LMFDB - Embedded newform 29.8.a.b.1.6

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			1.6
Root			$-1.69492$ 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)

$f(q)$	$=$	$q+1.69492 q^{2} +56.8671 q^{3} -125.127 q^{4} +194.958 q^{5} +96.3850 q^{6} +1221.62 q^{7} -429.029 q^{8} +1046.87 q^{9} +O(q^{10})$	\(q+1.69492 q^{2} +56.8671 q^{3} -125.127 q^{4} +194.958 q^{5} +96.3850 q^{6} +1221.62 q^{7} -429.029 q^{8} +1046.87 q^{9} +330.438 q^{10} +3778.54 q^{11} -7115.63 q^{12} -481.945 q^{13} +2070.54 q^{14} +11086.7 q^{15} +15289.1 q^{16} +24701.8 q^{17} +1774.36 q^{18} +6949.17 q^{19} -24394.6 q^{20} +69469.9 q^{21} +6404.30 q^{22} -50863.9 q^{23} -24397.7 q^{24} -40116.2 q^{25} -816.856 q^{26} -64835.9 q^{27} -152858. q^{28} -24389.0 q^{29} +18791.1 q^{30} -101452. q^{31} +80829.5 q^{32} +214874. q^{33} +41867.4 q^{34} +238165. q^{35} -130992. q^{36} -396099. q^{37} +11778.3 q^{38} -27406.8 q^{39} -83642.9 q^{40} -164861. q^{41} +117746. q^{42} -736832. q^{43} -472798. q^{44} +204096. q^{45} -86210.1 q^{46} +555959. q^{47} +869448. q^{48} +668808. q^{49} -67993.7 q^{50} +1.40472e6 q^{51} +60304.5 q^{52} +1.01769e6 q^{53} -109891. q^{54} +736657. q^{55} -524110. q^{56} +395179. q^{57} -41337.3 q^{58} -1.99379e6 q^{59} -1.38725e6 q^{60} +2.38696e6 q^{61} -171953. q^{62} +1.27888e6 q^{63} -1.82001e6 q^{64} -93959.2 q^{65} +364194. q^{66} +2.69917e6 q^{67} -3.09087e6 q^{68} -2.89248e6 q^{69} +403669. q^{70} -5.63766e6 q^{71} -449138. q^{72} +1.61311e6 q^{73} -671354. q^{74} -2.28130e6 q^{75} -869530. q^{76} +4.61593e6 q^{77} -46452.3 q^{78} +2.41702e6 q^{79} +2.98074e6 q^{80} -5.97654e6 q^{81} -279426. q^{82} +5.27756e6 q^{83} -8.69258e6 q^{84} +4.81582e6 q^{85} -1.24887e6 q^{86} -1.38693e6 q^{87} -1.62110e6 q^{88} -406995. q^{89} +345926. q^{90} -588753. q^{91} +6.36446e6 q^{92} -5.76930e6 q^{93} +942304. q^{94} +1.35480e6 q^{95} +4.59654e6 q^{96} +8.83259e6 q^{97} +1.13357e6 q^{98} +3.95564e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.69492	0.149811	0.0749054	−	0.997191i	$-0.476135\pi$
$2$	1.69492	0.149811	0.0749054	+	0.997191i	$0.476135\pi$
$3$	56.8671	1.21601	0.608005	−	0.793933i	$-0.291970\pi$
$3$	56.8671	1.21601	0.608005	+	0.793933i	$0.291970\pi$
$4$	−125.127	−0.977557
$5$	194.958	0.697504	0.348752	−	0.937215i	$-0.386606\pi$
$5$	194.958	0.697504	0.348752	+	0.937215i	$0.386606\pi$
$6$	96.3850	0.182171
$7$	1221.62	1.34615	0.673073	−	0.739576i	$-0.264974\pi$
$7$	1221.62	1.34615	0.673073	+	0.739576i	$0.264974\pi$
$8$	−429.029	−0.296259
$9$	1046.87	0.478679
$10$	330.438	0.104494
$11$	3778.54	0.855951	0.427976	−	0.903790i	$-0.359227\pi$
$11$	3778.54	0.855951	0.427976	+	0.903790i	$0.359227\pi$
$12$	−7115.63	−1.18872
$13$	−481.945	−0.0608409	−0.0304205	−	0.999537i	$-0.509685\pi$
$13$	−481.945	−0.0608409	−0.0304205	+	0.999537i	$0.509685\pi$
$14$	2070.54	0.201667
$15$	11086.7	0.848172
$16$	15289.1	0.933174
$17$	24701.8	1.21943	0.609715	−	0.792621i	$-0.291284\pi$
$17$	24701.8	1.21943	0.609715	+	0.792621i	$0.291284\pi$
$18$	1774.36	0.0717113
$19$	6949.17	0.232432	0.116216	−	0.993224i	$-0.462924\pi$
$19$	6949.17	0.232432	0.116216	+	0.993224i	$0.462924\pi$
$20$	−24394.6	−0.681850
$21$	69469.9	1.63693
$22$	6404.30	0.128231
$23$	−50863.9	−0.871690	−0.435845	−	0.900022i	$-0.643550\pi$
$23$	−50863.9	−0.871690	−0.435845	+	0.900022i	$0.643550\pi$
$24$	−24397.7	−0.360254
$25$	−40116.2	−0.513488
$26$	−816.856	−0.00911463
$27$	−64835.9	−0.633931
$28$	−152858.	−1.31593
$29$	−24389.0	−0.185695
$29$	−24389.0	−0.185695
$30$	18791.1	0.127065
$31$	−101452.	−0.611640	−0.305820	−	0.952089i	$-0.598931\pi$
$31$	−101452.	−0.611640	−0.305820	+	0.952089i	$0.598931\pi$
$32$	80829.5	0.436059
$33$	214874.	1.04085
$34$	41867.4	0.182684
$35$	238165.	0.938943
$36$	−130992.	−0.467936
$37$	−396099.	−1.28558	−0.642788	−	0.766044i	$-0.722222\pi$
$37$	−396099.	−1.28558	−0.642788	+	0.766044i	$0.722222\pi$
$38$	11778.3	0.0348208
$39$	−27406.8	−0.0739831
$40$	−83642.9	−0.206642
$41$	−164861.	−0.373573	−0.186786	−	0.982401i	$-0.559807\pi$
$41$	−164861.	−0.373573	−0.186786	+	0.982401i	$0.559807\pi$
$42$	117746.	0.245229
$43$	−736832.	−1.41328	−0.706641	−	0.707572i	$-0.749790\pi$
$43$	−736832.	−1.41328	−0.706641	+	0.707572i	$0.749790\pi$
$44$	−472798.	−0.836741
$45$	204096.	0.333881
$46$	−86210.1	−0.130589
$47$	555959.	0.781088	0.390544	−	0.920584i	$-0.372287\pi$
$47$	555959.	0.781088	0.390544	+	0.920584i	$0.372287\pi$
$48$	869448.	1.13475
$49$	668808.	0.812111
$50$	−67993.7	−0.0769261
$51$	1.40472e6	1.48284
$52$	60304.5	0.0594755
$53$	1.01769e6	0.938966	0.469483	−	0.882942i	$-0.344440\pi$
$53$	1.01769e6	0.938966	0.469483	+	0.882942i	$0.344440\pi$
$54$	−109891.	−0.0949698
$55$	736657.	0.597030
$56$	−524110.	−0.398809
$57$	395179.	0.282639
$58$	−41337.3	−0.0278192
$59$	−1.99379e6	−1.26386	−0.631928	−	0.775027i	$-0.717736\pi$
$59$	−1.99379e6	−1.26386	−0.631928	+	0.775027i	$0.717736\pi$
$60$	−1.38725e6	−0.829136
$61$	2.38696e6	1.34645	0.673226	−	0.739437i	$-0.264908\pi$
$61$	2.38696e6	1.34645	0.673226	+	0.739437i	$0.264908\pi$
$62$	−171953.	−0.0916303
$63$	1.27888e6	0.644372
$64$	−1.82001e6	−0.867847
$65$	−93959.2	−0.0424368
$66$	364194.	0.155930
$67$	2.69917e6	1.09640	0.548199	−	0.836348i	$-0.315314\pi$
$67$	2.69917e6	1.09640	0.548199	+	0.836348i	$0.315314\pi$
$68$	−3.09087e6	−1.19206
$69$	−2.89248e6	−1.05998
$70$	403669.	0.140664
$71$	−5.63766e6	−1.86937	−0.934684	−	0.355479i	$-0.884318\pi$
$71$	−5.63766e6	−1.86937	−0.934684	+	0.355479i	$0.884318\pi$
$72$	−449138.	−0.141813
$73$	1.61311e6	0.485326	0.242663	−	0.970111i	$-0.421979\pi$
$73$	1.61311e6	0.485326	0.242663	+	0.970111i	$0.421979\pi$
$74$	−671354.	−0.192593
$75$	−2.28130e6	−0.624406
$76$	−869530.	−0.227215
$77$	4.61593e6	1.15224
$78$	−46452.3	−0.0110835
$79$	2.41702e6	0.551551	0.275775	−	0.961222i	$-0.411065\pi$
$79$	2.41702e6	0.551551	0.275775	+	0.961222i	$0.411065\pi$
