LMFDB - Embedded newform 8.4.b.a.5.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [8,4,Mod(5,8)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	8.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.472015280046$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-7}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 2 $ x^2 - x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.1
Root			$0.500000 + 1.32288i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.4.b.a.5.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 2.64575i) q^{2} +5.29150i q^{3} +(-6.00000 + 5.29150i) q^{4} -10.5830i q^{5} +(14.0000 - 5.29150i) q^{6} -8.00000 q^{7} +(20.0000 + 10.5830i) q^{8} -1.00000 q^{9} +(-28.0000 + 10.5830i) q^{10} -15.8745i q^{11} +(-28.0000 - 31.7490i) q^{12} +52.9150i q^{13} +(8.00000 + 21.1660i) q^{14} +56.0000 q^{15} +(8.00000 - 63.4980i) q^{16} -14.0000 q^{17} +(1.00000 + 2.64575i) q^{18} -37.0405i q^{19} +(56.0000 + 63.4980i) q^{20} -42.3320i q^{21} +(-42.0000 + 15.8745i) q^{22} -152.000 q^{23} +(-56.0000 + 105.830i) q^{24} +13.0000 q^{25} +(140.000 - 52.9150i) q^{26} +137.579i q^{27} +(48.0000 - 42.3320i) q^{28} -158.745i q^{29} +(-56.0000 - 148.162i) q^{30} +224.000 q^{31} +(-176.000 + 42.3320i) q^{32} +84.0000 q^{33} +(14.0000 + 37.0405i) q^{34} +84.6640i q^{35} +(6.00000 - 5.29150i) q^{36} +243.409i q^{37} +(-98.0000 + 37.0405i) q^{38} -280.000 q^{39} +(112.000 - 211.660i) q^{40} -70.0000 q^{41} +(-112.000 + 42.3320i) q^{42} -439.195i q^{43} +(84.0000 + 95.2470i) q^{44} +10.5830i q^{45} +(152.000 + 402.154i) q^{46} +336.000 q^{47} +(336.000 + 42.3320i) q^{48} -279.000 q^{49} +(-13.0000 - 34.3948i) q^{50} -74.0810i q^{51} +(-280.000 - 317.490i) q^{52} +31.7490i q^{53} +(364.000 - 137.579i) q^{54} -168.000 q^{55} +(-160.000 - 84.6640i) q^{56} +196.000 q^{57} +(-420.000 + 158.745i) q^{58} +534.442i q^{59} +(-336.000 + 296.324i) q^{60} +95.2470i q^{61} +(-224.000 - 592.648i) q^{62} +8.00000 q^{63} +(288.000 + 423.320i) q^{64} +560.000 q^{65} +(-84.0000 - 222.243i) q^{66} +174.620i q^{67} +(84.0000 - 74.0810i) q^{68} -804.308i q^{69} +(224.000 - 84.6640i) q^{70} -72.0000 q^{71} +(-20.0000 - 10.5830i) q^{72} -294.000 q^{73} +(644.000 - 243.409i) q^{74} +68.7895i q^{75} +(196.000 + 222.243i) q^{76} +126.996i q^{77} +(280.000 + 740.810i) q^{78} -464.000 q^{79} +(-672.000 - 84.6640i) q^{80} -755.000 q^{81} +(70.0000 + 185.203i) q^{82} -545.025i q^{83} +(224.000 + 253.992i) q^{84} +148.162i q^{85} +(-1162.00 + 439.195i) q^{86} +840.000 q^{87} +(168.000 - 317.490i) q^{88} +266.000 q^{89} +(28.0000 - 10.5830i) q^{90} -423.320i q^{91} +(912.000 - 804.308i) q^{92} +1185.30i q^{93} +(-336.000 - 888.972i) q^{94} -392.000 q^{95} +(-224.000 - 931.304i) q^{96} +994.000 q^{97} +(279.000 + 738.165i) q^{98} +15.8745i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 12 q^{4} + 28 q^{6} - 16 q^{7} + 40 q^{8} - 2 q^{9} - 56 q^{10} - 56 q^{12} + 16 q^{14} + 112 q^{15} + 16 q^{16} - 28 q^{17} + 2 q^{18} + 112 q^{20} - 84 q^{22} - 304 q^{23} - 112 q^{24}+ \cdots + 558 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 12 * q^4 + 28 * q^6 - 16 * q^7 + 40 * q^8 - 2 * q^9 - 56 * q^10 - 56 * q^12 + 16 * q^14 + 112 * q^15 + 16 * q^16 - 28 * q^17 + 2 * q^18 + 112 * q^20 - 84 * q^22 - 304 * q^23 - 112 * q^24 + 26 * q^25 + 280 * q^26 + 96 * q^28 - 112 * q^30 + 448 * q^31 - 352 * q^32 + 168 * q^33 + 28 * q^34 + 12 * q^36 - 196 * q^38 - 560 * q^39 + 224 * q^40 - 140 * q^41 - 224 * q^42 + 168 * q^44 + 304 * q^46 + 672 * q^47 + 672 * q^48 - 558 * q^49 - 26 * q^50 - 560 * q^52 + 728 * q^54 - 336 * q^55 - 320 * q^56 + 392 * q^57 - 840 * q^58 - 672 * q^60 - 448 * q^62 + 16 * q^63 + 576 * q^64 + 1120 * q^65 - 168 * q^66 + 168 * q^68 + 448 * q^70 - 144 * q^71 - 40 * q^72 - 588 * q^73 + 1288 * q^74 + 392 * q^76 + 560 * q^78 - 928 * q^79 - 1344 * q^80 - 1510 * q^81 + 140 * q^82 + 448 * q^84 - 2324 * q^86 + 1680 * q^87 + 336 * q^88 + 532 * q^89 + 56 * q^90 + 1824 * q^92 - 672 * q^94 - 784 * q^95 - 448 * q^96 + 1988 * q^97 + 558 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.00000	−	2.64575i	−0.353553	−	0.935414i
$2$	−1.00000	−	2.64575i	−0.353553	−	0.935414i
$3$			5.29150i			1.01835i	0.860663	+	0.509175i	$0.170049\pi$
$3$			5.29150i			1.01835i	−0.860663	+	0.509175i	$0.829951\pi$
$4$	−6.00000	+	5.29150i	−0.750000	+	0.661438i
$5$		−	10.5830i		−	0.946573i	−0.880909	−	0.473286i	$-0.843068\pi$
$5$		−	10.5830i		−	0.946573i	0.880909	−	0.473286i	$-0.156932\pi$
$6$	14.0000	−	5.29150i	0.952579	−	0.360041i
$7$	−8.00000			−0.431959			−0.215980	−	0.976398i	$-0.569295\pi$
$7$	−8.00000			−0.431959			−0.215980	+	0.976398i	$0.569295\pi$
$8$	20.0000	+	10.5830i	0.883883	+	0.467707i
$9$	−1.00000			−0.0370370
$10$	−28.0000	+	10.5830i	−0.885438	+	0.334664i
$11$		−	15.8745i		−	0.435122i	−0.976047	−	0.217561i	$-0.930190\pi$
$11$		−	15.8745i		−	0.435122i	0.976047	−	0.217561i	$-0.0698101\pi$
$12$	−28.0000	−	31.7490i	−0.673575	−	0.763763i
$13$			52.9150i			1.12892i	0.825460	+	0.564461i	$0.190916\pi$
$13$			52.9150i			1.12892i	−0.825460	+	0.564461i	$0.809084\pi$
$14$	8.00000	+	21.1660i	0.152721	+	0.404061i
$15$	56.0000			0.963943
$16$	8.00000	−	63.4980i	0.125000	−	0.992157i
$17$	−14.0000			−0.199735			−0.0998676	−	0.995001i	$-0.531842\pi$
$17$	−14.0000			−0.199735			−0.0998676	+	0.995001i	$0.531842\pi$
$18$	1.00000	+	2.64575i	0.0130946	+	0.0346450i
$19$		−	37.0405i		−	0.447246i	−0.974676	−	0.223623i	$-0.928212\pi$
$19$		−	37.0405i		−	0.447246i	0.974676	−	0.223623i	$-0.0717885\pi$
$20$	56.0000	+	63.4980i	0.626099	+	0.709930i
$21$		−	42.3320i		−	0.439886i
$22$	−42.0000	+	15.8745i	−0.407020	+	0.153839i
$23$	−152.000			−1.37801			−0.689004	−	0.724757i	$-0.741952\pi$
$23$	−152.000			−1.37801			−0.689004	+	0.724757i	$0.741952\pi$
$24$	−56.0000	+	105.830i	−0.476290	+	0.900103i
$25$	13.0000			0.104000
$26$	140.000	−	52.9150i	1.05601	−	0.399134i
$27$			137.579i			0.980633i
$28$	48.0000	−	42.3320i	0.323970	−	0.285714i
$29$		−	158.745i		−	1.01649i	−0.861212	−	0.508245i	$-0.830294\pi$
$29$		−	158.745i		−	1.01649i	0.861212	−	0.508245i	$-0.169706\pi$
$30$	−56.0000	−	148.162i	−0.340805	−	0.901686i
$31$	224.000			1.29779			0.648897	−	0.760877i	$-0.275231\pi$
$31$	224.000			1.29779			0.648897	+	0.760877i	$0.275231\pi$
$32$	−176.000	+	42.3320i	−0.972272	+	0.233854i
$33$	84.0000			0.443107
$34$	14.0000	+	37.0405i	0.0706171	+	0.186835i
$35$			84.6640i			0.408881i
$36$	6.00000	−	5.29150i	0.0277778	−	0.0244977i
$37$			243.409i			1.08152i	0.841177	+	0.540760i	$0.181863\pi$
$37$			243.409i			1.08152i	−0.841177	+	0.540760i	$0.818137\pi$
$38$	−98.0000	+	37.0405i	−0.418361	+	0.158125i
$39$	−280.000			−1.14964
$40$	112.000	−	211.660i	0.442719	−	0.836660i
$41$	−70.0000			−0.266638			−0.133319	−	0.991073i	$-0.542564\pi$
$41$	−70.0000			−0.266638			−0.133319	+	0.991073i	$0.542564\pi$
$42$	−112.000	+	42.3320i	−0.411476	+	0.155523i
$43$		−	439.195i		−	1.55759i	−0.627276	−	0.778797i	$-0.715830\pi$
$43$		−	439.195i		−	1.55759i	0.627276	−	0.778797i	$-0.284170\pi$
$44$	84.0000	+	95.2470i	0.287806	+	0.326342i
$45$			10.5830i			0.0350583i
$46$	152.000	+	402.154i	0.487200	+	1.28901i
$47$	336.000			1.04278			0.521390	−	0.853319i	$-0.325414\pi$
$47$	336.000			1.04278			0.521390	+	0.853319i	$0.325414\pi$
$48$	336.000	+	42.3320i	1.01036	+	0.127294i
$49$	−279.000			−0.813411
$50$	−13.0000	−	34.3948i	−0.0367696	−	0.0972831i
$51$		−	74.0810i		−	0.203400i
$52$	−280.000	−	317.490i	−0.746712	−	0.846692i
$53$			31.7490i			0.0822842i	0.999153	+	0.0411421i	$0.0130996\pi$
$53$			31.7490i			0.0822842i	−0.999153	+	0.0411421i	$0.986900\pi$
$54$	364.000	−	137.579i	0.917299	−	0.346706i
$55$	−168.000			−0.411875
$56$	−160.000	−	84.6640i	−0.381802	−	0.202031i
$57$	196.000			0.455453
$58$	−420.000	+	158.745i	−0.950840	+	0.359384i
$59$			534.442i			1.17929i	0.807661	+	0.589647i	$0.200733\pi$
$59$			534.442i			1.17929i	−0.807661	+	0.589647i	$0.799267\pi$
$60$	−336.000	+	296.324i	−0.722957	+	0.637588i
$61$			95.2470i			0.199920i	0.994991	+	0.0999601i	$0.0318715\pi$
$61$			95.2470i			0.199920i	−0.994991	+	0.0999601i	$0.968128\pi$
