LMFDB - Embedded newform 10.26.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,26,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, 26, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 26 $
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:	$39.5996779952$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{95351}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 95351 $ x^2 - 95351
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$308.790$ 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)

$f(q)$	$=$	\(q+4096.00 q^{2} +618439. q^{3} +1.67772e7 q^{4} -2.44141e8 q^{5} +2.53313e9 q^{6} +4.78762e10 q^{7} +6.87195e10 q^{8} -4.64821e11 q^{9} -1.00000e12 q^{10} +3.58198e11 q^{11} +1.03757e13 q^{12} +7.76408e13 q^{13} +1.96101e14 q^{14} -1.50986e14 q^{15} +2.81475e14 q^{16} +1.50624e15 q^{17} -1.90391e15 q^{18} +4.83611e15 q^{19} -4.09600e15 q^{20} +2.96085e16 q^{21} +1.46718e15 q^{22} +2.59330e16 q^{23} +4.24988e16 q^{24} +5.96046e16 q^{25} +3.18017e17 q^{26} -8.11461e17 q^{27} +8.03229e17 q^{28} +9.30223e17 q^{29} -6.18439e17 q^{30} +3.10982e18 q^{31} +1.15292e18 q^{32} +2.21524e17 q^{33} +6.16957e18 q^{34} -1.16885e19 q^{35} -7.79841e18 q^{36} -4.54619e19 q^{37} +1.98087e19 q^{38} +4.80162e19 q^{39} -1.67772e19 q^{40} +1.02459e20 q^{41} +1.21276e20 q^{42} +4.58049e20 q^{43} +6.00957e18 q^{44} +1.13482e20 q^{45} +1.06222e20 q^{46} +1.51063e21 q^{47} +1.74075e20 q^{48} +9.51058e20 q^{49} +2.44141e20 q^{50} +9.31520e20 q^{51} +1.30260e21 q^{52} -2.00272e21 q^{53} -3.32374e21 q^{54} -8.74507e19 q^{55} +3.29002e21 q^{56} +2.99084e21 q^{57} +3.81019e21 q^{58} +2.00362e22 q^{59} -2.53313e21 q^{60} -2.40289e22 q^{61} +1.27378e22 q^{62} -2.22539e22 q^{63} +4.72237e21 q^{64} -1.89553e22 q^{65} +9.07362e20 q^{66} -5.68406e22 q^{67} +2.52706e22 q^{68} +1.60380e22 q^{69} -4.78762e22 q^{70} +2.06619e22 q^{71} -3.19423e22 q^{72} -3.20846e23 q^{73} -1.86212e23 q^{74} +3.68619e22 q^{75} +8.11365e22 q^{76} +1.71492e22 q^{77} +1.96674e23 q^{78} -4.28561e23 q^{79} -6.87195e22 q^{80} -1.08001e23 q^{81} +4.19671e23 q^{82} -1.11807e24 q^{83} +4.96748e23 q^{84} -3.67735e23 q^{85} +1.87617e24 q^{86} +5.75287e23 q^{87} +2.46152e22 q^{88} +1.75157e24 q^{89} +4.64821e23 q^{90} +3.71714e24 q^{91} +4.35084e23 q^{92} +1.92323e24 q^{93} +6.18754e24 q^{94} -1.18069e24 q^{95} +7.13012e23 q^{96} -1.28690e25 q^{97} +3.89553e24 q^{98} -1.66498e23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8192 q^{2} - 97092 q^{3} + 33554432 q^{4} - 488281250 q^{5} - 397688832 q^{6} - 16137160124 q^{7} + 137438953472 q^{8} - 800124539454 q^{9} - 2000000000000 q^{10} + 14416600801344 q^{11} - 1628933455872 q^{12}+ \cdots - 48\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 8192 * q^2 - 97092 * q^3 + 33554432 * q^4 - 488281250 * q^5 - 397688832 * q^6 - 16137160124 * q^7 + 137438953472 * q^8 - 800124539454 * q^9 - 2000000000000 * q^10 + 14416600801344 * q^11 - 1628933455872 * q^12 + 93404548866628 * q^13 - 66097807867904 * q^14 + 23704101562500 * q^15 + 562949953421312 * q^16 + 499266882181236 * q^17 - 3277310113603584 * q^18 - 3830204591906120 * q^19 - 8192000000000000 * q^20 + 75412053748282104 * q^21 + 59050396882305024 * q^22 + 169271186050723788 * q^23 - 6672111435251712 * q^24 + 119209289550781250 * q^25 + 382585032157708288 * q^26 + 34721228182863240 * q^27 - 270736621026934784 * q^28 + 569443622853716940 * q^29 + 97092000000000000 * q^30 + 3982769593868414584 * q^31 + 2305843009213693952 * q^32 - 9837705729224836224 * q^33 + 2044997149414342656 * q^34 + 3939736358398437500 * q^35 - 13423862225320280064 * q^36 + 28241444663789328196 * q^37 - 15688518008447467520 * q^38 + 36736718047624459512 * q^39 - 33554432000000000000 * q^40 + 36676428854020432524 * q^41 + 308887772152963497984 * q^42 + 909017314298263251628 * q^43 + 241870425629921378304 * q^44 + 195342905140136718750 * q^45 + 693334778063764635648 * q^46 + 954929084389204818996 * q^47 - 27328968438791012352 * q^48 + 3707694774551412650874 * q^49 + 488281250000000000000 * q^50 + 1652042752773544110744 * q^51 + 1567068291717973147648 * q^52 + 2753692919774994609588 * q^53 + 142218150637007831040 * q^54 - 3519677930015625000000 * q^55 - 1108937199726324875264 * q^56 + 9191867441696689119120 * q^57 + 2332441079208824586240 * q^58 + 458866752134906177880 * q^59 + 397688832000000000000 * q^60 - 26987853585082462424636 * q^61 + 16313424256485026136064 * q^62 - 789976870259963054652 * q^63 + 9444732965739290427392 * q^64 - 22803844938141601562500 * q^65 - 40295242666904929173504 * q^66 - 14159647018044347838524 * q^67 + 8376308324001147518976 * q^68 - 86524983849189139233048 * q^69 + 16137160124000000000000 * q^70 - 173327708998984655450136 * q^71 - 54984139674911867142144 * q^72 - 341978509295241035156732 * q^73 + 115676957342881088290816 * q^74 - 5787134170532226562500 * q^75 - 64260169762600826961920 * q^76 - 882775887628764911584128 * q^77 + 150473597123069786161152 * q^78 - 927961875376490258946800 * q^79 - 137438953472000000000000 * q^80 - 429372483438817686010518 * q^81 + 150226652586067691618304 * q^82 + 681902409230287477811148 * q^83 + 1265204314738538487742464 * q^84 - 121891328657528320312500 * q^85 + 3723334919365686278668288 * q^86 + 833435461987898381769960 * q^87 + 990701263380157965533184 * q^88 + 3822788098104790038225780 * q^89 + 800124539454000000000000 * q^90 + 2708056932935479178393864 * q^91 + 2839899250949179947614208 * q^92 + 1298609917529886715704336 * q^93 + 3911389529658182938607616 * q^94 + 935108542945830078125000 * q^95 - 111939454725287986593792 * q^96 - 16314734149871901683914364 * q^97 + 15186717796562586217979904 * q^98 - 4880327126898398506596288 * 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 $

$2$	4096.00	0.707107
$2$	4096.00	0.707107
$3$	618439.	0.671864	0.335932	−	0.941886i	$-0.390949\pi$
$3$	618439.	0.671864	0.335932	+	0.941886i	$0.390949\pi$
$4$	1.67772e7	0.500000
$5$	−2.44141e8	−0.447214
$5$	−2.44141e8	−0.447214
$6$	2.53313e9	0.475080
$7$	4.78762e10	1.30736	0.653678	−	0.756773i	$-0.273225\pi$
$7$	4.78762e10	1.30736	0.653678	+	0.756773i	$0.273225\pi$
$8$	6.87195e10	0.353553
$9$	−4.64821e11	−0.548598
$10$	−1.00000e12	−0.316228
$11$	3.58198e11	0.0344124	0.0172062	−	0.999852i	$-0.494523\pi$
$11$	3.58198e11	0.0344124	0.0172062	+	0.999852i	$0.494523\pi$
$12$	1.03757e13	0.335932
$13$	7.76408e13	0.924269	0.462134	−	0.886810i	$-0.347084\pi$
$13$	7.76408e13	0.924269	0.462134	+	0.886810i	$0.347084\pi$
$14$	1.96101e14	0.924440
$15$	−1.50986e14	−0.300467
$16$	2.81475e14	0.250000
$17$	1.50624e15	0.627023	0.313511	−	0.949584i	$-0.398495\pi$
$17$	1.50624e15	0.627023	0.313511	+	0.949584i	$0.398495\pi$
$18$	−1.90391e15	−0.387918
$19$	4.83611e15	0.501276	0.250638	−	0.968081i	$-0.419360\pi$
$19$	4.83611e15	0.501276	0.250638	+	0.968081i	$0.419360\pi$
$20$	−4.09600e15	−0.223607
$21$	2.96085e16	0.878366
$22$	1.46718e15	0.0243332
