LMFDB - Embedded newform 49.4.c.a.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,4,Mod(18,49)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("49.18");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	49.c (of order $3$, degree $2$, not minimal)

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:	no
Analytic conductor:	$2.89109359028$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.4.c.a.30.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(3.50000 - 6.06218i) q^{3} +(2.00000 - 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} -14.0000 q^{6} -24.0000 q^{8} +(-11.0000 - 19.0526i) q^{9} +(7.00000 - 12.1244i) q^{10} +(2.50000 - 4.33013i) q^{11} +(-14.0000 - 24.2487i) q^{12} +14.0000 q^{13} +49.0000 q^{15} +(8.00000 + 13.8564i) q^{16} +(-10.5000 + 18.1865i) q^{17} +(-22.0000 + 38.1051i) q^{18} +(24.5000 + 42.4352i) q^{19} +28.0000 q^{20} -10.0000 q^{22} +(79.5000 + 137.698i) q^{23} +(-84.0000 + 145.492i) q^{24} +(38.0000 - 65.8179i) q^{25} +(-14.0000 - 24.2487i) q^{26} +35.0000 q^{27} +58.0000 q^{29} +(-49.0000 - 84.8705i) q^{30} +(73.5000 - 127.306i) q^{31} +(-80.0000 + 138.564i) q^{32} +(-17.5000 - 30.3109i) q^{33} +42.0000 q^{34} -88.0000 q^{36} +(-109.500 - 189.660i) q^{37} +(49.0000 - 84.8705i) q^{38} +(49.0000 - 84.8705i) q^{39} +(-84.0000 - 145.492i) q^{40} -350.000 q^{41} -124.000 q^{43} +(-10.0000 - 17.3205i) q^{44} +(77.0000 - 133.368i) q^{45} +(159.000 - 275.396i) q^{46} +(262.500 + 454.663i) q^{47} +112.000 q^{48} -152.000 q^{50} +(73.5000 + 127.306i) q^{51} +(28.0000 - 48.4974i) q^{52} +(-151.500 + 262.406i) q^{53} +(-35.0000 - 60.6218i) q^{54} +35.0000 q^{55} +343.000 q^{57} +(-58.0000 - 100.459i) q^{58} +(-52.5000 + 90.9327i) q^{59} +(98.0000 - 169.741i) q^{60} +(-206.500 - 357.668i) q^{61} -294.000 q^{62} +448.000 q^{64} +(49.0000 + 84.8705i) q^{65} +(-35.0000 + 60.6218i) q^{66} +(-207.500 + 359.401i) q^{67} +(42.0000 + 72.7461i) q^{68} +1113.00 q^{69} -432.000 q^{71} +(264.000 + 457.261i) q^{72} +(-556.500 + 963.886i) q^{73} +(-219.000 + 379.319i) q^{74} +(-266.000 - 460.726i) q^{75} +196.000 q^{76} -196.000 q^{78} +(51.5000 + 89.2006i) q^{79} +(-56.0000 + 96.9948i) q^{80} +(419.500 - 726.595i) q^{81} +(350.000 + 606.218i) q^{82} -1092.00 q^{83} -147.000 q^{85} +(124.000 + 214.774i) q^{86} +(203.000 - 351.606i) q^{87} +(-60.0000 + 103.923i) q^{88} +(-164.500 - 284.922i) q^{89} -308.000 q^{90} +636.000 q^{92} +(-514.500 - 891.140i) q^{93} +(525.000 - 909.327i) q^{94} +(-171.500 + 297.047i) q^{95} +(560.000 + 969.948i) q^{96} +882.000 q^{97} -110.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 7 q^{3} + 4 q^{4} + 7 q^{5} - 28 q^{6} - 48 q^{8} - 22 q^{9} + 14 q^{10} + 5 q^{11} - 28 q^{12} + 28 q^{13} + 98 q^{15} + 16 q^{16} - 21 q^{17} - 44 q^{18} + 49 q^{19} + 56 q^{20} - 20 q^{22}+ \cdots - 220 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 + 7 * q^5 - 28 * q^6 - 48 * q^8 - 22 * q^9 + 14 * q^10 + 5 * q^11 - 28 * q^12 + 28 * q^13 + 98 * q^15 + 16 * q^16 - 21 * q^17 - 44 * q^18 + 49 * q^19 + 56 * q^20 - 20 * q^22 + 159 * q^23 - 168 * q^24 + 76 * q^25 - 28 * q^26 + 70 * q^27 + 116 * q^29 - 98 * q^30 + 147 * q^31 - 160 * q^32 - 35 * q^33 + 84 * q^34 - 176 * q^36 - 219 * q^37 + 98 * q^38 + 98 * q^39 - 168 * q^40 - 700 * q^41 - 248 * q^43 - 20 * q^44 + 154 * q^45 + 318 * q^46 + 525 * q^47 + 224 * q^48 - 304 * q^50 + 147 * q^51 + 56 * q^52 - 303 * q^53 - 70 * q^54 + 70 * q^55 + 686 * q^57 - 116 * q^58 - 105 * q^59 + 196 * q^60 - 413 * q^61 - 588 * q^62 + 896 * q^64 + 98 * q^65 - 70 * q^66 - 415 * q^67 + 84 * q^68 + 2226 * q^69 - 864 * q^71 + 528 * q^72 - 1113 * q^73 - 438 * q^74 - 532 * q^75 + 392 * q^76 - 392 * q^78 + 103 * q^79 - 112 * q^80 + 839 * q^81 + 700 * q^82 - 2184 * q^83 - 294 * q^85 + 248 * q^86 + 406 * q^87 - 120 * q^88 - 329 * q^89 - 616 * q^90 + 1272 * q^92 - 1029 * q^93 + 1050 * q^94 - 343 * q^95 + 1120 * q^96 + 1764 * q^97 - 220 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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	−	1.73205i	−0.353553	−	0.612372i	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	3.50000	−	6.06218i	0.673575	−	1.16667i	−0.303308	−	0.952893i	$-0.598091\pi$
$3$	3.50000	−	6.06218i	0.673575	−	1.16667i	0.976883	−	0.213774i	$-0.0685756\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	3.50000	+	6.06218i	0.313050	+	0.542218i	0.979021	−	0.203760i	$-0.0653161\pi$
$5$	3.50000	+	6.06218i	0.313050	+	0.542218i	−0.665971	+	0.745977i	$0.731983\pi$
$6$	−14.0000			−0.952579
$7$		0			0
$7$		0			0
$8$	−24.0000			−1.06066
$9$	−11.0000	−	19.0526i	−0.407407	−	0.705650i
$10$	7.00000	−	12.1244i	0.221359	−	0.383406i
$11$	2.50000	−	4.33013i	0.0685253	−	0.118689i	−0.829727	−	0.558169i	$-0.811504\pi$
$11$	2.50000	−	4.33013i	0.0685253	−	0.118689i	0.898252	+	0.439480i	$0.144837\pi$
$12$	−14.0000	−	24.2487i	−0.336788	−	0.583333i
$13$	14.0000			0.298685			0.149342	−	0.988786i	$-0.452284\pi$
$13$	14.0000			0.298685			0.149342	+	0.988786i	$0.452284\pi$
$14$		0			0
$15$	49.0000			0.843450
$16$	8.00000	+	13.8564i	0.125000	+	0.216506i
$17$	−10.5000	+	18.1865i	−0.149801	+	0.259464i	−0.931154	−	0.364626i	$-0.881197\pi$
$17$	−10.5000	+	18.1865i	−0.149801	+	0.259464i	0.781353	+	0.624090i	$0.214530\pi$
$18$	−22.0000	+	38.1051i	−0.288081	+	0.498970i
$19$	24.5000	+	42.4352i	0.295826	+	0.512385i	0.975177	−	0.221429i	$-0.0710720\pi$
$19$	24.5000	+	42.4352i	0.295826	+	0.512385i	−0.679351	+	0.733813i	$0.737739\pi$
$20$	28.0000			0.313050
$21$		0			0
$22$	−10.0000			−0.0969094
$23$	79.5000	+	137.698i	0.720735	+	1.24835i	0.960706	+	0.277569i	$0.0895287\pi$
$23$	79.5000	+	137.698i	0.720735	+	1.24835i	−0.239971	+	0.970780i	$0.577138\pi$
$24$	−84.0000	+	145.492i	−0.714435	+	1.23744i
$25$	38.0000	−	65.8179i	0.304000	−	0.526543i
$26$	−14.0000	−	24.2487i	−0.105601	−	0.182906i
$27$	35.0000			0.249472
$28$		0			0
$29$	58.0000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	58.0000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	−49.0000	−	84.8705i	−0.298205	−	0.516505i
$31$	73.5000	−	127.306i	0.425838	−	0.737574i	−0.570660	−	0.821186i	$-0.693313\pi$
$31$	73.5000	−	127.306i	0.425838	−	0.737574i	0.996498	+	0.0836128i	$0.0266459\pi$
$32$	−80.0000	+	138.564i	−0.441942	+	0.765466i
$33$	−17.5000	−	30.3109i	−0.0923139	−	0.159892i
$34$	42.0000			0.211851
$35$		0			0
$36$	−88.0000			−0.407407
$37$	−109.500	−	189.660i	−0.486532	−	0.842698i	0.513348	−	0.858181i	$-0.328405\pi$
$37$	−109.500	−	189.660i	−0.486532	−	0.842698i	−0.999880	+	0.0154821i	$0.995072\pi$
$38$	49.0000	−	84.8705i	0.209180	−	0.362311i
$39$	49.0000	−	84.8705i	0.201187	−	0.348466i
$40$	−84.0000	−	145.492i	−0.332039	−	0.575109i
$41$	−350.000			−1.33319			−0.666595	−	0.745420i	$-0.732249\pi$
$41$	−350.000			−1.33319			−0.666595	+	0.745420i	$0.732249\pi$
$42$		0			0
$43$	−124.000			−0.439763			−0.219882	−	0.975527i	$-0.570567\pi$
$43$	−124.000			−0.439763			−0.219882	+	0.975527i	$0.570567\pi$
$44$	−10.0000	−	17.3205i	−0.0342627	−	0.0593447i
$45$	77.0000	−	133.368i	0.255077	−	0.441807i
$46$	159.000	−	275.396i	0.509636	−	0.882716i
$47$	262.500	+	454.663i	0.814671	+	1.41105i	0.909564	+	0.415565i	$0.136416\pi$
$47$	262.500	+	454.663i	0.814671	+	1.41105i	−0.0948921	+	0.995488i	$0.530251\pi$
$48$	112.000			0.336788
$49$		0			0
$50$	−152.000			−0.429921
$51$	73.5000	+	127.306i	0.201805	+	0.349537i
$52$	28.0000	−	48.4974i	0.0746712	−	0.129334i
$53$	−151.500	+	262.406i	−0.392644	+	0.680079i	−0.992797	−	0.119806i	$-0.961773\pi$
$53$	−151.500	+	262.406i	−0.392644	+	0.680079i	0.600153	+	0.799885i	$0.295106\pi$
$54$	−35.0000	−	60.6218i	−0.0882018	−	0.152770i
$55$	35.0000			0.0858073
$56$		0			0
$57$	343.000			0.797043
$58$	−58.0000	−	100.459i	−0.131306	−	0.227429i
$59$	−52.5000	+	90.9327i	−0.115846	+	0.200651i	−0.918118	−	0.396308i	$-0.870291\pi$
$59$	−52.5000	+	90.9327i	−0.115846	+	0.200651i	0.802272	+	0.596959i	$0.203625\pi$
$60$	98.0000	−	169.741i	0.210862	−	0.365224i
$61$	−206.500	−	357.668i	−0.433436	−	0.750734i	0.563730	−	0.825959i	$-0.309366\pi$
$61$	−206.500	−	357.668i	−0.433436	−	0.750734i	−0.997167	+	0.0752252i	$0.976032\pi$
$62$	−294.000			−0.602226
$63$		0			0
