LMFDB - Embedded newform 74.6.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,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, 6, names="a")

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

chi := DirichletCharacter("74.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
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:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 870x^{3} - 2235x^{2} + 121361x + 481504 $ x^5 - x^4 - 870x^3 - 2235x^2 + 121361*x + 481504
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-4.15018$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} +8.15018 q^{3} +16.0000 q^{4} +86.4865 q^{5} +32.6007 q^{6} +72.3887 q^{7} +64.0000 q^{8} -176.574 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +8.15018 q^{3} +16.0000 q^{4} +86.4865 q^{5} +32.6007 q^{6} +72.3887 q^{7} +64.0000 q^{8} -176.574 q^{9} +345.946 q^{10} -547.665 q^{11} +130.403 q^{12} +630.075 q^{13} +289.555 q^{14} +704.881 q^{15} +256.000 q^{16} -202.123 q^{17} -706.298 q^{18} +2314.08 q^{19} +1383.78 q^{20} +589.982 q^{21} -2190.66 q^{22} -1349.30 q^{23} +521.612 q^{24} +4354.91 q^{25} +2520.30 q^{26} -3419.61 q^{27} +1158.22 q^{28} +634.921 q^{29} +2819.52 q^{30} -7380.03 q^{31} +1024.00 q^{32} -4463.57 q^{33} -808.493 q^{34} +6260.65 q^{35} -2825.19 q^{36} -1369.00 q^{37} +9256.33 q^{38} +5135.23 q^{39} +5535.13 q^{40} -496.112 q^{41} +2359.93 q^{42} -1239.89 q^{43} -8762.64 q^{44} -15271.3 q^{45} -5397.21 q^{46} -868.470 q^{47} +2086.45 q^{48} -11566.9 q^{49} +17419.6 q^{50} -1647.34 q^{51} +10081.2 q^{52} +13174.4 q^{53} -13678.4 q^{54} -47365.6 q^{55} +4632.88 q^{56} +18860.2 q^{57} +2539.68 q^{58} -30978.4 q^{59} +11278.1 q^{60} -45534.9 q^{61} -29520.1 q^{62} -12782.0 q^{63} +4096.00 q^{64} +54493.0 q^{65} -17854.3 q^{66} +46381.3 q^{67} -3233.97 q^{68} -10997.1 q^{69} +25042.6 q^{70} -79500.6 q^{71} -11300.8 q^{72} +15021.8 q^{73} -5476.00 q^{74} +35493.3 q^{75} +37025.3 q^{76} -39644.8 q^{77} +20540.9 q^{78} -9383.70 q^{79} +22140.5 q^{80} +15037.2 q^{81} -1984.45 q^{82} +65781.6 q^{83} +9439.70 q^{84} -17480.9 q^{85} -4959.57 q^{86} +5174.72 q^{87} -35050.5 q^{88} -142526. q^{89} -61085.2 q^{90} +45610.3 q^{91} -21588.8 q^{92} -60148.6 q^{93} -3473.88 q^{94} +200137. q^{95} +8345.79 q^{96} +148136. q^{97} -46267.5 q^{98} +96703.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 20 q^{2} + 19 q^{3} + 80 q^{4} + 95 q^{5} + 76 q^{6} + 170 q^{7} + 320 q^{8} + 598 q^{9}+O(q^{10}) $ 5 * q + 20 * q^2 + 19 * q^3 + 80 * q^4 + 95 * q^5 + 76 * q^6 + 170 * q^7 + 320 * q^8 + 598 * q^9	\( 5 q + 20 q^{2} + 19 q^{3} + 80 q^{4} + 95 q^{5} + 76 q^{6} + 170 q^{7} + 320 q^{8} + 598 q^{9} + 380 q^{10} + 903 q^{11} + 304 q^{12} + 1371 q^{13} + 680 q^{14} - 8 q^{15} + 1280 q^{16} + 2070 q^{17} + 2392 q^{18} + 2358 q^{19} + 1520 q^{20} + 2832 q^{21} + 3612 q^{22} + 2097 q^{23} + 1216 q^{24} - 390 q^{25} + 5484 q^{26} + 2614 q^{27} + 2720 q^{28} + 2927 q^{29} - 32 q^{30} - 5849 q^{31} + 5120 q^{32} - 11002 q^{33} + 8280 q^{34} - 10928 q^{35} + 9568 q^{36} - 6845 q^{37} + 9432 q^{38} - 9945 q^{39} + 6080 q^{40} - 14427 q^{41} + 11328 q^{42} - 6972 q^{43} + 14448 q^{44} - 6816 q^{45} + 8388 q^{46} - 18962 q^{47} + 4864 q^{48} - 11957 q^{49} - 1560 q^{50} - 67946 q^{51} + 21936 q^{52} - 23576 q^{53} + 10456 q^{54} - 31415 q^{55} + 10880 q^{56} - 70522 q^{57} + 11708 q^{58} - 18316 q^{59} - 128 q^{60} - 18695 q^{61} - 23396 q^{62} - 88094 q^{63} + 20480 q^{64} - 40706 q^{65} - 44008 q^{66} - 85273 q^{67} + 33120 q^{68} - 87171 q^{69} - 43712 q^{70} + 8760 q^{71} + 38272 q^{72} - 10425 q^{73} - 27380 q^{74} - 10542 q^{75} + 37728 q^{76} + 17238 q^{77} - 39780 q^{78} + 48425 q^{79} + 24320 q^{80} + 33449 q^{81} - 57708 q^{82} + 27704 q^{83} + 45312 q^{84} + 139062 q^{85} - 27888 q^{86} + 6227 q^{87} + 57792 q^{88} + 233646 q^{89} - 27264 q^{90} + 146434 q^{91} + 33552 q^{92} + 301866 q^{93} - 75848 q^{94} + 189498 q^{95} + 19456 q^{96} + 251694 q^{97} - 47828 q^{98} + 182486 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 + 19 * q^3 + 80 * q^4 + 95 * q^5 + 76 * q^6 + 170 * q^7 + 320 * q^8 + 598 * q^9 + 380 * q^10 + 903 * q^11 + 304 * q^12 + 1371 * q^13 + 680 * q^14 - 8 * q^15 + 1280 * q^16 + 2070 * q^17 + 2392 * q^18 + 2358 * q^19 + 1520 * q^20 + 2832 * q^21 + 3612 * q^22 + 2097 * q^23 + 1216 * q^24 - 390 * q^25 + 5484 * q^26 + 2614 * q^27 + 2720 * q^28 + 2927 * q^29 - 32 * q^30 - 5849 * q^31 + 5120 * q^32 - 11002 * q^33 + 8280 * q^34 - 10928 * q^35 + 9568 * q^36 - 6845 * q^37 + 9432 * q^38 - 9945 * q^39 + 6080 * q^40 - 14427 * q^41 + 11328 * q^42 - 6972 * q^43 + 14448 * q^44 - 6816 * q^45 + 8388 * q^46 - 18962 * q^47 + 4864 * q^48 - 11957 * q^49 - 1560 * q^50 - 67946 * q^51 + 21936 * q^52 - 23576 * q^53 + 10456 * q^54 - 31415 * q^55 + 10880 * q^56 - 70522 * q^57 + 11708 * q^58 - 18316 * q^59 - 128 * q^60 - 18695 * q^61 - 23396 * q^62 - 88094 * q^63 + 20480 * q^64 - 40706 * q^65 - 44008 * q^66 - 85273 * q^67 + 33120 * q^68 - 87171 * q^69 - 43712 * q^70 + 8760 * q^71 + 38272 * q^72 - 10425 * q^73 - 27380 * q^74 - 10542 * q^75 + 37728 * q^76 + 17238 * q^77 - 39780 * q^78 + 48425 * q^79 + 24320 * q^80 + 33449 * q^81 - 57708 * q^82 + 27704 * q^83 + 45312 * q^84 + 139062 * q^85 - 27888 * q^86 + 6227 * q^87 + 57792 * q^88 + 233646 * q^89 - 27264 * q^90 + 146434 * q^91 + 33552 * q^92 + 301866 * q^93 - 75848 * q^94 + 189498 * q^95 + 19456 * q^96 + 251694 * q^97 - 47828 * q^98 + 182486 * 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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	8.15018	0.522835	0.261417	−	0.965226i	$-0.415810\pi$
$3$	8.15018	0.522835	0.261417	+	0.965226i	$0.415810\pi$
$4$	16.0000	0.500000
$5$	86.4865	1.54712	0.773559	−	0.633725i	$-0.218475\pi$
$5$	86.4865	1.54712	0.773559	+	0.633725i	$0.218475\pi$
$6$	32.6007	0.369700
$7$	72.3887	0.558375	0.279187	−	0.960237i	$-0.409935\pi$
$7$	72.3887	0.558375	0.279187	+	0.960237i	$0.409935\pi$
$8$	64.0000	0.353553
$9$	−176.574	−0.726644
$10$	345.946	1.09398
$11$	−547.665	−1.36469	−0.682344	−	0.731032i	$-0.739039\pi$
$11$	−547.665	−1.36469	−0.682344	+	0.731032i	$0.739039\pi$
$12$	130.403	0.261417
$13$	630.075	1.03403	0.517016	−	0.855976i	$-0.327043\pi$
$13$	630.075	1.03403	0.517016	+	0.855976i	$0.327043\pi$
$14$	289.555	0.394831
$15$	704.881	0.808886
$16$	256.000	0.250000
$17$	−202.123	−0.169627	−0.0848134	−	0.996397i	$-0.527029\pi$
$17$	−202.123	−0.169627	−0.0848134	+	0.996397i	$0.527029\pi$
$18$	−706.298	−0.513815
$19$	2314.08	1.47060	0.735301	−	0.677741i	$-0.237041\pi$