$23$	2.59330e16	0.246749	0.123374	−	0.992360i	$-0.460628\pi$
$23$	2.59330e16	0.246749	0.123374	+	0.992360i	$0.460628\pi$
$24$	4.24988e16	0.237540
$25$	5.96046e16	0.200000
$26$	3.18017e17	0.653557
$27$	−8.11461e17	−1.04045
$28$	8.03229e17	0.653678
$29$	9.30223e17	0.488216	0.244108	−	0.969748i	$-0.421505\pi$
$29$	9.30223e17	0.488216	0.244108	+	0.969748i	$0.421505\pi$
$30$	−6.18439e17	−0.212462
$31$	3.10982e18	0.709110	0.354555	−	0.935035i	$-0.384632\pi$
$31$	3.10982e18	0.709110	0.354555	+	0.935035i	$0.384632\pi$
$32$	1.15292e18	0.176777
$33$	2.21524e17	0.0231205
$34$	6.16957e18	0.443372
$35$	−1.16885e19	−0.584667
$36$	−7.79841e18	−0.274299
$37$	−4.54619e19	−1.13534	−0.567670	−	0.823256i	$-0.692155\pi$
$37$	−4.54619e19	−1.13534	−0.567670	+	0.823256i	$0.692155\pi$
$38$	1.98087e19	0.354455
$39$	4.80162e19	0.620983
$40$	−1.67772e19	−0.158114
$41$	1.02459e20	0.709172	0.354586	−	0.935023i	$-0.384622\pi$
$41$	1.02459e20	0.709172	0.354586	+	0.935023i	$0.384622\pi$
$42$	1.21276e20	0.621098
$43$	4.58049e20	1.74806	0.874029	−	0.485874i	$-0.161498\pi$
$43$	4.58049e20	1.74806	0.874029	+	0.485874i	$0.161498\pi$
$44$	6.00957e18	0.0172062
$45$	1.13482e20	0.245341
$46$	1.06222e20	0.174478
$47$	1.51063e21	1.89642	0.948210	−	0.317644i	$-0.102892\pi$
$47$	1.51063e21	1.89642	0.948210	+	0.317644i	$0.102892\pi$
$48$	1.74075e20	0.167966
$49$	9.51058e20	0.709179
$50$	2.44141e20	0.141421
$51$	9.31520e20	0.421274
$52$	1.30260e21	0.462134
$53$	−2.00272e21	−0.559980	−0.279990	−	0.960003i	$-0.590331\pi$
$53$	−2.00272e21	−0.559980	−0.279990	+	0.960003i	$0.590331\pi$
$54$	−3.32374e21	−0.735708
$55$	−8.74507e19	−0.0153897
$56$	3.29002e21	0.462220
$57$	2.99084e21	0.336789
$58$	3.81019e21	0.345221
$59$	2.00362e22	1.46611	0.733053	−	0.680171i	$-0.238095\pi$
$59$	2.00362e22	1.46611	0.733053	+	0.680171i	$0.238095\pi$
$60$	−2.53313e21	−0.150233
$61$	−2.40289e22	−1.15908	−0.579538	−	0.814945i	$-0.696767\pi$
$61$	−2.40289e22	−1.15908	−0.579538	+	0.814945i	$0.696767\pi$
$62$	1.27378e22	0.501417
$63$	−2.22539e22	−0.717213
$64$	4.72237e21	0.125000
$65$	−1.89553e22	−0.413346
$66$	9.07362e20	0.0163486
$67$	−5.68406e22	−0.848640	−0.424320	−	0.905512i	$-0.639487\pi$
$67$	−5.68406e22	−0.848640	−0.424320	+	0.905512i	$0.639487\pi$
$68$	2.52706e22	0.313511
$69$	1.60380e22	0.165782
$70$	−4.78762e22	−0.413422
$71$	2.06619e22	0.149431	0.0747156	−	0.997205i	$-0.476195\pi$
$71$	2.06619e22	0.149431	0.0747156	+	0.997205i	$0.476195\pi$
$72$	−3.19423e22	−0.193959
$73$	−3.20846e23	−1.63969	−0.819843	−	0.572588i	$-0.805939\pi$
$73$	−3.20846e23	−1.63969	−0.819843	+	0.572588i	$0.805939\pi$
$74$	−1.86212e23	−0.802806
$75$	3.68619e22	0.134373
$76$	8.11365e22	0.250638
$77$	1.71492e22	0.0449892
$78$	1.96674e23	0.439101
$79$	−4.28561e23	−0.815969	−0.407985	−	0.912989i	$-0.633768\pi$
$79$	−4.28561e23	−0.815969	−0.407985	+	0.912989i	$0.633768\pi$
$80$	−6.87195e22	−0.111803
$81$	−1.08001e23	−0.150441
$82$	4.19671e23	0.501460
$83$	−1.11807e24	−1.14814	−0.574069	−	0.818807i	$-0.694636\pi$
$83$	−1.11807e24	−1.14814	−0.574069	+	0.818807i	$0.694636\pi$
$84$	4.96748e23	0.439183
$85$	−3.67735e23	−0.280413
$86$	1.87617e24	1.23606
$87$	5.75287e23	0.328015
$88$	2.46152e22	0.0121666
$89$	1.75157e24	0.751712	0.375856	−	0.926678i	$-0.377349\pi$
$89$	1.75157e24	0.751712	0.375856	+	0.926678i	$0.377349\pi$
$90$	4.64821e23	0.173482
$91$	3.71714e24	1.20835
$92$	4.35084e23	0.123374
$93$	1.92323e24	0.476426
$94$	6.18754e24	1.34097
$95$	−1.18069e24	−0.224177
$96$	7.13012e23	0.118770
$97$	−1.28690e25	−1.88320	−0.941601	−	0.336729i	$-0.890679\pi$
$97$	−1.28690e25	−1.88320	−0.941601	+	0.336729i	$0.890679\pi$
$98$	3.89553e24	0.501466
$99$	−1.66498e23	−0.0188786
$100$	1.00000e24	0.100000
$101$	−3.20176e24	−0.282730	−0.141365	−	0.989958i	$-0.545149\pi$
$101$	−3.20176e24	−0.282730	−0.141365	+	0.989958i	$0.545149\pi$
$102$	3.81551e24	0.297886
$103$	−5.43797e23	−0.0375813	−0.0187906	−	0.999823i	$-0.505982\pi$
$103$	−5.43797e23	−0.0375813	−0.0187906	+	0.999823i	$0.505982\pi$
$104$	5.33544e24	0.326778
$105$	−7.22864e24	−0.392817
$106$	−8.20316e24	−0.395966
$107$	−1.45562e25	−0.624816	−0.312408	−	0.949948i	$-0.601136\pi$
$107$	−1.45562e25	−0.624816	−0.312408	+	0.949948i	$0.601136\pi$
$108$	−1.36140e25	−0.520224
$109$	−3.33253e25	−1.13486	−0.567431	−	0.823421i	$-0.692063\pi$
$109$	−3.33253e25	−1.13486	−0.567431	+	0.823421i	$0.692063\pi$
$110$	−3.58198e23	−0.0108822
$111$	−2.81154e25	−0.762794
$112$	1.34759e25	0.326839
$113$	1.71253e25	0.371670	0.185835	−	0.982581i	$-0.440501\pi$
$113$	1.71253e25	0.371670	0.185835	+	0.982581i	$0.440501\pi$
$114$	1.22505e25	0.238146
$115$	−6.33130e24	−0.110349
$116$	1.56066e25	0.244108
$117$	−3.60891e25	−0.507052
$118$	8.20683e25	1.03669
$119$	7.21131e25	0.819742
$120$	−1.03757e25	−0.106231
$121$	−1.08219e26	−0.998816
$122$	−9.84225e25	−0.819590
$123$	6.33646e25	0.476467
$124$	5.21741e25	0.354555
$125$	−1.45519e25	−0.0894427
$126$	−9.11518e25	−0.507146
$127$	−2.80916e26	−1.41589	−0.707947	−	0.706266i	$-0.750378\pi$
$127$	−2.80916e26	−1.41589	−0.707947	+	0.706266i	$0.750378\pi$
$128$	1.93428e25	0.0883883
$129$	2.83275e26	1.17446
$130$	−7.76408e25	−0.292279
$131$	3.91683e26	1.33981	0.669906	−	0.742446i	$-0.266334\pi$
$131$	3.91683e26	1.33981	0.669906	+	0.742446i	$0.266334\pi$
$132$	3.71655e24	0.0115602
$133$	2.31535e26	0.655346
$134$	−2.32819e26	−0.600079
$135$	1.98110e26	0.465302
$136$	1.03508e26	0.221686
$137$	7.30593e24	0.0142780	0.00713902	−	0.999975i	$-0.497728\pi$
$137$	7.30593e24	0.0142780	0.00713902	+	0.999975i	$0.497728\pi$
$138$	6.56916e25	0.117225
$139$	9.32000e26	1.51961	0.759803	−	0.650154i	$-0.225295\pi$
$139$	9.32000e26	1.51961	0.759803	+	0.650154i	$0.225295\pi$
$140$	−1.96101e26	−0.292334
$141$	9.34233e26	1.27414
$142$	8.46313e25	0.105664
$143$	2.78108e25	0.0318063
$144$	−1.30836e26	−0.137150
$145$	−2.27105e26	−0.218337
$146$	−1.31419e27	−1.15943
$147$	5.88172e26	0.476472
$148$	−7.62723e26	−0.567670
$149$	−2.86893e27	−1.96287	−0.981434	−	0.191800i	$-0.938567\pi$
$149$	−2.86893e27	−1.96287	−0.981434	+	0.191800i	$0.938567\pi$
$150$	1.50986e26	0.0950160
$151$	6.35122e26	0.367828	0.183914	−	0.982942i	$-0.441123\pi$
$151$	6.35122e26	0.367828	0.183914	+	0.982942i	$0.441123\pi$
$152$	3.32335e26	0.177228
$153$	−7.00134e26	−0.343984
$154$	7.02429e25	0.0318122
$155$	−7.59233e26	−0.317124
$156$	8.05577e26	0.310492
$157$	−2.51786e27	−0.895954	−0.447977	−	0.894045i	$-0.647855\pi$
$157$	−2.51786e27	−0.895954	−0.447977	+	0.894045i	$0.647855\pi$
$158$	−1.75538e27	−0.576977
$159$	−1.23856e27	−0.376231
$160$	−2.81475e26	−0.0790569
$161$	1.24157e27	0.322588
$162$	−4.42374e26	−0.106378
$163$	−4.89494e26	−0.108994	−0.0544970	−	0.998514i	$-0.517356\pi$
$163$	−4.89494e26	−0.108994	−0.0544970	+	0.998514i	$0.517356\pi$
$164$	1.71897e27	0.354586
$165$	−5.40830e25	−0.0103398
$166$	−4.57963e27	−0.811856
$167$	2.73255e27	0.449378	0.224689	−	0.974430i	$-0.427863\pi$