$64$	448.000			0.875000
$65$	49.0000	+	84.8705i	0.0935031	+	0.161952i
$66$	−35.0000	+	60.6218i	−0.0652758	+	0.113061i
$67$	−207.500	+	359.401i	−0.378361	+	0.655340i	−0.990824	−	0.135159i	$-0.956845\pi$
$67$	−207.500	+	359.401i	−0.378361	+	0.655340i	0.612463	+	0.790499i	$0.290179\pi$
$68$	42.0000	+	72.7461i	0.0749007	+	0.129732i
$69$	1113.00			1.94188
$70$		0			0
$71$	−432.000			−0.722098			−0.361049	−	0.932547i	$-0.617581\pi$
$71$	−432.000			−0.722098			−0.361049	+	0.932547i	$0.617581\pi$
$72$	264.000	+	457.261i	0.432121	+	0.748455i
$73$	−556.500	+	963.886i	−0.892238	+	1.54540i	−0.0550526	+	0.998483i	$0.517533\pi$
$73$	−556.500	+	963.886i	−0.892238	+	1.54540i	−0.837186	+	0.546919i	$0.815801\pi$
$74$	−219.000	+	379.319i	−0.344030	+	0.595878i
$75$	−266.000	−	460.726i	−0.409534	−	0.709333i
$76$	196.000			0.295826
$77$		0			0
$78$	−196.000			−0.284521
$79$	51.5000	+	89.2006i	0.0733443	+	0.127036i	0.900365	−	0.435135i	$-0.143299\pi$
$79$	51.5000	+	89.2006i	0.0733443	+	0.127036i	−0.827021	+	0.562171i	$0.809966\pi$
$80$	−56.0000	+	96.9948i	−0.0782624	+	0.135554i
$81$	419.500	−	726.595i	0.575446	−	0.996701i
$82$	350.000	+	606.218i	0.471354	+	0.816409i
$83$	−1092.00			−1.44413			−0.722064	−	0.691827i	$-0.756806\pi$
$83$	−1092.00			−1.44413			−0.722064	+	0.691827i	$0.756806\pi$
$84$		0			0
$85$	−147.000			−0.187581
$86$	124.000	+	214.774i	0.155480	+	0.269299i
$87$	203.000	−	351.606i	0.250160	−	0.433289i
$88$	−60.0000	+	103.923i	−0.0726821	+	0.125889i
$89$	−164.500	−	284.922i	−0.195921	−	0.339345i	0.751281	−	0.659982i	$-0.229436\pi$
$89$	−164.500	−	284.922i	−0.195921	−	0.339345i	−0.947202	+	0.320637i	$0.896103\pi$
$90$	−308.000			−0.360734
$91$		0			0
$92$	636.000			0.720735
$93$	−514.500	−	891.140i	−0.573668	−	0.993623i
$94$	525.000	−	909.327i	0.576060	−	0.997765i
$95$	−171.500	+	297.047i	−0.185216	+	0.320804i
$96$	560.000	+	969.948i	0.595362	+	1.03120i
$97$	882.000			0.923232			0.461616	−	0.887080i	$-0.347270\pi$
$97$	882.000			0.923232			0.461616	+	0.887080i	$0.347270\pi$
$98$		0			0
$99$	−110.000			−0.111671
$100$	−152.000	−	263.272i	−0.152000	−	0.263272i
$101$	689.500	−	1194.25i	0.679285	−	1.17656i	−0.295911	−	0.955215i	$-0.595623\pi$
$101$	689.500	−	1194.25i	0.679285	−	1.17656i	0.975196	−	0.221341i	$-0.0710434\pi$
$102$	147.000	−	254.611i	0.142698	−	0.247160i
$103$	−339.500	−	588.031i	−0.324776	−	0.562529i	0.656691	−	0.754160i	$-0.271956\pi$
$103$	−339.500	−	588.031i	−0.324776	−	0.562529i	−0.981467	+	0.191631i	$0.938622\pi$
$104$	−336.000			−0.316803
$105$		0			0
$106$	606.000			0.555282
$107$	−228.500	−	395.774i	−0.206448	−	0.357578i	0.744145	−	0.668018i	$-0.232857\pi$
$107$	−228.500	−	395.774i	−0.206448	−	0.357578i	−0.950593	+	0.310440i	$0.899524\pi$
$108$	70.0000	−	121.244i	0.0623681	−	0.108025i
$109$	562.500	−	974.279i	0.494291	−	0.856137i	−0.505687	−	0.862717i	$-0.668761\pi$
$109$	562.500	−	974.279i	0.494291	−	0.856137i	0.999978	+	0.00657959i	$0.00209436\pi$
$110$	−35.0000	−	60.6218i	−0.0303374	−	0.0525460i
$111$	−1533.00			−1.31086
$112$		0			0
$113$	−1538.00			−1.28038			−0.640190	−	0.768217i	$-0.721144\pi$
$113$	−1538.00			−1.28038			−0.640190	+	0.768217i	$0.721144\pi$
$114$	−343.000	−	594.093i	−0.281797	−	0.488087i
$115$	−556.500	+	963.886i	−0.451251	+	0.781590i
$116$	116.000	−	200.918i	0.0928477	−	0.160817i
$117$	−154.000	−	266.736i	−0.121686	−	0.210767i
$118$	210.000			0.163831
$119$		0			0
$120$	−1176.00			−0.894614
$121$	653.000	+	1131.03i	0.490609	+	0.849759i
$122$	−413.000	+	715.337i	−0.306486	+	0.530849i
$123$	−1225.00	+	2121.76i	−0.898004	+	1.55539i
$124$	−294.000	−	509.223i	−0.212919	−	0.368787i
$125$	1407.00			1.00677
$126$		0			0
$127$	72.0000			0.0503068			0.0251534	−	0.999684i	$-0.491993\pi$
$127$	72.0000			0.0503068			0.0251534	+	0.999684i	$0.491993\pi$
$128$	192.000	+	332.554i	0.132583	+	0.229640i
$129$	−434.000	+	751.710i	−0.296214	+	0.513057i
$130$	98.0000	−	169.741i	0.0661167	−	0.114517i
$131$	1074.50	+	1861.09i	0.716637	+	1.24125i	0.962325	+	0.271903i	$0.0876531\pi$
$131$	1074.50	+	1861.09i	0.716637	+	1.24125i	−0.245687	+	0.969349i	$0.579014\pi$
$132$	−140.000			−0.0923139
$133$		0			0
$134$	830.000			0.535083
$135$	122.500	+	212.176i	0.0780972	+	0.135268i
$136$	252.000	−	436.477i	0.158888	−	0.275203i
$137$	562.500	−	974.279i	0.350786	−	0.607578i	−0.635602	−	0.772017i	$-0.719248\pi$
$137$	562.500	−	974.279i	0.350786	−	0.607578i	0.986387	+	0.164439i	$0.0525813\pi$
$138$	−1113.00	−	1927.77i	−0.686557	−	1.18915i
$139$	−252.000			−0.153772			−0.0768862	−	0.997040i	$-0.524498\pi$
$139$	−252.000			−0.153772			−0.0768862	+	0.997040i	$0.524498\pi$
$140$		0			0
$141$	3675.00			2.19497
$142$	432.000	+	748.246i	0.255300	+	0.442193i
$143$	35.0000	−	60.6218i	0.0204675	−	0.0354507i
$144$	176.000	−	304.841i	0.101852	−	0.176413i
$145$	203.000	+	351.606i	0.116264	+	0.201375i
$146$	2226.00			1.26182
$147$		0			0
$148$	−876.000			−0.486532
$149$	100.500	+	174.071i	0.0552569	+	0.0957078i	0.892331	−	0.451382i	$-0.149069\pi$
$149$	100.500	+	174.071i	0.0552569	+	0.0957078i	−0.837074	+	0.547090i	$0.815736\pi$
$150$	−532.000	+	921.451i	−0.289584	+	0.501574i
$151$	−809.500	+	1402.10i	−0.436266	+	0.755635i	−0.997398	−	0.0720914i	$-0.977033\pi$
$151$	−809.500	+	1402.10i	−0.436266	+	0.755635i	0.561132	+	0.827726i	$0.310366\pi$
$152$	−588.000	−	1018.45i	−0.313770	−	0.543466i
$153$	462.000			0.244121
$154$		0			0
$155$	1029.00			0.533234
$156$	−196.000	−	339.482i	−0.100593	−	0.174233i
$157$	339.500	−	588.031i	0.172580	−	0.298917i	−0.766741	−	0.641956i	$-0.778123\pi$
$157$	339.500	−	588.031i	0.172580	−	0.298917i	0.939321	+	0.343039i	$0.111456\pi$
$158$	103.000	−	178.401i	0.0518623	−	0.0898281i
$159$	1060.50	+	1836.84i	0.528950	+	0.916169i
$160$	−1120.00			−0.553399
$161$		0			0
$162$	−1678.00			−0.813803
$163$	233.500	+	404.434i	0.112203	+	0.194342i	0.916658	−	0.399672i	$-0.130876\pi$
$163$	233.500	+	404.434i	0.112203	+	0.194342i	−0.804455	+	0.594014i	$0.797543\pi$
$164$	−700.000	+	1212.44i	−0.333298	+	0.577288i
$165$	122.500	−	212.176i	0.0577976	−	0.100108i
$166$	1092.00	+	1891.40i	0.510576	+	0.884344i
$167$	−1204.00			−0.557894			−0.278947	−	0.960306i	$-0.589985\pi$
$167$	−1204.00			−0.557894			−0.278947	+	0.960306i	$0.589985\pi$
$168$		0			0
$169$	−2001.00			−0.910787
$170$	147.000	+	254.611i	0.0663199	+	0.114869i
$171$	539.000	−	933.575i	0.241043	−	0.417499i
$172$	−248.000	+	429.549i	−0.109941	+	0.190423i
$173$	−1410.50	−	2443.06i	−0.619875	−	1.07365i	−0.989508	−	0.144477i	$-0.953850\pi$
$173$	−1410.50	−	2443.06i	−0.619875	−	1.07365i	0.369633	−	0.929178i	$-0.379483\pi$
$174$	−812.000			−0.353779
$175$		0			0
$176$	80.0000			0.0342627
$177$	367.500	+	636.529i	0.156062	+	0.270307i
$178$	−329.000	+	569.845i	−0.138537	+	0.239953i
$179$	1626.50	−	2817.18i	0.679164	−	1.17635i	−0.296069	−	0.955166i	$-0.595676\pi$
$179$	1626.50	−	2817.18i	0.679164	−	1.17635i	0.975233	−	0.221180i	$-0.0709907\pi$
$180$	−308.000	−	533.472i	−0.127539	−	0.220903i
$181$	−1582.00			−0.649664			−0.324832	−	0.945772i	$-0.605308\pi$
$181$	−1582.00			−0.649664			−0.324832	+	0.945772i	$0.605308\pi$
$182$		0			0
$183$	−2891.00			−1.16781
$184$	−1908.00	−	3304.75i	−0.764454	−	1.32407i
$185$	766.500	−	1327.62i	0.304617	−	0.527613i
$186$	−1029.00	+	1782.28i	−0.405645	+	0.702597i
$187$	52.5000	+	90.9327i	0.0205304	+	0.0355597i
$188$	2100.00			0.814671
$189$		0			0
$190$	686.000			0.261935
$191$	−1278.50	−	2214.43i	−0.484340	−	0.838902i	0.515498	−	0.856891i	$-0.327607\pi$
$191$	−1278.50	−	2214.43i	−0.484340	−	0.838902i	−0.999838	+	0.0179887i	$0.994274\pi$
$192$	1568.00	−	2715.86i	0.589378	−	1.02083i
$193$	198.500	−	343.812i	0.0740329	−	0.128229i	−0.826632	−	0.562742i	$-0.809746\pi$
$193$	198.500	−	343.812i	0.0740329	−	0.128229i	0.900665	+	0.434514i	$0.143080\pi$
$194$	−882.000	−	1527.67i	−0.326412	−	0.565362i
$195$	686.000			0.251926
$196$		0			0
$197$	2914.00			1.05388			0.526939	−	0.849903i	$-0.323340\pi$
$197$	2914.00			1.05388			0.526939	+	0.849903i	$0.323340\pi$
$198$	110.000	+	190.526i	0.0394816	+	0.0683842i
$199$	1669.50	−	2891.66i	0.594712	−	1.03007i	−0.398875	−	0.917005i	$-0.630599\pi$
$199$	1669.50	−	2891.66i	0.594712	−	1.03007i	0.993587	−	0.113066i	$-0.0360673\pi$
