LMFDB - Embedded newform 74.8.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,8,Mod(1,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, 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("74.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	74.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:	$23.1164918858$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 10621x^{4} + 102052x^{3} + 31004503x^{2} - 305547358x - 22608804936 $ x^6 - 2x^5 - 10621x^4 + 102052x^3 + 31004503x^2 - 305547358*x - 22608804936
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$61.6850$ of defining polynomial
Character	$\chi$	$=$	74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} -56.6850 q^{3} +64.0000 q^{4} +360.557 q^{5} +453.480 q^{6} +1603.66 q^{7} -512.000 q^{8} +1026.19 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -56.6850 q^{3} +64.0000 q^{4} +360.557 q^{5} +453.480 q^{6} +1603.66 q^{7} -512.000 q^{8} +1026.19 q^{9} -2884.45 q^{10} -6804.46 q^{11} -3627.84 q^{12} +3812.29 q^{13} -12829.3 q^{14} -20438.2 q^{15} +4096.00 q^{16} -4261.18 q^{17} -8209.49 q^{18} +36752.8 q^{19} +23075.6 q^{20} -90903.7 q^{21} +54435.7 q^{22} +43547.9 q^{23} +29022.7 q^{24} +51876.2 q^{25} -30498.3 q^{26} +65800.7 q^{27} +102635. q^{28} -189320. q^{29} +163505. q^{30} +19996.5 q^{31} -32768.0 q^{32} +385711. q^{33} +34089.4 q^{34} +578212. q^{35} +65675.9 q^{36} -50653.0 q^{37} -294023. q^{38} -216099. q^{39} -184605. q^{40} -161085. q^{41} +727229. q^{42} +419058. q^{43} -435485. q^{44} +369998. q^{45} -348383. q^{46} -195644. q^{47} -232182. q^{48} +1.74820e6 q^{49} -415010. q^{50} +241545. q^{51} +243986. q^{52} +1.92611e6 q^{53} -526406. q^{54} -2.45339e6 q^{55} -821076. q^{56} -2.08333e6 q^{57} +1.51456e6 q^{58} +2.34699e6 q^{59} -1.30804e6 q^{60} +1.06839e6 q^{61} -159972. q^{62} +1.64566e6 q^{63} +262144. q^{64} +1.37455e6 q^{65} -3.08569e6 q^{66} +2.76451e6 q^{67} -272715. q^{68} -2.46851e6 q^{69} -4.62570e6 q^{70} +5.36844e6 q^{71} -525407. q^{72} -2.44360e6 q^{73} +405224. q^{74} -2.94060e6 q^{75} +2.35218e6 q^{76} -1.09121e7 q^{77} +1.72880e6 q^{78} -1.90275e6 q^{79} +1.47684e6 q^{80} -5.97418e6 q^{81} +1.28868e6 q^{82} -5.24367e6 q^{83} -5.81783e6 q^{84} -1.53640e6 q^{85} -3.35246e6 q^{86} +1.07316e7 q^{87} +3.48388e6 q^{88} -2.90811e6 q^{89} -2.95999e6 q^{90} +6.11363e6 q^{91} +2.78707e6 q^{92} -1.13350e6 q^{93} +1.56515e6 q^{94} +1.32515e7 q^{95} +1.85745e6 q^{96} -4.20555e6 q^{97} -1.39856e7 q^{98} -6.98264e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9}+O(q^{10}) $ 6 * q - 48 * q^2 + 28 * q^3 + 384 * q^4 - 14 * q^5 - 224 * q^6 - 980 * q^7 - 3072 * q^8 + 8254 * q^9	\( 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9} + 112 q^{10} + 2956 q^{11} + 1792 q^{12} + 2394 q^{13} + 7840 q^{14} - 28820 q^{15} + 24576 q^{16} - 45108 q^{17} - 66032 q^{18} + 11764 q^{19} - 896 q^{20} - 135378 q^{21} - 23648 q^{22} + 21052 q^{23} - 14336 q^{24} + 194744 q^{25} - 19152 q^{26} + 439240 q^{27} - 62720 q^{28} + 288454 q^{29} + 230560 q^{30} + 578868 q^{31} - 196608 q^{32} + 980174 q^{33} + 360864 q^{34} + 1243052 q^{35} + 528256 q^{36} - 303918 q^{37} - 94112 q^{38} + 1735296 q^{39} + 7168 q^{40} + 1176840 q^{41} + 1083024 q^{42} + 2669236 q^{43} + 189184 q^{44} + 2560692 q^{45} - 168416 q^{46} - 131044 q^{47} + 114688 q^{48} + 2460856 q^{49} - 1557952 q^{50} + 2899732 q^{51} + 153216 q^{52} + 983190 q^{53} - 3513920 q^{54} - 1200168 q^{55} + 501760 q^{56} - 163216 q^{57} - 2307632 q^{58} - 1215568 q^{59} - 1844480 q^{60} + 3136358 q^{61} - 4630944 q^{62} - 1444880 q^{63} + 1572864 q^{64} - 1302836 q^{65} - 7841392 q^{66} + 2179276 q^{67} - 2886912 q^{68} - 929514 q^{69} - 9944416 q^{70} + 325164 q^{71} - 4226048 q^{72} + 5011444 q^{73} + 2431344 q^{74} - 9374520 q^{75} + 752896 q^{76} - 26500426 q^{77} - 13882368 q^{78} + 3173032 q^{79} - 57344 q^{80} - 2565226 q^{81} - 9414720 q^{82} - 22567048 q^{83} - 8664192 q^{84} + 1486476 q^{85} - 21353888 q^{86} - 157228 q^{87} - 1513472 q^{88} + 26836996 q^{89} - 20485536 q^{90} + 17942380 q^{91} + 1347328 q^{92} + 16734948 q^{93} + 1048352 q^{94} - 4252048 q^{95} - 917504 q^{96} + 295792 q^{97} - 19686848 q^{98} + 25990712 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 + 28 * q^3 + 384 * q^4 - 14 * q^5 - 224 * q^6 - 980 * q^7 - 3072 * q^8 + 8254 * q^9 + 112 * q^10 + 2956 * q^11 + 1792 * q^12 + 2394 * q^13 + 7840 * q^14 - 28820 * q^15 + 24576 * q^16 - 45108 * q^17 - 66032 * q^18 + 11764 * q^19 - 896 * q^20 - 135378 * q^21 - 23648 * q^22 + 21052 * q^23 - 14336 * q^24 + 194744 * q^25 - 19152 * q^26 + 439240 * q^27 - 62720 * q^28 + 288454 * q^29 + 230560 * q^30 + 578868 * q^31 - 196608 * q^32 + 980174 * q^33 + 360864 * q^34 + 1243052 * q^35 + 528256 * q^36 - 303918 * q^37 - 94112 * q^38 + 1735296 * q^39 + 7168 * q^40 + 1176840 * q^41 + 1083024 * q^42 + 2669236 * q^43 + 189184 * q^44 + 2560692 * q^45 - 168416 * q^46 - 131044 * q^47 + 114688 * q^48 + 2460856 * q^49 - 1557952 * q^50 + 2899732 * q^51 + 153216 * q^52 + 983190 * q^53 - 3513920 * q^54 - 1200168 * q^55 + 501760 * q^56 - 163216 * q^57 - 2307632 * q^58 - 1215568 * q^59 - 1844480 * q^60 + 3136358 * q^61 - 4630944 * q^62 - 1444880 * q^63 + 1572864 * q^64 - 1302836 * q^65 - 7841392 * q^66 + 2179276 * q^67 - 2886912 * q^68 - 929514 * q^69 - 9944416 * q^70 + 325164 * q^71 - 4226048 * q^72 + 5011444 * q^73 + 2431344 * q^74 - 9374520 * q^75 + 752896 * q^76 - 26500426 * q^77 - 13882368 * q^78 + 3173032 * q^79 - 57344 * q^80 - 2565226 * q^81 - 9414720 * q^82 - 22567048 * q^83 - 8664192 * q^84 + 1486476 * q^85 - 21353888 * q^86 - 157228 * q^87 - 1513472 * q^88 + 26836996 * q^89 - 20485536 * q^90 + 17942380 * q^91 + 1347328 * q^92 + 16734948 * q^93 + 1048352 * q^94 - 4252048 * q^95 - 917504 * q^96 + 295792 * q^97 - 19686848 * q^98 + 25990712 * 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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	−56.6850	−1.21211	−0.606057	−	0.795421i	$-0.707250\pi$
$3$	−56.6850	−1.21211	−0.606057	+	0.795421i	$0.707250\pi$
$4$	64.0000	0.500000
$5$	360.557	1.28997	0.644984	−	0.764196i	$-0.276864\pi$
$5$	360.557	1.28997	0.644984	+	0.764196i	$0.276864\pi$
$6$	453.480	0.857094
$7$	1603.66	1.76714	0.883569	−	0.468302i	$-0.155134\pi$
$7$	1603.66	1.76714	0.883569	+	0.468302i	$0.155134\pi$
$8$	−512.000	−0.353553
$9$	1026.19	0.469221
$10$	−2884.45	−0.912145
$11$	−6804.46	−1.54141	−0.770707	−	0.637190i	$-0.780097\pi$
$11$	−6804.46	−1.54141	−0.770707	+	0.637190i	$0.780097\pi$
$12$	−3627.84	−0.606057
$13$	3812.29	0.481265	0.240632	−	0.970616i	$-0.422645\pi$
$13$	3812.29	0.481265	0.240632	+	0.970616i	$0.422645\pi$
$14$	−12829.3	−1.24955
$15$	−20438.2	−1.56359
$16$	4096.00	0.250000
