LMFDB - Embedded newform 74.8.a.b.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:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 2177x^{2} - 14018x + 634476 $ x^4 - 2x^3 - 2177x^2 - 14018*x + 634476
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			1.1
Root			$14.6748$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -82.6714 q^{3} +64.0000 q^{4} +114.337 q^{5} -661.371 q^{6} +130.721 q^{7} +512.000 q^{8} +4647.56 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -82.6714 q^{3} +64.0000 q^{4} +114.337 q^{5} -661.371 q^{6} +130.721 q^{7} +512.000 q^{8} +4647.56 q^{9} +914.695 q^{10} +2344.52 q^{11} -5290.97 q^{12} -5974.20 q^{13} +1045.76 q^{14} -9452.39 q^{15} +4096.00 q^{16} -19882.8 q^{17} +37180.5 q^{18} -7787.29 q^{19} +7317.56 q^{20} -10806.9 q^{21} +18756.2 q^{22} +4821.07 q^{23} -42327.8 q^{24} -65052.1 q^{25} -47793.6 q^{26} -203418. q^{27} +8366.12 q^{28} -246156. q^{29} -75619.1 q^{30} -67628.9 q^{31} +32768.0 q^{32} -193825. q^{33} -159062. q^{34} +14946.2 q^{35} +297444. q^{36} -50653.0 q^{37} -62298.3 q^{38} +493895. q^{39} +58540.4 q^{40} -242383. q^{41} -86454.9 q^{42} +660296. q^{43} +150049. q^{44} +531388. q^{45} +38568.6 q^{46} -310360. q^{47} -338622. q^{48} -806455. q^{49} -520417. q^{50} +1.64374e6 q^{51} -382349. q^{52} +859068. q^{53} -1.62735e6 q^{54} +268065. q^{55} +66929.0 q^{56} +643786. q^{57} -1.96925e6 q^{58} -1.22165e6 q^{59} -604953. q^{60} -1.70926e6 q^{61} -541031. q^{62} +607532. q^{63} +262144. q^{64} -683071. q^{65} -1.55060e6 q^{66} +1.29584e6 q^{67} -1.27250e6 q^{68} -398565. q^{69} +119569. q^{70} -518524. q^{71} +2.37955e6 q^{72} +872444. q^{73} -405224. q^{74} +5.37795e6 q^{75} -498387. q^{76} +306477. q^{77} +3.95116e6 q^{78} -4.72622e6 q^{79} +468324. q^{80} +6.65266e6 q^{81} -1.93906e6 q^{82} +1.69885e6 q^{83} -691639. q^{84} -2.27333e6 q^{85} +5.28237e6 q^{86} +2.03501e7 q^{87} +1.20039e6 q^{88} -4.21199e6 q^{89} +4.25110e6 q^{90} -780951. q^{91} +308549. q^{92} +5.59098e6 q^{93} -2.48288e6 q^{94} -890374. q^{95} -2.70898e6 q^{96} +1.31862e7 q^{97} -6.45164e6 q^{98} +1.08963e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} - 41 q^{3} + 256 q^{4} - 363 q^{5} - 328 q^{6} - 774 q^{7} + 2048 q^{8} - 1079 q^{9}+O(q^{10}) $ 4 * q + 32 * q^2 - 41 * q^3 + 256 * q^4 - 363 * q^5 - 328 * q^6 - 774 * q^7 + 2048 * q^8 - 1079 * q^9	\( 4 q + 32 q^{2} - 41 q^{3} + 256 q^{4} - 363 q^{5} - 328 q^{6} - 774 q^{7} + 2048 q^{8} - 1079 q^{9} - 2904 q^{10} - 309 q^{11} - 2624 q^{12} - 20827 q^{13} - 6192 q^{14} - 22940 q^{15} + 16384 q^{16} - 48756 q^{17} - 8632 q^{18} - 69068 q^{19} - 23232 q^{20} - 640 q^{21} - 2472 q^{22} - 50237 q^{23} - 20992 q^{24} - 3581 q^{25} - 166616 q^{26} - 368414 q^{27} - 49536 q^{28} - 205195 q^{29} - 183520 q^{30} - 172283 q^{31} + 131072 q^{32} - 205234 q^{33} - 390048 q^{34} - 584964 q^{35} - 69056 q^{36} - 202612 q^{37} - 552544 q^{38} + 329055 q^{39} - 185856 q^{40} - 1018945 q^{41} - 5120 q^{42} + 1263046 q^{43} - 19776 q^{44} + 1279606 q^{45} - 401896 q^{46} - 420930 q^{47} - 167936 q^{48} - 482790 q^{49} - 28648 q^{50} + 728262 q^{51} - 1332928 q^{52} + 2051230 q^{53} - 2947312 q^{54} - 1442891 q^{55} - 396288 q^{56} - 926198 q^{57} - 1641560 q^{58} + 357914 q^{59} - 1468160 q^{60} - 2507513 q^{61} - 1378264 q^{62} + 2879054 q^{63} + 1048576 q^{64} + 3097954 q^{65} - 1641872 q^{66} + 586879 q^{67} - 3120384 q^{68} - 252895 q^{69} - 4679712 q^{70} - 130272 q^{71} - 552448 q^{72} + 3517417 q^{73} - 1620896 q^{74} + 8154290 q^{75} - 4420352 q^{76} + 8777590 q^{77} + 2632440 q^{78} + 3790171 q^{79} - 1486848 q^{80} + 15888376 q^{81} - 8151560 q^{82} + 12973460 q^{83} - 40960 q^{84} + 14870322 q^{85} + 10104368 q^{86} + 23063695 q^{87} - 158208 q^{88} + 18852848 q^{89} + 10236848 q^{90} - 2046622 q^{91} - 3215168 q^{92} + 4005314 q^{93} - 3367440 q^{94} + 30367150 q^{95} - 1343488 q^{96} + 14580104 q^{97} - 3862320 q^{98} + 16949258 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 - 41 * q^3 + 256 * q^4 - 363 * q^5 - 328 * q^6 - 774 * q^7 + 2048 * q^8 - 1079 * q^9 - 2904 * q^10 - 309 * q^11 - 2624 * q^12 - 20827 * q^13 - 6192 * q^14 - 22940 * q^15 + 16384 * q^16 - 48756 * q^17 - 8632 * q^18 - 69068 * q^19 - 23232 * q^20 - 640 * q^21 - 2472 * q^22 - 50237 * q^23 - 20992 * q^24 - 3581 * q^25 - 166616 * q^26 - 368414 * q^27 - 49536 * q^28 - 205195 * q^29 - 183520 * q^30 - 172283 * q^31 + 131072 * q^32 - 205234 * q^33 - 390048 * q^34 - 584964 * q^35 - 69056 * q^36 - 202612 * q^37 - 552544 * q^38 + 329055 * q^39 - 185856 * q^40 - 1018945 * q^41 - 5120 * q^42 + 1263046 * q^43 - 19776 * q^44 + 1279606 * q^45 - 401896 * q^46 - 420930 * q^47 - 167936 * q^48 - 482790 * q^49 - 28648 * q^50 + 728262 * q^51 - 1332928 * q^52 + 2051230 * q^53 - 2947312 * q^54 - 1442891 * q^55 - 396288 * q^56 - 926198 * q^57 - 1641560 * q^58 + 357914 * q^59 - 1468160 * q^60 - 2507513 * q^61 - 1378264 * q^62 + 2879054 * q^63 + 1048576 * q^64 + 3097954 * q^65 - 1641872 * q^66 + 586879 * q^67 - 3120384 * q^68 - 252895 * q^69 - 4679712 * q^70 - 130272 * q^71 - 552448 * q^72 + 3517417 * q^73 - 1620896 * q^74 + 8154290 * q^75 - 4420352 * q^76 + 8777590 * q^77 + 2632440 * q^78 + 3790171 * q^79 - 1486848 * q^80 + 15888376 * q^81 - 8151560 * q^82 + 12973460 * q^83 - 40960 * q^84 + 14870322 * q^85 + 10104368 * q^86 + 23063695 * q^87 - 158208 * q^88 + 18852848 * q^89 + 10236848 * q^90 - 2046622 * q^91 - 3215168 * q^92 + 4005314 * q^93 - 3367440 * q^94 + 30367150 * q^95 - 1343488 * q^96 + 14580104 * q^97 - 3862320 * q^98 + 16949258 * 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
$3$	−82.6714	−1.76779	−0.883896	−	0.467684i	$-0.845088\pi$
$3$	−82.6714	−1.76779	−0.883896	+	0.467684i	$0.845088\pi$
$4$	64.0000	0.500000
$5$	114.337	0.409064	0.204532	−	0.978860i	$-0.434433\pi$
$5$	114.337	0.409064	0.204532	+	0.978860i	$0.434433\pi$
$6$	−661.371	−1.25002
$7$	130.721	0.144046	0.0720230	−	0.997403i	$-0.477055\pi$
$7$	130.721	0.144046	0.0720230	+	0.997403i	$0.477055\pi$
$8$	512.000	0.353553
$9$	4647.56	2.12509
$10$	914.695	0.289252
$11$	2344.52	0.531104	0.265552	−	0.964097i	$-0.414446\pi$
$11$	2344.52	0.531104	0.265552	+	0.964097i	$0.414446\pi$
$12$	−5290.97	−0.883896
$13$	−5974.20	−0.754185	−0.377092	−	0.926176i	$-0.623076\pi$
$13$	−5974.20	−0.754185	−0.377092	+	0.926176i	$0.623076\pi$
$14$	1045.76	0.101856
$15$	−9452.39	−0.723139
$16$	4096.00	0.250000
$17$	−19882.8	−0.981535	−0.490767	−	0.871291i	$-0.663284\pi$
$17$	−19882.8	−0.981535	−0.490767	+	0.871291i	$0.663284\pi$
$18$	37180.5	1.50266
$19$	−7787.29	−0.260465	−0.130232	−	0.991484i	$-0.541572\pi$
$19$	−7787.29	−0.260465	−0.130232	+	0.991484i	$0.541572\pi$
$20$	7317.56	0.204532
$21$	−10806.9	−0.254643
$22$	18756.2	0.375547
