LMFDB - Embedded newform 74.8.a.c.1.1

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			1.1
Root			$64.4910$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} -59.4910 q^{3} +64.0000 q^{4} +326.669 q^{5} +475.928 q^{6} -633.531 q^{7} -512.000 q^{8} +1352.18 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -59.4910 q^{3} +64.0000 q^{4} +326.669 q^{5} +475.928 q^{6} -633.531 q^{7} -512.000 q^{8} +1352.18 q^{9} -2613.35 q^{10} +4928.94 q^{11} -3807.43 q^{12} -10502.1 q^{13} +5068.25 q^{14} -19433.9 q^{15} +4096.00 q^{16} -26949.9 q^{17} -10817.5 q^{18} -28886.5 q^{19} +20906.8 q^{20} +37689.4 q^{21} -39431.6 q^{22} +62884.4 q^{23} +30459.4 q^{24} +28587.8 q^{25} +84017.0 q^{26} +49664.1 q^{27} -40546.0 q^{28} +234300. q^{29} +155471. q^{30} +134578. q^{31} -32768.0 q^{32} -293228. q^{33} +215599. q^{34} -206955. q^{35} +86539.8 q^{36} -50653.0 q^{37} +231092. q^{38} +624782. q^{39} -167255. q^{40} +89548.2 q^{41} -301515. q^{42} -133891. q^{43} +315452. q^{44} +441717. q^{45} -503075. q^{46} +1.29838e6 q^{47} -243675. q^{48} -422182. q^{49} -228702. q^{50} +1.60328e6 q^{51} -672136. q^{52} -1.28869e6 q^{53} -397313. q^{54} +1.61013e6 q^{55} +324368. q^{56} +1.71849e6 q^{57} -1.87440e6 q^{58} +1.69934e6 q^{59} -1.24377e6 q^{60} +542247. q^{61} -1.07662e6 q^{62} -856650. q^{63} +262144. q^{64} -3.43072e6 q^{65} +2.34582e6 q^{66} +598542. q^{67} -1.72480e6 q^{68} -3.74106e6 q^{69} +1.65564e6 q^{70} +1.28667e6 q^{71} -692318. q^{72} +5.37565e6 q^{73} +405224. q^{74} -1.70072e6 q^{75} -1.84874e6 q^{76} -3.12264e6 q^{77} -4.99826e6 q^{78} +4.37280e6 q^{79} +1.33804e6 q^{80} -5.91179e6 q^{81} -716385. q^{82} -1.49657e6 q^{83} +2.41212e6 q^{84} -8.80371e6 q^{85} +1.07113e6 q^{86} -1.39387e7 q^{87} -2.52362e6 q^{88} +9.71768e6 q^{89} -3.53373e6 q^{90} +6.65342e6 q^{91} +4.02460e6 q^{92} -8.00617e6 q^{93} -1.03870e7 q^{94} -9.43633e6 q^{95} +1.94940e6 q^{96} +816910. q^{97} +3.37745e6 q^{98} +6.66484e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−59.4910	−1.27212	−0.636059	−	0.771641i	$-0.719436\pi$
$3$	−59.4910	−1.27212	−0.636059	+	0.771641i	$0.719436\pi$
$4$	64.0000	0.500000
$5$	326.669	1.16873	0.584364	−	0.811492i	$-0.301344\pi$
$5$	326.669	1.16873	0.584364	+	0.811492i	$0.301344\pi$
$6$	475.928	0.899523
$7$	−633.531	−0.698111	−0.349056	−	0.937102i	$-0.613498\pi$
$7$	−633.531	−0.698111	−0.349056	+	0.937102i	$0.613498\pi$
$8$	−512.000	−0.353553
$9$	1352.18	0.618282
$10$	−2613.35	−0.826415
$11$	4928.94	1.11655	0.558277	−	0.829655i	$-0.311463\pi$
$11$	4928.94	1.11655	0.558277	+	0.829655i	$0.311463\pi$
$12$	−3807.43	−0.636059
$13$	−10502.1	−1.32579	−0.662896	−	0.748711i	$-0.730673\pi$
$13$	−10502.1	−1.32579	−0.662896	+	0.748711i	$0.730673\pi$
$14$	5068.25	0.493639
$15$	−19433.9	−1.48676
$16$	4096.00	0.250000
$17$	−26949.9	−1.33041	−0.665206	−	0.746660i	$-0.731656\pi$
$17$	−26949.9	−1.33041	−0.665206	+	0.746660i	$0.731656\pi$
$18$	−10817.5	−0.437192
$19$	−28886.5	−0.966178	−0.483089	−	0.875571i	$-0.660485\pi$
$19$	−28886.5	−0.966178	−0.483089	+	0.875571i	$0.660485\pi$
$20$	20906.8	0.584364
$21$	37689.4	0.888079
$22$	−39431.6	−0.789522
$23$	62884.4	1.07769	0.538847	−	0.842404i	$-0.318860\pi$
$23$	62884.4	1.07769	0.538847	+	0.842404i	$0.318860\pi$
$24$	30459.4	0.449761
$25$	28587.8	0.365924
$26$	84017.0	0.937477
$27$	49664.1	0.485589
$28$	−40546.0	−0.349056
$29$	234300.	1.78393	0.891967	−	0.452100i	$-0.149325\pi$
$29$	234300.	1.78393	0.891967	+	0.452100i	$0.149325\pi$
$30$	155471.	1.05130
$31$	134578.	0.811348	0.405674	−	0.914018i	$-0.367037\pi$
$31$	134578.	0.811348	0.405674	+	0.914018i	$0.367037\pi$
$32$	−32768.0	−0.176777
$33$	−293228.	−1.42039
$34$	215599.	0.940744
$35$	−206955.	−0.815902
$36$	86539.8	0.309141
$37$	−50653.0	−0.164399
$37$	−50653.0	−0.164399
$38$	231092.	0.683191
$39$	624782.	1.68656
$40$	−167255.	−0.413208
$41$	89548.2	0.202915	0.101457	−	0.994840i	$-0.467649\pi$
$41$	89548.2	0.202915	0.101457	+	0.994840i	$0.467649\pi$
$42$	−301515.	−0.627967
$43$	−133891.	−0.256811	−0.128405	−	0.991722i	$-0.540986\pi$
$43$	−133891.	−0.256811	−0.128405	+	0.991722i	$0.540986\pi$
$44$	315452.	0.558277
$45$	441717.	0.722604
$46$	−503075.	−0.762045
$47$	1.29838e6	1.82414	0.912072	−	0.410031i	$-0.134482\pi$
$47$	1.29838e6	1.82414	0.912072	+	0.410031i	$0.134482\pi$
$48$	−243675.	−0.318029
$49$	−422182.	−0.512641
$50$	−228702.	−0.258747
$51$	1.60328e6	1.69244
$52$	−672136.	−0.662896
$53$	−1.28869e6	−1.18901	−0.594503	−	0.804094i	$-0.702651\pi$
$53$	−1.28869e6	−1.18901	−0.594503	+	0.804094i	$0.702651\pi$
$54$	−397313.	−0.343364
$55$	1.61013e6	1.30495
$56$	324368.	0.246820
$57$	1.71849e6	1.22909
$58$	−1.87440e6	−1.26143
$59$	1.69934e6	1.07721	0.538603	−	0.842560i	$-0.318952\pi$
$59$	1.69934e6	1.07721	0.538603	+	0.842560i	$0.318952\pi$
$60$	−1.24377e6	−0.743379
$61$	542247.	0.305874	0.152937	−	0.988236i	$-0.451127\pi$
$61$	542247.	0.305874	0.152937	+	0.988236i	$0.451127\pi$
$62$	−1.07662e6	−0.573710
$63$	−856650.	−0.431630
$64$	262144.	0.125000
$65$	−3.43072e6	−1.54949
$66$	2.34582e6	1.00437
$67$	598542.	0.243127	0.121563	−	0.992584i	$-0.461209\pi$
$67$	598542.	0.243127	0.121563	+	0.992584i	$0.461209\pi$
$68$	−1.72480e6	−0.665206
$69$	−3.74106e6	−1.37095
$70$	1.65564e6	0.576930
$71$	1.28667e6	0.426640	0.213320	−	0.976982i	$-0.431572\pi$
$71$	1.28667e6	0.426640	0.213320	+	0.976982i	$0.431572\pi$
$72$	−692318.	−0.218596
$73$	5.37565e6	1.61734	0.808670	−	0.588263i	$-0.200188\pi$
$73$	5.37565e6	1.61734	0.808670	+	0.588263i	$0.200188\pi$
$74$	405224.	0.116248
$75$	−1.70072e6	−0.465498
$76$	−1.84874e6	−0.483089
$77$	−3.12264e6	−0.779478
$78$	−4.99826e6	−1.19258
$79$	4.37280e6	0.997848	0.498924	−	0.866646i	$-0.333729\pi$
$79$	4.37280e6	0.997848	0.498924	+	0.866646i	$0.333729\pi$
$80$	1.33804e6	0.292182
$81$	−5.91179e6	−1.23601
$82$	−716385.	−0.143482