$167$	2.73255e27	0.449378	0.224689	+	0.974430i	$0.427863\pi$
$168$	2.03468e27	0.310549
$169$	−1.02831e27	−0.145727
$170$	−1.50624e27	−0.198282
$171$	−2.24793e27	−0.274999
$172$	7.68478e27	0.874029
$173$	8.64082e27	0.914069	0.457034	−	0.889449i	$-0.348912\pi$
$173$	8.64082e27	0.914069	0.457034	+	0.889449i	$0.348912\pi$
$174$	2.35637e27	0.231942
$175$	2.85364e27	0.261471
$176$	1.00824e26	0.00860310
$177$	1.23912e28	0.985025
$178$	7.17441e27	0.531540
$179$	−2.03598e28	−1.40640	−0.703201	−	0.710991i	$-0.748247\pi$
$179$	−2.03598e28	−1.40640	−0.703201	+	0.710991i	$0.748247\pi$
$180$	1.90391e27	0.122670
$181$	1.34351e28	0.807718	0.403859	−	0.914821i	$-0.367669\pi$
$181$	1.34351e28	0.807718	0.403859	+	0.914821i	$0.367669\pi$
$182$	1.52254e28	0.854431
$183$	−1.48604e28	−0.778741
$184$	1.78210e27	0.0872388
$185$	1.10991e28	0.507739
$186$	7.87757e27	0.336884
$187$	5.39533e26	0.0215774
$188$	2.53441e28	0.948210
$189$	−3.88496e28	−1.36024
$190$	−4.83611e27	−0.158517
$191$	−1.46283e28	−0.449030	−0.224515	−	0.974471i	$-0.572080\pi$
$191$	−1.46283e28	−0.449030	−0.224515	+	0.974471i	$0.572080\pi$
$192$	2.92050e27	0.0839830
$193$	3.37927e28	0.910659	0.455330	−	0.890323i	$-0.349521\pi$
$193$	3.37927e28	0.910659	0.455330	+	0.890323i	$0.349521\pi$
$194$	−5.27113e28	−1.33163
$195$	−1.17227e28	−0.277712
$196$	1.59561e28	0.354590
$197$	−5.93119e28	−1.23684	−0.618420	−	0.785847i	$-0.712227\pi$
$197$	−5.93119e28	−1.23684	−0.618420	+	0.785847i	$0.712227\pi$
$198$	−6.81976e26	−0.0133492
$199$	−1.85919e28	−0.341712	−0.170856	−	0.985296i	$-0.554653\pi$
$199$	−1.85919e28	−0.341712	−0.170856	+	0.985296i	$0.554653\pi$
$200$	4.09600e27	0.0707107
$201$	−3.51525e28	−0.570171
$202$	−1.31144e28	−0.199920
$203$	4.45355e28	0.638272
$204$	1.56283e28	0.210637
$205$	−2.50144e28	−0.317151
$206$	−2.22739e27	−0.0265740
$207$	−1.20542e28	−0.135366
$208$	2.18540e28	0.231067
$209$	1.73229e27	0.0172501
$210$	−2.96085e28	−0.277764
$211$	1.59544e29	1.41042	0.705212	−	0.708996i	$-0.250852\pi$
$211$	1.59544e29	1.41042	0.705212	+	0.708996i	$0.250852\pi$
$212$	−3.36001e28	−0.279990
$213$	1.27782e28	0.100398
$214$	−5.96224e28	−0.441812
$215$	−1.11828e29	−0.781755
$216$	−5.57631e28	−0.367854
$217$	1.48886e29	0.927060
$218$	−1.36501e29	−0.802469
$219$	−1.98424e29	−1.10165
$220$	−1.46718e27	−0.00769484
$221$	1.16946e29	0.579538
$222$	−1.15161e29	−0.539377
$223$	2.93272e29	1.29855	0.649277	−	0.760552i	$-0.275072\pi$
$223$	2.93272e29	1.29855	0.649277	+	0.760552i	$0.275072\pi$
$224$	5.51975e28	0.231110
$225$	−2.77055e28	−0.109720
$226$	7.01452e28	0.262810
$227$	2.86033e29	1.01413	0.507065	−	0.861908i	$-0.330730\pi$
$227$	2.86033e29	1.01413	0.507065	+	0.861908i	$0.330730\pi$
$228$	5.01780e28	0.168395
$229$	−2.27815e29	−0.723833	−0.361916	−	0.932211i	$-0.617877\pi$
$229$	−2.27815e29	−0.723833	−0.361916	+	0.932211i	$0.617877\pi$
$230$	−2.59330e28	−0.0780288
$231$	1.06057e28	0.0302267
$232$	6.39244e28	0.172610
$233$	6.95835e29	1.78056	0.890281	−	0.455411i	$-0.150508\pi$
$233$	6.95835e29	1.78056	0.890281	+	0.455411i	$0.150508\pi$
$234$	−1.47821e29	−0.358540
$235$	−3.68806e29	−0.848105
$236$	3.36152e29	0.733053
$237$	−2.65039e29	−0.548220
$238$	2.95375e29	0.579645
$239$	1.46812e29	0.273393	0.136696	−	0.990613i	$-0.456352\pi$
$239$	1.46812e29	0.273393	0.136696	+	0.990613i	$0.456352\pi$
$240$	−4.24988e28	−0.0751167
$241$	7.86832e29	1.32029	0.660144	−	0.751139i	$-0.270495\pi$
$241$	7.86832e29	1.32029	0.660144	+	0.751139i	$0.270495\pi$
$242$	−4.43264e29	−0.706269
$243$	6.20749e29	0.939372
$244$	−4.03139e29	−0.579538
$245$	−2.32192e29	−0.317155
$246$	2.59541e29	0.336913
$247$	3.75480e29	0.463313
$248$	2.13705e29	0.250708
$249$	−6.91461e29	−0.771393
$250$	−5.96046e28	−0.0632456
$251$	−1.30352e30	−1.31582	−0.657910	−	0.753097i	$-0.728559\pi$
$251$	−1.30352e30	−1.31582	−0.657910	+	0.753097i	$0.728559\pi$
$252$	−3.73358e29	−0.358607
$253$	9.28916e27	0.00849121
$254$	−1.15063e30	−1.00119
$255$	−2.27422e29	−0.188400
$256$	7.92282e28	0.0625000
$257$	−2.21600e30	−1.66496	−0.832482	−	0.554052i	$-0.813081\pi$
$257$	−2.21600e30	−1.66496	−0.832482	+	0.554052i	$0.813081\pi$
$258$	1.16030e30	0.830467
$259$	−2.17654e30	−1.48429
$260$	−3.18017e29	−0.206673
$261$	−4.32387e29	−0.267835
$262$	1.60433e30	0.947390
$263$	3.37258e29	0.189896	0.0949479	−	0.995482i	$-0.469732\pi$
$263$	3.37258e29	0.189896	0.0949479	+	0.995482i	$0.469732\pi$
$264$	1.52230e28	0.00817431
$265$	4.88946e29	0.250431
$266$	9.48366e29	0.463399
$267$	1.08324e30	0.505048
$268$	−9.53627e29	−0.424320
$269$	−4.13865e30	−1.75774	−0.878871	−	0.477059i	$-0.841703\pi$
$269$	−4.13865e30	−1.75774	−0.878871	+	0.477059i	$0.841703\pi$
$270$	8.11461e29	0.329019
$271$	2.28080e29	0.0883021	0.0441511	−	0.999025i	$-0.485942\pi$
$271$	2.28080e29	0.0883021	0.0441511	+	0.999025i	$0.485942\pi$
$272$	4.23970e29	0.156756
$273$	2.29883e30	0.811846
$274$	2.99251e28	0.0100961
$275$	2.13503e28	0.00688248
$276$	2.69073e29	0.0828908
$277$	3.78637e30	1.11487	0.557437	−	0.830219i	$-0.311785\pi$
$277$	3.78637e30	1.11487	0.557437	+	0.830219i	$0.311785\pi$
$278$	3.81747e30	1.07452
$279$	−1.44551e30	−0.389017
$280$	−8.03229e29	−0.206711
$281$	4.87412e30	1.19969	0.599843	−	0.800118i	$-0.295230\pi$
$281$	4.87412e30	1.19969	0.599843	+	0.800118i	$0.295230\pi$
$282$	3.82662e30	0.900951
$283$	−7.79414e29	−0.175565	−0.0877825	−	0.996140i	$-0.527978\pi$
$283$	−7.79414e29	−0.175565	−0.0877825	+	0.996140i	$0.527978\pi$
$284$	3.46650e29	0.0747156
$285$	−7.30186e29	−0.150617
$286$	1.13913e29	0.0224904
$287$	4.90534e30	0.927140
$288$	−5.35902e29	−0.0969794
$289$	−3.50186e30	−0.606842
$290$	−9.30223e29	−0.154387
$291$	−7.95868e30	−1.26526
$292$	−5.38290e30	−0.819843
$293$	8.97738e30	1.31010	0.655050	−	0.755586i	$-0.272648\pi$
$293$	8.97738e30	1.31010	0.655050	+	0.755586i	$0.272648\pi$
$294$	2.40915e30	0.336917
$295$	−4.89165e30	−0.655663
$296$	−3.12412e30	−0.401403
$297$	−2.90664e29	−0.0358043
$298$	−1.17511e31	−1.38796
$299$	2.01346e30	0.228062
$300$	6.18439e29	0.0671864
$301$	2.19296e31	2.28533
$302$	2.60146e30	0.260094
$303$	−1.98009e30	−0.189956
$304$	1.36125e30	0.125319
$305$	5.86644e30	0.518354
$306$	−2.86775e30	−0.243233
$307$	−1.03718e31	−0.844547	−0.422274	−	0.906468i	$-0.638768\pi$
$307$	−1.03718e31	−0.844547	−0.422274	+	0.906468i	$0.638768\pi$
$308$	2.87715e29	0.0224946
$309$	−3.36306e29	−0.0252495
$310$	−3.10982e30	−0.224240
$311$	−3.85228e30	−0.266817	−0.133408	−	0.991061i	$-0.542592\pi$
$311$	−3.85228e30	−0.266817	−0.133408	+	0.991061i	$0.542592\pi$
$312$	3.29965e30	0.219551
$313$	−2.63756e31	−1.68616	−0.843079	−	0.537789i	$-0.819260\pi$
$313$	−2.63756e31	−1.68616	−0.843079	+	0.537789i	$0.819260\pi$
$314$	−1.03132e31	−0.633535
$315$	5.43307e30	0.320748
$316$	−7.19006e30	−0.407985
$317$	−3.65330e30	−0.199271	−0.0996355	−	0.995024i	$-0.531768\pi$
$317$	−3.65330e30	−0.199271	−0.0996355	+	0.995024i	$0.531768\pi$
$318$	−5.07316e30	−0.266035
$319$	3.33204e29	0.0168007
