i	$0.244069\pi$
$240$	1.85327e9	8.65363
$241$	1.62667e8	0.748581	0.374291	−	0.927311i	$-0.377886\pi$
$241$	1.62667e8	0.748581	0.374291	+	0.927311i	$0.377886\pi$
$242$	4.11496e8	1.86643
$243$	−2.66152e8	−1.18989
$244$	1.01484e9	4.47232
$245$	−1.52391e8	−0.662030
$246$	3.31035e8	1.41776
$247$	−1.62533e8	−0.686282
$248$	−1.10037e9	−4.58098
$249$	−2.70874e8	−1.11191
$250$	1.18726e8	0.480568
$251$	−9.86866e7	−0.393913	−0.196956	−	0.980412i	$-0.563106\pi$
$251$	−9.86866e7	−0.393913	−0.196956	+	0.980412i	$0.563106\pi$
$252$	7.60933e8	2.99533
$253$	−3.13193e7	−0.121588
$254$	4.86818e8	1.86401
$255$	−6.61230e8	−2.49725
$256$	1.10291e9	4.10868
$257$	1.41643e8	0.520509	0.260254	−	0.965540i	$-0.416194\pi$
$257$	1.41643e8	0.520509	0.260254	+	0.965540i	$0.416194\pi$
$258$	−7.11386e8	−2.57891
$259$	3.95962e7	0.141613
$260$	7.35892e8	2.59662
$261$	−7.98472e7	−0.277983
$262$	−9.29683e8	−3.19360
$263$	1.80962e8	0.613396	0.306698	−	0.951807i	$-0.400776\pi$
$263$	1.80962e8	0.613396	0.306698	+	0.951807i	$0.400776\pi$
$264$	3.45499e8	1.15567
$265$	8.95263e7	0.295522
$266$	4.26859e8	1.39059
$267$	−2.38372e7	−0.0766419
$268$	−4.60866e8	−1.46252
$269$	−2.27845e8	−0.713684	−0.356842	−	0.934165i	$-0.616146\pi$
$269$	−2.27845e8	−0.713684	−0.356842	+	0.934165i	$0.616146\pi$
$270$	−6.67880e8	−2.06502
$271$	−6.01958e8	−1.83727	−0.918636	−	0.395104i	$-0.870709\pi$
$271$	−6.01958e8	−1.83727	−0.918636	+	0.395104i	$0.870709\pi$
$272$	−1.58061e9	−4.76247
$273$	2.60244e8	0.774127
$274$	2.36978e7	0.0695954
$275$	−5.85497e7	−0.169770
$276$	9.06112e8	2.59418
$277$	−1.98459e8	−0.561036	−0.280518	−	0.959849i	$-0.590506\pi$
$277$	−1.98459e8	−0.561036	−0.280518	+	0.959849i	$0.590506\pi$
$278$	−1.55528e8	−0.434161
$279$	7.06601e8	1.94787
$280$	−1.24363e9	−3.38561
$281$	−3.68152e8	−0.989818	−0.494909	−	0.868945i	$-0.664799\pi$
$281$	−3.68152e8	−0.989818	−0.494909	+	0.868945i	$0.664799\pi$
$282$	1.87380e9	4.97567
$283$	2.58445e8	0.677821	0.338910	−	0.940819i	$-0.389942\pi$
$283$	2.58445e8	0.677821	0.338910	+	0.940819i	$0.389942\pi$
$284$	1.25186e9	3.24297
$285$	−8.31926e8	−2.12876
$286$	1.10091e8	0.278272
$287$	−1.31409e8	−0.328125
$288$	−2.67237e9	−6.59209
$289$	1.53609e8	0.374347
$290$	2.02801e8	0.488289
$291$	−1.61088e8	−0.383211
$292$	2.44560e7	0.0574838
$293$	−4.91702e8	−1.14200	−0.570999	−	0.820951i	$-0.693444\pi$
$293$	−4.91702e8	−1.14200	−0.570999	+	0.820951i	$0.693444\pi$
$294$	6.59576e8	1.51373
$295$	−5.88537e8	−1.33474
$296$	−3.11835e8	−0.698882
$297$	−7.36557e7	−0.163139
$298$	−4.65308e7	−0.101855
$299$	1.85788e8	0.401947
$300$	1.69393e9	3.62218
$301$	2.82395e8	0.596862
$302$	−6.72107e8	−1.40415
$303$	1.41035e9	2.91259
$304$	−1.98864e9	−4.05973
$305$	1.06507e9	2.14945
$306$	1.71577e9	3.42322
$307$	−4.21676e8	−0.831754	−0.415877	−	0.909421i	$-0.636525\pi$
$307$	−4.21676e8	−0.831754	−0.415877	+	0.909421i	$0.636525\pi$
$308$	−2.13140e8	−0.415660
$309$	−9.86031e8	−1.90124
$310$	−1.79467e9	−3.42152
$311$	8.55447e8	1.61262	0.806310	−	0.591494i	$-0.201461\pi$
$311$	8.55447e8	1.61262	0.806310	+	0.591494i	$0.201461\pi$
$312$	−2.04952e9	−3.82043
$313$	−417650.	−0.000769853 0	−0.000384926	−	1.00000i	$-0.500123\pi$
$313$	−417650.	−0.000769853 0	−0.000384926		1.00000i	$0.500123\pi$
$314$	9.57410e8	1.74520
$315$	7.98593e8	1.43959
$316$	−2.76680e8	−0.493257
$317$	−3.50781e8	−0.618484	−0.309242	−	0.950983i	$-0.600075\pi$
$317$	−3.50781e8	−0.618484	−0.309242	+	0.950983i	$0.600075\pi$
$318$	−3.87486e8	−0.675712
$319$	2.23655e7	0.0385755
$320$	3.57739e9	6.10297
$321$	−5.11649e8	−0.863385
$322$	−4.87933e8	−0.814451
$323$	7.09530e8	1.17155
$324$	−4.39646e8	−0.718118
$325$	3.47321e8	0.561228
$326$	1.47205e9	2.35321
$327$	−1.78532e9	−2.82357
$328$	1.03490e9	1.61934
$329$	−7.43832e8	−1.15157
$330$	5.63498e8	0.863165
$331$	4.95807e8	0.751475	0.375738	−	0.926726i	$-0.377389\pi$
$331$	4.95807e8	0.751475	0.375738	+	0.926726i	$0.377389\pi$
$332$	−1.31601e9	−1.97367
$333$	2.00244e8	0.297170
$334$	−1.33534e9	−1.96101
$335$	−4.83675e8	−0.702906
$336$	3.18416e9	4.57939
$337$	9.54347e8	1.35832	0.679159	−	0.733991i	$-0.262345\pi$
$337$	9.54347e8	1.35832	0.679159	+	0.733991i	$0.262345\pi$
$338$	7.31707e8	1.03069
$339$	3.71911e8	0.518490
$340$	−3.21250e9	−4.43268
$341$	−1.97922e8	−0.270304
$342$	2.15870e9	2.91810
$343$	−7.94973e8	−1.06371
$344$	−2.22397e9	−2.94560
$345$	9.50956e8	1.24679
$346$	2.24439e9	2.91294
$347$	−1.49821e8	−0.192495	−0.0962474	−	0.995357i	$-0.530684\pi$
$347$	−1.49821e8	−0.192495	−0.0962474	+	0.995357i	$0.530684\pi$
$348$	−6.47066e8	−0.823040
$349$	−9.98391e8	−1.25722	−0.628611	−	0.777720i	$-0.716376\pi$
