LMFDB - Embedded newform 10.16.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,16,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	10.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:	$14.2693505100$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{239569}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 59892 $ x^2 - x - 59892
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$245.229$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+128.000 q^{2} -5816.58 q^{3} +16384.0 q^{4} +78125.0 q^{5} -744522. q^{6} -2.56287e6 q^{7} +2.09715e6 q^{8} +1.94837e7 q^{9} +1.00000e7 q^{10} +1.14540e8 q^{11} -9.52988e7 q^{12} +2.84387e8 q^{13} -3.28048e8 q^{14} -4.54420e8 q^{15} +2.68435e8 q^{16} +7.76594e8 q^{17} +2.49391e9 q^{18} +3.74029e9 q^{19} +1.28000e9 q^{20} +1.49072e10 q^{21} +1.46612e10 q^{22} -2.76376e10 q^{23} -1.21982e10 q^{24} +6.10352e9 q^{25} +3.64016e10 q^{26} -2.98668e10 q^{27} -4.19901e10 q^{28} +1.59731e10 q^{29} -5.81658e10 q^{30} +2.79408e9 q^{31} +3.43597e10 q^{32} -6.66233e11 q^{33} +9.94040e10 q^{34} -2.00224e11 q^{35} +3.19221e11 q^{36} +6.85921e11 q^{37} +4.78758e11 q^{38} -1.65416e12 q^{39} +1.63840e11 q^{40} +9.09210e11 q^{41} +1.90812e12 q^{42} -4.11856e11 q^{43} +1.87663e12 q^{44} +1.52216e12 q^{45} -3.53762e12 q^{46} -4.29904e11 q^{47} -1.56138e12 q^{48} +1.82076e12 q^{49} +7.81250e11 q^{50} -4.51712e12 q^{51} +4.65940e12 q^{52} +1.11312e13 q^{53} -3.82295e12 q^{54} +8.94847e12 q^{55} -5.37473e12 q^{56} -2.17557e13 q^{57} +2.04456e12 q^{58} -2.98542e13 q^{59} -7.44522e12 q^{60} +1.56049e13 q^{61} +3.57642e11 q^{62} -4.99342e13 q^{63} +4.39805e12 q^{64} +2.22178e13 q^{65} -8.52778e13 q^{66} +6.47436e13 q^{67} +1.27237e13 q^{68} +1.60757e14 q^{69} -2.56287e13 q^{70} +1.38360e14 q^{71} +4.08602e13 q^{72} -5.76496e13 q^{73} +8.77978e13 q^{74} -3.55016e13 q^{75} +6.12810e13 q^{76} -2.93552e14 q^{77} -2.11733e14 q^{78} +1.85835e14 q^{79} +2.09715e13 q^{80} -1.05847e14 q^{81} +1.16379e14 q^{82} -3.07642e14 q^{83} +2.44239e14 q^{84} +6.06714e13 q^{85} -5.27175e13 q^{86} -9.29088e13 q^{87} +2.40209e14 q^{88} -1.81716e14 q^{89} +1.94837e14 q^{90} -7.28848e14 q^{91} -4.52815e14 q^{92} -1.62520e13 q^{93} -5.50277e13 q^{94} +2.92211e14 q^{95} -1.99856e14 q^{96} -1.82237e14 q^{97} +2.33057e14 q^{98} +2.23167e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 256 q^{2} - 1844 q^{3} + 32768 q^{4} + 156250 q^{5} - 236032 q^{6} - 984932 q^{7} + 4194304 q^{8} + 20916154 q^{9} + 20000000 q^{10} + 111552144 q^{11} - 30212096 q^{12} + 289313596 q^{13} - 126071296 q^{14}+ \cdots + 22\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 256 * q^2 - 1844 * q^3 + 32768 * q^4 + 156250 * q^5 - 236032 * q^6 - 984932 * q^7 + 4194304 * q^8 + 20916154 * q^9 + 20000000 * q^10 + 111552144 * q^11 - 30212096 * q^12 + 289313596 * q^13 - 126071296 * q^14 - 144062500 * q^15 + 536870912 * q^16 + 1421739348 * q^17 + 2677267712 * q^18 + 6159406120 * q^19 + 2560000000 * q^20 + 21175644704 * q^21 + 14278674432 * q^22 - 4330165884 * q^23 - 3867148288 * q^24 + 12207031250 * q^25 + 37032140288 * q^26 - 81178356680 * q^27 - 16137125888 * q^28 - 164295941940 * q^29 - 18440000000 * q^30 - 282710965016 * q^31 + 68719476736 * q^32 - 678104159568 * q^33 + 181982636544 * q^34 - 76947812500 * q^35 + 342690267136 * q^36 + 790105159228 * q^37 + 788403983360 * q^38 - 1634590297912 * q^39 + 327680000000 * q^40 - 374717265276 * q^41 + 2710482522112 * q^42 - 923824433204 * q^43 + 1827670327296 * q^44 + 1634074531250 * q^45 - 554261233152 * q^46 + 4796717212428 * q^47 - 494994980864 * q^48 - 436909177374 * q^49 + 1562500000000 * q^50 - 1954230185256 * q^51 + 4740113956864 * q^52 - 2768921292084 * q^53 - 10390829655040 * q^54 + 8715011250000 * q^55 - 2065552113664 * q^56 - 12145610545840 * q^57 - 21029880568320 * q^58 - 20737233989880 * q^59 - 2360320000000 * q^60 + 577887725164 * q^61 - 36187003522048 * q^62 - 47673833661364 * q^63 + 8796093022208 * q^64 + 22602624687500 * q^65 - 86797332424704 * q^66 + 86553258077668 * q^67 + 23293777477632 * q^68 + 253347375370848 * q^69 - 9849320000000 * q^70 + 73838906689464 * q^71 + 43864354193408 * q^72 + 39973727021476 * q^73 + 101133460381184 * q^74 - 11254882812500 * q^75 + 100915709870080 * q^76 - 298267692171504 * q^77 - 209227558132736 * q^78 + 421665304874800 * q^79 + 41943040000000 * q^80 - 330240444620318 * q^81 - 47963809955328 * q^82 - 721146660038964 * q^83 + 346941762830336 * q^84 + 111073386562500 * q^85 - 118249527450112 * q^86 - 809041723785720 * q^87 + 233941801893888 * q^88 + 363712836623220 * q^89 + 209161540000000 * q^90 - 721074767062936 * q^91 - 70945437843456 * q^92 - 1150443201950848 * q^93 + 613979803190784 * q^94 + 481203603125000 * q^95 - 63359357550592 * q^96 + 289030099396948 * q^97 - 55924374703872 * q^98 + 2227387596150288 * q^99

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 $

$2$	128.000	0.707107
$2$	128.000	0.707107
$3$	−5816.58	−1.53553	−0.767765	−	0.640732i	$-0.778631\pi$
$3$	−5816.58	−1.53553	−0.767765	+	0.640732i	$0.778631\pi$
$4$	16384.0	0.500000
$5$	78125.0	0.447214
$5$	78125.0	0.447214
$6$	−744522.	−1.08578
$7$	−2.56287e6	−1.17623	−0.588114	−	0.808778i	$-0.700129\pi$
$7$	−2.56287e6	−1.17623	−0.588114	+	0.808778i	$0.700129\pi$
$8$	2.09715e6	0.353553
$9$	1.94837e7	1.35785
$10$	1.00000e7	0.316228
$11$	1.14540e8	1.77220	0.886102	−	0.463491i	$-0.153403\pi$
$11$	1.14540e8	1.77220	0.886102	+	0.463491i	$0.153403\pi$
$12$	−9.52988e7	−0.767765
$13$	2.84387e8	1.25700	0.628500	−	0.777810i	$-0.283669\pi$
$13$	2.84387e8	1.25700	0.628500	+	0.777810i	$0.283669\pi$
$14$	−3.28048e8	−0.831719
$15$	−4.54420e8	−0.686710
$16$	2.68435e8	0.250000
$17$	7.76594e8	0.459015	0.229508	−	0.973307i	$-0.426288\pi$
$17$	7.76594e8	0.459015	0.229508	+	0.973307i	$0.426288\pi$
$18$	2.49391e9	0.960146
$19$	3.74029e9	0.959962	0.479981	−	0.877279i	$-0.340644\pi$
$19$	3.74029e9	0.959962	0.479981	+	0.877279i	$0.340644\pi$
$20$	1.28000e9	0.223607
$21$	1.49072e10	1.80613
$22$	1.46612e10	1.25314
$23$	−2.76376e10	−1.69255	−0.846277	−	0.532744i	$-0.821161\pi$
$23$	−2.76376e10	−1.69255	−0.846277	+	0.532744i	$0.821161\pi$
$24$	−1.21982e10	−0.542892
$25$	6.10352e9	0.200000
$26$	3.64016e10	0.888833
$27$	−2.98668e10	−0.549491
$28$	−4.19901e10	−0.588114
$29$	1.59731e10	0.171951	0.0859754	−	0.996297i	$-0.472599\pi$
$29$	1.59731e10	0.171951	0.0859754	+	0.996297i	$0.472599\pi$
$30$	−5.81658e10	−0.485577
$31$	2.79408e9	0.0182400	0.00912002	−	0.999958i	$-0.497097\pi$
$31$	2.79408e9	0.0182400	0.00912002	+	0.999958i	$0.497097\pi$
$32$	3.43597e10	0.176777
$33$	−6.66233e11	−2.72127
$34$	9.94040e10	0.324573
$35$	−2.00224e11	−0.526025
$36$	3.19221e11	0.678926
