LMFDB - Embedded newform 10.28.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,28,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, 28, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 28 $
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:	$46.1855574838$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{12929}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3232 $ x^2 - x - 3232
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$57.3529$ 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)

$f(q)$	$=$	\(q-8192.00 q^{2} -3.70167e6 q^{3} +6.71089e7 q^{4} -1.22070e9 q^{5} +3.03241e10 q^{6} +2.21874e11 q^{7} -5.49756e11 q^{8} +6.07675e12 q^{9} +1.00000e13 q^{10} -4.96342e12 q^{11} -2.48415e14 q^{12} -2.20961e14 q^{13} -1.81759e15 q^{14} +4.51864e15 q^{15} +4.50360e15 q^{16} -2.82835e16 q^{17} -4.97808e16 q^{18} -3.08583e17 q^{19} -8.19200e16 q^{20} -8.21302e17 q^{21} +4.06603e16 q^{22} -1.01717e18 q^{23} +2.03501e18 q^{24} +1.49012e18 q^{25} +1.81011e18 q^{26} +5.73331e18 q^{27} +1.48897e19 q^{28} -1.98720e19 q^{29} -3.70167e19 q^{30} -2.14960e20 q^{31} -3.68935e19 q^{32} +1.83729e19 q^{33} +2.31699e20 q^{34} -2.70842e20 q^{35} +4.07804e20 q^{36} -1.51125e21 q^{37} +2.52791e21 q^{38} +8.17924e20 q^{39} +6.71089e20 q^{40} +6.15572e21 q^{41} +6.72811e21 q^{42} +1.65500e22 q^{43} -3.33089e20 q^{44} -7.41791e21 q^{45} +8.33262e21 q^{46} -4.19797e21 q^{47} -1.66708e22 q^{48} -1.64845e22 q^{49} -1.22070e22 q^{50} +1.04696e23 q^{51} -1.48284e22 q^{52} +2.49598e23 q^{53} -4.69673e22 q^{54} +6.05886e21 q^{55} -1.21976e23 q^{56} +1.14227e24 q^{57} +1.62792e23 q^{58} +9.83832e23 q^{59} +3.03241e23 q^{60} -3.10904e23 q^{61} +1.76095e24 q^{62} +1.34827e24 q^{63} +3.02231e23 q^{64} +2.69728e23 q^{65} -1.50511e23 q^{66} -5.68487e24 q^{67} -1.89808e24 q^{68} +3.76521e24 q^{69} +2.21874e24 q^{70} -1.00834e25 q^{71} -3.34073e24 q^{72} +8.83463e24 q^{73} +1.23802e25 q^{74} -5.51592e24 q^{75} -2.07087e25 q^{76} -1.10125e24 q^{77} -6.70043e24 q^{78} -5.62142e25 q^{79} -5.49756e24 q^{80} -6.75617e25 q^{81} -5.04276e25 q^{82} +1.02556e26 q^{83} -5.51167e25 q^{84} +3.45258e25 q^{85} -1.35577e26 q^{86} +7.35596e25 q^{87} +2.72867e24 q^{88} -1.49929e26 q^{89} +6.07675e25 q^{90} -4.90254e25 q^{91} -6.82608e25 q^{92} +7.95709e26 q^{93} +3.43898e25 q^{94} +3.76689e26 q^{95} +1.36567e26 q^{96} -5.13532e26 q^{97} +1.35041e26 q^{98} -3.01615e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16384 q^{2} - 2245644 q^{3} + 134217728 q^{4} - 2441406250 q^{5} + 18396315648 q^{6} - 120196732292 q^{7} - 1099511627776 q^{8} + 571163616594 q^{9} + 20000000000000 q^{10} + 7112122732704 q^{11}+ \cdots - 96\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 16384 * q^2 - 2245644 * q^3 + 134217728 * q^4 - 2441406250 * q^5 + 18396315648 * q^6 - 120196732292 * q^7 - 1099511627776 * q^8 + 571163616594 * q^9 + 20000000000000 * q^10 + 7112122732704 * q^11 - 150702617788416 * q^12 - 323114990355404 * q^13 + 984651630936064 * q^14 + 2741264648437500 * q^15 + 9007199254740992 * q^16 - 11949781720794252 * q^17 - 4678972347138048 * q^18 - 310800626187534200 * q^19 - 163840000000000000 * q^20 - 1319365315134326376 * q^21 - 58262509426311168 * q^22 - 1207992822578557644 * q^23 + 1234555844922703872 * q^24 + 2980232238769531250 * q^25 + 2646958000991469568 * q^26 - 13386024338103046440 * q^27 - 8066266160628236288 * q^28 - 85089627076663724580 * q^29 - 22456440000000000000 * q^30 - 169891626304914480056 * q^31 - 73786976294838206464 * q^32 + 35955214564003682112 * q^33 + 97892611856746512384 * q^34 + 146724526723632812500 * q^35 + 38330141467754889216 * q^36 + 1001687425876018532308 * q^37 + 2546078729728280166400 * q^38 + 669184707607358092488 * q^39 + 1342177280000000000000 * q^40 + 6829708525832119000044 * q^41 + 10808240661580401672192 * q^42 + 15331910221739375128036 * q^43 + 477286477220341088256 * q^44 - 697221211662597656250 * q^45 + 9895877202563544219648 * q^46 + 44654607958183509227628 * q^47 - 10113481481606790119424 * q^48 + 34815266426190611168346 * q^49 - 24414062500000000000000 * q^50 + 128478598882379942153544 * q^51 - 21683879944122118701056 * q^52 + 259350970067880627435396 * q^53 + 109658311377740156436480 * q^54 - 8681790445195312500000 * q^55 + 66078852387866511671296 * q^56 + 1139044611805451608251600 * q^57 + 697054225012029231759360 * q^58 + 2082093442621301023169640 * q^59 + 183963156480000000000000 * q^60 + 677925769536334246319284 * q^61 + 1391752202689859420618752 * q^62 + 3231569874371732206566876 * q^63 + 604462909807314587353088 * q^64 + 394427478461186523437500 * q^65 - 294545117708318163861504 * q^66 + 2453617552336948143390028 * q^67 - 801936276330467429449728 * q^68 + 3487358239126020846890568 * q^69 - 1201967322920000000000000 * q^70 - 23890193584108132090228776 * q^71 - 314000518903848052457472 * q^72 - 13919420706136886544146204 * q^73 - 8205823392776343816667136 * q^74 - 3346270322799682617187500 * q^75 - 20857476953934071123148800 * q^76 - 5231935501660614540408384 * q^77 - 5481961124719477493661696 * q^78 - 53659327270981104663051920 * q^79 - 10995116277760000000000000 * q^80 - 53416489016311609709962998 * q^81 - 55948972243616718848360448 * q^82 + 5756571261014435461903716 * q^83 - 88541107499666650498596864 * q^84 + 14587135889641420898437500 * q^85 - 125599008536488961048870912 * q^86 - 21398789661957929503788840 * q^87 - 3909930821389034194993152 * q^88 + 174438127411287409220344020 * q^89 + 5711636165940000000000000 * q^90 - 14081455302088161819283816 * q^91 - 81067026043400554247356416 * q^92 + 861329117078544091150519632 * q^93 - 365810548393439307592728576 * q^94 + 379395295639079833984375000 * q^95 + 82849640297322824658321408 * q^96 - 21732067184289340167295292 * q^97 - 285206662563353486691090432 * q^98 - 96644441211111069636758112 * 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 $

$2$	−8192.00	−0.707107
$2$	−8192.00	−0.707107
$3$	−3.70167e6	−1.34048	−0.670240	−	0.742144i	$-0.733809\pi$
$3$	−3.70167e6	−1.34048	−0.670240	+	0.742144i	$0.733809\pi$
$4$	6.71089e7	0.500000
$5$	−1.22070e9	−0.447214
$5$	−1.22070e9	−0.447214
$6$	3.03241e10	0.947863
$7$	2.21874e11	0.865530	0.432765	−	0.901507i	$-0.357538\pi$
$7$	2.21874e11	0.865530	0.432765	+	0.901507i	$0.357538\pi$
$8$	−5.49756e11	−0.353553
$9$	6.07675e12	0.796889
$10$	1.00000e13	0.316228
$11$	−4.96342e12	−0.0433491	−0.0216745	−	0.999765i	$-0.506900\pi$
$11$	−4.96342e12	−0.0433491	−0.0216745	+	0.999765i	$0.506900\pi$
$12$	−2.48415e14	−0.670240
$13$	−2.20961e14	−0.202339	−0.101170	−	0.994869i	$-0.532258\pi$
$13$	−2.20961e14	−0.202339	−0.101170	+	0.994869i	$0.532258\pi$
$14$	−1.81759e15	−0.612022
$15$	4.51864e15	0.599481
$16$	4.50360e15	0.250000
$17$	−2.82835e16	−0.692585	−0.346293	−	0.938127i	$-0.612560\pi$
$17$	−2.82835e16	−0.692585	−0.346293	+	0.938127i	$0.612560\pi$
$18$	−4.97808e16	−0.563485
$19$	−3.08583e17	−1.68344	−0.841722	−	0.539911i	$-0.818458\pi$