$19$	2314.08	1.47060	0.735301	+	0.677741i	$0.237041\pi$
$20$	1383.78	0.773559
$21$	589.982	0.291938
$22$	−2190.66	−0.964980
$23$	−1349.30	−0.531850	−0.265925	−	0.963994i	$-0.585677\pi$
$23$	−1349.30	−0.531850	−0.265925	+	0.963994i	$0.585677\pi$
$24$	521.612	0.184850
$25$	4354.91	1.39357
$26$	2520.30	0.731171
$27$	−3419.61	−0.902749
$28$	1158.22	0.279187
$29$	634.921	0.140192	0.0700962	−	0.997540i	$-0.477669\pi$
$29$	634.921	0.140192	0.0700962	+	0.997540i	$0.477669\pi$
$30$	2819.52	0.571969
$31$	−7380.03	−1.37929	−0.689643	−	0.724150i	$-0.742232\pi$
$31$	−7380.03	−1.37929	−0.689643	+	0.724150i	$0.742232\pi$
$32$	1024.00	0.176777
$33$	−4463.57	−0.713506
$34$	−808.493	−0.119944
$35$	6260.65	0.863871
$36$	−2825.19	−0.363322
$37$	−1369.00	−0.164399
$37$	−1369.00	−0.164399
$38$	9256.33	1.03987
$39$	5135.23	0.540628
$40$	5535.13	0.546988
$41$	−496.112	−0.0460914	−0.0230457	−	0.999734i	$-0.507336\pi$
$41$	−496.112	−0.0460914	−0.0230457	+	0.999734i	$0.507336\pi$
$42$	2359.93	0.206431
$43$	−1239.89	−0.102262	−0.0511308	−	0.998692i	$-0.516283\pi$
$43$	−1239.89	−0.102262	−0.0511308	+	0.998692i	$0.516283\pi$
$44$	−8762.64	−0.682344
$45$	−15271.3	−1.12420
$46$	−5397.21	−0.376075
$47$	−868.470	−0.0573469	−0.0286735	−	0.999589i	$-0.509128\pi$
$47$	−868.470	−0.0573469	−0.0286735	+	0.999589i	$0.509128\pi$
$48$	2086.45	0.130709
$49$	−11566.9	−0.688217
$50$	17419.6	0.985404
$51$	−1647.34	−0.0886867
$52$	10081.2	0.517016
$53$	13174.4	0.644233	0.322116	−	0.946700i	$-0.395606\pi$
$53$	13174.4	0.644233	0.322116	+	0.946700i	$0.395606\pi$
$54$	−13678.4	−0.638340
$55$	−47365.6	−2.11133
$56$	4632.88	0.197415
$57$	18860.2	0.768881
$58$	2539.68	0.0991310
$59$	−30978.4	−1.15859	−0.579293	−	0.815119i	$-0.696671\pi$
$59$	−30978.4	−1.15859	−0.579293	+	0.815119i	$0.696671\pi$
$60$	11278.1	0.404443
$61$	−45534.9	−1.56682	−0.783411	−	0.621504i	$-0.786522\pi$
$61$	−45534.9	−1.56682	−0.783411	+	0.621504i	$0.786522\pi$
$62$	−29520.1	−0.975302
$63$	−12782.0	−0.405740
$64$	4096.00	0.125000
$65$	54493.0	1.59977
$66$	−17854.3	−0.504525
$67$	46381.3	1.26228	0.631141	−	0.775668i	$-0.282587\pi$
$67$	46381.3	1.26228	0.631141	+	0.775668i	$0.282587\pi$
$68$	−3233.97	−0.0848134
$69$	−10997.1	−0.278070
$70$	25042.6	0.610849
$71$	−79500.6	−1.87165	−0.935824	−	0.352467i	$-0.885343\pi$
$71$	−79500.6	−1.87165	−0.935824	+	0.352467i	$0.885343\pi$
$72$	−11300.8	−0.256907
$73$	15021.8	0.329925	0.164963	−	0.986300i	$-0.447250\pi$
$73$	15021.8	0.329925	0.164963	+	0.986300i	$0.447250\pi$
$74$	−5476.00	−0.116248
$75$	35493.3	0.728607
$76$	37025.3	0.735301
$77$	−39644.8	−0.762007
$78$	20540.9	0.382282
$79$	−9383.70	−0.169163	−0.0845817	−	0.996417i	$-0.526955\pi$
$79$	−9383.70	−0.169163	−0.0845817	+	0.996417i	$0.526955\pi$
$80$	22140.5	0.386779
$81$	15037.2	0.254656
$82$	−1984.45	−0.0325916
$83$	65781.6	1.04812	0.524058	−	0.851683i	$-0.324418\pi$
$83$	65781.6	1.04812	0.524058	+	0.851683i	$0.324418\pi$
$84$	9439.70	0.145969
$85$	−17480.9	−0.262432
$86$	−4959.57	−0.0723099
$87$	5174.72	0.0732975
$88$	−35050.5	−0.482490
$89$	−142526.	−1.90730	−0.953648	−	0.300925i	$-0.902705\pi$
$89$	−142526.	−1.90730	−0.953648	+	0.300925i	$0.902705\pi$
$90$	−61085.2	−0.794932
$91$	45610.3	0.577378
$92$	−21588.8	−0.265925
$93$	−60148.6	−0.721138
$94$	−3473.88	−0.0405504
$95$	200137.	2.27519
$96$	8345.79	0.0924250
$97$	148136.	1.59857	0.799284	−	0.600953i	$-0.205212\pi$
$97$	148136.	1.59857	0.799284	+	0.600953i	$0.205212\pi$
$98$	−46267.5	−0.486643
$99$	96703.6	0.991642
$100$	69678.6	0.696786
$101$	126299.	1.23196	0.615982	−	0.787760i	$-0.288759\pi$
$101$	126299.	1.23196	0.615982	+	0.787760i	$0.288759\pi$
$102$	−6589.37	−0.0627110
$103$	−44972.8	−0.417693	−0.208846	−	0.977948i	$-0.566971\pi$
$103$	−44972.8	−0.417693	−0.208846	+	0.977948i	$0.566971\pi$
$104$	40324.8	0.365586
$105$	51025.4	0.451662
$106$	52697.8	0.455541
$107$	116739.	0.985723	0.492862	−	0.870108i	$-0.335951\pi$
$107$	116739.	0.985723	0.492862	+	0.870108i	$0.335951\pi$
$108$	−54713.8	−0.451375
$109$	154202.	1.24315	0.621575	−	0.783354i	$-0.286493\pi$
$109$	154202.	1.24315	0.621575	+	0.783354i	$0.286493\pi$
$110$	−189462.	−1.49294
$111$	−11157.6	−0.0859535
$112$	18531.5	0.139594
$113$	39579.2	0.291589	0.145794	−	0.989315i	$-0.453426\pi$
$113$	39579.2	0.291589	0.145794	+	0.989315i	$0.453426\pi$
$114$	75440.8	0.543681
$115$	−116696.	−0.822835
$116$	10158.7	0.0700962
$117$	−111255.	−0.751373
$118$	−123914.	−0.819245
$119$	−14631.5	−0.0947153
$120$	45112.4	0.285984
$121$	138886.	0.862371
$122$	−182139.	−1.10791
$123$	−4043.40	−0.0240982
$124$	−118081.	−0.689643
$125$	106371.	0.608900
$126$	−51128.0	−0.286901
$127$	−144003.	−0.792252	−0.396126	−	0.918196i	$-0.629646\pi$
$127$	−144003.	−0.792252	−0.396126	+	0.918196i	$0.629646\pi$
$128$	16384.0	0.0883883
$129$	−10105.3	−0.0534659
$130$	217972.	1.13121
$131$	−1095.59	−0.00557791	−0.00278896	−	0.999996i	$-0.500888\pi$
$131$	−1095.59	−0.00557791	−0.00278896	+	0.999996i	$0.500888\pi$
$132$	−71417.1	−0.356753
$133$	167514.	0.821147
$134$	185525.	0.892568
$135$	−295750.	−1.39666
$136$	−12935.9	−0.0599721
$137$	−169635.	−0.772170	−0.386085	−	0.922463i	$-0.626173\pi$
$137$	−169635.	−0.772170	−0.386085	+	0.922463i	$0.626173\pi$
$138$	−43988.2	−0.196625
$139$	−374094.	−1.64227	−0.821134	−	0.570736i	$-0.806658\pi$
$139$	−374094.	−1.64227	−0.821134	+	0.570736i	$0.806658\pi$
$140$	100170.	0.431936
$141$	−7078.19	−0.0299830
$142$	−318002.	−1.32346
$143$	−345070.	−1.41113
$144$	−45203.1	−0.181661
$145$	54912.1	0.216894
$146$	60087.3	0.233292
$147$	−94272.1	−0.359824
$148$	−21904.0	−0.0821995
$149$	215642.	0.795733	0.397867	−	0.917443i	$-0.369751\pi$
$149$	215642.	0.795733	0.397867	+	0.917443i	$0.369751\pi$
$150$	141973.	0.515203
$151$	−352301.	−1.25739	−0.628697	−	0.777650i	$-0.716411\pi$
$151$	−352301.	−1.25739	−0.628697	+	0.777650i	$0.716411\pi$
$152$	148101.	0.519936
$153$	35689.8	0.123258
$154$	−158579.	−0.538820
$155$	−638273.	−2.13392
$156$	82163.7	0.270314
$157$	520870.	1.68647	0.843237	−	0.537541i	$-0.180647\pi$
$157$	520870.	1.68647	0.843237	+	0.537541i	$0.180647\pi$
$158$	−37534.8	−0.119617
$159$	107374.	0.336827
$160$	88562.1	0.273494
$161$	−97674.2	−0.296972
$162$	60148.6	0.180069
$163$	478521.	1.41069	0.705345	−	0.708864i	$-0.250792\pi$
$163$	478521.	1.41069	0.705345	+	0.708864i	$0.250792\pi$
$164$	−7937.79	−0.0230457
$165$	−386038.	−1.10388
$166$	263126.	0.741130
$167$	−93447.1	−0.259283	−0.129642	−	0.991561i	$-0.541383\pi$
$167$	−93447.1	−0.259283	−0.129642	+	0.991561i	$0.541383\pi$
$168$	37758.8	0.103216
$169$	25701.8	0.0692224
