LMFDB - Embedded newform 1470.2.m.c.97.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(97,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1470.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.m (of order $4$, degree $2$, 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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 32 x^{13} + 2 x^{12} + 352 x^{10} - 288 x^{9} + 2 x^{8} - 1440 x^{7} + 8800 x^{6} + \cdots + 390625 $ x^16 - 32x^13 + 2x^12 + 352x^10 - 288x^9 + 2x^8 - 1440x^7 + 8800x^6 + 1250x^4 - 100000*x^3 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.3
Root			$-0.410538 + 2.19806i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.c.1273.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(0.461873 + 2.18785i) q^{5} +1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(0.461873 + 2.18785i) q^{5} +1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(1.22045 - 1.87363i) q^{10} -2.98190 q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.960607 - 0.960607i) q^{13} +(1.22045 - 1.87363i) q^{15} -1.00000 q^{16} +(-1.62757 + 1.62757i) q^{17} +(0.707107 - 0.707107i) q^{18} +8.67101 q^{19} +(-2.18785 + 0.461873i) q^{20} +(2.10852 + 2.10852i) q^{22} +(1.36811 - 1.36811i) q^{23} -1.00000 q^{24} +(-4.57335 + 2.02101i) q^{25} +1.35850i q^{26} +(0.707107 - 0.707107i) q^{27} +2.00735i q^{29} +(-2.18785 + 0.461873i) q^{30} +0.179275i q^{31} +(0.707107 + 0.707107i) q^{32} +(2.10852 + 2.10852i) q^{33} +2.30173 q^{34} -1.00000 q^{36} +(-4.86644 - 4.86644i) q^{37} +(-6.13133 - 6.13133i) q^{38} +1.35850i q^{39} +(1.87363 + 1.22045i) q^{40} +5.14811i q^{41} +(-7.01377 + 7.01377i) q^{43} -2.98190i q^{44} +(-2.18785 + 0.461873i) q^{45} -1.93480 q^{46} +(0.202085 - 0.202085i) q^{47} +(0.707107 + 0.707107i) q^{48} +(4.66292 + 1.80477i) q^{50} +2.30173 q^{51} +(0.960607 - 0.960607i) q^{52} +(-7.01726 + 7.01726i) q^{53} -1.00000 q^{54} +(-1.37726 - 6.52395i) q^{55} +(-6.13133 - 6.13133i) q^{57} +(1.41941 - 1.41941i) q^{58} -7.09038 q^{59} +(1.87363 + 1.22045i) q^{60} +2.41715i q^{61} +(0.126767 - 0.126767i) q^{62} -1.00000i q^{64} +(1.65798 - 2.54534i) q^{65} -2.98190i q^{66} +(-6.29036 - 6.29036i) q^{67} +(-1.62757 - 1.62757i) q^{68} -1.93480 q^{69} -9.08488 q^{71} +(0.707107 + 0.707107i) q^{72} +(-8.78132 - 8.78132i) q^{73} +6.88219i q^{74} +(4.66292 + 1.80477i) q^{75} +8.67101i q^{76} +(0.960607 - 0.960607i) q^{78} +16.2755i q^{79} +(-0.461873 - 2.18785i) q^{80} -1.00000 q^{81} +(3.64026 - 3.64026i) q^{82} +(8.11428 + 8.11428i) q^{83} +(-4.31259 - 2.80914i) q^{85} +9.91897 q^{86} +(1.41941 - 1.41941i) q^{87} +(-2.10852 + 2.10852i) q^{88} -12.3037 q^{89} +(1.87363 + 1.22045i) q^{90} +(1.36811 + 1.36811i) q^{92} +(0.126767 - 0.126767i) q^{93} -0.285791 q^{94} +(4.00490 + 18.9709i) q^{95} -1.00000i q^{96} +(7.44633 - 7.44633i) q^{97} -2.98190i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{5}+O(q^{10}) $ 16 * q - 8 * q^5	$ 16 q - 8 q^{5} - 8 q^{13} - 16 q^{16} + 8 q^{17} + 48 q^{19} - 8 q^{22} - 8 q^{23} - 16 q^{24} + 8 q^{25} - 8 q^{33} - 16 q^{36} + 8 q^{37} + 8 q^{38} - 16 q^{47} + 8 q^{52} + 8 q^{53} - 16 q^{54} + 8 q^{57} + 24 q^{58} - 48 q^{59} + 8 q^{62} + 72 q^{65} - 48 q^{67} + 8 q^{68} - 16 q^{73} + 8 q^{78} + 8 q^{80} - 16 q^{81} + 16 q^{82} - 72 q^{85} + 24 q^{87} + 8 q^{88} + 64 q^{89} - 8 q^{92} + 8 q^{93} - 64 q^{94} + 48 q^{95} + 64 q^{97}+O(q^{100}) $ 16 * q - 8 * q^5 - 8 * q^13 - 16 * q^16 + 8 * q^17 + 48 * q^19 - 8 * q^22 - 8 * q^23 - 16 * q^24 + 8 * q^25 - 8 * q^33 - 16 * q^36 + 8 * q^37 + 8 * q^38 - 16 * q^47 + 8 * q^52 + 8 * q^53 - 16 * q^54 + 8 * q^57 + 24 * q^58 - 48 * q^59 + 8 * q^62 + 72 * q^65 - 48 * q^67 + 8 * q^68 - 16 * q^73 + 8 * q^78 + 8 * q^80 - 16 * q^81 + 16 * q^82 - 72 * q^85 + 24 * q^87 + 8 * q^88 + 64 * q^89 - 8 * q^92 + 8 * q^93 - 64 * q^94 + 48 * q^95 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$			1.00000i			0.500000i
$5$	0.461873	+	2.18785i	0.206556	+	0.978435i
$5$	0.461873	+	2.18785i	0.206556	+	0.978435i
$6$			1.00000i			0.408248i
$7$		0			0
$7$		0			0
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	1.22045	−	1.87363i	0.385940	−	0.592495i
$11$	−2.98190			−0.899077			−0.449539	−	0.893261i	$-0.648412\pi$
$11$	−2.98190			−0.899077			−0.449539	+	0.893261i	$0.648412\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−0.960607	−	0.960607i	−0.266425	−	0.266425i	0.561233	−	0.827658i	$-0.310327\pi$
$13$	−0.960607	−	0.960607i	−0.266425	−	0.266425i	−0.827658	+	0.561233i	$0.810327\pi$
$14$		0			0
$15$	1.22045	−	1.87363i	0.315118	−	0.483770i
$16$	−1.00000			−0.250000
$17$	−1.62757	+	1.62757i	−0.394743	+	0.394743i	−0.876374	−	0.481631i	$-0.840045\pi$
$17$	−1.62757	+	1.62757i	−0.394743	+	0.394743i	0.481631	+	0.876374i	$0.340045\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	8.67101			1.98927			0.994634	−	0.103461i	$-0.0329916\pi$
$19$	8.67101			1.98927			0.994634	+	0.103461i	$0.0329916\pi$
$20$	−2.18785	+	0.461873i	−0.489217	+	0.103278i
$21$		0			0
$22$	2.10852	+	2.10852i	0.449539	+	0.449539i
$23$	1.36811	−	1.36811i	0.285270	−	0.285270i	−0.549936	−	0.835207i	$-0.685348\pi$
$23$	1.36811	−	1.36811i	0.285270	−	0.285270i	0.835207	+	0.549936i	$0.185348\pi$
$24$	−1.00000			−0.204124
$25$	−4.57335	+	2.02101i	−0.914670	+	0.404203i
$26$			1.35850i			0.266425i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$			2.00735i			0.372756i	0.982478	+	0.186378i	$0.0596749\pi$
$29$			2.00735i			0.372756i	−0.982478	+	0.186378i	$0.940325\pi$
$30$	−2.18785	+	0.461873i	−0.399444	+	0.0843260i
$31$			0.179275i			0.0321988i	0.999870	+	0.0160994i	$0.00512481\pi$
$31$			0.179275i			0.0321988i	−0.999870	+	0.0160994i	$0.994875\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	2.10852	+	2.10852i	0.367047	+	0.367047i
$34$	2.30173			0.394743
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−4.86644	−	4.86644i	−0.800039	−	0.800039i	0.183063	−	0.983101i	$-0.441399\pi$
$37$	−4.86644	−	4.86644i	−0.800039	−	0.800039i	−0.983101	+	0.183063i	$0.941399\pi$
$38$	−6.13133	−	6.13133i	−0.994634	−	0.994634i
$39$			1.35850i			0.217535i
$40$	1.87363	+	1.22045i	0.296248	+	0.192970i
$41$			5.14811i			0.803999i	0.915640	+	0.402000i	$0.131685\pi$
$41$			5.14811i			0.803999i	−0.915640	+	0.402000i	$0.868315\pi$
$42$		0			0
$43$	−7.01377	+	7.01377i	−1.06959	+	1.06959i	−0.0722000	+	0.997390i	$0.523002\pi$
$43$	−7.01377	+	7.01377i	−1.06959	+	1.06959i	−0.997390	+	0.0722000i	$0.976998\pi$
$44$		−	2.98190i		−	0.449539i
$45$	−2.18785	+	0.461873i	−0.326145	+	0.0688519i
$46$	−1.93480			−0.285270
$47$	0.202085	−	0.202085i	0.0294771	−	0.0294771i	−0.692215	−	0.721692i	$-0.743365\pi$
$47$	0.202085	−	0.202085i	0.0294771	−	0.0294771i	0.721692	+	0.692215i	$0.243365\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		0			0
$50$	4.66292	+	1.80477i	0.659436	+	0.255233i
$51$	2.30173			0.322306
$52$	0.960607	−	0.960607i	0.133212	−	0.133212i
$53$	−7.01726	+	7.01726i	−0.963895	+	0.963895i	−0.999371	−	0.0354757i	$-0.988705\pi$
$53$	−7.01726	+	7.01726i	−0.963895	+	0.963895i	0.0354757	+	0.999371i	$0.488705\pi$
$54$	−1.00000			−0.136083
$55$	−1.37726	−	6.52395i	−0.185710	−	0.879689i
$56$		0			0
$57$	−6.13133	−	6.13133i	−0.812115	−	0.812115i
$58$	1.41941	−	1.41941i	0.186378	−	0.186378i
$59$	−7.09038			−0.923088			−0.461544	−	0.887117i	$-0.652704\pi$
$59$	−7.09038			−0.923088			−0.461544	+	0.887117i	$0.652704\pi$
$60$	1.87363	+	1.22045i	0.241885	+	0.157559i
$61$			2.41715i			0.309484i	0.987955	+	0.154742i	$0.0494547\pi$
$61$			2.41715i			0.309484i	−0.987955	+	0.154742i	$0.950545\pi$
$62$	0.126767	−	0.126767i	0.0160994	−	0.0160994i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	1.65798	−	2.54534i	0.205648	−	0.315711i
$66$		−	2.98190i		−	0.367047i
$67$	−6.29036	−	6.29036i	−0.768489	−	0.768489i	0.209351	−	0.977841i	$-0.432865\pi$