$80$	2.98074e6	0.650893
$81$	−5.97654e6	−1.24955
$82$	−279426.	−0.0559652
$83$	5.27756e6	1.01312	0.506559	−	0.862205i	$-0.330917\pi$
$83$	5.27756e6	1.01312	0.506559	+	0.862205i	$0.330917\pi$
$84$	−8.69258e6	−1.60019
$85$	4.81582e6	0.850558
$86$	−1.24887e6	−0.211725
$87$	−1.38693e6	−0.225807
$88$	−1.62110e6	−0.253584
$89$	−406995.	−0.0611961	−0.0305980	−	0.999532i	$-0.509741\pi$
$89$	−406995.	−0.0611961	−0.0305980	+	0.999532i	$0.509741\pi$
$90$	345926.	0.0500189
$91$	−588753.	−0.0819008
$92$	6.36446e6	0.852127
$93$	−5.76930e6	−0.743760
$94$	942304.	0.117016
$95$	1.35480e6	0.162122
$96$	4.59654e6	0.530252
$97$	8.83259e6	0.982623	0.491312	−	0.870984i	$-0.336518\pi$
$97$	8.83259e6	0.982623	0.491312	+	0.870984i	$0.336518\pi$
$98$	1.13357e6	0.121663
$99$	3.95564e6	0.409726
$100$	5.01964e6	0.501964
$101$	−8.58596e6	−0.829209	−0.414605	−	0.910002i	$-0.636080\pi$
$101$	−8.58596e6	−0.829209	−0.414605	+	0.910002i	$0.636080\pi$
$102$	2.38088e6	0.222145
$103$	−2.18840e7	−1.97332	−0.986658	−	0.162808i	$-0.947945\pi$
$103$	−2.18840e7	−1.97332	−0.986658	+	0.162808i	$0.947945\pi$
$104$	206769.	0.0180247
$105$	1.35437e7	1.14176
$106$	1.72490e6	0.140667
$107$	2.81023e6	0.221768	0.110884	−	0.993833i	$-0.464632\pi$
$107$	2.81023e6	0.221768	0.110884	+	0.993833i	$0.464632\pi$
$108$	8.11274e6	0.619704
$109$	2.32540e7	1.71991	0.859955	−	0.510370i	$-0.170492\pi$
$109$	2.32540e7	1.71991	0.859955	+	0.510370i	$0.170492\pi$
$110$	1.24857e6	0.0894415
$111$	−2.25250e7	−1.56327
$112$	1.86775e7	1.25619
$113$	−1.30285e7	−0.849417	−0.424708	−	0.905330i	$-0.639623\pi$
$113$	−1.30285e7	−0.849417	−0.424708	+	0.905330i	$0.639623\pi$
$114$	669795.	0.0423424
$115$	−9.91634e6	−0.608008
$116$	3.05173e6	0.181528
$117$	−504534.	−0.0291233
$118$	−3.37931e6	−0.189339
$119$	3.01761e7	1.64153
$120$	−4.75653e6	−0.251279
$121$	−5.20984e6	−0.267347
$122$	4.04570e6	0.201713
$123$	−9.37519e6	−0.454268
$124$	1.26944e7	0.597913
$125$	−2.30521e7	−1.05566
$126$	2.16759e6	0.0965339
$127$	3.57140e7	1.54712	0.773562	−	0.633721i	$-0.218473\pi$
$127$	3.57140e7	1.54712	0.773562	+	0.633721i	$0.218473\pi$
$128$	−1.34309e7	−0.566072
$129$	−4.19015e7	−1.71856
$130$	−159253.	−0.00635749
$131$	−5.07814e7	−1.97358	−0.986791	−	0.161997i	$-0.948206\pi$
$131$	−5.07814e7	−1.97358	−0.986791	+	0.161997i	$0.948206\pi$
$132$	−2.68867e7	−1.01749
$133$	8.48923e6	0.312887
$134$	4.57487e6	0.164252
$135$	−1.26403e7	−0.442170
$136$	−1.05978e7	−0.361268
$137$	1.65213e7	0.548936	0.274468	−	0.961596i	$-0.411498\pi$
$137$	1.65213e7	0.548936	0.274468	+	0.961596i	$0.411498\pi$
$138$	−4.90252e6	−0.158797
$139$	−7.80856e6	−0.246615	−0.123307	−	0.992369i	$-0.539350\pi$
$139$	−7.80856e6	−0.246615	−0.123307	+	0.992369i	$0.539350\pi$
$140$	−2.98009e7	−0.917870
$141$	3.16158e7	0.949811
$142$	−9.55537e6	−0.280052
$143$	−1.82105e6	−0.0520769
$144$	1.60057e7	0.446691
$145$	−4.75484e6	−0.129523
$146$	2.73408e6	0.0727071
$147$	3.80332e7	0.987535
$148$	4.95628e7	1.25672
$149$	−5.62280e7	−1.39252	−0.696259	−	0.717791i	$-0.745153\pi$
$149$	−5.62280e7	−1.39252	−0.696259	+	0.717791i	$0.745153\pi$
$150$	−3.86661e6	−0.0935428
$151$	4.24431e7	1.00320	0.501600	−	0.865100i	$-0.332745\pi$
$151$	4.24431e7	1.00320	0.501600	+	0.865100i	$0.332745\pi$
$152$	−2.98140e6	−0.0688600
$153$	2.58596e7	0.583716
$154$	7.82361e6	0.172617
$155$	−1.97790e7	−0.426621
$156$	3.42934e6	0.0723227
$157$	−5.65237e7	−1.16569	−0.582843	−	0.812585i	$-0.698060\pi$
$157$	−5.65237e7	−1.16569	−0.582843	+	0.812585i	$0.698060\pi$
$158$	4.09665e6	0.0826282
$159$	5.78731e7	1.14179
$160$	1.57584e7	0.304153
$161$	−6.21363e7	−1.17342
$162$	−1.01297e7	−0.187195
$163$	7.27759e7	1.31623	0.658113	−	0.752919i	$-0.271355\pi$
$163$	7.27759e7	1.31623	0.658113	+	0.752919i	$0.271355\pi$
$164$	2.06286e7	0.365189
$165$	4.18916e7	0.725994
$166$	8.94502e6	0.151776
$167$	6.10423e7	1.01420	0.507099	−	0.861888i	$-0.330718\pi$
$167$	6.10423e7	1.01420	0.507099	+	0.861888i	$0.330718\pi$
$168$	−2.98046e7	−0.484955
$169$	−6.25162e7	−0.996298
$170$	8.16241e6	0.127423
$171$	7.27488e6	0.111260
$172$	9.21978e7	1.38156
$173$	−3.69745e7	−0.542926	−0.271463	−	0.962449i	$-0.587507\pi$
$173$	−3.69745e7	−0.542926	−0.271463	+	0.962449i	$0.587507\pi$
$174$	−2.35073e6	−0.0338284
$175$	−4.90067e7	−0.691230
$176$	5.77705e7	0.798751
$177$	−1.13381e8	−1.53686
$178$	−689822.	−0.00916784
$179$	3.93463e7	0.512764	0.256382	−	0.966576i	$-0.417469\pi$
$179$	3.93463e7	0.512764	0.256382	+	0.966576i	$0.417469\pi$
$180$	−2.55380e7	−0.326387
$181$	−1.38709e7	−0.173872	−0.0869361	−	0.996214i	$-0.527708\pi$
$181$	−1.38709e7	−0.173872	−0.0869361	+	0.996214i	$0.527708\pi$
$182$	−997887.	−0.0122696
$183$	1.35740e8	1.63730
$184$	2.18221e7	0.258247
$185$	−7.72228e7	−0.896694
$186$	−9.77848e6	−0.111423
$187$	9.33365e7	1.04377
$188$	−6.95656e7	−0.763558
$189$	−7.92047e7	−0.853365
$190$	2.29627e6	0.0242876
$191$	7.69464e7	0.799045	0.399523	−	0.916723i	$-0.369176\pi$
$191$	7.69464e7	0.799045	0.399523	+	0.916723i	$0.369176\pi$
$192$	−1.03499e8	−1.05531
$193$	3.53821e7	0.354269	0.177134	−	0.984187i	$-0.443317\pi$
$193$	3.53821e7	0.354269	0.177134	+	0.984187i	$0.443317\pi$
$194$	1.49705e7	0.147208
$195$	−5.34319e6	−0.0516035
$196$	−8.36862e7	−0.793885
$197$	4.05030e7	0.377447	0.188723	−	0.982030i	$-0.439565\pi$
$197$	4.05030e7	0.377447	0.188723	+	0.982030i	$0.439565\pi$
$198$	6.70448e6	0.0613814
$199$	5.15925e7	0.464088	0.232044	−	0.972705i	$-0.425459\pi$
$199$	5.15925e7	0.464088	0.232044	+	0.972705i	$0.425459\pi$
$200$	1.72111e7	0.152126
$201$	1.53494e8	1.33323
$202$	−1.45525e7	−0.124225
$203$	−2.97940e7	−0.249973
$204$	−1.75769e8	−1.44956
$205$	−3.21411e7	−0.260569
$206$	−3.70916e7	−0.295624
$207$	−5.32479e7	−0.417260
$208$	−7.36852e6	−0.0567752
$209$	2.62577e7	0.198950
$210$	2.29555e7	0.171049
$211$	3.57068e7	0.261675	0.130837	−	0.991404i	$-0.458233\pi$
$211$	3.57068e7	0.261675	0.130837	+	0.991404i	$0.458233\pi$
