LMFDB - Embedded newform 464.2.u.h.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,2,Mod(49,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("464.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.u (of order $7$, degree $6$, 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:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 9 x^{9} - 5 x^{8} + 35 x^{7} + 197 x^{6} - 140 x^{5} - 80 x^{4} + \cdots + 4096 $ x^12 - 3x^11 + 13x^10 - 9x^9 - 5x^8 + 35x^7 + 197x^6 - 140x^5 - 80x^4 + 576x^3 + 3328x^2 + 3072*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			49.2
Root			$1.52179 - 1.90827i$ of defining polynomial
Character	$\chi$	$=$	464.49
Dual form			464.2.u.h.161.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52179 + 1.90827i) q^{3} +(2.60002 - 1.25211i) q^{5} +(1.89765 + 2.37957i) q^{7} +(-0.658071 + 2.88320i) q^{9} +O(q^{10})$	\(q+(1.52179 + 1.90827i) q^{3} +(2.60002 - 1.25211i) q^{5} +(1.89765 + 2.37957i) q^{7} +(-0.658071 + 2.88320i) q^{9} +(-1.22038 - 5.34685i) q^{11} +(0.0239308 + 0.104847i) q^{13} +(6.34605 + 3.05610i) q^{15} +0.816005 q^{17} +(-1.27358 + 1.59701i) q^{19} +(-1.65304 + 7.24243i) q^{21} +(-8.25746 - 3.97659i) q^{23} +(2.07491 - 2.60185i) q^{25} +(0.0938049 - 0.0451741i) q^{27} +(-5.37657 - 0.304047i) q^{29} +(-3.10086 + 1.49330i) q^{31} +(8.34605 - 10.4656i) q^{33} +(7.91340 + 3.81089i) q^{35} +(-1.31456 + 5.75946i) q^{37} +(-0.163659 + 0.205223i) q^{39} -2.43376 q^{41} +(4.94123 + 2.37957i) q^{43} +(1.89907 + 8.32035i) q^{45} +(1.31510 + 5.76182i) q^{47} +(-0.503658 + 2.20667i) q^{49} +(1.24179 + 1.55716i) q^{51} +(-3.55945 + 1.71414i) q^{53} +(-9.86785 - 12.3739i) q^{55} -4.98565 q^{57} -1.13359 q^{59} +(5.09132 + 6.38431i) q^{61} +(-8.10956 + 3.90536i) q^{63} +(0.193501 + 0.242642i) q^{65} +(0.212822 - 0.932434i) q^{67} +(-4.97776 - 21.8090i) q^{69} +(0.531778 + 2.32987i) q^{71} +(-8.01331 - 3.85900i) q^{73} +8.12261 q^{75} +(10.4074 - 13.0504i) q^{77} +(-0.934726 + 4.09530i) q^{79} +(8.22238 + 3.95969i) q^{81} +(9.64738 - 12.0974i) q^{83} +(2.12163 - 1.02172i) q^{85} +(-7.60183 - 10.7226i) q^{87} +(-4.99275 + 2.40438i) q^{89} +(-0.204080 + 0.255908i) q^{91} +(-7.56848 - 3.64479i) q^{93} +(-1.31170 + 5.74692i) q^{95} +(7.43305 - 9.32075i) q^{97} +16.2191 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - q^{7} - 11 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - q^7 - 11 * q^9	$ 12 q + 3 q^{3} - q^{7} - 11 q^{9} + 2 q^{11} + q^{13} + 9 q^{15} - 12 q^{17} + 6 q^{19} - 13 q^{21} - 35 q^{23} - 6 q^{25} - 39 q^{27} - 14 q^{29} + 8 q^{31} + 33 q^{33} + 18 q^{35} + 31 q^{37} + 22 q^{39} - 30 q^{41} + 5 q^{43} - 20 q^{45} + 33 q^{47} + 37 q^{49} + 15 q^{51} + 13 q^{53} - 36 q^{55} - 38 q^{57} - 38 q^{59} - 5 q^{61} - 4 q^{63} - 20 q^{65} + 7 q^{67} + 20 q^{69} - 3 q^{71} - 22 q^{73} + 2 q^{75} + 10 q^{77} + 60 q^{79} + 88 q^{81} + 39 q^{83} + 38 q^{85} - 9 q^{87} + 39 q^{89} - 61 q^{91} - 54 q^{93} - 55 q^{95} - 19 q^{97} + 8 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - q^7 - 11 * q^9 + 2 * q^11 + q^13 + 9 * q^15 - 12 * q^17 + 6 * q^19 - 13 * q^21 - 35 * q^23 - 6 * q^25 - 39 * q^27 - 14 * q^29 + 8 * q^31 + 33 * q^33 + 18 * q^35 + 31 * q^37 + 22 * q^39 - 30 * q^41 + 5 * q^43 - 20 * q^45 + 33 * q^47 + 37 * q^49 + 15 * q^51 + 13 * q^53 - 36 * q^55 - 38 * q^57 - 38 * q^59 - 5 * q^61 - 4 * q^63 - 20 * q^65 + 7 * q^67 + 20 * q^69 - 3 * q^71 - 22 * q^73 + 2 * q^75 + 10 * q^77 + 60 * q^79 + 88 * q^81 + 39 * q^83 + 38 * q^85 - 9 * q^87 + 39 * q^89 - 61 * q^91 - 54 * q^93 - 55 * q^95 - 19 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{7}\right)$

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			0
$2$		0			0
$3$	1.52179	+	1.90827i	0.878608	+	1.10174i	0.994104	+	0.108431i	$0.0345828\pi$
$3$	1.52179	+	1.90827i	0.878608	+	1.10174i	−0.115496	+	0.993308i	$0.536846\pi$
$4$		0			0
$5$	2.60002	−	1.25211i	1.16277	−	0.559959i	0.249922	−	0.968266i	$-0.419595\pi$
$5$	2.60002	−	1.25211i	1.16277	−	0.559959i	0.912844	+	0.408307i	$0.133881\pi$
$6$		0			0
$7$	1.89765	+	2.37957i	0.717242	+	0.899394i	0.998178	−	0.0603330i	$-0.0192162\pi$
$7$	1.89765	+	2.37957i	0.717242	+	0.899394i	−0.280936	+	0.959727i	$0.590645\pi$
$8$		0			0
$9$	−0.658071	+	2.88320i	−0.219357	+	0.961065i
$10$		0			0
$11$	−1.22038	−	5.34685i	−0.367959	−	1.61214i	−0.732377	−	0.680900i	$-0.761589\pi$
$11$	−1.22038	−	5.34685i	−0.367959	−	1.61214i	0.364417	−	0.931236i	$-0.381268\pi$
$12$		0			0
$13$	0.0239308	+	0.104847i	0.00663720	+	0.0290795i	0.978138	−	0.207956i	$-0.0666812\pi$
$13$	0.0239308	+	0.104847i	0.00663720	+	0.0290795i	−0.971501	+	0.237036i	$0.923824\pi$
$14$		0			0
$15$	6.34605	+	3.05610i	1.63854	+	0.789081i
$16$		0			0
$17$	0.816005			0.197910			0.0989551	−	0.995092i	$-0.468450\pi$
$17$	0.816005			0.197910			0.0989551	+	0.995092i	$0.468450\pi$
$18$		0			0
$19$	−1.27358	+	1.59701i	−0.292178	+	0.366380i	−0.906156	−	0.422943i	$-0.860997\pi$
$19$	−1.27358	+	1.59701i	−0.292178	+	0.366380i	0.613978	+	0.789323i	$0.289568\pi$
$20$		0			0
$21$	−1.65304	+	7.24243i	−0.360722	+	1.58043i
$22$		0			0
$23$	−8.25746	−	3.97659i	−1.72180	−	0.829175i	−0.988854	−	0.148889i	$-0.952430\pi$
$23$	−8.25746	−	3.97659i	−1.72180	−	0.829175i	−0.732946	−	0.680286i	$-0.761855\pi$
$24$		0			0
$25$	2.07491	−	2.60185i	0.414981	−	0.520370i
$26$		0			0
$27$	0.0938049	−	0.0451741i	0.0180528	−	0.00869375i
$28$		0			0
$29$	−5.37657	−	0.304047i	−0.998405	−	0.0564602i
$29$	−5.37657	−	0.304047i	−0.998405	−	0.0564602i
$30$		0			0
$31$	−3.10086	+	1.49330i	−0.556931	+	0.268204i	−0.691106	−	0.722754i	$-0.742876\pi$
$31$	−3.10086	+	1.49330i	−0.556931	+	0.268204i	0.134174	+	0.990958i	$0.457162\pi$
$32$		0			0
$33$	8.34605	−	10.4656i	1.45286	−	1.82183i
$34$		0			0
$35$	7.91340	+	3.81089i	1.33761	+	0.644158i
$36$		0			0
$37$	−1.31456	+	5.75946i	−0.216112	+	0.946850i	0.744207	+	0.667949i	$0.232827\pi$
$37$	−1.31456	+	5.75946i	−0.216112	+	0.946850i	−0.960320	+	0.278901i	$0.910030\pi$
$38$		0			0
$39$	−0.163659	+	0.205223i	−0.0262065	+	0.0328619i
$40$		0			0
$41$	−2.43376			−0.380090			−0.190045	−	0.981775i	$-0.560863\pi$
$41$	−2.43376			−0.380090			−0.190045	+	0.981775i	$0.560863\pi$
$42$		0			0
$43$	4.94123	+	2.37957i	0.753531	+	0.362881i	0.770890	−	0.636968i	$-0.219812\pi$
$43$	4.94123	+	2.37957i	0.753531	+	0.362881i	−0.0173595	+	0.999849i	$0.505526\pi$
$44$		0			0
$45$	1.89907	+	8.32035i	0.283096	+	1.24033i
$46$		0			0
$47$	1.31510	+	5.76182i	0.191827	+	0.840448i	0.975627	+	0.219435i	$0.0704214\pi$
$47$	1.31510	+	5.76182i	0.191827	+	0.840448i	−0.783800	+	0.621013i	$0.786721\pi$
$48$		0			0
$49$	−0.503658	+	2.20667i	−0.0719512	+	0.315239i
$50$		0			0
$51$	1.24179	+	1.55716i	0.173885	+	0.218045i
$52$		0			0
$53$	−3.55945	+	1.71414i	−0.488929	+	0.235456i	−0.662071	−	0.749441i	$-0.730322\pi$
$53$	−3.55945	+	1.71414i	−0.488929	+	0.235456i	0.173142	+	0.984897i	$0.444608\pi$
$54$		0			0
$55$	−9.86785	−	12.3739i	−1.33058	−	1.66849i
$56$		0			0
$57$	−4.98565			−0.660365
$58$		0			0
$59$	−1.13359			−0.147581			−0.0737904	−	0.997274i	$-0.523510\pi$