$83$	−1.49657e6	−0.287293	−0.143646	−	0.989629i	$-0.545883\pi$
$83$	−1.49657e6	−0.287293	−0.143646	+	0.989629i	$0.545883\pi$
$84$	2.41212e6	0.444040
$85$	−8.80371e6	−1.55489
$86$	1.07113e6	0.181593
$87$	−1.39387e7	−2.26937
$88$	−2.52362e6	−0.394761
$89$	9.71768e6	1.46116	0.730580	−	0.682827i	$-0.239250\pi$
$89$	9.71768e6	1.46116	0.730580	+	0.682827i	$0.239250\pi$
$90$	−3.53373e6	−0.510958
$91$	6.65342e6	0.925550
$92$	4.02460e6	0.538847
$93$	−8.00617e6	−1.03213
$94$	−1.03870e7	−1.28986
$95$	−9.43633e6	−1.12920
$96$	1.94940e6	0.224881
$97$	816910.	0.0908810	0.0454405	−	0.998967i	$-0.485531\pi$
$97$	816910.	0.0908810	0.0454405	+	0.998967i	$0.485531\pi$
$98$	3.37745e6	0.362492
$99$	6.66484e6	0.690345
$100$	1.82962e6	0.182962
$101$	1.46614e7	1.41596	0.707980	−	0.706233i	$-0.249607\pi$
$101$	1.46614e7	1.41596	0.707980	+	0.706233i	$0.249607\pi$
$102$	−1.28262e7	−1.19674
$103$	1.22739e7	1.10676	0.553378	−	0.832930i	$-0.313339\pi$
$103$	1.22739e7	1.10676	0.553378	+	0.832930i	$0.313339\pi$
$104$	5.37709e6	0.468738
$105$	1.23120e7	1.03792
$106$	1.03095e7	0.840754
$107$	6.90406e6	0.544831	0.272415	−	0.962180i	$-0.412178\pi$
$107$	6.90406e6	0.544831	0.272415	+	0.962180i	$0.412178\pi$
$108$	3.17850e6	0.242795
$109$	4.00824e6	0.296456	0.148228	−	0.988953i	$-0.452643\pi$
$109$	4.00824e6	0.296456	0.148228	+	0.988953i	$0.452643\pi$
$110$	−1.28811e7	−0.922736
$111$	3.01340e6	0.209135
$112$	−2.59494e6	−0.174528
$113$	−1.82237e7	−1.18812	−0.594062	−	0.804419i	$-0.702477\pi$
$113$	−1.82237e7	−1.18812	−0.594062	+	0.804419i	$0.702477\pi$
$114$	−1.37479e7	−0.869099
$115$	2.05424e7	1.25953
$116$	1.49952e7	0.891967
$117$	−1.42008e7	−0.819714
$118$	−1.35947e7	−0.761700
$119$	1.70736e7	0.928776
$120$	9.95015e6	0.525648
$121$	4.80732e6	0.246691
$122$	−4.33798e6	−0.216286
$123$	−5.32731e6	−0.258131
$124$	8.61297e6	0.405674
$125$	−1.61823e7	−0.741062
$126$	6.85320e6	0.305208
$127$	8.10569e6	0.351137	0.175569	−	0.984467i	$-0.443824\pi$
$127$	8.10569e6	0.351137	0.175569	+	0.984467i	$0.443824\pi$
$128$	−2.09715e6	−0.0883883
$129$	7.96534e6	0.326693
$130$	2.74458e7	1.09565
$131$	1.51186e7	0.587573	0.293786	−	0.955871i	$-0.405085\pi$
$131$	1.51186e7	0.587573	0.293786	+	0.955871i	$0.405085\pi$
$132$	−1.87666e7	−0.710193
$133$	1.83005e7	0.674500
$134$	−4.78834e6	−0.171917
$135$	1.62237e7	0.567522
$136$	1.37984e7	0.470372
$137$	511213.	0.0169856	0.00849278	−	0.999964i	$-0.497297\pi$
$137$	511213.	0.0169856	0.00849278	+	0.999964i	$0.497297\pi$
$138$	2.99285e7	0.969411
$139$	−3.70747e7	−1.17092	−0.585458	−	0.810703i	$-0.699085\pi$
$139$	−3.70747e7	−1.17092	−0.585458	+	0.810703i	$0.699085\pi$
$140$	−1.32451e7	−0.407951
$141$	−7.72419e7	−2.32052
$142$	−1.02933e7	−0.301680
$143$	−5.17644e7	−1.48032
$144$	5.53854e6	0.154571
$145$	7.65385e7	2.08493
$146$	−4.30052e7	−1.14363
$147$	2.51160e7	0.652139
$148$	−3.24179e6	−0.0821995
$149$	−6.15801e7	−1.52506	−0.762532	−	0.646950i	$-0.776044\pi$
$149$	−6.15801e7	−1.52506	−0.762532	+	0.646950i	$0.776044\pi$
$150$	1.36057e7	0.329157
$151$	−1.93912e7	−0.458338	−0.229169	−	0.973387i	$-0.573601\pi$
$151$	−1.93912e7	−0.458338	−0.229169	+	0.973387i	$0.573601\pi$
$152$	1.47899e7	0.341596
$153$	−3.64413e7	−0.822571
$154$	2.49811e7	0.551174
$155$	4.39624e7	0.948244
$156$	3.99861e7	0.843282
$157$	9.55496e7	1.97052	0.985258	−	0.171076i	$-0.0547244\pi$
$157$	9.55496e7	1.97052	0.985258	+	0.171076i	$0.0547244\pi$
$158$	−3.49824e7	−0.705585
$159$	7.66656e7	1.51255
$160$	−1.07043e7	−0.206604
$161$	−3.98392e7	−0.752350
$162$	4.72944e7	0.873991
$163$	1.46581e7	0.265106	0.132553	−	0.991176i	$-0.457682\pi$
$163$	1.46581e7	0.265106	0.132553	+	0.991176i	$0.457682\pi$
$164$	5.73108e6	0.101457
$165$	−9.57886e7	−1.66005
$166$	1.19726e7	0.203147
$167$	−7.81996e6	−0.129926	−0.0649632	−	0.997888i	$-0.520693\pi$
$167$	−7.81996e6	−0.129926	−0.0649632	+	0.997888i	$0.520693\pi$
$168$	−1.92970e7	−0.313983
$169$	4.75462e7	0.757726
$170$	7.04297e7	1.09947
$171$	−3.90598e7	−0.597371
$172$	−8.56905e6	−0.128405
$173$	7.42856e7	1.09079	0.545397	−	0.838178i	$-0.316379\pi$
$173$	7.42856e7	1.09079	0.545397	+	0.838178i	$0.316379\pi$
$174$	1.11510e8	1.60469
$175$	−1.81112e7	−0.255455
$176$	2.01890e7	0.279138
$177$	−1.01096e8	−1.37033
$178$	−7.77415e7	−1.03320
$179$	−9.99677e7	−1.30279	−0.651394	−	0.758739i	$-0.725816\pi$
$179$	−9.99677e7	−1.30279	−0.651394	+	0.758739i	$0.725816\pi$
$180$	2.82699e7	0.361302
$181$	1.00847e8	1.26411	0.632056	−	0.774922i	$-0.282211\pi$
$181$	1.00847e8	1.26411	0.632056	+	0.774922i	$0.282211\pi$
$182$	−5.32274e7	−0.654463
$183$	−3.22588e7	−0.389108
$184$	−3.21968e7	−0.381022
$185$	−1.65468e7	−0.192138
$186$	6.40493e7	0.729826
$187$	−1.32835e8	−1.48548
$188$	8.30962e7	0.912072
$189$	−3.14637e7	−0.338995
$190$	7.54906e7	0.798464
$191$	6.07867e6	0.0631236	0.0315618	−	0.999502i	$-0.489952\pi$
$191$	6.07867e6	0.0631236	0.0315618	+	0.999502i	$0.489952\pi$
$192$	−1.55952e7	−0.159015
$193$	−1.30742e8	−1.30907	−0.654537	−	0.756030i	$-0.727136\pi$
$193$	−1.30742e8	−1.30907	−0.654537	+	0.756030i	$0.727136\pi$
$194$	−6.53528e6	−0.0642625
$195$	2.04097e8	1.97113
$196$	−2.70196e7	−0.256320
$197$	−5.54311e7	−0.516561	−0.258280	−	0.966070i	$-0.583156\pi$
$197$	−5.54311e7	−0.516561	−0.258280	+	0.966070i	$0.583156\pi$
$198$	−5.33187e7	−0.488148
$199$	−6.82874e7	−0.614264	−0.307132	−	0.951667i	$-0.599369\pi$
$199$	−6.82874e7	−0.614264	−0.307132	+	0.951667i	$0.599369\pi$
$200$	−1.46369e7	−0.129374
$201$	−3.56079e7	−0.309286
$202$	−1.17291e8	−1.00123
$203$	−1.48436e8	−1.24538
$204$	1.02610e8	0.846221
$205$	2.92526e7	0.237152
$206$	−9.81911e7	−0.782595
$207$	8.50313e7	0.666319
$208$	−4.30167e7	−0.331448
$209$	−1.42380e8	−1.07879
$210$	−9.84957e7	−0.733922
$211$	−2.03378e8	−1.49045	−0.745223	−	0.666815i	$-0.767657\pi$
$211$	−2.03378e8	−1.49045	−0.745223	+	0.666815i	$0.767657\pi$
$212$	−8.24763e7	−0.594503