$62$	−224.000	−	592.648i	−0.458839	−	1.21397i
$63$	8.00000			0.0159985
$64$	288.000	+	423.320i	0.562500	+	0.826797i
$65$	560.000			1.06861
$66$	−84.0000	−	222.243i	−0.156662	−	0.414488i
$67$			174.620i			0.318406i	0.987246	+	0.159203i	$0.0508924\pi$
$67$			174.620i			0.318406i	−0.987246	+	0.159203i	$0.949108\pi$
$68$	84.0000	−	74.0810i	0.149801	−	0.132112i
$69$		−	804.308i		−	1.40329i
$70$	224.000	−	84.6640i	0.382473	−	0.144561i
$71$	−72.0000			−0.120350			−0.0601748	−	0.998188i	$-0.519166\pi$
$71$	−72.0000			−0.120350			−0.0601748	+	0.998188i	$0.519166\pi$
$72$	−20.0000	−	10.5830i	−0.0327364	−	0.0173225i
$73$	−294.000			−0.471371			−0.235686	−	0.971829i	$-0.575734\pi$
$73$	−294.000			−0.471371			−0.235686	+	0.971829i	$0.575734\pi$
$74$	644.000	−	243.409i	1.01167	−	0.382375i
$75$			68.7895i			0.105908i
$76$	196.000	+	222.243i	0.295826	+	0.335435i
$77$			126.996i			0.187955i
$78$	280.000	+	740.810i	0.406458	+	1.07539i
$79$	−464.000			−0.660811			−0.330406	−	0.943839i	$-0.607186\pi$
$79$	−464.000			−0.660811			−0.330406	+	0.943839i	$0.607186\pi$
$80$	−672.000	−	84.6640i	−0.939149	−	0.118322i
$81$	−755.000			−1.03567
$82$	70.0000	+	185.203i	0.0942708	+	0.249417i
$83$		−	545.025i		−	0.720774i	−0.932803	−	0.360387i	$-0.882645\pi$
$83$		−	545.025i		−	0.720774i	0.932803	−	0.360387i	$-0.117355\pi$
$84$	224.000	+	253.992i	0.290957	+	0.329914i
$85$			148.162i			0.189064i
$86$	−1162.00	+	439.195i	−1.45700	+	0.550693i
$87$	840.000			1.03514
$88$	168.000	−	317.490i	0.203510	−	0.384597i
$89$	266.000			0.316808			0.158404	−	0.987374i	$-0.449365\pi$
$89$	266.000			0.316808			0.158404	+	0.987374i	$0.449365\pi$
$90$	28.0000	−	10.5830i	0.0327940	−	0.0123950i
$91$		−	423.320i		−	0.487649i
$92$	912.000	−	804.308i	1.03351	−	0.911467i
$93$			1185.30i			1.32161i
$94$	−336.000	−	888.972i	−0.368678	−	0.975431i
$95$	−392.000			−0.423351
$96$	−224.000	−	931.304i	−0.238145	−	0.990113i
$97$	994.000			1.04047			0.520234	−	0.854024i	$-0.325845\pi$
$97$	994.000			1.04047			0.520234	+	0.854024i	$0.325845\pi$
$98$	279.000	+	738.165i	0.287584	+	0.760876i
$99$			15.8745i			0.0161156i
$100$	−78.0000	+	68.7895i	−0.0780000	+	0.0687895i
$101$			751.393i			0.740262i	0.928980	+	0.370131i	$0.120687\pi$
$101$			751.393i			0.740262i	−0.928980	+	0.370131i	$0.879313\pi$
$102$	−196.000	+	74.0810i	−0.190264	+	0.0719129i
$103$	1176.00			1.12500			0.562499	−	0.826798i	$-0.309840\pi$
$103$	1176.00			1.12500			0.562499	+	0.826798i	$0.309840\pi$
$104$	−560.000	+	1058.30i	−0.528005	+	0.997836i
$105$	−448.000			−0.416384
$106$	84.0000	−	31.7490i	0.0769698	−	0.0290919i
$107$		−	269.867i		−	0.243822i	−0.992541	−	0.121911i	$-0.961098\pi$
$107$		−	269.867i		−	0.243822i	0.992541	−	0.121911i	$-0.0389023\pi$
$108$	−728.000	−	825.474i	−0.648628	−	0.735475i
$109$		−	1894.36i		−	1.66465i	−0.554290	−	0.832324i	$-0.687010\pi$
$109$		−	1894.36i		−	1.66465i	0.554290	−	0.832324i	$-0.312990\pi$
$110$	168.000	+	444.486i	0.145620	+	0.385274i
$111$	−1288.00			−1.10137
$112$	−64.0000	+	507.984i	−0.0539949	+	0.428571i
$113$	−1710.00			−1.42357			−0.711784	−	0.702398i	$-0.752113\pi$
$113$	−1710.00			−1.42357			−0.711784	+	0.702398i	$0.752113\pi$
$114$	−196.000	−	518.567i	−0.161027	−	0.426037i
$115$			1608.62i			1.30439i
$116$	840.000	+	952.470i	0.672345	+	0.762368i
$117$		−	52.9150i		−	0.0418119i
$118$	1414.00	−	534.442i	1.10313	−	0.416944i
$119$	112.000			0.0862775
$120$	1120.00	+	592.648i	0.852013	+	0.450843i
$121$	1079.00			0.810669
$122$	252.000	−	95.2470i	0.187008	−	0.0706825i
$123$		−	370.405i		−	0.271531i
$124$	−1344.00	+	1185.30i	−0.973345	+	0.858409i
$125$		−	1460.45i		−	1.04502i
$126$	−8.00000	−	21.1660i	−0.00565632	−	0.0149652i
$127$	−1664.00			−1.16265			−0.581323	−	0.813673i	$-0.697465\pi$
$127$	−1664.00			−1.16265			−0.581323	+	0.813673i	$0.697465\pi$
$128$	832.000	−	1185.30i	0.574524	−	0.818488i
$129$	2324.00			1.58618
$130$	−560.000	−	1481.62i	−0.377810	−	0.999590i
$131$		−	672.021i		−	0.448204i	−0.974566	−	0.224102i	$-0.928055\pi$
$131$		−	672.021i		−	0.448204i	0.974566	−	0.224102i	$-0.0719449\pi$
$132$	−504.000	+	444.486i	−0.332330	+	0.293088i
$133$			296.324i			0.193192i
$134$	462.000	−	174.620i	0.297841	−	0.112573i
$135$	1456.00			0.928241
$136$	−280.000	−	148.162i	−0.176543	−	0.0934176i
$137$	−1062.00			−0.662283			−0.331142	−	0.943581i	$-0.607434\pi$
$137$	−1062.00			−0.662283			−0.331142	+	0.943581i	$0.607434\pi$
$138$	−2128.00	+	804.308i	−1.31266	+	0.496140i
$139$			2693.37i			1.64352i	0.569835	+	0.821759i	$0.307007\pi$
$139$			2693.37i			1.64352i	−0.569835	+	0.821759i	$0.692993\pi$
$140$	−448.000	−	507.984i	−0.270449	−	0.306661i
$141$			1777.94i			1.06191i
$142$	72.0000	+	190.494i	0.0425500	+	0.112577i
$143$	840.000			0.491219
$144$	−8.00000	+	63.4980i	−0.00462963	+	0.0367465i
$145$	−1680.00			−0.962182
$146$	294.000	+	777.851i	0.166655	+	0.440927i
$147$		−	1476.33i		−	0.828337i
$148$	−1288.00	−	1460.45i	−0.715358	−	0.811139i
$149$			793.725i			0.436406i	0.975903	+	0.218203i	$0.0700195\pi$
$149$			793.725i			0.436406i	−0.975903	+	0.218203i	$0.929980\pi$
$150$	182.000	−	68.7895i	0.0990683	−	0.0374443i
$151$	744.000			0.400966			0.200483	−	0.979697i	$-0.435749\pi$
$151$	744.000			0.400966			0.200483	+	0.979697i	$0.435749\pi$
$152$	392.000	−	740.810i	0.209180	−	0.395314i
$153$	14.0000			0.00739760
$154$	336.000	−	126.996i	0.175816	−	0.0664522i
$155$		−	2370.59i		−	1.22846i
$156$	1680.00	−	1481.62i	0.862229	−	0.760414i
$157$			179.911i			0.0914552i	0.998954	+	0.0457276i	$0.0145606\pi$
$157$			179.911i			0.0914552i	−0.998954	+	0.0457276i	$0.985439\pi$
$158$	464.000	+	1227.63i	0.233632	+	0.618132i
$159$	−168.000			−0.0837941
$160$	448.000	+	1862.61i	0.221359	+	0.920326i
$161$	1216.00			0.595244
$162$	755.000	+	1997.54i	0.366163	+	0.968776i
$163$		−	1772.65i		−	0.851809i	−0.904768	−	0.425905i	$-0.859956\pi$
$163$		−	1772.65i		−	0.851809i	0.904768	−	0.425905i	$-0.140044\pi$
$164$	420.000	−	370.405i	0.199979	−	0.176365i
$165$		−	888.972i		−	0.419433i
$166$	−1442.00	+	545.025i	−0.674222	+	0.254832i
$167$	−1960.00			−0.908200			−0.454100	−	0.890951i	$-0.650039\pi$
$167$	−1960.00			−0.908200			−0.454100	+	0.890951i	$0.650039\pi$
$168$	448.000	−	846.640i	0.205738	−	0.388808i
$169$	−603.000			−0.274465
$170$	392.000	−	148.162i	0.176853	−	0.0668442i
$171$			37.0405i			0.0165647i
$172$	2324.00	+	2635.17i	1.03025	+	1.16820i
$173$			2000.19i			0.879026i	0.898236	+	0.439513i	$0.144849\pi$
$173$			2000.19i			0.879026i	−0.898236	+	0.439513i	$0.855151\pi$
$174$	−840.000	−	2222.43i	−0.365978	−	0.968288i
$175$	−104.000			−0.0449238
$176$	−1008.00	−	126.996i	−0.431709	−	0.0543903i
$177$	−2828.00			−1.20094
$178$	−266.000	−	703.770i	−0.112009	−	0.296347i
$179$			3264.86i			1.36328i	0.731688	+	0.681639i	$0.238733\pi$
$179$			3264.86i			1.36328i	−0.731688	+	0.681639i	$0.761267\pi$
$180$	−56.0000	−	63.4980i	−0.0231889	−	0.0262937i
$181$		−	2338.84i		−	0.960469i	−0.877140	−	0.480235i	$-0.840552\pi$
$181$		−	2338.84i		−	0.960469i	0.877140	−	0.480235i	$-0.159448\pi$
$182$	−1120.00	+	423.320i	−0.456153	+	0.172410i
$183$	−504.000			−0.203589
$184$	−3040.00	−	1608.62i	−1.21800	−	0.644504i
$185$	2576.00			1.02374
$186$	3136.00	−	1185.30i	1.23625	−	0.467259i
$187$			222.243i			0.0869092i
$188$	−2016.00	+	1777.94i	−0.782085	+	0.689734i
$189$		−	1100.63i		−	0.423594i
$190$	392.000	+	1037.13i	0.149677	+	0.396009i
$191$	3904.00			1.47897			0.739486	−	0.673172i	$-0.235069\pi$
$191$	3904.00			1.47897			0.739486	+	0.673172i	$0.235069\pi$
$192$	−2240.00	+	1523.95i	−0.841969	+	0.572822i
$193$	3330.00			1.24196			0.620981	−	0.783826i	$-0.286734\pi$
$193$	3330.00			1.24196			0.620981	+	0.783826i	$0.286734\pi$
$194$	−994.000	−	2629.88i	−0.367861	−	0.973269i
$195$			2963.24i			1.08822i
$196$	1674.00	−	1476.33i	0.610058	−	0.538021i
$197$		−	1195.88i		−	0.432502i	−0.976338	−	0.216251i	$-0.930617\pi$
$197$		−	1195.88i		−	0.432502i	0.976338	−	0.216251i	$-0.0693829\pi$
$198$	42.0000	−	15.8745i	0.0150748	−	0.00569774i
$199$	−1736.00			−0.618401			−0.309200	−	0.950997i	$-0.600061\pi$
$199$	−1736.00			−0.618401			−0.309200	+	0.950997i	$0.600061\pi$