$59$	−1.13359			−0.147581			−0.0737904	+	0.997274i	$0.523510\pi$
$60$		0			0
$61$	5.09132	+	6.38431i	0.651876	+	0.817427i	0.992432	−	0.122797i	$-0.0391865\pi$
$61$	5.09132	+	6.38431i	0.651876	+	0.817427i	−0.340555	+	0.940224i	$0.610615\pi$
$62$		0			0
$63$	−8.10956	+	3.90536i	−1.02171	+	0.492029i
$64$		0			0
$65$	0.193501	+	0.242642i	0.0240008	+	0.0300961i
$66$		0			0
$67$	0.212822	−	0.932434i	0.0260003	−	0.113915i	−0.960263	−	0.279098i	$-0.909964\pi$
$67$	0.212822	−	0.932434i	0.0260003	−	0.113915i	0.986263	+	0.165183i	$0.0528216\pi$
$68$		0			0
$69$	−4.97776	−	21.8090i	−0.599252	−	2.62549i
$70$		0			0
$71$	0.531778	+	2.32987i	0.0631104	+	0.276505i	0.996631	−	0.0820198i	$-0.0261371\pi$
$71$	0.531778	+	2.32987i	0.0631104	+	0.276505i	−0.933520	+	0.358525i	$0.883280\pi$
$72$		0			0
$73$	−8.01331	−	3.85900i	−0.937886	−	0.451662i	−0.0984633	−	0.995141i	$-0.531393\pi$
$73$	−8.01331	−	3.85900i	−0.937886	−	0.451662i	−0.839423	+	0.543478i	$0.817107\pi$
$74$		0			0
$75$	8.12261			0.937918
$76$		0			0
$77$	10.4074	−	13.0504i	1.18603	−	1.48723i
$78$		0			0
$79$	−0.934726	+	4.09530i	−0.105165	+	0.460758i	0.894735	+	0.446598i	$0.147364\pi$
$79$	−0.934726	+	4.09530i	−0.105165	+	0.460758i	−0.999900	+	0.0141598i	$0.995493\pi$
$80$		0			0
$81$	8.22238	+	3.95969i	0.913598	+	0.439965i
$82$		0			0
$83$	9.64738	−	12.0974i	1.05894	−	1.32787i	0.116609	−	0.993178i	$-0.462798\pi$
$83$	9.64738	−	12.0974i	1.05894	−	1.32787i	0.942329	−	0.334688i	$-0.108631\pi$
$84$		0			0
$85$	2.12163	−	1.02172i	0.230123	−	0.110822i
$86$		0			0
$87$	−7.60183	−	10.7226i	−0.815002	−	1.14959i
$88$		0			0
$89$	−4.99275	+	2.40438i	−0.529231	+	0.254864i	−0.679364	−	0.733802i	$-0.737744\pi$
$89$	−4.99275	+	2.40438i	−0.529231	+	0.254864i	0.150133	+	0.988666i	$0.452030\pi$
$90$		0			0
$91$	−0.204080	+	0.255908i	−0.0213934	+	0.0268265i
$92$		0			0
$93$	−7.56848	−	3.64479i	−0.784815	−	0.377947i
$94$		0			0
$95$	−1.31170	+	5.74692i	−0.134577	+	0.589622i
$96$		0			0
$97$	7.43305	−	9.32075i	0.754712	−	0.946379i	−0.245020	−	0.969518i	$-0.578795\pi$
$97$	7.43305	−	9.32075i	0.754712	−	0.946379i	0.999732	+	0.0231388i	$0.00736597\pi$
$98$		0			0
$99$	16.2191			1.63008
$100$		0			0
$101$	8.47400	+	4.08086i	0.843194	+	0.406061i	0.805047	−	0.593211i	$-0.202140\pi$
$101$	8.47400	+	4.08086i	0.843194	+	0.406061i	0.0381473	+	0.999272i	$0.487854\pi$
$102$		0			0
$103$	−2.52053	−	11.0432i	−0.248355	−	1.08811i	−0.933181	−	0.359407i	$-0.882979\pi$
$103$	−2.52053	−	11.0432i	−0.248355	−	1.08811i	0.684826	−	0.728707i	$-0.259878\pi$
$104$		0			0
$105$	4.77035	+	20.9003i	0.465539	+	2.03966i
$106$		0			0
$107$	2.32690	−	10.1948i	0.224950	−	0.985570i	−0.728743	−	0.684787i	$-0.759895\pi$
$107$	2.32690	−	10.1948i	0.224950	−	0.985570i	0.953693	−	0.300782i	$-0.0972478\pi$
$108$		0			0
$109$	−8.68441	−	10.8899i	−0.831815	−	1.04306i	−0.998372	−	0.0570315i	$-0.981836\pi$
$109$	−8.68441	−	10.8899i	−0.831815	−	1.04306i	0.166557	−	0.986032i	$-0.446735\pi$
$110$		0			0
$111$	−12.9911	+	6.25618i	−1.23306	+	0.593810i
$112$		0			0
$113$	−8.17959	−	10.2569i	−0.769471	−	0.964886i	0.230496	−	0.973073i	$-0.425965\pi$
$113$	−8.17959	−	10.2569i	−0.769471	−	0.964886i	−0.999966	+	0.00818761i	$0.997394\pi$
$114$		0			0
$115$	−26.4487			−2.46635
$116$		0			0
$117$	−0.318044			−0.0294032
$118$		0			0
$119$	1.54849	+	1.94174i	0.141950	+	0.177999i
$120$		0			0
$121$	−17.1888	+	8.27769i	−1.56262	+	0.752517i
$122$		0			0
$123$	−3.70368	−	4.64427i	−0.333950	−	0.418760i
$124$		0			0
$125$	−1.07375	+	4.70440i	−0.0960390	+	0.420774i
$126$		0			0
$127$	−0.298178	−	1.30640i	−0.0264590	−	0.115925i	0.959974	−	0.280090i	$-0.0903642\pi$
$127$	−0.298178	−	1.30640i	−0.0264590	−	0.115925i	−0.986433	+	0.164165i	$0.947507\pi$
$128$		0			0
$129$	2.97867	+	13.0504i	0.262257	+	1.14902i
$130$		0			0
$131$	4.60153	+	2.21598i	0.402038	+	0.193611i	0.623965	−	0.781452i	$-0.285521\pi$
$131$	4.60153	+	2.21598i	0.402038	+	0.193611i	−0.221928	+	0.975063i	$0.571235\pi$
$132$		0			0
$133$	−6.21700			−0.539083
$134$		0			0
$135$	0.187332	−	0.234907i	0.0161230	−	0.0202176i
$136$		0			0
$137$	−0.265477	+	1.16313i	−0.0226812	+	0.0993729i	−0.985002	−	0.172545i	$-0.944801\pi$
$137$	−0.265477	+	1.16313i	−0.0226812	+	0.0993729i	0.962320	+	0.271918i	$0.0876580\pi$
$138$		0			0
$139$	9.08386	+	4.37456i	0.770483	+	0.371045i	0.777462	−	0.628931i	$-0.216507\pi$
$139$	9.08386	+	4.37456i	0.770483	+	0.371045i	−0.00697834	+	0.999976i	$0.502221\pi$
$140$		0			0
$141$	−8.99379	+	11.2779i	−0.757414	+	0.949767i
$142$		0			0
$143$	0.531399	−	0.255908i	0.0444378	−	0.0214001i
$144$		0			0
$145$	−14.3599	+	5.94151i	−1.19253	+	0.493415i
$146$		0			0
$147$	−4.97738	+	2.39698i	−0.410528	+	0.197700i
$148$		0			0
$149$	−1.09170	+	1.36895i	−0.0894359	+	0.112149i	−0.824536	−	0.565810i	$-0.808564\pi$
$149$	−1.09170	+	1.36895i	−0.0894359	+	0.112149i	0.735100	+	0.677959i	$0.237135\pi$
$150$		0			0
$151$	−0.508231	−	0.244751i	−0.0413593	−	0.0199176i	0.413090	−	0.910690i	$-0.364450\pi$
$151$	−0.508231	−	0.244751i	−0.0413593	−	0.0199176i	−0.454449	+	0.890773i	$0.650164\pi$
$152$		0			0
$153$	−0.536989	+	2.35270i	−0.0434130	+	0.190205i
$154$		0			0
$155$	−6.19255	+	7.76521i	−0.497398	+	0.623717i
$156$		0			0
$157$	17.3463			1.38439			0.692193	−	0.721712i	$-0.256645\pi$
$157$	17.3463			1.38439			0.692193	+	0.721712i	$0.256645\pi$
$158$		0			0
$159$	−8.68780	−	4.18382i	−0.688987	−	0.331799i
$160$		0			0
$161$	−6.20717	−	27.1954i	−0.489193	−	2.14330i
$162$		0			0
$163$	2.58544	+	11.3276i	0.202507	+	0.887243i	0.969404	+	0.245472i	$0.0789430\pi$
$163$	2.58544	+	11.3276i	0.202507	+	0.887243i	−0.766896	+	0.641771i	$0.778200\pi$
$164$		0			0
$165$	8.59588	−	37.6610i	0.669188	−	2.93190i
$166$		0			0
$167$	5.30395	+	6.65094i	0.410432	+	0.514665i	0.943484	−	0.331417i	$-0.107527\pi$
$167$	5.30395	+	6.65094i	0.410432	+	0.514665i	−0.533053	+	0.846082i	$0.678955\pi$
$168$		0			0
$169$	11.7022	−	5.63547i	0.900167	−	0.433498i
$170$		0			0
$171$	−3.76640	−	4.72292i	−0.288024	−	0.361170i
$172$		0			0
$173$	10.1868			0.774484			0.387242	−	0.921978i	$-0.373428\pi$
$173$	10.1868			0.774484			0.387242	+	0.921978i	$0.373428\pi$
$174$		0			0
$175$	10.1287			0.765660
$176$		0			0
$177$	−1.72509	−	2.16319i	−0.129666	−	0.162595i
$178$		0			0
$179$	4.31512	−	2.07805i	0.322527	−	0.155321i	−0.265613	−	0.964080i	$-0.585574\pi$
$179$	4.31512	−	2.07805i	0.322527	−	0.155321i	0.588141	+	0.808759i	$0.299860\pi$
$180$		0			0
$181$	0.459607	+	0.576329i	0.0341623	+	0.0428382i	0.798619	−	0.601837i	$-0.205564\pi$
$181$	0.459607	+	0.576329i	0.0341623	+	0.0428382i	−0.764457	+	0.644675i	$0.776993\pi$
$182$		0			0
$183$	−4.43504	+	19.4312i	−0.327848	+	1.43640i
$184$		0			0
$185$	3.79357	+	16.6207i	0.278909	+	1.22198i
$186$		0			0
$187$	−0.995839	−	4.36305i	−0.0728229	−	0.319058i
$188$		0			0
$189$	0.285503	+	0.137491i	0.0207673	+	0.0100010i
$190$		0			0
$191$	0.120340			0.00870752			0.00435376	−	0.999991i	$-0.498614\pi$
$191$	0.120340			0.00870752			0.00435376	+	0.999991i	$0.498614\pi$
$192$		0			0
$193$	−13.1799	+	16.5270i	−0.948707	+	1.18964i	0.0330411	+	0.999454i	$0.489481\pi$