$349$	−9.98391e8	−1.25722	−0.628611	+	0.777720i	$0.716376\pi$
$350$	−9.12165e8	−1.13720
$351$	4.36931e8	0.539309
$352$	7.48542e8	0.914780
$353$	1.40557e9	1.70075	0.850373	−	0.526180i	$-0.176376\pi$
$353$	1.40557e9	1.70075	0.850373	+	0.526180i	$0.176376\pi$
$354$	2.54730e9	3.05188
$355$	1.31382e9	1.55861
$356$	−1.15810e8	−0.136041
$357$	−1.13608e9	−1.32151
$358$	−8.78553e8	−1.01199
$359$	1.30123e9	1.48431	0.742155	−	0.670228i	$-0.233804\pi$
$359$	1.30123e9	1.48431	0.742155	+	0.670228i	$0.233804\pi$
$360$	−6.28922e9	−7.10458
$361$	−1.17891e6	−0.00131888
$362$	−1.24365e9	−1.37790
$363$	−1.37792e9	−1.51199
$364$	1.26436e9	1.37410
$365$	2.56664e7	0.0276274
$366$	−4.60980e9	−4.91471
$367$	8.12443e8	0.857950	0.428975	−	0.903316i	$-0.358875\pi$
$367$	8.12443e8	0.857950	0.428975	+	0.903316i	$0.358875\pi$
$368$	2.27317e9	2.37774
$369$	−6.64558e8	−0.688558
$370$	−5.08594e8	−0.521993
$371$	1.53818e8	0.156387
$372$	5.72616e9	5.76717
$373$	1.29059e9	1.28767	0.643837	−	0.765163i	$-0.277342\pi$
$373$	1.29059e9	1.28767	0.643837	+	0.765163i	$0.277342\pi$
$374$	−4.80594e8	−0.475038
$375$	−3.97560e8	−0.389308
$376$	5.85796e9	5.68315
$377$	−1.32674e8	−0.127523
$378$	−1.14751e9	−1.09278
$379$	4.40462e7	0.0415596	0.0207798	−	0.999784i	$-0.493385\pi$
$379$	4.40462e7	0.0415596	0.0207798	+	0.999784i	$0.493385\pi$
$380$	−4.04180e9	−3.77861
$381$	−1.63014e9	−1.51003
$382$	−3.96066e8	−0.363535
$383$	−1.42034e9	−1.29180	−0.645902	−	0.763421i	$-0.723518\pi$
$383$	−1.42034e9	−1.29180	−0.645902	+	0.763421i	$0.723518\pi$
$384$	−7.76259e9	−6.99596
$385$	−2.23689e8	−0.199771
$386$	1.91256e9	1.69262
$387$	1.42812e9	1.25249
$388$	−7.82625e8	−0.680209
$389$	8.67673e8	0.747365	0.373682	−	0.927557i	$-0.378095\pi$
$389$	8.67673e8	0.747365	0.373682	+	0.927557i	$0.378095\pi$
$390$	−3.34271e9	−2.85347
$391$	−8.11048e8	−0.686164
$392$	2.06200e9	1.72897
$393$	3.11309e9	2.58713
$394$	3.27125e9	2.69450
$395$	−2.90373e8	−0.237065
$396$	−1.07788e9	−0.872246
$397$	1.11899e7	0.00897550	0.00448775	−	0.999990i	$-0.498571\pi$
$397$	1.11899e7	0.00897550	0.00448775	+	0.999990i	$0.498571\pi$
$398$	−3.98322e9	−3.16697
$399$	−1.42936e9	−1.12651
$400$	4.24956e9	3.31997
$401$	−1.18782e9	−0.919906	−0.459953	−	0.887943i	$-0.652134\pi$
$401$	−1.18782e9	−0.919906	−0.459953	+	0.887943i	$0.652134\pi$
$402$	2.09344e9	1.60719
$403$	1.17409e9	0.893577
$404$	6.85202e9	5.16992
$405$	−4.61405e8	−0.345136
$406$	3.48439e8	0.258396
$407$	−5.60892e7	−0.0412381
$408$	8.94709e9	6.52185
$409$	−1.10619e9	−0.799462	−0.399731	−	0.916632i	$-0.630896\pi$
$409$	−1.10619e9	−0.799462	−0.399731	+	0.916632i	$0.630896\pi$
$410$	1.68789e9	1.20948
$411$	−7.93533e7	−0.0563792
$412$	−4.79050e9	−3.37474
$413$	−1.01119e9	−0.706327
$414$	−2.46756e9	−1.70910
$415$	−1.38114e9	−0.948567
$416$	−4.44040e9	−3.02410
$417$	5.20792e8	0.351713
$418$	−6.04659e8	−0.404942
$419$	2.88674e9	1.91716	0.958581	−	0.284819i	$-0.0919336\pi$
$419$	2.88674e9	1.91716	0.958581	+	0.284819i	$0.0919336\pi$
$420$	6.47164e9	4.26228
$421$	9.42877e8	0.615840	0.307920	−	0.951412i	$-0.400367\pi$
$421$	9.42877e8	0.615840	0.307920	+	0.951412i	$0.400367\pi$
$422$	−2.24060e9	−1.45135
$423$	−3.76168e9	−2.41652
$424$	−1.21138e9	−0.771790
$425$	−1.51621e9	−0.958072
$426$	−5.68645e9	−3.56375
$427$	1.82993e9	1.13746
$428$	−2.48578e9	−1.53253
$429$	−3.68644e8	−0.225427
$430$	−3.62722e9	−2.20006
$431$	4.00016e8	0.240662	0.120331	−	0.992734i	$-0.461604\pi$
$431$	4.00016e8	0.240662	0.120331	+	0.992734i	$0.461604\pi$
$432$	5.34597e9	3.19031
$433$	−2.34094e9	−1.38575	−0.692873	−	0.721060i	$-0.743655\pi$
$433$	−2.34094e9	−1.38575	−0.692873	+	0.721060i	$0.743655\pi$
$434$	−3.08349e9	−1.81062
$435$	−6.79090e8	−0.395562
$436$	−8.67374e9	−5.01192
$437$	−1.02042e9	−0.584916
$438$	−1.11089e8	−0.0631700
$439$	−7.14577e8	−0.403110	−0.201555	−	0.979477i	$-0.564599\pi$
$439$	−7.14577e8	−0.403110	−0.201555	+	0.979477i	$0.564599\pi$
$440$	1.76163e9	0.985897
$441$	−1.32411e9	−0.735171
$442$	2.85092e9	1.57039
$443$	2.19239e9	1.19813	0.599066	−	0.800699i	$-0.295539\pi$
$443$	2.19239e9	1.19813	0.599066	+	0.800699i	$0.295539\pi$
$444$	1.62274e9	0.879851
$445$	−1.21542e8	−0.0653830
$446$	−2.18536e9	−1.16641
$447$	1.55811e8	0.0825129
$448$	6.14643e9	3.22961
$449$	5.35068e8	0.278963	0.139482	−	0.990225i	$-0.455456\pi$
$449$	5.35068e8	0.278963	0.139482	+	0.990225i	$0.455456\pi$
$450$	−4.61297e9	−2.38636
$451$	1.86145e8	0.0955507
$452$	1.80688e9	0.920333
$453$	2.25059e9	1.13750
$454$	1.55987e9	0.782335
$455$	1.32694e9	0.660405
$456$	1.12568e10	5.55951
$457$	3.18626e9	1.56162	0.780808	−	0.624771i	$-0.214808\pi$
$457$	3.18626e9	1.56162	0.780808	+	0.624771i	$0.214808\pi$