$17$	−4261.18	−0.210358	−0.105179	−	0.994453i	$-0.533542\pi$
$17$	−4261.18	−0.210358	−0.105179	+	0.994453i	$0.533542\pi$
$18$	−8209.49	−0.331789
$19$	36752.8	1.22929	0.614643	−	0.788805i	$-0.289300\pi$
$19$	36752.8	1.22929	0.614643	+	0.788805i	$0.289300\pi$
$20$	23075.6	0.644984
$21$	−90903.7	−2.14197
$22$	54435.7	1.08994
$23$	43547.9	0.746311	0.373156	−	0.927769i	$-0.378276\pi$
$23$	43547.9	0.746311	0.373156	+	0.927769i	$0.378276\pi$
$24$	29022.7	0.428547
$25$	51876.2	0.664016
$26$	−30498.3	−0.340306
$27$	65800.7	0.643365
$28$	102635.	0.883569
$29$	−189320.	−1.44146	−0.720732	−	0.693214i	$-0.756194\pi$
$29$	−189320.	−1.44146	−0.720732	+	0.693214i	$0.756194\pi$
$30$	163505.	1.10562
$31$	19996.5	0.120556	0.0602780	−	0.998182i	$-0.480801\pi$
$31$	19996.5	0.120556	0.0602780	+	0.998182i	$0.480801\pi$
$32$	−32768.0	−0.176777
$33$	385711.	1.86837
$34$	34089.4	0.148745
$35$	578212.	2.27955
$36$	65675.9	0.234610
$37$	−50653.0	−0.164399
$37$	−50653.0	−0.164399
$38$	−294023.	−0.869237
$39$	−216099.	−0.583348
$40$	−184605.	−0.456072
$41$	−161085.	−0.365015	−0.182507	−	0.983204i	$-0.558421\pi$
$41$	−161085.	−0.365015	−0.182507	+	0.983204i	$0.558421\pi$
$42$	727229.	1.51460
$43$	419058.	0.803775	0.401888	−	0.915689i	$-0.368354\pi$
$43$	419058.	0.803775	0.401888	+	0.915689i	$0.368354\pi$
$44$	−435485.	−0.770707
$45$	369998.	0.605279
$46$	−348383.	−0.527722
$47$	−195644.	−0.274868	−0.137434	−	0.990511i	$-0.543886\pi$
$47$	−195644.	−0.274868	−0.137434	+	0.990511i	$0.543886\pi$
$48$	−232182.	−0.303029
$49$	1.74820e6	2.12277
$50$	−415010.	−0.469530
$51$	241545.	0.254978
$52$	243986.	0.240632
$53$	1.92611e6	1.77711	0.888556	−	0.458768i	$-0.151709\pi$
$53$	1.92611e6	1.77711	0.888556	+	0.458768i	$0.151709\pi$
$54$	−526406.	−0.454928
$55$	−2.45339e6	−1.98837
$56$	−821076.	−0.624777
$57$	−2.08333e6	−1.49004
$58$	1.51456e6	1.01927
$59$	2.34699e6	1.48775	0.743873	−	0.668321i	$-0.232987\pi$
$59$	2.34699e6	1.48775	0.743873	+	0.668321i	$0.232987\pi$
$60$	−1.30804e6	−0.781794
$61$	1.06839e6	0.602666	0.301333	−	0.953519i	$-0.402568\pi$
$61$	1.06839e6	0.602666	0.301333	+	0.953519i	$0.402568\pi$
$62$	−159972.	−0.0852460
$63$	1.64566e6	0.829177
$64$	262144.	0.125000
$65$	1.37455e6	0.620816
$66$	−3.08569e6	−1.32114
$67$	2.76451e6	1.12294	0.561470	−	0.827497i	$-0.310236\pi$
$67$	2.76451e6	1.12294	0.561470	+	0.827497i	$0.310236\pi$
$68$	−272715.	−0.105179
$69$	−2.46851e6	−0.904614
$70$	−4.62570e6	−1.61188
$71$	5.36844e6	1.78010	0.890049	−	0.455865i	$-0.150670\pi$
$71$	5.36844e6	1.78010	0.890049	+	0.455865i	$0.150670\pi$
$72$	−525407.	−0.165895
$73$	−2.44360e6	−0.735192	−0.367596	−	0.929986i	$-0.619819\pi$
$73$	−2.44360e6	−0.735192	−0.367596	+	0.929986i	$0.619819\pi$
$74$	405224.	0.116248
$75$	−2.94060e6	−0.804863
$76$	2.35218e6	0.614643
$77$	−1.09121e7	−2.72389
$78$	1.72880e6	0.412489
$79$	−1.90275e6	−0.434196	−0.217098	−	0.976150i	$-0.569659\pi$
$79$	−1.90275e6	−0.434196	−0.217098	+	0.976150i	$0.569659\pi$
$80$	1.47684e6	0.322492
$81$	−5.97418e6	−1.24905
$82$	1.28868e6	0.258104
$83$	−5.24367e6	−1.00661	−0.503306	−	0.864108i	$-0.667883\pi$
$83$	−5.24367e6	−1.00661	−0.503306	+	0.864108i	$0.667883\pi$
$84$	−5.81783e6	−1.07099
$85$	−1.53640e6	−0.271355
$86$	−3.35246e6	−0.568355
$87$	1.07316e7	1.74722
$88$	3.48388e6	0.544972
$89$	−2.90811e6	−0.437267	−0.218633	−	0.975807i	$-0.570160\pi$
$89$	−2.90811e6	−0.437267	−0.218633	+	0.975807i	$0.570160\pi$
$90$	−2.95999e6	−0.427997
$91$	6.11363e6	0.850461
$92$	2.78707e6	0.373156
$93$	−1.13350e6	−0.146128
$94$	1.56515e6	0.194361
$95$	1.32515e7	1.58574
$96$	1.85745e6	0.214274
$97$	−4.20555e6	−0.467867	−0.233933	−	0.972253i	$-0.575160\pi$
$97$	−4.20555e6	−0.467867	−0.233933	+	0.972253i	$0.575160\pi$
$98$	−1.39856e7	−1.50103
$99$	−6.98264e6	−0.723263
$100$	3.32008e6	0.332008
$101$	1.38804e7	1.34053	0.670266	−	0.742121i	$-0.266180\pi$
$101$	1.38804e7	1.34053	0.670266	+	0.742121i	$0.266180\pi$
$102$	−1.93236e6	−0.180296
$103$	−1.96461e6	−0.177152	−0.0885760	−	0.996069i	$-0.528232\pi$
$103$	−1.96461e6	−0.177152	−0.0885760	+	0.996069i	$0.528232\pi$
$104$	−1.95189e6	−0.170153
$105$	−3.27759e7	−2.76307
$106$	−1.54089e7	−1.25661
$107$	7.37489e6	0.581985	0.290993	−	0.956725i	$-0.406014\pi$
$107$	7.37489e6	0.581985	0.290993	+	0.956725i	$0.406014\pi$
$108$	4.21125e6	0.321683
$109$	5.72494e6	0.423427	0.211713	−	0.977332i	$-0.432096\pi$
$109$	5.72494e6	0.423427	0.211713	+	0.977332i	$0.432096\pi$
$110$	1.96272e7	1.40599
$111$	2.87126e6	0.199270
$112$	6.56861e6	0.441784
$113$	2.76008e7	1.79948	0.899741	−	0.436424i	$-0.143755\pi$
$113$	2.76008e7	1.79948	0.899741	+	0.436424i	$0.143755\pi$
$114$	1.66667e7	1.05361
$115$	1.57015e7	0.962717
$116$	−1.21165e7	−0.720732
$117$	3.91212e6	0.225819
$118$	−1.87759e7	−1.05200
$119$	−6.83350e6	−0.371731
$120$	1.04643e7	0.552812
$121$	2.68135e7	1.37596
$122$	−8.54715e6	−0.426149
$123$	9.13107e6	0.442440
$124$	1.27978e6	0.0602780
$125$	−9.46417e6	−0.433409
$126$	−1.31653e7	−0.586317
$127$	1.76605e7	0.765050	0.382525	−	0.923945i	$-0.375055\pi$
$127$	1.76605e7	0.765050	0.382525	+	0.923945i	$0.375055\pi$
$128$	−2.09715e6	−0.0883883
$129$	−2.37543e7	−0.974267
$130$	−1.09964e7	−0.438983
$131$	−79274.7	−0.00308095	−0.00154048	−	0.999999i	$-0.500490\pi$
$131$	−79274.7	−0.00308095	−0.00154048	+	0.999999i	$0.500490\pi$
$132$	2.46855e7	0.934185
$133$	5.89392e7	2.17232
$134$	−2.21161e7	−0.794038
$135$	2.37249e7	0.829920
$136$	2.18172e6	0.0743727
$137$	−5.54352e7	−1.84189	−0.920945	−	0.389694i	$-0.872581\pi$
$137$	−5.54352e7	−1.84189	−0.920945	+	0.389694i	$0.872581\pi$
$138$	1.97481e7	0.639659
$139$	−1.58433e7	−0.500373	−0.250187	−	0.968198i	$-0.580492\pi$
$139$	−1.58433e7	−0.500373	−0.250187	+	0.968198i	$0.580492\pi$
$140$	3.70056e7	1.13977
$141$	1.10901e7	0.333171
$142$	−4.29475e7	−1.25872
$143$	−2.59406e7	−0.741828
$144$	4.20326e6	0.117305
$145$	−6.82606e7	−1.85944
$146$	1.95488e7	0.519860
$147$	−9.90964e7	−2.57304
$148$	−3.24179e6	−0.0821995
$149$	−3.12918e7	−0.774959	−0.387479	−	0.921878i	$-0.626654\pi$
$149$	−3.12918e7	−0.774959	−0.387479	+	0.921878i	$0.626654\pi$
$150$	2.35248e7	0.569124
$151$	7.18061e7	1.69724	0.848618	−	0.529007i	$-0.177435\pi$
$151$	7.18061e7	1.69724	0.848618	+	0.529007i	$0.177435\pi$
$152$	−1.88174e7	−0.434618
$153$	−4.37276e6	−0.0987042
$154$	8.72966e7	1.92608
$155$	7.20989e6	0.155513
$156$	−1.38304e7	−0.291674
$157$	6.92052e7	1.42722	0.713608	−	0.700545i	$-0.247060\pi$
$157$	6.92052e7	1.42722	0.713608	+	0.700545i	$0.247060\pi$
$158$	1.52220e7	0.307023
$159$	−1.09181e8	−2.15406
$160$	−1.18147e7	−0.228036
$161$	6.98362e7	1.31883
$162$	4.77934e7	0.883214
$163$	5.19124e7	0.938889	0.469445	−	0.882962i	$-0.344454\pi$
$163$	5.19124e7	0.938889	0.469445	+	0.882962i	$0.344454\pi$
$164$	−1.03094e7	−0.182507
$165$	1.39071e8	2.41014