$193$	−13.1799	+	16.5270i	−0.948707	+	1.18964i	−0.981748	+	0.190187i	$0.939091\pi$
$194$		0			0
$195$	−0.168558	+	0.738502i	−0.0120707	+	0.0528853i
$196$		0			0
$197$	14.4345	+	6.95129i	1.02842	+	0.495259i	0.870487	−	0.492191i	$-0.163804\pi$
$197$	14.4345	+	6.95129i	1.02842	+	0.495259i	0.157929	+	0.987450i	$0.449518\pi$
$198$		0			0
$199$	−8.63982	+	10.8340i	−0.612461	+	0.768001i	−0.987262	−	0.159104i	$-0.949140\pi$
$199$	−8.63982	+	10.8340i	−0.612461	+	0.768001i	0.374801	+	0.927105i	$0.377711\pi$
$200$		0			0
$201$	2.10321	−	1.01285i	0.148349	−	0.0714410i
$202$		0			0
$203$	−9.47933	−	13.3709i	−0.665318	−	0.938455i
$204$		0			0
$205$	−6.32784	+	3.04733i	−0.441955	+	0.212834i
$206$		0			0
$207$	16.8993	−	21.1910i	1.17458	−	1.47288i
$208$		0			0
$209$	10.0932	+	4.86065i	0.698164	+	0.336218i
$210$		0			0
$211$	−5.41004	+	23.7029i	−0.372442	+	1.63178i	0.347455	+	0.937696i	$0.387046\pi$
$211$	−5.41004	+	23.7029i	−0.372442	+	1.63178i	−0.719898	+	0.694080i	$0.755811\pi$
$212$		0			0
$213$	−3.63676	+	4.56036i	−0.249187	+	0.312470i
$214$		0			0
$215$	15.8268			1.07938
$216$		0			0
$217$	−9.43774	−	4.54498i	−0.640676	−	0.308533i
$218$		0			0
$219$	−4.83058	−	21.1641i	−0.326420	−	1.43014i
$220$		0			0
$221$	0.0195276	+	0.0855561i	0.00131357	+	0.00575512i
$222$		0			0
$223$	2.31976	−	10.1636i	0.155343	−	0.680602i	−0.835937	−	0.548826i	$-0.815075\pi$
$223$	2.31976	−	10.1636i	0.155343	−	0.680602i	0.991280	−	0.131776i	$-0.0420679\pi$
$224$		0			0
$225$	6.13621	+	7.69457i	0.409081	+	0.512971i
$226$		0			0
$227$	18.9036	−	9.10351i	1.25468	−	0.604221i	0.315916	−	0.948787i	$-0.397688\pi$
$227$	18.9036	−	9.10351i	1.25468	−	0.604221i	0.938762	+	0.344566i	$0.111974\pi$
$228$		0			0
$229$	0.613583	+	0.769409i	0.0405467	+	0.0508440i	0.801691	−	0.597738i	$-0.203934\pi$
$229$	0.613583	+	0.769409i	0.0405467	+	0.0508440i	−0.761145	+	0.648582i	$0.775362\pi$
$230$		0			0
$231$	40.7415			2.68060
$232$		0			0
$233$	17.3778			1.13846			0.569229	−	0.822179i	$-0.307242\pi$
$233$	17.3778			1.13846			0.569229	+	0.822179i	$0.307242\pi$
$234$		0			0
$235$	10.6337	+	13.3342i	0.693666	+	0.869829i
$236$		0			0
$237$	−9.23740	+	4.44850i	−0.600033	+	0.288961i
$238$		0			0
$239$	0.718032	+	0.900383i	0.0464456	+	0.0582410i	0.804512	−	0.593937i	$-0.202427\pi$
$239$	0.718032	+	0.900383i	0.0464456	+	0.0582410i	−0.758066	+	0.652178i	$0.773856\pi$
$240$		0			0
$241$	4.38541	−	19.2137i	0.282489	−	1.23767i	−0.612102	−	0.790779i	$-0.709676\pi$
$241$	4.38541	−	19.2137i	0.282489	−	1.23767i	0.894591	−	0.446886i	$-0.147467\pi$
$242$		0			0
$243$	4.88711	+	21.4118i	0.313508	+	1.37357i
$244$		0			0
$245$	1.45346	+	6.36803i	0.0928582	+	0.406838i
$246$		0			0
$247$	−0.197920	−	0.0953135i	−0.0125934	−	0.00606465i
$248$		0			0
$249$	37.7665			2.39335
$250$		0			0
$251$	5.30247	−	6.64908i	0.334689	−	0.419686i	−0.585800	−	0.810456i	$-0.699220\pi$
$251$	5.30247	−	6.64908i	0.334689	−	0.419686i	0.920489	+	0.390769i	$0.127791\pi$
$252$		0			0
$253$	−11.1849	+	49.0044i	−0.703190	+	3.08088i
$254$		0			0
$255$	5.17841	+	2.49379i	0.324285	+	0.156167i
$256$		0			0
$257$	14.1670	−	17.7648i	0.883711	−	1.10814i	−0.109749	−	0.993959i	$-0.535005\pi$
$257$	14.1670	−	17.7648i	0.883711	−	1.10814i	0.993460	−	0.114179i	$-0.0364237\pi$
$258$		0			0
$259$	−16.1996	+	7.80133i	−1.00660	+	0.484751i
$260$		0			0
$261$	4.41479	−	15.3016i	0.273269	−	0.947147i
$262$		0			0
$263$	−23.4635	+	11.2994i	−1.44682	+	0.696753i	−0.982040	−	0.188672i	$-0.939582\pi$
$263$	−23.4635	+	11.2994i	−1.44682	+	0.696753i	−0.464782	+	0.885425i	$0.653867\pi$
$264$		0			0
$265$	−7.10838	+	8.91362i	−0.436664	+	0.547560i
$266$		0			0
$267$	−12.1861	−	5.86854i	−0.745780	−	0.359149i
$268$		0			0
$269$	−0.324096	+	1.41996i	−0.0197605	+	0.0865764i	−0.983847	−	0.179013i	$-0.942709\pi$
$269$	−0.324096	+	1.41996i	−0.0197605	+	0.0865764i	0.964086	+	0.265590i	$0.0855666\pi$
$270$		0			0
$271$	6.81360	−	8.54398i	0.413897	−	0.519010i	−0.530559	−	0.847648i	$-0.678018\pi$
$271$	6.81360	−	8.54398i	0.413897	−	0.519010i	0.944456	+	0.328638i	$0.106590\pi$
$272$		0			0
$273$	−0.798909			−0.0483522
$274$		0			0
$275$	−16.4439	−	7.91896i	−0.991604	−	0.477531i
$276$		0			0
$277$	0.550164	+	2.41043i	0.0330562	+	0.144829i	0.988763	−	0.149492i	$-0.0477638\pi$
$277$	0.550164	+	2.41043i	0.0330562	+	0.144829i	−0.955707	+	0.294321i	$0.904907\pi$
$278$		0			0
$279$	−2.26488	−	9.92309i	−0.135595	−	0.594080i
$280$		0			0
$281$	0.0415328	−	0.181967i	0.00247764	−	0.0108553i	−0.973674	−	0.227945i	$-0.926799\pi$
$281$	0.0415328	−	0.181967i	0.00247764	−	0.0108553i	0.976152	+	0.217090i	$0.0696565\pi$
$282$		0			0
$283$	11.5026	+	14.4238i	0.683758	+	0.857405i	0.995694	−	0.0926981i	$-0.0295491\pi$
$283$	11.5026	+	14.4238i	0.683758	+	0.857405i	−0.311937	+	0.950103i	$0.600978\pi$
$284$		0			0
$285$	−12.9628	+	6.24256i	−0.767850	+	0.369777i
$286$		0			0
$287$	−4.61841	−	5.79131i	−0.272616	−	0.341850i
$288$		0			0
$289$	−16.3341			−0.960832
$290$		0			0
$291$	29.0981			1.70576
$292$		0			0
$293$	−0.970339	−	1.21677i	−0.0566878	−	0.0710843i	0.752679	−	0.658387i	$-0.228761\pi$
$293$	−0.970339	−	1.21677i	−0.0566878	−	0.0710843i	−0.809367	+	0.587303i	$0.800190\pi$
$294$		0			0
$295$	−2.94736	+	1.41937i	−0.171602	+	0.0826391i
$296$		0			0
$297$	−0.356017	−	0.446431i	−0.0206582	−	0.0259046i
$298$		0			0
$299$	0.219328	−	0.960937i	0.0126840	−	0.0555724i
$300$		0			0
$301$	3.71434	+	16.2736i	0.214091	+	0.937995i
$302$		0			0
$303$	5.10829	+	22.3809i	0.293464	+	1.28575i
$304$		0			0
$305$	21.2314	+	10.2245i	1.21571	+	0.585453i
$306$		0			0
$307$	−19.6000			−1.11863			−0.559316	−	0.828955i	$-0.688936\pi$
$307$	−19.6000			−1.11863			−0.559316	+	0.828955i	$0.688936\pi$
$308$		0			0
$309$	17.2376	−	21.6152i	0.980611	−	1.22965i
$310$		0			0
$311$	−5.88970	+	25.8045i	−0.333974	+	1.46324i	0.477388	+	0.878693i	$0.341584\pi$
$311$	−5.88970	+	25.8045i	−0.333974	+	1.46324i	−0.811362	+	0.584544i	$0.801273\pi$
$312$		0			0
$313$	−19.6456	−	9.46081i	−1.11043	−	0.534756i	−0.213509	−	0.976941i	$-0.568489\pi$
$313$	−19.6456	−	9.46081i	−1.11043	−	0.534756i	−0.896924	+	0.442185i	$0.854204\pi$
$314$		0			0
$315$	−16.1951	+	20.3080i	−0.912492	+	1.14423i
$316$		0			0
$317$	−17.0540	+	8.21276i	−0.957846	+	0.461274i	−0.846430	−	0.532500i	$-0.821253\pi$
$317$	−17.0540	+	8.21276i	−0.957846	+	0.461274i	−0.111416	+	0.993774i	$0.535539\pi$
$318$		0			0
$319$	4.93579	+	29.1188i	0.276351	+	1.63034i
$320$		0			0
$321$	22.9955	−	11.0740i	1.28348	−	0.618093i
$322$		0			0
$323$	−1.03924	+	1.30317i	−0.0578251	+	0.0725104i
$324$		0			0
$325$	0.322452	+	0.155285i	0.0178864	+	0.00861364i
$326$		0			0
$327$	7.56498	−	33.1444i	0.418345	−	1.83289i
$328$		0			0
$329$	−11.2151	+	14.0633i	−0.618307	+	0.775333i
$330$		0			0
$331$	−17.7806			−0.977311			−0.488656	−	0.872477i	$-0.662513\pi$
$331$	−17.7806			−0.977311			−0.488656	+	0.872477i	$0.662513\pi$
$332$		0			0
$333$	−15.7406	−	7.58027i	−0.862579	−	0.415396i
$334$		0			0
$335$	−0.614164	−	2.69083i	−0.0335553	−	0.147016i
$336$		0			0