$458$	−1.75989e9	−0.855965
$459$	−1.90740e9	−0.920655
$460$	4.62009e9	2.21309
$461$	3.12207e9	1.48419	0.742094	−	0.670296i	$-0.233833\pi$
$461$	3.12207e9	1.48419	0.742094	+	0.670296i	$0.233833\pi$
$462$	9.68166e8	0.456776
$463$	3.15215e9	1.47595	0.737977	−	0.674825i	$-0.235781\pi$
$463$	3.15215e9	1.47595	0.737977	+	0.674825i	$0.235781\pi$
$464$	−1.62330e9	−0.754371
$465$	6.00956e9	2.77177
$466$	−6.14732e9	−2.81407
$467$	7.68753e8	0.349283	0.174642	−	0.984632i	$-0.444123\pi$
$467$	7.68753e8	0.349283	0.174642	+	0.984632i	$0.444123\pi$
$468$	6.39409e9	2.88349
$469$	−8.31020e8	−0.371969
$470$	9.55416e9	4.24473
$471$	−3.20594e9	−1.41378
$472$	7.96347e9	3.48582
$473$	−4.00021e8	−0.173808
$474$	1.25679e9	0.542048
$475$	−1.90762e9	−0.816702
$476$	−5.51951e9	−2.34572
$477$	7.77884e8	0.328171
$478$	−6.70850e9	−2.80949
$479$	1.41643e9	0.588873	0.294436	−	0.955671i	$-0.404868\pi$
$479$	1.41643e9	0.588873	0.294436	+	0.955671i	$0.404868\pi$
$480$	−2.27282e10	−9.38038
$481$	3.32725e8	0.136326
$482$	−3.58983e9	−1.46019
$483$	1.63387e9	0.659786
$484$	−6.69442e9	−2.68383
$485$	−8.21358e8	−0.326916
$486$	5.87360e9	2.32101
$487$	3.54792e9	1.39195	0.695974	−	0.718067i	$-0.254973\pi$
$487$	3.54792e9	1.39195	0.695974	+	0.718067i	$0.254973\pi$
$488$	−1.44114e10	−5.61353
$489$	−4.92923e9	−1.90633
$490$	3.36305e9	1.29136
$491$	−4.84906e8	−0.184872	−0.0924362	−	0.995719i	$-0.529465\pi$
$491$	−4.84906e8	−0.184872	−0.0924362	+	0.995719i	$0.529465\pi$
$492$	−5.38545e9	−2.03866
$493$	5.79180e8	0.217695
$494$	3.58688e9	1.33867
$495$	−1.13123e9	−0.419211
$496$	1.43652e10	5.28600
$497$	2.25732e9	0.824794
$498$	5.97781e9	2.16890
$499$	−4.20411e9	−1.51468	−0.757342	−	0.653018i	$-0.773503\pi$
$499$	−4.20411e9	−1.51468	−0.757342	+	0.653018i	$0.773503\pi$
$500$	−1.93149e9	−0.691031
$501$	4.47147e9	1.58861
$502$	2.17787e9	0.768369
$503$	−6.03464e8	−0.211428	−0.105714	−	0.994397i	$-0.533713\pi$
$503$	−6.03464e8	−0.211428	−0.105714	+	0.994397i	$0.533713\pi$
$504$	−1.08057e10	−3.75965
$505$	7.19114e9	2.48472
$506$	6.91172e8	0.237170
$507$	−2.45016e9	−0.834962
$508$	−7.91979e9	−2.68035
$509$	−3.03471e9	−1.02001	−0.510006	−	0.860171i	$-0.670357\pi$
$509$	−3.03471e9	−1.02001	−0.510006	+	0.860171i	$0.670357\pi$
$510$	1.45924e10	4.87116
$511$	4.40983e7	0.0146200
$512$	−1.08941e10	−3.58711
$513$	−2.39979e9	−0.784806
$514$	−3.12585e9	−1.01531
$515$	−5.02759e9	−1.62194
$516$	1.15732e10	3.70833
$517$	1.05366e9	0.335339
$518$	−8.73833e8	−0.276232
$519$	−7.51545e9	−2.35977
$520$	−1.04501e10	−3.25919
$521$	−4.88230e9	−1.51249	−0.756245	−	0.654289i	$-0.772968\pi$
$521$	−4.88230e9	−1.51249	−0.756245	+	0.654289i	$0.772968\pi$
$522$	1.76212e9	0.542235
$523$	4.28368e9	1.30936	0.654682	−	0.755904i	$-0.272802\pi$
$523$	4.28368e9	1.30936	0.654682	+	0.755904i	$0.272802\pi$
$524$	1.51246e10	4.59222
$525$	3.05443e9	0.921241
$526$	−3.99357e9	−1.19650
$527$	−5.12541e9	−1.52543
$528$	−4.51046e9	−1.33353
$529$	−2.23841e9	−0.657422
$530$	−1.97572e9	−0.576448
$531$	−5.11373e9	−1.48220
$532$	−6.94436e9	−1.99959
$533$	−1.10423e9	−0.315873
$534$	5.26054e8	0.149498
$535$	−2.60880e9	−0.736551
$536$	6.54459e9	1.83572
$537$	2.94188e9	0.819814
$538$	5.02821e9	1.39212
$539$	3.70888e8	0.102019
$540$	1.08654e10	2.96939
$541$	9.58437e8	0.260239	0.130120	−	0.991498i	$-0.458464\pi$
$541$	9.58437e8	0.260239	0.130120	+	0.991498i	$0.458464\pi$
$542$	1.32844e10	3.58380
$543$	4.16443e9	1.11624
$544$	1.93843e10	5.16244
$545$	−9.10302e9	−2.40878
$546$	−5.74323e9	−1.51002
$547$	−1.14779e9	−0.299851	−0.149926	−	0.988697i	$-0.547903\pi$
$547$	−1.14779e9	−0.299851	−0.149926	+	0.988697i	$0.547903\pi$
$548$	−3.85527e8	−0.100074
$549$	9.25424e9	2.38692
$550$	1.29211e9	0.331154
$551$	7.28694e8	0.185573
$552$	−1.28674e10	−3.25614
$553$	−4.98900e8	−0.125452
$554$	4.37970e9	1.09436
$555$	1.70305e9	0.422866
$556$	2.53020e9	0.624300
$557$	−5.96397e9	−1.46232	−0.731159	−	0.682207i	$-0.761020\pi$
$557$	−5.96397e9	−1.46232	−0.731159	+	0.682207i	$0.761020\pi$
$558$	−1.55937e10	−3.79953
$559$	2.37295e9	0.574576
$560$	1.62354e10	3.90666
$561$	1.60930e9	0.384827
$562$	8.12461e9	1.93075
$563$	−2.86789e9	−0.677302	−0.338651	−	0.940912i	$-0.609971\pi$
$563$	−2.86789e9	−0.677302	−0.338651	+	0.940912i	$0.609971\pi$
$564$	−3.04839e10	−7.15474
$565$	1.89631e9	0.442322
$566$	−5.70351e9	−1.32216
$567$	−7.92756e8	−0.182641
$568$	−1.77772e10	−4.07048
$569$	−5.88781e8	−0.133986	−0.0669932	−	0.997753i	$-0.521341\pi$
$569$	−5.88781e8	−0.133986	−0.0669932	+	0.997753i	$0.521341\pi$
$570$	1.83594e10	4.15238
$571$	6.81053e9	1.53093	0.765463	−	0.643479i	$-0.222510\pi$