$166$	4.19494e7	0.711782
$167$	−8.67223e7	−1.44087	−0.720433	−	0.693525i	$-0.756057\pi$
$167$	−8.67223e7	−1.44087	−0.720433	+	0.693525i	$0.756057\pi$
$168$	4.65427e7	0.757302
$169$	−4.82150e7	−0.768384
$170$	1.22912e7	0.191877
$171$	3.77152e7	0.576807
$172$	2.68197e7	0.401888
$173$	−3.39160e7	−0.498016	−0.249008	−	0.968501i	$-0.580105\pi$
$173$	−3.39160e7	−0.498016	−0.249008	+	0.968501i	$0.580105\pi$
$174$	−8.58528e7	−1.23547
$175$	8.31921e7	1.17341
$176$	−2.78711e7	−0.385353
$177$	−1.33039e8	−1.80332
$178$	2.32649e7	0.309194
$179$	1.35818e7	0.176999	0.0884994	−	0.996076i	$-0.471793\pi$
$179$	1.35818e7	0.176999	0.0884994	+	0.996076i	$0.471793\pi$
$180$	2.36799e7	0.302640
$181$	5.88225e7	0.737341	0.368671	−	0.929560i	$-0.379813\pi$
$181$	5.88225e7	0.737341	0.368671	+	0.929560i	$0.379813\pi$
$182$	−4.89091e7	−0.601367
$183$	−6.05619e7	−0.730500
$184$	−2.22965e7	−0.263861
$185$	−1.82633e7	−0.212069
$186$	9.06803e6	0.103328
$187$	2.89950e7	0.324248
$188$	−1.25212e7	−0.137434
$189$	1.05522e8	1.13691
$190$	−1.06012e8	−1.12129
$191$	−1.15450e8	−1.19888	−0.599442	−	0.800418i	$-0.704611\pi$
$191$	−1.15450e8	−1.19888	−0.599442	+	0.800418i	$0.704611\pi$
$192$	−1.48596e7	−0.151514
$193$	−1.96135e8	−1.96383	−0.981917	−	0.189311i	$-0.939375\pi$
$193$	−1.96135e8	−1.96383	−0.981917	+	0.189311i	$0.939375\pi$
$194$	3.36444e7	0.330832
$195$	−7.79161e7	−0.752500
$196$	1.11885e8	1.06139
$197$	−7.50680e7	−0.699557	−0.349778	−	0.936832i	$-0.613743\pi$
$197$	−7.50680e7	−0.699557	−0.349778	+	0.936832i	$0.613743\pi$
$198$	5.58611e7	0.511424
$199$	2.19532e8	1.97475	0.987375	−	0.158401i	$-0.0506340\pi$
$199$	2.19532e8	1.97475	0.987375	+	0.158401i	$0.0506340\pi$
$200$	−2.65606e7	−0.234765
$201$	−1.56706e8	−1.36113
$202$	−1.11043e8	−0.947900
$203$	−3.03606e8	−2.54726
$204$	1.54589e7	0.127489
$205$	−5.80801e7	−0.470857
$206$	1.57169e7	0.125265
$207$	4.46882e7	0.350185
$208$	1.56151e7	0.120316
$209$	−2.50083e8	−1.89484
$210$	2.62207e8	1.95379
$211$	1.64717e8	1.20712	0.603558	−	0.797319i	$-0.293749\pi$
$211$	1.64717e8	1.20712	0.603558	+	0.797319i	$0.293749\pi$
$212$	1.23271e8	0.888556
$213$	−3.04310e8	−2.15768
$214$	−5.89991e7	−0.411526
$215$	1.51094e8	1.03684
$216$	−3.36900e7	−0.227464
$217$	3.20677e7	0.213039
$218$	−4.57995e7	−0.299408
$219$	1.38516e8	0.891137
$220$	−1.57017e8	−0.994187
$221$	−1.62448e7	−0.101238
$222$	−2.29701e7	−0.140905
$223$	−2.83974e8	−1.71479	−0.857395	−	0.514659i	$-0.827918\pi$
$223$	−2.83974e8	−1.71479	−0.857395	+	0.514659i	$0.827918\pi$
$224$	−5.25489e7	−0.312389
$225$	5.32347e7	0.311570
$226$	−2.20807e8	−1.27243
$227$	1.12496e8	0.638332	0.319166	−	0.947699i	$-0.396597\pi$
$227$	1.12496e8	0.638332	0.319166	+	0.947699i	$0.396597\pi$
$228$	−1.33333e8	−0.745018
$229$	−2.41992e8	−1.33161	−0.665805	−	0.746125i	$-0.731912\pi$
$229$	−2.41992e8	−1.33161	−0.665805	+	0.746125i	$0.731912\pi$
$230$	−1.25612e8	−0.680744
$231$	6.18550e8	3.30167
$232$	9.69319e7	0.509634
$233$	3.30346e8	1.71089	0.855447	−	0.517891i	$-0.173283\pi$
$233$	3.30346e8	1.71089	0.855447	+	0.517891i	$0.173283\pi$
$234$	−3.12969e7	−0.159678
$235$	−7.05408e7	−0.354571
$236$	1.50207e8	0.743873
$237$	1.07857e8	0.526295
$238$	5.46680e7	0.262853
$239$	−2.89292e7	−0.137070	−0.0685352	−	0.997649i	$-0.521833\pi$
$239$	−2.89292e7	−0.137070	−0.0685352	+	0.997649i	$0.521833\pi$
$240$	−8.37147e7	−0.390897
$241$	1.09930e8	0.505891	0.252946	−	0.967480i	$-0.418601\pi$
$241$	1.09930e8	0.505891	0.252946	+	0.967480i	$0.418601\pi$
$242$	−2.14508e8	−0.972949
$243$	1.94740e8	0.870629
$244$	6.83772e7	0.301333
$245$	6.30324e8	2.73831
$246$	−7.30486e7	−0.312852
$247$	1.40112e8	0.591612
$248$	−1.02382e7	−0.0426230
$249$	2.97237e8	1.22013
$250$	7.57134e7	0.306466
$251$	−1.14733e8	−0.457962	−0.228981	−	0.973431i	$-0.573539\pi$
$251$	−1.14733e8	−0.457962	−0.228981	+	0.973431i	$0.573539\pi$
$252$	1.05322e8	0.414589
$253$	−2.96320e8	−1.15037
$254$	−1.41284e8	−0.540972
$255$	8.70906e7	0.328913
$256$	1.67772e7	0.0625000
$257$	5.37256e7	0.197431	0.0987154	−	0.995116i	$-0.468527\pi$
$257$	5.37256e7	0.197431	0.0987154	+	0.995116i	$0.468527\pi$
$258$	1.90034e8	0.688911
$259$	−8.12304e7	−0.290516
$260$	8.79710e7	0.310408
$261$	−1.94278e8	−0.676364
$262$	634197.	0.00217856
$263$	2.14600e8	0.727419	0.363709	−	0.931513i	$-0.381510\pi$
$263$	2.14600e8	0.727419	0.363709	+	0.931513i	$0.381510\pi$
$264$	−1.97484e8	−0.660568
$265$	6.94471e8	2.29242
$266$	−4.71513e8	−1.53606
$267$	1.64846e8	0.530017
$268$	1.76929e8	0.561470
$269$	4.40021e8	1.37829	0.689145	−	0.724623i	$-0.257986\pi$
$269$	4.40021e8	1.37829	0.689145	+	0.724623i	$0.257986\pi$
$270$	−1.89799e8	−0.586842
$271$	3.43478e8	1.04835	0.524175	−	0.851611i	$-0.324374\pi$
$271$	3.43478e8	1.04835	0.524175	+	0.851611i	$0.324374\pi$
$272$	−1.74538e7	−0.0525894
$273$	−3.46551e8	−1.03086
$274$	4.43481e8	1.30241
$275$	−3.52990e8	−1.02352
$276$	−1.57985e8	−0.452307
$277$	−1.11251e8	−0.314502	−0.157251	−	0.987559i	$-0.550263\pi$
$277$	−1.11251e8	−0.314502	−0.157251	+	0.987559i	$0.550263\pi$
$278$	1.26746e8	0.353817
$279$	2.05202e7	0.0565674
$280$	−2.96045e8	−0.805942
$281$	−3.99045e8	−1.07288	−0.536438	−	0.843940i	$-0.680231\pi$
$281$	−3.99045e8	−1.07288	−0.536438	+	0.843940i	$0.680231\pi$
$282$	−8.87206e7	−0.235588
$283$	−2.26808e8	−0.594847	−0.297423	−	0.954746i	$-0.596127\pi$
$283$	−2.26808e8	−0.594847	−0.297423	+	0.954746i	$0.596127\pi$
$284$	3.43580e8	0.890049
$285$	−7.51160e8	−1.92210
$286$	2.07525e8	0.524552
$287$	−2.58326e8	−0.645031
$288$	−3.36261e7	−0.0829473
$289$	−3.92181e8	−0.955750
$290$	5.46085e8	1.31482
$291$	2.38392e8	0.567108
$292$	−1.56391e8	−0.367596
$293$	3.64309e8	0.846122	0.423061	−	0.906101i	$-0.360956\pi$
$293$	3.64309e8	0.846122	0.423061	+	0.906101i	$0.360956\pi$
$294$	7.92771e8	1.81942
$295$	8.46223e8	1.91914
$296$	2.59343e7	0.0581238
$297$	−4.47738e8	−0.991692
$298$	2.50334e8	0.547979
$299$	1.66017e8	0.359173
$300$	−1.88199e8	−0.402432
$301$	6.72028e8	1.42038
$302$	−5.74449e8	−1.20013
$303$	−7.86810e8	−1.62488
$304$	1.50540e8	0.307322
$305$	3.85217e8	0.777420
$306$	3.49821e7	0.0697944
$307$	−6.39929e8	−1.26226	−0.631129	−	0.775678i	$-0.717408\pi$
$307$	−6.39929e8	−1.26226	−0.631129	+	0.775678i	$0.717408\pi$
$308$	−6.98372e8	−1.36195
$309$	1.11364e8	0.214729
$310$	−5.76791e7	−0.109965
$311$	−1.02265e9	−1.92781	−0.963907	−	0.266239i	$-0.914219\pi$
$311$	−1.02265e9	−1.92781	−0.963907	+	0.266239i	$0.914219\pi$
$312$	1.10643e8	0.206245
$313$	7.97524e7	0.147007	0.0735036	−	0.997295i	$-0.476582\pi$
$313$	7.97524e7	0.147007	0.0735036	+	0.997295i	$0.476582\pi$
$314$	−5.53641e8	−1.00919
$315$	5.93353e8	1.06961
$316$	−1.21776e8	−0.217098
$317$	−7.88946e8	−1.39104	−0.695520	−	0.718507i	$-0.744826\pi$
$317$	−7.88946e8	−1.39104	−0.695520	+	0.718507i	$0.744826\pi$
