LMFDB - Embedded newform 10.22.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,22,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, 22, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 22 $
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:	$27.9477344287$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{157921}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 39480 $ x^2 - x - 39480
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$199.196$ 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)

$f(q)$	$=$	\(q-1024.00 q^{2} -174616. q^{3} +1.04858e6 q^{4} -9.76562e6 q^{5} +1.78807e8 q^{6} -9.60462e8 q^{7} -1.07374e9 q^{8} +2.00304e10 q^{9} +1.00000e10 q^{10} +8.54661e10 q^{11} -1.83098e11 q^{12} +9.74302e11 q^{13} +9.83513e11 q^{14} +1.70523e12 q^{15} +1.09951e12 q^{16} -1.17045e13 q^{17} -2.05111e13 q^{18} +1.41128e13 q^{19} -1.02400e13 q^{20} +1.67712e14 q^{21} -8.75173e13 q^{22} -2.65862e13 q^{23} +1.87492e14 q^{24} +9.53674e13 q^{25} -9.97685e14 q^{26} -1.67108e15 q^{27} -1.00712e15 q^{28} +1.45075e15 q^{29} -1.74616e15 q^{30} -7.63253e15 q^{31} -1.12590e15 q^{32} -1.49237e16 q^{33} +1.19854e16 q^{34} +9.37951e15 q^{35} +2.10034e16 q^{36} +1.09912e16 q^{37} -1.44515e16 q^{38} -1.70129e17 q^{39} +1.04858e16 q^{40} +7.93639e16 q^{41} -1.71737e17 q^{42} -8.36751e16 q^{43} +8.96177e16 q^{44} -1.95609e17 q^{45} +2.72243e16 q^{46} +3.57127e17 q^{47} -1.91992e17 q^{48} +3.63941e17 q^{49} -9.76562e16 q^{50} +2.04379e18 q^{51} +1.02163e18 q^{52} -8.17016e17 q^{53} +1.71119e18 q^{54} -8.34630e17 q^{55} +1.03129e18 q^{56} -2.46432e18 q^{57} -1.48557e18 q^{58} +8.21011e17 q^{59} +1.78807e18 q^{60} +4.53683e18 q^{61} +7.81571e18 q^{62} -1.92384e19 q^{63} +1.15292e18 q^{64} -9.51466e18 q^{65} +1.52819e19 q^{66} +8.02826e18 q^{67} -1.22730e19 q^{68} +4.64238e18 q^{69} -9.60462e18 q^{70} -5.25728e19 q^{71} -2.15075e19 q^{72} +9.28698e18 q^{73} -1.12549e19 q^{74} -1.66527e19 q^{75} +1.47984e19 q^{76} -8.20869e19 q^{77} +1.74212e20 q^{78} +1.08861e19 q^{79} -1.07374e19 q^{80} +8.22724e19 q^{81} -8.12687e19 q^{82} -4.79994e19 q^{83} +1.75859e20 q^{84} +1.14302e20 q^{85} +8.56833e19 q^{86} -2.53325e20 q^{87} -9.17685e19 q^{88} +2.35270e20 q^{89} +2.00304e20 q^{90} -9.35779e20 q^{91} -2.78777e19 q^{92} +1.33276e21 q^{93} -3.65698e20 q^{94} -1.37820e20 q^{95} +1.96600e20 q^{96} +7.25967e20 q^{97} -3.72675e20 q^{98} +1.71192e21 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2048 q^{2} - 126692 q^{3} + 2097152 q^{4} - 19531250 q^{5} + 129732608 q^{6} - 292598684 q^{7} - 2147483648 q^{8} + 11866737826 q^{9} + 20000000000 q^{10} - 41326831776 q^{11} - 132846190592 q^{12}+ \cdots + 27\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 2048 * q^2 - 126692 * q^3 + 2097152 * q^4 - 19531250 * q^5 + 129732608 * q^6 - 292598684 * q^7 - 2147483648 * q^8 + 11866737826 * q^9 + 20000000000 * q^10 - 41326831776 * q^11 - 132846190592 * q^12 + 1887051472228 * q^13 + 299621052416 * q^14 + 1237226562500 * q^15 + 2199023255552 * q^16 - 3100413932364 * q^17 - 12151539533824 * q^18 + 7175794652440 * q^19 - 20480000000000 * q^20 + 199718603894264 * q^21 + 42318675738624 * q^22 - 357559990100052 * q^23 + 136034499166208 * q^24 + 190734863281250 * q^25 - 1932340707561472 * q^26 - 2563616231988920 * q^27 - 306811957673984 * q^28 - 2454584202185940 * q^29 - 1266920000000000 * q^30 - 4310677151243336 * q^31 - 2251799813685248 * q^32 - 21000167846983104 * q^33 + 3174823866740736 * q^34 + 2857409023437500 * q^35 + 12443176482635776 * q^36 - 32389201650205724 * q^37 - 7348013724098560 * q^38 - 126386038156081288 * q^39 + 20971520000000000 * q^40 - 16298035212712116 * q^41 - 204511850387726336 * q^42 - 161845702253479412 * q^43 - 43334323956350976 * q^44 - 115886111582031250 * q^45 + 366141429862453248 * q^46 + 153492993930726996 * q^47 - 139299327146196992 * q^48 + 251436016683357114 * q^49 - 195312500000000000 * q^50 + 2456129297437264344 * q^51 + 1978716884542947328 * q^52 + 604198357317820308 * q^53 + 2625143021556654080 * q^54 + 403582341562500000 * q^55 + 314175444658159616 * q^56 - 2796771718696561840 * q^57 + 2513494223038402560 * q^58 + 3110197357974672120 * q^59 + 1297326080000000000 * q^60 - 791142209760451676 * q^61 + 4414133402873176064 * q^62 - 24690614624666969692 * q^63 + 2305843009213693952 * q^64 - 18428237033476562500 * q^65 + 21504171875310698496 * q^66 - 5111819523383561564 * q^67 - 3251019639542513664 * q^68 - 11219196977510717208 * q^69 - 2925986840000000000 * q^70 - 82388741313238482456 * q^71 - 12741812718219034624 * q^72 + 10657918464992348548 * q^73 + 33166542489810661376 * q^74 - 12082290649414062500 * q^75 + 7524366053476925440 * q^76 - 166767237207340703808 * q^77 + 129419303071827238912 * q^78 + 28314166125451369360 * q^79 - 21474836480000000000 * q^80 + 124893157714537187242 * q^81 + 16689188057817206784 * q^82 - 10427725705926651732 * q^83 + 209420134797031768064 * q^84 + 30277479808242187500 * q^85 + 165729999107562917888 * q^86 - 440484049640705943960 * q^87 + 44374347731303399424 * q^88 + 478501472814113520180 * q^89 + 118667378260000000000 * q^90 - 326187611445407942776 * q^91 - 374928824179152125952 * q^92 + 1491957513759228855056 * q^93 - 157176825785064443904 * q^94 - 70076119652734375000 * q^95 + 142642510997705719808 * q^96 + 545226897779926992196 * q^97 - 257470481083757684736 * q^98 + 2747011580657571215712 * 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 $

$2$	−1024.00	−0.707107
$2$	−1024.00	−0.707107
$3$	−174616.	−1.70730	−0.853652	−	0.520844i	$-0.825617\pi$
$3$	−174616.	−1.70730	−0.853652	+	0.520844i	$0.825617\pi$
$4$	1.04858e6	0.500000
$5$	−9.76562e6	−0.447214
$5$	−9.76562e6	−0.447214
$6$	1.78807e8	1.20725
$7$	−9.60462e8	−1.28514	−0.642570	−	0.766227i	$-0.722132\pi$
$7$	−9.60462e8	−1.28514	−0.642570	+	0.766227i	$0.722132\pi$
$8$	−1.07374e9	−0.353553
$9$	2.00304e10	1.91489
$10$	1.00000e10	0.316228
$11$	8.54661e10	0.993507	0.496753	−	0.867892i	$-0.334525\pi$
$11$	8.54661e10	0.993507	0.496753	+	0.867892i	$0.334525\pi$
$12$	−1.83098e11	−0.853652
$13$	9.74302e11	1.96015	0.980073	−	0.198640i	$-0.0636523\pi$
$13$	9.74302e11	1.96015	0.980073	+	0.198640i	$0.0636523\pi$
$14$	9.83513e11	0.908732
$15$	1.70523e12	0.763529
$16$	1.09951e12	0.250000
$17$	−1.17045e13	−1.40812	−0.704058	−	0.710143i	$-0.748630\pi$
$17$	−1.17045e13	−1.40812	−0.704058	+	0.710143i	$0.748630\pi$
$18$	−2.05111e13	−1.35403
$19$	1.41128e13	0.528081	0.264041	−	0.964512i	$-0.414945\pi$
$19$	1.41128e13	0.528081	0.264041	+	0.964512i	$0.414945\pi$
$20$	−1.02400e13	−0.223607
$21$	1.67712e14	2.19413
$22$	−8.75173e13	−0.702515
$23$	−2.65862e13	−0.133818	−0.0669090	−	0.997759i	$-0.521314\pi$
$23$	−2.65862e13	−0.133818	−0.0669090	+	0.997759i	$0.521314\pi$
$24$	1.87492e14	0.603623
$25$	9.53674e13	0.200000