$571$	6.81053e9	1.53093	0.765463	+	0.643479i	$0.222510\pi$
$572$	−1.79101e9	−0.400139
$573$	1.32625e9	0.294499
$574$	2.90002e9	0.640043
$575$	2.18056e9	0.478332
$576$	3.10835e10	6.77722
$577$	6.57528e9	1.42495	0.712474	−	0.701698i	$-0.247575\pi$
$577$	6.57528e9	1.42495	0.712474	+	0.701698i	$0.247575\pi$
$578$	−3.38994e9	−0.730204
$579$	−6.40430e9	−1.37119
$580$	−3.29927e9	−0.702133
$581$	−2.37298e9	−0.501970
$582$	3.55499e9	0.747494
$583$	−2.17888e8	−0.0455401
$584$	−3.47291e8	−0.0721520
$585$	6.71054e9	1.38584
$586$	1.08512e10	2.22759
$587$	3.22998e9	0.659123	0.329561	−	0.944134i	$-0.393099\pi$
$587$	3.22998e9	0.659123	0.329561	+	0.944134i	$0.393099\pi$
$588$	−1.07303e10	−2.17667
$589$	−6.44852e9	−1.30034
$590$	1.29882e10	2.60355
$591$	−1.09540e10	−2.18281
$592$	4.07098e9	0.806442
$593$	1.64704e9	0.324350	0.162175	−	0.986762i	$-0.448149\pi$
$593$	1.64704e9	0.324350	0.162175	+	0.986762i	$0.448149\pi$
$594$	1.62548e9	0.318221
$595$	−5.79268e9	−1.12738
$596$	7.56987e8	0.146463
$597$	1.33380e10	2.56556
$598$	−4.10008e9	−0.784040
$599$	−2.22562e9	−0.423114	−0.211557	−	0.977366i	$-0.567853\pi$
$599$	−2.22562e9	−0.423114	−0.211557	+	0.977366i	$0.567853\pi$
$600$	−2.40548e10	−4.54646
$601$	−3.05479e9	−0.574012	−0.287006	−	0.957929i	$-0.592660\pi$
$601$	−3.05479e9	−0.574012	−0.287006	+	0.957929i	$0.592660\pi$
$602$	−6.23206e9	−1.16424
$603$	−4.20260e9	−0.780562
$604$	1.09342e10	2.01910
$605$	−7.02574e9	−1.28988
$606$	−3.11246e10	−5.68132
$607$	6.32843e9	1.14851	0.574256	−	0.818676i	$-0.305292\pi$
$607$	6.32843e9	1.14851	0.574256	+	0.818676i	$0.305292\pi$
$608$	2.43884e10	4.40068
$609$	−1.16677e9	−0.209326
$610$	−2.35045e10	−4.19273
$611$	−6.25039e9	−1.10857
$612$	−2.79131e10	−4.92240
$613$	−4.08769e9	−0.716747	−0.358373	−	0.933578i	$-0.616669\pi$
$613$	−4.08769e9	−0.716747	−0.358373	+	0.933578i	$0.616669\pi$
$614$	9.30580e9	1.62242
$615$	−5.65198e9	−0.979801
$616$	3.02673e9	0.521724
$617$	5.74557e9	0.984771	0.492385	−	0.870377i	$-0.336125\pi$
$617$	5.74557e9	0.984771	0.492385	+	0.870377i	$0.336125\pi$
$618$	2.17603e10	3.70856
$619$	7.82745e9	1.32649	0.663244	−	0.748404i	$-0.269179\pi$
$619$	7.82745e9	1.32649	0.663244	+	0.748404i	$0.269179\pi$
$620$	2.91966e10	4.91996
$621$	2.74315e9	0.459651
$622$	−1.88785e10	−3.14559
$623$	−2.08825e8	−0.0345998
$624$	2.67564e10	4.40840
$625$	−7.01513e9	−1.14936
$626$	9.21696e6	0.00150168
$627$	2.02473e9	0.328043
$628$	−1.55756e10	−2.50950
$629$	−1.45249e9	−0.232722
$630$	−1.76238e10	−2.80807
$631$	−8.67471e9	−1.37452	−0.687262	−	0.726410i	$-0.741188\pi$
$631$	−8.67471e9	−1.37452	−0.687262	+	0.726410i	$0.741188\pi$
$632$	3.92903e9	0.619121
$633$	7.50278e9	1.17573
$634$	7.74124e9	1.20642
$635$	−8.31176e9	−1.28820
$636$	6.30382e9	0.971637
$637$	−2.20013e9	−0.337257
$638$	−4.93575e8	−0.0752456
$639$	1.14156e10	1.73080
$640$	−3.95800e10	−5.96823
$641$	−2.90390e8	−0.0435490	−0.0217745	−	0.999763i	$-0.506932\pi$
$641$	−2.90390e8	−0.0435490	−0.0217745	+	0.999763i	$0.506932\pi$
$642$	1.12914e10	1.68412
$643$	7.73663e9	1.14766	0.573830	−	0.818974i	$-0.305457\pi$
$643$	7.73663e9	1.14766	0.573830	+	0.818974i	$0.305457\pi$
$644$	7.93794e9	1.17114
$645$	1.21460e10	1.78227
$646$	−1.56583e10	−2.28524
$647$	2.11912e9	0.307604	0.153802	−	0.988102i	$-0.450848\pi$
$647$	2.11912e9	0.307604	0.153802	+	0.988102i	$0.450848\pi$
$648$	6.24326e9	0.901361
$649$	1.43238e9	0.205684
$650$	−7.66488e9	−1.09473
$651$	1.03252e10	1.46678
$652$	−2.39480e10	−3.38378
$653$	−6.36948e9	−0.895174	−0.447587	−	0.894240i	$-0.647717\pi$
$653$	−6.36948e9	−0.895174	−0.447587	+	0.894240i	$0.647717\pi$
$654$	3.93995e10	5.50768
$655$	1.58731e10	2.20707
$656$	−1.35105e10	−1.86856
$657$	2.23012e8	0.0306796
$658$	1.64153e10	2.24626
$659$	−3.59109e9	−0.488796	−0.244398	−	0.969675i	$-0.578590\pi$
$659$	−3.59109e9	−0.488796	−0.244398	+	0.969675i	$0.578590\pi$
$660$	−9.16727e9	−1.24118
$661$	5.83457e9	0.785786	0.392893	−	0.919584i	$-0.371474\pi$
$661$	5.83457e9	0.785786	0.392893	+	0.919584i	$0.371474\pi$
$662$	−1.09418e10	−1.46583
$663$	−9.54646e9	−1.27217
$664$	1.86881e10	2.47729
$665$	−7.28804e9	−0.961026
$666$	−4.41911e9	−0.579663
$667$	−8.32954e8	−0.108688
$668$	2.17240e10	2.81983
$669$	7.31780e9	0.944907
$670$	1.06740e10	1.37109
$671$	−2.59215e9	−0.331231
$672$	−3.90501e10	−4.96398
$673$	−4.35317e9	−0.550494	−0.275247	−	0.961374i	$-0.588760\pi$
$673$	−4.35317e9	−0.550494	−0.275247	+	0.961374i	$0.588760\pi$
$674$	−2.10611e10	−2.64955
$675$	5.12817e9	0.641799
$676$	−1.19038e10	−1.48208
$677$	1.40182e9	0.173632	0.0868162	−	0.996224i	$-0.472331\pi$
$677$	1.40182e9	0.173632	0.0868162	+	0.996224i	$0.472331\pi$