$320$	−1.15292e30	−0.0559017
$321$	−9.00216e30	−0.419792
$322$	5.08548e30	0.228104
$323$	7.28436e30	0.314311
$324$	−1.81196e30	−0.0752206
$325$	4.62775e30	0.184854
$326$	−2.00497e30	−0.0770703
$327$	−2.06097e31	−0.762474
$328$	7.04092e30	0.250730
$329$	7.23231e31	2.47930
$330$	−2.21524e29	−0.00731133
$331$	−2.52293e31	−0.801781	−0.400890	−	0.916126i	$-0.631299\pi$
$331$	−2.52293e31	−0.801781	−0.400890	+	0.916126i	$0.631299\pi$
$332$	−1.87582e31	−0.574069
$333$	2.11316e31	0.622845
$334$	1.11925e31	0.317759
$335$	1.38771e31	0.379523
$336$	8.33405e30	0.219591
$337$	−2.57479e31	−0.653684	−0.326842	−	0.945079i	$-0.605985\pi$
$337$	−2.57479e31	−0.653684	−0.326842	+	0.945079i	$0.605985\pi$
$338$	−4.21196e30	−0.103045
$339$	1.05910e31	0.249712
$340$	−6.16957e30	−0.140207
$341$	1.11393e30	0.0244022
$342$	−9.20751e30	−0.194454
$343$	−1.86722e31	−0.380206
$344$	3.14769e31	0.618032
$345$	−3.91553e30	−0.0741398
$346$	3.53928e31	0.646344
$347$	−1.71059e31	−0.301319	−0.150660	−	0.988586i	$-0.548140\pi$
$347$	−1.71059e31	−0.301319	−0.150660	+	0.988586i	$0.548140\pi$
$348$	9.65171e30	0.164007
$349$	6.93560e31	1.13702	0.568508	−	0.822678i	$-0.307521\pi$
$349$	6.93560e31	1.13702	0.568508	+	0.822678i	$0.307521\pi$
$350$	1.16885e31	0.184888
$351$	−6.30025e31	−0.961653
$352$	4.12974e29	0.00608331
$353$	1.22234e31	0.173783	0.0868914	−	0.996218i	$-0.472307\pi$
$353$	1.22234e31	0.173783	0.0868914	+	0.996218i	$0.472307\pi$
$354$	5.07543e31	0.696518
$355$	−5.04442e30	−0.0668277
$356$	2.93864e31	0.375856
$357$	4.45976e31	0.550755
$358$	−8.33936e31	−0.994477
$359$	5.26279e31	0.606087	0.303044	−	0.952977i	$-0.401997\pi$
$359$	5.26279e31	0.606087	0.303044	+	0.952977i	$0.401997\pi$
$360$	7.79841e30	0.0867410
$361$	−6.96885e31	−0.748723
$362$	5.50303e31	0.571143
$363$	−6.69267e31	−0.671069
$364$	6.23633e31	0.604174
$365$	7.83315e31	0.733290
$366$	−6.08684e31	−0.550653
$367$	−1.04735e31	−0.0915729	−0.0457864	−	0.998951i	$-0.514579\pi$
$367$	−1.04735e31	−0.0915729	−0.0457864	+	0.998951i	$0.514579\pi$
$368$	7.29949e30	0.0616872
$369$	−4.76250e31	−0.389050
$370$	4.54619e31	0.359026
$371$	−9.58828e31	−0.732094
$372$	3.22665e31	0.238213
$373$	−1.24978e32	−0.892221	−0.446111	−	0.894978i	$-0.647191\pi$
$373$	−1.24978e32	−0.892221	−0.446111	+	0.894978i	$0.647191\pi$
$374$	2.20993e30	0.0152575
$375$	−8.99948e30	−0.0600934
$376$	1.03810e32	0.670486
$377$	7.22233e31	0.451243
$378$	−1.59128e32	−0.961832
$379$	−1.71176e32	−1.00104	−0.500522	−	0.865724i	$-0.666859\pi$
$379$	−1.71176e32	−1.00104	−0.500522	+	0.865724i	$0.666859\pi$
$380$	−1.98087e31	−0.112089
$381$	−1.73730e32	−0.951288
$382$	−5.99173e31	−0.317512
$383$	−2.63626e32	−1.35209	−0.676043	−	0.736862i	$-0.736307\pi$
$383$	−2.63626e32	−1.35209	−0.676043	+	0.736862i	$0.736307\pi$
$384$	1.19624e31	0.0593850
$385$	−4.18680e30	−0.0201198
$386$	1.38415e32	0.643933
$387$	−2.12911e32	−0.958982
$388$	−2.15905e32	−0.941601
$389$	3.01567e32	1.27354	0.636772	−	0.771052i	$-0.280269\pi$
$389$	3.01567e32	1.27354	0.636772	+	0.771052i	$0.280269\pi$
$390$	−4.80162e31	−0.196372
$391$	3.90614e31	0.154717
$392$	6.53562e31	0.250733
$393$	2.42232e32	0.900172
$394$	−2.42941e32	−0.874578
$395$	1.04629e32	0.364912
$396$	−2.79337e30	−0.00943929
$397$	3.60886e32	1.18165	0.590824	−	0.806800i	$-0.298803\pi$
$397$	3.60886e32	1.18165	0.590824	+	0.806800i	$0.298803\pi$
$398$	−7.61523e31	−0.241627
$399$	1.43190e32	0.440303
$400$	1.67772e31	0.0500000
$401$	3.40848e32	0.984591	0.492295	−	0.870428i	$-0.336158\pi$
$401$	3.40848e32	0.984591	0.492295	+	0.870428i	$0.336158\pi$
$402$	−1.43985e32	−0.403172
$403$	2.41449e32	0.655409
$404$	−5.37166e31	−0.141365
$405$	2.63676e31	0.0672794
$406$	1.82417e32	0.451327
$407$	−1.62844e31	−0.0390697
$408$	6.40136e31	0.148943
$409$	1.88820e32	0.426095	0.213048	−	0.977042i	$-0.431661\pi$
$409$	1.88820e32	0.426095	0.213048	+	0.977042i	$0.431661\pi$
$410$	−1.02459e32	−0.224260
$411$	4.51827e30	0.00959290
$412$	−9.12340e30	−0.0187906
$413$	9.59257e32	1.91672
$414$	−4.93741e31	−0.0957182
$415$	2.72967e32	0.513463
$416$	8.95138e31	0.163389
$417$	5.76386e32	1.02097
$418$	7.09545e30	0.0121977
$419$	−6.53498e32	−1.09036	−0.545179	−	0.838320i	$-0.683538\pi$
$419$	−6.53498e32	−1.09036	−0.545179	+	0.838320i	$0.683538\pi$
$420$	−1.21276e32	−0.196409
$421$	−8.06557e32	−1.26797	−0.633985	−	0.773345i	$-0.718582\pi$
$421$	−8.06557e32	−1.26797	−0.633985	+	0.773345i	$0.718582\pi$
$422$	6.53492e32	0.997321
$423$	−7.02172e32	−1.04037
$424$	−1.37626e32	−0.197983
$425$	8.97791e31	0.125405
$426$	5.23393e31	0.0709918
$427$	−1.15041e33	−1.51532
$428$	−2.44213e32	−0.312408
$429$	1.71993e31	0.0213695
$430$	−4.58049e32	−0.552785
$431$	−1.89617e32	−0.222285	−0.111143	−	0.993804i	$-0.535451\pi$
$431$	−1.89617e32	−0.222285	−0.111143	+	0.993804i	$0.535451\pi$
$432$	−2.28406e32	−0.260112
$433$	1.55976e33	1.72567	0.862835	−	0.505485i	$-0.168687\pi$
$433$	1.55976e33	1.72567	0.862835	+	0.505485i	$0.168687\pi$
$434$	6.09838e32	0.655530
$435$	−1.40451e32	−0.146693
$436$	−5.59106e32	−0.567431
$437$	1.25415e32	0.123689
$438$	−8.12744e32	−0.778982
$439$	−1.73749e33	−1.61851	−0.809254	−	0.587460i	$-0.800128\pi$
$439$	−1.73749e33	−1.61851	−0.809254	+	0.587460i	$0.800128\pi$
$440$	−6.00957e30	−0.00544108
$441$	−4.42072e32	−0.389055
$442$	4.79011e32	0.409795
$443$	2.09110e33	1.73912	0.869559	−	0.493830i	$-0.164403\pi$
$443$	2.09110e33	1.73912	0.869559	+	0.493830i	$0.164403\pi$
$444$	−4.71698e32	−0.381397
$445$	−4.27628e32	−0.336176
$446$	1.20124e33	0.918216
$447$	−1.77426e33	−1.31878
$448$	2.26089e32	0.163419
$449$	−2.57391e32	−0.180932	−0.0904659	−	0.995900i	$-0.528836\pi$
$449$	−2.57391e32	−0.180932	−0.0904659	+	0.995900i	$0.528836\pi$
$450$	−1.13482e32	−0.0775835
$451$	3.67006e31	0.0244043
$452$	2.87315e32	0.185835
$453$	3.92785e32	0.247131
$454$	1.17159e33	0.717098
$455$	−9.07506e32	−0.540390
$456$	2.05529e32	0.119073
$457$	−3.29162e33	−1.85548	−0.927742	−	0.373222i	$-0.878253\pi$
$457$	−3.29162e33	−1.85548	−0.927742	+	0.373222i	$0.878253\pi$
$458$	−9.33129e32	−0.511827
$459$	−1.22226e33	−0.652385
$460$	−1.06222e32	−0.0551747
$461$	2.82594e33	1.42857	0.714286	−	0.699854i	$-0.246752\pi$
$461$	2.82594e33	1.42857	0.714286	+	0.699854i	$0.246752\pi$
$462$	4.34410e31	0.0213735
$463$	3.15530e33	1.51105	0.755523	−	0.655122i	$-0.227383\pi$
$463$	3.15530e33	1.51105	0.755523	+	0.655122i	$0.227383\pi$
$464$	2.61834e32	0.122054
$465$	−4.69540e32	−0.213064
$466$	2.85014e33	1.25905
$467$	1.46352e33	0.629417	0.314709	−	0.949188i	$-0.398093\pi$
$467$	1.46352e33	0.629417	0.314709	+	0.949188i	$0.398093\pi$
$468$	−6.05475e32	−0.253526
$469$	−2.72131e33	−1.10947
$470$	−1.51063e33	−0.599701
$471$	−1.55714e33	−0.601960
$472$	1.37688e33	0.518347
$473$	1.64072e32	0.0601549
$474$	−1.08560e33	−0.387650
$475$	2.88255e32	0.100255
$476$	1.20986e33	0.409871
$477$	9.30909e32	0.307204
$478$	6.01341e32	0.193318
$479$	−9.44658e31	−0.0295856	−0.0147928	−	0.999891i	$-0.504709\pi$
