LMFDB - Embedded newform 10.24.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,24,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, 24, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 24 $
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:	$33.5204037345$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{219241}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 54810 $ x^2 - x - 54810
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$234.616$ 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)

$f(q)$	$=$	\(q-2048.00 q^{2} -248056. q^{3} +4.19430e6 q^{4} +4.88281e7 q^{5} +5.08019e8 q^{6} -5.53518e9 q^{7} -8.58993e9 q^{8} -3.26113e10 q^{9} -1.00000e11 q^{10} +1.14906e12 q^{11} -1.04042e12 q^{12} +5.00457e12 q^{13} +1.13361e13 q^{14} -1.21121e13 q^{15} +1.75922e13 q^{16} +2.66925e14 q^{17} +6.67879e13 q^{18} -8.29918e14 q^{19} +2.04800e14 q^{20} +1.37304e15 q^{21} -2.35328e15 q^{22} +4.09173e15 q^{23} +2.13079e15 q^{24} +2.38419e15 q^{25} -1.02494e16 q^{26} +3.14422e16 q^{27} -2.32162e16 q^{28} -7.61938e16 q^{29} +2.48056e16 q^{30} -9.68453e16 q^{31} -3.60288e16 q^{32} -2.85032e17 q^{33} -5.46662e17 q^{34} -2.70273e17 q^{35} -1.36782e17 q^{36} +4.73319e16 q^{37} +1.69967e18 q^{38} -1.24142e18 q^{39} -4.19430e17 q^{40} -2.15162e18 q^{41} -2.81198e18 q^{42} -7.08076e18 q^{43} +4.81952e18 q^{44} -1.59235e18 q^{45} -8.37987e18 q^{46} -1.89843e19 q^{47} -4.36385e18 q^{48} +3.26951e18 q^{49} -4.88281e18 q^{50} -6.62123e19 q^{51} +2.09907e19 q^{52} +3.73319e19 q^{53} -6.43937e19 q^{54} +5.61066e19 q^{55} +4.75469e19 q^{56} +2.05866e20 q^{57} +1.56045e20 q^{58} +2.48317e20 q^{59} -5.08019e19 q^{60} -2.46263e20 q^{61} +1.98339e20 q^{62} +1.80510e20 q^{63} +7.37870e19 q^{64} +2.44364e20 q^{65} +5.83747e20 q^{66} -8.02335e20 q^{67} +1.11956e21 q^{68} -1.01498e21 q^{69} +5.53518e20 q^{70} -9.67342e20 q^{71} +2.80129e20 q^{72} +1.76339e21 q^{73} -9.69358e19 q^{74} -5.91412e20 q^{75} -3.48093e21 q^{76} -6.36028e21 q^{77} +2.54242e21 q^{78} -6.00291e21 q^{79} +8.58993e20 q^{80} -4.72931e21 q^{81} +4.40652e21 q^{82} -1.90063e22 q^{83} +5.75893e21 q^{84} +1.30334e22 q^{85} +1.45014e22 q^{86} +1.89003e22 q^{87} -9.87039e21 q^{88} -4.51150e22 q^{89} +3.26113e21 q^{90} -2.77012e22 q^{91} +1.71620e22 q^{92} +2.40231e22 q^{93} +3.88798e22 q^{94} -4.05233e22 q^{95} +8.93717e21 q^{96} +1.75770e22 q^{97} -6.69595e21 q^{98} -3.74725e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4096 q^{2} - 18516 q^{3} + 8388608 q^{4} + 97656250 q^{5} + 37920768 q^{6} - 4415735108 q^{7} - 17179869184 q^{8} - 74065768326 q^{9} - 200000000000 q^{10} + 195017239824 q^{11} - 77661732864 q^{12}+ \cdots + 20\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 4096 * q^2 - 18516 * q^3 + 8388608 * q^4 + 97656250 * q^5 + 37920768 * q^6 - 4415735108 * q^7 - 17179869184 * q^8 - 74065768326 * q^9 - 200000000000 * q^10 + 195017239824 * q^11 - 77661732864 * q^12 + 2583183058684 * q^13 + 9043425501184 * q^14 - 904101562500 * q^15 + 35184372088832 * q^16 + 131668862600532 * q^17 + 151686693531648 * q^18 - 1760888418200 * q^19 + 409600000000000 * q^20 + 1629995023906464 * q^21 - 399395307159552 * q^22 + 4012836105342564 * q^23 + 159051228905472 * q^24 + 4768371582031250 * q^25 - 5290358904184832 * q^26 + 317121583931640 * q^27 - 18520935426424832 * q^28 - 108385465473787380 * q^29 + 1851600000000000 * q^30 - 282534241930647896 * q^31 - 72057594037927936 * q^32 - 504024591095725392 * q^33 - 269657830605889536 * q^34 - 215612065820312500 * q^35 - 310654348352815104 * q^36 - 326855967548366468 * q^37 + 3606299480473600 * q^38 - 1797221588702622072 * q^39 - 838860800000000000 * q^40 - 5378411403014673276 * q^41 - 3338229808960438272 * q^42 - 9824206470496391636 * q^43 + 817961589062762496 * q^44 - 3616492594042968750 * q^45 - 8218288343741571072 * q^46 - 18459008132084260308 * q^47 - 325736916798406656 * q^48 - 22846074207183681054 * q^49 - 9765625000000000000 * q^50 - 97258917604973930856 * q^51 + 10834655035770535936 * q^52 - 6735586459267392756 * q^53 - 649465003891998720 * q^54 + 9522326163281250000 * q^55 + 37930875753318055936 * q^56 + 395961513009676856400 * q^57 + 221973433290316554240 * q^58 + 404431460611319194440 * q^59 - 3792076800000000000 * q^60 + 267288639406230095404 * q^61 + 578630127473966891008 * q^62 + 134103369179566769004 * q^63 + 147573952589676412928 * q^64 + 126131985287304687500 * q^65 + 1032242362564045602816 * q^66 - 878259028011046311548 * q^67 + 552259237080861769728 * q^68 - 1033089938007493665312 * q^69 + 441573510800000000000 * q^70 - 1422290577065242851336 * q^71 + 636220105426565332992 * q^72 - 2737850090767514630876 * q^73 + 669401021539054526464 * q^74 - 44145584106445312500 * q^75 - 7385701336009932800 * q^76 - 7428286679002982182896 * q^77 + 3680709813662970003456 * q^78 - 16358236398140542679120 * q^79 + 1717986918400000000000 * q^80 - 7971119473850267877918 * q^81 + 11014986553374050869248 * q^82 - 24918314799609836009556 * q^83 + 6836694648750977581056 * q^84 + 6429143681666601562500 * q^85 + 20119974851576610070528 * q^86 + 11511051890670005309640 * q^87 - 1675185334400537591808 * q^88 - 69086711107654759066380 * q^89 + 7406576832600000000000 * q^90 - 30411848367847894491736 * q^91 + 16831054527982737555456 * q^92 - 18600007517643336450432 * q^93 + 37804048654508565110784 * q^94 - 85980879794921875000 * q^95 + 667109205603136831488 * q^96 + 142113717247845486800212 * q^97 + 46788759976312178798592 * q^98 + 2077038401308192249488 * 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 $

$2$	−2048.00	−0.707107
$2$	−2048.00	−0.707107
$3$	−248056.	−0.808455	−0.404227	−	0.914659i	$-0.632460\pi$
$3$	−248056.	−0.808455	−0.404227	+	0.914659i	$0.632460\pi$
$4$	4.19430e6	0.500000
$5$	4.88281e7	0.447214
$5$	4.88281e7	0.447214
$6$	5.08019e8	0.571664
$7$	−5.53518e9	−1.05805	−0.529023	−	0.848607i	$-0.677441\pi$
$7$	−5.53518e9	−1.05805	−0.529023	+	0.848607i	$0.677441\pi$
$8$	−8.58993e9	−0.353553
$9$	−3.26113e10	−0.346401
$10$	−1.00000e11	−0.316228
$11$	1.14906e12	1.21431	0.607153	−	0.794585i	$-0.292311\pi$
$11$	1.14906e12	1.21431	0.607153	+	0.794585i	$0.292311\pi$
$12$	−1.04042e12	−0.404227
$13$	5.00457e12	0.774495	0.387247	−	0.921976i	$-0.373426\pi$
$13$	5.00457e12	0.774495	0.387247	+	0.921976i	$0.373426\pi$
$14$	1.13361e13	0.748152
$15$	−1.21121e13	−0.361552
$16$	1.75922e13	0.250000
$17$	2.66925e14	1.88897	0.944487	−	0.328549i	$-0.106560\pi$
$17$	2.66925e14	1.88897	0.944487	+	0.328549i	$0.106560\pi$
$18$	6.67879e13	0.244943
$19$	−8.29918e14	−1.63444	−0.817219	−	0.576327i	$-0.804486\pi$
$19$	−8.29918e14	−1.63444	−0.817219	+	0.576327i	$0.804486\pi$
$20$	2.04800e14	0.223607
$21$	1.37304e15	0.855382
$22$	−2.35328e15	−0.858644
$23$	4.09173e15	0.895441	0.447721	−	0.894173i	$-0.352236\pi$
$23$	4.09173e15	0.895441	0.447721	+	0.894173i	$0.352236\pi$