$212$	−1.27341e8	−0.917892
$213$	−3.20598e8	−2.27317
$214$	4.76311e6	0.0332233
$215$	−1.43652e8	−0.985770
$216$	2.78165e7	0.187808
$217$	−1.23936e8	−0.823357
$218$	3.94136e7	0.257661
$219$	9.17329e7	0.590161
$220$	−9.21759e7	−0.583630
$221$	−1.19049e7	−0.0741913
$222$	−3.81780e7	−0.234195
$223$	−1.15795e8	−0.699235	−0.349618	−	0.936892i	$-0.613689\pi$
$223$	−1.15795e8	−0.699235	−0.349618	+	0.936892i	$0.613689\pi$
$224$	9.87429e7	0.586999
$225$	−4.19965e7	−0.245796
$226$	−2.20823e7	−0.127252
$227$	2.14422e8	1.21669	0.608344	−	0.793673i	$-0.291834\pi$
$227$	2.14422e8	1.21669	0.608344	+	0.793673i	$0.291834\pi$
$228$	−4.94477e7	−0.276296
$229$	3.56088e8	1.95945	0.979724	−	0.200352i	$-0.0642087\pi$
$229$	3.56088e8	1.95945	0.979724	+	0.200352i	$0.0642087\pi$
$230$	−1.68074e7	−0.0910861
$231$	2.62495e8	1.40113
$232$	1.04636e7	0.0550140
$233$	1.71224e8	0.886786	0.443393	−	0.896327i	$-0.353775\pi$
$233$	1.71224e8	0.886786	0.443393	+	0.896327i	$0.353775\pi$
$234$	−855143.	−0.00436298
$235$	1.08389e8	0.544812
$236$	2.49478e8	1.23549
$237$	1.37449e8	0.670691
$238$	5.11460e7	0.245919
$239$	−8.64239e7	−0.409488	−0.204744	−	0.978816i	$-0.565636\pi$
$239$	−8.64239e7	−0.409488	−0.204744	+	0.978816i	$0.565636\pi$
$240$	1.69506e8	0.791492
$241$	−1.85574e7	−0.0853998	−0.0426999	−	0.999088i	$-0.513596\pi$
$241$	−1.85574e7	−0.0853998	−0.0426999	+	0.999088i	$0.513596\pi$
$242$	−8.83024e6	−0.0400515
$243$	−1.98072e8	−0.885528
$244$	−2.98674e8	−1.31623
$245$	1.30390e8	0.566451
$246$	−1.58902e7	−0.0680543
$247$	−3.34912e6	−0.0141414
$248$	4.35260e7	0.181204
$249$	3.00120e8	1.23196
$250$	−3.90714e7	−0.158150
$251$	−1.19889e8	−0.478544	−0.239272	−	0.970953i	$-0.576909\pi$
$251$	−1.19889e8	−0.478544	−0.239272	+	0.970953i	$0.576909\pi$
$252$	−1.60022e8	−0.629910
$253$	−1.92191e8	−0.746125
$254$	6.05322e7	0.231776
$255$	2.73862e8	1.03429
$256$	2.10197e8	0.783044
$257$	−1.29768e8	−0.476873	−0.238436	−	0.971158i	$-0.576635\pi$
$257$	−1.29768e8	−0.476873	−0.238436	+	0.971158i	$0.576635\pi$
$258$	−7.10196e7	−0.257460
$259$	−4.83882e8	−1.73057
$260$	1.17569e7	0.0414844
$261$	−2.55321e7	−0.0888884
$262$	−8.60702e7	−0.295664
$263$	1.94163e8	0.658144	0.329072	−	0.944305i	$-0.393264\pi$
$263$	1.94163e8	0.658144	0.329072	+	0.944305i	$0.393264\pi$
$264$	−9.21875e7	−0.308360
$265$	1.98407e8	0.654932
$266$	1.43885e7	0.0468739
$267$	−2.31446e7	−0.0744150
$268$	−3.37740e8	−1.07179
$269$	−4.07419e8	−1.27617	−0.638085	−	0.769966i	$-0.720273\pi$
$269$	−4.07419e8	−1.27617	−0.638085	+	0.769966i	$0.720273\pi$
$270$	−2.14242e7	−0.0662418
$271$	3.87915e8	1.18398	0.591989	−	0.805946i	$-0.298343\pi$
$271$	3.87915e8	1.18398	0.591989	+	0.805946i	$0.298343\pi$
$272$	3.77668e8	1.13794
$273$	−3.34807e7	−0.0995922
$274$	2.80022e7	0.0822365
$275$	−1.51581e8	−0.439521
$276$	3.61929e8	1.03619
$277$	−2.85589e8	−0.807351	−0.403676	−	0.914902i	$-0.632268\pi$
$277$	−2.85589e8	−0.807351	−0.403676	+	0.914902i	$0.632268\pi$
$278$	−1.32348e7	−0.0369456
$279$	−1.06207e8	−0.292779
$280$	−1.02180e8	−0.278171
$281$	1.54293e8	0.414834	0.207417	−	0.978253i	$-0.433494\pi$
$281$	1.54293e8	0.414834	0.207417	+	0.978253i	$0.433494\pi$
$282$	5.35861e7	0.142292
$283$	−4.90133e8	−1.28547	−0.642734	−	0.766090i	$-0.722200\pi$
$283$	−4.90133e8	−1.28547	−0.642734	+	0.766090i	$0.722200\pi$
$284$	7.05425e8	1.82741
$285$	7.70435e7	0.197142
$286$	−3.08652e6	−0.00780168
$287$	−2.01398e8	−0.502884
$288$	8.46181e7	0.208732
$289$	1.99839e8	0.487010
$290$	−8.05905e6	−0.0194040
$291$	5.02284e8	1.19488
$292$	−2.01844e8	−0.474434
$293$	−7.85953e8	−1.82541	−0.912704	−	0.408621i	$-0.866010\pi$
$293$	−7.85953e8	−1.82541	−0.912704	+	0.408621i	$0.866010\pi$
$294$	6.44631e7	0.147943
$295$	−3.88706e8	−0.881545
$296$	1.69938e8	0.380864
$297$	−2.44985e8	−0.542614
$298$	−9.53017e7	−0.208614
$299$	2.45136e7	0.0530345
$300$	2.85452e8	0.610393
$301$	−9.00127e8	−1.90249
$302$	7.19374e7	0.150290
$303$	−4.88259e8	−1.00833
$304$	1.06247e8	0.216899
$305$	4.65358e8	0.939155
$306$	4.38298e7	0.0874469
$307$	3.88507e8	0.766328	0.383164	−	0.923680i	$-0.374834\pi$
$307$	3.88507e8	0.766328	0.383164	+	0.923680i	$0.374834\pi$
$308$	−5.77578e8	−1.12638
$309$	−1.24448e9	−2.39957
$310$	−3.35237e7	−0.0639125
$311$	2.89734e8	0.546183	0.273092	−	0.961988i	$-0.411954\pi$
$311$	2.89734e8	0.546183	0.273092	+	0.961988i	$0.411954\pi$
$312$	1.17583e7	0.0219182
$313$	7.85832e8	1.44852	0.724260	−	0.689527i	$-0.242181\pi$
$313$	7.85832e8	1.44852	0.724260	+	0.689527i	$0.242181\pi$
$314$	−9.58029e7	−0.174632
$315$	2.49328e8	0.449452
$316$	−3.02435e8	−0.539172
$317$	−8.53153e8	−1.50425	−0.752124	−	0.659021i	$-0.770971\pi$
$317$	−8.53153e8	−1.50425	−0.752124	+	0.659021i	$0.770971\pi$
$318$	9.80900e7	0.171053
$319$	−9.21547e7	−0.158946
$320$	−3.54826e8	−0.605327
$321$	1.59810e8	0.269672
$322$	−1.05316e8	−0.175792
$323$	1.71657e8	0.283434
$324$	7.47828e8	1.22150
$325$	1.93338e7	0.0312411
$326$	1.23349e8	0.197185
$327$	1.32239e9	2.09143
$328$	7.07303e7	0.110674
$329$	6.79170e8	1.05146
$330$	7.10027e7	0.108762
$331$	9.09954e8	1.37918	0.689591	−	0.724199i	$-0.257790\pi$
$331$	9.09954e8	1.37918	0.689591	+	0.724199i	$0.257790\pi$
$332$	−6.60367e8	−0.990380
$333$	−4.14664e8	−0.615378
$334$	1.03462e8	0.151938
$335$	5.26226e8	0.764742
$336$	1.06213e9	1.52754
$337$	8.09734e8	1.15249	0.576246	−	0.817276i	$-0.304517\pi$
$337$	8.09734e8	1.15249	0.576246	+	0.817276i	$0.304517\pi$
$338$	−1.05960e8	−0.149256
$339$	−7.40895e8	−1.03290
$340$	−6.02590e8	−0.831468
$341$	−3.83341e8	−0.523534
$342$	1.23303e7	0.0166680
$343$	−1.89027e8	−0.252926
$344$	3.16123e8	0.418698
$345$	−5.63914e8	−0.739343
$346$	−6.26686e7	−0.0813362
$347$	1.27779e9	1.64175	0.820875	−	0.571107i	$-0.193486\pi$
$347$	1.27779e9	1.64175	0.820875	+	0.571107i	$0.193486\pi$
$348$	1.73543e8	0.220739
$349$	−2.17985e8	−0.274496	−0.137248	−	0.990537i	$-0.543826\pi$