$337$	−0.631745	−	2.76785i	−0.0344133	−	0.150775i	0.954802	−	0.297242i	$-0.0960668\pi$
$337$	−0.631745	−	2.76785i	−0.0344133	−	0.150775i	−0.989216	+	0.146467i	$0.953210\pi$
$338$		0			0
$339$	7.12523	−	31.2177i	0.386990	−	1.69551i
$340$		0			0
$341$	11.7687	+	14.7574i	0.637309	+	0.799160i
$342$		0			0
$343$	12.9885	−	6.25495i	0.701315	−	0.337736i
$344$		0			0
$345$	−40.2495	−	50.4712i	−2.16696	−	2.71728i
$346$		0			0
$347$	7.14376			0.383497			0.191749	−	0.981444i	$-0.438584\pi$
$347$	7.14376			0.383497			0.191749	+	0.981444i	$0.438584\pi$
$348$		0			0
$349$	8.26091			0.442197			0.221098	−	0.975252i	$-0.429036\pi$
$349$	8.26091			0.442197			0.221098	+	0.975252i	$0.429036\pi$
$350$		0			0
$351$	0.00698121	+	0.00875416i	0.000372629	+	0.000467262i
$352$		0			0
$353$	−16.3812	+	7.88877i	−0.871883	+	0.419877i	−0.815653	−	0.578541i	$-0.803622\pi$
$353$	−16.3812	+	7.88877i	−0.871883	+	0.419877i	−0.0562300	+	0.998418i	$0.517908\pi$
$354$		0			0
$355$	4.29988	+	5.39188i	0.228214	+	0.286171i
$356$		0			0
$357$	−1.34889	+	5.90986i	−0.0713907	+	0.312783i
$358$		0			0
$359$	−4.40754	−	19.3107i	−0.232621	−	1.01918i	−0.947456	−	0.319887i	$-0.896355\pi$
$359$	−4.40754	−	19.3107i	−0.232621	−	1.01918i	0.714835	−	0.699294i	$-0.246502\pi$
$360$		0			0
$361$	3.29944	+	14.4558i	0.173655	+	0.760831i
$362$		0			0
$363$	−41.9539	−	20.2039i	−2.20201	−	1.06043i
$364$		0			0
$365$	−25.6667			−1.34345
$366$		0			0
$367$	−2.39019	+	2.99720i	−0.124767	+	0.156453i	−0.840292	−	0.542135i	$-0.817616\pi$
$367$	−2.39019	+	2.99720i	−0.124767	+	0.156453i	0.715525	+	0.698587i	$0.246188\pi$
$368$		0			0
$369$	1.60159	−	7.01701i	0.0833753	−	0.365291i
$370$		0			0
$371$	−10.8335	−	5.21714i	−0.562448	−	0.270860i
$372$		0			0
$373$	11.3336	−	14.2118i	0.586830	−	0.735861i	−0.396431	−	0.918064i	$-0.629751\pi$
$373$	11.3336	−	14.2118i	0.586830	−	0.735861i	0.983261	+	0.182203i	$0.0583229\pi$
$374$		0			0
$375$	−10.6113	+	5.11012i	−0.547964	+	0.263886i
$376$		0			0
$377$	−0.0967869	−	0.570996i	−0.00498478	−	0.0294078i
$378$		0			0
$379$	33.6665	−	16.2129i	1.72933	−	0.832803i	0.742744	−	0.669576i	$-0.233524\pi$
$379$	33.6665	−	16.2129i	1.72933	−	0.832803i	0.986589	−	0.163227i	$-0.0521902\pi$
$380$		0			0
$381$	2.03920	−	2.55708i	0.104472	−	0.131003i
$382$		0			0
$383$	−10.6536	−	5.13050i	−0.544373	−	0.262156i	0.141424	−	0.989949i	$-0.454832\pi$
$383$	−10.6536	−	5.13050i	−0.544373	−	0.262156i	−0.685797	+	0.727793i	$0.740546\pi$
$384$		0			0
$385$	10.7189	−	46.9625i	0.546285	−	2.39343i
$386$		0			0
$387$	−10.1125	+	12.6806i	−0.514045	+	0.644592i
$388$		0			0
$389$	−29.8660			−1.51426			−0.757132	−	0.653262i	$-0.773400\pi$
$389$	−29.8660			−1.51426			−0.757132	+	0.653262i	$0.773400\pi$
$390$		0			0
$391$	−6.73813	−	3.24491i	−0.340762	−	0.164102i
$392$		0			0
$393$	2.77389	+	12.1532i	0.139924	+	0.613049i
$394$		0			0
$395$	2.69744	+	11.8183i	0.135723	+	0.594641i
$396$		0			0
$397$	1.80314	−	7.90008i	0.0904971	−	0.396494i	−0.909310	−	0.416119i	$-0.863390\pi$
$397$	1.80314	−	7.90008i	0.0904971	−	0.396494i	0.999807	+	0.0196250i	$0.00624724\pi$
$398$		0			0
$399$	−9.46099	−	11.8637i	−0.473642	−	0.593928i
$400$		0			0
$401$	−5.35839	+	2.58047i	−0.267585	+	0.128862i	−0.562866	−	0.826548i	$-0.690301\pi$
$401$	−5.35839	+	2.58047i	−0.267585	+	0.128862i	0.295280	+	0.955411i	$0.404587\pi$
$402$		0			0
$403$	−0.230774	−	0.289382i	−0.0114957	−	0.0144151i
$404$		0			0
$405$	26.3363			1.30866
$406$		0			0
$407$	32.3993			1.60597
$408$		0			0
$409$	8.19234	+	10.2729i	0.405085	+	0.507960i	0.941971	−	0.335694i	$-0.108971\pi$
$409$	8.19234	+	10.2729i	0.405085	+	0.507960i	−0.536886	+	0.843655i	$0.680400\pi$
$410$		0			0
$411$	−2.62356	+	1.26344i	−0.129411	+	0.0623210i
$412$		0			0
$413$	−2.15115	−	2.69746i	−0.105851	−	0.132733i
$414$		0			0
$415$	9.93616	−	43.5332i	0.487747	−	2.13696i
$416$		0			0
$417$	5.47593	+	23.9916i	0.268157	+	1.17487i
$418$		0			0
$419$	4.93134	+	21.6056i	0.240912	+	1.05550i	0.940189	+	0.340653i	$0.110648\pi$
$419$	4.93134	+	21.6056i	0.240912	+	1.05550i	−0.699277	+	0.714850i	$0.746495\pi$
$420$		0			0
$421$	−21.4900	−	10.3490i	−1.04736	−	0.504381i	−0.170614	−	0.985338i	$-0.554575\pi$
$421$	−21.4900	−	10.3490i	−1.04736	−	0.504381i	−0.876744	+	0.480957i	$0.840289\pi$
$422$		0			0
$423$	−17.4779			−0.849804
$424$		0			0
$425$	1.69313	−	2.12312i	0.0821291	−	0.102987i
$426$		0			0
$427$	−5.53041	+	24.2303i	−0.267635	+	1.17259i
$428$		0			0
$429$	1.29702	+	0.624612i	0.0626208	+	0.0301566i
$430$		0			0
$431$	0.484432	−	0.607459i	0.0233343	−	0.0292603i	−0.770027	−	0.638011i	$-0.779758\pi$
$431$	0.484432	−	0.607459i	0.0233343	−	0.0292603i	0.793362	+	0.608751i	$0.208329\pi$
$432$		0			0
$433$	−0.551807	+	0.265736i	−0.0265182	+	0.0127705i	−0.447096	−	0.894486i	$-0.647542\pi$
$433$	−0.551807	+	0.265736i	−0.0265182	+	0.0127705i	0.420578	+	0.907257i	$0.361827\pi$
$434$		0			0
$435$	−33.1908	−	18.3608i	−1.59138	−	0.880335i
$436$		0			0
$437$	16.8672	−	8.12280i	0.806866	−	0.388566i
$438$		0			0
$439$	6.79310	−	8.51828i	0.324217	−	0.406555i	−0.592834	−	0.805325i	$-0.701991\pi$
$439$	6.79310	−	8.51828i	0.324217	−	0.406555i	0.917051	+	0.398769i	$0.130563\pi$
$440$		0			0
$441$	−6.03082	−	2.90429i	−0.287182	−	0.138300i
$442$		0			0
$443$	−7.74994	+	33.9547i	−0.368211	+	1.61324i	0.363482	+	0.931601i	$0.381588\pi$
$443$	−7.74994	+	33.9547i	−0.368211	+	1.61324i	−0.731692	+	0.681635i	$0.761269\pi$
$444$		0			0
$445$	−9.97073	+	12.5029i	−0.472658	+	0.592695i
$446$		0			0
$447$	−4.27368			−0.202138
$448$		0			0
$449$	−4.52504	−	2.17914i	−0.213550	−	0.102840i	0.324051	−	0.946040i	$-0.394955\pi$
$449$	−4.52504	−	2.17914i	−0.213550	−	0.102840i	−0.537601	+	0.843199i	$0.680669\pi$
$450$		0			0
$451$	2.97012	+	13.0130i	0.139858	+	0.612756i
$452$		0			0
$453$	−0.306372	−	1.34230i	−0.0143946	−	0.0630669i
$454$		0			0
$455$	−0.210189	+	0.920897i	−0.00985380	+	0.0431723i
$456$		0			0
$457$	23.8438	+	29.8992i	1.11537	+	1.39863i	0.907285	+	0.420516i	$0.138151\pi$
$457$	23.8438	+	29.8992i	1.11537	+	1.39863i	0.208083	+	0.978111i	$0.433278\pi$
$458$		0			0
$459$	0.0765452	−	0.0368622i	0.00357283	−	0.00172058i
$460$		0			0
$461$	16.2084	+	20.3246i	0.754898	+	0.946613i	0.999737	−	0.0229513i	$-0.00730628\pi$
$461$	16.2084	+	20.3246i	0.754898	+	0.946613i	−0.244838	+	0.969564i	$0.578735\pi$
$462$		0			0
$463$	−17.3502			−0.806331			−0.403166	−	0.915127i	$-0.632090\pi$
$463$	−17.3502			−0.806331			−0.403166	+	0.915127i	$0.632090\pi$
$464$		0			0
$465$	−24.2419			−1.12419
$466$		0			0
$467$	−18.2308	−	22.8606i	−0.843619	−	1.05786i	−0.997562	−	0.0697846i	$-0.977769\pi$
$467$	−18.2308	−	22.8606i	−0.843619	−	1.05786i	0.153943	−	0.988080i	$-0.450803\pi$
$468$		0			0
$469$	2.62265	−	1.26300i	0.121103	−	0.0583201i
$470$		0			0
$471$	26.3975	+	33.1014i	1.21633	+	1.52523i
$472$		0			0
$473$	6.69301	−	29.3240i	0.307745	−	1.34832i
$474$		0			0
$475$	1.51264	+	6.62731i	0.0694047	+	0.304082i
$476$		0			0
$477$	−2.59984	−	11.3906i	−0.119038	−	0.521541i
$478$		0			0
$479$	38.7300	+	18.6514i	1.76962	+	0.852204i	0.966616	+	0.256231i	$0.0824807\pi$