$26$	−9.97685e14	−1.38603
$27$	−1.67108e15	−1.56199
$28$	−1.00712e15	−0.642570
$29$	1.45075e15	0.640346	0.320173	−	0.947359i	$-0.396259\pi$
$29$	1.45075e15	0.640346	0.320173	+	0.947359i	$0.396259\pi$
$30$	−1.74616e15	−0.539897
$31$	−7.63253e15	−1.67252	−0.836259	−	0.548335i	$-0.815262\pi$
$31$	−7.63253e15	−1.67252	−0.836259	+	0.548335i	$0.815262\pi$
$32$	−1.12590e15	−0.176777
$33$	−1.49237e16	−1.69622
$34$	1.19854e16	0.995688
$35$	9.37951e15	0.574732
$36$	2.10034e16	0.957443
$37$	1.09912e16	0.375773	0.187886	−	0.982191i	$-0.439836\pi$
$37$	1.09912e16	0.375773	0.187886	+	0.982191i	$0.439836\pi$
$38$	−1.44515e16	−0.373410
$39$	−1.70129e17	−3.34656
$40$	1.04858e16	0.158114
$41$	7.93639e16	0.923406	0.461703	−	0.887035i	$-0.347239\pi$
$41$	7.93639e16	0.923406	0.461703	+	0.887035i	$0.347239\pi$
$42$	−1.71737e17	−1.55148
$43$	−8.36751e16	−0.590442	−0.295221	−	0.955429i	$-0.595393\pi$
$43$	−8.36751e16	−0.590442	−0.295221	+	0.955429i	$0.595393\pi$
$44$	8.96177e16	0.496753
$45$	−1.95609e17	−0.856363
$46$	2.72243e16	0.0946236
$47$	3.57127e17	0.990365	0.495183	−	0.868789i	$-0.335101\pi$
$47$	3.57127e17	0.990365	0.495183	+	0.868789i	$0.335101\pi$
$48$	−1.91992e17	−0.426826
$49$	3.63941e17	0.651586
$50$	−9.76562e16	−0.141421
$51$	2.04379e18	2.40408
$52$	1.02163e18	0.980073
$53$	−8.17016e17	−0.641702	−0.320851	−	0.947130i	$-0.603969\pi$
$53$	−8.17016e17	−0.641702	−0.320851	+	0.947130i	$0.603969\pi$
$54$	1.71119e18	1.10449
$55$	−8.34630e17	−0.444310
$56$	1.03129e18	0.454366
$57$	−2.46432e18	−0.901595
$58$	−1.48557e18	−0.452793
$59$	8.21011e17	0.209124	0.104562	−	0.994518i	$-0.466656\pi$
$59$	8.21011e17	0.209124	0.104562	+	0.994518i	$0.466656\pi$
$60$	1.78807e18	0.381765
$61$	4.53683e18	0.814310	0.407155	−	0.913359i	$-0.366521\pi$
$61$	4.53683e18	0.814310	0.407155	+	0.913359i	$0.366521\pi$
$62$	7.81571e18	1.18265
$63$	−1.92384e19	−2.46090
$64$	1.15292e18	0.125000
$65$	−9.51466e18	−0.876604
$66$	1.52819e19	1.19941
$67$	8.02826e18	0.538066	0.269033	−	0.963131i	$-0.413296\pi$
$67$	8.02826e18	0.538066	0.269033	+	0.963131i	$0.413296\pi$
$68$	−1.22730e19	−0.704058
$69$	4.64238e18	0.228468
$70$	−9.60462e18	−0.406397
$71$	−5.25728e19	−1.91668	−0.958338	−	0.285638i	$-0.907794\pi$
$71$	−5.25728e19	−1.91668	−0.958338	+	0.285638i	$0.907794\pi$
$72$	−2.15075e19	−0.677014
$73$	9.28698e18	0.252921	0.126460	−	0.991972i	$-0.459638\pi$
$73$	9.28698e18	0.252921	0.126460	+	0.991972i	$0.459638\pi$
$74$	−1.12549e19	−0.265711
$75$	−1.66527e19	−0.341461
$76$	1.47984e19	0.264041
$77$	−8.20869e19	−1.27680
$78$	1.74212e20	2.36638
$79$	1.08861e19	0.129356	0.0646781	−	0.997906i	$-0.479398\pi$
$79$	1.08861e19	0.129356	0.0646781	+	0.997906i	$0.479398\pi$
$80$	−1.07374e19	−0.111803
$81$	8.22724e19	0.751902
$82$	−8.12687e19	−0.652947
$83$	−4.79994e19	−0.339560	−0.169780	−	0.985482i	$-0.554306\pi$
$83$	−4.79994e19	−0.339560	−0.169780	+	0.985482i	$0.554306\pi$
$84$	1.75859e20	1.09706
$85$	1.14302e20	0.629728
$86$	8.56833e19	0.417506
$87$	−2.53325e20	−1.09327
$88$	−9.17685e19	−0.351258
$89$	2.35270e20	0.799783	0.399891	−	0.916563i	$-0.369048\pi$
$89$	2.35270e20	0.799783	0.399891	+	0.916563i	$0.369048\pi$
$90$	2.00304e20	0.605540
$91$	−9.35779e20	−2.51906
$92$	−2.78777e19	−0.0669090
$93$	1.33276e21	2.85549
$94$	−3.65698e20	−0.700294
$95$	−1.37820e20	−0.236165
$96$	1.96600e20	0.301812
$97$	7.25967e20	0.999571	0.499786	−	0.866149i	$-0.333412\pi$
$97$	7.25967e20	0.999571	0.499786	+	0.866149i	$0.333412\pi$
$98$	−3.72675e20	−0.460741
$99$	1.71192e21	1.90245
$100$	1.00000e20	0.100000
$101$	3.23940e20	0.291803	0.145902	−	0.989299i	$-0.453392\pi$
$101$	3.23940e20	0.291803	0.145902	+	0.989299i	$0.453392\pi$
$102$	−2.09284e21	−1.69994
$103$	5.76074e20	0.422364	0.211182	−	0.977447i	$-0.432269\pi$
$103$	5.76074e20	0.422364	0.211182	+	0.977447i	$0.432269\pi$
$104$	−1.04615e21	−0.693016
$105$	−1.63781e21	−0.981243
$106$	8.36624e20	0.453752
$107$	−3.09648e21	−1.52174	−0.760868	−	0.648907i	$-0.775226\pi$
$107$	−3.09648e21	−1.52174	−0.760868	+	0.648907i	$0.775226\pi$
$108$	−1.75225e21	−0.780994
$109$	−2.84500e21	−1.15108	−0.575539	−	0.817775i	$-0.695208\pi$
$109$	−2.84500e21	−1.15108	−0.575539	+	0.817775i	$0.695208\pi$
$110$	8.54661e20	0.314174
$111$	−1.91923e21	−0.641558
$112$	−1.05604e21	−0.321285
$113$	−5.61097e21	−1.55494	−0.777471	−	0.628919i	$-0.783498\pi$
$113$	−5.61097e21	−1.55494	−0.777471	+	0.628919i	$0.783498\pi$
$114$	2.52347e21	0.637524
$115$	2.59631e20	0.0598452
$116$	1.52123e21	0.320173
$117$	1.95156e22	3.75345
$118$	−8.40715e20	−0.147873
$119$	1.12417e22	1.80963
$120$	−1.83098e21	−0.269948
$121$	−9.57949e19	−0.0129448
$122$	−4.64572e21	−0.575804
$123$	−1.38582e22	−1.57653
$124$	−8.00329e21	−0.836259
$125$	−9.31323e20	−0.0894427
$126$	1.97001e22	1.74012
$127$	1.60366e22	1.30368	0.651842	−	0.758355i	$-0.273997\pi$
$127$	1.60366e22	1.30368	0.651842	+	0.758355i	$0.273997\pi$
$128$	−1.18059e21	−0.0883883
$129$	1.46110e22	1.00806
$130$	9.74302e21	0.619852
$131$	−1.39854e22	−0.820969	−0.410485	−	0.911868i	$-0.634640\pi$
$131$	−1.39854e22	−0.820969	−0.410485	+	0.911868i	$0.634640\pi$
$132$	−1.56487e22	−0.848109
$133$	−1.35548e22	−0.678659
$134$	−8.22093e21	−0.380470
$135$	1.63191e22	0.698542
$136$	1.25676e22	0.497844
$137$	−3.49305e22	−1.28127	−0.640633	−	0.767847i	$-0.721328\pi$
$137$	−3.49305e22	−1.28127	−0.640633	+	0.767847i	$0.721328\pi$
$138$	−4.75380e21	−0.161551
$139$	−1.16733e22	−0.367737	−0.183868	−	0.982951i	$-0.558862\pi$
$139$	−1.16733e22	−0.367737	−0.183868	+	0.982951i	$0.558862\pi$
$140$	9.83513e21	0.287366
$141$	−6.23601e22	−1.69085
$142$	5.38346e22	1.35529
$143$	8.32698e22	1.94742
$144$	2.20236e22	0.478722
$145$	−1.41675e22	−0.286371
$146$	−9.50986e21	−0.178842
$147$	−6.35499e22	−1.11246
$148$	1.15251e22	0.187886
$149$	−2.99897e22	−0.455530	−0.227765	−	0.973716i	$-0.573142\pi$
$149$	−2.99897e22	−0.455530	−0.227765	+	0.973716i	$0.573142\pi$
$150$	1.70523e22	0.241449
$151$	−8.80845e22	−1.16317	−0.581583	−	0.813487i	$-0.697566\pi$
$151$	−8.80845e22	−1.16317	−0.581583	+	0.813487i	$0.697566\pi$
$152$	−1.51535e22	−0.186705
$153$	−2.34445e23	−2.69638
$154$	8.40570e22	0.902831
$155$	7.45364e22	0.747972
$156$	−1.78393e23	−1.67328
$157$	1.76504e23	1.54813	0.774067	−	0.633104i	$-0.218219\pi$
$157$	1.76504e23	1.54813	0.774067	+	0.633104i	$0.218219\pi$
$158$	−1.11473e22	−0.0914686
$159$	1.42664e23	1.09558
$160$	1.09951e22	0.0790569
$161$	2.55351e22	0.171975
$162$	−8.42469e22	−0.531675
$163$	9.36633e22	0.554115	0.277057	−	0.960853i	$-0.410641\pi$
$163$	9.36633e22	0.554115	0.277057	+	0.960853i	$0.410641\pi$
$164$	8.32191e22	0.461703
$165$	1.45740e23	0.758571
$166$	4.91514e22	0.240105
$167$	−2.77263e23	−1.27166	−0.635828	−	0.771831i	$-0.719341\pi$
$167$	−2.77263e23	−1.27166	−0.635828	+	0.771831i	$0.719341\pi$
$168$	−1.80079e23	−0.775740
$169$	7.02199e23	2.84217
