LMFDB - Embedded newform 425.2.p.a.16.1

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			16.1
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-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} +(3.66123 + 1.89615i) 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} +(-4.88462 - 9.74572i) 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} +(6.35699 - 6.67748i) 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	−0.409969	−	0.912100i	$-0.634460\pi$
$3$	−0.355974	+	0.115663i	−0.205522	+	0.0667781i	0.204447	+	0.978878i	$0.434460\pi$
$4$	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	$0.0703607\pi$
$7$			1.16016i			0.438498i	−0.975669	+	0.219249i	$0.929639\pi$
$8$	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	−0.822834	−	0.568281i	$-0.807609\pi$
$11$	−0.0931875	+	0.128262i	−0.0280971	+	0.0386723i	0.794737	+	0.606954i	$0.207609\pi$
$12$	−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
$17$	3.66123	+	1.89615i	0.887979	+	0.459885i
$17$	3.66123	+	1.89615i	0.887979	+	0.459885i
$18$	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	$-0.477368\pi$
$23$	4.78500	−	6.58598i	0.997741	−	1.37327i	0.926701	−	0.375799i	$-0.122632\pi$
$24$			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	0.234767	−	0.972052i	$-0.424567\pi$
$29$	5.36392	−	1.74284i	0.996055	−	0.323638i	0.761288	+	0.648414i	$0.224567\pi$
$30$	1.24418	−	1.82995i	0.227156	−	0.334101i
$31$	5.75381	+	1.86952i	1.03341	+	0.335777i	0.776139	−	0.630562i	$-0.217175\pi$
$31$	5.75381	+	1.86952i	1.03341	+	0.335777i	0.257275	+	0.966338i	$0.417175\pi$
$32$	13.0693			2.31036
$33$	0.0183372	−	0.0564362i	0.00319210	−	0.00982428i
$34$	−4.88462	−	9.74572i	−0.837706	−	1.67138i
$35$	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	$-0.981634\pi$
$37$	−4.52969	−	6.23458i	−0.744676	−	1.02496i	0.253660	−	0.967293i	$-0.418366\pi$
$38$	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	0.371324	−	0.928503i	$-0.378904\pi$
$41$	−4.01143	−	5.52126i	−0.626480	−	0.862276i	−0.997805	+	0.0662271i	$0.978904\pi$
$42$	−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	−0.656483	−	0.754341i	$-0.727957\pi$
$61$	2.06036	−	2.83585i	0.263802	−	0.363093i	0.920285	+	0.391248i	$0.127957\pi$
$62$	−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	0.223297	−	0.974751i	$-0.428318\pi$
$71$	8.23143	−	2.67455i	0.976891	−	0.317411i	0.753595	+	0.657339i	$0.228318\pi$
$72$	6.98767	+	21.5058i	0.823504	+	2.53449i
$73$	−0.554257	+	0.762870i	−0.0648709	+	0.0892872i	−0.840220	−	0.542246i	$-0.817574\pi$
$73$	−0.554257	+	0.762870i	−0.0648709	+	0.0892872i	0.775349	+	0.631533i	$0.217574\pi$
$74$			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	0.442940	−	0.896551i	$-0.353936\pi$
$79$	11.8059	−	3.83596i	1.32827	−	0.431580i	0.885326	+	0.464972i	$0.153936\pi$
$80$	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
$85$	6.35699	−	6.67748i	0.689512	−	0.724274i
$86$	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	−0.0143469	−	0.999897i	$-0.504567\pi$
$97$	5.53280	−	1.79772i	0.561771	−	0.182530i	0.576118	+	0.817367i	$0.304567\pi$
$98$	−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	$0.183705\pi$
$102$	2.86602	+	2.90426i	0.283778	+	0.287564i
$103$	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	$0.155546\pi$
$107$			9.71197i			0.938892i	−0.882961	+	0.469446i	$0.844454\pi$
$108$	10.4101	+	3.38244i	1.00171	+	0.325475i
$109$	−6.14770	−	8.46159i	−0.588843	−	0.810473i	0.405787	−	0.913968i	$-0.366997\pi$