$19$	−3.08583e17	−1.68344	−0.841722	+	0.539911i	$0.818458\pi$
$20$	−8.19200e16	−0.223607
$21$	−8.21302e17	−1.16023
$22$	4.06603e16	0.0306524
$23$	−1.01717e18	−0.420790	−0.210395	−	0.977616i	$-0.567475\pi$
$23$	−1.01717e18	−0.420790	−0.210395	+	0.977616i	$0.567475\pi$
$24$	2.03501e18	0.473932
$25$	1.49012e18	0.200000
$26$	1.81011e18	0.143075
$27$	5.73331e18	0.272267
$28$	1.48897e19	0.432765
$29$	−1.98720e19	−0.359641	−0.179820	−	0.983699i	$-0.557552\pi$
$29$	−1.98720e19	−0.359641	−0.179820	+	0.983699i	$0.557552\pi$
$30$	−3.70167e19	−0.423897
$31$	−2.14960e20	−1.58115	−0.790577	−	0.612363i	$-0.790219\pi$
$31$	−2.14960e20	−1.58115	−0.790577	+	0.612363i	$0.790219\pi$
$32$	−3.68935e19	−0.176777
$33$	1.83729e19	0.0581086
$34$	2.31699e20	0.489732
$35$	−2.70842e20	−0.387077
$36$	4.07804e20	0.398444
$37$	−1.51125e21	−1.02003	−0.510015	−	0.860166i	$-0.670360\pi$
$37$	−1.51125e21	−1.02003	−0.510015	+	0.860166i	$0.670360\pi$
$38$	2.52791e21	1.19038
$39$	8.17924e20	0.271232
$40$	6.71089e20	0.158114
$41$	6.15572e21	1.03919	0.519597	−	0.854411i	$-0.326082\pi$
$41$	6.15572e21	1.03919	0.519597	+	0.854411i	$0.326082\pi$
$42$	6.72811e21	0.820404
$43$	1.65500e22	1.46883	0.734417	−	0.678698i	$-0.237455\pi$
$43$	1.65500e22	1.46883	0.734417	+	0.678698i	$0.237455\pi$
$44$	−3.33089e20	−0.0216745
$45$	−7.41791e21	−0.356380
$46$	8.33262e21	0.297544
$47$	−4.19797e21	−0.112129	−0.0560646	−	0.998427i	$-0.517855\pi$
$47$	−4.19797e21	−0.112129	−0.0560646	+	0.998427i	$0.517855\pi$
$48$	−1.66708e22	−0.335120
$49$	−1.64845e22	−0.250858
$50$	−1.22070e22	−0.141421
$51$	1.04696e23	0.928397
$52$	−1.48284e22	−0.101170
$53$	2.49598e23	1.31679	0.658396	−	0.752672i	$-0.271235\pi$
$53$	2.49598e23	1.31679	0.658396	+	0.752672i	$0.271235\pi$
$54$	−4.69673e22	−0.192522
$55$	6.05886e21	0.0193863
$56$	−1.21976e23	−0.306011
$57$	1.14227e24	2.25663
$58$	1.62792e23	0.254305
$59$	9.83832e23	1.22017	0.610083	−	0.792338i	$-0.291136\pi$
$59$	9.83832e23	1.22017	0.610083	+	0.792338i	$0.291136\pi$
$60$	3.03241e23	0.299741
$61$	−3.10904e23	−0.245852	−0.122926	−	0.992416i	$-0.539228\pi$
$61$	−3.10904e23	−0.245852	−0.122926	+	0.992416i	$0.539228\pi$
$62$	1.76095e24	1.11804
$63$	1.34827e24	0.689731
$64$	3.02231e23	0.125000
$65$	2.69728e23	0.0904888
$66$	−1.50511e23	−0.0410890
$67$	−5.68487e24	−1.26681	−0.633403	−	0.773822i	$-0.718343\pi$
$67$	−5.68487e24	−1.26681	−0.633403	+	0.773822i	$0.718343\pi$
$68$	−1.89808e24	−0.346293
$69$	3.76521e24	0.564061
$70$	2.21874e24	0.273705
$71$	−1.00834e25	−1.02712	−0.513560	−	0.858054i	$-0.671674\pi$
$71$	−1.00834e25	−1.02712	−0.513560	+	0.858054i	$0.671674\pi$
$72$	−3.34073e24	−0.281743
$73$	8.83463e24	0.618486	0.309243	−	0.950983i	$-0.399924\pi$
$73$	8.83463e24	0.618486	0.309243	+	0.950983i	$0.399924\pi$
$74$	1.23802e25	0.721270
$75$	−5.51592e24	−0.268096
$76$	−2.07087e25	−0.841722
$77$	−1.10125e24	−0.0375199
$78$	−6.70043e24	−0.191790
$79$	−5.62142e25	−1.35482	−0.677408	−	0.735608i	$-0.736897\pi$
$79$	−5.62142e25	−1.35482	−0.677408	+	0.735608i	$0.736897\pi$
$80$	−5.49756e24	−0.111803
$81$	−6.75617e25	−1.16186
$82$	−5.04276e25	−0.734821
$83$	1.02556e26	1.26884	0.634421	−	0.772987i	$-0.281238\pi$
$83$	1.02556e26	1.26884	0.634421	+	0.772987i	$0.281238\pi$
$84$	−5.51167e25	−0.580113
$85$	3.45258e25	0.309733
$86$	−1.35577e26	−1.03862
$87$	7.35596e25	0.482092
$88$	2.72867e24	0.0153262
$89$	−1.49929e26	−0.722972	−0.361486	−	0.932377i	$-0.617731\pi$
$89$	−1.49929e26	−0.722972	−0.361486	+	0.932377i	$0.617731\pi$
$90$	6.07675e25	0.251998
$91$	−4.90254e25	−0.175131
$92$	−6.82608e25	−0.210395
$93$	7.95709e26	2.11951
$94$	3.43898e25	0.0792873
$95$	3.76689e26	0.752859
$96$	1.36567e26	0.236966
$97$	−5.13532e26	−0.774728	−0.387364	−	0.921927i	$-0.626614\pi$
$97$	−5.13532e26	−0.774728	−0.387364	+	0.921927i	$0.626614\pi$
$98$	1.35041e26	0.177383
$99$	−3.01615e25	−0.0345444
$100$	1.00000e26	0.100000
$101$	−7.06297e26	−0.617517	−0.308758	−	0.951140i	$-0.599913\pi$
$101$	−7.06297e26	−0.617517	−0.308758	+	0.951140i	$0.599913\pi$
$102$	−8.57672e26	−0.656476
$103$	5.07949e26	0.340814	0.170407	−	0.985374i	$-0.445492\pi$
$103$	5.07949e26	0.340814	0.170407	+	0.985374i	$0.445492\pi$
$104$	1.21474e26	0.0715377
$105$	1.00257e27	0.518869
$106$	−2.04471e27	−0.931113
$107$	2.94045e27	1.17959	0.589797	−	0.807552i	$-0.299208\pi$
$107$	2.94045e27	1.17959	0.589797	+	0.807552i	$0.299208\pi$
$108$	3.84756e26	0.136133
$109$	5.73706e27	1.79239	0.896194	−	0.443663i	$-0.146321\pi$
$109$	5.73706e27	1.79239	0.896194	+	0.443663i	$0.146321\pi$
$110$	−4.96342e25	−0.0137082
$111$	5.59415e27	1.36733
$112$	9.99230e26	0.216382
$113$	5.78909e27	1.11186	0.555931	−	0.831228i	$-0.312362\pi$
$113$	5.78909e27	1.11186	0.555931	+	0.831228i	$0.312362\pi$
$114$	−9.35750e27	−1.59567
$115$	1.24166e27	0.188183
$116$	−1.33359e27	−0.179820
$117$	−1.34272e27	−0.161242
$118$	−8.05955e27	−0.862787
$119$	−6.27537e27	−0.599453
$120$	−2.48415e27	−0.211949
$121$	−1.30854e28	−0.998121
$122$	2.54692e27	0.173843
$123$	−2.27864e28	−1.39302
$124$	−1.44257e28	−0.790577
$125$	−1.81899e27	−0.0894427
$126$	−1.10450e28	−0.487714
$127$	3.77532e28	1.49832	0.749158	−	0.662392i	$-0.230459\pi$
$127$	3.77532e28	1.49832	0.749158	+	0.662392i	$0.230459\pi$
$128$	−2.47588e27	−0.0883883
$129$	−6.12625e28	−1.96895
$130$	−2.20961e27	−0.0639853
$131$	5.70081e28	1.48859	0.744293	−	0.667853i	$-0.232787\pi$
$131$	5.70081e28	1.48859	0.744293	+	0.667853i	$0.232787\pi$
$132$	1.23299e27	0.0290543
$133$	−6.84665e28	−1.45707
$134$	4.65704e28	0.895768
$135$	−6.99867e27	−0.121761
$136$	1.55490e28	0.244866
$137$	7.42178e28	1.05872	0.529359	−	0.848398i	$-0.322432\pi$
$137$	7.42178e28	1.05872	0.529359	+	0.848398i	$0.322432\pi$
$138$	−3.08446e28	−0.398852
$139$	1.13293e29	1.32893	0.664467	−	0.747317i	$-0.268658\pi$
$139$	1.13293e29	1.32893	0.664467	+	0.747317i	$0.268658\pi$
$140$	−1.81759e28	−0.193538
$141$	1.55395e28	0.150307
$142$	8.26036e28	0.726283
$143$	1.09672e27	0.00877121
$144$	2.73673e28	0.199222
$145$	2.42578e28	0.160836
$146$	−7.23733e28	−0.437336
$147$	6.10201e28	0.336270
$148$	−1.01418e29	−0.510015
$149$	−2.59311e29	−1.19071	−0.595355	−	0.803463i	$-0.702988\pi$
$149$	−2.59311e29	−1.19071	−0.595355	+	0.803463i	$0.702988\pi$
$150$	4.51864e28	0.189573
$151$	3.80757e29	1.46036	0.730179	−	0.683256i	$-0.239437\pi$
$151$	3.80757e29	1.46036	0.730179	+	0.683256i	$0.239437\pi$
$152$	1.69645e29	0.595188
$153$	−1.71872e29	−0.551913
$154$	9.02145e27	0.0265306
$155$	2.62402e29	0.707113
$156$	5.48899e28	0.135616
$157$	−1.65707e29	−0.375575	−0.187787	−	0.982210i	$-0.560132\pi$
$157$	−1.65707e29	−0.375575	−0.187787	+	0.982210i	$0.560132\pi$
$158$	4.60507e29	0.957999
$159$	−9.23930e29	−1.76513
$160$	4.50360e28	0.0790569
$161$	−2.25682e29	−0.364207
$162$	5.53465e29	0.821557
$163$	6.32120e29	0.863509	0.431754	−	0.901991i	$-0.357895\pi$
$163$	6.32120e29	0.863509	0.431754	+	0.901991i	$0.357895\pi$
$164$	4.13103e29	0.519597
$165$	−2.24279e28	−0.0259869