$318$	8.73451e8	1.52315
$319$	1.28822e9	2.22189
$320$	9.45178e7	0.161246
$321$	−4.18045e8	−0.705433
$322$	−5.58690e8	−0.932557
$323$	−1.56610e8	−0.258590
$324$	−3.82348e8	−0.624526
$325$	1.97767e8	0.319567
$326$	−4.15299e8	−0.663895
$327$	−3.24518e8	−0.513241
$328$	8.24753e7	0.129052
$329$	−3.13747e8	−0.485730
$330$	−1.11256e9	−1.70422
$331$	−4.83577e8	−0.732938	−0.366469	−	0.930430i	$-0.619433\pi$
$331$	−4.83577e8	−0.732938	−0.366469	+	0.930430i	$0.619433\pi$
$332$	−3.35595e8	−0.503306
$333$	−5.19794e7	−0.0771394
$334$	6.93779e8	1.01885
$335$	9.96763e8	1.44856
$336$	−3.72341e8	−0.535493
$337$	−1.42527e8	−0.202858	−0.101429	−	0.994843i	$-0.532342\pi$
$337$	−1.42527e8	−0.202858	−0.101429	+	0.994843i	$0.532342\pi$
$338$	3.85720e8	0.543330
$339$	−1.56455e9	−2.18118
$340$	−9.83294e7	−0.135677
$341$	−1.36066e8	−0.185827
$342$	−3.01722e8	−0.407864
$343$	1.48283e9	1.98410
$344$	−2.14558e8	−0.284177
$345$	−8.90039e8	−1.16692
$346$	2.71328e8	0.352151
$347$	−8.85934e8	−1.13828	−0.569139	−	0.822241i	$-0.692723\pi$
$347$	−8.85934e8	−1.13828	−0.569139	+	0.822241i	$0.692723\pi$
$348$	6.86822e8	0.873609
$349$	−3.31914e8	−0.417961	−0.208981	−	0.977920i	$-0.567015\pi$
$349$	−3.31914e8	−0.417961	−0.208981	+	0.977920i	$0.567015\pi$
$350$	−6.65537e8	−0.829724
$351$	2.50851e8	0.309629
$352$	2.22969e8	0.272486
$353$	−4.34687e8	−0.525975	−0.262988	−	0.964799i	$-0.584708\pi$
$353$	−4.34687e8	−0.525975	−0.262988	+	0.964799i	$0.584708\pi$
$354$	1.06431e9	1.27514
$355$	1.93563e9	2.29627
$356$	−1.86119e8	−0.218633
$357$	3.87357e8	0.450580
$358$	−1.08654e8	−0.125157
$359$	1.68930e9	1.92697	0.963486	−	0.267758i	$-0.0862829\pi$
$359$	1.68930e9	1.92697	0.963486	+	0.267758i	$0.0862829\pi$
$360$	−1.89439e8	−0.213999
$361$	4.56898e8	0.511145
$362$	−4.70580e8	−0.521379
$363$	−1.51992e9	−1.66782
$364$	3.91272e8	0.425230
$365$	−8.81059e8	−0.948374
$366$	4.84495e8	0.516542
$367$	−3.39873e8	−0.358910	−0.179455	−	0.983766i	$-0.557433\pi$
$367$	−3.39873e8	−0.358910	−0.179455	+	0.983766i	$0.557433\pi$
$368$	1.78372e8	0.186578
$369$	−1.65303e8	−0.171272
$370$	1.46106e8	0.149956
$371$	3.08883e9	3.14040
$372$	−7.25442e7	−0.0730639
$373$	−7.78423e8	−0.776667	−0.388333	−	0.921519i	$-0.626949\pi$
$373$	−7.78423e8	−0.776667	−0.388333	+	0.921519i	$0.626949\pi$
$374$	−2.31960e8	−0.229278
$375$	5.36476e8	0.525341
$376$	1.00170e8	0.0971805
$377$	−7.21743e8	−0.693725
$378$	−8.44178e8	−0.803920
$379$	1.47561e9	1.39231	0.696153	−	0.717893i	$-0.254893\pi$
$379$	1.47561e9	1.39231	0.696153	+	0.717893i	$0.254893\pi$
$380$	8.48095e8	0.792870
$381$	−1.00108e9	−0.927328
$382$	9.23600e8	0.847739
$383$	−1.53681e9	−1.39773	−0.698867	−	0.715252i	$-0.746312\pi$
$383$	−1.53681e9	−1.39773	−0.698867	+	0.715252i	$0.746312\pi$
$384$	1.18877e8	0.107137
$385$	−3.93442e9	−3.51373
$386$	1.56908e9	1.38864
$387$	4.30031e8	0.377148
$388$	−2.69155e8	−0.233933
$389$	9.07053e8	0.781284	0.390642	−	0.920543i	$-0.372253\pi$
$389$	9.07053e8	0.781284	0.390642	+	0.920543i	$0.372253\pi$
$390$	6.23329e8	0.532098
$391$	−1.85565e8	−0.156992
$392$	−8.95076e8	−0.750514
$393$	4.49368e6	0.00373446
$394$	6.00544e8	0.494661
$395$	−6.86048e8	−0.560099
$396$	−4.46889e8	−0.361632
$397$	5.73804e8	0.460253	0.230127	−	0.973161i	$-0.426086\pi$
$397$	5.73804e8	0.460253	0.230127	+	0.973161i	$0.426086\pi$
$398$	−1.75626e9	−1.39636
$399$	−3.34097e9	−2.63310
$400$	2.12485e8	0.166004
$401$	−3.21010e8	−0.248607	−0.124303	−	0.992244i	$-0.539670\pi$
$401$	−3.21010e8	−0.248607	−0.124303	+	0.992244i	$0.539670\pi$
$402$	1.25365e9	0.962465
$403$	7.62326e7	0.0580194
$404$	8.88346e8	0.670266
$405$	−2.15403e9	−1.61124
$406$	2.42885e9	1.80119
$407$	3.44666e8	0.253407
$408$	−1.23671e8	−0.0901482
$409$	−1.27539e9	−0.921743	−0.460872	−	0.887467i	$-0.652463\pi$
$409$	−1.27539e9	−0.921743	−0.460872	+	0.887467i	$0.652463\pi$
$410$	4.64641e8	0.332946
$411$	3.14234e9	2.23258
$412$	−1.25735e8	−0.0885760
$413$	3.76378e9	2.62905
$414$	−3.57506e8	−0.247618
$415$	−1.89064e9	−1.29850
$416$	−1.24921e8	−0.0850764
$417$	8.98077e8	0.606509
$418$	2.00066e9	1.33985
$419$	−2.17661e9	−1.44554	−0.722771	−	0.691087i	$-0.757132\pi$
$419$	−2.17661e9	−1.44554	−0.722771	+	0.691087i	$0.757132\pi$
$420$	−2.09766e9	−1.38154
$421$	−1.01489e9	−0.662875	−0.331438	−	0.943477i	$-0.607534\pi$
$421$	−1.01489e9	−0.662875	−0.331438	+	0.943477i	$0.607534\pi$
$422$	−1.31773e9	−0.853560
$423$	−2.00767e8	−0.128974
$424$	−9.86167e8	−0.628304
$425$	−2.21054e8	−0.139681
$426$	2.43448e9	1.52571
$427$	1.71334e9	1.06499
$428$	4.71993e8	0.290993
$429$	1.47044e9	0.899181
$430$	−1.20875e9	−0.733159
$431$	7.43582e8	0.447361	0.223681	−	0.974662i	$-0.428193\pi$
$431$	7.43582e8	0.447361	0.223681	+	0.974662i	$0.428193\pi$
$432$	2.69520e8	0.160841
$433$	−1.66611e9	−0.986273	−0.493136	−	0.869952i	$-0.664150\pi$
$433$	−1.66611e9	−0.986273	−0.493136	+	0.869952i	$0.664150\pi$
$434$	−2.56542e8	−0.150641
$435$	3.86935e9	2.25385
$436$	3.66396e8	0.211713
$437$	1.60051e9	0.917430
$438$	−1.10813e9	−0.630129
$439$	2.65790e9	1.49938	0.749692	−	0.661786i	$-0.230201\pi$
$439$	2.65790e9	1.49938	0.749692	+	0.661786i	$0.230201\pi$
$440$	1.25614e9	0.702996
$441$	1.79397e9	0.996050
$442$	1.29959e8	0.0715859
$443$	1.20975e9	0.661123	0.330561	−	0.943784i	$-0.392762\pi$
$443$	1.20975e9	0.661123	0.330561	+	0.943784i	$0.392762\pi$
$444$	1.83761e8	0.0996352
$445$	−1.04854e9	−0.564060
$446$	2.27179e9	1.21254
$447$	1.77377e9	0.939338
$448$	4.20391e8	0.220892
$449$	1.40983e9	0.735032	0.367516	−	0.930017i	$-0.380208\pi$
$449$	1.40983e9	0.735032	0.367516	+	0.930017i	$0.380208\pi$
$450$	−4.25877e8	−0.220313
$451$	1.09609e9	0.562639
$452$	1.76645e9	0.899741
$453$	−4.07033e9	−2.05724
$454$	−8.99969e8	−0.451369
$455$	2.20431e9	1.09707
$456$	1.06667e9	0.526807
$457$	−1.67800e9	−0.822407	−0.411203	−	0.911544i	$-0.634891\pi$
$457$	−1.67800e9	−0.822407	−0.411203	+	0.911544i	$0.634891\pi$
$458$	1.93594e9	0.941591
$459$	−2.80389e8	−0.135337
$460$	1.00490e9	0.481359
$461$	−5.09611e8	−0.242262	−0.121131	−	0.992637i	$-0.538652\pi$
$461$	−5.09611e8	−0.242262	−0.121131	+	0.992637i	$0.538652\pi$
$462$	−4.94840e9	−2.33463
$463$	−2.45905e9	−1.15142	−0.575711	−	0.817653i	$-0.695275\pi$
$463$	−2.45905e9	−1.15142	−0.575711	+	0.817653i	$0.695275\pi$
$464$	−7.75455e8	−0.360366
$465$	−4.08692e8	−0.188500
$466$	−2.64277e9	−1.20978
$467$	−1.18787e9	−0.539710	−0.269855	−	0.962901i	$-0.586976\pi$
$467$	−1.18787e9	−0.539710	−0.269855	+	0.962901i	$0.586976\pi$
$468$	2.50375e8	0.112910
$469$	4.43335e9	1.98439
$470$	5.64327e8	0.250719
$471$	−3.92289e9	−1.72995
$472$	−1.20166e9	−0.525998
$473$	−2.85146e9	−1.23895
$474$	−8.62857e8	−0.372147
$475$	1.90660e9	0.816266
$476$	−4.37344e8	−0.185865
$477$	1.97654e9	0.833858
$478$	2.31434e8	0.0969234