$24$	2.13079e15	0.285832
$25$	2.38419e15	0.200000
$26$	−1.02494e16	−0.547650
$27$	3.14422e16	1.08850
$28$	−2.32162e16	−0.529023
$29$	−7.61938e16	−1.15969	−0.579846	−	0.814726i	$-0.696887\pi$
$29$	−7.61938e16	−1.15969	−0.579846	+	0.814726i	$0.696887\pi$
$30$	2.48056e16	0.255656
$31$	−9.68453e16	−0.684572	−0.342286	−	0.939596i	$-0.611201\pi$
$31$	−9.68453e16	−0.684572	−0.342286	+	0.939596i	$0.611201\pi$
$32$	−3.60288e16	−0.176777
$33$	−2.85032e17	−0.981712
$34$	−5.46662e17	−1.33571
$35$	−2.70273e17	−0.473173
$36$	−1.36782e17	−0.173201
$37$	4.73319e16	0.0437355	0.0218678	−	0.999761i	$-0.493039\pi$
$37$	4.73319e16	0.0437355	0.0218678	+	0.999761i	$0.493039\pi$
$38$	1.69967e18	1.15572
$39$	−1.24142e18	−0.626144
$40$	−4.19430e17	−0.158114
$41$	−2.15162e18	−0.610592	−0.305296	−	0.952257i	$-0.598755\pi$
$41$	−2.15162e18	−0.610592	−0.305296	+	0.952257i	$0.598755\pi$
$42$	−2.81198e18	−0.604847
$43$	−7.08076e18	−1.16196	−0.580982	−	0.813916i	$-0.697331\pi$
$43$	−7.08076e18	−1.16196	−0.580982	+	0.813916i	$0.697331\pi$
$44$	4.81952e18	0.607153
$45$	−1.59235e18	−0.154915
$46$	−8.37987e18	−0.633173
$47$	−1.89843e19	−1.12013	−0.560065	−	0.828448i	$-0.689224\pi$
$47$	−1.89843e19	−1.12013	−0.560065	+	0.828448i	$0.689224\pi$
$48$	−4.36385e18	−0.202114
$49$	3.26951e18	0.119461
$50$	−4.88281e18	−0.141421
$51$	−6.62123e19	−1.52715
$52$	2.09907e19	0.387247
$53$	3.73319e19	0.553233	0.276616	−	0.960980i	$-0.410787\pi$
$53$	3.73319e19	0.553233	0.276616	+	0.960980i	$0.410787\pi$
$54$	−6.43937e19	−0.769689
$55$	5.61066e19	0.543054
$56$	4.75469e19	0.374076
$57$	2.05866e20	1.32137
$58$	1.56045e20	0.820026
$59$	2.48317e20	1.07203	0.536016	−	0.844208i	$-0.319929\pi$
$59$	2.48317e20	1.07203	0.536016	+	0.844208i	$0.319929\pi$
$60$	−5.08019e19	−0.180776
$61$	−2.46263e20	−0.724613	−0.362306	−	0.932059i	$-0.618011\pi$
$61$	−2.46263e20	−0.724613	−0.362306	+	0.932059i	$0.618011\pi$
$62$	1.98339e20	0.484065
$63$	1.80510e20	0.366508
$64$	7.37870e19	0.125000
$65$	2.44364e20	0.346365
$66$	5.83747e20	0.694175
$67$	−8.02335e20	−0.802594	−0.401297	−	0.915948i	$-0.631440\pi$
$67$	−8.02335e20	−0.802594	−0.401297	+	0.915948i	$0.631440\pi$
$68$	1.11956e21	0.944487
$69$	−1.01498e21	−0.723924
$70$	5.53518e20	0.334584
$71$	−9.67342e20	−0.496717	−0.248358	−	0.968668i	$-0.579891\pi$
$71$	−9.67342e20	−0.496717	−0.248358	+	0.968668i	$0.579891\pi$
$72$	2.80129e20	0.122471
$73$	1.76339e21	0.657864	0.328932	−	0.944354i	$-0.393311\pi$
$73$	1.76339e21	0.657864	0.328932	+	0.944354i	$0.393311\pi$
$74$	−9.69358e19	−0.0309257
$75$	−5.91412e20	−0.161691
$76$	−3.48093e21	−0.817219
$77$	−6.36028e21	−1.28479
$78$	2.54242e21	0.442751
$79$	−6.00291e21	−0.902921	−0.451461	−	0.892291i	$-0.649097\pi$
$79$	−6.00291e21	−0.902921	−0.451461	+	0.892291i	$0.649097\pi$
$80$	8.58993e20	0.111803
$81$	−4.72931e21	−0.533605
$82$	4.40652e21	0.431754
$83$	−1.90063e22	−1.61994	−0.809969	−	0.586472i	$-0.800516\pi$
$83$	−1.90063e22	−1.61994	−0.809969	+	0.586472i	$0.800516\pi$
$84$	5.75893e21	0.427691
$85$	1.30334e22	0.844775
$86$	1.45014e22	0.821633
$87$	1.89003e22	0.937558
$88$	−9.87039e21	−0.429322
$89$	−4.51150e22	−1.72320	−0.861601	−	0.507587i	$-0.830538\pi$
$89$	−4.51150e22	−1.72320	−0.861601	+	0.507587i	$0.830538\pi$
$90$	3.26113e21	0.109542
$91$	−2.77012e22	−0.819451
$92$	1.71620e22	0.447721
$93$	2.40231e22	0.553445
$94$	3.88798e22	0.792052
$95$	−4.05233e22	−0.730943
$96$	8.93717e21	0.142916
$97$	1.75770e22	0.249499	0.124750	−	0.992188i	$-0.460187\pi$
$97$	1.75770e22	0.249499	0.124750	+	0.992188i	$0.460187\pi$
$98$	−6.69595e21	−0.0844720
$99$	−3.74725e22	−0.420637
$100$	1.00000e22	0.100000
$101$	1.72636e23	1.53970	0.769850	−	0.638225i	$-0.220331\pi$
$101$	1.72636e23	1.53970	0.769850	+	0.638225i	$0.220331\pi$
$102$	1.35603e23	1.07986
$103$	−7.39196e22	−0.526176	−0.263088	−	0.964772i	$-0.584741\pi$
$103$	−7.39196e22	−0.526176	−0.263088	+	0.964772i	$0.584741\pi$
$104$	−4.29890e22	−0.273825
$105$	6.70428e22	0.382539
$106$	−7.64558e22	−0.391195
$107$	3.64152e23	1.67251	0.836255	−	0.548340i	$-0.184740\pi$
$107$	3.64152e23	1.67251	0.836255	+	0.548340i	$0.184740\pi$
$108$	1.31878e23	0.544252
$109$	2.32344e23	0.862434	0.431217	−	0.902248i	$-0.358084\pi$
$109$	2.32344e23	0.862434	0.431217	+	0.902248i	$0.358084\pi$
$110$	−1.14906e23	−0.383997
$111$	−1.17410e22	−0.0353582
$112$	−9.73760e22	−0.264512
$113$	−6.52015e23	−1.59902	−0.799512	−	0.600650i	$-0.794909\pi$
$113$	−6.52015e23	−1.59902	−0.799512	+	0.600650i	$0.794909\pi$
$114$	−4.21614e23	−0.934349
$115$	1.99792e23	0.400454
$116$	−3.19580e23	−0.579846
$117$	−1.63206e23	−0.268286
$118$	−5.08552e23	−0.758041
$119$	−1.47748e24	−1.99862
$120$	1.04042e23	0.127828
$121$	4.24918e23	0.474541
$122$	5.04347e23	0.512379
$123$	5.33723e23	0.493636
$124$	−4.06199e23	−0.342286
$125$	1.16415e23	0.0894427
$126$	−3.69683e23	−0.259160
$127$	−8.69127e23	−0.556340	−0.278170	−	0.960532i	$-0.589728\pi$
$127$	−8.69127e23	−0.556340	−0.278170	+	0.960532i	$0.589728\pi$
$128$	−1.51116e23	−0.0883883
$129$	1.75643e24	0.939396
$130$	−5.00457e23	−0.244917
$131$	1.54721e23	0.0693311	0.0346656	−	0.999399i	$-0.488963\pi$
$131$	1.54721e23	0.0693311	0.0346656	+	0.999399i	$0.488963\pi$
$132$	−1.19551e24	−0.490856
$133$	4.59375e24	1.72931
$134$	1.64318e24	0.567519
$135$	1.53527e24	0.486794
$136$	−2.29286e24	−0.667853
$137$	−5.27775e23	−0.141307	−0.0706533	−	0.997501i	$-0.522508\pi$
$137$	−5.27775e23	−0.141307	−0.0706533	+	0.997501i	$0.522508\pi$
$138$	2.07868e24	0.511891
$139$	−3.13469e24	−0.710435	−0.355217	−	0.934784i	$-0.615593\pi$
$139$	−3.13469e24	−0.710435	−0.355217	+	0.934784i	$0.615593\pi$
$140$	−1.13361e24	−0.236586
$141$	4.70917e24	0.905575
$142$	1.98112e24	0.351232
$143$	5.75057e24	0.940474
$144$	−5.73704e23	−0.0866003
$145$	−3.72040e24	−0.518630
$146$	−3.61143e24	−0.465180
$147$	−8.11022e23	−0.0965791
$148$	1.98525e23	0.0218678
$149$	−2.68240e24	−0.273453	−0.136726	−	0.990609i	$-0.543658\pi$
$149$	−2.68240e24	−0.273453	−0.136726	+	0.990609i	$0.543658\pi$
$150$	1.21121e24	0.114333
$151$	9.87063e24	0.863197	0.431599	−	0.902066i	$-0.357950\pi$
$151$	9.87063e24	0.863197	0.431599	+	0.902066i	$0.357950\pi$
$152$	7.12894e24	0.577861
$153$	−8.70476e24	−0.654343
$154$	1.30259e25	0.908485
$155$	−4.72877e24	−0.306150
$156$	−5.20687e24	−0.313072
$157$	−2.58352e25	−1.44333	−0.721666	−	0.692242i	$-0.756623\pi$
$157$	−2.58352e25	−1.44333	−0.721666	+	0.692242i	$0.756623\pi$
$158$	1.22940e25	0.638462
$159$	−9.26042e24	−0.447264
$160$	−1.75922e24	−0.0790569
$161$	−2.26485e25	−0.947418
$162$	9.68563e24	0.377316
$163$	−3.31455e24	−0.120301	−0.0601503	−	0.998189i	$-0.519158\pi$
$163$	−3.31455e24	−0.120301	−0.0601503	+	0.998189i	$0.519158\pi$
$164$	−9.02455e24	−0.305296
$165$	−1.39176e25	−0.439035
$166$	3.89248e25	1.14547
$167$	−9.23000e24	−0.253491	−0.126745	−	0.991935i	$-0.540453\pi$
$167$	−9.23000e24	−0.253491	−0.126745	+	0.991935i	$0.540453\pi$