$213$	−7.65452e7	−0.542737
$214$	−5.52325e7	−0.385254
$215$	−4.37382e7	−0.300142
$216$	−2.54280e7	−0.171682
$217$	−8.52591e7	−0.566411
$218$	−3.20659e7	−0.209626
$219$	−3.19803e8	−2.05745
$220$	1.03049e8	0.652473
$221$	2.83032e8	1.76385
$222$	−2.41072e7	−0.147881
$223$	2.51602e8	1.51931	0.759655	−	0.650326i	$-0.225368\pi$
$223$	2.51602e8	1.51931	0.759655	+	0.650326i	$0.225368\pi$
$224$	2.07595e7	0.123410
$225$	3.86559e7	0.226244
$226$	1.45789e8	0.840130
$227$	1.39422e8	0.791119	0.395559	−	0.918440i	$-0.370551\pi$
$227$	1.39422e8	0.791119	0.395559	+	0.918440i	$0.370551\pi$
$228$	1.09983e8	0.614546
$229$	6.53710e7	0.359717	0.179859	−	0.983692i	$-0.442436\pi$
$229$	6.53710e7	0.359717	0.179859	+	0.983692i	$0.442436\pi$
$230$	−1.64339e8	−0.890623
$231$	1.85769e8	0.991588
$232$	−1.19961e8	−0.630716
$233$	−1.58572e8	−0.821259	−0.410630	−	0.911802i	$-0.634691\pi$
$233$	−1.58572e8	−0.821259	−0.410630	+	0.911802i	$0.634691\pi$
$234$	1.13606e8	0.579626
$235$	4.24140e8	2.13193
$236$	1.08758e8	0.538603
$237$	−2.60142e8	−1.26938
$238$	−1.36589e8	−0.656744
$239$	1.38083e8	0.654257	0.327129	−	0.944980i	$-0.393919\pi$
$239$	1.38083e8	0.654257	0.327129	+	0.944980i	$0.393919\pi$
$240$	−7.96012e7	−0.371690
$241$	2.72955e8	1.25612	0.628060	−	0.778165i	$-0.283849\pi$
$241$	2.72955e8	1.25612	0.628060	+	0.778165i	$0.283849\pi$
$242$	−3.84585e7	−0.174437
$243$	2.43083e8	1.08676
$244$	3.47038e7	0.152937
$245$	−1.37914e8	−0.599137
$246$	4.26185e7	0.182526
$247$	3.03370e8	1.28095
$248$	−6.89038e7	−0.286855
$249$	8.90328e7	0.365470
$250$	1.29458e8	0.524010
$251$	−1.04504e8	−0.417133	−0.208566	−	0.978008i	$-0.566880\pi$
$251$	−1.04504e8	−0.417133	−0.208566	+	0.978008i	$0.566880\pi$
$252$	−5.48256e7	−0.215815
$253$	3.09954e8	1.20330
$254$	−6.48455e7	−0.248292
$255$	5.23742e8	1.97800
$256$	1.67772e7	0.0625000
$257$	−8.92962e7	−0.328146	−0.164073	−	0.986448i	$-0.552463\pi$
$257$	−8.92962e7	−0.328146	−0.164073	+	0.986448i	$0.552463\pi$
$258$	−6.37227e7	−0.231007
$259$	3.20902e7	0.114769
$260$	−2.19566e8	−0.774745
$261$	3.16816e8	1.10298
$262$	−1.20949e8	−0.415477
$263$	4.30716e8	1.45998	0.729989	−	0.683459i	$-0.239525\pi$
$263$	4.30716e8	1.45998	0.729989	+	0.683459i	$0.239525\pi$
$264$	1.50133e8	0.502183
$265$	−4.20976e8	−1.38962
$266$	−1.46404e8	−0.476943
$267$	−5.78115e8	−1.85877
$268$	3.83067e7	0.121563
$269$	3.96858e8	1.24309	0.621545	−	0.783379i	$-0.286505\pi$
$269$	3.96858e8	1.24309	0.621545	+	0.783379i	$0.286505\pi$
$270$	−1.29790e8	−0.401298
$271$	−4.25336e8	−1.29819	−0.649097	−	0.760706i	$-0.724853\pi$
$271$	−4.25336e8	−1.29819	−0.649097	+	0.760706i	$0.724853\pi$
$272$	−1.10387e8	−0.332603
$273$	−3.95819e8	−1.17741
$274$	−4.08971e6	−0.0120106
$275$	1.40908e8	0.408573
$276$	−2.39428e8	−0.685477
$277$	−3.85529e8	−1.08988	−0.544939	−	0.838475i	$-0.683447\pi$
$277$	−3.85529e8	−1.08988	−0.544939	+	0.838475i	$0.683447\pi$
$278$	2.96597e8	0.827962
$279$	1.81974e8	0.501642
$280$	1.05961e8	0.288465
$281$	6.68139e8	1.79637	0.898183	−	0.439622i	$-0.144888\pi$
$281$	6.68139e8	1.79637	0.898183	+	0.439622i	$0.144888\pi$
$282$	6.17935e8	1.64086
$283$	−6.06642e6	−0.0159104	−0.00795518	−	0.999968i	$-0.502532\pi$
$283$	−6.06642e6	−0.0159104	−0.00795518	+	0.999968i	$0.502532\pi$
$284$	8.23467e7	0.213320
$285$	5.61377e8	1.43647
$286$	4.14115e8	1.04674
$287$	−5.67315e7	−0.141657
$288$	−4.43084e7	−0.109298
$289$	3.15960e8	0.769998
$290$	−6.12308e8	−1.47427
$291$	−4.85988e7	−0.115611
$292$	3.44042e8	0.808670
$293$	−5.52559e8	−1.28334	−0.641670	−	0.766981i	$-0.721758\pi$
$293$	−5.52559e8	−1.28334	−0.641670	+	0.766981i	$0.721758\pi$
$294$	−2.00928e8	−0.461132
$295$	5.55123e8	1.25896
$296$	2.59343e7	0.0581238
$297$	2.44791e8	0.542187
$298$	4.92641e8	1.07838
$299$	−6.60420e8	−1.42880
$300$	−1.08846e8	−0.232749
$301$	8.48243e7	0.179282
$302$	1.55130e8	0.324094
$303$	−8.72222e8	−1.80127
$304$	−1.18319e8	−0.241544
$305$	1.77135e8	0.357484
$306$	2.91530e8	0.581645
$307$	−1.60387e8	−0.316363	−0.158181	−	0.987410i	$-0.550563\pi$
$307$	−1.60387e8	−0.316363	−0.158181	+	0.987410i	$0.550563\pi$
$308$	−1.99849e8	−0.389739
$309$	−7.30186e8	−1.40792
$310$	−3.51699e8	−0.670510
$311$	−3.88779e8	−0.732895	−0.366447	−	0.930439i	$-0.619426\pi$
$311$	−3.88779e8	−0.732895	−0.366447	+	0.930439i	$0.619426\pi$
$312$	−3.19889e8	−0.596290
$313$	−5.66353e8	−1.04396	−0.521978	−	0.852959i	$-0.674806\pi$
$313$	−5.66353e8	−1.04396	−0.521978	+	0.852959i	$0.674806\pi$
$314$	−7.64396e8	−1.39336
$315$	−2.79841e8	−0.504458
$316$	2.79859e8	0.498924
$317$	−5.85559e8	−1.03244	−0.516218	−	0.856457i	$-0.672661\pi$
$317$	−5.85559e8	−1.03244	−0.516218	+	0.856457i	$0.672661\pi$
$318$	−6.13325e8	−1.06954
$319$	1.15485e9	1.99186
$320$	8.56344e7	0.146091
$321$	−4.10730e8	−0.693089
$322$	3.18714e8	0.531992
$323$	7.78489e8	1.28542
$324$	−3.78355e8	−0.618005
$325$	−3.00233e8	−0.485139
$326$	−1.17265e8	−0.187459
$327$	−2.38454e8	−0.377127
$328$	−4.58487e7	−0.0717411
$329$	−8.22563e8	−1.27345
$330$	7.66309e8	1.17383
$331$	9.09836e8	1.37900	0.689501	−	0.724284i	$-0.257830\pi$
$331$	9.09836e8	1.37900	0.689501	+	0.724284i	$0.257830\pi$
$332$	−9.57807e7	−0.143646
$333$	−6.84922e7	−0.101645
$334$	6.25597e7	0.0918718
$335$	1.95525e8	0.284149
$336$	1.54376e8	0.222020
$337$	−7.44856e8	−1.06015	−0.530076	−	0.847950i	$-0.677836\pi$
$337$	−7.44856e8	−1.06015	−0.530076	+	0.847950i	$0.677836\pi$
$338$	−3.80369e8	−0.535793
$339$	1.08415e9	1.51143
$340$	−5.63438e8	−0.777445
$341$	6.63326e8	0.905913
$342$	3.12479e8	0.422405
$343$	7.89205e8	1.05599
$344$	6.85524e7	0.0907963
$345$	−1.22209e9	−1.60227
$346$	−5.94285e8	−0.771309
$347$	4.50778e8	0.579175	0.289588	−	0.957152i	$-0.406482\pi$
$347$	4.50778e8	0.579175	0.289588	+	0.957152i	$0.406482\pi$
$348$	−8.92079e8	−1.13469
$349$	−3.02416e8	−0.380817	−0.190408	−	0.981705i	$-0.560981\pi$