$166$	−8.40141e29	−0.897207
$167$	−1.17045e30	−1.15260	−0.576301	−	0.817237i	$-0.695504\pi$
$167$	−1.17045e30	−1.15260	−0.576301	+	0.817237i	$0.695504\pi$
$168$	4.51516e29	0.410202
$169$	−1.14371e30	−0.959059
$170$	−2.82835e29	−0.219015
$171$	−1.87518e30	−1.34152
$172$	1.11065e30	0.734417
$173$	−2.98638e29	−0.182609	−0.0913045	−	0.995823i	$-0.529104\pi$
$173$	−2.98638e29	−0.182609	−0.0913045	+	0.995823i	$0.529104\pi$
$174$	−6.02601e29	−0.340890
$175$	3.30617e29	0.173106
$176$	−2.23532e28	−0.0108373
$177$	−3.64182e30	−1.63561
$178$	1.22822e30	0.511219
$179$	2.50314e30	0.965983	0.482992	−	0.875625i	$-0.339550\pi$
$179$	2.50314e30	0.965983	0.482992	+	0.875625i	$0.339550\pi$
$180$	−4.97808e29	−0.178190
$181$	1.42305e30	0.472671	0.236336	−	0.971671i	$-0.424054\pi$
$181$	1.42305e30	0.472671	0.236336	+	0.971671i	$0.424054\pi$
$182$	4.01616e29	0.123836
$183$	1.15086e30	0.329559
$184$	5.59192e29	0.148772
$185$	1.84479e30	0.456171
$186$	−6.51845e30	−1.49872
$187$	1.40383e29	0.0300229
$188$	−2.81721e29	−0.0560646
$189$	1.27207e30	0.235655
$190$	−3.08583e30	−0.532352
$191$	7.99660e30	1.28515	0.642577	−	0.766221i	$-0.277865\pi$
$191$	7.99660e30	1.28515	0.642577	+	0.766221i	$0.277865\pi$
$192$	−1.11876e30	−0.167560
$193$	4.05061e30	0.565583	0.282792	−	0.959181i	$-0.408740\pi$
$193$	4.05061e30	0.565583	0.282792	+	0.959181i	$0.408740\pi$
$194$	4.20686e30	0.547816
$195$	−9.98442e29	−0.121299
$196$	−1.10625e30	−0.125429
$197$	3.68848e30	0.390439	0.195219	−	0.980760i	$-0.437458\pi$
$197$	3.68848e30	0.390439	0.195219	+	0.980760i	$0.437458\pi$
$198$	2.47083e29	0.0244266
$199$	−5.24093e30	−0.484052	−0.242026	−	0.970270i	$-0.577812\pi$
$199$	−5.24093e30	−0.484052	−0.242026	+	0.970270i	$0.577812\pi$
$200$	−8.19200e29	−0.0707107
$201$	2.10435e31	1.69813
$202$	5.78598e30	0.436650
$203$	−4.40908e30	−0.311280
$204$	7.02605e30	0.464199
$205$	−7.51431e30	−0.464742
$206$	−4.16112e30	−0.240992
$207$	−6.18106e30	−0.335323
$208$	−9.95119e29	−0.0505848
$209$	1.53163e30	0.0729757
$210$	−8.21302e30	−0.366896
$211$	4.12328e31	1.72754	0.863772	−	0.503882i	$-0.168095\pi$
$211$	4.12328e31	1.72754	0.863772	+	0.503882i	$0.168095\pi$
$212$	1.67503e31	0.658396
$213$	3.73256e31	1.37683
$214$	−2.40881e31	−0.834098
$215$	−2.02026e31	−0.656883
$216$	−3.15192e30	−0.0962608
$217$	−4.76938e31	−1.36854
$218$	−4.69980e31	−1.26741
$219$	−3.27029e31	−0.829069
$220$	4.06603e29	0.00969314
$221$	6.24955e30	0.140137
$222$	−4.58272e31	−0.966849
$223$	−7.30751e31	−1.45095	−0.725477	−	0.688246i	$-0.758381\pi$
$223$	−7.30751e31	−1.45095	−0.725477	+	0.688246i	$0.758381\pi$
$224$	−8.18569e30	−0.153006
$225$	9.05507e30	0.159378
$226$	−4.74242e31	−0.786206
$227$	−4.75425e31	−0.742562	−0.371281	−	0.928521i	$-0.621081\pi$
$227$	−4.75425e31	−0.742562	−0.371281	+	0.928521i	$0.621081\pi$
$228$	7.66567e31	1.12831
$229$	−1.75469e31	−0.243457	−0.121728	−	0.992563i	$-0.538844\pi$
$229$	−1.75469e31	−0.243457	−0.121728	+	0.992563i	$0.538844\pi$
$230$	−1.01717e31	−0.133066
$231$	4.07647e30	0.0502947
$232$	1.09248e31	0.127152
$233$	1.39810e32	1.53544	0.767722	−	0.640783i	$-0.221390\pi$
$233$	1.39810e32	1.53544	0.767722	+	0.640783i	$0.221390\pi$
$234$	1.09996e31	0.114015
$235$	5.12448e30	0.0501457
$236$	6.60238e31	0.610083
$237$	2.08086e32	1.81610
$238$	5.14078e31	0.423877
$239$	−1.11791e32	−0.871032	−0.435516	−	0.900181i	$-0.643434\pi$
$239$	−1.11791e32	−0.871032	−0.435516	+	0.900181i	$0.643434\pi$
$240$	2.03501e31	0.149870
$241$	−2.45179e32	−1.70708	−0.853538	−	0.521031i	$-0.825548\pi$
$241$	−2.45179e32	−1.70708	−0.853538	+	0.521031i	$0.825548\pi$
$242$	1.07195e32	0.705778
$243$	2.06371e32	1.28518
$244$	−2.08644e31	−0.122926
$245$	2.01226e31	0.112187
$246$	1.86666e32	0.985014
$247$	6.81848e31	0.340627
$248$	1.18175e32	0.559022
$249$	−3.79629e32	−1.70086
$250$	1.49012e31	0.0632456
$251$	−7.91625e31	−0.318364	−0.159182	−	0.987249i	$-0.550886\pi$
$251$	−7.91625e31	−0.318364	−0.159182	+	0.987249i	$0.550886\pi$
$252$	9.04809e31	0.344866
$253$	5.04862e30	0.0182409
$254$	−3.09274e32	−1.05947
$255$	−1.27803e32	−0.415192
$256$	2.02824e31	0.0625000
$257$	1.09612e32	0.320450	0.160225	−	0.987081i	$-0.448778\pi$
$257$	1.09612e32	0.320450	0.160225	+	0.987081i	$0.448778\pi$
$258$	5.01862e32	1.39225
$259$	−3.35306e32	−0.882866
$260$	1.81011e31	0.0452444
$261$	−1.20757e32	−0.286594
$262$	−4.67010e32	−1.05259
$263$	7.62148e32	1.63169	0.815843	−	0.578273i	$-0.196273\pi$
$263$	7.62148e32	1.63169	0.815843	+	0.578273i	$0.196273\pi$
$264$	−1.01006e31	−0.0205445
$265$	−3.04685e32	−0.588887
$266$	5.60877e32	1.03031
$267$	5.54989e32	0.969130
$268$	−3.81505e32	−0.633403
$269$	−5.43143e32	−0.857548	−0.428774	−	0.903412i	$-0.641054\pi$
$269$	−5.43143e32	−0.857548	−0.428774	+	0.903412i	$0.641054\pi$
$270$	5.73331e31	0.0860983
$271$	9.35499e32	1.33647	0.668233	−	0.743952i	$-0.267051\pi$
$271$	9.35499e32	1.33647	0.668233	+	0.743952i	$0.267051\pi$
$272$	−1.27378e32	−0.173146
$273$	1.81476e32	0.234759
$274$	−6.07992e32	−0.748627
$275$	−7.39607e30	−0.00866981
$276$	2.52679e32	0.282031
$277$	−7.26315e31	−0.0772055	−0.0386027	−	0.999255i	$-0.512291\pi$
$277$	−7.26315e31	−0.0772055	−0.0386027	+	0.999255i	$0.512291\pi$
$278$	−9.28097e32	−0.939699
$279$	−1.30626e33	−1.26000
$280$	1.48897e32	0.136852
$281$	−8.29253e32	−0.726360	−0.363180	−	0.931719i	$-0.618309\pi$
$281$	−8.29253e32	−0.726360	−0.363180	+	0.931719i	$0.618309\pi$
$282$	−1.27300e32	−0.106283
$283$	−8.40984e32	−0.669377	−0.334689	−	0.942329i	$-0.608631\pi$
$283$	−8.40984e32	−0.669377	−0.334689	+	0.942329i	$0.608631\pi$
$284$	−6.76688e32	−0.513560
$285$	−1.39438e33	−1.00919
$286$	−8.98434e30	−0.00620218
$287$	1.36579e33	0.899454
$288$	−2.24193e32	−0.140871
$289$	−8.67753e32	−0.520326
$290$	−1.98720e32	−0.113728
$291$	1.90093e33	1.03851
$292$	5.92882e32	0.309243
$293$	1.91703e33	0.954806	0.477403	−	0.878684i	$-0.341578\pi$
$293$	1.91703e33	0.954806	0.477403	+	0.878684i	$0.341578\pi$
$294$	−4.99876e32	−0.237779
$295$	−1.20097e33	−0.545675
$296$	8.30818e32	0.360635
$297$	−2.84568e31	−0.0118025
$298$	2.12427e33	0.841959
$299$	2.24754e32	0.0851424
$300$	−3.70167e32	−0.134048
$301$	3.67200e33	1.27132
$302$	−3.11916e33	−1.03263
$303$	2.61448e33	0.827769
$304$	−1.38974e33	−0.420861
$305$	3.79521e32	0.109948
$306$	1.40798e33	0.390262
$307$	1.55063e32	0.0411284	0.0205642	−	0.999789i	$-0.493454\pi$
$307$	1.55063e32	0.0411284	0.0205642	+	0.999789i	$0.493454\pi$
$308$	−7.39037e31	−0.0187600
$309$	−1.88026e33	−0.456855
$310$	−2.14960e33	−0.500004
$311$	3.36700e33	0.749856	0.374928	−	0.927054i	$-0.377667\pi$
$311$	3.36700e33	0.749856	0.374928	+	0.927054i	$0.377667\pi$
$312$	−4.49658e32	−0.0958949
$313$	9.72130e33	1.98553	0.992763	−	0.120088i	$-0.0383175\pi$
$313$	9.72130e33	1.98553	0.992763	+	0.120088i	$0.0383175\pi$
$314$	1.35747e33	0.265572
$315$	−1.64584e33	−0.308457
$316$	−3.77247e33	−0.677408
$317$	4.33019e33	0.745087	0.372543	−	0.928015i	$-0.378486\pi$
$317$	4.33019e33	0.745087	0.372543	+	0.928015i	$0.378486\pi$