$109$	−6.14770	−	8.46159i	−0.588843	−	0.810473i	−0.994630	+	0.103495i	$0.966997\pi$
$110$	−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	0.990698	−	0.136079i	$-0.0434502\pi$
$113$	5.90118	+	8.12228i	0.555136	+	0.764079i	−0.435562	+	0.900159i	$0.643450\pi$
$114$	−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
$119$	−2.19983	+	4.24760i	−0.201659	+	0.389377i
$120$	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	−0.672615	−	0.739992i	$-0.734829\pi$
$131$	−18.9049	−	6.14258i	−1.65173	−	0.536679i	−0.979114	+	0.203313i	$0.934829\pi$
$132$	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
$136$	23.2042	−	22.8987i	1.98974	−	1.96355i
$137$	−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	−0.939422	−	0.342763i	$-0.888637\pi$
$139$	−3.80974	+	5.24365i	−0.323138	+	0.444761i	0.616284	+	0.787524i	$0.288637\pi$
$140$	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
$153$	−11.6585	+	1.76741i	−0.942532	+	0.142887i
$154$	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	$0.111647\pi$
$163$	12.4569	+	17.1454i	0.975698	+	1.34293i	0.0365830	+	0.999331i	$0.488353\pi$
$164$	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	0.313899	−	0.949456i	$-0.398365\pi$
$167$	0.126289	+	0.0410339i	0.00977257	+	0.00317530i	−0.304127	+	0.952632i	$0.598365\pi$
$168$	−3.43342			−0.264894
$169$	1.05413	−	3.24428i	0.0810869	−	0.249560i
$170$	−23.9750	+	4.40391i	−1.83879	+	0.337764i
$171$	−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	−0.654815	−	0.755789i	$-0.727253\pi$
$173$	3.50306	−	4.82154i	0.266332	−	0.366575i	0.921147	+	0.389214i	$0.127253\pi$
$174$	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	0.223599	−	0.974681i	$-0.428220\pi$
$181$	−2.26572	−	0.736177i	−0.168410	−	0.0547196i	−0.392008	+	0.919962i	$0.628220\pi$
$182$		−	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
$187$	−0.584385	+	0.292898i	−0.0427344	+	0.0214188i
$188$	−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	$-0.834228\pi$
$193$		−	13.8247i		−	0.995126i	0.867428	−	0.497563i	$-0.165772\pi$
$194$	−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	−0.734355	−	0.678765i	$-0.762515\pi$
$197$	−13.0461	+	4.23892i	−0.929493	+	0.302010i	−0.195137	+	0.980776i	$0.562515\pi$
$198$	−0.704634	+	0.969845i	−0.0500761	+	0.0689239i
$199$			26.7064i			1.89316i	0.322463	+	0.946582i	$0.395489\pi$
$199$			26.7064i			1.89316i	−0.322463	+	0.946582i	$0.604511\pi$
$200$	−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
$204$	−1.15437	−	7.61460i	−0.0808217	−	0.533129i
$205$	−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	−0.949637	−	0.313352i	$-0.898548\pi$
$211$	−5.20269	+	7.16088i	−0.358168	+	0.492976i	0.591469	+	0.806327i	$0.298548\pi$
$212$	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
$221$	16.5143	−	2.50356i	1.11087	−	0.168407i
$222$	−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	$-0.537279\pi$
$227$	13.0145	−	17.9129i	0.863801	−	1.18892i	0.980650	−	0.195771i	$-0.0627208\pi$
$228$	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	−0.405798	−	0.913963i	$-0.633006\pi$
$233$	−19.4057	−	6.30529i	−1.27131	−	0.413073i	−0.865511	+	0.500889i	$0.833006\pi$
$234$	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
$238$	11.3066	−	5.66693i	0.732896	−	0.367332i
$239$	−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	0.877572	−	0.479445i	$-0.159162\pi$
$241$	2.33496	+	3.21379i	0.150408	+	0.207018i	−0.727164	+	0.686464i	$0.759162\pi$
$242$	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
