LMFDB - Embedded newform 425.2.p.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(16,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("425.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.p (of order $10$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$42$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			16.2
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.13901 - 1.55408i) q^{2} +(0.355974 - 0.115663i) q^{3} +(1.54215 + 4.74625i) q^{4} +(-0.624287 + 2.14715i) q^{5} +(-0.941180 - 0.305808i) q^{6} -1.16016i q^{7} +(2.44332 - 7.51977i) q^{8} +(-2.31371 + 1.68101i) q^{9} +(4.67220 - 3.62258i) q^{10} +(0.0931875 - 0.128262i) q^{11} +(1.09793 + 1.51117i) q^{12} +(3.27739 - 2.38116i) q^{13} +(-1.80297 + 2.48158i) q^{14} +(0.0261163 + 0.836538i) q^{15} +(-8.83779 + 6.42103i) q^{16} +(-4.07653 - 0.617997i) q^{17} +7.56146 q^{18} +(-0.651885 + 2.00629i) q^{19} +(-11.1537 + 0.348212i) q^{20} +(-0.134187 - 0.412986i) q^{21} +(-0.398657 + 0.129532i) q^{22} +(-4.78500 + 6.58598i) q^{23} -2.95945i q^{24} +(-4.22053 - 2.68088i) q^{25} -10.7109 q^{26} +(-1.28920 + 1.77444i) q^{27} +(5.50640 - 1.78914i) q^{28} +(-5.36392 + 1.74284i) q^{29} +(1.24418 - 1.82995i) q^{30} +(-5.75381 - 1.86952i) q^{31} +13.0693 q^{32} +(0.0183372 - 0.0564362i) q^{33} +(7.75930 + 7.65714i) q^{34} +(2.49103 + 0.724271i) q^{35} +(-11.5466 - 8.38908i) q^{36} +(4.52969 + 6.23458i) q^{37} +(4.51232 - 3.27839i) q^{38} +(0.891254 - 1.22671i) q^{39} +(14.6208 + 9.94068i) q^{40} +(4.01143 + 5.52126i) q^{41} +(-0.354785 + 1.09192i) q^{42} -5.21309 q^{43} +(0.752471 + 0.244493i) q^{44} +(-2.16497 - 6.01732i) q^{45} +(20.4703 - 6.65119i) q^{46} +(0.382134 + 1.17609i) q^{47} +(-2.40335 + 3.30793i) q^{48} +5.65404 q^{49} +(4.86145 + 12.2934i) q^{50} +(-1.52262 + 0.251512i) q^{51} +(16.3558 + 11.8832i) q^{52} +(-3.30742 - 10.1792i) q^{53} +(5.51523 - 1.79201i) q^{54} +(0.217222 + 0.280160i) q^{55} +(-8.72412 - 2.83464i) q^{56} +0.789588i q^{57} +(14.1820 + 4.60800i) q^{58} +(-6.36212 + 4.62235i) q^{59} +(-3.93014 + 1.41402i) q^{60} +(-2.06036 + 2.83585i) q^{61} +(9.40203 + 12.9408i) q^{62} +(1.95024 + 2.68427i) q^{63} +(-10.2798 - 7.46873i) q^{64} +(3.06669 + 8.52359i) q^{65} +(-0.126930 + 0.0922198i) q^{66} +(0.286942 - 0.883117i) q^{67} +(-3.35345 - 20.3013i) q^{68} +(-0.941581 + 2.89789i) q^{69} +(-4.20276 - 5.42048i) q^{70} +(-8.23143 + 2.67455i) q^{71} +(6.98767 + 21.5058i) q^{72} +(0.554257 - 0.762870i) q^{73} -20.3753i q^{74} +(-1.81248 - 0.466164i) q^{75} -10.5277 q^{76} +(-0.148804 - 0.108112i) q^{77} +(-3.81280 + 1.23885i) q^{78} +(-11.8059 + 3.83596i) q^{79} +(-8.26962 - 22.9846i) q^{80} +(2.39759 - 7.37902i) q^{81} -18.0441i q^{82} +(1.54222 - 4.74647i) q^{83} +(1.75320 - 1.27377i) q^{84} +(3.87186 - 8.36712i) q^{85} +(11.1508 + 8.10154i) q^{86} +(-1.70783 + 1.24081i) q^{87} +(-0.736811 - 1.01413i) q^{88} +(-0.191227 - 0.138935i) q^{89} +(-4.72052 + 16.2356i) q^{90} +(-2.76252 - 3.80229i) q^{91} +(-38.6379 - 12.5542i) q^{92} -2.26444 q^{93} +(1.01035 - 3.10952i) q^{94} +(-3.90086 - 2.65220i) q^{95} +(4.65235 - 1.51164i) q^{96} +(-5.53280 + 1.79772i) q^{97} +(-12.0940 - 8.78681i) q^{98} +0.453409i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) $ 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.13901	−	1.55408i	−1.51251	−	1.09890i	−0.965051	−	0.262064i	$-0.915597\pi$
$2$	−2.13901	−	1.55408i	−1.51251	−	1.09890i	−0.547454	−	0.836835i	$-0.684403\pi$
$3$	0.355974	−	0.115663i	0.205522	−	0.0667781i	−0.204447	−	0.978878i	$-0.565540\pi$
$3$	0.355974	−	0.115663i	0.205522	−	0.0667781i	0.409969	+	0.912100i	$0.365540\pi$
$4$	1.54215	+	4.74625i	0.771075	+	2.37312i
$5$	−0.624287	+	2.14715i	−0.279189	+	0.960236i
$5$	−0.624287	+	2.14715i	−0.279189	+	0.960236i
$6$	−0.941180	−	0.305808i	−0.384235	−	0.124846i
$7$		−	1.16016i		−	0.438498i	−0.975669	−	0.219249i	$-0.929639\pi$
$7$		−	1.16016i		−	0.438498i	0.975669	−	0.219249i	$-0.0703607\pi$
$8$	2.44332	−	7.51977i	0.863845	−	2.65864i
$9$	−2.31371	+	1.68101i	−0.771237	+	0.560337i
$10$	4.67220	−	3.62258i	1.47748	−	1.14556i
$11$	0.0931875	−	0.128262i	0.0280971	−	0.0386723i	−0.794737	−	0.606954i	$-0.792391\pi$
$11$	0.0931875	−	0.128262i	0.0280971	−	0.0386723i	0.822834	+	0.568281i	$0.192391\pi$
$12$	1.09793	+	1.51117i	0.316946	+	0.436238i
$13$	3.27739	−	2.38116i	0.908985	−	0.660416i	−0.0317732	−	0.999495i	$-0.510115\pi$
$13$	3.27739	−	2.38116i	0.908985	−	0.660416i	0.940758	+	0.339079i	$0.110115\pi$
$14$	−1.80297	+	2.48158i	−0.481865	+	0.663231i
$15$	0.0261163	+	0.836538i	0.00674320	+	0.215993i
$16$	−8.83779	+	6.42103i	−2.20945	+	1.60526i
$17$	−4.07653	−	0.617997i	−0.988703	−	0.149886i
$17$	−4.07653	−	0.617997i	−0.988703	−	0.149886i
$18$	7.56146			1.78225
$19$	−0.651885	+	2.00629i	−0.149553	+	0.460275i	−0.997568	−	0.0696956i	$-0.977797\pi$
$19$	−0.651885	+	2.00629i	−0.149553	+	0.460275i	0.848016	+	0.529971i	$0.177797\pi$
$20$	−11.1537	+	0.348212i	−2.49404	+	0.0778626i
$21$	−0.134187	−	0.412986i	−0.0292821	−	0.0901210i
$22$	−0.398657	+	0.129532i	−0.0849940	+	0.0276162i
$23$	−4.78500	+	6.58598i	−0.997741	+	1.37327i	−0.0710393	+	0.997474i	$0.522632\pi$
$23$	−4.78500	+	6.58598i	−0.997741	+	1.37327i	−0.926701	+	0.375799i	$0.877368\pi$
$24$		−	2.95945i		−	0.604095i
$25$	−4.22053	−	2.68088i	−0.844106	−	0.536176i
$26$	−10.7109			−2.10057
$27$	−1.28920	+	1.77444i	−0.248107	+	0.341491i
$28$	5.50640	−	1.78914i	1.04061	−	0.338115i
$29$	−5.36392	+	1.74284i	−0.996055	+	0.323638i	−0.761288	−	0.648414i	$-0.775433\pi$
$29$	−5.36392	+	1.74284i	−0.996055	+	0.323638i	−0.234767	+	0.972052i	$0.575433\pi$
$30$	1.24418	−	1.82995i	0.227156	−	0.334101i
$31$	−5.75381	−	1.86952i	−1.03341	−	0.335777i	−0.257275	−	0.966338i	$-0.582825\pi$
$31$	−5.75381	−	1.86952i	−1.03341	−	0.335777i	−0.776139	+	0.630562i	$0.782825\pi$
$32$	13.0693			2.31036
$33$	0.0183372	−	0.0564362i	0.00319210	−	0.00982428i
$34$	7.75930	+	7.65714i	1.33071	+	1.31319i
$35$	2.49103	+	0.724271i	0.421062	+	0.122424i
$36$	−11.5466	−	8.38908i	−1.92443	−	1.39818i
$37$	4.52969	+	6.23458i	0.744676	+	1.02496i	0.998336	+	0.0576651i	$0.0183656\pi$
$37$	4.52969	+	6.23458i	0.744676	+	1.02496i	−0.253660	+	0.967293i	$0.581634\pi$
$38$	4.51232	−	3.27839i	0.731995	−	0.531826i
$39$	0.891254	−	1.22671i	0.142715	−	0.196430i
$40$	14.6208	+	9.94068i	2.31175	+	1.57176i
$41$	4.01143	+	5.52126i	0.626480	+	0.862276i	0.997805	−	0.0662271i	$-0.0210962\pi$
$41$	4.01143	+	5.52126i	0.626480	+	0.862276i	−0.371324	+	0.928503i	$0.621096\pi$
$42$	−0.354785	+	1.09192i	−0.0547446	+	0.168486i
$43$	−5.21309			−0.794988			−0.397494	−	0.917605i	$-0.630120\pi$
$43$	−5.21309			−0.794988			−0.397494	+	0.917605i	$0.630120\pi$
$44$	0.752471	+	0.244493i	0.113439	+	0.0368586i
$45$	−2.16497	−	6.01732i	−0.322734	−	0.897010i
$46$	20.4703	−	6.65119i	3.01818	−	0.980665i
$47$	0.382134	+	1.17609i	0.0557400	+	0.171550i	0.975051	−	0.221983i	$-0.0712528\pi$
$47$	0.382134	+	1.17609i	0.0557400	+	0.171550i	−0.919311	+	0.393533i	$0.871253\pi$
$48$	−2.40335	+	3.30793i	−0.346894	+	0.477458i
$49$	5.65404			0.807719
$50$	4.86145	+	12.2934i	0.687512	+	1.73856i