$23$	4821.07	0.0826221	0.0413111	−	0.999146i	$-0.486847\pi$
$23$	4821.07	0.0826221	0.0413111	+	0.999146i	$0.486847\pi$
$24$	−42327.8	−0.625009
$25$	−65052.1	−0.832667
$26$	−47793.6	−0.533289
$27$	−203418.	−1.98892
$28$	8366.12	0.0720230
$29$	−246156.	−1.87421	−0.937105	−	0.349048i	$-0.886505\pi$
$29$	−246156.	−1.87421	−0.937105	+	0.349048i	$0.886505\pi$
$30$	−75619.1	−0.511337
$31$	−67628.9	−0.407724	−0.203862	−	0.979000i	$-0.565349\pi$
$31$	−67628.9	−0.407724	−0.203862	+	0.979000i	$0.565349\pi$
$32$	32768.0	0.176777
$33$	−193825.	−0.938881
$34$	−159062.	−0.694050
$35$	14946.2	0.0589240
$36$	297444.	1.06254
$37$	−50653.0	−0.164399
$37$	−50653.0	−0.164399
$38$	−62298.3	−0.184176
$39$	493895.	1.33324
$40$	58540.4	0.144626
$41$	−242383.	−0.549236	−0.274618	−	0.961553i	$-0.588551\pi$
$41$	−242383.	−0.549236	−0.274618	+	0.961553i	$0.588551\pi$
$42$	−86454.9	−0.180060
$43$	660296.	1.26648	0.633241	−	0.773955i	$-0.281724\pi$
$43$	660296.	1.26648	0.633241	+	0.773955i	$0.281724\pi$
$44$	150049.	0.265552
$45$	531388.	0.869296
$46$	38568.6	0.0584227
$47$	−310360.	−0.436037	−0.218019	−	0.975945i	$-0.569959\pi$
$47$	−310360.	−0.436037	−0.218019	+	0.975945i	$0.569959\pi$
$48$	−338622.	−0.441948
$49$	−806455.	−0.979251
$50$	−520417.	−0.588784
$51$	1.64374e6	1.73515
$52$	−382349.	−0.377092
$53$	859068.	0.792614	0.396307	−	0.918118i	$-0.370292\pi$
$53$	859068.	0.792614	0.396307	+	0.918118i	$0.370292\pi$
$54$	−1.62735e6	−1.40638
$55$	268065.	0.217255
$56$	66929.0	0.0509279
$57$	643786.	0.460447
$58$	−1.96925e6	−1.32527
$59$	−1.22165e6	−0.774396	−0.387198	−	0.921996i	$-0.626557\pi$
$59$	−1.22165e6	−0.774396	−0.387198	+	0.921996i	$0.626557\pi$
$60$	−604953.	−0.361570
$61$	−1.70926e6	−0.964170	−0.482085	−	0.876124i	$-0.660120\pi$
$61$	−1.70926e6	−0.964170	−0.482085	+	0.876124i	$0.660120\pi$
$62$	−541031.	−0.288305
$63$	607532.	0.306110
$64$	262144.	0.125000
$65$	−683071.	−0.308510
$66$	−1.55060e6	−0.663889
$67$	1.29584e6	0.526367	0.263184	−	0.964746i	$-0.415227\pi$
$67$	1.29584e6	0.526367	0.263184	+	0.964746i	$0.415227\pi$
$68$	−1.27250e6	−0.490767
$69$	−398565.	−0.146059
$70$	119569.	0.0416655
$71$	−518524.	−0.171935	−0.0859675	−	0.996298i	$-0.527398\pi$
$71$	−518524.	−0.171935	−0.0859675	+	0.996298i	$0.527398\pi$
$72$	2.37955e6	0.751331
$73$	872444.	0.262487	0.131243	−	0.991350i	$-0.458103\pi$
$73$	872444.	0.262487	0.131243	+	0.991350i	$0.458103\pi$
$74$	−405224.	−0.116248
$75$	5.37795e6	1.47198
$76$	−498387.	−0.130232
$77$	306477.	0.0765033
$78$	3.95116e6	0.942744
$79$	−4.72622e6	−1.07850	−0.539249	−	0.842147i	$-0.681292\pi$
$79$	−4.72622e6	−1.07850	−0.539249	+	0.842147i	$0.681292\pi$
$80$	468324.	0.102266
$81$	6.65266e6	1.39091
$82$	−1.93906e6	−0.388368
$83$	1.69885e6	0.326124	0.163062	−	0.986616i	$-0.447863\pi$
$83$	1.69885e6	0.326124	0.163062	+	0.986616i	$0.447863\pi$
$84$	−691639.	−0.127322
$85$	−2.27333e6	−0.401510
$86$	5.28237e6	0.895538
$87$	2.03501e7	3.31321
$88$	1.20039e6	0.187774
$89$	−4.21199e6	−0.633318	−0.316659	−	0.948539i	$-0.602561\pi$
$89$	−4.21199e6	−0.633318	−0.316659	+	0.948539i	$0.602561\pi$
$90$	4.25110e6	0.614685
$91$	−780951.	−0.108637
$92$	308549.	0.0413111
$93$	5.59098e6	0.720771
$94$	−2.48288e6	−0.308325
$95$	−890374.	−0.106547
$96$	−2.70898e6	−0.312504
$97$	1.31862e7	1.46697	0.733483	−	0.679708i	$-0.237894\pi$
$97$	1.31862e7	1.46697	0.733483	+	0.679708i	$0.237894\pi$
$98$	−6.45164e6	−0.692435
$99$	1.08963e7	1.12864
$100$	−4.16333e6	−0.416333
$101$	−1.96105e7	−1.89393	−0.946965	−	0.321336i	$-0.895868\pi$
$101$	−1.96105e7	−1.89393	−0.946965	+	0.321336i	$0.895868\pi$
$102$	1.31499e7	1.22694
$103$	−7.59111e6	−0.684502	−0.342251	−	0.939609i	$-0.611189\pi$
$103$	−7.59111e6	−0.684502	−0.342251	+	0.939609i	$0.611189\pi$
$104$	−3.05879e6	−0.266645
$105$	−1.23562e6	−0.104165
$106$	6.87254e6	0.560463
$107$	1.56821e7	1.23755	0.618773	−	0.785570i	$-0.287630\pi$
$107$	1.56821e7	1.23755	0.618773	+	0.785570i	$0.287630\pi$
$108$	−1.30188e7	−0.994459
$109$	−533820.	−0.0394823	−0.0197411	−	0.999805i	$-0.506284\pi$
$109$	−533820.	−0.0394823	−0.0197411	+	0.999805i	$0.506284\pi$
$110$	2.14452e6	0.153623
$111$	4.18756e6	0.290623
$112$	535432.	0.0360115
$113$	−1.42250e7	−0.927420	−0.463710	−	0.885987i	$-0.653482\pi$
$113$	−1.42250e7	−0.927420	−0.463710	+	0.885987i	$0.653482\pi$
$114$	5.15029e6	0.325585
$115$	551226.	0.0337977
$116$	−1.57540e7	−0.937105
$117$	−2.77655e7	−1.60271
$118$	−9.77317e6	−0.547581
$119$	−2.59909e6	−0.141386
$120$	−4.83962e6	−0.255668
$121$	−1.39904e7	−0.717929
$122$	−1.36741e7	−0.681771
$123$	2.00381e7	0.970934
$124$	−4.32825e6	−0.203862
$125$	−1.63704e7	−0.749678
$126$	4.86026e6	0.216452
$127$	−2.12729e7	−0.921537	−0.460768	−	0.887520i	$-0.652426\pi$
$127$	−2.12729e7	−0.921537	−0.460768	+	0.887520i	$0.652426\pi$
$128$	2.09715e6	0.0883883
$129$	−5.45876e7	−2.23888
$130$	−5.46457e6	−0.218149
$131$	1.89968e7	0.738297	0.369148	−	0.929370i	$-0.379649\pi$
$131$	1.89968e7	0.738297	0.369148	+	0.929370i	$0.379649\pi$
$132$	−1.24048e7	−0.469440
$133$	−1.01796e6	−0.0375189
$134$	1.03667e7	0.372198
$135$	−2.32582e7	−0.813594
$136$	−1.01800e7	−0.347025
$137$	5.66328e7	1.88168	0.940841	−	0.338848i	$-0.110037\pi$
$137$	5.66328e7	1.88168	0.940841	+	0.338848i	$0.110037\pi$
$138$	−3.18852e6	−0.103279
$139$	3.15115e7	0.995215	0.497607	−	0.867402i	$-0.334212\pi$
$139$	3.15115e7	0.995215	0.497607	+	0.867402i	$0.334212\pi$
$140$	956555.	0.0294620
$141$	2.56579e7	0.770823
$142$	−4.14819e6	−0.121576
$143$	−1.40066e7	−0.400551
$144$	1.90364e7	0.531272
$145$	−2.81447e7	−0.766671
$146$	6.97955e6	0.185606
$147$	6.66708e7	1.73111
$148$	−3.24179e6	−0.0821995
$149$	206567.	0.00511575	0.00255787	−	0.999997i	$-0.499186\pi$
$149$	206567.	0.00511575	0.00255787	+	0.999997i	$0.499186\pi$
$150$	4.30236e7	1.04085
$151$	3.08004e7	0.728009	0.364005	−	0.931397i	$-0.381409\pi$
$151$	3.08004e7	0.728009	0.364005	+	0.931397i	$0.381409\pi$
$152$	−3.98709e6	−0.0920882
$153$	−9.24064e7	−2.08585
$154$	2.45182e6	0.0540960
$155$	−7.73248e6	−0.166785
$156$	3.16093e7	0.666621
$157$	5.53862e7	1.14223	0.571114	−	0.820871i	$-0.306511\pi$
$157$	5.53862e7	1.14223	0.571114	+	0.820871i	$0.306511\pi$
$158$	−3.78097e7	−0.762613
$159$	−7.10204e7	−1.40118
$160$	3.74659e6	0.0723130
$161$	630214.	0.0119014
$162$	5.32213e7	0.983519
$163$	−1.01371e8	−1.83340	−0.916701	−	0.399574i	$-0.869158\pi$
$163$	−1.01371e8	−1.83340	−0.916701	+	0.399574i	$0.869158\pi$
$164$	−1.55125e7	−0.274618
$165$	−2.21613e7	−0.384062
$166$	1.35908e7	0.230605
$167$	−1.14227e8	−1.89785	−0.948926	−	0.315498i	$-0.897829\pi$
$167$	−1.14227e8	−1.89785	−0.948926	+	0.315498i	$0.897829\pi$
$168$	−5.53311e6	−0.0900299
$169$	−2.70575e7	−0.431205
$170$	−1.81867e7	−0.283911
$171$	−3.61919e7	−0.553510