$200$	260.000	+	137.579i	0.0919239	+	0.0486415i
$201$	−924.000			−0.324248
$202$	1988.00	−	751.393i	0.692451	−	0.261722i
$203$			1269.96i			0.439083i
$204$	392.000	+	444.486i	0.134537	+	0.152550i
$205$			740.810i			0.252392i
$206$	−1176.00	−	3111.40i	−0.397747	−	1.05234i
$207$	152.000			0.0510373
$208$	3360.00	+	423.320i	1.12007	+	0.141115i
$209$	−588.000			−0.194607
$210$	448.000	+	1185.30i	0.147214	+	0.389492i
$211$		−	2915.62i		−	0.951277i	−0.879641	−	0.475638i	$-0.842217\pi$
$211$		−	2915.62i		−	0.951277i	0.879641	−	0.475638i	$-0.157783\pi$
$212$	−168.000	−	190.494i	−0.0544259	−	0.0617132i
$213$		−	380.988i		−	0.122558i
$214$	−714.000	+	269.867i	−0.228075	+	0.0862042i
$215$	−4648.00			−1.47438
$216$	−1456.00	+	2751.58i	−0.458649	+	0.866766i
$217$	−1792.00			−0.560594
$218$	−5012.00	+	1894.36i	−1.55714	+	0.588542i
$219$		−	1555.70i		−	0.480021i
$220$	1008.00	−	888.972i	0.308906	−	0.272430i
$221$		−	740.810i		−	0.225486i
$222$	1288.00	+	3407.73i	0.389391	+	1.03023i
$223$	1568.00			0.470857			0.235428	−	0.971892i	$-0.424351\pi$
$223$	1568.00			0.470857			0.235428	+	0.971892i	$0.424351\pi$
$224$	1408.00	−	338.656i	0.419982	−	0.101015i
$225$	−13.0000			−0.00385185
$226$	1710.00	+	4524.23i	0.503308	+	1.33163i
$227$		−	1264.67i		−	0.369775i	−0.982760	−	0.184888i	$-0.940808\pi$
$227$		−	1264.67i		−	0.369775i	0.982760	−	0.184888i	$-0.0591922\pi$
$228$	−1176.00	+	1037.13i	−0.341590	+	0.301254i
$229$			5153.92i			1.48725i	0.668595	+	0.743626i	$0.266896\pi$
$229$			5153.92i			1.48725i	−0.668595	+	0.743626i	$0.733104\pi$
$230$	4256.00	−	1608.62i	1.22014	−	0.461170i
$231$	−672.000			−0.191404
$232$	1680.00	−	3174.90i	0.475420	−	0.898459i
$233$	−838.000			−0.235619			−0.117809	−	0.993036i	$-0.537587\pi$
$233$	−838.000			−0.235619			−0.117809	+	0.993036i	$0.537587\pi$
$234$	−140.000	+	52.9150i	−0.0391115	+	0.0147827i
$235$		−	3555.89i		−	0.987067i
$236$	−2828.00	−	3206.65i	−0.780030	−	0.884471i
$237$		−	2455.26i		−	0.672937i
$238$	−112.000	−	296.324i	−0.0305037	−	0.0807052i
$239$	6288.00			1.70183			0.850914	−	0.525305i	$-0.176049\pi$
$239$	6288.00			1.70183			0.850914	+	0.525305i	$0.176049\pi$
$240$	448.000	−	3555.89i	0.120493	−	0.956382i
$241$	−2926.00			−0.782076			−0.391038	−	0.920375i	$-0.627884\pi$
$241$	−2926.00			−0.782076			−0.391038	+	0.920375i	$0.627884\pi$
$242$	−1079.00	−	2854.77i	−0.286615	−	0.758311i
$243$		−	280.450i		−	0.0740364i
$244$	−504.000	−	571.482i	−0.132235	−	0.149940i
$245$			2952.66i			0.769953i
$246$	−980.000	+	370.405i	−0.253994	+	0.0960007i
$247$	1960.00			0.504906
$248$	4480.00	+	2370.59i	1.14710	+	0.606987i
$249$	2884.00			0.734000
$250$	−3864.00	+	1460.45i	−0.977523	+	0.369469i
$251$			5444.96i			1.36925i	0.728894	+	0.684627i	$0.240035\pi$
$251$			5444.96i			1.36925i	−0.728894	+	0.684627i	$0.759965\pi$
$252$	−48.0000	+	42.3320i	−0.0119989	+	0.0105820i
$253$			2412.93i			0.599602i
$254$	1664.00	+	4402.53i	0.411058	+	1.08756i
$255$	−784.000			−0.192533
$256$	−3968.00	−	1015.97i	−0.968750	−	0.248039i
$257$	2562.00			0.621841			0.310921	−	0.950436i	$-0.399363\pi$
$257$	2562.00			0.621841			0.310921	+	0.950436i	$0.399363\pi$
$258$	−2324.00	−	6148.73i	−0.560798	−	1.48373i
$259$		−	1947.27i		−	0.467172i
$260$	−3360.00	+	2963.24i	−0.801455	+	0.706817i
$261$			158.745i			0.0376478i
$262$	−1778.00	+	672.021i	−0.419257	+	0.158464i
$263$	−5896.00			−1.38237			−0.691184	−	0.722679i	$-0.742911\pi$
$263$	−5896.00			−1.38237			−0.691184	+	0.722679i	$0.742911\pi$
$264$	1680.00	+	888.972i	0.391655	+	0.207244i
$265$	336.000			0.0778880
$266$	784.000	−	296.324i	0.180715	−	0.0683038i
$267$			1407.54i			0.322622i
$268$	−924.000	−	1047.72i	−0.210606	−	0.238804i
$269$		−	5365.58i		−	1.21615i	−0.793878	−	0.608077i	$-0.791941\pi$
$269$		−	5365.58i		−	1.21615i	0.793878	−	0.608077i	$-0.208059\pi$
$270$	−1456.00	−	3852.21i	−0.328183	−	0.868290i
$271$	−1680.00			−0.376578			−0.188289	−	0.982114i	$-0.560294\pi$
$271$	−1680.00			−0.376578			−0.188289	+	0.982114i	$0.560294\pi$
$272$	−112.000	+	888.972i	−0.0249669	+	0.198169i
$273$	2240.00			0.496597
$274$	1062.00	+	2809.79i	0.234152	+	0.619509i
$275$		−	206.369i		−	0.0452527i
$276$	4256.00	+	4825.85i	0.928192	+	1.05247i
$277$		−	1576.87i		−	0.342039i	−0.985268	−	0.171019i	$-0.945294\pi$
$277$		−	1576.87i		−	0.342039i	0.985268	−	0.171019i	$-0.0547061\pi$
$278$	7126.00	−	2693.37i	1.53737	−	0.581072i
$279$	−224.000			−0.0480664
$280$	−896.000	+	1693.28i	−0.191237	+	0.361403i
$281$	−2742.00			−0.582114			−0.291057	−	0.956706i	$-0.594007\pi$
$281$	−2742.00			−0.582114			−0.291057	+	0.956706i	$0.594007\pi$
$282$	4704.00	−	1777.94i	0.993330	−	0.375444i
$283$			2989.70i			0.627983i	0.949426	+	0.313991i	$0.101666\pi$
$283$			2989.70i			0.627983i	−0.949426	+	0.313991i	$0.898334\pi$
$284$	432.000	−	380.988i	0.0902623	−	0.0796038i
$285$		−	2074.27i		−	0.431120i
$286$	−840.000	−	2222.43i	−0.173672	−	0.459493i
$287$	560.000			0.115177
$288$	176.000	−	42.3320i	0.0360101	−	0.00866124i
$289$	−4717.00			−0.960106
$290$	1680.00	+	4444.86i	0.340183	+	0.900039i
$291$			5259.75i			1.05956i
$292$	1764.00	−	1555.70i	0.353528	−	0.311783i
$293$		−	9238.96i		−	1.84214i	−0.389401	−	0.921068i	$-0.627318\pi$
$293$		−	9238.96i		−	1.84214i	0.389401	−	0.921068i	$-0.372682\pi$
$294$	−3906.00	+	1476.33i	−0.774839	+	0.292861i
$295$	5656.00			1.11629
$296$	−2576.00	+	4868.18i	−0.505834	+	0.955937i
$297$	2184.00			0.426695
$298$	2100.00	−	793.725i	0.408221	−	0.154293i
$299$		−	8043.08i		−	1.55566i
$300$	−364.000	−	412.737i	−0.0700518	−	0.0794313i
$301$			3513.56i			0.672818i
$302$	−744.000	−	1968.44i	−0.141763	−	0.375069i
$303$	−3976.00			−0.753846
$304$	−2352.00	−	296.324i	−0.443738	−	0.0559058i
$305$	1008.00			0.189239
$306$	−14.0000	−	37.0405i	−0.00261545	−	0.00691982i
$307$			2587.54i			0.481039i	0.970644	+	0.240520i	$0.0773178\pi$
$307$			2587.54i			0.481039i	−0.970644	+	0.240520i	$0.922682\pi$
$308$	−672.000	−	761.976i	−0.124321	−	0.140966i
$309$			6222.81i			1.14564i
$310$	−6272.00	+	2370.59i	−1.14912	+	0.434325i
$311$	−2744.00			−0.500315			−0.250157	−	0.968205i	$-0.580482\pi$
$311$	−2744.00			−0.500315			−0.250157	+	0.968205i	$0.580482\pi$
$312$	−5600.00	−	2963.24i	−1.01615	−	0.537694i
$313$	2282.00			0.412097			0.206048	−	0.978542i	$-0.433940\pi$
$313$	2282.00			0.412097			0.206048	+	0.978542i	$0.433940\pi$
$314$	476.000	−	179.911i	0.0855485	−	0.0323343i
$315$		−	84.6640i		−	0.0151437i
$316$	2784.00	−	2455.26i	0.495608	−	0.437085i
$317$			9577.62i			1.69695i	0.529237	+	0.848474i	$0.322478\pi$
$317$			9577.62i			1.69695i	−0.529237	+	0.848474i	$0.677522\pi$
$318$	168.000	+	444.486i	0.0296257	+	0.0783822i
$319$	−2520.00			−0.442298
$320$	4480.00	−	3047.91i	0.782624	−	0.532447i
$321$	1428.00			0.248297
$322$	−1216.00	−	3217.23i	−0.210450	−	0.556799i
$323$			518.567i			0.0893308i
$324$	4530.00	−	3995.08i	0.776749	−	0.685028i
$325$			687.895i			0.117408i
$326$	−4690.00	+	1772.65i	−0.796795	+	0.301160i
$327$	10024.0			1.69519
$328$	−1400.00	−	740.810i	−0.235677	−	0.124709i
$329$	−2688.00			−0.450438
$330$	−2352.00	+	888.972i	−0.392343	+	0.148292i
$331$		−	4249.08i		−	0.705590i	−0.935701	−	0.352795i	$-0.885231\pi$
$331$		−	4249.08i		−	0.705590i	0.935701	−	0.352795i	$-0.114769\pi$
$332$	2884.00	+	3270.15i	0.476747	+	0.540580i
$333$		−	243.409i		−	0.0400563i
$334$	1960.00	+	5185.67i	0.321097	+	0.849543i
$335$	1848.00			0.301394
$336$	−2688.00	−	338.656i	−0.436436	−	0.0549857i
$337$	6130.00			0.990868			0.495434	−	0.868646i	$-0.335009\pi$
$337$	6130.00			0.990868			0.495434	+	0.868646i	$0.335009\pi$
$338$	603.000	+	1595.39i	0.0970381	+	0.256739i
$339$		−	9048.47i		−	1.44969i
$340$	−784.000	−	888.972i	−0.125054	−	0.141798i
$341$		−	3555.89i		−	0.564699i
$342$	98.0000	−	37.0405i	0.0154948	−	0.00585650i
$343$	4976.00			0.783320
$344$	4648.00	−	8783.89i	0.728498	−	1.37673i
$345$	−8512.00			−1.32832
$346$	5292.00	−	2000.19i	0.822253	−	0.310783i
$347$			2481.71i			0.383935i	0.981401	+	0.191967i	$0.0614868\pi$
$347$			2481.71i			0.383935i	−0.981401	+	0.191967i	$0.938513\pi$
$348$	−5040.00	+	4444.86i	−0.776357	+	0.684683i