$51$	−1.52262	+	0.251512i	−0.213209	+	0.0352188i
$52$	16.3558	+	11.8832i	2.26815	+	1.64790i
$53$	−3.30742	−	10.1792i	−0.454310	−	1.39822i	−0.871944	−	0.489606i	$-0.837141\pi$
$53$	−3.30742	−	10.1792i	−0.454310	−	1.39822i	0.417634	−	0.908615i	$-0.362859\pi$
$54$	5.51523	−	1.79201i	0.750527	−	0.243861i
$55$	0.217222	+	0.280160i	0.0292902	+	0.0377768i
$56$	−8.72412	−	2.83464i	−1.16581	−	0.378794i
$57$			0.789588i			0.104584i
$58$	14.1820	+	4.60800i	1.86218	+	0.605060i
$59$	−6.36212	+	4.62235i	−0.828278	+	0.601779i	−0.919072	−	0.394091i	$-0.871060\pi$
$59$	−6.36212	+	4.62235i	−0.828278	+	0.601779i	0.0907936	+	0.995870i	$0.471060\pi$
$60$	−3.93014	+	1.41402i	−0.507379	+	0.182549i
$61$	−2.06036	+	2.83585i	−0.263802	+	0.363093i	−0.920285	−	0.391248i	$-0.872043\pi$
$61$	−2.06036	+	2.83585i	−0.263802	+	0.363093i	0.656483	+	0.754341i	$0.272043\pi$
$62$	9.40203	+	12.9408i	1.19406	+	1.64348i
$63$	1.95024	+	2.68427i	0.245707	+	0.338186i
$64$	−10.2798	−	7.46873i	−1.28498	−	0.933591i
$65$	3.06669	+	8.52359i	0.380376	+	1.05722i
$66$	−0.126930	+	0.0922198i	−0.0156240	+	0.0113515i
$67$	0.286942	−	0.883117i	0.0350555	−	0.107890i	−0.931998	−	0.362464i	$-0.881935\pi$
$67$	0.286942	−	0.883117i	0.0350555	−	0.107890i	0.967053	+	0.254575i	$0.0819354\pi$
$68$	−3.35345	−	20.3013i	−0.406665	−	2.46189i
$69$	−0.941581	+	2.89789i	−0.113353	+	0.348865i
$70$	−4.20276	−	5.42048i	−0.502326	−	0.647871i
$71$	−8.23143	+	2.67455i	−0.976891	+	0.317411i	−0.753595	−	0.657339i	$-0.771682\pi$
$71$	−8.23143	+	2.67455i	−0.976891	+	0.317411i	−0.223297	+	0.974751i	$0.571682\pi$
$72$	6.98767	+	21.5058i	0.823504	+	2.53449i
$73$	0.554257	−	0.762870i	0.0648709	−	0.0892872i	−0.775349	−	0.631533i	$-0.782426\pi$
$73$	0.554257	−	0.762870i	0.0648709	−	0.0892872i	0.840220	+	0.542246i	$0.182426\pi$
$74$		−	20.3753i		−	2.36858i
$75$	−1.81248	−	0.466164i	−0.209287	−	0.0538280i
$76$	−10.5277			−1.20761
$77$	−0.148804	−	0.108112i	−0.0169577	−	0.0123205i
$78$	−3.81280	+	1.23885i	−0.431714	+	0.140272i
$79$	−11.8059	+	3.83596i	−1.32827	+	0.431580i	−0.885326	−	0.464972i	$-0.846064\pi$
$79$	−11.8059	+	3.83596i	−1.32827	+	0.431580i	−0.442940	+	0.896551i	$0.646064\pi$
$80$	−8.26962	−	22.9846i	−0.924572	−	2.56976i
$81$	2.39759	−	7.37902i	0.266399	−	0.819892i
$82$		−	18.0441i		−	1.99264i
$83$	1.54222	−	4.74647i	0.169281	−	0.520993i	−0.830045	−	0.557696i	$-0.811686\pi$
$83$	1.54222	−	4.74647i	0.169281	−	0.520993i	0.999326	+	0.0367031i	$0.0116856\pi$
$84$	1.75320	−	1.27377i	0.191290	−	0.138980i
$85$	3.87186	−	8.36712i	0.419962	−	0.907542i
$86$	11.1508	+	8.10154i	1.20242	+	0.873612i
$87$	−1.70783	+	1.24081i	−0.183099	+	0.133029i
$88$	−0.736811	−	1.01413i	−0.0785443	−	0.108107i
$89$	−0.191227	−	0.138935i	−0.0202701	−	0.0147271i	0.577604	−	0.816317i	$-0.303988\pi$
$89$	−0.191227	−	0.138935i	−0.0202701	−	0.0147271i	−0.597874	+	0.801590i	$0.703988\pi$
$90$	−4.72052	+	16.2356i	−0.497586	+	1.71138i
$91$	−2.76252	−	3.80229i	−0.289591	−	0.398588i
$92$	−38.6379	−	12.5542i	−4.02828	−	1.30887i
$93$	−2.26444			−0.234812
$94$	1.01035	−	3.10952i	0.104209	−	0.320723i
$95$	−3.90086	−	2.65220i	−0.400220	−	0.272110i
$96$	4.65235	−	1.51164i	0.474829	−	0.154281i
$97$	−5.53280	+	1.79772i	−0.561771	+	0.182530i	−0.576118	−	0.817367i	$-0.695433\pi$
$97$	−5.53280	+	1.79772i	−0.561771	+	0.182530i	0.0143469	+	0.999897i	$0.495433\pi$
$98$	−12.0940	−	8.78681i	−1.22168	−	0.887602i
$99$			0.453409i			0.0455694i
$100$	6.21542	−	24.1660i	0.621542	−	2.41660i
$101$	16.8443			1.67607			0.838033	−	0.545619i	$-0.183705\pi$
$101$	16.8443			1.67607			0.838033	+	0.545619i	$0.183705\pi$
$102$	3.64776	+	1.82828i	0.361182	+	0.181027i
$103$	3.99627	+	12.2993i	0.393764	+	1.21188i	0.929920	+	0.367763i	$0.119876\pi$
$103$	3.99627	+	12.2993i	0.393764	+	1.21188i	−0.536155	+	0.844119i	$0.680124\pi$
$104$	−9.89809	−	30.4632i	−0.970587	−	2.98716i
$105$	0.970516	−	0.0302990i	0.0947126	−	0.00295688i
$106$	−8.74468	+	26.9134i	−0.849358	+	2.61406i
$107$		−	9.71197i		−	0.938892i	−0.882961	−	0.469446i	$-0.844454\pi$
$107$		−	9.71197i		−	0.938892i	0.882961	−	0.469446i	$-0.155546\pi$
$108$	−10.4101	−	3.38244i	−1.00171	−	0.325475i
$109$	6.14770	+	8.46159i	0.588843	+	0.810473i	0.994630	−	0.103495i	$-0.0330025\pi$
$109$	6.14770	+	8.46159i	0.588843	+	0.810473i	−0.405787	+	0.913968i	$0.633003\pi$
$110$	−0.0292478	−	0.936843i	−0.00278867	−	0.0893245i
$111$	2.33356	+	1.69543i	0.221492	+	0.160923i
$112$	7.44940	+	10.2532i	0.703902	+	0.968839i
$113$	−5.90118	−	8.12228i	−0.555136	−	0.764079i	0.435562	−	0.900159i	$-0.356550\pi$
$113$	−5.90118	−	8.12228i	−0.555136	−	0.764079i	−0.990698	+	0.136079i	$0.956550\pi$
$114$	1.22708	−	1.68893i	0.114927	−	0.158183i
$115$	−11.1539	−	14.3857i	−1.04011	−	1.34147i
$116$	−16.5439	−	22.7708i	−1.53607	−	2.11421i
$117$	−3.58018	+	11.0187i	−0.330987	+	1.01867i
$118$	20.7921			1.91407
$119$	−0.716974	+	4.72941i	−0.0657249	+	0.433545i
$120$	6.35439	+	1.84754i	0.580073	+	0.168657i
$121$	3.39142	+	10.4377i	0.308311	+	0.948883i
$122$	8.81425	−	2.86392i	0.798005	−	0.259288i
$123$	2.06657	+	1.50145i	0.186337	+	0.135381i
$124$		−	30.1921i		−	2.71133i
$125$	8.39108	−	7.38849i	0.750521	−	0.660847i
$126$		−	8.77248i		−	0.781515i
$127$	−3.26349	−	2.37107i	−0.289588	−	0.210398i	0.433501	−	0.901153i	$-0.357278\pi$
$127$	−3.26349	−	2.37107i	−0.289588	−	0.210398i	−0.723089	+	0.690755i	$0.757278\pi$
$128$	2.30430	+	7.09192i	0.203674	+	0.626843i
$129$	−1.85572	+	0.602961i	−0.163387	+	0.0530878i
$130$	6.68665	−	22.9979i	0.586458	−	2.01705i
$131$	18.9049	+	6.14258i	1.65173	+	0.536679i	0.979114	−	0.203313i	$-0.0651709\pi$
$131$	18.9049	+	6.14258i	1.65173	+	0.536679i	0.672615	+	0.739992i	$0.265171\pi$
$132$	0.296139			0.0257756
$133$	2.32762	+	0.756288i	0.201830	+	0.0655785i
$134$	−1.98620	+	1.44306i	−0.171582	+	0.124661i
$135$	−3.00515	−	3.87587i	−0.258643	−	0.333582i
$136$	−14.6075	+	29.1446i	−1.25258	+	2.49913i
$137$	−11.3659	+	8.25781i	−0.971055	+	0.705513i	−0.955692	−	0.294369i	$-0.904890\pi$
$137$	−11.3659	+	8.25781i	−0.971055	+	0.705513i	−0.0153631	+	0.999882i	$0.504890\pi$
$138$	6.51759	−	4.73531i	0.554814	−	0.403096i
$139$	3.80974	−	5.24365i	0.323138	−	0.444761i	−0.616284	−	0.787524i	$-0.711363\pi$
$139$	3.80974	−	5.24365i	0.323138	−	0.444761i	0.939422	+	0.342763i	$0.111363\pi$
$140$	0.403981	+	12.9400i	0.0341426	+	1.09363i
$141$	0.272060	+	0.374458i	0.0229116	+	0.0315351i
$142$	21.7635	+	7.07140i	1.82636	+	0.593419i
$143$		−	0.642258i		−	0.0537083i
$144$	9.65428	−	29.7128i	0.804523	−	2.47607i
$145$	−0.393528	−	12.6052i	−0.0326807	−	1.04680i
$146$	−2.37112	+	0.770423i	−0.196235	+	0.0637607i
$147$	2.01269	−	0.653963i	0.166004	−	0.0539380i
$148$	−22.6054	+	31.1137i	−1.85815	+	2.55753i
$149$	−15.4603			−1.26656			−0.633279	−	0.773924i	$-0.718291\pi$
$149$	−15.4603			−1.26656			−0.633279	+	0.773924i	$0.718291\pi$
$150$	3.15245	+	3.81386i	0.257396	+	0.311401i
$151$	15.4718			1.25908			0.629539	−	0.776969i	$-0.283244\pi$
$151$	15.4718			1.25908			0.629539	+	0.776969i	$0.283244\pi$
$152$	13.4941	+	9.80405i	1.09452	+	0.795213i
$153$	10.4708	−	5.42281i	0.846511	−	0.438409i
$154$	0.150277	+	0.462505i	0.0121097	+	0.0372697i