$170$	−69923.7	−0.185568
$171$	−408608.	−1.06860
$172$	−19838.3	−0.0511308
$173$	589744.	1.49813	0.749063	−	0.662499i	$-0.230504\pi$
$173$	589744.	1.49813	0.749063	+	0.662499i	$0.230504\pi$
$174$	20698.9	0.0518291
$175$	315246.	0.778135
$176$	−140202.	−0.341172
$177$	−252479.	−0.605749
$178$	−570103.	−1.34866
$179$	296703.	0.692134	0.346067	−	0.938210i	$-0.387517\pi$
$179$	296703.	0.692134	0.346067	+	0.938210i	$0.387517\pi$
$180$	−244341.	−0.562102
$181$	742997.	1.68574	0.842870	−	0.538117i	$-0.180864\pi$
$181$	742997.	1.68574	0.842870	+	0.538117i	$0.180864\pi$
$182$	182441.	0.408268
$183$	−371118.	−0.819189
$184$	−86355.3	−0.188037
$185$	−118400.	−0.254344
$186$	−240595.	−0.509922
$187$	110696.	0.231487
$188$	−13895.5	−0.0286735
$189$	−247541.	−0.504072
$190$	800548.	1.60880
$191$	−479890.	−0.951828	−0.475914	−	0.879492i	$-0.657883\pi$
$191$	−479890.	−0.951828	−0.475914	+	0.879492i	$0.657883\pi$
$192$	33383.2	0.0653543
$193$	865772.	1.67306	0.836528	−	0.547924i	$-0.184582\pi$
$193$	865772.	1.67306	0.836528	+	0.547924i	$0.184582\pi$
$194$	592544.	1.13036
$195$	444128.	0.836414
$196$	−185070.	−0.344109
$197$	250668.	0.460186	0.230093	−	0.973169i	$-0.426097\pi$
$197$	250668.	0.460186	0.230093	+	0.973169i	$0.426097\pi$
$198$	386815.	0.701197
$199$	89133.3	0.159554	0.0797769	−	0.996813i	$-0.474579\pi$
$199$	89133.3	0.159554	0.0797769	+	0.996813i	$0.474579\pi$
$200$	278714.	0.492702
$201$	378016.	0.659964
$202$	505198.	0.871130
$203$	45961.1	0.0782799
$204$	−26357.5	−0.0443434
$205$	−42907.0	−0.0713088
$206$	−179891.	−0.295353
$207$	238252.	0.386466
$208$	161299.	0.258508
$209$	−1.26734e6	−2.00691
$210$	204102.	0.319373
$211$	−141762.	−0.219207	−0.109603	−	0.993975i	$-0.534958\pi$
$211$	−141762.	−0.219207	−0.109603	+	0.993975i	$0.534958\pi$
$212$	210791.	0.322116
$213$	−647944.	−0.978563
$214$	466954.	0.697012
$215$	−107234.	−0.158211
$216$	−218855.	−0.319170
$217$	−534231.	−0.770158
$218$	616808.	0.879040
$219$	122431.	0.172496
$220$	−757849.	−1.05567
$221$	−127353.	−0.175399
$222$	−44630.4	−0.0607783
$223$	−1.07643e6	−1.44951	−0.724757	−	0.689004i	$-0.758048\pi$
$223$	−1.07643e6	−1.44951	−0.724757	+	0.689004i	$0.758048\pi$
$224$	74126.1	0.0987077
$225$	−768966.	−1.01263
$226$	158317.	0.206184
$227$	−75782.8	−0.0976126	−0.0488063	−	0.998808i	$-0.515542\pi$
$227$	−75782.8	−0.0976126	−0.0488063	+	0.998808i	$0.515542\pi$
$228$	301763.	0.384441
$229$	857042.	1.07997	0.539987	−	0.841673i	$-0.318429\pi$
$229$	857042.	1.07997	0.539987	+	0.841673i	$0.318429\pi$
$230$	−466785.	−0.581832
$231$	−323112.	−0.398404
$232$	40634.9	0.0495655
$233$	62998.3	0.0760219	0.0380110	−	0.999277i	$-0.487898\pi$
$233$	62998.3	0.0760219	0.0380110	+	0.999277i	$0.487898\pi$
$234$	−445021.	−0.531301
$235$	−75110.9	−0.0887224
$236$	−495654.	−0.579293
$237$	−76478.9	−0.0884445
$238$	−58525.8	−0.0669738
$239$	361959.	0.409888	0.204944	−	0.978774i	$-0.434299\pi$
$239$	361959.	0.409888	0.204944	+	0.978774i	$0.434299\pi$
$240$	180449.	0.202222
$241$	1.66031e6	1.84140	0.920699	−	0.390273i	$-0.127619\pi$
$241$	1.66031e6	1.84140	0.920699	+	0.390273i	$0.127619\pi$
$242$	555543.	0.609788
$243$	953521.	1.03589
$244$	−728558.	−0.783411
$245$	−1.00038e6	−1.06475
$246$	−16173.6	−0.0170400
$247$	1.45805e6	1.52065
$248$	−472322.	−0.487651
$249$	536132.	0.547991
$250$	425482.	0.430558
$251$	−1.28769e6	−1.29011	−0.645053	−	0.764138i	$-0.723165\pi$
$251$	−1.28769e6	−1.29011	−0.645053	+	0.764138i	$0.723165\pi$
$252$	−204512.	−0.202870
$253$	738965.	0.725809
$254$	−576013.	−0.560207
$255$	−142473.	−0.137209
$256$	65536.0	0.0625000
$257$	−341761.	−0.322767	−0.161384	−	0.986892i	$-0.551596\pi$
$257$	−341761.	−0.322767	−0.161384	+	0.986892i	$0.551596\pi$
$258$	−40421.4	−0.0378061
$259$	−99100.2	−0.0917963
$260$	871888.	0.799884
$261$	−112111.	−0.101870
$262$	−4382.38	−0.00394418
$263$	163367.	0.145638	0.0728188	−	0.997345i	$-0.476801\pi$
$263$	163367.	0.145638	0.0728188	+	0.997345i	$0.476801\pi$
$264$	−285668.	−0.252262
$265$	1.13941e6	0.996703
$266$	670054.	0.580639
$267$	−1.16161e6	−0.997200
$268$	742101.	0.631141
$269$	−1.64605e6	−1.38695	−0.693477	−	0.720479i	$-0.743922\pi$
$269$	−1.64605e6	−1.38695	−0.693477	+	0.720479i	$0.743922\pi$
$270$	−1.18300e6	−0.987587
$271$	1.96879e6	1.62846	0.814230	−	0.580542i	$-0.197159\pi$
$271$	1.96879e6	1.62846	0.814230	+	0.580542i	$0.197159\pi$
$272$	−51743.6	−0.0424067
$273$	371733.	0.301873
$274$	−678539.	−0.546007
$275$	−2.38503e6	−1.90179
$276$	−175953.	−0.139035
$277$	−186548.	−0.146080	−0.0730399	−	0.997329i	$-0.523270\pi$
$277$	−186548.	−0.146080	−0.0730399	+	0.997329i	$0.523270\pi$
$278$	−1.49638e6	−1.16126
$279$	1.30313e6	1.00225
$280$	400681.	0.305425
$281$	427381.	0.322886	0.161443	−	0.986882i	$-0.448385\pi$
$281$	427381.	0.322886	0.161443	+	0.986882i	$0.448385\pi$
$282$	−28312.8	−0.0212012
$283$	1.18605e6	0.880309	0.440155	−	0.897922i	$-0.354924\pi$
$283$	1.18605e6	0.880309	0.440155	+	0.897922i	$0.354924\pi$
$284$	−1.27201e6	−0.935824
$285$	1.63115e6	1.18955
$286$	−1.38028e6	−0.997820
$287$	−35912.9	−0.0257363
$288$	−180812.	−0.128454
$289$	−1.37900e6	−0.971227
$290$	219648.	0.153367
$291$	1.20734e6	0.835787
$292$	240349.	0.164963
$293$	−1.94748e6	−1.32527	−0.662634	−	0.748944i	$-0.730561\pi$
$293$	−1.94748e6	−1.32527	−0.662634	+	0.748944i	$0.730561\pi$
$294$	−377089.	−0.254434
$295$	−2.67921e6	−1.79247
$296$	−87616.0	−0.0581238
$297$	1.87280e6	1.23197
$298$	862568.	0.562668
$299$	−850162.	−0.549950
$300$	567893.	0.364304
$301$	−89754.2	−0.0571003
$302$	−1.40920e6	−0.889112
$303$	1.02936e6	0.644113
$304$	592405.	0.367650
$305$	−3.93815e6	−2.42406
$306$	142759.	0.0871567
$307$	−509958.	−0.308808	−0.154404	−	0.988008i	$-0.549346\pi$
$307$	−509958.	−0.308808	−0.154404	+	0.988008i	$0.549346\pi$
$308$	−634316.	−0.381004
$309$	−366537.	−0.218384
$310$	−2.55309e6	−1.50891
$311$	186378.	0.109268	0.0546340	−	0.998506i	$-0.482601\pi$
$311$	186378.	0.109268	0.0546340	+	0.998506i	$0.482601\pi$
$312$	328655.	0.191141
$313$	−2.06779e6	−1.19301	−0.596507	−	0.802608i	$-0.703445\pi$
$313$	−2.06779e6	−1.19301	−0.596507	+	0.802608i	$0.703445\pi$
$314$	2.08348e6	1.19252
$315$	−1.10547e6	−0.627727
$316$	−150139.	−0.0845817
$317$	2.99510e6	1.67403	0.837015	−	0.547180i	$-0.184299\pi$
$317$	2.99510e6	1.67403	0.837015	+	0.547180i	$0.184299\pi$
$318$	429497.	0.238173
$319$	−347724.	−0.191319
$320$	354249.	0.193390
$321$	951441.	0.515370
$322$	−390697.	−0.209991
$323$	−467730.	−0.249453
$324$	240594.	0.127328
$325$	2.74392e6	1.44100
$326$	1.91408e6	0.997509