$172$	4.22589e7	0.633241
$173$	−4.78631e7	−0.702813	−0.351407	−	0.936223i	$-0.614297\pi$
$173$	−4.78631e7	−0.702813	−0.351407	+	0.936223i	$0.614297\pi$
$174$	1.62801e8	2.34279
$175$	−8.50365e6	−0.119942
$176$	9.60315e6	0.132776
$177$	1.00995e8	1.36897
$178$	−3.36959e7	−0.447824
$179$	1.97413e7	0.257271	0.128635	−	0.991692i	$-0.458940\pi$
$179$	1.97413e7	0.257271	0.128635	+	0.991692i	$0.458940\pi$
$180$	3.40088e7	0.434648
$181$	6.57898e7	0.824676	0.412338	−	0.911031i	$-0.364712\pi$
$181$	6.57898e7	0.824676	0.412338	+	0.911031i	$0.364712\pi$
$182$	−6.24761e6	−0.0768181
$183$	1.41307e8	1.70445
$184$	2.46839e6	0.0292113
$185$	−5.79150e6	−0.0672497
$186$	4.47278e7	0.509662
$187$	−4.66155e7	−0.521297
$188$	−1.98631e7	−0.218019
$189$	−2.65910e7	−0.286495
$190$	−7.12299e6	−0.0753399
$191$	−6.84589e7	−0.710907	−0.355454	−	0.934694i	$-0.615674\pi$
$191$	−6.84589e7	−0.710907	−0.355454	+	0.934694i	$0.615674\pi$
$192$	−2.16718e7	−0.220974
$193$	9.33194e7	0.934375	0.467187	−	0.884158i	$-0.345267\pi$
$193$	9.33194e7	0.934375	0.467187	+	0.884158i	$0.345267\pi$
$194$	1.05490e8	1.03730
$195$	5.64704e7	0.545381
$196$	−5.16131e7	−0.489625
$197$	1.41425e8	1.31794	0.658970	−	0.752169i	$-0.270992\pi$
$197$	1.41425e8	1.31794	0.658970	+	0.752169i	$0.270992\pi$
$198$	8.71704e7	0.798070
$199$	1.09895e8	0.988531	0.494265	−	0.869311i	$-0.335437\pi$
$199$	1.09895e8	0.988531	0.494265	+	0.869311i	$0.335437\pi$
$200$	−3.33067e7	−0.294392
$201$	−1.07129e8	−0.930508
$202$	−1.56884e8	−1.33921
$203$	−3.21777e7	−0.269972
$204$	1.05199e8	0.867574
$205$	−2.77133e7	−0.224672
$206$	−6.07288e7	−0.484016
$207$	2.24062e7	0.175579
$208$	−2.44703e7	−0.188546
$209$	−1.82575e7	−0.138334
$210$	−9.88497e6	−0.0736560
$211$	1.70421e8	1.24892	0.624458	−	0.781058i	$-0.285320\pi$
$211$	1.70421e8	1.24892	0.624458	+	0.781058i	$0.285320\pi$
$212$	5.49804e7	0.396307
$213$	4.28671e7	0.303945
$214$	1.25457e8	0.875078
$215$	7.54961e7	0.518072
$216$	−1.04150e8	−0.703189
$217$	−8.84049e6	−0.0587310
$218$	−4.27056e6	−0.0279182
$219$	−7.21262e7	−0.464022
$220$	1.71562e7	0.108628
$221$	1.18784e8	0.740259
$222$	3.35004e7	0.205502
$223$	5.64211e7	0.340702	0.170351	−	0.985383i	$-0.445510\pi$
$223$	5.64211e7	0.340702	0.170351	+	0.985383i	$0.445510\pi$
$224$	4.28345e6	0.0254640
$225$	−3.02334e8	−1.76949
$226$	−1.13800e8	−0.655785
$227$	−1.82878e8	−1.03770	−0.518848	−	0.854866i	$-0.673639\pi$
$227$	−1.82878e8	−1.03770	−0.518848	+	0.854866i	$0.673639\pi$
$228$	4.12023e7	0.230224
$229$	1.93904e7	0.106700	0.0533498	−	0.998576i	$-0.483010\pi$
$229$	1.93904e7	0.106700	0.0533498	+	0.998576i	$0.483010\pi$
$230$	4.40981e6	0.0238986
$231$	−2.53369e7	−0.135242
$232$	−1.26032e8	−0.662633
$233$	−7.65219e7	−0.396314	−0.198157	−	0.980170i	$-0.563496\pi$
$233$	−7.65219e7	−0.396314	−0.198157	+	0.980170i	$0.563496\pi$
$234$	−2.22124e8	−1.13329
$235$	−3.54856e7	−0.178367
$236$	−7.81853e7	−0.387198
$237$	3.90723e8	1.90656
$238$	−2.07927e7	−0.0999750
$239$	3.45231e8	1.63575	0.817875	−	0.575396i	$-0.195152\pi$
$239$	3.45231e8	1.63575	0.817875	+	0.575396i	$0.195152\pi$
$240$	−3.87170e7	−0.180785
$241$	−2.61103e8	−1.20158	−0.600789	−	0.799408i	$-0.705147\pi$
$241$	−2.61103e8	−1.20158	−0.600789	+	0.799408i	$0.705147\pi$
$242$	−1.11923e8	−0.507652
$243$	−1.05109e8	−0.469913
$244$	−1.09393e8	−0.482085
$245$	−9.22075e7	−0.400576
$246$	1.60305e8	0.686554
$247$	4.65228e7	0.196439
$248$	−3.46260e7	−0.144152
$249$	−1.40447e8	−0.576519
$250$	−1.30963e8	−0.530102
$251$	1.56531e8	0.624804	0.312402	−	0.949950i	$-0.398866\pi$
$251$	1.56531e8	0.624804	0.312402	+	0.949950i	$0.398866\pi$
$252$	3.88821e7	0.153055
$253$	1.13031e7	0.0438809
$254$	−1.70183e8	−0.651625
$255$	1.87940e8	0.709787
$256$	1.67772e7	0.0625000
$257$	1.85640e8	0.682191	0.341095	−	0.940029i	$-0.389202\pi$
$257$	1.85640e8	0.682191	0.341095	+	0.940029i	$0.389202\pi$
$258$	−4.36701e8	−1.58312
$259$	−6.62139e6	−0.0236810
$260$	−4.37165e7	−0.154255
$261$	−1.14403e9	−3.98286
$262$	1.51974e8	0.522055
$263$	5.09760e8	1.72791	0.863953	−	0.503572i	$-0.167981\pi$
$263$	5.09760e8	1.72791	0.863953	+	0.503572i	$0.167981\pi$
$264$	−9.92383e7	−0.331945
$265$	9.82231e7	0.324230
$266$	−8.14368e6	−0.0265298
$267$	3.48211e8	1.11957
$268$	8.29336e7	0.263184
$269$	3.92417e8	1.22918	0.614589	−	0.788848i	$-0.289322\pi$
$269$	3.92417e8	1.22918	0.614589	+	0.788848i	$0.289322\pi$
$270$	−1.86066e8	−0.575298
$271$	−4.63684e8	−1.41524	−0.707619	−	0.706594i	$-0.750231\pi$
$271$	−4.63684e8	−1.41524	−0.707619	+	0.706594i	$0.750231\pi$
$272$	−8.14398e7	−0.245384
$273$	6.45623e7	0.192048
$274$	4.53063e8	1.33055
$275$	−1.52516e8	−0.442233
$276$	−2.55082e7	−0.0730293
$277$	1.93073e8	0.545811	0.272906	−	0.962041i	$-0.412015\pi$
$277$	1.93073e8	0.545811	0.272906	+	0.962041i	$0.412015\pi$
$278$	2.52092e8	0.703723
$279$	−3.14310e8	−0.866449
$280$	7.65244e6	0.0208328
$281$	3.95956e8	1.06457	0.532285	−	0.846565i	$-0.321333\pi$
$281$	3.95956e8	1.06457	0.532285	+	0.846565i	$0.321333\pi$
$282$	2.05263e8	0.545054
$283$	−5.52836e8	−1.44992	−0.724959	−	0.688792i	$-0.758142\pi$
$283$	−5.52836e8	−1.44992	−0.724959	+	0.688792i	$0.758142\pi$
$284$	−3.31855e7	−0.0859675
$285$	7.36085e7	0.188352
$286$	−1.12053e8	−0.283232
$287$	−3.16845e7	−0.0791151
$288$	1.52291e8	0.375666
$289$	−1.50141e7	−0.0365895
$290$	−2.25158e8	−0.542119
$291$	−1.09013e9	−2.59329
$292$	5.58364e7	0.131243
$293$	−8.34151e7	−0.193735	−0.0968675	−	0.995297i	$-0.530882\pi$
$293$	−8.34151e7	−0.193735	−0.0968675	+	0.995297i	$0.530882\pi$
$294$	5.33366e8	1.22408
$295$	−1.39679e8	−0.316778
$296$	−2.59343e7	−0.0581238
$297$	−4.76918e8	−1.05632
$298$	1.65254e6	0.00361738
$299$	−2.88020e7	−0.0623123
$300$	3.44189e8	0.735991
$301$	8.63143e7	0.182432
$302$	2.46403e8	0.514780
$303$	1.62123e9	3.34807
$304$	−3.18967e7	−0.0651162
$305$	−1.95431e8	−0.394407
$306$	−7.39252e8	−1.47492
$307$	8.49160e8	1.67496	0.837482	−	0.546466i	$-0.184027\pi$
$307$	8.49160e8	1.67496	0.837482	+	0.546466i	$0.184027\pi$
$308$	1.96145e7	0.0382517
$309$	6.27567e8	1.21006
$310$	−6.18598e7	−0.117935
$311$	3.12972e8	0.589990	0.294995	−	0.955499i	$-0.404682\pi$
$311$	3.12972e8	0.589990	0.294995	+	0.955499i	$0.404682\pi$
$312$	2.52874e8	0.471372
$313$	−3.68233e8	−0.678763	−0.339381	−	0.940649i	$-0.610218\pi$
$313$	−3.68233e8	−0.678763	−0.339381	+	0.940649i	$0.610218\pi$
$314$	4.43090e8	0.807677
$315$	6.94633e7	0.125219
$316$	−3.02478e8	−0.539249
$317$	8.20621e8	1.44689	0.723445	−	0.690382i	$-0.242558\pi$
$317$	8.20621e8	1.44689	0.723445	+	0.690382i	$0.242558\pi$
$318$	−5.68163e8	−0.990782
$319$	−5.77119e8	−0.995400
$320$	2.99727e7	0.0511330
$321$	−1.29646e9	−2.18772
$322$	5.04171e6	0.00841554
$323$	1.54833e8	0.255655
$324$	4.25770e8	0.695453
$325$	3.88634e8	0.627985
$326$	−8.10969e8	−1.29641