$255$	−1.49059	+	3.11228i	−0.0933441	+	0.194899i
$256$	−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	−0.103973	−	0.994580i	$-0.533155\pi$
$269$	−12.6730	−	4.11771i	−0.772688	−	0.251061i	−0.668715	+	0.743519i	$0.733155\pi$
$270$	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	$-0.283648\pi$
$272$	−44.5324	+	6.75107i	−2.70018	+	0.409344i
$273$	−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	−0.873366	−	0.487065i	$-0.838067\pi$
$277$	−2.33430	+	3.21289i	−0.140255	+	0.193044i	0.733111	+	0.680109i	$0.238067\pi$
$278$	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	0.598353	−	0.801232i	$-0.295822\pi$
$283$	10.2867	+	3.34234i	0.611478	+	0.198681i	0.0131253	+	0.999914i	$0.495822\pi$
$284$	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
$289$	9.80921	+	13.8845i	0.577012	+	0.816735i
$290$	−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
$306$	27.6842	+	14.3377i	1.58260	+	0.819631i
$307$	−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	−0.913345	−	0.407188i	$-0.866510\pi$
$311$	−4.30029	+	5.91884i	−0.243847	+	0.335627i	0.669497	+	0.742814i	$0.266510\pi$
$312$	7.04693	+	9.69927i	0.398954	+	0.549113i
$313$	−14.7613	−	20.3172i	−0.834357	−	1.14839i	−0.987096	−	0.160127i	$-0.948810\pi$
$313$	−14.7613	−	20.3172i	−0.834357	−	1.14839i	0.152740	−	0.988266i	$-0.451190\pi$
$314$	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	−0.731389	−	0.681961i	$-0.761127\pi$
$317$	−30.6939	−	9.97305i	−1.72394	−	0.560142i	−0.992552	+	0.121818i	$0.961127\pi$
$318$		−	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
$323$	−6.19094	+	6.10943i	−0.344473	+	0.339938i
$324$	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	$0.0348652\pi$
$337$	14.5173	+	19.9813i	0.790805	+	1.08845i	−0.203202	+	0.979137i	$0.565135\pi$
$338$	−7.29665	+	5.30132i	−0.396885	+	0.288354i
$339$	−3.04012	−	2.20877i	−0.165116	−	0.119964i
$340$	41.4964	+	19.8742i	2.25046	+	1.07783i
$341$	−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	−0.0806609	−	0.996742i	$-0.525703\pi$
$347$	8.19542	−	2.66285i	0.439953	−	0.142949i	0.520614	+	0.853792i	$0.325703\pi$
$348$	−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	−0.0661757	−	0.997808i	$-0.521080\pi$
$367$	−13.5290	−	4.39585i	−0.706210	−	0.229461i	−0.640034	+	0.768347i	$0.721080\pi$
$368$			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	−0.193297	−	0.981140i	$-0.561918\pi$
$379$	4.41964	−	1.43603i	0.227022	−	0.0737639i	0.420319	+	0.907376i	$0.361918\pi$
$380$	−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
$391$	30.0070	−	15.0397i	1.51752	−	0.760591i
$392$	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	−0.000495067	−	1.00000i	$-0.500158\pi$
$397$	11.6937	−	3.79951i	0.586890	−	0.190692i	0.587385	+	0.809308i	$0.300158\pi$
$398$	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	$-0.931841\pi$
$401$		−	8.51040i		−	0.424989i	0.977162	−	0.212495i	$-0.0681588\pi$
$402$	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
$408$	−5.61156	+	10.8352i	−0.277814	+	0.536423i
$409$	−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	0.434006	−	0.900910i	$-0.357100\pi$
$419$	5.23163	+	1.69986i	0.255582	+	0.0830436i	−0.178424	+	0.983954i	$0.557100\pi$
$420$	−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
$425$	−10.3690	−	17.8181i	−0.502970	−	0.864304i
$426$	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	0.144711	−	0.989474i	$-0.453775\pi$
$431$	−6.63952	−	2.15731i	−0.319814	−	0.103914i	−0.464525	+	0.885560i	$0.653775\pi$