$349$	−3.02416e8	−0.380817	−0.190408	+	0.981705i	$0.560981\pi$
$350$	1.44890e8	0.180634
$351$	−5.21579e8	−0.643791
$352$	−1.61512e8	−0.197381
$353$	1.84058e8	0.222712	0.111356	−	0.993781i	$-0.464481\pi$
$353$	1.84058e8	0.222712	0.111356	+	0.993781i	$0.464481\pi$
$354$	8.08765e8	0.968972
$355$	4.20315e8	0.498626
$356$	6.21932e8	0.730580
$357$	−1.01573e9	−1.18151
$358$	7.99741e8	0.921211
$359$	−1.70072e9	−1.94000	−0.969999	−	0.243111i	$-0.921832\pi$
$359$	−1.70072e9	−1.94000	−0.969999	+	0.243111i	$0.921832\pi$
$360$	−2.26159e8	−0.255479
$361$	−5.94426e7	−0.0665001
$362$	−8.06772e8	−0.893863
$363$	−2.85992e8	−0.313820
$364$	4.25819e8	0.462775
$365$	1.75606e9	1.89023
$366$	2.58071e8	0.275141
$367$	8.05279e8	0.850384	0.425192	−	0.905103i	$-0.360207\pi$
$367$	8.05279e8	0.850384	0.425192	+	0.905103i	$0.360207\pi$
$368$	2.57575e8	0.269424
$369$	1.21086e8	0.125459
$370$	1.32374e8	0.135862
$371$	8.16426e8	0.830058
$372$	−5.12395e8	−0.516065
$373$	1.35518e9	1.35212	0.676061	−	0.736846i	$-0.263686\pi$
$373$	1.35518e9	1.35212	0.676061	+	0.736846i	$0.263686\pi$
$374$	1.06268e9	1.05039
$375$	9.62701e8	0.942718
$376$	−6.64770e8	−0.644932
$377$	−2.46065e9	−2.36513
$378$	2.51710e8	0.239706
$379$	8.17165e8	0.771033	0.385516	−	0.922701i	$-0.374023\pi$
$379$	8.17165e8	0.771033	0.385516	+	0.922701i	$0.374023\pi$
$380$	−6.03925e8	−0.564599
$381$	−4.82216e8	−0.446688
$382$	−4.86294e7	−0.0446352
$383$	−4.22610e8	−0.384365	−0.192183	−	0.981359i	$-0.561557\pi$
$383$	−4.22610e8	−0.384365	−0.192183	+	0.981359i	$0.561557\pi$
$384$	1.24762e8	0.112440
$385$	−1.02007e9	−0.910998
$386$	1.04593e9	0.925655
$387$	−1.81046e8	−0.158782
$388$	5.22822e7	0.0454405
$389$	−5.23938e8	−0.451291	−0.225645	−	0.974210i	$-0.572449\pi$
$389$	−5.23938e8	−0.451291	−0.225645	+	0.974210i	$0.572449\pi$
$390$	−1.63278e9	−1.39380
$391$	−1.69473e9	−1.43378
$392$	2.16157e8	0.181246
$393$	−8.99420e8	−0.747462
$394$	4.43449e8	0.365264
$395$	1.42846e9	1.16621
$396$	4.26550e8	0.345173
$397$	9.30354e8	0.746245	0.373123	−	0.927782i	$-0.378287\pi$
$397$	9.30354e8	0.746245	0.373123	+	0.927782i	$0.378287\pi$
$398$	5.46299e8	0.434350
$399$	−1.08871e9	−0.858043
$400$	1.17096e8	0.0914809
$401$	−8.18251e8	−0.633697	−0.316848	−	0.948476i	$-0.602625\pi$
$401$	−8.18251e8	−0.633697	−0.316848	+	0.948476i	$0.602625\pi$
$402$	2.84863e8	0.218698
$403$	−1.41335e9	−1.07568
$404$	9.38330e8	0.707980
$405$	−1.93120e9	−1.44456
$406$	1.18749e9	0.880620
$407$	−2.49666e8	−0.183560
$408$	−8.20879e8	−0.598368
$409$	−4.85949e8	−0.351204	−0.175602	−	0.984461i	$-0.556187\pi$
$409$	−4.85949e8	−0.351204	−0.175602	+	0.984461i	$0.556187\pi$
$410$	−2.34021e8	−0.167692
$411$	−3.04126e7	−0.0216076
$412$	7.85529e8	0.553378
$413$	−1.07659e9	−0.752010
$414$	−6.80250e8	−0.471159
$415$	−4.88885e8	−0.335767
$416$	3.44134e8	0.234369
$417$	2.20561e9	1.48954
$418$	1.13904e9	0.762819
$419$	2.41129e9	1.60140	0.800700	−	0.599065i	$-0.204461\pi$
$419$	2.41129e9	1.60140	0.800700	+	0.599065i	$0.204461\pi$
$420$	7.87966e8	0.518961
$421$	1.26593e9	0.826841	0.413421	−	0.910540i	$-0.364334\pi$
$421$	1.26593e9	0.826841	0.413421	+	0.910540i	$0.364334\pi$
$422$	1.62703e9	1.05390
$423$	1.75565e9	1.12784
$424$	6.59810e8	0.420377
$425$	−7.70439e8	−0.486830
$426$	6.12361e8	0.383773
$427$	−3.43530e8	−0.213534
$428$	4.41860e8	0.272415
$429$	3.07952e9	1.88314
$430$	3.49906e8	0.212232
$431$	2.31185e9	1.39088	0.695440	−	0.718584i	$-0.255209\pi$
$431$	2.31185e9	1.39088	0.695440	+	0.718584i	$0.255209\pi$
$432$	2.03424e8	0.121397
$433$	−1.90291e9	−1.12644	−0.563222	−	0.826306i	$-0.690438\pi$
$433$	−1.90291e9	−1.12644	−0.563222	+	0.826306i	$0.690438\pi$
$434$	6.82073e8	0.400513
$435$	−4.55336e9	−2.65228
$436$	2.56527e8	0.148228
$437$	−1.81651e9	−1.04124
$438$	2.55843e9	1.45483
$439$	1.78517e9	1.00705	0.503527	−	0.863979i	$-0.332035\pi$
$439$	1.78517e9	1.00705	0.503527	+	0.863979i	$0.332035\pi$
$440$	−8.24389e8	−0.461368
$441$	−5.70867e8	−0.316957
$442$	−2.26425e9	−1.24723
$443$	−1.26054e9	−0.688882	−0.344441	−	0.938808i	$-0.611932\pi$
$443$	−1.26054e9	−0.688882	−0.344441	+	0.938808i	$0.611932\pi$
$444$	1.92858e8	0.104567
$445$	3.17447e9	1.70770
$446$	−2.01281e9	−1.07432
$447$	3.66346e9	1.94006
$448$	−1.66076e8	−0.0872639
$449$	−1.14767e8	−0.0598352	−0.0299176	−	0.999552i	$-0.509524\pi$
$449$	−1.14767e8	−0.0598352	−0.0299176	+	0.999552i	$0.509524\pi$
$450$	−3.09248e8	−0.159979
$451$	4.41378e8	0.226565
$452$	−1.16632e9	−0.594062
$453$	1.15360e9	0.583059
$454$	−1.11538e9	−0.559405
$455$	2.17347e9	1.08172
$456$	−8.79865e8	−0.434550
$457$	2.25206e8	0.110376	0.0551879	−	0.998476i	$-0.482424\pi$
$457$	2.25206e8	0.110376	0.0551879	+	0.998476i	$0.482424\pi$
$458$	−5.22968e8	−0.254358
$459$	−1.33844e9	−0.646034
$460$	1.31471e9	0.629765
$461$	3.42695e9	1.62913	0.814564	−	0.580074i	$-0.196976\pi$
$461$	3.42695e9	1.62913	0.814564	+	0.580074i	$0.196976\pi$
$462$	−1.48615e9	−0.701158
$463$	2.03034e9	0.950683	0.475342	−	0.879801i	$-0.342324\pi$
$463$	2.03034e9	0.950683	0.475342	+	0.879801i	$0.342324\pi$
$464$	9.59692e8	0.445984
$465$	−2.61537e9	−1.20628
$466$	1.26857e9	0.580718
$467$	2.63938e9	1.19920	0.599601	−	0.800299i	$-0.295326\pi$
$467$	2.63938e9	1.19920	0.599601	+	0.800299i	$0.295326\pi$
$468$	−9.08852e8	−0.409857
$469$	−3.79195e8	−0.169730
$470$	−3.39312e9	−1.50750
$471$	−5.68434e9	−2.50673
$472$	−8.70064e8	−0.380850
$473$	−6.59943e8	−0.286743
$474$	2.08114e9	0.897587
$475$	−8.25801e8	−0.353547
$476$	1.09271e9	0.464388
$477$	−1.74255e9	−0.735141
$478$	−1.10467e9	−0.462630
$479$	−3.66156e9	−1.52227	−0.761135	−	0.648594i	$-0.775357\pi$
$479$	−3.66156e9	−1.52227	−0.761135	+	0.648594i	$0.775357\pi$
$480$	6.36810e8	0.262824
$481$	5.31964e8	0.217959
$482$	−2.18364e9	−0.888211
$483$	2.37008e9	0.957078
$484$	3.07668e8	0.123346
$485$	2.66859e8	0.106215
$486$	−1.94467e9	−0.768455
$487$	9.76007e8	0.382914	0.191457	−	0.981501i	$-0.438679\pi$