$200$	−912.000	+	1579.63i	−0.322441	+	0.558484i
$201$	1452.50	+	2515.80i	0.509709	+	0.882841i
$202$	−2758.00			−0.960654
$203$		0			0
$204$	588.000			0.201805
$205$	−1225.00	−	2121.76i	−0.417355	−	0.722880i
$206$	−679.000	+	1176.06i	−0.229651	+	0.397768i
$207$	1749.00	−	3029.36i	0.587265	−	1.01717i
$208$	112.000	+	193.990i	0.0373356	+	0.0646671i
$209$	245.000			0.0810861
$210$		0			0
$211$	1780.00			0.580759			0.290380	−	0.956911i	$-0.406218\pi$
$211$	1780.00			0.580759			0.290380	+	0.956911i	$0.406218\pi$
$212$	606.000	+	1049.62i	0.196322	+	0.340040i
$213$	−1512.00	+	2618.86i	−0.486387	+	0.842448i
$214$	−457.000	+	791.547i	−0.145981	+	0.252846i
$215$	−434.000	−	751.710i	−0.137668	−	0.238447i
$216$	−840.000			−0.264605
$217$		0			0
$218$	−2250.00			−0.699033
$219$	3895.50	+	6747.20i	1.20198	+	2.08189i
$220$	70.0000	−	121.244i	0.0214518	−	0.0371556i
$221$	−147.000	+	254.611i	−0.0447434	+	0.0774978i
$222$	1533.00	+	2655.23i	0.463460	+	0.802737i
$223$	1400.00			0.420408			0.210204	−	0.977658i	$-0.432587\pi$
$223$	1400.00			0.420408			0.210204	+	0.977658i	$0.432587\pi$
$224$		0			0
$225$	−1672.00			−0.495407
$226$	1538.00	+	2663.89i	0.452682	+	0.784069i
$227$	−1102.50	+	1909.59i	−0.322359	+	0.558342i	−0.980974	−	0.194138i	$-0.937809\pi$
$227$	−1102.50	+	1909.59i	−0.322359	+	0.558342i	0.658615	+	0.752480i	$0.271142\pi$
$228$	686.000	−	1188.19i	0.199261	−	0.345130i
$229$	143.500	+	248.549i	0.0414094	+	0.0717231i	0.885987	−	0.463710i	$-0.153482\pi$
$229$	143.500	+	248.549i	0.0414094	+	0.0717231i	−0.844578	+	0.535433i	$0.820149\pi$
$230$	2226.00			0.638166
$231$		0			0
$232$	−1392.00			−0.393919
$233$	−2293.50	−	3972.46i	−0.644859	−	1.11693i	−0.984334	−	0.176314i	$-0.943583\pi$
$233$	−2293.50	−	3972.46i	−0.644859	−	1.11693i	0.339475	−	0.940615i	$-0.389751\pi$
$234$	−308.000	+	533.472i	−0.0860453	+	0.149035i
$235$	−1837.50	+	3182.64i	−0.510065	+	0.883459i
$236$	210.000	+	363.731i	0.0579230	+	0.100326i
$237$	721.000			0.197612
$238$		0			0
$239$	1668.00			0.451439			0.225720	−	0.974192i	$-0.427527\pi$
$239$	1668.00			0.451439			0.225720	+	0.974192i	$0.427527\pi$
$240$	392.000	+	678.964i	0.105431	+	0.182612i
$241$	−1704.50	+	2952.28i	−0.455587	+	0.789100i	−0.998722	−	0.0505456i	$-0.983904\pi$
$241$	−1704.50	+	2952.28i	−0.455587	+	0.789100i	0.543135	+	0.839646i	$0.317237\pi$
$242$	1306.00	−	2262.06i	0.346913	−	0.600870i
$243$	−2464.00	−	4267.77i	−0.650476	−	1.12666i
$244$	−1652.00			−0.433436
$245$		0			0
$246$	4900.00			1.26997
$247$	343.000	+	594.093i	0.0883586	+	0.153042i
$248$	−1764.00	+	3055.34i	−0.451670	+	0.782315i
$249$	−3822.00	+	6619.90i	−0.972729	+	1.68482i
$250$	−1407.00	−	2437.00i	−0.355946	−	0.616517i
$251$	4760.00			1.19701			0.598503	−	0.801121i	$-0.295762\pi$
$251$	4760.00			1.19701			0.598503	+	0.801121i	$0.295762\pi$
$252$		0			0
$253$	795.000			0.197554
$254$	−72.0000	−	124.708i	−0.0177861	−	0.0308065i
$255$	−514.500	+	891.140i	−0.126350	+	0.218845i
$256$	2176.00	−	3768.94i	0.531250	−	0.920152i
$257$	−402.500	−	697.150i	−0.0976936	−	0.169210i	0.813036	−	0.582213i	$-0.197813\pi$
$257$	−402.500	−	697.150i	−0.0976936	−	0.169210i	−0.910730	+	0.413003i	$0.864480\pi$
$258$	1736.00			0.418909
$259$		0			0
$260$	392.000			0.0935031
$261$	−638.000	−	1105.05i	−0.151307	−	0.262072i
$262$	2149.00	−	3722.18i	0.506739	−	0.877698i
$263$	128.500	−	222.569i	0.0301279	−	0.0521831i	−0.850568	−	0.525865i	$-0.823742\pi$
$263$	128.500	−	222.569i	0.0301279	−	0.0521831i	0.880696	+	0.473681i	$0.157075\pi$
$264$	420.000	+	727.461i	0.0979137	+	0.169591i
$265$	−2121.00			−0.491668
$266$		0			0
$267$	−2303.00			−0.527870
$268$	830.000	+	1437.60i	0.189180	+	0.327670i
$269$	1795.50	−	3109.90i	0.406965	−	0.704884i	−0.587583	−	0.809164i	$-0.699920\pi$
$269$	1795.50	−	3109.90i	0.406965	−	0.704884i	0.994548	+	0.104280i	$0.0332538\pi$
$270$	245.000	−	424.352i	0.0552231	−	0.0956491i
$271$	696.500	+	1206.37i	0.156123	+	0.270413i	0.933467	−	0.358662i	$-0.116767\pi$
$271$	696.500	+	1206.37i	0.156123	+	0.270413i	−0.777344	+	0.629075i	$0.783434\pi$
$272$	−336.000			−0.0749007
$273$		0			0
$274$	−2250.00			−0.496086
$275$	−190.000	−	329.090i	−0.0416634	−	0.0721631i
$276$	2226.00	−	3855.55i	0.485469	−	0.840857i
$277$	−207.500	+	359.401i	−0.0450089	+	0.0779577i	−0.887652	−	0.460514i	$-0.847665\pi$
$277$	−207.500	+	359.401i	−0.0450089	+	0.0779577i	0.842643	+	0.538472i	$0.180998\pi$
$278$	252.000	+	436.477i	0.0543667	+	0.0941660i
$279$	−3234.00			−0.693959
$280$		0			0
$281$	−4954.00			−1.05171			−0.525856	−	0.850574i	$-0.676255\pi$
$281$	−4954.00			−1.05171			−0.525856	+	0.850574i	$0.676255\pi$
$282$	−3675.00	−	6365.29i	−0.776039	−	1.34414i
$283$	−2138.50	+	3703.99i	−0.449190	+	0.778019i	−0.998333	−	0.0577087i	$-0.981621\pi$
$283$	−2138.50	+	3703.99i	−0.449190	+	0.778019i	0.549144	+	0.835728i	$0.314954\pi$
$284$	−864.000	+	1496.49i	−0.180525	+	0.312678i
$285$	1200.50	+	2079.33i	0.249514	+	0.432171i
$286$	−140.000			−0.0289454
$287$		0			0
$288$	3520.00			0.720201
$289$	2236.00	+	3872.87i	0.455119	+	0.788289i
$290$	406.000	−	703.213i	0.0822108	−	0.142393i
$291$	3087.00	−	5346.84i	0.621866	−	1.07710i
$292$	2226.00	+	3855.55i	0.446119	+	0.772701i
$293$	−7742.00			−1.54366			−0.771830	−	0.635829i	$-0.780658\pi$
$293$	−7742.00			−1.54366			−0.771830	+	0.635829i	$0.780658\pi$
$294$		0			0
$295$	−735.000			−0.145062
$296$	2628.00	+	4551.83i	0.516045	+	0.893817i
$297$	87.5000	−	151.554i	0.0170952	−	0.0296097i
$298$	201.000	−	348.142i	0.0390725	−	0.0676756i
$299$	1113.00	+	1927.77i	0.215272	+	0.372863i
$300$	−2128.00			−0.409534
$301$		0			0
$302$	3238.00			0.616973
$303$	−4826.50	−	8359.74i	−0.915100	−	1.58500i
$304$	−392.000	+	678.964i	−0.0739564	+	0.128096i
$305$	1445.50	−	2503.68i	0.271374	−	0.470034i
$306$	−462.000	−	800.207i	−0.0863097	−	0.149493i
$307$	7364.00			1.36901			0.684504	−	0.729009i	$-0.260019\pi$
$307$	7364.00			1.36901			0.684504	+	0.729009i	$0.260019\pi$
$308$		0			0
$309$	−4753.00			−0.875044
$310$	−1029.00	−	1782.28i	−0.188527	−	0.326538i
$311$	4987.50	−	8638.60i	0.909374	−	1.57508i	0.0944372	−	0.995531i	$-0.469895\pi$
$311$	4987.50	−	8638.60i	0.909374	−	1.57508i	0.814936	−	0.579550i	$-0.196772\pi$
$312$	−1176.00	+	2036.89i	−0.213391	+	0.369603i
$313$	−2376.50	−	4116.22i	−0.429162	−	0.743330i	0.567637	−	0.823279i	$-0.307858\pi$
$313$	−2376.50	−	4116.22i	−0.429162	−	0.743330i	−0.996799	+	0.0799485i	$0.974524\pi$
$314$	−1358.00			−0.244065
$315$		0			0
$316$	412.000			0.0733443
$317$	1738.50	+	3011.17i	0.308025	+	0.533515i	0.977930	−	0.208932i	$-0.0669987\pi$
$317$	1738.50	+	3011.17i	0.308025	+	0.533515i	−0.669905	+	0.742447i	$0.733665\pi$
$318$	2121.00	−	3673.68i	0.374024	−	0.647829i
$319$	145.000	−	251.147i	0.0254497	−	0.0440801i
$320$	1568.00	+	2715.86i	0.273918	+	0.474440i
$321$	−3199.00			−0.556233
$322$		0			0
$323$	−1029.00			−0.177260
$324$	−1678.00	−	2906.38i	−0.287723	−	0.498351i
$325$	532.000	−	921.451i	0.0908002	−	0.157270i
$326$	467.000	−	808.868i	0.0793397	−	0.137420i
$327$	−3937.50	−	6819.95i	−0.665885	−	1.15335i
$328$	8400.00			1.41406
$329$		0			0
$330$	−490.000			−0.0817382
$331$	−1670.50	−	2893.39i	−0.277399	−	0.480469i	0.693339	−	0.720612i	$-0.256139\pi$
$331$	−1670.50	−	2893.39i	−0.277399	−	0.480469i	−0.970738	+	0.240143i	$0.922806\pi$
$332$	−2184.00	+	3782.80i	−0.361032	+	0.625325i
$333$	−2409.00	+	4172.51i	−0.396434	+	0.686643i
$334$	1204.00	+	2085.39i	0.197245	+	0.341639i
$335$	−2905.00			−0.473782
$336$		0			0
$337$	7366.00			1.19066			0.595329	−	0.803482i	$-0.297022\pi$
$337$	7366.00			1.19066			0.595329	+	0.803482i	$0.297022\pi$
$338$	2001.00	+	3465.83i	0.322012	+	0.557741i
$339$	−5383.00	+	9323.63i	−0.862432	+	1.49378i
$340$	−294.000	+	509.223i	−0.0468953	+	0.0812250i
$341$	−367.500	−	636.529i	−0.0583614	−	0.101085i
$342$	−2156.00			−0.340886
$343$		0			0
$344$	2976.00			0.466439
$345$	3895.50	+	6747.20i	0.607903	+	1.05292i
$346$	−2821.00	+	4886.12i	−0.438318	+	0.759188i
$347$	−3707.50	+	6421.58i	−0.573571	+	0.993454i	0.422625	+	0.906305i	$0.361109\pi$
$347$	−3707.50	+	6421.58i	−0.573571	+	0.993454i	−0.996195	+	0.0871487i	$0.972224\pi$