$479$	−4.52784e9	−1.88242	−0.941211	−	0.337819i	$-0.890311\pi$
$479$	−4.52784e9	−1.88242	−0.941211	+	0.337819i	$0.890311\pi$
$480$	6.69717e8	0.276406
$481$	−1.93104e8	−0.0791194
$482$	−8.79441e8	−0.357719
$483$	−3.95866e9	−1.59858
$484$	1.71606e9	0.687979
$485$	−1.51634e9	−0.603533
$486$	−1.55792e9	−0.615628
$487$	1.83779e9	0.721014	0.360507	−	0.932757i	$-0.382604\pi$
$487$	1.83779e9	0.721014	0.360507	+	0.932757i	$0.382604\pi$
$488$	−5.47018e8	−0.213075
$489$	−2.94265e9	−1.13804
$490$	−5.04259e9	−1.93628
$491$	−5.11971e9	−1.95191	−0.975956	−	0.217965i	$-0.930058\pi$
$491$	−5.11971e9	−1.95191	−0.975956	+	0.217965i	$0.930058\pi$
$492$	5.84389e8	0.221220
$493$	8.06726e8	0.303223
$494$	−1.12090e9	−0.418333
$495$	−2.51764e9	−0.932986
$496$	8.19058e7	0.0301390
$497$	8.60918e9	3.14568
$498$	−2.37790e9	−0.862761
$499$	−1.51982e9	−0.547570	−0.273785	−	0.961791i	$-0.588276\pi$
$499$	−1.51982e9	−0.547570	−0.273785	+	0.961791i	$0.588276\pi$
$500$	−6.05707e8	−0.216704
$501$	4.91585e9	1.74649
$502$	9.17863e8	0.323828
$503$	2.54603e9	0.892021	0.446011	−	0.895028i	$-0.352844\pi$
$503$	2.54603e9	0.892021	0.446011	+	0.895028i	$0.352844\pi$
$504$	−8.42577e8	−0.293159
$505$	5.00468e9	1.72924
$506$	2.37056e9	0.813438
$507$	2.73306e9	0.931369
$508$	1.13027e9	0.382525
$509$	2.44937e9	0.823269	0.411635	−	0.911349i	$-0.364958\pi$
$509$	2.44937e9	0.823269	0.411635	+	0.911349i	$0.364958\pi$
$510$	−6.96725e8	−0.232576
$511$	−3.91872e9	−1.29919
$512$	−1.34218e8	−0.0441942
$513$	2.41836e9	0.790880
$514$	−4.29805e8	−0.139605
$515$	−7.08354e8	−0.228520
$516$	−1.52027e9	−0.487134
$517$	1.33125e9	0.423685
$518$	6.49843e8	0.205426
$519$	1.92253e9	0.603653
$520$	−7.03768e8	−0.219492
$521$	3.65748e9	1.13305	0.566526	−	0.824044i	$-0.308287\pi$
$521$	3.65748e9	1.13305	0.566526	+	0.824044i	$0.308287\pi$
$522$	1.55422e9	0.478262
$523$	4.56015e9	1.39387	0.696937	−	0.717133i	$-0.254546\pi$
$523$	4.56015e9	1.39387	0.696937	+	0.717133i	$0.254546\pi$
$524$	−5.07358e6	−0.00154048
$525$	−4.71574e9	−1.42230
$526$	−1.71680e9	−0.514363
$527$	−8.52088e7	−0.0253599
$528$	1.57987e9	0.467092
$529$	−1.50840e9	−0.443020
$530$	−5.55577e9	−1.62098
$531$	2.40845e9	0.698082
$532$	3.77211e9	1.08616
$533$	−6.14101e8	−0.175669
$534$	−1.31877e9	−0.374779
$535$	2.65907e9	0.750742
$536$	−1.41543e9	−0.397019
$537$	−7.69882e8	−0.214543
$538$	−3.52017e9	−0.974599
$539$	−1.18955e10	−3.27207
$540$	1.51839e9	0.414960
$541$	1.44423e9	0.392145	0.196073	−	0.980589i	$-0.437181\pi$
$541$	1.44423e9	0.392145	0.196073	+	0.980589i	$0.437181\pi$
$542$	−2.74782e9	−0.741295
$543$	−3.33435e9	−0.893742
$544$	1.39630e8	0.0371863
$545$	2.06417e9	0.546206
$546$	2.77241e9	0.728925
$547$	−2.42116e9	−0.632511	−0.316256	−	0.948674i	$-0.602426\pi$
$547$	−2.42116e9	−0.632511	−0.316256	+	0.948674i	$0.602426\pi$
$548$	−3.54785e9	−0.920945
$549$	1.09637e9	0.282784
$550$	2.82392e9	0.723740
$551$	−6.95804e9	−1.77197
$552$	1.26388e9	0.319829
$553$	−3.05136e9	−0.767284
$554$	8.90006e8	0.222387
$555$	1.03525e9	0.257052
$556$	−1.01397e9	−0.250187
$557$	7.78342e8	0.190843	0.0954217	−	0.995437i	$-0.469580\pi$
$557$	7.78342e8	0.190843	0.0954217	+	0.995437i	$0.469580\pi$
$558$	−1.64161e8	−0.0399992
$559$	1.59757e9	0.386829
$560$	2.36836e9	0.569887
$561$	−1.64358e9	−0.393026
$562$	3.19236e9	0.758638
$563$	−1.52702e9	−0.360632	−0.180316	−	0.983609i	$-0.557712\pi$
$563$	−1.52702e9	−0.360632	−0.180316	+	0.983609i	$0.557712\pi$
$564$	7.09765e8	0.166586
$565$	9.95167e9	2.32127
$566$	1.81446e9	0.420620
$567$	−9.58058e9	−2.20725
$568$	−2.74864e9	−0.629360
$569$	−6.14617e9	−1.39866	−0.699329	−	0.714800i	$-0.746518\pi$
$569$	−6.14617e9	−1.39866	−0.699329	+	0.714800i	$0.746518\pi$
$570$	6.00928e9	1.35913
$571$	7.49905e8	0.168570	0.0842849	−	0.996442i	$-0.473139\pi$
$571$	7.49905e8	0.168570	0.0842849	+	0.996442i	$0.473139\pi$
$572$	−1.66020e9	−0.370914
$573$	6.54428e9	1.45318
$574$	2.06660e9	0.456106
$575$	2.25910e9	0.495562
$576$	2.69008e8	0.0586526
$577$	−1.51301e9	−0.327888	−0.163944	−	0.986470i	$-0.552422\pi$
$577$	−1.51301e9	−0.327888	−0.163944	+	0.986470i	$0.552422\pi$
$578$	3.13745e9	0.675817
$579$	1.11179e10	2.38039
$580$	−4.36868e9	−0.929720
$581$	−8.40909e9	−1.77882
$582$	−1.90713e9	−0.401006
$583$	−1.31061e10	−2.73927
$584$	1.25113e9	0.259930
$585$	1.41054e9	0.291300
$586$	−2.91447e9	−0.598299
$587$	5.97756e9	1.21980	0.609902	−	0.792476i	$-0.291209\pi$
$587$	5.97756e9	1.21980	0.609902	+	0.792476i	$0.291209\pi$
$588$	−6.34217e9	−1.28652
$589$	7.34929e8	0.148198
$590$	−6.76978e9	−1.35704
$591$	4.25523e9	0.847943
$592$	−2.07475e8	−0.0410997
$593$	−7.24895e8	−0.142752	−0.0713762	−	0.997449i	$-0.522739\pi$
$593$	−7.24895e8	−0.142752	−0.0713762	+	0.997449i	$0.522739\pi$
$594$	3.58191e9	0.701232
$595$	−2.46386e9	−0.479521
$596$	−2.00268e9	−0.387479
$597$	−1.24442e10	−2.39362
$598$	−1.32814e9	−0.253974
$599$	3.20378e9	0.609073	0.304536	−	0.952501i	$-0.401498\pi$
$599$	3.20378e9	0.609073	0.304536	+	0.952501i	$0.401498\pi$
$600$	1.50559e9	0.284562
$601$	1.82721e9	0.343343	0.171672	−	0.985154i	$-0.445083\pi$
$601$	1.82721e9	0.343343	0.171672	+	0.985154i	$0.445083\pi$
$602$	−5.37623e9	−1.00436
$603$	2.83690e9	0.526906
$604$	4.59559e9	0.848618
$605$	9.66780e9	1.77494
$606$	6.29448e9	1.14896
$607$	−2.06764e9	−0.375245	−0.187623	−	0.982241i	$-0.560078\pi$
$607$	−2.06764e9	−0.375245	−0.187623	+	0.982241i	$0.560078\pi$
$608$	−1.20432e9	−0.217309
$609$	1.72099e10	3.08757
$610$	−3.08173e9	−0.549719
$611$	−7.45852e8	−0.132284
$612$	−2.79857e8	−0.0493521
$613$	−4.54512e9	−0.796955	−0.398477	−	0.917178i	$-0.630461\pi$
$613$	−4.54512e9	−0.796955	−0.398477	+	0.917178i	$0.630461\pi$
$614$	5.11944e9	0.892551
$615$	3.29227e9	0.570733
$616$	5.58698e9	0.963041
$617$	−4.98415e9	−0.854265	−0.427132	−	0.904189i	$-0.640476\pi$
$617$	−4.98415e9	−0.854265	−0.427132	+	0.904189i	$0.640476\pi$
$618$	−8.90911e8	−0.151836
$619$	−4.52382e9	−0.766635	−0.383317	−	0.923617i	$-0.625218\pi$
$619$	−4.52382e9	−0.766635	−0.383317	+	0.923617i	$0.625218\pi$
$620$	4.61433e8	0.0777567
$621$	2.86548e9	0.480151
$622$	8.18119e9	1.36317
$623$	−4.66364e9	−0.772710
$624$	−8.85143e8	−0.145837
$625$	−7.46520e9	−1.22310
$626$	−6.38019e8	−0.103950
$627$	1.41760e10	2.29676
$628$	4.42913e9	0.713608
$629$	2.15841e8	0.0345826
$630$	−4.74682e9	−0.756330
$631$	1.02552e9	0.162495	0.0812475	−	0.996694i	$-0.474110\pi$
$631$	1.02552e9	0.162495	0.0812475	+	0.996694i	$0.474110\pi$
$632$	9.74206e8	0.153511
$633$	−9.33696e9	−1.46316
$634$	6.31157e9	0.983614
$635$	6.36761e9	0.986890
$636$	−6.98761e9	−1.07703
$637$	6.66463e9	1.02162
$638$	−1.03058e10	−1.57111
$639$	5.50902e9	0.835259
$640$	−7.56143e8	−0.114018
$641$	−6.46595e8	−0.0969682	−0.0484841	−	0.998824i	$-0.515439\pi$
$641$	−6.46595e8	−0.0969682	−0.0484841	+	0.998824i	$0.515439\pi$