$678$	−8.20756e9	−1.01137
$679$	−1.41120e9	−0.173000
$680$	4.56195e10	5.56378
$681$	−5.22331e9	−0.633768
$682$	4.36785e9	0.527258
$683$	−2.09063e9	−0.251076	−0.125538	−	0.992089i	$-0.540066\pi$
$683$	−2.09063e9	−0.251076	−0.125538	+	0.992089i	$0.540066\pi$
$684$	−3.51187e10	−4.19607
$685$	−4.04608e8	−0.0480969
$686$	1.75439e10	2.07488
$687$	5.89308e9	0.693416
$688$	2.90337e10	3.39894
$689$	1.29253e9	0.150547
$690$	−2.09863e10	−2.43200
$691$	4.31774e9	0.497833	0.248916	−	0.968525i	$-0.419926\pi$
$691$	4.31774e9	0.497833	0.248916	+	0.968525i	$0.419926\pi$
$692$	−3.65128e10	−4.18865
$693$	−1.94361e9	−0.221841
$694$	3.30633e9	0.375482
$695$	2.65542e9	0.300045
$696$	9.18875e9	1.03306
$697$	4.82044e9	0.539228
$698$	2.20331e10	2.45234
$699$	2.05846e10	2.27967
$700$	1.48396e10	1.63523
$701$	1.20285e10	1.31886	0.659428	−	0.751768i	$-0.270799\pi$
$701$	1.20285e10	1.31886	0.659428	+	0.751768i	$0.270799\pi$
$702$	−9.64245e9	−1.05198
$703$	−1.82745e9	−0.198382
$704$	−8.70661e9	−0.940470
$705$	−3.19926e10	−3.43865
$706$	−3.10189e10	−3.31749
$707$	1.23553e10	1.31488
$708$	−4.14407e10	−4.38844
$709$	4.69177e9	0.494396	0.247198	−	0.968965i	$-0.420490\pi$
$709$	4.69177e9	0.494396	0.247198	+	0.968965i	$0.420490\pi$
$710$	−2.89942e10	−3.04023
$711$	−2.52302e9	−0.263255
$712$	1.64457e9	0.170755
$713$	7.37116e9	0.761593
$714$	2.50718e10	2.57775
$715$	−1.87965e9	−0.192312
$716$	1.42927e10	1.45519
$717$	2.24638e10	2.27597
$718$	−2.87164e10	−2.89531
$719$	−1.45057e9	−0.145542	−0.0727708	−	0.997349i	$-0.523184\pi$
$719$	−1.45057e9	−0.145542	−0.0727708	+	0.997349i	$0.523184\pi$
$720$	8.21053e10	8.19799
$721$	−8.63808e9	−0.858309
$722$	2.60169e7	0.00257262
$723$	1.20207e10	1.18290
$724$	2.02323e10	1.98135
$725$	−1.55716e9	−0.151758
$726$	3.04087e10	2.94930
$727$	−1.50239e10	−1.45015	−0.725073	−	0.688672i	$-0.758194\pi$
$727$	−1.50239e10	−1.45015	−0.725073	+	0.688672i	$0.758194\pi$
$728$	−1.79547e10	−1.72472
$729$	−1.69899e10	−1.62422
$730$	−5.66421e8	−0.0538901
$731$	−1.03590e10	−0.980860
$732$	7.49945e10	7.06709
$733$	1.07112e10	1.00456	0.502280	−	0.864705i	$-0.332495\pi$
$733$	1.07112e10	1.00456	0.502280	+	0.864705i	$0.332495\pi$
$734$	−1.79295e10	−1.67352
$735$	−1.12614e10	−1.04613
$736$	−2.78778e10	−2.57743
$737$	1.17716e9	0.108318
$738$	1.46659e10	1.34311
$739$	1.14070e10	1.03972	0.519859	−	0.854252i	$-0.325984\pi$
$739$	1.14070e10	1.03972	0.519859	+	0.854252i	$0.325984\pi$
$740$	8.27406e9	0.750598
$741$	−1.20109e10	−1.08445
$742$	−3.39455e9	−0.305049
$743$	1.77671e10	1.58912	0.794559	−	0.607187i	$-0.207702\pi$
$743$	1.77671e10	1.58912	0.794559	+	0.607187i	$0.207702\pi$
$744$	−8.13151e10	−7.23879
$745$	7.94452e8	0.0703916
$746$	−2.84814e10	−2.51175
$747$	−1.20005e10	−1.05336
$748$	7.81855e9	0.683079
$749$	−4.48227e9	−0.389773
$750$	8.77359e9	0.759386
$751$	−1.00842e9	−0.0868765	−0.0434382	−	0.999056i	$-0.513831\pi$
$751$	−1.00842e9	−0.0868765	−0.0434382	+	0.999056i	$0.513831\pi$
$752$	−7.64752e10	−6.55780
$753$	−7.29273e9	−0.622455
$754$	2.92792e9	0.248748
$755$	1.14753e10	0.970400
$756$	1.86682e10	1.57136
$757$	−1.41694e10	−1.18718	−0.593591	−	0.804767i	$-0.702290\pi$
$757$	−1.41694e10	−1.18718	−0.593591	+	0.804767i	$0.702290\pi$
$758$	−9.72039e8	−0.0810665
$759$	−2.31443e9	−0.192131
$760$	5.73961e10	4.74280
$761$	−1.23239e10	−1.01368	−0.506842	−	0.862039i	$-0.669187\pi$
$761$	−1.23239e10	−1.01368	−0.506842	+	0.862039i	$0.669187\pi$
$762$	3.59748e10	2.94548
$763$	−1.56402e10	−1.27470
$764$	6.44340e9	0.522744
$765$	−2.92945e10	−2.36576
$766$	3.13449e10	2.51980
$767$	−8.49695e9	−0.679954
$768$	8.15031e10	6.49247
$769$	−7.92692e9	−0.628583	−0.314291	−	0.949327i	$-0.601767\pi$
$769$	−7.92692e9	−0.628583	−0.314291	+	0.949327i	$0.601767\pi$
$770$	4.93650e9	0.389674
$771$	1.04671e10	0.822500
$772$	−3.11144e10	−2.43389
$773$	1.76622e10	1.37536	0.687679	−	0.726015i	$-0.258630\pi$
$773$	1.76622e10	1.37536	0.687679	+	0.726015i	$0.258630\pi$
$774$	−3.15165e10	−2.44312
$775$	1.37800e10	1.06339
$776$	1.11138e10	0.853779
$777$	2.92608e9	0.223775
$778$	−1.91483e10	−1.45781
$779$	6.06483e9	0.459661
$780$	5.43809e10	4.10313
$781$	−3.19756e9	−0.240182
$782$	1.78987e10	1.33844
$783$	−1.95892e9	−0.145831
$784$	−2.69192e10	−1.99506
$785$	−1.63465e10	−1.20609
$786$	−6.87016e10	−5.04648
$787$	2.48767e9	0.181920	0.0909601	−	0.995855i	$-0.471006\pi$
$787$	2.48767e9	0.181920	0.0909601	+	0.995855i	$0.471006\pi$
$788$	−5.32184e10	−3.87454
$789$	1.33727e10	0.969279
$790$	6.40813e9	0.462420
$791$	3.25811e9	0.234071
$792$	1.53066e10	1.09482
$793$	1.53768e10	1.09499
$794$	−2.46945e8	−0.0175077
$795$	6.61581e9	0.466980