$348$	−812.000	−	1406.43i	−0.125080	−	0.216645i
$349$	3878.00			0.594798			0.297399	−	0.954753i	$-0.403881\pi$
$349$	3878.00			0.594798			0.297399	+	0.954753i	$0.403881\pi$
$350$		0			0
$351$	490.000			0.0745136
$352$	400.000	+	692.820i	0.0605684	+	0.104908i
$353$	633.500	−	1097.25i	0.0955179	−	0.165442i	−0.814307	−	0.580435i	$-0.802883\pi$
$353$	633.500	−	1097.25i	0.0955179	−	0.165442i	0.909825	+	0.414993i	$0.136216\pi$
$354$	735.000	−	1273.06i	0.110353	−	0.191136i
$355$	−1512.00	−	2618.86i	−0.226052	−	0.391534i
$356$	−1316.00			−0.195921
$357$		0			0
$358$	−6506.00			−0.960483
$359$	−2342.50	−	4057.33i	−0.344380	−	0.596484i	0.640861	−	0.767657i	$-0.278578\pi$
$359$	−2342.50	−	4057.33i	−0.344380	−	0.596484i	−0.985241	+	0.171173i	$0.945244\pi$
$360$	−1848.00	+	3200.83i	−0.270550	+	0.468607i
$361$	2229.00	−	3860.74i	0.324974	−	0.562872i
$362$	1582.00	+	2740.10i	0.229691	+	0.397836i
$363$	9142.00			1.32185
$364$		0			0
$365$	−7791.00			−1.11726
$366$	2891.00	+	5007.36i	0.412882	+	0.715133i
$367$	−2320.50	+	4019.22i	−0.330052	+	0.571667i	−0.982522	−	0.186148i	$-0.940400\pi$
$367$	−2320.50	+	4019.22i	−0.330052	+	0.571667i	0.652470	+	0.757815i	$0.273733\pi$
$368$	−1272.00	+	2203.17i	−0.180184	+	0.312087i
$369$	3850.00	+	6668.40i	0.543152	+	0.940766i
$370$	−3066.00			−0.430794
$371$		0			0
$372$	−4116.00			−0.573668
$373$	4398.50	+	7618.43i	0.610578	+	1.05755i	0.991143	+	0.132798i	$0.0423963\pi$
$373$	4398.50	+	7618.43i	0.610578	+	1.05755i	−0.380565	+	0.924754i	$0.624270\pi$
$374$	105.000	−	181.865i	0.0145172	−	0.0251445i
$375$	4924.50	−	8529.48i	0.678134	−	1.17456i
$376$	−6300.00	−	10911.9i	−0.864090	−	1.49665i
$377$	812.000			0.110929
$378$		0			0
$379$	13680.0			1.85407			0.927037	−	0.374969i	$-0.122347\pi$
$379$	13680.0			1.85407			0.927037	+	0.374969i	$0.122347\pi$
$380$	686.000	+	1188.19i	0.0926080	+	0.160402i
$381$	252.000	−	436.477i	0.0338854	−	0.0586913i
$382$	−2557.00	+	4428.85i	−0.342480	+	0.593193i
$383$	4882.50	+	8456.74i	0.651395	+	1.12825i	0.982785	+	0.184755i	$0.0591490\pi$
$383$	4882.50	+	8456.74i	0.651395	+	1.12825i	−0.331390	+	0.943494i	$0.607518\pi$
$384$	2688.00			0.357217
$385$		0			0
$386$	−794.000			−0.104698
$387$	1364.00	+	2362.52i	0.179163	+	0.310319i
$388$	1764.00	−	3055.34i	0.230808	−	0.399771i
$389$	−865.500	+	1499.09i	−0.112809	+	0.195390i	−0.916902	−	0.399113i	$-0.869318\pi$
$389$	−865.500	+	1499.09i	−0.112809	+	0.195390i	0.804093	+	0.594504i	$0.202651\pi$
$390$	−686.000	−	1188.19i	−0.0890691	−	0.154272i
$391$	−3339.00			−0.431868
$392$		0			0
$393$	15043.0			1.93084
$394$	−2914.00	−	5047.20i	−0.372602	−	0.645366i
$395$	−360.500	+	624.404i	−0.0459208	+	0.0795372i
$396$	−220.000	+	381.051i	−0.0279177	+	0.0483549i
$397$	5491.50	+	9511.56i	0.694233	+	1.20245i	0.970439	+	0.241348i	$0.0775896\pi$
$397$	5491.50	+	9511.56i	0.694233	+	1.20245i	−0.276206	+	0.961099i	$0.589077\pi$
$398$	−6678.00			−0.841050
$399$		0			0
$400$	1216.00			0.152000
$401$	−3301.50	−	5718.37i	−0.411145	−	0.712124i	0.583870	−	0.811847i	$-0.301538\pi$
$401$	−3301.50	−	5718.37i	−0.411145	−	0.712124i	−0.995015	+	0.0997232i	$0.968204\pi$
$402$	2905.00	−	5031.61i	0.360418	−	0.624263i
$403$	1029.00	−	1782.28i	0.127191	−	0.220302i
$404$	−2758.00	−	4777.00i	−0.339643	−	0.588278i
$405$	5873.00			0.720572
$406$		0			0
$407$	−1095.00			−0.133359
$408$	−1764.00	−	3055.34i	−0.214047	−	0.370740i
$409$	5477.50	−	9487.31i	0.662213	−	1.14699i	−0.317820	−	0.948151i	$-0.602951\pi$
$409$	5477.50	−	9487.31i	0.662213	−	1.14699i	0.980033	−	0.198835i	$-0.0637158\pi$
$410$	−2450.00	+	4243.52i	−0.295114	+	0.511153i
$411$	−3937.50	−	6819.95i	−0.472561	−	0.818500i
$412$	−2716.00			−0.324776
$413$		0			0
$414$	−6996.00			−0.830518
$415$	−3822.00	−	6619.90i	−0.452083	−	0.783031i
$416$	−1120.00	+	1939.90i	−0.132001	+	0.228633i
$417$	−882.000	+	1527.67i	−0.103577	+	0.179401i
$418$	−245.000	−	424.352i	−0.0286683	−	0.0496549i
$419$	−6636.00			−0.773723			−0.386861	−	0.922138i	$-0.626441\pi$
$419$	−6636.00			−0.773723			−0.386861	+	0.922138i	$0.626441\pi$
$420$		0			0
$421$	−16630.0			−1.92517			−0.962585	−	0.270980i	$-0.912652\pi$
$421$	−16630.0			−1.92517			−0.962585	+	0.270980i	$0.912652\pi$
$422$	−1780.00	−	3083.05i	−0.205329	−	0.355641i
$423$	5775.00	−	10002.6i	0.663806	−	1.14975i
$424$	3636.00	−	6297.74i	0.416462	−	0.721333i
$425$	798.000	+	1382.18i	0.0910793	+	0.157754i
$426$	6048.00			0.687856
$427$		0			0
$428$	−1828.00			−0.206448
$429$	−245.000	−	424.352i	−0.0275728	−	0.0477574i
$430$	−868.000	+	1503.42i	−0.0973458	+	0.168608i
$431$	−2461.50	+	4263.44i	−0.275096	+	0.476480i	−0.970159	−	0.242468i	$-0.922043\pi$
$431$	−2461.50	+	4263.44i	−0.275096	+	0.476480i	0.695064	+	0.718948i	$0.255376\pi$
$432$	280.000	+	484.974i	0.0311840	+	0.0540123i
$433$	−8974.00			−0.995988			−0.497994	−	0.867180i	$-0.665930\pi$
$433$	−8974.00			−0.995988			−0.497994	+	0.867180i	$0.665930\pi$
$434$		0			0
$435$	2842.00			0.313249
$436$	−2250.00	−	3897.11i	−0.247146	−	0.428069i
$437$	−3895.50	+	6747.20i	−0.426423	+	0.738587i
$438$	7791.00	−	13494.4i	0.849928	−	1.47212i
$439$	−2089.50	−	3619.12i	−0.227167	−	0.393465i	0.729800	−	0.683660i	$-0.239613\pi$
$439$	−2089.50	−	3619.12i	−0.227167	−	0.393465i	−0.956967	+	0.290195i	$0.906280\pi$
$440$	−840.000			−0.0910123
$441$		0			0
$442$	588.000			0.0632767
$443$	6463.50	+	11195.1i	0.693206	+	1.20067i	0.970782	+	0.239964i	$0.0771356\pi$
$443$	6463.50	+	11195.1i	0.693206	+	1.20067i	−0.277576	+	0.960704i	$0.589531\pi$
$444$	−3066.00	+	5310.47i	−0.327716	+	0.567621i
$445$	1151.50	−	1994.46i	0.122666	−	0.212464i
$446$	−1400.00	−	2424.87i	−0.148637	−	0.257446i
$447$	1407.00			0.148879
$448$		0			0
$449$	−2826.00			−0.297032			−0.148516	−	0.988910i	$-0.547450\pi$
$449$	−2826.00			−0.297032			−0.148516	+	0.988910i	$0.547450\pi$
$450$	1672.00	+	2895.99i	0.175153	+	0.303374i
$451$	−875.000	+	1515.54i	−0.0913573	+	0.158235i
$452$	−3076.00	+	5327.79i	−0.320095	+	0.554421i
$453$	5666.50	+	9814.67i	0.587716	+	1.01795i
$454$	4410.00			0.455884
$455$		0			0
$456$	−8232.00			−0.845392
$457$	−4239.50	−	7343.03i	−0.433951	−	0.751625i	0.563259	−	0.826281i	$-0.309547\pi$
$457$	−4239.50	−	7343.03i	−0.433951	−	0.751625i	−0.997209	+	0.0746560i	$0.976214\pi$
$458$	287.000	−	497.099i	0.0292808	−	0.0507159i
$459$	−367.500	+	636.529i	−0.0373713	+	0.0647290i
$460$	2226.00	+	3855.55i	0.225626	+	0.390795i
$461$	−9338.00			−0.943414			−0.471707	−	0.881755i	$-0.656362\pi$
$461$	−9338.00			−0.943414			−0.471707	+	0.881755i	$0.656362\pi$
$462$		0			0
$463$	−4016.00			−0.403109			−0.201554	−	0.979477i	$-0.564599\pi$
$463$	−4016.00			−0.403109			−0.201554	+	0.979477i	$0.564599\pi$
$464$	464.000	+	803.672i	0.0464238	+	0.0804084i
$465$	3601.50	−	6237.98i	0.359173	−	0.622106i
$466$	−4587.00	+	7944.92i	−0.455984	+	0.789788i
$467$	−2929.50	−	5074.04i	−0.290281	−	0.502781i	0.683595	−	0.729861i	$-0.260415\pi$
$467$	−2929.50	−	5074.04i	−0.290281	−	0.502781i	−0.973876	+	0.227080i	$0.927082\pi$
$468$	−1232.00			−0.121686
$469$		0			0
$470$	7350.00			0.721341
$471$	−2376.50	−	4116.22i	−0.232491	−	0.402687i
$472$	1260.00	−	2182.38i	0.122873	−	0.212823i
$473$	−310.000	+	536.936i	−0.0301349	+	0.0521952i
$474$	−721.000	−	1248.81i	−0.0698663	−	0.121012i
$475$	3724.00			0.359724
$476$		0			0
$477$	6666.00			0.639864
$478$	−1668.00	−	2889.06i	−0.159608	−	0.276449i
$479$	3251.50	−	5631.76i	0.310156	−	0.537206i	−0.668240	−	0.743946i	$-0.732952\pi$
$479$	3251.50	−	5631.76i	0.310156	−	0.537206i	0.978396	+	0.206740i	$0.0662853\pi$
$480$	−3920.00	+	6789.64i	−0.372756	+	0.645632i
$481$	−1533.00	−	2655.23i	−0.145320	−	0.251701i
$482$	6818.00			0.644297
$483$		0			0
$484$	5224.00			0.490609
$485$	3087.00	+	5346.84i	0.289017	+	0.500593i
$486$	−4928.00	+	8535.55i	−0.459956	+	0.796667i
$487$	8024.50	−	13898.8i	0.746663	−	1.29326i	−0.202751	−	0.979230i	$-0.564988\pi$
$487$	8024.50	−	13898.8i	0.746663	−	1.29326i	0.949414	−	0.314028i	$-0.101678\pi$
$488$	4956.00	+	8584.04i	0.459729	+	0.796273i
$489$	3269.00			0.302309
$490$		0			0
$491$	8864.00			0.814718			0.407359	−	0.913268i	$-0.366450\pi$
$491$	8864.00			0.814718			0.407359	+	0.913268i	$0.366450\pi$