$318$	7.56884e33	1.24814
$319$	9.86332e31	0.0155901
$320$	−3.68935e32	−0.0559017
$321$	−1.08846e34	−1.58122
$322$	1.84879e33	0.257533
$323$	8.72782e33	1.16593
$324$	−4.53399e33	−0.580929
$325$	−3.29257e32	−0.0404678
$326$	−5.17833e33	−0.610593
$327$	−2.12367e34	−2.40266
$328$	−3.38414e33	−0.367411
$329$	−9.31419e32	−0.0970511
$330$	1.83729e32	0.0183755
$331$	4.05518e33	0.389343	0.194672	−	0.980868i	$-0.437636\pi$
$331$	4.05518e33	0.389343	0.194672	+	0.980868i	$0.437636\pi$
$332$	6.88243e33	0.634421
$333$	−9.18349e33	−0.812850
$334$	9.58830e33	0.815013
$335$	6.93953e33	0.566533
$336$	−3.69882e33	−0.290057
$337$	−1.02439e34	−0.771726	−0.385863	−	0.922556i	$-0.626096\pi$
$337$	−1.02439e34	−0.771726	−0.385863	+	0.922556i	$0.626096\pi$
$338$	9.36927e33	0.678157
$339$	−2.14293e34	−1.49043
$340$	2.31699e33	0.154867
$341$	1.06693e33	0.0685415
$342$	1.53615e34	0.948597
$343$	−1.82373e34	−1.08265
$344$	−9.09844e33	−0.519312
$345$	−4.59620e33	−0.252256
$346$	2.44644e33	0.129124
$347$	−1.38931e34	−0.705262	−0.352631	−	0.935763i	$-0.614713\pi$
$347$	−1.38931e34	−0.705262	−0.352631	+	0.935763i	$0.614713\pi$
$348$	4.93650e33	0.241046
$349$	−1.31006e34	−0.615386	−0.307693	−	0.951486i	$-0.599557\pi$
$349$	−1.31006e34	−0.615386	−0.307693	+	0.951486i	$0.599557\pi$
$350$	−2.70842e33	−0.122404
$351$	−1.26684e33	−0.0550902
$352$	1.83118e32	0.00766310
$353$	−1.98132e34	−0.797986	−0.398993	−	0.916954i	$-0.630640\pi$
$353$	−1.98132e34	−0.797986	−0.398993	+	0.916954i	$0.630640\pi$
$354$	2.98338e34	1.15655
$355$	1.23089e34	0.459342
$356$	−1.00616e34	−0.361486
$357$	2.32293e34	0.803555
$358$	−2.05057e34	−0.683053
$359$	−4.57990e32	−0.0146920	−0.00734600	−	0.999973i	$-0.502338\pi$
$359$	−4.57990e32	−0.0146920	−0.00734600	+	0.999973i	$0.502338\pi$
$360$	4.07804e33	0.125999
$361$	6.16230e34	1.83399
$362$	−1.16576e34	−0.334229
$363$	4.84377e34	1.33796
$364$	−3.29004e33	−0.0875653
$365$	−1.07845e34	−0.276595
$366$	−9.42786e33	−0.233034
$367$	5.67067e34	1.35096	0.675480	−	0.737379i	$-0.263937\pi$
$367$	5.67067e34	1.35096	0.675480	+	0.737379i	$0.263937\pi$
$368$	−4.58090e33	−0.105198
$369$	3.74068e34	0.828122
$370$	−1.51125e34	−0.322562
$371$	5.53793e34	1.13972
$372$	5.33991e34	1.05975
$373$	−8.62803e34	−1.65136	−0.825681	−	0.564137i	$-0.809209\pi$
$373$	−8.62803e34	−1.65136	−0.825681	+	0.564137i	$0.809209\pi$
$374$	−1.15002e33	−0.0212294
$375$	6.73330e33	0.119896
$376$	2.30786e33	0.0396436
$377$	4.39094e33	0.0727695
$378$	−1.04208e34	−0.166633
$379$	6.41552e34	0.989925	0.494963	−	0.868914i	$-0.335182\pi$
$379$	6.41552e34	0.989925	0.494963	+	0.868914i	$0.335182\pi$
$380$	2.52791e34	0.376430
$381$	−1.39750e35	−2.00846
$382$	−6.55081e34	−0.908741
$383$	−8.39805e34	−1.12459	−0.562296	−	0.826936i	$-0.690082\pi$
$383$	−8.39805e34	−1.12459	−0.562296	+	0.826936i	$0.690082\pi$
$384$	9.16489e33	0.118483
$385$	1.34430e33	0.0167794
$386$	−3.31826e34	−0.399928
$387$	1.00570e35	1.17050
$388$	−3.44626e34	−0.387364
$389$	7.41980e33	0.0805514	0.0402757	−	0.999189i	$-0.487176\pi$
$389$	7.41980e33	0.0805514	0.0402757	+	0.999189i	$0.487176\pi$
$390$	8.17924e33	0.0857710
$391$	2.87690e34	0.291433
$392$	9.06244e33	0.0886917
$393$	−2.11025e35	−1.99542
$394$	−3.02160e34	−0.276082
$395$	6.86208e34	0.605892
$396$	−2.02410e33	−0.0172722
$397$	−2.92884e34	−0.241559	−0.120780	−	0.992679i	$-0.538539\pi$
$397$	−2.92884e34	−0.241559	−0.120780	+	0.992679i	$0.538539\pi$
$398$	4.29337e34	0.342276
$399$	2.53440e35	1.95318
$400$	6.71089e33	0.0500000
$401$	−9.68409e34	−0.697605	−0.348803	−	0.937196i	$-0.613412\pi$
$401$	−9.68409e34	−0.697605	−0.348803	+	0.937196i	$0.613412\pi$
$402$	−1.72388e35	−1.20076
$403$	4.74976e34	0.319929
$404$	−4.73988e34	−0.308758
$405$	8.24728e34	0.519598
$406$	3.61192e34	0.220108
$407$	7.50096e33	0.0442173
$408$	−5.75574e34	−0.328238
$409$	6.56278e34	0.362096	0.181048	−	0.983474i	$-0.442051\pi$
$409$	6.56278e34	0.362096	0.181048	+	0.983474i	$0.442051\pi$
$410$	6.15572e34	0.328622
$411$	−2.74730e35	−1.41919
$412$	3.40879e34	0.170407
$413$	2.18286e35	1.05609
$414$	5.06353e34	0.237109
$415$	−1.25191e35	−0.567444
$416$	8.15202e33	0.0357689
$417$	−4.19374e35	−1.78141
$418$	−1.25471e34	−0.0516016
$419$	4.33969e35	1.72810	0.864050	−	0.503405i	$-0.167920\pi$
$419$	4.33969e35	1.72810	0.864050	+	0.503405i	$0.167920\pi$
$420$	6.72811e34	0.259434
$421$	−2.32277e35	−0.867356	−0.433678	−	0.901068i	$-0.642784\pi$
$421$	−2.32277e35	−0.867356	−0.433678	+	0.901068i	$0.642784\pi$
$422$	−3.37779e35	−1.22156
$423$	−2.55100e34	−0.0893545
$424$	−1.37218e35	−0.465556
$425$	−4.21457e34	−0.138517
$426$	−3.05771e35	−0.973569
$427$	−6.89813e34	−0.212792
$428$	1.97330e35	0.589797
$429$	−4.05970e33	−0.0117576
$430$	1.65500e35	0.464486
$431$	4.59488e35	1.24977	0.624887	−	0.780715i	$-0.285145\pi$
$431$	4.59488e35	1.24977	0.624887	+	0.780715i	$0.285145\pi$
$432$	2.58205e34	0.0680667
$433$	−2.35374e35	−0.601413	−0.300706	−	0.953717i	$-0.597222\pi$
$433$	−2.35374e35	−0.601413	−0.300706	+	0.953717i	$0.597222\pi$
$434$	3.90708e35	0.967701
$435$	−8.97945e34	−0.215598
$436$	3.85008e35	0.896194
$437$	3.13880e35	0.708377
$438$	2.67902e35	0.586240
$439$	−6.18421e34	−0.131224	−0.0656120	−	0.997845i	$-0.520900\pi$
$439$	−6.18421e34	−0.131224	−0.0656120	+	0.997845i	$0.520900\pi$
$440$	−3.33089e33	−0.00685409
$441$	−1.00172e35	−0.199906
$442$	−5.11963e34	−0.0990919
$443$	4.85749e34	0.0911930	0.0455965	−	0.998960i	$-0.485481\pi$
$443$	4.85749e34	0.0911930	0.0455965	+	0.998960i	$0.485481\pi$
$444$	3.75417e35	0.683665
$445$	1.83019e35	0.323323
$446$	5.98631e35	1.02598
$447$	9.59882e35	1.59612
$448$	6.70572e34	0.108191
$449$	3.57024e35	0.558949	0.279474	−	0.960153i	$-0.409840\pi$
$449$	3.57024e35	0.558949	0.279474	+	0.960153i	$0.409840\pi$
$450$	−7.41791e34	−0.112697
$451$	−3.05534e34	−0.0450481
$452$	3.88499e35	0.555931
$453$	−1.40944e36	−1.95758
$454$	3.89468e35	0.525071
$455$	5.98454e34	0.0783208
$456$	−6.27971e35	−0.797837
$457$	−1.26417e36	−1.55932	−0.779660	−	0.626203i	$-0.784608\pi$
$457$	−1.26417e36	−1.55932	−0.779660	+	0.626203i	$0.784608\pi$
$458$	1.43744e35	0.172150
$459$	−1.62158e35	−0.188568
$460$	8.33262e34	0.0940916
$461$	8.29211e35	0.909290	0.454645	−	0.890673i	$-0.349766\pi$
$461$	8.29211e35	0.909290	0.454645	+	0.890673i	$0.349766\pi$
$462$	−3.33944e34	−0.0355637
$463$	−1.37072e36	−1.41777	−0.708884	−	0.705325i	$-0.750801\pi$
$463$	−1.37072e36	−1.41777	−0.708884	+	0.705325i	$0.750801\pi$
$464$	−8.94956e34	−0.0899102
$465$	−9.71325e35	−0.947872
$466$	−1.14533e36	−1.08572
$467$	2.06002e35	0.189712	0.0948559	−	0.995491i	$-0.469761\pi$
$467$	2.06002e35	0.189712	0.0948559	+	0.995491i	$0.469761\pi$
$468$	−9.01087e34	−0.0806209
$469$	−1.26132e36	−1.09646
$470$	−4.19797e34	−0.0354583
$471$	6.13394e35	0.503451
$472$	−5.40867e35	−0.431394
$473$	−8.21444e34	−0.0636726
$474$	−1.70464e36	−1.28418
$475$	−4.59825e35	−0.336689
$476$	−4.21133e35	−0.299727
$477$	1.51675e36	1.04934
$478$	9.15790e35	0.615913