$642$	3.34436e9	0.498816
$643$	2.97547e9	0.441384	0.220692	−	0.975344i	$-0.429168\pi$
$643$	2.97547e9	0.441384	0.220692	+	0.975344i	$0.429168\pi$
$644$	4.46952e9	0.659417
$645$	−8.56477e9	−1.25677
$646$	1.25288e9	0.182851
$647$	8.15019e9	1.18305	0.591525	−	0.806287i	$-0.298526\pi$
$647$	8.15019e9	1.18305	0.591525	+	0.806287i	$0.298526\pi$
$648$	3.05878e9	0.441607
$649$	−1.59700e10	−2.29323
$650$	−1.58214e9	−0.225968
$651$	−1.81776e9	−0.258228
$652$	3.32239e9	0.469445
$653$	7.22353e9	1.01520	0.507602	−	0.861592i	$-0.330532\pi$
$653$	7.22353e9	1.01520	0.507602	+	0.861592i	$0.330532\pi$
$654$	2.59614e9	0.362916
$655$	−2.85830e7	−0.00397433
$656$	−6.59802e8	−0.0912537
$657$	−2.50759e9	−0.344968
$658$	2.50998e9	0.343463
$659$	−2.91517e9	−0.396794	−0.198397	−	0.980122i	$-0.563574\pi$
$659$	−2.91517e9	−0.396794	−0.198397	+	0.980122i	$0.563574\pi$
$660$	8.90052e9	1.20507
$661$	1.21040e10	1.63013	0.815065	−	0.579369i	$-0.196701\pi$
$661$	1.21040e10	1.63013	0.815065	+	0.579369i	$0.196701\pi$
$662$	3.86861e9	0.518266
$663$	9.20838e8	0.122712
$664$	2.68476e9	0.355891
$665$	2.12509e10	2.80222
$666$	4.15835e8	0.0545458
$667$	−8.24449e9	−1.07578
$668$	−5.55023e9	−0.720433
$669$	1.60970e10	2.07852
$670$	−7.97410e9	−1.02428
$671$	−7.26984e9	−0.928958
$672$	2.97873e9	0.378651
$673$	−4.16140e9	−0.526243	−0.263122	−	0.964763i	$-0.584752\pi$
$673$	−4.16140e9	−0.526243	−0.263122	+	0.964763i	$0.584752\pi$
$674$	1.14022e9	0.143443
$675$	3.41349e9	0.427205
$676$	−3.08576e9	−0.384192
$677$	4.12996e9	0.511547	0.255773	−	0.966737i	$-0.417670\pi$
$677$	4.12996e9	0.511547	0.255773	+	0.966737i	$0.417670\pi$
$678$	1.25164e10	1.54233
$679$	−6.74430e9	−0.826785
$680$	7.86635e8	0.0959383
$681$	−6.37684e9	−0.773732
$682$	1.08853e9	0.131399
$683$	1.54270e9	0.185272	0.0926361	−	0.995700i	$-0.470471\pi$
$683$	1.54270e9	0.185272	0.0926361	+	0.995700i	$0.470471\pi$
$684$	2.41377e9	0.288403
$685$	−1.99875e10	−2.37598
$686$	−1.18627e10	−1.40297
$687$	1.37173e10	1.61406
$688$	1.71646e9	0.200944
$689$	7.34288e9	0.855262
$690$	7.12031e9	0.825139
$691$	−8.98607e9	−1.03609	−0.518044	−	0.855354i	$-0.673340\pi$
$691$	−8.98607e9	−1.03609	−0.518044	+	0.855354i	$0.673340\pi$
$692$	−2.17063e9	−0.249008
$693$	−1.11978e10	−1.27811
$694$	7.08747e9	0.804884
$695$	−5.71241e9	−0.645465
$696$	−5.49458e9	−0.617735
$697$	6.86410e8	0.0767837
$698$	2.65531e9	0.295543
$699$	−1.87256e10	−2.07380
$700$	5.32429e9	0.586704
$701$	2.72692e9	0.298992	0.149496	−	0.988762i	$-0.452235\pi$
$701$	2.72692e9	0.298992	0.149496	+	0.988762i	$0.452235\pi$
$702$	−2.00681e9	−0.218941
$703$	−1.86164e9	−0.202093
$704$	−1.78375e9	−0.192677
$705$	3.99860e9	0.429780
$706$	3.47750e9	0.371921
$707$	2.22595e10	2.36891
$708$	−8.51450e9	−0.901659
$709$	8.71252e9	0.918083	0.459041	−	0.888415i	$-0.348193\pi$
$709$	8.71252e9	0.918083	0.459041	+	0.888415i	$0.348193\pi$
$710$	−1.54850e10	−1.62371
$711$	−1.95257e9	−0.203734
$712$	1.48895e9	0.154597
$713$	8.70808e8	0.0899723
$714$	−3.09885e9	−0.318608
$715$	−9.35305e9	−0.956934
$716$	8.69233e8	0.0884994
$717$	1.63985e9	0.166145
$718$	−1.35144e10	−1.36258
$719$	−1.14538e10	−1.14921	−0.574606	−	0.818430i	$-0.694845\pi$
$719$	−1.14538e10	−1.14921	−0.574606	+	0.818430i	$0.694845\pi$
$720$	1.51551e9	0.151320
$721$	−3.15058e9	−0.313052
$722$	−3.65518e9	−0.361434
$723$	−6.23139e9	−0.613198
$724$	3.76464e9	0.368671
$725$	−9.82121e9	−0.957155
$726$	1.21594e10	1.17932
$727$	7.31928e8	0.0706477	0.0353239	−	0.999376i	$-0.488754\pi$
$727$	7.31928e8	0.0706477	0.0353239	+	0.999376i	$0.488754\pi$
$728$	−3.13018e9	−0.300683
$729$	2.02670e9	0.193750
$730$	7.04847e9	0.670602
$731$	−1.78568e9	−0.169080
$732$	−3.87596e9	−0.365250
$733$	−3.27720e9	−0.307354	−0.153677	−	0.988121i	$-0.549112\pi$
$733$	−3.27720e9	−0.307354	−0.153677	+	0.988121i	$0.549112\pi$
$734$	2.71899e9	0.253788
$735$	−3.57299e10	−3.31914
$736$	−1.42698e9	−0.131930
$737$	−1.88110e10	−1.73091
$738$	1.32242e9	0.121108
$739$	−1.16807e10	−1.06467	−0.532334	−	0.846534i	$-0.678685\pi$
$739$	−1.16807e10	−1.06467	−0.532334	+	0.846534i	$0.678685\pi$
$740$	−1.16885e9	−0.106035
$741$	−7.94227e9	−0.717102
$742$	−2.47106e10	−2.22060
$743$	−1.40226e10	−1.25420	−0.627102	−	0.778937i	$-0.715759\pi$
$743$	−1.40226e10	−1.25420	−0.627102	+	0.778937i	$0.715759\pi$
$744$	5.80354e8	0.0516639
$745$	−1.12825e10	−0.999672
$746$	6.22738e9	0.549186
$747$	−5.38098e9	−0.472323
$748$	1.85568e9	0.162124
$749$	1.18268e10	1.02845
$750$	−4.29181e9	−0.371472
$751$	2.59621e9	0.223666	0.111833	−	0.993727i	$-0.464328\pi$
$751$	2.59621e9	0.223666	0.111833	+	0.993727i	$0.464328\pi$
$752$	−8.01358e8	−0.0687170
$753$	6.50363e9	0.555103
$754$	5.77394e9	0.490538
$755$	2.58902e10	2.18938
$756$	6.75342e9	0.568457
$757$	1.52457e10	1.27735	0.638676	−	0.769476i	$-0.279482\pi$
$757$	1.52457e10	1.27735	0.638676	+	0.769476i	$0.279482\pi$
$758$	−1.18049e10	−0.984509
$759$	1.67969e10	1.39439
$760$	−6.78476e9	−0.560643
$761$	5.69847e9	0.468718	0.234359	−	0.972150i	$-0.424701\pi$
$761$	5.69847e9	0.468718	0.234359	+	0.972150i	$0.424701\pi$
$762$	8.00868e9	0.655720
$763$	9.18088e9	0.748253
$764$	−7.38880e9	−0.599442
$765$	−1.57663e9	−0.127325
$766$	1.22945e10	0.988347
$767$	8.94740e9	0.716000
$768$	−9.51016e8	−0.0757571
$769$	−1.52942e10	−1.21279	−0.606395	−	0.795164i	$-0.707385\pi$
$769$	−1.52942e10	−1.21279	−0.606395	+	0.795164i	$0.707385\pi$
$770$	3.14754e10	2.48458
$771$	−3.04543e9	−0.239309
$772$	−1.25526e10	−0.981917
$773$	−1.28508e10	−1.00070	−0.500349	−	0.865824i	$-0.666795\pi$
$773$	−1.28508e10	−1.00070	−0.500349	+	0.865824i	$0.666795\pi$
$774$	−3.44025e9	−0.266684
$775$	1.03735e9	0.0800511
$776$	2.15324e9	0.165416
$777$	4.60454e9	0.352138
$778$	−7.25643e9	−0.552452
$779$	−5.92031e9	−0.448708
$780$	−4.98663e9	−0.376250
$781$	−3.65293e10	−2.74387
$782$	1.48452e9	0.111010
$783$	−1.24574e10	−0.927387
$784$	7.16061e9	0.530694
$785$	2.49524e10	1.84106
$786$	−3.59495e7	−0.00264067
$787$	4.14648e9	0.303227	0.151613	−	0.988440i	$-0.451553\pi$
$787$	4.14648e9	0.303227	0.151613	+	0.988440i	$0.451553\pi$
$788$	−4.80435e9	−0.349778
$789$	−1.21646e10	−0.881714
$790$	5.48838e9	0.396050
$791$	4.42625e10	3.17993
$792$	3.57511e9	0.255712
$793$	4.07303e9	0.290042
$794$	−4.59043e9	−0.325448
$795$	−3.93661e10	−2.77867
$796$	1.40500e10	0.987375
$797$	1.79688e10	1.25723	0.628614	−	0.777717i	$-0.283623\pi$
$797$	1.79688e10	1.25723	0.628614	+	0.777717i	$0.283623\pi$
$798$	2.67277e10	1.86188
$799$	8.33674e8	0.0578206
$800$	−1.69988e9	−0.117383
$801$	−2.98426e9	−0.205175
$802$	2.56808e9	0.175791
$803$	1.66274e10	1.13324
$804$	−1.00292e10	−0.680565
$805$	2.51799e10	1.70125
$806$	−6.09861e8	−0.0410259
$807$	−2.49426e10	−1.67065
$808$	−7.10677e9	−0.473950
$809$	2.12029e10	1.40791	0.703957	−	0.710243i	$-0.251415\pi$