$327$	1.25677e6	0.649962
$328$	−31751.2	−0.0162958
$329$	−62867.4	−0.0320211
$330$	−1.54415e6	−0.780559
$331$	1.92391e6	0.965193	0.482597	−	0.875843i	$-0.339694\pi$
$331$	1.92391e6	0.965193	0.482597	+	0.875843i	$0.339694\pi$
$332$	1.05251e6	0.524058
$333$	241730.	0.119460
$334$	−373788.	−0.183341
$335$	4.01136e6	1.95290
$336$	151035.	0.0729844
$337$	3.14534e6	1.50867	0.754334	−	0.656491i	$-0.227960\pi$
$337$	3.14534e6	1.50867	0.754334	+	0.656491i	$0.227960\pi$
$338$	102807.	0.0489476
$339$	322578.	0.152453
$340$	−279695.	−0.131216
$341$	4.04178e6	1.88229
$342$	−1.63443e6	−0.755617
$343$	−2.05395e6	−0.942658
$344$	−79353.1	−0.0361549
$345$	−951097.	−0.430206
$346$	2.35898e6	1.05934
$347$	2.77241e6	1.23604	0.618022	−	0.786161i	$-0.287934\pi$
$347$	2.77241e6	1.23604	0.618022	+	0.786161i	$0.287934\pi$
$348$	82795.5	0.0366487
$349$	514532.	0.226125	0.113062	−	0.993588i	$-0.463934\pi$
$349$	514532.	0.226125	0.113062	+	0.993588i	$0.463934\pi$
$350$	1.26099e6	0.550225
$351$	−2.15461e6	−0.933472
$352$	−560809.	−0.241245
$353$	−3.79653e6	−1.62163	−0.810813	−	0.585306i	$-0.800975\pi$
$353$	−3.79653e6	−1.62163	−0.810813	+	0.585306i	$0.800975\pi$
$354$	−1.00992e6	−0.428329
$355$	−6.87572e6	−2.89566
$356$	−2.28041e6	−0.953648
$357$	−119249.	−0.0495204
$358$	1.18681e6	0.489412
$359$	−90667.9	−0.0371294	−0.0185647	−	0.999828i	$-0.505910\pi$
$359$	−90667.9	−0.0371294	−0.0185647	+	0.999828i	$0.505910\pi$
$360$	−977364.	−0.397466
$361$	2.87888e6	1.16267
$362$	2.97199e6	1.19200
$363$	1.13194e6	0.450877
$364$	729766.	0.288689
$365$	1.29918e6	0.510433
$366$	−1.48447e6	−0.579254
$367$	2.55364e6	0.989680	0.494840	−	0.868984i	$-0.335227\pi$
$367$	2.55364e6	0.989680	0.494840	+	0.868984i	$0.335227\pi$
$368$	−345421.	−0.132963
$369$	87600.7	0.0334921
$370$	−473600.	−0.179849
$371$	953682.	0.359723
$372$	−962378.	−0.360569
$373$	−1.52707e6	−0.568313	−0.284157	−	0.958778i	$-0.591714\pi$
$373$	−1.52707e6	−0.568313	−0.284157	+	0.958778i	$0.591714\pi$
$374$	442783.	0.163686
$375$	866940.	0.318354
$376$	−55582.1	−0.0202752
$377$	400048.	0.144963
$378$	−990165.	−0.356433
$379$	−2.61755e6	−0.936044	−0.468022	−	0.883717i	$-0.655033\pi$
$379$	−2.61755e6	−0.936044	−0.468022	+	0.883717i	$0.655033\pi$
$380$	3.20219e6	1.13760
$381$	−1.17365e6	−0.414217
$382$	−1.91956e6	−0.673044
$383$	3.66325e6	1.27605	0.638027	−	0.770014i	$-0.279751\pi$
$383$	3.66325e6	1.27605	0.638027	+	0.770014i	$0.279751\pi$
$384$	133533.	0.0462125
$385$	−3.42874e6	−1.17891
$386$	3.46309e6	1.18303
$387$	218933.	0.0743078
$388$	2.37018e6	0.799284
$389$	−3.36151e6	−1.12632	−0.563158	−	0.826349i	$-0.690414\pi$
$389$	−3.36151e6	−1.12632	−0.563158	+	0.826349i	$0.690414\pi$
$390$	1.77651e6	0.591434
$391$	272725.	0.0902160
$392$	−740280.	−0.243322
$393$	−8929.30	−0.00291632
$394$	1.00267e6	0.325401
$395$	−811563.	−0.261716
$396$	1.54726e6	0.495821
$397$	−985380.	−0.313782	−0.156891	−	0.987616i	$-0.550147\pi$
$397$	−985380.	−0.313782	−0.156891	+	0.987616i	$0.550147\pi$
$398$	356533.	0.112822
$399$	1.36527e6	0.429324
$400$	1.11486e6	0.348393
$401$	4.02954e6	1.25139	0.625697	−	0.780066i	$-0.284815\pi$
$401$	4.02954e6	1.25139	0.625697	+	0.780066i	$0.284815\pi$
$402$	1.51207e6	0.466665
$403$	−4.64998e6	−1.42623
$404$	2.02079e6	0.615982
$405$	1.30051e6	0.393982
$406$	183844.	0.0553523
$407$	749753.	0.224353
$408$	−105430.	−0.0313555
$409$	−3.44664e6	−1.01880	−0.509398	−	0.860531i	$-0.670132\pi$
$409$	−3.44664e6	−1.01880	−0.509398	+	0.860531i	$0.670132\pi$
$410$	−171628.	−0.0504229
$411$	−1.38255e6	−0.403717
$412$	−719565.	−0.208846
$413$	−2.24249e6	−0.646926
$414$	953009.	0.273273
$415$	5.68922e6	1.62156
$416$	645197.	0.182793
$417$	−3.04894e6	−0.858634
$418$	−5.06937e6	−1.41910
$419$	1.56692e6	0.436025	0.218013	−	0.975946i	$-0.430043\pi$
$419$	1.56692e6	0.436025	0.218013	+	0.975946i	$0.430043\pi$
$420$	816407.	0.225831
$421$	−3.23318e6	−0.889047	−0.444524	−	0.895767i	$-0.646627\pi$
$421$	−3.23318e6	−0.889047	−0.444524	+	0.895767i	$0.646627\pi$
$422$	−567048.	−0.155003
$423$	153350.	0.0416708
$424$	843165.	0.227771
$425$	−880229.	−0.236387
$426$	−2.59178e6	−0.691948
$427$	−3.29621e6	−0.874874
$428$	1.86782e6	0.492862
$429$	−2.81238e6	−0.737788
$430$	−428935.	−0.111872
$431$	813652.	0.210982	0.105491	−	0.994420i	$-0.466359\pi$
$431$	813652.	0.210982	0.105491	+	0.994420i	$0.466359\pi$
$432$	−875420.	−0.225687
$433$	2.87403e6	0.736667	0.368334	−	0.929694i	$-0.379928\pi$
$433$	2.87403e6	0.736667	0.368334	+	0.929694i	$0.379928\pi$
$434$	−2.13693e6	−0.544584
$435$	447543.	0.113400
$436$	2.46723e6	0.621575
$437$	−3.12240e6	−0.782140
$438$	489723.	0.121973
$439$	91423.8	0.0226411	0.0113206	−	0.999936i	$-0.496396\pi$
$439$	91423.8	0.0226411	0.0113206	+	0.999936i	$0.496396\pi$
$440$	−3.03140e6	−0.746468
$441$	2.04241e6	0.500089
$442$	−509412.	−0.124026
$443$	−3.44676e6	−0.834453	−0.417227	−	0.908802i	$-0.636998\pi$
$443$	−3.44676e6	−0.834453	−0.417227	+	0.908802i	$0.636998\pi$
$444$	−178522.	−0.0429767
$445$	−1.23265e7	−2.95081
$446$	−4.30571e6	−1.02496
$447$	1.75752e6	0.416037
$448$	296504.	0.0697969
$449$	−5.00086e6	−1.17066	−0.585328	−	0.810797i	$-0.699034\pi$
$449$	−5.00086e6	−1.17066	−0.585328	+	0.810797i	$0.699034\pi$
$450$	−3.07586e6	−0.716038
$451$	271703.	0.0629004
$452$	633267.	0.145794
$453$	−2.87132e6	−0.657409
$454$	−303131.	−0.0690225
$455$	3.94468e6	0.893271
$456$	1.20705e6	0.271841
$457$	−144423.	−0.0323478	−0.0161739	−	0.999869i	$-0.505149\pi$
$457$	−144423.	−0.0323478	−0.0161739	+	0.999869i	$0.505149\pi$
$458$	3.42817e6	0.763657
$459$	691183.	0.153130
$460$	−1.86714e6	−0.411417
$461$	842104.	0.184550	0.0922748	−	0.995734i	$-0.470586\pi$
$461$	842104.	0.184550	0.0922748	+	0.995734i	$0.470586\pi$
$462$	−1.29245e6	−0.281714
$463$	417652.	0.0905444	0.0452722	−	0.998975i	$-0.485584\pi$
$463$	417652.	0.0905444	0.0452722	+	0.998975i	$0.485584\pi$
$464$	162540.	0.0350481
$465$	−5.20204e6	−1.11568
$466$	251993.	0.0537556
$467$	−1.92018e6	−0.407427	−0.203714	−	0.979031i	$-0.565301\pi$
$467$	−1.92018e6	−0.407427	−0.203714	+	0.979031i	$0.565301\pi$
$468$	−1.78008e6	−0.375687
$469$	3.35749e6	0.704826
$470$	−300444.	−0.0627362
$471$	4.24518e6	0.881747
$472$	−1.98262e6	−0.409622
$473$	679045.	0.139555
$474$	−305916.	−0.0625397
$475$	1.00776e7	2.04939
$476$	−234103.	−0.0473576
$477$	−2.32627e6	−0.468128
$478$	1.44784e6	0.289834
$479$	−6.92428e6	−1.37891	−0.689455	−	0.724329i	$-0.742150\pi$
$479$	−6.92428e6	−1.37891	−0.689455	+	0.724329i	$0.742150\pi$
$480$	721798.	0.142992
$481$	−862573.	−0.169994
$482$	6.64126e6	1.30207
$483$	−796063.	−0.155267