$487$	9.76007e8	0.382914	0.191457	+	0.981501i	$0.438679\pi$
$488$	−2.77631e8	−0.108143
$489$	−8.72024e8	−0.337247
$490$	1.10331e9	0.423654
$491$	5.15264e9	1.96447	0.982234	−	0.187662i	$-0.0600909\pi$
$491$	5.15264e9	1.96447	0.982234	+	0.187662i	$0.0600909\pi$
$492$	−3.40948e8	−0.129066
$493$	−6.31436e9	−2.37337
$494$	−2.42696e9	−0.905769
$495$	2.17720e9	0.806826
$496$	5.51230e8	0.202837
$497$	−8.15143e8	−0.297842
$498$	−7.12262e8	−0.258427
$499$	−6.78034e7	−0.0244286	−0.0122143	−	0.999925i	$-0.503888\pi$
$499$	−6.78034e7	−0.0244286	−0.0122143	+	0.999925i	$0.503888\pi$
$500$	−1.03567e9	−0.370531
$501$	4.65218e8	0.165282
$502$	8.36031e8	0.294958
$503$	−5.29745e9	−1.85600	−0.928002	−	0.372576i	$-0.878475\pi$
$503$	−5.29745e9	−1.85600	−0.928002	+	0.372576i	$0.878475\pi$
$504$	4.38605e8	0.152604
$505$	4.78943e9	1.65487
$506$	−2.47963e9	−0.850864
$507$	−2.82857e9	−0.963916
$508$	5.18764e8	0.175569
$509$	5.08156e9	1.70799	0.853994	−	0.520282i	$-0.174173\pi$
$509$	5.08156e9	1.70799	0.853994	+	0.520282i	$0.174173\pi$
$510$	−4.18994e9	−1.39866
$511$	−3.40564e9	−1.12908
$512$	−1.34218e8	−0.0441942
$513$	−1.43462e9	−0.469166
$514$	7.14369e8	0.232034
$515$	4.00950e9	1.29350
$516$	5.09782e8	0.163347
$517$	6.39964e9	2.03675
$518$	−2.56722e8	−0.0811538
$519$	−4.41933e9	−1.38762
$520$	1.75653e9	0.547827
$521$	4.55184e9	1.41012	0.705058	−	0.709150i	$-0.250921\pi$
$521$	4.55184e9	1.41012	0.705058	+	0.709150i	$0.250921\pi$
$522$	−2.53453e9	−0.779921
$523$	−2.31320e9	−0.707060	−0.353530	−	0.935423i	$-0.615019\pi$
$523$	−2.31320e9	−0.707060	−0.353530	+	0.935423i	$0.615019\pi$
$524$	9.67590e8	0.293786
$525$	1.07746e9	0.324969
$526$	−3.44573e9	−1.03236
$527$	−3.62686e9	−1.07943
$528$	−1.20106e9	−0.355097
$529$	5.49624e8	0.161425
$530$	3.36781e9	0.982612
$531$	2.29782e9	0.666018
$532$	1.17123e9	0.337250
$533$	−9.40446e8	−0.269023
$534$	4.62492e9	1.31435
$535$	2.25535e9	0.636759
$536$	−3.06454e8	−0.0859583
$537$	5.94718e9	1.65730
$538$	−3.17486e9	−0.878997
$539$	−2.08091e9	−0.572391
$540$	1.03832e9	0.283761
$541$	5.24683e8	0.142464	0.0712322	−	0.997460i	$-0.477307\pi$
$541$	5.24683e8	0.142464	0.0712322	+	0.997460i	$0.477307\pi$
$542$	3.40269e9	0.917962
$543$	−5.99946e9	−1.60810
$544$	8.83095e8	0.235186
$545$	1.30937e9	0.346477
$546$	3.16655e9	0.832554
$547$	−4.86419e9	−1.27073	−0.635367	−	0.772211i	$-0.719151\pi$
$547$	−4.86419e9	−1.27073	−0.635367	+	0.772211i	$0.719151\pi$
$548$	3.27176e7	0.00849278
$549$	7.33218e8	0.189117
$550$	−1.12726e9	−0.288905
$551$	−6.76810e9	−1.72360
$552$	1.91542e9	0.484705
$553$	−2.77030e9	−0.696609
$554$	3.08423e9	0.770661
$555$	9.84385e8	0.244422
$556$	−2.37278e9	−0.585458
$557$	5.18805e9	1.27207	0.636035	−	0.771660i	$-0.280573\pi$
$557$	5.18805e9	1.27207	0.636035	+	0.771660i	$0.280573\pi$
$558$	−1.45579e9	−0.354715
$559$	1.40614e9	0.340478
$560$	−8.47688e8	−0.203975
$561$	7.90247e9	1.88970
$562$	−5.34511e9	−1.27022
$563$	−5.86237e9	−1.38450	−0.692252	−	0.721656i	$-0.743381\pi$
$563$	−5.86237e9	−1.38450	−0.692252	+	0.721656i	$0.743381\pi$
$564$	−4.94348e9	−1.16026
$565$	−5.95312e9	−1.38859
$566$	4.85314e7	0.0112503
$567$	3.74530e9	0.862872
$568$	−6.58774e8	−0.150840
$569$	−6.72919e9	−1.53133	−0.765667	−	0.643238i	$-0.777591\pi$
$569$	−6.72919e9	−1.53133	−0.765667	+	0.643238i	$0.777591\pi$
$570$	−4.49102e9	−1.01574
$571$	−2.19206e9	−0.492748	−0.246374	−	0.969175i	$-0.579239\pi$
$571$	−2.19206e9	−0.492748	−0.246374	+	0.969175i	$0.579239\pi$
$572$	−3.31292e9	−0.740159
$573$	−3.61627e8	−0.0803007
$574$	4.53852e8	0.100167
$575$	1.79773e9	0.394354
$576$	3.54467e8	0.0772853
$577$	2.73158e9	0.591968	0.295984	−	0.955193i	$-0.404353\pi$
$577$	2.73158e9	0.591968	0.295984	+	0.955193i	$0.404353\pi$
$578$	−2.52768e9	−0.544471
$579$	7.77797e9	1.66529
$580$	4.89847e9	1.04247
$581$	9.48126e8	0.200562
$582$	3.88790e8	0.0817495
$583$	−6.35189e9	−1.32759
$584$	−2.75233e9	−0.571816
$585$	−4.63897e9	−0.958023
$586$	4.42047e9	0.907458
$587$	6.90154e9	1.40836	0.704178	−	0.710023i	$-0.251316\pi$
$587$	6.90154e9	1.40836	0.704178	+	0.710023i	$0.251316\pi$
$588$	1.60743e9	0.326070
$589$	−3.88748e9	−0.783906
$590$	−4.44098e9	−0.890220
$591$	3.29765e9	0.657126
$592$	−2.07475e8	−0.0410997
$593$	−2.98377e9	−0.587590	−0.293795	−	0.955869i	$-0.594918\pi$
$593$	−2.98377e9	−0.587590	−0.293795	+	0.955869i	$0.594918\pi$
$594$	−1.95833e9	−0.383384
$595$	5.57742e9	1.08549
$596$	−3.94112e9	−0.762532
$597$	4.06249e9	0.781416
$598$	5.28336e9	1.01031
$599$	−3.07774e9	−0.585110	−0.292555	−	0.956249i	$-0.594505\pi$
$599$	−3.07774e9	−0.585110	−0.292555	+	0.956249i	$0.594505\pi$
$600$	8.70767e8	0.164578
$601$	−7.73999e9	−1.45439	−0.727193	−	0.686433i	$-0.759176\pi$
$601$	−7.73999e9	−1.45439	−0.727193	+	0.686433i	$0.759176\pi$
$602$	−6.78595e8	−0.126772
$603$	8.09339e8	0.150321
$604$	−1.24104e9	−0.229169
$605$	1.57040e9	0.288315
$606$	6.97778e9	1.27369
$607$	4.77214e9	0.866070	0.433035	−	0.901377i	$-0.357443\pi$
$607$	4.77214e9	0.866070	0.433035	+	0.901377i	$0.357443\pi$
$608$	9.46552e8	0.170798
$609$	8.83062e9	1.58427
$610$	−1.41708e9	−0.252779
$611$	−1.36357e10	−2.41844
$612$	−2.33224e9	−0.411285
$613$	−3.63468e9	−0.637316	−0.318658	−	0.947870i	$-0.603232\pi$
$613$	−3.63468e9	−0.637316	−0.318658	+	0.947870i	$0.603232\pi$
$614$	1.28310e9	0.223702
$615$	−1.74027e9	−0.301685
$616$	1.59879e9	0.275587
$617$	3.37834e9	0.579035	0.289518	−	0.957173i	$-0.406505\pi$
$617$	3.37834e9	0.579035	0.289518	+	0.957173i	$0.406505\pi$
$618$	5.84149e9	0.995552
$619$	1.53489e8	0.0260111	0.0130056	−	0.999915i	$-0.495860\pi$
$619$	1.53489e8	0.0260111	0.0130056	+	0.999915i	$0.495860\pi$
$620$	2.81359e9	0.474122
$621$	3.12310e9	0.523317
$622$	3.11023e9	0.518235
$623$	−6.15645e9	−1.02005
$624$	2.55911e9	0.421641
$625$	−7.51968e9	−1.23202
$626$	4.53083e9	0.738188
$627$	8.47033e9	1.37235
$628$	6.11517e9	0.985258