$327$	4.41317e7	0.0697964
$328$	−1.24100e8	−0.194184
$329$	−4.05705e7	−0.0628094
$330$	−1.77290e8	−0.271573
$331$	3.11691e7	0.0472418	0.0236209	−	0.999721i	$-0.492481\pi$
$331$	3.11691e7	0.0472418	0.0236209	+	0.999721i	$0.492481\pi$
$332$	1.08727e8	0.163062
$333$	−2.35413e8	−0.349362
$334$	−9.13819e8	−1.34198
$335$	1.48162e8	0.215318
$336$	−4.42649e7	−0.0636608
$337$	−1.31728e9	−1.87487	−0.937437	−	0.348155i	$-0.886808\pi$
$337$	−1.31728e9	−1.87487	−0.937437	+	0.348155i	$0.886808\pi$
$338$	−2.16460e8	−0.304908
$339$	1.17600e9	1.63949
$340$	−1.45493e8	−0.200755
$341$	−1.58557e8	−0.216544
$342$	−2.89535e8	−0.391391
$343$	−2.13074e8	−0.285103
$344$	3.38071e8	0.447769
$345$	−4.55706e7	−0.0597473
$346$	−3.82905e8	−0.496964
$347$	1.01825e9	1.30829	0.654144	−	0.756370i	$-0.273029\pi$
$347$	1.01825e9	1.30829	0.654144	+	0.756370i	$0.273029\pi$
$348$	1.30241e9	1.65661
$349$	−1.02153e9	−1.28636	−0.643182	−	0.765713i	$-0.722386\pi$
$349$	−1.02153e9	−1.28636	−0.643182	+	0.765713i	$0.722386\pi$
$350$	−6.80292e7	−0.0848120
$351$	1.21526e9	1.50001
$352$	7.68252e7	0.0938868
$353$	1.14845e8	0.138964	0.0694818	−	0.997583i	$-0.477865\pi$
$353$	1.14845e8	0.138964	0.0694818	+	0.997583i	$0.477865\pi$
$354$	8.07962e8	0.968009
$355$	−5.92863e7	−0.0703324
$356$	−2.69567e8	−0.316659
$357$	2.14870e8	0.249941
$358$	1.57931e8	0.181918
$359$	1.15379e9	1.31612	0.658061	−	0.752965i	$-0.271377\pi$
$359$	1.15379e9	1.31612	0.658061	+	0.752965i	$0.271377\pi$
$360$	2.72070e8	0.307343
$361$	−8.33230e8	−0.932158
$362$	5.26318e8	0.583134
$363$	1.15661e9	1.26915
$364$	−4.99808e7	−0.0543186
$365$	9.97525e7	0.107374
$366$	1.13046e9	1.20523
$367$	−7.43776e7	−0.0785436	−0.0392718	−	0.999229i	$-0.512504\pi$
$367$	−7.43776e7	−0.0785436	−0.0392718	+	0.999229i	$0.512504\pi$
$368$	1.97471e7	0.0206555
$369$	−1.12649e9	−1.16717
$370$	−4.63320e7	−0.0475527
$371$	1.12298e8	0.114173
$372$	3.57823e8	0.360386
$373$	−1.22089e9	−1.21814	−0.609070	−	0.793117i	$-0.708457\pi$
$373$	−1.22089e9	−1.21814	−0.609070	+	0.793117i	$0.708457\pi$
$374$	−3.72924e8	−0.368613
$375$	1.35337e9	1.32527
$376$	−1.58904e8	−0.154162
$377$	1.47059e9	1.41350
$378$	−2.12728e8	−0.202583
$379$	−1.09902e9	−1.03698	−0.518490	−	0.855084i	$-0.673506\pi$
$379$	−1.09902e9	−1.03698	−0.518490	+	0.855084i	$0.673506\pi$
$380$	−5.69839e7	−0.0532733
$381$	1.75866e9	1.62908
$382$	−5.47671e8	−0.502687
$383$	−5.67152e8	−0.515827	−0.257913	−	0.966168i	$-0.583035\pi$
$383$	−5.67152e8	−0.515827	−0.257913	+	0.966168i	$0.583035\pi$
$384$	−1.73375e8	−0.156252
$385$	3.50416e7	0.0312947
$386$	7.46555e8	0.660703
$387$	3.06877e9	2.69138
$388$	8.43919e8	0.733483
$389$	−7.90877e8	−0.681217	−0.340608	−	0.940205i	$-0.610633\pi$
$389$	−7.90877e8	−0.681217	−0.340608	+	0.940205i	$0.610633\pi$
$390$	4.51763e8	0.385643
$391$	−9.58563e7	−0.0810965
$392$	−4.12905e8	−0.346217
$393$	−1.57049e9	−1.30515
$394$	1.13140e9	0.931925
$395$	−5.40381e8	−0.441174
$396$	6.97363e8	0.564321
$397$	−1.40683e9	−1.12843	−0.564217	−	0.825626i	$-0.690822\pi$
$397$	−1.40683e9	−1.12843	−0.564217	+	0.825626i	$0.690822\pi$
$398$	8.79156e8	0.698997
$399$	8.41562e7	0.0663255
$400$	−2.66453e8	−0.208167
$401$	−2.07896e9	−1.61005	−0.805027	−	0.593238i	$-0.797849\pi$
$401$	−2.07896e9	−1.61005	−0.805027	+	0.593238i	$0.797849\pi$
$402$	−8.57030e8	−0.657968
$403$	4.04029e8	0.307499
$404$	−1.25507e9	−0.946965
$405$	7.60644e8	0.568969
$406$	−2.57422e8	−0.190899
$407$	−1.18757e8	−0.0873129
$408$	8.41593e8	0.613468
$409$	−1.36197e8	−0.0984319	−0.0492160	−	0.998788i	$-0.515672\pi$
$409$	−1.36197e8	−0.0984319	−0.0492160	+	0.998788i	$0.515672\pi$
$410$	−2.21706e8	−0.158867
$411$	−4.68192e9	−3.32642
$412$	−4.85831e8	−0.342251
$413$	−1.59694e8	−0.111549
$414$	1.79250e8	0.124153
$415$	1.94242e8	0.133406
$416$	−1.95763e8	−0.133322
$417$	−2.60510e9	−1.75933
$418$	−1.46060e8	−0.0978168
$419$	8.70749e8	0.578287	0.289144	−	0.957286i	$-0.406629\pi$
$419$	8.70749e8	0.578287	0.289144	+	0.957286i	$0.406629\pi$
$420$	−7.90798e7	−0.0520826
$421$	−1.78983e9	−1.16903	−0.584514	−	0.811384i	$-0.698715\pi$
$421$	−1.78983e9	−1.16903	−0.584514	+	0.811384i	$0.698715\pi$
$422$	1.36336e9	0.883118
$423$	−1.44242e9	−0.926617
$424$	4.39843e8	0.280232
$425$	1.29342e9	0.817291
$426$	3.42937e8	0.214922
$427$	−2.23435e8	−0.138885
$428$	1.00366e9	0.618773
$429$	1.15795e9	0.708090
$430$	6.03969e8	0.366332
$431$	−2.43619e9	−1.46568	−0.732842	−	0.680399i	$-0.761807\pi$
$431$	−2.43619e9	−1.46568	−0.732842	+	0.680399i	$0.761807\pi$
$432$	−8.33201e8	−0.497229
$433$	1.60081e8	0.0947614	0.0473807	−	0.998877i	$-0.484913\pi$
$433$	1.60081e8	0.0947614	0.0473807	+	0.998877i	$0.484913\pi$
$434$	−7.07240e7	−0.0415291
$435$	2.32677e9	1.35532
$436$	−3.41645e7	−0.0197411
$437$	−3.75431e7	−0.0215201
$438$	−5.77009e8	−0.328113
$439$	−2.78349e9	−1.57023	−0.785115	−	0.619350i	$-0.787396\pi$
$439$	−2.78349e9	−1.57023	−0.785115	+	0.619350i	$0.787396\pi$
$440$	1.37249e8	0.0768114
$441$	−3.74805e9	−2.08099
$442$	9.50269e8	0.523442
$443$	−2.30211e9	−1.25809	−0.629046	−	0.777368i	$-0.716554\pi$
$443$	−2.30211e9	−1.25809	−0.629046	+	0.777368i	$0.716554\pi$
$444$	2.68004e8	0.145312
$445$	−4.81585e8	−0.259068
$446$	4.51369e8	0.240913
$447$	−1.70772e7	−0.00904357
$448$	3.42676e7	0.0180057
$449$	−1.65040e9	−0.860451	−0.430225	−	0.902721i	$-0.641566\pi$
$449$	−1.65040e9	−0.860451	−0.430225	+	0.902721i	$0.641566\pi$
$450$	−2.41867e9	−1.25122
$451$	−5.68272e8	−0.291701
$452$	−9.10398e8	−0.463710
$453$	−2.54631e9	−1.28697
$454$	−1.46302e9	−0.733763
$455$	−8.92914e7	−0.0444396
$456$	3.29619e8	0.162793
$457$	2.78651e8	0.136569	0.0682847	−	0.997666i	$-0.478247\pi$
$457$	2.78651e8	0.136569	0.0682847	+	0.997666i	$0.478247\pi$
$458$	1.55123e8	0.0754479
$459$	4.04452e9	1.95219
$460$	3.52785e7	0.0168989
$461$	3.50867e9	1.66798	0.833988	−	0.551783i	$-0.186052\pi$
$461$	3.50867e9	1.66798	0.833988	+	0.551783i	$0.186052\pi$
$462$	−2.02695e8	−0.0956305
$463$	−9.72895e8	−0.455546	−0.227773	−	0.973714i	$-0.573144\pi$
$463$	−9.72895e8	−0.455546	−0.227773	+	0.973714i	$0.573144\pi$
$464$	−1.00826e9	−0.468552
$465$	6.39255e8	0.294842
$466$	−6.12175e8	−0.280237
$467$	1.32759e9	0.603191	0.301596	−	0.953436i	$-0.402481\pi$
$467$	1.32759e9	0.603191	0.301596	+	0.953436i	$0.402481\pi$
$468$	−1.77699e9	−0.801354
$469$	1.69393e8	0.0758211
$470$	−2.83885e8	−0.126125
$471$	−4.57886e9	−2.01922
$472$	−6.25483e8	−0.273790
$473$	1.54808e9	0.672633
$474$	3.12579e9	1.34814
$475$	5.06580e8	0.216880
$476$	−1.66342e8	−0.0706930
$477$	3.99257e9	1.68437
$478$	2.76185e9	1.15665
$479$	4.21765e9	1.75346	0.876730	−	0.480983i	$-0.159720\pi$
$479$	4.21765e9	1.75346	0.876730	+	0.480983i	$0.159720\pi$
$480$	−3.09736e8	−0.127834
$481$	3.02611e8	0.123987
$482$	−2.08882e9	−0.849644