$479$	38.7300	+	18.6514i	1.76962	+	0.852204i	0.803004	+	0.595973i	$0.203234\pi$
$480$		0			0
$481$	−0.635324			−0.0289683
$482$		0			0
$483$	42.4501	−	53.2307i	1.93154	−	2.42208i
$484$		0			0
$485$	7.65555	−	33.5412i	0.347621	−	1.52303i
$486$		0			0
$487$	−9.00377	−	4.33599i	−0.408000	−	0.196482i	0.218616	−	0.975811i	$-0.429846\pi$
$487$	−9.00377	−	4.33599i	−0.408000	−	0.196482i	−0.626615	+	0.779329i	$0.715560\pi$
$488$		0			0
$489$	−17.6815	+	22.1719i	−0.799586	+	1.00265i
$490$		0			0
$491$	3.42912	−	1.65138i	0.154754	−	0.0745257i	−0.354904	−	0.934903i	$-0.615486\pi$
$491$	3.42912	−	1.65138i	0.154754	−	0.0745257i	0.509658	+	0.860377i	$0.329772\pi$
$492$		0			0
$493$	−4.38731	−	0.248104i	−0.197595	−	0.0111740i
$494$		0			0
$495$	42.1701	−	20.3080i	1.89540	−	0.912779i
$496$		0			0
$497$	−4.53497	+	5.68667i	−0.203421	+	0.255082i
$498$		0			0
$499$	−25.5824	−	12.3198i	−1.14522	−	0.551511i	−0.237629	−	0.971356i	$-0.576370\pi$
$499$	−25.5824	−	12.3198i	−1.14522	−	0.551511i	−0.907596	+	0.419845i	$0.862084\pi$
$500$		0			0
$501$	−4.62027	+	20.2427i	−0.206418	+	0.904377i
$502$		0			0
$503$	−1.01894	+	1.27771i	−0.0454321	+	0.0569701i	−0.804028	−	0.594591i	$-0.797314\pi$
$503$	−1.01894	+	1.27771i	−0.0454321	+	0.0569701i	0.758596	+	0.651561i	$0.225886\pi$
$504$		0			0
$505$	27.1423			1.20781
$506$		0			0
$507$	28.5623	+	13.7549i	1.26850	+	0.610875i
$508$		0			0
$509$	−8.11548	−	35.5563i	−0.359712	−	1.57600i	−0.753910	−	0.656978i	$-0.771835\pi$
$509$	−8.11548	−	35.5563i	−0.359712	−	1.57600i	0.394198	−	0.919026i	$-0.371023\pi$
$510$		0			0
$511$	−6.02363	−	26.3913i	−0.266470	−	1.16748i
$512$		0			0
$513$	−0.0473241	+	0.207340i	−0.00208941	+	0.00915430i
$514$		0			0
$515$	−20.3806	−	25.5565i	−0.898078	−	1.12615i
$516$		0			0
$517$	29.2027	−	14.0633i	1.28433	−	0.618502i
$518$		0			0
$519$	15.5021	+	19.4391i	0.680468	+	0.853280i
$520$		0			0
$521$	−37.4549			−1.64093			−0.820465	−	0.571697i	$-0.806285\pi$
$521$	−37.4549			−1.64093			−0.820465	+	0.571697i	$0.806285\pi$
$522$		0			0
$523$	−37.9515			−1.65950			−0.829751	−	0.558133i	$-0.811518\pi$
$523$	−37.9515			−1.65950			−0.829751	+	0.558133i	$0.811518\pi$
$524$		0			0
$525$	15.4138	+	19.3283i	0.672715	+	0.843558i
$526$		0			0
$527$	−2.53032	+	1.21854i	−0.110222	+	0.0530803i
$528$		0			0
$529$	38.0322	+	47.6909i	1.65357	+	2.07352i
$530$		0			0
$531$	0.745982	−	3.26836i	0.0323729	−	0.141835i
$532$		0			0
$533$	−0.0582417	−	0.255174i	−0.00252273	−	0.0110528i
$534$		0			0
$535$	−6.71499	−	29.4203i	−0.290314	−	1.27195i
$536$		0			0
$537$	10.5322	+	5.07204i	0.454498	+	0.218875i
$538$		0			0
$539$	12.4134			0.534683
$540$		0			0
$541$	15.7496	−	19.7494i	0.677128	−	0.849091i	−0.317958	−	0.948105i	$-0.602997\pi$
$541$	15.7496	−	19.7494i	0.677128	−	0.849091i	0.995086	+	0.0990135i	$0.0315687\pi$
$542$		0			0
$543$	−0.400363	+	1.75411i	−0.0171812	+	0.0752759i
$544$		0			0
$545$	−36.2150	−	17.4402i	−1.55128	−	0.747056i
$546$		0			0
$547$	9.32887	−	11.6980i	0.398874	−	0.500172i	−0.541318	−	0.840818i	$-0.682074\pi$
$547$	9.32887	−	11.6980i	0.398874	−	0.500172i	0.940192	+	0.340646i	$0.110646\pi$
$548$		0			0
$549$	−21.7577	+	10.4779i	−0.928595	+	0.447188i
$550$		0			0
$551$	7.33304	−	8.19923i	0.312398	−	0.349299i
$552$		0			0
$553$	−11.5188	+	5.54718i	−0.489831	+	0.235890i
$554$		0			0
$555$	−25.9437	+	32.5324i	−1.10125	+	1.38092i
$556$		0			0
$557$	−21.3547	−	10.2839i	−0.904827	−	0.435741i	−0.0771968	−	0.997016i	$-0.524597\pi$
$557$	−21.3547	−	10.2839i	−0.904827	−	0.435741i	−0.827630	+	0.561274i	$0.810311\pi$
$558$		0			0
$559$	−0.131245	+	0.575021i	−0.00555106	+	0.0243208i
$560$		0			0
$561$	6.81042	−	8.53999i	0.287536	−	0.360559i
$562$		0			0
$563$	−38.7490			−1.63308			−0.816538	−	0.577292i	$-0.804109\pi$
$563$	−38.7490			−1.63308			−0.816538	+	0.577292i	$0.804109\pi$
$564$		0			0
$565$	−34.1098	−	16.4264i	−1.43501	−	0.691065i
$566$		0			0
$567$	6.18079	+	27.0798i	0.259569	+	1.13725i
$568$		0			0
$569$	−0.256408	−	1.12340i	−0.0107492	−	0.0470953i	0.969269	−	0.246004i	$-0.0791175\pi$
$569$	−0.256408	−	1.12340i	−0.0107492	−	0.0470953i	−0.980018	+	0.198908i	$0.936260\pi$
$570$		0			0
$571$	3.71708	−	16.2856i	0.155555	−	0.681530i	−0.835658	−	0.549251i	$-0.814913\pi$
$571$	3.71708	−	16.2856i	0.155555	−	0.681530i	0.991212	−	0.132279i	$-0.0422296\pi$
$572$		0			0
$573$	0.183133	+	0.229642i	0.00765049	+	0.00959342i
$574$		0			0
$575$	−27.4800	+	13.2336i	−1.14599	+	0.551881i
$576$		0			0
$577$	−8.71275	−	10.9254i	−0.362717	−	0.454832i	0.566667	−	0.823947i	$-0.308232\pi$
$577$	−8.71275	−	10.9254i	−0.362717	−	0.454832i	−0.929384	+	0.369114i	$0.879661\pi$
$578$		0			0
$579$	−51.5950			−2.14422
$580$		0			0
$581$	47.0940			1.95379
$582$		0			0
$583$	13.5092	+	16.9400i	0.559492	+	0.701581i
$584$		0			0
$585$	−0.826922	+	0.398225i	−0.0341890	+	0.0164646i
$586$		0			0
$587$	22.9314	+	28.7551i	0.946480	+	1.18685i	0.982267	+	0.187489i	$0.0600350\pi$
$587$	22.9314	+	28.7551i	0.946480	+	1.18685i	−0.0357862	+	0.999359i	$0.511394\pi$
$588$		0			0
$589$	1.56437	−	6.85394i	0.0644587	−	0.282412i
$590$		0			0
$591$	8.70141	+	38.1234i	0.357928	+	1.56819i
$592$		0			0
$593$	−6.42262	−	28.1393i	−0.263745	−	1.15554i	−0.917152	−	0.398537i	$-0.869518\pi$
$593$	−6.42262	−	28.1393i	−0.263745	−	1.15554i	0.653407	−	0.757007i	$-0.273339\pi$
$594$		0			0
$595$	6.45737	+	3.10971i	0.264726	+	0.127486i
$596$		0			0
$597$	−33.8222			−1.38425
$598$		0			0
$599$	4.77557	−	5.98837i	0.195124	−	0.244678i	−0.674638	−	0.738148i	$-0.735700\pi$
$599$	4.77557	−	5.98837i	0.195124	−	0.244678i	0.869763	+	0.493470i	$0.164272\pi$
$600$		0			0
$601$	6.79389	−	29.7660i	0.277128	−	1.21418i	−0.624277	−	0.781203i	$-0.714606\pi$
$601$	6.79389	−	29.7660i	0.277128	−	1.21418i	0.901405	−	0.432976i	$-0.142537\pi$
$602$		0			0
$603$	2.54834	+	1.22722i	0.103776	+	0.0499761i
$604$		0			0
$605$	−34.3268	+	43.0444i	−1.39558	+	1.75000i
$606$		0			0
$607$	−15.6290	+	7.52654i	−0.634363	+	0.305493i	−0.723289	−	0.690545i	$-0.757371\pi$
$607$	−15.6290	+	7.52654i	−0.634363	+	0.305493i	0.0889265	+	0.996038i	$0.471656\pi$
$608$		0			0
$609$	11.0897	−	38.4369i	0.449378	−	1.55754i
$610$		0			0
$611$	−0.572641	+	0.275769i	−0.0231666	+	0.0111564i
$612$		0			0
$613$	26.2277	−	32.8885i	1.05933	−	1.32836i	0.117198	−	0.993109i	$-0.462609\pi$
$613$	26.2277	−	32.8885i	1.05933	−	1.32836i	0.942130	−	0.335247i	$-0.108820\pi$
$614$		0			0
$615$	−15.4448	−	7.43781i	−0.622793	−	0.299921i
$616$		0			0
$617$	−8.48563	+	37.1780i	−0.341619	+	1.49673i	0.454039	+	0.890982i	$0.349983\pi$
$617$	−8.48563	+	37.1780i	−0.341619	+	1.49673i	−0.795658	+	0.605747i	$0.792874\pi$
$618$		0			0
$619$	−6.89270	+	8.64317i	−0.277041	+	0.347398i	−0.900812	−	0.434208i	$-0.857028\pi$
$619$	−6.89270	+	8.64317i	−0.277041	+	0.347398i	0.623772	+	0.781607i	$0.285600\pi$
$620$		0			0
$621$	−0.954229			−0.0382919
$622$		0			0
$623$	−15.1959	−	7.31795i	−0.608810	−	0.293187i
$624$		0			0
$625$	6.80126	+	29.7983i	0.272050	+	1.19193i
$626$		0			0
$627$	6.08440	+	26.6575i	0.242988	+	1.06460i
$628$		0			0