$170$	−1.17045e23	−0.445285
$171$	2.82685e23	1.01122
$172$	−8.77397e22	−0.295221
$173$	−3.84494e23	−1.21732	−0.608661	−	0.793431i	$-0.708293\pi$
$173$	−3.84494e23	−1.21732	−0.608661	+	0.793431i	$0.708293\pi$
$174$	2.59405e23	0.773055
$175$	−9.15968e22	−0.257028
$176$	9.39710e22	0.248377
$177$	−1.43362e23	−0.357037
$178$	−2.40917e23	−0.565532
$179$	4.54367e22	0.100566	0.0502828	−	0.998735i	$-0.483988\pi$
$179$	4.54367e22	0.100566	0.0502828	+	0.998735i	$0.483988\pi$
$180$	−2.05111e23	−0.428182
$181$	8.61960e23	1.69770	0.848852	−	0.528630i	$-0.177294\pi$
$181$	8.61960e23	1.69770	0.848852	+	0.528630i	$0.177294\pi$
$182$	9.58238e23	1.78125
$183$	−7.92204e23	−1.39027
$184$	2.85467e22	0.0473118
$185$	−1.07336e23	−0.168051
$186$	−1.36475e24	−2.01914
$187$	−1.00034e24	−1.39897
$188$	3.74475e23	0.495183
$189$	1.60501e24	2.00737
$190$	1.41128e23	0.166994
$191$	−2.31575e23	−0.259323	−0.129661	−	0.991558i	$-0.541389\pi$
$191$	−2.31575e23	−0.259323	−0.129661	+	0.991558i	$0.541389\pi$
$192$	−2.01319e23	−0.213413
$193$	−1.13487e24	−1.13919	−0.569595	−	0.821926i	$-0.692900\pi$
$193$	−1.13487e24	−1.13919	−0.569595	+	0.821926i	$0.692900\pi$
$194$	−7.43390e23	−0.706804
$195$	1.66141e24	1.49663
$196$	3.81620e23	0.325793
$197$	−6.29771e23	−0.509668	−0.254834	−	0.966985i	$-0.582021\pi$
$197$	−6.29771e23	−0.509668	−0.254834	+	0.966985i	$0.582021\pi$
$198$	−1.75300e24	−1.34524
$199$	−7.13426e23	−0.519268	−0.259634	−	0.965707i	$-0.583602\pi$
$199$	−7.13426e23	−0.519268	−0.259634	+	0.965707i	$0.583602\pi$
$200$	−1.02400e23	−0.0707107
$201$	−1.40186e24	−0.918642
$202$	−3.31715e23	−0.206336
$203$	−1.39339e24	−0.822935
$204$	2.14307e24	1.20204
$205$	−7.75039e23	−0.412960
$206$	−5.89899e23	−0.298657
$207$	−5.32532e23	−0.256246
$208$	1.07126e24	0.490036
$209$	1.20617e24	0.524652
$210$	1.67712e24	0.693843
$211$	−2.57567e24	−1.01374	−0.506868	−	0.862024i	$-0.669197\pi$
$211$	−2.57567e24	−1.01374	−0.506868	+	0.862024i	$0.669197\pi$
$212$	−8.56703e23	−0.320851
$213$	9.18005e24	3.27235
$214$	3.17080e24	1.07603
$215$	8.17140e23	0.264054
$216$	1.79431e24	0.552246
$217$	7.33075e24	2.14942
$218$	2.91328e24	0.813934
$219$	−1.62165e24	−0.431812
$220$	−8.75173e23	−0.222155
$221$	−1.14037e25	−2.76011
$222$	1.96529e24	0.453650
$223$	−7.24650e24	−1.59561	−0.797806	−	0.602914i	$-0.794006\pi$
$223$	−7.24650e24	−1.59561	−0.797806	+	0.602914i	$0.794006\pi$
$224$	1.08138e24	0.227183
$225$	1.91025e24	0.382977
$226$	5.74563e24	1.09951
$227$	−1.55126e24	−0.283409	−0.141704	−	0.989909i	$-0.545258\pi$
$227$	−1.55126e24	−0.283409	−0.141704	+	0.989909i	$0.545258\pi$
$228$	−2.58403e24	−0.450798
$229$	−9.95437e24	−1.65860	−0.829299	−	0.558805i	$-0.811260\pi$
$229$	−9.95437e24	−1.65860	−0.829299	+	0.558805i	$0.811260\pi$
$230$	−2.65862e23	−0.0423170
$231$	1.43337e25	2.17988
$232$	−1.55773e24	−0.226396
$233$	−4.62738e23	−0.0642833	−0.0321417	−	0.999483i	$-0.510233\pi$
$233$	−4.62738e23	−0.0642833	−0.0321417	+	0.999483i	$0.510233\pi$
$234$	−1.99840e25	−2.65409
$235$	−3.48757e24	−0.442905
$236$	8.60892e23	0.104562
$237$	−1.90088e24	−0.220850
$238$	−1.15115e25	−1.27960
$239$	1.06208e25	1.12975	0.564873	−	0.825178i	$-0.308925\pi$
$239$	1.06208e25	1.12975	0.564873	+	0.825178i	$0.308925\pi$
$240$	1.87492e24	0.190882
$241$	1.67701e24	0.163439	0.0817195	−	0.996655i	$-0.473959\pi$
$241$	1.67701e24	0.163439	0.0817195	+	0.996655i	$0.473959\pi$
$242$	9.80940e22	0.00915337
$243$	3.11401e24	0.278262
$244$	4.75722e24	0.407155
$245$	−3.55411e24	−0.291398
$246$	1.41908e25	1.11478
$247$	1.37501e25	1.03512
$248$	8.19536e24	0.591324
$249$	8.38147e24	0.579732
$250$	9.53674e23	0.0632456
$251$	−2.15807e25	−1.37243	−0.686216	−	0.727398i	$-0.740730\pi$
$251$	−2.15807e25	−1.37243	−0.686216	+	0.727398i	$0.740730\pi$
$252$	−2.01729e25	−1.23045
$253$	−2.27222e24	−0.132949
$254$	−1.64214e25	−0.921843
$255$	−1.99589e25	−1.07514
$256$	1.20893e24	0.0625000
$257$	7.72467e24	0.383338	0.191669	−	0.981460i	$-0.438610\pi$
$257$	7.72467e24	0.383338	0.191669	+	0.981460i	$0.438610\pi$
$258$	−1.49617e25	−0.712809
$259$	−1.05566e25	−0.482921
$260$	−9.97685e24	−0.438302
$261$	2.90592e25	1.22619
$262$	1.43211e25	0.580513
$263$	1.35616e25	0.528174	0.264087	−	0.964499i	$-0.414929\pi$
$263$	1.35616e25	0.528174	0.264087	+	0.964499i	$0.414929\pi$
$264$	1.60243e25	0.599703
$265$	7.97867e24	0.286978
$266$	1.38801e25	0.479884
$267$	−4.10819e25	−1.36547
$268$	8.41824e24	0.269033
$269$	−2.23157e25	−0.685822	−0.342911	−	0.939368i	$-0.611413\pi$
$269$	−2.23157e25	−0.685822	−0.342911	+	0.939368i	$0.611413\pi$
$270$	−1.67108e25	−0.493944
$271$	8.79105e24	0.249956	0.124978	−	0.992160i	$-0.460114\pi$
$271$	8.79105e24	0.249956	0.124978	+	0.992160i	$0.460114\pi$
$272$	−1.28692e25	−0.352029
$273$	1.63402e26	4.30080
$274$	3.57689e25	0.905992
$275$	8.15068e24	0.198701
$276$	4.86789e24	0.114234
$277$	3.23947e25	0.731874	0.365937	−	0.930640i	$-0.380749\pi$
$277$	3.23947e25	0.731874	0.365937	+	0.930640i	$0.380749\pi$
$278$	1.19534e25	0.260029
$279$	−1.52882e26	−3.20268
$280$	−1.00712e25	−0.203199
$281$	1.62934e25	0.316662	0.158331	−	0.987386i	$-0.449389\pi$
$281$	1.62934e25	0.316662	0.158331	+	0.987386i	$0.449389\pi$
$282$	6.38568e25	1.19561
$283$	7.24900e25	1.30774	0.653869	−	0.756608i	$-0.273145\pi$
$283$	7.24900e25	1.30774	0.653869	+	0.756608i	$0.273145\pi$
$284$	−5.51266e25	−0.958338
$285$	2.40656e25	0.403206
$286$	−8.52682e25	−1.37703
$287$	−7.62260e25	−1.18671
$288$	−2.25522e25	−0.338507
$289$	6.79028e25	0.982790
$290$	1.45075e25	0.202495
$291$	−1.26765e26	−1.70657
$292$	9.73810e24	0.126460
$293$	−7.90881e25	−0.990835	−0.495418	−	0.868655i	$-0.664985\pi$
$293$	−7.90881e25	−0.990835	−0.495418	+	0.868655i	$0.664985\pi$
$294$	6.50751e25	0.786625
$295$	−8.01769e24	−0.0935229
$296$	−1.18017e25	−0.132856
$297$	−1.42821e26	−1.55185
$298$	3.07095e25	0.322108
$299$	−2.59030e25	−0.262303
$300$	−1.74616e25	−0.170730
$301$	8.03667e25	0.758801
$302$	9.01985e25	0.822482
$303$	−5.65651e25	−0.498197
$304$	1.55172e25	0.132020
$305$	−4.43050e25	−0.364170
$306$	2.40072e26	1.90663
$307$	−1.19014e26	−0.913363	−0.456682	−	0.889630i	$-0.650962\pi$
$307$	−1.19014e26	−0.913363	−0.456682	+	0.889630i	$0.650962\pi$
$308$	−8.60744e25	−0.638398
$309$	−1.00592e26	−0.721104
$310$	−7.63253e25	−0.528896
$311$	−1.66399e26	−1.11472	−0.557360	−	0.830271i	$-0.688186\pi$
$311$	−1.66399e26	−1.11472	−0.557360	+	0.830271i	$0.688186\pi$
$312$	1.82674e26	1.18319
$313$	2.24533e25	0.140626	0.0703128	−	0.997525i	$-0.477600\pi$
$313$	2.24533e25	0.140626	0.0703128	+	0.997525i	$0.477600\pi$
$314$	−1.80740e26	−1.09470
$315$	1.87875e26	1.10055
$316$	1.14149e25	0.0646781
$317$	1.10755e26	0.607076	0.303538	−	0.952819i	$-0.401832\pi$
$317$	1.10755e26	0.607076	0.303538	+	0.952819i	$0.401832\pi$
$318$	−1.46088e26	−0.774693
$319$	1.23990e26	0.636188
$320$	−1.12590e25	−0.0559017