$629$	1.36509e9	0.218719
$630$	2.23873e9	0.356705
$631$	−1.63395e9	−0.258902	−0.129451	−	0.991586i	$-0.541321\pi$
$631$	−1.63395e9	−0.258902	−0.129451	+	0.991586i	$0.541321\pi$
$632$	−2.23887e9	−0.352793
$633$	1.20992e10	1.89602
$634$	4.68447e9	0.730043
$635$	2.64788e9	0.410384
$636$	4.90660e9	0.756277
$637$	4.43381e9	0.679655
$638$	−9.23880e9	−1.40846
$639$	1.73981e9	0.263784
$640$	−6.85075e8	−0.103302
$641$	−9.11499e9	−1.36695	−0.683476	−	0.729973i	$-0.739532\pi$
$641$	−9.11499e9	−1.36695	−0.683476	+	0.729973i	$0.739532\pi$
$642$	3.28584e9	0.490088
$643$	−8.53904e9	−1.26669	−0.633346	−	0.773869i	$-0.718319\pi$
$643$	−8.53904e9	−1.26669	−0.633346	+	0.773869i	$0.718319\pi$
$644$	−2.54971e9	−0.376175
$645$	2.60203e9	0.381815
$646$	−6.22791e9	−0.908926
$647$	−2.95371e9	−0.428749	−0.214375	−	0.976752i	$-0.568771\pi$
$647$	−2.95371e9	−0.428749	−0.214375	+	0.976752i	$0.568771\pi$
$648$	3.02684e9	0.436995
$649$	8.37597e9	1.20276
$650$	2.40186e9	0.343045
$651$	5.07215e9	0.720541
$652$	9.38117e8	0.132553
$653$	1.57940e9	0.221970	0.110985	−	0.993822i	$-0.464599\pi$
$653$	1.57940e9	0.221970	0.110985	+	0.993822i	$0.464599\pi$
$654$	1.90763e9	0.266669
$655$	4.93878e9	0.686712
$656$	3.66789e8	0.0507286
$657$	7.26887e9	0.999973
$658$	6.58050e9	0.900468
$659$	5.08465e9	0.692089	0.346044	−	0.938218i	$-0.387525\pi$
$659$	5.08465e9	0.692089	0.346044	+	0.938218i	$0.387525\pi$
$660$	−6.13047e9	−0.830023
$661$	6.89277e9	0.928301	0.464150	−	0.885756i	$-0.346360\pi$
$661$	6.89277e9	0.928301	0.464150	+	0.885756i	$0.346360\pi$
$662$	−7.27869e9	−0.975102
$663$	−1.68378e10	−2.24383
$664$	7.66246e8	0.101573
$665$	5.97820e9	0.788306
$666$	5.47937e8	0.0718739
$667$	1.47338e10	1.92254
$668$	−5.00478e8	−0.0649632
$669$	−1.49681e10	−1.93274
$670$	−1.56420e9	−0.200924
$671$	2.67271e9	0.341525
$672$	−1.23501e9	−0.156992
$673$	−1.45890e9	−0.184490	−0.0922449	−	0.995736i	$-0.529404\pi$
$673$	−1.45890e9	−0.184490	−0.0922449	+	0.995736i	$0.529404\pi$
$674$	5.95885e9	0.749640
$675$	1.41979e9	0.177689
$676$	3.04295e9	0.378863
$677$	9.42301e9	1.16716	0.583579	−	0.812057i	$-0.301652\pi$
$677$	9.42301e9	1.16716	0.583579	+	0.812057i	$0.301652\pi$
$678$	−8.67317e9	−1.06874
$679$	−5.17537e8	−0.0634450
$680$	4.50750e9	0.549737
$681$	−8.29438e9	−1.00640
$682$	−5.30661e9	−0.640577
$683$	8.94405e9	1.07414	0.537071	−	0.843537i	$-0.319531\pi$
$683$	8.94405e9	1.07414	0.537071	+	0.843537i	$0.319531\pi$
$684$	−2.49983e9	−0.298685
$685$	1.66998e8	0.0198515
$686$	−6.31364e9	−0.746699
$687$	−3.88899e9	−0.457602
$688$	−5.48419e8	−0.0642027
$689$	1.35340e10	1.57637
$690$	9.77671e9	1.13298
$691$	−8.43588e9	−0.972652	−0.486326	−	0.873778i	$-0.661663\pi$
$691$	−8.43588e9	−0.972652	−0.486326	+	0.873778i	$0.661663\pi$
$692$	4.75428e9	0.545397
$693$	−4.22238e9	−0.481938
$694$	−3.60623e9	−0.409539
$695$	−1.21112e10	−1.36848
$696$	7.13663e9	0.802345
$697$	−2.41332e9	−0.269960
$698$	2.41933e9	0.269278
$699$	9.43360e9	1.04474
$700$	−1.15912e9	−0.127728
$701$	2.81188e9	0.308308	0.154154	−	0.988047i	$-0.450735\pi$
$701$	2.81188e9	0.308308	0.154154	+	0.988047i	$0.450735\pi$
$702$	4.17263e9	0.455229
$703$	1.46319e9	0.158839
$704$	1.29209e9	0.139569
$705$	−2.52326e10	−2.71206
$706$	−1.47247e9	−0.157481
$707$	−9.28845e9	−0.988497
$708$	−6.47012e9	−0.685167
$709$	−1.12427e10	−1.18470	−0.592352	−	0.805679i	$-0.701800\pi$
$709$	−1.12427e10	−1.18470	−0.592352	+	0.805679i	$0.701800\pi$
$710$	−3.36252e9	−0.352582
$711$	5.91282e9	0.616952
$712$	−4.97545e9	−0.516598
$713$	8.46284e9	0.874385
$714$	8.12581e9	0.835455
$715$	−1.69098e10	−1.73009
$716$	−6.39793e9	−0.651394
$717$	−8.21472e9	−0.832292
$718$	1.36057e10	1.37179
$719$	1.28416e10	1.28845	0.644225	−	0.764836i	$-0.277180\pi$
$719$	1.28416e10	1.28845	0.644225	+	0.764836i	$0.277180\pi$
$720$	1.80927e9	0.180651
$721$	−7.77588e9	−0.772639
$722$	4.75541e8	0.0470227
$723$	−1.62384e10	−1.59793
$724$	6.45418e9	0.632056
$725$	6.69811e9	0.652784
$726$	2.28794e9	0.221904
$727$	5.23755e9	0.505542	0.252771	−	0.967526i	$-0.418658\pi$
$727$	5.23755e9	0.505542	0.252771	+	0.967526i	$0.418658\pi$
$728$	−3.40655e9	−0.327231
$729$	−1.53219e9	−0.146476
$730$	−1.40485e10	−1.33659
$731$	3.60836e9	0.341664
$732$	−2.06457e9	−0.194554
$733$	−1.34926e10	−1.26541	−0.632706	−	0.774392i	$-0.718056\pi$
$733$	−1.34926e10	−1.26541	−0.632706	+	0.774392i	$0.718056\pi$
$734$	−6.44223e9	−0.601312
$735$	8.20464e9	0.762173
$736$	−2.06060e9	−0.190511
$737$	2.95018e9	0.271464
$738$	−9.68685e8	−0.0887126
$739$	−1.18887e10	−1.08362	−0.541810	−	0.840501i	$-0.682261\pi$
$739$	−1.18887e10	−1.08362	−0.541810	+	0.840501i	$0.682261\pi$
$740$	−1.05899e9	−0.0960688
$741$	−1.80478e10	−1.62952
$742$	−6.53141e9	−0.586939
$743$	1.78272e10	1.59449	0.797247	−	0.603653i	$-0.206289\pi$
$743$	1.78272e10	1.59449	0.797247	+	0.603653i	$0.206289\pi$
$744$	4.09916e9	0.364913
$745$	−2.01163e10	−1.78238
$746$	−1.08414e10	−0.956095
$747$	−2.02364e9	−0.177628
$748$	−8.50142e9	−0.742738
$749$	−4.37394e9	−0.380352
$750$	−7.70161e9	−0.666602
$751$	−9.32098e9	−0.803012	−0.401506	−	0.915856i	$-0.631513\pi$
$751$	−9.32098e9	−0.803012	−0.401506	+	0.915856i	$0.631513\pi$
$752$	5.31816e9	0.456036
$753$	6.21705e9	0.530642
$754$	1.96852e10	1.67240
$755$	−6.33451e9	−0.535672
$756$	−2.01368e9	−0.169498
$757$	−1.15006e10	−0.963572	−0.481786	−	0.876289i	$-0.660012\pi$
$757$	−1.15006e10	−0.963572	−0.481786	+	0.876289i	$0.660012\pi$
$758$	−6.53732e9	−0.545202
$759$	−1.84395e10	−1.53074
$760$	4.83140e9	0.399232
$761$	−4.33764e9	−0.356785	−0.178393	−	0.983959i	$-0.557090\pi$
$761$	−4.33764e9	−0.356785	−0.178393	+	0.983959i	$0.557090\pi$
$762$	3.85773e9	0.315856
$763$	−2.53934e9	−0.206959
$764$	3.89035e8	0.0315618
$765$	−1.19042e10	−0.961361
$766$	3.38088e9	0.271787
$767$	−1.78467e10	−1.42815
$768$	−9.98094e8	−0.0795073
$769$	1.87582e10	1.48747	0.743737	−	0.668472i	$-0.233051\pi$