$479$	−9.44658e31	−0.0295856	−0.0147928	+	0.999891i	$0.504709\pi$
$480$	−1.74075e32	−0.0531155
$481$	−3.52970e33	−1.04936
$482$	3.22286e33	0.933585
$483$	7.67838e32	0.216736
$484$	−1.81561e33	−0.499408
$485$	3.14184e33	0.842194
$486$	2.54259e33	0.664236
$487$	2.95578e33	0.752593	0.376296	−	0.926499i	$-0.377197\pi$
$487$	2.95578e33	0.752593	0.376296	+	0.926499i	$0.377197\pi$
$488$	−1.65126e33	−0.409795
$489$	−3.02722e32	−0.0732291
$490$	−9.51058e32	−0.224262
$491$	3.19357e33	0.734103	0.367052	−	0.930201i	$-0.380367\pi$
$491$	3.19357e33	0.734103	0.367052	+	0.930201i	$0.380367\pi$
$492$	1.06308e33	0.238233
$493$	1.40114e33	0.306123
$494$	1.53797e33	0.327612
$495$	4.06490e31	0.00844276
$496$	8.75336e32	0.177278
$497$	9.89214e32	0.195360
$498$	−2.83222e33	−0.545457
$499$	−3.38640e33	−0.636036	−0.318018	−	0.948085i	$-0.603017\pi$
$499$	−3.38640e33	−0.636036	−0.318018	+	0.948085i	$0.603017\pi$
$500$	−2.44141e32	−0.0447214
$501$	1.68992e33	0.301921
$502$	−5.33922e33	−0.930425
$503$	6.76442e33	1.14982	0.574911	−	0.818216i	$-0.305037\pi$
$503$	6.76442e33	1.14982	0.574911	+	0.818216i	$0.305037\pi$
$504$	−1.52927e33	−0.253573
$505$	7.81679e32	0.126441
$506$	3.80484e31	0.00600419
$507$	−6.35948e32	−0.0979089
$508$	−4.71299e33	−0.707947
$509$	6.69189e33	0.980791	0.490395	−	0.871500i	$-0.336852\pi$
$509$	6.69189e33	0.980791	0.490395	+	0.871500i	$0.336852\pi$
$510$	−9.31520e32	−0.133219
$511$	−1.53609e34	−2.14365
$512$	3.24519e32	0.0441942
$513$	−3.92432e33	−0.521551
$514$	−9.07672e33	−1.17731
$515$	1.32763e32	0.0168069
$516$	4.75257e33	0.587229
$517$	5.41105e32	0.0652603
$518$	−8.91511e33	−1.04955
$519$	5.34383e33	0.614130
$520$	−1.30260e33	−0.146140
$521$	−1.12229e34	−1.22923	−0.614616	−	0.788826i	$-0.710689\pi$
$521$	−1.12229e34	−1.22923	−0.614616	+	0.788826i	$0.710689\pi$
$522$	−1.77106e33	−0.189388
$523$	7.35349e33	0.767754	0.383877	−	0.923384i	$-0.374589\pi$
$523$	7.35349e33	0.767754	0.383877	+	0.923384i	$0.374589\pi$
$524$	6.57136e33	0.669906
$525$	1.76480e33	0.175673
$526$	1.38141e33	0.134277
$527$	4.68414e33	0.444628
$528$	6.23534e31	0.00578011
$529$	−1.03732e34	−0.939115
$530$	2.00272e33	0.177081
$531$	−9.31326e33	−0.804304
$532$	3.88451e33	0.327673
$533$	7.95499e33	0.655465
$534$	4.43694e33	0.357123
$535$	3.55377e33	0.279426
$536$	−3.90606e33	−0.300040
$537$	−1.25913e34	−0.944912
$538$	−1.69519e34	−1.24291
$539$	3.40667e32	0.0244046
$540$	3.32374e33	0.232651
$541$	6.91384e32	0.0472883	0.0236441	−	0.999720i	$-0.492473\pi$
$541$	6.91384e32	0.0472883	0.0236441	+	0.999720i	$0.492473\pi$
$542$	9.34216e32	0.0624390
$543$	8.30881e33	0.542677
$544$	1.73658e33	0.110843
$545$	8.13607e33	0.507526
$546$	9.41600e33	0.574062
$547$	1.40577e34	0.837672	0.418836	−	0.908062i	$-0.362438\pi$
$547$	1.40577e34	0.837672	0.418836	+	0.908062i	$0.362438\pi$
$548$	1.22573e32	0.00713902
$549$	1.11692e34	0.635867
$550$	8.74507e31	0.00486665
$551$	4.49866e33	0.244731
$552$	1.10212e33	0.0586127
$553$	−2.05178e34	−1.06676
$554$	1.55090e34	0.788335
$555$	6.86411e33	0.341132
$556$	1.56364e34	0.759803
$557$	−2.49292e34	−1.18445	−0.592227	−	0.805771i	$-0.701751\pi$
$557$	−2.49292e34	−1.18445	−0.592227	+	0.805771i	$0.701751\pi$
$558$	−5.92081e33	−0.275076
$559$	3.55633e34	1.61568
$560$	−3.29002e33	−0.146167
$561$	3.33669e32	0.0144971
$562$	1.99644e34	0.848306
$563$	−1.70240e34	−0.707466	−0.353733	−	0.935346i	$-0.615088\pi$
$563$	−1.70240e34	−0.707466	−0.353733	+	0.935346i	$0.615088\pi$
$564$	1.56738e34	0.637068
$565$	−4.18098e33	−0.166216
$566$	−3.19248e33	−0.124143
$567$	−5.17070e33	−0.196680
$568$	1.41988e33	0.0528319
$569$	1.90307e34	0.692709	0.346355	−	0.938104i	$-0.387419\pi$
$569$	1.90307e34	0.692709	0.346355	+	0.938104i	$0.387419\pi$
$570$	−2.99084e33	−0.106502
$571$	2.13655e34	0.744323	0.372162	−	0.928168i	$-0.378617\pi$
$571$	2.13655e34	0.744323	0.372162	+	0.928168i	$0.378617\pi$
$572$	4.66588e32	0.0159031
$573$	−9.04669e33	−0.301687
$574$	2.00923e34	0.655587
$575$	1.54573e33	0.0493497
$576$	−2.19506e33	−0.0685748
$577$	−2.06745e34	−0.632030	−0.316015	−	0.948754i	$-0.602345\pi$
$577$	−2.06745e34	−0.632030	−0.316015	+	0.948754i	$0.602345\pi$
$578$	−1.43436e34	−0.429102
$579$	2.08987e34	0.611839
$580$	−3.81019e33	−0.109168
$581$	−5.35291e34	−1.50103
$582$	−3.25988e34	−0.894672
$583$	−7.17372e32	−0.0192703
$584$	−2.20484e34	−0.579717
$585$	8.81082e33	0.226761
$586$	3.67713e34	0.926380
$587$	−5.55725e34	−1.37052	−0.685258	−	0.728301i	$-0.740310\pi$
$587$	−5.55725e34	−1.37052	−0.685258	+	0.728301i	$0.740310\pi$
$588$	9.86789e33	0.238236
$589$	1.50394e34	0.355460
$590$	−2.00362e34	−0.463624
$591$	−3.66808e34	−0.830989
$592$	−1.27964e34	−0.283835
$593$	−6.93628e34	−1.50641	−0.753204	−	0.657787i	$-0.771493\pi$
$593$	−6.93628e34	−1.50641	−0.753204	+	0.657787i	$0.771493\pi$
$594$	−1.19056e33	−0.0253175
$595$	−1.76057e34	−0.366600
$596$	−4.81326e34	−0.981434
$597$	−1.14979e34	−0.229584
$598$	8.24713e33	0.161264
$599$	−3.28492e34	−0.629056	−0.314528	−	0.949248i	$-0.601846\pi$
$599$	−3.28492e34	−0.629056	−0.314528	+	0.949248i	$0.601846\pi$
$600$	2.53313e33	0.0475080
$601$	−2.89648e34	−0.532034	−0.266017	−	0.963968i	$-0.585708\pi$
$601$	−2.89648e34	−0.532034	−0.266017	+	0.963968i	$0.585708\pi$
$602$	8.98237e34	1.61598
$603$	2.64207e34	0.465563
$604$	1.06556e34	0.183914
$605$	2.64206e34	0.446684
$606$	−8.11046e33	−0.134319
$607$	8.42327e34	1.36654	0.683270	−	0.730166i	$-0.260557\pi$
$607$	8.42327e34	1.36654	0.683270	+	0.730166i	$0.260557\pi$
$608$	5.57566e33	0.0886138
$609$	2.75425e34	0.428832
$610$	2.40289e34	0.366532
$611$	1.17286e35	1.75280
$612$	−1.17463e34	−0.171992
$613$	1.08389e34	0.155499	0.0777496	−	0.996973i	$-0.475227\pi$
$613$	1.08389e34	0.155499	0.0777496	+	0.996973i	$0.475227\pi$
$614$	−4.24829e34	−0.597185
$615$	−1.54699e34	−0.213083
$616$	1.17848e33	0.0159061
$617$	7.99721e33	0.105773	0.0528864	−	0.998601i	$-0.483158\pi$
$617$	7.99721e33	0.105773	0.0528864	+	0.998601i	$0.483158\pi$
$618$	−1.37751e33	−0.0178541
$619$	−6.34272e34	−0.805643	−0.402822	−	0.915279i	$-0.631970\pi$
$619$	−6.34272e34	−0.805643	−0.402822	+	0.915279i	$0.631970\pi$
$620$	−1.27378e34	−0.158562
$621$	−2.10436e34	−0.256729
$622$	−1.57789e34	−0.188668
$623$	8.38582e34	0.982755
$624$	1.35153e34	0.155246
$625$	3.55271e33	0.0400000
$626$	−1.08035e35	−1.19229
$627$	1.07131e33	0.0115897
$628$	−4.22427e34	−0.447977
$629$	−6.84766e34	−0.711884
$630$	2.22539e34	0.226803
$631$	1.41569e35	1.41449	0.707245	−	0.706968i	$-0.249938\pi$
$631$	1.41569e35	1.41449	0.707245	+	0.706968i	$0.249938\pi$
$632$	−2.94505e34	−0.288489
$633$	9.86683e34	0.947614
$634$	−1.49639e34	−0.140906
$635$	6.85831e34	0.633207
$636$	−2.07797e34	−0.188115
$637$	7.38409e34	0.655472
$638$	1.36480e33	0.0118799
$639$	−9.60410e33	−0.0819778
$640$	−4.72237e33	−0.0395285
$641$	−4.50631e34	−0.369910	−0.184955	−	0.982747i	$-0.559214\pi$
$641$	−4.50631e34	−0.369910	−0.184955	+	0.982747i	$0.559214\pi$