$484$	2.22217e6	0.431185
$485$	1.28118e7	2.47317
$486$	3.81408e6	0.732486
$487$	897036.	0.171391	0.0856954	−	0.996321i	$-0.472689\pi$
$487$	897036.	0.171391	0.0856954	+	0.996321i	$0.472689\pi$
$488$	−2.91423e6	−0.553955
$489$	3.90003e6	0.737558
$490$	−4.00151e6	−0.752894
$491$	−2.93583e6	−0.549575	−0.274788	−	0.961505i	$-0.588608\pi$
$491$	−2.93583e6	−0.549575	−0.274788	+	0.961505i	$0.588608\pi$
$492$	−64694.5	−0.0120491
$493$	−128332.	−0.0237804
$494$	5.83219e6	1.07526
$495$	8.36356e6	1.53419
$496$	−1.88929e6	−0.344821
$497$	−5.75494e6	−1.04508
$498$	2.14453e6	0.387488
$499$	9.14174e6	1.64353	0.821764	−	0.569827i	$-0.192990\pi$
$499$	9.14174e6	1.64353	0.821764	+	0.569827i	$0.192990\pi$
$500$	1.70193e6	0.304450
$501$	−761611.	−0.135562
$502$	−5.15074e6	−0.912243
$503$	−9.41511e6	−1.65923	−0.829613	−	0.558339i	$-0.811439\pi$
$503$	−9.41511e6	−1.65923	−0.829613	+	0.558339i	$0.811439\pi$
$504$	−818048.	−0.143451
$505$	1.09232e7	1.90599
$506$	2.95586e6	0.513225
$507$	209474.	0.0361919
$508$	−2.30405e6	−0.396126
$509$	−8.15537e6	−1.39524	−0.697620	−	0.716468i	$-0.745758\pi$
$509$	−8.15537e6	−1.39524	−0.697620	+	0.716468i	$0.745758\pi$
$510$	−569891.	−0.0970212
$511$	1.08741e6	0.184222
$512$	262144.	0.0441942
$513$	−7.91326e6	−1.32758
$514$	−1.36704e6	−0.228231
$515$	−3.88954e6	−0.646219
$516$	−161686.	−0.0267330
$517$	475630.	0.0782606
$518$	−396401.	−0.0649098
$519$	4.80652e6	0.783272
$520$	3.48755e6	0.565604
$521$	7.30997e6	1.17983	0.589917	−	0.807464i	$-0.299160\pi$
$521$	7.30997e6	1.17983	0.589917	+	0.807464i	$0.299160\pi$
$522$	−448443.	−0.0720330
$523$	−8.16574e6	−1.30539	−0.652696	−	0.757620i	$-0.726362\pi$
$523$	−8.16574e6	−1.30539	−0.652696	+	0.757620i	$0.726362\pi$
$524$	−17529.5	−0.00278896
$525$	2.56932e6	0.406836
$526$	653466.	0.102981
$527$	1.49168e6	0.233964
$528$	−1.14267e6	−0.178376
$529$	−4.61573e6	−0.717135
$530$	4.55765e6	0.704776
$531$	5.46999e6	0.841880
$532$	2.68022e6	0.410573
$533$	−312588.	−0.0476600
$534$	−4.64644e6	−0.705127
$535$	1.00963e7	1.52503
$536$	2.96840e6	0.446284
$537$	2.41819e6	0.361871
$538$	−6.58419e6	−0.980724
$539$	6.33477e6	0.939201
$540$	−4.73200e6	−0.698329
$541$	−854003.	−0.125449	−0.0627244	−	0.998031i	$-0.519979\pi$
$541$	−854003.	−0.125449	−0.0627244	+	0.998031i	$0.519979\pi$
$542$	7.87518e6	1.15150
$543$	6.05556e6	0.881363
$544$	−206974.	−0.0299860
$545$	1.33364e7	1.92330
$546$	1.48693e6	0.213456
$547$	−1.27761e7	−1.82571	−0.912854	−	0.408286i	$-0.866127\pi$
$547$	−1.27761e7	−1.82571	−0.912854	+	0.408286i	$0.866127\pi$
$548$	−2.71415e6	−0.386085
$549$	8.04030e6	1.13852
$550$	−9.54012e6	−1.34477
$551$	1.46926e6	0.206167
$552$	−703812.	−0.0983125
$553$	−679274.	−0.0944566
$554$	−746190.	−0.103294
$555$	−964982.	−0.132980
$556$	−5.98551e6	−0.821134
$557$	2.18352e6	0.298208	0.149104	−	0.988821i	$-0.452361\pi$
$557$	2.18352e6	0.298208	0.149104	+	0.988821i	$0.452361\pi$
$558$	5.21250e6	0.708697
$559$	−781225.	−0.105742
$560$	1.60273e6	0.215968
$561$	902192.	0.121030
$562$	1.70952e6	0.228315
$563$	−700806.	−0.0931809	−0.0465905	−	0.998914i	$-0.514836\pi$
$563$	−700806.	−0.0931809	−0.0465905	+	0.998914i	$0.514836\pi$
$564$	−113251.	−0.0149915
$565$	3.42306e6	0.451122
$566$	4.74418e6	0.622473
$567$	1.08852e6	0.142193
$568$	−5.08804e6	−0.661728
$569$	−6.21245e6	−0.804419	−0.402209	−	0.915548i	$-0.631758\pi$
$569$	−6.21245e6	−0.804419	−0.402209	+	0.915548i	$0.631758\pi$
$570$	6.52461e6	0.841138
$571$	9.58489e6	1.23026	0.615130	−	0.788426i	$-0.289104\pi$
$571$	9.58489e6	1.23026	0.615130	+	0.788426i	$0.289104\pi$
$572$	−5.52112e6	−0.705565
$573$	−3.91119e6	−0.497649
$574$	−143652.	−0.0181983
$575$	−5.87609e6	−0.741171
$576$	−723249.	−0.0908305
$577$	1.16906e7	1.46184	0.730919	−	0.682465i	$-0.239092\pi$
$577$	1.16906e7	1.46184	0.730919	+	0.682465i	$0.239092\pi$
$578$	−5.51601e6	−0.686761
$579$	7.05620e6	0.874731
$580$	878593.	0.108447
$581$	4.76185e6	0.585241
$582$	4.82934e6	0.590990
$583$	−7.21518e6	−0.879176
$584$	961397.	0.116646
$585$	−9.62207e6	−1.16246
$586$	−7.78991e6	−0.937105
$587$	7.92930e6	0.949816	0.474908	−	0.880036i	$-0.342481\pi$
$587$	7.92930e6	0.949816	0.474908	+	0.880036i	$0.342481\pi$
$588$	−1.50835e6	−0.179912
$589$	−1.70780e7	−2.02838
$590$	−1.07168e7	−1.26747
$591$	2.04299e6	0.240601
$592$	−350464.	−0.0410997
$593$	−4.38173e6	−0.511692	−0.255846	−	0.966718i	$-0.582354\pi$
$593$	−4.38173e6	−0.511692	−0.255846	+	0.966718i	$0.582354\pi$
$594$	7.49120e6	0.871134
$595$	−1.26542e6	−0.146536
$596$	3.45027e6	0.397867
$597$	726453.	0.0834203
$598$	−3.40065e6	−0.388874
$599$	−589355.	−0.0671135	−0.0335567	−	0.999437i	$-0.510683\pi$
$599$	−589355.	−0.0671135	−0.0335567	+	0.999437i	$0.510683\pi$
$600$	2.27157e6	0.257602
$601$	1.53813e6	0.173703	0.0868514	−	0.996221i	$-0.472319\pi$
$601$	1.53813e6	0.173703	0.0868514	+	0.996221i	$0.472319\pi$
$602$	−359017.	−0.0403760
$603$	−8.18976e6	−0.917229
$604$	−5.63682e6	−0.628697
$605$	1.20117e7	1.33419
$606$	4.11745e6	0.455457
$607$	−1.68219e7	−1.85312	−0.926559	−	0.376148i	$-0.877248\pi$
$607$	−1.68219e7	−1.85312	−0.926559	+	0.376148i	$0.877248\pi$
$608$	2.36962e6	0.259968
$609$	374592.	0.0409275
$610$	−1.57526e7	−1.71407
$611$	−547201.	−0.0592986
$612$	571037.	0.0616291
$613$	9.47846e6	1.01879	0.509397	−	0.860531i	$-0.329868\pi$
$613$	9.47846e6	1.01879	0.509397	+	0.860531i	$0.329868\pi$
$614$	−2.03983e6	−0.218360
$615$	−349700.	−0.0372827
$616$	−2.53726e6	−0.269410
$617$	7.29489e6	0.771446	0.385723	−	0.922615i	$-0.373952\pi$
$617$	7.29489e6	0.771446	0.385723	+	0.922615i	$0.373952\pi$
$618$	−1.46615e6	−0.154421
$619$	3.08760e6	0.323888	0.161944	−	0.986800i	$-0.448224\pi$
$619$	3.08760e6	0.323888	0.161944	+	0.986800i	$0.448224\pi$
$620$	−1.02124e7	−1.06696
$621$	4.61408e6	0.480127
$622$	745511.	0.0772641
$623$	−1.03173e7	−1.06499
$624$	1.31462e6	0.135157
$625$	−4.40948e6	−0.451531
$626$	−8.27116e6	−0.843588
$627$	−1.03291e7	−1.04928
$628$	8.33391e6	0.843237
$629$	276707.	0.0278865
$630$	−4.42188e6	−0.443870
$631$	−1.63390e6	−0.163362	−0.0816812	−	0.996659i	$-0.526029\pi$
$631$	−1.63390e6	−0.163362	−0.0816812	+	0.996659i	$0.526029\pi$
$632$	−600557.	−0.0598083
$633$	−1.15539e6	−0.114609
$634$	1.19804e7	1.18372
$635$	−1.24543e7	−1.22571
$636$	1.71799e6	0.168414
$637$	−7.28800e6	−0.711639
$638$	−1.39090e6	−0.135283
$639$	1.40378e7	1.36002
$640$	1.41699e6	0.136747
$641$	−9.64429e6	−0.927097	−0.463548	−	0.886072i	$-0.653424\pi$
$641$	−9.64429e6	−0.927097	−0.463548	+	0.886072i	$0.653424\pi$
$642$	3.80576e6	0.364422
$643$	−1.72986e6	−0.164999	−0.0824997	−	0.996591i	$-0.526290\pi$