$168$	−1.17943e25	−0.302423
$169$	−1.67082e25	−0.400158
$170$	−2.66925e25	−0.597346
$171$	2.70647e25	0.566171
$172$	−2.96989e25	−0.580982
$173$	2.50481e25	0.458400	0.229200	−	0.973379i	$-0.426389\pi$
$173$	2.50481e25	0.458400	0.229200	+	0.973379i	$0.426389\pi$
$174$	−3.87079e25	−0.662954
$175$	−1.31969e25	−0.211609
$176$	2.02145e25	0.303577
$177$	−6.15965e25	−0.866689
$178$	9.23955e25	1.21849
$179$	−7.76500e25	−0.960133	−0.480067	−	0.877232i	$-0.659388\pi$
$179$	−7.76500e25	−0.960133	−0.480067	+	0.877232i	$0.659388\pi$
$180$	−6.67879e24	−0.0774576
$181$	1.79026e26	1.94810	0.974050	−	0.226331i	$-0.0726731\pi$
$181$	1.79026e26	1.94810	0.974050	+	0.226331i	$0.0726731\pi$
$182$	5.67321e25	0.579439
$183$	6.10871e25	0.585817
$184$	−3.51477e25	−0.316586
$185$	2.31113e24	0.0195591
$186$	−4.91993e25	−0.391345
$187$	3.06713e26	2.29379
$188$	−7.96258e25	−0.560065
$189$	−1.74039e26	−1.15169
$190$	8.29918e25	0.516855
$191$	−1.87629e26	−1.10006	−0.550031	−	0.835144i	$-0.685384\pi$
$191$	−1.87629e26	−1.10006	−0.550031	+	0.835144i	$0.685384\pi$
$192$	−1.83033e25	−0.101057
$193$	3.19948e26	1.66407	0.832033	−	0.554726i	$-0.187177\pi$
$193$	3.19948e26	1.66407	0.832033	+	0.554726i	$0.187177\pi$
$194$	−3.59977e25	−0.176423
$195$	−6.06160e25	−0.280020
$196$	1.37133e25	0.0597307
$197$	2.32413e26	0.954770	0.477385	−	0.878694i	$-0.341585\pi$
$197$	2.32413e26	0.954770	0.477385	+	0.878694i	$0.341585\pi$
$198$	7.67436e25	0.297435
$199$	−1.44151e26	−0.527237	−0.263619	−	0.964627i	$-0.584916\pi$
$199$	−1.44151e26	−0.527237	−0.263619	+	0.964627i	$0.584916\pi$
$200$	−2.04800e25	−0.0707107
$201$	1.99024e26	0.648861
$202$	−3.53559e26	−1.08873
$203$	4.21747e26	1.22701
$204$	−2.77714e26	−0.763575
$205$	−1.05060e26	−0.273065
$206$	1.51387e26	0.372063
$207$	−1.33437e26	−0.310182
$208$	8.80414e25	0.193624
$209$	−9.53629e26	−1.98471
$210$	−1.37304e26	−0.270496
$211$	−9.00904e26	−1.68047	−0.840234	−	0.542223i	$-0.817583\pi$
$211$	−9.00904e26	−1.68047	−0.840234	+	0.542223i	$0.817583\pi$
$212$	1.56581e26	0.276616
$213$	2.39955e26	0.401573
$214$	−7.45783e26	−1.18264
$215$	−3.45740e26	−0.519646
$216$	−2.70087e26	−0.384844
$217$	5.36056e26	0.724308
$218$	−4.75840e26	−0.609833
$219$	−4.37420e26	−0.531853
$220$	2.35328e26	0.271527
$221$	1.33584e27	1.46300
$222$	2.40455e25	0.0250020
$223$	1.12234e27	1.10820	0.554100	−	0.832450i	$-0.313063\pi$
$223$	1.12234e27	1.10820	0.554100	+	0.832450i	$0.313063\pi$
$224$	1.99426e26	0.187038
$225$	−7.77514e25	−0.0692802
$226$	1.33533e27	1.13068
$227$	−1.38912e26	−0.111800	−0.0558999	−	0.998436i	$-0.517803\pi$
$227$	−1.38912e26	−0.111800	−0.0558999	+	0.998436i	$0.517803\pi$
$228$	8.63466e26	0.660685
$229$	−1.03506e27	−0.753105	−0.376553	−	0.926395i	$-0.622891\pi$
$229$	−1.03506e27	−0.753105	−0.376553	+	0.926395i	$0.622891\pi$
$230$	−4.09173e26	−0.283163
$231$	1.57771e27	1.03870
$232$	6.54500e26	0.410013
$233$	−1.03552e27	−0.617398	−0.308699	−	0.951160i	$-0.599894\pi$
$233$	−1.03552e27	−0.617398	−0.308699	+	0.951160i	$0.599894\pi$
$234$	3.34245e26	0.189707
$235$	−9.26967e26	−0.500938
$236$	1.04151e27	0.536016
$237$	1.48906e27	0.729971
$238$	3.02587e27	1.41324
$239$	−1.71220e27	−0.762041	−0.381021	−	0.924567i	$-0.624427\pi$
$239$	−1.71220e27	−0.762041	−0.381021	+	0.924567i	$0.624427\pi$
$240$	−2.13079e26	−0.0903880
$241$	−8.11502e26	−0.328166	−0.164083	−	0.986447i	$-0.552466\pi$
$241$	−8.11502e26	−0.328166	−0.164083	+	0.986447i	$0.552466\pi$
$242$	−8.70232e26	−0.335551
$243$	−1.78694e27	−0.657109
$244$	−1.03290e27	−0.362306
$245$	1.59644e26	0.0534248
$246$	−1.09306e27	−0.349053
$247$	−4.15338e27	−1.26586
$248$	8.31895e26	0.242033
$249$	4.71462e27	1.30965
$250$	−2.38419e26	−0.0632456
$251$	2.20197e27	0.557910	0.278955	−	0.960304i	$-0.410012\pi$
$251$	2.20197e27	0.557910	0.278955	+	0.960304i	$0.410012\pi$
$252$	7.57112e26	0.183254
$253$	4.70166e27	1.08734
$254$	1.77997e27	0.393392
$255$	−3.23302e27	−0.682962
$256$	3.09485e26	0.0625000
$257$	−8.24281e27	−1.59164	−0.795819	−	0.605534i	$-0.792959\pi$
$257$	−8.24281e27	−1.59164	−0.795819	+	0.605534i	$0.792959\pi$
$258$	−3.59716e27	−0.664253
$259$	−2.61991e26	−0.0462742
$260$	1.02494e27	0.173182
$261$	2.48478e27	0.401718
$262$	−3.16868e26	−0.0490245
$263$	1.16638e27	0.172722	0.0863610	−	0.996264i	$-0.472476\pi$
$263$	1.16638e27	0.172722	0.0863610	+	0.996264i	$0.472476\pi$
$264$	2.44841e27	0.347088
$265$	1.82285e27	0.247413
$266$	−9.40799e27	−1.22281
$267$	1.11911e28	1.39313
$268$	−3.36524e27	−0.401297
$269$	−1.48702e28	−1.69890	−0.849448	−	0.527673i	$-0.823065\pi$
$269$	−1.48702e28	−1.69890	−0.849448	+	0.527673i	$0.823065\pi$
$270$	−3.14422e27	−0.344215
$271$	−1.44238e28	−1.51333	−0.756665	−	0.653803i	$-0.773172\pi$
$271$	−1.44238e28	−1.51333	−0.756665	+	0.653803i	$0.773172\pi$
$272$	4.69579e27	0.472243
$273$	6.87146e27	0.662489
$274$	1.08088e27	0.0999188
$275$	2.73958e27	0.242861
$276$	−4.25713e27	−0.361962
$277$	−1.19544e28	−0.975013	−0.487507	−	0.873119i	$-0.662094\pi$
$277$	−1.19544e28	−0.975013	−0.487507	+	0.873119i	$0.662094\pi$
$278$	6.41984e27	0.502353
$279$	3.15825e27	0.237136
$280$	2.32162e27	0.167292
$281$	2.06996e28	1.43166	0.715831	−	0.698274i	$-0.246048\pi$
$281$	2.06996e28	1.43166	0.715831	+	0.698274i	$0.246048\pi$
$282$	−9.64438e27	−0.640338
$283$	−1.14948e28	−0.732753	−0.366376	−	0.930467i	$-0.619402\pi$
$283$	−1.14948e28	−0.732753	−0.366376	+	0.930467i	$0.619402\pi$
$284$	−4.05733e27	−0.248358
$285$	1.00521e28	0.590934
$286$	−1.17772e28	−0.665016
$287$	1.19096e28	0.646035
$288$	1.17495e27	0.0612356
$289$	5.12812e28	2.56822
$290$	7.61938e27	0.366727
$291$	−4.36008e27	−0.201709
$292$	7.39620e27	0.328932
$293$	−3.69791e28	−1.58117	−0.790586	−	0.612352i	$-0.790224\pi$
$293$	−3.69791e28	−1.58117	−0.790586	+	0.612352i	$0.790224\pi$
$294$	1.66097e27	0.0682917
$295$	1.21248e28	0.479427
$296$	−4.06578e26	−0.0154628
$297$	3.61291e28	1.32178
$298$	5.49356e27	0.193360
$299$	2.04774e28	0.693515
$300$	−2.48056e27	−0.0808455
$301$	3.91933e28	1.22941
$302$	−2.02150e28	−0.610372
$303$	−4.28235e28	−1.24478
$304$	−1.46001e28	−0.408610
$305$	−1.20246e28	−0.324057
$306$	1.78273e28	0.462690
$307$	−3.17969e28	−0.794866	−0.397433	−	0.917631i	$-0.630099\pi$
$307$	−3.17969e28	−0.794866	−0.397433	+	0.917631i	$0.630099\pi$
$308$	−2.66770e28	−0.642396
$309$	1.83362e28	0.425390
$310$	9.68453e27	0.216481
$311$	−4.33022e28	−0.932750	−0.466375	−	0.884587i	$-0.654440\pi$
$311$	−4.33022e28	−0.932750	−0.466375	+	0.884587i	$0.654440\pi$
$312$	1.06637e28	0.221375
$313$	4.55810e26	0.00912061	0.00456030	−	0.999990i	$-0.498548\pi$
$313$	4.55810e26	0.00912061	0.00456030	+	0.999990i	$0.498548\pi$
$314$	5.29105e28	1.02059
$315$	8.81394e27	0.163907
$316$	−2.51780e28	−0.451461
$317$	5.36147e28	0.927049	0.463524	−	0.886084i	$-0.346585\pi$
$317$	5.36147e28	0.927049	0.463524	+	0.886084i	$0.346585\pi$
$318$	1.89653e28	0.316263