$796$	6.48011e10	4.55393
$797$	−1.94471e10	−1.36066	−0.680332	−	0.732904i	$-0.738165\pi$
$797$	−1.94471e10	−1.36066	−0.680332	+	0.732904i	$0.738165\pi$
$798$	3.15440e10	2.19739
$799$	2.72858e10	1.89244
$800$	−5.21161e10	−3.59879
$801$	−1.05606e9	−0.0726065
$802$	2.62134e10	1.79438
$803$	−6.24666e7	−0.00425739
$804$	−3.40571e10	−2.31106
$805$	8.33081e9	0.562861
$806$	−2.59104e10	−1.74302
$807$	−1.68372e10	−1.12775
$808$	−9.73030e10	−6.48913
$809$	1.91310e10	1.27033	0.635167	−	0.772375i	$-0.280931\pi$
$809$	1.91310e10	1.27033	0.635167	+	0.772375i	$0.280931\pi$
$810$	1.01826e10	0.673224
$811$	1.21261e9	0.0798266	0.0399133	−	0.999203i	$-0.487292\pi$
$811$	1.21261e9	0.0798266	0.0399133	+	0.999203i	$0.487292\pi$
$812$	−5.66859e9	−0.371560
$813$	−4.44834e10	−2.90323
$814$	1.23781e9	0.0804394
$815$	−2.51332e10	−1.62628
$816$	−1.16803e11	−7.52558
$817$	−1.30331e10	−0.836127
$818$	2.44120e10	1.55944
$819$	1.15296e10	0.733367
$820$	−2.74594e10	−1.73917
$821$	1.93729e9	0.122178	0.0610890	−	0.998132i	$-0.480543\pi$
$821$	1.93729e9	0.122178	0.0610890	+	0.998132i	$0.480543\pi$
$822$	1.75122e9	0.109974
$823$	9.15703e9	0.572605	0.286302	−	0.958139i	$-0.407574\pi$
$823$	9.15703e9	0.572605	0.286302	+	0.958139i	$0.407574\pi$
$824$	6.80281e10	4.23588
$825$	−4.32670e9	−0.268267
$826$	2.23155e10	1.37777
$827$	2.73124e10	1.67916	0.839578	−	0.543239i	$-0.182802\pi$
$827$	2.73124e10	1.67916	0.839578	+	0.543239i	$0.182802\pi$
$828$	4.01435e10	2.45759
$829$	−9.35892e9	−0.570538	−0.285269	−	0.958447i	$-0.592083\pi$
$829$	−9.35892e9	−0.570538	−0.285269	+	0.958447i	$0.592083\pi$
$830$	3.04797e10	1.85028
$831$	−1.46657e10	−0.886540
$832$	5.16482e10	3.10902
$833$	9.60456e9	0.575731
$834$	−1.14932e10	−0.686054
$835$	2.27992e10	1.35524
$836$	9.83689e9	0.582285
$837$	1.73353e10	1.02186
$838$	−6.37064e10	−3.73963
$839$	9.38707e9	0.548735	0.274368	−	0.961625i	$-0.411531\pi$
$839$	9.38707e9	0.548735	0.274368	+	0.961625i	$0.411531\pi$
$840$	−9.19014e10	−5.34989
$841$	5.94823e8	0.0344828
$842$	−2.08080e10	−1.20126
$843$	−2.72057e10	−1.56410
$844$	3.64513e10	2.08696
$845$	−1.24929e10	−0.712304
$846$	8.30150e10	4.71368
$847$	−1.20712e10	−0.682586
$848$	1.58144e10	0.890570
$849$	1.90985e10	1.07108
$850$	3.34606e10	1.86882
$851$	2.08892e9	0.116190
$852$	9.25100e10	5.12449
$853$	−1.00111e10	−0.552280	−0.276140	−	0.961117i	$-0.589055\pi$
$853$	−1.00111e10	−0.552280	−0.276140	+	0.961117i	$0.589055\pi$
$854$	−4.03839e10	−2.21874
$855$	−3.68568e10	−2.01668
$856$	3.52996e10	1.92359
$857$	1.11853e10	0.607036	0.303518	−	0.952826i	$-0.401839\pi$
$857$	1.11853e10	0.607036	0.303518	+	0.952826i	$0.401839\pi$
$858$	8.13546e9	0.439720
$859$	−1.06684e10	−0.574282	−0.287141	−	0.957888i	$-0.592705\pi$
$859$	−1.06684e10	−0.574282	−0.287141	+	0.957888i	$0.592705\pi$
$860$	5.90095e10	3.16357
$861$	−9.71087e9	−0.518498
$862$	−8.82780e9	−0.469436
$863$	1.41277e10	0.748229	0.374114	−	0.927383i	$-0.377947\pi$
$863$	1.41277e10	0.748229	0.374114	+	0.927383i	$0.377947\pi$
$864$	−6.55622e10	−3.45824
$865$	−3.83199e10	−2.01311
$866$	5.16614e10	2.70305
$867$	1.13514e10	0.591537
$868$	5.01637e10	2.60358
$869$	7.06708e8	0.0365318
$870$	1.49866e10	0.771587
$871$	−6.98302e9	−0.358080
$872$	1.23173e11	6.29081
$873$	−7.13669e9	−0.363034
$874$	2.25192e10	1.14094
$875$	−3.48280e9	−0.175752
$876$	1.80725e9	0.0908350
$877$	4.77476e9	0.239030	0.119515	−	0.992832i	$-0.461866\pi$
$877$	4.77476e9	0.239030	0.119515	+	0.992832i	$0.461866\pi$
$878$	1.57697e10	0.786309
$879$	−3.63357e10	−1.80457
$880$	−2.29980e10	−1.13763
$881$	−1.54995e10	−0.763664	−0.381832	−	0.924232i	$-0.624707\pi$
$881$	−1.54995e10	−0.763664	−0.381832	+	0.924232i	$0.624707\pi$
$882$	2.92212e10	1.43403
$883$	−1.16646e10	−0.570173	−0.285086	−	0.958502i	$-0.592022\pi$
$883$	−1.16646e10	−0.570173	−0.285086	+	0.958502i	$0.592022\pi$
$884$	−4.63802e10	−2.25813
$885$	−4.34916e10	−2.10913
$886$	−4.83830e10	−2.33709
$887$	−7.82168e9	−0.376329	−0.188164	−	0.982138i	$-0.560254\pi$
$887$	−7.82168e9	−0.376329	−0.188164	+	0.982138i	$0.560254\pi$
$888$	−2.30440e10	−1.10436
$889$	−1.42807e10	−0.681701
$890$	2.68225e9	0.127537
$891$	1.12296e9	0.0531856
$892$	3.55526e10	1.67723
$893$	3.43295e10	1.61320
$894$	−3.43853e9	−0.160950
$895$	1.50001e10	0.699381
$896$	−6.80038e10	−3.15831
$897$	1.37294e10	0.635150
$898$	−1.18082e10	−0.544148
$899$	−5.26384e9	−0.241626
$900$	7.50461e10	3.43146
$901$	−5.64246e9	−0.256999
$902$	−4.10796e9	−0.186382
$903$	2.08684e10	0.943152
$904$	−2.56589e10	−1.15517
$905$	2.12336e10	0.952258
$906$	−4.96673e10	−2.21882
$907$	9.52932e9	0.424069	0.212034	−	0.977262i	$-0.431991\pi$