$809$	2.12029e10	1.40791	0.703957	+	0.710243i	$0.251415\pi$
$810$	1.72323e10	1.13932
$811$	−2.29918e10	−1.51356	−0.756782	−	0.653668i	$-0.773229\pi$
$811$	−2.29918e10	−1.51356	−0.756782	+	0.653668i	$0.773229\pi$
$812$	−1.94308e10	−1.27363
$813$	−1.94700e10	−1.27072
$814$	−2.75733e9	−0.179186
$815$	1.87174e10	1.21114
$816$	9.89367e8	0.0637444
$817$	1.54016e10	0.988070
$818$	1.02031e10	0.651771
$819$	6.27372e9	0.399054
$820$	−3.71713e9	−0.235429
$821$	−4.78390e9	−0.301704	−0.150852	−	0.988556i	$-0.548202\pi$
$821$	−4.78390e9	−0.301704	−0.150852	+	0.988556i	$0.548202\pi$
$822$	−2.51387e10	−1.57867
$823$	−1.60455e10	−1.00336	−0.501678	−	0.865054i	$-0.667284\pi$
$823$	−1.60455e10	−1.00336	−0.501678	+	0.865054i	$0.667284\pi$
$824$	1.00588e9	0.0626327
$825$	2.00092e10	1.24063
$826$	−3.01103e10	−1.85902
$827$	2.87357e10	1.76666	0.883328	−	0.468755i	$-0.155297\pi$
$827$	2.87357e10	1.76666	0.883328	+	0.468755i	$0.155297\pi$
$828$	2.86005e9	0.175092
$829$	1.71065e10	1.04285	0.521423	−	0.853298i	$-0.325401\pi$
$829$	1.71065e10	1.04285	0.521423	+	0.853298i	$0.325401\pi$
$830$	1.51251e10	0.918176
$831$	6.30625e9	0.381213
$832$	9.99369e8	0.0601581
$833$	−7.44937e9	−0.446542
$834$	−7.18462e9	−0.428867
$835$	−3.12683e10	−1.85867
$836$	−1.60053e10	−0.947420
$837$	1.31579e9	0.0775616
$838$	1.74129e10	1.02215
$839$	1.40929e8	0.00823823	0.00411911	−	0.999992i	$-0.498689\pi$
$839$	1.40929e8	0.00823823	0.00411911	+	0.999992i	$0.498689\pi$
$840$	1.67813e10	0.976894
$841$	1.85922e10	1.07782
$842$	8.11912e9	0.468723
$843$	2.26198e10	1.30045
$844$	1.05419e10	0.603558
$845$	−1.73842e10	−0.991191
$846$	1.60614e9	0.0911982
$847$	4.29999e10	2.43151
$848$	7.88934e9	0.444278
$849$	1.28566e10	0.721022
$850$	1.76843e9	0.0987693
$851$	−2.20583e9	−0.122693
$852$	−1.94758e10	−1.07884
$853$	−3.18982e9	−0.175973	−0.0879863	−	0.996122i	$-0.528043\pi$
$853$	−3.18982e9	−0.175973	−0.0879863	+	0.996122i	$0.528043\pi$
$854$	−1.37068e10	−0.753065
$855$	1.35985e10	0.744062
$856$	−3.77594e9	−0.205763
$857$	6.69698e8	0.0363451	0.0181725	−	0.999835i	$-0.494215\pi$
$857$	6.69698e8	0.0363451	0.0181725	+	0.999835i	$0.494215\pi$
$858$	−1.17635e10	−0.635817
$859$	2.27239e9	0.122323	0.0611613	−	0.998128i	$-0.480520\pi$
$859$	2.27239e9	0.122323	0.0611613	+	0.998128i	$0.480520\pi$
$860$	9.67003e9	0.518422
$861$	1.46432e10	0.781851
$862$	−5.94866e9	−0.316332
$863$	−3.40695e9	−0.180438	−0.0902191	−	0.995922i	$-0.528757\pi$
$863$	−3.40695e9	−0.180438	−0.0902191	+	0.995922i	$0.528757\pi$
$864$	−2.15616e9	−0.113732
$865$	−1.22287e10	−0.642425
$866$	1.33289e10	0.697400
$867$	2.22308e10	1.15848
$868$	2.05234e9	0.106520
$869$	1.29472e10	0.669276
$870$	−3.09548e10	−1.59372
$871$	1.05391e10	0.540431
$872$	−2.93117e9	−0.149704
$873$	−4.31568e9	−0.219533
$874$	−1.28041e10	−0.648721
$875$	−1.51773e10	−0.765892
$876$	8.86500e9	0.445569
$877$	7.72835e9	0.386890	0.193445	−	0.981111i	$-0.438034\pi$
$877$	7.72835e9	0.386890	0.193445	+	0.981111i	$0.438034\pi$
$878$	−2.12632e10	−1.06023
$879$	−2.06508e10	−1.02560
$880$	−1.00491e10	−0.497093
$881$	6.20300e9	0.305623	0.152812	−	0.988255i	$-0.451167\pi$
$881$	6.20300e9	0.305623	0.152812	+	0.988255i	$0.451167\pi$
$882$	−1.43518e10	−0.704314
$883$	3.00361e9	0.146819	0.0734094	−	0.997302i	$-0.476612\pi$
$883$	3.00361e9	0.146819	0.0734094	+	0.997302i	$0.476612\pi$
$884$	−1.03967e9	−0.0506189
$885$	−4.79681e10	−2.32622
$886$	−9.67799e9	−0.467485
$887$	−1.29120e10	−0.621244	−0.310622	−	0.950533i	$-0.600537\pi$
$887$	−1.29120e10	−0.621244	−0.310622	+	0.950533i	$0.600537\pi$
$888$	−1.47009e9	−0.0704527
$889$	2.83215e10	1.35195
$890$	8.38832e9	0.398850
$891$	4.06511e10	1.92531
$892$	−1.81743e10	−0.857395
$893$	−7.19047e9	−0.337892
$894$	−1.41902e10	−0.664213
$895$	4.89700e9	0.228323
$896$	−3.36313e9	−0.156194
$897$	−9.41068e9	−0.435359
$898$	−1.12787e10	−0.519746
$899$	−3.78575e9	−0.173777
$900$	3.40702e9	0.155785
$901$	−8.20749e9	−0.373829
$902$	−8.76875e9	−0.397846
$903$	−3.80939e10	−1.72166
$904$	−1.41316e10	−0.636213
$905$	2.12089e10	0.951146
$906$	3.25626e10	1.45469
$907$	6.25212e9	0.278229	0.139114	−	0.990276i	$-0.455574\pi$
$907$	6.25212e9	0.278229	0.139114	+	0.990276i	$0.455574\pi$
$908$	7.19975e9	0.319166
$909$	1.42439e10	0.629006
$910$	−1.76345e10	−0.775743
$911$	−1.74902e10	−0.766444	−0.383222	−	0.923656i	$-0.625186\pi$
$911$	−1.74902e10	−0.766444	−0.383222	+	0.923656i	$0.625186\pi$
$912$	−8.53333e9	−0.372509
$913$	3.56803e10	1.55161
$914$	1.34240e10	0.581529
$915$	−2.18360e10	−0.942322
$916$	−1.54875e10	−0.665805
$917$	−1.27130e8	−0.00544446
$918$	2.24311e9	0.0956976
$919$	−4.34787e10	−1.84787	−0.923937	−	0.382544i	$-0.875048\pi$
$919$	−4.34787e10	−1.84787	−0.923937	+	0.382544i	$0.875048\pi$
$920$	−8.03917e9	−0.340372
$921$	3.62744e10	1.53000
$922$	4.07688e9	0.171305
$923$	2.04660e10	0.856698
$924$	3.95872e10	1.65083
$925$	−2.62769e9	−0.109164
$926$	1.96724e10	0.814179
$927$	−2.01606e9	−0.0831234
$928$	6.20364e9	0.254817
$929$	1.50106e10	0.614249	0.307125	−	0.951669i	$-0.400633\pi$
$929$	1.50106e10	0.614249	0.307125	+	0.951669i	$0.400633\pi$
$930$	3.26954e9	0.133290
$931$	6.42511e10	2.60950
$932$	2.11421e10	0.855447
$933$	5.79688e10	2.33673
$934$	9.50297e9	0.381632
$935$	1.04544e10	0.418270
$936$	−2.00300e9	−0.0798392
$937$	−3.32777e10	−1.32149	−0.660747	−	0.750609i	$-0.729760\pi$
$937$	−3.32777e10	−1.32149	−0.660747	+	0.750609i	$0.729760\pi$
$938$	−3.54668e10	−1.40317
$939$	−4.52076e9	−0.178189
$940$	−4.51461e9	−0.177285
$941$	−4.53503e9	−0.177426	−0.0887129	−	0.996057i	$-0.528275\pi$
$941$	−4.53503e9	−0.177426	−0.0887129	+	0.996057i	$0.528275\pi$
$942$	3.13831e10	1.22326
$943$	−7.01490e9	−0.272415
$944$	9.61327e9	0.371937
$945$	3.80468e10	1.46658
$946$	2.28117e10	0.876070
$947$	−2.12973e10	−0.814890	−0.407445	−	0.913230i	$-0.633580\pi$
$947$	−2.12973e10	−0.814890	−0.407445	+	0.913230i	$0.633580\pi$
$948$	6.90285e9	0.263148
$949$	−9.31573e9	−0.353822
$950$	−1.52528e10	−0.577187
$951$	4.47214e10	1.68610
$952$	3.49875e9	0.131427
$953$	−3.81067e10	−1.42618	−0.713092	−	0.701070i	$-0.752706\pi$
$953$	−3.81067e10	−1.42618	−0.713092	+	0.701070i	$0.752706\pi$
$954$	−1.58124e10	−0.589627
$955$	−4.16263e10	−1.54652
$956$	−1.85147e9	−0.0685352
$957$	−7.30227e10	−2.69319
$958$	3.62227e10	1.33107
$959$	−8.88994e10	−3.25487
$960$	−5.35774e9	−0.195448
$961$	−2.71128e10	−0.985466
$962$	1.54483e9	0.0559459
$963$	7.56800e9	0.273080
$964$	7.03553e9	0.252946
$965$	−7.07179e10	−2.53328
$966$	3.16693e10	1.13037
$967$	3.86009e10	1.37279	0.686397	−	0.727227i	$-0.259191\pi$
$967$	3.86009e10	1.37279	0.686397	+	0.727227i	$0.259191\pi$
$968$	−1.37285e10	−0.486474
$969$	8.87745e9	0.313440
$970$	1.21307e10	0.426762
$971$	−4.11369e10	−1.44200	−0.720998	−	0.692938i	$-0.756316\pi$