$349$		−	328.073i		−	0.0503191i	−0.999683	−	0.0251595i	$-0.991991\pi$
$349$		−	328.073i		−	0.0503191i	0.999683	−	0.0251595i	$-0.00800937\pi$
$350$	104.000	+	275.158i	0.0158830	+	0.0420223i
$351$	−7280.00			−1.10706
$352$	672.000	+	2793.91i	0.101755	+	0.423057i
$353$	−10206.0			−1.53884			−0.769420	−	0.638743i	$-0.779455\pi$
$353$	−10206.0			−1.53884			−0.769420	+	0.638743i	$0.779455\pi$
$354$	2828.00	+	7482.18i	0.424595	+	1.12337i
$355$			761.976i			0.113920i
$356$	−1596.00	+	1407.54i	−0.237606	+	0.209549i
$357$			592.648i			0.0878607i
$358$	8638.00	−	3264.86i	1.27523	−	0.481992i
$359$	−3176.00			−0.466916			−0.233458	−	0.972367i	$-0.575004\pi$
$359$	−3176.00			−0.466916			−0.233458	+	0.972367i	$0.575004\pi$
$360$	−112.000	+	211.660i	−0.0163970	+	0.0309874i
$361$	5487.00			0.799971
$362$	−6188.00	+	2338.84i	−0.898437	+	0.339577i
$363$			5709.53i			0.825545i
$364$	2240.00	+	2539.92i	0.322549	+	0.365736i
$365$			3111.40i			0.446187i
$366$	504.000	+	1333.46i	0.0719795	+	0.190440i
$367$	−11760.0			−1.67266			−0.836331	−	0.548225i	$-0.815304\pi$
$367$	−11760.0			−1.67266			−0.836331	+	0.548225i	$0.815304\pi$
$368$	−1216.00	+	9651.70i	−0.172251	+	1.36720i
$369$	70.0000			0.00987549
$370$	−2576.00	−	6815.46i	−0.361946	−	0.957618i
$371$		−	253.992i		−	0.0355434i
$372$	−6272.00	−	7111.78i	−0.874161	−	0.991206i
$373$		−	10974.6i		−	1.52344i	−0.647908	−	0.761719i	$-0.724356\pi$
$373$		−	10974.6i		−	1.52344i	0.647908	−	0.761719i	$-0.275644\pi$
$374$	588.000	−	222.243i	0.0812961	−	0.0307271i
$375$	7728.00			1.06419
$376$	6720.00	+	3555.89i	0.921696	+	0.487715i
$377$	8400.00			1.14754
$378$	−2912.00	+	1100.63i	−0.396236	+	0.149763i
$379$			3074.36i			0.416674i	0.978057	+	0.208337i	$0.0668051\pi$
$379$			3074.36i			0.416674i	−0.978057	+	0.208337i	$0.933195\pi$
$380$	2352.00	−	2074.27i	0.317513	−	0.280020i
$381$		−	8805.06i		−	1.18398i
$382$	−3904.00	−	10329.0i	−0.522895	−	1.38345i
$383$	2688.00			0.358617			0.179309	−	0.983793i	$-0.442614\pi$
$383$	2688.00			0.358617			0.179309	+	0.983793i	$0.442614\pi$
$384$	6272.00	+	4402.53i	0.833507	+	0.585067i
$385$	1344.00			0.177913
$386$	−3330.00	−	8810.35i	−0.439100	−	1.16175i
$387$			439.195i			0.0576887i
$388$	−5964.00	+	5259.75i	−0.780351	+	0.688205i
$389$			10487.8i			1.36697i	0.729966	+	0.683484i	$0.239536\pi$
$389$			10487.8i			1.36697i	−0.729966	+	0.683484i	$0.760464\pi$
$390$	7840.00	−	2963.24i	1.01793	−	0.384742i
$391$	2128.00			0.275237
$392$	−5580.00	−	2952.66i	−0.718961	−	0.380438i
$393$	3556.00			0.456429
$394$	−3164.00	+	1195.88i	−0.404569	+	0.152913i
$395$			4910.51i			0.625506i
$396$	−84.0000	−	95.2470i	−0.0106595	−	0.0120867i
$397$		−	5704.24i		−	0.721127i	−0.932735	−	0.360564i	$-0.882584\pi$
$397$		−	5704.24i		−	0.721127i	0.932735	−	0.360564i	$-0.117416\pi$
$398$	1736.00	+	4593.02i	0.218638	+	0.578461i
$399$	−1568.00			−0.196737
$400$	104.000	−	825.474i	0.0130000	−	0.103184i
$401$	12402.0			1.54445			0.772227	−	0.635346i	$-0.219143\pi$
$401$	12402.0			1.54445			0.772227	+	0.635346i	$0.219143\pi$
$402$	924.000	+	2444.67i	0.114639	+	0.303307i
$403$			11853.0i			1.46511i
$404$	−3976.00	−	4508.36i	−0.489637	−	0.555196i
$405$			7990.17i			0.980333i
$406$	3360.00	−	1269.96i	0.410724	−	0.155239i
$407$	3864.00			0.470593
$408$	784.000	−	1481.62i	0.0951318	−	0.179782i
$409$	−12278.0			−1.48437			−0.742186	−	0.670194i	$-0.766211\pi$
$409$	−12278.0			−1.48437			−0.742186	+	0.670194i	$0.766211\pi$
$410$	1960.00	−	740.810i	0.236091	−	0.0892342i
$411$		−	5619.58i		−	0.674436i
$412$	−7056.00	+	6222.81i	−0.843748	+	0.744116i
$413$		−	4275.53i		−	0.509407i
$414$	−152.000	−	402.154i	−0.0180444	−	0.0477411i
$415$	−5768.00			−0.682265
$416$	−2240.00	−	9313.04i	−0.264002	−	1.09762i
$417$	−14252.0			−1.67368
$418$	588.000	+	1555.70i	0.0688039	+	0.182038i
$419$		−	8207.12i		−	0.956907i	−0.878113	−	0.478454i	$-0.841198\pi$
$419$		−	8207.12i		−	0.956907i	0.878113	−	0.478454i	$-0.158802\pi$
$420$	2688.00	−	2370.59i	0.312288	−	0.275412i
$421$		−	1449.87i		−	0.167844i	−0.996472	−	0.0839221i	$-0.973255\pi$
$421$		−	1449.87i		−	0.167844i	0.996472	−	0.0839221i	$-0.0267447\pi$
$422$	−7714.00	+	2915.62i	−0.889838	+	0.336327i
$423$	−336.000			−0.0386215
$424$	−336.000	+	634.980i	−0.0384849	+	0.0727296i
$425$	−182.000			−0.0207725
$426$	−1008.00	+	380.988i	−0.114643	+	0.0433308i
$427$		−	761.976i		−	0.0863574i
$428$	1428.00	+	1619.20i	0.161273	+	0.182867i
$429$			4444.86i			0.500233i
$430$	4648.00	+	12297.5i	0.521271	+	1.37915i
$431$	7632.00			0.852948			0.426474	−	0.904500i	$-0.359756\pi$
$431$	7632.00			0.852948			0.426474	+	0.904500i	$0.359756\pi$
$432$	8736.00	+	1100.63i	0.972942	+	0.122579i
$433$	3794.00			0.421081			0.210540	−	0.977585i	$-0.432478\pi$
$433$	3794.00			0.421081			0.210540	+	0.977585i	$0.432478\pi$
$434$	1792.00	+	4741.19i	0.198200	+	0.524388i
$435$		−	8889.72i		−	0.979838i
$436$	10024.0	+	11366.1i	1.10106	+	1.24849i
$437$			5630.16i			0.616309i
$438$	−4116.00	+	1555.70i	−0.449018	+	0.169713i
$439$	−1848.00			−0.200912			−0.100456	−	0.994942i	$-0.532030\pi$
$439$	−1848.00			−0.200912			−0.100456	+	0.994942i	$0.532030\pi$
$440$	−3360.00	−	1777.94i	−0.364049	−	0.192637i
$441$	279.000			0.0301263
$442$	−1960.00	+	740.810i	−0.210922	+	0.0797212i
$443$		−	12334.5i		−	1.32287i	−0.750004	−	0.661433i	$-0.769949\pi$
$443$		−	12334.5i		−	1.32287i	0.750004	−	0.661433i	$-0.230051\pi$
$444$	7728.00	−	6815.46i	0.826024	−	0.728485i
$445$		−	2815.08i		−	0.299882i
$446$	−1568.00	−	4148.54i	−0.166473	−	0.440446i
$447$	−4200.00			−0.444414
$448$	−2304.00	−	3386.56i	−0.242977	−	0.357143i
$449$	−3582.00			−0.376492			−0.188246	−	0.982122i	$-0.560280\pi$
$449$	−3582.00			−0.376492			−0.188246	+	0.982122i	$0.560280\pi$
$450$	13.0000	+	34.3948i	0.00136184	+	0.00360308i
$451$			1111.22i			0.116020i
$452$	10260.0	−	9048.47i	1.06768	−	0.941602i
$453$			3936.88i			0.408324i
$454$	−3346.00	+	1264.67i	−0.345893	+	0.130735i
$455$	−4480.00			−0.461595
$456$	3920.00	+	2074.27i	0.402568	+	0.213019i
$457$	2714.00			0.277802			0.138901	−	0.990306i	$-0.455643\pi$
$457$	2714.00			0.277802			0.138901	+	0.990306i	$0.455643\pi$
$458$	13636.0	−	5153.92i	1.39120	−	0.525823i
$459$		−	1926.11i		−	0.195867i
$460$	−8512.00	−	9651.70i	−0.862770	−	0.978289i
$461$			8349.99i			0.843596i	0.906690	+	0.421798i	$0.138601\pi$
$461$			8349.99i			0.843596i	−0.906690	+	0.421798i	$0.861399\pi$
$462$	672.000	+	1777.94i	0.0676716	+	0.179042i
$463$	2224.00			0.223236			0.111618	−	0.993751i	$-0.464397\pi$
$463$	2224.00			0.223236			0.111618	+	0.993751i	$0.464397\pi$
$464$	−10080.0	−	1269.96i	−1.00852	−	0.127061i
$465$	12544.0			1.25100
$466$	838.000	+	2217.14i	0.0833039	+	0.220401i
$467$			10292.0i			1.01982i	0.860228	+	0.509910i	$0.170321\pi$
$467$			10292.0i			1.01982i	−0.860228	+	0.509910i	$0.829679\pi$
$468$	280.000	+	317.490i	0.0276560	+	0.0313589i
$469$		−	1396.96i		−	0.137538i
$470$	−9408.00	+	3555.89i	−0.923316	+	0.348981i
$471$	−952.000			−0.0931334
$472$	−5656.00	+	10688.8i	−0.551565	+	1.04236i
$473$	−6972.00			−0.677744
$474$	−6496.00	+	2455.26i	−0.629475	+	0.237919i
$475$		−	481.527i		−	0.0465136i
$476$	−672.000	+	592.648i	−0.0647081	+	0.0570672i
$477$		−	31.7490i		−	0.00304756i
$478$	−6288.00	−	16636.5i	−0.601687	−	1.59191i
$479$	17696.0			1.68800			0.843999	−	0.536345i	$-0.180195\pi$
$479$	17696.0			1.68800			0.843999	+	0.536345i	$0.180195\pi$
$480$	−9856.00	+	2370.59i	−0.937214	+	0.225421i
$481$	−12880.0			−1.22095
$482$	2926.00	+	7741.47i	0.276505	+	0.731565i
$483$			6434.47i			0.606166i
$484$	−6474.00	+	5709.53i	−0.608002	+	0.536207i
$485$		−	10519.5i		−	0.984879i
$486$	−742.000	+	280.450i	−0.0692547	+	0.0261758i
$487$	1304.00			0.121334			0.0606672	−	0.998158i	$-0.480677\pi$
$487$	1304.00			0.121334			0.0606672	+	0.998158i	$0.480677\pi$
$488$	−1008.00	+	1904.94i	−0.0935041	+	0.176706i
$489$	9380.00			0.867440
$490$	7812.00	−	2952.66i	0.720225	−	0.272219i
$491$			16662.9i			1.53154i	0.643112	+	0.765772i	$0.277643\pi$
$491$			16662.9i			1.53154i	−0.643112	+	0.765772i	$0.722357\pi$
$492$	1960.00	+	2222.43i	0.179601	+	0.203648i
$493$			2222.43i			0.203029i