$629$	−1.07269	+	4.69975i	−0.0427708	+	0.187391i
$630$		0			0
$631$	3.27499	+	4.10671i	0.130375	+	0.163485i	0.842734	−	0.538330i	$-0.180945\pi$
$631$	3.27499	+	4.10671i	0.130375	+	0.163485i	−0.712359	+	0.701815i	$0.752373\pi$
$632$		0			0
$633$	−53.4645	+	25.7471i	−2.12502	+	1.02336i
$634$		0			0
$635$	−2.41103	−	3.02333i	−0.0956787	−	0.119977i
$636$		0			0
$637$	−0.243417			−0.00964452
$638$		0			0
$639$	−7.06742			−0.279583
$640$		0			0
$641$	26.6854	+	33.4624i	1.05401	+	1.32168i	0.944794	+	0.327666i	$0.106262\pi$
$641$	26.6854	+	33.4624i	1.05401	+	1.32168i	0.109215	+	0.994018i	$0.465166\pi$
$642$		0			0
$643$	5.14029	−	2.47543i	0.202713	−	0.0976215i	−0.329773	−	0.944060i	$-0.606972\pi$
$643$	5.14029	−	2.47543i	0.202713	−	0.0976215i	0.532486	+	0.846439i	$0.321258\pi$
$644$		0			0
$645$	24.0851	+	30.2018i	0.948350	+	1.18919i
$646$		0			0
$647$	−9.76368	+	42.7775i	−0.383850	+	1.68176i	0.301439	+	0.953485i	$0.402533\pi$
$647$	−9.76368	+	42.7775i	−0.383850	+	1.68176i	−0.685289	+	0.728271i	$0.740324\pi$
$648$		0			0
$649$	1.38341	+	6.06113i	0.0543037	+	0.237920i
$650$		0			0
$651$	−5.68926	−	24.9263i	−0.222979	−	0.976937i
$652$		0			0
$653$	7.72038	+	3.71794i	0.302122	+	0.145494i	0.578803	−	0.815468i	$-0.303520\pi$
$653$	7.72038	+	3.71794i	0.302122	+	0.145494i	−0.276681	+	0.960962i	$0.589234\pi$
$654$		0			0
$655$	14.7387			0.575890
$656$		0			0
$657$	16.3996	−	20.5644i	0.639809	−	0.802295i
$658$		0			0
$659$	9.14662	−	40.0740i	0.356302	−	1.56106i	−0.406021	−	0.913864i	$-0.633084\pi$
$659$	9.14662	−	40.0740i	0.356302	−	1.56106i	0.762323	−	0.647197i	$-0.224059\pi$
$660$		0			0
$661$	−3.77592	−	1.81839i	−0.146866	−	0.0707271i	0.359007	−	0.933335i	$-0.383115\pi$
$661$	−3.77592	−	1.81839i	−0.146866	−	0.0707271i	−0.505873	+	0.862608i	$0.668830\pi$
$662$		0			0
$663$	−0.133547	+	0.167463i	−0.00518653	+	0.00650371i
$664$		0			0
$665$	−16.1644	+	7.78434i	−0.626827	+	0.301864i
$666$		0			0
$667$	43.1878	+	23.8911i	1.67224	+	0.925066i
$668$		0			0
$669$	22.9250	−	11.0401i	0.886331	−	0.426835i
$670$		0			0
$671$	27.9226	−	35.0138i	1.07794	−	1.35169i
$672$		0			0
$673$	−24.2541	−	11.6801i	−0.934926	−	0.450237i	−0.0965493	−	0.995328i	$-0.530781\pi$
$673$	−24.2541	−	11.6801i	−0.934926	−	0.450237i	−0.838376	+	0.545092i	$0.816495\pi$
$674$		0			0
$675$	0.0771003	−	0.337798i	0.00296759	−	0.0130019i
$676$		0			0
$677$	4.81279	−	6.03505i	0.184971	−	0.231946i	−0.680697	−	0.732565i	$-0.738323\pi$
$677$	4.81279	−	6.03505i	0.184971	−	0.231946i	0.865668	+	0.500619i	$0.166894\pi$
$678$		0			0
$679$	36.2847			1.39248
$680$		0			0
$681$	46.1394	+	22.2196i	1.76806	+	0.851455i
$682$		0			0
$683$	−4.65093	−	20.3771i	−0.177963	−	0.779706i	−0.982569	−	0.185898i	$-0.940481\pi$
$683$	−4.65093	−	20.3771i	−0.177963	−	0.779706i	0.804606	−	0.593809i	$-0.202376\pi$
$684$		0			0
$685$	0.766115	+	3.35657i	0.0292718	+	0.128248i
$686$		0			0
$687$	−0.534492	+	2.34176i	−0.0203921	+	0.0893438i
$688$		0			0
$689$	−0.264904	−	0.332179i	−0.0100920	−	0.0126550i
$690$		0			0
$691$	10.6038	−	5.10652i	0.403387	−	0.194261i	−0.221178	−	0.975233i	$-0.570990\pi$
$691$	10.6038	−	5.10652i	0.403387	−	0.194261i	0.624566	+	0.780972i	$0.285276\pi$
$692$		0			0
$693$	30.7781	+	38.5945i	1.16916	+	1.46609i
$694$		0			0
$695$	29.0957			1.10366
$696$		0			0
$697$	−1.98596			−0.0752236
$698$		0			0
$699$	26.4455	+	33.1615i	1.00026	+	1.25428i
$700$		0			0
$701$	36.9078	−	17.7738i	1.39399	−	0.671309i	0.422055	−	0.906570i	$-0.361309\pi$
$701$	36.9078	−	17.7738i	1.39399	−	0.671309i	0.971932	+	0.235261i	$0.0755946\pi$
$702$		0			0
$703$	−7.52375	−	9.43448i	−0.283764	−	0.355828i
$704$		0			0
$705$	−9.26301	+	40.5839i	−0.348865	+	1.52848i
$706$		0			0
$707$	6.36994	+	27.9085i	0.239566	+	1.04961i
$708$		0			0
$709$	6.07130	+	26.6001i	0.228012	+	0.998988i	0.951258	+	0.308397i	$0.0997924\pi$
$709$	6.07130	+	26.6001i	0.228012	+	0.998988i	−0.723245	+	0.690591i	$0.757350\pi$
$710$		0			0
$711$	−11.1924	−	5.39000i	−0.419750	−	0.202141i
$712$		0			0
$713$	31.5435			1.18131
$714$		0			0
$715$	1.06123	−	1.33074i	0.0396876	−	0.0497667i
$716$		0			0
$717$	−0.625477	+	2.74039i	−0.0233589	+	0.102342i
$718$		0			0
$719$	−20.8338	−	10.0330i	−0.776971	−	0.374169i	0.00299195	−	0.999996i	$-0.499048\pi$
$719$	−20.8338	−	10.0330i	−0.776971	−	0.374169i	−0.779963	+	0.625826i	$0.784762\pi$
$720$		0			0
$721$	21.4949	−	26.9538i	0.800512	−	1.00381i
$722$		0			0
$723$	43.3386	−	20.8708i	1.61178	−	0.776193i
$724$		0			0
$725$	−11.9470	+	13.3582i	−0.443700	+	0.496110i
$726$		0			0
$727$	42.4462	−	20.4410i	1.57424	−	0.758116i	0.576005	−	0.817446i	$-0.304611\pi$
$727$	42.4462	−	20.4410i	1.57424	−	0.758116i	0.998238	+	0.0593302i	$0.0188965\pi$
$728$		0			0
$729$	−16.3521	+	20.5049i	−0.605635	+	0.759442i
$730$		0			0
$731$	4.03207	+	1.94174i	0.149131	+	0.0718179i
$732$		0			0
$733$	−5.43472	+	23.8111i	−0.200736	+	0.879482i	0.769754	+	0.638341i	$0.220379\pi$
$733$	−5.43472	+	23.8111i	−0.200736	+	0.879482i	−0.970490	+	0.241141i	$0.922478\pi$
$734$		0			0
$735$	−9.94004	+	12.4644i	−0.366644	+	0.459757i
$736$		0			0
$737$	−5.24531			−0.193213
$738$		0			0
$739$	−11.5585	−	5.56627i	−0.425185	−	0.204758i	0.209039	−	0.977907i	$-0.432966\pi$
$739$	−11.5585	−	5.56627i	−0.425185	−	0.204758i	−0.634225	+	0.773149i	$0.718681\pi$
$740$		0			0
$741$	−0.119310	−	0.522733i	−0.00438298	−	0.0192031i
$742$		0			0
$743$	0.0777472	+	0.340633i	0.00285227	+	0.0124966i	0.976334	−	0.216268i	$-0.0693885\pi$
$743$	0.0777472	+	0.340633i	0.00285227	+	0.0124966i	−0.973482	+	0.228765i	$0.926531\pi$
$744$		0			0
$745$	−1.12438	+	4.92624i	−0.0411942	+	0.180484i
$746$		0			0
$747$	28.5306	+	35.7763i	1.04388	+	1.30899i
$748$		0			0
$749$	28.6749	−	13.8091i	1.04776	−	0.504574i
$750$		0			0
$751$	−24.1412	−	30.2721i	−0.880926	−	1.10465i	−0.993816	−	0.111038i	$-0.964582\pi$
$751$	−24.1412	−	30.2721i	−0.880926	−	1.10465i	0.112891	−	0.993607i	$-0.463989\pi$
$752$		0			0
$753$	20.7575			0.756445
$754$		0			0
$755$	−1.62787			−0.0592442
$756$		0			0
$757$	−26.5780	−	33.3277i	−0.965993	−	1.21132i	−0.977404	−	0.211382i	$-0.932204\pi$
$757$	−26.5780	−	33.3277i	−0.965993	−	1.21132i	0.0114107	−	0.999935i	$-0.496368\pi$
$758$		0			0
$759$	−110.535	+	53.2307i	−4.01215	+	1.93215i
$760$		0			0
$761$	−5.40447	−	6.77699i	−0.195912	−	0.245666i	0.674166	−	0.738580i	$-0.264503\pi$
$761$	−5.40447	−	6.77699i	−0.195912	−	0.245666i	−0.870078	+	0.492914i	$0.835932\pi$
$762$		0			0
$763$	9.43338	−	41.3303i	0.341511	−	1.49626i
$764$		0			0
$765$	1.54965	+	6.78945i	0.0560276	+	0.245473i
$766$		0			0
$767$	−0.0271276	−	0.118854i	−0.000979522	−	0.00429157i
$768$		0			0
$769$	19.6592	+	9.46735i	0.708927	+	0.341401i	0.753358	−	0.657611i	$-0.228433\pi$
$769$	19.6592	+	9.46735i	0.708927	+	0.341401i	−0.0444304	+	0.999012i	$0.514147\pi$
$770$		0			0
$771$	55.4592			1.99731
$772$		0			0
$773$	−24.8461	+	31.1560i	−0.893652	+	1.12060i	0.0984470	+	0.995142i	$0.468613\pi$
$773$	−24.8461	+	31.1560i	−0.893652	+	1.12060i	−0.992099	+	0.125461i	$0.959959\pi$
$774$		0			0
$775$	−2.54866	+	11.1664i	−0.0915507	+	0.401110i