$37$	6.85921e11	1.18785	0.593924	−	0.804521i	$-0.297578\pi$
$37$	6.85921e11	1.18785	0.593924	+	0.804521i	$0.297578\pi$
$38$	4.78758e11	0.678795
$39$	−1.65416e12	−1.93016
$40$	1.63840e11	0.158114
$41$	9.09210e11	0.729097	0.364549	−	0.931184i	$-0.381223\pi$
$41$	9.09210e11	0.729097	0.364549	+	0.931184i	$0.381223\pi$
$42$	1.90812e12	1.27713
$43$	−4.11856e11	−0.231064	−0.115532	−	0.993304i	$-0.536857\pi$
$43$	−4.11856e11	−0.231064	−0.115532	+	0.993304i	$0.536857\pi$
$44$	1.87663e12	0.886102
$45$	1.52216e12	0.607249
$46$	−3.53762e12	−1.19682
$47$	−4.29904e11	−0.123776	−0.0618881	−	0.998083i	$-0.519712\pi$
$47$	−4.29904e11	−0.123776	−0.0618881	+	0.998083i	$0.519712\pi$
$48$	−1.56138e12	−0.383882
$49$	1.82076e12	0.383514
$50$	7.81250e11	0.141421
$51$	−4.51712e12	−0.704832
$52$	4.65940e12	0.628500
$53$	1.11312e13	1.30159	0.650793	−	0.759255i	$-0.274437\pi$
$53$	1.11312e13	1.30159	0.650793	+	0.759255i	$0.274437\pi$
$54$	−3.82295e12	−0.388549
$55$	8.94847e12	0.792553
$56$	−5.37473e12	−0.415860
$57$	−2.17557e13	−1.47405
$58$	2.04456e12	0.121588
$59$	−2.98542e13	−1.56177	−0.780883	−	0.624678i	$-0.785230\pi$
$59$	−2.98542e13	−1.56177	−0.780883	+	0.624678i	$0.785230\pi$
$60$	−7.44522e12	−0.343355
$61$	1.56049e13	0.635750	0.317875	−	0.948133i	$-0.397031\pi$
$61$	1.56049e13	0.635750	0.317875	+	0.948133i	$0.397031\pi$
$62$	3.57642e11	0.0128977
$63$	−4.99342e13	−1.59714
$64$	4.39805e12	0.125000
$65$	2.22178e13	0.562147
$66$	−8.52778e13	−1.92423
$67$	6.47436e13	1.30508	0.652538	−	0.757756i	$-0.273704\pi$
$67$	6.47436e13	1.30508	0.652538	+	0.757756i	$0.273704\pi$
$68$	1.27237e13	0.229508
$69$	1.60757e14	2.59897
$70$	−2.56287e13	−0.371956
$71$	1.38360e14	1.80540	0.902700	−	0.430270i	$-0.141582\pi$
$71$	1.38360e14	1.80540	0.902700	+	0.430270i	$0.141582\pi$
$72$	4.08602e13	0.480073
$73$	−5.76496e13	−0.610766	−0.305383	−	0.952230i	$-0.598784\pi$
$73$	−5.76496e13	−0.610766	−0.305383	+	0.952230i	$0.598784\pi$
$74$	8.77978e13	0.839935
$75$	−3.55016e13	−0.307106
$76$	6.12810e13	0.479981
$77$	−2.93552e14	−2.08452
$78$	−2.11733e14	−1.36483
$79$	1.85835e14	1.08874	0.544370	−	0.838846i	$-0.316769\pi$
$79$	1.85835e14	1.08874	0.544370	+	0.838846i	$0.316769\pi$
$80$	2.09715e13	0.111803
$81$	−1.05847e14	−0.514091
$82$	1.16379e14	0.515550
$83$	−3.07642e14	−1.24440	−0.622200	−	0.782859i	$-0.713761\pi$
$83$	−3.07642e14	−1.24440	−0.622200	+	0.782859i	$0.713761\pi$
$84$	2.44239e14	0.903067
$85$	6.06714e13	0.205278
$86$	−5.27175e13	−0.163387
$87$	−9.29088e13	−0.264036
$88$	2.40209e14	0.626568
$89$	−1.81716e14	−0.435480	−0.217740	−	0.976007i	$-0.569868\pi$
$89$	−1.81716e14	−0.435480	−0.217740	+	0.976007i	$0.569868\pi$
$90$	1.94837e14	0.429390
$91$	−7.28848e14	−1.47852
$92$	−4.52815e14	−0.846277
$93$	−1.62520e13	−0.0280081
$94$	−5.50277e13	−0.0875230
$95$	2.92211e14	0.429308
$96$	−1.99856e14	−0.271446
$97$	−1.82237e14	−0.229006	−0.114503	−	0.993423i	$-0.536528\pi$
$97$	−1.82237e14	−0.229006	−0.114503	+	0.993423i	$0.536528\pi$
$98$	2.33057e14	0.271185
$99$	2.23167e15	2.40639
$100$	1.00000e14	0.100000
$101$	−6.88940e14	−0.639398	−0.319699	−	0.947519i	$-0.603582\pi$
$101$	−6.88940e14	−0.639398	−0.319699	+	0.947519i	$0.603582\pi$
$102$	−5.78191e14	−0.498391
$103$	−1.74084e15	−1.39470	−0.697350	−	0.716731i	$-0.745637\pi$
$103$	−1.74084e15	−1.39470	−0.697350	+	0.716731i	$0.745637\pi$
$104$	5.96403e14	0.444416
$105$	1.16462e15	0.807728
$106$	1.42479e15	0.920360
$107$	2.39193e15	1.44002	0.720012	−	0.693962i	$-0.244136\pi$
$107$	2.39193e15	1.44002	0.720012	+	0.693962i	$0.244136\pi$
$108$	−4.89338e14	−0.274746
$109$	2.24908e15	1.17844	0.589218	−	0.807974i	$-0.299436\pi$
$109$	2.24908e15	1.17844	0.589218	+	0.807974i	$0.299436\pi$
$110$	1.14540e15	0.560420
$111$	−3.98971e15	−1.82398
$112$	−6.87966e14	−0.294057
$113$	−4.98952e14	−0.199513	−0.0997564	−	0.995012i	$-0.531806\pi$
$113$	−4.98952e14	−0.199513	−0.0997564	+	0.995012i	$0.531806\pi$
$114$	−2.78473e15	−1.04231
$115$	−2.15919e15	−0.756933
$116$	2.61703e14	0.0859754
$117$	5.54091e15	1.70682
$118$	−3.82134e15	−1.10433
$119$	−1.99031e15	−0.539907
$120$	−9.52988e14	−0.242789
$121$	8.94225e15	2.14070
$122$	1.99742e15	0.449543
$123$	−5.28849e15	−1.11955
$124$	4.57782e13	0.00912002
$125$	4.76837e14	0.0894427
$126$	−6.39158e15	−1.12935
$127$	−8.49486e15	−1.41458	−0.707291	−	0.706922i	$-0.750083\pi$
$127$	−8.49486e15	−1.41458	−0.707291	+	0.706922i	$0.750083\pi$
$128$	5.62950e14	0.0883883
$129$	2.39559e15	0.354805
$130$	2.84387e15	0.397498
$131$	3.46115e15	0.456758	0.228379	−	0.973572i	$-0.426657\pi$
$131$	3.46115e15	0.456758	0.228379	+	0.973572i	$0.426657\pi$
$132$	−1.09156e16	−1.36064
$133$	−9.58590e15	−1.12913
$134$	8.28718e15	0.922828
$135$	−2.33334e15	−0.245740
$136$	1.62864e15	0.162286
$137$	8.45917e14	0.0797854	0.0398927	−	0.999204i	$-0.487298\pi$
$137$	8.45917e14	0.0797854	0.0398927	+	0.999204i	$0.487298\pi$
$138$	2.05768e16	1.83775
$139$	−1.00576e16	−0.850912	−0.425456	−	0.904979i	$-0.639886\pi$
$139$	−1.00576e16	−0.850912	−0.425456	+	0.904979i	$0.639886\pi$
$140$	−3.28048e15	−0.263013
$141$	2.50057e15	0.190062
$142$	1.77101e16	1.27661
$143$	3.25738e16	2.22766
$144$	5.23011e15	0.339463
$145$	1.24790e15	0.0768987
$146$	−7.37914e15	−0.431876
$147$	−1.05906e16	−0.588897
$148$	1.12381e16	0.593924
$149$	1.57171e15	0.0789726	0.0394863	−	0.999220i	$-0.487428\pi$
$149$	1.57171e15	0.0789726	0.0394863	+	0.999220i	$0.487428\pi$
$150$	−4.54420e15	−0.217157
$151$	−6.62626e15	−0.301260	−0.150630	−	0.988590i	$-0.548130\pi$
$151$	−6.62626e15	−0.301260	−0.150630	+	0.988590i	$0.548130\pi$
$152$	7.84397e15	0.339398
$153$	1.51309e16	0.623274
$154$	−3.75747e16	−1.47398
$155$	2.18287e14	0.00815719
$156$	−2.71018e16	−0.965080
$157$	−3.43384e16	−1.16555	−0.582777	−	0.812632i	$-0.698034\pi$
$157$	−3.43384e16	−1.16555	−0.582777	+	0.812632i	$0.698034\pi$
$158$	2.37869e16	0.769855
$159$	−6.47455e16	−1.99862
$160$	2.68435e15	0.0790569
$161$	7.08318e16	1.99083
$162$	−1.35484e16	−0.363518
$163$	−5.08560e16	−1.30297	−0.651486	−	0.758661i	$-0.725854\pi$
$163$	−5.08560e16	−1.30297	−0.651486	+	0.758661i	$0.725854\pi$
$164$	1.48965e16	0.364549
$165$	−5.20495e16	−1.21699
$166$	−3.93782e16	−0.879923
$167$	3.23520e16	0.691078	0.345539	−	0.938404i	$-0.387696\pi$
$167$	3.23520e16	0.691078	0.345539	+	0.938404i	$0.387696\pi$
$168$	3.12626e16	0.638565
$169$	2.96902e16	0.580047
$170$	7.76594e15	0.145153
$171$	7.28747e16	1.30348
$172$	−6.74785e15	−0.115532
$173$	−1.02507e16	−0.168039	−0.0840193	−	0.996464i	$-0.526776\pi$
$173$	−1.02507e16	−0.168039	−0.0840193	+	0.996464i	$0.526776\pi$
$174$	−1.18923e16	−0.186701
$175$	−1.56425e16	−0.235246
$176$	3.07467e16	0.443051
$177$	1.73649e17	2.39814
$178$	−2.32596e16	−0.307931