$349$	−2.17985e8	−0.274496	−0.137248	+	0.990537i	$0.543826\pi$
$350$	−8.30623e7	−0.103554
$351$	3.12473e7	0.0385690
$352$	3.05417e8	0.373245
$353$	4.59736e8	0.556285	0.278142	−	0.960540i	$-0.410281\pi$
$353$	4.59736e8	0.556285	0.278142	+	0.960540i	$0.410281\pi$
$354$	−1.92172e8	−0.230238
$355$	−1.09911e9	−1.30389
$356$	5.09261e7	0.0598226
$357$	1.71603e9	1.99612
$358$	6.66886e7	0.0768176
$359$	−6.79111e8	−0.774659	−0.387329	−	0.921941i	$-0.626602\pi$
$359$	−6.79111e8	−0.774659	−0.387329	+	0.921941i	$0.626602\pi$
$360$	−8.75633e7	−0.0989153
$361$	−8.45581e8	−0.945976
$362$	−2.35100e7	−0.0260479
$363$	−2.96269e8	−0.325097
$364$	7.36690e7	0.0800627
$365$	3.14489e8	0.338517
$366$	2.30067e8	0.245285
$367$	−1.09300e9	−1.15422	−0.577110	−	0.816667i	$-0.695819\pi$
$367$	−1.09300e9	−1.15422	−0.577110	+	0.816667i	$0.695819\pi$
$368$	−7.77664e8	−0.813439
$369$	−1.72588e8	−0.178821
$370$	−1.30886e8	−0.134334
$371$	1.24323e9	1.26399
$372$	7.21897e8	0.727067
$373$	−5.71528e7	−0.0570239	−0.0285120	−	0.999593i	$-0.509077\pi$
$373$	−5.71528e7	−0.0570239	−0.0285120	+	0.999593i	$0.509077\pi$
$374$	1.58198e8	0.156369
$375$	−1.31091e9	−1.28370
$376$	−2.38523e8	−0.231405
$377$	1.17542e7	0.0112979
$378$	−1.34245e8	−0.127843
$379$	−6.60510e7	−0.0623221	−0.0311611	−	0.999514i	$-0.509920\pi$
$379$	−6.60510e7	−0.0623221	−0.0311611	+	0.999514i	$0.509920\pi$
$380$	−1.69522e8	−0.158483
$381$	2.03095e9	1.88132
$382$	1.30418e8	0.119706
$383$	2.83552e7	0.0257892	0.0128946	−	0.999917i	$-0.495895\pi$
$383$	2.83552e7	0.0257892	0.0128946	+	0.999917i	$0.495895\pi$
$384$	−7.63779e8	−0.688349
$385$	8.99914e8	0.803690
$386$	5.99697e7	0.0530733
$387$	−7.71368e8	−0.676508
$388$	−1.10520e9	−0.960570
$389$	−2.07510e9	−1.78738	−0.893689	−	0.448687i	$-0.851892\pi$
$389$	−2.07510e9	−1.78738	−0.893689	+	0.448687i	$0.851892\pi$
$390$	−9.05626e6	−0.00773077
$391$	−1.25643e9	−1.06297
$392$	−2.86938e8	−0.240596
$393$	−2.88779e9	−2.39989
$394$	6.86493e7	0.0565456
$395$	4.71218e8	0.384709
$396$	−4.94958e8	−0.400530
$397$	1.81933e9	1.45930	0.729648	−	0.683822i	$-0.239684\pi$
$397$	1.81933e9	1.45930	0.729648	+	0.683822i	$0.239684\pi$
$398$	8.74449e7	0.0695254
$399$	4.82758e8	0.380473
$400$	−6.13342e8	−0.479174
$401$	1.38849e9	1.07532	0.537659	−	0.843162i	$-0.319309\pi$
$401$	1.38849e9	1.07532	0.537659	+	0.843162i	$0.319309\pi$
$402$	2.60159e8	0.199732
$403$	4.88944e7	0.0372127
$404$	1.07434e9	0.810599
$405$	−1.16518e9	−0.871563
$406$	−5.04984e7	−0.0374487
$407$	−1.49667e9	−1.10039
$408$	−6.02666e8	−0.439305
$409$	1.31400e9	0.949649	0.474824	−	0.880081i	$-0.342512\pi$
$409$	1.31400e9	0.949649	0.474824	+	0.880081i	$0.342512\pi$
$410$	−5.44764e7	−0.0390360
$411$	9.39517e8	0.667511
$412$	2.73829e9	1.92903
$413$	−2.43565e9	−1.70134
$414$	−9.02508e7	−0.0625100
$415$	1.02890e9	0.706654
$416$	−3.89554e7	−0.0265302
$417$	−4.44050e8	−0.299886
$418$	4.45045e7	0.0298049
$419$	2.37736e9	1.57887	0.789433	−	0.613837i	$-0.210375\pi$
$419$	2.37736e9	1.57887	0.789433	+	0.613837i	$0.210375\pi$
$420$	−1.69469e9	−1.11614
$421$	7.37940e8	0.481985	0.240993	−	0.970527i	$-0.422527\pi$
$421$	7.37940e8	0.481985	0.240993	+	0.970527i	$0.422527\pi$
$422$	6.05200e7	0.0392017
$423$	5.82017e8	0.373891
$424$	−4.36619e8	−0.278177
$425$	−9.90943e8	−0.626163
$426$	−5.43386e8	−0.340545
$427$	2.91595e9	1.81252
$428$	−3.51637e8	−0.216791
$429$	−1.03558e8	−0.0633260
$430$	−2.43477e8	−0.147679
$431$	−6.15426e8	−0.370259	−0.185129	−	0.982714i	$-0.559270\pi$
$431$	−6.15426e8	−0.370259	−0.185129	+	0.982714i	$0.559270\pi$
$432$	−9.91284e8	−0.591568
$433$	6.59973e8	0.390678	0.195339	−	0.980736i	$-0.437419\pi$
$433$	6.59973e8	0.390678	0.195339	+	0.980736i	$0.437419\pi$
$434$	−2.10061e8	−0.123348
$435$	−2.70394e8	−0.157502
$436$	−2.90971e9	−1.68131
$437$	−3.53462e8	−0.202608
$438$	1.55480e8	0.0884125
$439$	1.81323e9	1.02288	0.511442	−	0.859318i	$-0.329111\pi$
$439$	1.81323e9	1.02288	0.511442	+	0.859318i	$0.329111\pi$
$440$	−3.16048e8	−0.176876
$441$	7.00156e8	0.388740
$442$	−2.01778e7	−0.0111147
$443$	2.64127e9	1.44344	0.721722	−	0.692183i	$-0.243351\pi$
$443$	2.64127e9	1.44344	0.721722	+	0.692183i	$0.243351\pi$
$444$	2.81849e9	1.52819
$445$	−7.93470e7	−0.0426845
$446$	−1.96263e8	−0.104753
$447$	−3.19753e9	−1.69331
$448$	−2.22336e9	−1.16825
$449$	8.21345e8	0.428217	0.214108	−	0.976810i	$-0.431315\pi$
$449$	8.21345e8	0.428217	0.214108	+	0.976810i	$0.431315\pi$
$450$	−7.11806e7	−0.0368229
$451$	−6.22934e8	−0.319760
$452$	1.63022e9	0.830353
$453$	2.41362e9	1.21990
$454$	3.63428e8	0.182273
$455$	−1.14782e8	−0.0571262
$456$	−1.69543e8	−0.0837344
$457$	1.52878e9	0.749268	0.374634	−	0.927173i	$-0.377768\pi$
$457$	1.52878e9	0.749268	0.374634	+	0.927173i	$0.377768\pi$
$458$	6.03540e8	0.293547
$459$	−1.60156e9	−0.773035
$460$	1.24080e9	0.594362
$461$	1.88695e9	0.897030	0.448515	−	0.893775i	$-0.351953\pi$
$461$	1.88695e9	0.897030	0.448515	+	0.893775i	$0.351953\pi$
$462$	4.44906e8	0.209904
$463$	3.90586e9	1.82887	0.914436	−	0.404731i	$-0.132635\pi$
$463$	3.90586e9	1.82887	0.914436	+	0.404731i	$0.132635\pi$
$464$	−3.72886e8	−0.173286
$465$	−1.12477e9	−0.518776
$466$	2.90210e8	0.132850
$467$	−1.52387e9	−0.692372	−0.346186	−	0.938166i	$-0.612523\pi$
$467$	−1.52387e9	−0.692372	−0.346186	+	0.938166i	$0.612523\pi$
$468$	6.31310e7	0.0284696
$469$	3.29735e9	1.47591
$470$	1.83710e8	0.0816188
$471$	−3.21434e9	−1.41749
$472$	8.55395e8	0.374429
$473$	−2.78415e9	−1.20970
$474$	2.32964e8	0.100477
$475$	−2.78774e8	−0.119351
$476$	−3.77586e9	−1.60469
$477$	1.06539e9	0.449463
$478$	−1.46481e8	−0.0613457
$479$	2.91492e8	0.121186	0.0605929	−	0.998163i	$-0.480701\pi$
$479$	2.91492e8	0.121186	0.0605929	+	0.998163i	$0.480701\pi$
$480$	8.96135e8	0.369853
$481$	1.90898e8	0.0782156
$482$	−3.14532e7	−0.0127938
$483$	−3.53351e9	−1.42689
$484$	6.51893e8	0.261347
$485$	1.72199e9	0.685384
$486$	−3.35716e8	−0.132662