$494$	−1960.00	−	5185.67i	−0.178511	−	0.472296i
$495$	168.000			0.0152546
$496$	1792.00	−	14223.6i	0.162224	−	1.28761i
$497$	576.000			0.0519862
$498$	−2884.00	−	7630.35i	−0.259508	−	0.686594i
$499$			3095.53i			0.277705i	0.990313	+	0.138853i	$0.0443414\pi$
$499$			3095.53i			0.277705i	−0.990313	+	0.138853i	$0.955659\pi$
$500$	7728.00	+	8762.73i	0.691213	+	0.783762i
$501$		−	10371.3i		−	0.924865i
$502$	14406.0	−	5444.96i	1.28082	−	0.484104i
$503$	−19320.0			−1.71260			−0.856298	−	0.516481i	$-0.827242\pi$
$503$	−19320.0			−1.71260			−0.856298	+	0.516481i	$0.827242\pi$
$504$	160.000	+	84.6640i	0.0141408	+	0.00748261i
$505$	7952.00			0.700712
$506$	6384.00	−	2412.93i	0.560876	−	0.211991i
$507$		−	3190.78i		−	0.279502i
$508$	9984.00	−	8805.06i	0.871985	−	0.769018i
$509$		−	4476.61i		−	0.389828i	−0.980820	−	0.194914i	$-0.937557\pi$
$509$		−	4476.61i		−	0.389828i	0.980820	−	0.194914i	$-0.0624427\pi$
$510$	784.000	+	2074.27i	0.0680708	+	0.180098i
$511$	2352.00			0.203613
$512$	1280.00	+	11514.3i	0.110485	+	0.993878i
$513$	5096.00			0.438585
$514$	−2562.00	−	6778.41i	−0.219854	−	0.581679i
$515$		−	12445.6i		−	1.06489i
$516$	−13944.0	+	12297.5i	−1.18963	+	1.04916i
$517$		−	5333.83i		−	0.453737i
$518$	−5152.00	+	1947.27i	−0.437000	+	0.165170i
$519$	−10584.0			−0.895156
$520$	11200.0	+	5926.48i	0.944524	+	0.499795i
$521$	−2982.00			−0.250756			−0.125378	−	0.992109i	$-0.540014\pi$
$521$	−2982.00			−0.250756			−0.125378	+	0.992109i	$0.540014\pi$
$522$	420.000	−	158.745i	0.0352163	−	0.0133105i
$523$			2016.06i			0.168559i	0.996442	+	0.0842794i	$0.0268588\pi$
$523$			2016.06i			0.168559i	−0.996442	+	0.0842794i	$0.973141\pi$
$524$	3556.00	+	4032.12i	0.296459	+	0.336153i
$525$		−	550.316i		−	0.0457481i
$526$	5896.00	+	15599.3i	0.488741	+	1.29309i
$527$	−3136.00			−0.259215
$528$	672.000	−	5333.83i	0.0553883	−	0.439631i
$529$	10937.0			0.898907
$530$	−336.000	−	888.972i	−0.0275376	−	0.0728575i
$531$		−	534.442i		−	0.0436776i
$532$	−1568.00	−	1777.94i	−0.127785	−	0.144894i
$533$		−	3704.05i		−	0.301014i
$534$	3724.00	−	1407.54i	0.301785	−	0.114064i
$535$	−2856.00			−0.230796
$536$	−1848.00	+	3492.39i	−0.148921	+	0.281433i
$537$	−17276.0			−1.38830
$538$	−14196.0	+	5365.58i	−1.13761	+	0.429975i
$539$			4428.99i			0.353933i
$540$	−8736.00	+	7704.43i	−0.696181	+	0.613974i
$541$			15419.4i			1.22539i	0.790321	+	0.612693i	$0.209914\pi$
$541$			15419.4i			1.22539i	−0.790321	+	0.612693i	$0.790086\pi$
$542$	1680.00	+	4444.86i	0.133141	+	0.352257i
$543$	12376.0			0.978094
$544$	2464.00	−	592.648i	0.194197	−	0.0467088i
$545$	−20048.0			−1.57571
$546$	−2240.00	−	5926.48i	−0.175574	−	0.464524i
$547$		−	12609.7i		−	0.985649i	−0.870129	−	0.492824i	$-0.835965\pi$
$547$		−	12609.7i		−	0.985649i	0.870129	−	0.492824i	$-0.164035\pi$
$548$	6372.00	−	5619.58i	0.496712	−	0.438059i
$549$		−	95.2470i		−	0.00740445i
$550$	−546.000	+	206.369i	−0.0423300	+	0.0159992i
$551$	−5880.00			−0.454621
$552$	8512.00	−	16086.2i	0.656331	−	1.24035i
$553$	3712.00			0.285444
$554$	−4172.00	+	1576.87i	−0.319948	+	0.120929i
$555$			13630.9i			1.04252i
$556$	−14252.0	−	16160.2i	−1.08709	−	1.23264i
$557$		−	7143.53i		−	0.543413i	−0.962380	−	0.271706i	$-0.912412\pi$
$557$		−	7143.53i		−	0.543413i	0.962380	−	0.271706i	$-0.0875880\pi$
$558$	224.000	+	592.648i	0.0169940	+	0.0449620i
$559$	23240.0			1.75840
$560$	5376.00	+	677.312i	0.405674	+	0.0511101i
$561$	−1176.00			−0.0885040
$562$	2742.00	+	7254.65i	0.205808	+	0.544518i
$563$		−	7572.14i		−	0.566834i	−0.958997	−	0.283417i	$-0.908532\pi$
$563$		−	7572.14i		−	0.566834i	0.958997	−	0.283417i	$-0.0914681\pi$
$564$	−9408.00	−	10667.7i	−0.702391	−	0.796436i
$565$			18096.9i			1.34751i
$566$	7910.00	−	2989.70i	0.587424	−	0.222025i
$567$	6040.00			0.447365
$568$	−1440.00	−	761.976i	−0.106375	−	0.0562884i
$569$	15594.0			1.14892			0.574459	−	0.818533i	$-0.305212\pi$
$569$	15594.0			1.14892			0.574459	+	0.818533i	$0.305212\pi$
$570$	−5488.00	+	2074.27i	−0.403275	+	0.152424i
$571$		−	16737.0i		−	1.22666i	−0.789827	−	0.613330i	$-0.789830\pi$
$571$		−	16737.0i		−	1.22666i	0.789827	−	0.613330i	$-0.210170\pi$
$572$	−5040.00	+	4444.86i	−0.368414	+	0.324911i
$573$			20658.0i			1.50611i
$574$	−560.000	−	1481.62i	−0.0407212	−	0.107738i
$575$	−1976.00			−0.143313
$576$	−288.000	−	423.320i	−0.0208333	−	0.0306221i
$577$	6594.00			0.475757			0.237879	−	0.971295i	$-0.423548\pi$
$577$	6594.00			0.475757			0.237879	+	0.971295i	$0.423548\pi$
$578$	4717.00	+	12480.0i	0.339449	+	0.898097i
$579$			17620.7i			1.26475i
$580$	10080.0	−	8889.72i	0.721637	−	0.636424i
$581$			4360.20i			0.311345i
$582$	13916.0	−	5259.75i	0.991128	−	0.374611i
$583$	504.000			0.0358037
$584$	−5880.00	−	3111.40i	−0.416637	−	0.220464i
$585$	−560.000			−0.0395780
$586$	−24444.0	+	9238.96i	−1.72316	+	0.651294i
$587$		−	23213.8i		−	1.63226i	−0.577868	−	0.816130i	$-0.696115\pi$
$587$		−	23213.8i		−	1.63226i	0.577868	−	0.816130i	$-0.303885\pi$
$588$	7812.00	+	8857.98i	0.547894	+	0.621253i
$589$		−	8297.08i		−	0.580433i
$590$	−5656.00	−	14964.4i	−0.394668	−	1.04419i
$591$	6328.00			0.440438
$592$	15456.0	+	1947.27i	1.07304	+	0.135190i
$593$	14322.0			0.991794			0.495897	−	0.868381i	$-0.334839\pi$
$593$	14322.0			0.991794			0.495897	+	0.868381i	$0.334839\pi$
$594$	−2184.00	−	5778.32i	−0.150860	−	0.399137i
$595$		−	1185.30i		−	0.0816679i
$596$	−4200.00	−	4762.35i	−0.288656	−	0.327305i
$597$		−	9186.05i		−	0.629749i
$598$	−21280.0	+	8043.08i	−1.45519	+	0.550010i
$599$	−16088.0			−1.09739			−0.548696	−	0.836022i	$-0.684876\pi$
$599$	−16088.0			−1.09739			−0.548696	+	0.836022i	$0.684876\pi$
$600$	−728.000	+	1375.79i	−0.0495341	+	0.0936107i
$601$	−21238.0			−1.44146			−0.720729	−	0.693217i	$-0.756193\pi$
$601$	−21238.0			−1.44146			−0.720729	+	0.693217i	$0.756193\pi$
$602$	9296.00	−	3513.56i	0.629363	−	0.237877i
$603$		−	174.620i		−	0.0117928i
$604$	−4464.00	+	3936.88i	−0.300724	+	0.265214i
$605$		−	11419.1i		−	0.767357i
$606$	3976.00	+	10519.5i	0.266525	+	0.705158i
$607$	−13664.0			−0.913681			−0.456841	−	0.889549i	$-0.651019\pi$
$607$	−13664.0			−0.913681			−0.456841	+	0.889549i	$0.651019\pi$
$608$	1568.00	+	6519.13i	0.104590	+	0.434845i
$609$	−6720.00			−0.447140
$610$	−1008.00	−	2666.92i	−0.0669061	−	0.177017i
$611$			17779.4i			1.17722i
$612$	−84.0000	+	74.0810i	−0.00554820	+	0.00489305i
$613$			20393.5i			1.34369i	0.740690	+	0.671846i	$0.234499\pi$
$613$			20393.5i			1.34369i	−0.740690	+	0.671846i	$0.765501\pi$
$614$	6846.00	−	2587.54i	0.449971	−	0.170073i
$615$	−3920.00			−0.257024
$616$	−1344.00	+	2539.92i	−0.0879080	+	0.166130i
$617$	−3782.00			−0.246771			−0.123385	−	0.992359i	$-0.539375\pi$
$617$	−3782.00			−0.246771			−0.123385	+	0.992359i	$0.539375\pi$
$618$	16464.0	−	6222.81i	1.07165	−	0.405045i
$619$			5825.94i			0.378295i	0.981949	+	0.189147i	$0.0605724\pi$
$619$			5825.94i			0.378295i	−0.981949	+	0.189147i	$0.939428\pi$
$620$	12544.0	+	14223.6i	0.812547	+	0.921342i
$621$		−	20912.0i		−	1.35132i
$622$	2744.00	+	7259.94i	0.176888	+	0.468002i
$623$	−2128.00			−0.136848
$624$	−2240.00	+	17779.4i	−0.143705	+	1.14062i
$625$	−13831.0			−0.885184
$626$	−2282.00	−	6037.60i	−0.145698	−	0.385481i
$627$		−	3111.40i		−	0.198178i
$628$	−952.000	−	1079.47i	−0.0604919	−	0.0685914i
$629$		−	3407.73i		−	0.216017i
$630$	−224.000	+	84.6640i	−0.0141657	+	0.00535412i
$631$	2056.00			0.129712			0.0648558	−	0.997895i	$-0.479341\pi$
$631$	2056.00			0.129712			0.0648558	+	0.997895i	$0.479341\pi$
$632$	−9280.00	−	4910.51i	−0.584080	−	0.309066i
$633$	15428.0			0.968733
$634$	25340.0	−	9577.62i	1.58735	−	0.599962i
$635$			17610.1i			1.10053i
$636$	1008.00	−	888.972i	0.0628456	−	0.0554246i
$637$		−	14763.3i		−	0.918278i
$638$	2520.00	+	6667.29i	0.156376	+	0.413731i
$639$	72.0000			0.00445740
$640$	−12544.0	−	8805.06i	−0.774758	−	0.543829i
$641$	11842.0			0.729689			0.364845	−	0.931068i	$-0.381122\pi$
$641$	11842.0			0.729689			0.364845	+	0.931068i	$0.381122\pi$
$642$	−1428.00	−	3778.13i	−0.0877861	−	0.232260i
$643$		−	16250.2i		−	0.996649i	−0.866991	−	0.498325i	$-0.833949\pi$
$643$		−	16250.2i		−	0.996649i	0.866991	−	0.498325i	$-0.166051\pi$