$479$	9.78763e35	0.639953	0.319977	−	0.947425i	$-0.396325\pi$
$479$	9.78763e35	0.639953	0.319977	+	0.947425i	$0.396325\pi$
$480$	−1.66708e35	−0.105974
$481$	3.33927e35	0.206392
$482$	2.00850e36	1.20708
$483$	8.35400e35	0.488212
$484$	−8.78144e35	−0.499060
$485$	6.26871e35	0.346469
$486$	−1.69059e36	−0.908760
$487$	1.92059e35	0.100414	0.0502068	−	0.998739i	$-0.484012\pi$
$487$	1.92059e35	0.100414	0.0502068	+	0.998739i	$0.484012\pi$
$488$	1.70921e35	0.0869217
$489$	−2.33990e36	−1.15752
$490$	−1.64845e35	−0.0793283
$491$	3.36034e36	1.57319	0.786597	−	0.617466i	$-0.211841\pi$
$491$	3.36034e36	1.57319	0.786597	+	0.617466i	$0.211841\pi$
$492$	−1.52917e36	−0.696510
$493$	5.62051e35	0.249082
$494$	−5.58570e35	−0.240860
$495$	3.68182e34	0.0154487
$496$	−9.68092e35	−0.395288
$497$	−2.23725e36	−0.889003
$498$	3.10992e36	1.20269
$499$	−4.56833e36	−1.71949	−0.859746	−	0.510722i	$-0.829378\pi$
$499$	−4.56833e36	−1.71949	−0.859746	+	0.510722i	$0.829378\pi$
$500$	−1.22070e35	−0.0447214
$501$	4.33261e36	1.54504
$502$	6.48500e35	0.225118
$503$	3.45540e36	1.16770	0.583850	−	0.811862i	$-0.301546\pi$
$503$	3.45540e36	1.16770	0.583850	+	0.811862i	$0.301546\pi$
$504$	−7.41220e35	−0.243857
$505$	8.62179e35	0.276162
$506$	−4.13583e34	−0.0128982
$507$	4.23363e36	1.28560
$508$	2.53357e36	0.749158
$509$	−1.49420e36	−0.430247	−0.215124	−	0.976587i	$-0.569015\pi$
$509$	−1.49420e36	−0.430247	−0.215124	+	0.976587i	$0.569015\pi$
$510$	1.04696e36	0.293585
$511$	1.96017e36	0.535318
$512$	−1.66153e35	−0.0441942
$513$	−1.76920e36	−0.458346
$514$	−8.97939e35	−0.226592
$515$	−6.20055e35	−0.152417
$516$	−4.11126e36	−0.984473
$517$	2.08363e34	0.00486069
$518$	2.74683e36	0.624281
$519$	1.10546e36	0.244784
$520$	−1.48284e35	−0.0319926
$521$	−3.77861e36	−0.794371	−0.397185	−	0.917738i	$-0.630013\pi$
$521$	−3.77861e36	−0.794371	−0.397185	+	0.917738i	$0.630013\pi$
$522$	9.89245e35	0.202652
$523$	6.89623e36	1.37670	0.688350	−	0.725379i	$-0.258335\pi$
$523$	6.89623e36	1.37670	0.688350	+	0.725379i	$0.258335\pi$
$524$	3.82575e36	0.744293
$525$	−1.22384e36	−0.232045
$526$	−6.24352e36	−1.15378
$527$	6.07982e36	1.09508
$528$	8.27443e34	0.0145271
$529$	−4.80859e36	−0.822936
$530$	2.49598e36	0.416406
$531$	5.97850e36	0.972336
$532$	−4.59471e36	−0.728536
$533$	−1.36017e36	−0.210270
$534$	−4.54647e36	−0.685279
$535$	−3.58941e36	−0.527530
$536$	3.12529e36	0.447884
$537$	−9.26580e36	−1.29488
$538$	4.44943e36	0.606378
$539$	8.18193e34	0.0108745
$540$	−4.69673e35	−0.0608807
$541$	−1.35606e36	−0.171442	−0.0857208	−	0.996319i	$-0.527319\pi$
$541$	−1.35606e36	−0.171442	−0.0857208	+	0.996319i	$0.527319\pi$
$542$	−7.66361e36	−0.945025
$543$	−5.26766e36	−0.633607
$544$	1.04348e36	0.122433
$545$	−7.00325e36	−0.801580
$546$	−1.48665e36	−0.166000
$547$	−7.28023e36	−0.793079	−0.396539	−	0.918018i	$-0.629789\pi$
$547$	−7.28023e36	−0.793079	−0.396539	+	0.918018i	$0.629789\pi$
$548$	4.98067e36	0.529359
$549$	−1.88928e36	−0.195916
$550$	6.05886e34	0.00613048
$551$	6.13217e36	0.605436
$552$	−2.06995e36	−0.199426
$553$	−1.24724e37	−1.17263
$554$	5.94997e35	0.0545925
$555$	−6.82879e36	−0.611489
$556$	7.60297e36	0.664467
$557$	2.29248e37	1.95551	0.977757	−	0.209740i	$-0.0672618\pi$
$557$	2.29248e37	1.95551	0.977757	+	0.209740i	$0.0672618\pi$
$558$	1.07009e37	0.890957
$559$	−3.65689e36	−0.297203
$560$	−1.21976e36	−0.0967692
$561$	−5.19651e35	−0.0402451
$562$	6.79324e36	0.513614
$563$	−9.81459e36	−0.724450	−0.362225	−	0.932091i	$-0.617983\pi$
$563$	−9.81459e36	−0.724450	−0.362225	+	0.932091i	$0.617983\pi$
$564$	1.04284e36	0.0751535
$565$	−7.06676e36	−0.497240
$566$	6.88934e36	0.473321
$567$	−1.49902e37	−1.00562
$568$	5.54343e36	0.363142
$569$	2.24316e37	1.43497	0.717487	−	0.696572i	$-0.245292\pi$
$569$	2.24316e37	1.43497	0.717487	+	0.696572i	$0.245292\pi$
$570$	1.14227e37	0.713607
$571$	−7.07828e34	−0.00431857	−0.00215929	−	0.999998i	$-0.500687\pi$
$571$	−7.07828e34	−0.00431857	−0.00215929	+	0.999998i	$0.500687\pi$
$572$	7.35997e34	0.00438561
$573$	−2.96008e37	−1.72272
$574$	−1.11886e37	−0.636010
$575$	−1.51569e36	−0.0841580
$576$	1.83659e36	0.0996111
$577$	1.36809e37	0.724837	0.362418	−	0.932016i	$-0.381951\pi$
$577$	1.36809e37	0.724837	0.362418	+	0.932016i	$0.381951\pi$
$578$	7.10863e36	0.367926
$579$	−1.49940e37	−0.758153
$580$	1.62792e36	0.0804182
$581$	2.27545e37	1.09822
$582$	−1.55724e37	−0.734336
$583$	−1.23886e36	−0.0570817
$584$	−4.85689e36	−0.218668
$585$	1.63907e36	0.0721095
$586$	−1.57043e37	−0.675150
$587$	1.21248e37	0.509402	0.254701	−	0.967020i	$-0.418023\pi$
$587$	1.21248e37	0.509402	0.254701	+	0.967020i	$0.418023\pi$
$588$	4.09499e36	0.168135
$589$	6.63329e37	2.66178
$590$	9.83832e36	0.385850
$591$	−1.36535e37	−0.523376
$592$	−6.80606e36	−0.255007
$593$	−6.58205e36	−0.241059	−0.120529	−	0.992710i	$-0.538459\pi$
$593$	−6.58205e36	−0.241059	−0.120529	+	0.992710i	$0.538459\pi$
$594$	2.33118e35	0.00834563
$595$	7.66036e36	0.268084
$596$	−1.74020e37	−0.595355
$597$	1.94002e37	0.648862
$598$	−1.84118e36	−0.0602047
$599$	1.55149e37	0.496005	0.248003	−	0.968759i	$-0.420226\pi$
$599$	1.55149e37	0.496005	0.248003	+	0.968759i	$0.420226\pi$
$600$	3.03241e36	0.0947863
$601$	5.61441e36	0.171593	0.0857964	−	0.996313i	$-0.472657\pi$
$601$	5.61441e36	0.171593	0.0857964	+	0.996313i	$0.472657\pi$
$602$	−3.00810e37	−0.898959
$603$	−3.45455e37	−1.00950
$604$	2.55522e37	0.730179
$605$	1.59733e37	0.446373
$606$	−2.14178e37	−0.585321
$607$	−2.30412e36	−0.0615825	−0.0307913	−	0.999526i	$-0.509803\pi$
$607$	−2.30412e36	−0.0615825	−0.0307913	+	0.999526i	$0.509803\pi$
$608$	1.13847e37	0.297594
$609$	1.63209e37	0.417265
$610$	−3.10904e36	−0.0777451
$611$	9.27587e35	0.0226881
$612$	−1.15341e37	−0.275957
$613$	4.94431e37	1.15715	0.578575	−	0.815629i	$-0.303609\pi$
$613$	4.94431e37	1.15715	0.578575	+	0.815629i	$0.303609\pi$
$614$	−1.27028e36	−0.0290821
$615$	2.78155e37	0.622977
$616$	6.05419e35	0.0132653
$617$	1.46372e37	0.313768	0.156884	−	0.987617i	$-0.449855\pi$
$617$	1.46372e37	0.313768	0.156884	+	0.987617i	$0.449855\pi$
$618$	1.54031e37	0.323045
$619$	−5.85835e37	−1.20213	−0.601065	−	0.799200i	$-0.705257\pi$
$619$	−5.85835e37	−1.20213	−0.601065	+	0.799200i	$0.705257\pi$
$620$	1.76095e37	0.353557
$621$	−5.83172e36	−0.114567
$622$	−2.75825e37	−0.530228
$623$	−3.32654e37	−0.625754
$624$	3.68360e36	0.0678079
$625$	2.22045e36	0.0400000
$626$	−7.96369e37	−1.40398
$627$	−5.66958e36	−0.0978226
$628$	−1.11204e37	−0.187787
$629$	4.27435e37	0.706458
$630$	1.34827e37	0.218112
$631$	4.50840e36	0.0713881	0.0356941	−	0.999363i	$-0.488636\pi$
$631$	4.50840e36	0.0713881	0.0356941	+	0.999363i	$0.488636\pi$
$632$	3.09041e37	0.479000
$633$	−1.52630e38	−2.31574
$634$	−3.54729e37	−0.526856
$635$	−4.60854e37	−0.670067
$636$	−6.20039e37	−0.882567
$637$	3.64242e36	0.0507584
$638$	−8.08003e35	−0.0110239
$639$	−6.12746e37	−0.818500
$640$	3.02231e36	0.0395285
$641$	−1.41328e38	−1.80986	−0.904929	−	0.425563i	$-0.860076\pi$