$67$	−6.29036	−	6.29036i	−0.768489	−	0.768489i	−0.977841	+	0.209351i	$0.932865\pi$
$68$	−1.62757	−	1.62757i	−0.197371	−	0.197371i
$69$	−1.93480			−0.232922
$70$		0			0
$71$	−9.08488			−1.07818			−0.539088	−	0.842249i	$-0.681231\pi$
$71$	−9.08488			−1.07818			−0.539088	+	0.842249i	$0.681231\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	−8.78132	−	8.78132i	−1.02778	−	1.02778i	−0.999603	−	0.0281728i	$-0.991031\pi$
$73$	−8.78132	−	8.78132i	−1.02778	−	1.02778i	−0.0281728	−	0.999603i	$-0.508969\pi$
$74$			6.88219i			0.800039i
$75$	4.66292	+	1.80477i	0.538427	+	0.208397i
$76$			8.67101i			0.994634i
$77$		0			0
$78$	0.960607	−	0.960607i	0.108767	−	0.108767i
$79$			16.2755i			1.83113i	0.402165	+	0.915567i	$0.368258\pi$
$79$			16.2755i			1.83113i	−0.402165	+	0.915567i	$0.631742\pi$
$80$	−0.461873	−	2.18785i	−0.0516389	−	0.244609i
$81$	−1.00000			−0.111111
$82$	3.64026	−	3.64026i	0.402000	−	0.402000i
$83$	8.11428	+	8.11428i	0.890658	+	0.890658i	0.994585	−	0.103927i	$-0.0331407\pi$
$83$	8.11428	+	8.11428i	0.890658	+	0.890658i	−0.103927	+	0.994585i	$0.533141\pi$
$84$		0			0
$85$	−4.31259	−	2.80914i	−0.467767	−	0.304694i
$86$	9.91897			1.06959
$87$	1.41941	−	1.41941i	0.152177	−	0.152177i
$88$	−2.10852	+	2.10852i	−0.224769	+	0.224769i
$89$	−12.3037			−1.30419			−0.652094	−	0.758138i	$-0.726109\pi$
$89$	−12.3037			−1.30419			−0.652094	+	0.758138i	$0.726109\pi$
$90$	1.87363	+	1.22045i	0.197498	+	0.128647i
$91$		0			0
$92$	1.36811	+	1.36811i	0.142635	+	0.142635i
$93$	0.126767	−	0.126767i	0.0131451	−	0.0131451i
$94$	−0.285791			−0.0294771
$95$	4.00490	+	18.9709i	0.410894	+	1.94637i
$96$		−	1.00000i		−	0.102062i
$97$	7.44633	−	7.44633i	0.756060	−	0.756060i	−0.219543	−	0.975603i	$-0.570457\pi$
$97$	7.44633	−	7.44633i	0.756060	−	0.756060i	0.975603	+	0.219543i	$0.0704566\pi$
$98$		0			0
$99$		−	2.98190i		−	0.299692i
$100$	−2.02101	−	4.57335i	−0.202101	−	0.457335i
$101$			13.0344i			1.29697i	0.761225	+	0.648487i	$0.224598\pi$
$101$			13.0344i			1.29697i	−0.761225	+	0.648487i	$0.775402\pi$
$102$	−1.62757	−	1.62757i	−0.161153	−	0.161153i
$103$	11.8321	+	11.8321i	1.16585	+	1.16585i	0.983173	+	0.182674i	$0.0584754\pi$
$103$	11.8321	+	11.8321i	1.16585	+	1.16585i	0.182674	+	0.983173i	$0.441525\pi$
$104$	−1.35850			−0.133212
$105$		0			0
$106$	9.92390			0.963895
$107$	−9.72604	−	9.72604i	−0.940251	−	0.940251i	0.0580616	−	0.998313i	$-0.481508\pi$
$107$	−9.72604	−	9.72604i	−0.940251	−	0.940251i	−0.998313	+	0.0580616i	$0.981508\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$		−	4.56620i		−	0.437363i	−0.975796	−	0.218681i	$-0.929824\pi$
$109$		−	4.56620i		−	0.437363i	0.975796	−	0.218681i	$-0.0701756\pi$
$110$	−3.63926	+	5.58699i	−0.346990	+	0.532699i
$111$			6.88219i			0.653229i
$112$		0			0
$113$	−11.4947	+	11.4947i	−1.08133	+	1.08133i	−0.0849397	+	0.996386i	$0.527070\pi$
$113$	−11.4947	+	11.4947i	−1.08133	+	1.08133i	−0.996386	+	0.0849397i	$0.972930\pi$
$114$			8.67101i			0.812115i
$115$	3.62510	+	2.36132i	0.338043	+	0.220194i
$116$	−2.00735			−0.186378
$117$	0.960607	−	0.960607i	0.0888082	−	0.0888082i
$118$	5.01365	+	5.01365i	0.461544	+	0.461544i
$119$		0			0
$120$	−0.461873	−	2.18785i	−0.0421630	−	0.199722i
$121$	−2.10826			−0.191660
$122$	1.70918	−	1.70918i	0.154742	−	0.154742i
$123$	3.64026	−	3.64026i	0.328231	−	0.328231i
$124$	−0.179275			−0.0160994
$125$	−6.53397	−	9.07233i	−0.584416	−	0.811454i
$126$		0			0
$127$	0.555238	+	0.555238i	0.0492694	+	0.0492694i	0.731312	−	0.682043i	$-0.238908\pi$
$127$	0.555238	+	0.555238i	0.0492694	+	0.0492694i	−0.682043	+	0.731312i	$0.738908\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	9.91897			0.873317
$130$	−2.97220	+	0.627456i	−0.260679	+	0.0550315i
$131$			21.7261i			1.89822i	0.314947	+	0.949109i	$0.398013\pi$
$131$			21.7261i			1.89822i	−0.314947	+	0.949109i	$0.601987\pi$
$132$	−2.10852	+	2.10852i	−0.183523	+	0.183523i
$133$		0			0
$134$			8.89591i			0.768489i
$135$	1.87363	+	1.22045i	0.161257	+	0.105039i
$136$			2.30173i			0.197371i
$137$	−0.263241	−	0.263241i	−0.0224902	−	0.0224902i	0.695772	−	0.718262i	$-0.255062\pi$
$137$	−0.263241	−	0.263241i	−0.0224902	−	0.0224902i	−0.718262	+	0.695772i	$0.755062\pi$
$138$	1.36811	+	1.36811i	0.116461	+	0.116461i
$139$	16.1794			1.37232			0.686159	−	0.727452i	$-0.259295\pi$
$139$	16.1794			1.37232			0.686159	+	0.727452i	$0.259295\pi$
$140$		0			0
$141$	−0.285791			−0.0240679
$142$	6.42398	+	6.42398i	0.539088	+	0.539088i
$143$	2.86444	+	2.86444i	0.239536	+	0.239536i
$144$		−	1.00000i		−	0.0833333i
$145$	−4.39178	+	0.927140i	−0.364717	+	0.0769948i
$146$			12.4187i			1.02778i
$147$		0			0
$148$	4.86644	−	4.86644i	0.400019	−	0.400019i
$149$			4.69989i			0.385030i	0.981294	+	0.192515i	$0.0616644\pi$
$149$			4.69989i			0.385030i	−0.981294	+	0.192515i	$0.938336\pi$
$150$	−2.02101	−	4.57335i	−0.165015	−	0.373412i
$151$	8.11372			0.660285			0.330143	−	0.943931i	$-0.392903\pi$
$151$	8.11372			0.660285			0.330143	+	0.943931i	$0.392903\pi$
$152$	6.13133	−	6.13133i	0.497317	−	0.497317i
$153$	−1.62757	−	1.62757i	−0.131581	−	0.131581i
$154$		0			0
$155$	−0.392226	+	0.0828022i	−0.0315044	+	0.00665084i
$156$	−1.35850			−0.108767
$157$	6.77980	−	6.77980i	0.541087	−	0.541087i	−0.382760	−	0.923848i	$-0.625027\pi$
$157$	6.77980	−	6.77980i	0.541087	−	0.541087i	0.923848	+	0.382760i	$0.125027\pi$
$158$	11.5085	−	11.5085i	0.915567	−	0.915567i
$159$	9.92390			0.787017
$160$	−1.22045	+	1.87363i	−0.0964849	+	0.148124i
$161$		0			0
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−4.53943	+	4.53943i	−0.355556	+	0.355556i	−0.862172	−	0.506616i	$-0.830896\pi$
$163$	−4.53943	+	4.53943i	−0.355556	+	0.355556i	0.506616	+	0.862172i	$0.330896\pi$
$164$	−5.14811			−0.402000
$165$	−3.63926	+	5.58699i	−0.283316	+	0.434947i
$166$		−	11.4753i		−	0.890658i
$167$	6.34259	−	6.34259i	0.490804	−	0.490804i	−0.417755	−	0.908560i	$-0.637183\pi$
$167$	6.34259	−	6.34259i	0.490804	−	0.490804i	0.908560	+	0.417755i	$0.137183\pi$
$168$		0			0
$169$		−	11.1545i		−	0.858036i
$170$	1.06310	+	5.03583i	0.0815364	+	0.386230i
$171$			8.67101i			0.663089i
$172$	−7.01377	−	7.01377i	−0.534795	−	0.534795i
$173$	−13.9572	−	13.9572i	−1.06115	−	1.06115i	−0.998004	−	0.0631450i	$-0.979887\pi$
$173$	−13.9572	−	13.9572i	−1.06115	−	1.06115i	−0.0631450	−	0.998004i	$-0.520113\pi$
$174$	−2.00735			−0.152177
$175$		0			0
$176$	2.98190			0.224769
$177$	5.01365	+	5.01365i	0.376849	+	0.376849i
$178$	8.70002	+	8.70002i	0.652094	+	0.652094i
$179$			8.00708i			0.598477i	0.954178	+	0.299238i	$0.0967326\pi$
$179$			8.00708i			0.598477i	−0.954178	+	0.299238i	$0.903267\pi$
$180$	−0.461873	−	2.18785i	−0.0344259	−	0.163072i
$181$			0.990829i			0.0736478i	0.999322	+	0.0368239i	$0.0117241\pi$
$181$			0.990829i			0.0736478i	−0.999322	+	0.0368239i	$0.988276\pi$
$182$		0			0
$183$	1.70918	−	1.70918i	0.126346	−	0.126346i
$184$		−	1.93480i		−	0.142635i
$185$	8.39936	−	12.8947i	0.617533	−	0.948038i
$186$	−0.179275			−0.0131451
$187$	4.85324	−	4.85324i	0.354904	−	0.354904i
$188$	0.202085	+	0.202085i	0.0147385	+	0.0147385i
$189$		0			0
$190$	10.5825	−	16.2463i	0.767737	−	1.17863i
$191$	−2.98374			−0.215896			−0.107948	−	0.994157i	$-0.534428\pi$
$191$	−2.98374			−0.215896			−0.107948	+	0.994157i	$0.534428\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	11.1285	−	11.1285i	0.801044	−	0.801044i	−0.182215	−	0.983259i	$-0.558327\pi$
$193$	11.1285	−	11.1285i	0.801044	−	0.801044i	0.983259	+	0.182215i	$0.0583266\pi$
$194$	−10.5307			−0.756060
$195$	−2.97220	+	0.627456i	−0.212844	+	0.0449330i
$196$		0			0
$197$	18.7450	+	18.7450i	1.33553	+	1.33553i	0.900340	+	0.435187i	$0.143318\pi$
$197$	18.7450	+	18.7450i	1.33553	+	1.33553i	0.435187	+	0.900340i	$0.356682\pi$
$198$	−2.10852	+	2.10852i	−0.149846	+	0.149846i
$199$	−12.5284			−0.888118			−0.444059	−	0.895998i	$-0.646462\pi$