$321$	5.40695e26	2.59806
$322$	−2.61479e25	−0.121605
$323$	−1.65183e26	−0.743599
$324$	8.62689e25	0.375951
$325$	9.29166e25	0.392029
$326$	−9.59112e25	−0.391818
$327$	4.96783e26	1.96524
$328$	−8.52164e25	−0.326473
$329$	−3.43007e26	−1.27276
$330$	−1.49237e26	−0.536391
$331$	−2.18220e26	−0.759803	−0.379901	−	0.925027i	$-0.624042\pi$
$331$	−2.18220e26	−0.759803	−0.379901	+	0.925027i	$0.624042\pi$
$332$	−5.03311e25	−0.169780
$333$	2.20157e26	0.719562
$334$	2.83918e26	0.899196
$335$	−7.84009e25	−0.240631
$336$	1.84401e26	0.548531
$337$	5.33804e26	1.53910	0.769551	−	0.638585i	$-0.220480\pi$
$337$	5.33804e26	1.53910	0.769551	+	0.638585i	$0.220480\pi$
$338$	−7.19052e26	−2.00972
$339$	9.79765e26	2.65476
$340$	1.19854e26	0.314864
$341$	−6.52322e26	−1.66166
$342$	−2.89469e26	−0.715037
$343$	1.86911e26	0.447761
$344$	8.98455e25	0.208753
$345$	−4.53357e25	−0.102174
$346$	3.93722e26	0.860776
$347$	−4.09971e26	−0.869548	−0.434774	−	0.900540i	$-0.643172\pi$
$347$	−4.09971e26	−0.869548	−0.434774	+	0.900540i	$0.643172\pi$
$348$	−2.65630e26	−0.546633
$349$	2.06527e26	0.412392	0.206196	−	0.978511i	$-0.433892\pi$
$349$	2.06527e26	0.412392	0.206196	+	0.978511i	$0.433892\pi$
$350$	9.37951e25	0.181746
$351$	−1.62814e27	−3.06172
$352$	−9.62263e25	−0.175629
$353$	2.63582e26	0.466961	0.233481	−	0.972361i	$-0.424988\pi$
$353$	2.63582e26	0.466961	0.233481	+	0.972361i	$0.424988\pi$
$354$	1.46802e26	0.252464
$355$	5.13406e26	0.857163
$356$	2.46699e26	0.399891
$357$	−1.96298e27	−3.08958
$358$	−4.65272e25	−0.0711107
$359$	2.72697e26	0.404751	0.202376	−	0.979308i	$-0.435134\pi$
$359$	2.72697e26	0.404751	0.202376	+	0.979308i	$0.435134\pi$
$360$	2.10034e26	0.302770
$361$	−5.15038e26	−0.721130
$362$	−8.82647e26	−1.20046
$363$	1.67273e25	0.0221007
$364$	−9.81236e26	−1.25953
$365$	−9.06931e25	−0.113110
$366$	8.11217e26	0.983072
$367$	−1.67539e26	−0.197297	−0.0986487	−	0.995122i	$-0.531452\pi$
$367$	−1.67539e26	−0.197297	−0.0986487	+	0.995122i	$0.531452\pi$
$368$	−2.92319e25	−0.0334545
$369$	1.58969e27	1.76822
$370$	1.09912e26	0.118830
$371$	7.84712e26	0.824678
$372$	1.39750e27	1.42775
$373$	9.92406e26	0.985704	0.492852	−	0.870113i	$-0.335954\pi$
$373$	9.92406e26	0.985704	0.492852	+	0.870113i	$0.335954\pi$
$374$	1.02434e27	0.989223
$375$	1.62624e26	0.152706
$376$	−3.83462e26	−0.350147
$377$	1.41347e27	1.25517
$378$	−1.64353e27	−1.41943
$379$	1.41427e25	0.0118801	0.00594007	−	0.999982i	$-0.498109\pi$
$379$	1.41427e25	0.0118801	0.00594007	+	0.999982i	$0.498109\pi$
$380$	−1.44515e26	−0.118083
$381$	−2.80024e27	−2.22578
$382$	2.37132e26	0.183369
$383$	2.51013e26	0.188847	0.0944234	−	0.995532i	$-0.469899\pi$
$383$	2.51013e26	0.188847	0.0944234	+	0.995532i	$0.469899\pi$
$384$	2.06150e26	0.150906
$385$	8.01630e26	0.571000
$386$	1.16211e27	0.805529
$387$	−1.67604e27	−1.13063
$388$	7.61232e26	0.499786
$389$	−2.50259e27	−1.59926	−0.799629	−	0.600495i	$-0.794970\pi$
$389$	−2.50259e27	−1.59926	−0.799629	+	0.600495i	$0.794970\pi$
$390$	−1.70129e27	−1.05828
$391$	3.11178e26	0.188431
$392$	−3.90779e26	−0.230371
$393$	2.44208e27	1.40164
$394$	6.44886e26	0.360390
$395$	−1.06309e26	−0.0578498
$396$	1.79508e27	0.951226
$397$	3.29042e26	0.169805	0.0849027	−	0.996389i	$-0.472942\pi$
$397$	3.29042e26	0.169805	0.0849027	+	0.996389i	$0.472942\pi$
$398$	7.30548e26	0.367178
$399$	2.36689e27	1.15868
$400$	1.04858e26	0.0500000
$401$	8.45309e26	0.392645	0.196322	−	0.980539i	$-0.437100\pi$
$401$	8.45309e26	0.392645	0.196322	+	0.980539i	$0.437100\pi$
$402$	1.43551e27	0.649578
$403$	−7.43638e27	−3.27838
$404$	3.39676e26	0.145902
$405$	−8.03441e26	−0.336261
$406$	1.42683e27	0.581903
$407$	9.39371e26	0.373333
$408$	−2.19450e27	−0.849971
$409$	−1.58724e27	−0.599167	−0.299583	−	0.954070i	$-0.596848\pi$
$409$	−1.58724e27	−0.599167	−0.299583	+	0.954070i	$0.596848\pi$
$410$	7.93639e26	0.292007
$411$	6.09943e27	2.18751
$412$	6.04057e26	0.211182
$413$	−7.88550e26	−0.268753
$414$	5.45313e26	0.181193
$415$	4.68745e26	0.151856
$416$	−1.09697e27	−0.346508
$417$	2.03834e27	0.627839
$418$	−1.23512e27	−0.370985
$419$	−1.46560e25	−0.00429308	−0.00214654	−	0.999998i	$-0.500683\pi$
$419$	−1.46560e25	−0.00429308	−0.00214654	+	0.999998i	$0.500683\pi$
$420$	−1.71737e27	−0.490621
$421$	−2.07639e27	−0.578559	−0.289280	−	0.957245i	$-0.593416\pi$
$421$	−2.07639e27	−0.578559	−0.289280	+	0.957245i	$0.593416\pi$
$422$	2.63749e27	0.716819
$423$	7.15340e27	1.89644
$424$	8.77264e26	0.226876
$425$	−1.11623e27	−0.281623
$426$	−9.40037e27	−2.31390
$427$	−4.35746e27	−1.04650
$428$	−3.24690e27	−0.760868
$429$	−1.45402e28	−3.32483
$430$	−8.36751e26	−0.186714
$431$	−2.88896e27	−0.629115	−0.314558	−	0.949238i	$-0.601856\pi$
$431$	−2.88896e27	−0.629115	−0.314558	+	0.949238i	$0.601856\pi$
$432$	−1.83737e27	−0.390497
$433$	6.58569e27	1.36609	0.683044	−	0.730377i	$-0.260656\pi$
$433$	6.58569e27	1.36609	0.683044	+	0.730377i	$0.260656\pi$
$434$	−7.50669e27	−1.51987
$435$	2.47387e27	0.488923
$436$	−2.98320e27	−0.575539
$437$	−3.75206e26	−0.0706668
$438$	1.66057e27	0.305337
$439$	−9.33293e26	−0.167548	−0.0837742	−	0.996485i	$-0.526697\pi$
$439$	−9.33293e26	−0.167548	−0.0837742	+	0.996485i	$0.526697\pi$
$440$	8.96177e26	0.157087
$441$	7.28987e27	1.24771
$442$	1.16774e28	1.95169
$443$	9.69019e27	1.58159	0.790793	−	0.612083i	$-0.209668\pi$
$443$	9.69019e27	1.58159	0.790793	+	0.612083i	$0.209668\pi$
$444$	−2.01246e27	−0.320779
$445$	−2.29756e27	−0.357674
$446$	7.42042e27	1.12827
$447$	5.23669e27	0.777728
$448$	−1.10734e27	−0.160643
$449$	−9.90883e27	−1.40422	−0.702111	−	0.712067i	$-0.747759\pi$
$449$	−9.90883e27	−1.40422	−0.702111	+	0.712067i	$0.747759\pi$
$450$	−1.95609e27	−0.270806
$451$	6.78293e27	0.917410
$452$	−5.88353e27	−0.777471
$453$	1.53810e28	1.98588
$454$	1.58849e27	0.200400
$455$	9.13847e27	1.12656
$456$	2.64605e27	0.318762
$457$	−1.41062e28	−1.66069	−0.830346	−	0.557248i	$-0.811857\pi$
$457$	−1.41062e28	−1.66069	−0.830346	+	0.557248i	$0.811857\pi$
$458$	1.01933e28	1.17281
$459$	1.95591e28	2.19946
$460$	2.72243e26	0.0299226
$461$	1.40343e26	0.0150776	0.00753880	−	0.999972i	$-0.497600\pi$
$461$	1.40343e26	0.0150776	0.00753880	+	0.999972i	$0.497600\pi$
$462$	−1.46777e28	−1.54141
$463$	−1.54202e28	−1.58303	−0.791514	−	0.611150i	$-0.790707\pi$
$463$	−1.54202e28	−1.58303	−0.791514	+	0.611150i	$0.790707\pi$
$464$	1.59512e27	0.160086
$465$	−1.30152e28	−1.27702
$466$	4.73844e26	0.0454552
$467$	1.42166e28	1.33343	0.666713	−	0.745314i	$-0.267701\pi$
$467$	1.42166e28	1.33343	0.666713	+	0.745314i	$0.267701\pi$
$468$	2.04636e28	1.87673
$469$	−7.71083e27	−0.691491
$470$	3.57127e27	0.313181
$471$	−3.08204e28	−2.64313
$472$	−8.81554e26	−0.0739363
$473$	−7.15138e27	−0.586608
$474$	1.94650e27	0.156165
$475$	1.34590e27	0.105616
$476$	1.17878e28	0.904813
$477$	−1.63651e28	−1.22879
$478$	−1.08757e28	−0.798851