$319$	−8.75515e28	−1.40822
$320$	3.60288e27	0.0559017
$321$	−9.03301e28	−1.35215
$322$	4.63841e28	0.669926
$323$	−2.21525e29	−3.08741
$324$	−1.98362e28	−0.266803
$325$	1.19318e28	0.154899
$326$	6.78820e27	0.0850653
$327$	−5.76343e28	−0.697239
$328$	1.84823e28	0.215877
$329$	1.05081e29	1.18515
$330$	2.85032e28	0.310445
$331$	3.04232e28	0.320025	0.160012	−	0.987115i	$-0.448847\pi$
$331$	3.04232e28	0.320025	0.160012	+	0.987115i	$0.448847\pi$
$332$	−7.97180e28	−0.809969
$333$	−1.54356e27	−0.0151500
$334$	1.89030e28	0.179245
$335$	−3.91765e28	−0.358931
$336$	2.41547e28	0.213846
$337$	5.57310e28	0.476819	0.238409	−	0.971165i	$-0.423374\pi$
$337$	5.57310e28	0.476819	0.238409	+	0.971165i	$0.423374\pi$
$338$	3.42183e28	0.282954
$339$	1.61736e29	1.29274
$340$	5.46662e28	0.422387
$341$	−1.11281e29	−0.831280
$342$	−5.54285e28	−0.400344
$343$	1.33394e29	0.931650
$344$	6.08233e28	0.410816
$345$	−4.95596e28	−0.323749
$346$	−5.12985e28	−0.324138
$347$	−2.05152e29	−1.25397	−0.626985	−	0.779031i	$-0.715711\pi$
$347$	−2.05152e29	−1.25397	−0.626985	+	0.779031i	$0.715711\pi$
$348$	7.92738e28	0.468779
$349$	2.36329e29	1.35215	0.676074	−	0.736834i	$-0.263680\pi$
$349$	2.36329e29	1.35215	0.676074	+	0.736834i	$0.263680\pi$
$350$	2.70273e28	0.149630
$351$	1.57355e29	0.843041
$352$	−4.13994e28	−0.214661
$353$	1.09725e29	0.550677	0.275339	−	0.961347i	$-0.411210\pi$
$353$	1.09725e29	0.550677	0.275339	+	0.961347i	$0.411210\pi$
$354$	1.26150e29	0.612841
$355$	−4.72335e28	−0.222139
$356$	−1.89226e29	−0.861601
$357$	3.66497e29	1.61579
$358$	1.59027e29	0.678917
$359$	−3.26602e29	−1.35031	−0.675153	−	0.737677i	$-0.735923\pi$
$359$	−3.26602e29	−1.35031	−0.675153	+	0.737677i	$0.735923\pi$
$360$	1.36782e28	0.0547708
$361$	4.30934e29	1.67139
$362$	−3.66644e29	−1.37752
$363$	−1.05404e29	−0.383645
$364$	−1.16187e29	−0.409726
$365$	8.61031e28	0.294206
$366$	−1.25106e29	−0.414235
$367$	−8.85081e28	−0.284003	−0.142002	−	0.989866i	$-0.545354\pi$
$367$	−8.85081e28	−0.284003	−0.142002	+	0.989866i	$0.545354\pi$
$368$	7.19825e28	0.223860
$369$	7.01671e28	0.211510
$370$	−4.73319e27	−0.0138304
$371$	−2.06639e29	−0.585346
$372$	1.00760e29	0.276723
$373$	−3.93901e29	−1.04890	−0.524452	−	0.851440i	$-0.675730\pi$
$373$	−3.93901e29	−1.04890	−0.524452	+	0.851440i	$0.675730\pi$
$374$	−6.28149e29	−1.62196
$375$	−2.88775e28	−0.0723104
$376$	1.63074e29	0.396026
$377$	−3.81317e29	−0.898175
$378$	3.56431e29	0.814366
$379$	1.29839e29	0.287777	0.143888	−	0.989594i	$-0.454039\pi$
$379$	1.29839e29	0.287777	0.143888	+	0.989594i	$0.454039\pi$
$380$	−1.69967e29	−0.365472
$381$	2.15592e29	0.449776
$382$	3.84265e29	0.777861
$383$	2.17964e29	0.428153	0.214076	−	0.976817i	$-0.431326\pi$
$383$	2.17964e29	0.428153	0.214076	+	0.976817i	$0.431326\pi$
$384$	3.74852e28	0.0714580
$385$	−3.10561e29	−0.574577
$386$	−6.55254e29	−1.17667
$387$	2.30913e29	0.402506
$388$	7.37232e28	0.124750
$389$	−9.04905e29	−1.48656	−0.743280	−	0.668980i	$-0.766731\pi$
$389$	−9.04905e29	−1.48656	−0.743280	+	0.668980i	$0.766731\pi$
$390$	1.24142e29	0.198004
$391$	1.09218e30	1.69147
$392$	−2.80849e28	−0.0422360
$393$	−3.83794e28	−0.0560511
$394$	−4.75982e29	−0.675125
$395$	−2.93111e29	−0.403799
$396$	−1.57171e29	−0.210319
$397$	1.18206e30	1.53656	0.768279	−	0.640116i	$-0.221114\pi$
$397$	1.18206e30	1.53656	0.768279	+	0.640116i	$0.221114\pi$
$398$	2.95221e29	0.372813
$399$	−1.13951e30	−1.39807
$400$	4.19430e28	0.0500000
$401$	9.75353e29	1.12980	0.564900	−	0.825159i	$-0.308915\pi$
$401$	9.75353e29	1.12980	0.564900	+	0.825159i	$0.308915\pi$
$402$	−4.07602e29	−0.458814
$403$	−4.84669e29	−0.530197
$404$	7.24089e29	0.769850
$405$	−2.30923e29	−0.238636
$406$	−8.63737e29	−0.867625
$407$	5.43874e28	0.0531084
$408$	5.68759e29	0.539929
$409$	3.52564e29	0.325402	0.162701	−	0.986675i	$-0.447979\pi$
$409$	3.52564e29	0.325402	0.162701	+	0.986675i	$0.447979\pi$
$410$	2.15162e29	0.193086
$411$	1.30918e29	0.114240
$412$	−3.10041e29	−0.263088
$413$	−1.37448e30	−1.13426
$414$	2.73278e29	0.219332
$415$	−9.28040e29	−0.724459
$416$	−1.80309e29	−0.136913
$417$	7.77579e29	0.574354
$418$	1.95303e30	1.40340
$419$	−1.40788e30	−0.984246	−0.492123	−	0.870526i	$-0.663779\pi$
$419$	−1.40788e30	−0.984246	−0.492123	+	0.870526i	$0.663779\pi$
$420$	2.81198e29	0.191269
$421$	7.36867e29	0.487691	0.243845	−	0.969814i	$-0.421591\pi$
$421$	7.36867e29	0.487691	0.243845	+	0.969814i	$0.421591\pi$
$422$	1.84505e30	1.18827
$423$	6.19102e29	0.388014
$424$	−3.20679e29	−0.195597
$425$	6.36398e29	0.377795
$426$	−4.91428e29	−0.283955
$427$	1.36311e30	0.766674
$428$	1.52736e30	0.836255
$429$	−1.42647e30	−0.760331
$430$	7.08076e29	0.367445
$431$	1.71259e30	0.865298	0.432649	−	0.901562i	$-0.357579\pi$
$431$	1.71259e30	0.865298	0.432649	+	0.901562i	$0.357579\pi$
$432$	5.53138e29	0.272126
$433$	3.34373e30	1.60184	0.800921	−	0.598770i	$-0.204343\pi$
$433$	3.34373e30	1.60184	0.800921	+	0.598770i	$0.204343\pi$
$434$	−1.09784e30	−0.512163
$435$	9.22868e29	0.419289
$436$	9.74520e29	0.431217
$437$	−3.39580e30	−1.46354
$438$	8.95837e29	0.376077
$439$	−3.95516e30	−1.61742	−0.808710	−	0.588208i	$-0.799834\pi$
$439$	−3.95516e30	−1.61742	−0.808710	+	0.588208i	$0.799834\pi$
$440$	−4.81952e29	−0.191999
$441$	−1.06623e29	−0.0413816
$442$	−2.73581e30	−1.03450
$443$	−3.40082e30	−1.25297	−0.626486	−	0.779433i	$-0.715507\pi$
$443$	−3.40082e30	−1.25297	−0.626486	+	0.779433i	$0.715507\pi$
$444$	−4.92452e28	−0.0176791
$445$	−2.20288e30	−0.770639
$446$	−2.29855e30	−0.783616
$447$	6.65387e29	0.221074
$448$	−4.08424e29	−0.132256
$449$	3.24298e30	1.02355	0.511777	−	0.859118i	$-0.328987\pi$
$449$	3.24298e30	1.02355	0.511777	+	0.859118i	$0.328987\pi$
$450$	1.59235e29	0.0489885
$451$	−2.47235e30	−0.741446
$452$	−2.73475e30	−0.799512
$453$	−2.44847e30	−0.697856
$454$	2.84491e29	0.0790545
$455$	−1.35260e30	−0.366470
$456$	−1.76838e30	−0.467175
$457$	−2.32028e30	−0.597729	−0.298864	−	0.954296i	$-0.596608\pi$
$457$	−2.32028e30	−0.597729	−0.298864	+	0.954296i	$0.596608\pi$
$458$	2.11979e30	0.532526
$459$	8.39270e30	2.05616
$460$	8.37987e29	0.200227
$461$	−1.77997e30	−0.414813	−0.207406	−	0.978255i	$-0.566502\pi$
$461$	−1.77997e30	−0.414813	−0.207406	+	0.978255i	$0.566502\pi$
$462$	−3.23114e30	−0.734469
$463$	−1.16490e30	−0.258291	−0.129145	−	0.991626i	$-0.541223\pi$
$463$	−1.16490e30	−0.258291	−0.129145	+	0.991626i	$0.541223\pi$
$464$	−1.34042e30	−0.289923
$465$	1.17300e30	0.247508
$466$	2.12074e30	0.436566
$467$	4.42414e30	0.888555	0.444278	−	0.895889i	$-0.353460\pi$
$467$	4.42414e30	0.888555	0.444278	+	0.895889i	$0.353460\pi$
$468$	−6.84534e29	−0.134143
$469$	4.44107e30	0.849181
$470$	1.89843e30	0.354216
$471$	6.40858e30	1.16687
$472$	−2.13302e30	−0.379020
$473$	−8.13625e30	−1.41098
$474$	−3.04959e30	−0.516167
$475$	−1.97868e30	−0.326888
$476$	−6.19699e30	−0.999311
$477$	−1.21744e30	−0.191640
$478$	3.50659e30	0.538845