$643$	−1.72986e6	−0.164999	−0.0824997	+	0.996591i	$0.526290\pi$
$644$	−1.56279e6	−0.148486
$645$	−873976.	−0.0827180
$646$	−1.87092e6	−0.176390
$647$	1.17832e7	1.10663	0.553315	−	0.832972i	$-0.313362\pi$
$647$	1.17832e7	1.10663	0.553315	+	0.832972i	$0.313362\pi$
$648$	962378.	0.0900343
$649$	1.69658e7	1.58111
$650$	1.09757e7	1.01894
$651$	−4.35408e6	−0.402665
$652$	7.65633e6	0.705345
$653$	−1.30181e7	−1.19471	−0.597357	−	0.801975i	$-0.703783\pi$
$653$	−1.30181e7	−1.19471	−0.597357	+	0.801975i	$0.703783\pi$
$654$	5.02710e6	0.459593
$655$	−94754.1	−0.00862968
$656$	−127005.	−0.0115229
$657$	−2.65247e6	−0.239738
$658$	−251470.	−0.0226423
$659$	−6.01603e6	−0.539630	−0.269815	−	0.962912i	$-0.586963\pi$
$659$	−6.01603e6	−0.539630	−0.269815	+	0.962912i	$0.586963\pi$
$660$	−6.17661e6	−0.551938
$661$	−2.02470e7	−1.80243	−0.901214	−	0.433375i	$-0.857323\pi$
$661$	−2.02470e7	−1.80243	−0.901214	+	0.433375i	$0.857323\pi$
$662$	7.69563e6	0.682495
$663$	−1.03795e6	−0.0917049
$664$	4.21002e6	0.370565
$665$	1.44877e7	1.27041
$666$	966922.	0.0844707
$667$	−856700.	−0.0745614
$668$	−1.49515e6	−0.129642
$669$	−8.77308e6	−0.757856
$670$	1.60454e7	1.38091
$671$	2.49378e7	2.13822
$672$	604141.	0.0516078
$673$	−1.94686e7	−1.65690	−0.828450	−	0.560062i	$-0.810777\pi$
$673$	−1.94686e7	−1.65690	−0.828450	+	0.560062i	$0.810777\pi$
$674$	1.25814e7	1.06679
$675$	−1.48921e7	−1.25805
$676$	411229.	0.0346112
$677$	−1.44777e7	−1.21402	−0.607011	−	0.794693i	$-0.707632\pi$
$677$	−1.44777e7	−1.21402	−0.607011	+	0.794693i	$0.707632\pi$
$678$	1.29031e6	0.107800
$679$	1.07234e7	0.892600
$680$	−1.11878e6	−0.0927838
$681$	−617643.	−0.0510352
$682$	1.61671e7	1.33098
$683$	−5.27087e6	−0.432345	−0.216173	−	0.976355i	$-0.569357\pi$
$683$	−5.27087e6	−0.432345	−0.216173	+	0.976355i	$0.569357\pi$
$684$	−6.53773e6	−0.534302
$685$	−1.46711e7	−1.19464
$686$	−8.21579e6	−0.666560
$687$	6.98505e6	0.564648
$688$	−317412.	−0.0255654
$689$	8.30089e6	0.666157
$690$	−3.80439e6	−0.304202
$691$	2.06077e7	1.64185	0.820926	−	0.571034i	$-0.193458\pi$
$691$	2.06077e7	1.64185	0.820926	+	0.571034i	$0.193458\pi$
$692$	9.43591e6	0.749063
$693$	7.00025e6	0.553708
$694$	1.10896e7	0.874015
$695$	−3.23541e7	−2.54078
$696$	331182.	0.0259146
$697$	100276.	0.00781834
$698$	2.05813e6	0.159894
$699$	513448.	0.0397469
$700$	5.04394e6	0.389068
$701$	4.04493e6	0.310897	0.155448	−	0.987844i	$-0.450318\pi$
$701$	4.04493e6	0.310897	0.155448	+	0.987844i	$0.450318\pi$
$702$	−8.61844e6	−0.660064
$703$	−3.16798e6	−0.241765
$704$	−2.24323e6	−0.170586
$705$	−612168.	−0.0463871
$706$	−1.51861e7	−1.14666
$707$	9.14266e6	0.687898
$708$	−4.03967e6	−0.302875
$709$	1.12046e7	0.837105	0.418553	−	0.908193i	$-0.362538\pi$
$709$	1.12046e7	0.837105	0.418553	+	0.908193i	$0.362538\pi$
$710$	−2.75029e7	−2.04754
$711$	1.65692e6	0.122922
$712$	−9.12164e6	−0.674331
$713$	9.95789e6	0.733573
$714$	−476996.	−0.0350162
$715$	−2.98439e7	−2.18318
$716$	4.74725e6	0.346067
$717$	2.95004e6	0.214304
$718$	−362672.	−0.0262544
$719$	−1.05518e7	−0.761206	−0.380603	−	0.924739i	$-0.624284\pi$
$719$	−1.05518e7	−0.761206	−0.380603	+	0.924739i	$0.624284\pi$
$720$	−3.90945e6	−0.281051
$721$	−3.25552e6	−0.233229
$722$	1.15155e7	0.822131
$723$	1.35319e7	0.962747
$724$	1.18879e7	0.842870
$725$	2.76502e6	0.195368
$726$	4.52778e6	0.318818
$727$	2.21445e7	1.55392	0.776962	−	0.629547i	$-0.216760\pi$
$727$	2.21445e7	1.55392	0.776962	+	0.629547i	$0.216760\pi$
$728$	2.91906e6	0.204134
$729$	4.11734e6	0.286945
$730$	5.19674e6	0.360931
$731$	250611.	0.0173463
$732$	−5.93788e6	−0.409594
$733$	1.47389e7	1.01322	0.506612	−	0.862174i	$-0.330898\pi$
$733$	1.47389e7	1.01322	0.506612	+	0.862174i	$0.330898\pi$
$734$	1.02146e7	0.699809
$735$	−8.15326e6	−0.556690
$736$	−1.38168e6	−0.0940187
$737$	−2.54014e7	−1.72262
$738$	350403.	0.0236825
$739$	−1.99208e7	−1.34183	−0.670913	−	0.741536i	$-0.734097\pi$
$739$	−1.99208e7	−1.34183	−0.670913	+	0.741536i	$0.734097\pi$
$740$	−1.89440e6	−0.127172
$741$	1.18833e7	0.795048
$742$	3.81473e6	0.254363
$743$	3.49348e6	0.232159	0.116080	−	0.993240i	$-0.462967\pi$
$743$	3.49348e6	0.232159	0.116080	+	0.993240i	$0.462967\pi$
$744$	−3.84951e6	−0.254961
$745$	1.86501e7	1.23109
$746$	−6.10829e6	−0.401858
$747$	−1.16154e7	−0.761607
$748$	1.77113e6	0.115744
$749$	8.45056e6	0.550403
$750$	3.46776e6	0.225110
$751$	1.19688e7	0.774373	0.387186	−	0.922001i	$-0.373447\pi$
$751$	1.19688e7	0.774373	0.387186	+	0.922001i	$0.373447\pi$
$752$	−222328.	−0.0143367
$753$	−1.04949e7	−0.674512
$754$	1.60019e6	0.102505
$755$	−3.04693e7	−1.94534
$756$	−3.96066e6	−0.252036
$757$	2.14264e7	1.35897	0.679483	−	0.733691i	$-0.262204\pi$
$757$	2.14264e7	1.35897	0.679483	+	0.733691i	$0.262204\pi$
$758$	−1.04702e7	−0.661883
$759$	6.02270e6	0.379478
$760$	1.28088e7	0.804402
$761$	3.99327e6	0.249958	0.124979	−	0.992159i	$-0.460114\pi$
$761$	3.99327e6	0.249958	0.124979	+	0.992159i	$0.460114\pi$
$762$	−4.69461e6	−0.292895
$763$	1.11625e7	0.694144
$764$	−7.67824e6	−0.475914
$765$	3.08669e6	0.190695
$766$	1.46530e7	0.902307
$767$	−1.95187e7	−1.19802
$768$	534130.	0.0326772
$769$	−3.07263e6	−0.187367	−0.0936837	−	0.995602i	$-0.529864\pi$
$769$	−3.07263e6	−0.187367	−0.0936837	+	0.995602i	$0.529864\pi$
$770$	−1.37149e7	−0.833618
$771$	−2.78541e6	−0.168754
$772$	1.38524e7	0.836528
$773$	1.38917e7	0.836190	0.418095	−	0.908403i	$-0.362698\pi$
$773$	1.38917e7	0.836190	0.418095	+	0.908403i	$0.362698\pi$
$774$	875733.	0.0525435
$775$	−3.21394e7	−1.92213
$776$	9.48070e6	0.565179
$777$	−807685.	−0.0479943
$778$	−1.34460e7	−0.796426
$779$	−1.14804e6	−0.0677821
$780$	7.10605e6	0.418207
$781$	4.35397e7	2.55421
$782$	1.09090e6	0.0637924
$783$	−2.17118e6	−0.126559
$784$	−2.96112e6	−0.172054
$785$	4.50482e7	2.60917
$786$	−35717.2	−0.00206215
$787$	3.21728e7	1.85162	0.925812	−	0.377985i	$-0.123383\pi$
$787$	3.21728e7	1.85162	0.925812	+	0.377985i	$0.123383\pi$
$788$	4.01069e6	0.230093
$789$	1.33147e6	0.0761444
$790$	−3.24625e6	−0.185061
$791$	2.86509e6	0.162816
$792$	6.18903e6	0.350598
$793$	−2.86904e7	−1.62014
$794$	−3.94152e6	−0.221877
$795$	9.28641e6	0.521111
$796$	1.42613e6	0.0797769
$797$	−2.52658e7	−1.40892	−0.704462	−	0.709742i	$-0.748812\pi$
$797$	−2.52658e7	−1.40892	−0.704462	+	0.709742i	$0.748812\pi$
$798$	5.46107e6	0.303578
$799$	175538.	0.00972757
$800$	4.45943e6	0.246351
$801$	2.51664e7	1.38592
$802$	1.61181e7	0.884869
$803$	−8.22692e6	−0.450245
$804$	6.04826e6	0.329982
$805$	−8.44750e6	−0.459450
$806$	−1.85999e7	−1.00849
$807$	−1.34156e7	−0.725147
$808$	8.08316e6	0.435565