$907$	9.52932e9	0.424069	0.212034	+	0.977262i	$0.431991\pi$
$908$	−2.53767e10	−1.12496
$909$	6.24830e10	2.75923
$910$	−2.92837e10	−1.28819
$911$	2.59809e9	0.113852	0.0569260	−	0.998378i	$-0.481870\pi$
$911$	2.59809e9	0.113852	0.0569260	+	0.998378i	$0.481870\pi$
$912$	−1.46956e11	−6.41513
$913$	3.36140e9	0.146175
$914$	−7.03162e10	−3.04610
$915$	7.87061e10	3.39652
$916$	2.86307e10	1.23083
$917$	2.72721e10	1.16796
$918$	4.20936e10	1.79584
$919$	8.94350e9	0.380105	0.190052	−	0.981774i	$-0.439134\pi$
$919$	8.94350e9	0.380105	0.190052	+	0.981774i	$0.439134\pi$
$920$	−6.56083e10	−2.77780
$921$	−3.11610e10	−1.31432
$922$	−6.88997e10	−2.89507
$923$	1.89682e10	0.793997
$924$	−1.57506e10	−0.656819
$925$	3.90513e9	0.162233
$926$	−6.95635e10	−2.87901
$927$	−4.36842e10	−1.80113
$928$	1.99079e10	0.817726
$929$	2.88780e10	1.18171	0.590856	−	0.806777i	$-0.298790\pi$
$929$	2.88780e10	1.18171	0.590856	+	0.806777i	$0.298790\pi$
$930$	−1.32622e11	−5.40663
$931$	1.20839e10	0.490778
$932$	1.00008e11	4.04648
$933$	6.32158e10	2.54824
$934$	−1.69653e10	−0.681314
$935$	8.20550e9	0.328295
$936$	−9.08001e10	−3.61927
$937$	2.86074e10	1.13603	0.568016	−	0.823018i	$-0.307711\pi$
$937$	2.86074e10	1.13603	0.568016	+	0.823018i	$0.307711\pi$
$938$	1.83394e10	0.725565
$939$	−3.08635e7	−0.00121651
$940$	−1.55432e11	−6.10369
$941$	4.92468e10	1.92670	0.963351	−	0.268246i	$-0.0864438\pi$
$941$	4.92468e10	1.92670	0.963351	+	0.268246i	$0.0864438\pi$
$942$	7.07506e10	2.75773
$943$	−6.93258e9	−0.269218
$944$	−1.03962e11	−4.02230
$945$	1.95921e10	0.755215
$946$	8.82790e9	0.339030
$947$	−4.35016e10	−1.66449	−0.832244	−	0.554410i	$-0.812944\pi$
$947$	−4.35016e10	−1.66449	−0.832244	+	0.554410i	$0.812944\pi$
$948$	−2.04461e10	−0.779436
$949$	3.70556e8	0.0140742
$950$	4.20984e10	1.59306
$951$	−2.59220e10	−0.977318
$952$	7.83805e10	2.94428
$953$	1.40959e10	0.527556	0.263778	−	0.964583i	$-0.415031\pi$
$953$	1.40959e10	0.527556	0.263778	+	0.964583i	$0.415031\pi$
$954$	−1.71668e10	−0.640133
$955$	6.76230e9	0.251236
$956$	1.09137e11	4.03990
$957$	1.65276e9	0.0609563
$958$	−3.12587e10	−1.14866
$959$	−6.95171e8	−0.0254523
$960$	2.64361e11	9.64381
$961$	1.90694e10	0.693113
$962$	−7.34278e9	−0.265918
$963$	−2.26676e10	−0.817925
$964$	5.84011e10	2.09967
$965$	−3.26543e10	−1.16975
$966$	−3.60573e10	−1.28698
$967$	−4.02387e9	−0.143104	−0.0715519	−	0.997437i	$-0.522795\pi$
$967$	−4.02387e9	−0.143104	−0.0715519	+	0.997437i	$0.522795\pi$
$968$	9.50651e10	3.36866
$969$	5.24327e10	1.85127
$970$	1.81262e10	0.637685
$971$	−3.56517e10	−1.24972	−0.624861	−	0.780736i	$-0.714844\pi$
$971$	−3.56517e10	−1.24972	−0.624861	+	0.780736i	$0.714844\pi$
$972$	−9.55546e10	−3.33749
$973$	4.56238e9	0.158780
$974$	−7.82977e10	−2.71514
$975$	2.56663e10	0.886843
$976$	1.88139e11	6.47746
$977$	−3.79562e10	−1.30212	−0.651060	−	0.759026i	$-0.725676\pi$
$977$	−3.79562e10	−1.30212	−0.651060	+	0.759026i	$0.725676\pi$
$978$	1.08781e11	3.71850
$979$	2.95807e8	0.0100755
$980$	−5.47119e10	−1.85691
$981$	−7.90951e10	−2.67490
$982$	1.07012e10	0.360613
$983$	−3.53123e10	−1.18574	−0.592868	−	0.805299i	$-0.702005\pi$
$983$	−3.53123e10	−1.18574	−0.592868	+	0.805299i	$0.702005\pi$
$984$	7.64768e10	2.55886
$985$	−5.58523e10	−1.86215
$986$	−1.27817e10	−0.424638
$987$	−5.49677e10	−1.81969
$988$	−5.83531e10	−1.92493
$989$	1.48979e10	0.489709
$990$	2.49647e10	0.817717
$991$	1.92381e10	0.627920	0.313960	−	0.949436i	$-0.398344\pi$
$991$	1.92381e10	0.627920	0.313960	+	0.949436i	$0.398344\pi$
$992$	−1.76173e11	−5.72993
$993$	3.66391e10	1.18747
$994$	−4.98159e10	−1.60885
$995$	6.80082e10	2.18867
$996$	−9.72500e10	−3.11876
$997$	−1.85218e10	−0.591901	−0.295951	−	0.955203i	$-0.595636\pi$
$997$	−1.85218e10	−0.591901	−0.295951	+	0.955203i	$0.595636\pi$
$998$	9.27788e10	2.95455
$999$	4.91266e9	0.155897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.8.a.b.1.1	✓	10
3.2	odd	2		261.8.a.f.1.10		10
4.3	odd	2		464.8.a.g.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.8.a.b.1.1	✓	10	1.1	even	1	trivial
261.8.a.f.1.10		10	3.2	odd	2