$479$	1.17747e31	1.76641	0.883207	−	0.468983i	$-0.155379\pi$
$479$	1.17747e31	1.76641	0.883207	+	0.468983i	$0.155379\pi$
$480$	4.36385e29	0.0639140
$481$	2.36876e29	0.0338729
$482$	1.66196e30	0.232048
$483$	5.61810e30	0.765945
$484$	1.78224e30	0.237270
$485$	8.58252e29	0.111580
$486$	3.65965e30	0.464646
$487$	8.71950e30	1.08121	0.540603	−	0.841278i	$-0.318196\pi$
$487$	8.71950e30	1.08121	0.540603	+	0.841278i	$0.318196\pi$
$488$	2.11538e30	0.256189
$489$	8.22195e29	0.0972575
$490$	−3.26951e29	−0.0377770
$491$	3.31430e30	0.374071	0.187036	−	0.982353i	$-0.440112\pi$
$491$	3.31430e30	0.374071	0.187036	+	0.982353i	$0.440112\pi$
$492$	2.23860e30	0.246818
$493$	−2.03380e31	−2.19063
$494$	8.50613e30	0.895101
$495$	−1.82971e30	−0.188115
$496$	−1.70372e30	−0.171143
$497$	5.35441e30	0.525549
$498$	−9.65554e30	−0.926060
$499$	−4.41221e30	−0.413523	−0.206762	−	0.978391i	$-0.566292\pi$
$499$	−4.41221e30	−0.413523	−0.206762	+	0.978391i	$0.566292\pi$
$500$	4.88281e29	0.0447214
$501$	2.28956e30	0.204936
$502$	−4.50964e30	−0.394502
$503$	8.86520e30	0.757978	0.378989	−	0.925401i	$-0.376272\pi$
$503$	8.86520e30	0.757978	0.378989	+	0.925401i	$0.376272\pi$
$504$	−1.55056e30	−0.129580
$505$	8.42950e30	0.688575
$506$	−9.62901e30	−0.768866
$507$	4.14456e30	0.323510
$508$	−3.64538e30	−0.278170
$509$	4.77364e30	0.356119	0.178059	−	0.984020i	$-0.443018\pi$
$509$	4.77364e30	0.356119	0.178059	+	0.984020i	$0.443018\pi$
$510$	6.62123e30	0.482927
$511$	−9.76070e30	−0.696050
$512$	−6.33825e29	−0.0441942
$513$	−2.60945e31	−1.77909
$514$	1.68813e31	1.12546
$515$	−3.60935e30	−0.235313
$516$	7.36699e30	0.469698
$517$	−2.18142e31	−1.36018
$518$	5.36558e29	0.0327208
$519$	−6.21334e30	−0.370596
$520$	−2.09907e30	−0.122458
$521$	−8.76488e30	−0.500164	−0.250082	−	0.968225i	$-0.580458\pi$
$521$	−8.76488e30	−0.500164	−0.250082	+	0.968225i	$0.580458\pi$
$522$	−5.08882e30	−0.284058
$523$	1.88160e31	1.02744	0.513721	−	0.857957i	$-0.328266\pi$
$523$	1.88160e31	1.02744	0.513721	+	0.857957i	$0.328266\pi$
$524$	6.48945e29	0.0346656
$525$	3.27357e30	0.171076
$526$	−2.38874e30	−0.122133
$527$	−2.58504e31	−1.29314
$528$	−5.01434e30	−0.245428
$529$	−4.13819e30	−0.198185
$530$	−3.73319e30	−0.174948
$531$	−8.09792e30	−0.371353
$532$	1.92676e31	0.864656
$533$	−1.07679e31	−0.472900
$534$	−2.29193e31	−0.985092
$535$	1.77808e31	0.747970
$536$	6.89201e30	0.283760
$537$	1.92616e31	0.776224
$538$	3.04542e31	1.20130
$539$	3.75687e30	0.145063
$540$	6.43937e30	0.243397
$541$	−2.61136e31	−0.966269	−0.483135	−	0.875546i	$-0.660502\pi$
$541$	−2.61136e31	−0.966269	−0.483135	+	0.875546i	$0.660502\pi$
$542$	2.95400e31	1.07009
$543$	−4.44084e31	−1.57495
$544$	−9.61697e30	−0.333927
$545$	1.13449e31	0.385692
$546$	−1.40728e31	−0.468450
$547$	3.35569e29	0.0109377	0.00546887	−	0.999985i	$-0.498259\pi$
$547$	3.35569e29	0.0109377	0.00546887	+	0.999985i	$0.498259\pi$
$548$	−2.21365e30	−0.0706533
$549$	8.03095e30	0.251007
$550$	−5.61066e30	−0.171729
$551$	6.32346e31	1.89544
$552$	8.71861e30	0.255946
$553$	3.32272e31	0.955332
$554$	2.44826e31	0.689438
$555$	−5.73290e29	−0.0158127
$556$	−1.31478e31	−0.355217
$557$	1.24154e31	0.328567	0.164284	−	0.986413i	$-0.447469\pi$
$557$	1.24154e31	0.328567	0.164284	+	0.986413i	$0.447469\pi$
$558$	−6.46810e30	−0.167681
$559$	−3.54362e31	−0.899935
$560$	−4.75469e30	−0.118293
$561$	−7.60822e31	−1.85443
$562$	−4.23929e31	−1.01234
$563$	6.53842e31	1.52977	0.764885	−	0.644166i	$-0.222796\pi$
$563$	6.53842e31	1.52977	0.764885	+	0.644166i	$0.222796\pi$
$564$	1.97517e31	0.452787
$565$	−3.18366e31	−0.715106
$566$	2.35413e31	0.518134
$567$	2.61776e31	0.564579
$568$	8.30940e30	0.175616
$569$	2.71677e31	0.562680	0.281340	−	0.959608i	$-0.409221\pi$
$569$	2.71677e31	0.562680	0.281340	+	0.959608i	$0.409221\pi$
$570$	−2.05866e31	−0.417854
$571$	5.92712e31	1.17904	0.589520	−	0.807754i	$-0.299317\pi$
$571$	5.92712e31	1.17904	0.589520	+	0.807754i	$0.299317\pi$
$572$	2.41197e31	0.470237
$573$	4.65426e31	0.889350
$574$	−2.43909e31	−0.456815
$575$	9.75545e30	0.179088
$576$	−2.40629e30	−0.0433001
$577$	−2.23935e31	−0.395003	−0.197502	−	0.980303i	$-0.563283\pi$
$577$	−2.23935e31	−0.395003	−0.197502	+	0.980303i	$0.563283\pi$
$578$	−1.05024e32	−1.81601
$579$	−7.93651e31	−1.34532
$580$	−1.56045e31	−0.259315
$581$	1.05203e32	1.71397
$582$	8.92945e30	0.142630
$583$	4.28968e31	0.671794
$584$	−1.51474e31	−0.232590
$585$	−7.96902e30	−0.119981
$586$	7.57332e31	1.11806
$587$	−6.49190e31	−0.939796	−0.469898	−	0.882721i	$-0.655709\pi$
$587$	−6.49190e31	−0.939796	−0.469898	+	0.882721i	$0.655709\pi$
$588$	−3.40167e30	−0.0482896
$589$	8.03736e31	1.11889
$590$	−2.48317e31	−0.339006
$591$	−5.76515e31	−0.771889
$592$	8.32672e29	0.0109339
$593$	1.27637e32	1.64379	0.821895	−	0.569638i	$-0.192917\pi$
$593$	1.27637e32	1.64379	0.821895	+	0.569638i	$0.192917\pi$
$594$	−7.39925e31	−0.934638
$595$	−7.21424e31	−0.893811
$596$	−1.12508e31	−0.136726
$597$	3.57575e31	0.426248
$598$	−4.19377e31	−0.490389
$599$	−4.35980e31	−0.500101	−0.250051	−	0.968233i	$-0.580447\pi$
$599$	−4.35980e31	−0.500101	−0.250051	+	0.968233i	$0.580447\pi$
$600$	5.08019e30	0.0571664
$601$	−8.94982e31	−0.988002	−0.494001	−	0.869461i	$-0.664466\pi$
$601$	−8.94982e31	−0.988002	−0.494001	+	0.869461i	$0.664466\pi$
$602$	−8.02679e31	−0.869326
$603$	2.61652e31	0.278019
$604$	4.14004e31	0.431599
$605$	2.07480e31	0.212221
$606$	8.77025e31	0.880191
$607$	−8.25995e31	−0.813406	−0.406703	−	0.913560i	$-0.633322\pi$
$607$	−8.25995e31	−0.813406	−0.406703	+	0.913560i	$0.633322\pi$
$608$	2.99009e31	0.288931
$609$	−1.04617e32	−0.991980
$610$	2.46263e31	0.229143
$611$	−9.50082e31	−0.867535
$612$	−3.65104e31	−0.327171
$613$	−1.75363e32	−1.54221	−0.771104	−	0.636710i	$-0.780295\pi$
$613$	−1.75363e32	−1.54221	−0.771104	+	0.636710i	$0.780295\pi$
$614$	6.51201e31	0.562055
$615$	2.60607e31	0.220761
$616$	5.46344e31	0.454243
$617$	−9.32726e31	−0.761158	−0.380579	−	0.924749i	$-0.624275\pi$
$617$	−9.32726e31	−0.761158	−0.380579	+	0.924749i	$0.624275\pi$
$618$	−3.75526e31	−0.300796
$619$	−2.11173e32	−1.66034	−0.830169	−	0.557512i	$-0.811756\pi$
$619$	−2.11173e32	−1.66034	−0.830169	+	0.557512i	$0.811756\pi$
$620$	−1.98339e31	−0.153075
$621$	1.28653e32	0.974692
$622$	8.86828e31	0.659554
$623$	2.49720e32	1.82323
$624$	−2.18392e31	−0.156536
$625$	5.68434e30	0.0400000
$626$	−9.33498e29	−0.00644924
$627$	2.36553e32	1.60455
$628$	−1.08361e32	−0.721666
$629$	1.26341e31	0.0826153
$630$	−1.80510e31	−0.115900
$631$	−1.01929e32	−0.642628	−0.321314	−	0.946973i	$-0.604125\pi$
$631$	−1.01929e32	−0.642628	−0.321314	+	0.946973i	$0.604125\pi$
$632$	5.15646e31	0.319231
$633$	2.23475e32	1.35858
$634$	−1.09803e32	−0.655522
$635$	−4.24379e31	−0.248803
$636$	−3.88410e31	−0.223632
$637$	1.63625e31	0.0925222
$638$	1.79306e32	0.995763
$639$	3.15463e31	0.172063
$640$	−7.37870e30	−0.0395285
$641$	−8.95507e31	−0.471196	−0.235598	−	0.971851i	$-0.575705\pi$