$492$	4900.00	+	8487.05i	0.449002	+	0.777695i
$493$	−609.000	+	1054.82i	−0.0556348	+	0.0963624i
$494$	686.000	−	1188.19i	0.0624789	−	0.108217i
$495$	−385.000	−	666.840i	−0.0349585	−	0.0605499i
$496$	2352.00			0.212919
$497$		0			0
$498$	15288.0			1.37565
$499$	5105.50	+	8842.99i	0.458023	+	0.793319i	0.998856	−	0.0478104i	$-0.0152243\pi$
$499$	5105.50	+	8842.99i	0.458023	+	0.793319i	−0.540833	+	0.841130i	$0.681891\pi$
$500$	2814.00	−	4873.99i	0.251692	−	0.435943i
$501$	−4214.00	+	7298.86i	−0.375784	+	0.650876i
$502$	−4760.00	−	8244.56i	−0.423206	−	0.733014i
$503$	1680.00			0.148921			0.0744607	−	0.997224i	$-0.476276\pi$
$503$	1680.00			0.148921			0.0744607	+	0.997224i	$0.476276\pi$
$504$		0			0
$505$	9653.00			0.850600
$506$	−795.000	−	1376.98i	−0.0698460	−	0.120977i
$507$	−7003.50	+	12130.4i	−0.613484	+	1.06259i
$508$	144.000	−	249.415i	0.0125767	−	0.0217835i
$509$	−4728.50	−	8190.00i	−0.411762	−	0.713193i	0.583320	−	0.812242i	$-0.301753\pi$
$509$	−4728.50	−	8190.00i	−0.411762	−	0.713193i	−0.995083	+	0.0990489i	$0.968420\pi$
$510$	2058.00			0.178686
$511$		0			0
$512$	−5632.00			−0.486136
$513$	857.500	+	1485.23i	0.0738003	+	0.127826i
$514$	−805.000	+	1394.30i	−0.0690798	+	0.119650i
$515$	2376.50	−	4116.22i	0.203342	−	0.352199i
$516$	1736.00	+	3006.84i	0.148107	+	0.256529i
$517$	2625.00			0.223302
$518$		0			0
$519$	−19747.0			−1.67013
$520$	−1176.00	−	2036.89i	−0.0991750	−	0.171776i
$521$	−9040.50	+	15658.6i	−0.760214	+	1.31673i	0.182526	+	0.983201i	$0.441573\pi$
$521$	−9040.50	+	15658.6i	−0.760214	+	1.31673i	−0.942740	+	0.333528i	$0.891761\pi$
$522$	−1276.00	+	2210.10i	−0.106990	+	0.185313i
$523$	10188.5	+	17647.0i	0.851839	+	1.47543i	0.879546	+	0.475813i	$0.157846\pi$
$523$	10188.5	+	17647.0i	0.851839	+	1.47543i	−0.0277071	+	0.999616i	$0.508821\pi$
$524$	8596.00			0.716637
$525$		0			0
$526$	−514.000			−0.0426073
$527$	1543.50	+	2673.42i	0.127582	+	0.220979i
$528$	280.000	−	484.974i	0.0230785	−	0.0399731i
$529$	−6557.00	+	11357.1i	−0.538917	+	0.933431i
$530$	2121.00	+	3673.68i	0.173831	+	0.301084i
$531$	2310.00			0.188786
$532$		0			0
$533$	−4900.00			−0.398204
$534$	2303.00	+	3988.91i	0.186630	+	0.323253i
$535$	1599.50	−	2770.42i	0.129257	−	0.223879i
$536$	4980.00	−	8625.61i	0.401312	−	0.695093i
$537$	−11385.5	−	19720.3i	−0.914936	−	1.58472i
$538$	−7182.00			−0.575535
$539$		0			0
$540$	980.000			0.0780972
$541$	3096.50	+	5363.30i	0.246079	+	0.426222i	0.962435	−	0.271514i	$-0.0875243\pi$
$541$	3096.50	+	5363.30i	0.246079	+	0.426222i	−0.716355	+	0.697736i	$0.754191\pi$
$542$	1393.00	−	2412.75i	0.110396	−	0.191211i
$543$	−5537.00	+	9590.37i	−0.437597	+	0.757941i
$544$	−1680.00	−	2909.85i	−0.132407	−	0.229336i
$545$	7875.00			0.618950
$546$		0			0
$547$	−18464.0			−1.44326			−0.721630	−	0.692279i	$-0.756607\pi$
$547$	−18464.0			−1.44326			−0.721630	+	0.692279i	$0.756607\pi$
$548$	−2250.00	−	3897.11i	−0.175393	−	0.303789i
$549$	−4543.00	+	7868.71i	−0.353170	+	0.611709i
$550$	−380.000	+	658.179i	−0.0294605	+	0.0510270i
$551$	1421.00	+	2461.24i	0.109867	+	0.190295i
$552$	−26712.0			−2.05967
$553$		0			0
$554$	830.000			0.0636522
$555$	−5365.50	−	9293.32i	−0.410365	−	0.710774i
$556$	−504.000	+	872.954i	−0.0384431	+	0.0665854i
$557$	4706.50	−	8151.90i	0.358027	−	0.620120i	−0.629604	−	0.776916i	$-0.716783\pi$
$557$	4706.50	−	8151.90i	0.358027	−	0.620120i	0.987631	+	0.156796i	$0.0501164\pi$
$558$	3234.00	+	5601.45i	0.245351	+	0.424961i
$559$	−1736.00			−0.131351
$560$		0			0
$561$	735.000			0.0553150
$562$	4954.00	+	8580.58i	0.371836	+	0.644039i
$563$	1599.50	−	2770.42i	0.119735	−	0.207387i	−0.799928	−	0.600097i	$-0.795129\pi$
$563$	1599.50	−	2770.42i	0.119735	−	0.207387i	0.919663	+	0.392709i	$0.128462\pi$
$564$	7350.00	−	12730.6i	0.548743	−	0.950450i
$565$	−5383.00	−	9323.63i	−0.400822	−	0.694244i
$566$	8554.00			0.635250
$567$		0			0
$568$	10368.0			0.765901
$569$	−10791.5	−	18691.4i	−0.795085	−	1.37713i	−0.922785	−	0.385314i	$-0.874093\pi$
$569$	−10791.5	−	18691.4i	−0.795085	−	1.37713i	0.127701	−	0.991813i	$-0.459240\pi$
$570$	2401.00	−	4158.65i	0.176433	−	0.305591i
$571$	−10133.5	+	17551.7i	−0.742686	+	1.28637i	0.208582	+	0.978005i	$0.433115\pi$
$571$	−10133.5	+	17551.7i	−0.742686	+	1.28637i	−0.951268	+	0.308365i	$0.900218\pi$
$572$	−140.000	−	242.487i	−0.0102337	−	0.0177253i
$573$	−17899.0			−1.30496
$574$		0			0
$575$	12084.0			0.876413
$576$	−4928.00	−	8535.55i	−0.356481	−	0.617444i
$577$	6975.50	−	12081.9i	0.503282	−	0.871710i	−0.496711	−	0.867916i	$-0.665459\pi$
$577$	6975.50	−	12081.9i	0.503282	−	0.871710i	0.999993	−	0.00379418i	$-0.00120773\pi$
$578$	4472.00	−	7745.73i	0.321818	−	0.557405i
$579$	−1389.50	−	2406.68i	−0.0997334	−	0.172743i
$580$	1624.00			0.116264
$581$		0			0
$582$	−12348.0			−0.879452
$583$	757.500	+	1312.03i	0.0538121	+	0.0932053i
$584$	13356.0	−	23133.3i	0.946362	−	1.63915i
$585$	1078.00	−	1867.15i	0.0761877	−	0.131961i
$586$	7742.00	+	13409.5i	0.545766	+	0.945295i
$587$	20972.0			1.47463			0.737314	−	0.675550i	$-0.236094\pi$
$587$	20972.0			1.47463			0.737314	+	0.675550i	$0.236094\pi$
$588$		0			0
$589$	7203.00			0.503895
$590$	735.000	+	1273.06i	0.0512872	+	0.0888321i
$591$	10199.0	−	17665.2i	0.709866	−	1.22952i
$592$	1752.00	−	3034.55i	0.121633	−	0.210675i
$593$	−94.5000	−	163.679i	−0.00654410	−	0.0113347i	0.862735	−	0.505657i	$-0.168750\pi$
$593$	−94.5000	−	163.679i	−0.00654410	−	0.0113347i	−0.869279	+	0.494322i	$0.835416\pi$
$594$	−350.000			−0.0241762
$595$		0			0
$596$	804.000			0.0552569
$597$	−11686.5	−	20241.6i	−0.801167	−	1.38766i
$598$	2226.00	−	3855.55i	0.152221	−	0.263654i
$599$	5140.50	−	8903.61i	0.350643	−	0.607331i	−0.635719	−	0.771920i	$-0.719296\pi$
$599$	5140.50	−	8903.61i	0.350643	−	0.607331i	0.986362	+	0.164589i	$0.0526297\pi$
$600$	6384.00	+	11057.4i	0.434376	+	0.752362i
$601$	6090.00			0.413338			0.206669	−	0.978411i	$-0.433738\pi$
$601$	6090.00			0.413338			0.206669	+	0.978411i	$0.433738\pi$
$602$		0			0
$603$	9130.00			0.616588
$604$	3238.00	+	5608.38i	0.218133	+	0.377817i
$605$	−4571.00	+	7917.20i	−0.307170	+	0.532033i
$606$	−9653.00	+	16719.5i	−0.647073	+	1.12076i
$607$	2474.50	+	4285.96i	0.165464	+	0.286593i	0.936820	−	0.349812i	$-0.113754\pi$
$607$	2474.50	+	4285.96i	0.165464	+	0.286593i	−0.771356	+	0.636404i	$0.780421\pi$
$608$	−7840.00			−0.522951
$609$		0			0
$610$	−5782.00			−0.383781
$611$	3675.00	+	6365.29i	0.243330	+	0.421460i
$612$	924.000	−	1600.41i	0.0610302	−	0.105707i
$613$	7898.50	−	13680.6i	0.520420	−	0.901394i	−0.479298	−	0.877652i	$-0.659109\pi$
$613$	7898.50	−	13680.6i	0.520420	−	0.901394i	0.999718	−	0.0237416i	$-0.00755791\pi$
$614$	−7364.00	−	12754.8i	−0.484018	−	0.838343i
$615$	−17150.0			−1.12448
$616$		0			0
$617$	−9378.00			−0.611903			−0.305951	−	0.952047i	$-0.598975\pi$
$617$	−9378.00			−0.611903			−0.305951	+	0.952047i	$0.598975\pi$
$618$	4753.00	+	8232.44i	0.309375	+	0.535853i
$619$	−12176.5	+	21090.3i	−0.790654	+	1.36945i	0.134908	+	0.990858i	$0.456926\pi$
$619$	−12176.5	+	21090.3i	−0.790654	+	1.36945i	−0.925562	+	0.378595i	$0.876407\pi$
$620$	2058.00	−	3564.56i	0.133308	−	0.230897i
$621$	2782.50	+	4819.43i	0.179803	+	0.311429i
$622$	−19950.0			−1.28605
$623$		0			0
$624$	1568.00			0.100593
$625$	174.500	+	302.243i	0.0111680	+	0.0193435i
$626$	−4753.00	+	8232.44i	−0.303463	+	0.525614i
$627$	857.500	−	1485.23i	0.0546176	−	0.0946005i
$628$	−1358.00	−	2352.12i	−0.0862900	−	0.149459i
$629$	4599.00			0.291533
$630$		0			0
$631$	−12640.0			−0.797449			−0.398725	−	0.917071i	$-0.630547\pi$
$631$	−12640.0			−0.797449			−0.398725	+	0.917071i	$0.630547\pi$
$632$	−1236.00	−	2140.81i	−0.0777934	−	0.134742i
$633$	6230.00	−	10790.7i	0.391185	−	0.677553i
$634$	3477.00	−	6022.34i	0.217806	−	0.377252i
$635$	252.000	+	436.477i	0.0157485	+	0.0272772i
$636$	8484.00			0.528950
$637$		0			0
$638$	−580.000			−0.0359913
$639$	4752.00	+	8230.71i	0.294188	+	0.509549i
$640$	−1344.00	+	2327.88i	−0.0830098	+	0.143777i
$641$	520.500	−	901.532i	0.0320726	−	0.0555513i	−0.849544	−	0.527518i	$-0.823123\pi$
$641$	520.500	−	901.532i	0.0320726	−	0.0555513i	0.881616	+	0.471967i	$0.156456\pi$
$642$	3199.00	+	5540.83i	0.196658	+	0.340622i