$487$	−1.73023e9	−0.678817	−0.339408	−	0.940639i	$-0.610227\pi$
$487$	−1.73023e9	−0.678817	−0.339408	+	0.940639i	$0.610227\pi$
$488$	−1.02408e9	−0.398899
$489$	4.13855e9	1.60054
$490$	2.21000e8	0.0848605
$491$	2.21877e9	0.845916	0.422958	−	0.906149i	$-0.360992\pi$
$491$	2.21877e9	0.845916	0.422958	+	0.906149i	$0.360992\pi$
$492$	1.17309e9	0.444073
$493$	−6.02452e8	−0.226443
$494$	−5.67647e6	−0.00211853
$495$	7.71185e8	0.285786
$496$	−1.55112e9	−0.570766
$497$	−6.88707e9	−2.51644
$498$	5.08678e8	0.184561
$499$	−2.14854e9	−0.774090	−0.387045	−	0.922061i	$-0.626504\pi$
$499$	−2.14854e9	−0.774090	−0.387045	+	0.922061i	$0.626504\pi$
$500$	2.88445e9	1.03197
$501$	3.47130e9	1.23328
$502$	−2.03202e8	−0.0716911
$503$	−3.88572e9	−1.36139	−0.680696	−	0.732566i	$-0.738323\pi$
$503$	−3.88572e9	−1.36139	−0.680696	+	0.732566i	$0.738323\pi$
$504$	−5.48676e8	−0.190901
$505$	−1.67390e9	−0.578377
$506$	−3.25748e8	−0.111778
$507$	−3.55512e9	−1.21151
$508$	−4.46879e9	−1.51240
$509$	−5.82488e9	−1.95783	−0.978915	−	0.204268i	$-0.934518\pi$
$509$	−5.82488e9	−1.95783	−0.978915	+	0.204268i	$0.934518\pi$
$510$	4.64173e8	0.154947
$511$	1.97060e9	0.653320
$512$	2.07543e9	0.683380
$513$	−4.50555e8	−0.147346
$514$	−2.19946e8	−0.0714407
$515$	−4.26647e9	−1.37640
$516$	5.24302e9	1.67999
$517$	2.10071e9	0.668574
$518$	−8.20139e8	−0.259259
$519$	−2.10263e9	−0.660203
$520$	4.03113e7	0.0125723
$521$	1.65024e9	0.511228	0.255614	−	0.966779i	$-0.417722\pi$
$521$	1.65024e9	0.511228	0.255614	+	0.966779i	$0.417722\pi$
$522$	−4.32748e7	−0.0133165
$523$	−7.75371e8	−0.237003	−0.118501	−	0.992954i	$-0.537809\pi$
$523$	−7.75371e8	−0.237003	−0.118501	+	0.992954i	$0.537809\pi$
$524$	6.35414e9	1.92929
$525$	−2.78687e9	−0.840542
$526$	3.29090e8	0.0985972
$527$	−2.50605e9	−0.745852
$528$	3.28524e9	0.971289
$529$	−8.17688e8	−0.240156
$530$	3.36283e8	0.0981160
$531$	−2.08724e9	−0.604982
$532$	−1.06223e9	−0.305865
$533$	7.94541e7	0.0227285
$534$	−3.92282e7	−0.0111482
$535$	5.47878e8	0.154684
$536$	−1.15802e9	−0.324818
$537$	2.23751e9	0.623526
$538$	−6.90541e8	−0.191184
$539$	2.52712e9	0.695128
$540$	1.58165e9	0.432246
$541$	−3.21338e9	−0.872512	−0.436256	−	0.899823i	$-0.643696\pi$
$541$	−3.21338e9	−0.872512	−0.436256	+	0.899823i	$0.643696\pi$
$542$	6.57483e8	0.177373
$543$	−7.88799e8	−0.211430
$544$	1.99663e9	0.531743
$545$	4.53357e9	1.19964
$546$	−5.67470e7	−0.0149200
$547$	7.38281e9	1.92871	0.964353	−	0.264618i	$-0.0852460\pi$
$547$	7.38281e9	1.92871	0.964353	+	0.264618i	$0.0852460\pi$
$548$	−2.06726e9	−0.536616
$549$	2.49884e9	0.644518
$550$	−2.56917e8	−0.0658450
$551$	−1.69483e8	−0.0431615
$552$	1.24096e9	0.314030
$553$	2.95268e9	0.742468
$554$	−4.84050e8	−0.120950
$555$	−4.39144e9	−1.09039
$556$	9.77063e8	0.241080
$557$	5.37040e9	1.31678	0.658391	−	0.752676i	$-0.271237\pi$
$557$	5.37040e9	1.31678	0.658391	+	0.752676i	$0.271237\pi$
$558$	−1.80013e8	−0.0438615
$559$	3.55113e8	0.0859854
$560$	3.64133e9	0.876197
$561$	5.30778e9	1.26924
$562$	2.61514e8	0.0621466
$563$	−7.49887e9	−1.77099	−0.885495	−	0.464648i	$-0.846181\pi$
$563$	−7.49887e9	−1.77099	−0.885495	+	0.464648i	$0.846181\pi$
$564$	−3.95600e9	−0.928494
$565$	−2.54002e9	−0.592472
$566$	−8.30734e8	−0.192577
$567$	−7.30105e9	−1.68207
$568$	2.41872e9	0.553818
$569$	−6.77706e9	−1.54223	−0.771114	−	0.636697i	$-0.780300\pi$
$569$	−6.77706e9	−1.54223	−0.771114	+	0.636697i	$0.780300\pi$
$570$	1.30582e8	0.0295340
$571$	−2.80866e9	−0.631353	−0.315677	−	0.948867i	$-0.602231\pi$
$571$	−2.80866e9	−0.631353	−0.315677	+	0.948867i	$0.602231\pi$
$572$	2.27863e8	0.0509081
$573$	4.37572e9	0.971647
$574$	−3.41352e8	−0.0753374
$575$	2.04047e9	0.447603
$576$	−1.90531e9	−0.415420
$577$	−1.45922e9	−0.316231	−0.158115	−	0.987421i	$-0.550542\pi$
$577$	−1.45922e9	−0.316231	−0.158115	+	0.987421i	$0.550542\pi$
$578$	3.38710e8	0.0729594
$579$	2.01208e9	0.430794
$580$	5.94960e8	0.126616
$581$	6.44717e9	1.36381
$582$	8.51329e8	0.179006
$583$	3.84538e9	0.803709
$584$	−6.92071e8	−0.143782
$585$	−9.83632e7	−0.0203136
$586$	−1.33213e9	−0.273466
$587$	4.88054e9	0.995944	0.497972	−	0.867193i	$-0.334078\pi$
$587$	4.88054e9	0.995944	0.497972	+	0.867193i	$0.334078\pi$
$588$	−4.75899e9	−0.965371
$589$	−7.05009e8	−0.142164
$590$	−6.58825e8	−0.132065
$591$	2.30329e9	0.458979
$592$	−6.05600e9	−1.19967
$593$	4.68395e9	0.922403	0.461201	−	0.887295i	$-0.347419\pi$
$593$	4.68395e9	0.922403	0.461201	+	0.887295i	$0.347419\pi$
$594$	−4.15228e8	−0.0812895
$595$	5.88309e9	1.14498
$596$	7.03566e9	1.36126
$597$	2.93392e9	0.564336
$598$	4.15485e7	0.00794514
$599$	−6.34418e9	−1.20610	−0.603048	−	0.797705i	$-0.706047\pi$
$599$	−6.34418e9	−1.20610	−0.603048	+	0.797705i	$0.706047\pi$
$600$	9.78743e8	0.184986
$601$	2.88037e9	0.541237	0.270618	−	0.962687i	$-0.412772\pi$
$601$	2.88037e9	0.541237	0.270618	+	0.962687i	$0.412772\pi$
$602$	−1.52564e9	−0.285013
$603$	2.82568e9	0.524823
$604$	−5.31078e9	−0.980685
$605$	−1.01570e9	−0.186476
$606$	−8.27558e8	−0.151058
$607$	−6.23334e9	−1.13126	−0.565628	−	0.824661i	$-0.691366\pi$
$607$	−6.23334e9	−1.13126	−0.565628	+	0.824661i	$0.691366\pi$
$608$	5.61698e8	0.101354
$609$	−1.69430e9	−0.303970
$610$	7.88742e8	0.140696
$611$	−2.67942e8	−0.0475221
$612$	−3.23574e9	−0.570615
$613$	7.55227e9	1.32424	0.662119	−	0.749399i	$-0.269657\pi$
$613$	7.55227e9	1.32424	0.662119	+	0.749399i	$0.269657\pi$
$614$	6.58487e8	0.114804
$615$	−1.82777e9	−0.316854
$616$	−1.98037e9	−0.341361
$617$	2.75554e9	0.472289	0.236145	−	0.971718i	$-0.424116\pi$
$617$	2.75554e9	0.472289	0.236145	+	0.971718i	$0.424116\pi$
$618$	−2.10929e9	−0.359482
$619$	−5.77979e9	−0.979479	−0.489739	−	0.871869i	$-0.662908\pi$
$619$	−5.77979e9	−0.979479	−0.489739	+	0.871869i	$0.662908\pi$
$620$	2.47489e9	0.417047
$621$	3.29781e9	0.552592
$622$	4.91075e8	0.0818242
$623$	−4.97192e8	−0.0823789
$624$	−4.19026e8	−0.0690391
$625$	−1.36012e9	−0.222842
$626$	1.33192e9	0.217004