$155$	7.60618	−	11.1872i	0.610943	−	0.898576i
$156$	7.19670	+	2.33835i	0.576197	+	0.187218i
$157$	−2.29408			−0.183087			−0.0915436	−	0.995801i	$-0.529180\pi$
$157$	−2.29408			−0.183087			−0.0915436	+	0.995801i	$0.529180\pi$
$158$	31.2142	+	10.1421i	2.48327	+	0.806864i
$159$	−2.35472	−	3.24099i	−0.186741	−	0.257027i
$160$	−8.15902	+	28.0619i	−0.645027	+	2.21849i
$161$	7.64077	+	5.55135i	0.602177	+	0.437507i
$162$	−16.5960	+	12.0577i	−1.30391	+	0.947345i
$163$	−12.4569	−	17.1454i	−0.975698	−	1.34293i	−0.939115	−	0.343603i	$-0.888353\pi$
$163$	−12.4569	−	17.1454i	−0.975698	−	1.34293i	−0.0365830	−	0.999331i	$-0.511647\pi$
$164$	−20.0191	+	27.5539i	−1.56323	+	2.15160i
$165$	0.109729	+	0.0746052i	0.00854243	+	0.00580801i
$166$	−10.6752	+	7.75599i	−0.828556	+	0.601982i
$167$	−0.126289	−	0.0410339i	−0.00977257	−	0.00317530i	0.304127	−	0.952632i	$-0.401635\pi$
$167$	−0.126289	−	0.0410339i	−0.00977257	−	0.00317530i	−0.313899	+	0.949456i	$0.601635\pi$
$168$	−3.43342			−0.264894
$169$	1.05413	−	3.24428i	0.0810869	−	0.249560i
$170$	−21.2851	+	11.8801i	−1.63249	+	0.911166i
$171$	−1.86433	−	5.73781i	−0.142569	−	0.438781i
$172$	−8.03936	−	24.7426i	−0.612995	−	1.88661i
$173$	−3.50306	+	4.82154i	−0.266332	+	0.366575i	−0.921147	−	0.389214i	$-0.872747\pi$
$173$	−3.50306	+	4.82154i	−0.266332	+	0.366575i	0.654815	+	0.755789i	$0.272747\pi$
$174$	5.58139			0.423124
$175$	−3.11024	+	4.89648i	−0.235112	+	0.370139i
$176$			1.73191i			0.130548i
$177$	−1.73012	+	2.38130i	−0.130044	+	0.178990i
$178$	0.193121	+	0.594364i	0.0144750	+	0.0445495i
$179$	5.72829	+	17.6299i	0.428153	+	1.31772i	0.899943	+	0.436008i	$0.143608\pi$
$179$	5.72829	+	17.6299i	0.428153	+	1.31772i	−0.471790	+	0.881711i	$0.656392\pi$
$180$	25.2210	−	19.5551i	1.87986	−	1.45755i
$181$	2.26572	+	0.736177i	0.168410	+	0.0547196i	0.392008	−	0.919962i	$-0.371780\pi$
$181$	2.26572	+	0.736177i	0.168410	+	0.0547196i	−0.223599	+	0.974681i	$0.571780\pi$
$182$			12.4263i			0.921098i
$183$	−0.405434	+	1.24780i	−0.0299705	+	0.0922397i
$184$	37.8338	+	52.0737i	2.78914	+	3.83893i
$185$	−16.2144	+	5.83377i	−1.19211	+	0.428907i
$186$	4.84365	+	3.51912i	0.355154	+	0.258034i
$187$	−0.459147	+	0.465272i	−0.0335761	+	0.0340241i
$188$	−4.99270	+	3.62741i	−0.364130	+	0.264556i
$189$	2.05863	+	1.49568i	0.149743	+	0.108795i
$190$	4.22223	+	11.7353i	0.306313	+	0.851368i
$191$	18.0124	−	13.0868i	1.30333	−	0.946925i	0.303348	−	0.952880i	$-0.401896\pi$
$191$	18.0124	−	13.0868i	1.30333	−	0.946925i	0.999982	+	0.00595506i	$0.00189557\pi$
$192$	−4.52321	−	1.46968i	−0.326434	−	0.106065i
$193$			13.8247i			0.995126i	0.867428	+	0.497563i	$0.165772\pi$
$193$			13.8247i			0.995126i	−0.867428	+	0.497563i	$0.834228\pi$
$194$	14.6285	+	4.75308i	1.05026	+	0.341251i
$195$	2.07753	+	2.67948i	0.148775	+	0.191881i
$196$	8.71937	+	26.8355i	0.622812	+	1.91682i
$197$	13.0461	−	4.23892i	0.929493	−	0.302010i	0.195137	−	0.980776i	$-0.437485\pi$
$197$	13.0461	−	4.23892i	0.929493	−	0.302010i	0.734355	+	0.678765i	$0.237485\pi$
$198$	0.704634	−	0.969845i	0.0500761	−	0.0689239i
$199$		−	26.7064i		−	1.89316i	−0.322463	−	0.946582i	$-0.604511\pi$
$199$		−	26.7064i		−	1.89316i	0.322463	−	0.946582i	$-0.395489\pi$
$200$	−30.4717	+	25.1872i	−2.15468	+	1.78100i
$201$		−	0.347555i		−	0.0245147i
$202$	−36.0300	−	26.1773i	−2.53506	−	1.84183i
$203$	2.02197	+	6.22299i	0.141915	+	0.436768i
$204$	−3.54185	−	6.83886i	−0.247979	−	0.478816i
$205$	−14.3593	+	5.16631i	−1.00290	+	0.360831i
$206$	10.5660	−	32.5187i	0.736166	−	2.26568i
$207$		−	23.2817i		−	1.61819i
$208$	−13.6754	+	42.0884i	−0.948216	+	2.91831i
$209$	0.196583	+	0.270573i	0.0135979	+	0.0187160i
$210$	−2.12303	−	1.44345i	−0.146503	−	0.0996074i
$211$	5.20269	−	7.16088i	0.358168	−	0.492976i	−0.591469	−	0.806327i	$-0.701452\pi$
$211$	5.20269	−	7.16088i	0.358168	−	0.492976i	0.949637	+	0.313352i	$0.101452\pi$
$212$	43.2125	−	31.3957i	2.96785	−	2.15627i
$213$	−2.62083	+	1.90415i	−0.179576	+	0.130470i
$214$	−15.0932	+	20.7740i	−1.03175	+	1.42008i
$215$	3.25446	−	11.1933i	0.221952	−	0.763376i
$216$	10.1934	+	14.0300i	0.693574	+	0.954623i
$217$	−2.16894	+	6.67532i	−0.147237	+	0.453150i
$218$		−	27.6534i		−	1.87292i
$219$	0.109066	−	0.335669i	0.00736997	−	0.0226824i
$220$	−0.994720	+	1.46304i	−0.0670640	+	0.0986379i
$221$	−14.8319	+	7.68146i	−0.997704	+	0.516711i
$222$	−2.35667	−	7.25308i	−0.158169	−	0.486795i
$223$	4.33472	+	3.14936i	0.290274	+	0.210897i	0.723386	−	0.690444i	$-0.242585\pi$
$223$	4.33472	+	3.14936i	0.290274	+	0.210897i	−0.433112	+	0.901340i	$0.642585\pi$
$224$		−	15.1625i		−	1.01309i
$225$	14.2717	−	0.891979i	0.951445	−	0.0594652i
$226$			26.5445i			1.76571i
$227$	−13.0145	+	17.9129i	−0.863801	+	1.18892i	0.116848	+	0.993150i	$0.462721\pi$
$227$	−13.0145	+	17.9129i	−0.863801	+	1.18892i	−0.980650	+	0.195771i	$0.937279\pi$
$228$	−3.74758	+	1.21766i	−0.248190	+	0.0806417i
$229$	−1.07460	−	3.30729i	−0.0710118	−	0.218552i	0.909252	−	0.416246i	$-0.136655\pi$
$229$	−1.07460	−	3.30729i	−0.0710118	−	0.218552i	−0.980264	+	0.197694i	$0.936655\pi$
$230$	1.50182	+	48.1050i	0.0990268	+	3.17195i
$231$	−0.0654749	−	0.0212741i	−0.00430793	−	0.00139973i
$232$			44.5938i			2.92772i
$233$	19.4057	+	6.30529i	1.27131	+	0.413073i	0.865511	−	0.500889i	$-0.166994\pi$
$233$	19.4057	+	6.30529i	1.27131	+	0.413073i	0.405798	+	0.913963i	$0.366994\pi$
$234$	24.7819	−	18.0051i	1.62004	−	1.17703i
$235$	−2.76380	+	0.0862845i	−0.180291	+	0.00562858i
$236$	−31.7502	−	23.0679i	−2.06676	−	1.50159i
$237$	−3.75891	+	2.73101i	−0.244168	+	0.177398i
$238$	8.88349	−	9.00200i	0.575831	−	0.583513i
$239$	−0.820630	−	0.596223i	−0.0530821	−	0.0385664i	0.560928	−	0.827865i	$-0.310445\pi$
$239$	−0.820630	−	0.596223i	−0.0530821	−	0.0385664i	−0.614010	+	0.789298i	$0.710445\pi$
$240$	−5.60225	−	7.22545i	−0.361623	−	0.466401i
$241$	−2.33496	−	3.21379i	−0.150408	−	0.207018i	0.727164	−	0.686464i	$-0.240838\pi$
$241$	−2.33496	−	3.21379i	−0.150408	−	0.207018i	−0.877572	+	0.479445i	$0.840838\pi$
$242$	8.96676	−	27.5969i	0.576405	−	1.77399i
$243$		−	9.48403i		−	0.608401i
$244$	−16.6370	−	5.40570i	−1.06508	−	0.346064i
$245$	−3.52974	+	12.1401i	−0.225507	+	0.775601i
$246$	−2.08703	−	6.42323i	−0.133064	−	0.409530i
$247$	2.64084	+	8.12765i	0.168032	+	0.517150i
$248$	−28.1168	+	38.6994i	−1.78542	+	2.45742i
$249$		−	1.86800i		−	0.118380i
$250$	−29.4309	+	2.76364i	−1.86137	+	0.174788i
$251$	−0.275968			−0.0174189			−0.00870946	−	0.999962i	$-0.502772\pi$
$251$	−0.275968			−0.0174189			−0.00870946	+	0.999962i	$0.502772\pi$
$252$	−9.73265	+	13.3958i	−0.613100	+	0.843859i
$253$	0.398827	+	1.22746i	0.0250740	+	0.0771699i
$254$	3.29581	+	10.1434i	0.206797	+	0.636456i
$255$	0.410515	−	3.42631i	0.0257074	−	0.214564i
$256$	−1.76061	+	5.41859i	−0.110038	+	0.338662i
$257$	5.55790			0.346692			0.173346	−	0.984861i	$-0.444542\pi$
$257$	5.55790			0.346692			0.173346	+	0.984861i	$0.444542\pi$
$258$	4.90645	+	1.59420i	0.305462	+	0.0992508i
$259$	7.23309	−	5.25515i	0.449442	−	0.326539i
$260$	−35.7258	+	27.6999i	−2.21562	+	1.71788i
$261$	9.48082	−	13.0492i	0.586848	−	0.807727i