$199$	−12.5284			−0.888118			−0.444059	+	0.895998i	$0.646462\pi$
$200$	−1.80477	+	4.66292i	−0.127617	+	0.329718i
$201$			8.89591i			0.627469i
$202$	9.21674	−	9.21674i	0.648487	−	0.648487i
$203$		0			0
$204$			2.30173i			0.161153i
$205$	−11.2633	+	2.37777i	−0.786661	+	0.166071i
$206$		−	16.7331i		−	1.16585i
$207$	1.36811	+	1.36811i	0.0950901	+	0.0950901i
$208$	0.960607	+	0.960607i	0.0666061	+	0.0666061i
$209$	−25.8561			−1.78850
$210$		0			0
$211$	−2.04533			−0.140806			−0.0704031	−	0.997519i	$-0.522429\pi$
$211$	−2.04533			−0.140806			−0.0704031	+	0.997519i	$0.522429\pi$
$212$	−7.01726	−	7.01726i	−0.481947	−	0.481947i
$213$	6.42398	+	6.42398i	0.440164	+	0.440164i
$214$			13.7547i			0.940251i
$215$	−18.5845	−	12.1056i	−1.26745	−	0.825594i
$216$		−	1.00000i		−	0.0680414i
$217$		0			0
$218$	−3.22879	+	3.22879i	−0.218681	+	0.218681i
$219$			12.4187i			0.839176i
$220$	6.52395	−	1.37726i	0.439844	−	0.0928548i
$221$	3.12691			0.210338
$222$	4.86644	−	4.86644i	0.326614	−	0.326614i
$223$	1.00154	+	1.00154i	0.0670680	+	0.0670680i	0.739845	−	0.672777i	$-0.234899\pi$
$223$	1.00154	+	1.00154i	0.0670680	+	0.0670680i	−0.672777	+	0.739845i	$0.734899\pi$
$224$		0			0
$225$	−2.02101	−	4.57335i	−0.134734	−	0.304890i
$226$	16.2559			1.08133
$227$	−5.86104	+	5.86104i	−0.389011	+	0.389011i	−0.874335	−	0.485324i	$-0.838702\pi$
$227$	−5.86104	+	5.86104i	−0.389011	+	0.389011i	0.485324	+	0.874335i	$0.338702\pi$
$228$	6.13133	−	6.13133i	0.406057	−	0.406057i
$229$	−16.9122			−1.11759			−0.558796	−	0.829305i	$-0.688737\pi$
$229$	−16.9122			−1.11759			−0.558796	+	0.829305i	$0.688737\pi$
$230$	−0.893630	−	4.23304i	−0.0589242	−	0.279118i
$231$		0			0
$232$	1.41941	+	1.41941i	0.0931889	+	0.0931889i
$233$	7.30362	−	7.30362i	0.478476	−	0.478476i	−0.426168	−	0.904644i	$-0.640137\pi$
$233$	7.30362	−	7.30362i	0.478476	−	0.478476i	0.904644	+	0.426168i	$0.140137\pi$
$234$	−1.35850			−0.0888082
$235$	0.535468	+	0.348793i	0.0349301	+	0.0227527i
$236$		−	7.09038i		−	0.461544i
$237$	11.5085	−	11.5085i	0.747557	−	0.747557i
$238$		0			0
$239$		−	0.400370i		−	0.0258978i	−0.999916	−	0.0129489i	$-0.995878\pi$
$239$		−	0.400370i		−	0.0258978i	0.999916	−	0.0129489i	$-0.00412187\pi$
$240$	−1.22045	+	1.87363i	−0.0787796	+	0.120943i
$241$			25.1974i			1.62311i	0.584279	+	0.811553i	$0.301377\pi$
$241$			25.1974i			1.62311i	−0.584279	+	0.811553i	$0.698623\pi$
$242$	1.49076	+	1.49076i	0.0958300	+	0.0958300i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−2.41715			−0.154742
$245$		0			0
$246$	−5.14811			−0.328231
$247$	−8.32944	−	8.32944i	−0.529990	−	0.529990i
$248$	0.126767	+	0.126767i	0.00804969	+	0.00804969i
$249$		−	11.4753i		−	0.727219i
$250$	−1.79489	+	11.0353i	−0.113519	+	0.697935i
$251$		−	5.28383i		−	0.333513i	−0.985998	−	0.166756i	$-0.946671\pi$
$251$		−	5.28383i		−	0.333513i	0.985998	−	0.166756i	$-0.0533293\pi$
$252$		0			0
$253$	−4.07957	+	4.07957i	−0.256480	+	0.256480i
$254$		−	0.785225i		−	0.0492694i
$255$	1.06310	+	5.03583i	0.0665742	+	0.315356i
$256$	1.00000			0.0625000
$257$	−11.3684	+	11.3684i	−0.709143	+	0.709143i	−0.966355	−	0.257212i	$-0.917196\pi$
$257$	−11.3684	+	11.3684i	−0.709143	+	0.709143i	0.257212	+	0.966355i	$0.417196\pi$
$258$	−7.01377	−	7.01377i	−0.436658	−	0.436658i
$259$		0			0
$260$	2.54534	+	1.65798i	0.157855	+	0.102824i
$261$	−2.00735			−0.124252
$262$	15.3627	−	15.3627i	0.949109	−	0.949109i
$263$	7.33228	−	7.33228i	0.452128	−	0.452128i	−0.443933	−	0.896060i	$-0.646417\pi$
$263$	7.33228	−	7.33228i	0.452128	−	0.452128i	0.896060	+	0.443933i	$0.146417\pi$
$264$	2.98190			0.183523
$265$	−18.5938	−	12.1116i	−1.14221	−	0.744010i
$266$		0			0
$267$	8.70002	+	8.70002i	0.532432	+	0.532432i
$268$	6.29036	−	6.29036i	0.384245	−	0.384245i
$269$	12.9743			0.791056			0.395528	−	0.918454i	$-0.370562\pi$
$269$	12.9743			0.791056			0.395528	+	0.918454i	$0.370562\pi$
$270$	−0.461873	−	2.18785i	−0.0281087	−	0.133148i
$271$		−	24.2245i		−	1.47153i	−0.677236	−	0.735765i	$-0.736823\pi$
$271$		−	24.2245i		−	1.47153i	0.677236	−	0.735765i	$-0.263177\pi$
$272$	1.62757	−	1.62757i	0.0986857	−	0.0986857i
$273$		0			0
$274$			0.372279i			0.0224902i
$275$	13.6373	−	6.02646i	0.822359	−	0.363409i
$276$		−	1.93480i		−	0.116461i
$277$	−20.6360	−	20.6360i	−1.23990	−	1.23990i	−0.960041	−	0.279858i	$-0.909713\pi$
$277$	−20.6360	−	20.6360i	−1.23990	−	1.23990i	−0.279858	−	0.960041i	$-0.590287\pi$
$278$	−11.4406	−	11.4406i	−0.686159	−	0.686159i
$279$	−0.179275			−0.0107329
$280$		0			0
$281$	−2.67650			−0.159667			−0.0798334	−	0.996808i	$-0.525439\pi$
$281$	−2.67650			−0.159667			−0.0798334	+	0.996808i	$0.525439\pi$
$282$	0.202085	+	0.202085i	0.0120340	+	0.0120340i
$283$	−9.28178	−	9.28178i	−0.551744	−	0.551744i	0.375200	−	0.926944i	$-0.377574\pi$
$283$	−9.28178	−	9.28178i	−0.551744	−	0.551744i	−0.926944	+	0.375200i	$0.877574\pi$
$284$		−	9.08488i		−	0.539088i
$285$	10.5825	−	16.2463i	0.626855	−	0.962348i
$286$		−	4.05093i		−	0.239536i
$287$		0			0
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$			11.7021i			0.688356i
$290$	3.76104	+	2.44987i	0.220856	+	0.143861i
$291$	−10.5307			−0.617320
$292$	8.78132	−	8.78132i	0.513888	−	0.513888i
$293$	−4.32212	−	4.32212i	−0.252501	−	0.252501i	0.569494	−	0.821995i	$-0.307139\pi$
$293$	−4.32212	−	4.32212i	−0.252501	−	0.252501i	−0.821995	+	0.569494i	$0.807139\pi$
$294$		0			0
$295$	−3.27485	−	15.5127i	−0.190669	−	0.903182i
$296$	−6.88219			−0.400019
$297$	−2.10852	+	2.10852i	−0.122349	+	0.122349i
$298$	3.32332	−	3.32332i	0.192515	−	0.192515i
$299$	−2.62843			−0.152006
$300$	−1.80477	+	4.66292i	−0.104199	+	0.269214i
$301$		0			0
$302$	−5.73727	−	5.73727i	−0.330143	−	0.330143i
$303$	9.21674	−	9.21674i	0.529488	−	0.529488i
$304$	−8.67101			−0.497317
$305$	−5.28836	+	1.11642i	−0.302810	+	0.0639258i
$306$			2.30173i			0.131581i
$307$	1.33625	−	1.33625i	0.0762637	−	0.0762637i	−0.667946	−	0.744210i	$-0.732826\pi$
$307$	1.33625	−	1.33625i	0.0762637	−	0.0762637i	0.744210	+	0.667946i	$0.232826\pi$
$308$		0			0
$309$		−	16.7331i		−	0.951911i
$310$	0.335896	+	0.218796i	0.0190776	+	0.0124268i
$311$			13.8982i			0.788094i	0.919090	+	0.394047i	$0.128925\pi$
$311$			13.8982i			0.788094i	−0.919090	+	0.394047i	$0.871075\pi$
$312$	0.960607	+	0.960607i	0.0543837	+	0.0543837i
$313$	2.99558	+	2.99558i	0.169320	+	0.169320i	0.786681	−	0.617360i	$-0.211798\pi$
$313$	2.99558	+	2.99558i	0.169320	+	0.169320i	−0.617360	+	0.786681i	$0.711798\pi$
$314$	−9.58809			−0.541087
$315$		0			0
$316$	−16.2755			−0.915567
$317$	−22.3508	−	22.3508i	−1.25534	−	1.25534i	−0.953291	−	0.302052i	$-0.902328\pi$
$317$	−22.3508	−	22.3508i	−1.25534	−	1.25534i	−0.302052	−	0.953291i	$-0.597672\pi$
$318$	−7.01726	−	7.01726i	−0.393508	−	0.393508i
$319$		−	5.98572i		−	0.335136i
$320$	2.18785	−	0.461873i	0.122304	−	0.0258195i
$321$			13.7547i			0.767712i
$322$		0			0
$323$	−14.1127	+	14.1127i	−0.785249	+	0.785249i
$324$		−	1.00000i		−	0.0555556i
$325$	6.33459	+	2.45179i	0.351380	+	0.136001i
$326$	6.41973			0.355556
$327$	−3.22879	+	3.22879i	−0.178553	+	0.178553i
$328$	3.64026	+	3.64026i	0.201000	+	0.201000i
$329$		0			0
$330$	6.52395	−	1.37726i	0.359131	−	0.0758156i
$331$	29.1052			1.59977			0.799885	−	0.600154i	$-0.204894\pi$
$331$	29.1052			1.59977			0.799885	+	0.600154i	$0.204894\pi$
$332$	−8.11428	+	8.11428i	−0.445329	+	0.445329i
$333$	4.86644	−	4.86644i	0.266680	−	0.266680i
$334$	−8.96978			−0.490804
$335$	10.8570	−	16.6677i	0.593181	−	0.910653i
$336$		0			0
$337$	8.28151	+	8.28151i	0.451123	+	0.451123i	0.895727	−	0.444604i	$-0.146656\pi$
$337$	8.28151	+	8.28151i	0.451123	+	0.451123i	−0.444604	+	0.895727i	$0.646656\pi$
$338$	−7.88740	+	7.88740i	−0.429018	+	0.429018i
$339$	16.2559			0.882899
$340$	2.80914	−	4.31259i	0.152347	−	0.233883i
$341$		−	0.534581i		−	0.0289492i