$627$	1.49320e9	0.241925
$628$	7.07265e9	1.13952
$629$	−9.78435e9	−1.56767
$630$	4.22589e8	0.0673328
$631$	9.51552e8	0.150775	0.0753876	−	0.997154i	$-0.475981\pi$
$631$	9.51552e8	0.150775	0.0753876	+	0.997154i	$0.475981\pi$
$632$	−1.03697e9	−0.163402
$633$	2.03054e9	0.318199
$634$	−1.44602e9	−0.225353
$635$	6.96273e9	1.07913
$636$	−7.24150e9	−1.11617
$637$	−3.22329e8	−0.0494096
$638$	−1.56194e8	−0.0238119
$639$	−5.90191e9	−0.894827
$640$	−2.61847e9	−0.394837
$641$	−4.78086e9	−0.716973	−0.358486	−	0.933535i	$-0.616707\pi$
$641$	−4.78086e9	−0.716973	−0.358486	+	0.933535i	$0.616707\pi$
$642$	2.70864e8	0.0403998
$643$	5.49821e9	0.815610	0.407805	−	0.913069i	$-0.366294\pi$
$643$	5.49821e9	0.815610	0.407805	+	0.913069i	$0.366294\pi$
$644$	7.77494e9	1.14709
$645$	−8.16905e9	−1.19871
$646$	2.90944e8	0.0424615
$647$	−8.28159e9	−1.20212	−0.601061	−	0.799203i	$-0.705255\pi$
$647$	−8.28159e9	−1.20212	−0.601061	+	0.799203i	$0.705255\pi$
$648$	2.56411e9	0.370190
$649$	−7.53361e9	−1.08180
$650$	3.27692e7	0.00468025
$651$	−7.04788e9	−1.00121
$652$	−9.10624e9	−1.28669
$653$	3.31982e8	0.0466571	0.0233286	−	0.999728i	$-0.492574\pi$
$653$	3.31982e8	0.0466571	0.0233286	+	0.999728i	$0.492574\pi$
$654$	2.24134e9	0.313318
$655$	−9.90026e9	−1.37658
$656$	−2.52058e9	−0.348608
$657$	1.68872e9	0.232315
$658$	1.15114e9	0.157520
$659$	4.29255e9	0.584274	0.292137	−	0.956376i	$-0.405634\pi$
$659$	4.29255e9	0.584274	0.292137	+	0.956376i	$0.405634\pi$
$660$	−5.24178e9	−0.709700
$661$	−1.67795e9	−0.225983	−0.112991	−	0.993596i	$-0.536043\pi$
$661$	−1.67795e9	−0.225983	−0.112991	+	0.993596i	$0.536043\pi$
$662$	1.54230e9	0.206616
$663$	−6.76998e8	−0.0902173
$664$	−2.26423e9	−0.300146
$665$	1.65505e9	0.218240
$666$	−7.02821e8	−0.0921903
$667$	1.24052e9	0.161869
$668$	−7.63805e9	−0.991437
$669$	−6.58494e9	−0.850277
$670$	8.91908e8	0.114567
$671$	9.01921e9	1.15250
$672$	5.61522e9	0.713797
$673$	−1.03688e10	−1.31121	−0.655607	−	0.755102i	$-0.727587\pi$
$673$	−1.03688e10	−1.31121	−0.655607	+	0.755102i	$0.727587\pi$
$674$	1.37243e9	0.172656
$675$	2.60097e9	0.325516
$676$	7.82249e9	0.973938
$677$	5.57174e9	0.690129	0.345065	−	0.938579i	$-0.387857\pi$
$677$	5.57174e9	0.690129	0.345065	+	0.938579i	$0.387857\pi$
$678$	−1.25575e9	−0.154739
$679$	1.07901e10	1.32276
$680$	−2.06613e9	−0.251986
$681$	1.21936e10	1.47951
$682$	−6.49731e8	−0.0784311
$683$	9.21223e9	1.10635	0.553175	−	0.833065i	$-0.313416\pi$
$683$	9.21223e9	1.10635	0.553175	+	0.833065i	$0.313416\pi$
$684$	−9.10286e8	−0.108763
$685$	3.22096e9	0.382885
$686$	−3.20384e8	−0.0378911
$687$	2.02497e10	2.38271
$688$	−1.12655e10	−1.31884
$689$	−4.90470e8	−0.0571275
$690$	−9.55787e8	−0.110762
$691$	9.17912e9	1.05835	0.529173	−	0.848514i	$-0.322502\pi$
$691$	9.17912e9	1.05835	0.529173	+	0.848514i	$0.322502\pi$
$692$	4.62652e9	0.530741
$693$	4.83228e9	0.551551
$694$	2.16575e9	0.245952
$695$	−1.52234e9	−0.172015
$696$	5.95035e8	0.0668975
$697$	−4.07237e9	−0.455546
$698$	−3.69465e8	−0.0411225
$699$	9.73702e9	1.07834
$700$	6.13208e9	0.675717
$701$	−7.13531e9	−0.782348	−0.391174	−	0.920317i	$-0.627931\pi$
$701$	−7.13531e9	−0.782348	−0.391174	+	0.920317i	$0.627931\pi$
$702$	5.29616e7	0.00577805
$703$	−2.75256e9	−0.298808
$704$	−6.87697e9	−0.742835
$705$	6.16376e9	0.662497
$706$	7.79214e8	0.0833375
$707$	−1.04888e10	−1.11624
$708$	1.41871e10	1.50237
$709$	7.88828e9	0.831228	0.415614	−	0.909541i	$-0.363567\pi$
$709$	7.88828e9	0.831228	0.415614	+	0.909541i	$0.363567\pi$
$710$	−1.86290e9	−0.195337
$711$	2.53031e9	0.264016
$712$	1.74613e8	0.0181299
$713$	5.16026e9	0.533161
$714$	2.90853e9	0.299040
$715$	−3.55028e8	−0.0363238
$716$	−4.92329e9	−0.501256
$717$	−4.91468e9	−0.497941
$718$	−1.15104e9	−0.116052
$719$	1.39767e10	1.40234	0.701168	−	0.712996i	$-0.252662\pi$
$719$	1.39767e10	1.40234	0.701168	+	0.712996i	$0.252662\pi$
$720$	3.12045e9	0.311569
$721$	−2.67339e10	−2.65637
$722$	−1.43319e9	−0.141717
$723$	−1.05530e9	−0.103847
$724$	1.73563e9	0.169970
$725$	9.78395e8	0.0953523
$726$	−5.02150e8	−0.0487030
$727$	−1.80038e10	−1.73777	−0.868886	−	0.495012i	$-0.835164\pi$
$727$	−1.80038e10	−1.73777	−0.868886	+	0.495012i	$0.835164\pi$
$728$	2.52592e8	0.0242639
$729$	1.80687e9	0.172735
$730$	5.33032e8	0.0507135
$731$	−1.82011e10	−1.72340
$732$	−1.69847e10	−1.60055
$733$	4.07079e9	0.381781	0.190891	−	0.981611i	$-0.438862\pi$
$733$	4.07079e9	0.381781	0.190891	+	0.981611i	$0.438862\pi$
$734$	−1.85254e9	−0.172915
$735$	7.41489e9	0.688809
$736$	−4.11131e9	−0.380108
$737$	1.01989e10	0.938464
$738$	−2.92523e8	−0.0267894
$739$	7.74559e9	0.705990	0.352995	−	0.935625i	$-0.385163\pi$
$739$	7.74559e9	0.705990	0.352995	+	0.935625i	$0.385163\pi$
$740$	9.66267e9	0.876569
$741$	−1.90455e8	−0.0171960
$742$	2.10717e9	0.189359
$743$	−7.06645e9	−0.632034	−0.316017	−	0.948754i	$-0.602346\pi$
$743$	−7.06645e9	−0.632034	−0.316017	+	0.948754i	$0.602346\pi$
$744$	2.47520e9	0.220346
$745$	−1.09621e10	−0.971287
$746$	−9.68693e7	−0.00854280
$747$	5.52493e9	0.484958
$748$	−1.16789e10	−1.02035
$749$	3.43303e9	0.298532
$750$	−2.22188e9	−0.192312
$751$	1.80210e9	0.155252	0.0776261	−	0.996983i	$-0.475266\pi$
$751$	1.80210e9	0.155252	0.0776261	+	0.996983i	$0.475266\pi$
$752$	8.50012e9	0.728891
$753$	−6.81776e9	−0.581914
$754$	1.99223e7	0.00169254
$755$	8.27463e9	0.699736
$756$	9.91067e9	0.834212
$757$	−2.57495e8	−0.0215742	−0.0107871	−	0.999942i	$-0.503434\pi$
$757$	−2.57495e8	−0.0215742	−0.0107871	+	0.999942i	$0.503434\pi$
$758$	−1.11951e8	−0.00933653
$759$	−1.09294e10	−0.907295
$760$	−5.81248e8	−0.0480302
$761$	1.91436e10	1.57462	0.787311	−	0.616556i	$-0.211473\pi$
$761$	1.91436e10	1.57462	0.787311	+	0.616556i	$0.211473\pi$
$762$	3.44229e9	0.281842
$763$	2.84076e10	2.31525
$764$	−9.62809e9	−0.781112
$765$	5.04154e9	0.407144
$766$	4.80597e7	0.00386350
$767$	9.60898e8	0.0768942
$768$	1.19533e10	0.952189
$769$	−1.35775e10	−1.07666	−0.538328	−	0.842735i	$-0.680944\pi$