$642$	−3.68728e34	−0.296837
$643$	1.18877e35	0.938561	0.469280	−	0.883049i	$-0.344513\pi$
$643$	1.18877e35	0.938561	0.469280	+	0.883049i	$0.344513\pi$
$644$	2.08301e34	0.161294
$645$	−6.91590e34	−0.525233
$646$	2.98367e34	0.222252
$647$	1.85298e34	0.135384	0.0676921	−	0.997706i	$-0.478436\pi$
$647$	1.85298e34	0.135384	0.0676921	+	0.997706i	$0.478436\pi$
$648$	−7.42181e33	−0.0531890
$649$	7.17694e33	0.0504522
$650$	1.89553e34	0.130711
$651$	9.20771e34	0.622858
$652$	−8.21234e33	−0.0544970
$653$	−1.84607e35	−1.20180	−0.600902	−	0.799323i	$-0.705192\pi$
$653$	−1.84607e35	−1.20180	−0.600902	+	0.799323i	$0.705192\pi$
$654$	−8.44173e34	−0.539150
$655$	−9.56258e34	−0.599182
$656$	2.88396e34	0.177293
$657$	1.49136e35	0.899530
$658$	2.96235e35	1.75313
$659$	−3.04390e35	−1.76752	−0.883758	−	0.467944i	$-0.844995\pi$
$659$	−3.04390e35	−1.76752	−0.883758	+	0.467944i	$0.844995\pi$
$660$	−9.07362e32	−0.00516989
$661$	2.88465e34	0.161278	0.0806389	−	0.996743i	$-0.474304\pi$
$661$	2.88465e34	0.161278	0.0806389	+	0.996743i	$0.474304\pi$
$662$	−1.03339e35	−0.566945
$663$	7.23240e34	0.389371
$664$	−7.68334e34	−0.405928
$665$	−5.65270e34	−0.293079
$666$	8.65552e34	0.440418
$667$	2.41235e34	0.120467
$668$	4.58446e34	0.224689
$669$	1.81371e35	0.872452
$670$	5.68406e34	0.268364
$671$	−8.60712e33	−0.0398865
$672$	3.41363e34	0.155275
$673$	−6.39436e34	−0.285502	−0.142751	−	0.989759i	$-0.545595\pi$
$673$	−6.39436e34	−0.285502	−0.142751	+	0.989759i	$0.545595\pi$
$674$	−1.05463e35	−0.462225
$675$	−4.83668e34	−0.208090
$676$	−1.72522e34	−0.0728636
$677$	6.00220e34	0.248858	0.124429	−	0.992229i	$-0.460290\pi$
$677$	6.00220e34	0.248858	0.124429	+	0.992229i	$0.460290\pi$
$678$	4.33806e34	0.176573
$679$	−6.16117e35	−2.46202
$680$	−2.52706e34	−0.0991410
$681$	1.76894e35	0.681358
$682$	4.56266e33	0.0172549
$683$	−3.76829e35	−1.39922	−0.699610	−	0.714525i	$-0.746643\pi$
$683$	−3.76829e35	−1.39922	−0.699610	+	0.714525i	$0.746643\pi$
$684$	−3.77140e34	−0.137499
$685$	−1.78367e33	−0.00638533
$686$	−7.64813e34	−0.268846
$687$	−1.40890e35	−0.486317
$688$	1.28929e35	0.437015
$689$	−1.55493e35	−0.517572
$690$	−1.60380e34	−0.0524248
$691$	−3.26709e35	−1.04878	−0.524392	−	0.851477i	$-0.675707\pi$
$691$	−3.26709e35	−1.04878	−0.524392	+	0.851477i	$0.675707\pi$
$692$	1.44969e35	0.457034
$693$	−7.97129e33	−0.0246810
$694$	−7.00657e34	−0.213065
$695$	−2.27539e35	−0.679588
$696$	3.95334e34	0.115971
$697$	1.54328e35	0.444667
$698$	2.84082e35	0.803991
$699$	4.30332e35	1.19630
$700$	4.78762e34	0.130736
$701$	3.88741e35	1.04276	0.521381	−	0.853324i	$-0.325417\pi$
$701$	3.88741e35	1.04276	0.521381	+	0.853324i	$0.325417\pi$
$702$	−2.58058e35	−0.679992
$703$	−2.19859e35	−0.569118
$704$	1.69154e33	0.00430155
$705$	−2.28084e35	−0.569811
$706$	5.00669e34	0.122883
$707$	−1.53288e35	−0.369628
$708$	2.07890e35	0.492512
$709$	4.23533e35	0.985848	0.492924	−	0.870072i	$-0.335928\pi$
$709$	4.23533e35	0.985848	0.492924	+	0.870072i	$0.335928\pi$
$710$	−2.06619e34	−0.0472543
$711$	1.99204e35	0.447639
$712$	1.20367e35	0.265770
$713$	8.06469e34	0.174972
$714$	1.82672e35	0.389443
$715$	−6.78975e33	−0.0142242
$716$	−3.41580e35	−0.703201
$717$	9.07941e34	0.183683
$718$	2.15564e35	0.428568
$719$	6.21554e35	1.21442	0.607208	−	0.794543i	$-0.292289\pi$
$719$	6.21554e35	1.21442	0.607208	+	0.794543i	$0.292289\pi$
$720$	3.19423e34	0.0613352
$721$	−2.60349e34	−0.0491321
$722$	−2.85444e35	−0.529427
$723$	4.86608e35	0.887055
$724$	2.25404e35	0.403859
$725$	5.54456e34	0.0976432
$726$	−2.74132e35	−0.474517
$727$	−4.24475e35	−0.722225	−0.361112	−	0.932522i	$-0.617603\pi$
$727$	−4.24475e35	−0.722225	−0.361112	+	0.932522i	$0.617603\pi$
$728$	2.55440e35	0.427216
$729$	4.75404e35	0.781572
$730$	3.20846e35	0.518514
$731$	6.89932e35	1.09607
$732$	−2.49317e35	−0.389371
$733$	7.04925e34	0.108229	0.0541145	−	0.998535i	$-0.482766\pi$
$733$	7.04925e34	0.108229	0.0541145	+	0.998535i	$0.482766\pi$
$734$	−4.28995e34	−0.0647518
$735$	−1.43597e35	−0.213085
$736$	2.98987e34	0.0436194
$737$	−2.03602e34	−0.0292037
$738$	−1.95072e35	−0.275100
$739$	−9.55082e35	−1.32430	−0.662148	−	0.749373i	$-0.730355\pi$
$739$	−9.55082e35	−1.32430	−0.662148	+	0.749373i	$0.730355\pi$
$740$	1.86212e35	0.253870
$741$	2.32212e35	0.311284
$742$	−3.92736e35	−0.517668
$743$	−1.29129e35	−0.167364	−0.0836820	−	0.996493i	$-0.526668\pi$
$743$	−1.29129e35	−0.167364	−0.0836820	+	0.996493i	$0.526668\pi$
$744$	1.32164e35	0.168442
$745$	7.00422e35	0.877821
$746$	−5.11909e35	−0.630896
$747$	5.19704e35	0.629867
$748$	9.05187e33	0.0107887
$749$	−6.96897e35	−0.816857
$750$	−3.68619e34	−0.0424924
$751$	−1.00002e36	−1.13373	−0.566864	−	0.823812i	$-0.691843\pi$
$751$	−1.00002e36	−1.13373	−0.566864	+	0.823812i	$0.691843\pi$
$752$	4.25204e35	0.474105
$753$	−8.06149e35	−0.884052
$754$	2.95827e35	0.319077
$755$	−1.55059e35	−0.164498
$756$	−6.51788e35	−0.680118
$757$	−4.62323e35	−0.474511	−0.237256	−	0.971447i	$-0.576248\pi$
$757$	−4.62323e35	−0.474511	−0.237256	+	0.971447i	$0.576248\pi$
$758$	−7.01138e35	−0.707846
$759$	5.74478e33	0.00570494
$760$	−8.11365e34	−0.0792586
$761$	1.71968e36	1.65249	0.826247	−	0.563308i	$-0.190471\pi$
$761$	1.71968e36	1.65249	0.826247	+	0.563308i	$0.190471\pi$
$762$	−7.11597e35	−0.672662
$763$	−1.59549e36	−1.48367
$764$	−2.45421e35	−0.224515
$765$	1.70931e35	0.153834
$766$	−1.07981e36	−0.956069
$767$	1.55563e36	1.35508
$768$	4.89978e34	0.0419915
$769$	1.91462e36	1.61437	0.807184	−	0.590299i	$-0.200990\pi$
$769$	1.91462e36	1.61437	0.807184	+	0.590299i	$0.200990\pi$
$770$	−1.71492e34	−0.0142268
$771$	−1.37046e36	−1.11863
$772$	5.66947e35	0.455330
$773$	−9.08398e35	−0.717848	−0.358924	−	0.933367i	$-0.616856\pi$
$773$	−9.08398e35	−0.717848	−0.358924	+	0.933367i	$0.616856\pi$
$774$	−8.72082e35	−0.678103
$775$	1.85360e35	0.141822
$776$	−8.84349e35	−0.665813
$777$	−1.34606e36	−0.997243
$778$	1.23522e36	0.900532
$779$	4.95503e35	0.355490
$780$	−1.96674e35	−0.138856
$781$	7.40106e33	0.00514229
$782$	1.59995e35	0.109402
$783$	−7.54839e35	−0.507963
$784$	2.67699e35	0.177295
$785$	6.14712e35	0.400683
$786$	9.92184e35	0.636518
$787$	5.77613e35	0.364714	0.182357	−	0.983232i	$-0.441627\pi$
$787$	5.77613e35	0.364714	0.182357	+	0.983232i	$0.441627\pi$
$788$	−9.95088e35	−0.618420
$789$	2.08574e35	0.127584
$790$	4.28561e35	0.258032
$791$	8.19893e35	0.485905
$792$	−1.14417e34	−0.00667459
$793$	−1.86563e36	−1.07130
$794$	1.47819e36	0.835552
$795$	3.02384e35	0.168256
$796$	−3.11920e35	−0.170856
$797$	1.37116e36	0.739364	0.369682	−	0.929158i	$-0.379467\pi$
$797$	1.37116e36	0.739364	0.369682	+	0.929158i	$0.379467\pi$
$798$	5.86507e35	0.311341
$799$	2.27537e36	1.18910
$800$	6.87195e34	0.0353553
$801$	−8.14165e35	−0.412388
$802$	1.39611e36	0.696211
$803$	−1.14926e35	−0.0564255
$804$	−5.89761e35	−0.285085
$805$	−3.03118e35	−0.144266
$806$	9.88975e35	0.463444
$807$	−2.55951e36	−1.18096
$808$	−2.20023e35	−0.0999600