$483$	−5.21006e7	−0.0210391
$484$	−8.95386e8	−0.358964
$485$	1.50767e9	0.600082
$486$	−8.40870e8	−0.332278
$487$	−1.37133e9	−0.538012	−0.269006	−	0.963139i	$-0.586695\pi$
$487$	−1.37133e9	−0.538012	−0.269006	+	0.963139i	$0.586695\pi$
$488$	−8.75141e8	−0.340886
$489$	8.38049e9	3.24107
$490$	−7.37660e8	−0.283250
$491$	8.25588e8	0.314759	0.157379	−	0.987538i	$-0.449695\pi$
$491$	8.25588e8	0.314759	0.157379	+	0.987538i	$0.449695\pi$
$492$	1.28244e9	0.485467
$493$	4.89427e9	1.83960
$494$	3.72183e8	0.138903
$495$	1.24585e9	0.461686
$496$	−2.77008e8	−0.101931
$497$	−6.77817e7	−0.0247665
$498$	−1.12357e9	−0.407661
$499$	4.64880e9	1.67490	0.837450	−	0.546514i	$-0.184045\pi$
$499$	4.64880e9	1.67490	0.837450	+	0.546514i	$0.184045\pi$
$500$	−1.04771e9	−0.374839
$501$	9.44334e9	3.35501
$502$	1.25225e9	0.441803
$503$	−5.35012e9	−1.87446	−0.937228	−	0.348716i	$-0.886618\pi$
$503$	−5.35012e9	−1.87446	−0.937228	+	0.348716i	$0.886618\pi$
$504$	3.11057e8	0.108226
$505$	−2.24220e9	−0.774738
$506$	9.04248e7	0.0310285
$507$	2.23688e9	0.762281
$508$	−1.36146e9	−0.460768
$509$	2.75912e9	0.927383	0.463691	−	0.885997i	$-0.346525\pi$
$509$	2.75912e9	0.927383	0.463691	+	0.885997i	$0.346525\pi$
$510$	1.50352e9	0.501895
$511$	1.14046e8	0.0378102
$512$	1.34218e8	0.0441942
$513$	1.58408e9	0.518043
$514$	1.48512e9	0.482382
$515$	−8.67943e8	−0.280005
$516$	−3.49361e9	−1.11944
$517$	−7.27646e8	−0.231581
$518$	−5.29711e7	−0.0167450
$519$	3.95691e9	1.24243
$520$	−3.49732e8	−0.109075
$521$	−4.81094e9	−1.49038	−0.745191	−	0.666851i	$-0.767642\pi$
$521$	−4.81094e9	−1.49038	−0.745191	+	0.666851i	$0.767642\pi$
$522$	−9.15222e9	−2.81631
$523$	−1.61447e9	−0.493486	−0.246743	−	0.969081i	$-0.579360\pi$
$523$	−1.61447e9	−0.493486	−0.246743	+	0.969081i	$0.579360\pi$
$524$	1.21580e9	0.369148
$525$	7.03009e8	0.212033
$526$	4.07808e9	1.22181
$527$	1.34465e9	0.400196
$528$	−7.93906e8	−0.234720
$529$	−3.38158e9	−0.993174
$530$	7.85785e8	0.229265
$531$	−5.67768e9	−1.64566
$532$	−6.51494e7	−0.0187594
$533$	1.44804e9	0.414225
$534$	2.78569e9	0.791659
$535$	1.79304e9	0.506236
$536$	6.63469e8	0.186099
$537$	−1.63204e9	−0.454801
$538$	3.13933e9	0.869159
$539$	−1.89075e9	−0.520084
$540$	−1.48852e9	−0.406797
$541$	6.90904e9	1.87598	0.937988	−	0.346667i	$-0.112687\pi$
$541$	6.90904e9	1.87598	0.937988	+	0.346667i	$0.112687\pi$
$542$	−3.70947e9	−1.00072
$543$	−5.43893e9	−1.45785
$544$	−6.51519e8	−0.173512
$545$	−6.10353e7	−0.0161508
$546$	5.16498e8	0.135798
$547$	−4.45727e9	−1.16443	−0.582215	−	0.813035i	$-0.697814\pi$
$547$	−4.45727e9	−1.16443	−0.582215	+	0.813035i	$0.697814\pi$
$548$	3.62450e9	0.940841
$549$	−7.94389e9	−2.04894
$550$	−1.22013e9	−0.312706
$551$	1.91689e9	0.488165
$552$	−2.04065e8	−0.0516395
$553$	−6.17814e8	−0.155353
$554$	1.54458e9	0.385947
$555$	4.78792e8	0.118883
$556$	2.01673e9	0.497607
$557$	−1.21053e9	−0.296813	−0.148406	−	0.988926i	$-0.547414\pi$
$557$	−1.21053e9	−0.296813	−0.148406	+	0.988926i	$0.547414\pi$
$558$	−2.51448e9	−0.612672
$559$	−3.94474e9	−0.955162
$560$	6.12195e7	0.0147310
$561$	3.85377e9	0.921544
$562$	3.16764e9	0.752765
$563$	3.68621e9	0.870565	0.435282	−	0.900294i	$-0.356649\pi$
$563$	3.68621e9	0.870565	0.435282	+	0.900294i	$0.356649\pi$
$564$	1.64211e9	0.385411
$565$	−1.62644e9	−0.379374
$566$	−4.42269e9	−1.02525
$567$	8.69639e8	0.200354
$568$	−2.65484e8	−0.0607882
$569$	4.78409e9	1.08869	0.544347	−	0.838860i	$-0.316777\pi$
$569$	4.78409e9	1.08869	0.544347	+	0.838860i	$0.316777\pi$
$570$	5.88868e8	0.133185
$571$	4.52250e9	1.01661	0.508303	−	0.861178i	$-0.330273\pi$
$571$	4.52250e9	1.01661	0.508303	+	0.861178i	$0.330273\pi$
$572$	−8.96424e8	−0.200275
$573$	5.65959e9	1.25674
$574$	−2.53476e8	−0.0559429
$575$	−3.13621e8	−0.0687967
$576$	1.21833e9	0.265636
$577$	−3.92270e9	−0.850100	−0.425050	−	0.905170i	$-0.639743\pi$
$577$	−3.92270e9	−0.850100	−0.425050	+	0.905170i	$0.639743\pi$
$578$	−1.20113e8	−0.0258727
$579$	−7.71484e9	−1.65178
$580$	−1.80126e9	−0.383336
$581$	2.22075e8	0.0469768
$582$	−8.72100e9	−1.83373
$583$	2.01410e9	0.420961
$584$	4.46691e8	0.0928031
$585$	−3.17461e9	−0.655610
$586$	−6.67321e8	−0.136991
$587$	4.45656e9	0.909424	0.454712	−	0.890638i	$-0.349742\pi$
$587$	4.45656e9	0.909424	0.454712	+	0.890638i	$0.349742\pi$
$588$	4.26693e9	0.865556
$589$	5.26646e8	0.106198
$590$	−1.11743e9	−0.223996
$591$	−1.16918e10	−2.32984
$592$	−2.07475e8	−0.0410997
$593$	3.49353e9	0.687976	0.343988	−	0.938974i	$-0.388222\pi$
$593$	3.49353e9	0.687976	0.343988	+	0.938974i	$0.388222\pi$
$594$	−3.81535e9	−0.746932
$595$	−2.97171e8	−0.0578359
$596$	1.32203e7	0.00255787
$597$	−9.08513e9	−1.74752
$598$	−2.30416e8	−0.0440615
$599$	−2.49362e9	−0.474063	−0.237032	−	0.971502i	$-0.576175\pi$
$599$	−2.49362e9	−0.474063	−0.237032	+	0.971502i	$0.576175\pi$
$600$	2.75351e9	0.520424
$601$	1.04034e10	1.95486	0.977429	−	0.211262i	$-0.0677574\pi$
$601$	1.04034e10	1.95486	0.977429	+	0.211262i	$0.0677574\pi$
$602$	6.90514e8	0.128999
$603$	6.02249e9	1.11858
$604$	1.97123e9	0.364005
$605$	−1.59962e9	−0.293679
$606$	1.29698e10	2.36745
$607$	3.56887e9	0.647694	0.323847	−	0.946110i	$-0.395024\pi$
$607$	3.56887e9	0.647694	0.323847	+	0.946110i	$0.395024\pi$
$608$	−2.55174e8	−0.0460441
$609$	2.66018e9	0.477255
$610$	−1.56345e9	−0.278888
$611$	1.85415e9	0.328853
$612$	−5.91401e9	−1.04292
$613$	−5.03005e8	−0.0881984	−0.0440992	−	0.999027i	$-0.514042\pi$
$613$	−5.03005e8	−0.0881984	−0.0440992	+	0.999027i	$0.514042\pi$
$614$	6.79328e9	1.18438
$615$	2.29110e9	0.397174
$616$	1.56916e8	0.0270480
$617$	−1.25403e9	−0.214936	−0.107468	−	0.994209i	$-0.534274\pi$
$617$	−1.25403e9	−0.214936	−0.107468	+	0.994209i	$0.534274\pi$
$618$	5.02054e9	0.855639
$619$	−9.27046e9	−1.57103	−0.785514	−	0.618843i	$-0.787602\pi$
$619$	−9.27046e9	−1.57103	−0.785514	+	0.618843i	$0.787602\pi$
$620$	−4.94878e8	−0.0833926
$621$	−9.80694e8	−0.164329
$622$	2.50378e9	0.417186
$623$	−5.50593e8	−0.0912269
$624$	2.02300e9	0.333310
$625$	3.21045e9	0.526001
$626$	−2.94587e9	−0.479958
$627$	1.50937e9	0.244545
$628$	3.54472e9	0.571114
$629$	1.00712e9	0.161363
$630$	5.55706e8	0.0885429
$631$	1.19395e9	0.189184	0.0945918	−	0.995516i	$-0.469845\pi$
$631$	1.19395e9	0.189184	0.0945918	+	0.995516i	$0.469845\pi$
$632$	−2.41982e9	−0.381306
$633$	−1.40889e10	−2.20782
$634$	6.56497e9	1.02311
$635$	−2.43227e9	−0.376967
$636$	−4.54530e9	−0.700589
$637$	4.81792e9	0.738536
$638$	−4.61695e9	−0.703854
$639$	−2.40987e9	−0.365377
$640$	2.39782e8	0.0361565
$641$	−6.01299e9	−0.901752	−0.450876	−	0.892587i	$-0.648888\pi$
$641$	−6.01299e9	−0.901752	−0.450876	+	0.892587i	$0.648888\pi$
$642$	−1.03717e10	−1.54695
$643$	−8.03723e9	−1.19225	−0.596126	−	0.802891i	$-0.703294\pi$
$643$	−8.03723e9	−1.19225	−0.596126	+	0.802891i	$0.703294\pi$
$644$	4.03337e7	0.00595069