$342$	6.13133	−	6.13133i	0.331545	−	0.331545i
$343$		0			0
$344$			9.91897i			0.534795i
$345$	−0.893630	−	4.23304i	−0.0481114	−	0.227899i
$346$			19.7385i			1.06115i
$347$	1.56698	+	1.56698i	0.0841199	+	0.0841199i	0.747915	−	0.663795i	$-0.231055\pi$
$347$	1.56698	+	1.56698i	0.0841199	+	0.0841199i	−0.663795	+	0.747915i	$0.731055\pi$
$348$	1.41941	+	1.41941i	0.0760884	+	0.0760884i
$349$	−29.6857			−1.58904			−0.794520	−	0.607237i	$-0.792278\pi$
$349$	−29.6857			−1.58904			−0.794520	+	0.607237i	$0.792278\pi$
$350$		0			0
$351$	−1.35850			−0.0725116
$352$	−2.10852	−	2.10852i	−0.112385	−	0.112385i
$353$	13.3833	+	13.3833i	0.712322	+	0.712322i	0.967020	−	0.254699i	$-0.0819763\pi$
$353$	13.3833	+	13.3833i	0.712322	+	0.712322i	−0.254699	+	0.967020i	$0.581976\pi$
$354$		−	7.09038i		−	0.376849i
$355$	−4.19605	−	19.8763i	−0.222703	−	1.05493i
$356$		−	12.3037i		−	0.652094i
$357$		0			0
$358$	5.66186	−	5.66186i	0.299238	−	0.299238i
$359$		−	35.0203i		−	1.84830i	−0.382028	−	0.924151i	$-0.624774\pi$
$359$		−	35.0203i		−	1.84830i	0.382028	−	0.924151i	$-0.375226\pi$
$360$	−1.22045	+	1.87363i	−0.0643233	+	0.0987492i
$361$	56.1865			2.95718
$362$	0.700622	−	0.700622i	0.0368239	−	0.0368239i
$363$	1.49076	+	1.49076i	0.0782448	+	0.0782448i
$364$		0			0
$365$	15.1563	−	23.2680i	0.793319	−	1.21790i
$366$	−2.41715			−0.126346
$367$	−0.0545117	+	0.0545117i	−0.00284549	+	0.00284549i	−0.708528	−	0.705683i	$-0.750640\pi$
$367$	−0.0545117	+	0.0545117i	−0.00284549	+	0.00284549i	0.705683	+	0.708528i	$0.250640\pi$
$368$	−1.36811	+	1.36811i	−0.0713176	+	0.0713176i
$369$	−5.14811			−0.268000
$370$	−15.0572	+	3.17870i	−0.782786	+	0.165253i
$371$		0			0
$372$	0.126767	+	0.126767i	0.00657254	+	0.00657254i
$373$	−4.00265	+	4.00265i	−0.207249	+	0.207249i	−0.803097	−	0.595848i	$-0.796816\pi$
$373$	−4.00265	+	4.00265i	−0.207249	+	0.207249i	0.595848	+	0.803097i	$0.296816\pi$
$374$	−6.86352			−0.354904
$375$	−1.79489	+	11.0353i	−0.0926880	+	0.569862i
$376$		−	0.285791i		−	0.0147385i
$377$	1.92828	−	1.92828i	0.0993113	−	0.0993113i
$378$		0			0
$379$		−	9.12109i		−	0.468519i	−0.972174	−	0.234259i	$-0.924734\pi$
$379$		−	9.12109i		−	0.468519i	0.972174	−	0.234259i	$-0.0752665\pi$
$380$	−18.9709	+	4.00490i	−0.973184	+	0.205447i
$381$		−	0.785225i		−	0.0402283i
$382$	2.10983	+	2.10983i	0.107948	+	0.107948i
$383$	1.26869	+	1.26869i	0.0648269	+	0.0648269i	0.738777	−	0.673950i	$-0.235404\pi$
$383$	1.26869	+	1.26869i	0.0648269	+	0.0648269i	−0.673950	+	0.738777i	$0.735404\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−15.7380			−0.801044
$387$	−7.01377	−	7.01377i	−0.356530	−	0.356530i
$388$	7.44633	+	7.44633i	0.378030	+	0.378030i
$389$		−	19.8245i		−	1.00514i	−0.864535	−	0.502572i	$-0.832387\pi$
$389$		−	19.8245i		−	1.00514i	0.864535	−	0.502572i	$-0.167613\pi$
$390$	2.54534	+	1.65798i	0.128888	+	0.0839553i
$391$			4.45337i			0.225217i
$392$		0			0
$393$	15.3627	−	15.3627i	0.774945	−	0.774945i
$394$		−	26.5095i		−	1.33553i
$395$	−35.6083	+	7.51720i	−1.79165	+	0.378231i
$396$	2.98190			0.149846
$397$	−17.2323	+	17.2323i	−0.864865	+	0.864865i	−0.991898	−	0.127034i	$-0.959454\pi$
$397$	−17.2323	+	17.2323i	−0.864865	+	0.864865i	0.127034	+	0.991898i	$0.459454\pi$
$398$	8.85895	+	8.85895i	0.444059	+	0.444059i
$399$		0			0
$400$	4.57335	−	2.02101i	0.228667	−	0.101051i
$401$	37.9336			1.89431			0.947157	−	0.320771i	$-0.103942\pi$
$401$	37.9336			1.89431			0.947157	+	0.320771i	$0.103942\pi$
$402$	6.29036	−	6.29036i	0.313734	−	0.313734i
$403$	0.172213	−	0.172213i	0.00857854	−	0.00857854i
$404$	−13.0344			−0.648487
$405$	−0.461873	−	2.18785i	−0.0229506	−	0.108715i
$406$		0			0
$407$	14.5113	+	14.5113i	0.719297	+	0.719297i
$408$	1.62757	−	1.62757i	0.0805765	−	0.0805765i
$409$	−2.07501			−0.102602			−0.0513012	−	0.998683i	$-0.516337\pi$
$409$	−2.07501			−0.102602			−0.0513012	+	0.998683i	$0.516337\pi$
$410$	9.64567	+	6.28300i	0.476366	+	0.310295i
$411$			0.372279i			0.0183632i
$412$	−11.8321	+	11.8321i	−0.582924	+	0.582924i
$413$		0			0
$414$		−	1.93480i		−	0.0950901i
$415$	−14.0050	+	21.5006i	−0.687481	+	1.05542i
$416$		−	1.35850i		−	0.0666061i
$417$	−11.4406	−	11.4406i	−0.560246	−	0.560246i
$418$	18.2830	+	18.2830i	0.894252	+	0.894252i
$419$	−12.9408			−0.632199			−0.316100	−	0.948726i	$-0.602373\pi$
$419$	−12.9408			−0.632199			−0.316100	+	0.948726i	$0.602373\pi$
$420$		0			0
$421$	6.83341			0.333040			0.166520	−	0.986038i	$-0.446747\pi$
$421$	6.83341			0.333040			0.166520	+	0.986038i	$0.446747\pi$
$422$	1.44627	+	1.44627i	0.0704031	+	0.0704031i
$423$	0.202085	+	0.202085i	0.00982570	+	0.00982570i
$424$			9.92390i			0.481947i
$425$	4.15409	−	10.7328i	0.201503	−	0.520615i
$426$		−	9.08488i		−	0.440164i
$427$		0			0
$428$	9.72604	−	9.72604i	0.470126	−	0.470126i
$429$		−	4.05093i		−	0.195581i
$430$	4.58130	+	21.7012i	0.220930	+	1.04652i
$431$	14.6990			0.708025			0.354012	−	0.935241i	$-0.384817\pi$
$431$	14.6990			0.708025			0.354012	+	0.935241i	$0.384817\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	3.88941	+	3.88941i	0.186913	+	0.186913i	0.794360	−	0.607447i	$-0.207806\pi$
$433$	3.88941	+	3.88941i	0.186913	+	0.186913i	−0.607447	+	0.794360i	$0.707806\pi$
$434$		0			0
$435$	3.76104	+	2.44987i	0.180328	+	0.117462i
$436$	4.56620			0.218681
$437$	11.8629	−	11.8629i	0.567479	−	0.567479i
$438$	8.78132	−	8.78132i	0.419588	−	0.419588i
$439$	34.1693			1.63081			0.815407	−	0.578888i	$-0.196513\pi$
$439$	34.1693			1.63081			0.815407	+	0.578888i	$0.196513\pi$
$440$	−5.58699	−	3.63926i	−0.266350	−	0.173495i
$441$		0			0
$442$	−2.21106	−	2.21106i	−0.105169	−	0.105169i
$443$	−3.60361	+	3.60361i	−0.171213	+	0.171213i	−0.787512	−	0.616299i	$-0.788631\pi$
$443$	−3.60361	+	3.60361i	−0.171213	+	0.171213i	0.616299	+	0.787512i	$0.288631\pi$
$444$	−6.88219			−0.326614
$445$	−5.68273	−	26.9186i	−0.269387	−	1.27606i
$446$		−	1.41639i		−	0.0670680i
$447$	3.32332	−	3.32332i	0.157188	−	0.157188i
$448$		0			0
$449$		−	30.3696i		−	1.43323i	−0.697468	−	0.716616i	$-0.745690\pi$
$449$		−	30.3696i		−	1.43323i	0.697468	−	0.716616i	$-0.254310\pi$
$450$	−1.80477	+	4.66292i	−0.0850778	+	0.219812i
$451$		−	15.3511i		−	0.722857i
$452$	−11.4947	−	11.4947i	−0.540663	−	0.540663i
$453$	−5.73727	−	5.73727i	−0.269560	−	0.269560i
$454$	8.28876			0.389011
$455$		0			0
$456$	−8.67101			−0.406057
$457$	6.16746	+	6.16746i	0.288501	+	0.288501i	0.836487	−	0.547986i	$-0.184605\pi$
$457$	6.16746	+	6.16746i	0.288501	+	0.288501i	−0.547986	+	0.836487i	$0.684605\pi$
$458$	11.9588	+	11.9588i	0.558796	+	0.558796i
$459$			2.30173i			0.107435i
$460$	−2.36132	+	3.62510i	−0.110097	+	0.169021i
$461$			27.4227i			1.27720i	0.769539	+	0.638600i	$0.220486\pi$
$461$			27.4227i			1.27720i	−0.769539	+	0.638600i	$0.779514\pi$
$462$		0			0
$463$	−17.0916	+	17.0916i	−0.794315	+	0.794315i	−0.982192	−	0.187878i	$-0.939839\pi$
$463$	−17.0916	+	17.0916i	−0.794315	+	0.794315i	0.187878	+	0.982192i	$0.439839\pi$
$464$		−	2.00735i		−	0.0931889i
$465$	0.335896	+	0.218796i	0.0155768	+	0.0101464i
$466$	−10.3289			−0.478476
$467$	11.2210	−	11.2210i	0.519245	−	0.519245i	−0.398098	−	0.917343i	$-0.630330\pi$
$467$	11.2210	−	11.2210i	0.519245	−	0.519245i	0.917343	+	0.398098i	$0.130330\pi$
$468$	0.960607	+	0.960607i	0.0444041	+	0.0444041i
$469$		0			0
$470$	−0.131999	−	0.625267i	−0.00608866	−	0.0288414i
$471$	−9.58809			−0.441796
$472$	−5.01365	+	5.01365i	−0.230772	+	0.230772i
$473$	20.9144	−	20.9144i	0.961644	−	0.961644i
$474$	−16.2755			−0.747557
$475$	−39.6556	+	17.5242i	−1.81952	+	0.804067i
$476$		0			0
$477$	−7.01726	−	7.01726i	−0.321298	−	0.321298i
$478$	−0.283104	+	0.283104i	−0.0129489	+	0.0129489i
$479$	−0.0440032			−0.00201056			−0.00100528	−	0.999999i	$-0.500320\pi$
$479$	−0.0440032			−0.00201056			−0.00100528	+	0.999999i	$0.500320\pi$
$480$	2.18785	−	0.461873i	0.0998611	−	0.0210815i