$769$	−1.35775e10	−1.07666	−0.538328	+	0.842735i	$0.680944\pi$
$770$	1.52528e9	0.120401
$771$	−7.37955e9	−0.579882
$772$	−4.42727e9	−0.346318
$773$	−1.25142e10	−0.974484	−0.487242	−	0.873267i	$-0.661997\pi$
$773$	−1.25142e10	−0.974484	−0.487242	+	0.873267i	$0.661997\pi$
$774$	−1.30740e9	−0.101348
$775$	4.06988e9	0.314070
$776$	−3.78944e9	−0.291111
$777$	−2.75170e10	−2.10439
$778$	−3.51713e9	−0.267769
$779$	−1.14565e9	−0.0868301
$780$	6.68579e8	0.0504454
$781$	−2.13021e10	−1.60009
$782$	−2.12954e9	−0.159244
$783$	1.58128e9	0.117718
$784$	1.02255e10	0.757841
$785$	−1.10198e10	−0.813071
$786$	−4.89457e9	−0.359530
$787$	−2.58346e9	−0.188925	−0.0944627	−	0.995528i	$-0.530113\pi$
$787$	−2.58346e9	−0.188925	−0.0944627	+	0.995528i	$0.530113\pi$
$788$	−5.06803e9	−0.368976
$789$	1.10415e10	0.800310
$790$	7.98675e8	0.0576335
$791$	−1.59159e10	−1.14344
$792$	−1.69709e9	−0.121385
$793$	−1.15038e9	−0.0819193
$794$	3.08360e9	0.218618
$795$	1.12828e10	0.796404
$796$	−6.45562e9	−0.453672
$797$	1.63651e10	1.14503	0.572514	−	0.819895i	$-0.305968\pi$
$797$	1.63651e10	1.14503	0.572514	+	0.819895i	$0.305968\pi$
$798$	8.18234e8	0.0569990
$799$	1.37332e10	0.952483
$800$	−3.24258e9	−0.223911
$801$	−4.26071e8	−0.0292933
$802$	2.35337e9	0.161094
$803$	6.09519e9	0.415416
$804$	−1.92063e10	−1.30331
$805$	−1.21140e10	−0.818468
$806$	8.28719e7	0.00557487
$807$	−2.31688e10	−1.55183
$808$	3.68363e9	0.245661
$809$	−9.60604e9	−0.637859	−0.318929	−	0.947779i	$-0.603323\pi$
$809$	−9.60604e9	−0.637859	−0.318929	+	0.947779i	$0.603323\pi$
$810$	−1.97487e9	−0.130570
$811$	−1.68869e10	−1.11168	−0.555838	−	0.831291i	$-0.687602\pi$
$811$	−1.68869e10	−1.11168	−0.555838	+	0.831291i	$0.687602\pi$
$812$	3.72805e9	0.244363
$813$	2.20596e10	1.43973
$814$	−2.53674e9	−0.164850
$815$	1.41883e10	0.918074
$816$	2.14769e10	1.38375
$817$	−5.12037e9	−0.328491
$818$	2.22712e9	0.142268
$819$	−6.16348e8	−0.0392042
$820$	4.02173e9	0.254721
$821$	−1.42229e10	−0.896992	−0.448496	−	0.893785i	$-0.648040\pi$
$821$	−1.42229e10	−0.896992	−0.448496	+	0.893785i	$0.648040\pi$
$822$	1.59240e9	0.100000
$823$	8.23523e9	0.514963	0.257482	−	0.966283i	$-0.417107\pi$
$823$	8.23523e9	0.514963	0.257482	+	0.966283i	$0.417107\pi$
$824$	9.38888e9	0.584613
$825$	−8.61996e9	−0.534461
$826$	−4.12823e9	−0.254879
$827$	−6.34613e9	−0.390157	−0.195079	−	0.980788i	$-0.562496\pi$
$827$	−6.34613e9	−0.390157	−0.195079	+	0.980788i	$0.562496\pi$
$828$	6.66277e9	0.407895
$829$	−3.05345e8	−0.0186144	−0.00930722	−	0.999957i	$-0.502963\pi$
$829$	−3.05345e8	−0.0186144	−0.00930722	+	0.999957i	$0.502963\pi$
$830$	1.74391e9	0.105864
$831$	−1.62406e10	−0.981747
$832$	8.77144e8	0.0528006
$833$	1.65208e10	0.990313
$834$	−7.52628e8	−0.0449261
$835$	1.19007e10	0.707408
$836$	−3.28555e9	−0.194485
$837$	6.57775e9	0.387738
$838$	4.02942e9	0.236531
$839$	6.59914e9	0.385763	0.192881	−	0.981222i	$-0.438217\pi$
$839$	6.59914e9	0.385763	0.192881	+	0.981222i	$0.438217\pi$
$840$	−5.81066e9	−0.338258
$841$	5.94823e8	0.0344828
$842$	1.25075e9	0.0722066
$843$	8.77420e9	0.504442
$844$	−4.46789e9	−0.255802
$845$	−1.21881e10	−0.694922
$846$	9.86470e8	0.0560129
$847$	−6.36444e9	−0.359888
$848$	1.55596e10	0.876218
$849$	−2.78724e10	−1.56314
$850$	−1.67956e9	−0.0938060
$851$	2.01471e10	1.12062
$852$	4.01155e10	2.22215
$853$	1.23204e10	0.679679	0.339839	−	0.940484i	$-0.389627\pi$
$853$	1.23204e10	0.679679	0.339839	+	0.940484i	$0.389627\pi$
$854$	4.94230e9	0.271535
$855$	1.41830e9	0.0776044
$856$	−1.20567e9	−0.0657009
$857$	−5.80631e9	−0.315114	−0.157557	−	0.987510i	$-0.550362\pi$
$857$	−5.80631e9	−0.315114	−0.157557	+	0.987510i	$0.550362\pi$
$858$	−1.75522e8	−0.00948692
$859$	2.15733e10	1.16129	0.580645	−	0.814157i	$-0.302800\pi$
$859$	2.15733e10	1.16129	0.580645	+	0.814157i	$0.302800\pi$
$860$	1.79747e10	0.963646
$861$	−1.14529e10	−0.611511
$862$	−1.04310e9	−0.0554688
$863$	−6.46792e9	−0.342552	−0.171276	−	0.985223i	$-0.554789\pi$
$863$	−6.46792e9	−0.342552	−0.171276	+	0.985223i	$0.554789\pi$
$864$	−5.24065e9	−0.276431
$865$	−7.20848e9	−0.378693
$866$	1.11860e9	0.0585277
$867$	1.13643e10	0.592209
$868$	1.55078e10	0.804878
$869$	9.13279e9	0.472101
$870$	−4.58295e8	−0.0235954
$871$	−1.30085e9	−0.0667059
$872$	−9.97667e9	−0.509539
$873$	9.24658e9	0.470361
$874$	−5.99088e8	−0.0303529
$875$	−2.81609e10	−1.42108
$876$	−1.14783e10	−0.576916
$877$	2.04649e10	1.02450	0.512249	−	0.858837i	$-0.328813\pi$
$877$	2.04649e10	1.02450	0.512249	+	0.858837i	$0.328813\pi$
$878$	3.07327e9	0.153239
$879$	−4.46949e10	−2.21971
$880$	1.12628e10	0.557132
$881$	−1.34314e10	−0.661767	−0.330883	−	0.943672i	$-0.607347\pi$
$881$	−1.34314e10	−0.661767	−0.330883	+	0.943672i	$0.607347\pi$
$882$	1.18671e9	0.0582375
$883$	3.26897e10	1.59789	0.798947	−	0.601401i	$-0.205391\pi$
$883$	3.26897e10	1.59789	0.798947	+	0.601401i	$0.205391\pi$
$884$	1.48963e9	0.0725262
$885$	−2.21046e10	−1.07197
$886$	4.47673e9	0.216244
$887$	3.80466e9	0.183056	0.0915278	−	0.995803i	$-0.470825\pi$
$887$	3.80466e9	0.183056	0.0915278	+	0.995803i	$0.470825\pi$
$888$	9.66389e9	0.463134
$889$	4.36288e10	2.08266
$890$	−1.34486e8	−0.00639460
$891$	−2.25826e10	−1.06955
$892$	1.44891e10	0.683542
$893$	3.86345e9	0.181550
$894$	−5.41954e9	−0.253677
$895$	7.67088e9	0.357655
$896$	−1.64075e10	−0.762016
$897$	1.39402e9	0.0644904
$898$	1.39211e9	0.0641515
$899$	2.47432e9	0.113579
$900$	5.25491e9	0.240279
$901$	2.51387e10	1.14500
$902$	−1.05582e9	−0.0479035
$903$	−5.11877e10	−2.31344
$904$	5.58962e9	0.251648
$905$	−2.70425e9	−0.121277
$906$	4.09088e9	0.182754
$907$	−1.63911e10	−0.729428	−0.364714	−	0.931120i	$-0.618833\pi$
$907$	−1.63911e10	−0.729428	−0.364714	+	0.931120i	$0.618833\pi$
$908$	−2.68301e10	−1.18938
$909$	−8.98839e9	−0.396925
$910$	−1.94546e8	−0.00855812
$911$	−1.03106e10	−0.451826	−0.225913	−	0.974148i	$-0.572536\pi$