$645$	−6.24137e9	−0.915843
$646$	1.23866e9	0.180775
$647$	−2.66241e9	−0.386465	−0.193233	−	0.981153i	$-0.561897\pi$
$647$	−2.66241e9	−0.386465	−0.193233	+	0.981153i	$0.561897\pi$
$648$	3.40616e9	0.491759
$649$	−2.86417e9	−0.411285
$650$	3.10907e9	0.444052
$651$	7.30856e8	0.103824
$652$	−6.48775e9	−0.916701
$653$	2.98529e9	0.419557	0.209779	−	0.977749i	$-0.432726\pi$
$653$	2.98529e9	0.419557	0.209779	+	0.977749i	$0.432726\pi$
$654$	3.53053e8	0.0493535
$655$	2.17203e9	0.302010
$656$	−9.92801e8	−0.137309
$657$	4.05474e9	0.557807
$658$	−3.24564e8	−0.0444129
$659$	−6.82535e9	−0.929022	−0.464511	−	0.885567i	$-0.653770\pi$
$659$	−6.82535e9	−0.929022	−0.464511	+	0.885567i	$0.653770\pi$
$660$	−1.41832e9	−0.192031
$661$	−5.93750e9	−0.799648	−0.399824	−	0.916592i	$-0.630929\pi$
$661$	−5.93750e9	−0.799648	−0.399824	+	0.916592i	$0.630929\pi$
$662$	2.49353e8	0.0334050
$663$	−9.82001e9	−1.30862
$664$	8.69813e8	0.115302
$665$	−1.16390e8	−0.0153476
$666$	−1.88330e9	−0.247036
$667$	−1.18674e9	−0.154851
$668$	−7.31055e9	−0.948926
$669$	−4.66442e9	−0.602290
$670$	1.18530e9	0.152253
$671$	−4.00739e9	−0.512074
$672$	−3.54119e8	−0.0450150
$673$	2.34747e9	0.296857	0.148428	−	0.988923i	$-0.452579\pi$
$673$	2.34747e9	0.296857	0.148428	+	0.988923i	$0.452579\pi$
$674$	−1.05382e10	−1.32574
$675$	1.32328e10	1.65611
$676$	−1.73168e9	−0.215603
$677$	2.16956e9	0.268727	0.134363	−	0.990932i	$-0.457101\pi$
$677$	2.16956e9	0.268727	0.134363	+	0.990932i	$0.457101\pi$
$678$	9.40798e9	1.15929
$679$	1.72371e9	0.211310
$680$	−1.16395e9	−0.141955
$681$	1.51188e10	1.83443
$682$	−1.26846e9	−0.153120
$683$	2.03106e9	0.243922	0.121961	−	0.992535i	$-0.461082\pi$
$683$	2.03106e9	0.243922	0.121961	+	0.992535i	$0.461082\pi$
$684$	−2.31628e9	−0.276755
$685$	6.47522e9	0.769728
$686$	−1.70459e9	−0.201598
$687$	−1.60303e9	−0.188622
$688$	2.70457e9	0.316620
$689$	−5.13224e9	−0.597778
$690$	−3.64565e8	−0.0422477
$691$	1.81275e9	0.209009	0.104504	−	0.994524i	$-0.466674\pi$
$691$	1.81275e9	0.209009	0.104504	+	0.994524i	$0.466674\pi$
$692$	−3.06324e9	−0.351407
$693$	1.42437e9	0.162576
$694$	8.14604e9	0.925099
$695$	3.60292e9	0.407106
$696$	1.04193e10	1.17140
$697$	4.81925e9	0.539094
$698$	−8.17227e9	−0.909597
$699$	6.32617e9	0.700601
$700$	−5.44234e8	−0.0599711
$701$	1.39158e10	1.52580	0.762898	−	0.646519i	$-0.223776\pi$
$701$	1.39158e10	1.52580	0.762898	+	0.646519i	$0.223776\pi$
$702$	9.72209e9	1.06067
$703$	3.94450e8	0.0428201
$704$	6.14602e8	0.0663880
$705$	2.93364e9	0.315316
$706$	9.18761e8	0.0982621
$707$	−2.56350e9	−0.272813
$708$	6.46369e9	0.684486
$709$	7.10889e9	0.749100	0.374550	−	0.927207i	$-0.377797\pi$
$709$	7.10889e9	0.749100	0.374550	+	0.927207i	$0.377797\pi$
$710$	−4.74291e8	−0.0497325
$711$	−2.19654e10	−2.29190
$712$	−2.15654e9	−0.223912
$713$	−3.26044e8	−0.0336870
$714$	1.71896e9	0.176735
$715$	−1.60147e9	−0.163851
$716$	1.26345e9	0.128635
$717$	−2.85407e10	−2.89166
$718$	9.23032e9	0.930639
$719$	−1.34368e10	−1.34818	−0.674088	−	0.738651i	$-0.735463\pi$
$719$	−1.34368e10	−1.34818	−0.674088	+	0.738651i	$0.735463\pi$
$720$	2.17656e9	0.217324
$721$	−9.92314e8	−0.0985997
$722$	−6.66584e9	−0.659135
$723$	2.15857e10	2.12414
$724$	4.21054e9	0.412338
$725$	1.60130e10	1.56059
$726$	9.25285e9	0.897423
$727$	1.28066e10	1.23612	0.618062	−	0.786129i	$-0.287918\pi$
$727$	1.28066e10	1.23612	0.618062	+	0.786129i	$0.287918\pi$
$728$	−3.99847e8	−0.0384091
$729$	−5.85987e9	−0.560198
$730$	7.98020e8	0.0759248
$731$	−1.31285e10	−1.24310
$732$	9.04364e9	0.852226
$733$	−1.30841e10	−1.22710	−0.613549	−	0.789657i	$-0.710259\pi$
$733$	−1.30841e10	−1.22710	−0.613549	+	0.789657i	$0.710259\pi$
$734$	−5.95021e8	−0.0555387
$735$	7.62293e9	0.708135
$736$	1.57977e8	0.0146057
$737$	3.03812e9	0.279556
$738$	−9.01192e9	−0.825316
$739$	−1.06618e10	−0.971800	−0.485900	−	0.874014i	$-0.661508\pi$
$739$	−1.06618e10	−0.971800	−0.485900	+	0.874014i	$0.661508\pi$
$740$	−3.70656e8	−0.0336248
$741$	−3.84611e9	−0.347262
$742$	8.98383e8	0.0807324
$743$	4.71447e9	0.421670	0.210835	−	0.977522i	$-0.432382\pi$
$743$	4.71447e9	0.421670	0.210835	+	0.977522i	$0.432382\pi$
$744$	2.86258e9	0.254831
$745$	2.36182e7	0.00209267
$746$	−9.76715e9	−0.861354
$747$	7.89553e9	0.693042
$748$	−2.98340e9	−0.260648
$749$	2.04998e9	0.178264
$750$	1.08269e10	0.937110
$751$	1.44861e10	1.24799	0.623996	−	0.781427i	$-0.285508\pi$
$751$	1.44861e10	1.24799	0.623996	+	0.781427i	$0.285508\pi$
$752$	−1.27124e9	−0.109009
$753$	−1.29407e10	−1.10452
$754$	1.17647e10	0.999496
$755$	3.52162e9	0.297802
$756$	−1.70182e9	−0.143248
$757$	1.05477e10	0.883737	0.441869	−	0.897080i	$-0.354316\pi$
$757$	1.05477e10	0.883737	0.441869	+	0.897080i	$0.354316\pi$
$758$	−8.79220e9	−0.733255
$759$	−9.34443e8	−0.0775723
$760$	−4.55872e8	−0.0376699
$761$	1.75003e9	0.143946	0.0719730	−	0.997407i	$-0.477070\pi$
$761$	1.75003e9	0.143946	0.0719730	+	0.997407i	$0.477070\pi$
$762$	1.40693e10	1.15194
$763$	−6.97813e7	−0.00568726
$764$	−4.38137e9	−0.355454
$765$	−1.05655e10	−0.853244
$766$	−4.53722e9	−0.364745
$767$	7.29835e9	0.584038
$768$	−1.38700e9	−0.110487
$769$	9.57155e8	0.0758997	0.0379498	−	0.999280i	$-0.487917\pi$
$769$	9.57155e8	0.0758997	0.0379498	+	0.999280i	$0.487917\pi$
$770$	2.80333e8	0.0221287
$771$	−1.53471e10	−1.20597
$772$	5.97244e9	0.467187
$773$	6.52807e9	0.508343	0.254171	−	0.967159i	$-0.418197\pi$
$773$	6.52807e9	0.508343	0.254171	+	0.967159i	$0.418197\pi$
$774$	2.45501e10	1.90310
$775$	4.39940e9	0.339498
$776$	6.75135e9	0.518651
$777$	5.47400e8	0.0418631
$778$	−6.32701e9	−0.481693
$779$	1.88751e9	0.143056
$780$	3.61411e9	0.272690
$781$	−1.21569e9	−0.0913154
$782$	−7.66850e8	−0.0573439
$783$	5.00727e10	3.72765
$784$	−3.30324e9	−0.244813
$785$	6.33268e9	0.467244
$786$	−1.25639e10	−0.922884
$787$	1.10475e10	0.807889	0.403944	−	0.914784i	$-0.367639\pi$
$787$	1.10475e10	0.807889	0.403944	+	0.914784i	$0.367639\pi$
$788$	9.05123e9	0.658970
$789$	−4.21426e10	−3.05458
$790$	−4.32305e9	−0.311957
$791$	−1.85950e9	−0.133591
$792$	5.57891e9	0.399035
$793$	1.02115e10	0.727162
$794$	−1.12547e10	−0.797924
$795$	−8.12024e9	−0.573171
$796$	7.03325e9	0.494265
$797$	−1.85828e10	−1.30019	−0.650095	−	0.759853i	$-0.725271\pi$
$797$	−1.85828e10	−1.30019	−0.650095	+	0.759853i	$0.725271\pi$
$798$	6.73249e8	0.0468992
$799$	6.17082e9	0.427986
$800$	−2.13163e9	−0.147196
$801$	−1.95755e10	−1.34586
$802$	−1.66317e10	−1.13848
$803$	2.04546e9	0.139408
$804$	−6.85624e9	−0.465254
$805$	7.20566e7	0.00486842
$806$	3.23223e9	0.217435
$807$	−3.24416e10	−2.17293
$808$	−1.00406e10	−0.669606
$809$	−9.21373e9	−0.611809	−0.305904	−	0.952062i	$-0.598959\pi$
$809$	−9.21373e9	−0.611809	−0.305904	+	0.952062i	$0.598959\pi$
$810$	6.08515e9	0.402322
$811$	−5.90313e8	−0.0388606	−0.0194303	−	0.999811i	$-0.506185\pi$