$481$			9.34949i			0.426300i
$482$	17.8172	−	17.8172i	0.811553	−	0.811553i
$483$		0			0
$484$		−	2.10826i		−	0.0958300i
$485$	19.7307	+	12.8522i	0.895924	+	0.583587i
$486$		−	1.00000i		−	0.0453609i
$487$	22.1406	+	22.1406i	1.00329	+	1.00329i	0.999995	+	0.00329256i	$0.00104806\pi$
$487$	22.1406	+	22.1406i	1.00329	+	1.00329i	0.00329256	+	0.999995i	$0.498952\pi$
$488$	1.70918	+	1.70918i	0.0773711	+	0.0773711i
$489$	6.41973			0.290310
$490$		0			0
$491$	24.8031			1.11935			0.559675	−	0.828712i	$-0.310926\pi$
$491$	24.8031			1.11935			0.559675	+	0.828712i	$0.310926\pi$
$492$	3.64026	+	3.64026i	0.164116	+	0.164116i
$493$	−3.26710	−	3.26710i	−0.147143	−	0.147143i
$494$			11.7796i			0.529990i
$495$	6.52395	−	1.37726i	0.293230	−	0.0619032i
$496$		−	0.179275i		−	0.00804969i
$497$		0			0
$498$	−8.11428	+	8.11428i	−0.363610	+	0.363610i
$499$			33.0665i			1.48026i	0.672465	+	0.740129i	$0.265236\pi$
$499$			33.0665i			1.48026i	−0.672465	+	0.740129i	$0.734764\pi$
$500$	9.07233	−	6.53397i	0.405727	−	0.292208i
$501$	−8.96978			−0.400740
$502$	−3.73623	+	3.73623i	−0.166756	+	0.166756i
$503$	15.9126	+	15.9126i	0.709510	+	0.709510i	0.966432	−	0.256922i	$-0.0827084\pi$
$503$	15.9126	+	15.9126i	0.709510	+	0.709510i	−0.256922	+	0.966432i	$0.582708\pi$
$504$		0			0
$505$	−28.5173	+	6.02025i	−1.26901	+	0.267897i
$506$	5.76938			0.256480
$507$	−7.88740	+	7.88740i	−0.350292	+	0.350292i
$508$	−0.555238	+	0.555238i	−0.0246347	+	0.0246347i
$509$	33.6114			1.48980			0.744900	−	0.667176i	$-0.232497\pi$
$509$	33.6114			1.48980			0.744900	+	0.667176i	$0.232497\pi$
$510$	2.80914	−	4.31259i	0.124391	−	0.190965i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	6.13133	−	6.13133i	0.270705	−	0.270705i
$514$	16.0774			0.709143
$515$	−20.4218	+	31.3516i	−0.899894	+	1.38152i
$516$			9.91897i			0.436658i
$517$	−0.602597	+	0.602597i	−0.0265022	+	0.0265022i
$518$		0			0
$519$			19.7385i			0.866425i
$520$	−0.627456	−	2.97220i	−0.0275158	−	0.130340i
$521$		−	37.0838i		−	1.62467i	−0.583189	−	0.812336i	$-0.698195\pi$
$521$		−	37.0838i		−	1.62467i	0.583189	−	0.812336i	$-0.301805\pi$
$522$	1.41941	+	1.41941i	0.0621259	+	0.0621259i
$523$	3.64979	+	3.64979i	0.159594	+	0.159594i	0.782387	−	0.622793i	$-0.214002\pi$
$523$	3.64979	+	3.64979i	0.159594	+	0.159594i	−0.622793	+	0.782387i	$0.714002\pi$
$524$	−21.7261			−0.949109
$525$		0			0
$526$	−10.3694			−0.452128
$527$	−0.291782	−	0.291782i	−0.0127102	−	0.0127102i
$528$	−2.10852	−	2.10852i	−0.0917617	−	0.0917617i
$529$			19.2566i			0.837242i
$530$	4.58358	+	21.7120i	0.199098	+	0.943108i
$531$		−	7.09038i		−	0.307696i
$532$		0			0
$533$	4.94531	−	4.94531i	0.214205	−	0.214205i
$534$		−	12.3037i		−	0.532432i
$535$	16.7869	−	25.7713i	0.725760	−	1.11419i
$536$	−8.89591			−0.384245
$537$	5.66186	−	5.66186i	0.244327	−	0.244327i
$538$	−9.17421	−	9.17421i	−0.395528	−	0.395528i
$539$		0			0
$540$	−1.22045	+	1.87363i	−0.0525197	+	0.0806284i
$541$	−41.0619			−1.76539			−0.882694	−	0.469949i	$-0.844272\pi$
$541$	−41.0619			−1.76539			−0.882694	+	0.469949i	$0.844272\pi$
$542$	−17.1293	+	17.1293i	−0.735765	+	0.735765i
$543$	0.700622	−	0.700622i	0.0300666	−	0.0300666i
$544$	−2.30173			−0.0986857
$545$	9.99015	−	2.10900i	0.427931	−	0.0903398i
$546$		0			0
$547$	8.69386	+	8.69386i	0.371723	+	0.371723i	0.868104	−	0.496382i	$-0.165338\pi$
$547$	8.69386	+	8.69386i	0.371723	+	0.371723i	−0.496382	+	0.868104i	$0.665338\pi$
$548$	0.263241	−	0.263241i	0.0112451	−	0.0112451i
$549$	−2.41715			−0.103161
$550$	−13.9044	−	5.38166i	−0.592884	−	0.229475i
$551$			17.4058i			0.741511i
$552$	−1.36811	+	1.36811i	−0.0582306	+	0.0582306i
$553$		0			0
$554$			29.1838i			1.23990i
$555$	−15.0572	+	3.17870i	−0.639142	+	0.134928i
$556$			16.1794i			0.686159i
$557$	−16.9052	−	16.9052i	−0.716298	−	0.716298i	0.251547	−	0.967845i	$-0.419061\pi$
$557$	−16.9052	−	16.9052i	−0.716298	−	0.716298i	−0.967845	+	0.251547i	$0.919061\pi$
$558$	0.126767	+	0.126767i	0.00536646	+	0.00536646i
$559$	13.4750			0.569930
$560$		0			0
$561$	−6.86352			−0.289778
$562$	1.89257	+	1.89257i	0.0798334	+	0.0798334i
$563$	6.12576	+	6.12576i	0.258170	+	0.258170i	0.824309	−	0.566139i	$-0.191564\pi$
$563$	6.12576	+	6.12576i	0.258170	+	0.258170i	−0.566139	+	0.824309i	$0.691564\pi$
$564$		−	0.285791i		−	0.0120340i
$565$	−30.4576	−	19.8395i	−1.28136	−	0.834653i
$566$			13.1264i			0.551744i
$567$		0			0
$568$	−6.42398	+	6.42398i	−0.269544	+	0.269544i
$569$		−	11.7783i		−	0.493774i	−0.969044	−	0.246887i	$-0.920592\pi$
$569$		−	11.7783i		−	0.493774i	0.969044	−	0.246887i	$-0.0794076\pi$
$570$	−18.9709	+	4.00490i	−0.794601	+	0.167747i
$571$	32.9997			1.38099			0.690497	−	0.723336i	$-0.257392\pi$
$571$	32.9997			1.38099			0.690497	+	0.723336i	$0.257392\pi$
$572$	−2.86444	+	2.86444i	−0.119768	+	0.119768i
$573$	2.10983	+	2.10983i	0.0881392	+	0.0881392i
$574$		0			0
$575$	−3.49187	+	9.02180i	−0.145621	+	0.376235i
$576$	1.00000			0.0416667
$577$	16.5978	−	16.5978i	0.690977	−	0.690977i	−0.271470	−	0.962447i	$-0.587510\pi$
$577$	16.5978	−	16.5978i	0.690977	−	0.690977i	0.962447	+	0.271470i	$0.0875097\pi$
$578$	8.27460	−	8.27460i	0.344178	−	0.344178i
$579$	−15.7380			−0.654050
$580$	−0.927140	−	4.39178i	−0.0384974	−	0.182359i
$581$		0			0
$582$	7.44633	+	7.44633i	0.308660	+	0.308660i
$583$	20.9248	−	20.9248i	0.866616	−	0.866616i
$584$	−12.4187			−0.513888
$585$	2.54534	+	1.65798i	0.105237	+	0.0685492i
$586$			6.11241i			0.252501i
$587$	5.05632	−	5.05632i	0.208697	−	0.208697i	−0.595017	−	0.803713i	$-0.702855\pi$
$587$	5.05632	−	5.05632i	0.208697	−	0.208697i	0.803713	+	0.595017i	$0.202855\pi$
$588$		0			0
$589$			1.55450i			0.0640519i
$590$	−8.65344	+	13.2848i	−0.356256	+	0.546925i
$591$		−	26.5095i		−	1.09045i
$592$	4.86644	+	4.86644i	0.200010	+	0.200010i
$593$	−22.5468	−	22.5468i	−0.925887	−	0.925887i	0.0715498	−	0.997437i	$-0.477206\pi$
$593$	−22.5468	−	22.5468i	−0.925887	−	0.925887i	−0.997437	+	0.0715498i	$0.977206\pi$
$594$	2.98190			0.122349
$595$		0			0
$596$	−4.69989			−0.192515
$597$	8.85895	+	8.85895i	0.362573	+	0.362573i
$598$	1.85858	+	1.85858i	0.0760030	+	0.0760030i
$599$			0.0359300i			0.00146806i	1.00000		0.000734031i	$0.000233649\pi$
$599$			0.0359300i			0.00146806i	−1.00000		0.000734031i	$0.999766\pi$
$600$	4.57335	−	2.02101i	0.186706	−	0.0825075i
$601$			24.8609i			1.01410i	0.861917	+	0.507049i	$0.169264\pi$
$601$			24.8609i			1.01410i	−0.861917	+	0.507049i	$0.830736\pi$
$602$		0			0
$603$	6.29036	−	6.29036i	0.256163	−	0.256163i
$604$			8.11372i			0.330143i
$605$	−0.973747	−	4.61255i	−0.0395884	−	0.187527i
$606$	−13.0344			−0.529488
$607$	−1.09064	+	1.09064i	−0.0442678	+	0.0442678i	−0.728894	−	0.684626i	$-0.759965\pi$
$607$	−1.09064	+	1.09064i	−0.0442678	+	0.0442678i	0.684626	+	0.728894i	$0.259965\pi$
$608$	6.13133	+	6.13133i	0.248658	+	0.248658i
$609$		0			0
$610$	4.52886	+	2.95001i	0.183368	+	0.119442i
$611$	−0.388248			−0.0157068
$612$	1.62757	−	1.62757i	0.0657905	−	0.0657905i
$613$	−16.4865	+	16.4865i	−0.665882	+	0.665882i	−0.956760	−	0.290878i	$-0.906053\pi$
$613$	−16.4865	+	16.4865i	−0.665882	+	0.665882i	0.290878	+	0.956760i	$0.406053\pi$
$614$	−1.88974			−0.0762637
$615$	9.64567	+	6.28300i	0.388951	+	0.253355i
$616$		0			0
$617$	5.22561	+	5.22561i	0.210375	+	0.210375i	0.804427	−	0.594052i	$-0.202473\pi$
$617$	5.22561	+	5.22561i	0.210375	+	0.210375i	−0.594052	+	0.804427i	$0.702473\pi$
$618$	−11.8321	+	11.8321i	−0.475955	+	0.475955i
$619$	−25.9888			−1.04458			−0.522289	−	0.852768i	$-0.674922\pi$
$619$	−25.9888			−1.04458			−0.522289	+	0.852768i	$0.674922\pi$
$620$	−0.0828022	−	0.392226i	−0.00332542	−	0.0157522i
$621$		−	1.93480i		−	0.0776407i
$622$	9.82751	−	9.82751i	0.394047	−	0.394047i
$623$		0			0
$624$		−	1.35850i		−	0.0543837i
$625$	16.8310	−	18.4856i	0.673241	−	0.739423i