$179$	−1.04290e17	−1.32387	−0.661933	−	0.749563i	$-0.730264\pi$
$179$	−1.04290e17	−1.32387	−0.661933	+	0.749563i	$0.730264\pi$
$180$	2.49391e16	0.303625
$181$	−1.35448e16	−0.158192	−0.0790959	−	0.996867i	$-0.525203\pi$
$181$	−1.35448e16	−0.158192	−0.0790959	+	0.996867i	$0.525203\pi$
$182$	−9.32926e16	−1.04547
$183$	−9.07669e16	−0.976213
$184$	−5.79604e16	−0.598408
$185$	5.35875e16	0.531222
$186$	−2.08025e15	−0.0198047
$187$	8.89514e16	0.813468
$188$	−7.04354e15	−0.0618881
$189$	7.65448e16	0.646327
$190$	3.74029e16	0.303567
$191$	1.60733e17	1.25417	0.627084	−	0.778952i	$-0.284248\pi$
$191$	1.60733e17	1.25417	0.627084	+	0.778952i	$0.284248\pi$
$192$	−2.55816e16	−0.191941
$193$	6.73174e16	0.485789	0.242895	−	0.970053i	$-0.421903\pi$
$193$	6.73174e16	0.485789	0.242895	+	0.970053i	$0.421903\pi$
$194$	−2.33263e16	−0.161932
$195$	−1.29231e17	−0.863193
$196$	2.98313e16	0.191757
$197$	9.46393e16	0.585565	0.292782	−	0.956179i	$-0.405419\pi$
$197$	9.46393e16	0.585565	0.292782	+	0.956179i	$0.405419\pi$
$198$	2.85654e17	1.70157
$199$	2.16580e16	0.124228	0.0621141	−	0.998069i	$-0.480216\pi$
$199$	2.16580e16	0.124228	0.0621141	+	0.998069i	$0.480216\pi$
$200$	1.28000e16	0.0707107
$201$	−3.76586e17	−2.00398
$202$	−8.81843e16	−0.452123
$203$	−4.09370e16	−0.202253
$204$	−7.40085e16	−0.352416
$205$	7.10321e16	0.326062
$206$	−2.22828e17	−0.986201
$207$	−5.38483e17	−2.29824
$208$	7.63396e16	0.314250
$209$	4.28415e17	1.70125
$210$	1.49072e17	0.571150
$211$	−3.78004e17	−1.39758	−0.698792	−	0.715325i	$-0.746279\pi$
$211$	−3.78004e17	−1.39758	−0.698792	+	0.715325i	$0.746279\pi$
$212$	1.82374e17	0.650793
$213$	−8.04783e17	−2.77225
$214$	3.06167e17	1.01825
$215$	−3.21762e16	−0.103335
$216$	−6.26352e16	−0.194274
$217$	−7.16086e15	−0.0214545
$218$	2.87882e17	0.833280
$219$	3.35323e17	0.937849
$220$	1.46612e17	0.396277
$221$	2.20853e17	0.576982
$222$	−5.10683e17	−1.28975
$223$	7.06105e16	0.172418	0.0862090	−	0.996277i	$-0.472525\pi$
$223$	7.06105e16	0.172418	0.0862090	+	0.996277i	$0.472525\pi$
$224$	−8.80596e16	−0.207930
$225$	1.18919e17	0.271570
$226$	−6.38659e16	−0.141077
$227$	6.99664e17	1.49519	0.747594	−	0.664156i	$-0.231209\pi$
$227$	6.99664e17	1.49519	0.747594	+	0.664156i	$0.231209\pi$
$228$	−3.56446e17	−0.737025
$229$	7.68134e16	0.153699	0.0768495	−	0.997043i	$-0.475514\pi$
$229$	7.68134e16	0.153699	0.0768495	+	0.997043i	$0.475514\pi$
$230$	−2.76376e17	−0.535232
$231$	1.70747e18	3.20084
$232$	3.34980e16	0.0607938
$233$	−7.01643e17	−1.23295	−0.616477	−	0.787373i	$-0.711441\pi$
$233$	−7.01643e17	−1.23295	−0.616477	+	0.787373i	$0.711441\pi$
$234$	7.09236e17	1.20690
$235$	−3.35862e16	−0.0553544
$236$	−4.89132e17	−0.780883
$237$	−1.08092e18	−1.67179
$238$	−2.54760e17	−0.381772
$239$	−4.82159e17	−0.700174	−0.350087	−	0.936717i	$-0.613848\pi$
$239$	−4.82159e17	−0.700174	−0.350087	+	0.936717i	$0.613848\pi$
$240$	−1.21982e17	−0.171677
$241$	1.37391e17	0.187426	0.0937129	−	0.995599i	$-0.470126\pi$
$241$	1.37391e17	0.187426	0.0937129	+	0.995599i	$0.470126\pi$
$242$	1.14461e18	1.51371
$243$	1.04422e18	1.33889
$244$	2.55670e17	0.317875
$245$	1.42247e17	0.171513
$246$	−6.76927e17	−0.791642
$247$	1.06369e18	1.20667
$248$	5.85960e15	0.00644883
$249$	1.78942e18	1.91081
$250$	6.10352e16	0.0632456
$251$	−6.45195e17	−0.648840	−0.324420	−	0.945913i	$-0.605169\pi$
$251$	−6.45195e17	−0.648840	−0.324420	+	0.945913i	$0.605169\pi$
$252$	−8.18122e17	−0.798572
$253$	−3.16563e18	−2.99955
$254$	−1.08734e18	−1.00026
$255$	−3.52900e17	−0.315210
$256$	7.20576e16	0.0625000
$257$	−1.22215e18	−1.02950	−0.514751	−	0.857339i	$-0.672116\pi$
$257$	−1.22215e18	−1.02950	−0.514751	+	0.857339i	$0.672116\pi$
$258$	3.06636e17	0.250885
$259$	−1.75793e18	−1.39718
$260$	3.64016e17	0.281074
$261$	3.11215e17	0.233484
$262$	4.43028e17	0.322977
$263$	1.57962e18	1.11914	0.559571	−	0.828783i	$-0.310966\pi$
$263$	1.57962e18	1.11914	0.559571	+	0.828783i	$0.310966\pi$
$264$	−1.39719e18	−0.962114
$265$	8.69625e17	0.582087
$266$	−1.22700e18	−0.798419
$267$	1.05696e18	0.668692
$268$	1.06076e18	0.652538
$269$	−1.84403e18	−1.10313	−0.551563	−	0.834134i	$-0.685968\pi$
$269$	−1.84403e18	−1.10313	−0.551563	+	0.834134i	$0.685968\pi$
$270$	−2.98668e17	−0.173764
$271$	−1.85427e18	−1.04931	−0.524655	−	0.851315i	$-0.675806\pi$
$271$	−1.85427e18	−1.04931	−0.524655	+	0.851315i	$0.675806\pi$
$272$	2.08465e17	0.114754
$273$	4.23940e18	2.27031
$274$	1.08277e17	0.0564168
$275$	6.99099e17	0.354441
$276$	2.63384e18	1.29948
$277$	2.28133e18	1.09544	0.547721	−	0.836661i	$-0.315496\pi$
$277$	2.28133e18	1.09544	0.547721	+	0.836661i	$0.315496\pi$
$278$	−1.28738e18	−0.601685
$279$	5.44389e16	0.0247673
$280$	−4.19901e17	−0.185978
$281$	−2.36990e18	−1.02196	−0.510979	−	0.859593i	$-0.670717\pi$
$281$	−2.36990e18	−1.02196	−0.510979	+	0.859593i	$0.670717\pi$
$282$	3.20073e17	0.134394
$283$	2.74133e18	1.12089	0.560445	−	0.828192i	$-0.310630\pi$
$283$	2.74133e18	1.12089	0.560445	+	0.828192i	$0.310630\pi$
$284$	2.26689e18	0.902700
$285$	−1.69967e18	−0.659215
$286$	4.16945e18	1.57519
$287$	−2.33019e18	−0.857585
$288$	6.69454e17	0.240036
$289$	−2.25932e18	−0.789305
$290$	1.59731e17	0.0543756
$291$	1.05999e18	0.351646
$292$	−9.44530e17	−0.305383
$293$	7.10128e17	0.223784	0.111892	−	0.993720i	$-0.464309\pi$
$293$	7.10128e17	0.223784	0.111892	+	0.993720i	$0.464309\pi$
$294$	−1.35559e18	−0.416413
$295$	−2.33236e18	−0.698443
$296$	1.43848e18	0.419968
$297$	−3.42096e18	−0.973810
$298$	2.01179e17	0.0558421
$299$	−7.85979e18	−2.12754
$300$	−5.81658e17	−0.153553
$301$	1.05553e18	0.271784
$302$	−8.48161e17	−0.213023
$303$	4.00727e18	0.981814
$304$	1.00403e18	0.239990
$305$	1.21913e18	0.284316
$306$	1.93676e18	0.440722
$307$	3.91067e18	0.868387	0.434194	−	0.900820i	$-0.357033\pi$
$307$	3.91067e18	0.868387	0.434194	+	0.900820i	$0.357033\pi$
$308$	−4.80956e18	−1.04226
$309$	1.01258e19	2.14160
$310$	2.79408e16	0.00576801
$311$	3.92589e18	0.791108	0.395554	−	0.918443i	$-0.370553\pi$
$311$	3.92589e18	0.791108	0.395554	+	0.918443i	$0.370553\pi$
$312$	−3.46903e18	−0.682414
$313$	−7.05946e18	−1.35578	−0.677889	−	0.735164i	$-0.737105\pi$
$313$	−7.05946e18	−1.35578	−0.677889	+	0.735164i	$0.737105\pi$
$314$	−4.39531e18	−0.824171
$315$	−3.90111e18	−0.714264
$316$	3.04472e18	0.544370
$317$	6.33185e18	1.10557	0.552785	−	0.833324i	$-0.313565\pi$
$317$	6.33185e18	1.10557	0.552785	+	0.833324i	$0.313565\pi$
$318$	−8.28742e18	−1.41324
$319$	1.82956e18	0.304732
$320$	3.43597e17	0.0559017
$321$	−1.39128e19	−2.21120
$322$	9.06647e18	1.40773
$323$	2.90469e18	0.440637
$324$	−1.73419e18	−0.257046
$325$	1.73576e18	0.251400
$326$	−6.50956e18	−0.921340
$327$	−1.30819e19	−1.80952
$328$	1.90675e18	0.257775