$641$	−8.95507e31	−0.471196	−0.235598	+	0.971851i	$0.575705\pi$
$642$	1.84996e32	0.956114
$643$	1.55072e32	0.787242	0.393621	−	0.919273i	$-0.371222\pi$
$643$	1.55072e32	0.787242	0.393621	+	0.919273i	$0.371222\pi$
$644$	−9.49947e31	−0.473709
$645$	8.57631e31	0.420110
$646$	4.53684e32	2.18313
$647$	−7.18599e31	−0.339693	−0.169847	−	0.985470i	$-0.554327\pi$
$647$	−7.18599e31	−0.339693	−0.169847	+	0.985470i	$0.554327\pi$
$648$	4.06245e31	0.188658
$649$	2.85332e32	1.30177
$650$	−2.44364e31	−0.109530
$651$	−1.32972e32	−0.585571
$652$	−1.39022e31	−0.0601503
$653$	1.03893e32	0.441658	0.220829	−	0.975313i	$-0.429124\pi$
$653$	1.03893e32	0.441658	0.220829	+	0.975313i	$0.429124\pi$
$654$	1.18035e32	0.493022
$655$	7.55472e30	0.0310058
$656$	−3.78517e31	−0.152648
$657$	−5.75065e31	−0.227885
$658$	−2.15207e32	−0.838028
$659$	−2.67825e31	−0.102487	−0.0512435	−	0.998686i	$-0.516318\pi$
$659$	−2.67825e31	−0.102487	−0.0512435	+	0.998686i	$0.516318\pi$
$660$	−5.83747e31	−0.219517
$661$	−3.87116e32	−1.43062	−0.715310	−	0.698807i	$-0.753715\pi$
$661$	−3.87116e32	−1.43062	−0.715310	+	0.698807i	$0.753715\pi$
$662$	−6.23068e31	−0.226292
$663$	−3.31364e32	−1.18277
$664$	1.63263e32	0.572735
$665$	2.24304e32	0.773371
$666$	3.16120e30	0.0107127
$667$	−3.11765e32	−1.03844
$668$	−3.87134e31	−0.126745
$669$	−2.78403e32	−0.895929
$670$	8.02335e31	0.253802
$671$	−2.82972e32	−0.879902
$672$	−4.94689e31	−0.151212
$673$	−2.33531e32	−0.701733	−0.350867	−	0.936425i	$-0.614113\pi$
$673$	−2.33531e32	−0.701733	−0.350867	+	0.936425i	$0.614113\pi$
$674$	−1.14137e32	−0.337162
$675$	7.49641e31	0.217701
$676$	−7.00791e31	−0.200079
$677$	6.22149e32	1.74632	0.873161	−	0.487432i	$-0.162066\pi$
$677$	6.22149e32	1.74632	0.873161	+	0.487432i	$0.162066\pi$
$678$	−3.31236e32	−0.914104
$679$	−9.72919e31	−0.263982
$680$	−1.11956e32	−0.298673
$681$	3.44579e31	0.0903851
$682$	2.27904e32	0.587804
$683$	−5.18176e32	−1.31413	−0.657067	−	0.753833i	$-0.728203\pi$
$683$	−5.18176e32	−1.31413	−0.657067	+	0.753833i	$0.728203\pi$
$684$	1.13518e32	0.283086
$685$	−2.57703e31	−0.0631942
$686$	−2.73190e32	−0.658776
$687$	2.56752e32	0.608851
$688$	−1.24566e32	−0.290491
$689$	1.86830e32	0.428476
$690$	1.01498e32	0.228925
$691$	5.78541e32	1.28333	0.641663	−	0.766987i	$-0.278245\pi$
$691$	5.78541e32	1.28333	0.641663	+	0.766987i	$0.278245\pi$
$692$	1.05059e32	0.229200
$693$	2.07417e32	0.445053
$694$	4.20151e32	0.886690
$695$	−1.53061e32	−0.317716
$696$	−1.62353e32	−0.331477
$697$	−5.74320e32	−1.15339
$698$	−4.84001e32	−0.956113
$699$	2.56867e32	0.499138
$700$	−5.53518e31	−0.105805
$701$	7.25665e32	1.36452	0.682259	−	0.731111i	$-0.260998\pi$
$701$	7.25665e32	1.36452	0.682259	+	0.731111i	$0.260998\pi$
$702$	−3.22263e32	−0.596120
$703$	−3.92816e31	−0.0714831
$704$	8.47860e31	0.151788
$705$	2.29940e32	0.404985
$706$	−2.24717e32	−0.389388
$707$	−9.55573e32	−1.62907
$708$	−2.58354e32	−0.433344
$709$	6.96702e32	1.14978	0.574891	−	0.818230i	$-0.305044\pi$
$709$	6.96702e32	1.14978	0.574891	+	0.818230i	$0.305044\pi$
$710$	9.67342e31	0.157076
$711$	1.95763e32	0.312773
$712$	3.87535e32	0.609244
$713$	−3.96265e32	−0.612994
$714$	−7.50586e32	−1.14254
$715$	2.80790e32	0.420593
$716$	−3.25688e32	−0.480067
$717$	4.24722e32	0.616076
$718$	6.68880e32	0.954811
$719$	7.58207e32	1.06514	0.532569	−	0.846387i	$-0.321227\pi$
$719$	7.58207e32	1.06514	0.532569	+	0.846387i	$0.321227\pi$
$720$	−2.80129e31	−0.0387288
$721$	4.09158e32	0.556719
$722$	−8.82552e32	−1.18185
$723$	2.01298e32	0.265307
$724$	7.50888e32	0.974050
$725$	−1.81660e32	−0.231938
$726$	2.15866e32	0.271278
$727$	2.69772e32	0.333696	0.166848	−	0.985983i	$-0.446641\pi$
$727$	2.69772e32	0.333696	0.166848	+	0.985983i	$0.446641\pi$
$728$	2.37952e32	0.289720
$729$	8.88493e32	1.06485
$730$	−1.76339e32	−0.208035
$731$	−1.89003e33	−2.19492
$732$	2.56218e32	0.292908
$733$	−3.67420e32	−0.413492	−0.206746	−	0.978395i	$-0.566287\pi$
$733$	−3.67420e32	−0.413492	−0.206746	+	0.978395i	$0.566287\pi$
$734$	1.81265e32	0.200821
$735$	−3.96007e31	−0.0431915
$736$	−1.47420e32	−0.158293
$737$	−9.21935e32	−0.974595
$738$	−1.43702e32	−0.149560
$739$	1.50918e33	1.54643	0.773216	−	0.634143i	$-0.218647\pi$
$739$	1.50918e33	1.54643	0.773216	+	0.634143i	$0.218647\pi$
$740$	9.69358e30	0.00977956
$741$	1.03027e33	1.02339
$742$	4.23197e32	0.413902
$743$	8.64193e32	0.832222	0.416111	−	0.909314i	$-0.363393\pi$
$743$	8.64193e32	0.832222	0.416111	+	0.909314i	$0.363393\pi$
$744$	−2.06357e32	−0.195672
$745$	−1.30977e32	−0.122292
$746$	8.06709e32	0.741687
$747$	6.19819e32	0.561148
$748$	1.28645e33	1.14690
$749$	−2.01565e33	−1.76959
$750$	5.91412e31	0.0511312
$751$	−8.02515e32	−0.683272	−0.341636	−	0.939832i	$-0.610981\pi$
$751$	−8.02515e32	−0.683272	−0.341636	+	0.939832i	$0.610981\pi$
$752$	−3.33975e32	−0.280033
$753$	−5.46213e32	−0.451045
$754$	7.80938e32	0.635106
$755$	4.81964e32	0.386033
$756$	−7.29971e32	−0.575844
$757$	−7.46047e32	−0.579647	−0.289823	−	0.957080i	$-0.593597\pi$
$757$	−7.46047e32	−0.579647	−0.289823	+	0.957080i	$0.593597\pi$
$758$	−2.65911e32	−0.203489
$759$	−1.16628e33	−0.879066
$760$	3.48093e32	0.258427
$761$	−2.23694e33	−1.63580	−0.817901	−	0.575359i	$-0.804863\pi$
$761$	−2.23694e33	−1.63580	−0.817901	+	0.575359i	$0.804863\pi$
$762$	−4.41533e32	−0.318040
$763$	−1.28606e33	−0.912495
$764$	−7.86974e32	−0.550031
$765$	−4.25037e32	−0.292631
$766$	−4.46390e32	−0.302750
$767$	1.24272e33	0.830283
$768$	−7.67697e31	−0.0505284
$769$	−8.84798e32	−0.573708	−0.286854	−	0.957974i	$-0.592609\pi$
$769$	−8.84798e32	−0.573708	−0.286854	+	0.957974i	$0.592609\pi$
$770$	6.36028e32	0.406287
$771$	2.04468e33	1.28677
$772$	1.34196e33	0.832033
$773$	4.12211e32	0.251800	0.125900	−	0.992043i	$-0.459818\pi$
$773$	4.12211e32	0.251800	0.125900	+	0.992043i	$0.459818\pi$
$774$	−4.72910e32	−0.284615
$775$	−2.30897e32	−0.136914
$776$	−1.50985e32	−0.0882114
$777$	6.49885e31	0.0374106
$778$	1.85325e33	1.05116
$779$	1.78567e33	0.997975
$780$	−2.54242e32	−0.140010
$781$	−1.11154e33	−0.603167
$782$	−2.23679e33	−1.19605
$783$	−2.39570e33	−1.26233
$784$	5.75178e31	0.0298653
$785$	−1.26148e33	−0.645477
$786$	7.86010e31	0.0396341
$787$	−9.29443e31	−0.0461863	−0.0230931	−	0.999733i	$-0.507351\pi$
$787$	−9.29443e31	−0.0461863	−0.0230931	+	0.999733i	$0.507351\pi$
$788$	9.74811e32	0.477385
$789$	−2.89327e32	−0.139638
$790$	6.00291e32	0.285529
$791$	3.60902e33	1.69184
$792$	3.21886e32	0.148718
$793$	−1.23244e33	−0.561209
$794$	−2.42086e33	−1.08651
$795$	−4.52169e32	−0.200022
$796$	−6.04612e32	−0.263619
$797$	−1.01244e32	−0.0435108	−0.0217554	−	0.999763i	$-0.506926\pi$
$797$	−1.01244e32	−0.0435108	−0.0217554	+	0.999763i	$0.506926\pi$
$798$	2.33371e33	0.988585
$799$	−5.06737e33	−2.11590
$800$	−8.58993e31	−0.0353553
$801$	1.47126e33	0.596919
$802$	−1.99752e33	−0.798890
$803$	2.02625e33	0.798848
$804$	8.34768e32	0.324430
$805$	−1.10588e33	−0.423698