$641$	−1.41328e38	−1.80986	−0.904929	+	0.425563i	$0.860076\pi$
$642$	8.91663e37	1.11809
$643$	−4.71217e37	−0.578592	−0.289296	−	0.957240i	$-0.593421\pi$
$643$	−4.71217e37	−0.578592	−0.289296	+	0.957240i	$0.593421\pi$
$644$	−1.51453e37	−0.182103
$645$	7.47833e37	0.880539
$646$	−7.14983e37	−0.824436
$647$	−3.72863e37	−0.421057	−0.210529	−	0.977588i	$-0.567519\pi$
$647$	−3.72863e37	−0.421057	−0.210529	+	0.977588i	$0.567519\pi$
$648$	3.71424e37	0.410778
$649$	−4.88317e36	−0.0528930
$650$	2.69728e36	0.0286151
$651$	1.76547e38	1.83450
$652$	4.24208e37	0.431754
$653$	5.32316e37	0.530691	0.265345	−	0.964153i	$-0.414514\pi$
$653$	5.32316e37	0.530691	0.265345	+	0.964153i	$0.414514\pi$
$654$	1.73971e38	1.69894
$655$	−6.95899e37	−0.665716
$656$	2.77229e37	0.259799
$657$	5.36859e37	0.492865
$658$	7.63019e36	0.0686255
$659$	1.58587e38	1.39738	0.698692	−	0.715423i	$-0.253766\pi$
$659$	1.58587e38	1.39738	0.698692	+	0.715423i	$0.253766\pi$
$660$	−1.50511e36	−0.0129935
$661$	1.90328e38	1.60984	0.804922	−	0.593380i	$-0.202207\pi$
$661$	1.90328e38	1.60984	0.804922	+	0.593380i	$0.202207\pi$
$662$	−3.32201e37	−0.275307
$663$	−2.31338e37	−0.187851
$664$	−5.63809e37	−0.448604
$665$	8.35772e37	0.651622
$666$	7.52312e37	0.574772
$667$	2.02131e37	0.151333
$668$	−7.85474e37	−0.576301
$669$	2.70500e38	1.94498
$670$	−5.68487e37	−0.400599
$671$	1.54314e36	0.0106574
$672$	3.03007e37	0.205101
$673$	−2.51031e38	−1.66542	−0.832709	−	0.553711i	$-0.813211\pi$
$673$	−2.51031e38	−1.66542	−0.832709	+	0.553711i	$0.813211\pi$
$674$	8.39183e37	0.545693
$675$	8.54329e36	0.0544533
$676$	−7.67531e37	−0.479529
$677$	−2.63747e38	−1.61525	−0.807627	−	0.589694i	$-0.799248\pi$
$677$	−2.63747e38	−1.61525	−0.807627	+	0.589694i	$0.799248\pi$
$678$	1.75549e38	1.05389
$679$	−1.13939e38	−0.670550
$680$	−1.89808e37	−0.109507
$681$	1.75987e38	0.995390
$682$	−8.74033e36	−0.0484662
$683$	−1.50962e38	−0.820707	−0.410353	−	0.911927i	$-0.634595\pi$
$683$	−1.50962e38	−0.820707	−0.410353	+	0.911927i	$0.634595\pi$
$684$	−1.25842e38	−0.670759
$685$	−9.05979e37	−0.473473
$686$	1.49400e38	0.765553
$687$	6.49529e37	0.326349
$688$	7.45344e37	0.367209
$689$	−5.51514e37	−0.266439
$690$	3.76521e37	0.178372
$691$	5.64059e36	0.0262042	0.0131021	−	0.999914i	$-0.495829\pi$
$691$	5.64059e36	0.0262042	0.0131021	+	0.999914i	$0.495829\pi$
$692$	−2.00412e37	−0.0913045
$693$	−6.69203e36	−0.0298992
$694$	1.13812e38	0.498695
$695$	−1.38297e38	−0.594318
$696$	−4.04398e37	−0.170445
$697$	−1.74105e38	−0.719730
$698$	1.07320e38	0.435144
$699$	−5.17531e38	−2.05823
$700$	2.21874e37	0.0865530
$701$	−1.95153e38	−0.746761	−0.373381	−	0.927678i	$-0.621801\pi$
$701$	−1.95153e38	−0.746761	−0.373381	+	0.927678i	$0.621801\pi$
$702$	1.03779e37	0.0389547
$703$	4.66346e38	1.71716
$704$	−1.50010e36	−0.00541863
$705$	−1.89691e37	−0.0672193
$706$	1.62309e38	0.564261
$707$	−1.56709e38	−0.534479
$708$	−2.44398e38	−0.817804
$709$	3.20482e38	1.05215	0.526077	−	0.850437i	$-0.323662\pi$
$709$	3.20482e38	1.05215	0.526077	+	0.850437i	$0.323662\pi$
$710$	−1.00834e38	−0.324804
$711$	−3.41600e38	−1.07964
$712$	8.24245e37	0.255609
$713$	2.18649e38	0.665334
$714$	−1.90295e38	−0.568200
$715$	−1.33877e36	−0.00392261
$716$	1.67983e38	0.482992
$717$	4.13812e38	1.16760
$718$	3.75185e36	0.0103888
$719$	−6.47800e38	−1.76036	−0.880179	−	0.474642i	$-0.842578\pi$
$719$	−6.47800e38	−1.76036	−0.880179	+	0.474642i	$0.842578\pi$
$720$	−3.34073e37	−0.0890949
$721$	1.12700e38	0.294985
$722$	−5.04816e38	−1.29682
$723$	9.07570e38	2.28830
$724$	9.54992e37	0.236336
$725$	−2.96116e37	−0.0719282
$726$	−3.96801e38	−0.946082
$727$	2.86591e37	0.0670729	0.0335365	−	0.999437i	$-0.489323\pi$
$727$	2.86591e37	0.0670729	0.0335365	+	0.999437i	$0.489323\pi$
$728$	2.69520e37	0.0619180
$729$	−2.48719e38	−0.560903
$730$	8.83463e37	0.195582
$731$	−4.68092e38	−1.01729
$732$	7.72331e37	0.164780
$733$	3.01689e38	0.631910	0.315955	−	0.948774i	$-0.397675\pi$
$733$	3.01689e38	0.631910	0.315955	+	0.948774i	$0.397675\pi$
$734$	−4.64541e38	−0.955272
$735$	−7.44874e37	−0.150385
$736$	3.75268e37	0.0743859
$737$	2.82164e37	0.0549149
$738$	−3.06436e38	−0.585571
$739$	−7.89496e37	−0.148132	−0.0740662	−	0.997253i	$-0.523598\pi$
$739$	−7.89496e37	−0.148132	−0.0740662	+	0.997253i	$0.523598\pi$
$740$	1.23802e38	0.228086
$741$	−2.52398e38	−0.456604
$742$	−4.53667e38	−0.805906
$743$	5.54426e38	0.967152	0.483576	−	0.875302i	$-0.339338\pi$
$743$	5.54426e38	0.967152	0.483576	+	0.875302i	$0.339338\pi$
$744$	−4.37446e38	−0.749358
$745$	3.16541e38	0.532501
$746$	7.06808e38	1.16769
$747$	6.23209e38	1.01113
$748$	9.42094e36	0.0150115
$749$	6.52407e38	1.02097
$750$	−5.51592e37	−0.0847795
$751$	7.27919e38	1.09886	0.549432	−	0.835538i	$-0.314844\pi$
$751$	7.27919e38	1.09886	0.549432	+	0.835538i	$0.314844\pi$
$752$	−1.89060e37	−0.0280323
$753$	2.93033e38	0.426761
$754$	−3.59706e37	−0.0514558
$755$	−4.64792e38	−0.653092
$756$	8.53671e37	0.117827
$757$	6.83088e37	0.0926151	0.0463076	−	0.998927i	$-0.485255\pi$
$757$	6.83088e37	0.0926151	0.0463076	+	0.998927i	$0.485255\pi$
$758$	−5.25559e38	−0.699983
$759$	−1.86883e37	−0.0244515
$760$	−2.07087e38	−0.266176
$761$	−6.08504e38	−0.768371	−0.384185	−	0.923256i	$-0.625518\pi$
$761$	−6.08504e38	−0.768371	−0.384185	+	0.923256i	$0.625518\pi$
$762$	1.14483e39	1.42020
$763$	1.27290e39	1.55137
$764$	5.36643e38	0.642577
$765$	2.09805e38	0.246823
$766$	6.87969e38	0.795207
$767$	−2.17388e38	−0.246887
$768$	−7.50788e37	−0.0837801
$769$	2.25503e38	0.247256	0.123628	−	0.992329i	$-0.460547\pi$
$769$	2.25503e38	0.247256	0.123628	+	0.992329i	$0.460547\pi$
$770$	−1.10125e37	−0.0118648
$771$	−4.05746e38	−0.429557
$772$	2.71832e38	0.282792
$773$	−1.63456e39	−1.67101	−0.835504	−	0.549484i	$-0.814824\pi$
$773$	−1.63456e39	−1.67101	−0.835504	+	0.549484i	$0.814824\pi$
$774$	−8.23870e38	−0.827667
$775$	−3.20315e38	−0.316231
$776$	2.82317e38	0.273908
$777$	1.24119e39	1.18347
$778$	−6.07830e37	−0.0569584
$779$	−1.89955e39	−1.74943
$780$	−6.70043e37	−0.0606493
$781$	5.00483e37	0.0445247
$782$	−2.35676e38	−0.206074
$783$	−1.13932e38	−0.0979182
$784$	−7.42395e37	−0.0627145
$785$	2.02279e38	0.167962
$786$	1.72872e39	1.41098
$787$	2.62879e38	0.210910	0.105455	−	0.994424i	$-0.466370\pi$
$787$	2.62879e38	0.210910	0.105455	+	0.994424i	$0.466370\pi$
$788$	2.47529e38	0.195219
$789$	−2.82122e39	−2.18724
$790$	−5.62142e38	−0.428430
$791$	1.28445e39	0.962350
$792$	1.65814e37	0.0122133
$793$	6.86975e37	0.0497454
$794$	2.39931e38	0.170808
$795$	1.12784e39	0.789392
$796$	−3.51713e38	−0.242026
$797$	−2.10383e39	−1.42339	−0.711693	−	0.702490i	$-0.752071\pi$
$797$	−2.10383e39	−1.42339	−0.711693	+	0.702490i	$0.752071\pi$
$798$	−2.07618e39	−1.38110
$799$	1.18733e38	0.0776590
$800$	−5.49756e37	−0.0353553
$801$	−9.11084e38	−0.576129
$802$	7.93321e38	0.493281
$803$	−4.38500e37	−0.0268108
$804$	1.41220e39	0.849065
$805$	2.75491e38	0.162878
$806$	−3.89101e38	−0.226224
$807$	2.01053e39	1.14953
$808$	3.88291e38	0.218325