$329$	1.10179e18	0.145589
$330$	−6.66233e18	−0.860541
$331$	6.29584e18	0.794957	0.397478	−	0.917612i	$-0.369885\pi$
$331$	6.29584e18	0.794957	0.397478	+	0.917612i	$0.369885\pi$
$332$	−5.04040e18	−0.622200
$333$	1.33643e19	1.61292
$334$	4.14105e18	0.488666
$335$	5.05809e18	0.583647
$336$	4.00161e18	0.451533
$337$	−5.64981e18	−0.623461	−0.311730	−	0.950171i	$-0.600909\pi$
$337$	−5.64981e18	−0.623461	−0.311730	+	0.950171i	$0.600909\pi$
$338$	3.80035e18	0.410155
$339$	2.90219e18	0.306358
$340$	9.94040e17	0.102639
$341$	3.20035e17	0.0323251
$342$	9.32796e18	0.921703
$343$	7.50103e18	0.725129
$344$	−8.63724e17	−0.0816934
$345$	1.25591e19	1.16229
$346$	−1.31209e18	−0.118821
$347$	9.94333e17	0.0881172	0.0440586	−	0.999029i	$-0.485971\pi$
$347$	9.94333e17	0.0881172	0.0440586	+	0.999029i	$0.485971\pi$
$348$	−1.52222e18	−0.132018
$349$	−1.39253e19	−1.18199	−0.590996	−	0.806674i	$-0.701265\pi$
$349$	−1.39253e19	−1.18199	−0.590996	+	0.806674i	$0.701265\pi$
$350$	−2.00224e18	−0.166344
$351$	−8.49374e18	−0.690710
$352$	3.93558e18	0.313284
$353$	4.63332e18	0.361062	0.180531	−	0.983569i	$-0.442218\pi$
$353$	4.63332e18	0.361062	0.180531	+	0.983569i	$0.442218\pi$
$354$	2.22271e19	1.69574
$355$	1.08094e19	0.807399
$356$	−2.97723e18	−0.217740
$357$	1.15768e19	0.829043
$358$	−1.33491e19	−0.936115
$359$	1.14313e19	0.785030	0.392515	−	0.919746i	$-0.371605\pi$
$359$	1.14313e19	0.785030	0.392515	+	0.919746i	$0.371605\pi$
$360$	3.19221e18	0.214695
$361$	−1.19132e18	−0.0784738
$362$	−1.73374e18	−0.111858
$363$	−5.20133e19	−3.28711
$364$	−1.19415e19	−0.739259
$365$	−4.50387e18	−0.273143
$366$	−1.16182e19	−0.690287
$367$	−1.89910e19	−1.10549	−0.552743	−	0.833352i	$-0.686419\pi$
$367$	−1.89910e19	−1.10549	−0.552743	+	0.833352i	$0.686419\pi$
$368$	−7.41893e18	−0.423138
$369$	1.77148e19	0.990006
$370$	6.85921e18	0.375631
$371$	−2.85278e19	−1.53096
$372$	−2.66272e17	−0.0140041
$373$	−2.59363e18	−0.133688	−0.0668439	−	0.997763i	$-0.521293\pi$
$373$	−2.59363e18	−0.133688	−0.0668439	+	0.997763i	$0.521293\pi$
$374$	1.13858e19	0.575209
$375$	−2.77356e18	−0.137342
$376$	−9.01573e17	−0.0437615
$377$	4.54255e18	0.216142
$378$	9.79774e18	0.457022
$379$	−2.69599e19	−1.23289	−0.616446	−	0.787397i	$-0.711428\pi$
$379$	−2.69599e19	−1.23289	−0.616446	+	0.787397i	$0.711428\pi$
$380$	4.78758e18	0.214654
$381$	4.94110e19	2.17213
$382$	2.05739e19	0.886830
$383$	7.21341e17	0.0304895	0.0152447	−	0.999884i	$-0.495147\pi$
$383$	7.21341e17	0.0304895	0.0152447	+	0.999884i	$0.495147\pi$
$384$	−3.27444e18	−0.135723
$385$	−2.29338e19	−0.932224
$386$	8.61663e18	0.343505
$387$	−8.02447e18	−0.313750
$388$	−2.98577e18	−0.114503
$389$	1.58276e19	0.595378	0.297689	−	0.954663i	$-0.403784\pi$
$389$	1.58276e19	0.595378	0.297689	+	0.954663i	$0.403784\pi$
$390$	−1.65416e19	−0.610370
$391$	−2.14632e19	−0.776908
$392$	3.81840e18	0.135593
$393$	−2.01321e19	−0.701365
$394$	1.21138e19	0.414057
$395$	1.45183e19	0.486899
$396$	3.65637e19	1.20319
$397$	−1.94707e19	−0.628713	−0.314356	−	0.949305i	$-0.601789\pi$
$397$	−1.94707e19	−0.628713	−0.314356	+	0.949305i	$0.601789\pi$
$398$	2.77222e18	0.0878426
$399$	5.57571e19	1.73382
$400$	1.63840e18	0.0500000
$401$	1.04806e19	0.313908	0.156954	−	0.987606i	$-0.449833\pi$
$401$	1.04806e19	0.313908	0.156954	+	0.987606i	$0.449833\pi$
$402$	−4.82030e19	−1.41703
$403$	7.94600e17	0.0229277
$404$	−1.12876e19	−0.319699
$405$	−8.26929e18	−0.229909
$406$	−5.23994e18	−0.143015
$407$	7.85656e19	2.10511
$408$	−9.47309e18	−0.249196
$409$	7.27248e17	0.0187827	0.00939134	−	0.999956i	$-0.497011\pi$
$409$	7.27248e17	0.0187827	0.00939134	+	0.999956i	$0.497011\pi$
$410$	9.09210e18	0.230561
$411$	−4.92034e18	−0.122513
$412$	−2.85220e19	−0.697350
$413$	7.65126e19	1.83699
$414$	−6.89258e19	−1.62510
$415$	−2.40345e19	−0.556512
$416$	9.77147e18	0.222208
$417$	5.85010e19	1.30660
$418$	5.48371e19	1.20296
$419$	4.89919e19	1.05565	0.527824	−	0.849354i	$-0.323008\pi$
$419$	4.89919e19	1.05565	0.527824	+	0.849354i	$0.323008\pi$
$420$	1.90812e19	0.403864
$421$	−4.22149e18	−0.0877707	−0.0438854	−	0.999037i	$-0.513974\pi$
$421$	−4.22149e18	−0.0877707	−0.0438854	+	0.999037i	$0.513974\pi$
$422$	−4.83845e19	−0.988241
$423$	−8.37611e18	−0.168070
$424$	2.33438e19	0.460180
$425$	4.73995e18	0.0918031
$426$	−1.03012e20	−1.96027
$427$	−3.99933e19	−0.747787
$428$	3.91893e19	0.720012
$429$	−1.89468e20	−3.42063
$430$	−4.11856e18	−0.0730688
$431$	1.61261e18	0.0281157	0.0140579	−	0.999901i	$-0.495525\pi$
$431$	1.61261e18	0.0281157	0.0140579	+	0.999901i	$0.495525\pi$
$432$	−8.01731e18	−0.137373
$433$	−6.08830e19	−1.02527	−0.512633	−	0.858608i	$-0.671330\pi$
$433$	−6.08830e19	−1.02527	−0.512633	+	0.858608i	$0.671330\pi$
$434$	−9.16591e17	−0.0151706
$435$	−7.25850e18	−0.118080
$436$	3.68489e19	0.589218
$437$	−1.03373e20	−1.62479
$438$	4.29214e19	0.663159
$439$	5.81533e19	0.883264	0.441632	−	0.897196i	$-0.354400\pi$
$439$	5.81533e19	0.883264	0.441632	+	0.897196i	$0.354400\pi$
$440$	1.87663e19	0.280210
$441$	3.54750e19	0.520755
$442$	2.82692e19	0.407988
$443$	1.06230e20	1.50736	0.753682	−	0.657239i	$-0.228276\pi$
$443$	1.06230e20	1.50736	0.753682	+	0.657239i	$0.228276\pi$
$444$	−6.53674e19	−0.911988
$445$	−1.41966e19	−0.194752
$446$	9.03814e18	0.121918
$447$	−9.14200e18	−0.121265
$448$	−1.12716e19	−0.147029
$449$	−1.17735e20	−1.51028	−0.755140	−	0.655564i	$-0.772431\pi$
$449$	−1.17735e20	−1.51028	−0.755140	+	0.655564i	$0.772431\pi$
$450$	1.52216e19	0.192029
$451$	1.04141e20	1.29211
$452$	−8.17483e18	−0.0997564
$453$	3.85421e19	0.462593
$454$	8.95570e19	1.05726
$455$	−5.69413e19	−0.661213
$456$	−4.56251e19	−0.521155
$457$	1.15681e20	1.29984	0.649918	−	0.760004i	$-0.274803\pi$
$457$	1.15681e20	1.29984	0.649918	+	0.760004i	$0.274803\pi$
$458$	9.83212e18	0.108682
$459$	−2.31944e19	−0.252225
$460$	−3.53762e19	−0.378466
$461$	−8.04744e19	−0.847034	−0.423517	−	0.905888i	$-0.639205\pi$
$461$	−8.04744e19	−0.847034	−0.423517	+	0.905888i	$0.639205\pi$
$462$	2.18556e20	2.26333
$463$	−9.29651e19	−0.947245	−0.473623	−	0.880728i	$-0.657054\pi$
$463$	−9.29651e19	−0.947245	−0.473623	+	0.880728i	$0.657054\pi$
$464$	4.28775e18	0.0429877
$465$	−1.26969e18	−0.0125256
$466$	−8.98103e19	−0.871830
$467$	1.37482e19	0.131332	0.0656659	−	0.997842i	$-0.479083\pi$
$467$	1.37482e19	0.131332	0.0656659	+	0.997842i	$0.479083\pi$
$468$	9.07823e19	0.853409
$469$	−1.65930e20	−1.53507
$470$	−4.29904e18	−0.0391415
$471$	1.99732e20	1.78974
$472$	−6.26089e19	−0.552167
$473$	−4.71741e19	−0.409492
$474$	−1.38358e20	−1.18213
$475$	2.28289e19	0.191992
$476$	−3.26093e19	−0.269953
$477$	2.16877e20	1.76736
$478$	−6.17164e19	−0.495098
$479$	6.69948e19	0.529084	0.264542	−	0.964374i	$-0.414779\pi$