$643$	−9548.00			−0.585593			−0.292797	−	0.956175i	$-0.594586\pi$
$643$	−9548.00			−0.585593			−0.292797	+	0.956175i	$0.594586\pi$
$644$		0			0
$645$	−6076.00			−0.370918
$646$	1029.00	+	1782.28i	0.0626710	+	0.108549i
$647$	−1620.50	+	2806.79i	−0.0984674	+	0.170551i	−0.911050	−	0.412295i	$-0.864727\pi$
$647$	−1620.50	+	2806.79i	−0.0984674	+	0.170551i	0.812583	+	0.582845i	$0.198061\pi$
$648$	−10068.0	+	17438.3i	−0.610352	+	1.05716i
$649$	262.500	+	454.663i	0.0158768	+	0.0274994i
$650$	−2128.00			−0.128411
$651$		0			0
$652$	1868.00			0.112203
$653$	4426.50	+	7666.92i	0.265272	+	0.459464i	0.967635	−	0.252355i	$-0.0812051\pi$
$653$	4426.50	+	7666.92i	0.265272	+	0.459464i	−0.702363	+	0.711819i	$0.747872\pi$
$654$	−7875.00	+	13639.9i	−0.470851	+	0.815539i
$655$	−7521.50	+	13027.6i	−0.448686	+	0.777147i
$656$	−2800.00	−	4849.74i	−0.166649	−	0.288644i
$657$	24486.0			1.45402
$658$		0			0
$659$	7044.00			0.416381			0.208191	−	0.978088i	$-0.433243\pi$
$659$	7044.00			0.416381			0.208191	+	0.978088i	$0.433243\pi$
$660$	−490.000	−	848.705i	−0.0288988	−	0.0500542i
$661$	−6044.50	+	10469.4i	−0.355679	+	0.616054i	−0.987234	−	0.159277i	$-0.949084\pi$
$661$	−6044.50	+	10469.4i	−0.355679	+	0.616054i	0.631555	+	0.775331i	$0.282417\pi$
$662$	−3341.00	+	5786.78i	−0.196151	+	0.339743i
$663$	1029.00	+	1782.28i	0.0602761	+	0.104401i
$664$	26208.0			1.53173
$665$		0			0
$666$	9636.00			0.560642
$667$	4611.00	+	7986.49i	0.267674	+	0.463625i
$668$	−2408.00	+	4170.78i	−0.139474	+	0.241575i
$669$	4900.00	−	8487.05i	0.283176	−	0.490476i
$670$	2905.00	+	5031.61i	0.167507	+	0.290131i
$671$	−2065.00			−0.118805
$672$		0			0
$673$	982.000			0.0562456			0.0281228	−	0.999604i	$-0.491047\pi$
$673$	982.000			0.0562456			0.0281228	+	0.999604i	$0.491047\pi$
$674$	−7366.00	−	12758.3i	−0.420961	−	0.729126i
$675$	1330.00	−	2303.63i	0.0758396	−	0.131358i
$676$	−4002.00	+	6931.67i	−0.227697	+	0.394383i
$677$	−15256.5	−	26425.0i	−0.866108	−	1.50014i	−0.865943	−	0.500143i	$-0.833281\pi$
$677$	−15256.5	−	26425.0i	−0.866108	−	1.50014i	−0.000164659	−	1.00000i	$-0.500052\pi$
$678$	21532.0			1.21966
$679$		0			0
$680$	3528.00			0.198960
$681$	7717.50	+	13367.1i	0.434266	+	0.752171i
$682$	−735.000	+	1273.06i	−0.0412677	+	0.0714778i
$683$	−5737.50	+	9937.64i	−0.321434	+	0.556740i	−0.980784	−	0.195096i	$-0.937498\pi$
$683$	−5737.50	+	9937.64i	−0.321434	+	0.556740i	0.659350	+	0.751836i	$0.270831\pi$
$684$	−2156.00	−	3734.30i	−0.120522	−	0.208749i
$685$	7875.00			0.439253
$686$		0			0
$687$	2009.00			0.111569
$688$	−992.000	−	1718.19i	−0.0549704	−	0.0952116i
$689$	−2121.00	+	3673.68i	−0.117277	+	0.203129i
$690$	7791.00	−	13494.4i	0.429853	−	0.744527i
$691$	−14157.5	−	24521.5i	−0.779416	−	1.34999i	−0.932279	−	0.361741i	$-0.882182\pi$
$691$	−14157.5	−	24521.5i	−0.779416	−	1.34999i	0.152862	−	0.988248i	$-0.451151\pi$
$692$	−11284.0			−0.619875
$693$		0			0
$694$	14830.0			0.811151
$695$	−882.000	−	1527.67i	−0.0481384	−	0.0833781i
$696$	−4872.00	+	8438.55i	−0.265334	+	0.459573i
$697$	3675.00	−	6365.29i	0.199714	−	0.345915i
$698$	−3878.00	−	6716.89i	−0.210293	−	0.364238i
$699$	−32109.0			−1.73744
$700$		0			0
$701$	10614.0			0.571876			0.285938	−	0.958248i	$-0.407695\pi$
$701$	10614.0			0.571876			0.285938	+	0.958248i	$0.407695\pi$
$702$	−490.000	−	848.705i	−0.0263445	−	0.0456301i
$703$	5365.50	−	9293.32i	0.287857	−	0.498583i
$704$	1120.00	−	1939.90i	0.0599596	−	0.103853i
$705$	12862.5	+	22278.5i	0.687134	+	1.19015i
$706$	−2534.00			−0.135083
$707$		0			0
$708$	2940.00			0.156062
$709$	−5149.50	−	8919.20i	−0.272769	−	0.472451i	0.696801	−	0.717265i	$-0.254606\pi$
$709$	−5149.50	−	8919.20i	−0.272769	−	0.472451i	−0.969570	+	0.244814i	$0.921273\pi$
$710$	−3024.00	+	5237.72i	−0.159843	+	0.276857i
$711$	1133.00	−	1962.41i	0.0597621	−	0.103511i
$712$	3948.00	+	6838.14i	0.207806	+	0.359930i
$713$	23373.0			1.22767
$714$		0			0
$715$	490.000			0.0256293
$716$	−6506.00	−	11268.7i	−0.339582	−	0.588173i
$717$	5838.00	−	10111.7i	0.304078	−	0.526679i
$718$	−4685.00	+	8114.66i	−0.243513	+	0.421778i
$719$	16264.5	+	28170.9i	0.843621	+	1.46119i	0.886813	+	0.462128i	$0.152914\pi$
$719$	16264.5	+	28170.9i	0.843621	+	1.46119i	−0.0431924	+	0.999067i	$0.513753\pi$
$720$	2464.00			0.127539
$721$		0			0
$722$	−8916.00			−0.459583
$723$	11931.5	+	20666.0i	0.613744	+	1.06304i
$724$	−3164.00	+	5480.21i	−0.162416	+	0.281313i
$725$	2204.00	−	3817.44i	0.112903	−	0.195553i
$726$	−9142.00	−	15834.4i	−0.467344	−	0.809463i
$727$	−29456.0			−1.50270			−0.751350	−	0.659904i	$-0.770597\pi$
$727$	−29456.0			−1.50270			−0.751350	+	0.659904i	$0.770597\pi$
$728$		0			0
$729$	−11843.0			−0.601687
$730$	7791.00	+	13494.4i	0.395011	+	0.684179i
$731$	1302.00	−	2255.13i	0.0658772	−	0.114103i
$732$	−5782.00	+	10014.7i	−0.291952	+	0.505676i
$733$	13933.5	+	24133.5i	0.702109	+	1.21609i	0.967725	+	0.252009i	$0.0810912\pi$
$733$	13933.5	+	24133.5i	0.702109	+	1.21609i	−0.265616	+	0.964079i	$0.585575\pi$
$734$	9282.00			0.466764
$735$		0			0
$736$	−25440.0			−1.27409
$737$	1037.50	+	1797.00i	0.0518546	+	0.0898147i
$738$	7700.00	−	13336.8i	0.384066	−	0.665222i
$739$	−9769.50	+	16921.3i	−0.486302	+	0.842299i	−0.999876	−	0.0157460i	$-0.994988\pi$
$739$	−9769.50	+	16921.3i	−0.486302	+	0.842299i	0.513574	+	0.858045i	$0.328321\pi$
$740$	−3066.00	−	5310.47i	−0.152309	−	0.263806i
$741$	4802.00			0.238065
$742$		0			0
$743$	1248.00			0.0616214			0.0308107	−	0.999525i	$-0.490191\pi$
$743$	1248.00			0.0616214			0.0308107	+	0.999525i	$0.490191\pi$
$744$	12348.0	+	21387.4i	0.608467	+	1.05390i
$745$	−703.500	+	1218.50i	−0.0345963	+	0.0599226i
$746$	8797.00	−	15236.9i	0.431744	−	0.747803i
$747$	12012.0	+	20805.4i	0.588348	+	1.01905i
$748$	420.000			0.0205304
$749$		0			0
$750$	−19698.0			−0.959026
$751$	−14046.5	−	24329.3i	−0.682509	−	1.18214i	−0.974213	−	0.225631i	$-0.927556\pi$
$751$	−14046.5	−	24329.3i	−0.682509	−	1.18214i	0.291704	−	0.956509i	$-0.405778\pi$
$752$	−4200.00	+	7274.61i	−0.203668	+	0.352763i
$753$	16660.0	−	28856.0i	0.806274	−	1.39651i
$754$	−812.000	−	1406.43i	−0.0392192	−	0.0679297i
$755$	−11333.0			−0.546292
$756$		0			0
$757$	35954.0			1.72625			0.863124	−	0.504991i	$-0.168504\pi$
$757$	35954.0			1.72625			0.863124	+	0.504991i	$0.168504\pi$
$758$	−13680.0	−	23694.5i	−0.655514	−	1.13538i
$759$	2782.50	−	4819.43i	0.133068	−	0.230480i
$760$	4116.00	−	7129.12i	0.196451	−	0.340264i
$761$	−430.500	−	745.648i	−0.0205067	−	0.0355187i	0.855590	−	0.517654i	$-0.173195\pi$
$761$	−430.500	−	745.648i	−0.0205067	−	0.0355187i	−0.876097	+	0.482136i	$0.839861\pi$
$762$	−1008.00			−0.0479212
$763$		0			0
$764$	−10228.0			−0.484340
$765$	1617.00	+	2800.73i	0.0764219	+	0.132367i
$766$	9765.00	−	16913.5i	0.460605	−	0.797792i
$767$	−735.000	+	1273.06i	−0.0346014	+	0.0599315i
$768$	−15232.0	−	26382.6i	−0.715674	−	1.23958i
$769$	−24710.0			−1.15873			−0.579366	−	0.815067i	$-0.696700\pi$
$769$	−24710.0			−1.15873			−0.579366	+	0.815067i	$0.696700\pi$
$770$		0			0
$771$	−5635.00			−0.263216
$772$	−794.000	−	1375.25i	−0.0370164	−	0.0641143i
$773$	8249.50	−	14288.6i	0.383847	−	0.664843i	−0.607761	−	0.794120i	$-0.707932\pi$
$773$	8249.50	−	14288.6i	0.383847	−	0.664843i	0.991609	+	0.129277i	$0.0412656\pi$
$774$	2728.00	−	4725.03i	0.126687	−	0.219429i
$775$	−5586.00	−	9675.24i	−0.258910	−	0.448445i
$776$	−21168.0			−0.979236
$777$		0			0
$778$	3462.00			0.159536
$779$	−8575.00	−	14852.3i	−0.394392	−	0.683107i
$780$	1372.00	−	2376.37i	0.0629814	−	0.109087i
$781$	−1080.00	+	1870.61i	−0.0494820	+	0.0857053i
$782$	3339.00	+	5783.32i	0.152688	+	0.264464i
$783$	2030.00			0.0926517
$784$		0			0
$785$	4753.00			0.216104
$786$	−15043.0	−	26055.2i	−0.682654	−	1.18239i
$787$	8235.50	−	14264.3i	0.373016	−	0.646083i	−0.617012	−	0.786954i	$-0.711657\pi$
$787$	8235.50	−	14264.3i	0.373016	−	0.646083i	0.990028	+	0.140871i	$0.0449902\pi$
$788$	5828.00	−	10094.4i	0.263469	−	0.456342i
$789$	−899.500	−	1557.98i	−0.0405869	−	0.0702985i
$790$	1442.00			0.0649418
$791$		0			0
$792$	2640.00			0.118445
$793$	−2891.00	−	5007.36i	−0.129461	−	0.224233i
$794$	10983.0	−	19023.1i	0.490897	−	0.850258i
$795$	−7423.50	+	12857.9i	−0.331175	+	0.573613i