$479$	1.82659e28	1.31256	0.656280	−	0.754518i	$-0.272129\pi$
$479$	1.82659e28	1.31256	0.656280	+	0.754518i	$0.272129\pi$
$480$	−1.91992e27	−0.134974
$481$	1.07087e28	0.736569
$482$	−1.71725e27	−0.115569
$483$	−4.45883e27	−0.293613
$484$	−1.00448e26	−0.00647241
$485$	−7.08952e27	−0.447022
$486$	−3.18875e27	−0.196761
$487$	3.19696e28	1.93056	0.965280	−	0.261218i	$-0.0841243\pi$
$487$	3.19696e28	1.93056	0.965280	+	0.261218i	$0.0841243\pi$
$488$	−4.87139e27	−0.287902
$489$	−1.63551e28	−0.946042
$490$	3.63941e27	0.206050
$491$	−1.06661e28	−0.591086	−0.295543	−	0.955329i	$-0.595501\pi$
$491$	−1.06661e28	−0.591086	−0.295543	+	0.955329i	$0.595501\pi$
$492$	−1.45314e28	−0.788267
$493$	−1.69803e28	−0.901681
$494$	−1.40801e28	−0.731937
$495$	−1.67180e28	−0.850802
$496$	−8.39205e27	−0.418129
$497$	5.04942e28	2.46320
$498$	−8.58262e27	−0.409932
$499$	−1.19664e28	−0.559638	−0.279819	−	0.960053i	$-0.590275\pi$
$499$	−1.19664e28	−0.559638	−0.279819	+	0.960053i	$0.590275\pi$
$500$	−9.76563e26	−0.0447214
$501$	4.84146e28	2.17110
$502$	2.20986e28	0.970456
$503$	−3.75074e28	−1.61307	−0.806534	−	0.591188i	$-0.798659\pi$
$503$	−3.75074e28	−1.61307	−0.806534	+	0.591188i	$0.798659\pi$
$504$	2.06571e28	0.870059
$505$	−3.16348e27	−0.130498
$506$	2.32675e27	0.0940092
$507$	−1.22615e29	−4.85245
$508$	1.68156e28	0.651842
$509$	3.27640e28	1.24411	0.622057	−	0.782972i	$-0.286297\pi$
$509$	3.27640e28	1.24411	0.622057	+	0.782972i	$0.286297\pi$
$510$	2.04379e28	0.760237
$511$	−8.91979e27	−0.325039
$512$	−1.23794e27	−0.0441942
$513$	−2.35836e28	−0.824857
$514$	−7.91006e27	−0.271061
$515$	−5.62572e27	−0.188887
$516$	1.53208e28	0.504032
$517$	3.05223e28	0.983934
$518$	1.08099e28	0.341477
$519$	6.71388e28	2.07834
$520$	1.02163e28	0.309926
$521$	−5.49377e27	−0.163333	−0.0816667	−	0.996660i	$-0.526024\pi$
$521$	−5.49377e27	−0.163333	−0.0816667	+	0.996660i	$0.526024\pi$
$522$	−2.97566e28	−0.867047
$523$	9.60628e27	0.274339	0.137170	−	0.990548i	$-0.456199\pi$
$523$	9.60628e27	0.274339	0.137170	+	0.990548i	$0.456199\pi$
$524$	−1.46648e28	−0.410485
$525$	1.59943e28	0.438825
$526$	−1.38871e28	−0.373475
$527$	8.93347e28	2.35510
$528$	−1.64088e28	−0.424054
$529$	−3.87648e28	−0.982093
$530$	−8.17016e27	−0.202924
$531$	1.64452e28	0.400448
$532$	−1.42133e28	−0.339329
$533$	7.73244e28	1.81001
$534$	4.20679e28	0.965534
$535$	3.02391e28	0.680541
$536$	−8.62027e27	−0.190235
$537$	−7.93397e27	−0.171696
$538$	2.28513e28	0.484949
$539$	3.11046e28	0.647355
$540$	1.71119e28	0.349271
$541$	−7.34453e28	−1.47026	−0.735128	−	0.677929i	$-0.762878\pi$
$541$	−7.34453e28	−1.47026	−0.735128	+	0.677929i	$0.762878\pi$
$542$	−9.00204e27	−0.176745
$543$	−1.50512e29	−2.89850
$544$	1.31781e28	0.248922
$545$	2.77832e28	0.514777
$546$	−1.67324e29	−3.04113
$547$	4.12363e28	0.735212	0.367606	−	0.929982i	$-0.380178\pi$
$547$	4.12363e28	0.735212	0.367606	+	0.929982i	$0.380178\pi$
$548$	−3.66273e28	−0.640633
$549$	9.08745e28	1.55931
$550$	−8.34630e27	−0.140503
$551$	2.04742e28	0.338155
$552$	−4.98472e27	−0.0807756
$553$	−1.04557e28	−0.166241
$554$	−3.31722e28	−0.517513
$555$	1.87425e28	0.286914
$556$	−1.22403e28	−0.183868
$557$	−8.83426e27	−0.130224	−0.0651119	−	0.997878i	$-0.520740\pi$
$557$	−8.83426e27	−0.130224	−0.0651119	+	0.997878i	$0.520740\pi$
$558$	1.56552e29	2.26464
$559$	−8.15248e28	−1.15735
$560$	1.03129e28	0.143683
$561$	1.74675e29	2.38847
$562$	−1.66845e28	−0.223914
$563$	−1.06900e29	−1.40811	−0.704057	−	0.710143i	$-0.748630\pi$
$563$	−1.06900e29	−1.40811	−0.704057	+	0.710143i	$0.748630\pi$
$564$	−6.53893e28	−0.845427
$565$	5.47946e28	0.695391
$566$	−7.42298e28	−0.924711
$567$	−7.90195e28	−0.966300
$568$	5.64496e28	0.677647
$569$	−1.27688e29	−1.50477	−0.752386	−	0.658723i	$-0.771097\pi$
$569$	−1.27688e29	−1.50477	−0.752386	+	0.658723i	$0.771097\pi$
$570$	−2.46432e28	−0.285109
$571$	−8.59333e28	−0.976073	−0.488037	−	0.872823i	$-0.662287\pi$
$571$	−8.59333e28	−0.976073	−0.488037	+	0.872823i	$0.662287\pi$
$572$	8.73147e28	0.973709
$573$	4.04366e28	0.442743
$574$	7.80555e28	0.839128
$575$	−2.53546e27	−0.0267636
$576$	2.30935e28	0.239361
$577$	−1.28637e29	−1.30925	−0.654623	−	0.755956i	$-0.727172\pi$
$577$	−1.28637e29	−1.30925	−0.654623	+	0.755956i	$0.727172\pi$
$578$	−6.95325e28	−0.694937
$579$	1.98167e29	1.94494
$580$	−1.48557e28	−0.143186
$581$	4.61016e28	0.436382
$582$	1.29808e29	1.20673
$583$	−6.98271e28	−0.637536
$584$	−9.97182e27	−0.0894210
$585$	−1.90582e29	−1.67860
$586$	8.09863e28	0.700626
$587$	−3.48294e28	−0.295969	−0.147985	−	0.988990i	$-0.547279\pi$
$587$	−3.48294e28	−0.295969	−0.147985	+	0.988990i	$0.547279\pi$
$588$	−6.66369e28	−0.556228
$589$	−1.07716e29	−0.883225
$590$	8.21011e27	0.0661307
$591$	1.09968e29	0.870158
$592$	1.20849e28	0.0939432
$593$	−8.77330e28	−0.670021	−0.335011	−	0.942214i	$-0.608740\pi$
$593$	−8.77330e28	−0.670021	−0.335011	+	0.942214i	$0.608740\pi$
$594$	1.46248e29	1.09732
$595$	−1.09782e29	−0.809290
$596$	−3.14465e28	−0.227765
$597$	1.24576e29	0.886548
$598$	2.65247e28	0.185476
$599$	−1.00705e29	−0.691944	−0.345972	−	0.938245i	$-0.612451\pi$
$599$	−1.00705e29	−0.691944	−0.345972	+	0.938245i	$0.612451\pi$
$600$	1.78807e28	0.120725
$601$	−1.06089e29	−0.703861	−0.351930	−	0.936026i	$-0.614475\pi$
$601$	−1.06089e29	−0.703861	−0.351930	+	0.936026i	$0.614475\pi$
$602$	−8.22955e28	−0.536554
$603$	1.60809e29	1.03034
$604$	−9.23633e28	−0.581583
$605$	9.35497e26	0.00578910
$606$	5.79227e28	0.352278
$607$	5.05632e28	0.302241	0.151120	−	0.988515i	$-0.451712\pi$
$607$	5.05632e28	0.302241	0.151120	+	0.988515i	$0.451712\pi$
$608$	−1.58896e28	−0.0933525
$609$	2.43309e29	1.40500
$610$	4.53683e28	0.257507
$611$	3.47950e29	1.94126
$612$	−2.45834e29	−1.34819
$613$	1.21126e29	0.652985	0.326493	−	0.945200i	$-0.394133\pi$
$613$	1.21126e29	0.652985	0.326493	+	0.945200i	$0.394133\pi$
$614$	1.21870e29	0.645845
$615$	1.35334e29	0.705048
$616$	8.81402e28	0.451415
$617$	7.11151e28	0.358070	0.179035	−	0.983843i	$-0.442702\pi$
$617$	7.11151e28	0.358070	0.179035	+	0.983843i	$0.442702\pi$
$618$	1.03006e29	0.509898
$619$	−1.87344e28	−0.0911774	−0.0455887	−	0.998960i	$-0.514516\pi$
$619$	−1.87344e28	−0.0911774	−0.0455887	+	0.998960i	$0.514516\pi$
$620$	7.81571e28	0.373986
$621$	4.44277e28	0.209022
$622$	1.70392e29	0.788225
$623$	−2.25968e29	−1.02783
$624$	−1.87058e29	−0.836641
$625$	9.09495e27	0.0400000
$626$	−2.29922e28	−0.0994374
$627$	−2.10616e29	−0.895741
$628$	1.85078e29	0.774067
$629$	−1.28646e29	−0.529131
$630$	−1.92384e29	−0.778204
$631$	1.18886e29	0.472956	0.236478	−	0.971637i	$-0.424007\pi$
$631$	1.18886e29	0.472956	0.236478	+	0.971637i	$0.424007\pi$
$632$	−1.16888e28	−0.0457343
$633$	4.49753e29	1.73075
$634$	−1.13414e29	−0.429267
$635$	−1.56607e29	−0.583025
$636$	1.49594e29	0.547790
$637$	3.54588e29	1.27720
$638$	−1.26966e29	−0.449853
$639$	−1.05305e30	−3.67021
$640$	1.15292e28	0.0395285