$479$	6.69948e19	0.529084	0.264542	+	0.964374i	$0.414779\pi$
$480$	−1.56138e19	−0.121394
$481$	1.95067e20	1.49312
$482$	1.75860e19	0.132530
$483$	−4.11999e20	−3.05698
$484$	1.46510e20	1.07035
$485$	−1.42372e19	−0.102415
$486$	1.33661e20	0.946741
$487$	−1.80792e19	−0.126099	−0.0630495	−	0.998010i	$-0.520083\pi$
$487$	−1.80792e19	−0.126099	−0.0630495	+	0.998010i	$0.520083\pi$
$488$	3.27258e19	0.224772
$489$	2.95808e20	2.00075
$490$	1.82076e19	0.121278
$491$	−1.08152e20	−0.709450	−0.354725	−	0.934971i	$-0.615426\pi$
$491$	−1.08152e20	−0.709450	−0.354725	+	0.934971i	$0.615426\pi$
$492$	−8.66467e19	−0.559775
$493$	1.24046e19	0.0789280
$494$	1.36153e20	0.853245
$495$	1.74349e20	1.07617
$496$	7.50029e17	0.00456001
$497$	−3.54599e20	−2.12356
$498$	2.29046e20	1.35115
$499$	6.92079e19	0.402163	0.201081	−	0.979575i	$-0.435554\pi$
$499$	6.92079e19	0.402163	0.201081	+	0.979575i	$0.435554\pi$
$500$	7.81250e18	0.0447214
$501$	−1.88178e20	−1.06117
$502$	−8.25849e19	−0.458799
$503$	1.85647e20	1.01608	0.508040	−	0.861333i	$-0.330370\pi$
$503$	1.85647e20	1.01608	0.508040	+	0.861333i	$0.330370\pi$
$504$	−1.04720e20	−0.564675
$505$	−5.38235e19	−0.285947
$506$	−4.05200e20	−2.12100
$507$	−1.72695e20	−0.890679
$508$	−1.39180e20	−0.707291
$509$	−1.26957e20	−0.635730	−0.317865	−	0.948136i	$-0.602966\pi$
$509$	−1.26957e20	−0.635730	−0.317865	+	0.948136i	$0.602966\pi$
$510$	−4.51712e19	−0.222887
$511$	1.47748e20	0.718400
$512$	9.22337e18	0.0441942
$513$	−1.11711e20	−0.527490
$514$	−1.56436e20	−0.727968
$515$	−1.36003e20	−0.623728
$516$	3.92494e19	0.177403
$517$	−4.92413e19	−0.219357
$518$	−2.25015e20	−0.987956
$519$	5.96242e19	0.258028
$520$	4.65940e19	0.198749
$521$	−1.53600e20	−0.645817	−0.322908	−	0.946430i	$-0.604661\pi$
$521$	−1.53600e20	−0.645817	−0.322908	+	0.946430i	$0.604661\pi$
$522$	3.98355e19	0.165098
$523$	4.35314e20	1.77844	0.889222	−	0.457477i	$-0.151247\pi$
$523$	4.35314e20	1.77844	0.889222	+	0.457477i	$0.151247\pi$
$524$	5.67075e19	0.228379
$525$	9.09860e19	0.361227
$526$	2.02192e20	0.791352
$527$	2.16986e18	0.00837246
$528$	−1.78841e20	−0.680318
$529$	4.97204e20	1.86474
$530$	1.11312e20	0.411598
$531$	−5.81670e20	−2.12064
$532$	−1.57055e20	−0.564567
$533$	2.58568e20	0.916475
$534$	1.35292e20	0.472837
$535$	1.86869e20	0.643998
$536$	1.35777e20	0.461414
$537$	6.06610e20	2.03284
$538$	−2.36035e20	−0.780027
$539$	2.08550e20	0.679664
$540$	−3.82295e19	−0.122870
$541$	−1.00466e20	−0.318448	−0.159224	−	0.987243i	$-0.550899\pi$
$541$	−1.00466e20	−0.318448	−0.159224	+	0.987243i	$0.550899\pi$
$542$	−2.37347e20	−0.741975
$543$	7.87845e19	0.242908
$544$	2.66836e19	0.0811432
$545$	1.75709e20	0.527013
$546$	5.42644e20	1.60535
$547$	−3.68217e20	−1.07448	−0.537240	−	0.843429i	$-0.680533\pi$
$547$	−3.68217e20	−1.07448	−0.537240	+	0.843429i	$0.680533\pi$
$548$	1.38595e19	0.0398927
$549$	3.04040e20	0.863254
$550$	8.94847e19	0.250627
$551$	5.97441e19	0.165066
$552$	3.37131e20	0.918873
$553$	−4.76271e20	−1.28061
$554$	2.92010e20	0.774594
$555$	−3.11696e20	−0.815707
$556$	−1.64784e20	−0.425456
$557$	8.61313e19	0.219405	0.109703	−	0.993964i	$-0.465010\pi$
$557$	8.61313e19	0.219405	0.109703	+	0.993964i	$0.465010\pi$
$558$	6.96818e18	0.0175131
$559$	−1.17127e20	−0.290447
$560$	−5.37473e19	−0.131506
$561$	−5.17393e20	−1.24910
$562$	−3.03348e20	−0.722634
$563$	−4.59219e20	−1.07946	−0.539731	−	0.841838i	$-0.681474\pi$
$563$	−4.59219e20	−1.07946	−0.539731	+	0.841838i	$0.681474\pi$
$564$	4.09693e19	0.0950310
$565$	−3.89806e19	−0.0892248
$566$	3.50890e20	0.792589
$567$	2.71272e20	0.604689
$568$	2.90162e20	0.638305
$569$	−7.18099e20	−1.55899	−0.779493	−	0.626410i	$-0.784523\pi$
$569$	−7.18099e20	−1.55899	−0.779493	+	0.626410i	$0.784523\pi$
$570$	−2.17557e20	−0.466135
$571$	1.98256e20	0.419233	0.209616	−	0.977784i	$-0.432778\pi$
$571$	1.98256e20	0.419233	0.209616	+	0.977784i	$0.432778\pi$
$572$	5.33690e20	1.11383
$573$	−9.34918e20	−1.92581
$574$	−2.98264e20	−0.606404
$575$	−1.68687e20	−0.338511
$576$	8.56901e19	0.169731
$577$	1.51016e20	0.295259	0.147630	−	0.989043i	$-0.452836\pi$
$577$	1.51016e20	0.295259	0.147630	+	0.989043i	$0.452836\pi$
$578$	−2.89194e20	−0.558123
$579$	−3.91557e20	−0.745943
$580$	2.04456e19	0.0384494
$581$	7.88447e20	1.46370
$582$	1.35679e20	0.248651
$583$	1.27497e21	2.30668
$584$	−1.20900e20	−0.215938
$585$	4.32884e20	0.763312
$586$	9.08964e19	0.158239
$587$	−4.98278e20	−0.856418	−0.428209	−	0.903680i	$-0.640855\pi$
$587$	−4.98278e20	−0.856418	−0.428209	+	0.903680i	$0.640855\pi$
$588$	−1.73516e20	−0.294448
$589$	1.04507e19	0.0175097
$590$	−2.98542e20	−0.493874
$591$	−5.50477e20	−0.899152
$592$	1.84125e20	0.296962
$593$	1.37436e20	0.218871	0.109436	−	0.993994i	$-0.465096\pi$
$593$	1.37436e20	0.218871	0.109436	+	0.993994i	$0.465096\pi$
$594$	−4.37882e20	−0.688587
$595$	−1.55493e20	−0.241454
$596$	2.57510e19	0.0394863
$597$	−1.25975e20	−0.190756
$598$	−1.00605e21	−1.50440
$599$	−1.07343e21	−1.58516	−0.792582	−	0.609765i	$-0.791264\pi$
$599$	−1.07343e21	−1.58516	−0.792582	+	0.609765i	$0.791264\pi$
$600$	−7.44522e19	−0.108578
$601$	−1.27438e20	−0.183544	−0.0917721	−	0.995780i	$-0.529253\pi$
$601$	−1.27438e20	−0.183544	−0.0917721	+	0.995780i	$0.529253\pi$
$602$	1.35108e20	0.192180
$603$	1.26144e21	1.77210
$604$	−1.08565e20	−0.150630
$605$	6.98613e20	0.957352
$606$	5.12931e20	0.694248
$607$	−3.63227e20	−0.485582	−0.242791	−	0.970079i	$-0.578063\pi$
$607$	−3.63227e20	−0.485582	−0.242791	+	0.970079i	$0.578063\pi$
$608$	1.28516e20	0.169699
$609$	2.38113e20	0.310566
$610$	1.56049e20	0.201042
$611$	−1.22259e20	−0.155587
$612$	2.47905e20	0.311637
$613$	1.06315e21	1.32021	0.660104	−	0.751174i	$-0.270512\pi$
$613$	1.06315e21	1.32021	0.660104	+	0.751174i	$0.270512\pi$
$614$	5.00566e20	0.614042
$615$	−4.13164e20	−0.500678
$616$	−6.15624e20	−0.736988
$617$	8.94081e20	1.05740	0.528699	−	0.848810i	$-0.322680\pi$
$617$	8.94081e20	1.05740	0.528699	+	0.848810i	$0.322680\pi$
$618$	1.29610e21	1.51434
$619$	−1.24002e21	−1.43136	−0.715681	−	0.698427i	$-0.753884\pi$
$619$	−1.24002e21	−1.43136	−0.715681	+	0.698427i	$0.753884\pi$
$620$	3.57642e18	0.00407860
$621$	8.25448e20	0.930043
$622$	5.02514e20	0.559398
$623$	4.65715e20	0.512224
$624$	−4.44035e20	−0.482540
$625$	3.72529e19	0.0400000
$626$	−9.03610e20	−0.958680
$627$	−2.49191e21	−2.61231
$628$	−5.62600e20	−0.582777
$629$	5.32682e20	0.545240
$630$	−4.99342e20	−0.505061
$631$	1.22882e21	1.22820	0.614099	−	0.789229i	$-0.289519\pi$
$631$	1.22882e21	1.22820	0.614099	+	0.789229i	$0.289519\pi$
$632$	3.89724e20	0.384927
$633$	2.19869e21	2.14603
$634$	8.10477e20	0.781756
$635$	−6.63661e20	−0.632620
$636$	−1.06079e21	−0.999312
$637$	5.17800e20	0.482076
$638$	2.34184e20	0.215478
$639$	2.69577e21	2.45146