$644$	−7296.00	+	6434.47i	−0.446433	+	0.393717i
$645$		−	24594.9i		−	1.50143i
$646$	1372.00	−	518.567i	0.0835613	−	0.0315832i
$647$	19320.0			1.17395			0.586976	−	0.809604i	$-0.300318\pi$
$647$	19320.0			1.17395			0.586976	+	0.809604i	$0.300318\pi$
$648$	−15100.0	−	7990.17i	−0.915407	−	0.484388i
$649$	8484.00			0.513137
$650$	1820.00	−	687.895i	0.109825	−	0.0415100i
$651$		−	9482.37i		−	0.570881i
$652$	9380.00	+	10635.9i	0.563419	+	0.638857i
$653$		−	2317.68i		−	0.138894i	−0.997586	−	0.0694470i	$-0.977877\pi$
$653$		−	2317.68i		−	0.138894i	0.997586	−	0.0694470i	$-0.0221235\pi$
$654$	−10024.0	−	26521.0i	−0.599342	−	1.58571i
$655$	−7112.00			−0.424258
$656$	−560.000	+	4444.86i	−0.0333298	+	0.264547i
$657$	294.000			0.0174582
$658$	2688.00	+	7111.78i	0.159254	+	0.421347i
$659$			27732.8i			1.63932i	0.572847	+	0.819662i	$0.305839\pi$
$659$			27732.8i			1.63932i	−0.572847	+	0.819662i	$0.694161\pi$
$660$	4704.00	+	5333.83i	0.277429	+	0.314575i
$661$			22467.7i			1.32208i	0.750352	+	0.661039i	$0.229884\pi$
$661$			22467.7i			1.32208i	−0.750352	+	0.661039i	$0.770116\pi$
$662$	−11242.0	+	4249.08i	−0.660019	+	0.249464i
$663$	3920.00			0.229623
$664$	5768.00	−	10900.5i	0.337111	−	0.637080i
$665$	3136.00			0.182870
$666$	−644.000	+	243.409i	−0.0374692	+	0.0141620i
$667$			24129.3i			1.40073i
$668$	11760.0	−	10371.3i	0.681150	−	0.600718i
$669$			8297.08i			0.479497i
$670$	−1848.00	−	4889.35i	−0.106559	−	0.281928i
$671$	1512.00			0.0869897
$672$	1792.00	+	7450.44i	0.102869	+	0.427689i
$673$	−10078.0			−0.577234			−0.288617	−	0.957445i	$-0.593195\pi$
$673$	−10078.0			−0.577234			−0.288617	+	0.957445i	$0.593195\pi$
$674$	−6130.00	−	16218.5i	−0.350325	−	0.926872i
$675$			1788.53i			0.101986i
$676$	3618.00	−	3190.78i	0.205849	−	0.181542i
$677$			16160.2i			0.917413i	0.888588	+	0.458707i	$0.151687\pi$
$677$			16160.2i			0.917413i	−0.888588	+	0.458707i	$0.848313\pi$
$678$	−23940.0	+	9048.47i	−1.35606	+	0.512543i
$679$	−7952.00			−0.449440
$680$	−1568.00	+	2963.24i	−0.0884266	+	0.167110i
$681$	6692.00			0.376561
$682$	−9408.00	+	3555.89i	−0.528227	+	0.199651i
$683$		−	16356.0i		−	0.916320i	−0.888870	−	0.458160i	$-0.848509\pi$
$683$		−	16356.0i		−	0.916320i	0.888870	−	0.458160i	$-0.151491\pi$
$684$	−196.000	−	222.243i	−0.0109565	−	0.0124235i
$685$			11239.2i			0.626899i
$686$	−4976.00	−	13165.3i	−0.276945	−	0.732729i
$687$	−27272.0			−1.51454
$688$	−27888.0	−	3513.56i	−1.54538	−	0.194699i
$689$	−1680.00			−0.0928925
$690$	8512.00	+	22520.6i	0.469632	+	1.24253i
$691$		−	29246.1i		−	1.61009i	−0.593211	−	0.805047i	$-0.702140\pi$
$691$		−	29246.1i		−	1.61009i	0.593211	−	0.805047i	$-0.297860\pi$
$692$	−10584.0	−	12001.1i	−0.581421	−	0.659269i
$693$		−	126.996i		−	0.00696130i
$694$	6566.00	−	2481.71i	0.359138	−	0.135742i
$695$	28504.0			1.55571
$696$	16800.0	+	8889.72i	0.914946	+	0.484144i
$697$	980.000			0.0532570
$698$	−868.000	+	328.073i	−0.0470692	+	0.0177905i
$699$		−	4434.28i		−	0.239943i
$700$	624.000	−	550.316i	0.0336928	−	0.0297143i
$701$			2465.84i			0.132858i	0.997791	+	0.0664290i	$0.0211606\pi$
$701$			2465.84i			0.132858i	−0.997791	+	0.0664290i	$0.978839\pi$
$702$	7280.00	+	19261.1i	0.391404	+	1.03556i
$703$	9016.00			0.483705
$704$	6720.00	−	4571.86i	0.359758	−	0.244756i
$705$	18816.0			1.00518
$706$	10206.0	+	27002.5i	0.544062	+	1.43945i
$707$		−	6011.15i		−	0.319763i
$708$	16968.0	−	14964.4i	0.900701	−	0.794344i
$709$		−	31674.9i		−	1.67782i	−0.544267	−	0.838912i	$-0.683192\pi$
$709$		−	31674.9i		−	1.67782i	0.544267	−	0.838912i	$-0.316808\pi$
$710$	2016.00	−	761.976i	0.106562	−	0.0402767i
$711$	464.000			0.0244745
$712$	5320.00	+	2815.08i	0.280022	+	0.148174i
$713$	−34048.0			−1.78837
$714$	1568.00	−	592.648i	0.0821862	−	0.0310635i
$715$		−	8889.72i		−	0.464975i
$716$	−17276.0	−	19589.1i	−0.901724	−	1.02246i
$717$			33273.0i			1.73306i
$718$	3176.00	+	8402.91i	0.165080	+	0.436760i
$719$	−9296.00			−0.482173			−0.241086	−	0.970504i	$-0.577504\pi$
$719$	−9296.00			−0.482173			−0.241086	+	0.970504i	$0.577504\pi$
$720$	672.000	+	84.6640i	0.0347833	+	0.00438228i
$721$	−9408.00			−0.485953
$722$	−5487.00	−	14517.2i	−0.282832	−	0.748304i
$723$		−	15482.9i		−	0.796427i
$724$	12376.0	+	14033.1i	0.635291	+	0.720352i
$725$		−	2063.69i		−	0.105715i
$726$	15106.0	−	5709.53i	0.772226	−	0.291874i
$727$	21672.0			1.10560			0.552799	−	0.833315i	$-0.313560\pi$
$727$	21672.0			1.10560			0.552799	+	0.833315i	$0.313560\pi$
$728$	4480.00	−	8466.40i	0.228077	−	0.431024i
$729$	−18901.0			−0.960270
$730$	8232.00	−	3111.40i	0.417370	−	0.157751i
$731$			6148.73i			0.311106i
$732$	3024.00	−	2666.92i	0.152692	−	0.134661i
$733$		−	9471.79i		−	0.477283i	−0.971108	−	0.238642i	$-0.923298\pi$
$733$		−	9471.79i		−	0.477283i	0.971108	−	0.238642i	$-0.0767021\pi$
$734$	11760.0	+	31114.0i	0.591375	+	1.56463i
$735$	−15624.0			−0.784082
$736$	26752.0	−	6434.47i	1.33980	−	0.322252i
$737$	2772.00			0.138545
$738$	−70.0000	−	185.203i	−0.00349151	−	0.00923767i
$739$			6863.08i			0.341627i	0.985303	+	0.170814i	$0.0546396\pi$
$739$			6863.08i			0.341627i	−0.985303	+	0.170814i	$0.945360\pi$
$740$	−15456.0	+	13630.9i	−0.767803	+	0.677138i
$741$			10371.3i			0.514171i
$742$	−672.000	+	253.992i	−0.0332478	+	0.0125665i
$743$	17432.0			0.860724			0.430362	−	0.902656i	$-0.358386\pi$
$743$	17432.0			0.860724			0.430362	+	0.902656i	$0.358386\pi$
$744$	−12544.0	+	23705.9i	−0.618125	+	1.16815i
$745$	8400.00			0.413090
$746$	−29036.0	+	10974.6i	−1.42504	+	0.538616i
$747$			545.025i			0.0266953i
$748$	−1176.00	−	1333.46i	−0.0574851	−	0.0651819i
$749$			2158.93i			0.105321i
$750$	−7728.00	−	20446.4i	−0.376249	−	0.995461i
$751$	−11632.0			−0.565190			−0.282595	−	0.959239i	$-0.591195\pi$
$751$	−11632.0			−0.565190			−0.282595	+	0.959239i	$0.591195\pi$
$752$	2688.00	−	21335.3i	0.130347	−	1.03460i
$753$	−28812.0			−1.39438
$754$	−8400.00	−	22224.3i	−0.405716	−	1.07342i
$755$		−	7873.76i		−	0.379543i
$756$	5824.00	+	6603.80i	0.280181	+	0.317695i
$757$		−	16731.7i		−	0.803336i	−0.915785	−	0.401668i	$-0.868431\pi$
$757$		−	16731.7i		−	0.803336i	0.915785	−	0.401668i	$-0.131569\pi$
$758$	8134.00	−	3074.36i	0.389763	−	0.147316i
$759$	−12768.0			−0.610605
$760$	−7840.00	−	4148.54i	−0.374193	−	0.198004i
$761$	39466.0			1.87995			0.939975	−	0.341244i	$-0.110848\pi$
$761$	39466.0			1.87995			0.939975	+	0.341244i	$0.110848\pi$
$762$	−23296.0	+	8805.06i	−1.10751	+	0.418601i
$763$			15154.9i			0.719060i
$764$	−23424.0	+	20658.0i	−1.10923	+	0.978248i
$765$		−	148.162i		−	0.00700237i
$766$	−2688.00	−	7111.78i	−0.126790	−	0.335456i
$767$	−28280.0			−1.33133
$768$	5376.00	−	20996.7i	0.252591	−	0.986527i
$769$	35266.0			1.65374			0.826869	−	0.562395i	$-0.190120\pi$
$769$	35266.0			1.65374			0.826869	+	0.562395i	$0.190120\pi$
$770$	−1344.00	−	3555.89i	−0.0629018	−	0.166423i
$771$			13556.8i			0.633252i
$772$	−19980.0	+	17620.7i	−0.931471	+	0.821481i
$773$			16244.9i			0.755872i	0.925832	+	0.377936i	$0.123366\pi$
$773$			16244.9i			0.755872i	−0.925832	+	0.377936i	$0.876634\pi$
$774$	1162.00	−	439.195i	0.0539628	−	0.0203960i
$775$	2912.00			0.134970
$776$	19880.0	+	10519.5i	0.919653	+	0.486634i
$777$	10304.0			0.475745
$778$	27748.0	−	10487.8i	1.27868	−	0.483296i
$779$			2592.84i			0.119253i
$780$	−15680.0	−	17779.4i	−0.719787	−	0.816162i
$781$			1142.96i			0.0523668i
$782$	−2128.00	−	5630.16i	−0.0973109	−	0.257460i
$783$	21840.0			0.996805
$784$	−2232.00	+	17716.0i	−0.101676	+	0.807031i
$785$	1904.00			0.0865690
$786$	−3556.00	−	9408.29i	−0.161372	−	0.426950i
$787$			34844.5i			1.57824i	0.614240	+	0.789119i	$0.289463\pi$
$787$			34844.5i			1.57824i	−0.614240	+	0.789119i	$0.710537\pi$
$788$	6328.00	+	7175.28i	0.286073	+	0.324376i
$789$		−	31198.7i		−	1.40774i
$790$	12992.0	−	4910.51i	0.585107	−	0.221150i
$791$	13680.0			0.614924
$792$	−168.000	+	317.490i	−0.00753740	+	0.0142443i
$793$	−5040.00			−0.225694
$794$	−15092.0	+	5704.24i	−0.674553	+	0.254957i
$795$			1777.94i			0.0793172i
$796$	10416.0	−	9186.05i	0.463801	−	0.409034i
$797$			2550.50i			0.113354i	0.998393	+	0.0566772i	$0.0180506\pi$