$776$		0			0
$777$	−39.5395	−	19.0412i	−1.41847	−	0.683100i
$778$		0			0
$779$	3.09958	−	3.88675i	0.111054	−	0.139257i
$780$		0			0
$781$	11.8085	−	5.68667i	0.422541	−	0.203485i
$782$		0			0
$783$	−0.518084	+	0.214361i	−0.0185148	+	0.00766062i
$784$		0			0
$785$	45.1008	−	21.7194i	1.60972	−	0.775199i
$786$		0			0
$787$	−20.3075	+	25.4648i	−0.723885	+	0.907723i	−0.998551	−	0.0538171i	$-0.982861\pi$
$787$	−20.3075	+	25.4648i	−0.723885	+	0.907723i	0.274666	+	0.961540i	$0.411433\pi$
$788$		0			0
$789$	−57.2690	−	27.5793i	−2.03883	−	0.981849i
$790$		0			0
$791$	8.88502	−	38.9278i	0.315915	−	1.38411i
$792$		0			0
$793$	−0.547540	+	0.686593i	−0.0194437	+	0.0243816i
$794$		0			0
$795$	−27.8271			−0.986924
$796$		0			0
$797$	12.2356	+	5.89234i	0.433406	+	0.208717i	0.637849	−	0.770161i	$-0.279824\pi$
$797$	12.2356	+	5.89234i	0.433406	+	0.208717i	−0.204444	+	0.978878i	$0.565539\pi$
$798$		0			0
$799$	1.07313	+	4.70167i	0.0379645	+	0.166333i
$800$		0			0
$801$	−3.64672	−	15.9773i	−0.128851	−	0.564532i
$802$		0			0
$803$	−10.8542	+	47.5554i	−0.383037	+	1.67819i
$804$		0			0
$805$	−50.1903	−	62.9366i	−1.76897	−	2.21822i
$806$		0			0
$807$	−3.20287	+	1.54242i	−0.112746	+	0.0542958i
$808$		0			0
$809$	1.47559	+	1.85033i	0.0518789	+	0.0650541i	0.807094	−	0.590423i	$-0.201039\pi$
$809$	1.47559	+	1.85033i	0.0518789	+	0.0650541i	−0.755215	+	0.655477i	$0.772468\pi$
$810$		0			0
$811$	45.5629			1.59993			0.799965	−	0.600047i	$-0.204852\pi$
$811$	45.5629			1.59993			0.799965	+	0.600047i	$0.204852\pi$
$812$		0			0
$813$	26.6731			0.935466
$814$		0			0
$815$	20.9055	+	26.2147i	0.732288	+	0.918260i
$816$		0			0
$817$	−10.0932	+	4.86065i	−0.353118	+	0.170053i
$818$		0			0
$819$	−0.603535	−	0.756809i	−0.0210892	−	0.0264450i
$820$		0			0
$821$	−8.65549	+	37.9222i	−0.302079	+	1.32349i	0.564904	+	0.825156i	$0.308913\pi$
$821$	−8.65549	+	37.9222i	−0.302079	+	1.32349i	−0.866983	+	0.498337i	$0.833944\pi$
$822$		0			0
$823$	2.12762	+	9.32173i	0.0741643	+	0.324935i	0.998377	−	0.0569419i	$-0.0181350\pi$
$823$	2.12762	+	9.32173i	0.0741643	+	0.324935i	−0.924213	+	0.381877i	$0.875278\pi$
$824$		0			0
$825$	−9.91270	−	43.4304i	−0.345116	−	1.51205i
$826$		0			0
$827$	1.10499	+	0.532133i	0.0384241	+	0.0185041i	0.452997	−	0.891512i	$-0.350355\pi$
$827$	1.10499	+	0.532133i	0.0384241	+	0.0185041i	−0.414573	+	0.910016i	$0.636069\pi$
$828$		0			0
$829$	45.1704			1.56883			0.784417	−	0.620234i	$-0.212962\pi$
$829$	45.1704			1.56883			0.784417	+	0.620234i	$0.212962\pi$
$830$		0			0
$831$	−3.76251	+	4.71803i	−0.130520	+	0.163667i
$832$		0			0
$833$	−0.410987	+	1.80065i	−0.0142399	+	0.0623890i
$834$		0			0
$835$	22.1181	+	10.6515i	0.765427	+	0.368610i
$836$		0			0
$837$	−0.223418	+	0.280157i	−0.00772245	+	0.00968364i
$838$		0			0
$839$	−4.06270	+	1.95649i	−0.140260	+	0.0675456i	−0.502697	−	0.864463i	$-0.667659\pi$
$839$	−4.06270	+	1.95649i	−0.140260	+	0.0675456i	0.362437	+	0.932008i	$0.381945\pi$
$840$		0			0
$841$	28.8151	+	3.26947i	0.993624	+	0.112740i
$842$		0			0
$843$	0.410447	−	0.197661i	0.0141365	−	0.00680779i
$844$		0			0
$845$	23.3697	−	29.3047i	0.803943	−	1.00811i
$846$		0			0
$847$	−52.3156	−	25.1939i	−1.79759	−	0.865672i
$848$		0			0
$849$	−10.0199	+	43.9000i	−0.343882	+	1.50665i
$850$		0			0
$851$	33.7579	−	42.3311i	1.15721	−	1.45109i
$852$		0			0
$853$	−11.4706			−0.392747			−0.196373	−	0.980529i	$-0.562916\pi$
$853$	−11.4706			−0.392747			−0.196373	+	0.980529i	$0.562916\pi$
$854$		0			0
$855$	−15.7063	−	7.56377i	−0.537145	−	0.258675i
$856$		0			0
$857$	1.15292	+	5.05126i	0.0393829	+	0.172548i	0.990795	−	0.135374i	$-0.0432236\pi$
$857$	1.15292	+	5.05126i	0.0393829	+	0.172548i	−0.951412	+	0.307922i	$0.900366\pi$
$858$		0			0
$859$	5.49148	+	24.0598i	0.187367	+	0.820908i	0.977998	+	0.208615i	$0.0668956\pi$
$859$	5.49148	+	24.0598i	0.187367	+	0.820908i	−0.790631	+	0.612293i	$0.790247\pi$
$860$		0			0
$861$	4.02310	−	17.6263i	0.137107	−	0.600704i
$862$		0			0
$863$	−22.5934	−	28.3313i	−0.769089	−	0.964407i	0.230874	−	0.972984i	$-0.425842\pi$
$863$	−22.5934	−	28.3313i	−0.769089	−	0.964407i	−0.999963	+	0.00857620i	$0.997270\pi$
$864$		0			0
$865$	26.4858	−	12.7549i	0.900544	−	0.433679i
$866$		0			0
$867$	−24.8572	−	31.1699i	−0.844194	−	1.05859i
$868$		0			0
$869$	23.0377			0.781500
$870$		0			0
$871$	0.102856			0.00348516
$872$		0			0
$873$	21.9821	+	27.5647i	0.743981	+	0.932923i
$874$		0			0
$875$	−13.2321	+	6.37222i	−0.447325	+	0.215420i
$876$		0			0
$877$	−17.0627	−	21.3959i	−0.576166	−	0.722490i	0.405287	−	0.914189i	$-0.367171\pi$
$877$	−17.0627	−	21.3959i	−0.576166	−	0.722490i	−0.981454	+	0.191700i	$0.938600\pi$
$878$		0			0
$879$	0.845262	−	3.70334i	0.0285100	−	0.124910i
$880$		0			0
$881$	0.706293	+	3.09447i	0.0237956	+	0.104255i	0.985431	−	0.170075i	$-0.0544010\pi$
$881$	0.706293	+	3.09447i	0.0237956	+	0.104255i	−0.961636	+	0.274330i	$0.911544\pi$
$882$		0			0
$883$	1.93077	+	8.45926i	0.0649756	+	0.284677i	0.996969	−	0.0777983i	$-0.0247890\pi$
$883$	1.93077	+	8.45926i	0.0649756	+	0.284677i	−0.931994	+	0.362475i	$0.881932\pi$
$884$		0			0
$885$	−7.19382	−	3.46436i	−0.241817	−	0.116453i
$886$		0			0
$887$	−2.46214			−0.0826706			−0.0413353	−	0.999145i	$-0.513161\pi$
$887$	−2.46214			−0.0826706			−0.0413353	+	0.999145i	$0.513161\pi$
$888$		0			0
$889$	2.54285	−	3.18863i	0.0852843	−	0.106943i
$890$		0			0
$891$	11.1374	−	48.7962i	0.373117	−	1.63473i
$892$		0			0
$893$	−10.8766	−	5.23789i	−0.363971	−	0.175279i
$894$		0			0
$895$	8.61747	−	10.8060i	0.288050	−	0.361204i
$896$		0			0
$897$	2.16750	−	1.04381i	0.0723706	−	0.0348519i
$898$		0			0
$899$	17.1260	−	7.08601i	0.571186	−	0.236332i
$900$		0			0
$901$	−2.90453	+	1.39875i	−0.0967640	+	0.0465991i
$902$		0			0
$903$	−25.4019	+	31.8530i	−0.845323	+	1.06000i
$904$		0			0
$905$	1.91661	+	0.922992i	0.0637104	+	0.0306813i
$906$		0			0
$907$	1.53955	−	6.74521i	0.0511199	−	0.223971i	−0.942915	−	0.333034i	$-0.891928\pi$
$907$	1.53955	−	6.74521i	0.0511199	−	0.223971i	0.994035	+	0.109063i	$0.0347849\pi$
$908$		0			0
$909$	−17.3424	+	21.7467i	−0.575212	+	0.721292i
$910$		0			0
$911$	−51.8794			−1.71884			−0.859421	−	0.511269i	$-0.829176\pi$
$911$	−51.8794			−1.71884			−0.859421	+	0.511269i	$0.829176\pi$
$912$		0			0
$913$	−76.4567	−	36.8196i	−2.53035	−	1.21855i
$914$		0			0
$915$	12.7987	+	56.0747i	0.423112	+	1.85377i
$916$		0			0
$917$	3.45899	+	15.1548i	0.114226	+	0.500456i
$918$		0			0
$919$	−6.03103	+	26.4237i	−0.198945	+	0.871636i	0.772621	+	0.634868i	$0.218945\pi$
$919$	−6.03103	+	26.4237i	−0.198945	+	0.871636i	−0.971566	+	0.236769i	$0.923912\pi$
$920$		0			0
$921$	−29.8272	−	37.4021i	−0.982838	−	1.23244i
$922$		0			0
$923$	−0.231555	+	0.111511i	−0.00762173	+	0.00367043i
$924$		0			0
$925$	12.2577	+	15.3706i	0.403030	+	0.505384i
$926$		0			0
$927$	33.4983			1.10023
$928$		0			0
$929$	−40.7022			−1.33539			−0.667697	−	0.744433i	$-0.732720\pi$
$929$	−40.7022			−1.33539			−0.667697	+	0.744433i	$0.732720\pi$
$930$		0			0
$931$	−2.88264	−	3.61471i	−0.0944746	−	0.118467i
$932$		0			0
$933$	−58.2048	+	28.0299i	−1.90554	+	0.917659i