$806$	9.92603e32	0.374906
$807$	3.68865e33	1.37348
$808$	−1.48293e33	−0.544366
$809$	−3.30371e33	−1.19562	−0.597811	−	0.801637i	$-0.703963\pi$
$809$	−3.30371e33	−1.19562	−0.597811	+	0.801637i	$0.703963\pi$
$810$	4.72931e32	0.168741
$811$	3.27520e33	1.15212	0.576061	−	0.817407i	$-0.304589\pi$
$811$	3.27520e33	1.15212	0.576061	+	0.817407i	$0.304589\pi$
$812$	1.76893e33	0.613504
$813$	3.57792e33	1.22346
$814$	−1.11385e32	−0.0375533
$815$	−1.61843e32	−0.0538000
$816$	−1.16482e33	−0.381787
$817$	5.87645e33	1.89916
$818$	−7.22051e32	−0.230094
$819$	9.03373e32	0.283859
$820$	−4.40652e32	−0.136533
$821$	−2.62789e32	−0.0802900	−0.0401450	−	0.999194i	$-0.512782\pi$
$821$	−2.62789e32	−0.0802900	−0.0401450	+	0.999194i	$0.512782\pi$
$822$	−2.68120e32	−0.0807799
$823$	1.32429e33	0.393447	0.196724	−	0.980459i	$-0.436970\pi$
$823$	1.32429e33	0.393447	0.196724	+	0.980459i	$0.436970\pi$
$824$	6.34964e32	0.186031
$825$	−6.79570e32	−0.196342
$826$	2.81493e33	0.802042
$827$	6.86820e32	0.192988	0.0964938	−	0.995334i	$-0.469237\pi$
$827$	6.86820e32	0.192988	0.0964938	+	0.995334i	$0.469237\pi$
$828$	−5.59674e32	−0.155091
$829$	−3.52526e33	−0.963416	−0.481708	−	0.876332i	$-0.659983\pi$
$829$	−3.52526e33	−0.963416	−0.481708	+	0.876332i	$0.659983\pi$
$830$	1.90063e33	0.512270
$831$	2.96536e33	0.788254
$832$	3.69272e32	0.0968118
$833$	8.72712e32	0.225659
$834$	−1.59248e33	−0.406130
$835$	−4.50684e32	−0.113365
$836$	−3.99981e33	−0.992355
$837$	−3.04503e33	−0.745159
$838$	2.88333e33	0.695967
$839$	7.77027e33	1.85001	0.925004	−	0.379958i	$-0.124061\pi$
$839$	7.77027e33	1.85001	0.925004	+	0.379958i	$0.124061\pi$
$840$	−5.75893e32	−0.135248
$841$	1.48877e33	0.344885
$842$	−1.50910e33	−0.344850
$843$	−5.13468e33	−1.15743
$844$	−3.77867e33	−0.840234
$845$	−8.15828e32	−0.178956
$846$	−1.26792e33	−0.274368
$847$	−2.35200e33	−0.502086
$848$	6.56750e32	0.138308
$849$	2.85136e33	0.592397
$850$	−1.30334e33	−0.267141
$851$	1.93670e32	0.0391626
$852$	1.00644e33	0.200787
$853$	−5.19512e33	−1.02254	−0.511272	−	0.859419i	$-0.670825\pi$
$853$	−5.19512e33	−1.02254	−0.511272	+	0.859419i	$0.670825\pi$
$854$	−2.79165e33	−0.542120
$855$	1.32152e33	0.253199
$856$	−3.12804e33	−0.591322
$857$	9.62211e33	1.79469	0.897347	−	0.441325i	$-0.145491\pi$
$857$	9.62211e33	1.79469	0.897347	+	0.441325i	$0.145491\pi$
$858$	2.92140e33	0.537635
$859$	−6.92148e33	−1.25683	−0.628417	−	0.777877i	$-0.716297\pi$
$859$	−6.92148e33	−1.25683	−0.628417	+	0.777877i	$0.716297\pi$
$860$	−1.45014e33	−0.259823
$861$	−2.95425e33	−0.522290
$862$	−3.50739e33	−0.611858
$863$	4.39935e33	0.757294	0.378647	−	0.925541i	$-0.376389\pi$
$863$	4.39935e33	0.757294	0.378647	+	0.925541i	$0.376389\pi$
$864$	−1.13283e33	−0.192422
$865$	1.22305e33	0.205003
$866$	−6.84795e33	−1.13267
$867$	−1.27206e34	−2.07629
$868$	2.24838e33	0.362154
$869$	−6.89772e33	−1.09642
$870$	−1.89003e33	−0.296482
$871$	−4.01535e33	−0.621605
$872$	−1.99582e33	−0.304917
$873$	−5.73208e32	−0.0864269
$874$	6.95460e33	1.03488
$875$	−6.44380e32	−0.0946345
$876$	−1.83467e33	−0.265927
$877$	−8.80187e33	−1.25916	−0.629578	−	0.776937i	$-0.716772\pi$
$877$	−8.80187e33	−1.25916	−0.629578	+	0.776937i	$0.716772\pi$
$878$	8.10018e33	1.14369
$879$	9.17290e33	1.27831
$880$	9.87039e32	0.135764
$881$	6.20312e33	0.842146	0.421073	−	0.907027i	$-0.361654\pi$
$881$	6.20312e33	0.842146	0.421073	+	0.907027i	$0.361654\pi$
$882$	2.18364e32	0.0292612
$883$	−7.33525e32	−0.0970213	−0.0485106	−	0.998823i	$-0.515447\pi$
$883$	−7.33525e32	−0.0970213	−0.0485106	+	0.998823i	$0.515447\pi$
$884$	5.60293e33	0.731500
$885$	−3.00764e33	−0.387595
$886$	6.96489e33	0.885985
$887$	−5.08588e33	−0.638623	−0.319311	−	0.947650i	$-0.603452\pi$
$887$	−5.08588e33	−0.638623	−0.319311	+	0.947650i	$0.603452\pi$
$888$	1.00854e32	0.0125010
$889$	4.81078e33	0.588634
$890$	4.51150e33	0.544924
$891$	−5.43428e33	−0.647960
$892$	4.70743e33	0.554100
$893$	1.57554e34	1.83079
$894$	−1.36271e33	−0.156323
$895$	−3.79150e33	−0.429385
$896$	8.36453e32	0.0935189
$897$	−5.07954e33	−0.560675
$898$	−6.64162e33	−0.723763
$899$	7.37901e33	0.793892
$900$	−3.26113e32	−0.0346401
$901$	9.96481e33	1.04504
$902$	5.06337e33	0.524282
$903$	−9.72215e33	−0.993924
$904$	5.60076e33	0.565341
$905$	8.74148e33	0.871217
$906$	5.01447e33	0.493458
$907$	1.39867e34	1.35904	0.679521	−	0.733656i	$-0.262188\pi$
$907$	1.39867e34	1.35904	0.679521	+	0.733656i	$0.262188\pi$
$908$	−5.82638e32	−0.0558999
$909$	−5.62989e33	−0.533354
$910$	2.77012e33	0.259133
$911$	−1.11628e34	−1.03112	−0.515561	−	0.856853i	$-0.672417\pi$
$911$	−1.11628e34	−1.03112	−0.515561	+	0.856853i	$0.672417\pi$
$912$	3.62164e33	0.330342
$913$	−2.18394e34	−1.96710
$914$	4.75194e33	0.422658
$915$	2.98277e33	0.261985
$916$	−4.34134e33	−0.376553
$917$	−8.56407e32	−0.0733555
$918$	−1.71883e34	−1.45392
$919$	8.24058e33	0.688382	0.344191	−	0.938900i	$-0.388153\pi$
$919$	8.24058e33	0.688382	0.344191	+	0.938900i	$0.388153\pi$
$920$	−1.71620e33	−0.141582
$921$	7.88743e33	0.642613
$922$	3.64538e33	0.293317
$923$	−4.84113e33	−0.384705
$924$	6.61738e33	0.519348
$925$	1.12848e32	0.00874711
$926$	2.38572e33	0.182639
$927$	2.41061e33	0.182268
$928$	2.74517e33	0.205006
$929$	1.03061e33	0.0760178	0.0380089	−	0.999277i	$-0.487898\pi$
$929$	1.03061e33	0.0760178	0.0380089	+	0.999277i	$0.487898\pi$
$930$	−2.40231e33	−0.175015
$931$	−2.71342e33	−0.195252
$932$	−4.34328e33	−0.308699
$933$	1.07414e34	0.754086
$934$	−9.06063e33	−0.628303
$935$	1.49762e34	1.02582
$936$	1.40193e33	0.0948533
$937$	−1.43845e34	−0.961368	−0.480684	−	0.876894i	$-0.659612\pi$
$937$	−1.43845e34	−0.961368	−0.480684	+	0.876894i	$0.659612\pi$
$938$	−9.09532e33	−0.600462
$939$	−1.13066e32	−0.00737360
$940$	−3.88798e33	−0.250469
$941$	−9.09450e33	−0.578760	−0.289380	−	0.957214i	$-0.593449\pi$
$941$	−9.09450e33	−0.578760	−0.289380	+	0.957214i	$0.593449\pi$
$942$	−1.31248e34	−0.825100
$943$	−8.80386e33	−0.546750
$944$	4.36843e33	0.268008
$945$	−8.49798e33	−0.515050
$946$	1.66630e34	0.997714
$947$	9.97145e33	0.589839	0.294920	−	0.955522i	$-0.404707\pi$
$947$	9.97145e33	0.589839	0.294920	+	0.955522i	$0.404707\pi$
$948$	6.24556e33	0.364986
$949$	8.82502e33	0.509512
$950$	4.05233e33	0.231145
$951$	−1.32995e34	−0.749477
$952$	1.26914e34	0.706619
$953$	−7.81126e33	−0.429688	−0.214844	−	0.976648i	$-0.568924\pi$
$953$	−7.81126e33	−0.429688	−0.214844	+	0.976648i	$0.568924\pi$
$954$	2.49332e33	0.135510
$955$	−9.16159e33	−0.491962
$956$	−7.18149e33	−0.381021
$957$	2.17177e34	1.13848
$958$	−2.41146e34	−1.24904
$959$	2.92133e33	0.149509
$960$	−8.93717e32	−0.0451940
$961$	−1.06343e34	−0.531361
$962$	−4.85122e32	−0.0239518
$963$	−1.18755e34	−0.579360
$964$	−3.40368e33	−0.164083
$965$	1.56225e34	0.744193
$966$	−1.15059e34	−0.541605
$967$	9.65442e33	0.449078	0.224539	−	0.974465i	$-0.427912\pi$
$967$	9.65442e33	0.449078	0.224539	+	0.974465i	$0.427912\pi$