$262$	−30.8916	−	42.5187i	−1.90849	−	2.62681i
$263$	9.27346	−	6.73757i	0.571826	−	0.415456i	−0.263942	−	0.964539i	$-0.585023\pi$
$263$	9.27346	−	6.73757i	0.571826	−	0.415456i	0.835768	+	0.549082i	$0.185023\pi$
$264$	−0.379584	−	0.275784i	−0.0233618	−	0.0169733i
$265$	23.9211	−	0.746805i	1.46946	−	0.0458758i
$266$	−3.80345	−	5.23500i	−0.233205	−	0.320979i
$267$	−0.0841416	−	0.0273393i	−0.00514938	−	0.00167314i
$268$	4.63400			0.283067
$269$	12.6730	+	4.11771i	0.772688	+	0.251061i	0.668715	−	0.743519i	$-0.266845\pi$
$269$	12.6730	+	4.11771i	0.772688	+	0.251061i	0.103973	+	0.994580i	$0.466845\pi$
$270$	0.404629	+	12.9608i	0.0246249	+	0.788767i
$271$	−5.54966	−	17.0801i	−0.337118	−	1.03754i	−0.965669	−	0.259775i	$-0.916352\pi$
$271$	−5.54966	−	17.0801i	−0.337118	−	1.03754i	0.628551	−	0.777768i	$-0.283648\pi$
$272$	39.9957	−	20.7138i	2.42509	−	1.25596i
$273$	−1.42317	−	1.03400i	−0.0861343	−	0.0625802i
$274$	37.1450			2.24401
$275$	−0.737155	+	0.291508i	−0.0444521	+	0.0175786i
$276$	−15.2062			−0.915303
$277$	2.33430	−	3.21289i	0.140255	−	0.193044i	−0.733111	−	0.680109i	$-0.761933\pi$
$277$	2.33430	−	3.21289i	0.140255	−	0.193044i	0.873366	+	0.487065i	$0.161933\pi$
$278$	−16.2981	+	5.29557i	−0.977494	+	0.317607i
$279$	16.4553	−	5.34666i	0.985155	−	0.320096i
$280$	11.5327	−	16.9624i	0.689214	−	1.01370i
$281$	−0.340613	+	1.04830i	−0.0203193	+	0.0625364i	−0.960702	−	0.277582i	$-0.910467\pi$
$281$	−0.340613	+	1.04830i	−0.0203193	+	0.0625364i	0.940383	+	0.340118i	$0.110467\pi$
$282$		−	1.22377i		−	0.0728745i
$283$	−10.2867	−	3.34234i	−0.611478	−	0.198681i	−0.0131253	−	0.999914i	$-0.504178\pi$
$283$	−10.2867	−	3.34234i	−0.611478	−	0.198681i	−0.598353	+	0.801232i	$0.704178\pi$
$284$	−25.3882	−	34.9439i	−1.50651	−	2.07354i
$285$	−1.69537	−	0.492929i	−0.100425	−	0.0291986i
$286$	−0.998120	+	1.37379i	−0.0590200	+	0.0812341i
$287$	6.40553	−	4.65389i	0.378107	−	0.274710i
$288$	−30.2387	+	21.9697i	−1.78183	+	1.29458i
$289$	16.2362	+	5.03857i	0.955068	+	0.296386i
$290$	−18.7477	+	27.5741i	−1.10090	+	1.61921i
$291$	−1.76161	+	1.27988i	−0.103267	+	0.0750280i
$292$	4.47552	+	1.45418i	0.261910	+	0.0850997i
$293$	20.4738			1.19609			0.598047	−	0.801461i	$-0.295944\pi$
$293$	20.4738			1.19609			0.598047	+	0.801461i	$0.295944\pi$
$294$	−5.32147	−	1.72905i	−0.310354	−	0.100840i
$295$	−5.95311	−	16.5461i	−0.346604	−	0.963353i
$296$	57.9501	−	18.8291i	3.36828	−	1.09442i
$297$	0.107454	+	0.330711i	0.00623514	+	0.0191898i
$298$	33.0697	+	24.0265i	1.91567	+	1.39182i
$299$			32.9787i			1.90721i
$300$	−0.582585	−	9.32138i	−0.0336356	−	0.538170i
$301$			6.04800i			0.348601i
$302$	−33.0943	−	24.0444i	−1.90436	−	1.38360i
$303$	5.99612	−	1.94826i	0.344468	−	0.111925i
$304$	−7.12126	−	21.9170i	−0.408432	−	1.25702i
$305$	−4.80274	−	6.19429i	−0.275004	−	0.354684i
$306$	−30.8245	−	4.67296i	−1.76212	−	0.267136i
$307$	−28.2888			−1.61453			−0.807263	−	0.590192i	$-0.799052\pi$
$307$	−28.2888			−1.61453			−0.807263	+	0.590192i	$0.799052\pi$
$308$	0.283650	−	0.872984i	0.0161624	−	0.0497429i
$309$	2.84514	+	3.91600i	0.161854	+	0.222773i
$310$	−33.6554	+	12.1088i	−1.91150	+	0.687736i
$311$	4.30029	−	5.91884i	0.243847	−	0.335627i	−0.669497	−	0.742814i	$-0.733490\pi$
$311$	4.30029	−	5.91884i	0.243847	−	0.335627i	0.913345	+	0.407188i	$0.133490\pi$
$312$	−7.04693	−	9.69927i	−0.398954	−	0.549113i
$313$	14.7613	+	20.3172i	0.834357	+	1.14839i	0.987096	+	0.160127i	$0.0511904\pi$
$313$	14.7613	+	20.3172i	0.834357	+	1.14839i	−0.152740	+	0.988266i	$0.548810\pi$
$314$	4.90704	+	3.56518i	0.276920	+	0.201194i
$315$	−6.98104	+	2.51170i	−0.393337	+	0.141518i
$316$	−36.4129	−	50.1180i	−2.04838	−	2.81936i
$317$	30.6939	+	9.97305i	1.72394	+	0.560142i	0.992552	−	0.121818i	$-0.0388725\pi$
$317$	30.6939	+	9.97305i	1.72394	+	0.560142i	0.731389	+	0.681961i	$0.238873\pi$
$318$			10.5919i			0.593964i
$319$	−0.276310	+	0.850396i	−0.0154704	+	0.0476130i
$320$	22.4541	−	17.4097i	1.25522	−	0.973233i
$321$	−1.12332	−	3.45721i	−0.0626974	−	0.192963i
$322$	−7.71643	−	23.7487i	−0.430020	−	1.32346i
$323$	3.89731	−	7.77585i	0.216852	−	0.432660i
$324$	38.7201			2.15112
$325$	−20.2159	+	1.26350i	−1.12138	+	0.0700861i
$326$			56.0331i			3.10339i
$327$	3.16712	+	2.30105i	0.175142	+	0.127248i
$328$	51.3198	−	16.6748i	2.83366	−	0.920713i
$329$	1.36445	−	0.443336i	0.0752244	−	0.0244419i
$330$	−0.118770	−	0.330109i	−0.00653805	−	0.0181719i
$331$	−4.31303	+	13.2741i	−0.237065	+	0.729612i	0.759775	+	0.650186i	$0.225309\pi$
$331$	−4.31303	+	13.2741i	−0.237065	+	0.729612i	−0.996841	+	0.0794267i	$0.974691\pi$
$332$	24.9063			1.36691
$333$	−20.9608	−	6.81057i	−1.14864	−	0.373217i
$334$	0.206364	+	0.284035i	0.0112917	+	0.0155417i
$335$	1.71705	+	1.16743i	0.0938126	+	0.0637833i
$336$	3.83772	+	2.78826i	0.209365	+	0.152112i
$337$	−14.5173	−	19.9813i	−0.790805	−	1.08845i	−0.994007	−	0.109313i	$-0.965135\pi$
$337$	−14.5173	−	19.9813i	−0.790805	−	1.08845i	0.203202	−	0.979137i	$-0.434865\pi$
$338$	−7.29665	+	5.30132i	−0.396885	+	0.288354i
$339$	−3.04012	−	2.20877i	−0.165116	−	0.119964i
$340$	45.6834	+	5.47344i	2.47753	+	0.296839i
$341$	−0.775971	+	0.563776i	−0.0420212	+	0.0305302i
$342$	−4.92920	+	15.1705i	−0.266541	+	0.820328i
$343$		−	14.6807i		−	0.792682i
$344$	−12.7372	+	39.2012i	−0.686746	+	2.11359i
$345$	−5.63439	−	3.83083i	−0.303345	−	0.206245i
$346$	14.9861	−	4.86928i	0.805658	−	0.261774i
$347$	−8.19542	+	2.66285i	−0.439953	+	0.142949i	−0.520614	−	0.853792i	$-0.674297\pi$
$347$	−8.19542	+	2.66285i	−0.439953	+	0.142949i	0.0806609	+	0.996742i	$0.474297\pi$
$348$	−8.52295	−	6.19229i	−0.456878	−	0.331942i
$349$	−10.5358			−0.563966			−0.281983	−	0.959419i	$-0.590992\pi$
$349$	−10.5358			−0.563966			−0.281983	+	0.959419i	$0.590992\pi$
$350$	14.2623	−	5.64004i	0.762354	−	0.301473i
$351$			8.88533i			0.474264i
$352$	1.21790	−	1.67630i	0.0649143	−	0.0893468i
$353$	−2.62310	−	8.07307i	−0.139614	−	0.429686i	0.856666	−	0.515872i	$-0.172532\pi$
$353$	−2.62310	−	8.07307i	−0.139614	−	0.429686i	−0.996279	+	0.0861859i	$0.972532\pi$
$354$	7.40146	−	2.40488i	0.393383	−	0.127818i
$355$	−0.603905	−	19.3438i	−0.0320520	−	1.02666i
$356$	0.364518	−	1.12187i	0.0193194	−	0.0594590i
$357$	0.291794	+	1.76648i	0.0154434	+	0.0934919i
$358$	15.1454	−	46.6126i	0.800457	−	2.46355i
$359$	−16.7441	+	12.1653i	−0.883719	+	0.642059i	−0.934233	−	0.356664i	$-0.883914\pi$
$359$	−16.7441	+	12.1653i	−0.883719	+	0.642059i	0.0505141	+	0.998723i	$0.483914\pi$
$360$	−50.5386	+	1.57779i	−2.66362	+	0.0831569i
$361$	11.7711	+	8.55218i	0.619529	+	0.450114i
$362$	−3.70231	−	5.09580i	−0.194589	−	0.267829i
$363$	2.41452	+	3.32330i	0.126729	+	0.174428i
$364$	13.7864	−	18.9753i	0.722603	−	0.994577i
$365$	1.29198	+	1.66633i	0.0676255	+	0.0872194i
$366$	2.80640	−	2.03897i	0.146693	−	0.106579i
$367$	13.5290	+	4.39585i	0.706210	+	0.229461i	0.640034	−	0.768347i	$-0.278920\pi$
$367$	13.5290	+	4.39585i	0.706210	+	0.229461i	0.0661757	+	0.997808i	$0.478920\pi$
$368$		−	88.9301i		−	4.63580i
$369$	−18.5626	−	6.03135i	−0.966330	−	0.313980i
$370$	43.7489	+	12.7200i	2.27439	+	0.661282i
$371$	−11.8095	+	3.83713i	−0.613117	+	0.199214i