$934$		0			0
$935$	−8.05221	−	10.0972i	−0.263335	−	0.330212i
$936$		0			0
$937$	−0.650756	+	2.85115i	−0.0212593	+	0.0931429i	−0.984445	−	0.175695i	$-0.943783\pi$
$937$	−0.650756	+	2.85115i	−0.0212593	+	0.0931429i	0.963185	+	0.268838i	$0.0866397\pi$
$938$		0			0
$939$	−11.8427	−	51.8864i	−0.386473	−	1.69325i
$940$		0			0
$941$	−6.71794	−	29.4332i	−0.218999	−	0.959496i	−0.958220	−	0.286033i	$-0.907663\pi$
$941$	−6.71794	−	29.4332i	−0.218999	−	0.959496i	0.739221	−	0.673463i	$-0.235194\pi$
$942$		0			0
$943$	20.0967	+	9.67806i	0.654438	+	0.315161i
$944$		0			0
$945$	0.914469			0.0297477
$946$		0			0
$947$	−15.7987	+	19.8109i	−0.513388	+	0.643768i	−0.969190	−	0.246313i	$-0.920781\pi$
$947$	−15.7987	+	19.8109i	−0.513388	+	0.643768i	0.455802	+	0.890081i	$0.349352\pi$
$948$		0			0
$949$	0.212842	−	0.932524i	0.00690916	−	0.0302710i
$950$		0			0
$951$	−41.6248	−	20.0454i	−1.34978	−	0.650017i
$952$		0			0
$953$	20.7525	−	26.0228i	0.672240	−	0.842962i	−0.322374	−	0.946612i	$-0.604481\pi$
$953$	20.7525	−	26.0228i	0.672240	−	0.842962i	0.994614	+	0.103650i	$0.0330523\pi$
$954$		0			0
$955$	0.312888	−	0.150679i	0.0101248	−	0.00487585i
$956$		0			0
$957$	−48.0552	+	53.7316i	−1.55340	+	1.73690i
$958$		0			0
$959$	−3.27153	+	1.57549i	−0.105643	+	0.0508751i
$960$		0			0
$961$	−11.9428	+	14.9758i	−0.385251	+	0.483089i
$962$		0			0
$963$	27.8624	+	13.4178i	0.897853	+	0.432383i
$964$		0			0
$965$	−13.5744	+	59.4732i	−0.436974	+	1.91451i
$966$		0			0
$967$	23.4997	−	29.4677i	0.755699	−	0.947617i	−0.244055	−	0.969761i	$-0.578478\pi$
$967$	23.4997	−	29.4677i	0.755699	−	0.947617i	0.999755	+	0.0221443i	$0.00704932\pi$
$968$		0			0
$969$	−4.06831			−0.130693
$970$		0			0
$971$	−20.9811	−	10.1040i	−0.673316	−	0.324252i	0.0657974	−	0.997833i	$-0.479041\pi$
$971$	−20.9811	−	10.1040i	−0.673316	−	0.324252i	−0.739113	+	0.673581i	$0.764755\pi$
$972$		0			0
$973$	6.82837	+	29.9171i	0.218908	+	0.959097i
$974$		0			0
$975$	0.194380	+	0.851635i	0.00622515	+	0.0272742i
$976$		0			0
$977$	3.26264	−	14.2946i	0.104381	−	0.457324i	−0.895543	−	0.444976i	$-0.853212\pi$
$977$	3.26264	−	14.2946i	0.104381	−	0.457324i	0.999924	−	0.0123481i	$-0.00393061\pi$
$978$		0			0
$979$	18.9489	+	23.7612i	0.605611	+	0.759412i
$980$		0			0
$981$	37.1127	−	17.8725i	1.18492	−	0.570626i
$982$		0			0
$983$	−10.7639	−	13.4975i	−0.343316	−	0.430504i	0.579958	−	0.814646i	$-0.303069\pi$
$983$	−10.7639	−	13.4975i	−0.343316	−	0.430504i	−0.923274	+	0.384142i	$0.874497\pi$
$984$		0			0
$985$	46.2338			1.47313
$986$		0			0
$987$	−43.9035			−1.39746
$988$		0			0
$989$	−31.3395	−	39.2985i	−0.996537	−	1.24962i
$990$		0			0
$991$	8.47342	−	4.08058i	0.269167	−	0.129624i	−0.294432	−	0.955672i	$-0.595131\pi$
$991$	8.47342	−	4.08058i	0.269167	−	0.129624i	0.563599	+	0.826048i	$0.309416\pi$
$992$		0			0
$993$	−27.0584	−	33.9302i	−0.858673	−	1.07674i
$994$		0			0
$995$	−8.89844	+	38.9866i	−0.282100	+	1.23596i
$996$		0			0
$997$	10.3569	+	45.3765i	0.328006	+	1.43709i	0.822925	+	0.568150i	$0.192341\pi$
$997$	10.3569	+	45.3765i	0.328006	+	1.43709i	−0.494919	+	0.868939i	$0.664802\pi$
$998$		0			0
$999$	0.136866	+	0.599650i	0.00433025	+	0.0189721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.u.h.49.2		12
4.3	odd	2		58.2.d.b.49.1	yes	12
12.11	even	2		522.2.k.h.397.1		12
29.16	even	7	inner	464.2.u.h.161.2		12
116.19	even	28		1682.2.b.i.1681.6		12
116.39	even	28		1682.2.b.i.1681.7		12
116.83	odd	14		1682.2.a.t.1.1		6
116.91	odd	14		1682.2.a.q.1.6		6
116.103	odd	14		58.2.d.b.45.1	✓	12
348.335	even	14		522.2.k.h.451.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.d.b.45.1	✓	12	116.103	odd	14
58.2.d.b.49.1	yes	12	4.3	odd	2
464.2.u.h.49.2		12	1.1	even	1	trivial
464.2.u.h.161.2		12	29.16	even	7	inner
522.2.k.h.397.1		12	12.11	even	2
522.2.k.h.451.1		12	348.335	even	14
1682.2.a.q.1.6		6	116.91	odd	14
1682.2.a.t.1.1		6	116.83	odd	14
1682.2.b.i.1681.6		12	116.19	even	28
1682.2.b.i.1681.7		12	116.39	even	28

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.u (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.52179 + 1.90827i) q^{3} +(2.60002 - 1.25211i) q^{5} +(1.89765 + 2.37957i) q^{7} +(-0.658071 + 2.88320i) q^{9} +O(q^{10})\)	\(q+(1.52179 + 1.90827i) q^{3} +(2.60002 - 1.25211i) q^{5} +(1.89765 + 2.37957i) q^{7} +(-0.658071 + 2.88320i) q^{9} +(-1.22038 - 5.34685i) q^{11} +(0.0239308 + 0.104847i) q^{13} +(6.34605 + 3.05610i) q^{15} +0.816005 q^{17} +(-1.27358 + 1.59701i) q^{19} +(-1.65304 + 7.24243i) q^{21} +(-8.25746 - 3.97659i) q^{23} +(2.07491 - 2.60185i) q^{25} +(0.0938049 - 0.0451741i) q^{27} +(-5.37657 - 0.304047i) q^{29} +(-3.10086 + 1.49330i) q^{31} +(8.34605 - 10.4656i) q^{33} +(7.91340 + 3.81089i) q^{35} +(-1.31456 + 5.75946i) q^{37} +(-0.163659 + 0.205223i) q^{39} -2.43376 q^{41} +(4.94123 + 2.37957i) q^{43} +(1.89907 + 8.32035i) q^{45} +(1.31510 + 5.76182i) q^{47} +(-0.503658 + 2.20667i) q^{49} +(1.24179 + 1.55716i) q^{51} +(-3.55945 + 1.71414i) q^{53} +(-9.86785 - 12.3739i) q^{55} -4.98565 q^{57} -1.13359 q^{59} +(5.09132 + 6.38431i) q^{61} +(-8.10956 + 3.90536i) q^{63} +(0.193501 + 0.242642i) q^{65} +(0.212822 - 0.932434i) q^{67} +(-4.97776 - 21.8090i) q^{69} +(0.531778 + 2.32987i) q^{71} +(-8.01331 - 3.85900i) q^{73} +8.12261 q^{75} +(10.4074 - 13.0504i) q^{77} +(-0.934726 + 4.09530i) q^{79} +(8.22238 + 3.95969i) q^{81} +(9.64738 - 12.0974i) q^{83} +(2.12163 - 1.02172i) q^{85} +(-7.60183 - 10.7226i) q^{87} +(-4.99275 + 2.40438i) q^{89} +(-0.204080 + 0.255908i) q^{91} +(-7.56848 - 3.64479i) q^{93} +(-1.31170 + 5.74692i) q^{95} +(7.43305 - 9.32075i) q^{97} +16.2191 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - q^{7} - 11 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - q^7 - 11 * q^9	\( 12 q + 3 q^{3} - q^{7} - 11 q^{9} + 2 q^{11} + q^{13} + 9 q^{15} - 12 q^{17} + 6 q^{19} - 13 q^{21} - 35 q^{23} - 6 q^{25} - 39 q^{27} - 14 q^{29} + 8 q^{31} + 33 q^{33} + 18 q^{35} + 31 q^{37} + 22 q^{39} - 30 q^{41} + 5 q^{43} - 20 q^{45} + 33 q^{47} + 37 q^{49} + 15 q^{51} + 13 q^{53} - 36 q^{55} - 38 q^{57} - 38 q^{59} - 5 q^{61} - 4 q^{63} - 20 q^{65} + 7 q^{67} + 20 q^{69} - 3 q^{71} - 22 q^{73} + 2 q^{75} + 10 q^{77} + 60 q^{79} + 88 q^{81} + 39 q^{83} + 38 q^{85} - 9 q^{87} + 39 q^{89} - 61 q^{91} - 54 q^{93} - 55 q^{95} - 19 q^{97} + 8 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - q^7 - 11 * q^9 + 2 * q^11 + q^13 + 9 * q^15 - 12 * q^17 + 6 * q^19 - 13 * q^21 - 35 * q^23 - 6 * q^25 - 39 * q^27 - 14 * q^29 + 8 * q^31 + 33 * q^33 + 18 * q^35 + 31 * q^37 + 22 * q^39 - 30 * q^41 + 5 * q^43 - 20 * q^45 + 33 * q^47 + 37 * q^49 + 15 * q^51 + 13 * q^53 - 36 * q^55 - 38 * q^57 - 38 * q^59 - 5 * q^61 - 4 * q^63 - 20 * q^65 + 7 * q^67 + 20 * q^69 - 3 * q^71 - 22 * q^73 + 2 * q^75 + 10 * q^77 + 60 * q^79 + 88 * q^81 + 39 * q^83 + 38 * q^85 - 9 * q^87 + 39 * q^89 - 61 * q^91 - 54 * q^93 - 55 * q^95 - 19 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

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Database

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