$968$	−3.65002e33	−0.167775
$969$	5.49508e34	2.49603
$970$	−1.75770e33	−0.0788987
$971$	−2.59685e34	−1.15193	−0.575965	−	0.817474i	$-0.695374\pi$
$971$	−2.59685e34	−1.15193	−0.575965	+	0.817474i	$0.695374\pi$
$972$	−7.49496e33	−0.328554
$973$	1.73511e34	0.751673
$974$	−1.78575e34	−0.764529
$975$	−2.95976e33	−0.125229
$976$	−4.33230e33	−0.181153
$977$	−7.90048e33	−0.326487	−0.163244	−	0.986586i	$-0.552196\pi$
$977$	−7.90048e33	−0.326487	−0.163244	+	0.986586i	$0.552196\pi$
$978$	−1.68386e33	−0.0687714
$979$	−5.18400e34	−2.09249
$980$	6.69595e32	0.0267124
$981$	−7.57703e33	−0.298748
$982$	−6.78769e33	−0.264508
$983$	9.20116e33	0.354387	0.177193	−	0.984176i	$-0.443298\pi$
$983$	9.20116e33	0.354387	0.177193	+	0.984176i	$0.443298\pi$
$984$	−4.58464e33	−0.174527
$985$	1.13483e34	0.426986
$986$	4.16522e34	1.54901
$987$	−2.60661e34	−0.958140
$988$	−1.74206e34	−0.632932
$989$	−2.89726e34	−1.04047
$990$	3.74725e33	0.133017
$991$	2.65253e34	0.930708	0.465354	−	0.885125i	$-0.345927\pi$
$991$	2.65253e34	0.930708	0.465354	+	0.885125i	$0.345927\pi$
$992$	3.48922e33	0.121016
$993$	−7.54667e33	−0.258725
$994$	−1.09658e34	−0.371619
$995$	−7.03861e33	−0.235788
$996$	1.97746e34	0.654824
$997$	4.79679e34	1.57021	0.785103	−	0.619365i	$-0.212610\pi$
$997$	4.79679e34	1.57021	0.785103	+	0.619365i	$0.212610\pi$
$998$	9.03621e33	0.292405
$999$	1.48822e33	0.0476063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.24.a.a.1.1	✓	2
5.2	odd	4		50.24.b.d.49.2		4
5.3	odd	4		50.24.b.d.49.3		4
5.4	even	2		50.24.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.24.a.a.1.1	✓	2	1.1	even	1	trivial
50.24.a.d.1.2		2	5.4	even	2
50.24.b.d.49.2		4	5.2	odd	4
50.24.b.d.49.3		4	5.3	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:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-2048.00 q^{2} -248056. q^{3} +4.19430e6 q^{4} +4.88281e7 q^{5} +5.08019e8 q^{6} -5.53518e9 q^{7} -8.58993e9 q^{8} -3.26113e10 q^{9} -1.00000e11 q^{10} +1.14906e12 q^{11} -1.04042e12 q^{12} +5.00457e12 q^{13} +1.13361e13 q^{14} -1.21121e13 q^{15} +1.75922e13 q^{16} +2.66925e14 q^{17} +6.67879e13 q^{18} -8.29918e14 q^{19} +2.04800e14 q^{20} +1.37304e15 q^{21} -2.35328e15 q^{22} +4.09173e15 q^{23} +2.13079e15 q^{24} +2.38419e15 q^{25} -1.02494e16 q^{26} +3.14422e16 q^{27} -2.32162e16 q^{28} -7.61938e16 q^{29} +2.48056e16 q^{30} -9.68453e16 q^{31} -3.60288e16 q^{32} -2.85032e17 q^{33} -5.46662e17 q^{34} -2.70273e17 q^{35} -1.36782e17 q^{36} +4.73319e16 q^{37} +1.69967e18 q^{38} -1.24142e18 q^{39} -4.19430e17 q^{40} -2.15162e18 q^{41} -2.81198e18 q^{42} -7.08076e18 q^{43} +4.81952e18 q^{44} -1.59235e18 q^{45} -8.37987e18 q^{46} -1.89843e19 q^{47} -4.36385e18 q^{48} +3.26951e18 q^{49} -4.88281e18 q^{50} -6.62123e19 q^{51} +2.09907e19 q^{52} +3.73319e19 q^{53} -6.43937e19 q^{54} +5.61066e19 q^{55} +4.75469e19 q^{56} +2.05866e20 q^{57} +1.56045e20 q^{58} +2.48317e20 q^{59} -5.08019e19 q^{60} -2.46263e20 q^{61} +1.98339e20 q^{62} +1.80510e20 q^{63} +7.37870e19 q^{64} +2.44364e20 q^{65} +5.83747e20 q^{66} -8.02335e20 q^{67} +1.11956e21 q^{68} -1.01498e21 q^{69} +5.53518e20 q^{70} -9.67342e20 q^{71} +2.80129e20 q^{72} +1.76339e21 q^{73} -9.69358e19 q^{74} -5.91412e20 q^{75} -3.48093e21 q^{76} -6.36028e21 q^{77} +2.54242e21 q^{78} -6.00291e21 q^{79} +8.58993e20 q^{80} -4.72931e21 q^{81} +4.40652e21 q^{82} -1.90063e22 q^{83} +5.75893e21 q^{84} +1.30334e22 q^{85} +1.45014e22 q^{86} +1.89003e22 q^{87} -9.87039e21 q^{88} -4.51150e22 q^{89} +3.26113e21 q^{90} -2.77012e22 q^{91} +1.71620e22 q^{92} +2.40231e22 q^{93} +3.88798e22 q^{94} -4.05233e22 q^{95} +8.93717e21 q^{96} +1.75770e22 q^{97} -6.69595e21 q^{98} -3.74725e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4096 q^{2} - 18516 q^{3} + 8388608 q^{4} + 97656250 q^{5} + 37920768 q^{6} - 4415735108 q^{7} - 17179869184 q^{8} - 74065768326 q^{9} - 200000000000 q^{10} + 195017239824 q^{11} - 77661732864 q^{12}+ \cdots + 20\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 4096 * q^2 - 18516 * q^3 + 8388608 * q^4 + 97656250 * q^5 + 37920768 * q^6 - 4415735108 * q^7 - 17179869184 * q^8 - 74065768326 * q^9 - 200000000000 * q^10 + 195017239824 * q^11 - 77661732864 * q^12 + 2583183058684 * q^13 + 9043425501184 * q^14 - 904101562500 * q^15 + 35184372088832 * q^16 + 131668862600532 * q^17 + 151686693531648 * q^18 - 1760888418200 * q^19 + 409600000000000 * q^20 + 1629995023906464 * q^21 - 399395307159552 * q^22 + 4012836105342564 * q^23 + 159051228905472 * q^24 + 4768371582031250 * q^25 - 5290358904184832 * q^26 + 317121583931640 * q^27 - 18520935426424832 * q^28 - 108385465473787380 * q^29 + 1851600000000000 * q^30 - 282534241930647896 * q^31 - 72057594037927936 * q^32 - 504024591095725392 * q^33 - 269657830605889536 * q^34 - 215612065820312500 * q^35 - 310654348352815104 * q^36 - 326855967548366468 * q^37 + 3606299480473600 * q^38 - 1797221588702622072 * q^39 - 838860800000000000 * q^40 - 5378411403014673276 * q^41 - 3338229808960438272 * q^42 - 9824206470496391636 * q^43 + 817961589062762496 * q^44 - 3616492594042968750 * q^45 - 8218288343741571072 * q^46 - 18459008132084260308 * q^47 - 325736916798406656 * q^48 - 22846074207183681054 * q^49 - 9765625000000000000 * q^50 - 97258917604973930856 * q^51 + 10834655035770535936 * q^52 - 6735586459267392756 * q^53 - 649465003891998720 * q^54 + 9522326163281250000 * q^55 + 37930875753318055936 * q^56 + 395961513009676856400 * q^57 + 221973433290316554240 * q^58 + 404431460611319194440 * q^59 - 3792076800000000000 * q^60 + 267288639406230095404 * q^61 + 578630127473966891008 * q^62 + 134103369179566769004 * q^63 + 147573952589676412928 * q^64 + 126131985287304687500 * q^65 + 1032242362564045602816 * q^66 - 878259028011046311548 * q^67 + 552259237080861769728 * q^68 - 1033089938007493665312 * q^69 + 441573510800000000000 * q^70 - 1422290577065242851336 * q^71 + 636220105426565332992 * q^72 - 2737850090767514630876 * q^73 + 669401021539054526464 * q^74 - 44145584106445312500 * q^75 - 7385701336009932800 * q^76 - 7428286679002982182896 * q^77 + 3680709813662970003456 * q^78 - 16358236398140542679120 * q^79 + 1717986918400000000000 * q^80 - 7971119473850267877918 * q^81 + 11014986553374050869248 * q^82 - 24918314799609836009556 * q^83 + 6836694648750977581056 * q^84 + 6429143681666601562500 * q^85 + 20119974851576610070528 * q^86 + 11511051890670005309640 * q^87 - 1675185334400537591808 * q^88 - 69086711107654759066380 * q^89 + 7406576832600000000000 * q^90 - 30411848367847894491736 * q^91 + 16831054527982737555456 * q^92 - 18600007517643336450432 * q^93 + 37804048654508565110784 * q^94 - 85980879794921875000 * q^95 + 667109205603136831488 * q^96 + 142113717247845486800212 * q^97 + 46788759976312178798592 * q^98 + 2077038401308192249488 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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