$809$	2.31714e7	1.24475	0.622373	−	0.782721i	$-0.286169\pi$
$809$	2.31714e7	1.24475	0.622373	+	0.782721i	$0.286169\pi$
$810$	5.20204e6	0.278587
$811$	−2.73212e7	−1.45864	−0.729320	−	0.684173i	$-0.760163\pi$
$811$	−2.73212e7	−1.45864	−0.729320	+	0.684173i	$0.760163\pi$
$812$	735378.	0.0391400
$813$	1.60460e7	0.851415
$814$	2.99901e6	0.158642
$815$	4.13856e7	2.18250
$816$	−421720.	−0.0221717
$817$	−2.86921e6	−0.150386
$818$	−1.37865e7	−0.720397
$819$	−8.05362e6	−0.419548
$820$	−686512.	−0.0356544
$821$	−2.96438e7	−1.53489	−0.767444	−	0.641116i	$-0.778472\pi$
$821$	−2.96438e7	−1.53489	−0.767444	+	0.641116i	$0.778472\pi$
$822$	−5.53021e6	−0.285471
$823$	5.06577e6	0.260703	0.130351	−	0.991468i	$-0.458389\pi$
$823$	5.06577e6	0.260703	0.130351	+	0.991468i	$0.458389\pi$
$824$	−2.87826e6	−0.147677
$825$	−1.94384e7	−0.994321
$826$	−8.96994e6	−0.457446
$827$	−1.94380e7	−0.988297	−0.494149	−	0.869377i	$-0.664520\pi$
$827$	−1.94380e7	−0.988297	−0.494149	+	0.869377i	$0.664520\pi$
$828$	3.81204e6	0.193233
$829$	−1.76995e7	−0.894487	−0.447244	−	0.894412i	$-0.647594\pi$
$829$	−1.76995e7	−0.894487	−0.447244	+	0.894412i	$0.647594\pi$
$830$	2.27569e7	1.14661
$831$	−1.52040e6	−0.0763756
$832$	2.58079e6	0.129254
$833$	2.33793e6	0.116740
$834$	−1.21957e7	−0.607146
$835$	−8.08191e6	−0.401142
$836$	−2.02775e7	−1.00346
$837$	2.52368e7	1.24515
$838$	6.26768e6	0.308316
$839$	2.32202e7	1.13884	0.569418	−	0.822048i	$-0.307168\pi$
$839$	2.32202e7	1.13884	0.569418	+	0.822048i	$0.307168\pi$
$840$	3.26563e6	0.159687
$841$	−2.01080e7	−0.980346
$842$	−1.29327e7	−0.628651
$843$	3.48323e6	0.168816
$844$	−2.26819e6	−0.109603
$845$	2.22286e6	0.107095
$846$	613399.	0.0294657
$847$	1.00538e7	0.481526
$848$	3.37266e6	0.161058
$849$	9.66649e6	0.460256
$850$	−3.52092e6	−0.167151
$851$	1.84719e6	0.0874357
$852$	−1.03671e7	−0.489281
$853$	1.91589e7	0.901565	0.450783	−	0.892634i	$-0.351145\pi$
$853$	1.91589e7	0.901565	0.450783	+	0.892634i	$0.351145\pi$
$854$	−1.31848e7	−0.618629
$855$	−3.53391e7	−1.65325
$856$	7.47127e6	0.348506
$857$	−1.54920e6	−0.0720537	−0.0360268	−	0.999351i	$-0.511470\pi$
$857$	−1.54920e6	−0.0720537	−0.0360268	+	0.999351i	$0.511470\pi$
$858$	−1.12495e7	−0.521695
$859$	−1.68565e6	−0.0779442	−0.0389721	−	0.999240i	$-0.512408\pi$
$859$	−1.68565e6	−0.0779442	−0.0389721	+	0.999240i	$0.512408\pi$
$860$	−1.71574e6	−0.0791053
$861$	−292697.	−0.0134558
$862$	3.25461e6	0.149187
$863$	−2.69694e7	−1.23266	−0.616330	−	0.787488i	$-0.711381\pi$
$863$	−2.69694e7	−1.23266	−0.616330	+	0.787488i	$0.711381\pi$
$864$	−3.50168e6	−0.159585
$865$	5.10049e7	2.31778
$866$	1.14961e7	0.520902
$867$	−1.12391e7	−0.507791
$868$	−8.54770e6	−0.385079
$869$	5.13912e6	0.230855
$870$	1.79017e6	0.0801857
$871$	2.92237e7	1.30524
$872$	9.86893e6	0.439520
$873$	−2.61570e7	−1.16159
$874$	−1.24896e7	−0.553056
$875$	7.70003e6	0.339995
$876$	1.95889e6	0.0862482
$877$	−5.06132e6	−0.222211	−0.111105	−	0.993809i	$-0.535439\pi$
$877$	−5.06132e6	−0.222211	−0.111105	+	0.993809i	$0.535439\pi$
$878$	365695.	0.0160097
$879$	−1.58723e7	−0.692896
$880$	−1.21256e7	−0.527833
$881$	−3.88615e7	−1.68686	−0.843431	−	0.537237i	$-0.819468\pi$
$881$	−3.88615e7	−1.68686	−0.843431	+	0.537237i	$0.819468\pi$
$882$	8.16966e6	0.353616
$883$	−1.92859e6	−0.0832412	−0.0416206	−	0.999133i	$-0.513252\pi$
$883$	−1.92859e6	−0.0832412	−0.0416206	+	0.999133i	$0.513252\pi$
$884$	−2.03765e6	−0.0876997
$885$	−2.18361e7	−0.937165
$886$	−1.37870e7	−0.590047
$887$	1.85945e7	0.793554	0.396777	−	0.917915i	$-0.370129\pi$
$887$	1.85945e7	0.793554	0.396777	+	0.917915i	$0.370129\pi$
$888$	−714087.	−0.0303891
$889$	−1.04242e7	−0.442373
$890$	−4.93062e7	−2.08654
$891$	−8.23532e6	−0.347525
$892$	−1.72228e7	−0.724757
$893$	−2.00971e6	−0.0843345
$894$	7.03009e6	0.294183
$895$	2.56608e7	1.07081
$896$	1.18602e6	0.0493538
$897$	−6.92897e6	−0.287533
$898$	−2.00035e7	−0.827779
$899$	−4.68574e6	−0.193365
$900$	−1.23035e7	−0.506315
$901$	−2.66286e6	−0.109279
$902$	1.08681e6	0.0444773
$903$	−731513.	−0.0298540
$904$	2.53307e6	0.103092
$905$	6.42592e7	2.60804
$906$	−1.14853e7	−0.464859
$907$	3.30031e7	1.33210	0.666050	−	0.745907i	$-0.267984\pi$
$907$	3.30031e7	1.33210	0.666050	+	0.745907i	$0.267984\pi$
$908$	−1.21252e6	−0.0488063
$909$	−2.23013e7	−0.895199
$910$	1.57787e7	0.631638
$911$	5.71390e6	0.228106	0.114053	−	0.993475i	$-0.463617\pi$
$911$	5.71390e6	0.228106	0.114053	+	0.993475i	$0.463617\pi$
$912$	4.82821e6	0.192220
$913$	−3.60263e7	−1.43035
$914$	−577691.	−0.0228734
$915$	−3.20967e7	−1.26738
$916$	1.37127e7	0.539987
$917$	−79308.7	−0.00311457
$918$	2.76473e6	0.108280
$919$	4.75764e7	1.85825	0.929123	−	0.369772i	$-0.120564\pi$
$919$	4.75764e7	1.85825	0.929123	+	0.369772i	$0.120564\pi$
$920$	−7.46857e6	−0.290916
$921$	−4.15625e6	−0.161455
$922$	3.36842e6	0.130496
$923$	−5.00913e7	−1.93534
$924$	−5.16979e6	−0.199202
$925$	−5.96187e6	−0.229102
$926$	1.67061e6	0.0640246
$927$	7.94105e6	0.303514
$928$	650159.	0.0247828
$929$	−929095.	−0.0353200	−0.0176600	−	0.999844i	$-0.505622\pi$
$929$	−929095.	−0.0353200	−0.0176600	+	0.999844i	$0.505622\pi$
$930$	−2.08082e7	−0.788908
$931$	−2.67667e7	−1.01209
$932$	1.00797e6	0.0380110
$933$	1.51901e6	0.0571291
$934$	−7.68072e6	−0.288094
$935$	9.57369e6	0.358138
$936$	−7.12033e6	−0.265651
$937$	−5.53593e6	−0.205988	−0.102994	−	0.994682i	$-0.532842\pi$
$937$	−5.53593e6	−0.205988	−0.102994	+	0.994682i	$0.532842\pi$
$938$	1.34299e7	0.498387
$939$	−1.68529e7	−0.623749
$940$	−1.20177e6	−0.0443612
$941$	4.67972e7	1.72284	0.861422	−	0.507889i	$-0.169574\pi$
$941$	4.67972e7	1.72284	0.861422	+	0.507889i	$0.169574\pi$
$942$	1.69807e7	0.623489
$943$	669405.	0.0245137
$944$	−7.93046e6	−0.289647
$945$	−2.14090e7	−0.779859
$946$	2.71618e6	0.0986804
$947$	−1.18266e7	−0.428535	−0.214268	−	0.976775i	$-0.568737\pi$
$947$	−1.18266e7	−0.428535	−0.214268	+	0.976775i	$0.568737\pi$
$948$	−1.22366e6	−0.0442222
$949$	9.46488e6	0.341153
$950$	4.03105e7	1.44914
$951$	2.44106e7	0.875241
$952$	−936413.	−0.0334869
$953$	−3.92659e7	−1.40050	−0.700251	−	0.713897i	$-0.746929\pi$
$953$	−3.92659e7	−1.40050	−0.700251	+	0.713897i	$0.746929\pi$
$954$	−9.30509e6	−0.331016
$955$	−4.15040e7	−1.47259
$956$	5.79135e6	0.204944
$957$	−2.83401e6	−0.100028
$958$	−2.76971e7	−0.975036
$959$	−1.22796e7	−0.431161
$960$	2.88719e6	0.101111
$961$	2.58357e7	0.902428
$962$	−3.45029e6	−0.120204
$963$	−2.06131e7	−0.716270
$964$	2.65650e7	0.920699
$965$	7.48776e7	2.58841
$966$	−3.18425e6	−0.109790
$967$	−3.03166e7	−1.04259	−0.521296	−	0.853376i	$-0.674551\pi$
$967$	−3.03166e7	−1.04259	−0.521296	+	0.853376i	$0.674551\pi$