$641$	−4.05009e29	−1.36602	−0.683008	−	0.730411i	$-0.739329\pi$
$641$	−4.05009e29	−1.36602	−0.683008	+	0.730411i	$0.739329\pi$
$642$	−5.53672e29	−1.83711
$643$	2.92040e29	0.953296	0.476648	−	0.879094i	$-0.341852\pi$
$643$	2.92040e29	0.953296	0.476648	+	0.879094i	$0.341852\pi$
$644$	2.67754e28	0.0859875
$645$	−1.42686e29	−0.450820
$646$	1.69147e29	0.525804
$647$	−1.30263e29	−0.398407	−0.199203	−	0.979958i	$-0.563835\pi$
$647$	−1.30263e29	−0.398407	−0.199203	+	0.979958i	$0.563835\pi$
$648$	−8.83393e28	−0.265838
$649$	7.01686e28	0.207766
$650$	−9.51466e28	−0.277206
$651$	−1.28007e30	−3.66971
$652$	9.82131e28	0.277057
$653$	−1.49980e29	−0.416337	−0.208169	−	0.978093i	$-0.566750\pi$
$653$	−1.49980e29	−0.416337	−0.208169	+	0.978093i	$0.566750\pi$
$654$	−5.08706e29	−1.38963
$655$	1.36576e29	0.367149
$656$	8.72616e28	0.230852
$657$	1.86022e29	0.484314
$658$	3.51239e29	0.899976
$659$	3.09551e29	0.780613	0.390307	−	0.920685i	$-0.372369\pi$
$659$	3.09551e29	0.780613	0.390307	+	0.920685i	$0.372369\pi$
$660$	1.52819e29	0.379286
$661$	−1.06593e29	−0.260383	−0.130191	−	0.991489i	$-0.541559\pi$
$661$	−1.06593e29	−0.260383	−0.130191	+	0.991489i	$0.541559\pi$
$662$	2.23457e29	0.537262
$663$	1.99127e30	4.71235
$664$	5.15390e28	0.120053
$665$	1.32371e29	0.303505
$666$	−2.25441e29	−0.508807
$667$	−3.85701e28	−0.0856898
$668$	−2.90732e29	−0.635828
$669$	1.26535e30	2.72419
$670$	8.02826e28	0.170151
$671$	3.87746e29	0.809022
$672$	−1.88827e29	−0.387870
$673$	−7.90406e29	−1.59842	−0.799212	−	0.601049i	$-0.794750\pi$
$673$	−7.90406e29	−1.59842	−0.799212	+	0.601049i	$0.794750\pi$
$674$	−5.46615e29	−1.08831
$675$	−1.59367e29	−0.312398
$676$	7.36309e29	1.42108
$677$	−3.48611e29	−0.662461	−0.331230	−	0.943550i	$-0.607464\pi$
$677$	−3.48611e29	−0.662461	−0.331230	+	0.943550i	$0.607464\pi$
$678$	−1.00328e30	−1.87720
$679$	−6.97264e29	−1.28459
$680$	−1.22730e29	−0.222643
$681$	2.70875e29	0.483865
$682$	6.67978e29	1.17497
$683$	3.87738e28	0.0671617	0.0335808	−	0.999436i	$-0.489309\pi$
$683$	3.87738e28	0.0671617	0.0335808	+	0.999436i	$0.489309\pi$
$684$	2.96417e29	0.505608
$685$	3.41118e29	0.572999
$686$	−1.91397e29	−0.316615
$687$	1.73819e30	2.83173
$688$	−9.20017e28	−0.147611
$689$	−7.96020e29	−1.25783
$690$	4.64238e28	0.0722479
$691$	7.13503e29	1.09364	0.546822	−	0.837249i	$-0.315837\pi$
$691$	7.13503e29	1.09364	0.546822	+	0.837249i	$0.315837\pi$
$692$	−4.03171e29	−0.608661
$693$	−1.64423e30	−2.44492
$694$	4.19810e29	0.614863
$695$	1.13997e29	0.164457
$696$	2.72005e29	0.386528
$697$	−9.28913e29	−1.30026
$698$	−2.11484e29	−0.291605
$699$	8.08015e28	0.109751
$700$	−9.60462e28	−0.128514
$701$	−8.08128e28	−0.106522	−0.0532612	−	0.998581i	$-0.516962\pi$
$701$	−8.08128e28	−0.106522	−0.0532612	+	0.998581i	$0.516962\pi$
$702$	1.66721e30	2.16497
$703$	1.55116e29	0.198439
$704$	9.85357e28	0.124188
$705$	6.08986e29	0.756173
$706$	−2.69908e29	−0.330191
$707$	−3.11132e29	−0.375008
$708$	−1.50326e29	−0.178519
$709$	7.67692e28	0.0898259	0.0449129	−	0.998991i	$-0.485699\pi$
$709$	7.67692e28	0.0898259	0.0449129	+	0.998991i	$0.485699\pi$
$710$	−5.25728e29	−0.606106
$711$	2.18052e29	0.247702
$712$	−2.52620e29	−0.282766
$713$	2.02920e29	0.223813
$714$	2.01009e30	2.18466
$715$	−8.13181e29	−0.870911
$716$	4.76438e28	0.0502828
$717$	−1.85457e30	−1.92882
$718$	−2.79241e29	−0.286202
$719$	4.77523e29	0.482326	0.241163	−	0.970485i	$-0.422471\pi$
$719$	4.77523e29	0.482326	0.241163	+	0.970485i	$0.422471\pi$
$720$	−2.15075e29	−0.214091
$721$	−5.53297e29	−0.542797
$722$	5.27399e29	0.509916
$723$	−2.92832e29	−0.279040
$724$	9.03830e29	0.848852
$725$	1.38355e29	0.128069
$726$	−1.71288e28	−0.0156276
$727$	−8.17519e29	−0.735168	−0.367584	−	0.929990i	$-0.619815\pi$
$727$	−8.17519e29	−0.735168	−0.367584	+	0.929990i	$0.619815\pi$
$728$	1.00479e30	0.890623
$729$	−1.40435e30	−1.22698
$730$	9.28698e28	0.0799805
$731$	9.79373e29	0.831411
$732$	−8.30686e29	−0.695137
$733$	−1.25004e30	−1.03118	−0.515588	−	0.856837i	$-0.672426\pi$
$733$	−1.25004e30	−1.03118	−0.515588	+	0.856837i	$0.672426\pi$
$734$	1.71560e29	0.139510
$735$	6.20604e29	0.497505
$736$	2.99334e28	0.0236559
$737$	6.86144e29	0.534572
$738$	−1.62784e30	−1.25032
$739$	1.41926e30	1.07472	0.537359	−	0.843354i	$-0.319422\pi$
$739$	1.41926e30	1.07472	0.537359	+	0.843354i	$0.319422\pi$
$740$	−1.12549e29	−0.0840253
$741$	−2.40099e30	−1.76726
$742$	−8.03545e29	−0.583135
$743$	−4.94344e29	−0.353709	−0.176855	−	0.984237i	$-0.556592\pi$
$743$	−4.94344e29	−0.353709	−0.176855	+	0.984237i	$0.556592\pi$
$744$	−1.43104e30	−1.00957
$745$	2.92869e29	0.203719
$746$	−1.01622e30	−0.696998
$747$	−9.61447e29	−0.650218
$748$	−1.04893e30	−0.699486
$749$	2.97405e30	1.95564
$750$	−1.66527e29	−0.107979
$751$	−1.81607e30	−1.16121	−0.580607	−	0.814184i	$-0.697185\pi$
$751$	−1.81607e30	−1.16121	−0.580607	+	0.814184i	$0.697185\pi$
$752$	3.92666e29	0.247591
$753$	3.76833e30	2.34316
$754$	−1.44740e30	−0.887540
$755$	8.60200e29	0.520183
$756$	1.68297e30	1.00369
$757$	−3.23429e30	−1.90227	−0.951136	−	0.308772i	$-0.900082\pi$
$757$	−3.23429e30	−1.90227	−0.951136	+	0.308772i	$0.900082\pi$
$758$	−1.44822e28	−0.00840053
$759$	3.96766e29	0.226984
$760$	1.47984e29	0.0834970
$761$	5.91876e29	0.329376	0.164688	−	0.986346i	$-0.447338\pi$
$761$	5.91876e29	0.329376	0.164688	+	0.986346i	$0.447338\pi$
$762$	2.86745e30	1.57387
$763$	2.73252e30	1.47930
$764$	−2.42824e29	−0.129661
$765$	2.28950e30	1.20586
$766$	−2.57038e29	−0.133535
$767$	7.99912e29	0.409912
$768$	−2.11098e29	−0.106706
$769$	3.65919e30	1.82456	0.912281	−	0.409565i	$-0.134320\pi$
$769$	3.65919e30	1.82456	0.912281	+	0.409565i	$0.134320\pi$
$770$	−8.20869e29	−0.403758
$771$	−1.34885e30	−0.654475
$772$	−1.19000e30	−0.569595
$773$	−3.12612e30	−1.47612	−0.738059	−	0.674736i	$-0.764257\pi$
$773$	−3.12612e30	−1.47612	−0.738059	+	0.674736i	$0.764257\pi$
$774$	1.71627e30	0.799476
$775$	−7.27895e29	−0.334503
$776$	−7.79501e29	−0.353402
$777$	1.84335e30	0.824492
$778$	2.56265e30	1.13085
$779$	1.12005e30	0.487633
$780$	1.74212e30	0.748314
$781$	−4.49319e30	−1.90423
$782$	−3.18646e29	−0.133241
$783$	−2.42433e30	−1.00021
$784$	4.00157e29	0.162897
$785$	−1.72367e30	−0.692346
$786$	−2.50069e30	−0.991112
$787$	1.94010e30	0.758735	0.379368	−	0.925246i	$-0.376142\pi$
$787$	1.94010e30	0.758735	0.379368	+	0.925246i	$0.376142\pi$
$788$	−6.60363e29	−0.254834
$789$	−2.36808e30	−0.901753
$790$	1.08861e29	0.0409060
$791$	5.38912e30	1.99832
$792$	−1.83816e30	−0.672618
$793$	4.42024e30	1.59617
$794$	−3.36939e29	−0.120071
$795$	−1.39320e30	−0.489959
$796$	−7.48081e29	−0.259634
$797$	1.87837e30	0.643383	0.321691	−	0.946845i	$-0.395749\pi$
$797$	1.87837e30	0.643383	0.321691	+	0.946845i	$0.395749\pi$
$798$	−2.42369e30	−0.819308
$799$	−4.17999e30	−1.39455
$800$	−1.07374e29	−0.0353553
$801$	4.71255e30	1.53149