$811$	−5.90313e8	−0.0388606	−0.0194303	+	0.999811i	$0.506185\pi$
$812$	−2.05937e9	−0.134986
$813$	3.83334e10	2.50185
$814$	−9.50056e8	−0.0617396
$815$	−1.15904e10	−0.749978
$816$	6.73275e9	0.433787
$817$	−5.14192e9	−0.329874
$818$	−1.08958e9	−0.0696019
$819$	−3.62952e9	−0.230864
$820$	−1.77365e9	−0.112336
$821$	4.22037e9	0.266164	0.133082	−	0.991105i	$-0.457513\pi$
$821$	4.22037e9	0.266164	0.133082	+	0.991105i	$0.457513\pi$
$822$	−3.74553e10	−2.35214
$823$	3.49867e8	0.0218778	0.0109389	−	0.999940i	$-0.496518\pi$
$823$	3.49867e8	0.0218778	0.0109389	+	0.999940i	$0.496518\pi$
$824$	−3.88665e9	−0.242008
$825$	1.26087e10	0.781775
$826$	−1.27755e9	−0.0788768
$827$	2.50807e10	1.54195	0.770976	−	0.636864i	$-0.219769\pi$
$827$	2.50807e10	1.54195	0.770976	+	0.636864i	$0.219769\pi$
$828$	1.43400e9	0.0877896
$829$	−1.89801e10	−1.15706	−0.578532	−	0.815660i	$-0.696374\pi$
$829$	−1.89801e10	−1.15706	−0.578532	+	0.815660i	$0.696374\pi$
$830$	1.55393e9	0.0943320
$831$	−1.59616e10	−0.964880
$832$	−1.56610e9	−0.0942731
$833$	1.60346e10	0.961169
$834$	−2.08408e10	−1.24404
$835$	−1.30604e10	−0.776343
$836$	−1.16848e9	−0.0691669
$837$	1.37570e10	0.810930
$838$	6.96599e9	0.408911
$839$	−8.08351e9	−0.472534	−0.236267	−	0.971688i	$-0.575924\pi$
$839$	−8.08351e9	−0.472534	−0.236267	+	0.971688i	$0.575924\pi$
$840$	−6.32638e8	−0.0368280
$841$	4.33431e10	2.51266
$842$	−1.43186e10	−0.826627
$843$	−3.27342e10	−1.88194
$844$	1.09069e10	0.624458
$845$	−3.09367e9	−0.176390
$846$	−1.15394e10	−0.655217
$847$	−1.82883e9	−0.103415
$848$	3.51874e9	0.198154
$849$	4.57037e10	2.56315
$850$	1.03473e10	0.577912
$851$	−2.44202e8	−0.0135830
$852$	2.74349e9	0.151973
$853$	7.31648e9	0.403627	0.201814	−	0.979424i	$-0.435316\pi$
$853$	7.31648e9	0.403627	0.201814	+	0.979424i	$0.435316\pi$
$854$	−1.78748e9	−0.0982063
$855$	−4.13807e9	−0.226421
$856$	8.02925e9	0.437539
$857$	1.69375e10	0.919214	0.459607	−	0.888122i	$-0.347990\pi$
$857$	1.69375e10	0.919214	0.459607	+	0.888122i	$0.347990\pi$
$858$	9.26358e9	0.500695
$859$	−3.12574e10	−1.68258	−0.841292	−	0.540581i	$-0.818204\pi$
$859$	−3.12574e10	−1.68258	−0.841292	+	0.540581i	$0.818204\pi$
$860$	4.83175e9	0.259036
$861$	2.61940e9	0.139859
$862$	−1.94895e10	−1.03640
$863$	−1.82116e10	−0.964517	−0.482258	−	0.876029i	$-0.660183\pi$
$863$	−1.82116e10	−0.964517	−0.482258	+	0.876029i	$0.660183\pi$
$864$	−6.66561e9	−0.351594
$865$	−5.47252e9	−0.287495
$866$	1.28065e9	0.0670065
$867$	1.24124e9	0.0646827
$868$	−5.65792e8	−0.0293655
$869$	−1.10807e10	−0.572794
$870$	1.86141e10	0.958353
$871$	−7.74159e9	−0.396978
$872$	−2.73316e8	−0.0139591
$873$	6.12839e10	3.11743
$874$	−3.00345e8	−0.0152170
$875$	−2.13995e9	−0.107988
$876$	−4.61608e9	−0.232011
$877$	−4.59540e9	−0.230051	−0.115026	−	0.993363i	$-0.536695\pi$
$877$	−4.59540e9	−0.230051	−0.115026	+	0.993363i	$0.536695\pi$
$878$	−2.22679e10	−1.11032
$879$	6.89604e9	0.342483
$880$	1.09799e9	0.0543138
$881$	2.03239e10	1.00136	0.500680	−	0.865632i	$-0.333083\pi$
$881$	2.03239e10	1.00136	0.500680	+	0.865632i	$0.333083\pi$
$882$	−2.99844e10	−1.47148
$883$	3.32637e10	1.62595	0.812976	−	0.582297i	$-0.197846\pi$
$883$	3.32637e10	1.62595	0.812976	+	0.582297i	$0.197846\pi$
$884$	7.60215e9	0.370129
$885$	1.15475e10	0.559997
$886$	−1.84168e10	−0.889605
$887$	−8.51025e8	−0.0409458	−0.0204729	−	0.999790i	$-0.506517\pi$
$887$	−8.51025e8	−0.0409458	−0.0204729	+	0.999790i	$0.506517\pi$
$888$	2.14403e9	0.102751
$889$	−2.78080e9	−0.132744
$890$	−3.85268e9	−0.183188
$891$	1.55973e10	0.738715
$892$	3.61095e9	0.170351
$893$	2.41687e9	0.113572
$894$	−1.36617e8	−0.00639477
$895$	2.25716e9	0.105240
$896$	2.74141e8	0.0127320
$897$	2.38111e9	0.110155
$898$	−1.32032e10	−0.608431
$899$	1.66473e10	0.764161
$900$	−1.93494e10	−0.884744
$901$	−1.70807e10	−0.777979
$902$	−4.54617e9	−0.206264
$903$	−7.13572e9	−0.322501
$904$	−7.28318e9	−0.327893
$905$	7.52219e9	0.337345
$906$	−2.03705e10	−0.910024
$907$	−2.88263e10	−1.28282	−0.641408	−	0.767200i	$-0.721649\pi$
$907$	−2.88263e10	−1.28282	−0.641408	+	0.767200i	$0.721649\pi$
$908$	−1.17042e10	−0.518848
$909$	−9.11411e10	−4.02477
$910$	−7.14331e8	−0.0314235
$911$	−1.58607e10	−0.695039	−0.347519	−	0.937673i	$-0.612976\pi$
$911$	−1.58607e10	−0.695039	−0.347519	+	0.937673i	$0.612976\pi$
$912$	2.63695e9	0.115112
$913$	3.98300e9	0.173206
$914$	2.22920e9	0.0965691
$915$	1.61566e10	0.697229
$916$	1.24099e9	0.0533498
$917$	2.48327e9	0.106349
$918$	3.23562e10	1.38041
$919$	2.56364e9	0.108956	0.0544782	−	0.998515i	$-0.482650\pi$
$919$	2.56364e9	0.108956	0.0544782	+	0.998515i	$0.482650\pi$
$920$	2.82228e8	0.0119493
$921$	−7.02013e10	−2.96099
$922$	2.80694e10	1.17944
$923$	3.09776e9	0.129671
$924$	−1.62156e9	−0.0676210
$925$	3.29508e9	0.136890
$926$	−7.78316e9	−0.322120
$927$	−3.52801e10	−1.45463
$928$	−8.06605e9	−0.331317
$929$	3.94497e10	1.61431	0.807157	−	0.590336i	$-0.201005\pi$
$929$	3.94497e10	1.61431	0.807157	+	0.590336i	$0.201005\pi$
$930$	5.11404e9	0.208484
$931$	6.28010e9	0.255060
$932$	−4.89740e9	−0.198157
$933$	−2.58739e10	−1.04298
$934$	1.06207e10	0.426520
$935$	−5.32987e9	−0.213244
$936$	−1.42159e10	−0.566643
$937$	3.28786e9	0.130564	0.0652822	−	0.997867i	$-0.479205\pi$
$937$	3.28786e9	0.130564	0.0652822	+	0.997867i	$0.479205\pi$
$938$	1.35514e9	0.0536136
$939$	3.04424e10	1.19991
$940$	−2.27108e9	−0.0891835
$941$	1.85752e9	0.0726724	0.0363362	−	0.999340i	$-0.488431\pi$
$941$	1.85752e9	0.0726724	0.0363362	+	0.999340i	$0.488431\pi$
$942$	−3.66308e10	−1.42780
$943$	−1.16855e9	−0.0453790
$944$	−5.00386e9	−0.193599
$945$	−3.04033e9	−0.117195
$946$	1.23846e10	0.475624
$947$	1.06515e10	0.407556	0.203778	−	0.979017i	$-0.434678\pi$
$947$	1.06515e10	0.407556	0.203778	+	0.979017i	$0.434678\pi$
$948$	2.50063e10	0.953279
$949$	−5.21215e9	−0.197964
$950$	4.05264e9	0.153358
$951$	−6.78419e10	−2.55780
$952$	−1.33073e9	−0.0499875
$953$	−5.95593e9	−0.222907	−0.111454	−	0.993770i	$-0.535551\pi$
$953$	−5.95593e9	−0.222907	−0.111454	+	0.993770i	$0.535551\pi$
$954$	3.19406e10	1.19103
$955$	−7.82737e9	−0.290807
$956$	2.20948e10	0.817875
$957$	4.77112e10	1.75966
$958$	3.37412e10	1.23988
$959$	7.40308e9	0.271049
$960$	−2.47789e9	−0.0903924
$961$	−2.29389e10	−0.833761
$962$	2.42089e9	0.0876722
$963$	7.28837e10	2.62989
$964$	−1.67106e10	−0.600789
$965$	1.06698e10	0.382219
$966$	−4.16805e8	−0.0148769
$967$	−1.98986e10	−0.707669	−0.353834	−	0.935308i	$-0.615122\pi$
$967$	−1.98986e10	−0.707669	−0.353834	+	0.935308i	$0.615122\pi$
$968$	−7.16308e9	−0.253826
$969$	−1.28003e10	−0.451945
$970$	1.20614e10	0.424322
$971$	4.28048e10	1.50046	0.750231	−	0.661176i	$-0.229942\pi$
$971$	4.28048e10	1.50046	0.750231	+	0.661176i	$0.229942\pi$
$972$	−6.72696e9	−0.234956
$973$	4.11920e9	0.143357