$971$	−4.11369e10	−1.44200	−0.720998	+	0.692938i	$0.756316\pi$
$972$	1.24634e10	0.435315
$973$	−2.54073e10	−0.884228
$974$	−1.47023e10	−0.509834
$975$	−1.12104e10	−0.387352
$976$	4.37614e9	0.150667
$977$	9.69080e9	0.332452	0.166226	−	0.986088i	$-0.446842\pi$
$977$	9.69080e9	0.332452	0.166226	+	0.986088i	$0.446842\pi$
$978$	2.35412e10	0.804717
$979$	1.97881e10	0.674009
$980$	4.03407e10	1.36915
$981$	5.87485e9	0.198681
$982$	4.09577e10	1.38021
$983$	−3.21349e10	−1.07905	−0.539523	−	0.841971i	$-0.681395\pi$
$983$	−3.21349e10	−1.07905	−0.539523	+	0.841971i	$0.681395\pi$
$984$	−4.67511e9	−0.156426
$985$	−2.70663e10	−0.902405
$986$	−6.45381e9	−0.214411
$987$	1.77848e10	0.588760
$988$	8.96719e9	0.295806
$989$	1.82491e10	0.599866
$990$	2.01411e10	0.659721
$991$	−6.24879e9	−0.203957	−0.101978	−	0.994787i	$-0.532517\pi$
$991$	−6.24879e9	−0.203957	−0.101978	+	0.994787i	$0.532517\pi$
$992$	−6.55247e8	−0.0213115
$993$	2.74115e10	0.888405
$994$	−6.88734e10	−2.22433
$995$	7.91538e10	2.54736
$996$	1.90232e10	0.610064
$997$	−2.81770e10	−0.900454	−0.450227	−	0.892914i	$-0.648657\pi$
$997$	−2.81770e10	−0.900454	−0.450227	+	0.892914i	$0.648657\pi$
$998$	1.21585e10	0.387190
$999$	−3.33300e9	−0.105769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.a.c.1.2	✓	6
4.3	odd	2		592.8.a.c.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.a.c.1.2	✓	6	1.1	even	1	trivial
592.8.a.c.1.5		6	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	74.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -56.6850 q^{3} +64.0000 q^{4} +360.557 q^{5} +453.480 q^{6} +1603.66 q^{7} -512.000 q^{8} +1026.19 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -56.6850 q^{3} +64.0000 q^{4} +360.557 q^{5} +453.480 q^{6} +1603.66 q^{7} -512.000 q^{8} +1026.19 q^{9} -2884.45 q^{10} -6804.46 q^{11} -3627.84 q^{12} +3812.29 q^{13} -12829.3 q^{14} -20438.2 q^{15} +4096.00 q^{16} -4261.18 q^{17} -8209.49 q^{18} +36752.8 q^{19} +23075.6 q^{20} -90903.7 q^{21} +54435.7 q^{22} +43547.9 q^{23} +29022.7 q^{24} +51876.2 q^{25} -30498.3 q^{26} +65800.7 q^{27} +102635. q^{28} -189320. q^{29} +163505. q^{30} +19996.5 q^{31} -32768.0 q^{32} +385711. q^{33} +34089.4 q^{34} +578212. q^{35} +65675.9 q^{36} -50653.0 q^{37} -294023. q^{38} -216099. q^{39} -184605. q^{40} -161085. q^{41} +727229. q^{42} +419058. q^{43} -435485. q^{44} +369998. q^{45} -348383. q^{46} -195644. q^{47} -232182. q^{48} +1.74820e6 q^{49} -415010. q^{50} +241545. q^{51} +243986. q^{52} +1.92611e6 q^{53} -526406. q^{54} -2.45339e6 q^{55} -821076. q^{56} -2.08333e6 q^{57} +1.51456e6 q^{58} +2.34699e6 q^{59} -1.30804e6 q^{60} +1.06839e6 q^{61} -159972. q^{62} +1.64566e6 q^{63} +262144. q^{64} +1.37455e6 q^{65} -3.08569e6 q^{66} +2.76451e6 q^{67} -272715. q^{68} -2.46851e6 q^{69} -4.62570e6 q^{70} +5.36844e6 q^{71} -525407. q^{72} -2.44360e6 q^{73} +405224. q^{74} -2.94060e6 q^{75} +2.35218e6 q^{76} -1.09121e7 q^{77} +1.72880e6 q^{78} -1.90275e6 q^{79} +1.47684e6 q^{80} -5.97418e6 q^{81} +1.28868e6 q^{82} -5.24367e6 q^{83} -5.81783e6 q^{84} -1.53640e6 q^{85} -3.35246e6 q^{86} +1.07316e7 q^{87} +3.48388e6 q^{88} -2.90811e6 q^{89} -2.95999e6 q^{90} +6.11363e6 q^{91} +2.78707e6 q^{92} -1.13350e6 q^{93} +1.56515e6 q^{94} +1.32515e7 q^{95} +1.85745e6 q^{96} -4.20555e6 q^{97} -1.39856e7 q^{98} -6.98264e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9}+O(q^{10}) \) 6 * q - 48 * q^2 + 28 * q^3 + 384 * q^4 - 14 * q^5 - 224 * q^6 - 980 * q^7 - 3072 * q^8 + 8254 * q^9	\( 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9} + 112 q^{10} + 2956 q^{11} + 1792 q^{12} + 2394 q^{13} + 7840 q^{14} - 28820 q^{15} + 24576 q^{16} - 45108 q^{17} - 66032 q^{18} + 11764 q^{19} - 896 q^{20} - 135378 q^{21} - 23648 q^{22} + 21052 q^{23} - 14336 q^{24} + 194744 q^{25} - 19152 q^{26} + 439240 q^{27} - 62720 q^{28} + 288454 q^{29} + 230560 q^{30} + 578868 q^{31} - 196608 q^{32} + 980174 q^{33} + 360864 q^{34} + 1243052 q^{35} + 528256 q^{36} - 303918 q^{37} - 94112 q^{38} + 1735296 q^{39} + 7168 q^{40} + 1176840 q^{41} + 1083024 q^{42} + 2669236 q^{43} + 189184 q^{44} + 2560692 q^{45} - 168416 q^{46} - 131044 q^{47} + 114688 q^{48} + 2460856 q^{49} - 1557952 q^{50} + 2899732 q^{51} + 153216 q^{52} + 983190 q^{53} - 3513920 q^{54} - 1200168 q^{55} + 501760 q^{56} - 163216 q^{57} - 2307632 q^{58} - 1215568 q^{59} - 1844480 q^{60} + 3136358 q^{61} - 4630944 q^{62} - 1444880 q^{63} + 1572864 q^{64} - 1302836 q^{65} - 7841392 q^{66} + 2179276 q^{67} - 2886912 q^{68} - 929514 q^{69} - 9944416 q^{70} + 325164 q^{71} - 4226048 q^{72} + 5011444 q^{73} + 2431344 q^{74} - 9374520 q^{75} + 752896 q^{76} - 26500426 q^{77} - 13882368 q^{78} + 3173032 q^{79} - 57344 q^{80} - 2565226 q^{81} - 9414720 q^{82} - 22567048 q^{83} - 8664192 q^{84} + 1486476 q^{85} - 21353888 q^{86} - 157228 q^{87} - 1513472 q^{88} + 26836996 q^{89} - 20485536 q^{90} + 17942380 q^{91} + 1347328 q^{92} + 16734948 q^{93} + 1048352 q^{94} - 4252048 q^{95} - 917504 q^{96} + 295792 q^{97} - 19686848 q^{98} + 25990712 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 + 28 * q^3 + 384 * q^4 - 14 * q^5 - 224 * q^6 - 980 * q^7 - 3072 * q^8 + 8254 * q^9 + 112 * q^10 + 2956 * q^11 + 1792 * q^12 + 2394 * q^13 + 7840 * q^14 - 28820 * q^15 + 24576 * q^16 - 45108 * q^17 - 66032 * q^18 + 11764 * q^19 - 896 * q^20 - 135378 * q^21 - 23648 * q^22 + 21052 * q^23 - 14336 * q^24 + 194744 * q^25 - 19152 * q^26 + 439240 * q^27 - 62720 * q^28 + 288454 * q^29 + 230560 * q^30 + 578868 * q^31 - 196608 * q^32 + 980174 * q^33 + 360864 * q^34 + 1243052 * q^35 + 528256 * q^36 - 303918 * q^37 - 94112 * q^38 + 1735296 * q^39 + 7168 * q^40 + 1176840 * q^41 + 1083024 * q^42 + 2669236 * q^43 + 189184 * q^44 + 2560692 * q^45 - 168416 * q^46 - 131044 * q^47 + 114688 * q^48 + 2460856 * q^49 - 1557952 * q^50 + 2899732 * q^51 + 153216 * q^52 + 983190 * q^53 - 3513920 * q^54 - 1200168 * q^55 + 501760 * q^56 - 163216 * q^57 - 2307632 * q^58 - 1215568 * q^59 - 1844480 * q^60 + 3136358 * q^61 - 4630944 * q^62 - 1444880 * q^63 + 1572864 * q^64 - 1302836 * q^65 - 7841392 * q^66 + 2179276 * q^67 - 2886912 * q^68 - 929514 * q^69 - 9944416 * q^70 + 325164 * q^71 - 4226048 * q^72 + 5011444 * q^73 + 2431344 * q^74 - 9374520 * q^75 + 752896 * q^76 - 26500426 * q^77 - 13882368 * q^78 + 3173032 * q^79 - 57344 * q^80 - 2565226 * q^81 - 9414720 * q^82 - 22567048 * q^83 - 8664192 * q^84 + 1486476 * q^85 - 21353888 * q^86 - 157228 * q^87 - 1513472 * q^88 + 26836996 * q^89 - 20485536 * q^90 + 17942380 * q^91 + 1347328 * q^92 + 16734948 * q^93 + 1048352 * q^94 - 4252048 * q^95 - 917504 * q^96 + 295792 * q^97 - 19686848 * q^98 + 25990712 * q^99

Introduction

L-functions

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