$911$	−1.03106e10	−0.451826	−0.225913	+	0.974148i	$0.572536\pi$
$912$	6.04194e9	0.263751
$913$	1.99415e10	0.867180
$914$	2.59115e9	0.112248
$915$	2.64636e10	1.14202
$916$	−4.45564e10	−1.91547
$917$	−6.20355e10	−2.65673
$918$	−2.71451e9	−0.115809
$919$	4.05387e10	1.72292	0.861460	−	0.507825i	$-0.169550\pi$
$919$	4.05387e10	1.72292	0.861460	+	0.507825i	$0.169550\pi$
$920$	4.25440e9	0.180128
$921$	2.20933e10	0.931862
$922$	3.19822e9	0.134385
$923$	2.71704e9	0.113734
$924$	−3.28452e10	−1.36968
$925$	1.58900e10	0.660128
$926$	6.62011e9	0.273985
$927$	−2.29097e10	−0.944585
$928$	−1.97135e9	−0.0809741
$929$	−1.31491e10	−0.538072	−0.269036	−	0.963130i	$-0.586705\pi$
$929$	−1.31491e10	−0.538072	−0.269036	+	0.963130i	$0.586705\pi$
$930$	−1.90640e9	−0.0777182
$931$	4.64766e9	0.188760
$932$	−2.14248e10	−0.866884
$933$	1.64764e10	0.664164
$934$	−2.58283e9	−0.103725
$935$	1.81967e10	0.728036
$936$	2.16460e8	0.00862804
$937$	4.42551e9	0.175742	0.0878709	−	0.996132i	$-0.471994\pi$
$937$	4.42551e9	0.175742	0.0878709	+	0.996132i	$0.471994\pi$
$938$	5.58874e9	0.221108
$939$	4.46880e10	1.76141
$940$	−1.35624e10	−0.532585
$941$	−3.78750e10	−1.48180	−0.740899	−	0.671617i	$-0.765600\pi$
$941$	−3.78750e10	−1.48180	−0.740899	+	0.671617i	$0.765600\pi$
$942$	−5.44804e9	−0.212355
$943$	8.38549e9	0.325640
$944$	−3.04833e10	−1.17940
$945$	−1.54416e10	−0.595225
$946$	−4.71889e9	−0.181226
$947$	4.79393e10	1.83428	0.917142	−	0.398560i	$-0.130490\pi$
$947$	4.79393e10	1.83428	0.917142	+	0.398560i	$0.130490\pi$
$948$	−1.71986e10	−0.655638
$949$	−7.77430e8	−0.0295277
$950$	−4.72499e8	−0.0178800
$951$	−4.85164e10	−1.82918
$952$	−1.29465e10	−0.486319
$953$	−5.67436e9	−0.212369	−0.106185	−	0.994346i	$-0.533863\pi$
$953$	−5.67436e9	−0.212369	−0.106185	+	0.994346i	$0.533863\pi$
$954$	1.80575e9	0.0673344
$955$	1.50013e10	0.557338
$956$	1.08140e10	0.400298
$957$	−5.24057e9	−0.193280
$958$	4.94054e8	0.0181549
$959$	2.01827e10	0.738948
$960$	−2.01779e10	−0.736084
$961$	−1.72201e10	−0.625897
$962$	3.23556e8	0.0117175
$963$	2.94195e9	0.106156
$964$	2.32203e9	0.0834831
$965$	6.89804e9	0.247104
$966$	−5.98901e9	−0.213764
$967$	−5.07626e10	−1.80531	−0.902655	−	0.430366i	$-0.858385\pi$
$967$	−5.07626e10	−1.80531	−0.902655	+	0.430366i	$0.858385\pi$
$968$	2.23517e9	0.0792041
$969$	9.76163e9	0.344658
$970$	2.91862e9	0.102678
$971$	2.95757e8	0.0103674	0.00518368	−	0.999987i	$-0.498350\pi$
$971$	2.95757e8	0.0103674	0.00518368	+	0.999987i	$0.498350\pi$
$972$	2.47843e10	0.865654
$973$	−9.53908e9	−0.331980
$974$	−2.93259e9	−0.101694
$975$	1.09946e9	0.0379895
$976$	3.64945e10	1.25647
$977$	1.61711e10	0.554763	0.277382	−	0.960760i	$-0.410533\pi$
$977$	1.61711e10	0.554763	0.277382	+	0.960760i	$0.410533\pi$
$978$	7.01450e9	0.239779
$979$	−1.53784e9	−0.0523809
$980$	−1.63153e10	−0.553738
$981$	2.43440e10	0.823285
$982$	3.76063e9	0.126727
$983$	−2.97882e10	−1.00025	−0.500123	−	0.865954i	$-0.666712\pi$
$983$	−2.97882e10	−1.00025	−0.500123	+	0.865954i	$0.666712\pi$
$984$	4.02223e9	0.134581
$985$	7.89641e9	0.263271
$986$	−1.02110e9	−0.0339235
$987$	3.86224e10	1.27858
$988$	4.19066e8	0.0138240
$989$	3.74782e10	1.23194
$990$	1.30709e9	0.0428138
$991$	−6.67808e9	−0.217968	−0.108984	−	0.994043i	$-0.534760\pi$
$991$	−6.67808e9	−0.217968	−0.108984	+	0.994043i	$0.534760\pi$
$992$	−8.20034e9	−0.266711
$993$	5.17465e10	1.67710
$994$	−1.16730e10	−0.376991
$995$	1.00584e10	0.323703
$996$	−3.75532e10	−1.20431
$997$	−1.52367e10	−0.486920	−0.243460	−	0.969911i	$-0.578282\pi$
$997$	−1.52367e10	−0.486920	−0.243460	+	0.969911i	$0.578282\pi$
$998$	−3.64159e9	−0.115967
$999$	2.56814e10	0.814966

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.8.a.b.1.6	✓	10
3.2	odd	2		261.8.a.f.1.5		10
4.3	odd	2		464.8.a.g.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.8.a.b.1.6	✓	10	1.1	even	1	trivial
261.8.a.f.1.5		10	3.2	odd	2
464.8.a.g.1.3		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)

\(f(q)\)	\(=\)	\(q+1.69492 q^{2} +56.8671 q^{3} -125.127 q^{4} +194.958 q^{5} +96.3850 q^{6} +1221.62 q^{7} -429.029 q^{8} +1046.87 q^{9} +O(q^{10})\)	\(q+1.69492 q^{2} +56.8671 q^{3} -125.127 q^{4} +194.958 q^{5} +96.3850 q^{6} +1221.62 q^{7} -429.029 q^{8} +1046.87 q^{9} +330.438 q^{10} +3778.54 q^{11} -7115.63 q^{12} -481.945 q^{13} +2070.54 q^{14} +11086.7 q^{15} +15289.1 q^{16} +24701.8 q^{17} +1774.36 q^{18} +6949.17 q^{19} -24394.6 q^{20} +69469.9 q^{21} +6404.30 q^{22} -50863.9 q^{23} -24397.7 q^{24} -40116.2 q^{25} -816.856 q^{26} -64835.9 q^{27} -152858. q^{28} -24389.0 q^{29} +18791.1 q^{30} -101452. q^{31} +80829.5 q^{32} +214874. q^{33} +41867.4 q^{34} +238165. q^{35} -130992. q^{36} -396099. q^{37} +11778.3 q^{38} -27406.8 q^{39} -83642.9 q^{40} -164861. q^{41} +117746. q^{42} -736832. q^{43} -472798. q^{44} +204096. q^{45} -86210.1 q^{46} +555959. q^{47} +869448. q^{48} +668808. q^{49} -67993.7 q^{50} +1.40472e6 q^{51} +60304.5 q^{52} +1.01769e6 q^{53} -109891. q^{54} +736657. q^{55} -524110. q^{56} +395179. q^{57} -41337.3 q^{58} -1.99379e6 q^{59} -1.38725e6 q^{60} +2.38696e6 q^{61} -171953. q^{62} +1.27888e6 q^{63} -1.82001e6 q^{64} -93959.2 q^{65} +364194. q^{66} +2.69917e6 q^{67} -3.09087e6 q^{68} -2.89248e6 q^{69} +403669. q^{70} -5.63766e6 q^{71} -449138. q^{72} +1.61311e6 q^{73} -671354. q^{74} -2.28130e6 q^{75} -869530. q^{76} +4.61593e6 q^{77} -46452.3 q^{78} +2.41702e6 q^{79} +2.98074e6 q^{80} -5.97654e6 q^{81} -279426. q^{82} +5.27756e6 q^{83} -8.69258e6 q^{84} +4.81582e6 q^{85} -1.24887e6 q^{86} -1.38693e6 q^{87} -1.62110e6 q^{88} -406995. q^{89} +345926. q^{90} -588753. q^{91} +6.36446e6 q^{92} -5.76930e6 q^{93} +942304. q^{94} +1.35480e6 q^{95} +4.59654e6 q^{96} +8.83259e6 q^{97} +1.13357e6 q^{98} +3.95564e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9}+O(q^{10}) \) 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

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