$974$	−1.09707e10	−0.380432
$975$	−3.21289e10	−1.11015
$976$	−7.00113e9	−0.241042
$977$	−3.09752e10	−1.06263	−0.531316	−	0.847174i	$-0.678302\pi$
$977$	−3.09752e10	−1.06263	−0.531316	+	0.847174i	$0.678302\pi$
$978$	6.70439e10	2.29178
$979$	−9.87509e9	−0.336358
$980$	−5.90128e9	−0.200288
$981$	−2.48096e9	−0.0839032
$982$	6.60470e9	0.222568
$983$	−1.77744e10	−0.596839	−0.298420	−	0.954435i	$-0.596459\pi$
$983$	−1.77744e10	−0.596839	−0.298420	+	0.954435i	$0.596459\pi$
$984$	1.02595e10	0.343277
$985$	1.61701e10	0.539122
$986$	3.91542e10	1.30080
$987$	3.35402e9	0.111034
$988$	2.97746e9	0.0982193
$989$	3.18333e9	0.104639
$990$	9.96679e9	0.326462
$991$	−5.34227e10	−1.74369	−0.871843	−	0.489786i	$-0.837075\pi$
$991$	−5.34227e10	−1.74369	−0.871843	+	0.489786i	$0.837075\pi$
$992$	−2.21606e9	−0.0720761
$993$	−2.57679e9	−0.0835136
$994$	−5.42254e8	−0.0175126
$995$	1.25650e10	0.404372
$996$	−8.98859e9	−0.288260
$997$	1.20062e10	0.383682	0.191841	−	0.981426i	$-0.438554\pi$
$997$	1.20062e10	0.383682	0.191841	+	0.981426i	$0.438554\pi$
$998$	3.71904e10	1.18433
$999$	1.03037e10	0.326976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.a.b.1.1	✓	4
4.3	odd	2		592.8.a.a.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.a.b.1.1	✓	4	1.1	even	1	trivial
592.8.a.a.1.4		4	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)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -82.6714 q^{3} +64.0000 q^{4} +114.337 q^{5} -661.371 q^{6} +130.721 q^{7} +512.000 q^{8} +4647.56 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -82.6714 q^{3} +64.0000 q^{4} +114.337 q^{5} -661.371 q^{6} +130.721 q^{7} +512.000 q^{8} +4647.56 q^{9} +914.695 q^{10} +2344.52 q^{11} -5290.97 q^{12} -5974.20 q^{13} +1045.76 q^{14} -9452.39 q^{15} +4096.00 q^{16} -19882.8 q^{17} +37180.5 q^{18} -7787.29 q^{19} +7317.56 q^{20} -10806.9 q^{21} +18756.2 q^{22} +4821.07 q^{23} -42327.8 q^{24} -65052.1 q^{25} -47793.6 q^{26} -203418. q^{27} +8366.12 q^{28} -246156. q^{29} -75619.1 q^{30} -67628.9 q^{31} +32768.0 q^{32} -193825. q^{33} -159062. q^{34} +14946.2 q^{35} +297444. q^{36} -50653.0 q^{37} -62298.3 q^{38} +493895. q^{39} +58540.4 q^{40} -242383. q^{41} -86454.9 q^{42} +660296. q^{43} +150049. q^{44} +531388. q^{45} +38568.6 q^{46} -310360. q^{47} -338622. q^{48} -806455. q^{49} -520417. q^{50} +1.64374e6 q^{51} -382349. q^{52} +859068. q^{53} -1.62735e6 q^{54} +268065. q^{55} +66929.0 q^{56} +643786. q^{57} -1.96925e6 q^{58} -1.22165e6 q^{59} -604953. q^{60} -1.70926e6 q^{61} -541031. q^{62} +607532. q^{63} +262144. q^{64} -683071. q^{65} -1.55060e6 q^{66} +1.29584e6 q^{67} -1.27250e6 q^{68} -398565. q^{69} +119569. q^{70} -518524. q^{71} +2.37955e6 q^{72} +872444. q^{73} -405224. q^{74} +5.37795e6 q^{75} -498387. q^{76} +306477. q^{77} +3.95116e6 q^{78} -4.72622e6 q^{79} +468324. q^{80} +6.65266e6 q^{81} -1.93906e6 q^{82} +1.69885e6 q^{83} -691639. q^{84} -2.27333e6 q^{85} +5.28237e6 q^{86} +2.03501e7 q^{87} +1.20039e6 q^{88} -4.21199e6 q^{89} +4.25110e6 q^{90} -780951. q^{91} +308549. q^{92} +5.59098e6 q^{93} -2.48288e6 q^{94} -890374. q^{95} -2.70898e6 q^{96} +1.31862e7 q^{97} -6.45164e6 q^{98} +1.08963e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} - 41 q^{3} + 256 q^{4} - 363 q^{5} - 328 q^{6} - 774 q^{7} + 2048 q^{8} - 1079 q^{9}+O(q^{10}) \) 4 * q + 32 * q^2 - 41 * q^3 + 256 * q^4 - 363 * q^5 - 328 * q^6 - 774 * q^7 + 2048 * q^8 - 1079 * q^9	\( 4 q + 32 q^{2} - 41 q^{3} + 256 q^{4} - 363 q^{5} - 328 q^{6} - 774 q^{7} + 2048 q^{8} - 1079 q^{9} - 2904 q^{10} - 309 q^{11} - 2624 q^{12} - 20827 q^{13} - 6192 q^{14} - 22940 q^{15} + 16384 q^{16} - 48756 q^{17} - 8632 q^{18} - 69068 q^{19} - 23232 q^{20} - 640 q^{21} - 2472 q^{22} - 50237 q^{23} - 20992 q^{24} - 3581 q^{25} - 166616 q^{26} - 368414 q^{27} - 49536 q^{28} - 205195 q^{29} - 183520 q^{30} - 172283 q^{31} + 131072 q^{32} - 205234 q^{33} - 390048 q^{34} - 584964 q^{35} - 69056 q^{36} - 202612 q^{37} - 552544 q^{38} + 329055 q^{39} - 185856 q^{40} - 1018945 q^{41} - 5120 q^{42} + 1263046 q^{43} - 19776 q^{44} + 1279606 q^{45} - 401896 q^{46} - 420930 q^{47} - 167936 q^{48} - 482790 q^{49} - 28648 q^{50} + 728262 q^{51} - 1332928 q^{52} + 2051230 q^{53} - 2947312 q^{54} - 1442891 q^{55} - 396288 q^{56} - 926198 q^{57} - 1641560 q^{58} + 357914 q^{59} - 1468160 q^{60} - 2507513 q^{61} - 1378264 q^{62} + 2879054 q^{63} + 1048576 q^{64} + 3097954 q^{65} - 1641872 q^{66} + 586879 q^{67} - 3120384 q^{68} - 252895 q^{69} - 4679712 q^{70} - 130272 q^{71} - 552448 q^{72} + 3517417 q^{73} - 1620896 q^{74} + 8154290 q^{75} - 4420352 q^{76} + 8777590 q^{77} + 2632440 q^{78} + 3790171 q^{79} - 1486848 q^{80} + 15888376 q^{81} - 8151560 q^{82} + 12973460 q^{83} - 40960 q^{84} + 14870322 q^{85} + 10104368 q^{86} + 23063695 q^{87} - 158208 q^{88} + 18852848 q^{89} + 10236848 q^{90} - 2046622 q^{91} - 3215168 q^{92} + 4005314 q^{93} - 3367440 q^{94} + 30367150 q^{95} - 1343488 q^{96} + 14580104 q^{97} - 3862320 q^{98} + 16949258 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 - 41 * q^3 + 256 * q^4 - 363 * q^5 - 328 * q^6 - 774 * q^7 + 2048 * q^8 - 1079 * q^9 - 2904 * q^10 - 309 * q^11 - 2624 * q^12 - 20827 * q^13 - 6192 * q^14 - 22940 * q^15 + 16384 * q^16 - 48756 * q^17 - 8632 * q^18 - 69068 * q^19 - 23232 * q^20 - 640 * q^21 - 2472 * q^22 - 50237 * q^23 - 20992 * q^24 - 3581 * q^25 - 166616 * q^26 - 368414 * q^27 - 49536 * q^28 - 205195 * q^29 - 183520 * q^30 - 172283 * q^31 + 131072 * q^32 - 205234 * q^33 - 390048 * q^34 - 584964 * q^35 - 69056 * q^36 - 202612 * q^37 - 552544 * q^38 + 329055 * q^39 - 185856 * q^40 - 1018945 * q^41 - 5120 * q^42 + 1263046 * q^43 - 19776 * q^44 + 1279606 * q^45 - 401896 * q^46 - 420930 * q^47 - 167936 * q^48 - 482790 * q^49 - 28648 * q^50 + 728262 * q^51 - 1332928 * q^52 + 2051230 * q^53 - 2947312 * q^54 - 1442891 * q^55 - 396288 * q^56 - 926198 * q^57 - 1641560 * q^58 + 357914 * q^59 - 1468160 * q^60 - 2507513 * q^61 - 1378264 * q^62 + 2879054 * q^63 + 1048576 * q^64 + 3097954 * q^65 - 1641872 * q^66 + 586879 * q^67 - 3120384 * q^68 - 252895 * q^69 - 4679712 * q^70 - 130272 * q^71 - 552448 * q^72 + 3517417 * q^73 - 1620896 * q^74 + 8154290 * q^75 - 4420352 * q^76 + 8777590 * q^77 + 2632440 * q^78 + 3790171 * q^79 - 1486848 * q^80 + 15888376 * q^81 - 8151560 * q^82 + 12973460 * q^83 - 40960 * q^84 + 14870322 * q^85 + 10104368 * q^86 + 23063695 * q^87 - 158208 * q^88 + 18852848 * q^89 + 10236848 * q^90 - 2046622 * q^91 - 3215168 * q^92 + 4005314 * q^93 - 3367440 * q^94 + 30367150 * q^95 - 1343488 * q^96 + 14580104 * q^97 - 3862320 * q^98 + 16949258 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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