$626$		−	4.23639i		−	0.169320i
$627$	18.2830	+	18.2830i	0.730154	+	0.730154i
$628$	6.77980	+	6.77980i	0.270544	+	0.270544i
$629$	15.8409			0.631619
$630$		0			0
$631$	1.56613			0.0623468			0.0311734	−	0.999514i	$-0.490076\pi$
$631$	1.56613			0.0623468			0.0311734	+	0.999514i	$0.490076\pi$
$632$	11.5085	+	11.5085i	0.457784	+	0.457784i
$633$	1.44627	+	1.44627i	0.0574839	+	0.0574839i
$634$			31.6087i			1.25534i
$635$	−0.958326	+	1.47122i	−0.0380300	+	0.0583838i
$636$			9.92390i			0.393508i
$637$		0			0
$638$	−4.23255	+	4.23255i	−0.167568	+	0.167568i
$639$		−	9.08488i		−	0.359392i
$640$	−1.87363	−	1.22045i	−0.0740619	−	0.0482424i
$641$	−27.1075			−1.07068			−0.535341	−	0.844636i	$-0.679817\pi$
$641$	−27.1075			−1.07068			−0.535341	+	0.844636i	$0.679817\pi$
$642$	9.72604	−	9.72604i	0.383856	−	0.383856i
$643$	24.8300	+	24.8300i	0.979200	+	0.979200i	0.999788	−	0.0205877i	$-0.00655374\pi$
$643$	24.8300	+	24.8300i	0.979200	+	0.979200i	−0.0205877	+	0.999788i	$0.506554\pi$
$644$		0			0
$645$	4.58130	+	21.7012i	0.180389	+	0.854483i
$646$	19.9583			0.785249
$647$	1.65076	−	1.65076i	0.0648980	−	0.0648980i	−0.673913	−	0.738811i	$-0.735388\pi$
$647$	1.65076	−	1.65076i	0.0648980	−	0.0648980i	0.738811	+	0.673913i	$0.235388\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	21.1428			0.829928
$650$	−2.74555	−	6.21291i	−0.107689	−	0.243690i
$651$		0			0
$652$	−4.53943	−	4.53943i	−0.177778	−	0.177778i
$653$	−25.5390	+	25.5390i	−0.999419	+	0.999419i	−1.00000		0.000580655i	$-0.999815\pi$
$653$	−25.5390	+	25.5390i	−0.999419	+	0.999419i	0.000580655		1.00000i	$0.499815\pi$
$654$	4.56620			0.178553
$655$	−47.5334	+	10.0347i	−1.85728	+	0.392088i
$656$		−	5.14811i		−	0.201000i
$657$	8.78132	−	8.78132i	0.342592	−	0.342592i
$658$		0			0
$659$		−	13.1119i		−	0.510768i	−0.966840	−	0.255384i	$-0.917798\pi$
$659$		−	13.1119i		−	0.510768i	0.966840	−	0.255384i	$-0.0822019\pi$
$660$	−5.58699	−	3.63926i	−0.217473	−	0.141658i
$661$		−	10.4554i		−	0.406669i	−0.979109	−	0.203334i	$-0.934822\pi$
$661$		−	10.4554i		−	0.406669i	0.979109	−	0.203334i	$-0.0651779\pi$
$662$	−20.5805	−	20.5805i	−0.799885	−	0.799885i
$663$	−2.21106	−	2.21106i	−0.0858703	−	0.0858703i
$664$	11.4753			0.445329
$665$		0			0
$666$	−6.88219			−0.266680
$667$	2.74627	+	2.74627i	0.106336	+	0.106336i
$668$	6.34259	+	6.34259i	0.245402	+	0.245402i
$669$		−	1.41639i		−	0.0547608i
$670$	−19.4629	+	4.10878i	−0.751917	+	0.158736i
$671$		−	7.20771i		−	0.278250i
$672$		0			0
$673$	17.0926	−	17.0926i	0.658871	−	0.658871i	−0.296242	−	0.955113i	$-0.595733\pi$
$673$	17.0926	−	17.0926i	0.658871	−	0.658871i	0.955113	+	0.296242i	$0.0957335\pi$
$674$		−	11.7118i		−	0.451123i
$675$	−1.80477	+	4.66292i	−0.0694658	+	0.179476i
$676$	11.1545			0.429018
$677$	20.1314	−	20.1314i	0.773714	−	0.773714i	−0.205040	−	0.978754i	$-0.565732\pi$
$677$	20.1314	−	20.1314i	0.773714	−	0.773714i	0.978754	+	0.205040i	$0.0657323\pi$
$678$	−11.4947	−	11.4947i	−0.441449	−	0.441449i
$679$		0			0
$680$	−5.03583	+	1.06310i	−0.193115	+	0.0407682i
$681$	8.28876			0.317626
$682$	−0.378006	+	0.378006i	−0.0144746	+	0.0144746i
$683$	−32.8781	+	32.8781i	−1.25805	+	1.25805i	−0.306022	+	0.952024i	$0.598998\pi$
$683$	−32.8781	+	32.8781i	−1.25805	+	1.25805i	−0.952024	+	0.306022i	$0.901002\pi$
$684$	−8.67101			−0.331545
$685$	0.454348	−	0.697515i	0.0173597	−	0.0266507i
$686$		0			0
$687$	11.9588	+	11.9588i	0.456255	+	0.456255i
$688$	7.01377	−	7.01377i	0.267398	−	0.267398i
$689$	13.4817			0.513611
$690$	−2.36132	+	3.62510i	−0.0898939	+	0.138005i
$691$		−	15.9822i		−	0.607991i	−0.952673	−	0.303996i	$-0.901679\pi$
$691$		−	15.9822i		−	0.607991i	0.952673	−	0.303996i	$-0.0983208\pi$
$692$	13.9572	−	13.9572i	0.530575	−	0.530575i
$693$		0			0
$694$		−	2.21605i		−	0.0841199i
$695$	7.47281	+	35.3980i	0.283460	+	1.34272i
$696$		−	2.00735i		−	0.0760884i
$697$	−8.37888	−	8.37888i	−0.317373	−	0.317373i
$698$	20.9910	+	20.9910i	0.794520	+	0.794520i
$699$	−10.3289			−0.390674
$700$		0			0
$701$	−32.0051			−1.20882			−0.604408	−	0.796675i	$-0.706590\pi$
$701$	−32.0051			−1.20882			−0.604408	+	0.796675i	$0.706590\pi$
$702$	0.960607	+	0.960607i	0.0362558	+	0.0362558i
$703$	−42.1970	−	42.1970i	−1.59149	−	1.59149i
$704$			2.98190i			0.112385i
$705$	−0.131999	−	0.625267i	−0.00497137	−	0.0235489i
$706$		−	18.9269i		−	0.712322i
$707$		0			0
$708$	−5.01365	+	5.01365i	−0.188425	+	0.188425i
$709$			1.77069i			0.0664998i	0.999447	+	0.0332499i	$0.0105857\pi$
$709$			1.77069i			0.0664998i	−0.999447	+	0.0332499i	$0.989414\pi$
$710$	−11.0876	+	17.0217i	−0.416111	+	0.638814i
$711$	−16.2755			−0.610378
$712$	−8.70002	+	8.70002i	−0.326047	+	0.326047i
$713$	0.245268	+	0.245268i	0.00918535	+	0.00918535i
$714$		0			0
$715$	−4.94395	+	7.58996i	−0.184893	+	0.283848i
$716$	−8.00708			−0.299238
$717$	−0.283104	+	0.283104i	−0.0105727	+	0.0105727i
$718$	−24.7631	+	24.7631i	−0.924151	+	0.924151i
$719$	10.8718			0.405451			0.202725	−	0.979236i	$-0.435020\pi$
$719$	10.8718			0.405451			0.202725	+	0.979236i	$0.435020\pi$
$720$	2.18785	−	0.461873i	0.0815362	−	0.0172130i
$721$		0			0
$722$	−39.7298	−	39.7298i	−1.47859	−	1.47859i
$723$	17.8172	−	17.8172i	0.662630	−	0.662630i
$724$	−0.990829			−0.0368239
$725$	−4.05688	−	9.18031i	−0.150669	−	0.340948i
$726$		−	2.10826i		−	0.0782448i
$727$	9.64027	−	9.64027i	0.357538	−	0.357538i	−0.505367	−	0.862905i	$-0.668643\pi$
$727$	9.64027	−	9.64027i	0.357538	−	0.357538i	0.862905	+	0.505367i	$0.168643\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	−27.1701	+	5.73584i	−1.00561	+	0.212293i
$731$		−	22.8308i		−	0.844426i
$732$	1.70918	+	1.70918i	0.0631732	+	0.0631732i
$733$	−6.07900	−	6.07900i	−0.224533	−	0.224533i	0.585871	−	0.810404i	$-0.300752\pi$
$733$	−6.07900	−	6.07900i	−0.224533	−	0.224533i	−0.810404	+	0.585871i	$0.800752\pi$
$734$	0.0770912			0.00284549
$735$		0			0
$736$	1.93480			0.0713176
$737$	18.7572	+	18.7572i	0.690931	+	0.690931i
$738$	3.64026	+	3.64026i	0.134000	+	0.134000i
$739$			27.0495i			0.995032i	0.867455	+	0.497516i	$0.165754\pi$
$739$			27.0495i			0.995032i	−0.867455	+	0.497516i	$0.834246\pi$
$740$	12.8947	+	8.39936i	0.474019	+	0.308767i
$741$			11.7796i			0.432735i
$742$		0			0
$743$	24.6470	−	24.6470i	0.904210	−	0.904210i	−0.0915872	−	0.995797i	$-0.529194\pi$
$743$	24.6470	−	24.6470i	0.904210	−	0.904210i	0.995797	+	0.0915872i	$0.0291940\pi$
$744$		−	0.179275i		−	0.00657254i
$745$	−10.2826	+	2.17075i	−0.376727	+	0.0795301i
$746$	5.66060			0.207249
$747$	−8.11428	+	8.11428i	−0.296886	+	0.296886i
$748$	4.85324	+	4.85324i	0.177452	+	0.177452i
$749$		0			0
$750$	9.07233	−	6.53397i	0.331275	−	0.238587i
$751$	−28.9452			−1.05623			−0.528113	−	0.849174i	$-0.677100\pi$
$751$	−28.9452			−1.05623			−0.528113	+	0.849174i	$0.677100\pi$
$752$	−0.202085	+	0.202085i	−0.00736927	+	0.00736927i
$753$	−3.73623	+	3.73623i	−0.136156	+	0.136156i
$754$	−2.72699			−0.0993113
$755$	3.74750	+	17.7516i	0.136386	+	0.646046i
$756$		0			0
$757$	16.4988	+	16.4988i	0.599661	+	0.599661i	0.940222	−	0.340562i	$-0.110617\pi$
$757$	16.4988	+	16.4988i	0.599661	+	0.599661i	−0.340562	+	0.940222i	$0.610617\pi$
$758$	−6.44958	+	6.44958i	−0.234259	+	0.234259i
$759$	5.76938			0.209415
$760$	16.2463	+	10.5825i	0.589316	+	0.383868i
$761$			47.2049i			1.71118i	0.517658	+	0.855588i	$0.326804\pi$
$761$			47.2049i			1.71118i	−0.517658	+	0.855588i	$0.673196\pi$
$762$	−0.555238	+	0.555238i	−0.0201141	+	0.0201141i
$763$		0			0
$764$		−	2.98374i		−	0.107948i
$765$	2.80914	−	4.31259i	0.101565	−	0.155922i
$766$		−	1.79420i		−	0.0648269i
$767$	6.81107	+	6.81107i	0.245933	+	0.245933i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	5.30753			0.191394			0.0956971	−	0.995410i	$-0.469492\pi$
$769$	5.30753			0.191394			0.0956971	+	0.995410i	$0.469492\pi$
$770$		0			0
$771$	16.0774			0.579013