$802$	−8.65597e29	−0.277642
$803$	7.93722e29	0.251278
$804$	−1.46996e30	−0.459321
$805$	−2.49366e29	−0.0769095
$806$	7.61486e30	2.31816
$807$	3.89668e30	1.17091
$808$	−3.47828e29	−0.103168
$809$	3.76184e30	1.10139	0.550694	−	0.834707i	$-0.314363\pi$
$809$	3.76184e30	1.10139	0.550694	+	0.834707i	$0.314363\pi$
$810$	8.22724e29	0.237772
$811$	−1.39769e30	−0.398741	−0.199370	−	0.979924i	$-0.563890\pi$
$811$	−1.39769e30	−0.398741	−0.199370	+	0.979924i	$0.563890\pi$
$812$	−1.46108e30	−0.411467
$813$	−1.53506e30	−0.426751
$814$	−9.61916e29	−0.263986
$815$	−9.14681e29	−0.247808
$816$	2.24717e30	0.601020
$817$	−1.18089e30	−0.311801
$818$	1.62533e30	0.423675
$819$	−1.87440e31	−4.82372
$820$	−8.12687e29	−0.206480
$821$	3.06130e30	0.767897	0.383948	−	0.923355i	$-0.374564\pi$
$821$	3.06130e30	0.767897	0.383948	+	0.923355i	$0.374564\pi$
$822$	−6.24581e30	−1.54680
$823$	−2.80656e30	−0.686239	−0.343120	−	0.939292i	$-0.611484\pi$
$823$	−2.80656e30	−0.686239	−0.343120	+	0.939292i	$0.611484\pi$
$824$	−6.18554e29	−0.149328
$825$	−1.42324e30	−0.339243
$826$	8.07475e29	0.190037
$827$	−1.80807e30	−0.420153	−0.210077	−	0.977685i	$-0.567371\pi$
$827$	−1.80807e30	−0.420153	−0.210077	+	0.977685i	$0.567371\pi$
$828$	−5.58401e29	−0.128123
$829$	6.48512e30	1.46925	0.734625	−	0.678473i	$-0.237358\pi$
$829$	6.48512e30	1.46925	0.734625	+	0.678473i	$0.237358\pi$
$830$	−4.79994e29	−0.107378
$831$	−5.65663e30	−1.24953
$832$	1.12329e30	0.245018
$833$	−4.25974e30	−0.917509
$834$	−2.08726e30	−0.443949
$835$	2.70765e30	0.568702
$836$	1.26476e30	0.262326
$837$	1.27546e31	2.61245
$838$	1.50078e28	0.00303566
$839$	5.47358e30	1.09338	0.546690	−	0.837335i	$-0.315888\pi$
$839$	5.47358e30	1.09338	0.546690	+	0.837335i	$0.315888\pi$
$840$	1.75859e30	0.346922
$841$	−3.02816e30	−0.589957
$842$	2.12623e30	0.409103
$843$	−2.84509e30	−0.540639
$844$	−2.70079e30	−0.506868
$845$	−6.85741e30	−1.27106
$846$	−7.32508e30	−1.34098
$847$	9.20073e28	0.0166359
$848$	−8.98318e29	−0.160426
$849$	−1.26579e31	−2.23271
$850$	1.14302e30	0.199138
$851$	−2.92213e29	−0.0502851
$852$	9.62598e30	1.63617
$853$	−7.71396e30	−1.29513	−0.647564	−	0.762011i	$-0.724212\pi$
$853$	−7.71396e30	−1.29513	−0.647564	+	0.762011i	$0.724212\pi$
$854$	4.46203e30	0.739989
$855$	−2.76060e30	−0.452229
$856$	3.32482e30	0.538015
$857$	1.69666e29	0.0271205	0.0135602	−	0.999908i	$-0.495684\pi$
$857$	1.69666e29	0.0271205	0.0135602	+	0.999908i	$0.495684\pi$
$858$	1.48892e31	2.35101
$859$	4.91435e30	0.766545	0.383273	−	0.923635i	$-0.374797\pi$
$859$	4.91435e30	0.766545	0.383273	+	0.923635i	$0.374797\pi$
$860$	8.56833e29	0.132027
$861$	1.33103e31	2.02607
$862$	2.95829e30	0.444851
$863$	1.11211e31	1.65209	0.826047	−	0.563602i	$-0.190585\pi$
$863$	1.11211e31	1.65209	0.826047	+	0.563602i	$0.190585\pi$
$864$	1.88147e30	0.276123
$865$	3.75482e30	0.544403
$866$	−6.74375e30	−0.965970
$867$	−1.18569e31	−1.67792
$868$	7.68685e30	1.07471
$869$	9.30391e29	0.128516
$870$	−2.53325e30	−0.345721
$871$	7.82194e30	1.05469
$872$	3.05480e30	0.406967
$873$	1.45414e31	1.91406
$874$	3.84211e29	0.0499689
$875$	8.94500e29	0.114946
$876$	−1.70043e30	−0.215906
$877$	−1.05245e31	−1.32041	−0.660203	−	0.751088i	$-0.729530\pi$
$877$	−1.05245e31	−1.32041	−0.660203	+	0.751088i	$0.729530\pi$
$878$	9.55692e29	0.118475
$879$	1.38101e31	1.69166
$880$	−9.17685e29	−0.111077
$881$	−8.70976e30	−1.04174	−0.520870	−	0.853636i	$-0.674392\pi$
$881$	−8.70976e30	−1.04174	−0.520870	+	0.853636i	$0.674392\pi$
$882$	−7.46483e30	−0.882267
$883$	7.95603e30	0.929199	0.464600	−	0.885521i	$-0.346198\pi$
$883$	7.95603e30	0.929199	0.464600	+	0.885521i	$0.346198\pi$
$884$	−1.19576e31	−1.38006
$885$	1.40002e30	0.159672
$886$	−9.92275e30	−1.11835
$887$	−1.08949e31	−1.21346	−0.606729	−	0.794909i	$-0.707519\pi$
$887$	−1.08949e31	−1.21346	−0.606729	+	0.794909i	$0.707519\pi$
$888$	2.06076e30	0.226825
$889$	−1.54025e31	−1.67542
$890$	2.35270e30	0.252913
$891$	7.03150e30	0.747020
$892$	−7.59851e30	−0.797806
$893$	5.04007e30	0.522993
$894$	−5.36237e30	−0.549937
$895$	−4.43718e29	−0.0449743
$896$	1.13391e30	0.113591
$897$	4.52308e30	0.447830
$898$	1.01466e31	0.992935
$899$	−1.10729e31	−1.07099
$900$	2.00304e30	0.191489
$901$	9.56274e30	0.903591
$902$	−6.94572e30	−0.648707
$903$	−1.40333e31	−1.29550
$904$	6.02473e30	0.549755
$905$	−8.41758e30	−0.759236
$906$	−1.57501e31	−1.40423
$907$	7.14477e30	0.629668	0.314834	−	0.949147i	$-0.398051\pi$
$907$	7.14477e30	0.629668	0.314834	+	0.949147i	$0.398051\pi$
$908$	−1.62661e30	−0.141704
$909$	6.48864e30	0.558770
$910$	−9.35779e30	−0.796597
$911$	−9.25953e30	−0.779194	−0.389597	−	0.920985i	$-0.627386\pi$
$911$	−9.25953e30	−0.779194	−0.389597	+	0.920985i	$0.627386\pi$
$912$	−2.70955e30	−0.225399
$913$	−4.10233e30	−0.337355
$914$	1.44447e31	1.17429
$915$	7.73636e30	0.621749
$916$	−1.04379e31	−0.829299
$917$	1.34325e31	1.05506
$918$	−2.00285e31	−1.55525
$919$	2.16799e31	1.66435	0.832174	−	0.554515i	$-0.187096\pi$
$919$	2.16799e31	1.66435	0.832174	+	0.554515i	$0.187096\pi$
$920$	−2.78777e29	−0.0211585
$921$	2.07817e31	1.55939
$922$	−1.43712e29	−0.0106615
$923$	−5.12218e31	−3.75696
$924$	1.50300e31	1.08994
$925$	1.04820e30	0.0751545
$926$	1.57903e31	1.11937
$927$	1.15390e31	0.808779
$928$	−1.63340e30	−0.113198
$929$	−1.54089e31	−1.05586	−0.527929	−	0.849289i	$-0.677031\pi$
$929$	−1.54089e31	−1.05586	−0.527929	+	0.849289i	$0.677031\pi$
$930$	1.33276e31	0.902987
$931$	5.13623e30	0.344091
$932$	−4.85216e29	−0.0321417
$933$	2.90558e31	1.90316
$934$	−1.45578e31	−0.942875
$935$	9.76891e30	0.625639
$936$	−2.09548e31	−1.32705
$937$	−2.18719e31	−1.36969	−0.684843	−	0.728691i	$-0.740129\pi$
$937$	−2.18719e31	−1.36969	−0.684843	+	0.728691i	$0.740129\pi$
$938$	7.89589e30	0.488958
$939$	−3.92070e30	−0.240091
$940$	−3.65698e30	−0.221452
$941$	−5.71240e29	−0.0342080	−0.0171040	−	0.999854i	$-0.505445\pi$
$941$	−5.71240e29	−0.0342080	−0.0171040	+	0.999854i	$0.505445\pi$
$942$	3.15601e31	1.86898
$943$	−2.10999e30	−0.123568
$944$	9.02711e29	0.0522809
$945$	−1.56739e31	−0.897725
$946$	7.32302e30	0.414795
$947$	6.38251e29	0.0357534	0.0178767	−	0.999840i	$-0.494309\pi$
$947$	6.38251e29	0.0357534	0.0178767	+	0.999840i	$0.494309\pi$
$948$	−1.99322e30	−0.110425
$949$	9.04832e30	0.495761
$950$	−1.37820e30	−0.0746820
$951$	−1.93397e31	−1.03646
$952$	−1.20707e31	−0.639800
$953$	−2.06863e31	−1.08444	−0.542222	−	0.840235i	$-0.682417\pi$
$953$	−2.06863e31	−1.08444	−0.542222	+	0.840235i	$0.682417\pi$
$954$	1.67579e31	0.868884
$955$	2.26147e30	0.115973
$956$	1.11368e31	0.564873
$957$	−2.16507e31	−1.08617
$958$	−1.87043e31	−0.928120
$959$	3.35494e31	1.64661
$960$	1.96600e30	0.0954412
$961$	3.74300e31	1.79731
$962$	−1.09657e31	−0.520833
$963$	−6.20238e31	−2.91395
$964$	1.75847e30	0.0817195
$965$	1.10828e31	0.509461
$966$	4.56584e30	0.207616
$967$	2.49286e31	1.12129	0.560647	−	0.828055i	$-0.310552\pi$