$372$	−3.49211	−	10.7476i	−0.181057	−	0.557237i
$373$	−24.1497	−	17.5458i	−1.25043	−	0.908487i	−0.252179	−	0.967681i	$-0.581147\pi$
$373$	−24.1497	−	17.5458i	−1.25043	−	0.908487i	−0.998247	+	0.0591937i	$0.981147\pi$
$374$	1.70519	−	0.281670i	0.0881731	−	0.0145648i
$375$	2.13243	−	3.60065i	0.110118	−	0.185937i
$376$	9.77759			0.504241
$377$	−13.4297	+	18.4843i	−0.691663	+	0.951992i
$378$	−2.07901	−	6.39853i	−0.106933	−	0.329105i
$379$	−4.41964	+	1.43603i	−0.227022	+	0.0737639i	−0.420319	−	0.907376i	$-0.638082\pi$
$379$	−4.41964	+	1.43603i	−0.227022	+	0.0737639i	0.193297	+	0.981140i	$0.438082\pi$
$380$	6.57229	−	22.6045i	0.337151	−	1.15959i
$381$	−1.43596	−	0.466573i	−0.0735667	−	0.0239033i
$382$	−58.8664			−3.01187
$383$	−1.53572	+	4.72645i	−0.0784715	+	0.241510i	−0.982595	−	0.185761i	$-0.940525\pi$
$383$	−1.53572	+	4.72645i	−0.0784715	+	0.241510i	0.904123	+	0.427271i	$0.140525\pi$
$384$	1.64055	+	2.25802i	0.0837188	+	0.115229i
$385$	0.325029	−	0.252011i	0.0165650	−	0.0128437i
$386$	21.4847	−	29.5712i	1.09354	−	1.50513i
$387$	12.0616	−	8.76325i	0.613124	−	0.445461i
$388$	−17.0648	−	23.4877i	−0.866335	−	1.19241i
$389$	−7.21454	−	5.24167i	−0.365792	−	0.265763i	0.389672	−	0.920954i	$-0.372588\pi$
$389$	−7.21454	−	5.24167i	−0.365792	−	0.265763i	−0.755464	+	0.655191i	$0.772588\pi$
$390$	−0.279728	−	8.96005i	−0.0141646	−	0.453710i
$391$	23.5763	−	23.8908i	1.19230	−	1.20821i
$392$	13.8146	−	42.5171i	0.697744	−	2.14744i
$393$	7.44013			0.375305
$394$	−34.4932	−	11.2075i	−1.73774	−	0.564626i
$395$	−0.866147	−	27.7438i	−0.0435806	−	1.39594i
$396$	−2.15199	+	0.699225i	−0.108142	+	0.0351374i
$397$	−11.6937	+	3.79951i	−0.586890	+	0.190692i	−0.587385	−	0.809308i	$-0.699842\pi$
$397$	−11.6937	+	3.79951i	−0.586890	+	0.190692i	0.000495067		1.00000i	$0.499842\pi$
$398$	−41.5038	+	57.1251i	−2.08040	+	2.86342i
$399$	0.916046			0.0458597
$400$	54.5142	−	3.40713i	2.72571	−	0.170357i
$401$			8.51040i			0.424989i	0.977162	+	0.212495i	$0.0681588\pi$
$401$			8.51040i			0.424989i	−0.977162	+	0.212495i	$0.931841\pi$
$402$	−0.540128	+	0.743423i	−0.0269391	+	0.0370786i
$403$	−23.3091	+	7.57359i	−1.16111	+	0.377267i
$404$	25.9764	+	79.9471i	1.29237	+	3.97752i
$405$	14.3471	+	9.75462i	0.712914	+	0.484711i
$406$	5.34600	−	16.4533i	0.265318	−	0.816564i
$407$	1.22177			0.0605608
$408$	−1.82893	+	12.0643i	−0.0905456	+	0.597270i
$409$	−32.5839	+	23.6736i	−1.61117	+	1.17058i	−0.751492	+	0.659742i	$0.770666\pi$
$409$	−32.5839	+	23.6736i	−1.61117	+	1.17058i	−0.859676	+	0.510840i	$0.829334\pi$
$410$	38.7434	+	11.2647i	1.91340	+	0.556323i
$411$	−3.09085	+	4.25418i	−0.152460	+	0.209843i
$412$	−52.2125	+	37.9346i	−2.57232	+	1.86890i
$413$	5.36266	+	7.38106i	0.263879	+	0.363198i
$414$	−36.1816	+	49.7996i	−1.77823	+	2.44752i
$415$	9.22861	+	6.27454i	0.453015	+	0.308005i
$416$	42.8334	−	31.1203i	2.10008	−	1.52580i
$417$	0.749671	−	2.30725i	0.0367116	−	0.112987i
$418$		−	0.884263i		−	0.0432507i
$419$	−5.23163	−	1.69986i	−0.255582	−	0.0830436i	0.178424	−	0.983954i	$-0.442900\pi$
$419$	−5.23163	−	1.69986i	−0.255582	−	0.0830436i	−0.434006	+	0.900910i	$0.642900\pi$
$420$	1.64049	+	4.55958i	0.0800476	+	0.222485i
$421$	8.87870	+	27.3258i	0.432721	+	1.33178i	0.895404	+	0.445256i	$0.146887\pi$
$421$	8.87870	+	27.3258i	0.432721	+	1.33178i	−0.462682	+	0.886524i	$0.653113\pi$
$422$	−22.2571	+	7.23179i	−1.08346	+	0.352038i
$423$	−2.86116	−	2.07876i	−0.139114	−	0.101073i
$424$	−84.6264			−4.10982
$425$	15.5483	+	13.5370i	0.754205	+	0.656639i
$426$	8.56516			0.414984
$427$	3.29003	+	2.39034i	0.159216	+	0.115677i
$428$	46.0954	−	14.9773i	2.22811	−	0.723956i
$429$	−0.0742856	−	0.228627i	−0.00358654	−	0.0110382i
$430$	−24.3566	+	18.8848i	−1.17458	+	0.910707i
$431$	6.63952	+	2.15731i	0.319814	+	0.103914i	0.464525	−	0.885560i	$-0.346225\pi$
$431$	6.63952	+	2.15731i	0.319814	+	0.103914i	−0.144711	+	0.989474i	$0.546225\pi$
$432$		−	23.9601i		−	1.15278i
$433$	−5.97762	+	18.3972i	−0.287266	+	0.884114i	0.698444	+	0.715664i	$0.253876\pi$
$433$	−5.97762	+	18.3972i	−0.287266	+	0.884114i	−0.985710	+	0.168449i	$0.946124\pi$
$434$	15.0133	−	10.9078i	0.720664	−	0.523593i
$435$	−1.59804	−	4.44161i	−0.0766202	−	0.212959i
$436$	−30.6801	+	42.2276i	−1.46931	+	2.02233i
$437$	−10.0942	−	13.8934i	−0.482869	−	0.664612i
$438$	−0.754948	+	0.548502i	−0.0360728	+	0.0262084i
$439$	−14.3775	+	19.7889i	−0.686200	+	0.944473i	−0.999987	−	0.00502013i	$-0.998402\pi$
$439$	−14.3775	+	19.7889i	−0.686200	+	0.944473i	0.313788	+	0.949493i	$0.398402\pi$
$440$	2.63748	−	0.948936i	0.125737	−	0.0452388i
$441$	−13.0818	+	9.50449i	−0.622943	+	0.452595i
$442$	43.6632	+	6.61929i	2.07684	+	0.314848i
$443$	−31.6552			−1.50399			−0.751993	−	0.659171i	$-0.770907\pi$
$443$	−31.6552			−1.50399			−0.751993	+	0.659171i	$0.770907\pi$
$444$	−4.44824	+	13.6903i	−0.211104	+	0.649712i
$445$	0.417695	−	0.323859i	0.0198006	−	0.0153524i
$446$	−4.37764	−	13.4730i	−0.207287	−	0.637964i
$447$	−5.50347	+	1.78819i	−0.260305	+	0.0845783i
$448$	−8.66490	+	11.9262i	−0.409378	+	0.563460i
$449$		−	23.4934i		−	1.10872i	−0.832276	−	0.554362i	$-0.812962\pi$
$449$		−	23.4934i		−	1.10872i	0.832276	−	0.554362i	$-0.187038\pi$
$450$	−31.9134	−	20.2714i	−1.50441	−	0.955601i
$451$	1.08198			0.0509485
$452$	29.4498	−	40.5342i	1.38520	−	1.90657i
$453$	5.50756	−	1.78952i	0.258768	−	0.0840788i
$454$	55.6761	−	18.0903i	2.61301	−	0.849018i
$455$	9.88870	−	3.55784i	0.463590	−	0.166794i
$456$	5.93752	+	1.92922i	0.278050	+	0.0903439i
$457$	30.5760			1.43028			0.715142	−	0.698979i	$-0.246362\pi$
$457$	30.5760			1.43028			0.715142	+	0.698979i	$0.246362\pi$
$458$	−2.84120	+	8.74433i	−0.132761	+	0.408596i
$459$	6.35207	−	6.43682i	0.296489	−	0.300445i
$460$	51.0769	−	75.1240i	2.38147	−	3.50268i
$461$	4.86925	+	3.53772i	0.226783	+	0.164768i	0.695375	−	0.718647i	$-0.255238\pi$
$461$	4.86925	+	3.53772i	0.226783	+	0.164768i	−0.468591	+	0.883415i	$0.655238\pi$
$462$	0.106989	+	0.147258i	0.00497760	+	0.00685108i
$463$	−4.83170	+	3.51044i	−0.224548	+	0.163144i	−0.694372	−	0.719617i	$-0.744318\pi$
$463$	−4.83170	+	3.51044i	−0.224548	+	0.163144i	0.469823	+	0.882760i	$0.344318\pi$
$464$	36.2143	−	49.8448i	1.68121	−	2.31398i
$465$	1.41366	−	4.86210i	0.0655569	−	0.225475i
$466$	−31.7100	−	43.6450i	−1.46894	−	2.02182i
$467$	−8.59414	+	26.4500i	−0.397689	+	1.22396i	0.529158	+	0.848523i	$0.322508\pi$
$467$	−8.59414	+	26.4500i	−0.397689	+	1.22396i	−0.926847	+	0.375439i	$0.877492\pi$
$468$	−57.8184			−2.67266
$469$	−1.02455	−	0.332898i	−0.0473095	−	0.0153718i
$470$	6.04588	+	4.11060i	0.278876	+	0.189608i
$471$	−0.816632	+	0.265340i	−0.0376284	+	0.0122262i
$472$	19.2143	+	59.1356i	0.884411	+	2.72194i
$473$	−0.485795	+	0.668639i	−0.0223369	+	0.0307440i
$474$	12.2845			0.564247
$475$	8.12993	−	6.72001i	0.373027	−	0.308335i
$476$	−23.5527	+	3.89053i	−1.07953	+	0.178322i
$477$	24.7638	+	17.9919i	1.13385	+	0.823794i
$478$	0.828755	+	2.55065i	0.0379064	+	0.116664i
$479$	28.7904	−	9.35456i	1.31547	−	0.427421i	0.434530	−	0.900657i	$-0.356914\pi$
$479$	28.7904	−	9.35456i	1.31547	−	0.427421i	0.880935	+	0.473237i	$0.156914\pi$
$480$	0.341323	+	10.9330i	0.0155792	+	0.499021i