$797$			2550.50i			0.113354i	−0.998393	+	0.0566772i	$0.981949\pi$
$798$	1568.00	+	4148.54i	0.0695571	+	0.184031i
$799$	−4704.00			−0.208280
$800$	−2288.00	+	550.316i	−0.101116	+	0.0243208i
$801$	−266.000			−0.0117336
$802$	−12402.0	−	32812.6i	−0.546047	−	1.44471i
$803$			4667.11i			0.205104i
$804$	5544.00	−	4889.35i	0.243186	−	0.214470i
$805$		−	12868.9i		−	0.563441i
$806$	31360.0	−	11853.0i	1.37048	−	0.517994i
$807$	28392.0			1.23847
$808$	−7952.00	+	15027.9i	−0.346226	+	0.654305i
$809$	−24390.0			−1.05996			−0.529979	−	0.848010i	$-0.677800\pi$
$809$	−24390.0			−1.05996			−0.529979	+	0.848010i	$0.677800\pi$
$810$	21140.0	−	7990.17i	0.917017	−	0.346600i
$811$		−	9582.91i		−	0.414922i	−0.978243	−	0.207461i	$-0.933480\pi$
$811$		−	9582.91i		−	0.414922i	0.978243	−	0.207461i	$-0.0665200\pi$
$812$	−6720.00	−	7619.76i	−0.290426	−	0.329312i
$813$		−	8889.72i		−	0.383489i
$814$	−3864.00	−	10223.2i	−0.166380	−	0.440199i
$815$	−18760.0			−0.806300
$816$	−4704.00	−	592.648i	−0.201805	−	0.0254250i
$817$	−16268.0			−0.696628
$818$	12278.0	+	32484.5i	0.524805	+	1.38850i
$819$			423.320i			0.0180611i
$820$	−3920.00	−	4444.86i	−0.166942	−	0.189294i
$821$		−	8773.31i		−	0.372948i	−0.982460	−	0.186474i	$-0.940294\pi$
$821$		−	8773.31i		−	0.372948i	0.982460	−	0.186474i	$-0.0597061\pi$
$822$	−14868.0	+	5619.58i	−0.630877	+	0.238449i
$823$	−21688.0			−0.918586			−0.459293	−	0.888285i	$-0.651897\pi$
$823$	−21688.0			−0.918586			−0.459293	+	0.888285i	$0.651897\pi$
$824$	23520.0	+	12445.6i	0.994367	+	0.526169i
$825$	1092.00			0.0460831
$826$	−11312.0	+	4275.53i	−0.476507	+	0.180103i
$827$		−	19446.3i		−	0.817670i	−0.912608	−	0.408835i	$-0.865935\pi$
$827$		−	19446.3i		−	0.817670i	0.912608	−	0.408835i	$-0.134065\pi$
$828$	−912.000	+	804.308i	−0.0382780	+	0.0337580i
$829$		−	19546.8i		−	0.818925i	−0.912327	−	0.409462i	$-0.865716\pi$
$829$		−	19546.8i		−	0.818925i	0.912327	−	0.409462i	$-0.134284\pi$
$830$	5768.00	+	15260.7i	0.241217	+	0.638200i
$831$	8344.00			0.348315
$832$	−22400.0	+	15239.5i	−0.933390	+	0.635019i
$833$	3906.00			0.162467
$834$	14252.0	+	37707.2i	0.591734	+	1.56558i
$835$			20742.7i			0.859677i
$836$	3528.00	−	3111.40i	0.145955	−	0.128720i
$837$			30817.7i			1.27266i
$838$	−21714.0	+	8207.12i	−0.895105	+	0.338318i
$839$	−18760.0			−0.771951			−0.385976	−	0.922509i	$-0.626135\pi$
$839$	−18760.0			−0.771951			−0.385976	+	0.922509i	$0.626135\pi$
$840$	−8960.00	−	4741.19i	−0.368035	−	0.194746i
$841$	−811.000			−0.0332527
$842$	−3836.00	+	1449.87i	−0.157004	+	0.0593419i
$843$		−	14509.3i		−	0.592796i
$844$	15428.0	+	17493.7i	0.629210	+	0.713458i
$845$			6381.55i			0.259801i
$846$	336.000	+	888.972i	0.0136547	+	0.0361271i
$847$	−8632.00			−0.350176
$848$	2016.00	+	253.992i	0.0816388	+	0.0102855i
$849$	−15820.0			−0.639506
$850$	182.000	+	481.527i	0.00734417	+	0.0194309i
$851$		−	36998.2i		−	1.49034i
$852$	2016.00	+	2285.93i	0.0810646	+	0.0919186i
$853$			28732.9i			1.15333i	0.816979	+	0.576667i	$0.195647\pi$
$853$			28732.9i			1.15333i	−0.816979	+	0.576667i	$0.804353\pi$
$854$	−2016.00	+	761.976i	−0.0807800	+	0.0305320i
$855$	392.000			0.0156797
$856$	2856.00	−	5397.33i	0.114037	−	0.215511i
$857$	8778.00			0.349884			0.174942	−	0.984579i	$-0.444026\pi$
$857$	8778.00			0.349884			0.174942	+	0.984579i	$0.444026\pi$
$858$	11760.0	−	4444.86i	0.467925	−	0.176859i
$859$		−	5646.03i		−	0.224261i	−0.993693	−	0.112130i	$-0.964233\pi$
$859$		−	5646.03i		−	0.224261i	0.993693	−	0.112130i	$-0.0357675\pi$
$860$	27888.0	−	24594.9i	1.10578	−	0.975208i
$861$			2963.24i			0.117290i
$862$	−7632.00	−	20192.4i	−0.301563	−	0.797860i
$863$	−9312.00			−0.367305			−0.183652	−	0.982991i	$-0.558792\pi$
$863$	−9312.00			−0.367305			−0.183652	+	0.982991i	$0.558792\pi$
$864$	−5824.00	−	24213.9i	−0.229325	−	0.953442i
$865$	21168.0			0.832062
$866$	−3794.00	−	10038.0i	−0.148875	−	0.393885i
$867$		−	24960.0i		−	0.977724i
$868$	10752.0	−	9482.37i	0.420445	−	0.370798i
$869$			7365.77i			0.287534i
$870$	−23520.0	+	8889.72i	−0.916555	+	0.346425i
$871$	−9240.00			−0.359455
$872$	20048.0	−	37887.2i	0.778568	−	1.47135i
$873$	−994.000			−0.0385359
$874$	14896.0	−	5630.16i	0.576504	−	0.217898i
$875$			11683.6i			0.451405i
$876$	8232.00	+	9334.21i	0.317504	+	0.360016i
$877$			137.579i			0.00529728i	0.999996	+	0.00264864i	$0.000843089\pi$
$877$			137.579i			0.00529728i	−0.999996	+	0.00264864i	$0.999157\pi$
$878$	1848.00	+	4889.35i	0.0710330	+	0.187936i
$879$	48888.0			1.87594
$880$	−1344.00	+	10667.7i	−0.0514844	+	0.408644i
$881$	−31150.0			−1.19123			−0.595613	−	0.803272i	$-0.703091\pi$
$881$	−31150.0			−1.19123			−0.595613	+	0.803272i	$0.703091\pi$
$882$	−279.000	−	738.165i	−0.0106513	−	0.0281806i
$883$			12577.9i			0.479366i	0.970851	+	0.239683i	$0.0770435\pi$
$883$			12577.9i			0.479366i	−0.970851	+	0.239683i	$0.922957\pi$
$884$	3920.00	+	4444.86i	0.149145	+	0.169114i
$885$			29928.7i			1.13677i
$886$	−32634.0	+	12334.5i	−1.23743	+	0.467704i
$887$	37128.0			1.40545			0.702726	−	0.711460i	$-0.251966\pi$
$887$	37128.0			1.40545			0.702726	+	0.711460i	$0.251966\pi$
$888$	−25760.0	−	13630.9i	−0.973479	−	0.515116i
$889$	13312.0			0.502216
$890$	−7448.00	+	2815.08i	−0.280514	+	0.106024i
$891$			11985.3i			0.450641i
$892$	−9408.00	+	8297.08i	−0.353143	+	0.311442i
$893$		−	12445.6i		−	0.466379i
$894$	4200.00	+	11112.2i	0.157124	+	0.415711i
$895$	34552.0			1.29044
$896$	−6656.00	+	9482.37i	−0.248171	+	0.353553i
$897$	42560.0			1.58421
$898$	3582.00	+	9477.08i	0.133110	+	0.352176i
$899$		−	35558.9i		−	1.31919i
$900$	78.0000	−	68.7895i	0.00288889	−	0.00254776i
$901$		−	444.486i		−	0.0164351i
$902$	2940.00	−	1111.22i	0.108527	−	0.0410193i
$903$	−18592.0			−0.685164
$904$	−34200.0	−	18096.9i	−1.25827	−	0.665813i
$905$	−24752.0			−0.909154
$906$	10416.0	−	3936.88i	0.381952	−	0.144364i
$907$			35204.4i			1.28880i	0.764688	+	0.644400i	$0.222893\pi$
$907$			35204.4i			1.28880i	−0.764688	+	0.644400i	$0.777107\pi$
$908$	6692.00	+	7588.01i	0.244584	+	0.277332i
$909$		−	751.393i		−	0.0274171i
$910$	4480.00	+	11853.0i	0.163198	+	0.431782i
$911$	−10512.0			−0.382303			−0.191152	−	0.981561i	$-0.561222\pi$
$911$	−10512.0			−0.382303			−0.191152	+	0.981561i	$0.561222\pi$
$912$	1568.00	−	12445.6i	0.0569317	−	0.451881i
$913$	−8652.00			−0.313625
$914$	−2714.00	−	7180.57i	−0.0982179	−	0.259860i
$915$			5333.83i			0.192712i
$916$	−27272.0	−	30923.5i	−0.983725	−	1.11544i
$917$			5376.17i			0.193606i
$918$	−5096.00	+	1926.11i	−0.183217	+	0.0692495i
$919$	−46104.0			−1.65488			−0.827438	−	0.561557i	$-0.810202\pi$
$919$	−46104.0			−1.65488			−0.827438	+	0.561557i	$0.810202\pi$
$920$	−17024.0	+	32172.3i	−0.610070	+	1.15292i
$921$	−13692.0			−0.489866
$922$	22092.0	−	8349.99i	0.789112	−	0.298256i
$923$		−	3809.88i		−	0.135865i
$924$	4032.00	−	3555.89i	0.143553	−	0.126602i
$925$			3164.32i			0.112478i
$926$	−2224.00	−	5884.15i	−0.0789257	−	0.208818i
$927$	−1176.00			−0.0416666
$928$	6720.00	+	27939.1i	0.237710	+	0.988305i
$929$	−5726.00			−0.202222			−0.101111	−	0.994875i	$-0.532240\pi$
$929$	−5726.00			−0.202222			−0.101111	+	0.994875i	$0.532240\pi$
$930$	−12544.0	−	33188.3i	−0.442295	−	1.17020i
$931$			10334.3i			0.363795i
$932$	5028.00	−	4434.28i	0.176714	−	0.155847i
$933$		−	14519.9i		−	0.509496i
$934$	27230.0	−	10292.0i	0.953954	−	0.360561i
$935$	2352.00			0.0822659
$936$	560.000	−	1058.30i	0.0195557	−	0.0369569i
$937$	1274.00			0.0444181			0.0222091	−	0.999753i	$-0.492930\pi$
$937$	1274.00			0.0444181			0.0222091	+	0.999753i	$0.492930\pi$
$938$	−3696.00	+	1396.96i	−0.128655	+	0.0486271i
$939$			12075.2i			0.419659i
$940$	18816.0	+	21335.3i	0.652883	+	0.740300i
$941$		−	26446.9i		−	0.916201i	−0.888900	−	0.458101i	$-0.848530\pi$
$941$		−	26446.9i		−	0.916201i	0.888900	−	0.458101i	$-0.151470\pi$
$942$	952.000	+	2518.76i	0.0329276	+	0.0871183i
$943$	10640.0			0.367430
$944$	33936.0	+	4275.53i	1.17005	+	0.147412i
$945$	−11648.0			−0.400962
$946$	6972.00	+	18446.2i	0.239619	+	0.633971i
$947$			23922.9i			0.820897i	0.911884	+	0.410448i	$0.134628\pi$
$947$			23922.9i			0.820897i	−0.911884	+	0.410448i	$0.865372\pi$
$948$	12992.0	+	14731.5i	0.445106	+	0.504703i