$809$	3.20140e39	1.77025	0.885125	−	0.465354i	$-0.154073\pi$
$809$	3.20140e39	1.77025	0.885125	+	0.465354i	$0.154073\pi$
$810$	−6.75617e38	−0.367411
$811$	6.63176e38	0.354689	0.177344	−	0.984149i	$-0.443249\pi$
$811$	6.63176e38	0.354689	0.177344	+	0.984149i	$0.443249\pi$
$812$	−2.95888e38	−0.155640
$813$	−3.46291e39	−1.79151
$814$	−6.14479e37	−0.0312664
$815$	−7.71631e38	−0.386173
$816$	4.71510e38	0.232099
$817$	−5.10704e39	−2.47270
$818$	−5.37623e38	−0.256040
$819$	−2.97915e38	−0.139560
$820$	−5.04276e38	−0.232371
$821$	−3.63383e39	−1.64715	−0.823573	−	0.567211i	$-0.808022\pi$
$821$	−3.63383e39	−1.64715	−0.823573	+	0.567211i	$0.808022\pi$
$822$	2.25059e39	1.00352
$823$	3.19652e39	1.40210	0.701051	−	0.713111i	$-0.252714\pi$
$823$	3.19652e39	1.40210	0.701051	+	0.713111i	$0.252714\pi$
$824$	−2.79248e38	−0.120496
$825$	2.73778e37	0.0116217
$826$	−1.78820e39	−0.746768
$827$	−2.85534e39	−1.17310	−0.586549	−	0.809914i	$-0.699514\pi$
$827$	−2.85534e39	−1.17310	−0.586549	+	0.809914i	$0.699514\pi$
$828$	−4.14804e38	−0.167662
$829$	2.36694e39	0.941240	0.470620	−	0.882336i	$-0.344030\pi$
$829$	2.36694e39	0.941240	0.470620	+	0.882336i	$0.344030\pi$
$830$	1.02556e39	0.401243
$831$	2.68858e38	0.103492
$832$	−6.67813e37	−0.0252924
$833$	4.66239e38	0.173741
$834$	3.43551e39	1.25965
$835$	1.42877e39	0.515459
$836$	1.02786e38	0.0364879
$837$	−1.23243e39	−0.430495
$838$	−3.55507e39	−1.22195
$839$	2.29389e39	0.775866	0.387933	−	0.921688i	$-0.373189\pi$
$839$	2.29389e39	0.775866	0.387933	+	0.921688i	$0.373189\pi$
$840$	−5.51167e38	−0.183448
$841$	−2.65824e39	−0.870658
$842$	1.90281e39	0.613313
$843$	3.06962e39	0.973672
$844$	2.76708e39	0.863772
$845$	1.39613e39	0.428904
$846$	2.08978e38	0.0631831
$847$	−2.90330e39	−0.863903
$848$	1.12409e39	0.329198
$849$	3.11304e39	0.897287
$850$	3.45258e38	0.0979463
$851$	1.53719e39	0.429219
$852$	2.50488e39	0.688417
$853$	1.11980e39	0.302919	0.151460	−	0.988463i	$-0.451603\pi$
$853$	1.11980e39	0.302919	0.151460	+	0.988463i	$0.451603\pi$
$854$	5.65095e38	0.150467
$855$	2.28904e39	0.599945
$856$	−1.61653e39	−0.417049
$857$	4.56953e39	1.16046	0.580231	−	0.814452i	$-0.302962\pi$
$857$	4.56953e39	1.16046	0.580231	+	0.814452i	$0.302962\pi$
$858$	3.32570e37	0.00831391
$859$	3.49246e39	0.859455	0.429728	−	0.902959i	$-0.358610\pi$
$859$	3.49246e39	0.859455	0.429728	+	0.902959i	$0.358610\pi$
$860$	−1.35577e39	−0.328441
$861$	−5.05571e39	−1.20570
$862$	−3.76413e39	−0.883723
$863$	7.89699e39	1.82522	0.912612	−	0.408827i	$-0.134062\pi$
$863$	7.89699e39	1.82522	0.912612	+	0.408827i	$0.134062\pi$
$864$	−2.11522e38	−0.0481304
$865$	3.64548e38	0.0816652
$866$	1.92819e39	0.425263
$867$	3.21213e39	0.697487
$868$	−3.20068e39	−0.684268
$869$	2.79015e38	0.0587300
$870$	7.35596e38	0.152451
$871$	1.25613e39	0.256325
$872$	−3.15398e39	−0.633705
$873$	−3.12061e39	−0.617372
$874$	−2.57131e39	−0.500898
$875$	−4.03586e38	−0.0774153
$876$	−2.19465e39	−0.414534
$877$	−2.35733e39	−0.438456	−0.219228	−	0.975674i	$-0.570354\pi$
$877$	−2.35733e39	−0.438456	−0.219228	+	0.975674i	$0.570354\pi$
$878$	5.06610e38	0.0927894
$879$	−7.09620e39	−1.27990
$880$	2.72867e37	0.00484657
$881$	4.52972e39	0.792312	0.396156	−	0.918183i	$-0.370344\pi$
$881$	4.52972e39	0.792312	0.396156	+	0.918183i	$0.370344\pi$
$882$	8.20610e38	0.141355
$883$	−9.79510e39	−1.66165	−0.830824	−	0.556535i	$-0.812131\pi$
$883$	−9.79510e39	−1.66165	−0.830824	+	0.556535i	$0.812131\pi$
$884$	4.19400e38	0.0700686
$885$	4.44558e39	0.731466
$886$	−3.97926e38	−0.0644832
$887$	−9.29591e39	−1.48362	−0.741811	−	0.670609i	$-0.766033\pi$
$887$	−9.29591e39	−1.48362	−0.741811	+	0.670609i	$0.766033\pi$
$888$	−3.07541e39	−0.483424
$889$	8.37643e39	1.29684
$890$	−1.49929e39	−0.228624
$891$	3.35337e38	0.0503654
$892$	−4.90399e39	−0.725477
$893$	1.29542e39	0.188763
$894$	−7.86336e39	−1.12863
$895$	−3.05559e39	−0.432001
$896$	−5.49332e38	−0.0765028
$897$	−8.31963e38	−0.114132
$898$	−2.92474e39	−0.395236
$899$	4.27168e39	0.568647
$900$	6.07675e38	0.0796889
$901$	−7.05952e39	−0.911991
$902$	2.50294e38	0.0318538
$903$	−1.35925e40	−1.70418
$904$	−3.18258e39	−0.393103
$905$	−1.73712e39	−0.211385
$906$	1.15461e40	1.38422
$907$	1.36999e40	1.61815	0.809077	−	0.587703i	$-0.199967\pi$
$907$	1.36999e40	1.61815	0.809077	+	0.587703i	$0.199967\pi$
$908$	−3.19052e39	−0.371281
$909$	−4.29199e39	−0.492092
$910$	−4.90254e38	−0.0553812
$911$	−3.75210e39	−0.417615	−0.208807	−	0.977957i	$-0.566958\pi$
$911$	−3.75210e39	−0.417615	−0.208807	+	0.977957i	$0.566958\pi$
$912$	5.14434e39	0.564156
$913$	−5.09029e38	−0.0550031
$914$	1.03560e40	1.10261
$915$	−1.40486e39	−0.147383
$916$	−1.17755e39	−0.121728
$917$	1.26486e40	1.28842
$918$	1.32840e39	0.133338
$919$	9.82750e39	0.972039	0.486019	−	0.873948i	$-0.338448\pi$
$919$	9.82750e39	0.972039	0.486019	+	0.873948i	$0.338448\pi$
$920$	−6.82608e38	−0.0665328
$921$	−5.73993e38	−0.0551318
$922$	−6.79290e39	−0.642965
$923$	2.22805e39	0.207827
$924$	2.73567e38	0.0251474
$925$	−2.25194e39	−0.204006
$926$	1.12289e40	1.00251
$927$	3.08668e39	0.271591
$928$	7.33148e38	0.0635761
$929$	−3.06657e39	−0.262084	−0.131042	−	0.991377i	$-0.541832\pi$
$929$	−3.06657e39	−0.262084	−0.131042	+	0.991377i	$0.541832\pi$
$930$	7.95709e39	0.670246
$931$	5.08683e39	0.422306
$932$	9.38251e39	0.767722
$933$	−1.24635e40	−1.00517
$934$	−1.68757e39	−0.134146
$935$	−1.71366e38	−0.0134267
$936$	7.38171e38	0.0570076
$937$	5.24978e39	0.399629	0.199814	−	0.979834i	$-0.435966\pi$
$937$	5.24978e39	0.399629	0.199814	+	0.979834i	$0.435966\pi$
$938$	1.03327e40	0.775314
$939$	−3.59850e40	−2.66156
$940$	3.43898e38	0.0250728
$941$	4.32653e39	0.310942	0.155471	−	0.987840i	$-0.450310\pi$
$941$	4.32653e39	0.310942	0.155471	+	0.987840i	$0.450310\pi$
$942$	−5.02492e39	−0.355994
$943$	−6.26138e39	−0.437283
$944$	4.43078e39	0.305041
$945$	−1.55282e39	−0.105388
$946$	6.72927e38	0.0450233
$947$	1.94230e39	0.128113	0.0640564	−	0.997946i	$-0.479596\pi$
$947$	1.94230e39	0.128113	0.0640564	+	0.997946i	$0.479596\pi$
$948$	1.39644e40	0.908052
$949$	−1.95211e39	−0.125144
$950$	3.76689e39	0.238075
$951$	−1.60289e40	−0.998775
$952$	3.44992e39	0.211939
$953$	3.12687e40	1.89389	0.946946	−	0.321393i	$-0.104151\pi$
$953$	3.12687e40	1.89389	0.946946	+	0.321393i	$0.104151\pi$
$954$	−1.24252e40	−0.741993
$955$	−9.76147e39	−0.574738
$956$	−7.50215e39	−0.435516
$957$	−3.65107e38	−0.0208982
$958$	−8.01803e39	−0.452515
$959$	1.64670e40	0.916353
$960$	1.36567e39	0.0749352
$961$	2.77249e40	1.50004
$962$	−2.73553e39	−0.145941
$963$	1.78684e40	0.940005
$964$	−1.64537e40	−0.853538
$965$	−4.94459e39	−0.252937
$966$	−6.84360e39	−0.345218
$967$	8.16162e39	0.405994	0.202997	−	0.979179i	$-0.434932\pi$
$967$	8.16162e39	0.405994	0.202997	+	0.979179i	$0.434932\pi$
$968$	7.19375e39	0.352889
$969$	−3.23075e40	−1.56290
$970$	−5.13532e39	−0.244991
$971$	−2.55969e40	−1.20428	−0.602140	−	0.798391i	$-0.705685\pi$
$971$	−2.55969e40	−1.20428	−0.602140	+	0.798391i	$0.705685\pi$
$972$	1.38493e40	0.642590