$481$	29.6911	+	9.64723i	1.35380	+	0.439876i
$482$			10.5030i			0.478399i
$483$	3.36201	+	1.09238i	0.152977	+	0.0497051i
$484$	−44.3099	+	32.1930i	−2.01409	+	1.46332i
$485$	−0.405918	−	13.0021i	−0.0184318	−	0.590393i
$486$	−14.7389	+	20.2864i	−0.668571	+	0.920209i
$487$	17.8876	+	24.6201i	0.810563	+	1.11564i	0.991236	+	0.132101i	$0.0421723\pi$
$487$	17.8876	+	24.6201i	0.810563	+	1.11564i	−0.180674	+	0.983543i	$0.557828\pi$
$488$	16.2908	+	22.4223i	0.737449	+	1.01501i
$489$	−6.41742	−	4.66253i	−0.290206	−	0.210847i
$490$	26.4168	−	20.4822i	1.19339	−	0.925292i
$491$	−12.1606	+	8.83517i	−0.548799	+	0.398726i	−0.827342	−	0.561698i	$-0.810148\pi$
$491$	−12.1606	+	8.83517i	−0.548799	+	0.398726i	0.278544	+	0.960424i	$0.410148\pi$
$492$	−3.93931	+	12.1239i	−0.177598	+	0.546589i
$493$	22.9432	−	3.78986i	1.03331	−	0.170687i
$494$	6.98225	−	21.4892i	0.314146	−	0.966843i
$495$	−0.973540	−	0.283057i	−0.0437573	−	0.0127225i
$496$	62.8552	−	20.4229i	2.82228	−	0.917015i
$497$	3.10290	+	9.54976i	0.139184	+	0.428365i
$498$	−2.90302	+	3.99566i	−0.130087	+	0.179050i
$499$			20.5765i			0.921130i	0.887626	+	0.460565i	$0.152353\pi$
$499$			20.5765i			0.921130i	−0.887626	+	0.460565i	$0.847647\pi$
$500$	48.0079	+	28.4320i	2.14698	+	1.27152i
$501$	−0.0497019			−0.00222052
$502$	0.590296	+	0.428875i	0.0263462	+	0.0191416i
$503$	8.18400	−	2.65914i	0.364906	−	0.118565i	−0.120824	−	0.992674i	$-0.538554\pi$
$503$	8.18400	−	2.65914i	0.364906	−	0.118565i	0.485730	+	0.874109i	$0.338554\pi$
$504$	24.9501	−	8.10679i	1.11137	−	0.361105i
$505$	−10.5156	+	36.1672i	−0.467940	+	1.60942i
$506$	1.05448	−	3.24536i	0.0468774	−	0.144274i
$507$		−	1.27680i		−	0.0567048i
$508$	6.22088	−	19.1459i	0.276007	−	0.849461i
$509$	20.5422	−	14.9248i	0.910518	−	0.661530i	−0.0306282	−	0.999531i	$-0.509751\pi$
$509$	20.5422	−	14.9248i	0.910518	−	0.661530i	0.941146	+	0.338001i	$0.109751\pi$
$510$	−6.20285	+	6.69093i	−0.274667	+	0.296279i
$511$	−0.885049	−	0.643026i	−0.0391523	−	0.0284458i
$512$	24.2523	−	17.6204i	1.07181	−	0.778717i
$513$	−2.71963	−	3.74325i	−0.120075	−	0.165269i
$514$	−11.8884	−	8.63741i	−0.524374	−	0.380980i
$515$	−28.9032	+	0.902344i	−1.27363	+	0.0397620i
$516$	−5.72361	−	7.87788i	−0.251968	−	0.346804i
$517$	0.186457	+	0.0605836i	0.00820037	+	0.00266446i
$518$	−23.6385			−1.03862
$519$	−0.689323	+	2.12152i	−0.0302579	+	0.0931244i
$520$	71.5884	−	2.23495i	3.13936	−	0.0980092i
$521$	−10.0997	+	3.28159i	−0.442475	+	0.143769i	−0.521777	−	0.853082i	$-0.674731\pi$
$521$	−10.0997	+	3.28159i	−0.442475	+	0.143769i	0.0793021	+	0.996851i	$0.474731\pi$
$522$	−40.5591	+	13.1784i	−1.77522	+	0.576805i
$523$	15.4162	+	11.2005i	0.674104	+	0.489765i	0.871397	−	0.490579i	$-0.163215\pi$
$523$	15.4162	+	11.2005i	0.674104	+	0.489765i	−0.197292	+	0.980345i	$0.563215\pi$
$524$			99.2002i			4.33358i
$525$	−0.540823	+	2.10276i	−0.0236035	+	0.0917720i
$526$	−30.3067			−1.32143
$527$	22.3002	+	11.1770i	0.971411	+	0.486878i
$528$	0.200318	+	0.616515i	0.00871772	+	0.0268304i
$529$	−13.3716	−	41.1535i	−0.581373	−	1.78928i
$530$	−52.3279	−	35.5778i	−2.27298	−	1.54540i
$531$	6.94990	−	21.3896i	0.301600	−	0.928229i
$532$			12.2138i			0.529534i
$533$	26.2941	+	8.54346i	1.13892	+	0.370058i
$534$	0.137492	+	0.189242i	0.00594986	+	0.00818928i
$535$	20.8531	+	6.06305i	0.901558	+	0.262129i
$536$	−5.93974	−	4.31548i	−0.256558	−	0.186400i
$537$	4.07825	+	5.61323i	0.175990	+	0.242229i
$538$	−20.7084	−	28.5027i	−0.892803	−	1.22884i
$539$	0.526886	−	0.725196i	0.0226946	−	0.0312364i
$540$	13.7615	−	20.2404i	0.592199	−	0.871008i
$541$	14.3045	+	19.6884i	0.614998	+	0.846472i	0.996977	−	0.0776993i	$-0.0247574\pi$
$541$	14.3045	+	19.6884i	0.614998	+	0.846472i	−0.381979	+	0.924171i	$0.624757\pi$
$542$	−14.6731	+	45.1591i	−0.630262	+	1.93975i
$543$	0.891687			0.0382660
$544$	−53.2776	−	8.07682i	−2.28426	−	0.346291i
$545$	−22.0062	+	7.91760i	−0.942644	+	0.339153i
$546$	1.43726	+	4.42344i	0.0615092	+	0.189306i
$547$	−23.8001	+	7.73314i	−1.01762	+	0.330645i	−0.769885	−	0.638183i	$-0.779686\pi$
$547$	−23.8001	+	7.73314i	−1.01762	+	0.330645i	−0.247736	+	0.968828i	$0.579686\pi$
$548$	−56.7216	−	41.2106i	−2.42303	−	1.76043i
$549$		−	10.0248i		−	0.427849i
$550$	2.02980	+	0.522059i	0.0865511	+	0.0222607i
$551$		−	11.8977i		−	0.506860i
$552$	19.4909	+	14.1609i	0.829586	+	0.602730i
$553$	4.45032	+	13.6967i	0.189247	+	0.582442i
$554$	−9.98616	+	3.24470i	−0.424271	+	0.137854i
$555$	−5.09717	+	3.95208i	−0.216363	+	0.167756i
$556$	30.7629	+	9.99546i	1.30464	+	0.423902i
$557$	29.6870			1.25788			0.628940	−	0.777454i	$-0.283489\pi$
$557$	29.6870			1.25788			0.628940	+	0.777454i	$0.283489\pi$
$558$	−43.5072	−	14.1363i	−1.84181	−	0.598439i
$559$	−17.0853	+	12.4132i	−0.722632	+	0.525023i
$560$	−26.6658	+	9.59406i	−1.12684	+	0.405423i
$561$	−0.109630	+	0.218731i	−0.00462857	+	0.00923485i
$562$	2.35771	−	1.71298i	0.0994542	−	0.0722577i
$563$	−20.0297	+	14.5524i	−0.844152	+	0.613312i	−0.923527	−	0.383533i	$-0.874707\pi$
$563$	−20.0297	+	14.5524i	−0.844152	+	0.613312i	0.0793756	+	0.996845i	$0.474707\pi$
$564$	−1.35772	+	1.86873i	−0.0571701	+	0.0786879i
$565$	21.1238	−	7.60011i	0.888685	−	0.319739i
$566$	16.8090	+	23.1356i	0.706533	+	0.972460i
$567$	−8.56083	−	2.78158i	−0.359521	−	0.116815i
$568$			68.4333i			2.87140i
$569$	4.55310	−	14.0130i	0.190876	−	0.587456i	−0.809124	−	0.587638i	$-0.800058\pi$
$569$	4.55310	−	14.0130i	0.190876	−	0.587456i	1.00000		0.000182164i	$5.79846e-5\pi$
$570$	2.86035	+	3.68911i	0.119807	+	0.154520i
$571$	−13.9916	+	4.54614i	−0.585529	+	0.190250i	−0.586776	−	0.809749i	$-0.699603\pi$
$571$	−13.9916	+	4.54614i	−0.585529	+	0.190250i	0.00124675	+	0.999999i	$0.499603\pi$
$572$	3.04832	−	0.990459i	0.127457	−	0.0414132i
$573$	4.89829	−	6.74192i	0.204629	−	0.281648i
$574$	−20.9340			−0.873767
$575$	37.8514	−	14.9684i	1.57851	−	0.624224i
$576$	36.3395			1.51415
$577$	4.88320	+	3.54785i	0.203290	+	0.147699i	0.684773	−	0.728757i	$-0.259902\pi$
$577$	4.88320	+	3.54785i	0.203290	+	0.147699i	−0.481483	+	0.876456i	$0.659902\pi$
$578$	−26.8989	−	36.0098i	−1.11885	−	1.49781i
$579$	1.59901	+	4.92125i	0.0664526	+	0.204520i
$580$	59.2205	−	21.3069i	2.45900	−	0.884720i
$581$	−5.50665	−	1.78922i	−0.228454	−	0.0742293i
$582$	5.75712			0.238640
$583$	−1.61381	−	0.524359i	−0.0668372	−	0.0217167i
$584$	−4.38238	−	6.03183i	−0.181344	−	0.249599i
$585$	−21.4237	−	14.5660i	−0.885760	−	0.602229i
$586$	−43.7936	−	31.8179i	−1.80910	−	1.31439i
$587$	−36.3862	+	26.4361i	−1.50182	+	1.09113i	−0.532166	+	0.846640i	$0.678622\pi$
$587$	−36.3862	+	26.4361i	−1.50182	+	1.09113i	−0.969651	+	0.244494i	$0.921378\pi$
$588$	6.20774	+	8.54423i	0.256003	+	0.352358i
$589$	7.50163	−	10.3251i	0.309099	−	0.425439i
$590$	−12.9802	+	44.6439i	−0.534388	+	1.83796i
$591$	4.15377	−	3.01789i	0.170863	−	0.124140i
$592$	−80.0648	−	26.0146i	−3.29064	−	1.06920i
$593$	−24.3317			−0.999182			−0.499591	−	0.866261i	$-0.666516\pi$
$593$	−24.3317			−0.999182			−0.499591	+	0.866261i	$0.666516\pi$
$594$	0.284105	−	0.874384i	0.0116570	−	0.0358764i
$595$	−9.70718	−	4.49196i	−0.397955	−	0.184153i