$949$		−	15557.0i		−	0.532141i
$950$	−1274.00	+	481.527i	−0.0435095	+	0.0164450i
$951$	−50680.0			−1.72809
$952$	2240.00	+	1185.30i	0.0762593	+	0.0403526i
$953$	38250.0			1.30015			0.650073	−	0.759872i	$-0.274738\pi$
$953$	38250.0			1.30015			0.650073	+	0.759872i	$0.274738\pi$
$954$	−84.0000	+	31.7490i	−0.00285073	+	0.00107748i
$955$		−	41316.1i		−	1.39995i
$956$	−37728.0	+	33273.0i	−1.27637	+	1.12565i
$957$		−	13334.6i		−	0.450414i
$958$	−17696.0	−	46819.2i	−0.596797	−	1.57898i
$959$	8496.00			0.286079
$960$	16128.0	+	23705.9i	0.542218	+	0.796985i
$961$	20385.0			0.684267
$962$	12880.0	+	34077.3i	0.431671	+	1.14210i
$963$			269.867i			0.00903046i
$964$	17556.0	−	15482.9i	0.586557	−	0.517294i
$965$		−	35241.4i		−	1.17561i
$966$	17024.0	−	6434.47i	0.567017	−	0.214312i
$967$	4664.00			0.155103			0.0775513	−	0.996988i	$-0.475290\pi$
$967$	4664.00			0.155103			0.0775513	+	0.996988i	$0.475290\pi$
$968$	21580.0	+	11419.1i	0.716537	+	0.379156i
$969$	−2744.00			−0.0909701
$970$	−27832.0	+	10519.5i	−0.921270	+	0.348207i
$971$			30971.2i			1.02360i	0.859106	+	0.511798i	$0.171020\pi$
$971$			30971.2i			1.02360i	−0.859106	+	0.511798i	$0.828980\pi$
$972$	1484.00	+	1682.70i	0.0489705	+	0.0555273i
$973$		−	21547.0i		−	0.709933i
$974$	−1304.00	−	3450.06i	−0.0428982	−	0.113498i
$975$	−3640.00			−0.119562
$976$	6048.00	+	761.976i	0.198352	+	0.0249900i
$977$	−4814.00			−0.157639			−0.0788196	−	0.996889i	$-0.525115\pi$
$977$	−4814.00			−0.157639			−0.0788196	+	0.996889i	$0.525115\pi$
$978$	−9380.00	−	24817.1i	−0.306686	−	0.811416i
$979$		−	4222.62i		−	0.137850i
$980$	−15624.0	−	17716.0i	−0.509276	−	0.577465i
$981$			1894.36i			0.0616536i
$982$	44086.0	−	16662.9i	1.43263	−	0.541483i
$983$	−12376.0			−0.401560			−0.200780	−	0.979636i	$-0.564348\pi$
$983$	−12376.0			−0.401560			−0.200780	+	0.979636i	$0.564348\pi$
$984$	3920.00	−	7408.10i	0.126997	−	0.240002i
$985$	−12656.0			−0.409395
$986$	5880.00	−	2222.43i	0.189916	−	0.0717816i
$987$		−	14223.6i		−	0.458704i
$988$	−11760.0	+	10371.3i	−0.378680	+	0.333964i
$989$			66757.6i			2.14638i
$990$	−168.000	−	444.486i	−0.00539332	−	0.0142694i
$991$	45344.0			1.45348			0.726740	−	0.686912i	$-0.241034\pi$
$991$	45344.0			1.45348			0.726740	+	0.686912i	$0.241034\pi$
$992$	−39424.0	+	9482.37i	−1.26181	+	0.303494i
$993$	22484.0			0.718538
$994$	−576.000	−	1523.95i	−0.0183799	−	0.0486286i
$995$			18372.1i			0.585361i
$996$	−17304.0	+	15260.7i	−0.550500	+	0.485496i
$997$		−	26002.4i		−	0.825984i	−0.910735	−	0.412992i	$-0.864484\pi$
$997$		−	26002.4i		−	0.825984i	0.910735	−	0.412992i	$-0.135516\pi$
$998$	8190.00	−	3095.53i	0.259769	−	0.0981836i
$999$	−33488.0			−1.06057

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.4.b.a.5.1	✓	2
3.2	odd	2		72.4.d.b.37.2		2
4.3	odd	2		32.4.b.a.17.1		2
5.2	odd	4		200.4.f.a.149.3		4
5.3	odd	4		200.4.f.a.149.2		4
5.4	even	2		200.4.d.a.101.2		2
8.3	odd	2		32.4.b.a.17.2		2
8.5	even	2	inner	8.4.b.a.5.2	yes	2
12.11	even	2		288.4.d.a.145.2		2
16.3	odd	4		256.4.a.j.1.2		2
16.5	even	4		256.4.a.l.1.2		2
16.11	odd	4		256.4.a.j.1.1		2
16.13	even	4		256.4.a.l.1.1		2
20.3	even	4		800.4.f.a.49.3		4
20.7	even	4		800.4.f.a.49.2		4
20.19	odd	2		800.4.d.a.401.2		2
24.5	odd	2		72.4.d.b.37.1		2
24.11	even	2		288.4.d.a.145.1		2
40.3	even	4		800.4.f.a.49.1		4
40.13	odd	4		200.4.f.a.149.4		4
40.19	odd	2		800.4.d.a.401.1		2
40.27	even	4		800.4.f.a.49.4		4
40.29	even	2		200.4.d.a.101.1		2
40.37	odd	4		200.4.f.a.149.1		4
48.5	odd	4		2304.4.a.bn.1.1		2
48.11	even	4		2304.4.a.v.1.1		2
48.29	odd	4		2304.4.a.bn.1.2		2
48.35	even	4		2304.4.a.v.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.4.b.a.5.1	✓	2	1.1	even	1	trivial
8.4.b.a.5.2	yes	2	8.5	even	2	inner
32.4.b.a.17.1		2	4.3	odd	2
32.4.b.a.17.2		2	8.3	odd	2
72.4.d.b.37.1		2	24.5	odd	2
72.4.d.b.37.2		2	3.2	odd	2
200.4.d.a.101.1		2	40.29	even	2
200.4.d.a.101.2		2	5.4	even	2
200.4.f.a.149.1		4	40.37	odd	4
200.4.f.a.149.2		4	5.3	odd	4
200.4.f.a.149.3		4	5.2	odd	4
200.4.f.a.149.4		4	40.13	odd	4
256.4.a.j.1.1		2	16.11	odd	4
256.4.a.j.1.2		2	16.3	odd	4
256.4.a.l.1.1		2	16.13	even	4
256.4.a.l.1.2		2	16.5	even	4
288.4.d.a.145.1		2	24.11	even	2
288.4.d.a.145.2		2	12.11	even	2
800.4.d.a.401.1		2	40.19	odd	2
800.4.d.a.401.2		2	20.19	odd	2
800.4.f.a.49.1		4	40.3	even	4
800.4.f.a.49.2		4	20.7	even	4
800.4.f.a.49.3		4	20.3	even	4
800.4.f.a.49.4		4	40.27	even	4
2304.4.a.v.1.1		2	48.11	even	4
2304.4.a.v.1.2		2	48.35	even	4
2304.4.a.bn.1.1		2	48.5	odd	4
2304.4.a.bn.1.2		2	48.29	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 2.64575i) q^{2} +5.29150i q^{3} +(-6.00000 + 5.29150i) q^{4} -10.5830i q^{5} +(14.0000 - 5.29150i) q^{6} -8.00000 q^{7} +(20.0000 + 10.5830i) q^{8} -1.00000 q^{9} +(-28.0000 + 10.5830i) q^{10} -15.8745i q^{11} +(-28.0000 - 31.7490i) q^{12} +52.9150i q^{13} +(8.00000 + 21.1660i) q^{14} +56.0000 q^{15} +(8.00000 - 63.4980i) q^{16} -14.0000 q^{17} +(1.00000 + 2.64575i) q^{18} -37.0405i q^{19} +(56.0000 + 63.4980i) q^{20} -42.3320i q^{21} +(-42.0000 + 15.8745i) q^{22} -152.000 q^{23} +(-56.0000 + 105.830i) q^{24} +13.0000 q^{25} +(140.000 - 52.9150i) q^{26} +137.579i q^{27} +(48.0000 - 42.3320i) q^{28} -158.745i q^{29} +(-56.0000 - 148.162i) q^{30} +224.000 q^{31} +(-176.000 + 42.3320i) q^{32} +84.0000 q^{33} +(14.0000 + 37.0405i) q^{34} +84.6640i q^{35} +(6.00000 - 5.29150i) q^{36} +243.409i q^{37} +(-98.0000 + 37.0405i) q^{38} -280.000 q^{39} +(112.000 - 211.660i) q^{40} -70.0000 q^{41} +(-112.000 + 42.3320i) q^{42} -439.195i q^{43} +(84.0000 + 95.2470i) q^{44} +10.5830i q^{45} +(152.000 + 402.154i) q^{46} +336.000 q^{47} +(336.000 + 42.3320i) q^{48} -279.000 q^{49} +(-13.0000 - 34.3948i) q^{50} -74.0810i q^{51} +(-280.000 - 317.490i) q^{52} +31.7490i q^{53} +(364.000 - 137.579i) q^{54} -168.000 q^{55} +(-160.000 - 84.6640i) q^{56} +196.000 q^{57} +(-420.000 + 158.745i) q^{58} +534.442i q^{59} +(-336.000 + 296.324i) q^{60} +95.2470i q^{61} +(-224.000 - 592.648i) q^{62} +8.00000 q^{63} +(288.000 + 423.320i) q^{64} +560.000 q^{65} +(-84.0000 - 222.243i) q^{66} +174.620i q^{67} +(84.0000 - 74.0810i) q^{68} -804.308i q^{69} +(224.000 - 84.6640i) q^{70} -72.0000 q^{71} +(-20.0000 - 10.5830i) q^{72} -294.000 q^{73} +(644.000 - 243.409i) q^{74} +68.7895i q^{75} +(196.000 + 222.243i) q^{76} +126.996i q^{77} +(280.000 + 740.810i) q^{78} -464.000 q^{79} +(-672.000 - 84.6640i) q^{80} -755.000 q^{81} +(70.0000 + 185.203i) q^{82} -545.025i q^{83} +(224.000 + 253.992i) q^{84} +148.162i q^{85} +(-1162.00 + 439.195i) q^{86} +840.000 q^{87} +(168.000 - 317.490i) q^{88} +266.000 q^{89} +(28.0000 - 10.5830i) q^{90} -423.320i q^{91} +(912.000 - 804.308i) q^{92} +1185.30i q^{93} +(-336.000 - 888.972i) q^{94} -392.000 q^{95} +(-224.000 - 931.304i) q^{96} +994.000 q^{97} +(279.000 + 738.165i) q^{98} +15.8745i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 12 q^{4} + 28 q^{6} - 16 q^{7} + 40 q^{8} - 2 q^{9} - 56 q^{10} - 56 q^{12} + 16 q^{14} + 112 q^{15} + 16 q^{16} - 28 q^{17} + 2 q^{18} + 112 q^{20} - 84 q^{22} - 304 q^{23} - 112 q^{24}+ \cdots + 558 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 12 * q^4 + 28 * q^6 - 16 * q^7 + 40 * q^8 - 2 * q^9 - 56 * q^10 - 56 * q^12 + 16 * q^14 + 112 * q^15 + 16 * q^16 - 28 * q^17 + 2 * q^18 + 112 * q^20 - 84 * q^22 - 304 * q^23 - 112 * q^24 + 26 * q^25 + 280 * q^26 + 96 * q^28 - 112 * q^30 + 448 * q^31 - 352 * q^32 + 168 * q^33 + 28 * q^34 + 12 * q^36 - 196 * q^38 - 560 * q^39 + 224 * q^40 - 140 * q^41 - 224 * q^42 + 168 * q^44 + 304 * q^46 + 672 * q^47 + 672 * q^48 - 558 * q^49 - 26 * q^50 - 560 * q^52 + 728 * q^54 - 336 * q^55 - 320 * q^56 + 392 * q^57 - 840 * q^58 - 672 * q^60 - 448 * q^62 + 16 * q^63 + 576 * q^64 + 1120 * q^65 - 168 * q^66 + 168 * q^68 + 448 * q^70 - 144 * q^71 - 40 * q^72 - 588 * q^73 + 1288 * q^74 + 392 * q^76 + 560 * q^78 - 928 * q^79 - 1344 * q^80 - 1510 * q^81 + 140 * q^82 + 448 * q^84 - 2324 * q^86 + 1680 * q^87 + 336 * q^88 + 532 * q^89 + 56 * q^90 + 1824 * q^92 - 672 * q^94 - 784 * q^95 - 448 * q^96 + 1988 * q^97 + 558 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more