$796$	−6678.00	−	11566.6i	−0.297356	−	0.515036i
$797$	36470.0			1.62087			0.810435	−	0.585828i	$-0.199231\pi$
$797$	36470.0			1.62087			0.810435	+	0.585828i	$0.199231\pi$
$798$		0			0
$799$	−11025.0			−0.488156
$800$	6080.00	+	10530.9i	0.268701	+	0.465403i
$801$	−3619.00	+	6268.29i	−0.159639	+	0.276503i
$802$	−6603.00	+	11436.7i	−0.290723	+	0.503547i
$803$	2782.50	+	4819.43i	0.122282	+	0.211798i
$804$	11620.0			0.509709
$805$		0			0
$806$	−4116.00			−0.179876
$807$	−12568.5	−	21769.3i	−0.548243	−	0.949585i
$808$	−16548.0	+	28662.0i	−0.720491	+	1.24793i
$809$	−17875.5	+	30961.3i	−0.776847	+	1.34554i	0.156904	+	0.987614i	$0.449849\pi$
$809$	−17875.5	+	30961.3i	−0.776847	+	1.34554i	−0.933751	+	0.357924i	$0.883485\pi$
$810$	−5873.00	−	10172.3i	−0.254761	−	0.441259i
$811$	16492.0			0.714072			0.357036	−	0.934091i	$-0.383787\pi$
$811$	16492.0			0.714072			0.357036	+	0.934091i	$0.383787\pi$
$812$		0			0
$813$	9751.00			0.420643
$814$	1095.00	+	1896.60i	0.0471495	+	0.0816654i
$815$	−1634.50	+	2831.04i	−0.0702504	+	0.121677i
$816$	−1176.00	+	2036.89i	−0.0504513	+	0.0873842i
$817$	−3038.00	−	5261.97i	−0.130093	−	0.225328i
$818$	−21910.0			−0.936510
$819$		0			0
$820$	−9800.00			−0.417355
$821$	20736.5	+	35916.7i	0.881497	+	1.52680i	0.849677	+	0.527304i	$0.176797\pi$
$821$	20736.5	+	35916.7i	0.881497	+	1.52680i	0.0318198	+	0.999494i	$0.489870\pi$
$822$	−7875.00	+	13639.9i	−0.334151	+	0.578767i
$823$	12532.5	−	21706.9i	0.530809	−	0.919387i	−0.468545	−	0.883440i	$-0.655222\pi$
$823$	12532.5	−	21706.9i	0.530809	−	0.919387i	0.999354	−	0.0359479i	$-0.0114450\pi$
$824$	8148.00	+	14112.7i	0.344477	+	0.596652i
$825$	−2660.00			−0.112254
$826$		0			0
$827$	9732.00			0.409208			0.204604	−	0.978845i	$-0.434409\pi$
$827$	9732.00			0.409208			0.204604	+	0.978845i	$0.434409\pi$
$828$	−6996.00	−	12117.4i	−0.293633	−	0.508587i
$829$	13877.5	−	24036.5i	0.581406	−	1.00702i	−0.413907	−	0.910319i	$-0.635836\pi$
$829$	13877.5	−	24036.5i	0.581406	−	1.00702i	0.995313	−	0.0967055i	$-0.0308305\pi$
$830$	−7644.00	+	13239.8i	−0.319671	+	0.553687i
$831$	1452.50	+	2515.80i	0.0606338	+	0.105021i
$832$	6272.00			0.261349
$833$		0			0
$834$	3528.00			0.146480
$835$	−4214.00	−	7298.86i	−0.174648	−	0.302500i
$836$	490.000	−	848.705i	0.0202715	−	0.0351113i
$837$	2572.50	−	4455.70i	0.106235	−	0.184004i
$838$	6636.00	+	11493.9i	0.273552	+	0.473806i
$839$	−21112.0			−0.868733			−0.434367	−	0.900736i	$-0.643028\pi$
$839$	−21112.0			−0.868733			−0.434367	+	0.900736i	$0.643028\pi$
$840$		0			0
$841$	−21025.0			−0.862069
$842$	16630.0	+	28804.0i	0.680650	+	1.17892i
$843$	−17339.0	+	30032.0i	−0.708407	+	1.22700i
$844$	3560.00	−	6166.10i	0.145190	−	0.251476i
$845$	−7003.50	−	12130.4i	−0.285122	−	0.493845i
$846$	−23100.0			−0.938764
$847$		0			0
$848$	−4848.00			−0.196322
$849$	14969.5	+	25927.9i	0.605126	+	1.04811i
$850$	1596.00	−	2764.35i	0.0644028	−	0.111549i
$851$	17410.5	−	30155.9i	0.701321	−	1.21472i
$852$	6048.00	+	10475.4i	0.243194	+	0.421224i
$853$	21238.0			0.852492			0.426246	−	0.904607i	$-0.359836\pi$
$853$	21238.0			0.852492			0.426246	+	0.904607i	$0.359836\pi$
$854$		0			0
$855$	7546.00			0.301834
$856$	5484.00	+	9498.57i	0.218971	+	0.379269i
$857$	−17804.5	+	30838.3i	−0.709673	+	1.22919i	0.255305	+	0.966861i	$0.417824\pi$
$857$	−17804.5	+	30838.3i	−0.709673	+	1.22919i	−0.964978	+	0.262330i	$0.915509\pi$
$858$	−490.000	+	848.705i	−0.0194969	+	0.0337696i
$859$	1088.50	+	1885.34i	0.0432353	+	0.0748858i	0.886833	−	0.462090i	$-0.152900\pi$
$859$	1088.50	+	1885.34i	0.0432353	+	0.0748858i	−0.843598	+	0.536975i	$0.819567\pi$
$860$	−3472.00			−0.137668
$861$		0			0
$862$	9846.00			0.389044
$863$	16123.5	+	27926.7i	0.635980	+	1.10155i	0.986307	+	0.164921i	$0.0527371\pi$
$863$	16123.5	+	27926.7i	0.635980	+	1.10155i	−0.350327	+	0.936627i	$0.613930\pi$
$864$	−2800.00	+	4849.74i	−0.110252	+	0.190962i
$865$	9873.50	−	17101.4i	0.388103	−	0.672214i
$866$	8974.00	+	15543.4i	0.352135	+	0.609916i
$867$	31304.0			1.22623
$868$		0			0
$869$	515.000			0.0201038
$870$	−2842.00	−	4922.49i	−0.110750	−	0.191825i
$871$	−2905.00	+	5031.61i	−0.113011	+	0.195740i
$872$	−13500.0	+	23382.7i	−0.524275	+	0.908071i
$873$	−9702.00	−	16804.4i	−0.376132	−	0.651479i
$874$	15582.0			0.603054
$875$		0			0
$876$	31164.0			1.20198
$877$	−13815.5	−	23929.1i	−0.531946	−	0.921357i	−0.999305	−	0.0372891i	$-0.988128\pi$
$877$	−13815.5	−	23929.1i	−0.531946	−	0.921357i	0.467359	−	0.884068i	$-0.345206\pi$
$878$	−4179.00	+	7238.24i	−0.160631	+	0.278222i
$879$	−27097.0	+	46933.4i	−1.03977	+	1.80094i
$880$	280.000	+	484.974i	0.0107259	+	0.0185778i
$881$	−24402.0			−0.933172			−0.466586	−	0.884476i	$-0.654516\pi$
$881$	−24402.0			−0.933172			−0.466586	+	0.884476i	$0.654516\pi$
$882$		0			0
$883$	−19612.0			−0.747448			−0.373724	−	0.927540i	$-0.621919\pi$
$883$	−19612.0			−0.747448			−0.373724	+	0.927540i	$0.621919\pi$
$884$	588.000	+	1018.45i	0.0223717	+	0.0387489i
$885$	−2572.50	+	4455.70i	−0.0977103	+	0.169239i
$886$	12927.0	−	22390.2i	0.490170	−	0.849000i
$887$	1130.50	+	1958.08i	0.0427942	+	0.0741218i	0.886629	−	0.462481i	$-0.153041\pi$
$887$	1130.50	+	1958.08i	0.0427942	+	0.0741218i	−0.843835	+	0.536603i	$0.819707\pi$
$888$	36792.0			1.39038
$889$		0			0
$890$	−4606.00			−0.173476
$891$	−2097.50	−	3632.98i	−0.0788652	−	0.136599i
$892$	2800.00	−	4849.74i	0.105102	−	0.182042i
$893$	−12862.5	+	22278.5i	−0.482001	+	0.834851i
$894$	−1407.00	−	2437.00i	−0.0526366	−	0.0911693i
$895$	22771.0			0.850448
$896$		0			0
$897$	15582.0			0.580009
$898$	2826.00	+	4894.78i	0.105017	+	0.181894i
$899$	4263.00	−	7383.73i	0.158152	−	0.273928i
$900$	−3344.00	+	5791.98i	−0.123852	+	0.214518i
$901$	−3181.50	−	5510.52i	−0.117637	−	0.203754i
$902$	3500.00			0.129199
$903$		0			0
$904$	36912.0			1.35805
$905$	−5537.00	−	9590.37i	−0.203377	−	0.352259i
$906$	11333.0	−	19629.3i	0.415578	−	0.719802i
$907$	11916.5	−	20640.0i	0.436252	−	0.755611i	−0.561145	−	0.827718i	$-0.689639\pi$
$907$	11916.5	−	20640.0i	0.436252	−	0.755611i	0.997397	+	0.0721066i	$0.0229722\pi$
$908$	4410.00	+	7638.34i	0.161180	+	0.279171i
$909$	−30338.0			−1.10698
$910$		0			0
$911$	31824.0			1.15738			0.578692	−	0.815546i	$-0.303563\pi$
$911$	31824.0			1.15738			0.578692	+	0.815546i	$0.303563\pi$
$912$	2744.00	+	4752.75i	0.0996304	+	0.172565i
$913$	−2730.00	+	4728.50i	−0.0989593	+	0.171402i
$914$	−8479.00	+	14686.1i	−0.306849	+	0.531479i
$915$	−10118.5	−	17525.8i	−0.365582	−	0.633206i
$916$	1148.00			0.0414094
$917$		0			0
$918$	1470.00			0.0528510
$919$	8409.50	+	14565.7i	0.301854	+	0.522826i	0.976556	−	0.215264i	$-0.0690612\pi$
$919$	8409.50	+	14565.7i	0.301854	+	0.522826i	−0.674702	+	0.738090i	$0.735728\pi$
$920$	13356.0	−	23133.3i	0.478624	−	0.829001i
$921$	25774.0	−	44641.9i	0.922130	−	1.59718i
$922$	9338.00	+	16173.9i	0.333547	+	0.577721i
$923$	−6048.00			−0.215680
$924$		0			0
$925$	−16644.0			−0.591623
$926$	4016.00	+	6955.92i	0.142520	+	0.246853i
$927$	−7469.00	+	12936.7i	−0.264632	+	0.458357i
$928$	−4640.00	+	8036.72i	−0.164133	+	0.284287i
$929$	899.500	+	1557.98i	0.0317671	+	0.0550222i	0.881472	−	0.472237i	$-0.156553\pi$
$929$	899.500	+	1557.98i	0.0317671	+	0.0550222i	−0.849705	+	0.527259i	$0.823220\pi$
$930$	−14406.0			−0.507948
$931$		0			0
$932$	−18348.0			−0.644859
$933$	−34912.5	−	60470.2i	−1.22506	−	2.12187i
$934$	−5859.00	+	10148.1i	−0.205259	+	0.355520i
$935$	−367.500	+	636.529i	−0.0128540	+	0.0222639i
$936$	3696.00	+	6401.66i	0.129068	+	0.223552i
$937$	−14154.0			−0.493480			−0.246740	−	0.969082i	$-0.579359\pi$
$937$	−14154.0			−0.493480			−0.246740	+	0.969082i	$0.579359\pi$
$938$		0			0
$939$	−33271.0			−1.15629
$940$	7350.00	+	12730.6i	0.255033	+	0.441729i
$941$	6023.50	−	10433.0i	0.208672	−	0.361431i	−0.742624	−	0.669708i	$-0.766419\pi$
$941$	6023.50	−	10433.0i	0.208672	−	0.361431i	0.951296	+	0.308277i	$0.0997525\pi$
$942$	−4753.00	+	8232.44i	−0.164396	+	0.284742i
$943$	−27825.0	−	48194.3i	−0.960877	−	1.66429i
$944$	−1680.00			−0.0579230
$945$		0			0
$946$	1240.00			0.0426172
$947$	12189.5	+	21112.8i	0.418274	+	0.724472i	0.995766	−	0.0919245i	$-0.0293018\pi$
$947$	12189.5	+	21112.8i	0.418274	+	0.724472i	−0.577492	+	0.816396i	$0.695969\pi$