$640$	4.39805e19	0.0395285
$641$	−1.91614e21	−1.70213	−0.851063	−	0.525063i	$-0.824042\pi$
$641$	−1.91614e21	−1.70213	−0.851063	+	0.525063i	$0.824042\pi$
$642$	−1.78084e21	−1.56355
$643$	−8.56056e20	−0.742882	−0.371441	−	0.928457i	$-0.621136\pi$
$643$	−8.56056e20	−0.742882	−0.371441	+	0.928457i	$0.621136\pi$
$644$	1.16051e21	0.995415
$645$	1.87156e20	0.158674
$646$	3.71800e20	0.311577
$647$	1.91833e21	1.58906	0.794531	−	0.607224i	$-0.207717\pi$
$647$	1.91833e21	1.58906	0.794531	+	0.607224i	$0.207717\pi$
$648$	−2.21977e20	−0.181759
$649$	−3.41951e21	−2.76777
$650$	2.22178e20	0.177767
$651$	4.16517e19	0.0329439
$652$	−8.33224e20	−0.651486
$653$	−1.17776e21	−0.910353	−0.455176	−	0.890401i	$-0.650424\pi$
$653$	−1.17776e21	−0.910353	−0.455176	+	0.890401i	$0.650424\pi$
$654$	−1.67449e21	−1.27953
$655$	2.70403e20	0.204268
$656$	2.44064e20	0.182274
$657$	−1.12323e21	−0.829329
$658$	1.41029e20	0.102947
$659$	3.65308e20	0.263644	0.131822	−	0.991273i	$-0.457917\pi$
$659$	3.65308e20	0.263644	0.131822	+	0.991273i	$0.457917\pi$
$660$	−8.52778e20	−0.608495
$661$	2.48240e21	1.75130	0.875650	−	0.482947i	$-0.160433\pi$
$661$	2.48240e21	1.75130	0.875650	+	0.482947i	$0.160433\pi$
$662$	8.05867e20	0.562119
$663$	−1.28461e21	−0.885973
$664$	−6.45172e20	−0.439961
$665$	−7.48898e20	−0.504964
$666$	1.71062e21	1.14051
$667$	−4.41459e20	−0.291036
$668$	5.30055e20	0.345539
$669$	−4.10711e20	−0.264753
$670$	6.47436e20	0.412701
$671$	1.78739e21	1.12668
$672$	5.12206e20	0.319282
$673$	−2.25249e21	−1.38851	−0.694257	−	0.719728i	$-0.744267\pi$
$673$	−2.25249e21	−1.38851	−0.694257	+	0.719728i	$0.744267\pi$
$674$	−7.23175e20	−0.440853
$675$	−1.82293e20	−0.109898
$676$	4.86444e20	0.290023
$677$	1.00846e21	0.594628	0.297314	−	0.954780i	$-0.403909\pi$
$677$	1.00846e21	0.594628	0.297314	+	0.954780i	$0.403909\pi$
$678$	3.71481e20	0.216628
$679$	4.67049e20	0.269364
$680$	1.27237e20	0.0725767
$681$	−4.06965e21	−2.29591
$682$	4.09644e19	0.0228573
$683$	1.61840e20	0.0893160	0.0446580	−	0.999002i	$-0.485780\pi$
$683$	1.61840e20	0.0893160	0.0446580	+	0.999002i	$0.485780\pi$
$684$	1.19398e21	0.651742
$685$	6.60873e19	0.0356811
$686$	9.60132e20	0.512743
$687$	−4.46791e20	−0.236009
$688$	−1.10557e20	−0.0577659
$689$	3.16557e21	1.63609
$690$	1.60757e21	0.821865
$691$	−2.04771e21	−1.03558	−0.517788	−	0.855509i	$-0.673244\pi$
$691$	−2.04771e21	−1.03558	−0.517788	+	0.855509i	$0.673244\pi$
$692$	−1.67948e20	−0.0840193
$693$	−5.71948e21	−2.83046
$694$	1.27275e20	0.0623083
$695$	−7.85752e20	−0.380539
$696$	−1.94844e20	−0.0933507
$697$	7.06087e20	0.334667
$698$	−1.78244e21	−0.835795
$699$	4.08116e21	1.89324
$700$	−2.56287e20	−0.117623
$701$	−2.28411e21	−1.03713	−0.518564	−	0.855039i	$-0.673533\pi$
$701$	−2.28411e21	−1.03713	−0.518564	+	0.855039i	$0.673533\pi$
$702$	−1.08720e21	−0.488406
$703$	2.56555e21	1.14029
$704$	5.03754e20	0.221525
$705$	1.95357e20	0.0849983
$706$	5.93065e20	0.255310
$707$	1.76567e21	0.752078
$708$	2.84507e21	1.19907
$709$	7.23937e20	0.301894	0.150947	−	0.988542i	$-0.451768\pi$
$709$	7.23937e20	0.301894	0.150947	+	0.988542i	$0.451768\pi$
$710$	1.38360e21	0.570918
$711$	3.62075e21	1.47835
$712$	−3.81086e20	−0.153965
$713$	−7.72217e19	−0.0308722
$714$	1.48183e21	0.586222
$715$	2.54483e21	0.996239
$716$	−1.70868e21	−0.661933
$717$	2.80452e21	1.07514
$718$	1.46320e21	0.555100
$719$	−2.52991e20	−0.0949815	−0.0474907	−	0.998872i	$-0.515122\pi$
$719$	−2.52991e20	−0.0949815	−0.0474907	+	0.998872i	$0.515122\pi$
$720$	4.08602e20	0.151812
$721$	4.46156e21	1.64049
$722$	−1.52489e20	−0.0554893
$723$	−7.99143e20	−0.287798
$724$	−2.21918e20	−0.0790959
$725$	9.74921e19	0.0343902
$726$	−6.65770e21	−2.32434
$727$	−2.20533e21	−0.762019	−0.381009	−	0.924571i	$-0.624423\pi$
$727$	−2.20533e21	−0.762019	−0.381009	+	0.924571i	$0.624423\pi$
$728$	−1.52851e21	−0.522735
$729$	−4.55502e21	−1.54182
$730$	−5.76496e20	−0.193141
$731$	−3.19845e20	−0.106062
$732$	−1.48713e21	−0.488106
$733$	−1.83621e21	−0.596544	−0.298272	−	0.954481i	$-0.596410\pi$
$733$	−1.83621e21	−0.596544	−0.298272	+	0.954481i	$0.596410\pi$
$734$	−2.43085e21	−0.781697
$735$	−8.27388e20	−0.263363
$736$	−9.49622e20	−0.299204
$737$	7.41575e21	2.31286
$738$	2.26749e21	0.700040
$739$	−1.19943e21	−0.366556	−0.183278	−	0.983061i	$-0.558671\pi$
$739$	−1.19943e21	−0.366556	−0.183278	+	0.983061i	$0.558671\pi$
$740$	8.77978e20	0.265611
$741$	−6.18705e21	−1.85288
$742$	−3.65156e21	−1.08255
$743$	5.61963e20	0.164927	0.0824635	−	0.996594i	$-0.473721\pi$
$743$	5.61963e20	0.164927	0.0824635	+	0.996594i	$0.473721\pi$
$744$	−3.40829e19	−0.00990236
$745$	1.22790e20	0.0353176
$746$	−3.31985e20	−0.0945315
$747$	−5.99399e21	−1.68971
$748$	1.45738e21	0.406734
$749$	−6.13021e21	−1.69380
$750$	−3.55016e20	−0.0971154
$751$	−6.45789e21	−1.74901	−0.874503	−	0.485020i	$-0.838812\pi$
$751$	−6.45789e21	−1.74901	−0.874503	+	0.485020i	$0.838812\pi$
$752$	−1.15401e20	−0.0309441
$753$	3.75283e21	0.996314
$754$	5.81446e20	0.152835
$755$	−5.17676e20	−0.134727
$756$	1.25411e21	0.323164
$757$	−2.17355e21	−0.554561	−0.277281	−	0.960789i	$-0.589433\pi$
$757$	−2.17355e21	−0.554561	−0.277281	+	0.960789i	$0.589433\pi$
$758$	−3.45087e21	−0.871786
$759$	1.84131e22	4.60589
$760$	6.12810e20	0.151783
$761$	6.38965e21	1.56708	0.783542	−	0.621339i	$-0.213411\pi$
$761$	6.38965e21	1.56708	0.783542	+	0.621339i	$0.213411\pi$
$762$	6.32461e21	1.53593
$763$	−5.76410e21	−1.38611
$764$	2.63345e21	0.627084
$765$	1.18210e21	0.278737
$766$	9.23317e19	0.0215593
$767$	−8.49016e21	−1.96314
$768$	−4.19129e20	−0.0959706
$769$	−4.63352e21	−1.05066	−0.525331	−	0.850898i	$-0.676059\pi$
$769$	−4.63352e21	−1.05066	−0.525331	+	0.850898i	$0.676059\pi$
$770$	−2.93552e21	−0.659182
$771$	7.10876e21	1.58083
$772$	1.10293e21	0.242895
$773$	−2.62638e21	−0.572811	−0.286406	−	0.958108i	$-0.592460\pi$
$773$	−2.62638e21	−0.572811	−0.286406	+	0.958108i	$0.592460\pi$
$774$	−1.02713e21	−0.221855
$775$	1.70537e19	0.00364801
$776$	−3.82178e20	−0.0809660
$777$	1.02251e22	2.14541
$778$	2.02593e21	0.420996
$779$	3.40071e21	0.699905
$780$	−2.11733e21	−0.431597
$781$	1.58478e22	3.19954
$782$	−2.74729e21	−0.549357
$783$	−4.77066e20	−0.0944854
$784$	4.88755e20	0.0958784
$785$	−2.68269e21	−0.521252
$786$	−2.57691e21	−0.495940
$787$	−9.12707e21	−1.73989	−0.869944	−	0.493151i	$-0.835845\pi$
$787$	−9.12707e21	−1.73989	−0.869944	+	0.493151i	$0.835845\pi$
$788$	1.55057e21	0.292782
$789$	−9.18799e21	−1.71847
$790$	1.85835e21	0.344290
$791$	1.27875e21	0.234673
$792$	4.68015e21	0.850787
$793$	4.43782e21	0.799137
$794$	−2.49225e21	−0.444567
$795$	−5.05824e21	−0.893812
$796$	3.54845e20	0.0621141
$797$	−6.57555e21	−1.14024	−0.570118	−	0.821563i	$-0.693102\pi$