$973$	2.51367e40	1.15023
$974$	−1.57334e39	−0.0710032
$975$	1.21880e39	0.0542464
$976$	−1.40019e39	−0.0614629
$977$	−1.33514e40	−0.578028	−0.289014	−	0.957325i	$-0.593327\pi$
$977$	−1.33514e40	−0.578028	−0.289014	+	0.957325i	$0.593327\pi$
$978$	1.91684e40	0.818488
$979$	7.44162e38	0.0313402
$980$	1.35041e39	0.0560936
$981$	3.48627e40	1.42833
$982$	−2.75279e40	−1.11242
$983$	1.76204e40	0.702333	0.351167	−	0.936313i	$-0.385785\pi$
$983$	1.76204e40	0.702333	0.351167	+	0.936313i	$0.385785\pi$
$984$	1.25270e40	0.492507
$985$	−4.50253e39	−0.174610
$986$	−4.60432e39	−0.176128
$987$	3.44780e39	0.130095
$988$	4.57581e39	0.170313
$989$	−1.68340e40	−0.618071
$990$	−3.01615e38	−0.0109239
$991$	−7.00587e39	−0.250304	−0.125152	−	0.992138i	$-0.539942\pi$
$991$	−7.00587e39	−0.250304	−0.125152	+	0.992138i	$0.539942\pi$
$992$	7.93061e39	0.279511
$993$	−1.50109e40	−0.521907
$994$	1.83275e40	0.628620
$995$	6.39762e39	0.216475
$996$	−2.54765e40	−0.850430
$997$	−1.98983e40	−0.655287	−0.327644	−	0.944801i	$-0.606255\pi$
$997$	−1.98983e40	−0.655287	−0.327644	+	0.944801i	$0.606255\pi$
$998$	3.74238e40	1.21586
$999$	−8.66446e39	−0.277720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.28.a.b.1.1	✓	2
5.2	odd	4		50.28.b.d.49.2		4
5.3	odd	4		50.28.b.d.49.3		4
5.4	even	2		50.28.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.28.a.b.1.1	✓	2	1.1	even	1	trivial
50.28.a.d.1.2		2	5.4	even	2
50.28.b.d.49.2		4	5.2	odd	4
50.28.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:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-8192.00 q^{2} -3.70167e6 q^{3} +6.71089e7 q^{4} -1.22070e9 q^{5} +3.03241e10 q^{6} +2.21874e11 q^{7} -5.49756e11 q^{8} +6.07675e12 q^{9} +1.00000e13 q^{10} -4.96342e12 q^{11} -2.48415e14 q^{12} -2.20961e14 q^{13} -1.81759e15 q^{14} +4.51864e15 q^{15} +4.50360e15 q^{16} -2.82835e16 q^{17} -4.97808e16 q^{18} -3.08583e17 q^{19} -8.19200e16 q^{20} -8.21302e17 q^{21} +4.06603e16 q^{22} -1.01717e18 q^{23} +2.03501e18 q^{24} +1.49012e18 q^{25} +1.81011e18 q^{26} +5.73331e18 q^{27} +1.48897e19 q^{28} -1.98720e19 q^{29} -3.70167e19 q^{30} -2.14960e20 q^{31} -3.68935e19 q^{32} +1.83729e19 q^{33} +2.31699e20 q^{34} -2.70842e20 q^{35} +4.07804e20 q^{36} -1.51125e21 q^{37} +2.52791e21 q^{38} +8.17924e20 q^{39} +6.71089e20 q^{40} +6.15572e21 q^{41} +6.72811e21 q^{42} +1.65500e22 q^{43} -3.33089e20 q^{44} -7.41791e21 q^{45} +8.33262e21 q^{46} -4.19797e21 q^{47} -1.66708e22 q^{48} -1.64845e22 q^{49} -1.22070e22 q^{50} +1.04696e23 q^{51} -1.48284e22 q^{52} +2.49598e23 q^{53} -4.69673e22 q^{54} +6.05886e21 q^{55} -1.21976e23 q^{56} +1.14227e24 q^{57} +1.62792e23 q^{58} +9.83832e23 q^{59} +3.03241e23 q^{60} -3.10904e23 q^{61} +1.76095e24 q^{62} +1.34827e24 q^{63} +3.02231e23 q^{64} +2.69728e23 q^{65} -1.50511e23 q^{66} -5.68487e24 q^{67} -1.89808e24 q^{68} +3.76521e24 q^{69} +2.21874e24 q^{70} -1.00834e25 q^{71} -3.34073e24 q^{72} +8.83463e24 q^{73} +1.23802e25 q^{74} -5.51592e24 q^{75} -2.07087e25 q^{76} -1.10125e24 q^{77} -6.70043e24 q^{78} -5.62142e25 q^{79} -5.49756e24 q^{80} -6.75617e25 q^{81} -5.04276e25 q^{82} +1.02556e26 q^{83} -5.51167e25 q^{84} +3.45258e25 q^{85} -1.35577e26 q^{86} +7.35596e25 q^{87} +2.72867e24 q^{88} -1.49929e26 q^{89} +6.07675e25 q^{90} -4.90254e25 q^{91} -6.82608e25 q^{92} +7.95709e26 q^{93} +3.43898e25 q^{94} +3.76689e26 q^{95} +1.36567e26 q^{96} -5.13532e26 q^{97} +1.35041e26 q^{98} -3.01615e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16384 q^{2} - 2245644 q^{3} + 134217728 q^{4} - 2441406250 q^{5} + 18396315648 q^{6} - 120196732292 q^{7} - 1099511627776 q^{8} + 571163616594 q^{9} + 20000000000000 q^{10} + 7112122732704 q^{11}+ \cdots - 96\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 16384 * q^2 - 2245644 * q^3 + 134217728 * q^4 - 2441406250 * q^5 + 18396315648 * q^6 - 120196732292 * q^7 - 1099511627776 * q^8 + 571163616594 * q^9 + 20000000000000 * q^10 + 7112122732704 * q^11 - 150702617788416 * q^12 - 323114990355404 * q^13 + 984651630936064 * q^14 + 2741264648437500 * q^15 + 9007199254740992 * q^16 - 11949781720794252 * q^17 - 4678972347138048 * q^18 - 310800626187534200 * q^19 - 163840000000000000 * q^20 - 1319365315134326376 * q^21 - 58262509426311168 * q^22 - 1207992822578557644 * q^23 + 1234555844922703872 * q^24 + 2980232238769531250 * q^25 + 2646958000991469568 * q^26 - 13386024338103046440 * q^27 - 8066266160628236288 * q^28 - 85089627076663724580 * q^29 - 22456440000000000000 * q^30 - 169891626304914480056 * q^31 - 73786976294838206464 * q^32 + 35955214564003682112 * q^33 + 97892611856746512384 * q^34 + 146724526723632812500 * q^35 + 38330141467754889216 * q^36 + 1001687425876018532308 * q^37 + 2546078729728280166400 * q^38 + 669184707607358092488 * q^39 + 1342177280000000000000 * q^40 + 6829708525832119000044 * q^41 + 10808240661580401672192 * q^42 + 15331910221739375128036 * q^43 + 477286477220341088256 * q^44 - 697221211662597656250 * q^45 + 9895877202563544219648 * q^46 + 44654607958183509227628 * q^47 - 10113481481606790119424 * q^48 + 34815266426190611168346 * q^49 - 24414062500000000000000 * q^50 + 128478598882379942153544 * q^51 - 21683879944122118701056 * q^52 + 259350970067880627435396 * q^53 + 109658311377740156436480 * q^54 - 8681790445195312500000 * q^55 + 66078852387866511671296 * q^56 + 1139044611805451608251600 * q^57 + 697054225012029231759360 * q^58 + 2082093442621301023169640 * q^59 + 183963156480000000000000 * q^60 + 677925769536334246319284 * q^61 + 1391752202689859420618752 * q^62 + 3231569874371732206566876 * q^63 + 604462909807314587353088 * q^64 + 394427478461186523437500 * q^65 - 294545117708318163861504 * q^66 + 2453617552336948143390028 * q^67 - 801936276330467429449728 * q^68 + 3487358239126020846890568 * q^69 - 1201967322920000000000000 * q^70 - 23890193584108132090228776 * q^71 - 314000518903848052457472 * q^72 - 13919420706136886544146204 * q^73 - 8205823392776343816667136 * q^74 - 3346270322799682617187500 * q^75 - 20857476953934071123148800 * q^76 - 5231935501660614540408384 * q^77 - 5481961124719477493661696 * q^78 - 53659327270981104663051920 * q^79 - 10995116277760000000000000 * q^80 - 53416489016311609709962998 * q^81 - 55948972243616718848360448 * q^82 + 5756571261014435461903716 * q^83 - 88541107499666650498596864 * q^84 + 14587135889641420898437500 * q^85 - 125599008536488961048870912 * q^86 - 21398789661957929503788840 * q^87 - 3909930821389034194993152 * q^88 + 174438127411287409220344020 * q^89 + 5711636165940000000000000 * q^90 - 14081455302088161819283816 * q^91 - 81067026043400554247356416 * q^92 + 861329117078544091150519632 * q^93 - 365810548393439307592728576 * q^94 + 379395295639079833984375000 * q^95 + 82849640297322824658321408 * q^96 - 21732067184289340167295292 * q^97 - 285206662563353486691090432 * q^98 - 96644441211111069636758112 * q^99

Introduction

L-functions

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