$968$	8.88868e6	0.304894
$969$	−3.81209e6	−0.130423
$970$	5.12470e7	1.74880
$971$	−2.49823e7	−0.850325	−0.425162	−	0.905117i	$-0.639783\pi$
$971$	−2.49823e7	−0.850325	−0.425162	+	0.905117i	$0.639783\pi$
$972$	1.52563e7	0.517946
$973$	−2.70802e7	−0.917001
$974$	3.58814e6	0.121192
$975$	2.23635e7	0.753403
$976$	−1.16569e7	−0.391705
$977$	4.25521e7	1.42621	0.713107	−	0.701056i	$-0.247288\pi$
$977$	4.25521e7	1.42621	0.713107	+	0.701056i	$0.247288\pi$
$978$	1.56001e7	0.521532
$979$	7.80563e7	2.60286
$980$	−1.60060e7	−0.532376
$981$	−2.72281e7	−0.903328
$982$	−1.17433e7	−0.388608
$983$	5.62326e7	1.85611	0.928056	−	0.372441i	$-0.121479\pi$
$983$	5.62326e7	1.85611	0.928056	+	0.372441i	$0.121479\pi$
$984$	−258778.	−0.00852000
$985$	2.16794e7	0.711961
$986$	−513329.	−0.0168153
$987$	−512381.	−0.0167417
$988$	2.33287e7	0.760325
$989$	1.67299e6	0.0543879
$990$	3.34542e7	1.08483
$991$	4.04052e7	1.30693	0.653467	−	0.756955i	$-0.273314\pi$
$991$	4.04052e7	1.30693	0.653467	+	0.756955i	$0.273314\pi$
$992$	−7.55715e6	−0.243825
$993$	1.56802e7	0.504636
$994$	−2.30198e7	−0.738984
$995$	7.70882e6	0.246848
$996$	8.57811e6	0.273996
$997$	−4.43031e7	−1.41155	−0.705775	−	0.708436i	$-0.749401\pi$
$997$	−4.43031e7	−1.41155	−0.705775	+	0.708436i	$0.749401\pi$
$998$	3.65669e7	1.16215
$999$	4.68145e6	0.148411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.a.e.1.3	✓	5
3.2	odd	2		666.6.a.l.1.1		5
4.3	odd	2		592.6.a.e.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.a.e.1.3	✓	5	1.1	even	1	trivial
592.6.a.e.1.3		5	4.3	odd	2
666.6.a.l.1.1		5	3.2	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +8.15018 q^{3} +16.0000 q^{4} +86.4865 q^{5} +32.6007 q^{6} +72.3887 q^{7} +64.0000 q^{8} -176.574 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +8.15018 q^{3} +16.0000 q^{4} +86.4865 q^{5} +32.6007 q^{6} +72.3887 q^{7} +64.0000 q^{8} -176.574 q^{9} +345.946 q^{10} -547.665 q^{11} +130.403 q^{12} +630.075 q^{13} +289.555 q^{14} +704.881 q^{15} +256.000 q^{16} -202.123 q^{17} -706.298 q^{18} +2314.08 q^{19} +1383.78 q^{20} +589.982 q^{21} -2190.66 q^{22} -1349.30 q^{23} +521.612 q^{24} +4354.91 q^{25} +2520.30 q^{26} -3419.61 q^{27} +1158.22 q^{28} +634.921 q^{29} +2819.52 q^{30} -7380.03 q^{31} +1024.00 q^{32} -4463.57 q^{33} -808.493 q^{34} +6260.65 q^{35} -2825.19 q^{36} -1369.00 q^{37} +9256.33 q^{38} +5135.23 q^{39} +5535.13 q^{40} -496.112 q^{41} +2359.93 q^{42} -1239.89 q^{43} -8762.64 q^{44} -15271.3 q^{45} -5397.21 q^{46} -868.470 q^{47} +2086.45 q^{48} -11566.9 q^{49} +17419.6 q^{50} -1647.34 q^{51} +10081.2 q^{52} +13174.4 q^{53} -13678.4 q^{54} -47365.6 q^{55} +4632.88 q^{56} +18860.2 q^{57} +2539.68 q^{58} -30978.4 q^{59} +11278.1 q^{60} -45534.9 q^{61} -29520.1 q^{62} -12782.0 q^{63} +4096.00 q^{64} +54493.0 q^{65} -17854.3 q^{66} +46381.3 q^{67} -3233.97 q^{68} -10997.1 q^{69} +25042.6 q^{70} -79500.6 q^{71} -11300.8 q^{72} +15021.8 q^{73} -5476.00 q^{74} +35493.3 q^{75} +37025.3 q^{76} -39644.8 q^{77} +20540.9 q^{78} -9383.70 q^{79} +22140.5 q^{80} +15037.2 q^{81} -1984.45 q^{82} +65781.6 q^{83} +9439.70 q^{84} -17480.9 q^{85} -4959.57 q^{86} +5174.72 q^{87} -35050.5 q^{88} -142526. q^{89} -61085.2 q^{90} +45610.3 q^{91} -21588.8 q^{92} -60148.6 q^{93} -3473.88 q^{94} +200137. q^{95} +8345.79 q^{96} +148136. q^{97} -46267.5 q^{98} +96703.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 20 q^{2} + 19 q^{3} + 80 q^{4} + 95 q^{5} + 76 q^{6} + 170 q^{7} + 320 q^{8} + 598 q^{9}+O(q^{10}) \) 5 * q + 20 * q^2 + 19 * q^3 + 80 * q^4 + 95 * q^5 + 76 * q^6 + 170 * q^7 + 320 * q^8 + 598 * q^9	\( 5 q + 20 q^{2} + 19 q^{3} + 80 q^{4} + 95 q^{5} + 76 q^{6} + 170 q^{7} + 320 q^{8} + 598 q^{9} + 380 q^{10} + 903 q^{11} + 304 q^{12} + 1371 q^{13} + 680 q^{14} - 8 q^{15} + 1280 q^{16} + 2070 q^{17} + 2392 q^{18} + 2358 q^{19} + 1520 q^{20} + 2832 q^{21} + 3612 q^{22} + 2097 q^{23} + 1216 q^{24} - 390 q^{25} + 5484 q^{26} + 2614 q^{27} + 2720 q^{28} + 2927 q^{29} - 32 q^{30} - 5849 q^{31} + 5120 q^{32} - 11002 q^{33} + 8280 q^{34} - 10928 q^{35} + 9568 q^{36} - 6845 q^{37} + 9432 q^{38} - 9945 q^{39} + 6080 q^{40} - 14427 q^{41} + 11328 q^{42} - 6972 q^{43} + 14448 q^{44} - 6816 q^{45} + 8388 q^{46} - 18962 q^{47} + 4864 q^{48} - 11957 q^{49} - 1560 q^{50} - 67946 q^{51} + 21936 q^{52} - 23576 q^{53} + 10456 q^{54} - 31415 q^{55} + 10880 q^{56} - 70522 q^{57} + 11708 q^{58} - 18316 q^{59} - 128 q^{60} - 18695 q^{61} - 23396 q^{62} - 88094 q^{63} + 20480 q^{64} - 40706 q^{65} - 44008 q^{66} - 85273 q^{67} + 33120 q^{68} - 87171 q^{69} - 43712 q^{70} + 8760 q^{71} + 38272 q^{72} - 10425 q^{73} - 27380 q^{74} - 10542 q^{75} + 37728 q^{76} + 17238 q^{77} - 39780 q^{78} + 48425 q^{79} + 24320 q^{80} + 33449 q^{81} - 57708 q^{82} + 27704 q^{83} + 45312 q^{84} + 139062 q^{85} - 27888 q^{86} + 6227 q^{87} + 57792 q^{88} + 233646 q^{89} - 27264 q^{90} + 146434 q^{91} + 33552 q^{92} + 301866 q^{93} - 75848 q^{94} + 189498 q^{95} + 19456 q^{96} + 251694 q^{97} - 47828 q^{98} + 182486 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 + 19 * q^3 + 80 * q^4 + 95 * q^5 + 76 * q^6 + 170 * q^7 + 320 * q^8 + 598 * q^9 + 380 * q^10 + 903 * q^11 + 304 * q^12 + 1371 * q^13 + 680 * q^14 - 8 * q^15 + 1280 * q^16 + 2070 * q^17 + 2392 * q^18 + 2358 * q^19 + 1520 * q^20 + 2832 * q^21 + 3612 * q^22 + 2097 * q^23 + 1216 * q^24 - 390 * q^25 + 5484 * q^26 + 2614 * q^27 + 2720 * q^28 + 2927 * q^29 - 32 * q^30 - 5849 * q^31 + 5120 * q^32 - 11002 * q^33 + 8280 * q^34 - 10928 * q^35 + 9568 * q^36 - 6845 * q^37 + 9432 * q^38 - 9945 * q^39 + 6080 * q^40 - 14427 * q^41 + 11328 * q^42 - 6972 * q^43 + 14448 * q^44 - 6816 * q^45 + 8388 * q^46 - 18962 * q^47 + 4864 * q^48 - 11957 * q^49 - 1560 * q^50 - 67946 * q^51 + 21936 * q^52 - 23576 * q^53 + 10456 * q^54 - 31415 * q^55 + 10880 * q^56 - 70522 * q^57 + 11708 * q^58 - 18316 * q^59 - 128 * q^60 - 18695 * q^61 - 23396 * q^62 - 88094 * q^63 + 20480 * q^64 - 40706 * q^65 - 44008 * q^66 - 85273 * q^67 + 33120 * q^68 - 87171 * q^69 - 43712 * q^70 + 8760 * q^71 + 38272 * q^72 - 10425 * q^73 - 27380 * q^74 - 10542 * q^75 + 37728 * q^76 + 17238 * q^77 - 39780 * q^78 + 48425 * q^79 + 24320 * q^80 + 33449 * q^81 - 57708 * q^82 + 27704 * q^83 + 45312 * q^84 + 139062 * q^85 - 27888 * q^86 + 6227 * q^87 + 57792 * q^88 + 233646 * q^89 - 27264 * q^90 + 146434 * q^91 + 33552 * q^92 + 301866 * q^93 - 75848 * q^94 + 189498 * q^95 + 19456 * q^96 + 251694 * q^97 - 47828 * q^98 + 182486 * q^99

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