$772$	11.1285	+	11.1285i	0.400522	+	0.400522i
$773$	30.1160	+	30.1160i	1.08320	+	1.08320i	0.996209	+	0.0869880i	$0.0277242\pi$
$773$	30.1160	+	30.1160i	1.08320	+	1.08320i	0.0869880	+	0.996209i	$0.472276\pi$
$774$			9.91897i			0.356530i
$775$	−0.362317	−	0.819887i	−0.0130148	−	0.0294512i
$776$		−	10.5307i		−	0.378030i
$777$		0			0
$778$	−14.0181	+	14.0181i	−0.502572	+	0.502572i
$779$			44.6393i			1.59937i
$780$	−0.627456	−	2.97220i	−0.0224665	−	0.106422i
$781$	27.0902			0.969364
$782$	3.14901	−	3.14901i	0.112608	−	0.112608i
$783$	1.41941	+	1.41941i	0.0507256	+	0.0507256i
$784$		0			0
$785$	17.9646	+	11.7018i	0.641183	+	0.417654i
$786$	−21.7261			−0.774945
$787$	−19.9216	+	19.9216i	−0.710128	+	0.710128i	−0.966562	−	0.256433i	$-0.917453\pi$
$787$	−19.9216	+	19.9216i	−0.710128	+	0.710128i	0.256433	+	0.966562i	$0.417453\pi$
$788$	−18.7450	+	18.7450i	−0.667763	+	0.667763i
$789$	−10.3694			−0.369161
$790$	30.4943	+	19.8634i	1.08494	+	0.706707i
$791$		0			0
$792$	−2.10852	−	2.10852i	−0.0749231	−	0.0749231i
$793$	2.32193	−	2.32193i	0.0824543	−	0.0824543i
$794$	24.3702			0.864865
$795$	4.58358	+	21.7120i	0.162563	+	0.770045i
$796$		−	12.5284i		−	0.444059i
$797$	−11.2338	+	11.2338i	−0.397922	+	0.397922i	−0.877500	−	0.479577i	$-0.840790\pi$
$797$	−11.2338	+	11.2338i	−0.397922	+	0.397922i	0.479577	+	0.877500i	$0.340790\pi$
$798$		0			0
$799$			0.657813i			0.0232717i
$800$	−4.66292	−	1.80477i	−0.164859	−	0.0638084i
$801$		−	12.3037i		−	0.434729i
$802$	−26.8231	−	26.8231i	−0.947157	−	0.947157i
$803$	26.1850	+	26.1850i	0.924050	+	0.924050i
$804$	−8.89591			−0.313734
$805$		0			0
$806$	−0.243546			−0.00857854
$807$	−9.17421	−	9.17421i	−0.322947	−	0.322947i
$808$	9.21674	+	9.21674i	0.324244	+	0.324244i
$809$		−	13.0198i		−	0.457752i	−0.973456	−	0.228876i	$-0.926495\pi$
$809$		−	13.0198i		−	0.457752i	0.973456	−	0.228876i	$-0.0735050\pi$
$810$	−1.22045	+	1.87363i	−0.0428822	+	0.0658328i
$811$		−	45.1419i		−	1.58514i	−0.609778	−	0.792572i	$-0.708741\pi$
$811$		−	45.1419i		−	1.58514i	0.609778	−	0.792572i	$-0.291259\pi$
$812$		0			0
$813$	−17.1293	+	17.1293i	−0.600750	+	0.600750i
$814$		−	20.5220i		−	0.719297i
$815$	−12.0282	−	7.83495i	−0.421330	−	0.274446i
$816$	−2.30173			−0.0805765
$817$	−60.8165	+	60.8165i	−2.12770	+	2.12770i
$818$	1.46725	+	1.46725i	0.0513012	+	0.0513012i
$819$		0			0
$820$	−2.37777	−	11.2633i	−0.0830353	−	0.393330i
$821$	−38.7475			−1.35230			−0.676148	−	0.736766i	$-0.736352\pi$
$821$	−38.7475			−1.35230			−0.676148	+	0.736766i	$0.736352\pi$
$822$	0.263241	−	0.263241i	0.00918159	−	0.00918159i
$823$	−34.8021	+	34.8021i	−1.21312	+	1.21312i	−0.243131	+	0.969993i	$0.578175\pi$
$823$	−34.8021	+	34.8021i	−1.21312	+	1.21312i	−0.969993	+	0.243131i	$0.921825\pi$
$824$	16.7331			0.582924
$825$	−13.9044	−	5.38166i	−0.484088	−	0.187365i
$826$		0			0
$827$	13.1555	+	13.1555i	0.457462	+	0.457462i	0.897821	−	0.440360i	$-0.145149\pi$
$827$	13.1555	+	13.1555i	0.457462	+	0.457462i	−0.440360	+	0.897821i	$0.645149\pi$
$828$	−1.36811	+	1.36811i	−0.0475451	+	0.0475451i
$829$	−15.3802			−0.534175			−0.267087	−	0.963672i	$-0.586061\pi$
$829$	−15.3802			−0.534175			−0.267087	+	0.963672i	$0.586061\pi$
$830$	25.1063	−	5.30014i	0.871451	−	0.183971i
$831$			29.1838i			1.01237i
$832$	−0.960607	+	0.960607i	−0.0333031	+	0.0333031i
$833$		0			0
$834$			16.1794i			0.560246i
$835$	16.8061	+	10.9471i	0.581599	+	0.378842i
$836$		−	25.8561i		−	0.894252i
$837$	0.126767	+	0.126767i	0.00438170	+	0.00438170i
$838$	9.15053	+	9.15053i	0.316100	+	0.316100i
$839$	33.7835			1.16634			0.583168	−	0.812352i	$-0.301813\pi$
$839$	33.7835			1.16634			0.583168	+	0.812352i	$0.301813\pi$
$840$		0			0
$841$	24.9705			0.861053
$842$	−4.83195	−	4.83195i	−0.166520	−	0.166520i
$843$	1.89257	+	1.89257i	0.0651837	+	0.0651837i
$844$		−	2.04533i		−	0.0704031i
$845$	24.4043	−	5.15194i	0.839532	−	0.177232i
$846$		−	0.285791i		−	0.00982570i
$847$		0			0
$848$	7.01726	−	7.01726i	0.240974	−	0.240974i
$849$			13.1264i			0.450497i
$850$	−10.5266	+	4.65182i	−0.361059	+	0.159556i
$851$	−13.3156			−0.456455
$852$	−6.42398	+	6.42398i	−0.220082	+	0.220082i
$853$	31.2527	+	31.2527i	1.07007	+	1.07007i	0.997352	+	0.0727187i	$0.0231675\pi$
$853$	31.2527	+	31.2527i	1.07007	+	1.07007i	0.0727187	+	0.997352i	$0.476832\pi$
$854$		0			0
$855$	−18.9709	+	4.00490i	−0.648789	+	0.136965i
$856$	−13.7547			−0.470126
$857$	12.0706	−	12.0706i	0.412323	−	0.412323i	−0.470224	−	0.882547i	$-0.655827\pi$
$857$	12.0706	−	12.0706i	0.412323	−	0.412323i	0.882547	+	0.470224i	$0.155827\pi$
$858$	−2.86444	+	2.86444i	−0.0977903	+	0.0977903i
$859$	21.5661			0.735826			0.367913	−	0.929860i	$-0.380072\pi$
$859$	21.5661			0.735826			0.367913	+	0.929860i	$0.380072\pi$
$860$	12.1056	−	18.5845i	0.412797	−	0.633727i
$861$		0			0
$862$	−10.3937	−	10.3937i	−0.354012	−	0.354012i
$863$	11.6912	−	11.6912i	0.397973	−	0.397973i	−0.479544	−	0.877518i	$-0.659198\pi$
$863$	11.6912	−	11.6912i	0.397973	−	0.397973i	0.877518	+	0.479544i	$0.159198\pi$
$864$	1.00000			0.0340207
$865$	24.0898	−	36.9828i	0.819079	−	1.25745i
$866$		−	5.50045i		−	0.186913i
$867$	8.27460	−	8.27460i	0.281020	−	0.281020i
$868$		0			0
$869$		−	48.5319i		−	1.64633i
$870$	−0.927140	−	4.39178i	−0.0314330	−	0.148895i
$871$			12.0851i			0.409489i
$872$	−3.22879	−	3.22879i	−0.109341	−	0.109341i
$873$	7.44633	+	7.44633i	0.252020	+	0.252020i
$874$	−16.7767			−0.567479
$875$		0			0
$876$	−12.4187			−0.419588
$877$	−17.8666	−	17.8666i	−0.603312	−	0.603312i	0.337878	−	0.941190i	$-0.390291\pi$
$877$	−17.8666	−	17.8666i	−0.603312	−	0.603312i	−0.941190	+	0.337878i	$0.890291\pi$
$878$	−24.1614	−	24.1614i	−0.815407	−	0.815407i
$879$			6.11241i			0.206166i
$880$	1.37726	+	6.52395i	0.0464274	+	0.219922i
$881$		−	0.521687i		−	0.0175761i	−0.999961	−	0.00878804i	$-0.997203\pi$
$881$		−	0.521687i		−	0.0175761i	0.999961	−	0.00878804i	$-0.00279736\pi$
$882$		0			0
$883$	−17.5835	+	17.5835i	−0.591732	+	0.591732i	−0.938099	−	0.346367i	$-0.887415\pi$
$883$	−17.5835	+	17.5835i	−0.591732	+	0.591732i	0.346367	+	0.938099i	$0.387415\pi$
$884$			3.12691i			0.105169i
$885$	−8.65344	+	13.2848i	−0.290882	+	0.446563i
$886$	5.09627			0.171213
$887$	26.5408	−	26.5408i	0.891153	−	0.891153i	−0.103479	−	0.994632i	$-0.532997\pi$
$887$	26.5408	−	26.5408i	0.891153	−	0.891153i	0.994632	+	0.103479i	$0.0329974\pi$
$888$	4.86644	+	4.86644i	0.163307	+	0.163307i
$889$		0			0
$890$	−15.0160	+	23.0526i	−0.503338	+	0.772725i
$891$	2.98190			0.0998975
$892$	−1.00154	+	1.00154i	−0.0335340	+	0.0335340i
$893$	1.75228	−	1.75228i	0.0586378	−	0.0586378i
$894$	−4.69989			−0.157188
$895$	−17.5183	+	3.69825i	−0.585571	+	0.123619i
$896$		0			0
$897$	1.85858	+	1.85858i	0.0620562	+	0.0620562i
$898$	−21.4746	+	21.4746i	−0.716616	+	0.716616i
$899$	−0.359868			−0.0120023
$900$	4.57335	−	2.02101i	0.152445	−	0.0673671i
$901$		−	22.8421i		−	0.760981i
$902$	−10.8549	+	10.8549i	−0.361429	+	0.361429i
$903$		0			0
$904$			16.2559i			0.540663i
$905$	−2.16778	+	0.457637i	−0.0720595	+	0.0152124i
$906$			8.11372i			0.269560i
$907$	−27.0193	−	27.0193i	−0.897160	−	0.897160i	0.0980241	−	0.995184i	$-0.468748\pi$
$907$	−27.0193	−	27.0193i	−0.897160	−	0.897160i	−0.995184	+	0.0980241i	$0.968748\pi$
$908$	−5.86104	−	5.86104i	−0.194505	−	0.194505i
$909$	−13.0344			−0.432325
$910$		0			0
$911$	7.44947			0.246812			0.123406	−	0.992356i	$-0.460618\pi$
$911$	7.44947			0.246812			0.123406	+	0.992356i	$0.460618\pi$
$912$	6.13133	+	6.13133i	0.203029	+	0.203029i
$913$	−24.1960	−	24.1960i	−0.800771	−	0.800771i
$914$		−	8.72210i		−	0.288501i
$915$	4.52886	+	2.95001i	0.149719	+	0.0975242i
$916$		−	16.9122i		−	0.558796i
$917$		0			0
$918$	1.62757	−	1.62757i	0.0537177	−	0.0537177i
$919$		−	18.4266i		−	0.607836i	−0.952698	−	0.303918i	$-0.901705\pi$
$919$		−	18.4266i		−	0.607836i	0.952698	−	0.303918i	$-0.0982949\pi$