$769$	1.87582e10	1.48747	0.743737	+	0.668472i	$0.233051\pi$
$770$	8.16056e9	0.644173
$771$	5.31232e9	0.417440
$772$	−8.36748e9	−0.654537
$773$	1.53052e10	1.19182	0.595909	−	0.803052i	$-0.296792\pi$
$773$	1.53052e10	1.19182	0.595909	+	0.803052i	$0.296792\pi$
$774$	1.44837e9	0.112276
$775$	3.84728e9	0.296891
$776$	−4.18258e8	−0.0321313
$777$	−1.90908e9	−0.145999
$778$	4.19151e9	0.319111
$779$	−2.58673e9	−0.196052
$780$	1.30622e10	0.985566
$781$	6.34191e9	0.476367
$782$	1.35578e10	1.01383
$783$	1.16363e10	0.866260
$784$	−1.72926e9	−0.128160
$785$	3.12131e10	2.30300
$786$	7.19536e9	0.528535
$787$	2.16684e10	1.58458	0.792291	−	0.610144i	$-0.208888\pi$
$787$	2.16684e10	1.58458	0.792291	+	0.610144i	$0.208888\pi$
$788$	−3.54759e9	−0.258280
$789$	−2.56238e10	−1.85726
$790$	−1.14277e10	−0.824637
$791$	1.15453e10	0.829442
$792$	−3.41240e9	−0.244074
$793$	−5.69475e9	−0.405526
$794$	−7.44283e9	−0.527675
$795$	2.50443e10	1.76776
$796$	−4.37040e9	−0.307132
$797$	1.78039e10	1.24570	0.622848	−	0.782343i	$-0.285976\pi$
$797$	1.78039e10	1.24570	0.622848	+	0.782343i	$0.285976\pi$
$798$	8.70972e9	0.606728
$799$	−3.49912e10	−2.42686
$800$	−9.36765e8	−0.0646868
$801$	1.31401e10	0.903409
$802$	6.54601e9	0.448091
$803$	2.64963e10	1.80585
$804$	−2.27891e9	−0.154643
$805$	−1.30142e10	−0.879292
$806$	1.13068e10	0.760620
$807$	−2.36095e10	−1.58136
$808$	−7.50664e9	−0.500617
$809$	−1.86192e10	−1.23635	−0.618174	−	0.786041i	$-0.712127\pi$
$809$	−1.86192e10	−1.23635	−0.618174	+	0.786041i	$0.712127\pi$
$810$	1.54496e10	1.02146
$811$	−2.08368e10	−1.37170	−0.685849	−	0.727743i	$-0.740569\pi$
$811$	−2.08368e10	−1.37170	−0.685849	+	0.727743i	$0.740569\pi$
$812$	−9.49991e9	−0.622692
$813$	2.53037e10	1.65146
$814$	1.99733e9	0.129797
$815$	4.78834e9	0.309837
$816$	6.56703e9	0.423110
$817$	3.86765e9	0.248125
$818$	3.88759e9	0.248338
$819$	8.99665e9	0.572252
$820$	1.87217e9	0.118576
$821$	2.50241e10	1.57818	0.789091	−	0.614277i	$-0.210552\pi$
$821$	2.50241e10	1.57818	0.789091	+	0.614277i	$0.210552\pi$
$822$	2.43301e8	0.0152789
$823$	1.73792e10	1.08675	0.543375	−	0.839490i	$-0.317146\pi$
$823$	1.73792e10	1.08675	0.543375	+	0.839490i	$0.317146\pi$
$824$	−6.28423e9	−0.391297
$825$	−8.38274e9	−0.519753
$826$	8.61269e9	0.531751
$827$	−1.05928e10	−0.651241	−0.325620	−	0.945501i	$-0.605573\pi$
$827$	−1.05928e10	−0.651241	−0.325620	+	0.945501i	$0.605573\pi$
$828$	5.44200e9	0.333160
$829$	6.89516e9	0.420343	0.210171	−	0.977665i	$-0.432598\pi$
$829$	6.89516e9	0.420343	0.210171	+	0.977665i	$0.432598\pi$
$830$	3.91108e9	0.237423
$831$	2.29355e10	1.38645
$832$	−2.75307e9	−0.165724
$833$	1.13778e10	0.682024
$834$	−1.76449e10	−1.05327
$835$	−2.55454e9	−0.151848
$836$	−9.11231e9	−0.539395
$837$	6.68368e9	0.393982
$838$	−1.92903e10	−1.13236
$839$	2.84284e10	1.66182	0.830912	−	0.556404i	$-0.187819\pi$
$839$	2.84284e10	1.66182	0.830912	+	0.556404i	$0.187819\pi$
$840$	−6.30373e9	−0.366961
$841$	3.76465e10	2.18242
$842$	−1.01274e10	−0.584665
$843$	−3.97483e10	−2.28519
$844$	−1.30162e10	−0.745223
$845$	1.55319e10	0.885575
$846$	−1.40452e10	−0.797500
$847$	−3.04558e9	−0.172218
$848$	−5.27848e9	−0.297251
$849$	3.60898e8	0.0202399
$850$	6.16351e9	0.344241
$851$	−3.18528e9	−0.177172
$852$	−4.89889e9	−0.271368
$853$	−2.95280e10	−1.62897	−0.814484	−	0.580186i	$-0.802980\pi$
$853$	−2.95280e10	−1.62897	−0.814484	+	0.580186i	$0.802980\pi$
$854$	2.74824e9	0.150991
$855$	−1.27596e10	−0.698164
$856$	−3.53488e9	−0.192627
$857$	2.71240e10	1.47204	0.736021	−	0.676959i	$-0.236702\pi$
$857$	2.71240e10	1.47204	0.736021	+	0.676959i	$0.236702\pi$
$858$	−2.46361e10	−1.33158
$859$	−2.96758e8	−0.0159745	−0.00798723	−	0.999968i	$-0.502542\pi$
$859$	−2.96758e8	−0.0159745	−0.00798723	+	0.999968i	$0.502542\pi$
$860$	−2.79924e9	−0.150071
$861$	3.37502e9	0.180204
$862$	−1.84948e10	−0.983501
$863$	−3.21034e9	−0.170025	−0.0850126	−	0.996380i	$-0.527093\pi$
$863$	−3.21034e9	−0.170025	−0.0850126	+	0.996380i	$0.527093\pi$
$864$	−1.62739e9	−0.0858409
$865$	2.42668e10	1.27484
$866$	1.52232e10	0.796516
$867$	−1.87968e10	−0.979528
$868$	−5.45658e9	−0.283205
$869$	2.15533e10	1.11415
$870$	3.64269e10	1.87544
$871$	−6.28597e9	−0.322336
$872$	−2.05222e9	−0.104813
$873$	1.10461e9	0.0561901
$874$	1.45321e10	0.736271
$875$	1.02520e10	0.517344
$876$	−2.04674e10	−1.02872
$877$	3.21311e10	1.60852	0.804261	−	0.594277i	$-0.202562\pi$
$877$	3.21311e10	1.60852	0.804261	+	0.594277i	$0.202562\pi$
$878$	−1.42813e10	−0.712095
$879$	3.28723e10	1.63256
$880$	6.59511e9	0.326237
$881$	2.94649e9	0.145174	0.0725871	−	0.997362i	$-0.476874\pi$
$881$	2.94649e9	0.145174	0.0725871	+	0.997362i	$0.476874\pi$
$882$	4.56694e9	0.224122
$883$	−1.54320e10	−0.754328	−0.377164	−	0.926146i	$-0.623101\pi$
$883$	−1.54320e10	−0.754328	−0.377164	+	0.926146i	$0.623101\pi$
$884$	1.81140e10	0.881926
$885$	−3.30248e10	−1.60155
$886$	1.00844e10	0.487113
$887$	−3.90897e10	−1.88074	−0.940372	−	0.340147i	$-0.889523\pi$
$887$	−3.90897e10	−1.88074	−0.940372	+	0.340147i	$0.889523\pi$
$888$	−1.54286e9	−0.0739403
$889$	−5.13520e9	−0.245133
$890$	−2.53957e10	−1.20752
$891$	−2.91389e10	−1.38007
$892$	1.61025e10	0.759655
$893$	−3.75056e10	−1.76245
$894$	−2.93077e10	−1.37183
$895$	−3.26564e10	−1.52260
$896$	1.32861e9	0.0617049
$897$	3.92891e10	1.81760
$898$	9.18140e8	0.0423099
$899$	3.15315e10	1.44739
$900$	2.47398e9	0.113122
$901$	3.47302e10	1.58187
$902$	−3.53102e9	−0.160206
$903$	−5.04629e9	−0.228068
$904$	9.33053e9	0.420065
$905$	3.29435e10	1.47740
$906$	−9.22882e9	−0.412285
$907$	2.70491e10	1.20373	0.601863	−	0.798599i	$-0.294425\pi$
$907$	2.70491e10	1.20373	0.601863	+	0.798599i	$0.294425\pi$
$908$	8.92303e9	0.395559
$909$	1.98249e10	0.875463
$910$	−1.73877e10	−0.764889
$911$	1.42537e10	0.624616	0.312308	−	0.949981i	$-0.398898\pi$
$911$	1.42537e10	0.624616	0.312308	+	0.949981i	$0.398898\pi$