$967$	2.49286e31	1.12129	0.560647	+	0.828055i	$0.310552\pi$
$968$	1.02859e29	0.00457668
$969$	2.88436e31	1.26955
$970$	7.25967e30	0.316092
$971$	4.80972e30	0.207166	0.103583	−	0.994621i	$-0.466969\pi$
$971$	4.80972e30	0.207166	0.103583	+	0.994621i	$0.466969\pi$
$972$	3.26528e30	0.139131
$973$	1.12117e31	0.472594
$974$	−3.27369e31	−1.36511
$975$	−1.62247e31	−0.669313
$976$	4.98830e30	0.203577
$977$	1.25924e31	0.508411	0.254205	−	0.967150i	$-0.418186\pi$
$977$	1.25924e31	0.508411	0.254205	+	0.967150i	$0.418186\pi$
$978$	1.67476e31	0.668953
$979$	2.01076e31	0.794589
$980$	−3.72675e30	−0.145699
$981$	−5.69865e31	−2.20418
$982$	1.09221e31	0.417961
$983$	1.94974e31	0.738185	0.369093	−	0.929393i	$-0.379669\pi$
$983$	1.94974e31	0.738185	0.369093	+	0.929393i	$0.379669\pi$
$984$	1.48801e31	0.557389
$985$	6.15011e30	0.227930
$986$	1.73878e31	0.637585
$987$	5.98945e31	2.17299
$988$	1.44181e31	0.517558
$989$	2.22461e30	0.0790118
$990$	1.71192e31	0.601608
$991$	−1.67935e31	−0.583941	−0.291971	−	0.956427i	$-0.594311\pi$
$991$	−1.67935e31	−0.583941	−0.291971	+	0.956427i	$0.594311\pi$
$992$	8.59346e30	0.295662
$993$	3.81047e31	1.29721
$994$	−5.17060e31	−1.74174
$995$	6.96705e30	0.232224
$996$	8.78861e30	0.289866
$997$	2.24576e31	0.732932	0.366466	−	0.930431i	$-0.380568\pi$
$997$	2.24576e31	0.732932	0.366466	+	0.930431i	$0.380568\pi$
$998$	1.22536e31	0.395724
$999$	−1.83671e31	−0.586953

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.22.a.b.1.1	✓	2
4.3	odd	2		80.22.a.d.1.2		2
5.2	odd	4		50.22.b.f.49.2		4
5.3	odd	4		50.22.b.f.49.3		4
5.4	even	2		50.22.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.22.a.b.1.1	✓	2	1.1	even	1	trivial
50.22.a.f.1.2		2	5.4	even	2
50.22.b.f.49.2		4	5.2	odd	4
50.22.b.f.49.3		4	5.3	odd	4
80.22.a.d.1.2		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-1024.00 q^{2} -174616. q^{3} +1.04858e6 q^{4} -9.76562e6 q^{5} +1.78807e8 q^{6} -9.60462e8 q^{7} -1.07374e9 q^{8} +2.00304e10 q^{9} +1.00000e10 q^{10} +8.54661e10 q^{11} -1.83098e11 q^{12} +9.74302e11 q^{13} +9.83513e11 q^{14} +1.70523e12 q^{15} +1.09951e12 q^{16} -1.17045e13 q^{17} -2.05111e13 q^{18} +1.41128e13 q^{19} -1.02400e13 q^{20} +1.67712e14 q^{21} -8.75173e13 q^{22} -2.65862e13 q^{23} +1.87492e14 q^{24} +9.53674e13 q^{25} -9.97685e14 q^{26} -1.67108e15 q^{27} -1.00712e15 q^{28} +1.45075e15 q^{29} -1.74616e15 q^{30} -7.63253e15 q^{31} -1.12590e15 q^{32} -1.49237e16 q^{33} +1.19854e16 q^{34} +9.37951e15 q^{35} +2.10034e16 q^{36} +1.09912e16 q^{37} -1.44515e16 q^{38} -1.70129e17 q^{39} +1.04858e16 q^{40} +7.93639e16 q^{41} -1.71737e17 q^{42} -8.36751e16 q^{43} +8.96177e16 q^{44} -1.95609e17 q^{45} +2.72243e16 q^{46} +3.57127e17 q^{47} -1.91992e17 q^{48} +3.63941e17 q^{49} -9.76562e16 q^{50} +2.04379e18 q^{51} +1.02163e18 q^{52} -8.17016e17 q^{53} +1.71119e18 q^{54} -8.34630e17 q^{55} +1.03129e18 q^{56} -2.46432e18 q^{57} -1.48557e18 q^{58} +8.21011e17 q^{59} +1.78807e18 q^{60} +4.53683e18 q^{61} +7.81571e18 q^{62} -1.92384e19 q^{63} +1.15292e18 q^{64} -9.51466e18 q^{65} +1.52819e19 q^{66} +8.02826e18 q^{67} -1.22730e19 q^{68} +4.64238e18 q^{69} -9.60462e18 q^{70} -5.25728e19 q^{71} -2.15075e19 q^{72} +9.28698e18 q^{73} -1.12549e19 q^{74} -1.66527e19 q^{75} +1.47984e19 q^{76} -8.20869e19 q^{77} +1.74212e20 q^{78} +1.08861e19 q^{79} -1.07374e19 q^{80} +8.22724e19 q^{81} -8.12687e19 q^{82} -4.79994e19 q^{83} +1.75859e20 q^{84} +1.14302e20 q^{85} +8.56833e19 q^{86} -2.53325e20 q^{87} -9.17685e19 q^{88} +2.35270e20 q^{89} +2.00304e20 q^{90} -9.35779e20 q^{91} -2.78777e19 q^{92} +1.33276e21 q^{93} -3.65698e20 q^{94} -1.37820e20 q^{95} +1.96600e20 q^{96} +7.25967e20 q^{97} -3.72675e20 q^{98} +1.71192e21 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2048 q^{2} - 126692 q^{3} + 2097152 q^{4} - 19531250 q^{5} + 129732608 q^{6} - 292598684 q^{7} - 2147483648 q^{8} + 11866737826 q^{9} + 20000000000 q^{10} - 41326831776 q^{11} - 132846190592 q^{12}+ \cdots + 27\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 2048 * q^2 - 126692 * q^3 + 2097152 * q^4 - 19531250 * q^5 + 129732608 * q^6 - 292598684 * q^7 - 2147483648 * q^8 + 11866737826 * q^9 + 20000000000 * q^10 - 41326831776 * q^11 - 132846190592 * q^12 + 1887051472228 * q^13 + 299621052416 * q^14 + 1237226562500 * q^15 + 2199023255552 * q^16 - 3100413932364 * q^17 - 12151539533824 * q^18 + 7175794652440 * q^19 - 20480000000000 * q^20 + 199718603894264 * q^21 + 42318675738624 * q^22 - 357559990100052 * q^23 + 136034499166208 * q^24 + 190734863281250 * q^25 - 1932340707561472 * q^26 - 2563616231988920 * q^27 - 306811957673984 * q^28 - 2454584202185940 * q^29 - 1266920000000000 * q^30 - 4310677151243336 * q^31 - 2251799813685248 * q^32 - 21000167846983104 * q^33 + 3174823866740736 * q^34 + 2857409023437500 * q^35 + 12443176482635776 * q^36 - 32389201650205724 * q^37 - 7348013724098560 * q^38 - 126386038156081288 * q^39 + 20971520000000000 * q^40 - 16298035212712116 * q^41 - 204511850387726336 * q^42 - 161845702253479412 * q^43 - 43334323956350976 * q^44 - 115886111582031250 * q^45 + 366141429862453248 * q^46 + 153492993930726996 * q^47 - 139299327146196992 * q^48 + 251436016683357114 * q^49 - 195312500000000000 * q^50 + 2456129297437264344 * q^51 + 1978716884542947328 * q^52 + 604198357317820308 * q^53 + 2625143021556654080 * q^54 + 403582341562500000 * q^55 + 314175444658159616 * q^56 - 2796771718696561840 * q^57 + 2513494223038402560 * q^58 + 3110197357974672120 * q^59 + 1297326080000000000 * q^60 - 791142209760451676 * q^61 + 4414133402873176064 * q^62 - 24690614624666969692 * q^63 + 2305843009213693952 * q^64 - 18428237033476562500 * q^65 + 21504171875310698496 * q^66 - 5111819523383561564 * q^67 - 3251019639542513664 * q^68 - 11219196977510717208 * q^69 - 2925986840000000000 * q^70 - 82388741313238482456 * q^71 - 12741812718219034624 * q^72 + 10657918464992348548 * q^73 + 33166542489810661376 * q^74 - 12082290649414062500 * q^75 + 7524366053476925440 * q^76 - 166767237207340703808 * q^77 + 129419303071827238912 * q^78 + 28314166125451369360 * q^79 - 21474836480000000000 * q^80 + 124893157714537187242 * q^81 + 16689188057817206784 * q^82 - 10427725705926651732 * q^83 + 209420134797031768064 * q^84 + 30277479808242187500 * q^85 + 165729999107562917888 * q^86 - 440484049640705943960 * q^87 + 44374347731303399424 * q^88 + 478501472814113520180 * q^89 + 118667378260000000000 * q^90 - 326187611445407942776 * q^91 - 374928824179152125952 * q^92 + 1491957513759228855056 * q^93 - 157176825785064443904 * q^94 - 70076119652734375000 * q^95 + 142642510997705719808 * q^96 + 545226897779926992196 * q^97 - 257470481083757684736 * q^98 + 2747011580657571215712 * q^99

Introduction

L-functions

Modular forms

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