$920$	4.23304	−	0.893630i	0.139559	−	0.0294621i
$921$	−1.88974			−0.0622690
$922$	19.3907	−	19.3907i	0.638600	−	0.638600i
$923$	8.72700	+	8.72700i	0.287253	+	0.287253i
$924$		0			0
$925$	32.0911	+	12.4208i	1.05515	+	0.408393i
$926$	24.1712			0.794315
$927$	−11.8321	+	11.8321i	−0.388616	+	0.388616i
$928$	−1.41941	+	1.41941i	−0.0465945	+	0.0465945i
$929$	48.3933			1.58773			0.793867	−	0.608092i	$-0.208065\pi$
$929$	48.3933			1.58773			0.793867	+	0.608092i	$0.208065\pi$
$930$	−0.0828022	−	0.392226i	−0.00271519	−	0.0128616i
$931$		0			0
$932$	7.30362	+	7.30362i	0.239238	+	0.239238i
$933$	9.82751	−	9.82751i	0.321738	−	0.321738i
$934$	−15.8689			−0.519245
$935$	12.8597	+	8.37657i	0.420558	+	0.273943i
$936$		−	1.35850i		−	0.0444041i
$937$	−4.99590	+	4.99590i	−0.163209	+	0.163209i	−0.783987	−	0.620778i	$-0.786817\pi$
$937$	−4.99590	+	4.99590i	−0.163209	+	0.163209i	0.620778	+	0.783987i	$0.286817\pi$
$938$		0			0
$939$		−	4.23639i		−	0.138249i
$940$	−0.348793	+	0.535468i	−0.0113764	+	0.0174650i
$941$			10.9082i			0.355598i	0.984067	+	0.177799i	$0.0568976\pi$
$941$			10.9082i			0.355598i	−0.984067	+	0.177799i	$0.943102\pi$
$942$	6.77980	+	6.77980i	0.220898	+	0.220898i
$943$	7.04317	+	7.04317i	0.229357	+	0.229357i
$944$	7.09038			0.230772
$945$		0			0
$946$	−29.5774			−0.961644
$947$	4.37732	+	4.37732i	0.142244	+	0.142244i	0.774643	−	0.632399i	$-0.217930\pi$
$947$	4.37732	+	4.37732i	0.142244	+	0.142244i	−0.632399	+	0.774643i	$0.717930\pi$
$948$	11.5085	+	11.5085i	0.373779	+	0.373779i
$949$			16.8708i			0.547650i
$950$	40.4322	+	15.6492i	1.31179	+	0.507728i
$951$			31.6087i			1.02498i
$952$		0			0
$953$	−6.54107	+	6.54107i	−0.211886	+	0.211886i	−0.805068	−	0.593182i	$-0.797871\pi$
$953$	−6.54107	+	6.54107i	−0.211886	+	0.211886i	0.593182	+	0.805068i	$0.297871\pi$
$954$			9.92390i			0.321298i
$955$	−1.37811	−	6.52797i	−0.0445946	−	0.211240i
$956$	0.400370			0.0129489
$957$	−4.23255	+	4.23255i	−0.136819	+	0.136819i
$958$	0.0311150	+	0.0311150i	0.00100528	+	0.00100528i
$959$		0			0
$960$	−1.87363	−	1.22045i	−0.0604713	−	0.0393898i
$961$	30.9679			0.998963
$962$	6.61109	−	6.61109i	0.213150	−	0.213150i
$963$	9.72604	−	9.72604i	0.313417	−	0.313417i
$964$	−25.1974			−0.811553
$965$	29.4873	+	19.2074i	0.949230	+	0.618309i
$966$		0			0
$967$	−35.8084	−	35.8084i	−1.15152	−	1.15152i	−0.986248	−	0.165272i	$-0.947150\pi$
$967$	−35.8084	−	35.8084i	−1.15152	−	1.15152i	−0.165272	−	0.986248i	$-0.552850\pi$
$968$	−1.49076	+	1.49076i	−0.0479150	+	0.0479150i
$969$	19.9583			0.641153
$970$	−4.86384	−	23.0395i	−0.156168	−	0.739755i
$971$			10.0030i			0.321011i	0.987035	+	0.160505i	$0.0513124\pi$
$971$			10.0030i			0.321011i	−0.987035	+	0.160505i	$0.948688\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$		0			0
$974$		−	31.3116i		−	1.00329i
$975$	−2.74555	−	6.21291i	−0.0879281	−	0.198972i
$976$		−	2.41715i		−	0.0773711i
$977$	30.0543	+	30.0543i	0.961521	+	0.961521i	0.999287	−	0.0377658i	$-0.0120241\pi$
$977$	30.0543	+	30.0543i	0.961521	+	0.961521i	−0.0377658	+	0.999287i	$0.512024\pi$
$978$	−4.53943	−	4.53943i	−0.145155	−	0.145155i
$979$	36.6884			1.17257
$980$		0			0
$981$	4.56620			0.145788
$982$	−17.5385	−	17.5385i	−0.559675	−	0.559675i
$983$	−5.35375	−	5.35375i	−0.170758	−	0.170758i	0.616554	−	0.787312i	$-0.288528\pi$
$983$	−5.35375	−	5.35375i	−0.170758	−	0.170758i	−0.787312	+	0.616554i	$0.788528\pi$
$984$		−	5.14811i		−	0.164116i
$985$	−32.3534	+	49.6690i	−1.03087	+	1.58259i
$986$			4.62037i			0.147143i
$987$		0			0
$988$	8.32944	−	8.32944i	0.264995	−	0.264995i
$989$			19.1912i			0.610245i
$990$	−5.58699	−	3.63926i	−0.177566	−	0.115663i
$991$	−22.1160			−0.702538			−0.351269	−	0.936274i	$-0.614250\pi$
$991$	−22.1160			−0.702538			−0.351269	+	0.936274i	$0.614250\pi$
$992$	−0.126767	+	0.126767i	−0.00402485	+	0.00402485i
$993$	−20.5805	−	20.5805i	−0.653103	−	0.653103i
$994$		0			0
$995$	−5.78654	−	27.4103i	−0.183446	−	0.868965i
$996$	11.4753			0.363610
$997$	−16.4225	+	16.4225i	−0.520107	+	0.520107i	−0.917604	−	0.397497i	$-0.869879\pi$
$997$	−16.4225	+	16.4225i	−0.520107	+	0.520107i	0.397497	+	0.917604i	$0.369879\pi$
$998$	23.3815	−	23.3815i	0.740129	−	0.740129i
$999$	−6.88219			−0.217743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.c.97.3	✓	16
5.3	odd	4		1470.2.m.f.1273.2	yes	16
7.6	odd	2		1470.2.m.f.97.2	yes	16
35.13	even	4	inner	1470.2.m.c.1273.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.c.97.3	✓	16	1.1	even	1	trivial
1470.2.m.c.1273.3	yes	16	35.13	even	4	inner
1470.2.m.f.97.2	yes	16	7.6	odd	2
1470.2.m.f.1273.2	yes	16	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(0.461873 + 2.18785i) q^{5} +1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(0.461873 + 2.18785i) q^{5} +1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(1.22045 - 1.87363i) q^{10} -2.98190 q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.960607 - 0.960607i) q^{13} +(1.22045 - 1.87363i) q^{15} -1.00000 q^{16} +(-1.62757 + 1.62757i) q^{17} +(0.707107 - 0.707107i) q^{18} +8.67101 q^{19} +(-2.18785 + 0.461873i) q^{20} +(2.10852 + 2.10852i) q^{22} +(1.36811 - 1.36811i) q^{23} -1.00000 q^{24} +(-4.57335 + 2.02101i) q^{25} +1.35850i q^{26} +(0.707107 - 0.707107i) q^{27} +2.00735i q^{29} +(-2.18785 + 0.461873i) q^{30} +0.179275i q^{31} +(0.707107 + 0.707107i) q^{32} +(2.10852 + 2.10852i) q^{33} +2.30173 q^{34} -1.00000 q^{36} +(-4.86644 - 4.86644i) q^{37} +(-6.13133 - 6.13133i) q^{38} +1.35850i q^{39} +(1.87363 + 1.22045i) q^{40} +5.14811i q^{41} +(-7.01377 + 7.01377i) q^{43} -2.98190i q^{44} +(-2.18785 + 0.461873i) q^{45} -1.93480 q^{46} +(0.202085 - 0.202085i) q^{47} +(0.707107 + 0.707107i) q^{48} +(4.66292 + 1.80477i) q^{50} +2.30173 q^{51} +(0.960607 - 0.960607i) q^{52} +(-7.01726 + 7.01726i) q^{53} -1.00000 q^{54} +(-1.37726 - 6.52395i) q^{55} +(-6.13133 - 6.13133i) q^{57} +(1.41941 - 1.41941i) q^{58} -7.09038 q^{59} +(1.87363 + 1.22045i) q^{60} +2.41715i q^{61} +(0.126767 - 0.126767i) q^{62} -1.00000i q^{64} +(1.65798 - 2.54534i) q^{65} -2.98190i q^{66} +(-6.29036 - 6.29036i) q^{67} +(-1.62757 - 1.62757i) q^{68} -1.93480 q^{69} -9.08488 q^{71} +(0.707107 + 0.707107i) q^{72} +(-8.78132 - 8.78132i) q^{73} +6.88219i q^{74} +(4.66292 + 1.80477i) q^{75} +8.67101i q^{76} +(0.960607 - 0.960607i) q^{78} +16.2755i q^{79} +(-0.461873 - 2.18785i) q^{80} -1.00000 q^{81} +(3.64026 - 3.64026i) q^{82} +(8.11428 + 8.11428i) q^{83} +(-4.31259 - 2.80914i) q^{85} +9.91897 q^{86} +(1.41941 - 1.41941i) q^{87} +(-2.10852 + 2.10852i) q^{88} -12.3037 q^{89} +(1.87363 + 1.22045i) q^{90} +(1.36811 + 1.36811i) q^{92} +(0.126767 - 0.126767i) q^{93} -0.285791 q^{94} +(4.00490 + 18.9709i) q^{95} -1.00000i q^{96} +(7.44633 - 7.44633i) q^{97} -2.98190i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5}+O(q^{10}) \) 16 * q - 8 * q^5	\( 16 q - 8 q^{5} - 8 q^{13} - 16 q^{16} + 8 q^{17} + 48 q^{19} - 8 q^{22} - 8 q^{23} - 16 q^{24} + 8 q^{25} - 8 q^{33} - 16 q^{36} + 8 q^{37} + 8 q^{38} - 16 q^{47} + 8 q^{52} + 8 q^{53} - 16 q^{54} + 8 q^{57} + 24 q^{58} - 48 q^{59} + 8 q^{62} + 72 q^{65} - 48 q^{67} + 8 q^{68} - 16 q^{73} + 8 q^{78} + 8 q^{80} - 16 q^{81} + 16 q^{82} - 72 q^{85} + 24 q^{87} + 8 q^{88} + 64 q^{89} - 8 q^{92} + 8 q^{93} - 64 q^{94} + 48 q^{95} + 64 q^{97}+O(q^{100}) \) 16 * q - 8 * q^5 - 8 * q^13 - 16 * q^16 + 8 * q^17 + 48 * q^19 - 8 * q^22 - 8 * q^23 - 16 * q^24 + 8 * q^25 - 8 * q^33 - 16 * q^36 + 8 * q^37 + 8 * q^38 - 16 * q^47 + 8 * q^52 + 8 * q^53 - 16 * q^54 + 8 * q^57 + 24 * q^58 - 48 * q^59 + 8 * q^62 + 72 * q^65 - 48 * q^67 + 8 * q^68 - 16 * q^73 + 8 * q^78 + 8 * q^80 - 16 * q^81 + 16 * q^82 - 72 * q^85 + 24 * q^87 + 8 * q^88 + 64 * q^89 - 8 * q^92 + 8 * q^93 - 64 * q^94 + 48 * q^95 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more