$596$	−23.8421	−	73.3785i	−0.976611	−	3.00570i
$597$	−3.08894	−	9.50678i	−0.126422	−	0.389087i
$598$	51.2515	−	70.5416i	2.09583	−	2.88466i
$599$	−11.7623			−0.480593			−0.240297	−	0.970699i	$-0.577245\pi$
$599$	−11.7623			−0.480593			−0.240297	+	0.970699i	$0.577245\pi$
$600$	−7.93392	+	12.4904i	−0.323901	+	0.509920i
$601$		−	3.33100i		−	0.135874i	−0.997690	−	0.0679372i	$-0.978358\pi$
$601$		−	3.33100i		−	0.135874i	0.997690	−	0.0679372i	$-0.0216417\pi$
$602$	9.39906	−	12.9367i	0.383077	−	0.527261i
$603$	0.820627	+	2.52563i	0.0334185	+	0.102852i
$604$	23.8598	+	73.4330i	0.970843	+	2.98795i
$605$	−24.5286	+	0.765771i	−0.997229	+	0.0311330i
$606$	−15.8535	−	5.15111i	−0.644004	−	0.209250i
$607$		−	43.2234i		−	1.75439i	−0.480139	−	0.877193i	$-0.659414\pi$
$607$		−	43.2234i		−	1.75439i	0.480139	−	0.877193i	$-0.340586\pi$
$608$	−8.51970	+	26.2210i	−0.345520	+	1.06340i
$609$	1.43954	+	1.98136i	0.0583331	+	0.0802886i
$610$	0.646664	+	20.7135i	0.0261827	+	0.838663i
$611$	4.05286	+	2.94458i	0.163961	+	0.119125i
$612$	41.8855	+	41.3341i	1.69312	+	1.67083i
$613$	−18.4231	+	13.3852i	−0.744101	+	0.540621i	−0.893993	−	0.448081i	$-0.852108\pi$
$613$	−18.4231	+	13.3852i	−0.744101	+	0.540621i	0.149892	+	0.988702i	$0.452108\pi$
$614$	60.5098	+	43.9630i	2.44198	+	1.77420i
$615$	−4.51398	+	3.49991i	−0.182021	+	0.141130i
$616$	−1.17655	+	0.854816i	−0.0474047	+	0.0344415i
$617$	31.3252	+	10.1782i	1.26111	+	0.409758i	0.861888	−	0.507099i	$-0.169282\pi$
$617$	31.3252	+	10.1782i	1.26111	+	0.409758i	0.399217	+	0.916856i	$0.369282\pi$
$618$		−	12.7979i		−	0.514807i
$619$	−29.0420	−	9.43631i	−1.16730	−	0.379277i	−0.339663	−	0.940547i	$-0.610313\pi$
$619$	−29.0420	−	9.43631i	−1.16730	−	0.379277i	−0.827633	+	0.561270i	$0.810313\pi$
$620$	64.8270	+	18.8485i	2.60352	+	0.756974i
$621$	−5.51757	−	16.9813i	−0.221413	−	0.681438i
$622$	−18.3967	+	5.97745i	−0.737640	+	0.239674i
$623$	−0.161186	+	0.221854i	−0.00645779	+	0.00888838i
$624$			16.5641i			0.663096i
$625$	10.6258	+	22.6295i	0.425032	+	0.905179i
$626$		−	66.3987i		−	2.65382i
$627$	0.101274	+	0.0735798i	0.00404449	+	0.00293849i
$628$	−3.53781	−	10.8883i	−0.141174	−	0.434489i
$629$	−14.6124	−	28.2148i	−0.582636	−	1.12500i
$630$	18.8359	+	5.47654i	0.750439	+	0.218191i
$631$	5.29714	−	16.3029i	0.210876	−	0.649009i	−0.788545	−	0.614977i	$-0.789165\pi$
$631$	5.29714	−	16.3029i	0.210876	−	0.649009i	0.999421	−	0.0340320i	$-0.0108348\pi$
$632$			98.1500i			3.90420i
$633$	1.02377	−	3.15085i	0.0406913	−	0.125235i
$634$	−50.1555	−	69.0331i	−1.99193	−	2.74166i
$635$	7.12840	−	5.52699i	0.282882	−	0.219332i
$636$	11.7512	−	16.1742i	0.465966	−	0.641347i
$637$	18.5305	−	13.4632i	0.734205	−	0.533431i
$638$	1.91261	−	1.38959i	0.0757210	−	0.0550145i
$639$	14.5492	−	20.0253i	0.575558	−	0.792187i
$640$	−16.6660	+	0.520304i	−0.658781	+	0.0205668i
$641$	−4.92690	−	6.78130i	−0.194601	−	0.267845i	0.700555	−	0.713598i	$-0.252936\pi$
$641$	−4.92690	−	6.78130i	−0.194601	−	0.267845i	−0.895156	+	0.445753i	$0.852936\pi$
$642$	−2.97000	+	9.14072i	−0.117217	+	0.360755i
$643$			29.7140i			1.17180i	0.810382	+	0.585902i	$0.199260\pi$
$643$			29.7140i			1.17180i	−0.810382	+	0.585902i	$0.800740\pi$
$644$	−14.5649	+	44.8260i	−0.573936	+	1.76639i
$645$	−0.136147	−	4.36095i	−0.00536077	−	0.171712i
$646$	−20.4206	+	10.5759i	−0.803440	+	0.416102i
$647$	−1.80257	−	5.54775i	−0.0708665	−	0.218105i	0.909350	−	0.416031i	$-0.136579\pi$
$647$	−1.80257	−	5.54775i	−0.0708665	−	0.218105i	−0.980217	+	0.197926i	$0.936579\pi$
$648$	−49.6305	−	36.0587i	−1.94967	−	1.41652i
$649$			1.24676i			0.0489397i
$650$	45.2056	+	28.7145i	1.77311	+	1.12628i
$651$			2.62711i			0.102964i
$652$	62.1661	−	85.5643i	2.43461	−	3.35096i
$653$	−41.5529	+	13.5014i	−1.62609	+	0.528349i	−0.973368	−	0.229248i	$-0.926373\pi$
$653$	−41.5529	+	13.5014i	−1.62609	+	0.528349i	−0.652722	+	0.757597i	$0.726373\pi$
$654$	−3.19848	−	9.84389i	−0.125070	−	0.384927i
$655$	−24.9911	+	36.7570i	−0.976484	+	1.43621i
$656$	−70.9044	−	23.0382i	−2.76835	−	0.899492i
$657$			2.69677i			0.105211i
$658$	−3.60754	−	1.17216i	−0.140636	−	0.0456955i
$659$	20.6806	−	15.0253i	0.805602	−	0.585304i	−0.106950	−	0.994264i	$-0.534109\pi$
$659$	20.6806	−	15.0253i	0.805602	−	0.585304i	0.912552	+	0.408960i	$0.134109\pi$
$660$	−0.184876	+	0.635856i	−0.00719627	+	0.0247507i
$661$	−4.20146	−	3.05254i	−0.163418	−	0.118730i	0.503071	−	0.864245i	$-0.332203\pi$
$661$	−4.20146	−	3.05254i	−0.163418	−	0.118730i	−0.666489	+	0.745515i	$0.732203\pi$
$662$	29.8546	−	21.6907i	1.16033	−	0.843031i
$663$	−4.39132	+	4.44991i	−0.170545	+	0.172820i
$664$	−31.9242	−	23.1943i	−1.23890	−	0.900114i
$665$	−3.07697	+	4.52561i	−0.119320	+	0.175496i
$666$	34.2511	+	47.1425i	1.32720	+	1.82674i
$667$	14.1880	−	43.6662i	0.549362	−	1.69076i
$668$		−	0.662682i		−	0.0256399i
$669$	1.90731	+	0.619723i	0.0737410	+	0.0239599i
$670$	−1.85851	−	5.16556i	−0.0718006	−	0.199563i
$671$	0.171730	+	0.528531i	0.00662957	+	0.0204037i
$672$	−1.75374	−	5.39746i	−0.0676520	−	0.208211i
$673$	6.62456	−	9.11792i	0.255358	−	0.351470i	−0.662021	−	0.749486i	$-0.730301\pi$
$673$	6.62456	−	9.11792i	0.255358	−	0.351470i	0.917379	+	0.398015i	$0.130301\pi$
$674$			65.3010i			2.51530i
$675$	10.1982	−	4.03287i	0.392528	−	0.155225i
$676$	17.0238			0.654760
$677$	−11.6342	+	16.0131i	−0.447139	+	0.615434i	−0.971780	−	0.235890i	$-0.924200\pi$
$677$	−11.6342	+	16.0131i	−0.447139	+	0.615434i	0.524641	+	0.851324i	$0.324200\pi$
$678$	3.07022	+	9.44916i	0.117911	+	0.362893i
$679$	2.08563	+	6.41892i	0.0800393	+	0.246336i
$680$	−53.4586	−	49.5590i	−2.05005	−	1.90050i
$681$	−2.56096	+	7.88182i	−0.0981362	+	0.302032i
$682$	2.53596			0.0971069
$683$	10.1306	+	3.29164i	0.387638	+	0.125951i	0.496351	−	0.868122i	$-0.334673\pi$
$683$	10.1306	+	3.29164i	0.387638	+	0.125951i	−0.108713	+	0.994073i	$0.534673\pi$
$684$	24.3580	−	17.6971i	0.931352	−	0.676667i
$685$	−10.6352	−	29.5596i	−0.406350	−	1.12941i
$686$	−22.8149	+	31.4020i	−0.871077	+	1.19893i
$687$	−0.765063	−	1.05302i	−0.0291890	−	0.0401752i
$688$	46.0722	−	33.4734i	1.75648	−	1.27616i
$689$	−35.0781	−	25.4857i	−1.33637	−	0.970928i
$690$	6.09858	+	16.9505i	0.232169	+	0.645293i
$691$	−24.7486	−	34.0636i	−0.941483	−	1.29584i	−0.955208	−	0.295934i	$-0.904369\pi$
$691$	−24.7486	−	34.0636i	−0.941483	−	1.29584i	0.0137256	−	0.999906i	$-0.495631\pi$
$692$	−28.2865	−	9.19084i	−1.07529	−	0.349383i
$693$	0.526026			0.0199821
$694$	21.6683	+	7.04046i	0.822518	+	0.267252i
$695$	8.88056	+	11.4536i	0.336859	+	0.434461i
$696$	5.15785	+	15.8742i	0.195508	+	0.601711i
$697$	−12.9406	−	24.9866i	−0.490160	−	0.946436i
$698$	22.5360	+	16.3734i	0.853002	+	0.619742i
$699$	7.63722			0.288866
$700$	−28.0364	−	7.21086i	−1.05968	−	0.272545i
$701$	−24.9855			−0.943688			−0.471844	−	0.881682i	$-0.656411\pi$
$701$	−24.9855			−0.943688			−0.471844	+	0.881682i	$0.656411\pi$
$702$	13.8085	−	19.0058i	0.521168	−	0.717326i
$703$	−15.4612	+	5.02366i	−0.583132	+	0.189471i
$704$	−1.91590	+	0.622514i	−0.0722083	+	0.0234619i
$705$	−0.973862	+	0.350385i	−0.0366778	+	0.0131963i
$706$	−6.93536	+	21.3449i	−0.261016	+	0.803324i
$707$		−	19.5420i		−	0.734952i