$797$	−6.57555e21	−1.14024	−0.570118	+	0.821563i	$0.693102\pi$
$798$	7.13691e21	1.22600
$799$	−3.33861e20	−0.0568152
$800$	2.09715e20	0.0353553
$801$	−3.54049e21	−0.591317
$802$	1.34151e21	0.221966
$803$	−6.60320e21	−1.08240
$804$	−6.16999e21	−1.00199
$805$	5.53373e21	0.890326
$806$	1.01709e20	0.0162123
$807$	1.07259e22	1.69388
$808$	−1.44481e21	−0.226061
$809$	1.80991e21	0.280572	0.140286	−	0.990111i	$-0.455198\pi$
$809$	1.80991e21	0.280572	0.140286	+	0.990111i	$0.455198\pi$
$810$	−1.05847e21	−0.162570
$811$	3.19559e21	0.486290	0.243145	−	0.969990i	$-0.421821\pi$
$811$	3.19559e21	0.486290	0.243145	+	0.969990i	$0.421821\pi$
$812$	−6.70712e20	−0.101127
$813$	1.07855e22	1.61125
$814$	1.00564e22	1.48854
$815$	−3.97312e21	−0.582707
$816$	−1.21256e21	−0.176208
$817$	−1.54046e21	−0.221812
$818$	9.30877e19	0.0132814
$819$	−1.42006e22	−2.00761
$820$	1.16379e21	0.163031
$821$	−8.98711e21	−1.24752	−0.623758	−	0.781617i	$-0.714395\pi$
$821$	−8.98711e21	−1.24752	−0.623758	+	0.781617i	$0.714395\pi$
$822$	−6.29804e20	−0.0866297
$823$	5.82230e21	0.793589	0.396795	−	0.917907i	$-0.370123\pi$
$823$	5.82230e21	0.793589	0.396795	+	0.917907i	$0.370123\pi$
$824$	−3.65081e21	−0.493101
$825$	−4.06636e21	−0.544254
$826$	9.79361e21	1.29895
$827$	1.32555e22	1.74223	0.871113	−	0.491083i	$-0.163399\pi$
$827$	1.32555e22	1.74223	0.871113	+	0.491083i	$0.163399\pi$
$828$	−8.82251e21	−1.14912
$829$	−1.11966e22	−1.44520	−0.722598	−	0.691269i	$-0.757052\pi$
$829$	−1.11966e22	−1.44520	−0.722598	+	0.691269i	$0.757052\pi$
$830$	−3.07642e21	−0.393514
$831$	−1.32695e22	−1.68208
$832$	1.25075e21	0.157125
$833$	1.41399e21	0.176039
$834$	7.48812e21	0.923906
$835$	2.52750e21	0.309060
$836$	7.01915e21	0.850623
$837$	−8.34502e19	−0.0100227
$838$	6.27096e21	0.746455
$839$	−1.04808e21	−0.123646	−0.0618228	−	0.998087i	$-0.519691\pi$
$839$	−1.04808e21	−0.123646	−0.0618228	+	0.998087i	$0.519691\pi$
$840$	2.44239e21	0.285575
$841$	−8.37405e21	−0.970433
$842$	−5.40350e20	−0.0620633
$843$	1.37847e22	1.56925
$844$	−6.19322e21	−0.698792
$845$	2.31955e21	0.259405
$846$	−1.07214e21	−0.118843
$847$	−2.29179e22	−2.51796
$848$	2.98801e21	0.325397
$849$	−1.59452e22	−1.72116
$850$	6.06714e20	0.0649146
$851$	−1.89572e22	−2.01050
$852$	−1.31856e22	−1.38612
$853$	9.43153e21	0.982799	0.491399	−	0.870934i	$-0.336486\pi$
$853$	9.43153e21	0.982799	0.491399	+	0.870934i	$0.336486\pi$
$854$	−5.11914e21	−0.528765
$855$	5.69334e21	0.582936
$856$	5.01624e21	0.509125
$857$	1.23081e22	1.23832	0.619161	−	0.785264i	$-0.287473\pi$
$857$	1.23081e22	1.23832	0.619161	+	0.785264i	$0.287473\pi$
$858$	−2.42519e22	−2.41875
$859$	1.76754e22	1.74752	0.873759	−	0.486360i	$-0.161675\pi$
$859$	1.76754e22	1.74752	0.873759	+	0.486360i	$0.161675\pi$
$860$	−5.27175e20	−0.0516674
$861$	1.35537e22	1.31685
$862$	2.06414e20	0.0198808
$863$	4.26192e21	0.406934	0.203467	−	0.979082i	$-0.434779\pi$
$863$	4.26192e21	0.406934	0.203467	+	0.979082i	$0.434779\pi$
$864$	−1.02622e21	−0.0971372
$865$	−8.00838e20	−0.0751491
$866$	−7.79302e21	−0.724973
$867$	1.31415e22	1.21200
$868$	−1.17324e20	−0.0107272
$869$	2.12856e22	1.92947
$870$	−9.29088e20	−0.0834954
$871$	1.84122e22	1.64048
$872$	4.71666e21	0.416640
$873$	−3.55064e21	−0.310957
$874$	−1.32317e22	−1.14890
$875$	−1.22207e21	−0.105205
$876$	5.49394e21	0.468924
$877$	−3.22309e21	−0.272757	−0.136378	−	0.990657i	$-0.543546\pi$
$877$	−3.22309e21	−0.272757	−0.136378	+	0.990657i	$0.543546\pi$
$878$	7.44363e21	0.624562
$879$	−4.13051e21	−0.343627
$880$	2.40209e21	0.198138
$881$	−1.48852e22	−1.21740	−0.608702	−	0.793399i	$-0.708310\pi$
$881$	−1.48852e22	−1.21740	−0.608702	+	0.793399i	$0.708310\pi$
$882$	4.54080e21	0.368229
$883$	−8.42699e21	−0.677590	−0.338795	−	0.940860i	$-0.610019\pi$
$883$	−8.42699e21	−0.677590	−0.338795	+	0.940860i	$0.610019\pi$
$884$	3.61846e21	0.288491
$885$	1.35664e22	1.07248
$886$	1.35974e22	1.06587
$887$	−1.54780e22	−1.20306	−0.601529	−	0.798851i	$-0.705442\pi$
$887$	−1.54780e22	−1.20306	−0.601529	+	0.798851i	$0.705442\pi$
$888$	−8.36703e21	−0.644873
$889$	2.17712e22	1.66387
$890$	−1.81716e21	−0.137711
$891$	−1.21237e22	−0.911074
$892$	1.15688e21	0.0862090
$893$	−1.60797e21	−0.118820
$894$	−1.17018e21	−0.0857471
$895$	−8.14764e21	−0.592051
$896$	−1.44277e21	−0.103965
$897$	4.57171e22	3.26690
$898$	−1.50701e22	−1.06793
$899$	4.46301e19	0.00313639
$900$	1.94837e21	0.135785
$901$	8.64442e21	0.597448
$902$	1.33301e22	0.913659
$903$	−6.13960e21	−0.417332
$904$	−1.04638e21	−0.0705384
$905$	−1.05819e21	−0.0707455
$906$	4.93339e21	0.327103
$907$	−2.19678e22	−1.44455	−0.722275	−	0.691606i	$-0.756903\pi$
$907$	−2.19678e22	−1.44455	−0.722275	+	0.691606i	$0.756903\pi$
$908$	1.14633e22	0.747594
$909$	−1.34231e22	−0.868207
$910$	−7.28848e21	−0.467549
$911$	1.84376e22	1.17305	0.586525	−	0.809931i	$-0.300496\pi$
$911$	1.84376e22	1.17305	0.586525	+	0.809931i	$0.300496\pi$
$912$	−5.84001e21	−0.368512
$913$	−3.52374e22	−2.20533
$914$	1.48071e22	0.919123
$915$	−7.09117e21	−0.436576
$916$	1.25851e21	0.0768495
$917$	−8.87050e21	−0.537252
$918$	−2.96888e21	−0.178350
$919$	−1.29719e22	−0.772927	−0.386464	−	0.922305i	$-0.626304\pi$
$919$	−1.29719e22	−0.772927	−0.386464	+	0.922305i	$0.626304\pi$
$920$	−4.52815e21	−0.267616
$921$	−2.27467e22	−1.33343
$922$	−1.03007e22	−0.598944
$923$	3.93479e22	2.26939
$924$	2.79752e22	1.60042
$925$	4.18653e21	0.237570
$926$	−1.18995e22	−0.669803
$927$	−3.39180e22	−1.89379
$928$	5.48831e20	0.0303969
$929$	2.38798e22	1.31194	0.655969	−	0.754788i	$-0.272260\pi$
$929$	2.38798e22	1.31194	0.655969	+	0.754788i	$0.272260\pi$
$930$	−1.62520e20	−0.00885694
$931$	6.81016e21	0.368158
$932$	−1.14957e22	−0.616477
$933$	−2.28353e22	−1.21477
$934$	1.75977e21	0.0928655
$935$	6.94933e21	0.363794
$936$	1.16201e22	0.603451
$937$	−1.55876e22	−0.803033	−0.401516	−	0.915852i	$-0.631517\pi$
$937$	−1.55876e22	−0.803033	−0.401516	+	0.915852i	$0.631517\pi$
$938$	−2.12390e22	−1.08546
$939$	4.10619e22	2.08184
$940$	−5.50277e20	−0.0276772
$941$	−1.19037e21	−0.0593964	−0.0296982	−	0.999559i	$-0.509455\pi$
$941$	−1.19037e21	−0.0593964	−0.0296982	+	0.999559i	$0.509455\pi$
$942$	2.55657e22	1.26554
$943$	−2.51284e22	−1.23404
$944$	−8.01393e21	−0.390441
$945$	5.98007e21	0.289046
$946$	−6.03829e21	−0.289554
$947$	−1.18652e22	−0.564482	−0.282241	−	0.959343i	$-0.591078\pi$
$947$	−1.18652e22	−0.564482	−0.282241	+	0.959343i	$0.591078\pi$
$948$	−1.77098e22	−0.835896
$949$	−1.63948e22	−0.767732
$950$	2.92211e21	0.135759
$951$	−3.68297e22	−1.69763
$952$	−4.17399e21	−0.190886
$953$	−7.68749e21	−0.348809	−0.174404	−	0.984674i	$-0.555800\pi$
$953$	−7.68749e21	−0.348809	−0.174404	+	0.984674i	$0.555800\pi$
$954$	2.77602e22	1.24971
$955$	1.25573e22	0.560881