$432$			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	−0.313788	−	0.949493i	$-0.601598\pi$
$439$	14.3775	−	19.7889i	0.686200	−	0.944473i	0.999987	+	0.00502013i	$0.00159796\pi$
$440$	2.63748	−	0.948936i	0.125737	−	0.0452388i
$441$	−13.0818	+	9.50449i	−0.622943	+	0.452595i
$442$	−39.2150	−	20.3094i	−1.86527	−	0.966022i
$443$	−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	$0.187038\pi$
$449$			23.4934i			1.10872i	−0.832276	+	0.554362i	$0.812962\pi$
$450$	−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
$459$	8.08467	−	4.05209i	0.377360	−	0.189136i
$460$	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	−0.880935	−	0.473237i	$-0.843086\pi$
$479$	−28.7904	+	9.35456i	−1.31547	+	0.427421i	−0.434530	+	0.900657i	$0.643086\pi$
$480$	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	$-0.957828\pi$
$487$	−17.8876	−	24.6201i	−0.810563	−	1.11564i	0.180674	−	0.983543i	$-0.442172\pi$
$488$	−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	$-0.847647\pi$
$499$		−	20.5765i		−	0.921130i	0.887626	−	0.460565i	$-0.152353\pi$
$500$	−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	−0.485730	−	0.874109i	$-0.661446\pi$
$503$	−8.18400	+	2.65914i	−0.364906	+	0.118565i	0.120824	+	0.992674i	$0.461446\pi$
$504$	−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	$0.109751\pi$
$510$	8.02510	−	4.34069i	0.355357	−	0.192209i
$511$	−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	−0.0793021	−	0.996851i	$-0.525269\pi$
$521$	10.0997	−	3.28159i	0.442475	−	0.143769i	0.521777	+	0.853082i	$0.325269\pi$
$522$	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
$527$	17.5211	+	17.7549i	0.763231	+	0.773413i
$528$	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	0.381979	−	0.924171i	$-0.375243\pi$
$541$	−14.3045	−	19.6884i	−0.614998	−	0.846472i	−0.996977	+	0.0776993i	$0.975243\pi$
$542$	−14.6731	+	45.1591i	−0.630262	+	1.93975i
$543$	0.891687			0.0382660
$544$	47.8499	+	24.7815i	2.05155	+	1.06250i
$545$	−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	0.247736	−	0.968828i	$-0.420314\pi$
$547$	23.8001	−	7.73314i	1.01762	−	0.330645i	0.769885	+	0.638183i	$0.220314\pi$
$548$	−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
$561$	0.174148	−	0.171856i	0.00735255	−	0.00725575i
$562$	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	−0.00124675	−	0.999999i	$-0.500397\pi$
$571$	13.9916	−	4.54614i	0.585529	−	0.190250i	0.586776	+	0.809749i	$0.300397\pi$
$572$	−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	$0.659902\pi$
$578$	0.595646	−	44.9433i	0.0247756	−	1.86939i
$579$	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
$595$	7.74692	+	7.37510i	0.317593	+	0.302350i
$596$	−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	$0.0216417\pi$
$601$			3.33100i			0.135874i	−0.997690	+	0.0679372i	$0.978358\pi$
$602$	−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	$0.340586\pi$
$607$			43.2234i			1.75439i	−0.480139	+	0.877193i	$0.659414\pi$
$608$	−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
$612$	−26.3677	−	52.6084i	−1.06585	−	2.12657i
$613$	−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	−0.399217	−	0.916856i	$-0.630718\pi$
$617$	−31.3252	−	10.1782i	−1.26111	−	0.409758i	−0.861888	+	0.507099i	$0.830718\pi$
$618$			12.7979i			0.514807i
$619$	29.0420	+	9.43631i	1.16730	+	0.379277i	0.827633	−	0.561270i	$-0.189687\pi$
$619$	29.0420	+	9.43631i	1.16730	+	0.379277i	0.339663	+	0.940547i	$0.389687\pi$