$708$	−13.9704	−	4.53924i	−0.525038	−	0.170595i
$709$	11.0352	+	15.1887i	0.414437	+	0.570424i	0.964294	−	0.264835i	$-0.0853175\pi$
$709$	11.0352	+	15.1887i	0.414437	+	0.570424i	−0.549856	+	0.835259i	$0.685318\pi$
$710$	−28.7701	+	42.3151i	−1.07972	+	1.58806i
$711$	20.8671	−	28.7211i	0.782578	−	1.07713i
$712$	−1.51199	+	1.09852i	−0.0566641	+	0.0411689i
$713$	39.8446	−	28.9488i	1.49219	−	1.08414i
$714$	2.12109	−	4.23197i	0.0793800	−	0.158378i
$715$	1.37903	+	0.400953i	0.0515727	+	0.0149948i
$716$	−74.8419	+	54.3758i	−2.79697	+	2.03212i
$717$	−0.361084	−	0.117323i	−0.0134849	−	0.00438152i
$718$	54.7215			2.04219
$719$	−42.2776	−	13.7368i	−1.57669	−	0.512298i	−0.615489	−	0.788146i	$-0.711041\pi$
$719$	−42.2776	−	13.7368i	−1.57669	−	0.512298i	−0.961201	+	0.275848i	$0.911041\pi$
$720$	57.7709	+	39.2785i	2.15300	+	1.46382i
$721$	14.2691	−	4.63630i	0.531408	−	0.172665i
$722$	−11.8876	−	36.5863i	−0.442411	−	1.36160i
$723$	−1.20290	−	0.873959i	−0.0447364	−	0.0325029i
$724$			11.8890i			0.441850i
$725$	27.3109	+	7.02429i	1.01430	+	0.260875i
$726$		−	10.8609i		−	0.403086i
$727$	−34.2286	−	24.8685i	−1.26947	−	0.922323i	−0.270288	−	0.962780i	$-0.587119\pi$
$727$	−34.2286	−	24.8685i	−1.26947	−	0.922323i	−0.999181	+	0.0404561i	$0.987119\pi$
$728$	−35.3421	+	11.4833i	−1.30986	+	0.425601i
$729$	6.09582	+	18.7610i	0.225771	+	0.694852i
$730$	−0.173959	−	5.57212i	−0.00643851	−	0.206233i
$731$	21.2513	+	3.22167i	0.786007	+	0.119158i
$732$	−6.54759			−0.242006
$733$	−2.20558	+	6.78807i	−0.0814648	+	0.250723i	−0.983491	−	0.180959i	$-0.942080\pi$
$733$	−2.20558	+	6.78807i	−0.0814648	+	0.250723i	0.902026	+	0.431682i	$0.142080\pi$
$734$	−22.1072	−	30.4279i	−0.815991	−	1.12311i
$735$	0.147663	+	4.72982i	0.00544662	+	0.174462i
$736$	−62.5368	+	86.0745i	−2.30514	+	3.17275i
$737$	−0.0865305	−	0.119099i	−0.00318739	−	0.00438707i
$738$	30.3323	+	41.7488i	1.11655	+	1.53679i
$739$	7.62443	+	5.53947i	0.280469	+	0.203773i	0.719122	−	0.694884i	$-0.244544\pi$
$739$	7.62443	+	5.53947i	0.280469	+	0.203773i	−0.438653	+	0.898657i	$0.644544\pi$
$740$	−52.6936	−	67.9611i	−1.93705	−	2.49830i
$741$	1.88014	+	2.58779i	0.0690686	+	0.0950648i
$742$	31.2237	+	10.1452i	1.14626	+	0.372442i
$743$		−	42.7211i		−	1.56729i	−0.621212	−	0.783643i	$-0.713359\pi$
$743$		−	42.7211i		−	1.56729i	0.621212	−	0.783643i	$-0.286641\pi$
$744$	−5.53276	+	17.0281i	−0.202841	+	0.624280i
$745$	9.65166	−	33.1956i	0.353610	−	1.21619i
$746$	24.3888	+	75.0611i	0.892939	+	2.74818i
$747$	4.41061	+	13.5744i	0.161376	+	0.496663i
$748$	−2.91637	−	1.46171i	−0.106633	−	0.0534453i
$749$	−11.2674			−0.411702
$750$	−10.1570	+	4.38785i	−0.370880	+	0.160221i
$751$		−	9.89387i		−	0.361032i	−0.983572	−	0.180516i	$-0.942223\pi$
$751$		−	9.89387i		−	0.361032i	0.983572	−	0.180516i	$-0.0577768\pi$
$752$	−10.9289	−	7.94032i	−0.398536	−	0.289554i
$753$	−0.0982374	+	0.0319193i	−0.00357997	+	0.00116320i
$754$	57.4522	−	18.6674i	2.09229	−	0.679825i
$755$	−9.65884	+	33.2203i	−0.351521	+	1.20901i
$756$	−3.92416	+	12.0773i	−0.142720	+	0.439248i
$757$	9.09007			0.330384			0.165192	−	0.986261i	$-0.447176\pi$
$757$	9.09007			0.330384			0.165192	+	0.986261i	$0.447176\pi$
$758$	11.6853	+	3.79680i	0.424431	+	0.137906i
$759$	0.283944	+	0.390816i	0.0103065	+	0.0141857i
$760$	−29.4750	+	22.8534i	−1.06917	+	0.828979i
$761$	−24.5587	−	17.8429i	−0.890251	−	0.646805i	0.0456924	−	0.998956i	$-0.485451\pi$
$761$	−24.5587	−	17.8429i	−0.890251	−	0.646805i	−0.935943	+	0.352150i	$0.885451\pi$
$762$	2.34644	+	3.22960i	0.0850027	+	0.116996i
$763$	9.81677	−	7.13230i	0.355391	−	0.258207i
$764$	89.8908	+	65.3095i	3.25214	+	2.36282i
$765$	5.10685	+	25.8677i	0.184639	+	0.935250i
$766$	10.6302	−	7.72328i	0.384084	−	0.279054i
$767$	−9.84459	+	30.2985i	−0.355467	+	1.09402i
$768$			2.13252i			0.0769505i
$769$	5.94738	−	18.3041i	0.214468	−	0.660064i	−0.784723	−	0.619847i	$-0.787195\pi$
$769$	5.94738	−	18.3041i	0.214468	−	0.660064i	0.999191	−	0.0402177i	$-0.0128052\pi$
$770$	−1.08688	+	0.0339320i	−0.0391686	+	0.00122282i
$771$	1.97847	−	0.642844i	0.0712528	−	0.0231514i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.13901 - 1.55408i) q^{2} +(0.355974 - 0.115663i) q^{3} +(1.54215 + 4.74625i) q^{4} +(-0.624287 + 2.14715i) q^{5} +(-0.941180 - 0.305808i) q^{6} -1.16016i q^{7} +(2.44332 - 7.51977i) q^{8} +(-2.31371 + 1.68101i) q^{9} +(4.67220 - 3.62258i) q^{10} +(0.0931875 - 0.128262i) q^{11} +(1.09793 + 1.51117i) q^{12} +(3.27739 - 2.38116i) q^{13} +(-1.80297 + 2.48158i) q^{14} +(0.0261163 + 0.836538i) q^{15} +(-8.83779 + 6.42103i) q^{16} +(-4.07653 - 0.617997i) q^{17} +7.56146 q^{18} +(-0.651885 + 2.00629i) q^{19} +(-11.1537 + 0.348212i) q^{20} +(-0.134187 - 0.412986i) q^{21} +(-0.398657 + 0.129532i) q^{22} +(-4.78500 + 6.58598i) q^{23} -2.95945i q^{24} +(-4.22053 - 2.68088i) q^{25} -10.7109 q^{26} +(-1.28920 + 1.77444i) q^{27} +(5.50640 - 1.78914i) q^{28} +(-5.36392 + 1.74284i) q^{29} +(1.24418 - 1.82995i) q^{30} +(-5.75381 - 1.86952i) q^{31} +13.0693 q^{32} +(0.0183372 - 0.0564362i) q^{33} +(7.75930 + 7.65714i) q^{34} +(2.49103 + 0.724271i) q^{35} +(-11.5466 - 8.38908i) q^{36} +(4.52969 + 6.23458i) q^{37} +(4.51232 - 3.27839i) q^{38} +(0.891254 - 1.22671i) q^{39} +(14.6208 + 9.94068i) q^{40} +(4.01143 + 5.52126i) q^{41} +(-0.354785 + 1.09192i) q^{42} -5.21309 q^{43} +(0.752471 + 0.244493i) q^{44} +(-2.16497 - 6.01732i) q^{45} +(20.4703 - 6.65119i) q^{46} +(0.382134 + 1.17609i) q^{47} +(-2.40335 + 3.30793i) q^{48} +5.65404 q^{49} +(4.86145 + 12.2934i) q^{50} +(-1.52262 + 0.251512i) q^{51} +(16.3558 + 11.8832i) q^{52} +(-3.30742 - 10.1792i) q^{53} +(5.51523 - 1.79201i) q^{54} +(0.217222 + 0.280160i) q^{55} +(-8.72412 - 2.83464i) q^{56} +0.789588i q^{57} +(14.1820 + 4.60800i) q^{58} +(-6.36212 + 4.62235i) q^{59} +(-3.93014 + 1.41402i) q^{60} +(-2.06036 + 2.83585i) q^{61} +(9.40203 + 12.9408i) q^{62} +(1.95024 + 2.68427i) q^{63} +(-10.2798 - 7.46873i) q^{64} +(3.06669 + 8.52359i) q^{65} +(-0.126930 + 0.0922198i) q^{66} +(0.286942 - 0.883117i) q^{67} +(-3.35345 - 20.3013i) q^{68} +(-0.941581 + 2.89789i) q^{69} +(-4.20276 - 5.42048i) q^{70} +(-8.23143 + 2.67455i) q^{71} +(6.98767 + 21.5058i) q^{72} +(0.554257 - 0.762870i) q^{73} -20.3753i q^{74} +(-1.81248 - 0.466164i) q^{75} -10.5277 q^{76} +(-0.148804 - 0.108112i) q^{77} +(-3.81280 + 1.23885i) q^{78} +(-11.8059 + 3.83596i) q^{79} +(-8.26962 - 22.9846i) q^{80} +(2.39759 - 7.37902i) q^{81} -18.0441i q^{82} +(1.54222 - 4.74647i) q^{83} +(1.75320 - 1.27377i) q^{84} +(3.87186 - 8.36712i) q^{85} +(11.1508 + 8.10154i) q^{86} +(-1.70783 + 1.24081i) q^{87} +(-0.736811 - 1.01413i) q^{88} +(-0.191227 - 0.138935i) q^{89} +(-4.72052 + 16.2356i) q^{90} +(-2.76252 - 3.80229i) q^{91} +(-38.6379 - 12.5542i) q^{92} -2.26444 q^{93} +(1.01035 - 3.10952i) q^{94} +(-3.90086 - 2.65220i) q^{95} +(4.65235 - 1.51164i) q^{96} +(-5.53280 + 1.79772i) q^{97} +(-12.0940 - 8.78681i) q^{98} +0.453409i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) \) 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

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