$809$	3.58962e36	1.60580	0.802902	−	0.596111i	$-0.203288\pi$
$809$	3.58962e36	1.60580	0.802902	+	0.596111i	$0.203288\pi$
$810$	1.08001e35	0.0475737
$811$	1.03429e35	0.0448624	0.0224312	−	0.999748i	$-0.492859\pi$
$811$	1.03429e35	0.0448624	0.0224312	+	0.999748i	$0.492859\pi$
$812$	7.47182e35	0.319136
$813$	1.41054e35	0.0593270
$814$	−6.67007e34	−0.0276265
$815$	1.19505e35	0.0487436
$816$	2.62200e35	0.105319
$817$	2.21518e36	0.876259
$818$	7.73407e35	0.301295
$819$	−1.72781e36	−0.662898
$820$	−4.19671e35	−0.158576
$821$	−2.70025e36	−1.00488	−0.502439	−	0.864612i	$-0.667564\pi$
$821$	−2.70025e36	−1.00488	−0.502439	+	0.864612i	$0.667564\pi$
$822$	1.85069e34	0.00678320
$823$	−2.53917e36	−0.916630	−0.458315	−	0.888790i	$-0.651547\pi$
$823$	−2.53917e36	−0.916630	−0.458315	+	0.888790i	$0.651547\pi$
$824$	−3.73695e34	−0.0132870
$825$	1.32039e34	0.00462409
$826$	3.92912e36	1.35533
$827$	2.67322e36	0.908270	0.454135	−	0.890933i	$-0.349948\pi$
$827$	2.67322e36	0.908270	0.454135	+	0.890933i	$0.349948\pi$
$828$	−2.02236e35	−0.0676830
$829$	−5.79155e36	−1.90925	−0.954626	−	0.297806i	$-0.903745\pi$
$829$	−5.79155e36	−1.90925	−0.954626	+	0.297806i	$0.903745\pi$
$830$	1.11807e36	0.363073
$831$	2.34164e36	0.749044
$832$	3.66648e35	0.115534
$833$	1.43252e36	0.444672
$834$	2.36088e36	0.721934
$835$	−6.67126e35	−0.200968
$836$	2.90630e34	0.00862504
$837$	−2.52349e36	−0.737792
$838$	−2.67673e36	−0.770999
$839$	−2.27845e36	−0.646568	−0.323284	−	0.946302i	$-0.604787\pi$
$839$	−2.27845e36	−0.646568	−0.323284	+	0.946302i	$0.604787\pi$
$840$	−4.96748e35	−0.138882
$841$	−2.76505e36	−0.761645
$842$	−3.30366e36	−0.896590
$843$	3.01435e36	0.806026
$844$	2.67671e36	0.705212
$845$	2.51053e35	0.0651712
$846$	−2.87610e36	−0.735655
$847$	−5.18110e36	−1.30581
$848$	−5.63717e35	−0.139995
$849$	−4.82020e35	−0.117956
$850$	3.67735e35	0.0886744
$851$	−1.17896e36	−0.280144
$852$	2.14382e35	0.0501988
$853$	3.72321e36	0.859122	0.429561	−	0.903038i	$-0.358668\pi$
$853$	3.72321e36	0.859122	0.429561	+	0.903038i	$0.358668\pi$
$854$	−4.71209e36	−1.07150
$855$	5.48811e35	0.122983
$856$	−1.00030e36	−0.220906
$857$	1.02353e36	0.222761	0.111381	−	0.993778i	$-0.464473\pi$
$857$	1.02353e36	0.222761	0.111381	+	0.993778i	$0.464473\pi$
$858$	7.04483e34	0.0151105
$859$	1.85947e36	0.393074	0.196537	−	0.980496i	$-0.437030\pi$
$859$	1.85947e36	0.393074	0.196537	+	0.980496i	$0.437030\pi$
$860$	−1.87617e36	−0.390878
$861$	3.03365e36	0.622912
$862$	−7.76670e35	−0.157180
$863$	8.67106e36	1.72957	0.864783	−	0.502146i	$-0.167456\pi$
$863$	8.67106e36	1.72957	0.864783	+	0.502146i	$0.167456\pi$
$864$	−9.35550e35	−0.183927
$865$	−2.10958e36	−0.408784
$866$	6.38876e36	1.22023
$867$	−2.16569e36	−0.407716
$868$	2.49790e36	0.463530
$869$	−1.53510e35	−0.0280794
$870$	−5.75287e35	−0.103727
$871$	−4.41315e36	−0.784372
$872$	−2.29010e36	−0.401235
$873$	5.98177e36	1.03312
$874$	5.13700e35	0.0874614
$875$	−6.96690e35	−0.116933
$876$	−3.32900e36	−0.550823
$877$	−7.14177e36	−1.16496	−0.582480	−	0.812845i	$-0.697918\pi$
$877$	−7.14177e36	−1.16496	−0.582480	+	0.812845i	$0.697918\pi$
$878$	−7.11674e36	−1.14446
$879$	5.55196e36	0.880209
$880$	−2.46152e34	−0.00384742
$881$	−3.00182e36	−0.462579	−0.231290	−	0.972885i	$-0.574294\pi$
$881$	−3.00182e36	−0.462579	−0.231290	+	0.972885i	$0.574294\pi$
$882$	−1.81073e36	−0.275103
$883$	−2.65767e36	−0.398100	−0.199050	−	0.979989i	$-0.563786\pi$
$883$	−2.65767e36	−0.398100	−0.199050	+	0.979989i	$0.563786\pi$
$884$	1.96203e36	0.289769
$885$	−3.02519e36	−0.440516
$886$	8.56516e36	1.22974
$887$	2.39194e36	0.338613	0.169307	−	0.985563i	$-0.445847\pi$
$887$	2.39194e36	0.338613	0.169307	+	0.985563i	$0.445847\pi$
$888$	−1.93208e36	−0.269688
$889$	−1.34492e37	−1.85108
$890$	−1.75157e36	−0.237712
$891$	−3.86859e34	−0.00517704
$892$	4.92029e36	0.649277
$893$	7.30557e36	0.950629
$894$	−7.26736e36	−0.932519
$895$	4.97064e36	0.628962
$896$	9.26060e35	0.115555
$897$	1.24520e36	0.153227
$898$	−1.05428e36	−0.127938
$899$	2.89282e36	0.346199
$900$	−4.64821e35	−0.0548598
$901$	−3.01659e36	−0.351121
$902$	1.50326e35	0.0172564
$903$	1.35621e37	1.53543
$904$	1.17684e36	0.131405
$905$	−3.28006e36	−0.361222
$906$	1.60885e36	0.174748
$907$	1.27834e37	1.36948	0.684741	−	0.728787i	$-0.259915\pi$
$907$	1.27834e37	1.36948	0.684741	+	0.728787i	$0.259915\pi$
$908$	4.79885e36	0.507065
$909$	1.48824e36	0.155105
$910$	−3.71714e36	−0.382113
$911$	1.51675e37	1.53792	0.768961	−	0.639296i	$-0.220774\pi$
$911$	1.51675e37	1.53792	0.768961	+	0.639296i	$0.220774\pi$
$912$	8.41848e35	0.0841973
$913$	−4.00492e35	−0.0395102
$914$	−1.34825e37	−1.31203
$915$	3.62804e36	0.348264
$916$	−3.82210e36	−0.361916
$917$	1.87523e37	1.75161
$918$	−5.00636e36	−0.461306
$919$	−1.63543e36	−0.148658	−0.0743292	−	0.997234i	$-0.523682\pi$
$919$	−1.63543e36	−0.148658	−0.0743292	+	0.997234i	$0.523682\pi$
$920$	−4.35084e35	−0.0390144
$921$	−6.41432e36	−0.567421
$922$	1.15751e37	1.01015
$923$	1.60421e36	0.138115
$924$	1.77934e35	0.0151133
$925$	−2.70974e36	−0.227068
$926$	1.29241e37	1.06847
$927$	2.52769e35	0.0206170
$928$	1.07247e36	0.0863052
$929$	−7.47115e36	−0.593186	−0.296593	−	0.955004i	$-0.595850\pi$
$929$	−7.47115e36	−0.593186	−0.296593	+	0.955004i	$0.595850\pi$
$930$	−1.92323e36	−0.150659
$931$	4.59943e36	0.355494
$932$	1.16742e37	0.890281
$933$	−2.38240e36	−0.179265
$934$	5.99459e36	0.445065
$935$	−1.31722e35	−0.00964969
$936$	−2.48002e36	−0.179270
$937$	−2.45447e37	−1.75070	−0.875351	−	0.483488i	$-0.839370\pi$
$937$	−2.45447e37	−1.75070	−0.875351	+	0.483488i	$0.839370\pi$
$938$	−1.11465e37	−0.784517
$939$	−1.63117e37	−1.13287
$940$	−6.18754e36	−0.424052
$941$	−1.35589e36	−0.0916968	−0.0458484	−	0.998948i	$-0.514599\pi$
$941$	−1.35589e36	−0.0916968	−0.0458484	+	0.998948i	$0.514599\pi$
$942$	−6.37806e36	−0.425650
$943$	2.65707e36	0.174987
$944$	5.63969e36	0.366527
$945$	9.48477e36	0.608316
$946$	6.72040e35	0.0425359
$947$	−2.07354e37	−1.29520	−0.647601	−	0.761980i	$-0.724227\pi$
$947$	−2.07354e37	−1.29520	−0.647601	+	0.761980i	$0.724227\pi$
$948$	−4.44661e36	−0.274110
$949$	−2.49107e37	−1.51551
$950$	1.18069e36	0.0708911
$951$	−2.25934e36	−0.133883
$952$	4.95558e36	0.289823
$953$	−2.04124e37	−1.17823	−0.589117	−	0.808048i	$-0.700524\pi$
$953$	−2.04124e37	−1.17823	−0.589117	+	0.808048i	$0.700524\pi$
$954$	3.81300e36	0.217226
$955$	3.57135e36	0.200812
$956$	2.46309e36	0.136696
$957$	2.06067e35	0.0112878
$958$	−3.86932e35	−0.0209202
$959$	3.49780e35	0.0186665
$960$	−7.13012e35	−0.0375584
$961$	−9.56182e36	−0.497163
$962$	−1.44576e37	−0.742009
$963$	6.76605e36	0.342773
$964$	1.32008e37	0.660144
$965$	−8.25016e36	−0.407259
$966$	3.14506e36	0.153255
$967$	−1.88209e37	−0.905333	−0.452666	−	0.891680i	$-0.649527\pi$
$967$	−1.88209e37	−0.905333	−0.452666	+	0.891680i	$0.649527\pi$
$968$	−7.43674e36	−0.353135
$969$	4.50494e36	0.211174
$970$	1.28690e37	0.595521
$971$	−2.62810e37	−1.20061	−0.600305	−	0.799771i	$-0.704954\pi$