$912$	7.03892e9	0.307273
$913$	−7.37653e9	−0.320778
$914$	−1.80165e9	−0.0780475
$915$	−1.05380e10	−0.454761
$916$	4.18375e9	0.179859
$917$	−9.57809e9	−0.410191
$918$	1.07075e10	0.456815
$919$	1.68941e9	0.0718012	0.0359006	−	0.999355i	$-0.488570\pi$
$919$	1.68941e9	0.0718012	0.0359006	+	0.999355i	$0.488570\pi$
$920$	−1.05177e10	−0.445311
$921$	9.54160e9	0.402451
$922$	−2.74156e10	−1.15197
$923$	−1.35127e10	−0.565637
$924$	1.18892e10	0.495794
$925$	−1.44806e9	−0.0601575
$926$	−1.62427e10	−0.672235
$927$	1.65966e10	0.684288
$928$	−7.67753e9	−0.315358
$929$	−4.53109e10	−1.85416	−0.927080	−	0.374863i	$-0.877690\pi$
$929$	−4.53109e10	−1.85416	−0.927080	+	0.374863i	$0.877690\pi$
$930$	2.09229e10	0.852967
$931$	1.21953e10	0.495302
$932$	−1.01486e10	−0.410630
$933$	2.31289e10	0.932328
$934$	−2.11150e10	−0.847964
$935$	−4.33930e10	−1.73612
$936$	7.27081e9	0.289813
$937$	5.33576e9	0.211889	0.105944	−	0.994372i	$-0.466213\pi$
$937$	5.33576e9	0.211889	0.105944	+	0.994372i	$0.466213\pi$
$938$	3.03356e9	0.120017
$939$	3.36929e10	1.32803
$940$	2.71450e10	1.06596
$941$	−7.02739e9	−0.274935	−0.137468	−	0.990506i	$-0.543896\pi$
$941$	−7.02739e9	−0.274935	−0.137468	+	0.990506i	$0.543896\pi$
$942$	4.54747e10	1.77252
$943$	5.63118e9	0.218680
$944$	6.96051e9	0.269302
$945$	−1.02782e10	−0.396193
$946$	5.27955e9	0.202758
$947$	3.18352e10	1.21810	0.609049	−	0.793133i	$-0.291551\pi$
$947$	3.18352e10	1.21810	0.609049	+	0.793133i	$0.291551\pi$
$948$	−1.66491e10	−0.634690
$949$	−5.64558e10	−2.14426
$950$	6.60641e9	0.249996
$951$	3.48355e10	1.31338
$952$	−8.74169e9	−0.328372
$953$	−1.79825e10	−0.673015	−0.336508	−	0.941681i	$-0.609246\pi$
$953$	−1.79825e10	−0.673015	−0.336508	+	0.941681i	$0.609246\pi$
$954$	1.39404e10	0.519823
$955$	1.98572e9	0.0737743
$956$	8.83733e9	0.327129
$957$	−6.87032e10	−2.53388
$958$	2.92925e10	1.07641
$959$	−3.23869e8	−0.0118578
$960$	−5.09448e9	−0.185845
$961$	−9.40146e9	−0.341715
$962$	−4.25571e9	−0.154120
$963$	9.33556e9	0.336859
$964$	1.74691e10	0.628060
$965$	−4.27093e10	−1.52995
$966$	−1.89606e10	−0.676756
$967$	1.60417e10	0.570503	0.285251	−	0.958453i	$-0.407923\pi$
$967$	1.60417e10	0.570503	0.285251	+	0.958453i	$0.407923\pi$
$968$	−2.46135e9	−0.0872186
$969$	−4.63131e10	−1.63520
$970$	−2.13487e9	−0.0751054
$971$	−2.80778e10	−0.984228	−0.492114	−	0.870531i	$-0.663776\pi$
$971$	−2.80778e10	−0.984228	−0.492114	+	0.870531i	$0.663776\pi$
$972$	1.55573e10	0.543380
$973$	2.34879e10	0.817429
$974$	−7.80805e9	−0.270761
$975$	1.78612e10	0.617154
$976$	2.22104e9	0.0764685
$977$	−3.10512e9	−0.106524	−0.0532621	−	0.998581i	$-0.516962\pi$
$977$	−3.10512e9	−0.106524	−0.0532621	+	0.998581i	$0.516962\pi$
$978$	6.97619e9	0.238469
$979$	4.78979e10	1.63146
$980$	−8.82648e9	−0.299569
$981$	5.41987e9	0.183294
$982$	−4.12211e10	−1.38909
$983$	−2.95037e9	−0.0990692	−0.0495346	−	0.998772i	$-0.515774\pi$
$983$	−2.95037e9	−0.0990692	−0.0495346	+	0.998772i	$0.515774\pi$
$984$	2.72758e9	0.0912631
$985$	−1.81076e10	−0.603719
$986$	5.05149e10	1.67823
$987$	4.89351e10	1.61998
$988$	1.94157e10	0.640476
$989$	−8.41968e9	−0.276763
$990$	−1.74176e10	−0.570512
$991$	−5.38667e10	−1.75818	−0.879089	−	0.476658i	$-0.841848\pi$
$991$	−5.38667e10	−1.75818	−0.879089	+	0.476658i	$0.841848\pi$
$992$	−4.40984e9	−0.143427
$993$	−5.41271e10	−1.75425
$994$	6.52115e9	0.210606
$995$	−2.23074e10	−0.717907
$996$	5.69810e9	0.182735
$997$	1.66452e10	0.531931	0.265965	−	0.963983i	$-0.414309\pi$
$997$	1.66452e10	0.531931	0.265965	+	0.963983i	$0.414309\pi$
$998$	5.42427e8	0.0172737
$999$	−2.51563e9	−0.0798304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.a.c.1.1	✓	6
4.3	odd	2		592.8.a.c.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.a.c.1.1	✓	6	1.1	even	1	trivial
592.8.a.c.1.6		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)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -59.4910 q^{3} +64.0000 q^{4} +326.669 q^{5} +475.928 q^{6} -633.531 q^{7} -512.000 q^{8} +1352.18 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -59.4910 q^{3} +64.0000 q^{4} +326.669 q^{5} +475.928 q^{6} -633.531 q^{7} -512.000 q^{8} +1352.18 q^{9} -2613.35 q^{10} +4928.94 q^{11} -3807.43 q^{12} -10502.1 q^{13} +5068.25 q^{14} -19433.9 q^{15} +4096.00 q^{16} -26949.9 q^{17} -10817.5 q^{18} -28886.5 q^{19} +20906.8 q^{20} +37689.4 q^{21} -39431.6 q^{22} +62884.4 q^{23} +30459.4 q^{24} +28587.8 q^{25} +84017.0 q^{26} +49664.1 q^{27} -40546.0 q^{28} +234300. q^{29} +155471. q^{30} +134578. q^{31} -32768.0 q^{32} -293228. q^{33} +215599. q^{34} -206955. q^{35} +86539.8 q^{36} -50653.0 q^{37} +231092. q^{38} +624782. q^{39} -167255. q^{40} +89548.2 q^{41} -301515. q^{42} -133891. q^{43} +315452. q^{44} +441717. q^{45} -503075. q^{46} +1.29838e6 q^{47} -243675. q^{48} -422182. q^{49} -228702. q^{50} +1.60328e6 q^{51} -672136. q^{52} -1.28869e6 q^{53} -397313. q^{54} +1.61013e6 q^{55} +324368. q^{56} +1.71849e6 q^{57} -1.87440e6 q^{58} +1.69934e6 q^{59} -1.24377e6 q^{60} +542247. q^{61} -1.07662e6 q^{62} -856650. q^{63} +262144. q^{64} -3.43072e6 q^{65} +2.34582e6 q^{66} +598542. q^{67} -1.72480e6 q^{68} -3.74106e6 q^{69} +1.65564e6 q^{70} +1.28667e6 q^{71} -692318. q^{72} +5.37565e6 q^{73} +405224. q^{74} -1.70072e6 q^{75} -1.84874e6 q^{76} -3.12264e6 q^{77} -4.99826e6 q^{78} +4.37280e6 q^{79} +1.33804e6 q^{80} -5.91179e6 q^{81} -716385. q^{82} -1.49657e6 q^{83} +2.41212e6 q^{84} -8.80371e6 q^{85} +1.07113e6 q^{86} -1.39387e7 q^{87} -2.52362e6 q^{88} +9.71768e6 q^{89} -3.53373e6 q^{90} +6.65342e6 q^{91} +4.02460e6 q^{92} -8.00617e6 q^{93} -1.03870e7 q^{94} -9.43633e6 q^{95} +1.94940e6 q^{96} +816910. q^{97} +3.37745e6 q^{98} +6.66484e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9}+O(q^{10}) \) 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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