464.8.a.g.1.2		10	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-22.0686 q^{2} +73.8979 q^{3} +359.023 q^{4} +376.792 q^{5} -1630.82 q^{6} +647.379 q^{7} -5098.36 q^{8} +3273.90 q^{9} +O(q^{10})\)	\(q-22.0686 q^{2} +73.8979 q^{3} +359.023 q^{4} +376.792 q^{5} -1630.82 q^{6} +647.379 q^{7} -5098.36 q^{8} +3273.90 q^{9} -8315.26 q^{10} -917.032 q^{11} +26531.1 q^{12} +5439.90 q^{13} -14286.7 q^{14} +27844.1 q^{15} +66558.6 q^{16} -23747.6 q^{17} -72250.4 q^{18} -29878.0 q^{19} +135277. q^{20} +47840.0 q^{21} +20237.6 q^{22} +34152.9 q^{23} -376758. q^{24} +63846.9 q^{25} -120051. q^{26} +80319.7 q^{27} +232424. q^{28} -24389.0 q^{29} -614481. q^{30} +215829. q^{31} -816266. q^{32} -67766.7 q^{33} +524076. q^{34} +243927. q^{35} +1.17541e6 q^{36} +61163.9 q^{37} +659365. q^{38} +401997. q^{39} -1.92102e6 q^{40} -202987. q^{41} -1.05576e6 q^{42} +436213. q^{43} -329236. q^{44} +1.23358e6 q^{45} -753706. q^{46} -1.14899e6 q^{47} +4.91854e6 q^{48} -404443. q^{49} -1.40901e6 q^{50} -1.75490e6 q^{51} +1.95305e6 q^{52} +237602. q^{53} -1.77254e6 q^{54} -345530. q^{55} -3.30057e6 q^{56} -2.20792e6 q^{57} +538231. q^{58} -1.56197e6 q^{59} +9.99668e6 q^{60} +2.82667e6 q^{61} -4.76303e6 q^{62} +2.11945e6 q^{63} +9.49434e6 q^{64} +2.04971e6 q^{65} +1.49552e6 q^{66} -1.28367e6 q^{67} -8.52593e6 q^{68} +2.52383e6 q^{69} -5.38313e6 q^{70} +3.48686e6 q^{71} -1.66915e7 q^{72} +68118.2 q^{73} -1.34980e6 q^{74} +4.71816e6 q^{75} -1.07269e7 q^{76} -593667. q^{77} -8.87151e6 q^{78} -770647. q^{79} +2.50787e7 q^{80} -1.22456e6 q^{81} +4.47963e6 q^{82} -3.66552e6 q^{83} +1.71756e7 q^{84} -8.94789e6 q^{85} -9.62660e6 q^{86} -1.80230e6 q^{87} +4.67535e6 q^{88} -322570. q^{89} -2.72233e7 q^{90} +3.52167e6 q^{91} +1.22617e7 q^{92} +1.59493e7 q^{93} +2.53566e7 q^{94} -1.12578e7 q^{95} -6.03203e7 q^{96} -2.17987e6 q^{97} +8.92550e6 q^{98} -3.00227e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9}+O(q^{10}) \) 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9} + 8496 q^{10} + 7384 q^{11} + 49720 q^{12} + 20820 q^{13} + 50976 q^{14} + 43516 q^{15} + 122082 q^{16} - 11620 q^{17} + 66060 q^{18} + 75068 q^{19} - 42914 q^{20} + 51480 q^{21} - 36950 q^{22} + 62040 q^{23} - 205942 q^{24} + 261022 q^{25} - 201528 q^{26} - 28060 q^{27} - 24980 q^{28} - 243890 q^{29} - 1284894 q^{30} + 200600 q^{31} - 1761460 q^{32} - 1068000 q^{33} - 503932 q^{34} + 107528 q^{35} - 26300 q^{36} - 367740 q^{37} + 766880 q^{38} + 392692 q^{39} - 865000 q^{40} + 932764 q^{41} - 2058060 q^{42} + 1443560 q^{43} - 1325912 q^{44} + 4245684 q^{45} + 1760460 q^{46} - 286960 q^{47} + 3187120 q^{48} + 4713194 q^{49} - 3682652 q^{50} + 1451016 q^{51} + 2560210 q^{52} + 3953220 q^{53} - 3147534 q^{54} + 3981316 q^{55} + 2082464 q^{56} + 2050640 q^{57} + 6712320 q^{59} + 7476756 q^{60} + 1905196 q^{61} - 8048490 q^{62} + 3643800 q^{63} + 8445458 q^{64} + 4667544 q^{65} - 12425580 q^{66} - 2718200 q^{67} - 17699740 q^{68} + 1109064 q^{69} - 30441624 q^{70} + 3447736 q^{71} - 22466840 q^{72} - 2554460 q^{73} - 4214584 q^{74} + 1088084 q^{75} - 8294848 q^{76} - 3967800 q^{77} - 24809970 q^{78} + 4187744 q^{79} - 17715290 q^{80} + 5161402 q^{81} + 7020500 q^{82} + 3498720 q^{83} + 22947224 q^{84} + 1817072 q^{85} - 361638 q^{86} - 1951120 q^{87} + 15118470 q^{88} - 303268 q^{89} - 28959160 q^{90} + 27215080 q^{91} - 10783380 q^{92} + 1097360 q^{93} + 55641726 q^{94} - 8810536 q^{95} - 53327238 q^{96} + 4908620 q^{97} + 40120080 q^{98} - 14408716 q^{99}+O(q^{100}) \) 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9 + 8496 * q^10 + 7384 * q^11 + 49720 * q^12 + 20820 * q^13 + 50976 * q^14 + 43516 * q^15 + 122082 * q^16 - 11620 * q^17 + 66060 * q^18 + 75068 * q^19 - 42914 * q^20 + 51480 * q^21 - 36950 * q^22 + 62040 * q^23 - 205942 * q^24 + 261022 * q^25 - 201528 * q^26 - 28060 * q^27 - 24980 * q^28 - 243890 * q^29 - 1284894 * q^30 + 200600 * q^31 - 1761460 * q^32 - 1068000 * q^33 - 503932 * q^34 + 107528 * q^35 - 26300 * q^36 - 367740 * q^37 + 766880 * q^38 + 392692 * q^39 - 865000 * q^40 + 932764 * q^41 - 2058060 * q^42 + 1443560 * q^43 - 1325912 * q^44 + 4245684 * q^45 + 1760460 * q^46 - 286960 * q^47 + 3187120 * q^48 + 4713194 * q^49 - 3682652 * q^50 + 1451016 * q^51 + 2560210 * q^52 + 3953220 * q^53 - 3147534 * q^54 + 3981316 * q^55 + 2082464 * q^56 + 2050640 * q^57 + 6712320 * q^59 + 7476756 * q^60 + 1905196 * q^61 - 8048490 * q^62 + 3643800 * q^63 + 8445458 * q^64 + 4667544 * q^65 - 12425580 * q^66 - 2718200 * q^67 - 17699740 * q^68 + 1109064 * q^69 - 30441624 * q^70 + 3447736 * q^71 - 22466840 * q^72 - 2554460 * q^73 - 4214584 * q^74 + 1088084 * q^75 - 8294848 * q^76 - 3967800 * q^77 - 24809970 * q^78 + 4187744 * q^79 - 17715290 * q^80 + 5161402 * q^81 + 7020500 * q^82 + 3498720 * q^83 + 22947224 * q^84 + 1817072 * q^85 - 361638 * q^86 - 1951120 * q^87 + 15118470 * q^88 - 303268 * q^89 - 28959160 * q^90 + 27215080 * q^91 - 10783380 * q^92 + 1097360 * q^93 + 55641726 * q^94 - 8810536 * q^95 - 53327238 * q^96 + 4908620 * q^97 + 40120080 * q^98 - 14408716 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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