$971$	−2.62810e37	−1.20061	−0.600305	+	0.799771i	$0.704954\pi$
$972$	1.04144e37	0.469686
$973$	4.46206e37	1.98667
$974$	1.21069e37	0.532163
$975$	2.86199e36	0.124197
$976$	−6.76354e36	−0.289769
$977$	6.14194e36	0.259791	0.129895	−	0.991528i	$-0.458536\pi$
$977$	6.14194e36	0.259791	0.129895	+	0.991528i	$0.458536\pi$
$978$	−1.23995e36	−0.0517808
$979$	6.27407e35	0.0258682
$980$	−3.89553e36	−0.158577
$981$	1.54903e37	0.622584
$982$	1.30808e37	0.519089
$983$	−5.02851e37	−1.97025	−0.985123	−	0.171849i	$-0.945026\pi$
$983$	−5.02851e37	−1.97025	−0.985123	+	0.171849i	$0.945026\pi$
$984$	4.35438e36	0.168457
$985$	1.44804e37	0.553132
$986$	5.73908e36	0.216461
$987$	4.47275e37	1.66575
$988$	6.29951e36	0.231657
$989$	1.18786e37	0.431331
$990$	1.66498e35	0.00596993
$991$	−2.22624e37	−0.788226	−0.394113	−	0.919062i	$-0.628948\pi$
$991$	−2.22624e37	−0.788226	−0.394113	+	0.919062i	$0.628948\pi$
$992$	3.58538e36	0.125354
$993$	−1.56028e37	−0.538688
$994$	4.05182e36	0.138140
$995$	4.53903e36	0.152818
$996$	−1.16008e37	−0.385697
$997$	−7.44693e36	−0.244505	−0.122253	−	0.992499i	$-0.539012\pi$
$997$	−7.44693e36	−0.244505	−0.122253	+	0.992499i	$0.539012\pi$
$998$	−1.38707e37	−0.449745
$999$	3.68905e37	1.18126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.26.a.d.1.2	✓	2
5.2	odd	4		50.26.b.d.49.3		4
5.3	odd	4		50.26.b.d.49.2		4
5.4	even	2		50.26.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.a.d.1.2	✓	2	1.1	even	1	trivial
50.26.a.d.1.1		2	5.4	even	2
50.26.b.d.49.2		4	5.3	odd	4
50.26.b.d.49.3		4	5.2	odd	4

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:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+4096.00 q^{2} +618439. q^{3} +1.67772e7 q^{4} -2.44141e8 q^{5} +2.53313e9 q^{6} +4.78762e10 q^{7} +6.87195e10 q^{8} -4.64821e11 q^{9} -1.00000e12 q^{10} +3.58198e11 q^{11} +1.03757e13 q^{12} +7.76408e13 q^{13} +1.96101e14 q^{14} -1.50986e14 q^{15} +2.81475e14 q^{16} +1.50624e15 q^{17} -1.90391e15 q^{18} +4.83611e15 q^{19} -4.09600e15 q^{20} +2.96085e16 q^{21} +1.46718e15 q^{22} +2.59330e16 q^{23} +4.24988e16 q^{24} +5.96046e16 q^{25} +3.18017e17 q^{26} -8.11461e17 q^{27} +8.03229e17 q^{28} +9.30223e17 q^{29} -6.18439e17 q^{30} +3.10982e18 q^{31} +1.15292e18 q^{32} +2.21524e17 q^{33} +6.16957e18 q^{34} -1.16885e19 q^{35} -7.79841e18 q^{36} -4.54619e19 q^{37} +1.98087e19 q^{38} +4.80162e19 q^{39} -1.67772e19 q^{40} +1.02459e20 q^{41} +1.21276e20 q^{42} +4.58049e20 q^{43} +6.00957e18 q^{44} +1.13482e20 q^{45} +1.06222e20 q^{46} +1.51063e21 q^{47} +1.74075e20 q^{48} +9.51058e20 q^{49} +2.44141e20 q^{50} +9.31520e20 q^{51} +1.30260e21 q^{52} -2.00272e21 q^{53} -3.32374e21 q^{54} -8.74507e19 q^{55} +3.29002e21 q^{56} +2.99084e21 q^{57} +3.81019e21 q^{58} +2.00362e22 q^{59} -2.53313e21 q^{60} -2.40289e22 q^{61} +1.27378e22 q^{62} -2.22539e22 q^{63} +4.72237e21 q^{64} -1.89553e22 q^{65} +9.07362e20 q^{66} -5.68406e22 q^{67} +2.52706e22 q^{68} +1.60380e22 q^{69} -4.78762e22 q^{70} +2.06619e22 q^{71} -3.19423e22 q^{72} -3.20846e23 q^{73} -1.86212e23 q^{74} +3.68619e22 q^{75} +8.11365e22 q^{76} +1.71492e22 q^{77} +1.96674e23 q^{78} -4.28561e23 q^{79} -6.87195e22 q^{80} -1.08001e23 q^{81} +4.19671e23 q^{82} -1.11807e24 q^{83} +4.96748e23 q^{84} -3.67735e23 q^{85} +1.87617e24 q^{86} +5.75287e23 q^{87} +2.46152e22 q^{88} +1.75157e24 q^{89} +4.64821e23 q^{90} +3.71714e24 q^{91} +4.35084e23 q^{92} +1.92323e24 q^{93} +6.18754e24 q^{94} -1.18069e24 q^{95} +7.13012e23 q^{96} -1.28690e25 q^{97} +3.89553e24 q^{98} -1.66498e23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8192 q^{2} - 97092 q^{3} + 33554432 q^{4} - 488281250 q^{5} - 397688832 q^{6} - 16137160124 q^{7} + 137438953472 q^{8} - 800124539454 q^{9} - 2000000000000 q^{10} + 14416600801344 q^{11} - 1628933455872 q^{12}+ \cdots - 48\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 8192 * q^2 - 97092 * q^3 + 33554432 * q^4 - 488281250 * q^5 - 397688832 * q^6 - 16137160124 * q^7 + 137438953472 * q^8 - 800124539454 * q^9 - 2000000000000 * q^10 + 14416600801344 * q^11 - 1628933455872 * q^12 + 93404548866628 * q^13 - 66097807867904 * q^14 + 23704101562500 * q^15 + 562949953421312 * q^16 + 499266882181236 * q^17 - 3277310113603584 * q^18 - 3830204591906120 * q^19 - 8192000000000000 * q^20 + 75412053748282104 * q^21 + 59050396882305024 * q^22 + 169271186050723788 * q^23 - 6672111435251712 * q^24 + 119209289550781250 * q^25 + 382585032157708288 * q^26 + 34721228182863240 * q^27 - 270736621026934784 * q^28 + 569443622853716940 * q^29 + 97092000000000000 * q^30 + 3982769593868414584 * q^31 + 2305843009213693952 * q^32 - 9837705729224836224 * q^33 + 2044997149414342656 * q^34 + 3939736358398437500 * q^35 - 13423862225320280064 * q^36 + 28241444663789328196 * q^37 - 15688518008447467520 * q^38 + 36736718047624459512 * q^39 - 33554432000000000000 * q^40 + 36676428854020432524 * q^41 + 308887772152963497984 * q^42 + 909017314298263251628 * q^43 + 241870425629921378304 * q^44 + 195342905140136718750 * q^45 + 693334778063764635648 * q^46 + 954929084389204818996 * q^47 - 27328968438791012352 * q^48 + 3707694774551412650874 * q^49 + 488281250000000000000 * q^50 + 1652042752773544110744 * q^51 + 1567068291717973147648 * q^52 + 2753692919774994609588 * q^53 + 142218150637007831040 * q^54 - 3519677930015625000000 * q^55 - 1108937199726324875264 * q^56 + 9191867441696689119120 * q^57 + 2332441079208824586240 * q^58 + 458866752134906177880 * q^59 + 397688832000000000000 * q^60 - 26987853585082462424636 * q^61 + 16313424256485026136064 * q^62 - 789976870259963054652 * q^63 + 9444732965739290427392 * q^64 - 22803844938141601562500 * q^65 - 40295242666904929173504 * q^66 - 14159647018044347838524 * q^67 + 8376308324001147518976 * q^68 - 86524983849189139233048 * q^69 + 16137160124000000000000 * q^70 - 173327708998984655450136 * q^71 - 54984139674911867142144 * q^72 - 341978509295241035156732 * q^73 + 115676957342881088290816 * q^74 - 5787134170532226562500 * q^75 - 64260169762600826961920 * q^76 - 882775887628764911584128 * q^77 + 150473597123069786161152 * q^78 - 927961875376490258946800 * q^79 - 137438953472000000000000 * q^80 - 429372483438817686010518 * q^81 + 150226652586067691618304 * q^82 + 681902409230287477811148 * q^83 + 1265204314738538487742464 * q^84 - 121891328657528320312500 * q^85 + 3723334919365686278668288 * q^86 + 833435461987898381769960 * q^87 + 990701263380157965533184 * q^88 + 3822788098104790038225780 * q^89 + 800124539454000000000000 * q^90 + 2708056932935479178393864 * q^91 + 2839899250949179947614208 * q^92 + 1298609917529886715704336 * q^93 + 3911389529658182938607616 * q^94 + 935108542945830078125000 * q^95 - 111939454725287986593792 * q^96 - 16314734149871901683914364 * q^97 + 15186717796562586217979904 * q^98 - 4880327126898398506596288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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