$956$	−7.89970e21	−0.350087
$957$	−1.06418e22	−0.467925
$958$	8.57533e21	0.374119
$959$	−2.16798e21	−0.0938459
$960$	−1.99856e21	−0.0858387
$961$	−2.34575e22	−0.999667
$962$	2.49686e22	1.05580
$963$	4.66036e22	1.95534
$964$	2.25101e21	0.0937129
$965$	5.25917e21	0.217251
$966$	−5.27358e22	−2.16161
$967$	2.96436e22	1.20568	0.602840	−	0.797862i	$-0.294036\pi$
$967$	2.96436e22	1.20568	0.602840	+	0.797862i	$0.294036\pi$
$968$	1.87533e22	0.756853
$969$	−1.68954e22	−0.676611
$970$	−1.82237e21	−0.0724182
$971$	3.79674e22	1.49715	0.748577	−	0.663047i	$-0.230737\pi$
$971$	3.79674e22	1.49715	0.748577	+	0.663047i	$0.230737\pi$
$972$	1.71085e22	0.669447
$973$	2.57764e22	1.00087
$974$	−2.31414e21	−0.0891655
$975$	−1.00962e22	−0.386032
$976$	4.18890e21	0.158937
$977$	−1.73025e21	−0.0651479	−0.0325739	−	0.999469i	$-0.510370\pi$
$977$	−1.73025e21	−0.0651479	−0.0325739	+	0.999469i	$0.510370\pi$
$978$	3.78634e22	1.41474
$979$	−2.08138e22	−0.771758
$980$	2.33057e21	0.0857563
$981$	4.38203e22	1.60014
$982$	−1.38434e22	−0.501657
$983$	2.72751e22	0.980878	0.490439	−	0.871476i	$-0.336836\pi$
$983$	2.72751e22	0.980878	0.490439	+	0.871476i	$0.336836\pi$
$984$	−1.10908e22	−0.395821
$985$	7.39370e21	0.261873
$986$	1.58779e21	0.0558106
$987$	−6.40864e21	−0.223556
$988$	1.74275e22	0.603335
$989$	1.13827e22	0.391088
$990$	2.23167e22	0.760967
$991$	4.94891e22	1.67478	0.837389	−	0.546607i	$-0.184081\pi$
$991$	4.94891e22	1.67478	0.837389	+	0.546607i	$0.184081\pi$
$992$	9.60038e19	0.00322441
$993$	−3.66202e22	−1.22068
$994$	−4.53887e22	−1.50159
$995$	1.69203e21	0.0555565
$996$	2.93179e22	0.955406
$997$	6.46309e21	0.209039	0.104519	−	0.994523i	$-0.466670\pi$
$997$	6.46309e21	0.209039	0.104519	+	0.994523i	$0.466670\pi$
$998$	8.85861e21	0.284372
$999$	−2.04863e22	−0.652712

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.16.a.d.1.1	✓	2
3.2	odd	2		90.16.a.j.1.1		2
4.3	odd	2		80.16.a.f.1.2		2
5.2	odd	4		50.16.b.e.49.4		4
5.3	odd	4		50.16.b.e.49.1		4
5.4	even	2		50.16.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.16.a.d.1.1	✓	2	1.1	even	1	trivial
50.16.a.f.1.2		2	5.4	even	2
50.16.b.e.49.1		4	5.3	odd	4
50.16.b.e.49.4		4	5.2	odd	4
80.16.a.f.1.2		2	4.3	odd	2
90.16.a.j.1.1		2	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+128.000 q^{2} -5816.58 q^{3} +16384.0 q^{4} +78125.0 q^{5} -744522. q^{6} -2.56287e6 q^{7} +2.09715e6 q^{8} +1.94837e7 q^{9} +1.00000e7 q^{10} +1.14540e8 q^{11} -9.52988e7 q^{12} +2.84387e8 q^{13} -3.28048e8 q^{14} -4.54420e8 q^{15} +2.68435e8 q^{16} +7.76594e8 q^{17} +2.49391e9 q^{18} +3.74029e9 q^{19} +1.28000e9 q^{20} +1.49072e10 q^{21} +1.46612e10 q^{22} -2.76376e10 q^{23} -1.21982e10 q^{24} +6.10352e9 q^{25} +3.64016e10 q^{26} -2.98668e10 q^{27} -4.19901e10 q^{28} +1.59731e10 q^{29} -5.81658e10 q^{30} +2.79408e9 q^{31} +3.43597e10 q^{32} -6.66233e11 q^{33} +9.94040e10 q^{34} -2.00224e11 q^{35} +3.19221e11 q^{36} +6.85921e11 q^{37} +4.78758e11 q^{38} -1.65416e12 q^{39} +1.63840e11 q^{40} +9.09210e11 q^{41} +1.90812e12 q^{42} -4.11856e11 q^{43} +1.87663e12 q^{44} +1.52216e12 q^{45} -3.53762e12 q^{46} -4.29904e11 q^{47} -1.56138e12 q^{48} +1.82076e12 q^{49} +7.81250e11 q^{50} -4.51712e12 q^{51} +4.65940e12 q^{52} +1.11312e13 q^{53} -3.82295e12 q^{54} +8.94847e12 q^{55} -5.37473e12 q^{56} -2.17557e13 q^{57} +2.04456e12 q^{58} -2.98542e13 q^{59} -7.44522e12 q^{60} +1.56049e13 q^{61} +3.57642e11 q^{62} -4.99342e13 q^{63} +4.39805e12 q^{64} +2.22178e13 q^{65} -8.52778e13 q^{66} +6.47436e13 q^{67} +1.27237e13 q^{68} +1.60757e14 q^{69} -2.56287e13 q^{70} +1.38360e14 q^{71} +4.08602e13 q^{72} -5.76496e13 q^{73} +8.77978e13 q^{74} -3.55016e13 q^{75} +6.12810e13 q^{76} -2.93552e14 q^{77} -2.11733e14 q^{78} +1.85835e14 q^{79} +2.09715e13 q^{80} -1.05847e14 q^{81} +1.16379e14 q^{82} -3.07642e14 q^{83} +2.44239e14 q^{84} +6.06714e13 q^{85} -5.27175e13 q^{86} -9.29088e13 q^{87} +2.40209e14 q^{88} -1.81716e14 q^{89} +1.94837e14 q^{90} -7.28848e14 q^{91} -4.52815e14 q^{92} -1.62520e13 q^{93} -5.50277e13 q^{94} +2.92211e14 q^{95} -1.99856e14 q^{96} -1.82237e14 q^{97} +2.33057e14 q^{98} +2.23167e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 256 q^{2} - 1844 q^{3} + 32768 q^{4} + 156250 q^{5} - 236032 q^{6} - 984932 q^{7} + 4194304 q^{8} + 20916154 q^{9} + 20000000 q^{10} + 111552144 q^{11} - 30212096 q^{12} + 289313596 q^{13} - 126071296 q^{14}+ \cdots + 22\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 256 * q^2 - 1844 * q^3 + 32768 * q^4 + 156250 * q^5 - 236032 * q^6 - 984932 * q^7 + 4194304 * q^8 + 20916154 * q^9 + 20000000 * q^10 + 111552144 * q^11 - 30212096 * q^12 + 289313596 * q^13 - 126071296 * q^14 - 144062500 * q^15 + 536870912 * q^16 + 1421739348 * q^17 + 2677267712 * q^18 + 6159406120 * q^19 + 2560000000 * q^20 + 21175644704 * q^21 + 14278674432 * q^22 - 4330165884 * q^23 - 3867148288 * q^24 + 12207031250 * q^25 + 37032140288 * q^26 - 81178356680 * q^27 - 16137125888 * q^28 - 164295941940 * q^29 - 18440000000 * q^30 - 282710965016 * q^31 + 68719476736 * q^32 - 678104159568 * q^33 + 181982636544 * q^34 - 76947812500 * q^35 + 342690267136 * q^36 + 790105159228 * q^37 + 788403983360 * q^38 - 1634590297912 * q^39 + 327680000000 * q^40 - 374717265276 * q^41 + 2710482522112 * q^42 - 923824433204 * q^43 + 1827670327296 * q^44 + 1634074531250 * q^45 - 554261233152 * q^46 + 4796717212428 * q^47 - 494994980864 * q^48 - 436909177374 * q^49 + 1562500000000 * q^50 - 1954230185256 * q^51 + 4740113956864 * q^52 - 2768921292084 * q^53 - 10390829655040 * q^54 + 8715011250000 * q^55 - 2065552113664 * q^56 - 12145610545840 * q^57 - 21029880568320 * q^58 - 20737233989880 * q^59 - 2360320000000 * q^60 + 577887725164 * q^61 - 36187003522048 * q^62 - 47673833661364 * q^63 + 8796093022208 * q^64 + 22602624687500 * q^65 - 86797332424704 * q^66 + 86553258077668 * q^67 + 23293777477632 * q^68 + 253347375370848 * q^69 - 9849320000000 * q^70 + 73838906689464 * q^71 + 43864354193408 * q^72 + 39973727021476 * q^73 + 101133460381184 * q^74 - 11254882812500 * q^75 + 100915709870080 * q^76 - 298267692171504 * q^77 - 209227558132736 * q^78 + 421665304874800 * q^79 + 41943040000000 * q^80 - 330240444620318 * q^81 - 47963809955328 * q^82 - 721146660038964 * q^83 + 346941762830336 * q^84 + 111073386562500 * q^85 - 118249527450112 * q^86 - 809041723785720 * q^87 + 233941801893888 * q^88 + 363712836623220 * q^89 + 209161540000000 * q^90 - 721074767062936 * q^91 - 70945437843456 * q^92 - 1150443201950848 * q^93 + 613979803190784 * q^94 + 481203603125000 * q^95 - 63359357550592 * q^96 + 289030099396948 * q^97 - 55924374703872 * q^98 + 2227387596150288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more