$948$	1442.00	−	2497.62i	0.0494029	−	0.0855684i
$949$	−7791.00	+	13494.4i	−0.266498	+	0.461588i
$950$	−3724.00	−	6450.16i	−0.127182	−	0.220285i
$951$	24339.0			0.829912
$952$		0			0
$953$	−52330.0			−1.77874			−0.889368	−	0.457192i	$-0.848855\pi$
$953$	−52330.0			−1.77874			−0.889368	+	0.457192i	$0.848855\pi$
$954$	−6666.00	−	11545.9i	−0.226226	−	0.391835i
$955$	8949.50	−	15501.0i	0.303245	−	0.525236i
$956$	3336.00	−	5778.12i	0.112860	−	0.195479i
$957$	−1015.00	−	1758.03i	−0.0342845	−	0.0593825i
$958$	−13006.0			−0.438627
$959$		0			0
$960$	21952.0			0.738018
$961$	4091.00	+	7085.82i	0.137323	+	0.237851i
$962$	−3066.00	+	5310.47i	−0.102757	+	0.177980i
$963$	−5027.00	+	8707.02i	−0.168217	+	0.291360i
$964$	6818.00	+	11809.1i	0.227794	+	0.394550i
$965$	2779.00			0.0927038
$966$		0			0
$967$	−12416.0			−0.412897			−0.206449	−	0.978457i	$-0.566191\pi$
$967$	−12416.0			−0.412897			−0.206449	+	0.978457i	$0.566191\pi$
$968$	−15672.0	−	27144.7i	−0.520369	−	0.901305i
$969$	−3601.50	+	6237.98i	−0.119398	+	0.206804i
$970$	6174.00	−	10693.7i	0.204366	−	0.353973i
$971$	18406.5	+	31881.0i	0.608334	+	1.05367i	0.991515	+	0.129993i	$0.0414954\pi$
$971$	18406.5	+	31881.0i	0.608334	+	1.05367i	−0.383181	+	0.923673i	$0.625171\pi$
$972$	−19712.0			−0.650476
$973$		0			0
$974$	−32098.0			−1.05594
$975$	−3724.00	−	6450.16i	−0.122321	−	0.211867i
$976$	3304.00	−	5722.70i	0.108359	−	0.187683i
$977$	−17497.5	+	30306.6i	−0.572973	+	0.992418i	0.423286	+	0.905996i	$0.360877\pi$
$977$	−17497.5	+	30306.6i	−0.572973	+	0.992418i	−0.996259	+	0.0864221i	$0.972457\pi$
$978$	−3269.00	−	5662.07i	−0.106883	−	0.185126i
$979$	−1645.00			−0.0537022
$980$		0			0
$981$	−24750.0			−0.805511
$982$	−8864.00	−	15352.9i	−0.288046	−	0.498911i
$983$	−7150.50	+	12385.0i	−0.232010	+	0.401853i	−0.958399	−	0.285430i	$-0.907863\pi$
$983$	−7150.50	+	12385.0i	−0.232010	+	0.401853i	0.726390	+	0.687283i	$0.241197\pi$
$984$	29400.0	−	50922.3i	0.952477	−	1.64974i
$985$	10199.0	+	17665.2i	0.329916	+	0.571431i
$986$	2436.00			0.0786796
$987$		0			0
$988$	2744.00			0.0883586
$989$	−9858.00	−	17074.6i	−0.316953	−	0.548978i
$990$	−770.000	+	1333.68i	−0.0247194	+	0.0428153i
$991$	1332.50	−	2307.96i	0.0427127	−	0.0739805i	−0.843879	−	0.536534i	$-0.819733\pi$
$991$	1332.50	−	2307.96i	0.0427127	−	0.0739805i	0.886591	+	0.462553i	$0.153067\pi$
$992$	11760.0	+	20368.9i	0.376392	+	0.651929i
$993$	−23387.0			−0.747396
$994$		0			0
$995$	23373.0			0.744697
$996$	15288.0	+	26479.6i	0.486364	+	0.842408i
$997$	12435.5	−	21538.9i	0.395021	−	0.684197i	−0.598083	−	0.801434i	$-0.704071\pi$
$997$	12435.5	−	21538.9i	0.395021	−	0.684197i	0.993104	+	0.117237i	$0.0374039\pi$
$998$	10211.0	−	17686.0i	0.323871	−	0.560962i
$999$	−3832.50	−	6638.08i	−0.121376	−	0.210230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.4.c.a.18.1		2
3.2	odd	2		441.4.e.k.361.1		2
7.2	even	3	inner	49.4.c.a.30.1		2
7.3	odd	6		49.4.a.d.1.1		1
7.4	even	3		49.4.a.c.1.1		1
7.5	odd	6		7.4.c.a.2.1	✓	2
7.6	odd	2		7.4.c.a.4.1	yes	2
21.2	odd	6		441.4.e.k.226.1		2
21.5	even	6		63.4.e.b.37.1		2
21.11	odd	6		441.4.a.e.1.1		1
21.17	even	6		441.4.a.d.1.1		1
21.20	even	2		63.4.e.b.46.1		2
28.3	even	6		784.4.a.b.1.1		1
28.11	odd	6		784.4.a.r.1.1		1
28.19	even	6		112.4.i.c.65.1		2
28.27	even	2		112.4.i.c.81.1		2
35.4	even	6		1225.4.a.d.1.1		1
35.12	even	12		175.4.k.a.149.1		4
35.13	even	4		175.4.k.a.74.1		4
35.19	odd	6		175.4.e.a.51.1		2
35.24	odd	6		1225.4.a.c.1.1		1
35.27	even	4		175.4.k.a.74.2		4
35.33	even	12		175.4.k.a.149.2		4
35.34	odd	2		175.4.e.a.151.1		2
56.5	odd	6		448.4.i.f.65.1		2
56.13	odd	2		448.4.i.f.193.1		2
56.19	even	6		448.4.i.a.65.1		2
56.27	even	2		448.4.i.a.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.4.c.a.2.1	✓	2	7.5	odd	6
7.4.c.a.4.1	yes	2	7.6	odd	2
49.4.a.c.1.1		1	7.4	even	3
49.4.a.d.1.1		1	7.3	odd	6
49.4.c.a.18.1		2	1.1	even	1	trivial
49.4.c.a.30.1		2	7.2	even	3	inner
63.4.e.b.37.1		2	21.5	even	6
63.4.e.b.46.1		2	21.20	even	2
112.4.i.c.65.1		2	28.19	even	6
112.4.i.c.81.1		2	28.27	even	2
175.4.e.a.51.1		2	35.19	odd	6
175.4.e.a.151.1		2	35.34	odd	2
175.4.k.a.74.1		4	35.13	even	4
175.4.k.a.74.2		4	35.27	even	4
175.4.k.a.149.1		4	35.12	even	12
175.4.k.a.149.2		4	35.33	even	12
441.4.a.d.1.1		1	21.17	even	6
441.4.a.e.1.1		1	21.11	odd	6
441.4.e.k.226.1		2	21.2	odd	6
441.4.e.k.361.1		2	3.2	odd	2
448.4.i.a.65.1		2	56.19	even	6
448.4.i.a.193.1		2	56.27	even	2
448.4.i.f.65.1		2	56.5	odd	6
448.4.i.f.193.1		2	56.13	odd	2
784.4.a.b.1.1		1	28.3	even	6
784.4.a.r.1.1		1	28.11	odd	6
1225.4.a.c.1.1		1	35.24	odd	6
1225.4.a.d.1.1		1	35.4	even	6

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(3.50000 - 6.06218i) q^{3} +(2.00000 - 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} -14.0000 q^{6} -24.0000 q^{8} +(-11.0000 - 19.0526i) q^{9} +(7.00000 - 12.1244i) q^{10} +(2.50000 - 4.33013i) q^{11} +(-14.0000 - 24.2487i) q^{12} +14.0000 q^{13} +49.0000 q^{15} +(8.00000 + 13.8564i) q^{16} +(-10.5000 + 18.1865i) q^{17} +(-22.0000 + 38.1051i) q^{18} +(24.5000 + 42.4352i) q^{19} +28.0000 q^{20} -10.0000 q^{22} +(79.5000 + 137.698i) q^{23} +(-84.0000 + 145.492i) q^{24} +(38.0000 - 65.8179i) q^{25} +(-14.0000 - 24.2487i) q^{26} +35.0000 q^{27} +58.0000 q^{29} +(-49.0000 - 84.8705i) q^{30} +(73.5000 - 127.306i) q^{31} +(-80.0000 + 138.564i) q^{32} +(-17.5000 - 30.3109i) q^{33} +42.0000 q^{34} -88.0000 q^{36} +(-109.500 - 189.660i) q^{37} +(49.0000 - 84.8705i) q^{38} +(49.0000 - 84.8705i) q^{39} +(-84.0000 - 145.492i) q^{40} -350.000 q^{41} -124.000 q^{43} +(-10.0000 - 17.3205i) q^{44} +(77.0000 - 133.368i) q^{45} +(159.000 - 275.396i) q^{46} +(262.500 + 454.663i) q^{47} +112.000 q^{48} -152.000 q^{50} +(73.5000 + 127.306i) q^{51} +(28.0000 - 48.4974i) q^{52} +(-151.500 + 262.406i) q^{53} +(-35.0000 - 60.6218i) q^{54} +35.0000 q^{55} +343.000 q^{57} +(-58.0000 - 100.459i) q^{58} +(-52.5000 + 90.9327i) q^{59} +(98.0000 - 169.741i) q^{60} +(-206.500 - 357.668i) q^{61} -294.000 q^{62} +448.000 q^{64} +(49.0000 + 84.8705i) q^{65} +(-35.0000 + 60.6218i) q^{66} +(-207.500 + 359.401i) q^{67} +(42.0000 + 72.7461i) q^{68} +1113.00 q^{69} -432.000 q^{71} +(264.000 + 457.261i) q^{72} +(-556.500 + 963.886i) q^{73} +(-219.000 + 379.319i) q^{74} +(-266.000 - 460.726i) q^{75} +196.000 q^{76} -196.000 q^{78} +(51.5000 + 89.2006i) q^{79} +(-56.0000 + 96.9948i) q^{80} +(419.500 - 726.595i) q^{81} +(350.000 + 606.218i) q^{82} -1092.00 q^{83} -147.000 q^{85} +(124.000 + 214.774i) q^{86} +(203.000 - 351.606i) q^{87} +(-60.0000 + 103.923i) q^{88} +(-164.500 - 284.922i) q^{89} -308.000 q^{90} +636.000 q^{92} +(-514.500 - 891.140i) q^{93} +(525.000 - 909.327i) q^{94} +(-171.500 + 297.047i) q^{95} +(560.000 + 969.948i) q^{96} +882.000 q^{97} -110.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 7 q^{3} + 4 q^{4} + 7 q^{5} - 28 q^{6} - 48 q^{8} - 22 q^{9} + 14 q^{10} + 5 q^{11} - 28 q^{12} + 28 q^{13} + 98 q^{15} + 16 q^{16} - 21 q^{17} - 44 q^{18} + 49 q^{19} + 56 q^{20} - 20 q^{22}+ \cdots - 220 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 + 7 * q^5 - 28 * q^6 - 48 * q^8 - 22 * q^9 + 14 * q^10 + 5 * q^11 - 28 * q^12 + 28 * q^13 + 98 * q^15 + 16 * q^16 - 21 * q^17 - 44 * q^18 + 49 * q^19 + 56 * q^20 - 20 * q^22 + 159 * q^23 - 168 * q^24 + 76 * q^25 - 28 * q^26 + 70 * q^27 + 116 * q^29 - 98 * q^30 + 147 * q^31 - 160 * q^32 - 35 * q^33 + 84 * q^34 - 176 * q^36 - 219 * q^37 + 98 * q^38 + 98 * q^39 - 168 * q^40 - 700 * q^41 - 248 * q^43 - 20 * q^44 + 154 * q^45 + 318 * q^46 + 525 * q^47 + 224 * q^48 - 304 * q^50 + 147 * q^51 + 56 * q^52 - 303 * q^53 - 70 * q^54 + 70 * q^55 + 686 * q^57 - 116 * q^58 - 105 * q^59 + 196 * q^60 - 413 * q^61 - 588 * q^62 + 896 * q^64 + 98 * q^65 - 70 * q^66 - 415 * q^67 + 84 * q^68 + 2226 * q^69 - 864 * q^71 + 528 * q^72 - 1113 * q^73 - 438 * q^74 - 532 * q^75 + 392 * q^76 - 392 * q^78 + 103 * q^79 - 112 * q^80 + 839 * q^81 + 700 * q^82 - 2184 * q^83 - 294 * q^85 + 248 * q^86 + 406 * q^87 - 120 * q^88 - 329 * q^89 - 616 * q^90 + 1272 * q^92 - 1029 * q^93 + 1050 * q^94 - 343 * q^95 + 1120 * q^96 + 1764 * q^97 - 220 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more