$620$	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
$629$	−4.76251	−	31.4152i	−0.189894	−	1.25261i
$630$	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	0.895156	−	0.445753i	$-0.147064\pi$
$641$	4.92690	+	6.78130i	0.194601	+	0.267845i	−0.700555	+	0.713598i	$0.747064\pi$
$642$	−2.97000	+	9.14072i	−0.117217	+	0.360755i
$643$		−	29.7140i		−	1.17180i	−0.810382	−	0.585902i	$-0.800740\pi$
$643$		−	29.7140i		−	1.17180i	0.810382	−	0.585902i	$-0.199260\pi$
$644$	−14.5649	+	44.8260i	−0.573936	+	1.76639i
$645$	−0.136147	−	4.36095i	−0.00536077	−	0.171712i
$646$	22.7370	−	3.44690i	0.894575	−	0.135617i
$647$	−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	0.652722	−	0.757597i	$-0.273627\pi$
$653$	41.5529	−	13.5014i	1.62609	−	0.528349i	0.973368	+	0.229248i	$0.0736268\pi$
$654$	−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
$663$	−5.58911	+	2.80130i	−0.217063	+	0.108793i
$664$	−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	−0.917379	−	0.398015i	$-0.869699\pi$
$673$	−6.62456	+	9.11792i	−0.255358	+	0.351470i	0.662021	+	0.749486i	$0.269699\pi$
$674$		−	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	−0.524641	−	0.851324i	$-0.675800\pi$
$677$	11.6342	−	16.0131i	0.447139	−	0.615434i	0.971780	+	0.235890i	$0.0758005\pi$
$678$	3.07022	+	9.44916i	0.117911	+	0.362893i
$679$	2.08563	+	6.41892i	0.0800393	+	0.246336i
$680$	−34.6809	−	64.1183i	−1.32995	−	2.45883i
$681$	−2.56096	+	7.88182i	−0.0981362	+	0.302032i
$682$	2.53596			0.0971069
$683$	−10.1306	−	3.29164i	−0.387638	−	0.125951i	0.108713	−	0.994073i	$-0.465327\pi$
$683$	−10.1306	−	3.29164i	−0.387638	−	0.125951i	−0.496351	+	0.868122i	$0.665327\pi$
$684$	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	$0.0956309\pi$
$691$	24.7486	+	34.0636i	0.941483	+	1.29584i	−0.0137256	+	0.999906i	$0.504369\pi$
$692$	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
$697$	−4.21762	−	27.8209i	−0.159754	−	1.05379i
$698$	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	0.549856	−	0.835259i	$-0.314682\pi$
$709$	−11.0352	−	15.1887i	−0.414437	−	0.570424i	−0.964294	+	0.264835i	$0.914682\pi$
$710$	−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
$714$	−3.36939	+	3.32503i	−0.126096	+	0.124436i
$715$	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	0.961201	−	0.275848i	$-0.0889586\pi$
$719$	42.2776	+	13.7368i	1.57669	+	0.512298i	0.615489	+	0.788146i	$0.288959\pi$
$720$	−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
$731$	−19.0863	−	9.88481i	−0.705933	−	0.365603i
$732$	−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	$0.286641\pi$
$743$			42.7211i			1.56729i	−0.621212	+	0.783643i	$0.713359\pi$
$744$	−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
$748$	−2.29137	−	2.32194i	−0.0837809	−	0.0848986i
$749$	−11.2674			−0.411702
$750$	−10.1570	+	4.38785i	−0.370880	+	0.160221i
$751$			9.89387i			0.361032i	0.983572	+	0.180516i	$0.0577768\pi$
$751$			9.89387i			0.361032i	−0.983572	+	0.180516i	$0.942223\pi$
$752$	−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
$765$	−3.48332	+	26.1359i	−0.125940	+	0.944946i
$766$	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
$772$

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} +(3.66123 + 1.89615i) 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} +(-4.88462 - 9.74572i) 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} +(6.35699 - 6.67748i) 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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